LMFDB - Embedded newform 91.8.f.a.22.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.19
Character	$\chi$	$=$	91.22
Dual form			91.8.f.a.29.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.11392 - 10.5896i) q^{2} +(-32.6404 + 56.5348i) q^{3} +(-10.7599 - 18.6367i) q^{4} -72.0010 q^{5} +(399.121 + 691.298i) q^{6} +(171.500 + 297.047i) q^{7} +1302.02 q^{8} +(-1037.29 - 1796.63i) q^{9} +O(q^{10})$	\(q+(6.11392 - 10.5896i) q^{2} +(-32.6404 + 56.5348i) q^{3} +(-10.7599 - 18.6367i) q^{4} -72.0010 q^{5} +(399.121 + 691.298i) q^{6} +(171.500 + 297.047i) q^{7} +1302.02 q^{8} +(-1037.29 - 1796.63i) q^{9} +(-440.208 + 762.462i) q^{10} +(-1731.44 + 2998.95i) q^{11} +1404.83 q^{12} +(6757.23 + 4133.81i) q^{13} +4194.15 q^{14} +(2350.14 - 4070.56i) q^{15} +(9337.72 - 16173.4i) q^{16} +(-2819.23 - 4883.05i) q^{17} -25367.6 q^{18} +(-16998.0 - 29441.4i) q^{19} +(774.725 + 1341.86i) q^{20} -22391.3 q^{21} +(21171.8 + 36670.6i) q^{22} +(-42542.6 + 73686.0i) q^{23} +(-42498.5 + 73609.5i) q^{24} -72940.9 q^{25} +(85088.6 - 46282.7i) q^{26} -7339.19 q^{27} +(3690.65 - 6392.40i) q^{28} +(-86557.6 + 149922. i) q^{29} +(-28737.1 - 49774.1i) q^{30} -129350. q^{31} +(-30850.7 - 53434.9i) q^{32} +(-113030. - 195773. i) q^{33} -68946.2 q^{34} +(-12348.2 - 21387.7i) q^{35} +(-22322.3 + 38663.3i) q^{36} +(-79482.0 + 137667. i) q^{37} -415697. q^{38} +(-454262. + 247089. i) q^{39} -93746.8 q^{40} +(185401. - 321124. i) q^{41} +(-136898. + 237115. i) q^{42} +(-148840. - 257798. i) q^{43} +74520.8 q^{44} +(74685.7 + 129359. i) q^{45} +(520204. + 901020. i) q^{46} +838918. q^{47} +(609573. + 1.05581e6i) q^{48} +(-58824.5 + 101887. i) q^{49} +(-445954. + 772415. i) q^{50} +368083. q^{51} +(4333.47 - 170412. i) q^{52} -712974. q^{53} +(-44871.2 + 77719.2i) q^{54} +(124666. - 215927. i) q^{55} +(223297. + 386761. i) q^{56} +2.21928e6 q^{57} +(1.05841e6 + 1.83322e6i) q^{58} +(-163838. - 283775. i) q^{59} -101149. q^{60} +(-482597. - 835883. i) q^{61} +(-790833. + 1.36976e6i) q^{62} +(355790. - 616246. i) q^{63} +1.63598e6 q^{64} +(-486527. - 297638. i) q^{65} -2.76422e6 q^{66} +(-2.39613e6 + 4.15022e6i) q^{67} +(-60669.5 + 105083. i) q^{68} +(-2.77721e6 - 4.81028e6i) q^{69} -301983. q^{70} +(-852954. - 1.47736e6i) q^{71} +(-1.35057e6 - 2.33926e6i) q^{72} +3.27634e6 q^{73} +(971892. + 1.68337e6i) q^{74} +(2.38082e6 - 4.12370e6i) q^{75} +(-365794. + 633575. i) q^{76} -1.18777e6 q^{77} +(-160743. + 6.32115e6i) q^{78} -7.68282e6 q^{79} +(-672325. + 1.16450e6i) q^{80} +(2.50810e6 - 4.34416e6i) q^{81} +(-2.26705e6 - 3.92665e6i) q^{82} -411017. q^{83} +(240929. + 417301. i) q^{84} +(202988. + 351585. i) q^{85} -3.63997e6 q^{86} +(-5.65054e6 - 9.78703e6i) q^{87} +(-2.25438e6 + 3.90469e6i) q^{88} +(-2.71121e6 + 4.69596e6i) q^{89} +1.82649e6 q^{90} +(-69070.2 + 2.71616e6i) q^{91} +1.83102e6 q^{92} +(4.22202e6 - 7.31275e6i) q^{93} +(5.12907e6 - 8.88381e6i) q^{94} +(1.22387e6 + 2.11981e6i) q^{95} +4.02791e6 q^{96} +(3.42895e6 + 5.93911e6i) q^{97} +(719296. + 1.24586e6i) q^{98} +7.18401e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	6.11392	−	10.5896i	0.540399	−	0.935998i	−0.458482	−	0.888704i	$-0.651607\pi$
$2$	6.11392	−	10.5896i	0.540399	−	0.935998i	0.998881	−	0.0472947i	$-0.0150600\pi$
$3$	−32.6404	+	56.5348i	−0.697960	+	1.20890i	0.271212	+	0.962520i	$0.412575\pi$
$3$	−32.6404	+	56.5348i	−0.697960	+	1.20890i	−0.969173	+	0.246383i	$0.920758\pi$
$4$	−10.7599	−	18.6367i	−0.0840619	−	0.145599i
$5$	−72.0010			−0.257598			−0.128799	−	0.991671i	$-0.541112\pi$
$5$	−72.0010			−0.257598			−0.128799	+	0.991671i	$0.541112\pi$
$6$	399.121	+	691.298i	0.754354	+	1.30658i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$	1302.02			0.899090
$9$	−1037.29	−	1796.63i	−0.474297	−	0.821506i
$10$	−440.208	+	762.462i	−0.139206	+	0.241112i
$11$	−1731.44	+	2998.95i	−0.392224	+	0.679351i	−0.992743	−	0.120259i	$-0.961627\pi$
$11$	−1731.44	+	2998.95i	−0.392224	+	0.679351i	0.600519	+	0.799611i	$0.294961\pi$
$12$	1404.83			0.234687
$13$	6757.23	+	4133.81i	0.853035	+	0.521854i
$13$	6757.23	+	4133.81i	0.853035	+	0.521854i
$14$	4194.15			0.408503
$15$	2350.14	−	4070.56i	0.179794	−	0.311411i
$16$	9337.72	−	16173.4i	0.569929	−	0.987146i
$17$	−2819.23	−	4883.05i	−0.139175	−	0.241057i	0.788010	−	0.615663i	$-0.211112\pi$
$17$	−2819.23	−	4883.05i	−0.139175	−	0.241057i	−0.927184	+	0.374605i	$0.877778\pi$
$18$	−25367.6			−1.02524
$19$	−16998.0	−	29441.4i	−0.568539	−	0.984738i	−0.996711	−	0.0810411i	$-0.974176\pi$
$19$	−16998.0	−	29441.4i	−0.568539	−	0.984738i	0.428172	−	0.903697i	$-0.359158\pi$
$20$	774.725	+	1341.86i	0.0216542	+	0.0375062i
$21$	−22391.3			−0.527608
$22$	21171.8	+	36670.6i	0.423914	+	0.734241i
$23$	−42542.6	+	73686.0i	−0.729083	+	1.26281i	0.228188	+	0.973617i	$0.426720\pi$
$23$	−42542.6	+	73686.0i	−0.729083	+	1.26281i	−0.957271	+	0.289192i	$0.906614\pi$
$24$	−42498.5	+	73609.5i	−0.627529	+	1.08691i
$25$	−72940.9			−0.933643
$26$	85088.6	−	46282.7i	0.949433	−	0.516430i
$27$	−7339.19			−0.0717588
$28$	3690.65	−	6392.40i	0.0317724	−	0.0550314i
$29$	−86557.6	+	149922.i	−0.659041	+	1.14149i	0.321824	+	0.946800i	$0.395704\pi$
$29$	−86557.6	+	149922.i	−0.659041	+	1.14149i	−0.980864	+	0.194692i	$0.937629\pi$
$30$	−28737.1	−	49774.1i	−0.194320	−	0.336573i
$31$	−129350.			−0.779829			−0.389914	−	0.920851i	$-0.627495\pi$
$31$	−129350.			−0.779829			−0.389914	+	0.920851i	$0.627495\pi$
$32$	−30850.7	−	53434.9i	−0.166433	−	0.288271i
$33$	−113030.	−	195773.i	−0.547513	−	0.948320i
$34$	−68946.2			−0.300839
$35$	−12348.2	−	21387.7i	−0.0486815	−	0.0843189i
$36$	−22322.3	+	38663.3i	−0.0797406	+	0.138115i
$37$	−79482.0	+	137667.i	−0.257966	+	0.446810i	−0.965697	−	0.259672i	$-0.916386\pi$
$37$	−79482.0	+	137667.i	−0.257966	+	0.446810i	0.707731	+	0.706482i	$0.249719\pi$
$38$	−415697.			−1.22895
$39$	−454262.	+	247089.i	−1.22625	+	0.667003i
$40$	−93746.8			−0.231604
$41$	185401.	−	321124.i	0.420116	−	0.727662i	−0.575835	−	0.817566i	$-0.695323\pi$
$41$	185401.	−	321124.i	0.420116	−	0.727662i	0.995950	+	0.0899042i	$0.0286561\pi$
$42$	−136898.	+	237115.i	−0.285119	+	0.493841i
$43$	−148840.	−	257798.i	−0.285482	−	0.494470i	0.687244	−	0.726427i	$-0.258820\pi$
$43$	−148840.	−	257798.i	−0.285482	−	0.494470i	−0.972726	+	0.231957i	$0.925487\pi$
$44$	74520.8			0.131884
$45$	74685.7	+	129359.i	0.122178	+	0.211619i
$46$	520204.	+	901020.i	0.787991	+	1.36484i
$47$	838918.			1.17863			0.589314	−	0.807904i	$-0.299398\pi$
$47$	838918.			1.17863			0.589314	+	0.807904i	$0.299398\pi$
$48$	609573.	+	1.05581e6i	0.795576	+	1.37798i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	−445954.	+	772415.i	−0.504540	+	0.873888i
$51$	368083.			0.388553
$52$	4333.47	−	170412.i	0.00427390	−	0.168069i
$53$	−712974.			−0.657822			−0.328911	−	0.944361i	$-0.606682\pi$
$53$	−712974.			−0.657822			−0.328911	+	0.944361i	$0.606682\pi$
$54$	−44871.2	+	77719.2i	−0.0387784	+	0.0671661i
$55$	124666.	−	215927.i	0.101036	−	0.175000i
$56$	223297.	+	386761.i	0.169912	+	0.294296i
$57$	2.21928e6			1.58727
$58$	1.05841e6	+	1.83322e6i	0.712290	+	1.23372i
$59$	−163838.	−	283775.i	−0.103856	−	0.179884i	0.809414	−	0.587238i	$-0.199785\pi$
$59$	−163838.	−	283775.i	−0.103856	−	0.179884i	−0.913270	+	0.407354i	$0.866451\pi$
$60$	−101149.			−0.0604551
$61$	−482597.	−	835883.i	−0.272226	−	0.471510i	0.697205	−	0.716872i	$-0.254427\pi$
$61$	−482597.	−	835883.i	−0.272226	−	0.471510i	−0.969432	+	0.245362i	$0.921093\pi$
$62$	−790833.	+	1.36976e6i	−0.421419	+	0.729919i
$63$	355790.	−	616246.i	0.179267	−	0.310500i
$64$	1.63598e6			0.780097
$65$	−486527.	−	297638.i	−0.219741	−	0.134429i
$66$	−2.76422e6			−1.18350
$67$	−2.39613e6	+	4.15022e6i	−0.973305	+	1.68581i	−0.287886	+	0.957665i	$0.592952\pi$
$67$	−2.39613e6	+	4.15022e6i	−0.973305	+	1.68581i	−0.685419	+	0.728149i	$0.740381\pi$
$68$	−60669.5	+	105083.i	−0.0233986	+	0.0405275i
$69$	−2.77721e6	−	4.81028e6i	−1.01774	−	1.76278i
$70$	−301983.			−0.105230
$71$	−852954.	−	1.47736e6i	−0.282827	−	0.489871i	0.689253	−	0.724521i	$-0.257939\pi$
$71$	−852954.	−	1.47736e6i	−0.282827	−	0.489871i	−0.972080	+	0.234650i	$0.924606\pi$
$72$	−1.35057e6	−	2.33926e6i	−0.426436	−	0.738608i
$73$	3.27634e6			0.985731			0.492866	−	0.870105i	$-0.335949\pi$
$73$	3.27634e6			0.985731			0.492866	+	0.870105i	$0.335949\pi$
$74$	971892.	+	1.68337e6i	0.278809	+	0.482912i
$75$	2.38082e6	−	4.12370e6i	0.651646	−	1.12868i
$76$	−365794.	+	633575.i	−0.0955849	+	0.165558i
$77$	−1.18777e6			−0.296493
$78$	−160743.	+	6.32115e6i	−0.0383530	+	1.50822i
$79$	−7.68282e6			−1.75318			−0.876589	−	0.481240i	$-0.840187\pi$
$79$	−7.68282e6			−1.75318			−0.876589	+	0.481240i	$0.840187\pi$
$80$	−672325.	+	1.16450e6i	−0.146813	+	0.254287i
$81$	2.50810e6	−	4.34416e6i	0.524382	−	0.908256i
$82$	−2.26705e6	−	3.92665e6i	−0.454060	−	0.786455i
$83$	−411017.			−0.0789017			−0.0394509	−	0.999222i	$-0.512561\pi$
$83$	−411017.			−0.0789017			−0.0394509	+	0.999222i	$0.512561\pi$
$84$	240929.	+	417301.i	0.0443518	+	0.0768195i
$85$	202988.	+	351585.i	0.0358511	+	0.0620960i
$86$	−3.63997e6			−0.617098
$87$	−5.65054e6	−	9.78703e6i	−0.919968	−	1.59343i
$88$	−2.25438e6	+	3.90469e6i	−0.352644	+	0.610798i
$89$	−2.71121e6	+	4.69596e6i	−0.407661	+	0.706089i	−0.994627	−	0.103522i	$-0.966989\pi$
$89$	−2.71121e6	+	4.69596e6i	−0.407661	+	0.706089i	0.586966	+	0.809611i	$0.300322\pi$
$90$	1.82649e6			0.264100
$91$	−69070.2	+	2.71616e6i	−0.00960828	+	0.377842i
$92$	1.83102e6			0.245152
$93$	4.22202e6	−	7.31275e6i	0.544290	−	0.942737i
$94$	5.12907e6	−	8.88381e6i	0.636929	−	1.10319i
$95$	1.22387e6	+	2.11981e6i	0.146455	+	0.253667i
$96$	4.02791e6			0.464655
$97$	3.42895e6	+	5.93911e6i	0.381469	+	0.660724i	0.991273	−	0.131829i	$-0.0420849\pi$
$97$	3.42895e6	+	5.93911e6i	0.381469	+	0.660724i	−0.609803	+	0.792553i	$0.708752\pi$
$98$	719296.	+	1.24586e6i	0.0771998	+	0.133714i
$99$	7.18401e6			0.744122
$100$	784838.	+	1.35938e6i	0.0784838	+	0.135938i
$101$	4.59813e6	−	7.96420e6i	0.444075	−	0.769161i	−0.553912	−	0.832575i	$-0.686866\pi$
$101$	4.59813e6	−	7.96420e6i	0.444075	−	0.769161i	0.997987	+	0.0634144i	$0.0201990\pi$
$102$	2.25043e6	−	3.89786e6i	0.209974	−	0.363685i
$103$	−1.43896e6			−0.129754			−0.0648768	−	0.997893i	$-0.520665\pi$
$103$	−1.43896e6			−0.129754			−0.0648768	+	0.997893i	$0.520665\pi$
$104$	8.79805e6	+	5.38231e6i	0.766955	+	0.469193i
$105$	1.61219e6			0.135911
$106$	−4.35906e6	+	7.55012e6i	−0.355486	+	0.615720i
$107$	7.28621e6	−	1.26201e7i	0.574988	−	0.995908i	−0.421055	−	0.907035i	$-0.638340\pi$
$107$	7.28621e6	−	1.26201e7i	0.574988	−	0.995908i	0.996043	−	0.0888731i	$-0.0283265\pi$
$108$	78969.1	+	136779.i	0.00603218	+	0.0104480i
$109$	1.58679e7			1.17362			0.586809	−	0.809725i	$-0.300384\pi$
$109$	1.58679e7			1.17362			0.586809	+	0.809725i	$0.300384\pi$
$110$	−1.52439e6	−	2.64032e6i	−0.109200	−	0.189139i
$111$	−5.18864e6	−	8.98699e6i	−0.360100	−	0.623712i
$112$	6.40567e6			0.430826
$113$	1.31058e7	+	2.26999e7i	0.854454	+	1.47996i	0.877151	+	0.480215i	$0.159442\pi$
$113$	1.31058e7	+	2.26999e7i	0.854454	+	1.47996i	−0.0226965	+	0.999742i	$0.507225\pi$
$114$	1.35685e7	−	2.35014e7i	0.857759	−	1.48568i
$115$	3.06311e6	−	5.30546e6i	0.187811	−	0.325298i
$116$	3.72541e6			0.221601
$117$	417759.	−	1.64282e7i	0.0241143	−	0.948287i
$118$	−4.00676e6			−0.224495
$119$	966997.	−	1.67489e6i	0.0526030	−	0.0911111i
$120$	3.05993e6	−	5.29995e6i	0.161651	−	0.279987i
$121$	3.74780e6	+	6.49138e6i	0.192321	+	0.333110i
$122$	−1.18022e7			−0.588443
$123$	1.21031e7	+	2.09632e7i	0.586448	+	1.01576i
$124$	1.39179e6	+	2.41066e6i	0.0655539	+	0.113543i
$125$	1.08769e7			0.498104
$126$	−4.35054e6	−	7.53535e6i	−0.193752	−	0.335588i
$127$	−1.99625e7	+	3.45761e7i	−0.864773	+	1.49783i	0.00249901	+	0.999997i	$0.499205\pi$
$127$	−1.99625e7	+	3.45761e7i	−0.864773	+	1.49783i	−0.867272	+	0.497834i	$0.834129\pi$
$128$	1.39511e7	−	2.41641e7i	0.587997	−	1.01844i
$129$	1.94327e7			0.797022
$130$	−6.12646e6	+	3.33240e6i	−0.244573	+	0.133032i
$131$	−2.23636e7			−0.869145			−0.434572	−	0.900637i	$-0.643100\pi$
$131$	−2.23636e7			−0.869145			−0.434572	+	0.900637i	$0.643100\pi$
$132$	−2.43239e6	+	4.21301e6i	−0.0920500	+	0.159435i
$133$	5.83031e6	−	1.00984e7i	0.214888	−	0.372196i
$134$	2.92995e7	+	5.07482e7i	1.05195	+	1.82202i
$135$	528429.			0.0184850
$136$	−3.67070e6	−	6.35784e6i	−0.125130	−	0.216732i
$137$	−5.65117e6	−	9.78811e6i	−0.187766	−	0.325220i	0.756739	−	0.653717i	$-0.226791\pi$
$137$	−5.65117e6	−	9.78811e6i	−0.187766	−	0.325220i	−0.944505	+	0.328497i	$0.893458\pi$
$138$	−6.79186e7			−2.19995
$139$	−434111.	−	751902.i	−0.0137103	−	0.0237470i	0.859089	−	0.511827i	$-0.171031\pi$
$139$	−434111.	−	751902.i	−0.0137103	−	0.0237470i	−0.872799	+	0.488079i	$0.837698\pi$
$140$	−265731.	+	460259.i	−0.00818453	+	0.0141760i
$141$	−2.73826e7	+	4.74280e7i	−0.822636	+	1.42485i
$142$	−2.08596e7			−0.611358
$143$	−2.40968e7	+	1.31071e7i	−0.689102	+	0.374827i
$144$	−3.87436e7			−1.08126
$145$	6.23223e6	−	1.07945e7i	0.169768	−	0.294047i
$146$	2.00312e7	−	3.46951e7i	0.532688	−	0.922643i
$147$	−3.84011e6	−	6.65126e6i	−0.0997086	−	0.172700i
$148$	3.42088e6			0.0867405
$149$	−1.34363e7	−	2.32724e7i	−0.332758	−	0.576354i	0.650293	−	0.759683i	$-0.274646\pi$
$149$	−1.34363e7	−	2.32724e7i	−0.332758	−	0.576354i	−0.983052	+	0.183329i	$0.941313\pi$
$150$	−2.91122e7	−	5.04239e7i	−0.704297	−	1.21988i
$151$	5.71461e7			1.35073			0.675363	−	0.737485i	$-0.263987\pi$
$151$	5.71461e7			1.35073			0.675363	+	0.737485i	$0.263987\pi$
$152$	−2.21318e7	−	3.83333e7i	−0.511168	−	0.885368i
$153$	−5.84871e6	+	1.01303e7i	−0.132020	+	0.228666i
$154$	−7.26192e6	+	1.25780e7i	−0.160225	+	0.277517i
$155$	9.31330e6			0.200883
$156$	9.49277e6	+	5.80731e6i	0.200197	+	0.122473i
$157$	−3.52998e7			−0.727986			−0.363993	−	0.931402i	$-0.618587\pi$
$157$	−3.52998e7			−0.727986			−0.363993	+	0.931402i	$0.618587\pi$
$158$	−4.69721e7	+	8.13581e7i	−0.947415	+	1.64097i
$159$	2.32717e7	−	4.03078e7i	0.459133	−	0.795242i
$160$	2.22128e6	+	3.84737e6i	0.0428729	+	0.0742581i
$161$	−2.91842e7			−0.551135
$162$	−3.06686e7	−	5.31196e7i	−0.566751	−	0.981641i
$163$	3.63722e7	+	6.29985e7i	0.657829	+	1.13939i	0.981176	+	0.193113i	$0.0618585\pi$
$163$	3.63722e7	+	6.29985e7i	0.657829	+	1.13939i	−0.323347	+	0.946280i	$0.604808\pi$
$164$	−7.97961e6			−0.141263
$165$	8.13826e6	+	1.40959e7i	0.141038	+	0.244286i
$166$	−2.51292e6	+	4.35251e6i	−0.0426384	+	0.0738519i
$167$	2.80895e6	−	4.86524e6i	0.0466698	−	0.0808344i	−0.841747	−	0.539872i	$-0.818472\pi$
$167$	2.80895e6	−	4.86524e6i	0.0466698	−	0.0808344i	0.888417	+	0.459038i	$0.151806\pi$
$168$	−2.91539e7			−0.474367
$169$	2.85717e7	+	5.58662e7i	0.455337	+	0.890319i
$170$	4.96419e6			0.0774957
$171$	−3.52636e7	+	6.10784e7i	−0.539313	+	0.934117i
$172$	−3.20301e6	+	5.54777e6i	−0.0479964	+	0.0831322i
$173$	2.65236e7	+	4.59402e7i	0.389467	+	0.674576i	0.992378	−	0.123232i	$-0.0393260\pi$
$173$	2.65236e7	+	4.59402e7i	0.389467	+	0.674576i	−0.602911	+	0.797808i	$0.705993\pi$
$174$	−1.38188e8			−1.98860
$175$	−1.25094e7	−	2.16668e7i	−0.176442	−	0.305606i
$176$	3.23354e7	+	5.60066e7i	0.447079	+	0.774364i
$177$	2.13909e7			0.289949
$178$	3.31523e7	+	5.74214e7i	0.440599	+	0.763140i
$179$	−1.36729e6	+	2.36822e6i	−0.0178187	+	0.0308629i	−0.874797	−	0.484489i	$-0.839006\pi$
$179$	−1.36729e6	+	2.36822e6i	−0.0178187	+	0.0308629i	0.856979	+	0.515352i	$0.172339\pi$
$180$	1.60722e6	−	2.78380e6i	0.0205411	−	0.0355782i
$181$	1.18574e8			1.48633			0.743165	−	0.669108i	$-0.233324\pi$
$181$	1.18574e8			1.48633			0.743165	+	0.669108i	$0.233324\pi$
$182$	2.83408e7	+	1.73378e7i	0.348467	+	0.213179i
$183$	6.30086e7			0.760013
$184$	−5.53914e7	+	9.59407e7i	−0.655511	+	1.13538i
$185$	5.72278e6	−	9.91215e6i	0.0664517	−	0.115098i
$186$	−5.16262e7	−	8.94191e7i	−0.588267	−	1.01891i
$187$	1.95254e7			0.218350
$188$	−9.02669e6	−	1.56347e7i	−0.0990777	−	0.171608i
$189$	−1.25867e6	−	2.18008e6i	−0.0135611	−	0.0234886i
$190$	2.99306e7			0.316576
$191$	−4.80314e7	−	8.31928e7i	−0.498779	−	0.863911i	0.501220	−	0.865320i	$-0.332885\pi$
$191$	−4.80314e7	−	8.31928e7i	−0.498779	−	0.863911i	−0.999999	+	0.00140922i	$0.999551\pi$
$192$	−5.33991e7	+	9.24899e7i	−0.544477	+	0.943061i
$193$	−4.77412e7	+	8.26902e7i	−0.478016	+	0.827948i	−0.999682	−	0.0252013i	$-0.991977\pi$
$193$	−4.77412e7	+	8.26902e7i	−0.478016	+	0.827948i	0.521666	+	0.853150i	$0.325311\pi$
$194$	8.38571e7			0.824582
$195$	3.27073e7	−	1.77907e7i	0.315881	−	0.171819i
$196$	2.53179e6			0.0240177
$197$	6.80345e7	−	1.17839e8i	0.634012	−	1.09814i	−0.352712	−	0.935732i	$-0.614740\pi$
$197$	6.80345e7	−	1.17839e8i	0.634012	−	1.09814i	0.986724	−	0.162409i	$-0.0519264\pi$
$198$	4.39225e7	−	7.60759e7i	0.402123	−	0.696497i
$199$	1.00450e8	+	1.73985e8i	0.903578	+	1.56504i	0.822815	+	0.568309i	$0.192402\pi$
$199$	1.00450e8	+	1.73985e8i	0.903578	+	1.56504i	0.0807627	+	0.996733i	$0.474264\pi$
$200$	−9.49706e7			−0.839429
$201$	−1.56421e8	−	2.70930e8i	−1.35866	−	2.35326i
$202$	−5.62252e7	−	9.73848e7i	−0.479955	−	0.831307i
$203$	−5.93785e7			−0.498188
$204$	−3.96055e6	−	6.85987e6i	−0.0326625	−	0.0565731i
$205$	−1.33491e7	+	2.31213e7i	−0.108221	+	0.187445i
$206$	−8.79770e6	+	1.52381e7i	−0.0701187	+	0.121449i
$207$	1.76516e8			1.38321
$208$	1.29955e8	−	7.06870e7i	1.00132	−	0.544651i
$209$	1.17724e8			0.891978
$210$	9.85682e6	−	1.70725e7i	0.0734462	−	0.127213i
$211$	−7.25080e7	+	1.25587e8i	−0.531370	+	0.920360i	0.467959	+	0.883750i	$0.344989\pi$
$211$	−7.25080e7	+	1.25587e8i	−0.531370	+	0.920360i	−0.999330	+	0.0366102i	$0.988344\pi$
$212$	7.67155e6	+	1.32875e7i	0.0552977	+	0.0957785i
$213$	1.11363e8			0.789609
$214$	−8.90946e7	−	1.54316e8i	−0.621446	−	1.07638i
$215$	1.07166e7	+	1.85617e7i	0.0735398	+	0.127375i
$216$	−9.55578e6			−0.0645176
$217$	−2.21835e7	−	3.84229e7i	−0.147374	−	0.255259i
$218$	9.70150e7	−	1.68035e8i	0.634222	−	1.09850i
$219$	−1.06941e8	+	1.85227e8i	−0.688001	+	1.19165i
$220$	−5.36557e6			−0.0339732
$221$	1.13542e6	−	4.46501e7i	0.00707595	−	0.278259i
$222$	−1.26892e8			−0.778391
$223$	−1.06815e8	+	1.85009e8i	−0.645007	+	1.11718i	0.339293	+	0.940681i	$0.389812\pi$
$223$	−1.06815e8	+	1.85009e8i	−0.645007	+	1.11718i	−0.984300	+	0.176504i	$0.943521\pi$
$224$	1.05818e7	−	1.83282e7i	0.0629058	−	0.108956i
$225$	7.56606e7	+	1.31048e8i	0.442824	+	0.766994i
$226$	3.20511e8			1.84698
$227$	−4.39080e6	−	7.60509e6i	−0.0249146	−	0.0431533i	0.853299	−	0.521421i	$-0.174598\pi$
$227$	−4.39080e6	−	7.60509e6i	−0.0249146	−	0.0431533i	−0.878214	+	0.478268i	$0.841265\pi$
$228$	−2.38793e7	−	4.13602e7i	−0.133429	−	0.231106i
$229$	−1.79184e8			−0.985994			−0.492997	−	0.870031i	$-0.664099\pi$
$229$	−1.79184e8			−0.985994			−0.492997	+	0.870031i	$0.664099\pi$
$230$	−3.74552e7	−	6.48743e7i	−0.202985	−	0.351581i
$231$	3.87692e7	−	6.71503e7i	0.206940	−	0.358431i
$232$	−1.12700e8	+	1.95202e8i	−0.592537	+	1.02630i
$233$	3.20992e8			1.66245			0.831224	−	0.555938i	$-0.187641\pi$
$233$	3.20992e8			1.66245			0.831224	+	0.555938i	$0.187641\pi$
$234$	−1.71414e8	−	1.04865e8i	−0.874564	−	0.535024i
$235$	−6.04029e7			−0.303613
$236$	−3.52576e6	+	6.10679e6i	−0.0174607	+	0.0302428i
$237$	2.50770e8	−	4.34347e8i	1.22365	−	2.11942i
$238$	−1.18243e7	−	2.04802e7i	−0.0568532	−	0.0984727i
$239$	−1.00381e8			−0.475618			−0.237809	−	0.971312i	$-0.576429\pi$
$239$	−1.00381e8			−0.475618			−0.237809	+	0.971312i	$0.576429\pi$
$240$	−4.38899e7	−	7.60195e7i	−0.204939	−	0.354965i
$241$	1.41521e8	+	2.45122e8i	0.651272	+	1.12804i	0.982814	+	0.184596i	$0.0590978\pi$
$241$	1.41521e8	+	2.45122e8i	0.651272	+	1.12804i	−0.331542	+	0.943440i	$0.607569\pi$
$242$	9.16549e7			0.415721
$243$	1.55705e8	+	2.69690e8i	0.696116	+	1.20571i
$244$	−1.03854e7	+	1.79881e7i	−0.0457677	+	0.0792720i
$245$	4.23542e6	−	7.33596e6i	0.0183999	−	0.0318695i
$246$	2.95990e8			1.26766
$247$	6.84580e6	−	2.69209e8i	0.0289058	−	1.13671i
$248$	−1.68416e8			−0.701136
$249$	1.34157e7	−	2.32368e7i	0.0550703	−	0.0953845i
$250$	6.65004e7	−	1.15182e8i	0.269175	−	0.466224i
$251$	−5.28797e7	−	9.15903e7i	−0.211072	−	0.365588i	0.740978	−	0.671529i	$-0.234362\pi$
$251$	−5.28797e7	−	9.15903e7i	−0.211072	−	0.365588i	−0.952050	+	0.305941i	$0.901029\pi$
$252$	−1.53131e7			−0.0602782
$253$	−1.47320e8	−	2.55166e8i	−0.571927	−	0.990607i
$254$	2.44098e8	+	4.22791e8i	0.934645	+	1.61885i
$255$	−2.65023e7			−0.100091
$256$	−6.58894e7	−	1.14124e8i	−0.245457	−	0.425144i
$257$	−1.89203e7	+	3.27708e7i	−0.0695282	+	0.120426i	−0.898694	−	0.438577i	$-0.855483\pi$
$257$	−1.89203e7	+	3.27708e7i	−0.0695282	+	0.120426i	0.829165	+	0.559003i	$0.188816\pi$
$258$	1.18810e8	−	2.05785e8i	0.430710	−	0.746011i
$259$	−5.45246e7			−0.195004
$260$	−312014.	+	1.22698e7i	−0.00110095	+	0.0432944i
$261$	3.59141e8			1.25032
$262$	−1.36729e8	+	2.36822e8i	−0.469685	+	0.813518i
$263$	6.56553e7	−	1.13718e8i	0.222548	−	0.385465i	−0.733033	−	0.680193i	$-0.761896\pi$
$263$	6.56553e7	−	1.13718e8i	0.222548	−	0.385465i	0.955581	+	0.294728i	$0.0952291\pi$
$264$	−1.47167e8	−	2.54901e8i	−0.492263	−	0.852625i
$265$	5.13348e7			0.169454
$266$	−7.12921e7	−	1.23482e8i	−0.232250	−	0.402269i
$267$	−1.76990e8	−	3.06556e8i	−0.569062	−	0.985644i
$268$	1.03129e8			0.327271
$269$	−1.25894e8	−	2.18054e8i	−0.394340	−	0.683017i	0.598677	−	0.800991i	$-0.295693\pi$
$269$	−1.25894e8	−	2.18054e8i	−0.394340	−	0.683017i	−0.993017	+	0.117974i	$0.962360\pi$
$270$	3.23077e6	−	5.59586e6i	0.00998925	−	0.0173019i
$271$	−3.13743e8	+	5.43419e8i	−0.957595	+	1.65860i	−0.229282	+	0.973360i	$0.573638\pi$
$271$	−3.13743e8	+	5.43419e8i	−0.957595	+	1.65860i	−0.728314	+	0.685244i	$0.759696\pi$
$272$	−1.05301e8			−0.317278
$273$	−1.51303e8	−	9.25614e7i	−0.450068	−	0.275334i
$274$	−1.38203e8			−0.405873
$275$	1.26293e8	−	2.18746e8i	0.366197	−	0.634271i
$276$	−5.97652e7	+	1.03516e8i	−0.171107	+	0.296365i
$277$	−1.35389e8	−	2.34501e8i	−0.382740	−	0.662926i	0.608713	−	0.793391i	$-0.291686\pi$
$277$	−1.35389e8	−	2.34501e8i	−0.382740	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$278$	−1.06165e7			−0.0296362
$279$	1.34173e8	+	2.32394e8i	0.369870	+	0.640634i
$280$	−1.60776e7	−	2.78472e7i	−0.0437691	−	0.0758103i
$281$	3.70629e7			0.0996477			0.0498238	−	0.998758i	$-0.484134\pi$
$281$	3.70629e7			0.0996477			0.0498238	+	0.998758i	$0.484134\pi$
$282$	3.34830e8	+	5.79942e8i	0.889103	+	1.53997i
$283$	8.16967e7	−	1.41503e8i	0.214265	−	0.371118i	−0.738780	−	0.673947i	$-0.764598\pi$
$283$	8.16967e7	−	1.41503e8i	0.214265	−	0.371118i	0.953045	+	0.302829i	$0.0979310\pi$
$284$	−1.83554e7	+	3.17926e7i	−0.0475500	+	0.0823591i
$285$	−1.59791e8			−0.408878
$286$	−8.52676e6	+	3.35312e8i	−0.0215528	+	0.847555i
$287$	1.27185e8			0.317578
$288$	−6.40020e7	+	1.10855e8i	−0.157877	+	0.273452i
$289$	1.89273e8	−	3.27831e8i	0.461261	−	0.798927i
$290$	−7.62067e7	−	1.31994e8i	−0.183485	−	0.317805i
$291$	−4.47688e8			−1.06500
$292$	−3.52531e7	−	6.10602e7i	−0.0828624	−	0.143522i
$293$	2.06071e8	+	3.56926e8i	0.478609	+	0.828975i	0.999699	−	0.0245263i	$-0.00780774\pi$
$293$	2.06071e8	+	3.56926e8i	0.478609	+	0.828975i	−0.521090	+	0.853502i	$0.674474\pi$
$294$	−9.39124e7			−0.215530
$295$	1.17965e7	+	2.04321e7i	0.0267531	+	0.0463378i
$296$	−1.03487e8	+	1.79245e8i	−0.231935	+	0.401723i
$297$	1.27074e7	−	2.20098e7i	0.0281455	−	0.0487494i
$298$	−3.28594e8			−0.719289
$299$	−5.92074e8	+	3.22050e8i	−1.28093	+	0.696745i
$300$	−1.02470e8			−0.219114
$301$	5.10520e7	−	8.84247e7i	0.107902	−	0.186892i
$302$	3.49387e8	−	6.05155e8i	0.729931	−	1.26428i
$303$	3.00169e8	+	5.19909e8i	0.619894	+	1.07369i
$304$	−6.34890e8			−1.29611
$305$	3.47475e7	+	6.01844e7i	0.0701251	+	0.121460i
$306$	7.15170e7	+	1.23871e8i	0.142687	+	0.247141i
$307$	4.62250e8			0.911786			0.455893	−	0.890035i	$-0.349320\pi$
$307$	4.62250e8			0.911786			0.455893	+	0.890035i	$0.349320\pi$
$308$	1.27803e7	+	2.21361e7i	0.0249238	+	0.0431693i
$309$	4.69683e7	−	8.13515e7i	0.0905629	−	0.156860i
$310$	5.69407e7	−	9.86242e7i	0.108557	−	0.188026i
$311$	6.00765e8			1.13251			0.566256	−	0.824229i	$-0.308391\pi$
$311$	6.00765e8			1.13251			0.566256	+	0.824229i	$0.308391\pi$
$312$	−5.91459e8	+	3.21716e8i	−1.10251	+	0.599696i
$313$	−3.07836e8			−0.567433			−0.283717	−	0.958908i	$-0.591568\pi$
$313$	−3.07836e8			−0.567433			−0.283717	+	0.958908i	$0.591568\pi$
$314$	−2.15820e8	+	3.73811e8i	−0.393403	+	0.681394i
$315$	−2.56172e7	+	4.43703e7i	−0.0461790	+	0.0799844i
$316$	8.26666e7	+	1.43183e8i	0.147375	+	0.255262i
$317$	−2.23707e7			−0.0394433			−0.0197216	−	0.999806i	$-0.506278\pi$
$317$	−2.23707e7			−0.0394433			−0.0197216	+	0.999806i	$0.506278\pi$
$318$	−2.84563e8	−	4.92877e8i	−0.496230	−	0.859496i
$319$	−2.99739e8	−	5.19163e8i	−0.516983	−	0.895440i
$320$	−1.17792e8			−0.200952
$321$	4.75649e8	+	8.23849e8i	0.802637	+	1.39021i
$322$	−1.78430e8	+	3.09050e8i	−0.297833	+	0.515861i
$323$	−9.58427e7	+	1.66004e8i	−0.158252	+	0.274101i
$324$	−1.07948e8			−0.176322
$325$	−4.92878e8	−	3.01524e8i	−0.796430	−	0.487225i
$326$	8.89507e8			1.42196
$327$	−5.17934e8	+	8.97088e8i	−0.819139	+	1.41879i
$328$	2.41396e8	−	4.18111e8i	0.377722	−	0.654234i
$329$	1.43874e8	+	2.49198e8i	0.222740	+	0.385797i
$330$	1.99026e8			0.304868
$331$	8.92864e7	+	1.54649e8i	0.135328	+	0.234395i	0.925723	−	0.378203i	$-0.123458\pi$
$331$	8.92864e7	+	1.54649e8i	0.135328	+	0.234395i	−0.790395	+	0.612598i	$0.790125\pi$
$332$	4.42251e6	+	7.66001e6i	0.00663263	+	0.0114880i
$333$	3.29783e8			0.489410
$334$	−3.43473e7	−	5.94913e7i	−0.0504406	−	0.0873657i
$335$	1.72524e8	−	2.98820e8i	0.250722	−	0.434263i
$336$	−2.09084e8	+	3.62143e8i	−0.300699	+	0.520827i
$337$	7.21290e7			0.102661			0.0513305	−	0.998682i	$-0.483654\pi$
$337$	7.21290e7			0.102661			0.0513305	+	0.998682i	$0.483654\pi$
$338$	7.66287e8	+	3.89975e7i	1.07940	+	0.0549324i
$339$	−1.71111e9			−2.38550
$340$	4.36826e6	−	7.56605e6i	0.00602743	−	0.0104398i
$341$	2.23961e8	−	3.87913e8i	0.305867	−	0.529778i
$342$	4.31198e8	+	7.46856e8i	0.582888	+	1.00959i
$343$	−4.03536e7			−0.0539949
$344$	−1.93793e8	−	3.35659e8i	−0.256674	−	0.444573i
$345$	1.99962e8	+	3.46345e8i	0.262169	+	0.454090i
$346$	6.48651e8			0.841870
$347$	−4.03267e7	−	6.98479e7i	−0.0518131	−	0.0897430i	0.838956	−	0.544200i	$-0.183167\pi$
$347$	−4.03267e7	−	6.98479e7i	−0.0518131	−	0.0897430i	−0.890769	+	0.454457i	$0.849833\pi$
$348$	−1.21599e8	+	2.10615e8i	−0.154669	+	0.267894i
$349$	1.02821e8	−	1.78092e8i	0.129478	−	0.224262i	−0.793997	−	0.607922i	$-0.792003\pi$
$349$	1.02821e8	−	1.78092e8i	0.129478	−	0.224262i	0.923474	+	0.383660i	$0.125337\pi$
$350$	−3.05925e8			−0.381396
$351$	−4.95926e7	−	3.03388e7i	−0.0612127	−	0.0374476i
$352$	2.13665e8			0.261116
$353$	4.04619e8	−	7.00821e8i	0.489593	−	0.847999i	−0.510336	−	0.859975i	$-0.670479\pi$
$353$	4.04619e8	−	7.00821e8i	0.489593	−	0.847999i	0.999928	+	0.0119759i	$0.00381214\pi$
$354$	1.30782e8	−	2.26521e8i	0.156688	−	0.271392i
$355$	6.14135e7	+	1.06371e8i	0.0728559	+	0.126190i
$356$	1.16690e8			0.137075
$357$	6.31263e7	+	1.09338e8i	0.0734296	+	0.127184i
$358$	1.67191e7	+	2.89582e7i	0.0192584	+	0.0333566i
$359$	−3.08338e8			−0.351719			−0.175860	−	0.984415i	$-0.556270\pi$
$359$	−3.08338e8			−0.351719			−0.175860	+	0.984415i	$0.556270\pi$
$360$	9.72424e7	+	1.68429e8i	0.109849	+	0.190264i
$361$	−1.30928e8	+	2.26774e8i	−0.146473	+	0.253699i
$362$	7.24953e8	−	1.25566e9i	0.803211	−	1.39120i
$363$	−4.89318e8			−0.536931
$364$	5.13636e7	−	2.79384e7i	0.0558213	−	0.0303632i
$365$	−2.35899e8			−0.253923
$366$	3.85229e8	−	6.67236e8i	0.410710	−	0.711371i
$367$	1.19282e7	−	2.06602e7i	0.0125963	−	0.0218174i	−0.859659	−	0.510869i	$-0.829324\pi$
$367$	1.19282e7	−	2.06602e7i	0.0125963	−	0.0218174i	0.872255	+	0.489052i	$0.162657\pi$
$368$	7.94502e8	+	1.37612e9i	0.831051	+	1.43942i
$369$	−7.69257e8			−0.797039
$370$	−6.99772e7	−	1.21204e8i	−0.0718208	−	0.124397i
$371$	−1.22275e8	−	2.11787e8i	−0.124317	−	0.215323i
$372$	−1.81714e8			−0.183016
$373$	7.81913e8	+	1.35431e9i	0.780149	+	1.35126i	0.931855	+	0.362832i	$0.118190\pi$
$373$	7.81913e8	+	1.35431e9i	0.780149	+	1.35126i	−0.151706	+	0.988426i	$0.548477\pi$
$374$	1.19376e8	−	2.06766e8i	0.117996	−	0.204375i
$375$	−3.55026e8	+	6.14922e8i	−0.347656	+	0.602159i
$376$	1.09229e9			1.05969
$377$	−1.20464e9	+	6.55246e8i	−1.15788	+	0.629810i
$378$	−3.07816e7			−0.0293137
$379$	5.13513e8	−	8.89430e8i	0.484523	−	0.839218i	−0.515319	−	0.856998i	$-0.672327\pi$
$379$	5.13513e8	−	8.89430e8i	0.484523	−	0.839218i	0.999842	+	0.0177805i	$0.00566002\pi$
$380$	2.63376e7	−	4.56180e7i	0.0246225	−	0.0426475i
$381$	−1.30317e9	−	2.25715e9i	−1.20715	−	2.09085i
$382$	−1.17464e9			−1.07816
$383$	2.58986e8	+	4.48576e8i	0.235548	+	0.407982i	0.959432	−	0.281940i	$-0.0909781\pi$
$383$	2.58986e8	+	4.48576e8i	0.235548	+	0.407982i	−0.723884	+	0.689922i	$0.757645\pi$
$384$	9.10741e8	+	1.57745e9i	0.820797	+	1.42166i
$385$	8.55206e7			0.0763762
$386$	5.83771e8	+	1.01112e9i	0.516639	+	0.894845i
$387$	−3.08779e8	+	5.34821e8i	−0.270807	+	0.469051i
$388$	7.37904e7	−	1.27809e8i	0.0641341	−	0.111083i
$389$	−1.29178e9			−1.11267			−0.556334	−	0.830959i	$-0.687793\pi$
$389$	−1.29178e9			−1.11267			−0.556334	+	0.830959i	$0.687793\pi$
$390$	1.15736e7	−	4.55129e8i	0.00987969	−	0.388515i
$391$	4.79750e8			0.405879
$392$	−7.65908e7	+	1.32659e8i	−0.0642207	+	0.111234i
$393$	7.29956e8	−	1.26432e9i	0.606628	−	1.05071i
$394$	−8.31915e8	−	1.44092e9i	−0.685239	−	1.18687i
$395$	5.53171e8			0.451616
$396$	−7.72995e7	−	1.33887e8i	−0.0625523	−	0.108344i
$397$	−1.02710e9	−	1.77899e9i	−0.823848	−	1.42695i	−0.902797	−	0.430068i	$-0.858490\pi$
$397$	−1.02710e9	−	1.77899e9i	−0.823848	−	1.42695i	0.0789487	−	0.996879i	$-0.474844\pi$
$398$	2.45658e9			1.95317
$399$	3.80607e8	+	6.59231e8i	0.299966	+	0.519556i
$400$	−6.81101e8	+	1.17970e9i	−0.532110	+	0.921642i
$401$	1.42257e8	−	2.46397e8i	0.110172	−	0.190823i	−0.805668	−	0.592368i	$-0.798193\pi$
$401$	1.42257e8	−	2.46397e8i	0.110172	−	0.190823i	0.915839	+	0.401545i	$0.131527\pi$
$402$	−3.82539e9			−2.93687
$403$	−8.74045e8	−	5.34707e8i	−0.665221	−	0.406957i
$404$	−1.97902e8			−0.149319
$405$	−1.80586e8	+	3.12784e8i	−0.135080	+	0.233965i
$406$	−3.63035e8	+	6.28796e8i	−0.269220	+	0.466303i
$407$	−2.75237e8	−	4.76724e8i	−0.202361	−	0.350499i
$408$	4.79252e8			0.349344
$409$	−1.06010e9	−	1.83615e9i	−0.766154	−	1.32702i	−0.939634	−	0.342181i	$-0.888835\pi$
$409$	−1.06010e9	−	1.83615e9i	−0.766154	−	1.32702i	0.173480	−	0.984837i	$-0.444499\pi$
$410$	1.63230e8	+	2.82723e8i	0.116965	+	0.202590i
$411$	7.37825e8			0.524212
$412$	1.54831e7	+	2.68176e7i	0.0109073	+	0.0188921i
$413$	5.61963e7	−	9.73348e7i	0.0392539	−	0.0679897i
$414$	1.07920e9	−	1.86923e9i	0.747484	−	1.29468i
$415$	2.95936e7			0.0203250
$416$	1.24249e7	−	4.88603e8i	0.00846183	−	0.332759i
$417$	5.66781e7			0.0382771
$418$	7.19756e8	−	1.24665e9i	0.482024	−	0.834890i
$419$	−1.85525e8	+	3.21340e8i	−0.123212	+	0.213410i	−0.921033	−	0.389485i	$-0.872653\pi$
$419$	−1.85525e8	+	3.21340e8i	−0.123212	+	0.213410i	0.797820	+	0.602895i	$0.205986\pi$
$420$	−1.73471e7	−	3.00460e7i	−0.0114249	−	0.0197886i
$421$	−1.24211e9			−0.811285			−0.405643	−	0.914032i	$-0.632952\pi$
$421$	−1.24211e9			−0.811285			−0.405643	+	0.914032i	$0.632952\pi$
$422$	8.86615e8	+	1.53566e9i	0.574304	+	0.994723i
$423$	−8.70199e8	−	1.50723e9i	−0.559020	−	0.968251i
$424$	−9.28307e8			−0.591441
$425$	2.05637e8	+	3.56174e8i	0.129939	+	0.225062i
$426$	6.80864e8	−	1.17929e9i	0.426704	−	0.739073i
$427$	1.65531e8	−	2.86708e8i	0.102892	−	0.178214i
$428$	−3.13596e8			−0.193338
$429$	4.55218e7	−	1.79013e9i	0.0278368	−	1.09467i
$430$	2.62082e8			0.158963
$431$	6.61648e8	−	1.14601e9i	0.398068	−	0.689473i	−0.595420	−	0.803415i	$-0.703014\pi$
$431$	6.61648e8	−	1.14601e9i	0.398068	−	0.689473i	0.993487	+	0.113941i	$0.0363476\pi$
$432$	−6.85313e7	+	1.18700e8i	−0.0408974	+	0.0708364i
$433$	−1.04054e9	−	1.80226e9i	−0.615957	−	1.06687i	−0.990216	−	0.139544i	$-0.955436\pi$
$433$	−1.04054e9	−	1.80226e9i	−0.615957	−	1.06687i	0.374259	−	0.927324i	$-0.377897\pi$
$434$	−5.42511e8			−0.318563
$435$	4.06845e8	+	7.04676e8i	0.236982	+	0.410466i
$436$	−1.70737e8	−	2.95726e8i	−0.0986566	−	0.170878i
$437$	2.89256e9			1.65805
$438$	1.30765e9	+	2.26492e9i	0.743590	+	1.28794i
$439$	−2.80560e8	+	4.85944e8i	−0.158270	+	0.274132i	−0.934245	−	0.356632i	$-0.883925\pi$
$439$	−2.80560e8	+	4.85944e8i	−0.158270	+	0.274132i	0.775975	+	0.630764i	$0.217258\pi$
$440$	1.62317e8	−	2.81142e8i	0.0908406	−	0.157341i
$441$	2.44072e8			0.135513
$442$	−4.65885e8	−	2.85011e8i	−0.256626	−	0.156994i
$443$	3.56356e9			1.94747			0.973736	−	0.227678i	$-0.0731134\pi$
$443$	3.56356e9			1.94747			0.973736	+	0.227678i	$0.0731134\pi$
$444$	−1.11659e8	+	1.93399e8i	−0.0605414	+	0.104861i
$445$	1.95210e8	−	3.38114e8i	0.105013	−	0.181887i
$446$	1.30611e9	+	2.26225e9i	0.697122	+	1.20745i
$447$	1.75427e9			0.929008
$448$	2.80571e8	+	4.85963e8i	0.147424	+	0.255347i
$449$	6.94728e8	+	1.20330e9i	0.362203	+	0.627355i	0.988323	−	0.152372i	$-0.0486912\pi$
$449$	6.94728e8	+	1.20330e9i	0.362203	+	0.627355i	−0.626120	+	0.779727i	$0.715358\pi$
$450$	1.85033e9			0.957206
$451$	6.42023e8	+	1.11202e9i	0.329559	+	0.570812i
$452$	2.82035e8	−	4.88498e8i	0.143654	−	0.248816i
$453$	−1.86527e9	+	3.23074e9i	−0.942754	+	1.63290i
$454$	−1.07380e8			−0.0538552
$455$	4.97312e6	−	1.95566e8i	0.00247508	−	0.0973316i
$456$	2.88956e9			1.42710
$457$	1.62605e8	−	2.81640e8i	0.0796943	−	0.138035i	−0.823424	−	0.567427i	$-0.807939\pi$
$457$	1.62605e8	−	2.81640e8i	0.0796943	−	0.138035i	0.903118	+	0.429392i	$0.141272\pi$
$458$	−1.09551e9	+	1.89749e9i	−0.532830	+	0.922889i
$459$	2.06909e7	+	3.58377e7i	0.00998699	+	0.0172980i
$460$	−1.31835e8			−0.0631509
$461$	3.33605e8	+	5.77821e8i	0.158591	+	0.274688i	0.934361	−	0.356328i	$-0.115971\pi$
$461$	3.33605e8	+	5.77821e8i	0.158591	+	0.274688i	−0.775770	+	0.631016i	$0.782638\pi$
$462$	−4.74064e8	−	8.21102e8i	−0.223661	−	0.387392i
$463$	−2.80071e8			−0.131140			−0.0655700	−	0.997848i	$-0.520887\pi$
$463$	−2.80071e8			−0.131140			−0.0655700	+	0.997848i	$0.520887\pi$
$464$	1.61650e9	+	2.79986e9i	0.751213	+	1.30114i
$465$	−3.03990e8	+	5.26525e8i	−0.140208	+	0.242848i
$466$	1.96252e9	−	3.39918e9i	0.898385	−	1.55605i
$467$	2.64435e8			0.120146			0.0600730	−	0.998194i	$-0.480867\pi$
$467$	2.64435e8			0.120146			0.0600730	+	0.998194i	$0.480867\pi$
$468$	−3.10663e8	+	1.68981e8i	−0.140097	+	0.0762038i
$469$	−1.64375e9			−0.735749
$470$	−3.69298e8	+	6.39643e8i	−0.164072	+	0.284181i
$471$	1.15220e9	−	1.99566e9i	0.508105	−	0.880064i
$472$	−2.13320e8	−	3.69481e8i	−0.0933759	−	0.161732i
$473$	1.03083e9			0.447892
$474$	−3.06637e9	−	5.31112e9i	−1.32252	−	2.29067i
$475$	1.23985e9	+	2.14748e9i	0.530812	+	0.919394i
$476$	−4.16193e7			−0.0176876
$477$	7.39559e8	+	1.28095e9i	0.312003	+	0.540405i
$478$	−6.13720e8	+	1.06299e9i	−0.257024	+	0.445178i
$479$	−7.25491e8	+	1.25659e9i	−0.301618	+	0.522418i	−0.976503	−	0.215505i	$-0.930860\pi$
$479$	−7.25491e8	+	1.25659e9i	−0.301618	+	0.522418i	0.674884	+	0.737923i	$0.264193\pi$
$480$	−2.90013e8			−0.119694
$481$	−1.10617e9	+	6.01683e8i	−0.453224	+	0.246524i
$482$	3.46100e9			1.40779
$483$	9.52585e8	−	1.64992e9i	0.384670	−	0.666268i
$484$	8.06521e7	−	1.39693e8i	0.0323338	−	0.0560038i
$485$	−2.46887e8	−	4.27622e8i	−0.0982659	−	0.170202i
$486$	3.80788e9			1.50472
$487$	3.64863e8	+	6.31962e8i	0.143146	+	0.247936i	0.928680	−	0.370883i	$-0.120945\pi$
$487$	3.64863e8	+	6.31962e8i	0.143146	+	0.247936i	−0.785534	+	0.618819i	$0.787612\pi$
$488$	−6.28352e8	−	1.08834e9i	−0.244756	−	0.423930i
$489$	−4.74881e9			−1.83655
$490$	−5.17900e7	−	8.97029e7i	−0.0198866	−	0.0344445i
$491$	−1.78915e9	+	3.09890e9i	−0.682121	+	1.18147i	0.292211	+	0.956354i	$0.405609\pi$
$491$	−1.78915e9	+	3.09890e9i	−0.682121	+	1.18147i	−0.974332	+	0.225115i	$0.927724\pi$
$492$	2.60457e8	−	4.51126e8i	0.0985959	−	0.170773i
$493$	9.76104e8			0.366887
$494$	−2.80896e9	−	1.71841e9i	−1.04834	−	0.641333i
$495$	−5.17256e8			−0.191685
$496$	−1.20783e9	+	2.09202e9i	−0.444447	+	0.769805i
$497$	2.92563e8	−	5.06734e8i	0.106899	−	0.185154i
$498$	−1.64045e8	−	2.84135e8i	−0.0595198	−	0.103091i
$499$	1.64473e9			0.592576			0.296288	−	0.955099i	$-0.404251\pi$
$499$	1.64473e9			0.592576			0.296288	+	0.955099i	$0.404251\pi$
$500$	−1.17034e8	−	2.02710e8i	−0.0418715	−	0.0725236i
$501$	1.83370e8	+	3.17606e8i	0.0651473	+	0.112838i
$502$	−1.29321e9			−0.456253
$503$	−2.50638e9	−	4.34117e9i	−0.878130	−	1.52097i	−0.853391	−	0.521271i	$-0.825458\pi$
$503$	−2.50638e9	−	4.34117e9i	−0.878130	−	1.52097i	−0.0247385	−	0.999694i	$-0.507875\pi$
$504$	4.63246e8	−	8.02365e8i	0.161178	−	0.279168i
$505$	−3.31070e8	+	5.73430e8i	−0.114393	+	0.198135i
$506$	−3.60281e9			−1.23627
$507$	−4.09098e9	−	2.08196e8i	−1.39412	−	0.0709488i
$508$	8.59181e8			0.290778
$509$	−2.26175e9	+	3.91747e9i	−0.760208	+	1.31672i	0.182535	+	0.983199i	$0.441570\pi$
$509$	−2.26175e9	+	3.91747e9i	−0.760208	+	1.31672i	−0.942743	+	0.333520i	$0.891764\pi$
$510$	−1.62033e8	+	2.80650e8i	−0.0540889	+	0.0936847i
$511$	5.61892e8	+	9.73225e8i	0.186286	+	0.322656i
$512$	1.96012e9			0.645415
$513$	1.24752e8	+	2.16076e8i	0.0407977	+	0.0706636i
$514$	2.31354e8	+	4.00716e8i	0.0751459	+	0.130157i
$515$	1.03607e8			0.0334243
$516$	−2.09095e8	−	3.62163e8i	−0.0669991	−	0.116046i
$517$	−1.45254e9	+	2.51587e9i	−0.462286	+	0.800702i
$518$	−3.33359e8	+	5.77395e8i	−0.105380	+	0.182523i
$519$	−3.46296e9			−1.08733
$520$	−6.33468e8	−	3.87531e8i	−0.197566	−	0.120864i
$521$	5.50079e9			1.70409			0.852045	−	0.523468i	$-0.175362\pi$
$521$	5.50079e9			1.70409			0.852045	+	0.523468i	$0.175362\pi$
$522$	2.19575e9	−	3.80316e9i	0.675674	−	1.17030i
$523$	−2.65921e9	+	4.60588e9i	−0.812824	+	1.40785i	0.0980560	+	0.995181i	$0.468738\pi$
$523$	−2.65921e9	+	4.60588e9i	−0.812824	+	1.40785i	−0.910880	+	0.412671i	$0.864596\pi$
$524$	2.40631e8	+	4.16784e8i	0.0730620	+	0.126547i
$525$	1.63324e9			0.492598
$526$	−8.02822e8	−	1.39053e9i	−0.240530	−	0.416610i
$527$	3.64667e8	+	6.31621e8i	0.108532	+	0.187983i
$528$	−4.22176e9			−1.24817
$529$	−1.91734e9	−	3.32093e9i	−0.563124	−	0.975359i
$530$	3.13857e8	−	5.43616e8i	0.0915727	−	0.158609i
$531$	−3.39893e8	+	5.88713e8i	−0.0985171	+	0.170637i
$532$	−2.50935e8			−0.0722554
$533$	2.58027e9	−	1.40350e9i	0.738107	−	0.401482i
$534$	−4.32841e9			−1.23008
$535$	−5.24614e8	+	9.08659e8i	−0.148116	+	0.256544i
$536$	−3.11981e9	+	5.40368e9i	−0.875089	+	1.51570i
$537$	−8.92580e7	−	1.54599e8i	−0.0248735	−	0.0430822i
$538$	−3.07881e9			−0.852404
$539$	−2.03702e8	−	3.52823e8i	−0.0560319	−	0.0970502i
$540$	−5.68585e6	−	9.84819e6i	−0.00155388	−	0.00269140i
$541$	−2.91206e9			−0.790696			−0.395348	−	0.918531i	$-0.629376\pi$
$541$	−2.91206e9			−0.790696			−0.395348	+	0.918531i	$0.629376\pi$
$542$	3.83640e9	+	6.64484e9i	1.03497	+	1.79262i
$543$	−3.87031e9	+	6.70357e9i	−1.03740	+	1.79683i
$544$	−1.73951e8	+	3.01291e8i	−0.0463265	+	0.0802399i
$545$	−1.14250e9			−0.302322
$546$	−1.90524e9	+	1.03633e9i	−0.500929	+	0.272473i
$547$	−2.39955e9			−0.626865			−0.313433	−	0.949610i	$-0.601479\pi$
$547$	−2.39955e9			−0.626865			−0.313433	+	0.949610i	$0.601479\pi$
$548$	−1.21612e8	+	2.10639e8i	−0.0315679	+	0.0546772i
$549$	−1.00118e9	+	1.73410e9i	−0.258232	+	0.447271i
$550$	−1.54429e9	−	2.67479e9i	−0.395785	−	0.685519i
$551$	5.88523e9			1.49876
$552$	−3.61599e9	−	6.26308e9i	−0.915041	−	1.58490i
$553$	−1.31760e9	−	2.28216e9i	−0.331319	−	0.573862i
$554$	−3.31103e9			−0.827330
$555$	3.73587e8	+	6.47072e8i	0.0927613	+	0.160667i
$556$	−9.34199e6	+	1.61808e7i	−0.00230504	+	0.00399244i
$557$	−1.83306e8	+	3.17495e8i	−0.0449452	+	0.0778474i	−0.887623	−	0.460571i	$-0.847645\pi$
$557$	−1.83306e8	+	3.17495e8i	−0.0449452	+	0.0778474i	0.842678	+	0.538418i	$0.180978\pi$
$558$	3.28128e9			0.799510
$559$	5.99440e7	−	2.35728e9i	0.0145146	−	0.570780i
$560$	−4.61215e8			−0.110980
$561$	−6.37315e8	+	1.10386e9i	−0.152400	+	0.263964i
$562$	2.26599e8	−	3.92482e8i	0.0538495	−	0.0932701i
$563$	9.71663e8	+	1.68297e9i	0.229476	+	0.397463i	0.957653	−	0.287926i	$-0.0929656\pi$
$563$	9.71663e8	+	1.68297e9i	0.229476	+	0.397463i	−0.728177	+	0.685389i	$0.759632\pi$
$564$	1.17854e9			0.276609
$565$	−9.43630e8	−	1.63441e9i	−0.220106	−	0.381235i
$566$	−9.98973e8	−	1.73027e9i	−0.231577	−	0.401104i
$567$	1.72056e9			0.396395
$568$	−1.11056e9	−	1.92355e9i	−0.254287	−	0.440438i
$569$	−2.47483e9	+	4.28653e9i	−0.563186	+	0.975467i	0.434030	+	0.900899i	$0.357091\pi$
$569$	−2.47483e9	+	4.28653e9i	−0.563186	+	0.975467i	−0.997216	+	0.0745685i	$0.976242\pi$
$570$	−9.76946e8	+	1.69212e9i	−0.220957	+	0.382710i
$571$	2.64854e9			0.595361			0.297681	−	0.954666i	$-0.403787\pi$
$571$	2.64854e9			0.595361			0.297681	+	0.954666i	$0.403787\pi$
$572$	5.03554e8	+	3.08055e8i	0.112502	+	0.0688243i
$573$	6.27105e9			1.39251
$574$	7.77600e8	−	1.34684e9i	0.171619	−	0.297252i
$575$	3.10310e9	−	5.37472e9i	0.680703	−	1.17901i
$576$	−1.69698e9	−	2.93926e9i	−0.369998	−	0.640855i
$577$	1.19981e8			0.0260014			0.0130007	−	0.999915i	$-0.495862\pi$
$577$	1.19981e8			0.0260014			0.0130007	+	0.999915i	$0.495862\pi$
$578$	−2.31440e9	−	4.00866e9i	−0.498530	−	0.863479i
$579$	−3.11658e9	−	5.39808e9i	−0.667273	−	1.15575i
$580$	−2.68233e8			−0.0570841
$581$	−7.04894e7	−	1.22091e8i	−0.0149110	−	0.0258266i
$582$	−2.73713e9	+	4.74085e9i	−0.575526	+	0.996840i
$583$	1.23447e9	−	2.13817e9i	0.258013	−	0.446892i
$584$	4.26586e9			0.886261
$585$	−3.00790e7	+	1.18285e9i	−0.00621181	+	0.244277i
$586$	5.03961e9			1.03456
$587$	3.05512e9	−	5.29162e9i	0.623440	−	1.07983i	−0.365400	−	0.930851i	$-0.619068\pi$
$587$	3.05512e9	−	5.29162e9i	0.623440	−	1.07983i	0.988840	−	0.148979i	$-0.0475988\pi$
$588$	−8.26385e7	+	1.43134e8i	−0.0167634	+	0.0290350i
$589$	2.19869e9	+	3.80824e9i	0.443363	+	0.767928i
$590$	2.88490e8			0.0578295
$591$	4.44134e9	+	7.69263e9i	0.885030	+	1.53292i
$592$	1.48436e9	+	2.57099e9i	0.294045	+	0.509301i
$593$	5.03328e9			0.991196			0.495598	−	0.868552i	$-0.334949\pi$
$593$	5.03328e9			0.991196			0.495598	+	0.868552i	$0.334949\pi$
$594$	−1.55384e8	−	2.69133e8i	−0.0304196	−	0.0526882i
$595$	−6.96247e7	+	1.20594e8i	−0.0135505	+	0.0234701i
$596$	−2.89148e8	+	5.00819e8i	−0.0559446	+	0.0968988i
$597$	−1.31149e10			−2.52265
$598$	−2.09508e8	+	8.23882e9i	−0.0400632	+	1.57547i
$599$	7.15002e9			1.35929			0.679647	−	0.733539i	$-0.262133\pi$
$599$	7.15002e9			1.35929			0.679647	+	0.733539i	$0.262133\pi$
$600$	3.09987e9	−	5.36914e9i	0.585888	−	1.01479i
$601$	3.06771e9	−	5.31343e9i	0.576439	−	0.998422i	−0.419445	−	0.907781i	$-0.637775\pi$
$601$	3.06771e9	−	5.31343e9i	0.576439	−	0.998422i	0.995884	−	0.0906407i	$-0.0288915\pi$
$602$	−6.24256e8	−	1.08124e9i	−0.116620	−	0.201993i
$603$	9.94191e9			1.84654
$604$	−6.14888e8	−	1.06502e9i	−0.113545	−	0.196665i
$605$	−2.69845e8	−	4.67386e8i	−0.0495417	−	0.0858087i
$606$	7.34084e9			1.33996
$607$	−2.57446e8	−	4.45910e8i	−0.0467225	−	0.0809258i	0.841718	−	0.539917i	$-0.181544\pi$
$607$	−2.57446e8	−	4.45910e8i	−0.0467225	−	0.0809258i	−0.888441	+	0.458991i	$0.848211\pi$
$608$	−1.04880e9	+	1.81657e9i	−0.189247	+	0.327786i
$609$	1.93814e9	−	3.35695e9i	0.347715	−	0.602261i
$610$	8.49772e8			0.151582
$611$	5.66876e9	+	3.46793e9i	1.00541	+	0.615072i
$612$	2.51727e8			0.0443914
$613$	−3.14064e9	+	5.43974e9i	−0.550689	+	0.953821i	0.447536	+	0.894266i	$0.352302\pi$
$613$	−3.14064e9	+	5.43974e9i	−0.550689	+	0.953821i	−0.998225	+	0.0595551i	$0.981032\pi$
$614$	2.82616e9	−	4.89505e9i	0.492728	−	0.853430i
$615$	−8.71437e8	−	1.50937e9i	−0.151068	−	0.261658i
$616$	−1.54650e9			−0.266574
$617$	4.18571e8	+	7.24987e8i	0.0717417	+	0.124260i	0.899665	−	0.436582i	$-0.143811\pi$
$617$	4.18571e8	+	7.24987e8i	0.0717417	+	0.124260i	−0.827923	+	0.560842i	$0.810478\pi$
$618$	−5.74321e8	−	9.94753e8i	−0.0978802	−	0.169533i
$619$	9.22789e9			1.56381			0.781907	−	0.623395i	$-0.214247\pi$
$619$	9.22789e9			1.56381			0.781907	+	0.623395i	$0.214247\pi$
$620$	−1.00210e8	−	1.73570e8i	−0.0168866	−	0.0292484i
$621$	3.12228e8	−	5.40796e8i	0.0523181	−	0.0906176i
$622$	3.67303e9	−	6.36187e9i	0.612009	−	1.06003i
$623$	−1.85989e9			−0.308163
$624$	−2.45500e8	+	9.65422e9i	−0.0404489	+	1.59064i
$625$	4.91536e9			0.805332
$626$	−1.88209e9	+	3.25987e9i	−0.306640	+	0.531117i
$627$	−3.84256e9	+	6.65551e9i	−0.622565	+	1.07831i
$628$	3.79823e8	+	6.57872e8i	0.0611959	+	0.105994i
$629$	8.96313e8			0.143609
$630$	3.13243e8	+	5.42552e8i	0.0499102	+	0.0864470i
$631$	−4.69303e7	−	8.12857e7i	−0.00743620	−	0.0128799i	0.862283	−	0.506426i	$-0.169034\pi$
$631$	−4.69303e7	−	8.12857e7i	−0.00743620	−	0.0128799i	−0.869720	+	0.493546i	$0.835700\pi$
$632$	−1.00032e10			−1.57626
$633$	−4.73337e9	−	8.19844e9i	−0.741750	−	1.28475i
$634$	−1.36773e8	+	2.36897e8i	−0.0213151	+	0.0369188i
$635$	1.43732e9	−	2.48951e9i	0.222764	−	0.385839i
$636$	−1.00161e9			−0.154383
$637$	−8.18672e8	+	4.45305e8i	−0.125494	+	0.0682604i
$638$	−7.33032e9			−1.11751
$639$	−1.76952e9	+	3.06489e9i	−0.268288	+	0.464689i
$640$	−1.00450e9	+	1.73984e9i	−0.151467	+	0.262349i
$641$	2.06428e9	+	3.57544e9i	0.309575	+	0.536199i	0.978269	−	0.207338i	$-0.0664800\pi$
$641$	2.06428e9	+	3.57544e9i	0.309575	+	0.536199i	−0.668695	+	0.743537i	$0.733147\pi$
$642$	1.16323e10			1.73498
$643$	−6.52524e8	−	1.13020e9i	−0.0967961	−	0.167656i	0.813561	−	0.581480i	$-0.197526\pi$
$643$	−6.52524e8	−	1.13020e9i	−0.0967961	−	0.167656i	−0.910357	+	0.413824i	$0.864193\pi$
$644$	3.14020e8	+	5.43899e8i	0.0463294	+	0.0802450i
$645$	−1.39918e9			−0.205312
$646$	1.17195e9	+	2.02987e9i	0.171039	+	0.296248i
$647$	2.98586e9	−	5.17167e9i	0.433416	−	0.750699i	−0.563749	−	0.825946i	$-0.690641\pi$
$647$	2.98586e9	−	5.17167e9i	0.433416	−	0.750699i	0.997165	+	0.0752475i	$0.0239747\pi$
$648$	3.26560e9	−	5.65619e9i	0.471466	−	0.816604i
$649$	1.13470e9			0.162939
$650$	−6.20643e9	+	3.37590e9i	−0.886432	+	0.482161i
$651$	2.89631e9			0.411444
$652$	7.82725e8	−	1.35572e9i	0.110597	−	0.191559i
$653$	5.71540e9	−	9.89937e9i	0.803250	−	1.39127i	−0.114216	−	0.993456i	$-0.536436\pi$
$653$	5.71540e9	−	9.89937e9i	0.803250	−	1.39127i	0.917466	−	0.397814i	$-0.130231\pi$
$654$	6.33321e9	+	1.09694e10i	0.885323	+	1.53343i
$655$	1.61020e9			0.223890
$656$	−3.46245e9	−	5.99714e9i	−0.478873	−	0.829432i
$657$	−3.39850e9	−	5.88638e9i	−0.467529	−	0.809785i
$658$	3.51854e9			0.481473
$659$	−1.24865e9	−	2.16273e9i	−0.169959	−	0.294377i	0.768446	−	0.639914i	$-0.221030\pi$
$659$	−1.24865e9	−	2.16273e9i	−0.169959	−	0.294377i	−0.938405	+	0.345537i	$0.887697\pi$
$660$	1.75134e8	−	3.03341e8i	0.0237119	−	0.0410703i
$661$	3.71101e9	−	6.42766e9i	0.499789	−	0.865661i	−0.500211	−	0.865904i	$-0.666744\pi$
$661$	3.71101e9	−	6.42766e9i	0.499789	−	0.865661i	1.00000		0.000243173i	$7.74045e-5\pi$
$662$	2.18356e9			0.292524
$663$	2.48722e9	+	1.52159e9i	0.331449	+	0.202768i
$664$	−5.35153e8			−0.0709397
$665$	−4.19788e8	+	7.27095e8i	−0.0553547	+	0.0958772i
$666$	2.01626e9	−	3.49227e9i	0.264477	−	0.458087i
$667$	−7.36478e9	−	1.27562e10i	−0.960991	−	1.66448i
$668$	−1.20896e8			−0.0156926
$669$	−6.97295e9	−	1.20775e10i	−0.900378	−	1.55950i
$670$	−2.10959e9	−	3.65392e9i	−0.270980	−	0.469350i
$671$	3.34236e9			0.427094
$672$	6.90787e8	+	1.19648e9i	0.0878115	+	0.152094i
$673$	−3.12644e8	+	5.41515e8i	−0.0395364	+	0.0684791i	−0.885116	−	0.465370i	$-0.845921\pi$
$673$	−3.12644e8	+	5.41515e8i	−0.0395364	+	0.0684791i	0.845580	+	0.533849i	$0.179255\pi$
$674$	4.40991e8	−	7.63818e8i	0.0554779	−	0.0960905i
$675$	5.35327e8			0.0669971
$676$	7.33734e8	−	1.13360e9i	0.0913535	−	0.141139i
$677$	−1.44081e10			−1.78463			−0.892314	−	0.451415i	$-0.850920\pi$
$677$	−1.44081e10			−1.78463			−0.892314	+	0.451415i	$0.850920\pi$
$678$	−1.04616e10	+	1.81200e10i	−1.28912	+	2.23282i
$679$	−1.17613e9	+	2.03711e9i	−0.144182	+	0.249730i
$680$	2.64294e8	+	4.57771e8i	0.0322334	+	0.0558299i
$681$	5.73270e8			0.0695575
$682$	−2.73856e9	−	4.74333e9i	−0.330581	−	0.572583i
$683$	−5.77842e9	−	1.00085e10i	−0.693964	−	1.20198i	−0.970529	−	0.240985i	$-0.922529\pi$
$683$	−5.77842e9	−	1.00085e10i	−0.693964	−	1.20198i	0.276565	−	0.960995i	$-0.410804\pi$
$684$	1.51774e9			0.181343
$685$	4.06890e8	+	7.04753e8i	0.0483682	+	0.0837761i
$686$	−2.46719e8	+	4.27329e8i	−0.0291788	+	0.0505392i
$687$	5.84862e9	−	1.01301e10i	0.688185	−	1.19197i
$688$	−5.55930e9			−0.650819
$689$	−4.81773e9	−	2.94730e9i	−0.561145	−	0.343287i
$690$	4.89021e9			0.566703
$691$	−6.40845e9	+	1.10998e10i	−0.738890	+	1.27979i	0.214106	+	0.976811i	$0.431316\pi$
$691$	−6.40845e9	+	1.10998e10i	−0.738890	+	1.27979i	−0.952996	+	0.302984i	$0.902017\pi$
$692$	5.70783e8	−	9.88625e8i	0.0654786	−	0.113412i
$693$	1.23206e9	+	2.13399e9i	0.140626	+	0.243571i
$694$	−9.86217e8			−0.111999
$695$	3.12564e7	+	5.41376e7i	0.00353177	+	0.00611720i
$696$	−7.35713e9	−	1.27429e10i	−0.827134	−	1.43264i
$697$	−2.09076e9			−0.233878
$698$	−1.25728e9	−	2.17768e9i	−0.139939	−	0.242382i
$699$	−1.04773e10	+	1.81472e10i	−1.16032	+	2.00974i
$700$	−2.69199e8	+	4.66267e8i	−0.0296641	+	0.0513797i
$701$	−3.62493e9			−0.397454			−0.198727	−	0.980055i	$-0.563681\pi$
$701$	−3.62493e9			−0.397454			−0.198727	+	0.980055i	$0.563681\pi$
$702$	−6.24481e8	+	3.39677e8i	−0.0681302	+	0.0370584i
$703$	5.40414e9			0.586655
$704$	−2.83261e9	+	4.90622e9i	−0.305972	+	0.529960i
$705$	1.97157e9	−	3.41486e9i	0.211910	−	0.367038i
$706$	−4.94761e9	−	8.56952e9i	−0.529151	−	0.916516i
$707$	3.15432e9			0.335689
$708$	−2.30164e8	−	3.98656e8i	−0.0243737	−	0.0422165i
$709$	6.04518e9	+	1.04706e10i	0.637012	+	1.10334i	0.986085	+	0.166241i	$0.0531631\pi$
$709$	6.04518e9	+	1.04706e10i	0.637012	+	1.10334i	−0.349073	+	0.937095i	$0.613504\pi$
$710$	1.50191e9			0.157485
$711$	7.96930e9	+	1.38032e10i	0.831527	+	1.44025i
$712$	−3.53006e9	+	6.11424e9i	−0.366524	+	0.634838i
$713$	5.50287e9	−	9.53126e9i	0.568560	−	0.984775i
$714$	1.54379e9			0.158725
$715$	1.73499e9	−	9.43725e8i	0.177512	−	0.0965549i
$716$	5.88480e7			0.00599150
$717$	3.27647e9	−	5.67501e9i	0.331963	−	0.574976i
$718$	−1.88515e9	+	3.26518e9i	−0.190069	+	0.329209i
$719$	6.62275e9	+	1.14709e10i	0.664488	+	1.15093i	0.979424	+	0.201814i	$0.0646838\pi$
$719$	6.62275e9	+	1.14709e10i	0.664488	+	1.15093i	−0.314935	+	0.949113i	$0.601983\pi$
$720$	2.78958e9			0.278532
$721$	−2.46782e8	−	4.27440e8i	−0.0245211	−	0.0424719i
$722$	1.60097e9	+	2.77296e9i	0.158308	+	0.274197i
$723$	−1.84772e10			−1.81825
$724$	−1.27585e9	−	2.20984e9i	−0.124944	−	0.216409i
$725$	6.31359e9	−	1.09355e10i	0.615309	−	1.06575i
$726$	−2.99165e9	+	5.18169e9i	−0.290157	+	0.502566i
$727$	6.14238e9			0.592880			0.296440	−	0.955052i	$-0.404201\pi$
$727$	6.14238e9			0.592880			0.296440	+	0.955052i	$0.404201\pi$
$728$	−8.99308e7	+	3.53650e9i	−0.00863871	+	0.339714i
$729$	−9.35868e9			−0.894681
$730$	−1.44227e9	+	2.49808e9i	−0.137220	+	0.237671i
$731$	−8.39228e8	+	1.45359e9i	−0.0794638	+	0.137635i
$732$	−6.77968e8	−	1.17427e9i	−0.0638881	−	0.110657i
$733$	8.43952e9			0.791505			0.395752	−	0.918357i	$-0.370484\pi$
$733$	8.43952e9			0.791505			0.395752	+	0.918357i	$0.370484\pi$
$734$	−1.45856e8	−	2.52630e8i	−0.0136141	−	0.0235802i
$735$	2.76491e8	+	4.78897e8i	0.0256848	+	0.0444874i
$736$	5.24988e9			0.485374
$737$	−8.29753e9	−	1.43717e10i	−0.763506	−	1.32243i
$738$	−4.70317e9	+	8.14614e9i	−0.430719	+	0.746027i
$739$	−6.44326e9	+	1.11601e10i	−0.587287	+	1.01721i	0.407299	+	0.913295i	$0.366471\pi$
$739$	−6.44326e9	+	1.11601e10i	−0.587287	+	1.01721i	−0.994586	+	0.103916i	$0.966863\pi$
$740$	−2.46307e8			−0.0223442
$741$	1.49962e10	+	9.17410e9i	1.35400	+	0.828323i
$742$	−2.99032e9			−0.268722
$743$	−9.26733e9	+	1.60515e10i	−0.828884	+	1.43567i	0.0700299	+	0.997545i	$0.477691\pi$
$743$	−9.26733e9	+	1.60515e10i	−0.828884	+	1.43567i	−0.898914	+	0.438125i	$0.855643\pi$
$744$	5.49716e9	−	9.52136e9i	0.489365	−	0.847606i
$745$	9.67429e8	+	1.67564e9i	0.0857180	+	0.148468i
$746$	1.91222e10			1.68637
$747$	4.26343e8	+	7.38447e8i	0.0374228	+	0.0648183i
$748$	−2.10091e8	−	3.63889e8i	−0.0183549	−	0.0317917i
$749$	4.99834e9			0.434650
$750$	4.34119e9	+	7.51917e9i	0.375746	+	0.650812i
$751$	−8.84498e9	+	1.53200e10i	−0.762004	+	1.31983i	0.179813	+	0.983701i	$0.442451\pi$
$751$	−8.84498e9	+	1.53200e10i	−0.762004	+	1.31983i	−0.941816	+	0.336128i	$0.890883\pi$
$752$	7.83358e9	−	1.35682e10i	0.671735	−	1.16348i
$753$	6.90405e9			0.589280
$754$	−4.26266e8	+	1.67628e10i	−0.0362144	+	1.42412i
$755$	−4.11458e9			−0.347945
$756$	−2.70864e7	+	4.69150e7i	−0.00227995	+	0.00394899i
$757$	7.10445e8	−	1.23053e9i	0.0595243	−	0.103099i	−0.834728	−	0.550663i	$-0.814375\pi$
$757$	7.10445e8	−	1.23053e9i	0.0595243	−	0.103099i	0.894252	+	0.447564i	$0.147708\pi$
$758$	−6.27915e9	−	1.08758e10i	−0.523671	−	0.907025i
$759$	1.92343e10			1.59673
$760$	1.59351e9	+	2.76004e9i	0.131676	+	0.228070i
$761$	−4.43204e9	−	7.67653e9i	−0.364551	−	0.631420i	0.624153	−	0.781302i	$-0.285444\pi$
$761$	−4.43204e9	−	7.67653e9i	−0.364551	−	0.631420i	−0.988704	+	0.149882i	$0.952111\pi$
$762$	−3.18698e10			−2.60938
$763$	2.72135e9	+	4.71351e9i	0.221793	+	0.384157i
$764$	−1.03363e9	+	1.79030e9i	−0.0838566	+	0.145244i
$765$	4.21113e8	−	7.29389e8i	0.0340082	−	0.0589039i
$766$	6.33367e9			0.509160
$767$	6.59842e7	−	2.59481e9i	0.00528027	−	0.207645i
$768$	8.60261e9			0.685277
$769$	−5.76826e9	+	9.99091e9i	−0.457407	+	0.792251i	−0.998823	−	0.0485032i	$-0.984555\pi$
$769$	−5.76826e9	+	9.99091e9i	−0.457407	+	0.792251i	0.541417	+	0.840755i	$0.317888\pi$
$770$	5.22865e8	−	9.05630e8i	0.0412736	−	0.0714880i
$771$	−1.23513e9	−	2.13931e9i	−0.0970559	−	0.168106i
$772$	2.05477e9			0.160732
$773$	−5.49559e9	−	9.51865e9i	−0.427944	−	0.741220i	0.568747	−	0.822513i	$-0.307428\pi$
$773$	−5.49559e9	−	9.51865e9i	−0.427944	−	0.741220i	−0.996690	+	0.0812928i	$0.974095\pi$
$774$	3.77570e9	+	6.53970e9i	0.292687	+	0.506950i
$775$	9.43488e9			0.728082
$776$	4.46456e9	+	7.73285e9i	0.342975	+	0.594050i
$777$	1.77970e9	−	3.08254e9i	0.136105	−	0.235741i
$778$	−7.89785e9	+	1.36795e10i	−0.601285	+	1.04146i
$779$	−1.26058e10			−0.955409
$780$	−6.83488e8	−	4.18132e8i	−0.0515703	−	0.0315487i
$781$	5.90736e9			0.443726
$782$	2.93315e9	−	5.08037e9i	0.219337	−	0.379902i
$783$	6.35263e8	−	1.10031e9i	0.0472920	−	0.0819121i
$784$	1.09857e9	+	1.90278e9i	0.0814184	+	0.141021i
$785$	2.54162e9			0.187528
$786$	−8.92578e9	−	1.54599e10i	−0.655643	−	1.13561i
$787$	−6.67857e9	−	1.15676e10i	−0.488396	−	0.845926i	0.511515	−	0.859274i	$-0.329084\pi$
$787$	−6.67857e9	−	1.15676e10i	−0.488396	−	0.845926i	−0.999911	+	0.0133480i	$0.995751\pi$
$788$	−2.92818e9			−0.213185
$789$	4.28603e9	+	7.42361e9i	0.310660	+	0.538079i
$790$	3.38204e9	−	5.85786e9i	0.244053	−	0.422712i
$791$	−4.49529e9	+	7.78606e9i	−0.322953	+	0.559371i
$792$	9.35374e9			0.669032
$793$	1.94362e8	−	7.64321e9i	0.0138406	−	0.544277i
$794$	−2.51185e10			−1.78083
$795$	−1.67559e9	+	2.90220e9i	−0.118272	+	0.204853i
$796$	2.16168e9	−	3.74413e9i	0.151913	−	0.263121i
$797$	−5.21231e9	−	9.02799e9i	−0.364692	−	0.631665i	0.624035	−	0.781397i	$-0.285492\pi$
$797$	−5.21231e9	−	9.02799e9i	−0.364692	−	0.631665i	−0.988727	+	0.149732i	$0.952159\pi$
$798$	9.30800e9			0.648405
$799$	−2.36510e9	−	4.09648e9i	−0.164035	−	0.284117i
$800$	2.25028e9	+	3.89759e9i	0.155389	+	0.269142i
$801$	1.12492e10			0.773409
$802$	−1.73950e9	−	3.01290e9i	−0.119073	−	0.206241i
$803$	−5.67279e9	+	9.82556e9i	−0.386627	+	0.669658i
$804$	−3.36616e9	+	5.83036e9i	−0.228422	+	0.395639i
$805$	2.10129e9			0.141972
$806$	−1.10062e10	+	5.98665e9i	−0.740396	+	0.402727i
$807$	1.64369e10			1.10093
$808$	5.98686e9	−	1.03696e10i	0.399264	−	0.691545i
$809$	−8.69150e9	+	1.50541e10i	−0.577132	+	0.999622i	0.418675	+	0.908136i	$0.362495\pi$
$809$	−8.69150e9	+	1.50541e10i	−0.577132	+	0.999622i	−0.995806	+	0.0914853i	$0.970839\pi$
$810$	2.20817e9	+	3.82467e9i	0.145994	+	0.252869i
$811$	−5.75582e9			−0.378908			−0.189454	−	0.981890i	$-0.560672\pi$
$811$	−5.75582e9			−0.378908			−0.189454	+	0.981890i	$0.560672\pi$
$812$	6.38908e8	+	1.10662e9i	0.0418786	+	0.0725359i
$813$	−2.04814e10	−	3.54748e10i	−1.33673	−	2.31528i
$814$	−6.73110e9			−0.437422
$815$	−2.61883e9	−	4.53595e9i	−0.169456	−	0.293506i
$816$	3.43706e9	−	5.95316e9i	0.221448	−	0.383559i
$817$	−5.05996e9	+	8.76410e9i	−0.324616	+	0.562251i
$818$	−2.59255e10			−1.65612
$819$	4.95159e9	−	2.69335e9i	0.314957	−	0.171316i
$820$	5.74540e8			0.0363891
$821$	−1.26985e10	+	2.19944e10i	−0.800849	+	1.38711i	0.118209	+	0.992989i	$0.462285\pi$
$821$	−1.26985e10	+	2.19944e10i	−0.800849	+	1.38711i	−0.919058	+	0.394122i	$0.871049\pi$
$822$	4.51100e9	−	7.81328e9i	0.283283	−	0.490661i
$823$	1.20213e10	+	2.08215e10i	0.751714	+	1.30201i	0.946992	+	0.321259i	$0.104106\pi$
$823$	1.20213e10	+	2.08215e10i	0.751714	+	1.30201i	−0.195278	+	0.980748i	$0.562561\pi$
$824$	−1.87356e9			−0.116660
$825$	8.24449e9	+	1.42799e10i	0.511182	+	0.885392i
$826$	−6.87159e8	−	1.19019e9i	−0.0424255	−	0.0734831i
$827$	1.03283e9			0.0634978			0.0317489	−	0.999496i	$-0.489892\pi$
$827$	1.03283e9			0.0634978			0.0317489	+	0.999496i	$0.489892\pi$
$828$	−1.89930e9	−	3.28968e9i	−0.116275	−	0.201394i
$829$	−6.68177e9	+	1.15732e10i	−0.407334	+	0.705523i	−0.994590	−	0.103878i	$-0.966875\pi$
$829$	−6.68177e9	+	1.15732e10i	−0.407334	+	0.705523i	0.587256	+	0.809401i	$0.300208\pi$
$830$	1.80933e8	−	3.13385e8i	0.0109836	−	0.0190241i
$831$	1.76766e10			1.06855
$832$	1.10547e10	+	6.76284e9i	0.665450	+	0.407097i
$833$	6.63360e8			0.0397642
$834$	3.46525e8	−	6.00199e8i	0.0206849	−	0.0358273i
$835$	−2.02247e8	+	3.50302e8i	−0.0120221	+	0.0208228i
$836$	−1.26670e9	−	2.19400e9i	−0.0749813	−	0.129871i
$837$	9.49322e8			0.0559596
$838$	2.26857e9	+	3.92929e9i	0.133168	+	0.230653i
$839$	9.56288e9	+	1.65634e10i	0.559013	+	0.968239i	0.997579	+	0.0695402i	$0.0221532\pi$
$839$	9.56288e9	+	1.65634e10i	0.559013	+	0.968239i	−0.438566	+	0.898699i	$0.644513\pi$
$840$	2.09911e9			0.122196
$841$	−6.35950e9	−	1.10150e10i	−0.368669	−	0.638554i
$842$	−7.59417e9	+	1.31535e10i	−0.438418	+	0.759362i
$843$	−1.20975e9	+	2.09534e9i	−0.0695501	+	0.120464i
$844$	3.12072e9			0.178672
$845$	−2.05719e9	−	4.02242e9i	−0.117294	−	0.229345i
$846$	−2.12813e10			−1.20837
$847$	−1.28550e9	+	2.22654e9i	−0.0726906	+	0.125904i
$848$	−6.65755e9	+	1.15312e10i	−0.374912	+	0.649366i
$849$	5.33322e9	+	9.23741e9i	0.299097	+	0.518052i
$850$	5.02900e9			0.280876
$851$	−6.76275e9	−	1.17134e10i	−0.376157	−	0.651524i
$852$	−1.19826e9	−	2.07544e9i	−0.0663760	−	0.114967i
$853$	3.51283e10			1.93792			0.968959	−	0.247222i	$-0.0795178\pi$
$853$	3.51283e10			1.93792			0.968959	+	0.247222i	$0.0795178\pi$
$854$	−2.02408e9	−	3.50581e9i	−0.111205	−	0.192613i
$855$	2.53902e9	−	4.39770e9i	0.138926	−	0.240627i
$856$	9.48680e9	−	1.64316e10i	0.516966	−	0.895411i
$857$	2.84685e10			1.54501			0.772507	−	0.635006i	$-0.219003\pi$
$857$	2.84685e10			1.54501			0.772507	+	0.635006i	$0.219003\pi$
$858$	−1.86785e10	−	1.14268e10i	−1.00957	−	0.617615i
$859$	2.83134e10			1.52411			0.762055	−	0.647513i	$-0.224191\pi$
$859$	2.83134e10			1.52411			0.762055	+	0.647513i	$0.224191\pi$
$860$	2.30620e8	−	3.99445e8i	0.0123638	−	0.0214147i
$861$	−4.15137e9	+	7.19039e9i	−0.221657	+	0.383921i
$862$	−8.09052e9	−	1.40132e10i	−0.430231	−	0.745181i
$863$	−3.14662e10			−1.66650			−0.833252	−	0.552893i	$-0.813524\pi$
$863$	−3.14662e10			−1.66650			−0.833252	+	0.552893i	$0.813524\pi$
$864$	2.26419e8	+	3.92169e8i	0.0119430	+	0.0206859i
$865$	−1.90972e9	−	3.30774e9i	−0.100326	−	0.173770i
$866$	−2.54470e10			−1.33145
$867$	1.23559e10	+	2.14010e10i	0.643884	+	1.11524i
$868$	−4.77385e8	+	8.26855e8i	−0.0247770	+	0.0429151i
$869$	1.33024e10	−	2.30404e10i	0.687638	−	1.19102i
$870$	9.94966e9			0.512260
$871$	−3.33474e10	+	1.81388e10i	−1.71001	+	0.930135i
$872$	2.06603e10			1.05519
$873$	7.11361e9	−	1.23211e10i	0.361859	−	0.626759i
$874$	1.76849e10	−	3.06311e10i	0.896007	−	1.55193i
$875$	1.86539e9	+	3.23094e9i	0.0941327	+	0.163043i
$876$	4.60270e9			0.231339
$877$	4.45390e9	+	7.71439e9i	0.222968	+	0.386192i	0.955708	−	0.294317i	$-0.0950922\pi$
$877$	4.45390e9	+	7.71439e9i	0.222968	+	0.386192i	−0.732740	+	0.680509i	$0.761759\pi$
$878$	3.43064e9	+	5.94204e9i	0.171058	+	0.296282i
$879$	−2.69050e10			−1.33620
$880$	−2.32818e9	−	4.03253e9i	−0.115167	−	0.199475i
$881$	1.06161e10	−	1.83876e10i	0.523057	−	0.905960i	−0.476583	−	0.879129i	$-0.658125\pi$
$881$	1.06161e10	−	1.83876e10i	0.523057	−	0.905960i	0.999640	−	0.0268312i	$-0.00854167\pi$
$882$	1.49223e9	−	2.58462e9i	0.0732313	−	0.126840i
$883$	−3.13490e10			−1.53236			−0.766181	−	0.642625i	$-0.777845\pi$
$883$	−3.13490e10			−1.53236			−0.766181	+	0.642625i	$0.777845\pi$
$884$	−8.44349e8	+	4.59271e8i	−0.0411092	+	0.0223607i
$885$	−1.54016e9			−0.0746905
$886$	2.17873e10	−	3.77368e10i	1.05241	−	1.82283i
$887$	−1.32271e10	+	2.29101e10i	−0.636405	+	1.10229i	0.349811	+	0.936820i	$0.386246\pi$
$887$	−1.32271e10	+	2.29101e10i	−0.636405	+	1.10229i	−0.986216	+	0.165465i	$0.947087\pi$
$888$	−6.75572e9	−	1.17013e10i	−0.323762	−	0.560773i
$889$	−1.36943e10			−0.653707
$890$	−2.38700e9	−	4.13440e9i	−0.113498	−	0.196584i
$891$	8.68527e9	+	1.50433e10i	0.411350	+	0.712479i
$892$	4.59727e9			0.216882
$893$	−1.42599e10	−	2.46989e10i	−0.670096	−	1.16064i
$894$	1.07254e10	−	1.85770e10i	0.502035	−	0.869550i
$895$	9.84466e7	−	1.70514e8i	0.00459008	−	0.00795025i
$896$	9.57048e9			0.444484
$897$	1.11850e9	−	4.39846e10i	0.0517443	−	2.03483i
$898$	1.69900e10			0.782937
$899$	1.11962e10	−	1.93924e10i	0.513939	−	0.890169i
$900$	1.62821e9	−	2.82013e9i	0.0744493	−	0.128950i
$901$	2.01004e9	+	3.48149e9i	0.0915520	+	0.158573i
$902$	1.57011e10			0.712373
$903$	3.33271e9	+	5.77243e9i	0.150623	+	0.260887i
$904$	1.70640e10	+	2.95557e10i	0.768231	+	1.33062i
$905$	−8.53746e9			−0.382877
$906$	2.28082e10	+	3.95050e10i	1.01893	+	1.76483i
$907$	−1.42799e10	+	2.47335e10i	−0.635476	+	1.10068i	0.350938	+	0.936399i	$0.385863\pi$
$907$	−1.42799e10	+	2.47335e10i	−0.635476	+	1.10068i	−0.986414	+	0.164278i	$0.947470\pi$
$908$	−9.44894e7	+	1.63660e8i	−0.00418873	+	0.00725510i
$909$	−1.90783e10			−0.842494
$910$	−2.04057e9	−	1.24834e9i	−0.0897647	−	0.0549146i
$911$	3.22154e10			1.41172			0.705860	−	0.708351i	$-0.250561\pi$
$911$	3.22154e10			1.41172			0.705860	+	0.708351i	$0.250561\pi$
$912$	2.07231e10	−	3.58934e10i	0.904632	−	1.56687i
$913$	7.11652e8	−	1.23262e9i	0.0309471	−	0.0536020i
$914$	−1.98831e9	−	3.44385e9i	−0.0861335	−	0.149188i
$915$	−4.53668e9			−0.195778
$916$	1.92800e9	+	3.33940e9i	0.0828846	+	0.143560i
$917$	−3.83536e9	−	6.64303e9i	−0.164253	−	0.284494i
$918$	5.06009e8			0.0215878
$919$	−1.84088e9	−	3.18849e9i	−0.0782385	−	0.135513i	0.824252	−	0.566224i	$-0.191596\pi$
$919$	−1.84088e9	−	3.18849e9i	−0.0782385	−	0.135513i	−0.902490	+	0.430711i	$0.858263\pi$
$920$	3.98824e9	−	6.90783e9i	0.168859	−	0.292472i
$921$	−1.50880e10	+	2.61332e10i	−0.636390	+	1.10226i
$922$	8.15854e9			0.342810
$923$	3.43520e8	−	1.35088e10i	0.0143796	−	0.565472i
$924$	−1.66862e9			−0.0695832
$925$	5.79748e9	−	1.00415e10i	0.240848	−	0.417161i
$926$	−1.71233e9	+	2.96585e9i	−0.0708679	+	0.122747i
$927$	1.49262e9	+	2.58529e9i	0.0615418	+	0.106593i
$928$	1.06814e10			0.438745
$929$	−1.82634e10	−	3.16331e10i	−0.747354	−	1.29445i	−0.949087	−	0.315014i	$-0.897991\pi$
$929$	−1.82634e10	−	3.16331e10i	−0.747354	−	1.29445i	0.201733	−	0.979440i	$-0.435343\pi$
$930$	3.71713e9	+	6.43826e9i	0.151537	+	0.262469i
$931$	3.99960e9			0.162440
$932$	−3.45385e9	−	5.98224e9i	−0.139749	−	0.242052i
$933$	−1.96092e10	+	3.39641e10i	−0.790449	+	1.36910i
$934$	1.61673e9	−	2.80026e9i	0.0649267	−	0.112456i
$935$	−1.40584e9			−0.0562467
$936$	5.43931e8	−	2.13899e10i	0.0216809	−	0.852596i
$937$	−9.20129e9			−0.365393			−0.182696	−	0.983169i	$-0.558483\pi$
$937$	−9.20129e9			−0.365393			−0.182696	+	0.983169i	$0.558483\pi$
$938$	−1.00497e10	+	1.74066e10i	−0.397598	+	0.688660i
$939$	1.00479e10	−	1.74035e10i	0.396046	−	0.685972i
$940$	6.49930e8	+	1.12571e9i	0.0255223	+	0.0442059i
$941$	−3.93466e10			−1.53937			−0.769686	−	0.638423i	$-0.779587\pi$
$941$	−3.93466e10			−1.53937			−0.769686	+	0.638423i	$0.779587\pi$
$942$	−1.40889e10	−	2.44027e10i	−0.549159	−	0.951172i
$943$	1.57749e10	+	2.73229e10i	0.612599	+	1.06105i
$944$	−6.11948e9			−0.236762
$945$	9.06255e7	+	1.56968e8i	0.00349333	+	0.00605062i
$946$	6.30241e9	−	1.09161e10i	0.242040	−	0.419226i
$947$	−2.26461e10	+	3.92241e10i	−0.866498	+	1.50082i	−0.000946463		1.00000i	$0.500301\pi$
$947$	−2.26461e10	+	3.92241e10i	−0.866498	+	1.50082i	−0.865552	+	0.500819i	$0.833032\pi$
$948$	−1.07931e10			−0.411449
$949$	2.21390e10	+	1.35438e10i	0.840863	+	0.514408i
$950$	3.03213e10			1.14740
$951$	7.30189e8	−	1.26472e9i	0.0275298	−	0.0476831i
$952$	1.25905e9	−	2.18074e9i	0.0472949	−	0.0819171i
$953$	−3.56611e7	−	6.17669e7i	−0.00133466	−	0.00231169i	0.865357	−	0.501155i	$-0.167092\pi$
$953$	−3.56611e7	−	6.17669e7i	−0.00133466	−	0.00231169i	−0.866692	+	0.498844i	$0.833758\pi$
$954$	1.80864e10			0.674424
$955$	3.45831e9	+	5.98996e9i	0.128485	+	0.222542i
$956$	1.08009e9	+	1.87077e9i	0.0399814	+	0.0692498i
$957$	3.91344e10			1.44333
$958$	8.87118e9	+	1.53653e10i	0.325988	+	0.564628i
$959$	1.93835e9	−	3.35732e9i	0.0709687	−	0.122921i
$960$	3.84478e9	−	6.65936e9i	0.140256	−	0.242931i
$961$	−1.07813e10			−0.391867
$962$	−3.91421e8	+	1.53925e10i	−0.0141753	+	0.557438i
$963$	−3.02316e10			−1.09086
$964$	3.04552e9	−	5.27500e9i	0.109494	−	0.189650i
$965$	3.43741e9	−	5.95377e9i	0.123136	−	0.213278i
$966$	−1.16480e10	−	2.01750e10i	−0.415751	−	0.720101i
$967$	8.55631e9			0.304294			0.152147	−	0.988358i	$-0.451381\pi$
$967$	8.55631e9			0.304294			0.152147	+	0.988358i	$0.451381\pi$
$968$	4.87971e9	+	8.45191e9i	0.172914	+	0.299496i
$969$	−6.25668e9	−	1.08369e10i	−0.220908	−	0.382623i
$970$	−6.03780e9			−0.212411
$971$	−1.17889e10	−	2.04189e10i	−0.413243	−	0.715758i	0.581999	−	0.813189i	$-0.302271\pi$
$971$	−1.17889e10	−	2.04189e10i	−0.413243	−	0.715758i	−0.995242	+	0.0974317i	$0.968937\pi$
$972$	3.35075e9	−	5.80368e9i	0.117034	−	0.202708i
$973$	1.48900e8	−	2.57902e8i	0.00518203	−	0.00897553i
$974$	8.92298e9			0.309424
$975$	3.31343e10	−	1.80229e10i	1.14488	−	0.622743i
$976$	−1.80254e10			−0.620599
$977$	1.64409e10	−	2.84764e10i	0.564019	−	0.976910i	−0.433121	−	0.901336i	$-0.642588\pi$
$977$	1.64409e10	−	2.84764e10i	0.564019	−	0.976910i	0.997140	−	0.0755742i	$-0.0240790\pi$
$978$	−2.90338e10	+	5.02881e10i	−0.992472	+	1.71901i
$979$	−9.38863e9	−	1.62616e10i	−0.319788	−	0.553890i
$980$	−1.82291e8			−0.00618692
$981$	−1.64596e10	−	2.85088e10i	−0.556644	−	0.964135i
$982$	2.18774e10	+	3.78928e10i	0.737235	+	1.27693i
$983$	2.33197e10			0.783043			0.391522	−	0.920169i	$-0.371949\pi$
$983$	2.33197e10			0.783043			0.391522	+	0.920169i	$0.371949\pi$
$984$	1.57585e10	+	2.72946e10i	0.527270	+	0.913258i
$985$	−4.89855e9	+	8.48454e9i	−0.163321	+	0.282879i
$986$	5.96782e9	−	1.03366e10i	0.198265	−	0.343405i
$987$	−1.87845e10			−0.621854
$988$	−5.09083e9	+	2.76908e9i	−0.167934	+	0.0913454i
$989$	2.53281e10			0.832561
$990$	−3.16246e9	+	5.47754e9i	−0.103586	+	0.179417i
$991$	8.66081e9	−	1.50010e10i	0.282684	−	0.489622i	−0.689361	−	0.724418i	$-0.742109\pi$
$991$	8.66081e9	−	1.50010e10i	0.282684	−	0.489622i	0.972045	+	0.234795i	$0.0754420\pi$
$992$	3.99052e9	+	6.91179e9i	0.129789	+	0.224802i
$993$	−1.16574e10			−0.377814
$994$	−3.57741e9	−	6.19626e9i	−0.115536	−	0.200114i
$995$	−7.23252e9	−	1.25271e10i	−0.232760	−	0.403153i
$996$	−5.77410e8			−0.0185172
$997$	−1.09229e10	−	1.89189e10i	−0.349063	−	0.604594i	0.637021	−	0.770847i	$-0.280167\pi$
$997$	−1.09229e10	−	1.89189e10i	−0.349063	−	0.604594i	−0.986083	+	0.166253i	$0.946833\pi$
$998$	1.00558e10	−	1.74171e10i	0.320227	−	0.554650i
$999$	5.83333e8	−	1.01036e9i	0.0185113	−	0.0320626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.f.a.22.19	✓	48
13.3	even	3	inner	91.8.f.a.29.19	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.f.a.22.19	✓	48	1.1	even	1	trivial
91.8.f.a.29.19	yes	48	13.3	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.11392 - 10.5896i) q^{2} +(-32.6404 + 56.5348i) q^{3} +(-10.7599 - 18.6367i) q^{4} -72.0010 q^{5} +(399.121 + 691.298i) q^{6} +(171.500 + 297.047i) q^{7} +1302.02 q^{8} +(-1037.29 - 1796.63i) q^{9} +O(q^{10})\)	\(q+(6.11392 - 10.5896i) q^{2} +(-32.6404 + 56.5348i) q^{3} +(-10.7599 - 18.6367i) q^{4} -72.0010 q^{5} +(399.121 + 691.298i) q^{6} +(171.500 + 297.047i) q^{7} +1302.02 q^{8} +(-1037.29 - 1796.63i) q^{9} +(-440.208 + 762.462i) q^{10} +(-1731.44 + 2998.95i) q^{11} +1404.83 q^{12} +(6757.23 + 4133.81i) q^{13} +4194.15 q^{14} +(2350.14 - 4070.56i) q^{15} +(9337.72 - 16173.4i) q^{16} +(-2819.23 - 4883.05i) q^{17} -25367.6 q^{18} +(-16998.0 - 29441.4i) q^{19} +(774.725 + 1341.86i) q^{20} -22391.3 q^{21} +(21171.8 + 36670.6i) q^{22} +(-42542.6 + 73686.0i) q^{23} +(-42498.5 + 73609.5i) q^{24} -72940.9 q^{25} +(85088.6 - 46282.7i) q^{26} -7339.19 q^{27} +(3690.65 - 6392.40i) q^{28} +(-86557.6 + 149922. i) q^{29} +(-28737.1 - 49774.1i) q^{30} -129350. q^{31} +(-30850.7 - 53434.9i) q^{32} +(-113030. - 195773. i) q^{33} -68946.2 q^{34} +(-12348.2 - 21387.7i) q^{35} +(-22322.3 + 38663.3i) q^{36} +(-79482.0 + 137667. i) q^{37} -415697. q^{38} +(-454262. + 247089. i) q^{39} -93746.8 q^{40} +(185401. - 321124. i) q^{41} +(-136898. + 237115. i) q^{42} +(-148840. - 257798. i) q^{43} +74520.8 q^{44} +(74685.7 + 129359. i) q^{45} +(520204. + 901020. i) q^{46} +838918. q^{47} +(609573. + 1.05581e6i) q^{48} +(-58824.5 + 101887. i) q^{49} +(-445954. + 772415. i) q^{50} +368083. q^{51} +(4333.47 - 170412. i) q^{52} -712974. q^{53} +(-44871.2 + 77719.2i) q^{54} +(124666. - 215927. i) q^{55} +(223297. + 386761. i) q^{56} +2.21928e6 q^{57} +(1.05841e6 + 1.83322e6i) q^{58} +(-163838. - 283775. i) q^{59} -101149. q^{60} +(-482597. - 835883. i) q^{61} +(-790833. + 1.36976e6i) q^{62} +(355790. - 616246. i) q^{63} +1.63598e6 q^{64} +(-486527. - 297638. i) q^{65} -2.76422e6 q^{66} +(-2.39613e6 + 4.15022e6i) q^{67} +(-60669.5 + 105083. i) q^{68} +(-2.77721e6 - 4.81028e6i) q^{69} -301983. q^{70} +(-852954. - 1.47736e6i) q^{71} +(-1.35057e6 - 2.33926e6i) q^{72} +3.27634e6 q^{73} +(971892. + 1.68337e6i) q^{74} +(2.38082e6 - 4.12370e6i) q^{75} +(-365794. + 633575. i) q^{76} -1.18777e6 q^{77} +(-160743. + 6.32115e6i) q^{78} -7.68282e6 q^{79} +(-672325. + 1.16450e6i) q^{80} +(2.50810e6 - 4.34416e6i) q^{81} +(-2.26705e6 - 3.92665e6i) q^{82} -411017. q^{83} +(240929. + 417301. i) q^{84} +(202988. + 351585. i) q^{85} -3.63997e6 q^{86} +(-5.65054e6 - 9.78703e6i) q^{87} +(-2.25438e6 + 3.90469e6i) q^{88} +(-2.71121e6 + 4.69596e6i) q^{89} +1.82649e6 q^{90} +(-69070.2 + 2.71616e6i) q^{91} +1.83102e6 q^{92} +(4.22202e6 - 7.31275e6i) q^{93} +(5.12907e6 - 8.88381e6i) q^{94} +(1.22387e6 + 2.11981e6i) q^{95} +4.02791e6 q^{96} +(3.42895e6 + 5.93911e6i) q^{97} +(719296. + 1.24586e6i) q^{98} +7.18401e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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