LMFDB - Embedded newform 115.2.l.a.102.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			102.4
Character	$\chi$	$=$	115.102
Dual form			115.2.l.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0452482 + 0.632652i) q^{2} +(-1.67360 + 0.364069i) q^{3} +(1.58144 + 0.227377i) q^{4} +(-0.673353 + 2.13227i) q^{5} +(-0.154602 - 1.07528i) q^{6} +(-0.171765 + 0.0937908i) q^{7} +(-0.485055 + 2.22976i) q^{8} +(-0.0605071 + 0.0276327i) q^{9} +(-1.31852 - 0.522480i) q^{10} +(2.33306 + 2.02161i) q^{11} +(-2.72948 + 0.195216i) q^{12} +(0.0682068 - 0.124911i) q^{13} +(-0.0515649 - 0.112911i) q^{14} +(0.350628 - 3.81372i) q^{15} +(1.67726 + 0.492487i) q^{16} +(0.702107 + 0.525590i) q^{17} +(-0.0147440 - 0.0395303i) q^{18} +(1.07365 - 7.46738i) q^{19} +(-1.54970 + 3.21896i) q^{20} +(0.253320 - 0.219503i) q^{21} +(-1.38454 + 1.38454i) q^{22} +(1.56765 - 4.53238i) q^{23} -3.90832i q^{24} +(-4.09319 - 2.87155i) q^{25} +(0.0759392 + 0.0488032i) q^{26} +(4.20456 - 3.14750i) q^{27} +(-0.292962 + 0.109269i) q^{28} +(3.41800 - 0.491434i) q^{29} +(2.39689 + 0.394389i) q^{30} +(-0.282325 + 0.181439i) q^{31} +(-1.98236 + 5.31490i) q^{32} +(-4.64062 - 2.53397i) q^{33} +(-0.364285 + 0.420407i) q^{34} +(-0.0843292 - 0.429405i) q^{35} +(-0.101971 + 0.0299415i) q^{36} +(7.03930 + 2.62552i) q^{37} +(4.67567 + 1.01713i) q^{38} +(-0.0686744 + 0.233884i) q^{39} +(-4.42785 - 2.53569i) q^{40} +(-3.88633 + 8.50988i) q^{41} +(0.127407 + 0.170195i) q^{42} +(0.170122 + 0.782038i) q^{43} +(3.22994 + 3.72754i) q^{44} +(-0.0181778 - 0.147624i) q^{45} +(2.79649 + 1.19686i) q^{46} +(-4.49497 - 4.49497i) q^{47} +(-2.98636 - 0.213588i) q^{48} +(-3.76378 + 5.85655i) q^{49} +(2.00190 - 2.45963i) q^{50} +(-1.36640 - 0.624012i) q^{51} +(0.136267 - 0.182031i) q^{52} +(-0.955623 - 1.75009i) q^{53} +(1.80102 + 2.80244i) q^{54} +(-5.88161 + 3.61347i) q^{55} +(-0.125816 - 0.428489i) q^{56} +(0.921788 + 12.8883i) q^{57} +(0.156248 + 2.18464i) q^{58} +(-2.49768 - 8.50633i) q^{59} +(1.42165 - 5.95145i) q^{60} +(-5.60557 - 8.72243i) q^{61} +(-0.102013 - 0.186823i) q^{62} +(0.00780132 - 0.0104213i) q^{63} +(-0.0925946 - 0.0422865i) q^{64} +(0.220418 + 0.229545i) q^{65} +(1.81310 - 2.82124i) q^{66} +(8.30923 + 0.594288i) q^{67} +(0.990833 + 0.990833i) q^{68} +(-0.973521 + 8.15612i) q^{69} +(0.275480 - 0.0339213i) q^{70} +(4.40447 + 5.08303i) q^{71} +(-0.0322650 - 0.148320i) q^{72} +(4.04711 + 5.40630i) q^{73} +(-1.97956 + 4.33463i) q^{74} +(7.89580 + 3.31562i) q^{75} +(3.39582 - 11.5651i) q^{76} +(-0.590347 - 0.128422i) q^{77} +(-0.144860 - 0.0540298i) q^{78} +(3.57517 - 1.04977i) q^{79} +(-2.17950 + 3.24475i) q^{80} +(-5.76017 + 6.64759i) q^{81} +(-5.20795 - 2.84375i) q^{82} +(-3.02763 + 8.11740i) q^{83} +(0.450520 - 0.289532i) q^{84} +(-1.59347 + 1.14318i) q^{85} +(-0.502456 + 0.0722422i) q^{86} +(-5.54144 + 2.06685i) q^{87} +(-5.63937 + 4.22158i) q^{88} +(-6.56977 - 4.22214i) q^{89} +(0.0942173 - 0.00482048i) q^{90} +0.0278526i q^{91} +(3.50971 - 6.81125i) q^{92} +(0.406442 - 0.406442i) q^{93} +(3.04714 - 2.64036i) q^{94} +(15.1996 + 7.31749i) q^{95} +(1.38268 - 9.61674i) q^{96} +(-4.54643 - 12.1894i) q^{97} +(-3.53486 - 2.64616i) q^{98} +(-0.197029 - 0.0578530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0452482	+	0.632652i	−0.0319953	+	0.447353i	0.956052	+	0.293199i	$0.0947197\pi$
$2$	−0.0452482	+	0.632652i	−0.0319953	+	0.447353i	−0.988047	+	0.154154i	$0.950735\pi$
$3$	−1.67360	+	0.364069i	−0.966253	+	0.210196i	−0.667893	−	0.744258i	$-0.732803\pi$
$3$	−1.67360	+	0.364069i	−0.966253	+	0.210196i	−0.298361	+	0.954453i	$0.596440\pi$
$4$	1.58144	+	0.227377i	0.790721	+	0.113688i
$5$	−0.673353	+	2.13227i	−0.301133	+	0.953582i
$5$	−0.673353	+	2.13227i	−0.301133	+	0.953582i
$6$	−0.154602	−	1.07528i	−0.0631160	−	0.438981i
$7$	−0.171765	+	0.0937908i	−0.0649211	+	0.0354496i	−0.511382	−	0.859354i	$-0.670866\pi$
$7$	−0.171765	+	0.0937908i	−0.0649211	+	0.0354496i	0.446461	+	0.894803i	$0.352684\pi$
$8$	−0.485055	+	2.22976i	−0.171493	+	0.788339i
$9$	−0.0605071	+	0.0276327i	−0.0201690	+	0.00921089i
$10$	−1.31852	−	0.522480i	−0.416953	−	0.165223i
$11$	2.33306	+	2.02161i	0.703445	+	0.609539i	0.931342	−	0.364147i	$-0.118639\pi$
$11$	2.33306	+	2.02161i	0.703445	+	0.609539i	−0.227897	+	0.973685i	$0.573185\pi$
$12$	−2.72948	+	0.195216i	−0.787933	+	0.0563541i
$13$	0.0682068	−	0.124911i	0.0189172	−	0.0346442i	−0.868049	−	0.496478i	$-0.834626\pi$
$13$	0.0682068	−	0.124911i	0.0189172	−	0.0346442i	0.886967	+	0.461834i	$0.152808\pi$
$14$	−0.0515649	−	0.112911i	−0.0137813	−	0.0301768i
$15$	0.350628	−	3.81372i	0.0905317	−	0.984699i
$16$	1.67726	+	0.492487i	0.419314	+	0.123122i
$17$	0.702107	+	0.525590i	0.170286	+	0.127474i	0.681022	−	0.732263i	$-0.261536\pi$
$17$	0.702107	+	0.525590i	0.170286	+	0.127474i	−0.510736	+	0.859738i	$0.670627\pi$
$18$	−0.0147440	−	0.0395303i	−0.00347520	−	0.00931737i
$19$	1.07365	−	7.46738i	0.246311	−	1.71313i	−0.372868	−	0.927884i	$-0.621626\pi$
$19$	1.07365	−	7.46738i	0.246311	−	1.71313i	0.619180	−	0.785249i	$-0.287465\pi$
$20$	−1.54970	+	3.21896i	−0.346523	+	0.719782i
$21$	0.253320	−	0.219503i	0.0552789	−	0.0478994i
$22$	−1.38454	+	1.38454i	−0.295186	+	0.295186i
$23$	1.56765	−	4.53238i	0.326878	−	0.945067i
$23$	1.56765	−	4.53238i	0.326878	−	0.945067i
$24$		−	3.90832i		−	0.797782i
$25$	−4.09319	−	2.87155i	−0.818638	−	0.574310i
$26$	0.0759392	+	0.0488032i	0.0148929	+	0.00957109i
$27$	4.20456	−	3.14750i	0.809169	−	0.605736i
$28$	−0.292962	+	0.109269i	−0.0553647	+	0.0206500i
$29$	3.41800	−	0.491434i	0.634706	−	0.0912569i	0.182551	−	0.983196i	$-0.441565\pi$
$29$	3.41800	−	0.491434i	0.634706	−	0.0912569i	0.452155	+	0.891939i	$0.350655\pi$
$30$	2.39689	+	0.394389i	0.437611	+	0.0720053i
$31$	−0.282325	+	0.181439i	−0.0507070	+	0.0325874i	−0.565749	−	0.824578i	$-0.691413\pi$
$31$	−0.282325	+	0.181439i	−0.0507070	+	0.0325874i	0.515042	+	0.857165i	$0.327776\pi$
$32$	−1.98236	+	5.31490i	−0.350434	+	0.939551i
$33$	−4.64062	−	2.53397i	−0.807828	−	0.441108i
$34$	−0.364285	+	0.420407i	−0.0624743	+	0.0720992i
$35$	−0.0843292	−	0.429405i	−0.0142542	−	0.0725826i
$36$	−0.101971	+	0.0299415i	−0.0169952	+	0.00499025i
$37$	7.03930	+	2.62552i	1.15725	+	0.431633i	0.853487	−	0.521113i	$-0.174483\pi$
$37$	7.03930	+	2.62552i	1.15725	+	0.431633i	0.303766	+	0.952747i	$0.401756\pi$
$38$	4.67567	+	1.01713i	0.758494	+	0.165000i
$39$	−0.0686744	+	0.233884i	−0.0109967	+	0.0374514i
$40$	−4.42785	−	2.53569i	−0.700104	−	0.400927i
$41$	−3.88633	+	8.50988i	−0.606943	+	1.32902i	0.317702	+	0.948191i	$0.397089\pi$
$41$	−3.88633	+	8.50988i	−0.606943	+	1.32902i	−0.924645	+	0.380830i	$0.875638\pi$
$42$	0.127407	+	0.170195i	0.0196593	+	0.0262617i
$43$	0.170122	+	0.782038i	0.0259433	+	0.119260i	0.988297	−	0.152539i	$-0.0487451\pi$
$43$	0.170122	+	0.782038i	0.0259433	+	0.119260i	−0.962354	+	0.271799i	$0.912381\pi$
$44$	3.22994	+	3.72754i	0.486931	+	0.561948i
$45$	−0.0181778	−	0.147624i	−0.00270978	−	0.0220065i
$46$	2.79649	+	1.19686i	0.412319	+	0.176467i
$47$	−4.49497	−	4.49497i	−0.655659	−	0.655659i	0.298691	−	0.954350i	$-0.403450\pi$
$47$	−4.49497	−	4.49497i	−0.655659	−	0.655659i	−0.954350	+	0.298691i	$0.903450\pi$
$48$	−2.98636	−	0.213588i	−0.431043	−	0.0308288i
$49$	−3.76378	+	5.85655i	−0.537683	+	0.836651i
$50$	2.00190	−	2.45963i	0.283111	−	0.347845i
$51$	−1.36640	−	0.624012i	−0.191334	−	0.0873792i
$52$	0.136267	−	0.182031i	0.0188968	−	0.0252432i
$53$	−0.955623	−	1.75009i	−0.131265	−	0.240394i	0.803777	−	0.594930i	$-0.202820\pi$
$53$	−0.955623	−	1.75009i	−0.131265	−	0.240394i	−0.935042	+	0.354537i	$0.884639\pi$
$54$	1.80102	+	2.80244i	0.245088	+	0.381364i
$55$	−5.88161	+	3.61347i	−0.793075	+	0.487241i
$56$	−0.125816	−	0.428489i	−0.0168128	−	0.0572592i
$57$	0.921788	+	12.8883i	0.122094	+	1.70709i
$58$	0.156248	+	2.18464i	0.0205164	+	0.286857i
$59$	−2.49768	−	8.50633i	−0.325171	−	1.10743i	−0.946184	−	0.323630i	$-0.895097\pi$
$59$	−2.49768	−	8.50633i	−0.325171	−	1.10743i	0.621013	−	0.783800i	$-0.286721\pi$
$60$	1.42165	−	5.95145i	0.183534	−	0.768329i
$61$	−5.60557	−	8.72243i	−0.717719	−	1.11679i	−0.988066	−	0.154030i	$-0.950775\pi$
$61$	−5.60557	−	8.72243i	−0.717719	−	1.11679i	0.270347	−	0.962763i	$-0.412862\pi$
$62$	−0.102013	−	0.186823i	−0.0129557	−	0.0237266i
$63$	0.00780132	−	0.0104213i	0.000982873	−	0.00131297i
$64$	−0.0925946	−	0.0422865i	−0.0115743	−	0.00528582i
$65$	0.220418	+	0.229545i	0.0273395	+	0.0284716i
$66$	1.81310	−	2.82124i	0.223177	−	0.347271i
$67$	8.30923	+	0.594288i	1.01513	+	0.0726038i	0.568979	−	0.822352i	$-0.307338\pi$
$67$	8.30923	+	0.594288i	1.01513	+	0.0726038i	0.446155	+	0.894956i	$0.352793\pi$
$68$	0.990833	+	0.990833i	0.120156	+	0.120156i
$69$	−0.973521	+	8.15612i	−0.117198	+	0.981882i
$70$	0.275480	−	0.0339213i	0.0329261	−	0.00405437i
$71$	4.40447	+	5.08303i	0.522714	+	0.603245i	0.954308	−	0.298823i	$-0.0965941\pi$
$71$	4.40447	+	5.08303i	0.522714	+	0.603245i	−0.431594	+	0.902068i	$0.642049\pi$
$72$	−0.0322650	−	0.148320i	−0.00380246	−	0.0174796i
$73$	4.04711	+	5.40630i	0.473678	+	0.632760i	0.972210	−	0.234112i	$-0.0752181\pi$
$73$	4.04711	+	5.40630i	0.473678	+	0.632760i	−0.498532	+	0.866872i	$0.666127\pi$
$74$	−1.97956	+	4.33463i	−0.230119	+	0.503890i
$75$	7.89580	+	3.31562i	0.911729	+	0.382854i
$76$	3.39582	−	11.5651i	0.389527	−	1.32661i
$77$	−0.590347	−	0.128422i	−0.0672763	−	0.0146351i
$78$	−0.144860	−	0.0540298i	−0.0164021	−	0.00611767i
$79$	3.57517	−	1.04977i	0.402239	−	0.118108i	−0.0743546	−	0.997232i	$-0.523690\pi$
$79$	3.57517	−	1.04977i	0.402239	−	0.118108i	0.476593	+	0.879124i	$0.341871\pi$
$80$	−2.17950	+	3.24475i	−0.243676	+	0.362775i
$81$	−5.76017	+	6.64759i	−0.640019	+	0.738621i
$82$	−5.20795	−	2.84375i	−0.575121	−	0.314040i
$83$	−3.02763	+	8.11740i	−0.332326	+	0.891000i	0.658097	+	0.752933i	$0.271362\pi$
$83$	−3.02763	+	8.11740i	−0.332326	+	0.891000i	−0.990423	+	0.138067i	$0.955911\pi$
$84$	0.450520	−	0.289532i	0.0491558	−	0.0315905i
$85$	−1.59347	+	1.14318i	−0.172836	+	0.123995i
$86$	−0.502456	+	0.0722422i	−0.0541812	+	0.00779008i
$87$	−5.54144	+	2.06685i	−0.594105	+	0.221590i
$88$	−5.63937	+	4.22158i	−0.601159	+	0.450022i
$89$	−6.56977	−	4.22214i	−0.696395	−	0.447546i	0.143959	−	0.989584i	$-0.454017\pi$
$89$	−6.56977	−	4.22214i	−0.696395	−	0.447546i	−0.840354	+	0.542038i	$0.817653\pi$
$90$	0.0942173	−	0.00482048i	0.00993138	−	0.000508124i
$91$			0.0278526i			0.00291974i
$92$	3.50971	−	6.81125i	0.365912	−	0.710121i
$93$	0.406442	−	0.406442i	0.0421461	−	0.0421461i
$94$	3.04714	−	2.64036i	0.314289	−	0.272333i
$95$	15.1996	+	7.31749i	1.55944	+	0.750759i
$96$	1.38268	−	9.61674i	0.141119	−	0.981504i
$97$	−4.54643	−	12.1894i	−0.461620	−	1.23765i	−0.934323	−	0.356428i	$-0.883994\pi$
$97$	−4.54643	−	12.1894i	−0.461620	−	1.23765i	0.472703	−	0.881222i	$-0.343278\pi$
$98$	−3.53486	−	2.64616i	−0.357075	−	0.267303i
$99$	−0.197029	−	0.0578530i	−0.0198022	−	0.00581445i
$100$	−5.82022	−	5.47188i	−0.582022	−	0.547188i
$101$	4.62209	+	10.1210i	0.459915	+	1.00707i	0.987507	+	0.157575i	$0.0503678\pi$
$101$	4.62209	+	10.1210i	0.459915	+	1.00707i	−0.527592	+	0.849498i	$0.676905\pi$
$102$	0.456610	−	0.836218i	0.0452111	−	0.0827979i
$103$	5.63058	−	0.402707i	0.554797	−	0.0396799i	0.208874	−	0.977943i	$-0.433020\pi$
$103$	5.63058	−	0.402707i	0.554797	−	0.0396799i	0.345924	+	0.938263i	$0.387566\pi$
$104$	0.245438	+	0.212674i	0.0240672	+	0.0208544i
$105$	0.297466	+	0.687950i	0.0290298	+	0.0671370i
$106$	1.15044	−	0.525389i	0.111741	−	0.0510303i
$107$	3.70255	−	17.0203i	0.357939	−	1.64542i	−0.348254	−	0.937400i	$-0.613225\pi$
$107$	3.70255	−	17.0203i	0.357939	−	1.64542i	0.706193	−	0.708019i	$-0.250411\pi$
$108$	7.36494	−	4.02156i	0.708692	−	0.386975i
$109$	−1.08276	−	7.53075i	−0.103709	−	0.721315i	−0.973632	−	0.228126i	$-0.926740\pi$
$109$	−1.08276	−	7.53075i	−0.103709	−	0.721315i	0.869922	−	0.493189i	$-0.164169\pi$
$110$	−2.01994	−	3.88451i	−0.192594	−	0.370374i
$111$	−12.7368	−	1.83128i	−1.20893	−	0.173817i
$112$	−0.334285	+	0.0727192i	−0.0315870	+	0.00687132i
$113$	0.628483	−	8.78734i	0.0591227	−	0.826644i	−0.878225	−	0.478248i	$-0.841272\pi$
$113$	0.628483	−	8.78734i	0.0591227	−	0.826644i	0.937348	−	0.348396i	$-0.113273\pi$
$114$	−8.19551			−0.767579
$115$	8.60870	+	6.39456i	0.802765	+	0.596296i
$116$	5.51710			0.512250
$117$	−0.000675360		0.00944276i	−6.24370e−5		0.000872983i
$118$	5.49456	−	1.19527i	0.505816	−	0.110033i
$119$	−0.169893	−	0.0244269i	−0.0155741	−	0.00223921i
$120$	8.33361	+	2.63168i	0.760751	+	0.240238i
$121$	−0.209189	−	1.45494i	−0.0190172	−	0.132268i
$122$	5.77191	−	3.15170i	0.522564	−	0.285341i
$123$	3.40598	−	15.6570i	0.307107	−	1.41175i
$124$	−0.487735	+	0.222741i	−0.0437999	+	0.0200028i
$125$	8.87909	−	6.79424i	0.794170	−	0.607695i
$126$	0.00624009	+	0.00540707i	0.000555911	+	0.000481700i
$127$	−21.8775	+	1.56471i	−1.94131	+	0.138845i	−0.987080	−	0.160228i	$-0.948777\pi$
$127$	−21.8775	+	1.56471i	−1.94131	+	0.138845i	−0.954230	+	0.299073i	$0.903323\pi$
$128$	−5.40620	+	9.90071i	−0.477845	+	0.875107i
$129$	−0.569432	−	1.24688i	−0.0501357	−	0.109782i
$130$	−0.155196	+	0.129062i	−0.0136116	+	0.0113194i
$131$	−17.6458	−	5.18128i	−1.54172	−	0.452691i	−0.603109	−	0.797659i	$-0.706071\pi$
$131$	−17.6458	−	5.18128i	−1.54172	−	0.452691i	−0.938614	+	0.344968i	$0.887890\pi$
$132$	−6.76270	−	5.06250i	−0.588618	−	0.440634i
$133$	0.515956	+	1.38333i	0.0447391	+	0.119950i
$134$	−0.751955	+	5.22996i	−0.0649590	+	0.451800i
$135$	3.88017	+	11.0847i	0.333952	+	0.954016i
$136$	−1.51250	+	1.31059i	−0.129696	+	0.112382i
$137$	−5.31898	+	5.31898i	−0.454431	+	0.454431i	−0.896822	−	0.442391i	$-0.854130\pi$
$137$	−5.31898	+	5.31898i	−0.454431	+	0.454431i	0.442391	+	0.896822i	$0.354130\pi$
$138$	−5.11594	−	0.984950i	−0.435498	−	0.0838445i
$139$			16.5816i			1.40643i	0.710975	+	0.703217i	$0.248254\pi$
$139$			16.5816i			1.40643i	−0.710975	+	0.703217i	$0.751746\pi$
$140$	−0.0357250	−	0.698253i	−0.00301932	−	0.0590132i
$141$	9.15926	+	5.88630i	0.771349	+	0.495716i
$142$	−3.41508	+	2.55650i	−0.286587	+	0.214537i
$143$	0.411653	−	0.153539i	0.0344241	−	0.0128395i
$144$	−0.115095	+	0.0165481i	−0.00959122	+	0.00137901i
$145$	−1.25365	+	7.61901i	−0.104110	+	0.632725i
$146$	−3.60343	+	2.31579i	−0.298222	+	0.191656i
$147$	4.16687	−	11.1718i	0.343677	−	0.921435i
$148$	10.5353	+	5.75268i	0.865993	+	0.472868i
$149$	−8.33524	+	9.61937i	−0.682849	+	0.788050i	−0.986329	−	0.164788i	$-0.947306\pi$
$149$	−8.33524	+	9.61937i	−0.682849	+	0.788050i	0.303480	+	0.952838i	$0.401851\pi$
$150$	−2.45490	+	4.84527i	−0.200442	+	0.395615i
$151$	0.986154	−	0.289561i	0.0802521	−	0.0235641i	−0.241360	−	0.970436i	$-0.577593\pi$
$151$	0.986154	−	0.289561i	0.0802521	−	0.0235641i	0.321612	+	0.946872i	$0.395775\pi$
$152$	16.1297	+	6.01606i	1.30829	+	0.487967i
$153$	−0.0570059	−	0.0124009i	−0.00460865	−	0.00100255i
$154$	0.107959	−	0.367674i	0.00869956	−	0.0296280i
$155$	−0.196774	−	0.724167i	−0.0158052	−	0.0581665i
$156$	−0.161784	+	0.354258i	−0.0129531	+	0.0283634i
$157$	10.2561	+	13.7006i	0.818526	+	1.09342i	0.994048	+	0.108948i	$0.0347481\pi$
$157$	10.2561	+	13.7006i	0.818526	+	1.09342i	−0.175521	+	0.984476i	$0.556161\pi$
$158$	0.502366	+	2.30934i	0.0399661	+	0.183721i
$159$	2.23649	+	2.58104i	0.177365	+	0.204690i
$160$	−9.99801	−	7.80574i	−0.790412	−	0.617098i
$161$	0.155828	+	0.925536i	0.0122810	+	0.0729425i
$162$	−3.94497	−	3.94497i	−0.309946	−	0.309946i
$163$	−4.99602	−	0.357322i	−0.391318	−	0.0279876i	−0.125706	−	0.992068i	$-0.540120\pi$
$163$	−4.99602	−	0.357322i	−0.391318	−	0.0279876i	−0.265612	+	0.964080i	$0.585574\pi$
$164$	−8.08096	+	12.5742i	−0.631017	+	0.981881i
$165$	8.52790	−	8.18882i	0.663896	−	0.637499i
$166$	−4.99849	−	2.28274i	−0.387958	−	0.177175i
$167$	4.90538	−	6.55282i	0.379590	−	0.507073i	−0.569537	−	0.821965i	$-0.692878\pi$
$167$	4.90538	−	6.55282i	0.379590	−	0.507073i	0.949127	+	0.314893i	$0.101969\pi$
$168$	0.366565	+	0.671313i	0.0282811	+	0.0517929i
$169$	7.01738	+	10.9193i	0.539798	+	0.839943i
$170$	−0.651131	−	1.05984i	−0.0499395	−	0.0812859i
$171$	0.141380	+	0.481497i	0.0108116	+	0.0368210i
$172$	0.0912205	+	1.27543i	0.00695550	+	0.0972505i
$173$	−1.23899	−	17.3233i	−0.0941985	−	1.31707i	−0.796262	−	0.604952i	$-0.793192\pi$
$173$	−1.23899	−	17.3233i	−0.0941985	−	1.31707i	0.702063	−	0.712114i	$-0.252262\pi$
$174$	−1.05686	−	3.59932i	−0.0801201	−	0.272864i
$175$	0.972392	+	0.109328i	0.0735059	+	0.00826442i
$176$	2.91753	+	4.53976i	0.219917	+	0.342198i
$177$	7.27702	+	13.3269i	0.546974	+	1.00171i
$178$	2.96841	−	3.96534i	0.222492	−	0.297215i
$179$	−11.4047	−	5.20834i	−0.852425	−	0.389290i	−0.0592208	−	0.998245i	$-0.518862\pi$
$179$	−11.4047	−	5.20834i	−0.852425	−	0.389290i	−0.793205	+	0.608955i	$0.791589\pi$
$180$	0.00481926	−	0.237592i	0.000359207	−	0.0177091i
$181$	14.0743	−	21.9000i	1.04613	−	1.62782i	0.310322	−	0.950631i	$-0.399563\pi$
$181$	14.0743	−	21.9000i	1.04613	−	1.62782i	0.735812	−	0.677186i	$-0.236801\pi$
$182$	−0.0176210	−	0.00126028i	−0.00130616	−	9.34181e-5i
$183$	12.5570	+	12.5570i	0.928243	+	0.928243i
$184$	9.34572	+	5.69394i	0.688976	+	0.419763i
$185$	−10.3383	+	13.2418i	−0.760085	+	0.973558i
$186$	0.238746	+	0.275527i	0.0175057	+	0.0202026i
$187$	0.575520	+	2.64562i	0.0420862	+	0.193467i
$188$	−6.08648	−	8.13058i	−0.443902	−	0.592984i
$189$	−0.426991	+	0.934980i	−0.0310590	+	0.0680098i
$190$	−5.31718	+	9.28493i	−0.385749	+	0.673599i
$191$	3.50213	−	11.9272i	0.253406	−	0.863020i	−0.730284	−	0.683144i	$-0.760612\pi$
$191$	3.50213	−	11.9272i	0.253406	−	0.863020i	0.983689	−	0.179876i	$-0.0575697\pi$
$192$	0.170362	+	0.0370599i	0.0122948	+	0.00267457i
$193$	10.6245	+	3.96275i	0.764771	+	0.285245i	0.701422	−	0.712747i	$-0.252549\pi$
$193$	10.6245	+	3.96275i	0.764771	+	0.285245i	0.0633493	+	0.997991i	$0.479822\pi$
$194$	7.91739	−	2.32476i	0.568436	−	0.166908i
$195$	−0.452462	−	0.303919i	−0.0324015	−	0.0217641i
$196$	−7.28384	+	8.40600i	−0.520274	+	0.600429i
$197$	−6.09462	−	3.32791i	−0.434224	−	0.237104i	0.247243	−	0.968954i	$-0.420476\pi$
$197$	−6.09462	−	3.32791i	−0.434224	−	0.237104i	−0.681466	+	0.731850i	$0.738657\pi$
$198$	0.0455161	−	0.122033i	0.00323469	−	0.00867253i
$199$	−17.0426	+	10.9526i	−1.20812	+	0.776411i	−0.980343	−	0.197302i	$-0.936782\pi$
$199$	−17.0426	+	10.9526i	−1.20812	+	0.776411i	−0.227777	+	0.973713i	$0.573146\pi$
$200$	8.38829	−	7.73398i	0.593141	−	0.546875i
$201$	−14.1227	+	2.03054i	−0.996138	+	0.143223i
$202$	−6.61219	+	2.46622i	−0.465232	+	0.173523i
$203$	−0.541000	+	0.404988i	−0.0379708	+	0.0284246i
$204$	−2.01899	−	1.29753i	−0.141358	−	0.0908450i
$205$	−15.5285	−	14.0169i	−1.08456	−	0.978982i
$206$			3.58042i			0.249460i
$207$	0.0303877	+	0.317560i	0.00211209	+	0.0220719i
$208$	0.175917	−	0.175917i	0.0121977	−	0.0121977i
$209$	17.6010	−	15.2514i	1.21749	−	1.05496i
$210$	−0.448693	+	0.157064i	−0.0309627	+	0.0108385i
$211$	−0.733595	+	5.10227i	−0.0505028	+	0.351255i	0.948864	+	0.315684i	$0.102234\pi$
$211$	−0.733595	+	5.10227i	−0.0505028	+	0.351255i	−0.999367	+	0.0355706i	$0.988675\pi$
$212$	−1.11333	−	2.98496i	−0.0764639	−	0.205008i
$213$	−9.22189	−	6.90342i	−0.631874	−	0.473015i
$214$	10.6004	+	3.11257i	0.724630	+	0.212771i
$215$	−1.78207	−	0.163841i	−0.121536	−	0.0111739i
$216$	4.97872	+	10.9019i	0.338759	+	0.741779i
$217$	0.0314762	−	0.0576444i	0.00213674	−	0.00391316i
$218$	4.81334	−	0.344257i	0.326000	−	0.0233160i
$219$	−8.74151	−	7.57456i	−0.590696	−	0.511841i
$220$	−10.1230	+	4.37716i	−0.682495	+	0.295108i
$221$	0.113541	−	0.0518523i	0.00763757	−	0.00348796i
$222$	1.73488	−	7.97513i	0.116438	−	0.535255i
$223$	−10.7757	+	5.88395i	−0.721591	+	0.394019i	−0.797679	−	0.603083i	$-0.793939\pi$
$223$	−10.7757	+	5.88395i	−0.721591	+	0.394019i	0.0760877	+	0.997101i	$0.475757\pi$
$224$	−0.157990	−	1.09884i	−0.0105561	−	0.0734195i
$225$	0.327016	+	0.0606433i	0.0218010	+	0.00404288i
$226$	5.53089	+	0.795223i	0.367910	+	0.0528974i
$227$	5.04440	−	1.09734i	0.334808	−	0.0728331i	−0.0420184	−	0.999117i	$-0.513379\pi$
$227$	5.04440	−	1.09734i	0.334808	−	0.0728331i	0.376827	+	0.926284i	$0.377015\pi$
$228$	−1.47274	+	20.5917i	−0.0975349	+	1.36372i
$229$	16.5896			1.09627			0.548137	−	0.836389i	$-0.315337\pi$
$229$	16.5896			1.09627			0.548137	+	0.836389i	$0.315337\pi$
$230$	−4.43506	+	5.15697i	−0.292439	+	0.340040i
$231$	1.03476			0.0680822
$232$	−0.562136	+	7.85968i	−0.0369060	+	0.516013i
$233$	−9.08066	+	1.97538i	−0.594894	+	0.129411i	−0.499924	−	0.866069i	$-0.666639\pi$
$233$	−9.08066	+	1.97538i	−0.594894	+	0.129411i	−0.0949691	+	0.995480i	$0.530275\pi$
$234$	−0.00594342		0.000854535i	−0.000388534		5.58627e-5i
$235$	12.6112	−	6.55781i	0.822665	−	0.427784i
$236$	−2.01580	−	14.0202i	−0.131217	−	0.912636i
$237$	−5.60122	+	3.05850i	−0.363838	+	0.198671i
$238$	0.0231411	−	0.106378i	0.00150001	−	0.00689545i
$239$	3.59581	−	1.64215i	0.232594	−	0.106222i	−0.295709	−	0.955278i	$-0.595556\pi$
$239$	3.59581	−	1.64215i	0.232594	−	0.106222i	0.528303	+	0.849056i	$0.322829\pi$
$240$	2.46630	−	6.22391i	0.159199	−	0.401752i
$241$	4.61704	+	4.00069i	0.297409	+	0.257707i	0.790763	−	0.612122i	$-0.209684\pi$
$241$	4.61704	+	4.00069i	0.297409	+	0.257707i	−0.493354	+	0.869829i	$0.664229\pi$
$242$	0.929939	−	0.0665106i	0.0597788	−	0.00427546i
$243$	−0.331233	+	0.606607i	−0.0212486	+	0.0389139i
$244$	−6.88160	−	15.0686i	−0.440549	−	0.964668i
$245$	−9.95343	−	11.9689i	−0.635901	−	0.764668i
$246$	9.75134	+	2.86325i	0.621723	+	0.182554i
$247$	−0.859530	−	0.643436i	−0.0546906	−	0.0409409i
$248$	−0.267623	−	0.717525i	−0.0169941	−	0.0455629i
$249$	2.11175	−	14.6875i	0.133827	−	0.930785i
$250$	3.89663	+	5.92480i	0.246444	+	0.374718i
$251$	4.28686	−	3.71459i	0.270584	−	0.234463i	−0.508990	−	0.860772i	$-0.669981\pi$
$251$	4.28686	−	3.71459i	0.270584	−	0.234463i	0.779574	+	0.626310i	$0.215436\pi$
$252$	0.0147069	−	0.0147069i	0.000926447	−	0.000926447i
$253$	12.8201	−	7.40515i	0.805995	−	0.465558i
$254$		−	13.9116i		−	0.872893i
$255$	2.25063	−	2.49335i	0.140940	−	0.156140i
$256$	−6.19035	−	3.97830i	−0.386897	−	0.248644i
$257$	−18.5185	+	13.8628i	−1.15515	+	0.864737i	−0.992536	−	0.121952i	$-0.961085\pi$
$257$	−18.5185	+	13.8628i	−1.15515	+	0.864737i	−0.162618	+	0.986689i	$0.551994\pi$
$258$	0.814608	−	0.303833i	0.0507153	−	0.0189158i
$259$	−1.45536	+	0.209249i	−0.0904314	+	0.0130021i
$260$	0.296385	+	0.413130i	0.0183810	+	0.0256212i
$261$	−0.193233	+	0.124184i	−0.0119608	+	0.00768677i
$262$	4.07639	−	10.9292i	0.251840	−	0.675210i
$263$	−22.9578	−	12.5359i	−1.41564	−	0.772998i	−0.424451	−	0.905451i	$-0.639533\pi$
$263$	−22.9578	−	12.5359i	−1.41564	−	0.772998i	−0.991189	+	0.132453i	$0.957715\pi$
$264$	7.90110	−	9.11836i	0.486279	−	0.561196i
$265$	4.37515	−	0.859220i	0.268763	−	0.0527815i
$266$	−0.898514	+	0.263828i	−0.0550915	+	0.0161763i
$267$	12.5323	+	4.67431i	0.766966	+	0.286063i
$268$	13.0054	+	2.82916i	0.794433	+	0.172818i
$269$	5.70242	−	19.4206i	0.347683	−	1.18410i	−0.581212	−	0.813752i	$-0.697421\pi$
$269$	5.70242	−	19.4206i	0.347683	−	1.18410i	0.928894	−	0.370345i	$-0.120761\pi$
$270$	−7.18831	+	1.95324i	−0.437466	+	0.118870i
$271$	3.29990	−	7.22577i	0.200455	−	0.438934i	−0.782532	−	0.622610i	$-0.786072\pi$
$271$	3.29990	−	7.22577i	0.200455	−	0.438934i	0.982987	+	0.183676i	$0.0587996\pi$
$272$	0.918766	+	1.22733i	0.0557084	+	0.0744177i
$273$	−0.0101403	−	0.0466141i	−0.000613717	−	0.00282121i
$274$	−3.12439	−	3.60574i	−0.188751	−	0.217831i
$275$	−3.74452	−	14.9743i	−0.225803	−	0.902987i
$276$	−3.39408	+	12.6771i	−0.204300	+	0.763070i
$277$	2.42021	+	2.42021i	0.145416	+	0.145416i	0.776067	−	0.630651i	$-0.217212\pi$
$277$	2.42021	+	2.42021i	0.145416	+	0.145416i	−0.630651	+	0.776067i	$0.717212\pi$
$278$	−10.4904	−	0.750288i	−0.629172	−	0.0449993i
$279$	0.0120690	−	0.0187797i	0.000722553	−	0.00112431i
$280$	0.998374	+	0.0202508i	0.0596643	+	0.00121021i
$281$	0.296073	+	0.135212i	0.0176623	+	0.00806608i	0.424227	−	0.905556i	$-0.360546\pi$
$281$	0.296073	+	0.135212i	0.0176623	+	0.00806608i	−0.406564	+	0.913622i	$0.633273\pi$
$282$	−4.13842	+	5.52828i	−0.246439	+	0.329204i
$283$	12.8604	+	23.5521i	0.764471	+	1.40002i	0.911672	+	0.410918i	$0.134792\pi$
$283$	12.8604	+	23.5521i	0.764471	+	1.40002i	−0.147201	+	0.989107i	$0.547026\pi$
$284$	5.80965	+	9.03999i	0.344739	+	0.536425i
$285$	−28.1020	−	6.71286i	−1.66462	−	0.397635i
$286$	0.0785100	+	0.267380i	0.00464239	+	0.0158105i
$287$	−0.130613	−	1.82620i	−0.00770982	−	0.107797i
$288$	−0.0269183	−	0.376367i	−0.00158618	−	0.0221776i
$289$	−4.57275	−	15.5733i	−0.268985	−	0.916079i
$290$	−4.76346	−	1.13787i	−0.279720	−	0.0668180i
$291$	12.0467	+	18.7450i	0.706190	+	1.09885i
$292$	5.17100	+	9.46997i	0.302610	+	0.554188i
$293$	−5.21528	+	6.96681i	−0.304680	+	0.407005i	−0.926584	−	0.376089i	$-0.877269\pi$
$293$	−5.21528	+	6.96681i	−0.304680	+	0.407005i	0.621903	+	0.783094i	$0.286360\pi$
$294$	6.87932	+	3.14168i	0.401210	+	0.183227i
$295$	19.8197	+	0.402017i	1.15395	+	0.0234063i
$296$	−9.26873	+	14.4224i	−0.538734	+	0.838287i
$297$	16.1725	+	1.15668i	0.938425	+	0.0671175i
$298$	−5.70856	−	5.70856i	−0.330688	−	0.330688i
$299$	−0.459221	−	0.504957i	−0.0265575	−	0.0292024i
$300$	11.7329	+	7.03878i	0.677397	+	0.406384i
$301$	−0.102569	−	0.118371i	−0.00591198	−	0.00682279i
$302$	0.138570	+	0.636994i	0.00797379	+	0.0366549i
$303$	−11.4203	−	15.2557i	−0.656077	−	0.876416i
$304$	5.47837	−	11.9959i	0.314206	−	0.688015i
$305$	22.3731	−	6.07933i	1.28108	−	0.348101i
$306$	0.0104248	−	0.0355038i	0.000595949	−	0.00202962i
$307$	−21.2410	−	4.62069i	−1.21229	−	0.263717i	−0.439418	−	0.898283i	$-0.644815\pi$
$307$	−21.2410	−	4.62069i	−1.21229	−	0.263717i	−0.772869	+	0.634566i	$0.781179\pi$
$308$	−0.904400	−	0.337324i	−0.0515330	−	0.0192208i
$309$	−9.27672	+	2.72389i	−0.527734	+	0.154957i
$310$	0.467049	−	0.0917221i	0.0265266	−	0.00520947i
$311$	11.0480	−	12.7501i	0.626474	−	0.722990i	−0.350449	−	0.936582i	$-0.613971\pi$
$311$	11.0480	−	12.7501i	0.626474	−	0.722990i	0.976923	+	0.213592i	$0.0685164\pi$
$312$	−0.488194	−	0.266574i	−0.0276385	−	0.0150918i
$313$	−8.81628	+	23.6374i	−0.498326	+	1.33606i	0.407807	+	0.913068i	$0.366294\pi$
$313$	−8.81628	+	23.6374i	−0.498326	+	1.33606i	−0.906132	+	0.422994i	$0.860979\pi$
$314$	−9.13175	+	5.86862i	−0.515335	+	0.331186i
$315$	0.0169681	+	0.0236518i	0.000956045	+	0.00133263i
$316$	5.89262	−	0.847231i	0.331486	−	0.0476605i
$317$	22.9628	−	8.56468i	1.28972	−	0.481040i	0.391334	−	0.920249i	$-0.372014\pi$
$317$	22.9628	−	8.56468i	1.28972	−	0.481040i	0.898385	+	0.439208i	$0.144741\pi$
$318$	−1.73410	+	1.29813i	−0.0972434	+	0.0727955i
$319$	8.96789	+	5.76331i	0.502105	+	0.322683i
$320$	0.152515	−	0.168963i	0.00852587	−	0.00944534i
$321$			29.8332i			1.66513i
$322$	−0.592593	+	0.0567060i	−0.0330239	+	0.00316010i
$323$	4.67859	−	4.67859i	0.260324	−	0.260324i
$324$	−10.6209	+	9.20304i	−0.590049	+	0.511280i
$325$	−0.637872	+	0.315427i	−0.0353828	+	0.0174967i
$326$	0.452121	−	3.14457i	0.0250407	−	0.174162i
$327$	4.55382	+	12.2093i	0.251827	+	0.675174i
$328$	−17.0899	−	12.7933i	−0.943633	−	0.706395i
$329$	1.19367	+	0.350492i	0.0658089	+	0.0193232i
$330$	4.79480	+	5.76572i	0.263945	+	0.317393i
$331$	0.362741	+	0.794293i	0.0199381	+	0.0436583i	0.919339	−	0.393466i	$-0.128724\pi$
$331$	0.362741	+	0.794293i	0.0199381	+	0.0436583i	−0.899401	+	0.437125i	$0.855997\pi$
$332$	−6.63373	+	12.1488i	−0.364073	+	0.666751i
$333$	−0.498478	+	0.0356518i	−0.0273164	+	0.00195371i
$334$	3.92370	+	3.39990i	0.214695	+	0.186034i
$335$	−6.86223	+	17.3174i	−0.374924	+	0.946150i
$336$	0.532984	−	0.243406i	0.0290767	−	0.0132789i
$337$	1.37093	−	6.30208i	0.0746795	−	0.343296i	−0.924613	−	0.380908i	$-0.875611\pi$
$337$	1.37093	−	6.30208i	0.0746795	−	0.343296i	0.999292	+	0.0376120i	$0.0119751\pi$
$338$	−7.22561	+	3.94548i	−0.393022	+	0.214606i
$339$	2.14737	+	14.9353i	0.116629	+	0.811174i
$340$	−2.77991	+	1.44555i	−0.150762	+	0.0783958i
$341$	−1.02548	−	0.147442i	−0.0555329	−	0.00798443i
$342$	−0.311017	+	0.0676577i	−0.0168179	+	0.00365851i
$343$	0.194924	−	2.72540i	0.0105249	−	0.147158i
$344$	−1.82628			−0.0984662
$345$	−16.7356	−	7.56777i	−0.901013	−	0.407435i
$346$	11.0157			0.592207
$347$	−1.02315	+	14.3054i	−0.0549253	+	0.767956i	0.893120	+	0.449819i	$0.148512\pi$
$347$	−1.02315	+	14.3054i	−0.0549253	+	0.767956i	−0.948045	+	0.318137i	$0.896943\pi$
$348$	−9.23342	+	2.00861i	−0.494963	+	0.107673i
$349$	26.0154	+	3.74046i	1.39257	+	0.200222i	0.797437	−	0.603402i	$-0.206188\pi$
$349$	26.0154	+	3.74046i	1.39257	+	0.200222i	0.595138	+	0.803624i	$0.297098\pi$
$350$	−0.113166	+	0.610239i	−0.00604895	+	0.0326187i
$351$	−0.106378	−	0.739879i	−0.00567806	−	0.0394918i
$352$	−15.3696	+	8.39245i	−0.819204	+	0.447319i
$353$	−3.12048	+	14.3446i	−0.166086	+	0.763486i	0.816450	+	0.577416i	$0.195939\pi$
$353$	−3.12048	+	14.3446i	−0.166086	+	0.763486i	−0.982536	+	0.186070i	$0.940425\pi$
$354$	−8.76054	+	4.00080i	−0.465617	+	0.212640i
$355$	−13.8042	+	5.96887i	−0.732650	+	0.316795i
$356$	−9.42970	−	8.17088i	−0.499773	−	0.433056i
$357$	0.293226	−	0.0209719i	0.0155192	−	0.00110995i
$358$	3.81111	−	6.97952i	0.201423	−	0.368879i
$359$	−6.34071	−	13.8842i	−0.334650	−	0.732781i	0.665254	−	0.746617i	$-0.268323\pi$
$359$	−6.34071	−	13.8842i	−0.334650	−	0.732781i	−0.999904	+	0.0138356i	$0.995596\pi$
$360$	0.337984	+	0.0310738i	0.0178133	+	0.00163773i
$361$	−36.3786	−	10.6817i	−1.91466	−	0.562196i
$362$	13.2183	+	9.89507i	0.694737	+	0.520073i
$363$	0.879800	+	2.35883i	0.0461775	+	0.123807i
$364$	−0.00633304	+	0.0440472i	−0.000331941	+	0.00230870i
$365$	−14.2529	+	4.98919i	−0.746029	+	0.261146i
$366$	−8.51242	+	7.37606i	−0.444951	+	0.385553i
$367$	10.4062	−	10.4062i	0.543199	−	0.543199i	−0.381266	−	0.924465i	$-0.624512\pi$
$367$	10.4062	−	10.4062i	0.543199	−	0.543199i	0.924465	+	0.381266i	$0.124512\pi$
$368$	4.86149	−	6.82992i	0.253423	−	0.356034i
$369$		−	0.622298i		−	0.0323955i
$370$	−7.90967	−	7.13970i	−0.411204	−	0.371175i
$371$	0.328285	+	0.210976i	0.0170437	+	0.0109533i
$372$	0.735180	−	0.550349i	0.0381173	−	0.0285343i
$373$	−17.1142	+	6.38327i	−0.886140	+	0.330513i	−0.750991	−	0.660312i	$-0.770424\pi$
$373$	−17.1142	+	6.38327i	−0.886140	+	0.330513i	−0.135149	+	0.990825i	$0.543151\pi$
$374$	−1.69980	+	0.244394i	−0.0878945	+	0.0126373i
$375$	−12.3865	+	14.6034i	−0.639635	+	0.754119i
$376$	12.2030	−	7.84240i	0.629322	−	0.404441i
$377$	0.171745	−	0.460466i	0.00884531	−	0.0237152i
$378$	−0.572196	−	0.312443i	−0.0294306	−	0.0160703i
$379$	2.12189	−	2.44879i	0.108994	−	0.125786i	−0.698631	−	0.715482i	$-0.746207\pi$
$379$	2.12189	−	2.44879i	0.108994	−	0.125786i	0.807625	+	0.589696i	$0.200752\pi$
$380$	22.3734	+	15.0282i	1.14773	+	0.770931i
$381$	36.0444	−	10.5836i	1.84661	−	0.542214i
$382$	7.38729	+	2.75532i	0.377967	+	0.140974i
$383$	24.7699	+	5.38836i	1.26568	+	0.275332i	0.794804	−	0.606866i	$-0.207573\pi$
$383$	24.7699	+	5.38836i	1.26568	+	0.275332i	0.470878	+	0.882198i	$0.343937\pi$
$384$	5.44326	−	18.5380i	0.277775	−	0.946016i
$385$	0.671344	−	1.17231i	0.0342148	−	0.0597464i
$386$	−2.98778	+	6.54233i	−0.152074	+	0.332996i
$387$	−0.0319034	−	0.0426179i	−0.00162174	−	0.00216639i
$388$	−4.41831	−	20.3106i	−0.224306	−	1.03112i
$389$	−8.46700	−	9.77144i	−0.429294	−	0.495432i	0.499352	−	0.866399i	$-0.333572\pi$
$389$	−8.46700	−	9.77144i	−0.429294	−	0.495432i	−0.928646	+	0.370968i	$0.879026\pi$
$390$	0.212748	−	0.272499i	0.0107729	−	0.0137985i
$391$	3.48283	−	2.35827i	0.176134	−	0.119263i
$392$	−11.2331	−	11.2331i	−0.567356	−	0.567356i
$393$	31.4184	+	2.24709i	1.58485	+	0.113351i
$394$	2.38118	−	3.70519i	0.119962	−	0.186665i
$395$	−0.168966	+	8.33012i	−0.00850160	+	0.419134i
$396$	−0.298436	−	0.136291i	−0.0149970	−	0.00684889i
$397$	−13.2178	+	17.6569i	−0.663382	+	0.886174i	−0.998429	−	0.0560269i	$-0.982157\pi$
$397$	−13.2178	+	17.6569i	−0.663382	+	0.886174i	0.335047	+	0.942201i	$0.391248\pi$
$398$	−6.15806	−	11.2776i	−0.308675	−	0.565297i
$399$	−1.36713	−	2.12730i	−0.0684423	−	0.106498i
$400$	−5.45113	−	6.83217i	−0.272557	−	0.341608i
$401$	6.39755	+	21.7880i	0.319478	+	1.08804i	0.950098	+	0.311951i	$0.100982\pi$
$401$	6.39755	+	21.7880i	0.319478	+	1.08804i	−0.630620	+	0.776092i	$0.717199\pi$
$402$	−0.645597	−	9.02663i	−0.0321995	−	0.450207i
$403$	0.00340735	+	0.0476410i	0.000169732	+	0.00237317i
$404$	5.00829	+	17.0567i	0.249172	+	0.848601i
$405$	−10.2959	−	16.7584i	−0.511605	−	0.832733i
$406$	−0.231737	−	0.360590i	−0.0115009	−	0.0178958i
$407$	11.1153	+	20.3562i	0.550967	+	1.00902i
$408$	2.05417	−	2.74406i	0.101697	−	0.135851i
$409$	9.91080	+	4.52611i	0.490058	+	0.223802i	0.645089	−	0.764108i	$-0.276820\pi$
$409$	9.91080	+	4.52611i	0.490058	+	0.223802i	−0.155031	+	0.987910i	$0.549548\pi$
$410$	9.57045	−	9.18992i	0.472651	−	0.453858i
$411$	6.96537	−	10.8383i	0.343576	−	0.534615i
$412$	8.99600	+	0.643407i	0.443201	+	0.0316984i
$413$	1.22683	+	1.22683i	0.0603684	+	0.0603684i
$414$	−0.202280	+	0.00485584i	−0.00994150	+	0.000238651i
$415$	−15.2699	−	11.9216i	−0.749568	−	0.585209i
$416$	0.528682	+	0.610131i	0.0259208	+	0.0299142i
$417$	−6.03686	−	27.7510i	−0.295626	−	1.35897i
$418$	8.85239	+	11.8254i	0.432985	+	0.578400i
$419$	−13.3850	+	29.3090i	−0.653898	+	1.43184i	0.234203	+	0.972188i	$0.424752\pi$
$419$	−13.3850	+	29.3090i	−0.653898	+	1.43184i	−0.888101	+	0.459649i	$0.847975\pi$
$420$	0.314002	+	1.15559i	0.0153217	+	0.0563870i
$421$	3.93444	−	13.3995i	0.191753	−	0.653050i	−0.806348	−	0.591442i	$-0.798559\pi$
$421$	3.93444	−	13.3995i	0.191753	−	0.653050i	0.998100	−	0.0616082i	$-0.0196229\pi$
$422$	−3.19477	−	0.694979i	−0.155519	−	0.0338310i
$423$	0.396185	+	0.147770i	0.0192632	+	0.00718480i
$424$	4.36582	−	1.28192i	0.212023	−	0.0622555i
$425$	−1.36460	−	4.16747i	−0.0661927	−	0.202152i
$426$	4.78474	−	5.52188i	0.231821	−	0.267536i
$427$	1.78092	+	0.972458i	0.0861850	+	0.0470606i
$428$	9.72540	−	26.0748i	0.470095	−	1.26037i
$429$	−0.633043	+	0.406832i	−0.0305636	+	0.0196420i
$430$	0.184290	−	1.12002i	0.00888725	−	0.0540121i
$431$	2.74180	−	0.394211i	0.132068	−	0.0189885i	−0.0759639	−	0.997111i	$-0.524203\pi$
$431$	2.74180	−	0.394211i	0.132068	−	0.0189885i	0.208032	+	0.978122i	$0.433294\pi$
$432$	8.60223	−	3.20847i	0.413875	−	0.154367i
$433$	9.75986	−	7.30614i	0.469029	−	0.351111i	−0.338473	−	0.940976i	$-0.609910\pi$
$433$	9.75986	−	7.30614i	0.469029	−	0.351111i	0.807501	+	0.589866i	$0.200819\pi$
$434$	0.0350446	+	0.0225218i	0.00168219	+	0.00108108i
$435$	−0.675746	−	13.2076i	−0.0323995	−	0.633256i
$436$		−	12.1556i		−	0.582149i
$437$	−32.1619	−	16.5724i	−1.53851	−	0.792766i
$438$	5.18760	−	5.18760i	0.247873	−	0.247873i
$439$	−16.0315	+	13.8914i	−0.765140	+	0.662998i	−0.947328	−	0.320266i	$-0.896228\pi$
$439$	−16.0315	+	13.8914i	−0.765140	+	0.662998i	0.182187	+	0.983264i	$0.441682\pi$
$440$	−5.20428	−	14.8673i	−0.248104	−	0.708771i
$441$	0.0659031	−	0.458366i	0.00313824	−	0.0218270i
$442$	0.0276669	+	0.0741780i	0.00131598	+	0.00352829i
$443$	18.3197	+	13.7140i	0.870397	+	0.651571i	0.938187	−	0.346129i	$-0.112504\pi$
$443$	18.3197	+	13.7140i	0.870397	+	0.651571i	−0.0677903	+	0.997700i	$0.521595\pi$
$444$	−19.7262	−	5.79213i	−0.936163	−	0.274882i
$445$	13.4265	−	11.1656i	0.636479	−	0.529299i
$446$	−3.23492	−	7.08348i	−0.153178	−	0.335412i
$447$	10.4477	−	19.1336i	0.494161	−	0.904987i
$448$	0.0198706	−	0.00142117i	0.000938798	−	6.71442e-5i
$449$	21.0185	+	18.2126i	0.991925	+	0.859508i	0.990082	−	0.140490i	$-0.0448679\pi$
$449$	21.0185	+	18.2126i	0.991925	+	0.859508i	0.00184293	+	0.999998i	$0.499413\pi$
$450$	−0.0531630	+	0.204143i	−0.00250613	+	0.00962340i
$451$	−26.2707	+	11.9974i	−1.23704	+	0.564937i
$452$	2.99195	−	13.7538i	0.140729	−	0.646923i
$453$	−1.54501	+	0.843637i	−0.0725907	+	0.0396375i
$454$	0.465986	+	3.24100i	0.0218698	+	0.152108i
$455$	−0.0593894	−	0.0187546i	−0.00278422	−	0.000879231i
$456$	−29.1849	−	4.19615i	−1.36671	−	0.196503i
$457$	−39.4237	+	8.57611i	−1.84416	+	0.401173i	−0.992431	−	0.122802i	$-0.960812\pi$
$457$	−39.4237	+	8.57611i	−1.84416	+	0.401173i	−0.851733	+	0.523976i	$0.824448\pi$
$458$	−0.750651	+	10.4955i	−0.0350756	+	0.490421i
$459$	4.60635			0.215006
$460$	12.1602	+	12.0700i	0.566971	+	0.562768i
$461$	9.74476			0.453859			0.226929	−	0.973911i	$-0.427131\pi$
$461$	9.74476			0.453859			0.226929	+	0.973911i	$0.427131\pi$
$462$	−0.0468210	+	0.654643i	−0.00217831	+	0.0304567i
$463$	9.37152	−	2.03865i	0.435531	−	0.0947440i	0.0105462	−	0.999944i	$-0.496643\pi$
$463$	9.37152	−	2.03865i	0.435531	−	0.0947440i	0.424985	+	0.905200i	$0.360279\pi$
$464$	5.97488	+	0.859058i	0.277377	+	0.0398808i
$465$	0.592967	+	1.14033i	0.0274982	+	0.0528813i
$466$	−0.838843	−	5.83428i	−0.0388586	−	0.270268i
$467$	−5.69780	+	3.11123i	−0.263663	+	0.143971i	−0.605643	−	0.795736i	$-0.707084\pi$
$467$	−5.69780	+	3.11123i	−0.263663	+	0.143971i	0.341981	+	0.939707i	$0.388902\pi$
$468$	−0.00321511	+	0.0147796i	−0.000148618	+	0.000683188i
$469$	−1.48297	+	0.677252i	−0.0684774	+	0.0312726i
$470$	3.57818	+	8.27524i	0.165049	+	0.381708i
$471$	−22.1526	−	19.1953i	−1.02074	−	0.884473i
$472$	20.1786	−	1.44320i	0.928795	−	0.0664287i
$473$	−1.18407	+	2.16846i	−0.0544436	+	0.0997061i
$474$	−1.68152	−	3.68202i	−0.0772348	−	0.169121i
$475$	−25.8376	+	27.4824i	−1.18551	+	1.26098i
$476$	−0.263122	−	0.0772595i	−0.0120602	−	0.00354118i
$477$	0.106182	+	0.0794867i	0.00486173	+	0.00363944i
$478$	0.876207	+	2.34920i	0.0400768	+	0.107450i
$479$	1.67535	−	11.6523i	0.0765487	−	0.532408i	−0.915079	−	0.403275i	$-0.867872\pi$
$479$	1.67535	−	11.6523i	0.0765487	−	0.532408i	0.991627	−	0.129132i	$-0.0412192\pi$
$480$	19.5745	+	9.42371i	0.893449	+	0.430132i
$481$	0.808086	−	0.700210i	0.0368455	−	0.0319268i
$482$	−2.73995	+	2.73995i	−0.124802	+	0.124802i
$483$	−0.597753	−	1.49224i	−0.0271987	−	0.0678995i
$484$		−	2.34847i		−	0.106749i
$485$	29.0526	−	1.48643i	1.31921	−	0.0674953i
$486$	−0.368784	−	0.237003i	−0.0167284	−	0.0107507i
$487$	−12.8124	+	9.59126i	−0.580586	+	0.434621i	−0.848782	−	0.528743i	$-0.822663\pi$
$487$	−12.8124	+	9.59126i	−0.580586	+	0.434621i	0.268196	+	0.963364i	$0.413573\pi$
$488$	22.1679	−	8.26821i	1.00350	−	0.374284i
$489$	8.49142	−	1.22088i	0.383996	−	0.0552102i
$490$	8.02255	−	5.75549i	0.362422	−	0.260006i
$491$	−4.32259	+	2.77796i	−0.195076	+	0.125368i	−0.634533	−	0.772896i	$-0.718807\pi$
$491$	−4.32259	+	2.77796i	−0.195076	+	0.125368i	0.439457	+	0.898264i	$0.355171\pi$
$492$	8.94640	−	23.9862i	0.403335	−	1.08138i
$493$	2.65809	+	1.45143i	0.119714	+	0.0653690i
$494$	0.445964	−	0.514669i	0.0200648	−	0.0231561i
$495$	0.256029	−	0.381165i	0.0115076	−	0.0171321i
$496$	−0.562888	+	0.165279i	−0.0252744	+	0.00742123i
$497$	−1.23328	−	0.459988i	−0.0553200	−	0.0206333i
$498$	9.19655	+	2.00059i	0.412107	+	0.0896485i
$499$	−9.59724	+	32.6852i	−0.429631	+	1.46319i	0.405986	+	0.913879i	$0.366928\pi$
$499$	−9.59724	+	32.6852i	−0.429631	+	1.46319i	−0.835618	+	0.549311i	$0.814890\pi$
$500$	15.5866	−	8.72579i	0.697055	−	0.390229i
$501$	−5.82396	+	12.7527i	−0.260196	+	0.569749i
$502$	2.15607	+	2.88017i	0.0962300	+	0.128548i
$503$	0.334058	+	1.53564i	0.0148949	+	0.0684709i	0.983994	−	0.178199i	$-0.0570272\pi$
$503$	0.334058	+	1.53564i	0.0148949	+	0.0684709i	−0.969099	+	0.246670i	$0.920664\pi$
$504$	0.0194530	+	0.0224500i	0.000866506	+	0.00100000i
$505$	−24.6930	+	3.04058i	−1.09882	+	0.135304i
$506$	4.10479	+	8.44576i	0.182480	+	0.375460i
$507$	−15.7196	−	15.7196i	−0.698134	−	0.698134i
$508$	−34.9537	−	2.49994i	−1.55082	−	0.110917i
$509$	10.9905	−	17.1015i	0.487145	−	0.758012i	−0.507468	−	0.861670i	$-0.669419\pi$
$509$	10.9905	−	17.1015i	0.487145	−	0.758012i	0.994613	+	0.103659i	$0.0330549\pi$
$510$	1.47559	+	1.53669i	0.0653401	+	0.0680457i
$511$	−1.20221	−	0.549032i	−0.0531828	−	0.0242878i
$512$	−10.7234	+	14.3248i	−0.473911	+	0.633072i
$513$	−18.9893	−	34.7764i	−0.838399	−	1.53541i
$514$	−7.93239	−	12.3430i	−0.349883	−	0.544428i
$515$	−2.93269	+	12.2771i	−0.129230	+	0.540994i
$516$	−0.617011	−	2.10135i	−0.0271624	−	0.0925066i
$517$	−1.39997	−	19.5741i	−0.0615706	−	0.860869i
$518$	−0.0665294	−	0.930202i	−0.00292313	−	0.0408707i
$519$	8.38045	+	28.5412i	0.367861	+	1.25282i
$520$	−0.618745	+	0.380138i	−0.0271338	+	0.0166701i
$521$	19.6254	+	30.5377i	0.859804	+	1.33788i	0.940025	+	0.341104i	$0.110801\pi$
$521$	19.6254	+	30.5377i	0.859804	+	1.33788i	−0.0802212	+	0.996777i	$0.525563\pi$
$522$	−0.0698215	−	0.127869i	−0.00305600	−	0.00559666i
$523$	1.45985	−	1.95013i	0.0638346	−	0.0852730i	−0.767488	−	0.641064i	$-0.778493\pi$
$523$	1.45985	−	1.95013i	0.0638346	−	0.0852730i	0.831322	+	0.555791i	$0.187584\pi$
$524$	−26.7277	−	12.2061i	−1.16761	−	0.533228i
$525$	−1.66720	+	0.171047i	−0.0727625	+	0.00746510i
$526$	8.96968	−	13.9571i	0.391096	−	0.608558i
$527$	−0.293585	−	0.0209976i	−0.0127888	−	0.000914670i
$528$	−6.53556	−	6.53556i	−0.284424	−	0.284424i
$529$	−18.0849	−	14.2104i	−0.786302	−	0.617843i
$530$	0.345620	+	2.80683i	0.0150128	+	0.121921i
$531$	0.386180	+	0.445676i	0.0167588	+	0.0193407i
$532$	0.501417	+	2.30498i	0.0217392	+	0.0999334i
$533$	0.797907	+	1.06588i	0.0345612	+	0.0461683i
$534$	−3.52428	+	7.71709i	−0.152510	+	0.333951i
$535$	33.7989	+	19.3556i	1.46126	+	0.836814i
$536$	−5.35555	+	18.2393i	−0.231325	+	0.787819i
$537$	20.9831	+	4.56458i	0.905486	+	0.196976i
$538$	12.0285	+	4.48640i	0.518585	+	0.193422i
$539$	−20.6208	+	6.05482i	−0.888201	+	0.260799i
$540$	3.61587	+	18.4120i	0.155602	+	0.792327i
$541$	23.9206	−	27.6058i	1.02843	−	1.18687i	0.0462450	−	0.998930i	$-0.485275\pi$
$541$	23.9206	−	27.6058i	1.02843	−	1.18687i	0.982181	−	0.187937i	$-0.0601800\pi$
$542$	4.42208	+	2.41464i	0.189945	+	0.103718i
$543$	−15.5816	+	41.7759i	−0.668671	+	1.79278i
$544$	−4.18529	+	2.68972i	−0.179443	+	0.115321i
$545$	16.7867	+	2.76212i	0.719064	+	0.118316i
$546$	0.0299493	−	0.00430606i	0.00128171	−	0.000184282i
$547$	38.6516	−	14.4163i	1.65262	−	0.616396i	0.661571	−	0.749883i	$-0.269890\pi$
$547$	38.6516	−	14.4163i	1.65262	−	0.616396i	0.991051	+	0.133487i	$0.0426175\pi$
$548$	−9.62107	+	7.20225i	−0.410992	+	0.307665i
$549$	0.580200	+	0.372872i	0.0247624	+	0.0159138i
$550$	9.64298	−	1.69142i	0.411178	−	0.0721223i
$551$		−	26.0511i		−	1.10981i
$552$	−17.7140	−	6.12688i	−0.753957	−	0.260777i
$553$	−0.515632	+	0.515632i	−0.0219269	+	0.0219269i
$554$	−1.64066	+	1.42164i	−0.0697050	+	0.0603997i
$555$	12.4812	−	25.9253i	0.529797	−	1.10047i
$556$	−3.77028	+	26.2229i	−0.159895	+	1.11210i
$557$	4.73958	+	12.7073i	0.200822	+	0.538426i	0.997852	−	0.0655152i	$-0.0208691\pi$
$557$	4.73958	+	12.7073i	0.200822	+	0.538426i	−0.797029	+	0.603941i	$0.793596\pi$
$558$	0.0113349	+	0.00848523i	0.000479846	+	0.000359208i
$559$	0.109289	+	0.0320901i	0.00462243	+	0.00135727i
$560$	0.0700345	−	0.761753i	0.00295950	−	0.0321899i
$561$	−1.92638	−	4.21818i	−0.0813318	−	0.178092i
$562$	−0.0989391	+	0.181193i	−0.00417349	+	0.00764318i
$563$	−21.1473	+	1.51248i	−0.891251	+	0.0637435i	−0.509449	−	0.860501i	$-0.670151\pi$
$563$	−21.1473	+	1.51248i	−0.891251	+	0.0637435i	−0.381802	+	0.924244i	$0.624696\pi$
$564$	13.1464	+	11.3914i	0.553564	+	0.479666i
$565$	18.3138	+	7.25709i	0.770469	+	0.305308i
$566$	−15.4822	+	7.07047i	−0.650764	+	0.297194i
$567$	0.365913	−	1.68207i	0.0153669	−	0.0706405i
$568$	−13.4703	+	7.35537i	−0.565203	+	0.308624i
$569$	0.120169	+	0.835792i	0.00503773	+	0.0350382i	0.992185	−	0.124773i	$-0.0398204\pi$
$569$	0.120169	+	0.835792i	0.00503773	+	0.0350382i	−0.987148	+	0.159812i	$0.948911\pi$
$570$	5.51847	−	17.4751i	0.231143	−	0.731950i
$571$	−25.5215	−	3.66943i	−1.06804	−	0.153561i	−0.414194	−	0.910189i	$-0.635937\pi$
$571$	−25.5215	−	3.66943i	−1.06804	−	0.153561i	−0.653846	+	0.756628i	$0.726846\pi$
$572$	0.685916	−	0.149212i	0.0286796	−	0.00623886i
$573$	−1.51885	+	21.2363i	−0.0634510	+	0.887161i
$574$	1.16126			0.0484701
$575$	−19.4316	+	14.0503i	−0.810356	+	0.585938i
$576$	0.00677112			0.000282130
$577$	1.51556	−	21.1902i	0.0630934	−	0.882161i	−0.863081	−	0.505066i	$-0.831468\pi$
$577$	1.51556	−	21.1902i	0.0630934	−	0.882161i	0.926174	−	0.377096i	$-0.123077\pi$
$578$	10.0594	−	2.18829i	0.418416	−	0.0910209i
$579$	−19.2239	−	2.76398i	−0.798919	−	0.114867i
$580$	−3.71496	+	11.7640i	−0.154255	+	0.488472i
$581$	−0.241296	−	1.67825i	−0.0100106	−	0.0696255i
$582$	−12.4042	+	6.77319i	−0.514170	+	0.280758i
$583$	1.30848	−	6.01498i	0.0541916	−	0.249115i
$584$	−14.0178	+	6.40173i	−0.580062	+	0.264905i
$585$	−0.0196798	−	0.00779836i	−0.000813660	−	0.000322423i
$586$	−4.17158	−	3.61470i	−0.172326	−	0.149322i
$587$	1.93346	−	0.138284i	0.0798026	−	0.00570759i	−0.0313808	−	0.999508i	$-0.509990\pi$
$587$	1.93346	−	0.138284i	0.0798026	−	0.00570759i	0.111183	+	0.993800i	$0.464536\pi$
$588$	9.12987	−	16.7201i	0.376509	−	0.689526i
$589$	1.05176	+	2.30303i	0.0433369	+	0.0948946i
$590$	−1.15114	+	12.5208i	−0.0473917	+	0.515471i
$591$	11.4115	+	3.35073i	0.469408	+	0.137831i
$592$	10.5137	+	7.87044i	0.432109	+	0.323473i
$593$	1.30615	+	3.50192i	0.0536371	+	0.143807i	0.961005	−	0.276530i	$-0.0891846\pi$
$593$	1.30615	+	3.50192i	0.0536371	+	0.143807i	−0.907368	+	0.420337i	$0.861912\pi$
$594$	−1.46355	+	10.1792i	−0.0600504	+	0.417660i
$595$	0.166483	−	0.345811i	0.00682513	−	0.0141768i
$596$	−15.3689	+	13.3172i	−0.629535	+	0.545495i
$597$	24.5350	−	24.5350i	1.00415	−	1.00415i
$598$	0.340241	−	0.267679i	0.0139135	−	0.0109462i
$599$			30.7152i			1.25499i	0.778622	+	0.627494i	$0.215919\pi$
$599$			30.7152i			1.25499i	−0.778622	+	0.627494i	$0.784081\pi$
$600$	−11.2229	+	15.9975i	−0.458174	+	0.653095i
$601$	−5.73269	−	3.68418i	−0.233841	−	0.150281i	0.418473	−	0.908229i	$-0.362565\pi$
$601$	−5.73269	−	3.68418i	−0.233841	−	0.150281i	−0.652314	+	0.757949i	$0.726202\pi$
$602$	0.0795287	−	0.0595344i	0.00324135	−	0.00242644i
$603$	−0.519189	+	0.193648i	−0.0211430	+	0.00788594i
$604$	1.62538	−	0.233695i	0.0661359	−	0.00950891i
$605$	3.24320	+	0.533642i	0.131855	+	0.0216956i
$606$	10.1683	−	6.53476i	0.413058	−	0.265456i
$607$	5.35178	−	14.3487i	0.217222	−	0.582395i	−0.781939	−	0.623355i	$-0.785769\pi$
$607$	5.35178	−	14.3487i	0.217222	−	0.582395i	0.999161	+	0.0409605i	$0.0130418\pi$
$608$	37.5600	+	20.5093i	1.52326	+	0.831763i
$609$	0.757974	−	0.874749i	0.0307147	−	0.0354466i
$610$	2.83376	+	14.4295i	0.114735	+	0.584233i
$611$	−0.868060	+	0.254885i	−0.0351180	+	0.0103116i
$612$	−0.0873318	−	0.0325731i	−0.00353018	−	0.00131669i
$613$	−44.8300	−	9.75216i	−1.81066	−	0.393886i	−0.825348	−	0.564624i	$-0.809021\pi$
$613$	−44.8300	−	9.75216i	−1.81066	−	0.393886i	−0.985316	+	0.170738i	$0.945385\pi$
$614$	3.88441	−	13.2291i	0.156762	−	0.533882i
$615$	31.0917	+	17.8052i	1.25374	+	0.717975i
$616$	0.572702	−	1.25404i	0.0230748	−	0.0505268i
$617$	16.2881	+	21.7584i	0.655736	+	0.875961i	0.997972	−	0.0636532i	$-0.0202751\pi$
$617$	16.2881	+	21.7584i	0.655736	+	0.875961i	−0.342236	+	0.939614i	$0.611184\pi$
$618$	−1.30352	−	5.99219i	−0.0524353	−	0.241041i
$619$	−6.85826	−	7.91486i	−0.275657	−	0.318125i	0.600993	−	0.799255i	$-0.294772\pi$
$619$	−6.85826	−	7.91486i	−0.275657	−	0.318125i	−0.876650	+	0.481130i	$0.840227\pi$
$620$	−0.146527	−	1.18997i	−0.00588468	−	0.0477903i
$621$	−7.67436	−	23.9909i	−0.307961	−	0.962720i
$622$	7.56645	+	7.56645i	0.303387	+	0.303387i
$623$	1.52446	+	0.109031i	0.0610760	+	0.00436824i
$624$	−0.230369	+	0.358462i	−0.00922215	+	0.0143499i
$625$	8.50842	+	23.5076i	0.340337	+	0.940304i
$626$	−14.5553	−	6.64719i	−0.581747	−	0.265675i
$627$	−23.9045	+	31.9327i	−0.954653	+	1.27527i
$628$	13.1042	+	23.9986i	0.522916	+	0.957649i
$629$	3.56239	+	5.54318i	0.142042	+	0.221021i
$630$	−0.0157311	+	0.00966471i	−0.000626743	+	0.000385051i
$631$	1.07019	+	3.64475i	0.0426037	+	0.145095i	0.978048	−	0.208379i	$-0.0668186\pi$
$631$	1.07019	+	3.64475i	0.0426037	+	0.145095i	−0.935445	+	0.353474i	$0.885000\pi$
$632$	0.606571	+	8.48098i	0.0241281	+	0.337355i
$633$	−0.629834	−	8.80623i	−0.0250337	−	0.350016i
$634$	4.37944	+	14.9150i	0.173930	+	0.592350i
$635$	11.3949	−	47.7023i	0.452192	−	1.89301i
$636$	2.95000	+	4.59029i	0.116975	+	0.182017i
$637$	0.474835	+	0.869596i	0.0188137	+	0.0344546i
$638$	−4.05195	+	5.41277i	−0.160418	+	0.214294i
$639$	−0.406959	−	0.185852i	−0.0160991	−	0.00735220i
$640$	−17.4707	−	18.1942i	−0.690592	−	0.719188i
$641$	−6.36323	+	9.90138i	−0.251333	+	0.391081i	−0.943879	−	0.330293i	$-0.892853\pi$
$641$	−6.36323	+	9.90138i	−0.251333	+	0.391081i	0.692546	+	0.721374i	$0.256489\pi$
$642$	−18.8741	−	1.34990i	−0.744900	−	0.0532763i
$643$	12.7726	+	12.7726i	0.503701	+	0.503701i	0.912586	−	0.408885i	$-0.134082\pi$
$643$	12.7726	+	12.7726i	0.503701	+	0.503701i	−0.408885	+	0.912586i	$0.634082\pi$
$644$	0.0359870	+	1.49911i	0.00141809	+	0.0590733i
$645$	3.04212	−	0.374593i	0.119784	−	0.0147496i
$646$	2.74823	+	3.17162i	0.108127	+	0.124786i
$647$	−5.54103	−	25.4717i	−0.217840	−	1.00140i	−0.948037	−	0.318160i	$-0.896935\pi$
$647$	−5.54103	−	25.4717i	−0.217840	−	1.00140i	0.730197	−	0.683237i	$-0.239428\pi$
$648$	−12.0285	−	16.0682i	−0.472525	−	0.631220i
$649$	11.3692	−	24.8952i	0.446282	−	0.977220i
$650$	−0.170693	−	0.417824i	−0.00669513	−	0.0163884i
$651$	−0.0316920	+	0.107933i	−0.00124211	+	0.00423023i
$652$	−7.81966	−	1.70106i	−0.306242	−	0.0666188i
$653$	29.1500	+	10.8724i	1.14073	+	0.425469i	0.847617	−	0.530609i	$-0.178037\pi$
$653$	29.1500	+	10.8724i	1.14073	+	0.425469i	0.293111	+	0.956079i	$0.405310\pi$
$654$	−7.93027	+	2.32854i	−0.310098	+	0.0910530i
$655$	22.9298	−	34.1369i	0.895941	−	1.33384i
$656$	−10.7094	+	12.3593i	−0.418131	+	0.482549i
$657$	−0.394269	−	0.215287i	−0.0153819	−	0.00839916i
$658$	−0.275751	+	0.739316i	−0.0107499	+	0.0288215i
$659$	0.0162657	−	0.0104533i	0.000633622	−	0.000407204i	−0.540324	−	0.841457i	$-0.681698\pi$
$659$	0.0162657	−	0.0104533i	0.000633622	−	0.000407204i	0.540958	+	0.841050i	$0.318062\pi$
$660$	15.3483	−	11.0111i	0.597433	−	0.428606i
$661$	35.4326	−	5.09444i	1.37817	−	0.198151i	0.586919	−	0.809646i	$-0.300341\pi$
$661$	35.4326	−	5.09444i	1.37817	−	0.198151i	0.791248	+	0.611495i	$0.209432\pi$
$662$	−0.518924	+	0.193549i	−0.0201686	+	0.00752249i
$663$	−0.171144	+	0.128117i	−0.00664667	+	0.00497564i
$664$	−16.6313	−	10.6883i	−0.645419	−	0.414786i
$665$	−3.29707	+	0.168689i	−0.127855	+	0.00654149i
$666$		−	0.316976i		−	0.0122826i
$667$	3.13086	−	16.2621i	0.121228	−	0.629669i
$668$	9.24754	−	9.24754i	0.357798	−	0.357798i
$669$	15.8920	−	13.7705i	0.614419	−	0.532397i
$670$	−10.6454	−	5.12499i	−0.411267	−	0.197996i
$671$	4.55522	−	31.6823i	0.175852	−	1.22308i
$672$	0.664466	+	1.78150i	0.0256323	+	0.0687229i
$673$	−20.0631	−	15.0190i	−0.773374	−	0.578940i	0.138042	−	0.990426i	$-0.455919\pi$
$673$	−20.0631	−	15.0190i	−0.773374	−	0.578940i	−0.911416	+	0.411486i	$0.865010\pi$
$674$	3.92499	+	1.15248i	0.151185	+	0.0443919i
$675$	−26.2483	+	0.809698i	−1.01030	+	0.0311653i
$676$	8.61479	+	18.8638i	0.331338	+	0.725529i
$677$	−16.1282	+	29.5365i	−0.619856	+	1.13518i	0.359521	+	0.933137i	$0.382940\pi$
$677$	−16.1282	+	29.5365i	−0.619856	+	1.13518i	−0.979376	+	0.202044i	$0.935242\pi$
$678$	−9.54602	+	0.682745i	−0.366613	+	0.0262207i
$679$	1.92418	+	1.66731i	0.0738431	+	0.0639854i
$680$	−1.77609	−	4.10756i	−0.0681099	−	0.157518i
$681$	−8.04279	+	3.67302i	−0.308201	+	0.140750i
$682$	0.139681	−	0.642101i	0.00534865	−	0.0245873i
$683$	17.8768	−	9.76146i	0.684036	−	0.373512i	−0.0993455	−	0.995053i	$-0.531675\pi$
$683$	17.8768	−	9.76146i	0.684036	−	0.373512i	0.783382	+	0.621541i	$0.213493\pi$
$684$	0.114103	+	0.793606i	0.00436285	+	0.0303443i
$685$	−7.75998	−	14.9231i	−0.296494	−	0.570182i
$686$	1.71541	+	0.246638i	0.0654946	+	0.00941670i
$687$	−27.7644	+	6.03978i	−1.05928	+	0.230432i
$688$	−0.0998053	+	1.39546i	−0.00380504	+	0.0532014i
$689$	−0.283787			−0.0108114
$690$	5.54502	−	10.2454i	0.211095	−	0.390034i
$691$	−9.06622			−0.344895			−0.172448	−	0.985019i	$-0.555168\pi$
$691$	−9.06622			−0.344895			−0.172448	+	0.985019i	$0.555168\pi$
$692$	1.97953	−	27.6775i	0.0752506	−	1.05214i
$693$	0.0392689	−	0.00854242i	0.00149170	−	0.000324500i
$694$	−9.00407	−	1.29459i	−0.341790	−	0.0491420i
$695$	−35.3566	−	11.1653i	−1.34115	−	0.423523i
$696$	−1.92068	−	13.3586i	−0.0728032	−	0.506357i
$697$	−7.20133	+	3.93222i	−0.272770	+	0.148944i
$698$	−3.54356	+	16.2895i	−0.134126	+	0.616566i
$699$	14.4782	−	6.61198i	0.547616	−	0.250088i
$700$	1.51292	+	0.393995i	0.0571831	+	0.0148916i
$701$	−2.88463	−	2.49955i	−0.108951	−	0.0944066i	0.598682	−	0.800987i	$-0.295691\pi$
$701$	−2.88463	−	2.49955i	−0.108951	−	0.0944066i	−0.707633	+	0.706580i	$0.750237\pi$
$702$	0.472899	−	0.0338224i	0.0178484	−	0.00127654i
$703$	27.1635	−	49.7462i	1.02449	−	1.87621i
$704$	−0.130542	−	0.285847i	−0.00491999	−	0.0107733i
$705$	−18.7186	+	15.5665i	−0.704984	+	0.586268i
$706$	−8.93395	−	2.62324i	−0.336234	−	0.0987271i
$707$	−1.74317	−	1.30492i	−0.0655585	−	0.0490765i
$708$	8.47796	+	22.7303i	0.318621	+	0.854256i
$709$	−0.496317	+	3.45196i	−0.0186396	+	0.129641i	−0.997016	−	0.0771888i	$-0.975406\pi$
$709$	−0.496317	+	3.45196i	−0.0186396	+	0.129641i	0.978377	+	0.206830i	$0.0663147\pi$
$710$	−3.15160	−	9.00332i	−0.118278	−	0.337889i
$711$	−0.187316	+	0.162310i	−0.00702488	+	0.00608710i
$712$	12.6011	−	12.6011i	0.472244	−	0.472244i
$713$	0.379764	+	1.56404i	0.0142223	+	0.0585736i
$714$			0.186459i			0.00697805i
$715$	0.0501986	+	0.981143i	0.00187732	+	0.0366927i
$716$	−16.8516	−	10.8298i	−0.629773	−	0.404730i
$717$	−5.42009	+	4.05743i	−0.202417	+	0.151528i
$718$	9.07079	−	3.38323i	0.338519	−	0.126261i
$719$	−1.41127	+	0.202910i	−0.0526314	+	0.00756725i	−0.168580	−	0.985688i	$-0.553918\pi$
$719$	−1.41127	+	0.202910i	−0.0526314	+	0.00756725i	0.115949	+	0.993255i	$0.463009\pi$
$720$	0.0422142	−	0.256556i	0.00157323	−	0.00956128i
$721$	−0.929367	+	0.597268i	−0.0346114	+	0.0222434i
$722$	8.40388	−	22.5317i	0.312760	−	0.838542i
$723$	−9.18360	−	5.01462i	−0.341542	−	0.186496i
$724$	27.2372	−	31.4335i	1.01226	−	1.16822i
$725$	−15.4017	−	7.80341i	−0.572004	−	0.289811i
$726$	−1.53213	+	0.449874i	−0.0568627	+	0.0166964i
$727$	6.16192	+	2.29828i	0.228533	+	0.0852384i	0.461122	−	0.887337i	$-0.347447\pi$
$727$	6.16192	+	2.29828i	0.228533	+	0.0852384i	−0.232589	+	0.972575i	$0.574720\pi$
$728$	−0.0621046	−	0.0135100i	−0.00230175	−	0.000500715i
$729$	7.76788	−	26.4550i	0.287699	−	0.979814i
$730$	−2.51151	−	9.24285i	−0.0929551	−	0.342093i
$731$	−0.291588	+	0.638488i	−0.0107848	+	0.0236153i
$732$	17.0030	+	22.7134i	0.628451	+	0.839512i
$733$	−2.58919	−	11.9023i	−0.0956338	−	0.439621i	−0.999919	−	0.0126935i	$-0.995959\pi$
$733$	−2.58919	−	11.9023i	−0.0956338	−	0.439621i	0.904286	−	0.426928i	$-0.140404\pi$
$734$	6.11264	+	7.05436i	0.225622	+	0.260381i
$735$	21.0156	+	16.4075i	0.775171	+	0.605199i
$736$	20.9815	+	17.3167i	0.773389	+	0.638302i
$737$	18.1845	+	18.1845i	0.669836	+	0.669836i
$738$	0.393698	+	0.0281578i	0.0144922	+	0.00103650i
$739$	7.74807	−	12.0562i	0.285017	−	0.443496i	−0.668993	−	0.743269i	$-0.733274\pi$
$739$	7.74807	−	12.0562i	0.285017	−	0.443496i	0.954011	+	0.299773i	$0.0969108\pi$
$740$	−19.3603	+	18.5905i	−0.711697	+	0.683399i
$741$	1.67276	+	0.763926i	0.0614506	+	0.0280635i
$742$	−0.148329	+	0.198144i	−0.00544533	+	0.00727410i
$743$	−9.02949	−	16.5363i	−0.331260	−	0.606657i	0.657967	−	0.753047i	$-0.271417\pi$
$743$	−9.02949	−	16.5363i	−0.331260	−	0.606657i	−0.989227	+	0.146389i	$0.953235\pi$
$744$	0.709122	+	1.10342i	0.0259977	+	0.0404532i
$745$	−14.8986	−	24.2502i	−0.545842	−	0.888460i
$746$	−3.26400	−	11.1162i	−0.119504	−	0.406992i
$747$	−0.0411121	−	0.574822i	−0.00150421	−	0.0210316i
$748$	0.308597	+	4.31476i	0.0112834	+	0.157763i
$749$	0.960384	+	3.27077i	0.0350917	+	0.119511i
$750$	−8.67843	−	8.49711i	−0.316892	−	0.310270i
$751$	15.9579	+	24.8310i	0.582313	+	0.906096i	0.999997	−	0.00249615i	$-0.000794549\pi$
$751$	15.9579	+	24.8310i	0.582313	+	0.906096i	−0.417684	+	0.908592i	$0.637158\pi$
$752$	−5.32550	−	9.75293i	−0.194201	−	0.355653i
$753$	−5.82212	+	7.77744i	−0.212170	+	0.283426i
$754$	0.283543	+	0.129490i	0.0103260	+	0.00471575i
$755$	−0.0466065	+	2.29773i	−0.00169619	+	0.0836229i
$756$	−0.887854	+	1.38153i	−0.0322909	+	0.0502457i
$757$	−21.7294	−	1.55412i	−0.789770	−	0.0564854i	−0.329374	−	0.944199i	$-0.606838\pi$
$757$	−21.7294	−	1.55412i	−0.789770	−	0.0564854i	−0.460395	+	0.887714i	$0.652292\pi$
$758$	1.45322	+	1.45322i	0.0527834	+	0.0527834i
$759$	−18.7598	+	17.0607i	−0.680937	+	0.619263i
$760$	−23.6889	+	30.3420i	−0.859285	+	1.10062i
$761$	−12.8439	−	14.8227i	−0.465593	−	0.537323i	0.473588	−	0.880747i	$-0.342959\pi$
$761$	−12.8439	−	14.8227i	−0.465593	−	0.537323i	−0.939180	+	0.343424i	$0.888413\pi$
$762$	5.06479	+	23.2825i	0.183478	+	0.843435i
$763$	0.892296	+	1.19197i	0.0323033	+	0.0431521i
$764$	8.25039	−	18.0658i	0.298488	−	0.653599i
$765$	0.0648272	−	0.113202i	0.00234383	−	0.00409283i
$766$	−4.52975	+	15.4269i	−0.163667	+	0.557397i
$767$	−1.23290	−	0.268200i	−0.0445173	−	0.00968415i
$768$	11.8085	+	4.40436i	0.426104	+	0.158929i
$769$	−0.293488	+	0.0861757i	−0.0105834	+	0.00310758i	−0.287020	−	0.957925i	$-0.592665\pi$
$769$	−0.293488	+	0.0861757i	−0.0105834	+	0.00310758i	0.276437	+	0.961032i	$0.410846\pi$
$770$	0.711287	+	0.477772i	0.0256330	+	0.0172177i
$771$	25.9456	−	29.9428i	0.934407	−	1.07836i
$772$	15.9010	+	8.68263i	0.572291	+	0.312495i
$773$	−7.03246	+	18.8547i	−0.252940	+	0.678158i	0.746972	+	0.664856i	$0.231507\pi$
$773$	−7.03246	+	18.8547i	−0.252940	+	0.678158i	−0.999912	+	0.0133021i	$0.995766\pi$
$774$	0.0284059	−	0.0182554i	0.00102103	−	0.000656175i
$775$	1.67662	+	0.0680443i	0.0602260	+	0.00244422i
$776$	29.3848	−	4.22490i	1.05485	−	0.151665i
$777$	2.35950	−	0.880049i	0.0846467	−	0.0315716i
$778$	6.56504	−	4.91453i	0.235368	−	0.176194i
$779$	59.3739	+	38.1573i	2.12729	+	1.36713i
$780$	−0.646438	−	0.583510i	−0.0231462	−	0.0208930i
$781$			20.7632i			0.742964i
$782$	1.33437	+	2.31013i	0.0477171	+	0.0826101i
$783$	12.8244	−	12.8244i	0.458306	−	0.458306i
$784$	−9.19710	+	7.96933i	−0.328468	+	0.284619i
$785$	−36.1193	+	12.6435i	−1.28915	+	0.451267i
$786$	−2.84325	+	19.7752i	−0.101415	+	0.705359i
$787$	7.36810	+	19.7546i	0.262644	+	0.704177i	0.999601	+	0.0282370i	$0.00898931\pi$
$787$	7.36810	+	19.7546i	0.262644	+	0.704177i	−0.736957	+	0.675940i	$0.763738\pi$
$788$	−8.88159	−	6.64868i	−0.316394	−	0.236849i
$789$	42.9861	+	12.6219i	1.53035	+	0.449351i
$790$	−5.26242	−	0.483819i	−0.187229	−	0.0172135i
$791$	0.716221	+	1.56830i	0.0254659	+	0.0557625i
$792$	0.224568	−	0.411266i	0.00797969	−	0.0146137i
$793$	−1.47187	+	0.105270i	−0.0522676	+	0.00373825i
$794$	−10.5726	−	9.16121i	−0.375207	−	0.325119i
$795$	−7.00944	+	3.03085i	−0.248599	+	0.107493i
$796$	−29.4423	+	13.4458i	−1.04355	+	0.476575i
$797$	4.78441	−	21.9936i	0.169472	−	0.779052i	−0.811414	−	0.584471i	$-0.801302\pi$
$797$	4.78441	−	21.9936i	0.169472	−	0.779052i	0.980887	−	0.194580i	$-0.0623345\pi$
$798$	1.40770	−	0.768663i	0.0498321	−	0.0272104i
$799$	−0.793435	−	5.51846i	−0.0280697	−	0.195229i
$800$	23.3762	−	16.0625i	0.826472	−	0.567895i
$801$	0.514187	+	0.0739289i	0.0181679	+	0.00261215i
$802$	−14.0737	+	3.06155i	−0.496961	+	0.108107i
$803$	−1.48728	+	20.7949i	−0.0524850	+	0.733837i
$804$	−22.7959			−0.803949
$805$	−2.07842	−	0.290945i	−0.0732548	−	0.0102545i
$806$	−0.0302943			−0.00106707
$807$	−2.47310	+	34.5785i	−0.0870573	+	1.21722i
$808$	−24.8093	+	5.39693i	−0.872788	+	0.189863i
$809$	−36.4611	−	5.24231i	−1.28190	−	0.184310i	−0.532504	−	0.846428i	$-0.678749\pi$
$809$	−36.4611	−	5.24231i	−1.28190	−	0.184310i	−0.749400	+	0.662118i	$0.769658\pi$
$810$	11.0681	−	5.75541i	0.388894	−	0.202224i
$811$	2.23766	+	15.5633i	0.0785750	+	0.546501i	0.990645	+	0.136466i	$0.0435744\pi$
$811$	2.23766	+	15.5633i	0.0785750	+	0.546501i	−0.912070	+	0.410035i	$0.865516\pi$
$812$	−0.947645	+	0.517454i	−0.0332558	+	0.0181591i
$813$	−2.89203	+	13.2944i	−0.101428	+	0.466256i
$814$	−13.3814	+	6.11106i	−0.469017	+	0.214193i
$815$	4.12599	−	10.4123i	0.144527	−	0.364726i
$816$	−1.98448	−	1.71956i	−0.0694707	−	0.0601967i
$817$	6.02242	−	0.430732i	0.210698	−	0.0150694i
$818$	−3.31190	+	6.06529i	−0.115798	+	0.212068i
$819$	−0.000769641	−	0.00168528i	−2.68934e−5	−	5.88884e-5i
$820$	−21.3703	−	25.6977i	−0.746285	−	0.897403i
$821$	18.5294	+	5.44073i	0.646682	+	0.189883i	0.588594	−	0.808429i	$-0.299682\pi$
$821$	18.5294	+	5.44073i	0.646682	+	0.189883i	0.0580876	+	0.998311i	$0.481500\pi$
$822$	6.54172	+	4.89707i	0.228169	+	0.170805i
$823$	−5.33967	−	14.3162i	−0.186129	−	0.499032i	0.810050	−	0.586360i	$-0.199440\pi$
$823$	−5.33967	−	14.3162i	−0.186129	−	0.499032i	−0.996180	+	0.0873287i	$0.972167\pi$
$824$	−1.83320	+	12.7502i	−0.0638625	+	0.444173i
$825$	11.7185	+	23.6978i	0.407987	+	0.825051i
$826$	−0.831669	+	0.720645i	−0.0289375	+	0.0250745i
$827$	15.0227	−	15.0227i	0.522391	−	0.522391i	−0.395902	−	0.918293i	$-0.629568\pi$
$827$	15.0227	−	15.0227i	0.522391	−	0.522391i	0.918293	+	0.395902i	$0.129568\pi$
$828$	−0.0241494	+	0.509111i	−0.000839249	+	0.0176928i
$829$			37.7158i			1.30992i	0.755661	+	0.654962i	$0.227316\pi$
$829$			37.7158i			1.30992i	−0.755661	+	0.654962i	$0.772684\pi$
$830$	8.23317	−	9.12108i	0.285778	−	0.316597i
$831$	−4.93159	−	3.16934i	−0.171075	−	0.109943i
$832$	−0.0115977	+	0.00868189i	−0.000402076	+	0.000300991i
$833$	−5.72072	+	2.13372i	−0.198211	+	0.0739290i
$834$	17.8299	−	2.56355i	0.617398	−	0.0887685i
$835$	10.6694	+	14.8720i	0.369229	+	0.514666i
$836$	31.3028	−	20.1171i	1.08263	−	0.695764i
$837$	−0.615974	+	1.65149i	−0.0212912	+	0.0570838i
$838$	−17.9367	−	9.79420i	−0.619614	−	0.338335i
$839$	15.5246	−	17.9164i	0.535970	−	0.618543i	−0.421586	−	0.906788i	$-0.638527\pi$
$839$	15.5246	−	17.9164i	0.535970	−	0.618543i	0.957556	+	0.288246i	$0.0930720\pi$
$840$	−1.67825	+	0.329586i	−0.0579052	+	0.0113718i
$841$	−16.3841	+	4.81081i	−0.564969	+	0.165890i
$842$	8.29918	+	3.09543i	0.286008	+	0.106676i
$843$	−0.544735	−	0.118500i	−0.0187617	−	0.00408135i
$844$	−2.32028	+	7.90214i	−0.0798672	+	0.272003i
$845$	−28.0080	+	7.61046i	−0.963506	+	0.261808i
$846$	−0.111413	+	0.243961i	−0.00383047	+	0.00838756i
$847$	0.172392	+	0.230289i	0.00592346	+	0.00791281i
$848$	−0.740927	−	3.40599i	−0.0254435	−	0.116962i
$849$	−30.0977	−	34.7346i	−1.03295	−	1.19209i
$850$	2.69831	−	0.674745i	0.0925512	−	0.0231436i
$851$	22.9350	−	27.7889i	0.786203	−	0.952590i
$852$	−13.0142	−	13.0142i	−0.445859	−	0.445859i
$853$	2.98919	+	0.213791i	0.102348	+	0.00732006i	0.122419	−	0.992478i	$-0.460935\pi$
$853$	2.98919	+	0.213791i	0.102348	+	0.00732006i	−0.0200713	+	0.999799i	$0.506389\pi$
$854$	−0.695811	+	1.08270i	−0.0238102	+	0.0370494i
$855$	−1.12188	−	0.0227560i	−0.0383676	−	0.000778238i
$856$	36.1554	+	16.5116i	1.23576	+	0.564355i
$857$	−31.6373	+	42.2625i	−1.08071	+	1.44366i	−0.194193	+	0.980963i	$0.562209\pi$
$857$	−31.6373	+	42.2625i	−1.08071	+	1.44366i	−0.886517	+	0.462696i	$0.846882\pi$
$858$	−0.228739	−	0.418905i	−0.00780903	−	0.0143012i
$859$	−28.8098	−	44.8289i	−0.982977	−	1.52954i	−0.841963	−	0.539535i	$-0.818600\pi$
$859$	−28.8098	−	44.8289i	−0.982977	−	1.52954i	−0.141014	−	0.990008i	$-0.545036\pi$
$860$	−2.78099	−	0.664307i	−0.0948309	−	0.0226527i
$861$	0.883458	+	3.00878i	0.0301082	+	0.102539i
$862$	0.125337	+	1.75244i	0.00426900	+	0.0596884i
$863$	−3.32241	−	46.4534i	−0.113096	−	1.58129i	−0.664651	−	0.747154i	$-0.731420\pi$
$863$	−3.32241	−	46.4534i	−0.113096	−	1.58129i	0.551555	−	0.834139i	$-0.314035\pi$
$864$	8.39370	+	28.5863i	0.285559	+	0.972526i
$865$	37.7723	+	9.02284i	1.28430	+	0.306786i
$866$	4.18063	+	6.50518i	0.142064	+	0.221055i
$867$	13.3227	+	24.3987i	0.452463	+	0.828625i
$868$	0.0628848	−	0.0840043i	0.00213445	−	0.00285129i
$869$	10.4633	+	4.77844i	0.354944	+	0.162097i
$870$	8.38639	+	0.170107i	0.284325	+	0.00576718i
$871$	0.640979	−	0.997383i	0.0217188	−	0.0337950i
$872$	17.3170	+	1.23853i	0.586426	+	0.0419420i
$873$	0.611918	+	0.611918i	0.0207103	+	0.0207103i
$874$	11.9398	−	19.5974i	0.403871	−	0.662892i
$875$	−0.887881	+	1.99979i	−0.0300158	+	0.0676053i
$876$	−12.1019	−	13.9663i	−0.408885	−	0.471879i
$877$	7.42725	+	34.1425i	0.250801	+	1.15291i	0.914396	+	0.404820i	$0.132666\pi$
$877$	7.42725	+	34.1425i	0.250801	+	1.15291i	−0.663596	+	0.748091i	$0.730970\pi$
$878$	−8.06300	−	10.7709i	−0.272113	−	0.363500i
$879$	6.19190	−	13.5584i	0.208848	−	0.457312i
$880$	−11.6445	+	3.16411i	−0.392538	+	0.106662i
$881$	2.81610	−	9.59077i	0.0948769	−	0.323121i	−0.898355	−	0.439271i	$-0.855237\pi$
$881$	2.81610	−	9.59077i	0.0948769	−	0.323121i	0.993232	+	0.116149i	$0.0370551\pi$
$882$	0.287004	+	0.0624340i	0.00966394	+	0.00210226i
$883$	19.9409	+	7.43756i	0.671064	+	0.250294i	0.661819	−	0.749664i	$-0.269785\pi$
$883$	19.9409	+	7.43756i	0.671064	+	0.250294i	0.00924435	+	0.999957i	$0.497057\pi$
$884$	0.191348	−	0.0561848i	0.00643573	−	0.00188970i
$885$	−33.3165	+	6.54291i	−1.11992	+	0.219938i
$886$	−9.50511	+	10.9695i	−0.319331	+	0.368527i
$887$	−15.3253	−	8.36823i	−0.514572	−	0.280978i	0.200909	−	0.979610i	$-0.435610\pi$
$887$	−15.3253	−	8.36823i	−0.514572	−	0.280978i	−0.715481	+	0.698632i	$0.753792\pi$
$888$	10.2614	−	27.5118i	0.344349	−	0.923236i
$889$	3.61103	−	2.32067i	0.121110	−	0.0778327i
$890$	6.45640	+	8.99955i	0.216419	+	0.301665i
$891$	−26.8777	+	3.86443i	−0.900436	+	0.129463i
$892$	−18.3789	+	6.85499i	−0.615372	+	0.229522i
$893$	−38.3916	+	28.7396i	−1.28473	+	0.961734i
$894$	11.6322	+	7.47554i	0.389038	+	0.250019i
$895$	18.7850	−	20.8108i	0.627913	−	0.695630i
$896$		−	2.20765i		−	0.0737523i
$897$	0.952392	+	0.677907i	0.0317994	+	0.0226346i
$898$	−12.4733	+	12.4733i	−0.416240	+	0.416240i
$899$	−0.875820	+	0.758902i	−0.0292102	+	0.0253108i
$900$	0.503367	+	0.170260i	0.0167789	+	0.00567532i
$901$	0.248883	−	1.73102i	0.00829149	−	0.0576686i
$902$	−6.40150	−	17.1631i	−0.213147	−	0.571469i
$903$	0.214755	+	0.160763i	0.00714659	+	0.00534987i
$904$	19.2888	+	5.66371i	0.641537	+	0.188372i
$905$	37.2199	+	44.7567i	1.23723	+	1.48776i
$906$	−0.463820	−	1.01562i	−0.0154094	−	0.0337419i
$907$	21.4410	−	39.2663i	0.711938	−	1.30382i	−0.231683	−	0.972791i	$-0.574423\pi$
$907$	21.4410	−	39.2663i	0.711938	−	1.30382i	0.943622	−	0.331026i	$-0.107395\pi$
$908$	8.22693	−	0.588402i	0.273020	−	0.0195268i
$909$	−0.559338	−	0.484669i	−0.0185521	−	0.0160755i
$910$	0.0145524	−	0.0367242i	0.000482408	−	0.00121740i
$911$	−22.6399	+	10.3393i	−0.750095	+	0.342557i	−0.753509	−	0.657437i	$-0.771640\pi$
$911$	−22.6399	+	10.3393i	−0.750095	+	0.342557i	0.00341443	+	0.999994i	$0.498913\pi$
$912$	−4.80123	+	22.0709i	−0.158985	+	0.730841i
$913$	−23.4739	+	12.8177i	−0.776872	+	0.424204i
$914$	−3.64184	−	25.3296i	−0.120461	−	0.837827i
$915$	−35.2304	+	18.3197i	−1.16468	+	0.605632i
$916$	26.2355	+	3.77210i	0.866847	+	0.124634i
$917$	3.51689	−	0.765053i	0.116138	−	0.0252643i
$918$	−0.208429	+	2.91421i	−0.00687917	+	0.0961834i
$919$	−24.9235			−0.822150			−0.411075	−	0.911602i	$-0.634847\pi$
$919$	−24.9235			−0.822150			−0.411075	+	0.911602i	$0.634847\pi$
$920$	−18.4340	+	16.0936i	−0.607752	+	0.530591i
$921$	37.2311			1.22681
$922$	−0.440932	+	6.16504i	−0.0145213	+	0.203035i
$923$	0.935343	−	0.203471i	0.0307872	−	0.00669734i
$924$	1.63641	+	0.235281i	0.0538340	+	0.00774016i
$925$	−21.2739	−	30.9604i	−0.699481	−	1.01797i
$926$	0.865711	+	6.02115i	0.0284490	+	0.197867i
$927$	−0.329562	+	0.179955i	−0.0108242	+	0.00591048i
$928$	−4.16376	+	19.1405i	−0.136682	+	0.628318i
$929$	−0.933878	+	0.426488i	−0.0306395	+	0.0139926i	−0.430676	−	0.902507i	$-0.641725\pi$
$929$	−0.933878	+	0.426488i	−0.0306395	+	0.0139926i	0.400036	+	0.916499i	$0.368998\pi$
$930$	−0.748260	+	0.323544i	−0.0245364	+	0.0106094i
$931$	39.6921	+	34.3934i	1.30086	+	1.12720i
$932$	−14.8097	+	1.05921i	−0.485107	+	0.0346956i
$933$	−13.8480	+	25.3607i	−0.453363	+	0.830273i
$934$	−1.71051	−	3.74550i	−0.0559697	−	0.122557i
$935$	−6.02872	−	0.554272i	−0.197160	−	0.0181266i
$936$	−0.0207275	−	0.00608614i	−0.000677500	−	0.000198932i
$937$	7.34182	+	5.49602i	0.239847	+	0.179547i	0.712439	−	0.701734i	$-0.247591\pi$
$937$	7.34182	+	5.49602i	0.239847	+	0.179547i	−0.472592	+	0.881281i	$0.656682\pi$
$938$	−0.361363	−	0.968851i	−0.0117989	−	0.0316341i
$939$	6.14929	−	42.7692i	0.200674	−	1.39572i
$940$	21.4350	−	7.50329i	0.699132	−	0.244730i
$941$	−11.2095	+	9.71311i	−0.365420	+	0.316638i	−0.818145	−	0.575012i	$-0.804997\pi$
$941$	−11.2095	+	9.71311i	−0.365420	+	0.316638i	0.452725	+	0.891650i	$0.350452\pi$
$942$	13.1463	−	13.1463i	0.428330	−	0.428330i
$943$	32.4776	+	30.9549i	1.05762	+	1.00803i
$944$		−	15.4974i		−	0.504397i
$945$	−1.70612	−	1.54003i	−0.0555000	−	0.0500973i
$946$	−1.31831	−	0.847224i	−0.0428618	−	0.0275456i
$947$	3.87889	−	2.90370i	0.126047	−	0.0943577i	−0.534394	−	0.845235i	$-0.679460\pi$
$947$	3.87889	−	2.90370i	0.126047	−	0.0943577i	0.660441	+	0.750878i	$0.270369\pi$
$948$	−9.55344	+	3.56325i	−0.310281	+	0.115729i
$949$	0.951349	−	0.136783i	0.0308821	−	0.00444017i
$950$	−16.2177	−	17.5897i	−0.526171	−	0.570686i
$951$	−35.3124	+	22.6939i	−1.14508	+	0.735900i
$952$	0.136874	−	0.366972i	0.00443610	−	0.0118936i
$953$	−22.1425	−	12.0907i	−0.717267	−	0.391658i	0.0787799	−	0.996892i	$-0.474898\pi$
$953$	−22.1425	−	12.0907i	−0.717267	−	0.391658i	−0.796047	+	0.605234i	$0.793079\pi$
$954$	−0.0550919	+	0.0635795i	−0.00178367	+	0.00205846i
$955$	23.0738	+	15.4987i	0.746652	+	0.501527i
$956$	6.05996	−	1.77936i	0.195993	−	0.0575487i
$957$	−17.1069	−	6.38054i	−0.552987	−	0.206254i
$958$	7.29605	+	1.58716i	0.235725	+	0.0512788i
$959$	0.414744	−	1.41249i	0.0133928	−	0.0456116i
$960$	−0.193735	+	0.338303i	−0.00625278	+	0.0109187i
$961$	−12.8311	+	28.0961i	−0.413906	+	0.906327i
$962$	0.406425	+	0.542920i	0.0131037	+	0.0175045i
$963$	0.246287	+	1.13216i	0.00793649	+	0.0364834i
$964$	6.39191	+	7.37666i	0.205870	+	0.237586i
$965$	−15.6037	+	19.9861i	−0.502302	+	0.643375i
$966$	0.971119	−	0.310648i	0.0312452	−	0.00999494i
$967$	−31.6406	−	31.6406i	−1.01749	−	1.01749i	−0.999844	−	0.0176482i	$-0.994382\pi$
$967$	−31.6406	−	31.6406i	−1.01749	−	1.01749i	−0.0176482	−	0.999844i	$-0.505618\pi$
$968$	3.34565	+	0.239285i	0.107533	+	0.00769092i
$969$	−6.12676	+	9.53343i	−0.196820	+	0.306258i
$970$	−0.374183	+	18.4474i	−0.0120143	+	0.592312i
$971$	3.89604	+	1.77926i	0.125030	+	0.0570993i	0.476948	−	0.878932i	$-0.341743\pi$
$971$	3.89604	+	1.77926i	0.125030	+	0.0570993i	−0.351918	+	0.936031i	$0.614470\pi$
$972$	−0.661753	+	0.883999i	−0.0212257	+	0.0283543i
$973$	−1.55520	−	2.84814i	−0.0498575	−	0.0913073i
$974$	−5.48819	−	8.53979i	−0.175853	−	0.273633i
$975$	0.952706	−	0.760128i	0.0305110	−	0.0243436i
$976$	−5.10629	−	17.3904i	−0.163448	−	0.556654i
$977$	−0.917337	−	12.8260i	−0.0293482	−	0.410342i	−0.990797	−	0.135357i	$-0.956782\pi$
$977$	−0.917337	−	12.8260i	−0.0293482	−	0.410342i	0.961449	−	0.274984i	$-0.0886727\pi$
$978$	0.388172	+	5.42736i	0.0124124	+	0.173548i
$979$	−6.79218	−	23.1320i	−0.217079	−	0.739303i
$980$	−13.0193	−	21.1914i	−0.415887	−	0.676933i
$981$	0.273609	+	0.425744i	0.00873567	+	0.0135930i
$982$	−1.56189	−	2.86040i	−0.0498420	−	0.0912789i
$983$	−3.07935	+	4.11353i	−0.0982159	+	0.131201i	−0.846957	−	0.531662i	$-0.821568\pi$
$983$	−3.07935	+	4.11353i	−0.0982159	+	0.131201i	0.748741	+	0.662863i	$0.230659\pi$
$984$	33.2593	+	15.1890i	1.06027	+	0.484209i
$985$	11.1999	−	10.7545i	0.356857	−	0.342668i
$986$	−1.03852	+	1.61597i	−0.0330733	+	0.0514630i
$987$	−2.12532	−	0.152006i	−0.0676497	−	0.00483840i
$988$	−1.21299	−	1.21299i	−0.0385905	−	0.0385905i
$989$	3.81118	+	0.454906i	0.121189	+	0.0144652i
$990$	0.229560	+	0.179224i	0.00729590	+	0.00569612i
$991$	2.02548	+	2.33753i	0.0643416	+	0.0742541i	0.787008	−	0.616943i	$-0.211629\pi$
$991$	2.02548	+	2.33753i	0.0643416	+	0.0742541i	−0.722666	+	0.691197i	$0.757084\pi$
$992$	−0.404663	−	1.86021i	−0.0128481	−	0.0590616i
$993$	−0.896261	−	1.19726i	−0.0284420	−	0.0379940i
$994$	0.346816	−	0.759421i	0.0110003	−	0.0240874i
$995$	−11.8783	−	43.7145i	−0.376568	−	1.38584i
$996$	6.67922	−	22.7473i	0.211639	−	0.720777i
$997$	35.3791	+	7.69626i	1.12047	+	0.243743i	0.734393	−	0.678724i	$-0.237467\pi$
$997$	35.3791	+	7.69626i	1.12047	+	0.243743i	0.386075	+	0.922467i	$0.373830\pi$
$998$	−20.2441	−	7.55066i	−0.640816	−	0.239012i
$999$	37.8610	−	11.1170i	1.19787	−	0.351726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.102.4	yes	200
5.2	odd	4		575.2.r.b.493.4		200
5.3	odd	4	inner	115.2.l.a.33.7	yes	200
5.4	even	2		575.2.r.b.332.7		200
23.7	odd	22	inner	115.2.l.a.7.7	✓	200
115.7	even	44		575.2.r.b.168.7		200
115.53	even	44	inner	115.2.l.a.53.4	yes	200
115.99	odd	22		575.2.r.b.7.4		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.7	✓	200	23.7	odd	22	inner
115.2.l.a.33.7	yes	200	5.3	odd	4	inner
115.2.l.a.53.4	yes	200	115.53	even	44	inner
115.2.l.a.102.4	yes	200	1.1	even	1	trivial
575.2.r.b.7.4		200	115.99	odd	22
575.2.r.b.168.7		200	115.7	even	44
575.2.r.b.332.7		200	5.4	even	2
575.2.r.b.493.4		200	5.2	odd	4

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0452482 + 0.632652i) q^{2} +(-1.67360 + 0.364069i) q^{3} +(1.58144 + 0.227377i) q^{4} +(-0.673353 + 2.13227i) q^{5} +(-0.154602 - 1.07528i) q^{6} +(-0.171765 + 0.0937908i) q^{7} +(-0.485055 + 2.22976i) q^{8} +(-0.0605071 + 0.0276327i) q^{9} +(-1.31852 - 0.522480i) q^{10} +(2.33306 + 2.02161i) q^{11} +(-2.72948 + 0.195216i) q^{12} +(0.0682068 - 0.124911i) q^{13} +(-0.0515649 - 0.112911i) q^{14} +(0.350628 - 3.81372i) q^{15} +(1.67726 + 0.492487i) q^{16} +(0.702107 + 0.525590i) q^{17} +(-0.0147440 - 0.0395303i) q^{18} +(1.07365 - 7.46738i) q^{19} +(-1.54970 + 3.21896i) q^{20} +(0.253320 - 0.219503i) q^{21} +(-1.38454 + 1.38454i) q^{22} +(1.56765 - 4.53238i) q^{23} -3.90832i q^{24} +(-4.09319 - 2.87155i) q^{25} +(0.0759392 + 0.0488032i) q^{26} +(4.20456 - 3.14750i) q^{27} +(-0.292962 + 0.109269i) q^{28} +(3.41800 - 0.491434i) q^{29} +(2.39689 + 0.394389i) q^{30} +(-0.282325 + 0.181439i) q^{31} +(-1.98236 + 5.31490i) q^{32} +(-4.64062 - 2.53397i) q^{33} +(-0.364285 + 0.420407i) q^{34} +(-0.0843292 - 0.429405i) q^{35} +(-0.101971 + 0.0299415i) q^{36} +(7.03930 + 2.62552i) q^{37} +(4.67567 + 1.01713i) q^{38} +(-0.0686744 + 0.233884i) q^{39} +(-4.42785 - 2.53569i) q^{40} +(-3.88633 + 8.50988i) q^{41} +(0.127407 + 0.170195i) q^{42} +(0.170122 + 0.782038i) q^{43} +(3.22994 + 3.72754i) q^{44} +(-0.0181778 - 0.147624i) q^{45} +(2.79649 + 1.19686i) q^{46} +(-4.49497 - 4.49497i) q^{47} +(-2.98636 - 0.213588i) q^{48} +(-3.76378 + 5.85655i) q^{49} +(2.00190 - 2.45963i) q^{50} +(-1.36640 - 0.624012i) q^{51} +(0.136267 - 0.182031i) q^{52} +(-0.955623 - 1.75009i) q^{53} +(1.80102 + 2.80244i) q^{54} +(-5.88161 + 3.61347i) q^{55} +(-0.125816 - 0.428489i) q^{56} +(0.921788 + 12.8883i) q^{57} +(0.156248 + 2.18464i) q^{58} +(-2.49768 - 8.50633i) q^{59} +(1.42165 - 5.95145i) q^{60} +(-5.60557 - 8.72243i) q^{61} +(-0.102013 - 0.186823i) q^{62} +(0.00780132 - 0.0104213i) q^{63} +(-0.0925946 - 0.0422865i) q^{64} +(0.220418 + 0.229545i) q^{65} +(1.81310 - 2.82124i) q^{66} +(8.30923 + 0.594288i) q^{67} +(0.990833 + 0.990833i) q^{68} +(-0.973521 + 8.15612i) q^{69} +(0.275480 - 0.0339213i) q^{70} +(4.40447 + 5.08303i) q^{71} +(-0.0322650 - 0.148320i) q^{72} +(4.04711 + 5.40630i) q^{73} +(-1.97956 + 4.33463i) q^{74} +(7.89580 + 3.31562i) q^{75} +(3.39582 - 11.5651i) q^{76} +(-0.590347 - 0.128422i) q^{77} +(-0.144860 - 0.0540298i) q^{78} +(3.57517 - 1.04977i) q^{79} +(-2.17950 + 3.24475i) q^{80} +(-5.76017 + 6.64759i) q^{81} +(-5.20795 - 2.84375i) q^{82} +(-3.02763 + 8.11740i) q^{83} +(0.450520 - 0.289532i) q^{84} +(-1.59347 + 1.14318i) q^{85} +(-0.502456 + 0.0722422i) q^{86} +(-5.54144 + 2.06685i) q^{87} +(-5.63937 + 4.22158i) q^{88} +(-6.56977 - 4.22214i) q^{89} +(0.0942173 - 0.00482048i) q^{90} +0.0278526i q^{91} +(3.50971 - 6.81125i) q^{92} +(0.406442 - 0.406442i) q^{93} +(3.04714 - 2.64036i) q^{94} +(15.1996 + 7.31749i) q^{95} +(1.38268 - 9.61674i) q^{96} +(-4.54643 - 12.1894i) q^{97} +(-3.53486 - 2.64616i) q^{98} +(-0.197029 - 0.0578530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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