LMFDB - Embedded newform 250.2.h.a.229.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(9,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("250.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.h (of order $50$, degree $20$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.9
Character	$\chi$	$=$	250.229
Dual form			250.2.h.a.119.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248690 + 0.968583i) q^{2} +(-0.302937 + 0.0577884i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.17551 - 0.516852i) q^{5} +(-0.131310 - 0.279049i) q^{6} +(-1.43378 + 1.97343i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-2.70090 + 1.06936i) q^{9} +O(q^{10})$	\(q+(0.248690 + 0.968583i) q^{2} +(-0.302937 + 0.0577884i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.17551 - 0.516852i) q^{5} +(-0.131310 - 0.279049i) q^{6} +(-1.43378 + 1.97343i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-2.70090 + 1.06936i) q^{9} +(-0.0404148 - 2.23570i) q^{10} +(-1.19537 + 0.306918i) q^{11} +(0.237626 - 0.196582i) q^{12} +(0.169154 + 0.427233i) q^{13} +(-2.26800 - 0.897963i) q^{14} +(0.688913 + 0.0308542i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-2.41467 + 4.39227i) q^{17} +(-1.70745 - 2.35010i) q^{18} +(0.360057 - 1.88749i) q^{19} +(2.15541 - 0.595142i) q^{20} +(0.320304 - 0.680681i) q^{21} +(-0.594552 - 1.08149i) q^{22} +(2.22360 + 0.139897i) q^{23} +(0.249501 + 0.181273i) q^{24} +(4.46573 + 2.24884i) q^{25} +(-0.371744 + 0.270088i) q^{26} +(1.53758 - 0.975777i) q^{27} +(0.305724 - 2.42006i) q^{28} +(-1.14691 - 0.144888i) q^{29} +(0.141441 + 0.674943i) q^{30} +(-4.68679 - 2.57659i) q^{31} +(0.951057 + 0.309017i) q^{32} +(0.344386 - 0.162056i) q^{33} +(-4.85478 - 1.24650i) q^{34} +(4.13918 - 3.55217i) q^{35} +(1.85165 - 2.23826i) q^{36} +(8.74702 + 5.55103i) q^{37} +(1.91773 - 0.120653i) q^{38} +(-0.0759321 - 0.119650i) q^{39} +(1.11247 + 1.93969i) q^{40} +(-0.216691 - 3.44420i) q^{41} +(0.738953 + 0.140963i) q^{42} +(1.59932 - 0.519652i) q^{43} +(0.899650 - 0.844828i) q^{44} +(6.42854 - 0.930448i) q^{45} +(0.417485 + 2.18853i) q^{46} +(-8.37392 + 8.91732i) q^{47} +(-0.113530 + 0.286743i) q^{48} +(0.324423 + 0.998472i) q^{49} +(-1.06760 + 4.88469i) q^{50} +(0.477672 - 1.47012i) q^{51} +(-0.354052 - 0.292897i) q^{52} +(-2.18855 - 1.02985i) q^{53} +(1.32750 + 1.24661i) q^{54} +(2.75917 - 0.0498775i) q^{55} +(2.42006 - 0.305724i) q^{56} +0.592597i q^{57} +(-0.144888 - 1.14691i) q^{58} +(1.33560 + 1.61446i) q^{59} +(-0.618563 + 0.304849i) q^{60} +(-0.490097 + 7.78987i) q^{61} +(1.33008 - 5.18032i) q^{62} +(1.76218 - 6.86326i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-0.147180 - 1.01688i) q^{65} +(0.242609 + 0.293264i) q^{66} +(0.559393 + 4.42805i) q^{67} -5.01225i q^{68} +(-0.681696 + 0.0861182i) q^{69} +(4.46995 + 3.12575i) q^{70} +(-10.7020 - 10.0498i) q^{71} +(2.62842 + 1.23684i) q^{72} +(11.4816 + 9.49844i) q^{73} +(-3.20134 + 9.85270i) q^{74} +(-1.48279 - 0.423189i) q^{75} +(0.593783 + 1.82747i) q^{76} +(1.10821 - 2.79903i) q^{77} +(0.0970073 - 0.103302i) q^{78} +(-0.991073 - 5.19539i) q^{79} +(-1.60209 + 1.55990i) q^{80} +(5.94332 - 5.58115i) q^{81} +(3.28211 - 1.06642i) q^{82} +(-4.76523 - 0.909015i) q^{83} +(0.0472359 + 0.750793i) q^{84} +(7.52331 - 8.30742i) q^{85} +(0.901061 + 1.41985i) q^{86} +(0.355814 - 0.0223859i) q^{87} +(1.04202 + 0.661286i) q^{88} +(-3.35848 + 4.05971i) q^{89} +(2.49993 + 5.99519i) q^{90} +(-1.08564 - 0.278746i) q^{91} +(-2.01595 + 0.948634i) q^{92} +(1.56870 + 0.509702i) q^{93} +(-10.7197 - 5.89319i) q^{94} +(-1.75886 + 3.92016i) q^{95} +(-0.305968 - 0.0386528i) q^{96} +(-0.409457 + 3.24118i) q^{97} +(-0.886423 + 0.562541i) q^{98} +(2.90036 - 2.10724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 10 q^{5}+O(q^{10}) $ 240 * q + 10 * q^5	$ 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) $ 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$3$	−0.302937	+	0.0577884i	−0.174901	+	0.0333642i	−0.274088	−	0.961705i	$-0.588376\pi$
$3$	−0.302937	+	0.0577884i	−0.174901	+	0.0333642i	0.0991867	+	0.995069i	$0.468376\pi$
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	−2.17551	−	0.516852i	−0.972920	−	0.231143i
$5$	−2.17551	−	0.516852i	−0.972920	−	0.231143i
$6$	−0.131310	−	0.279049i	−0.0536072	−	0.113921i
$7$	−1.43378	+	1.97343i	−0.541918	+	0.745886i	−0.988888	−	0.148663i	$-0.952503\pi$
$7$	−1.43378	+	1.97343i	−0.541918	+	0.745886i	0.446970	+	0.894549i	$0.352503\pi$
$8$	−0.684547	−	0.728969i	−0.242024	−	0.257729i
$9$	−2.70090	+	1.06936i	−0.900299	+	0.356454i
$10$	−0.0404148	−	2.23570i	−0.0127803	−	0.706991i
$11$	−1.19537	+	0.306918i	−0.360417	+	0.0925394i	−0.424556	−	0.905402i	$-0.639570\pi$
$11$	−1.19537	+	0.306918i	−0.360417	+	0.0925394i	0.0641391	+	0.997941i	$0.479570\pi$
$12$	0.237626	−	0.196582i	0.0685968	−	0.0567482i
$13$	0.169154	+	0.427233i	0.0469148	+	0.118493i	0.951344	−	0.308130i	$-0.0997031\pi$
$13$	0.169154	+	0.427233i	0.0469148	+	0.118493i	−0.904430	+	0.426623i	$0.859703\pi$
$14$	−2.26800	−	0.897963i	−0.606147	−	0.239991i
$15$	0.688913	+	0.0308542i	0.177877	+	0.00796651i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−2.41467	+	4.39227i	−0.585644	+	1.06528i	0.403028	+	0.915188i	$0.367958\pi$
$17$	−2.41467	+	4.39227i	−0.585644	+	1.06528i	−0.988672	+	0.150095i	$0.952042\pi$
$18$	−1.70745	−	2.35010i	−0.402450	−	0.553925i
$19$	0.360057	−	1.88749i	0.0826028	−	0.433019i	−0.916828	−	0.399282i	$-0.869259\pi$
$19$	0.360057	−	1.88749i	0.0826028	−	0.433019i	0.999431	−	0.0337364i	$-0.0107407\pi$
$20$	2.15541	−	0.595142i	0.481965	−	0.133078i
$21$	0.320304	−	0.680681i	0.0698961	−	0.148537i
$22$	−0.594552	−	1.08149i	−0.126759	−	0.230574i
$23$	2.22360	+	0.139897i	0.463652	+	0.0291705i	0.292899	−	0.956143i	$-0.405380\pi$
$23$	2.22360	+	0.139897i	0.463652	+	0.0291705i	0.170753	+	0.985314i	$0.445380\pi$
$24$	0.249501	+	0.181273i	0.0509292	+	0.0370022i
$25$	4.46573	+	2.24884i	0.893146	+	0.449767i
$26$	−0.371744	+	0.270088i	−0.0729051	+	0.0529686i
$27$	1.53758	−	0.975777i	0.295907	−	0.187788i
$28$	0.305724	−	2.42006i	0.0577765	−	0.457348i
$29$	−1.14691	−	0.144888i	−0.212975	−	0.0269050i	0.0181215	−	0.999836i	$-0.494231\pi$
$29$	−1.14691	−	0.144888i	−0.212975	−	0.0269050i	−0.231097	+	0.972931i	$0.574231\pi$
$30$	0.141441	+	0.674943i	0.0258235	+	0.123227i
$31$	−4.68679	−	2.57659i	−0.841773	−	0.462768i	0.00166297	−	0.999999i	$-0.499471\pi$
$31$	−4.68679	−	2.57659i	−0.841773	−	0.462768i	−0.843436	+	0.537230i	$0.819471\pi$
$32$	0.951057	+	0.309017i	0.168125	+	0.0546270i
$33$	0.344386	−	0.162056i	0.0599498	−	0.0282102i
$34$	−4.85478	−	1.24650i	−0.832589	−	0.213772i
$35$	4.13918	−	3.55217i	0.699649	−	0.600427i
$36$	1.85165	−	2.23826i	0.308608	−	0.373043i
$37$	8.74702	+	5.55103i	1.43800	+	0.912583i	0.999907	+	0.0136544i	$0.00434647\pi$
$37$	8.74702	+	5.55103i	1.43800	+	0.912583i	0.438094	+	0.898929i	$0.355654\pi$
$38$	1.91773	−	0.120653i	0.311097	−	0.0195725i
$39$	−0.0759321	−	0.119650i	−0.0121589	−	0.0191593i
$40$	1.11247	+	1.93969i	0.175898	+	0.306692i
$41$	−0.216691	−	3.44420i	−0.0338414	−	0.537894i	−0.978027	−	0.208479i	$-0.933149\pi$
$41$	−0.216691	−	3.44420i	−0.0338414	−	0.537894i	0.944185	−	0.329415i	$-0.106851\pi$
$42$	0.738953	+	0.140963i	0.114023	+	0.0217510i
$43$	1.59932	−	0.519652i	0.243895	−	0.0792461i	−0.184519	−	0.982829i	$-0.559073\pi$
$43$	1.59932	−	0.519652i	0.243895	−	0.0792461i	0.428413	+	0.903583i	$0.359073\pi$
$44$	0.899650	−	0.844828i	0.135627	−	0.127363i
$45$	6.42854	−	0.930448i	0.958311	−	0.138703i
$46$	0.417485	+	2.18853i	0.0615548	+	0.322681i
$47$	−8.37392	+	8.91732i	−1.22146	+	1.30072i	−0.281453	+	0.959575i	$0.590816\pi$
$47$	−8.37392	+	8.91732i	−1.22146	+	1.30072i	−0.940009	+	0.341150i	$0.889184\pi$
$48$	−0.113530	+	0.286743i	−0.0163866	+	0.0413878i
$49$	0.324423	+	0.998472i	0.0463462	+	0.142639i
$50$	−1.06760	+	4.88469i	−0.150982	+	0.690800i
$51$	0.477672	−	1.47012i	0.0668875	−	0.205859i
$52$	−0.354052	−	0.292897i	−0.0490981	−	0.0406175i
$53$	−2.18855	−	1.02985i	−0.300620	−	0.141461i	0.269553	−	0.962986i	$-0.413124\pi$
$53$	−2.18855	−	1.02985i	−0.300620	−	0.141461i	−0.570174	+	0.821524i	$0.693124\pi$
$54$	1.32750	+	1.24661i	0.180650	+	0.169642i
$55$	2.75917	−	0.0498775i	0.372047	−	0.00672549i
$56$	2.42006	−	0.305724i	0.323394	−	0.0408541i
$57$			0.592597i			0.0784914i
$58$	−0.144888	−	1.14691i	−0.0190247	−	0.150596i
$59$	1.33560	+	1.61446i	0.173880	+	0.210185i	0.850253	−	0.526375i	$-0.176449\pi$
$59$	1.33560	+	1.61446i	0.173880	+	0.210185i	−0.676373	+	0.736560i	$0.736449\pi$
$60$	−0.618563	+	0.304849i	−0.0798562	+	0.0393558i
$61$	−0.490097	+	7.78987i	−0.0627505	+	0.997390i	0.833125	+	0.553085i	$0.186550\pi$
$61$	−0.490097	+	7.78987i	−0.0627505	+	0.997390i	−0.895875	+	0.444305i	$0.853450\pi$
$62$	1.33008	−	5.18032i	0.168920	−	0.657901i
$63$	1.76218	−	6.86326i	0.222014	−	0.864689i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−0.147180	−	1.01688i	−0.0182554	−	0.126128i
$66$	0.242609	+	0.293264i	0.0298632	+	0.0360984i
$67$	0.559393	+	4.42805i	0.0683408	+	0.540973i	0.988701	+	0.149901i	$0.0478956\pi$
$67$	0.559393	+	4.42805i	0.0683408	+	0.540973i	−0.920360	+	0.391072i	$0.872104\pi$
$68$		−	5.01225i		−	0.607825i
$69$	−0.681696	+	0.0861182i	−0.0820666	+	0.0103674i
$70$	4.46995	+	3.12575i	0.534261	+	0.373599i
$71$	−10.7020	−	10.0498i	−1.27009	−	1.19269i	−0.971162	−	0.238419i	$-0.923371\pi$
$71$	−10.7020	−	10.0498i	−1.27009	−	1.19269i	−0.298928	−	0.954276i	$-0.596629\pi$
$72$	2.62842	+	1.23684i	0.309763	+	0.145763i
$73$	11.4816	+	9.49844i	1.34382	+	1.11171i	0.983899	+	0.178728i	$0.0571982\pi$
$73$	11.4816	+	9.49844i	1.34382	+	1.11171i	0.359926	+	0.932981i	$0.382802\pi$
$74$	−3.20134	+	9.85270i	−0.372148	+	1.14535i
$75$	−1.48279	−	0.423189i	−0.171218	−	0.0488657i
$76$	0.593783	+	1.82747i	0.0681115	+	0.209626i
$77$	1.10821	−	2.79903i	0.126293	−	0.318979i
$78$	0.0970073	−	0.103302i	0.0109839	−	0.0116967i
$79$	−0.991073	−	5.19539i	−0.111504	−	0.584527i	−0.993553	−	0.113368i	$-0.963836\pi$
$79$	−0.991073	−	5.19539i	−0.111504	−	0.584527i	0.882049	−	0.471158i	$-0.156164\pi$
$80$	−1.60209	+	1.55990i	−0.179119	+	0.174403i
$81$	5.94332	−	5.58115i	0.660369	−	0.620127i
$82$	3.28211	−	1.06642i	0.362448	−	0.117767i
$83$	−4.76523	−	0.909015i	−0.523051	−	0.0997774i	−0.0809077	−	0.996722i	$-0.525782\pi$
$83$	−4.76523	−	0.909015i	−0.523051	−	0.0997774i	−0.442144	+	0.896944i	$0.645782\pi$
$84$	0.0472359	+	0.750793i	0.00515386	+	0.0819183i
$85$	7.52331	−	8.30742i	0.816017	−	0.901067i
$86$	0.901061	+	1.41985i	0.0971639	+	0.153106i
$87$	0.355814	−	0.0223859i	0.0381473	−	0.00240002i
$88$	1.04202	+	0.661286i	0.111080	+	0.0704933i
$89$	−3.35848	+	4.05971i	−0.355998	+	0.430328i	−0.917861	−	0.396903i	$-0.870085\pi$
$89$	−3.35848	+	4.05971i	−0.355998	+	0.430328i	0.561862	+	0.827231i	$0.310085\pi$
$90$	2.49993	+	5.99519i	0.263516	+	0.631948i
$91$	−1.08564	−	0.278746i	−0.113806	−	0.0292205i
$92$	−2.01595	+	0.948634i	−0.210177	+	0.0989020i
$93$	1.56870	+	0.509702i	0.162667	+	0.0528536i
$94$	−10.7197	−	5.89319i	−1.10565	−	0.607836i
$95$	−1.75886	+	3.92016i	−0.180455	+	0.402199i
$96$	−0.305968	−	0.0386528i	−0.0312278	−	0.00394498i
$97$	−0.409457	+	3.24118i	−0.0415740	+	0.329092i	0.957587	+	0.288144i	$0.0930381\pi$
$97$	−0.409457	+	3.24118i	−0.0415740	+	0.329092i	−0.999161	+	0.0409488i	$0.986962\pi$
$98$	−0.886423	+	0.562541i	−0.0895422	+	0.0568252i
$99$	2.90036	−	2.10724i	0.291497	−	0.211785i
$100$	−4.99673	+	0.180711i	−0.499673	+	0.0180711i
$101$	−5.28668	−	3.84100i	−0.526044	−	0.382194i	0.292832	−	0.956164i	$-0.405402\pi$
$101$	−5.28668	−	3.84100i	−0.526044	−	0.382194i	−0.818876	+	0.573970i	$0.805402\pi$
$102$	1.54273	+	0.0970603i	0.152753	+	0.00961040i
$103$	−3.32009	−	6.03921i	−0.327138	−	0.595061i	0.660682	−	0.750666i	$-0.270267\pi$
$103$	−3.32009	−	6.03921i	−0.327138	−	0.595061i	−0.987819	+	0.155605i	$0.950267\pi$
$104$	0.195646	−	0.415769i	0.0191847	−	0.0407695i
$105$	−1.04864	+	1.31528i	−0.102337	+	0.128358i
$106$	0.453228	−	2.37591i	0.0440214	−	0.230768i
$107$	2.76744	+	3.80905i	0.267539	+	0.368235i	0.921557	−	0.388244i	$-0.126918\pi$
$107$	2.76744	+	3.80905i	0.267539	+	0.368235i	−0.654018	+	0.756479i	$0.726918\pi$
$108$	−0.877306	+	1.59581i	−0.0844188	+	0.153557i
$109$	−5.27169	+	8.30685i	−0.504936	+	0.795652i	−0.997199	−	0.0747948i	$-0.976170\pi$
$109$	−5.27169	+	8.30685i	−0.504936	+	0.795652i	0.492263	+	0.870447i	$0.336170\pi$
$110$	0.734489	+	2.66008i	0.0700308	+	0.253629i
$111$	−2.97059	−	1.17614i	−0.281955	−	0.111634i
$112$	0.897963	+	2.26800i	0.0848495	+	0.214305i
$113$	3.21129	−	2.65661i	0.302093	−	0.249913i	−0.474010	−	0.880520i	$-0.657194\pi$
$113$	3.21129	−	2.65661i	0.302093	−	0.249913i	0.776103	+	0.630607i	$0.217194\pi$
$114$	−0.573980	+	0.147373i	−0.0537581	+	0.0138027i
$115$	−4.76517	−	1.45362i	−0.444354	−	0.135551i
$116$	1.07484	−	0.425560i	0.0997966	−	0.0395123i
$117$	−0.913734	−	0.973028i	−0.0844747	−	0.0899564i
$118$	−1.23159	+	1.69514i	−0.113377	+	0.156050i
$119$	−5.20573	−	11.0627i	−0.477208	−	1.01412i
$120$	−0.449102	−	0.523317i	−0.0409972	−	0.0477721i
$121$	−8.30467	+	4.56553i	−0.754970	+	0.415048i
$122$	−7.66702	+	1.46256i	−0.694139	+	0.132414i
$123$	0.264679	+	1.03086i	0.0238653	+	0.0929492i
$124$	5.34835			0.480296
$125$	−8.55294	−	7.20050i	−0.764999	−	0.644032i
$126$	7.08587			0.631260
$127$	−4.62531	−	18.0144i	−0.410430	−	1.59852i	−0.752332	−	0.658785i	$-0.771071\pi$
$127$	−4.62531	−	18.0144i	−0.410430	−	1.59852i	0.341901	−	0.939736i	$-0.388929\pi$
$128$	−0.982287	+	0.187381i	−0.0868227	+	0.0165623i
$129$	−0.454465	+	0.249844i	−0.0400134	+	0.0219976i
$130$	0.948331	−	0.395444i	0.0831741	−	0.0346827i
$131$	−7.98034	−	16.9591i	−0.697245	−	1.48172i	−0.868081	−	0.496422i	$-0.834647\pi$
$131$	−7.98034	−	16.9591i	−0.697245	−	1.48172i	0.170836	−	0.985300i	$-0.445353\pi$
$132$	−0.223717	+	0.307919i	−0.0194720	+	0.0268009i
$133$	3.20857	+	3.41678i	0.278219	+	0.296273i
$134$	−4.14982	+	1.64303i	−0.358490	+	0.141936i
$135$	−3.84936	+	1.32812i	−0.331300	+	0.114306i
$136$	4.85478	−	1.24650i	0.416294	−	0.106886i
$137$	−2.05164	+	1.69727i	−0.175284	+	0.145007i	−0.720929	−	0.693009i	$-0.756285\pi$
$137$	−2.05164	+	1.69727i	−0.175284	+	0.145007i	0.545645	+	0.838016i	$0.316285\pi$
$138$	−0.252944	−	0.638863i	−0.0215320	−	0.0543836i
$139$	14.6033	+	5.78184i	1.23863	+	0.490409i	0.893889	−	0.448288i	$-0.147966\pi$
$139$	14.6033	+	5.78184i	1.23863	+	0.490409i	0.344743	+	0.938697i	$0.387966\pi$
$140$	−1.91592	+	5.10686i	−0.161925	+	0.431608i
$141$	2.02146	−	3.18531i	0.170237	−	0.268251i
$142$	7.07262	−	12.8650i	0.593521	−	1.07961i
$143$	−0.333327	−	0.458785i	−0.0278742	−	0.0383655i
$144$	−0.544322	+	2.85344i	−0.0453602	+	0.237786i
$145$	2.42023	+	0.907987i	0.200989	+	0.0754042i
$146$	−6.34466	+	13.4831i	−0.525088	+	1.11587i
$147$	−0.155980	−	0.283727i	−0.0128650	−	0.0234014i
$148$	−10.3393	−	0.650494i	−0.849885	−	0.0534702i
$149$	7.24263	+	5.26208i	0.593339	+	0.431086i	0.843508	−	0.537116i	$-0.180486\pi$
$149$	7.24263	+	5.26208i	0.593339	+	0.431086i	−0.250169	+	0.968202i	$0.580486\pi$
$150$	0.0411385	−	1.54145i	0.00335894	−	0.125859i
$151$	−13.6960	+	9.95069i	−1.11456	+	0.809776i	−0.983376	−	0.181582i	$-0.941878\pi$
$151$	−13.6960	+	9.95069i	−1.11456	+	0.809776i	−0.131185	+	0.991358i	$0.541878\pi$
$152$	−1.62239	+	1.02960i	−0.131593	+	0.0835118i
$153$	1.82486	−	14.4452i	0.147531	−	1.16783i
$154$	2.98669	+	0.377307i	0.240675	+	0.0304043i
$155$	8.86447	+	8.02778i	0.712012	+	0.644807i
$156$	0.124182	+	0.0682694i	0.00994249	+	0.00546593i
$157$	−17.2707	−	5.61161i	−1.37836	−	0.447855i	−0.476227	−	0.879322i	$-0.657996\pi$
$157$	−17.2707	−	5.61161i	−1.37836	−	0.447855i	−0.902129	+	0.431467i	$0.857996\pi$
$158$	4.78569	−	2.25198i	0.380729	−	0.179158i
$159$	0.722507	+	0.185508i	0.0572986	+	0.0147118i
$160$	−1.90932	−	1.16383i	−0.150945	−	0.0920085i
$161$	−3.46423	+	4.18753i	−0.273019	+	0.330024i
$162$	6.88385	+	4.36862i	0.540846	+	0.343231i
$163$	12.0069	−	0.755409i	0.940452	−	0.0591682i	0.414842	−	0.909894i	$-0.363837\pi$
$163$	12.0069	−	0.755409i	0.940452	−	0.0591682i	0.525610	+	0.850725i	$0.323837\pi$
$164$	1.84915	+	2.91379i	0.144394	+	0.227529i
$165$	−0.832974	+	0.174558i	−0.0648470	+	0.0135893i
$166$	−0.304606	−	4.84158i	−0.0236420	−	0.375779i
$167$	−19.7071	−	3.75934i	−1.52498	−	0.290906i	−0.644361	−	0.764722i	$-0.722876\pi$
$167$	−19.7071	−	3.75934i	−1.52498	−	0.290906i	−0.880624	+	0.473815i	$0.842876\pi$
$168$	−0.715459	+	0.232467i	−0.0551988	+	0.0179352i
$169$	9.32268	−	8.75458i	0.717129	−	0.673429i
$170$	9.91740	+	5.22098i	0.760630	+	0.400431i
$171$	1.04593	+	5.48294i	0.0799840	+	0.419291i
$172$	−1.15115	+	1.22585i	−0.0877746	+	0.0934705i
$173$	−6.87541	+	17.3653i	−0.522728	+	1.32026i	0.393398	+	0.919368i	$0.371299\pi$
$173$	−6.87541	+	17.3653i	−0.522728	+	1.32026i	−0.916126	+	0.400891i	$0.868701\pi$
$174$	0.110170	+	0.339068i	0.00835196	+	0.0257047i
$175$	−10.8408	+	5.58846i	−0.819487	+	0.422448i
$176$	−0.381371	+	1.17374i	−0.0287469	+	0.0884738i
$177$	−0.497900	−	0.411899i	−0.0374245	−	0.0309602i
$178$	−4.76739	−	2.24336i	−0.357331	−	0.168147i
$179$	12.5060	+	11.7439i	0.934742	+	0.877781i	0.992709	−	0.120537i	$-0.0384618\pi$
$179$	12.5060	+	11.7439i	0.934742	+	0.877781i	−0.0579669	+	0.998319i	$0.518462\pi$
$180$	−5.18513	+	3.91233i	−0.386477	+	0.291608i
$181$	6.92517	−	0.874853i	0.514744	−	0.0650273i	0.136330	−	0.990664i	$-0.456469\pi$
$181$	6.92517	−	0.874853i	0.514744	−	0.0650273i	0.378414	+	0.925636i	$0.376469\pi$
$182$		−	1.12086i		−	0.0830835i
$183$	−0.301695	−	2.38817i	−0.0223020	−	0.176538i
$184$	−1.42018	−	1.71670i	−0.104697	−	0.126557i
$185$	−16.1602	−	16.5973i	−1.18812	−	1.22025i
$186$	−0.103569	+	1.64618i	−0.00759402	+	0.120703i
$187$	1.53835	−	5.99149i	0.112496	−	0.438141i
$188$	3.04217	−	11.8485i	0.221873	−	0.864139i
$189$	−0.278923	+	4.43335i	−0.0202887	+	0.322479i
$190$	−4.23441	−	0.728698i	−0.307196	−	0.0528653i
$191$	13.4842	+	16.2996i	0.975680	+	1.17939i	0.983771	+	0.179427i	$0.0574243\pi$
$191$	13.4842	+	16.2996i	0.975680	+	1.17939i	−0.00809160	+	0.999967i	$0.502576\pi$
$192$	−0.0386528	−	0.305968i	−0.00278952	−	0.0220814i
$193$			18.9472i			1.36385i	0.731423	+	0.681924i	$0.238856\pi$
$193$			18.9472i			1.36385i	−0.731423	+	0.681924i	$0.761144\pi$
$194$	−3.24118	+	0.409457i	−0.232703	+	0.0293973i
$195$	0.103350	+	0.299546i	0.00740106	+	0.0214509i
$196$	−0.765312	−	0.718676i	−0.0546651	−	0.0513340i
$197$	21.9475	+	10.3277i	1.56370	+	0.735820i	0.996162	−	0.0875285i	$-0.0278969\pi$
$197$	21.9475	+	10.3277i	1.56370	+	0.735820i	0.567536	+	0.823349i	$0.307897\pi$
$198$	2.76232	+	2.28519i	0.196310	+	0.162402i
$199$	3.11587	−	9.58966i	0.220878	−	0.679793i	−0.777806	−	0.628505i	$-0.783667\pi$
$199$	3.11587	−	9.58966i	0.220878	−	0.679793i	0.998684	−	0.0512882i	$-0.0163327\pi$
$200$	−1.41767	−	4.79481i	−0.100244	−	0.339044i
$201$	−0.425351	−	1.30910i	−0.0300020	−	0.0923366i
$202$	2.40558	−	6.07581i	0.169256	−	0.427492i
$203$	1.93034	−	2.05560i	0.135483	−	0.144275i
$204$	0.289650	+	1.51840i	0.0202796	+	0.106309i
$205$	−1.30873	+	7.60491i	−0.0914055	+	0.531150i
$206$	5.02381	−	4.71767i	0.350025	−	0.328696i
$207$	−6.15531	+	1.99998i	−0.427824	+	0.139008i
$208$	0.451362	+	0.0861019i	0.0312963	+	0.00597010i
$209$	0.148903	+	2.36675i	0.0102998	+	0.163711i
$210$	−1.53475	−	0.688596i	−0.105908	−	0.0475176i
$211$	10.6716	+	16.8157i	0.734663	+	1.15764i	0.982031	+	0.188721i	$0.0604343\pi$
$211$	10.6716	+	16.8157i	0.734663	+	1.15764i	−0.247368	+	0.968922i	$0.579566\pi$
$212$	2.41398	−	0.151875i	0.165793	−	0.0104308i
$213$	3.82279	+	2.42602i	0.261933	+	0.166228i
$214$	−3.00115	+	3.62777i	−0.205155	+	0.247989i
$215$	−3.74793	+	0.303897i	−0.255607	+	0.0207256i
$216$	−1.76386	−	0.452881i	−0.120015	−	0.0308147i
$217$	11.8045	−	5.55479i	0.801344	−	0.377084i
$218$	−9.35689	−	3.04024i	−0.633728	−	0.205911i
$219$	−4.02712	−	2.21393i	−0.272128	−	0.149603i
$220$	−2.39385	+	1.37295i	−0.161394	+	0.0925642i
$221$	−2.28498	−	0.288660i	−0.153704	−	0.0194173i
$222$	0.400433	−	3.16975i	0.0268753	−	0.212740i
$223$	4.71519	−	2.99235i	0.315752	−	0.200383i	−0.368500	−	0.929628i	$-0.620129\pi$
$223$	4.71519	−	2.99235i	0.315752	−	0.200383i	0.684253	+	0.729245i	$0.260129\pi$
$224$	−1.97343	+	1.43378i	−0.131855	+	0.0957984i
$225$	−14.4663	−	1.29840i	−0.964420	−	0.0865601i
$226$	3.37176	+	2.44973i	0.224286	+	0.162954i
$227$	2.42854	+	0.152791i	0.161188	+	0.0101411i	0.143179	−	0.989697i	$-0.454267\pi$
$227$	2.42854	+	0.152791i	0.161188	+	0.0101411i	0.0180085	+	0.999838i	$0.494267\pi$
$228$	−0.285486	−	0.519297i	−0.0189068	−	0.0343913i
$229$	6.77269	−	14.3927i	0.447552	−	0.951096i	−0.546007	−	0.837780i	$-0.683853\pi$
$229$	6.77269	−	14.3927i	0.447552	−	0.951096i	0.993559	−	0.113316i	$-0.0361471\pi$
$230$	0.222902	−	4.97696i	0.0146977	−	0.328171i
$231$	−0.173968	+	0.911972i	−0.0114463	+	0.0600034i
$232$	0.679493	+	0.935242i	0.0446109	+	0.0614016i
$233$	−6.97274	+	12.6834i	−0.456799	+	0.830915i	−0.999962	−	0.00871280i	$-0.997227\pi$
$233$	−6.97274	+	12.6834i	−0.456799	+	0.830915i	0.543163	+	0.839627i	$0.317227\pi$
$234$	0.715222	−	1.12701i	0.0467555	−	0.0736749i
$235$	22.8265	−	15.0717i	1.48904	−	0.983168i
$236$	−1.94817	−	0.771334i	−0.126815	−	0.0502096i
$237$	0.600466	+	1.51660i	0.0390045	+	0.0985141i
$238$	9.42056	−	7.79337i	0.610644	−	0.505169i
$239$	15.7268	−	4.03795i	1.01728	−	0.261193i	0.297001	−	0.954877i	$-0.404013\pi$
$239$	15.7268	−	4.03795i	1.01728	−	0.261193i	0.720280	+	0.693684i	$0.244013\pi$
$240$	0.395189	−	0.565136i	0.0255093	−	0.0364794i
$241$	21.7123	−	8.59651i	1.39861	−	0.553750i	0.456704	−	0.889619i	$-0.349030\pi$
$241$	21.7123	−	8.59651i	1.39861	−	0.553750i	0.941909	+	0.335869i	$0.109030\pi$
$242$	−6.48738	−	6.90836i	−0.417025	−	0.444086i
$243$	−4.68912	+	6.45402i	−0.300807	+	0.414026i
$244$	−3.32332	−	7.06242i	−0.212754	−	0.452125i
$245$	−0.189726	−	2.33987i	−0.0121211	−	0.149489i
$246$	−0.932647	+	0.512727i	−0.0594634	+	0.0326903i
$247$	0.867302	−	0.165447i	0.0551851	−	0.0105271i
$248$	1.33008	+	5.18032i	0.0844602	+	0.328951i
$249$	1.49610			0.0948112
$250$	4.84725	−	10.0749i	0.306567	−	0.637194i
$251$	26.3283			1.66183			0.830915	−	0.556399i	$-0.187818\pi$
$251$	26.3283			1.66183			0.830915	+	0.556399i	$0.187818\pi$
$252$	1.76218	+	6.86326i	0.111007	+	0.432345i
$253$	−2.70096	+	0.515235i	−0.169808	+	0.0323926i
$254$	16.2982	−	8.96000i	1.02264	−	0.562201i
$255$	−1.79902	+	2.95139i	−0.112659	+	0.184823i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	−8.39199	+	11.5506i	−0.523478	+	0.720506i	−0.986119	−	0.166040i	$-0.946902\pi$
$257$	−8.39199	+	11.5506i	−0.523478	+	0.720506i	0.462641	+	0.886546i	$0.346902\pi$
$258$	−0.355016	−	0.378054i	−0.0221023	−	0.0235366i
$259$	−23.4959	+	9.30267i	−1.45996	+	0.578040i
$260$	0.618861	+	0.820194i	0.0383801	+	0.0508663i
$261$	3.25262	−	0.835130i	0.201332	−	0.0516932i
$262$	14.4417	−	11.9472i	0.892208	−	0.738099i
$263$	3.22990	+	8.15779i	0.199164	+	0.503031i	0.994693	−	0.102884i	$-0.0328071\pi$
$263$	3.22990	+	8.15779i	0.199164	+	0.503031i	−0.795529	+	0.605915i	$0.792807\pi$
$264$	−0.353882	−	0.140112i	−0.0217799	−	0.00862327i
$265$	4.22894	+	3.37162i	0.259782	+	0.207117i
$266$	−2.51150	+	3.95749i	−0.153990	+	0.242649i
$267$	0.782806	−	1.42392i	0.0479070	−	0.0871424i
$268$	−2.62343	−	3.61084i	−0.160252	−	0.220567i
$269$	2.02710	−	10.6264i	0.123595	−	0.647906i	−0.865534	−	0.500851i	$-0.833021\pi$
$269$	2.02710	−	10.6264i	0.123595	−	0.647906i	0.989128	−	0.147055i	$-0.0469795\pi$
$270$	−2.24369	−	3.39813i	−0.136547	−	0.206804i
$271$	−4.47971	+	9.51988i	−0.272123	+	0.578291i	−0.993445	−	0.114308i	$-0.963535\pi$
$271$	−4.47971	+	9.51988i	−0.272123	+	0.578291i	0.721322	+	0.692600i	$0.243535\pi$
$272$	2.41467	+	4.39227i	0.146411	+	0.266321i
$273$	0.344990	+	0.0217050i	0.0208798	+	0.00131364i
$274$	−2.15417	−	1.56510i	−0.130138	−	0.0945509i
$275$	−6.02840	−	1.31757i	−0.363526	−	0.0794527i
$276$	0.555887	−	0.403876i	0.0334605	−	0.0243104i
$277$	18.5414	−	11.7667i	1.11405	−	0.706995i	0.154345	−	0.988017i	$-0.450673\pi$
$277$	18.5414	−	11.7667i	1.11405	−	0.706995i	0.959701	+	0.281022i	$0.0906734\pi$
$278$	−1.96851	+	15.5824i	−0.118063	+	0.934568i
$279$	15.4138	+	1.94722i	0.922803	+	0.116577i
$280$	−5.42288	−	0.585703i	−0.324079	−	0.0350024i
$281$	−12.7494	−	7.00905i	−0.760566	−	0.418125i	0.0537443	−	0.998555i	$-0.482884\pi$
$281$	−12.7494	−	7.00905i	−0.760566	−	0.418125i	−0.814310	+	0.580430i	$0.802884\pi$
$282$	3.58795	+	1.16580i	0.213659	+	0.0694221i
$283$	−15.8548	+	7.46069i	−0.942468	+	0.443492i	−0.834713	−	0.550686i	$-0.814366\pi$
$283$	−15.8548	+	7.46069i	−0.942468	+	0.443492i	−0.107755	+	0.994177i	$0.534366\pi$
$284$	14.2197	+	3.65101i	0.843787	+	0.216648i
$285$	0.306285	−	1.28920i	0.0181427	−	0.0763658i
$286$	0.361476	−	0.436950i	0.0213745	−	0.0258374i
$287$	7.10758	+	4.51061i	0.419547	+	0.266253i
$288$	−2.89916	+	0.182400i	−0.170834	+	0.0107480i
$289$	−4.35235	−	6.85821i	−0.256021	−	0.403424i
$290$	−0.277575	+	2.57000i	−0.0162997	+	0.150916i
$291$	−0.0632631	−	1.00554i	−0.00370855	−	0.0589457i
$292$	−14.6374	−	2.79222i	−0.856586	−	0.163403i
$293$	−9.97405	+	3.24077i	−0.582691	+	0.189328i	−0.585506	−	0.810668i	$-0.699104\pi$
$293$	−9.97405	+	3.24077i	−0.582691	+	0.189328i	0.00281502	+	0.999996i	$0.499104\pi$
$294$	0.236022	−	0.221640i	0.0137651	−	0.0129263i
$295$	−2.07118	−	4.20259i	−0.120589	−	0.244684i
$296$	−1.94122	−	10.1762i	−0.112831	−	0.591482i
$297$	−1.53849	+	1.63832i	−0.0892722	+	0.0950652i
$298$	−3.29559	+	8.32371i	−0.190908	+	0.482180i
$299$	0.316361	+	0.973660i	0.0182956	+	0.0563082i
$300$	1.50325	−	0.343497i	0.0867905	−	0.0198318i
$301$	−1.26758	+	3.90122i	−0.0730622	+	0.224862i
$302$	−13.0441	−	10.7910i	−0.750604	−	0.620954i
$303$	1.82350	+	0.858073i	0.104757	+	0.0492950i
$304$	−1.40073	−	1.31537i	−0.0803373	−	0.0754417i
$305$	5.09242	−	16.6937i	0.291591	−	0.955877i
$306$	14.4452	−	1.82486i	0.825779	−	0.104320i
$307$		−	29.5835i		−	1.68842i	−0.536015	−	0.844209i	$-0.680071\pi$
$307$		−	29.5835i		−	1.68842i	0.536015	−	0.844209i	$-0.319929\pi$
$308$	0.377307	+	2.98669i	0.0214991	+	0.170183i
$309$	1.35478	+	1.63764i	0.0770705	+	0.0931622i
$310$	−5.57106	+	10.5824i	−0.316415	+	0.601040i
$311$	−0.724026	+	11.5081i	−0.0410558	+	0.652563i	0.922657	+	0.385622i	$0.126013\pi$
$311$	−0.724026	+	11.5081i	−0.0410558	+	0.652563i	−0.963713	+	0.266941i	$0.913987\pi$
$312$	−0.0352419	+	0.137258i	−0.00199518	+	0.00777071i
$313$	−3.75487	+	14.6243i	−0.212238	+	0.826612i	0.769856	+	0.638218i	$0.220328\pi$
$313$	−3.75487	+	14.6243i	−0.212238	+	0.826612i	−0.982094	+	0.188394i	$0.939672\pi$
$314$	1.14025	−	18.1237i	0.0643478	−	1.02278i
$315$	−7.38094	+	14.0203i	−0.415869	+	0.789956i
$316$	3.37138	+	4.07530i	0.189655	+	0.229253i
$317$	1.44913	+	11.4710i	0.0813910	+	0.644276i	0.979055	+	0.203596i	$0.0652628\pi$
$317$	1.44913	+	11.4710i	0.0813910	+	0.644276i	−0.897664	+	0.440680i	$0.854737\pi$
$318$			0.745943i			0.0418304i
$319$	1.41545	−	0.178812i	0.0792497	−	0.0100116i
$320$	0.652433	−	2.13877i	0.0364721	−	0.119561i
$321$	−1.05848	−	0.993979i	−0.0590786	−	0.0554785i
$322$	−4.91749	−	2.31400i	−0.274041	−	0.128954i
$323$	7.42093	+	6.13913i	0.412911	+	0.341590i
$324$	−2.51943	+	7.75401i	−0.139968	+	0.430778i
$325$	−0.205384	+	2.28831i	−0.0113926	+	0.126932i
$326$	3.71767	+	11.4418i	0.205903	+	0.633703i
$327$	1.11695	−	2.82110i	0.0617676	−	0.156007i
$328$	−2.36238	+	2.51568i	−0.130441	+	0.138905i
$329$	−5.59134	−	29.3108i	−0.308260	−	1.61596i
$330$	−0.376226	−	0.763394i	−0.0207106	−	0.0420235i
$331$	−16.3027	+	15.3093i	−0.896078	+	0.841473i	−0.988025	−	0.154291i	$-0.950691\pi$
$331$	−16.3027	+	15.3093i	−0.896078	+	0.841473i	0.0919476	+	0.995764i	$0.470691\pi$
$332$	4.61372	−	1.49909i	0.253211	−	0.0822732i
$333$	−29.5609	−	5.63904i	−1.61993	−	0.309017i
$334$	−1.25974	−	20.0229i	−0.0689297	−	1.09561i
$335$	1.07168	−	9.92242i	0.0585521	−	0.542120i
$336$	−0.403091	−	0.635169i	−0.0219904	−	0.0346513i
$337$	8.02874	−	0.505125i	0.437353	−	0.0275159i	0.157412	−	0.987533i	$-0.449685\pi$
$337$	8.02874	−	0.505125i	0.437353	−	0.0275159i	0.279941	+	0.960017i	$0.409685\pi$
$338$	10.7980	+	6.85261i	0.587333	+	0.372733i
$339$	−0.819299	+	0.990362i	−0.0444982	+	0.0537891i
$340$	−2.59059	+	10.9042i	−0.140495	+	0.591365i
$341$	6.39324	+	1.64151i	0.346214	+	0.0888925i
$342$	−5.05057	+	2.37662i	−0.273103	+	0.128513i
$343$	−18.6749	−	6.06784i	−1.00835	−	0.327633i
$344$	−1.47362	−	0.810130i	−0.0794524	−	0.0436793i
$345$	1.52755	+	0.164984i	0.0822405	+	0.00888245i
$346$	−18.5296	−	2.34083i	−0.996157	−	0.125844i
$347$	−1.52286	+	12.0547i	−0.0817515	+	0.647130i	0.896993	+	0.442045i	$0.145747\pi$
$347$	−1.52286	+	12.0547i	−0.0817515	+	0.647130i	−0.978744	+	0.205084i	$0.934253\pi$
$348$	−0.301018	+	0.191032i	−0.0161362	+	0.0102404i
$349$	−24.9382	+	18.1187i	−1.33491	+	0.969871i	−0.335298	+	0.942112i	$0.608837\pi$
$349$	−24.9382	+	18.1187i	−1.33491	+	0.969871i	−0.999615	+	0.0277582i	$0.991163\pi$
$350$	−8.10888	−	9.11041i	−0.433438	−	0.486972i
$351$	0.676972	+	0.491849i	0.0361341	+	0.0262529i
$352$	−1.23171	−	0.0774924i	−0.0656501	−	0.00413036i
$353$	−10.8249	−	19.6904i	−0.576151	−	1.04801i	−0.990450	−	0.137874i	$-0.955973\pi$
$353$	−10.8249	−	19.6904i	−0.576151	−	1.04801i	0.414299	−	0.910141i	$-0.364027\pi$
$354$	0.275136	−	0.584693i	0.0146233	−	0.0310761i
$355$	18.0880	+	27.3949i	0.960013	+	1.45397i
$356$	0.987281	−	5.17551i	0.0523258	−	0.274301i
$357$	2.21631	+	3.05049i	0.117299	+	0.161449i
$358$	−8.26484	+	15.0337i	−0.436810	+	0.794555i
$359$	−2.04416	+	3.22108i	−0.107887	+	0.170002i	−0.893982	−	0.448104i	$-0.852100\pi$
$359$	−2.04416	+	3.22108i	−0.107887	+	0.170002i	0.786095	+	0.618106i	$0.212100\pi$
$360$	−5.07891	−	4.04927i	−0.267682	−	0.213415i
$361$	14.2328	+	5.63516i	0.749094	+	0.296587i
$362$	2.56959	+	6.49004i	0.135055	+	0.341109i
$363$	2.25196	−	1.86298i	0.118197	−	0.0977813i
$364$	1.08564	−	0.278746i	0.0569032	−	0.0146103i
$365$	−20.0692	−	26.5983i	−1.05047	−	1.39222i
$366$	2.23811	−	0.886130i	0.116988	−	0.0463187i
$367$	−11.2810	−	12.0130i	−0.588861	−	0.627074i	0.363665	−	0.931530i	$-0.381525\pi$
$367$	−11.2810	−	12.0130i	−0.588861	−	0.627074i	−0.952526	+	0.304456i	$0.901525\pi$
$368$	1.30958	−	1.80249i	0.0682667	−	0.0939611i
$369$	4.26836	+	9.07072i	0.222202	+	0.472203i
$370$	12.0569	−	19.7801i	0.626810	−	1.02832i
$371$	5.17024	−	2.84236i	0.268426	−	0.147568i
$372$	−1.62021	+	0.309072i	−0.0840042	+	0.0160247i
$373$	2.16871	+	8.44658i	0.112292	+	0.437347i	0.999722	−	0.0235955i	$-0.00751139\pi$
$373$	2.16871	+	8.44658i	0.112292	+	0.437347i	−0.887430	+	0.460943i	$0.847511\pi$
$374$	6.18583			0.319862
$375$	3.00711	+	1.68704i	0.155287	+	0.0871183i
$376$	12.2328			0.630858
$377$	−0.132103	−	0.514505i	−0.00680363	−	0.0264984i
$378$	−4.36344	+	0.832370i	−0.224431	+	0.0428125i
$379$	−10.0582	+	5.52955i	−0.516656	+	0.284034i	−0.718673	−	0.695348i	$-0.755250\pi$
$379$	−10.0582	+	5.52955i	−0.516656	+	0.284034i	0.202017	+	0.979382i	$0.435250\pi$
$380$	−0.347249	−	4.28260i	−0.0178135	−	0.219693i
$381$	2.44221	+	5.18995i	0.125118	+	0.265889i
$382$	−12.4341	+	17.1141i	−0.636184	+	0.875632i
$383$	5.50880	+	5.86627i	0.281486	+	0.299753i	0.854138	−	0.520046i	$-0.174085\pi$
$383$	5.50880	+	5.86627i	0.281486	+	0.299753i	−0.572652	+	0.819799i	$0.694085\pi$
$384$	0.286743	−	0.113530i	0.0146328	−	0.00579354i
$385$	−3.85762	+	5.51654i	−0.196602	+	0.281149i
$386$	−18.3519	+	4.71197i	−0.934088	+	0.239833i
$387$	−3.76391	+	3.11378i	−0.191330	+	0.158282i
$388$	−1.20264	−	3.03753i	−0.0610549	−	0.154207i
$389$	28.2046	+	11.1670i	1.43003	+	0.566190i	0.950331	−	0.311242i	$-0.100745\pi$
$389$	28.2046	+	11.1670i	1.43003	+	0.566190i	0.479701	+	0.877432i	$0.340745\pi$
$390$	−0.264433	+	0.174597i	−0.0133901	+	0.00884108i
$391$	−5.98373	+	9.42885i	−0.302610	+	0.476837i
$392$	0.505772	−	0.919996i	0.0255453	−	0.0464668i
$393$	3.39758	+	4.67637i	0.171385	+	0.235892i
$394$	−4.54513	+	23.8264i	−0.228980	+	1.20036i
$395$	−0.529150	+	11.8149i	−0.0266244	+	0.594471i
$396$	−1.52644	+	3.24384i	−0.0767064	+	0.163009i
$397$	−4.56926	−	8.31145i	−0.229325	−	0.417140i	0.736462	−	0.676479i	$-0.236495\pi$
$397$	−4.56926	−	8.31145i	−0.229325	−	0.417140i	−0.965786	+	0.259339i	$0.916495\pi$
$398$	10.0633	+	0.633127i	0.504426	+	0.0317358i
$399$	−1.16945	−	0.849654i	−0.0585456	−	0.0425359i
$400$	4.29161	−	2.56555i	0.214581	−	0.128278i
$401$	20.4630	−	14.8672i	1.02187	−	0.742433i	0.0552058	−	0.998475i	$-0.482419\pi$
$401$	20.4630	−	14.8672i	1.02187	−	0.742433i	0.966666	+	0.256042i	$0.0824185\pi$
$402$	1.16219	−	0.737548i	0.0579647	−	0.0367855i
$403$	0.308015	−	2.43819i	0.0153433	−	0.121455i
$404$	6.48317	+	0.819015i	0.322550	+	0.0407475i
$405$	−15.8144	+	9.07005i	−0.785824	+	0.450695i
$406$	2.47108	+	1.35849i	0.122637	+	0.0674205i
$407$	−12.1596	−	3.95090i	−0.602730	−	0.195839i
$408$	−1.39866	+	0.658161i	−0.0692441	+	0.0325838i
$409$	−28.7326	−	7.37729i	−1.42074	−	0.364783i	−0.541313	−	0.840821i	$-0.682072\pi$
$409$	−28.7326	−	7.37729i	−1.42074	−	0.364783i	−0.879425	+	0.476038i	$0.842072\pi$
$410$	−7.69146	+	0.623653i	−0.379854	+	0.0308000i
$411$	0.523438	−	0.632727i	0.0258193	−	0.0312101i
$412$	5.81883	+	3.69274i	0.286673	+	0.181928i
$413$	−5.10098	+	0.320926i	−0.251003	+	0.0157918i
$414$	−3.46791	−	5.46456i	−0.170439	−	0.268568i
$415$	9.89699	+	4.44049i	0.485824	+	0.217975i
$416$	0.0288523	+	0.458595i	0.00141460	+	0.0224844i
$417$	−4.75800	−	0.907637i	−0.233000	−	0.0444472i
$418$	−2.25536	+	0.732811i	−0.110313	+	0.0358430i
$419$	16.6578	−	15.6427i	0.813788	−	0.764198i	−0.161089	−	0.986940i	$-0.551501\pi$
$419$	16.6578	−	15.6427i	0.813788	−	0.764198i	0.974877	+	0.222742i	$0.0715007\pi$
$420$	0.285286	−	1.65778i	0.0139205	−	0.0808912i
$421$	−3.42688	−	17.9643i	−0.167016	−	0.875529i	−0.962855	−	0.270020i	$-0.912970\pi$
$421$	−3.42688	−	17.9643i	−0.167016	−	0.875529i	0.795839	−	0.605509i	$-0.207030\pi$
$422$	−13.6335	+	14.5182i	−0.663669	+	0.706736i
$423$	13.0813	−	33.0395i	0.636033	−	1.60644i
$424$	0.747435	+	2.30037i	0.0362986	+	0.111716i
$425$	−20.6608	+	14.1845i	−1.00219	+	0.688049i
$426$	−1.39911	+	4.30602i	−0.0677871	+	0.208627i
$427$	−14.6701	−	12.1361i	−0.709934	−	0.587308i
$428$	−4.26015	−	2.00468i	−0.205922	−	0.0968996i
$429$	0.127490	+	0.119721i	0.00615526	+	0.00578017i
$430$	−1.22642	−	3.55461i	−0.0591434	−	0.171419i
$431$	−17.5252	+	2.21395i	−0.844161	+	0.106642i	−0.535506	−	0.844531i	$-0.679879\pi$
$431$	−17.5252	+	2.21395i	−0.844161	+	0.106642i	−0.308656	+	0.951174i	$0.599879\pi$
$432$		−	1.82107i		−	0.0876162i
$433$	−0.263020	−	2.08202i	−0.0126399	−	0.100055i	0.984533	−	0.175201i	$-0.0560577\pi$
$433$	−0.263020	−	2.08202i	−0.0126399	−	0.100055i	−0.997173	+	0.0751461i	$0.976058\pi$
$434$	8.31595	+	10.0523i	0.399178	+	0.482524i
$435$	−0.785649	−	0.135202i	−0.0376690	−	0.00648245i
$436$	0.617759	−	9.81900i	0.0295853	−	0.470245i
$437$	1.06468	−	4.14664i	0.0509304	−	0.198361i
$438$	1.14287	−	4.45118i	0.0546084	−	0.212686i
$439$	−0.149343	+	2.37374i	−0.00712775	+	0.113292i	−0.999982	−	0.00604312i	$-0.998076\pi$
$439$	−0.149343	+	2.37374i	−0.00712775	+	0.113292i	0.992854	+	0.119335i	$0.0380764\pi$
$440$	−1.92514	−	1.97721i	−0.0917776	−	0.0942596i
$441$	−1.94396	−	2.34985i	−0.0925696	−	0.111897i
$442$	−0.288660	−	2.28498i	−0.0137301	−	0.108685i
$443$		−	29.8191i		−	1.41675i	−0.705837	−	0.708375i	$-0.749429\pi$
$443$		−	29.8191i		−	1.41675i	0.705837	−	0.708375i	$-0.250571\pi$
$444$	3.16975	−	0.400433i	0.150430	−	0.0190037i
$445$	9.40469	−	7.09612i	0.445825	−	0.336388i
$446$	4.07096	+	3.82288i	0.192765	+	0.181019i
$447$	−2.49815	−	1.17554i	−0.118158	−	0.0556012i
$448$	−1.87951	−	1.55486i	−0.0887983	−	0.0734604i
$449$	−6.14889	+	18.9243i	−0.290184	+	0.893095i	0.694612	+	0.719384i	$0.255576\pi$
$449$	−6.14889	+	18.9243i	−0.290184	+	0.893095i	−0.984797	+	0.173711i	$0.944424\pi$
$450$	−2.34001	−	14.3347i	−0.110309	−	0.675745i
$451$	1.31612	+	4.05059i	0.0619734	+	0.190735i
$452$	−1.53424	+	3.87506i	−0.0721647	+	0.182267i
$453$	3.57398	−	3.80590i	0.167920	−	0.178817i
$454$	0.455963	+	2.39024i	0.0213994	+	0.112180i
$455$	2.21776	+	1.16753i	0.103970	+	0.0547348i
$456$	0.431985	−	0.405661i	0.0202295	−	0.0189968i
$457$	−6.18256	+	2.00884i	−0.289208	+	0.0939694i	−0.450028	−	0.893014i	$-0.648586\pi$
$457$	−6.18256	+	2.00884i	−0.289208	+	0.0939694i	0.160820	+	0.986984i	$0.448586\pi$
$458$	15.6248	+	2.98059i	0.730100	+	0.139274i
$459$	0.573130	+	9.10965i	0.0267514	+	0.425202i
$460$	4.87603	−	1.02182i	0.227346	−	0.0476426i
$461$	−2.65015	−	4.17596i	−0.123430	−	0.194494i	0.776994	−	0.629508i	$-0.216743\pi$
$461$	−2.65015	−	4.17596i	−0.123430	−	0.194494i	−0.900424	+	0.435014i	$0.856743\pi$
$462$	−0.926585	+	0.0582958i	−0.0431086	+	0.00271217i
$463$	−12.9884	−	8.24266i	−0.603620	−	0.383069i	0.198615	−	0.980078i	$-0.436356\pi$
$463$	−12.9884	−	8.24266i	−0.603620	−	0.383069i	−0.802235	+	0.597009i	$0.796356\pi$
$464$	−0.736877	+	0.890731i	−0.0342086	+	0.0413511i
$465$	−3.14929	−	1.91965i	−0.146045	−	0.0890217i
$466$	−14.0189	−	3.59945i	−0.649415	−	0.166741i
$467$	5.93211	−	2.79144i	0.274505	−	0.129172i	−0.283600	−	0.958943i	$-0.591529\pi$
$467$	5.93211	−	2.79144i	0.274505	−	0.129172i	0.558105	+	0.829770i	$0.311529\pi$
$468$	1.26947	+	0.412476i	0.0586813	+	0.0190667i
$469$	−9.54050	−	5.24493i	−0.440539	−	0.242188i
$470$	20.2749	+	18.3612i	0.935212	+	0.846939i
$471$	5.55624	+	0.701917i	0.256018	+	0.0323426i
$472$	0.262612	−	2.07879i	0.0120877	−	0.0956838i
$473$	−1.75229	+	1.11204i	−0.0805704	+	0.0511315i
$474$	−1.31963	+	0.958766i	−0.0606125	+	0.0440376i
$475$	5.85256	−	7.61929i	0.268534	−	0.349597i
$476$	9.89132	+	7.18647i	0.453368	+	0.329391i
$477$	7.01234	+	0.441179i	0.321073	+	0.0202002i
$478$	7.82218	+	14.2285i	0.357778	+	0.650796i
$479$	4.46251	−	9.48331i	0.203897	−	0.433303i	−0.776558	−	0.630046i	$-0.783036\pi$
$479$	4.46251	−	9.48331i	0.203897	−	0.433303i	0.980455	+	0.196742i	$0.0630362\pi$
$480$	0.645661	+	0.242230i	0.0294702	+	0.0110562i
$481$	−0.891994	+	4.67600i	−0.0406714	+	0.213207i
$482$	13.7261	+	18.8923i	0.625205	+	0.860521i
$483$	0.807454	−	1.46875i	0.0367404	−	0.0668306i
$484$	5.07797	−	8.00161i	0.230817	−	0.363709i
$485$	2.56599	−	6.83962i	0.116516	−	0.310571i
$486$	−7.41739	−	2.93675i	−0.336460	−	0.133214i
$487$	7.80278	+	19.7076i	0.353578	+	0.893035i	0.992329	+	0.123622i	$0.0394511\pi$
$487$	7.80278	+	19.7076i	0.353578	+	0.893035i	−0.638752	+	0.769413i	$0.720549\pi$
$488$	6.01406	−	4.97527i	0.272244	−	0.225220i
$489$	−3.59368	+	0.922701i	−0.162512	+	0.0417260i
$490$	2.21918	−	0.765667i	0.100252	−	0.0345893i
$491$	39.6392	−	15.6943i	1.78889	−	0.708272i	0.793931	−	0.608007i	$-0.208031\pi$
$491$	39.6392	−	15.6943i	1.78889	−	0.708272i	0.994961	−	0.100265i	$-0.0319691\pi$
$492$	−0.728559	−	0.775836i	−0.0328460	−	0.0349774i
$493$	3.40579	−	4.68767i	0.153389	−	0.211122i
$494$	0.375938	+	0.798909i	0.0169143	+	0.0359446i
$495$	−7.39891	+	3.08527i	−0.332556	+	0.138672i
$496$	−4.68679	+	2.57659i	−0.210443	+	0.115692i
$497$	35.1769	−	6.71035i	1.57790	−	0.301000i
$498$	0.372064	+	1.44909i	0.0166726	+	0.0649354i
$499$	22.7517			1.01851			0.509253	−	0.860617i	$-0.329922\pi$
$499$	22.7517			1.01851			0.509253	+	0.860617i	$0.329922\pi$
$500$	10.9639	+	2.18943i	0.490319	+	0.0979143i
$501$	6.18728			0.276427
$502$	6.54759	+	25.5012i	0.292233	+	1.13817i
$503$	22.7325	−	4.33647i	1.01359	−	0.193353i	0.346281	−	0.938131i	$-0.387444\pi$
$503$	22.7325	−	4.33647i	1.01359	−	0.193353i	0.667313	+	0.744777i	$0.267444\pi$
$504$	−6.20940	+	3.41365i	−0.276589	+	0.152056i
$505$	9.51603	+	11.0886i	0.423458	+	0.493435i
$506$	−1.17075	−	2.48797i	−0.0520461	−	0.110604i
$507$	−2.31828	+	3.19083i	−0.102958	+	0.141710i
$508$	12.7317	+	13.5579i	0.564878	+	0.601534i
$509$	−18.4839	+	7.31828i	−0.819283	+	0.324377i	−0.740112	−	0.672484i	$-0.765227\pi$
$509$	−18.4839	+	7.31828i	−0.819283	+	0.324377i	−0.0791713	+	0.996861i	$0.525227\pi$
$510$	−3.30606	−	1.00852i	−0.146395	−	0.0446579i
$511$	−35.2066	+	9.03953i	−1.55745	+	0.399885i
$512$	0.770513	−	0.637424i	0.0340522	−	0.0281704i
$513$	−1.28815	−	3.25349i	−0.0568732	−	0.143645i
$514$	−13.2747	−	5.25583i	−0.585522	−	0.231825i
$515$	4.10152	+	14.8544i	0.180735	+	0.654563i
$516$	0.277887	−	0.437880i	0.0122333	−	0.0192766i
$517$	7.27303	−	13.2296i	0.319867	−	0.581837i
$518$	−14.8536	−	20.4442i	−0.652629	−	0.898267i
$519$	1.07931	−	5.65792i	0.0473763	−	0.248355i
$520$	−0.640522	+	0.803392i	−0.0280887	+	0.0352311i
$521$	11.9964	−	25.4937i	0.525574	−	1.11690i	−0.449144	−	0.893459i	$-0.648271\pi$
$521$	11.9964	−	25.4937i	0.525574	−	1.11690i	0.974717	−	0.223441i	$-0.0717291\pi$
$522$	1.61779	+	2.94274i	0.0708086	+	0.128800i
$523$	18.4743	+	1.16230i	0.807825	+	0.0508240i	0.461331	−	0.887228i	$-0.347372\pi$
$523$	18.4743	+	1.16230i	0.807825	+	0.0508240i	0.346494	+	0.938052i	$0.387372\pi$
$524$	15.1633	+	11.0168i	0.662413	+	0.481271i
$525$	2.96113	−	2.31943i	0.129234	−	0.101228i
$526$	−7.09826	+	5.15719i	−0.309499	+	0.224864i
$527$	22.6341	−	14.3641i	0.985958	−	0.625708i
$528$	0.0477030	−	0.377608i	0.00207601	−	0.0164333i
$529$	−17.8938	−	2.26051i	−0.777992	−	0.0982832i
$530$	−2.21400	+	4.93457i	−0.0961699	+	0.214344i
$531$	−5.33376	−	2.93226i	−0.231465	−	0.127249i
$532$	−4.45774	−	1.44841i	−0.193268	−	0.0627965i
$533$	1.43482	−	0.675177i	0.0621492	−	0.0292452i
$534$	1.57386	+	0.404099i	0.0681076	+	0.0174871i
$535$	−4.05189	−	9.71701i	−0.175179	−	0.420103i
$536$	2.84498	−	3.43899i	0.122884	−	0.148542i
$537$	−4.46720	−	2.83497i	−0.192774	−	0.122338i
$538$	10.7967	−	0.679272i	0.465480	−	0.0292855i
$539$	−0.694255	−	1.09397i	−0.0299037	−	0.0471207i
$540$	2.73339	−	3.01828i	0.117626	−	0.129886i
$541$	−1.14797	−	18.2465i	−0.0493552	−	0.784478i	−0.942395	−	0.334501i	$-0.891432\pi$
$541$	−1.14797	−	18.2465i	−0.0493552	−	0.784478i	0.893040	−	0.449977i	$-0.148568\pi$
$542$	−10.3349	−	1.97148i	−0.443920	−	0.0846822i
$543$	−2.04734	+	0.665220i	−0.0878597	+	0.0285473i
$544$	−3.65378	+	3.43112i	−0.156654	+	0.147108i
$545$	15.7620	−	15.3470i	0.675172	−	0.657393i
$546$	0.0647726	+	0.339550i	0.00277201	+	0.0145314i
$547$	9.89824	−	10.5406i	0.423218	−	0.450682i	−0.481656	−	0.876360i	$-0.659965\pi$
$547$	9.89824	−	10.5406i	0.423218	−	0.450682i	0.904874	+	0.425679i	$0.139965\pi$
$548$	0.980205	−	2.47571i	0.0418723	−	0.105757i
$549$	−7.00648	−	21.5637i	−0.299029	−	0.920318i
$550$	−0.223023	−	6.16667i	−0.00950972	−	0.262948i
$551$	−0.686426	+	2.11260i	−0.0292427	+	0.0899999i
$552$	0.529430	+	0.437983i	0.0225341	+	0.0186418i
$553$	11.6737	+	5.49323i	0.496416	+	0.233596i
$554$	16.0081	+	15.0326i	0.680120	+	0.638675i
$555$	5.85466	+	4.09406i	0.248517	+	0.173783i
$556$	−15.5824	+	1.96851i	−0.660839	+	0.0834834i
$557$		−	17.1402i		−	0.726252i	−0.931740	−	0.363126i	$-0.881710\pi$
$557$		−	17.1402i		−	0.726252i	0.931740	−	0.363126i	$-0.118290\pi$
$558$	1.94722	+	15.4138i	0.0824325	+	0.652520i
$559$	0.492544	+	0.595383i	0.0208324	+	0.0251820i
$560$	−0.781315	−	5.39817i	−0.0330166	−	0.228114i
$561$	−0.119786	+	1.90395i	−0.00505737	+	0.0803847i
$562$	3.61819	−	14.0919i	0.152624	−	0.594433i
$563$	−4.56226	+	17.7688i	−0.192276	+	0.748867i	0.797144	+	0.603789i	$0.206343\pi$
$563$	−4.56226	+	17.7688i	−0.192276	+	0.748867i	−0.989420	+	0.145077i	$0.953657\pi$
$564$	−0.236883	+	3.76515i	−0.00997458	+	0.158541i
$565$	−8.35928	+	4.11973i	−0.351678	+	0.173319i
$566$	−11.1692	−	13.5013i	−0.469477	−	0.567500i
$567$	2.49259	+	19.7308i	0.104679	+	0.828618i
$568$			14.6810i			0.616000i
$569$	−21.8121	+	2.75551i	−0.914412	+	0.115517i	−0.568437	−	0.822727i	$-0.692452\pi$
$569$	−21.8121	+	2.75551i	−0.914412	+	0.115517i	−0.345975	+	0.938244i	$0.612452\pi$
$570$	1.32487	−	0.0239497i	0.0554927	−	0.00100314i
$571$	11.9478	+	11.2197i	0.500000	+	0.469531i	0.893032	−	0.449994i	$-0.148574\pi$
$571$	11.9478	+	11.2197i	0.500000	+	0.469531i	−0.393032	+	0.919525i	$0.628574\pi$
$572$	0.513118	+	0.241455i	0.0214545	+	0.0100957i
$573$	−5.02678	−	4.15852i	−0.209997	−	0.173725i
$574$	−2.60131	+	8.00602i	−0.108577	+	0.334165i
$575$	9.61539	+	5.62525i	0.400989	+	0.234589i
$576$	−0.897660	−	2.76271i	−0.0374025	−	0.115113i
$577$	−1.80554	+	4.56029i	−0.0751658	+	0.189847i	−0.962501	−	0.271277i	$-0.912554\pi$
$577$	−1.80554	+	4.56029i	−0.0751658	+	0.189847i	0.887335	+	0.461125i	$0.152554\pi$
$578$	5.56036	−	5.92119i	0.231281	−	0.246289i
$579$	−1.09493	−	5.73981i	−0.0455036	−	0.238538i
$580$	−2.55829	+	0.370279i	−0.106227	+	0.0153750i
$581$	8.62616	−	8.10050i	0.357873	−	0.336066i
$582$	0.958214	−	0.311343i	0.0397193	−	0.0129056i
$583$	2.93220	+	0.559348i	0.121439	+	0.0231658i
$584$	−0.935660	−	14.8719i	−0.0387179	−	0.615403i
$585$	1.48493	+	2.58910i	0.0613943	+	0.107046i
$586$	−5.61940	−	8.85476i	−0.232135	−	0.365787i
$587$	−39.9197	+	2.51153i	−1.64766	+	0.103662i	−0.859274	−	0.511516i	$-0.829084\pi$
$587$	−39.9197	+	2.51153i	−1.64766	+	0.103662i	−0.788388	+	0.615178i	$0.789084\pi$
$588$	0.273373	+	0.173488i	0.0112737	+	0.00715451i
$589$	−6.55078	+	7.91853i	−0.269920	+	0.326277i
$590$	3.55548	−	3.05125i	0.146377	−	0.125618i
$591$	−7.24556	−	1.86034i	−0.298042	−	0.0765243i
$592$	9.37378	−	4.41096i	0.385260	−	0.181290i
$593$	14.2726	+	4.63745i	0.586105	+	0.190437i	0.587034	−	0.809562i	$-0.300296\pi$
$593$	14.2726	+	4.63745i	0.586105	+	0.190437i	−0.000928529		1.00000i	$0.500296\pi$
$594$	−1.96946	−	1.08272i	−0.0808079	−	0.0444245i
$595$	5.60734	+	26.7577i	0.229879	+	1.09696i
$596$	−8.88179	−	1.12203i	−0.363812	−	0.0459602i
$597$	−0.389742	+	3.08513i	−0.0159511	+	0.126266i
$598$	−0.864395	+	0.548562i	−0.0353477	+	0.0224324i
$599$	−24.0518	+	17.4747i	−0.982731	+	0.713996i	−0.958317	−	0.285706i	$-0.907772\pi$
$599$	−24.0518	+	17.4747i	−0.982731	+	0.713996i	−0.0244140	+	0.999702i	$0.507772\pi$
$600$	0.706550	+	1.37060i	0.0288448	+	0.0559546i
$601$	−4.37000	−	3.17499i	−0.178256	−	0.129511i	0.495079	−	0.868848i	$-0.335139\pi$
$601$	−4.37000	−	3.17499i	−0.178256	−	0.129511i	−0.673335	+	0.739337i	$0.735139\pi$
$602$	−4.09389	−	0.257566i	−0.166854	−	0.0104976i
$603$	−6.24605	−	11.3615i	−0.254359	−	0.462677i
$604$	7.20807	−	15.3179i	0.293292	−	0.623278i
$605$	20.4266	−	5.64010i	0.830460	−	0.229303i
$606$	−0.377630	+	1.97960i	−0.0153402	+	0.0804159i
$607$	27.2798	+	37.5475i	1.10725	+	1.52400i	0.825401	+	0.564547i	$0.190949\pi$
$607$	27.2798	+	37.5475i	1.10725	+	1.52400i	0.281854	+	0.959457i	$0.409051\pi$
$608$	0.925700	−	1.68384i	0.0375421	−	0.0682888i
$609$	−0.465982	+	0.734270i	−0.0188825	+	0.0297541i
$610$	17.4356	+	0.780885i	0.705948	+	0.0316171i
$611$	−5.22626	−	2.06922i	−0.211432	−	0.0837117i
$612$	5.35991	+	13.5376i	0.216661	+	0.547224i
$613$	14.8893	−	12.3175i	0.601374	−	0.497500i	−0.286197	−	0.958171i	$-0.592391\pi$
$613$	14.8893	−	12.3175i	0.601374	−	0.497500i	0.887571	+	0.460671i	$0.152391\pi$
$614$	28.6540	−	7.35711i	1.15638	−	0.296909i
$615$	−0.0430132	−	2.37944i	−0.00173446	−	0.0959484i
$616$	−2.79903	+	1.10821i	−0.112776	+	0.0446512i
$617$	9.91675	+	10.5603i	0.399233	+	0.425140i	0.896904	−	0.442226i	$-0.145811\pi$
$617$	9.91675	+	10.5603i	0.399233	+	0.425140i	−0.497670	+	0.867366i	$0.665811\pi$
$618$	−1.24927	+	1.71948i	−0.0502531	+	0.0691675i
$619$	11.5849	+	24.6192i	0.465636	+	0.989527i	0.990394	+	0.138276i	$0.0441560\pi$
$619$	11.5849	+	24.6192i	0.465636	+	0.989527i	−0.524758	+	0.851252i	$0.675844\pi$
$620$	−11.6354	−	2.76430i	−0.467289	−	0.111017i
$621$	3.55547	−	1.95463i	0.142676	−	0.0784368i
$622$	−11.3266	+	2.16066i	−0.454154	+	0.0866346i
$623$	−3.19622	−	12.4485i	−0.128054	−	0.498737i
$624$	−0.141710			−0.00567295
$625$	14.8855	+	20.0854i	0.595419	+	0.803416i
$626$	−15.0986			−0.603462
$627$	−0.181879	−	0.708372i	−0.00726355	−	0.0282896i
$628$	17.8379	−	3.40276i	0.711809	−	0.135785i
$629$	−45.5028	+	25.0154i	−1.81432	+	0.997428i
$630$	−15.4154	−	3.66234i	−0.614165	−	0.145911i
$631$	−5.93155	−	12.6052i	−0.236131	−	0.501804i	0.751279	−	0.659985i	$-0.229437\pi$
$631$	−5.93155	−	12.6052i	−0.236131	−	0.501804i	−0.987410	+	0.158180i	$0.949437\pi$
$632$	−3.10884	+	4.27895i	−0.123663	+	0.170207i
$633$	−4.20458	−	4.47742i	−0.167117	−	0.177962i
$634$	−10.7502	+	4.25632i	−0.426947	+	0.169040i
$635$	0.751663	+	41.5812i	0.0298288	+	1.65010i
$636$	−0.722507	+	0.185508i	−0.0286493	+	0.00735589i
$637$	−0.371703	+	0.307500i	−0.0147274	+	0.0121836i
$638$	0.525201	+	1.32651i	0.0207929	+	0.0525169i
$639$	39.6518	+	15.6993i	1.56860	+	0.621053i
$640$	2.23383	+	0.100046i	0.0882998	+	0.00395466i
$641$	−7.14638	+	11.2609i	−0.282265	+	0.444779i	−0.955646	−	0.294517i	$-0.904841\pi$
$641$	−7.14638	+	11.2609i	−0.282265	+	0.444779i	0.673381	+	0.739295i	$0.264841\pi$
$642$	0.699518	−	1.27242i	0.0276078	−	0.0502184i
$643$	−4.23016	−	5.82231i	−0.166821	−	0.229610i	0.717419	−	0.696642i	$-0.245323\pi$
$643$	−4.23016	−	5.82231i	−0.166821	−	0.229610i	−0.884240	+	0.467032i	$0.845323\pi$
$644$	1.01837	−	5.33847i	0.0401293	−	0.210365i
$645$	1.11783	−	0.308649i	0.0440144	−	0.0121530i
$646$	−4.10074	+	8.71452i	−0.161342	+	0.342868i
$647$	3.57507	+	6.50303i	0.140551	+	0.255661i	0.937208	−	0.348770i	$-0.113401\pi$
$647$	3.57507	+	6.50303i	0.140551	+	0.255661i	−0.796658	+	0.604431i	$0.793401\pi$
$648$	−8.13696	−	0.511934i	−0.319650	−	0.0201107i
$649$	−2.09204	−	1.51996i	−0.0821198	−	0.0596635i
$650$	−2.26749	+	0.370148i	−0.0889384	+	0.0145184i
$651$	−3.25503	+	2.36492i	−0.127575	+	0.0926885i
$652$	−10.1578	+	6.44633i	−0.397810	+	0.252458i
$653$	3.28605	−	26.0117i	0.128593	−	1.01792i	−0.787321	−	0.616543i	$-0.788533\pi$
$653$	3.28605	−	26.0117i	0.128593	−	1.01792i	0.915914	−	0.401375i	$-0.131467\pi$
$654$	3.01024	+	0.380282i	0.117710	+	0.0148702i
$655$	8.59602	+	41.0194i	0.335874	+	1.60276i
$656$	−3.02415	−	1.66254i	−0.118073	−	0.0649112i
$657$	−41.1680	−	13.3763i	−1.60612	−	0.521859i
$658$	26.9994	−	12.7050i	1.05255	−	0.495291i
$659$	33.9019	+	8.70453i	1.32063	+	0.339080i	0.842257	−	0.539076i	$-0.181226\pi$
$659$	33.9019	+	8.70453i	1.32063	+	0.339080i	0.478374	+	0.878156i	$0.341226\pi$
$660$	0.645847	−	0.554255i	0.0251396	−	0.0215743i
$661$	−29.6743	+	35.8701i	−1.15420	+	1.39518i	−0.249905	+	0.968270i	$0.580399\pi$
$661$	−29.6743	+	35.8701i	−1.15420	+	1.39518i	−0.904292	+	0.426914i	$0.859601\pi$
$662$	−18.8826	−	11.9833i	−0.733894	−	0.465743i
$663$	0.708886	−	0.0445993i	0.0275309	−	0.00173209i
$664$	2.59938	+	4.09596i	0.100875	+	0.158954i
$665$	−5.21433	−	9.09162i	−0.202203	−	0.352558i
$666$	−1.88961	−	30.0345i	−0.0732210	−	1.16381i
$667$	−2.52999	−	0.482622i	−0.0979617	−	0.0186872i
$668$	19.0806	−	6.19966i	0.738250	−	0.239872i
$669$	−1.25548	+	1.17898i	−0.0485398	+	0.0455819i
$670$	9.87721	−	1.42960i	0.381590	−	0.0552301i
$671$	−1.80501	−	9.46218i	−0.0696815	−	0.365283i
$672$	0.514970	−	0.548387i	0.0198654	−	0.0211545i
$673$	2.43177	−	6.14194i	0.0937377	−	0.236754i	−0.875341	−	0.483506i	$-0.839363\pi$
$673$	2.43177	−	6.14194i	0.0937377	−	0.236754i	0.969079	+	0.246752i	$0.0793631\pi$
$674$	2.48592	+	7.65088i	0.0957541	+	0.294701i
$675$	9.06077	−	0.899793i	0.348749	−	0.0346331i
$676$	−3.95197	+	12.1629i	−0.151999	+	0.467805i
$677$	12.4855	+	10.3289i	0.479855	+	0.396971i	0.845661	−	0.533721i	$-0.179207\pi$
$677$	12.4855	+	10.3289i	0.479855	+	0.396971i	−0.365806	+	0.930691i	$0.619207\pi$
$678$	−1.16300	−	0.547266i	−0.0446647	−	0.0210176i
$679$	−5.80917	−	5.45518i	−0.222936	−	0.209351i
$680$	−11.2059	+	0.202569i	−0.429727	+	0.00776817i
$681$	−0.744525	+	0.0940554i	−0.0285303	+	0.00360421i
$682$			6.60061i			0.252751i
$683$	−0.416016	−	3.29311i	−0.0159184	−	0.126007i	0.982153	−	0.188084i	$-0.0602277\pi$
$683$	−0.416016	−	3.29311i	−0.0159184	−	0.126007i	−0.998071	+	0.0620766i	$0.980228\pi$
$684$	−3.55798	−	4.30085i	−0.136043	−	0.164447i
$685$	5.34062	−	2.63204i	0.204055	−	0.100565i
$686$	1.23295	−	19.5972i	0.0470743	−	0.748225i
$687$	−1.21997	+	4.75147i	−0.0465448	+	0.181280i
$688$	0.418204	−	1.62880i	0.0159439	−	0.0620973i
$689$	0.0697865	−	1.10923i	0.00265866	−	0.0422581i
$690$	0.220085	+	1.52059i	0.00837851	+	0.0578878i
$691$	−16.6465	−	20.1221i	−0.633262	−	0.765482i	0.352099	−	0.935963i	$-0.385468\pi$
$691$	−16.6465	−	20.1221i	−0.633262	−	0.765482i	−0.985361	+	0.170481i	$0.945468\pi$
$692$	−2.34083	−	18.5296i	−0.0889850	−	0.704389i
$693$			8.74497i			0.332194i
$694$	−12.0547	+	1.52286i	−0.457590	+	0.0578070i
$695$	−28.7813	−	20.1262i	−1.09174	−	0.763430i
$696$	−0.259890	−	0.244053i	−0.00985111	−	0.00925081i
$697$	15.6511	+	7.36486i	0.592828	+	0.278964i
$698$	−23.7513	−	19.6488i	−0.899001	−	0.743718i
$699$	1.37935	−	4.24521i	0.0521719	−	0.160569i
$700$	6.80759	−	10.1198i	0.257303	−	0.382492i
$701$	−4.30999	−	13.2648i	−0.162786	−	0.501005i	0.836080	−	0.548607i	$-0.184842\pi$
$701$	−4.30999	−	13.2648i	−0.162786	−	0.501005i	−0.998866	+	0.0476028i	$0.984842\pi$
$702$	−0.308040	+	0.778021i	−0.0116262	+	0.0293645i
$703$	13.6269	−	14.5112i	0.513949	−	0.547300i
$704$	−0.231255	−	1.21228i	−0.00871575	−	0.0456896i
$705$	−6.04404	+	5.88489i	−0.227632	+	0.221638i
$706$	16.3798	−	15.3816i	0.616460	−	0.578895i
$707$	15.1599	−	4.92574i	0.570146	−	0.185252i
$708$	0.634747	+	0.121084i	0.0238553	+	0.00455063i
$709$	−3.03915	−	48.3059i	−0.114138	−	1.81417i	−0.473311	−	0.880895i	$-0.656941\pi$
$709$	−3.03915	−	48.3059i	−0.114138	−	1.81417i	0.359173	−	0.933271i	$-0.383059\pi$
$710$	−22.0359	+	24.3326i	−0.826992	+	0.913186i
$711$	8.23253	+	12.9724i	0.308744	+	0.486503i
$712$	5.25844	−	0.330833i	0.197068	−	0.0123985i
$713$	−10.0611	−	6.38496i	−0.376791	−	0.239119i
$714$	−2.40348	+	2.90530i	−0.0899478	+	0.108728i
$715$	0.488034	+	1.17037i	0.0182514	+	0.0437695i
$716$	−16.6168	−	4.26646i	−0.620997	−	0.159445i
$717$	−4.53088	+	2.13207i	−0.169209	+	0.0796237i
$718$	−3.62824	−	1.17889i	−0.135405	−	0.0439957i
$719$	−19.0802	−	10.4894i	−0.711571	−	0.391189i	0.0844750	−	0.996426i	$-0.473079\pi$
$719$	−19.0802	−	10.4894i	−0.711571	−	0.391189i	−0.796046	+	0.605236i	$0.793079\pi$
$720$	2.65898	−	5.92636i	0.0990945	−	0.220862i
$721$	16.6782	+	2.10695i	0.621130	+	0.0784669i
$722$	−1.91857	+	15.1871i	−0.0714018	+	0.565204i
$723$	−6.08069	+	3.85893i	−0.226143	+	0.143515i
$724$	−5.64711	+	4.10287i	−0.209873	+	0.152482i
$725$	−4.79595	−	3.22624i	−0.178117	−	0.119819i
$726$	2.36449	+	1.71791i	0.0877546	+	0.0637575i
$727$	−27.0922	−	1.70450i	−1.00479	−	0.0632163i	−0.448143	−	0.893962i	$-0.647914\pi$
$727$	−27.0922	−	1.70450i	−1.00479	−	0.0632163i	−0.556652	+	0.830746i	$0.687914\pi$
$728$	0.539977	+	0.982215i	0.0200129	+	0.0364033i
$729$	−9.36666	+	19.9052i	−0.346913	+	0.737228i
$730$	20.7717	−	26.0534i	0.768794	−	0.964280i
$731$	−1.57939	+	8.27945i	−0.0584158	+	0.306227i
$732$	1.41488	+	1.94742i	0.0522957	+	0.0719788i
$733$	−1.01617	+	1.84841i	−0.0375332	+	0.0682726i	−0.894408	−	0.447252i	$-0.852403\pi$
$733$	−1.01617	+	1.84841i	−0.0375332	+	0.0682726i	0.856875	+	0.515524i	$0.172403\pi$
$734$	8.83013	−	13.9141i	0.325926	−	0.513577i
$735$	0.192692	+	0.697870i	0.00710757	+	0.0257413i
$736$	2.07154	+	0.820180i	0.0763579	+	0.0302322i
$737$	−2.02773	−	5.12147i	−0.0746925	−	0.188652i
$738$	−7.72425	+	6.39006i	−0.284334	+	0.235221i
$739$	−36.7323	+	9.43125i	−1.35122	+	0.346934i	−0.853811	−	0.520583i	$-0.825715\pi$
$739$	−36.7323	+	9.43125i	−1.35122	+	0.346934i	−0.497408	+	0.867517i	$0.665715\pi$
$740$	22.1571	+	6.75904i	0.814511	+	0.248467i
$741$	−0.253177	+	0.100240i	−0.00930070	+	0.00368241i
$742$	4.03885	+	4.30094i	0.148271	+	0.157893i
$743$	1.44565	−	1.98977i	0.0530358	−	0.0729975i	−0.781675	−	0.623686i	$-0.785635\pi$
$743$	1.44565	−	1.98977i	0.0530358	−	0.0729975i	0.834711	+	0.550688i	$0.185635\pi$
$744$	−0.702293	−	1.49245i	−0.0257473	−	0.0547159i
$745$	−13.0367	−	15.1911i	−0.477629	−	0.556558i
$746$	−7.64187	+	4.20116i	−0.279789	+	0.153815i
$747$	13.8425	−	2.64059i	0.506469	−	0.0966141i
$748$	1.53835	+	5.99149i	0.0562478	+	0.219071i
$749$	−11.4848			−0.419645
$750$	−0.886199	+	3.33219i	−0.0323594	+	0.121674i
$751$	−54.4091			−1.98542			−0.992708	−	0.120542i	$-0.961537\pi$
$751$	−54.4091			−1.98542			−0.992708	+	0.120542i	$0.961537\pi$
$752$	3.04217	+	11.8485i	0.110937	+	0.432069i
$753$	−7.97584	+	1.52147i	−0.290656	+	0.0554456i
$754$	0.465489	−	0.255905i	0.0169521	−	0.00931949i
$755$	34.9388	−	14.5691i	1.27155	−	0.530224i
$756$	−1.89136	−	4.01935i	−0.0687882	−	0.146182i
$757$	−0.919309	+	1.26532i	−0.0334128	+	0.0459888i	−0.825397	−	0.564553i	$-0.809048\pi$
$757$	−0.919309	+	1.26532i	−0.0334128	+	0.0459888i	0.791984	+	0.610542i	$0.209048\pi$
$758$	−7.85721	−	8.36707i	−0.285387	−	0.303906i
$759$	0.788446	−	0.312168i	0.0286188	−	0.0113310i
$760$	4.06169	−	1.40138i	0.147333	−	0.0508333i
$761$	18.6848	−	4.79745i	0.677324	−	0.173907i	0.105669	−	0.994401i	$-0.466302\pi$
$761$	18.6848	−	4.79745i	0.677324	−	0.173907i	0.571655	+	0.820494i	$0.306302\pi$
$762$	−4.41955	+	3.65617i	−0.160103	+	0.132449i
$763$	−8.83453	−	22.3135i	−0.319832	−	0.807802i
$764$	−19.6686	−	7.78736i	−0.711586	−	0.281737i
$765$	−11.4360	+	30.4826i	−0.413471	+	1.10210i
$766$	−4.31199	+	6.79461i	−0.155799	+	0.245499i
$767$	−0.463831	+	0.843705i	−0.0167480	+	0.0304644i
$768$	0.181273	+	0.249501i	0.00654113	+	0.00900309i
$769$	−8.32643	+	43.6487i	−0.300259	+	1.57401i	0.437672	+	0.899135i	$0.355803\pi$
$769$	−8.32643	+	43.6487i	−0.300259	+	1.57401i	−0.737930	+	0.674877i	$0.764197\pi$
$770$	−6.30258	−	2.36451i	−0.227129	−	0.0852111i
$771$	1.87476	−	3.98407i	0.0675178	−	0.143483i
$772$	−9.12787	−	16.6035i	−0.328519	−	0.597574i
$773$	30.0788	+	1.89240i	1.08186	+	0.0680649i	0.593698	−	0.804688i	$-0.297667\pi$
$773$	30.0788	+	1.89240i	1.08186	+	0.0680649i	0.488163	+	0.872753i	$0.337667\pi$
$774$	−3.95200	−	2.87130i	−0.142052	−	0.103207i
$775$	−15.1356	−	22.0462i	−0.543688	−	0.791922i
$776$	2.64301	−	1.92026i	0.0948787	−	0.0689334i
$777$	6.58019	−	4.17591i	0.236063	−	0.149810i
$778$	−3.80197	+	30.0957i	−0.136307	+	1.07898i
$779$	−6.57890	−	0.831109i	−0.235714	−	0.0297776i
$780$	−0.234874	−	0.212705i	−0.00840983	−	0.00761605i
$781$	15.8773	+	8.72861i	0.568134	+	0.312334i
$782$	−10.6207	−	3.45088i	−0.379796	−	0.123403i
$783$	−1.90484	+	0.896349i	−0.0680734	+	0.0320329i
$784$	1.01687	+	0.261089i	0.0363169	+	0.00932459i
$785$	34.6724	+	21.1345i	1.23751	+	0.754324i
$786$	−3.68451	+	4.45381i	−0.131422	+	0.158862i
$787$	−2.75621	−	1.74914i	−0.0982482	−	0.0623502i	0.485795	−	0.874073i	$-0.338530\pi$
$787$	−2.75621	−	1.74914i	−0.0982482	−	0.0623502i	−0.584043	+	0.811723i	$0.698530\pi$
$788$	−24.2082	+	1.52305i	−0.862381	+	0.0542564i
$789$	−1.44988	−	2.28465i	−0.0516172	−	0.0813357i
$790$	−11.5753	+	2.42572i	−0.411830	+	0.0863031i
$791$	0.638348	+	10.1462i	0.0226970	+	0.360759i
$792$	−3.52154	−	0.671770i	−0.125133	−	0.0238703i
$793$	−3.41099	+	1.10830i	−0.121128	+	0.0393569i
$794$	6.91400	−	6.49268i	0.245369	−	0.230417i
$795$	−1.47595	−	0.777005i	−0.0523464	−	0.0275575i
$796$	1.88940	+	9.90456i	0.0669679	+	0.351058i
$797$	−19.2413	+	20.4899i	−0.681563	+	0.725790i	−0.973001	−	0.230799i	$-0.925866\pi$
$797$	−19.2413	+	20.4899i	−0.681563	+	0.725790i	0.291439	+	0.956589i	$0.405866\pi$
$798$	0.532130	−	1.34401i	0.0188372	−	0.0475774i
$799$	−18.9470	−	58.3129i	−0.670297	−	2.06296i
$800$	3.55223	+	3.51876i	0.125590	+	0.124407i
$801$	4.72962	−	14.5563i	0.167113	−	0.514321i
$802$	19.4891	+	16.1228i	0.688183	+	0.569314i
$803$	−16.6400	−	7.83021i	−0.587214	−	0.276322i
$804$	1.00340	+	0.942256i	0.0353872	+	0.0332308i
$805$	9.70081	−	7.31955i	0.341909	−	0.257980i
$806$	2.43819	−	0.308015i	0.0858817	−	0.0108494i
$807$			3.33629i			0.117443i
$808$	0.819015	+	6.48317i	0.0288128	+	0.228077i
$809$	22.6465	+	27.3749i	0.796208	+	0.962450i	0.999862	−	0.0165930i	$-0.00528197\pi$
$809$	22.6465	+	27.3749i	0.796208	+	0.962450i	−0.203655	+	0.979043i	$0.565282\pi$
$810$	−12.7180	−	13.0619i	−0.446864	−	0.458949i
$811$	1.38170	−	21.9615i	0.0485180	−	0.771171i	−0.896274	−	0.443500i	$-0.853736\pi$
$811$	1.38170	−	21.9615i	0.0485180	−	0.771171i	0.944792	−	0.327670i	$-0.106264\pi$
$812$	−0.701275	+	2.73128i	−0.0246099	+	0.0958493i
$813$	0.806935	−	3.14280i	0.0283004	−	0.110223i
$814$	0.802801	−	12.7602i	0.0281382	−	0.447243i
$815$	−26.5116	−	4.56237i	−0.928661	−	0.159813i
$816$	−0.985317	−	1.19104i	−0.0344930	−	0.0416949i
$817$	−0.404987	−	3.20580i	−0.0141687	−	0.112157i
$818$		−	29.6646i		−	1.03720i
$819$	3.23029	−	0.408081i	0.112876	−	0.0142595i
$820$	−2.51685	−	7.29472i	−0.0878921	−	0.254743i
$821$	−15.8677	−	14.9008i	−0.553788	−	0.520041i	0.356347	−	0.934354i	$-0.384022\pi$
$821$	−15.8677	−	14.9008i	−0.553788	−	0.520041i	−0.910135	+	0.414312i	$0.864022\pi$
$822$	0.743023	+	0.349640i	0.0259159	+	0.0121951i
$823$	9.85998	+	8.15688i	0.343697	+	0.284331i	0.793217	−	0.608940i	$-0.208405\pi$
$823$	9.85998	+	8.15688i	0.343697	+	0.284331i	−0.449520	+	0.893271i	$0.648405\pi$
$824$	−2.12964	+	6.55436i	−0.0741896	+	0.228332i
$825$	1.90237	+	0.0507707i	0.0662320	+	0.00176761i
$826$	−1.57941	−	4.86091i	−0.0549546	−	0.169133i
$827$	9.83047	−	24.8289i	0.341839	−	0.863386i	−0.652564	−	0.757733i	$-0.726307\pi$
$827$	9.83047	−	24.8289i	0.341839	−	0.863386i	0.994403	−	0.105653i	$-0.0336932\pi$
$828$	4.43044	−	4.71794i	0.153969	−	0.163960i
$829$	−2.67361	−	14.0156i	−0.0928584	−	0.486781i	−0.998085	−	0.0618522i	$-0.980299\pi$
$829$	−2.67361	−	14.0156i	−0.0928584	−	0.486781i	0.905227	−	0.424928i	$-0.139701\pi$
$830$	−1.83970	+	10.6904i	−0.0638570	+	0.371068i
$831$	−4.93691	+	4.63607i	−0.171259	+	0.160823i
$832$	−0.437012	+	0.141994i	−0.0151507	+	0.00492275i
$833$	−5.16894	−	0.986028i	−0.179093	−	0.0341638i
$834$	−0.304145	−	4.83424i	−0.0105317	−	0.167396i
$835$	40.9302	+	18.3642i	1.41645	+	0.635518i
$836$	−1.27067	−	2.00226i	−0.0439472	−	0.0692497i
$837$	−9.72049	+	0.611561i	−0.335989	+	0.0211386i
$838$	19.2939	+	12.2443i	0.666498	+	0.422972i
$839$	−30.0123	+	36.2787i	−1.03614	+	1.25248i	−0.0691663	+	0.997605i	$0.522034\pi$
$839$	−30.0123	+	36.2787i	−1.03614	+	1.25248i	−0.966974	+	0.254874i	$0.917966\pi$
$840$	1.67664	−	0.135949i	0.0578496	−	0.00469067i
$841$	−26.7945	−	6.87966i	−0.923949	−	0.237230i
$842$	16.5477	−	7.78677i	0.570273	−	0.268350i
$843$	4.26731	+	1.38653i	0.146974	+	0.0477548i
$844$	−17.4526	−	9.59466i	−0.600744	−	0.330262i
$845$	−24.8064	+	14.2273i	−0.853367	+	0.489433i
$846$	35.2547	+	4.45370i	1.21208	+	0.153122i
$847$	2.89732	−	22.9346i	0.0995530	−	0.788043i
$848$	−2.04222	+	1.29603i	−0.0701300	+	0.0445059i
$849$	4.37186	−	3.17634i	0.150042	−	0.109012i
$850$	−18.8770	−	16.4841i	−0.647475	−	0.565401i
$851$	18.6733	+	13.5669i	0.640112	+	0.465069i
$852$	−4.51868	−	0.284291i	−0.154807	−	0.00973966i
$853$	12.7879	+	23.2610i	0.437848	+	0.796442i	0.999522	−	0.0309162i	$-0.00984249\pi$
$853$	12.7879	+	23.2610i	0.437848	+	0.796442i	−0.561674	+	0.827359i	$0.689842\pi$
$854$	8.10655	−	17.2273i	0.277401	−	0.589506i
$855$	0.558437	−	12.4688i	0.0190981	−	0.426424i
$856$	0.882238	−	4.62485i	0.0301543	−	0.158074i
$857$	33.3264	+	45.8699i	1.13841	+	1.56689i	0.771012	+	0.636821i	$0.219751\pi$
$857$	33.3264	+	45.8699i	1.13841	+	1.56689i	0.367397	+	0.930064i	$0.380249\pi$
$858$	−0.0842541	+	0.153258i	−0.00287639	+	0.00523213i
$859$	−7.27240	+	11.4595i	−0.248131	+	0.390992i	−0.945449	−	0.325770i	$-0.894377\pi$
$859$	−7.27240	+	11.4595i	−0.248131	+	0.390992i	0.697318	+	0.716762i	$0.254377\pi$
$860$	3.13794	−	2.07189i	0.107003	−	0.0706508i
$861$	−2.41381	−	0.955696i	−0.0822625	−	0.0325700i
$862$	−6.50275	−	16.4241i	−0.221485	−	0.559406i
$863$	−43.1832	+	35.7243i	−1.46997	+	1.21607i	−0.543667	+	0.839301i	$0.682965\pi$
$863$	−43.1832	+	35.7243i	−1.46997	+	1.21607i	−0.926308	+	0.376768i	$0.877035\pi$
$864$	1.76386	−	0.452881i	0.0600076	−	0.0154073i
$865$	23.9328	−	34.2249i	0.813741	−	1.16368i
$866$	1.95120	−	0.772533i	0.0663043	−	0.0262517i
$867$	1.71482	+	1.82609i	0.0582382	+	0.0620174i
$868$	−7.66835	+	10.5546i	−0.260281	+	0.358246i
$869$	2.77926	+	5.90622i	0.0942798	+	0.200355i
$870$	−0.0644284	−	0.794590i	−0.00218433	−	0.0269391i
$871$	−1.79719	+	0.988013i	−0.0608954	+	0.0334776i
$872$	9.66415	−	1.84354i	0.327269	−	0.0624300i
$873$	−2.36010	−	9.19197i	−0.0798771	−	0.311101i
$874$	4.28114			0.144812
$875$	26.4727	−	6.55470i	0.894941	−	0.221589i
$876$	4.59556			0.155270
$877$	10.8232	+	42.1537i	0.365474	+	1.42343i	0.839712	+	0.543032i	$0.182724\pi$
$877$	10.8232	+	42.1537i	0.365474	+	1.42343i	−0.474238	+	0.880397i	$0.657276\pi$
$878$	−2.33630	+	0.445674i	−0.0788464	+	0.0150408i
$879$	2.83424	−	1.55813i	0.0955964	−	0.0525546i
$880$	1.43633	−	2.35637i	0.0484185	−	0.0794333i
$881$	20.5566	+	43.6850i	0.692569	+	1.47178i	0.872758	+	0.488153i	$0.162329\pi$
$881$	20.5566	+	43.6850i	0.692569	+	1.47178i	−0.180189	+	0.983632i	$0.557671\pi$
$882$	1.79258	−	2.46727i	0.0603592	−	0.0830774i
$883$	7.31677	+	7.79157i	0.246229	+	0.262207i	0.840197	−	0.542282i	$-0.182439\pi$
$883$	7.31677	+	7.79157i	0.246229	+	0.262207i	−0.593968	+	0.804489i	$0.702439\pi$
$884$	2.14140	−	0.847841i	0.0720232	−	0.0285160i
$885$	0.870299	+	1.15343i	0.0292548	+	0.0387722i
$886$	28.8823	−	7.41571i	0.970320	−	0.249136i
$887$	−2.72999	+	2.25844i	−0.0916640	+	0.0758311i	−0.682127	−	0.731233i	$-0.738945\pi$
$887$	−2.72999	+	2.25844i	−0.0916640	+	0.0758311i	0.590463	+	0.807064i	$0.298945\pi$
$888$	1.17614	+	2.97059i	0.0394686	+	0.0996863i
$889$	42.1818	+	16.7010i	1.41473	+	0.560133i
$890$	9.21203	+	7.34450i	0.308788	+	0.246188i
$891$	−5.39150	+	8.49564i	−0.180622	+	0.284615i
$892$	−2.69038	+	4.89377i	−0.0900804	+	0.163856i
$893$	13.8162	+	19.0164i	0.462342	+	0.636359i
$894$	0.517344	−	2.71201i	0.0173026	−	0.0907032i
$895$	−21.1371	−	32.0128i	−0.706536	−	1.07007i
$896$	1.03860	−	2.20714i	0.0346972	−	0.0737353i
$897$	−0.152104	−	0.276676i	−0.00507860	−	0.00923795i
$898$	−19.8590	−	1.24942i	−0.662703	−	0.0416937i
$899$	5.00200	+	3.63416i	0.166826	+	0.121206i
$900$	13.3024	−	5.83139i	0.443414	−	0.194380i
$901$	9.80803	−	7.12595i	0.326753	−	0.237400i
$902$	−3.59602	+	2.28211i	−0.119735	+	0.0759858i
$903$	0.158553	−	1.25508i	0.00527631	−	0.0417663i
$904$	−4.13487	−	0.522355i	−0.137524	−	0.0173733i
$905$	−15.5180	−	1.67603i	−0.515835	−	0.0557132i
$906$	4.57515	+	2.51521i	0.151999	+	0.0835622i
$907$	−52.9780	−	17.2136i	−1.75911	−	0.571568i	−0.761998	−	0.647579i	$-0.775781\pi$
$907$	−52.9780	−	17.2136i	−1.75911	−	0.571568i	−0.997107	+	0.0760114i	$0.975781\pi$
$908$	−2.20175	+	1.03607i	−0.0730677	+	0.0343831i
$909$	18.3862	+	4.72077i	0.609832	+	0.156578i
$910$	−0.579317	+	2.43844i	−0.0192042	+	0.0808336i
$911$	23.3743	−	28.2546i	0.774424	−	0.936118i	−0.224843	−	0.974395i	$-0.572187\pi$
$911$	23.3743	−	28.2546i	0.774424	−	0.936118i	0.999267	+	0.0382767i	$0.0121868\pi$
$912$	0.500346	+	0.317529i	0.0165681	+	0.0105144i
$913$	5.97519	−	0.375927i	0.197750	−	0.0124414i
$914$	−3.48326	−	5.48875i	−0.115216	−	0.181552i
$915$	−0.577984	+	5.35142i	−0.0191076	+	0.176912i
$916$	0.998782	+	15.8752i	0.0330007	+	0.524531i
$917$	44.9096	+	8.56696i	1.48305	+	0.282906i
$918$	−8.68092	+	2.82060i	−0.286513	+	0.0930937i
$919$	32.1289	−	30.1710i	1.05983	−	0.995251i	0.0598389	−	0.998208i	$-0.480941\pi$
$919$	32.1289	−	30.1710i	1.05983	−	0.995251i	0.999996	+	0.00295719i	$0.000941304\pi$
$920$	2.20234	+	4.46873i	0.0726090	+	0.147330i
$921$	1.70958	+	8.96194i	0.0563326	+	0.295306i
$922$	3.38570	−	3.60541i	0.111502	−	0.118738i
$923$	2.48334	−	6.27221i	0.0817402	−	0.206452i
$924$	−0.286897	−	0.882977i	−0.00943821	−	0.0290478i
$925$	26.5785	+	44.4600i	0.873895	+	1.46184i
$926$	4.75363	−	14.6302i	0.156214	−	0.480777i
$927$	15.4253	+	12.7609i	0.506634	+	0.419124i
$928$	−1.04600	−	0.492210i	−0.0343366	−	0.0161576i
$929$	−15.0297	−	14.1138i	−0.493107	−	0.463058i	0.397651	−	0.917537i	$-0.369826\pi$
$929$	−15.0297	−	14.1138i	−0.493107	−	0.463058i	−0.890758	+	0.454479i	$0.849826\pi$
$930$	1.07614	−	3.52775i	0.0352881	−	0.115679i
$931$	2.00141	−	0.252837i	0.0655937	−	0.00828641i
$932$		−	14.4737i		−	0.474100i
$933$	−0.445698	−	3.52807i	−0.0145915	−	0.115504i
$934$	4.17900	+	5.05154i	0.136741	+	0.165291i
$935$	−6.44342	+	12.2395i	−0.210722	+	0.400274i
$936$	−0.0838128	+	1.33217i	−0.00273951	+	0.0435432i
$937$	4.30577	−	16.7699i	0.140663	−	0.547847i	−0.858710	−	0.512461i	$-0.828734\pi$
$937$	4.30577	−	16.7699i	0.140663	−	0.547847i	0.999374	−	0.0353862i	$-0.0112661\pi$
$938$	2.70753	−	10.5451i	0.0884039	−	0.344311i
$939$	0.292379	−	4.64723i	0.00954142	−	0.151656i
$940$	−12.7422	+	24.2042i	−0.415604	+	0.789453i
$941$	33.6165	+	40.6354i	1.09587	+	1.32468i	0.941632	+	0.336643i	$0.109291\pi$
$941$	33.6165	+	40.6354i	1.09587	+	1.32468i	0.154236	+	0.988034i	$0.450709\pi$
$942$	0.701917	+	5.55624i	0.0228697	+	0.181032i
$943$		−	7.68884i		−	0.250383i
$944$	2.07879	−	0.262612i	0.0676587	−	0.00854728i
$945$	2.89819	−	9.50066i	0.0942780	−	0.309057i
$946$	−1.51288	−	1.42069i	−0.0491879	−	0.0461905i
$947$	−0.0328543	−	0.0154601i	−0.00106762	−	0.000502385i	0.425245	−	0.905078i	$-0.360188\pi$
$947$	−0.0328543	−	0.0154601i	−0.00106762	−	0.000502385i	−0.426313	+	0.904576i	$0.640188\pi$
$948$	−1.25682	−	1.03973i	−0.0408197	−	0.0337690i
$949$	−2.11589	+	6.51204i	−0.0686847	+	0.211390i
$950$	8.83539	+	3.77385i	0.286658	+	0.122440i
$951$	−1.10189	−	3.39126i	−0.0357311	−	0.109969i
$952$	−4.50082	+	11.3678i	−0.145872	+	0.368432i
$953$	−30.3076	+	32.2743i	−0.981759	+	1.04547i	0.0171996	+	0.999852i	$0.494525\pi$
$953$	−30.3076	+	32.2743i	−0.981759	+	1.04547i	−0.998959	+	0.0456156i	$0.985475\pi$
$954$	1.31658	+	6.90175i	0.0426258	+	0.223452i
$955$	−20.9105	−	42.4292i	−0.676649	−	1.37298i
$956$	−11.8362	+	11.1149i	−0.382810	+	0.359482i
$957$	−0.418458	+	0.135965i	−0.0135268	+	0.00439513i
$958$	10.2952	+	1.96391i	0.332621	+	0.0634509i
$959$	−0.407831	−	6.48228i	−0.0131695	−	0.209324i
$960$	−0.0740505	+	0.685616i	−0.00238997	+	0.0221282i
$961$	−1.28340	−	2.02232i	−0.0414001	−	0.0652362i
$962$	−4.75092	+	0.298903i	−0.153176	+	0.00963701i
$963$	−11.5478	−	7.32847i	−0.372124	−	0.236157i
$964$	−14.8852	+	17.9932i	−0.479421	+	0.579521i
$965$	9.79288	−	41.2198i	0.315244	−	1.32691i
$966$	1.62341	+	0.416822i	0.0522325	+	0.0134110i
$967$	−20.5244	+	9.65805i	−0.660020	+	0.310582i	−0.726460	−	0.687208i	$-0.758836\pi$
$967$	−20.5244	+	9.65805i	−0.660020	+	0.310582i	0.0664400	+	0.997790i	$0.478836\pi$
$968$	9.01306	+	2.92852i	0.289691	+	0.0941263i
$969$	−2.60285	−	1.43093i	−0.0836155	−	0.0459680i
$970$	7.26287	+	0.784432i	0.233197	+	0.0251866i
$971$	15.5016	+	1.95830i	0.497469	+	0.0628449i	0.370065	−	0.929006i	$-0.379336\pi$
$971$	15.5016	+	1.95830i	0.497469	+	0.0628449i	0.127404	+	0.991851i	$0.459336\pi$
$972$	0.999859	−	7.91470i	0.0320705	−	0.253864i
$973$	−32.3479	+	20.5286i	−1.03703	+	0.658117i
$974$	−17.1479	+	12.4587i	−0.549456	+	0.399203i
$975$	−0.0700193	−	0.705083i	−0.00224241	−	0.0225807i
$976$	6.31460	+	4.58782i	0.202125	+	0.146853i
$977$	−24.8103	−	1.56093i	−0.793753	−	0.0499387i	−0.339264	−	0.940691i	$-0.610178\pi$
$977$	−24.8103	−	1.56093i	−0.793753	−	0.0499387i	−0.454489	+	0.890753i	$0.650178\pi$
$978$	−1.78742	−	3.25131i	−0.0571555	−	0.103966i
$979$	2.76862	−	5.88363i	0.0884856	−	0.188042i
$980$	1.29350	+	1.95904i	0.0413193	+	0.0625793i
$981$	5.35527	−	28.0733i	0.170980	−	0.896311i
$982$	25.0591	+	34.4909i	0.799667	+	1.10065i
$983$	28.3101	−	51.4960i	0.902953	−	1.64247i	0.145716	−	0.989327i	$-0.453452\pi$
$983$	28.3101	−	51.4960i	0.902953	−	1.64247i	0.757238	−	0.653139i	$-0.226548\pi$
$984$	0.570277	−	0.898612i	0.0181798	−	0.0286467i
$985$	−42.4093	−	33.8118i	−1.35127	−	1.07733i
$986$	5.38738	+	2.13302i	0.171569	+	0.0679291i
$987$	3.38765	+	8.55623i	0.107830	+	0.272348i
$988$	−0.680318	+	0.562808i	−0.0216438	+	0.0179053i
$989$	3.62895	−	0.931756i	0.115394	−	0.0296281i
$990$	−4.82837	−	6.39918i	−0.153456	−	0.203379i
$991$	36.0961	−	14.2915i	1.14663	−	0.453983i	0.283504	−	0.958971i	$-0.408503\pi$
$991$	36.0961	−	14.2915i	1.14663	−	0.453983i	0.863126	+	0.504988i	$0.168503\pi$
$992$	−3.66120	−	3.89878i	−0.116243	−	0.123786i
$993$	4.05400	−	5.57986i	0.128650	−	0.177071i
$994$	15.2477	+	32.4029i	0.483627	+	1.02776i
$995$	−11.7350	+	19.2520i	−0.372026	+	0.610330i
$996$	−1.31104	+	0.720750i	−0.0415419	+	0.0228378i
$997$	0.229094	−	0.0437020i	0.00725548	−	0.00138406i	−0.183752	−	0.982973i	$-0.558824\pi$
$997$	0.229094	−	0.0437020i	0.00725548	−	0.00138406i	0.191008	+	0.981589i	$0.438824\pi$
$998$	5.65812	+	22.0369i	0.179105	+	0.697566i
$999$	18.8658			0.596888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.h.a.229.9	yes	240
125.119	even	50	inner	250.2.h.a.119.9	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.h.a.119.9	✓	240	125.119	even	50	inner
250.2.h.a.229.9	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.302937 + 0.0577884i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.17551 - 0.516852i) q^{5} +(-0.131310 - 0.279049i) q^{6} +(-1.43378 + 1.97343i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-2.70090 + 1.06936i) q^{9} +O(q^{10})\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.302937 + 0.0577884i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.17551 - 0.516852i) q^{5} +(-0.131310 - 0.279049i) q^{6} +(-1.43378 + 1.97343i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-2.70090 + 1.06936i) q^{9} +(-0.0404148 - 2.23570i) q^{10} +(-1.19537 + 0.306918i) q^{11} +(0.237626 - 0.196582i) q^{12} +(0.169154 + 0.427233i) q^{13} +(-2.26800 - 0.897963i) q^{14} +(0.688913 + 0.0308542i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-2.41467 + 4.39227i) q^{17} +(-1.70745 - 2.35010i) q^{18} +(0.360057 - 1.88749i) q^{19} +(2.15541 - 0.595142i) q^{20} +(0.320304 - 0.680681i) q^{21} +(-0.594552 - 1.08149i) q^{22} +(2.22360 + 0.139897i) q^{23} +(0.249501 + 0.181273i) q^{24} +(4.46573 + 2.24884i) q^{25} +(-0.371744 + 0.270088i) q^{26} +(1.53758 - 0.975777i) q^{27} +(0.305724 - 2.42006i) q^{28} +(-1.14691 - 0.144888i) q^{29} +(0.141441 + 0.674943i) q^{30} +(-4.68679 - 2.57659i) q^{31} +(0.951057 + 0.309017i) q^{32} +(0.344386 - 0.162056i) q^{33} +(-4.85478 - 1.24650i) q^{34} +(4.13918 - 3.55217i) q^{35} +(1.85165 - 2.23826i) q^{36} +(8.74702 + 5.55103i) q^{37} +(1.91773 - 0.120653i) q^{38} +(-0.0759321 - 0.119650i) q^{39} +(1.11247 + 1.93969i) q^{40} +(-0.216691 - 3.44420i) q^{41} +(0.738953 + 0.140963i) q^{42} +(1.59932 - 0.519652i) q^{43} +(0.899650 - 0.844828i) q^{44} +(6.42854 - 0.930448i) q^{45} +(0.417485 + 2.18853i) q^{46} +(-8.37392 + 8.91732i) q^{47} +(-0.113530 + 0.286743i) q^{48} +(0.324423 + 0.998472i) q^{49} +(-1.06760 + 4.88469i) q^{50} +(0.477672 - 1.47012i) q^{51} +(-0.354052 - 0.292897i) q^{52} +(-2.18855 - 1.02985i) q^{53} +(1.32750 + 1.24661i) q^{54} +(2.75917 - 0.0498775i) q^{55} +(2.42006 - 0.305724i) q^{56} +0.592597i q^{57} +(-0.144888 - 1.14691i) q^{58} +(1.33560 + 1.61446i) q^{59} +(-0.618563 + 0.304849i) q^{60} +(-0.490097 + 7.78987i) q^{61} +(1.33008 - 5.18032i) q^{62} +(1.76218 - 6.86326i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-0.147180 - 1.01688i) q^{65} +(0.242609 + 0.293264i) q^{66} +(0.559393 + 4.42805i) q^{67} -5.01225i q^{68} +(-0.681696 + 0.0861182i) q^{69} +(4.46995 + 3.12575i) q^{70} +(-10.7020 - 10.0498i) q^{71} +(2.62842 + 1.23684i) q^{72} +(11.4816 + 9.49844i) q^{73} +(-3.20134 + 9.85270i) q^{74} +(-1.48279 - 0.423189i) q^{75} +(0.593783 + 1.82747i) q^{76} +(1.10821 - 2.79903i) q^{77} +(0.0970073 - 0.103302i) q^{78} +(-0.991073 - 5.19539i) q^{79} +(-1.60209 + 1.55990i) q^{80} +(5.94332 - 5.58115i) q^{81} +(3.28211 - 1.06642i) q^{82} +(-4.76523 - 0.909015i) q^{83} +(0.0472359 + 0.750793i) q^{84} +(7.52331 - 8.30742i) q^{85} +(0.901061 + 1.41985i) q^{86} +(0.355814 - 0.0223859i) q^{87} +(1.04202 + 0.661286i) q^{88} +(-3.35848 + 4.05971i) q^{89} +(2.49993 + 5.99519i) q^{90} +(-1.08564 - 0.278746i) q^{91} +(-2.01595 + 0.948634i) q^{92} +(1.56870 + 0.509702i) q^{93} +(-10.7197 - 5.89319i) q^{94} +(-1.75886 + 3.92016i) q^{95} +(-0.305968 - 0.0386528i) q^{96} +(-0.409457 + 3.24118i) q^{97} +(-0.886423 + 0.562541i) q^{98} +(2.90036 - 2.10724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 10 q^{5}+O(q^{10}) \) 240 * q + 10 * q^5	\( 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) \) 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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