LMFDB - Embedded newform 43.7.f.a.22.15

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			22.15
Character	$\chi$	$=$	43.22
Dual form			43.7.f.a.2.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.79658 - 5.80715i) q^{2} +(-16.1345 - 33.5037i) q^{3} +(14.0012 + 17.5569i) q^{4} +(-177.830 + 40.5886i) q^{5} -239.682 q^{6} +522.371i q^{7} +(543.278 - 124.000i) q^{8} +(-407.649 + 511.176i) q^{9} +O(q^{10})$	\(q+(2.79658 - 5.80715i) q^{2} +(-16.1345 - 33.5037i) q^{3} +(14.0012 + 17.5569i) q^{4} +(-177.830 + 40.5886i) q^{5} -239.682 q^{6} +522.371i q^{7} +(543.278 - 124.000i) q^{8} +(-407.649 + 511.176i) q^{9} +(-261.612 + 1146.20i) q^{10} +(-95.4353 + 119.672i) q^{11} +(362.319 - 752.362i) q^{12} +(-664.158 - 2909.87i) q^{13} +(3033.49 + 1460.85i) q^{14} +(4229.08 + 5303.09i) q^{15} +(479.428 - 2100.51i) q^{16} +(-1681.88 + 7368.81i) q^{17} +(1828.45 + 3796.82i) q^{18} +(-2144.88 + 1710.48i) q^{19} +(-3202.44 - 2553.86i) q^{20} +(17501.4 - 8428.21i) q^{21} +(428.062 + 888.880i) q^{22} +(-14961.4 + 18761.0i) q^{23} +(-12920.0 - 16201.1i) q^{24} +(15898.6 - 7656.35i) q^{25} +(-18755.4 - 4280.80i) q^{26} +(-2725.63 - 622.108i) q^{27} +(-9171.22 + 7313.81i) q^{28} +(-12713.6 + 26400.2i) q^{29} +(42622.8 - 9728.38i) q^{30} +(5284.73 + 2544.99i) q^{31} +(17025.9 + 13577.7i) q^{32} +(5549.26 + 1266.58i) q^{33} +(38088.3 + 30374.4i) q^{34} +(-21202.3 - 92893.5i) q^{35} -14682.2 q^{36} -54282.8i q^{37} +(3934.72 + 17239.1i) q^{38} +(-86775.3 + 69201.0i) q^{39} +(-91578.3 + 44101.8i) q^{40} +(-18943.7 - 9122.82i) q^{41} -125203. i q^{42} +(62267.7 - 49437.7i) q^{43} -3437.28 q^{44} +(51744.5 - 107448. i) q^{45} +(67107.3 + 139350. i) q^{46} +(-88169.2 - 110561. i) q^{47} +(-78110.2 + 17828.1i) q^{48} -155223. q^{49} -113737. i q^{50} +(274018. - 62542.9i) q^{51} +(41789.3 - 52402.1i) q^{52} +(-10575.4 + 46333.7i) q^{53} +(-11235.1 + 14088.4i) q^{54} +(12114.0 - 25154.9i) q^{55} +(64773.8 + 283793. i) q^{56} +(91913.9 + 44263.4i) q^{57} +(117755. + 147660. i) q^{58} +(-50268.6 + 220241. i) q^{59} +(-33893.9 + 148499. i) q^{60} +(-84478.6 - 175422. i) q^{61} +(29558.3 - 23572.0i) q^{62} +(-267024. - 212944. i) q^{63} +(250697. - 120729. i) q^{64} +(236215. + 490505. i) q^{65} +(22874.2 - 28683.3i) q^{66} +(-26697.3 - 33477.4i) q^{67} +(-152922. + 73643.2i) q^{68} +(869957. + 198562. i) q^{69} +(-598741. - 136659. i) q^{70} +(23306.4 - 18586.2i) q^{71} +(-158081. + 328259. i) q^{72} +(-237553. + 54220.0i) q^{73} +(-315228. - 151806. i) q^{74} +(-513032. - 409129. i) q^{75} +(-60061.5 - 13708.6i) q^{76} +(-62513.3 - 49852.7i) q^{77} +(159187. + 697444. i) q^{78} -250032. q^{79} +392994. i q^{80} +(129195. + 566039. i) q^{81} +(-105955. + 84496.5i) q^{82} +(530384. - 255419. i) q^{83} +(393013. + 189265. i) q^{84} -1.37866e6i q^{85} +(-112956. - 499855. i) q^{86} +1.08963e6 q^{87} +(-37008.6 + 76849.1i) q^{88} +(-60323.4 - 125263. i) q^{89} +(-479263. - 600976. i) q^{90} +(1.52003e6 - 346937. i) q^{91} -538862. q^{92} -218120. i q^{93} +(-888615. + 202821. i) q^{94} +(311998. - 391233. i) q^{95} +(180199. - 789502. i) q^{96} +(21744.4 - 27266.6i) q^{97} +(-434093. + 901403. i) q^{98} +(-22269.4 - 97568.4i) 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 $

$2$	2.79658	−	5.80715i	0.349572	−	0.725894i	−0.649844	−	0.760068i	$-0.725166\pi$
$2$	2.79658	−	5.80715i	0.349572	−	0.725894i	0.999416	+	0.0341737i	$0.0108799\pi$
$3$	−16.1345	−	33.5037i	−0.597575	−	1.24088i	−0.952088	−	0.305825i	$-0.901068\pi$
$3$	−16.1345	−	33.5037i	−0.597575	−	1.24088i	0.354513	−	0.935051i	$-0.384647\pi$
$4$	14.0012	+	17.5569i	0.218768	+	0.274327i
$5$	−177.830	+	40.5886i	−1.42264	+	0.324709i	−0.863494	−	0.504358i	$-0.831729\pi$
$5$	−177.830	+	40.5886i	−1.42264	+	0.324709i	−0.559149	+	0.829067i	$0.688872\pi$
$6$	−239.682			−1.10964
$7$			522.371i			1.52295i	0.648195	+	0.761474i	$0.275524\pi$
$7$			522.371i			1.52295i	−0.648195	+	0.761474i	$0.724476\pi$
$8$	543.278	−	124.000i	1.06109	−	0.242187i
$9$	−407.649	+	511.176i	−0.559189	+	0.701201i
$10$	−261.612	+	1146.20i	−0.261612	+	1.14620i
$11$	−95.4353	+	119.672i	−0.0717020	+	0.0899114i	−0.816389	−	0.577503i	$-0.804027\pi$
$11$	−95.4353	+	119.672i	−0.0717020	+	0.0899114i	0.744687	+	0.667414i	$0.232599\pi$
$12$	362.319	−	752.362i	0.209675	−	0.435395i
$13$	−664.158	−	2909.87i	−0.302302	−	1.32447i	−0.866642	−	0.498930i	$-0.833726\pi$
$13$	−664.158	−	2909.87i	−0.302302	−	1.32447i	0.564340	−	0.825543i	$-0.309131\pi$
$14$	3033.49	+	1460.85i	1.10550	+	0.532381i
$15$	4229.08	+	5303.09i	1.25306	+	1.57129i
$16$	479.428	−	2100.51i	0.117048	−	0.512820i
$17$	−1681.88	+	7368.81i	−0.342333	+	1.49986i	0.451802	+	0.892118i	$0.350781\pi$
$17$	−1681.88	+	7368.81i	−0.342333	+	1.49986i	−0.794135	+	0.607741i	$0.792076\pi$
$18$	1828.45	+	3796.82i	0.313521	+	0.651033i
$19$	−2144.88	+	1710.48i	−0.312710	+	0.249378i	−0.767249	−	0.641349i	$-0.778375\pi$
$19$	−2144.88	+	1710.48i	−0.312710	+	0.249378i	0.454540	+	0.890726i	$0.349804\pi$
$20$	−3202.44	−	2553.86i	−0.400305	−	0.319233i
$21$	17501.4	−	8428.21i	1.88979	−	0.910076i
$22$	428.062	+	888.880i	0.0402012	+	0.0834786i
$23$	−14961.4	+	18761.0i	−1.22967	+	1.54196i	−0.485021	+	0.874503i	$0.661188\pi$
$23$	−14961.4	+	18761.0i	−1.22967	+	1.54196i	−0.744650	+	0.667455i	$0.767384\pi$
$24$	−12920.0	−	16201.1i	−0.934604	−	1.17196i
$25$	15898.6	−	7656.35i	1.01751	−	0.490007i
$26$	−18755.4	−	4280.80i	−1.06710	−	0.243559i
$27$	−2725.63	−	622.108i	−0.138477	−	0.0316064i
$28$	−9171.22	+	7313.81i	−0.417785	+	0.333173i
$29$	−12713.6	+	26400.2i	−0.521286	+	1.08246i	0.459644	+	0.888103i	$0.347977\pi$
$29$	−12713.6	+	26400.2i	−0.521286	+	1.08246i	−0.980931	+	0.194359i	$0.937737\pi$
$30$	42622.8	−	9728.38i	1.57862	−	0.360310i
$31$	5284.73	+	2544.99i	0.177394	+	0.0854282i	0.520473	−	0.853878i	$-0.325756\pi$
$31$	5284.73	+	2544.99i	0.177394	+	0.0854282i	−0.343079	+	0.939306i	$0.611470\pi$
$32$	17025.9	+	13577.7i	0.519591	+	0.414360i
$33$	5549.26	+	1266.58i	0.154416	+	0.0352445i
$34$	38088.3	+	30374.4i	0.969069	+	0.772807i
$35$	−21202.3	−	92893.5i	−0.494515	−	2.16661i
$36$	−14682.2			−0.314691
$37$		−	54282.8i		−	1.07166i	−0.844326	−	0.535830i	$-0.819999\pi$
$37$		−	54282.8i		−	1.07166i	0.844326	−	0.535830i	$-0.180001\pi$
$38$	3934.72	+	17239.1i	0.0717072	+	0.314170i
$39$	−86775.3	+	69201.0i	−1.46286	+	1.16659i
$40$	−91578.3	+	44101.8i	−1.43091	+	0.689090i
$41$	−18943.7	−	9122.82i	−0.274861	−	0.132366i	0.291376	−	0.956609i	$-0.405887\pi$
$41$	−18943.7	−	9122.82i	−0.274861	−	0.132366i	−0.566237	+	0.824242i	$0.691601\pi$
$42$		−	125203.i		−	1.68993i
$43$	62267.7	−	49437.7i	0.783173	−	0.621804i
$43$	62267.7	−	49437.7i	0.783173	−	0.621804i
$44$	−3437.28			−0.0403512
$45$	51744.5	−	107448.i	0.567841	−	1.17913i
$46$	67107.3	+	139350.i	0.689440	+	1.43164i
$47$	−88169.2	−	110561.i	−0.849226	−	1.06490i	−0.997116	−	0.0758921i	$-0.975820\pi$
$47$	−88169.2	−	110561.i	−0.849226	−	1.06490i	0.147890	−	0.989004i	$-0.452752\pi$
$48$	−78110.2	+	17828.1i	−0.706292	+	0.161206i
$49$	−155223.			−1.31937
$50$		−	113737.i		−	0.909897i
$51$	274018.	−	62542.9i	2.06571	−	0.471485i
$52$	41789.3	−	52402.1i	0.297204	−	0.372682i
$53$	−10575.4	+	46333.7i	−0.0710342	+	0.311221i	−0.997946	−	0.0640575i	$-0.979596\pi$
$53$	−10575.4	+	46333.7i	−0.0710342	+	0.311221i	0.926912	+	0.375279i	$0.122453\pi$
$54$	−11235.1	+	14088.4i	−0.0713504	+	0.0894706i
$55$	12114.0	−	25154.9i	0.0728113	−	0.151194i
$56$	64773.8	+	283793.i	0.368838	+	1.61598i
$57$	91913.9	+	44263.4i	0.496314	+	0.239012i
$58$	117755.	+	147660.i	0.603526	+	0.756797i
$59$	−50268.6	+	220241.i	−0.244760	+	1.07237i	0.691863	+	0.722028i	$0.256790\pi$
$59$	−50268.6	+	220241.i	−0.244760	+	1.07237i	−0.936624	+	0.350337i	$0.886067\pi$
$60$	−33893.9	+	148499.i	−0.156916	+	0.687495i
$61$	−84478.6	−	175422.i	−0.372184	−	0.772847i	0.627801	−	0.778374i	$-0.283955\pi$
$61$	−84478.6	−	175422.i	−0.372184	−	0.772847i	−0.999985	+	0.00552657i	$0.998241\pi$
$62$	29558.3	−	23572.0i	0.124024	−	0.0989056i
$63$	−267024.	−	212944.i	−1.06789	−	0.851617i
$64$	250697.	−	120729.i	0.956333	−	0.460546i
$65$	236215.	+	490505.i	0.860137	+	1.78609i
$66$	22874.2	−	28683.3i	0.0795634	−	0.0997694i
$67$	−26697.3	−	33477.4i	−0.0887654	−	0.111308i	0.735465	−	0.677562i	$-0.236964\pi$
$67$	−26697.3	−	33477.4i	−0.0887654	−	0.111308i	−0.824231	+	0.566254i	$0.808392\pi$
$68$	−152922.	+	73643.2i	−0.486343	+	0.234210i
$69$	869957.	+	198562.i	2.64820	+	0.604434i
$70$	−598741.	−	136659.i	−1.74560	−	0.398422i
$71$	23306.4	−	18586.2i	0.0651179	−	0.0519298i	−0.590390	−	0.807118i	$-0.701026\pi$
$71$	23306.4	−	18586.2i	0.0651179	−	0.0519298i	0.655508	+	0.755188i	$0.272455\pi$
$72$	−158081.	+	328259.i	−0.423528	+	0.879465i
$73$	−237553.	+	54220.0i	−0.610650	+	0.139377i	−0.516652	−	0.856196i	$-0.672822\pi$
$73$	−237553.	+	54220.0i	−0.610650	+	0.139377i	−0.0939980	+	0.995572i	$0.529965\pi$
$74$	−315228.	−	151806.i	−0.777912	−	0.374623i
$75$	−513032.	−	409129.i	−1.21608	−	0.969788i
$76$	−60061.5	−	13708.6i	−0.136822	−	0.0312287i
$77$	−62513.3	−	49852.7i	−0.136930	−	0.109198i
$78$	159187.	+	697444.i	0.335447	+	1.46969i
$79$	−250032.			−0.507124			−0.253562	−	0.967319i	$-0.581602\pi$
$79$	−250032.			−0.507124			−0.253562	+	0.967319i	$0.581602\pi$
$80$			392994.i			0.767567i
$81$	129195.	+	566039.i	0.243103	+	1.06510i
$82$	−105955.	+	84496.5i	−0.192168	+	0.153249i
$83$	530384.	−	255419.i	0.927590	−	0.446704i	0.0918150	−	0.995776i	$-0.470733\pi$
$83$	530384.	−	255419.i	0.927590	−	0.446704i	0.835775	+	0.549072i	$0.185019\pi$
$84$	393013.	+	189265.i	0.663084	+	0.319324i
$85$		−	1.37866e6i		−	2.24492i
$86$	−112956.	−	499855.i	−0.177588	−	0.785866i
$87$	1.08963e6			1.65471
$88$	−37008.6	+	76849.1i	−0.0543068	+	0.112769i
$89$	−60323.4	−	125263.i	−0.0855689	−	0.177686i	0.853793	−	0.520612i	$-0.174296\pi$
$89$	−60323.4	−	125263.i	−0.0855689	−	0.177686i	−0.939362	+	0.342926i	$0.888582\pi$
$90$	−479263.	−	600976.i	−0.657425	−	0.824384i
$91$	1.52003e6	−	346937.i	2.01710	−	0.460391i
$92$	−538862.			−0.692013
$93$		−	218120.i		−	0.271173i
$94$	−888615.	+	202821.i	−1.06987	+	0.244190i
$95$	311998.	−	391233.i	0.363899	−	0.456315i
$96$	180199.	−	789502.i	0.203675	−	0.892359i
$97$	21744.4	−	27266.6i	0.0238249	−	0.0298755i	−0.769776	−	0.638314i	$-0.779632\pi$
$97$	21744.4	−	27266.6i	0.0238249	−	0.0298755i	0.793601	+	0.608438i	$0.208204\pi$
$98$	−434093.	+	901403.i	−0.461216	+	0.957725i
$99$	−22269.4	−	97568.4i	−0.0229510	−	0.100555i
$100$	357020.	+	171932.i	0.357020	+	0.171932i
$101$	328837.	+	412349.i	0.319166	+	0.400221i	0.915371	−	0.402610i	$-0.131897\pi$
$101$	328837.	+	412349.i	0.319166	+	0.400221i	−0.596205	+	0.802832i	$0.703326\pi$
$102$	403117.	−	1.76617e6i	0.379867	−	1.66430i
$103$	171707.	−	752298.i	0.157136	−	0.688459i	−0.833567	−	0.552419i	$-0.813705\pi$
$103$	171707.	−	752298.i	0.157136	−	0.688459i	0.990703	−	0.136041i	$-0.0434378\pi$
$104$	−721644.	−	1.49851e6i	−0.641539	−	1.33217i
$105$	−2.77018e6	+	2.20915e6i	−2.39299	+	1.90835i
$106$	239492.	+	190989.i	0.201082	+	0.160358i
$107$	271265.	−	130634.i	0.221433	−	0.106637i	−0.319879	−	0.947458i	$-0.603642\pi$
$107$	271265.	−	130634.i	0.221433	−	0.106637i	0.541312	+	0.840822i	$0.317928\pi$
$108$	−27239.7	−	56563.9i	−0.0216238	−	0.0449022i
$109$	−1.57218e6	+	1.97145e6i	−1.21401	+	1.52232i	−0.428412	+	0.903584i	$0.640927\pi$
$109$	−1.57218e6	+	1.97145e6i	−1.21401	+	1.52232i	−0.785598	+	0.618737i	$0.787645\pi$
$110$	−112201.	−	140695.i	−0.0842982	−	0.105707i
$111$	−1.81867e6	+	875826.i	−1.32980	+	0.640397i
$112$	1.09725e6	+	250440.i	0.780999	+	0.178258i
$113$	−730706.	−	166779.i	−0.506416	−	0.115586i	−0.0383229	−	0.999265i	$-0.512202\pi$
$113$	−730706.	−	166779.i	−0.506416	−	0.115586i	−0.468093	+	0.883679i	$0.655059\pi$
$114$	514089.	−	409972.i	0.346995	−	0.276720i
$115$	1.89911e6	−	3.94354e6i	1.24869	−	2.59294i
$116$	−641511.	+	146421.i	−0.410989	+	0.0938055i
$117$	1.75820e6	+	846703.i	1.09777	+	0.528656i
$118$	1.13840e6	+	907840.i	0.692862	+	0.552539i
$119$	−3.84925e6	−	878567.i	−2.28421	−	0.521356i
$120$	2.95514e6	+	2.35665e6i	1.71015	+	1.36380i
$121$	388996.	+	1.70430e6i	0.219578	+	0.962034i
$122$	−1.25495e6			−0.691110
$123$			781877.i			0.420168i
$124$	29310.2	+	128416.i	0.0153728	+	0.0673527i
$125$	−288226.	+	229852.i	−0.147571	+	0.117684i
$126$	−1.98335e6	+	955132.i	−0.991490	+	0.477476i
$127$	1.94325e6	+	935821.i	0.948676	+	0.456858i	0.843222	−	0.537566i	$-0.180656\pi$
$127$	1.94325e6	+	935821.i	0.948676	+	0.456858i	0.105454	+	0.994424i	$0.466370\pi$
$128$		−	399737.i		−	0.190609i
$129$	−2.66101e6	−	1.28854e6i	−1.23959	−	0.600247i
$130$	3.50903e6			1.59719
$131$	1.17174e6	−	2.43315e6i	0.521217	−	1.08232i	−0.459732	−	0.888058i	$-0.652055\pi$
$131$	1.17174e6	−	2.43315e6i	0.521217	−	1.08232i	0.980950	−	0.194262i	$-0.0622311\pi$
$132$	55458.8	+	115161.i	0.0241128	+	0.0500708i
$133$	−893507.	−	1.12042e6i	−0.379789	−	0.476241i
$134$	−269070.	+	61413.4i	−0.111828	+	0.0255240i
$135$	509951.			0.207266
$136$			4.21186e6i			1.67439i
$137$	3.51514e6	−	802307.i	1.36704	−	0.312017i	0.524847	−	0.851197i	$-0.324123\pi$
$137$	3.51514e6	−	802307.i	1.36704	−	0.312017i	0.842191	+	0.539179i	$0.181265\pi$
$138$	3.58598e6	−	4.49668e6i	1.36449	−	1.71102i
$139$	−709025.	+	3.10644e6i	−0.264008	+	1.15669i	0.652852	+	0.757486i	$0.273572\pi$
$139$	−709025.	+	3.10644e6i	−0.264008	+	1.15669i	−0.916860	+	0.399209i	$0.869285\pi$
$140$	1.33406e6	−	1.67286e6i	0.486175	−	0.609644i
$141$	−2.28162e6	+	4.73783e6i	−0.813928	+	1.69014i
$142$	−42755.0	−	187322.i	−0.0149321	−	0.0654219i
$143$	411614.	+	198223.i	0.140761	+	0.0677869i
$144$	878293.	+	1.10134e6i	0.294138	+	0.368838i
$145$	1.18933e6	−	5.21078e6i	0.390119	−	1.70922i
$146$	−349472.	+	1.53114e6i	−0.112293	+	0.491989i
$147$	2.50445e6	+	5.20054e6i	0.788424	+	1.63718i
$148$	953037.	−	760022.i	0.293985	−	0.234445i
$149$	2.16304e6	+	1.72496e6i	0.653890	+	0.521460i	0.893301	−	0.449458i	$-0.148383\pi$
$149$	2.16304e6	+	1.72496e6i	0.653890	+	0.521460i	−0.239411	+	0.970918i	$0.576954\pi$
$150$	−3.81061e6	+	1.83509e6i	−1.12907	+	0.543731i
$151$	442594.	+	919055.i	0.128551	+	0.266938i	0.955303	−	0.295627i	$-0.0955287\pi$
$151$	442594.	+	919055.i	0.128551	+	0.266938i	−0.826753	+	0.562566i	$0.809814\pi$
$152$	−953164.	+	1.19523e6i	−0.271417	+	0.340346i
$153$	−3.08114e6	−	3.86362e6i	−0.860274	−	1.07875i
$154$	−464325.	+	223607.i	−0.127134	+	0.0612243i
$155$	−1.04308e6	−	238077.i	−0.280107	−	0.0639326i
$156$	−2.42991e6	−	554611.i	−0.640054	−	0.146088i
$157$	−873085.	+	696262.i	−0.225610	+	0.179918i	−0.729771	−	0.683692i	$-0.760373\pi$
$157$	−873085.	+	696262.i	−0.225610	+	0.179918i	0.504161	+	0.863610i	$0.331802\pi$
$158$	−699233.	+	1.45197e6i	−0.177276	+	0.368118i
$159$	1.72298e6	−	393258.i	0.428635	−	0.0978333i
$160$	−3.57883e6	−	1.72347e6i	−0.873738	−	0.420770i
$161$	−9.80021e6	−	7.81541e6i	−2.34832	−	1.87273i
$162$	3.64838e6	+	832719.i	0.858134	+	0.195864i
$163$	−172707.	−	137730.i	−0.0398794	−	0.0318027i	0.603347	−	0.797479i	$-0.293833\pi$
$163$	−172707.	−	137730.i	−0.0398794	−	0.0318027i	−0.643227	+	0.765676i	$0.722405\pi$
$164$	−105066.	−	460323.i	−0.0238193	−	0.104359i
$165$	−1.03824e6			−0.231123
$166$		−	3.79432e6i		−	0.829487i
$167$	1.58784e6	+	6.95677e6i	0.340923	+	1.49368i	0.797129	+	0.603809i	$0.206351\pi$
$167$	1.58784e6	+	6.95677e6i	0.340923	+	1.49368i	−0.456206	+	0.889874i	$0.650792\pi$
$168$	8.46300e6	−	6.74902e6i	1.78483	−	1.42335i
$169$	−3.67741e6	+	1.77095e6i	−0.761872	+	0.366898i
$170$	−8.00611e6	−	3.85554e6i	−1.62958	−	0.784763i
$171$		−	1.79368e6i		−	0.358722i
$172$	1.73979e6	+	401043.i	0.341911	+	0.0788144i
$173$	−4.38581e6			−0.847056			−0.423528	−	0.905883i	$-0.639208\pi$
$173$	−4.38581e6			−0.847056			−0.423528	+	0.905883i	$0.639208\pi$
$174$	3.04724e6	−	6.32765e6i	0.578440	−	1.20114i
$175$	3.99946e6	+	8.30496e6i	0.746255	+	1.54961i
$176$	205618.	+	257837.i	0.0377158	+	0.0472942i
$177$	8.18995e6	−	1.86930e6i	1.47694	−	0.337101i
$178$	−896120.			−0.158894
$179$			4.55544e6i			0.794276i	0.917759	+	0.397138i	$0.129997\pi$
$179$			4.55544e6i			0.794276i	−0.917759	+	0.397138i	$0.870003\pi$
$180$	2.61095e6	−	595931.i	0.447693	−	0.102183i
$181$	767509.	−	962426.i	0.129434	−	0.162305i	−0.712891	−	0.701274i	$-0.752615\pi$
$181$	767509.	−	962426.i	0.129434	−	0.162305i	0.842325	+	0.538970i	$0.181186\pi$
$182$	2.23617e6	−	9.79729e6i	0.370929	−	1.62514i
$183$	−4.51425e6	+	5.66069e6i	−0.736600	+	0.923668i
$184$	−5.80184e6	+	1.20476e7i	−0.931348	+	1.93396i
$185$	2.20326e6	+	9.65313e6i	0.347978	+	1.52459i
$186$	−1.26666e6	−	609990.i	−0.196843	−	0.0947946i
$187$	−721330.	−	904519.i	−0.110308	−	0.138322i
$188$	706632.	−	3.09596e6i	0.106346	−	0.465931i
$189$	324971.	−	1.42379e6i	0.0481349	−	0.210893i
$190$	−1.39942e6	−	2.90593e6i	−0.204027	−	0.423667i
$191$	−1.00040e6	+	797789.i	−0.143573	+	0.114495i	−0.692642	−	0.721281i	$-0.743554\pi$
$191$	−1.00040e6	+	797789.i	−0.143573	+	0.114495i	0.549070	+	0.835777i	$0.314982\pi$
$192$	−8.08975e6	−	6.45136e6i	−1.14296	−	0.911481i
$193$	9.29999e6	−	4.47864e6i	1.29363	−	0.622980i	0.344774	−	0.938686i	$-0.387956\pi$
$193$	9.29999e6	−	4.47864e6i	1.29363	−	0.622980i	0.948857	+	0.315706i	$0.102241\pi$
$194$	−97531.4	−	202526.i	−0.0133579	−	0.0277380i
$195$	1.26225e7	−	1.58281e7i	1.70232	−	2.13465i
$196$	−2.17330e6	−	2.72523e6i	−0.288637	−	0.361939i
$197$	−1.03397e7	+	4.97934e6i	−1.35241	+	0.651288i	−0.962931	−	0.269747i	$-0.913060\pi$
$197$	−1.03397e7	+	4.97934e6i	−1.35241	+	0.651288i	−0.389481	+	0.921034i	$0.627346\pi$
$198$	−628873.	−	143536.i	−0.0810153	−	0.0184912i
$199$	4.55466e6	+	1.03957e6i	0.577959	+	0.131915i	0.501500	−	0.865157i	$-0.332782\pi$
$199$	4.55466e6	+	1.03957e6i	0.577959	+	0.131915i	0.0764584	+	0.997073i	$0.475639\pi$
$200$	7.68796e6	−	6.13094e6i	0.960995	−	0.766368i
$201$	−690867.	+	1.43460e6i	−0.0850759	+	0.176662i
$202$	3.31419e6	−	756442.i	0.402090	−	0.0917744i
$203$	−1.37907e7	−	6.64125e6i	−1.64853	−	0.793892i
$204$	4.93463e6	+	3.93524e6i	0.581252	+	0.463533i
$205$	3.73905e6	+	853415.i	0.434010	+	0.0990600i
$206$	−3.88852e6	−	3.10099e6i	−0.444818	−	0.354731i
$207$	−3.49117e6	−	1.52958e7i	−0.393604	−	1.72449i
$208$	−6.43063e6			−0.714601
$209$		−	419922.i		−	0.0459970i
$210$	5.08183e6	+	2.22649e7i	0.548734	+	2.40416i
$211$	−170424.	+	135909.i	−0.0181420	+	0.0144677i	−0.632519	−	0.774545i	$-0.717979\pi$
$211$	−170424.	+	135909.i	−0.0181420	+	0.0144677i	0.614377	+	0.789013i	$0.289407\pi$
$212$	−961543.	+	463055.i	−0.100916	+	0.0485987i
$213$	−998745.	−	480970.i	−0.103351	−	0.0497713i
$214$		−	1.94061e6i		−	0.198014i
$215$	−9.06649e6	+	1.13189e7i	−0.912271	+	1.13891i
$216$	−1.55792e6			−0.154591
$217$	−1.32943e6	+	2.76059e6i	−0.130103	+	0.270161i
$218$	7.05179e6	+	1.46432e7i	0.680659	+	1.41340i
$219$	5.64937e6	+	7.08409e6i	0.537858	+	0.674453i
$220$	611252.	−	139514.i	0.0574054	−	0.0131024i
$221$	2.25593e7			2.09001
$222$			1.30106e7i			1.18916i
$223$	274088.	−	62558.8i	0.0247159	−	0.00564123i	−0.210145	−	0.977670i	$-0.567394\pi$
$223$	274088.	−	62558.8i	0.0247159	−	0.00564123i	0.234861	+	0.972029i	$0.424537\pi$
$224$	−7.09262e6	+	8.89387e6i	−0.631049	+	0.791310i
$225$	−2.56730e6	+	1.12481e7i	−0.225387	+	0.987485i
$226$	−3.01199e6	+	3.77691e6i	−0.260932	+	0.327199i
$227$	6.25548e6	−	1.29896e7i	0.534790	−	1.11050i	−0.442141	−	0.896946i	$-0.645781\pi$
$227$	6.25548e6	−	1.29896e7i	0.534790	−	1.11050i	0.976931	−	0.213557i	$-0.0685049\pi$
$228$	509773.	+	2.23346e6i	0.0430103	+	0.188440i
$229$	−7.72302e6	−	3.71921e6i	−0.643103	−	0.309702i	0.0837585	−	0.996486i	$-0.473308\pi$
$229$	−7.72302e6	−	3.71921e6i	−0.643103	−	0.309702i	−0.726862	+	0.686784i	$0.759022\pi$
$230$	−1.75897e7	−	2.20568e7i	−1.44569	−	1.81284i
$231$	−661626.	+	2.89877e6i	−0.0536756	+	0.235168i
$232$	−3.63343e6	+	1.59191e7i	−0.290973	+	1.27484i
$233$	−3.71383e6	−	7.71186e6i	−0.293599	−	0.609665i	0.701034	−	0.713128i	$-0.252722\pi$
$233$	−3.71383e6	−	7.71186e6i	−0.293599	−	0.609665i	−0.994633	+	0.103463i	$0.967008\pi$
$234$	9.83387e6	−	7.84225e6i	0.767497	−	0.612059i
$235$	2.01667e7	+	1.60824e7i	1.55393	+	1.23922i
$236$	−4.57057e6	+	2.20107e6i	−0.347724	+	0.167455i
$237$	4.03414e6	+	8.37698e6i	0.303044	+	0.629278i
$238$	−1.58667e7	+	1.98962e7i	−1.17694	+	1.47584i
$239$	−9.62477e6	−	1.20691e7i	−0.705012	−	0.884057i	0.292375	−	0.956304i	$-0.405555\pi$
$239$	−9.62477e6	−	1.20691e7i	−0.705012	−	0.884057i	−0.997387	+	0.0722464i	$0.976983\pi$
$240$	1.31668e7	−	6.34077e6i	0.952456	−	0.458679i
$241$	−4.52386e6	−	1.03254e6i	−0.323190	−	0.0737661i	0.0578478	−	0.998325i	$-0.481576\pi$
$241$	−4.52386e6	−	1.03254e6i	−0.323190	−	0.0737661i	−0.381038	+	0.924559i	$0.624433\pi$
$242$	1.09850e7	+	2.50726e6i	0.775093	+	0.176910i
$243$	1.52865e7	−	1.21905e7i	1.06534	−	0.849580i
$244$	1.89706e6	−	3.93929e6i	0.130591	−	0.271174i
$245$	2.76034e7	−	6.30028e6i	1.87700	−	0.428412i
$246$	4.54048e6	+	2.18658e6i	0.304997	+	0.146879i
$247$	6.40181e6	+	5.10527e6i	0.424827	+	0.338788i
$248$	3.18665e6	+	727333.i	0.208920	+	0.0476846i
$249$	−1.71150e7	−	1.36487e7i	−1.10861	−	0.884086i
$250$	528742.	+	2.31657e6i	0.0338395	+	0.148260i
$251$	−2.33150e7			−1.47439			−0.737197	−	0.675677i	$-0.763851\pi$
$251$	−2.33150e7			−1.47439			−0.737197	+	0.675677i	$0.763851\pi$
$252$		−	7.66957e6i		−	0.479258i
$253$	−817323.	−	3.58092e6i	−0.0504698	−	0.221123i
$254$	1.08689e7	−	8.66767e6i	0.663262	−	0.528934i
$255$	−4.61903e7	+	2.22441e7i	−2.78567	+	1.34151i
$256$	1.37233e7	+	6.60878e6i	0.817971	+	0.393914i
$257$		−	3.30112e6i		−	0.194474i	−0.995261	−	0.0972370i	$-0.969000\pi$
$257$		−	3.30112e6i		−	0.194474i	0.995261	−	0.0972370i	$-0.0310005\pi$
$258$	−1.49245e7	+	1.18494e7i	−0.869041	+	0.689979i
$259$	2.83558e7			1.63208
$260$	−5.30447e6	+	1.10148e7i	−0.301802	+	0.626698i
$261$	−8.31242e6	−	1.72609e7i	−0.467526	−	0.970828i
$262$	−1.08528e7	−	1.36090e7i	−0.603446	−	0.756698i
$263$	2.16239e7	−	4.93551e6i	1.18868	−	0.271309i	0.417952	−	0.908469i	$-0.362748\pi$
$263$	2.16239e7	−	4.93551e6i	1.18868	−	0.271309i	0.770732	+	0.637160i	$0.219891\pi$
$264$	3.17184e6			0.172385
$265$		−	8.66878e6i		−	0.465822i
$266$	−9.00522e6	+	2.05538e6i	−0.478464	+	0.109206i
$267$	−3.22348e6	+	4.04211e6i	−0.169352	+	0.212361i
$268$	213966.	−	937445.i	0.0111158	−	0.0487014i
$269$	−2.27891e7	+	2.85766e7i	−1.17077	+	1.46809i	−0.316243	+	0.948678i	$0.602422\pi$
$269$	−2.27891e7	+	2.85766e7i	−1.17077	+	1.46809i	−0.854522	+	0.519415i	$0.826150\pi$
$270$	1.42612e6	−	2.96136e6i	0.0724543	−	0.150453i
$271$	−2.86872e6	−	1.25687e7i	−0.144139	−	0.631512i	−0.994448	−	0.105229i	$-0.966442\pi$
$271$	−2.86872e6	−	1.25687e7i	−0.144139	−	0.631512i	0.850309	−	0.526283i	$-0.176415\pi$
$272$	1.46719e7	+	7.06563e6i	0.729089	+	0.351111i
$273$	−3.61486e7	−	4.53290e7i	−1.77666	−	2.22786i
$274$	5.17123e6	−	2.26567e7i	0.251387	−	1.10140i
$275$	−601034.	+	2.63330e6i	−0.0289002	+	0.126620i
$276$	8.69428e6	+	1.80539e7i	0.413529	+	0.858702i
$277$	−4.93314e6	+	3.93405e6i	−0.232105	+	0.185098i	−0.732635	−	0.680621i	$-0.761710\pi$
$277$	−4.93314e6	+	3.93405e6i	−0.232105	+	0.185098i	0.500530	+	0.865719i	$0.333138\pi$
$278$	1.60567e7	+	1.28048e7i	0.747348	+	0.595990i
$279$	−3.45525e6	+	1.66396e6i	−0.159099	+	0.0766180i
$280$	−2.30375e7	−	4.78379e7i	−1.04945	−	2.17920i
$281$	620076.	−	777551.i	0.0279464	−	0.0350437i	−0.767662	−	0.640855i	$-0.778580\pi$
$281$	620076.	−	777551.i	0.0279464	−	0.0350437i	0.795608	+	0.605811i	$0.207151\pi$
$282$	2.11326e7	+	2.64994e7i	0.942336	+	1.18165i
$283$	3.75547e7	−	1.80854e7i	1.65693	−	0.797936i	0.657938	−	0.753072i	$-0.271429\pi$
$283$	3.75547e7	−	1.80854e7i	1.65693	−	0.797936i	0.998993	−	0.0448638i	$-0.0142854\pi$
$284$	652634.	+	148959.i	0.0284914	+	0.00650299i
$285$	−1.81417e7	−	4.14072e6i	−0.783688	−	0.178872i
$286$	2.30222e6	−	1.83596e6i	0.0984122	−	0.0784811i
$287$	4.76550e6	−	9.89566e6i	0.201587	−	0.418600i
$288$	−1.38812e7	+	3.16830e6i	−0.581099	+	0.132632i
$289$	−2.97234e7	−	1.43140e7i	−1.23142	−	0.593019i
$290$	−2.69338e7	−	2.14790e7i	−1.10434	−	0.880682i
$291$	−1.26437e6	−	288583.i	−0.0513090	−	0.0117109i
$292$	−4.27795e6	−	3.41155e6i	−0.171825	−	0.137026i
$293$	4.26893e6	+	1.87034e7i	0.169713	+	0.743563i	0.986113	+	0.166075i	$0.0531095\pi$
$293$	4.26893e6	+	1.87034e7i	0.169713	+	0.743563i	−0.816400	+	0.577487i	$0.804033\pi$
$294$	3.72042e7			1.46403
$295$		−	4.12059e7i		−	1.60507i
$296$	−6.73104e6	−	2.94906e7i	−0.259542	−	1.13713i
$297$	334571.	−	266811.i	0.0127708	−	0.0101844i
$298$	1.60662e7	−	7.73709e6i	0.607107	−	0.292367i
$299$	6.45287e7	+	3.10754e7i	2.41401	+	1.16253i
$300$		−	1.47355e7i		−	0.545760i
$301$	2.58249e7	+	3.25269e7i	0.946975	+	1.19273i
$302$	6.57484e6			0.238707
$303$	8.50956e6	−	1.76703e7i	0.305900	−	0.635208i
$304$	2.56457e6	+	5.32539e6i	0.0912840	+	0.189553i
$305$	2.21430e7	+	2.77664e7i	0.780435	+	0.978634i
$306$	−3.10533e7	+	7.08771e6i	−1.08379	+	0.247367i
$307$	−2.83562e7			−0.980015			−0.490008	−	0.871718i	$-0.663006\pi$
$307$	−2.83562e7			−0.980015			−0.490008	+	0.871718i	$0.663006\pi$
$308$		−	1.79553e6i		−	0.0614528i
$309$	−2.79752e7	+	6.38515e6i	−0.948194	+	0.216419i
$310$	−4.29961e6	+	5.39155e6i	−0.144326	+	0.180979i
$311$	−7.91532e6	+	3.46793e7i	−0.263140	+	1.15289i	0.654683	+	0.755904i	$0.272802\pi$
$311$	−7.91532e6	+	3.46793e7i	−0.263140	+	1.15289i	−0.917823	+	0.396990i	$0.870055\pi$
$312$	−3.85622e7	+	4.83555e7i	−1.26969	+	1.59214i
$313$	−3.72738e6	+	7.73998e6i	−0.121554	+	0.252410i	−0.952863	−	0.303401i	$-0.901878\pi$
$313$	−3.72738e6	+	7.73998e6i	−0.121554	+	0.252410i	0.831309	+	0.555811i	$0.187592\pi$
$314$	1.60165e6	+	7.01729e6i	0.0517344	+	0.226663i
$315$	5.61280e7	+	2.70298e7i	1.79576	+	0.864792i
$316$	−3.50073e6	−	4.38978e6i	−0.110942	−	0.139117i
$317$	−3.67453e6	+	1.60992e7i	−0.115352	+	0.505388i	0.883935	+	0.467611i	$0.154885\pi$
$317$	−3.67453e6	+	1.60992e7i	−0.115352	+	0.505388i	−0.999286	+	0.0377778i	$0.987972\pi$
$318$	2.53473e6	−	1.11054e7i	0.0788225	−	0.345344i
$319$	−1.94603e6	−	4.04098e6i	−0.0599484	−	0.124484i
$320$	−3.96813e7	+	3.16448e7i	−1.21098	+	0.965722i
$321$	−8.75346e6	−	6.98065e6i	−0.264646	−	0.211048i
$322$	−7.27923e7	+	3.50549e7i	−2.18031	+	1.04998i
$323$	−8.99678e6	−	1.86820e7i	−0.266980	−	0.554391i
$324$	−8.12902e6	+	1.01935e7i	−0.239003	+	0.299700i
$325$	−3.28381e7	−	4.11777e7i	−0.956596	−	1.19953i
$326$	−1.28281e6	+	617767.i	−0.0370262	+	0.0178309i
$327$	9.14171e7	+	2.08654e7i	2.61447	+	0.596736i
$328$	−1.14229e7	−	2.60721e6i	−0.323710	−	0.0738847i
$329$	5.77537e7	−	4.60571e7i	1.62178	−	1.29333i
$330$	−2.90351e6	+	6.02919e6i	−0.0807943	+	0.167771i
$331$	1.46982e7	−	3.35476e6i	0.405303	−	0.0925077i	−0.0150093	−	0.999887i	$-0.504778\pi$
$331$	1.46982e7	−	3.35476e6i	0.405303	−	0.0925077i	0.420312	+	0.907380i	$0.361921\pi$
$332$	1.19104e7	+	5.73573e6i	0.325470	+	0.156738i
$333$	2.77480e7	+	2.21283e7i	0.751449	+	0.599261i
$334$	4.48396e7	+	1.02343e7i	1.20343	+	0.274676i
$335$	6.10640e6	+	4.86969e6i	0.162424	+	0.129529i
$336$	−9.31292e6	−	4.08025e7i	−0.245509	−	1.07565i
$337$	−4.37573e7			−1.14330			−0.571651	−	0.820497i	$-0.693697\pi$
$337$	−4.37573e7			−1.14330			−0.571651	+	0.820497i	$0.693697\pi$
$338$			2.63079e7i			0.681296i
$339$	6.20188e6	+	2.71722e7i	0.159193	+	0.697471i
$340$	2.42051e7	−	1.93029e7i	0.615842	−	0.491118i
$341$	−808914.	+	389553.i	−0.0204004	+	0.00982433i
$342$	−1.04162e7	−	5.01618e6i	−0.260394	−	0.125399i
$343$		−	1.96275e7i		−	0.486389i
$344$	2.76984e7	−	3.45796e7i	0.680424	−	0.849463i
$345$	−1.62764e8			−3.96371
$346$	−1.22653e7	+	2.54691e7i	−0.296107	+	0.614873i
$347$	−3.35045e7	−	6.95727e7i	−0.801889	−	1.66514i	−0.745288	−	0.666742i	$-0.767688\pi$
$347$	−3.35045e7	−	6.95727e7i	−0.801889	−	1.66514i	−0.0566004	−	0.998397i	$-0.518026\pi$
$348$	1.52561e7	+	1.91305e7i	0.361998	+	0.453931i
$349$	−2.63089e7	+	6.00484e6i	−0.618909	+	0.141262i	−0.520468	−	0.853881i	$-0.674243\pi$
$349$	−2.63089e7	+	6.00484e6i	−0.618909	+	0.141262i	−0.0984409	+	0.995143i	$0.531386\pi$
$350$	5.94130e7			1.38573
$351$			8.34441e6i			0.192963i
$352$	−3.24975e6	+	741735.i	−0.0745113	+	0.0170067i
$353$	−1.16882e7	+	1.46565e7i	−0.265719	+	0.333201i	−0.896734	−	0.442569i	$-0.854067\pi$
$353$	−1.16882e7	+	1.46565e7i	−0.265719	+	0.333201i	0.631015	+	0.775771i	$0.282639\pi$
$354$	1.20485e7	−	5.27880e7i	0.271596	−	1.18994i
$355$	−3.39020e6	+	4.25117e6i	−0.0757775	+	0.0950219i
$356$	1.35463e6	−	2.81292e6i	0.0300242	−	0.0623458i
$357$	3.26706e7	+	1.43139e8i	0.718047	+	3.14597i
$358$	2.64542e7	+	1.27397e7i	0.576561	+	0.277657i
$359$	1.05599e7	+	1.32417e7i	0.228232	+	0.286194i	0.882741	−	0.469861i	$-0.155696\pi$
$359$	1.05599e7	+	1.32417e7i	0.228232	+	0.286194i	−0.654509	+	0.756055i	$0.727124\pi$
$360$	1.47880e7	−	6.47907e7i	0.316959	−	1.38869i
$361$	−8.79395e6	+	3.85288e7i	−0.186923	+	0.818962i
$362$	−3.44256e6	−	7.14854e6i	−0.0725697	−	0.150692i
$363$	5.08241e7	−	4.05309e7i	1.06255	−	0.847357i
$364$	2.73733e7	+	2.18295e7i	0.567576	+	0.452626i
$365$	4.00435e7	−	1.92839e7i	0.823480	−	0.396567i
$366$	2.02480e7	+	4.20455e7i	0.412990	+	0.857583i
$367$	−1.05355e7	+	1.32111e7i	−0.213137	+	0.267265i	−0.876895	−	0.480682i	$-0.840389\pi$
$367$	−1.05355e7	+	1.32111e7i	−0.213137	+	0.267265i	0.663758	+	0.747947i	$0.268960\pi$
$368$	3.22348e7	+	4.04212e7i	0.646817	+	0.811083i
$369$	1.23858e7	−	5.96466e6i	0.246515	−	0.118715i
$370$	6.22188e7	+	1.42010e7i	1.22833	+	0.280359i
$371$	−2.42034e7	−	5.52427e6i	−0.473974	−	0.108181i
$372$	3.82951e6	−	3.05393e6i	0.0743900	−	0.0593241i
$373$	1.73335e7	−	3.59934e7i	0.334010	−	0.693579i	−0.664549	−	0.747245i	$-0.731376\pi$
$373$	1.73335e7	−	3.59934e7i	0.334010	−	0.693579i	0.998559	+	0.0536655i	$0.0170905\pi$
$374$	−7.26993e6	+	1.65931e6i	−0.138968	+	0.0317186i
$375$	1.23513e7	+	5.94806e6i	0.234217	+	0.112793i
$376$	−6.16098e7	−	4.91322e7i	−1.15901	−	0.924278i
$377$	8.52648e7	+	1.94611e7i	1.59128	+	0.363199i
$378$	−7.35938e6	−	5.86891e6i	−0.136259	−	0.108663i
$379$	−4.44294e6	−	1.94658e7i	−0.0816118	−	0.357565i	0.917589	−	0.397530i	$-0.130132\pi$
$379$	−4.44294e6	−	1.94658e7i	−0.0816118	−	0.357565i	−0.999201	+	0.0399650i	$0.987275\pi$
$380$	1.12372e7			0.204789
$381$		−	8.02051e7i		−	1.45020i
$382$	1.83520e6	+	8.04054e6i	0.0329225	+	0.144243i
$383$	−2.65311e7	+	2.11578e7i	−0.472236	+	0.376595i	−0.830494	−	0.557027i	$-0.811942\pi$
$383$	−2.65311e7	+	2.11578e7i	−0.472236	+	0.376595i	0.358259	+	0.933622i	$0.383371\pi$
$384$	−1.33927e7	+	6.44956e6i	−0.236523	+	0.113903i
$385$	1.31402e7	+	6.32799e6i	0.230261	+	0.110888i
$386$		−	6.65313e7i		−	1.15682i
$387$	−112010.	+	5.19830e7i	−0.00193252	+	0.896868i
$388$	783163.			0.0134078
$389$	−3.10497e7	+	6.44754e7i	−0.527484	+	1.09533i	0.451665	+	0.892188i	$0.350830\pi$
$389$	−3.10497e7	+	6.44754e7i	−0.527484	+	1.09533i	−0.979149	+	0.203144i	$0.934884\pi$
$390$	−5.66166e7	−	1.17566e8i	−0.954442	−	1.98192i
$391$	−1.13083e8	−	1.41801e8i	−1.89176	−	2.37220i
$392$	−8.43291e7	+	1.92476e7i	−1.39997	+	0.319534i
$393$	−1.00425e8			−1.65449
$394$			7.39693e7i			1.20938i
$395$	4.44632e7	−	1.01484e7i	0.721456	−	0.164668i
$396$	1.40120e6	−	1.75705e6i	0.0225640	−	0.0282943i
$397$	−1.59068e7	+	6.96923e7i	−0.254221	+	1.11381i	0.673101	+	0.739551i	$0.264962\pi$
$397$	−1.59068e7	+	6.96923e7i	−0.254221	+	1.11381i	−0.927322	+	0.374264i	$0.877895\pi$
$398$	1.87744e7	−	2.35424e7i	0.297795	−	0.373423i
$399$	−2.31219e7	+	4.80132e7i	−0.364004	+	0.755861i
$400$	−8.46004e6	−	3.70658e7i	−0.132188	−	0.579154i
$401$	−1.00126e7	−	4.82181e6i	−0.155279	−	0.0747785i	0.354630	−	0.935007i	$-0.384607\pi$
$401$	−1.00126e7	−	4.82181e6i	−0.155279	−	0.0747785i	−0.509909	+	0.860228i	$0.670321\pi$
$402$	6.39888e6	+	8.02395e6i	0.0984977	+	0.123512i
$403$	3.89569e6	−	1.70681e7i	0.0595209	−	0.260778i
$404$	−2.63546e6	+	1.15467e7i	−0.0399680	+	0.175111i
$405$	−4.59495e7	−	9.54152e7i	−0.691697	−	1.43632i
$406$	−7.71335e7	+	6.15119e7i	−1.15256	+	0.919139i
$407$	6.49613e6	+	5.18049e6i	0.0963544	+	0.0768401i
$408$	1.41113e8	−	6.79563e7i	2.07771	−	1.00057i
$409$	3.83549e7	+	7.96448e7i	0.560597	+	1.16409i	0.968025	+	0.250855i	$0.0807117\pi$
$409$	3.83549e7	+	7.96448e7i	0.560597	+	1.16409i	−0.407427	+	0.913238i	$0.633574\pi$
$410$	1.54125e7	−	1.93266e7i	0.223625	−	0.280417i
$411$	−8.35953e7	−	1.04825e8i	−1.20408	−	1.50987i
$412$	1.56121e7	−	7.51840e6i	0.223239	−	0.107506i
$413$	−1.15048e8	−	2.62589e7i	−1.63316	−	0.372758i
$414$	−9.85884e7	−	2.25022e7i	−1.38939	−	0.317120i
$415$	−8.39512e7	+	6.69489e7i	−1.17458	+	0.936697i
$416$	2.82015e7	−	5.85610e7i	0.391735	−	0.813445i
$417$	1.15517e8	−	2.63660e7i	1.59308	−	0.363610i
$418$	−2.43855e6	−	1.17434e6i	−0.0333890	−	0.0160793i
$419$	4.91612e7	+	3.92048e7i	0.668314	+	0.532963i	0.897830	−	0.440342i	$-0.145143\pi$
$419$	4.91612e7	+	3.92048e7i	0.668314	+	0.532963i	−0.229516	+	0.973305i	$0.573714\pi$
$420$	−7.75716e7	−	1.77052e7i	−1.04702	−	0.238975i
$421$	1.78034e7	+	1.41977e7i	0.238592	+	0.190271i	0.735485	−	0.677541i	$-0.236954\pi$
$421$	1.78034e7	+	1.41977e7i	0.238592	+	0.190271i	−0.496893	+	0.867812i	$0.665526\pi$
$422$	312639.	+	1.36976e6i	0.00416012	+	0.0182267i
$423$	9.24580e7			1.22158
$424$			2.64834e7i			0.347437i
$425$	2.96786e7	+	1.30031e8i	0.386614	+	1.69387i
$426$	−5.58614e6	+	4.45479e6i	−0.0722575	+	0.0576234i
$427$	9.16352e7	−	4.41292e7i	1.17701	−	0.566817i
$428$	6.09156e6	+	2.93354e6i	0.0776957	+	0.0374163i
$429$		−	1.69888e7i		−	0.215175i
$430$	4.03754e7	+	8.43047e7i	0.507822	+	1.06034i
$431$	6.99118e7			0.873210			0.436605	−	0.899653i	$-0.356181\pi$
$431$	6.99118e7			0.873210			0.436605	+	0.899653i	$0.356181\pi$
$432$	−2.61349e6	+	5.42697e6i	−0.0324168	+	0.0673141i
$433$	5.73791e7	+	1.19149e8i	0.706789	+	1.46766i	0.876114	+	0.482103i	$0.160127\pi$
$433$	5.73791e7	+	1.19149e8i	0.706789	+	1.46766i	−0.169325	+	0.985560i	$0.554159\pi$
$434$	1.23133e7	+	1.54404e7i	0.150628	+	0.188882i
$435$	−1.93769e8	+	4.42266e7i	−2.35406	+	0.537299i
$436$	−5.66249e7			−0.683200
$437$		−	6.58312e7i		−	0.788838i
$438$	5.69373e7	−	1.29956e7i	0.677602	−	0.154658i
$439$	7.94195e7	−	9.95889e7i	0.938714	−	1.17711i	−0.0452915	−	0.998974i	$-0.514422\pi$
$439$	7.94195e7	−	9.95889e7i	0.938714	−	1.17711i	0.984006	−	0.178137i	$-0.0570069\pi$
$440$	3.46205e6	−	1.51682e7i	0.0406420	−	0.178064i
$441$	6.32765e7	−	7.93462e7i	0.737779	−	0.925146i
$442$	6.30888e7	−	1.31005e8i	0.730610	−	1.51713i
$443$	7.09396e6	+	3.10807e7i	0.0815977	+	0.357503i	0.999200	−	0.0399974i	$-0.0127350\pi$
$443$	7.09396e6	+	3.10807e7i	0.0815977	+	0.357503i	−0.917602	+	0.397500i	$0.869878\pi$
$444$	−4.08403e7	−	1.96677e7i	−0.466595	−	0.224700i
$445$	1.58116e7	+	1.98271e7i	0.179430	+	0.224998i
$446$	403220.	−	1.76662e6i	0.00454504	−	0.0199131i
$447$	2.28931e7	−	1.00301e8i	0.256319	−	1.12301i
$448$	6.30655e7	+	1.30957e8i	0.701388	+	1.45645i
$449$	−3.70120e7	+	2.95161e7i	−0.408888	+	0.326077i	−0.806239	−	0.591589i	$-0.798501\pi$
$449$	−3.70120e7	+	2.95161e7i	−0.408888	+	0.326077i	0.397352	+	0.917666i	$0.369929\pi$
$450$	5.81396e7	+	4.63648e7i	0.638021	+	0.508804i
$451$	2.89965e6	−	1.39640e6i	0.0316093	−	0.0152223i
$452$	−7.30261e6	−	1.51640e7i	−0.0790793	−	0.164210i
$453$	2.36507e7	−	2.96570e7i	0.254419	−	0.319031i
$454$	−5.79389e7	−	7.26531e7i	−0.619160	−	0.776402i
$455$	−2.56226e8	+	1.23392e8i	−2.72013	+	1.30994i
$456$	5.54234e7	+	1.26500e7i	0.584519	+	0.133413i
$457$	1.04253e8	+	2.37951e7i	1.09230	+	0.249309i	0.730476	−	0.682939i	$-0.239298\pi$
$457$	1.04253e8	+	2.37951e7i	1.09230	+	0.249309i	0.361820	+	0.932248i	$0.382156\pi$
$458$	−4.31960e7	+	3.44477e7i	−0.449622	+	0.358562i
$459$	9.16839e6	−	1.90384e7i	0.0948102	−	0.196875i
$460$	9.58261e7	−	2.18717e7i	0.984487	−	0.224703i
$461$	6.16340e7	+	2.96813e7i	0.629096	+	0.302957i	0.721131	−	0.692799i	$-0.243623\pi$
$461$	6.16340e7	+	2.96813e7i	0.629096	+	0.302957i	−0.0920343	+	0.995756i	$0.529337\pi$
$462$	1.49833e7	+	1.19488e7i	0.151944	+	0.121171i
$463$	−8.24919e7	−	1.88282e7i	−0.831129	−	0.189700i	−0.214271	−	0.976774i	$-0.568738\pi$
$463$	−8.24919e7	−	1.88282e7i	−0.831129	−	0.189700i	−0.616858	+	0.787074i	$0.711595\pi$
$464$	4.93586e7	+	3.93622e7i	0.494093	+	0.394026i
$465$	8.85320e6	+	3.87884e7i	0.0880524	+	0.385783i
$466$	−5.51700e7			−0.545186
$467$		−	1.47361e8i		−	1.44688i	−0.690387	−	0.723440i	$-0.742560\pi$
$467$		−	1.47361e8i		−	1.44688i	0.690387	−	0.723440i	$-0.257440\pi$
$468$	9.75131e6	+	4.27233e7i	0.0951318	+	0.416800i
$469$	1.74876e7	−	1.39459e7i	0.169517	−	0.135185i
$470$	1.49791e8	−	7.21353e7i	1.44275	−	0.694791i
$471$	3.74142e7	+	1.80177e7i	0.358074	+	0.172440i
$472$			1.25885e8i			1.19715i
$473$	−26222.8	+	1.21698e7i	−0.000247797	+	0.115001i
$474$	5.99282e7			0.562725
$475$	−2.10044e7	+	4.36161e7i	−0.195988	+	0.406974i
$476$	−3.84691e7	−	7.98819e7i	−0.356690	−	0.740675i
$477$	−1.93736e7	−	2.42938e7i	−0.178507	−	0.223841i
$478$	−9.70034e7	+	2.21404e7i	−0.888185	+	0.202722i
$479$	9.76513e7			0.888529			0.444264	−	0.895896i	$-0.353465\pi$
$479$	9.76513e7			0.888529			0.444264	+	0.895896i	$0.353465\pi$
$480$			1.47711e8i			1.33564i
$481$	−1.57956e8	+	3.60523e7i	−1.41938	+	0.323965i
$482$	−1.86475e7	+	2.33832e7i	−0.166525	+	0.208815i
$483$	−1.03723e8	+	4.54441e8i	−0.920522	+	4.03307i
$484$	−2.44759e7	+	3.06918e7i	−0.215875	+	0.270699i
$485$	−2.76010e6	+	5.73140e6i	−0.0241935	+	0.0502384i
$486$	−2.80426e7	−	1.22863e8i	−0.244292	−	1.07031i
$487$	9.92166e7	+	4.77802e7i	0.859009	+	0.413677i	0.810914	−	0.585166i	$-0.198971\pi$
$487$	9.92166e7	+	4.77802e7i	0.859009	+	0.413677i	0.0480952	+	0.998843i	$0.484685\pi$
$488$	−6.76475e7	−	8.48273e7i	−0.582093	−	0.729922i
$489$	−1.82790e6	+	8.00854e6i	−0.0156324	+	0.0684899i
$490$	4.06082e7	−	1.77916e8i	0.345164	−	1.51226i
$491$	1.21237e7	+	2.51752e7i	0.102422	+	0.212681i	0.945882	−	0.324511i	$-0.105200\pi$
$491$	1.21237e7	+	2.51752e7i	0.102422	+	0.212681i	−0.843460	+	0.537191i	$0.819485\pi$
$492$	−1.37273e7	+	1.09472e7i	−0.115263	+	0.0919193i
$493$	−1.73155e8	−	1.38086e8i	−1.44509	−	1.15242i
$494$	4.75503e7	−	2.28990e7i	0.394432	−	0.189948i
$495$	7.92034e6	+	1.64467e7i	0.0653022	+	0.135601i
$496$	7.87944e6	−	9.88050e6i	0.0645729	−	0.0809718i
$497$	9.70892e6	+	1.21746e7i	0.0790864	+	0.0991712i
$498$	−1.27124e8	+	6.12195e7i	−1.02929	+	0.495681i
$499$	1.42322e8	+	3.24840e7i	1.14543	+	0.261438i	0.752795	−	0.658255i	$-0.228705\pi$
$499$	1.42322e8	+	3.24840e7i	1.14543	+	0.261438i	0.392638	+	0.919693i	$0.371562\pi$
$500$	−8.07098e6	−	1.84215e6i	−0.0645679	−	0.0147372i
$501$	2.07458e8	−	1.65443e8i	1.64975	−	1.31563i
$502$	−6.52021e7	+	1.35394e8i	−0.515408	+	1.07025i
$503$	−2.03649e8	+	4.64815e7i	−1.60021	+	0.365238i	−0.927251	−	0.374440i	$-0.877835\pi$
$503$	−2.03649e8	+	4.64815e7i	−1.60021	+	0.365238i	−0.672961	+	0.739678i	$0.734978\pi$
$504$	−1.71473e8	−	8.25770e7i	−1.33938	−	0.645012i
$505$	−7.52139e7	−	5.99811e7i	−0.584015	−	0.465736i
$506$	−2.30807e7	−	5.26802e6i	−0.178155	−	0.0406626i
$507$	1.18667e8	+	9.46334e7i	0.910551	+	0.726140i
$508$	1.07777e7	+	4.72201e7i	0.0822117	+	0.360193i
$509$	−9.08791e7			−0.689145			−0.344573	−	0.938760i	$-0.611976\pi$
$509$	−9.08791e7			−0.689145			−0.344573	+	0.938760i	$0.611976\pi$
$510$			3.30441e8i			2.49106i
$511$	−2.83230e7	−	1.24091e8i	−0.212264	−	0.929988i
$512$	9.67581e7	−	7.71620e7i	0.720904	−	0.574902i
$513$	6.91025e6	−	3.32780e6i	0.0511849	−	0.0246493i
$514$	−1.91701e7	−	9.23183e6i	−0.141168	−	0.0679827i
$515$			1.40751e8i			1.03046i
$516$	−1.46343e7	−	6.47601e7i	−0.106518	−	0.471366i
$517$	2.16455e7			0.156637
$518$	7.92991e7	−	1.64666e8i	0.570531	−	1.18472i
$519$	7.07630e7	+	1.46941e8i	0.506179	+	1.05109i
$520$	1.89153e8	+	2.37190e8i	1.34525	+	1.68689i
$521$	8.23525e7	−	1.87964e7i	0.582323	−	0.132911i	0.0787957	−	0.996891i	$-0.474893\pi$
$521$	8.23525e7	−	1.87964e7i	0.582323	−	0.132911i	0.503527	+	0.863979i	$0.332035\pi$
$522$	−1.23483e8			−0.868152
$523$		−	7.93006e7i		−	0.554334i	−0.960822	−	0.277167i	$-0.910605\pi$
$523$		−	7.93006e7i		−	0.554334i	0.960822	−	0.277167i	$-0.0893955\pi$
$524$	5.91244e7	−	1.34948e7i	0.410935	−	0.0937932i
$525$	2.13717e8	−	2.67993e8i	1.47694	−	1.85202i
$526$	3.18116e7	−	1.39376e8i	0.218589	−	0.957701i
$527$	−2.76418e7	+	3.46618e7i	−0.188858	+	0.236820i
$528$	5.32094e6	−	1.10490e7i	0.0361482	−	0.0750625i
$529$	−9.51906e7	−	4.17057e8i	−0.643024	−	2.81727i
$530$	−5.03409e7	−	2.42429e7i	−0.338138	−	0.162839i
$531$	−9.20900e7	−	1.15477e8i	−0.615077	−	0.771282i
$532$	7.16101e6	−	3.13744e7i	0.0475597	−	0.208373i
$533$	−1.39646e7	+	6.11827e7i	−0.0922243	+	0.404061i
$534$	1.44585e7	+	3.00233e7i	0.0949508	+	0.197167i
$535$	−4.29369e7	+	3.42410e7i	−0.280394	+	0.223607i
$536$	−1.86553e7	−	1.48771e7i	−0.121145	−	0.0966102i
$537$	1.52624e8	−	7.34999e7i	0.985599	−	0.474639i
$538$	1.02217e8	+	2.12256e8i	0.656413	+	1.36306i
$539$	1.48137e7	−	1.85758e7i	0.0946016	−	0.118627i
$540$	7.13990e6	+	8.95316e6i	0.0453431	+	0.0568584i
$541$	−1.92816e8	+	9.28553e7i	−1.21773	+	0.586428i	−0.928679	−	0.370885i	$-0.879054\pi$
$541$	−1.92816e8	+	9.28553e7i	−1.21773	+	0.586428i	−0.289052	+	0.957313i	$0.593340\pi$
$542$	−8.10108e7	−	1.84902e7i	−0.508798	−	0.116130i
$543$	−4.46282e7	−	1.01861e7i	−0.278747	−	0.0636221i
$544$	−1.28687e8	+	1.02625e8i	−0.799354	+	0.637464i
$545$	1.99563e8	−	4.14396e8i	1.23279	−	2.55992i
$546$	−3.64325e8	+	8.31547e7i	−2.23826	+	0.510868i
$547$	9.60037e7	+	4.62330e7i	0.586578	+	0.282481i	0.703541	−	0.710655i	$-0.251601\pi$
$547$	9.60037e7	+	4.62330e7i	0.586578	+	0.282481i	−0.116962	+	0.993136i	$0.537316\pi$
$548$	6.33020e7	+	5.04817e7i	0.384659	+	0.306755i
$549$	1.24109e8	+	2.83270e7i	0.750043	+	0.171192i
$550$	1.36112e7	+	1.08545e7i	0.0818101	+	0.0652414i
$551$	−1.78878e7	−	7.83715e7i	−0.106931	−	0.468493i
$552$	4.97250e8			2.95636
$553$		−	1.30609e8i		−	0.772323i
$554$	9.04972e6	+	3.96494e7i	0.0532238	+	0.233189i
$555$	2.87867e8	−	2.29566e8i	1.68388	−	1.34285i
$556$	−6.44666e7	+	3.10455e7i	−0.375069	+	0.180624i
$557$	−1.22429e8	−	5.89589e7i	−0.708468	−	0.341180i	0.0447073	−	0.999000i	$-0.485764\pi$
$557$	−1.22429e8	−	5.89589e7i	−0.708468	−	0.341180i	−0.753175	+	0.657820i	$0.771479\pi$
$558$			2.47186e7i			0.142273i
$559$	−1.85213e8	−	1.48356e8i	−1.06032	−	0.849319i
$560$	−2.05289e8			−1.16897
$561$	−1.86664e7	+	3.87612e7i	−0.105724	+	0.219537i
$562$	−2.78127e6	−	5.77536e6i	−0.0156687	−	0.0325365i
$563$	−1.44329e8	−	1.80983e8i	−0.808779	−	1.01418i	−0.999471	−	0.0325264i	$-0.989645\pi$
$563$	−1.44329e8	−	1.80983e8i	−0.808779	−	1.01418i	0.190692	−	0.981650i	$-0.438927\pi$
$564$	−1.15127e8	+	2.62770e7i	−0.641712	+	0.146467i
$565$	1.36711e8			0.757981
$566$		−	2.68663e8i		−	1.48169i
$567$	−2.95683e8	+	6.74877e7i	−1.62210	+	0.370233i
$568$	1.03572e7	−	1.29875e7i	0.0565192	−	0.0708728i
$569$	−3.55906e7	+	1.55933e8i	−0.193196	+	0.846448i	0.781676	+	0.623685i	$0.214365\pi$
$569$	−3.55906e7	+	1.55933e8i	−0.193196	+	0.846448i	−0.974872	+	0.222764i	$0.928492\pi$
$570$	−7.47804e7	+	9.37717e7i	−0.403797	+	0.506346i
$571$	1.45641e8	−	3.02427e8i	0.782304	−	1.62447i	0.00125654	−	0.999999i	$-0.499600\pi$
$571$	1.45641e8	−	3.02427e8i	0.782304	−	1.62447i	0.781047	−	0.624472i	$-0.214686\pi$
$572$	2.28289e6	+	1.00020e7i	0.0121983	+	0.0534441i
$573$	4.28698e7	+	2.06450e7i	0.227870	+	0.109736i
$574$	−4.41385e7	−	5.53480e7i	−0.233390	−	0.292662i
$575$	−9.42242e7	+	4.12823e8i	−0.495631	+	2.17150i
$576$	−4.04825e7	+	1.77365e8i	−0.211836	+	0.928114i
$577$	1.40675e8	+	2.92115e8i	0.732301	+	1.52064i	0.849534	+	0.527534i	$0.176883\pi$
$577$	1.40675e8	+	2.92115e8i	0.732301	+	1.52064i	−0.117233	+	0.993104i	$0.537402\pi$
$578$	−1.66248e8	+	1.32578e8i	−0.860938	+	0.686575i
$579$	−3.00102e8	−	2.39323e8i	−1.54608	−	1.23296i
$580$	1.08137e8	−	5.20761e7i	0.554231	−	0.266904i
$581$	1.33424e8	+	2.77057e8i	0.680307	+	1.41267i
$582$	−5.21174e6	+	6.53532e6i	−0.0264371	+	0.0331511i
$583$	−4.53559e6	−	5.68745e6i	−0.0228891	−	0.0287020i
$584$	−1.22334e8	+	5.89130e7i	−0.614199	+	0.295782i
$585$	−3.47027e8	−	7.92067e7i	−1.73339	−	0.395635i
$586$	1.20552e8	+	2.75152e7i	0.599075	+	0.136735i
$587$	1.84146e8	−	1.46851e8i	0.910431	−	0.726044i	−0.0516915	−	0.998663i	$-0.516461\pi$
$587$	1.84146e8	−	1.46851e8i	0.910431	−	0.726044i	0.962122	+	0.272619i	$0.0878898\pi$
$588$	−5.62401e7	+	1.16784e8i	−0.276640	+	0.574448i
$589$	−1.56883e7	+	3.58074e6i	−0.0767766	+	0.0175238i
$590$	−2.39289e8	−	1.15236e8i	−1.16511	−	0.561088i
$591$	3.33652e8	+	2.66079e8i	1.61634	+	1.28898i
$592$	−1.14022e8	−	2.60247e7i	−0.549569	−	0.125436i
$593$	2.22346e8	+	1.77315e8i	1.06627	+	0.850319i	0.989180	−	0.146705i	$-0.0468670\pi$
$593$	2.22346e8	+	1.77315e8i	1.06627	+	0.850319i	0.0770860	+	0.997024i	$0.475438\pi$
$594$	−613761.	−	2.68906e6i	−0.00292846	−	0.0128304i
$595$	7.20174e8			3.41890
$596$			6.21277e7i			0.293458i
$597$	−3.86578e7	−	1.69371e8i	−0.181683	−	0.796005i
$598$	3.60919e8	−	2.87824e8i	1.68774	−	1.34593i
$599$	−1.88919e8	+	9.09788e7i	−0.879015	+	0.423311i	−0.818265	−	0.574842i	$-0.805064\pi$
$599$	−1.88919e8	+	9.09788e7i	−0.879015	+	0.423311i	−0.0607501	+	0.998153i	$0.519349\pi$
$600$	−3.29450e8	−	1.58655e8i	−1.52523	−	0.734514i
$601$		−	2.87692e8i		−	1.32527i	−0.748943	−	0.662635i	$-0.769438\pi$
$601$		−	2.87692e8i		−	1.32527i	0.748943	−	0.662635i	$-0.230562\pi$
$602$	2.61110e8	−	5.90050e7i	1.19683	−	0.270458i
$603$	2.79960e7			0.127686
$604$	−9.93894e6	+	2.06384e7i	−0.0451055	+	0.0936625i
$605$	−1.38351e8	−	2.87288e8i	−0.624762	−	1.29733i
$606$	−7.88164e7	−	9.88327e7i	−0.354159	−	0.444102i
$607$	−6.71927e7	+	1.53363e7i	−0.300439	+	0.0685731i	−0.370083	−	0.928999i	$-0.620671\pi$
$607$	−6.71927e7	+	1.53363e7i	−0.300439	+	0.0685731i	0.0696443	+	0.997572i	$0.477814\pi$
$608$	−5.97430e7			−0.265813
$609$			5.69192e8i			2.52004i
$610$	2.23169e8	−	5.09368e7i	0.983204	−	0.224410i
$611$	−2.63159e8	+	3.29990e8i	−1.15370	+	1.44670i
$612$	2.46938e7	−	1.08190e8i	0.107729	−	0.471992i
$613$	−3.11351e7	+	3.90421e7i	−0.135166	+	0.169493i	−0.844808	−	0.535070i	$-0.820285\pi$
$613$	−3.11351e7	+	3.90421e7i	−0.135166	+	0.169493i	0.709642	+	0.704563i	$0.248857\pi$
$614$	−7.93003e7	+	1.64669e8i	−0.342586	+	0.711387i
$615$	−3.17353e7	−	1.39041e8i	−0.136432	−	0.597749i
$616$	−4.01438e7	−	1.93322e7i	−0.171742	−	0.0827065i
$617$	−1.91046e7	−	2.39565e7i	−0.0813361	−	0.101992i	0.739499	−	0.673158i	$-0.235063\pi$
$617$	−1.91046e7	−	2.39565e7i	−0.0813361	−	0.101992i	−0.820835	+	0.571166i	$0.806491\pi$
$618$	−4.11552e7	+	1.80313e8i	−0.174365	+	0.763942i
$619$	−4.55054e7	+	1.99372e8i	−0.191863	+	0.840607i	0.783744	+	0.621084i	$0.213307\pi$
$619$	−4.55054e7	+	1.99372e8i	−0.191863	+	0.840607i	−0.975607	+	0.219523i	$0.929550\pi$
$620$	−1.04245e7	−	2.16467e7i	−0.0437401	−	0.0908272i
$621$	5.24507e7	−	4.18280e7i	0.219016	−	0.174660i
$622$	1.79252e8	+	1.42949e8i	0.744892	+	0.594032i
$623$	6.54338e7	−	3.15112e7i	0.270606	−	0.130317i
$624$	1.03755e8	+	2.15450e8i	0.427027	+	0.886731i
$625$	−1.29983e8	+	1.62993e8i	−0.532410	+	0.667621i
$626$	3.45234e7	+	4.32909e7i	0.140731	+	0.176471i
$627$	−1.40689e7	+	6.77524e6i	−0.0570767	+	0.0274867i
$628$	−2.44484e7	−	5.58019e6i	−0.0987124	−	0.0225305i
$629$	3.99999e8	+	9.12972e7i	1.60734	+	0.366865i
$630$	3.13933e8	−	2.50353e8i	1.25550	−	1.00122i
$631$	−1.75181e8	+	3.63767e8i	−0.697266	+	1.44789i	0.187698	+	0.982227i	$0.439897\pi$
$631$	−1.75181e8	+	3.63767e8i	−0.697266	+	1.44789i	−0.884964	+	0.465660i	$0.845817\pi$
$632$	−1.35837e8	+	3.10038e7i	−0.538103	+	0.122819i
$633$	7.30316e6	+	3.51702e6i	0.0287938	+	0.0138664i
$634$	8.32142e7	+	6.63611e7i	0.326535	+	0.260403i
$635$	−3.83553e8	−	8.75435e7i	−1.49797	−	0.341903i
$636$	3.10281e7	+	2.47441e7i	0.120610	+	0.0961833i
$637$	1.03093e8	+	4.51678e8i	0.398849	+	1.74747i
$638$	−2.89088e7			−0.111319
$639$			1.94903e7i			0.0746993i
$640$	1.62248e7	+	7.10854e7i	0.0618926	+	0.271169i
$641$	−1.37545e8	+	1.09689e8i	−0.522242	+	0.416474i	−0.848809	−	0.528700i	$-0.822680\pi$
$641$	−1.37545e8	+	1.09689e8i	−0.522242	+	0.416474i	0.326567	+	0.945174i	$0.394108\pi$
$642$	−6.50174e7	+	3.13107e7i	−0.245711	+	0.118328i
$643$	−9.36142e7	−	4.50822e7i	−0.352135	−	0.169579i	0.249451	−	0.968387i	$-0.419750\pi$
$643$	−9.36142e7	−	4.50822e7i	−0.352135	−	0.169579i	−0.601586	+	0.798808i	$0.705464\pi$
$644$		−	2.81486e8i		−	1.05390i
$645$	5.25508e8	+	1.21136e8i	1.95839	+	0.451433i
$646$	−1.33649e8			−0.495758
$647$	7.53005e7	−	1.56363e8i	0.278026	−	0.577326i	−0.714461	−	0.699675i	$-0.753328\pi$
$647$	7.53005e7	−	1.56363e8i	0.278026	−	0.577326i	0.992487	+	0.122348i	$0.0390425\pi$
$648$	1.40377e8	+	2.91496e8i	0.515907	+	1.07129i
$649$	−2.15593e7	−	2.70346e7i	−0.0788681	−	0.0988974i
$650$	−3.30960e8	+	7.55394e7i	−1.20513	+	0.275064i
$651$	1.13940e8			0.412983
$652$		−	4.96058e6i		−	0.0178974i
$653$	1.68144e8	−	3.83779e7i	0.603869	−	0.137829i	0.0903541	−	0.995910i	$-0.471200\pi$
$653$	1.68144e8	−	3.83779e7i	0.603869	−	0.137829i	0.513515	+	0.858080i	$0.328343\pi$
$654$	3.76823e8	−	4.72522e8i	1.34711	−	1.68923i
$655$	−1.09613e8	+	4.80248e8i	−0.390068	+	1.70900i
$656$	−2.82448e7	+	3.54178e7i	−0.100052	+	0.125461i
$657$	6.91224e7	−	1.43534e8i	0.243738	−	0.506126i
$658$	−1.05948e8	−	4.64187e8i	−0.371889	−	1.62935i
$659$	−7.78758e6	−	3.75030e6i	−0.0272111	−	0.0131042i	0.420229	−	0.907418i	$-0.361950\pi$
$659$	−7.78758e6	−	3.75030e6i	−0.0272111	−	0.0131042i	−0.447440	+	0.894314i	$0.647664\pi$
$660$	−1.45365e7	−	1.82282e7i	−0.0505624	−	0.0634033i
$661$	−7.04126e7	+	3.08498e8i	−0.243807	+	1.06819i	0.693712	+	0.720253i	$0.255974\pi$
$661$	−7.04126e7	+	3.08498e8i	−0.243807	+	1.06819i	−0.937519	+	0.347935i	$0.886883\pi$
$662$	2.16230e7	−	9.47364e7i	0.0745318	−	0.326545i
$663$	−3.63983e8	−	7.55819e8i	−1.24894	−	2.59344i
$664$	2.56474e8	−	2.04531e8i	0.876070	−	0.698642i
$665$	2.04369e8	+	1.62979e8i	0.694945	+	0.554200i
$666$	2.06102e8	−	9.92536e7i	0.697686	−	0.335988i
$667$	−3.05080e8	−	6.33504e8i	−1.02810	−	2.13487i
$668$	−9.99078e7	+	1.25280e8i	−0.335174	+	0.420295i
$669$	−6.51823e6	−	8.17360e6i	−0.0217696	−	0.0272983i
$670$	4.53561e7	−	2.18423e7i	0.150803	−	0.0726231i
$671$	2.90553e7	+	6.63169e6i	0.0961741	+	0.0219511i
$672$	4.12413e8	+	9.41306e7i	1.35902	+	0.310187i
$673$	9.23677e7	−	7.36608e7i	0.303023	−	0.241652i	−0.460159	−	0.887836i	$-0.652208\pi$
$673$	9.23677e7	−	7.36608e7i	0.303023	−	0.241652i	0.763182	+	0.646184i	$0.223636\pi$
$674$	−1.22371e8	+	2.54106e8i	−0.399667	+	0.829917i
$675$	−4.80968e7	+	1.09778e7i	−0.156388	+	0.0356946i
$676$	−8.25804e7	−	3.97686e7i	−0.267323	−	0.128736i
$677$	3.32933e7	+	2.65505e7i	0.107298	+	0.0855672i	0.675669	−	0.737205i	$-0.263855\pi$
$677$	3.32933e7	+	2.65505e7i	0.107298	+	0.0855672i	−0.568371	+	0.822772i	$0.692426\pi$
$678$	1.75137e8	+	3.99739e7i	0.561939	+	0.128259i
$679$	1.42433e7	+	1.13586e7i	0.0454989	+	0.0362841i
$680$	−1.70954e8	−	7.48997e8i	−0.543690	−	2.38206i
$681$	−5.36130e8			−1.69757
$682$			5.78691e6i			0.0182429i
$683$	4.62698e7	+	2.02721e8i	0.145223	+	0.636264i	0.994174	+	0.107791i	$0.0343778\pi$
$683$	4.62698e7	+	2.02721e8i	0.145223	+	0.636264i	−0.848951	+	0.528472i	$0.822765\pi$
$684$	3.14915e7	−	2.51137e7i	0.0984069	−	0.0784769i
$685$	−5.92534e8	+	2.85349e8i	−1.84349	+	0.887779i
$686$	−1.13980e8	−	5.48899e7i	−0.353067	−	0.170028i
$687$			3.18757e8i			0.983082i
$688$	−7.39917e7	−	1.54496e8i	−0.227205	−	0.474408i
$689$	1.41849e8			0.433678
$690$	−4.55183e8	+	9.45197e8i	−1.38560	+	2.87723i
$691$	−1.44536e8	−	3.00131e8i	−0.438067	−	0.909656i	−0.996772	−	0.0802890i	$-0.974416\pi$
$691$	−1.44536e8	−	3.00131e8i	−0.438067	−	0.909656i	0.558704	−	0.829367i	$-0.311299\pi$
$692$	−6.14065e7	−	7.70013e7i	−0.185309	−	0.232370i
$693$	5.09670e7	−	1.16329e7i	0.153140	−	0.0349532i
$694$	−4.97717e8			−1.48903
$695$		−	5.81198e8i		−	1.73129i
$696$	5.91972e8	−	1.35114e8i	1.75579	−	0.400748i
$697$	9.90854e7	−	1.24249e8i	0.292625	−	0.366940i
$698$	−3.87039e7	+	1.69573e8i	−0.113812	+	0.498644i
$699$	−1.98455e8	+	2.48854e8i	−0.581071	+	0.728640i
$700$	−8.98123e7	+	1.86497e8i	−0.261844	+	0.543724i
$701$	−1.47310e8	−	6.45407e8i	−0.427639	−	1.87361i	−0.483783	−	0.875188i	$-0.660738\pi$
$701$	−1.47310e8	−	6.45407e8i	−0.427639	−	1.87361i	0.0561438	−	0.998423i	$-0.482119\pi$
$702$	4.84573e7	+	2.33358e7i	0.140071	+	0.0674545i
$703$	9.28497e7	+	1.16430e8i	0.267248	+	0.335118i
$704$	−9.47742e6	+	4.15233e7i	−0.0271626	+	0.119007i
$705$	2.13439e8	−	9.35139e8i	0.609126	−	2.66876i
$706$	5.24258e7	+	1.08863e8i	0.148981	+	0.309362i
$707$	−2.15399e8	+	1.71775e8i	−0.609517	+	0.486073i
$708$	1.47488e8	+	1.17618e8i	0.415582	+	0.331416i
$709$	5.37367e8	−	2.58782e8i	1.50776	−	0.726098i	0.516287	−	0.856416i	$-0.327314\pi$
$709$	5.37367e8	−	2.58782e8i	1.50776	−	0.726098i	0.991472	+	0.130317i	$0.0415996\pi$
$710$	1.52063e7	+	3.15761e7i	0.0424862	+	0.0882235i
$711$	1.01925e8	−	1.27810e8i	0.283578	−	0.355596i
$712$	−4.83049e7	−	6.05725e7i	−0.133829	−	0.167817i
$713$	−1.26814e8	+	6.10702e7i	−0.349862	+	0.168485i
$714$	9.22598e8	+	2.10577e8i	2.53465	+	0.578517i
$715$	−8.12431e7	−	1.85432e7i	−0.222264	−	0.0507302i
$716$	−7.99795e7	+	6.37815e7i	−0.217891	+	0.173762i
$717$	−2.49067e8	+	5.17194e8i	−0.675709	+	1.40312i
$718$	1.06428e8	−	2.42915e7i	0.287530	−	0.0656268i
$719$	1.06920e8	+	5.14900e7i	0.287656	+	0.138528i	0.572147	−	0.820151i	$-0.306111\pi$
$719$	1.06920e8	+	5.14900e7i	0.287656	+	0.138528i	−0.284492	+	0.958678i	$0.591825\pi$
$720$	−2.00889e8	−	1.60204e8i	−0.538219	−	0.429215i
$721$	3.92979e8	+	8.96949e7i	1.04849	+	0.239311i
$722$	1.99150e8	+	1.58817e8i	0.529137	+	0.421973i
$723$	3.83964e7	+	1.68226e8i	0.101596	+	0.445120i
$724$	2.76432e7			0.0728405
$725$			5.17065e8i			1.35685i
$726$	−9.32355e7	−	4.08491e8i	−0.243653	−	1.06751i
$727$	4.36694e7	−	3.48252e7i	0.113651	−	0.0906338i	−0.565015	−	0.825081i	$-0.691130\pi$
$727$	4.36694e7	−	3.48252e7i	0.113651	−	0.0906338i	0.678666	+	0.734447i	$0.262558\pi$
$728$	7.82779e8	−	3.76966e8i	2.02883	−	0.977031i
$729$	−2.73728e8	−	1.31821e8i	−0.706541	−	0.340252i
$730$		−	2.86468e8i		−	0.736388i
$731$	2.59570e8	+	5.41987e8i	0.664512	+	1.38751i
$732$	−1.62589e8			−0.414531
$733$	−7.78283e7	+	1.61612e8i	−0.197618	+	0.410357i	−0.976104	−	0.217304i	$-0.930274\pi$
$733$	−7.78283e7	+	1.61612e8i	−0.197618	+	0.410357i	0.778486	+	0.627662i	$0.215988\pi$
$734$	4.72557e7	+	9.81275e7i	0.119500	+	0.248143i
$735$	−6.56449e8	−	8.23161e8i	−1.65325	−	2.07311i
$736$	−5.09464e8	+	1.16282e8i	−1.27785	+	0.291661i
$737$	6.55418e6			0.0163725
$738$		−	8.86066e7i		−	0.220443i
$739$	−6.08801e8	+	1.38955e8i	−1.50849	+	0.344303i	−0.895239	−	0.445586i	$-0.852995\pi$
$739$	−6.08801e8	+	1.38955e8i	−1.50849	+	0.344303i	−0.613250	+	0.789889i	$0.710138\pi$
$740$	−1.38631e8	+	1.73837e8i	−0.342109	+	0.428991i
$741$	6.77553e7	−	2.96855e8i	0.166528	−	0.729609i
$742$	−9.97670e7	+	1.25104e8i	−0.244217	+	0.306238i
$743$	4.67108e7	−	9.69960e7i	0.113881	−	0.236476i	−0.836236	−	0.548369i	$-0.815249\pi$
$743$	4.67108e7	−	9.69960e7i	0.113881	−	0.236476i	0.950117	+	0.311893i	$0.100963\pi$
$744$	−2.70468e7	−	1.18500e8i	−0.0656745	−	0.287739i
$745$	−4.54667e8	−	2.18956e8i	−1.09958	−	0.529528i
$746$	−1.60545e8	−	2.01317e8i	−0.386705	−	0.484912i
$747$	−8.56463e7	+	3.75241e8i	−0.205469	+	0.900219i
$748$	5.78109e6	−	2.53286e7i	0.0138135	−	0.0605211i
$749$	6.82396e7	+	1.41701e8i	0.162402	+	0.337231i
$750$	6.90826e7	−	5.50915e7i	0.163751	−	0.130587i
$751$	5.17093e8	+	4.12368e8i	1.22081	+	0.973565i	0.999998	−	0.00175085i	$-0.000557313\pi$
$751$	5.17093e8	+	4.12368e8i	1.22081	+	0.973565i	0.220814	+	0.975316i	$0.429129\pi$
$752$	−2.74505e8	+	1.32195e8i	−0.645501	+	0.310857i
$753$	3.76176e8	+	7.81137e8i	0.881061	+	1.82954i
$754$	3.51464e8	−	4.40721e8i	0.819910	−	1.02813i
$755$	−1.16010e8	−	1.45472e8i	−0.269559	−	0.338016i
$756$	2.95474e7	−	1.42293e7i	0.0683838	−	0.0329319i
$757$	−1.84927e8	−	4.22083e7i	−0.426297	−	0.0972994i	0.00398934	−	0.999992i	$-0.498730\pi$
$757$	−1.84927e8	−	4.22083e7i	−0.426297	−	0.0972994i	−0.430286	+	0.902693i	$0.641587\pi$
$758$	−1.25466e8	−	2.86368e7i	−0.288083	−	0.0657532i
$759$	−1.06787e8	+	8.51598e7i	−0.244227	+	0.194764i
$760$	1.20989e8	−	2.51236e8i	0.275616	−	0.572323i
$761$	−8.44713e7	+	1.92800e7i	−0.191670	+	0.0437475i	−0.317278	−	0.948332i	$-0.602769\pi$
$761$	−8.44713e7	+	1.92800e7i	−0.191670	+	0.0437475i	0.125608	+	0.992080i	$0.459912\pi$
$762$	−4.65763e8	−	2.24300e8i	−1.05269	−	0.506949i
$763$	−1.02983e9	−	8.21261e8i	−2.31842	−	1.84888i
$764$	−2.80134e7	−	6.39388e6i	−0.0628183	−	0.0143379i
$765$	7.04739e8	+	5.62011e8i	1.57414	+	1.25534i
$766$	4.86706e7	+	2.13240e8i	0.108288	+	0.474440i
$767$	6.74259e8			1.49431
$768$		−	5.66409e8i		−	1.25039i
$769$	6.14872e7	+	2.69393e8i	0.135209	+	0.592389i	0.996450	+	0.0841917i	$0.0268308\pi$
$769$	6.14872e7	+	2.69393e8i	0.135209	+	0.592389i	−0.861241	+	0.508197i	$0.830312\pi$
$770$	7.34953e7	−	5.86105e7i	0.160986	−	0.128382i
$771$	−1.10599e8	+	5.32619e7i	−0.241318	+	0.116213i
$772$	2.08842e8	+	1.00573e8i	0.453905	+	0.218589i
$773$			5.20031e8i			1.12588i	0.826499	+	0.562938i	$0.190329\pi$
$773$			5.20031e8i			1.12588i	−0.826499	+	0.562938i	$0.809671\pi$
$774$	3.01560e8	+	1.46025e8i	0.650356	+	0.314923i
$775$	1.03505e8			0.222360
$776$	8.43219e6	−	1.75096e7i	0.0180449	−	0.0374707i
$777$	−4.57507e8	−	9.50022e8i	−0.975291	−	2.02521i
$778$	2.87586e8	+	3.60621e8i	0.610701	+	0.765795i
$779$	5.62364e7	−	1.28356e7i	0.118961	−	0.0271521i
$780$	4.54623e8			0.958004
$781$			4.56291e6i			0.00957831i
$782$	−1.13971e9	+	2.60131e8i	−2.38327	+	0.543966i
$783$	5.10765e7	−	6.40479e7i	0.106399	−	0.133420i
$784$	−7.44183e7	+	3.26048e8i	−0.154430	+	0.676601i
$785$	1.27001e8	−	1.59254e8i	0.262541	−	0.329216i
$786$	−2.80846e8	+	5.83184e8i	−0.578364	+	1.20099i
$787$	1.08855e8	+	4.76926e8i	0.223319	+	0.978423i	0.954960	+	0.296733i	$0.0958972\pi$
$787$	1.08855e8	+	4.76926e8i	0.223319	+	0.978423i	−0.731642	+	0.681689i	$0.761246\pi$
$788$	−2.32189e8	−	1.11817e8i	−0.474530	−	0.228522i
$789$	−5.14249e8	−	6.44847e8i	−1.04699	−	1.31288i
$790$	6.54113e7	−	2.86586e8i	0.132670	−	0.581264i
$791$	8.71205e7	−	3.81700e8i	0.176032	−	0.771245i
$792$	−2.41969e7	−	5.02453e7i	−0.0487062	−	0.101139i
$793$	−4.54346e8	+	3.62329e8i	−0.911103	+	0.726580i
$794$	3.60229e8	+	2.87273e8i	0.719643	+	0.573896i
$795$	−2.90436e8	+	1.39867e8i	−0.578028	+	0.278364i
$796$	4.55189e7	+	9.45209e7i	0.0902511	+	0.187408i
$797$	−7.14033e7	+	8.95369e7i	−0.141040	+	0.176859i	−0.847335	−	0.531059i	$-0.821794\pi$
$797$	−7.14033e7	+	8.95369e7i	−0.141040	+	0.176859i	0.706294	+	0.707918i	$0.250366\pi$
$798$	2.14158e8	+	2.68545e8i	0.421430	+	0.528456i
$799$	9.62990e8	−	4.63752e8i	1.88791	−	0.909170i
$800$	3.74644e8	+	8.55101e7i	0.731727	+	0.167012i
$801$	8.86222e7	+	2.02274e7i	0.172443	+	0.0393589i
$802$	−5.60020e7	+	4.46601e7i	−0.108563	+	0.0865758i
$803$	1.61823e7	−	3.36030e7i	0.0312532	−	0.0648980i
$804$	−3.48601e7	+	7.95659e6i	−0.0670749	+	0.0153094i
$805$	2.05999e9	+	9.92040e8i	3.94892	+	1.90170i
$806$	−8.82227e7	−	7.03553e7i	−0.168490	−	0.134367i
$807$	1.32511e9	+	3.02448e8i	2.52134	+	0.575480i
$808$	2.29781e8	+	1.83244e8i	0.435592	+	0.347373i
$809$	−1.48706e8	−	6.51525e8i	−0.280856	−	1.23051i	−0.896698	−	0.442642i	$-0.854041\pi$
$809$	−1.48706e8	−	6.51525e8i	−0.280856	−	1.23051i	0.615842	−	0.787870i	$-0.288816\pi$
$810$	−6.82592e8			−1.28442
$811$			6.43331e8i			1.20607i	0.797715	+	0.603034i	$0.206042\pi$
$811$			6.43331e8i			1.20607i	−0.797715	+	0.603034i	$0.793958\pi$
$812$	−7.64860e7	−	3.35107e8i	−0.142861	−	0.625915i
$813$	−3.74811e8	+	2.98902e8i	−0.697495	+	0.556234i
$814$	4.82509e7	−	2.32364e7i	0.0894606	−	0.0430820i
$815$	3.63029e7	+	1.74826e7i	0.0670608	+	0.0322948i
$816$		−	6.05564e8i		−	1.11452i
$817$	−4.89942e7	+	2.12546e8i	−0.0898419	+	0.389750i
$818$	5.69772e8			1.04098
$819$	−4.42293e8	+	9.18432e8i	−0.805116	+	1.67184i
$820$	3.73678e7	+	7.75950e7i	0.0677728	+	0.140732i
$821$	6.17788e8	+	7.74682e8i	1.11637	+	1.39989i	0.906523	+	0.422157i	$0.138727\pi$
$821$	6.17788e8	+	7.74682e8i	1.11637	+	1.39989i	0.209852	+	0.977733i	$0.432702\pi$
$822$	−8.42516e8	+	1.92299e8i	−1.51692	+	0.346227i
$823$	−3.05536e8			−0.548105			−0.274052	−	0.961715i	$-0.588364\pi$
$823$	−3.05536e8			−0.548105			−0.274052	+	0.961715i	$0.588364\pi$
$824$		−	4.29998e8i		−	0.768573i
$825$	9.79227e7	−	2.23502e7i	0.174390	−	0.0398034i
$826$	−4.74230e8	+	5.94665e8i	−0.841489	+	1.05519i
$827$	5.53320e7	−	2.42425e8i	0.0978272	−	0.428609i	−0.902169	−	0.431383i	$-0.858026\pi$
$827$	5.53320e7	−	2.42425e8i	0.0978272	−	0.428609i	0.999996	+	0.00277389i	$0.000882957\pi$
$828$	2.19667e8	−	2.75453e8i	0.386966	−	0.485240i
$829$	2.21295e7	−	4.59524e7i	0.0388426	−	0.0806574i	−0.880645	−	0.473778i	$-0.842890\pi$
$829$	2.21295e7	−	4.59524e7i	0.0388426	−	0.0806574i	0.919487	+	0.393120i	$0.128604\pi$
$830$	1.54006e8	+	6.74746e8i	0.269342	+	1.18006i
$831$	2.11399e8	+	1.01804e8i	0.368383	+	0.177404i
$832$	−5.17809e8	−	6.49311e8i	−0.899082	−	1.12741i
$833$	2.61067e8	−	1.14381e9i	0.451665	−	1.97887i
$834$	1.69941e8	−	7.44559e8i	0.292954	−	1.28352i
$835$	−5.64732e8	−	1.17268e9i	−0.970025	−	2.01428i
$836$	7.37253e6	−	5.87940e6i	0.0126182	−	0.0100627i
$837$	−1.28210e7	−	1.02244e7i	−0.0218648	−	0.0174366i
$838$	3.65151e8	−	1.75848e8i	0.620499	−	0.298816i
$839$	3.28350e8	+	6.81827e8i	0.555970	+	1.15448i	0.969748	+	0.244107i	$0.0784947\pi$
$839$	3.28350e8	+	6.81827e8i	0.555970	+	1.15448i	−0.413778	+	0.910378i	$0.635791\pi$
$840$	−1.23105e9	+	1.54368e9i	−2.07700	+	2.60447i
$841$	−1.64465e8	−	2.06233e8i	−0.276495	−	0.346713i
$842$	1.32237e8	−	6.36820e7i	0.221522	−	0.106679i
$843$	−3.60555e7	−	8.22942e6i	−0.0601850	−	0.0137368i
$844$	−4.77228e6	−	1.08924e6i	−0.00793777	−	0.00181174i
$845$	5.82075e8	−	4.64190e8i	0.964737	−	0.769352i
$846$	2.58566e8	−	5.36918e8i	0.427032	−	0.886741i
$847$	−8.90279e8	+	2.03200e8i	−1.46513	+	0.334406i
$848$	9.22544e7	+	4.44274e7i	0.151286	+	0.0728556i
$849$	−1.21185e9	−	9.66420e8i	−1.98028	−	1.57922i
$850$	8.38106e8	+	1.91292e8i	1.36472	+	0.311488i
$851$	1.01840e9	+	8.12146e8i	1.65245	+	1.31779i
$852$	−5.53924e6	−	2.42690e7i	−0.00895636	−	0.0392404i
$853$	6.29178e8			1.01374			0.506870	−	0.862022i	$-0.330802\pi$
$853$	6.29178e8			1.01374			0.506870	+	0.862022i	$0.330802\pi$
$854$		−	6.55551e8i		−	1.05253i
$855$	7.28032e7	+	3.18972e8i	0.116480	+	0.510333i
$856$	1.31174e8	−	1.04607e8i	0.209134	−	0.166779i
$857$	−7.93564e8	+	3.82160e8i	−1.26078	+	0.607160i	−0.940381	−	0.340123i	$-0.889531\pi$
$857$	−7.93564e8	+	3.82160e8i	−1.26078	+	0.607160i	−0.320399	+	0.947283i	$0.603817\pi$
$858$	−9.86566e7	−	4.75105e7i	−0.156194	−	0.0752191i
$859$		−	2.03267e8i		−	0.320691i	−0.987061	−	0.160346i	$-0.948739\pi$
$859$		−	2.03267e8i		−	0.320691i	0.987061	−	0.160346i	$-0.0512608\pi$
$860$	−3.25666e8	−	701727.i	−0.512009	−	0.00110325i
$861$	−4.08430e8			−0.639894
$862$	1.95514e8	−	4.05988e8i	0.305250	−	0.633858i
$863$	−5.20267e8	−	1.08035e9i	−0.809457	−	1.68086i	−0.729422	−	0.684064i	$-0.760211\pi$
$863$	−5.20267e8	−	1.08035e9i	−0.809457	−	1.68086i	−0.0800352	−	0.996792i	$-0.525503\pi$
$864$	−3.79597e7	−	4.75999e7i	−0.0588547	−	0.0738014i
$865$	7.79931e8	−	1.78014e8i	1.20506	−	0.275047i
$866$	8.52381e8			1.31244
$867$			1.22679e9i			1.88241i
$868$	−6.70810e7	+	1.53108e7i	−0.102575	+	0.0234120i
$869$	2.38619e7	−	2.99218e7i	0.0363618	−	0.0455962i
$870$	−2.85061e8	+	1.24893e9i	−0.432892	+	1.89662i
$871$	−7.96836e7	+	9.99200e7i	−0.120591	+	0.151216i
$872$	−6.09670e8	+	1.26599e9i	−0.919487	+	1.90933i
$873$	5.07394e6	+	2.22304e7i	0.00762610	+	0.0334121i
$874$	−3.82292e8	−	1.84102e8i	−0.572613	−	0.275756i
$875$	−1.20068e8	−	1.50561e8i	−0.179227	−	0.224744i
$876$	−4.52769e7	+	1.98371e8i	−0.0673541	+	0.295098i
$877$	5.39243e7	−	2.36258e8i	0.0799439	−	0.350257i	−0.919098	−	0.394030i	$-0.871081\pi$
$877$	5.39243e7	−	2.36258e8i	0.0799439	−	0.350257i	0.999042	+	0.0437727i	$0.0139377\pi$
$878$	−3.56225e8	−	7.39709e8i	−0.526309	−	1.09289i
$879$	5.57755e8	−	4.44795e8i	0.821253	−	0.654927i
$880$	−4.70305e7	−	3.75055e7i	−0.0690130	−	0.0550361i
$881$	−3.61637e8	+	1.74155e8i	−0.528866	+	0.254688i	−0.679208	−	0.733946i	$-0.737677\pi$
$881$	−3.61637e8	+	1.74155e8i	−0.528866	+	0.254688i	0.150342	+	0.988634i	$0.451962\pi$
$882$	−2.83818e8	−	5.89354e8i	−0.413651	−	0.858955i
$883$	−3.46066e8	+	4.33953e8i	−0.502663	+	0.630320i	−0.966828	−	0.255429i	$-0.917783\pi$
$883$	−3.46066e8	+	4.33953e8i	−0.502663	+	0.630320i	0.464164	+	0.885749i	$0.346355\pi$
$884$	3.15856e8	+	3.96071e8i	0.457228	+	0.573345i
$885$	−1.38055e9	+	6.64838e8i	−1.99169	+	0.959149i
$886$	2.00329e8	+	4.57238e7i	0.288033	+	0.0657418i
$887$	−1.27098e6	−	290093.i	−0.00182124	−	0.000415687i	0.221610	−	0.975135i	$-0.428869\pi$
$887$	−1.27098e6	−	290093.i	−0.00182124	−	0.000415687i	−0.223431	+	0.974720i	$0.571726\pi$
$888$	−8.79442e8	+	7.01331e8i	−1.25594	+	1.00158i
$889$	−4.88846e8	+	1.01510e9i	−0.695772	+	1.44479i
$890$	1.59357e8	−	3.63723e7i	0.226049	−	0.0515942i
$891$	−8.00689e7	−	3.85591e7i	−0.113196	−	0.0545123i
$892$	4.93589e6	+	3.93624e6i	0.00695458	+	0.00554609i
$893$	3.78224e8	+	8.63272e7i	0.531123	+	0.121225i
$894$	−5.18442e8	−	4.13443e8i	−0.725583	−	0.578633i
$895$	−1.84899e8	−	8.10097e8i	−0.257909	−	1.12997i
$896$	2.08811e8			0.290288
$897$		−	2.66334e9i		−	3.69019i
$898$	6.78976e7	+	2.97479e8i	0.0937617	+	0.410797i
$899$	−1.34376e8	+	1.07162e8i	−0.184946	+	0.147489i
$900$	−2.33426e8	+	1.12412e8i	−0.320201	+	0.154201i
$901$	−3.23638e8	−	1.55856e8i	−0.442471	−	0.213083i
$902$		−	2.07438e7i		−	0.0282663i
$903$	6.73098e8	−	1.39003e9i	0.914145	−	1.88783i
$904$	−4.17656e8			−0.565345
$905$	−9.74229e7	+	2.02301e8i	−0.131436	+	0.272930i
$906$	−1.06082e8	−	2.20281e8i	−0.142645	−	0.296206i
$907$	−2.65691e8	−	3.33166e8i	−0.356086	−	0.446518i	0.571234	−	0.820787i	$-0.306465\pi$
$907$	−2.65691e8	−	3.33166e8i	−0.356086	−	0.446518i	−0.927320	+	0.374269i	$0.877894\pi$
$908$	3.15642e8	−	7.20432e7i	0.421635	−	0.0962355i
$909$	−3.44833e8			−0.459110
$910$			1.83302e9i			2.43244i
$911$	3.08801e8	−	7.04817e7i	0.408435	−	0.0932226i	−0.0133669	−	0.999911i	$-0.504255\pi$
$911$	3.08801e8	−	7.04817e7i	0.408435	−	0.0932226i	0.421802	+	0.906688i	$0.361398\pi$
$912$	1.37042e8	−	1.71845e8i	0.180663	−	0.226544i
$913$	−2.00508e7	+	8.78482e7i	−0.0263462	+	0.115430i
$914$	4.29733e8	−	5.38869e8i	0.562808	−	0.705739i
$915$	5.73011e8	−	1.18987e9i	0.747996	−	1.55323i
$916$	−4.28334e7	−	1.87666e8i	−0.0557310	−	0.244173i
$917$	1.27101e9	+	6.12086e8i	1.64832	+	0.793787i
$918$	−8.49185e7	−	1.06484e8i	−0.109768	−	0.137644i
$919$	2.69693e8	−	1.18160e9i	0.347475	−	1.52239i	−0.435418	−	0.900228i	$-0.643399\pi$
$919$	2.69693e8	−	1.18160e9i	0.347475	−	1.52239i	0.782893	−	0.622157i	$-0.213743\pi$
$920$	5.42746e8	−	2.37793e9i	0.697000	−	3.05376i
$921$	4.57513e8	+	9.50037e8i	0.585632	+	1.21608i
$922$	3.44728e8	−	2.74912e8i	0.439829	−	0.350752i
$923$	−6.95626e7	−	5.54743e7i	−0.0884649	−	0.0705484i
$924$	−6.01570e7	+	2.89701e7i	−0.0762553	+	0.0367226i
$925$	−4.15608e8	−	8.63019e8i	−0.525120	−	1.09042i
$926$	−3.40034e8	+	4.26389e8i	−0.428242	+	0.536998i
$927$	3.14560e8	+	3.94446e8i	0.394880	+	0.495163i
$928$	−5.74916e8	+	2.76865e8i	−0.719384	+	0.346437i
$929$	−1.06416e9	−	2.42887e8i	−1.32727	−	0.302941i	−0.500625	−	0.865664i	$-0.666897\pi$
$929$	−1.06416e9	−	2.42887e8i	−1.32727	−	0.302941i	−0.826645	+	0.562723i	$0.809754\pi$
$930$	2.50009e8	+	5.70629e7i	0.310818	+	0.0709422i
$931$	3.32934e8	−	2.65506e8i	0.412581	−	0.329022i
$932$	8.33983e7	−	1.73178e8i	0.103017	−	0.213917i
$933$	1.28959e9	−	2.94341e8i	1.58784	−	0.362415i
$934$	−8.55749e8	−	4.12107e8i	−1.05028	−	0.505789i
$935$	1.64988e8	+	1.31573e8i	0.201844	+	0.160965i
$936$	1.06018e9	+	2.41979e8i	1.29286	+	0.295087i
$937$	−4.15666e8	−	3.31482e8i	−0.505272	−	0.402941i	0.337406	−	0.941359i	$-0.390451\pi$
$937$	−4.15666e8	−	3.31482e8i	−0.505272	−	0.402941i	−0.842678	+	0.538418i	$0.819022\pi$
$938$	−3.20806e7	−	1.40554e8i	−0.0388717	−	0.170308i
$939$	3.19457e8			0.385848
$940$			5.79236e8i			0.697384i
$941$	−1.93668e7	−	8.48516e7i	−0.0232429	−	0.101834i	0.961976	−	0.273134i	$-0.0880603\pi$
$941$	−1.93668e7	−	8.48516e7i	−0.0232429	−	0.101834i	−0.985219	+	0.171300i	$0.945203\pi$
$942$	2.09263e8	−	1.66882e8i	0.250346	−	0.199644i
$943$	4.54578e8	−	2.18913e8i	0.542092	−	0.261058i
$944$	4.38519e8	+	2.11180e8i	0.521282	+	0.251036i
$945$			2.66384e8i			0.315655i
$946$	7.05987e7	+	3.41861e7i	0.0833918	+	0.0403809i
$947$	1.38631e9			1.63234			0.816168	−	0.577815i	$-0.196094\pi$
$947$	1.38631e9			1.63234			0.816168	+	0.577815i	$0.196094\pi$
$948$	−9.05911e7	+	1.88114e8i	−0.106331	+	0.220799i
$949$	3.15546e8	+	6.55237e8i	0.369202	+	0.766655i
$950$	1.94545e8	+	2.43952e8i	0.226908	+	0.284534i
$951$	5.98667e8	−	1.36642e8i	0.696056	−	0.158870i
$952$	−2.20016e9			−2.55001
$953$		−	6.07906e7i		−	0.0702357i	−0.999383	−	0.0351179i	$-0.988819\pi$
$953$		−	6.07906e7i		−	0.0702357i	0.999383	−	0.0351179i	$-0.0111807\pi$
$954$	−1.95257e8	+	4.45662e7i	−0.224886	+	0.0513288i
$955$	1.45520e8	−	1.82476e8i	0.167075	−	0.209506i
$956$	7.71377e7	−	3.37962e8i	0.0882862	−	0.386807i
$957$	−1.03989e8	+	1.30398e8i	−0.118646	+	0.148777i
$958$	2.73089e8	−	5.67076e8i	0.310605	−	0.644978i
$959$	4.19102e8	+	1.83621e9i	0.475187	+	2.08193i
$960$	1.70046e9	+	8.18896e8i	1.92199	+	0.925582i
$961$	−5.31898e8	−	6.66979e8i	−0.599319	−	0.751523i
$962$	−2.32374e8	+	1.01810e9i	−0.261013	+	1.14357i
$963$	−4.38038e7	+	1.91917e8i	−0.0490493	+	0.214899i
$964$	−4.52111e7	−	9.38818e7i	−0.0504677	−	0.104797i
$965$	−1.47204e9	+	1.17391e9i	−1.63809	+	1.30633i
$966$	2.34894e9	+	1.87322e9i	2.60579	+	2.07805i
$967$	−9.68086e8	+	4.66206e8i	−1.07062	+	0.515582i	−0.884306	−	0.466908i	$-0.845368\pi$
$967$	−9.68086e8	+	4.66206e8i	−1.07062	+	0.515582i	−0.186312	+	0.982491i	$0.559654\pi$
$968$	4.22665e8	+	8.77674e8i	0.465984	+	0.967625i
$969$	−4.80757e8	+	6.02850e8i	−0.528390	+	0.662580i
$970$	2.55643e7	+	3.20566e7i	0.0280104	+	0.0351239i
$971$	3.02728e8	−	1.45786e8i	0.330670	−	0.159242i	−0.261181	−	0.965290i	$-0.584112\pi$
$971$	3.02728e8	−	1.45786e8i	0.330670	−	0.159242i	0.591851	+	0.806048i	$0.298398\pi$
$972$	4.28056e8	+	9.77011e7i	0.466125	+	0.106390i
$973$	−1.62272e9	−	3.70374e8i	−1.76159	−	0.402071i
$974$	5.54934e8	−	4.42545e8i	0.600571	−	0.478940i
$975$	−8.49777e8	+	1.76458e9i	−0.916835	+	1.90383i
$976$	−4.08977e8	+	9.33463e7i	−0.439895	+	0.100403i
$977$	−1.32299e9	−	6.37119e8i	−1.41864	−	0.683183i	−0.441796	−	0.897116i	$-0.645658\pi$
$977$	−1.32299e9	−	6.37119e8i	−1.41864	−	0.683183i	−0.976848	+	0.213933i	$0.931373\pi$
$978$	4.13949e7	+	3.30114e7i	0.0442518	+	0.0352896i
$979$	2.07475e7	+	4.73547e6i	0.0221114	+	0.00504679i
$980$	4.97092e8	+	3.96418e8i	0.528152	+	0.421187i
$981$	−3.66860e8	−	1.60732e9i	−0.388592	−	1.70253i
$982$	1.80101e8			0.190187
$983$		−	1.58220e9i		−	1.66572i	−0.553484	−	0.832860i	$-0.686702\pi$
$983$		−	1.58220e9i		−	1.66572i	0.553484	−	0.832860i	$-0.313298\pi$
$984$	9.69523e7	+	4.24776e8i	0.101759	+	0.445836i
$985$	1.63661e9	−	1.30515e9i	1.71252	−	1.36569i
$986$	−1.28613e9	+	6.19367e8i	−1.34170	+	0.646127i
$987$	−2.47491e9	−	1.19185e9i	−2.57400	−	1.23957i
$988$			1.83876e8i			0.190657i
$989$	−4.11095e6	+	1.90786e9i	−0.00424966	+	1.97223i
$990$	1.17659e8			0.121260
$991$	−7.02427e8	+	1.45860e9i	−0.721739	+	1.49871i	0.139345	+	0.990244i	$0.455500\pi$
$991$	−7.02427e8	+	1.45860e9i	−0.721739	+	1.49871i	−0.861084	+	0.508463i	$0.830214\pi$
$992$	5.54223e7	+	1.15086e8i	0.0567740	+	0.117892i
$993$	−3.49545e8	−	4.38315e8i	−0.356989	−	0.447650i
$994$	9.78516e7	−	2.23340e7i	0.0996342	−	0.0227409i
$995$	−8.52152e8			−0.865063
$996$		−	4.91584e8i		−	0.497530i
$997$	1.81642e9	−	4.14586e8i	1.83287	−	0.418340i	0.840517	−	0.541785i	$-0.182251\pi$
$997$	1.81642e9	−	4.14586e8i	1.83287	−	0.418340i	0.992351	+	0.123445i	$0.0393942\pi$
$998$	5.86654e8	−	7.35641e8i	0.590188	−	0.740072i
$999$	−3.37698e7	+	1.47955e8i	−0.0338713	+	0.148400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.22.15	yes	126
43.2	odd	14	inner	43.7.f.a.2.15	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.15	✓	126	43.2	odd	14	inner
43.7.f.a.22.15	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)

\(f(q)\)	\(=\)	\(q+(2.79658 - 5.80715i) q^{2} +(-16.1345 - 33.5037i) q^{3} +(14.0012 + 17.5569i) q^{4} +(-177.830 + 40.5886i) q^{5} -239.682 q^{6} +522.371i q^{7} +(543.278 - 124.000i) q^{8} +(-407.649 + 511.176i) q^{9} +O(q^{10})\)	\(q+(2.79658 - 5.80715i) q^{2} +(-16.1345 - 33.5037i) q^{3} +(14.0012 + 17.5569i) q^{4} +(-177.830 + 40.5886i) q^{5} -239.682 q^{6} +522.371i q^{7} +(543.278 - 124.000i) q^{8} +(-407.649 + 511.176i) q^{9} +(-261.612 + 1146.20i) q^{10} +(-95.4353 + 119.672i) q^{11} +(362.319 - 752.362i) q^{12} +(-664.158 - 2909.87i) q^{13} +(3033.49 + 1460.85i) q^{14} +(4229.08 + 5303.09i) q^{15} +(479.428 - 2100.51i) q^{16} +(-1681.88 + 7368.81i) q^{17} +(1828.45 + 3796.82i) q^{18} +(-2144.88 + 1710.48i) q^{19} +(-3202.44 - 2553.86i) q^{20} +(17501.4 - 8428.21i) q^{21} +(428.062 + 888.880i) q^{22} +(-14961.4 + 18761.0i) q^{23} +(-12920.0 - 16201.1i) q^{24} +(15898.6 - 7656.35i) q^{25} +(-18755.4 - 4280.80i) q^{26} +(-2725.63 - 622.108i) q^{27} +(-9171.22 + 7313.81i) q^{28} +(-12713.6 + 26400.2i) q^{29} +(42622.8 - 9728.38i) q^{30} +(5284.73 + 2544.99i) q^{31} +(17025.9 + 13577.7i) q^{32} +(5549.26 + 1266.58i) q^{33} +(38088.3 + 30374.4i) q^{34} +(-21202.3 - 92893.5i) q^{35} -14682.2 q^{36} -54282.8i q^{37} +(3934.72 + 17239.1i) q^{38} +(-86775.3 + 69201.0i) q^{39} +(-91578.3 + 44101.8i) q^{40} +(-18943.7 - 9122.82i) q^{41} -125203. i q^{42} +(62267.7 - 49437.7i) q^{43} -3437.28 q^{44} +(51744.5 - 107448. i) q^{45} +(67107.3 + 139350. i) q^{46} +(-88169.2 - 110561. i) q^{47} +(-78110.2 + 17828.1i) q^{48} -155223. q^{49} -113737. i q^{50} +(274018. - 62542.9i) q^{51} +(41789.3 - 52402.1i) q^{52} +(-10575.4 + 46333.7i) q^{53} +(-11235.1 + 14088.4i) q^{54} +(12114.0 - 25154.9i) q^{55} +(64773.8 + 283793. i) q^{56} +(91913.9 + 44263.4i) q^{57} +(117755. + 147660. i) q^{58} +(-50268.6 + 220241. i) q^{59} +(-33893.9 + 148499. i) q^{60} +(-84478.6 - 175422. i) q^{61} +(29558.3 - 23572.0i) q^{62} +(-267024. - 212944. i) q^{63} +(250697. - 120729. i) q^{64} +(236215. + 490505. i) q^{65} +(22874.2 - 28683.3i) q^{66} +(-26697.3 - 33477.4i) q^{67} +(-152922. + 73643.2i) q^{68} +(869957. + 198562. i) q^{69} +(-598741. - 136659. i) q^{70} +(23306.4 - 18586.2i) q^{71} +(-158081. + 328259. i) q^{72} +(-237553. + 54220.0i) q^{73} +(-315228. - 151806. i) q^{74} +(-513032. - 409129. i) q^{75} +(-60061.5 - 13708.6i) q^{76} +(-62513.3 - 49852.7i) q^{77} +(159187. + 697444. i) q^{78} -250032. q^{79} +392994. i q^{80} +(129195. + 566039. i) q^{81} +(-105955. + 84496.5i) q^{82} +(530384. - 255419. i) q^{83} +(393013. + 189265. i) q^{84} -1.37866e6i q^{85} +(-112956. - 499855. i) q^{86} +1.08963e6 q^{87} +(-37008.6 + 76849.1i) q^{88} +(-60323.4 - 125263. i) q^{89} +(-479263. - 600976. i) q^{90} +(1.52003e6 - 346937. i) q^{91} -538862. q^{92} -218120. i q^{93} +(-888615. + 202821. i) q^{94} +(311998. - 391233. i) q^{95} +(180199. - 789502. i) q^{96} +(21744.4 - 27266.6i) q^{97} +(-434093. + 901403. i) q^{98} +(-22269.4 - 97568.4i) 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

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Representations

Groups

Database

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