LMFDB - Embedded newform 50.3.f.b.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	50.47
Dual form			50.3.f.b.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26007 + 0.642040i) q^{2} +(0.185739 - 0.0294182i) q^{3} +(1.17557 - 1.61803i) q^{4} +(4.66951 + 1.78765i) q^{5} +(-0.215157 + 0.156321i) q^{6} +(7.34278 + 7.34278i) q^{7} +(-0.442463 + 2.79360i) q^{8} +(-8.52588 + 2.77022i) q^{9} +O(q^{10})$	\(q+(-1.26007 + 0.642040i) q^{2} +(0.185739 - 0.0294182i) q^{3} +(1.17557 - 1.61803i) q^{4} +(4.66951 + 1.78765i) q^{5} +(-0.215157 + 0.156321i) q^{6} +(7.34278 + 7.34278i) q^{7} +(-0.442463 + 2.79360i) q^{8} +(-8.52588 + 2.77022i) q^{9} +(-7.03167 + 0.745442i) q^{10} +(5.47552 - 16.8519i) q^{11} +(0.170750 - 0.335116i) q^{12} +(7.48219 + 3.81236i) q^{13} +(-13.9668 - 4.53808i) q^{14} +(0.919900 + 0.194668i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-29.4384 - 4.66258i) q^{17} +(8.96464 - 8.96464i) q^{18} +(-9.36667 - 12.8921i) q^{19} +(8.38181 - 5.45392i) q^{20} +(1.57985 + 1.14783i) q^{21} +(3.92004 + 24.7502i) q^{22} +(-3.14877 - 6.17981i) q^{23} +0.531898i q^{24} +(18.6086 + 16.6949i) q^{25} -11.8758 q^{26} +(-3.01011 + 1.53373i) q^{27} +(20.5128 - 3.24891i) q^{28} +(-13.3163 + 18.3284i) q^{29} +(-1.28413 + 0.345317i) q^{30} +(13.0736 - 9.49852i) q^{31} +(4.00000 + 4.00000i) q^{32} +(0.521266 - 3.29114i) q^{33} +(40.0881 - 13.0254i) q^{34} +(21.1609 + 47.4135i) q^{35} +(-5.54045 + 17.0518i) q^{36} +(0.504956 - 0.991031i) q^{37} +(20.0799 + 10.2312i) q^{38} +(1.50189 + 0.487993i) q^{39} +(-7.06007 + 12.2538i) q^{40} +(-14.4667 - 44.5241i) q^{41} +(-2.72768 - 0.432022i) q^{42} +(8.20366 - 8.20366i) q^{43} +(-20.8301 - 28.6702i) q^{44} +(-44.7638 - 2.30567i) q^{45} +(7.93537 + 5.76538i) q^{46} +(-5.42280 - 34.2382i) q^{47} +(-0.341500 - 0.670231i) q^{48} +58.8327i q^{49} +(-34.1670 - 9.08929i) q^{50} -5.60502 q^{51} +(14.9644 - 7.62473i) q^{52} +(-31.2370 + 4.94745i) q^{53} +(2.80825 - 3.86522i) q^{54} +(55.6933 - 68.9019i) q^{55} +(-23.7617 + 17.2639i) q^{56} +(-2.11902 - 2.11902i) q^{57} +(5.01203 - 31.6447i) q^{58} +(58.9939 - 19.1683i) q^{59} +(1.39639 - 1.25958i) q^{60} +(-19.9613 + 61.4346i) q^{61} +(-10.3753 + 20.3626i) q^{62} +(-82.9447 - 42.2624i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(28.1230 + 31.1774i) q^{65} +(1.45621 + 4.48176i) q^{66} +(-59.8348 - 9.47690i) q^{67} +(-42.1511 + 42.1511i) q^{68} +(-0.766649 - 1.05520i) q^{69} +(-57.1056 - 46.1583i) q^{70} +(66.2647 + 48.1441i) q^{71} +(-3.96652 - 25.0436i) q^{72} +(23.7464 + 46.6049i) q^{73} +1.57297i q^{74} +(3.94749 + 2.55346i) q^{75} -31.8711 q^{76} +(163.945 - 83.5344i) q^{77} +(-2.20580 + 0.349364i) q^{78} +(1.37219 - 1.88866i) q^{79} +(1.02878 - 19.9735i) q^{80} +(64.7589 - 47.0501i) q^{81} +(46.8154 + 46.8154i) q^{82} +(-15.3387 + 96.8447i) q^{83} +(3.71446 - 1.20690i) q^{84} +(-129.128 - 74.3974i) q^{85} +(-5.07014 + 15.6043i) q^{86} +(-1.93418 + 3.79604i) q^{87} +(44.6549 + 22.7528i) q^{88} +(-6.69713 - 2.17603i) q^{89} +(57.8861 - 25.8348i) q^{90} +(26.9467 + 82.9333i) q^{91} +(-13.7008 - 2.16999i) q^{92} +(2.14885 - 2.14885i) q^{93} +(28.8154 + 39.6610i) q^{94} +(-20.6912 - 76.9441i) q^{95} +(0.860630 + 0.625284i) q^{96} +(-1.05060 - 6.63322i) q^{97} +(-37.7729 - 74.1335i) q^{98} +158.846i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−1.26007	+	0.642040i	−0.630037	+	0.321020i
$2$	−1.26007	+	0.642040i	−0.630037	+	0.321020i
$3$	0.185739	−	0.0294182i	0.0619131	−	0.00980607i	−0.125401	−	0.992106i	$-0.540022\pi$
$3$	0.185739	−	0.0294182i	0.0619131	−	0.00980607i	0.187314	+	0.982300i	$0.440022\pi$
$4$	1.17557	−	1.61803i	0.293893	−	0.404508i
$5$	4.66951	+	1.78765i	0.933902	+	0.357530i
$5$	4.66951	+	1.78765i	0.933902	+	0.357530i
$6$	−0.215157	+	0.156321i	−0.0358596	+	0.0260535i
$7$	7.34278	+	7.34278i	1.04897	+	1.04897i	0.998738	+	0.0502302i	$0.0159955\pi$
$7$	7.34278	+	7.34278i	1.04897	+	1.04897i	0.0502302	+	0.998738i	$0.484004\pi$
$8$	−0.442463	+	2.79360i	−0.0553079	+	0.349201i
$9$	−8.52588	+	2.77022i	−0.947319	+	0.307803i
$10$	−7.03167	+	0.745442i	−0.703167	+	0.0745442i
$11$	5.47552	−	16.8519i	0.497775	−	1.53199i	−0.314812	−	0.949154i	$-0.601942\pi$
$11$	5.47552	−	16.8519i	0.497775	−	1.53199i	0.812587	−	0.582840i	$-0.198058\pi$
$12$	0.170750	−	0.335116i	0.0142292	−	0.0279263i
$13$	7.48219	+	3.81236i	0.575553	+	0.293259i	0.717436	−	0.696625i	$-0.245316\pi$
$13$	7.48219	+	3.81236i	0.575553	+	0.293259i	−0.141883	+	0.989883i	$0.545316\pi$
$14$	−13.9668	−	4.53808i	−0.997628	−	0.324149i
$15$	0.919900	+	0.194668i	0.0613267	+	0.0129778i
$16$	−1.23607	−	3.80423i	−0.0772542	−	0.237764i
$17$	−29.4384	−	4.66258i	−1.73167	−	0.274269i	−0.790563	−	0.612381i	$-0.790212\pi$
$17$	−29.4384	−	4.66258i	−1.73167	−	0.274269i	−0.941106	+	0.338111i	$0.890212\pi$
$18$	8.96464	−	8.96464i	0.498035	−	0.498035i
$19$	−9.36667	−	12.8921i	−0.492983	−	0.678532i	0.487952	−	0.872870i	$-0.337744\pi$
$19$	−9.36667	−	12.8921i	−0.492983	−	0.678532i	−0.980935	+	0.194338i	$0.937744\pi$
$20$	8.38181	−	5.45392i	0.419091	−	0.272696i
$21$	1.57985	+	1.14783i	0.0752311	+	0.0546586i
$22$	3.92004	+	24.7502i	0.178184	+	1.12501i
$23$	−3.14877	−	6.17981i	−0.136903	−	0.268688i	0.812369	−	0.583144i	$-0.198178\pi$
$23$	−3.14877	−	6.17981i	−0.136903	−	0.268688i	−0.949272	+	0.314457i	$0.898178\pi$
$24$			0.531898i			0.0221624i
$25$	18.6086	+	16.6949i	0.744345	+	0.667795i
$26$	−11.8758			−0.456761
$27$	−3.01011	+	1.53373i	−0.111486	+	0.0568048i
$28$	20.5128	−	3.24891i	0.732600	−	0.116032i
$29$	−13.3163	+	18.3284i	−0.459184	+	0.632012i	−0.974339	−	0.225084i	$-0.927734\pi$
$29$	−13.3163	+	18.3284i	−0.459184	+	0.632012i	0.515155	+	0.857097i	$0.327734\pi$
$30$	−1.28413	+	0.345317i	−0.0428042	+	0.0115106i
$31$	13.0736	−	9.49852i	0.421729	−	0.306404i	−0.356604	−	0.934256i	$-0.616066\pi$
$31$	13.0736	−	9.49852i	0.421729	−	0.306404i	0.778333	+	0.627852i	$0.216066\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	0.521266	−	3.29114i	0.0157959	−	0.0997316i
$34$	40.0881	−	13.0254i	1.17906	−	0.383100i
$35$	21.1609	+	47.4135i	0.604596	+	1.35467i
$36$	−5.54045	+	17.0518i	−0.153901	+	0.473660i
$37$	0.504956	−	0.991031i	0.0136474	−	0.0267846i	−0.884082	−	0.467332i	$-0.845215\pi$
$37$	0.504956	−	0.991031i	0.0136474	−	0.0267846i	0.897730	+	0.440547i	$0.145215\pi$
$38$	20.0799	+	10.2312i	0.528419	+	0.269243i
$39$	1.50189	+	0.487993i	0.0385099	+	0.0125126i
$40$	−7.06007	+	12.2538i	−0.176502	+	0.306345i
$41$	−14.4667	−	44.5241i	−0.352847	−	1.08595i	−0.957247	−	0.289271i	$-0.906587\pi$
$41$	−14.4667	−	44.5241i	−0.352847	−	1.08595i	0.604400	−	0.796681i	$-0.293413\pi$
$42$	−2.72768	−	0.432022i	−0.0649448	−	0.0102862i
$43$	8.20366	−	8.20366i	0.190783	−	0.190783i	−0.605252	−	0.796034i	$-0.706927\pi$
$43$	8.20366	−	8.20366i	0.190783	−	0.190783i	0.796034	+	0.605252i	$0.206927\pi$
$44$	−20.8301	−	28.6702i	−0.473412	−	0.651596i
$45$	−44.7638	−	2.30567i	−0.994752	−	0.0512371i
$46$	7.93537	+	5.76538i	0.172508	+	0.125334i
$47$	−5.42280	−	34.2382i	−0.115379	−	0.728472i	−0.975764	−	0.218827i	$-0.929777\pi$
$47$	−5.42280	−	34.2382i	−0.115379	−	0.728472i	0.860385	−	0.509645i	$-0.170223\pi$
$48$	−0.341500	−	0.670231i	−0.00711458	−	0.0139631i
$49$			58.8327i			1.20067i
$50$	−34.1670	−	9.08929i	−0.683340	−	0.181786i
$51$	−5.60502			−0.109902
$52$	14.9644	−	7.62473i	0.287776	−	0.146629i
$53$	−31.2370	+	4.94745i	−0.589377	+	0.0933481i	−0.443998	−	0.896028i	$-0.646440\pi$
$53$	−31.2370	+	4.94745i	−0.589377	+	0.0933481i	−0.145379	+	0.989376i	$0.546440\pi$
$54$	2.80825	−	3.86522i	0.0520046	−	0.0715782i
$55$	55.6933	−	68.9019i	1.01261	−	1.25276i
$56$	−23.7617	+	17.2639i	−0.424316	+	0.308284i
$57$	−2.11902	−	2.11902i	−0.0371758	−	0.0371758i
$58$	5.01203	−	31.6447i	0.0864143	−	0.545598i
$59$	58.9939	−	19.1683i	0.999897	−	0.324886i	0.237073	−	0.971492i	$-0.423812\pi$
$59$	58.9939	−	19.1683i	0.999897	−	0.324886i	0.762825	+	0.646605i	$0.223812\pi$
$60$	1.39639	−	1.25958i	0.0232731	−	0.0209931i
$61$	−19.9613	+	61.4346i	−0.327234	+	1.00712i	0.643188	+	0.765709i	$0.277612\pi$
$61$	−19.9613	+	61.4346i	−0.327234	+	1.00712i	−0.970422	+	0.241415i	$0.922388\pi$
$62$	−10.3753	+	20.3626i	−0.167343	+	0.328429i
$63$	−82.9447	−	42.2624i	−1.31658	−	0.670832i
$64$	−7.60845	−	2.47214i	−0.118882	−	0.0386271i
$65$	28.1230	+	31.1774i	0.432661	+	0.479652i
$66$	1.45621	+	4.48176i	0.0220638	+	0.0679054i
$67$	−59.8348	−	9.47690i	−0.893057	−	0.141446i	−0.306993	−	0.951712i	$-0.599323\pi$
$67$	−59.8348	−	9.47690i	−0.893057	−	0.141446i	−0.586063	+	0.810265i	$0.699323\pi$
$68$	−42.1511	+	42.1511i	−0.619869	+	0.619869i
$69$	−0.766649	−	1.05520i	−0.0111109	−	0.0152928i
$70$	−57.1056	−	46.1583i	−0.815794	−	0.659405i
$71$	66.2647	+	48.1441i	0.933306	+	0.678086i	0.946800	−	0.321823i	$-0.104295\pi$
$71$	66.2647	+	48.1441i	0.933306	+	0.678086i	−0.0134942	+	0.999909i	$0.504295\pi$
$72$	−3.96652	−	25.0436i	−0.0550906	−	0.347828i
$73$	23.7464	+	46.6049i	0.325293	+	0.638423i	0.994510	−	0.104644i	$-0.0333703\pi$
$73$	23.7464	+	46.6049i	0.325293	+	0.638423i	−0.669217	+	0.743067i	$0.733370\pi$
$74$			1.57297i			0.0212564i
$75$	3.94749	+	2.55346i	0.0526331	+	0.0340461i
$76$	−31.8711			−0.419356
$77$	163.945	−	83.5344i	2.12916	−	1.08486i
$78$	−2.20580	+	0.349364i	−0.0282795	+	0.00447903i
$79$	1.37219	−	1.88866i	0.0173695	−	0.0239071i	−0.800244	−	0.599675i	$-0.795297\pi$
$79$	1.37219	−	1.88866i	0.0173695	−	0.0239071i	0.817613	+	0.575768i	$0.195297\pi$
$80$	1.02878	−	19.9735i	0.0128598	−	0.249669i
$81$	64.7589	−	47.0501i	0.799493	−	0.580865i
$82$	46.8154	+	46.8154i	0.570919	+	0.570919i
$83$	−15.3387	+	96.8447i	−0.184804	+	1.16680i	0.704574	+	0.709631i	$0.251138\pi$
$83$	−15.3387	+	96.8447i	−0.184804	+	1.16680i	−0.889378	+	0.457174i	$0.848862\pi$
$84$	3.71446	−	1.20690i	0.0442197	−	0.0143679i
$85$	−129.128	−	74.3974i	−1.51915	−	0.875263i
$86$	−5.07014	+	15.6043i	−0.0589551	+	0.181445i
$87$	−1.93418	+	3.79604i	−0.0222319	+	0.0436326i
$88$	44.6549	+	22.7528i	0.507442	+	0.258555i
$89$	−6.69713	−	2.17603i	−0.0752486	−	0.0244498i	0.271151	−	0.962537i	$-0.412596\pi$
$89$	−6.69713	−	2.17603i	−0.0752486	−	0.0244498i	−0.346399	+	0.938087i	$0.612596\pi$
$90$	57.8861	−	25.8348i	0.643178	−	0.287054i
$91$	26.9467	+	82.9333i	0.296117	+	0.911355i
$92$	−13.7008	−	2.16999i	−0.148921	−	0.0235868i
$93$	2.14885	−	2.14885i	0.0231059	−	0.0231059i
$94$	28.8154	+	39.6610i	0.306547	+	0.421925i
$95$	−20.6912	−	76.9441i	−0.217802	−	0.809938i
$96$	0.860630	+	0.625284i	0.00896489	+	0.00651338i
$97$	−1.05060	−	6.63322i	−0.0108309	−	0.0683837i	0.981681	−	0.190533i	$-0.0610215\pi$
$97$	−1.05060	−	6.63322i	−0.0108309	−	0.0683837i	−0.992512	+	0.122149i	$0.961021\pi$
$98$	−37.7729	−	74.1335i	−0.385438	−	0.756465i
$99$			158.846i			1.60450i
$100$	48.8886	−	10.4834i	0.488886	−	0.104834i
$101$	−40.1366			−0.397392			−0.198696	−	0.980061i	$-0.563671\pi$
$101$	−40.1366			−0.397392			−0.198696	+	0.980061i	$0.563671\pi$
$102$	7.06274	−	3.59865i	0.0692426	−	0.0352809i
$103$	−72.1217	+	11.4230i	−0.700211	+	0.110903i	−0.496382	−	0.868104i	$-0.665339\pi$
$103$	−72.1217	+	11.4230i	−0.700211	+	0.110903i	−0.203829	+	0.979007i	$0.565339\pi$
$104$	−13.9608	+	19.2154i	−0.134239	+	0.184764i
$105$	5.32522	+	8.18402i	0.0507164	+	0.0779431i
$106$	36.1844	−	26.2895i	0.341363	−	0.248014i
$107$	85.6650	+	85.6650i	0.800608	+	0.800608i	0.983190	−	0.182583i	$-0.0584457\pi$
$107$	85.6650	+	85.6650i	0.800608	+	0.800608i	−0.182583	+	0.983190i	$0.558446\pi$
$108$	−1.05697	+	6.67347i	−0.00978680	+	0.0617914i
$109$	181.039	−	58.8232i	1.66091	−	0.539662i	0.679847	−	0.733354i	$-0.262046\pi$
$109$	181.039	−	58.8232i	1.66091	−	0.539662i	0.981062	+	0.193692i	$0.0620461\pi$
$110$	−25.9399	+	122.579i	−0.235817	+	1.11435i
$111$	0.0646357	−	0.198928i	0.000582304	−	0.00179215i
$112$	18.8574	−	37.0097i	0.168370	−	0.330444i
$113$	−3.42176	−	1.74347i	−0.0302811	−	0.0154290i	0.438784	−	0.898592i	$-0.355409\pi$
$113$	−3.42176	−	1.74347i	−0.0302811	−	0.0154290i	−0.469065	+	0.883163i	$0.655409\pi$
$114$	4.03062	+	1.30963i	0.0353563	+	0.0114880i
$115$	−3.65589	−	34.4856i	−0.0317904	−	0.299875i
$116$	14.0016	+	43.0926i	0.120704	+	0.371488i
$117$	−74.3533	−	11.7764i	−0.635498	−	0.100653i
$118$	−62.0299	+	62.0299i	−0.525677	+	0.525677i
$119$	−181.923	−	250.396i	−1.52877	−	2.10416i
$120$	−0.950847	+	2.48370i	−0.00792372	+	0.0206975i
$121$	−156.115	−	113.424i	−1.29021	−	0.937391i
$122$	−14.2907	−	90.2280i	−0.117137	−	0.739574i
$123$	−3.99686	−	7.84428i	−0.0324948	−	0.0637746i
$124$		−	32.3197i		−	0.260643i
$125$	57.0486	+	111.223i	0.456389	+	0.889780i
$126$	131.651			1.04485
$127$	−143.728	+	73.2331i	−1.13172	+	0.576638i	−0.916542	−	0.399937i	$-0.869032\pi$
$127$	−143.728	+	73.2331i	−1.13172	+	0.576638i	−0.215174	+	0.976576i	$0.569032\pi$
$128$	11.1744	−	1.76985i	0.0873001	−	0.0138270i
$129$	1.28240	−	1.76508i	0.00994112	−	0.0136828i
$130$	−55.4541	−	21.2297i	−0.426570	−	0.163306i
$131$	−150.705	+	109.494i	−1.15042	+	0.835828i	−0.988537	−	0.150982i	$-0.951757\pi$
$131$	−150.705	+	109.494i	−1.15042	+	0.835828i	−0.161882	+	0.986810i	$0.551757\pi$
$132$	−4.71240	−	4.71240i	−0.0357000	−	0.0357000i
$133$	25.8865	−	163.441i	0.194636	−	1.22888i
$134$	81.4808	−	26.4747i	0.608065	−	0.197572i
$135$	−16.7975	+	1.78074i	−0.124426	+	0.0131907i
$136$	26.0508	−	80.1761i	0.191550	−	0.589530i
$137$	6.75798	−	13.2633i	0.0493283	−	0.0968122i	−0.865027	−	0.501726i	$-0.832699\pi$
$137$	6.75798	−	13.2633i	0.0493283	−	0.0968122i	0.914355	+	0.404914i	$0.132699\pi$
$138$	1.64352	+	0.837413i	0.0119095	+	0.00606821i
$139$	−47.7855	−	15.5264i	−0.343780	−	0.111701i	0.132038	−	0.991245i	$-0.457848\pi$
$139$	−47.7855	−	15.5264i	−0.343780	−	0.111701i	−0.475818	+	0.879544i	$0.657848\pi$
$140$	101.593	+	21.4989i	0.725662	+	0.153563i
$141$	−2.01445	−	6.19985i	−0.0142869	−	0.0439705i
$142$	−114.409	−	18.1206i	−0.805696	−	0.127610i
$143$	105.215	−	105.215i	0.735766	−	0.735766i
$144$	21.0771	+	29.0102i	0.146369	+	0.201460i
$145$	−94.9454	+	61.7795i	−0.654796	+	0.426066i
$146$	−59.8444	−	43.4795i	−0.409893	−	0.297805i
$147$	1.73075	+	10.9275i	0.0117738	+	0.0743370i
$148$	−1.00991	−	1.98206i	−0.00682372	−	0.0133923i
$149$			188.734i			1.26667i	0.773877	+	0.633335i	$0.218315\pi$
$149$			188.734i			1.26667i	−0.773877	+	0.633335i	$0.781685\pi$
$150$	−6.61354	−	0.683106i	−0.0440903	−	0.00455404i
$151$	68.5434			0.453930			0.226965	−	0.973903i	$-0.427120\pi$
$151$	68.5434			0.453930			0.226965	+	0.973903i	$0.427120\pi$
$152$	40.1599	−	20.4625i	0.264210	−	0.134622i
$153$	263.904	−	41.7983i	1.72486	−	0.273192i
$154$	−152.951	+	210.519i	−0.993188	+	1.36701i
$155$	78.0273	−	20.9825i	0.503402	−	0.135371i
$156$	2.55516	−	1.85644i	0.0163793	−	0.0119002i
$157$	10.9153	+	10.9153i	0.0695245	+	0.0695245i	0.741014	−	0.671490i	$-0.234345\pi$
$157$	10.9153	+	10.9153i	0.0695245	+	0.0695245i	−0.671490	+	0.741014i	$0.734345\pi$
$158$	−0.516468	+	3.26085i	−0.00326879	+	0.0206383i
$159$	−5.65639	+	1.83787i	−0.0355748	+	0.0115589i
$160$	11.5274	+	25.8286i	0.0720465	+	0.161429i
$161$	22.2563	−	68.4977i	0.138238	−	0.425452i
$162$	−51.3930	+	100.864i	−0.317240	+	0.622620i
$163$	42.5428	+	21.6766i	0.260999	+	0.132986i	0.579594	−	0.814905i	$-0.303211\pi$
$163$	42.5428	+	21.6766i	0.260999	+	0.132986i	−0.318595	+	0.947891i	$0.603211\pi$
$164$	−89.0481	−	28.9335i	−0.542976	−	0.176424i
$165$	8.31746	−	14.4362i	0.0504089	−	0.0874921i
$166$	−42.8503	−	131.880i	−0.258134	−	0.794455i
$167$	119.073	+	18.8593i	0.713012	+	0.112930i	0.502394	−	0.864639i	$-0.332453\pi$
$167$	119.073	+	18.8593i	0.713012	+	0.112930i	0.210618	+	0.977569i	$0.432453\pi$
$168$	−3.90561	+	3.90561i	−0.0232477	+	0.0232477i
$169$	−57.8867	−	79.6742i	−0.342525	−	0.471445i
$170$	210.476	+	10.8411i	1.23810	+	0.0637712i
$171$	115.573	+	83.9688i	0.675866	+	0.491045i
$172$	−3.62982	−	22.9178i	−0.0211036	−	0.133243i
$173$	150.570	+	295.510i	0.870347	+	1.70815i	0.689036	+	0.724727i	$0.258034\pi$
$173$	150.570	+	295.510i	0.870347	+	1.70815i	0.181312	+	0.983426i	$0.441966\pi$
$174$		−	6.02510i		−	0.0346270i
$175$	14.0523	+	259.226i	0.0802989	+	1.48129i
$176$	−70.8767			−0.402708
$177$	10.3936	−	5.29580i	0.0587209	−	0.0299198i
$178$	9.83597	−	1.55786i	0.0552583	−	0.00875205i
$179$	166.183	−	228.732i	0.928398	−	1.27783i	−0.0320838	−	0.999485i	$-0.510214\pi$
$179$	166.183	−	228.732i	0.928398	−	1.27783i	0.960481	−	0.278344i	$-0.0897857\pi$
$180$	−56.3537	+	69.7189i	−0.313076	+	0.387327i
$181$	22.1737	−	16.1101i	0.122506	−	0.0890061i	−0.524845	−	0.851198i	$-0.675877\pi$
$181$	22.1737	−	16.1101i	0.122506	−	0.0890061i	0.647351	+	0.762192i	$0.275877\pi$
$182$	−87.2013	−	87.2013i	−0.479128	−	0.479128i
$183$	−1.90030	+	11.9980i	−0.0103842	+	0.0655630i
$184$	18.6572	−	6.06208i	0.101398	−	0.0329461i
$185$	4.12951	−	3.72495i	0.0223217	−	0.0201348i
$186$	−1.32806	+	4.08735i	−0.00714012	+	0.0219750i
$187$	−239.764	+	470.563i	−1.28216	+	2.51638i
$188$	−61.7735	−	31.4751i	−0.328582	−	0.167421i
$189$	−33.3644	−	10.8408i	−0.176531	−	0.0573585i
$190$	75.4736	+	83.6707i	0.397229	+	0.440372i
$191$	−49.7113	−	152.996i	−0.260269	−	0.801025i	−0.992746	−	0.120233i	$-0.961636\pi$
$191$	−49.7113	−	152.996i	−0.260269	−	0.801025i	0.732477	−	0.680792i	$-0.238364\pi$
$192$	−1.48591	−	0.235346i	−0.00773913	−	0.00122576i
$193$	190.941	−	190.941i	0.989331	−	0.989331i	−0.0106129	−	0.999944i	$-0.503378\pi$
$193$	190.941	−	190.941i	0.989331	−	0.989331i	0.999944	+	0.0106129i	$0.00337827\pi$
$194$	5.58262	+	7.68382i	0.0287764	+	0.0396073i
$195$	6.14072	+	4.96353i	0.0314909	+	0.0254540i
$196$	95.1933	+	69.1620i	0.485680	+	0.352867i
$197$	−24.6140	−	155.407i	−0.124944	−	0.788868i	−0.967983	−	0.251015i	$-0.919236\pi$
$197$	−24.6140	−	155.407i	−0.124944	−	0.788868i	0.843039	−	0.537853i	$-0.180764\pi$
$198$	−101.985	−	200.158i	−0.515077	−	1.01090i
$199$		−	213.484i		−	1.07279i	−0.843968	−	0.536393i	$-0.819787\pi$
$199$		−	213.484i		−	1.07279i	0.843968	−	0.536393i	$-0.180213\pi$
$200$	−54.8725	+	44.5983i	−0.274363	+	0.222991i
$201$	−11.3925			−0.0566789
$202$	50.5751	−	25.7693i	0.250372	−	0.127571i
$203$	−232.360	+	36.8022i	−1.14463	+	0.181292i
$204$	−6.58910	+	9.06912i	−0.0322995	+	0.0444565i
$205$	12.0407	−	233.767i	0.0587353	−	1.14033i
$206$	83.5447	−	60.6988i	0.405557	−	0.294654i
$207$	43.9655	+	43.9655i	0.212394	+	0.212394i
$208$	5.25460	−	33.1763i	0.0252625	−	0.159501i
$209$	−268.544	+	87.2554i	−1.28490	+	0.417490i
$210$	−11.9646	−	6.89347i	−0.0569744	−	0.0328260i
$211$	8.19988	−	25.2366i	0.0388620	−	0.119605i	−0.929743	−	0.368208i	$-0.879971\pi$
$211$	8.19988	−	25.2366i	0.0388620	−	0.119605i	0.968605	+	0.248603i	$0.0799714\pi$
$212$	−28.7161	+	56.3586i	−0.135453	+	0.265842i
$213$	13.7243	+	6.99286i	0.0644332	+	0.0328303i
$214$	−162.945	−	52.9439i	−0.761423	−	0.247401i
$215$	52.9723	−	23.6418i	0.246383	−	0.109962i
$216$	−2.95277	−	9.08769i	−0.0136702	−	0.0420726i
$217$	165.742	+	26.2509i	0.763788	+	0.120972i
$218$	−190.356	+	190.356i	−0.873192	+	0.873192i
$219$	5.78166	+	7.95778i	0.0264003	+	0.0363369i
$220$	−46.0143	−	171.113i	−0.209156	−	0.777785i
$221$	−202.488	−	147.116i	−0.916235	−	0.665684i
$222$	0.0462741	+	0.292163i	0.000208442	+	0.00131605i
$223$	−85.5448	−	167.891i	−0.383609	−	0.752875i	0.615777	−	0.787921i	$-0.288842\pi$
$223$	−85.5448	−	167.891i	−0.383609	−	0.752875i	−0.999386	+	0.0350456i	$0.988842\pi$
$224$			58.7422i			0.262242i
$225$	−204.903	−	90.7883i	−0.910682	−	0.403504i
$226$	5.43105			0.0240312
$227$	65.5445	−	33.3966i	0.288742	−	0.147122i	−0.303620	−	0.952793i	$-0.598195\pi$
$227$	65.5445	−	33.3966i	0.288742	−	0.147122i	0.592362	+	0.805672i	$0.298195\pi$
$228$	−5.91970	+	0.937589i	−0.0259636	+	0.00411223i
$229$	−115.180	+	158.531i	−0.502969	+	0.692277i	−0.982714	−	0.185131i	$-0.940729\pi$
$229$	−115.180	+	158.531i	−0.502969	+	0.692277i	0.479745	+	0.877408i	$0.340729\pi$
$230$	26.7478	+	41.1072i	0.116295	+	0.178727i
$231$	27.9937	−	20.3386i	0.121185	−	0.0880459i
$232$	−45.3102	−	45.3102i	−0.195303	−	0.195303i
$233$	−42.5249	+	268.492i	−0.182510	+	1.15233i	0.710970	+	0.703223i	$0.248256\pi$
$233$	−42.5249	+	268.492i	−0.182510	+	1.15233i	−0.893480	+	0.449103i	$0.851744\pi$
$234$	101.252	−	32.8986i	0.432699	−	0.140592i
$235$	35.8840	−	169.570i	0.152698	−	0.721573i
$236$	38.3366	−	117.988i	0.162443	−	0.499949i
$237$	0.199309	−	0.391166i	0.000840965	−	0.00165049i
$238$	390.000	+	198.715i	1.63866	+	0.834937i
$239$	113.170	+	36.7711i	0.473514	+	0.153854i	0.536046	−	0.844189i	$-0.319917\pi$
$239$	113.170	+	36.7711i	0.473514	+	0.153854i	−0.0625316	+	0.998043i	$0.519917\pi$
$240$	−0.396499	−	3.74013i	−0.00165208	−	0.0155839i
$241$	104.021	+	320.142i	0.431621	+	1.32839i	0.896510	+	0.443023i	$0.146094\pi$
$241$	104.021	+	320.142i	0.431621	+	1.32839i	−0.464890	+	0.885369i	$0.653906\pi$
$242$	269.539	+	42.6909i	1.11380	+	0.176409i
$243$	32.1437	−	32.1437i	0.132279	−	0.132279i
$244$	75.9373	+	104.519i	0.311218	+	0.428355i
$245$	−105.172	+	274.720i	−0.429274	+	1.12131i
$246$	10.0727	+	7.31823i	0.0409458	+	0.0297489i
$247$	−20.9337	−	132.170i	−0.0847519	−	0.535102i
$248$	20.7505	+	40.7252i	0.0836715	+	0.164215i
$249$			18.4391i			0.0740526i
$250$	−143.295	−	103.521i	−0.573179	−	0.414084i
$251$	−24.6454			−0.0981890			−0.0490945	−	0.998794i	$-0.515634\pi$
$251$	−24.6454			−0.0981890			−0.0490945	+	0.998794i	$0.515634\pi$
$252$	−165.889	+	84.5249i	−0.658291	+	0.335416i
$253$	−121.383	+	19.2252i	−0.479775	+	0.0759888i
$254$	134.089	−	184.558i	0.527911	−	0.726607i
$255$	−26.1727	−	10.0198i	−0.102638	−	0.0392934i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−20.8782	−	20.8782i	−0.0812381	−	0.0812381i	0.665320	−	0.746558i	$-0.268295\pi$
$257$	−20.8782	−	20.8782i	−0.0812381	−	0.0812381i	−0.746558	+	0.665320i	$0.768295\pi$
$258$	−0.482674	+	3.04748i	−0.00187083	+	0.0118119i
$259$	10.9847	−	3.56914i	0.0424120	−	0.0137805i
$260$	83.5066	−	8.85272i	0.321179	−	0.0340489i
$261$	62.7597	−	193.155i	0.240459	−	0.740056i
$262$	119.600	−	234.728i	0.456489	−	0.895910i
$263$	−272.419	−	138.804i	−1.03581	−	0.527774i	−0.148487	−	0.988914i	$-0.547440\pi$
$263$	−272.419	−	138.804i	−1.03581	−	0.527774i	−0.887327	+	0.461141i	$0.847440\pi$
$264$	8.96351	+	2.91242i	0.0339527	+	0.0110319i
$265$	−154.706	−	32.7385i	−0.583795	−	0.123542i
$266$	72.3168	+	222.568i	0.271868	+	0.836722i
$267$	−1.30793	−	0.207156i	−0.00489863	−	0.000775867i
$268$	−85.6740	+	85.6740i	−0.319679	+	0.319679i
$269$	28.2649	+	38.9033i	0.105074	+	0.144622i	0.858316	−	0.513122i	$-0.171511\pi$
$269$	28.2649	+	38.9033i	0.105074	+	0.144622i	−0.753242	+	0.657744i	$0.771511\pi$
$270$	20.0228	−	13.0285i	0.0741585	−	0.0482538i
$271$	265.655	+	193.010i	0.980276	+	0.712212i	0.957770	−	0.287535i	$-0.0928356\pi$
$271$	265.655	+	193.010i	0.980276	+	0.712212i	0.0225057	+	0.999747i	$0.492836\pi$
$272$	18.6503	+	117.753i	0.0685674	+	0.432917i
$273$	7.44480	+	14.6112i	0.0272703	+	0.0535211i
$274$			21.0516i			0.0768306i
$275$	383.233	−	222.178i	1.39357	−	0.807921i
$276$	−2.60860			−0.00945146
$277$	3.09125	−	1.57507i	0.0111597	−	0.00568617i	−0.448402	−	0.893832i	$-0.648007\pi$
$277$	3.09125	−	1.57507i	0.0111597	−	0.00568617i	0.459561	+	0.888146i	$0.348007\pi$
$278$	70.1818	−	11.1157i	0.252452	−	0.0399845i
$279$	−85.1508	+	117.200i	−0.305200	+	0.420072i
$280$	−141.817	+	38.1364i	−0.506490	+	0.136201i
$281$	−333.008	+	241.945i	−1.18508	+	0.861013i	−0.992736	−	0.120314i	$-0.961610\pi$
$281$	−333.008	+	241.945i	−1.18508	+	0.861013i	−0.192347	+	0.981327i	$0.561610\pi$
$282$	6.51890	+	6.51890i	0.0231167	+	0.0231167i
$283$	−15.6043	+	98.5216i	−0.0551388	+	0.348133i	0.944660	+	0.328052i	$0.106392\pi$
$283$	−15.6043	+	98.5216i	−0.0551388	+	0.348133i	−0.999798	+	0.0200805i	$0.993608\pi$
$284$	155.798	−	50.6217i	0.548583	−	0.178246i
$285$	−6.10672	−	13.6828i	−0.0214271	−	0.0480100i
$286$	−65.0262	+	200.130i	−0.227364	+	0.699755i
$287$	220.704	−	433.156i	0.769004	−	1.50926i
$288$	−45.1844	−	23.0226i	−0.156890	−	0.0799396i
$289$	570.023	+	185.212i	1.97240	+	0.640871i
$290$	79.9733	−	138.805i	0.275770	−	0.478639i
$291$	−0.390275	−	1.20114i	−0.00134115	−	0.00412764i
$292$	103.324	+	16.3649i	0.353849	+	0.0560441i
$293$	−34.4622	+	34.4622i	−0.117618	+	0.117618i	−0.763466	−	0.645848i	$-0.776504\pi$
$293$	−34.4622	+	34.4622i	−0.117618	+	0.117618i	0.645848	+	0.763466i	$0.276504\pi$
$294$	−9.19679	−	12.6583i	−0.0312816	−	0.0430554i
$295$	309.739	+	15.9539i	1.04996	+	0.0540809i
$296$	2.54512	+	1.84914i	0.00859839	+	0.00624710i
$297$	9.36435	+	59.1242i	0.0315298	+	0.199071i
$298$	−121.175	−	237.819i	−0.406626	−	0.798049i
$299$		−	58.2428i		−	0.194792i
$300$	8.77213	−	3.38539i	0.0292404	−	0.0112846i
$301$	120.475			0.400250
$302$	−86.3697	+	44.0076i	−0.285993	+	0.145720i
$303$	−7.45494	+	1.18075i	−0.0246038	+	0.00389685i
$304$	−37.4667	+	51.5684i	−0.123246	+	0.169633i
$305$	−203.033	+	251.185i	−0.665681	+	0.823559i
$306$	−305.703	+	222.106i	−0.999028	+	0.725836i
$307$	−270.723	−	270.723i	−0.881835	−	0.881835i	0.111886	−	0.993721i	$-0.464311\pi$
$307$	−270.723	−	270.723i	−0.881835	−	0.881835i	−0.993721	+	0.111886i	$0.964311\pi$
$308$	57.5680	−	363.470i	0.186909	−	1.18010i
$309$	−13.0598	+	4.24338i	−0.0422647	+	0.0137326i
$310$	−84.8485	+	76.5360i	−0.273705	+	0.246890i
$311$	−131.481	+	404.658i	−0.422769	+	1.30115i	0.482345	+	0.875981i	$0.339785\pi$
$311$	−131.481	+	404.658i	−0.422769	+	1.30115i	−0.905114	+	0.425169i	$0.860215\pi$
$312$	−2.02779	+	3.97976i	−0.00649933	+	0.0127556i
$313$	−432.163	−	220.198i	−1.38071	−	0.703507i	−0.403342	−	0.915049i	$-0.632151\pi$
$313$	−432.163	−	220.198i	−1.38071	−	0.703507i	−0.977369	+	0.211542i	$0.932151\pi$
$314$	−20.7622	−	6.74606i	−0.0661217	−	0.0214843i
$315$	−311.761	−	345.621i	−0.989717	−	1.09721i
$316$	−1.44281	−	4.44051i	−0.00456585	−	0.0140522i
$317$	−185.598	−	29.3958i	−0.585482	−	0.0927312i	−0.143336	−	0.989674i	$-0.545783\pi$
$317$	−185.598	−	29.3958i	−0.585482	−	0.0927312i	−0.442146	+	0.896943i	$0.645783\pi$
$318$	5.94748	−	5.94748i	0.0187028	−	0.0187028i
$319$	235.954	+	324.763i	0.739669	+	1.01807i
$320$	−31.1084	−	25.1449i	−0.0972138	−	0.0785778i
$321$	18.4315	+	13.3912i	0.0574189	+	0.0417173i
$322$	15.9337	+	100.602i	0.0494836	+	0.312427i
$323$	215.629	+	423.196i	0.667582	+	1.31020i
$324$		−	160.093i		−	0.494114i
$325$	75.5863	+	195.857i	0.232573	+	0.602637i
$326$	−67.5243			−0.207130
$327$	31.8956	−	16.2516i	0.0975400	−	0.0496991i
$328$	130.784	−	20.7141i	0.398731	−	0.0631527i
$329$	211.585	−	291.222i	0.643116	−	0.885173i
$330$	−1.21201	+	23.5308i	−0.00367276	+	0.0713055i
$331$	437.596	−	317.932i	1.32204	−	0.960519i	0.322137	−	0.946693i	$-0.395599\pi$
$331$	437.596	−	317.932i	1.32204	−	0.960519i	0.999904	−	0.0138259i	$-0.00440105\pi$
$332$	138.666	+	138.666i	0.417670	+	0.417670i
$333$	−1.55981	+	9.84825i	−0.00468411	+	0.0295743i
$334$	−162.149	+	52.6855i	−0.485476	+	0.157741i
$335$	−262.458	−	151.216i	−0.783456	−	0.451391i
$336$	2.41380	−	7.42891i	0.00718393	−	0.0221099i
$337$	288.832	−	566.865i	0.857068	−	1.68209i	0.134365	−	0.990932i	$-0.457101\pi$
$337$	288.832	−	566.865i	0.857068	−	1.68209i	0.722703	−	0.691159i	$-0.242899\pi$
$338$	124.096	+	63.2298i	0.367147	+	0.187071i
$339$	−0.686845	−	0.223169i	−0.00202609	−	0.000658317i
$340$	−272.176	+	121.474i	−0.800518	+	0.357275i
$341$	−88.4837	−	272.325i	−0.259483	−	0.798606i
$342$	−199.542	−	31.6043i	−0.583456	−	0.0924103i
$343$	−72.1993	+	72.1993i	−0.210494	+	0.210494i
$344$	19.2880	+	26.5476i	0.0560696	+	0.0771732i
$345$	−1.69355	−	6.29778i	−0.00490883	−	0.0182544i
$346$	−379.459	−	275.693i	−1.09670	−	0.796800i
$347$	27.7630	+	175.289i	0.0800086	+	0.505154i	0.994851	+	0.101344i	$0.0323143\pi$
$347$	27.7630	+	175.289i	0.0800086	+	0.505154i	−0.914843	+	0.403810i	$0.867686\pi$
$348$	3.86836	+	7.59207i	0.0111160	+	0.0218163i
$349$			43.7714i			0.125420i	0.998032	+	0.0627098i	$0.0199743\pi$
$349$			43.7714i			0.125420i	−0.998032	+	0.0627098i	$0.980026\pi$
$350$	−184.140	−	317.621i	−0.526115	−	0.907489i
$351$	−28.3694			−0.0808244
$352$	89.3098	−	45.5056i	0.253721	−	0.129277i
$353$	−193.566	+	30.6578i	−0.548344	+	0.0868492i	−0.424459	−	0.905447i	$-0.639536\pi$
$353$	−193.566	+	30.6578i	−0.548344	+	0.0868492i	−0.123886	+	0.992296i	$0.539536\pi$
$354$	−9.69658	+	13.3462i	−0.0273915	+	0.0377011i
$355$	223.359	+	343.267i	0.629180	+	0.966950i
$356$	−11.3938	+	8.27810i	−0.0320051	+	0.0232531i
$357$	−41.1564	−	41.1564i	−0.115284	−	0.115284i
$358$	−62.5483	+	394.915i	−0.174716	+	1.10311i
$359$	−539.276	+	175.221i	−1.50216	+	0.488082i	−0.940647	−	0.339386i	$-0.889781\pi$
$359$	−539.276	+	175.221i	−1.50216	+	0.488082i	−0.561513	+	0.827468i	$0.689781\pi$
$360$	26.2475	−	124.032i	0.0729097	−	0.344534i
$361$	33.0830	−	101.819i	0.0916428	−	0.282047i
$362$	−17.5971	+	34.5363i	−0.0486108	+	0.0954041i
$363$	−32.3334	−	16.4747i	−0.0890729	−	0.0453849i
$364$	165.867	+	53.8933i	0.455678	+	0.148059i
$365$	27.5708	+	260.072i	0.0755365	+	0.712526i
$366$	−5.30869	−	16.3385i	−0.0145046	−	0.0446406i
$367$	115.036	+	18.2199i	0.313449	+	0.0496455i	0.311177	−	0.950352i	$-0.399277\pi$
$367$	115.036	+	18.2199i	0.313449	+	0.0496455i	0.00227212	+	0.999997i	$0.499277\pi$
$368$	−19.6173	+	19.6173i	−0.0533079	+	0.0533079i
$369$	246.683	+	339.530i	0.668518	+	0.920137i
$370$	−2.81192	+	7.34502i	−0.00759979	+	0.0198514i
$371$	−265.694	−	193.038i	−0.716157	−	0.520318i
$372$	−0.950787	−	6.00304i	−0.00255588	−	0.0161372i
$373$	−172.404	−	338.361i	−0.462208	−	0.907134i	−0.998026	−	0.0628006i	$-0.979997\pi$
$373$	−172.404	−	338.361i	−0.462208	−	0.907134i	0.535818	−	0.844333i	$-0.320003\pi$
$374$		−	746.882i		−	1.99701i
$375$	13.8681	+	18.9801i	0.0369817	+	0.0506136i
$376$	98.0474			0.260764
$377$	−169.510	+	86.3695i	−0.449628	+	0.229097i
$378$	49.0018	−	7.76113i	0.129634	−	0.0205321i
$379$	164.027	−	225.764i	0.432790	−	0.595684i	−0.535801	−	0.844344i	$-0.679990\pi$
$379$	164.027	−	225.764i	0.432790	−	0.595684i	0.968591	+	0.248660i	$0.0799903\pi$
$380$	−148.822	−	56.9742i	−0.391637	−	0.149932i
$381$	−24.5415	+	17.8305i	−0.0644135	+	0.0467991i
$382$	160.869	+	160.869i	0.421124	+	0.421124i
$383$	93.8837	−	592.759i	0.245127	−	1.54767i	−0.491200	−	0.871047i	$-0.663442\pi$
$383$	93.8837	−	592.759i	0.245127	−	1.54767i	0.736327	−	0.676626i	$-0.236558\pi$
$384$	2.02346	−	0.657463i	0.00526943	−	0.00171214i
$385$	914.875	−	96.9879i	2.37630	−	0.251917i
$386$	−118.008	+	363.191i	−0.305720	+	0.940909i
$387$	−47.2174	+	92.6693i	−0.122009	+	0.239456i
$388$	−11.9678	−	6.09792i	−0.0308449	−	0.0157163i
$389$	−268.657	−	87.2921i	−0.690636	−	0.224401i	−0.0573901	−	0.998352i	$-0.518278\pi$
$389$	−268.657	−	87.2921i	−0.690636	−	0.224401i	−0.633246	+	0.773951i	$0.718278\pi$
$390$	−10.9245	−	2.31183i	−0.0280117	−	0.00592778i
$391$	63.8809	+	196.605i	0.163378	+	0.502826i
$392$	−164.355	−	26.0313i	−0.419274	−	0.0664064i
$393$	−24.7707	+	24.7707i	−0.0630298	+	0.0630298i
$394$	130.793	+	180.021i	0.331962	+	0.456906i
$395$	9.78372	−	6.36612i	0.0247689	−	0.0161168i
$396$	257.018	+	186.735i	0.649035	+	0.471552i
$397$	93.0080	+	587.229i	0.234277	+	1.47917i	0.771772	+	0.635900i	$0.219371\pi$
$397$	93.0080	+	587.229i	0.234277	+	1.47917i	−0.537495	+	0.843267i	$0.680629\pi$
$398$	137.065	+	269.006i	0.344385	+	0.675895i
$399$		−	31.1190i		−	0.0779924i
$400$	40.5095	−	91.4274i	0.101274	−	0.228569i
$401$	338.722			0.844693			0.422346	−	0.906435i	$-0.361207\pi$
$401$	338.722			0.844693			0.422346	+	0.906435i	$0.361207\pi$
$402$	14.3553	−	7.31441i	0.0357098	−	0.0181950i
$403$	134.031	−	21.2284i	0.332583	−	0.0526759i
$404$	−47.1834	+	64.9424i	−0.116791	+	0.160748i
$405$	386.501	−	103.935i	0.954324	−	0.256629i
$406$	269.162	−	195.558i	0.662961	−	0.481669i
$407$	−13.9359	−	13.9359i	−0.0342405	−	0.0342405i
$408$	2.48002	−	15.6582i	0.00607848	−	0.0383780i
$409$	−771.108	+	250.548i	−1.88535	+	0.612587i	−0.901739	+	0.432281i	$0.857709\pi$
$409$	−771.108	+	250.548i	−1.88535	+	0.612587i	−0.983611	+	0.180306i	$0.942291\pi$
$410$	134.915	+	302.294i	0.329062	+	0.737303i
$411$	0.865040	−	2.66232i	0.00210472	−	0.00647766i
$412$	−66.3014	+	130.124i	−0.160926	+	0.315835i
$413$	573.928	+	292.431i	1.38966	+	0.708065i
$414$	−83.6274	−	27.1722i	−0.201998	−	0.0656333i
$415$	−244.748	+	424.797i	−0.589755	+	1.02361i
$416$	14.6793	+	45.1782i	0.0352867	+	0.108601i
$417$	−9.33239	−	1.47811i	−0.0223798	−	0.00354462i
$418$	282.364	−	282.364i	0.675513	−	0.675513i
$419$	23.3449	+	32.1315i	0.0557158	+	0.0766862i	0.835966	−	0.548782i	$-0.184908\pi$
$419$	23.3449	+	32.1315i	0.0557158	+	0.0766862i	−0.780250	+	0.625468i	$0.784908\pi$
$420$	19.5022	+	1.00451i	0.0464338	+	0.00239169i
$421$	201.243	+	146.212i	0.478012	+	0.347296i	0.800556	−	0.599258i	$-0.204538\pi$
$421$	201.243	+	146.212i	0.478012	+	0.347296i	−0.322543	+	0.946555i	$0.604538\pi$
$422$	5.87047	+	37.0647i	0.0139111	+	0.0878310i
$423$	141.082	+	276.888i	0.333526	+	0.654582i
$424$		−	89.4528i		−	0.210974i
$425$	−469.967	−	578.234i	−1.10580	−	1.36055i
$426$	−21.7833			−0.0511345
$427$	−597.671	+	304.529i	−1.39970	+	0.713182i
$428$	239.314	−	37.9036i	0.559145	−	0.0885599i
$429$	16.4472	−	22.6377i	0.0383386	−	0.0527685i
$430$	−51.5700	+	63.8007i	−0.119930	+	0.148374i
$431$	553.004	−	401.781i	1.28307	−	0.932206i	0.283430	−	0.958993i	$-0.408528\pi$
$431$	553.004	−	401.781i	1.28307	−	0.932206i	0.999641	+	0.0267868i	$0.00852751\pi$
$432$	9.55536	+	9.55536i	0.0221189	+	0.0221189i
$433$	−73.5249	+	464.218i	−0.169803	+	1.07210i	0.744665	+	0.667439i	$0.232609\pi$
$433$	−73.5249	+	464.218i	−0.169803	+	1.07210i	−0.914468	+	0.404658i	$0.867391\pi$
$434$	−225.701	+	73.3348i	−0.520049	+	0.168974i
$435$	−15.8176	+	14.2680i	−0.0363624	+	0.0328000i
$436$	117.646	−	362.078i	0.269831	−	0.830455i
$437$	−50.1773	+	98.4786i	−0.114822	+	0.225351i
$438$	−12.3945	−	6.31533i	−0.0282980	−	0.0144186i
$439$	−342.493	−	111.283i	−0.780166	−	0.253491i	−0.108255	−	0.994123i	$-0.534526\pi$
$439$	−342.493	−	111.283i	−0.780166	−	0.253491i	−0.671911	+	0.740632i	$0.734526\pi$
$440$	167.843	+	186.072i	0.381460	+	0.422890i
$441$	−162.980	−	501.600i	−0.369569	−	1.13742i
$442$	349.604	+	55.3718i	0.790959	+	0.125276i
$443$	−111.700	+	111.700i	−0.252144	+	0.252144i	−0.821849	−	0.569705i	$-0.807057\pi$
$443$	−111.700	+	111.700i	−0.252144	+	0.252144i	0.569705	+	0.821849i	$0.307057\pi$
$444$	−0.245889	−	0.338437i	−0.000553804	−	0.000762245i
$445$	−27.3823	−	22.1331i	−0.0615333	−	0.0497373i
$446$	215.586	+	156.632i	0.483376	+	0.351193i
$447$	5.55221	+	35.0553i	0.0124211	+	0.0784235i
$448$	−37.7148	−	74.0195i	−0.0841849	−	0.165222i
$449$		−	289.169i		−	0.644029i	−0.946735	−	0.322014i	$-0.895640\pi$
$449$		−	289.169i		−	0.644029i	0.946735	−	0.322014i	$-0.104360\pi$
$450$	316.483	−	17.1562i	0.703296	−	0.0381248i
$451$	−829.529			−1.83931
$452$	−6.84352	+	3.48695i	−0.0151405	+	0.00771448i
$453$	12.7312	−	2.01642i	0.0281042	−	0.00445127i
$454$	−61.1490	+	84.1644i	−0.134689	+	0.185384i
$455$	−22.4278	+	435.429i	−0.0492919	+	0.956987i
$456$	6.85729	−	4.98212i	0.0150379	−	0.0109257i
$457$	−383.361	−	383.361i	−0.838864	−	0.838864i	0.149845	−	0.988709i	$-0.452122\pi$
$457$	−383.361	−	383.361i	−0.838864	−	0.838864i	−0.988709	+	0.149845i	$0.952122\pi$
$458$	43.3516	−	273.711i	0.0946542	−	0.597623i
$459$	95.7640	−	31.1156i	0.208636	−	0.0677900i
$460$	−60.0966	−	34.6249i	−0.130645	−	0.0752715i
$461$	133.417	−	410.614i	0.289407	−	0.890703i	−0.695636	−	0.718395i	$-0.744877\pi$
$461$	133.417	−	410.614i	0.289407	−	0.890703i	0.985043	−	0.172309i	$-0.0551227\pi$
$462$	−22.2159	+	43.6012i	−0.0480864	+	0.0943748i
$463$	−87.4829	−	44.5748i	−0.188948	−	0.0962738i	0.356957	−	0.934121i	$-0.383814\pi$
$463$	−87.4829	−	44.5748i	−0.188948	−	0.0962738i	−0.545905	+	0.837847i	$0.683814\pi$
$464$	86.1851	+	28.0032i	0.185744	+	0.0603518i
$465$	13.8755	−	6.19269i	0.0298397	−	0.0133176i
$466$	−118.798	−	365.622i	−0.254931	−	0.784597i
$467$	416.998	+	66.0461i	0.892930	+	0.141426i	0.586005	−	0.810307i	$-0.300700\pi$
$467$	416.998	+	66.0461i	0.892930	+	0.141426i	0.306925	+	0.951734i	$0.400700\pi$
$468$	−106.462	+	106.462i	−0.227483	+	0.227483i
$469$	−369.767	−	508.940i	−0.788415	−	1.08516i
$470$	63.6539	+	236.709i	0.135434	+	0.503637i
$471$	2.34852	+	1.70630i	0.00498624	+	0.00362271i
$472$	27.4460	+	173.287i	0.0581482	+	0.367134i
$473$	−93.3282	−	183.167i	−0.197311	−	0.387245i
$474$			0.620862i			0.00130983i
$475$	40.9313	−	396.280i	0.0861712	−	0.834273i
$476$	−619.012			−1.30045
$477$	252.617	−	128.715i	0.529595	−	0.269842i
$478$	−166.211	+	26.3252i	−0.347722	+	0.0550737i
$479$	−331.632	+	456.452i	−0.692343	+	0.952928i	0.307656	+	0.951498i	$0.400455\pi$
$479$	−331.632	+	456.452i	−0.692343	+	0.952928i	−0.999999	+	0.00143028i	$0.999545\pi$
$480$	2.90093	+	4.45827i	0.00604361	+	0.00928807i
$481$	7.55634	−	5.49000i	0.0157097	−	0.0114137i
$482$	−336.618	−	336.618i	−0.698377	−	0.698377i
$483$	2.11878	−	13.3774i	0.00438671	−	0.0276966i
$484$	−367.049	+	119.261i	−0.758365	+	0.246408i
$485$	6.95208	−	32.8520i	0.0143342	−	0.0677361i
$486$	−19.8659	+	61.1409i	−0.0408763	+	0.125804i
$487$	85.8690	−	168.527i	0.176322	−	0.346052i	−0.785884	−	0.618374i	$-0.787792\pi$
$487$	85.8690	−	168.527i	0.176322	−	0.346052i	0.962206	+	0.272322i	$0.0877916\pi$
$488$	−162.792	−	82.9465i	−0.333590	−	0.169972i
$489$	8.53956	+	2.77467i	0.0174633	+	0.00567417i
$490$	−43.8564	−	413.692i	−0.0895028	−	0.844269i
$491$	−182.614	−	562.028i	−0.371922	−	1.14466i	−0.945532	−	0.325530i	$-0.894457\pi$
$491$	−182.614	−	562.028i	−0.371922	−	1.14466i	0.573609	−	0.819129i	$-0.305543\pi$
$492$	−17.3909	−	2.75445i	−0.0353474	−	0.00559847i
$493$	477.469	−	477.469i	0.968496	−	0.968496i
$494$	111.237	+	153.104i	0.225175	+	0.309927i
$495$	−283.960	+	741.732i	−0.573658	+	1.49845i
$496$	−52.2944	−	37.9941i	−0.105432	−	0.0766010i
$497$	133.055	+	840.078i	0.267717	+	1.69030i
$498$	−11.8386	−	23.2346i	−0.0237724	−	0.0466559i
$499$		−	284.999i		−	0.571140i	−0.958358	−	0.285570i	$-0.907817\pi$
$499$		−	284.999i		−	0.571140i	0.958358	−	0.285570i	$-0.0921829\pi$
$500$	247.027	+	38.4433i	0.494053	+	0.0768866i
$501$	22.6713			0.0452522
$502$	31.0551	−	15.8233i	0.0618627	−	0.0315206i
$503$	215.718	−	34.1664i	0.428863	−	0.0679252i	0.0617280	−	0.998093i	$-0.480339\pi$
$503$	215.718	−	34.1664i	0.428863	−	0.0679252i	0.367135	+	0.930168i	$0.380339\pi$
$504$	154.765	−	213.015i	0.307073	−	0.422649i
$505$	−187.418	−	71.7501i	−0.371125	−	0.142079i
$506$	140.608	−	102.158i	0.277882	−	0.201893i
$507$	−13.0957	−	13.0957i	−0.0258298	−	0.0258298i
$508$	−50.4688	+	318.647i	−0.0993480	+	0.627259i
$509$	324.255	−	105.357i	0.637044	−	0.206988i	0.0273511	−	0.999626i	$-0.491293\pi$
$509$	324.255	−	105.357i	0.637044	−	0.206988i	0.609693	+	0.792638i	$0.291293\pi$
$510$	39.4127	−	4.17822i	0.0772797	−	0.00819259i
$511$	−167.845	+	516.573i	−0.328464	+	1.01091i
$512$	10.2726	−	20.1612i	0.0200637	−	0.0393773i
$513$	47.9678	+	24.4408i	0.0935044	+	0.0476429i
$514$	39.7127	+	12.9034i	0.0772620	+	0.0251039i
$515$	−357.193	−	75.5886i	−0.693579	−	0.146774i
$516$	−1.34840	−	4.14995i	−0.00261318	−	0.00804253i
$517$	−606.672	−	96.0875i	−1.17345	−	0.185856i
$518$	−11.5500	+	11.5500i	−0.0222973	+	0.0222973i
$519$	36.6602	+	50.4584i	0.0706361	+	0.0972223i
$520$	−99.5407	+	64.7696i	−0.191424	+	0.124557i
$521$	528.326	+	383.851i	1.01406	+	0.736759i	0.965057	−	0.262040i	$-0.0843952\pi$
$521$	528.326	+	383.851i	1.01406	+	0.736759i	0.0490042	+	0.998799i	$0.484395\pi$
$522$	44.9310	+	283.683i	0.0860747	+	0.543454i
$523$	−91.9041	−	180.372i	−0.175725	−	0.344880i	0.786298	−	0.617847i	$-0.211995\pi$
$523$	−91.9041	−	180.372i	−0.175725	−	0.344880i	−0.962023	+	0.272967i	$0.911995\pi$
$524$			372.563i			0.710998i
$525$	10.2360	+	47.7350i	0.0194972	+	0.0909238i
$526$	432.386			0.822027
$527$	−429.153	+	218.664i	−0.814332	+	0.414923i
$528$	−13.1646	+	2.08506i	−0.0249329	+	0.00394899i
$529$	282.663	−	389.052i	0.534335	−	0.735449i
$530$	215.960	−	58.0742i	0.407472	−	0.109574i
$531$	−449.875	+	326.853i	−0.847221	+	0.615542i
$532$	−234.022	−	234.022i	−0.439891	−	0.439891i
$533$	61.4991	−	388.290i	0.115383	−	0.728499i
$534$	1.78110	−	0.578713i	0.00333538	−	0.00108373i
$535$	246.875	+	553.153i	0.461448	+	1.03393i
$536$	52.9494	−	162.962i	0.0987862	−	0.304033i
$537$	24.1379	−	47.3732i	0.0449495	−	0.0882183i
$538$	−60.5933	−	30.8738i	−0.112627	−	0.0573863i
$539$	991.445	+	322.140i	1.83941	+	0.597662i
$540$	−16.8654	+	29.2724i	−0.0312322	+	0.0542081i
$541$	327.863	+	1009.06i	0.606031	+	1.86517i	0.489542	+	0.871980i	$0.337164\pi$
$541$	327.863	+	1009.06i	0.606031	+	1.86517i	0.116489	+	0.993192i	$0.462836\pi$
$542$	−458.664	−	72.6453i	−0.846244	−	0.134032i
$543$	3.64459	−	3.64459i	0.00671195	−	0.00671195i
$544$	−99.1032	−	136.404i	−0.182175	−	0.250742i
$545$	950.519	+	48.9588i	1.74407	+	0.0898326i
$546$	−18.7620	−	13.6314i	−0.0343626	−	0.0249659i
$547$	−98.2103	−	620.075i	−0.179544	−	1.13359i	−0.898641	−	0.438684i	$-0.855445\pi$
$547$	−98.2103	−	620.075i	−0.179544	−	1.13359i	0.719098	−	0.694909i	$-0.244555\pi$
$548$	−13.5160	−	26.5266i	−0.0246641	−	0.0484061i
$549$		−	579.081i		−	1.05479i
$550$	−340.254	+	526.012i	−0.618644	+	0.956385i
$551$	361.021			0.655210
$552$	3.28703	−	1.67483i	0.00595477	−	0.00303411i
$553$	23.9437	−	3.79231i	0.0432978	−	0.00685770i
$554$	−2.88394	+	3.96941i	−0.00520568	+	0.00716500i
$555$	0.657431	−	0.813351i	0.00118456	−	0.00146550i
$556$	−81.2975	+	59.0661i	−0.146218	+	0.106234i
$557$	410.470	+	410.470i	0.736930	+	0.736930i	0.971983	−	0.235053i	$-0.0755263\pi$
$557$	410.470	+	410.470i	0.736930	+	0.736930i	−0.235053	+	0.971983i	$0.575526\pi$
$558$	32.0492	−	202.351i	0.0574359	−	0.362636i
$559$	92.6566	−	30.1060i	0.165754	−	0.0538568i
$560$	154.215	−	139.107i	0.275384	−	0.248405i
$561$	−30.6904	+	94.4555i	−0.0547067	+	0.168370i
$562$	264.277	−	518.673i	0.470244	−	0.922905i
$563$	581.018	+	296.043i	1.03200	+	0.525832i	0.886113	−	0.463469i	$-0.153395\pi$
$563$	581.018	+	296.043i	1.03200	+	0.525832i	0.145890	+	0.989301i	$0.453395\pi$
$564$	−12.3997	−	4.02890i	−0.0219853	−	0.00714345i
$565$	−12.8612	−	14.2581i	−0.0227632	−	0.0252355i
$566$	−43.5922	−	134.163i	−0.0770181	−	0.237037i
$567$	820.988	+	130.032i	1.44795	+	0.229333i
$568$	−163.815	+	163.815i	−0.288407	+	0.288407i
$569$	422.211	+	581.123i	0.742022	+	1.02131i	0.998500	+	0.0547557i	$0.0174380\pi$
$569$	422.211	+	581.123i	0.742022	+	1.02131i	−0.256478	+	0.966550i	$0.582562\pi$
$570$	16.4798	+	13.3206i	0.0289120	+	0.0233695i
$571$	−882.819	−	641.406i	−1.54609	−	1.12330i	−0.946365	−	0.323099i	$-0.895275\pi$
$571$	−882.819	−	641.406i	−1.54609	−	1.12330i	−0.599728	−	0.800204i	$-0.704725\pi$
$572$	−46.5536	−	293.928i	−0.0813874	−	0.513860i
$573$	−13.7342	−	26.9549i	−0.0239689	−	0.0470417i
$574$			687.509i			1.19775i
$575$	44.5769	−	167.566i	0.0775250	−	0.291420i
$576$	71.7171			0.124509
$577$	380.981	−	194.120i	0.660279	−	0.336429i	−0.0915372	−	0.995802i	$-0.529178\pi$
$577$	380.981	−	194.120i	0.660279	−	0.336429i	0.751816	+	0.659373i	$0.229178\pi$
$578$	−837.184	+	132.597i	−1.44841	+	0.229406i
$579$	29.8481	−	41.0823i	0.0515511	−	0.0709539i
$580$	−11.6536	+	226.251i	−0.0200924	+	0.390088i
$581$	−823.738	+	598.481i	−1.41779	+	1.03009i
$582$	1.26296	+	1.26296i	0.00217003	+	0.00217003i
$583$	−87.6647	+	553.493i	−0.150368	+	0.949388i
$584$	−140.703	+	45.7170i	−0.240929	+	0.0782826i
$585$	−326.141	−	187.907i	−0.557506	−	0.321209i
$586$	21.2988	−	65.5510i	0.0363461	−	0.111862i
$587$	190.949	−	374.759i	0.325296	−	0.638430i	−0.669214	−	0.743070i	$-0.733369\pi$
$587$	190.949	−	374.759i	0.325296	−	0.638430i	0.994510	+	0.104640i	$0.0333689\pi$
$588$	19.7157	+	10.0457i	0.0335302	+	0.0170845i
$589$	−244.912	−	79.5767i	−0.415810	−	0.135105i
$590$	−400.537	+	178.762i	−0.678876	+	0.302986i
$591$	−9.14358	−	28.1411i	−0.0154714	−	0.0476160i
$592$	−4.39427	−	0.695983i	−0.00742275	−	0.00117565i
$593$	−80.9820	+	80.9820i	−0.136563	+	0.136563i	−0.772084	−	0.635521i	$-0.780785\pi$
$593$	−80.9820	+	80.9820i	−0.136563	+	0.136563i	0.635521	+	0.772084i	$0.280785\pi$
$594$	−49.7599	−	68.4886i	−0.0837708	−	0.115301i
$595$	−401.872	−	1494.44i	−0.675416	−	2.51166i
$596$	305.378	+	221.870i	0.512379	+	0.372265i
$597$	−6.28033	−	39.6524i	−0.0105198	−	0.0664195i
$598$	37.3942	+	73.3902i	0.0625321	+	0.122726i
$599$			412.824i			0.689188i	0.938752	+	0.344594i	$0.111983\pi$
$599$			412.824i			0.689188i	−0.938752	+	0.344594i	$0.888017\pi$
$600$	−8.87998	+	9.89790i	−0.0148000	+	0.0164965i
$601$	−213.346			−0.354986			−0.177493	−	0.984122i	$-0.556799\pi$
$601$	−213.346			−0.354986			−0.177493	+	0.984122i	$0.556799\pi$
$602$	−151.808	+	77.3499i	−0.252172	+	0.128488i
$603$	536.397	−	84.9570i	0.889547	−	0.140890i
$604$	80.5776	−	110.906i	0.133407	−	0.183618i
$605$	−526.219	−	808.715i	−0.869783	−	1.33672i
$606$	8.63569	−	6.27419i	0.0142503	−	0.0103535i
$607$	769.147	+	769.147i	1.26713	+	1.26713i	0.947565	+	0.319564i	$0.103536\pi$
$607$	769.147	+	769.147i	1.26713	+	1.26713i	0.319564	+	0.947565i	$0.396464\pi$
$608$	14.1018	−	89.0351i	0.0231937	−	0.146439i
$609$	−42.0757	+	13.6712i	−0.0690898	+	0.0224486i
$610$	94.5653	−	446.867i	0.155025	−	0.732569i
$611$	89.9541	−	276.850i	0.147224	−	0.453110i
$612$	242.607	−	476.143i	0.396417	−	0.778011i
$613$	−505.327	−	257.477i	−0.824351	−	0.420028i	−0.00968113	−	0.999953i	$-0.503082\pi$
$613$	−505.327	−	257.477i	−0.824351	−	0.420028i	−0.814670	+	0.579926i	$0.803082\pi$
$614$	514.946	+	167.316i	0.838675	+	0.272502i
$615$	−4.64057	−	43.7739i	−0.00754564	−	0.0711771i
$616$	160.822	+	494.960i	0.261075	+	0.803506i
$617$	−583.605	−	92.4339i	−0.945875	−	0.149812i	−0.335602	−	0.942004i	$-0.608940\pi$
$617$	−583.605	−	92.4339i	−0.945875	−	0.149812i	−0.610272	+	0.792192i	$0.708940\pi$
$618$	13.7319	−	13.7319i	0.0222199	−	0.0222199i
$619$	403.441	+	555.290i	0.651763	+	0.897075i	0.999174	−	0.0406379i	$-0.0129390\pi$
$619$	403.441	+	555.290i	0.651763	+	0.897075i	−0.347411	+	0.937713i	$0.612939\pi$
$620$	57.7762	−	150.917i	0.0931875	−	0.243415i
$621$	18.9563	+	13.7726i	0.0305255	+	0.0221781i
$622$	−94.1302	−	594.315i	−0.151335	−	0.955490i
$623$	−33.1974	−	65.1536i	−0.0532864	−	0.104580i
$624$		−	6.31671i		−	0.0101229i
$625$	67.5624	+	621.338i	0.108100	+	0.994140i
$626$	685.932			1.09574
$627$	−47.3123	+	24.1068i	−0.0754583	+	0.0384479i
$628$	30.4932	−	4.82964i	0.0485560	−	0.00769051i
$629$	−19.4858	+	26.8200i	−0.0309791	+	0.0426390i
$630$	614.744	+	235.345i	0.975784	+	0.373563i
$631$	130.769	−	95.0090i	0.207240	−	0.150569i	−0.479324	−	0.877638i	$-0.659118\pi$
$631$	130.769	−	95.0090i	0.207240	−	0.150569i	0.686564	+	0.727069i	$0.259118\pi$
$632$	4.66902	+	4.66902i	0.00738770	+	0.00738770i
$633$	0.780623	−	4.92866i	0.00123321	−	0.00778619i
$634$	252.740	−	82.1203i	0.398644	−	0.129527i
$635$	−802.054	+	85.0275i	−1.26308	+	0.133902i
$636$	−3.67574	+	11.3128i	−0.00577947	+	0.0177874i
$637$	−224.292	+	440.197i	−0.352106	+	0.691047i
$638$	−505.831	−	257.734i	−0.792838	−	0.403971i
$639$	−698.335	−	226.903i	−1.09286	−	0.355090i
$640$	55.3429	+	11.7116i	0.0864733	+	0.0182993i
$641$	244.269	+	751.783i	0.381075	+	1.17283i	0.939288	+	0.343131i	$0.111487\pi$
$641$	244.269	+	751.783i	0.381075	+	1.17283i	−0.558212	+	0.829698i	$0.688513\pi$
$642$	−31.8227	−	5.04022i	−0.0495681	−	0.00785081i
$643$	−365.724	+	365.724i	−0.568778	+	0.568778i	−0.931786	−	0.363008i	$-0.881750\pi$
$643$	−365.724	+	365.724i	−0.568778	+	0.568778i	0.363008	+	0.931786i	$0.381750\pi$
$644$	−84.6678	−	116.535i	−0.131472	−	0.180955i
$645$	9.14354	−	5.94956i	0.0141760	−	0.00922413i
$646$	−543.417	−	394.815i	−0.841202	−	0.611169i
$647$	−200.810	−	1267.86i	−0.310371	−	1.95960i	−0.279755	−	0.960071i	$-0.590253\pi$
$647$	−200.810	−	1267.86i	−0.310371	−	1.95960i	−0.0306158	−	0.999531i	$-0.509747\pi$
$648$	102.786	+	201.729i	0.158620	+	0.311310i
$649$		−	1099.12i		−	1.69356i
$650$	−220.992	−	198.265i	−0.339988	−	0.305023i
$651$	31.5570			0.0484747
$652$	85.0856	−	43.3533i	0.130499	−	0.0664928i
$653$	−668.189	+	105.831i	−1.02326	+	0.162069i	−0.645440	−	0.763811i	$-0.723326\pi$
$653$	−668.189	+	105.831i	−1.02326	+	0.162069i	−0.377820	+	0.925879i	$0.623326\pi$
$654$	−29.7566	+	40.9565i	−0.0454994	+	0.0626246i
$655$	−899.454	+	241.874i	−1.37321	+	0.369273i
$656$	−151.498	+	110.070i	−0.230942	+	0.167789i
$657$	−331.565	−	331.565i	−0.504665	−	0.504665i
$658$	−79.6368	+	502.807i	−0.121029	+	0.764144i
$659$	202.168	−	65.6882i	0.306779	−	0.0996786i	−0.151582	−	0.988445i	$-0.548437\pi$
$659$	202.168	−	65.6882i	0.306779	−	0.0996786i	0.458361	+	0.888766i	$0.348437\pi$
$660$	−13.5805	−	30.4287i	−0.0205765	−	0.0461041i
$661$	−178.262	+	548.635i	−0.269686	+	0.830007i	0.720891	+	0.693048i	$0.243733\pi$
$661$	−178.262	+	548.635i	−0.269686	+	0.830007i	−0.990577	+	0.136959i	$0.956267\pi$
$662$	−347.278	+	681.571i	−0.524589	+	1.02956i
$663$	−41.9378	−	21.3684i	−0.0632546	−	0.0322299i
$664$	−263.759	−	85.7005i	−0.397228	−	0.129067i
$665$	413.053	−	716.914i	0.621132	−	1.07807i
$666$	−4.35749	−	13.4110i	−0.00654278	−	0.0201366i
$667$	155.196	+	24.5806i	0.232678	+	0.0368525i
$668$	170.494	−	170.494i	0.255230	−	0.255230i
$669$	−20.8281	−	28.6674i	−0.0311332	−	0.0428511i
$670$	427.803	+	22.0350i	0.638511	+	0.0328881i
$671$	925.992	+	672.773i	1.38002	+	1.00264i
$672$	1.72809	+	10.9107i	0.00257156	+	0.0162362i
$673$	−156.148	−	306.458i	−0.232018	−	0.455361i	0.745417	−	0.666599i	$-0.232251\pi$
$673$	−156.148	−	306.458i	−0.232018	−	0.455361i	−0.977435	+	0.211238i	$0.932251\pi$
$674$			899.732i			1.33491i
$675$	−81.6195	−	21.7129i	−0.120918	−	0.0321672i
$676$	−196.966			−0.291369
$677$	658.650	−	335.599i	0.972895	−	0.495715i	0.106087	−	0.994357i	$-0.466168\pi$
$677$	658.650	−	335.599i	0.972895	−	0.495715i	0.866808	+	0.498642i	$0.166168\pi$
$678$	1.00876	−	0.159772i	0.00148784	−	0.000235651i
$679$	40.9920	−	56.4206i	0.0603711	−	0.0830936i
$680$	264.971	−	327.814i	0.389664	−	0.482079i
$681$	11.1917	−	8.13126i	0.0164342	−	0.0119402i
$682$	286.339	+	286.339i	0.419852	+	0.419852i
$683$	78.6646	−	496.669i	0.115175	−	0.727187i	−0.860741	−	0.509043i	$-0.830000\pi$
$683$	78.6646	−	496.669i	0.115175	−	0.727187i	0.975916	−	0.218144i	$-0.0700004\pi$
$684$	271.729	−	88.2900i	0.397264	−	0.129079i
$685$	55.2665	−	49.8521i	0.0806810	−	0.0727768i
$686$	44.6216	−	137.331i	0.0650461	−	0.200191i
$687$	−16.7297	+	32.8339i	−0.0243518	+	0.0477931i
$688$	−41.3489	−	21.0683i	−0.0601001	−	0.0306225i
$689$	−252.582	−	82.0690i	−0.366593	−	0.119113i
$690$	6.17741	+	6.84834i	0.00895278	+	0.00992513i
$691$	−148.890	−	458.235i	−0.215470	−	0.663148i	−0.999120	−	0.0419455i	$-0.986644\pi$
$691$	−148.890	−	458.235i	−0.215470	−	0.663148i	0.783650	−	0.621203i	$-0.213356\pi$
$692$	655.152	+	103.766i	0.946751	+	0.149951i
$693$	−1166.37	+	1166.37i	−1.68307	+	1.68307i
$694$	−147.526	−	203.052i	−0.212573	−	0.292581i
$695$	−195.379	−	157.924i	−0.281121	−	0.227229i
$696$	−9.74882	−	7.08294i	−0.0140069	−	0.0101766i
$697$	218.280	+	1378.17i	0.313171	+	1.97729i
$698$	−28.1030	−	55.1552i	−0.0402622	−	0.0790189i
$699$			51.1205i			0.0731337i
$700$	435.955	+	282.001i	0.622794	+	0.402859i
$701$	462.142			0.659260			0.329630	−	0.944110i	$-0.393076\pi$
$701$	462.142			0.659260			0.329630	+	0.944110i	$0.393076\pi$
$702$	35.7475	−	18.2143i	0.0509223	−	0.0259462i
$703$	−17.5062	+	2.77272i	−0.0249022	+	0.00394412i
$704$	−83.3205	+	114.681i	−0.118353	+	0.162899i
$705$	1.67664	−	32.5514i	0.00237821	−	0.0461722i
$706$	224.223	−	162.908i	0.317597	−	0.230748i
$707$	−294.714	−	294.714i	−0.416851	−	0.416851i
$708$	3.64962	−	23.0428i	0.00515483	−	0.0325463i
$709$	1195.01	−	388.281i	1.68548	−	0.547647i	0.699521	−	0.714613i	$-0.253397\pi$
$709$	1195.01	−	388.281i	1.68548	−	0.547647i	0.985963	+	0.166966i	$0.0533970\pi$
$710$	−501.840	−	289.137i	−0.706817	−	0.407235i
$711$	−6.46712	+	19.9038i	−0.00909581	+	0.0279940i
$712$	9.04220	−	17.7463i	0.0126997	−	0.0249246i
$713$	−99.8649	−	50.8837i	−0.140063	−	0.0713656i
$714$	78.2842	+	25.4361i	0.109642	+	0.0356248i
$715$	679.387	−	303.214i	0.950192	−	0.424075i
$716$	−174.735	−	537.780i	−0.244044	−	0.751089i
$717$	22.1018	+	3.50059i	0.0308254	+	0.00488227i
$718$	567.028	−	567.028i	0.789732	−	0.789732i
$719$	−332.930	−	458.239i	−0.463046	−	0.637328i	0.512091	−	0.858931i	$-0.328871\pi$
$719$	−332.930	−	458.239i	−0.463046	−	0.637328i	−0.975137	+	0.221603i	$0.928871\pi$
$720$	46.5599	+	173.142i	0.0646665	+	0.240475i
$721$	−613.450	−	445.697i	−0.850832	−	0.618166i
$722$	23.6848	+	149.540i	0.0328045	+	0.207119i
$723$	28.7387	+	56.4029i	0.0397493	+	0.0780123i
$724$		−	54.8163i		−	0.0757131i
$725$	−553.788	+	118.751i	−0.763846	+	0.163795i
$726$	51.3199			0.0706886
$727$	762.004	−	388.260i	1.04815	−	0.534058i	0.156919	−	0.987611i	$-0.449844\pi$
$727$	762.004	−	388.260i	1.04815	−	0.534058i	0.891229	+	0.453553i	$0.149844\pi$
$728$	−243.606	+	38.5834i	−0.334623	+	0.0529991i
$729$	−418.426	+	575.914i	−0.573973	+	0.790006i
$730$	−201.718	−	310.008i	−0.276326	−	0.424669i
$731$	−279.753	+	203.252i	−0.382698	+	0.278047i
$732$	17.1793	+	17.1793i	0.0234690	+	0.0234690i
$733$	−37.5132	+	236.849i	−0.0511777	+	0.323123i	0.948796	+	0.315889i	$0.102303\pi$
$733$	−37.5132	+	236.849i	−0.0511777	+	0.323123i	−0.999974	+	0.00723420i	$0.997697\pi$
$734$	−156.652	+	50.8992i	−0.213422	+	0.0693449i
$735$	−11.4528	+	54.1202i	−0.0155821	+	0.0736329i
$736$	12.1242	−	37.3143i	0.0164731	−	0.0506988i
$737$	−487.331	+	956.441i	−0.661236	+	1.29775i
$738$	−528.831	−	269.453i	−0.716573	−	0.365112i
$739$	510.511	+	165.875i	0.690814	+	0.224459i	0.633324	−	0.773887i	$-0.281690\pi$
$739$	510.511	+	165.875i	0.690814	+	0.224459i	0.0574900	+	0.998346i	$0.481690\pi$
$740$	−1.17256	−	11.0606i	−0.00158454	−	0.0149468i
$741$	−7.77643	−	23.9334i	−0.0104945	−	0.0322988i
$742$	458.732	+	72.6561i	0.618238	+	0.0979192i
$743$	747.446	−	747.446i	1.00598	−	1.00598i	0.00600177	−	0.999982i	$-0.498090\pi$
$743$	747.446	−	747.446i	1.00598	−	1.00598i	0.999982	−	0.00600177i	$-0.00191043\pi$
$744$	5.05225	+	6.95382i	0.00679066	+	0.00934654i
$745$	−337.390	+	881.295i	−0.452872	+	1.18295i
$746$	434.482	+	315.670i	0.582416	+	0.423150i
$747$	−137.506	−	868.178i	−0.184077	−	1.16222i
$748$	479.528	+	941.127i	0.641080	+	1.25819i
$749$			1258.04i			1.67962i
$750$	−29.6609	−	15.0125i	−0.0395478	−	0.0200166i
$751$	−436.245			−0.580885			−0.290443	−	0.956892i	$-0.593803\pi$
$751$	−436.245			−0.580885			−0.290443	+	0.956892i	$0.593803\pi$
$752$	−123.547	+	62.9503i	−0.164291	+	0.0837105i
$753$	−4.57762	+	0.725024i	−0.00607918	+	0.000962848i
$754$	158.142	−	217.664i	0.209737	−	0.288679i
$755$	320.064	+	122.531i	0.423926	+	0.162293i
$756$	−56.7629	+	41.2407i	−0.0750833	+	0.0545512i
$757$	−160.414	−	160.414i	−0.211907	−	0.211907i	0.593170	−	0.805077i	$-0.297876\pi$
$757$	−160.414	−	160.414i	−0.211907	−	0.211907i	−0.805077	+	0.593170i	$0.797876\pi$
$758$	−61.7369	+	389.792i	−0.0814471	+	0.514237i
$759$	−21.9800	+	7.14174i	−0.0289592	+	0.00940940i
$760$	224.107	−	23.7580i	0.294877	−	0.0312606i
$761$	296.697	−	913.138i	0.389877	−	1.19992i	−0.543002	−	0.839731i	$-0.682713\pi$
$761$	296.697	−	913.138i	0.389877	−	1.19992i	0.932880	−	0.360188i	$-0.117287\pi$
$762$	19.4763	−	38.2243i	0.0255594	−	0.0501632i
$763$	1761.26	+	897.404i	2.30833	+	1.17615i
$764$	−305.991	−	99.4226i	−0.400512	−	0.130134i
$765$	1307.02	+	276.590i	1.70853	+	0.361556i
$766$	262.274	+	807.196i	0.342394	+	1.05378i
$767$	514.480	+	81.4857i	0.670769	+	0.106239i
$768$	−2.12759	+	2.12759i	−0.00277030	+	0.00277030i
$769$	−710.831	−	978.375i	−0.924358	−	1.27227i	−0.962020	−	0.272979i	$-0.911991\pi$
$769$	−710.831	−	978.375i	−0.924358	−	1.27227i	0.0376621	−	0.999291i	$-0.488009\pi$
$770$	−1090.54	+	709.598i	−1.41629	+	0.921556i
$771$	−4.49210	−	3.26370i	−0.00582632	−	0.00423307i
$772$	−84.4843	−	533.413i	−0.109436	−	0.690950i
$773$	6.43059	+	12.6208i	0.00831901	+	0.0163270i	0.895129	−	0.445808i	$-0.147084\pi$
$773$	6.43059	+	12.6208i	0.00831901	+	0.0163270i	−0.886810	+	0.462135i	$0.847084\pi$
$774$		−	147.086i		−	0.190033i
$775$	401.858	+	41.5075i	0.518527	+	0.0535581i
$776$	18.9955			0.0244787
$777$	1.93529	−	0.986080i	0.00249072	−	0.00126909i
$778$	394.573	−	62.4942i	0.507163	−	0.0803268i
$779$	−438.504	+	603.549i	−0.562906	+	0.774774i
$780$	15.2500	−	4.10091i	0.0195513	−	0.00525758i
$781$	1174.16	−	853.074i	1.50340	−	1.09228i
$782$	−206.723	−	206.723i	−0.264351	−	0.264351i
$783$	11.9729	−	75.5941i	0.0152911	−	0.0965442i
$784$	223.813	−	72.7212i	0.285476	−	0.0927566i
$785$	31.4565	+	70.4821i	0.0400720	+	0.0897861i
$786$	15.3091	−	47.1167i	0.0194773	−	0.0599449i
$787$	−618.435	+	1213.75i	−0.785813	+	1.54224i	0.0534821	+	0.998569i	$0.482968\pi$
$787$	−618.435	+	1213.75i	−0.785813	+	1.54224i	−0.839295	+	0.543676i	$0.817032\pi$
$788$	−280.389	−	142.865i	−0.355824	−	0.181301i
$789$	−54.6823	−	17.7674i	−0.0693058	−	0.0225188i
$790$	−8.24091	+	14.3033i	−0.0104315	+	0.0181055i
$791$	−12.3233	−	37.9271i	−0.0155794	−	0.0479483i
$792$	−443.753	−	70.2835i	−0.560294	−	0.0887418i
$793$	−383.565	+	383.565i	−0.483689	+	0.483689i
$794$	−494.221	−	680.237i	−0.622445	−	0.856722i
$795$	−29.6980	−	1.52967i	−0.0373560	−	0.00192411i
$796$	−345.425	−	250.966i	−0.433951	−	0.315284i
$797$	−41.8758	−	264.394i	−0.0525418	−	0.331736i	−0.999932	−	0.0116553i	$-0.996290\pi$
$797$	−41.8758	−	264.394i	−0.0525418	−	0.331736i	0.947390	−	0.320081i	$-0.103710\pi$
$798$	19.9796	+	39.2122i	0.0250371	+	0.0491381i
$799$			1033.20i			1.29312i
$800$	7.65504	+	141.214i	0.00956879	+	0.176518i
$801$	63.1270			0.0788102
$802$	−426.814	+	217.473i	−0.532187	+	0.271163i
$803$	915.406	−	144.986i	1.13998	−	0.180556i
$804$	−13.3926	+	18.4334i	−0.0166575	+	0.0229271i
$805$	226.376	−	280.064i	0.281212	−	0.347906i
$806$	−155.259	+	112.802i	−0.192629	+	0.139953i
$807$	6.39436	+	6.39436i	0.00792362	+	0.00792362i
$808$	17.7590	−	112.126i	0.0219789	−	0.138770i
$809$	459.152	−	149.188i	0.567555	−	0.184410i	−0.0111627	−	0.999938i	$-0.503553\pi$
$809$	459.152	−	149.188i	0.567555	−	0.184410i	0.578718	+	0.815528i	$0.303553\pi$
$810$	−420.290	+	379.115i	−0.518876	+	0.468043i
$811$	−108.992	+	335.444i	−0.134393	+	0.413618i	−0.995495	−	0.0948136i	$-0.969774\pi$
$811$	−108.992	+	335.444i	−0.134393	+	0.413618i	0.861102	+	0.508431i	$0.169774\pi$
$812$	−213.608	+	419.230i	−0.263064	+	0.516293i
$813$	55.0205	+	28.0343i	0.0676759	+	0.0344826i
$814$	26.5076	+	8.61286i	0.0325647	+	0.0105809i
$815$	159.904	+	177.271i	0.196201	+	0.217510i
$816$	6.92819	+	21.3228i	0.00849043	+	0.0261309i
$817$	−182.603	−	28.9215i	−0.223505	−	0.0353997i
$818$	810.791	−	810.791i	0.991187	−	0.991187i
$819$	−459.488	−	632.431i	−0.561035	−	0.772199i
$820$	−364.088	−	294.292i	−0.444010	−	0.358893i
$821$	−499.761	−	363.098i	−0.608723	−	0.442263i	0.240242	−	0.970713i	$-0.422773\pi$
$821$	−499.761	−	363.098i	−0.608723	−	0.442263i	−0.848964	+	0.528450i	$0.822773\pi$
$822$	0.619300	+	3.91011i	0.000753406	+	0.00475682i
$823$	−704.006	−	1381.69i	−0.855415	−	1.67885i	−0.726474	−	0.687194i	$-0.758842\pi$
$823$	−704.006	−	1381.69i	−0.855415	−	1.67885i	−0.128941	−	0.991652i	$-0.541158\pi$
$824$		−	206.534i		−	0.250648i
$825$	64.6453	−	52.5412i	0.0783579	−	0.0636863i
$826$	−910.943			−1.10284
$827$	−1331.37	+	678.366i	−1.60988	+	0.820273i	−0.610272	+	0.792192i	$0.708940\pi$
$827$	−1331.37	+	678.366i	−1.60988	+	0.820273i	−0.999606	+	0.0280811i	$0.991060\pi$
$828$	122.822	−	19.4531i	0.148336	−	0.0234941i
$829$	−292.387	+	402.436i	−0.352699	+	0.485448i	−0.948096	−	0.317983i	$-0.896994\pi$
$829$	−292.387	+	402.436i	−0.352699	+	0.485448i	0.595398	+	0.803431i	$0.296994\pi$
$830$	35.6645	−	692.414i	0.0429692	−	0.834234i
$831$	0.527831	−	0.383491i	0.000635175	−	0.000461482i
$832$	−47.5032	−	47.5032i	−0.0570952	−	0.0570952i
$833$	274.312	−	1731.94i	0.329306	−	2.07916i
$834$	12.7085	−	4.12924i	0.0152380	−	0.00495113i
$835$	522.299	+	300.924i	0.625507	+	0.360388i
$836$	−174.511	+	537.089i	−0.208745	+	0.642451i
$837$	−24.7848	+	48.6430i	−0.0296115	+	0.0581159i
$838$	−50.0460	−	25.4997i	−0.0597207	−	0.0304292i
$839$	−877.533	−	285.128i	−1.04593	−	0.339842i	−0.264858	−	0.964287i	$-0.585325\pi$
$839$	−877.533	−	285.128i	−1.04593	−	0.339842i	−0.781069	+	0.624445i	$0.785325\pi$
$840$	−25.2191	+	11.2554i	−0.0300228	+	0.0133993i
$841$	101.279	+	311.706i	0.120427	+	0.370637i
$842$	−347.455	−	55.0314i	−0.412654	−	0.0653580i
$843$	−54.7351	+	54.7351i	−0.0649290	+	0.0649290i
$844$	−31.1942	−	42.9351i	−0.0369600	−	0.0508710i
$845$	−127.873	−	475.521i	−0.151329	−	0.562746i
$846$	−355.546	−	258.320i	−0.420268	−	0.305342i
$847$	−313.469	−	1979.17i	−0.370094	−	2.33668i
$848$	57.4323	+	112.717i	0.0677267	+	0.132921i
$849$			18.7584i			0.0220947i
$850$	963.442	+	426.880i	1.13346	+	0.502212i
$851$	−7.71438			−0.00906508
$852$	27.4485	−	13.9857i	0.0322166	−	0.0164152i
$853$	203.617	−	32.2497i	0.238707	−	0.0378074i	−0.0359348	−	0.999354i	$-0.511441\pi$
$853$	203.617	−	32.2497i	0.238707	−	0.0378074i	0.274641	+	0.961547i	$0.411441\pi$
$854$	557.590	−	767.457i	0.652916	−	0.898662i
$855$	389.563	+	598.697i	0.455629	+	0.700230i
$856$	−277.218	+	201.411i	−0.323853	+	0.235293i
$857$	71.7689	+	71.7689i	0.0837444	+	0.0837444i	0.747738	−	0.663994i	$-0.231140\pi$
$857$	71.7689	+	71.7689i	0.0837444	+	0.0837444i	−0.663994	+	0.747738i	$0.731140\pi$
$858$	−6.19045	+	39.0849i	−0.00721497	+	0.0455535i
$859$	1025.56	−	333.225i	1.19390	−	0.387922i	0.356387	−	0.934339i	$-0.384009\pi$
$859$	1025.56	−	333.225i	1.19390	−	0.387922i	0.837513	+	0.546417i	$0.184009\pi$
$860$	24.0194	−	113.504i	0.0279296	−	0.131981i
$861$	28.2507	−	86.9468i	0.0328115	−	0.100984i
$862$	−438.866	+	861.324i	−0.509126	+	0.999215i
$863$	−1102.23	−	561.612i	−1.27720	−	0.650767i	−0.322005	−	0.946738i	$-0.604357\pi$
$863$	−1102.23	−	561.612i	−1.27720	−	0.650767i	−0.955197	+	0.295971i	$0.904357\pi$
$864$	−18.1754	−	5.90554i	−0.0210363	−	0.00683511i
$865$	174.820	+	1649.06i	0.202104	+	1.90642i
$866$	−205.399	−	632.154i	−0.237182	−	0.729970i
$867$	111.324	+	17.6320i	0.128402	+	0.0203368i
$868$	237.316	−	237.316i	0.273406	−	0.273406i
$869$	−24.3141	−	33.4655i	−0.0279794	−	0.0385103i
$870$	10.7708	−	28.1343i	0.0123802	−	0.0323383i
$871$	−411.566	−	299.020i	−0.472521	−	0.343306i
$872$	84.2255	+	531.779i	0.0965889	+	0.609838i
$873$	27.3328	+	53.6436i	0.0313090	+	0.0614475i
$874$		−	156.306i		−	0.178840i
$875$	−397.787	+	1235.58i	−0.454614	+	1.41209i
$876$	19.6727			0.0224574
$877$	109.372	−	55.7280i	0.124712	−	0.0635439i	−0.390521	−	0.920594i	$-0.627705\pi$
$877$	109.372	−	55.7280i	0.124712	−	0.0635439i	0.515233	+	0.857050i	$0.327705\pi$
$878$	503.014	−	79.6696i	0.572909	−	0.0907399i
$879$	−5.38717	+	7.41480i	−0.00612874	+	0.00843549i
$880$	−330.959	−	126.703i	−0.376090	−	0.143980i
$881$	−44.4342	+	32.2833i	−0.0504361	+	0.0366440i	−0.612718	−	0.790302i	$-0.709924\pi$
$881$	−44.4342	+	32.2833i	−0.0504361	+	0.0366440i	0.562282	+	0.826946i	$0.309924\pi$
$882$	527.414	+	527.414i	0.597975	+	0.597975i
$883$	−183.327	+	1157.48i	−0.207619	+	1.31085i	0.635071	+	0.772454i	$0.280971\pi$
$883$	−183.327	+	1157.48i	−0.207619	+	1.31085i	−0.842690	+	0.538399i	$0.819029\pi$
$884$	−476.078	+	154.687i	−0.538549	+	0.174985i
$885$	58.0000	−	6.14871i	0.0655367	−	0.00694769i
$886$	69.0343	−	212.466i	0.0779168	−	0.239803i
$887$	−45.8334	+	89.9531i	−0.0516724	+	0.101413i	−0.915399	−	0.402548i	$-0.868125\pi$
$887$	−45.8334	+	89.9531i	−0.0516724	+	0.101413i	0.863726	+	0.503961i	$0.168125\pi$
$888$	0.527128	+	0.268585i	0.000593612	+	0.000302461i
$889$	−1593.10	−	517.628i	−1.79201	−	0.582259i
$890$	48.7141	+	10.3088i	0.0547349	+	0.0115829i
$891$	−438.296	−	1348.94i	−0.491915	−	1.51396i
$892$	−372.218	−	58.9535i	−0.417284	−	0.0660913i
$893$	−390.609	+	390.609i	−0.437412	+	0.437412i
$894$	−29.5031	−	40.6075i	−0.0330012	−	0.0454223i
$895$	1184.89	−	770.987i	1.32389	−	0.861438i
$896$	95.0469	+	69.0556i	0.106079	+	0.0770710i
$897$	−1.71340	−	10.8180i	−0.00191014	−	0.0120602i
$898$	185.658	+	364.374i	0.206746	+	0.405762i
$899$			366.103i			0.407234i
$900$	−387.777	+	224.813i	−0.430863	+	0.249792i
$901$	942.634			1.04621
$902$	1045.27	−	532.591i	1.15883	−	0.590455i
$903$	22.3770	−	3.54416i	0.0247807	−	0.00392488i
$904$	6.38458	−	8.78762i	0.00706259	−	0.00972082i
$905$	132.339	−	35.5876i	0.146231	−	0.0393233i
$906$	−14.7476	+	10.7148i	−0.0162777	+	0.0118265i
$907$	394.165	+	394.165i	0.434581	+	0.434581i	0.890183	−	0.455602i	$-0.150576\pi$
$907$	394.165	+	394.165i	0.434581	+	0.434581i	−0.455602	+	0.890183i	$0.650576\pi$
$908$	23.0154	−	145.313i	0.0253473	−	0.160037i
$909$	342.200	−	111.187i	0.376457	−	0.122318i
$910$	−251.302	−	563.072i	−0.276156	−	0.618761i
$911$	337.243	−	1037.93i	0.370190	−	1.13933i	−0.576477	−	0.817114i	$-0.695573\pi$
$911$	337.243	−	1037.93i	0.370190	−	1.13933i	0.946667	−	0.322214i	$-0.104427\pi$
$912$	−5.44198	+	10.6805i	−0.00596708	+	0.0117111i
$913$	1548.03	+	788.762i	1.69555	+	0.863924i
$914$	729.196	+	236.930i	0.797807	+	0.259223i
$915$	−30.3217	+	52.6278i	−0.0331385	+	0.0575168i
$916$	121.107	+	372.730i	0.132213	+	0.406910i
$917$	−1910.58	−	302.606i	−2.08351	−	0.329995i
$918$	−100.692	+	100.692i	−0.109687	+	0.109687i
$919$	650.818	+	895.775i	0.708181	+	0.974728i	0.999834	+	0.0182035i	$0.00579467\pi$
$919$	650.818	+	895.775i	0.708181	+	0.974728i	−0.291653	+	0.956524i	$0.594205\pi$
$920$	97.9567	+	5.04550i	0.106475	+	0.00548424i
$921$	−58.2481	−	42.3197i	−0.0632444	−	0.0459498i
$922$	95.5158	+	603.063i	0.103596	+	0.654081i
$923$	312.262	+	612.848i	0.338312	+	0.663975i
$924$		−	69.2042i		−	0.0748963i
$925$	25.9417	−	10.0116i	0.0280451	−	0.0108233i
$926$	138.854			0.149950
$927$	583.257	−	297.184i	0.629187	−	0.320587i
$928$	−126.579	+	20.0481i	−0.136400	+	0.0216036i
$929$	−30.4145	+	41.8620i	−0.0327390	+	0.0450613i	−0.825073	−	0.565027i	$-0.808866\pi$
$929$	−30.4145	+	41.8620i	−0.0327390	+	0.0450613i	0.792334	+	0.610088i	$0.208866\pi$
$930$	−13.5081	+	16.7118i	−0.0145249	+	0.0179697i
$931$	758.478	−	551.066i	0.814691	−	0.591908i
$932$	384.438	+	384.438i	0.412487	+	0.412487i
$933$	−12.5169	+	79.0287i	−0.0134158	+	0.0847039i
$934$	−567.853	+	184.507i	−0.607979	+	0.197545i
$935$	−1960.78	+	1768.69i	−2.09709	+	1.89164i
$936$	65.7972	−	202.503i	0.0702962	−	0.216349i
$937$	434.814	−	853.370i	0.464049	−	0.910747i	−0.533827	−	0.845594i	$-0.679247\pi$
$937$	434.814	−	853.370i	0.464049	−	0.910747i	0.997875	−	0.0651528i	$-0.0207535\pi$
$938$	792.693	+	403.897i	0.845088	+	0.430594i
$939$	−86.7473	−	28.1859i	−0.0923827	−	0.0300170i
$940$	−232.185	−	257.403i	−0.247006	−	0.273833i
$941$	168.148	+	517.505i	0.178690	+	0.549953i	0.999783	−	0.0208427i	$-0.00663493\pi$
$941$	168.148	+	517.505i	0.178690	+	0.549953i	−0.821092	+	0.570795i	$0.806635\pi$
$942$	−4.05482	−	0.642220i	−0.00430448	−	0.000681762i
$943$	−229.598	+	229.598i	−0.243476	+	0.243476i
$944$	−145.841	−	200.733i	−0.154493	−	0.212641i
$945$	−136.416	−	110.265i	−0.144356	−	0.116682i
$946$	235.201	+	170.883i	0.248627	+	0.180638i
$947$	230.479	+	1455.19i	0.243378	+	1.53663i	0.742352	+	0.670010i	$0.233710\pi$
$947$	230.479	+	1455.19i	0.243378	+	1.53663i	−0.498974	+	0.866617i	$0.666290\pi$
$948$	−0.398618	−	0.782331i	−0.000420483	−	0.000825244i
$949$			439.236i			0.462841i
$950$	202.851	+	525.621i	0.213527	+	0.553286i
$951$	−35.3376			−0.0371583
$952$	780.001	−	397.430i	0.819328	−	0.417469i
$953$	353.665	−	56.0150i	0.371107	−	0.0587776i	0.0319045	−	0.999491i	$-0.489843\pi$
$953$	353.665	−	56.0150i	0.371107	−	0.0587776i	0.339203	+	0.940713i	$0.389843\pi$
$954$	−235.676	+	324.380i	−0.247040	+	0.340021i
$955$	41.3749	−	803.281i	0.0433245	−	0.841132i
$956$	192.536	−	139.886i	0.201398	−	0.146324i
$957$	53.3799	+	53.3799i	0.0557784	+	0.0557784i
$958$	124.820	−	788.085i	0.130293	−	0.822635i
$959$	147.012	−	47.7670i	0.153297	−	0.0498091i
$960$	−6.51777	−	3.75524i	−0.00678935	−	0.00391171i
$961$	−216.268	+	665.606i	−0.225045	+	0.692618i
$962$	−5.99675	+	11.7693i	−0.00623363	+	0.0122342i
$963$	−967.681	−	493.058i	−1.00486	−	0.512002i
$964$	640.285	+	208.041i	0.664196	+	0.215810i
$965$	1232.93	−	550.265i	1.27765	−	0.570223i
$966$	5.91903	+	18.2169i	0.00612736	+	0.0188581i
$967$	−520.029	−	82.3645i	−0.537775	−	0.0851753i	−0.118362	−	0.992971i	$-0.537764\pi$
$967$	−520.029	−	82.3645i	−0.537775	−	0.0851753i	−0.419414	+	0.907795i	$0.637764\pi$
$968$	385.938	−	385.938i	0.398696	−	0.398696i
$969$	52.5004	+	72.2606i	0.0541800	+	0.0745723i
$970$	12.3321	+	45.8594i	0.0127136	+	0.0472778i
$971$	712.193	+	517.438i	0.733463	+	0.532892i	0.890657	−	0.454675i	$-0.150245\pi$
$971$	712.193	+	517.438i	0.733463	+	0.532892i	−0.157194	+	0.987568i	$0.550245\pi$
$972$	−14.2224	−	89.7968i	−0.0146321	−	0.0923835i
$973$	−236.871	−	464.885i	−0.243444	−	0.477785i
$974$			267.488i			0.274629i
$975$	19.8011	+	34.1547i	0.0203088	+	0.0350305i
$976$	258.384			0.264738
$977$	134.349	−	68.4541i	0.137512	−	0.0700656i	−0.383881	−	0.923383i	$-0.625413\pi$
$977$	134.349	−	68.4541i	0.137512	−	0.0700656i	0.521393	+	0.853317i	$0.325413\pi$
$978$	−12.5419	+	1.98644i	−0.0128240	+	0.00203113i
$979$	−73.3406	+	100.945i	−0.0749138	+	0.103110i
$980$	320.869	+	493.125i	0.327417	+	0.503188i
$981$	−1380.56	+	1003.04i	−1.40730	+	1.02247i
$982$	590.951	+	590.951i	0.601783	+	0.601783i
$983$	−49.2021	+	310.650i	−0.0500530	+	0.316022i	0.949941	+	0.312431i	$0.101143\pi$
$983$	−49.2021	+	310.650i	−0.0500530	+	0.316022i	−0.999994	+	0.00359144i	$0.998857\pi$
$984$	23.6823	−	7.69484i	0.0240674	−	0.00781996i
$985$	162.877	−	769.675i	0.165358	−	0.781396i
$986$	−295.092	+	908.199i	−0.299282	+	0.921095i
$987$	30.7324	−	60.3158i	0.0311372	−	0.0611102i
$988$	−238.465	−	121.504i	−0.241361	−	0.122980i
$989$	−76.5285	−	24.8656i	−0.0773797	−	0.0251422i
$990$	−118.410	−	1116.95i	−0.119606	−	1.12823i
$991$	−81.9066	−	252.083i	−0.0826505	−	0.254372i	0.901189	−	0.433427i	$-0.142696\pi$
$991$	−81.9066	−	252.083i	−0.0826505	−	0.254372i	−0.983839	+	0.179055i	$0.942696\pi$
$992$	90.2885	+	14.3003i	0.0910166	+	0.0144156i
$993$	71.9257	−	71.9257i	0.0724327	−	0.0724327i
$994$	−707.023	−	973.134i	−0.711291	−	0.979008i
$995$	381.635	−	996.867i	0.383553	−	1.00188i
$996$	29.8351	+	21.6765i	0.0299549	+	0.0217635i
$997$	−17.1081	−	108.016i	−0.0171596	−	0.108342i	0.977622	−	0.210370i	$-0.0674668\pi$
$997$	−17.1081	−	108.016i	−0.0171596	−	0.108342i	−0.994782	+	0.102028i	$0.967467\pi$
$998$	182.981	+	359.120i	0.183347	+	0.359839i
$999$			3.75758i			0.00376134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.b.47.2	yes	24
4.3	odd	2		400.3.bg.b.97.2		24
5.2	odd	4		250.3.f.d.243.2		24
5.3	odd	4		250.3.f.f.243.2		24
5.4	even	2		250.3.f.e.7.2		24
25.6	even	5		250.3.f.f.107.2		24
25.8	odd	20	inner	50.3.f.b.33.2	✓	24
25.17	odd	20		250.3.f.e.143.2		24
25.19	even	10		250.3.f.d.107.2		24
100.83	even	20		400.3.bg.b.33.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.33.2	✓	24	25.8	odd	20	inner
50.3.f.b.47.2	yes	24	1.1	even	1	trivial
250.3.f.d.107.2		24	25.19	even	10
250.3.f.d.243.2		24	5.2	odd	4
250.3.f.e.7.2		24	5.4	even	2
250.3.f.e.143.2		24	25.17	odd	20
250.3.f.f.107.2		24	25.6	even	5
250.3.f.f.243.2		24	5.3	odd	4
400.3.bg.b.33.2		24	100.83	even	20
400.3.bg.b.97.2		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26007 + 0.642040i) q^{2} +(0.185739 - 0.0294182i) q^{3} +(1.17557 - 1.61803i) q^{4} +(4.66951 + 1.78765i) q^{5} +(-0.215157 + 0.156321i) q^{6} +(7.34278 + 7.34278i) q^{7} +(-0.442463 + 2.79360i) q^{8} +(-8.52588 + 2.77022i) q^{9} +O(q^{10})\)	\(q+(-1.26007 + 0.642040i) q^{2} +(0.185739 - 0.0294182i) q^{3} +(1.17557 - 1.61803i) q^{4} +(4.66951 + 1.78765i) q^{5} +(-0.215157 + 0.156321i) q^{6} +(7.34278 + 7.34278i) q^{7} +(-0.442463 + 2.79360i) q^{8} +(-8.52588 + 2.77022i) q^{9} +(-7.03167 + 0.745442i) q^{10} +(5.47552 - 16.8519i) q^{11} +(0.170750 - 0.335116i) q^{12} +(7.48219 + 3.81236i) q^{13} +(-13.9668 - 4.53808i) q^{14} +(0.919900 + 0.194668i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-29.4384 - 4.66258i) q^{17} +(8.96464 - 8.96464i) q^{18} +(-9.36667 - 12.8921i) q^{19} +(8.38181 - 5.45392i) q^{20} +(1.57985 + 1.14783i) q^{21} +(3.92004 + 24.7502i) q^{22} +(-3.14877 - 6.17981i) q^{23} +0.531898i q^{24} +(18.6086 + 16.6949i) q^{25} -11.8758 q^{26} +(-3.01011 + 1.53373i) q^{27} +(20.5128 - 3.24891i) q^{28} +(-13.3163 + 18.3284i) q^{29} +(-1.28413 + 0.345317i) q^{30} +(13.0736 - 9.49852i) q^{31} +(4.00000 + 4.00000i) q^{32} +(0.521266 - 3.29114i) q^{33} +(40.0881 - 13.0254i) q^{34} +(21.1609 + 47.4135i) q^{35} +(-5.54045 + 17.0518i) q^{36} +(0.504956 - 0.991031i) q^{37} +(20.0799 + 10.2312i) q^{38} +(1.50189 + 0.487993i) q^{39} +(-7.06007 + 12.2538i) q^{40} +(-14.4667 - 44.5241i) q^{41} +(-2.72768 - 0.432022i) q^{42} +(8.20366 - 8.20366i) q^{43} +(-20.8301 - 28.6702i) q^{44} +(-44.7638 - 2.30567i) q^{45} +(7.93537 + 5.76538i) q^{46} +(-5.42280 - 34.2382i) q^{47} +(-0.341500 - 0.670231i) q^{48} +58.8327i q^{49} +(-34.1670 - 9.08929i) q^{50} -5.60502 q^{51} +(14.9644 - 7.62473i) q^{52} +(-31.2370 + 4.94745i) q^{53} +(2.80825 - 3.86522i) q^{54} +(55.6933 - 68.9019i) q^{55} +(-23.7617 + 17.2639i) q^{56} +(-2.11902 - 2.11902i) q^{57} +(5.01203 - 31.6447i) q^{58} +(58.9939 - 19.1683i) q^{59} +(1.39639 - 1.25958i) q^{60} +(-19.9613 + 61.4346i) q^{61} +(-10.3753 + 20.3626i) q^{62} +(-82.9447 - 42.2624i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(28.1230 + 31.1774i) q^{65} +(1.45621 + 4.48176i) q^{66} +(-59.8348 - 9.47690i) q^{67} +(-42.1511 + 42.1511i) q^{68} +(-0.766649 - 1.05520i) q^{69} +(-57.1056 - 46.1583i) q^{70} +(66.2647 + 48.1441i) q^{71} +(-3.96652 - 25.0436i) q^{72} +(23.7464 + 46.6049i) q^{73} +1.57297i q^{74} +(3.94749 + 2.55346i) q^{75} -31.8711 q^{76} +(163.945 - 83.5344i) q^{77} +(-2.20580 + 0.349364i) q^{78} +(1.37219 - 1.88866i) q^{79} +(1.02878 - 19.9735i) q^{80} +(64.7589 - 47.0501i) q^{81} +(46.8154 + 46.8154i) q^{82} +(-15.3387 + 96.8447i) q^{83} +(3.71446 - 1.20690i) q^{84} +(-129.128 - 74.3974i) q^{85} +(-5.07014 + 15.6043i) q^{86} +(-1.93418 + 3.79604i) q^{87} +(44.6549 + 22.7528i) q^{88} +(-6.69713 - 2.17603i) q^{89} +(57.8861 - 25.8348i) q^{90} +(26.9467 + 82.9333i) q^{91} +(-13.7008 - 2.16999i) q^{92} +(2.14885 - 2.14885i) q^{93} +(28.8154 + 39.6610i) q^{94} +(-20.6912 - 76.9441i) q^{95} +(0.860630 + 0.625284i) q^{96} +(-1.05060 - 6.63322i) q^{97} +(-37.7729 - 74.1335i) q^{98} +158.846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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