LMFDB - Embedded newform 490.2.s.a.223.21

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			223.21
Character	$\chi$	$=$	490.223
Dual form			490.2.s.a.167.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.330279 - 0.943883i) q^{2} +(-0.137913 - 0.219487i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.72144 - 1.42712i) q^{5} +(-0.252720 + 0.0576817i) q^{6} +(-1.39792 + 2.24629i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.27250 - 2.64237i) q^{9} +O(q^{10})$	\(q+(0.330279 - 0.943883i) q^{2} +(-0.137913 - 0.219487i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.72144 - 1.42712i) q^{5} +(-0.252720 + 0.0576817i) q^{6} +(-1.39792 + 2.24629i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.27250 - 2.64237i) q^{9} +(-1.91558 + 1.15349i) q^{10} +(-4.36362 + 2.10141i) q^{11} +(-0.0290234 + 0.257589i) q^{12} +(0.751866 - 2.14871i) q^{13} +(1.65853 + 2.06138i) q^{14} +(-0.0758253 + 0.574651i) q^{15} +(0.222521 + 0.974928i) q^{16} +(-0.298283 + 2.64734i) q^{17} +(-2.07381 - 2.07381i) q^{18} -6.43091 q^{19} +(0.456081 + 2.18906i) q^{20} +(0.685824 - 0.00296620i) q^{21} +(0.542272 + 4.81280i) q^{22} +(-4.88587 + 0.550506i) q^{23} +(0.233549 + 0.112471i) q^{24} +(0.926683 + 4.91338i) q^{25} +(-1.77980 - 1.41935i) q^{26} +(-1.52823 + 0.172190i) q^{27} +(2.49348 - 0.884629i) q^{28} +(1.98342 - 1.58173i) q^{29} +(0.517360 + 0.261365i) q^{30} -0.764596i q^{31} +(0.993712 + 0.111964i) q^{32} +(1.06303 + 0.667948i) q^{33} +(2.40026 + 1.15591i) q^{34} +(5.61215 - 1.87185i) q^{35} +(-2.64237 + 1.27250i) q^{36} +(5.31523 + 0.598883i) q^{37} +(-2.12399 + 6.07003i) q^{38} +(-0.575306 + 0.131310i) q^{39} +(2.21685 + 0.292514i) q^{40} +(-5.47826 - 1.25038i) q^{41} +(0.223713 - 0.648317i) q^{42} +(2.02132 - 3.21691i) q^{43} +(4.72182 + 1.07773i) q^{44} +(-5.96148 + 2.73266i) q^{45} +(-1.09409 + 4.79352i) q^{46} +(-8.99806 - 3.14856i) q^{47} +(0.183296 - 0.183296i) q^{48} +(-3.09163 - 6.28027i) q^{49} +(4.94372 + 0.748104i) q^{50} +(0.622194 - 0.299633i) q^{51} +(-1.92753 + 1.21115i) q^{52} +(5.91348 - 0.666290i) q^{53} +(-0.342215 + 1.49934i) q^{54} +(10.5106 + 2.60995i) q^{55} +(-0.0114428 - 2.64573i) q^{56} +(0.886906 + 1.41150i) q^{57} +(-0.837882 - 2.39453i) q^{58} +(-2.62131 - 11.4847i) q^{59} +(0.417572 - 0.402004i) q^{60} +(-1.25986 + 1.00471i) q^{61} +(-0.721689 - 0.252530i) q^{62} +(4.15667 + 6.55222i) q^{63} +(0.433884 - 0.900969i) q^{64} +(-4.36074 + 2.62587i) q^{65} +(0.981562 - 0.782770i) q^{66} +(7.59992 - 7.59992i) q^{67} +(1.88380 - 1.88380i) q^{68} +(0.794655 + 0.996466i) q^{69} +(0.0867711 - 5.91544i) q^{70} +(-7.82703 + 9.81479i) q^{71} +(0.328370 + 2.91436i) q^{72} +(6.88935 - 2.41069i) q^{73} +(2.32078 - 4.81916i) q^{74} +(0.950622 - 0.881014i) q^{75} +(5.02789 + 4.00961i) q^{76} +(1.37963 - 12.7396i) q^{77} +(-0.0660704 + 0.586391i) q^{78} -2.08985i q^{79} +(1.00828 - 1.99584i) q^{80} +(-5.23717 - 6.56720i) q^{81} +(-2.98956 + 4.75786i) q^{82} +(1.38846 - 0.485844i) q^{83} +(-0.538048 - 0.425285i) q^{84} +(4.29153 - 4.13154i) q^{85} +(-2.36879 - 2.97037i) q^{86} +(-0.620708 - 0.217195i) q^{87} +(2.57677 - 4.10090i) q^{88} +(-9.91674 - 4.77565i) q^{89} +(0.610364 + 6.52949i) q^{90} +(3.77557 + 4.69264i) q^{91} +(4.16317 + 2.61589i) q^{92} +(-0.167819 + 0.105448i) q^{93} +(-5.94374 + 7.45322i) q^{94} +(11.0704 + 9.17765i) q^{95} +(-0.112471 - 0.233549i) q^{96} +(3.47917 + 3.47917i) q^{97} +(-6.94895 + 0.843890i) q^{98} +14.2043i 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 $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.330279	−	0.943883i	0.233543	−	0.667426i
$2$	0.330279	−	0.943883i	0.233543	−	0.667426i
$3$	−0.137913	−	0.219487i	−0.0796241	−	0.126721i	0.804538	−	0.593901i	$-0.202413\pi$
$3$	−0.137913	−	0.219487i	−0.0796241	−	0.126721i	−0.884162	+	0.467180i	$0.845270\pi$
$4$	−0.781831	−	0.623490i	−0.390916	−	0.311745i
$5$	−1.72144	−	1.42712i	−0.769850	−	0.638225i
$5$	−1.72144	−	1.42712i	−0.769850	−	0.638225i
$6$	−0.252720	+	0.0576817i	−0.103173	+	0.0235485i
$7$	−1.39792	+	2.24629i	−0.528365	+	0.849017i
$7$	−1.39792	+	2.24629i	−0.528365	+	0.849017i
$8$	−0.846724	+	0.532032i	−0.299362	+	0.188102i
$9$	1.27250	−	2.64237i	0.424166	−	0.880789i
$10$	−1.91558	+	1.15349i	−0.605761	+	0.364765i
$11$	−4.36362	+	2.10141i	−1.31568	+	0.633599i	−0.954309	−	0.298823i	$-0.903406\pi$
$11$	−4.36362	+	2.10141i	−1.31568	+	0.633599i	−0.361372	+	0.932422i	$0.617692\pi$
$12$	−0.0290234	+	0.257589i	−0.00837832	+	0.0743597i
$13$	0.751866	−	2.14871i	0.208530	−	0.595945i	−0.791351	−	0.611362i	$-0.790622\pi$
$13$	0.751866	−	2.14871i	0.208530	−	0.595945i	0.999881	+	0.0154173i	$0.00490769\pi$
$14$	1.65853	+	2.06138i	0.443261	+	0.550926i
$15$	−0.0758253	+	0.574651i	−0.0195780	+	0.148374i
$16$	0.222521	+	0.974928i	0.0556302	+	0.243732i
$17$	−0.298283	+	2.64734i	−0.0723444	+	0.642074i	0.904253	+	0.426997i	$0.140429\pi$
$17$	−0.298283	+	2.64734i	−0.0723444	+	0.642074i	−0.976597	+	0.215076i	$0.931000\pi$
$18$	−2.07381	−	2.07381i	−0.488801	−	0.488801i
$19$	−6.43091			−1.47535			−0.737676	−	0.675155i	$-0.764077\pi$
$19$	−6.43091			−1.47535			−0.737676	+	0.675155i	$0.764077\pi$
$20$	0.456081	+	2.18906i	0.101983	+	0.489489i
$21$	0.685824	−	0.00296620i	0.149659	−	0.000647278i
$22$	0.542272	+	4.81280i	0.115613	+	1.02609i
$23$	−4.88587	+	0.550506i	−1.01878	+	0.114788i	−0.605523	−	0.795828i	$-0.707036\pi$
$23$	−4.88587	+	0.550506i	−1.01878	+	0.114788i	−0.413253	+	0.910616i	$0.635607\pi$
$24$	0.233549	+	0.112471i	0.0476729	+	0.0229581i
$25$	0.926683	+	4.91338i	0.185337	+	0.982675i
$26$	−1.77980	−	1.41935i	−0.349048	−	0.278357i
$27$	−1.52823	+	0.172190i	−0.294108	+	0.0331380i
$28$	2.49348	−	0.884629i	0.471223	−	0.167179i
$29$	1.98342	−	1.58173i	0.368312	−	0.293719i	−0.421791	−	0.906693i	$-0.638598\pi$
$29$	1.98342	−	1.58173i	0.368312	−	0.293719i	0.790103	+	0.612974i	$0.210027\pi$
$30$	0.517360	+	0.261365i	0.0944566	+	0.0477186i
$31$		−	0.764596i		−	0.137325i	−0.997640	−	0.0686627i	$-0.978127\pi$
$31$		−	0.764596i		−	0.137325i	0.997640	−	0.0686627i	$-0.0218732\pi$
$32$	0.993712	+	0.111964i	0.175665	+	0.0197927i
$33$	1.06303	+	0.667948i	0.185050	+	0.116275i
$34$	2.40026	+	1.15591i	0.411642	+	0.198236i
$35$	5.61215	−	1.87185i	0.948626	−	0.316400i
$36$	−2.64237	+	1.27250i	−0.440394	+	0.212083i
$37$	5.31523	+	0.598883i	0.873818	+	0.0984557i	0.537471	−	0.843282i	$-0.319380\pi$
$37$	5.31523	+	0.598883i	0.873818	+	0.0984557i	0.336347	+	0.941738i	$0.390808\pi$
$38$	−2.12399	+	6.07003i	−0.344557	+	0.984689i
$39$	−0.575306	+	0.131310i	−0.0921228	+	0.0210264i
$40$	2.21685	+	0.292514i	0.350515	+	0.0462505i
$41$	−5.47826	−	1.25038i	−0.855560	−	0.195276i	−0.227824	−	0.973702i	$-0.573161\pi$
$41$	−5.47826	−	1.25038i	−0.855560	−	0.195276i	−0.627736	+	0.778426i	$0.716018\pi$
$42$	0.223713	−	0.648317i	0.0345197	−	0.100038i
$43$	2.02132	−	3.21691i	0.308248	−	0.490574i	−0.656293	−	0.754506i	$-0.727877\pi$
$43$	2.02132	−	3.21691i	0.308248	−	0.490574i	0.964541	+	0.263932i	$0.0850194\pi$
$44$	4.72182	+	1.07773i	0.711842	+	0.162473i
$45$	−5.96148	+	2.73266i	−0.888685	+	0.407362i
$46$	−1.09409	+	4.79352i	−0.161315	+	0.706765i
$47$	−8.99806	−	3.14856i	−1.31250	−	0.459264i	−0.418863	−	0.908050i	$-0.637571\pi$
$47$	−8.99806	−	3.14856i	−1.31250	−	0.459264i	−0.893640	+	0.448785i	$0.851857\pi$
$48$	0.183296	−	0.183296i	0.0264565	−	0.0264565i
$49$	−3.09163	−	6.28027i	−0.441661	−	0.897182i
$50$	4.94372	+	0.748104i	0.699147	+	0.105798i
$51$	0.622194	−	0.299633i	0.0871246	−	0.0419570i
$52$	−1.92753	+	1.21115i	−0.267300	+	0.167956i
$53$	5.91348	−	0.666290i	0.812280	−	0.0915219i	0.303954	−	0.952687i	$-0.401693\pi$
$53$	5.91348	−	0.666290i	0.812280	−	0.0915219i	0.508326	+	0.861165i	$0.330265\pi$
$54$	−0.342215	+	1.49934i	−0.0465695	+	0.204034i
$55$	10.5106	+	2.60995i	1.41726	+	0.351925i
$56$	−0.0114428	−	2.64573i	−0.00152911	−	0.353550i
$57$	0.886906	+	1.41150i	0.117474	+	0.186958i
$58$	−0.837882	−	2.39453i	−0.110019	−	0.314417i
$59$	−2.62131	−	11.4847i	−0.341265	−	1.49518i	−0.796406	−	0.604762i	$-0.793268\pi$
$59$	−2.62131	−	11.4847i	−0.341265	−	1.49518i	0.455141	−	0.890419i	$-0.349589\pi$
$60$	0.417572	−	0.402004i	0.0539083	−	0.0518985i
$61$	−1.25986	+	1.00471i	−0.161309	+	0.128640i	−0.700818	−	0.713340i	$-0.747181\pi$
$61$	−1.25986	+	1.00471i	−0.161309	+	0.128640i	0.539509	+	0.841980i	$0.318610\pi$
$62$	−0.721689	−	0.252530i	−0.0916546	−	0.0320713i
$63$	4.15667	+	6.55222i	0.523691	+	0.825502i
$64$	0.433884	−	0.900969i	0.0542355	−	0.112621i
$65$	−4.36074	+	2.62587i	−0.540884	+	0.325699i
$66$	0.981562	−	0.782770i	0.120822	−	0.0963523i
$67$	7.59992	−	7.59992i	0.928478	−	0.928478i	−0.0691296	−	0.997608i	$-0.522022\pi$
$67$	7.59992	−	7.59992i	0.928478	−	0.928478i	0.997608	+	0.0691296i	$0.0220222\pi$
$68$	1.88380	−	1.88380i	0.228444	−	0.228444i
$69$	0.794655	+	0.996466i	0.0956652	+	0.119960i
$70$	0.0867711	−	5.91544i	0.0103711	−	0.707031i
$71$	−7.82703	+	9.81479i	−0.928898	+	1.16480i	0.0571545	+	0.998365i	$0.481797\pi$
$71$	−7.82703	+	9.81479i	−0.928898	+	1.16480i	−0.986052	+	0.166436i	$0.946774\pi$
$72$	0.328370	+	2.91436i	0.0386988	+	0.343461i
$73$	6.88935	−	2.41069i	0.806338	−	0.282150i	0.104535	−	0.994521i	$-0.466665\pi$
$73$	6.88935	−	2.41069i	0.806338	−	0.282150i	0.701803	+	0.712371i	$0.252379\pi$
$74$	2.32078	−	4.81916i	0.269786	−	0.560216i
$75$	0.950622	−	0.881014i	0.109768	−	0.101731i
$76$	5.02789	+	4.00961i	0.576738	+	0.459933i
$77$	1.37963	−	12.7396i	0.157224	−	1.45181i
$78$	−0.0660704	+	0.586391i	−0.00748100	+	0.0663957i
$79$		−	2.08985i		−	0.235126i	−0.993065	−	0.117563i	$-0.962492\pi$
$79$		−	2.08985i		−	0.235126i	0.993065	−	0.117563i	$-0.0375082\pi$
$80$	1.00828	−	1.99584i	0.112729	−	0.223142i
$81$	−5.23717	−	6.56720i	−0.581907	−	0.729689i
$82$	−2.98956	+	4.75786i	−0.330142	+	0.525418i
$83$	1.38846	−	0.485844i	0.152403	−	0.0533283i	−0.252999	−	0.967466i	$-0.581417\pi$
$83$	1.38846	−	0.485844i	0.152403	−	0.0533283i	0.405403	+	0.914138i	$0.367131\pi$
$84$	−0.538048	−	0.425285i	−0.0587058	−	0.0464024i
$85$	4.29153	−	4.13154i	0.465482	−	0.448128i
$86$	−2.36879	−	2.97037i	−0.255433	−	0.320303i
$87$	−0.620708	−	0.217195i	−0.0665469	−	0.0232858i
$88$	2.57677	−	4.10090i	0.274684	−	0.437157i
$89$	−9.91674	−	4.77565i	−1.05117	−	0.506218i	−0.173179	−	0.984890i	$-0.555404\pi$
$89$	−9.91674	−	4.77565i	−1.05117	−	0.506218i	−0.877994	+	0.478672i	$0.841118\pi$
$90$	0.610364	+	6.52949i	0.0643380	+	0.688268i
$91$	3.77557	+	4.69264i	0.395787	+	0.491922i
$92$	4.16317	+	2.61589i	0.434040	+	0.272725i
$93$	−0.167819	+	0.105448i	−0.0174020	+	0.0109344i
$94$	−5.94374	+	7.45322i	−0.613050	+	0.768741i
$95$	11.0704	+	9.17765i	1.13580	+	0.941607i
$96$	−0.112471	−	0.233549i	−0.0114790	−	0.0238365i
$97$	3.47917	+	3.47917i	0.353256	+	0.353256i	0.861319	−	0.508064i	$-0.169639\pi$
$97$	3.47917	+	3.47917i	0.353256	+	0.353256i	−0.508064	+	0.861319i	$0.669639\pi$
$98$	−6.94895	+	0.843890i	−0.701950	+	0.0852458i
$99$			14.2043i			1.42759i
$100$	2.33893	−	4.41921i	0.233893	−	0.441921i
$101$	−13.6557	−	3.11684i	−1.35880	−	0.310137i	−0.519808	−	0.854283i	$-0.673996\pi$
$101$	−13.6557	−	3.11684i	−1.35880	−	0.310137i	−0.838990	+	0.544147i	$0.816853\pi$
$102$	−0.0773208	−	0.686241i	−0.00765590	−	0.0679480i
$103$	−1.93029	−	3.07204i	−0.190197	−	0.302698i	0.737989	−	0.674813i	$-0.235776\pi$
$103$	−1.93029	−	3.07204i	−0.190197	−	0.302698i	−0.928187	+	0.372115i	$0.878633\pi$
$104$	0.506559	+	2.21938i	0.0496722	+	0.217628i
$105$	−1.18483	−	0.973643i	−0.115628	−	0.0950179i
$106$	1.32420	−	5.80170i	0.128618	−	0.563511i
$107$	12.7686	−	4.46791i	1.23438	−	0.431929i	0.367305	−	0.930101i	$-0.380281\pi$
$107$	12.7686	−	4.46791i	1.23438	−	0.431929i	0.867079	+	0.498171i	$0.165995\pi$
$108$	1.30218	+	0.818211i	0.125302	+	0.0787324i
$109$	1.41331	+	2.93477i	0.135371	+	0.281100i	0.957624	−	0.288022i	$-0.0929976\pi$
$109$	1.41331	+	2.93477i	0.135371	+	0.281100i	−0.822253	+	0.569122i	$0.807283\pi$
$110$	5.93493	−	9.05881i	0.565874	−	0.863724i
$111$	−0.601592	−	1.24922i	−0.0571006	−	0.118571i
$112$	−2.50104	−	0.863027i	−0.236326	−	0.0815484i
$113$	4.60519	+	13.1609i	0.433220	+	1.23807i	0.929148	+	0.369707i	$0.120542\pi$
$113$	4.60519	+	13.1609i	0.433220	+	1.23807i	−0.495929	+	0.868363i	$0.665172\pi$
$114$	1.62522	−	0.370946i	0.152216	−	0.0347423i
$115$	9.19636	+	6.02505i	0.857565	+	0.561838i
$116$	−2.53689			−0.235544
$117$	−4.72093	−	4.72093i	−0.436450	−	0.436450i
$118$	−11.7060	−	1.31895i	−1.07762	−	0.121419i
$119$	−5.52971	−	4.37080i	−0.506908	−	0.400671i
$120$	−0.241530	−	0.526913i	−0.0220485	−	0.0481003i
$121$	7.76687	−	9.73935i	0.706079	−	0.885396i
$122$	0.532221	+	1.52100i	0.0481850	+	0.137705i
$123$	0.481081	+	1.37485i	0.0433776	+	0.123966i
$124$	−0.476718	+	0.597785i	−0.0428105	+	0.0536827i
$125$	5.41673	−	9.78055i	0.484487	−	0.874799i
$126$	7.55739	−	1.75935i	0.673266	−	0.156735i
$127$	−14.6471	−	1.65034i	−1.29972	−	0.146444i	−0.565158	−	0.824983i	$-0.691185\pi$
$127$	−14.6471	−	1.65034i	−1.29972	−	0.146444i	−0.734564	+	0.678539i	$0.762613\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.984837			−0.0867101
$130$	1.03825	+	4.98330i	0.0910604	+	0.437064i
$131$	8.33247	−	1.90183i	0.728011	−	0.166164i	0.157577	−	0.987507i	$-0.449632\pi$
$131$	8.33247	−	1.90183i	0.728011	−	0.166164i	0.570435	+	0.821343i	$0.306775\pi$
$132$	−0.414654	−	1.18501i	−0.0360910	−	0.103142i
$133$	8.98991	−	14.4457i	0.779524	−	1.25260i
$134$	−4.66334	−	9.68353i	−0.402852	−	0.836530i
$135$	2.87648	+	1.88454i	0.247568	+	0.162196i
$136$	−1.15591	−	2.40026i	−0.0991180	−	0.205821i
$137$	5.64947	+	3.54980i	0.482667	+	0.303280i	0.751298	−	0.659963i	$-0.229428\pi$
$137$	5.64947	+	3.54980i	0.482667	+	0.303280i	−0.268631	+	0.963243i	$0.586571\pi$
$138$	1.20301	−	0.420950i	0.102407	−	0.0358336i
$139$	3.74261	−	16.3974i	0.317444	−	1.39081i	−0.524574	−	0.851365i	$-0.675776\pi$
$139$	3.74261	−	16.3974i	0.317444	−	1.39081i	0.842018	−	0.539449i	$-0.181367\pi$
$140$	−5.55483	−	2.03565i	−0.469469	−	0.172044i
$141$	0.549881	+	2.40919i	0.0463084	+	0.202890i
$142$	6.67891	+	10.6294i	0.560482	+	0.892001i
$143$	1.23446	+	10.9561i	0.103231	+	0.916197i
$144$	2.85927	+	0.652611i	0.238273	+	0.0543842i
$145$	−5.67164	−	0.107732i	−0.471004	−	0.00894662i
$146$		−	7.29895i		−	0.604065i
$147$	−0.952065	+	1.54470i	−0.0785250	+	0.127405i
$148$	−3.78222	−	3.78222i	−0.310896	−	0.310896i
$149$	−6.35489	−	13.1961i	−0.520613	−	1.08106i	−0.981119	−	0.193407i	$-0.938046\pi$
$149$	−6.35489	−	13.1961i	−0.520613	−	1.08106i	0.460505	−	0.887657i	$-0.347668\pi$
$150$	−0.517604	−	1.18826i	−0.0422622	−	0.0970207i
$151$	−1.40900	+	1.76683i	−0.114663	+	0.143782i	−0.835850	−	0.548957i	$-0.815025\pi$
$151$	−1.40900	+	1.76683i	−0.114663	+	0.143782i	0.721188	+	0.692740i	$0.243596\pi$
$152$	5.44521	−	3.42145i	0.441665	−	0.277516i
$153$	6.61567	+	4.15690i	0.534845	+	0.336066i
$154$	−11.5690	−	5.50982i	−0.932256	−	0.443994i
$155$	−1.09117	+	1.31620i	−0.0876446	+	0.105720i
$156$	0.531663	+	0.256035i	0.0425671	+	0.0204992i
$157$	−6.05052	+	9.62934i	−0.482884	+	0.768505i	−0.995956	−	0.0898400i	$-0.971364\pi$
$157$	−6.05052	+	9.62934i	−0.482884	+	0.768505i	0.513072	+	0.858345i	$0.328507\pi$
$158$	−1.97257	−	0.690232i	−0.156929	−	0.0549119i
$159$	−0.961789	−	1.20604i	−0.0762748	−	0.0956456i
$160$	−1.55083	−	1.61088i	−0.122604	−	0.127351i
$161$	5.59348	−	11.7446i	0.440828	−	0.925608i
$162$	−7.92840	+	2.77427i	−0.622914	+	0.217967i
$163$	−10.1445	+	16.1448i	−0.794576	+	1.26456i	0.165884	+	0.986145i	$0.446952\pi$
$163$	−10.1445	+	16.1448i	−0.794576	+	1.26456i	−0.960461	+	0.278416i	$0.910191\pi$
$164$	3.50348	+	4.39322i	0.273575	+	0.343053i
$165$	−0.876704	−	2.66690i	−0.0682513	−	0.207618i
$166$		−	1.47101i		−	0.114172i
$167$	−0.904974	+	8.03187i	−0.0700290	+	0.621525i	0.908856	+	0.417111i	$0.136957\pi$
$167$	−0.904974	+	8.03187i	−0.0700290	+	0.621525i	−0.978885	+	0.204414i	$0.934471\pi$
$168$	−0.579125	+	0.367392i	−0.0446805	+	0.0283449i
$169$	6.11216	+	4.87429i	0.470166	+	0.374945i
$170$	−2.48229	−	5.41527i	−0.190383	−	0.415332i
$171$	−8.18331	+	16.9928i	−0.625793	+	1.29947i
$172$	−3.58604	+	1.25481i	−0.273433	+	0.0956784i
$173$	−1.65486	−	14.6873i	−0.125816	−	1.11665i	−0.884940	−	0.465705i	$-0.845801\pi$
$173$	−1.65486	−	14.6873i	−0.125816	−	1.11665i	0.759124	−	0.650946i	$-0.225628\pi$
$174$	−0.410014	+	0.514141i	−0.0310831	+	0.0389769i
$175$	−12.3323	−	4.78692i	−0.932234	−	0.361857i
$176$	−3.01972	−	3.78661i	−0.227620	−	0.285426i
$177$	−2.15923	+	2.15923i	−0.162298	+	0.162298i
$178$	−7.78295	+	7.78295i	−0.583357	+	0.583357i
$179$	9.21090	−	7.34545i	0.688455	−	0.549025i	−0.215578	−	0.976487i	$-0.569164\pi$
$179$	9.21090	−	7.34545i	0.688455	−	0.549025i	0.904033	+	0.427462i	$0.140592\pi$
$180$	6.36466	+	1.58044i	0.474394	+	0.117799i
$181$	−7.01952	+	14.5762i	−0.521757	+	1.08344i	0.459041	+	0.888415i	$0.348193\pi$
$181$	−7.01952	+	14.5762i	−0.521757	+	1.08344i	−0.980798	+	0.195025i	$0.937521\pi$
$182$	5.67629	−	2.01382i	0.420755	−	0.149274i
$183$	0.394272	+	0.137962i	0.0291455	+	0.0101984i
$184$	3.84410	−	3.06557i	0.283391	−	0.225997i
$185$	−8.29515	−	8.61638i	−0.609872	−	0.633489i
$186$	0.0441032	+	0.193229i	0.00323381	+	0.0141682i
$187$	−4.26154	−	12.1788i	−0.311635	−	0.890602i
$188$	5.07187	+	8.07184i	0.369904	+	0.588700i
$189$	1.74956	−	3.67355i	0.127261	−	0.267211i
$190$	12.3190	−	7.41798i	0.893711	−	0.538157i
$191$	−0.119783	+	0.524803i	−0.00866719	+	0.0379734i	−0.979077	−	0.203492i	$-0.934771\pi$
$191$	−0.119783	+	0.524803i	−0.00866719	+	0.0379734i	0.970409	+	0.241465i	$0.0776280\pi$
$192$	−0.257589	+	0.0290234i	−0.0185899	+	0.00209458i
$193$	6.13364	−	3.85402i	0.441509	−	0.277418i	−0.292878	−	0.956150i	$-0.594613\pi$
$193$	6.13364	−	3.85402i	0.441509	−	0.277418i	0.734386	+	0.678732i	$0.237470\pi$
$194$	4.43302	−	2.13483i	0.318272	−	0.153272i
$195$	1.17775	+	0.594987i	0.0843403	+	0.0426079i
$196$	−1.49856	+	6.83771i	−0.107040	+	0.488408i
$197$	−15.4981	+	15.4981i	−1.10420	+	1.10420i	−0.110299	+	0.993898i	$0.535181\pi$
$197$	−15.4981	+	15.4981i	−1.10420	+	1.10420i	−0.993898	+	0.110299i	$0.964819\pi$
$198$	13.4072	+	4.69139i	0.952810	+	0.333402i
$199$	−1.29948	+	5.69341i	−0.0921180	+	0.403595i	−0.999874	−	0.0159043i	$-0.994937\pi$
$199$	−1.29948	+	5.69341i	−0.0921180	+	0.403595i	0.907756	+	0.419500i	$0.137794\pi$
$200$	−3.39872	−	3.66725i	−0.240326	−	0.259314i
$201$	−2.71621	−	0.619958i	−0.191587	−	0.0437285i
$202$	−7.45214	+	11.8600i	−0.524330	+	0.834467i
$203$	0.780343	+	6.66646i	0.0547693	+	0.467894i
$204$	−0.673269	−	0.153669i	−0.0471383	−	0.0107590i
$205$	7.64603	+	9.97054i	0.534022	+	0.696373i
$206$	−3.53719	+	0.807340i	−0.246448	+	0.0562500i
$207$	−4.76262	+	13.6108i	−0.331025	+	0.946015i
$208$	2.26214	+	0.254882i	0.156851	+	0.0176729i
$209$	28.0620	−	13.5140i	1.94109	−	0.934781i
$210$	−1.31033	+	0.796772i	−0.0904215	+	0.0549825i
$211$	12.6980	+	6.11505i	0.874169	+	0.420978i	0.816491	−	0.577358i	$-0.195916\pi$
$211$	12.6980	+	6.11505i	0.874169	+	0.420978i	0.0576776	+	0.998335i	$0.481630\pi$
$212$	−5.03877	−	3.16607i	−0.346064	−	0.217447i
$213$	3.23367	+	0.364347i	0.221568	+	0.0249647i
$214$		−	13.5277i		−	0.924734i
$215$	−8.07047	+	2.65305i	−0.550402	+	0.180937i
$216$	1.20238	−	0.958864i	0.0818114	−	0.0652424i
$217$	1.71750	+	1.06885i	0.116592	+	0.0725580i
$218$	3.23687	−	0.364707i	0.219228	−	0.0247011i
$219$	−1.47925	−	1.17966i	−0.0999583	−	0.0797141i
$220$	−6.59028	−	8.59382i	−0.444316	−	0.579395i
$221$	5.46409	+	2.63137i	0.367554	+	0.177005i
$222$	−1.37781	+	0.155242i	−0.0924726	+	0.0104192i
$223$	1.88752	+	16.7522i	0.126397	+	1.12181i	0.883474	+	0.468481i	$0.155199\pi$
$223$	1.88752	+	16.7522i	0.126397	+	1.12181i	−0.757076	+	0.653327i	$0.773373\pi$
$224$	−1.64064	+	2.07565i	−0.109620	+	0.138685i
$225$	14.1621	+	3.80362i	0.944143	+	0.253574i
$226$	13.9433			0.927496
$227$	7.99697	+	7.99697i	0.530777	+	0.530777i	0.920804	−	0.390026i	$-0.127534\pi$
$227$	7.99697	+	7.99697i	0.530777	+	0.530777i	−0.390026	+	0.920804i	$0.627534\pi$
$228$	0.186647	−	1.65653i	0.0123610	−	0.109707i
$229$	4.42493	+	19.3869i	0.292407	+	1.28112i	0.881164	+	0.472810i	$0.156760\pi$
$229$	4.42493	+	19.3869i	0.292407	+	1.28112i	−0.588757	+	0.808310i	$0.700382\pi$
$230$	8.72430	−	6.69034i	0.575264	−	0.441148i
$231$	−2.98644	+	1.45414i	−0.196493	+	0.0956753i
$232$	−0.837882	+	2.39453i	−0.0550096	+	0.157208i
$233$	1.98331	−	17.6024i	0.129931	−	1.15317i	−0.744363	−	0.667775i	$-0.767247\pi$
$233$	1.98331	−	17.6024i	0.129931	−	1.15317i	0.874294	−	0.485396i	$-0.161325\pi$
$234$	−6.01523	+	2.89678i	−0.393228	+	0.189369i
$235$	10.9962	+	18.2613i	0.717315	+	1.19124i
$236$	−5.11118	+	10.6135i	−0.332709	+	0.690878i
$237$	−0.458695	+	0.288217i	−0.0297954	+	0.0187217i
$238$	−5.95188	+	3.77582i	−0.385803	+	0.244750i
$239$	−25.4277	+	5.80371i	−1.64478	+	0.375411i	−0.941899	−	0.335896i	$-0.890961\pi$
$239$	−25.4277	+	5.80371i	−1.64478	+	0.375411i	−0.702882	+	0.711307i	$0.748104\pi$
$240$	−0.577116	+	0.0539477i	−0.0372527	+	0.00348231i
$241$	−6.00836	−	4.79151i	−0.387032	−	0.308648i	0.410573	−	0.911828i	$-0.365329\pi$
$241$	−6.00836	−	4.79151i	−0.387032	−	0.308648i	−0.797605	+	0.603180i	$0.793900\pi$
$242$	−6.62758	−	10.5477i	−0.426037	−	0.678034i
$243$	−2.24295	+	6.40998i	−0.143885	+	0.411201i
$244$	1.61143			0.103161
$245$	−3.64064	+	15.2232i	−0.232592	+	0.972574i
$246$	1.45659			0.0928688
$247$	−4.83518	+	13.8182i	−0.307655	+	0.879228i
$248$	0.406790	+	0.647402i	0.0258312	+	0.0411101i
$249$	−0.298123	−	0.237746i	−0.0188928	−	0.0150665i
$250$	−7.44266	−	8.34307i	−0.470715	−	0.527662i
$251$	−21.7145	+	4.95619i	−1.37060	+	0.312832i	−0.843573	−	0.537014i	$-0.819552\pi$
$251$	−21.7145	+	4.95619i	−1.37060	+	0.312832i	−0.527032	+	0.849846i	$0.676695\pi$
$252$	0.835429	−	7.71437i	0.0526271	−	0.485960i
$253$	20.1633	−	12.6694i	1.26765	−	0.796519i
$254$	−6.39536	+	13.2801i	−0.401281	+	0.833268i
$255$	−1.49868	−	0.372144i	−0.0938509	−	0.0233046i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−1.92367	+	17.0730i	−0.119995	+	1.06499i	0.778999	+	0.627026i	$0.215728\pi$
$257$	−1.92367	+	17.0730i	−0.119995	+	1.06499i	−0.898994	+	0.437961i	$0.855701\pi$
$258$	−0.325271	+	0.929572i	−0.0202505	+	0.0578726i
$259$	−8.77554	+	11.1023i	−0.545286	+	0.689866i
$260$	5.04657	+	0.665895i	0.312975	+	0.0412971i
$261$	−1.65560	−	7.25366i	−0.102479	−	0.448991i
$262$	0.956933	−	8.49301i	0.0591195	−	0.524700i
$263$	4.68612	+	4.68612i	0.288958	+	0.288958i	0.836668	−	0.547710i	$-0.184500\pi$
$263$	4.68612	+	4.68612i	0.288958	+	0.288958i	−0.547710	+	0.836668i	$0.684500\pi$
$264$	−1.25547			−0.0772685
$265$	−11.1306	−	7.29225i	−0.683745	−	0.447959i
$266$	−10.6659	−	13.2565i	−0.653966	−	0.812810i
$267$	0.319453	+	2.83522i	0.0195502	+	0.173513i
$268$	−10.6803	+	1.20338i	−0.652405	+	0.0735084i
$269$	−15.6211	−	7.52271i	−0.952434	−	0.458668i	−0.107895	−	0.994162i	$-0.534411\pi$
$269$	−15.6211	−	7.52271i	−0.952434	−	0.458668i	−0.844539	+	0.535494i	$0.820125\pi$
$270$	2.72883	−	2.09264i	0.166071	−	0.127354i
$271$	9.27689	+	7.39807i	0.563531	+	0.449401i	0.863357	−	0.504593i	$-0.168357\pi$
$271$	9.27689	+	7.39807i	0.563531	+	0.449401i	−0.299827	+	0.953994i	$0.596929\pi$
$272$	−2.64734	+	0.298283i	−0.160518	+	0.0180861i
$273$	0.509274	−	1.47587i	0.0308226	−	0.0893234i
$274$	5.21650	−	4.16002i	0.315140	−	0.251316i
$275$	−14.3687	−	19.4928i	−0.866465	−	1.17546i
$276$		−	1.27453i		−	0.0767175i
$277$	−3.94862	−	0.444903i	−0.237250	−	0.0267316i	−0.00746110	−	0.999972i	$-0.502375\pi$
$277$	−3.94862	−	0.444903i	−0.237250	−	0.0267316i	−0.229789	+	0.973241i	$0.573804\pi$
$278$	−14.2412	−	8.94832i	−0.854129	−	0.536685i
$279$	−2.02034	−	0.972946i	−0.120955	−	0.0582487i
$280$	−3.75606	+	4.57078i	−0.224467	+	0.273156i
$281$	−17.3621	+	8.36113i	−1.03573	+	0.498783i	−0.872915	−	0.487873i	$-0.837773\pi$
$281$	−17.3621	+	8.36113i	−1.03573	+	0.498783i	−0.162819	+	0.986656i	$0.552059\pi$
$282$	2.45561	+	0.276680i	0.146229	+	0.0164761i
$283$	9.03793	−	25.8289i	0.537249	−	1.53537i	−0.280534	−	0.959844i	$-0.590512\pi$
$283$	9.03793	−	25.8289i	0.537249	−	1.53537i	0.817783	−	0.575526i	$-0.195203\pi$
$284$	12.2388	−	2.79344i	0.726242	−	0.165760i
$285$	0.487626	−	3.69553i	0.0288845	−	0.218904i
$286$	10.7490	+	2.45339i	0.635603	+	0.145072i
$287$	10.4669	−	10.5578i	0.617841	−	0.623208i
$288$	1.56035	−	2.48328i	0.0919443	−	0.146329i
$289$	9.65435	+	2.20354i	0.567903	+	0.129620i
$290$	−1.97491	+	5.31778i	−0.115971	+	0.312271i
$291$	0.283810	−	1.24345i	0.0166373	−	0.0728926i
$292$	−6.88935	−	2.41069i	−0.403169	−	0.141075i
$293$	−14.9146	+	14.9146i	−0.871318	+	0.871318i	−0.992616	−	0.121298i	$-0.961294\pi$
$293$	−14.9146	+	14.9146i	−0.871318	+	0.871318i	0.121298	+	0.992616i	$0.461294\pi$
$294$	1.14357	+	1.40882i	0.0666946	+	0.0821642i
$295$	−11.8776	+	23.5111i	−0.691540	+	1.36887i
$296$	−4.81916	+	2.32078i	−0.280108	+	0.134893i
$297$	6.30677	−	3.96280i	0.365956	−	0.229945i
$298$	−14.5544	+	1.63989i	−0.843116	+	0.0949964i
$299$	−2.49064	+	10.9122i	−0.144038	+	0.631070i
$300$	−1.29253	+	0.0961012i	−0.0746242	+	0.00554841i
$301$	4.40046	+	9.03746i	0.253638	+	0.520910i
$302$	1.20232	+	1.91348i	0.0691855	+	0.110108i
$303$	1.19920	+	3.42712i	0.0688922	+	0.196883i
$304$	−1.43101	−	6.26967i	−0.0820742	−	0.359590i
$305$	3.60261	+	0.0684308i	0.206285	+	0.00391834i
$306$	6.10865	−	4.87149i	0.349208	−	0.278484i
$307$	2.63902	+	0.923432i	0.150617	+	0.0527031i	0.404534	−	0.914523i	$-0.367434\pi$
$307$	2.63902	+	0.923432i	0.150617	+	0.0527031i	−0.253918	+	0.967226i	$0.581719\pi$
$308$	−9.02162	+	9.10000i	−0.514055	+	0.518521i
$309$	−0.408062	+	0.847350i	−0.0232138	+	0.0482041i
$310$	0.881953	+	1.46465i	0.0500915	+	0.0831864i
$311$	19.8219	−	15.8075i	1.12400	−	0.896359i	0.128555	−	0.991702i	$-0.458966\pi$
$311$	19.8219	−	15.8075i	1.12400	−	0.896359i	0.995444	+	0.0953429i	$0.0303948\pi$
$312$	0.417265	−	0.417265i	0.0236230	−	0.0236230i
$313$	−19.4389	+	19.4389i	−1.09875	+	1.09875i	−0.104196	+	0.994557i	$0.533227\pi$
$313$	−19.4389	+	19.4389i	−1.09875	+	1.09875i	−0.994557	+	0.104196i	$0.966773\pi$
$314$	7.09062	+	8.89135i	0.400147	+	0.501768i
$315$	2.19534	−	17.2113i	0.123693	−	0.969745i
$316$	−1.30300	+	1.63391i	−0.0732993	+	0.0919145i
$317$	−2.64562	−	23.4806i	−0.148593	−	1.31880i	−0.817705	−	0.575638i	$-0.804754\pi$
$317$	−2.64562	−	23.4806i	−0.148593	−	1.31880i	0.669112	−	0.743162i	$-0.266675\pi$
$318$	−1.45602	+	0.509485i	−0.0816498	+	0.0285705i
$319$	−5.33104	+	11.0700i	−0.298481	+	0.619802i
$320$	−2.03269	+	0.931758i	−0.113631	+	0.0520869i
$321$	−2.74160	−	2.18635i	−0.153021	−	0.122030i
$322$	−9.23817	−	9.15860i	−0.514823	−	0.510389i
$323$	1.91823	−	17.0248i	0.106733	−	0.947285i
$324$			8.39976i			0.466653i
$325$	11.2542	+	1.70303i	0.624268	+	0.0944669i
$326$	11.8883	+	14.9075i	0.658434	+	0.825650i
$327$	0.449231	−	0.714946i	0.0248425	−	0.0395366i
$328$	5.30381	−	1.85588i	0.292854	−	0.102474i
$329$	19.6512	−	15.8108i	1.08340	−	0.871678i
$330$	−2.80680	−	0.0533146i	−0.154509	−	0.00293487i
$331$	−1.59380	−	1.99857i	−0.0876033	−	0.109851i	0.736098	−	0.676875i	$-0.236666\pi$
$331$	−1.59380	−	1.99857i	−0.0876033	−	0.109851i	−0.823701	+	0.567024i	$0.808095\pi$
$332$	−1.38846	−	0.485844i	−0.0762017	−	0.0266641i
$333$	8.34608	−	13.2827i	0.457362	−	0.727888i
$334$	7.28225	+	3.50695i	0.398467	+	0.191892i
$335$	−23.9287	+	2.23681i	−1.30737	+	0.122210i
$336$	0.155502	+	0.667969i	0.00848333	+	0.0364407i
$337$	11.2820	+	7.08897i	0.614571	+	0.386161i	0.803046	−	0.595917i	$-0.203211\pi$
$337$	11.2820	+	7.08897i	0.614571	+	0.386161i	−0.188475	+	0.982078i	$0.560354\pi$
$338$	6.61948	−	4.15929i	0.360052	−	0.226236i
$339$	2.25353	−	2.82584i	0.122395	−	0.153478i
$340$	−5.93123	+	0.554440i	−0.321666	+	0.0300687i
$341$	1.60673	+	3.33641i	0.0870092	+	0.180677i
$342$	13.3365	+	13.3365i	0.721153	+	0.721153i
$343$	18.4292	+	1.83465i	0.995081	+	0.0990620i
$344$			3.79924i			0.204841i
$345$	0.0541241	−	2.84942i	0.00291394	−	0.153407i
$346$	−14.4096	−	3.28890i	−0.774666	−	0.176812i
$347$	−1.16712	−	10.3585i	−0.0626545	−	0.556074i	−0.985350	−	0.170544i	$-0.945447\pi$
$347$	−1.16712	−	10.3585i	−0.0626545	−	0.556074i	0.922696	−	0.385530i	$-0.125981\pi$
$348$	0.349870	+	0.556815i	0.0187550	+	0.0298484i
$349$	2.98588	+	13.0820i	0.159830	+	0.700263i	0.989801	+	0.142456i	$0.0454999\pi$
$349$	2.98588	+	13.0820i	0.159830	+	0.700263i	−0.829971	+	0.557807i	$0.811643\pi$
$350$	−8.59139	+	10.0592i	−0.459229	+	0.537688i
$351$	−0.779036	+	3.41318i	−0.0415819	+	0.182182i
$352$	−4.57147	+	1.59963i	−0.243660	+	0.0852603i
$353$	9.94862	+	6.25113i	0.529511	+	0.332714i	0.770110	−	0.637911i	$-0.220201\pi$
$353$	9.94862	+	6.25113i	0.529511	+	0.332714i	−0.240599	+	0.970625i	$0.577344\pi$
$354$	1.32492	+	2.75122i	0.0704185	+	0.146225i
$355$	27.4806	−	5.72545i	1.45852	−	0.303875i
$356$	4.77565	+	9.91674i	0.253109	+	0.525586i
$357$	−0.196717	+	1.81649i	−0.0104114	+	0.0961389i
$358$	−3.89108	−	11.1201i	−0.205650	−	0.587714i
$359$	32.7076	−	7.46530i	1.72624	−	0.394004i	0.759653	−	0.650329i	$-0.225369\pi$
$359$	32.7076	−	7.46530i	1.72624	−	0.394004i	0.966591	+	0.256325i	$0.0825119\pi$
$360$	3.59387	−	5.48551i	0.189413	−	0.289112i
$361$	22.3566			1.17666
$362$	11.4398	+	11.4398i	0.601264	+	0.601264i
$363$	−3.20882	−	0.361547i	−0.168419	−	0.0189763i
$364$	−0.0260491	−	6.02288i	−0.00136534	−	0.315685i
$365$	−15.2999	−	5.68206i	−0.800834	−	0.297412i
$366$	0.260440	−	0.326581i	0.0136134	−	0.0170707i
$367$	−5.06682	−	14.4802i	−0.264486	−	0.755858i	−0.997162	−	0.0752805i	$-0.976015\pi$
$367$	−5.06682	−	14.4802i	−0.264486	−	0.755858i	0.732676	−	0.680577i	$-0.238271\pi$
$368$	−1.62391	−	4.64088i	−0.0846523	−	0.241922i
$369$	−10.2750	+	12.8845i	−0.534896	+	0.670738i
$370$	−10.8726	+	4.98384i	−0.565238	+	0.259098i
$371$	−6.76991	+	14.2148i	−0.351476	+	0.737996i
$372$	0.196952	+	0.0221911i	0.0102115	+	0.00115056i
$373$	−24.5478	−	24.5478i	−1.27104	−	1.27104i	−0.945544	−	0.325494i	$-0.894469\pi$
$373$	−24.5478	−	24.5478i	−1.27104	−	1.27104i	−0.325494	−	0.945544i	$-0.605531\pi$
$374$	−12.9029			−0.667191
$375$	−2.89374	+	0.159962i	−0.149432	+	0.00826038i
$376$	9.29401	−	2.12130i	0.479302	−	0.109398i
$377$	−1.90740	−	5.45104i	−0.0982361	−	0.280743i
$378$	−2.88956	−	2.86467i	−0.148623	−	0.147343i
$379$	−14.3512	−	29.8006i	−0.737173	−	1.53076i	−0.843920	−	0.536469i	$-0.819758\pi$
$379$	−14.3512	−	29.8006i	−0.737173	−	1.53076i	0.106747	−	0.994286i	$-0.465957\pi$
$380$	−2.93302	−	14.0777i	−0.150461	−	0.722169i
$381$	1.65780	+	3.44246i	0.0849318	+	0.176363i
$382$	0.455791	+	0.286393i	0.0233203	+	0.0146531i
$383$	−19.4110	+	6.79221i	−0.991857	+	0.347066i	−0.776946	−	0.629568i	$-0.783232\pi$
$383$	−19.4110	+	6.79221i	−0.991857	+	0.347066i	−0.214912	+	0.976634i	$0.568946\pi$
$384$	−0.0576817	+	0.252720i	−0.00294356	+	0.0128966i
$385$	−20.5558	+	19.9614i	−1.04762	+	1.01733i
$386$	−1.61193	−	7.06234i	−0.0820452	−	0.359464i
$387$	−5.92814	−	9.43457i	−0.301344	−	0.479586i
$388$	−0.550897	−	4.88934i	−0.0279675	−	0.248219i
$389$	−30.7268	−	7.01320i	−1.55791	−	0.355583i	−0.645144	−	0.764061i	$-0.723203\pi$
$389$	−30.7268	−	7.01320i	−1.55791	−	0.355583i	−0.912768	+	0.408478i	$0.866060\pi$
$390$	0.950584	−	0.915145i	0.0481347	−	0.0463401i
$391$		−	13.0988i		−	0.662433i
$392$	5.95906	+	3.67282i	0.300978	+	0.185505i
$393$	−1.56658	−	1.56658i	−0.0790237	−	0.0790237i
$394$	9.50973	+	19.7472i	0.479093	+	0.994847i
$395$	−2.98245	+	3.59754i	−0.150063	+	0.181012i
$396$	8.85625	−	11.1054i	0.445043	−	0.558066i
$397$	6.27664	−	3.94388i	0.315016	−	0.197937i	−0.365238	−	0.930914i	$-0.619012\pi$
$397$	6.27664	−	3.94388i	0.315016	−	0.197937i	0.680254	+	0.732977i	$0.261870\pi$
$398$	4.94472	+	3.10698i	0.247857	+	0.155739i
$399$	−4.41047	+	0.0190754i	−0.220800	+	0.000954962i
$400$	−4.58398	+	1.99678i	−0.229199	+	0.0998389i
$401$	10.2625	+	4.94215i	0.512484	+	0.246799i	0.672208	−	0.740363i	$-0.265346\pi$
$401$	10.2625	+	4.94215i	0.512484	+	0.246799i	−0.159724	+	0.987162i	$0.551060\pi$
$402$	−1.48228	+	2.35903i	−0.0739293	+	0.117658i
$403$	−1.64289	−	0.574874i	−0.0818384	−	0.0286365i
$404$	8.73318	+	10.9511i	0.434492	+	0.544836i
$405$	−0.356704	+	18.7791i	−0.0177248	+	0.933139i
$406$	6.55010	+	1.46524i	0.325076	+	0.0727187i
$407$	−24.4521	+	8.55617i	−1.21205	+	0.424114i
$408$	−0.367413	+	0.584734i	−0.0181896	+	0.0289486i
$409$	−8.24959	−	10.3447i	−0.407916	−	0.511511i	0.534858	−	0.844942i	$-0.320365\pi$
$409$	−8.24959	−	10.3447i	−0.407916	−	0.511511i	−0.942774	+	0.333431i	$0.891794\pi$
$410$	11.9364	−	3.92390i	0.589495	−	0.193788i
$411$		−	1.72955i		−	0.0853125i
$412$	−0.406224	+	3.60534i	−0.0200132	+	0.177622i
$413$	29.4624	+	10.1665i	1.44975	+	0.500261i
$414$	11.2740	+	8.99072i	0.554087	+	0.441870i
$415$	−3.08350	−	1.14515i	−0.151363	−	0.0562130i
$416$	0.987717	−	2.05102i	0.0484268	−	0.100559i
$417$	−4.11519	+	1.43997i	−0.201522	+	0.0705154i
$418$	−3.48730	−	30.9507i	−0.170570	−	1.51385i
$419$	13.3403	−	16.7282i	0.651716	−	0.817225i	−0.340698	−	0.940173i	$-0.610663\pi$
$419$	13.3403	−	16.7282i	0.651716	−	0.817225i	0.992413	+	0.122948i	$0.0392347\pi$
$420$	0.319284	+	1.49996i	0.0155795	+	0.0731904i
$421$	−9.13345	−	11.4530i	−0.445137	−	0.558184i	0.507752	−	0.861503i	$-0.330477\pi$
$421$	−9.13345	−	11.4530i	−0.445137	−	0.558184i	−0.952889	+	0.303319i	$0.901905\pi$
$422$	9.96579	−	9.96579i	0.485127	−	0.485127i
$423$	−19.7696	+	19.7696i	−0.961233	+	0.961233i
$424$	−4.65260	+	3.71033i	−0.225950	+	0.180189i
$425$	−13.2838	+	0.987666i	−0.644358	+	0.0479088i
$426$	1.41192	−	2.93187i	0.0684075	−	0.142050i
$427$	−0.495672	−	4.23452i	−0.0239873	−	0.204923i
$428$	−12.7686	−	4.46791i	−0.617192	−	0.215965i
$429$	2.23448	−	1.78194i	0.107882	−	0.0860329i
$430$	−0.161339	+	8.49383i	−0.00778044	+	0.409609i
$431$	−0.879090	−	3.85154i	−0.0423443	−	0.185522i	0.949333	−	0.314273i	$-0.101761\pi$
$431$	−0.879090	−	3.85154i	−0.0423443	−	0.185522i	−0.991677	+	0.128750i	$0.958903\pi$
$432$	−0.507936	−	1.45160i	−0.0244381	−	0.0698400i
$433$	4.34366	+	6.91290i	0.208743	+	0.332213i	0.934643	−	0.355588i	$-0.115719\pi$
$433$	4.34366	+	6.91290i	0.208743	+	0.332213i	−0.725900	+	0.687800i	$0.758576\pi$
$434$	1.57612	−	1.26811i	0.0756562	−	0.0608710i
$435$	0.758547	+	1.25971i	0.0363695	+	0.0603985i
$436$	0.724828	−	3.17568i	0.0347130	−	0.152087i
$437$	31.4206	−	3.54025i	1.50305	−	0.169353i
$438$	−1.60203	+	1.00662i	−0.0765478	+	0.0480982i
$439$	3.40301	−	1.63880i	0.162417	−	0.0782159i	−0.350909	−	0.936409i	$-0.614127\pi$
$439$	3.40301	−	1.63880i	0.162417	−	0.0782159i	0.513326	+	0.858194i	$0.328413\pi$
$440$	−10.2882	+	3.38209i	−0.490470	+	0.161235i
$441$	−20.5289	+	0.177579i	−0.977565	+	0.00845613i
$442$	4.28838	−	4.28838i	0.203977	−	0.203977i
$443$	−20.1159	−	7.03885i	−0.955734	−	0.334426i	−0.193044	−	0.981190i	$-0.561836\pi$
$443$	−20.1159	−	7.03885i	−0.955734	−	0.334426i	−0.762690	+	0.646764i	$0.776122\pi$
$444$	−0.308532	+	1.35177i	−0.0146423	+	0.0641519i
$445$	10.2556	+	22.3733i	0.486164	+	1.06060i
$446$	16.4355	+	3.75129i	0.778243	+	0.177629i
$447$	−2.01995	+	3.21473i	−0.0955402	+	0.152051i
$448$	1.41730	+	2.23411i	0.0669611	+	0.105552i
$449$	−24.4024	−	5.56969i	−1.15162	−	0.262850i	−0.396247	−	0.918144i	$-0.629688\pi$
$449$	−24.4024	−	5.56969i	−1.15162	−	0.262850i	−0.755374	+	0.655294i	$0.772545\pi$
$450$	8.26763	−	12.1112i	0.389740	−	0.570925i
$451$	26.5326	−	6.05589i	1.24937	−	0.285161i
$452$	4.60519	−	13.1609i	0.216610	−	0.619035i
$453$	0.582115	+	0.0655886i	0.0273502	+	0.00308162i
$454$	10.1894	−	4.90697i	0.478214	−	0.230296i
$455$	0.197531	−	13.4662i	0.00926038	−	0.631307i
$456$	−1.50193	−	0.723291i	−0.0703343	−	0.0338712i
$457$	−23.9402	−	15.0426i	−1.11987	−	0.703663i	−0.160847	−	0.986979i	$-0.551422\pi$
$457$	−23.9402	−	15.0426i	−1.11987	−	0.703663i	−0.959026	+	0.283317i	$0.908565\pi$
$458$	19.7604	+	2.22646i	0.923343	+	0.104036i
$459$		−	4.09710i		−	0.191236i
$460$	−3.43345	−	10.4444i	−0.160085	−	0.486973i
$461$	26.3242	−	20.9929i	1.22604	−	0.977735i	0.226048	−	0.974116i	$-0.427419\pi$
$461$	26.3242	−	20.9929i	1.22604	−	0.977735i	0.999993	−	0.00361899i	$-0.00115196\pi$
$462$	0.386179	+	3.29912i	0.0179667	+	0.153489i
$463$	33.9942	−	3.83022i	1.57984	−	0.178006i	0.721991	−	0.691902i	$-0.243227\pi$
$463$	33.9942	−	3.83022i	1.57984	−	0.178006i	0.857852	+	0.513897i	$0.171799\pi$
$464$	1.98342	+	1.58173i	0.0920780	+	0.0734297i
$465$	0.439376	+	0.0579757i	0.0203756	+	0.00268856i
$466$	−15.9596	−	7.68572i	−0.739312	−	0.356034i
$467$	36.4932	−	4.11179i	1.68870	−	0.190271i	0.785315	−	0.619096i	$-0.212501\pi$
$467$	36.4932	−	4.11179i	1.68870	−	0.190271i	0.903388	+	0.428825i	$0.141072\pi$
$468$	0.747520	+	6.63442i	0.0345541	+	0.306676i
$469$	6.44752	+	27.6957i	0.297719	+	1.27887i
$470$	20.8684	−	4.34783i	0.962586	−	0.200550i
$471$	2.94796			0.135835
$472$	8.32976	+	8.32976i	0.383408	+	0.383408i
$473$	−2.06022	+	18.2850i	−0.0947292	+	0.840745i
$474$	0.120546	+	0.528146i	0.00553686	+	0.0242586i
$475$	−5.95942	−	31.5975i	−0.273437	−	1.44979i
$476$	1.59815	+	6.86495i	0.0732510	+	0.314654i
$477$	5.76431	−	16.4734i	0.263929	−	0.754267i
$478$	−2.92021	+	25.9176i	−0.133568	+	1.18544i
$479$	29.7133	−	14.3091i	1.35763	−	0.653802i	0.393526	−	0.919314i	$-0.371255\pi$
$479$	29.7133	−	14.3091i	1.35763	−	0.653802i	0.964108	+	0.265512i	$0.0855410\pi$
$480$	−0.139689	+	0.562548i	−0.00637590	+	0.0256767i
$481$	5.28316	−	10.9706i	0.240891	−	0.500216i
$482$	−6.50706	+	4.08865i	−0.296388	+	0.186233i
$483$	−3.34922	+	0.392042i	−0.152395	+	0.0178385i
$484$	−12.1448	+	2.77197i	−0.552035	+	0.125998i
$485$	−1.02399	−	10.9543i	−0.0464970	−	0.497410i
$486$	5.30948	+	4.23417i	0.240843	+	0.192066i
$487$	−18.6223	−	29.6373i	−0.843858	−	1.34299i	−0.937715	−	0.347407i	$-0.887062\pi$
$487$	−18.6223	−	29.6373i	−0.843858	−	1.34299i	0.0938566	−	0.995586i	$-0.470080\pi$
$488$	0.532221	−	1.52100i	0.0240925	−	0.0688524i
$489$	4.94264			0.223514
$490$	13.1665	+	8.46424i	0.594802	+	0.382376i
$491$	40.4813			1.82689			0.913447	−	0.406957i	$-0.133410\pi$
$491$	40.4813			1.82689			0.913447	+	0.406957i	$0.133410\pi$
$492$	0.481081	−	1.37485i	0.0216888	−	0.0619831i
$493$	3.59574	+	5.72259i	0.161944	+	0.257732i
$494$	11.4458	+	9.12769i	0.514969	+	0.410674i
$495$	20.2712	−	24.4518i	0.911123	−	1.09903i
$496$	0.745426	−	0.170139i	0.0334706	−	0.00763945i
$497$	−11.1053	−	31.3021i	−0.498139	−	1.40409i
$498$	−0.322868	+	0.202871i	−0.0144681	+	0.00909088i
$499$	−18.0500	+	37.4812i	−0.808029	+	1.67789i	−0.0755088	+	0.997145i	$0.524058\pi$
$499$	−18.0500	+	37.4812i	−0.808029	+	1.67789i	−0.732521	+	0.680745i	$0.761656\pi$
$500$	−10.3330	+	4.26946i	−0.462108	+	0.190936i
$501$	1.88770	−	0.909069i	0.0843363	−	0.0406142i
$502$	−2.49377	+	22.1328i	−0.111303	+	0.987837i
$503$	−0.326113	+	0.931976i	−0.0145406	+	0.0415548i	−0.950925	−	0.309422i	$-0.899865\pi$
$503$	−0.326113	+	0.931976i	−0.0145406	+	0.0415548i	0.936384	+	0.350976i	$0.114150\pi$
$504$	−7.00554	−	3.33644i	−0.312052	−	0.148617i
$505$	19.0594	+	24.8538i	0.848133	+	1.10598i
$506$	−5.29895	−	23.2162i	−0.235567	−	1.03209i
$507$	0.226897	−	2.01377i	0.0100769	−	0.0894347i
$508$	10.4226	+	10.4226i	0.462429	+	0.462429i
$509$	−35.6764			−1.58133			−0.790664	−	0.612251i	$-0.790264\pi$
$509$	−35.6764			−1.58133			−0.790664	+	0.612251i	$0.790264\pi$
$510$	−0.846243	+	1.29167i	−0.0374723	+	0.0571959i
$511$	−4.21568	+	18.8454i	−0.186491	+	0.833673i
$512$	0.111964	+	0.993712i	0.00494818	+	0.0439163i
$513$	9.82790	−	1.10734i	0.433912	−	0.0488902i
$514$	15.4796	+	7.45459i	0.682776	+	0.328808i
$515$	−1.06129	+	8.04308i	−0.0467658	+	0.354420i
$516$	0.769977	+	0.614036i	0.0338963	+	0.0270314i
$517$	45.8805	−	5.16950i	2.01782	−	0.227354i
$518$	7.58094	+	11.9500i	0.333088	+	0.525051i
$519$	−2.99544	+	2.38878i	−0.131485	+	0.104856i
$520$	2.29530	−	4.54344i	0.100656	−	0.199243i
$521$		−	37.3854i		−	1.63789i	−0.573875	−	0.818943i	$-0.694560\pi$
$521$		−	37.3854i		−	1.63789i	0.573875	−	0.818943i	$-0.305440\pi$
$522$	−7.39342	−	0.833039i	−0.323601	−	0.0364611i
$523$	6.37950	+	4.00850i	0.278956	+	0.175280i	0.664242	−	0.747518i	$-0.268754\pi$
$523$	6.37950	+	4.00850i	0.278956	+	0.175280i	−0.385286	+	0.922797i	$0.625897\pi$
$524$	−7.70036	−	3.70830i	−0.336392	−	0.161998i
$525$	0.650115	+	3.36696i	0.0283734	+	0.146946i
$526$	5.97087	−	2.87542i	0.260342	−	0.125374i
$527$	2.02414	+	0.228066i	0.0881731	+	0.00993472i
$528$	−0.414654	+	1.18501i	−0.0180455	+	0.0515711i
$529$	1.14537	−	0.261424i	0.0497987	−	0.0113662i
$530$	−10.5592	+	8.09747i	−0.458663	+	0.351732i
$531$	−33.6824	−	7.68779i	−1.46169	−	0.333622i
$532$	−16.0353	+	5.68897i	−0.695220	+	0.246648i
$533$	−6.80561	+	10.8311i	−0.294784	+	0.469145i
$534$	2.78163	+	0.634889i	0.120373	+	0.0274743i
$535$	−28.3565	−	10.5310i	−1.22596	−	0.455294i
$536$	−2.39164	+	10.4784i	−0.103303	+	0.452600i
$537$	−2.88254	−	1.00864i	−0.124391	−	0.0435262i
$538$	−12.2599	+	12.2599i	−0.528561	+	0.528561i
$539$	26.6881	+	20.9080i	1.14954	+	0.900570i
$540$	−1.07393	−	3.26685i	−0.0462146	−	0.140583i
$541$	26.7156	−	12.8655i	1.14859	−	0.553133i	0.239981	−	0.970777i	$-0.422859\pi$
$541$	26.7156	−	12.8655i	1.14859	−	0.553133i	0.908610	+	0.417645i	$0.137144\pi$
$542$	10.0469	−	6.31287i	0.431550	−	0.271161i
$543$	4.16737	−	0.469550i	0.178839	−	0.0201503i
$544$	−0.592816	+	2.59730i	−0.0254168	+	0.111358i
$545$	1.75533	−	7.06897i	0.0751901	−	0.302801i
$546$	−1.22484	−	0.968142i	−0.0524184	−	0.0414327i
$547$	−7.39391	−	11.7673i	−0.316141	−	0.503135i	0.650419	−	0.759575i	$-0.274593\pi$
$547$	−7.39391	−	11.7673i	−0.316141	−	0.503135i	−0.966560	+	0.256440i	$0.917450\pi$
$548$	−2.20367	−	6.29773i	−0.0941362	−	0.269026i
$549$	1.05163	+	4.60751i	0.0448827	+	0.196644i
$550$	−23.1446	+	7.12433i	−0.986888	+	0.303782i
$551$	−12.7552	+	10.1719i	−0.543390	+	0.433339i
$552$	−1.20301	−	0.420950i	−0.0512033	−	0.0179168i
$553$	4.69440	+	2.92144i	0.199626	+	0.124232i
$554$	−1.72408	+	3.58010i	−0.0732493	+	0.152104i
$555$	−0.747177	+	3.00899i	−0.0317159	+	0.127725i
$556$	−13.1497	+	10.4866i	−0.557673	+	0.444729i
$557$	−5.27775	+	5.27775i	−0.223625	+	0.223625i	−0.810023	−	0.586398i	$-0.800546\pi$
$557$	−5.27775	+	5.27775i	−0.223625	+	0.223625i	0.586398	+	0.810023i	$0.300546\pi$
$558$	−1.58562	+	1.58562i	−0.0671248	+	0.0671248i
$559$	−5.39244	−	6.76191i	−0.228076	−	0.285998i
$560$	3.07373	+	5.05491i	0.129889	+	0.213609i
$561$	−2.08537	+	2.61497i	−0.0880443	+	0.110404i
$562$	2.15760	+	19.1493i	0.0910131	+	0.807763i
$563$	19.1973	−	6.71742i	0.809069	−	0.283106i	0.106127	−	0.994353i	$-0.466155\pi$
$563$	19.1973	−	6.71742i	0.809069	−	0.283106i	0.702942	+	0.711247i	$0.251869\pi$
$564$	1.07219	−	2.22642i	0.0451473	−	0.0937494i
$565$	10.8545	−	29.2277i	0.456654	−	1.22962i
$566$	−21.3945	−	17.0615i	−0.899276	−	0.717149i
$567$	22.0730	−	2.58375i	0.926978	−	0.108507i
$568$	1.40556	−	12.4747i	0.0589758	−	0.523425i
$569$			12.6436i			0.530049i	0.964242	+	0.265024i	$0.0853800\pi$
$569$			12.6436i			0.530049i	−0.964242	+	0.265024i	$0.914620\pi$
$570$	−3.32710	−	1.68082i	−0.139357	−	0.0704017i
$571$	4.67126	+	5.85757i	0.195486	+	0.245132i	0.869908	−	0.493215i	$-0.164178\pi$
$571$	4.67126	+	5.85757i	0.195486	+	0.245132i	−0.674422	+	0.738346i	$0.735607\pi$
$572$	5.86589	−	9.33552i	0.245265	−	0.390338i
$573$	0.131707	−	0.0460864i	0.00550215	−	0.00192529i
$574$	−6.50835	−	13.3665i	−0.271653	−	0.557909i
$575$	−7.23250	−	23.4960i	−0.301616	−	0.979851i
$576$	−1.82857	−	2.29296i	−0.0761906	−	0.0955400i
$577$	25.1912	+	8.81480i	1.04872	+	0.366965i	0.798987	−	0.601349i	$-0.205370\pi$
$577$	25.1912	+	8.81480i	1.04872	+	0.366965i	0.249738	+	0.968313i	$0.419655\pi$
$578$	5.26851	−	8.38479i	0.219141	−	0.348761i
$579$	−1.69182	−	0.814736i	−0.0703095	−	0.0338593i
$580$	4.36709	+	3.62044i	0.181334	+	0.150330i
$581$	−0.849616	+	3.79806i	−0.0352480	+	0.157570i
$582$	−1.07994	−	0.678571i	−0.0447649	−	0.0281277i
$583$	−24.4041	+	15.3341i	−1.01071	+	0.635073i
$584$	−4.55082	+	5.70655i	−0.188314	+	0.236139i
$585$	1.38947	+	14.8641i	0.0574474	+	0.614554i
$586$	9.15164	+	19.0036i	0.378051	+	0.785031i
$587$	−11.3983	−	11.3983i	−0.470460	−	0.470460i	0.431604	−	0.902063i	$-0.357948\pi$
$587$	−11.3983	−	11.3983i	−0.470460	−	0.470460i	−0.902063	+	0.431604i	$0.857948\pi$
$588$	1.70746	−	0.614095i	0.0704145	−	0.0253249i
$589$			4.91705i			0.202603i
$590$	18.2688	+	18.9763i	0.752115	+	0.781241i
$591$	5.53904	+	1.26425i	0.227846	+	0.0520043i
$592$	0.598883	+	5.31523i	0.0246139	+	0.218455i
$593$	−23.4051	−	37.2491i	−0.961133	−	1.52964i	−0.843879	−	0.536533i	$-0.819734\pi$
$593$	−23.4051	−	37.2491i	−0.961133	−	1.52964i	−0.117254	−	0.993102i	$-0.537409\pi$
$594$	−1.65743	−	7.26168i	−0.0680052	−	0.297950i
$595$	3.28140	+	15.4156i	0.134524	+	0.631978i
$596$	−3.25916	+	14.2793i	−0.133500	+	0.584903i
$597$	1.42885	−	0.499975i	0.0584788	−	0.0204626i
$598$	9.47726	+	5.95496i	0.387554	+	0.243516i
$599$	13.6561	+	28.3573i	0.557975	+	1.15865i	0.969009	+	0.247027i	$0.0794536\pi$
$599$	13.6561	+	28.3573i	0.557975	+	1.15865i	−0.411034	+	0.911620i	$0.634832\pi$
$600$	−0.336187	+	1.25174i	−0.0137248	+	0.0511019i
$601$	−2.90785	−	6.03821i	−0.118614	−	0.246304i	0.833206	−	0.552963i	$-0.186503\pi$
$601$	−2.90785	−	6.03821i	−0.118614	−	0.246304i	−0.951819	+	0.306660i	$0.900789\pi$
$602$	9.98369	−	1.16864i	0.406905	−	0.0476302i
$603$	−10.4109	−	29.7526i	−0.423965	−	1.21162i
$604$	2.20320	−	0.502865i	0.0896468	−	0.0204613i
$605$	−27.2694	+	5.68145i	−1.10866	+	0.230984i
$606$	3.63087			0.147494
$607$	−4.97699	−	4.97699i	−0.202010	−	0.202010i	0.598851	−	0.800861i	$-0.295624\pi$
$607$	−4.97699	−	4.97699i	−0.202010	−	0.202010i	−0.800861	+	0.598851i	$0.795624\pi$
$608$	−6.39047	−	0.720033i	−0.259168	−	0.0292012i
$609$	1.35559	−	1.09067i	0.0549311	−	0.0441961i
$610$	1.25446	−	3.37784i	0.0507915	−	0.136765i
$611$	−13.5307	+	16.9669i	−0.547392	+	0.686408i
$612$	−2.58055	−	7.37480i	−0.104313	−	0.298109i
$613$	−5.88161	−	16.8087i	−0.237556	−	0.678897i	−0.999511	−	0.0312665i	$-0.990046\pi$
$613$	−5.88161	−	16.8087i	−0.237556	−	0.678897i	0.761955	−	0.647630i	$-0.224240\pi$
$614$	1.74322	−	2.18593i	0.0703508	−	0.0882171i
$615$	1.13392	−	3.05328i	0.0457241	−	0.123120i
$616$	5.60968	+	11.5209i	0.226021	+	0.464190i
$617$	11.6416	+	1.31169i	0.468673	+	0.0528068i	0.343143	−	0.939283i	$-0.388508\pi$
$617$	11.6416	+	1.31169i	0.468673	+	0.0528068i	0.125530	+	0.992090i	$0.459937\pi$
$618$	0.665025	+	0.665025i	0.0267512	+	0.0267512i
$619$	−1.29434			−0.0520240			−0.0260120	−	0.999662i	$-0.508281\pi$
$619$	−1.29434			−0.0520240			−0.0260120	+	0.999662i	$0.508281\pi$
$620$	1.67375	−	0.348718i	0.0672193	−	0.0140048i
$621$	7.37194	−	1.68260i	0.295826	−	0.0675203i
$622$	−8.37364	−	23.9305i	−0.335752	−	0.959525i
$623$	24.5903	−	15.5999i	0.985191	−	0.624996i
$624$	−0.256035	−	0.531663i	−0.0102496	−	0.0212836i
$625$	−23.2825	+	9.10629i	−0.931301	+	0.364251i
$626$	11.9278	+	24.7683i	0.476731	+	0.989942i
$627$	−6.83627	−	4.29551i	−0.273014	−	0.171546i
$628$	10.7343	−	3.75609i	0.428345	−	0.149884i
$629$	−3.17089	+	13.8926i	−0.126432	+	0.553933i
$630$	−15.5204	−	7.75666i	−0.618346	−	0.309033i
$631$	−1.48119	−	6.48950i	−0.0589651	−	0.258343i	0.936850	−	0.349731i	$-0.113727\pi$
$631$	−1.48119	−	6.48950i	−0.0589651	−	0.258343i	−0.995815	+	0.0913877i	$0.970870\pi$
$632$	1.11186	+	1.76952i	0.0442276	+	0.0703878i
$633$	−0.409048	−	3.63040i	−0.0162582	−	0.144296i
$634$	−23.0367	−	5.25798i	−0.914904	−	0.208821i
$635$	22.8589	+	23.7441i	0.907127	+	0.942255i
$636$			1.54259i			0.0611676i
$637$	−15.8190	+	1.92108i	−0.626770	+	0.0761159i
$638$	8.68808	+	8.68808i	0.343964	+	0.343964i
$639$	15.9744	+	33.1712i	0.631937	+	1.31223i
$640$	0.208116	+	2.22636i	0.00822651	+	0.0880047i
$641$	−7.22164	+	9.05565i	−0.285238	+	0.357677i	−0.903721	−	0.428121i	$-0.859176\pi$
$641$	−7.22164	+	9.05565i	−0.285238	+	0.357677i	0.618484	+	0.785797i	$0.287747\pi$
$642$	−2.96916	+	1.86564i	−0.117183	+	0.0736311i
$643$	−16.3644	−	10.2825i	−0.645351	−	0.405501i	0.169209	−	0.985580i	$-0.445879\pi$
$643$	−16.3644	−	10.2825i	−0.645351	−	0.405501i	−0.814560	+	0.580079i	$0.803022\pi$
$644$	−11.6958	+	5.69486i	−0.460880	+	0.224409i
$645$	1.69533	+	1.40548i	0.0667537	+	0.0553406i
$646$	−15.4359	−	7.43352i	−0.607316	−	0.292468i
$647$	5.28304	−	8.40791i	0.207698	−	0.330549i	−0.726588	−	0.687073i	$-0.758895\pi$
$647$	5.28304	−	8.40791i	0.207698	−	0.330549i	0.934286	+	0.356524i	$0.116038\pi$
$648$	7.92840	+	2.77427i	0.311457	+	0.108983i
$649$	35.5725	+	44.6065i	1.39634	+	1.75096i
$650$	5.32447	−	10.0601i	0.208843	−	0.394591i
$651$	−0.00226794	−	0.524378i	−8.88877e−5	−	0.0205520i
$652$	17.9974	−	6.29757i	0.704833	−	0.246632i
$653$	−20.6799	+	32.9118i	−0.809266	+	1.28794i	0.145135	+	0.989412i	$0.453638\pi$
$653$	−20.6799	+	32.9118i	−0.809266	+	1.28794i	−0.954401	+	0.298527i	$0.903505\pi$
$654$	−0.526454	−	0.660153i	−0.0205860	−	0.0258140i
$655$	−17.0579	−	8.61751i	−0.666509	−	0.336714i
$656$		−	5.61914i		−	0.219391i
$657$	2.39676	−	21.2718i	0.0935063	−	0.829892i
$658$	−8.43319	−	23.7704i	−0.328760	−	0.926666i
$659$	34.1565	+	27.2389i	1.33055	+	1.06108i	0.992793	+	0.119843i	$0.0382391\pi$
$659$	34.1565	+	27.2389i	1.33055	+	1.06108i	0.337755	+	0.941234i	$0.390332\pi$
$660$	−0.977350	+	2.63168i	−0.0380433	+	0.102438i
$661$	−18.5089	+	38.4342i	−0.719914	+	1.49492i	0.143085	+	0.989710i	$0.454298\pi$
$661$	−18.5089	+	38.4342i	−0.719914	+	1.49492i	−0.862999	+	0.505206i	$0.831417\pi$
$662$	−2.41281	+	0.844280i	−0.0937766	+	0.0328139i
$663$	−0.176017	−	1.56220i	−0.00683595	−	0.0606708i
$664$	−0.917159	+	1.15008i	−0.0355927	+	0.0446318i
$665$	−36.0912	+	12.0377i	−1.39956	+	0.466801i
$666$	−9.78079	−	12.2647i	−0.378998	−	0.475248i
$667$	−8.82000	+	8.82000i	−0.341512	+	0.341512i
$668$	5.71533	−	5.71533i	0.221133	−	0.221133i
$669$	3.41657	−	2.72463i	0.132092	−	0.105340i
$670$	−5.79187	+	23.3247i	−0.223760	+	0.901112i
$671$	3.38627	−	7.03166i	0.130725	−	0.271454i
$672$	0.681843	+	0.0738403i	0.0263027	+	0.00284845i
$673$	−42.9088	−	15.0144i	−1.65401	−	0.578764i	−0.667813	−	0.744329i	$-0.732769\pi$
$673$	−42.9088	−	15.0144i	−1.65401	−	0.578764i	−0.986199	+	0.165566i	$0.947055\pi$
$674$	10.4174	−	8.30758i	0.401262	−	0.319996i
$675$	−2.26222	−	7.34919i	−0.0870728	−	0.282871i
$676$	−1.73961	−	7.62174i	−0.0669082	−	0.293144i
$677$	15.6569	+	44.7449i	0.601744	+	1.71969i	0.690213	+	0.723607i	$0.257517\pi$
$677$	15.6569	+	44.7449i	0.601744	+	1.71969i	−0.0884685	+	0.996079i	$0.528197\pi$
$678$	−1.92297	−	3.06038i	−0.0738511	−	0.117533i
$679$	−12.6788	+	2.95161i	−0.486568	+	0.113272i
$680$	−1.43563	+	5.78151i	−0.0550540	+	0.221711i
$681$	0.652347	−	2.85812i	0.0249980	−	0.109523i
$682$	3.67985	−	0.414619i	0.140909	−	0.0158766i
$683$	−1.71322	+	1.07649i	−0.0655547	+	0.0411907i	−0.564411	−	0.825494i	$-0.690897\pi$
$683$	−1.71322	+	1.07649i	−0.0655547	+	0.0411907i	0.498856	+	0.866685i	$0.333754\pi$
$684$	16.9928	−	8.18331i	0.649737	−	0.312897i
$685$	−4.65923	−	14.1732i	−0.178020	−	0.541530i
$686$	7.81847	−	16.7890i	0.298510	−	0.641008i
$687$	3.64492	−	3.64492i	0.139062	−	0.139062i
$688$	3.58604	+	1.25481i	0.136717	+	0.0478392i
$689$	3.01448	−	13.2073i	0.114843	−	0.503159i
$690$	−2.67164	−	0.992189i	−0.101708	−	0.0377720i
$691$	−13.2009	−	3.01301i	−0.502185	−	0.114620i	−0.0360782	−	0.999349i	$-0.511487\pi$
$691$	−13.2009	−	3.01301i	−0.502185	−	0.114620i	−0.466107	+	0.884729i	$0.654344\pi$
$692$	−7.86354	+	12.5147i	−0.298927	+	0.475739i
$693$	−31.9070	−	19.8565i	−1.21205	−	0.754287i
$694$	−10.1627	−	2.31957i	−0.385771	−	0.0880497i
$695$	−29.8437	+	22.8860i	−1.13204	+	0.868116i
$696$	0.641123	−	0.146332i	0.0243017	−	0.00554671i
$697$	4.94424	−	14.1298i	0.187276	−	0.535205i
$698$	13.3340	+	1.50239i	0.504701	+	0.0568662i
$699$	−4.13703	+	1.99229i	−0.156477	+	0.0753552i
$700$	6.65718	+	11.4316i	0.251618	+	0.432075i
$701$	6.74422	+	3.24785i	0.254726	+	0.122669i	0.556890	−	0.830587i	$-0.311995\pi$
$701$	6.74422	+	3.24785i	0.254726	+	0.122669i	−0.302164	+	0.953256i	$0.597709\pi$
$702$	2.96435	+	1.86262i	0.111882	+	0.0703001i
$703$	−34.1818	−	3.85136i	−1.28919	−	0.145257i
$704$			4.84325i			0.182537i
$705$	2.49160	−	4.93201i	0.0938392	−	0.185750i
$706$	9.18616	−	7.32572i	0.345726	−	0.275707i
$707$	26.0910	−	26.3177i	0.981253	−	0.989777i
$708$	3.03442	−	0.341897i	0.114040	−	0.0128493i
$709$	−16.0677	−	12.8136i	−0.603436	−	0.481224i	0.273474	−	0.961879i	$-0.411827\pi$
$709$	−16.0677	−	12.8136i	−0.603436	−	0.481224i	−0.876909	+	0.480656i	$0.840399\pi$
$710$	3.67210	−	27.8294i	0.137811	−	1.04442i
$711$	−5.52214	−	2.65932i	−0.207096	−	0.0997323i
$712$	10.9375	−	1.23237i	0.409902	−	0.0461848i
$713$	0.420915	+	3.73572i	0.0157634	+	0.139904i
$714$	1.64958	+	0.785627i	0.0617342	+	0.0294014i
$715$	13.5106	−	20.6220i	0.505268	−	0.771218i
$716$	−11.7812			−0.440284
$717$	4.78065	+	4.78065i	0.178537	+	0.178537i
$718$	3.75627	−	33.3378i	0.140183	−	1.24416i
$719$	3.45923	+	15.1559i	0.129007	+	0.565218i	0.997572	+	0.0696423i	$0.0221858\pi$
$719$	3.45923	+	15.1559i	0.129007	+	0.565218i	−0.868565	+	0.495576i	$0.834957\pi$
$720$	−3.99071	−	5.20394i	−0.148725	−	0.193939i
$721$	9.59910	−	0.0415163i	0.357489	−	0.00154615i
$722$	7.38392	−	21.1020i	0.274801	−	0.785336i
$723$	−0.223044	+	1.97957i	−0.00829509	+	0.0736210i
$724$	14.5762	−	7.01952i	0.541720	−	0.260878i
$725$	9.60961	+	8.27953i	0.356892	+	0.307494i
$726$	−1.40106	+	2.90934i	−0.0519983	+	0.107976i
$727$	−14.6833	+	9.22612i	−0.544573	+	0.342178i	−0.776059	−	0.630660i	$-0.782784\pi$
$727$	−14.6833	+	9.22612i	−0.544573	+	0.342178i	0.231486	+	0.972838i	$0.425641\pi$
$728$	−5.69350	−	1.96464i	−0.211015	−	0.0728145i
$729$	−22.8512	+	5.21565i	−0.846343	+	0.193172i
$730$	−10.4164	+	12.5647i	−0.385530	+	0.465039i
$731$	7.91333	+	6.31067i	0.292685	+	0.233408i
$732$	−0.222237	−	0.353688i	−0.00821411	−	0.0130727i
$733$	12.5929	−	35.9884i	0.465129	−	1.32926i	−0.437645	−	0.899148i	$-0.644187\pi$
$733$	12.5929	−	35.9884i	0.465129	−	1.32926i	0.902774	−	0.430115i	$-0.141527\pi$
$734$	−15.3410			−0.566248
$735$	3.84339	−	1.30040i	0.141766	−	0.0479661i
$736$	−4.91679			−0.181235
$737$	−17.1926	+	49.1337i	−0.633299	+	1.80986i
$738$	8.76780	+	13.9539i	0.322747	+	0.513649i
$739$	−19.2945	−	15.3869i	−0.709760	−	0.566015i	0.200680	−	0.979657i	$-0.435685\pi$
$739$	−19.2945	−	15.3869i	−0.709760	−	0.566015i	−0.910440	+	0.413642i	$0.864256\pi$
$740$	1.11318	+	11.9085i	0.0409215	+	0.437765i
$741$	3.69974	−	0.844442i	0.135913	−	0.0310214i
$742$	11.1812	+	11.0849i	0.410474	+	0.406938i
$743$	−8.21267	+	5.16036i	−0.301293	+	0.189315i	−0.674191	−	0.738557i	$-0.735507\pi$
$743$	−8.21267	+	5.16036i	−0.301293	+	0.189315i	0.372897	+	0.927873i	$0.378364\pi$
$744$	0.0859949	−	0.178570i	0.00315273	−	0.00654671i
$745$	−7.89277	+	31.7854i	−0.289169	+	1.16453i
$746$	−31.2779	+	15.0627i	−1.14517	+	0.551483i
$747$	0.483035	−	4.28706i	0.0176733	−	0.156855i
$748$	−4.26154	+	12.1788i	−0.155817	+	0.445301i
$749$	−7.81324	+	34.9277i	−0.285489	+	1.27623i
$750$	−0.804758	+	2.78419i	−0.0293856	+	0.101664i
$751$	−0.628520	−	2.75372i	−0.0229350	−	0.100485i	0.962165	−	0.272468i	$-0.0878398\pi$
$751$	−0.628520	−	2.75372i	−0.0229350	−	0.100485i	−0.985100	+	0.171983i	$0.944983\pi$
$752$	1.06736	−	9.47308i	0.0389226	−	0.345448i
$753$	4.08253	+	4.08253i	0.148776	+	0.148776i
$754$	−5.77512			−0.210317
$755$	4.94697	−	1.03068i	0.180038	−	0.0375102i
$756$	−3.65828	+	1.78127i	−0.133050	+	0.0647840i
$757$	1.30887	+	11.6165i	0.0475717	+	0.422210i	0.994815	+	0.101696i	$0.0324271\pi$
$757$	1.30887	+	11.6165i	0.0475717	+	0.422210i	−0.947244	+	0.320514i	$0.896144\pi$
$758$	−32.8682	+	3.70336i	−1.19383	+	0.134512i
$759$	−5.56155	−	2.67830i	−0.201872	−	0.0972162i
$760$	−14.2564	−	1.88113i	−0.517133	−	0.0682358i
$761$	−4.97952	−	3.97104i	−0.180507	−	0.143950i	0.529068	−	0.848580i	$-0.322542\pi$
$761$	−4.97952	−	3.97104i	−0.180507	−	0.143950i	−0.709575	+	0.704630i	$0.751113\pi$
$762$	3.79682	−	0.427799i	0.137544	−	0.0154975i
$763$	−8.56803	−	0.927877i	−0.310184	−	0.0335914i
$764$	0.420860	−	0.335624i	0.0152262	−	0.0121425i
$765$	−5.45608	−	16.5972i	−0.197265	−	0.600072i
$766$			20.5651i			0.743046i
$767$	−26.6482	−	3.00253i	−0.962209	−	0.108415i
$768$	0.219487	+	0.137913i	0.00792007	+	0.00497651i
$769$	−35.0292	−	16.8692i	−1.26318	−	0.608318i	−0.322169	−	0.946682i	$-0.604412\pi$
$769$	−35.0292	−	16.8692i	−1.26318	−	0.608318i	−0.941015	+	0.338365i	$0.890126\pi$
$770$	12.0521	+	25.9951i	0.434329	+	0.936798i
$771$	4.01261	−	1.93237i	0.144511	−	0.0695927i
$772$	−7.19841	−	0.811066i	−0.259077	−	0.0291909i
$773$	−10.2825	+	29.3858i	−0.369838	+	1.05694i	0.597154	+	0.802127i	$0.296298\pi$
$773$	−10.2825	+	29.3858i	−0.369838	+	1.05694i	−0.966992	+	0.254808i	$0.917988\pi$
$774$	−10.8631	+	2.47943i	−0.390465	+	0.0891211i
$775$	3.75675	−	0.708538i	0.134946	−	0.0254514i
$776$	−4.79692	−	1.09487i	−0.172199	−	0.0393034i
$777$	3.64709	+	0.394962i	0.130838	+	0.0141692i
$778$	−16.7681	+	26.6862i	−0.601165	+	0.956748i
$779$	35.2302	+	8.04106i	1.26225	+	0.288101i
$780$	−0.549832	−	1.19949i	−0.0196871	−	0.0429487i
$781$	13.5293	−	59.2758i	0.484117	−	2.12105i
$782$	−12.3637	−	4.32625i	−0.442125	−	0.154706i
$783$	−2.75876	+	2.75876i	−0.0985901	+	0.0985901i
$784$	5.43486	−	4.41160i	0.194102	−	0.157557i
$785$	24.1578	−	7.94151i	0.862228	−	0.283445i
$786$	−1.99608	+	0.961263i	−0.0711979	+	0.0342871i
$787$	19.4981	−	12.2515i	0.695034	−	0.436719i	−0.137640	−	0.990482i	$-0.543952\pi$
$787$	19.4981	−	12.2515i	0.695034	−	0.436719i	0.832674	+	0.553764i	$0.186809\pi$
$788$	21.7799	−	2.45400i	0.775876	−	0.0874202i
$789$	0.382267	−	1.67482i	0.0136091	−	0.0596251i
$790$	2.41061	+	4.00328i	0.0857658	+	0.142430i
$791$	−36.0008	−	8.05330i	−1.28004	−	0.286342i
$792$	−7.55715	−	12.0271i	−0.268532	−	0.427366i
$793$	1.21158	+	3.46249i	0.0430243	+	0.122957i
$794$	−1.64951	−	7.22700i	−0.0585391	−	0.256477i
$795$	−0.0655076	+	3.44871i	−0.00232331	+	0.122313i
$796$	4.56576	−	3.64107i	0.161829	−	0.129054i
$797$	29.7627	+	10.4144i	1.05425	+	0.368898i	0.801101	−	0.598529i	$-0.204248\pi$
$797$	29.7627	+	10.4144i	1.05425	+	0.368898i	0.253149	+	0.967427i	$0.418534\pi$
$798$	−1.43868	+	4.16927i	−0.0509288	+	0.147591i
$799$	11.0193	−	22.8818i	0.389834	−	0.809498i
$800$	0.370733	+	4.98624i	0.0131074	+	0.176290i
$801$	−25.2380	+	20.1267i	−0.891742	+	0.711141i
$802$	8.05430	−	8.05430i	0.284407	−	0.284407i
$803$	−24.9967	+	24.9967i	−0.882114	+	0.882114i
$804$	1.73708	+	2.17823i	0.0612622	+	0.0768204i
$805$	−26.3898	+	12.2351i	−0.930118	+	0.431231i
$806$	−1.08523	+	1.36083i	−0.0382255	+	0.0479333i
$807$	0.503209	+	4.46611i	0.0177138	+	0.157214i
$808$	13.2209	−	4.62620i	0.465110	−	0.162749i
$809$	−6.90959	+	14.3479i	−0.242928	+	0.504446i	−0.986408	−	0.164312i	$-0.947460\pi$
$809$	−6.90959	+	14.3479i	−0.242928	+	0.504446i	0.743480	+	0.668758i	$0.233174\pi$
$810$	17.6074	+	6.53902i	0.618662	+	0.229758i
$811$	19.3478	+	15.4294i	0.679393	+	0.541798i	0.901260	−	0.433279i	$-0.142644\pi$
$811$	19.3478	+	15.4294i	0.679393	+	0.541798i	−0.221867	+	0.975077i	$0.571215\pi$
$812$	3.54638	−	5.69859i	0.124453	−	0.199981i
$813$	0.344379	−	3.05645i	0.0120779	−	0.107194i
$814$			25.9059i			0.908001i
$815$	40.5036	−	13.3150i	1.41878	−	0.466403i
$816$	0.430572	+	0.539920i	0.0150730	+	0.0189010i
$817$	−12.9989	+	20.6877i	−0.454775	+	0.723770i
$818$	−12.4888	+	4.37003i	−0.436661	+	0.152794i
$819$	17.2041	−	4.00508i	0.601159	−	0.139949i
$820$	0.238622	−	12.5625i	0.00833305	−	0.438702i
$821$	−11.2287	−	14.0804i	−0.391885	−	0.491409i	0.546277	−	0.837605i	$-0.316045\pi$
$821$	−11.2287	−	14.0804i	−0.391885	−	0.491409i	−0.938162	+	0.346196i	$0.887473\pi$
$822$	−1.63249	−	0.571235i	−0.0569398	−	0.0199241i
$823$	−1.41497	+	2.25192i	−0.0493229	+	0.0784970i	−0.870476	−	0.492212i	$-0.836189\pi$
$823$	−1.41497	+	2.25192i	−0.0493229	+	0.0784970i	0.821153	+	0.570709i	$0.193331\pi$
$824$	3.26885	+	1.57420i	0.113876	+	0.0548397i
$825$	−2.29678	+	5.84205i	−0.0799637	+	0.203394i
$826$	19.3268	−	24.4512i	0.672465	−	0.850767i
$827$	−29.1303	−	18.3038i	−1.01296	−	0.636485i	−0.0801232	−	0.996785i	$-0.525531\pi$
$827$	−29.1303	−	18.3038i	−1.01296	−	0.636485i	−0.932836	+	0.360300i	$0.882674\pi$
$828$	12.2098	−	7.67190i	0.424318	−	0.266617i
$829$	28.4166	−	35.6333i	0.986951	−	1.23760i	0.0156167	−	0.999878i	$-0.495029\pi$
$829$	28.4166	−	35.6333i	0.986951	−	1.23760i	0.971334	−	0.237719i	$-0.0763997\pi$
$830$	−2.09930	+	2.53225i	−0.0728678	+	0.0878956i
$831$	0.446916	+	0.928031i	0.0155034	+	0.0321930i
$832$	−1.60970	−	1.60970i	−0.0558062	−	0.0558062i
$833$	17.5482	−	6.31128i	0.608009	−	0.218673i
$834$			4.35985i			0.150969i
$835$	13.0203	−	12.5348i	0.450585	−	0.433786i
$836$	−30.3656	−	6.93075i	−1.05022	−	0.239705i
$837$	0.131656	+	1.16848i	0.00455069	+	0.0403885i
$838$	−11.3834	−	18.1166i	−0.393234	−	0.625829i
$839$	−0.288854	−	1.26555i	−0.00997233	−	0.0436917i	0.969697	−	0.244311i	$-0.0785617\pi$
$839$	−0.288854	−	1.26555i	−0.00997233	−	0.0436917i	−0.979669	+	0.200619i	$0.935705\pi$
$840$	1.52124	+	0.194037i	0.0524877	+	0.00669493i
$841$	−5.02100	+	21.9985i	−0.173138	+	0.758567i
$842$	−13.8269	+	4.83823i	−0.476505	+	0.166736i
$843$	4.22962	+	2.65764i	0.145676	+	0.0915341i
$844$	−6.11505	−	12.6980i	−0.210489	−	0.437084i
$845$	−3.56553	−	17.1135i	−0.122658	−	0.588723i
$846$	12.1307	+	25.1897i	0.417063	+	0.866041i
$847$	11.0199	+	31.0615i	0.378649	+	1.06729i
$848$	1.96546	+	5.61696i	0.0674941	+	0.192887i
$849$	−6.91557	+	1.57843i	−0.237342	+	0.0541717i
$850$	−3.45511	+	12.8645i	−0.118509	+	0.441250i
$851$	−26.2992			−0.901526
$852$	−2.30102	−	2.30102i	−0.0788316	−	0.0788316i
$853$	−21.9231	−	2.47014i	−0.750631	−	0.0845758i	−0.271644	−	0.962398i	$-0.587567\pi$
$853$	−21.9231	−	2.47014i	−0.750631	−	0.0845758i	−0.478987	+	0.877822i	$0.658996\pi$
$854$	−4.16061	−	0.930718i	−0.142373	−	0.0318485i
$855$	38.3378	−	17.5735i	1.31112	−	0.601002i
$856$	−8.43438	+	10.5764i	−0.288281	+	0.361493i
$857$	9.89250	+	28.2711i	0.337921	+	0.965724i	0.979985	+	0.199072i	$0.0637929\pi$
$857$	9.89250	+	28.2711i	0.337921	+	0.965724i	−0.642063	+	0.766652i	$0.721921\pi$
$858$	−0.943941	−	2.69763i	−0.0322256	−	0.0920955i
$859$	17.0940	−	21.4353i	0.583241	−	0.731361i	−0.399421	−	0.916768i	$-0.630789\pi$
$859$	17.0940	−	21.4353i	0.583241	−	0.731361i	0.982662	+	0.185406i	$0.0593601\pi$
$860$	7.96390	+	2.95762i	0.271567	+	0.100854i
$861$	−3.76083	−	0.841288i	−0.128169	−	0.0286710i
$862$	−3.92575	−	0.442326i	−0.133712	−	0.0150657i
$863$	−22.2172	−	22.2172i	−0.756282	−	0.756282i	0.219362	−	0.975644i	$-0.429603\pi$
$863$	−22.2172	−	22.2172i	−0.756282	−	0.756282i	−0.975644	+	0.219362i	$0.929603\pi$
$864$	−1.53790			−0.0523204
$865$	−18.1117	+	27.6448i	−0.615816	+	0.939953i
$866$	7.95959	−	1.81673i	0.270478	−	0.0617348i
$867$	−0.847811	−	2.42290i	−0.0287932	−	0.0822861i
$868$	−0.676384	−	1.90650i	−0.0229580	−	0.0647109i
$869$	4.39162	+	9.11929i	0.148976	+	0.309351i
$870$	1.43955	−	0.299924i	0.0488054	−	0.0101684i
$871$	−10.6159	−	22.0441i	−0.359706	−	0.746937i
$872$	−2.75807	−	1.73301i	−0.0934002	−	0.0586872i
$873$	13.6205	−	4.76600i	0.460983	−	0.161305i
$874$	7.03599	−	30.8267i	0.237996	−	1.04273i
$875$	14.3978	+	25.8400i	0.486733	+	0.873551i
$876$	0.421016	+	1.84459i	0.0142248	+	0.0623230i
$877$	27.1108	+	43.1466i	0.915467	+	1.45696i	0.889312	+	0.457300i	$0.151183\pi$
$877$	27.1108	+	43.1466i	0.915467	+	1.45696i	0.0261549	+	0.999658i	$0.491674\pi$
$878$	−0.422896	−	3.75331i	−0.0142721	−	0.126668i
$879$	5.33047	+	1.21665i	0.179792	+	0.0410364i
$880$	−0.205674	+	10.8279i	−0.00693325	+	0.365008i
$881$		−	36.2991i		−	1.22295i	−0.791264	−	0.611474i	$-0.790577\pi$
$881$		−	36.2991i		−	1.22295i	0.791264	−	0.611474i	$-0.209423\pi$
$882$	−6.61264	+	19.4355i	−0.222659	+	0.654428i
$883$	−21.9641	−	21.9641i	−0.739151	−	0.739151i	0.233262	−	0.972414i	$-0.425060\pi$
$883$	−21.9641	−	21.9641i	−0.739151	−	0.739151i	−0.972414	+	0.233262i	$0.925060\pi$
$884$	−2.63137	−	5.46409i	−0.0885025	−	0.183777i
$885$	6.79846	−	0.635507i	0.228528	−	0.0213623i
$886$	−13.2877	+	16.6623i	−0.446409	+	0.559779i
$887$	−22.2180	+	13.9605i	−0.746007	+	0.468747i	−0.850630	−	0.525765i	$-0.823779\pi$
$887$	−22.2180	+	13.9605i	−0.746007	+	0.468747i	0.104623	+	0.994512i	$0.466636\pi$
$888$	1.17401	+	0.737678i	0.0393971	+	0.0247548i
$889$	24.1827	−	30.5946i	0.811061	−	1.02611i
$890$	24.5050	−	2.29068i	0.821410	−	0.0767838i
$891$	36.6534	+	17.6513i	1.22793	+	0.591342i
$892$	8.96908	−	14.2742i	0.300307	−	0.477936i
$893$	57.8657	+	20.2481i	1.93640	+	0.677577i
$894$	2.36718	+	2.96835i	0.0791704	+	0.0992766i
$895$	−26.3388	−	0.500300i	−0.880409	−	0.0167232i
$896$	2.57685	−	0.599885i	0.0860864	−	0.0200408i
$897$	2.73859	−	0.958273i	0.0914388	−	0.0319958i
$898$	−13.3167	+	21.1935i	−0.444385	+	0.707235i
$899$	−1.20938	−	1.51652i	−0.0403351	−	0.0505786i
$900$	−8.70089	−	11.8037i	−0.290030	−	0.393458i
$901$			15.8537i			0.528165i
$902$	3.04710	−	27.0438i	0.101457	−	0.900460i
$903$	1.37673	−	2.21223i	0.0458146	−	0.0736184i
$904$	−10.9013	−	8.69352i	−0.362573	−	0.289142i
$905$	32.8856	−	15.0743i	1.09315	−	0.501087i
$906$	0.254169	−	0.527786i	0.00844418	−	0.0175345i
$907$	−45.5979	+	15.9554i	−1.51405	+	0.529790i	−0.954295	−	0.298867i	$-0.903391\pi$
$907$	−45.5979	+	15.9554i	−1.51405	+	0.529790i	−0.559757	+	0.828657i	$0.689106\pi$
$908$	−1.26625	−	11.2383i	−0.0420221	−	0.372956i
$909$	−25.6127	+	32.1173i	−0.849520	+	1.06526i
$910$	−12.6453	−	4.63406i	−0.419188	−	0.153618i
$911$	16.3043	+	20.4449i	0.540185	+	0.677371i	0.974757	−	0.223266i	$-0.0716719\pi$
$911$	16.3043	+	20.4449i	0.540185	+	0.677371i	−0.434572	+	0.900637i	$0.643101\pi$
$912$	−1.17876	+	1.17876i	−0.0390326	+	0.0390326i
$913$	−5.03776	+	5.03776i	−0.166726	+	0.166726i
$914$	−22.1054	+	17.6285i	−0.731181	+	0.583098i
$915$	−0.481827	−	0.800165i	−0.0159287	−	0.0264526i
$916$	8.62797	−	17.9162i	0.285076	−	0.591967i
$917$	−7.37608	+	21.3757i	−0.243580	+	0.705889i
$918$	−3.86718	−	1.35319i	−0.127636	−	0.0446618i
$919$	33.7070	−	26.8805i	1.11189	−	0.886704i	0.117565	−	0.993065i	$-0.462491\pi$
$919$	33.7070	−	26.8805i	1.11189	−	0.886704i	0.994328	+	0.106361i	$0.0339199\pi$
$920$	−10.9923	−	0.208796i	−0.362405	−	0.00688381i
$921$	−0.161273	−	0.706584i	−0.00531413	−	0.0232827i
$922$	−11.1205	−	31.7805i	−0.366233	−	1.04663i
$923$	15.2042	+	24.1974i	0.500454	+	0.796468i
$924$	3.24153	+	0.725124i	0.106639	+	0.0238548i
$925$	1.98300	+	26.6707i	0.0652006	+	0.876927i
$926$	7.61228	−	33.3516i	0.250155	−	1.09600i
$927$	−10.5738	+	1.19138i	−0.347288	+	0.0391299i
$928$	2.14805	−	1.34971i	0.0705131	−	0.0443063i
$929$	−34.0550	+	16.4000i	−1.11731	+	0.538068i	−0.899060	−	0.437825i	$-0.855749\pi$
$929$	−34.0550	+	16.4000i	−1.11731	+	0.538068i	−0.218249	+	0.975893i	$0.570035\pi$
$930$	0.199839	−	0.395571i	0.00655298	−	0.0129713i
$931$	19.8820	+	40.3879i	0.651605	+	1.32366i
$932$	−12.5255	+	12.5255i	−0.410287	+	0.410287i
$933$	−6.20324	−	2.17061i	−0.203085	−	0.0710625i
$934$	8.17188	−	35.8033i	0.267392	−	1.17152i
$935$	−10.0446	+	27.0467i	−0.328493	+	0.884523i
$936$	6.50901	+	1.48564i	0.212754	+	0.0485596i
$937$	−2.66068	+	4.23445i	−0.0869206	+	0.138333i	−0.887355	−	0.461087i	$-0.847459\pi$
$937$	−2.66068	+	4.23445i	−0.0869206	+	0.138333i	0.800434	+	0.599421i	$0.204602\pi$
$938$	28.2710	+	3.06161i	0.923081	+	0.0999652i
$939$	6.94748	+	1.58572i	0.226722	+	0.0517479i
$940$	2.78854	−	21.1333i	0.0909522	−	0.689293i
$941$	2.22083	−	0.506889i	0.0723969	−	0.0165241i	−0.186169	−	0.982518i	$-0.559607\pi$
$941$	2.22083	−	0.506889i	0.0723969	−	0.0165241i	0.258566	+	0.965994i	$0.416750\pi$
$942$	0.973651	−	2.78253i	0.0317233	−	0.0906599i
$943$	27.4544	+	3.09337i	0.894039	+	0.100734i
$944$	10.6135	−	5.11118i	0.345439	−	0.166355i
$945$	−8.25433	+	3.82696i	−0.268513	+	0.124491i
$946$	16.5785	+	7.98376i	0.539012	+	0.259575i
$947$	22.4009	+	14.0754i	0.727933	+	0.457391i	0.844338	−	0.535811i	$-0.179994\pi$
$947$	22.4009	+	14.0754i	0.727933	+	0.457391i	−0.116405	+	0.993202i	$0.537137\pi$
$948$	0.538322	+	0.0606544i	0.0174839	+	0.00196996i
$949$		−	16.6157i		−	0.539369i
$950$	−31.7926	−	4.81099i	−1.03149	−	0.156089i
$951$	−4.78882	+	3.81896i	−0.155288	+	0.123838i
$952$	7.00755	+	0.758883i	0.227116	+	0.0245955i
$953$	25.2299	−	2.84273i	0.817278	−	0.0920851i	0.306580	−	0.951845i	$-0.400815\pi$
$953$	25.2299	−	2.84273i	0.817278	−	0.0920851i	0.510699	+	0.859760i	$0.329387\pi$
$954$	−13.6452	−	10.8817i	−0.441779	−	0.352307i
$955$	0.955154	−	0.732471i	0.0309080	−	0.0237022i
$956$	23.4987	+	11.3164i	0.760003	+	0.365998i
$957$	3.16495	−	0.356604i	0.102308	−	0.0115274i
$958$	−3.69250	−	32.7719i	−0.119299	−	1.05881i
$959$	−15.8714	+	7.72800i	−0.512514	+	0.249550i
$960$	0.484843	+	0.317648i	0.0156483	+	0.0102520i
$961$	30.4154			0.981142
$962$	−8.61005	−	8.61005i	−0.277599	−	0.277599i
$963$	4.44209	−	39.4246i	0.143144	−	1.27044i
$964$	1.71007	+	7.49230i	0.0550776	+	0.241311i
$965$	−16.0588	−	2.11896i	−0.516951	−	0.0682117i
$966$	−0.736133	+	3.29075i	−0.0236847	+	0.105878i
$967$	17.2030	−	49.1634i	0.553211	−	1.58099i	−0.239181	−	0.970975i	$-0.576879\pi$
$967$	17.2030	−	49.1634i	0.553211	−	1.58099i	0.792392	−	0.610012i	$-0.208835\pi$
$968$	−1.39475	+	12.3788i	−0.0448290	+	0.397869i
$969$	−4.00128	+	1.92691i	−0.128540	+	0.0619014i
$970$	−10.6778	−	2.65146i	−0.342844	−	0.0851332i
$971$	11.1191	−	23.0891i	0.356830	−	0.740966i	−0.642857	−	0.765987i	$-0.722251\pi$
$971$	11.1191	−	23.0891i	0.356830	−	0.740966i	0.999687	+	0.0250207i	$0.00796516\pi$
$972$	5.75017	−	3.61307i	0.184437	−	0.115889i
$973$	31.6015	+	31.3293i	1.01310	+	1.00437i
$974$	−34.1247	+	7.78873i	−1.09343	+	0.249567i
$975$	−1.17830	−	2.70501i	−0.0377359	−	0.0866298i
$976$	−1.25986	−	1.00471i	−0.0403273	−	0.0321599i
$977$	−6.75260	−	10.7467i	−0.216035	−	0.343818i	0.721072	−	0.692860i	$-0.243650\pi$
$977$	−6.75260	−	10.7467i	−0.216035	−	0.343818i	−0.937107	+	0.349043i	$0.886507\pi$
$978$	1.63245	−	4.66528i	0.0522000	−	0.149179i
$979$	53.3085			1.70375
$980$	12.3379	−	9.63207i	0.394119	−	0.307685i
$981$	9.55316			0.305009
$982$	13.3701	−	38.2096i	0.426658	−	1.21932i
$983$	23.2715	+	37.0364i	0.742245	+	1.18128i	0.977825	+	0.209422i	$0.0671581\pi$
$983$	23.2715	+	37.0364i	0.742245	+	1.18128i	−0.235580	+	0.971855i	$0.575699\pi$
$984$	−1.13881	−	0.908169i	−0.0363039	−	0.0289514i
$985$	48.7967	−	4.56142i	1.55479	−	0.145339i
$986$	6.58905	−	1.50391i	0.209838	−	0.0478942i
$987$	−6.18042	−	2.13267i	−0.196725	−	0.0678835i
$988$	12.3958	−	7.78878i	0.394362	−	0.247794i
$989$	−8.10498	+	16.8302i	−0.257723	+	0.535168i
$990$	−16.3845	−	27.2096i	−0.520734	−	0.864777i
$991$	−31.8441	+	15.3353i	−1.01156	+	0.487143i	−0.864847	−	0.502036i	$-0.832584\pi$
$991$	−31.8441	+	15.3353i	−1.01156	+	0.487143i	−0.146715	+	0.989179i	$0.546870\pi$
$992$	0.0856076	−	0.759788i	0.00271804	−	0.0241233i
$993$	−0.218854	+	0.625448i	−0.00694511	+	0.0198480i
$994$	−33.2134	+	0.143648i	−1.05346	+	0.00455625i
$995$	10.3621	−	7.94633i	0.328502	−	0.251916i
$996$	0.0848504	+	0.371754i	0.00268859	+	0.0117795i
$997$	−0.290169	+	2.57532i	−0.00918976	+	0.0815614i	−0.997470	−	0.0710895i	$-0.977352\pi$
$997$	−0.290169	+	2.57532i	−0.00918976	+	0.0815614i	0.988280	+	0.152651i	$0.0487810\pi$
$998$	29.4164	+	29.4164i	0.931159	+	0.931159i
$999$	−8.22600			−0.260259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.s.a.223.21	yes	336
5.2	odd	4	inner	490.2.s.a.27.21	✓	336
49.20	odd	14	inner	490.2.s.a.363.21	yes	336
245.167	even	28	inner	490.2.s.a.167.21	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.s.a.27.21	✓	336	5.2	odd	4	inner
490.2.s.a.167.21	yes	336	245.167	even	28	inner
490.2.s.a.223.21	yes	336	1.1	even	1	trivial
490.2.s.a.363.21	yes	336	49.20	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)

\(f(q)\)	\(=\)	\(q+(0.330279 - 0.943883i) q^{2} +(-0.137913 - 0.219487i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.72144 - 1.42712i) q^{5} +(-0.252720 + 0.0576817i) q^{6} +(-1.39792 + 2.24629i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.27250 - 2.64237i) q^{9} +O(q^{10})\)	\(q+(0.330279 - 0.943883i) q^{2} +(-0.137913 - 0.219487i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.72144 - 1.42712i) q^{5} +(-0.252720 + 0.0576817i) q^{6} +(-1.39792 + 2.24629i) q^{7} +(-0.846724 + 0.532032i) q^{8} +(1.27250 - 2.64237i) q^{9} +(-1.91558 + 1.15349i) q^{10} +(-4.36362 + 2.10141i) q^{11} +(-0.0290234 + 0.257589i) q^{12} +(0.751866 - 2.14871i) q^{13} +(1.65853 + 2.06138i) q^{14} +(-0.0758253 + 0.574651i) q^{15} +(0.222521 + 0.974928i) q^{16} +(-0.298283 + 2.64734i) q^{17} +(-2.07381 - 2.07381i) q^{18} -6.43091 q^{19} +(0.456081 + 2.18906i) q^{20} +(0.685824 - 0.00296620i) q^{21} +(0.542272 + 4.81280i) q^{22} +(-4.88587 + 0.550506i) q^{23} +(0.233549 + 0.112471i) q^{24} +(0.926683 + 4.91338i) q^{25} +(-1.77980 - 1.41935i) q^{26} +(-1.52823 + 0.172190i) q^{27} +(2.49348 - 0.884629i) q^{28} +(1.98342 - 1.58173i) q^{29} +(0.517360 + 0.261365i) q^{30} -0.764596i q^{31} +(0.993712 + 0.111964i) q^{32} +(1.06303 + 0.667948i) q^{33} +(2.40026 + 1.15591i) q^{34} +(5.61215 - 1.87185i) q^{35} +(-2.64237 + 1.27250i) q^{36} +(5.31523 + 0.598883i) q^{37} +(-2.12399 + 6.07003i) q^{38} +(-0.575306 + 0.131310i) q^{39} +(2.21685 + 0.292514i) q^{40} +(-5.47826 - 1.25038i) q^{41} +(0.223713 - 0.648317i) q^{42} +(2.02132 - 3.21691i) q^{43} +(4.72182 + 1.07773i) q^{44} +(-5.96148 + 2.73266i) q^{45} +(-1.09409 + 4.79352i) q^{46} +(-8.99806 - 3.14856i) q^{47} +(0.183296 - 0.183296i) q^{48} +(-3.09163 - 6.28027i) q^{49} +(4.94372 + 0.748104i) q^{50} +(0.622194 - 0.299633i) q^{51} +(-1.92753 + 1.21115i) q^{52} +(5.91348 - 0.666290i) q^{53} +(-0.342215 + 1.49934i) q^{54} +(10.5106 + 2.60995i) q^{55} +(-0.0114428 - 2.64573i) q^{56} +(0.886906 + 1.41150i) q^{57} +(-0.837882 - 2.39453i) q^{58} +(-2.62131 - 11.4847i) q^{59} +(0.417572 - 0.402004i) q^{60} +(-1.25986 + 1.00471i) q^{61} +(-0.721689 - 0.252530i) q^{62} +(4.15667 + 6.55222i) q^{63} +(0.433884 - 0.900969i) q^{64} +(-4.36074 + 2.62587i) q^{65} +(0.981562 - 0.782770i) q^{66} +(7.59992 - 7.59992i) q^{67} +(1.88380 - 1.88380i) q^{68} +(0.794655 + 0.996466i) q^{69} +(0.0867711 - 5.91544i) q^{70} +(-7.82703 + 9.81479i) q^{71} +(0.328370 + 2.91436i) q^{72} +(6.88935 - 2.41069i) q^{73} +(2.32078 - 4.81916i) q^{74} +(0.950622 - 0.881014i) q^{75} +(5.02789 + 4.00961i) q^{76} +(1.37963 - 12.7396i) q^{77} +(-0.0660704 + 0.586391i) q^{78} -2.08985i q^{79} +(1.00828 - 1.99584i) q^{80} +(-5.23717 - 6.56720i) q^{81} +(-2.98956 + 4.75786i) q^{82} +(1.38846 - 0.485844i) q^{83} +(-0.538048 - 0.425285i) q^{84} +(4.29153 - 4.13154i) q^{85} +(-2.36879 - 2.97037i) q^{86} +(-0.620708 - 0.217195i) q^{87} +(2.57677 - 4.10090i) q^{88} +(-9.91674 - 4.77565i) q^{89} +(0.610364 + 6.52949i) q^{90} +(3.77557 + 4.69264i) q^{91} +(4.16317 + 2.61589i) q^{92} +(-0.167819 + 0.105448i) q^{93} +(-5.94374 + 7.45322i) q^{94} +(11.0704 + 9.17765i) q^{95} +(-0.112471 - 0.233549i) q^{96} +(3.47917 + 3.47917i) q^{97} +(-6.94895 + 0.843890i) q^{98} +14.2043i 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

Varieties

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Representations

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Database

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