LMFDB - Embedded newform 930.2.br.a.11.15

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			11.15
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-0.730003 - 1.57070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.17965 - 1.26824i) q^{6} +(0.0245947 + 0.234003i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.93419 + 2.29323i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-0.730003 - 1.57070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.17965 - 1.26824i) q^{6} +(0.0245947 + 0.234003i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.93419 + 2.29323i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-1.45178 - 0.646376i) q^{11} +(-1.51382 - 0.841637i) q^{12} +(-1.21131 - 5.69874i) q^{13} +(0.0957017 + 0.214950i) q^{14} +(1.41755 + 0.995264i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.90661 + 1.73934i) q^{17} +(-1.13088 + 2.77869i) q^{18} +(0.572761 + 0.121744i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.349594 - 0.209453i) q^{21} +(-1.58047 - 0.166114i) q^{22} +(-7.46724 - 5.42527i) q^{23} +(-1.69981 - 0.332649i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.91303 - 5.04551i) q^{26} +(5.01394 + 1.36397i) 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} +(0.0445444 + 2.75217i) q^{33} +(-3.17793 + 2.86142i) q^{34} +(-0.138301 - 0.190355i) q^{35} +(-0.216867 + 2.99215i) q^{36} +(0.834092 + 0.481563i) q^{37} +(0.582349 - 0.0612073i) q^{38} +(-8.06676 + 6.06270i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(5.53676 + 4.98532i) q^{41} +(0.267759 - 0.307232i) q^{42} +(0.201044 - 0.945836i) q^{43} +(-1.55445 + 0.330408i) q^{44} +(0.528444 - 2.95309i) q^{45} +(-8.77827 - 2.85223i) q^{46} +(-7.81614 - 2.53962i) q^{47} +(-1.71941 + 0.208901i) q^{48} +(6.79288 - 1.44387i) q^{49} +(0.207912 - 0.978148i) q^{50} +(5.58381 + 4.86639i) q^{51} +(-4.32960 - 3.89839i) q^{52} +(0.193679 - 1.84273i) q^{53} +(5.19003 - 0.252181i) q^{54} +(1.58047 - 0.166114i) q^{55} +(0.203769 + 0.117646i) q^{56} +(-0.226894 - 0.988508i) q^{57} +(-1.04510 - 1.43845i) q^{58} +(-2.88510 + 2.59776i) q^{59} +(1.73182 - 0.0280299i) 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} +(0.892832 + 2.60371i) q^{66} +(2.84513 + 4.92790i) q^{67} +(-2.13816 + 3.70340i) q^{68} +(-3.07036 + 15.6893i) q^{69} +(-0.190355 - 0.138301i) q^{70} +(13.9140 + 1.46242i) q^{71} +(0.718372 + 2.91272i) q^{72} +(-6.83385 + 15.3491i) q^{73} +(0.942080 + 0.200245i) q^{74} +(-1.72527 - 0.153149i) q^{75} +(0.534933 - 0.238167i) q^{76} +(0.115548 - 0.355619i) q^{77} +(-5.79847 + 8.25873i) q^{78} +(-5.16130 - 11.5925i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-1.51780 - 8.87109i) q^{81} +(6.80632 + 3.03037i) q^{82} +(10.2545 - 11.3888i) q^{83} +(0.159714 - 0.374937i) q^{84} +(2.51356 - 3.45962i) q^{85} +(-0.101076 - 0.961670i) q^{86} +(-2.25496 + 2.09744i) q^{87} +(-1.37627 + 0.794588i) q^{88} +(-14.8213 + 10.7683i) q^{89} +(-0.409975 - 2.97185i) q^{90} +(1.30373 - 0.423607i) q^{91} -9.23002 q^{92} +(5.53277 + 7.89864i) q^{93} -8.21838 q^{94} +(-0.556897 + 0.180947i) q^{95} +(-1.57070 + 0.730003i) q^{96} +(5.67058 - 4.11992i) q^{97} +(6.01423 - 3.47232i) q^{98} +(4.29032 - 2.07906i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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
$3$	−0.730003	−	1.57070i	−0.421467	−	0.906844i
$3$	−0.730003	−	1.57070i	−0.421467	−	0.906844i
$4$	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
$6$	−1.17965	−	1.26824i	−0.481589	−	0.517757i
$7$	0.0245947	+	0.234003i	0.00929591	+	0.0884447i	0.998186	−	0.0602027i	$-0.0191747\pi$
$7$	0.0245947	+	0.234003i	0.00929591	+	0.0884447i	−0.988890	+	0.148647i	$0.952508\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.93419	+	2.29323i	−0.644731	+	0.764410i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−1.45178	−	0.646376i	−0.437729	−	0.194890i	0.176027	−	0.984385i	$-0.443675\pi$
$11$	−1.45178	−	0.646376i	−0.437729	−	0.194890i	−0.613756	+	0.789496i	$0.710342\pi$
$12$	−1.51382	−	0.841637i	−0.437002	−	0.242960i
$13$	−1.21131	−	5.69874i	−0.335956	−	1.58055i	−0.744381	−	0.667755i	$-0.767255\pi$
$13$	−1.21131	−	5.69874i	−0.335956	−	1.58055i	0.408425	−	0.912792i	$-0.366078\pi$
$14$	0.0957017	+	0.214950i	0.0255774	+	0.0574477i
$15$	1.41755	+	0.995264i	0.366010	+	0.256976i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.90661	+	1.73934i	−0.947493	+	0.421851i	−0.821518	−	0.570182i	$-0.806873\pi$
$17$	−3.90661	+	1.73934i	−0.947493	+	0.421851i	−0.125975	+	0.992033i	$0.540206\pi$
$18$	−1.13088	+	2.77869i	−0.266551	+	0.654943i
$19$	0.572761	+	0.121744i	0.131400	+	0.0279300i	0.273142	−	0.961974i	$-0.411937\pi$
$19$	0.572761	+	0.121744i	0.131400	+	0.0279300i	−0.141742	+	0.989904i	$0.545270\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	0.349594	−	0.209453i	0.0762876	−	0.0457065i
$22$	−1.58047	−	0.166114i	−0.336957	−	0.0354156i
$23$	−7.46724	−	5.42527i	−1.55703	−	1.13125i	−0.938394	−	0.345568i	$-0.887686\pi$
$23$	−7.46724	−	5.42527i	−1.55703	−	1.13125i	−0.618635	−	0.785679i	$-0.712314\pi$
$24$	−1.69981	−	0.332649i	−0.346972	−	0.0679017i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.91303	−	5.04551i	−0.571292	−	0.989507i
$27$	5.01394	+	1.36397i	0.964933	+	0.262496i
$28$	0.157441	+	0.174856i	0.0297535	+	0.0330446i
$29$	−0.549440	−	1.69100i	−0.102028	−	0.314011i	0.886993	−	0.461783i	$-0.152790\pi$
$29$	−0.549440	−	1.69100i	−0.102028	−	0.314011i	−0.989022	+	0.147771i	$0.952790\pi$
$30$	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
$33$	0.0445444	+	2.75217i	0.00775418	+	0.479092i
$34$	−3.17793	+	2.86142i	−0.545010	+	0.490729i
$35$	−0.138301	−	0.190355i	−0.0233771	−	0.0321759i
$36$	−0.216867	+	2.99215i	−0.0361446	+	0.498692i
$37$	0.834092	+	0.481563i	0.137124	+	0.0791685i	0.566993	−	0.823723i	$-0.308107\pi$
$37$	0.834092	+	0.481563i	0.137124	+	0.0791685i	−0.429869	+	0.902891i	$0.641440\pi$
$38$	0.582349	−	0.0612073i	0.0944695	−	0.00992914i
$39$	−8.06676	+	6.06270i	−1.29171	+	0.970808i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	5.53676	+	4.98532i	0.864697	+	0.778576i	0.976582	−	0.215145i	$-0.0690223\pi$
$41$	5.53676	+	4.98532i	0.864697	+	0.778576i	−0.111886	+	0.993721i	$0.535689\pi$
$42$	0.267759	−	0.307232i	0.0413161	−	0.0474070i
$43$	0.201044	−	0.945836i	0.0306589	−	0.144239i	−0.960156	−	0.279465i	$-0.909843\pi$
$43$	0.201044	−	0.945836i	0.0306589	−	0.144239i	0.990815	+	0.135226i	$0.0431762\pi$
$44$	−1.55445	+	0.330408i	−0.234342	+	0.0498109i
$45$	0.528444	−	2.95309i	0.0787758	−	0.440221i
$46$	−8.77827	−	2.85223i	−1.29429	−	0.420539i
$47$	−7.81614	−	2.53962i	−1.14010	−	0.370442i	−0.322695	−	0.946503i	$-0.604589\pi$
$47$	−7.81614	−	2.53962i	−1.14010	−	0.370442i	−0.817406	+	0.576061i	$0.804589\pi$
$48$	−1.71941	+	0.208901i	−0.248175	+	0.0301523i
$49$	6.79288	−	1.44387i	0.970412	−	0.206267i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	5.58381	+	4.86639i	0.781890	+	0.681432i
$52$	−4.32960	−	3.89839i	−0.600408	−	0.540610i
$53$	0.193679	−	1.84273i	0.0266038	−	0.253119i	−0.973134	−	0.230238i	$-0.926050\pi$
$53$	0.193679	−	1.84273i	0.0266038	−	0.253119i	0.999738	−	0.0228807i	$-0.00728379\pi$
$54$	5.19003	−	0.252181i	0.706274	−	0.0343174i
$55$	1.58047	−	0.166114i	0.213110	−	0.0223988i
$56$	0.203769	+	0.117646i	0.0272297	+	0.0157211i
$57$	−0.226894	−	0.988508i	−0.0300528	−	0.130931i
$58$	−1.04510	−	1.43845i	−0.137228	−	0.188878i
$59$	−2.88510	+	2.59776i	−0.375608	+	0.338199i	−0.835215	−	0.549923i	$-0.814657\pi$
$59$	−2.88510	+	2.59776i	−0.375608	+	0.338199i	0.459607	+	0.888122i	$0.347990\pi$
$60$	1.73182	−	0.0280299i	0.223578	−	0.00361864i
$61$		−	5.54239i		−	0.709630i	−0.934937	−	0.354815i	$-0.884544\pi$
$61$		−	5.54239i		−	0.709630i	0.934937	−	0.354815i	$-0.115456\pi$
$62$	−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
$66$	0.892832	+	2.60371i	0.109900	+	0.320494i
$67$	2.84513	+	4.92790i	0.347588	+	0.602039i	0.985820	−	0.167804i	$-0.0536676\pi$
$67$	2.84513	+	4.92790i	0.347588	+	0.602039i	−0.638233	+	0.769843i	$0.720334\pi$
$68$	−2.13816	+	3.70340i	−0.259290	+	0.449104i
$69$	−3.07036	+	15.6893i	−0.369628	+	1.88876i
$70$	−0.190355	−	0.138301i	−0.0227518	−	0.0165301i
$71$	13.9140	+	1.46242i	1.65129	+	0.173558i	0.883918	−	0.467642i	$-0.154896\pi$
$71$	13.9140	+	1.46242i	1.65129	+	0.173558i	0.767374	+	0.641199i	$0.221563\pi$
$72$	0.718372	+	2.91272i	0.0846610	+	0.343267i
$73$	−6.83385	+	15.3491i	−0.799842	+	1.79647i	−0.233380	+	0.972386i	$0.574978\pi$
$73$	−6.83385	+	15.3491i	−0.799842	+	1.79647i	−0.566462	+	0.824088i	$0.691688\pi$
$74$	0.942080	+	0.200245i	0.109515	+	0.0232780i
$75$	−1.72527	−	0.153149i	−0.199217	−	0.0176841i
$76$	0.534933	−	0.238167i	0.0613610	−	0.0273197i
$77$	0.115548	−	0.355619i	0.0131679	−	0.0405265i
$78$	−5.79847	+	8.25873i	−0.656547	+	0.935117i
$79$	−5.16130	−	11.5925i	−0.580691	−	1.30425i	−0.930108	−	0.367286i	$-0.880287\pi$
$79$	−5.16130	−	11.5925i	−0.580691	−	1.30425i	0.349417	−	0.936967i	$-0.386380\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−1.51780	−	8.87109i	−0.168645	−	0.985677i
$82$	6.80632	+	3.03037i	0.751632	+	0.334648i
$83$	10.2545	−	11.3888i	1.12558	−	1.25008i	0.160806	−	0.986986i	$-0.448591\pi$
$83$	10.2545	−	11.3888i	1.12558	−	1.25008i	0.964770	−	0.263093i	$-0.0847426\pi$
$84$	0.159714	−	0.374937i	0.0174262	−	0.0409090i
$85$	2.51356	−	3.45962i	0.272634	−	0.375248i
$86$	−0.101076	−	0.961670i	−0.0108993	−	0.103699i
$87$	−2.25496	+	2.09744i	−0.241757	+	0.224869i
$88$	−1.37627	+	0.794588i	−0.146710	+	0.0847033i
$89$	−14.8213	+	10.7683i	−1.57105	+	1.14144i	−0.644915	+	0.764255i	$0.723107\pi$
$89$	−14.8213	+	10.7683i	−1.57105	+	1.14144i	−0.926139	+	0.377182i	$0.876893\pi$
$90$	−0.409975	−	2.97185i	−0.0432151	−	0.313261i
$91$	1.30373	−	0.423607i	0.136668	−	0.0444061i
$92$	−9.23002			−0.962296
$93$	5.53277	+	7.89864i	0.573721	+	0.819050i
$94$	−8.21838			−0.847661
$95$	−0.556897	+	0.180947i	−0.0571365	+	0.0185648i
$96$	−1.57070	+	0.730003i	−0.160309	+	0.0745056i
$97$	5.67058	−	4.11992i	0.575760	−	0.418314i	−0.261433	−	0.965222i	$-0.584195\pi$
$97$	5.67058	−	4.11992i	0.575760	−	0.418314i	0.837193	+	0.546907i	$0.184195\pi$
$98$	6.01423	−	3.47232i	0.607529	−	0.350757i
$99$	4.29032	−	2.07906i	0.431193	−	0.208953i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	5.98156	−	8.23291i	0.595187	−	0.819205i	−0.400070	−	0.916485i	$-0.631014\pi$
$101$	5.98156	−	8.23291i	0.595187	−	0.819205i	0.995257	+	0.0972795i	$0.0310141\pi$
$102$	6.81432	+	2.90272i	0.674718	+	0.287412i
$103$	6.82296	−	7.57767i	0.672287	−	0.746650i	−0.306424	−	0.951895i	$-0.599133\pi$
$103$	6.82296	−	7.57767i	0.672287	−	0.746650i	0.978711	+	0.205245i	$0.0657992\pi$
$104$	−5.32237	−	2.36967i	−0.521901	−	0.232365i
$105$	−0.198030	+	0.356189i	−0.0193258	+	0.0347605i
$106$	−0.385236	−	1.81239i	−0.0374174	−	0.176035i
$107$	−7.56288	−	16.9865i	−0.731131	−	1.64215i	−0.766070	−	0.642757i	$-0.777790\pi$
$107$	−7.56288	−	16.9865i	−0.731131	−	1.64215i	0.0349393	−	0.999389i	$-0.488876\pi$
$108$	4.85808	−	1.84365i	0.467469	−	0.177405i
$109$	−3.61225	+	11.1174i	−0.345990	+	1.06485i	0.615061	+	0.788480i	$0.289131\pi$
$109$	−3.61225	+	11.1174i	−0.345990	+	1.06485i	−0.961051	+	0.276370i	$0.910869\pi$
$110$	1.45178	−	0.646376i	0.138422	−	0.0616295i
$111$	0.147501	−	1.66165i	0.0140002	−	0.157717i
$112$	0.230150	+	0.0489199i	0.0217471	+	0.00462249i
$113$	3.90181	−	8.76362i	0.367052	−	0.824412i	−0.631736	−	0.775184i	$-0.717657\pi$
$113$	3.90181	−	8.76362i	0.367052	−	0.824412i	0.998788	−	0.0492280i	$-0.0156761\pi$
$114$	−0.521255	−	0.870013i	−0.0488200	−	0.0814842i
$115$	9.17946	+	0.964800i	0.855989	+	0.0899681i
$116$	−1.43845	−	1.04510i	−0.133557	−	0.0970348i
$117$	15.4114	+	8.24466i	1.42479	+	0.762219i
$118$	−1.94114	+	3.36216i	−0.178697	+	0.309512i
$119$	−0.503091	−	0.871380i	−0.0461183	−	0.0798792i
$120$	1.63840	−	0.561821i	0.149565	−	0.0512870i
$121$	−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
$126$	−0.678034	−	0.196288i	−0.0604041	−	0.0174867i
$127$	10.1245	−	9.11616i	0.898406	−	0.808928i	−0.0838490	−	0.996478i	$-0.526721\pi$
$127$	10.1245	−	9.11616i	0.898406	−	0.808928i	0.982255	+	0.187550i	$0.0600547\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−1.63239	+	0.374684i	−0.143724	+	0.0329891i
$130$	5.04551	+	2.91303i	0.442521	+	0.255490i
$131$	−2.96849	+	0.312000i	−0.259358	+	0.0272596i	−0.233315	−	0.972401i	$-0.574957\pi$
$131$	−2.96849	+	0.312000i	−0.259358	+	0.0272596i	−0.0260429	+	0.999661i	$0.508291\pi$
$132$	1.65372	+	2.20037i	0.143938	+	0.191518i
$133$	−0.0144016	+	0.137022i	−0.00124877	+	0.0118813i
$134$	4.22868	+	3.80752i	0.365303	+	0.328920i
$135$	−5.02418	+	1.32574i	−0.432413	+	0.114101i
$136$	−0.889097	+	4.18287i	−0.0762395	+	0.358678i
$137$	9.57679	−	2.03561i	0.818201	−	0.173914i	0.220246	−	0.975444i	$-0.429314\pi$
$137$	9.57679	−	2.03561i	0.818201	−	0.173914i	0.597954	+	0.801530i	$0.295981\pi$
$138$	1.92816	+	15.8702i	0.164136	+	1.35096i
$139$	1.51445	+	0.492075i	0.128454	+	0.0417373i	0.372539	−	0.928017i	$-0.378487\pi$
$139$	1.51445	+	0.492075i	0.128454	+	0.0417373i	−0.244084	+	0.969754i	$0.578487\pi$
$140$	−0.223776	−	0.0727091i	−0.0189125	−	0.00614504i
$141$	1.71683	+	14.1307i	0.144583	+	1.19002i
$142$	13.6850	−	2.90883i	1.14842	−	0.244103i
$143$	−1.92498	+	9.05630i	−0.160975	+	0.757326i
$144$	1.58329	+	2.54817i	0.131941	+	0.212348i
$145$	1.32133	+	1.18973i	0.109731	+	0.0988018i
$146$	−1.75625	+	16.7096i	−0.145348	+	1.38290i
$147$	−7.22671	−	9.61554i	−0.596049	−	0.793077i
$148$	0.957850	−	0.100674i	0.0787348	−	0.00827536i
$149$	14.5438	+	8.39688i	1.19148	+	0.687899i	0.958641	−	0.284617i	$-0.0918666\pi$
$149$	14.5438	+	8.39688i	1.19148	+	0.687899i	0.232835	+	0.972516i	$0.425200\pi$
$150$	−1.68815	+	0.387484i	−0.137837	+	0.0316379i
$151$	−4.30219	−	5.92146i	−0.350107	−	0.481881i	0.597252	−	0.802054i	$-0.296259\pi$
$151$	−4.30219	−	5.92146i	−0.350107	−	0.481881i	−0.947359	+	0.320172i	$0.896259\pi$
$152$	0.435153	−	0.391814i	0.0352956	−	0.0317803i
$153$	3.56744	−	12.3230i	0.288411	−	0.996253i
$154$		−	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	−0.984140	−	0.177394i	$-0.943233\pi$
$157$	−3.66155	−	11.2691i	−0.292224	−	0.899372i	0.691916	−	0.721978i	$-0.256767\pi$
$158$	−8.49095	−	9.43016i	−0.675504	−	0.750223i
$159$	−3.03576	+	1.04099i	−0.240752	+	0.0825557i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	1.08587	−	1.88079i	0.0855788	−	0.148227i
$162$	−4.18484	−	7.96788i	−0.328792	−	0.626016i
$163$	1.36435	+	0.991259i	0.106864	+	0.0776414i	0.639934	−	0.768430i	$-0.278962\pi$
$163$	1.36435	+	0.991259i	0.106864	+	0.0776414i	−0.533070	+	0.846071i	$0.678962\pi$
$164$	7.40963	+	0.778784i	0.578595	+	0.0608128i
$165$	−1.41466	−	2.36118i	−0.110131	−	0.183817i
$166$	6.23328	−	14.0002i	0.483796	−	1.08662i
$167$	8.24880	+	1.75334i	0.638311	+	0.135677i	0.515689	−	0.856776i	$-0.327536\pi$
$167$	8.24880	+	1.75334i	0.638311	+	0.135677i	0.122623	+	0.992453i	$0.460869\pi$
$168$	0.0360346	−	0.405941i	0.00278013	−	0.0313190i
$169$	−19.1323	+	8.51826i	−1.47172	+	0.655251i
$170$	1.32146	−	4.06702i	0.101351	−	0.311926i
$171$	−1.38702	+	1.07800i	−0.106068	+	0.0824364i
$172$	−0.393301	−	0.883368i	−0.0299889	−	0.0673562i
$173$	4.41054	+	20.7500i	0.335327	+	1.57759i	0.746088	+	0.665847i	$0.231930\pi$
$173$	4.41054	+	20.7500i	0.335327	+	1.57759i	−0.410761	+	0.911743i	$0.634737\pi$
$174$	−1.49645	+	2.69161i	−0.113446	+	0.204050i
$175$	0.214950	+	0.0957017i	0.0162487	+	0.00723437i
$176$	−1.06337	+	1.18099i	−0.0801542	+	0.0890203i
$177$	6.18643	+	2.63526i	0.465001	+	0.198078i
$178$	−10.7683	+	14.8213i	−0.807118	+	1.11090i
$179$	−0.299958	−	2.85391i	−0.0224199	−	0.213312i	−0.999996	−	0.00273012i	$-0.999131\pi$
$179$	−0.299958	−	2.85391i	−0.0224199	−	0.213312i	0.977576	−	0.210581i	$-0.0675357\pi$
$180$	−1.30826	−	2.69971i	−0.0975122	−	0.201225i
$181$	7.52031	−	4.34186i	0.558981	−	0.322728i	−0.193756	−	0.981050i	$-0.562067\pi$
$181$	7.52031	−	4.34186i	0.558981	−	0.322728i	0.752736	+	0.658322i	$0.228734\pi$
$182$	1.10902	−	0.805749i	0.0822059	−	0.0597261i
$183$	−8.70542	+	4.04596i	−0.643523	+	0.299086i
$184$	−8.77827	+	2.85223i	−0.647143	+	0.210269i
$185$	−0.963126			−0.0708105
$186$	7.70279	+	5.80233i	0.564796	+	0.425448i
$187$	6.79582			0.496960
$188$	−7.81614	+	2.53962i	−0.570051	+	0.185221i
$189$	−0.195856	+	1.20682i	−0.0142464	+	0.0877834i
$190$	−0.473725	+	0.344182i	−0.0343676	+	0.0249696i
$191$	12.6416	−	7.29863i	0.914713	−	0.528110i	0.0327687	−	0.999463i	$-0.489568\pi$
$191$	12.6416	−	7.29863i	0.914713	−	0.528110i	0.881945	+	0.471353i	$0.156234\pi$
$192$	−1.26824	+	1.17965i	−0.0915274	+	0.0851337i
$193$	−2.15689	−	20.5214i	−0.155256	−	1.47716i	−0.743640	−	0.668581i	$-0.766902\pi$
$193$	−2.15689	−	20.5214i	−0.155256	−	1.47716i	0.588384	−	0.808582i	$-0.299764\pi$
$194$	4.11992	−	5.67058i	0.295793	−	0.407124i
$195$	3.95467	−	9.28383i	0.283200	−	0.664829i
$196$	4.64687	−	5.16087i	0.331919	−	0.368634i
$197$	−2.14512	−	0.955070i	−0.152834	−	0.0680460i	0.328894	−	0.944367i	$-0.393324\pi$
$197$	−2.14512	−	0.955070i	−0.152834	−	0.0680460i	−0.481728	+	0.876321i	$0.659991\pi$
$198$	3.43787	−	3.30308i	0.244319	−	0.234740i
$199$	−3.17450	−	14.9348i	−0.225034	−	1.05870i	−0.935050	−	0.354516i	$-0.884646\pi$
$199$	−3.17450	−	14.9348i	−0.225034	−	1.05870i	0.710016	−	0.704186i	$-0.248688\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	5.66330	−	8.06622i	0.399459	−	0.568947i
$202$	3.14469	−	9.67837i	0.221260	−	0.680968i
$203$	0.382186	−	0.170160i	0.0268242	−	0.0119429i
$204$	7.37780	+	0.654913i	0.516549	+	0.0458531i
$205$	−7.28764	−	1.54903i	−0.508991	−	0.108189i
$206$	4.14740	−	9.31520i	0.288963	−	0.649021i
$207$	26.8845	−	6.63059i	1.86860	−	0.460858i
$208$	−5.79414	−	0.608989i	−0.401751	−	0.0422258i
$209$	−0.752832	−	0.546965i	−0.0520745	−	0.0378343i
$210$	−0.0782695	+	0.399950i	−0.00540111	+	0.0275992i
$211$	−8.45337	+	14.6417i	−0.581954	+	1.00797i	0.413294	+	0.910598i	$0.364378\pi$
$211$	−8.45337	+	14.6417i	−0.581954	+	1.00797i	−0.995248	+	0.0973762i	$0.968955\pi$
$212$	−0.926441	−	1.60464i	−0.0636282	−	0.110207i
$213$	−7.86026	−	22.9223i	−0.538576	−	1.57061i
$214$	−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
$219$	29.0975	−	0.470948i	1.96623	−	0.0318237i
$220$	1.18099	−	1.06337i	0.0796221	−	0.0716921i
$221$	14.6441	+	20.1559i	0.985071	+	1.35583i
$222$	−0.373196	−	1.62590i	−0.0250473	−	0.109123i
$223$	−11.1904	−	6.46079i	−0.749366	−	0.432647i	0.0760988	−	0.997100i	$-0.475754\pi$
$223$	−11.1904	−	6.46079i	−0.749366	−	0.432647i	−0.825465	+	0.564454i	$0.809087\pi$
$224$	0.234003	−	0.0245947i	0.0156350	−	0.00164330i
$225$	1.01890	+	2.82167i	0.0679266	+	0.188112i
$226$	1.00274	−	9.54042i	0.0667012	−	0.634619i
$227$	−1.41382	−	1.27301i	−0.0938386	−	0.0844926i	0.620876	−	0.783909i	$-0.286777\pi$
$227$	−1.41382	−	1.27301i	−0.0938386	−	0.0844926i	−0.714715	+	0.699416i	$0.753444\pi$
$228$	−0.764592	−	0.666355i	−0.0506363	−	0.0441305i
$229$	−4.34732	+	20.4526i	−0.287279	+	1.35154i	0.563542	+	0.826087i	$0.309438\pi$
$229$	−4.34732	+	20.4526i	−0.287279	+	1.35154i	−0.850821	+	0.525455i	$0.823895\pi$
$230$	9.02832	−	1.91903i	0.595310	−	0.126537i
$231$	−0.642920	+	0.0781123i	−0.0423010	+	0.00513941i
$232$	−1.69100	−	0.549440i	−0.111020	−	0.0360725i
$233$	9.30190	+	3.02237i	0.609388	+	0.198002i	0.597423	−	0.801926i	$-0.296191\pi$
$233$	9.30190	+	3.02237i	0.609388	+	0.198002i	0.0119648	+	0.999928i	$0.496191\pi$
$234$	17.2049	+	3.07875i	1.12472	+	0.201264i
$235$	8.03879	−	1.70870i	0.524393	−	0.111463i
$236$	−0.807173	+	3.79745i	−0.0525425	+	0.247193i
$237$	−14.4405	+	16.5694i	−0.938012	+	1.07630i
$238$	−0.747739	−	0.673268i	−0.0484687	−	0.0436415i
$239$	−1.09867	+	10.4532i	−0.0710672	+	0.676159i	0.899761	+	0.436383i	$0.143741\pi$
$239$	−1.09867	+	10.4532i	−0.0710672	+	0.676159i	−0.970828	+	0.239776i	$0.922926\pi$
$240$	1.38460	−	1.04062i	0.0893755	−	0.0671716i
$241$	−15.5369	+	1.63300i	−1.00082	+	0.105190i	−0.590743	−	0.806860i	$-0.701165\pi$
$241$	−15.5369	+	1.63300i	−1.00082	+	0.105190i	−0.410078	+	0.912051i	$0.634498\pi$
$242$	−7.33915	−	4.23726i	−0.471779	−	0.272381i
$243$	−12.8258	+	8.85994i	−0.822776	+	0.568365i
$244$	−3.25773	−	4.48389i	−0.208555	−	0.287051i
$245$	−5.16087	+	4.64687i	−0.329716	+	0.296878i
$246$	−0.208835	−	12.9029i	−0.0133148	−	0.822656i
$247$		−	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	$-0.108996\pi$
$251$	8.07287	+	8.96583i	0.509555	+	0.565918i	−0.432389	+	0.901687i	$0.642329\pi$
$252$	−0.705505	+	0.0228434i	−0.0444426	+	0.00143900i
$253$	7.33406	+	12.7030i	0.461088	+	0.798629i
$254$	6.81194	−	11.7986i	0.427419	−	0.740312i
$255$	−7.26892	−	1.42251i	−0.455198	−	0.0890813i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.91475	−	0.201248i	−0.119439	−	0.0125535i	0.0446205	−	0.999004i	$-0.485792\pi$
$257$	−1.91475	−	0.201248i	−0.119439	−	0.0125535i	−0.164059	+	0.986450i	$0.552459\pi$
$258$	−1.43671	+	0.860781i	−0.0894455	+	0.0535899i
$259$	−0.0921729	+	0.207024i	−0.00572734	+	0.0128638i
$260$	5.69874	+	1.21131i	0.353421	+	0.0751220i
$261$	4.94058	+	2.01073i	0.305814	+	0.124461i
$262$	−2.72678	+	1.21404i	−0.168461	+	0.0750038i
$263$	−0.545687	+	1.67945i	−0.0336485	+	0.103559i	−0.966470	−	0.256779i	$-0.917339\pi$
$263$	−0.545687	+	1.67945i	−0.0336485	+	0.103559i	0.932822	+	0.360338i	$0.117339\pi$
$264$	2.25274	+	1.58165i	0.138646	+	0.0973438i
$265$	0.753635	+	1.69269i	0.0462954	+	0.103981i
$266$	0.0286454	+	0.134766i	0.00175636	+	0.00826302i
$267$	27.7333	+	15.4189i	1.69725	+	0.943621i
$268$	5.19831	+	2.31443i	0.317537	+	0.141377i
$269$	−9.65595	+	10.7240i	−0.588734	+	0.653855i	−0.961737	−	0.273975i	$-0.911661\pi$
$269$	−9.65595	+	10.7240i	−0.588734	+	0.653855i	0.373003	+	0.927830i	$0.378328\pi$
$270$	−4.36861	+	2.81341i	−0.265865	+	0.171219i
$271$	2.62225	−	3.60922i	0.159290	−	0.219245i	−0.721910	−	0.691987i	$-0.756736\pi$
$271$	2.62225	−	3.60922i	0.159290	−	0.219245i	0.881201	+	0.472742i	$0.156736\pi$
$272$	0.446997	+	4.25290i	0.0271032	+	0.257870i
$273$	−1.61709	−	1.73853i	−0.0978705	−	0.105221i
$274$	8.47903	−	4.89537i	0.512237	−	0.295740i
$275$	−1.28567	+	0.934094i	−0.0775288	+	0.0563280i
$276$	6.73794	+	14.4976i	0.405576	+	0.872652i
$277$	10.1435	−	3.29584i	0.609466	−	0.198028i	0.0120084	−	0.999928i	$-0.496178\pi$
$277$	10.1435	−	3.29584i	0.609466	−	0.198028i	0.597458	+	0.801900i	$0.296178\pi$
$278$	1.59239			0.0955051
$279$	8.36745	−	14.4563i	0.500946	−	0.865479i
$280$	−0.235292			−0.0140614
$281$	7.01729	−	2.28006i	0.418617	−	0.136017i	−0.0921322	−	0.995747i	$-0.529368\pi$
$281$	7.01729	−	2.28006i	0.418617	−	0.136017i	0.510749	+	0.859730i	$0.329368\pi$
$282$	5.99944	+	12.9086i	0.357262	+	0.768696i
$283$	4.17492	−	3.03325i	0.248173	−	0.180308i	−0.456744	−	0.889598i	$-0.650984\pi$
$283$	4.17492	−	3.03325i	0.248173	−	0.180308i	0.704917	+	0.709290i	$0.250984\pi$
$284$	12.1163	−	6.99534i	0.718969	−	0.415097i
$285$	0.690750	+	0.742627i	0.0409165	+	0.0439894i
$286$	0.967790	+	9.20791i	0.0572266	+	0.544475i
$287$	−1.03040	+	1.41823i	−0.0608228	+	0.0837154i
$288$	2.29323	+	1.93419i	0.135130	+	0.113973i
$289$	0.861122	−	0.956372i	0.0506542	−	0.0562572i
$290$	1.62431	+	0.723188i	0.0953826	+	0.0424671i
$291$	−10.6107	−	5.89922i	−0.622009	−	0.345819i
$292$	3.49326	+	16.4345i	0.204428	+	0.961756i
$293$	1.81354	+	4.07328i	0.105948	+	0.237963i	0.958738	−	0.284290i	$-0.0917580\pi$
$293$	1.81354	+	4.07328i	0.105948	+	0.237963i	−0.852790	+	0.522254i	$0.825091\pi$
$294$	−9.84438	−	6.91175i	−0.574136	−	0.403101i
$295$	1.19969	−	3.69228i	0.0698488	−	0.214973i
$296$	0.879860	−	0.391739i	0.0511408	−	0.0227694i
$297$	−6.39752	−	5.22108i	−0.371222	−	0.302958i
$298$	16.4268	+	3.49162i	0.951577	+	0.202264i
$299$	−21.8721	+	49.1256i	−1.26490	+	2.84101i
$300$	−1.48579	+	0.890187i	−0.0857820	+	0.0513949i
$301$	0.226273	+	0.0237822i	0.0130421	+	0.00137078i
$302$	−5.92146	−	4.30219i	−0.340742	−	0.247563i
$303$	−17.2980	−	3.38518i	−0.993743	−	0.194474i
$304$	0.292778	−	0.507107i	0.0167920	−	0.0290846i
$305$	2.77119	+	4.79985i	0.158678	+	0.274839i
$306$	−0.415169	−	12.8222i	−0.0237336	−	0.732999i
$307$	−15.4805	−	17.1928i	−0.883516	−	0.981244i	0.116412	−	0.993201i	$-0.462861\pi$
$307$	−15.4805	−	17.1928i	−0.883516	−	0.981244i	−0.999929	+	0.0119566i	$0.996194\pi$
$308$	−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	$0.901027\pi$
$312$	0.163304	+	10.0897i	0.00924525	+	0.571217i
$313$	−14.5839	+	13.1314i	−0.824332	+	0.742232i	−0.968950	−	0.247255i	$-0.920471\pi$
$313$	−14.5839	+	13.1314i	−0.824332	+	0.742232i	0.144618	+	0.989488i	$0.453805\pi$
$314$	−6.96468	−	9.58606i	−0.393040	−	0.540973i
$315$	0.704028	+	0.0510271i	0.0396675	+	0.00287505i
$316$	−10.9895	−	6.34476i	−0.618205	−	0.356921i
$317$	17.0520	−	1.79223i	0.957734	−	0.100662i	0.387253	−	0.921973i	$-0.373424\pi$
$317$	17.0520	−	1.79223i	0.957734	−	0.100662i	0.570480	+	0.821311i	$0.306757\pi$
$318$	−2.56550	+	1.92814i	−0.143866	+	0.108125i
$319$	−0.295355	+	2.81012i	−0.0165367	+	0.157336i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	−21.1598	+	24.2792i	−1.18102	+	1.35513i
$322$	0.451532	−	2.12429i	0.0251629	−	0.118382i
$323$	−2.44931	+	0.520617i	−0.136283	+	0.0289679i
$324$	−6.44223	−	6.28472i	−0.357901	−	0.349151i
$325$	−5.54091	−	1.80035i	−0.307354	−	0.0998655i
$326$	1.60389	+	0.521136i	0.0888313	+	0.0288630i
$327$	20.0990	−	2.44195i	1.11148	−	0.135040i
$328$	7.28764	−	1.54903i	0.402392	−	0.0855311i
$329$	0.402042	−	1.89146i	0.0221653	−	0.104280i
$330$	−2.07507	−	1.80846i	−0.114229	−	0.0995524i
$331$	10.3314	+	9.30240i	0.567863	+	0.511306i	0.902298	−	0.431113i	$-0.141879\pi$
$331$	10.3314	+	9.30240i	0.567863	+	0.511306i	−0.334435	+	0.942419i	$0.608546\pi$
$332$	1.60191	−	15.2411i	0.0879161	−	0.836466i
$333$	−2.71763	+	0.981329i	−0.148925	+	0.0537765i
$334$	8.38689	−	0.881497i	0.458910	−	0.0482334i
$335$	−4.92790	−	2.84513i	−0.269240	−	0.155446i
$336$	−0.0911717	−	0.397208i	−0.00497382	−	0.0216695i
$337$	3.32897	+	4.58194i	0.181341	+	0.249594i	0.890004	−	0.455953i	$-0.150701\pi$
$337$	3.32897	+	4.58194i	0.181341	+	0.249594i	−0.708663	+	0.705547i	$0.750701\pi$
$338$	−15.5636	+	14.0136i	−0.846551	+	0.762238i
$339$	−16.6133	+	0.268890i	−0.902313	+	0.0146041i
$340$		−	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
$345$	−5.18562	−	15.1225i	−0.279184	−	0.814167i
$346$	10.6068	+	18.3715i	0.570223	+	0.987656i
$347$	−2.00119	+	3.46616i	−0.107429	+	0.186073i	−0.914728	−	0.404070i	$-0.867595\pi$
$347$	−2.00119	+	3.46616i	−0.107429	+	0.186073i	0.807299	+	0.590143i	$0.200929\pi$
$348$	−0.591459	+	3.02230i	−0.0317055	+	0.162012i
$349$	−13.8018	−	10.0276i	−0.738791	−	0.536763i	0.153541	−	0.988142i	$-0.450932\pi$
$349$	−13.8018	−	10.0276i	−0.738791	−	0.536763i	−0.892332	+	0.451379i	$0.850932\pi$
$350$	0.234003	+	0.0245947i	0.0125080	+	0.00131464i
$351$	1.69950	−	30.2253i	0.0907126	−	1.61331i
$352$	−0.646376	+	1.45178i	−0.0344519	+	0.0773803i
$353$	−12.8098	−	2.72281i	−0.681798	−	0.144921i	−0.146023	−	0.989281i	$-0.546647\pi$
$353$	−12.8098	−	2.72281i	−0.681798	−	0.144921i	−0.535775	+	0.844361i	$0.679981\pi$
$354$	6.69798	+	0.594567i	0.355994	+	0.0316009i
$355$	−12.7811	+	5.69052i	−0.678352	+	0.302022i
$356$	−5.66123	+	17.4235i	−0.300045	+	0.923442i
$357$	−1.00142	+	1.42631i	−0.0530006	+	0.0754886i
$358$	−1.16719	−	2.62154i	−0.0616877	−	0.138553i
$359$	−4.89049	−	23.0079i	−0.258110	−	1.21431i	−0.895954	−	0.444147i	$-0.853507\pi$
$359$	−4.89049	−	23.0079i	−0.258110	−	1.21431i	0.637844	−	0.770166i	$-0.279827\pi$
$360$	−2.07849	−	2.16330i	−0.109546	−	0.114016i
$361$	−17.0441	−	7.58854i	−0.897059	−	0.399397i
$362$	5.81054	−	6.45325i	0.305395	−	0.339176i
$363$	−5.75242	+	13.5042i	−0.301924	+	0.708784i
$364$	0.805749	−	1.10902i	0.0422327	−	0.0581284i
$365$	−1.75625	−	16.7096i	−0.0919264	−	0.874621i
$366$	−7.02908	+	6.53806i	−0.367416	+	0.341750i
$367$	16.0420	−	9.26187i	0.837387	−	0.483466i	−0.0189881	−	0.999820i	$-0.506044\pi$
$367$	16.0420	−	9.26187i	0.837387	−	0.483466i	0.856375	+	0.516354i	$0.172711\pi$
$368$	−7.46724	+	5.42527i	−0.389257	+	0.282812i
$369$	−22.1416	+	3.05450i	−1.15265	+	0.159011i
$370$	−0.915988	+	0.297622i	−0.0476199	+	0.0154727i
$371$	0.435968			0.0226343
$372$	9.11881	+	3.13805i	0.472788	+	0.162700i
$373$	−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
$375$	1.57070	−	0.730003i	0.0811106	−	0.0376972i
$376$	−6.64881	+	4.83064i	−0.342886	+	0.249121i
$377$	−8.97105	+	5.17944i	−0.462033	+	0.266755i
$378$	0.186658	+	1.20828i	0.00960065	+	0.0621471i
$379$	−0.262801	−	2.50039i	−0.0134992	−	0.128436i	0.985697	−	0.168528i	$-0.0539015\pi$
$379$	−0.262801	−	2.50039i	−0.0134992	−	0.128436i	−0.999196	+	0.0400922i	$0.987235\pi$
$380$	−0.344182	+	0.473725i	−0.0176561	+	0.0243016i
$381$	−21.7097	−	9.24776i	−1.11222	−	0.473777i
$382$	9.76747	−	10.8479i	0.499747	−	0.555025i
$383$	−4.62812	−	2.06057i	−0.236486	−	0.105290i	0.285072	−	0.958506i	$-0.407982\pi$
$383$	−4.62812	−	2.06057i	−0.236486	−	0.105290i	−0.521558	+	0.853216i	$0.674649\pi$
$384$	−0.841637	+	1.51382i	−0.0429496	+	0.0772517i
$385$	0.0777423	+	0.365749i	0.00396211	+	0.0186403i
$386$	−8.39278	−	18.8505i	−0.427181	−	0.959465i
$387$	1.78016	+	2.29047i	0.0904907	+	0.116431i
$388$	2.16597	−	6.66616i	0.109960	−	0.338423i
$389$	31.3934	−	13.9772i	1.59171	−	0.708675i	0.596155	−	0.802869i	$-0.296694\pi$
$389$	31.3934	−	13.9772i	1.59171	−	0.708675i	0.995554	+	0.0941947i	$0.0300276\pi$
$390$	0.892253	−	10.0515i	0.0451810	−	0.508978i
$391$	38.6080	+	8.20639i	1.95249	+	0.415015i
$392$	2.82464	−	6.34424i	0.142666	−	0.320433i
$393$	2.65706	+	4.43484i	0.134031	+	0.223708i
$394$	−2.33527	−	0.245446i	−0.117649	−	0.0123654i
$395$	10.2660	+	7.45872i	0.516541	+	0.375289i
$396$	2.24890	−	4.20378i	0.113011	−	0.211248i
$397$	−13.6799	+	23.6942i	−0.686573	+	1.18918i	0.286367	+	0.958120i	$0.407552\pi$
$397$	−13.6799	+	23.6942i	−0.686573	+	1.18918i	−0.972940	+	0.231059i	$0.925781\pi$
$398$	−7.63424	−	13.2229i	−0.382670	−	0.662804i
$399$	0.225733	−	0.0774058i	0.0113008	−	0.00387514i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	3.23828	+	9.96640i	0.161712	+	0.497698i	0.998779	−	0.0494023i	$-0.0157316\pi$
$401$	3.23828	+	9.96640i	0.161712	+	0.497698i	−0.837067	+	0.547100i	$0.815732\pi$
$402$	2.89352	−	9.42149i	0.144316	−	0.469901i
$403$	12.1950	+	30.0585i	0.607478	+	1.49732i
$404$		−	10.1764i		−	0.506297i
$405$	5.75000	+	6.92369i	0.285720	+	0.344041i
$406$	0.310898	−	0.279934i	0.0154296	−	0.0138929i
$407$	−0.899650	−	1.23826i	−0.0445940	−	0.0613784i
$408$	7.21908	−	1.65701i	0.357398	−	0.0820340i
$409$	8.60533	+	4.96829i	0.425506	+	0.245666i	0.697430	−	0.716653i	$-0.254327\pi$
$409$	8.60533	+	4.96829i	0.425506	+	0.245666i	−0.271924	+	0.962319i	$0.587660\pi$
$410$	−7.40963	+	0.778784i	−0.365936	+	0.0384614i
$411$	−10.1884	−	13.5563i	−0.502557	−	0.668681i
$412$	1.06585	−	10.1409i	0.0525107	−	0.499606i
$413$	−0.678840	−	0.611231i	−0.0334036	−	0.0300767i
$414$	23.5197	−	14.6138i	1.15593	−	0.718230i
$415$	−3.18627	+	14.9902i	−0.156408	+	0.735840i
$416$	−5.69874	+	1.21131i	−0.279404	+	0.0593891i
$417$	−0.332652	−	2.73796i	−0.0162900	−	0.134079i
$418$	−0.885008	−	0.287556i	−0.0432871	−	0.0140648i
$419$	−14.2183	−	4.61982i	−0.694611	−	0.225693i	−0.0596301	−	0.998221i	$-0.518992\pi$
$419$	−14.2183	−	4.61982i	−0.694611	−	0.225693i	−0.634981	+	0.772528i	$0.718992\pi$
$420$	0.0491527	+	0.404562i	0.00239841	+	0.0197406i
$421$	−10.5391	+	2.24015i	−0.513643	+	0.109178i	−0.457439	−	0.889241i	$-0.651233\pi$
$421$	−10.5391	+	2.24015i	−0.513643	+	0.109178i	−0.0562045	+	0.998419i	$0.517900\pi$
$422$	−3.51511	+	16.5373i	−0.171113	+	0.805023i
$423$	20.9419	−	13.0121i	1.01823	−	0.632670i
$424$	−1.37696	−	1.23982i	−0.0668711	−	0.0602110i
$425$	−0.446997	+	4.25290i	−0.0216826	+	0.206296i
$426$	−14.5589	−	19.3715i	−0.705383	−	0.938552i
$427$	1.29693	−	0.136313i	0.0627630	−	0.00659666i
$428$	−16.1029	−	9.29702i	−0.778363	−	0.449388i
$429$	15.6300	−	3.58757i	0.754622	−	0.173209i
$430$	0.568369	+	0.782292i	0.0274092	+	0.0377255i
$431$	−28.8964	+	26.0184i	−1.39189	+	1.25326i	−0.461275	+	0.887257i	$0.652608\pi$
$431$	−28.8964	+	26.0184i	−1.39189	+	1.25326i	−0.930613	+	0.366005i	$0.880725\pi$
$432$	2.84660	−	4.34705i	0.136957	−	0.209148i
$433$			15.0113i			0.721398i	0.932682	+	0.360699i	$0.117462\pi$
$433$			15.0113i			0.721398i	−0.932682	+	0.360699i	$0.882538\pi$
$434$	−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
$438$	27.5278	−	9.43952i	1.31533	−	0.451038i
$439$	−2.56978	−	4.45100i	−0.122649	−	0.212435i	0.798162	−	0.602442i	$-0.205806\pi$
$439$	−2.56978	−	4.45100i	−0.122649	−	0.212435i	−0.920812	+	0.390008i	$0.872472\pi$
$440$	0.794588	−	1.37627i	0.0378805	−	0.0656109i
$441$	−9.82761	+	18.3704i	−0.467981	+	0.874779i
$442$	20.1559	+	14.6441i	0.958720	+	0.696551i
$443$	27.6026	+	2.90115i	1.31144	+	0.137838i	0.734309	−	0.678816i	$-0.237506\pi$
$443$	27.6026	+	2.90115i	1.31144	+	0.137838i	0.577129	+	0.816653i	$0.304173\pi$
$444$	−0.857362	−	1.43100i	−0.0406886	−	0.0679124i
$445$	7.45146	−	16.7363i	0.353233	−	0.793375i
$446$	−12.6392	−	2.68655i	−0.598484	−	0.127212i
$447$	2.57194	−	28.9737i	0.121649	−	1.37041i
$448$	0.214950	−	0.0957017i	0.0101554	−	0.00452148i
$449$	5.18694	−	15.9638i	0.244787	−	0.753376i	−0.750885	−	0.660433i	$-0.770373\pi$
$449$	5.18694	−	15.9638i	0.244787	−	0.753376i	0.995671	−	0.0929430i	$-0.0296274\pi$
$450$	1.84098	+	2.36871i	0.0867844	+	0.111662i
$451$	−4.81579	−	10.8164i	−0.226767	−	0.509326i
$452$	−1.99449	−	9.38334i	−0.0938130	−	0.441355i
$453$	−6.16022	+	11.0801i	−0.289432	+	0.520590i
$454$	−1.73800	−	0.773810i	−0.0815686	−	0.0363167i
$455$	−0.917259	+	1.01872i	−0.0430018	+	0.0477583i
$456$	−0.933085	−	0.397470i	−0.0436957	−	0.0186132i
$457$	−10.2081	+	14.0503i	−0.477516	+	0.657245i	−0.978025	−	0.208486i	$-0.933146\pi$
$457$	−10.2081	+	14.0503i	−0.477516	+	0.657245i	0.500509	+	0.865731i	$0.333146\pi$
$458$	2.18564	+	20.7949i	0.102128	+	0.971683i
$459$	−21.9599	+	3.39243i	−1.02500	+	0.158345i
$460$	7.99343	−	4.61501i	0.372696	−	0.215176i
$461$	7.22933	−	5.25242i	0.336704	−	0.244629i	−0.406566	−	0.913621i	$-0.633274\pi$
$461$	7.22933	−	5.25242i	0.336704	−	0.244629i	0.743270	+	0.668992i	$0.233274\pi$
$462$	−0.587315	+	0.272962i	−0.0273244	+	0.0126994i
$463$	32.0277	−	10.4064i	1.48845	−	0.483628i	0.551827	−	0.833958i	$-0.313931\pi$
$463$	32.0277	−	10.4064i	1.48845	−	0.483628i	0.936626	+	0.350330i	$0.113931\pi$
$464$	−1.77803			−0.0825428
$465$	−8.74084	−	4.07404i	−0.405347	−	0.188929i
$466$	9.78060			0.453077
$467$	−20.2617	+	6.58343i	−0.937600	+	0.304645i	−0.737667	−	0.675165i	$-0.764073\pi$
$467$	−20.2617	+	6.58343i	−0.937600	+	0.304645i	−0.199933	+	0.979810i	$0.564073\pi$
$468$	17.3142	−	2.38854i	0.800349	−	0.110410i
$469$	−1.08317	+	0.786968i	−0.0500160	+	0.0363388i
$470$	7.11733	−	4.10919i	0.328298	−	0.189543i
$471$	−15.0274	+	13.9777i	−0.692427	+	0.644057i
$472$	0.405810	+	3.86102i	0.0186789	+	0.177718i
$473$	−0.903238	+	1.24320i	−0.0415309	+	0.0571624i
$474$	−8.61352	+	20.2208i	−0.395632	+	0.928771i
$475$	0.391814	−	0.435153i	0.0179777	−	0.0199662i
$476$	−0.919194	−	0.409251i	−0.0421312	−	0.0187580i
$477$	3.85120	+	4.00835i	0.176334	+	0.183530i
$478$	2.18531	+	10.2811i	0.0999536	+	0.470245i
$479$	−10.1769	−	22.8578i	−0.464997	−	1.04440i	−0.982080	−	0.188465i	$-0.939649\pi$
$479$	−10.1769	−	22.8578i	−0.464997	−	1.04440i	0.517083	−	0.855935i	$-0.327018\pi$
$480$	0.995264	−	1.41755i	0.0454274	−	0.0647020i
$481$	1.73397	−	5.33660i	0.0790620	−	0.243328i
$482$	−14.2719	+	6.35424i	−0.650065	+	0.289428i
$483$	−3.74684	−	0.332600i	−0.170487	−	0.0151338i
$484$	−8.28933	−	1.76195i	−0.376788	−	0.0800887i
$485$	−2.85091	+	6.40324i	−0.129453	+	0.290756i
$486$	−9.46020	+	12.3897i	−0.429124	+	0.562008i
$487$	−40.0422	−	4.20860i	−1.81448	−	0.190710i	−0.864421	−	0.502768i	$-0.832315\pi$
$487$	−40.0422	−	4.20860i	−1.81448	−	0.190710i	−0.950063	+	0.312058i	$0.898982\pi$
$488$	−4.48389	−	3.25773i	−0.202976	−	0.147471i
$489$	0.560990	−	2.86661i	0.0253688	−	0.129632i
$490$	−3.47232	+	6.01423i	−0.156863	+	0.271695i
$491$	−9.92842	−	17.1965i	−0.448063	−	0.776068i	0.550197	−	0.835035i	$-0.314553\pi$
$491$	−9.92842	−	17.1965i	−0.448063	−	0.776068i	−0.998260	+	0.0589669i	$0.981219\pi$
$492$	−4.18582	−	12.2068i	−0.188711	−	0.550326i
$493$	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
$498$	−26.5404	+	0.429560i	−1.18930	+	0.0192491i
$499$	8.13030	−	7.32055i	0.363962	−	0.327713i	−0.466777	−	0.884375i	$-0.654585\pi$
$499$	8.13030	−	7.32055i	0.363962	−	0.327713i	0.830739	+	0.556662i	$0.187918\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	−3.26768	−	14.2363i	−0.145989	−	0.636032i
$502$	10.4483	+	6.03236i	0.466333	+	0.269237i
$503$	−2.89209	+	0.303971i	−0.128952	+	0.0135534i	−0.168784	−	0.985653i	$-0.553984\pi$
$503$	−2.89209	+	0.303971i	−0.128952	+	0.0135534i	0.0398326	+	0.999206i	$0.487318\pi$
$504$	−0.663916	+	0.239738i	−0.0295732	+	0.0106788i
$505$	−1.06373	+	10.1207i	−0.0473352	+	0.450365i
$506$	10.9005	+	9.81489i	0.484588	+	0.436325i
$507$	27.3463	+	23.8328i	1.21449	+	1.05845i
$508$	2.83257	−	13.3262i	0.125675	−	0.591253i
$509$	−10.8821	+	2.31307i	−0.482343	+	0.102525i	−0.442664	−	0.896687i	$-0.645967\pi$
$509$	−10.8821	+	2.31307i	−0.482343	+	0.102525i	−0.0396784	+	0.999213i	$0.512633\pi$
$510$	−7.35274	+	0.893329i	−0.325585	+	0.0395573i
$511$	−3.75980	−	1.22163i	−0.166324	−	0.0540419i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	2.70573	+	1.39165i	0.119461	+	0.0614427i
$514$	−1.88322	+	0.400292i	−0.0830654	+	0.0176561i
$515$	−2.12003	+	9.97394i	−0.0934195	+	0.439504i
$516$	−1.10039	+	1.26262i	−0.0484422	+	0.0555837i
$517$	9.70580	+	8.73914i	0.426861	+	0.384347i
$518$	−0.0236878	+	0.225374i	−0.00104078	+	0.00990237i
$519$	29.3722	−	22.0752i	1.28930	−	0.968992i
$520$	5.79414	−	0.608989i	0.254090	−	0.0267059i
$521$	−18.8898	−	10.9060i	−0.827575	−	0.477801i	0.0254466	−	0.999676i	$-0.491899\pi$
$521$	−18.8898	−	10.9060i	−0.827575	−	0.477801i	−0.853022	+	0.521875i	$0.825233\pi$
$522$	5.32012	+	0.385596i	0.232855	+	0.0168771i
$523$	−16.0372	−	22.0733i	−0.701256	−	0.965196i	−0.999941	−	0.0108445i	$-0.996548\pi$
$523$	−16.0372	−	22.0733i	−0.701256	−	0.965196i	0.298685	−	0.954352i	$-0.403452\pi$
$524$	−2.21817	+	1.99725i	−0.0969011	+	0.0872501i
$525$	−0.00659519	−	0.407484i	−0.000287838	−	0.0177840i
$526$			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
$531$	−0.376914	−	11.6408i	−0.0163567	−	0.505166i
$532$	0.0688883	+	0.119318i	0.00298669	+	0.00517309i
$533$	21.7034	−	37.5913i	0.940077	−	1.62826i
$534$	31.1407	+	6.09417i	1.34759	+	0.263721i
$535$	15.0429	+	10.9293i	0.650361	+	0.472515i
$536$	5.65908	+	0.594794i	0.244435	+	0.0256912i
$537$	−4.26367	+	2.55451i	−0.183991	+	0.110235i
$538$	−5.86945	+	13.1830i	−0.253050	+	0.568360i
$539$	−10.7951	−	2.29456i	−0.464977	−	0.0988339i
$540$	−3.28540	+	4.02569i	−0.141381	+	0.173238i
$541$	10.2641	−	4.56986i	0.441287	−	0.196474i	−0.174052	−	0.984737i	$-0.555686\pi$
$541$	10.2641	−	4.56986i	0.441287	−	0.196474i	0.615339	+	0.788263i	$0.289019\pi$
$542$	1.37860	−	4.24289i	0.0592159	−	0.182248i
$543$	−12.3096	−	8.64258i	−0.528255	−	0.370889i
$544$	1.73934	+	3.90661i	0.0745734	+	0.167495i
$545$	−2.43038	−	11.4340i	−0.104106	−	0.489780i
$546$	−2.07518	−	1.15374i	−0.0888094	−	0.0493753i
$547$	1.09364	+	0.486922i	0.0467608	+	0.0208193i	0.429984	−	0.902837i	$-0.358519\pi$
$547$	1.09364	+	0.486922i	0.0467608	+	0.0208193i	−0.383223	+	0.923656i	$0.625186\pi$
$548$	6.55129	−	7.27594i	0.279857	−	0.310813i
$549$	12.7100	+	10.7200i	0.542448	+	0.457520i
$550$	−0.934094	+	1.28567i	−0.0398299	+	0.0548211i
$551$	−0.108828	−	1.03543i	−0.00463624	−	0.0441109i
$552$	10.8882	+	11.7059i	0.463431	+	0.498236i
$553$	2.58573	−	1.49287i	0.109956	−	0.0634833i
$554$	8.62861	−	6.26905i	0.366594	−	0.266346i
$555$	0.703085	+	1.51278i	0.0298443	+	0.0642140i
$556$	1.51445	−	0.492075i	0.0642270	−	0.0208686i
$557$	−25.7087			−1.08931			−0.544656	−	0.838659i	$-0.683340\pi$
$557$	−25.7087			−1.08931			−0.544656	+	0.838659i	$0.683340\pi$
$558$	3.49066	−	16.3345i	0.147771	−	0.691494i
$559$	−5.63360			−0.238276
$560$	−0.223776	+	0.0727091i	−0.00945625	+	0.00307252i
$561$	−4.96097	−	10.6742i	−0.209452	−	0.450665i
$562$	5.96927	−	4.33693i	0.251798	−	0.182942i
$563$	5.87739	−	3.39331i	0.247702	−	0.143011i	−0.371009	−	0.928629i	$-0.620988\pi$
$563$	5.87739	−	3.39331i	0.247702	−	0.143011i	0.618712	+	0.785618i	$0.287655\pi$
$564$	9.69479	+	10.4229i	0.408224	+	0.438883i
$565$	1.00274	+	9.54042i	0.0421855	+	0.401369i
$566$	3.03325	−	4.17492i	0.127497	−	0.175485i
$567$	2.03853	−	0.573352i	0.0856102	−	0.0240785i
$568$	9.36159	−	10.3971i	0.392804	−	0.436253i
$569$	22.0862	+	9.83340i	0.925901	+	0.412238i	0.813592	−	0.581436i	$-0.197509\pi$
$569$	22.0862	+	9.83340i	0.925901	+	0.412238i	0.112309	+	0.993673i	$0.464175\pi$
$570$	0.886427	+	0.492826i	0.0371283	+	0.0206422i
$571$	−7.17071	−	33.7356i	−0.300085	−	1.41179i	−0.827158	−	0.561969i	$-0.810044\pi$
$571$	−7.17071	−	33.7356i	−0.300085	−	1.41179i	0.527073	−	0.849820i	$-0.323289\pi$
$572$	3.76582	+	8.45818i	0.157457	+	0.353654i
$573$	−20.6923	−	14.5281i	−0.864435	−	0.606921i
$574$	−0.541715	+	1.66723i	−0.0226108	+	0.0695888i
$575$	−8.43204	+	3.75419i	−0.351641	+	0.156560i
$576$	2.77869	+	1.13088i	0.115779	+	0.0471199i
$577$	−21.5034	−	4.57069i	−0.895198	−	0.190280i	−0.262733	−	0.964869i	$-0.584624\pi$
$577$	−21.5034	−	4.57069i	−0.895198	−	0.190280i	−0.632466	+	0.774588i	$0.717957\pi$
$578$	0.523440	−	1.17567i	0.0217722	−	0.0489012i
$579$	−30.6584	+	18.3685i	−1.27412	+	0.763369i
$580$	1.76829	+	0.185854i	0.0734241	+	0.00771718i
$581$	2.91721	+	2.11947i	0.121026	+	0.0879306i
$582$	−11.9143	−	2.33161i	−0.493865	−	0.0966484i
$583$	−1.47228	+	2.55006i	−0.0609755	+	0.105613i
$584$	8.40083	+	14.5507i	0.347629	+	0.602111i
$585$	−17.4690	+	0.565626i	−0.722255	+	0.0233858i
$586$	2.98349	+	3.31350i	0.123247	+	0.136880i
$587$	−11.4484	−	35.2347i	−0.472528	−	1.45429i	−0.849263	−	0.527970i	$-0.822953\pi$
$587$	−11.4484	−	35.2347i	−0.472528	−	1.45429i	0.376735	−	0.926321i	$-0.377047\pi$
$588$	−11.4984	−	3.53138i	−0.474186	−	0.145632i
$589$	−3.25842	−	0.109067i	−0.134261	−	0.00449404i
$590$		−	3.88229i		−	0.159831i
$591$	0.0658178	+	4.06655i	0.00270738	+	0.167275i
$592$	0.715742	−	0.644457i	0.0294168	−	0.0264870i
$593$	−1.72205	−	2.37020i	−0.0707161	−	0.0973323i	0.772194	−	0.635387i	$-0.219159\pi$
$593$	−1.72205	−	2.37020i	−0.0707161	−	0.0973323i	−0.842910	+	0.538055i	$0.819159\pi$
$594$	−7.69780	−	2.98860i	−0.315845	−	0.122624i
$595$	0.871380	+	0.503091i	0.0357231	+	0.0206247i
$596$	16.7018	−	1.75543i	0.684131	−	0.0719050i
$597$	−21.1407	+	15.8886i	−0.865232	+	0.650279i
$598$	−5.62098	+	53.4801i	−0.229859	+	2.18696i
$599$	−24.6722	−	22.2149i	−1.00808	−	0.907677i	−0.0123414	−	0.999924i	$-0.503928\pi$
$599$	−24.6722	−	22.2149i	−1.00808	−	0.907677i	−0.995736	+	0.0922467i	$0.970595\pi$
$600$	−1.13799	+	1.30575i	−0.0464581	+	0.0533071i
$601$	2.06812	−	9.72973i	0.0843603	−	0.396884i	−0.915626	−	0.402030i	$-0.868305\pi$
$601$	2.06812	−	9.72973i	0.0843603	−	0.396884i	0.999987	+	0.00514613i	$0.00163807\pi$
$602$	0.222547	−	0.0473039i	0.00907035	−	0.00192796i
$603$	−16.8038	−	3.00698i	−0.684305	−	0.122454i
$604$	−6.96109	−	2.26180i	−0.283243	−	0.0920312i
$605$	8.05975	+	2.61877i	0.327675	+	0.106468i
$606$	−17.4974	+	2.12587i	−0.710785	+	0.0863576i
$607$	45.4447	−	9.65957i	1.84454	−	0.392070i	0.853007	−	0.521900i	$-0.174776\pi$
$607$	45.4447	−	9.65957i	1.84454	−	0.392070i	0.991536	+	0.129830i	$0.0414431\pi$
$608$	0.121744	−	0.572761i	0.00493737	−	0.0232285i
$609$	−0.546267	−	0.476082i	−0.0221359	−	0.0192918i
$610$	4.11880	+	3.70858i	0.166765	+	0.150156i
$611$	−5.00490	+	47.6185i	−0.202477	+	1.92644i
$612$	−4.35714	−	12.0664i	−0.176127	−	0.487755i
$613$	−0.770411	+	0.0809734i	−0.0311166	+	0.00327049i	−0.120074	−	0.992765i	$-0.538313\pi$
$613$	−0.770411	+	0.0809734i	−0.0311166	+	0.00327049i	0.0889574	+	0.996035i	$0.471647\pi$
$614$	−20.0357	−	11.5676i	−0.808573	−	0.466830i
$615$	2.88693	+	12.5775i	0.116412	+	0.507173i
$616$	−0.219784	−	0.302507i	−0.00885537	−	0.0121884i
$617$	−30.1490	+	27.1463i	−1.21375	+	1.09287i	−0.220684	+	0.975345i	$0.570829\pi$
$617$	−30.1490	+	27.1463i	−1.21375	+	1.09287i	−0.993070	+	0.117524i	$0.962504\pi$
$618$	−17.6590	+	0.285814i	−0.710349	+	0.0114971i
$619$			43.2387i			1.73791i	0.494890	+	0.868956i	$0.335209\pi$
$619$			43.2387i			1.73791i	−0.494890	+	0.868956i	$0.664791\pi$
$620$	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
$624$	3.27320	+	9.54542i	0.131033	+	0.382123i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−9.81231	+	16.9954i	−0.392179	+	0.679273i
$627$	−0.309547	+	1.58176i	−0.0123621	+	0.0631694i
$628$	−9.58606	−	6.96468i	−0.382526	−	0.277921i
$629$	−4.09608	−	0.430515i	−0.163321	−	0.0171658i
$630$	0.685339	−	0.169027i	0.0273045	−	0.00673420i
$631$	−11.4622	+	25.7445i	−0.456302	+	1.02487i	0.528140	+	0.849158i	$0.322890\pi$
$631$	−11.4622	+	25.7445i	−0.456302	+	1.02487i	−0.984441	+	0.175713i	$0.943777\pi$
$632$	−12.4122	−	2.63830i	−0.493732	−	0.104946i
$633$	29.1686	+	2.58924i	1.15935	+	0.102913i
$634$	15.6635	−	6.97386i	0.622079	−	0.276967i
$635$	−4.21001	+	12.9571i	−0.167069	+	0.514186i
$636$	−1.84411	+	2.62655i	−0.0731236	+	0.104150i
$637$	−16.4565	−	36.9619i	−0.652031	−	1.46448i
$638$	0.587474	+	2.76385i	0.0232583	+	0.109422i
$639$	−30.2661	+	29.0795i	−1.19731	+	1.15037i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	27.1348	−	30.1363i	1.07176	−	1.19031i	0.0908480	−	0.995865i	$-0.471042\pi$
$641$	27.1348	−	30.1363i	1.07176	−	1.19031i	0.980913	−	0.194447i	$-0.0622911\pi$
$642$	−12.6214	+	29.6296i	−0.498128	+	1.16939i
$643$	−4.57473	+	6.29658i	−0.180410	+	0.248313i	−0.889638	−	0.456666i	$-0.849044\pi$
$643$	−4.57473	+	6.29658i	−0.180410	+	0.248313i	0.709228	+	0.704979i	$0.249044\pi$
$644$	−0.227009	−	2.15985i	−0.00894542	−	0.0851100i
$645$	1.22635	−	1.14068i	0.0482873	−	0.0449142i
$646$	−2.16855	+	1.25201i	−0.0853206	+	0.0492598i
$647$	−0.364013	+	0.264471i	−0.0143108	+	0.0103974i	−0.594918	−	0.803787i	$-0.702815\pi$
$647$	−0.364013	+	0.264471i	−0.0143108	+	0.0103974i	0.580607	+	0.814184i	$0.302815\pi$
$648$	−8.06901	−	3.98637i	−0.316981	−	0.156599i
$649$	5.86767	−	1.90652i	0.230326	−	0.0748376i
$650$	−5.82606			−0.228517
$651$	−1.71223	+	1.48895i	−0.0671074	+	0.0583564i
$652$	1.68643			0.0660457
$653$	11.7108	−	3.80507i	0.458279	−	0.148904i	−0.0707745	−	0.997492i	$-0.522547\pi$
$653$	11.7108	−	3.80507i	0.458279	−	0.148904i	0.529054	+	0.848588i	$0.322547\pi$
$654$	18.3606	−	8.53335i	0.717958	−	0.333680i
$655$	2.41478	−	1.75444i	0.0943534	−	0.0685518i
$656$	6.45227	−	3.72522i	0.251919	−	0.145446i
$657$	−21.9810	−	45.3596i	−0.857560	−	1.76965i
$658$	−0.202128	−	1.92312i	−0.00787978	−	0.0749711i
$659$	−9.03461	+	12.4351i	−0.351938	+	0.484402i	−0.947881	−	0.318626i	$-0.896779\pi$
$659$	−9.03461	+	12.4351i	−0.351938	+	0.484402i	0.595942	+	0.803027i	$0.296779\pi$
$660$	−2.53235	−	1.07872i	−0.0985717	−	0.0419890i
$661$	−29.1471	+	32.3712i	−1.13369	+	1.25909i	−0.171960	+	0.985104i	$0.555010\pi$
$661$	−29.1471	+	32.3712i	−1.13369	+	1.25909i	−0.961733	+	0.273989i	$0.911657\pi$
$662$	12.7003	+	5.65454i	0.493611	+	0.219770i
$663$	20.9686	−	37.7154i	0.814354	−	1.46475i
$664$	−3.18627	−	14.9902i	−0.123651	−	0.581733i
$665$	−0.0560388	−	0.125865i	−0.00217309	−	0.00488084i
$666$	−2.28137	+	1.77309i	−0.0884013	+	0.0687059i
$667$	−5.07134	+	15.6080i	−0.196363	+	0.604344i
$668$	7.70401	−	3.43004i	0.298077	−	0.132712i
$669$	−1.97892	+	22.2932i	−0.0765096	+	0.861904i
$670$	−5.56591	−	1.18307i	−0.215030	−	0.0457060i
$671$	−3.58247	+	8.04635i	−0.138300	+	0.310626i
$672$	−0.209453	−	0.349594i	−0.00807984	−	0.0134859i
$673$	8.32249	+	0.874729i	0.320808	+	0.0337183i	0.263564	−	0.964642i	$-0.415102\pi$
$673$	8.32249	+	0.874729i	0.320808	+	0.0337183i	0.0572443	+	0.998360i	$0.481769\pi$
$674$	4.58194	+	3.32897i	0.176490	+	0.128227i
$675$	3.68820	−	3.66021i	0.141959	−	0.140882i
$676$	−10.4715	+	18.1371i	−0.402749	+	0.697582i
$677$	−6.75184	−	11.6945i	−0.259494	−	0.449458i	0.706612	−	0.707601i	$-0.250223\pi$
$677$	−6.75184	−	11.6945i	−0.259494	−	0.449458i	−0.966107	+	0.258144i	$0.916889\pi$
$678$	−15.7171	+	5.38953i	−0.603613	+	0.206984i
$679$	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	$0.970105\pi$
$684$	−0.488490	+	1.68738i	−0.0186779	+	0.0645188i
$685$	−7.27594	+	6.55129i	−0.277999	+	0.250312i
$686$	1.92856	+	2.65443i	0.0736326	+	0.101347i
$687$	35.2984	−	8.10208i	1.34672	−	0.309114i
$688$	−0.837418	−	0.483483i	−0.0319263	−	0.0184326i
$689$	−10.7359	+	1.12838i	−0.409004	+	0.0429880i
$690$	−9.60492	−	12.7799i	−0.365653	−	0.486522i
$691$	−1.20449	+	11.4599i	−0.0458208	+	0.435956i	0.947429	+	0.319965i	$0.103671\pi$
$691$	−1.20449	+	11.4599i	−0.0458208	+	0.435956i	−0.993250	+	0.115991i	$0.962996\pi$
$692$	15.7647	+	14.1946i	0.599285	+	0.539599i
$693$	0.592024	+	0.952812i	0.0224891	+	0.0361943i
$694$	−0.832141	+	3.91491i	−0.0315876	+	0.148608i
$695$	−1.55759	+	0.331076i	−0.0590828	+	0.0125584i
$696$	0.371432	+	3.05715i	0.0140791	+	0.115881i
$697$	−30.3011	−	9.84544i	−1.14774	−	0.372922i
$698$	−16.2249	−	5.27180i	−0.614123	−	0.199541i
$699$	−2.04318	−	16.8168i	−0.0772801	−	0.636071i
$700$	0.230150	−	0.0489199i	0.00869885	−	0.00184900i
$701$	3.35523	−	15.7851i	0.126725	−	0.596196i	−0.868254	−	0.496119i	$-0.834758\pi$
$701$	3.35523	−	15.7851i	0.126725	−	0.596196i	0.994980	−	0.100077i	$-0.0319088\pi$
$702$	−7.72382	−	29.2712i	−0.291517	−	1.10477i
$703$	0.419108	+	0.377366i	0.0158069	+	0.0142326i
$704$	−0.166114	+	1.58047i	−0.00626066	+	0.0595662i
$705$	−8.55219	−	11.3792i	−0.322094	−	0.428564i
$706$	−13.0243	+	1.36890i	−0.490174	+	0.0515194i
$707$	2.07364	+	1.19722i	0.0779872	+	0.0450259i
$708$	6.55389	−	1.50432i	0.246310	−	0.0565360i
$709$	−2.19797	−	3.02524i	−0.0825464	−	0.113615i	0.765747	−	0.643142i	$-0.222370\pi$
$709$	−2.19797	−	3.02524i	−0.0825464	−	0.113615i	−0.848293	+	0.529527i	$0.822370\pi$
$710$	−10.3971	+	9.36159i	−0.390196	+	0.351334i
$711$	36.5671	+	10.5860i	1.37137	+	0.397006i
$712$			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
$717$	17.2208	−	5.90516i	0.643123	−	0.220532i
$718$	−11.7610	−	20.3706i	−0.438916	−	0.760224i
$719$	13.0738	−	22.6444i	0.487570	−	0.844495i	−0.512328	−	0.858790i	$-0.671217\pi$
$719$	13.0738	−	22.6444i	0.487570	−	0.844495i	0.999898	+	0.0142945i	$0.00455024\pi$
$720$	−2.64526	−	1.41514i	−0.0985830	−	0.0527390i
$721$	1.94100	+	1.41022i	0.0722867	+	0.0525194i
$722$	−18.5549	−	1.95020i	−0.690543	−	0.0725789i
$723$	13.9069	+	23.2117i	0.517204	+	0.863253i
$724$	3.53198	−	7.93296i	0.131265	−	0.294826i
$725$	−1.73917	−	0.369672i	−0.0645912	−	0.0137293i
$726$	−1.29786	+	14.6208i	−0.0481681	+	0.542629i
$727$	−25.5520	+	11.3765i	−0.947671	+	0.421931i	−0.821583	−	0.570089i	$-0.806909\pi$
$727$	−25.5520	+	11.3765i	−0.947671	+	0.421931i	−0.126088	+	0.992019i	$0.540242\pi$
$728$	0.423607	−	1.30373i	0.0156999	−	0.0483194i
$729$	23.2792	+	13.6777i	0.862192	+	0.506582i
$730$	−6.83385	−	15.3491i	−0.252932	−	0.568095i
$731$	0.859727	+	4.04470i	0.0317982	+	0.149599i
$732$	−4.66468	+	8.39017i	−0.172412	+	0.310110i
$733$	44.4161	+	19.7753i	1.64054	+	0.730418i	0.999318	−	0.0369334i	$-0.0117589\pi$
$733$	44.4161	+	19.7753i	1.64054	+	0.730418i	0.641227	+	0.767351i	$0.278426\pi$
$734$	12.3948	−	13.7658i	0.457500	−	0.508106i
$735$	11.0663	+	4.71395i	0.408186	+	0.173877i
$736$	−5.42527	+	7.46724i	−0.199978	+	0.275246i
$737$	−0.945231	−	8.99327i	−0.0348180	−	0.331271i
$738$	−20.1141	+	9.74714i	−0.740409	+	0.358797i
$739$	15.3823	−	8.88098i	0.565847	−	0.326692i	−0.189642	−	0.981853i	$-0.560733\pi$
$739$	15.3823	−	8.88098i	0.565847	−	0.326692i	0.755489	+	0.655161i	$0.227399\pi$
$740$	−0.779186	+	0.566111i	−0.0286434	+	0.0208107i
$741$	−5.35842	+	2.49040i	−0.196846	+	0.0914870i
$742$	0.414630	−	0.134721i	0.0152215	−	0.00494578i
$743$	−46.6306			−1.71071			−0.855356	−	0.518040i	$-0.826662\pi$
$743$	−46.6306			−1.71071			−0.855356	+	0.518040i	$0.826662\pi$
$744$	9.64221	+	0.166598i	0.353501	+	0.00610778i
$745$	−16.7938			−0.615275
$746$	−3.56127	+	1.15713i	−0.130387	+	0.0423654i
$747$	6.28290	+	45.5439i	0.229879	+	1.66637i
$748$	5.49794	−	3.99449i	0.201024	−	0.146053i
$749$	3.78888	−	2.18751i	0.138443	−	0.0799299i
$750$	1.26824	−	1.17965i	0.0463096	−	0.0430746i
$751$	−2.34540	−	22.3150i	−0.0855849	−	0.814286i	−0.950156	−	0.311775i	$-0.899076\pi$
$751$	−2.34540	−	22.3150i	−0.0855849	−	0.814286i	0.864571	−	0.502511i	$-0.167590\pi$
$752$	−4.83064	+	6.64881i	−0.176155	+	0.242457i
$753$	8.18940	−	19.2251i	0.298438	−	0.700603i
$754$	−6.93144	+	7.69815i	−0.252428	+	0.280350i
$755$	6.68654	+	2.97704i	0.243348	+	0.108346i
$756$	0.550901	+	1.09146i	0.0200361	+	0.0396960i
$757$	−0.327100	−	1.53889i	−0.0118887	−	0.0559318i	0.971803	−	0.235793i	$-0.0757686\pi$
$757$	−0.327100	−	1.53889i	−0.0118887	−	0.0559318i	−0.983692	+	0.179861i	$0.942435\pi$
$758$	−1.02260	−	2.29680i	−0.0371426	−	0.0834235i
$759$	14.5987	−	20.7928i	0.529898	−	0.754731i
$760$	−0.180947	+	0.556897i	−0.00656364	+	0.0202008i
$761$	41.7285	−	18.5787i	1.51266	−	0.673478i	0.528202	−	0.849119i	$-0.322866\pi$
$761$	41.7285	−	18.5787i	1.51266	−	0.673478i	0.984454	+	0.175641i	$0.0561998\pi$
$762$	−23.5048	−	2.08648i	−0.851491	−	0.0755852i
$763$	−2.69033	−	0.571848i	−0.0973965	−	0.0207023i
$764$	5.93724	−	13.3353i	0.214802	−	0.482453i
$765$	3.07199	+	12.4557i	0.111068	+	0.450338i
$766$	−5.03836	−	0.529553i	−0.182043	−	0.0191335i
$767$	18.2987	+	13.2948i	0.660728	+	0.480047i
$768$	−0.332649	+	1.69981i	−0.0120034	+	0.0613365i
$769$	25.3988	−	43.9920i	0.915905	−	1.58639i	0.110333	−	0.993895i	$-0.464808\pi$
$769$	25.3988	−	43.9920i	0.915905	−	1.58639i	0.805571	−	0.592499i	$-0.201859\pi$
$770$	0.186960	+	0.323824i	0.00673756	+	0.0116698i
$771$	1.08167	+	3.15441i	0.0389555	+	0.113603i
$772$	−13.8071	−	15.3344i	−0.496929	−	0.551896i
$773$	2.16622	+	6.66695i	0.0779137	+	0.239794i	0.982426	−	0.186655i	$-0.0597646\pi$
$773$	2.16622	+	6.66695i	0.0779137	+	0.239794i	−0.904512	+	0.426448i	$0.859765\pi$
$774$	2.40083	+	1.62826i	0.0862960	+	0.0585267i
$775$	−1.89672	+	5.23474i	−0.0681321	+	0.188037i
$776$		−	7.00922i		−	0.251616i
$777$	0.392458	−	0.00635200i	0.0140794	−	0.000227877i
$778$	25.5377	−	22.9942i	0.915571	−	0.824384i
$779$	2.56431	+	3.52946i	0.0918758	+	0.126456i
$780$	−2.25750	−	9.83527i	−0.0808316	−	0.352159i
$781$	−19.2549	−	11.1168i	−0.688994	−	0.397791i
$782$	39.2543	−	4.12580i	1.40373	−	0.147538i
$783$	−0.448384	−	9.22800i	−0.0160239	−	0.329782i
$784$	0.725912	−	6.90659i	0.0259254	−	0.246664i
$785$	8.80554	+	7.92855i	0.314283	+	0.282982i
$786$	3.89746	+	3.39670i	0.139018	+	0.121156i
$787$	−7.05806	+	33.2056i	−0.251593	+	1.18365i	0.652995	+	0.757362i	$0.273512\pi$
$787$	−7.05806	+	33.2056i	−0.251593	+	1.18365i	−0.904587	+	0.426288i	$0.859821\pi$
$788$	−2.29682	+	0.488204i	−0.0818207	+	0.0173915i
$789$	3.03626	−	0.368894i	0.108094	−	0.0131330i
$790$	12.0685	+	3.92128i	0.429376	+	0.139513i
$791$	2.14667	+	0.697497i	0.0763269	+	0.0248001i
$792$	0.839791	−	4.69298i	0.0298407	−	0.166758i
$793$	−31.5847	+	6.71353i	−1.12160	+	0.238404i
$794$	−5.68841	+	26.7619i	−0.201874	+	0.949743i
$795$	2.10855	−	2.41940i	0.0747827	−	0.0858074i
$796$	−11.3467	−	10.2166i	−0.402173	−	0.362118i
$797$	0.827795	−	7.87594i	0.0293220	−	0.278980i	−0.970030	−	0.242985i	$-0.921873\pi$
$797$	0.827795	−	7.87594i	0.0293220	−	0.278980i	0.999352	−	0.0359949i	$-0.0114600\pi$
$798$	0.190765	−	0.143373i	0.00675302	−	0.00507534i
$799$	34.9519	−	3.67359i	1.23651	−	0.129962i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	3.97304	−	54.8166i	0.140380	−	1.93685i
$802$	6.15957	+	8.47792i	0.217502	+	0.299366i
$803$	19.8425	−	17.8663i	0.700228	−	0.630488i
$804$	−0.159497	−	9.85452i	−0.00562503	−	0.347542i
$805$			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	$-0.0835903\pi$
$809$	17.2533	+	19.1618i	0.606595	+	0.673692i	−0.359121	+	0.933291i	$0.616924\pi$
$810$	7.60812	+	4.80797i	0.267322	+	0.168935i
$811$	10.8354	+	18.7675i	0.380483	+	0.659016i	0.991131	−	0.132886i	$-0.0424245\pi$
$811$	10.8354	+	18.7675i	0.380483	+	0.659016i	−0.610648	+	0.791902i	$0.709091\pi$
$812$	0.209177	−	0.362306i	0.00734068	−	0.0127144i
$813$	−7.58325	−	1.48403i	−0.265956	−	0.0520471i
$814$	−1.23826	−	0.899650i	−0.0434011	−	0.0315327i
$815$	−1.67719	−	0.176280i	−0.0587495	−	0.00617482i
$816$	6.35371	−	3.80672i	0.222424	−	0.133262i
$817$	0.230300	−	0.517262i	0.00805717	−	0.0180967i
$818$	9.71944	+	2.06593i	0.339832	+	0.0722336i
$819$	−1.55023	+	3.80909i	−0.0541696	+	0.133100i
$820$	−6.80632	+	3.03037i	−0.237687	+	0.105825i
$821$	−1.39325	+	4.28798i	−0.0486247	+	0.149652i	−0.972421	−	0.233233i	$-0.925069\pi$
$821$	−1.39325	+	4.28798i	−0.0486247	+	0.149652i	0.923796	+	0.382885i	$0.125069\pi$
$822$	−13.8789	−	9.74437i	−0.484081	−	0.339874i
$823$	13.5279	+	30.3842i	0.471554	+	1.05913i	0.980174	+	0.198137i	$0.0634891\pi$
$823$	13.5279	+	30.3842i	0.471554	+	1.05913i	−0.508620	+	0.860991i	$0.669844\pi$
$824$	−2.12003	−	9.97394i	−0.0738546	−	0.347459i
$825$	2.40572	+	1.33751i	0.0837565	+	0.0465661i
$826$	−0.834496	−	0.371542i	−0.0290358	−	0.0129276i
$827$	18.2763	−	20.2979i	0.635529	−	0.705826i	−0.336236	−	0.941778i	$-0.609154\pi$
$827$	18.2763	−	20.2979i	0.635529	−	0.705826i	0.971765	+	0.235951i	$0.0758206\pi$
$828$	17.8526	−	21.1666i	0.620422	−	0.735589i
$829$	20.6267	−	28.3902i	0.716394	−	0.986032i	−0.283242	−	0.959049i	$-0.591410\pi$
$829$	20.6267	−	28.3902i	0.716394	−	0.986032i	0.999636	−	0.0269836i	$-0.00859020\pi$
$830$	1.60191	+	15.2411i	0.0556031	+	0.529028i
$831$	−12.5816	−	13.5265i	−0.436450	−	0.469228i
$832$	−5.04551	+	2.91303i	−0.174922	+	0.100991i
$833$	−24.0258	+	17.4558i	−0.832444	+	0.604806i
$834$	−1.16245	−	2.50116i	−0.0402523	−	0.0866082i
$835$	−8.02034	+	2.60597i	−0.277555	+	0.0901832i
$836$	−0.930552			−0.0321838
$837$	−28.8148	−	2.58957i	−0.995986	−	0.0895085i
$838$	−14.9500			−0.516441
$839$	−35.2953	+	11.4681i	−1.21853	+	0.395924i	−0.846546	−	0.532316i	$-0.821322\pi$
$839$	−35.2953	+	11.4681i	−1.21853	+	0.395924i	−0.371983	+	0.928240i	$0.621322\pi$
$840$	0.171764	+	0.369572i	0.00592641	+	0.0127515i
$841$	20.9039	−	15.1876i	0.720824	−	0.523709i
$842$	−9.33102	+	5.38727i	−0.321568	+	0.185657i
$843$	−8.70393	−	9.35761i	−0.299779	−	0.322293i
$844$	1.76724	+	16.8141i	0.0608308	+	0.578766i
$845$	12.3100	−	16.9432i	0.423475	−	0.582864i
$846$	15.8959	−	18.8466i	0.546513	−	0.647961i
$847$	1.33424	−	1.48182i	0.0458449	−	0.0509159i
$848$	−1.69269	−	0.753635i	−0.0581273	−	0.0258799i
$849$	−7.81203	−	4.34325i	−0.268108	−	0.149060i
$850$	0.889097	+	4.18287i	0.0304958	+	0.143471i
$851$	−3.61576	−	8.12112i	−0.123947	−	0.278389i
$852$	−19.8325	−	13.9244i	−0.679450	−	0.477043i
$853$	−2.27727	+	7.00872i	−0.0779723	+	0.239974i	−0.982443	−	0.186561i	$-0.940266\pi$
$853$	−2.27727	+	7.00872i	−0.0779723	+	0.239974i	0.904471	+	0.426535i	$0.140266\pi$
$854$	1.19133	−	0.530416i	0.0407666	−	0.0181505i
$855$	0.662194	−	1.62708i	0.0226465	−	0.0556450i
$856$	−18.1877	−	3.86592i	−0.621643	−	0.132134i
$857$	−20.8740	+	46.8837i	−0.713041	+	1.60152i	0.0831972	+	0.996533i	$0.473487\pi$
$857$	−20.8740	+	46.8837i	−0.713041	+	1.60152i	−0.796238	+	0.604983i	$0.793180\pi$
$858$	13.7564	−	8.24190i	0.469634	−	0.281374i
$859$	−14.6635	−	1.54120i	−0.500312	−	0.0525849i	−0.148988	−	0.988839i	$-0.547602\pi$
$859$	−14.6635	−	1.54120i	−0.500312	−	0.0525849i	−0.351324	+	0.936254i	$0.614268\pi$
$860$	0.782292	+	0.568369i	0.0266760	+	0.0193812i
$861$	2.97981	+	0.583143i	0.101552	+	0.0198735i
$862$	−19.4419	+	33.6744i	−0.662195	+	1.14696i
$863$	13.9762	+	24.2074i	0.475754	+	0.824030i	0.999614	−	0.0277742i	$-0.00884195\pi$
$863$	13.9762	+	24.2074i	0.475754	+	0.824030i	−0.523860	+	0.851804i	$0.675509\pi$
$864$	1.36397	−	5.01394i	0.0464032	−	0.170578i
$865$	−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
$870$	−0.0498378	−	3.07923i	−0.00168966	−	0.104396i
$871$	24.6366	−	22.1828i	0.834778	−	0.751637i
$872$	6.87090	+	9.45698i	0.232678	+	0.320254i
$873$	−1.52007	+	20.9726i	−0.0514466	+	0.709817i
$874$	−4.68061	−	2.70235i	−0.158324	−	0.0914084i
$875$	−0.234003	+	0.0245947i	−0.00791073	+	0.000831452i
$876$	23.2636	−	17.4841i	0.786003	−	0.590733i
$877$	2.23390	−	21.2541i	0.0754333	−	0.717700i	−0.889807	−	0.456337i	$-0.849161\pi$
$877$	2.23390	−	21.2541i	0.0754333	−	0.717700i	0.965240	−	0.261363i	$-0.0841721\pi$
$878$	−3.81944	−	3.43904i	−0.128900	−	0.116062i
$879$	5.07401	−	5.82203i	0.171142	−	0.196372i
$880$	0.330408	−	1.55445i	0.0111381	−	0.0524004i
$881$	27.9985	−	5.95125i	0.943292	−	0.200503i	0.289501	−	0.957178i	$-0.406511\pi$
$881$	27.9985	−	5.95125i	0.943292	−	0.200503i	0.653791	+	0.756675i	$0.273177\pi$
$882$	−3.66985	+	20.5081i	−0.123570	+	0.690545i
$883$	43.9681	+	14.2861i	1.47965	+	0.480766i	0.934007	−	0.357255i	$-0.116287\pi$
$883$	43.9681	+	14.2861i	1.47965	+	0.480766i	0.545638	+	0.838021i	$0.316287\pi$
$884$	23.6947	+	7.69888i	0.796939	+	0.258941i
$885$	−6.67523	+	0.811015i	−0.224386	+	0.0272620i
$886$	27.1481	−	5.77051i	0.912058	−	0.193864i
$887$	9.30543	−	43.7786i	0.312446	−	1.46994i	−0.489215	−	0.872163i	$-0.662717\pi$
$887$	9.30543	−	43.7786i	0.312446	−	1.46994i	0.801661	−	0.597779i	$-0.203950\pi$
$888$	−1.25760	−	1.09602i	−0.0422024	−	0.0367802i
$889$	2.38222	+	2.14496i	0.0798969	+	0.0719395i
$890$	1.91497	−	18.2198i	0.0641901	−	0.610728i
$891$	−3.53053	+	13.8600i	−0.118277	+	0.464327i
$892$	−12.8508	+	1.35067i	−0.430277	+	0.0452239i
$893$	−4.16760	−	2.40616i	−0.139463	−	0.0805192i
$894$	−6.50731	−	28.3504i	−0.217637	−	0.948179i
$895$	1.68673	+	2.32158i	0.0563811	+	0.0776019i
$896$	0.174856	−	0.157441i	0.00584152	−	0.00525973i
$897$	93.1282	−	1.50730i	3.10946	−	0.0503271i
$898$		−	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
$903$	−0.127825	−	0.372768i	−0.00425375	−	0.0124049i
$904$	−4.79649	−	8.30776i	−0.159529	−	0.276312i
$905$	−4.34186	+	7.52031i	−0.144328	+	0.249984i
$906$	−2.43477	+	12.4414i	−0.0808897	+	0.413339i
$907$	23.8416	+	17.3220i	0.791649	+	0.575166i	0.908452	−	0.417989i	$-0.137265\pi$
$907$	23.8416	+	17.3220i	0.791649	+	0.575166i	−0.116804	+	0.993155i	$0.537265\pi$
$908$	−1.89206	−	0.198864i	−0.0627902	−	0.00659952i
$909$	7.31047	+	29.6411i	0.242473	+	0.983134i
$910$	−0.557564	+	1.25231i	−0.0184831	+	0.0415136i
$911$	25.1099	+	5.33727i	0.831928	+	0.176832i	0.604139	−	0.796879i	$-0.293517\pi$
$911$	25.1099	+	5.33727i	0.831928	+	0.176832i	0.227789	+	0.973711i	$0.426850\pi$
$912$	−1.01024	−	0.0896772i	−0.0334524	−	0.00296951i
$913$	−22.2487	+	9.90577i	−0.736325	+	0.327833i
$914$	−5.36673	+	16.5171i	−0.177516	+	0.546337i
$915$	5.51614	−	7.85662i	0.182358	−	0.259732i
$916$	8.50465	+	19.1018i	0.281002	+	0.631140i
$917$	−0.146018	−	0.686960i	−0.00482194	−	0.0226854i
$918$	−19.8368	+	10.0124i	−0.654712	+	0.330458i
$919$	38.1654	+	16.9923i	1.25896	+	0.560526i	0.924247	−	0.381794i	$-0.124694\pi$
$919$	38.1654	+	16.9923i	1.25896	+	0.560526i	0.334714	+	0.942320i	$0.391360\pi$
$920$	6.17609	−	6.85924i	0.203620	−	0.226143i
$921$	−15.7039	+	36.8659i	−0.517462	+	1.21477i
$922$	5.25242	−	7.22933i	0.172979	−	0.238085i
$923$	−8.52017	−	81.0640i	−0.280445	−	2.66825i
$924$	−0.474220	+	0.441093i	−0.0156007	+	0.0145109i
$925$	0.834092	−	0.481563i	0.0274248	−	0.0158337i
$926$	27.2444	−	19.7942i	0.895306	−	0.650478i
$927$	4.18042	+	30.3033i	0.137303	+	0.995291i
$928$	−1.69100	+	0.549440i	−0.0555099	+	0.0180363i
$929$	−36.4849			−1.19703			−0.598516	−	0.801111i	$-0.704243\pi$
$929$	−36.4849			−1.19703			−0.598516	+	0.801111i	$0.704243\pi$
$930$	−9.57198	−	1.17357i	−0.313877	−	0.0384829i
$931$	4.06648			0.133273
$932$	9.30190	−	3.02237i	0.304694	−	0.0990010i
$933$	16.9492	−	7.87737i	0.554893	−	0.257894i
$934$	−17.2356	+	12.5224i	−0.563967	+	0.409746i
$935$	−5.88536	+	3.39791i	−0.192472	+	0.111124i
$936$	15.7287	−	7.62202i	0.514108	−	0.249133i
$937$	−0.854868	−	8.13353i	−0.0279273	−	0.265711i	−0.999572	−	0.0292638i	$-0.990684\pi$
$937$	−0.854868	−	8.13353i	−0.0279273	−	0.265711i	0.971644	−	0.236447i	$-0.0759830\pi$
$938$	−0.786968	+	1.08317i	−0.0256954	+	0.0353667i
$939$	31.2718	+	13.3210i	1.02052	+	0.434714i
$940$	5.49917	−	6.10745i	0.179363	−	0.199203i
$941$	4.82534	+	2.14838i	0.157302	+	0.0700352i	0.483877	−	0.875136i	$-0.339228\pi$
$941$	4.82534	+	2.14838i	0.157302	+	0.0700352i	−0.326576	+	0.945171i	$0.605895\pi$
$942$	−9.97258	+	17.9373i	−0.324924	+	0.584428i
$943$	−14.2976	−	67.2650i	−0.465595	−	2.19045i
$944$	1.57907	+	3.54665i	0.0513943	+	0.115434i
$945$	−0.433794	−	1.14307i	−0.0141113	−	0.0371839i
$946$	−0.474860	+	1.46147i	−0.0154390	+	0.0475165i
$947$	43.3109	−	19.2832i	1.40741	−	0.626621i	0.444340	−	0.895858i	$-0.353438\pi$
$947$	43.3109	−	19.2832i	1.40741	−	0.626621i	0.963074	+	0.269237i	$0.0867716\pi$
$948$	−1.94338	+	21.8928i	−0.0631181	+	0.711046i
$949$	95.7483	+	20.3519i	3.10812	+	0.660652i
$950$	0.238167	−	0.534933i	0.00772717	−	0.0173555i
$951$	−15.2630	−	25.4752i	−0.494938	−	0.826089i
$952$	−1.00067	−	0.105175i	−0.0324319	−	0.00340873i
$953$	−6.88120	−	4.99948i	−0.222904	−	0.161949i	0.470729	−	0.882278i	$-0.343991\pi$
$953$	−6.88120	−	4.99948i	−0.222904	−	0.161949i	−0.693633	+	0.720329i	$0.743991\pi$
$954$	4.90135	+	2.62208i	0.158687	+	0.0848930i
$955$	−7.29863	+	12.6416i	−0.236178	+	0.409072i
$956$	5.25537	+	9.10258i	0.169971	+	0.294398i
$957$	4.62946	−	1.58748i	0.149649	−	0.0513159i
$958$	−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
$963$	53.5820	+	15.5117i	1.72666	+	0.499859i
$964$	−11.6098	+	10.4535i	−0.373926	+	0.336684i
$965$	12.1286	+	16.6936i	0.390434	+	0.537386i
$966$	−3.66624	+	0.841517i	−0.117959	+	0.0270754i
$967$	−34.8024	−	20.0932i	−1.11917	−	0.646153i	−0.177981	−	0.984034i	$-0.556957\pi$
$967$	−34.8024	−	20.0932i	−1.11917	−	0.646153i	−0.941189	+	0.337881i	$0.890290\pi$
$968$	−8.42810	+	0.885829i	−0.270889	+	0.0284716i
$969$	2.60574	+	3.46708i	0.0837083	+	0.111379i
$970$	−0.732663	+	6.97082i	−0.0235244	+	0.223820i
$971$	−3.05008	−	2.74631i	−0.0978819	−	0.0881332i	0.618737	−	0.785598i	$-0.287645\pi$
$971$	−3.05008	−	2.74631i	−0.0978819	−	0.0881332i	−0.716619	+	0.697465i	$0.754311\pi$
$972$	−5.16856	+	14.7067i	−0.165782	+	0.471716i
$973$	−0.0778994	+	0.366488i	−0.00249734	+	0.0117491i
$974$	−39.3829	+	8.37110i	−1.26191	+	0.268227i
$975$	1.21707	+	10.0174i	0.0389775	+	0.320812i
$976$	−5.27112	−	1.71269i	−0.168725	−	0.0548219i
$977$	−57.2743	−	18.6095i	−1.83237	−	0.595372i	−0.999096	−	0.0425075i	$-0.986465\pi$
$977$	−57.2743	−	18.6095i	−1.83237	−	0.595372i	−0.833271	−	0.552865i	$-0.813535\pi$
$978$	−0.352297	−	2.89966i	−0.0112652	−	0.0927209i
$979$	28.4777	−	6.05312i	0.910150	−	0.193458i
$980$	−1.44387	+	6.79288i	−0.0461228	+	0.216991i
$981$	−18.5079	−	29.7868i	−0.590911	−	0.951019i
$982$	−14.7565	−	13.2868i	−0.470899	−	0.423999i
$983$	−1.38652	+	13.1919i	−0.0442233	+	0.420756i	0.949904	+	0.312541i	$0.101180\pi$
$983$	−1.38652	+	13.1919i	−0.0442233	+	0.420756i	−0.994128	+	0.108215i	$0.965486\pi$
$984$	−7.75306	−	10.3159i	−0.247159	−	0.328858i
$985$	2.33527	−	0.245446i	0.0744078	−	0.00782057i
$986$	6.58475	+	3.80170i	0.209701	+	0.121071i
$987$	−3.26441	+	0.749284i	−0.103907	+	0.0238500i
$988$	−2.00522	−	2.75995i	−0.0637946	−	0.0878057i
$989$	−6.63266	+	5.97207i	−0.210906	+	0.189901i
$990$	−1.32574	+	4.57949i	−0.0421348	+	0.145546i
$991$			1.71913i			0.0546099i	0.999627	+	0.0273049i	$0.00869251\pi$
$991$			1.71913i			0.0546099i	−0.999627	+	0.0273049i	$0.991307\pi$
$992$	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
$996$	−25.1086	+	8.60996i	−0.795598	+	0.272817i
$997$	3.86651	+	6.69699i	0.122454	+	0.212096i	0.920735	−	0.390189i	$-0.127590\pi$
$997$	3.86651	+	6.69699i	0.122454	+	0.212096i	−0.798281	+	0.602285i	$0.794257\pi$
$998$	5.47020	−	9.47466i	0.173156	−	0.299915i
$999$	3.52525	+	3.55220i	0.111534	+	0.112387i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.10	✓	176	3.2	odd	2	inner
930.2.br.a.11.15	yes	176	1.1	even	1	trivial
930.2.br.a.761.10	yes	176	31.17	odd	30	inner
930.2.br.a.761.15	yes	176	93.17	even	30	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.730003 - 1.57070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.17965 - 1.26824i) q^{6} +(0.0245947 + 0.234003i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.93419 + 2.29323i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.730003 - 1.57070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.17965 - 1.26824i) q^{6} +(0.0245947 + 0.234003i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.93419 + 2.29323i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-1.45178 - 0.646376i) q^{11} +(-1.51382 - 0.841637i) q^{12} +(-1.21131 - 5.69874i) q^{13} +(0.0957017 + 0.214950i) q^{14} +(1.41755 + 0.995264i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.90661 + 1.73934i) q^{17} +(-1.13088 + 2.77869i) q^{18} +(0.572761 + 0.121744i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.349594 - 0.209453i) q^{21} +(-1.58047 - 0.166114i) q^{22} +(-7.46724 - 5.42527i) q^{23} +(-1.69981 - 0.332649i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.91303 - 5.04551i) q^{26} +(5.01394 + 1.36397i) 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} +(0.0445444 + 2.75217i) q^{33} +(-3.17793 + 2.86142i) q^{34} +(-0.138301 - 0.190355i) q^{35} +(-0.216867 + 2.99215i) q^{36} +(0.834092 + 0.481563i) q^{37} +(0.582349 - 0.0612073i) q^{38} +(-8.06676 + 6.06270i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(5.53676 + 4.98532i) q^{41} +(0.267759 - 0.307232i) q^{42} +(0.201044 - 0.945836i) q^{43} +(-1.55445 + 0.330408i) q^{44} +(0.528444 - 2.95309i) q^{45} +(-8.77827 - 2.85223i) q^{46} +(-7.81614 - 2.53962i) q^{47} +(-1.71941 + 0.208901i) q^{48} +(6.79288 - 1.44387i) q^{49} +(0.207912 - 0.978148i) q^{50} +(5.58381 + 4.86639i) q^{51} +(-4.32960 - 3.89839i) q^{52} +(0.193679 - 1.84273i) q^{53} +(5.19003 - 0.252181i) q^{54} +(1.58047 - 0.166114i) q^{55} +(0.203769 + 0.117646i) q^{56} +(-0.226894 - 0.988508i) q^{57} +(-1.04510 - 1.43845i) q^{58} +(-2.88510 + 2.59776i) q^{59} +(1.73182 - 0.0280299i) 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} +(0.892832 + 2.60371i) q^{66} +(2.84513 + 4.92790i) q^{67} +(-2.13816 + 3.70340i) q^{68} +(-3.07036 + 15.6893i) q^{69} +(-0.190355 - 0.138301i) q^{70} +(13.9140 + 1.46242i) q^{71} +(0.718372 + 2.91272i) q^{72} +(-6.83385 + 15.3491i) q^{73} +(0.942080 + 0.200245i) q^{74} +(-1.72527 - 0.153149i) q^{75} +(0.534933 - 0.238167i) q^{76} +(0.115548 - 0.355619i) q^{77} +(-5.79847 + 8.25873i) q^{78} +(-5.16130 - 11.5925i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-1.51780 - 8.87109i) q^{81} +(6.80632 + 3.03037i) q^{82} +(10.2545 - 11.3888i) q^{83} +(0.159714 - 0.374937i) q^{84} +(2.51356 - 3.45962i) q^{85} +(-0.101076 - 0.961670i) q^{86} +(-2.25496 + 2.09744i) q^{87} +(-1.37627 + 0.794588i) q^{88} +(-14.8213 + 10.7683i) q^{89} +(-0.409975 - 2.97185i) q^{90} +(1.30373 - 0.423607i) q^{91} -9.23002 q^{92} +(5.53277 + 7.89864i) q^{93} -8.21838 q^{94} +(-0.556897 + 0.180947i) q^{95} +(-1.57070 + 0.730003i) q^{96} +(5.67058 - 4.11992i) q^{97} +(6.01423 - 3.47232i) q^{98} +(4.29032 - 2.07906i) 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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