LMFDB - Embedded newform 175.2.x.a.103.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.18
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50521 + 0.131292i) q^{2} +(-0.971802 - 1.20007i) q^{3} +(4.26979 + 0.448773i) q^{4} +(-1.53208 + 1.62872i) q^{5} +(-2.27701 - 3.13403i) q^{6} +(2.61863 - 0.377880i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.127953 - 0.601973i) q^{9} +O(q^{10})$	\(q+(2.50521 + 0.131292i) q^{2} +(-0.971802 - 1.20007i) q^{3} +(4.26979 + 0.448773i) q^{4} +(-1.53208 + 1.62872i) q^{5} +(-2.27701 - 3.13403i) q^{6} +(2.61863 - 0.377880i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.127953 - 0.601973i) q^{9} +(-4.05202 + 3.87914i) q^{10} +(-5.16938 + 1.09879i) q^{11} +(-3.61083 - 5.56019i) q^{12} +(-2.31369 - 1.17888i) q^{13} +(6.60982 - 0.602863i) q^{14} +(3.44346 + 0.255818i) q^{15} +(5.71816 + 1.21543i) q^{16} +(0.412480 + 1.07455i) q^{17} +(0.399585 - 1.49127i) q^{18} +(0.136615 + 1.29981i) q^{19} +(-7.27259 + 6.26674i) q^{20} +(-2.99827 - 2.77532i) q^{21} +(-13.0946 + 2.07399i) q^{22} +(-0.453175 + 8.64709i) q^{23} +(-4.44200 - 7.69377i) q^{24} +(-0.305462 - 4.99066i) q^{25} +(-5.64150 - 3.25712i) q^{26} +(-4.97446 + 2.53461i) q^{27} +(11.3506 - 0.438300i) q^{28} +(1.59083 - 2.18958i) q^{29} +(8.59301 + 1.09298i) q^{30} +(2.42584 - 5.44852i) q^{31} +(3.05145 + 0.817633i) q^{32} +(6.34224 + 5.13584i) q^{33} +(0.892268 + 2.74612i) q^{34} +(-3.39648 + 4.84395i) q^{35} +(0.816484 - 2.51288i) q^{36} +(2.70277 - 1.75520i) q^{37} +(0.171595 + 3.27423i) q^{38} +(0.833698 + 3.92224i) q^{39} +(-10.1715 + 7.87600i) q^{40} +(6.10496 - 1.98362i) q^{41} +(-7.14692 - 7.34642i) q^{42} +(-3.37188 - 3.37188i) q^{43} +(-22.5653 + 2.37171i) q^{44} +(0.784411 + 1.13067i) q^{45} +(-2.27060 + 21.6033i) q^{46} +(6.65848 + 2.55595i) q^{47} +(-4.09831 - 8.04338i) q^{48} +(6.71441 - 1.97905i) q^{49} +(-0.110010 - 12.5428i) q^{50} +(0.888688 - 1.53925i) q^{51} +(-9.34992 - 6.07191i) q^{52} +(2.65234 - 2.14782i) q^{53} +(-12.7948 + 5.69663i) q^{54} +(6.13029 - 10.1029i) q^{55} +(15.2199 + 0.209504i) q^{56} +(1.42711 - 1.42711i) q^{57} +(4.27283 - 5.27650i) q^{58} +(1.17763 - 1.30789i) q^{59} +(14.5881 + 2.63762i) q^{60} +(3.10590 - 2.79657i) q^{61} +(6.79258 - 13.3312i) q^{62} +(0.107588 - 1.62469i) q^{63} +(-3.58241 - 1.16399i) q^{64} +(5.46483 - 1.96221i) q^{65} +(15.2143 + 13.6991i) q^{66} +(0.225467 - 0.0865487i) q^{67} +(1.27897 + 4.77320i) q^{68} +(10.8176 - 7.85941i) q^{69} +(-9.14488 + 11.6892i) q^{70} +(-8.50997 - 6.18285i) q^{71} +(1.26883 - 3.30543i) q^{72} +(-6.73286 + 10.3677i) q^{73} +(7.00145 - 4.04229i) q^{74} +(-5.69232 + 5.21651i) q^{75} +5.61123i q^{76} +(-13.1215 + 4.83072i) q^{77} +(1.57363 + 9.93549i) q^{78} +(1.88229 + 4.22770i) q^{79} +(-10.7403 + 7.45114i) q^{80} +(6.18926 + 2.75564i) q^{81} +(15.5546 - 4.16785i) q^{82} +(1.46786 - 9.26772i) q^{83} +(-11.5565 - 13.1956i) q^{84} +(-2.38209 - 0.974476i) q^{85} +(-8.00457 - 8.88998i) q^{86} +(-4.17363 + 0.218731i) q^{87} +(-30.3628 + 1.59125i) q^{88} +(-3.01084 - 3.34388i) q^{89} +(1.81667 + 2.93556i) q^{90} +(-6.50417 - 2.21276i) q^{91} +(-5.81555 + 36.7179i) q^{92} +(-8.89606 + 2.38369i) q^{93} +(16.3453 + 7.27740i) q^{94} +(-2.32633 - 1.76890i) q^{95} +(-1.98418 - 4.45654i) q^{96} +(1.20511 + 7.60880i) q^{97} +(17.0808 - 4.07639i) q^{98} +3.25242i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	2.50521	+	0.131292i	1.77145	+	0.0928378i	0.909898	−	0.414831i	$-0.136159\pi$
$2$	2.50521	+	0.131292i	1.77145	+	0.0928378i	0.861552	+	0.507669i	$0.169493\pi$
$3$	−0.971802	−	1.20007i	−0.561070	−	0.692864i	0.415124	−	0.909765i	$-0.363738\pi$
$3$	−0.971802	−	1.20007i	−0.561070	−	0.692864i	−0.976194	+	0.216901i	$0.930405\pi$
$4$	4.26979	+	0.448773i	2.13490	+	0.224387i
$5$	−1.53208	+	1.62872i	−0.685167	+	0.728386i
$5$	−1.53208	+	1.62872i	−0.685167	+	0.728386i
$6$	−2.27701	−	3.13403i	−0.929584	−	1.27946i
$7$	2.61863	−	0.377880i	0.989748	−	0.142825i
$7$	2.61863	−	0.377880i	0.989748	−	0.142825i
$8$	5.68228	+	0.899985i	2.00899	+	0.318193i
$9$	0.127953	−	0.601973i	0.0426511	−	0.200658i
$10$	−4.05202	+	3.87914i	−1.28136	+	1.22669i
$11$	−5.16938	+	1.09879i	−1.55863	+	0.331296i	−0.904964	−	0.425489i	$-0.860102\pi$
$11$	−5.16938	+	1.09879i	−1.55863	+	0.331296i	−0.653664	+	0.756785i	$0.726769\pi$
$12$	−3.61083	−	5.56019i	−1.04236	−	1.60509i
$13$	−2.31369	−	1.17888i	−0.641702	−	0.326963i	0.102683	−	0.994714i	$-0.467257\pi$
$13$	−2.31369	−	1.17888i	−0.641702	−	0.326963i	−0.744385	+	0.667751i	$0.767257\pi$
$14$	6.60982	−	0.602863i	1.76655	−	0.161122i
$15$	3.44346	+	0.255818i	0.889099	+	0.0660518i
$16$	5.71816	+	1.21543i	1.42954	+	0.303858i
$17$	0.412480	+	1.07455i	0.100041	+	0.260616i	0.974462	−	0.224552i	$-0.0720919\pi$
$17$	0.412480	+	1.07455i	0.100041	+	0.260616i	−0.874421	+	0.485168i	$0.838759\pi$
$18$	0.399585	−	1.49127i	0.0941830	−	0.351496i
$19$	0.136615	+	1.29981i	0.0313417	+	0.298197i	0.998953	+	0.0457513i	$0.0145682\pi$
$19$	0.136615	+	1.29981i	0.0313417	+	0.298197i	−0.967611	+	0.252445i	$0.918765\pi$
$20$	−7.27259	+	6.26674i	−1.62620	+	1.40129i
$21$	−2.99827	−	2.77532i	−0.654276	−	0.605625i
$22$	−13.0946	+	2.07399i	−2.79179	+	0.442176i
$23$	−0.453175	+	8.64709i	−0.0944935	+	1.80304i	0.382311	+	0.924034i	$0.375128\pi$
$23$	−0.453175	+	8.64709i	−0.0944935	+	1.80304i	−0.476805	+	0.879009i	$0.658205\pi$
$24$	−4.44200	−	7.69377i	−0.906720	−	1.57048i
$25$	−0.305462	−	4.99066i	−0.0610924	−	0.998132i
$26$	−5.64150	−	3.25712i	−1.10639	−	0.638774i
$27$	−4.97446	+	2.53461i	−0.957335	+	0.487786i
$28$	11.3506	−	0.438300i	2.14506	−	0.0828309i
$29$	1.59083	−	2.18958i	0.295409	−	0.406595i	−0.635353	−	0.772222i	$-0.719145\pi$
$29$	1.59083	−	2.18958i	0.295409	−	0.406595i	0.930762	+	0.365627i	$0.119145\pi$
$30$	8.59301	+	1.09298i	1.56886	+	0.199549i
$31$	2.42584	−	5.44852i	0.435693	−	0.978583i	−0.553619	−	0.832770i	$-0.686754\pi$
$31$	2.42584	−	5.44852i	0.435693	−	0.978583i	0.989312	−	0.145813i	$-0.0465797\pi$
$32$	3.05145	+	0.817633i	0.539425	+	0.144538i
$33$	6.34224	+	5.13584i	1.10404	+	0.894036i
$34$	0.892268	+	2.74612i	0.153023	+	0.470955i
$35$	−3.39648	+	4.84395i	−0.574111	+	0.818778i
$36$	0.816484	−	2.51288i	0.136081	−	0.418813i
$37$	2.70277	−	1.75520i	0.444333	−	0.288553i	−0.303015	−	0.952986i	$-0.597993\pi$
$37$	2.70277	−	1.75520i	0.444333	−	0.288553i	0.747348	+	0.664433i	$0.231327\pi$
$38$	0.171595	+	3.27423i	0.0278364	+	0.531151i
$39$	0.833698	+	3.92224i	0.133499	+	0.628061i
$40$	−10.1715	+	7.87600i	−1.60826	+	1.24530i
$41$	6.10496	−	1.98362i	0.953434	−	0.309790i	0.209324	−	0.977846i	$-0.432874\pi$
$41$	6.10496	−	1.98362i	0.953434	−	0.309790i	0.744110	+	0.668057i	$0.232874\pi$
$42$	−7.14692	−	7.34642i	−1.10279	−	1.13358i
$43$	−3.37188	−	3.37188i	−0.514207	−	0.514207i	0.401605	−	0.915813i	$-0.368452\pi$
$43$	−3.37188	−	3.37188i	−0.514207	−	0.514207i	−0.915813	+	0.401605i	$0.868452\pi$
$44$	−22.5653	+	2.37171i	−3.40185	+	0.357549i
$45$	0.784411	+	1.13067i	0.116933	+	0.168551i
$46$	−2.27060	+	21.6033i	−0.334781	+	3.18523i
$47$	6.65848	+	2.55595i	0.971239	+	0.372824i	0.791688	−	0.610925i	$-0.209202\pi$
$47$	6.65848	+	2.55595i	0.971239	+	0.372824i	0.179551	+	0.983749i	$0.442536\pi$
$48$	−4.09831	−	8.04338i	−0.591539	−	1.16096i
$49$	6.71441	−	1.97905i	0.959202	−	0.282722i
$50$	−0.110010	−	12.5428i	−0.0155578	−	1.77381i
$51$	0.888688	−	1.53925i	0.124441	−	0.215538i
$52$	−9.34992	−	6.07191i	−1.29660	−	0.842022i
$53$	2.65234	−	2.14782i	0.364326	−	0.295026i	−0.429624	−	0.903008i	$-0.641354\pi$
$53$	2.65234	−	2.14782i	0.364326	−	0.295026i	0.793951	+	0.607982i	$0.208021\pi$
$54$	−12.7948	+	5.69663i	−1.74116	+	0.775213i
$55$	6.13029	−	10.1029i	0.826608	−	1.36228i
$56$	15.2199	+	0.209504i	2.03384	+	0.0279961i
$57$	1.42711	−	1.42711i	0.189025	−	0.189025i
$58$	4.27283	−	5.27650i	0.561050	−	0.692839i
$59$	1.17763	−	1.30789i	0.153315	−	0.170273i	−0.661595	−	0.749862i	$-0.730120\pi$
$59$	1.17763	−	1.30789i	0.153315	−	0.170273i	0.814909	+	0.579588i	$0.196787\pi$
$60$	14.5881	+	2.63762i	1.88331	+	0.340516i
$61$	3.10590	−	2.79657i	0.397670	−	0.358064i	−0.445900	−	0.895083i	$-0.647116\pi$
$61$	3.10590	−	2.79657i	0.397670	−	0.358064i	0.843570	+	0.537019i	$0.180450\pi$
$62$	6.79258	−	13.3312i	0.862658	−	1.69306i
$63$	0.107588	−	1.62469i	0.0135549	−	0.204692i
$64$	−3.58241	−	1.16399i	−0.447801	−	0.145499i
$65$	5.46483	−	1.96221i	0.677829	−	0.243382i
$66$	15.2143	+	13.6991i	1.87276	+	1.68624i
$67$	0.225467	−	0.0865487i	0.0275452	−	0.0105736i	−0.344556	−	0.938766i	$-0.611971\pi$
$67$	0.225467	−	0.0865487i	0.0275452	−	0.0105736i	0.372102	+	0.928192i	$0.378637\pi$
$68$	1.27897	+	4.77320i	0.155098	+	0.578835i
$69$	10.8176	−	7.85941i	1.30228	−	0.946162i
$70$	−9.14488	+	11.6892i	−1.09302	+	1.39713i
$71$	−8.50997	−	6.18285i	−1.00995	−	0.733770i	−0.0457493	−	0.998953i	$-0.514568\pi$
$71$	−8.50997	−	6.18285i	−1.00995	−	0.733770i	−0.964198	+	0.265183i	$0.914568\pi$
$72$	1.26883	−	3.30543i	0.149534	−	0.389548i
$73$	−6.73286	+	10.3677i	−0.788022	+	1.21345i	0.185001	+	0.982738i	$0.440771\pi$
$73$	−6.73286	+	10.3677i	−0.788022	+	1.21345i	−0.973023	+	0.230709i	$0.925896\pi$
$74$	7.00145	−	4.04229i	0.813902	−	0.469907i
$75$	−5.69232	+	5.21651i	−0.657292	+	0.602351i
$76$			5.61123i			0.643652i
$77$	−13.1215	+	4.83072i	−1.49533	+	0.550511i
$78$	1.57363	+	9.93549i	0.178178	+	1.12497i
$79$	1.88229	+	4.22770i	0.211775	+	0.475653i	0.987932	−	0.154885i	$-0.0495007\pi$
$79$	1.88229	+	4.22770i	0.211775	+	0.475653i	−0.776158	+	0.630539i	$0.782834\pi$
$80$	−10.7403	+	7.45114i	−1.20080	+	0.833063i
$81$	6.18926	+	2.75564i	0.687696	+	0.306182i
$82$	15.5546	−	4.16785i	1.71772	−	0.460262i
$83$	1.46786	−	9.26772i	0.161119	−	1.01726i	−0.766094	−	0.642729i	$-0.777802\pi$
$83$	1.46786	−	9.26772i	0.161119	−	1.01726i	0.927213	−	0.374536i	$-0.122198\pi$
$84$	−11.5565	−	13.1956i	−1.26092	−	1.43976i
$85$	−2.38209	−	0.974476i	−0.258374	−	0.105697i
$86$	−8.00457	−	8.88998i	−0.863155	−	0.958631i
$87$	−4.17363	+	0.218731i	−0.447460	+	0.0234504i
$88$	−30.3628	+	1.59125i	−3.23668	+	0.169627i
$89$	−3.01084	−	3.34388i	−0.319148	−	0.354450i	0.562129	−	0.827050i	$-0.309982\pi$
$89$	−3.01084	−	3.34388i	−0.319148	−	0.354450i	−0.881277	+	0.472599i	$0.843316\pi$
$90$	1.81667	+	2.93556i	0.191493	+	0.309435i
$91$	−6.50417	−	2.21276i	−0.681822	−	0.231960i
$92$	−5.81555	+	36.7179i	−0.606313	+	3.82811i
$93$	−8.89606	+	2.38369i	−0.922479	+	0.247177i
$94$	16.3453	+	7.27740i	1.68589	+	0.750606i
$95$	−2.32633	−	1.76890i	−0.238677	−	0.181486i
$96$	−1.98418	−	4.45654i	−0.202510	−	0.454844i
$97$	1.20511	+	7.60880i	0.122361	+	0.772556i	0.970201	+	0.242303i	$0.0779029\pi$
$97$	1.20511	+	7.60880i	0.122361	+	0.772556i	−0.847840	+	0.530253i	$0.822097\pi$
$98$	17.0808	−	4.07639i	1.72543	−	0.411778i
$99$			3.25242i			0.326881i
$100$	0.935416	−	21.4462i	0.0935416	−	2.14462i
$101$	8.71392	−	5.03098i	0.867067	−	0.500602i	0.000694788	−	1.00000i	$-0.499779\pi$
$101$	8.71392	−	5.03098i	0.867067	−	0.500602i	0.866373	+	0.499398i	$0.166446\pi$
$102$	2.42844	−	3.73947i	0.240451	−	0.370263i
$103$	−4.87969	+	12.7120i	−0.480811	+	1.25255i	0.451945	+	0.892046i	$0.350730\pi$
$103$	−4.87969	+	12.7120i	−0.480811	+	1.25255i	−0.932756	+	0.360509i	$0.882603\pi$
$104$	−12.0861	−	8.78103i	−1.18514	−	0.861051i
$105$	9.11382	−	0.631326i	0.889418	−	0.0616111i
$106$	6.92665	−	5.03251i	0.672776	−	0.488800i
$107$	5.12202	+	19.1156i	0.495164	+	1.84798i	0.529108	+	0.848555i	$0.322527\pi$
$107$	5.12202	+	19.1156i	0.495164	+	1.84798i	−0.0339437	+	0.999424i	$0.510807\pi$
$108$	−22.3774	+	8.58987i	−2.15326	+	0.826560i
$109$	5.38155	+	4.84557i	0.515459	+	0.464121i	0.885331	−	0.464961i	$-0.153932\pi$
$109$	5.38155	+	4.84557i	0.515459	+	0.464121i	−0.369872	+	0.929083i	$0.620598\pi$
$110$	16.6841	−	24.5050i	1.59077	−	2.33646i
$111$	−4.73293	−	1.53782i	−0.449230	−	0.145964i
$112$	15.4330	+	1.02198i	1.45828	+	0.0965685i
$113$	0.227796	−	0.447075i	0.0214293	−	0.0420573i	−0.880044	−	0.474893i	$-0.842487\pi$
$113$	0.227796	−	0.447075i	0.0214293	−	0.0420573i	0.901473	+	0.432835i	$0.142487\pi$
$114$	3.76257	−	3.38783i	0.352397	−	0.317299i
$115$	−13.3894	−	13.9861i	−1.24857	−	1.30421i
$116$	7.77512	−	8.63515i	0.721902	−	0.801753i
$117$	−1.00570	+	1.24194i	−0.0929771	+	0.114817i
$118$	3.12193	−	3.12193i	0.287397	−	0.287397i
$119$	1.48618	+	2.65797i	0.136238	+	0.243655i
$120$	19.3365	+	4.55269i	1.76517	+	0.415602i
$121$	15.4662	−	6.88599i	1.40602	−	0.625999i
$122$	8.14810	−	6.59820i	0.737694	−	0.597373i
$123$	−8.31330	−	5.39872i	−0.749585	−	0.486786i
$124$	12.8030	−	22.1754i	1.14974	−	1.99141i
$125$	8.59638	+	7.14858i	0.768884	+	0.639388i
$126$	0.482842	−	4.05607i	0.0430149	−	0.361344i
$127$	0.723490	+	1.41993i	0.0641993	+	0.125998i	0.920876	−	0.389855i	$-0.127475\pi$
$127$	0.723490	+	1.41993i	0.0641993	+	0.125998i	−0.856677	+	0.515853i	$0.827475\pi$
$128$	−14.7204	−	5.65063i	−1.30111	−	0.499449i
$129$	−0.769711	+	7.32332i	−0.0677693	+	0.644782i
$130$	13.9482	−	4.19826i	1.22333	−	0.368211i
$131$	−18.1424	+	1.90684i	−1.58511	+	0.166602i	−0.855699	−	0.517474i	$-0.826872\pi$
$131$	−18.1424	+	1.90684i	−1.58511	+	0.166602i	−0.729411	+	0.684076i	$0.760206\pi$
$132$	24.7752	+	24.7752i	2.15641	+	2.15641i
$133$	0.848917	+	3.35209i	0.0736105	+	0.290663i
$134$	0.576205	−	0.187220i	0.0497765	−	0.0161734i
$135$	3.49309	−	11.9852i	0.300637	−	1.03152i
$136$	1.37675	+	6.47710i	0.118055	+	0.555407i
$137$	0.447778	+	8.54412i	0.0382563	+	0.729973i	0.948669	+	0.316271i	$0.102431\pi$
$137$	0.447778	+	8.54412i	0.0382563	+	0.729973i	−0.910412	+	0.413702i	$0.864236\pi$
$138$	28.1321	−	18.2692i	2.39476	−	1.55518i
$139$	−1.62016	+	4.98635i	−0.137420	+	0.422937i	−0.995959	−	0.0898130i	$-0.971373\pi$
$139$	−1.62016	+	4.98635i	−0.137420	+	0.422937i	0.858538	+	0.512750i	$0.171373\pi$
$140$	−16.6761	+	19.1584i	−1.40939	+	1.61918i
$141$	−3.40339	−	10.4746i	−0.286617	−	0.882116i
$142$	−20.5075	−	16.6066i	−1.72095	−	1.39360i
$143$	13.2557	+	3.55185i	1.10850	+	0.297021i
$144$	1.46332	−	3.28666i	0.121943	−	0.273888i
$145$	1.12895	+	5.94563i	0.0937540	+	0.493757i
$146$	−18.2284	+	25.0893i	−1.50859	+	2.07640i
$147$	−8.90009	−	6.13455i	−0.734067	−	0.505969i
$148$	12.3280	−	6.28141i	1.01335	−	0.516329i
$149$	−3.28424	−	1.89616i	−0.269056	−	0.155339i	0.359403	−	0.933183i	$-0.382980\pi$
$149$	−3.28424	−	1.89616i	−0.269056	−	0.155339i	−0.628458	+	0.777843i	$0.716314\pi$
$150$	−14.9453	+	12.3211i	−1.22028	+	1.00601i
$151$	−4.87556	−	8.44472i	−0.396768	−	0.687222i	0.596557	−	0.802570i	$-0.296535\pi$
$151$	−4.87556	−	8.44472i	−0.396768	−	0.687222i	−0.993325	+	0.115349i	$0.963202\pi$
$152$	−0.393521	+	7.50884i	−0.0319188	+	0.609047i
$153$	0.699626	−	0.110810i	0.0565614	−	0.00895845i
$154$	−33.5063	+	10.3792i	−2.70001	+	0.836381i
$155$	5.15754	+	12.2986i	0.414263	+	0.987845i
$156$	1.79952	+	17.1213i	0.144077	+	1.37080i
$157$	4.24841	−	15.8553i	0.339060	−	1.26539i	−0.560340	−	0.828263i	$-0.689329\pi$
$157$	4.24841	−	15.8553i	0.339060	−	1.26539i	0.899400	−	0.437127i	$-0.144004\pi$
$158$	4.16047	+	10.8384i	0.330990	+	0.862257i
$159$	−5.15509	−	1.09575i	−0.408825	−	0.0868985i
$160$	−6.00676	+	3.71728i	−0.474876	+	0.293876i
$161$	2.08087	+	22.8147i	0.163995	+	1.79805i
$162$	15.1436	+	7.71605i	1.18979	+	0.606230i
$163$	−3.33023	−	5.12810i	−0.260843	−	0.401664i	0.683848	−	0.729625i	$-0.260305\pi$
$163$	−3.33023	−	5.12810i	−0.260843	−	0.401664i	−0.944691	+	0.327961i	$0.893639\pi$
$164$	26.9571	−	5.72991i	2.10500	−	0.447431i
$165$	−18.0817	+	2.46121i	−1.40766	+	0.191605i
$166$	4.89408	−	23.0249i	0.379855	−	1.78708i
$167$	−19.8065	−	3.13704i	−1.53267	−	0.242752i	−0.667647	−	0.744478i	$-0.732698\pi$
$167$	−19.8065	−	3.13704i	−1.53267	−	0.242752i	−0.865026	+	0.501726i	$0.832698\pi$
$168$	−14.5393	−	18.4686i	−1.12173	−	1.42488i
$169$	−3.67782	−	5.06208i	−0.282909	−	0.389391i
$170$	−5.83969	−	2.75402i	−0.447883	−	0.211224i
$171$	0.799931	+	0.0840761i	0.0611723	+	0.00642946i
$172$	−12.8840	−	15.9105i	−0.982398	−	1.21316i
$173$	−11.9566	−	0.626618i	−0.909042	−	0.0476409i	−0.407920	−	0.913018i	$-0.633746\pi$
$173$	−11.9566	−	0.626618i	−0.909042	−	0.0476409i	−0.501122	+	0.865377i	$0.667079\pi$
$174$	−10.4845			−0.794831
$175$	−2.68576	−	12.9532i	−0.203025	−	0.979174i
$176$	−30.8948			−2.32879
$177$	−2.71400	−	0.142234i	−0.203996	−	0.0106910i
$178$	−7.10376	−	8.77241i	−0.532449	−	0.657520i
$179$	22.0600	+	2.31860i	1.64884	+	0.173300i	0.882885	−	0.469590i	$-0.155598\pi$
$179$	22.0600	+	2.31860i	1.64884	+	0.173300i	0.765958	+	0.642890i	$0.222265\pi$
$180$	2.84186	+	5.17976i	0.211820	+	0.386076i
$181$	1.61496	+	2.22281i	0.120039	+	0.165220i	0.864808	−	0.502103i	$-0.167440\pi$
$181$	1.61496	+	2.22281i	0.120039	+	0.165220i	−0.744769	+	0.667323i	$0.767440\pi$
$182$	−16.0038	−	6.39737i	−1.18628	−	0.474205i
$183$	−6.37441	−	1.00961i	−0.471210	−	0.0746323i
$184$	−10.3573	+	48.7273i	−0.763552	+	3.59223i
$185$	−1.28213	+	7.09117i	−0.0942641	+	0.521353i
$186$	−22.5995	+	4.80366i	−1.65707	+	0.352222i
$187$	−3.31296	−	5.10151i	−0.242268	−	0.373060i
$188$	27.2833	+	13.9015i	1.98984	+	1.01387i
$189$	−12.0685	+	8.51695i	−0.877852	+	0.619517i
$190$	−5.59571	−	4.73690i	−0.405955	−	0.343651i
$191$	−21.0814	−	4.48100i	−1.52540	−	0.324234i	−0.632525	−	0.774540i	$-0.717982\pi$
$191$	−21.0814	−	4.48100i	−1.52540	−	0.324234i	−0.892874	+	0.450306i	$0.851315\pi$
$192$	2.08451	+	5.43033i	0.150436	+	0.391900i
$193$	1.63297	−	6.09432i	0.117544	−	0.438679i	−0.881921	−	0.471397i	$-0.843750\pi$
$193$	1.63297	−	6.09432i	0.117544	−	0.438679i	0.999465	+	0.0327186i	$0.0104165\pi$
$194$	2.02009	+	19.2198i	0.145034	+	1.37990i
$195$	−7.66553	−	4.65133i	−0.548940	−	0.333088i
$196$	29.5573	−	5.43690i	2.11124	−	0.388350i
$197$	−1.85729	+	0.294166i	−0.132326	+	0.0209584i	−0.222246	−	0.974991i	$-0.571339\pi$
$197$	−1.85729	+	0.294166i	−0.132326	+	0.0209584i	0.0899199	+	0.995949i	$0.471339\pi$
$198$	−0.427019	+	8.14800i	−0.0303469	+	0.579053i
$199$	−6.41745	−	11.1153i	−0.454921	−	0.787946i	0.543763	−	0.839239i	$-0.316999\pi$
$199$	−6.41745	−	11.1153i	−0.454921	−	0.787946i	−0.998684	+	0.0512931i	$0.983666\pi$
$200$	2.75580	−	28.6332i	0.194864	−	2.02468i
$201$	−0.322974	−	0.186469i	−0.0227808	−	0.0131525i
$202$	22.4907	−	11.4596i	1.58244	−	0.806294i
$203$	3.33838	−	6.33484i	0.234308	−	0.444619i
$204$	4.48529	−	6.17347i	0.314033	−	0.432229i
$205$	−6.12252	+	12.9823i	−0.427615	+	0.906726i
$206$	−13.8937	+	31.2056i	−0.968016	+	2.17420i
$207$	5.14733	+	1.37922i	0.357764	+	0.0958626i
$208$	−11.7972	−	9.55317i	−0.817988	−	0.662393i
$209$	−2.13443	−	6.56910i	−0.147642	−	0.454394i
$210$	22.9149	−	0.385029i	1.58128	−	0.0265695i
$211$	−0.550856	+	1.69536i	−0.0379225	+	0.116713i	−0.968226	−	0.250078i	$-0.919544\pi$
$211$	−0.550856	+	1.69536i	−0.0379225	+	0.116713i	0.930303	+	0.366791i	$0.119544\pi$
$212$	12.2888	−	7.98045i	0.843999	−	0.548099i
$213$	0.850112	+	16.2211i	0.0582487	+	1.11145i
$214$	10.3220	+	48.5612i	0.705597	+	3.31957i
$215$	10.6579	−	0.325861i	0.726859	−	0.0222236i
$216$	−30.5474	+	9.92544i	−2.07849	+	0.675341i
$217$	4.29347	−	15.1843i	0.291460	−	1.03078i
$218$	12.8457	+	12.8457i	0.870022	+	0.870022i
$219$	18.9850	−	1.99541i	1.28289	−	0.134837i
$220$	30.7090	−	40.3862i	2.07040	−	2.72284i
$221$	0.312415	−	2.97243i	0.0210153	−	0.199947i
$222$	−11.6551	−	4.47396i	−0.782237	−	0.300273i
$223$	2.23679	+	4.38996i	0.149787	+	0.293973i	0.953692	−	0.300784i	$-0.0972483\pi$
$223$	2.23679	+	4.38996i	0.149787	+	0.293973i	−0.803906	+	0.594757i	$0.797248\pi$
$224$	8.29957	+	0.987994i	0.554538	+	0.0660131i
$225$	−3.04333	−	0.454692i	−0.202889	−	0.0303128i
$226$	0.629375	−	1.09011i	0.0418654	−	0.0725130i
$227$	11.5388	+	7.49336i	0.765855	+	0.497352i	0.867481	−	0.497471i	$-0.165738\pi$
$227$	11.5388	+	7.49336i	0.765855	+	0.497352i	−0.101626	+	0.994823i	$0.532404\pi$
$228$	6.73389	−	5.45300i	0.445963	−	0.361134i
$229$	−1.56660	+	0.697493i	−0.103524	+	0.0460916i	−0.457845	−	0.889032i	$-0.651379\pi$
$229$	−1.56660	+	0.697493i	−0.103524	+	0.0460916i	0.354321	+	0.935124i	$0.384712\pi$
$230$	−31.7070	−	36.7961i	−2.09070	−	2.42626i
$231$	18.5487	+	11.0523i	1.22041	+	0.727185i
$232$	11.0101	−	11.0101i	0.722849	−	0.722849i
$233$	14.5817	−	18.0068i	0.955276	−	1.17967i	−0.0283779	−	0.999597i	$-0.509034\pi$
$233$	14.5817	−	18.0068i	0.955276	−	1.17967i	0.983654	−	0.180070i	$-0.0576325\pi$
$234$	−2.68255	+	2.97927i	−0.175364	+	0.194761i
$235$	−14.3643	+	6.92888i	−0.937020	+	0.451990i
$236$	5.61519	−	5.05594i	0.365518	−	0.329114i
$237$	3.24434	−	6.36738i	0.210743	−	0.413606i
$238$	3.37422	+	6.85389i	0.218718	+	0.444272i
$239$	−0.970343	−	0.315283i	−0.0627662	−	0.0203940i	0.277466	−	0.960736i	$-0.410506\pi$
$239$	−0.970343	−	0.315283i	−0.0627662	−	0.0203940i	−0.340232	+	0.940342i	$0.610506\pi$
$240$	19.3793	+	5.64810i	1.25093	+	0.364583i
$241$	−4.91023	−	4.42119i	−0.316296	−	0.284794i	0.495655	−	0.868519i	$-0.334928\pi$
$241$	−4.91023	−	4.42119i	−0.316296	−	0.284794i	−0.811951	+	0.583725i	$0.801595\pi$
$242$	39.6501	−	15.2203i	2.54881	−	0.978395i
$243$	1.62717	+	6.07267i	0.104383	+	0.389562i
$244$	14.5166	−	10.5469i	0.929329	−	0.675197i
$245$	−7.06369	+	13.9680i	−0.451283	+	0.892381i
$246$	−20.1177	−	14.6164i	−1.28266	−	0.931908i
$247$	1.21624	−	3.16841i	0.0773874	−	0.201601i
$248$	18.6879	−	28.7768i	1.18668	−	1.82733i
$249$	−12.5484	+	7.24484i	−0.795224	+	0.459123i
$250$	20.5972	+	19.0373i	1.30268	+	1.20403i
$251$			13.1515i			0.830114i	0.909795	+	0.415057i	$0.136238\pi$
$251$			13.1515i			0.830114i	−0.909795	+	0.415057i	$0.863762\pi$
$252$	1.18850	−	6.88883i	0.0748684	−	0.433955i
$253$	−7.15867	−	45.1981i	−0.450062	−	2.84158i
$254$	1.62607	+	3.65221i	0.102029	+	0.229160i
$255$	1.14547	+	3.80568i	0.0717322	+	0.238321i
$256$	−29.2535	−	13.0245i	−1.82835	−	0.814032i
$257$	−17.3530	+	4.64973i	−1.08245	+	0.290042i	−0.755600	−	0.655033i	$-0.772655\pi$
$257$	−17.3530	+	4.64973i	−1.08245	+	0.290042i	−0.326852	+	0.945075i	$0.605988\pi$
$258$	−2.88978	+	18.2454i	−0.179910	+	1.13591i
$259$	6.41429	−	5.61754i	0.398565	−	0.349057i
$260$	24.2143	−	5.92576i	1.50171	−	0.367500i
$261$	−1.11452	−	1.23780i	−0.0689870	−	0.0766178i
$262$	−45.7009	+	2.39508i	−2.82341	+	0.147969i
$263$	−3.28134	+	0.171968i	−0.202336	+	0.0106040i	−0.153235	−	0.988190i	$-0.548969\pi$
$263$	−3.28134	+	0.171968i	−0.202336	+	0.0106040i	−0.0491014	+	0.998794i	$0.515636\pi$
$264$	31.4162	+	34.8912i	1.93353	+	2.14741i
$265$	−0.565393	+	7.61055i	−0.0347318	+	0.467512i
$266$	1.68661	+	8.50915i	0.103413	+	0.521729i
$267$	−1.08696	+	6.86282i	−0.0665211	+	0.419998i
$268$	1.00154	−	0.268361i	0.0611787	−	0.0163928i
$269$	−6.22712	−	2.77249i	−0.379674	−	0.169042i	0.208021	−	0.978124i	$-0.433298\pi$
$269$	−6.22712	−	2.77249i	−0.379674	−	0.169042i	−0.587695	+	0.809083i	$0.699965\pi$
$270$	10.3245	−	29.5669i	0.628329	−	1.79938i
$271$	5.26961	+	11.8357i	0.320106	+	0.718970i	0.999896	−	0.0144371i	$-0.00459563\pi$
$271$	5.26961	+	11.8357i	0.320106	+	0.718970i	−0.679790	+	0.733407i	$0.737929\pi$
$272$	1.05259	+	6.64576i	0.0638224	+	0.402959i
$273$	3.66528	+	9.95585i	0.221833	+	0.602555i
$274$			21.4636i			1.29666i
$275$	7.06272	+	25.4630i	0.425898	+	1.53548i
$276$	49.7158	−	28.7034i	2.99254	−	1.72774i
$277$	0.805962	−	1.24107i	0.0484255	−	0.0745688i	−0.813629	−	0.581385i	$-0.802511\pi$
$277$	0.805962	−	1.24107i	0.0484255	−	0.0745688i	0.862054	+	0.506816i	$0.169178\pi$
$278$	−4.71352	+	12.2791i	−0.282698	+	0.736454i
$279$	−2.96947	−	2.15745i	−0.177777	−	0.129163i
$280$	−23.6593	+	24.4679i	−1.41391	+	1.46224i
$281$	−7.47301	+	5.42946i	−0.445802	+	0.323894i	−0.787936	−	0.615757i	$-0.788850\pi$
$281$	−7.47301	+	5.42946i	−0.445802	+	0.323894i	0.342134	+	0.939651i	$0.388850\pi$
$282$	−7.15097	−	26.6878i	−0.425834	−	1.58923i
$283$	9.60322	−	3.68633i	0.570852	−	0.219130i	−0.0557822	−	0.998443i	$-0.517765\pi$
$283$	9.60322	−	3.68633i	0.570852	−	0.219130i	0.626634	+	0.779313i	$0.284432\pi$
$284$	−33.5611	−	30.2186i	−1.99148	−	1.79314i
$285$	0.137917	+	4.51080i	0.00816947	+	0.267197i
$286$	32.7419	+	10.6385i	1.93607	+	0.629068i
$287$	15.2370	−	7.50130i	0.899414	−	0.442788i
$288$	0.882636	−	1.73227i	0.0520098	−	0.102075i
$289$	11.6490	−	10.4888i	0.685232	−	0.616986i
$290$	2.04763	+	15.0433i	0.120241	+	0.883371i
$291$	7.95999	−	8.84047i	0.466623	−	0.518237i
$292$	−33.4007	+	41.2464i	−1.95463	+	2.41376i
$293$	3.40255	−	3.40255i	0.198779	−	0.198779i	−0.600697	−	0.799476i	$-0.705110\pi$
$293$	3.40255	−	3.40255i	0.198779	−	0.198779i	0.799476	+	0.600697i	$0.205110\pi$
$294$	−21.4912	−	16.5369i	−1.25339	−	0.964449i
$295$	0.325966	+	3.92183i	0.0189785	+	0.228338i
$296$	16.9376	−	7.54109i	0.984476	−	0.438317i
$297$	22.9299	−	18.5682i	1.33053	−	1.07744i
$298$	−7.97877	−	5.18147i	−0.462198	−	0.300155i
$299$	11.2424	−	19.4724i	0.650166	−	1.12612i
$300$	−26.6461	+	19.7189i	−1.53841	+	1.13847i
$301$	−10.1039	−	7.55554i	−0.582378	−	0.435494i
$302$	−11.1056	−	21.7959i	−0.639054	−	1.25421i
$303$	−14.5058	−	5.56824i	−0.833334	−	0.319887i
$304$	−0.798641	+	7.59856i	−0.0458052	+	0.435807i
$305$	−0.203664	+	9.34321i	−0.0116618	+	0.534991i
$306$	1.76726	−	0.185746i	0.101027	−	0.0106184i
$307$	23.4485	+	23.4485i	1.33828	+	1.33828i	0.897727	+	0.440551i	$0.145217\pi$
$307$	23.4485	+	23.4485i	1.33828	+	1.33828i	0.440551	+	0.897727i	$0.354783\pi$
$308$	−58.1939	+	14.7376i	−3.31590	+	0.839753i
$309$	19.9975	−	6.49758i	1.13762	−	0.369634i
$310$	11.3060	+	31.4877i	0.642138	+	1.78838i
$311$	−5.22121	−	24.5639i	−0.296068	−	1.39289i	−0.834865	−	0.550454i	$-0.814454\pi$
$311$	−5.22121	−	24.5639i	−0.296068	−	1.39289i	0.538797	−	0.842435i	$-0.318879\pi$
$312$	1.20735	+	23.0376i	0.0683527	+	1.30425i
$313$	−6.25005	+	4.05883i	−0.353274	+	0.229419i	−0.709059	−	0.705149i	$-0.750880\pi$
$313$	−6.25005	+	4.05883i	−0.353274	+	0.229419i	0.355785	+	0.934568i	$0.384213\pi$
$314$	12.7248	−	39.1630i	0.718104	−	2.21010i
$315$	2.48134	+	2.66439i	0.139808	+	0.150122i
$316$	6.13972	+	18.8961i	0.345386	+	1.06299i
$317$	20.6799	+	16.7463i	1.16150	+	0.940565i	0.998935	−	0.0461327i	$-0.0146897\pi$
$317$	20.6799	+	16.7463i	1.16150	+	0.940565i	0.162566	+	0.986698i	$0.448023\pi$
$318$	−12.7707	−	3.42190i	−0.716146	−	0.191891i
$319$	−5.81770	+	13.0668i	−0.325729	+	0.731599i
$320$	7.38435	−	4.05141i	0.412798	−	0.226481i
$321$	17.9626	−	24.7234i	1.00258	−	1.37993i
$322$	2.21760	+	57.4289i	0.123582	+	3.20039i
$323$	−1.34035	+	0.682945i	−0.0745793	+	0.0380001i
$324$	25.1902	+	14.5436i	1.39946	+	0.807976i
$325$	−5.17666	+	11.9069i	−0.287150	+	0.660478i
$326$	−7.66963	−	13.2842i	−0.424782	−	0.735743i
$327$	0.585248	−	11.1672i	0.0323643	−	0.617547i
$328$	36.4753	−	5.77712i	2.01401	−	0.318988i
$329$	18.4019	+	4.17697i	1.01453	+	0.230284i
$330$	−45.6215	+	3.79187i	−2.51138	+	0.208735i
$331$	0.707809	+	6.73435i	0.0389047	+	0.370153i	0.996601	+	0.0823741i	$0.0262503\pi$
$331$	0.707809	+	6.73435i	0.0389047	+	0.370153i	−0.957697	+	0.287779i	$0.907083\pi$
$332$	10.4266	−	38.9125i	0.572233	−	2.13560i
$333$	−0.710755	−	1.85158i	−0.0389491	−	0.101466i
$334$	−49.2076	−	10.4594i	−2.69252	−	0.572313i
$335$	−0.204470	+	0.499822i	−0.0111714	+	0.0273082i
$336$	−13.7714	−	19.5139i	−0.751289	−	1.06457i
$337$	18.6572	+	9.50634i	1.01633	+	0.517843i	0.881079	−	0.472969i	$-0.156818\pi$
$337$	18.6572	+	9.50634i	1.01633	+	0.517843i	0.135246	+	0.990812i	$0.456818\pi$
$338$	−8.54909	−	13.1644i	−0.465009	−	0.716051i
$339$	−0.757897	+	0.161096i	−0.0411633	+	0.00874953i
$340$	−9.73370	−	5.22983i	−0.527884	−	0.283627i
$341$	−6.55332	+	30.8310i	−0.354882	+	1.66959i
$342$	1.99296	+	0.315653i	0.107767	+	0.0170686i
$343$	16.8347	−	7.71965i	0.908988	−	0.416822i
$344$	−16.1253	−	22.1946i	−0.869420	−	1.19665i
$345$	−3.77257	+	29.6600i	−0.203108	+	1.59684i
$346$	−29.8715	−	3.13962i	−1.60590	−	0.168787i
$347$	−6.31710	−	7.80097i	−0.339120	−	0.418778i	0.578847	−	0.815436i	$-0.303503\pi$
$347$	−6.31710	−	7.80097i	−0.339120	−	0.418778i	−0.917966	+	0.396659i	$0.870170\pi$
$348$	−17.9187	−	0.939079i	−0.960543	−	0.0503399i
$349$	−18.7086			−1.00145			−0.500725	−	0.865607i	$-0.666933\pi$
$349$	−18.7086			−1.00145			−0.500725	+	0.865607i	$0.666933\pi$
$350$	−5.02773	−	32.8032i	−0.268744	−	1.75341i
$351$	14.4974			0.773812
$352$	−16.6725	−	0.873769i	−0.888647	−	0.0465720i
$353$	−6.39971	−	7.90298i	−0.340622	−	0.420633i	0.577835	−	0.816154i	$-0.303898\pi$
$353$	−6.39971	−	7.90298i	−0.340622	−	0.420633i	−0.918457	+	0.395520i	$0.870564\pi$
$354$	−6.78045	−	0.712654i	−0.360377	−	0.0378771i
$355$	23.1081	−	4.38773i	1.22645	−	0.232877i
$356$	−11.3550	−	15.6288i	−0.601815	−	0.828327i
$357$	1.74549	−	4.36654i	0.0923810	−	0.231102i
$358$	54.9606	+	8.70490i	2.90476	+	0.460068i
$359$	0.676610	−	3.18320i	0.0357101	−	0.168003i	−0.956679	−	0.291145i	$-0.905964\pi$
$359$	0.676610	−	3.18320i	0.0357101	−	0.168003i	0.992389	+	0.123142i	$0.0392971\pi$
$360$	3.43966	+	7.13075i	0.181286	+	0.375824i
$361$	16.9140	−	3.59517i	0.890209	−	0.189220i
$362$	3.75399	+	5.78063i	0.197305	+	0.303823i
$363$	−23.2938	−	11.8688i	−1.22261	−	0.622949i
$364$	−26.7784	−	12.3669i	−1.40357	−	0.648203i
$365$	−6.57080	−	26.8501i	−0.343931	−	1.40540i
$366$	−15.8367	−	3.36619i	−0.827796	−	0.175954i
$367$	4.45137	+	11.5962i	0.232360	+	0.605317i	0.999339	−	0.0363544i	$-0.0115745\pi$
$367$	4.45137	+	11.5962i	0.232360	+	0.605317i	−0.766979	+	0.641672i	$0.778241\pi$
$368$	−13.1013	+	48.8946i	−0.682951	+	2.54881i
$369$	−0.412937	−	3.92883i	−0.0214966	−	0.204527i
$370$	−4.14302	+	17.5965i	−0.215386	+	0.914800i
$371$	6.13386	−	6.62660i	0.318454	−	0.344036i
$372$	−39.0541	+	6.18556i	−2.02486	+	0.320706i
$373$	−1.01730	+	19.4113i	−0.0526740	+	1.00508i	0.836631	+	0.547766i	$0.184522\pi$
$373$	−1.01730	+	19.4113i	−0.0526740	+	1.00508i	−0.889305	+	0.457314i	$0.848812\pi$
$374$	−7.62987	−	13.2153i	−0.394531	−	0.683348i
$375$	0.224851	−	17.2633i	0.0116113	−	0.891473i
$376$	35.5350	+	20.5162i	1.83258	+	1.05804i
$377$	−6.26194	+	3.19062i	−0.322506	+	0.164325i
$378$	−31.3522	+	19.7522i	−1.61259	+	1.01595i
$379$	−13.2455	+	18.2308i	−0.680373	+	0.936453i	−0.999938	−	0.0111109i	$-0.996463\pi$
$379$	−13.2455	+	18.2308i	−0.680373	+	0.936453i	0.319565	+	0.947564i	$0.396463\pi$
$380$	−9.13912	−	8.59685i	−0.468827	−	0.441009i
$381$	1.00093	−	2.24813i	0.0512793	−	0.115175i
$382$	−52.2251	−	13.9937i	−2.67207	−	0.715979i
$383$	−14.5624	−	11.7924i	−0.744103	−	0.602563i	0.180464	−	0.983582i	$-0.442240\pi$
$383$	−14.5624	−	11.7924i	−0.744103	−	0.602563i	−0.924567	+	0.381019i	$0.875573\pi$
$384$	7.52412	+	23.1569i	0.383964	+	1.18172i
$385$	12.2353	−	28.7723i	0.623566	−	1.46637i
$386$	4.89106	−	15.0531i	0.248949	−	0.766185i
$387$	−2.46123	+	1.59834i	−0.125111	+	0.0812482i
$388$	1.73097	+	33.0288i	0.0878765	+	1.67678i
$389$	0.257457	+	1.21124i	0.0130536	+	0.0614124i	0.984192	−	0.177103i	$-0.0566726\pi$
$389$	0.257457	+	1.21124i	0.0130536	+	0.0614124i	−0.971139	+	0.238515i	$0.923339\pi$
$390$	−18.5931	−	12.6590i	−0.941497	−	0.641012i
$391$	−9.47862	+	3.07979i	−0.479354	+	0.155752i
$392$	39.9343	−	5.20267i	2.01699	−	0.262775i
$393$	19.9192	+	19.9192i	1.00479	+	1.00479i
$394$	−4.69152	+	0.493098i	−0.236355	+	0.0248419i
$395$	−9.76957	−	3.41144i	−0.491560	−	0.171648i
$396$	−1.45960	+	13.8872i	−0.0733477	+	0.697857i
$397$	7.53582	+	2.89273i	0.378212	+	0.145182i	0.540045	−	0.841636i	$-0.318407\pi$
$397$	7.53582	+	2.89273i	0.378212	+	0.145182i	−0.161833	+	0.986818i	$0.551741\pi$
$398$	−14.6177	−	28.6888i	−0.732718	−	1.43804i
$399$	3.19778	−	4.27633i	0.160089	−	0.214084i
$400$	4.31913	−	28.9087i	0.215956	−	1.44543i
$401$	−8.24579	+	14.2821i	−0.411775	+	0.713215i	−0.995084	−	0.0990353i	$-0.968424\pi$
$401$	−8.24579	+	14.2821i	−0.411775	+	0.713215i	0.583309	+	0.812250i	$0.301758\pi$
$402$	−0.784636	−	0.509548i	−0.0391341	−	0.0254140i
$403$	−12.0358	+	9.74640i	−0.599546	+	0.485503i
$404$	39.4644	−	17.5707i	1.96343	−	0.874174i
$405$	−13.9706	+	5.85872i	−0.694205	+	0.291122i
$406$	9.19505	−	15.4318i	0.456343	−	0.765868i
$407$	−12.0431	+	12.0431i	−0.596953	+	0.596953i
$408$	6.43508	−	7.94666i	0.318584	−	0.393418i
$409$	7.37013	−	8.18536i	0.364430	−	0.404740i	−0.532845	−	0.846213i	$-0.678877\pi$
$409$	7.37013	−	8.18536i	0.364430	−	0.404740i	0.897275	+	0.441473i	$0.145544\pi$
$410$	−17.0427	+	31.7196i	−0.841678	+	1.56652i
$411$	9.81843	−	8.84055i	0.484307	−	0.436072i
$412$	−26.5401	+	52.0879i	−1.30754	+	2.56619i
$413$	2.58955	−	3.86989i	0.127424	−	0.190425i
$414$	12.7141	+	4.13105i	0.624862	+	0.203030i
$415$	12.8456	+	16.5896i	0.630568	+	0.814353i
$416$	−6.09621	−	5.48905i	−0.298891	−	0.269123i
$417$	7.55847	−	2.90142i	0.370140	−	0.142083i
$418$	−4.48472	−	16.7372i	−0.219355	−	0.818644i
$419$	−27.4976	+	19.9782i	−1.34334	+	0.975997i	−0.344031	+	0.938958i	$0.611792\pi$
$419$	−27.4976	+	19.9782i	−1.34334	+	0.975997i	−0.999314	+	0.0370384i	$0.988208\pi$
$420$	39.1974	+	1.39441i	1.91264	+	0.0680401i
$421$	−1.53583	−	1.11585i	−0.0748519	−	0.0543831i	0.549730	−	0.835342i	$-0.314731\pi$
$421$	−1.53583	−	1.11585i	−0.0748519	−	0.0543831i	−0.624582	+	0.780959i	$0.714731\pi$
$422$	−1.60260	+	4.17491i	−0.0780133	+	0.203232i
$423$	2.39059	−	3.68118i	0.116234	−	0.178985i
$424$	17.0043	−	9.81745i	0.825803	−	0.476778i
$425$	5.23670	−	2.38678i	0.254017	−	0.115776i
$426$			40.7489i			1.97429i
$427$	7.07643	−	8.49682i	0.342452	−	0.411190i
$428$	13.2914	+	83.9184i	0.642463	+	4.05635i
$429$	−8.61941	−	19.3595i	−0.416149	−	0.934686i
$430$	26.7429	+	0.582945i	1.28966	+	0.0281121i
$431$	29.6452	+	13.1989i	1.42796	+	0.635769i	0.967721	−	0.252025i	$-0.0810966\pi$
$431$	29.6452	+	13.1989i	1.42796	+	0.635769i	0.460240	+	0.887794i	$0.347763\pi$
$432$	−31.5254	+	8.44720i	−1.51677	+	0.406416i
$433$	3.83767	−	24.2301i	0.184426	−	1.16442i	−0.705633	−	0.708578i	$-0.749337\pi$
$433$	3.83767	−	24.2301i	0.184426	−	1.16442i	0.890059	−	0.455845i	$-0.150663\pi$
$434$	12.7496	−	37.4762i	0.612002	−	1.79891i
$435$	6.03808	−	7.13279i	0.289504	−	0.341991i
$436$	20.8035	+	23.1047i	0.996309	+	1.10651i
$437$	−11.3015	+	0.592285i	−0.540623	+	0.0283329i
$438$	47.8234	−	2.50632i	2.28509	−	0.119757i
$439$	−14.9441	−	16.5971i	−0.713244	−	0.792138i	0.272182	−	0.962246i	$-0.412255\pi$
$439$	−14.9441	−	16.5971i	−0.713244	−	0.792138i	−0.985425	+	0.170108i	$0.945588\pi$
$440$	43.9265	−	51.8904i	2.09411	−	2.47378i
$441$	−0.332206	−	4.29512i	−0.0158193	−	0.204530i
$442$	1.17292	−	7.40554i	0.0557903	−	0.352246i
$443$	−4.79492	+	1.28480i	−0.227814	+	0.0610425i	−0.370920	−	0.928665i	$-0.620958\pi$
$443$	−4.79492	+	1.28480i	−0.227814	+	0.0610425i	0.143106	+	0.989707i	$0.454291\pi$
$444$	−19.5185	−	8.69019i	−0.926307	−	0.412418i
$445$	10.0591	+	0.219269i	0.476847	+	0.0103943i
$446$	5.02727	+	11.2914i	0.238048	+	0.534665i
$447$	0.916100	+	5.78403i	0.0433301	+	0.273575i
$448$	−9.82084	−	1.69435i	−0.463991	−	0.0800504i
$449$			2.68091i			0.126520i	0.997997	+	0.0632600i	$0.0201497\pi$
$449$			2.68091i			0.126520i	−0.997997	+	0.0632600i	$0.979850\pi$
$450$	−7.56448	−	1.53866i	−0.356593	−	0.0725333i
$451$	−29.3793	+	16.9621i	−1.38342	+	0.798716i
$452$	1.17328	−	1.80669i	0.0551864	−	0.0849795i
$453$	−5.39622	+	14.0576i	−0.253537	+	0.660485i
$454$	27.9232	+	20.2874i	1.31050	+	0.952135i
$455$	13.5689	−	7.20334i	0.636118	−	0.337698i
$456$	9.39359	−	6.82484i	0.439895	−	0.319603i
$457$	−8.07135	−	30.1227i	−0.377562	−	1.40908i	−0.849565	−	0.527484i	$-0.823136\pi$
$457$	−8.07135	−	30.1227i	−0.377562	−	1.40908i	0.472003	−	0.881597i	$-0.343531\pi$
$458$	−4.01623	+	1.54168i	−0.187666	+	0.0720382i
$459$	−4.77542	−	4.29981i	−0.222897	−	0.200698i
$460$	−50.8933	−	65.7267i	−2.37291	−	3.06452i
$461$	13.2462	+	4.30394i	0.616936	+	0.200455i	0.600779	−	0.799415i	$-0.294857\pi$
$461$	13.2462	+	4.30394i	0.616936	+	0.200455i	0.0161563	+	0.999869i	$0.494857\pi$
$462$	45.0173	+	30.1235i	2.09439	+	1.40147i
$463$	−4.86495	+	9.54799i	−0.226093	+	0.443733i	−0.975988	−	0.217824i	$-0.930104\pi$
$463$	−4.86495	+	9.54799i	−0.226093	+	0.443733i	0.749895	+	0.661557i	$0.230104\pi$
$464$	11.7579	−	10.5868i	0.545846	−	0.491482i
$465$	9.74711	−	18.1412i	0.452011	−	0.841278i
$466$	38.8943	−	43.1964i	1.80174	−	2.00104i
$467$	22.8241	−	28.1854i	1.05617	−	1.30427i	0.105384	−	0.994432i	$-0.466393\pi$
$467$	22.8241	−	28.1854i	1.05617	−	1.30427i	0.950790	−	0.309835i	$-0.100274\pi$
$468$	−4.85148	+	4.85148i	−0.224260	+	0.224260i
$469$	0.557709	−	0.311838i	0.0257526	−	0.0143993i
$470$	−36.8952	+	15.4724i	−1.70185	+	0.713688i
$471$	−23.1561	+	10.3098i	−1.06698	+	0.475050i
$472$	7.86872	−	6.37197i	0.362187	−	0.293294i
$473$	21.1355	+	13.7256i	0.971813	+	0.631103i
$474$	8.96374	−	15.5257i	0.411718	−	0.713117i
$475$	6.44518	−	1.07884i	0.295725	−	0.0495008i
$476$	5.15285	+	12.0159i	0.236181	+	0.550749i
$477$	−0.953555	−	1.87146i	−0.0436603	−	0.0856881i
$478$	−2.38952	−	0.917250i	−0.109294	−	0.0419540i
$479$	−1.71663	+	16.3326i	−0.0784349	+	0.746258i	0.882655	+	0.470022i	$0.155754\pi$
$479$	−1.71663	+	16.3326i	−0.0784349	+	0.746258i	−0.961090	+	0.276236i	$0.910913\pi$
$480$	10.2984	+	3.59610i	0.470055	+	0.164139i
$481$	−8.32255	+	0.874735i	−0.379476	+	0.0398845i
$482$	−11.7207	−	11.7207i	−0.533863	−	0.533863i
$483$	25.3572	−	24.6686i	1.15379	−	1.12246i
$484$	69.1277	−	22.4609i	3.14217	−	1.02095i
$485$	−14.2389	−	9.69449i	−0.646557	−	0.440204i
$486$	3.27910	+	15.4270i	0.148743	+	0.699781i
$487$	1.69116	+	32.2692i	0.0766337	+	1.46226i	0.718546	+	0.695480i	$0.244808\pi$
$487$	1.69116	+	32.2692i	0.0766337	+	1.46226i	−0.641912	+	0.766778i	$0.721859\pi$
$488$	20.1655	−	13.0956i	0.912848	−	0.592810i
$489$	−2.91778	+	8.98001i	−0.131947	+	0.406090i
$490$	−19.5299	+	34.0653i	−0.882272	+	1.53891i
$491$	7.15620	+	22.0245i	0.322955	+	0.993953i	0.972355	+	0.233506i	$0.0750199\pi$
$491$	7.15620	+	22.0245i	0.322955	+	0.993953i	−0.649401	+	0.760447i	$0.724980\pi$
$492$	−33.0733	−	26.7822i	−1.49106	−	1.20744i
$493$	3.00899	+	0.806257i	0.135518	+	0.0363120i
$494$	3.46292	−	7.77785i	0.155804	−	0.349942i
$495$	−5.29729	−	4.98297i	−0.238095	−	0.223968i
$496$	20.4936	−	28.2070i	0.920191	−	1.26653i
$497$	−24.6208	−	12.9748i	−1.10439	−	0.582001i
$498$	−32.3876	+	16.5023i	−1.45132	+	0.739487i
$499$	−15.3858	−	8.88299i	−0.688763	−	0.397657i	0.114386	−	0.993436i	$-0.463510\pi$
$499$	−15.3858	−	8.88299i	−0.688763	−	0.397657i	−0.803148	+	0.595779i	$0.796843\pi$
$500$	33.4967	+	34.3808i	1.49802	+	1.53756i
$501$	15.4833	+	26.8179i	0.691743	+	1.19813i
$502$	−1.72669	+	32.9472i	−0.0770659	+	1.47051i
$503$	10.3863	−	1.64503i	0.463104	−	0.0733484i	0.0794771	−	0.996837i	$-0.474675\pi$
$503$	10.3863	−	1.64503i	0.463104	−	0.0733484i	0.383627	+	0.923488i	$0.374675\pi$
$504$	2.07355	−	9.13514i	0.0923632	−	0.406912i
$505$	−5.15635	+	21.9004i	−0.229455	+	0.974555i
$506$	−11.9998	−	114.170i	−0.533456	−	5.07550i
$507$	−2.50077	+	9.33299i	−0.111063	+	0.414493i
$508$	2.45193	+	6.38748i	0.108787	+	0.283399i
$509$	−15.2768	−	3.24718i	−0.677131	−	0.143929i	−0.143506	−	0.989650i	$-0.545838\pi$
$509$	−15.2768	−	3.24718i	−0.677131	−	0.143929i	−0.533626	+	0.845721i	$0.679171\pi$
$510$	2.36999	+	9.68442i	0.104945	+	0.428833i
$511$	−13.7131	+	29.6933i	−0.606632	+	1.31356i
$512$	−43.4780	−	22.1532i	−1.92148	−	0.979041i
$513$	−3.97410	−	6.11958i	−0.175461	−	0.270186i
$514$	−44.0835	+	9.37023i	−1.94444	+	0.413303i
$515$	−13.2283	−	27.4235i	−0.582908	−	1.20842i
$516$	−6.57302	+	30.9236i	−0.289361	+	1.36134i
$517$	−37.2287	−	5.89644i	−1.63731	−	0.259325i
$518$	16.8067	−	13.2310i	0.738444	−	0.581335i
$519$	10.8674	+	14.9577i	0.477027	+	0.656572i
$520$	32.8187	−	6.23156i	1.43919	−	0.273272i
$521$	29.5560	+	3.10646i	1.29487	+	0.136096i	0.726780	−	0.686870i	$-0.241016\pi$
$521$	29.5560	+	3.10646i	1.29487	+	0.136096i	0.568090	+	0.822966i	$0.307682\pi$
$522$	−2.62959	−	3.24727i	−0.115094	−	0.142129i
$523$	34.4270	+	1.80424i	1.50539	+	0.0788939i	0.787088	−	0.616841i	$-0.211588\pi$
$523$	34.4270	+	1.80424i	1.50539	+	0.0788939i	0.718298	+	0.695735i	$0.244921\pi$
$524$	−78.3201			−3.42143
$525$	−12.9348	+	15.8111i	−0.564523	+	0.690053i
$526$	−8.24303			−0.359413
$527$	6.85529	+	0.359271i	0.298621	+	0.0156501i
$528$	30.0237	+	37.0761i	1.30661	+	1.61353i
$529$	−51.6928	−	5.43313i	−2.24751	−	0.236223i
$530$	−2.41564	+	18.9918i	−0.104929	+	0.824950i
$531$	−0.636635	−	0.876253i	−0.0276276	−	0.0380261i
$532$	2.12037	+	14.6937i	0.0919297	+	0.637053i
$533$	−16.4634	−	2.60755i	−0.713110	−	0.112946i
$534$	−3.62411	+	17.0501i	−0.156831	+	0.737830i
$535$	−38.9814	−	20.9443i	−1.68531	−	0.905503i
$536$	1.35906	−	0.288877i	0.0587024	−	0.0124776i
$537$	−18.6555	−	28.7269i	−0.805043	−	1.23966i
$538$	−15.2362	−	7.76325i	−0.656881	−	0.334697i
$539$	−32.5348	+	17.6082i	−1.40137	+	0.758439i
$540$	20.2934	−	49.6068i	0.873290	−	2.13474i
$541$	34.9045	+	7.41919i	1.50066	+	0.318976i	0.883714	−	0.468027i	$-0.155035\pi$
$541$	34.9045	+	7.41919i	1.50066	+	0.318976i	0.616949	+	0.787003i	$0.288369\pi$
$542$	11.6475	+	30.3429i	0.500304	+	1.30334i
$543$	1.09811	−	4.09821i	0.0471245	−	0.175871i
$544$	0.380076	+	3.61618i	0.0162956	+	0.155042i
$545$	−16.1370	+	1.34124i	−0.691235	+	0.0574525i
$546$	7.87517	+	25.4227i	0.337026	+	1.08799i
$547$	9.01623	−	1.42803i	0.385506	−	0.0610582i	0.0393265	−	0.999226i	$-0.487479\pi$
$547$	9.01623	−	1.42803i	0.385506	−	0.0610582i	0.346180	+	0.938168i	$0.387479\pi$
$548$	−1.92245	+	36.6826i	−0.0821230	+	1.56700i
$549$	−1.28605	−	2.22750i	−0.0548872	−	0.0950674i
$550$	14.3505	+	64.7174i	0.611907	+	2.75956i
$551$	3.06337	+	1.76864i	0.130504	+	0.0753466i
$552$	68.5417	−	34.9238i	2.91733	−	1.48645i
$553$	6.52659	+	10.3595i	0.277539	+	0.440530i
$554$	2.18205	−	3.00333i	0.0927063	−	0.127599i
$555$	9.75591	−	5.35255i	0.414115	−	0.227203i
$556$	−9.15550	+	20.5636i	−0.388280	+	0.872091i
$557$	−38.0569	−	10.1973i	−1.61252	−	0.432074i	−0.663730	−	0.747972i	$-0.731028\pi$
$557$	−38.0569	−	10.1973i	−1.61252	−	0.432074i	−0.948793	+	0.315898i	$0.897694\pi$
$558$	−7.15588	−	5.79472i	−0.302933	−	0.245310i
$559$	3.82643	+	11.7765i	0.161841	+	0.498095i
$560$	−25.3091	+	23.5703i	−1.06951	+	0.996027i
$561$	−2.90266	+	8.93346i	−0.122550	+	0.377171i
$562$	−19.4343	+	12.6208i	−0.819786	+	0.532375i
$563$	−1.89184	−	36.0984i	−0.0797313	−	1.52136i	−0.686877	−	0.726774i	$-0.741019\pi$
$563$	−1.89184	−	36.0984i	−0.0797313	−	1.52136i	0.607145	−	0.794591i	$-0.292315\pi$
$564$	−9.83106	−	46.2515i	−0.413962	−	1.94754i
$565$	0.379159	+	1.05597i	0.0159513	+	0.0444251i
$566$	24.5421	−	7.97420i	1.03158	−	0.335181i
$567$	17.2487	+	4.87719i	0.724376	+	0.204823i
$568$	−42.7916	−	42.7916i	−1.79549	−	1.79549i
$569$	17.0565	−	1.79271i	0.715047	−	0.0751544i	0.259983	−	0.965613i	$-0.416283\pi$
$569$	17.0565	−	1.79271i	0.715047	−	0.0751544i	0.455064	+	0.890459i	$0.349616\pi$
$570$	−0.246724	+	11.3186i	−0.0103341	+	0.474084i
$571$	3.85429	−	36.6711i	0.161297	−	1.53464i	−0.552039	−	0.833818i	$-0.686150\pi$
$571$	3.85429	−	36.6711i	0.161297	−	1.53464i	0.713337	−	0.700822i	$-0.247183\pi$
$572$	55.0051	+	21.1145i	2.29988	+	0.882840i
$573$	15.1094	+	29.6540i	0.631206	+	1.23881i
$574$	39.1568	−	16.7918i	1.63437	−	0.700878i
$575$	43.2931	−	0.379716i	1.80545	−	0.0158352i
$576$	−1.15907	+	2.00758i	−0.0482948	+	0.0836490i
$577$	1.79573	+	1.16616i	0.0747572	+	0.0485479i	0.581476	−	0.813563i	$-0.302475\pi$
$577$	1.79573	+	1.16616i	0.0747572	+	0.0485479i	−0.506719	+	0.862111i	$0.669142\pi$
$578$	30.5602	−	24.7471i	1.27114	−	1.02934i
$579$	−8.90056	+	3.96278i	−0.369895	+	0.164688i
$580$	2.15213	+	25.8932i	0.0893625	+	1.07516i
$581$	0.341697	−	24.8234i	0.0141760	−	1.02985i
$582$	21.1021	−	21.1021i	0.874712	−	0.874712i
$583$	−11.3509	+	14.0173i	−0.470108	+	0.580535i
$584$	−47.5888	+	52.8527i	−1.96924	+	2.18706i
$585$	−0.481954	−	3.54075i	−0.0199264	−	0.146392i
$586$	8.97082	−	8.07737i	0.370581	−	0.333673i
$587$	8.93180	−	17.5297i	0.368655	−	0.723526i	−0.629933	−	0.776649i	$-0.716918\pi$
$587$	8.93180	−	17.5297i	0.368655	−	0.723526i	0.998588	+	0.0531234i	$0.0169177\pi$
$588$	−35.2485	−	30.1874i	−1.45362	−	1.24491i
$589$	7.41344	+	2.40877i	0.305466	+	0.0992518i
$590$	0.301706	+	9.86781i	0.0124210	+	0.406251i
$591$	2.15794	+	1.94302i	0.0887657	+	0.0799250i
$592$	17.5882	−	6.75148i	0.722871	−	0.277484i
$593$	6.07582	+	22.6753i	0.249504	+	0.931161i	0.971066	+	0.238811i	$0.0767578\pi$
$593$	6.07582	+	22.6753i	0.249504	+	0.931161i	−0.721562	+	0.692350i	$0.756576\pi$
$594$	59.8820	−	43.5068i	2.45699	−	1.78511i
$595$	−6.60603	−	1.65165i	−0.270821	−	0.0677109i
$596$	−13.1721	−	9.57009i	−0.539550	−	0.392006i
$597$	−7.10276	+	18.5033i	−0.290697	+	0.757291i
$598$	30.7212	−	47.3065i	1.25628	−	1.93451i
$599$	20.7625	−	11.9873i	0.848334	−	0.489786i	−0.0117543	−	0.999931i	$-0.503742\pi$
$599$	20.7625	−	11.9873i	0.848334	−	0.489786i	0.860088	+	0.510145i	$0.170408\pi$
$600$	−37.0401	+	24.5187i	−1.51216	+	1.00097i
$601$		−	18.5996i		−	0.758692i	−0.925255	−	0.379346i	$-0.876149\pi$
$601$		−	18.5996i		−	0.758692i	0.925255	−	0.379346i	$-0.123851\pi$
$602$	−24.3203	−	20.2548i	−0.991223	−	0.825523i
$603$	−0.0232507	−	0.146799i	−0.000946843	−	0.00597813i
$604$	−17.0279	−	38.2452i	−0.692855	−	1.55618i
$605$	−12.4801	+	35.7400i	−0.507387	+	1.45304i
$606$	−35.6089	−	15.8541i	−1.44651	−	0.644029i
$607$	6.91436	−	1.85270i	0.280645	−	0.0751987i	−0.115751	−	0.993278i	$-0.536927\pi$
$607$	6.91436	−	1.85270i	0.280645	−	0.0751987i	0.396396	+	0.918080i	$0.370261\pi$
$608$	−0.645892	+	4.07800i	−0.0261944	+	0.165385i
$609$	−10.8465	+	2.14991i	−0.439523	+	0.0871186i
$610$	−1.73691	+	23.3800i	−0.0703256	+	0.946627i
$611$	−12.3925	−	13.7632i	−0.501346	−	0.556801i
$612$	3.03699	−	0.159162i	0.122763	−	0.00643373i
$613$	−4.04570	+	0.212026i	−0.163404	+	0.00856367i	−0.133863	−	0.991000i	$-0.542738\pi$
$613$	−4.04570	+	0.212026i	−0.163404	+	0.00856367i	−0.0295417	+	0.999564i	$0.509405\pi$
$614$	55.6649	+	61.8221i	2.24645	+	2.49494i
$615$	21.5296	−	5.26877i	0.868159	−	0.212457i
$616$	−78.9075	+	15.6404i	−3.17927	+	0.630168i
$617$	−1.01342	+	6.39846i	−0.0407986	+	0.257592i	−0.999654	−	0.0263025i	$-0.991627\pi$
$617$	−1.01342	+	6.39846i	−0.0407986	+	0.257592i	0.958855	+	0.283895i	$0.0916267\pi$
$618$	50.9510	−	13.6523i	2.04955	−	0.549175i
$619$	32.9743	+	14.6811i	1.32535	+	0.590084i	0.942648	−	0.333788i	$-0.108327\pi$
$619$	32.9743	+	14.6811i	1.32535	+	0.590084i	0.382701	+	0.923872i	$0.374994\pi$
$620$	16.5024	+	54.8269i	0.662750	+	2.20190i
$621$	−19.6627	−	44.1632i	−0.789038	−	1.77221i
$622$	−9.85518	−	62.2232i	−0.395157	−	2.49492i
$623$	−9.14785	−	7.61863i	−0.366501	−	0.305234i
$624$			23.4413i			0.938403i
$625$	−24.8134	+	3.04891i	−0.992535	+	0.121957i
$626$	−16.1906	+	9.34763i	−0.647106	+	0.373607i
$627$	−5.80917	+	8.94534i	−0.231996	+	0.357242i
$628$	25.2553	−	65.7922i	1.00779	−	2.62540i
$629$	3.00088	+	2.18027i	0.119653	+	0.0869330i
$630$	5.86646	+	7.00064i	0.233725	+	0.278912i
$631$	4.47810	−	3.25353i	0.178270	−	0.129521i	−0.495072	−	0.868852i	$-0.664858\pi$
$631$	4.47810	−	3.25353i	0.178270	−	0.129521i	0.673342	+	0.739331i	$0.264858\pi$
$632$	6.89085	+	25.7170i	0.274103	+	1.02297i
$633$	2.56988	−	0.986486i	0.102144	−	0.0392093i
$634$	49.6089	+	44.6681i	1.97022	+	1.77400i
$635$	−3.42111	−	0.997081i	−0.135763	−	0.0395680i
$636$	−21.5194	−	6.99208i	−0.853301	−	0.277254i
$637$	−17.8681	−	3.33660i	−0.707961	−	0.132201i
$638$	−16.2901	+	31.9712i	−0.644932	+	1.26575i
$639$	−4.81079	+	4.33166i	−0.190312	+	0.171358i
$640$	31.7561	−	15.3182i	1.25527	−	0.605504i
$641$	−14.4112	+	16.0053i	−0.569208	+	0.632170i	−0.957177	−	0.289503i	$-0.906510\pi$
$641$	−14.4112	+	16.0053i	−0.569208	+	0.632170i	0.387969	+	0.921672i	$0.373177\pi$
$642$	48.2461	−	59.5790i	1.90412	−	2.35139i
$643$	−18.0306	+	18.0306i	−0.711059	+	0.711059i	−0.966757	−	0.255698i	$-0.917695\pi$
$643$	−18.0306	+	18.0306i	−0.711059	+	0.711059i	0.255698	+	0.966757i	$0.417695\pi$
$644$	−1.35378	+	98.3481i	−0.0533462	+	3.87546i
$645$	−10.7484	−	12.4735i	−0.423217	−	0.491146i
$646$	−3.44753	+	1.53494i	−0.135641	+	0.0603914i
$647$	−20.9404	+	16.9572i	−0.823253	+	0.666657i	−0.945421	−	0.325853i	$-0.894349\pi$
$647$	−20.9404	+	16.9572i	−0.823253	+	0.666657i	0.122168	+	0.992509i	$0.461015\pi$
$648$	32.6891	+	21.2285i	1.28415	+	0.833936i
$649$	−4.65054	+	8.05497i	−0.182550	+	0.316185i
$650$	−14.5319	+	29.1497i	−0.569989	+	1.14335i
$651$	−22.3947	+	9.60365i	−0.877718	+	0.376397i
$652$	−11.9180	−	23.3904i	−0.466746	−	0.916040i
$653$	−29.2233	−	11.2178i	−1.14360	−	0.438985i	−0.288512	−	0.957476i	$-0.593161\pi$
$653$	−29.2233	−	11.2178i	−1.14360	−	0.438985i	−0.855083	+	0.518491i	$0.826494\pi$
$654$	2.93234	−	27.8993i	0.114663	−	1.09095i
$655$	24.6899	−	32.4703i	0.964714	−	1.26872i
$656$	37.3201	−	3.92250i	1.45710	−	0.153148i
$657$	5.37958	+	5.37958i	0.209878	+	0.209878i
$658$	45.5522	+	12.8802i	1.77581	+	0.502124i
$659$	39.1971	−	12.7359i	1.52690	−	0.496121i	0.579175	−	0.815203i	$-0.303375\pi$
$659$	39.1971	−	12.7359i	1.52690	−	0.496121i	0.947727	+	0.319082i	$0.103375\pi$
$660$	−78.3095	+	2.39429i	−3.04819	+	0.0931978i
$661$	−5.70180	−	26.8249i	−0.221774	−	1.04337i	−0.938304	−	0.345810i	$-0.887604\pi$
$661$	−5.70180	−	26.8249i	−0.221774	−	1.04337i	0.716530	−	0.697556i	$-0.245729\pi$
$662$	0.889040	+	16.9639i	0.0345535	+	0.659320i
$663$	−3.87075	+	2.51369i	−0.150327	+	0.0976237i
$664$	16.6816	−	51.3407i	0.647372	−	1.99241i
$665$	−6.76023	−	3.75302i	−0.262150	−	0.145536i
$666$	−1.53749	−	4.73191i	−0.0595766	−	0.183358i
$667$	18.2126	+	14.7483i	0.705195	+	0.571055i
$668$	−83.1619	−	22.2832i	−3.21763	−	0.862161i
$669$	3.09456	−	6.95049i	0.119642	−	0.268721i
$670$	−0.577863	+	1.22531i	−0.0223248	+	0.0473380i
$671$	−12.9828	+	17.8692i	−0.501194	+	0.689834i
$672$	−6.87987	−	10.9202i	−0.265397	−	0.421257i
$673$	−21.6856	+	11.0493i	−0.835917	+	0.425921i	−0.818901	−	0.573934i	$-0.805416\pi$
$673$	−21.6856	+	11.0493i	−0.835917	+	0.425921i	−0.0170154	+	0.999855i	$0.505416\pi$
$674$	45.4922	+	26.2649i	1.75229	+	1.01169i
$675$	14.1689	+	24.0516i	0.545361	+	0.925746i
$676$	−13.4318	−	23.2645i	−0.516607	−	0.894790i
$677$	0.669964	−	12.7837i	0.0257488	−	0.491317i	−0.955068	−	0.296386i	$-0.904219\pi$
$677$	0.669964	−	12.7837i	0.0257488	−	0.491317i	0.980817	−	0.194931i	$-0.0624482\pi$
$678$	−1.91984	+	0.304073i	−0.0737310	+	0.0116778i
$679$	6.03096	+	19.4692i	0.231447	+	0.747160i
$680$	−12.6587	−	7.68109i	−0.485438	−	0.294556i
$681$	−2.22079	−	21.1295i	−0.0851010	−	0.809682i
$682$	−20.4653	+	76.3776i	−0.783657	+	2.92465i
$683$	−5.17320	−	13.4766i	−0.197947	−	0.515670i	0.798297	−	0.602265i	$-0.205735\pi$
$683$	−5.17320	−	13.4766i	−0.197947	−	0.515670i	−0.996244	+	0.0865949i	$0.972401\pi$
$684$	3.37781	+	0.717975i	0.129154	+	0.0274525i
$685$	−14.6020	−	12.3610i	−0.557914	−	0.472288i
$686$	43.1880	−	17.1291i	1.64892	−	0.653991i
$687$	2.35946	+	1.20221i	0.0900192	+	0.0458671i
$688$	−15.1827	−	23.3793i	−0.578834	−	0.891326i
$689$	−8.66871	+	1.84259i	−0.330252	+	0.0701971i
$690$	−13.3452	+	73.8092i	−0.508043	+	2.80987i
$691$	−7.52679	+	35.4108i	−0.286333	+	1.34709i	0.566136	+	0.824312i	$0.308438\pi$
$691$	−7.52679	+	35.4108i	−0.286333	+	1.34709i	−0.852469	+	0.522778i	$0.824896\pi$
$692$	−50.7709	−	8.04132i	−1.93002	−	0.305685i
$693$	1.22903	+	8.51688i	0.0466868	+	0.323530i
$694$	−14.8014	−	20.3724i	−0.561855	−	0.773327i
$695$	−5.63915	−	10.2783i	−0.213905	−	0.389877i
$696$	−23.9126	−	2.51332i	−0.906405	−	0.0952670i
$697$	4.64966	+	5.74185i	0.176119	+	0.217488i
$698$	−46.8690	−	2.45630i	−1.77402	−	0.0929723i
$699$	−35.7800			−1.35333
$700$	−5.65458	−	56.5130i	−0.213723	−	2.13599i
$701$	−21.7031			−0.819713			−0.409856	−	0.912150i	$-0.634421\pi$
$701$	−21.7031			−0.819713			−0.409856	+	0.912150i	$0.634421\pi$
$702$	36.3189	+	1.90339i	1.37077	+	0.0718390i
$703$	2.65067	+	3.27330i	0.0999718	+	0.123455i
$704$	19.7978	+	2.08083i	0.746158	+	0.0784244i
$705$	22.2744	+	10.5047i	0.838902	+	0.395629i
$706$	−14.9950	−	20.6389i	−0.564345	−	0.776754i
$707$	20.9174	−	16.4671i	0.786680	−	0.619308i
$708$	−11.5244	−	1.82528i	−0.433112	−	0.0685982i
$709$	7.86441	−	36.9992i	0.295354	−	1.38953i	−0.540852	−	0.841118i	$-0.681898\pi$
$709$	7.86441	−	36.9992i	0.295354	−	1.38953i	0.836206	−	0.548415i	$-0.184768\pi$
$710$	58.4667	−	7.95828i	2.19422	−	0.298669i
$711$	2.78581	−	0.592142i	0.104476	−	0.0222071i
$712$	−14.0990	−	21.7106i	−0.528383	−	0.813638i
$713$	46.0145	+	23.4456i	1.72326	+	0.878043i
$714$	4.94611	−	10.7099i	0.185103	−	0.400809i
$715$	−26.0937	+	16.1481i	−0.975851	+	0.603904i
$716$	93.1512	+	19.7999i	3.48122	+	0.739957i
$717$	0.564617	+	1.47088i	0.0210860	+	0.0549309i
$718$	2.11298	−	7.88575i	0.0788557	−	0.294294i
$719$	−2.69624	−	25.6530i	−0.100553	−	0.956696i	−0.922204	−	0.386705i	$-0.873613\pi$
$719$	−2.69624	−	25.6530i	−0.100553	−	0.956696i	0.821651	−	0.569991i	$-0.193053\pi$
$720$	3.11113	+	7.41876i	0.115945	+	0.276481i
$721$	−7.97447	+	35.1320i	−0.296985	+	1.30838i
$722$	42.8450	−	6.78599i	1.59453	−	0.252548i
$723$	−0.533992	+	10.1892i	−0.0198594	+	0.378939i
$724$	5.89803	+	10.2157i	0.219198	+	0.379663i
$725$	−11.4134	−	7.27043i	−0.423883	−	0.270017i
$726$	−56.7975	−	32.7920i	−2.10795	−	1.21703i
$727$	16.7072	−	8.51272i	0.619634	−	0.315719i	−0.115845	−	0.993267i	$-0.536957\pi$
$727$	16.7072	−	8.51272i	0.619634	−	0.315719i	0.735478	+	0.677548i	$0.236957\pi$
$728$	−34.9670	−	18.4272i	−1.29596	−	0.682956i
$729$	17.6531	−	24.2974i	0.653818	−	0.899904i
$730$	−12.9360	−	68.1278i	−0.478783	−	2.52152i
$731$	2.23241	−	5.01408i	0.0825687	−	0.185452i
$732$	−26.7643	−	7.17148i	−0.989238	−	0.265065i
$733$	26.9713	+	21.8410i	0.996209	+	0.806714i	0.981165	−	0.193173i	$-0.0618778\pi$
$733$	26.9713	+	21.8410i	0.996209	+	0.806714i	0.0150442	+	0.999887i	$0.495211\pi$
$734$	9.62911	+	29.6354i	0.355417	+	1.09386i
$735$	23.6271	−	5.09714i	0.871500	−	0.188011i
$736$	−8.45298	+	26.0156i	−0.311581	+	0.958948i
$737$	−1.07043	+	0.695143i	−0.0394297	+	0.0256059i
$738$	−0.518667	−	9.89676i	−0.0190924	−	0.364305i
$739$	3.56779	+	16.7851i	0.131243	+	0.617451i	0.993771	+	0.111441i	$0.0355466\pi$
$739$	3.56779	+	16.7851i	0.131243	+	0.617451i	−0.862528	+	0.506010i	$0.831120\pi$
$740$	−8.65676	+	29.7024i	−0.318229	+	1.09188i
$741$	−4.98427	+	1.61949i	−0.183102	+	0.0594934i
$742$	16.2366	−	15.7957i	0.596065	−	0.579878i
$743$	−27.5202	−	27.5202i	−1.00962	−	1.00962i	−0.999953	−	0.00966488i	$-0.996924\pi$
$743$	−27.5202	−	27.5202i	−1.00962	−	1.00962i	−0.00966488	−	0.999953i	$-0.503076\pi$
$744$	−52.6952	+	5.53849i	−1.93190	+	0.203051i
$745$	8.12004	−	2.44405i	0.297495	−	0.0895430i
$746$	−5.09712	+	48.4959i	−0.186619	+	1.77556i
$747$	−5.39110	−	2.06945i	−0.197250	−	0.0757172i
$748$	−11.8562	−	23.2692i	−0.433507	−	0.850805i
$749$	20.6361	+	48.1212i	0.754026	+	1.75831i
$750$	2.82984	−	43.2187i	0.103331	−	1.57812i
$751$	19.5835	−	33.9196i	0.714612	−	1.23774i	−0.248497	−	0.968633i	$-0.579937\pi$
$751$	19.5835	−	33.9196i	0.714612	−	1.23774i	0.963109	−	0.269112i	$-0.0867301\pi$
$752$	34.9676	+	22.7083i	1.27514	+	0.828085i
$753$	15.7828	−	12.7806i	0.575156	−	0.465752i
$754$	−16.1064	+	7.17102i	−0.586559	+	0.261153i
$755$	21.2239	+	4.99706i	0.772415	+	0.181862i
$756$	−55.3520	+	30.9496i	−2.01313	+	1.12563i
$757$	−5.61158	+	5.61158i	−0.203956	+	0.203956i	−0.801693	−	0.597736i	$-0.796067\pi$
$757$	−5.61158	+	5.61158i	−0.203956	+	0.203956i	0.597736	+	0.801693i	$0.296067\pi$
$758$	−35.5762	+	43.9330i	−1.29219	+	1.59572i
$759$	−47.2842	+	52.5145i	−1.71631	+	1.90615i
$760$	−11.6269	−	12.1451i	−0.421752	−	0.440548i
$761$	−19.8262	+	17.8516i	−0.718698	+	0.647119i	−0.945050	−	0.326927i	$-0.893987\pi$
$761$	−19.8262	+	17.8516i	−0.718698	+	0.647119i	0.226352	+	0.974046i	$0.427320\pi$
$762$	2.80271	−	5.50062i	0.101531	−	0.199267i
$763$	15.9233	+	10.6552i	0.576463	+	0.385743i
$764$	−88.0024	−	28.5937i	−3.18382	−	1.03448i
$765$	−0.891405	+	1.30927i	−0.0322288	+	0.0473366i
$766$	−34.9336	−	31.4543i	−1.26220	−	1.13649i
$767$

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.50521 + 0.131292i) q^{2} +(-0.971802 - 1.20007i) q^{3} +(4.26979 + 0.448773i) q^{4} +(-1.53208 + 1.62872i) q^{5} +(-2.27701 - 3.13403i) q^{6} +(2.61863 - 0.377880i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.127953 - 0.601973i) q^{9} +O(q^{10})\)	\(q+(2.50521 + 0.131292i) q^{2} +(-0.971802 - 1.20007i) q^{3} +(4.26979 + 0.448773i) q^{4} +(-1.53208 + 1.62872i) q^{5} +(-2.27701 - 3.13403i) q^{6} +(2.61863 - 0.377880i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.127953 - 0.601973i) q^{9} +(-4.05202 + 3.87914i) q^{10} +(-5.16938 + 1.09879i) q^{11} +(-3.61083 - 5.56019i) q^{12} +(-2.31369 - 1.17888i) q^{13} +(6.60982 - 0.602863i) q^{14} +(3.44346 + 0.255818i) q^{15} +(5.71816 + 1.21543i) q^{16} +(0.412480 + 1.07455i) q^{17} +(0.399585 - 1.49127i) q^{18} +(0.136615 + 1.29981i) q^{19} +(-7.27259 + 6.26674i) q^{20} +(-2.99827 - 2.77532i) q^{21} +(-13.0946 + 2.07399i) q^{22} +(-0.453175 + 8.64709i) q^{23} +(-4.44200 - 7.69377i) q^{24} +(-0.305462 - 4.99066i) q^{25} +(-5.64150 - 3.25712i) q^{26} +(-4.97446 + 2.53461i) q^{27} +(11.3506 - 0.438300i) q^{28} +(1.59083 - 2.18958i) q^{29} +(8.59301 + 1.09298i) q^{30} +(2.42584 - 5.44852i) q^{31} +(3.05145 + 0.817633i) q^{32} +(6.34224 + 5.13584i) q^{33} +(0.892268 + 2.74612i) q^{34} +(-3.39648 + 4.84395i) q^{35} +(0.816484 - 2.51288i) q^{36} +(2.70277 - 1.75520i) q^{37} +(0.171595 + 3.27423i) q^{38} +(0.833698 + 3.92224i) q^{39} +(-10.1715 + 7.87600i) q^{40} +(6.10496 - 1.98362i) q^{41} +(-7.14692 - 7.34642i) q^{42} +(-3.37188 - 3.37188i) q^{43} +(-22.5653 + 2.37171i) q^{44} +(0.784411 + 1.13067i) q^{45} +(-2.27060 + 21.6033i) q^{46} +(6.65848 + 2.55595i) q^{47} +(-4.09831 - 8.04338i) q^{48} +(6.71441 - 1.97905i) q^{49} +(-0.110010 - 12.5428i) q^{50} +(0.888688 - 1.53925i) q^{51} +(-9.34992 - 6.07191i) q^{52} +(2.65234 - 2.14782i) q^{53} +(-12.7948 + 5.69663i) q^{54} +(6.13029 - 10.1029i) q^{55} +(15.2199 + 0.209504i) q^{56} +(1.42711 - 1.42711i) q^{57} +(4.27283 - 5.27650i) q^{58} +(1.17763 - 1.30789i) q^{59} +(14.5881 + 2.63762i) q^{60} +(3.10590 - 2.79657i) q^{61} +(6.79258 - 13.3312i) q^{62} +(0.107588 - 1.62469i) q^{63} +(-3.58241 - 1.16399i) q^{64} +(5.46483 - 1.96221i) q^{65} +(15.2143 + 13.6991i) q^{66} +(0.225467 - 0.0865487i) q^{67} +(1.27897 + 4.77320i) q^{68} +(10.8176 - 7.85941i) q^{69} +(-9.14488 + 11.6892i) q^{70} +(-8.50997 - 6.18285i) q^{71} +(1.26883 - 3.30543i) q^{72} +(-6.73286 + 10.3677i) q^{73} +(7.00145 - 4.04229i) q^{74} +(-5.69232 + 5.21651i) q^{75} +5.61123i q^{76} +(-13.1215 + 4.83072i) q^{77} +(1.57363 + 9.93549i) q^{78} +(1.88229 + 4.22770i) q^{79} +(-10.7403 + 7.45114i) q^{80} +(6.18926 + 2.75564i) q^{81} +(15.5546 - 4.16785i) q^{82} +(1.46786 - 9.26772i) q^{83} +(-11.5565 - 13.1956i) q^{84} +(-2.38209 - 0.974476i) q^{85} +(-8.00457 - 8.88998i) q^{86} +(-4.17363 + 0.218731i) q^{87} +(-30.3628 + 1.59125i) q^{88} +(-3.01084 - 3.34388i) q^{89} +(1.81667 + 2.93556i) q^{90} +(-6.50417 - 2.21276i) q^{91} +(-5.81555 + 36.7179i) q^{92} +(-8.89606 + 2.38369i) q^{93} +(16.3453 + 7.27740i) q^{94} +(-2.32633 - 1.76890i) q^{95} +(-1.98418 - 4.45654i) q^{96} +(1.20511 + 7.60880i) q^{97} +(17.0808 - 4.07639i) q^{98} +3.25242i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more