LMFDB - Embedded newform 490.2.s.a.237.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(13,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([21, 22]))

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

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

chi := DirichletCharacter("490.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.s (of order $28$, degree $12$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			237.15
Character	$\chi$	$=$	490.237
Dual form			490.2.s.a.153.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.111964 - 0.993712i) q^{2} +(-2.84935 - 0.997032i) q^{3} +(-0.974928 - 0.222521i) q^{4} +(1.00157 + 1.99921i) q^{5} +(-1.30979 + 2.71981i) q^{6} +(-2.64158 + 0.148532i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(4.77926 + 3.81133i) q^{9} +O(q^{10})$	\(q+(0.111964 - 0.993712i) q^{2} +(-2.84935 - 0.997032i) q^{3} +(-0.974928 - 0.222521i) q^{4} +(1.00157 + 1.99921i) q^{5} +(-1.30979 + 2.71981i) q^{6} +(-2.64158 + 0.148532i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(4.77926 + 3.81133i) q^{9} +(2.09878 - 0.771433i) q^{10} +(1.99492 + 2.50155i) q^{11} +(2.55606 + 1.60608i) q^{12} +(0.776361 - 6.89040i) q^{13} +(-0.148165 + 2.64160i) q^{14} +(-0.860553 - 6.69507i) q^{15} +(0.900969 + 0.433884i) q^{16} +(3.20963 + 2.01674i) q^{17} +(4.32247 - 4.32247i) q^{18} -0.0628586 q^{19} +(-0.531593 - 2.17196i) q^{20} +(7.67489 + 2.21052i) q^{21} +(2.70918 - 1.70229i) q^{22} +(0.310155 + 0.493609i) q^{23} +(1.88216 - 2.36016i) q^{24} +(-2.99371 + 4.00471i) q^{25} +(-6.76015 - 1.54296i) q^{26} +(-4.99955 - 7.95674i) q^{27} +(2.60840 + 0.442999i) q^{28} +(5.50817 - 1.25720i) q^{29} +(-6.74932 + 0.105532i) q^{30} -9.67170i q^{31} +(0.532032 - 0.846724i) q^{32} +(-3.19010 - 9.11680i) q^{33} +(2.36343 - 2.96364i) q^{34} +(-2.94268 - 5.13231i) q^{35} +(-3.81133 - 4.77926i) q^{36} +(-0.436099 + 0.694047i) q^{37} +(-0.00703793 + 0.0624634i) q^{38} +(-9.08208 + 18.8591i) q^{39} +(-2.21782 + 0.285068i) q^{40} +(-0.156997 - 0.326007i) q^{41} +(3.05593 - 7.37913i) q^{42} +(8.04854 - 2.81630i) q^{43} +(-1.38825 - 2.88274i) q^{44} +(-2.83289 + 13.3721i) q^{45} +(0.525232 - 0.252938i) q^{46} +(3.19598 + 0.360100i) q^{47} +(-2.13458 - 2.13458i) q^{48} +(6.95588 - 0.784718i) q^{49} +(3.64434 + 3.42327i) q^{50} +(-7.13461 - 8.94652i) q^{51} +(-2.29015 + 6.54488i) q^{52} +(3.07947 + 4.90094i) q^{53} +(-8.46648 + 4.07724i) q^{54} +(-3.00308 + 6.49375i) q^{55} +(0.732261 - 2.54240i) q^{56} +(0.179107 + 0.0626721i) q^{57} +(-0.632579 - 5.61430i) q^{58} +(6.67638 + 3.21518i) q^{59} +(-0.650816 + 6.71870i) q^{60} +(0.362413 - 0.0827185i) q^{61} +(-9.61089 - 1.08289i) q^{62} +(-13.1909 - 9.35805i) q^{63} +(-0.781831 - 0.623490i) q^{64} +(14.5530 - 5.34911i) q^{65} +(-9.41665 + 2.14929i) q^{66} +(6.34785 + 6.34785i) q^{67} +(-2.68039 - 2.68039i) q^{68} +(-0.391598 - 1.71570i) q^{69} +(-5.42952 + 2.34954i) q^{70} +(1.24555 - 5.45713i) q^{71} +(-5.17594 + 3.25226i) q^{72} +(14.5303 - 1.63717i) q^{73} +(0.640856 + 0.511065i) q^{74} +(12.5230 - 8.42602i) q^{75} +(0.0612826 + 0.0139874i) q^{76} +(-5.64129 - 6.31173i) q^{77} +(17.7237 + 11.1365i) q^{78} +11.6804i q^{79} +(0.0349587 + 2.23579i) q^{80} +(2.23162 + 9.77738i) q^{81} +(-0.341535 + 0.119508i) q^{82} +(-9.29856 + 1.04770i) q^{83} +(-6.99057 - 3.86292i) q^{84} +(-0.817227 + 8.43664i) q^{85} +(-1.89745 - 8.31326i) q^{86} +(-16.9482 - 1.90960i) q^{87} +(-3.02005 + 1.05676i) q^{88} +(6.28381 - 7.87965i) q^{89} +(12.9708 + 4.31228i) q^{90} +(-1.02737 + 18.3168i) q^{91} +(-0.192541 - 0.550250i) q^{92} +(-9.64300 + 27.5581i) q^{93} +(0.715672 - 3.13556i) q^{94} +(-0.0629574 - 0.125668i) q^{95} +(-2.36016 + 1.88216i) q^{96} +(-6.93159 + 6.93159i) q^{97} +(-0.000972913 - 7.00000i) q^{98} +19.5588i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 28 q^{6} + 8 q^{7}+O(q^{10}) $ 336 * q + 28 * q^6 + 8 * q^7	$ 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98}+O(q^{100}) $ 336 * q + 28 * q^6 + 8 * q^7 + 8 * q^11 + 44 * q^15 + 56 * q^16 + 28 * q^17 - 16 * q^21 - 20 * q^22 + 8 * q^23 - 8 * q^25 - 28 * q^26 - 8 * q^28 - 24 * q^30 + 8 * q^35 + 76 * q^36 - 24 * q^37 - 56 * q^41 - 112 * q^42 - 24 * q^43 + 112 * q^45 - 68 * q^46 - 84 * q^47 - 32 * q^50 - 80 * q^51 - 100 * q^53 + 84 * q^55 - 20 * q^56 + 92 * q^57 - 80 * q^58 - 112 * q^61 - 32 * q^67 + 52 * q^70 + 16 * q^71 - 84 * q^75 + 16 * q^77 - 80 * q^78 + 12 * q^81 + 140 * q^83 + 40 * q^85 - 8 * q^86 - 28 * q^87 - 8 * q^88 - 84 * q^90 + 124 * q^91 + 8 * q^92 + 20 * q^93 - 56 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.111964	−	0.993712i	0.0791708	−	0.702661i
$2$	0.111964	−	0.993712i	0.0791708	−	0.702661i
$3$	−2.84935	−	0.997032i	−1.64508	−	0.575637i	−0.660535	−	0.750795i	$-0.729671\pi$
$3$	−2.84935	−	0.997032i	−1.64508	−	0.575637i	−0.984540	+	0.175158i	$0.943956\pi$
$4$	−0.974928	−	0.222521i	−0.487464	−	0.111260i
$5$	1.00157	+	1.99921i	0.447916	+	0.894075i
$5$	1.00157	+	1.99921i	0.447916	+	0.894075i
$6$	−1.30979	+	2.71981i	−0.534719	+	1.11036i
$7$	−2.64158	+	0.148532i	−0.998423	+	0.0561398i
$7$	−2.64158	+	0.148532i	−0.998423	+	0.0561398i
$8$	−0.330279	+	0.943883i	−0.116771	+	0.333713i
$9$	4.77926	+	3.81133i	1.59309	+	1.27044i
$10$	2.09878	−	0.771433i	0.663694	−	0.243949i
$11$	1.99492	+	2.50155i	0.601490	+	0.754245i	0.985609	−	0.169038i	$-0.0540662\pi$
$11$	1.99492	+	2.50155i	0.601490	+	0.754245i	−0.384119	+	0.923284i	$0.625495\pi$
$12$	2.55606	+	1.60608i	0.737870	+	0.463634i
$13$	0.776361	−	6.89040i	0.215324	−	1.91105i	−0.165164	−	0.986266i	$-0.552815\pi$
$13$	0.776361	−	6.89040i	0.215324	−	1.91105i	0.380488	−	0.924786i	$-0.375756\pi$
$14$	−0.148165	+	2.64160i	−0.0395987	+	0.705997i
$15$	−0.860553	−	6.69507i	−0.222194	−	1.72866i
$16$	0.900969	+	0.433884i	0.225242	+	0.108471i
$17$	3.20963	+	2.01674i	0.778449	+	0.489132i	0.861713	−	0.507395i	$-0.169392\pi$
$17$	3.20963	+	2.01674i	0.778449	+	0.489132i	−0.0832641	+	0.996528i	$0.526535\pi$
$18$	4.32247	−	4.32247i	1.01882	−	1.01882i
$19$	−0.0628586			−0.0144208			−0.00721038	−	0.999974i	$-0.502295\pi$
$19$	−0.0628586			−0.0144208			−0.00721038	+	0.999974i	$0.502295\pi$
$20$	−0.531593	−	2.17196i	−0.118868	−	0.485665i
$21$	7.67489	+	2.21052i	1.67480	+	0.482375i
$22$	2.70918	−	1.70229i	0.577599	−	0.362929i
$23$	0.310155	+	0.493609i	0.0646719	+	0.102925i	0.877495	−	0.479586i	$-0.159213\pi$
$23$	0.310155	+	0.493609i	0.0646719	+	0.102925i	−0.812823	+	0.582511i	$0.802070\pi$
$24$	1.88216	−	2.36016i	0.384195	−	0.481766i
$25$	−2.99371	+	4.00471i	−0.598742	+	0.800942i
$26$	−6.76015	−	1.54296i	−1.32577	−	0.302599i
$27$	−4.99955	−	7.95674i	−0.962164	−	1.53127i
$28$	2.60840	+	0.442999i	0.492941	+	0.0837189i
$29$	5.50817	−	1.25720i	1.02284	−	0.233457i	0.321974	−	0.946749i	$-0.395654\pi$
$29$	5.50817	−	1.25720i	1.02284	−	0.233457i	0.700867	+	0.713292i	$0.252796\pi$
$30$	−6.74932	+	0.105532i	−1.23225	+	0.0192674i
$31$		−	9.67170i		−	1.73709i	−0.495611	−	0.868545i	$-0.665056\pi$
$31$		−	9.67170i		−	1.73709i	0.495611	−	0.868545i	$-0.334944\pi$
$32$	0.532032	−	0.846724i	0.0940509	−	0.149681i
$33$	−3.19010	−	9.11680i	−0.555326	−	1.58703i
$34$	2.36343	−	2.96364i	0.405324	−	0.508261i
$35$	−2.94268	−	5.13231i	−0.497403	−	0.867519i
$36$	−3.81133	−	4.77926i	−0.635221	−	0.796543i
$37$	−0.436099	+	0.694047i	−0.0716942	+	0.114101i	−0.880647	−	0.473773i	$-0.842892\pi$
$37$	−0.436099	+	0.694047i	−0.0716942	+	0.114101i	0.808953	+	0.587873i	$0.200035\pi$
$38$	−0.00703793	+	0.0624634i	−0.00114170	+	0.0101329i
$39$	−9.08208	+	18.8591i	−1.45430	+	3.01988i
$40$	−2.21782	+	0.285068i	−0.350669	+	0.0450733i
$41$	−0.156997	−	0.326007i	−0.0245188	−	0.0509137i	0.888350	−	0.459167i	$-0.151852\pi$
$41$	−0.156997	−	0.326007i	−0.0245188	−	0.0509137i	−0.912869	+	0.408254i	$0.866138\pi$
$42$	3.05593	−	7.37913i	0.471541	−	1.13862i
$43$	8.04854	−	2.81630i	1.22739	−	0.429482i	0.362756	−	0.931884i	$-0.381836\pi$
$43$	8.04854	−	2.81630i	1.22739	−	0.429482i	0.864634	+	0.502402i	$0.167550\pi$
$44$	−1.38825	−	2.88274i	−0.209287	−	0.434589i
$45$	−2.83289	+	13.3721i	−0.422303	+	1.99339i
$46$	0.525232	−	0.252938i	0.0774412	−	0.0372937i
$47$	3.19598	+	0.360100i	0.466181	+	0.0525260i	0.341931	−	0.939725i	$-0.388919\pi$
$47$	3.19598	+	0.360100i	0.466181	+	0.0525260i	0.124250	+	0.992251i	$0.460348\pi$
$48$	−2.13458	−	2.13458i	−0.308101	−	0.308101i
$49$	6.95588	−	0.784718i	0.993697	−	0.112103i
$50$	3.64434	+	3.42327i	0.515388	+	0.484123i
$51$	−7.13461	−	8.94652i	−0.999045	−	1.25276i
$52$	−2.29015	+	6.54488i	−0.317587	+	0.907612i
$53$	3.07947	+	4.90094i	0.422997	+	0.673197i	0.988444	−	0.151589i	$-0.0484389\pi$
$53$	3.07947	+	4.90094i	0.422997	+	0.673197i	−0.565446	+	0.824785i	$0.691296\pi$
$54$	−8.46648	+	4.07724i	−1.15214	+	0.554842i
$55$	−3.00308	+	6.49375i	−0.404935	+	0.875617i
$56$	0.732261	−	2.54240i	0.0978525	−	0.339742i
$57$	0.179107	+	0.0626721i	0.0237232	+	0.00830112i
$58$	−0.632579	−	5.61430i	−0.0830617	−	0.737193i
$59$	6.67638	+	3.21518i	0.869191	+	0.418580i	0.814665	−	0.579932i	$-0.196921\pi$
$59$	6.67638	+	3.21518i	0.869191	+	0.418580i	0.0545262	+	0.998512i	$0.482635\pi$
$60$	−0.650816	+	6.71870i	−0.0840200	+	0.867380i
$61$	0.362413	−	0.0827185i	0.0464023	−	0.0105910i	−0.199257	−	0.979947i	$-0.563853\pi$
$61$	0.362413	−	0.0827185i	0.0464023	−	0.0105910i	0.245659	+	0.969356i	$0.420996\pi$
$62$	−9.61089	−	1.08289i	−1.22058	−	0.137527i
$63$	−13.1909	−	9.35805i	−1.66190	−	1.17900i
$64$	−0.781831	−	0.623490i	−0.0977289	−	0.0779362i
$65$	14.5530	−	5.34911i	1.80507	−	0.663476i
$66$	−9.41665	+	2.14929i	−1.15911	+	0.264559i
$67$	6.34785	+	6.34785i	0.775513	+	0.775513i	0.979064	−	0.203551i	$-0.0652482\pi$
$67$	6.34785	+	6.34785i	0.775513	+	0.775513i	−0.203551	+	0.979064i	$0.565248\pi$
$68$	−2.68039	−	2.68039i	−0.325045	−	0.325045i
$69$	−0.391598	−	1.71570i	−0.0471429	−	0.206546i
$70$	−5.42952	+	2.34954i	−0.648952	+	0.280823i
$71$	1.24555	−	5.45713i	0.147820	−	0.647642i	−0.845668	−	0.533709i	$-0.820798\pi$
$71$	1.24555	−	5.45713i	0.147820	−	0.647642i	0.993488	−	0.113933i	$-0.0363450\pi$
$72$	−5.17594	+	3.25226i	−0.609990	+	0.383282i
$73$	14.5303	−	1.63717i	1.70064	−	0.191616i	0.792384	−	0.610023i	$-0.208840\pi$
$73$	14.5303	−	1.63717i	1.70064	−	0.191616i	0.908260	+	0.418407i	$0.137411\pi$
$74$	0.640856	+	0.511065i	0.0744980	+	0.0594102i
$75$	12.5230	−	8.42602i	1.44603	−	0.972953i
$76$	0.0612826	+	0.0139874i	0.00702960	+	0.00160446i
$77$	−5.64129	−	6.31173i	−0.642885	−	0.719288i
$78$	17.7237	+	11.1365i	2.00681	+	1.26096i
$79$			11.6804i			1.31415i	0.753827	+	0.657073i	$0.228206\pi$
$79$			11.6804i			1.31415i	−0.753827	+	0.657073i	$0.771794\pi$
$80$	0.0349587	+	2.23579i	0.00390850	+	0.249969i
$81$	2.23162	+	9.77738i	0.247958	+	1.08638i
$82$	−0.341535	+	0.119508i	−0.0377162	+	0.0131975i
$83$	−9.29856	+	1.04770i	−1.02065	+	0.115000i	−0.606397	−	0.795162i	$-0.707386\pi$
$83$	−9.29856	+	1.04770i	−1.02065	+	0.115000i	−0.414253	+	0.910162i	$0.635957\pi$
$84$	−6.99057	−	3.86292i	−0.762734	−	0.421479i
$85$	−0.817227	+	8.43664i	−0.0886407	+	0.915083i
$86$	−1.89745	−	8.31326i	−0.204607	−	0.896441i
$87$	−16.9482	−	1.90960i	−1.81704	−	0.204731i
$88$	−3.02005	+	1.05676i	−0.321938	+	0.112651i
$89$	6.28381	−	7.87965i	0.666083	−	0.835242i	−0.327907	−	0.944710i	$-0.606343\pi$
$89$	6.28381	−	7.87965i	0.666083	−	0.835242i	0.993990	+	0.109468i	$0.0349148\pi$
$90$	12.9708	+	4.31228i	1.36724	+	0.454554i
$91$	−1.02737	+	18.3168i	−0.107698	+	1.92013i
$92$	−0.192541	−	0.550250i	−0.0200738	−	0.0573675i
$93$	−9.64300	+	27.5581i	−0.999933	+	2.85764i
$94$	0.715672	−	3.13556i	0.0738159	−	0.323409i
$95$	−0.0629574	−	0.125668i	−0.00645930	−	0.0128932i
$96$	−2.36016	+	1.88216i	−0.240883	+	0.192098i
$97$	−6.93159	+	6.93159i	−0.703797	+	0.703797i	−0.965223	−	0.261427i	$-0.915807\pi$
$97$	−6.93159	+	6.93159i	−0.703797	+	0.703797i	0.261427	+	0.965223i	$0.415807\pi$
$98$	−0.000972913	−	7.00000i	−9.82790e−5	−	0.707107i
$99$			19.5588i			1.96574i
$100$	3.80978	−	3.23814i	0.380978	−	0.323814i
$101$	2.99135	+	6.21161i	0.297651	+	0.618078i	0.995135	−	0.0985219i	$-0.0314115\pi$
$101$	2.99135	+	6.21161i	0.297651	+	0.618078i	−0.697484	+	0.716600i	$0.745697\pi$
$102$	−9.68909	+	6.08806i	−0.959363	+	0.602808i
$103$	−12.1932	−	4.26657i	−1.20143	−	0.420398i	−0.345958	−	0.938250i	$-0.612446\pi$
$103$	−12.1932	−	4.26657i	−1.20143	−	0.420398i	−0.855470	+	0.517852i	$0.826732\pi$
$104$	6.24731	+	3.00855i	0.612600	+	0.295012i
$105$	3.26765	+	17.5577i	0.318890	+	1.71346i
$106$	5.21492	−	2.51137i	0.506518	−	0.243926i
$107$	8.78075	−	0.989353i	0.848867	−	0.0956444i	0.323196	−	0.946332i	$-0.395243\pi$
$107$	8.78075	−	0.989353i	0.848867	−	0.0956444i	0.525671	+	0.850688i	$0.323814\pi$
$108$	3.10366	+	8.86975i	0.298650	+	0.853492i
$109$	−5.46584	+	4.35886i	−0.523532	+	0.417503i	−0.849271	−	0.527957i	$-0.822958\pi$
$109$	−5.46584	+	4.35886i	−0.523532	+	0.417503i	0.325739	+	0.945460i	$0.394387\pi$
$110$	6.11668	+	3.71126i	0.583202	+	0.353855i
$111$	1.93459	−	1.54278i	0.183623	−	0.146434i
$112$	−2.44443	−	1.01232i	−0.230977	−	0.0956548i
$113$	0.0699776	+	0.621069i	0.00658294	+	0.0584252i	0.996574	−	0.0827035i	$-0.0263554\pi$
$113$	0.0699776	+	0.621069i	0.00658294	+	0.0584252i	−0.989991	+	0.141129i	$0.954927\pi$
$114$	0.0823316	−	0.170963i	0.00771106	−	0.0160122i
$115$	−0.676188	+	1.11445i	−0.0630548	+	0.103923i
$116$	−5.64982			−0.524573
$117$	29.9720	−	29.9720i	2.77091	−	2.77091i
$118$	3.94248	−	6.27442i	0.362935	−	0.577607i
$119$	−8.77804	−	4.85065i	−0.804681	−	0.444659i
$120$	6.60359	+	1.39898i	0.602822	+	0.127709i
$121$	0.169685	−	0.743440i	0.0154259	−	0.0675855i
$122$	−0.0416209	−	0.369396i	−0.00376818	−	0.0334436i
$123$	0.122300	+	1.08544i	0.0110274	+	0.0978708i
$124$	−2.15216	+	9.42921i	−0.193269	+	0.846768i
$125$	−11.0047	−	1.97406i	−0.984289	−	0.176565i
$126$	−10.7761	+	12.0602i	−0.960013	+	1.07441i
$127$	4.11272	−	6.54536i	0.364945	−	0.580807i	−0.612894	−	0.790165i	$-0.709995\pi$
$127$	4.11272	−	6.54536i	0.364945	−	0.580807i	0.977839	+	0.209358i	$0.0671375\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−25.7411			−2.26638
$130$	−3.68607	−	15.0604i	−0.323289	−	1.32088i
$131$	−8.30317	+	17.2417i	−0.725451	+	1.50641i	0.131666	+	0.991294i	$0.457967\pi$
$131$	−8.30317	+	17.2417i	−0.725451	+	1.50641i	−0.857118	+	0.515121i	$0.827747\pi$
$132$	1.08144	+	9.59808i	0.0941277	+	0.835406i
$133$	0.166046	−	0.00933652i	0.0143980	−	0.000809579i
$134$	7.01867	−	5.59720i	0.606321	−	0.483525i
$135$	10.8998	−	17.9644i	0.938106	−	1.54613i
$136$	−2.96364	+	2.36343i	−0.254130	+	0.202662i
$137$	−6.85744	−	19.5974i	−0.585870	−	1.67432i	−0.728915	−	0.684605i	$-0.759975\pi$
$137$	−6.85744	−	19.5974i	−0.585870	−	1.67432i	0.143044	−	0.989716i	$-0.454311\pi$
$138$	−1.74876	+	0.197038i	−0.148864	+	0.0167730i
$139$	11.6334	−	5.60236i	0.986733	−	0.475186i	0.130317	−	0.991472i	$-0.458400\pi$
$139$	11.6334	−	5.60236i	0.986733	−	0.475186i	0.856416	+	0.516287i	$0.172686\pi$
$140$	1.72685	+	5.65844i	0.145946	+	0.478226i
$141$	−8.74744	−	4.21255i	−0.736668	−	0.354760i
$142$	−5.28336	−	1.84873i	−0.443369	−	0.155142i
$143$	18.7854	−	11.8037i	1.57092	−	0.987073i
$144$	2.65229	+	5.50753i	0.221024	+	0.458961i
$145$	8.03024	+	9.75283i	0.666876	+	0.809928i
$146$		−	14.6222i		−	1.21015i
$147$	−20.6022	−	4.69929i	−1.69924	−	0.387591i
$148$	0.579605	−	0.579605i	0.0476432	−	0.0476432i
$149$	2.54714	−	2.03128i	0.208670	−	0.166409i	−0.513578	−	0.858043i	$-0.671680\pi$
$149$	2.54714	−	2.03128i	0.208670	−	0.166409i	0.722248	+	0.691634i	$0.243109\pi$
$150$	−6.97091	−	13.3876i	−0.569172	−	1.09310i
$151$	1.37722	−	6.03399i	0.112077	−	0.491039i	−0.887468	−	0.460869i	$-0.847538\pi$
$151$	1.37722	−	6.03399i	0.112077	−	0.491039i	0.999545	−	0.0301705i	$-0.00960503\pi$
$152$	0.0207609	−	0.0593312i	0.00168393	−	0.00481240i
$153$	7.65316	+	21.8715i	0.618721	+	1.76820i
$154$	−6.90366	+	4.89913i	−0.556313	+	0.394783i
$155$	19.3358	−	9.68690i	1.55309	−	0.778071i
$156$	13.0509	−	16.3653i	1.04491	−	1.31028i
$157$	−15.3072	+	5.35620i	−1.22164	+	0.427472i	−0.862618	−	0.505856i	$-0.831177\pi$
$157$	−15.3072	+	5.35620i	−1.22164	+	0.427472i	−0.359026	+	0.933328i	$0.616891\pi$
$158$	11.6069	+	1.30779i	0.923398	+	0.104042i
$159$	−3.88810	−	17.0349i	−0.308346	−	1.35095i
$160$	2.22565	+	0.215591i	0.175953	+	0.0170439i
$161$	−0.892617	−	1.25784i	−0.0703480	−	0.0991317i
$162$	9.96576	−	1.12287i	0.782984	−	0.0882211i
$163$	7.07989	−	2.47736i	0.554540	−	0.194042i	−0.0384375	−	0.999261i	$-0.512238\pi$
$163$	7.07989	−	2.47736i	0.554540	−	0.194042i	0.592977	+	0.805219i	$0.297952\pi$
$164$	0.0805171	+	0.352768i	0.00628733	+	0.0275466i
$165$	15.0313	−	15.5088i	1.17019	−	1.20736i
$166$			9.35740i			0.726275i
$167$	−0.823807	−	0.517632i	−0.0637481	−	0.0400556i	0.499781	−	0.866152i	$-0.333414\pi$
$167$	−0.823807	−	0.517632i	−0.0637481	−	0.0400556i	−0.563529	+	0.826096i	$0.690557\pi$
$168$	−4.62133	+	6.51411i	−0.356543	+	0.502574i
$169$	−34.2008	−	7.80610i	−2.63083	−	0.600469i
$170$	8.29210	+	1.75669i	0.635975	+	0.134732i
$171$	−0.300417	−	0.239575i	−0.0229735	−	0.0183208i
$172$	−8.47343	+	0.954726i	−0.646093	+	0.0727972i
$173$	−3.21405	+	2.01952i	−0.244360	+	0.153541i	−0.648644	−	0.761092i	$-0.724663\pi$
$173$	−3.21405	+	2.01952i	−0.244360	+	0.153541i	0.404284	+	0.914633i	$0.367521\pi$
$174$	−3.79519	+	16.6278i	−0.287713	+	1.26055i
$175$	7.31329	−	11.0234i	0.552833	−	0.833292i
$176$	0.711978	+	3.11938i	0.0536674	+	0.235132i
$177$	−15.8178	−	15.8178i	−1.18894	−	1.18894i
$178$	−7.12654	−	7.12654i	−0.534157	−	0.534157i
$179$	16.8438	−	3.84449i	1.25897	−	0.287351i	0.459562	−	0.888146i	$-0.348006\pi$
$179$	16.8438	−	3.84449i	1.25897	−	0.287351i	0.799403	+	0.600795i	$0.205149\pi$
$180$	5.73743	−	12.4064i	0.427643	−	0.924720i
$181$	4.27755	+	3.41123i	0.317948	+	0.253555i	0.769438	−	0.638721i	$-0.220536\pi$
$181$	4.27755	+	3.41123i	0.317948	+	0.253555i	−0.451491	+	0.892276i	$0.649108\pi$
$182$	18.0866	+	3.07175i	1.34067	+	0.227693i
$183$	−1.11512	−	0.125644i	−0.0824318	−	0.00928784i
$184$	−0.568347	+	0.129722i	−0.0418991	+	0.00956320i
$185$	−1.82433	−	0.176717i	−0.134128	−	0.0129925i
$186$	26.3052	+	12.6679i	1.92879	+	0.928855i
$187$	1.35797	+	12.0523i	0.0993043	+	0.881350i
$188$	−3.03572	−	1.06224i	−0.221403	−	0.0774721i
$189$	14.3885	+	20.2758i	1.04661	+	1.47484i
$190$	−0.131927	+	0.0484912i	−0.00957096	+	0.00351792i
$191$	−13.8482	+	6.66895i	−1.00202	+	0.482548i	−0.861624	−	0.507547i	$-0.830552\pi$
$191$	−13.8482	+	6.66895i	−1.00202	+	0.482548i	−0.140398	+	0.990095i	$0.544838\pi$
$192$	1.60608	+	2.55606i	0.115909	+	0.184467i
$193$	−3.90593	+	11.1625i	−0.281155	+	0.803494i	0.713539	+	0.700615i	$0.247091\pi$
$193$	−3.90593	+	11.1625i	−0.281155	+	0.803494i	−0.994694	+	0.102879i	$0.967195\pi$
$194$	6.11192	+	7.66410i	0.438810	+	0.550250i
$195$	−46.7998	+	0.731757i	−3.35140	+	0.0524022i
$196$	−6.95609	−	0.782785i	−0.496864	−	0.0559132i
$197$	10.7364	+	10.7364i	0.764940	+	0.764940i	0.977211	−	0.212271i	$-0.0680859\pi$
$197$	10.7364	+	10.7364i	0.764940	+	0.764940i	−0.212271	+	0.977211i	$0.568086\pi$
$198$	19.4358	+	2.18989i	1.38125	+	0.155629i
$199$	3.03337	−	1.46080i	0.215030	−	0.103553i	−0.323268	−	0.946307i	$-0.604782\pi$
$199$	3.03337	−	1.46080i	0.215030	−	0.103553i	0.538298	+	0.842754i	$0.319067\pi$
$200$	−2.79122	−	4.14838i	−0.197369	−	0.293335i
$201$	−11.7583	−	24.4163i	−0.829364	−	1.72219i
$202$	6.50748	−	2.27707i	0.457865	−	0.160214i
$203$	−14.3635	+	4.13914i	−1.00812	+	0.290511i
$204$	4.96494	+	10.3098i	0.347616	+	0.721831i
$205$	0.494514	−	0.640389i	0.0345384	−	0.0447267i
$206$	−5.60495	+	11.6388i	−0.390515	+	0.810913i
$207$	−0.398996	+	3.54119i	−0.0277322	+	0.246130i
$208$	3.68911	−	5.87118i	0.255794	−	0.407093i
$209$	−0.125398	−	0.157244i	−0.00867395	−	0.0108768i
$210$	17.8132	−	1.28126i	1.22923	−	0.0884154i
$211$	7.59734	−	9.52676i	0.523022	−	0.655849i	−0.448225	−	0.893921i	$-0.647944\pi$
$211$	7.59734	−	9.52676i	0.523022	−	0.655849i	0.971248	+	0.238071i	$0.0765152\pi$
$212$	−1.91170	−	5.46331i	−0.131296	−	0.375222i
$213$	−8.98996	+	14.3074i	−0.615982	+	0.980329i
$214$		−	8.83631i		−	0.604038i
$215$	13.6916	+	13.2700i	0.933758	+	0.905007i
$216$	9.16148	−	2.09105i	0.623360	−	0.142278i
$217$	1.43656	+	25.5486i	0.0975199	+	1.73435i
$218$	3.71947	+	5.91951i	0.251914	+	0.400920i
$219$	−43.0343	−	9.82230i	−2.90799	−	0.663730i
$220$	4.37278	−	5.66269i	0.294813	−	0.381778i
$221$	16.3880	−	20.5499i	1.10238	−	1.38234i
$222$	−1.31648	−	2.09516i	−0.0883561	−	0.140618i
$223$	4.71059	−	2.95986i	0.315444	−	0.198207i	−0.364998	−	0.931008i	$-0.618930\pi$
$223$	4.71059	−	2.95986i	0.315444	−	0.198207i	0.680443	+	0.732801i	$0.261788\pi$
$224$	−1.27964	+	2.31571i	−0.0854995	+	0.154725i
$225$	−29.5710	+	7.72953i	−1.97140	+	0.515302i
$226$	0.624998			0.0415743
$227$	−5.19988	+	5.19988i	−0.345128	+	0.345128i	−0.858291	−	0.513163i	$-0.828474\pi$
$227$	−5.19988	+	5.19988i	−0.345128	+	0.345128i	0.513163	+	0.858291i	$0.328474\pi$
$228$	−0.160670	−	0.100956i	−0.0106406	−	0.00668596i
$229$	−2.44413	−	1.17703i	−0.161513	−	0.0777805i	0.351381	−	0.936233i	$-0.385712\pi$
$229$	−2.44413	−	1.17703i	−0.161513	−	0.0777805i	−0.512894	+	0.858452i	$0.671427\pi$
$230$	1.03174	+	0.796715i	0.0680306	+	0.0525338i
$231$	9.78105	+	23.6089i	0.643546	+	1.55335i
$232$	−0.632579	+	5.61430i	−0.0415309	+	0.368597i
$233$	−14.5263	−	9.12745i	−0.951647	−	0.597959i	−0.0357448	−	0.999361i	$-0.511380\pi$
$233$	−14.5263	−	9.12745i	−0.951647	−	0.597959i	−0.915902	+	0.401402i	$0.868523\pi$
$234$	−26.4277	−	33.1393i	−1.72764	−	2.16639i
$235$	2.48108	+	6.75011i	0.161848	+	0.440328i
$236$	−5.79355	−	4.62020i	−0.377128	−	0.300749i
$237$	11.6457	−	33.2816i	0.756471	−	2.16187i
$238$	−5.80298	+	8.17974i	−0.376151	+	0.530214i
$239$	6.10417	−	12.6754i	0.394846	−	0.819906i	−0.604876	−	0.796320i	$-0.706777\pi$
$239$	6.10417	−	12.6754i	0.394846	−	0.819906i	0.999722	−	0.0235860i	$-0.00750837\pi$
$240$	2.12955	−	6.40543i	0.137462	−	0.413469i
$241$	−27.7341	−	6.33012i	−1.78651	−	0.407759i	−0.804099	−	0.594495i	$-0.797352\pi$
$241$	−27.7341	−	6.33012i	−1.78651	−	0.407759i	−0.982410	+	0.186736i	$0.940209\pi$
$242$	−0.719767	−	0.251857i	−0.0462684	−	0.0161900i
$243$	0.233259	−	2.07023i	0.0149636	−	0.132805i
$244$	−0.371734			−0.0237978
$245$	8.53563	+	13.1203i	0.545321	+	0.838227i
$246$	1.09231			0.0696430
$247$	−0.0488010	+	0.433121i	−0.00310513	+	0.0275588i
$248$	9.12896	+	3.19436i	0.579690	+	0.202842i
$249$	27.5395	+	6.28571i	1.74524	+	0.398341i
$250$	−3.19378	+	10.7145i	−0.201992	+	0.677642i
$251$	3.81764	−	7.92741i	0.240967	−	0.500374i	−0.745052	−	0.667007i	$-0.767575\pi$
$251$	3.81764	−	7.92741i	0.240967	−	0.500374i	0.986019	+	0.166633i	$0.0532895\pi$
$252$	10.7778	+	12.0587i	0.678937	+	0.759625i
$253$	−0.616053	+	1.76058i	−0.0387309	+	0.110687i
$254$	−6.04373	−	4.81971i	−0.379217	−	0.302416i
$255$	10.7402	−	23.2242i	0.672576	−	1.45436i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	6.20170	+	3.89679i	0.386851	+	0.243075i	0.711390	−	0.702798i	$-0.248066\pi$
$257$	6.20170	+	3.89679i	0.386851	+	0.243075i	−0.324538	+	0.945873i	$0.605209\pi$
$258$	−2.88209	+	25.5792i	−0.179431	+	1.59249i
$259$	1.04890	−	1.89816i	0.0651756	−	0.117946i
$260$	−15.3784	+	1.97666i	−0.953726	+	0.122587i
$261$	31.1166	+	14.9849i	1.92607	+	0.927545i
$262$	16.2036	+	10.1814i	1.00106	+	0.629010i
$263$	−4.47348	+	4.47348i	−0.275847	+	0.275847i	−0.831448	−	0.555602i	$-0.812488\pi$
$263$	−4.47348	+	4.47348i	−0.275847	+	0.275847i	0.555602	+	0.831448i	$0.312488\pi$
$264$	9.65882			0.594459
$265$	−6.71373	+	11.0652i	−0.412421	+	0.679727i
$266$	0.00931344	−	0.166047i	0.000571044	−	0.0101810i
$267$	−25.7611	+	16.1868i	−1.57655	+	0.990614i
$268$	−4.77617	−	7.60123i	−0.291751	−	0.464319i
$269$	10.6785	−	13.3905i	0.651082	−	0.816432i	−0.341257	−	0.939970i	$-0.610853\pi$
$269$	10.6785	−	13.3905i	0.651082	−	0.816432i	0.992340	+	0.123538i	$0.0394242\pi$
$270$	−16.6311	−	12.8426i	−1.01213	−	0.781579i
$271$	−17.1212	−	3.90780i	−1.04004	−	0.237382i	−0.331795	−	0.943351i	$-0.607654\pi$
$271$	−17.1212	−	3.90780i	−1.04004	−	0.237382i	−0.708242	+	0.705970i	$0.750511\pi$
$272$	2.01674	+	3.20963i	0.122283	+	0.194612i
$273$	21.1898	−	51.1668i	1.28247	−	3.09676i
$274$	−20.2420	+	4.62010i	−1.22286	+	0.279111i
$275$	−15.9902	+	0.500164i	−0.964244	+	0.0301610i
$276$			1.75983i			0.105929i
$277$	−3.64759	+	5.80510i	−0.219162	+	0.348795i	−0.938151	−	0.346227i	$-0.887463\pi$
$277$	−3.64759	+	5.80510i	−0.219162	+	0.348795i	0.718988	+	0.695022i	$0.244605\pi$
$278$	−4.26460	−	12.1875i	−0.255774	−	0.730960i
$279$	36.8620	−	46.2235i	2.20687	−	2.76733i
$280$	5.81621	−	1.08245i	0.347585	−	0.0646887i
$281$	−4.69831	−	5.89150i	−0.280278	−	0.351457i	0.621688	−	0.783265i	$-0.286447\pi$
$281$	−4.69831	−	5.89150i	−0.280278	−	0.351457i	−0.901966	+	0.431808i	$0.857876\pi$
$282$	−5.16546	+	8.22079i	−0.307599	+	0.489541i
$283$	−1.80243	+	15.9970i	−0.107144	+	0.950925i	0.819010	+	0.573779i	$0.194523\pi$
$283$	−1.80243	+	15.9970i	−0.107144	+	0.950925i	−0.926154	+	0.377146i	$0.876905\pi$
$284$	−2.42865	+	5.04314i	−0.144114	+	0.299256i
$285$	0.0540932	+	0.420843i	0.00320420	+	0.0249286i
$286$	−9.62615	−	19.9889i	−0.569206	−	1.18197i
$287$	0.463141	+	0.837854i	0.0273384	+	0.0494569i
$288$	5.76986	−	2.01896i	0.339992	−	0.118968i
$289$	−1.14156	−	2.37048i	−0.0671508	−	0.139440i
$290$	10.5906	−	6.88778i	0.621902	−	0.404464i
$291$	26.6616	−	12.8395i	1.56293	−	0.752668i
$292$	−14.5303	−	1.63717i	−0.850322	−	0.0958082i
$293$	−17.8318	−	17.8318i	−1.04175	−	1.04175i	−0.999090	−	0.0426567i	$-0.986418\pi$
$293$	−17.8318	−	17.8318i	−1.04175	−	1.04175i	−0.0426567	−	0.999090i	$-0.513582\pi$
$294$	−6.97645	+	19.9465i	−0.406875	+	1.16330i
$295$	0.259052	+	16.5677i	0.0150826	+	0.964612i
$296$	−0.511065	−	0.640856i	−0.0297051	−	0.0372490i
$297$	9.93047	−	28.3796i	0.576224	−	1.64675i
$298$	−1.73332	−	2.75856i	−0.100408	−	0.159799i
$299$	3.64196	−	1.75387i	0.210620	−	0.101429i
$300$	−14.0840	+	5.42814i	−0.813137	+	0.313394i
$301$	−20.8425	+	8.63496i	−1.20134	+	0.497711i
$302$	−5.84185	−	2.04415i	−0.336161	−	0.117628i
$303$	−2.33025	−	20.6816i	−0.133870	−	1.18812i
$304$	−0.0566337	−	0.0272733i	−0.00324816	−	0.00156423i
$305$	0.528355	+	0.641693i	0.0302535	+	0.0367432i
$306$	22.5908	−	5.15621i	1.29143	−	0.294761i
$307$	25.7191	+	2.89785i	1.46787	+	0.165389i	0.809417	−	0.587234i	$-0.199783\pi$
$307$	25.7191	+	2.89785i	1.46787	+	0.165389i	0.658451	+	0.752623i	$0.271212\pi$
$308$	4.09536	+	7.40878i	0.233355	+	0.422155i
$309$	30.4887	+	24.3140i	1.73444	+	1.38317i
$310$	−7.46107	−	20.2988i	−0.423760	−	1.15289i
$311$	16.8159	−	3.83813i	0.953544	−	0.217640i	0.282675	−	0.959216i	$-0.408778\pi$
$311$	16.8159	−	3.83813i	0.953544	−	0.217640i	0.670869	+	0.741576i	$0.265921\pi$
$312$	−14.8012	−	14.8012i	−0.837953	−	0.837953i
$313$	13.2374	+	13.2374i	0.748224	+	0.748224i	0.974146	−	0.225922i	$-0.0725393\pi$
$313$	13.2374	+	13.2374i	0.748224	+	0.748224i	−0.225922	+	0.974146i	$0.572539\pi$
$314$	3.60867	+	15.8106i	0.203649	+	0.892244i
$315$	5.49713	−	35.7442i	0.309728	−	2.01395i
$316$	2.59913	−	11.3875i	0.146212	−	0.640599i
$317$	−0.536362	+	0.337018i	−0.0301251	+	0.0189288i	−0.547010	−	0.837126i	$-0.684234\pi$
$317$	−0.536362	+	0.337018i	−0.0301251	+	0.0189288i	0.516885	+	0.856055i	$0.327091\pi$
$318$	−17.3631	+	1.95635i	−0.973673	+	0.109707i
$319$	14.1333	+	11.2709i	0.791313	+	0.631051i
$320$	0.463429	−	2.18752i	0.0259065	−	0.122286i
$321$	−26.0059	−	5.93568i	−1.45151	−	0.331297i
$322$	−1.34987	+	0.746171i	−0.0752254	+	0.0415825i
$323$	−0.201753	−	0.126770i	−0.0112258	−	0.00705366i
$324$		−	10.0288i		−	0.557157i
$325$	25.2698	+	23.7369i	1.40172	+	1.31669i
$326$	−1.66909	−	7.31275i	−0.0924422	−	0.405016i
$327$	19.9200	−	6.97032i	1.10158	−	0.385460i
$328$	0.359565	−	0.0405133i	0.0198537	−	0.00223697i
$329$	−8.49591	−	0.476528i	−0.468395	−	0.0262718i
$330$	−13.7283	−	16.6732i	−0.755720	−	0.917831i
$331$	1.99132	+	8.72455i	0.109453	+	0.479544i	0.999710	+	0.0240859i	$0.00766753\pi$
$331$	1.99132	+	8.72455i	0.109453	+	0.479544i	−0.890257	+	0.455459i	$0.849475\pi$
$332$	9.29856	+	1.04770i	0.510325	+	0.0574998i
$333$	−4.72947	+	1.65491i	−0.259173	+	0.0906887i
$334$	−0.606614	+	0.760670i	−0.0331925	+	0.0416220i
$335$	−6.33288	+	19.0485i	−0.346002	+	1.04073i
$336$	5.95573	+	5.32162i	0.324911	+	0.290318i
$337$	10.8942	+	31.1338i	0.593444	+	1.69596i	0.711260	+	0.702929i	$0.248125\pi$
$337$	10.8942	+	31.1338i	0.593444	+	1.69596i	−0.117816	+	0.993035i	$0.537589\pi$
$338$	−11.5863	+	33.1117i	−0.630211	+	1.80104i
$339$	0.419834	−	1.83941i	0.0228023	−	0.0999033i
$340$	2.67407	−	8.04327i	0.145022	−	0.436208i
$341$	24.1942	−	19.2943i	1.31019	−	1.04484i
$342$	−0.271705	+	0.271705i	−0.0146921	+	0.0146921i
$343$	−18.2579	+	3.10607i	−0.985836	+	0.167712i
$344$			8.52705i			0.459748i
$345$	3.03784	−	2.50129i	0.163552	−	0.134665i
$346$	1.64696	+	3.41995i	0.0885413	+	0.183858i
$347$	−6.69896	+	4.20924i	−0.359619	+	0.225964i	−0.699707	−	0.714430i	$-0.746686\pi$
$347$	−6.69896	+	4.20924i	−0.359619	+	0.225964i	0.340088	+	0.940394i	$0.389543\pi$
$348$	16.0983	+	5.63306i	0.862962	+	0.301963i
$349$	4.54614	+	2.18931i	0.243350	+	0.117191i	0.551584	−	0.834120i	$-0.314024\pi$
$349$	4.54614	+	2.18931i	0.243350	+	0.117191i	−0.308234	+	0.951311i	$0.599738\pi$
$350$	−10.1353	−	8.50154i	−0.541753	−	0.454426i
$351$	−58.7065	+	28.2716i	−3.13352	+	1.50902i
$352$	3.17948	−	0.358242i	0.169467	−	0.0190943i
$353$	0.988265	+	2.82430i	0.0526001	+	0.150322i	0.967186	−	0.254069i	$-0.0817691\pi$
$353$	0.988265	+	2.82430i	0.0526001	+	0.150322i	−0.914586	+	0.404391i	$0.867483\pi$
$354$	−17.4893	+	13.9473i	−0.929547	+	0.741289i
$355$	12.1575	−	2.97558i	0.645252	−	0.157927i
$356$	−7.87965	+	6.28381i	−0.417621	+	0.333041i
$357$	20.1755	+	22.5732i	1.06780	+	1.19470i
$358$	−1.93441	−	17.1683i	−0.102237	−	0.907375i
$359$	−5.74928	+	11.9385i	−0.303436	+	0.630091i	−0.995810	−	0.0914480i	$-0.970850\pi$
$359$	−5.74928	+	11.9385i	−0.303436	+	0.630091i	0.692374	+	0.721539i	$0.256565\pi$
$360$	−11.6860	−	7.09044i	−0.615908	−	0.373699i
$361$	−18.9960			−0.999792
$362$	3.86872	−	3.86872i	0.203335	−	0.203335i
$363$	−1.22473	+	1.94914i	−0.0642815	+	0.102303i
$364$	5.07750	−	17.6290i	0.266133	−	0.924010i
$365$	17.8262	+	27.4094i	0.933066	+	1.43468i
$366$	−0.249707	+	1.09404i	−0.0130524	+	0.0571863i
$367$	−0.387828	−	3.44207i	−0.0202445	−	0.179675i	0.979521	−	0.201343i	$-0.0645307\pi$
$367$	−0.387828	−	3.44207i	−0.0202445	−	0.179675i	−0.999765	+	0.0216687i	$0.993102\pi$
$368$	0.0652712	+	0.579298i	0.00340250	+	0.0301980i
$369$	0.492192	−	2.15644i	0.0256225	−	0.112260i
$370$	−0.379866	+	1.79308i	−0.0197483	+	0.0932176i
$371$	−8.86260	−	12.4888i	−0.460123	−	0.648388i
$372$	15.5335	−	24.7214i	0.805374	−	1.28175i
$373$	−5.24073	+	5.24073i	−0.271355	+	0.271355i	−0.829645	−	0.558291i	$-0.811457\pi$
$373$	−5.24073	+	5.24073i	−0.271355	+	0.271355i	0.558291	+	0.829645i	$0.311457\pi$
$374$	12.1285			0.627152
$375$	29.3881	+	16.5968i	1.51759	+	0.857056i
$376$	−1.39546	+	2.89770i	−0.0719652	+	0.149437i
$377$	−4.38630	−	38.9295i	−0.225906	−	2.00497i
$378$	21.7593	−	12.0279i	1.11918	−	0.618648i
$379$	17.2268	−	13.7379i	0.884881	−	0.705669i	−0.0716093	−	0.997433i	$-0.522813\pi$
$379$	17.2268	−	13.7379i	0.884881	−	0.705669i	0.956490	+	0.291764i	$0.0942420\pi$
$380$	0.0334152	+	0.136526i	0.00171417	+	0.00700366i
$381$	−18.2445	+	14.5495i	−0.934696	+	0.745396i
$382$	5.07651	+	14.5078i	0.259737	+	0.742285i
$383$	12.8148	−	1.44388i	0.654805	−	0.0737788i	0.221690	−	0.975117i	$-0.428843\pi$
$383$	12.8148	−	1.44388i	0.654805	−	0.0737788i	0.433115	+	0.901339i	$0.357414\pi$
$384$	2.71981	−	1.30979i	0.138795	−	0.0668399i
$385$	6.96833	−	17.5998i	0.355139	−	0.896969i
$386$	10.6550	+	5.13117i	0.542324	+	0.261170i
$387$	49.1999	+	17.2158i	2.50097	+	0.875127i
$388$	8.30023	−	5.21538i	0.421380	−	0.264771i
$389$	−5.91417	−	12.2809i	−0.299860	−	0.622666i	0.695538	−	0.718489i	$-0.255166\pi$
$389$	−5.91417	−	12.2809i	−0.299860	−	0.622666i	−0.995398	+	0.0958231i	$0.969452\pi$
$390$	−4.51276	+	46.5874i	−0.228512	+	2.35905i
$391$			2.20981i			0.111755i
$392$	−1.55670	+	6.82471i	−0.0786251	+	0.344700i
$393$	40.8492	−	40.8492i	2.06057	−	2.06057i
$394$	11.8710	−	9.46684i	0.598054	−	0.476932i
$395$	−23.3516	+	11.6987i	−1.17495	+	0.588628i
$396$	4.35225	−	19.0684i	0.218709	−	0.958225i
$397$	8.50153	−	24.2960i	0.426679	−	1.21938i	−0.507212	−	0.861822i	$-0.669324\pi$
$397$	8.50153	−	24.2960i	0.426679	−	1.21938i	0.933891	−	0.357558i	$-0.116391\pi$
$398$	−1.11198	−	3.17786i	−0.0557385	−	0.159292i
$399$	−0.482433	−	0.138950i	−0.0241519	−	0.00695621i
$400$	−4.43482	+	2.30920i	−0.221741	+	0.115460i
$401$	−5.57931	+	6.99623i	−0.278617	+	0.349375i	−0.901375	−	0.433040i	$-0.857441\pi$
$401$	−5.57931	+	6.99623i	−0.278617	+	0.349375i	0.622757	+	0.782415i	$0.286012\pi$
$402$	−25.5793	+	8.95058i	−1.27578	+	0.446414i
$403$	−66.6419	−	7.50874i	−3.31967	−	0.374037i
$404$	−1.53414	−	6.72151i	−0.0763264	−	0.334408i
$405$	−17.3119	+	14.2542i	−0.860237	+	0.708298i
$406$	2.50491	+	14.7367i	0.124317	+	0.731368i
$407$	−2.60617	+	0.293645i	−0.129183	+	0.0145555i
$408$	10.8009	−	3.77939i	0.534723	−	0.187108i
$409$	−5.92913	−	25.9772i	−0.293176	−	1.28449i	−0.880077	−	0.474831i	$-0.842509\pi$
$409$	−5.92913	−	25.9772i	−0.293176	−	1.28449i	0.586901	−	0.809659i	$-0.300348\pi$
$410$	−0.580994	−	0.563105i	−0.0286933	−	0.0278098i
$411$			62.6771i			3.09163i
$412$	10.9381	+	6.87283i	0.538879	+	0.338600i
$413$	−18.1138	−	7.50149i	−0.891319	−	0.369124i
$414$	3.47425	+	0.792975i	0.170750	+	0.0389726i
$415$	−11.4077	−	17.5405i	−0.559984	−	0.861028i
$416$	−5.42122	−	4.32328i	−0.265797	−	0.211966i
$417$	−38.7335	+	4.36421i	−1.89679	+	0.213716i
$418$	−0.170295	+	0.107004i	−0.00832941	+	0.00523372i
$419$	−6.17168	+	27.0399i	−0.301506	+	1.32099i	0.566347	+	0.824167i	$0.308356\pi$
$419$	−6.17168	+	27.0399i	−0.301506	+	1.32099i	−0.867854	+	0.496820i	$0.834501\pi$
$420$	0.721240	−	17.8446i	0.0351929	−	0.870729i
$421$	−5.59848	−	24.5285i	−0.272853	−	1.19545i	−0.906628	−	0.421930i	$-0.861353\pi$
$421$	−5.59848	−	24.5285i	−0.272853	−	1.19545i	0.633775	−	0.773517i	$-0.281504\pi$
$422$	−8.61623	−	8.61623i	−0.419431	−	0.419431i
$423$	13.9019	+	13.9019i	0.675935	+	0.675935i
$424$	−5.64300	+	1.28798i	−0.274048	+	0.0625498i
$425$	−17.6852	+	6.81609i	−0.857856	+	0.330629i
$426$	13.2109	+	10.5354i	0.640071	+	0.510440i
$427$	−0.945057	+	0.272337i	−0.0457345	+	0.0131793i
$428$	−8.78075	−	0.989353i	−0.424434	−	0.0478222i
$429$	−65.2950	+	14.9032i	−3.15247	+	0.719531i
$430$	14.7195	−	12.1197i	0.709839	−	0.584465i
$431$	7.63678	+	3.67768i	0.367851	+	0.177148i	0.608672	−	0.793422i	$-0.291703\pi$
$431$	7.63678	+	3.67768i	0.367851	+	0.177148i	−0.240821	+	0.970569i	$0.577417\pi$
$432$	−1.05214	−	9.33799i	−0.0506211	−	0.449274i
$433$	17.4395	+	6.10236i	0.838091	+	0.293261i	0.714991	−	0.699133i	$-0.246431\pi$
$433$	17.4395	+	6.10236i	0.838091	+	0.293261i	0.123100	+	0.992394i	$0.460716\pi$
$434$	25.5488	+	1.43301i	1.22638	+	0.0687865i
$435$	−13.1571	−	35.7957i	−0.630836	−	1.71627i
$436$	6.29874	−	3.03331i	0.301655	−	0.145269i
$437$	−0.0194959	−	0.0310276i	−0.000932617	−	0.00148425i
$438$	−14.5789	+	41.6640i	−0.696605	+	1.99078i
$439$	3.91183	+	4.90528i	0.186701	+	0.234116i	0.866369	−	0.499404i	$-0.166448\pi$
$439$	3.91183	+	4.90528i	0.186701	+	0.234116i	−0.679668	+	0.733520i	$0.737876\pi$
$440$	−5.13749	−	4.97930i	−0.244920	−	0.237379i
$441$	36.2347	+	22.7608i	1.72546	+	1.08385i
$442$	−18.5858	−	18.5858i	−0.884036	−	0.884036i
$443$	29.9722	+	3.37706i	1.42402	+	0.160449i	0.790114	−	0.612959i	$-0.210021\pi$
$443$	29.9722	+	3.37706i	1.42402	+	0.160449i	0.633908	+	0.773408i	$0.281450\pi$
$444$	−2.22939	+	1.07362i	−0.105802	+	0.0509515i
$445$	22.0468	+	4.67065i	1.04512	+	0.221410i
$446$	−2.41383	−	5.01237i	−0.114298	−	0.237343i
$447$	−9.28297	+	3.24825i	−0.439069	+	0.153637i
$448$	2.15788	+	1.53087i	0.101950	+	0.0723268i
$449$	10.5131	+	21.8307i	0.496144	+	1.03025i	0.987254	+	0.159155i	$0.0508771\pi$
$449$	10.5131	+	21.8307i	0.496144	+	1.03025i	−0.491110	+	0.871098i	$0.663409\pi$
$450$	4.37003	+	30.2505i	0.206005	+	1.42602i
$451$	0.502326	−	1.04309i	0.0236536	−	0.0491173i
$452$	0.0699776	−	0.621069i	0.00329147	−	0.0292126i
$453$	−9.94027	+	15.8199i	−0.467035	+	0.743282i
$454$	4.58498	+	5.74939i	0.215184	+	0.269832i
$455$	−37.6483	+	16.2917i	−1.76498	+	0.763766i
$456$	−0.118310	+	0.148356i	−0.00554039	+	0.00694743i
$457$	−2.34872	−	6.71226i	−0.109869	−	0.313986i	0.875801	−	0.482672i	$-0.160334\pi$
$457$	−2.34872	−	6.71226i	−0.109869	−	0.313986i	−0.985670	+	0.168685i	$0.946048\pi$
$458$	−1.44329	+	2.29698i	−0.0674404	+	0.107331i
$459$		−	35.6210i		−	1.66264i
$460$	0.907223	−	0.936044i	0.0422995	−	0.0436433i
$461$	31.3543	−	7.15642i	1.46032	−	0.333308i	0.582707	−	0.812682i	$-0.301994\pi$
$461$	31.3543	−	7.15642i	1.46032	−	0.333308i	0.877610	+	0.479375i	$0.159136\pi$
$462$	24.5556	−	7.07619i	1.14243	−	0.329214i
$463$	−13.3420	−	21.2337i	−0.620056	−	0.986813i	−0.998135	−	0.0610403i	$-0.980558\pi$
$463$	−13.3420	−	21.2337i	−0.620056	−	0.986813i	0.378079	−	0.925773i	$-0.376585\pi$
$464$	5.50817	+	1.25720i	0.255710	+	0.0583642i
$465$	−64.7527	+	8.32301i	−3.00284	+	0.385970i
$466$	−10.6965	+	13.4130i	−0.495505	+	0.621344i
$467$	10.1274	+	16.1177i	0.468642	+	0.745839i	0.994500	−	0.104733i	$-0.0333987\pi$
$467$	10.1274	+	16.1177i	0.468642	+	0.745839i	−0.525858	+	0.850572i	$0.676256\pi$
$468$	−35.8899	+	22.5511i	−1.65901	+	1.04243i
$469$	−17.7112	−	15.8255i	−0.817828	−	0.730753i
$470$	6.98546	−	1.70971i	0.322215	−	0.0788631i
$471$	48.9558			2.25576
$472$	−5.23982	+	5.23982i	−0.241182	+	0.241182i
$473$	23.1013	+	14.5155i	1.06220	+	0.667424i
$474$	−31.7684	−	15.2988i	−1.45917	−	0.702699i
$475$	0.188180	−	0.251731i	0.00863431	−	0.0115502i
$476$	7.47858	+	6.68233i	0.342780	+	0.306284i
$477$	−3.96155	+	35.1597i	−0.181387	+	1.60985i
$478$	−11.9123	−	7.48498i	−0.544855	−	0.342355i
$479$	20.8340	+	26.1250i	0.951929	+	1.19368i	0.980981	+	0.194103i	$0.0621796\pi$
$479$	20.8340	+	26.1250i	0.951929	+	1.19368i	−0.0290523	+	0.999578i	$0.509249\pi$
$480$	−6.12672	−	2.83334i	−0.279645	−	0.129324i
$481$	4.44369	+	3.54373i	0.202615	+	0.161580i
$482$	−9.39555	+	26.8509i	−0.427956	+	1.22303i
$483$	1.28927	+	4.47400i	0.0586640	+	0.203574i
$484$	−0.330862	+	0.687042i	−0.0150392	+	0.0312292i
$485$	−20.8002	−	6.91525i	−0.944490	−	0.314005i
$486$	−2.03109	−	0.463584i	−0.0921323	−	0.0210286i
$487$	−4.83666	−	1.69242i	−0.219170	−	0.0766909i	0.218461	−	0.975846i	$-0.429897\pi$
$487$	−4.83666	−	1.69242i	−0.219170	−	0.0766909i	−0.437631	+	0.899155i	$0.644182\pi$
$488$	−0.0416209	+	0.369396i	−0.00188409	+	0.0167218i
$489$	−22.6431			−1.02396
$490$	13.9935	−	7.01295i	0.632163	−	0.316813i
$491$	−34.1101			−1.53937			−0.769685	−	0.638424i	$-0.779587\pi$
$491$	−34.1101			−1.53937			−0.769685	+	0.638424i	$0.779587\pi$
$492$	0.122300	−	1.08544i	0.00551370	−	0.0489354i
$493$	20.2146	+	7.07341i	0.910421	+	0.318570i
$494$	0.424934	+	0.0969883i	0.0191187	+	0.00436371i
$495$	−39.1023	+	19.5896i	−1.75752	+	0.880485i
$496$	4.19639	−	8.71390i	0.188424	−	0.391266i
$497$	−2.47967	+	14.6004i	−0.111228	+	0.654919i
$498$	9.32963	−	26.6625i	0.418071	−	1.19478i
$499$	13.5363	+	10.7949i	0.605969	+	0.483244i	0.877753	−	0.479114i	$-0.159042\pi$
$499$	13.5363	+	10.7949i	0.605969	+	0.483244i	−0.271784	+	0.962358i	$0.587613\pi$
$500$	10.2895	+	4.37334i	0.460161	+	0.195582i
$501$	1.83122	+	2.29628i	0.0818130	+	0.102590i
$502$	−7.45013	−	4.68123i	−0.332515	−	0.208933i
$503$	4.11710	−	36.5403i	0.183572	−	1.62925i	−0.477292	−	0.878745i	$-0.658382\pi$
$503$	4.11710	−	36.5403i	0.183572	−	1.62925i	0.660865	−	0.750505i	$-0.270190\pi$
$504$	13.1896	−	9.35989i	0.587511	−	0.416922i
$505$	−9.42228	+	12.2017i	−0.419286	+	0.542970i
$506$	1.68053	+	0.809302i	0.0747088	+	0.0359779i
$507$	89.6672	+	56.3416i	3.98226	+	2.50222i
$508$	−5.46609	+	5.46609i	−0.242518	+	0.242518i
$509$	−16.9394			−0.750824			−0.375412	−	0.926858i	$-0.622499\pi$
$509$	−16.9394			−0.750824			−0.375412	+	0.926858i	$0.622499\pi$
$510$	−21.8756	−	13.2729i	−0.968670	−	0.587735i
$511$	−38.1398	+	6.48293i	−1.68720	+	0.286788i
$512$	0.846724	−	0.532032i	0.0374203	−	0.0235127i
$513$	0.314265	+	0.500150i	0.0138751	+	0.0220821i
$514$	4.56665	−	5.72640i	0.201426	−	0.252581i
$515$	−3.68254	−	28.6500i	−0.162272	−	1.26247i
$516$	25.0957	+	5.72793i	1.10478	+	0.252158i
$517$	5.47491	+	8.71326i	0.240786	+	0.383209i
$518$	−1.76878	−	1.25483i	−0.0777158	−	0.0551342i
$519$	11.1715	−	2.54982i	0.490374	−	0.111925i
$520$	0.242403	+	15.5030i	0.0106301	+	0.679851i
$521$			20.9736i			0.918870i	0.888211	+	0.459435i	$0.151948\pi$
$521$			20.9736i			0.918870i	−0.888211	+	0.459435i	$0.848052\pi$
$522$	18.3747	−	29.2431i	0.804238	−	1.27994i
$523$	4.08023	+	11.6606i	0.178416	+	0.509883i	0.998010	−	0.0630617i	$-0.0200865\pi$
$523$	4.08023	+	11.6606i	0.178416	+	0.509883i	−0.819594	+	0.572945i	$0.805801\pi$
$524$	11.9316	−	14.9618i	0.521236	−	0.653609i
$525$	−31.8289	+	24.1181i	−1.38913	+	1.05260i
$526$	3.94448	+	4.94622i	0.171988	+	0.215666i
$527$	19.5053	−	31.0426i	0.849666	−	1.35224i
$528$	1.08144	−	9.59808i	0.0470638	−	0.417703i
$529$	9.83187	−	20.4161i	0.427473	−	0.887656i
$530$	10.2439	+	7.91042i	0.444966	+	0.343607i
$531$	19.6540	+	40.8120i	0.852913	+	1.77109i
$532$	−0.163960	−	0.0278463i	−0.00710859	−	0.00120729i
$533$	−2.36820	+	0.828670i	−0.102578	+	0.0358937i
$534$	13.2007	+	27.4114i	0.571248	+	1.18621i
$535$	10.7725	+	16.5637i	0.465735	+	0.716111i
$536$	−8.08819	+	3.89507i	−0.349357	+	0.168241i
$537$	−51.8271	−	5.83951i	−2.23650	−	0.251993i
$538$	−12.1107	−	12.1107i	−0.522128	−	0.522128i
$539$	15.8394	+	15.8350i	0.682252	+	0.682062i
$540$	−14.6240	+	15.0886i	−0.629316	+	0.649308i
$541$	14.7342	+	18.4761i	0.633472	+	0.794349i	0.990170	−	0.139871i	$-0.0446687\pi$
$541$	14.7342	+	18.4761i	0.633472	+	0.794349i	−0.356697	+	0.934220i	$0.616097\pi$
$542$	−5.80019	+	16.5760i	−0.249139	+	0.711999i
$543$	−8.78715	−	13.9847i	−0.377093	−	0.600139i
$544$	3.41525	−	1.64470i	0.146428	−	0.0705158i
$545$	−14.1887	−	6.56167i	−0.607778	−	0.281071i
$546$	−48.4726	−	26.7855i	−2.07444	−	1.14631i
$547$	−4.32500	−	1.51338i	−0.184924	−	0.0647076i	0.236229	−	0.971697i	$-0.424089\pi$
$547$	−4.32500	−	1.51338i	−0.184924	−	0.0647076i	−0.421152	+	0.906990i	$0.638374\pi$
$548$	2.32467	+	20.6320i	0.0993049	+	0.881355i
$549$	2.04733	+	0.985944i	0.0873781	+	0.0420791i
$550$	−1.29331	+	15.9456i	−0.0551470	+	0.679924i
$551$	−0.346236	+	0.0790261i	−0.0147501	+	0.00336663i
$552$	1.74876	+	0.197038i	0.0744322	+	0.00838649i
$553$	−1.73491	−	30.8547i	−0.0737759	−	1.31207i
$554$	5.36020	+	4.27462i	0.227733	+	0.181611i
$555$	5.02198	+	2.32245i	0.213171	+	0.0985824i
$556$	−12.5884	+	2.87322i	−0.533866	+	0.121851i
$557$	−5.77704	−	5.77704i	−0.244781	−	0.244781i	0.574044	−	0.818825i	$-0.305374\pi$
$557$	−5.77704	−	5.77704i	−0.244781	−	0.244781i	−0.818825	+	0.574044i	$0.805374\pi$
$558$	−41.8057	−	41.8057i	−1.76977	−	1.76977i
$559$	−13.1569	−	57.6441i	−0.556477	−	2.43808i
$560$	−0.424433	−	5.90084i	−0.0179356	−	0.249356i
$561$	8.14718	−	35.6951i	0.343974	−	1.50705i
$562$	−6.38050	+	4.00913i	−0.269145	+	0.169115i
$563$	−33.8225	+	3.81088i	−1.42545	+	0.160609i	−0.790745	−	0.612146i	$-0.790306\pi$
$563$	−33.8225	+	3.81088i	−1.42545	+	0.160609i	−0.634704	+	0.772756i	$0.718878\pi$
$564$	7.59075	+	6.05342i	0.319628	+	0.254895i
$565$	−1.17156	+	0.761945i	−0.0492879	+	0.0320553i
$566$	15.6946	+	3.58220i	0.659695	+	0.150571i
$567$	−7.34726	−	25.4962i	−0.308556	−	1.07074i
$568$	4.73951	+	2.97803i	0.198866	+	0.124955i
$569$			27.2578i			1.14270i	0.820705	+	0.571352i	$0.193581\pi$
$569$			27.2578i			1.14270i	−0.820705	+	0.571352i	$0.806419\pi$
$570$	0.424253	−	0.00663358i	0.0177700	−	0.000277850i
$571$	1.36873	+	5.99681i	0.0572797	+	0.250959i	0.995459	−	0.0951907i	$-0.0303461\pi$
$571$	1.36873	+	5.99681i	0.0572797	+	0.250959i	−0.938179	+	0.346150i	$0.887489\pi$
$572$	−20.9410	+	7.32758i	−0.875588	+	0.306381i
$573$	46.1077	−	5.19509i	1.92618	−	0.217028i
$574$	0.884441	−	0.366419i	0.0369159	−	0.0152941i
$575$	−2.90528	−	0.235640i	−0.121158	−	0.00982687i
$576$	−1.36025	−	5.95963i	−0.0566770	−	0.248318i
$577$	3.42779	+	0.386220i	0.142701	+	0.0160785i	0.183026	−	0.983108i	$-0.441411\pi$
$577$	3.42779	+	0.386220i	0.142701	+	0.0160785i	−0.0403250	+	0.999187i	$0.512839\pi$
$578$	−2.48339	+	0.868975i	−0.103295	+	0.0361446i
$579$	22.2587	−	27.9116i	0.925042	−	1.15997i
$580$	−5.65870	−	11.2952i	−0.234965	−	0.469008i
$581$	24.4073	−	4.14871i	1.01258	−	0.172117i
$582$	−9.77366	−	27.9315i	−0.405131	−	1.15780i
$583$	−6.11666	+	17.4804i	−0.253326	+	0.723965i
$584$	−3.25376	+	14.2556i	−0.134641	+	0.589902i
$585$	89.9395	+	29.9013i	3.71854	+	1.23627i
$586$	−19.7162	+	15.7232i	−0.814470	+	0.649518i
$587$	−22.9645	+	22.9645i	−0.947845	+	0.947845i	−0.998706	−	0.0508606i	$-0.983804\pi$
$587$	−22.9645	+	22.9645i	−0.947845	+	0.947845i	0.0508606	+	0.998706i	$0.483804\pi$
$588$	19.0399	+	9.16588i	0.785193	+	0.377995i
$589$			0.607950i			0.0250501i
$590$	16.4926	+	1.59758i	0.678989	+	0.0657712i
$591$	−19.8874	−	41.2965i	−0.818057	−	1.69871i
$592$	−0.694047	+	0.436099i	−0.0285252	+	0.0179236i
$593$	−23.5804	−	8.25112i	−0.968329	−	0.338833i	−0.200647	−	0.979664i	$-0.564304\pi$
$593$	−23.5804	−	8.25112i	−0.968329	−	0.338833i	−0.767682	+	0.640831i	$0.778590\pi$
$594$	−27.0893	−	13.0455i	−1.11149	−	0.535265i
$595$	0.905658	−	22.4074i	0.0371284	−	0.918616i
$596$	−2.93528	+	1.41356i	−0.120234	+	0.0579016i
$597$	−10.0996	+	1.13795i	−0.413350	+	0.0465733i
$598$	−1.33508	−	3.81543i	−0.0545953	−	0.156024i
$599$	13.7320	−	10.9509i	0.561075	−	0.447443i	−0.301432	−	0.953488i	$-0.597464\pi$
$599$	13.7320	−	10.9509i	0.561075	−	0.447443i	0.862507	+	0.506045i	$0.168893\pi$
$600$	3.81711	+	14.6032i	0.155833	+	0.596171i
$601$	−5.00272	+	3.98954i	−0.204065	+	0.162737i	−0.720190	−	0.693777i	$-0.755945\pi$
$601$	−5.00272	+	3.98954i	−0.204065	+	0.162737i	0.516125	+	0.856513i	$0.327374\pi$
$602$	6.24704	+	21.6783i	0.254610	+	0.883541i
$603$	6.14425	+	54.5318i	0.250213	+	2.22070i
$604$	−2.68538	+	5.57625i	−0.109267	+	0.226894i
$605$	1.65625	−	0.405371i	0.0673360	−	0.0164807i
$606$	−20.8124			−0.845447
$607$	−16.3894	+	16.3894i	−0.665225	+	0.665225i	−0.956607	−	0.291382i	$-0.905885\pi$
$607$	−16.3894	+	16.3894i	−0.665225	+	0.665225i	0.291382	+	0.956607i	$0.405885\pi$
$608$	−0.0334428	+	0.0532239i	−0.00135628	+	0.00215852i
$609$	45.0536	+	2.52702i	1.82567	+	0.102400i
$610$	0.696815	−	0.453186i	0.0282132	−	0.0183490i
$611$	4.96247	−	21.7420i	0.200760	−	0.879587i
$612$	−2.59442	−	23.0261i	−0.104873	−	0.930775i
$613$	−1.85938	−	16.5024i	−0.0750995	−	0.666526i	−0.973712	−	0.227783i	$-0.926852\pi$
$613$	−1.85938	−	16.5024i	−0.0750995	−	0.666526i	0.898612	−	0.438743i	$-0.144576\pi$
$614$	5.75926	−	25.2330i	0.232425	−	1.01832i
$615$	−2.04753	+	1.33165i	−0.0825646	+	0.0536973i
$616$	7.82073	−	3.24009i	0.315106	−	0.130547i
$617$	4.54408	−	7.23187i	0.182938	−	0.291144i	−0.742648	−	0.669682i	$-0.766430\pi$
$617$	4.54408	−	7.23187i	0.182938	−	0.291144i	0.925586	+	0.378538i	$0.123573\pi$
$618$	27.5747	−	27.5747i	1.10922	−	1.10922i
$619$	6.89250			0.277033			0.138517	−	0.990360i	$-0.455767\pi$
$619$	6.89250			0.277033			0.138517	+	0.990360i	$0.455767\pi$
$620$	−21.0065	+	5.14141i	−0.843643	+	0.206484i
$621$	2.37688	−	4.93565i	0.0953810	−	0.198061i
$622$	−1.93121	−	17.1399i	−0.0774343	−	0.687249i
$623$	−15.4288	+	21.7481i	−0.618142	+	0.871318i
$624$	−16.3653	+	13.0509i	−0.655138	+	0.522455i
$625$	−7.07542	−	23.9779i	−0.283017	−	0.959115i
$626$	14.6363	−	11.6721i	0.584985	−	0.466510i
$627$	0.200526	+	0.573069i	0.00800822	+	0.0228862i
$628$	16.1152	−	1.81575i	0.643068	−	0.0724564i
$629$	−2.79943	+	1.34813i	−0.111621	+	0.0537537i
$630$	−34.9039	−	9.46464i	−1.39061	−	0.377080i
$631$	4.33717	+	2.08867i	0.172660	+	0.0831487i	0.518217	−	0.855249i	$-0.326596\pi$
$631$	4.33717	+	2.08867i	0.172660	+	0.0831487i	−0.345557	+	0.938398i	$0.612310\pi$
$632$	−11.0249	−	3.85779i	−0.438548	−	0.153454i
$633$	−31.1460	+	19.5703i	−1.23794	+	0.777851i
$634$	0.274846	+	0.570723i	0.0109155	+	0.0226663i
$635$	17.2048	+	1.66656i	0.682750	+	0.0661355i
$636$			17.4729i			0.692847i
$637$	−0.00674617	−	48.5380i	−0.000267293	−	1.92314i
$638$	12.7825	−	12.7825i	0.506064	−	0.506064i
$639$	26.7517	−	21.3338i	1.05828	−	0.843952i
$640$	−2.12188	−	0.705439i	−0.0838745	−	0.0278849i
$641$	8.98430	−	39.3628i	0.354858	−	1.55474i	−0.410944	−	0.911661i	$-0.634801\pi$
$641$	8.98430	−	39.3628i	0.354858	−	1.55474i	0.765802	−	0.643076i	$-0.222342\pi$
$642$	−8.81009	+	25.1778i	−0.347707	+	0.993688i
$643$	5.82164	+	16.6373i	0.229583	+	0.656110i	0.999831	+	0.0183662i	$0.00584648\pi$
$643$	5.82164	+	16.6373i	0.229583	+	0.656110i	−0.770248	+	0.637744i	$0.779868\pi$
$644$	0.590341	+	1.42493i	0.0232627	+	0.0561501i
$645$	−25.7815	−	51.4619i	−1.01515	−	2.02631i
$646$	−0.148562	+	0.186291i	−0.00584508	+	0.00732950i
$647$	−37.5621	+	13.1435i	−1.47672	+	0.516726i	−0.944109	−	0.329635i	$-0.893074\pi$
$647$	−37.5621	+	13.1435i	−1.47672	+	0.516726i	−0.532610	+	0.846361i	$0.678789\pi$
$648$	−9.96576	−	1.12287i	−0.391492	−	0.0441106i
$649$	5.27592	+	23.1153i	0.207098	+	0.907355i
$650$	26.4170	−	22.4533i	1.03616	−	0.880689i
$651$	21.3795	−	74.2292i	0.837928	−	2.90927i
$652$	−7.45365	+	0.839824i	−0.291907	+	0.0328901i
$653$	−15.3689	+	5.37780i	−0.601430	+	0.210450i	−0.613784	−	0.789474i	$-0.710353\pi$
$653$	−15.3689	+	5.37780i	−0.601430	+	0.210450i	0.0123535	+	0.999924i	$0.496068\pi$
$654$	−4.69616	−	20.5752i	−0.183634	−	0.804554i
$655$	−42.7861	+	0.668999i	−1.67179	+	0.0261400i
$656$		−	0.361840i		−	0.0141275i
$657$	75.6838	+	47.5553i	2.95271	+	1.85531i
$658$	−1.42477	+	8.38914i	−0.0555434	+	0.327043i
$659$	−45.2316	−	10.3238i	−1.76197	−	0.402159i	−0.785683	−	0.618629i	$-0.787688\pi$
$659$	−45.2316	−	10.3238i	−1.76197	−	0.402159i	−0.976289	+	0.216470i	$0.930546\pi$
$660$	−18.1055	+	11.7752i	−0.704755	+	0.458349i
$661$	39.4984	+	31.4990i	1.53631	+	1.22517i	0.884262	+	0.466991i	$0.154662\pi$
$661$	39.4984	+	31.4990i	1.53631	+	1.22517i	0.652050	+	0.758176i	$0.273909\pi$
$662$	8.89265	−	1.00196i	0.345622	−	0.0389423i
$663$	−67.1841	+	42.2146i	−2.60921	+	1.63948i
$664$	2.08222	−	9.12279i	0.0808057	−	0.354033i
$665$	0.184973	+	0.322610i	0.00717293	+	0.0125103i
$666$	1.11498	+	4.88502i	0.0432044	+	0.189291i
$667$	2.32896	+	2.32896i	0.0901775	+	0.0901775i
$668$	0.687968	+	0.687968i	0.0266183	+	0.0266183i
$669$	−16.3732	+	3.73708i	−0.633025	+	0.144484i
$670$	18.2197	+	8.42582i	0.703889	+	0.325518i
$671$	0.929909	+	0.741578i	0.0358987	+	0.0286283i
$672$	5.95499	−	5.32245i	0.229719	−	0.205318i
$673$	17.9875	+	2.02670i	0.693366	+	0.0781236i	0.451613	−	0.892214i	$-0.350849\pi$
$673$	17.9875	+	2.02670i	0.693366	+	0.0781236i	0.241753	+	0.970338i	$0.422278\pi$
$674$	32.1578	−	7.33980i	1.23867	−	0.282719i
$675$	46.8316	+	3.79840i	1.80255	+	0.146201i
$676$	31.6063	+	15.2208i	1.21563	+	0.585414i
$677$	−0.0530267	−	0.470625i	−0.00203798	−	0.0180876i	0.992652	−	0.121004i	$-0.0386113\pi$
$677$	−0.0530267	−	0.470625i	−0.00203798	−	0.0180876i	−0.994690	+	0.102916i	$0.967183\pi$
$678$	−1.78084	−	0.623144i	−0.0683928	−	0.0239317i
$679$	17.2808	−	19.3399i	0.663176	−	0.742198i
$680$	−7.69330	−	3.55781i	−0.295024	−	0.136436i
$681$	20.0008	−	9.63186i	0.766431	−	0.369094i
$682$	−16.4640	−	26.2024i	−0.630441	−	1.00334i
$683$	7.91062	−	22.6072i	0.302691	−	0.865042i	−0.687607	−	0.726083i	$-0.741339\pi$
$683$	7.91062	−	22.6072i	0.302691	−	0.865042i	0.990298	−	0.138959i	$-0.0443756\pi$
$684$	0.239575	+	0.300417i	0.00916038	+	0.0114867i
$685$	32.3112	−	33.3377i	1.23455	−	1.27377i
$686$	1.04229	+	18.4909i	0.0397950	+	0.705986i
$687$	5.79066	+	5.79066i	0.220928	+	0.220928i
$688$	8.47343	+	0.954726i	0.323046	+	0.0363986i
$689$	36.1602	−	17.4138i	1.37760	−	0.663415i
$690$	−2.14543	−	3.29880i	−0.0816751	−	0.125583i
$691$	−6.83076	−	14.1842i	−0.259854	−	0.539593i	0.729697	−	0.683770i	$-0.239661\pi$
$691$	−6.83076	−	14.1842i	−0.259854	−	0.539593i	−0.989552	+	0.144177i	$0.953947\pi$
$692$	3.58285	−	1.25369i	0.136200	−	0.0476583i
$693$	−2.90511	−	51.6662i	−0.110356	−	1.96264i
$694$	3.43272	+	7.12813i	0.130304	+	0.270580i
$695$	22.8520	+	17.6465i	0.866826	+	0.669370i
$696$	7.40008	−	15.3664i	0.280499	−	0.582463i
$697$	0.153571	−	1.36298i	0.00581693	−	0.0516267i
$698$	2.68455	−	4.27243i	0.101612	−	0.161714i
$699$	32.2901	+	40.4905i	1.22132	+	1.53149i
$700$	−9.58287	+	9.11968i	−0.362198	+	0.344692i
$701$	17.6076	−	22.0793i	0.665031	−	0.833922i	−0.328850	−	0.944382i	$-0.606661\pi$
$701$	17.6076	−	22.0793i	0.665031	−	0.833922i	0.993881	+	0.110460i	$0.0352325\pi$
$702$	21.5208	+	61.5028i	0.812249	+	2.32127i
$703$	0.0274126	−	0.0436269i	0.00103389	−	0.00164542i
$704$		−	3.19960i		−	0.120589i
$705$	−0.339411	−	21.7072i	−0.0127830	−	0.817539i
$706$	2.91719	−	0.665830i	0.109790	−	0.0250588i
$707$	−8.82452	−	15.9641i	−0.331880	−	0.600394i
$708$	11.9014	+	18.9409i	0.447282	+	0.711844i
$709$	−23.9326	−	5.46247i	−0.898809	−	0.205147i	−0.251935	−	0.967744i	$-0.581067\pi$
$709$	−23.9326	−	5.46247i	−0.898809	−	0.205147i	−0.646874	+	0.762597i	$0.723924\pi$
$710$	−1.59566	−	12.4142i	−0.0598841	−	0.465896i
$711$	−44.5178	+	55.8235i	−1.66955	+	2.09355i
$712$	5.36206	+	8.53367i	0.200952	+	0.319813i
$713$	4.77404	−	2.99973i	0.178789	−	0.112341i
$714$	24.6902	−	17.5212i	0.924008	−	0.655715i
$715$	42.4130	+	25.7339i	1.58616	+	0.962392i
$716$	−17.2770			−0.645671
$717$	−30.0308	+	30.0308i	−1.12152	+	1.12152i
$718$	11.2197	+	7.04982i	0.418717	+	0.263097i
$719$	−40.7497	−	19.6240i	−1.51971	−	0.731852i	−0.526715	−	0.850042i	$-0.676577\pi$
$719$	−40.7497	−	19.6240i	−1.51971	−	0.731852i	−0.992991	+	0.118190i	$0.962291\pi$
$720$	−8.35427	+	10.8187i	−0.311345	+	0.403188i
$721$	32.8429	+	9.45941i	1.22313	+	0.352287i
$722$	−2.12688	+	18.8766i	−0.0791544	+	0.702515i
$723$	72.7129	+	45.6885i	2.70422	+	1.69918i
$724$	−3.41123	−	4.27755i	−0.126777	−	0.158974i
$725$	−11.4551	+	25.8223i	−0.425432	+	0.959017i
$726$	1.79976	+	1.43526i	0.0667954	+	0.0532676i
$727$	8.74399	−	24.9889i	0.324296	−	0.926786i	−0.660155	−	0.751129i	$-0.729509\pi$
$727$	8.74399	−	24.9889i	0.324296	−	0.926786i	0.984451	−	0.175657i	$-0.0562049\pi$
$728$	−16.9496	−	7.01939i	−0.628195	−	0.260156i
$729$	10.3253	−	21.4407i	0.382419	−	0.794100i
$730$	29.2330	−	14.6452i	1.08196	−	0.542044i
$731$	31.5126	+	7.19254i	1.16553	+	0.266026i
$732$	1.05920	+	0.370630i	0.0391492	+	0.0136989i
$733$	2.07538	−	18.4195i	0.0766559	−	0.680340i	−0.895347	−	0.445370i	$-0.853072\pi$
$733$	2.07538	−	18.4195i	0.0766559	−	0.680340i	0.972003	−	0.234970i	$-0.0754993\pi$
$734$	−3.46385			−0.127853
$735$	−11.2396	−	45.8948i	−0.414580	−	1.69285i
$736$	0.582964			0.0214883
$737$	−3.21601	+	28.5429i	−0.118463	+	1.05139i
$738$	−2.08777	−	0.730542i	−0.0768518	−	0.0268916i
$739$	−39.8482	−	9.09509i	−1.46584	−	0.334568i	−0.586183	−	0.810178i	$-0.699370\pi$
$739$	−39.8482	−	9.09509i	−1.46584	−	0.334568i	−0.879656	+	0.475610i	$0.842227\pi$
$740$	1.73927	+	0.578238i	0.0639368	+	0.0212565i
$741$	0.570887	−	1.18546i	0.0209721	−	0.0435489i
$742$	−13.4026	+	7.40857i	−0.492025	+	0.271977i
$743$	1.68655	−	4.81987i	0.0618734	−	0.176824i	−0.908797	−	0.417239i	$-0.862998\pi$
$743$	1.68655	−	4.81987i	0.0618734	−	0.176824i	0.970670	+	0.240415i	$0.0772835\pi$
$744$	−22.8268	−	18.2037i	−0.836870	−	0.667381i
$745$	6.61211	+	3.05781i	0.242249	+	0.112030i
$746$	4.62100	+	5.79456i	0.169187	+	0.212154i
$747$	−48.4333	−	30.4327i	−1.77208	−	1.11347i
$748$	1.35797	−	12.0523i	0.0496521	−	0.440675i
$749$	−23.0481	+	3.91768i	−0.842159	+	0.143149i
$750$	19.7829	−	27.3450i	0.722369	−	0.998499i
$751$	−39.8172	−	19.1750i	−1.45295	−	0.699704i	−0.469846	−	0.882749i	$-0.655690\pi$
$751$	−39.8172	−	19.1750i	−1.45295	−	0.699704i	−0.983105	+	0.183045i	$0.941405\pi$
$752$	2.72323	+	1.71112i	0.0993062	+	0.0623982i
$753$	−18.7817	+	18.7817i	−0.684443	+	0.684443i
$754$	−39.1758			−1.42670
$755$	13.4426	−	3.29012i	0.489227	−	0.119740i
$756$	−9.51600	−	22.9691i	−0.346094	−	0.835380i
$757$	22.1027	−	13.8880i	0.803335	−	0.504769i	−0.0666918	−	0.997774i	$-0.521244\pi$
$757$	22.1027	−	13.8880i	0.803335	−	0.504769i	0.870027	+	0.493005i	$0.164102\pi$
$758$	−11.7227	−	18.6566i	−0.425789	−	0.677640i
$759$	3.51071	−	4.40229i	0.127431	−	0.159793i
$760$	0.139409	−	0.0179190i	0.00505691	−	0.000649991i
$761$	10.9620	+	2.50201i	0.397373	+	0.0906978i	0.416537	−	0.909119i	$-0.363243\pi$
$761$	10.9620	+	2.50201i	0.397373	+	0.0906978i	−0.0191645	+	0.999816i	$0.506101\pi$
$762$	12.4153	+	19.7589i	0.449759	+	0.715788i
$763$	13.7910	−	12.3261i	0.499268	−	0.446236i
$764$	14.9850	−	3.42023i	0.542138	−	0.123740i
$765$	−36.0606	+	37.2062i	−1.30377	+	1.34519i
$766$		−	12.8959i		−	0.465947i
$767$	27.3371	−	43.5068i	0.987087	−	1.57094i
$768$	−0.997032	−	2.84935i	−0.0359773	−	0.102817i
$769$	−13.3382	+	16.7255i	−0.480987	+	0.603138i	−0.961823	−	0.273672i	$-0.911762\pi$
$769$	−13.3382	+	16.7255i	−0.480987	+	0.603138i	0.480836	+	0.876810i	$0.340333\pi$
$770$	−16.7089	−	8.89507i	−0.602148	−	0.320556i
$771$	−13.7856	−	17.2866i	−0.496477	−	0.622562i
$772$	6.29189	−	10.0135i	0.226450	−	0.360393i
$773$	0.155344	−	1.37872i	0.00558734	−	0.0495890i	−0.990609	−	0.136724i	$-0.956343\pi$
$773$	0.155344	−	1.37872i	0.00558734	−	0.0495890i	0.996197	+	0.0871351i	$0.0277712\pi$
$774$	22.6162	−	46.9630i	0.812921	−	1.68805i
$775$	38.7324	+	28.9543i	1.39131	+	1.04007i
$776$	−4.25326	−	8.83198i	−0.152683	−	0.317049i
$777$	−4.88121	+	4.36273i	−0.175113	+	0.156512i
$778$	−12.8658	+	4.50196i	−0.461263	+	0.161403i
$779$	0.00986859	+	0.0204923i	0.000353579	+	0.000734215i
$780$	45.7892	+	9.70052i	1.63952	+	0.347334i
$781$	16.1360	−	7.77071i	0.577393	−	0.278058i
$782$	2.19591	+	0.247420i	0.0785256	+	0.00884771i
$783$	−37.5416	−	37.5416i	−1.34163	−	1.34163i
$784$	6.60750	+	2.31104i	0.235982	+	0.0825370i
$785$	−26.0394	−	25.2376i	−0.929386	−	0.900770i
$786$	−36.0187	−	45.1660i	−1.28474	−	1.61102i
$787$	−0.164892	+	0.471234i	−0.00587777	+	0.0167977i	−0.946785	−	0.321867i	$-0.895690\pi$
$787$	−0.164892	+	0.471234i	−0.00587777	+	0.0167977i	0.940907	+	0.338665i	$0.109975\pi$
$788$	−8.07818	−	12.8563i	−0.287773	−	0.457988i
$789$	17.2067	−	8.28633i	0.612576	−	0.295001i
$790$	9.01063	+	24.5146i	0.320584	+	0.872190i
$791$	−0.277100	−	1.63021i	−0.00985254	−	0.0579635i
$792$	−18.4612	−	6.45987i	−0.655992	−	0.229542i
$793$	−0.288599	−	2.56139i	−0.0102485	−	0.0909577i
$794$	−23.1913	−	11.1684i	−0.823029	−	0.396350i
$795$	30.1621	−	24.8348i	1.06974	−	0.880798i
$796$	−3.28238	+	0.749181i	−0.116341	+	0.0265540i
$797$	−35.1841	−	3.96430i	−1.24629	−	0.140423i	−0.535928	−	0.844263i	$-0.680038\pi$
$797$	−35.1841	−	3.96430i	−1.24629	−	0.140423i	−0.710358	+	0.703841i	$0.751467\pi$
$798$	−0.192092	+	0.463842i	−0.00679998	+	0.0164198i
$799$	9.53167	+	7.60125i	0.337206	+	0.268913i
$800$	1.79814	+	4.66548i	0.0635737	+	0.164950i
$801$	60.0639	−	13.7092i	2.12225	−	0.484391i
$802$	6.32755	+	6.32755i	0.223434	+	0.223434i
$803$	33.0822	+	33.0822i	1.16745	+	1.16745i
$804$	6.03033	+	26.4206i	0.212673	+	0.931782i
$805$	1.62067	−	3.04435i	0.0571212	−	0.107299i
$806$	−14.9230	+	65.3821i	−0.525642	+	2.30299i
$807$	−43.7777	+	27.5074i	−1.54105	+	0.968305i
$808$	−6.85102	+	0.771924i	−0.241018	+	0.0271562i
$809$	−23.3817	−	18.6463i	−0.822058	−	0.655570i	0.119345	−	0.992853i	$-0.461921\pi$
$809$	−23.3817	−	18.6463i	−0.822058	−	0.655570i	−0.941403	+	0.337283i	$0.890492\pi$
$810$	12.2263	+	18.7990i	0.429588	+	0.660531i
$811$	0.741569	+	0.169258i	0.0260400	+	0.00594346i	0.235521	−	0.971869i	$-0.424320\pi$
$811$	0.741569	+	0.169258i	0.0260400	+	0.00594346i	−0.209481	+	0.977813i	$0.567177\pi$
$812$	14.9245	−	0.839180i	0.523746	−	0.0294494i
$813$	44.8881	+	28.2051i	1.57429	+	0.989195i
$814$			2.62267i			0.0919244i
$815$	12.0438	+	11.6730i	0.421876	+	0.408886i
$816$	−2.54631	−	11.1561i	−0.0891388	−	0.390543i
$817$	−0.505920	+	0.177029i	−0.0176999	+	0.00619346i
$818$	−26.4777	+	2.98332i	−0.925771	+	0.104309i
$819$	−74.7216	+	83.6252i	−2.61098	+	2.92210i
$820$	−0.624615	+	0.514293i	−0.0218125	+	0.0179599i
$821$	6.80821	+	29.8287i	0.237608	+	1.04103i	0.943152	+	0.332363i	$0.107846\pi$
$821$	6.80821	+	29.8287i	0.237608	+	1.04103i	−0.705543	+	0.708667i	$0.749297\pi$
$822$	62.2830	+	7.01761i	2.17237	+	0.244767i
$823$	−15.4631	+	5.41077i	−0.539010	+	0.188608i	−0.586035	−	0.810286i	$-0.699312\pi$
$823$	−15.4631	+	5.41077i	−0.539010	+	0.188608i	0.0470247	+	0.998894i	$0.485026\pi$
$824$	8.05429	−	10.0998i	0.280585	−	0.351842i
$825$	46.0604	+	14.5176i	1.60362	+	0.505437i
$826$	−9.48242	+	17.1600i	−0.329935	+	0.597071i
$827$	1.12124	+	3.20431i	0.0389893	+	0.111425i	0.961732	−	0.273991i	$-0.0883438\pi$
$827$	1.12124	+	3.20431i	0.0389893	+	0.111425i	−0.922743	+	0.385416i	$0.874058\pi$
$828$	1.17698	−	3.36362i	0.0409029	−	0.116894i
$829$	−7.95033	+	34.8327i	−0.276126	+	1.20979i	0.626520	+	0.779406i	$0.284479\pi$
$829$	−7.95033	+	34.8327i	−0.276126	+	1.20979i	−0.902646	+	0.430384i	$0.858378\pi$
$830$	−18.7074	+	9.37211i	−0.649345	+	0.325311i
$831$	16.1811	−	12.9040i	0.561318	−	0.447636i
$832$	−4.90308	+	4.90308i	−0.169984	+	0.169984i
$833$	23.9084	+	11.5096i	0.828375	+	0.398783i
$834$			38.9785i			1.34972i
$835$	0.209756	−	2.16541i	0.00725889	−	0.0749371i
$836$	0.0872638	+	0.181205i	0.00301808	+	0.00626711i
$837$	−76.9552	+	48.3542i	−2.65996	+	1.67136i
$838$	26.1789	+	9.16039i	0.904334	+	0.316440i
$839$	−27.5127	−	13.2494i	−0.949845	−	0.457421i	−0.106213	−	0.994343i	$-0.533873\pi$
$839$	−27.5127	−	13.2494i	−0.949845	−	0.457421i	−0.843632	+	0.536922i	$0.819587\pi$
$840$	−17.6517	−	2.71467i	−0.609041	−	0.0936650i
$841$	2.63127	−	1.26715i	0.0907335	−	0.0436950i
$842$	−25.0011	+	2.81695i	−0.861596	+	0.0970785i
$843$	7.51314	+	21.4713i	0.258766	+	0.739512i
$844$	−9.52676	+	7.59734i	−0.327925	+	0.261511i
$845$	−18.6484	−	76.1930i	−0.641526	−	2.62112i
$846$	15.3710	−	12.2580i	0.528467	−	0.421439i
$847$	−0.337813	+	1.98906i	−0.0116074	+	0.0683449i
$848$	0.648064	+	5.75173i	0.0222546	+	0.197515i
$849$	21.0853	−	43.7842i	0.723647	−	1.50267i
$850$	4.79312	+	18.3371i	0.164403	+	0.628958i
$851$	−0.477847			−0.0163804
$852$	11.9483	−	11.9483i	0.409341	−	0.409341i
$853$	−25.6542	+	40.8284i	−0.878383	+	1.39794i	0.0387033	+	0.999251i	$0.487677\pi$
$853$	−25.6542	+	40.8284i	−0.878383	+	1.39794i	−0.917087	+	0.398688i	$0.869466\pi$
$854$	0.164812	+	0.969607i	0.00563976	+	0.0331793i
$855$	0.178072	−	0.840550i	0.00608993	−	0.0287462i
$856$	−1.96626	+	8.61477i	−0.0672055	+	0.294447i
$857$	−2.07781	−	18.4410i	−0.0709765	−	0.629934i	−0.977964	−	0.208775i	$-0.933052\pi$
$857$	−2.07781	−	18.4410i	−0.0709765	−	0.629934i	0.906987	−	0.421158i	$-0.138376\pi$
$858$	7.49873	+	66.5531i	0.256002	+	2.27208i
$859$	−4.82132	+	21.1236i	−0.164501	+	0.720727i	0.823632	+	0.567125i	$0.191944\pi$
$859$	−4.82132	+	21.1236i	−0.164501	+	0.720727i	−0.988133	+	0.153602i	$0.950913\pi$
$860$	−10.3954	−	15.9840i	−0.354482	−	0.545049i
$861$	−0.484287	−	2.84911i	−0.0165045	−	0.0970974i
$862$	4.50960	−	7.17699i	0.153598	−	0.244449i
$863$	18.0944	−	18.0944i	0.615941	−	0.615941i	−0.328547	−	0.944488i	$-0.606559\pi$
$863$	18.0944	−	18.0944i	0.615941	−	0.615941i	0.944488	+	0.328547i	$0.106559\pi$
$864$	−9.39708			−0.319695
$865$	−7.25655	−	4.40287i	−0.246730	−	0.149702i
$866$	8.01660	−	16.6466i	0.272415	−	0.565676i
$867$	0.889273	+	7.89251i	0.0302013	+	0.268044i
$868$	4.28455	−	25.2277i	0.145427	−	0.856283i
$869$	−29.2190	+	23.3014i	−0.991188	+	0.790446i
$870$	−37.0437	+	9.06656i	−1.25590	+	0.307385i
$871$	48.6674	−	38.8110i	1.64903	−	1.31506i
$872$	−2.30900	−	6.59875i	−0.0781927	−	0.223462i
$873$	−59.5464	+	6.70927i	−2.01534	+	0.227074i
$874$	−0.0330154	+	0.0158994i	−0.00111676	+	0.000537804i
$875$	29.3630	+	3.58008i	0.992649	+	0.121029i
$876$	39.7697	+	19.1521i	1.34369	+	0.647088i
$877$	35.7854	+	12.5218i	1.20839	+	0.422832i	0.857940	−	0.513750i	$-0.171744\pi$
$877$	35.7854	+	12.5218i	1.20839	+	0.422832i	0.350446	+	0.936583i	$0.386030\pi$
$878$	5.31242	−	3.33802i	0.179286	−	0.112653i
$879$	33.0303	+	68.5881i	1.11408	+	2.31342i
$880$	−5.52321	+	4.54768i	−0.186187	+	0.153302i
$881$			32.8023i			1.10514i	0.833467	+	0.552569i	$0.186352\pi$
$881$			32.8023i			1.10514i	−0.833467	+	0.552569i	$0.813648\pi$
$882$	26.6747	−	33.4585i	0.898182	−	1.12661i
$883$	27.7958	−	27.7958i	0.935403	−	0.935403i	−0.0626334	−	0.998037i	$-0.519950\pi$
$883$	27.7958	−	27.7958i	0.935403	−	0.935403i	0.998037	+	0.0626334i	$0.0199499\pi$
$884$	−20.5499	+	16.3880i	−0.691168	+	0.551188i
$885$	15.7805	−	47.4657i	0.530454	−	1.59554i
$886$	6.71165	−	29.4056i	0.225482	−	0.987902i
$887$	0.492905	−	1.40864i	0.0165501	−	0.0472976i	−0.935312	−	0.353824i	$-0.884881\pi$
$887$	0.492905	−	1.40864i	0.0165501	−	0.0472976i	0.951862	+	0.306527i	$0.0991668\pi$
$888$	0.817253	+	2.33557i	0.0274252	+	0.0783768i
$889$	−9.89189	+	17.9010i	−0.331763	+	0.600379i
$890$	7.10974	−	21.3852i	0.238319	−	0.716834i
$891$	−20.0067	+	25.0876i	−0.670249	+	0.840465i
$892$	−5.25112	+	1.83745i	−0.175820	+	0.0615222i
$893$	−0.200895	−	0.0226354i	−0.00672269	−	0.000757465i
$894$	2.18846	+	9.58829i	0.0731932	+	0.320680i
$895$	24.5562	+	29.8238i	0.820824	+	0.996901i
$896$	1.76285	−	1.97291i	0.0588927	−	0.0659102i
$897$	−12.1259	+	1.36626i	−0.404872	+	0.0456181i
$898$	22.8705	−	8.00273i	0.763198	−	0.267055i
$899$	−12.1593	−	53.2734i	−0.405535	−	1.77677i
$900$	30.5495	−	0.955573i	1.01832	−	0.0318524i
$901$			21.9407i			0.730951i
$902$	−0.980290	−	0.615957i	−0.0326401	−	0.0205091i
$903$	67.9971	−	3.82338i	2.26280	−	0.127234i
$904$	−0.609328	−	0.139075i	−0.0202660	−	0.00462557i
$905$	−2.53551	+	11.9683i	−0.0842831	+	0.397841i
$906$	14.6074	+	11.6490i	0.485299	+	0.387013i
$907$	27.5196	−	3.10072i	0.913774	−	0.102958i	0.357459	−	0.933929i	$-0.383643\pi$
$907$	27.5196	−	3.10072i	0.913774	−	0.102958i	0.556315	+	0.830971i	$0.312215\pi$
$908$	6.22659	−	3.91243i	0.206637	−	0.129838i
$909$	−9.37805	+	41.0879i	−0.311050	+	1.36280i
$910$	11.9740	+	39.2356i	0.396934	+	1.30065i
$911$	3.19916	+	14.0164i	0.105993	+	0.464385i	0.999871	+	0.0160745i	$0.00511691\pi$
$911$	3.19916	+	14.0164i	0.105993	+	0.464385i	−0.893878	+	0.448310i	$0.852026\pi$
$912$	0.134177	+	0.134177i	0.00444305	+	0.00444305i
$913$	−21.1707	−	21.1707i	−0.700649	−	0.700649i
$914$	−6.93303	+	1.58242i	−0.229324	+	0.0523418i
$915$	−0.865682	−	2.35520i	−0.0286186	−	0.0778605i
$916$	2.12094	+	1.69139i	0.0700778	+	0.0558852i
$917$	19.3725	−	46.7786i	0.639737	−	1.54477i
$918$	−35.3970	−	3.98828i	−1.16827	−	0.131633i
$919$	−32.6832	+	7.45972i	−1.07812	+	0.246073i	−0.724471	−	0.689306i	$-0.757916\pi$
$919$	−32.6832	+	7.45972i	−1.07812	+	0.246073i	−0.353647	+	0.935379i	$0.615059\pi$
$920$	−0.828582	−	1.00632i	−0.0273175	−	0.0331775i
$921$	−70.3937	−	33.8998i	−2.31955	−	1.11704i
$922$	−3.60085	−	31.9585i	−0.118588	−	1.05250i
$923$	−36.6348	−	12.8191i	−1.20585	−	0.421945i
$924$	−4.28234	−	25.1935i	−0.140879	−	0.828804i
$925$	−1.47391	−	3.82423i	−0.0484617	−	0.125740i
$926$	−22.5940	+	10.8807i	−0.742485	+	0.357562i
$927$	−42.0129	−	66.8632i	−1.37989	−	2.19608i
$928$	1.86602	−	5.33277i	0.0612550	−	0.175057i
$929$	−19.9884	−	25.0647i	−0.655799	−	0.822346i	0.337079	−	0.941476i	$-0.390561\pi$
$929$	−19.9884	−	25.0647i	−0.655799	−	0.822346i	−0.992879	+	0.119130i	$0.961990\pi$
$930$	1.02067	+	65.2774i	0.0334692	+	2.14053i
$931$	−0.437237	+	0.0493263i	−0.0143299	+	0.00161660i
$932$	12.1310	+	12.1310i	0.397364	+	0.397364i
$933$	−51.7413	−	5.82984i	−1.69393	−	0.190861i
$934$	17.1503	−	8.25915i	0.561175	−	0.270248i
$935$	−22.7350	+	14.7861i	−0.743513	+	0.483557i
$936$	18.3909	+	38.1892i	0.601127	+	1.24825i
$937$	−28.0140	+	9.80253i	−0.915178	+	0.320235i	−0.746461	−	0.665430i	$-0.768248\pi$
$937$	−28.0140	+	9.80253i	−0.915178	+	0.320235i	−0.168718	+	0.985664i	$0.553963\pi$
$938$	−17.7090	+	15.8280i	−0.578220	+	0.516801i
$939$	−24.5200	−	50.9163i	−0.800180	−	1.66159i
$940$	−0.916837	−	7.13296i	−0.0299039	−	0.232652i
$941$	17.4645	−	36.2654i	0.569326	−	1.18222i	−0.395290	−	0.918557i	$-0.629356\pi$
$941$	17.4645	−	36.2654i	0.569326	−	1.18222i	0.964615	−	0.263661i	$-0.0849299\pi$
$942$	5.48131	−	48.6480i	0.178591	−	1.58504i
$943$	0.112227	−	0.178608i	0.00365460	−	0.00581627i
$944$	4.62020	+	5.79355i	0.150375	+	0.188564i
$945$	−26.1244	+	49.0734i	−0.849827	+	1.59636i
$946$	17.0108	−	21.3308i	0.553067	−	0.693525i
$947$	16.8839	+	48.2515i	0.548654	+	1.56796i	0.799958	+	0.600056i	$0.204855\pi$
$947$	16.8839	+	48.2515i	0.548654	+	1.56796i	−0.251304	+	0.967908i	$0.580859\pi$
$948$	−18.7596	+	29.8557i	−0.609283	+	0.969668i
$949$		−	101.391i		−	3.29128i
$950$	−0.229078	−	0.215182i	−0.00743228	−	0.00698143i
$951$	1.86430	−	0.425515i	0.0604542	−	0.0137983i
$952$	7.47765	−	6.68337i	0.242352	−	0.216609i
$953$	4.08748	+	6.50518i	0.132406	+	0.210724i	0.906346	−	0.422535i	$-0.138860\pi$
$953$	4.08748	+	6.50518i	0.132406	+	0.210724i	−0.773940	+	0.633259i	$0.781717\pi$
$954$	34.4951	+	7.87328i	1.11682	+	0.254907i
$955$	−27.2026	−	21.0061i	−0.880257	−	0.679742i
$956$	−8.77167	+	10.9993i	−0.283696	+	0.355744i
$957$	−29.0333	−	46.2062i	−0.938514	−	1.49364i
$958$	28.2934	−	17.7779i	0.914118	−	0.574378i
$959$	21.0253	+	50.7496i	0.678942	+	1.63879i
$960$	−3.50150	+	5.77096i	−0.113010	+	0.186257i
$961$	−62.5418			−2.01748
$962$	4.01898	−	4.01898i	0.129577	−	0.129577i
$963$	45.7362	+	28.7380i	1.47383	+	0.926068i
$964$	25.6301	+	12.3428i	0.825491	+	0.397536i
$965$	−26.2283	+	3.37126i	−0.844318	+	0.108525i
$966$	4.59022	−	0.780238i	0.147688	−	0.0251038i
$967$	−2.92084	+	25.9232i	−0.0939280	+	0.833634i	0.855105	+	0.518456i	$0.173493\pi$
$967$	−2.92084	+	25.9232i	−0.0939280	+	0.833634i	−0.949033	+	0.315178i	$0.897936\pi$
$968$	0.645677	+	0.405706i	0.0207529	+	0.0130399i
$969$	0.448472	+	0.562366i	0.0144070	+	0.0180658i
$970$	−9.20065	+	19.8952i	−0.295415	+	0.638796i
$971$	−13.3229	−	10.6247i	−0.427552	−	0.340961i	0.385954	−	0.922518i	$-0.373872\pi$
$971$	−13.3229	−	10.6247i	−0.427552	−	0.340961i	−0.813506	+	0.581557i	$0.802444\pi$
$972$	−0.688080	+	1.96642i	−0.0220702	+	0.0630729i
$973$	−29.8984	+	16.5270i	−0.958500	+	0.529831i
$974$	−2.22331	+	4.61676i	−0.0712396	+	0.147930i
$975$	−48.3363	−	92.8298i	−1.54800	−	2.97293i
$976$	0.362413	+	0.0827185i	0.0116006	+	0.00264775i
$977$	12.3420	+	4.31864i	0.394854	+	0.138166i	0.520401	−	0.853922i	$-0.325783\pi$
$977$	12.3420	+	4.31864i	0.394854	+	0.138166i	−0.125546	+	0.992088i	$0.540068\pi$
$978$	−2.53523	+	22.5008i	−0.0810676	+	0.719495i
$979$	32.2470			1.03062
$980$	−5.40207	−	14.6907i	−0.172563	−	0.469278i
$981$	−42.7357			−1.36445
$982$	−3.81912	+	33.8957i	−0.121873	+	1.08165i
$983$	14.1181	+	4.94014i	0.450297	+	0.157566i	0.545894	−	0.837854i	$-0.316190\pi$
$983$	14.1181	+	4.94014i	0.450297	+	0.157566i	−0.0955966	+	0.995420i	$0.530476\pi$
$984$	−1.06492	−	0.243061i	−0.0339485	−	0.00774852i
$985$	−10.7111	+	32.2178i	−0.341285	+	1.02654i
$986$	9.29225	−	19.2956i	0.295926	−	0.614496i
$987$	23.7328	+	9.82850i	0.755422	+	0.312845i
$988$	0.143956	−	0.411402i	0.00457985	−	0.0130885i
$989$	3.88645	+	3.09934i	0.123582	+	0.0985533i
$990$	15.0883	+	41.0497i	0.479538	+	1.30465i
$991$	−7.43675	−	9.32539i	−0.236236	−	0.296231i	0.649555	−	0.760314i	$-0.274955\pi$
$991$	−7.43675	−	9.32539i	−0.236236	−	0.296231i	−0.885791	+	0.464084i	$0.846384\pi$
$992$	−8.18927	−	5.14566i	−0.260009	−	0.163375i
$993$	3.02468	−	26.8447i	0.0959852	−	0.851892i
$994$	14.2310	+	4.09881i	0.451380	+	0.130006i
$995$	5.95858	+	4.60127i	0.188900	+	0.145870i
$996$	−25.4503	−	12.2562i	−0.806424	−	0.388353i
$997$	−46.5247	−	29.2334i	−1.47345	−	0.925831i	−0.998961	−	0.0455699i	$-0.985490\pi$
$997$	−46.5247	−	29.2334i	−1.47345	−	0.925831i	−0.474490	−	0.880261i	$-0.657368\pi$
$998$	12.2426	−	12.2426i	0.387532	−	0.387532i
$999$	7.70265			0.243701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.s.a.237.15	yes	336
5.3	odd	4	inner	490.2.s.a.433.14	yes	336
49.6	odd	14	inner	490.2.s.a.447.14	yes	336
245.153	even	28	inner	490.2.s.a.153.15	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.s.a.153.15	✓	336	245.153	even	28	inner
490.2.s.a.237.15	yes	336	1.1	even	1	trivial
490.2.s.a.433.14	yes	336	5.3	odd	4	inner
490.2.s.a.447.14	yes	336	49.6	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.111964 - 0.993712i) q^{2} +(-2.84935 - 0.997032i) q^{3} +(-0.974928 - 0.222521i) q^{4} +(1.00157 + 1.99921i) q^{5} +(-1.30979 + 2.71981i) q^{6} +(-2.64158 + 0.148532i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(4.77926 + 3.81133i) q^{9} +O(q^{10})\)	\(q+(0.111964 - 0.993712i) q^{2} +(-2.84935 - 0.997032i) q^{3} +(-0.974928 - 0.222521i) q^{4} +(1.00157 + 1.99921i) q^{5} +(-1.30979 + 2.71981i) q^{6} +(-2.64158 + 0.148532i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(4.77926 + 3.81133i) q^{9} +(2.09878 - 0.771433i) q^{10} +(1.99492 + 2.50155i) q^{11} +(2.55606 + 1.60608i) q^{12} +(0.776361 - 6.89040i) q^{13} +(-0.148165 + 2.64160i) q^{14} +(-0.860553 - 6.69507i) q^{15} +(0.900969 + 0.433884i) q^{16} +(3.20963 + 2.01674i) q^{17} +(4.32247 - 4.32247i) q^{18} -0.0628586 q^{19} +(-0.531593 - 2.17196i) q^{20} +(7.67489 + 2.21052i) q^{21} +(2.70918 - 1.70229i) q^{22} +(0.310155 + 0.493609i) q^{23} +(1.88216 - 2.36016i) q^{24} +(-2.99371 + 4.00471i) q^{25} +(-6.76015 - 1.54296i) q^{26} +(-4.99955 - 7.95674i) q^{27} +(2.60840 + 0.442999i) q^{28} +(5.50817 - 1.25720i) q^{29} +(-6.74932 + 0.105532i) q^{30} -9.67170i q^{31} +(0.532032 - 0.846724i) q^{32} +(-3.19010 - 9.11680i) q^{33} +(2.36343 - 2.96364i) q^{34} +(-2.94268 - 5.13231i) q^{35} +(-3.81133 - 4.77926i) q^{36} +(-0.436099 + 0.694047i) q^{37} +(-0.00703793 + 0.0624634i) q^{38} +(-9.08208 + 18.8591i) q^{39} +(-2.21782 + 0.285068i) q^{40} +(-0.156997 - 0.326007i) q^{41} +(3.05593 - 7.37913i) q^{42} +(8.04854 - 2.81630i) q^{43} +(-1.38825 - 2.88274i) q^{44} +(-2.83289 + 13.3721i) q^{45} +(0.525232 - 0.252938i) q^{46} +(3.19598 + 0.360100i) q^{47} +(-2.13458 - 2.13458i) q^{48} +(6.95588 - 0.784718i) q^{49} +(3.64434 + 3.42327i) q^{50} +(-7.13461 - 8.94652i) q^{51} +(-2.29015 + 6.54488i) q^{52} +(3.07947 + 4.90094i) q^{53} +(-8.46648 + 4.07724i) q^{54} +(-3.00308 + 6.49375i) q^{55} +(0.732261 - 2.54240i) q^{56} +(0.179107 + 0.0626721i) q^{57} +(-0.632579 - 5.61430i) q^{58} +(6.67638 + 3.21518i) q^{59} +(-0.650816 + 6.71870i) q^{60} +(0.362413 - 0.0827185i) q^{61} +(-9.61089 - 1.08289i) q^{62} +(-13.1909 - 9.35805i) q^{63} +(-0.781831 - 0.623490i) q^{64} +(14.5530 - 5.34911i) q^{65} +(-9.41665 + 2.14929i) q^{66} +(6.34785 + 6.34785i) q^{67} +(-2.68039 - 2.68039i) q^{68} +(-0.391598 - 1.71570i) q^{69} +(-5.42952 + 2.34954i) q^{70} +(1.24555 - 5.45713i) q^{71} +(-5.17594 + 3.25226i) q^{72} +(14.5303 - 1.63717i) q^{73} +(0.640856 + 0.511065i) q^{74} +(12.5230 - 8.42602i) q^{75} +(0.0612826 + 0.0139874i) q^{76} +(-5.64129 - 6.31173i) q^{77} +(17.7237 + 11.1365i) q^{78} +11.6804i q^{79} +(0.0349587 + 2.23579i) q^{80} +(2.23162 + 9.77738i) q^{81} +(-0.341535 + 0.119508i) q^{82} +(-9.29856 + 1.04770i) q^{83} +(-6.99057 - 3.86292i) q^{84} +(-0.817227 + 8.43664i) q^{85} +(-1.89745 - 8.31326i) q^{86} +(-16.9482 - 1.90960i) q^{87} +(-3.02005 + 1.05676i) q^{88} +(6.28381 - 7.87965i) q^{89} +(12.9708 + 4.31228i) q^{90} +(-1.02737 + 18.3168i) q^{91} +(-0.192541 - 0.550250i) q^{92} +(-9.64300 + 27.5581i) q^{93} +(0.715672 - 3.13556i) q^{94} +(-0.0629574 - 0.125668i) q^{95} +(-2.36016 + 1.88216i) q^{96} +(-6.93159 + 6.93159i) q^{97} +(-0.000972913 - 7.00000i) q^{98} +19.5588i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 28 q^{6} + 8 q^{7}+O(q^{10}) \) 336 * q + 28 * q^6 + 8 * q^7	\( 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98}+O(q^{100}) \) 336 * q + 28 * q^6 + 8 * q^7 + 8 * q^11 + 44 * q^15 + 56 * q^16 + 28 * q^17 - 16 * q^21 - 20 * q^22 + 8 * q^23 - 8 * q^25 - 28 * q^26 - 8 * q^28 - 24 * q^30 + 8 * q^35 + 76 * q^36 - 24 * q^37 - 56 * q^41 - 112 * q^42 - 24 * q^43 + 112 * q^45 - 68 * q^46 - 84 * q^47 - 32 * q^50 - 80 * q^51 - 100 * q^53 + 84 * q^55 - 20 * q^56 + 92 * q^57 - 80 * q^58 - 112 * q^61 - 32 * q^67 + 52 * q^70 + 16 * q^71 - 84 * q^75 + 16 * q^77 - 80 * q^78 + 12 * q^81 + 140 * q^83 + 40 * q^85 - 8 * q^86 - 28 * q^87 - 8 * q^88 - 84 * q^90 + 124 * q^91 + 8 * q^92 + 20 * q^93 - 56 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

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