LMFDB - Embedded newform 930.2.br.a.761.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.10
Character	$\chi$	$=$	930.761
Dual form			930.2.br.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(1.48579 - 0.890187i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.68815 + 0.387484i) q^{6} +(0.0245947 - 0.234003i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.41514 - 2.64526i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.48579 - 0.890187i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.68815 + 0.387484i) q^{6} +(0.0245947 - 0.234003i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.41514 - 2.64526i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(1.45178 - 0.646376i) q^{11} +(1.72527 + 0.153149i) q^{12} +(-1.21131 + 5.69874i) q^{13} +(-0.0957017 + 0.214950i) q^{14} +(1.73182 - 0.0280299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.90661 + 1.73934i) q^{17} +(-2.16330 + 2.07849i) q^{18} +(0.572761 - 0.121744i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-0.171764 - 0.369572i) q^{21} +(-1.58047 + 0.166114i) q^{22} +(7.46724 - 5.42527i) q^{23} +(-1.59350 - 0.678790i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.91303 - 5.04551i) q^{26} +(-0.252181 - 5.19003i) q^{27} +(0.157441 - 0.174856i) q^{28} +(0.549440 - 1.69100i) q^{29} +(-1.65572 - 0.508505i) q^{30} +(-5.48177 - 0.974763i) q^{31} -1.00000i q^{32} +(1.58165 - 2.25274i) q^{33} +(-3.17793 - 2.86142i) q^{34} +(0.138301 - 0.190355i) q^{35} +(2.69971 - 1.30826i) q^{36} +(0.834092 - 0.481563i) q^{37} +(-0.582349 - 0.0612073i) q^{38} +(3.27320 + 9.54542i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-5.53676 + 4.98532i) q^{41} +(0.0491527 + 0.404562i) q^{42} +(0.201044 + 0.945836i) q^{43} +(1.55445 + 0.330408i) q^{44} +(2.54817 - 1.58329i) q^{45} +(-8.77827 + 2.85223i) q^{46} +(7.81614 - 2.53962i) q^{47} +(1.30575 + 1.13799i) q^{48} +(6.79288 + 1.44387i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(7.35274 - 0.893329i) q^{51} +(-4.32960 + 3.89839i) q^{52} +(-0.193679 - 1.84273i) q^{53} +(-1.36397 + 5.01394i) q^{54} +(1.58047 + 0.166114i) q^{55} +(-0.203769 + 0.117646i) q^{56} +(0.742627 - 0.690750i) q^{57} +(-1.04510 + 1.43845i) q^{58} +(2.88510 + 2.59776i) q^{59} +(1.41755 + 0.995264i) q^{60} +5.54239i q^{61} +(4.91226 + 2.62102i) q^{62} +(-0.584193 - 0.396205i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.89839 + 4.32960i) q^{65} +(-2.20037 + 1.65372i) q^{66} +(2.84513 - 4.92790i) q^{67} +(2.13816 + 3.70340i) q^{68} +(6.26524 - 14.7080i) q^{69} +(-0.190355 + 0.138301i) q^{70} +(-13.9140 + 1.46242i) q^{71} +(-2.97185 + 0.409975i) q^{72} +(-6.83385 - 15.3491i) q^{73} +(-0.942080 + 0.200245i) q^{74} +(1.51382 + 0.841637i) q^{75} +(0.534933 + 0.238167i) q^{76} +(-0.115548 - 0.355619i) q^{77} +(-0.163304 - 10.0897i) q^{78} +(-5.16130 + 11.5925i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-4.99478 - 7.48680i) q^{81} +(6.80632 - 3.03037i) q^{82} +(-10.2545 - 11.3888i) q^{83} +(0.0782695 - 0.399950i) q^{84} +(2.51356 + 3.45962i) q^{85} +(0.101076 - 0.961670i) q^{86} +(-0.688956 - 3.00158i) q^{87} +(-1.37627 - 0.794588i) q^{88} +(14.8213 + 10.7683i) q^{89} +(-2.91272 + 0.718372i) q^{90} +(1.30373 + 0.423607i) q^{91} +9.23002 q^{92} +(-9.01248 + 3.43151i) q^{93} -8.21838 q^{94} +(0.556897 + 0.180947i) q^{95} +(-0.890187 - 1.48579i) q^{96} +(5.67058 + 4.11992i) q^{97} +(-6.01423 - 3.47232i) q^{98} +(0.344640 - 4.75505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.48579	−	0.890187i	0.857820	−	0.513949i
$3$	1.48579	−	0.890187i	0.857820	−	0.513949i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.68815	+	0.387484i	−0.689185	+	0.158190i
$7$	0.0245947	−	0.234003i	0.00929591	−	0.0884447i	−0.988890	−	0.148647i	$-0.952508\pi$
$7$	0.0245947	−	0.234003i	0.00929591	−	0.0884447i	0.998186	+	0.0602027i	$0.0191747\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	1.41514	−	2.64526i	0.471712	−	0.881753i
$10$	−0.669131	−	0.743145i	−0.211598	−	0.235003i
$11$	1.45178	−	0.646376i	0.437729	−	0.194890i	−0.176027	−	0.984385i	$-0.556325\pi$
$11$	1.45178	−	0.646376i	0.437729	−	0.194890i	0.613756	+	0.789496i	$0.289658\pi$
$12$	1.72527	+	0.153149i	0.498042	+	0.0442102i
$13$	−1.21131	+	5.69874i	−0.335956	+	1.58055i	0.408425	+	0.912792i	$0.366078\pi$
$13$	−1.21131	+	5.69874i	−0.335956	+	1.58055i	−0.744381	+	0.667755i	$0.767255\pi$
$14$	−0.0957017	+	0.214950i	−0.0255774	+	0.0574477i
$15$	1.73182	−	0.0280299i	0.447155	−	0.00723728i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.90661	+	1.73934i	0.947493	+	0.421851i	0.821518	−	0.570182i	$-0.193127\pi$
$17$	3.90661	+	1.73934i	0.947493	+	0.421851i	0.125975	+	0.992033i	$0.459794\pi$
$18$	−2.16330	+	2.07849i	−0.509896	+	0.489905i
$19$	0.572761	−	0.121744i	0.131400	−	0.0279300i	−0.141742	−	0.989904i	$-0.545270\pi$
$19$	0.572761	−	0.121744i	0.131400	−	0.0279300i	0.273142	+	0.961974i	$0.411937\pi$
$20$	0.406737	+	0.913545i	0.0909491	+	0.204275i
$21$	−0.171764	−	0.369572i	−0.0374819	−	0.0806473i
$22$	−1.58047	+	0.166114i	−0.336957	+	0.0354156i
$23$	7.46724	−	5.42527i	1.55703	−	1.13125i	0.618635	−	0.785679i	$-0.287686\pi$
$23$	7.46724	−	5.42527i	1.55703	−	1.13125i	0.938394	−	0.345568i	$-0.112314\pi$
$24$	−1.59350	−	0.678790i	−0.325272	−	0.138557i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.91303	−	5.04551i	0.571292	−	0.989507i
$27$	−0.252181	−	5.19003i	−0.0485322	−	0.998822i
$28$	0.157441	−	0.174856i	0.0297535	−	0.0330446i
$29$	0.549440	−	1.69100i	0.102028	−	0.314011i	−0.886993	−	0.461783i	$-0.847210\pi$
$29$	0.549440	−	1.69100i	0.102028	−	0.314011i	0.989022	+	0.147771i	$0.0472100\pi$
$30$	−1.65572	−	0.508505i	−0.302292	−	0.0928399i
$31$	−5.48177	−	0.974763i	−0.984556	−	0.175073i
$31$	−5.48177	−	0.974763i	−0.984556	−	0.175073i
$32$		−	1.00000i		−	0.176777i
$33$	1.58165	−	2.25274i	0.275330	−	0.392151i
$34$	−3.17793	−	2.86142i	−0.545010	−	0.490729i
$35$	0.138301	−	0.190355i	0.0233771	−	0.0321759i
$36$	2.69971	−	1.30826i	0.449952	−	0.218044i
$37$	0.834092	−	0.481563i	0.137124	−	0.0791685i	−0.429869	−	0.902891i	$-0.641440\pi$
$37$	0.834092	−	0.481563i	0.137124	−	0.0791685i	0.566993	+	0.823723i	$0.308107\pi$
$38$	−0.582349	−	0.0612073i	−0.0944695	−	0.00992914i
$39$	3.27320	+	9.54542i	0.524132	+	1.52849i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	−5.53676	+	4.98532i	−0.864697	+	0.778576i	−0.976582	−	0.215145i	$-0.930978\pi$
$41$	−5.53676	+	4.98532i	−0.864697	+	0.778576i	0.111886	+	0.993721i	$0.464311\pi$
$42$	0.0491527	+	0.404562i	0.00758443	+	0.0624253i
$43$	0.201044	+	0.945836i	0.0306589	+	0.144239i	0.990815	−	0.135226i	$-0.0431762\pi$
$43$	0.201044	+	0.945836i	0.0306589	+	0.144239i	−0.960156	+	0.279465i	$0.909843\pi$
$44$	1.55445	+	0.330408i	0.234342	+	0.0498109i
$45$	2.54817	−	1.58329i	0.379859	−	0.236023i
$46$	−8.77827	+	2.85223i	−1.29429	+	0.420539i
$47$	7.81614	−	2.53962i	1.14010	−	0.370442i	0.322695	−	0.946503i	$-0.395411\pi$
$47$	7.81614	−	2.53962i	1.14010	−	0.370442i	0.817406	+	0.576061i	$0.195411\pi$
$48$	1.30575	+	1.13799i	0.188469	+	0.164254i
$49$	6.79288	+	1.44387i	0.970412	+	0.206267i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	7.35274	−	0.893329i	1.02959	−	0.125091i
$52$	−4.32960	+	3.89839i	−0.600408	+	0.540610i
$53$	−0.193679	−	1.84273i	−0.0266038	−	0.253119i	−0.999738	−	0.0228807i	$-0.992716\pi$
$53$	−0.193679	−	1.84273i	−0.0266038	−	0.253119i	0.973134	−	0.230238i	$-0.0739505\pi$
$54$	−1.36397	+	5.01394i	−0.185613	+	0.682311i
$55$	1.58047	+	0.166114i	0.213110	+	0.0223988i
$56$	−0.203769	+	0.117646i	−0.0272297	+	0.0157211i
$57$	0.742627	−	0.690750i	0.0983633	−	0.0914921i
$58$	−1.04510	+	1.43845i	−0.137228	+	0.188878i
$59$	2.88510	+	2.59776i	0.375608	+	0.338199i	0.835215	−	0.549923i	$-0.185343\pi$
$59$	2.88510	+	2.59776i	0.375608	+	0.338199i	−0.459607	+	0.888122i	$0.652010\pi$
$60$	1.41755	+	0.995264i	0.183005	+	0.128488i
$61$			5.54239i			0.709630i	0.934937	+	0.354815i	$0.115456\pi$
$61$			5.54239i			0.709630i	−0.934937	+	0.354815i	$0.884544\pi$
$62$	4.91226	+	2.62102i	0.623857	+	0.332869i
$63$	−0.584193	−	0.396205i	−0.0736014	−	0.0499171i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.89839	+	4.32960i	−0.483536	+	0.537021i
$66$	−2.20037	+	1.65372i	−0.270847	+	0.203559i
$67$	2.84513	−	4.92790i	0.347588	−	0.602039i	−0.638233	−	0.769843i	$-0.720334\pi$
$67$	2.84513	−	4.92790i	0.347588	−	0.602039i	0.985820	+	0.167804i	$0.0536676\pi$
$68$	2.13816	+	3.70340i	0.259290	+	0.449104i
$69$	6.26524	−	14.7080i	0.754247	−	1.77064i
$70$	−0.190355	+	0.138301i	−0.0227518	+	0.0165301i
$71$	−13.9140	+	1.46242i	−1.65129	+	0.173558i	−0.883918	−	0.467642i	$-0.845104\pi$
$71$	−13.9140	+	1.46242i	−1.65129	+	0.173558i	−0.767374	+	0.641199i	$0.778437\pi$
$72$	−2.97185	+	0.409975i	−0.350236	+	0.0483160i
$73$	−6.83385	−	15.3491i	−0.799842	−	1.79647i	−0.566462	−	0.824088i	$-0.691688\pi$
$73$	−6.83385	−	15.3491i	−0.799842	−	1.79647i	−0.233380	−	0.972386i	$-0.574978\pi$
$74$	−0.942080	+	0.200245i	−0.109515	+	0.0232780i
$75$	1.51382	+	0.841637i	0.174801	+	0.0971839i
$76$	0.534933	+	0.238167i	0.0613610	+	0.0273197i
$77$	−0.115548	−	0.355619i	−0.0131679	−	0.0405265i
$78$	−0.163304	−	10.0897i	−0.0184905	−	1.14243i
$79$	−5.16130	+	11.5925i	−0.580691	+	1.30425i	0.349417	+	0.936967i	$0.386380\pi$
$79$	−5.16130	+	11.5925i	−0.580691	+	1.30425i	−0.930108	+	0.367286i	$0.880287\pi$
$80$	−0.207912	+	0.978148i	−0.0232452	+	0.109360i
$81$	−4.99478	−	7.48680i	−0.554976	−	0.831867i
$82$	6.80632	−	3.03037i	0.751632	−	0.334648i
$83$	−10.2545	−	11.3888i	−1.12558	−	1.25008i	−0.964770	−	0.263093i	$-0.915257\pi$
$83$	−10.2545	−	11.3888i	−1.12558	−	1.25008i	−0.160806	−	0.986986i	$-0.551409\pi$
$84$	0.0782695	−	0.399950i	0.00853991	−	0.0436382i
$85$	2.51356	+	3.45962i	0.272634	+	0.375248i
$86$	0.101076	−	0.961670i	0.0108993	−	0.103699i
$87$	−0.688956	−	3.00158i	−0.0738638	−	0.321803i
$88$	−1.37627	−	0.794588i	−0.146710	−	0.0847033i
$89$	14.8213	+	10.7683i	1.57105	+	1.14144i	0.926139	+	0.377182i	$0.123107\pi$
$89$	14.8213	+	10.7683i	1.57105	+	1.14144i	0.644915	+	0.764255i	$0.276893\pi$
$90$	−2.91272	+	0.718372i	−0.307028	+	0.0757231i
$91$	1.30373	+	0.423607i	0.136668	+	0.0444061i
$92$	9.23002			0.962296
$93$	−9.01248	+	3.43151i	−0.934550	+	0.355831i
$94$	−8.21838			−0.847661
$95$	0.556897	+	0.180947i	0.0571365	+	0.0185648i
$96$	−0.890187	−	1.48579i	−0.0908543	−	0.151643i
$97$	5.67058	+	4.11992i	0.575760	+	0.418314i	0.837193	−	0.546907i	$-0.184195\pi$
$97$	5.67058	+	4.11992i	0.575760	+	0.418314i	−0.261433	+	0.965222i	$0.584195\pi$
$98$	−6.01423	−	3.47232i	−0.607529	−	0.350757i
$99$	0.344640	−	4.75505i	0.0346377	−	0.477901i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−5.98156	−	8.23291i	−0.595187	−	0.819205i	0.400070	−	0.916485i	$-0.368986\pi$
$101$	−5.98156	−	8.23291i	−0.595187	−	0.819205i	−0.995257	+	0.0972795i	$0.968986\pi$
$102$	−7.26892	−	1.42251i	−0.719731	−	0.140850i
$103$	6.82296	+	7.57767i	0.672287	+	0.746650i	0.978711	−	0.205245i	$-0.0657992\pi$
$103$	6.82296	+	7.57767i	0.672287	+	0.746650i	−0.306424	+	0.951895i	$0.599133\pi$
$104$	5.32237	−	2.36967i	0.521901	−	0.232365i
$105$	0.0360346	−	0.405941i	0.00351661	−	0.0396158i
$106$	−0.385236	+	1.81239i	−0.0374174	+	0.176035i
$107$	7.56288	−	16.9865i	0.731131	−	1.64215i	−0.0349393	−	0.999389i	$-0.511124\pi$
$107$	7.56288	−	16.9865i	0.731131	−	1.64215i	0.766070	−	0.642757i	$-0.222210\pi$
$108$	2.84660	−	4.34705i	0.273915	−	0.418295i
$109$	−3.61225	−	11.1174i	−0.345990	−	1.06485i	−0.961051	−	0.276370i	$-0.910869\pi$
$109$	−3.61225	−	11.1174i	−0.345990	−	1.06485i	0.615061	−	0.788480i	$-0.289131\pi$
$110$	−1.45178	−	0.646376i	−0.138422	−	0.0616295i
$111$	0.810603	−	1.45800i	0.0769390	−	0.138387i
$112$	0.230150	−	0.0489199i	0.0217471	−	0.00462249i
$113$	−3.90181	−	8.76362i	−0.367052	−	0.824412i	−0.998788	−	0.0492280i	$-0.984324\pi$
$113$	−3.90181	−	8.76362i	−0.367052	−	0.824412i	0.631736	−	0.775184i	$-0.282343\pi$
$114$	−0.919733	+	0.427458i	−0.0861409	+	0.0400351i
$115$	9.17946	−	0.964800i	0.855989	−	0.0899681i
$116$	1.43845	−	1.04510i	0.133557	−	0.0970348i
$117$	13.3605	+	11.2687i	1.23518	+	1.04179i
$118$	−1.94114	−	3.36216i	−0.178697	−	0.309512i
$119$	0.503091	−	0.871380i	0.0461183	−	0.0798792i
$120$	−1.04062	−	1.38460i	−0.0949949	−	0.126396i
$121$	−5.67056	+	6.29780i	−0.515506	+	0.572527i
$122$	1.71269	−	5.27112i	0.155060	−	0.477225i
$123$	−3.78859	+	12.3359i	−0.341606	+	1.11229i
$124$	−3.86190	−	4.01071i	−0.346809	−	0.360172i
$125$			1.00000i			0.0894427i
$126$	0.433166	+	0.557339i	0.0385895	+	0.0496517i
$127$	10.1245	+	9.11616i	0.898406	+	0.808928i	0.982255	−	0.187550i	$-0.0600547\pi$
$127$	10.1245	+	9.11616i	0.898406	+	0.808928i	−0.0838490	+	0.996478i	$0.526721\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	1.14068	+	1.22635i	0.100431	+	0.107974i
$130$	5.04551	−	2.91303i	0.442521	−	0.255490i
$131$	2.96849	+	0.312000i	0.259358	+	0.0272596i	0.233315	−	0.972401i	$-0.425043\pi$
$131$	2.96849	+	0.312000i	0.259358	+	0.0272596i	0.0260429	+	0.999661i	$0.491709\pi$
$132$	2.60371	−	0.892832i	0.226624	−	0.0777111i
$133$	−0.0144016	−	0.137022i	−0.00124877	−	0.0118813i
$134$	−4.22868	+	3.80752i	−0.365303	+	0.328920i
$135$	2.37662	−	4.62079i	0.204547	−	0.397694i
$136$	−0.889097	−	4.18287i	−0.0762395	−	0.358678i
$137$	−9.57679	−	2.03561i	−0.818201	−	0.173914i	−0.220246	−	0.975444i	$-0.570686\pi$
$137$	−9.57679	−	2.03561i	−0.818201	−	0.173914i	−0.597954	+	0.801530i	$0.704019\pi$
$138$	−10.5036	+	12.0521i	−0.894129	+	1.02594i
$139$	1.51445	−	0.492075i	0.128454	−	0.0417373i	−0.244084	−	0.969754i	$-0.578487\pi$
$139$	1.51445	−	0.492075i	0.128454	−	0.0417373i	0.372539	+	0.928017i	$0.378487\pi$
$140$	0.223776	−	0.0727091i	0.0189125	−	0.00614504i
$141$	9.35240	−	10.7312i	0.787614	−	0.903727i
$142$	13.6850	+	2.90883i	1.14842	+	0.244103i
$143$	1.92498	+	9.05630i	0.160975	+	0.757326i
$144$	2.95309	+	0.528444i	0.246091	+	0.0440370i
$145$	1.32133	−	1.18973i	0.109731	−	0.0988018i
$146$	1.75625	+	16.7096i	0.145348	+	1.38290i
$147$	11.3781	−	3.90164i	0.938450	−	0.321802i
$148$	0.957850	+	0.100674i	0.0787348	+	0.00827536i
$149$	−14.5438	+	8.39688i	−1.19148	+	0.687899i	−0.958641	−	0.284617i	$-0.908133\pi$
$149$	−14.5438	+	8.39688i	−1.19148	+	0.687899i	−0.232835	+	0.972516i	$0.574800\pi$
$150$	−1.17965	−	1.26824i	−0.0963177	−	0.103551i
$151$	−4.30219	+	5.92146i	−0.350107	+	0.481881i	−0.947359	−	0.320172i	$-0.896259\pi$
$151$	−4.30219	+	5.92146i	−0.350107	+	0.481881i	0.597252	+	0.802054i	$0.296259\pi$
$152$	−0.435153	−	0.391814i	−0.0352956	−	0.0317803i
$153$	10.1294	−	7.87261i	0.818912	−	0.636462i
$154$			0.373920i			0.0301313i
$155$	−4.25997	−	3.58506i	−0.342169	−	0.287959i
$156$	−2.96258	+	9.64634i	−0.237196	+	0.772326i
$157$	−3.66155	+	11.2691i	−0.292224	+	0.899372i	0.691916	+	0.721978i	$0.256767\pi$
$157$	−3.66155	+	11.2691i	−0.292224	+	0.899372i	−0.984140	+	0.177394i	$0.943233\pi$
$158$	8.49095	−	9.43016i	0.675504	−	0.750223i
$159$	−1.92814	−	2.56550i	−0.152912	−	0.203457i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−1.08587	−	1.88079i	−0.0855788	−	0.148227i
$162$	2.43677	+	8.66384i	0.191451	+	0.680696i
$163$	1.36435	−	0.991259i	0.106864	−	0.0776414i	−0.533070	−	0.846071i	$-0.678962\pi$
$163$	1.36435	−	0.991259i	0.106864	−	0.0776414i	0.639934	+	0.768430i	$0.278962\pi$
$164$	−7.40963	+	0.778784i	−0.578595	+	0.0608128i
$165$	2.49612	−	1.16010i	0.194322	−	0.0903138i
$166$	6.23328	+	14.0002i	0.483796	+	1.08662i
$167$	−8.24880	+	1.75334i	−0.638311	+	0.135677i	−0.515689	−	0.856776i	$-0.672464\pi$
$167$	−8.24880	+	1.75334i	−0.638311	+	0.135677i	−0.122623	+	0.992453i	$0.539131\pi$
$168$	−0.198030	+	0.356189i	−0.0152784	+	0.0274806i
$169$	−19.1323	−	8.51826i	−1.47172	−	0.655251i
$170$	−1.32146	−	4.06702i	−0.101351	−	0.311926i
$171$	0.488490	−	1.68738i	0.0373558	−	0.129038i
$172$	−0.393301	+	0.883368i	−0.0299889	+	0.0673562i
$173$	−4.41054	+	20.7500i	−0.335327	+	1.57759i	0.410761	+	0.911743i	$0.365263\pi$
$173$	−4.41054	+	20.7500i	−0.335327	+	1.57759i	−0.746088	+	0.665847i	$0.768070\pi$
$174$	−0.272302	+	3.06757i	−0.0206432	+	0.232552i
$175$	0.214950	−	0.0957017i	0.0162487	−	0.00723437i
$176$	1.06337	+	1.18099i	0.0801542	+	0.0890203i
$177$	6.59914	+	1.29144i	0.496022	+	0.0970706i
$178$	−10.7683	−	14.8213i	−0.807118	−	1.11090i
$179$	0.299958	−	2.85391i	0.0224199	−	0.213312i	−0.977576	−	0.210581i	$-0.932464\pi$
$179$	0.299958	−	2.85391i	0.0224199	−	0.213312i	0.999996	−	0.00273012i	$-0.000869026\pi$
$180$	2.99215	+	0.216867i	0.223022	+	0.0161643i
$181$	7.52031	+	4.34186i	0.558981	+	0.322728i	0.752736	−	0.658322i	$-0.228734\pi$
$181$	7.52031	+	4.34186i	0.558981	+	0.322728i	−0.193756	+	0.981050i	$0.562067\pi$
$182$	−1.10902	−	0.805749i	−0.0822059	−	0.0597261i
$183$	4.93376	+	8.23482i	0.364714	+	0.608735i
$184$	−8.77827	−	2.85223i	−0.647143	−	0.210269i
$185$	0.963126			0.0708105
$186$	9.63177	−	0.478551i	0.706236	−	0.0350890i
$187$	6.79582			0.496960
$188$	7.81614	+	2.53962i	0.570051	+	0.185221i
$189$	−1.22068	−	0.0686361i	−0.0887916	−	0.00499254i
$190$	−0.473725	−	0.344182i	−0.0343676	−	0.0249696i
$191$	−12.6416	−	7.29863i	−0.914713	−	0.528110i	−0.0327687	−	0.999463i	$-0.510432\pi$
$191$	−12.6416	−	7.29863i	−0.914713	−	0.528110i	−0.881945	+	0.471353i	$0.843766\pi$
$192$	0.387484	+	1.68815i	0.0279642	+	0.121832i
$193$	−2.15689	+	20.5214i	−0.155256	+	1.47716i	0.588384	+	0.808582i	$0.299764\pi$
$193$	−2.15689	+	20.5214i	−0.155256	+	1.47716i	−0.743640	+	0.668581i	$0.766902\pi$
$194$	−4.11992	−	5.67058i	−0.295793	−	0.407124i
$195$	−1.93803	+	9.90318i	−0.138785	+	0.709181i
$196$	4.64687	+	5.16087i	0.331919	+	0.368634i
$197$	2.14512	−	0.955070i	0.152834	−	0.0680460i	−0.328894	−	0.944367i	$-0.606676\pi$
$197$	2.14512	−	0.955070i	0.152834	−	0.0680460i	0.481728	+	0.876321i	$0.340009\pi$
$198$	−1.79716	+	4.41582i	−0.127719	+	0.313819i
$199$	−3.17450	+	14.9348i	−0.225034	+	1.05870i	0.710016	+	0.704186i	$0.248688\pi$
$199$	−3.17450	+	14.9348i	−0.225034	+	1.05870i	−0.935050	+	0.354516i	$0.884646\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	−0.159497	−	9.85452i	−0.0112501	−	0.695084i
$202$	3.14469	+	9.67837i	0.221260	+	0.680968i
$203$	−0.382186	−	0.170160i	−0.0268242	−	0.0119429i
$204$	6.47357	+	3.59911i	0.453241	+	0.251988i
$205$	−7.28764	+	1.54903i	−0.508991	+	0.108189i
$206$	−4.14740	−	9.31520i	−0.288963	−	0.649021i
$207$	−3.78408	−	27.4303i	−0.263012	−	1.90654i
$208$	−5.79414	+	0.608989i	−0.401751	+	0.0422258i
$209$	0.752832	−	0.546965i	0.0520745	−	0.0378343i
$210$	−0.159714	+	0.374937i	−0.0110213	+	0.0258731i
$211$	−8.45337	−	14.6417i	−0.581954	−	1.00797i	−0.995248	−	0.0973762i	$-0.968955\pi$
$211$	−8.45337	−	14.6417i	−0.581954	−	1.00797i	0.413294	−	0.910598i	$-0.364378\pi$
$212$	0.926441	−	1.60464i	0.0636282	−	0.110207i
$213$	−19.3715	+	14.5589i	−1.32731	+	0.997562i
$214$	−12.4418	+	13.8181i	−0.850507	+	0.944583i
$215$	−0.298809	+	0.919640i	−0.0203786	+	0.0627189i
$216$	−4.05059	+	3.25464i	−0.275608	+	0.221450i
$217$	−0.362920	+	1.25878i	−0.0246366	+	0.0854513i
$218$			11.6895i			0.791711i
$219$	−23.8172	−	16.7221i	−1.60942	−	1.12997i
$220$	1.18099	+	1.06337i	0.0796221	+	0.0716921i
$221$	−14.6441	+	20.1559i	−0.985071	+	1.35583i
$222$	−1.22148	+	1.13615i	−0.0819801	+	0.0762533i
$223$	−11.1904	+	6.46079i	−0.749366	+	0.432647i	−0.825465	−	0.564454i	$-0.809087\pi$
$223$	−11.1904	+	6.46079i	−0.749366	+	0.432647i	0.0760988	+	0.997100i	$0.475754\pi$
$224$	−0.234003	−	0.0245947i	−0.0156350	−	0.00164330i
$225$	2.99843	−	0.0970856i	0.199895	−	0.00647237i
$226$	1.00274	+	9.54042i	0.0667012	+	0.634619i
$227$	1.41382	−	1.27301i	0.0938386	−	0.0844926i	−0.620876	−	0.783909i	$-0.713223\pi$
$227$	1.41382	−	1.27301i	0.0938386	−	0.0844926i	0.714715	+	0.699416i	$0.246556\pi$
$228$	1.00681	−	0.122323i	0.0666776	−	0.00810107i
$229$	−4.34732	−	20.4526i	−0.287279	−	1.35154i	−0.850821	−	0.525455i	$-0.823895\pi$
$229$	−4.34732	−	20.4526i	−0.287279	−	1.35154i	0.563542	−	0.826087i	$-0.309438\pi$
$230$	−9.02832	−	1.91903i	−0.595310	−	0.126537i
$231$	−0.488246	−	0.425515i	−0.0321242	−	0.0279969i
$232$	−1.69100	+	0.549440i	−0.111020	+	0.0360725i
$233$	−9.30190	+	3.02237i	−0.609388	+	0.198002i	−0.597423	−	0.801926i	$-0.703809\pi$
$233$	−9.30190	+	3.02237i	−0.609388	+	0.198002i	−0.0119648	+	0.999928i	$0.503809\pi$
$234$	−9.22436	−	14.8458i	−0.603015	−	0.970500i
$235$	8.03879	+	1.70870i	0.524393	+	0.111463i
$236$	0.807173	+	3.79745i	0.0525425	+	0.247193i
$237$	2.65086	+	21.8185i	0.172192	+	1.41726i
$238$	−0.747739	+	0.673268i	−0.0484687	+	0.0436415i
$239$	1.09867	+	10.4532i	0.0710672	+	0.676159i	0.970828	+	0.239776i	$0.0770741\pi$
$239$	1.09867	+	10.4532i	0.0710672	+	0.676159i	−0.899761	+	0.436383i	$0.856259\pi$
$240$	0.561821	+	1.63840i	0.0362654	+	0.105758i
$241$	−15.5369	−	1.63300i	−1.00082	−	0.105190i	−0.410078	−	0.912051i	$-0.634498\pi$
$241$	−15.5369	−	1.63300i	−1.00082	−	0.105190i	−0.590743	+	0.806860i	$0.701165\pi$
$242$	7.33915	−	4.23726i	0.471779	−	0.272381i
$243$	−14.0858	−	6.67751i	−0.903607	−	0.428363i
$244$	−3.25773	+	4.48389i	−0.208555	+	0.287051i
$245$	5.16087	+	4.64687i	0.329716	+	0.296878i
$246$	7.41516	−	10.5614i	0.472773	−	0.673369i
$247$			3.41149i			0.217068i
$248$	2.43351	+	5.00780i	0.154528	+	0.317996i
$249$	−25.3741	−	7.79289i	−1.60802	−	0.493854i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−8.07287	+	8.96583i	−0.509555	+	0.565918i	−0.941944	−	0.335769i	$-0.891004\pi$
$251$	−8.07287	+	8.96583i	−0.509555	+	0.565918i	0.432389	+	0.901687i	$0.357671\pi$
$252$	−0.239738	−	0.663916i	−0.0151021	−	0.0418228i
$253$	7.33406	−	12.7030i	0.461088	−	0.798629i
$254$	−6.81194	−	11.7986i	−0.427419	−	0.740312i
$255$	6.81432	+	2.90272i	0.426729	+	0.181776i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.91475	−	0.201248i	0.119439	−	0.0125535i	−0.0446205	−	0.999004i	$-0.514208\pi$
$257$	1.91475	−	0.201248i	0.119439	−	0.0125535i	0.164059	+	0.986450i	$0.447541\pi$
$258$	−0.705888	−	1.51881i	−0.0439467	−	0.0945572i
$259$	−0.0921729	−	0.207024i	−0.00572734	−	0.0128638i
$260$	−5.69874	+	1.21131i	−0.353421	+	0.0751220i
$261$	−3.69561	−	3.84641i	−0.228752	−	0.238087i
$262$	−2.72678	−	1.21404i	−0.168461	−	0.0750038i
$263$	0.545687	+	1.67945i	0.0336485	+	0.103559i	0.966470	−	0.256779i	$-0.0826612\pi$
$263$	0.545687	+	1.67945i	0.0336485	+	0.103559i	−0.932822	+	0.360338i	$0.882661\pi$
$264$	−2.75217	+	0.0445444i	−0.169384	+	0.00274152i
$265$	0.753635	−	1.69269i	0.0462954	−	0.103981i
$266$	−0.0286454	+	0.134766i	−0.00175636	+	0.00826302i
$267$	31.6071	+	2.80570i	1.93432	+	0.171706i
$268$	5.19831	−	2.31443i	0.317537	−	0.141377i
$269$	9.65595	+	10.7240i	0.588734	+	0.653855i	0.961737	−	0.273975i	$-0.0883386\pi$
$269$	9.65595	+	10.7240i	0.588734	+	0.653855i	−0.373003	+	0.927830i	$0.621672\pi$
$270$	−3.68820	+	3.66021i	−0.224457	+	0.222754i
$271$	2.62225	+	3.60922i	0.159290	+	0.219245i	0.881201	−	0.472742i	$-0.156736\pi$
$271$	2.62225	+	3.60922i	0.159290	+	0.219245i	−0.721910	+	0.691987i	$0.756736\pi$
$272$	−0.446997	+	4.25290i	−0.0271032	+	0.257870i
$273$	2.31416	−	0.531172i	0.140059	−	0.0321480i
$274$	8.47903	+	4.89537i	0.512237	+	0.295740i
$275$	1.28567	+	0.934094i	0.0775288	+	0.0563280i
$276$	13.7139	−	8.21644i	0.825477	−	0.494572i
$277$	10.1435	+	3.29584i	0.609466	+	0.198028i	0.597458	−	0.801900i	$-0.296178\pi$
$277$	10.1435	+	3.29584i	0.609466	+	0.198028i	0.0120084	+	0.999928i	$0.496178\pi$
$278$	−1.59239			−0.0955051
$279$	−10.3360	+	13.1213i	−0.618797	+	0.785551i
$280$	−0.235292			−0.0140614
$281$	−7.01729	−	2.28006i	−0.418617	−	0.136017i	0.0921322	−	0.995747i	$-0.470632\pi$
$281$	−7.01729	−	2.28006i	−0.418617	−	0.136017i	−0.510749	+	0.859730i	$0.670632\pi$
$282$	−12.2108	+	7.31589i	−0.727141	+	0.435655i
$283$	4.17492	+	3.03325i	0.248173	+	0.180308i	0.704917	−	0.709290i	$-0.250984\pi$
$283$	4.17492	+	3.03325i	0.248173	+	0.180308i	−0.456744	+	0.889598i	$0.650984\pi$
$284$	−12.1163	−	6.99534i	−0.718969	−	0.415097i
$285$	0.988508	−	0.226894i	0.0585542	−	0.0134400i
$286$	0.967790	−	9.20791i	0.0572266	−	0.544475i
$287$	1.03040	+	1.41823i	0.0608228	+	0.0837154i
$288$	−2.64526	−	1.41514i	−0.155873	−	0.0833877i
$289$	0.861122	+	0.956372i	0.0506542	+	0.0562572i
$290$	−1.62431	+	0.723188i	−0.0953826	+	0.0424671i
$291$	12.0928	+	1.07345i	0.708891	+	0.0629269i
$292$	3.49326	−	16.4345i	0.204428	−	0.961756i
$293$	−1.81354	+	4.07328i	−0.105948	+	0.237963i	−0.958738	−	0.284290i	$-0.908242\pi$
$293$	−1.81354	+	4.07328i	−0.105948	+	0.237963i	0.852790	+	0.522254i	$0.174909\pi$
$294$	−12.0269	+	0.194657i	−0.701422	+	0.0113526i
$295$	1.19969	+	3.69228i	0.0698488	+	0.214973i
$296$	−0.879860	−	0.391739i	−0.0511408	−	0.0227694i
$297$	−3.72082	−	7.37180i	−0.215904	−	0.427755i
$298$	16.4268	−	3.49162i	0.951577	−	0.202264i
$299$	21.8721	+	49.1256i	1.26490	+	2.84101i
$300$	0.730003	+	1.57070i	0.0421467	+	0.0906844i
$301$	0.226273	−	0.0237822i	0.0130421	−	0.00137078i
$302$	5.92146	−	4.30219i	0.340742	−	0.247563i
$303$	−16.2162	−	6.90766i	−0.931594	−	0.396835i
$304$	0.292778	+	0.507107i	0.0167920	+	0.0290846i
$305$	−2.77119	+	4.79985i	−0.158678	+	0.274839i
$306$	−12.0664	+	4.35714i	−0.689789	+	0.249081i
$307$	−15.4805	+	17.1928i	−0.883516	+	0.981244i	−0.999929	−	0.0119566i	$-0.996194\pi$
$307$	−15.4805	+	17.1928i	−0.883516	+	0.981244i	0.116412	+	0.993201i	$0.462861\pi$
$308$	0.115548	−	0.355619i	0.00658393	−	0.0202633i
$309$	16.8830	+	5.18510i	0.960442	+	0.294970i
$310$	2.94363	+	4.72600i	0.167187	+	0.268418i
$311$			10.7909i			0.611895i	0.952048	+	0.305947i	$0.0989731\pi$
$311$			10.7909i			0.611895i	−0.952048	+	0.305947i	$0.901027\pi$
$312$	5.79847	−	8.25873i	0.328273	−	0.467559i
$313$	−14.5839	−	13.1314i	−0.824332	−	0.742232i	0.144618	−	0.989488i	$-0.453805\pi$
$313$	−14.5839	−	13.1314i	−0.824332	−	0.742232i	−0.968950	+	0.247255i	$0.920471\pi$
$314$	6.96468	−	9.58606i	0.393040	−	0.540973i
$315$	−0.307823	−	0.635220i	−0.0173439	−	0.0357906i
$316$	−10.9895	+	6.34476i	−0.618205	+	0.356921i
$317$	−17.0520	−	1.79223i	−0.957734	−	0.100662i	−0.387253	−	0.921973i	$-0.626576\pi$
$317$	−17.0520	−	1.79223i	−0.957734	−	0.100662i	−0.570480	+	0.821311i	$0.693243\pi$
$318$	1.04099	+	3.03576i	0.0583757	+	0.170237i
$319$	−0.295355	−	2.81012i	−0.0165367	−	0.157336i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	−3.88432	−	31.9707i	−0.216801	−	1.78443i
$322$	0.451532	+	2.12429i	0.0251629	+	0.118382i
$323$	2.44931	+	0.520617i	0.136283	+	0.0289679i
$324$	0.359767	−	8.99281i	0.0199870	−	0.499600i
$325$	−5.54091	+	1.80035i	−0.307354	+	0.0998655i
$326$	−1.60389	+	0.521136i	−0.0888313	+	0.0288630i
$327$	−15.2636	−	13.3025i	−0.844076	−	0.735628i
$328$	7.28764	+	1.54903i	0.402392	+	0.0855311i
$329$	−0.402042	−	1.89146i	−0.0221653	−	0.104280i
$330$	−2.73244	+	0.331981i	−0.150416	+	0.0182749i
$331$	10.3314	−	9.30240i	0.567863	−	0.511306i	−0.334435	−	0.942419i	$-0.608546\pi$
$331$	10.3314	−	9.30240i	0.567863	−	0.511306i	0.902298	+	0.431113i	$0.141879\pi$
$332$	−1.60191	−	15.2411i	−0.0879161	−	0.836466i
$333$	−0.0935057	−	2.88787i	−0.00512408	−	0.158254i
$334$	8.38689	+	0.881497i	0.458910	+	0.0482334i
$335$	4.92790	−	2.84513i	0.269240	−	0.155446i
$336$	0.298406	−	0.277561i	0.0162794	−	0.0151422i
$337$	3.32897	−	4.58194i	0.181341	−	0.249594i	−0.708663	−	0.705547i	$-0.750701\pi$
$337$	3.32897	−	4.58194i	0.181341	−	0.249594i	0.890004	+	0.455953i	$0.150701\pi$
$338$	15.5636	+	14.0136i	0.846551	+	0.762238i
$339$	−13.5985	−	9.54754i	−0.738570	−	0.518551i
$340$			4.27632i			0.231916i
$341$	−8.58841	+	2.12814i	−0.465089	+	0.115245i
$342$	−0.986012	+	1.45385i	−0.0533174	+	0.0786150i
$343$	1.01390	−	3.12047i	0.0547456	−	0.168490i
$344$	0.647027	−	0.718596i	0.0348854	−	0.0387441i
$345$	12.7799	−	9.60492i	0.688046	−	0.517112i
$346$	10.6068	−	18.3715i	0.570223	−	0.987656i
$347$	2.00119	+	3.46616i	0.107429	+	0.186073i	0.914728	−	0.404070i	$-0.132405\pi$
$347$	2.00119	+	3.46616i	0.107429	+	0.186073i	−0.807299	+	0.590143i	$0.799071\pi$
$348$	1.20691	−	2.83328i	0.0646969	−	0.151880i
$349$	−13.8018	+	10.0276i	−0.738791	+	0.536763i	−0.892332	−	0.451379i	$-0.850932\pi$
$349$	−13.8018	+	10.0276i	−0.738791	+	0.536763i	0.153541	+	0.988142i	$0.450932\pi$
$350$	−0.234003	+	0.0245947i	−0.0125080	+	0.00131464i
$351$	29.8821	+	4.84960i	1.59499	+	0.258852i
$352$	−0.646376	−	1.45178i	−0.0344519	−	0.0773803i
$353$	12.8098	−	2.72281i	0.681798	−	0.144921i	0.146023	−	0.989281i	$-0.453353\pi$
$353$	12.8098	−	2.72281i	0.681798	−	0.144921i	0.535775	+	0.844361i	$0.320019\pi$
$354$	−5.87708	−	3.26748i	−0.312363	−	0.173665i
$355$	−12.7811	−	5.69052i	−0.678352	−	0.302022i
$356$	5.66123	+	17.4235i	0.300045	+	0.923442i
$357$	−0.0282032	−	1.74253i	−0.00149267	−	0.0922245i
$358$	−1.16719	+	2.62154i	−0.0616877	+	0.138553i
$359$	4.89049	−	23.0079i	0.258110	−	1.21431i	−0.637844	−	0.770166i	$-0.720173\pi$
$359$	4.89049	−	23.0079i	0.258110	−	1.21431i	0.895954	−	0.444147i	$-0.146493\pi$
$360$	−2.77869	−	1.13088i	−0.146450	−	0.0596025i
$361$	−17.0441	+	7.58854i	−0.897059	+	0.399397i
$362$	−5.81054	−	6.45325i	−0.305395	−	0.339176i
$363$	−2.81904	+	14.4051i	−0.147961	+	0.756069i
$364$	0.805749	+	1.10902i	0.0422327	+	0.0581284i
$365$	1.75625	−	16.7096i	0.0919264	−	0.874621i
$366$	−2.14759	−	9.35639i	−0.112256	−	0.489066i
$367$	16.0420	+	9.26187i	0.837387	+	0.483466i	0.856375	−	0.516354i	$-0.172711\pi$
$367$	16.0420	+	9.26187i	0.837387	+	0.483466i	−0.0189881	+	0.999820i	$0.506044\pi$
$368$	7.46724	+	5.42527i	0.389257	+	0.282812i
$369$	5.35219	+	21.7011i	0.278624	+	1.12971i
$370$	−0.915988	−	0.297622i	−0.0476199	−	0.0154727i
$371$	−0.435968			−0.0226343
$372$	−9.30824	−	2.52125i	−0.482610	−	0.130721i
$373$	−3.74454			−0.193885			−0.0969424	−	0.995290i	$-0.530906\pi$
$373$	−3.74454			−0.193885			−0.0969424	+	0.995290i	$0.530906\pi$
$374$	−6.46321	−	2.10003i	−0.334205	−	0.108590i
$375$	0.890187	+	1.48579i	0.0459690	+	0.0767258i
$376$	−6.64881	−	4.83064i	−0.342886	−	0.249121i
$377$	8.97105	+	5.17944i	0.462033	+	0.266755i
$378$	1.13973	+	0.442489i	0.0586213	+	0.0227592i
$379$	−0.262801	+	2.50039i	−0.0134992	+	0.128436i	−0.999196	−	0.0400922i	$-0.987235\pi$
$379$	−0.262801	+	2.50039i	−0.0134992	+	0.128436i	0.985697	+	0.168528i	$0.0539015\pi$
$380$	0.344182	+	0.473725i	0.0176561	+	0.0243016i
$381$	23.1580	+	4.53197i	1.18642	+	0.232180i
$382$	9.76747	+	10.8479i	0.499747	+	0.555025i
$383$	4.62812	−	2.06057i	0.236486	−	0.105290i	−0.285072	−	0.958506i	$-0.592018\pi$
$383$	4.62812	−	2.06057i	0.236486	−	0.105290i	0.521558	+	0.853216i	$0.325351\pi$
$384$	0.153149	−	1.72527i	0.00781533	−	0.0880422i
$385$	0.0777423	−	0.365749i	0.00396211	−	0.0186403i
$386$	8.39278	−	18.8505i	0.427181	−	0.959465i
$387$	2.78648	+	0.806674i	0.141645	+	0.0410055i
$388$	2.16597	+	6.66616i	0.109960	+	0.338423i
$389$	−31.3934	−	13.9772i	−1.59171	−	0.708675i	−0.596155	−	0.802869i	$-0.703306\pi$
$389$	−31.3934	−	13.9772i	−1.59171	−	0.708675i	−0.995554	+	0.0941947i	$0.969972\pi$
$390$	4.90343	−	8.81959i	0.248295	−	0.446598i
$391$	38.6080	−	8.20639i	1.95249	−	0.415015i
$392$	−2.82464	−	6.34424i	−0.142666	−	0.320433i
$393$	4.68828	−	2.17894i	0.236493	−	0.109913i
$394$	−2.33527	+	0.245446i	−0.117649	+	0.0123654i
$395$	−10.2660	+	7.45872i	−0.516541	+	0.375289i
$396$	3.07377	−	3.64434i	0.154463	−	0.183135i
$397$	−13.6799	−	23.6942i	−0.686573	−	1.18918i	−0.972940	−	0.231059i	$-0.925781\pi$
$397$	−13.6799	−	23.6942i	−0.686573	−	1.18918i	0.286367	−	0.958120i	$-0.407552\pi$
$398$	7.63424	−	13.2229i	0.382670	−	0.662804i
$399$	−0.143373	−	0.190765i	−0.00717761	−	0.00955021i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	−3.23828	+	9.96640i	−0.161712	+	0.497698i	−0.998779	−	0.0494023i	$-0.984268\pi$
$401$	−3.23828	+	9.96640i	−0.161712	+	0.497698i	0.837067	+	0.547100i	$0.184268\pi$
$402$	−2.89352	+	9.42149i	−0.144316	+	0.469901i
$403$	12.1950	−	30.0585i	0.607478	−	1.49732i
$404$		−	10.1764i		−	0.506297i
$405$	−0.582208	−	8.98115i	−0.0289302	−	0.446277i
$406$	0.310898	+	0.279934i	0.0154296	+	0.0138929i
$407$	0.899650	−	1.23826i	0.0445940	−	0.0613784i
$408$	−5.04455	−	5.42340i	−0.249742	−	0.268498i
$409$	8.60533	−	4.96829i	0.425506	−	0.245666i	−0.271924	−	0.962319i	$-0.587660\pi$
$409$	8.60533	−	4.96829i	0.425506	−	0.245666i	0.697430	+	0.716653i	$0.254327\pi$
$410$	7.40963	+	0.778784i	0.365936	+	0.0384614i
$411$	−16.0412	+	5.50065i	−0.791252	+	0.271327i
$412$	1.06585	+	10.1409i	0.0525107	+	0.499606i
$413$	0.678840	−	0.611231i	0.0334036	−	0.0300767i
$414$	−4.87755	+	27.2571i	−0.239719	+	1.33961i
$415$	−3.18627	−	14.9902i	−0.156408	−	0.735840i
$416$	5.69874	+	1.21131i	0.279404	+	0.0593891i
$417$	1.81212	−	2.07926i	0.0887397	−	0.101822i
$418$	−0.885008	+	0.287556i	−0.0432871	+	0.0140648i
$419$	14.2183	−	4.61982i	0.694611	−	0.225693i	0.0596301	−	0.998221i	$-0.481008\pi$
$419$	14.2183	−	4.61982i	0.694611	−	0.225693i	0.634981	+	0.772528i	$0.281008\pi$
$420$	0.267759	−	0.307232i	0.0130653	−	0.0149914i
$421$	−10.5391	−	2.24015i	−0.513643	−	0.109178i	−0.0562045	−	0.998419i	$-0.517900\pi$
$421$	−10.5391	−	2.24015i	−0.513643	−	0.109178i	−0.457439	+	0.889241i	$0.651233\pi$
$422$	3.51511	+	16.5373i	0.171113	+	0.805023i
$423$	4.34296	−	24.2696i	0.211162	−	1.18003i
$424$	−1.37696	+	1.23982i	−0.0668711	+	0.0602110i
$425$	0.446997	+	4.25290i	0.0216826	+	0.206296i
$426$	22.9223	−	7.86026i	1.11059	−	0.380831i
$427$	1.29693	+	0.136313i	0.0627630	+	0.00659666i
$428$	16.1029	−	9.29702i	0.778363	−	0.449388i
$429$	10.9219	+	11.7422i	0.527315	+	0.566917i
$430$	0.568369	−	0.782292i	0.0274092	−	0.0377255i
$431$	28.8964	+	26.0184i	1.39189	+	1.25326i	0.930613	+	0.366005i	$0.119275\pi$
$431$	28.8964	+	26.0184i	1.39189	+	1.25326i	0.461275	+	0.887257i	$0.347392\pi$
$432$	4.85808	−	1.84365i	0.233735	−	0.0887024i
$433$		−	15.0113i		−	0.721398i	−0.932682	−	0.360699i	$-0.882538\pi$
$433$		−	15.0113i		−	0.721398i	0.932682	−	0.360699i	$-0.117462\pi$
$434$	0.734140	−	1.08502i	0.0352398	−	0.0520826i
$435$	0.904135	−	2.94392i	0.0433500	−	0.141150i
$436$	3.61225	−	11.1174i	0.172995	−	0.532425i
$437$	3.61645	−	4.01648i	0.172998	−	0.192134i
$438$	17.4841	+	23.2636i	0.835422	+	1.11158i
$439$	−2.56978	+	4.45100i	−0.122649	+	0.212435i	−0.920812	−	0.390008i	$-0.872472\pi$
$439$	−2.56978	+	4.45100i	−0.122649	+	0.212435i	0.798162	+	0.602442i	$0.205806\pi$
$440$	−0.794588	−	1.37627i	−0.0378805	−	0.0656109i
$441$	13.4323	−	15.9256i	0.639631	−	0.758364i
$442$	20.1559	−	14.6441i	0.958720	−	0.696551i
$443$	−27.6026	+	2.90115i	−1.31144	+	0.137838i	−0.734309	−	0.678816i	$-0.762494\pi$
$443$	−27.6026	+	2.90115i	−1.31144	+	0.137838i	−0.577129	+	0.816653i	$0.695827\pi$
$444$	1.51278	−	0.703085i	0.0717934	−	0.0333669i
$445$	7.45146	+	16.7363i	0.353233	+	0.793375i
$446$	12.6392	−	2.68655i	0.598484	−	0.127212i
$447$	−14.1343	+	25.4227i	−0.668527	+	1.20245i
$448$	0.214950	+	0.0957017i	0.0101554	+	0.00452148i
$449$	−5.18694	−	15.9638i	−0.244787	−	0.753376i	−0.995671	−	0.0929430i	$-0.970373\pi$
$449$	−5.18694	−	15.9638i	−0.244787	−	0.753376i	0.750885	−	0.660433i	$-0.229627\pi$
$450$	−2.88168	−	0.834232i	−0.135844	−	0.0393261i
$451$	−4.81579	+	10.8164i	−0.226767	+	0.509326i
$452$	1.99449	−	9.38334i	0.0938130	−	0.441355i
$453$	−1.12094	+	12.6278i	−0.0526666	+	0.593305i
$454$	−1.73800	+	0.773810i	−0.0815686	+	0.0363167i
$455$	0.917259	+	1.01872i	0.0430018	+	0.0477583i
$456$	−0.995333	−	0.194785i	−0.0466108	−	0.00912164i
$457$	−10.2081	−	14.0503i	−0.477516	−	0.657245i	0.500509	−	0.865731i	$-0.333146\pi$
$457$	−10.2081	−	14.0503i	−0.477516	−	0.657245i	−0.978025	+	0.208486i	$0.933146\pi$
$458$	−2.18564	+	20.7949i	−0.102128	+	0.971683i
$459$	8.04204	−	20.7141i	0.375370	−	0.966850i
$460$	7.99343	+	4.61501i	0.372696	+	0.215176i
$461$	−7.22933	−	5.25242i	−0.336704	−	0.244629i	0.406566	−	0.913621i	$-0.366726\pi$
$461$	−7.22933	−	5.25242i	−0.336704	−	0.244629i	−0.743270	+	0.668992i	$0.766726\pi$
$462$	0.332858	+	0.555565i	0.0154860	+	0.0258472i
$463$	32.0277	+	10.4064i	1.48845	+	0.483628i	0.936626	−	0.350330i	$-0.113931\pi$
$463$	32.0277	+	10.4064i	1.48845	+	0.483628i	0.551827	+	0.833958i	$0.313931\pi$
$464$	1.77803			0.0825428
$465$	−9.52079	−	1.53446i	−0.441516	−	0.0711591i
$466$	9.78060			0.453077
$467$	20.2617	+	6.58343i	0.937600	+	0.304645i	0.737667	−	0.675165i	$-0.235927\pi$
$467$	20.2617	+	6.58343i	0.937600	+	0.304645i	0.199933	+	0.979810i	$0.435927\pi$
$468$	4.18528	+	16.9697i	0.193465	+	0.784424i
$469$	−1.08317	−	0.786968i	−0.0500160	−	0.0363388i
$470$	−7.11733	−	4.10919i	−0.328298	−	0.189543i
$471$	4.59131	+	20.0030i	0.211556	+	0.921688i
$472$	0.405810	−	3.86102i	0.0186789	−	0.177718i
$473$	0.903238	+	1.24320i	0.0415309	+	0.0571624i
$474$	4.22116	−	21.5697i	0.193884	−	0.990731i
$475$	0.391814	+	0.435153i	0.0179777	+	0.0199662i
$476$	0.919194	−	0.409251i	0.0421312	−	0.0187580i
$477$	−5.14858	−	2.09538i	−0.235737	−	0.0959411i
$478$	2.18531	−	10.2811i	0.0999536	−	0.470245i
$479$	10.1769	−	22.8578i	0.464997	−	1.04440i	−0.517083	−	0.855935i	$-0.672982\pi$
$479$	10.1769	−	22.8578i	0.464997	−	1.04440i	0.982080	−	0.188465i	$-0.0603510\pi$
$480$	−0.0280299	−	1.73182i	−0.00127938	−	0.0790466i
$481$	1.73397	+	5.33660i	0.0790620	+	0.243328i
$482$	14.2719	+	6.35424i	0.650065	+	0.289428i
$483$	−3.28763	−	1.82782i	−0.149592	−	0.0831688i
$484$	−8.28933	+	1.76195i	−0.376788	+	0.0800887i
$485$	2.85091	+	6.40324i	0.129453	+	0.290756i
$486$	11.3330	+	10.7035i	0.514074	+	0.485519i
$487$	−40.0422	+	4.20860i	−1.81448	+	0.190710i	−0.950063	−	0.312058i	$-0.898982\pi$
$487$	−40.0422	+	4.20860i	−1.81448	+	0.190710i	−0.864421	+	0.502768i	$0.832315\pi$
$488$	4.48389	−	3.25773i	0.202976	−	0.147471i
$489$	1.14473	−	2.68733i	0.0517666	−	0.121525i
$490$	−3.47232	−	6.01423i	−0.156863	−	0.271695i
$491$	9.92842	−	17.1965i	0.448063	−	0.776068i	−0.550197	−	0.835035i	$-0.685447\pi$
$491$	9.92842	−	17.1965i	0.448063	−	0.776068i	0.998260	+	0.0589669i	$0.0187807\pi$
$492$	−10.3159	+	7.75306i	−0.465076	+	0.349535i
$493$	5.08767	−	5.65043i	0.229137	−	0.254483i
$494$	1.05421	−	3.24452i	0.0474310	−	0.145978i
$495$	2.67599	−	3.94568i	0.120277	−	0.177345i
$496$	−0.766906	−	5.51469i	−0.0344351	−	0.247617i
$497$			3.29189i			0.147661i
$498$	21.7241	+	15.2525i	0.973480	+	0.683481i
$499$	8.13030	+	7.32055i	0.363962	+	0.327713i	0.830739	−	0.556662i	$-0.187918\pi$
$499$	8.13030	+	7.32055i	0.363962	+	0.327713i	−0.466777	+	0.884375i	$0.654585\pi$
$500$	−0.587785	+	0.809017i	−0.0262866	+	0.0361803i
$501$	−10.6952	+	9.94806i	−0.477825	+	0.444447i
$502$	10.4483	−	6.03236i	0.466333	−	0.269237i
$503$	2.89209	+	0.303971i	0.128952	+	0.0135534i	0.168784	−	0.985653i	$-0.446016\pi$
$503$	2.89209	+	0.303971i	0.128952	+	0.0135534i	−0.0398326	+	0.999206i	$0.512682\pi$
$504$	0.0228434	+	0.705505i	0.00101753	+	0.0314257i
$505$	−1.06373	−	10.1207i	−0.0473352	−	0.450365i
$506$	−10.9005	+	9.81489i	−0.484588	+	0.436325i
$507$	−36.0095	+	4.37501i	−1.59924	+	0.194301i
$508$	2.83257	+	13.3262i	0.125675	+	0.591253i
$509$	10.8821	+	2.31307i	0.482343	+	0.102525i	0.442664	−	0.896687i	$-0.354033\pi$
$509$	10.8821	+	2.31307i	0.482343	+	0.102525i	0.0396784	+	0.999213i	$0.487367\pi$
$510$	−5.58381	−	4.86639i	−0.247255	−	0.215488i
$511$	−3.75980	+	1.22163i	−0.166324	+	0.0540419i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−0.776295	−	2.94194i	−0.0342742	−	0.129890i
$514$	−1.88322	−	0.400292i	−0.0830654	−	0.0176561i
$515$	2.12003	+	9.97394i	0.0934195	+	0.439504i
$516$	0.202001	+	1.66261i	0.00889258	+	0.0731923i
$517$	9.70580	−	8.73914i	0.426861	−	0.384347i
$518$	0.0236878	+	0.225374i	0.00104078	+	0.00990237i
$519$	11.9182	+	34.7563i	0.523151	+	1.52563i
$520$	5.79414	+	0.608989i	0.254090	+	0.0267059i
$521$	18.8898	−	10.9060i	0.827575	−	0.477801i	−0.0254466	−	0.999676i	$-0.508101\pi$
$521$	18.8898	−	10.9060i	0.827575	−	0.477801i	0.853022	+	0.521875i	$0.174767\pi$
$522$	2.32612	+	4.80016i	0.101812	+	0.210097i
$523$	−16.0372	+	22.0733i	−0.701256	+	0.965196i	0.298685	+	0.954352i	$0.403452\pi$
$523$	−16.0372	+	22.0733i	−0.701256	+	0.965196i	−0.999941	+	0.0108445i	$0.996548\pi$
$524$	2.21817	+	1.99725i	0.0969011	+	0.0872501i
$525$	0.234177	−	0.333538i	0.0102203	−	0.0145568i
$526$		−	1.76588i		−	0.0769960i
$527$	−19.7197	−	13.3427i	−0.859005	−	0.581216i
$528$	2.63124	+	0.808104i	0.114510	+	0.0351682i
$529$	19.2188	−	59.1493i	0.835599	−	2.57171i
$530$	−1.23982	+	1.37696i	−0.0538543	+	0.0598113i
$531$	10.9546	−	3.95566i	0.475387	−	0.171661i
$532$	0.0688883	−	0.119318i	0.00298669	−	0.00517309i
$533$	−21.7034	−	37.5913i	−0.940077	−	1.62826i
$534$	−29.1931	−	12.4355i	−1.26331	−	0.538137i
$535$	15.0429	−	10.9293i	0.650361	−	0.472515i
$536$	−5.65908	+	0.594794i	−0.244435	+	0.0256912i
$537$	−2.09484	−	4.50733i	−0.0903990	−	0.194506i
$538$	−5.86945	−	13.1830i	−0.253050	−	0.568360i
$539$	10.7951	−	2.29456i	0.464977	−	0.0988339i
$540$	4.63876	−	2.34135i	0.199620	−	0.100756i
$541$	10.2641	+	4.56986i	0.441287	+	0.196474i	0.615339	−	0.788263i	$-0.289019\pi$
$541$	10.2641	+	4.56986i	0.441287	+	0.196474i	−0.174052	+	0.984737i	$0.555686\pi$
$542$	−1.37860	−	4.24289i	−0.0592159	−	0.182248i
$543$	15.0387	−	0.243403i	0.645371	−	0.0104454i
$544$	1.73934	−	3.90661i	0.0745734	−	0.167495i
$545$	2.43038	−	11.4340i	0.104106	−	0.489780i
$546$	−2.36503	−	0.209940i	−0.101214	−	0.00898458i
$547$	1.09364	−	0.486922i	0.0467608	−	0.0208193i	−0.383223	−	0.923656i	$-0.625186\pi$
$547$	1.09364	−	0.486922i	0.0467608	−	0.0208193i	0.429984	+	0.902837i	$0.358519\pi$
$548$	−6.55129	−	7.27594i	−0.279857	−	0.310813i
$549$	14.6610	+	7.84323i	0.625718	+	0.334741i
$550$	−0.934094	−	1.28567i	−0.0398299	−	0.0548211i
$551$	0.108828	−	1.03543i	0.00463624	−	0.0441109i
$552$	−15.5817	+	3.57648i	−0.663200	+	0.152225i
$553$	2.58573	+	1.49287i	0.109956	+	0.0634833i
$554$	−8.62861	−	6.26905i	−0.366594	−	0.266346i
$555$	1.43100	−	0.857362i	0.0607427	−	0.0363930i
$556$	1.51445	+	0.492075i	0.0642270	+	0.0208686i
$557$	25.7087			1.08931			0.544656	−	0.838659i	$-0.316660\pi$
$557$	25.7087			1.08931			0.544656	+	0.838659i	$0.316660\pi$
$558$	13.8848	−	9.28510i	0.587789	−	0.393070i
$559$	−5.63360			−0.238276
$560$	0.223776	+	0.0727091i	0.00945625	+	0.00307252i
$561$	10.0972	−	6.04955i	0.426302	−	0.255412i
$562$	5.96927	+	4.33693i	0.251798	+	0.182942i
$563$	−5.87739	−	3.39331i	−0.247702	−	0.143011i	0.371009	−	0.928629i	$-0.379012\pi$
$563$	−5.87739	−	3.39331i	−0.247702	−	0.143011i	−0.618712	+	0.785618i	$0.712345\pi$
$564$	13.8739	−	3.18449i	0.584195	−	0.134091i
$565$	1.00274	−	9.54042i	0.0421855	−	0.401369i
$566$	−3.03325	−	4.17492i	−0.127497	−	0.175485i
$567$	−1.87478	+	0.984657i	−0.0787332	+	0.0413517i
$568$	9.36159	+	10.3971i	0.392804	+	0.436253i
$569$	−22.0862	+	9.83340i	−0.925901	+	0.412238i	−0.813592	−	0.581436i	$-0.802491\pi$
$569$	−22.0862	+	9.83340i	−0.925901	+	0.412238i	−0.112309	+	0.993673i	$0.535825\pi$
$570$	−1.01024	−	0.0896772i	−0.0423144	−	0.00375616i
$571$	−7.17071	+	33.7356i	−0.300085	+	1.41179i	0.527073	+	0.849820i	$0.323289\pi$
$571$	−7.17071	+	33.7356i	−0.300085	+	1.41179i	−0.827158	+	0.561969i	$0.810044\pi$
$572$	−3.76582	+	8.45818i	−0.157457	+	0.353654i
$573$	−25.2799	+	0.409159i	−1.05608	+	0.0170929i
$574$	−0.541715	−	1.66723i	−0.0226108	−	0.0695888i
$575$	8.43204	+	3.75419i	0.351641	+	0.156560i
$576$	2.07849	+	2.16330i	0.0866037	+	0.0901377i
$577$	−21.5034	+	4.57069i	−0.895198	+	0.190280i	−0.632466	−	0.774588i	$-0.717957\pi$
$577$	−21.5034	+	4.57069i	−0.895198	+	0.190280i	−0.262733	+	0.964869i	$0.584624\pi$
$578$	−0.523440	−	1.17567i	−0.0217722	−	0.0489012i
$579$	15.0632	+	32.4105i	0.626005	+	1.34693i
$580$	1.76829	−	0.185854i	0.0734241	−	0.00771718i
$581$	−2.91721	+	2.11947i	−0.121026	+	0.0879306i
$582$	−11.1692	−	4.75779i	−0.462978	−	0.197217i
$583$	−1.47228	−	2.55006i	−0.0609755	−	0.105613i
$584$	−8.40083	+	14.5507i	−0.347629	+	0.602111i
$585$	5.93617	+	16.4392i	0.245430	+	0.679679i
$586$	2.98349	−	3.31350i	0.123247	−	0.136880i
$587$	11.4484	−	35.2347i	0.472528	−	1.45429i	−0.376735	−	0.926321i	$-0.622953\pi$
$587$	11.4484	−	35.2347i	0.472528	−	1.45429i	0.849263	−	0.527970i	$-0.177047\pi$
$588$	11.4984	+	3.53138i	0.474186	+	0.145632i
$589$	−3.25842	+	0.109067i	−0.134261	+	0.00449404i
$590$		−	3.88229i		−	0.159831i
$591$	2.33701	−	3.32859i	0.0961317	−	0.136920i
$592$	0.715742	+	0.644457i	0.0294168	+	0.0264870i
$593$	1.72205	−	2.37020i	0.0707161	−	0.0973323i	−0.772194	−	0.635387i	$-0.780841\pi$
$593$	1.72205	−	2.37020i	0.0707161	−	0.0973323i	0.842910	+	0.538055i	$0.180841\pi$
$594$	1.26070	+	8.16079i	0.0517272	+	0.334841i
$595$	0.871380	−	0.503091i	0.0357231	−	0.0206247i
$596$	−16.7018	−	1.75543i	−0.684131	−	0.0719050i
$597$	8.57815	+	25.0159i	0.351080	+	1.02383i
$598$	−5.62098	−	53.4801i	−0.229859	−	2.18696i
$599$	24.6722	−	22.2149i	1.00808	−	0.907677i	0.0123414	−	0.999924i	$-0.496072\pi$
$599$	24.6722	−	22.2149i	1.00808	−	0.907677i	0.995736	+	0.0922467i	$0.0294049\pi$
$600$	−0.208901	−	1.71941i	−0.00852836	−	0.0701945i
$601$	2.06812	+	9.72973i	0.0843603	+	0.396884i	0.999987	−	0.00514613i	$-0.00163807\pi$
$601$	2.06812	+	9.72973i	0.0843603	+	0.396884i	−0.915626	+	0.402030i	$0.868305\pi$
$602$	−0.222547	−	0.0473039i	−0.00907035	−	0.00192796i
$603$	−9.00934	−	14.4997i	−0.366889	−	0.590475i
$604$	−6.96109	+	2.26180i	−0.283243	+	0.0920312i
$605$	−8.05975	+	2.61877i	−0.327675	+	0.106468i
$606$	13.2879	+	11.5806i	0.539784	+	0.470432i
$607$	45.4447	+	9.65957i	1.84454	+	0.392070i	0.991536	−	0.129830i	$-0.0414431\pi$
$607$	45.4447	+	9.65957i	1.84454	+	0.392070i	0.853007	+	0.521900i	$0.174776\pi$
$608$	−0.121744	−	0.572761i	−0.00493737	−	0.0232285i
$609$	−0.719322	+	0.0873948i	−0.0291484	+	0.00354141i
$610$	4.11880	−	3.70858i	0.166765	−	0.150156i
$611$	5.00490	+	47.6185i	0.202477	+	1.92644i
$612$	12.8222	−	0.415169i	0.518309	−	0.0167822i
$613$	−0.770411	−	0.0809734i	−0.0311166	−	0.00327049i	0.0889574	−	0.996035i	$-0.471647\pi$
$613$	−0.770411	−	0.0809734i	−0.0311166	−	0.00327049i	−0.120074	+	0.992765i	$0.538313\pi$
$614$	20.0357	−	11.5676i	0.808573	−	0.466830i
$615$	−9.44896	+	8.78889i	−0.381019	+	0.354402i
$616$	−0.219784	+	0.302507i	−0.00885537	+	0.0121884i
$617$	30.1490	+	27.1463i	1.21375	+	1.09287i	0.993070	+	0.117524i	$0.0374957\pi$
$617$	30.1490	+	27.1463i	1.21375	+	1.09287i	0.220684	+	0.975345i	$0.429171\pi$
$618$	−14.4544	−	10.1485i	−0.581442	−	0.408231i
$619$		−	43.2387i		−	1.73791i	−0.494890	−	0.868956i	$-0.664791\pi$
$619$		−	43.2387i		−	1.73791i	0.494890	−	0.868956i	$-0.335209\pi$
$620$	−1.33915	−	5.40432i	−0.0537815	−	0.217043i
$621$	−30.0404	−	37.3871i	−1.20548	−	1.50029i
$622$	3.33457	−	10.2627i	0.133704	−	0.411498i
$623$	2.88433	−	3.20338i	0.115558	−	0.128341i
$624$	−8.06676	+	6.06270i	−0.322929	+	0.242702i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.81231	+	16.9954i	0.392179	+	0.679273i
$627$	0.631649	−	1.48284i	0.0252256	−	0.0592187i
$628$	−9.58606	+	6.96468i	−0.382526	+	0.277921i
$629$	4.09608	−	0.430515i	0.163321	−	0.0171658i
$630$	0.0964637	+	0.699253i	0.00384320	+	0.0278589i
$631$	−11.4622	−	25.7445i	−0.456302	−	1.02487i	−0.984441	−	0.175713i	$-0.943777\pi$
$631$	−11.4622	−	25.7445i	−0.456302	−	1.02487i	0.528140	−	0.849158i	$-0.322890\pi$
$632$	12.4122	−	2.63830i	0.493732	−	0.104946i
$633$	−25.5937	−	14.2293i	−1.01726	−	0.565566i
$634$	15.6635	+	6.97386i	0.622079	+	0.276967i
$635$	4.21001	+	12.9571i	0.167069	+	0.514186i
$636$	−0.0519360	−	3.20887i	−0.00205940	−	0.127240i
$637$	−16.4565	+	36.9619i	−0.652031	+	1.46448i
$638$	−0.587474	+	2.76385i	−0.0232583	+	0.109422i
$639$	−15.8218	+	38.8758i	−0.625899	+	1.53790i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−27.1348	−	30.1363i	−1.07176	−	1.19031i	−0.980913	−	0.194447i	$-0.937709\pi$
$641$	−27.1348	−	30.1363i	−1.07176	−	1.19031i	−0.0908480	−	0.995865i	$-0.528958\pi$
$642$	−6.18529	+	31.6063i	−0.244114	+	1.24740i
$643$	−4.57473	−	6.29658i	−0.180410	−	0.248313i	0.709228	−	0.704979i	$-0.249044\pi$
$643$	−4.57473	−	6.29658i	−0.180410	−	0.248313i	−0.889638	+	0.456666i	$0.849044\pi$
$644$	0.227009	−	2.15985i	0.00894542	−	0.0851100i
$645$	0.374684	+	1.63239i	0.0147532	+	0.0642752i
$646$	−2.16855	−	1.25201i	−0.0853206	−	0.0492598i
$647$	0.364013	+	0.264471i	0.0143108	+	0.0103974i	0.594918	−	0.803787i	$-0.297185\pi$
$647$	0.364013	+	0.264471i	0.0143108	+	0.0103974i	−0.580607	+	0.814184i	$0.697185\pi$
$648$	−3.12109	+	8.44149i	−0.122608	+	0.331613i
$649$	5.86767	+	1.90652i	0.230326	+	0.0748376i
$650$	5.82606			0.228517
$651$	0.581323	+	2.19334i	0.0227839	+	0.0859638i
$652$	1.68643			0.0660457
$653$	−11.7108	−	3.80507i	−0.458279	−	0.148904i	0.0707745	−	0.997492i	$-0.477453\pi$
$653$	−11.7108	−	3.80507i	−0.458279	−	0.148904i	−0.529054	+	0.848588i	$0.677453\pi$
$654$	10.4058	+	17.3681i	0.406899	+	0.679146i
$655$	2.41478	+	1.75444i	0.0943534	+	0.0685518i
$656$	−6.45227	−	3.72522i	−0.251919	−	0.145446i
$657$	−50.2731	−	3.64373i	−1.96134	−	0.142156i
$658$	−0.202128	+	1.92312i	−0.00787978	+	0.0749711i
$659$	9.03461	+	12.4351i	0.351938	+	0.484402i	0.947881	−	0.318626i	$-0.103221\pi$
$659$	9.03461	+	12.4351i	0.351938	+	0.484402i	−0.595942	+	0.803027i	$0.703221\pi$
$660$	2.70129	+	0.528638i	0.105148	+	0.0205772i
$661$	−29.1471	−	32.3712i	−1.13369	−	1.25909i	−0.961733	−	0.273989i	$-0.911657\pi$
$661$	−29.1471	−	32.3712i	−1.13369	−	1.25909i	−0.171960	−	0.985104i	$-0.555010\pi$
$662$	−12.7003	+	5.65454i	−0.493611	+	0.219770i
$663$	−3.81556	+	42.9835i	−0.148184	+	1.66934i
$664$	−3.18627	+	14.9902i	−0.123651	+	0.581733i
$665$	0.0560388	−	0.125865i	0.00217309	−	0.00488084i
$666$	−0.803470	+	2.77542i	−0.0311338	+	0.107545i
$667$	−5.07134	−	15.6080i	−0.196363	−	0.604344i
$668$	−7.70401	−	3.43004i	−0.298077	−	0.132712i
$669$	−10.8753	+	19.5609i	−0.420463	+	0.756269i
$670$	−5.56591	+	1.18307i	−0.215030	+	0.0457060i
$671$	3.58247	+	8.04635i	0.138300	+	0.310626i
$672$	−0.369572	+	0.171764i	−0.0142566	+	0.00662592i
$673$	8.32249	−	0.874729i	0.320808	−	0.0337183i	0.0572443	−	0.998360i	$-0.481769\pi$
$673$	8.32249	−	0.874729i	0.320808	−	0.0337183i	0.263564	+	0.964642i	$0.415102\pi$
$674$	−4.58194	+	3.32897i	−0.176490	+	0.128227i
$675$	4.36861	−	2.81341i	0.168148	−	0.108288i
$676$	−10.4715	−	18.1371i	−0.402749	−	0.697582i
$677$	6.75184	−	11.6945i	0.259494	−	0.449458i	−0.706612	−	0.707601i	$-0.749777\pi$
$677$	6.75184	−	11.6945i	0.259494	−	0.449458i	0.966107	+	0.258144i	$0.0831108\pi$
$678$	9.98261	+	13.2824i	0.383380	+	0.510108i
$679$	1.10354	−	1.22560i	0.0423499	−	0.0470343i
$680$	1.32146	−	4.06702i	0.0506755	−	0.155963i
$681$	0.967422	−	3.14999i	0.0370717	−	0.120708i
$682$	8.82570	+	0.629984i	0.337953	+	0.0241233i
$683$			4.90180i			0.187562i	0.995593	+	0.0937811i	$0.0298954\pi$
$683$			4.90180i			0.187562i	−0.995593	+	0.0937811i	$0.970105\pi$
$684$	1.38702	−	1.07800i	0.0530339	−	0.0412182i
$685$	−7.27594	−	6.55129i	−0.277999	−	0.250312i
$686$	−1.92856	+	2.65443i	−0.0736326	+	0.101347i
$687$	−24.6658	−	26.5182i	−0.941059	−	1.01173i
$688$	−0.837418	+	0.483483i	−0.0319263	+	0.0184326i
$689$	10.7359	+	1.12838i	0.409004	+	0.0429880i
$690$	−15.1225	+	5.18562i	−0.575703	+	0.197413i
$691$	−1.20449	−	11.4599i	−0.0458208	−	0.435956i	−0.993250	−	0.115991i	$-0.962996\pi$
$691$	−1.20449	−	11.4599i	−0.0458208	−	0.435956i	0.947429	−	0.319965i	$-0.103671\pi$
$692$	−15.7647	+	14.1946i	−0.599285	+	0.539599i
$693$	−1.10422	−	0.197596i	−0.0419458	−	0.00750604i
$694$	−0.832141	−	3.91491i	−0.0315876	−	0.148608i
$695$	1.55759	+	0.331076i	0.0590828	+	0.0125584i
$696$	−2.02337	+	2.32166i	−0.0766956	+	0.0880023i
$697$	−30.3011	+	9.84544i	−1.14774	+	0.372922i
$698$	16.2249	−	5.27180i	0.614123	−	0.199541i
$699$	−11.1302	+	12.7710i	−0.420982	+	0.483045i
$700$	0.230150	+	0.0489199i	0.00869885	+	0.00184900i
$701$	−3.35523	−	15.7851i	−0.126725	−	0.596196i	−0.994980	−	0.100077i	$-0.968091\pi$
$701$	−3.35523	−	15.7851i	−0.126725	−	0.596196i	0.868254	−	0.496119i	$-0.165242\pi$
$702$	−26.9210	−	13.8463i	−1.01607	−	0.522596i
$703$	0.419108	−	0.377366i	0.0158069	−	0.0142326i
$704$	0.166114	+	1.58047i	0.00626066	+	0.0595662i
$705$	13.4650	−	4.61726i	0.507121	−	0.173896i
$706$	−13.0243	−	1.36890i	−0.490174	−	0.0515194i
$707$	−2.07364	+	1.19722i	−0.0779872	+	0.0450259i
$708$	4.57973	+	4.92368i	0.172117	+	0.185043i
$709$	−2.19797	+	3.02524i	−0.0825464	+	0.113615i	−0.848293	−	0.529527i	$-0.822370\pi$
$709$	−2.19797	+	3.02524i	−0.0825464	+	0.113615i	0.765747	+	0.643142i	$0.222370\pi$
$710$	10.3971	+	9.36159i	0.390196	+	0.351334i
$711$	23.3611	+	30.0579i	0.876110	+	1.12726i
$712$		−	18.3201i		−	0.686576i
$713$	−46.2221	+	22.4613i	−1.73103	+	0.841183i
$714$	−0.511649	+	1.66596i	−0.0191480	+	0.0623470i
$715$	−2.86107	+	8.80548i	−0.106998	+	0.329306i
$716$	1.92016	−	2.13255i	0.0717597	−	0.0796973i
$717$	10.9377	+	14.5532i	0.408475	+	0.543498i
$718$	−11.7610	+	20.3706i	−0.438916	+	0.760224i
$719$	−13.0738	−	22.6444i	−0.487570	−	0.844495i	0.512328	−	0.858790i	$-0.328783\pi$
$719$	−13.0738	−	22.6444i	−0.487570	−	0.844495i	−0.999898	+	0.0142945i	$0.995450\pi$
$720$	2.29323	+	1.93419i	0.0854636	+	0.0720831i
$721$	1.94100	−	1.41022i	0.0722867	−	0.0525194i
$722$	18.5549	−	1.95020i	0.690543	−	0.0725789i
$723$	−24.5382	+	11.4045i	−0.912587	+	0.424137i
$724$	3.53198	+	7.93296i	0.131265	+	0.294826i
$725$	1.73917	−	0.369672i	0.0645912	−	0.0137293i
$726$	7.13248	−	12.8289i	0.264711	−	0.476125i
$727$	−25.5520	−	11.3765i	−0.947671	−	0.421931i	−0.126088	−	0.992019i	$-0.540242\pi$
$727$	−25.5520	−	11.3765i	−0.947671	−	0.421931i	−0.821583	+	0.570089i	$0.806909\pi$
$728$	−0.423607	−	1.30373i	−0.0156999	−	0.0483194i
$729$	−26.8728	+	2.61765i	−0.995289	+	0.0969500i
$730$	−6.83385	+	15.3491i	−0.252932	+	0.568095i
$731$	−0.859727	+	4.04470i	−0.0317982	+	0.149599i
$732$	−0.848809	+	9.56210i	−0.0313729	+	0.353425i
$733$	44.4161	−	19.7753i	1.64054	−	0.730418i	0.641227	−	0.767351i	$-0.278426\pi$
$733$	44.4161	−	19.7753i	1.64054	−	0.730418i	0.999318	+	0.0369334i	$0.0117589\pi$
$734$	−12.3948	−	13.7658i	−0.457500	−	0.508106i
$735$	11.8045	+	2.31013i	0.435417	+	0.0852103i
$736$	−5.42527	−	7.46724i	−0.199978	−	0.275246i
$737$	0.945231	−	8.99327i	0.0348180	−	0.331271i
$738$	1.61576	−	22.2929i	0.0594769	−	0.820611i
$739$	15.3823	+	8.88098i	0.565847	+	0.326692i	0.755489	−	0.655161i	$-0.227399\pi$
$739$	15.3823	+	8.88098i	0.565847	+	0.326692i	−0.189642	+	0.981853i	$0.560733\pi$
$740$	0.779186	+	0.566111i	0.0286434	+	0.0208107i
$741$	3.03686	+	5.06875i	0.111562	+	0.186205i
$742$	0.414630	+	0.134721i	0.0152215	+	0.00494578i
$743$	46.6306			1.71071			0.855356	−	0.518040i	$-0.173338\pi$
$743$	46.6306			1.71071			0.855356	+	0.518040i	$0.173338\pi$
$744$	8.07355	+	5.27426i	0.295991	+	0.193364i
$745$	−16.7938			−0.615275
$746$	3.56127	+	1.15713i	0.130387	+	0.0423654i
$747$	−44.6377	+	11.0091i	−1.63321	+	0.402803i
$748$	5.49794	+	3.99449i	0.201024	+	0.146053i
$749$	−3.78888	−	2.18751i	−0.138443	−	0.0799299i
$750$	−0.387484	−	1.68815i	−0.0141489	−	0.0616426i
$751$	−2.34540	+	22.3150i	−0.0855849	+	0.814286i	0.864571	+	0.502511i	$0.167590\pi$
$751$	−2.34540	+	22.3150i	−0.0855849	+	0.814286i	−0.950156	+	0.311775i	$0.899076\pi$
$752$	4.83064	+	6.64881i	0.176155	+	0.242457i
$753$	−4.01332	+	20.5077i	−0.146253	+	0.747342i
$754$	−6.93144	−	7.69815i	−0.252428	−	0.280350i
$755$	−6.68654	+	2.97704i	−0.243348	+	0.108346i
$756$	−0.947210	−	0.773027i	−0.0344497	−	0.0281147i
$757$	−0.327100	+	1.53889i	−0.0118887	+	0.0559318i	−0.983692	−	0.179861i	$-0.942435\pi$
$757$	−0.327100	+	1.53889i	−0.0118887	+	0.0559318i	0.971803	+	0.235793i	$0.0757686\pi$
$758$	1.02260	−	2.29680i	0.0371426	−	0.0834235i
$759$	−0.411145	−	25.4026i	−0.0149236	−	0.922056i
$760$	−0.180947	−	0.556897i	−0.00656364	−	0.0202008i
$761$	−41.7285	−	18.5787i	−1.51266	−	0.673478i	−0.528202	−	0.849119i	$-0.677134\pi$
$761$	−41.7285	−	18.5787i	−1.51266	−	0.673478i	−0.984454	+	0.175641i	$0.943800\pi$
$762$	−20.6241	−	11.4664i	−0.747132	−	0.415383i
$763$	−2.69033	+	0.571848i	−0.0973965	+	0.0207023i
$764$	−5.93724	−	13.3353i	−0.214802	−	0.482453i
$765$	12.7086	−	1.75318i	0.459481	−	0.0633865i
$766$	−5.03836	+	0.529553i	−0.182043	+	0.0191335i
$767$	−18.2987	+	13.2948i	−0.660728	+	0.480047i
$768$	−0.678790	+	1.59350i	−0.0244937	+	0.0575005i
$769$	25.3988	+	43.9920i	0.915905	+	1.58639i	0.805571	+	0.592499i	$0.201859\pi$
$769$	25.3988	+	43.9920i	0.915905	+	1.58639i	0.110333	+	0.993895i	$0.464808\pi$
$770$	−0.186960	+	0.323824i	−0.00673756	+	0.0116698i
$771$	2.66576	−	2.00350i	0.0960052	−	0.0721542i
$772$	−13.8071	+	15.3344i	−0.496929	+	0.551896i
$773$	−2.16622	+	6.66695i	−0.0779137	+	0.239794i	−0.982426	−	0.186655i	$-0.940235\pi$
$773$	−2.16622	+	6.66695i	−0.0779137	+	0.239794i	0.904512	+	0.426448i	$0.140235\pi$
$774$	−2.40083	−	1.62826i	−0.0862960	−	0.0585267i
$775$	−1.89672	−	5.23474i	−0.0681321	−	0.188037i
$776$		−	7.00922i		−	0.251616i
$777$	−0.321239	−	0.225542i	−0.0115244	−	0.00809128i
$778$	25.5377	+	22.9942i	0.915571	+	0.824384i
$779$	−2.56431	+	3.52946i	−0.0918758	+	0.126456i
$780$	−7.38884	+	6.87269i	−0.264563	+	0.246082i
$781$	−19.2549	+	11.1168i	−0.688994	+	0.397791i
$782$	−39.2543	−	4.12580i	−1.40373	−	0.147538i
$783$	−8.91491	−	2.42517i	−0.318593	−	0.0866686i
$784$	0.725912	+	6.90659i	0.0259254	+	0.246664i
$785$	−8.80554	+	7.92855i	−0.314283	+	0.282982i
$786$	−5.13215	+	0.623536i	−0.183058	+	0.0222408i
$787$	−7.05806	−	33.2056i	−0.251593	−	1.18365i	−0.904587	−	0.426288i	$-0.859821\pi$
$787$	−7.05806	−	33.2056i	−0.251593	−	1.18365i	0.652995	−	0.757362i	$-0.273512\pi$
$788$	2.29682	+	0.488204i	0.0818207	+	0.0173915i
$789$	2.30580	+	2.00955i	0.0820886	+	0.0715417i
$790$	12.0685	−	3.92128i	0.429376	−	0.139513i
$791$	−2.14667	+	0.697497i	−0.0763269	+	0.0248001i
$792$	−4.04949	+	2.51613i	−0.143892	+	0.0894068i
$793$	−31.5847	−	6.71353i	−1.12160	−	0.238404i
$794$	5.68841	+	26.7619i	0.201874	+	0.949743i
$795$	−0.387069	−	3.18586i	−0.0137279	−	0.112991i
$796$	−11.3467	+	10.2166i	−0.402173	+	0.362118i
$797$	−0.827795	−	7.87594i	−0.0293220	−	0.278980i	−0.999352	−	0.0359949i	$-0.988540\pi$
$797$	−0.827795	−	7.87594i	−0.0293220	−	0.278980i	0.970030	−	0.242985i	$-0.0781267\pi$
$798$	0.0774058	+	0.225733i	0.00274013	+	0.00799087i
$799$	34.9519	+	3.67359i	1.23651	+	0.129962i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	49.4591	−	23.9675i	1.74755	−	0.846851i
$802$	6.15957	−	8.47792i	0.217502	−	0.299366i
$803$	−19.8425	−	17.8663i	−0.700228	−	0.630488i
$804$	5.66330	−	8.06622i	0.199729	−	0.284474i
$805$		−	2.17175i		−	0.0765440i
$806$	−20.8867	+	24.8189i	−0.735704	+	0.874207i
$807$	23.8931	+	7.33803i	0.841076	+	0.258311i
$808$	−3.14469	+	9.67837i	−0.110630	+	0.340484i
$809$	−17.2533	+	19.1618i	−0.606595	+	0.673692i	−0.965717	−	0.259599i	$-0.916410\pi$
$809$	−17.2533	+	19.1618i	−0.606595	+	0.673692i	0.359121	+	0.933291i	$0.383076\pi$
$810$	−2.22161	+	8.72149i	−0.0780596	+	0.306442i
$811$	10.8354	−	18.7675i	0.380483	−	0.659016i	−0.610648	−	0.791902i	$-0.709091\pi$
$811$	10.8354	−	18.7675i	0.380483	−	0.659016i	0.991131	+	0.132886i	$0.0424245\pi$
$812$	−0.209177	−	0.362306i	−0.00734068	−	0.0127144i
$813$	7.10899	+	3.02825i	0.249323	+	0.106205i
$814$	−1.23826	+	0.899650i	−0.0434011	+	0.0315327i
$815$	1.67719	−	0.176280i	0.0587495	−	0.00617482i
$816$	3.12173	+	6.71681i	0.109282	+	0.235136i
$817$	0.230300	+	0.517262i	0.00805717	+	0.0180967i
$818$	−9.71944	+	2.06593i	−0.339832	+	0.0722336i
$819$	2.96551	−	2.84924i	0.103623	−	0.0995605i
$820$	−6.80632	−	3.03037i	−0.237687	−	0.105825i
$821$	1.39325	+	4.28798i	0.0486247	+	0.149652i	0.972421	−	0.233233i	$-0.0749306\pi$
$821$	1.39325	+	4.28798i	0.0486247	+	0.149652i	−0.923796	+	0.382885i	$0.874931\pi$
$822$	16.9558	−	0.274433i	0.591403	−	0.00957196i
$823$	13.5279	−	30.3842i	0.471554	−	1.05913i	−0.508620	−	0.860991i	$-0.669844\pi$
$823$	13.5279	−	30.3842i	0.471554	−	1.05913i	0.980174	−	0.198137i	$-0.0634891\pi$
$824$	2.12003	−	9.97394i	0.0738546	−	0.347459i
$825$	2.74175	+	0.243380i	0.0954555	+	0.00847340i
$826$	−0.834496	+	0.371542i	−0.0290358	+	0.0129276i
$827$	−18.2763	−	20.2979i	−0.635529	−	0.705826i	0.336236	−	0.941778i	$-0.390846\pi$
$827$	−18.2763	−	20.2979i	−0.635529	−	0.705826i	−0.971765	+	0.235951i	$0.924179\pi$
$828$	13.0617	−	24.4158i	0.453927	−	0.848507i
$829$	20.6267	+	28.3902i	0.716394	+	0.986032i	0.999636	+	0.0269836i	$0.00859020\pi$
$829$	20.6267	+	28.3902i	0.716394	+	0.986032i	−0.283242	+	0.959049i	$0.591410\pi$
$830$	−1.60191	+	15.2411i	−0.0556031	+	0.529028i
$831$	18.0051	−	4.13273i	0.624589	−	0.143363i
$832$	−5.04551	−	2.91303i	−0.174922	−	0.100991i
$833$	24.0258	+	17.4558i	0.832444	+	0.604806i
$834$	−2.36595	+	1.41752i	−0.0819262	+	0.0490848i
$835$	−8.02034	−	2.60597i	−0.277555	−	0.0901832i
$836$	0.930552			0.0321838
$837$	−3.67665	+	28.6964i	−0.127084	+	0.991892i
$838$	−14.9500			−0.516441
$839$	35.2953	+	11.4681i	1.21853	+	0.395924i	0.846546	−	0.532316i	$-0.178678\pi$
$839$	35.2953	+	11.4681i	1.21853	+	0.395924i	0.371983	+	0.928240i	$0.378678\pi$
$840$	−0.349594	+	0.209453i	−0.0120621	+	0.00722683i
$841$	20.9039	+	15.1876i	0.720824	+	0.523709i
$842$	9.33102	+	5.38727i	0.321568	+	0.185657i
$843$	−12.4559	+	2.85902i	−0.429004	+	0.0984698i
$844$	1.76724	−	16.8141i	0.0608308	−	0.578766i
$845$	−12.3100	−	16.9432i	−0.423475	−	0.582864i
$846$	−11.6301	+	21.7397i	−0.399852	+	0.747428i
$847$	1.33424	+	1.48182i	0.0458449	+	0.0509159i
$848$	1.69269	−	0.753635i	0.0581273	−	0.0258799i
$849$	8.90321	+	0.790320i	0.305557	+	0.0271237i
$850$	0.889097	−	4.18287i	0.0304958	−	0.143471i
$851$	3.61576	−	8.12112i	0.123947	−	0.278389i
$852$	−24.2294	+	0.392157i	−0.830085	+	0.0134351i
$853$	−2.27727	−	7.00872i	−0.0779723	−	0.239974i	0.904471	−	0.426535i	$-0.140266\pi$
$853$	−2.27727	−	7.00872i	−0.0779723	−	0.239974i	−0.982443	+	0.186561i	$0.940266\pi$
$854$	−1.19133	−	0.530416i	−0.0407666	−	0.0181505i
$855$	1.26674	−	1.21707i	0.0433215	−	0.0416230i
$856$	−18.1877	+	3.86592i	−0.621643	+	0.132134i
$857$	20.8740	+	46.8837i	0.713041	+	1.60152i	0.796238	+	0.604983i	$0.206820\pi$
$857$	20.8740	+	46.8837i	0.713041	+	1.60152i	−0.0831972	+	0.996533i	$0.526513\pi$
$858$	−6.75882	−	14.5425i	−0.230742	−	0.496473i
$859$	−14.6635	+	1.54120i	−0.500312	+	0.0525849i	−0.351324	−	0.936254i	$-0.614268\pi$
$859$	−14.6635	+	1.54120i	−0.500312	+	0.0525849i	−0.148988	+	0.988839i	$0.547602\pi$
$860$	−0.782292	+	0.568369i	−0.0266760	+	0.0193812i
$861$	2.79345	+	1.18994i	0.0952005	+	0.0405529i
$862$	−19.4419	−	33.6744i	−0.662195	−	1.14696i
$863$	−13.9762	+	24.2074i	−0.475754	+	0.824030i	−0.999614	−	0.0277742i	$-0.991158\pi$
$863$	−13.9762	+	24.2074i	−0.475754	+	0.824030i	0.523860	+	0.851804i	$0.324491\pi$
$864$	−5.19003	+	0.252181i	−0.176568	+	0.00857936i
$865$	−14.1946	+	15.7647i	−0.482632	+	0.536017i
$866$	−4.63875	+	14.2766i	−0.157631	+	0.485139i
$867$	2.13079	+	0.654408i	0.0723656	+	0.0222249i
$868$	−1.03350	+	0.805052i	−0.0350792	+	0.0273252i
$869$			20.1659i			0.684081i
$870$	−1.76960	+	2.52044i	−0.0599952	+	0.0854510i
$871$	24.6366	+	22.1828i	0.834778	+	0.751637i
$872$	−6.87090	+	9.45698i	−0.232678	+	0.320254i
$873$	18.9229	−	9.16990i	0.640442	−	0.310354i
$874$	−4.68061	+	2.70235i	−0.158324	+	0.0914084i
$875$	0.234003	+	0.0245947i	0.00791073	+	0.000831452i
$876$	−9.43952	−	27.5278i	−0.318932	−	0.930080i
$877$	2.23390	+	21.2541i	0.0754333	+	0.717700i	0.965240	+	0.261363i	$0.0841721\pi$
$877$	2.23390	+	21.2541i	0.0754333	+	0.717700i	−0.889807	+	0.456337i	$0.849161\pi$
$878$	3.81944	−	3.43904i	0.128900	−	0.116062i
$879$	0.931440	+	7.66642i	0.0314167	+	0.258582i
$880$	0.330408	+	1.55445i	0.0111381	+	0.0524004i
$881$	−27.9985	−	5.95125i	−0.943292	−	0.200503i	−0.289501	−	0.957178i	$-0.593489\pi$
$881$	−27.9985	−	5.95125i	−0.943292	−	0.200503i	−0.653791	+	0.756675i	$0.726823\pi$
$882$	−17.6961	+	10.9954i	−0.595860	+	0.370234i
$883$	43.9681	−	14.2861i	1.47965	−	0.480766i	0.545638	−	0.838021i	$-0.316287\pi$
$883$	43.9681	−	14.2861i	1.47965	−	0.480766i	0.934007	+	0.357255i	$0.116287\pi$
$884$	−23.6947	+	7.69888i	−0.796939	+	0.258941i
$885$	5.06930	+	4.41799i	0.170403	+	0.148509i
$886$	27.1481	+	5.77051i	0.912058	+	0.193864i
$887$	−9.30543	−	43.7786i	−0.312446	−	1.46994i	−0.801661	−	0.597779i	$-0.796050\pi$
$887$	−9.30543	−	43.7786i	−0.312446	−	1.46994i	0.489215	−	0.872163i	$-0.337283\pi$
$888$	−1.65601	+	0.201198i	−0.0555719	+	0.00675177i
$889$	2.38222	−	2.14496i	0.0798969	−	0.0719395i
$890$	−1.91497	−	18.2198i	−0.0641901	−	0.610728i
$891$	−12.0906	−	7.64071i	−0.405051	−	0.255973i
$892$	−12.8508	−	1.35067i	−0.430277	−	0.0452239i
$893$	4.16760	−	2.40616i	0.139463	−	0.0805192i
$894$	21.2985	−	19.8107i	0.712329	−	0.662569i
$895$	1.68673	−	2.32158i	0.0563811	−	0.0776019i
$896$	−0.174856	−	0.157441i	−0.00584152	−	0.00525973i
$897$	76.2283	+	53.5200i	2.54519	+	1.78698i
$898$			16.7853i			0.560132i
$899$	−4.66023	+	8.73412i	−0.155427	+	0.291299i
$900$	2.48285	+	1.68389i	0.0827615	+	0.0561296i
$901$	2.44850	−	7.53572i	0.0815714	−	0.251051i
$902$	7.92255	−	8.79888i	0.263792	−	0.292971i
$903$	0.315023	−	0.236760i	0.0104833	−	0.00787889i
$904$	−4.79649	+	8.30776i	−0.159529	+	0.276312i
$905$	4.34186	+	7.52031i	0.144328	+	0.249984i
$906$	4.96828	−	11.6634i	0.165060	−	0.387489i
$907$	23.8416	−	17.3220i	0.791649	−	0.575166i	−0.116804	−	0.993155i	$-0.537265\pi$
$907$	23.8416	−	17.3220i	0.791649	−	0.575166i	0.908452	+	0.417989i	$0.137265\pi$
$908$	1.89206	−	0.198864i	0.0627902	−	0.00659952i
$909$	−30.2429	+	4.17208i	−1.00309	+	0.138379i
$910$	−0.557564	−	1.25231i	−0.0184831	−	0.0415136i
$911$	−25.1099	+	5.33727i	−0.831928	+	0.176832i	−0.604139	−	0.796879i	$-0.706483\pi$
$911$	−25.1099	+	5.33727i	−0.831928	+	0.176832i	−0.227789	+	0.973711i	$0.573150\pi$
$912$	0.886427	+	0.492826i	0.0293525	+	0.0163191i
$913$	−22.2487	−	9.90577i	−0.736325	−	0.327833i
$914$	5.36673	+	16.5171i	0.177516	+	0.546337i
$915$	0.155352	+	9.59844i	0.00513579	+	0.317315i
$916$	8.50465	−	19.1018i	0.281002	−	0.631140i
$917$	0.146018	−	0.686960i	0.00482194	−	0.0226854i
$918$	−14.0494	+	17.2151i	−0.463700	+	0.568184i
$919$	38.1654	−	16.9923i	1.25896	−	0.560526i	0.334714	−	0.942320i	$-0.391360\pi$
$919$	38.1654	−	16.9923i	1.25896	−	0.560526i	0.924247	+	0.381794i	$0.124694\pi$
$920$	−6.17609	−	6.85924i	−0.203620	−	0.226143i
$921$	−7.69590	+	39.3254i	−0.253588	+	1.29581i
$922$	5.25242	+	7.22933i	0.172979	+	0.238085i
$923$	8.52017	−	81.0640i	0.280445	−	2.66825i
$924$	−0.144888	−	0.631233i	−0.00476646	−	0.0207660i
$925$	0.834092	+	0.481563i	0.0274248	+	0.0158337i
$926$	−27.2444	−	19.7942i	−0.895306	−	0.650478i
$927$	29.7003	−	7.32507i	0.975486	−	0.240587i
$928$	−1.69100	−	0.549440i	−0.0555099	−	0.0180363i
$929$	36.4849			1.19703			0.598516	−	0.801111i	$-0.295757\pi$
$929$	36.4849			1.19703			0.598516	+	0.801111i	$0.295757\pi$
$930$	8.58063	+	4.40145i	0.281370	+	0.144329i
$931$	4.06648			0.133273
$932$	−9.30190	−	3.02237i	−0.304694	−	0.0990010i
$933$	9.60590	+	16.0330i	0.314483	+	0.524896i
$934$	−17.2356	−	12.5224i	−0.563967	−	0.409746i
$935$	5.88536	+	3.39791i	0.192472	+	0.111124i
$936$	1.26348	−	17.4324i	0.0412982	−	0.569797i
$937$	−0.854868	+	8.13353i	−0.0279273	+	0.265711i	0.971644	+	0.236447i	$0.0759830\pi$
$937$	−0.854868	+	8.13353i	−0.0279273	+	0.265711i	−0.999572	+	0.0292638i	$0.990684\pi$
$938$	0.786968	+	1.08317i	0.0256954	+	0.0353667i
$939$	−33.3581	−	6.52811i	−1.08860	−	0.213037i
$940$	5.49917	+	6.10745i	0.179363	+	0.199203i
$941$	−4.82534	+	2.14838i	−0.157302	+	0.0700352i	−0.483877	−	0.875136i	$-0.660772\pi$
$941$	−4.82534	+	2.14838i	−0.157302	+	0.0700352i	0.326576	+	0.945171i	$0.394105\pi$
$942$	1.81466	−	20.4427i	0.0591249	−	0.666060i
$943$	−14.2976	+	67.2650i	−0.465595	+	2.19045i
$944$	−1.57907	+	3.54665i	−0.0513943	+	0.115434i
$945$	−1.02282	−	0.669782i	−0.0332725	−	0.0217880i
$946$	−0.474860	−	1.46147i	−0.0154390	−	0.0475165i
$947$	−43.3109	−	19.2832i	−1.40741	−	0.626621i	−0.444340	−	0.895858i	$-0.646562\pi$
$947$	−43.3109	−	19.2832i	−1.40741	−	0.626621i	−0.963074	+	0.269237i	$0.913228\pi$
$948$	−10.6800	+	19.2096i	−0.346870	+	0.623900i
$949$	95.7483	−	20.3519i	3.10812	−	0.660652i
$950$	−0.238167	−	0.534933i	−0.00772717	−	0.0173555i
$951$	−26.9310	+	12.5165i	−0.873299	+	0.405877i
$952$	−1.00067	+	0.105175i	−0.0324319	+	0.00340873i
$953$	6.88120	−	4.99948i	0.222904	−	0.161949i	−0.470729	−	0.882278i	$-0.656009\pi$
$953$	6.88120	−	4.99948i	0.222904	−	0.161949i	0.693633	+	0.720329i	$0.256009\pi$
$954$	4.24908	+	3.58383i	0.137569	+	0.116031i
$955$	−7.29863	−	12.6416i	−0.236178	−	0.409072i
$956$	−5.25537	+	9.10258i	−0.169971	+	0.294398i
$957$	−2.94036	−	3.91232i	−0.0950484	−	0.126467i
$958$	−16.7423	+	18.5942i	−0.540919	+	0.600752i
$959$	−0.711876	+	2.19093i	−0.0229877	+	0.0707488i
$960$	−0.508505	+	1.65572i	−0.0164119	+	0.0534383i
$961$	29.0997	+	10.6869i	0.938699	+	0.344737i
$962$		−	5.61123i		−	0.180913i
$963$	−34.2312	−	44.0440i	−1.10308	−	1.41930i
$964$	−11.6098	−	10.4535i	−0.373926	−	0.336684i
$965$	−12.1286	+	16.6936i	−0.390434	+	0.537386i
$966$	2.56189	+	2.75430i	0.0824276	+	0.0886181i
$967$	−34.8024	+	20.0932i	−1.11917	+	0.646153i	−0.941189	−	0.337881i	$-0.890290\pi$
$967$	−34.8024	+	20.0932i	−1.11917	+	0.646153i	−0.177981	+	0.984034i	$0.556957\pi$
$968$	8.42810	+	0.885829i	0.270889	+	0.0284716i
$969$	4.10260	−	1.40682i	0.131795	−	0.0451934i
$970$	−0.732663	−	6.97082i	−0.0235244	−	0.223820i
$971$	3.05008	−	2.74631i	0.0978819	−	0.0881332i	−0.618737	−	0.785598i	$-0.712355\pi$
$971$	3.05008	−	2.74631i	0.0978819	−	0.0881332i	0.716619	+	0.697465i	$0.245689\pi$
$972$	−7.47074	−	13.6817i	−0.239624	−	0.438840i
$973$	−0.0778994	−	0.366488i	−0.00249734	−	0.0117491i
$974$	39.3829	+	8.37110i	1.26191	+	0.268227i
$975$	−6.62997	+	7.60738i	−0.212329	+	0.243631i
$976$	−5.27112	+	1.71269i	−0.168725	+	0.0548219i
$977$	57.2743	−	18.6095i	1.83237	−	0.595372i	0.833271	−	0.552865i	$-0.186465\pi$
$977$	57.2743	−	18.6095i	1.83237	−	0.595372i	0.999096	−	0.0425075i	$-0.0135346\pi$
$978$	−1.91913	+	2.20206i	−0.0613672	+	0.0704141i
$979$	28.4777	+	6.05312i	0.910150	+	0.193458i
$980$	1.44387	+	6.79288i	0.0461228	+	0.216991i
$981$	−34.5201	−	6.17724i	−1.10214	−	0.197224i
$982$	−14.7565	+	13.2868i	−0.470899	+	0.423999i
$983$	1.38652	+	13.1919i	0.0442233	+	0.420756i	0.994128	+	0.108215i	$0.0345135\pi$
$983$	1.38652	+	13.1919i	0.0442233	+	0.420756i	−0.949904	+	0.312541i	$0.898820\pi$
$984$	12.2068	−	4.18582i	0.389139	−	0.133439i
$985$	2.33527	+	0.245446i	0.0744078	+	0.00782057i
$986$	−6.58475	+	3.80170i	−0.209701	+	0.121071i
$987$	−2.28110	−	2.45242i	−0.0726083	−	0.0780613i
$988$	−2.00522	+	2.75995i	−0.0637946	+	0.0878057i
$989$	6.63266	+	5.97207i	0.210906	+	0.189901i
$990$	−3.76430	+	2.92563i	−0.119637	+	0.0929827i
$991$		−	1.71913i		−	0.0546099i	−0.999627	−	0.0273049i	$-0.991307\pi$
$991$		−	1.71913i		−	0.0546099i	0.999627	−	0.0273049i	$-0.00869251\pi$
$992$	−0.974763	+	5.48177i	−0.0309488	+	0.174046i
$993$	7.06935	−	23.0182i	0.224339	−	0.730462i
$994$	1.01725	−	3.13077i	0.0322652	−	0.0993021i
$995$	−10.2166	+	11.3467i	−0.323888	+	0.359714i
$996$	−15.9476	−	21.2191i	−0.505318	−	0.672353i
$997$	3.86651	−	6.69699i	0.122454	−	0.212096i	−0.798281	−	0.602285i	$-0.794257\pi$
$997$	3.86651	−	6.69699i	0.122454	−	0.212096i	0.920735	+	0.390189i	$0.127590\pi$
$998$	−5.47020	−	9.47466i	−0.173156	−	0.299915i
$999$	−2.70967	−	4.20752i	−0.0857301	−	0.133120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.761.10	yes	176
3.2	odd	2	inner	930.2.br.a.761.15	yes	176
31.11	odd	30	inner	930.2.br.a.11.15	yes	176
93.11	even	30	inner	930.2.br.a.11.10	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.10	✓	176	93.11	even	30	inner
930.2.br.a.11.15	yes	176	31.11	odd	30	inner
930.2.br.a.761.10	yes	176	1.1	even	1	trivial
930.2.br.a.761.15	yes	176	3.2	odd	2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.48579 - 0.890187i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.68815 + 0.387484i) q^{6} +(0.0245947 - 0.234003i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.41514 - 2.64526i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.48579 - 0.890187i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.68815 + 0.387484i) q^{6} +(0.0245947 - 0.234003i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.41514 - 2.64526i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(1.45178 - 0.646376i) q^{11} +(1.72527 + 0.153149i) q^{12} +(-1.21131 + 5.69874i) q^{13} +(-0.0957017 + 0.214950i) q^{14} +(1.73182 - 0.0280299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.90661 + 1.73934i) q^{17} +(-2.16330 + 2.07849i) q^{18} +(0.572761 - 0.121744i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-0.171764 - 0.369572i) q^{21} +(-1.58047 + 0.166114i) q^{22} +(7.46724 - 5.42527i) q^{23} +(-1.59350 - 0.678790i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.91303 - 5.04551i) q^{26} +(-0.252181 - 5.19003i) q^{27} +(0.157441 - 0.174856i) q^{28} +(0.549440 - 1.69100i) q^{29} +(-1.65572 - 0.508505i) q^{30} +(-5.48177 - 0.974763i) q^{31} -1.00000i q^{32} +(1.58165 - 2.25274i) q^{33} +(-3.17793 - 2.86142i) q^{34} +(0.138301 - 0.190355i) q^{35} +(2.69971 - 1.30826i) q^{36} +(0.834092 - 0.481563i) q^{37} +(-0.582349 - 0.0612073i) q^{38} +(3.27320 + 9.54542i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-5.53676 + 4.98532i) q^{41} +(0.0491527 + 0.404562i) q^{42} +(0.201044 + 0.945836i) q^{43} +(1.55445 + 0.330408i) q^{44} +(2.54817 - 1.58329i) q^{45} +(-8.77827 + 2.85223i) q^{46} +(7.81614 - 2.53962i) q^{47} +(1.30575 + 1.13799i) q^{48} +(6.79288 + 1.44387i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(7.35274 - 0.893329i) q^{51} +(-4.32960 + 3.89839i) q^{52} +(-0.193679 - 1.84273i) q^{53} +(-1.36397 + 5.01394i) q^{54} +(1.58047 + 0.166114i) q^{55} +(-0.203769 + 0.117646i) q^{56} +(0.742627 - 0.690750i) q^{57} +(-1.04510 + 1.43845i) q^{58} +(2.88510 + 2.59776i) q^{59} +(1.41755 + 0.995264i) q^{60} +5.54239i q^{61} +(4.91226 + 2.62102i) q^{62} +(-0.584193 - 0.396205i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.89839 + 4.32960i) q^{65} +(-2.20037 + 1.65372i) q^{66} +(2.84513 - 4.92790i) q^{67} +(2.13816 + 3.70340i) q^{68} +(6.26524 - 14.7080i) q^{69} +(-0.190355 + 0.138301i) q^{70} +(-13.9140 + 1.46242i) q^{71} +(-2.97185 + 0.409975i) q^{72} +(-6.83385 - 15.3491i) q^{73} +(-0.942080 + 0.200245i) q^{74} +(1.51382 + 0.841637i) q^{75} +(0.534933 + 0.238167i) q^{76} +(-0.115548 - 0.355619i) q^{77} +(-0.163304 - 10.0897i) q^{78} +(-5.16130 + 11.5925i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-4.99478 - 7.48680i) q^{81} +(6.80632 - 3.03037i) q^{82} +(-10.2545 - 11.3888i) q^{83} +(0.0782695 - 0.399950i) q^{84} +(2.51356 + 3.45962i) q^{85} +(0.101076 - 0.961670i) q^{86} +(-0.688956 - 3.00158i) q^{87} +(-1.37627 - 0.794588i) q^{88} +(14.8213 + 10.7683i) q^{89} +(-2.91272 + 0.718372i) q^{90} +(1.30373 + 0.423607i) q^{91} +9.23002 q^{92} +(-9.01248 + 3.43151i) q^{93} -8.21838 q^{94} +(0.556897 + 0.180947i) q^{95} +(-0.890187 - 1.48579i) q^{96} +(5.67058 + 4.11992i) q^{97} +(-6.01423 - 3.47232i) q^{98} +(0.344640 - 4.75505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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