LMFDB - Embedded newform 930.2.br.b.11.7

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			11.7
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.145925 + 1.72589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.672113 - 1.59633i) q^{6} +(-0.228500 - 2.17403i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.95741 + 0.503701i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.145925 + 1.72589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.672113 - 1.59633i) q^{6} +(-0.228500 - 2.17403i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.95741 + 0.503701i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.37174 - 1.50120i) q^{11} +(1.13251 + 1.31050i) q^{12} +(-0.565435 - 2.66016i) q^{13} +(0.889128 + 1.99701i) q^{14} +(-0.989321 - 1.42170i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.18937 - 1.86523i) q^{17} +(2.65701 - 1.39294i) q^{18} +(7.02672 + 1.49358i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(3.71880 - 0.711610i) q^{21} +(3.67062 + 0.385797i) q^{22} +(4.43137 + 3.21958i) q^{23} +(-1.48205 - 0.896399i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.35980 + 2.35524i) q^{26} +(-1.30089 - 5.03067i) q^{27} +(-1.46272 - 1.62452i) q^{28} +(1.85284 + 5.70246i) q^{29} +(1.38023 + 1.04640i) q^{30} +(3.69419 - 4.16569i) q^{31} +1.00000i q^{32} +(2.09889 - 6.03833i) q^{33} +(-3.40794 + 3.06853i) q^{34} +(1.28490 + 1.76851i) q^{35} +(-2.09653 + 2.14583i) q^{36} +(-2.33106 - 1.34584i) q^{37} +(-7.14435 + 0.750901i) q^{38} +(4.50865 - 1.36406i) q^{39} +(0.104528 - 0.994522i) q^{40} +(4.55509 + 4.10142i) q^{41} +(-3.31689 + 1.82595i) q^{42} +(0.429934 - 2.02268i) q^{43} +(-3.61018 + 0.767368i) q^{44} +(2.30934 - 1.91492i) q^{45} +(-5.20938 - 1.69263i) q^{46} +(-10.3554 - 3.36468i) q^{47} +(1.68651 + 0.394548i) q^{48} +(2.17284 - 0.461852i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(3.83052 + 6.95823i) q^{51} +(-2.02105 - 1.81976i) q^{52} +(0.296898 - 2.82480i) q^{53} +(2.79179 + 4.38246i) q^{54} +(3.67062 - 0.385797i) q^{55} +(1.89313 + 1.09300i) q^{56} +(-1.55238 + 12.3453i) q^{57} +(-3.52431 - 4.85080i) q^{58} +(2.06251 - 1.85710i) q^{59} +(-1.63603 - 0.568675i) q^{60} -15.3542i q^{61} +(-2.22611 + 5.10337i) q^{62} +(1.77083 + 6.31440i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.81976 + 2.02105i) q^{65} +(-0.130211 + 6.39139i) q^{66} +(2.98226 + 5.16542i) q^{67} +(2.29292 - 3.97146i) q^{68} +(-4.91000 + 8.11788i) q^{69} +(-1.76851 - 1.28490i) q^{70} +(11.8911 + 1.24981i) q^{71} +(1.33082 - 2.68866i) q^{72} +(0.731646 - 1.64330i) q^{73} +(2.63285 + 0.559630i) q^{74} +(1.56763 + 0.736572i) q^{75} +(6.56264 - 2.92187i) q^{76} +(-2.49320 + 7.67329i) q^{77} +(-3.86646 + 2.69055i) q^{78} +(4.31032 + 9.68114i) q^{79} +(0.207912 + 0.978148i) q^{80} +(8.49257 - 2.97930i) q^{81} +(-5.59956 - 2.49308i) q^{82} +(-0.948324 + 1.05322i) q^{83} +(2.59030 - 2.76156i) q^{84} +(-2.69549 + 3.71002i) q^{85} +(0.216151 + 2.05654i) q^{86} +(-9.57145 + 4.02993i) q^{87} +(3.19636 - 1.84542i) q^{88} +(2.65594 - 1.92965i) q^{89} +(-1.60457 + 2.53483i) q^{90} +(-5.65407 + 1.83712i) q^{91} +5.47747 q^{92} +(7.72861 + 5.76790i) q^{93} +10.8883 q^{94} +(-6.83210 + 2.21989i) q^{95} +(-1.72589 + 0.145925i) q^{96} +(-8.91550 + 6.47749i) q^{97} +(-1.92378 + 1.11069i) q^{98} +(10.7278 + 2.74131i) 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} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 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 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * 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
$3$	0.145925	+	1.72589i	0.0842496	+	0.996445i
$3$	0.145925	+	1.72589i	0.0842496	+	0.996445i
$4$	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
$6$	−0.672113	−	1.59633i	−0.274389	−	0.651698i
$7$	−0.228500	−	2.17403i	−0.0863647	−	0.821706i	−0.948872	−	0.315661i	$-0.897774\pi$
$7$	−0.228500	−	2.17403i	−0.0863647	−	0.821706i	0.862507	−	0.506045i	$-0.168893\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−2.95741	+	0.503701i	−0.985804	+	0.167900i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−3.37174	−	1.50120i	−1.01662	−	0.452628i	−0.170350	−	0.985384i	$-0.554490\pi$
$11$	−3.37174	−	1.50120i	−1.01662	−	0.452628i	−0.846269	+	0.532755i	$0.821157\pi$
$12$	1.13251	+	1.31050i	0.326927	+	0.378310i
$13$	−0.565435	−	2.66016i	−0.156824	−	0.737797i	−0.984329	−	0.176340i	$-0.943574\pi$
$13$	−0.565435	−	2.66016i	−0.156824	−	0.737797i	0.827506	−	0.561457i	$-0.189759\pi$
$14$	0.889128	+	1.99701i	0.237629	+	0.533724i
$15$	−0.989321	−	1.42170i	−0.255442	−	0.367083i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.18937	−	1.86523i	1.01607	−	0.452385i	0.169995	−	0.985445i	$-0.445625\pi$
$17$	4.18937	−	1.86523i	1.01607	−	0.452385i	0.846077	+	0.533060i	$0.178958\pi$
$18$	2.65701	−	1.39294i	0.626264	−	0.328319i
$19$	7.02672	+	1.49358i	1.61204	+	0.342650i	0.923812	−	0.382846i	$-0.125056\pi$
$19$	7.02672	+	1.49358i	1.61204	+	0.342650i	0.688227	+	0.725495i	$0.258389\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	3.71880	−	0.711610i	0.811508	−	0.155286i
$22$	3.67062	+	0.385797i	0.782578	+	0.0822522i
$23$	4.43137	+	3.21958i	0.924004	+	0.671328i	0.944517	−	0.328462i	$-0.106530\pi$
$23$	4.43137	+	3.21958i	0.924004	+	0.671328i	−0.0205136	+	0.999790i	$0.506530\pi$
$24$	−1.48205	−	0.896399i	−0.302522	−	0.182977i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.35980	+	2.35524i	0.266678	+	0.461900i
$27$	−1.30089	−	5.03067i	−0.250357	−	0.968154i
$28$	−1.46272	−	1.62452i	−0.276429	−	0.307005i
$29$	1.85284	+	5.70246i	0.344064	+	1.05892i	0.962083	+	0.272756i	$0.0879353\pi$
$29$	1.85284	+	5.70246i	0.344064	+	1.05892i	−0.618019	+	0.786163i	$0.712065\pi$
$30$	1.38023	+	1.04640i	0.251995	+	0.191046i
$31$	3.69419	−	4.16569i	0.663496	−	0.748180i
$31$	3.69419	−	4.16569i	0.663496	−	0.748180i
$32$			1.00000i			0.176777i
$33$	2.09889	−	6.03833i	0.365369	−	1.05114i
$34$	−3.40794	+	3.06853i	−0.584458	+	0.526248i
$35$	1.28490	+	1.76851i	0.217188	+	0.298933i
$36$	−2.09653	+	2.14583i	−0.349421	+	0.357638i
$37$	−2.33106	−	1.34584i	−0.383224	−	0.221254i	0.295996	−	0.955189i	$-0.404348\pi$
$37$	−2.33106	−	1.34584i	−0.383224	−	0.221254i	−0.679220	+	0.733935i	$0.737682\pi$
$38$	−7.14435	+	0.750901i	−1.15897	+	0.121812i
$39$	4.50865	−	1.36406i	0.721961	−	0.218425i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	4.55509	+	4.10142i	0.711386	+	0.640535i	0.943200	−	0.332225i	$-0.107799\pi$
$41$	4.55509	+	4.10142i	0.711386	+	0.640535i	−0.231814	+	0.972760i	$0.574466\pi$
$42$	−3.31689	+	1.82595i	−0.511807	+	0.281751i
$43$	0.429934	−	2.02268i	0.0655643	−	0.308456i	−0.933130	−	0.359539i	$-0.882934\pi$
$43$	0.429934	−	2.02268i	0.0655643	−	0.308456i	0.998694	+	0.0510832i	$0.0162674\pi$
$44$	−3.61018	+	0.767368i	−0.544255	+	0.115685i
$45$	2.30934	−	1.91492i	0.344257	−	0.285460i
$46$	−5.20938	−	1.69263i	−0.768082	−	0.249565i
$47$	−10.3554	−	3.36468i	−1.51049	−	0.490789i	−0.567436	−	0.823418i	$-0.692064\pi$
$47$	−10.3554	−	3.36468i	−1.51049	−	0.490789i	−0.943058	+	0.332629i	$0.892064\pi$
$48$	1.68651	+	0.394548i	0.243427	+	0.0569480i
$49$	2.17284	−	0.461852i	0.310406	−	0.0659789i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	3.83052	+	6.95823i	0.536380	+	0.974347i
$52$	−2.02105	−	1.81976i	−0.280269	−	0.252356i
$53$	0.296898	−	2.82480i	0.0407821	−	0.388016i	−0.955024	−	0.296528i	$-0.904171\pi$
$53$	0.296898	−	2.82480i	0.0407821	−	0.388016i	0.995806	−	0.0914875i	$-0.0291622\pi$
$54$	2.79179	+	4.38246i	0.379914	+	0.596377i
$55$	3.67062	−	0.385797i	0.494946	−	0.0520209i
$56$	1.89313	+	1.09300i	0.252981	+	0.146059i
$57$	−1.55238	+	12.3453i	−0.205618	+	1.63518i
$58$	−3.52431	−	4.85080i	−0.462765	−	0.636941i
$59$	2.06251	−	1.85710i	0.268517	−	0.241773i	−0.523862	−	0.851803i	$-0.675509\pi$
$59$	2.06251	−	1.85710i	0.268517	−	0.241773i	0.792378	+	0.610030i	$0.208843\pi$
$60$	−1.63603	−	0.568675i	−0.211211	−	0.0734156i
$61$		−	15.3542i		−	1.96590i	−0.183874	−	0.982950i	$-0.558864\pi$
$61$		−	15.3542i		−	1.96590i	0.183874	−	0.982950i	$-0.441136\pi$
$62$	−2.22611	+	5.10337i	−0.282717	+	0.648129i
$63$	1.77083	+	6.31440i	0.223103	+	0.795540i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	1.81976	+	2.02105i	0.225714	+	0.250681i
$66$	−0.130211	+	6.39139i	−0.0160279	+	0.786725i
$67$	2.98226	+	5.16542i	0.364341	+	0.631056i	0.988670	−	0.150105i	$-0.0479611\pi$
$67$	2.98226	+	5.16542i	0.364341	+	0.631056i	−0.624330	+	0.781161i	$0.714628\pi$
$68$	2.29292	−	3.97146i	0.278057	−	0.481610i
$69$	−4.91000	+	8.11788i	−0.591094	+	0.977278i
$70$	−1.76851	−	1.28490i	−0.211378	−	0.153575i
$71$	11.8911	+	1.24981i	1.41122	+	0.148325i	0.779272	−	0.626686i	$-0.215589\pi$
$71$	11.8911	+	1.24981i	1.41122	+	0.148325i	0.631948	+	0.775011i	$0.282256\pi$
$72$	1.33082	−	2.68866i	0.156839	−	0.316862i
$73$	0.731646	−	1.64330i	0.0856327	−	0.192334i	−0.865653	−	0.500644i	$-0.833097\pi$
$73$	0.731646	−	1.64330i	0.0856327	−	0.192334i	0.951286	+	0.308310i	$0.0997633\pi$
$74$	2.63285	+	0.559630i	0.306063	+	0.0650557i
$75$	1.56763	+	0.736572i	0.181014	+	0.0850520i
$76$	6.56264	−	2.92187i	0.752786	−	0.335162i
$77$	−2.49320	+	7.67329i	−0.284127	+	0.874453i
$78$	−3.86646	+	2.69055i	−0.437790	+	0.304645i
$79$	4.31032	+	9.68114i	0.484949	+	1.08921i	0.975938	+	0.218047i	$0.0699687\pi$
$79$	4.31032	+	9.68114i	0.484949	+	1.08921i	−0.490989	+	0.871166i	$0.663365\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	8.49257	−	2.97930i	0.943619	−	0.331033i
$82$	−5.59956	−	2.49308i	−0.618368	−	0.275315i
$83$	−0.948324	+	1.05322i	−0.104092	+	0.115606i	−0.792939	−	0.609300i	$-0.791450\pi$
$83$	−0.948324	+	1.05322i	−0.104092	+	0.115606i	0.688847	+	0.724906i	$0.258117\pi$
$84$	2.59030	−	2.76156i	0.282624	−	0.301311i
$85$	−2.69549	+	3.71002i	−0.292367	+	0.402409i
$86$	0.216151	+	2.05654i	0.0233082	+	0.221762i
$87$	−9.57145	+	4.02993i	−1.02617	+	0.432054i
$88$	3.19636	−	1.84542i	0.340733	−	0.196722i
$89$	2.65594	−	1.92965i	0.281529	−	0.204543i	−0.438055	−	0.898948i	$-0.644332\pi$
$89$	2.65594	−	1.92965i	0.281529	−	0.204543i	0.719584	+	0.694405i	$0.244332\pi$
$90$	−1.60457	+	2.53483i	−0.169137	+	0.267194i
$91$	−5.65407	+	1.83712i	−0.592708	+	0.192582i
$92$	5.47747			0.571066
$93$	7.72861	+	5.76790i	0.801419	+	0.598103i
$94$	10.8883			1.12305
$95$	−6.83210	+	2.21989i	−0.700959	+	0.227755i
$96$	−1.72589	+	0.145925i	−0.176148	+	0.0148934i
$97$	−8.91550	+	6.47749i	−0.905231	+	0.657689i	−0.939804	−	0.341713i	$-0.888993\pi$
$97$	−8.91550	+	6.47749i	−0.905231	+	0.657689i	0.0345729	+	0.999402i	$0.488993\pi$
$98$	−1.92378	+	1.11069i	−0.194331	+	0.112197i
$99$	10.7278	+	2.74131i	1.07818	+	0.275512i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−3.79042	+	5.21707i	−0.377161	+	0.519117i	−0.954830	−	0.297154i	$-0.903963\pi$
$101$	−3.79042	+	5.21707i	−0.377161	+	0.519117i	0.577669	+	0.816271i	$0.303963\pi$
$102$	−5.79325	−	5.43397i	−0.573617	−	0.538044i
$103$	7.22868	−	8.02826i	0.712263	−	0.791048i	−0.273015	−	0.962010i	$-0.588021\pi$
$103$	7.22868	−	8.02826i	0.712263	−	0.791048i	0.985278	+	0.170962i	$0.0546875\pi$
$104$	2.48447	+	1.10616i	0.243623	+	0.108468i
$105$	−2.86477	+	2.47567i	−0.279573	+	0.241601i
$106$	0.590543	+	2.77829i	0.0573586	+	0.269851i
$107$	−8.22008	−	18.4626i	−0.794665	−	1.78485i	−0.592641	−	0.805467i	$-0.701915\pi$
$107$	−8.22008	−	18.4626i	−0.794665	−	1.78485i	−0.202024	−	0.979380i	$-0.564752\pi$
$108$	−4.00940	−	3.30526i	−0.385805	−	0.318048i
$109$	−4.07983	+	12.5564i	−0.390777	+	1.20269i	0.541424	+	0.840749i	$0.317885\pi$
$109$	−4.07983	+	12.5564i	−0.390777	+	1.20269i	−0.932202	+	0.361939i	$0.882115\pi$
$110$	−3.37174	+	1.50120i	−0.321483	+	0.143134i
$111$	1.98261	−	4.21955i	0.188181	−	0.400502i
$112$	−2.13823	−	0.454496i	−0.202044	−	0.0429458i
$113$	4.46461	−	10.0277i	0.419995	−	0.943324i	−0.572371	−	0.819995i	$-0.693976\pi$
$113$	4.46461	−	10.0277i	0.419995	−	0.943324i	0.992366	−	0.123329i	$-0.0393572\pi$
$114$	−2.33851	−	12.2208i	−0.219022	−	1.14458i
$115$	−5.44746	−	0.572552i	−0.507979	−	0.0533907i
$116$	4.85080	+	3.52431i	0.450385	+	0.327224i
$117$	3.01215	+	7.58239i	0.278474	+	0.700992i
$118$	−1.38769	+	2.40356i	−0.127748	+	0.221265i
$119$	−5.01233	−	8.68162i	−0.459480	−	0.795843i
$120$	1.73169	+	0.0352796i	0.158081	+	0.00322058i
$121$	1.75463	+	1.94872i	0.159512	+	0.177156i
$122$	4.74470	+	14.6027i	0.429565	+	1.32206i
$123$	−6.41392	+	8.46010i	−0.578323	+	0.762822i
$124$	0.540130	−	5.54150i	0.0485051	−	0.497642i
$125$			1.00000i			0.0894427i
$126$	−3.63541	−	5.45814i	−0.323868	−	0.486250i
$127$	10.9690	−	9.87650i	0.973338	−	0.876397i	−0.0190163	−	0.999819i	$-0.506053\pi$
$127$	10.9690	−	9.87650i	0.973338	−	0.876397i	0.992354	+	0.123422i	$0.0393868\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	3.55366	+	0.446861i	0.312883	+	0.0393439i
$130$	−2.35524	−	1.35980i	−0.206568	−	0.119262i
$131$	19.8470	−	2.08600i	1.73404	−	0.182255i	0.815814	−	0.578315i	$-0.196289\pi$
$131$	19.8470	−	2.08600i	1.73404	−	0.182255i	0.918225	+	0.396060i	$0.129623\pi$
$132$	−1.85121	−	6.11881i	−0.161127	−	0.532574i
$133$	1.64147	−	15.6176i	0.142334	−	1.35421i
$134$	−4.43250	−	3.99104i	−0.382909	−	0.344773i
$135$	3.64194	+	3.70624i	0.313449	+	0.318983i
$136$	−0.953450	+	4.48563i	−0.0817577	+	0.384640i
$137$	5.43517	−	1.15528i	0.464358	−	0.0987024i	0.0302095	−	0.999544i	$-0.490383\pi$
$137$	5.43517	−	1.15528i	0.464358	−	0.0987024i	0.434149	+	0.900841i	$0.357049\pi$
$138$	2.16112	−	9.23783i	0.183967	−	0.786377i
$139$	5.01572	+	1.62971i	0.425428	+	0.138230i	0.513903	−	0.857848i	$-0.328199\pi$
$139$	5.01572	+	1.62971i	0.425428	+	0.138230i	−0.0884746	+	0.996078i	$0.528199\pi$
$140$	2.07901	+	0.675512i	0.175709	+	0.0570912i
$141$	4.29597	−	18.3633i	0.361786	−	1.54647i
$142$	−11.6954	+	2.48593i	−0.981453	+	0.208614i
$143$	−2.08693	+	9.81822i	−0.174518	+	0.821041i
$144$	−0.434843	+	2.96832i	−0.0362369	+	0.247360i
$145$	−4.45583	−	4.01205i	−0.370037	−	0.333183i
$146$	−0.188028	+	1.78897i	−0.0155613	+	0.148056i
$147$	1.11418	+	3.68270i	0.0918959	+	0.303744i
$148$	−2.67693	+	0.281356i	−0.220042	+	0.0231274i
$149$	−12.4377	−	7.18089i	−1.01893	−	0.588281i	−0.105138	−	0.994458i	$-0.533529\pi$
$149$	−12.4377	−	7.18089i	−1.01893	−	0.588281i	−0.913795	+	0.406176i	$0.866862\pi$
$150$	−1.71852	−	0.216097i	−0.140316	−	0.0176443i
$151$	13.9180	+	19.1565i	1.13263	+	1.55893i	0.782975	+	0.622054i	$0.213701\pi$
$151$	13.9180	+	19.1565i	1.13263	+	1.55893i	0.349656	+	0.936878i	$0.386299\pi$
$152$	−5.33853	+	4.80683i	−0.433012	+	0.389886i
$153$	−11.4502	+	7.62644i	−0.925693	+	0.616561i
$154$		−	8.06818i		−	0.650152i
$155$	−1.11642	+	5.45469i	−0.0896727	+	0.438131i
$156$	2.84580	−	3.75367i	0.227846	−	0.300534i
$157$	−3.20316	−	9.85832i	−0.255640	−	0.786779i	−0.993703	−	0.112047i	$-0.964259\pi$
$157$	−3.20316	−	9.85832i	−0.255640	−	0.786779i	0.738063	−	0.674732i	$-0.235741\pi$
$158$	−7.09099	−	7.87534i	−0.564129	−	0.626529i
$159$	4.91862	+	0.100207i	0.390072	+	0.00794691i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	5.98689	−	10.3696i	0.471833	−	0.817238i
$162$	−7.15626	+	5.45783i	−0.562249	+	0.428808i
$163$	7.20253	+	5.23294i	0.564145	+	0.409876i	0.832974	−	0.553312i	$-0.186636\pi$
$163$	7.20253	+	5.23294i	0.564145	+	0.409876i	−0.268828	+	0.963188i	$0.586636\pi$
$164$	6.09590	+	0.640705i	0.476010	+	0.0500307i
$165$	1.20148	+	6.27879i	0.0935349	+	0.488803i
$166$	0.576447	−	1.29472i	0.0447409	−	0.100490i
$167$	−11.1787	−	2.37611i	−0.865036	−	0.183869i	−0.246037	−	0.969260i	$-0.579128\pi$
$167$	−11.1787	−	2.37611i	−0.865036	−	0.183869i	−0.619000	+	0.785391i	$0.712462\pi$
$168$	−1.61015	+	3.42684i	−0.124226	+	0.264387i
$169$	5.11934	−	2.27928i	0.393795	−	0.175329i
$170$	1.41710	−	4.36139i	0.108687	−	0.334504i
$171$	−21.5332	−	0.877754i	−1.64669	−	0.0671235i
$172$	−0.841077	−	1.88909i	−0.0641315	−	0.144042i
$173$	−2.49687	−	11.7469i	−0.189834	−	0.893098i	−0.965185	−	0.261568i	$-0.915761\pi$
$173$	−2.49687	−	11.7469i	−0.189834	−	0.893098i	0.775351	−	0.631530i	$-0.217573\pi$
$174$	7.85767	−	6.79043i	0.595689	−	0.514781i
$175$	−1.99701	−	0.889128i	−0.150960	−	0.0672118i
$176$	−2.46965	+	2.74282i	−0.186157	+	0.206748i
$177$	3.50612	+	3.28868i	0.263536	+	0.247193i
$178$	−1.92965	+	2.65594i	−0.144634	+	0.199071i
$179$	−1.99102	−	18.9433i	−0.148816	−	1.41589i	−0.772899	−	0.634529i	$-0.781194\pi$
$179$	−1.99102	−	18.9433i	−0.148816	−	1.41589i	0.624083	−	0.781358i	$-0.285473\pi$
$180$	0.742734	−	2.90660i	0.0553602	−	0.216645i
$181$	−10.2133	+	5.89665i	−0.759148	+	0.438294i	−0.828990	−	0.559264i	$-0.811084\pi$
$181$	−10.2133	+	5.89665i	−0.759148	+	0.438294i	0.0698417	+	0.997558i	$0.477751\pi$
$182$	4.80964	−	3.49441i	0.356514	−	0.259023i
$183$	26.4996	−	2.24055i	1.95891	−	0.165626i
$184$	−5.20938	+	1.69263i	−0.384041	+	0.124782i
$185$	2.69167			0.197896
$186$	−9.13272	−	3.09732i	−0.669644	−	0.227107i
$187$	−16.9256			−1.23772
$188$	−10.3554	+	3.36468i	−0.755247	+	0.245395i
$189$	−10.6396	+	3.97769i	−0.773915	+	0.289334i
$190$	5.81173	−	4.22247i	0.421628	−	0.306330i
$191$	−9.12036	+	5.26564i	−0.659926	+	0.381009i	−0.792249	−	0.610198i	$-0.791090\pi$
$191$	−9.12036	+	5.26564i	−0.659926	+	0.381009i	0.132323	+	0.991207i	$0.457757\pi$
$192$	1.59633	−	0.672113i	0.115205	−	0.0485056i
$193$	1.50082	+	14.2794i	0.108032	+	1.02785i	0.905458	+	0.424436i	$0.139528\pi$
$193$	1.50082	+	14.2794i	0.108032	+	1.02785i	−0.797426	+	0.603416i	$0.793806\pi$
$194$	6.47749	−	8.91550i	0.465056	−	0.640095i
$195$	−3.22257	+	3.43564i	−0.230773	+	0.246031i
$196$	1.48640	−	1.65081i	0.106171	−	0.117915i
$197$	−12.7875	−	5.69337i	−0.911074	−	0.405636i	−0.102975	−	0.994684i	$-0.532836\pi$
$197$	−12.7875	−	5.69337i	−0.911074	−	0.405636i	−0.808098	+	0.589048i	$0.799503\pi$
$198$	−11.0498	+	0.707930i	−0.785279	+	0.0503104i
$199$	−2.32358	−	10.9316i	−0.164714	−	0.774920i	−0.980493	−	0.196555i	$-0.937025\pi$
$199$	−2.32358	−	10.9316i	−0.164714	−	0.774920i	0.815779	−	0.578364i	$-0.196309\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−8.47977	+	5.90082i	−0.598117	+	0.416211i
$202$	1.99274	−	6.13303i	0.140209	−	0.431518i
$203$	11.9739	−	5.33114i	0.840405	−	0.374172i
$204$	7.18890	+	3.37780i	0.503324	+	0.236493i
$205$	−5.99554	−	1.27439i	−0.418747	−	0.0890073i
$206$	−4.39401	+	9.86911i	−0.306145	+	0.687614i
$207$	−14.7271	−	7.28953i	−1.02360	−	0.506657i
$208$	−2.70470	−	0.284275i	−0.187537	−	0.0197109i
$209$	−21.4501	−	15.5844i	−1.48374	−	1.07800i
$210$	1.95953	−	3.23976i	0.135221	−	0.223565i
$211$	2.89490	−	5.01412i	0.199293	−	0.345186i	−0.749006	−	0.662563i	$-0.769469\pi$
$211$	2.89490	−	5.01412i	0.199293	−	0.345186i	0.948300	+	0.317377i	$0.102802\pi$
$212$	−1.42018	−	2.45982i	−0.0975382	−	0.168941i
$213$	−0.421826	+	20.7052i	−0.0289031	+	1.41870i
$214$	13.5230	+	15.0188i	0.924415	+	1.02667i
$215$	0.639006	+	1.96666i	0.0435798	+	0.134125i
$216$	4.83455	+	1.90451i	0.328949	+	0.129586i
$217$	−9.90045	−	7.07941i	−0.672086	−	0.480582i
$218$		−	13.2026i		−	0.894194i
$219$	2.94293	+	1.02294i	0.198865	+	0.0691242i
$220$	2.74282	−	2.46965i	0.184921	−	0.166504i
$221$	−7.33064	−	10.0898i	−0.493112	−	0.678711i
$222$	−0.581664	+	4.62569i	−0.0390387	+	0.310456i
$223$	2.36191	+	1.36365i	0.158165	+	0.0913169i	0.576994	−	0.816749i	$-0.304226\pi$
$223$	2.36191	+	1.36365i	0.158165	+	0.0913169i	−0.418828	+	0.908065i	$0.637559\pi$
$224$	2.17403	−	0.228500i	0.145258	−	0.0152673i
$225$	−1.04249	+	2.81304i	−0.0694992	+	0.187536i
$226$	−1.14737	+	10.9165i	−0.0763221	+	0.726156i
$227$	17.3935	+	15.6612i	1.15445	+	1.03947i	0.998664	+	0.0516759i	$0.0164563\pi$
$227$	17.3935	+	15.6612i	1.15445	+	1.03947i	0.155782	+	0.987792i	$0.450210\pi$
$228$	6.00049	+	10.9000i	0.397392	+	0.721872i
$229$	−1.39905	+	6.58202i	−0.0924519	+	0.434952i	0.907439	+	0.420184i	$0.138034\pi$
$229$	−1.39905	+	6.58202i	−0.0924519	+	0.434952i	−0.999891	+	0.0147683i	$0.995299\pi$
$230$	5.35777	−	1.13883i	0.353281	−	0.0750922i
$231$	−13.6071	−	3.18328i	−0.895282	−	0.209444i
$232$	−5.70246	−	1.85284i	−0.374385	−	0.121645i
$233$	−0.931250	−	0.302581i	−0.0610082	−	0.0198228i	0.278354	−	0.960479i	$-0.410211\pi$
$233$	−0.931250	−	0.302581i	−0.0610082	−	0.0198228i	−0.339362	+	0.940656i	$0.610211\pi$
$234$	−5.20781	−	6.28048i	−0.340445	−	0.410568i
$235$	10.6504	−	2.26381i	0.694755	−	0.147675i
$236$	0.577035	−	2.71474i	0.0375618	−	0.176714i
$237$	−16.0796	+	8.85187i	−1.04448	+	0.574990i
$238$	7.44978	+	6.70781i	0.482898	+	0.434803i
$239$	1.32521	−	12.6086i	0.0857209	−	0.815580i	−0.864212	−	0.503127i	$-0.832183\pi$
$239$	1.32521	−	12.6086i	0.0857209	−	0.815580i	0.949933	−	0.312453i	$-0.101151\pi$
$240$	−1.65784	+	0.501569i	−0.107013	+	0.0323761i
$241$	−4.19226	+	0.440624i	−0.270047	+	0.0283831i	−0.238584	−	0.971122i	$-0.576683\pi$
$241$	−4.19226	+	0.440624i	−0.270047	+	0.0283831i	−0.0314630	+	0.999505i	$0.510017\pi$
$242$	−2.27094	−	1.31113i	−0.145982	−	0.0842826i
$243$	6.38123	+	14.2225i	0.409356	+	0.912375i
$244$	−9.02495	−	12.4218i	−0.577763	−	0.795223i
$245$	−1.65081	+	1.48640i	−0.105467	+	0.0949625i
$246$	3.48568	−	10.0280i	0.222239	−	0.639365i
$247$		−	19.5367i		−	1.24309i
$248$	1.19872	+	5.43719i	0.0761191	+	0.345262i
$249$	−1.95613	−	1.48301i	−0.123965	−	0.0939822i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	6.40209	+	7.11024i	0.404096	+	0.448794i	0.910504	−	0.413500i	$-0.135694\pi$
$251$	6.40209	+	7.11024i	0.404096	+	0.448794i	−0.506408	+	0.862294i	$0.669027\pi$
$252$	5.14414	+	4.06759i	0.324051	+	0.256234i
$253$	−10.1082	−	17.5079i	−0.635498	−	1.10072i
$254$	−7.38010	+	12.7827i	−0.463068	+	0.802058i
$255$	−6.79644	−	4.11074i	−0.425610	−	0.257425i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−9.79588	−	1.02959i	−0.611050	−	0.0642240i	−0.206051	−	0.978541i	$-0.566061\pi$
$257$	−9.79588	−	1.02959i	−0.611050	−	0.0642240i	−0.404999	+	0.914317i	$0.632728\pi$
$258$	−3.51782	+	0.673153i	−0.219010	+	0.0419087i
$259$	−2.39324	+	5.37531i	−0.148709	+	0.334005i
$260$	2.66016	+	0.565435i	0.164976	+	0.0350668i
$261$	−8.35194	−	15.9312i	−0.516972	−	0.986119i
$262$	−18.2310	+	8.11696i	−1.12631	+	0.501467i
$263$	4.46155	−	13.7312i	0.275111	−	0.846704i	−0.714079	−	0.700065i	$-0.753154\pi$
$263$	4.46155	−	13.7312i	0.275111	−	0.846704i	0.989190	−	0.146639i	$-0.0468456\pi$
$264$	3.65142	+	5.24728i	0.224729	+	0.322948i
$265$	1.15528	+	2.59479i	0.0709681	+	0.159397i
$266$	3.26496	+	15.3604i	0.200188	+	0.941809i
$267$	3.71794	+	4.30228i	0.227534	+	0.263295i
$268$	5.44885	+	2.42599i	0.332842	+	0.148191i
$269$	−4.96616	+	5.51548i	−0.302792	+	0.336285i	−0.875269	−	0.483636i	$-0.839316\pi$
$269$	−4.96616	+	5.51548i	−0.302792	+	0.336285i	0.572477	+	0.819921i	$0.305983\pi$
$270$	−4.60899	−	2.39943i	−0.280494	−	0.146024i
$271$	−4.36890	+	6.01328i	−0.265392	+	0.365280i	−0.920827	−	0.389971i	$-0.872485\pi$
$271$	−4.36890	+	6.01328i	−0.265392	+	0.365280i	0.655435	+	0.755251i	$0.272485\pi$
$272$	−0.479351	−	4.56072i	−0.0290649	−	0.276534i
$273$	−3.99574	−	9.49024i	−0.241833	−	0.574375i
$274$	−4.81216	+	2.77830i	−0.290713	+	0.167843i
$275$	−2.98595	+	2.16942i	−0.180059	+	0.130821i
$276$	0.799298	+	9.45353i	0.0481121	+	0.569035i
$277$	−19.3130	+	6.27518i	−1.16041	+	0.377039i	−0.825054	−	0.565054i	$-0.808855\pi$
$277$	−19.3130	+	6.27518i	−1.16041	+	0.377039i	−0.335352	+	0.942093i	$0.608855\pi$
$278$	−5.27384			−0.316304
$279$	−8.82698	+	14.1804i	−0.528457	+	0.848960i
$280$	−2.18600			−0.130639
$281$	−24.9934	+	8.12085i	−1.49098	+	0.484449i	−0.937373	−	0.348327i	$-0.886750\pi$
$281$	−24.9934	+	8.12085i	−1.49098	+	0.484449i	−0.553609	+	0.832777i	$0.686750\pi$
$282$	1.58888	+	18.7921i	0.0946162	+	1.11905i
$283$	0.177341	−	0.128846i	0.0105418	−	0.00765908i	−0.582502	−	0.812829i	$-0.697926\pi$
$283$	0.177341	−	0.128846i	0.0105418	−	0.00765908i	0.593044	+	0.805170i	$0.297926\pi$
$284$	10.3548	−	5.97832i	0.614442	−	0.354748i
$285$	−4.82826	−	11.4675i	−0.286001	−	0.679279i
$286$	−1.04921	−	9.98258i	−0.0620412	−	0.590282i
$287$	7.87578	−	10.8401i	0.464892	−	0.639869i
$288$	−0.503701	−	2.95741i	−0.0296808	−	0.174267i
$289$	2.69656	−	2.99483i	0.158621	−	0.176167i
$290$	5.47754	+	2.43876i	0.321652	+	0.143209i
$291$	−12.4804	−	14.4420i	−0.731616	−	0.846603i
$292$	−0.373996	−	1.75951i	−0.0218865	−	0.102968i
$293$	2.36345	+	5.30840i	0.138074	+	0.310120i	0.969327	−	0.245775i	$-0.0790423\pi$
$293$	2.36345	+	5.30840i	0.138074	+	0.310120i	−0.831253	+	0.555895i	$0.812376\pi$
$294$	−2.19766	−	3.15816i	−0.128170	−	0.184187i
$295$	−0.857642	+	2.63955i	−0.0499338	+	0.153681i
$296$	2.45897	−	1.09480i	0.142925	−	0.0636341i
$297$	−3.16576	+	18.9150i	−0.183696	+	1.09756i
$298$	14.0479	+	2.98598i	0.813775	+	0.172973i
$299$	6.05895	−	13.6086i	0.350398	−	0.787007i
$300$	1.70118	−	0.325530i	0.0982180	−	0.0187945i
$301$	−4.49560	−	0.472507i	−0.259122	−	0.0272348i
$302$	−19.1565	−	13.9180i	−1.10233	−	0.800891i
$303$	−9.55721	−	5.78056i	−0.549048	−	0.332085i
$304$	3.59185	−	6.22127i	0.206007	−	0.356814i
$305$	7.67708	+	13.2971i	0.439588	+	0.761390i
$306$	8.53308	−	10.7915i	0.487804	−	0.616908i
$307$	17.0895	+	18.9798i	0.975349	+	1.08323i	0.996511	+	0.0834589i	$0.0265967\pi$
$307$	17.0895	+	18.9798i	0.975349	+	1.08323i	−0.0211621	+	0.999776i	$0.506737\pi$
$308$	2.49320	+	7.67329i	0.142063	+	0.437226i
$309$	14.9108	+	11.3044i	0.848244	+	0.643085i
$310$	−0.623816	−	5.53271i	−0.0354304	−	0.314237i
$311$		−	10.2077i		−	0.578825i	−0.957204	−	0.289413i	$-0.906540\pi$
$311$		−	10.2077i		−	0.578825i	0.957204	−	0.289413i	$-0.0934600\pi$
$312$	−1.54656	+	4.44935i	−0.0875570	+	0.251895i
$313$	16.9992	−	15.3061i	0.960849	−	0.865153i	−0.0300785	−	0.999548i	$-0.509576\pi$
$313$	16.9992	−	15.3061i	0.960849	−	0.865153i	0.990928	+	0.134395i	$0.0429091\pi$
$314$	6.09277	+	8.38598i	0.343835	+	0.473248i
$315$	−4.69078	−	4.58302i	−0.264296	−	0.258224i
$316$	9.17755	+	5.29866i	0.516278	+	0.298073i
$317$	−13.6421	+	1.43384i	−0.766214	+	0.0805324i	−0.479569	−	0.877504i	$-0.659207\pi$
$317$	−13.6421	+	1.43384i	−0.766214	+	0.0805324i	−0.286646	+	0.958037i	$0.592540\pi$
$318$	−4.70885	+	1.42463i	−0.264059	+	0.0798895i
$319$	2.31321	−	22.0087i	0.129515	−	1.23225i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	30.6650	−	16.8811i	1.71155	−	0.942213i
$322$	−2.48949	+	11.7121i	−0.138734	+	0.652691i
$323$	32.2234	−	6.84930i	1.79296	−	0.381105i
$324$	5.11945	−	7.40211i	0.284414	−	0.411229i
$325$	−2.58649	−	0.840401i	−0.143472	−	0.0466170i
$326$	−8.46708	−	2.75112i	−0.468948	−	0.152370i
$327$	−22.2664	−	5.20906i	−1.23134	−	0.288062i
$328$	−5.99554	+	1.27439i	−0.331048	+	0.0703665i
$329$	−4.94870	+	23.2818i	−0.272831	+	1.28357i
$330$	−3.08293	−	5.60021i	−0.169710	−	0.308281i
$331$	−11.6143	−	10.4576i	−0.638382	−	0.574802i	0.285074	−	0.958506i	$-0.407982\pi$
$331$	−11.6143	−	10.4576i	−0.638382	−	0.574802i	−0.923456	+	0.383703i	$0.874648\pi$
$332$	−0.148143	+	1.40948i	−0.00813039	+	0.0773555i
$333$	7.57180	+	2.80604i	0.414932	+	0.153770i
$334$	11.3659	−	1.19460i	0.621913	−	0.0653656i
$335$	−5.16542	−	2.98226i	−0.282217	−	0.162938i
$336$	0.472390	−	3.75669i	0.0257710	−	0.204944i
$337$	15.4268	+	21.2331i	0.840351	+	1.15664i	0.985907	+	0.167293i	$0.0535027\pi$
$337$	15.4268	+	21.2331i	0.840351	+	1.15664i	−0.145557	+	0.989350i	$0.546497\pi$
$338$	−4.16444	+	3.74968i	−0.226516	+	0.203956i
$339$	17.9582	+	6.24215i	0.975355	+	0.339027i
$340$			4.58584i			0.248702i
$341$	−18.7094	+	8.49994i	−1.01317	+	0.460297i
$342$	20.7505	−	5.81934i	1.12206	−	0.314674i
$343$	−6.22916	−	19.1714i	−0.336343	−	1.03516i
$344$	1.38367	+	1.53672i	0.0746026	+	0.0828546i
$345$	0.193243	−	9.48529i	0.0104039	−	0.510671i
$346$	6.00465	+	10.4004i	0.322812	+	0.559127i
$347$	−1.43457	+	2.48476i	−0.0770120	+	0.133389i	−0.901959	−	0.431821i	$-0.857871\pi$
$347$	−1.43457	+	2.48476i	−0.0770120	+	0.133389i	0.824947	+	0.565209i	$0.191205\pi$
$348$	−5.37473	+	8.88624i	−0.288116	+	0.476353i
$349$	−22.0255	−	16.0025i	−1.17900	−	0.856593i	−0.186941	−	0.982371i	$-0.559857\pi$
$349$	−22.0255	−	16.0025i	−1.17900	−	0.856593i	−0.992058	+	0.125778i	$0.959857\pi$
$350$	2.17403	+	0.228500i	0.116207	+	0.0122138i
$351$	−12.6468	+	6.30511i	−0.675039	+	0.336542i
$352$	1.50120	−	3.37174i	0.0800141	−	0.179715i
$353$	−2.56334	−	0.544856i	−0.136433	−	0.0289997i	0.139189	−	0.990266i	$-0.455550\pi$
$353$	−2.56334	−	0.544856i	−0.136433	−	0.0289997i	−0.275622	+	0.961266i	$0.588884\pi$
$354$	−4.35078	−	2.04427i	−0.231241	−	0.108652i
$355$	−10.9229	+	4.86321i	−0.579729	+	0.258112i
$356$	1.01448	−	3.12224i	0.0537673	−	0.165479i
$357$	14.2521	−	9.91761i	0.754302	−	0.524896i
$358$	7.74737	+	17.4009i	0.409461	+	0.919665i
$359$	7.14471	+	33.6132i	0.377084	+	1.77404i	0.600815	+	0.799388i	$0.294843\pi$
$359$	7.14471	+	33.6132i	0.377084	+	1.77404i	−0.223732	+	0.974651i	$0.571824\pi$
$360$	0.191808	+	2.99386i	0.0101091	+	0.157790i
$361$	29.7866	+	13.2619i	1.56772	+	0.697993i
$362$	7.89125	−	8.76413i	0.414755	−	0.460632i
$363$	−3.10723	+	3.31267i	−0.163087	+	0.173870i
$364$	−3.49441	+	4.80964i	−0.183157	+	0.252094i
$365$	0.188028	+	1.78897i	0.00984183	+	0.0936388i
$366$	−24.5103	+	10.3197i	−1.28117	+	0.539421i
$367$	10.5384	−	6.08435i	0.550100	−	0.317601i	−0.199062	−	0.979987i	$-0.563790\pi$
$367$	10.5384	−	6.08435i	0.550100	−	0.317601i	0.749162	+	0.662386i	$0.230456\pi$
$368$	4.43137	−	3.21958i	0.231001	−	0.167832i
$369$	−15.5372	−	9.83520i	−0.808833	−	0.512000i
$370$	−2.55993	+	0.831773i	−0.133085	+	0.0432418i
$371$	−6.20903			−0.322357
$372$	9.64286	+	0.123565i	0.499959	+	0.00640655i
$373$	−21.1831			−1.09682			−0.548411	−	0.836209i	$-0.684767\pi$
$373$	−21.1831			−1.09682			−0.548411	+	0.836209i	$0.684767\pi$
$374$	16.0972	−	5.23029i	0.832366	−	0.270452i
$375$	−1.72589	+	0.145925i	−0.0891247	+	0.00753552i
$376$	8.80885	−	6.40000i	0.454282	−	0.330055i
$377$	14.1218	−	8.15323i	0.727310	−	0.419913i
$378$	8.88967	−	7.07081i	0.457235	−	0.363683i
$379$	−0.363458	−	3.45807i	−0.0186696	−	0.177629i	0.981213	−	0.192925i	$-0.0617976\pi$
$379$	−0.363458	−	3.45807i	−0.0186696	−	0.177629i	−0.999883	+	0.0152962i	$0.995131\pi$
$380$	−4.22247	+	5.81173i	−0.216608	+	0.298136i
$381$	18.6464	+	17.4900i	0.955285	+	0.896041i
$382$	7.04681	−	7.82627i	0.360546	−	0.400427i
$383$	3.33636	+	1.48544i	0.170480	+	0.0759026i	0.490202	−	0.871609i	$-0.336923\pi$
$383$	3.33636	+	1.48544i	0.170480	+	0.0759026i	−0.319722	+	0.947511i	$0.603590\pi$
$384$	−1.31050	+	1.13251i	−0.0668764	+	0.0577932i
$385$	−1.67747	−	7.89187i	−0.0854917	−	0.402207i
$386$	−5.83994	−	13.1167i	−0.297245	−	0.667623i
$387$	−0.252666	+	6.19845i	−0.0128437	+	0.315085i
$388$	−3.40542	+	10.4808i	−0.172884	+	0.532082i
$389$	26.6684	−	11.8736i	1.35214	−	0.602013i	0.402522	−	0.915411i	$-0.368134\pi$
$389$	26.6684	−	11.8736i	1.35214	−	0.602013i	0.949622	+	0.313397i	$0.101467\pi$
$390$	2.00318	−	4.26331i	0.101435	−	0.215881i
$391$	24.5699	+	5.22249i	1.24255	+	0.264113i
$392$	−0.903519	+	2.02934i	−0.0456346	+	0.102497i
$393$	6.49638	+	33.9494i	0.327699	+	1.71252i
$394$	13.9210	+	1.46316i	0.701330	+	0.0737128i
$395$	−8.57341	−	6.22895i	−0.431375	−	0.313412i
$396$	10.2903	−	4.08787i	0.517105	−	0.205423i
$397$	−4.66581	+	8.08142i	−0.234170	+	0.405595i	−0.959031	−	0.283300i	$-0.908571\pi$
$397$	−4.66581	+	8.08142i	−0.234170	+	0.405595i	0.724861	+	0.688895i	$0.241904\pi$
$398$	5.58790	+	9.67853i	0.280096	+	0.485141i
$399$	27.1938	+	0.554017i	1.36139	+	0.0277356i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	9.34516	+	28.7614i	0.466675	+	1.43628i	0.856864	+	0.515543i	$0.172410\pi$
$401$	9.34516	+	28.7614i	0.466675	+	1.43628i	−0.390189	+	0.920735i	$0.627590\pi$
$402$	6.24129	−	8.23240i	0.311287	−	0.410595i
$403$	−13.1702	−	7.47172i	−0.656056	−	0.372193i
$404$			6.44865i			0.320832i
$405$	−5.86513	+	6.82644i	−0.291441	+	0.339208i
$406$	−9.74047	+	8.77036i	−0.483411	+	0.435266i
$407$	5.83937	+	8.03720i	0.289447	+	0.398389i
$408$	−7.88085	−	0.990989i	−0.390160	−	0.0490612i
$409$	12.4271	+	7.17477i	0.614479	+	0.354769i	0.774716	−	0.632309i	$-0.217893\pi$
$409$	12.4271	+	7.17477i	0.614479	+	0.354769i	−0.160238	+	0.987078i	$0.551226\pi$
$410$	6.09590	−	0.640705i	0.301055	−	0.0316422i
$411$	2.78702	+	9.21194i	0.137474	+	0.454392i
$412$	1.12923	−	10.7439i	0.0556332	−	0.529314i
$413$	−4.50867	−	4.05962i	−0.221857	−	0.199761i
$414$	16.2589	+	2.38184i	0.799080	+	0.117061i
$415$	0.294662	−	1.38628i	0.0144644	−	0.0680497i
$416$	2.66016	−	0.565435i	0.130425	−	0.0277227i
$417$	−2.08078	+	8.89442i	−0.101896	+	0.435561i
$418$	25.2162	+	8.19323i	1.23336	+	0.400744i
$419$	−0.514090	−	0.167038i	−0.0251149	−	0.00816033i	0.296433	−	0.955054i	$-0.404203\pi$
$419$	−0.514090	−	0.167038i	−0.0251149	−	0.00816033i	−0.321548	+	0.946893i	$0.604203\pi$
$420$	−0.862483	+	3.68673i	−0.0420848	+	0.179894i
$421$	−17.5901	+	3.73890i	−0.857290	+	0.182223i	−0.615530	−	0.788113i	$-0.711058\pi$
$421$	−17.5901	+	3.73890i	−0.857290	+	0.182223i	−0.241760	+	0.970336i	$0.577725\pi$
$422$	−1.20377	+	5.66329i	−0.0585985	+	0.275684i
$423$	32.3200	+	4.73471i	1.57145	+	0.230210i
$424$	2.11080	+	1.90057i	0.102509	+	0.0922998i
$425$	0.479351	−	4.56072i	0.0232519	−	0.221227i
$426$	−5.99709	−	19.8222i	−0.290560	−	0.960388i
$427$	−33.3804	+	3.50842i	−1.61539	+	0.169784i
$428$	−17.5022	−	10.1049i	−0.846002	−	0.488440i
$429$	−17.2497	−	2.16909i	−0.832825	−	0.104725i
$430$	−1.21546	−	1.67294i	−0.0586148	−	0.0806763i
$431$	15.0404	−	13.5425i	0.724472	−	0.652317i	−0.222021	−	0.975042i	$-0.571265\pi$
$431$	15.0404	−	13.5425i	0.724472	−	0.652317i	0.946493	+	0.322725i	$0.104599\pi$
$432$	−5.18645	−	0.317341i	−0.249533	−	0.0152681i
$433$			33.0377i			1.58769i	0.608120	+	0.793845i	$0.291924\pi$
$433$			33.0377i			1.58769i	−0.608120	+	0.793845i	$0.708076\pi$
$434$	11.6035	+	3.67352i	0.556988	+	0.176334i
$435$	6.27415	−	8.27575i	0.300823	−	0.396792i
$436$	4.07983	+	12.5564i	0.195389	+	0.601344i
$437$	26.3293	+	29.2416i	1.25950	+	1.39882i
$438$	−3.11500	−	0.0634618i	−0.148841	−	0.00303232i
$439$	0.0919831	+	0.159319i	0.00439011	+	0.00760390i	0.868212	−	0.496193i	$-0.165269\pi$
$439$	0.0919831	+	0.159319i	0.00439011	+	0.00760390i	−0.863822	+	0.503797i	$0.831936\pi$
$440$	−1.84542	+	3.19636i	−0.0879768	+	0.152380i
$441$	−6.19336	+	2.46035i	−0.294922	+	0.117160i
$442$	10.0898	+	7.33064i	0.479921	+	0.348683i
$443$	17.6901	+	1.85930i	0.840481	+	0.0883381i	0.514979	−	0.857203i	$-0.327800\pi$
$443$	17.6901	+	1.85930i	0.840481	+	0.0883381i	0.325502	+	0.945541i	$0.394467\pi$
$444$	−0.876221	−	4.57903i	−0.0415836	−	0.217311i
$445$	−1.33528	+	2.99910i	−0.0632986	+	0.142171i
$446$	−2.66771	−	0.567038i	−0.126320	−	0.0268500i
$447$	10.5785	−	22.5139i	0.500345	−	1.06487i
$448$	−1.99701	+	0.889128i	−0.0943500	+	0.0420073i
$449$	3.59150	−	11.0535i	0.169493	−	0.521646i	−0.829846	−	0.557992i	$-0.811572\pi$
$449$	3.59150	−	11.0535i	0.169493	−	0.521646i	0.999339	+	0.0363460i	$0.0115718\pi$
$450$	0.122187	−	2.99751i	0.00575995	−	0.141304i
$451$	−9.20156	−	20.6670i	−0.433285	−	0.973173i
$452$	−2.28218	−	10.7368i	−0.107344	−	0.505016i
$453$	−31.0310	+	26.8164i	−1.45797	+	1.25994i
$454$	−21.3817	−	9.51976i	−1.00349	−	0.446785i
$455$	3.97801	−	4.41803i	0.186492	−	0.207120i
$456$	−9.07510	−	8.51229i	−0.424981	−	0.398625i
$457$	10.4017	−	14.3168i	0.486573	−	0.669710i	−0.493178	−	0.869928i	$-0.664165\pi$
$457$	10.4017	−	14.3168i	0.486573	−	0.669710i	0.979751	+	0.200218i	$0.0641650\pi$
$458$	−0.703379	−	6.69220i	−0.0328667	−	0.312706i
$459$	−14.8333	−	18.6489i	−0.692359	−	0.870457i
$460$	−4.74363	+	2.73874i	−0.221173	+	0.127694i
$461$	30.0510	−	21.8334i	1.39962	−	1.01688i	0.404885	−	0.914368i	$-0.367312\pi$
$461$	30.0510	−	21.8334i	1.39962	−	1.01688i	0.994732	−	0.102513i	$-0.0326883\pi$
$462$	13.9248	−	1.17735i	0.647841	−	0.0547751i
$463$	7.50915	−	2.43987i	0.348980	−	0.113390i	−0.129282	−	0.991608i	$-0.541267\pi$
$463$	7.50915	−	2.43987i	0.348980	−	0.113390i	0.478261	+	0.878217i	$0.341267\pi$
$464$	5.99592			0.278353
$465$	−9.57712	−	1.13084i	−0.444128	−	0.0524415i
$466$	0.979174			0.0453594
$467$	−33.9339	+	11.0258i	−1.57027	+	0.510212i	−0.959527	−	0.281616i	$-0.909130\pi$
$467$	−33.9339	+	11.0258i	−1.57027	+	0.510212i	−0.610744	+	0.791828i	$0.709130\pi$
$468$	6.89370	+	4.36378i	0.318661	+	0.201716i
$469$	10.5483	−	7.66381i	0.487076	−	0.353882i
$470$	−9.42958	+	5.44417i	−0.434954	+	0.251121i
$471$	16.5470	−	6.96688i	0.762444	−	0.321017i
$472$	0.290107	+	2.76018i	0.0133533	+	0.127048i
$473$	−4.48607	+	6.17454i	−0.206270	+	0.283906i
$474$	12.5573	−	13.3875i	0.576774	−	0.614908i
$475$	4.80683	−	5.33853i	0.220553	−	0.244948i
$476$	−9.15799	−	4.07740i	−0.419756	−	0.186887i
$477$	0.544802	+	8.50363i	0.0249448	+	0.389355i
$478$	2.63591	+	12.4010i	0.120564	+	0.567207i
$479$	−8.71390	−	19.5717i	−0.398148	−	0.894256i	−0.995718	−	0.0924392i	$-0.970534\pi$
$479$	−8.71390	−	19.5717i	−0.398148	−	0.894256i	0.597570	−	0.801817i	$-0.296133\pi$
$480$	1.42170	−	0.989321i	0.0648916	−	0.0451561i
$481$	−2.26208	+	6.96198i	−0.103142	+	0.317439i
$482$	3.85092	−	1.71454i	0.175404	−	0.0780951i
$483$	18.7704	+	8.81954i	0.854084	+	0.401303i
$484$	2.56496	+	0.545198i	0.116589	+	0.0247817i
$485$	4.48230	−	10.0674i	0.203531	−	0.457138i
$486$	−10.4639	−	11.5545i	−0.474653	−	0.524123i
$487$	34.2088	+	3.59549i	1.55015	+	0.162927i	0.840572	−	0.541700i	$-0.182219\pi$
$487$	34.2088	+	3.59549i	1.55015	+	0.162927i	0.709577	+	0.704628i	$0.248886\pi$
$488$	12.4218	+	9.02495i	0.562308	+	0.408540i
$489$	−7.98047	+	13.1944i	−0.360889	+	0.596672i
$490$	1.11069	−	1.92378i	0.0501760	−	0.0869074i
$491$	−1.67715	−	2.90492i	−0.0756889	−	0.131097i	0.825697	−	0.564114i	$-0.190782\pi$
$491$	−1.67715	−	2.90492i	−0.0756889	−	0.131097i	−0.901386	+	0.433017i	$0.857449\pi$
$492$	−0.216246	+	10.6144i	−0.00974912	+	0.478533i
$493$	18.3986	+	20.4337i	0.828633	+	0.920290i
$494$	6.03719	+	18.5805i	0.271626	+	0.835978i
$495$	−10.6612	+	2.98985i	−0.479185	+	0.134384i
$496$	−2.82024	−	4.80065i	−0.126632	−	0.215556i
$497$		−	26.1373i		−	1.17242i
$498$	2.31867	+	0.805953i	0.103902	+	0.0361156i
$499$	−18.4916	+	16.6499i	−0.827799	+	0.745354i	−0.969640	−	0.244535i	$-0.921365\pi$
$499$	−18.4916	+	16.6499i	−0.827799	+	0.745354i	0.141841	+	0.989889i	$0.454698\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	2.46966	−	19.6400i	0.110336	−	0.877452i
$502$	−8.28593	−	4.78389i	−0.369819	−	0.213515i
$503$	−37.9553	+	3.98926i	−1.69234	+	0.177872i	−0.901095	−	0.433623i	$-0.857235\pi$
$503$	−37.9553	+	3.98926i	−1.69234	+	0.177872i	−0.791248	+	0.611495i	$0.790568\pi$
$504$	−6.14933	−	2.27888i	−0.273913	−	0.101510i
$505$	0.674067	−	6.41332i	0.0299956	−	0.285389i
$506$	15.0237	+	13.5274i	0.667887	+	0.601368i
$507$	4.68082	+	8.50282i	0.207883	+	0.377624i
$508$	3.06882	−	14.4376i	0.136157	−	0.640567i
$509$	−8.18192	+	1.73912i	−0.362657	+	0.0770852i	−0.385637	−	0.922651i	$-0.626018\pi$
$509$	−8.18192	+	1.73912i	−0.362657	+	0.0770852i	0.0229793	+	0.999736i	$0.492685\pi$
$510$	7.73409	+	1.80933i	0.342471	+	0.0801186i
$511$	−3.73977	−	1.21513i	−0.165438	−	0.0537540i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−1.62732	−	37.2921i	−0.0718478	−	1.64649i
$514$	9.63460	−	2.04790i	0.424964	−	0.0903289i
$515$	−2.24609	+	10.5670i	−0.0989745	+	0.465638i
$516$	3.13763	−	1.72727i	0.138127	−	0.0760390i
$517$	29.8648	+	26.8904i	1.31345	+	1.18264i
$518$	0.615046	−	5.85178i	0.0270236	−	0.257112i
$519$	19.9095	−	6.02349i	0.873929	−	0.264402i
$520$	−2.70470	+	0.284275i	−0.118609	+	0.0124663i
$521$	19.5869	+	11.3085i	0.858119	+	0.495435i	0.863382	−	0.504551i	$-0.168342\pi$
$521$	19.5869	+	11.3085i	0.858119	+	0.495435i	−0.00526273	+	0.999986i	$0.501675\pi$
$522$	12.8662	+	12.5706i	0.563138	+	0.550201i
$523$	−20.9331	−	28.8119i	−0.915339	−	1.25986i	−0.965310	−	0.261105i	$-0.915913\pi$
$523$	−20.9331	−	28.8119i	−0.915339	−	1.25986i	0.0499715	−	0.998751i	$-0.484087\pi$
$524$	14.8304	−	13.3534i	0.647870	−	0.583345i
$525$	1.24313	−	3.57638i	0.0542545	−	0.156086i
$526$			14.4379i			0.629521i
$527$	7.70637	−	24.3421i	0.335695	−	1.06036i
$528$	−5.09420	−	3.86211i	−0.221697	−	0.168077i
$529$	2.16395	+	6.65994i	0.0940846	+	0.289563i
$530$	−1.90057	−	2.11080i	−0.0825554	−	0.0916871i
$531$	−5.16428	+	6.53109i	−0.224111	+	0.283425i
$532$	−7.85180	−	13.5997i	−0.340419	−	0.589622i
$533$	8.33485	−	14.4364i	0.361022	−	0.625309i
$534$	−4.86545	−	2.94281i	−0.210549	−	0.127348i
$535$	16.3501	+	11.8790i	0.706877	+	0.513576i
$536$	−5.93184	−	0.623461i	−0.256216	−	0.0269294i
$537$	32.4035	−	6.20058i	1.39832	−	0.267575i
$538$	3.01872	−	6.78016i	0.130146	−	0.292313i
$539$	−8.01961	−	1.70462i	−0.345429	−	0.0734232i
$540$	5.12487	+	0.857735i	0.220539	+	0.0369110i
$541$	−32.6644	+	14.5431i	−1.40435	+	0.625257i	−0.962364	−	0.271764i	$-0.912393\pi$
$541$	−32.6644	+	14.5431i	−1.40435	+	0.625257i	−0.441987	+	0.897022i	$0.645726\pi$
$542$	2.29687	−	7.06903i	0.0986589	−	0.303641i
$543$	−11.6674	−	16.7666i	−0.500694	−	0.719523i
$544$	1.86523	+	4.18937i	0.0799711	+	0.179618i
$545$	−2.74498	−	12.9141i	−0.117582	−	0.553180i
$546$	6.73282	+	7.79100i	0.288138	+	0.333424i
$547$	−24.3829	−	10.8560i	−1.04254	−	0.464167i	−0.187244	−	0.982313i	$-0.559956\pi$
$547$	−24.3829	−	10.8560i	−1.04254	−	0.464167i	−0.855292	+	0.518146i	$0.826622\pi$
$548$	3.71809	−	4.12936i	0.158829	−	0.176397i
$549$	7.73390	+	45.4086i	0.330075	+	1.93799i
$550$	2.16942	−	2.98595i	0.0925043	−	0.127321i
$551$	4.50234	+	42.8369i	0.191806	+	1.82491i
$552$	−3.68148	−	8.74384i	−0.156694	−	0.372163i
$553$	20.0622	−	11.5829i	0.853130	−	0.492555i
$554$	16.4286	−	11.9361i	0.697986	−	0.507116i
$555$	0.392782	+	4.64554i	0.0166726	+	0.197192i
$556$	5.01572	−	1.62971i	0.212714	−	0.0691150i
$557$	4.47753			0.189719			0.0948595	−	0.995491i	$-0.469760\pi$
$557$	4.47753			0.189719			0.0948595	+	0.995491i	$0.469760\pi$
$558$	4.01296	−	16.2141i	0.169882	−	0.686396i
$559$	−5.62376			−0.237860
$560$	2.07901	−	0.675512i	0.0878543	−	0.0285456i
$561$	−2.46986	−	29.2117i	−0.104278	−	1.23332i
$562$	21.2607	−	15.4468i	0.896827	−	0.651583i
$563$	1.56813	−	0.905361i	0.0660889	−	0.0381564i	−0.466591	−	0.884473i	$-0.654518\pi$
$563$	1.56813	−	0.905361i	0.0660889	−	0.0381564i	0.532680	+	0.846317i	$0.321185\pi$
$564$	−7.31819	−	17.3814i	−0.308151	−	0.731887i
$565$	1.14737	+	10.9165i	0.0482703	+	0.459262i
$566$	−0.128846	+	0.177341i	−0.00541579	+	0.00745420i
$567$	−8.41763	−	17.7823i	−0.353507	−	0.746787i
$568$	−8.00056	+	8.88552i	−0.335696	+	0.372828i
$569$	−38.3816	−	17.0886i	−1.60904	−	0.716391i	−0.611827	−	0.790992i	$-0.709565\pi$
$569$	−38.3816	−	17.0886i	−1.60904	−	0.716391i	−0.997214	+	0.0746005i	$0.976232\pi$
$570$	8.13561	+	9.41427i	0.340763	+	0.394320i
$571$	6.36279	+	29.9346i	0.266274	+	1.25272i	0.884432	+	0.466668i	$0.154546\pi$
$571$	6.36279	+	29.9346i	0.266274	+	1.25272i	−0.618158	+	0.786054i	$0.712121\pi$
$572$	4.08265	+	9.16978i	0.170704	+	0.383408i
$573$	−10.4188	−	14.9724i	−0.435253	−	0.625480i
$574$	−4.14054	+	12.7433i	−0.172823	+	0.531894i
$575$	5.00392	−	2.22789i	0.208678	−	0.0929093i
$576$	1.39294	+	2.65701i	0.0580391	+	0.110709i
$577$	−26.5441	−	5.64213i	−1.10505	−	0.234885i	−0.380958	−	0.924592i	$-0.624406\pi$
$577$	−26.5441	−	5.64213i	−1.10505	−	0.234885i	−0.724088	+	0.689707i	$0.757739\pi$
$578$	−1.63913	+	3.68154i	−0.0681786	+	0.153132i
$579$	−24.4257	+	4.67397i	−1.01510	+	0.194244i
$580$	−5.96307	−	0.626744i	−0.247603	−	0.0260241i
$581$	2.50642	+	1.82102i	0.103984	+	0.0755487i
$582$	16.3324	+	9.87846i	0.677000	+	0.409475i
$583$	−5.24164	+	9.07879i	−0.217087	+	0.376005i
$584$	0.899410	+	1.55782i	0.0372179	+	0.0644632i
$585$	−6.39979	−	5.06047i	−0.264599	−	0.209225i
$586$	−3.88817	−	4.31825i	−0.160619	−	0.178385i
$587$	−0.133143	−	0.409772i	−0.00549541	−	0.0169131i	0.948271	−	0.317461i	$-0.102830\pi$
$587$	−0.133143	−	0.409772i	−0.00549541	−	0.0169131i	−0.953767	+	0.300548i	$0.902830\pi$
$588$	3.06603	+	2.32447i	0.126441	+	0.0958595i
$589$	32.1798	−	23.7536i	1.32595	−	0.978749i
$590$		−	2.77539i		−	0.114261i
$591$	7.96014	−	22.9007i	0.327436	−	0.942009i
$592$	−2.00030	+	1.80108i	−0.0822120	+	0.0740240i
$593$	12.1674	+	16.7470i	0.499657	+	0.687719i	0.982132	−	0.188191i	$-0.0602623\pi$
$593$	12.1674	+	16.7470i	0.499657	+	0.687719i	−0.482476	+	0.875909i	$0.660262\pi$
$594$	−2.83426	−	18.9676i	−0.116291	−	0.778248i
$595$	8.68162	+	5.01233i	0.355912	+	0.205486i
$596$	−14.2831	+	1.50121i	−0.585059	+	0.0614921i
$597$	18.5277	−	5.60544i	0.758287	−	0.229415i
$598$	−1.55711	+	14.8149i	−0.0636749	+	0.605826i
$599$	11.9576	+	10.7667i	0.488576	+	0.439916i	0.876233	−	0.481888i	$-0.160049\pi$
$599$	11.9576	+	10.7667i	0.488576	+	0.439916i	−0.387657	+	0.921804i	$0.626715\pi$
$600$	−1.51733	+	0.835293i	−0.0619447	+	0.0341007i
$601$	−5.02182	+	23.6258i	−0.204845	+	0.963718i	0.748803	+	0.662792i	$0.230629\pi$
$601$	−5.02182	+	23.6258i	−0.204845	+	0.963718i	−0.953648	+	0.300925i	$0.902705\pi$
$602$	4.42158	−	0.939837i	0.180210	−	0.0383049i
$603$	−11.4216	−	13.7741i	−0.465123	−	0.560925i
$604$	22.5198	+	7.31712i	0.916317	+	0.297729i
$605$	−2.49392	−	0.810322i	−0.101392	−	0.0329443i
$606$	10.8757	+	2.54430i	0.441797	+	0.103355i
$607$	7.76425	−	1.65034i	0.315141	−	0.0669853i	−0.0476258	−	0.998865i	$-0.515165\pi$
$607$	7.76425	−	1.65034i	0.315141	−	0.0669853i	0.362767	+	0.931880i	$0.381832\pi$
$608$	−1.49358	+	7.02672i	−0.0605725	+	0.284971i
$609$	10.9483	+	19.8878i	0.443646	+	0.805893i
$610$	−11.4104	−	10.2739i	−0.461992	−	0.415980i
$611$	−3.09528	+	29.4496i	−0.125222	+	1.19140i
$612$	−4.78069	+	12.9002i	−0.193248	+	0.521459i
$613$	−31.7438	+	3.33641i	−1.28212	+	0.134756i	−0.720976	−	0.692960i	$-0.756306\pi$
$613$	−31.7438	+	3.33641i	−1.28212	+	0.134756i	−0.561146	+	0.827717i	$0.689639\pi$
$614$	−22.1182	−	12.7699i	−0.892616	−	0.515352i
$615$	1.32457	−	10.5336i	0.0534116	−	0.424757i
$616$	−4.74236	−	6.52729i	−0.191075	−	0.262992i
$617$	−19.2548	+	17.3371i	−0.775168	+	0.697964i	−0.958502	−	0.285086i	$-0.907978\pi$
$617$	−19.2548	+	17.3371i	−0.775168	+	0.697964i	0.183334	+	0.983051i	$0.441311\pi$
$618$	−17.6742	−	6.14345i	−0.710962	−	0.247126i
$619$			39.8751i			1.60271i	0.598187	+	0.801357i	$0.295888\pi$
$619$			39.8751i			1.60271i	−0.598187	+	0.801357i	$0.704112\pi$
$620$	2.30299	+	5.06915i	0.0924901	+	0.203582i
$621$	10.4319	−	26.4811i	0.418618	−	1.06265i
$622$	3.15435	+	9.70809i	0.126478	+	0.389259i
$623$	−4.80200	−	5.33316i	−0.192388	−	0.213669i
$624$	0.0959463	−	4.70950i	0.00384093	−	0.188531i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.4373	+	19.8100i	−0.457127	+	0.791767i
$627$	23.7670	−	39.2948i	0.949162	−	1.56928i
$628$	−8.38598	−	6.09277i	−0.334637	−	0.243128i
$629$	−12.2760	−	1.29026i	−0.489475	−	0.0514459i
$630$	5.87743	+	2.90918i	0.234162	+	0.115904i
$631$	8.46078	−	19.0032i	0.336818	−	0.756506i	−0.663150	−	0.748487i	$-0.730781\pi$
$631$	8.46078	−	19.0032i	0.336818	−	0.756506i	0.999968	−	0.00801934i	$-0.00255266\pi$
$632$	−10.3657	−	2.20331i	−0.412327	−	0.0876429i
$633$	9.07627	+	4.26461i	0.360749	+	0.169503i
$634$	12.5313	−	5.57929i	0.497681	−	0.221582i
$635$	−4.56115	+	14.0378i	−0.181004	+	0.557072i
$636$	4.03815	−	2.81002i	0.160123	−	0.111425i
$637$	−2.45721	−	5.51897i	−0.0973580	−	0.218670i
$638$	4.60107	+	21.6463i	0.182158	+	0.856987i
$639$	−35.7966	+	2.29338i	−1.41609	+	0.0907245i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−6.80511	+	7.55784i	−0.268786	+	0.298517i	−0.862394	−	0.506237i	$-0.831036\pi$
$641$	−6.80511	+	7.55784i	−0.268786	+	0.298517i	0.593609	+	0.804754i	$0.297703\pi$
$642$	−23.9476	+	25.5309i	−0.945135	+	1.00762i
$643$	13.9285	−	19.1709i	0.549286	−	0.756028i	−0.440629	−	0.897689i	$-0.645244\pi$
$643$	13.9285	−	19.1709i	0.549286	−	0.756028i	0.989915	+	0.141662i	$0.0452445\pi$
$644$	−1.25160	−	11.9082i	−0.0493199	−	0.469248i
$645$	−3.30099	+	1.38984i	−0.129977	+	0.0547249i
$646$	−28.5297	+	16.4717i	−1.12249	+	0.648069i
$647$	26.4307	−	19.2031i	1.03910	−	0.754950i	0.0689898	−	0.997617i	$-0.478022\pi$
$647$	26.4307	−	19.2031i	1.03910	−	0.754950i	0.970110	+	0.242668i	$0.0780224\pi$
$648$	−2.58150	+	8.62182i	−0.101411	+	0.338697i
$649$	−9.74214	+	3.16541i	−0.382413	+	0.124253i
$650$	2.71959			0.106671
$651$	10.7736	−	18.1202i	0.422250	−	0.710186i
$652$	8.90281			0.348661
$653$	−32.4979	+	10.5592i	−1.27174	+	0.413214i	−0.865664	−	0.500625i	$-0.833103\pi$
$653$	−32.4979	+	10.5592i	−1.27174	+	0.413214i	−0.406077	+	0.913839i	$0.633103\pi$
$654$	22.7863	−	1.92659i	0.891015	−	0.0753356i
$655$	−16.1450	+	11.7300i	−0.630837	+	0.458330i
$656$	5.30829	−	3.06474i	0.207254	−	0.119658i
$657$	−1.33605	+	5.22846i	−0.0521241	+	0.203982i
$658$	−2.48798	−	23.6716i	−0.0969916	−	0.922813i
$659$	−10.3301	+	14.2182i	−0.402403	+	0.553861i	−0.961345	−	0.275346i	$-0.911208\pi$
$659$	−10.3301	+	14.2182i	−0.402403	+	0.553861i	0.558942	+	0.829207i	$0.311208\pi$
$660$	4.66260	+	4.37344i	0.181491	+	0.170236i
$661$	11.7988	−	13.1039i	0.458920	−	0.509682i	−0.468623	−	0.883398i	$-0.655250\pi$
$661$	11.7988	−	13.1039i	0.458920	−	0.509682i	0.927543	+	0.373716i	$0.121917\pi$
$662$	14.2775	+	6.35674i	0.554910	+	0.247062i
$663$	16.3441	−	14.1242i	0.634753	−	0.548540i
$664$	−0.294662	−	1.38628i	−0.0114351	−	0.0537980i
$665$	6.38723	+	14.3459i	0.247686	+	0.556312i
$666$	−8.06832	−	0.328887i	−0.312641	−	0.0127441i
$667$	−10.1489	+	31.2350i	−0.392966	+	1.20943i
$668$	−10.4404	+	4.64838i	−0.403952	+	0.179851i
$669$	−2.00886	+	4.27540i	−0.0776668	+	0.165297i
$670$	5.83417	+	1.24009i	0.225394	+	0.0479089i
$671$	−23.0496	+	51.7703i	−0.889821	+	1.99857i
$672$	0.711610	+	3.71880i	0.0274510	+	0.143456i
$673$	9.73347	+	1.02303i	0.375198	+	0.0394349i	0.290251	−	0.956951i	$-0.406261\pi$
$673$	9.73347	+	1.02303i	0.375198	+	0.0394349i	0.0849470	+	0.996385i	$0.472928\pi$
$674$	−21.2331	−	15.4268i	−0.817870	−	0.594218i
$675$	−5.00714	−	1.38873i	−0.192725	−	0.0534523i
$676$	2.80191	−	4.85304i	0.107766	−	0.186655i
$677$	−0.202661	−	0.351020i	−0.00778891	−	0.0134908i	0.862105	−	0.506730i	$-0.169146\pi$
$677$	−0.202661	−	0.351020i	−0.00778891	−	0.0134908i	−0.869894	+	0.493239i	$0.835813\pi$
$678$	−19.0082	−	0.387253i	−0.730005	−	0.0148723i
$679$	16.1194	+	17.9024i	0.618607	+	0.687033i
$680$	−1.41710	−	4.36139i	−0.0543434	−	0.167252i
$681$	−24.4913	+	32.3046i	−0.938510	+	1.23792i
$682$	15.1671	−	13.8654i	0.580777	−	0.530935i
$683$			21.3556i			0.817150i	0.912725	+	0.408575i	$0.133974\pi$
$683$			21.3556i			0.817150i	−0.912725	+	0.408575i	$0.866026\pi$
$684$	−17.9367	+	11.9468i	−0.685826	+	0.456797i
$685$	−4.12936	+	3.71809i	−0.157775	+	0.142061i
$686$	11.8486	+	16.3082i	0.452380	+	0.622648i
$687$	−11.5640	−	1.45413i	−0.441195	−	0.0554787i
$688$	−1.79082	−	1.03393i	−0.0682746	−	0.0394183i
$689$	−7.68230	+	0.807442i	−0.292672	+	0.0307611i
$690$	2.74733	+	9.08076i	0.104589	+	0.345699i
$691$	0.259829	−	2.47210i	0.00988435	−	0.0940433i	−0.988467	−	0.151433i	$-0.951611\pi$
$691$	0.259829	−	2.47210i	0.00988435	−	0.0940433i	0.998352	+	0.0573899i	$0.0182778\pi$
$692$	−8.92465	−	8.03579i	−0.339264	−	0.305475i
$693$	3.50839	−	23.9489i	0.133273	−	0.909744i
$694$	0.596530	−	2.80645i	0.0226440	−	0.106531i
$695$	−5.15860	+	1.09649i	−0.195677	+	0.0415924i
$696$	2.36567	−	10.1122i	0.0896707	−	0.383302i
$697$	26.7331	+	8.68611i	1.01259	+	0.329010i
$698$	25.8926	+	8.41300i	0.980048	+	0.318437i
$699$	0.386331	−	1.65139i	0.0146124	−	0.0624614i
$700$	−2.13823	+	0.454496i	−0.0808177	+	0.0171783i
$701$	−3.89924	+	18.3445i	−0.147272	+	0.692861i	0.841109	+	0.540866i	$0.181903\pi$
$701$	−3.89924	+	18.3445i	−0.147272	+	0.692861i	−0.988381	+	0.151995i	$0.951430\pi$
$702$	10.0795	−	9.90460i	0.380425	−	0.373825i
$703$	−14.3696	−	12.9384i	−0.541959	−	0.487982i
$704$	−0.385797	+	3.67062i	−0.0145403	+	0.138342i
$705$	5.46125	+	18.0511i	0.205683	+	0.679844i
$706$	2.60626	−	0.273928i	0.0980877	−	0.0103094i
$707$	12.2082	+	7.04839i	0.459135	+	0.265082i
$708$	4.76955	+	0.599754i	0.179251	+	0.0225401i
$709$	1.27468	+	1.75444i	0.0478715	+	0.0658894i	0.832282	−	0.554353i	$-0.187034\pi$
$709$	1.27468	+	1.75444i	0.0478715	+	0.0658894i	−0.784410	+	0.620242i	$0.787034\pi$
$710$	8.88552	−	8.00056i	0.333468	−	0.300256i
$711$	−17.6238	−	26.4600i	−0.660944	−	0.992327i
$712$			3.28292i			0.123033i
$713$	29.7821	−	6.56598i	1.11535	−	0.245898i
$714$	−10.4899	+	13.8364i	−0.392573	+	0.517813i
$715$	−3.10178	−	9.54630i	−0.116000	−	0.357011i
$716$	−12.7454	−	14.1551i	−0.476316	−	0.529003i
$717$	21.9544	+	0.447276i	0.819903	+	0.0167038i
$718$	−17.1821	−	29.7602i	−0.641230	−	1.11064i
$719$	16.5506	−	28.6664i	0.617232	−	1.06908i	−0.372757	−	0.927929i	$-0.621587\pi$
$719$	16.5506	−	28.6664i	0.617232	−	1.06908i	0.989989	−	0.141148i	$-0.0450792\pi$
$720$	−1.10757	−	2.78806i	−0.0412769	−	0.103905i
$721$	−19.1054	−	13.8809i	−0.711523	−	0.516952i
$722$	−32.4269	−	3.40821i	−1.20680	−	0.126840i
$723$	−1.37222	−	7.17109i	−0.0510336	−	0.266696i
$724$	−4.79676	+	10.7737i	−0.178270	+	0.400402i
$725$	5.86489	+	1.24662i	0.217817	+	0.0462983i
$726$	1.93148	−	4.11073i	0.0716840	−	0.152563i
$727$	7.87455	−	3.50598i	0.292051	−	0.130029i	−0.255481	−	0.966814i	$-0.582234\pi$
$727$	7.87455	−	3.50598i	0.292051	−	0.130029i	0.547532	+	0.836785i	$0.315567\pi$
$728$	1.83712	−	5.65407i	0.0680882	−	0.209554i
$729$	−23.6154	+	13.0887i	−0.874643	+	0.484768i
$730$	−0.731646	−	1.64330i	−0.0270794	−	0.0608214i
$731$	−1.97161	−	9.27568i	−0.0729225	−	0.343074i
$732$	20.1217	−	17.3887i	0.743719	−	0.642706i
$733$	2.05609	+	0.915431i	0.0759435	+	0.0338122i	0.444357	−	0.895850i	$-0.353432\pi$
$733$	2.05609	+	0.915431i	0.0759435	+	0.0338122i	−0.368413	+	0.929662i	$0.620099\pi$
$734$	−8.14245	+	9.04311i	−0.300543	+	0.333787i
$735$	−2.80626	−	2.63222i	−0.103510	−	0.0970910i
$736$	−3.21958	+	4.43137i	−0.118675	+	0.163342i
$737$	−2.30109	−	21.8934i	−0.0847618	−	0.806455i
$738$	17.8160	+	4.55258i	0.655815	+	0.167583i
$739$	−34.8580	+	20.1253i	−1.28227	+	0.740320i	−0.977263	−	0.212030i	$-0.931993\pi$
$739$	−34.8580	+	20.1253i	−1.28227	+	0.740320i	−0.305008	+	0.952350i	$0.598659\pi$
$740$	2.17761	−	1.58213i	0.0800505	−	0.0581601i
$741$	33.7183	−	2.85089i	1.23867	−	0.104730i
$742$	5.90514	−	1.91870i	0.216784	−	0.0704375i
$743$	−9.56261			−0.350818			−0.175409	−	0.984496i	$-0.556125\pi$
$743$	−9.56261			−0.350818			−0.175409	+	0.984496i	$0.556125\pi$
$744$	−9.20909	+	2.86229i	−0.337622	+	0.104937i
$745$	14.3618			0.526175
$746$	20.1464	−	6.54595i	0.737611	−	0.239664i
$747$	2.27408	−	3.59248i	0.0832041	−	0.131442i
$748$	−13.6931	+	9.94861i	−0.500669	+	0.363757i
$749$	−38.2599	+	22.0894i	−1.39799	+	0.807129i
$750$	1.59633	−	0.672113i	0.0582897	−	0.0245421i
$751$	3.86289	+	36.7530i	0.140959	+	1.34114i	0.804927	+	0.593374i	$0.202205\pi$
$751$	3.86289	+	36.7530i	0.140959	+	1.34114i	−0.663968	+	0.747761i	$0.731129\pi$
$752$	−6.40000	+	8.80885i	−0.233384	+	0.321226i
$753$	−11.3373	+	12.0869i	−0.413154	+	0.440470i
$754$	−10.9111	+	12.1181i	−0.397361	+	0.441314i
$755$	−21.6316	−	9.63100i	−0.787254	−	0.350508i
$756$	−6.26957	+	9.47180i	−0.228022	+	0.344486i
$757$	9.57884	+	45.0649i	0.348149	+	1.63791i	0.708943	+	0.705266i	$0.249173\pi$
$757$	9.57884	+	45.0649i	0.348149	+	1.63791i	−0.360794	+	0.932646i	$0.617494\pi$
$758$	1.41427	+	3.17651i	0.0513687	+	0.115376i
$759$	28.7418	−	20.0005i	1.04326	−	0.725974i
$760$	2.21989	−	6.83210i	0.0805237	−	0.247826i
$761$	27.2571	−	12.1356i	0.988069	−	0.439917i	0.151904	−	0.988395i	$-0.451459\pi$
$761$	27.2571	−	12.1356i	0.988069	−	0.439917i	0.836165	+	0.548479i	$0.184793\pi$
$762$	−23.1385	−	10.8719i	−0.838220	−	0.393849i
$763$	28.2303	+	6.00054i	1.02201	+	0.217234i
$764$	−4.28346	+	9.62081i	−0.154970	+	0.348069i
$765$	6.10293	−	12.3298i	0.220652	−	0.445784i
$766$	−3.63209	−	0.381749i	−0.131233	−	0.0137931i
$767$	−6.10640	−	4.43656i	−0.220489	−	0.160195i
$768$	0.896399	−	1.48205i	0.0323460	−	0.0534788i
$769$	−1.03301	+	1.78922i	−0.0372512	+	0.0645210i	−0.884050	−	0.467392i	$-0.845194\pi$
$769$	−1.03301	+	1.78922i	−0.0372512	+	0.0645210i	0.846799	+	0.531913i	$0.178527\pi$
$770$	4.03409	+	6.98725i	0.145378	+	0.251803i
$771$	0.347499	−	17.0569i	0.0125149	−	0.614289i
$772$	9.60740	+	10.6701i	0.345778	+	0.384025i
$773$	9.43346	+	29.0332i	0.339298	+	1.04425i	0.964566	+	0.263842i	$0.0849896\pi$
$773$	9.43346	+	29.0332i	0.339298	+	1.04425i	−0.625268	+	0.780410i	$0.715010\pi$
$774$	−1.67513	−	5.97316i	−0.0602112	−	0.214701i
$775$	−1.76050	−	5.28211i	−0.0632390	−	0.189739i
$776$		−	11.0202i		−	0.395601i
$777$	−9.62644	−	3.34609i	−0.345347	−	0.120040i
$778$	−21.6941	+	19.5334i	−0.777770	+	0.700307i
$779$	25.8816	+	35.6229i	0.927303	+	1.27632i
$780$	−0.587697	+	4.67367i	−0.0210429	+	0.167344i
$781$	−38.2177	−	22.0650i	−1.36754	−	0.789548i
$782$	−24.9812	+	2.62563i	−0.893326	+	0.0938924i
$783$	26.2768	−	16.7393i	0.939058	−	0.598214i
$784$	0.232198	−	2.20922i	0.00829279	−	0.0789006i
$785$	7.70318	+	6.93597i	0.274938	+	0.247555i
$786$	−16.6693	−	30.2803i	−0.594576	−	1.08006i
$787$	−4.25960	+	20.0399i	−0.151839	+	0.714344i	0.834685	+	0.550727i	$0.185649\pi$
$787$	−4.25960	+	20.0399i	−0.151839	+	0.714344i	−0.986524	+	0.163617i	$0.947684\pi$
$788$	−13.6918	+	2.91028i	−0.487750	+	0.103675i
$789$	24.3497	+	5.69643i	0.866871	+	0.202798i
$790$	10.0787	+	3.27475i	0.358582	+	0.116510i
$791$	−22.8206	−	7.41487i	−0.811408	−	0.263642i
$792$	−8.52340	+	7.06767i	−0.302866	+	0.251139i
$793$	−40.8446	+	8.68179i	−1.45043	+	0.308299i
$794$	1.94015	−	9.12770i	0.0688534	−	0.323930i
$795$	−4.30975	+	2.37253i	−0.152851	+	0.0841449i
$796$	−8.30524	−	7.47807i	−0.294371	−	0.265053i
$797$	−0.0364211	+	0.346523i	−0.00129010	+	0.0122745i	−0.995148	−	0.0983892i	$-0.968631\pi$
$797$	−0.0364211	+	0.346523i	−0.00129010	+	0.0122745i	0.993858	+	0.110664i	$0.0352977\pi$
$798$	−26.0340	+	7.87644i	−0.921594	+	0.278823i
$799$	−49.6587	+	5.21933i	−1.75680	+	0.184647i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−6.88274	+	7.04458i	−0.243190	+	0.248908i
$802$	−17.7755	−	24.4659i	−0.627676	−	0.863922i
$803$	−4.93385	+	4.44246i	−0.174112	+	0.156771i
$804$	−3.39187	+	9.75815i	−0.119622	+	0.344143i
$805$			11.9738i			0.422020i
$806$	14.8345	+	3.03620i	0.522524	+	0.106946i
$807$	−10.2438	−	7.76621i	−0.360599	−	0.273384i
$808$	−1.99274	−	6.13303i	−0.0701044	−	0.215759i
$809$	−3.55440	−	3.94756i	−0.124966	−	0.138789i	0.677415	−	0.735601i	$-0.263100\pi$
$809$	−3.55440	−	3.94756i	−0.124966	−	0.138789i	−0.802381	+	0.596812i	$0.796434\pi$
$810$	3.46859	−	8.30475i	0.121874	−	0.291799i
$811$	7.80808	+	13.5240i	0.274179	+	0.474892i	0.969928	−	0.243393i	$-0.0782606\pi$
$811$	7.80808	+	13.5240i	0.274179	+	0.474892i	−0.695749	+	0.718285i	$0.744927\pi$
$812$	6.55355	−	11.3511i	0.229984	−	0.398345i
$813$	−11.0158	−	6.66277i	−0.386341	−	0.233674i
$814$	−8.03720	−	5.83937i	−0.281704	−	0.204670i
$815$	−8.85404	−	0.930597i	−0.310144	−	0.0325974i
$816$	7.80136	−	1.49283i	0.273102	−	0.0522595i
$817$	6.04204	−	13.5707i	0.211384	−	0.474777i
$818$	−14.0360	−	2.98344i	−0.490756	−	0.104313i
$819$	15.7961	−	8.28108i	0.551959	−	0.289364i
$820$	−5.59956	+	2.49308i	−0.195545	+	0.0870623i
$821$	8.14824	−	25.0777i	0.284376	−	0.875218i	−0.702210	−	0.711970i	$-0.747803\pi$
$821$	8.14824	−	25.0777i	0.284376	−	0.875218i	0.986585	−	0.163248i	$-0.0521969\pi$
$822$	−5.49726	−	7.89984i	−0.191739	−	0.275539i
$823$	−11.2849	−	25.3462i	−0.393366	−	0.883514i	−0.996318	−	0.0857363i	$-0.972676\pi$
$823$	−11.2849	−	25.3462i	−0.393366	−	0.883514i	0.602952	−	0.797777i	$-0.293991\pi$
$824$	2.24609	+	10.5670i	0.0782462	+	0.368119i
$825$	−4.17991	−	4.83685i	−0.145526	−	0.168398i
$826$	5.54249	+	2.46767i	0.192848	+	0.0858614i
$827$	23.1122	−	25.6687i	0.803690	−	0.892588i	−0.192366	−	0.981323i	$-0.561616\pi$
$827$	23.1122	−	25.6687i	0.803690	−	0.892588i	0.996055	+	0.0887356i	$0.0282826\pi$
$828$	−16.1991	+	2.75901i	−0.562959	+	0.0958821i
$829$	−9.25079	+	12.7326i	−0.321293	+	0.442222i	−0.938861	−	0.344295i	$-0.888118\pi$
$829$	−9.25079	+	12.7326i	−0.321293	+	0.442222i	0.617568	+	0.786517i	$0.288118\pi$
$830$	0.148143	+	1.40948i	0.00514211	+	0.0489239i
$831$	−13.6485	−	32.4165i	−0.473462	−	1.12452i
$832$	−2.35524	+	1.35980i	−0.0816532	+	0.0471425i
$833$	8.24140	−	5.98773i	0.285548	−	0.207462i
$834$	−0.769584	−	9.10209i	−0.0266485	−	0.315180i
$835$	10.8691	−	3.53159i	0.376142	−	0.122216i
$836$	−26.5138			−0.917000
$837$	−25.7620	−	13.1651i	−0.890464	−	0.455054i
$838$	0.540546			0.0186728
$839$	11.2449	−	3.65369i	0.388217	−	0.126139i	−0.108404	−	0.994107i	$-0.534574\pi$
$839$	11.2449	−	3.65369i	0.388217	−	0.126139i	0.496621	+	0.867968i	$0.334574\pi$
$840$	−0.318992	−	3.77281i	−0.0110063	−	0.130174i
$841$	−5.62348	+	4.08570i	−0.193913	+	0.140886i
$842$	15.5738	−	8.99155i	0.536709	−	0.309869i
$843$	−17.6629	−	41.9509i	−0.608342	−	1.44487i
$844$	−0.605200	−	5.75809i	−0.0208318	−	0.198202i
$845$	−3.29384	+	4.53358i	−0.113311	+	0.155960i
$846$	−32.2013	+	5.48446i	−1.10710	+	0.188560i
$847$	3.83564	−	4.25990i	0.131794	−	0.146372i
$848$	−2.59479	−	1.15528i	−0.0891056	−	0.0396724i
$849$	0.248252	+	0.287270i	0.00852000	+	0.00985907i
$850$	0.953450	+	4.48563i	0.0327031	+	0.153856i
$851$	−5.99675	−	13.4689i	−0.205566	−	0.461708i
$852$	11.8290	+	16.9988i	0.405254	+	0.582370i
$853$	15.0978	−	46.4663i	0.516940	−	1.59098i	−0.262785	−	0.964854i	$-0.584641\pi$
$853$	15.0978	−	46.4663i	0.516940	−	1.59098i	0.779725	−	0.626122i	$-0.215359\pi$
$854$	30.6625	−	13.6518i	1.04925	−	0.467156i
$855$	19.0872	−	10.0064i	0.652768	−	0.342213i
$856$	19.7682	+	4.20186i	0.675663	+	0.143617i
$857$	−12.2561	+	27.5277i	−0.418661	+	0.940328i	0.573939	+	0.818898i	$0.305415\pi$
$857$	−12.2561	+	27.5277i	−0.418661	+	0.940328i	−0.992600	+	0.121430i	$0.961252\pi$
$858$	17.0758	−	3.26753i	0.582957	−	0.111552i
$859$	36.7520	+	3.86279i	1.25396	+	0.131797i	0.708121	−	0.706091i	$-0.249543\pi$
$859$	36.7520	+	3.86279i	1.25396	+	0.131797i	0.545842	+	0.837888i	$0.316210\pi$
$860$	1.67294	+	1.21546i	0.0570468	+	0.0414469i
$861$	19.8581	+	12.0109i	0.676762	+	0.409331i
$862$	−10.1194	+	17.5274i	−0.344670	+	0.596985i
$863$	−5.92627	−	10.2646i	−0.201733	−	0.349411i	0.747354	−	0.664426i	$-0.231324\pi$
$863$	−5.92627	−	10.2646i	−0.201733	−	0.349411i	−0.949087	+	0.315015i	$0.897991\pi$
$864$	5.03067	−	1.30089i	0.171147	−	0.0442573i
$865$	8.03579	+	8.92465i	0.273225	+	0.303447i
$866$	−10.2092	−	31.4207i	−0.346923	−	1.06772i
$867$	5.56225	+	4.21695i	0.188904	+	0.143215i
$868$	−12.1708	+	0.0919725i	−0.413104	+	0.00312175i
$869$		−	39.1130i		−	1.32682i
$870$	−3.40973	+	9.80953i	−0.115601	+	0.332574i
$871$	12.0546	−	10.8540i	0.408454	−	0.367774i
$872$	−7.76031	−	10.6811i	−0.262797	−	0.361709i
$873$	23.1041	−	23.6473i	0.781955	−	0.800341i
$874$	−34.0768	−	19.6742i	−1.15266	−	0.665491i
$875$	2.17403	−	0.228500i	0.0734956	−	0.00772470i
$876$	2.98215	−	0.902233i	0.100758	−	0.0304836i
$877$	−0.710708	+	6.76193i	−0.0239989	+	0.228334i	0.975948	+	0.218005i	$0.0699548\pi$
$877$	−0.710708	+	6.76193i	−0.0239989	+	0.228334i	−0.999947	+	0.0103297i	$0.996712\pi$
$878$	−0.136714	−	0.123097i	−0.00461386	−	0.00415434i
$879$	−8.81685	+	4.85370i	−0.297385	+	0.163711i
$880$	0.767368	−	3.61018i	0.0258680	−	0.121699i
$881$	5.18548	−	1.10221i	0.174703	−	0.0371343i	−0.119729	−	0.992807i	$-0.538203\pi$
$881$	5.18548	−	1.10221i	0.174703	−	0.0371343i	0.294433	+	0.955672i	$0.404869\pi$
$882$	5.12995	−	4.25379i	0.172734	−	0.143232i
$883$	−11.4622	−	3.72430i	−0.385735	−	0.125333i	0.109729	−	0.993962i	$-0.465002\pi$
$883$	−11.4622	−	3.72430i	−0.385735	−	0.125333i	−0.495463	+	0.868629i	$0.665002\pi$
$884$	−11.8612	−	3.85394i	−0.398936	−	0.129622i
$885$	−4.68073	−	1.09502i	−0.157341	−	0.0368088i
$886$	−17.3988	+	3.69823i	−0.584525	+	0.124245i
$887$	8.10250	−	38.1193i	0.272055	−	1.27992i	−0.603719	−	0.797198i	$-0.706315\pi$
$887$	8.10250	−	38.1193i	0.272055	−	1.27992i	0.875774	−	0.482722i	$-0.160352\pi$
$888$	2.24834	+	4.08415i	0.0754492	+	0.137055i
$889$	−23.9782	−	21.5901i	−0.804203	−	0.724107i
$890$	0.343159	−	3.26494i	0.0115027	−	0.109441i
$891$	−33.1073	−	2.70359i	−1.10914	−	0.0905735i
$892$	2.71236	−	0.285081i	0.0908166	−	0.00954521i
$893$	−67.7392	−	39.1093i	−2.26681	−	1.30874i
$894$	−3.10354	+	24.6810i	−0.103798	+	0.825455i
$895$	11.1959	+	15.4099i	0.374238	+	0.515095i
$896$	1.62452	−	1.46272i	0.0542713	−	0.0488661i
$897$	24.3712	+	8.47126i	0.813730	+	0.282847i
$898$			11.6223i			0.387842i
$899$	30.5994	+	13.3476i	1.02055	+	0.445167i
$900$	0.810075	+	2.88856i	0.0270025	+	0.0962853i
$901$	−4.02508	−	12.3879i	−0.134095	−	0.412701i
$902$	15.1377	+	16.8121i	0.504029	+	0.559781i
$903$	0.159477	−	7.82788i	0.00530706	−	0.260495i
$904$	5.48833	+	9.50606i	0.182539	+	0.316167i
$905$	5.89665	−	10.2133i	0.196011	−	0.339501i
$906$	21.2256	−	35.0930i	0.705172	−	1.16589i
$907$	22.9450	+	16.6705i	0.761875	+	0.553535i	0.899485	−	0.436952i	$-0.143942\pi$
$907$	22.9450	+	16.6705i	0.761875	+	0.553535i	−0.137610	+	0.990487i	$0.543942\pi$
$908$	23.2770	+	2.44651i	0.772475	+	0.0811904i
$909$	8.58200	−	17.3383i	0.284647	−	0.575073i
$910$	−2.41807	+	5.43107i	−0.0801581	+	0.180038i
$911$	10.2922	+	2.18767i	0.340995	+	0.0724807i	0.375226	−	0.926933i	$-0.377565\pi$
$911$	10.2922	+	2.18767i	0.340995	+	0.0724807i	−0.0342314	+	0.999414i	$0.510898\pi$
$912$	11.2614	+	5.29131i	0.372901	+	0.175213i
$913$	4.77860	−	2.12757i	0.158148	−	0.0704122i
$914$	−5.46852	+	16.8304i	−0.180883	+	0.556699i
$915$	−21.8291	+	15.1902i	−0.721647	+	0.502172i
$916$	2.73696	+	6.14731i	0.0904316	+	0.203113i
$917$	−9.07005	−	42.6712i	−0.299520	−	1.40913i
$918$	19.8701	+	13.1524i	0.655812	+	0.434095i
$919$	−34.2566	−	15.2520i	−1.13002	−	0.503118i	−0.245397	−	0.969423i	$-0.578918\pi$
$919$	−34.2566	−	15.2520i	−1.13002	−	0.503118i	−0.884624	+	0.466305i	$0.845585\pi$
$920$	3.66514	−	4.07055i	0.120836	−	0.134202i
$921$	−30.2633	+	32.2643i	−0.997211	+	1.06314i
$922$	−21.8334	+	30.0510i	−0.719043	+	0.989678i
$923$	−3.39898	−	32.3391i	−0.111879	−	1.06445i
$924$	−12.8795	+	5.42273i	−0.423703	+	0.178395i
$925$	−2.33106	+	1.34584i	−0.0766447	+	0.0442508i
$926$	−6.38766	+	4.64091i	−0.209912	+	0.152510i
$927$	−17.3343	+	27.3840i	−0.569334	+	0.899407i
$928$	−5.70246	+	1.85284i	−0.187192	+	0.0608225i
$929$	−55.3918			−1.81734			−0.908672	−	0.417510i	$-0.862903\pi$
$929$	−55.3918			−1.81734			−0.908672	+	0.417510i	$0.862903\pi$
$930$	9.45783	−	1.88400i	0.310134	−	0.0617787i
$931$	15.9578			0.522995
$932$	−0.931250	+	0.302581i	−0.0305041	+	0.00991138i
$933$	17.6174	−	1.48955i	0.576767	−	0.0487658i
$934$	28.8659	−	20.9723i	0.944520	−	0.686234i
$935$	14.6580	−	8.46279i	0.479367	−	0.276763i
$936$	−7.90478	−	2.01994i	−0.258376	−	0.0660237i
$937$	2.33085	+	22.1766i	0.0761457	+	0.724478i	0.964278	+	0.264891i	$0.0853359\pi$
$937$	2.33085	+	22.1766i	0.0761457	+	0.724478i	−0.888133	+	0.459587i	$0.847997\pi$
$938$	−7.66381	+	10.5483i	−0.250232	+	0.344415i
$939$	28.8973	+	27.1052i	0.943028	+	0.884544i
$940$	7.28572	−	8.09161i	0.237634	−	0.263919i
$941$	13.4969	+	6.00921i	0.439986	+	0.195895i	0.614760	−	0.788714i	$-0.289253\pi$
$941$	13.4969	+	6.00921i	0.439986	+	0.195895i	−0.174774	+	0.984609i	$0.555919\pi$
$942$	−13.5842	+	11.7392i	−0.442598	+	0.382484i
$943$	6.98044	+	32.8404i	0.227314	+	1.06943i
$944$	−1.12885	−	2.53544i	−0.0367410	−	0.0825216i
$945$	7.22530	−	8.76456i	0.235039	−	0.285111i
$946$	2.35846	−	7.25861i	0.0766803	−	0.235998i
$947$	−39.9597	+	17.7912i	−1.29852	+	0.578137i	−0.935395	−	0.353605i	$-0.884956\pi$
$947$	−39.9597	+	17.7912i	−1.29852	+	0.578137i	−0.363122	+	0.931742i	$0.618289\pi$
$948$	−7.80569	+	16.6127i	−0.253517	+	0.539555i
$949$	−4.78516	−	1.01712i	−0.155333	−	0.0330170i
$950$	−2.92187	+	6.56264i	−0.0947981	+	0.212920i
$951$	−4.46536	−	23.3355i	−0.144799	−	0.756705i
$952$	9.96975	+	1.04786i	0.323122	+	0.0339614i
$953$	10.2091	+	7.41738i	0.330707	+	0.240272i	0.740730	−	0.671802i	$-0.234480\pi$
$953$	10.2091	+	7.41738i	0.330707	+	0.240272i	−0.410024	+	0.912075i	$0.634480\pi$
$954$	−3.14590	−	7.91908i	−0.101852	−	0.256390i
$955$	5.26564	−	9.12036i	0.170392	−	0.295128i
$956$	−6.33901	−	10.9795i	−0.205018	−	0.355102i
$957$	38.3222	+	0.780736i	1.23878	+	0.0252376i
$958$	14.3354	+	15.9211i	0.463156	+	0.514387i
$959$	−3.75355	−	11.5522i	−0.121209	−	0.373041i
$960$	−1.04640	+	1.38023i	−0.0337726	+	0.0445468i
$961$	−3.70594	−	30.7777i	−0.119546	−	0.992829i
$962$		−	7.32026i		−	0.236015i
$963$	33.6098	+	50.4611i	1.08306	+	1.62609i
$964$	−3.13262	+	2.82062i	−0.100895	+	0.0908461i
$965$	−8.43944	−	11.6159i	−0.271675	−	0.373929i
$966$	−20.5771	−	2.58750i	−0.662058	−	0.0832515i
$967$	36.3692	+	20.9978i	1.16956	+	0.675243i	0.953575	−	0.301154i	$-0.0973719\pi$
$967$	36.3692	+	20.9978i	1.16956	+	0.675243i	0.215980	+	0.976398i	$0.430705\pi$
$968$	−2.60789	+	0.274101i	−0.0838209	+	0.00880993i
$969$	16.5233	+	54.6147i	0.530806	+	1.75448i
$970$	−1.15192	+	10.9598i	−0.0369859	+	0.351898i
$971$	21.1277	+	19.0235i	0.678021	+	0.610493i	0.934460	−	0.356068i	$-0.115883\pi$
$971$	21.1277	+	19.0235i	0.678021	+	0.610493i	−0.256439	+	0.966560i	$0.582549\pi$
$972$	13.5223	+	7.75546i	0.433728	+	0.248757i
$973$	2.39694	−	11.2767i	0.0768424	−	0.361515i
$974$	−33.6456	+	7.15159i	−1.07807	+	0.229152i
$975$	1.07301	−	4.58663i	0.0343638	−	0.146890i
$976$	−14.6027	−	4.74470i	−0.467420	−	0.151874i
$977$	−3.23480	−	1.05105i	−0.103491	−	0.0336261i	0.256814	−	0.966461i	$-0.417327\pi$
$977$	−3.23480	−	1.05105i	−0.103491	−	0.0336261i	−0.360305	+	0.932835i	$0.617327\pi$
$978$	3.51258	−	15.0147i	0.112320	−	0.480118i
$979$	−11.8519	+	2.51921i	−0.378790	+	0.0805142i
$980$	−0.461852	+	2.17284i	−0.0147533	+	0.0694090i
$981$	5.74106	−	39.1896i	0.183298	−	1.25123i
$982$	2.49274	+	2.24447i	0.0795464	+	0.0716239i
$983$	1.07992	−	10.2747i	0.0344440	−	0.327713i	−0.963709	−	0.266956i	$-0.913982\pi$
$983$	1.07992	−	10.2747i	0.0344440	−	0.327713i	0.998153	−	0.0607565i	$-0.0193513\pi$
$984$	−3.07436	−	10.1617i	−0.0980070	−	0.323943i
$985$	13.9210	−	1.46316i	0.443560	−	0.0466201i
$986$	−23.8125	−	13.7482i	−0.758345	−	0.437831i
$987$	−40.9041	−	5.14354i	−1.30199	−	0.163721i
$988$	−11.4834	−	15.8056i	−0.365336	−	0.502842i
$989$	8.41736	−	7.57903i	0.267657	−	0.240999i
$990$	9.21548	−	6.13801i	0.292887	−	0.195079i
$991$		−	22.5140i		−	0.715181i	−0.933878	−	0.357591i	$-0.883598\pi$
$991$		−	22.5140i		−	0.715181i	0.933878	−	0.357591i	$-0.116402\pi$
$992$	4.16569	+	3.69419i	0.132261	+	0.117291i
$993$	16.3539	−	21.5711i	0.518975	−	0.684540i
$994$	8.07686	+	24.8580i	0.256183	+	0.788449i
$995$	7.47807	+	8.30524i	0.237071	+	0.263294i
$996$	−2.45424	−	0.0500000i	−0.0777654	−	0.00158431i
$997$	10.5595	+	18.2896i	0.334424	+	0.579239i	0.983374	−	0.181592i	$-0.0581250\pi$
$997$	10.5595	+	18.2896i	0.334424	+	0.579239i	−0.648950	+	0.760831i	$0.724792\pi$
$998$	12.4415	−	21.5493i	0.393828	−	0.682130i
$999$	−3.73801	+	13.4776i	−0.118265	+	0.426412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.7	✓	176
3.2	odd	2	inner	930.2.br.b.11.13	yes	176
31.17	odd	30	inner	930.2.br.b.761.13	yes	176
93.17	even	30	inner	930.2.br.b.761.7	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.7	✓	176	1.1	even	1	trivial
930.2.br.b.11.13	yes	176	3.2	odd	2	inner
930.2.br.b.761.7	yes	176	93.17	even	30	inner
930.2.br.b.761.13	yes	176	31.17	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.145925 + 1.72589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.672113 - 1.59633i) q^{6} +(-0.228500 - 2.17403i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.95741 + 0.503701i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.145925 + 1.72589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.672113 - 1.59633i) q^{6} +(-0.228500 - 2.17403i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.95741 + 0.503701i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.37174 - 1.50120i) q^{11} +(1.13251 + 1.31050i) q^{12} +(-0.565435 - 2.66016i) q^{13} +(0.889128 + 1.99701i) q^{14} +(-0.989321 - 1.42170i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.18937 - 1.86523i) q^{17} +(2.65701 - 1.39294i) q^{18} +(7.02672 + 1.49358i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(3.71880 - 0.711610i) q^{21} +(3.67062 + 0.385797i) q^{22} +(4.43137 + 3.21958i) q^{23} +(-1.48205 - 0.896399i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.35980 + 2.35524i) q^{26} +(-1.30089 - 5.03067i) q^{27} +(-1.46272 - 1.62452i) q^{28} +(1.85284 + 5.70246i) q^{29} +(1.38023 + 1.04640i) q^{30} +(3.69419 - 4.16569i) q^{31} +1.00000i q^{32} +(2.09889 - 6.03833i) q^{33} +(-3.40794 + 3.06853i) q^{34} +(1.28490 + 1.76851i) q^{35} +(-2.09653 + 2.14583i) q^{36} +(-2.33106 - 1.34584i) q^{37} +(-7.14435 + 0.750901i) q^{38} +(4.50865 - 1.36406i) q^{39} +(0.104528 - 0.994522i) q^{40} +(4.55509 + 4.10142i) q^{41} +(-3.31689 + 1.82595i) q^{42} +(0.429934 - 2.02268i) q^{43} +(-3.61018 + 0.767368i) q^{44} +(2.30934 - 1.91492i) q^{45} +(-5.20938 - 1.69263i) q^{46} +(-10.3554 - 3.36468i) q^{47} +(1.68651 + 0.394548i) q^{48} +(2.17284 - 0.461852i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(3.83052 + 6.95823i) q^{51} +(-2.02105 - 1.81976i) q^{52} +(0.296898 - 2.82480i) q^{53} +(2.79179 + 4.38246i) q^{54} +(3.67062 - 0.385797i) q^{55} +(1.89313 + 1.09300i) q^{56} +(-1.55238 + 12.3453i) q^{57} +(-3.52431 - 4.85080i) q^{58} +(2.06251 - 1.85710i) q^{59} +(-1.63603 - 0.568675i) q^{60} -15.3542i q^{61} +(-2.22611 + 5.10337i) q^{62} +(1.77083 + 6.31440i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.81976 + 2.02105i) q^{65} +(-0.130211 + 6.39139i) q^{66} +(2.98226 + 5.16542i) q^{67} +(2.29292 - 3.97146i) q^{68} +(-4.91000 + 8.11788i) q^{69} +(-1.76851 - 1.28490i) q^{70} +(11.8911 + 1.24981i) q^{71} +(1.33082 - 2.68866i) q^{72} +(0.731646 - 1.64330i) q^{73} +(2.63285 + 0.559630i) q^{74} +(1.56763 + 0.736572i) q^{75} +(6.56264 - 2.92187i) q^{76} +(-2.49320 + 7.67329i) q^{77} +(-3.86646 + 2.69055i) q^{78} +(4.31032 + 9.68114i) q^{79} +(0.207912 + 0.978148i) q^{80} +(8.49257 - 2.97930i) q^{81} +(-5.59956 - 2.49308i) q^{82} +(-0.948324 + 1.05322i) q^{83} +(2.59030 - 2.76156i) q^{84} +(-2.69549 + 3.71002i) q^{85} +(0.216151 + 2.05654i) q^{86} +(-9.57145 + 4.02993i) q^{87} +(3.19636 - 1.84542i) q^{88} +(2.65594 - 1.92965i) q^{89} +(-1.60457 + 2.53483i) q^{90} +(-5.65407 + 1.83712i) q^{91} +5.47747 q^{92} +(7.72861 + 5.76790i) q^{93} +10.8883 q^{94} +(-6.83210 + 2.21989i) q^{95} +(-1.72589 + 0.145925i) q^{96} +(-8.91550 + 6.47749i) q^{97} +(-1.92378 + 1.11069i) q^{98} +(10.7278 + 2.74131i) 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	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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