LMFDB - Embedded newform 43.7.f.a.22.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(2,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([9]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.f (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$21$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			22.14
Character	$\chi$	$=$	43.22
Dual form			43.7.f.a.2.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.61426 - 5.42856i) q^{2} +(1.01637 + 2.11052i) q^{3} +(17.2684 + 21.6539i) q^{4} +(-102.842 + 23.4731i) q^{5} +14.1142 q^{6} -486.006i q^{7} +(538.641 - 122.941i) q^{8} +(451.103 - 565.665i) q^{9} +O(q^{10})$	\(q+(2.61426 - 5.42856i) q^{2} +(1.01637 + 2.11052i) q^{3} +(17.2684 + 21.6539i) q^{4} +(-102.842 + 23.4731i) q^{5} +14.1142 q^{6} -486.006i q^{7} +(538.641 - 122.941i) q^{8} +(451.103 - 565.665i) q^{9} +(-141.431 + 619.650i) q^{10} +(609.196 - 763.908i) q^{11} +(-28.1498 + 58.4537i) q^{12} +(-77.4782 - 339.454i) q^{13} +(-2638.32 - 1270.55i) q^{14} +(-154.067 - 193.193i) q^{15} +(346.320 - 1517.33i) q^{16} +(664.284 - 2910.42i) q^{17} +(-1891.45 - 3927.64i) q^{18} +(2015.78 - 1607.53i) q^{19} +(-2284.20 - 1821.59i) q^{20} +(1025.73 - 493.964i) q^{21} +(-2554.33 - 5304.11i) q^{22} +(-5367.87 + 6731.09i) q^{23} +(806.931 + 1011.86i) q^{24} +(-4052.10 + 1951.39i) q^{25} +(-2045.30 - 466.826i) q^{26} +(3317.21 + 757.131i) q^{27} +(10523.9 - 8392.54i) q^{28} +(1624.49 - 3373.30i) q^{29} +(-1451.53 + 331.303i) q^{30} +(4571.58 + 2201.56i) q^{31} +(20313.7 + 16199.6i) q^{32} +(2231.41 + 509.306i) q^{33} +(-14062.8 - 11214.7i) q^{34} +(11408.1 + 49982.0i) q^{35} +20038.6 q^{36} -14590.2i q^{37} +(-3456.81 - 15145.3i) q^{38} +(637.679 - 508.532i) q^{39} +(-52509.3 + 25287.1i) q^{40} +(34086.8 + 16415.3i) q^{41} -6859.57i q^{42} +(-42282.4 + 67331.7i) q^{43} +27061.4 q^{44} +(-33114.5 + 68763.0i) q^{45} +(22507.2 + 46736.6i) q^{46} +(48965.7 + 61401.1i) q^{47} +(3554.34 - 811.255i) q^{48} -118553. q^{49} +27098.5i q^{50} +(6817.66 - 1556.09i) q^{51} +(6012.58 - 7539.53i) q^{52} +(28175.5 - 123445. i) q^{53} +(12782.2 - 16028.3i) q^{54} +(-44719.8 + 92861.7i) q^{55} +(-59750.3 - 261783. i) q^{56} +(5441.51 + 2620.49i) q^{57} +(-14065.3 - 17637.4i) q^{58} +(16530.9 - 72426.4i) q^{59} +(1522.90 - 6672.27i) q^{60} +(-7616.39 - 15815.6i) q^{61} +(23902.6 - 19061.7i) q^{62} +(-274917. - 219239. i) q^{63} +(230788. - 111142. i) q^{64} +(15936.1 + 33091.6i) q^{65} +(8598.29 - 10781.9i) q^{66} +(213761. + 268047. i) q^{67} +(74492.9 - 35873.9i) q^{68} +(-19661.9 - 4487.69i) q^{69} +(301154. + 68736.4i) q^{70} +(393246. - 313603. i) q^{71} +(173439. - 360150. i) q^{72} +(-521532. + 119036. i) q^{73} +(-79203.8 - 38142.5i) q^{74} +(-8236.89 - 6568.70i) q^{75} +(69618.5 + 15890.0i) q^{76} +(-371264. - 296073. i) q^{77} +(-1093.54 - 4791.12i) q^{78} -197625. q^{79} +164175. i q^{80} +(-115593. - 506446. i) q^{81} +(178223. - 142128. i) q^{82} +(-833718. + 401497. i) q^{83} +(28408.9 + 13681.0i) q^{84} +314907. i q^{85} +(254978. + 405555. i) q^{86} +8770.51 q^{87} +(234222. - 486368. i) q^{88} +(503044. + 1.04458e6i) q^{89} +(286715. + 359529. i) q^{90} +(-164977. + 37654.9i) q^{91} -238448. q^{92} +11886.0i q^{93} +(461329. - 105295. i) q^{94} +(-169573. + 212638. i) q^{95} +(-13543.4 + 59337.4i) q^{96} +(-983626. + 1.23343e6i) q^{97} +(-309928. + 643573. i) q^{98} +(-157306. - 689202. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) $ 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.61426	−	5.42856i	0.326782	−	0.678571i	−0.671253	−	0.741229i	$-0.734243\pi$
$2$	2.61426	−	5.42856i	0.326782	−	0.678571i	0.998035	+	0.0626580i	$0.0199577\pi$
$3$	1.01637	+	2.11052i	0.0376435	+	0.0781675i	0.918942	−	0.394392i	$-0.129045\pi$
$3$	1.01637	+	2.11052i	0.0376435	+	0.0781675i	−0.881299	+	0.472559i	$0.843330\pi$
$4$	17.2684	+	21.6539i	0.269818	+	0.338342i
$5$	−102.842	+	23.4731i	−0.822738	+	0.187785i	−0.613111	−	0.789997i	$-0.710082\pi$
$5$	−102.842	+	23.4731i	−0.822738	+	0.187785i	−0.209627	+	0.977781i	$0.567225\pi$
$6$	14.1142			0.0653434
$7$		−	486.006i		−	1.41693i	−0.705747	−	0.708464i	$-0.749389\pi$
$7$		−	486.006i		−	1.41693i	0.705747	−	0.708464i	$-0.250611\pi$
$8$	538.641	−	122.941i	1.05203	−	0.240120i
$9$	451.103	−	565.665i	0.618797	−	0.775946i
$10$	−141.431	+	619.650i	−0.141431	+	0.619650i
$11$	609.196	−	763.908i	0.457698	−	0.573935i	−0.498413	−	0.866940i	$-0.666084\pi$
$11$	609.196	−	763.908i	0.457698	−	0.573935i	0.956111	+	0.293005i	$0.0946551\pi$
$12$	−28.1498	+	58.4537i	−0.0162904	+	0.0338274i
$13$	−77.4782	−	339.454i	−0.0352655	−	0.154508i	0.954230	−	0.299075i	$-0.0966782\pi$
$13$	−77.4782	−	339.454i	−0.0352655	−	0.154508i	−0.989495	+	0.144567i	$0.953821\pi$
$14$	−2638.32	−	1270.55i	−0.961485	−	0.463027i
$15$	−154.067	−	193.193i	−0.0456493	−	0.0572425i
$16$	346.320	−	1517.33i	0.0845508	−	0.370441i
$17$	664.284	−	2910.42i	0.135209	−	0.592391i	−0.861240	−	0.508198i	$-0.830312\pi$
$17$	664.284	−	2910.42i	0.135209	−	0.592391i	0.996449	−	0.0841927i	$-0.0268311\pi$
$18$	−1891.45	−	3927.64i	−0.324323	−	0.673463i
$19$	2015.78	−	1607.53i	0.293888	−	0.234368i	−0.465434	−	0.885082i	$-0.654102\pi$
$19$	2015.78	−	1607.53i	0.293888	−	0.234368i	0.759323	+	0.650714i	$0.225530\pi$
$20$	−2284.20	−	1821.59i	−0.285525	−	0.227699i
$21$	1025.73	−	493.964i	0.110758	−	0.0533381i
$22$	−2554.33	−	5304.11i	−0.239888	−	0.498132i
$23$	−5367.87	+	6731.09i	−0.441182	+	0.553225i	−0.951854	−	0.306550i	$-0.900825\pi$
$23$	−5367.87	+	6731.09i	−0.441182	+	0.553225i	0.510672	+	0.859776i	$0.329397\pi$
$24$	806.931	+	1011.86i	0.0583718	+	0.0731959i
$25$	−4052.10	+	1951.39i	−0.259334	+	0.124889i
$26$	−2045.30	−	466.826i	−0.116369	−	0.0265604i
$27$	3317.21	+	757.131i	0.168532	+	0.0384662i
$28$	10523.9	−	8392.54i	0.479406	−	0.382313i
$29$	1624.49	−	3373.30i	0.0666077	−	0.138312i	−0.865007	−	0.501760i	$-0.832686\pi$
$29$	1624.49	−	3373.30i	0.0666077	−	0.138312i	0.931615	+	0.363448i	$0.118400\pi$
$30$	−1451.53	+	331.303i	−0.0537605	+	0.0122705i
$31$	4571.58	+	2201.56i	0.153455	+	0.0739001i	0.509035	−	0.860746i	$-0.330002\pi$
$31$	4571.58	+	2201.56i	0.153455	+	0.0739001i	−0.355580	+	0.934646i	$0.615717\pi$
$32$	20313.7	+	16199.6i	0.619925	+	0.494374i
$33$	2231.41	+	509.306i	0.0620924	+	0.0141722i
$34$	−14062.8	−	11214.7i	−0.357795	−	0.285332i
$35$	11408.1	+	49982.0i	0.266077	+	1.16576i
$36$	20038.6			0.429498
$37$		−	14590.2i		−	0.288042i	−0.989575	−	0.144021i	$-0.953997\pi$
$37$		−	14590.2i		−	0.288042i	0.989575	−	0.144021i	$-0.0460033\pi$
$38$	−3456.81	−	15145.3i	−0.0629977	−	0.276011i
$39$	637.679	−	508.532i	0.0107500	−	0.00857283i
$40$	−52509.3	+	25287.1i	−0.820457	+	0.395111i
$41$	34086.8	+	16415.3i	0.494577	+	0.238176i	0.664509	−	0.747280i	$-0.268641\pi$
$41$	34086.8	+	16415.3i	0.494577	+	0.238176i	−0.169932	+	0.985456i	$0.554355\pi$
$42$		−	6859.57i		−	0.0925868i
$43$	−42282.4	+	67331.7i	−0.531807	+	0.846866i
$43$	−42282.4	+	67331.7i	−0.531807	+	0.846866i
$44$	27061.4			0.317681
$45$	−33114.5	+	68763.0i	−0.363397	+	0.754601i
$46$	22507.2	+	46736.6i	0.231232	+	0.480158i
$47$	48965.7	+	61401.1i	0.471627	+	0.591401i	0.959569	−	0.281475i	$-0.0908236\pi$
$47$	48965.7	+	61401.1i	0.471627	+	0.591401i	−0.487942	+	0.872876i	$0.662252\pi$
$48$	3554.34	−	811.255i	0.0321392	−	0.00733557i
$49$	−118553.			−1.00768
$50$			27098.5i			0.216788i
$51$	6817.66	−	1556.09i	0.0513954	−	0.0117307i
$52$	6012.58	−	7539.53i	0.0427613	−	0.0536209i
$53$	28175.5	−	123445.i	0.189253	−	0.829173i	−0.787758	−	0.615985i	$-0.788758\pi$
$53$	28175.5	−	123445.i	0.189253	−	0.829173i	0.977011	−	0.213188i	$-0.0683848\pi$
$54$	12782.2	−	16028.3i	0.0811752	−	0.101790i
$55$	−44719.8	+	92861.7i	−0.268789	+	0.558147i
$56$	−59750.3	−	261783.i	−0.340233	−	1.49066i
$57$	5441.51	+	2620.49i	0.0293829	+	0.0141501i
$58$	−14065.3	−	17637.4i	−0.0720884	−	0.0903960i
$59$	16530.9	−	72426.4i	0.0804895	−	0.352648i	−0.918606	−	0.395175i	$-0.870684\pi$
$59$	16530.9	−	72426.4i	0.0804895	−	0.352648i	0.999095	+	0.0425276i	$0.0135410\pi$
$60$	1522.90	−	6672.27i	0.00705048	−	0.0308902i
$61$	−7616.39	−	15815.6i	−0.0335552	−	0.0696780i	0.883517	−	0.468398i	$-0.155169\pi$
$61$	−7616.39	−	15815.6i	−0.0335552	−	0.0696780i	−0.917073	+	0.398720i	$0.869454\pi$
$62$	23902.6	−	19061.7i	0.100293	−	0.0799809i
$63$	−274917.	−	219239.i	−1.09946	−	0.876790i
$64$	230788.	−	111142.i	0.880387	−	0.423972i
$65$	15936.1	+	33091.6i	0.0580285	+	0.120497i
$66$	8598.29	−	10781.9i	0.0299075	−	0.0375028i
$67$	213761.	+	268047.i	0.710728	+	0.891224i	0.997774	−	0.0666924i	$-0.0212446\pi$
$67$	213761.	+	268047.i	0.710728	+	0.891224i	−0.287046	+	0.957917i	$0.592673\pi$
$68$	74492.9	−	35873.9i	0.236912	−	0.114091i
$69$	−19661.9	−	4487.69i	−0.0598518	−	0.0136608i
$70$	301154.	+	68736.4i	0.878000	+	0.200398i
$71$	393246.	−	313603.i	1.09873	−	0.876205i	0.105735	−	0.994394i	$-0.466280\pi$
$71$	393246.	−	313603.i	1.09873	−	0.876205i	0.992991	+	0.118190i	$0.0377091\pi$
$72$	173439.	−	360150.i	0.464675	−	0.964907i
$73$	−521532.	+	119036.i	−1.34064	+	0.305992i	−0.831899	−	0.554927i	$-0.812746\pi$
$73$	−521532.	+	119036.i	−1.34064	+	0.305992i	−0.508741	+	0.860919i	$0.669889\pi$
$74$	−79203.8	−	38142.5i	−0.195457	−	0.0941271i
$75$	−8236.89	−	6568.70i	−0.0195245	−	0.0155702i
$76$	69618.5	+	15890.0i	0.158593	+	0.0361978i
$77$	−371264.	−	296073.i	−0.813224	−	0.648525i
$78$	−1093.54	−	4791.12i	−0.00230436	−	0.0100961i
$79$	−197625.			−0.400831			−0.200415	−	0.979711i	$-0.564229\pi$
$79$	−197625.			−0.400831			−0.200415	+	0.979711i	$0.564229\pi$
$80$			164175.i			0.320653i
$81$	−115593.	−	506446.i	−0.217509	−	0.952968i
$82$	178223.	−	142128.i	0.323238	−	0.257774i
$83$	−833718.	+	401497.i	−1.45809	+	0.702180i	−0.983979	−	0.178284i	$-0.942945\pi$
$83$	−833718.	+	401497.i	−1.45809	+	0.702180i	−0.474113	+	0.880464i	$0.657231\pi$
$84$	28408.9	+	13681.0i	0.0479309	+	0.0230823i
$85$			314907.i			0.512773i
$86$	254978.	+	405555.i	0.400873	+	0.637609i
$87$	8770.51			0.0133189
$88$	234222.	−	486368.i	0.343701	−	0.713702i
$89$	503044.	+	1.04458e6i	0.713569	+	1.48174i	0.869479	+	0.493970i	$0.164455\pi$
$89$	503044.	+	1.04458e6i	0.713569	+	1.48174i	−0.155910	+	0.987771i	$0.549831\pi$
$90$	286715.	+	359529.i	0.393298	+	0.493181i
$91$	−164977.	+	37654.9i	−0.218927	+	0.0499686i
$92$	−238448.			−0.306218
$93$			11886.0i			0.0147771i
$94$	461329.	−	105295.i	0.555427	−	0.126773i
$95$	−169573.	+	212638.i	−0.197782	+	0.248011i
$96$	−13543.4	+	59337.4i	−0.0153078	+	0.0670679i
$97$	−983626.	+	1.23343e6i	−1.07774	+	1.35145i	−0.145605	+	0.989343i	$0.546513\pi$
$97$	−983626.	+	1.23343e6i	−1.07774	+	1.35145i	−0.932138	+	0.362103i	$0.882059\pi$
$98$	−309928.	+	643573.i	−0.329293	+	0.683785i
$99$	−157306.	−	689202.i	−0.162121	−	0.710298i
$100$	−112228.	−	54046.3i	−0.112228	−	0.0540463i
$101$	303004.	+	379954.i	0.294092	+	0.368780i	0.906823	−	0.421512i	$-0.138500\pi$
$101$	303004.	+	379954.i	0.294092	+	0.368780i	−0.612731	+	0.790292i	$0.709929\pi$
$102$	9375.81	−	41078.1i	0.00883503	−	0.0387088i
$103$	−285048.	+	1.24888e6i	−0.260859	+	1.14290i	0.659463	+	0.751737i	$0.270784\pi$
$103$	−285048.	+	1.24888e6i	−0.260859	+	1.14290i	−0.920322	+	0.391161i	$0.872073\pi$
$104$	−83466.0	−	173319.i	−0.0742010	−	0.154080i
$105$	−93893.2	+	74877.3i	−0.0811084	+	0.0646818i
$106$	−596470.	−	475669.i	−0.500808	−	0.399381i
$107$	1.91340e6	−	921447.i	1.56191	−	0.752175i	0.564590	−	0.825372i	$-0.309034\pi$
$107$	1.91340e6	−	921447.i	1.56191	−	0.752175i	0.997318	+	0.0731968i	$0.0233201\pi$
$108$	40888.0	+	84904.7i	0.0324582	+	0.0674001i
$109$	705875.	−	885139.i	0.545065	−	0.683490i	−0.430654	−	0.902517i	$-0.641717\pi$
$109$	705875.	−	885139.i	0.545065	−	0.683490i	0.975719	+	0.219028i	$0.0702885\pi$
$110$	387196.	+	485529.i	0.290906	+	0.364785i
$111$	30792.9	−	14829.1i	0.0225155	−	0.0108429i
$112$	−737430.	−	168314.i	−0.524888	−	0.119802i
$113$	2.03407e6	+	464263.i	1.40971	+	0.321757i	0.858588	−	0.512666i	$-0.171342\pi$
$113$	2.03407e6	+	464263.i	1.40971	+	0.321757i	0.551123	+	0.834424i	$0.314199\pi$
$114$	28451.0	−	22688.9i	0.0192036	−	0.0153144i
$115$	394044.	−	818241.i	0.259090	−	0.538007i
$116$	101097.	−	23074.8i	0.0647688	−	0.0147831i
$117$	−226968.	−	109302.i	−0.141712	−	0.0682450i
$118$	−349956.	−	279080.i	−0.212994	−	0.169857i
$119$	−1.41448e6	−	322846.i	−0.839375	−	0.191582i
$120$	−106738.	−	85120.8i	−0.0617697	−	0.0492597i
$121$	181774.	+	796406.i	0.102607	+	0.449550i
$122$	−105767.			−0.0582467
$123$			88624.9i			0.0476256i
$124$	31271.6	+	137010.i	0.0164016	+	0.0718599i
$125$	1.65956e6	−	1.32346e6i	0.849696	−	0.677610i
$126$	−1.90886e6	+	919256.i	−0.954248	+	0.459542i
$127$	−2.61592e6	−	1.25976e6i	−1.27706	−	0.615002i	−0.332430	−	0.943128i	$-0.607869\pi$
$127$	−2.61592e6	−	1.25976e6i	−1.27706	−	0.615002i	−0.944634	+	0.328126i	$0.893583\pi$
$128$			119459.i			0.0569623i
$129$	−185080.	−	20803.7i	−0.0862164	−	0.00969104i
$130$	221301.			0.100729
$131$	444997.	−	924047.i	0.197945	−	0.411036i	−0.778243	−	0.627963i	$-0.783889\pi$
$131$	444997.	−	924047.i	0.197945	−	0.411036i	0.976188	+	0.216927i	$0.0696033\pi$
$132$	27504.5	+	57113.6i	0.0119586	+	0.0248324i
$133$	−781269.	−	979681.i	−0.332082	−	0.416418i
$134$	2.01394e6	−	459668.i	0.837012	−	0.191043i
$135$	−358921.			−0.145881
$136$		−	1.64934e6i		−	0.655682i
$137$	2.48239e6	−	566589.i	0.965402	−	0.220347i	0.289369	−	0.957218i	$-0.406555\pi$
$137$	2.48239e6	−	566589.i	0.965402	−	0.220347i	0.676033	+	0.736871i	$0.263697\pi$
$138$	−75763.0	+	95003.7i	−0.0288283	+	0.0361496i
$139$	−212764.	+	932178.i	−0.0792233	+	0.347100i	−0.998968	−	0.0454168i	$-0.985538\pi$
$139$	−212764.	+	932178.i	−0.0792233	+	0.347100i	0.919745	+	0.392517i	$0.128396\pi$
$140$	−885304.	+	1.11014e6i	−0.322633	+	0.404569i
$141$	−79820.8	+	165750.i	−0.0284747	+	0.0591283i
$142$	−674369.	−	2.95460e6i	−0.235522	−	1.03189i
$143$	−306511.	−	147608.i	−0.104819	−	0.0504780i
$144$	−702073.	−	880372.i	−0.235123	−	0.294835i
$145$	−87885.0	+	385049.i	−0.0288278	+	0.126303i
$146$	−717223.	+	3.14236e6i	−0.230460	+	1.00971i
$147$	−120494.	−	250209.i	−0.0379327	−	0.0787681i
$148$	315934.	−	251949.i	0.0974566	−	0.0777190i
$149$	1.04762e6	+	835446.i	0.316697	+	0.252557i	0.768916	−	0.639349i	$-0.220796\pi$
$149$	1.04762e6	+	835446.i	0.316697	+	0.252557i	−0.452220	+	0.891907i	$0.649368\pi$
$150$	−57192.0	+	27542.2i	−0.0169458	+	0.00816065i
$151$	−1.26697e6	−	2.63089e6i	−0.367990	−	0.764139i	0.631951	−	0.775008i	$-0.282254\pi$
$151$	−1.26697e6	−	2.63089e6i	−0.367990	−	0.764139i	−0.999941	+	0.0108697i	$0.996540\pi$
$152$	888150.	−	1.11370e6i	0.252904	−	0.317131i
$153$	−1.34666e6	−	1.68866e6i	−0.375997	−	0.471485i
$154$	−2.57783e6	+	1.24142e6i	−0.705817	+	0.339904i
$155$	−521829.	−	119104.i	−0.140131	−	0.0319839i
$156$	22023.4	+	5026.69i	0.00580109	+	0.00132406i
$157$	3.30672e6	−	2.63702e6i	0.854473	−	0.681419i	−0.0949287	−	0.995484i	$-0.530262\pi$
$157$	3.30672e6	−	2.63702e6i	0.854473	−	0.681419i	0.949402	+	0.314065i	$0.101691\pi$
$158$	−516643.	+	1.07282e6i	−0.130984	+	0.271992i
$159$	289170.	−	66001.1i	0.0719385	−	0.0164195i
$160$	−2.46936e6	−	1.18918e6i	−0.602872	−	0.290328i
$161$	3.27135e6	+	2.60882e6i	0.783880	+	0.625124i
$162$	−3.05147e6	−	696477.i	−0.717734	−	0.163818i
$163$	2.00398e6	+	1.59812e6i	0.462732	+	0.369017i	0.826930	−	0.562305i	$-0.190085\pi$
$163$	2.00398e6	+	1.59812e6i	0.462732	+	0.369017i	−0.364198	+	0.931322i	$0.618657\pi$
$164$	233168.	+	1.02158e6i	0.0528612	+	0.231600i
$165$	−241439.			−0.0537471
$166$			5.57551e6i			1.21888i
$167$	1.54684e6	+	6.77715e6i	0.332121	+	1.45512i	0.815016	+	0.579438i	$0.196728\pi$
$167$	1.54684e6	+	6.77715e6i	0.332121	+	1.45512i	−0.482896	+	0.875678i	$0.660415\pi$
$168$	491770.	−	392174.i	0.103713	−	0.0827086i
$169$	4.23958e6	−	2.04167e6i	0.878340	−	0.422986i
$170$	1.70949e6	+	823247.i	0.347952	+	0.167565i
$171$		−	1.86542e6i		−	0.373067i
$172$	−2.18814e6	+	247133.i	−0.430021	+	0.0485675i
$173$	−1.73894e6			−0.335851			−0.167926	−	0.985800i	$-0.553707\pi$
$173$	−1.73894e6			−0.335851			−0.167926	+	0.985800i	$0.553707\pi$
$174$	22928.4	−	47611.3i	0.00435237	−	0.00903779i
$175$	948386.	+	1.96934e6i	0.176958	+	0.367458i
$176$	−948121.	−	1.18891e6i	−0.173910	−	0.218077i
$177$	169659.	−	38723.6i	0.0305955	−	0.00698322i
$178$	6.98567e6			1.23865
$179$			2.43668e6i			0.424854i	0.977177	+	0.212427i	$0.0681368\pi$
$179$			2.43668e6i			0.424854i	−0.977177	+	0.212427i	$0.931863\pi$
$180$	−2.06082e6	+	470369.i	−0.353364	+	0.0806531i
$181$	4.82977e6	−	6.05634e6i	0.814500	−	1.02135i	−0.184756	−	0.982784i	$-0.559150\pi$
$181$	4.82977e6	−	6.05634e6i	0.814500	−	1.02135i	0.999256	−	0.0385661i	$-0.0122790\pi$
$182$	−226880.	+	994028.i	−0.0376342	+	0.164886i
$183$	25638.1	−	32149.1i	0.00418342	−	0.00524585i
$184$	−2.06383e6	+	4.28558e6i	−0.331298	+	0.687948i
$185$	342477.	+	1.50049e6i	0.0540898	+	0.236983i
$186$	64524.1	+	31073.2i	0.0100273	+	0.00482888i
$187$	−1.81861e6	−	2.28046e6i	−0.278109	−	0.348737i
$188$	−484012.	+	2.12059e6i	−0.0728421	+	0.319142i
$189$	367970.	−	1.61218e6i	0.0545038	−	0.238797i
$190$	711013.	+	1.47643e6i	0.103661	+	0.215255i
$191$	−959769.	+	765390.i	−0.137742	+	0.109846i	−0.689937	−	0.723869i	$-0.742362\pi$
$191$	−959769.	+	765390.i	−0.137742	+	0.109846i	0.552195	+	0.833715i	$0.313790\pi$
$192$	469134.	+	374122.i	0.0662816	+	0.0528578i
$193$	−8.18989e6	+	3.94404e6i	−1.13922	+	0.548618i	−0.905777	−	0.423754i	$-0.860712\pi$
$193$	−8.18989e6	+	3.94404e6i	−1.13922	+	0.548618i	−0.233439	+	0.972371i	$0.574998\pi$
$194$	4.12429e6	+	8.56418e6i	0.564865	+	1.17295i
$195$	−53643.5	+	67266.8i	−0.00723458	+	0.00907188i
$196$	−2.04722e6	−	2.56713e6i	−0.271892	−	0.340941i
$197$	−1.15644e6	+	556914.i	−0.151261	+	0.0728433i	−0.507983	−	0.861367i	$-0.669609\pi$
$197$	−1.15644e6	+	556914.i	−0.151261	+	0.0728433i	0.356722	+	0.934211i	$0.383894\pi$
$198$	−4.15261e6	−	947807.i	−0.534966	−	0.122102i
$199$	−1.12394e7	−	2.56533e6i	−1.42622	−	0.325525i	−0.561372	−	0.827564i	$-0.689726\pi$
$199$	−1.12394e7	−	2.56533e6i	−1.42622	−	0.325525i	−0.864845	+	0.502039i	$0.832583\pi$
$200$	−1.94272e6	+	1.54927e6i	−0.242840	+	0.193659i
$201$	−348459.	+	723583.i	−0.0429105	+	0.0891046i
$202$	2.85474e6	−	651575.i	0.346347	−	0.0790516i
$203$	−1.63944e6	−	789515.i	−0.195979	−	0.0943783i
$204$	151425.	+	120758.i	0.0178364	+	0.0142241i
$205$	−3.89088e6	−	888067.i	−0.451633	−	0.103082i
$206$	6.03442e6	+	4.81229e6i	0.690293	+	0.550490i
$207$	1.38608e6	+	6.07283e6i	0.156271	+	0.684668i
$208$	−541896.			−0.0602179
$209$		−	2.51917e6i		−	0.275942i
$210$	161015.	+	705454.i	0.0173864	+	0.0761747i
$211$	8.47054e6	−	6.75503e6i	0.901704	−	0.719085i	−0.0585290	−	0.998286i	$-0.518641\pi$
$211$	8.47054e6	−	6.75503e6i	0.901704	−	0.719085i	0.960233	+	0.279201i	$0.0900696\pi$
$212$	3.15960e6	−	1.52158e6i	0.331608	−	0.159694i
$213$	1.06155e6	+	511216.i	0.109851	+	0.0529012i
$214$		−	1.27959e7i		−	1.30566i
$215$	2.76793e6	−	7.91704e6i	0.278509	−	0.796614i
$216$	1.87987e6			0.186537
$217$	1.06997e6	−	2.22182e6i	0.104711	−	0.217435i
$218$	−2.95969e6	−	6.14587e6i	−0.285678	−	0.593217i
$219$	−781300.	−	979719.i	−0.0743850	−	0.0932758i
$220$	−2.78305e6	+	635214.i	−0.261369	+	0.0596557i
$221$	−1.03942e6			−0.0962974
$222$		−	205928.i		−	0.0188216i
$223$	−1.43776e7	+	3.28160e6i	−1.29650	+	0.295918i	−0.814454	−	0.580228i	$-0.802963\pi$
$223$	−1.43776e7	+	3.28160e6i	−1.29650	+	0.295918i	−0.482046	+	0.876146i	$0.660106\pi$
$224$	7.87312e6	−	9.87258e6i	0.700492	−	0.878389i
$225$	−724081.	+	3.17241e6i	−0.0635681	+	0.278510i
$226$	7.83786e6	−	9.82837e6i	0.679004	−	0.851444i
$227$	2.71076e6	−	5.62896e6i	0.231747	−	0.481227i	−0.752372	−	0.658739i	$-0.771090\pi$
$227$	2.71076e6	−	5.62896e6i	0.231747	−	0.481227i	0.984119	+	0.177511i	$0.0568046\pi$
$228$	37222.3	+	163081.i	0.00314050	+	0.0137594i
$229$	−916747.	−	441482.i	−0.0763384	−	0.0367626i	0.395325	−	0.918541i	$-0.370632\pi$
$229$	−916747.	−	441482.i	−0.0763384	−	0.0367626i	−0.471663	+	0.881779i	$0.656346\pi$
$230$	−3.41174e6	−	4.27819e6i	−0.280409	−	0.351622i
$231$	247526.	−	1.08448e6i	0.0200810	−	0.0879804i
$232$	460302.	−	2.01672e6i	0.0368620	−	0.161503i
$233$	1.02680e7	+	2.13216e7i	0.811739	+	1.68559i	0.724363	+	0.689419i	$0.242134\pi$
$233$	1.02680e7	+	2.13216e7i	0.811739	+	1.68559i	0.0873762	+	0.996175i	$0.472152\pi$
$234$	−1.18671e6	+	946367.i	−0.0926181	+	0.0738605i
$235$	−6.47702e6	−	5.16525e6i	−0.499081	−	0.398004i
$236$	1.85377e6	−	892730.i	0.141033	−	0.0679179i
$237$	−200861.	−	417092.i	−0.0150887	−	0.0313319i
$238$	−5.45041e6	+	6.83460e6i	−0.404295	+	0.506970i
$239$	−1.10288e7	−	1.38297e7i	−0.807858	−	1.01302i	−0.999502	−	0.0315578i	$-0.989953\pi$
$239$	−1.10288e7	−	1.38297e7i	−0.807858	−	1.01302i	0.191644	−	0.981465i	$-0.438618\pi$
$240$	−346494.	+	166863.i	−0.0250647	+	0.0120705i
$241$	1.86593e7	+	4.25885e6i	1.33304	+	0.304258i	0.828916	−	0.559373i	$-0.188958\pi$
$241$	1.86593e7	+	4.25885e6i	1.33304	+	0.304258i	0.504124	+	0.863631i	$0.331815\pi$
$242$	4.79854e6	+	1.09524e6i	0.338582	+	0.0772791i
$243$	2.89066e6	−	2.30522e6i	0.201455	−	0.160655i
$244$	210946.	−	438034.i	0.0145212	−	0.0301535i
$245$	1.21923e7	−	2.78280e6i	0.829060	−	0.189228i
$246$	481106.	+	231688.i	0.0323173	+	0.0155632i
$247$	−701862.	−	559716.i	−0.0465759	−	0.0371430i
$248$	2.73311e6	+	623814.i	0.179185	+	0.0408978i
$249$	−1.69474e6	−	1.35151e6i	−0.109775	−	0.0875429i
$250$	−2.84595e6	−	1.24689e7i	−0.182141	−	0.798010i
$251$	−1.01361e6			−0.0640987			−0.0320493	−	0.999486i	$-0.510203\pi$
$251$	−1.01361e6			−0.0640987			−0.0320493	+	0.999486i	$0.510203\pi$
$252$		−	9.73891e6i		−	0.608567i
$253$	1.87185e6	+	8.20111e6i	0.115587	+	0.506420i
$254$	−1.36774e7	+	1.09073e7i	−0.834644	+	0.665607i
$255$	−664617.	+	320063.i	−0.0400821	+	0.0193025i
$256$	1.54189e7	+	7.42537e6i	0.919040	+	0.442586i
$257$		−	6.32313e6i		−	0.372505i	−0.982502	−	0.186253i	$-0.940366\pi$
$257$		−	6.32313e6i		−	0.372505i	0.982502	−	0.186253i	$-0.0596343\pi$
$258$	−596780.	+	950331.i	−0.0347501	+	0.0553370i
$259$	−7.09092e6			−0.408135
$260$	−441371.	+	916516.i	−0.0251121	+	0.0521459i
$261$	−1.17534e6	−	2.44062e6i	−0.0661063	−	0.137271i
$262$	−3.85291e6	−	4.83139e6i	−0.214232	−	0.268639i
$263$	−2.33310e7	+	5.32515e6i	−1.28253	+	0.292728i	−0.808873	−	0.587983i	$-0.799922\pi$
$263$	−2.33310e7	+	5.32515e6i	−1.28253	+	0.292728i	−0.473653	+	0.880712i	$0.657065\pi$
$264$	1.26455e6			0.0687263
$265$			1.33567e7i			0.717731i
$266$	−7.36070e6	+	1.68003e6i	−0.391088	+	0.0892632i
$267$	−1.69333e6	+	2.12337e6i	−0.0889627	+	0.111556i
$268$	−2.11296e6	+	9.25749e6i	−0.109771	+	0.480938i
$269$	−6.68068e6	+	8.37731e6i	−0.343213	+	0.430375i	−0.923241	−	0.384221i	$-0.874470\pi$
$269$	−6.68068e6	+	8.37731e6i	−0.343213	+	0.430375i	0.580028	+	0.814596i	$0.303042\pi$
$270$	−938313.	+	1.94843e6i	−0.0476712	+	0.0989903i
$271$	7.44838e6	+	3.26335e7i	0.374243	+	1.63967i	0.714717	+	0.699413i	$0.246555\pi$
$271$	7.44838e6	+	3.26335e7i	0.374243	+	1.63967i	−0.340474	+	0.940254i	$0.610588\pi$
$272$	−4.18600e6	−	2.01587e6i	−0.208014	−	0.100174i
$273$	−247150.	−	309916.i	−0.0121471	−	0.0152320i
$274$	3.41384e6	−	1.49570e7i	0.165956	−	0.727099i
$275$	−977842.	+	4.28420e6i	−0.0470187	+	0.206002i
$276$	−242353.	−	503251.i	−0.0115271	−	0.0239363i
$277$	1.00708e6	−	803121.i	0.0473833	−	0.0377870i	−0.599512	−	0.800366i	$-0.704639\pi$
$277$	1.00708e6	−	803121.i	0.0473833	−	0.0377870i	0.646895	+	0.762579i	$0.276067\pi$
$278$	4.50417e6	+	3.59196e6i	0.209643	+	0.167185i
$279$	3.30760e6	−	1.59286e6i	0.152300	−	0.0733439i
$280$	1.22897e7	+	2.55198e7i	0.559844	+	1.16253i
$281$	−2.54542e6	+	3.19186e6i	−0.114721	+	0.143855i	−0.835876	−	0.548918i	$-0.815040\pi$
$281$	−2.54542e6	+	3.19186e6i	−0.114721	+	0.143855i	0.721156	+	0.692773i	$0.243611\pi$
$282$	691110.	+	866625.i	0.0308177	+	0.0386442i
$283$	−3.28203e7	+	1.58054e7i	−1.44805	+	0.697343i	−0.982255	−	0.187550i	$-0.939945\pi$
$283$	−3.28203e7	+	1.58054e7i	−1.44805	+	0.697343i	−0.465794	+	0.884893i	$0.654231\pi$
$284$	1.35814e7	+	3.09988e6i	0.592913	+	0.135329i
$285$	−621128.	−	141768.i	−0.0268316	−	0.00612414i
$286$	−1.60260e6	+	1.27803e6i	−0.0685057	+	0.0546315i
$287$	7.97794e6	−	1.65664e7i	0.337478	−	0.700780i
$288$	1.83271e7	−	4.18305e6i	0.767215	−	0.175112i
$289$	1.37179e7	+	6.60622e6i	0.568324	+	0.273690i
$290$	1.86051e6	+	1.48371e6i	0.0762849	+	0.0608352i
$291$	−3.60291e6	−	822341.i	−0.146209	−	0.0333713i
$292$	−1.15836e7	−	9.23762e6i	−0.465259	−	0.371032i
$293$	3.08235e6	+	1.35046e7i	0.122540	+	0.536884i	0.998513	+	0.0545225i	$0.0173637\pi$
$293$	3.08235e6	+	1.35046e7i	0.122540	+	0.536884i	−0.875972	+	0.482361i	$0.839779\pi$
$294$	−1.67328e6			−0.0658455
$295$			7.83652e6i			0.305251i
$296$	−1.79374e6	−	7.85888e6i	−0.0691646	−	0.303030i
$297$	2.59921e6	−	2.07280e6i	0.0992136	−	0.0791202i
$298$	7.27401e6	−	3.50298e6i	0.274869	−	0.132370i
$299$	2.70079e6	+	1.30063e6i	0.101036	+	0.0486565i
$300$		−	291791.i		−	0.0108071i
$301$	3.27236e7	+	2.05495e7i	1.19995	+	0.753532i
$302$	−1.75942e7			−0.638774
$303$	−493937.	+	1.02567e6i	−0.0177559	+	0.0368706i
$304$	−1.74104e6	−	3.61531e6i	−0.0619711	−	0.128684i
$305$	1.15453e6	+	1.44773e6i	0.0406916	+	0.0510256i
$306$	−1.26875e7	+	2.89584e6i	−0.442805	+	0.101067i
$307$	−5.14760e7			−1.77905			−0.889527	−	0.456882i	$-0.848966\pi$
$307$	−5.14760e7			−1.77905			−0.889527	+	0.456882i	$0.848966\pi$
$308$		−	1.31520e7i		−	0.450132i
$309$	−2.92549e6	+	667725.i	−0.0991571	+	0.0226320i
$310$	−2.01076e6	+	2.52142e6i	−0.0674956	+	0.0846368i
$311$	−3.58168e6	+	1.56924e7i	−0.119071	+	0.521684i	0.879850	+	0.475251i	$0.157643\pi$
$311$	−3.58168e6	+	1.56924e7i	−0.119071	+	0.521684i	−0.998921	+	0.0464333i	$0.985214\pi$
$312$	280961.	−	352313.i	0.00925085	−	0.0116002i
$313$	1.85893e7	−	3.86012e7i	0.606221	−	1.25883i	−0.341546	−	0.939865i	$-0.610950\pi$
$313$	1.85893e7	−	3.86012e7i	0.606221	−	1.25883i	0.947766	−	0.318965i	$-0.103335\pi$
$314$	−5.67062e6	−	2.48446e7i	−0.183164	−	0.802496i
$315$	3.34193e7	+	1.60939e7i	1.06922	+	0.514907i
$316$	−3.41267e6	−	4.27935e6i	−0.108151	−	0.135618i
$317$	1.12019e7	−	4.90786e7i	0.351652	−	1.54069i	−0.421715	−	0.906728i	$-0.638572\pi$
$317$	1.12019e7	−	4.90786e7i	0.351652	−	1.54069i	0.773367	−	0.633959i	$-0.218571\pi$
$318$	397673.	−	1.74232e6i	0.0123665	−	0.0541810i
$319$	−1.58725e6	−	3.29596e6i	−0.0488961	−	0.101534i
$320$	−2.11259e7	+	1.68474e7i	−0.644712	+	0.514141i
$321$	3.88947e6	+	3.10175e6i	0.117591	+	0.0937759i
$322$	2.27143e7	−	1.09386e7i	0.680349	−	0.327639i
$323$	−3.33953e6	−	6.93461e6i	−0.0991010	−	0.205785i
$324$	8.97041e6	−	1.12485e7i	0.263741	−	0.330721i
$325$	976356.	+	1.22431e6i	0.0284419	+	0.0356650i
$326$	1.39144e7	−	6.70082e6i	0.401617	−	0.193408i
$327$	2.58554e6	+	590132.i	0.0739448	+	0.0168774i
$328$	2.03787e7	+	4.65130e6i	0.577503	+	0.131811i
$329$	2.98413e7	−	2.37976e7i	0.837973	−	0.668261i
$330$	−631183.	+	1.31066e6i	−0.0175636	+	0.0364712i
$331$	−4.14229e6	+	945450.i	−0.114224	+	0.0260708i	−0.279251	−	0.960218i	$-0.590086\pi$
$331$	−4.14229e6	+	945450.i	−0.114224	+	0.0260708i	0.165027	+	0.986289i	$0.447229\pi$
$332$	−2.30909e7	−	1.11200e7i	−0.630997	−	0.303872i
$333$	−8.25316e6	−	6.58168e6i	−0.223505	−	0.178239i
$334$	4.08340e7	+	9.32010e6i	1.09593	+	0.250139i
$335$	−2.82755e7	−	2.25490e7i	−0.752101	−	0.599780i
$336$	−394275.	−	1.72743e6i	−0.0103940	−	0.0455390i
$337$	4.15530e6			0.108571			0.0542853	−	0.998525i	$-0.482712\pi$
$337$	4.15530e6			0.108571			0.0542853	+	0.998525i	$0.482712\pi$
$338$		−	2.83523e7i		−	0.734240i
$339$	1.08754e6	+	4.76481e6i	0.0279155	+	0.122306i
$340$	−6.81894e6	+	5.43793e6i	−0.173492	+	0.138356i
$341$	4.46678e6	−	2.15109e6i	0.112650	−	0.0542494i
$342$	−1.01265e7	−	4.87668e6i	−0.253153	−	0.121912i
$343$			439359.i			0.0108877i
$344$	−1.44972e7	+	4.14659e7i	−0.356130	+	1.01863i
$345$	2.12741e6			0.0518077
$346$	−4.54604e6	+	9.43996e6i	−0.109750	+	0.227899i
$347$	−2.59331e7	−	5.38506e7i	−0.620677	−	1.28885i	−0.939991	−	0.341200i	$-0.889167\pi$
$347$	−2.59331e7	−	5.38506e7i	−0.620677	−	1.28885i	0.319314	−	0.947649i	$-0.396548\pi$
$348$	151453.	+	189915.i	0.00359368	+	0.00450633i
$349$	−6.23044e7	+	1.42206e7i	−1.46569	+	0.334534i	−0.879601	−	0.475711i	$-0.842191\pi$
$349$	−6.23044e7	+	1.42206e7i	−1.46569	+	0.334534i	−0.586090	+	0.810246i	$0.699333\pi$
$350$	1.31700e7			0.307173
$351$		−	1.18470e6i		−	0.0273960i
$352$	2.47500e7	−	5.64904e6i	0.567477	−	0.129523i
$353$	−1.62729e7	+	2.04056e7i	−0.369948	+	0.463900i	−0.931606	−	0.363469i	$-0.881592\pi$
$353$	−1.62729e7	+	2.04056e7i	−0.369948	+	0.463900i	0.561658	+	0.827369i	$0.310164\pi$
$354$	233319.	−	1.02224e6i	0.00525946	−	0.0230432i
$355$	−3.30811e7	+	4.14824e7i	−0.739426	+	0.927211i
$356$	−1.39325e7	+	2.89311e7i	−0.308801	+	0.641231i
$357$	−756267.	−	3.31342e6i	−0.0166215	−	0.0728236i
$358$	1.32277e7	+	6.37012e6i	0.288294	+	0.138835i
$359$	−3.46189e7	−	4.34107e7i	−0.748221	−	0.938239i	0.251339	−	0.967899i	$-0.419129\pi$
$359$	−3.46189e7	−	4.34107e7i	−0.748221	−	0.938239i	−0.999560	+	0.0296598i	$0.990558\pi$
$360$	−9.38303e6	+	4.11098e7i	−0.201111	+	0.881125i
$361$	−8.98948e6	+	3.93855e7i	−0.191079	+	0.837172i
$362$	−2.02510e7	−	4.20516e7i	−0.426894	−	0.886455i
$363$	−1.49608e6	+	1.19308e6i	−0.0312777	+	0.0249431i
$364$	−3.66426e6	−	2.92215e6i	−0.0759770	−	0.0605896i
$365$	5.08414e7	−	2.44839e7i	1.04553	−	0.503503i
$366$	−107499.	−	223224.i	−0.00219261	−	0.00455300i
$367$	2.83224e7	−	3.55152e7i	0.572970	−	0.718482i	−0.407926	−	0.913015i	$-0.633748\pi$
$367$	2.83224e7	−	3.55152e7i	0.572970	−	0.718482i	0.980896	+	0.194533i	$0.0623192\pi$
$368$	8.35427e6	+	1.04759e7i	0.167635	+	0.210208i
$369$	2.46622e7	−	1.18767e7i	0.490854	−	0.236383i
$370$	9.04082e6	+	2.06351e6i	0.178485	+	0.0407381i
$371$	−5.99950e7	−	1.36935e7i	−1.17488	−	0.268158i
$372$	−257379.	+	205253.i	−0.00499970	+	0.00398712i
$373$	3.65907e7	−	7.59814e7i	0.705090	−	1.46413i	−0.172643	−	0.984984i	$-0.555231\pi$
$373$	3.65907e7	−	7.59814e7i	0.705090	−	1.46413i	0.877733	−	0.479150i	$-0.159055\pi$
$374$	−1.71340e7	+	3.91072e6i	−0.327524	+	0.0747552i
$375$	4.47992e6	+	2.15742e6i	0.0849526	+	0.0409110i
$376$	3.39237e7	+	2.70532e7i	0.638175	+	0.508927i
$377$	−1.27094e6	−	290085.i	−0.0237193	−	0.00541378i
$378$	−7.78987e6	−	6.21221e6i	−0.144230	−	0.115019i
$379$	2.68155e6	+	1.17486e7i	0.0492571	+	0.215809i	0.993567	−	0.113249i	$-0.0361258\pi$
$379$	2.68155e6	+	1.17486e7i	0.0492571	+	0.215809i	−0.944310	+	0.329058i	$0.893269\pi$
$380$	−7.53270e6			−0.137278
$381$		−	6.80133e6i		−	0.122976i
$382$	1.64589e6	+	7.21109e6i	0.0295263	+	0.129363i
$383$	8.13855e7	−	6.49028e7i	1.44861	−	1.15523i	0.489564	−	0.871967i	$-0.337156\pi$
$383$	8.13855e7	−	6.49028e7i	1.44861	−	1.15523i	0.959044	−	0.283259i	$-0.0914155\pi$
$384$	−252120.	+	121415.i	−0.00445260	+	0.00214426i
$385$	4.51313e7	+	2.17341e7i	0.790854	+	0.380855i
$386$			5.47701e7i			0.952318i
$387$	1.90135e7	+	5.42912e7i	0.328042	+	0.936691i
$388$	−4.36941e7			−0.748045
$389$	−2.52969e7	+	5.25296e7i	−0.429753	+	0.892391i	0.567846	+	0.823135i	$0.307777\pi$
$389$	−2.52969e7	+	5.25296e7i	−0.429753	+	0.892391i	−0.997599	+	0.0692562i	$0.977937\pi$
$390$	224924.	+	467060.i	0.00379178	+	0.00787370i
$391$	1.60245e7	+	2.00941e7i	0.268074	+	0.336154i
$392$	−6.38576e7	+	1.45751e7i	−1.06012	+	0.241965i
$393$	2.40250e6			0.0395810
$394$			7.73375e6i			0.126445i
$395$	2.03242e7	−	4.63887e6i	0.329779	−	0.0752698i
$396$	1.22075e7	−	1.53077e7i	0.196580	−	0.246504i
$397$	−2.06807e7	+	9.06083e7i	−0.330518	+	1.44809i	0.487613	+	0.873060i	$0.337868\pi$
$397$	−2.06807e7	+	9.06083e7i	−0.330518	+	1.44809i	−0.818131	+	0.575032i	$0.804989\pi$
$398$	−4.33089e7	+	5.43076e7i	−0.686954	+	0.861413i
$399$	1.27358e6	−	2.64461e6i	0.0200496	−	0.0416335i
$400$	1.55757e6	+	6.82416e6i	0.0243370	+	0.106628i
$401$	7.23519e7	+	3.48428e7i	1.12206	+	0.540356i	0.900529	−	0.434797i	$-0.143180\pi$
$401$	7.23519e7	+	3.48428e7i	1.12206	+	0.540356i	0.221533	+	0.975153i	$0.428894\pi$
$402$	3.01705e6	+	3.78326e6i	0.0464413	+	0.0582356i
$403$	393130.	−	1.72242e6i	0.00600650	−	0.0263162i
$404$	−2.99510e6	+	1.31224e7i	−0.0454221	+	0.199007i
$405$	2.37757e7	+	4.93707e7i	0.357905	+	0.743198i
$406$	−8.57186e6	+	6.83583e6i	−0.128085	+	0.102144i
$407$	−1.11456e7	−	8.88829e6i	−0.165317	−	0.131836i
$408$	3.48096e6	−	1.67634e6i	0.0512530	−	0.0246821i
$409$	−5.25467e7	−	1.09114e8i	−0.768026	−	1.59482i	−0.803394	−	0.595448i	$-0.796975\pi$
$409$	−5.25467e7	−	1.09114e8i	−0.768026	−	1.59482i	0.0353684	−	0.999374i	$-0.488740\pi$
$410$	−1.49927e7	+	1.88002e7i	−0.217534	+	0.272779i
$411$	3.71883e6	+	4.66327e6i	0.0535650	+	0.0671684i
$412$	−3.19653e7	+	1.53937e7i	−0.457075	+	0.220116i
$413$	−3.51997e7	−	8.03410e6i	−0.499676	−	0.114048i
$414$	3.65903e7	+	8.35150e6i	0.515662	+	0.117697i
$415$	7.63171e7	−	6.08608e7i	1.06777	−	0.851517i
$416$	3.92517e6	−	8.15069e6i	0.0545228	−	0.113218i
$417$	−2.18363e6	+	498399.i	−0.0301142	+	0.00687336i
$418$	−1.36755e7	−	6.58576e6i	−0.187246	−	0.0901731i
$419$	4.74066e6	+	3.78055e6i	0.0644461	+	0.0513940i	0.655183	−	0.755470i	$-0.272591\pi$
$419$	4.74066e6	+	3.78055e6i	0.0644461	+	0.0513940i	−0.590737	+	0.806864i	$0.701163\pi$
$420$	−3.24277e6	−	740140.i	−0.0437691	−	0.00999001i
$421$	9.90509e7	+	7.89905e7i	1.32743	+	1.05859i	0.993239	+	0.116087i	$0.0370352\pi$
$421$	9.90509e7	+	7.89905e7i	1.32743	+	1.05859i	0.334193	+	0.942505i	$0.391536\pi$
$422$	−1.45259e7	−	6.36423e7i	−0.193289	−	0.846854i
$423$	5.68210e7			0.750737
$424$		−	6.99564e7i		−	0.917762i
$425$	2.98761e6	+	1.30896e7i	0.0389186	+	0.170513i
$426$	5.55034e6	−	4.42625e6i	0.0717945	−	0.0572542i
$427$	−7.68648e6	+	3.70161e6i	−0.0987288	+	0.0475453i
$428$	5.29943e7	+	2.55207e7i	0.675923	+	0.325508i
$429$		−	796923.i		−	0.0100936i
$430$	−3.57421e7	−	3.57231e7i	−0.449547	−	0.449308i
$431$	−1.06466e8			−1.32978			−0.664890	−	0.746941i	$-0.731522\pi$
$431$	−1.06466e8			−1.32978			−0.664890	+	0.746941i	$0.731522\pi$
$432$	2.29763e6	−	4.77108e6i	0.0284989	−	0.0591787i
$433$	1.39680e7	+	2.90048e7i	0.172056	+	0.357278i	0.969110	−	0.246631i	$-0.0793234\pi$
$433$	1.39680e7	+	2.90048e7i	0.172056	+	0.357278i	−0.797053	+	0.603909i	$0.793609\pi$
$434$	−9.26410e6	−	1.16168e7i	−0.113327	−	0.142108i
$435$	−901979.	+	205871.i	−0.0109579	+	0.00250108i
$436$	3.13560e7			0.378321
$437$			2.21974e7i			0.265985i
$438$	−7.36099e6	+	1.68010e6i	−0.0876019	+	0.0199946i
$439$	−2.47684e7	+	3.10585e7i	−0.292755	+	0.367103i	−0.906357	−	0.422512i	$-0.861148\pi$
$439$	−2.47684e7	+	3.10585e7i	−0.292755	+	0.367103i	0.613603	+	0.789615i	$0.289720\pi$
$440$	−1.26714e7	+	5.55171e7i	−0.148753	+	0.651731i
$441$	−5.34796e7	+	6.70613e7i	−0.623552	+	0.781909i
$442$	−2.71732e6	+	5.64256e6i	−0.0314683	+	0.0653446i
$443$	−2.04106e7	−	8.94248e7i	−0.234771	−	1.02860i	−0.945625	−	0.325260i	$-0.894548\pi$
$443$	−2.04106e7	−	8.94248e7i	−0.234771	−	1.02860i	0.710853	−	0.703340i	$-0.248309\pi$
$444$	852851.	+	410711.i	0.00974370	+	0.00469232i
$445$	−7.62537e7	−	9.56191e7i	−0.865328	−	1.08509i
$446$	−1.97725e7	+	8.66288e7i	−0.222872	+	0.976468i
$447$	−698457.	+	3.06014e6i	−0.00782019	+	0.0342625i
$448$	−5.40156e7	−	1.12164e8i	−0.600738	−	1.24744i
$449$	−2.36662e7	+	1.88731e7i	−0.261450	+	0.208500i	−0.745438	−	0.666575i	$-0.767759\pi$
$449$	−2.36662e7	+	1.88731e7i	−0.261450	+	0.208500i	0.483987	+	0.875075i	$0.339188\pi$
$450$	1.53287e7	+	1.22242e7i	0.168216	+	0.134148i
$451$	3.33053e7	−	1.60390e7i	0.363064	−	0.174843i
$452$	2.50720e7	+	5.20625e7i	0.271502	+	0.563780i
$453$	4.26484e6	−	5.34794e6i	0.0458784	−	0.0575296i
$454$	−2.34705e7	−	2.94311e7i	−0.250816	−	0.314513i
$455$	1.60827e7	−	7.74503e6i	0.170736	−	0.0822222i
$456$	3.25319e6	+	742519.i	0.0343095	+	0.00783093i
$457$	−4.99753e7	−	1.14065e7i	−0.523609	−	0.119510i	−0.0474570	−	0.998873i	$-0.515112\pi$
$457$	−4.99753e7	−	1.14065e7i	−0.523609	−	0.119510i	−0.476152	+	0.879363i	$0.657969\pi$
$458$	−4.79323e6	+	3.82247e6i	−0.0498921	+	0.0397876i
$459$	4.40713e6	−	9.15150e6i	0.0455741	−	0.0946355i
$460$	2.45226e7	−	5.59712e6i	0.251937	−	0.0575031i
$461$	−6.83480e7	−	3.29147e7i	−0.697627	−	0.335959i	0.0512339	−	0.998687i	$-0.483685\pi$
$461$	−6.83480e7	−	3.29147e7i	−0.697627	−	0.335959i	−0.748861	+	0.662727i	$0.769399\pi$
$462$	−5.24008e6	−	4.17882e6i	−0.0531388	−	0.0423768i
$463$	−3.01568e7	−	6.88308e6i	−0.303838	−	0.0693490i	0.0678839	−	0.997693i	$-0.478375\pi$
$463$	−3.01568e7	−	6.88308e6i	−0.303838	−	0.0693490i	−0.371722	+	0.928344i	$0.621232\pi$
$464$	−4.55580e6	−	3.63313e6i	−0.0456048	−	0.0363686i
$465$	−279002.	−	1.22239e6i	−0.00277490	−	0.0121576i
$466$	1.42589e8			1.40906
$467$			1.73581e6i			0.0170432i	0.999964	+	0.00852160i	$0.00271254\pi$
$467$			1.73581e6i			0.0170432i	−0.999964	+	0.00852160i	$0.997287\pi$
$468$	−1.55256e6	−	6.80221e6i	−0.0151464	−	0.0663609i
$469$	1.30273e8	−	1.03889e8i	1.26280	−	1.00705i
$470$	−4.49725e7	+	2.16576e7i	−0.433165	+	0.208601i
$471$	8.92635e6	+	4.29870e6i	0.0854301	+	0.0411410i
$472$		−	4.10442e7i		−	0.390324i
$473$	2.56770e7	+	7.33180e7i	0.242639	+	0.692831i
$474$	−2.78931e6			−0.0261916
$475$	−5.03122e6	+	1.04474e7i	−0.0469453	+	0.0974829i
$476$	−1.74349e7	−	3.62040e7i	−0.161659	−	0.335688i
$477$	−5.71184e7	−	7.16242e7i	−0.526285	−	0.659940i
$478$	−1.03908e8	+	2.37162e7i	−0.951401	+	0.217151i
$479$	1.28183e8			1.16633			0.583167	−	0.812352i	$-0.301813\pi$
$479$	1.28183e8			1.16633			0.583167	+	0.812352i	$0.301813\pi$
$480$		−	6.42029e6i		−	0.0580539i
$481$	−4.95270e6	+	1.13042e6i	−0.0445048	+	0.0101579i
$482$	7.18996e7	−	9.01592e7i	0.642074	−	0.805136i
$483$	−2.18105e6	+	9.55579e6i	−0.0193564	+	0.0848057i
$484$	−1.41063e7	+	1.76888e7i	−0.124416	+	0.156013i
$485$	7.22060e7	−	1.49937e8i	0.632919	−	1.31427i
$486$	−4.95713e6	−	2.17186e7i	−0.0431838	−	0.189201i
$487$	−3.78494e7	−	1.82273e7i	−0.327697	−	0.157811i	0.262800	−	0.964850i	$-0.415354\pi$
$487$	−3.78494e7	−	1.82273e7i	−0.327697	−	0.157811i	−0.590497	+	0.807040i	$0.701068\pi$
$488$	−6.04689e6	−	7.58256e6i	−0.0520323	−	0.0652464i
$489$	−1.33607e6	+	5.85372e6i	−0.0114262	+	0.0500617i
$490$	1.67671e7	−	7.34614e7i	0.142518	−	0.624412i
$491$	8.35082e7	+	1.73407e8i	0.705480	+	1.46494i	0.877363	+	0.479827i	$0.159300\pi$
$491$	8.35082e7	+	1.73407e8i	0.705480	+	1.46494i	−0.171883	+	0.985117i	$0.554985\pi$
$492$	−1.91907e6	+	1.53041e6i	−0.0161137	+	0.0128503i
$493$	−8.73858e6	−	6.96878e6i	−0.0729289	−	0.0581589i
$494$	−4.87330e6	+	2.34686e6i	−0.0404243	+	0.0194673i
$495$	3.23554e7	+	6.71866e7i	0.266766	+	0.553945i
$496$	4.92372e6	−	6.17414e6i	0.0403504	−	0.0505978i
$497$	−1.52413e8	−	1.91120e8i	−1.24152	−	1.55682i
$498$	−1.17672e7	+	5.66680e6i	−0.0952766	+	0.0458828i
$499$	8.32958e7	+	1.90117e7i	0.670380	+	0.153010i	0.544146	−	0.838991i	$-0.316854\pi$
$499$	8.32958e7	+	1.90117e7i	0.670380	+	0.153010i	0.126234	+	0.992000i	$0.459711\pi$
$500$	5.73159e7	+	1.30820e7i	0.458528	+	0.104656i
$501$	−1.27312e7	+	1.01528e7i	−0.101241	+	0.0807366i
$502$	−2.64983e6	+	5.50244e6i	−0.0209463	+	0.0434955i
$503$	−5.82375e7	+	1.32923e7i	−0.457613	+	0.104447i	−0.445113	−	0.895475i	$-0.646836\pi$
$503$	−5.82375e7	+	1.32923e7i	−0.457613	+	0.104447i	−0.0125006	+	0.999922i	$0.503979\pi$
$504$	−1.75035e8	−	8.42924e7i	−1.36720	−	0.658411i
$505$	−4.00803e7	−	3.19629e7i	−0.311212	−	0.248183i
$506$	4.94137e7	+	1.12784e7i	0.381414	+	0.0870552i
$507$	8.61799e6	+	6.87262e6i	0.0661275	+	0.0527349i
$508$	−1.78940e7	−	7.83987e7i	−0.136495	−	0.598023i
$509$	4.11004e7			0.311669			0.155834	−	0.987783i	$-0.450193\pi$
$509$	4.11004e7			0.311669			0.155834	+	0.987783i	$0.450193\pi$
$510$			4.44464e6i			0.0335063i
$511$	5.78523e7	+	2.53468e8i	0.433569	+	1.89959i
$512$	7.46408e7	−	5.95240e7i	0.556117	−	0.443489i
$513$	7.90386e6	−	3.80630e6i	0.0585446	−	0.0281936i
$514$	−3.43255e7	−	1.65303e7i	−0.252771	−	0.121728i
$515$		−	1.35128e8i		−	0.989291i
$516$	−2.74555e6	−	4.36694e6i	−0.0199839	−	0.0317854i
$517$	7.67345e7			0.555289
$518$	−1.85375e7	+	3.84935e7i	−0.133371	+	0.276948i
$519$	−1.76741e6	−	3.67007e6i	−0.0126426	−	0.0262526i
$520$	1.26522e7	+	1.58653e7i	0.0899818	+	0.112834i
$521$	2.26119e7	−	5.16102e6i	0.159891	−	0.0364940i	−0.141826	−	0.989892i	$-0.545297\pi$
$521$	2.26119e7	−	5.16102e6i	0.159891	−	0.0364940i	0.301717	+	0.953398i	$0.402440\pi$
$522$	−1.63217e7			−0.114751
$523$			1.45802e8i			1.01920i	0.860412	+	0.509599i	$0.170206\pi$
$523$			1.45802e8i			1.01920i	−0.860412	+	0.509599i	$0.829794\pi$
$524$	2.76936e7	−	6.32088e6i	0.192480	−	0.0439322i
$525$	−3.19243e6	+	4.00318e6i	−0.0220619	+	0.0276648i
$526$	−3.20854e7	+	1.40575e8i	−0.220470	+	0.965943i
$527$	9.44428e6	−	1.18428e7i	0.0645263	−	0.0809135i
$528$	1.54557e6	−	3.20940e6i	0.0104999	−	0.0218033i
$529$	1.64475e7	+	7.20611e7i	0.111105	+	0.486781i
$530$	7.25078e7	+	3.49179e7i	0.487031	+	0.234542i
$531$	−3.35120e7	−	4.20227e7i	−0.223829	−	0.280673i
$532$	7.72262e6	−	3.38350e7i	0.0512896	−	0.224715i
$533$	2.93127e6	−	1.28427e7i	0.0193586	−	0.0848156i
$534$	7.10005e6	+	1.47434e7i	0.0466270	+	0.0968219i
$535$	−1.75150e8	+	1.39677e8i	−1.14379	+	0.912145i
$536$	1.48094e8	+	1.18101e8i	0.961711	+	0.766939i
$537$	−5.14267e6	+	2.47658e6i	−0.0332098	+	0.0159930i
$538$	2.80117e7	+	5.81669e7i	0.179884	+	0.373533i
$539$	−7.22220e7	+	9.05635e7i	−0.461215	+	0.578345i
$540$	−6.19799e6	−	7.77203e6i	−0.0393613	−	0.0493575i
$541$	−2.63767e8	+	1.27024e8i	−1.66583	+	0.802219i	−0.667485	+	0.744623i	$0.732629\pi$
$541$	−2.63767e8	+	1.27024e8i	−1.66583	+	0.802219i	−0.998340	+	0.0575962i	$0.981656\pi$
$542$	1.96625e8	+	4.48784e7i	1.23493	+	0.281864i
$543$	1.76909e7	+	4.03783e6i	0.110497	+	0.0252202i
$544$	6.06417e7	−	4.83602e7i	0.376682	−	0.300394i
$545$	−5.18168e7	+	1.07599e8i	−0.320097	+	0.664687i
$546$	−2.32851e6	+	531468.i	−0.0143054	+	0.00326512i
$547$	4.47452e7	+	2.15481e7i	0.273391	+	0.131658i	0.565556	−	0.824710i	$-0.308662\pi$
$547$	4.47452e7	+	2.15481e7i	0.273391	+	0.131658i	−0.292165	+	0.956368i	$0.594376\pi$
$548$	5.51357e7	+	4.39693e7i	0.335036	+	0.267182i
$549$	−1.23821e7	−	2.82613e6i	−0.0748303	−	0.0170795i
$550$	2.07008e7	+	1.65083e7i	0.124422	+	0.0992234i
$551$	−2.14806e6	−	9.41124e6i	−0.0128408	−	0.0562590i
$552$	−1.11424e7			−0.0662464
$553$			9.60470e7i			0.567948i
$554$	−1.72702e6	−	7.56658e6i	−0.0101571	−	0.0445011i
$555$	−2.81873e6	+	2.24786e6i	−0.0164882	+	0.0131489i
$556$	−2.38593e7	+	1.14901e7i	−0.138814	+	0.0668494i
$557$	−1.65874e8	−	7.98808e7i	−0.959872	−	0.462250i	−0.112735	−	0.993625i	$-0.535961\pi$
$557$	−1.65874e8	−	7.98808e7i	−0.959872	−	0.462250i	−0.847137	+	0.531375i	$0.821676\pi$
$558$		−	2.21197e7i		−	0.127314i
$559$	2.61320e7	+	9.13619e6i	0.149602	+	0.0523034i
$560$	7.97898e7			0.454343
$561$	2.96458e6	−	6.15602e6i	0.0167909	−	0.0348667i
$562$	1.06728e7	+	2.21624e7i	0.0601271	+	0.124855i
$563$	−1.32434e8	−	1.66067e8i	−0.742121	−	0.930590i	0.257240	−	0.966348i	$-0.417187\pi$
$563$	−1.32434e8	−	1.66067e8i	−0.742121	−	0.930590i	−0.999360	+	0.0357574i	$0.988616\pi$
$564$	−4.96750e6	+	1.13380e6i	−0.0276886	+	0.00631973i
$565$	−2.20086e8			−1.22024
$566$			2.19487e8i			1.21048i
$567$	−2.46136e8	+	5.61789e7i	−1.35029	+	0.308194i
$568$	1.73264e8	−	2.17266e8i	0.945503	−	1.18562i
$569$	−1.85537e7	+	8.12893e7i	−0.100715	+	0.441262i	0.899277	+	0.437379i	$0.144093\pi$
$569$	−1.85537e7	+	8.12893e7i	−0.100715	+	0.441262i	−0.999992	+	0.00388303i	$0.998764\pi$
$570$	−2.39339e6	+	3.00121e6i	−0.0129238	+	0.0162059i
$571$	5.65005e7	−	1.17325e8i	0.303490	−	0.630203i	−0.692326	−	0.721585i	$-0.743414\pi$
$571$	5.65005e7	−	1.17325e8i	0.303490	−	0.630203i	0.995816	+	0.0913815i	$0.0291283\pi$
$572$	−2.09667e6	−	9.18610e6i	−0.0112032	−	0.0490844i
$573$	−2.59086e6	−	1.24769e6i	−0.0137714	−	0.00663198i
$574$	−6.90752e7	−	8.66176e7i	−0.365247	−	0.458005i
$575$	8.61615e6	−	3.77498e7i	0.0453221	−	0.198569i
$576$	4.12402e7	−	1.80685e8i	0.215801	−	0.945486i
$577$	−3.06430e7	−	6.36308e7i	−0.159516	−	0.331238i	0.805858	−	0.592109i	$-0.201704\pi$
$577$	−3.06430e7	−	6.36308e7i	−0.159516	−	0.331238i	−0.965374	+	0.260871i	$0.915990\pi$
$578$	7.17245e7	−	5.71984e7i	0.371436	−	0.296211i
$579$	−1.66480e7	−	1.32763e7i	−0.0857681	−	0.0683978i
$580$	−9.85544e6	+	4.74613e6i	−0.0505117	+	0.0243252i
$581$	1.95130e8	+	4.05192e8i	0.994938	+	2.06601i
$582$	−1.38831e7	+	1.74088e7i	−0.0704233	+	0.0883080i
$583$	−7.71361e7	−	9.67256e7i	−0.389271	−	0.488130i
$584$	−2.66284e8	+	1.28236e8i	−1.33692	+	0.643829i
$585$	2.59076e7	+	5.91323e6i	0.129407	+	0.0295364i
$586$	8.13689e7	+	1.85719e7i	0.404358	+	0.0922920i
$587$	1.10311e8	−	8.79702e7i	0.545387	−	0.434932i	−0.311642	−	0.950200i	$-0.600879\pi$
$587$	1.10311e8	−	8.79702e7i	0.545387	−	0.434932i	0.857029	+	0.515268i	$0.172307\pi$
$588$	3.33725e6	−	6.92986e6i	0.0164156	−	0.0340873i
$589$	1.27544e7	−	2.91110e6i	0.0624185	−	0.0142466i
$590$	4.25411e7	+	2.04867e7i	0.207135	+	0.0997507i
$591$	−2.35076e6	−	1.87467e6i	−0.0113880	−	0.00908159i
$592$	−2.21381e7	−	5.05288e6i	−0.106703	−	0.0243542i
$593$	1.79045e8	+	1.42783e8i	0.858613	+	0.684721i	0.950391	−	0.311059i	$-0.100684\pi$
$593$	1.79045e8	+	1.42783e8i	0.858613	+	0.684721i	−0.0917780	+	0.995779i	$0.529255\pi$
$594$	−4.45732e6	−	1.95288e7i	−0.0212674	−	0.0931786i
$595$	1.53047e8			0.726562
$596$			3.71117e7i			0.175296i
$597$	−6.00929e6	−	2.63284e7i	−0.0282423	−	0.123738i
$598$	1.41211e7	−	1.12612e7i	0.0660338	−	0.0526602i
$599$	−9.09512e7	+	4.37998e7i	−0.423183	+	0.203794i	−0.633340	−	0.773874i	$-0.718317\pi$
$599$	−9.09512e7	+	4.37998e7i	−0.423183	+	0.203794i	0.210158	+	0.977668i	$0.432602\pi$
$600$	−5.24429e6	−	2.52552e6i	−0.0242791	−	0.0116922i
$601$		−	1.62986e8i		−	0.750803i	−0.926862	−	0.375402i	$-0.877505\pi$
$601$		−	1.62986e8i		−	0.750803i	0.926862	−	0.375402i	$-0.122495\pi$
$602$	1.97102e8	−	1.23921e8i	0.903446	−	0.568008i
$603$	2.48053e8			1.13134
$604$	3.50904e7	−	7.28660e7i	0.159249	−	0.330685i
$605$	−3.73882e7	−	7.76373e7i	−0.168837	−	0.350594i
$606$	4.27664e6	+	5.36274e6i	0.0192170	+	0.0240973i
$607$	−2.31342e8	+	5.28024e7i	−1.03440	+	0.236095i	−0.705828	−	0.708383i	$-0.749425\pi$
$607$	−2.31342e8	+	5.28024e7i	−1.03440	+	0.236095i	−0.328573	+	0.944479i	$0.606568\pi$
$608$	6.69893e7			0.298054
$609$		−	4.26252e6i		−	0.0188719i
$610$	1.08773e7	−	2.48268e6i	0.0479218	−	0.0109378i
$611$	1.70491e7	−	2.13789e7i	0.0747442	−	0.0937263i
$612$	1.33113e7	−	5.83208e7i	0.0580721	−	0.254431i
$613$	6.52690e7	−	8.18448e7i	0.283352	−	0.355312i	−0.619704	−	0.784836i	$-0.712747\pi$
$613$	6.52690e7	−	8.18448e7i	0.283352	−	0.355312i	0.903055	+	0.429524i	$0.141319\pi$
$614$	−1.34571e8	+	2.79441e8i	−0.581364	+	1.20721i
$615$	−2.08030e6	−	9.11438e6i	−0.00894335	−	0.0391834i
$616$	−2.36378e8	−	1.13833e8i	−1.01126	−	0.486999i
$617$	−1.92922e8	−	2.41916e8i	−0.821344	−	1.02993i	−0.998949	−	0.0458314i	$-0.985406\pi$
$617$	−1.92922e8	−	2.41916e8i	−0.821344	−	1.02993i	0.177605	−	0.984102i	$-0.443165\pi$
$618$	−4.02321e6	+	1.76268e7i	−0.0170454	+	0.0746808i
$619$	7.13660e7	−	3.12675e8i	0.300898	−	1.31832i	−0.567877	−	0.823114i	$-0.692235\pi$
$619$	7.13660e7	−	3.12675e8i	0.300898	−	1.31832i	0.868775	−	0.495207i	$-0.164908\pi$
$620$	−6.43208e6	−	1.33564e7i	−0.0269884	−	0.0560419i
$621$	−2.29026e7	+	1.82642e7i	−0.0956336	+	0.0762653i
$622$	7.58236e7	+	6.04673e7i	0.315089	+	0.251275i
$623$	5.07673e8	−	2.44482e8i	2.09952	−	1.01108i
$624$	−550768.	−	1.14368e6i	−0.00226681	−	0.00470708i
$625$	−9.57930e7	+	1.20121e8i	−0.392368	+	0.492014i
$626$	−1.60952e8	−	2.01827e8i	−0.656103	−	0.822727i
$627$	5.31676e6	−	2.56042e6i	0.0215697	−	0.0103874i
$628$	1.14203e8	+	2.60662e7i	0.461105	+	0.105244i
$629$	−4.24635e7	−	9.69202e6i	−0.170633	−	0.0389460i
$630$	1.74733e8	−	1.39345e8i	0.698801	−	0.557275i
$631$	−4.56312e7	+	9.47542e7i	−0.181624	+	0.377147i	−0.971826	−	0.235700i	$-0.924262\pi$
$631$	−4.56312e7	+	9.47542e7i	−0.181624	+	0.377147i	0.790201	+	0.612847i	$0.209976\pi$
$632$	−1.06449e8	+	2.42963e7i	−0.421687	+	0.0962474i
$633$	2.28659e7	+	1.10116e7i	0.0901523	+	0.0434150i
$634$	−2.37142e8	−	1.89114e8i	−0.930551	−	0.742090i
$635$	2.98597e8	+	6.81529e7i	1.16618	+	0.266172i
$636$	6.42267e6	+	5.12191e6i	0.0249657	+	0.0199095i
$637$	9.18528e6	+	4.02433e7i	0.0355365	+	0.155695i
$638$	−2.20418e7			−0.0848762
$639$		−	3.63913e8i		−	1.39475i
$640$	−2.80406e6	−	1.22854e7i	−0.0106966	−	0.0468651i
$641$	4.88536e7	−	3.89594e7i	0.185491	−	0.147924i	−0.526342	−	0.850273i	$-0.676437\pi$
$641$	4.88536e7	−	3.89594e7i	0.185491	−	0.147924i	0.711833	+	0.702349i	$0.247865\pi$
$642$	2.70061e7	−	1.30055e7i	0.102060	−	0.0491496i
$643$	−1.12694e8	−	5.42705e7i	−0.423904	−	0.204141i	0.209755	−	0.977754i	$-0.432733\pi$
$643$	−1.12694e8	−	5.42705e7i	−0.423904	−	0.204141i	−0.633659	+	0.773613i	$0.718448\pi$
$644$			1.15887e8i			0.433889i
$645$	1.95223e7	−	2.20490e6i	0.0727533	−	0.00821692i
$646$	−4.63754e7			−0.172024
$647$	−6.99913e7	+	1.45338e8i	−0.258423	+	0.536621i	−0.989301	−	0.145887i	$-0.953396\pi$
$647$	−6.99913e7	+	1.45338e8i	−0.258423	+	0.536621i	0.730878	+	0.682508i	$0.239111\pi$
$648$	−1.24526e8	−	2.58582e8i	−0.457653	−	0.950326i
$649$	−4.52566e7	−	5.67499e7i	−0.165557	−	0.207602i
$650$	9.19871e6	−	2.09954e6i	0.0334955	−	0.00764513i
$651$	5.77669e6			0.0209380
$652$			7.09907e7i			0.256129i
$653$	−5.15400e7	+	1.17637e7i	−0.185099	+	0.0422478i	−0.314066	−	0.949401i	$-0.601691\pi$
$653$	−5.15400e7	+	1.17637e7i	−0.185099	+	0.0422478i	0.128966	+	0.991649i	$0.458834\pi$
$654$	9.96283e6	−	1.24930e7i	0.0356164	−	0.0446615i
$655$	−2.40743e7	+	1.05476e8i	−0.0856703	+	0.375346i
$656$	3.67123e7	−	4.60358e7i	0.130047	−	0.163074i
$657$	−1.67930e8	+	3.48710e8i	−0.592150	+	1.22961i
$658$	−5.11742e7	−	2.24209e8i	−0.179628	−	0.787000i
$659$	2.59599e8	+	1.25016e8i	0.907084	+	0.436829i	0.828442	−	0.560074i	$-0.189227\pi$
$659$	2.59599e8	+	1.25016e8i	0.907084	+	0.436829i	0.0786416	+	0.996903i	$0.474942\pi$
$660$	−4.16925e6	−	5.22808e6i	−0.0145020	−	0.0181849i
$661$	2.00354e7	−	8.77806e7i	0.0693733	−	0.303944i	−0.928324	−	0.371773i	$-0.878750\pi$
$661$	2.00354e7	−	8.77806e7i	0.0693733	−	0.303944i	0.997697	+	0.0678286i	$0.0216071\pi$
$662$	−5.69657e6	+	2.49583e7i	−0.0196354	+	0.0860283i
$663$	−1.05644e6	−	2.19372e6i	−0.00362497	−	0.00752733i
$664$	−3.99714e8	+	3.18762e8i	−1.36535	+	1.08883i
$665$	1.03344e8	+	8.24138e7i	0.351414	+	0.280243i
$666$	−5.73050e7	+	2.75966e7i	−0.193986	+	0.0934185i
$667$	1.39859e7	+	2.90420e7i	0.0471317	+	0.0978700i
$668$	−1.20040e8	+	1.50525e8i	−0.402714	+	0.504987i
$669$	−2.15389e7	−	2.70090e7i	−0.0719359	−	0.0902048i
$670$	−1.96328e8	+	9.45466e7i	−0.652767	+	0.314356i
$671$	−1.67215e7	−	3.81658e6i	−0.0553488	−	0.0126330i
$672$	2.88383e7	+	6.58216e6i	0.0950304	+	0.0216901i
$673$	1.61975e8	−	1.29171e8i	0.531378	−	0.423760i	−0.320695	−	0.947182i	$-0.603917\pi$
$673$	1.61975e8	−	1.29171e8i	0.531378	−	0.423760i	0.852073	+	0.523423i	$0.175345\pi$
$674$	1.08630e7	−	2.25573e7i	0.0354790	−	0.0736728i
$675$	−1.49191e7	+	3.40519e6i	−0.0485100	+	0.0110721i
$676$	1.17421e8	+	5.65469e7i	0.380106	+	0.183049i
$677$	−3.47863e8	−	2.77412e8i	−1.12110	−	0.894044i	−0.125909	−	0.992042i	$-0.540185\pi$
$677$	−3.47863e8	−	2.77412e8i	−1.12110	−	0.894044i	−0.995187	+	0.0979982i	$0.968756\pi$
$678$	2.87092e7	+	6.55268e6i	0.0921153	+	0.0210247i
$679$	5.99454e8	+	4.78049e8i	1.91490	+	1.52708i
$680$	3.87150e7	+	1.69622e8i	0.123127	+	0.539454i
$681$	1.46352e7			0.0463401
$682$		−	2.98717e7i		−	0.0941687i
$683$	−7.75309e6	−	3.39685e7i	−0.0243340	−	0.106614i	0.961302	−	0.275495i	$-0.0888418\pi$
$683$	−7.75309e6	−	3.39685e7i	−0.0243340	−	0.106614i	−0.985636	+	0.168881i	$0.945985\pi$
$684$	4.03935e7	−	3.22127e7i	0.126224	−	0.100660i
$685$	−2.41995e8	+	1.16539e8i	−0.752895	+	0.362575i
$686$	2.38509e6	+	1.14860e6i	0.00738809	+	0.00355792i
$687$		−	2.38353e6i		−	0.00735105i
$688$	8.75210e7	+	8.74745e7i	0.268749	+	0.268606i
$689$	−4.40869e7			−0.134788
$690$	5.56160e6	−	1.15488e7i	0.0169298	−	0.0351552i
$691$	4.92143e7	+	1.02194e8i	0.149162	+	0.309737i	0.962140	−	0.272557i	$-0.0878694\pi$
$691$	4.92143e7	+	1.02194e8i	0.149162	+	0.309737i	−0.812978	+	0.582294i	$0.802155\pi$
$692$	−3.00287e7	−	3.76548e7i	−0.0906188	−	0.113632i
$693$	−3.34956e8	+	7.64516e7i	−1.00644	+	0.229714i
$694$	−3.60127e8			−1.07740
$695$		−	1.00862e8i		−	0.300449i
$696$	4.72416e6	−	1.07826e6i	0.0140119	−	0.00319812i
$697$	7.04187e7	−	8.83022e7i	0.207965	−	0.260779i
$698$	−8.56826e7	+	3.75400e8i	−0.251957	+	1.10390i
$699$	−3.45637e7	+	4.33415e7i	−0.101202	+	0.126903i
$700$	−2.62668e7	+	5.45436e7i	−0.0765796	+	0.159019i
$701$	−9.67754e7	−	4.24001e8i	−0.280938	−	1.23087i	−0.896593	−	0.442855i	$-0.853966\pi$
$701$	−9.67754e7	−	4.24001e8i	−0.280938	−	1.23087i	0.615655	−	0.788016i	$-0.288892\pi$
$702$	−6.43123e6	−	3.09712e6i	−0.0185901	−	0.00895254i
$703$	−2.34542e7	−	2.94106e7i	−0.0675078	−	0.0846521i
$704$	5.56932e7	−	2.44008e8i	0.159619	−	0.699336i
$705$	4.31830e6	−	1.89197e7i	0.0123238	−	0.0539942i
$706$	6.82314e7	+	1.41684e8i	0.193897	+	0.402630i
$707$	1.84660e8	−	1.47262e8i	0.522535	−	0.416707i
$708$	3.76825e6	+	3.00508e6i	0.0106179	+	0.00846752i
$709$	1.32315e8	−	6.37195e7i	0.371253	−	0.178786i	−0.238949	−	0.971032i	$-0.576803\pi$
$709$	1.32315e8	−	6.37195e7i	0.371253	−	0.178786i	0.610202	+	0.792246i	$0.291088\pi$
$710$	1.38707e8	+	2.88028e8i	0.387547	+	0.804749i
$711$	−8.91492e7	+	1.11790e8i	−0.248033	+	0.311023i
$712$	3.99383e8	+	5.00810e8i	1.10649	+	1.38750i
$713$	−3.93585e7	+	1.89541e7i	−0.108585	+	0.0522919i
$714$	−1.99642e7	−	4.55670e6i	−0.0548476	−	0.0125186i
$715$	3.49871e7	+	7.98558e6i	0.0957172	+	0.0218468i
$716$	−5.27636e7	+	4.20776e7i	−0.143746	+	0.114634i
$717$	1.79785e7	−	3.73327e7i	0.0487748	−	0.101282i
$718$	−3.26161e8	+	7.44440e7i	−0.881167	+	0.201121i
$719$	4.07065e8	+	1.96032e8i	1.09516	+	0.527400i	0.892133	−	0.451773i	$-0.149208\pi$
$719$	4.07065e8	+	1.96032e8i	1.09516	+	0.527400i	0.203025	+	0.979174i	$0.434923\pi$
$720$	9.28678e7	+	7.40596e7i	0.248810	+	0.198419i
$721$	6.06962e8	+	1.38535e8i	1.61940	+	0.369619i
$722$	1.90306e8	+	1.51764e8i	0.505639	+	0.403234i
$723$	9.97637e6	+	4.37093e7i	0.0263972	+	0.115654i
$724$	2.14546e8			0.565332
$725$			1.68389e7i			0.0441877i
$726$	2.56559e6	+	1.12406e7i	0.00670468	+	0.0293751i
$727$	3.22701e8	−	2.57345e8i	0.839840	−	0.669750i	−0.106006	−	0.994366i	$-0.533806\pi$
$727$	3.22701e8	−	2.57345e8i	0.839840	−	0.669750i	0.945846	+	0.324615i	$0.105235\pi$
$728$	−8.42341e7	+	4.05650e7i	−0.218320	+	0.105137i
$729$	−3.33388e8	−	1.60551e8i	−0.860533	−	0.414411i
$730$		−	3.40003e8i		−	0.874005i
$731$	1.67876e8	+	1.67787e8i	0.429770	+	0.429542i
$732$	1.13888e6			0.00290365
$733$	−1.64914e8	+	3.42448e8i	−0.418742	+	0.869526i	0.579759	+	0.814788i	$0.303147\pi$
$733$	−1.64914e8	+	3.42448e8i	−0.418742	+	0.869526i	−0.998501	+	0.0547383i	$0.982568\pi$
$734$	−1.18754e8	−	2.46596e8i	−0.300304	−	0.623588i
$735$	1.82651e7	+	2.29037e7i	0.0460001	+	0.0576823i
$736$	−2.18082e8	+	4.97759e7i	−0.547000	+	0.124849i
$737$	3.34986e8			0.836804
$738$		−	1.64929e8i		−	0.410325i
$739$	2.59792e8	−	5.92959e7i	0.643714	−	0.146924i	0.111812	−	0.993729i	$-0.464335\pi$
$739$	2.59792e8	−	5.92959e7i	0.643714	−	0.146924i	0.531902	+	0.846806i	$0.321477\pi$
$740$	−2.65773e7	+	3.33269e7i	−0.0655868	+	0.0822433i
$741$	467939.	−	2.05018e6i	0.00115010	−	0.00503891i
$742$	−2.31178e8	+	2.89888e8i	−0.565894	+	0.709609i
$743$	−1.02698e8	+	2.13255e8i	−0.250378	+	0.519916i	−0.987840	−	0.155473i	$-0.950310\pi$
$743$	−1.02698e8	+	2.13255e8i	−0.250378	+	0.519916i	0.737462	+	0.675389i	$0.236024\pi$
$744$	1.46129e6	+	6.40231e6i	0.00354827	+	0.0155460i
$745$	−1.27350e8	−	6.13284e7i	−0.307985	−	0.148318i
$746$	−3.16812e8	−	3.97270e8i	−0.763108	−	0.956907i
$747$	−1.48979e8	+	6.52722e8i	−0.357408	+	1.56591i
$748$	1.79764e7	−	7.87599e7i	0.0429535	−	0.188192i
$749$	−4.47829e8	−	9.29926e8i	−1.06578	−	2.21311i
$750$	2.34234e7	−	1.86795e7i	0.0555220	−	0.0442773i
$751$	5.05111e7	+	4.02812e7i	0.119252	+	0.0951005i	0.681300	−	0.732004i	$-0.261415\pi$
$751$	5.05111e7	+	4.02812e7i	0.119252	+	0.0951005i	−0.562048	+	0.827105i	$0.689986\pi$
$752$	1.10123e8	−	5.30326e7i	0.258956	−	0.124707i
$753$	−1.03020e6	−	2.13924e6i	−0.00241290	−	0.00501043i
$754$	−4.89732e6	+	6.14104e6i	−0.0114247	+	0.0143261i
$755$	1.92053e8	+	2.40827e8i	0.446253	+	0.559583i
$756$	4.12642e7	−	1.98718e7i	0.0955011	−	0.0459909i
$757$	1.49884e8	+	3.42100e7i	0.345515	+	0.0788615i	0.391757	−	0.920069i	$-0.371867\pi$
$757$	1.49884e8	+	3.42100e7i	0.345515	+	0.0788615i	−0.0462421	+	0.998930i	$0.514725\pi$
$758$	7.07885e7	+	1.61570e7i	0.162538	+	0.0370983i
$759$	−1.54061e7	+	1.22860e7i	−0.0352345	+	0.0280986i
$760$	−6.51972e7	+	1.35383e8i	−0.148521	+	0.308407i
$761$	−3.33341e8	+	7.60830e7i	−0.756372	+	0.172637i	−0.583283	−	0.812269i	$-0.698232\pi$
$761$	−3.33341e8	+	7.60830e7i	−0.756372	+	0.172637i	−0.173089	+	0.984906i	$0.555375\pi$
$762$	−3.69215e7	−	1.77804e7i	−0.0834477	−	0.0401863i
$763$	−4.30183e8	−	3.43059e8i	−0.968455	−	0.772317i
$764$	−3.31473e7	−	7.56566e6i	−0.0743307	−	0.0169655i
$765$	1.78132e8	+	1.42055e8i	0.397884	+	0.317302i
$766$	−1.39566e8	−	6.11479e8i	−0.310523	−	1.36049i
$767$	−2.58662e7			−0.0573254
$768$			4.00889e7i			0.0884995i
$769$	2.97864e7	+	1.30503e8i	0.0654997	+	0.286973i	0.997061	−	0.0766112i	$-0.0244100\pi$
$769$	2.97864e7	+	1.30503e8i	0.0654997	+	0.286973i	−0.931561	+	0.363584i	$0.881553\pi$
$770$	2.35970e8	−	1.88180e8i	0.516874	−	0.412193i
$771$	1.33451e7	−	6.42666e6i	0.0291178	−	0.0140224i
$772$	−2.26830e8	−	1.09236e8i	−0.493002	−	0.237417i
$773$			1.93628e8i			0.419207i	0.977786	+	0.209604i	$0.0672173\pi$
$773$			1.93628e8i			0.419207i	−0.977786	+	0.209604i	$0.932783\pi$
$774$	3.44430e8	+	3.87152e7i	0.742810	+	0.0834945i
$775$	−2.28206e7			−0.0490255
$776$	−3.78183e8	+	7.85304e8i	−0.809313	+	1.68055i
$777$	−7.20703e6	−	1.49655e7i	−0.0153636	−	0.0319029i
$778$	2.19028e8	+	2.74652e8i	0.465115	+	0.583235i
$779$	9.50994e7	−	2.17058e7i	0.201171	−	0.0459160i
$780$	−2.38292e6			−0.00502142
$781$		−	4.91450e8i		−	1.03163i
$782$	1.50974e8	−	3.44589e7i	0.315706	−	0.0720578i
$783$	7.94281e6	−	9.95997e6i	0.0165458	−	0.0207478i
$784$	−4.10573e7	+	1.79884e8i	−0.0852005	+	0.373288i
$785$	−2.78171e8	+	3.48816e8i	−0.575047	+	0.721086i
$786$	6.28077e6	−	1.30421e7i	0.0129344	−	0.0268585i
$787$	−1.86848e8	−	8.18634e8i	−0.383322	−	1.67944i	−0.686990	−	0.726667i	$-0.741068\pi$
$787$	−1.86848e8	−	8.18634e8i	−0.383322	−	1.67944i	0.303668	−	0.952778i	$-0.401789\pi$
$788$	−3.20293e7	−	1.54245e7i	−0.0654588	−	0.0315233i
$789$	−3.49519e7	−	4.38282e7i	−0.0711605	−	0.0892325i
$790$	2.79504e7	−	1.22459e8i	0.0566899	−	0.248375i
$791$	2.25635e8	−	9.88570e8i	0.455907	−	1.99746i
$792$	−1.69463e8	−	3.51893e8i	−0.341113	−	0.708329i
$793$	−4.77857e6	+	3.81078e6i	−0.00958249	+	0.00764178i
$794$	4.37808e8	+	3.49140e8i	0.874626	+	0.697491i
$795$	−2.81896e7	+	1.35754e7i	−0.0561032	+	0.0270179i
$796$	−1.38538e8	−	2.87676e8i	−0.274681	−	0.570381i
$797$	3.53611e7	−	4.43414e7i	0.0698474	−	0.0875859i	−0.745680	−	0.666304i	$-0.767875\pi$
$797$	3.53611e7	−	4.43414e7i	0.0698474	−	0.0875859i	0.815528	+	0.578718i	$0.196447\pi$
$798$	−1.10270e7	−	1.38274e7i	−0.0216994	−	0.0272102i
$799$	2.11230e8	−	1.01723e8i	0.414109	−	0.199424i
$800$	−1.13925e8	−	2.60026e7i	−0.222509	−	0.0507863i
$801$	8.17808e8	+	1.86659e8i	1.59131	+	0.363205i
$802$	3.78293e8	−	3.01679e8i	0.733340	−	0.584819i
$803$	−2.26782e8	+	4.70918e8i	−0.437988	+	0.909492i
$804$	−2.16857e7	+	4.94962e6i	−0.0417258	+	0.00952365i
$805$	−3.97670e8	−	1.91508e8i	−0.762316	−	0.367112i
$806$	−8.32251e6	−	6.63698e6i	−0.0158946	−	0.0126755i
$807$	−2.44705e7	−	5.58524e6i	−0.0465611	−	0.0106273i
$808$	2.09922e8	+	1.67408e8i	0.397946	+	0.317352i
$809$	−1.08437e8	−	4.75092e8i	−0.204800	−	0.897289i	−0.967965	−	0.251085i	$-0.919213\pi$
$809$	−1.08437e8	−	4.75092e8i	−0.204800	−	0.897289i	0.763165	−	0.646204i	$-0.223645\pi$
$810$	3.30168e8			0.621269
$811$			5.11753e6i			0.00959396i	0.999988	+	0.00479698i	$0.00152693\pi$
$811$			5.11753e6i			0.00959396i	−0.999988	+	0.00479698i	$0.998473\pi$
$812$	−1.12145e7	−	4.91339e7i	−0.0209465	−	0.0917727i
$813$	−6.13034e7	+	4.88878e7i	−0.114081	+	0.0909764i
$814$	−7.73880e7	+	3.72681e7i	−0.143483	+	0.0690978i
$815$	−2.43606e8	−	1.17315e8i	−0.450003	−	0.216710i
$816$		−	1.08835e7i		−	0.0200308i
$817$	2.30059e7	+	2.03696e8i	0.0421864	+	0.373522i
$818$	−7.29705e8			−1.33318
$819$	−5.31215e7	+	1.10308e8i	−0.0966982	+	0.200796i
$820$	−4.79590e7	−	9.95880e7i	−0.0869819	−	0.180620i
$821$	−5.14594e8	−	6.45280e8i	−0.929897	−	1.16605i	−0.985851	−	0.167621i	$-0.946391\pi$
$821$	−5.14594e8	−	6.45280e8i	−0.929897	−	1.16605i	0.0559541	−	0.998433i	$-0.482180\pi$
$822$	3.50369e7	−	7.99694e6i	0.0630826	−	0.0143982i
$823$	−6.16346e8			−1.10567			−0.552834	−	0.833291i	$-0.686454\pi$
$823$	−6.16346e8			−1.10567			−0.552834	+	0.833291i	$0.686454\pi$
$824$			7.07741e8i			1.26501i
$825$	−1.00358e7	+	2.29060e6i	−0.0178726	+	0.00407931i
$826$	−1.35635e8	+	1.70081e8i	−0.240675	+	0.301797i
$827$	−1.98124e8	+	8.68039e8i	−0.350285	+	1.53470i	0.426240	+	0.904610i	$0.359838\pi$
$827$	−1.98124e8	+	8.68039e8i	−0.350285	+	1.53470i	−0.776525	+	0.630087i	$0.783019\pi$
$828$	−1.07565e8	+	1.34882e8i	−0.189487	+	0.237609i
$829$	3.30251e8	−	6.85773e8i	0.579670	−	1.20370i	−0.380630	−	0.924727i	$-0.624293\pi$
$829$	3.30251e8	−	6.85773e8i	0.579670	−	1.20370i	0.960300	−	0.278969i	$-0.0899927\pi$
$830$	−1.30874e8	−	5.73398e8i	−0.228887	−	1.00282i
$831$	2.71858e6	+	1.30920e6i	0.00473738	+	0.00228140i
$832$	−5.56086e7	−	6.97310e7i	−0.0965544	−	0.121075i
$833$	−7.87528e7	+	3.45039e8i	−0.136248	+	0.596943i
$834$	−3.00298e6	+	1.31569e7i	−0.00517672	+	0.0226807i
$835$	−3.18161e8	−	6.60668e8i	−0.546497	−	1.13481i
$836$	5.45497e7	−	4.35020e7i	0.0933628	−	0.0744543i
$837$	1.34980e7	+	1.07643e7i	0.0230194	+	0.0183573i
$838$	3.29162e7	−	1.58516e7i	0.0559343	−	0.0269365i
$839$	6.05975e7	+	1.25832e8i	0.102605	+	0.213062i	0.945951	−	0.324309i	$-0.105132\pi$
$839$	6.05975e7	+	1.25832e8i	0.102605	+	0.213062i	−0.843346	+	0.537371i	$0.819418\pi$
$840$	−4.13692e7	+	5.18754e7i	−0.0697974	+	0.0875232i
$841$	3.62126e8	+	4.54092e8i	0.608796	+	0.763406i
$842$	6.87750e8	−	3.31203e8i	1.15211	−	0.554827i
$843$	−9.32359e6	−	2.12805e6i	−0.0155633	−	0.00355221i
$844$	2.92545e8	+	6.67715e7i	0.486593	+	0.111062i
$845$	−3.88083e8	+	3.09486e8i	−0.643213	+	0.512945i
$846$	1.48545e8	−	3.08457e8i	0.245328	−	0.509428i
$847$	3.87058e8	−	8.83435e7i	0.636980	−	0.145387i
$848$	−1.77548e8	−	8.55028e7i	−0.291158	−	0.140215i
$849$	−6.67154e7	−	5.32037e7i	−0.109019	−	0.0869399i
$850$	7.88679e7	+	1.80011e7i	0.128423	+	0.0293118i
$851$	9.82079e7	+	7.83182e7i	0.159352	+	0.127079i
$852$	7.26147e6	+	3.18146e7i	0.0117410	+	0.0514407i
$853$	1.08028e9			1.74056			0.870282	−	0.492554i	$-0.163937\pi$
$853$	1.08028e9			1.74056			0.870282	+	0.492554i	$0.163937\pi$
$854$			5.14035e7i			0.0825314i
$855$	4.37870e7	+	1.91844e8i	0.0700563	+	0.306937i
$856$	9.17354e8	−	7.31566e8i	1.46257	−	1.16636i
$857$	−3.82573e8	+	1.84237e8i	−0.607815	+	0.292708i	−0.712363	−	0.701812i	$-0.752375\pi$
$857$	−3.82573e8	+	1.84237e8i	−0.607815	+	0.292708i	0.104548	+	0.994520i	$0.466661\pi$
$858$	−4.32615e6	−	2.08336e6i	−0.00684920	−	0.00329840i
$859$			5.15368e8i			0.813089i	0.913631	+	0.406545i	$0.133266\pi$
$859$			5.15368e8i			0.813089i	−0.913631	+	0.406545i	$0.866734\pi$
$860$	2.19232e8	−	7.67781e7i	0.344675	−	0.120710i
$861$	4.30723e7			0.0674820
$862$	−2.78330e8	+	5.77958e8i	−0.434549	+	0.902350i
$863$	−3.08588e8	−	6.40789e8i	−0.480116	−	0.996972i	−0.990562	−	0.137062i	$-0.956234\pi$
$863$	−3.08588e8	−	6.40789e8i	−0.480116	−	0.996972i	0.510446	−	0.859910i	$-0.329480\pi$
$864$	5.51195e7	+	6.91176e7i	0.0854602	+	0.107164i
$865$	1.78837e8	−	4.08183e7i	0.276317	−	0.0630676i
$866$	1.93970e8			0.298663
$867$			3.56664e7i			0.0547271i
$868$	6.65876e7	−	1.51982e7i	0.101820	−	0.0232398i
$869$	−1.20392e8	+	1.50967e8i	−0.183459	+	0.230051i
$870$	−1.24042e6	+	5.43465e6i	−0.00188370	+	0.00825304i
$871$	7.44280e7	−	9.33298e7i	0.112637	−	0.141243i
$872$	2.71393e8	−	5.63554e8i	0.409307	−	0.849935i
$873$	2.53991e8	+	1.11281e9i	0.381747	+	1.67254i
$874$	1.20500e8	+	5.80297e7i	0.180490	+	0.0869193i
$875$	−6.43209e8	−	8.06558e8i	−0.960125	−	1.20396i
$876$	7.72292e6	−	3.38363e7i	0.0114887	−	0.0503351i
$877$	2.84216e7	−	1.24523e8i	0.0421357	−	0.184609i	−0.949481	−	0.313826i	$-0.898389\pi$
$877$	2.84216e7	−	1.24523e8i	0.0421357	−	0.184609i	0.991616	+	0.129217i	$0.0412464\pi$
$878$	1.03852e8	+	2.15652e8i	0.153438	+	0.318617i
$879$	−2.53690e7	+	2.02311e7i	−0.0373540	+	0.0297888i
$880$	1.25414e8	+	1.00014e8i	0.184034	+	0.146762i
$881$	6.20873e8	−	2.98997e8i	0.907978	−	0.437259i	0.0792139	−	0.996858i	$-0.474759\pi$
$881$	6.20873e8	−	2.98997e8i	0.907978	−	0.437259i	0.828764	+	0.559599i	$0.189045\pi$
$882$	2.24237e8	+	4.65633e8i	0.326815	+	0.678638i
$883$	−5.48134e8	+	6.87338e8i	−0.796167	+	0.998362i	0.203646	+	0.979045i	$0.434721\pi$
$883$	−5.48134e8	+	6.87338e8i	−0.796167	+	0.998362i	−0.999813	+	0.0193175i	$0.993851\pi$
$884$	−1.79491e7	−	2.25075e7i	−0.0259828	−	0.0325814i
$885$	−1.65392e7	+	7.96484e6i	−0.0238607	+	0.0114907i
$886$	−5.38807e8	−	1.22979e8i	−0.774697	−	0.176820i
$887$	4.37797e8	+	9.99243e7i	0.627338	+	0.143186i	0.524359	−	0.851498i	$-0.324305\pi$
$887$	4.37797e8	+	9.99243e7i	0.627338	+	0.143186i	0.102980	+	0.994683i	$0.467162\pi$
$888$	1.47632e7	−	1.17733e7i	0.0210835	−	0.0168135i
$889$	−6.12251e8	+	1.27135e9i	−0.871413	+	1.80951i
$890$	−7.18422e8	+	1.63975e8i	−1.01908	+	0.232599i
$891$	−4.57297e8	−	2.20223e8i	−0.646495	−	0.311336i
$892$	−3.19338e8	−	2.54663e8i	−0.449941	−	0.358816i
$893$	1.97408e8	+	4.50571e7i	0.277211	+	0.0632716i
$894$	1.47862e7	+	1.17916e7i	0.0206940	+	0.0165029i
$895$	−5.71964e7	−	2.50594e8i	−0.0797811	−	0.349544i
$896$	5.80577e7			0.0807115
$897$			7.02201e6i			0.00972935i
$898$	4.05846e7	+	1.77813e8i	0.0560444	+	0.245546i
$899$	1.48530e7	−	1.18449e7i	0.0204426	−	0.0163024i
$900$	−8.11985e7	+	3.91032e7i	−0.111383	+	0.0536394i
$901$	−3.40559e8	−	1.64005e8i	−0.465606	−	0.224224i
$902$		−	2.22730e8i		−	0.303500i
$903$	−1.01107e7	+	8.99499e7i	−0.0137315	+	0.122162i
$904$	1.15271e9			1.56032
$905$	−3.54544e8	+	7.36218e8i	−0.478326	+	0.993254i
$906$	−1.78822e7	−	3.71328e7i	−0.0240457	−	0.0499314i
$907$	2.58025e8	+	3.23553e8i	0.345812	+	0.433635i	0.924072	−	0.382218i	$-0.124840\pi$
$907$	2.58025e8	+	3.23553e8i	0.345812	+	0.433635i	−0.578260	+	0.815852i	$0.696268\pi$
$908$	1.68699e8	−	3.85045e7i	0.225349	−	0.0514344i
$909$	3.51613e8			0.468137
$910$		−	1.07554e8i		−	0.142725i
$911$	−1.87298e8	+	4.27496e7i	−0.247730	+	0.0565427i	−0.344583	−	0.938756i	$-0.611980\pi$
$911$	−1.87298e8	+	4.27496e7i	−0.247730	+	0.0565427i	0.0968527	+	0.995299i	$0.469122\pi$
$912$	5.86065e6	−	7.34902e6i	0.00772611	−	0.00968824i
$913$	−2.01191e8	+	8.81474e8i	−0.264360	+	1.15824i
$914$	−1.92570e8	+	2.41475e8i	−0.252202	+	0.316252i
$915$	−1.88204e6	+	3.90809e6i	−0.00245677	+	0.00510154i
$916$	−6.27094e6	−	2.74748e7i	−0.00815918	−	0.0357477i
$917$	−4.49092e8	−	2.16272e8i	−0.582409	−	0.280473i
$918$	−3.81581e7	−	4.78488e7i	−0.0493241	−	0.0618505i
$919$	−2.39976e8	+	1.05140e9i	−0.309187	+	1.35464i	0.546638	+	0.837369i	$0.315907\pi$
$919$	−2.39976e8	+	1.05140e9i	−0.309187	+	1.35464i	−0.855825	+	0.517266i	$0.826950\pi$
$920$	1.11653e8	−	4.89183e8i	0.143386	−	0.628214i
$921$	−5.23188e7	−	1.08641e8i	−0.0669698	−	0.139064i
$922$	−3.57359e8	+	2.84984e8i	−0.455944	+	0.363603i
$923$	−1.36922e8	−	1.09192e8i	−0.174128	−	0.138862i
$924$	2.77576e7	−	1.33673e7i	0.0351856	−	0.0169445i
$925$	2.84711e7	+	5.91209e7i	0.0359732	+	0.0746991i
$926$	−1.16203e8	+	1.45714e8i	−0.146347	+	0.183513i
$927$	5.77860e8	+	7.24613e8i	0.725409	+	0.909635i
$928$	8.76457e7	−	4.22079e7i	0.109670	−	0.0528142i
$929$	5.00905e8	+	1.14328e8i	0.624752	+	0.142596i	0.523166	−	0.852231i	$-0.324751\pi$
$929$	5.00905e8	+	1.14328e8i	0.624752	+	0.142596i	0.101587	+	0.994827i	$0.467608\pi$
$930$	−7.36519e6	−	1.68106e6i	−0.00915661	−	0.00208994i
$931$	−2.38977e8	+	1.90577e8i	−0.296146	+	0.236169i
$932$	−2.84385e8	+	5.90531e8i	−0.351284	+	0.729450i
$933$	−3.67594e7	+	8.39010e6i	−0.0452610	+	0.0103305i
$934$	9.42294e6	+	4.53785e6i	0.0115650	+	0.00556942i
$935$	2.40559e8	+	1.91840e8i	0.294298	+	0.234695i
$936$	−1.35692e8	−	3.09709e7i	−0.165473	−	0.0377681i
$937$	9.47928e8	+	7.55947e8i	1.15228	+	0.918909i	0.997613	−	0.0690580i	$-0.0219994\pi$
$937$	9.47928e8	+	7.55947e8i	1.15228	+	0.918909i	0.154663	+	0.987967i	$0.450571\pi$
$938$	−2.23402e8	−	9.78786e8i	−0.270693	−	1.18599i
$939$	1.00362e8			0.121220
$940$		−	2.29448e8i		−	0.276249i
$941$	−3.11270e8	−	1.36376e9i	−0.373566	−	1.63670i	−0.716676	−	0.697406i	$-0.754337\pi$
$941$	−3.11270e8	−	1.36376e9i	−0.373566	−	1.63670i	0.343110	−	0.939295i	$-0.388520\pi$
$942$	4.66716e7	−	3.72193e7i	0.0558341	−	0.0445262i
$943$	−2.93466e8	+	1.41326e8i	−0.349964	+	0.168534i
$944$	−1.04170e8	−	5.01654e7i	−0.123830	−	0.0596333i
$945$			1.74438e8i			0.206702i
$946$	4.65138e8	+	5.22832e7i	0.549425	+	0.0617574i
$947$	−1.11957e9			−1.31826			−0.659128	−	0.752030i	$-0.729075\pi$
$947$	−1.11957e9			−1.31826			−0.659128	+	0.752030i	$0.729075\pi$
$948$	5.56311e6	−	1.15519e7i	0.00652969	−	0.0135590i
$949$	8.08147e7	+	1.67814e8i	0.0945566	+	0.196349i
$950$	4.35616e7	+	5.46246e7i	0.0508082	+	0.0637114i
$951$	1.14967e8	−	2.62404e7i	0.133669	−	0.0305091i
$952$	−8.01589e8			−0.929054
$953$			8.32042e8i			0.961316i	0.876908	+	0.480658i	$0.159602\pi$
$953$			8.32042e8i			0.961316i	−0.876908	+	0.480658i	$0.840398\pi$
$954$	−5.38139e8	+	1.22827e8i	−0.619797	+	0.141465i
$955$	8.07387e7	−	1.01243e8i	0.0926983	−	0.116240i
$956$	1.09017e8	−	4.77633e8i	0.124773	−	0.546664i
$957$	5.34296e6	−	6.69986e6i	0.00609602	−	0.00764416i
$958$	3.35103e8	−	6.95848e8i	0.381137	−	0.791440i
$959$	−2.75366e8	−	1.20646e9i	−0.312215	−	1.36791i
$960$	−5.70286e7	−	2.74635e7i	−0.0644583	−	0.0310415i
$961$	−5.37297e8	−	6.73749e8i	−0.605403	−	0.759151i
$962$	−6.81108e6	+	2.98413e7i	−0.00765052	+	0.0335191i
$963$	3.41912e8	−	1.49801e9i	0.382856	−	1.67740i
$964$	2.29994e8	+	4.77588e8i	0.256736	+	0.533117i
$965$	7.49688e8	−	5.97856e8i	0.834255	−	0.665296i
$966$	4.61724e7	+	3.68213e7i	0.0512214	+	0.0408477i
$967$	−4.53374e8	+	2.18333e8i	−0.501391	+	0.241457i	−0.667445	−	0.744659i	$-0.732612\pi$
$967$	−4.53374e8	+	2.18333e8i	−0.501391	+	0.241457i	0.166053	+	0.986117i	$0.446898\pi$
$968$	1.95822e8	+	4.06629e8i	0.215892	+	0.448304i
$969$	1.12414e7	−	1.40963e7i	0.0123552	−	0.0154929i
$970$	−6.25179e8	−	7.83950e8i	−0.684998	−	0.858960i
$971$	−1.42017e9	+	6.83920e8i	−1.55126	+	0.747046i	−0.996390	−	0.0848920i	$-0.972945\pi$
$971$	−1.42017e9	+	6.83920e8i	−1.55126	+	0.747046i	−0.554868	+	0.831939i	$0.687231\pi$
$972$	9.98340e7	+	2.27865e7i	0.108713	+	0.0248129i
$973$	4.53044e8	+	1.03404e8i	0.491816	+	0.112254i
$974$	−1.97896e8	+	1.57817e8i	−0.214171	+	0.170796i
$975$	−1.59159e6	+	3.30498e6i	−0.00171719	+	0.00356578i
$976$	−2.66351e7	+	6.07930e6i	−0.0286487	+	0.00653889i
$977$	7.31769e8	+	3.52401e8i	0.784675	+	0.377880i	0.782923	−	0.622119i	$-0.213728\pi$
$977$	7.31769e8	+	3.52401e8i	0.784675	+	0.377880i	0.00175249	+	0.999998i	$0.499442\pi$
$978$	2.82844e7	+	2.25561e7i	0.0302365	+	0.0241128i
$979$	1.10442e9	+	2.52076e8i	1.17702	+	0.268648i
$980$	2.70799e8	+	2.15955e8i	0.287719	+	0.229448i
$981$	−1.82270e8	−	7.98577e8i	−0.193067	−	0.845882i
$982$	1.15966e9			1.22461
$983$		−	8.03136e8i		−	0.845529i	−0.906240	−	0.422764i	$-0.861060\pi$
$983$		−	8.03136e8i		−	0.845529i	0.906240	−	0.422764i	$-0.138940\pi$
$984$	1.08957e7	+	4.77370e7i	0.0114359	+	0.0501038i
$985$	1.05859e8	−	8.44196e7i	0.110769	−	0.0883354i
$986$	−6.06754e7	+	2.92197e7i	−0.0632968	+	0.0304821i
$987$	8.05554e7	+	3.87934e7i	0.0837805	+	0.0403466i
$988$		−	2.48634e7i		−	0.0257804i
$989$	−2.26250e8	−	6.46034e8i	−0.233884	−	0.667831i
$990$	4.49312e8			0.463066
$991$	3.35244e8	−	6.96141e8i	0.344461	−	0.715281i	−0.654715	−	0.755876i	$-0.727211\pi$
$991$	3.35244e8	−	6.96141e8i	0.344461	−	0.715281i	0.999176	+	0.0405955i	$0.0129255\pi$
$992$	5.72013e7	+	1.18780e8i	0.0585964	+	0.121677i
$993$	−6.20550e6	−	7.78145e6i	−0.00633766	−	0.00794718i
$994$	−1.43596e9	+	3.27747e8i	−1.46212	+	0.333718i
$995$	1.21611e9			1.23453
$996$		−	6.00360e7i		−	0.0607622i
$997$	−2.96364e8	+	6.76431e7i	−0.299047	+	0.0682556i	−0.369412	−	0.929266i	$-0.620441\pi$
$997$	−2.96364e8	+	6.76431e7i	−0.299047	+	0.0682556i	0.0703646	+	0.997521i	$0.477584\pi$
$998$	3.20963e8	−	4.02475e8i	0.322897	−	0.404899i
$999$	1.10467e7	−	4.83987e7i	0.0110799	−	0.0485442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.22.14	yes	126
43.2	odd	14	inner	43.7.f.a.2.14	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.14	✓	126	43.2	odd	14	inner
43.7.f.a.22.14	yes	126	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.61426 - 5.42856i) q^{2} +(1.01637 + 2.11052i) q^{3} +(17.2684 + 21.6539i) q^{4} +(-102.842 + 23.4731i) q^{5} +14.1142 q^{6} -486.006i q^{7} +(538.641 - 122.941i) q^{8} +(451.103 - 565.665i) q^{9} +O(q^{10})\)	\(q+(2.61426 - 5.42856i) q^{2} +(1.01637 + 2.11052i) q^{3} +(17.2684 + 21.6539i) q^{4} +(-102.842 + 23.4731i) q^{5} +14.1142 q^{6} -486.006i q^{7} +(538.641 - 122.941i) q^{8} +(451.103 - 565.665i) q^{9} +(-141.431 + 619.650i) q^{10} +(609.196 - 763.908i) q^{11} +(-28.1498 + 58.4537i) q^{12} +(-77.4782 - 339.454i) q^{13} +(-2638.32 - 1270.55i) q^{14} +(-154.067 - 193.193i) q^{15} +(346.320 - 1517.33i) q^{16} +(664.284 - 2910.42i) q^{17} +(-1891.45 - 3927.64i) q^{18} +(2015.78 - 1607.53i) q^{19} +(-2284.20 - 1821.59i) q^{20} +(1025.73 - 493.964i) q^{21} +(-2554.33 - 5304.11i) q^{22} +(-5367.87 + 6731.09i) q^{23} +(806.931 + 1011.86i) q^{24} +(-4052.10 + 1951.39i) q^{25} +(-2045.30 - 466.826i) q^{26} +(3317.21 + 757.131i) q^{27} +(10523.9 - 8392.54i) q^{28} +(1624.49 - 3373.30i) q^{29} +(-1451.53 + 331.303i) q^{30} +(4571.58 + 2201.56i) q^{31} +(20313.7 + 16199.6i) q^{32} +(2231.41 + 509.306i) q^{33} +(-14062.8 - 11214.7i) q^{34} +(11408.1 + 49982.0i) q^{35} +20038.6 q^{36} -14590.2i q^{37} +(-3456.81 - 15145.3i) q^{38} +(637.679 - 508.532i) q^{39} +(-52509.3 + 25287.1i) q^{40} +(34086.8 + 16415.3i) q^{41} -6859.57i q^{42} +(-42282.4 + 67331.7i) q^{43} +27061.4 q^{44} +(-33114.5 + 68763.0i) q^{45} +(22507.2 + 46736.6i) q^{46} +(48965.7 + 61401.1i) q^{47} +(3554.34 - 811.255i) q^{48} -118553. q^{49} +27098.5i q^{50} +(6817.66 - 1556.09i) q^{51} +(6012.58 - 7539.53i) q^{52} +(28175.5 - 123445. i) q^{53} +(12782.2 - 16028.3i) q^{54} +(-44719.8 + 92861.7i) q^{55} +(-59750.3 - 261783. i) q^{56} +(5441.51 + 2620.49i) q^{57} +(-14065.3 - 17637.4i) q^{58} +(16530.9 - 72426.4i) q^{59} +(1522.90 - 6672.27i) q^{60} +(-7616.39 - 15815.6i) q^{61} +(23902.6 - 19061.7i) q^{62} +(-274917. - 219239. i) q^{63} +(230788. - 111142. i) q^{64} +(15936.1 + 33091.6i) q^{65} +(8598.29 - 10781.9i) q^{66} +(213761. + 268047. i) q^{67} +(74492.9 - 35873.9i) q^{68} +(-19661.9 - 4487.69i) q^{69} +(301154. + 68736.4i) q^{70} +(393246. - 313603. i) q^{71} +(173439. - 360150. i) q^{72} +(-521532. + 119036. i) q^{73} +(-79203.8 - 38142.5i) q^{74} +(-8236.89 - 6568.70i) q^{75} +(69618.5 + 15890.0i) q^{76} +(-371264. - 296073. i) q^{77} +(-1093.54 - 4791.12i) q^{78} -197625. q^{79} +164175. i q^{80} +(-115593. - 506446. i) q^{81} +(178223. - 142128. i) q^{82} +(-833718. + 401497. i) q^{83} +(28408.9 + 13681.0i) q^{84} +314907. i q^{85} +(254978. + 405555. i) q^{86} +8770.51 q^{87} +(234222. - 486368. i) q^{88} +(503044. + 1.04458e6i) q^{89} +(286715. + 359529. i) q^{90} +(-164977. + 37654.9i) q^{91} -238448. q^{92} +11886.0i q^{93} +(461329. - 105295. i) q^{94} +(-169573. + 212638. i) q^{95} +(-13543.4 + 59337.4i) q^{96} +(-983626. + 1.23343e6i) q^{97} +(-309928. + 643573. i) q^{98} +(-157306. - 689202. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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