LMFDB - Embedded newform 930.2.br.b.11.19

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			11.19
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(1.16166 + 1.28473i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.50181 + 0.862882i) q^{6} +(-0.480398 - 4.57068i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.301087 + 2.98485i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(1.16166 + 1.28473i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.50181 + 0.862882i) q^{6} +(-0.480398 - 4.57068i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.301087 + 2.98485i) q^{9} +(0.669131 - 0.743145i) q^{10} +(0.516409 + 0.229920i) q^{11} +(1.69495 + 0.356565i) q^{12} +(-1.00968 - 4.75019i) q^{13} +(-1.86930 - 4.19852i) q^{14} +(1.64840 + 0.531782i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.72428 - 0.767698i) q^{17} +(0.636020 + 2.93180i) q^{18} +(0.927360 + 0.197116i) q^{19} +(0.406737 - 0.913545i) q^{20} +(5.31405 - 5.92676i) q^{21} +(0.562183 + 0.0590878i) q^{22} +(1.21642 + 0.883780i) q^{23} +(1.72218 - 0.184656i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.42816 - 4.20569i) q^{26} +(-4.18450 + 3.08057i) q^{27} +(-3.07523 - 3.41539i) q^{28} +(0.844119 + 2.59793i) q^{29} +(1.73205 - 0.00362720i) q^{30} +(4.21421 + 3.63874i) q^{31} -1.00000i q^{32} +(0.304506 + 0.930537i) q^{33} +(1.40265 - 1.26296i) q^{34} +(-2.70138 - 3.71812i) q^{35} +(1.51087 + 2.59177i) q^{36} +(-3.87698 - 2.23838i) q^{37} +(0.942884 - 0.0991011i) q^{38} +(4.92982 - 6.81528i) q^{39} +(0.104528 - 0.994522i) q^{40} +(6.77733 + 6.10233i) q^{41} +(3.22249 - 7.27882i) q^{42} +(-2.64923 + 12.4637i) q^{43} +(0.552927 - 0.117528i) q^{44} +(1.23168 + 2.73550i) q^{45} +(1.42999 + 0.464631i) q^{46} +(-9.02610 - 2.93276i) q^{47} +(1.58083 - 0.707801i) q^{48} +(-13.8133 + 2.93610i) q^{49} +(0.207912 - 0.978148i) q^{50} +(2.98932 + 1.32343i) q^{51} +(-3.60894 - 3.24951i) q^{52} +(0.0116490 - 0.110832i) q^{53} +(-3.02775 + 4.22288i) q^{54} +(0.562183 - 0.0590878i) q^{55} +(-3.98013 - 2.29793i) q^{56} +(0.824036 + 1.42039i) q^{57} +(1.60561 + 2.20993i) q^{58} +(2.10574 - 1.89601i) q^{59} +(1.64615 - 0.538682i) q^{60} +4.31193i q^{61} +(5.13239 + 2.15838i) q^{62} +(13.7874 - 0.0577467i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.24951 - 3.60894i) q^{65} +(0.577154 + 0.790896i) q^{66} +(-3.48591 - 6.03777i) q^{67} +(0.943729 - 1.63459i) q^{68} +(0.277644 + 2.58943i) q^{69} +(-3.71812 - 2.70138i) q^{70} +(9.48638 + 0.997059i) q^{71} +(2.23782 + 1.99804i) q^{72} +(-3.17525 + 7.13174i) q^{73} +(-4.37893 - 0.930770i) q^{74} +(1.69344 - 0.363661i) q^{75} +(0.866112 - 0.385618i) q^{76} +(0.802808 - 2.47079i) q^{77} +(2.58250 - 8.00512i) q^{78} +(5.71023 + 12.8254i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.81869 - 1.79740i) q^{81} +(8.33135 + 3.70936i) q^{82} +(6.99219 - 7.76562i) q^{83} +(0.815493 - 7.91837i) q^{84} +(1.10942 - 1.52699i) q^{85} +(1.33191 + 12.6723i) q^{86} +(-2.35707 + 4.10239i) q^{87} +(0.489546 - 0.282640i) q^{88} +(-1.50357 + 1.09240i) q^{89} +(2.01671 + 2.22101i) q^{90} +(-21.2265 + 6.89692i) q^{91} +1.50358 q^{92} +(0.220672 + 9.64113i) q^{93} -9.49061 q^{94} +(0.901676 - 0.292972i) q^{95} +(1.28473 - 1.16166i) q^{96} +(-1.12756 + 0.819221i) q^{97} +(-12.2299 + 7.06094i) q^{98} +(-0.841761 + 1.47218i) 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
$3$	1.16166	+	1.28473i	0.670685	+	0.741742i
$3$	1.16166	+	1.28473i	0.670685	+	0.741742i
$4$	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
$6$	1.50181	+	0.862882i	0.613111	+	0.352270i
$7$	−0.480398	−	4.57068i	−0.181573	−	1.72755i	−0.583700	−	0.811970i	$-0.698395\pi$
$7$	−0.480398	−	4.57068i	−0.181573	−	1.72755i	0.402126	−	0.915584i	$-0.368271\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−0.301087	+	2.98485i	−0.100362	+	0.994951i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	0.516409	+	0.229920i	0.155703	+	0.0693235i	0.483109	−	0.875560i	$-0.339508\pi$
$11$	0.516409	+	0.229920i	0.155703	+	0.0693235i	−0.327406	+	0.944884i	$0.606174\pi$
$12$	1.69495	+	0.356565i	0.489290	+	0.102931i
$13$	−1.00968	−	4.75019i	−0.280036	−	1.31747i	−0.863098	−	0.505037i	$-0.831479\pi$
$13$	−1.00968	−	4.75019i	−0.280036	−	1.31747i	0.583062	−	0.812428i	$-0.301855\pi$
$14$	−1.86930	−	4.19852i	−0.499592	−	1.12210i
$15$	1.64840	+	0.531782i	0.425614	+	0.137306i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.72428	−	0.767698i	0.418199	−	0.186194i	−0.186839	−	0.982390i	$-0.559824\pi$
$17$	1.72428	−	0.767698i	0.418199	−	0.186194i	0.605038	+	0.796196i	$0.293158\pi$
$18$	0.636020	+	2.93180i	0.149911	+	0.691033i
$19$	0.927360	+	0.197116i	0.212751	+	0.0452216i	0.313054	−	0.949735i	$-0.398648\pi$
$19$	0.927360	+	0.197116i	0.212751	+	0.0452216i	−0.100303	+	0.994957i	$0.531981\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	5.31405	−	5.92676i	1.15962	−	1.29333i
$22$	0.562183	+	0.0590878i	0.119858	+	0.0125976i
$23$	1.21642	+	0.883780i	0.253641	+	0.184281i	0.707339	−	0.706875i	$-0.249896\pi$
$23$	1.21642	+	0.883780i	0.253641	+	0.184281i	−0.453698	+	0.891156i	$0.649896\pi$
$24$	1.72218	−	0.184656i	0.351538	−	0.0376927i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.42816	−	4.20569i	−0.476200	−	0.824803i
$27$	−4.18450	+	3.08057i	−0.805308	+	0.592856i
$28$	−3.07523	−	3.41539i	−0.581163	−	0.645447i
$29$	0.844119	+	2.59793i	0.156749	+	0.482424i	0.998334	−	0.0577011i	$-0.0183770\pi$
$29$	0.844119	+	2.59793i	0.156749	+	0.482424i	−0.841585	+	0.540125i	$0.818377\pi$
$30$	1.73205	−	0.00362720i	0.316227	−	0.000662233i
$31$	4.21421	+	3.63874i	0.756895	+	0.653537i
$31$	4.21421	+	3.63874i	0.756895	+	0.653537i
$32$		−	1.00000i		−	0.176777i
$33$	0.304506	+	0.930537i	0.0530076	+	0.161986i
$34$	1.40265	−	1.26296i	0.240553	−	0.216595i
$35$	−2.70138	−	3.71812i	−0.456616	−	0.628478i
$36$	1.51087	+	2.59177i	0.251811	+	0.431962i
$37$	−3.87698	−	2.23838i	−0.637372	−	0.367987i	0.146229	−	0.989251i	$-0.453286\pi$
$37$	−3.87698	−	2.23838i	−0.637372	−	0.367987i	−0.783602	+	0.621264i	$0.786620\pi$
$38$	0.942884	−	0.0991011i	0.152956	−	0.0160763i
$39$	4.92982	−	6.81528i	0.789403	−	1.09132i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	6.77733	+	6.10233i	1.05844	+	0.953025i	0.998978	−	0.0452059i	$-0.0143944\pi$
$41$	6.77733	+	6.10233i	1.05844	+	0.953025i	0.0594633	+	0.998230i	$0.481061\pi$
$42$	3.22249	−	7.27882i	0.497241	−	1.12315i
$43$	−2.64923	+	12.4637i	−0.404004	+	1.90069i	0.0295506	+	0.999563i	$0.490592\pi$
$43$	−2.64923	+	12.4637i	−0.404004	+	1.90069i	−0.433555	+	0.901127i	$0.642741\pi$
$44$	0.552927	−	0.117528i	0.0833569	−	0.0177180i
$45$	1.23168	+	2.73550i	0.183608	+	0.407785i
$46$	1.42999	+	0.464631i	0.210840	+	0.0685061i
$47$	−9.02610	−	2.93276i	−1.31659	−	0.427787i	−0.435269	−	0.900300i	$-0.643347\pi$
$47$	−9.02610	−	2.93276i	−1.31659	−	0.427787i	−0.881323	+	0.472514i	$0.843347\pi$
$48$	1.58083	−	0.707801i	0.228173	−	0.102162i
$49$	−13.8133	+	2.93610i	−1.97333	+	0.419443i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	2.98932	+	1.32343i	0.418588	+	0.185318i
$52$	−3.60894	−	3.24951i	−0.500470	−	0.450625i
$53$	0.0116490	−	0.110832i	0.00160011	−	0.0152240i	−0.993693	−	0.112137i	$-0.964230\pi$
$53$	0.0116490	−	0.110832i	0.00160011	−	0.0152240i	0.995293	+	0.0969134i	$0.0308970\pi$
$54$	−3.02775	+	4.22288i	−0.412025	+	0.574661i
$55$	0.562183	−	0.0590878i	0.0758047	−	0.00796740i
$56$	−3.98013	−	2.29793i	−0.531867	−	0.307073i
$57$	0.824036	+	1.42039i	0.109146	+	0.188136i
$58$	1.60561	+	2.20993i	0.210827	+	0.290178i
$59$	2.10574	−	1.89601i	0.274143	−	0.246840i	−0.520578	−	0.853814i	$-0.674284\pi$
$59$	2.10574	−	1.89601i	0.274143	−	0.246840i	0.794722	+	0.606974i	$0.207617\pi$
$60$	1.64615	−	0.538682i	0.212518	−	0.0695435i
$61$			4.31193i			0.552087i	0.961145	+	0.276043i	$0.0890233\pi$
$61$			4.31193i			0.552087i	−0.961145	+	0.276043i	$0.910977\pi$
$62$	5.13239	+	2.15838i	0.651814	+	0.274115i
$63$	13.7874	−	0.0577467i	1.73705	−	0.00727540i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−3.24951	−	3.60894i	−0.403052	−	0.447634i
$66$	0.577154	+	0.790896i	0.0710427	+	0.0973525i
$67$	−3.48591	−	6.03777i	−0.425871	−	0.737631i	0.570630	−	0.821207i	$-0.306699\pi$
$67$	−3.48591	−	6.03777i	−0.425871	−	0.737631i	−0.996501	+	0.0835763i	$0.973366\pi$
$68$	0.943729	−	1.63459i	0.114444	−	0.198223i
$69$	0.277644	+	2.58943i	0.0334244	+	0.311731i
$70$	−3.71812	−	2.70138i	−0.444401	−	0.322876i
$71$	9.48638	+	0.997059i	1.12583	+	0.118329i	0.649086	−	0.760715i	$-0.275152\pi$
$71$	9.48638	+	0.997059i	1.12583	+	0.118329i	0.476740	+	0.879044i	$0.341818\pi$
$72$	2.23782	+	1.99804i	0.263730	+	0.235471i
$73$	−3.17525	+	7.13174i	−0.371635	+	0.834707i	0.626821	+	0.779163i	$0.284356\pi$
$73$	−3.17525	+	7.13174i	−0.371635	+	0.834707i	−0.998456	+	0.0555435i	$0.982311\pi$
$74$	−4.37893	−	0.930770i	−0.509040	−	0.108200i
$75$	1.69344	−	0.363661i	0.195542	−	0.0419919i
$76$	0.866112	−	0.385618i	0.0993499	−	0.0442334i
$77$	0.802808	−	2.47079i	0.0914885	−	0.281573i
$78$	2.58250	−	8.00512i	0.292411	−	0.906401i
$79$	5.71023	+	12.8254i	0.642451	+	1.44297i	0.881606	+	0.471986i	$0.156463\pi$
$79$	5.71023	+	12.8254i	0.642451	+	1.44297i	−0.239155	+	0.970981i	$0.576870\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	−8.81869	−	1.79740i	−0.979855	−	0.199711i
$82$	8.33135	+	3.70936i	0.920044	+	0.409630i
$83$	6.99219	−	7.76562i	0.767493	−	0.852387i	−0.225042	−	0.974349i	$-0.572252\pi$
$83$	6.99219	−	7.76562i	0.767493	−	0.852387i	0.992535	+	0.121962i	$0.0389186\pi$
$84$	0.815493	−	7.91837i	0.0889775	−	0.863965i
$85$	1.10942	−	1.52699i	0.120333	−	0.165625i
$86$	1.33191	+	12.6723i	0.143624	+	1.36649i
$87$	−2.35707	+	4.10239i	−0.252705	+	0.439822i
$88$	0.489546	−	0.282640i	0.0521858	−	0.0301295i
$89$	−1.50357	+	1.09240i	−0.159378	+	0.115795i	−0.664616	−	0.747185i	$-0.731405\pi$
$89$	−1.50357	+	1.09240i	−0.159378	+	0.115795i	0.505238	+	0.862980i	$0.331405\pi$
$90$	2.01671	+	2.22101i	0.212580	+	0.234115i
$91$	−21.2265	+	6.89692i	−2.22515	+	0.722993i
$92$	1.50358			0.156759
$93$	0.220672	+	9.64113i	0.0228827	+	0.999738i
$94$	−9.49061			−0.978881
$95$	0.901676	−	0.292972i	0.0925100	−	0.0300583i
$96$	1.28473	−	1.16166i	0.131123	−	0.118562i
$97$	−1.12756	+	0.819221i	−0.114486	+	0.0831793i	−0.643555	−	0.765400i	$-0.722541\pi$
$97$	−1.12756	+	0.819221i	−0.114486	+	0.0831793i	0.529069	+	0.848579i	$0.322541\pi$
$98$	−12.2299	+	7.06094i	−1.23541	+	0.713263i
$99$	−0.841761	+	1.47218i	−0.0846001	+	0.147959i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	8.22058	−	11.3147i	0.817978	−	1.12585i	−0.172065	−	0.985086i	$-0.555044\pi$
$101$	8.22058	−	11.3147i	0.817978	−	1.12585i	0.990043	−	0.140765i	$-0.0449562\pi$
$102$	3.25197	+	0.334912i	0.321993	+	0.0331612i
$103$	−2.70848	+	3.00807i	−0.266874	+	0.296394i	−0.861655	−	0.507494i	$-0.830572\pi$
$103$	−2.70848	+	3.00807i	−0.266874	+	0.296394i	0.594781	+	0.803888i	$0.297239\pi$
$104$	−4.43646	−	1.97524i	−0.435031	−	0.193688i
$105$	1.63872	−	7.78975i	0.159923	−	0.760202i
$106$	−0.0231703	−	0.109008i	−0.00225050	−	0.0105878i
$107$	7.04877	+	15.8318i	0.681431	+	1.53052i	0.839658	+	0.543116i	$0.182755\pi$
$107$	7.04877	+	15.8318i	0.681431	+	1.53052i	−0.158227	+	0.987403i	$0.550578\pi$
$108$	−1.57462	+	4.95182i	−0.151518	+	0.476490i
$109$	−0.326699	+	1.00548i	−0.0312921	+	0.0963071i	−0.965483	−	0.260467i	$-0.916123\pi$
$109$	−0.326699	+	1.00548i	−0.0312921	+	0.0963071i	0.934191	+	0.356774i	$0.116123\pi$
$110$	0.516409	−	0.229920i	0.0492376	−	0.0219220i
$111$	−1.62802	−	7.58113i	−0.154525	−	0.719569i
$112$	−4.49542	−	0.955532i	−0.424778	−	0.0902893i
$113$	3.02132	−	6.78599i	0.284221	−	0.638372i	−0.713860	−	0.700289i	$-0.753055\pi$
$113$	3.02132	−	6.78599i	0.284221	−	0.638372i	0.998081	+	0.0619167i	$0.0197213\pi$
$114$	1.22263	+	1.09623i	0.114510	+	0.102672i
$115$	1.49534	+	0.157167i	0.139441	+	0.0146559i
$116$	2.20993	+	1.60561i	0.205187	+	0.149077i
$117$	14.4826	−	1.58354i	1.33892	−	0.146398i
$118$	1.41677	−	2.45392i	0.130425	−	0.225902i
$119$	−4.33724	−	7.51232i	−0.397594	−	0.688653i
$120$	1.39912	−	1.02101i	0.127722	−	0.0932047i
$121$	−7.14662	−	7.93713i	−0.649693	−	0.721557i
$122$	1.33246	+	4.10089i	0.120635	+	0.371277i
$123$	0.0330793	+	15.7959i	0.00298266	+	1.42427i
$124$	5.54817	+	0.466750i	0.498240	+	0.0419154i
$125$		−	1.00000i		−	0.0894427i
$126$	13.0948	−	4.31547i	1.16658	−	0.384453i
$127$	9.12726	−	8.21822i	0.809914	−	0.729249i	−0.156100	−	0.987741i	$-0.549892\pi$
$127$	9.12726	−	8.21822i	0.809914	−	0.729249i	0.966013	+	0.258492i	$0.0832255\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−19.0900	+	11.0750i	−1.68078	+	0.975098i
$130$	−4.20569	−	2.42816i	−0.368863	−	0.212963i
$131$	−20.8565	+	2.19210i	−1.82224	+	0.191525i	−0.953021	−	0.302904i	$-0.902044\pi$
$131$	−20.8565	+	2.19210i	−1.82224	+	0.191525i	−0.869218	+	0.494429i	$0.835377\pi$
$132$	0.793306	+	0.573836i	0.0690484	+	0.0499460i
$133$	0.455454	−	4.33336i	0.0394929	−	0.375750i
$134$	−5.18107	−	4.66506i	−0.447576	−	0.402999i
$135$	−2.08360	+	4.76011i	−0.179328	+	0.409685i
$136$	0.392424	−	1.84621i	0.0336501	−	0.158311i
$137$	2.49684	−	0.530719i	0.213319	−	0.0453424i	−0.100012	−	0.994986i	$-0.531888\pi$
$137$	2.49684	−	0.530719i	0.213319	−	0.0453424i	0.313332	+	0.949644i	$0.398555\pi$
$138$	1.06423	+	2.37690i	0.0905935	+	0.202335i
$139$	−8.76782	−	2.84884i	−0.743677	−	0.241635i	−0.0874187	−	0.996172i	$-0.527862\pi$
$139$	−8.76782	−	2.84884i	−0.743677	−	0.241635i	−0.656258	+	0.754536i	$0.727862\pi$
$140$	−4.37092	−	1.42020i	−0.369410	−	0.120029i
$141$	−6.71746	−	15.0030i	−0.565712	−	1.26348i
$142$	9.33019	−	1.98319i	0.782972	−	0.166426i
$143$	0.570753	−	2.68518i	0.0477288	−	0.224546i
$144$	2.74572	+	1.20872i	0.228810	+	0.100727i
$145$	2.02999	+	1.82782i	0.168582	+	0.151792i
$146$	−0.816018	+	7.76389i	−0.0675342	+	0.642545i
$147$	−19.8185	−	14.3356i	−1.63460	−	1.18238i
$148$	−4.45223	+	0.467948i	−0.365971	+	0.0384651i
$149$	−6.19718	−	3.57794i	−0.507693	−	0.293116i	0.224192	−	0.974545i	$-0.428026\pi$
$149$	−6.19718	−	3.57794i	−0.507693	−	0.293116i	−0.731885	+	0.681429i	$0.761359\pi$
$150$	1.49818	−	0.869165i	0.122326	−	0.0709670i
$151$	−4.64699	−	6.39603i	−0.378167	−	0.520502i	0.576931	−	0.816793i	$-0.304250\pi$
$151$	−4.64699	−	6.39603i	−0.378167	−	0.520502i	−0.955098	+	0.296291i	$0.904250\pi$
$152$	0.704559	−	0.634388i	0.0571473	−	0.0514557i
$153$	1.77231	+	5.37786i	0.143283	+	0.434774i
$154$		−	2.59794i		−	0.209348i
$155$	5.46898	+	1.04413i	0.439279	+	0.0838669i
$156$	−0.0176148	−	8.41136i	−0.00141031	−	0.673448i
$157$	−3.14740	−	9.68670i	−0.251190	−	0.773083i	−0.994556	−	0.104199i	$-0.966772\pi$
$157$	−3.14740	−	9.68670i	−0.251190	−	0.773083i	0.743367	−	0.668884i	$-0.233228\pi$
$158$	9.39401	+	10.4331i	0.747347	+	0.830013i
$159$	0.155922	−	0.113784i	0.0123655	−	0.00902365i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	3.45511	−	5.98442i	0.272301	−	0.471639i
$162$	−8.94250	+	1.01570i	−0.702589	+	0.0798009i
$163$	−6.43301	−	4.67385i	−0.503872	−	0.366084i	0.306622	−	0.951831i	$-0.400801\pi$
$163$	−6.43301	−	4.67385i	−0.503872	−	0.366084i	−0.810494	+	0.585747i	$0.800801\pi$
$164$	9.06984	+	0.953278i	0.708235	+	0.0744385i
$165$	0.728978	+	0.653616i	0.0567509	+	0.0508839i
$166$	4.25026	−	9.54624i	0.329884	−	0.740932i
$167$	−21.1368	−	4.49276i	−1.63561	−	0.347660i	−0.703743	−	0.710454i	$-0.748489\pi$
$167$	−21.1368	−	4.49276i	−1.63561	−	0.347660i	−0.931869	+	0.362794i	$0.881823\pi$
$168$	−1.67133	−	7.78282i	−0.128946	−	0.600458i
$169$	−9.66873	+	4.30480i	−0.743749	+	0.331138i
$170$	0.583256	−	1.79508i	0.0447337	−	0.137676i
$171$	−0.867579	+	2.70868i	−0.0663455	+	0.207138i
$172$	5.18268	+	11.6405i	0.395176	+	0.887579i
$173$	1.64417	+	7.73521i	0.125004	+	0.588097i	0.995405	+	0.0957541i	$0.0305262\pi$
$173$	1.64417	+	7.73521i	0.125004	+	0.588097i	−0.870401	+	0.492343i	$0.836140\pi$
$174$	−0.974002	+	4.62998i	−0.0738389	+	0.350998i
$175$	−4.19852	−	1.86930i	−0.317378	−	0.141306i
$176$	0.378246	−	0.420085i	0.0285114	−	0.0316651i
$177$	4.88203	+	0.502787i	0.366955	+	0.0377918i
$178$	−1.09240	+	1.50357i	−0.0818792	+	0.112697i
$179$	1.86441	+	17.7387i	0.139353	+	1.32585i	0.811029	+	0.585006i	$0.198908\pi$
$179$	1.86441	+	17.7387i	0.139353	+	1.32585i	−0.671676	+	0.740845i	$0.734425\pi$
$180$	2.60434	+	1.48911i	0.194116	+	0.110991i
$181$	3.59547	−	2.07585i	0.267250	−	0.154297i	−0.360388	−	0.932803i	$-0.617356\pi$
$181$	3.59547	−	2.07585i	0.267250	−	0.154297i	0.627637	+	0.778506i	$0.284022\pi$
$182$	−18.0564	+	13.1187i	−1.33843	+	0.972424i
$183$	−5.53969	+	5.00901i	−0.409506	+	0.370276i
$184$	1.42999	−	0.464631i	0.105420	−	0.0342530i
$185$	−4.47675			−0.329138
$186$	3.18914	+	9.10106i	0.233839	+	0.667322i
$187$	1.06694			0.0780225
$188$	−9.02610	+	2.93276i	−0.658296	+	0.213893i
$189$	16.0905	+	17.6461i	1.17041	+	1.28357i
$190$	0.767011	−	0.557266i	0.0556448	−	0.0404283i
$191$	−14.2033	+	8.20029i	−1.02772	+	0.593352i	−0.916330	−	0.400425i	$-0.868863\pi$
$191$	−14.2033	+	8.20029i	−1.02772	+	0.593352i	−0.111387	+	0.993777i	$0.535529\pi$
$192$	0.862882	−	1.50181i	0.0622732	−	0.108384i
$193$	0.106420	+	1.01252i	0.00766031	+	0.0728830i	0.997684	−	0.0680168i	$-0.0216671\pi$
$193$	0.106420	+	1.01252i	0.00766031	+	0.0728830i	−0.990024	+	0.140900i	$0.955000\pi$
$194$	−0.819221	+	1.12756i	−0.0588166	+	0.0809542i
$195$	0.861708	−	8.36712i	0.0617082	−	0.599182i
$196$	−9.44938	+	10.4946i	−0.674956	+	0.749614i
$197$	17.3968	+	7.74555i	1.23947	+	0.551847i	0.918567	−	0.395265i	$-0.129347\pi$
$197$	17.3968	+	7.74555i	1.23947	+	0.551847i	0.320902	+	0.947112i	$0.396014\pi$
$198$	−0.345634	+	1.66024i	−0.0245631	+	0.117988i
$199$	5.77308	+	27.1602i	0.409242	+	1.92533i	0.377955	+	0.925824i	$0.376627\pi$
$199$	5.77308	+	27.1602i	0.409242	+	1.92533i	0.0312875	+	0.999510i	$0.490039\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	3.70749	−	11.4923i	0.261506	−	0.810605i
$202$	4.32181	−	13.3012i	0.304082	−	0.935868i
$203$	11.4688	−	5.10624i	0.804952	−	0.358388i
$204$	3.19630	−	0.686394i	0.223786	−	0.0480572i
$205$	8.92051	+	1.89611i	0.623035	+	0.132430i
$206$	−1.64637	+	3.69781i	−0.114708	+	0.257639i
$207$	−3.00420	+	3.36474i	−0.208806	+	0.233865i
$208$	−4.82971	−	0.507623i	−0.334880	−	0.0351973i
$209$	0.433576	+	0.315011i	0.0299911	+	0.0217898i
$210$	−0.848650	−	7.91489i	−0.0585624	−	0.546179i
$211$	−0.124531	+	0.215695i	−0.00857310	+	0.0148490i	−0.870280	−	0.492557i	$-0.836062\pi$
$211$	−0.124531	+	0.215695i	−0.00857310	+	0.0148490i	0.861707	+	0.507406i	$0.169396\pi$
$212$	−0.0557215	−	0.0965124i	−0.00382697	−	0.00662850i
$213$	9.73900	+	13.3457i	0.667306	+	0.914434i
$214$	11.5961	+	12.8788i	0.792692	+	0.880373i
$215$	3.93753	+	12.1185i	0.268537	+	0.826472i
$216$	0.0326446	+	5.19605i	0.00222118	+	0.353546i
$217$	14.6070	−	21.0098i	0.991588	−	1.42624i
$218$			1.05722i			0.0716039i
$219$	−12.8510	+	4.20530i	−0.868388	+	0.284168i
$220$	0.420085	−	0.378246i	0.0283221	−	0.0255013i
$221$	−5.38769	−	7.41551i	−0.362415	−	0.498821i
$222$	−3.89104	−	6.70700i	−0.261149	−	0.450144i
$223$	−13.8417	−	7.99152i	−0.926910	−	0.535152i	−0.0410768	−	0.999156i	$-0.513079\pi$
$223$	−13.8417	−	7.99152i	−0.926910	−	0.535152i	−0.885833	+	0.464004i	$0.846412\pi$
$224$	−4.57068	+	0.480398i	−0.305391	+	0.0320979i
$225$	2.43442	+	1.75318i	0.162294	+	0.116878i
$226$	0.776457	−	7.38749i	0.0516491	−	0.491409i
$227$	10.5420	+	9.49207i	0.699698	+	0.630011i	0.940194	−	0.340639i	$-0.110644\pi$
$227$	10.5420	+	9.49207i	0.699698	+	0.630011i	−0.240496	+	0.970650i	$0.577310\pi$
$228$	1.50155	+	0.664767i	0.0994423	+	0.0440253i
$229$	5.03234	−	23.6753i	0.332547	−	1.56451i	−0.420966	−	0.907076i	$-0.638309\pi$
$229$	5.03234	−	23.6753i	0.332547	−	1.56451i	0.753513	−	0.657433i	$-0.228358\pi$
$230$	1.47072	−	0.312611i	0.0969764	−	0.0206130i
$231$	4.10690	−	1.83883i	0.270214	−	0.120986i
$232$	2.59793	+	0.844119i	0.170563	+	0.0554191i
$233$	−20.1250	−	6.53900i	−1.31843	−	0.428384i	−0.436475	−	0.899716i	$-0.643773\pi$
$233$	−20.1250	−	6.53900i	−1.31843	−	0.428384i	−0.881956	+	0.471332i	$0.843773\pi$
$234$	13.2844	−	5.98141i	0.868431	−	0.391017i
$235$	−9.28321	+	1.97321i	−0.605570	+	0.128718i
$236$	0.589128	−	2.77163i	0.0383489	−	0.180418i
$237$	−9.84386	+	22.2349i	−0.639427	+	1.44431i
$238$	−6.44640	−	5.80436i	−0.417858	−	0.376241i
$239$	−1.38479	+	13.1754i	−0.0895746	+	0.852245i	0.853819	+	0.520570i	$0.174280\pi$
$239$	−1.38479	+	13.1754i	−0.0895746	+	0.852245i	−0.943394	+	0.331675i	$0.892386\pi$
$240$	1.01514	−	1.40339i	0.0655268	−	0.0905883i
$241$	18.1386	−	1.90645i	1.16841	−	0.122805i	0.499614	−	0.866248i	$-0.333475\pi$
$241$	18.1386	−	1.90645i	1.16841	−	0.122805i	0.668799	+	0.743443i	$0.266809\pi$
$242$	−9.24955	−	5.34023i	−0.594584	−	0.343283i
$243$	−7.93515	−	13.4176i	−0.509040	−	0.860743i
$244$	2.53449	+	3.48843i	0.162254	+	0.223324i
$245$	−10.4946	+	9.44938i	−0.670476	+	0.603699i
$246$	4.91267	+	15.0126i	0.313220	+	0.957168i
$247$		−	4.60416i		−	0.292956i
$248$	5.42085	−	1.27057i	0.344225	−	0.0806814i
$249$	18.0993	−	0.0379030i	1.14700	−	0.00240201i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	0.111052	+	0.123336i	0.00700953	+	0.00778488i	0.746639	−	0.665229i	$-0.231666\pi$
$251$	0.111052	+	0.123336i	0.00700953	+	0.00778488i	−0.739630	+	0.673014i	$0.764999\pi$
$252$	11.1203	−	8.15077i	0.700515	−	0.513450i
$253$	0.424970	+	0.736070i	0.0267177	+	0.0462764i
$254$	6.14097	−	10.6365i	0.385319	−	0.667392i
$255$	3.25054	−	0.348529i	0.203557	−	0.0218258i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	10.0097	+	1.05206i	0.624385	+	0.0656255i	0.411437	−	0.911438i	$-0.365027\pi$
$257$	10.0097	+	1.05206i	0.624385	+	0.0656255i	0.212948	+	0.977064i	$0.431694\pi$
$258$	−14.7333	+	16.4321i	−0.917256	+	1.02302i
$259$	−8.36841	+	18.7958i	−0.519988	+	1.16791i
$260$	−4.75019	−	1.00968i	−0.294594	−	0.0626179i
$261$	−8.00860	+	1.73737i	−0.495720	+	0.107540i
$262$	−19.1583	+	8.52982i	−1.18360	+	0.526974i
$263$	1.41186	−	4.34527i	0.0870592	−	0.267941i	−0.898044	−	0.439906i	$-0.855012\pi$
$263$	1.41186	−	4.34527i	0.0870592	−	0.267941i	0.985103	+	0.171965i	$0.0550117\pi$
$264$	0.931804	+	0.300606i	0.0573486	+	0.0185010i
$265$	−0.0453279	−	0.101808i	−0.00278447	−	0.00625403i
$266$	−0.905919	−	4.26201i	−0.0555454	−	0.261321i
$267$	−3.15008	−	0.662679i	−0.192782	−	0.0405553i
$268$	−6.36907	−	2.83569i	−0.389053	−	0.173218i
$269$	4.45749	−	4.95054i	0.271778	−	0.301840i	−0.591770	−	0.806107i	$-0.701571\pi$
$269$	4.45749	−	4.95054i	0.271778	−	0.301840i	0.863548	+	0.504267i	$0.168237\pi$
$270$	−0.510669	+	5.17100i	−0.0310783	+	0.314697i
$271$	3.64164	−	5.01229i	0.221214	−	0.304475i	−0.683957	−	0.729522i	$-0.739743\pi$
$271$	3.64164	−	5.01229i	0.221214	−	0.304475i	0.905171	+	0.425047i	$0.139743\pi$
$272$	−0.197293	−	1.87712i	−0.0119626	−	0.113817i
$273$	−33.5187	−	19.2586i	−2.02865	−	1.16558i
$274$	2.21063	−	1.27631i	0.133549	−	0.0771046i
$275$	0.457321	−	0.332263i	0.0275775	−	0.0200362i
$276$	1.74665	+	1.93170i	0.105136	+	0.116274i
$277$	20.4613	−	6.64829i	1.22940	−	0.399457i	0.378905	−	0.925436i	$-0.376301\pi$
$277$	20.4613	−	6.64829i	1.22940	−	0.399457i	0.850498	+	0.525979i	$0.176301\pi$
$278$	−9.21903			−0.552921
$279$	−12.1299	+	11.4832i	−0.726201	+	0.687483i
$280$	−4.59585			−0.274655
$281$	−13.2811	+	4.31528i	−0.792282	+	0.257428i	−0.677075	−	0.735914i	$-0.736753\pi$
$281$	−13.2811	+	4.31528i	−0.792282	+	0.257428i	−0.115206	+	0.993342i	$0.536753\pi$
$282$	−11.0249	−	12.1929i	−0.656521	−	0.726077i
$283$	−10.6337	+	7.72580i	−0.632105	+	0.459251i	−0.857129	−	0.515102i	$-0.827754\pi$
$283$	−10.6337	+	7.72580i	−0.632105	+	0.459251i	0.225024	+	0.974353i	$0.427754\pi$
$284$	8.26070	−	4.76932i	0.490182	−	0.283007i
$285$	1.42383	+	0.818080i	0.0843406	+	0.0484589i
$286$	−0.286949	−	2.73013i	−0.0169676	−	0.161436i
$287$	24.6360	−	33.9085i	1.45422	−	2.00156i
$288$	2.98485	+	0.301087i	0.175884	+	0.0177417i
$289$	−8.99145	+	9.98601i	−0.528909	+	0.587412i
$290$	2.49547	+	1.11105i	0.146539	+	0.0652433i
$291$	−2.36233	−	0.496959i	−0.138482	−	0.0291323i
$292$	1.62310	+	7.63607i	0.0949845	+	0.446867i
$293$	−4.84034	−	10.8716i	−0.282776	−	0.635125i	0.715186	−	0.698934i	$-0.246342\pi$
$293$	−4.84034	−	10.8716i	−0.282776	−	0.635125i	−0.997962	+	0.0638088i	$0.979675\pi$
$294$	−23.2784	−	7.50977i	−1.35763	−	0.437978i
$295$	0.875614	−	2.69486i	0.0509802	−	0.156901i
$296$	−4.08972	+	1.82086i	−0.237710	+	0.105835i
$297$	−2.86920	+	0.628733i	−0.166488	+	0.0364828i
$298$	−6.99951	−	1.48779i	−0.405471	−	0.0861855i
$299$	2.96992	−	6.67056i	0.171755	−	0.385768i
$300$	1.15627	−	1.28959i	0.0667573	−	0.0744544i
$301$	58.2401	+	6.12128i	3.35690	+	0.352825i
$302$	−6.39603	−	4.64699i	−0.368050	−	0.267404i
$303$	24.0859	−	2.58253i	1.38370	−	0.148363i
$304$	0.474039	−	0.821060i	0.0271880	−	0.0470910i
$305$	2.15597	+	3.73424i	0.123450	+	0.213822i
$306$	3.34742	+	4.56698i	0.191359	+	0.261077i
$307$	2.14205	+	2.37898i	0.122253	+	0.135776i	0.801164	−	0.598445i	$-0.204214\pi$
$307$	2.14205	+	2.37898i	0.122253	+	0.135776i	−0.678911	+	0.734221i	$0.737548\pi$
$308$	−0.802808	−	2.47079i	−0.0457443	−	0.140786i
$309$	−7.01090	+	0.0146820i	−0.398836	+	0.000835230i
$310$	5.52397	−	0.696978i	0.313740	−	0.0395857i
$311$			10.7395i			0.608980i	0.952516	+	0.304490i	$0.0984860\pi$
$311$			10.7395i			0.608980i	−0.952516	+	0.304490i	$0.901514\pi$
$312$	−2.61601	−	7.99423i	−0.148102	−	0.452584i
$313$	−9.60134	+	8.64508i	−0.542700	+	0.488649i	−0.894279	−	0.447509i	$-0.852311\pi$
$313$	−9.60134	+	8.64508i	−0.542700	+	0.488649i	0.351580	+	0.936158i	$0.385645\pi$
$314$	−5.98671	−	8.24000i	−0.337850	−	0.465010i
$315$	11.9114	−	6.94373i	0.671132	−	0.391235i
$316$	12.1582	+	7.01956i	0.683954	+	0.394881i
$317$	29.2721	−	3.07662i	1.64408	−	0.172800i	0.763210	−	0.646151i	$-0.223622\pi$
$317$	29.2721	−	3.07662i	1.64408	−	0.172800i	0.880874	+	0.473350i	$0.156956\pi$
$318$	0.113130	−	0.156398i	0.00634401	−	0.00877035i
$319$	−0.161406	+	1.53567i	−0.00903699	+	0.0859812i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	−12.1514	+	27.4470i	−0.678224	+	1.53194i
$322$	1.43672	−	6.75921i	0.0800650	−	0.376676i
$323$	1.75035	−	0.372049i	0.0973922	−	0.0207014i
$324$	−8.19096	+	3.72937i	−0.455053	+	0.207187i
$325$	−4.61863	−	1.50068i	−0.256195	−	0.0832429i
$326$	−7.56245	−	2.45719i	−0.418845	−	0.136091i
$327$	−1.67128	+	0.748301i	−0.0924221	+	0.0413811i
$328$	8.92051	−	1.89611i	0.492553	−	0.104695i
$329$	−9.06858	+	42.6643i	−0.499967	+	2.35216i
$330$	0.895278	+	0.396359i	0.0492834	+	0.0218188i
$331$	14.5635	+	13.1131i	0.800485	+	0.720760i	0.964035	−	0.265775i	$-0.0856280\pi$
$331$	14.5635	+	13.1131i	0.800485	+	0.720760i	−0.163550	+	0.986535i	$0.552295\pi$
$332$	1.09229	−	10.3924i	0.0599471	−	0.570358i
$333$	7.84853	−	10.8983i	0.430097	−	0.597222i
$334$	−21.4906	+	2.25875i	−1.17591	+	0.123593i
$335$	−6.03777	−	3.48591i	−0.329879	−	0.190456i
$336$	−3.99455	−	6.88543i	−0.217921	−	0.375631i
$337$	−10.8198	−	14.8922i	−0.589393	−	0.811229i	0.405293	−	0.914187i	$-0.367169\pi$
$337$	−10.8198	−	14.8922i	−0.589393	−	0.811229i	−0.994686	+	0.102957i	$0.967169\pi$
$338$	−7.86526	+	7.08191i	−0.427814	+	0.385205i
$339$	12.2279	−	4.00143i	0.664130	−	0.217328i
$340$		−	1.88746i		−	0.102362i
$341$	1.33964	+	2.84801i	0.0725454	+	0.154228i
$342$	0.0119126	+	2.84421i	0.000644157	+	0.153797i
$343$	10.1145	+	31.1292i	0.546130	+	1.68082i
$344$	8.52613	+	9.46923i	0.459698	+	0.510547i
$345$	1.53516	+	2.10369i	0.0826503	+	0.113259i
$346$	3.95401	+	6.84855i	0.212569	+	0.368180i
$347$	−6.62158	+	11.4689i	−0.355465	+	0.615683i	−0.987197	−	0.159503i	$-0.949011\pi$
$347$	−6.62158	+	11.4689i	−0.355465	+	0.615683i	0.631733	+	0.775186i	$0.282344\pi$
$348$	0.504410	+	4.70435i	0.0270392	+	0.252180i
$349$	−15.6867	−	11.3970i	−0.839688	−	0.610069i	0.0825957	−	0.996583i	$-0.473679\pi$
$349$	−15.6867	−	11.3970i	−0.839688	−	0.610069i	−0.922283	+	0.386514i	$0.873679\pi$
$350$	−4.57068	−	0.480398i	−0.244313	−	0.0256783i
$351$	18.8583	+	16.7668i	1.00658	+	0.894945i
$352$	0.229920	−	0.516409i	0.0122548	−	0.0275247i
$353$	19.0711	+	4.05369i	1.01505	+	0.215756i	0.685261	−	0.728298i	$-0.259688\pi$
$353$	19.0711	+	4.05369i	1.01505	+	0.215756i	0.329792	+	0.944054i	$0.393021\pi$
$354$	4.79845	−	1.03045i	0.255035	−	0.0547678i
$355$	8.71398	−	3.87971i	0.462490	−	0.205914i
$356$	−0.574311	+	1.76755i	−0.0304384	+	0.0936798i
$357$	4.61294	−	14.2990i	0.244142	−	0.756782i
$358$	7.25471	+	16.2944i	0.383423	+	0.861183i
$359$	2.44588	+	11.5070i	0.129089	+	0.607315i	0.994364	+	0.106018i	$0.0338102\pi$
$359$	2.44588	+	11.5070i	0.129089	+	0.607315i	−0.865275	+	0.501297i	$0.832856\pi$
$360$	2.93703	+	0.611439i	0.154795	+	0.0322257i
$361$	−16.5362	−	7.36240i	−0.870327	−	0.387495i
$362$	2.77803	−	3.08531i	0.146010	−	0.162160i
$363$	1.89515	−	18.4018i	0.0994696	−	0.965842i
$364$	−13.1187	+	18.0564i	−0.687608	+	0.946411i
$365$	0.816018	+	7.76389i	0.0427123	+	0.406381i
$366$	−3.72069	+	6.47571i	−0.194484	+	0.338491i
$367$	−23.6599	+	13.6600i	−1.23504	+	0.713048i	−0.968075	−	0.250659i	$-0.919353\pi$
$367$	−23.6599	+	13.6600i	−1.23504	+	0.713048i	−0.266961	+	0.963707i	$0.586019\pi$
$368$	1.21642	−	0.883780i	0.0634102	−	0.0460702i
$369$	−20.2551	+	18.3920i	−1.05444	+	0.957449i
$370$	−4.25765	+	1.38339i	−0.221344	+	0.0719192i
$371$	−0.512176			−0.0265908
$372$	5.84544	+	7.67013i	0.303072	+	0.397678i
$373$	−20.8084			−1.07742			−0.538709	−	0.842492i	$-0.681088\pi$
$373$	−20.8084			−1.07742			−0.538709	+	0.842492i	$0.681088\pi$
$374$	1.01472	−	0.329703i	0.0524700	−	0.0170485i
$375$	1.28473	−	1.16166i	0.0663434	−	0.0599879i
$376$	−7.67806	+	5.57844i	−0.395966	+	0.287686i
$377$	11.4884	−	6.63281i	0.591681	−	0.341607i
$378$	20.7560	+	11.8102i	1.06757	+	0.607452i
$379$	−3.54880	−	33.7646i	−0.182290	−	1.73437i	−0.578037	−	0.816011i	$-0.696181\pi$
$379$	−3.54880	−	33.7646i	−0.182290	−	1.73437i	0.395747	−	0.918359i	$-0.370486\pi$
$380$	0.557266	−	0.767011i	0.0285872	−	0.0393468i
$381$	21.1610	+	2.17932i	1.08411	+	0.111650i
$382$	−10.9741	+	12.1880i	−0.561486	+	0.623593i
$383$	15.7351	+	7.00570i	0.804024	+	0.357974i	0.767249	−	0.641349i	$-0.221625\pi$
$383$	15.7351	+	7.00570i	0.804024	+	0.357974i	0.0367747	+	0.999324i	$0.488292\pi$
$384$	0.356565	−	1.69495i	0.0181959	−	0.0864951i
$385$	−0.540143	−	2.54117i	−0.0275282	−	0.129510i
$386$	0.414099	+	0.930081i	0.0210771	+	0.0473399i
$387$	−36.4045	−	11.6602i	−1.85055	−	0.592722i
$388$	−0.430690	+	1.32553i	−0.0218650	+	0.0672935i
$389$	30.6031	−	13.6254i	1.55164	−	0.690834i	0.561060	−	0.827775i	$-0.310394\pi$
$389$	30.6031	−	13.6254i	1.55164	−	0.690834i	0.990579	+	0.136941i	$0.0437272\pi$
$390$	−1.76605	−	8.22389i	−0.0894274	−	0.416433i
$391$	2.77592	+	0.590040i	0.140384	+	0.0298396i
$392$	−5.74389	+	12.9010i	−0.290110	+	0.651598i
$393$	−27.0444	−	24.2486i	−1.36421	−	1.22318i
$394$	18.9388	+	1.99055i	0.954124	+	0.100283i
$395$	11.3579	+	8.25199i	0.571477	+	0.415203i
$396$	0.184326	+	1.68579i	0.00926271	+	0.0847142i
$397$	18.2364	−	31.5864i	0.915260	−	1.58528i	0.108740	−	0.994070i	$-0.465318\pi$
$397$	18.2364	−	31.5864i	0.915260	−	1.58528i	0.806520	−	0.591207i	$-0.201348\pi$
$398$	13.8835	+	24.0469i	0.695916	+	1.20536i
$399$	6.09630	−	4.44876i	0.305197	−	0.222716i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−7.41431	−	22.8189i	−0.370253	−	1.13952i	−0.946626	−	0.322335i	$-0.895532\pi$
$401$	−7.41431	−	22.8189i	−0.370253	−	1.13952i	0.576373	−	0.817187i	$-0.304468\pi$
$402$	−0.0252882	−	12.0755i	−0.00126126	−	0.602272i
$403$	13.0297	−	23.6923i	0.649054	−	1.18020i
$404$		−	13.9857i		−	0.695814i
$405$	−8.53591	+	2.85275i	−0.424153	+	0.141755i
$406$	9.32956	−	8.40037i	0.463018	−	0.416903i
$407$	−1.48746	−	2.04731i	−0.0737306	−	0.101482i
$408$	2.82776	−	1.64051i	0.139995	−	0.0812174i
$409$	−6.67674	−	3.85482i	−0.330143	−	0.190608i	0.325761	−	0.945452i	$-0.394379\pi$
$409$	−6.67674	−	3.85482i	−0.330143	−	0.190608i	−0.655905	+	0.754844i	$0.727713\pi$
$410$	9.06984	−	0.953278i	0.447927	−	0.0470791i
$411$	3.58231	+	2.59126i	0.176702	+	0.127817i
$412$	−0.423106	+	4.02558i	−0.0208449	+	0.198326i
$413$	−9.67766	−	8.71380i	−0.476206	−	0.428778i
$414$	−1.81740	+	4.12840i	−0.0893205	+	0.202900i
$415$	2.17261	−	10.2213i	0.106649	−	0.501745i
$416$	−4.75019	+	1.00968i	−0.232897	+	0.0495038i
$417$	−6.52524	−	14.5737i	−0.319542	−	0.713678i
$418$	0.509699	+	0.165611i	0.0249302	+	0.00810031i
$419$	34.7375	+	11.2869i	1.69704	+	0.551401i	0.988092	−	0.153863i	$-0.0491716\pi$
$419$	34.7375	+	11.2869i	1.69704	+	0.551401i	0.708945	+	0.705264i	$0.249172\pi$
$420$	−3.25295	−	7.26526i	−0.158728	−	0.354508i
$421$	−32.9456	+	7.00280i	−1.60567	+	0.341296i	−0.921606	−	0.388127i	$-0.873122\pi$
$421$	−32.9456	+	7.00280i	−1.60567	+	0.341296i	−0.684063	+	0.729422i	$0.739789\pi$
$422$	−0.0517831	+	0.243620i	−0.00252076	+	0.0118592i
$423$	11.4715	−	26.0586i	0.557763	−	1.26701i
$424$	−0.0828183	−	0.0745699i	−0.00402201	−	0.00362143i
$425$	0.197293	−	1.87712i	0.00957012	−	0.0910536i
$426$	13.3864	+	9.68302i	0.648573	+	0.469144i
$427$	19.7085	−	2.07144i	0.953759	−	0.100244i
$428$	15.0083	+	8.66503i	0.725453	+	0.418840i
$429$	4.11277	−	2.38601i	0.198566	−	0.115198i
$430$	7.48962	+	10.3086i	0.361182	+	0.497124i
$431$	−7.96826	+	7.17466i	−0.383818	+	0.345591i	−0.838343	−	0.545143i	$-0.816475\pi$
$431$	−7.96826	+	7.17466i	−0.383818	+	0.345591i	0.454526	+	0.890734i	$0.349809\pi$
$432$	1.63671	+	4.93165i	0.0787465	+	0.237274i
$433$		−	3.58072i		−	0.172078i	−0.996292	−	0.0860392i	$-0.972579\pi$
$433$		−	3.58072i		−	0.172078i	0.996292	−	0.0860392i	$-0.0274210\pi$
$434$	7.39969	−	24.4954i	0.355196	−	1.17582i
$435$	0.00990815	+	4.73131i	0.000475059	+	0.226849i
$436$	0.326699	+	1.00548i	0.0156460	+	0.0481535i
$437$	0.953851	+	1.05936i	0.0456289	+	0.0506760i
$438$	−10.9225	+	7.97065i	−0.521896	+	0.380852i
$439$	14.5806	+	25.2544i	0.695895	+	1.20533i	0.969878	+	0.243591i	$0.0783256\pi$
$439$	14.5806	+	25.2544i	0.695895	+	1.20533i	−0.273983	+	0.961735i	$0.588341\pi$
$440$	0.282640	−	0.489546i	0.0134743	−	0.0233382i
$441$	−4.60485	−	42.1146i	−0.219278	−	2.00546i
$442$	−7.41551	−	5.38769i	−0.352720	−	0.256266i
$443$	−17.7222	−	1.86268i	−0.842007	−	0.0884985i	−0.326303	−	0.945265i	$-0.605803\pi$
$443$	−17.7222	−	1.86268i	−0.842007	−	0.0884985i	−0.515704	+	0.856767i	$0.672470\pi$
$444$	−5.77317	−	5.17634i	−0.273983	−	0.245658i
$445$	−0.755924	+	1.69783i	−0.0358342	+	0.0804850i
$446$	−15.6338	−	3.32306i	−0.740280	−	0.157351i
$447$	−2.60231	−	12.1181i	−0.123085	−	0.573166i
$448$	−4.19852	+	1.86930i	−0.198362	+	0.0883162i
$449$	−2.87099	+	8.83599i	−0.135490	+	0.416996i	−0.995666	−	0.0930018i	$-0.970354\pi$
$449$	−2.87099	+	8.83599i	−0.135490	+	0.416996i	0.860176	+	0.509998i	$0.170354\pi$
$450$	2.85703	+	0.915093i	0.134682	+	0.0431379i
$451$	2.09682	+	4.70954i	0.0987355	+	0.221764i
$452$	−1.54441	−	7.26586i	−0.0726428	−	0.341757i
$453$	2.81898	−	13.4002i	0.132447	−	0.629595i
$454$	12.9593	+	5.76983i	0.608208	+	0.270792i
$455$	−14.9343	+	16.5862i	−0.700129	+	0.777572i
$456$	1.63348	+	0.168228i	0.0764947	+	0.00787799i
$457$	6.37627	−	8.77618i	0.298269	−	0.410532i	−0.633409	−	0.773817i	$-0.718345\pi$
$457$	6.37627	−	8.77618i	0.298269	−	0.410532i	0.931678	+	0.363285i	$0.118345\pi$
$458$	−2.53003	−	24.0716i	−0.118221	−	1.12479i
$459$	−4.85030	+	8.52420i	−0.226393	+	0.397876i
$460$	1.30214	−	0.751788i	0.0607124	−	0.0350523i
$461$	19.5268	−	14.1871i	0.909454	−	0.660757i	−0.0314228	−	0.999506i	$-0.510004\pi$
$461$	19.5268	−	14.1871i	0.909454	−	0.660757i	0.940877	+	0.338749i	$0.110004\pi$
$462$	3.33767	−	3.01793i	0.155282	−	0.140407i
$463$	−25.6083	+	8.32064i	−1.19012	+	0.386693i	−0.836117	−	0.548552i	$-0.815179\pi$
$463$	−25.6083	+	8.32064i	−1.19012	+	0.386693i	−0.354002	+	0.935245i	$0.615179\pi$
$464$	2.73163			0.126813
$465$	5.01167	+	8.23912i	0.232411	+	0.382080i
$466$	−21.1606			−0.980248
$467$	19.3442	−	6.28531i	0.895142	−	0.290849i	0.174912	−	0.984584i	$-0.444036\pi$
$467$	19.3442	−	6.28531i	0.895142	−	0.290849i	0.720230	+	0.693735i	$0.244036\pi$
$468$	10.7859	−	9.79378i	0.498578	−	0.452718i
$469$	−25.9221	+	18.8335i	−1.19697	+	0.869650i
$470$	−8.21911	+	4.74530i	−0.379119	+	0.218885i
$471$	8.78863	−	15.2962i	0.404959	−	0.704814i
$472$	−0.296186	−	2.81802i	−0.0136331	−	0.129710i
$473$	−4.23373	+	5.82723i	−0.194667	+	0.267936i
$474$	−2.49111	+	24.1885i	−0.114421	+	1.11102i
$475$	0.634388	−	0.704559i	0.0291077	−	0.0323274i
$476$	−7.92453	−	3.52823i	−0.363220	−	0.161716i
$477$	0.327311	+	0.0681406i	0.0149866	+	0.00311994i
$478$	2.75441	+	12.9585i	0.125984	+	0.592706i
$479$	−8.76637	−	19.6896i	−0.400546	−	0.899640i	−0.995400	−	0.0958067i	$-0.969457\pi$
$479$	−8.76637	−	19.6896i	−0.400546	−	0.899640i	0.594854	−	0.803834i	$-0.297210\pi$
$480$	0.531782	−	1.64840i	0.0242724	−	0.0752386i
$481$	−6.71819	+	20.6765i	−0.306323	+	0.942765i
$482$	16.6618	−	7.41829i	0.758922	−	0.337894i
$483$	11.7021	−	2.51298i	0.532462	−	0.114344i
$484$	−10.4471	−	2.22059i	−0.474867	−	0.100936i
$485$	−0.566886	+	1.27325i	−0.0257410	+	0.0578152i
$486$	−11.6931	−	10.3088i	−0.530408	−	0.467619i
$487$	−6.28113	−	0.660174i	−0.284625	−	0.0299153i	−0.0388599	−	0.999245i	$-0.512373\pi$
$487$	−6.28113	−	0.660174i	−0.284625	−	0.0299153i	−0.245765	+	0.969329i	$0.579039\pi$
$488$	3.48843	+	2.53449i	0.157914	+	0.114731i
$489$	−1.46831	−	13.6941i	−0.0663994	−	0.619270i
$490$	−7.06094	+	12.2299i	−0.318981	+	0.552491i
$491$	−2.64454	−	4.58048i	−0.119347	−	0.206714i	0.800162	−	0.599784i	$-0.204747\pi$
$491$	−2.64454	−	4.58048i	−0.119347	−	0.206714i	−0.919509	+	0.393069i	$0.871413\pi$
$492$	9.31137	+	12.7597i	0.419789	+	0.575253i
$493$	3.44992	+	3.83153i	0.155377	+	0.172563i
$494$	−1.42276	−	4.37882i	−0.0640132	−	0.197012i
$495$	0.00710271	+	1.69582i	0.000319243	+	0.0762216i
$496$	4.76291	−	2.88352i	0.213861	−	0.129474i
$497$		−	43.8382i		−	1.96641i
$498$	17.2018	−	5.62904i	0.770829	−	0.252243i
$499$	25.4800	−	22.9423i	1.14064	−	1.02704i	0.141331	−	0.989962i	$-0.454862\pi$
$499$	25.4800	−	22.9423i	1.14064	−	1.02704i	0.999312	−	0.0370775i	$-0.0118048\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−18.7818	−	32.3742i	−0.839107	−	1.44637i
$502$	0.143729	+	0.0829822i	0.00641496	+	0.00370368i
$503$	−12.1005	+	1.27181i	−0.539534	+	0.0567073i	−0.370376	−	0.928882i	$-0.620771\pi$
$503$	−12.1005	+	1.27181i	−0.539534	+	0.0567073i	−0.169157	+	0.985589i	$0.554105\pi$
$504$	8.05734	−	11.1882i	0.358902	−	0.498363i
$505$	1.46190	−	13.9091i	0.0650538	−	0.618946i
$506$	0.631629	+	0.568721i	0.0280793	+	0.0252828i
$507$	−16.7623	−	7.42104i	−0.744441	−	0.329580i
$508$	2.55356	−	12.0136i	0.113296	−	0.533015i
$509$	11.4546	−	2.43475i	0.507716	−	0.107918i	0.0530703	−	0.998591i	$-0.483099\pi$
$509$	11.4546	−	2.43475i	0.507716	−	0.107918i	0.454646	+	0.890672i	$0.349766\pi$
$510$	2.98375	−	1.33594i	0.132123	−	0.0591566i
$511$	34.1223	+	11.0870i	1.50948	+	0.490460i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−4.48777	+	2.03196i	−0.198140	+	0.0897134i
$514$	9.84485	−	2.09259i	0.434238	−	0.0923000i
$515$	−0.841576	+	3.95930i	−0.0370843	+	0.174468i
$516$	−8.93443	+	20.1807i	−0.393316	+	0.888405i
$517$	−3.98686	−	3.58978i	−0.175342	−	0.157878i
$518$	−2.15062	+	20.4618i	−0.0944929	+	0.899040i
$519$	−8.02773	+	11.0980i	−0.352378	+	0.487149i
$520$	−4.82971	+	0.507623i	−0.211797	+	0.0222607i
$521$	−25.8959	−	14.9510i	−1.13452	−	0.655015i	−0.189452	−	0.981890i	$-0.560671\pi$
$521$	−25.8959	−	14.9510i	−1.13452	−	0.655015i	−0.945068	+	0.326874i	$0.894005\pi$
$522$	−7.07975	+	4.12713i	−0.309872	+	0.180640i
$523$	9.18368	+	12.6403i	0.401574	+	0.552720i	0.961138	−	0.276068i	$-0.0890313\pi$
$523$	9.18368	+	12.6403i	0.401574	+	0.552720i	−0.559564	+	0.828787i	$0.689031\pi$
$524$	−15.5848	+	14.0326i	−0.680824	+	0.613016i
$525$	−2.47570	−	7.56548i	−0.108049	−	0.330185i
$526$		−	4.56889i		−	0.199213i
$527$	10.0599	+	3.03896i	0.438217	+	0.132379i
$528$	0.979091	−	0.00205038i	0.0426095	−	8.92314e-5i
$529$	−6.40878	−	19.7242i	−0.278643	−	0.857574i
$530$	−0.0745699	−	0.0828183i	−0.00323911	−	0.00359740i
$531$	5.02531	+	6.85618i	0.218080	+	0.297533i
$532$	−2.17861	−	3.77347i	−0.0944549	−	0.163601i
$533$	22.1443	−	38.3550i	0.959175	−	1.66134i
$534$	−3.20069	+	0.343184i	−0.138507	+	0.0148510i
$535$	14.0203	+	10.1864i	0.606151	+	0.440395i
$536$	−6.93362	−	0.728753i	−0.299487	−	0.0314773i
$537$	−20.6237	+	23.0016i	−0.889978	+	0.992593i
$538$	2.70952	−	6.08569i	0.116816	−	0.262373i
$539$	−7.80837	−	1.65972i	−0.336330	−	0.0714892i
$540$	1.11225	+	5.07572i	0.0478637	+	0.218424i
$541$	−14.8215	+	6.59894i	−0.637225	+	0.283711i	−0.699810	−	0.714329i	$-0.746732\pi$
$541$	−14.8215	+	6.59894i	−0.637225	+	0.283711i	0.0625854	+	0.998040i	$0.480065\pi$
$542$	1.91452	−	5.89230i	0.0822358	−	0.253096i
$543$	6.84364	+	2.20780i	0.293689	+	0.0947457i
$544$	−0.767698	−	1.72428i	−0.0329148	−	0.0739278i
$545$	0.219808	+	1.03412i	0.00941555	+	0.0442967i
$546$	−37.8295	−	7.95813i	−1.61895	−	0.340577i
$547$	13.1188	+	5.84087i	0.560920	+	0.249738i	0.667555	−	0.744561i	$-0.267341\pi$
$547$	13.1188	+	5.84087i	0.560920	+	0.249738i	−0.106635	+	0.994298i	$0.534008\pi$
$548$	1.70803	−	1.89696i	0.0729636	−	0.0810343i
$549$	−12.8705	−	1.29827i	−0.549299	−	0.0554086i
$550$	0.332263	−	0.457321i	0.0141677	−	0.0195002i
$551$	0.270707	+	2.57561i	0.0115325	+	0.109725i
$552$	2.25809	+	1.29741i	0.0961105	+	0.0552214i
$553$	55.8775	−	32.2609i	2.37615	−	1.37187i
$554$	17.4055	−	12.6458i	0.739487	−	0.537269i
$555$	−5.20047	−	5.75144i	−0.220748	−	0.244135i
$556$	−8.76782	+	2.84884i	−0.371838	+	0.120818i
$557$	−23.6826			−1.00346			−0.501732	−	0.865023i	$-0.667304\pi$
$557$	−23.6826			−1.00346			−0.501732	+	0.865023i	$0.667304\pi$
$558$	−7.98775	+	14.6696i	−0.338148	+	0.621012i
$559$	61.8796			2.61723
$560$	−4.37092	+	1.42020i	−0.184705	+	0.0600143i
$561$	1.23942	+	1.37074i	0.0523285	+	0.0578725i
$562$	−11.2975	+	8.20815i	−0.476558	+	0.346240i
$563$	26.1212	−	15.0811i	1.10088	−	0.635593i	0.164427	−	0.986389i	$-0.447422\pi$
$563$	26.1212	−	15.0811i	1.10088	−	0.635593i	0.936452	+	0.350796i	$0.114089\pi$
$564$	−14.2531	−	8.18928i	−0.600163	−	0.344831i
$565$	−0.776457	−	7.38749i	−0.0326658	−	0.310794i
$566$	−7.72580	+	10.6337i	−0.324740	+	0.446966i
$567$	−3.97885	+	41.1709i	−0.167096	+	1.72901i
$568$	6.38259	−	7.08859i	0.267808	−	0.297430i
$569$	30.5701	+	13.6107i	1.28157	+	0.570590i	0.930682	−	0.365830i	$-0.119215\pi$
$569$	30.5701	+	13.6107i	1.28157	+	0.570590i	0.350883	+	0.936419i	$0.385881\pi$
$570$	1.60695	+	0.338051i	0.0673076	+	0.0141594i
$571$	−8.29677	−	39.0333i	−0.347209	−	1.63349i	−0.711842	−	0.702340i	$-0.752139\pi$
$571$	−8.29677	−	39.0333i	−0.347209	−	1.63349i	0.364633	−	0.931151i	$-0.381194\pi$
$572$	−1.11656	−	2.50784i	−0.0466858	−	0.104858i
$573$	−27.0347	−	8.72154i	−1.12939	−	0.364348i
$574$	12.9519	−	39.8619i	0.540602	−	1.66380i
$575$	1.37359	−	0.611560i	0.0572825	−	0.0255038i
$576$	2.93180	−	0.636020i	0.122159	−	0.0265008i
$577$	29.4890	+	6.26808i	1.22764	+	0.260944i	0.775699	−	0.631102i	$-0.217397\pi$
$577$	29.4890	+	6.26808i	1.22764	+	0.260944i	0.451944	+	0.892046i	$0.350731\pi$
$578$	−5.46553	+	12.2758i	−0.227336	+	0.510605i
$579$	−1.17720	+	1.31293i	−0.0489227	+	0.0545635i
$580$	2.71666	+	0.285533i	0.112803	+	0.0118561i
$581$	−38.8532	−	28.2285i	−1.61190	−	1.17111i
$582$	−2.40027	+	0.257362i	−0.0994946	+	0.0106680i
$583$	0.0314982	−	0.0545565i	0.00130452	−	0.00225950i
$584$	3.90333	+	6.76077i	0.161521	+	0.279763i
$585$	11.7505	−	8.61269i	0.485825	−	0.356091i
$586$	−7.96295	−	8.84375i	−0.328946	−	0.365332i
$587$	−0.684066	−	2.10534i	−0.0282344	−	0.0868966i	0.935946	−	0.352143i	$-0.114547\pi$
$587$	−0.684066	−	2.10534i	−0.0282344	−	0.0868966i	−0.964181	+	0.265246i	$0.914547\pi$
$588$	−24.4598	+	0.0512229i	−1.00870	+	0.00211239i
$589$	3.19084	+	4.20511i	0.131476	+	0.173269i
$590$		−	2.83355i		−	0.116655i
$591$	10.2582	+	31.3480i	0.421966	+	1.28948i
$592$	−3.32688	+	2.99553i	−0.136734	+	0.123116i
$593$	26.9270	+	37.0619i	1.10576	+	1.52195i	0.827520	+	0.561437i	$0.189751\pi$
$593$	26.9270	+	37.0619i	1.10576	+	1.52195i	0.278240	+	0.960511i	$0.410249\pi$
$594$	−2.53448	+	1.48459i	−0.103991	+	0.0609135i
$595$	−7.51232	−	4.33724i	−0.307975	−	0.177810i
$596$	−7.11668	+	0.747994i	−0.291511	+	0.0306390i
$597$	−28.1873	+	38.9678i	−1.15363	+	1.59485i
$598$	0.763249	−	7.26183i	0.0312116	−	0.296958i
$599$	−20.4922	−	18.4512i	−0.837287	−	0.753897i	0.134209	−	0.990953i	$-0.457151\pi$
$599$	−20.4922	−	18.4512i	−0.837287	−	0.753897i	−0.971496	+	0.237056i	$0.923817\pi$
$600$	0.701173	−	1.58378i	0.0286253	−	0.0646575i
$601$	1.36595	−	6.42627i	0.0557181	−	0.262133i	−0.941468	−	0.337103i	$-0.890553\pi$
$601$	1.36595	−	6.42627i	0.0557181	−	0.262133i	0.997186	+	0.0749702i	$0.0238862\pi$
$602$	57.2812	−	12.1755i	2.33461	−	0.496236i
$603$	19.0714	−	8.58703i	0.776648	−	0.349691i
$604$	−7.51899	−	2.44307i	−0.305943	−	0.0994070i
$605$	−10.1577	−	3.30044i	−0.412970	−	0.134182i
$606$	22.1090	−	9.89908i	0.898115	−	0.402123i
$607$	33.9229	−	7.21053i	1.37689	−	0.292666i	0.540748	−	0.841185i	$-0.318141\pi$
$607$	33.9229	−	7.21053i	1.37689	−	0.292666i	0.836139	+	0.548518i	$0.184808\pi$
$608$	0.197116	−	0.927360i	0.00799413	−	0.0376094i
$609$	19.8830	+	8.80264i	0.805700	+	0.356701i
$610$	3.20439	+	2.88525i	0.129742	+	0.116820i
$611$	−4.81765	+	45.8368i	−0.194901	+	1.85436i
$612$	4.59486	+	3.30904i	0.185736	+	0.133760i
$613$	−8.70831	+	0.915280i	−0.351725	+	0.0369678i	−0.278744	−	0.960365i	$-0.589918\pi$
$613$	−8.70831	+	0.915280i	−0.351725	+	0.0369678i	−0.0729815	+	0.997333i	$0.523251\pi$
$614$	2.77235	+	1.60062i	0.111883	+	0.0645957i
$615$	7.92661	+	13.6631i	0.319632	+	0.550950i
$616$	−1.52703	−	2.10178i	−0.0615259	−	0.0846831i
$617$	−7.52209	+	6.77292i	−0.302828	+	0.272667i	−0.806508	−	0.591223i	$-0.798646\pi$
$617$	−7.52209	+	6.77292i	−0.302828	+	0.272667i	0.503681	+	0.863890i	$0.331979\pi$
$618$	−6.66323	+	2.18045i	−0.268034	+	0.0877106i
$619$			38.2325i			1.53669i	0.640034	+	0.768347i	$0.278920\pi$
$619$			38.2325i			1.53669i	−0.640034	+	0.768347i	$0.721080\pi$
$620$	5.03823	−	2.36987i	0.202340	−	0.0951761i
$621$	−7.81266	+	0.0490836i	−0.313511	+	0.00196966i
$622$	3.31868	+	10.2139i	0.133067	+	0.409538i
$623$	5.71534	+	6.34752i	0.228980	+	0.254308i
$624$	−4.95832	−	6.79458i	−0.198492	−	0.272001i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.45994	+	11.1889i	−0.258191	+	0.447200i
$627$	0.0989623	+	0.922966i	0.00395217	+	0.0368597i
$628$	−8.24000	−	5.98671i	−0.328812	−	0.238896i
$629$	−8.40340	−	0.883232i	−0.335065	−	0.0352168i
$630$	9.18269	−	10.2847i	0.365847	−	0.409753i
$631$	−16.1501	+	36.2738i	−0.642926	+	1.44404i	0.238229	+	0.971209i	$0.423433\pi$
$631$	−16.1501	+	36.2738i	−0.642926	+	1.44404i	−0.881155	+	0.472827i	$0.843234\pi$
$632$	13.7323	+	2.91890i	0.546243	+	0.116108i
$633$	−0.421774	+	0.0905744i	−0.0167640	+	0.00360001i
$634$	26.8887	−	11.9716i	1.06789	−	0.475453i
$635$	3.79533	−	11.6808i	0.150613	−	0.463539i
$636$	0.0592634	−	0.183702i	0.00234995	−	0.00728426i
$637$	27.8941	+	62.6512i	1.10520	+	2.48233i
$638$	0.321043	+	1.51039i	0.0127102	+	0.0597969i
$639$	−5.83229	+	28.0152i	−0.230722	+	1.10827i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	10.0008	−	11.1070i	0.395006	−	0.438699i	−0.512532	−	0.858668i	$-0.671292\pi$
$641$	10.0008	−	11.1070i	0.395006	−	0.438699i	0.907538	+	0.419969i	$0.137959\pi$
$642$	−3.07506	+	29.8586i	−0.121363	+	1.17843i
$643$	4.57814	−	6.30126i	0.180544	−	0.248498i	−0.709147	−	0.705061i	$-0.750920\pi$
$643$	4.57814	−	6.30126i	0.180544	−	0.248498i	0.889691	+	0.456563i	$0.150920\pi$
$644$	−0.722315	−	6.87236i	−0.0284632	−	0.270809i
$645$	−10.9949	+	19.1362i	−0.432925	+	0.753488i
$646$	1.54972	−	0.894728i	0.0609727	−	0.0352026i
$647$	34.5060	−	25.0700i	1.35657	−	0.985605i	0.357914	−	0.933754i	$-0.383488\pi$
$647$	34.5060	−	25.0700i	1.35657	−	0.985605i	0.998655	−	0.0518506i	$-0.0165120\pi$
$648$	−6.63762	+	6.07799i	−0.260750	+	0.238766i
$649$	1.52335	−	0.494967i	0.0597968	−	0.0194291i
$650$	−4.85631			−0.190480
$651$	43.9605	−	5.64020i	1.72295	−	0.221057i
$652$	−7.95163			−0.311410
$653$	10.5038	−	3.41290i	0.411047	−	0.133557i	−0.0961918	−	0.995363i	$-0.530666\pi$
$653$	10.5038	−	3.41290i	0.411047	−	0.133557i	0.507239	+	0.861806i	$0.330666\pi$
$654$	−1.35825	+	1.22813i	−0.0531116	+	0.0480237i
$655$	−16.9662	+	12.3267i	−0.662924	+	0.481642i
$656$	7.89798	−	4.55990i	0.308364	−	0.178034i
$657$	−20.3312	−	11.6249i	−0.793194	−	0.453532i
$658$	4.55927	+	43.3785i	0.177739	+	1.69107i
$659$	−21.4601	+	29.5373i	−0.835966	+	1.15061i	0.150818	+	0.988562i	$0.451809\pi$
$659$	−21.4601	+	29.5373i	−0.835966	+	1.15061i	−0.986783	+	0.162046i	$0.948191\pi$
$660$	0.973941	+	0.100304i	0.0379106	+	0.00390432i
$661$	4.92255	−	5.46704i	0.191465	−	0.212643i	−0.639767	−	0.768569i	$-0.720969\pi$
$661$	4.92255	−	5.46704i	0.191465	−	0.212643i	0.831232	+	0.555925i	$0.187636\pi$
$662$	17.9029	+	7.97089i	0.695816	+	0.309797i
$663$	3.26830	−	15.5361i	0.126930	−	0.603371i
$664$	−2.17261	−	10.2213i	−0.0843135	−	0.396664i
$665$	−1.77224	−	3.98053i	−0.0687247	−	0.154358i
$666$	4.09665	−	12.7902i	0.158742	−	0.495611i
$667$	−1.26920	+	3.90619i	−0.0491435	+	0.151248i
$668$	−19.7408	+	8.78916i	−0.763794	+	0.340063i
$669$	−5.81240	−	27.0664i	−0.224720	−	1.04645i
$670$	−6.81947	−	1.44952i	−0.263459	−	0.0559999i
$671$	−0.991399	+	2.22672i	−0.0382726	+	0.0859616i
$672$	−5.92676	−	5.31405i	−0.228630	−	0.204994i
$673$	2.26597	+	0.238163i	0.0873466	+	0.00918050i	0.148101	−	0.988972i	$-0.452684\pi$
$673$	2.26597	+	0.238163i	0.0873466	+	0.00918050i	−0.0607543	+	0.998153i	$0.519351\pi$
$674$	−14.8922	−	10.8198i	−0.573626	−	0.416764i
$675$	0.575601	+	5.16417i	0.0221549	+	0.198769i
$676$	−5.29187	+	9.16579i	−0.203534	+	0.352531i
$677$	−0.445412	−	0.771476i	−0.0171186	−	0.0296502i	0.857339	−	0.514752i	$-0.172116\pi$
$677$	−0.445412	−	0.771476i	−0.0171186	−	0.0296502i	−0.874458	+	0.485102i	$0.838783\pi$
$678$	10.3929	−	7.58422i	0.399139	−	0.291270i
$679$	4.28607	+	4.76017i	0.164484	+	0.182678i
$680$	−0.583256	−	1.79508i	−0.0223669	−	0.0688381i
$681$	0.0514542	+	24.5703i	0.00197173	+	0.941534i
$682$	2.15415	+	2.29465i	0.0824868	+	0.0878665i
$683$			6.63621i			0.253928i	0.991907	+	0.126964i	$0.0405232\pi$
$683$			6.63621i			0.253928i	−0.991907	+	0.126964i	$0.959477\pi$
$684$	0.890238	+	2.70132i	0.0340391	+	0.103288i
$685$	1.89696	−	1.70803i	0.0724793	−	0.0652607i
$686$	19.2389	+	26.4800i	0.734544	+	1.01101i
$687$	36.2624	−	21.0375i	1.38350	−	0.802630i
$688$	11.0350	+	6.37105i	0.420705	+	0.242894i
$689$	−0.538237	+	0.0565710i	−0.0205052	+	0.00215518i
$690$	2.11010	+	1.52634i	0.0803301	+	0.0581066i
$691$	4.77691	−	45.4493i	0.181722	−	1.72897i	−0.400807	−	0.916162i	$-0.631270\pi$
$691$	4.77691	−	45.4493i	0.181722	−	1.72897i	0.582530	−	0.812809i	$-0.302063\pi$
$692$	5.87681	+	5.29150i	0.223403	+	0.201153i
$693$	7.13323	+	3.14019i	0.270969	+	0.119286i
$694$	−2.75341	+	12.9538i	−0.104518	+	0.491718i
$695$	−9.01758	+	1.91674i	−0.342056	+	0.0727063i
$696$	1.93345	+	4.31823i	0.0732871	+	0.163682i
$697$	16.3708	+	5.31918i	0.620086	+	0.201478i
$698$	−18.4408	−	5.99177i	−0.697994	−	0.226792i
$699$	−14.9775	−	33.4513i	−0.566502	−	1.26525i
$700$	−4.49542	+	0.955532i	−0.169911	+	0.0361157i
$701$	−9.01448	+	42.4098i	−0.340472	+	1.60180i	0.391310	+	0.920259i	$0.372022\pi$
$701$	−9.01448	+	42.4098i	−0.340472	+	1.60180i	−0.731783	+	0.681538i	$0.761311\pi$
$702$	23.1165	+	10.1186i	0.872478	+	0.381903i
$703$	−3.15414	−	2.84000i	−0.118961	−	0.107113i
$704$	0.0590878	−	0.562183i	0.00222696	−	0.0211881i
$705$	−13.3190	−	9.63427i	−0.501623	−	0.362848i
$706$	19.3904	−	2.03801i	0.729766	−	0.0767015i
$707$	−55.6648	−	32.1381i	−2.09349	−	1.20868i
$708$	4.24517	−	2.46282i	0.159543	−	0.0925584i
$709$	−16.7918	−	23.1119i	−0.630628	−	0.867984i	0.367445	−	0.930045i	$-0.380233\pi$
$709$	−16.7918	−	23.1119i	−0.630628	−	0.867984i	−0.998072	+	0.0620609i	$0.980233\pi$
$710$	7.08859	−	6.38259i	0.266030	−	0.239534i
$711$	−40.0011	+	13.1826i	−1.50016	+	0.494387i
$712$			1.85851i			0.0696506i
$713$	1.91040	+	8.15067i	0.0715451	+	0.305245i
$714$	−0.0314641	−	15.0246i	−0.00117751	−	0.562282i
$715$	−0.848305	−	2.61081i	−0.0317248	−	0.0976389i
$716$	11.9349	+	13.2550i	0.446027	+	0.495363i
$717$	−18.5355	+	13.5262i	−0.692222	+	0.505147i
$718$	5.88202	+	10.1880i	0.219515	+	0.380211i
$719$	2.29211	−	3.97006i	0.0854814	−	0.148058i	−0.820115	−	0.572199i	$-0.806091\pi$
$719$	2.29211	−	3.97006i	0.0854814	−	0.148058i	0.905596	+	0.424141i	$0.139424\pi$
$720$	2.98223	−	0.326079i	0.111141	−	0.0121522i
$721$	15.0501	+	10.9345i	0.560494	+	0.407222i
$722$	−18.0020	−	1.89209i	−0.669965	−	0.0704161i
$723$	23.5202	+	21.0887i	0.874727	+	0.784297i
$724$	1.68865	−	3.79276i	0.0627581	−	0.140957i
$725$	2.67193	+	0.567937i	0.0992331	+	0.0210927i
$726$	−3.88406	−	18.0868i	−0.144151	−	0.671262i
$727$	−30.5255	+	13.5908i	−1.13213	+	0.504055i	−0.885307	−	0.465006i	$-0.846052\pi$
$727$	−30.5255	+	13.5908i	−1.13213	+	0.504055i	−0.246819	+	0.969062i	$0.579385\pi$
$728$	−6.89692	+	21.2265i	−0.255617	+	0.786708i
$729$	8.02016	−	25.7813i	0.297043	−	0.954864i
$730$	3.17525	+	7.13174i	0.117521	+	0.263958i
$731$	5.00031	+	23.5246i	0.184943	+	0.870090i
$732$	−1.53748	+	7.30852i	−0.0568271	+	0.270131i
$733$	−25.6819	−	11.4343i	−0.948583	−	0.422337i	−0.126667	−	0.991945i	$-0.540428\pi$
$733$	−25.6819	−	11.4343i	−0.948583	−	0.422337i	−0.821916	+	0.569609i	$0.807095\pi$
$734$	−18.2807	+	20.3028i	−0.674753	+	0.749389i
$735$	−24.3311	−	2.50580i	−0.897467	−	0.0924278i
$736$	0.883780	−	1.21642i	0.0325766	−	0.0448378i
$737$	−0.411949	−	3.91944i	−0.0151743	−	0.144374i
$738$	−13.5803	+	23.7510i	−0.499899	+	0.874287i
$739$	4.62354	−	2.66940i	0.170080	−	0.0981956i	−0.412544	−	0.910938i	$-0.635360\pi$
$739$	4.62354	−	2.66940i	0.170080	−	0.0981956i	0.582623	+	0.812742i	$0.302026\pi$
$740$	−3.62177	+	2.63137i	−0.133139	+	0.0967311i
$741$	5.91512	−	5.34847i	0.217298	−	0.196481i
$742$	−0.487108	+	0.158271i	−0.0178823	+	0.00581031i
$743$	−51.7169			−1.89731			−0.948655	−	0.316314i	$-0.897555\pi$
$743$	−51.7169			−1.89731			−0.948655	+	0.316314i	$0.897555\pi$
$744$	7.92954	+	5.48838i	0.290711	+	0.201214i
$745$	−7.15588			−0.262171
$746$	−19.7900	+	6.43015i	−0.724562	+	0.235424i
$747$	21.0740	+	23.2088i	0.771056	+	0.849165i
$748$	0.863173	−	0.627132i	0.0315607	−	0.0229302i
$749$	68.9759	−	39.8232i	2.52032	−	1.45511i
$750$	0.862882	−	1.50181i	0.0315080	−	0.0548384i
$751$	−4.04236	−	38.4605i	−0.147508	−	1.40344i	−0.778495	−	0.627650i	$-0.784017\pi$
$751$	−4.04236	−	38.4605i	−0.147508	−	1.40344i	0.630987	−	0.775793i	$-0.282650\pi$
$752$	−5.57844	+	7.67806i	−0.203425	+	0.279990i
$753$	−0.0294489	+	0.285946i	−0.00107318	+	0.0104205i
$754$	8.87644	−	9.85828i	0.323261	−	0.359017i
$755$	−7.22243	−	3.21563i	−0.262851	−	0.117029i
$756$	23.3896	+	4.81824i	0.850673	+	0.175238i
$757$	9.59651	+	45.1480i	0.348791	+	1.64093i	0.706944	+	0.707269i	$0.250073\pi$
$757$	9.59651	+	45.1480i	0.348791	+	1.64093i	−0.358153	+	0.933663i	$0.616593\pi$
$758$	−13.8089	−	31.0154i	−0.501563	−	1.12653i
$759$	−0.451984	+	1.40104i	−0.0164060	+	0.0508545i
$760$	0.292972	−	0.901676i	0.0106272	−	0.0327072i
$761$	−5.25115	+	2.33796i	−0.190354	+	0.0847510i	−0.499700	−	0.866198i	$-0.666556\pi$
$761$	−5.25115	+	2.33796i	−0.190354	+	0.0847510i	0.309346	+	0.950949i	$0.399890\pi$
$762$	20.7988	−	4.46646i	0.753460	−	0.161803i
$763$	4.75265	+	1.01021i	0.172057	+	0.0365720i
$764$	−6.67072	+	14.9827i	−0.241338	+	0.542054i
$765$	4.22379	+	3.77121i	0.152712	+	0.136348i
$766$	17.1298	+	1.80042i	0.618925	+	0.0650517i
$767$	−11.1325	−	8.08827i	−0.401973	−	0.292050i
$768$	−0.184656	−	1.72218i	−0.00666318	−	0.0621438i
$769$	7.04604	−	12.2041i	0.254087	−	0.440091i	−0.710560	−	0.703636i	$-0.751558\pi$
$769$	7.04604	−	12.2041i	0.254087	−	0.440091i	0.964647	+	0.263545i	$0.0848918\pi$
$770$	−1.29897	−	2.24988i	−0.0468117	−	0.0810802i
$771$	10.2762	+	14.0819i	0.370089	+	0.507146i
$772$	0.681242	+	0.756596i	0.0245184	+	0.0272305i
$773$	−0.742095	−	2.28393i	−0.0266913	−	0.0821473i	0.936824	−	0.349802i	$-0.113751\pi$
$773$	−0.742095	−	2.28393i	−0.0266913	−	0.0821473i	−0.963515	+	0.267655i	$0.913751\pi$
$774$	−38.2260	+	0.160104i	−1.37400	+	0.00575482i
$775$	5.25835	−	1.83025i	0.188885	−	0.0657443i
$776$			1.39374i			0.0500324i
$777$	−33.8688	+	11.0831i	−1.21504	+	0.397604i
$778$	24.8948	−	22.4154i	0.892522	−	0.803630i
$779$	5.08215	+	6.99499i	0.182087	+	0.250621i
$780$	−4.22093	−	7.27564i	−0.151134	−	0.260510i
$781$	4.66960	+	2.69600i	0.167092	+	0.0964704i
$782$	2.82239	−	0.296645i	0.100928	−	0.0106080i
$783$	−11.5353	−	8.27069i	−0.412239	−	0.295570i
$784$	−1.47614	+	14.0445i	−0.0527192	+	0.501590i
$785$	−7.56908	−	6.81523i	−0.270152	−	0.243246i
$786$	−33.2140	−	14.7046i	−1.18470	−	0.524494i
$787$	−3.97119	+	18.6830i	−0.141558	+	0.665977i	0.848945	+	0.528482i	$0.177238\pi$
$787$	−3.97119	+	18.6830i	−0.141558	+	0.665977i	−0.990502	+	0.137495i	$0.956095\pi$
$788$	18.6270	−	3.95929i	0.663560	−	0.141044i
$789$	7.22262	−	3.23386i	0.257132	−	0.115128i
$790$	13.3520	+	4.33833i	0.475043	+	0.154351i
$791$	−32.4680	−	10.5495i	−1.15443	−	0.375097i
$792$	0.696242	+	1.54632i	0.0247399	+	0.0549462i
$793$	20.4825	−	4.35369i	0.727355	−	0.154604i
$794$	7.58313	−	35.6758i	0.269115	−	1.26609i
$795$	0.0781408	−	0.176501i	0.00277137	−	0.00625985i
$796$	20.6349	+	18.5797i	0.731384	+	0.658541i
$797$	−2.51574	+	23.9357i	−0.0891120	+	0.847844i	0.855090	+	0.518479i	$0.173501\pi$
$797$	−2.51574	+	23.9357i	−0.0891120	+	0.847844i	−0.944202	+	0.329366i	$0.893165\pi$
$798$	4.42318	−	6.11488i	0.156579	−	0.216464i
$799$	−17.8150	+	1.87243i	−0.630249	+	0.0662418i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−2.80796	−	4.81683i	−0.0992145	−	0.170194i
$802$	−14.1029	−	19.4109i	−0.497989	−	0.685423i
$803$	−3.27946	+	2.95284i	−0.115730	+	0.104203i
$804$	−3.75559	−	11.4767i	−0.132449	−	0.404751i
$805$		−	6.91022i		−	0.243553i
$806$	5.07064	−	26.5591i	0.178606	−	0.935504i
$807$	11.5382	−	0.0241630i	0.406165	−	0.000850577i
$808$	−4.32181	−	13.3012i	−0.152041	−	0.467934i
$809$	−32.3544	−	35.9333i	−1.13752	−	1.26335i	−0.960237	−	0.279186i	$-0.909935\pi$
$809$	−32.3544	−	35.9333i	−1.13752	−	1.26335i	−0.177285	−	0.984160i	$-0.556731\pi$
$810$	−7.23658	+	5.35087i	−0.254268	+	0.188011i
$811$	19.0527	+	33.0003i	0.669031	+	1.15880i	0.978175	+	0.207781i	$0.0666241\pi$
$811$	19.0527	+	33.0003i	0.669031	+	1.15880i	−0.309144	+	0.951015i	$0.600043\pi$
$812$	6.27708	−	10.8722i	0.220282	−	0.381540i
$813$	10.6698	−	1.14404i	0.374207	−	0.0401232i
$814$	−2.04731	−	1.48746i	−0.0717583	−	0.0521354i
$815$	−7.90807	−	0.831172i	−0.277008	−	0.0291147i
$816$	2.18241	−	2.43404i	0.0763997	−	0.0852086i
$817$	−4.91359	+	11.0361i	−0.171905	+	0.386104i
$818$	−7.54116	−	1.60292i	−0.263670	−	0.0560449i
$819$	−14.1953	−	65.4346i	−0.496023	−	2.28647i
$820$	8.33135	−	3.70936i	0.290943	−	0.129536i
$821$	−0.594068	+	1.82835i	−0.0207331	+	0.0638100i	−0.960888	−	0.276938i	$-0.910680\pi$
$821$	−0.594068	+	1.82835i	−0.0207331	+	0.0638100i	0.940155	+	0.340748i	$0.110680\pi$
$822$	4.20772	+	1.35744i	0.146761	+	0.0473461i
$823$	3.60580	+	8.09876i	0.125690	+	0.282305i	0.965420	−	0.260700i	$-0.0839533\pi$
$823$	3.60580	+	8.09876i	0.125690	+	0.282305i	−0.839730	+	0.543005i	$0.817287\pi$
$824$	0.841576	+	3.95930i	0.0293177	+	0.137929i
$825$	0.958122	+	0.201559i	0.0333575	+	0.00701738i
$826$	−11.8967	−	5.29676i	−0.413939	−	0.184298i
$827$	14.2338	−	15.8082i	0.494957	−	0.549706i	−0.442971	−	0.896536i	$-0.646075\pi$
$827$	14.2338	−	15.8082i	0.494957	−	0.549706i	0.937928	+	0.346830i	$0.112742\pi$
$828$	−0.452707	+	4.48795i	−0.0157326	+	0.155967i
$829$	−9.34434	+	12.8614i	−0.324542	+	0.446694i	−0.939847	−	0.341595i	$-0.889033\pi$
$829$	−9.34434	+	12.8614i	−0.324542	+	0.446694i	0.615305	+	0.788289i	$0.289033\pi$
$830$	−1.09229	−	10.3924i	−0.0379139	−	0.360726i
$831$	32.3104	+	18.5643i	1.12084	+	0.643989i
$832$	−4.20569	+	2.42816i	−0.145806	+	0.0841811i
$833$	−21.5639	+	15.6671i	−0.747145	+	0.542833i
$834$	−10.7094	−	11.8440i	−0.370836	−	0.410125i
$835$	−20.5514	+	6.67754i	−0.711209	+	0.231086i
$836$	0.535929			0.0185355
$837$	−28.8438	−	2.24414i	−0.996987	−	0.0775688i
$838$	36.5251			1.26174
$839$	−29.5912	+	9.61478i	−1.02160	+	0.331939i	−0.771465	−	0.636271i	$-0.780476\pi$
$839$	−29.5912	+	9.61478i	−1.02160	+	0.331939i	−0.250138	+	0.968210i	$0.580476\pi$
$840$	−5.33883	−	5.90445i	−0.184207	−	0.203723i
$841$	17.4248	−	12.6598i	0.600855	−	0.436546i
$842$	−29.1691	+	16.8408i	−1.00523	+	0.580372i
$843$	−20.9721	−	12.0497i	−0.722317	−	0.415015i
$844$	0.0260342	+	0.247698i	0.000896133	+	0.00852613i
$845$	−6.22097	+	8.56243i	−0.214008	+	0.294557i
$846$	2.85749	−	28.3281i	0.0982427	−	0.973939i
$847$	−32.8448	+	36.4779i	−1.12856	+	1.25340i
$848$	−0.101808	−	0.0453279i	−0.00349611	−	0.00155657i
$849$	−22.2783	−	4.68666i	−0.764590	−	0.160846i
$850$	−0.392424	−	1.84621i	−0.0134600	−	0.0633245i
$851$	−2.73780	−	6.14920i	−0.0938506	−	0.210792i
$852$	15.7234	+	5.07248i	0.538676	+	0.173780i
$853$	8.68579	−	26.7321i	0.297396	−	0.915290i	−0.685011	−	0.728533i	$-0.740202\pi$
$853$	8.68579	−	26.7321i	0.297396	−	0.915290i	0.982406	−	0.186757i	$-0.0597976\pi$
$854$	18.1038	−	8.06031i	0.619498	−	0.275818i
$855$	0.602997	+	2.77958i	0.0206220	+	0.0950596i
$856$	16.9514	+	3.60312i	0.579386	+	0.123152i
$857$	3.10897	−	6.98285i	0.106200	−	0.238530i	−0.852627	−	0.522520i	$-0.824992\pi$
$857$	3.10897	−	6.98285i	0.106200	−	0.238530i	0.958827	+	0.283991i	$0.0916585\pi$
$858$	3.17416	−	3.54014i	0.108364	−	0.120859i
$859$	0.947801	+	0.0996179i	0.0323385	+	0.00339892i	0.120684	−	0.992691i	$-0.461491\pi$
$859$	0.947801	+	0.0996179i	0.0323385	+	0.00339892i	−0.0883454	+	0.996090i	$0.528158\pi$
$860$	10.3086	+	7.48962i	0.351520	+	0.255394i
$861$	72.1822	−	7.73952i	2.45996	−	0.263762i
$862$	−5.36118	+	9.28583i	−0.182602	+	0.316277i
$863$	−18.8307	−	32.6157i	−0.641004	−	1.11025i	−0.985209	−	0.171357i	$-0.945185\pi$
$863$	−18.8307	−	32.6157i	−0.641004	−	1.11025i	0.344205	−	0.938894i	$-0.388148\pi$
$864$	3.08057	+	4.18450i	0.104803	+	0.142360i
$865$	5.29150	+	5.87681i	0.179916	+	0.199817i
$866$	−1.10650	−	3.40547i	−0.0376005	−	0.115722i
$867$	−23.2744	+	0.0487405i	−0.790440	+	0.00165531i
$868$	−0.531962	−	25.5831i	−0.0180560	−	0.868347i
$869$			7.93603i			0.269211i
$870$	1.47148	+	4.49668i	0.0498877	+	0.152452i
$871$	−25.1609	+	22.6550i	−0.852544	+	0.767634i
$872$	0.621418	+	0.855309i	0.0210439	+	0.0289644i
$873$	−2.10576	−	3.61226i	−0.0712692	−	0.122256i
$874$	1.23453	+	0.712754i	0.0417585	+	0.0241093i
$875$	−4.57068	+	0.480398i	−0.154517	+	0.0162404i
$876$	−7.92483	+	10.9558i	−0.267755	+	0.370161i
$877$	−1.15497	+	10.9888i	−0.0390007	+	0.371067i	0.957562	+	0.288227i	$0.0930657\pi$
$877$	−1.15497	+	10.9888i	−0.0390007	+	0.371067i	−0.996563	+	0.0828401i	$0.973601\pi$
$878$	21.6710	+	19.5127i	0.731362	+	0.658521i
$879$	8.34427	−	18.8477i	0.281445	−	0.635716i
$880$	0.117528	−	0.552927i	0.00396188	−	0.0186392i
$881$	−49.8721	+	10.6007i	−1.68024	+	0.357145i	−0.946603	−	0.322402i	$-0.895510\pi$
$881$	−49.8721	+	10.6007i	−1.68024	+	0.357145i	−0.733632	+	0.679547i	$0.762176\pi$
$882$	−17.3936	−	38.6304i	−0.585673	−	1.30075i
$883$	−53.4174	−	17.3564i	−1.79764	−	0.584088i	−0.797814	−	0.602903i	$-0.794011\pi$
$883$	−53.4174	−	17.3564i	−1.79764	−	0.584088i	−0.999823	+	0.0188154i	$0.994011\pi$
$884$	−8.71746	−	2.83247i	−0.293200	−	0.0952664i
$885$	4.47935	−	2.00559i	0.150572	−	0.0674170i
$886$	−17.4304	+	3.70495i	−0.585586	+	0.124470i
$887$	−2.00922	+	9.45265i	−0.0674631	+	0.317389i	−0.998920	−	0.0464627i	$-0.985205\pi$
$887$	−2.00922	+	9.45265i	−0.0674631	+	0.317389i	0.931457	+	0.363852i	$0.118538\pi$
$888$	−7.09019	−	3.13898i	−0.237931	−	0.105337i
$889$	−41.9476	−	37.7698i	−1.40688	−	1.26676i
$890$	−0.194267	+	1.84833i	−0.00651185	+	0.0619561i
$891$	−4.14079	−	2.95578i	−0.138722	−	0.0990225i
$892$	−15.8955	+	1.67068i	−0.532220	+	0.0559386i
$893$	−7.79235	−	4.49892i	−0.260761	−	0.150551i
$894$	−6.21964	−	10.7208i	−0.208016	−	0.358558i
$895$	10.4840	+	14.4299i	0.350440	+	0.482340i
$896$	−3.41539	+	3.07523i	−0.114100	+	0.102736i
$897$	12.0199	−	3.93336i	0.401334	−	0.131331i
$898$			9.29071i			0.310035i
$899$	−5.89590	+	14.0198i	−0.196639	+	0.467585i
$900$	2.99997	−	0.0125650i	0.0999991	−	0.000418832i
$901$	−0.0649998	−	0.200049i	−0.00216546	−	0.00666459i
$902$	3.44952	+	3.83109i	0.114857	+	0.127561i
$903$	59.7910	+	81.9339i	1.98972	+	2.72659i
$904$	−3.71409	−	6.43300i	−0.123529	−	0.213958i
$905$	2.07585	−	3.59547i	0.0690035	−	0.119518i
$906$	−1.45987	−	13.6154i	−0.0485011	−	0.452343i
$907$	−40.0109	−	29.0696i	−1.32854	−	0.965242i	−0.999783	−	0.0208275i	$-0.993370\pi$
$907$	−40.0109	−	29.0696i	−1.32854	−	0.965242i	−0.328758	−	0.944414i	$-0.606630\pi$
$908$	14.1080	+	1.48281i	0.468189	+	0.0492087i
$909$	31.2975	+	27.9439i	1.03807	+	0.926841i
$910$	−9.07791	+	20.3893i	−0.300930	+	0.675900i
$911$	13.6434	+	2.89999i	0.452025	+	0.0960809i	0.428298	−	0.903638i	$-0.359113\pi$
$911$	13.6434	+	2.89999i	0.452025	+	0.0960809i	0.0237271	+	0.999718i	$0.492447\pi$
$912$	1.60552	−	0.344779i	0.0531640	−	0.0114168i
$913$	5.39630	−	2.40259i	0.178591	−	0.0795140i
$914$	3.35220	−	10.3170i	0.110881	−	0.341257i
$915$	−2.29301	+	7.10777i	−0.0758046	+	0.234976i
$916$	−9.84475	−	22.1117i	−0.325280	−	0.730590i
$917$	20.0388	+	94.2752i	0.661740	+	3.11324i
$918$	−1.97879	+	9.60582i	−0.0653097	+	0.317039i
$919$	25.1223	+	11.1851i	0.828707	+	0.368964i	0.776846	−	0.629690i	$-0.216818\pi$
$919$	25.1223	+	11.1851i	0.828707	+	0.368964i	0.0518605	+	0.998654i	$0.483485\pi$
$920$	1.00609	−	1.11738i	0.0331698	−	0.0368388i
$921$	−0.568030	+	5.51553i	−0.0187172	+	0.181743i
$922$	14.1871	−	19.5268i	0.467226	−	0.643081i
$923$	−4.84203	−	46.0688i	−0.159377	−	1.51637i
$924$	2.24172	−	3.90162i	0.0737471	−	0.128354i
$925$	−3.87698	+	2.23838i	−0.127474	+	0.0735974i
$926$	−21.7837	+	15.8268i	−0.715857	+	0.520101i
$927$	−8.16316	−	8.99010i	−0.268113	−	0.295273i
$928$	2.59793	−	0.844119i	0.0852813	−	0.0277096i
$929$	24.7489			0.811986			0.405993	−	0.913876i	$-0.366926\pi$
$929$	24.7489			0.811986			0.405993	+	0.913876i	$0.366926\pi$
$930$	7.31241	+	6.28718i	0.239783	+	0.206165i
$931$	−13.3886			−0.438795
$932$	−20.1250	+	6.53900i	−0.659215	+	0.214192i
$933$	−13.7974	+	12.4756i	−0.451706	+	0.408434i
$934$	16.4551	−	11.9554i	0.538429	−	0.391191i
$935$	0.923998	−	0.533471i	0.0302180	−	0.0174464i
$936$	7.23156	−	12.6475i	0.236371	−	0.413395i
$937$	2.16440	+	20.5929i	0.0707078	+	0.672739i	0.971265	+	0.238001i	$0.0764923\pi$
$937$	2.16440	+	20.5929i	0.0707078	+	0.672739i	−0.900557	+	0.434738i	$0.856841\pi$
$938$	−18.8335	+	25.9221i	−0.614935	+	0.846386i
$939$	−22.2601	−	2.29251i	−0.726432	−	0.0748134i
$940$	−6.35046	+	7.05290i	−0.207129	+	0.230040i
$941$	−17.6372	−	7.85258i	−0.574956	−	0.255987i	0.0985952	−	0.995128i	$-0.468565\pi$
$941$	−17.6372	−	7.85258i	−0.574956	−	0.255987i	−0.673551	+	0.739141i	$0.735232\pi$
$942$	3.63169	−	17.2634i	0.118327	−	0.562473i
$943$	2.85095	+	13.4127i	0.0928397	+	0.436776i
$944$	−1.15251	−	2.58857i	−0.0375109	−	0.0842509i
$945$	22.7579	+	7.23673i	0.740313	+	0.235411i
$946$	−2.22580	+	6.85032i	−0.0723671	+	0.222723i
$947$	−44.4790	+	19.8033i	−1.44537	+	0.643522i	−0.971493	−	0.237067i	$-0.923814\pi$
$947$	−44.4790	+	19.8033i	−1.44537	+	0.643522i	−0.473880	+	0.880589i	$0.657147\pi$
$948$	5.10548	+	23.7745i	0.165818	+	0.772159i
$949$	37.0831	+	7.88226i	1.20377	+	0.255869i
$950$	0.385618	−	0.866112i	0.0125111	−	0.0281004i
$951$	37.9569	+	34.0329i	1.23084	+	1.10359i
$952$	−8.62696	−	0.906730i	−0.279601	−	0.0293873i
$953$	5.14905	+	3.74100i	0.166794	+	0.121183i	0.668051	−	0.744116i	$-0.267129\pi$
$953$	5.14905	+	3.74100i	0.166794	+	0.121183i	−0.501257	+	0.865299i	$0.667129\pi$
$954$	0.332348	−	0.0363392i	0.0107602	−	0.00117652i
$955$	−8.20029	+	14.2033i	−0.265355	+	0.459609i
$956$	6.62398	+	11.4731i	0.214235	+	0.371066i
$957$	−2.16043	+	1.57657i	−0.0698369	+	0.0509632i
$958$	−14.4217	−	16.0170i	−0.465945	−	0.517484i
$959$	−3.62522	−	11.1573i	−0.117064	−	0.360287i
$960$	−0.00362720	−	1.73205i	−0.000117067	−	0.0559016i
$961$	4.51916	+	30.6688i	0.145779	+	0.989317i
$962$			21.7405i			0.700942i
$963$	−49.3779	+	16.2728i	−1.59118	+	0.524384i
$964$	13.5539	−	12.2040i	0.436541	−	0.393064i
$965$	0.598424	+	0.823661i	0.0192640	+	0.0265146i
$966$	10.3528	−	6.00612i	0.333095	−	0.193244i
$967$	−20.6194	−	11.9046i	−0.663076	−	0.382827i	0.130372	−	0.991465i	$-0.458383\pi$
$967$	−20.6194	−	11.9046i	−0.663076	−	0.382827i	−0.793448	+	0.608638i	$0.791716\pi$
$968$	−10.6220	+	1.11641i	−0.341402	+	0.0358828i
$969$	2.51130	+	1.81654i	0.0806746	+	0.0583558i
$970$	−0.145686	+	1.38611i	−0.00467769	+	0.0445052i
$971$	10.3662	+	9.33380i	0.332668	+	0.299536i	0.818489	−	0.574523i	$-0.194812\pi$
$971$	10.3662	+	9.33380i	0.332668	+	0.299536i	−0.485820	+	0.874059i	$0.661479\pi$
$972$	−14.3064	−	6.19094i	−0.458877	−	0.198574i
$973$	−8.80908	+	41.4435i	−0.282406	+	1.32862i
$974$	−6.17772	+	1.31311i	−0.197947	+	0.0420749i
$975$	−3.43730	−	7.67699i	−0.110082	−	0.245861i
$976$	4.10089	+	1.33246i	0.131266	+	0.0426510i
$977$	35.4761	+	11.5269i	1.13498	+	0.368778i	0.815467	−	0.578803i	$-0.196480\pi$
$977$	35.4761	+	11.5269i	1.13498	+	0.368778i	0.319515	+	0.947581i	$0.396480\pi$
$978$	−5.62817	−	12.5702i	−0.179969	−	0.401950i
$979$	−1.02762	+	0.218427i	−0.0328429	+	0.00698097i
$980$	−2.93610	+	13.8133i	−0.0937904	+	0.441249i
$981$	−2.90283	−	1.27788i	−0.0926803	−	0.0407997i
$982$	−3.93056	−	3.53909i	−0.125429	−	0.112937i
$983$	−4.88618	+	46.4889i	−0.155845	+	1.48276i	0.584970	+	0.811055i	$0.301106\pi$
$983$	−4.88618	+	46.4889i	−0.155845	+	1.48276i	−0.740815	+	0.671709i	$0.765560\pi$
$984$	12.7986	+	9.25784i	0.408005	+	0.295129i
$985$	18.9388	−	1.99055i	0.603441	−	0.0634242i
$986$	4.46508	+	2.57791i	0.142197	+	0.0820975i
$987$	−65.3469	+	37.9108i	−2.08002	+	1.20671i
$988$	−2.70626	−	3.72484i	−0.0860975	−	0.118503i
$989$	−14.2377	+	12.8197i	−0.452733	+	0.407643i
$990$	0.530793	+	1.61063i	0.0168697	+	0.0511892i
$991$		−	20.1987i		−	0.641634i	−0.947141	−	0.320817i	$-0.896043\pi$
$991$		−	20.1987i		−	0.641634i	0.947141	−	0.320817i	$-0.103957\pi$
$992$	3.63874	−	4.21421i	0.115530	−	0.133801i
$993$	0.0710828	+	33.9432i	0.00225575	+	1.07716i
$994$	−13.5467	−	41.6926i	−0.429677	−	1.32241i
$995$	18.5797	+	20.6349i	0.589017	+	0.654169i
$996$	14.6204	−	10.6692i	0.463264	−	0.338066i
$997$	−6.19765	−	10.7346i	−0.196282	−	0.339970i	0.751038	−	0.660259i	$-0.229553\pi$
$997$	−6.19765	−	10.7346i	−0.196282	−	0.339970i	−0.947320	+	0.320289i	$0.896220\pi$
$998$	17.1434	−	29.6932i	0.542665	−	0.939923i
$999$	23.1187	−	2.57682i	0.731444	−	0.0815271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.19	yes	176
3.2	odd	2	inner	930.2.br.b.11.3	✓	176
31.17	odd	30	inner	930.2.br.b.761.3	yes	176
93.17	even	30	inner	930.2.br.b.761.19	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.3	✓	176	3.2	odd	2	inner
930.2.br.b.11.19	yes	176	1.1	even	1	trivial
930.2.br.b.761.3	yes	176	31.17	odd	30	inner
930.2.br.b.761.19	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.16166 + 1.28473i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.50181 + 0.862882i) q^{6} +(-0.480398 - 4.57068i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.301087 + 2.98485i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.16166 + 1.28473i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.50181 + 0.862882i) q^{6} +(-0.480398 - 4.57068i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.301087 + 2.98485i) q^{9} +(0.669131 - 0.743145i) q^{10} +(0.516409 + 0.229920i) q^{11} +(1.69495 + 0.356565i) q^{12} +(-1.00968 - 4.75019i) q^{13} +(-1.86930 - 4.19852i) q^{14} +(1.64840 + 0.531782i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.72428 - 0.767698i) q^{17} +(0.636020 + 2.93180i) q^{18} +(0.927360 + 0.197116i) q^{19} +(0.406737 - 0.913545i) q^{20} +(5.31405 - 5.92676i) q^{21} +(0.562183 + 0.0590878i) q^{22} +(1.21642 + 0.883780i) q^{23} +(1.72218 - 0.184656i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.42816 - 4.20569i) q^{26} +(-4.18450 + 3.08057i) q^{27} +(-3.07523 - 3.41539i) q^{28} +(0.844119 + 2.59793i) q^{29} +(1.73205 - 0.00362720i) q^{30} +(4.21421 + 3.63874i) q^{31} -1.00000i q^{32} +(0.304506 + 0.930537i) q^{33} +(1.40265 - 1.26296i) q^{34} +(-2.70138 - 3.71812i) q^{35} +(1.51087 + 2.59177i) q^{36} +(-3.87698 - 2.23838i) q^{37} +(0.942884 - 0.0991011i) q^{38} +(4.92982 - 6.81528i) q^{39} +(0.104528 - 0.994522i) q^{40} +(6.77733 + 6.10233i) q^{41} +(3.22249 - 7.27882i) q^{42} +(-2.64923 + 12.4637i) q^{43} +(0.552927 - 0.117528i) q^{44} +(1.23168 + 2.73550i) q^{45} +(1.42999 + 0.464631i) q^{46} +(-9.02610 - 2.93276i) q^{47} +(1.58083 - 0.707801i) q^{48} +(-13.8133 + 2.93610i) q^{49} +(0.207912 - 0.978148i) q^{50} +(2.98932 + 1.32343i) q^{51} +(-3.60894 - 3.24951i) q^{52} +(0.0116490 - 0.110832i) q^{53} +(-3.02775 + 4.22288i) q^{54} +(0.562183 - 0.0590878i) q^{55} +(-3.98013 - 2.29793i) q^{56} +(0.824036 + 1.42039i) q^{57} +(1.60561 + 2.20993i) q^{58} +(2.10574 - 1.89601i) q^{59} +(1.64615 - 0.538682i) q^{60} +4.31193i q^{61} +(5.13239 + 2.15838i) q^{62} +(13.7874 - 0.0577467i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.24951 - 3.60894i) q^{65} +(0.577154 + 0.790896i) q^{66} +(-3.48591 - 6.03777i) q^{67} +(0.943729 - 1.63459i) q^{68} +(0.277644 + 2.58943i) q^{69} +(-3.71812 - 2.70138i) q^{70} +(9.48638 + 0.997059i) q^{71} +(2.23782 + 1.99804i) q^{72} +(-3.17525 + 7.13174i) q^{73} +(-4.37893 - 0.930770i) q^{74} +(1.69344 - 0.363661i) q^{75} +(0.866112 - 0.385618i) q^{76} +(0.802808 - 2.47079i) q^{77} +(2.58250 - 8.00512i) q^{78} +(5.71023 + 12.8254i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.81869 - 1.79740i) q^{81} +(8.33135 + 3.70936i) q^{82} +(6.99219 - 7.76562i) q^{83} +(0.815493 - 7.91837i) q^{84} +(1.10942 - 1.52699i) q^{85} +(1.33191 + 12.6723i) q^{86} +(-2.35707 + 4.10239i) q^{87} +(0.489546 - 0.282640i) q^{88} +(-1.50357 + 1.09240i) q^{89} +(2.01671 + 2.22101i) q^{90} +(-21.2265 + 6.89692i) q^{91} +1.50358 q^{92} +(0.220672 + 9.64113i) q^{93} -9.49061 q^{94} +(0.901676 - 0.292972i) q^{95} +(1.28473 - 1.16166i) q^{96} +(-1.12756 + 0.819221i) q^{97} +(-12.2299 + 7.06094i) q^{98} +(-0.841761 + 1.47218i) 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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