LMFDB - Embedded newform 43.7.f.a.2.17

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			2.17
Character	$\chi$	$=$	43.2
Dual form			43.7.f.a.22.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.58164 + 7.43735i) q^{2} +(3.11543 - 6.46926i) q^{3} +(-2.58264 + 3.23853i) q^{4} +(50.0201 + 11.4168i) q^{5} +59.2725 q^{6} -578.950i q^{7} +(481.727 + 109.951i) q^{8} +(422.379 + 529.646i) q^{9} +O(q^{10})$	\(q+(3.58164 + 7.43735i) q^{2} +(3.11543 - 6.46926i) q^{3} +(-2.58264 + 3.23853i) q^{4} +(50.0201 + 11.4168i) q^{5} +59.2725 q^{6} -578.950i q^{7} +(481.727 + 109.951i) q^{8} +(422.379 + 529.646i) q^{9} +(94.2435 + 412.908i) q^{10} +(177.289 + 222.313i) q^{11} +(12.9049 + 26.7972i) q^{12} +(522.456 - 2289.03i) q^{13} +(4305.85 - 2073.59i) q^{14} +(229.692 - 288.025i) q^{15} +(966.619 + 4235.03i) q^{16} +(1016.14 + 4452.02i) q^{17} +(-2426.35 + 5038.38i) q^{18} +(-268.840 - 214.393i) q^{19} +(-166.158 + 132.506i) q^{20} +(-3745.38 - 1803.68i) q^{21} +(-1018.43 + 2114.80i) q^{22} +(11991.2 + 15036.5i) q^{23} +(2212.09 - 2773.87i) q^{24} +(-11706.0 - 5637.30i) q^{25} +(18895.6 - 4312.79i) q^{26} +(9845.54 - 2247.18i) q^{27} +(1874.95 + 1495.22i) q^{28} +(-10841.4 - 22512.5i) q^{29} +(2964.82 + 676.700i) q^{30} +(-12411.4 + 5977.03i) q^{31} +(-3311.16 + 2640.56i) q^{32} +(1990.53 - 454.326i) q^{33} +(-29471.7 + 23502.9i) q^{34} +(6609.74 - 28959.2i) q^{35} -2806.13 q^{36} -86593.0i q^{37} +(631.627 - 2767.34i) q^{38} +(-13180.7 - 10511.2i) q^{39} +(22840.8 + 10999.5i) q^{40} +(-100062. + 48187.1i) q^{41} -34315.8i q^{42} +(50098.1 - 61737.7i) q^{43} -1177.84 q^{44} +(15080.6 + 31315.2i) q^{45} +(-68883.4 + 143038. i) q^{46} +(-68513.9 + 85913.7i) q^{47} +(30409.0 + 6940.65i) q^{48} -217535. q^{49} -107252. i q^{50} +(31967.0 + 7296.25i) q^{51} +(6063.78 + 7603.74i) q^{52} +(16805.6 + 73630.1i) q^{53} +(51976.2 + 65176.1i) q^{54} +(6329.91 + 13144.2i) q^{55} +(63656.2 - 278896. i) q^{56} +(-2224.52 + 1071.27i) q^{57} +(128603. - 161263. i) q^{58} +(82828.7 + 362896. i) q^{59} +(339.565 + 1487.73i) q^{60} +(-23746.6 + 49310.3i) q^{61} +(-88906.4 - 70900.5i) q^{62} +(306639. - 244536. i) q^{63} +(218982. + 105456. i) q^{64} +(52266.7 - 108533. i) q^{65} +(10508.3 + 13177.0i) q^{66} +(-227135. + 284818. i) q^{67} +(-17042.3 - 8207.16i) q^{68} +(134633. - 30729.0i) q^{69} +(239053. - 54562.3i) q^{70} +(-41341.7 - 32968.9i) q^{71} +(145236. + 301586. i) q^{72} +(57019.6 + 13014.4i) q^{73} +(644022. - 310145. i) q^{74} +(-72938.3 + 58166.3i) q^{75} +(1388.64 - 316.948i) q^{76} +(128708. - 102641. i) q^{77} +(30967.3 - 135676. i) q^{78} -442938. q^{79} +222873. i q^{80} +(-93757.7 + 410780. i) q^{81} +(-716769. - 571604. i) q^{82} +(-183088. - 88170.7i) q^{83} +(15514.3 - 7471.27i) q^{84} +234292. i q^{85} +(638598. + 151475. i) q^{86} -179415. q^{87} +(60961.2 + 126587. i) q^{88} +(-244378. + 507456. i) q^{89} +(-178889. + 224319. i) q^{90} +(-1.32524e6 - 302476. i) q^{91} -79665.1 q^{92} +98913.7i q^{93} +(-884362. - 201850. i) q^{94} +(-10999.8 - 13793.3i) q^{95} +(6766.78 + 29647.2i) q^{96} +(540180. + 677364. i) q^{97} +(-779130. - 1.61788e6i) q^{98} +(-42864.2 + 187801. 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	3.58164	+	7.43735i	0.447705	+	0.929668i	0.995652	+	0.0931552i	$0.0296953\pi$
$2$	3.58164	+	7.43735i	0.447705	+	0.929668i	−0.547947	+	0.836513i	$0.684590\pi$
$3$	3.11543	−	6.46926i	0.115386	−	0.239602i	−0.835275	−	0.549832i	$-0.814692\pi$
$3$	3.11543	−	6.46926i	0.115386	−	0.239602i	0.950662	+	0.310230i	$0.100406\pi$
$4$	−2.58264	+	3.23853i	−0.0403538	+	0.0506021i
$5$	50.0201	+	11.4168i	0.400161	+	0.0913341i	0.417865	−	0.908509i	$-0.362779\pi$
$5$	50.0201	+	11.4168i	0.400161	+	0.0913341i	−0.0177040	+	0.999843i	$0.505636\pi$
$6$	59.2725			0.274410
$7$		−	578.950i		−	1.68790i	−0.536420	−	0.843951i	$-0.680224\pi$
$7$		−	578.950i		−	1.68790i	0.536420	−	0.843951i	$-0.319776\pi$
$8$	481.727	+	109.951i	0.940873	+	0.214748i
$9$	422.379	+	529.646i	0.579395	+	0.726538i
$10$	94.2435	+	412.908i	0.0942435	+	0.412908i
$11$	177.289	+	222.313i	0.133200	+	0.167027i	0.843958	−	0.536409i	$-0.180220\pi$
$11$	177.289	+	222.313i	0.133200	+	0.167027i	−0.710759	+	0.703436i	$0.751648\pi$
$12$	12.9049	+	26.7972i	0.00746809	+	0.0155077i
$13$	522.456	−	2289.03i	0.237804	−	1.04189i	−0.705174	−	0.709035i	$-0.749131\pi$
$13$	522.456	−	2289.03i	0.237804	−	1.04189i	0.942978	−	0.332855i	$-0.108012\pi$
$14$	4305.85	−	2073.59i	1.56919	−	0.755682i
$15$	229.692	−	288.025i	0.0680570	−	0.0853407i
$16$	966.619	+	4235.03i	0.235991	+	1.03394i
$17$	1016.14	+	4452.02i	0.206828	+	0.906171i	0.966662	+	0.256055i	$0.0824227\pi$
$17$	1016.14	+	4452.02i	0.206828	+	0.906171i	−0.759835	+	0.650116i	$0.774720\pi$
$18$	−2426.35	+	5038.38i	−0.416042	+	0.863919i
$19$	−268.840	−	214.393i	−0.0391953	−	0.0312572i	0.603696	−	0.797214i	$-0.293694\pi$
$19$	−268.840	−	214.393i	−0.0391953	−	0.0312572i	−0.642892	+	0.765957i	$0.722265\pi$
$20$	−166.158	+	132.506i	−0.0207697	+	0.0165633i
$21$	−3745.38	−	1803.68i	−0.404425	−	0.194761i
$22$	−1018.43	+	2114.80i	−0.0956456	+	0.198610i
$23$	11991.2	+	15036.5i	0.985550	+	1.23584i	0.971769	+	0.235936i	$0.0758156\pi$
$23$	11991.2	+	15036.5i	0.985550	+	1.23584i	0.0137817	+	0.999905i	$0.495613\pi$
$24$	2212.09	−	2773.87i	0.160018	−	0.200656i
$25$	−11706.0	−	5637.30i	−0.749182	−	0.360787i
$26$	18895.6	−	4312.79i	1.07508	−	0.245379i
$27$	9845.54	−	2247.18i	0.500205	−	0.114169i
$28$	1874.95	+	1495.22i	0.0854114	+	0.0681133i
$29$	−10841.4	−	22512.5i	−0.444522	−	0.923059i	−0.996041	−	0.0888969i	$-0.971666\pi$
$29$	−10841.4	−	22512.5i	−0.444522	−	0.923059i	0.551519	−	0.834162i	$-0.314048\pi$
$30$	2964.82	+	676.700i	0.109808	+	0.0250630i
$31$	−12411.4	+	5977.03i	−0.416616	+	0.200632i	−0.630436	−	0.776241i	$-0.717124\pi$
$31$	−12411.4	+	5977.03i	−0.416616	+	0.200632i	0.213819	+	0.976873i	$0.431410\pi$
$32$	−3311.16	+	2640.56i	−0.101048	+	0.0805835i
$33$	1990.53	−	454.326i	0.0553895	−	0.0126423i
$34$	−29471.7	+	23502.9i	−0.749841	+	0.597978i
$35$	6609.74	−	28959.2i	0.154163	−	0.675433i
$36$	−2806.13			−0.0601451
$37$		−	86593.0i		−	1.70953i	−0.519012	−	0.854767i	$-0.673700\pi$
$37$		−	86593.0i		−	1.70953i	0.519012	−	0.854767i	$-0.326300\pi$
$38$	631.627	−	2767.34i	0.0115109	−	0.0504326i
$39$	−13180.7	−	10511.2i	−0.222200	−	0.177198i
$40$	22840.8	+	10999.5i	0.356887	+	0.171868i
$41$	−100062.	+	48187.1i	−1.45183	+	0.699165i	−0.982912	−	0.184076i	$-0.941071\pi$
$41$	−100062.	+	48187.1i	−1.45183	+	0.699165i	−0.468919	+	0.883241i	$0.655356\pi$
$42$		−	34315.8i		−	0.463176i
$43$	50098.1	−	61737.7i	0.630109	−	0.776506i
$43$	50098.1	−	61737.7i	0.630109	−	0.776506i
$44$	−1177.84			−0.0138270
$45$	15080.6	+	31315.2i	0.165493	+	0.343651i
$46$	−68883.4	+	143038.i	−0.707687	+	1.46953i
$47$	−68513.9	+	85913.7i	−0.659911	+	0.827502i	−0.993334	−	0.115276i	$-0.963225\pi$
$47$	−68513.9	+	85913.7i	−0.659911	+	0.827502i	0.333423	+	0.942777i	$0.391796\pi$
$48$	30409.0	+	6940.65i	0.274965	+	0.0627590i
$49$	−217535.			−1.84901
$50$		−	107252.i		−	0.858017i
$51$	31967.0	+	7296.25i	0.240986	+	0.0550034i
$52$	6063.78	+	7603.74i	0.0431254	+	0.0540776i
$53$	16805.6	+	73630.1i	0.112882	+	0.494570i	0.999487	+	0.0320409i	$0.0102007\pi$
$53$	16805.6	+	73630.1i	0.112882	+	0.494570i	−0.886604	+	0.462529i	$0.846942\pi$
$54$	51976.2	+	65176.1i	0.330083	+	0.413911i
$55$	6329.91	+	13144.2i	0.0380460	+	0.0790034i
$56$	63656.2	−	278896.i	0.362474	−	1.58810i
$57$	−2224.52	+	1071.27i	−0.0120119	+	0.00578462i
$58$	128603.	−	161263.i	0.659124	−	0.826516i
$59$	82828.7	+	362896.i	0.403297	+	1.76696i	0.613897	+	0.789386i	$0.289601\pi$
$59$	82828.7	+	362896.i	0.403297	+	1.76696i	−0.210600	+	0.977572i	$0.567542\pi$
$60$	339.565	+	1487.73i	0.00157206	+	0.00688765i
$61$	−23746.6	+	49310.3i	−0.104619	+	0.217244i	−0.946707	−	0.322097i	$-0.895612\pi$
$61$	−23746.6	+	49310.3i	−0.104619	+	0.217244i	0.842088	+	0.539341i	$0.181327\pi$
$62$	−88906.4	−	70900.5i	−0.373042	−	0.297491i
$63$	306639.	−	244536.i	1.22632	−	0.977961i
$64$	218982.	+	105456.i	0.835352	+	0.402284i
$65$	52266.7	−	108533.i	0.190320	−	0.395204i
$66$	10508.3	+	13177.0i	0.0365512	+	0.0458338i
$67$	−227135.	+	284818.i	−0.755194	+	0.946984i	−0.999743	−	0.0226530i	$-0.992789\pi$
$67$	−227135.	+	284818.i	−0.755194	+	0.946984i	0.244549	+	0.969637i	$0.421360\pi$
$68$	−17042.3	−	8207.16i	−0.0542004	−	0.0261015i
$69$	134633.	−	30729.0i	0.409829	−	0.0935409i
$70$	239053.	−	54562.3i	0.696948	−	0.159074i
$71$	−41341.7	−	32968.9i	−0.115508	−	0.0921149i	0.564032	−	0.825753i	$-0.309249\pi$
$71$	−41341.7	−	32968.9i	−0.115508	−	0.0921149i	−0.679541	+	0.733638i	$0.737821\pi$
$72$	145236.	+	301586.i	0.389114	+	0.808004i
$73$	57019.6	+	13014.4i	0.146574	+	0.0334545i	0.295178	−	0.955442i	$-0.404621\pi$
$73$	57019.6	+	13014.4i	0.146574	+	0.0334545i	−0.148605	+	0.988897i	$0.547478\pi$
$74$	644022.	−	310145.i	1.58930	−	0.765366i
$75$	−72938.3	+	58166.3i	−0.172891	+	0.137876i
$76$	1388.64	−	316.948i	0.00316336	−	0.000722016i
$77$	128708.	−	102641.i	0.281925	−	0.224828i
$78$	30967.3	−	135676.i	0.0652558	−	0.285904i
$79$	−442938.			−0.898383			−0.449192	−	0.893435i	$-0.648288\pi$
$79$	−442938.			−0.898383			−0.449192	+	0.893435i	$0.648288\pi$
$80$			222873.i			0.435298i
$81$	−93757.7	+	410780.i	−0.176422	+	0.772954i
$82$	−716769.	−	571604.i	−1.29998	−	1.03670i
$83$	−183088.	−	88170.7i	−0.320204	−	0.154202i	0.266876	−	0.963731i	$-0.414008\pi$
$83$	−183088.	−	88170.7i	−0.320204	−	0.154202i	−0.587080	+	0.809529i	$0.699723\pi$
$84$	15514.3	−	7471.27i	0.0261754	−	0.0126054i
$85$			234292.i			0.381505i
$86$	638598.	+	151475.i	1.00400	+	0.238147i
$87$	−179415.			−0.272459
$88$	60961.2	+	126587.i	0.0894552	+	0.185756i
$89$	−244378.	+	507456.i	−0.346651	+	0.719827i	−0.999284	−	0.0378470i	$-0.987950\pi$
$89$	−244378.	+	507456.i	−0.346651	+	0.719827i	0.652633	+	0.757674i	$0.273664\pi$
$90$	−178889.	+	224319.i	−0.245389	+	0.307708i
$91$	−1.32524e6	−	302476.i	−1.75861	−	0.401391i
$92$	−79665.1			−0.102307
$93$			98913.7i			0.122972i
$94$	−884362.	−	201850.i	−1.06475	−	0.243022i
$95$	−10999.8	−	13793.3i	−0.0128296	−	0.0160878i
$96$	6766.78	+	29647.2i	0.00764836	+	0.0335097i
$97$	540180.	+	677364.i	0.591865	+	0.742176i	0.984085	−	0.177696i	$-0.0568642\pi$
$97$	540180.	+	677364.i	0.591865	+	0.742176i	−0.392220	+	0.919871i	$0.628293\pi$
$98$	−779130.	−	1.61788e6i	−0.827812	−	1.71897i
$99$	−42864.2	+	187801.i	−0.0441763	+	0.193549i
$100$	48488.9	−	23351.0i	0.0484889	−	0.0233510i
$101$	821650.	−	1.03032e6i	0.797486	−	1.00002i	−0.202300	−	0.979324i	$-0.564842\pi$
$101$	821650.	−	1.03032e6i	0.797486	−	1.00002i	0.999786	−	0.0206917i	$-0.00658685\pi$
$102$	60229.3	+	263882.i	0.0567555	+	0.248662i
$103$	180295.	+	789924.i	0.164995	+	0.722892i	0.987949	+	0.154783i	$0.0494678\pi$
$103$	180295.	+	789924.i	0.164995	+	0.722892i	−0.822953	+	0.568109i	$0.807675\pi$
$104$	503363.	−	1.04524e6i	0.447488	−	0.929218i
$105$	−166752.	−	132980.i	−0.144047	−	0.114873i
$106$	−487421.	+	388705.i	−0.409248	+	0.326364i
$107$	−376500.	−	181313.i	−0.307336	−	0.148005i	0.273858	−	0.961770i	$-0.411700\pi$
$107$	−376500.	−	181313.i	−0.307336	−	0.148005i	−0.581194	+	0.813765i	$0.697414\pi$
$108$	−18149.9	+	37688.8i	−0.0144080	+	0.0299186i
$109$	−352147.	−	441578.i	−0.271922	−	0.340980i	0.627055	−	0.778975i	$-0.284260\pi$
$109$	−352147.	−	441578.i	−0.271922	−	0.340980i	−0.898977	+	0.437995i	$0.855689\pi$
$110$	−75086.4	+	94155.4i	−0.0564135	+	0.0707403i
$111$	−560193.	−	269775.i	−0.409608	−	0.197257i
$112$	2.45187e6	−	559624.i	1.74520	−	0.398330i
$113$	−2.52952e6	+	577346.i	−1.75308	+	0.400129i	−0.973956	−	0.226738i	$-0.927194\pi$
$113$	−2.52952e6	+	577346.i	−1.75308	+	0.400129i	−0.779126	+	0.626867i	$0.784337\pi$
$114$	−15934.8	−	12707.6i	−0.0107556	−	0.00857727i
$115$	428133.	+	889027.i	0.281504	+	0.584550i
$116$	100907.	+	23031.4i	0.0646469	+	0.0147552i
$117$	1.43305e6	−	690121.i	0.894754	−	0.430891i
$118$	−2.40232e6	+	1.91579e6i	−1.46213	+	1.16601i
$119$	2.57750e6	−	588297.i	1.52953	−	0.349105i
$120$	142318.	−	113495.i	0.0823598	−	0.0656797i
$121$	376218.	−	1.64832e6i	0.212365	−	0.930432i
$122$	−451789.			−0.248803
$123$			797448.i			0.428536i
$124$	12697.5	−	55631.3i	0.00665967	−	0.0291779i
$125$	−1.14794e6	−	915452.i	−0.587745	−	0.468711i
$126$	2.91697e6	+	1.40474e6i	1.45821	+	0.702237i
$127$	3.35137e6	−	1.61393e6i	1.63610	−	0.787906i	0.636238	−	0.771493i	$-0.280490\pi$
$127$	3.35137e6	−	1.61393e6i	1.63610	−	0.787906i	0.999865	−	0.0164131i	$-0.00522468\pi$
$128$			2.27740e6i			1.08595i
$129$	−243320.	−	516437.i	−0.113347	−	0.240574i
$130$	994396.			0.452616
$131$	−625955.	−	1.29981e6i	−0.278439	−	0.578184i	0.714110	−	0.700033i	$-0.246832\pi$
$131$	−625955.	−	1.29981e6i	−0.278439	−	0.578184i	−0.992549	+	0.121850i	$0.961117\pi$
$132$	−3669.48	+	7619.76i	−0.00159545	+	0.00331299i
$133$	−124123.	+	155645.i	−0.0527591	+	0.0661578i
$134$	−2.93180e6	−	669165.i	−1.21848	−	0.278111i
$135$	518130.			0.210590
$136$			2.25638e6i			0.897008i
$137$	−722150.	−	164826.i	−0.280844	−	0.0641009i	0.0797785	−	0.996813i	$-0.474579\pi$
$137$	−722150.	−	164826.i	−0.280844	−	0.0641009i	−0.360623	+	0.932712i	$0.617436\pi$
$138$	710747.	+	891249.i	0.270444	+	0.339127i
$139$	754618.	+	3.30620e6i	0.280985	+	1.23108i	0.896533	+	0.442976i	$0.146077\pi$
$139$	754618.	+	3.30620e6i	0.280985	+	1.23108i	−0.615548	+	0.788099i	$0.711065\pi$
$140$	76714.6	+	96197.1i	0.0279572	+	0.0350573i
$141$	342348.	+	710893.i	0.122127	+	0.253598i
$142$	97130.3	−	425556.i	0.0339226	−	0.148625i
$143$	601507.	−	289670.i	0.205699	−	0.0990595i
$144$	−1.83479e6	+	2.30075e6i	−0.614467	+	0.770518i
$145$	−285271.	−	1.24985e6i	−0.0935735	−	0.409972i
$146$	107431.	+	470688.i	0.0345201	+	0.151243i
$147$	−677714.	+	1.40729e6i	−0.213351	+	0.443028i
$148$	280434.	+	223639.i	0.0865060	+	0.0689862i
$149$	556385.	−	443702.i	0.168196	−	0.134132i	−0.535774	−	0.844361i	$-0.679980\pi$
$149$	556385.	−	443702.i	0.168196	−	0.134132i	0.703971	+	0.710229i	$0.251409\pi$
$150$	−693842.	−	334136.i	−0.205583	−	0.0990034i
$151$	1.54172e6	−	3.20141e6i	0.447790	−	0.929846i	−0.547851	−	0.836576i	$-0.684554\pi$
$151$	1.54172e6	−	3.20141e6i	0.447790	−	0.929846i	0.995641	−	0.0932700i	$-0.0297320\pi$
$152$	−105935.	−	132838.i	−0.0301654	−	0.0378262i
$153$	−1.92880e6	+	2.41863e6i	−0.538533	+	0.675299i
$154$	1.22437e6	+	589623.i	0.335235	+	0.161440i
$155$	−689059.	+	157273.i	−0.185038	+	0.0422338i
$156$	68081.9	−	15539.2i	0.0179332	−	0.00409314i
$157$	2.16811e6	+	1.72901e6i	0.560250	+	0.446785i	0.862221	−	0.506533i	$-0.169073\pi$
$157$	2.16811e6	+	1.72901e6i	0.560250	+	0.446785i	−0.301970	+	0.953317i	$0.597644\pi$
$158$	−1.58644e6	−	3.29428e6i	−0.402210	−	0.835198i
$159$	528689.	+	120670.i	0.131525	+	0.0300197i
$160$	−195771.	+	94278.4i	−0.0477957	+	0.0230172i
$161$	8.70537e6	−	6.94230e6i	2.08598	−	1.66351i
$162$	−3.39092e6	+	773954.i	−0.797576	+	0.182041i
$163$	−10003.0	+	7977.13i	−0.00230976	+	0.00184197i	−0.624644	−	0.780910i	$-0.714756\pi$
$163$	−10003.0	+	7977.13i	−0.00230976	+	0.00184197i	0.622334	+	0.782752i	$0.286184\pi$
$164$	102368.	−	448503.i	0.0232077	−	0.101680i
$165$	104754.			0.0233194
$166$		−	1.67749e6i		−	0.366720i
$167$	304309.	−	1.33326e6i	0.0653379	−	0.286264i	−0.931695	−	0.363242i	$-0.881670\pi$
$167$	304309.	−	1.33326e6i	0.0653379	−	0.286264i	0.997033	+	0.0769777i	$0.0245270\pi$
$168$	−1.60593e6	−	1.28069e6i	−0.338688	−	0.270095i
$169$	−617895.	−	297563.i	−0.128013	−	0.0616479i
$170$	−1.74251e6	+	839147.i	−0.354673	+	0.170801i
$171$		−	232945.i		−	0.0465871i
$172$	70554.0	+	321691.i	0.0138655	+	0.0632198i
$173$	−5.33809e6			−1.03097			−0.515487	−	0.856897i	$-0.672389\pi$
$173$	−5.33809e6			−1.03097			−0.515487	+	0.856897i	$0.672389\pi$
$174$	−642599.	−	1.33437e6i	−0.121981	−	0.253296i
$175$	−3.26372e6	+	6.77718e6i	−0.608973	+	1.26455i
$176$	−770132.	+	965715.i	−0.141263	+	0.177138i
$177$	2.60572e6	+	594738.i	0.469902	+	0.107252i
$178$	−4.64940e6			−0.824398
$179$		−	2.03960e6i		−	0.355620i	−0.984065	−	0.177810i	$-0.943099\pi$
$179$		−	2.03960e6i		−	0.355620i	0.984065	−	0.177810i	$-0.0569012\pi$
$180$	−140363.	−	32036.9i	−0.0240677	−	0.00549330i
$181$	−1.07031e6	−	1.34213e6i	−0.180499	−	0.226339i	0.683348	−	0.730093i	$-0.260523\pi$
$181$	−1.07031e6	−	1.34213e6i	−0.180499	−	0.226339i	−0.863847	+	0.503754i	$0.831952\pi$
$182$	−2.49689e6	−	1.09396e7i	−0.414176	−	1.81463i
$183$	245020.	+	307245.i	0.0399805	+	0.0501340i
$184$	4.12321e6	+	8.56192e6i	0.661883	+	1.37442i
$185$	988612.	−	4.33139e6i	0.156139	−	0.684089i
$186$	−735655.	+	354273.i	−0.114324	+	0.0550553i
$187$	−809590.	+	1.01519e6i	−0.123806	+	0.155247i
$188$	−101287.	−	443769.i	−0.0152434	−	0.0667857i
$189$	−1.30101e6	−	5.70008e6i	−0.192705	−	0.844297i
$190$	63188.1	−	131211.i	0.00921243	−	0.0191298i
$191$	−2.85051e6	−	2.27321e6i	−0.409093	−	0.326241i	0.397227	−	0.917720i	$-0.369973\pi$
$191$	−2.85051e6	−	2.27321e6i	−0.409093	−	0.326241i	−0.806320	+	0.591479i	$0.798544\pi$
$192$	1.36445e6	−	1.08811e6i	0.192776	−	0.153734i
$193$	2.90303e6	+	1.39803e6i	0.403813	+	0.194466i	0.624755	−	0.780821i	$-0.285199\pi$
$193$	2.90303e6	+	1.39803e6i	0.403813	+	0.194466i	−0.220942	+	0.975287i	$0.570913\pi$
$194$	−3.10306e6	+	6.44357e6i	−0.424996	+	0.882514i
$195$	−539294.	−	676253.i	−0.0727313	−	0.0912022i
$196$	561814.	−	704493.i	0.0746147	−	0.0935639i
$197$	−1.34191e6	−	646231.i	−0.175520	−	0.0845258i	0.344061	−	0.938947i	$-0.388197\pi$
$197$	−1.34191e6	−	646231.i	−0.175520	−	0.0845258i	−0.519580	+	0.854422i	$0.673912\pi$
$198$	−1.55026e6	+	353837.i	−0.199714	+	0.0455835i
$199$	122987.	−	28071.1i	0.0156063	−	0.00356205i	−0.214711	−	0.976678i	$-0.568881\pi$
$199$	122987.	−	28071.1i	0.0156063	−	0.00356205i	0.230317	+	0.973116i	$0.426024\pi$
$200$	−5.01926e6	−	4.00272e6i	−0.627407	−	0.500340i
$201$	1.13494e6	+	2.35672e6i	0.139760	+	0.290215i
$202$	1.06057e7	+	2.42068e6i	1.28672	+	0.293686i
$203$	−1.30336e7	+	6.27666e6i	−1.55803	+	0.750309i
$204$	−106188.	+	84682.5i	−0.0125080	+	0.00997478i
$205$	−5.55524e6	+	1.26795e6i	−0.644824	+	0.147177i
$206$	−5.22918e6	+	4.17014e6i	−0.598181	+	0.477033i
$207$	−2.89919e6	+	1.27022e7i	−0.326863	+	1.43208i
$208$	1.01991e7			1.13337
$209$		−	97776.2i		−	0.0107101i
$210$	391776.	−	1.71648e6i	0.0423038	−	0.185345i
$211$	1.07975e7	+	8.61068e6i	1.14941	+	0.916622i	0.997422	−	0.0717611i	$-0.0228619\pi$
$211$	1.07975e7	+	8.61068e6i	1.14941	+	0.916622i	0.151985	+	0.988383i	$0.451433\pi$
$212$	−281856.	−	135735.i	−0.0295815	−	0.0142457i
$213$	−342082.	+	164738.i	−0.0353990	+	0.0170473i
$214$		−	3.44956e6i		−	0.351984i
$215$	3.21076e6	−	2.51617e6i	0.323067	−	0.253177i
$216$	4.98994e6			0.495147
$217$	3.46040e6	+	7.18560e6i	0.338647	+	0.703208i
$218$	2.02291e6	−	4.20061e6i	0.195257	−	0.405456i
$219$	261834.	−	328330.i	0.0249284	−	0.0312592i
$220$	−58915.8	−	13447.1i	−0.00553304	−	0.00126288i
$221$	1.07217e7			0.993314
$222$		−	5.13258e6i		−	0.469112i
$223$	739310.	+	168743.i	0.0666672	+	0.0152163i	0.255724	−	0.966750i	$-0.417686\pi$
$223$	739310.	+	168743.i	0.0666672	+	0.0152163i	−0.189057	+	0.981966i	$0.560543\pi$
$224$	1.52875e6	+	1.91700e6i	0.136017	+	0.170560i
$225$	−1.95858e6	−	8.58109e6i	−0.171947	−	0.753347i
$226$	−1.33537e7	−	1.67450e7i	−1.15685	−	1.45064i
$227$	6.79547e6	+	1.41109e7i	0.580954	+	1.20636i	0.959743	+	0.280880i	$0.0906264\pi$
$227$	6.79547e6	+	1.41109e7i	0.580954	+	1.20636i	−0.378789	+	0.925483i	$0.623659\pi$
$228$	2275.79	−	9970.89i	0.000192012	−	0.000841258i
$229$	1.76310e7	−	8.49063e6i	1.46815	−	0.707023i	0.482510	−	0.875891i	$-0.339725\pi$
$229$	1.76310e7	−	8.49063e6i	1.46815	−	0.707023i	0.985639	+	0.168867i	$0.0540110\pi$
$230$	−5.07859e6	+	6.36834e6i	−0.417407	+	0.523411i
$231$	−263032.	−	1.15242e6i	−0.0213389	−	0.0934920i
$232$	−2.74735e6	−	1.20369e7i	−0.220014	−	0.963942i
$233$	7.81027e6	−	1.62182e7i	0.617445	−	1.28214i	−0.324345	−	0.945939i	$-0.605144\pi$
$233$	7.81027e6	−	1.62182e7i	0.617445	−	1.28214i	0.941791	−	0.336200i	$-0.109142\pi$
$234$	1.02653e7	+	8.18633e6i	0.801171	+	0.638913i
$235$	−4.40793e6	+	3.51521e6i	−0.339650	+	0.270862i
$236$	−1.38917e6	−	668988.i	−0.105686	−	0.0508959i
$237$	−1.37994e6	+	2.86548e6i	−0.103661	+	0.215255i
$238$	1.36070e7	+	1.70627e7i	1.00933	+	1.26566i
$239$	4.08976e6	−	5.12840e6i	0.299574	−	0.375654i	−0.609147	−	0.793057i	$-0.708488\pi$
$239$	4.08976e6	−	5.12840e6i	0.299574	−	0.375654i	0.908722	+	0.417403i	$0.137060\pi$
$240$	1.44182e6	+	694344.i	0.104298	+	0.0502274i
$241$	−8.82371e6	+	2.01395e6i	−0.630377	+	0.143879i	−0.525760	−	0.850633i	$-0.676219\pi$
$241$	−8.82371e6	+	2.01395e6i	−0.630377	+	0.143879i	−0.104617	+	0.994513i	$0.533362\pi$
$242$	1.36066e7	−	3.10561e6i	0.960070	−	0.219130i
$243$	8.12117e6	+	6.47642e6i	0.565978	+	0.451352i
$244$	−98364.0	−	204255.i	−0.00677121	−	0.0140606i
$245$	−1.08811e7	−	2.48354e6i	−0.739903	−	0.168878i
$246$	−5.93090e6	+	2.85617e6i	−0.398396	+	0.191858i
$247$	−631210.	+	503373.i	−0.0418873	+	0.0334040i
$248$	−6.63610e6	+	1.51465e6i	−0.435069	+	0.0993016i
$249$	−1.14080e6	+	909757.i	−0.0738943	+	0.0589287i
$250$	2.69703e6	−	1.18164e7i	0.172610	−	0.756252i
$251$	3.13063e6			0.197975			0.0989874	−	0.995089i	$-0.468440\pi$
$251$	3.13063e6			0.197975			0.0989874	+	0.995089i	$0.468440\pi$
$252$			1.62461e6i			0.101519i
$253$	−1.21690e6	+	5.33159e6i	−0.0751439	+	0.329227i
$254$	2.40068e7	+	1.91447e7i	1.46498	+	1.16828i
$255$	1.51569e6	+	729919.i	0.0914093	+	0.0440204i
$256$	−2.92296e6	+	1.40762e6i	−0.174222	+	0.0839008i
$257$		−	1.27984e7i		−	0.753976i	−0.926218	−	0.376988i	$-0.876960\pi$
$257$		−	1.27984e7i		−	0.753976i	0.926218	−	0.376988i	$-0.123040\pi$
$258$	2.96944e6	−	3.65935e6i	0.172908	−	0.213081i
$259$	−5.01331e7			−2.88553
$260$	216501.	+	449569.i	0.0123180	+	0.0255786i
$261$	7.34446e6	−	1.52509e7i	0.413084	−	0.857778i
$262$	7.42519e6	−	9.31089e6i	0.412861	−	0.517711i
$263$	−2.39205e7	−	5.45970e6i	−1.31493	−	0.300125i	−0.493159	−	0.869939i	$-0.664158\pi$
$263$	−2.39205e7	−	5.45970e6i	−1.31493	−	0.300125i	−0.821773	+	0.569815i	$0.807015\pi$
$264$	1.00885e6			0.0548294
$265$			3.87485e6i			0.208218i
$266$	−1.60215e6	−	365680.i	−0.0851253	−	0.0194293i
$267$	2.52152e6	+	3.16189e6i	0.132473	+	0.166116i
$268$	−335784.	−	1.47117e6i	−0.0174444	−	0.0764288i
$269$	−1.84502e6	−	2.31359e6i	−0.0947862	−	0.118858i	0.732176	−	0.681115i	$-0.238505\pi$
$269$	−1.84502e6	−	2.31359e6i	−0.0947862	−	0.118858i	−0.826963	+	0.562257i	$0.809933\pi$
$270$	1.85576e6	+	3.85352e6i	0.0942821	+	0.195779i
$271$	−5.13785e6	+	2.25104e7i	−0.258151	+	1.13103i	0.665075	+	0.746776i	$0.268399\pi$
$271$	−5.13785e6	+	2.25104e7i	−0.258151	+	1.13103i	−0.923226	+	0.384257i	$0.874458\pi$
$272$	−1.78722e7	+	8.60681e6i	−0.888120	+	0.427696i
$273$	−6.08548e6	+	7.63095e6i	−0.299093	+	0.375051i
$274$	−1.36061e6	−	5.96123e6i	−0.0661427	−	0.289790i
$275$	−822091.	−	3.60182e6i	−0.0395296	−	0.173190i
$276$	−248191.	+	515374.i	−0.0118048	+	0.0245129i
$277$	−2.22074e7	−	1.77098e7i	−1.04486	−	0.833250i	−0.0585741	−	0.998283i	$-0.518655\pi$
$277$	−2.22074e7	−	1.77098e7i	−1.04486	−	0.833250i	−0.986288	+	0.165033i	$0.947227\pi$
$278$	−2.18866e7	+	1.74540e7i	−1.01869	+	0.812381i
$279$	−8.40803e6	−	4.04909e6i	−0.387152	−	0.186443i
$280$	6.36818e6	−	1.32237e7i	0.290096	−	0.602390i
$281$	−3.95318e6	−	4.95713e6i	−0.178167	−	0.223414i	0.684727	−	0.728800i	$-0.259922\pi$
$281$	−3.95318e6	−	4.95713e6i	−0.178167	−	0.223414i	−0.862894	+	0.505386i	$0.831350\pi$
$282$	−4.06099e6	+	5.09232e6i	−0.181086	+	0.227074i
$283$	−2.47287e7	−	1.19087e7i	−1.09104	−	0.525418i	−0.200211	−	0.979753i	$-0.564163\pi$
$283$	−2.47287e7	−	1.19087e7i	−1.09104	−	0.525418i	−0.890831	+	0.454334i	$0.849877\pi$
$284$	213542.	−	48739.6i	0.00932241	−	0.00212778i
$285$	−123501.	+	28188.3i	−0.00533502	+	0.00121768i
$286$	4.30876e6	+	3.43612e6i	0.184185	+	0.146883i
$287$	2.78980e7	+	5.79307e7i	1.18012	+	2.45055i
$288$	−2.79712e6	−	638425.i	−0.117094	−	0.0267259i
$289$	2.95929e6	−	1.42512e6i	0.122601	−	0.0590415i
$290$	8.27385e6	−	6.59817e6i	0.339245	−	0.270539i
$291$	6.06493e6	−	1.38428e6i	0.246120	−	0.0561753i
$292$	−189409.	+	151049.i	−0.00760767	+	0.00606692i
$293$	−679058.	+	2.97515e6i	−0.0269963	+	0.118278i	−0.986631	−	0.162972i	$-0.947892\pi$
$293$	−679058.	+	2.97515e6i	−0.0269963	+	0.118278i	0.959634	+	0.281250i	$0.0907491\pi$
$294$	−1.28938e7			−0.507387
$295$			1.90977e7i			0.743903i
$296$	9.52100e6	−	4.17142e7i	0.367119	−	1.60845i
$297$	2.24508e6	+	1.79039e6i	0.0856963	+	0.0683406i
$298$	5.29274e6	+	2.54885e6i	0.200001	+	0.0963153i
$299$	4.06838e7	−	1.95923e7i	1.52198	−	0.732946i
$300$		−	386436.i		−	0.0143124i
$301$	−3.57431e7	−	2.90043e7i	−1.31067	−	1.06356i
$302$	2.93319e7			1.06493
$303$	−4.10559e6	−	8.52535e6i	−0.147587	−	0.306467i
$304$	648096.	−	1.34578e6i	0.0230684	−	0.0479021i
$305$	−1.75077e6	+	2.19540e6i	−0.0617063	+	0.0773773i
$306$	−2.48965e7	−	5.68246e6i	−0.868907	−	0.198322i
$307$	1.07951e7			0.373087			0.186544	−	0.982447i	$-0.440271\pi$
$307$	1.07951e7			0.373087			0.186544	+	0.982447i	$0.440271\pi$
$308$			681912.i			0.0233387i
$309$	5.67192e6	+	1.29458e6i	0.192245	+	0.0438786i
$310$	−3.63766e6	−	4.56148e6i	−0.122106	−	0.153116i
$311$	−6.37397e6	−	2.79262e7i	−0.211899	−	0.928389i	−0.963275	−	0.268516i	$-0.913467\pi$
$311$	−6.37397e6	−	2.79262e7i	−0.211899	−	0.928389i	0.751377	−	0.659874i	$-0.229390\pi$
$312$	−5.19376e6	−	6.51277e6i	−0.171009	−	0.214438i
$313$	−2.15879e7	−	4.48278e7i	−0.704009	−	1.46189i	−0.878753	−	0.477276i	$-0.841624\pi$
$313$	−2.15879e7	−	4.48278e7i	−0.704009	−	1.46189i	0.174744	−	0.984614i	$-0.444090\pi$
$314$	−5.09386e6	+	2.23177e7i	−0.164535	+	0.720875i
$315$	1.81299e7	−	8.73091e6i	0.580049	−	0.279337i
$316$	1.14395e6	−	1.43447e6i	0.0362532	−	0.0454601i
$317$	6.16553e6	+	2.70129e7i	0.193550	+	0.847997i	0.974676	+	0.223623i	$0.0717885\pi$
$317$	6.16553e6	+	2.70129e7i	0.193550	+	0.847997i	−0.781126	+	0.624373i	$0.785354\pi$
$318$	996108.	+	4.36423e6i	0.0309760	+	0.135715i
$319$	3.08275e6	−	6.40140e6i	0.0949657	−	0.197198i
$320$	9.74956e6	+	7.77501e6i	0.297533	+	0.237275i
$321$	−2.34592e6	+	1.87081e6i	−0.0709249	+	0.0565607i
$322$	8.28118e7	+	3.98801e7i	2.48042	+	1.19451i
$323$	681301.	−	1.41474e6i	0.0202177	−	0.0419825i
$324$	−1.08818e6	−	1.36453e6i	−0.0319938	−	0.0401190i
$325$	−1.90198e7	+	2.38501e7i	−0.554059	+	0.694768i
$326$	−95155.8	−	45824.6i	−0.00274652	−	0.00132265i
$327$	−3.95378e6	+	902423.i	−0.113076	+	0.0258088i
$328$	−5.35006e7	+	1.22112e7i	−1.51613	+	0.346048i
$329$	4.97398e7	+	3.96662e7i	1.39674	+	1.11386i
$330$	375189.	+	779088.i	0.0104402	+	0.0216793i
$331$	4.20241e7	+	9.59173e6i	1.15882	+	0.264492i	0.758368	−	0.651827i	$-0.225997\pi$
$331$	4.20241e7	+	9.59173e6i	1.15882	+	0.264492i	0.400448	+	0.916319i	$0.368854\pi$
$332$	758396.	−	365224.i	0.0207244	−	0.00998034i
$333$	4.58637e7	−	3.65750e7i	1.24204	−	0.990495i
$334$	1.10059e7	−	2.51202e6i	0.295383	−	0.0674192i
$335$	−1.46130e7	+	1.16535e7i	−0.388691	+	0.309971i
$336$	4.01829e6	−	1.76053e7i	0.105931	−	0.464114i
$337$	1.63945e7			0.428360			0.214180	−	0.976794i	$-0.431292\pi$
$337$	1.63945e7			0.428360			0.214180	+	0.976794i	$0.431292\pi$
$338$		−	5.66126e6i		−	0.146610i
$339$	−4.14554e6	+	1.81628e7i	−0.106410	+	0.466212i
$340$	−758761.	−	605092.i	−0.0193049	−	0.0153952i
$341$	−3.52917e6	−	1.69956e6i	−0.0890041	−	0.0428621i
$342$	1.73249e6	−	834325.i	0.0433105	−	0.0208573i
$343$			5.78288e7i			1.43305i
$344$	3.09217e7	−	2.42324e7i	0.759606	−	0.595279i
$345$	7.08517e6			0.172541
$346$	−1.91191e7	−	3.97013e7i	−0.461572	−	0.958464i
$347$	−1.85327e7	+	3.84835e7i	−0.443557	+	0.921056i	0.552598	+	0.833448i	$0.313636\pi$
$347$	−1.85327e7	+	3.84835e7i	−0.443557	+	0.921056i	−0.996155	+	0.0876077i	$0.972078\pi$
$348$	463365.	−	581041.i	0.0109948	−	0.0137870i
$349$	−4.24599e7	−	9.69120e6i	−0.998856	−	0.227982i	−0.308322	−	0.951282i	$-0.599767\pi$
$349$	−4.24599e7	−	9.69120e6i	−0.998856	−	0.227982i	−0.690534	+	0.723300i	$0.742624\pi$
$350$	−6.20936e7			−1.44825
$351$		−	2.37108e7i		−	0.548308i
$352$	−1.17406e6	−	267972.i	−0.0269192	−	0.00614414i
$353$	4.89607e7	+	6.13947e7i	1.11307	+	1.39575i	0.909002	+	0.416792i	$0.136845\pi$
$353$	4.89607e7	+	6.13947e7i	1.11307	+	1.39575i	0.204070	+	0.978956i	$0.434583\pi$
$354$	4.90946e6	+	2.15097e7i	0.110668	+	0.484870i
$355$	−1.69152e6	−	2.12110e6i	−0.0378087	−	0.0474107i
$356$	−1.01227e6	−	2.10200e6i	−0.0224361	−	0.0465890i
$357$	4.22417e6	−	1.85073e7i	0.0928403	−	0.406760i
$358$	1.51692e7	−	7.30511e6i	0.330609	−	0.159213i
$359$	−1.24096e7	+	1.55612e7i	−0.268211	+	0.336325i	−0.897638	−	0.440734i	$-0.854718\pi$
$359$	−1.24096e7	+	1.55612e7i	−0.268211	+	0.336325i	0.629427	+	0.777060i	$0.283290\pi$
$360$	3.82159e6	+	1.67435e7i	0.0819100	+	0.358871i
$361$	−1.04424e7	−	4.57511e7i	−0.221962	−	0.972478i
$362$	6.14842e6	−	1.27673e7i	0.129610	−	0.269137i
$363$	−9.49131e6	−	7.56907e6i	−0.198430	−	0.158242i
$364$	4.40219e6	−	3.51063e6i	0.0912777	−	0.0727915i
$365$	2.70355e6	+	1.30196e6i	0.0555975	+	0.0267744i
$366$	−1.40752e6	+	2.92274e6i	−0.0287085	+	0.0596138i
$367$	3.33087e7	+	4.17678e7i	0.673844	+	0.844974i	0.994771	−	0.102130i	$-0.0325659\pi$
$367$	3.33087e7	+	4.17678e7i	0.673844	+	0.844974i	−0.320927	+	0.947104i	$0.603994\pi$
$368$	−5.20891e7	+	6.53176e7i	−1.04521	+	1.31065i
$369$	−6.77860e7	−	3.26440e7i	−1.34915	−	0.649718i
$370$	3.57549e7	−	8.16083e6i	0.705880	−	0.161112i
$371$	4.26281e7	−	9.72960e6i	0.834785	−	0.190534i
$372$	−320335.	−	255459.i	−0.00622266	−	0.00496241i
$373$	2.92670e6	+	6.07736e6i	0.0563965	+	0.117109i	0.927262	−	0.374412i	$-0.122155\pi$
$373$	2.92670e6	+	6.07736e6i	0.0563965	+	0.117109i	−0.870866	+	0.491521i	$0.836441\pi$
$374$	−1.04500e7	−	2.38515e6i	−0.199757	−	0.0455932i
$375$	−9.49862e6	+	4.57430e6i	−0.180122	+	0.0867422i
$376$	−4.24513e7	+	3.38538e7i	−0.798597	+	0.636860i
$377$	−5.71960e7	+	1.30546e7i	−1.06743	+	0.243635i
$378$	3.77337e7	−	3.00916e7i	0.698641	−	0.557148i
$379$	2.12327e7	−	9.30263e7i	0.390020	−	1.70879i	−0.274559	−	0.961570i	$-0.588532\pi$
$379$	2.12327e7	−	9.30263e7i	0.390020	−	1.70879i	0.664579	−	0.747218i	$-0.268611\pi$
$380$	73078.4			0.00133180
$381$		−	2.67090e7i		−	0.482928i
$382$	6.69713e6	−	2.93420e7i	0.120143	−	0.526381i
$383$	−2.57976e7	−	2.05729e7i	−0.459179	−	0.366183i	0.366411	−	0.930453i	$-0.380586\pi$
$383$	−2.57976e7	−	2.05729e7i	−0.459179	−	0.366183i	−0.825590	+	0.564270i	$0.809158\pi$
$384$	1.47331e7	+	7.09509e6i	0.260196	+	0.125304i
$385$	7.60983e6	−	3.66470e6i	0.133350	−	0.0642179i
$386$			2.65981e7i			0.462475i
$387$	5.38595e7	+	457575.i	0.929243	+	0.00789459i
$388$	−3.58876e6			−0.0614397
$389$	4.55319e7	+	9.45480e7i	0.773512	+	1.60621i	0.795123	+	0.606448i	$0.207406\pi$
$389$	4.55319e7	+	9.45480e7i	0.773512	+	1.60621i	−0.0216113	+	0.999766i	$0.506880\pi$
$390$	3.09797e6	−	6.43301e6i	0.0522256	−	0.108448i
$391$	−5.47579e7	+	6.86642e7i	−0.916044	+	1.14868i
$392$	−1.04792e8	−	2.39182e7i	−1.73969	−	0.397072i
$393$	−1.03589e7			−0.170662
$394$		−	1.22948e7i		−	0.201018i
$395$	−2.21558e7	−	5.05692e6i	−0.359498	−	0.0820531i
$396$	−497495.	−	623839.i	−0.00801131	−	0.0100459i
$397$	−2.09413e7	−	9.17500e7i	−0.334683	−	1.46634i	−0.809950	−	0.586499i	$-0.800506\pi$
$397$	−2.09413e7	−	9.17500e7i	−0.334683	−	1.46634i	0.475268	−	0.879841i	$-0.342351\pi$
$398$	649270.	+	814159.i	0.0102986	+	0.0129140i
$399$	620213.	+	1.28789e6i	0.00976387	+	0.0202749i
$400$	1.25589e7	−	5.50243e7i	0.196233	−	0.859754i
$401$	5.89525e7	−	2.83900e7i	0.914259	−	0.440284i	0.0832410	−	0.996529i	$-0.473473\pi$
$401$	5.89525e7	−	2.83900e7i	0.914259	−	0.440284i	0.831018	+	0.556246i	$0.187759\pi$
$402$	−1.34628e7	+	1.68818e7i	−0.207233	+	0.259861i
$403$	7.19717e6	+	3.15329e7i	0.109963	+	0.481779i
$404$	1.21469e6	+	5.32188e6i	0.0184213	+	0.0807089i
$405$	−9.37955e6	+	1.94768e7i	−0.141194	+	0.293193i
$406$	−9.33634e7	−	7.44548e7i	−1.39508	−	1.11254i
$407$	1.92507e7	−	1.53520e7i	0.285538	−	0.227709i
$408$	1.45971e7	+	7.02961e6i	0.214925	+	0.103502i
$409$	4.93935e7	−	1.02567e8i	0.721937	−	1.49912i	−0.138937	−	0.990301i	$-0.544369\pi$
$409$	4.93935e7	−	1.02567e8i	0.721937	−	1.49912i	0.860875	−	0.508817i	$-0.169917\pi$
$410$	−2.93270e7	−	3.67749e7i	−0.425516	−	0.533580i
$411$	−3.31611e6	+	4.15827e6i	−0.0477643	+	0.0598945i
$412$	−3.02383e6	−	1.45620e6i	−0.0432380	−	0.0208223i
$413$	2.10099e8	−	4.79537e7i	2.98245	−	0.680725i
$414$	−1.04854e8	+	2.39323e7i	−1.47770	+	0.337275i
$415$	−8.15148e6	−	6.50059e6i	−0.114049	−	0.0909512i
$416$	4.31439e6	+	8.95892e6i	0.0599293	+	0.124444i
$417$	2.37396e7	+	5.41841e6i	0.327390	+	0.0747247i
$418$	727195.	−	350199.i	0.00995685	−	0.00479497i
$419$	−2.25149e7	+	1.79551e7i	−0.306076	+	0.244087i	−0.764466	−	0.644664i	$-0.776997\pi$
$419$	−2.25149e7	+	1.79551e7i	−0.306076	+	0.244087i	0.458391	+	0.888751i	$0.348426\pi$
$420$	861323.	−	196591.i	0.0116257	−	0.00265348i
$421$	−2.41749e7	+	1.92789e7i	−0.323980	+	0.258366i	−0.771950	−	0.635683i	$-0.780719\pi$
$421$	−2.41749e7	+	1.92789e7i	−0.323980	+	0.258366i	0.447970	+	0.894049i	$0.352147\pi$
$422$	−2.53681e7	+	1.11145e8i	−0.337559	+	1.47894i
$423$	−7.44427e7			−0.983560
$424$			3.73174e7i			0.489569i
$425$	1.32024e7	−	5.78435e7i	0.171983	−	0.753508i
$426$	−2.45043e6	−	1.95415e6i	−0.0316966	−	0.0252772i
$427$	2.85482e7	+	1.37481e7i	0.366687	+	0.176587i
$428$	1.55955e6	−	751042.i	0.0198916	−	0.00957928i
$429$		−	4.79375e6i		−	0.0607161i
$430$	3.02134e7	+	1.48675e7i	0.380009	+	0.186996i
$431$	−9.34751e7			−1.16752			−0.583760	−	0.811926i	$-0.698419\pi$
$431$	−9.34751e7			−1.16752			−0.583760	+	0.811926i	$0.698419\pi$
$432$	1.90338e7	+	3.95240e7i	0.236088	+	0.490241i
$433$	−5.61461e7	+	1.16589e8i	−0.691602	+	1.43613i	0.198378	+	0.980126i	$0.436433\pi$
$433$	−5.61461e7	+	1.16589e8i	−0.691602	+	1.43613i	−0.889979	+	0.456001i	$0.849281\pi$
$434$	−4.10479e7	+	5.14724e7i	−0.502136	+	0.629659i
$435$	−8.97436e6	−	2.04834e6i	−0.109027	−	0.0248848i
$436$	2.33954e6			0.0282274
$437$		−	6.61324e6i		−	0.0792447i
$438$	3.37969e6	+	771393.i	0.0402212	+	0.00918023i
$439$	4.95506e7	+	6.21345e7i	0.585673	+	0.734411i	0.983069	−	0.183236i	$-0.0586573\pi$
$439$	4.95506e7	+	6.21345e7i	0.585673	+	0.734411i	−0.397396	+	0.917647i	$0.630086\pi$
$440$	1.60407e6	+	7.02789e6i	0.0188307	+	0.0825025i
$441$	−9.18820e7	−	1.15216e8i	−1.07131	−	1.34338i
$442$	3.84012e7	+	7.97409e7i	0.444711	+	0.923452i
$443$	2.73048e7	−	1.19630e8i	0.314071	−	1.37604i	−0.533700	−	0.845674i	$-0.679199\pi$
$443$	2.73048e7	−	1.19630e8i	0.314071	−	1.37604i	0.847771	−	0.530362i	$-0.177944\pi$
$444$	2.32045e6	−	1.11747e6i	0.0265109	−	0.0127670i
$445$	−1.80173e7	+	2.25930e7i	−0.204461	+	0.256386i
$446$	1.39294e6	+	6.10288e6i	0.0157010	+	0.0687908i
$447$	−1.13705e6	−	4.98172e6i	−0.0127308	−	0.0557773i
$448$	6.10540e7	−	1.26780e8i	0.679016	−	1.40999i
$449$	−1.13858e7	−	9.07986e6i	−0.125784	−	0.100309i	0.558578	−	0.829452i	$-0.311347\pi$
$449$	−1.13858e7	−	9.07986e6i	−0.125784	−	0.100309i	−0.684361	+	0.729143i	$0.739919\pi$
$450$	5.68057e7	−	4.53010e7i	0.623382	−	0.497130i
$451$	−2.84524e7	−	1.37020e7i	−0.310163	−	0.149367i
$452$	4.66309e6	−	9.68300e6i	0.0504962	−	0.104856i
$453$	−1.59077e7	−	1.99476e7i	−0.171124	−	0.214583i
$454$	−8.06090e7	+	1.01080e8i	−0.861422	+	1.08019i
$455$	−6.28351e7	−	3.02598e7i	−0.667065	−	0.321242i
$456$	−1.18940e6	+	271472.i	−0.0125439	+	0.00286306i
$457$	5.75871e7	−	1.31439e7i	0.603360	−	0.137713i	0.0900803	−	0.995935i	$-0.471288\pi$
$457$	5.75871e7	−	1.31439e7i	0.603360	−	0.137713i	0.513279	+	0.858222i	$0.328430\pi$
$458$	1.26296e8	+	1.00717e8i	1.31459	+	1.04835i
$459$	2.00090e7	+	4.15490e7i	0.206912	+	0.429658i
$460$	−3.98486e6	−	909518.i	−0.0409392	−	0.00934411i
$461$	−1.15388e8	+	5.55678e7i	−1.17776	+	0.567180i	−0.917258	−	0.398293i	$-0.869603\pi$
$461$	−1.15388e8	+	5.55678e7i	−1.17776	+	0.567180i	−0.260503	+	0.965473i	$0.583888\pi$
$462$	7.62885e6	−	6.08381e6i	0.0773630	−	0.0616949i
$463$	9.60847e7	−	2.19307e7i	0.968080	−	0.220958i	0.290882	−	0.956759i	$-0.406051\pi$
$463$	9.60847e7	−	2.19307e7i	0.968080	−	0.220958i	0.677198	+	0.735801i	$0.263194\pi$
$464$	8.48616e7	−	6.76749e7i	0.849488	−	0.677444i
$465$	−1.12927e6	+	4.94768e6i	−0.0112316	+	0.0492088i
$466$	1.48594e8			1.46840
$467$			3.49532e6i			0.0343191i	0.999853	+	0.0171596i	$0.00546232\pi$
$467$			3.49532e6i			0.0343191i	−0.999853	+	0.0171596i	$0.994538\pi$
$468$	−1.46608e6	+	6.42332e6i	−0.0143028	+	0.0626645i
$469$	1.64895e8	+	1.31500e8i	1.59842	+	1.27469i
$470$	−4.19314e7	−	2.01931e7i	−0.403874	−	0.194496i
$471$	1.79400e7	−	8.63945e6i	0.171696	−	0.0826844i
$472$			1.83924e8i			1.74909i
$473$	2.26069e7	+	192062.i	0.213628	+	0.00181492i
$474$	−2.62540e7			−0.246525
$475$	1.93844e6	+	4.02521e6i	0.0180872	+	0.0375585i
$476$	−4.75154e6	+	9.86667e6i	−0.0440568	+	0.0914850i
$477$	−3.18996e7	+	4.00008e7i	−0.293920	+	0.368564i
$478$	5.27898e7	+	1.20489e7i	0.483355	+	0.110323i
$479$	6.73725e7			0.613022			0.306511	−	0.951867i	$-0.400838\pi$
$479$	6.73725e7			0.613022			0.306511	+	0.951867i	$0.400838\pi$
$480$			1.56021e6i			0.0141078i
$481$	−1.98214e8	−	4.52411e7i	−1.78114	−	0.406535i
$482$	−4.65818e7	−	5.84117e7i	−0.415983	−	0.521626i
$483$	−1.77906e7	−	7.79456e7i	−0.157888	−	0.691752i
$484$	4.36649e6	+	5.47541e6i	0.0385121	+	0.0482926i
$485$	1.92865e7	+	4.00489e7i	0.169055	+	0.351047i
$486$	−1.90803e7	+	8.35961e7i	−0.166217	+	0.728245i
$487$	7.59609e7	−	3.65809e7i	0.657663	−	0.316714i	−0.0751218	−	0.997174i	$-0.523935\pi$
$487$	7.59609e7	−	3.65809e7i	0.657663	−	0.316714i	0.732785	+	0.680461i	$0.238220\pi$
$488$	−1.68611e7	+	2.11431e7i	−0.145086	+	0.181932i
$489$	20442.4	+	89564.2i	0.000174826	+	0.000765963i
$490$	−2.05012e7	−	8.98217e7i	−0.174257	−	0.763472i
$491$	8.79323e6	−	1.82593e7i	0.0742855	−	0.154255i	−0.860519	−	0.509419i	$-0.829860\pi$
$491$	8.79323e6	−	1.82593e7i	0.0742855	−	0.154255i	0.934804	+	0.355163i	$0.115575\pi$
$492$	−2.58256e6	−	2.05953e6i	−0.0216848	−	0.0172931i
$493$	8.92095e7	−	7.11422e7i	0.744510	−	0.593727i
$494$	−6.00452e6	−	2.89162e6i	−0.0498078	−	0.0239862i
$495$	−4.28815e6	+	8.90443e6i	−0.0353553	+	0.0734160i
$496$	−3.73100e7	−	4.67853e7i	−0.305760	−	0.383411i
$497$	−1.90874e7	+	2.39348e7i	−0.155481	+	0.194967i
$498$	−1.08521e7	−	5.22610e6i	−0.0878670	−	0.0423145i
$499$	−2.46911e7	+	5.63557e6i	−0.198718	+	0.0453562i	−0.320721	−	0.947174i	$-0.603925\pi$
$499$	−2.46911e7	+	5.63557e6i	−0.198718	+	0.0453562i	0.122003	+	0.992530i	$0.461068\pi$
$500$	5.92944e6	−	1.35336e6i	0.0474355	−	0.0108269i
$501$	−7.67718e6	−	6.12235e6i	−0.0610504	−	0.0486861i
$502$	1.12128e7	+	2.32835e7i	0.0886342	+	0.184051i
$503$	1.37058e8	+	3.12826e7i	1.07696	+	0.245810i	0.723980	−	0.689821i	$-0.242311\pi$
$503$	1.37058e8	+	3.12826e7i	1.07696	+	0.245810i	0.352982	+	0.935630i	$0.385168\pi$
$504$	1.74603e8	−	8.40845e7i	1.36383	−	0.656787i
$505$	5.28619e7	−	4.21560e7i	0.410458	−	0.327329i
$506$	−4.40114e7	+	1.00453e7i	−0.339714	+	0.0775376i
$507$	−3.85002e6	+	3.07029e6i	−0.0295419	+	0.0235589i
$508$	−3.42861e6	+	1.50217e7i	−0.0261533	+	0.114585i
$509$	3.93027e7			0.298036			0.149018	−	0.988834i	$-0.452389\pi$
$509$	3.93027e7			0.298036			0.149018	+	0.988834i	$0.452389\pi$
$510$			1.38870e7i			0.104689i
$511$	7.53467e6	−	3.30115e7i	0.0564679	−	0.247402i
$512$	9.30170e7	+	7.41786e7i	0.693030	+	0.552673i
$513$	−3.12866e6	−	1.50668e6i	−0.0231743	−	0.0111601i
$514$	9.51864e7	−	4.58394e7i	0.700948	−	0.337559i
$515$			4.15705e7i			0.304343i
$516$	2.30091e6	+	545773.i	0.0167475	+	0.00397249i
$517$	−3.12465e7			−0.226115
$518$	−1.79558e8	−	3.72857e8i	−1.29186	−	2.68258i
$519$	−1.66305e7	+	3.45335e7i	−0.118960	+	0.247024i
$520$	3.71116e7	−	4.65364e7i	0.263936	−	0.330966i
$521$	−2.71403e8	−	6.19460e7i	−1.91912	−	0.438026i	−0.998914	−	0.0465886i	$-0.985165\pi$
$521$	−2.71403e8	−	6.19460e7i	−1.91912	−	0.438026i	−0.920205	−	0.391438i	$-0.871978\pi$
$522$	1.39732e8			0.982388
$523$		−	8.02910e7i		−	0.561257i	−0.959817	−	0.280628i	$-0.909457\pi$
$523$		−	8.02910e7i		−	0.561257i	0.959817	−	0.280628i	$-0.0905428\pi$
$524$	5.82609e6	+	1.32977e6i	0.0404933	+	0.00924234i
$525$	3.36754e7	+	4.22276e7i	0.232721	+	0.291823i
$526$	−4.50689e7	−	1.97460e8i	−0.309685	−	1.35682i
$527$	−3.92216e7	−	4.91823e7i	−0.267975	−	0.336029i
$528$	3.84817e6	+	7.99080e6i	0.0261428	+	0.0542861i
$529$	−4.93659e7	+	2.16286e8i	−0.333473	+	1.46104i
$530$	−2.88186e7	+	1.38783e7i	−0.193573	+	0.0932199i
$531$	−1.57221e8	+	1.97149e8i	−1.05009	+	1.31678i
$532$	−183497.	−	803953.i	−0.00121869	−	0.00533944i
$533$	5.80240e7	+	2.54220e8i	0.383201	+	1.67891i
$534$	−1.44849e7	+	3.00782e7i	−0.0951242	+	0.197527i
$535$	−1.67626e7	−	1.33677e7i	−0.109466	−	0.0872963i
$536$	−1.40733e8	+	1.12231e8i	−0.913906	+	0.728815i
$537$	−1.31947e7	−	6.35423e6i	−0.0852073	−	0.0410337i
$538$	1.05987e7	−	2.20085e7i	0.0680624	−	0.141333i
$539$	−3.85664e7	−	4.83608e7i	−0.246288	−	0.308835i
$540$	−1.33815e6	+	1.67798e6i	−0.00849811	+	0.0106563i
$541$	−1.94645e7	−	9.37360e6i	−0.122928	−	0.0591990i	0.371409	−	0.928469i	$-0.378875\pi$
$541$	−1.94645e7	−	9.37360e6i	−0.122928	−	0.0591990i	−0.494337	+	0.869270i	$0.664589\pi$
$542$	−1.85820e8	+	4.24121e7i	−1.16706	+	0.266374i
$543$	−1.20171e7	+	2.74282e6i	−0.0750585	+	0.0171316i
$544$	−1.51204e7	−	1.20581e7i	−0.0939220	−	0.0749003i
$545$	−1.25730e7	−	2.61082e7i	−0.0776696	−	0.161283i
$546$	−7.85499e7	−	1.79285e7i	−0.482578	−	0.110145i
$547$	−2.61035e8	+	1.25708e8i	−1.59491	+	0.768068i	−0.999378	−	0.0352630i	$-0.988773\pi$
$547$	−2.61035e8	+	1.25708e8i	−1.59491	+	0.768068i	−0.595532	+	0.803331i	$0.703059\pi$
$548$	2.39885e6	−	1.91302e6i	0.0145768	−	0.0116246i
$549$	−3.61470e7	+	8.25032e6i	−0.218452	+	0.0498602i
$550$	2.38435e7	−	1.90146e7i	0.143312	−	0.114287i
$551$	−1.91190e6	+	8.37660e6i	−0.0114291	+	0.0500741i
$552$	6.82349e7			0.405685
$553$			2.56439e8i			1.51638i
$554$	5.21752e7	−	2.28595e8i	0.306856	−	1.34442i
$555$	−2.49410e7	−	1.98897e7i	−0.145893	−	0.116346i
$556$	−1.26561e7	−	6.09488e6i	−0.0736338	−	0.0354602i
$557$	3.57073e7	−	1.71957e7i	0.206629	−	0.0995073i	−0.327707	−	0.944779i	$-0.606276\pi$
$557$	3.57073e7	−	1.71957e7i	0.206629	−	0.0995073i	0.534336	+	0.845272i	$0.320562\pi$
$558$		−	7.70358e7i		−	0.443394i
$559$	−1.15145e8	−	1.46931e8i	−0.659191	−	0.841161i
$560$	1.29032e8			0.734740
$561$	4.04533e6	+	8.40022e6i	0.0229121	+	0.0475775i
$562$	2.27090e7	−	4.71558e7i	0.127935	−	0.265660i
$563$	8.79199e7	−	1.10248e8i	0.492677	−	0.617797i	−0.471883	−	0.881661i	$-0.656426\pi$
$563$	8.79199e7	−	1.10248e8i	0.492677	−	0.617797i	0.964560	+	0.263864i	$0.0849971\pi$
$564$	−3.18641e6	−	727278.i	−0.0177609	−	0.00405381i
$565$	−1.33118e8			−0.738060
$566$		−	2.26568e8i		−	1.24954i
$567$	2.37821e8	+	5.42811e7i	1.30467	+	0.297783i
$568$	−1.62905e7	−	2.04276e7i	−0.0888973	−	0.111474i
$569$	−2.57416e7	−	1.12781e8i	−0.139733	−	0.612210i	−0.995493	−	0.0948368i	$-0.969767\pi$
$569$	−2.57416e7	−	1.12781e8i	−0.139733	−	0.612210i	0.855760	−	0.517373i	$-0.173090\pi$
$570$	−651982.	−	817560.i	−0.00352056	−	0.00441464i
$571$	−5.22253e7	−	1.08447e8i	−0.280526	−	0.582517i	0.712329	−	0.701845i	$-0.247640\pi$
$571$	−5.22253e7	−	1.08447e8i	−0.280526	−	0.582517i	−0.992855	+	0.119328i	$0.961926\pi$
$572$	−615371.	+	2.69612e6i	−0.00328813	+	0.0144062i
$573$	−2.35865e7	+	1.13587e7i	−0.125372	+	0.0603759i
$574$	−3.30930e8	+	4.14974e8i	−1.74985	+	2.19424i
$575$	−5.56034e7	−	2.43614e8i	−0.292481	−	1.28144i
$576$	3.66390e7	+	1.60526e8i	0.191724	+	0.839996i
$577$	−1.17400e8	+	2.43784e8i	−0.611141	+	1.26905i	0.334058	+	0.942553i	$0.391582\pi$
$577$	−1.17400e8	+	2.43784e8i	−0.611141	+	1.26905i	−0.945199	+	0.326495i	$0.894132\pi$
$578$	2.11982e7	+	1.69050e7i	0.109778	+	0.0875451i
$579$	1.80884e7	−	1.44250e7i	0.0931889	−	0.0743157i
$580$	4.78444e6	+	2.30406e6i	0.0245215	+	0.0118089i
$581$	−5.10465e7	+	1.05999e8i	−0.260278	+	0.540473i
$582$	3.20178e7	+	4.01490e7i	0.162414	+	0.203660i
$583$	−1.33895e7	+	1.67899e7i	−0.0675706	+	0.0847309i
$584$	2.60370e7	+	1.25387e7i	0.130723	+	0.0629529i
$585$	7.95603e7	−	1.81591e7i	0.397401	−	0.0907042i
$586$	−2.45593e7	+	5.60551e6i	−0.122046	+	0.0278562i
$587$	2.61801e8	+	2.08779e8i	1.29437	+	1.03222i	0.996995	+	0.0774608i	$0.0246813\pi$
$587$	2.61801e8	+	2.08779e8i	1.29437	+	1.03222i	0.297371	+	0.954762i	$0.403890\pi$
$588$	−2.80725e6	−	5.82932e6i	−0.0138086	−	0.0286739i
$589$	4.61812e6	+	1.05406e6i	0.0226006	+	0.00515844i
$590$	−1.42037e8	+	6.84012e7i	−0.691583	+	0.333049i
$591$	−8.36127e6	+	6.66789e6i	−0.0405051	+	0.0323018i
$592$	3.66724e8	−	8.37024e7i	1.76756	−	0.403434i
$593$	6.97062e7	−	5.55888e7i	0.334277	−	0.266577i	−0.441937	−	0.897046i	$-0.645709\pi$
$593$	6.97062e7	−	5.55888e7i	0.334277	−	0.266577i	0.776215	+	0.630469i	$0.217137\pi$
$594$	−5.27470e6	+	2.31100e7i	−0.0251674	+	0.110266i
$595$	1.35643e8			0.643942
$596$			2.94780e6i			0.0139238i
$597$	201560.	−	883090.i	0.000947285	−	0.00415033i
$598$	2.91429e8	+	2.32407e8i	1.36279	+	1.08679i
$599$	−1.75001e8	−	8.42758e7i	−0.814252	−	0.392123i	−0.0200667	−	0.999799i	$-0.506388\pi$
$599$	−1.75001e8	−	8.42758e7i	−0.814252	−	0.392123i	−0.794185	+	0.607675i	$0.792102\pi$
$600$	−4.15318e7	+	2.00007e7i	−0.192277	+	0.0925957i
$601$		−	3.48723e8i		−	1.60641i	−0.595702	−	0.803206i	$-0.703126\pi$
$601$		−	3.48723e8i		−	1.60641i	0.595702	−	0.803206i	$-0.296874\pi$
$602$	8.76964e7	−	3.69716e8i	0.401969	−	1.69465i
$603$	−2.46789e8			−1.12558
$604$	6.38617e6	+	1.32610e7i	0.0289821	+	0.0601820i
$605$	3.76369e7	−	7.81538e7i	0.169960	−	0.352926i
$606$	4.87012e7	−	6.10694e7i	0.218838	−	0.274414i
$607$	−2.48915e7	−	5.68131e6i	−0.111297	−	0.0254029i	0.166510	−	0.986040i	$-0.446750\pi$
$607$	−2.48915e7	−	5.68131e6i	−0.111297	−	0.0254029i	−0.277807	+	0.960637i	$0.589607\pi$
$608$	1.45629e6			0.00647944
$609$			1.03872e8i			0.459884i
$610$	−2.25985e7	−	5.15797e6i	−0.0995614	−	0.0227242i
$611$	1.60864e8	+	2.01717e8i	0.705236	+	0.884337i
$612$	−2.85143e6	−	1.24929e7i	−0.0124397	−	0.0545017i
$613$	−4.83516e7	−	6.06310e7i	−0.209908	−	0.263216i	0.665721	−	0.746201i	$-0.268124\pi$
$613$	−4.83516e7	−	6.06310e7i	−0.209908	−	0.263216i	−0.875629	+	0.482984i	$0.839553\pi$
$614$	3.86640e7	+	8.02867e7i	0.167033	+	0.346847i
$615$	−9.10428e6	+	3.98885e7i	−0.0391400	+	0.171483i
$616$	7.32878e7	−	3.52935e7i	0.313537	−	0.150992i
$617$	1.46263e7	−	1.83408e7i	0.0622702	−	0.0780843i	−0.749721	−	0.661754i	$-0.769812\pi$
$617$	1.46263e7	−	1.83408e7i	0.0622702	−	0.0780843i	0.811991	+	0.583670i	$0.198384\pi$
$618$	1.06865e7	+	4.68207e7i	0.0452763	+	0.198368i
$619$	−4.45941e7	−	1.95380e8i	−0.188021	−	0.823773i	−0.977659	−	0.210199i	$-0.932589\pi$
$619$	−4.45941e7	−	1.95380e8i	−0.188021	−	0.823773i	0.789638	−	0.613573i	$-0.210268\pi$
$620$	1.27026e6	−	2.63772e6i	0.00532988	−	0.0110676i
$621$	1.51849e8	+	1.21096e8i	0.634071	+	0.505655i
$622$	1.84867e8	−	1.47427e8i	0.768226	−	0.612640i
$623$	2.93792e8	+	1.41483e8i	1.21500	+	0.585112i
$624$	3.17747e7	−	6.59809e7i	0.130776	−	0.271559i
$625$	7.96061e7	+	9.98229e7i	0.326067	+	0.408875i
$626$	2.56080e8	−	3.21114e8i	1.04388	−	1.30899i
$627$	−632539.	−	304615.i	−0.00256617	−	0.00123580i
$628$	−1.11989e7	+	2.55608e6i	−0.0452165	+	0.0103204i
$629$	3.85514e8	−	8.79910e7i	1.54913	−	0.353579i
$630$	1.29870e8	+	1.03568e8i	0.519381	+	0.414192i
$631$	−1.33283e8	−	2.76764e8i	−0.530500	−	1.10159i	−0.978249	−	0.207435i	$-0.933488\pi$
$631$	−1.33283e8	−	2.76764e8i	−0.530500	−	1.10159i	0.447749	−	0.894159i	$-0.352226\pi$
$632$	−2.13375e8	−	4.87015e7i	−0.845265	−	0.192926i
$633$	8.93434e7	−	4.30255e7i	0.352250	−	0.169635i
$634$	−1.78822e8	+	1.42606e8i	−0.701702	+	0.559589i
$635$	1.86062e8	−	4.24674e7i	0.726667	−	0.165857i
$636$	−1.75621e6	+	1.40053e6i	−0.00682660	+	0.00544403i
$637$	−1.13652e8	+	4.97943e8i	−0.439703	+	1.92647i
$638$	5.86508e7			0.225846
$639$		−	3.58219e7i		−	0.137292i
$640$	−2.60006e7	+	1.13916e8i	−0.0991843	+	0.434555i
$641$	1.60219e8	+	1.27770e8i	0.608330	+	0.485127i	0.878536	−	0.477676i	$-0.158521\pi$
$641$	1.60219e8	+	1.27770e8i	0.608330	+	0.485127i	−0.270207	+	0.962802i	$0.587092\pi$
$642$	−2.23161e7	−	1.07469e7i	−0.0843361	−	0.0406141i
$643$	−2.70333e8	+	1.30185e8i	−1.01687	+	0.489699i	−0.866631	−	0.498950i	$-0.833719\pi$
$643$	−2.70333e8	+	1.30185e8i	−1.01687	+	0.489699i	−0.150241	+	0.988649i	$0.548005\pi$
$644$			4.61221e7i			0.172684i
$645$	−6.27485e6	−	2.86102e7i	−0.0233843	−	0.106621i
$646$	1.29621e7			0.0480813
$647$	−8.71565e7	−	1.80982e8i	−0.321801	−	0.668226i	0.675827	−	0.737060i	$-0.263786\pi$
$647$	−8.71565e7	−	1.80982e8i	−0.321801	−	0.668226i	−0.997628	+	0.0688337i	$0.978072\pi$
$648$	−9.03313e7	+	1.87575e8i	−0.331981	+	0.689366i
$649$	−6.59919e7	+	8.27513e7i	−0.241411	+	0.302720i
$650$	−2.45503e8	−	5.60345e7i	−0.893958	−	0.204040i
$651$	5.72661e7			0.207565
$652$		−	52997.1i		−	0.000191210i
$653$	−5.84915e7	−	1.33503e7i	−0.210065	−	0.0479459i	0.116193	−	0.993227i	$-0.462931\pi$
$653$	−5.84915e7	−	1.33503e7i	−0.210065	−	0.0479459i	−0.326258	+	0.945281i	$0.605788\pi$
$654$	−2.08726e7	−	2.61734e7i	−0.0746180	−	0.0935681i
$655$	−1.64707e7	−	7.21630e7i	−0.0586123	−	0.256797i
$656$	−3.00796e8	−	3.77186e8i	−1.06552	−	1.33611i
$657$	1.71909e7	+	3.56972e7i	0.0606180	+	0.125875i
$658$	−1.16861e8	+	5.12002e8i	−0.410197	+	1.79719i
$659$	−1.62993e8	+	7.84935e7i	−0.569526	+	0.274269i	−0.696405	−	0.717649i	$-0.745218\pi$
$659$	−1.62993e8	+	7.84935e7i	−0.569526	+	0.274269i	0.126879	+	0.991918i	$0.459504\pi$
$660$	−270541.	+	339248.i	−0.000941026	+	0.00118001i
$661$	5.41312e7	+	2.37164e8i	0.187432	+	0.821192i	0.977964	+	0.208772i	$0.0669467\pi$
$661$	5.41312e7	+	2.37164e8i	0.187432	+	0.821192i	−0.790533	+	0.612420i	$0.790196\pi$
$662$	7.91781e7	+	3.46902e8i	0.272917	+	1.19573i
$663$	3.34027e7	−	6.93614e7i	0.114615	−	0.238000i
$664$	−7.85042e7	−	6.26050e7i	−0.268157	−	0.213848i
$665$	−7.98561e6	+	6.36831e6i	−0.0271546	+	0.0216551i
$666$	4.36288e8	+	2.10105e8i	1.47690	+	0.711237i
$667$	2.08507e8	−	4.32969e8i	0.702656	−	1.45908i
$668$	3.53190e6	+	4.42886e6i	0.0118489	+	0.0148581i
$669$	3.39491e6	−	4.25708e6i	0.0113384	−	0.0142178i
$670$	−1.39009e8	−	6.69434e7i	−0.462189	−	0.222579i
$671$	−1.51723e7	+	3.46298e6i	−0.0502208	+	0.0114626i
$672$	1.71643e7	−	3.91763e6i	0.0565610	−	0.0129097i
$673$	−2.36195e8	−	1.88359e8i	−0.774863	−	0.617932i	0.154121	−	0.988052i	$-0.450745\pi$
$673$	−2.36195e8	−	1.88359e8i	−0.774863	−	0.617932i	−0.928984	+	0.370120i	$0.879317\pi$
$674$	5.87192e7	+	1.21932e8i	0.191779	+	0.398233i
$675$	−1.27920e8	−	2.91968e7i	−0.415935	−	0.0949345i
$676$	2.55947e6	−	1.23258e6i	0.00828533	−	0.00399000i
$677$	−3.40652e8	+	2.71661e8i	−1.09786	+	0.875511i	−0.992898	−	0.118966i	$-0.962042\pi$
$677$	−3.40652e8	+	2.71661e8i	−1.09786	+	0.875511i	−0.104958	+	0.994477i	$0.533471\pi$
$678$	−1.49931e8	+	3.42207e7i	−0.481062	+	0.109799i
$679$	3.92160e8	−	3.12737e8i	1.25272	−	0.999011i
$680$	−2.57606e7	+	1.12865e8i	−0.0819274	+	0.358948i
$681$	1.12458e8			0.356082
$682$		−	3.23349e7i		−	0.101934i
$683$	−2.80335e7	+	1.22823e8i	−0.0879863	+	0.385493i	−0.999678	−	0.0253823i	$-0.991920\pi$
$683$	−2.80335e7	+	1.22823e8i	−0.0879863	+	0.385493i	0.911692	+	0.410875i	$0.134777\pi$
$684$	754401.	+	601615.i	0.00235740	+	0.00187997i
$685$	−3.42402e7	−	1.64892e7i	−0.106528	−	0.0513013i
$686$	−4.30093e8	+	2.07122e8i	−1.33226	+	0.641584i
$687$		−	1.40511e8i		−	0.433352i
$688$	3.09887e8	+	1.52490e8i	0.951564	+	0.468249i
$689$	1.77322e8			0.542131
$690$	2.53765e7	+	5.26948e7i	0.0772475	+	0.160406i
$691$	6.89828e7	−	1.43244e8i	0.209077	−	0.434153i	−0.769888	−	0.638179i	$-0.779688\pi$
$691$	6.89828e7	−	1.43244e8i	0.209077	−	0.434153i	0.978966	+	0.204025i	$0.0654024\pi$
$692$	1.37864e7	−	1.72876e7i	0.0416038	−	0.0521695i
$693$	1.08727e8	+	2.48163e7i	0.326692	+	0.0745653i
$694$	−3.52592e8			−1.05486
$695$			1.73992e8i			0.518292i
$696$	−8.64290e7	−	1.97269e7i	−0.256349	−	0.0585100i
$697$	−3.16207e8	−	3.96511e8i	−0.933842	−	1.17100i
$698$	−7.99992e7	−	3.50499e8i	−0.235244	−	1.03067i
$699$	−8.05874e7	−	1.01053e8i	−0.235958	−	0.295882i
$700$	−1.35191e7	−	2.80727e7i	−0.0394143	−	0.0818446i
$701$	1.02560e8	−	4.49345e8i	0.297731	−	1.30444i	−0.575766	−	0.817615i	$-0.695296\pi$
$701$	1.02560e8	−	4.49345e8i	0.297731	−	1.30444i	0.873497	−	0.486830i	$-0.161847\pi$
$702$	1.76345e8	−	8.49234e7i	0.509744	−	0.245480i
$703$	−1.85649e7	+	2.32797e7i	−0.0534352	+	0.0670056i
$704$	1.53788e7	+	6.73789e7i	0.0440762	+	0.193110i
$705$	9.00818e6	+	3.94674e7i	0.0257081	+	0.112635i
$706$	−2.81255e8	+	5.84031e8i	−0.799255	+	1.65967i
$707$	−5.96502e8	−	4.75695e8i	−1.68793	−	1.34608i
$708$	−8.65572e6	+	6.90270e6i	−0.0243895	+	0.0194500i
$709$	3.98167e8	+	1.91747e8i	1.11719	+	0.538010i	0.899023	−	0.437901i	$-0.144278\pi$
$709$	3.98167e8	+	1.91747e8i	1.11719	+	0.538010i	0.218167	+	0.975912i	$0.429992\pi$
$710$	9.71694e6	−	2.01774e7i	0.0271490	−	0.0563756i
$711$	−1.87088e8	−	2.34600e8i	−0.520518	−	0.652710i
$712$	−1.73519e8	+	2.17586e8i	−0.480736	+	0.602824i
$713$	−2.38701e8	−	1.14952e8i	−0.658546	−	0.317139i
$714$	1.52775e8	−	3.48698e7i	0.419717	−	0.0957977i
$715$	3.33945e7	−	7.62209e6i	0.0913603	−	0.0208524i
$716$	6.60531e6	+	5.26756e6i	0.0179951	+	0.0143506i
$717$	−2.04356e7	−	4.24349e7i	−0.0554408	−	0.115124i
$718$	−1.60181e8	−	3.65602e7i	−0.432750	−	0.0987724i
$719$	1.10081e8	−	5.30120e7i	0.296159	−	0.142622i	−0.279904	−	0.960028i	$-0.590303\pi$
$719$	1.10081e8	−	5.30120e7i	0.296159	−	0.142622i	0.576063	+	0.817406i	$0.304588\pi$
$720$	−1.18044e8	+	9.41366e7i	−0.316260	+	0.252209i
$721$	4.57327e8	−	1.04382e8i	1.22017	−	0.278496i
$722$	3.02866e8	−	2.41527e8i	0.804708	−	0.641733i
$723$	−1.44609e7	+	6.33572e7i	−0.0382631	+	0.167641i
$724$	7.11078e6			0.0187371
$725$			3.24647e8i			0.851917i
$726$	2.22993e7	−	9.76998e7i	0.0582750	−	0.255319i
$727$	3.43158e7	+	2.73659e7i	0.0893080	+	0.0712208i	0.667126	−	0.744945i	$-0.267524\pi$
$727$	3.43158e7	+	2.73659e7i	0.0893080	+	0.0712208i	−0.577818	+	0.816166i	$0.696096\pi$
$728$	−6.05144e8	−	2.91422e8i	−1.56843	−	0.755315i
$729$	−2.09543e8	+	1.00910e8i	−0.540866	+	0.260467i
$730$			2.47704e7i			0.0636743i
$731$	3.25764e8	+	1.60303e8i	0.833971	+	0.410384i
$732$	−1.62782e6			−0.00415025
$733$	−1.84430e8	−	3.82974e8i	−0.468296	−	0.972427i	−0.992661	−	0.120933i	$-0.961411\pi$
$733$	−1.84430e8	−	3.82974e8i	−0.468296	−	0.972427i	0.524364	−	0.851494i	$-0.324303\pi$
$734$	−1.91342e8	+	3.97325e8i	−0.483862	+	1.00475i
$735$	−4.99660e7	+	6.26554e7i	−0.125838	+	0.157796i
$736$	−7.94094e7	−	1.81247e7i	−0.199177	−	0.0454608i
$737$	−1.03587e8			−0.258764
$738$		−	6.21067e8i		−	1.54515i
$739$	7.77853e8	+	1.77540e8i	1.92737	+	0.439909i	0.997382	+	0.0723098i	$0.0230370\pi$
$739$	7.77853e8	+	1.77540e8i	1.92737	+	0.439909i	0.929984	+	0.367599i	$0.119820\pi$
$740$	1.14741e7	+	1.43881e7i	0.0283155	+	0.0355065i
$741$	1.28996e6	+	5.65168e6i	0.00317045	+	0.0138907i
$742$	2.25041e8	+	2.82192e8i	0.550871	+	0.690770i
$743$	−6.64018e7	−	1.37885e8i	−0.161888	−	0.336163i	0.804208	−	0.594348i	$-0.202590\pi$
$743$	−6.64018e7	−	1.37885e8i	−0.161888	−	0.336163i	−0.966095	+	0.258185i	$0.916876\pi$
$744$	−1.08757e7	+	4.76494e7i	−0.0264081	+	0.115701i
$745$	3.28961e7	−	1.58419e7i	0.0795565	−	0.0383124i
$746$	−3.47171e7	+	4.35338e7i	−0.0836231	+	0.104860i
$747$	−3.06334e7	−	1.34213e8i	−0.0734908	−	0.321984i
$748$	−1.19686e6	−	5.24377e6i	−0.00285981	−	0.0125296i
$749$	−1.04971e8	+	2.17975e8i	−0.249819	+	0.518754i
$750$	−6.80412e7	−	5.42611e7i	−0.161283	−	0.128619i
$751$	3.32583e8	−	2.65226e8i	0.785199	−	0.626175i	−0.146581	−	0.989199i	$-0.546827\pi$
$751$	3.32583e8	−	2.65226e8i	0.785199	−	0.626175i	0.931780	+	0.363023i	$0.118255\pi$
$752$	−4.30074e8	−	2.07113e8i	−1.01132	−	0.487028i
$753$	9.75325e6	−	2.02528e7i	0.0228436	−	0.0474352i
$754$	−3.01947e8	−	3.78629e8i	−0.704395	−	0.883284i
$755$	1.13667e8	−	1.42534e8i	0.264115	−	0.331190i
$756$	2.18199e7	+	1.05079e7i	0.0504996	+	0.0243193i
$757$	5.02868e8	−	1.14776e8i	1.15922	−	0.264585i	0.400685	−	0.916216i	$-0.368772\pi$
$757$	5.02868e8	−	1.14776e8i	1.15922	−	0.264585i	0.758536	+	0.651631i	$0.225915\pi$
$758$	7.67917e8	−	1.75272e8i	1.76322	−	0.402443i
$759$	3.07003e7	+	2.44827e7i	0.0702129	+	0.0559930i
$760$	−3.78230e6	−	7.85402e6i	−0.00861618	−	0.0178917i
$761$	−3.56214e8	−	8.13034e7i	−0.808270	−	0.184482i	−0.201633	−	0.979461i	$-0.564625\pi$
$761$	−3.56214e8	−	8.13034e7i	−0.808270	−	0.184482i	−0.606637	+	0.794979i	$0.707482\pi$
$762$	1.98644e8	−	9.56618e7i	0.448962	−	0.216209i
$763$	−2.55652e8	+	2.03876e8i	−0.575540	+	0.458978i
$764$	1.47237e7	−	3.36059e6i	0.0330170	−	0.00753590i
$765$	−1.24092e8	+	9.89597e7i	−0.277178	+	0.221042i
$766$	6.06100e7	−	2.65550e8i	0.134852	−	0.590826i
$767$	8.73955e8			1.93688
$768$			2.32947e7i			0.0514249i
$769$	−5.27334e7	+	2.31040e8i	−0.115960	+	0.508052i	0.883272	+	0.468861i	$0.155335\pi$
$769$	−5.27334e7	+	2.31040e8i	−0.115960	+	0.508052i	−0.999232	+	0.0391913i	$0.987522\pi$
$770$	5.45113e7	+	4.34713e7i	0.119403	+	0.0952205i
$771$	−8.27964e7	−	3.98726e7i	−0.180654	−	0.0869985i
$772$	−1.20251e7	+	5.79096e6i	−0.0261358	+	0.0125863i
$773$			7.68647e8i			1.66414i	0.554674	+	0.832068i	$0.312843\pi$
$773$			7.68647e8i			1.66414i	−0.554674	+	0.832068i	$0.687157\pi$
$774$	1.89502e8	+	4.02211e8i	0.408687	+	0.867422i
$775$	1.78982e8			0.384507
$776$	1.85742e8	+	3.85698e8i	0.397490	+	0.825396i
$777$	−1.56186e8	+	3.24324e8i	−0.332950	+	0.691378i
$778$	−5.40107e8	+	6.77273e8i	−1.14694	+	1.43822i
$779$	3.72316e7	+	8.49787e6i	0.0787588	+	0.0179762i
$780$	3.58287e6			0.00755001
$781$		−	1.50358e7i		−	0.0315627i
$782$	−7.06802e8	−	1.61323e8i	−1.47801	−	0.337346i
$783$	−1.57329e8	−	1.97285e8i	−0.327736	−	0.410968i
$784$	−2.10273e8	−	9.21266e8i	−0.436350	−	1.91178i
$785$	8.87094e7	+	1.11238e8i	0.183384	+	0.229956i
$786$	−3.71019e7	−	7.70429e7i	−0.0764062	−	0.158659i
$787$	−2.12718e8	+	9.31977e8i	−0.436395	+	1.91197i	−0.0269476	+	0.999637i	$0.508579\pi$
$787$	−2.12718e8	+	9.31977e8i	−0.436395	+	1.91197i	−0.409447	+	0.912334i	$0.634278\pi$
$788$	5.55852e6	−	2.67684e6i	0.0113601	−	0.00547072i
$789$	−1.09843e8	+	1.37739e8i	−0.223636	+	0.280430i
$790$	−4.17440e7	−	1.82893e8i	−0.0846668	−	0.370949i
$791$	3.34254e8	+	1.46446e9i	0.675379	+	2.95903i
$792$	−4.12977e7	+	8.57556e7i	−0.0831287	+	0.172618i
$793$	1.00466e8	+	8.01191e7i	0.201465	+	0.160663i
$794$	6.07372e8	−	4.84363e8i	1.21337	−	0.967631i
$795$	2.50674e7	+	1.20718e7i	0.0498894	+	0.0240255i
$796$	−226723.	+	470796.i	−0.000449529	+	0.000933456i
$797$	−3.97336e8	−	4.98244e8i	−0.784843	−	0.984162i	−0.999971	−	0.00757642i	$-0.997588\pi$
$797$	−3.97336e8	−	4.98244e8i	−0.784843	−	0.984162i	0.215128	−	0.976586i	$-0.430983\pi$
$798$	−7.35707e6	+	9.22548e6i	−0.0144776	+	0.0181543i
$799$	−4.52109e8	−	2.17724e8i	−0.886346	−	0.426842i
$800$	5.36459e7	−	1.22443e7i	0.104777	−	0.0239147i
$801$	−3.71992e8	+	8.49047e7i	−0.723829	+	0.165209i
$802$	4.22293e8	+	3.36767e8i	0.818636	+	0.652840i
$803$	7.21568e6	+	1.49835e7i	0.0139358	+	0.0289379i
$804$	−1.05635e7	−	2.41104e6i	−0.0203254	−	0.00463913i
$805$	5.14703e8	−	2.47868e8i	0.986663	−	0.475152i
$806$	−2.08743e8	+	1.66467e8i	−0.398664	+	0.317924i
$807$	−2.07152e7	+	4.72812e6i	−0.0394157	+	0.00899637i
$808$	5.09096e8	−	4.05990e8i	0.965084	−	0.769629i
$809$	4.19989e7	−	1.84009e8i	0.0793218	−	0.347531i	−0.919657	−	0.392724i	$-0.871533\pi$
$809$	4.19989e7	−	1.84009e8i	0.0793218	−	0.347531i	0.998978	+	0.0451923i	$0.0143900\pi$
$810$	−1.78450e8			−0.335785
$811$		−	4.15151e8i		−	0.778293i	−0.921176	−	0.389147i	$-0.872770\pi$
$811$		−	4.15151e8i		−	0.778293i	0.921176	−	0.389147i	$-0.127230\pi$
$812$	1.33340e7	−	5.84202e7i	0.0249054	−	0.109118i
$813$	1.29619e8	+	1.03368e8i	0.241211	+	0.192359i
$814$	1.83127e8	+	8.81893e7i	0.339531	+	0.163509i
$815$	−591424.	+	284815.i	−0.00109251	+	0.000526126i
$816$			1.42434e8i			0.262146i
$817$	−2.67045e7	+	5.85690e6i	−0.0489687	+	0.0107399i
$818$	9.39733e8			1.71690
$819$	−3.99546e8	−	8.29665e8i	−0.727302	−	1.51026i
$820$	1.02409e7	−	2.12655e7i	0.0185736	−	0.0385686i
$821$	−1.87093e8	+	2.34607e8i	−0.338087	+	0.423948i	−0.921591	−	0.388163i	$-0.873110\pi$
$821$	−1.87093e8	+	2.34607e8i	−0.338087	+	0.423948i	0.583504	+	0.812110i	$0.301681\pi$
$822$	−4.28036e7	−	9.76964e6i	−0.0770664	−	0.0175899i
$823$	1.31959e8			0.236722			0.118361	−	0.992971i	$-0.462236\pi$
$823$	1.31959e8			0.236722			0.118361	+	0.992971i	$0.462236\pi$
$824$			4.00351e8i			0.715582i
$825$	−2.58623e7	−	5.90289e6i	−0.0460580	−	0.0105124i
$826$	1.10915e9	+	1.39083e9i	1.96811	+	2.46793i
$827$	2.29251e8	+	1.00441e9i	0.405317	+	1.77581i	0.605286	+	0.796008i	$0.293059\pi$
$827$	2.29251e8	+	1.00441e9i	0.405317	+	1.77581i	−0.199969	+	0.979802i	$0.564084\pi$
$828$	−3.36488e7	−	4.21943e7i	−0.0592760	−	0.0743298i
$829$	−7.56657e7	−	1.57121e8i	−0.132811	−	0.275786i	0.823948	−	0.566665i	$-0.191767\pi$
$829$	−7.56657e7	−	1.57121e8i	−0.132811	−	0.275786i	−0.956760	+	0.290879i	$0.906052\pi$
$830$	1.91515e7	−	8.39081e7i	0.0334941	−	0.146747i
$831$	−1.83755e8	+	8.84919e7i	−0.320211	+	0.154206i
$832$	3.55802e8	−	4.46161e8i	0.617786	−	0.774679i
$833$	−2.21046e8	−	9.68468e8i	−0.382427	−	1.67552i
$834$	4.47281e7	+	1.95967e8i	0.0771049	+	0.337819i
$835$	3.04431e7	−	6.32158e7i	0.0522914	−	0.108584i
$836$	316651.	+	252521.i	0.000541954	+	0.000432194i
$837$	−1.08766e8	+	8.67377e7i	−0.185488	+	0.147922i
$838$	−2.14178e8	−	1.03143e8i	−0.363952	−	0.175270i
$839$	3.30053e8	−	6.85361e8i	0.558853	−	1.16047i	−0.409829	−	0.912162i	$-0.634412\pi$
$839$	3.30053e8	−	6.85361e8i	0.558853	−	1.16047i	0.968681	−	0.248307i	$-0.0798741\pi$
$840$	−6.57077e7	−	8.23949e7i	−0.110861	−	0.139015i
$841$	−1.84091e7	+	2.30843e7i	−0.0309488	+	0.0388086i
$842$	−2.29969e8	−	1.10747e8i	−0.385242	−	0.185523i
$843$	−4.43848e7	+	1.01305e7i	−0.0740886	+	0.0169102i
$844$	−5.57720e7	+	1.27296e7i	−0.0927659	+	0.0211732i
$845$	−2.75100e7	−	2.19385e7i	−0.0455953	−	0.0363610i
$846$	−2.66627e8	−	5.53656e8i	−0.440344	−	0.914385i
$847$	−9.54294e8	−	2.17811e8i	−1.57048	−	0.358451i
$848$	−2.95581e8	+	1.42344e8i	−0.484718	+	0.233428i
$849$	−1.54081e8	+	1.22876e8i	−0.251783	+	0.200790i
$850$	4.77488e8	−	1.08984e8i	0.777510	−	0.177462i
$851$	1.30205e9	−	1.03835e9i	2.11271	−	1.68483i
$852$	349967.	−	1.53330e6i	0.000565858	−	0.00247919i
$853$	−4.46112e7			−0.0718782			−0.0359391	−	0.999354i	$-0.511442\pi$
$853$	−4.46112e7			−0.0718782			−0.0359391	+	0.999354i	$0.511442\pi$
$854$			2.61563e8i			0.419956i
$855$	2.65948e6	−	1.16520e7i	0.00425499	−	0.0186423i
$856$	−1.61435e8	−	1.28740e8i	−0.257381	−	0.205254i
$857$	8.40396e8	+	4.04713e8i	1.33518	+	0.642991i	0.958961	−	0.283538i	$-0.0915082\pi$
$857$	8.40396e8	+	4.04713e8i	1.33518	+	0.642991i	0.376223	+	0.926529i	$0.377223\pi$
$858$	3.56528e7	−	1.71695e7i	0.0564458	−	0.0271829i
$859$			2.71643e8i			0.428568i	0.976771	+	0.214284i	$0.0687417\pi$
$859$			2.71643e8i			0.428568i	−0.976771	+	0.214284i	$0.931258\pi$
$860$	−143548.	+	1.68965e7i	−0.000225685	+	0.0265645i
$861$	4.61683e8			0.723327
$862$	−3.34794e8	−	6.95207e8i	−0.522704	−	1.08541i
$863$	−2.09981e8	+	4.36030e8i	−0.326698	+	0.678396i	−0.998029	−	0.0627621i	$-0.980009\pi$
$863$	−2.09981e8	+	4.36030e8i	−0.326698	+	0.678396i	0.671330	+	0.741159i	$0.265723\pi$
$864$	−2.66663e7	+	3.34385e7i	−0.0413449	+	0.0518448i
$865$	−2.67012e8	−	6.09438e7i	−0.412556	−	0.0941632i
$866$	−1.06821e9			−1.64475
$867$		−	2.35843e7i		−	0.0361880i
$868$	−3.22078e7	−	7.35122e6i	−0.0492495	−	0.0112409i
$869$	−7.85279e7	−	9.84709e7i	−0.119664	−	0.150054i
$870$	−1.69087e7	−	7.40818e7i	−0.0256775	−	0.112500i
$871$	5.33289e8	+	6.68723e8i	0.807064	+	1.01203i
$872$	−1.21087e8	−	2.51439e8i	−0.182620	−	0.379213i
$873$	−1.30603e8	+	5.72208e8i	−0.196295	+	0.860025i
$874$	4.91850e7	−	2.36862e7i	0.0736712	−	0.0354782i
$875$	−5.30001e8	+	6.64600e8i	−0.791139	+	0.992057i
$876$	387082.	+	1.69592e6i	0.000575825	+	0.00252285i
$877$	2.52746e8	+	1.10735e9i	0.374702	+	1.64168i	0.713382	+	0.700775i	$0.247162\pi$
$877$	2.52746e8	+	1.10735e9i	0.374702	+	1.64168i	−0.338680	+	0.940901i	$0.609981\pi$
$878$	−2.84643e8	+	5.91068e8i	−0.420550	+	0.873281i
$879$	1.71314e7	+	1.36619e7i	0.0252248	+	0.0201161i
$880$	−4.95475e7	+	3.95128e7i	−0.0727065	+	0.0579815i
$881$	1.21580e8	+	5.85498e7i	0.177801	+	0.0856244i	0.520667	−	0.853760i	$-0.325683\pi$
$881$	1.21580e8	+	5.85498e7i	0.177801	+	0.0856244i	−0.342866	+	0.939384i	$0.611398\pi$
$882$	5.27816e8	−	1.09602e9i	0.769266	−	1.59740i
$883$	−6.76450e8	−	8.48241e8i	−0.982547	−	1.23208i	−0.972686	−	0.232124i	$-0.925432\pi$
$883$	−6.76450e8	−	8.48241e8i	−0.982547	−	1.23208i	−0.00986123	−	0.999951i	$-0.503139\pi$
$884$	−2.76903e7	+	3.47226e7i	−0.0400840	+	0.0502638i
$885$	1.23548e8	+	5.94977e7i	0.178241	+	0.0858362i
$886$	9.87528e8	−	2.25397e8i	1.41987	−	0.324076i
$887$	−1.31534e9	+	3.00218e8i	−1.88481	+	0.430195i	−0.999400	−	0.0346219i	$-0.988977\pi$
$887$	−1.31534e9	+	3.00218e8i	−1.88481	+	0.430195i	−0.885407	+	0.464817i	$0.846120\pi$
$888$	−2.40198e8	−	1.91552e8i	−0.343029	−	0.273556i
$889$	−9.34387e8	−	1.94027e9i	−1.32991	−	2.76158i
$890$	−2.32563e8	−	5.30811e7i	−0.329892	−	0.0752956i
$891$	−1.07944e8	+	5.19830e7i	−0.152604	+	0.0734900i
$892$	−2.45585e6	+	1.95848e6i	−0.00346025	+	0.00275946i
$893$	3.68386e7	−	8.40817e6i	0.0517308	−	0.0118072i
$894$	3.29783e7	−	2.62993e7i	0.0461547	−	0.0368071i
$895$	2.32856e7	−	1.02021e8i	0.0324802	−	0.142305i
$896$	1.31850e9			1.83298
$897$		−	3.24233e8i		−	0.449241i
$898$	2.67503e7	−	1.17201e8i	0.0369402	−	0.161846i
$899$	2.69115e8	+	2.14612e8i	0.370390	+	0.295376i
$900$	3.28485e7	+	1.58190e7i	0.0450596	+	0.0216996i
$901$	−3.10725e8	+	1.49637e8i	−0.424817	+	0.204581i
$902$		−	2.60686e8i		−	0.355221i
$903$	−2.98991e8	+	1.40870e8i	−0.406065	+	0.191318i
$904$	−1.28202e9			−1.73536
$905$	−3.82144e7	−	7.93531e7i	−0.0515563	−	0.107058i
$906$	9.13815e7	−	1.89756e8i	0.122878	−	0.255159i
$907$	2.28752e8	−	2.86845e8i	0.306579	−	0.384438i	−0.604545	−	0.796571i	$-0.706645\pi$
$907$	2.28752e8	−	2.86845e8i	0.306579	−	0.384438i	0.911123	+	0.412134i	$0.135216\pi$
$908$	−6.32490e7	−	1.44362e7i	−0.0844882	−	0.0192839i
$909$	8.92751e8			1.18861
$910$		−	5.75706e8i		−	0.763971i
$911$	−6.46089e8	−	1.47466e8i	−0.854549	−	0.195045i	−0.227262	−	0.973834i	$-0.572977\pi$
$911$	−6.46089e8	−	1.47466e8i	−0.854549	−	0.195045i	−0.627287	+	0.778788i	$0.715835\pi$
$912$	−6.68713e6	−	8.38540e6i	−0.00881567	−	0.0110545i
$913$	−1.28580e7	−	5.63346e7i	−0.0168951	−	0.0740223i
$914$	3.04011e8	+	3.81218e8i	0.398154	+	0.499270i
$915$	8.74818e6	+	1.81658e7i	0.0114197	+	0.0237132i
$916$	−1.80374e7	+	7.90268e7i	−0.0234686	+	0.102822i
$917$	−7.52525e8	+	3.62397e8i	−0.975917	+	0.469977i
$918$	−2.37350e8	+	2.97627e8i	−0.306804	+	0.384720i
$919$	1.32075e8	+	5.78660e8i	0.170167	+	0.745551i	0.985929	+	0.167163i	$0.0534607\pi$
$919$	1.32075e8	+	5.78660e8i	0.170167	+	0.745551i	−0.815762	+	0.578388i	$0.803682\pi$
$920$	1.08494e8	+	4.75342e8i	0.139329	+	0.610440i
$921$	3.36313e7	−	6.98361e7i	0.0430492	−	0.0893925i
$922$	−8.26555e8	−	6.59155e8i	−1.05458	−	0.840998i
$923$	−9.70662e7	+	7.74077e7i	−0.123442	+	0.0984417i
$924$	4.41146e6	+	2.12445e6i	0.00559200	+	0.00269296i
$925$	−4.88151e8	+	1.01366e9i	−0.616778	+	1.28075i
$926$	5.07247e8	+	6.36067e8i	0.638832	+	0.801070i
$927$	−3.42227e8	+	4.29139e8i	−0.429611	+	0.538715i
$928$	9.53433e7	+	4.59149e7i	0.119302	+	0.0574526i
$929$	−5.83740e8	+	1.33235e8i	−0.728069	+	0.166177i	−0.570461	−	0.821325i	$-0.693235\pi$
$929$	−5.83740e8	+	1.33235e8i	−0.728069	+	0.166177i	−0.157608	+	0.987502i	$0.550378\pi$
$930$	−4.08422e7	+	9.32197e6i	−0.0507762	+	0.0115893i
$931$	5.84821e7	+	4.66379e7i	0.0724726	+	0.0577949i
$932$	3.23520e7	+	6.71797e7i	0.0399626	+	0.0829832i
$933$	−2.00519e8	−	4.57672e7i	−0.246894	−	0.0563520i
$934$	−2.59959e7	+	1.25190e7i	−0.0319054	+	0.0153648i
$935$	−5.20860e7	+	4.15372e7i	−0.0637216	+	0.0508163i
$936$	7.66219e8	−	1.74884e8i	0.934384	−	0.213267i
$937$	1.09942e9	−	8.76759e8i	1.33643	−	1.06577i	0.344524	−	0.938778i	$-0.388040\pi$
$937$	1.09942e9	−	8.76759e8i	1.33643	−	1.06577i	0.991904	−	0.126988i	$-0.0405310\pi$
$938$	−3.87413e8	+	1.69737e9i	−0.469425	+	2.05668i
$939$	−3.57259e8			−0.431505
$940$		−	2.33538e7i		−	0.0281173i
$941$	1.28415e8	−	5.62622e8i	0.154116	−	0.675224i	−0.837547	−	0.546365i	$-0.816011\pi$
$941$	1.28415e8	−	5.62622e8i	0.154116	−	0.675224i	0.991663	−	0.128860i	$-0.0411316\pi$
$942$	1.28509e8	+	1.02483e8i	0.153738	+	0.122602i
$943$	−1.92442e9	−	9.26753e8i	−2.29491	−	1.10517i
$944$	−1.45681e9	+	7.01564e8i	−1.73176	+	0.833972i
$945$		−	2.99972e8i		−	0.355455i
$946$	7.95413e7	+	1.68823e8i	0.0939549	+	0.199416i
$947$	8.82744e8			1.03941			0.519703	−	0.854347i	$-0.326043\pi$
$947$	8.82744e8			1.03941			0.519703	+	0.854347i	$0.326043\pi$
$948$	−5.71605e6	−	1.18695e7i	−0.00670921	−	0.0139318i
$949$	5.95805e7	−	1.23720e8i	0.0697117	−	0.144758i
$950$	−2.29941e7	+	2.88337e7i	−0.0268192	+	0.0336302i
$951$	1.93962e8	+	4.42706e7i	0.225515	+	0.0514723i
$952$	1.30633e9			1.51406
$953$		−	2.34013e7i		−	0.0270372i	−0.999909	−	0.0135186i	$-0.995697\pi$
$953$		−	2.34013e7i		−	0.0270372i	0.999909	−	0.0135186i	$-0.00430323\pi$
$954$	−4.11752e8	−	9.39798e7i	−0.474232	−	0.108240i
$955$	−1.16630e8	−	1.46250e8i	−0.133906	−	0.167913i
$956$	6.04610e6	+	2.64897e7i	0.00691993	+	0.0303182i
$957$	−3.18082e7	−	3.98863e7i	−0.0362914	−	0.0455080i
$958$	2.41304e8	+	5.01073e8i	0.274453	+	0.569907i
$959$	−9.54261e7	+	4.18089e8i	−0.108196	+	0.474038i
$960$	8.06727e7	−	3.88499e7i	0.0911827	−	0.0439113i
$961$	−4.35031e8	+	5.45512e8i	−0.490174	+	0.614658i
$962$	−3.73457e8	−	1.63622e9i	−0.419484	−	1.83788i
$963$	−6.29940e7	−	2.75995e8i	−0.0705375	−	0.309045i
$964$	1.62663e7	−	3.37772e7i	0.0181575	−	0.0377045i
$965$	1.29249e8	+	1.03073e8i	0.143829	+	0.114700i
$966$	5.15989e8	−	4.11487e8i	0.572412	−	0.456484i
$967$	6.65354e8	+	3.20417e8i	0.735823	+	0.354354i	0.763971	−	0.645250i	$-0.223247\pi$
$967$	6.65354e8	+	3.20417e8i	0.735823	+	0.354354i	−0.0281486	+	0.999604i	$0.508961\pi$
$968$	3.62469e8	−	7.52674e8i	0.399617	−	0.829814i
$969$	−7.02975e6	−	8.81503e6i	−0.00772624	−	0.00968840i
$970$	−2.28780e8	+	2.86881e8i	−0.250671	+	0.314331i
$971$	9.42287e7	+	4.53782e7i	0.102926	+	0.0495666i	0.484638	−	0.874715i	$-0.338951\pi$
$971$	9.42287e7	+	4.53782e7i	0.102926	+	0.0495666i	−0.381712	+	0.924281i	$0.624665\pi$
$972$	−4.19482e7	+	9.57440e6i	−0.0456788	+	0.0104259i
$973$	1.91413e9	−	4.36887e8i	2.07793	−	0.474275i
$974$	5.44129e8	+	4.33928e8i	0.588877	+	0.469614i
$975$	9.50374e7	+	1.97347e8i	0.102537	+	0.212920i
$976$	−2.31784e8	−	5.29033e7i	−0.249307	−	0.0569027i
$977$	−3.14809e8	+	1.51604e8i	−0.337570	+	0.162565i	−0.594987	−	0.803735i	$-0.702843\pi$
$977$	−3.14809e8	+	1.51604e8i	−0.337570	+	0.162565i	0.257417	+	0.966300i	$0.417129\pi$
$978$	−592902.	+	472824.i	−0.000633821	+	0.000505455i
$979$	−1.56139e8	+	3.56378e7i	−0.166404	+	0.0379807i
$980$	3.61451e7	−	2.88247e7i	0.0384035	−	0.0306258i
$981$	8.51409e7	−	3.73027e8i	0.0901844	−	0.395123i
$982$	1.67295e8			0.176664
$983$			2.74695e8i			0.289194i	0.989491	+	0.144597i	$0.0461886\pi$
$983$			2.74695e8i			0.289194i	−0.989491	+	0.144597i	$0.953811\pi$
$984$	−8.76803e7	+	3.84153e8i	−0.0920273	+	0.403198i
$985$	−5.97448e7	−	4.76449e7i	−0.0625160	−	0.0498548i
$986$	8.48626e8	+	4.08677e8i	0.885290	+	0.426333i
$987$	4.11572e8	−	1.98202e8i	0.428049	−	0.206138i
$988$		−	3.34423e6i		−	0.00346757i
$989$	1.52905e9	+	1.29904e7i	1.58064	+	0.0134287i
$990$	−8.15839e7			−0.0840812
$991$	7.84452e7	+	1.62893e8i	0.0806019	+	0.167372i	0.937375	−	0.348322i	$-0.113248\pi$
$991$	7.84452e7	+	1.62893e8i	0.0806019	+	0.167372i	−0.856773	+	0.515694i	$0.827534\pi$
$992$	2.53135e7	−	5.25640e7i	0.0259308	−	0.0538460i
$993$	1.92975e8	−	2.41982e8i	0.197084	−	0.247136i
$994$	−2.46376e8	−	5.62336e7i	−0.250864	−	0.0572581i
$995$	6.47232e6			0.00657039
$996$		−	6.04409e6i		−	0.00611720i
$997$	8.65658e8	+	1.97581e8i	0.873496	+	0.199370i	0.635691	−	0.771943i	$-0.280715\pi$
$997$	8.65658e8	+	1.97581e8i	0.873496	+	0.199370i	0.237804	+	0.971313i	$0.423572\pi$
$998$	−1.30348e8	−	1.63451e8i	−0.131133	−	0.164436i
$999$	−1.94590e8	−	8.52555e8i	−0.195175	−	0.855117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.17	✓	126
43.22	odd	14	inner	43.7.f.a.22.17	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.17	✓	126	1.1	even	1	trivial
43.7.f.a.22.17	yes	126	43.22	odd	14	inner

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)

\(f(q)\)	\(=\)	\(q+(3.58164 + 7.43735i) q^{2} +(3.11543 - 6.46926i) q^{3} +(-2.58264 + 3.23853i) q^{4} +(50.0201 + 11.4168i) q^{5} +59.2725 q^{6} -578.950i q^{7} +(481.727 + 109.951i) q^{8} +(422.379 + 529.646i) q^{9} +O(q^{10})\)	\(q+(3.58164 + 7.43735i) q^{2} +(3.11543 - 6.46926i) q^{3} +(-2.58264 + 3.23853i) q^{4} +(50.0201 + 11.4168i) q^{5} +59.2725 q^{6} -578.950i q^{7} +(481.727 + 109.951i) q^{8} +(422.379 + 529.646i) q^{9} +(94.2435 + 412.908i) q^{10} +(177.289 + 222.313i) q^{11} +(12.9049 + 26.7972i) q^{12} +(522.456 - 2289.03i) q^{13} +(4305.85 - 2073.59i) q^{14} +(229.692 - 288.025i) q^{15} +(966.619 + 4235.03i) q^{16} +(1016.14 + 4452.02i) q^{17} +(-2426.35 + 5038.38i) q^{18} +(-268.840 - 214.393i) q^{19} +(-166.158 + 132.506i) q^{20} +(-3745.38 - 1803.68i) q^{21} +(-1018.43 + 2114.80i) q^{22} +(11991.2 + 15036.5i) q^{23} +(2212.09 - 2773.87i) q^{24} +(-11706.0 - 5637.30i) q^{25} +(18895.6 - 4312.79i) q^{26} +(9845.54 - 2247.18i) q^{27} +(1874.95 + 1495.22i) q^{28} +(-10841.4 - 22512.5i) q^{29} +(2964.82 + 676.700i) q^{30} +(-12411.4 + 5977.03i) q^{31} +(-3311.16 + 2640.56i) q^{32} +(1990.53 - 454.326i) q^{33} +(-29471.7 + 23502.9i) q^{34} +(6609.74 - 28959.2i) q^{35} -2806.13 q^{36} -86593.0i q^{37} +(631.627 - 2767.34i) q^{38} +(-13180.7 - 10511.2i) q^{39} +(22840.8 + 10999.5i) q^{40} +(-100062. + 48187.1i) q^{41} -34315.8i q^{42} +(50098.1 - 61737.7i) q^{43} -1177.84 q^{44} +(15080.6 + 31315.2i) q^{45} +(-68883.4 + 143038. i) q^{46} +(-68513.9 + 85913.7i) q^{47} +(30409.0 + 6940.65i) q^{48} -217535. q^{49} -107252. i q^{50} +(31967.0 + 7296.25i) q^{51} +(6063.78 + 7603.74i) q^{52} +(16805.6 + 73630.1i) q^{53} +(51976.2 + 65176.1i) q^{54} +(6329.91 + 13144.2i) q^{55} +(63656.2 - 278896. i) q^{56} +(-2224.52 + 1071.27i) q^{57} +(128603. - 161263. i) q^{58} +(82828.7 + 362896. i) q^{59} +(339.565 + 1487.73i) q^{60} +(-23746.6 + 49310.3i) q^{61} +(-88906.4 - 70900.5i) q^{62} +(306639. - 244536. i) q^{63} +(218982. + 105456. i) q^{64} +(52266.7 - 108533. i) q^{65} +(10508.3 + 13177.0i) q^{66} +(-227135. + 284818. i) q^{67} +(-17042.3 - 8207.16i) q^{68} +(134633. - 30729.0i) q^{69} +(239053. - 54562.3i) q^{70} +(-41341.7 - 32968.9i) q^{71} +(145236. + 301586. i) q^{72} +(57019.6 + 13014.4i) q^{73} +(644022. - 310145. i) q^{74} +(-72938.3 + 58166.3i) q^{75} +(1388.64 - 316.948i) q^{76} +(128708. - 102641. i) q^{77} +(30967.3 - 135676. i) q^{78} -442938. q^{79} +222873. i q^{80} +(-93757.7 + 410780. i) q^{81} +(-716769. - 571604. i) q^{82} +(-183088. - 88170.7i) q^{83} +(15514.3 - 7471.27i) q^{84} +234292. i q^{85} +(638598. + 151475. i) q^{86} -179415. q^{87} +(60961.2 + 126587. i) q^{88} +(-244378. + 507456. i) q^{89} +(-178889. + 224319. i) q^{90} +(-1.32524e6 - 302476. i) q^{91} -79665.1 q^{92} +98913.7i q^{93} +(-884362. - 201850. i) q^{94} +(-10999.8 - 13793.3i) q^{95} +(6766.78 + 29647.2i) q^{96} +(540180. + 677364. i) q^{97} +(-779130. - 1.61788e6i) q^{98} +(-42864.2 + 187801. 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

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