LMFDB - Embedded newform 755.2.t.b.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(81,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.t (of order $25$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [520,0,0,-140,0,-5,0,0,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$520$
Relative dimension:	$26$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	755.81
Dual form			755.2.t.b.261.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.23996 - 1.62742i) q^{2} +(-0.643868 + 0.0813395i) q^{3} +(1.75087 + 5.38861i) q^{4} +(-0.968583 + 0.248690i) q^{5} +(1.57461 + 0.865650i) q^{6} +(-0.657273 + 0.794506i) q^{7} +(3.13652 - 9.65321i) q^{8} +(-2.49780 + 0.641326i) q^{9} +(2.57431 + 1.01924i) q^{10} +(-1.56584 - 0.197812i) q^{11} +(-1.56563 - 3.32714i) q^{12} +(-0.0938114 + 0.491777i) q^{13} +(2.76526 - 0.709999i) q^{14} +(0.603411 - 0.238908i) q^{15} +(-13.5679 + 9.85764i) q^{16} +(2.43225 + 2.94009i) q^{17} +(6.63867 + 2.62844i) q^{18} +(1.99294 + 6.13364i) q^{19} +(-3.03595 - 4.78390i) q^{20} +(0.358572 - 0.565019i) q^{21} +(3.18549 + 2.99138i) q^{22} +(-1.51841 - 4.67317i) q^{23} +(-1.23432 + 6.47051i) q^{24} +(0.876307 - 0.481754i) q^{25} +(1.01046 - 0.948888i) q^{26} +(3.36632 - 1.33282i) q^{27} +(-5.43208 - 2.15071i) q^{28} +(-0.676279 - 0.635068i) q^{29} +(-1.74042 - 0.446864i) q^{30} +(0.0104192 + 0.165608i) q^{31} +26.1341 q^{32} +1.02428 q^{33} +(-0.663371 - 10.5440i) q^{34} +(0.439038 - 0.933003i) q^{35} +(-7.82917 - 12.3368i) q^{36} +(1.24430 - 6.52286i) q^{37} +(5.51794 - 16.9825i) q^{38} +(0.0204013 - 0.324270i) q^{39} +(-0.637323 + 10.1300i) q^{40} +(-9.04519 - 4.97263i) q^{41} +(-1.72271 + 0.682070i) q^{42} +(-4.75776 - 5.75114i) q^{43} +(-1.67565 - 8.78404i) q^{44} +(2.25984 - 1.24235i) q^{45} +(-4.20407 + 12.9388i) q^{46} +(3.05953 + 1.68199i) q^{47} +(7.93411 - 7.45062i) q^{48} +(1.11244 + 5.83160i) q^{49} +(-2.74691 - 0.347015i) q^{50} +(-1.80520 - 1.69519i) q^{51} +(-2.81425 + 0.355522i) q^{52} +(3.54782 - 7.53949i) q^{53} +(-9.70949 - 2.49297i) q^{54} +(1.56584 - 0.197812i) q^{55} +(5.60799 + 8.83677i) q^{56} +(-1.78210 - 3.78715i) q^{57} +(0.481311 + 2.52312i) q^{58} +(5.18696 - 3.76855i) q^{59} +(2.34387 + 2.83325i) q^{60} +(3.74338 + 0.472899i) q^{61} +(0.246176 - 0.387911i) q^{62} +(1.13220 - 2.40604i) q^{63} +(-31.4035 - 22.8159i) q^{64} +(-0.0314357 - 0.499657i) q^{65} +(-2.29435 - 1.66695i) q^{66} +(-12.5492 - 3.22209i) q^{67} +(-11.5845 + 18.2542i) q^{68} +(1.35777 + 2.88540i) q^{69} +(-2.50182 + 1.37539i) q^{70} +(3.42012 - 4.13422i) q^{71} +(-1.64354 + 26.1233i) q^{72} +(2.74431 - 3.31730i) q^{73} +(-13.4026 + 12.5859i) q^{74} +(-0.525040 + 0.381464i) q^{75} +(-29.5624 + 21.4784i) q^{76} +(1.18635 - 1.11405i) q^{77} +(-0.573423 + 0.693149i) q^{78} +(0.785118 - 12.4791i) q^{79} +(10.6901 - 12.9221i) q^{80} +(4.72045 - 2.59509i) q^{81} +(12.1682 + 25.8588i) q^{82} +(-6.69424 + 10.5484i) q^{83} +(3.67248 + 0.942933i) q^{84} +(-3.08701 - 2.24284i) q^{85} +(1.29763 + 20.6252i) q^{86} +(0.487091 + 0.353892i) q^{87} +(-6.82080 + 14.4949i) q^{88} +(-0.162373 + 0.255859i) q^{89} +(-7.08377 - 0.894889i) q^{90} +(-0.329060 - 0.397765i) q^{91} +(22.5234 - 16.3642i) q^{92} +(-0.0201790 - 0.105782i) q^{93} +(-4.11591 - 8.74675i) q^{94} +(-3.45570 - 5.44532i) q^{95} +(-16.8269 + 2.12573i) q^{96} +(-5.41459 - 1.39023i) q^{97} +(6.99867 - 14.8729i) q^{98} +(4.03802 - 0.510120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 520 q - 140 q^{4} - 5 q^{6} + 5 q^{10} + 5 q^{11} - 20 q^{13} - 15 q^{14} - 160 q^{16} + 25 q^{17} + 25 q^{18} + 5 q^{20} - 30 q^{23} + 20 q^{24} - 15 q^{26} - 45 q^{27} - 145 q^{28} - 25 q^{29} - 30 q^{31}+ \cdots - 60 q^{99}+O(q^{100}) $ 520 * q - 140 * q^4 - 5 * q^6 + 5 * q^10 + 5 * q^11 - 20 * q^13 - 15 * q^14 - 160 * q^16 + 25 * q^17 + 25 * q^18 + 5 * q^20 - 30 * q^23 + 20 * q^24 - 15 * q^26 - 45 * q^27 - 145 * q^28 - 25 * q^29 - 30 * q^31 + 45 * q^34 + 10 * q^35 - 20 * q^36 - 30 * q^37 - 65 * q^38 + 30 * q^39 - 45 * q^40 + 5 * q^41 + 245 * q^42 + 50 * q^46 + 95 * q^47 + 290 * q^48 - 10 * q^49 + 5 * q^50 - 5 * q^51 - 55 * q^52 + 135 * q^53 - 390 * q^54 - 5 * q^55 + 150 * q^56 + 30 * q^58 + 20 * q^59 + 35 * q^60 + 10 * q^61 - 60 * q^62 - 30 * q^63 - 200 * q^64 + 25 * q^65 + 200 * q^66 - 60 * q^67 - 130 * q^68 + 10 * q^69 - 30 * q^70 - 30 * q^71 + 425 * q^72 + 30 * q^73 + 120 * q^74 - 15 * q^75 + 15 * q^76 + 40 * q^77 - 5 * q^78 + 215 * q^79 - 15 * q^80 - 100 * q^81 - 100 * q^82 - 5 * q^83 - 45 * q^84 - 15 * q^85 + 140 * q^86 - 20 * q^87 + 135 * q^88 - 15 * q^89 - 20 * q^90 - 10 * q^91 + 180 * q^92 + 100 * q^93 - 65 * q^94 - 55 * q^95 + 35 * q^96 + 15 * q^97 - 160 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$e\left(\frac{4}{25}\right)$	$1$

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 $

$2$	−2.23996	−	1.62742i	−1.58389	−	1.15076i	−0.912060	−	0.410057i	$-0.865509\pi$
$2$	−2.23996	−	1.62742i	−1.58389	−	1.15076i	−0.671829	−	0.740706i	$-0.734491\pi$
$3$	−0.643868	+	0.0813395i	−0.371737	+	0.0469614i	−0.308983	−	0.951068i	$-0.599989\pi$
$3$	−0.643868	+	0.0813395i	−0.371737	+	0.0469614i	−0.0627546	+	0.998029i	$0.519989\pi$
$4$	1.75087	+	5.38861i	0.875433	+	2.69431i
$5$	−0.968583	+	0.248690i	−0.433164	+	0.111217i
$5$	−0.968583	+	0.248690i	−0.433164	+	0.111217i
$6$	1.57461	+	0.865650i	0.642832	+	0.353400i
$7$	−0.657273	+	0.794506i	−0.248426	+	0.300295i	−0.879955	−	0.475057i	$-0.842428\pi$
$7$	−0.657273	+	0.794506i	−0.248426	+	0.300295i	0.631529	+	0.775352i	$0.282428\pi$
$8$	3.13652	−	9.65321i	1.10893	−	3.41292i
$9$	−2.49780	+	0.641326i	−0.832600	+	0.213775i
$10$	2.57431	+	1.01924i	0.814068	+	0.322312i
$11$	−1.56584	−	0.197812i	−0.472119	−	0.0596424i	−0.114325	−	0.993443i	$-0.536471\pi$
$11$	−1.56584	−	0.197812i	−0.472119	−	0.0596424i	−0.357793	+	0.933801i	$0.616471\pi$
$12$	−1.56563	−	3.32714i	−0.451959	−	0.960463i
$13$	−0.0938114	+	0.491777i	−0.0260186	+	0.136394i	−0.992926	−	0.118732i	$-0.962117\pi$
$13$	−0.0938114	+	0.491777i	−0.0260186	+	0.136394i	0.966908	+	0.255126i	$0.0821171\pi$
$14$	2.76526	−	0.709999i	0.739047	−	0.189755i
$15$	0.603411	−	0.238908i	0.155800	−	0.0616857i
$16$	−13.5679	+	9.85764i	−3.39197	+	2.46441i
$17$	2.43225	+	2.94009i	0.589908	+	0.713077i	0.978014	−	0.208538i	$-0.0668706\pi$
$17$	2.43225	+	2.94009i	0.589908	+	0.713077i	−0.388106	+	0.921615i	$0.626871\pi$
$18$	6.63867	+	2.62844i	1.56475	+	0.619529i
$19$	1.99294	+	6.13364i	0.457212	+	1.40715i	0.868518	+	0.495657i	$0.165073\pi$
$19$	1.99294	+	6.13364i	0.457212	+	1.40715i	−0.411306	+	0.911497i	$0.634927\pi$
$20$	−3.03595	−	4.78390i	−0.678860	−	1.06971i
$21$	0.358572	−	0.565019i	0.0782469	−	0.123297i
$22$	3.18549	+	2.99138i	0.679149	+	0.637764i
$23$	−1.51841	−	4.67317i	−0.316610	−	0.974424i	−0.975087	−	0.221824i	$-0.928799\pi$
$23$	−1.51841	−	4.67317i	−0.316610	−	0.974424i	0.658477	−	0.752601i	$-0.271201\pi$
$24$	−1.23432	+	6.47051i	−0.251954	+	1.32079i
$25$	0.876307	−	0.481754i	0.175261	−	0.0963507i
$26$	1.01046	−	0.948888i	0.198168	−	0.186092i
$27$	3.36632	−	1.33282i	0.647849	−	0.256502i
$28$	−5.43208	−	2.15071i	−1.02657	−	0.406447i
$29$	−0.676279	−	0.635068i	−0.125582	−	0.117929i	0.619212	−	0.785224i	$-0.287452\pi$
$29$	−0.676279	−	0.635068i	−0.125582	−	0.117929i	−0.744794	+	0.667295i	$0.767452\pi$
$30$	−1.74042	−	0.446864i	−0.317756	−	0.0815858i
$31$	0.0104192	+	0.165608i	0.00187134	+	0.0297441i	0.998852	−	0.0479115i	$-0.0152565\pi$
$31$	0.0104192	+	0.165608i	0.00187134	+	0.0297441i	−0.996980	+	0.0776556i	$0.975257\pi$
$32$	26.1341			4.61989
$33$	1.02428			0.178305
$34$	−0.663371	−	10.5440i	−0.113767	−	1.80828i
$35$	0.439038	−	0.933003i	0.0742109	−	0.157706i
$36$	−7.82917	−	12.3368i	−1.30486	−	2.05613i
$37$	1.24430	−	6.52286i	0.204562	−	1.07235i	−0.720764	−	0.693180i	$-0.756209\pi$
$37$	1.24430	−	6.52286i	0.204562	−	1.07235i	0.925326	−	0.379171i	$-0.123791\pi$
$38$	5.51794	−	16.9825i	0.895127	−	2.75492i
$39$	0.0204013	−	0.324270i	0.00326683	−	0.0519248i
$40$	−0.637323	+	10.1300i	−0.100770	+	1.60169i
$41$	−9.04519	−	4.97263i	−1.41262	−	0.776595i	−0.421158	−	0.906987i	$-0.638376\pi$
$41$	−9.04519	−	4.97263i	−1.41262	−	0.776595i	−0.991462	+	0.130392i	$0.958376\pi$
$42$	−1.72271	+	0.682070i	−0.265820	+	0.105246i
$43$	−4.75776	−	5.75114i	−0.725551	−	0.877041i	0.270778	−	0.962642i	$-0.412719\pi$
$43$	−4.75776	−	5.75114i	−0.725551	−	0.877041i	−0.996329	+	0.0856011i	$0.972719\pi$
$44$	−1.67565	−	8.78404i	−0.252613	−	1.32424i
$45$	2.25984	−	1.24235i	0.336876	−	0.185199i
$46$	−4.20407	+	12.9388i	−0.619857	+	1.90772i
$47$	3.05953	+	1.68199i	0.446279	+	0.245344i	0.689013	−	0.724749i	$-0.258044\pi$
$47$	3.05953	+	1.68199i	0.446279	+	0.245344i	−0.242734	+	0.970093i	$0.578044\pi$
$48$	7.93411	−	7.45062i	1.14519	−	1.07540i
$49$	1.11244	+	5.83160i	0.158919	+	0.833085i
$50$	−2.74691	−	0.347015i	−0.388471	−	0.0490754i
$51$	−1.80520	−	1.69519i	−0.252778	−	0.237374i
$52$	−2.81425	+	0.355522i	−0.390266	+	0.0493020i
$53$	3.54782	−	7.53949i	0.487330	−	1.03563i	−0.498346	−	0.866978i	$-0.666059\pi$
$53$	3.54782	−	7.53949i	0.487330	−	1.03563i	0.985676	−	0.168651i	$-0.0539410\pi$
$54$	−9.70949	−	2.49297i	−1.32129	−	0.339251i
$55$	1.56584	−	0.197812i	0.211138	−	0.0266729i
$56$	5.60799	+	8.83677i	0.749399	+	1.18086i
$57$	−1.78210	−	3.78715i	−0.236045	−	0.501620i
$58$	0.481311	+	2.52312i	0.0631992	+	0.331302i
$59$	5.18696	−	3.76855i	0.675285	−	0.490623i	−0.196505	−	0.980503i	$-0.562959\pi$
$59$	5.18696	−	3.76855i	0.675285	−	0.490623i	0.871790	+	0.489879i	$0.162959\pi$
$60$	2.34387	+	2.83325i	0.302593	+	0.365772i
$61$	3.74338	+	0.472899i	0.479291	+	0.0605486i	0.361267	−	0.932462i	$-0.382344\pi$
$61$	3.74338	+	0.472899i	0.479291	+	0.0605486i	0.118024	+	0.993011i	$0.462344\pi$
$62$	0.246176	−	0.387911i	0.0312644	−	0.0492648i
$63$	1.13220	−	2.40604i	0.142644	−	0.303133i
$64$	−31.4035	−	22.8159i	−3.92543	−	2.85199i
$65$	−0.0314357	−	0.499657i	−0.00389912	−	0.0619748i
$66$	−2.29435	−	1.66695i	−0.282415	−	0.205187i
$67$	−12.5492	−	3.22209i	−1.53313	−	0.393641i	−0.614550	−	0.788878i	$-0.710662\pi$
$67$	−12.5492	−	3.22209i	−1.53313	−	0.393641i	−0.918579	+	0.395237i	$0.870662\pi$
$68$	−11.5845	+	18.2542i	−1.40482	+	2.21364i
$69$	1.35777	+	2.88540i	0.163456	+	0.347362i
$70$	−2.50182	+	1.37539i	−0.299024	+	0.164390i
$71$	3.42012	−	4.13422i	0.405894	−	0.490641i	−0.527470	−	0.849574i	$-0.676859\pi$
$71$	3.42012	−	4.13422i	0.405894	−	0.490641i	0.933364	+	0.358932i	$0.116859\pi$
$72$	−1.64354	+	26.1233i	−0.193693	+	3.07866i
$73$	2.74431	−	3.31730i	0.321197	−	0.388261i	−0.585058	−	0.810991i	$-0.698928\pi$
$73$	2.74431	−	3.31730i	0.321197	−	0.388261i	0.906255	+	0.422730i	$0.138928\pi$
$74$	−13.4026	+	12.5859i	−1.55803	+	1.46308i
$75$	−0.525040	+	0.381464i	−0.0606264	+	0.0440477i
$76$	−29.5624	+	21.4784i	−3.39104	+	2.46374i
$77$	1.18635	−	1.11405i	0.135197	−	0.126958i
$78$	−0.573423	+	0.693149i	−0.0649274	+	0.0784837i
$79$	0.785118	−	12.4791i	0.0883327	−	1.40401i	−0.665233	−	0.746636i	$-0.731668\pi$
$79$	0.785118	−	12.4791i	0.0883327	−	1.40401i	0.753566	−	0.657372i	$-0.228332\pi$
$80$	10.6901	−	12.9221i	1.19519	−	1.44474i
$81$	4.72045	−	2.59509i	0.524494	−	0.288343i
$82$	12.1682	+	25.8588i	1.34376	+	2.85563i
$83$	−6.69424	+	10.5484i	−0.734788	+	1.15784i	0.247212	+	0.968961i	$0.420486\pi$
$83$	−6.69424	+	10.5484i	−0.734788	+	1.15784i	−0.982000	+	0.188879i	$0.939514\pi$
$84$	3.67248	+	0.942933i	0.400701	+	0.102882i
$85$	−3.08701	−	2.24284i	−0.334833	−	0.243271i
$86$	1.29763	+	20.6252i	0.139927	+	2.22407i
$87$	0.487091	+	0.353892i	0.0522216	+	0.0379412i
$88$	−6.82080	+	14.4949i	−0.727100	+	1.54517i
$89$	−0.162373	+	0.255859i	−0.0172115	+	0.0271210i	−0.852825	−	0.522197i	$-0.825113\pi$
$89$	−0.162373	+	0.255859i	−0.0172115	+	0.0271210i	0.835613	+	0.549318i	$0.185113\pi$
$90$	−7.08377	−	0.894889i	−0.746695	−	0.0943296i
$91$	−0.329060	−	0.397765i	−0.0344949	−	0.0416971i
$92$	22.5234	−	16.3642i	2.34823	−	1.70609i
$93$	−0.0201790	−	0.105782i	−0.00209247	−	0.0109691i
$94$	−4.11591	−	8.74675i	−0.424524	−	0.902159i
$95$	−3.45570	−	5.44532i	−0.354548	−	0.558678i
$96$	−16.8269	+	2.12573i	−1.71739	+	0.216956i
$97$	−5.41459	−	1.39023i	−0.549768	−	0.141157i	−0.0364195	−	0.999337i	$-0.511595\pi$
$97$	−5.41459	−	1.39023i	−0.549768	−	0.141157i	−0.513349	+	0.858180i	$0.671595\pi$
$98$	6.99867	−	14.8729i	0.706973	−	1.50239i
$99$	4.03802	−	0.510120i	0.405836	−	0.0512690i
$100$	4.13028	+	3.87859i	0.413028	+	0.387859i
$101$	−9.66066	−	1.22043i	−0.961272	−	0.121437i	−0.370993	−	0.928636i	$-0.620982\pi$
$101$	−9.66066	−	1.22043i	−0.961272	−	0.121437i	−0.590279	+	0.807199i	$0.700982\pi$
$102$	1.28477	+	6.73498i	0.127211	+	0.666862i
$103$	−13.3298	+	12.5175i	−1.31342	+	1.23339i	−0.359569	+	0.933118i	$0.617076\pi$
$103$	−13.3298	+	12.5175i	−1.31342	+	1.23339i	−0.953855	+	0.300269i	$0.902924\pi$
$104$	4.45298	+	2.44805i	0.436651	+	0.240051i
$105$	−0.206792	+	0.636442i	−0.0201809	+	0.0621103i
$106$	−20.2169	+	11.1143i	−1.96364	+	1.07952i
$107$	−1.08291	−	5.67679i	−0.104689	−	0.548796i	−0.995527	−	0.0944765i	$-0.969882\pi$
$107$	−1.08291	−	5.67679i	−0.104689	−	0.548796i	0.890839	−	0.454320i	$-0.150118\pi$
$108$	13.0760	+	15.8062i	1.25824	+	1.52095i
$109$	13.9774	−	5.53404i	1.33879	−	0.530065i	0.413909	−	0.910318i	$-0.364163\pi$
$109$	13.9774	−	5.53404i	1.33879	−	0.530065i	0.924882	+	0.380253i	$0.124163\pi$
$110$	−3.82934	−	2.10520i	−0.365113	−	0.200723i
$111$	−0.270601	+	4.30107i	−0.0256843	+	0.408240i
$112$	1.08584	−	17.2589i	0.102602	−	1.63081i
$113$	5.01261	−	15.4272i	0.471547	−	1.45127i	−0.379011	−	0.925392i	$-0.623736\pi$
$113$	5.01261	−	15.4272i	0.471547	−	1.45127i	0.850558	−	0.525881i	$-0.176264\pi$
$114$	−2.17148	+	11.3833i	−0.203378	+	1.06614i
$115$	2.63287	+	4.14875i	0.245517	+	0.386873i
$116$	2.23806	−	4.75613i	0.207799	−	0.441595i
$117$	−0.0810670	−	1.28852i	−0.00749465	−	0.119124i
$118$	−17.7516			−1.63417
$119$	−3.93457			−0.360682
$120$	−0.413613	−	6.57419i	−0.0377575	−	0.600139i
$121$	−8.24169	−	2.11611i	−0.749244	−	0.192373i
$122$	−7.61541	−	7.15135i	−0.689467	−	0.647453i
$123$	6.22838	+	2.46599i	0.561594	+	0.222351i
$124$	−0.874154	+	0.346102i	−0.0785014	+	0.0310809i
$125$	−0.728969	+	0.684547i	−0.0652009	+	0.0612278i
$126$	−6.45173	+	3.54687i	−0.574766	+	0.315980i
$127$	2.35766	−	12.3593i	0.209209	−	1.09671i	−0.710377	−	0.703821i	$-0.751476\pi$
$127$	2.35766	−	12.3593i	0.209209	−	1.09671i	0.919586	−	0.392889i	$-0.128524\pi$
$128$	17.0594	+	52.5035i	1.50786	+	4.64070i
$129$	3.53116	+	3.31598i	0.310901	+	0.291956i
$130$	−0.742739	+	1.17037i	−0.0651425	+	0.102648i
$131$	−4.47189	−	7.04658i	−0.390711	−	0.615662i	0.590857	−	0.806777i	$-0.298790\pi$
$131$	−4.47189	−	7.04658i	−0.390711	−	0.615662i	−0.981568	+	0.191114i	$0.938790\pi$
$132$	1.79338	+	5.51947i	0.156094	+	0.480408i
$133$	−6.18312	−	2.44807i	−0.536145	−	0.212275i
$134$	22.8660	+	27.6402i	1.97532	+	2.38775i
$135$	−2.92910	+	2.12812i	−0.252097	+	0.183159i
$136$	36.0101	−	14.2574i	3.08784	−	1.22256i
$137$	−8.58887	+	2.20525i	−0.733797	+	0.188407i	−0.597056	−	0.802200i	$-0.703663\pi$
$137$	−8.58887	+	2.20525i	−0.733797	+	0.188407i	−0.136741	+	0.990607i	$0.543663\pi$
$138$	1.65443	−	8.67284i	0.140835	−	0.738281i
$139$	−4.73057	−	10.0530i	−0.401241	−	0.852681i	−0.998709	−	0.0507887i	$-0.983827\pi$
$139$	−4.73057	−	10.0530i	−0.401241	−	0.852681i	0.597468	−	0.801893i	$-0.296173\pi$
$140$	5.79628	+	0.732241i	0.489875	+	0.0618857i
$141$	−2.10675	−	0.834121i	−0.177420	−	0.0702456i
$142$	−14.3891	+	3.69448i	−1.20750	+	0.310034i
$143$	0.244173	−	0.751487i	0.0204188	−	0.0628425i
$144$	27.5679	−	33.3238i	2.29732	−	2.77699i
$145$	0.812968	+	0.446933i	0.0675133	+	0.0371158i
$146$	−11.5458	+	2.96446i	−0.955537	+	0.245340i
$147$	−1.19060	−	3.66429i	−0.0981991	−	0.302226i
$148$	37.3278	−	4.71559i	3.06832	−	0.387619i
$149$	11.3687	+	8.25982i	0.931357	+	0.676671i	0.946325	−	0.323217i	$-0.104764\pi$
$149$	11.3687	+	8.25982i	0.931357	+	0.676671i	−0.0149675	+	0.999888i	$0.504764\pi$
$150$	1.79687			0.146714
$151$	12.1097	−	2.08663i	0.985477	−	0.169807i
$151$	12.1097	−	2.08663i	0.985477	−	0.169807i
$152$	65.4602			5.30952
$153$	−7.96084	−	5.78389i	−0.643596	−	0.467600i
$154$	−4.47040	+	0.564743i	−0.360235	+	0.0455083i
$155$	−0.0512769	−	0.157814i	−0.00411866	−	0.0126759i
$156$	1.78308	−	0.457818i	0.142761	−	0.0366548i
$157$	−1.09201	−	0.600336i	−0.0871517	−	0.0479120i	0.437582	−	0.899179i	$-0.355835\pi$
$157$	−1.09201	−	0.600336i	−0.0871517	−	0.0479120i	−0.524734	+	0.851267i	$0.675835\pi$
$158$	−22.0674	+	26.6749i	−1.75559	+	2.12214i
$159$	−1.67107	+	5.14302i	−0.132524	+	0.407868i
$160$	−25.3130	+	6.49928i	−2.00117	+	0.513813i
$161$	4.71087	+	1.86517i	0.371269	+	0.146996i
$162$	−14.7969	−	1.86929i	−1.16256	−	0.146865i
$163$	−1.55286	−	3.30000i	−0.121629	−	0.258476i	0.834735	−	0.550652i	$-0.185621\pi$
$163$	−1.55286	−	3.30000i	−0.121629	−	0.258476i	−0.956365	+	0.292176i	$0.905621\pi$
$164$	10.9587	−	57.4474i	0.855729	−	4.48589i
$165$	−0.992104	+	0.254729i	−0.0772352	+	0.0198306i
$166$	32.1616	−	12.7337i	2.49622	−	0.988325i
$167$	6.70891	−	4.87431i	0.519151	−	0.377186i	−0.297133	−	0.954836i	$-0.596030\pi$
$167$	6.70891	−	4.87431i	0.519151	−	0.377186i	0.816284	+	0.577651i	$0.196030\pi$
$168$	−4.32958	−	5.23357i	−0.334034	−	0.403778i
$169$	11.8541	+	4.69335i	0.911850	+	0.361027i
$170$	3.26471	+	10.0478i	0.250392	+	0.770628i
$171$	−8.91163	−	14.0425i	−0.681489	−	1.07386i
$172$	22.6605	−	35.7072i	1.72784	−	2.72265i
$173$	−1.94503	−	1.82651i	−0.147878	−	0.138867i	0.607078	−	0.794642i	$-0.292342\pi$
$173$	−1.94503	−	1.82651i	−0.147878	−	0.138867i	−0.754956	+	0.655776i	$0.772342\pi$
$174$	−0.515130	−	1.58541i	−0.0390519	−	0.120189i
$175$	−0.193216	+	1.01287i	−0.0146058	+	0.0765661i
$176$	23.1951	−	12.7516i	1.74839	−	0.961188i
$177$	−3.03319	+	2.84835i	−0.227988	+	0.214095i
$178$	0.780100	−	0.308863i	0.0584710	−	0.0231503i
$179$	6.85352	+	2.71350i	0.512256	+	0.202817i	0.610010	−	0.792394i	$-0.291166\pi$
$179$	6.85352	+	2.71350i	0.512256	+	0.202817i	−0.0977532	+	0.995211i	$0.531166\pi$
$180$	10.6512	+	10.0022i	0.793896	+	0.745518i
$181$	20.3013	+	5.21249i	1.50899	+	0.387442i	0.910438	−	0.413646i	$-0.135745\pi$
$181$	20.3013	+	5.21249i	1.50899	+	0.387442i	0.598547	+	0.801087i	$0.295745\pi$
$182$	0.0897476	+	1.42650i	0.00665254	+	0.105739i
$183$	−2.44871			−0.181014
$184$	−49.8736			−3.67673
$185$	0.416959	+	6.62738i	0.0306555	+	0.487254i
$186$	−0.126952	+	0.269788i	−0.00930860	+	0.0197818i
$187$	−3.22694	−	5.08484i	−0.235977	−	0.371840i
$188$	−3.70677	+	19.4316i	−0.270344	+	1.41719i
$189$	−1.15366	+	3.55059i	−0.0839162	+	0.258268i
$190$	−1.12121	+	17.8212i	−0.0813414	+	1.29288i
$191$	0.852673	−	13.5528i	0.0616972	−	0.980649i	−0.838426	−	0.545015i	$-0.816524\pi$
$191$	0.852673	−	13.5528i	0.0616972	−	0.980649i	0.900124	−	0.435634i	$-0.143476\pi$
$192$	22.0755	+	12.1361i	1.59316	+	0.875849i
$193$	9.39879	−	3.72124i	0.676540	−	0.267861i	−0.00462704	−	0.999989i	$-0.501473\pi$
$193$	9.39879	−	3.72124i	0.676540	−	0.267861i	0.681167	+	0.732128i	$0.261473\pi$
$194$	9.86596	+	11.9259i	0.708334	+	0.856229i
$195$	0.0608823	+	0.319156i	0.00435987	+	0.0228552i
$196$	−29.4765	+	16.2048i	−2.10546	+	1.15749i
$197$	2.12496	−	6.53996i	0.151397	−	0.465953i	−0.846381	−	0.532578i	$-0.821223\pi$
$197$	2.12496	−	6.53996i	0.151397	−	0.465953i	0.997778	+	0.0666252i	$0.0212232\pi$
$198$	−9.87517	−	5.42892i	−0.701798	−	0.385816i
$199$	−5.93309	+	5.57154i	−0.420585	+	0.394956i	−0.865737	−	0.500499i	$-0.833150\pi$
$199$	−5.93309	+	5.57154i	−0.420585	+	0.394956i	0.445152	+	0.895455i	$0.353150\pi$
$200$	−1.90192	−	9.97020i	−0.134486	−	0.704999i
$201$	8.34211	+	1.05385i	0.588407	+	0.0743331i
$202$	19.6533	+	18.4557i	1.38280	+	1.29854i
$203$	0.949066	−	0.119895i	0.0666114	−	0.00841497i
$204$	5.97407	−	12.6956i	0.418269	−	0.888866i
$205$	9.99766	+	2.56696i	0.698267	+	0.179284i
$206$	50.2295	−	6.34546i	3.49965	−	0.442109i
$207$	6.78970	+	10.6989i	0.471917	+	0.743622i
$208$	−3.57494	−	7.59713i	−0.247877	−	0.526766i
$209$	−1.90732	−	9.99853i	−0.131932	−	0.691613i
$210$	1.49897	−	1.08906i	0.103439	−	0.0751525i
$211$	11.0326	+	13.3361i	0.759516	+	0.918097i	0.998600	−	0.0529022i	$-0.0168472\pi$
$211$	11.0326	+	13.3361i	0.759516	+	0.918097i	−0.239084	+	0.970999i	$0.576847\pi$
$212$	46.8391	+	5.91716i	3.21693	+	0.406392i
$213$	−1.86583	+	2.94008i	−0.127845	+	0.201451i
$214$	−6.81289	+	14.4781i	−0.465720	+	0.989704i
$215$	6.03853	+	4.38725i	0.411825	+	0.299208i
$216$	−2.30747	−	36.6762i	−0.157004	−	2.49550i
$217$	−0.138425	−	0.100572i	−0.00939689	−	0.00682724i
$218$	−40.3150	−	10.3511i	−2.73048	−	0.701067i
$219$	−1.49715	+	2.35913i	−0.101168	+	0.159415i
$220$	3.80751	+	8.09136i	0.256702	+	0.545519i
$221$	−1.67404	+	0.920312i	−0.112608	+	0.0619069i
$222$	7.60580	−	9.19384i	0.510468	−	0.617050i
$223$	−0.317626	+	5.04852i	−0.0212698	+	0.338074i	0.972973	+	0.230920i	$0.0741737\pi$
$223$	−0.317626	+	5.04852i	−0.0212698	+	0.338074i	−0.994242	+	0.107154i	$0.965826\pi$
$224$	−17.1772	+	20.7637i	−1.14770	+	1.38733i
$225$	−1.87988	+	1.76532i	−0.125325	+	0.117688i
$226$	−36.3347	+	26.3987i	−2.41695	+	1.75602i
$227$	−19.9157	+	14.4696i	−1.32185	+	0.960382i	−0.321946	+	0.946758i	$0.604337\pi$
$227$	−19.9157	+	14.4696i	−1.32185	+	0.960382i	−0.999907	+	0.0136243i	$0.995663\pi$
$228$	17.2873	−	16.2338i	1.14488	−	1.07511i
$229$	−11.6660	+	14.1018i	−0.770911	+	0.931872i	−0.999129	−	0.0417384i	$-0.986710\pi$
$229$	−11.6660	+	14.1018i	−0.770911	+	0.931872i	0.228217	+	0.973610i	$0.426710\pi$
$230$	0.854244	−	13.5778i	0.0563272	−	0.895295i
$231$	−0.673234	+	0.813800i	−0.0442956	+	0.0535441i
$232$	−8.25161	+	4.53636i	−0.541745	+	0.297827i
$233$	−5.87546	−	12.4860i	−0.384914	−	0.817984i	−0.999574	−	0.0291915i	$-0.990707\pi$
$233$	−5.87546	−	12.4860i	−0.384914	−	0.817984i	0.614660	−	0.788792i	$-0.289293\pi$
$234$	−1.91539	+	3.01817i	−0.125213	+	0.197304i
$235$	−3.38171	−	0.868275i	−0.220598	−	0.0566400i
$236$	29.3889	+	21.3523i	1.91306	+	1.38992i
$237$	0.509530	+	8.09875i	0.0330976	+	0.526071i
$238$	8.81328	+	6.40322i	0.571280	+	0.415059i
$239$	−10.7269	+	22.7959i	−0.693868	+	1.47454i	0.177606	+	0.984102i	$0.443165\pi$
$239$	−10.7269	+	22.7959i	−0.693868	+	1.47454i	−0.871473	+	0.490443i	$0.836835\pi$
$240$	−5.83195	+	9.18968i	−0.376451	+	0.593191i
$241$	−4.87939	−	0.616410i	−0.314309	−	0.0397065i	−0.0334037	−	0.999442i	$-0.510635\pi$
$241$	−4.87939	−	0.616410i	−0.314309	−	0.0397065i	−0.280905	+	0.959735i	$0.590635\pi$
$242$	15.0172	+	18.1527i	0.965344	+	1.16690i
$243$	−11.6156	+	8.43921i	−0.745140	+	0.541376i
$244$	4.00589	+	20.9996i	0.256451	+	1.34436i
$245$	−2.52775	−	5.37173i	−0.161492	−	0.343187i
$246$	−9.93809	−	15.6599i	−0.633629	−	0.998440i
$247$	−3.20334	+	0.404676i	−0.203824	+	0.0257489i
$248$	1.63133	+	0.418854i	0.103589	+	0.0265972i
$249$	3.45220	−	7.33630i	0.218774	−	0.464919i
$250$	2.74691	−	0.347015i	0.173730	−	0.0219472i
$251$	−13.5305	−	12.7060i	−0.854039	−	0.801996i	0.127782	−	0.991802i	$-0.459214\pi$
$251$	−13.5305	−	12.7060i	−0.854039	−	0.801996i	−0.981822	+	0.189806i	$0.939214\pi$
$252$	14.9476	+	1.88832i	0.941608	+	0.118953i
$253$	1.45317	+	7.61780i	0.0913602	+	0.478927i
$254$	−25.3949	+	23.8474i	−1.59342	+	1.49632i
$255$	2.17006	+	1.19300i	0.135894	+	0.0747086i
$256$	23.2430	−	71.5347i	1.45269	−	4.47092i
$257$	9.68468	−	5.32420i	0.604114	−	0.332114i	−0.150173	−	0.988660i	$-0.547983\pi$
$257$	9.68468	−	5.32420i	0.604114	−	0.332114i	0.754287	+	0.656545i	$0.227983\pi$
$258$	−2.51314	−	13.1744i	−0.156461	−	0.820200i
$259$	4.36461	+	5.27590i	0.271204	+	0.327829i
$260$	2.63742	−	1.04423i	0.163566	−	0.0647602i
$261$	2.09650	+	1.15256i	0.129770	+	0.0713416i
$262$	−1.45092	+	23.0617i	−0.0896381	+	1.42476i
$263$	0.646941	−	10.2828i	0.0398921	−	0.634066i	−0.926388	−	0.376572i	$-0.877103\pi$
$263$	0.646941	−	10.2828i	0.0398921	−	0.634066i	0.966280	−	0.257495i	$-0.0828971\pi$
$264$	3.21268	−	9.88763i	0.197727	−	0.608541i
$265$	−1.56136	+	8.18493i	−0.0959135	+	0.502796i
$266$	9.86588	+	15.5461i	0.604916	+	0.953195i
$267$	0.0837354	−	0.177947i	0.00512452	−	0.0108902i
$268$	−4.60939	−	73.2642i	−0.281564	−	4.47532i
$269$	12.5036			0.762358			0.381179	−	0.924501i	$-0.375518\pi$
$269$	12.5036			0.762358			0.381179	+	0.924501i	$0.375518\pi$
$270$	10.0244			0.610067
$271$	−1.52831	−	24.2919i	−0.0928385	−	1.47563i	−0.718498	−	0.695529i	$-0.755170\pi$
$271$	−1.52831	−	24.2919i	−0.0928385	−	1.47563i	0.625659	−	0.780097i	$-0.284830\pi$
$272$	−61.9829	−	15.9145i	−3.75826	−	0.964958i
$273$	0.244225	+	0.229343i	0.0147812	+	0.0138805i
$274$	22.8276	+	9.03808i	1.37906	+	0.546010i
$275$	−1.46745	+	0.581006i	−0.0884907	+	0.0350360i
$276$	−13.1710	+	12.3684i	−0.792803	+	0.744492i
$277$	−1.05257	+	0.578657i	−0.0632430	+	0.0347681i	−0.513061	−	0.858352i	$-0.671489\pi$
$277$	−1.05257	+	0.578657i	−0.0632430	+	0.0347681i	0.449818	+	0.893120i	$0.351489\pi$
$278$	−5.76417	+	30.2169i	−0.345712	+	1.81229i
$279$	−0.132234	−	0.406973i	−0.00791662	−	0.0243649i
$280$	−7.62942	−	7.16450i	−0.455945	−	0.428161i
$281$	12.3910	−	19.5251i	0.739184	−	1.16477i	−0.241733	−	0.970343i	$-0.577716\pi$
$281$	12.3910	−	19.5251i	0.739184	−	1.16477i	0.980917	−	0.194426i	$-0.0622843\pi$
$282$	3.36156	+	5.29697i	0.200178	+	0.315430i
$283$	−0.817412	−	2.51574i	−0.0485901	−	0.149545i	0.923818	−	0.382833i	$-0.125052\pi$
$283$	−0.817412	−	2.51574i	−0.0485901	−	0.149545i	−0.972408	+	0.233288i	$0.925052\pi$
$284$	28.2659	+	11.1912i	1.67727	+	0.664079i
$285$	2.66794	+	3.22498i	0.158035	+	0.191031i
$286$	−1.76993	+	1.28593i	−0.104658	+	0.0760384i
$287$	9.89594	−	3.91808i	0.584139	−	0.231277i
$288$	−65.2777	+	16.7605i	−3.84652	+	0.987619i
$289$	0.457213	−	2.39679i	0.0268949	−	0.140988i
$290$	−1.09366	−	2.32415i	−0.0642222	−	0.136479i
$291$	3.59936	+	0.454705i	0.210998	+	0.0266553i
$292$	22.6806	+	8.97987i	1.32728	+	0.525507i
$293$	−0.326723	+	0.0838882i	−0.0190874	+	0.00490080i	−0.258221	−	0.966086i	$-0.583136\pi$
$293$	−0.326723	+	0.0838882i	−0.0190874	+	0.00490080i	0.239134	+	0.970987i	$0.423136\pi$
$294$	−3.29646	+	10.1455i	−0.192254	+	0.591696i
$295$	−4.08681	+	4.94010i	−0.237943	+	0.287624i
$296$	−59.0637	−	32.4706i	−3.43301	−	1.88731i
$297$	−5.53477	+	1.42109i	−0.321160	+	0.0824599i
$298$	−12.0231	−	37.0033i	−0.696479	−	2.14354i
$299$	2.44060	−	0.308320i	0.141144	−	0.0178306i
$300$	−2.97484	−	2.16135i	−0.171752	−	0.124785i
$301$	7.69646			0.443617
$302$	−30.5211	−	15.0337i	−1.75629	−	0.865095i
$303$	6.31946			0.363044
$304$	−87.5032	−	63.5748i	−5.01865	−	3.64626i
$305$	−3.74338	+	0.472899i	−0.214346	+	0.0270781i
$306$	8.41910	+	25.9113i	0.481288	+	1.48125i
$307$	12.8438	−	3.29773i	0.733035	−	0.188211i	0.136320	−	0.990665i	$-0.456472\pi$
$307$	12.8438	−	3.29773i	0.733035	−	0.188211i	0.596715	+	0.802453i	$0.296472\pi$
$308$	8.08034	+	4.44220i	0.460420	+	0.253118i
$309$	7.56446	−	9.14387i	0.430327	−	0.520176i
$310$	−0.141972	+	0.436946i	−0.00806349	+	0.0248169i
$311$	−24.8806	+	6.38824i	−1.41085	+	0.362244i	−0.875839	−	0.482603i	$-0.839691\pi$
$311$	−24.8806	+	6.38824i	−1.41085	+	0.362244i	−0.535008	+	0.844847i	$0.679691\pi$
$312$	−3.06626	−	1.21402i	−0.173593	−	0.0687301i
$313$	30.0736	+	3.79918i	1.69986	+	0.214742i	0.914582	−	0.404399i	$-0.132519\pi$
$313$	30.0736	+	3.79918i	1.69986	+	0.214742i	0.785279	+	0.619142i	$0.212519\pi$
$314$	1.46905	+	3.12189i	0.0829032	+	0.176178i
$315$	−0.498269	+	2.61202i	−0.0280743	+	0.147171i
$316$	68.6196	−	17.6185i	3.86016	−	0.991120i
$317$	−20.8819	+	8.26775i	−1.17285	+	0.464363i	−0.872094	−	0.489339i	$-0.837238\pi$
$317$	−20.8819	+	8.26775i	−1.17285	+	0.464363i	−0.300753	+	0.953702i	$0.597238\pi$
$318$	12.1130	−	8.80060i	0.679263	−	0.493513i
$319$	0.933321	+	1.12819i	0.0522560	+	0.0631666i
$320$	36.0910	+	14.2894i	2.01755	+	0.798803i
$321$	1.15900	+	3.56702i	0.0646889	+	0.199092i
$322$	−7.51674	−	11.8445i	−0.418892	−	0.660067i
$323$	−13.1861	+	20.7780i	−0.733695	+	1.15612i
$324$	22.2488	+	20.8930i	1.23604	+	1.16072i
$325$	0.154708	+	0.476141i	0.00858164	+	0.0264116i
$326$	−1.89215	+	9.91901i	−0.104797	+	0.549363i
$327$	−8.54946	+	4.70011i	−0.472786	+	0.259916i
$328$	−76.3722	+	71.7183i	−4.21695	+	3.95998i
$329$	−3.34730	+	1.32529i	−0.184543	+	0.0730657i
$330$	2.63682	+	1.04399i	0.145152	+	0.0574699i
$331$	1.40836	+	1.32253i	0.0774102	+	0.0726930i	0.722287	−	0.691594i	$-0.243091\pi$
$331$	1.40836	+	1.32253i	0.0774102	+	0.0726930i	−0.644876	+	0.764287i	$0.723091\pi$
$332$	−68.5621	−	17.6038i	−3.76283	−	0.966132i
$333$	1.07526	+	17.0908i	0.0589240	+	0.936570i
$334$	−22.9603			−1.25633
$335$	12.9562			0.707875
$336$	0.704694	+	11.2008i	0.0384442	+	0.611053i
$337$	7.55890	−	16.0635i	0.411759	−	0.875033i	−0.586138	−	0.810212i	$-0.699352\pi$
$337$	7.55890	−	16.0635i	0.411759	−	0.875033i	0.997897	−	0.0648215i	$-0.0206478\pi$
$338$	−18.9145	−	29.8045i	−1.02881	−	1.62115i
$339$	−1.97262	+	10.3408i	−0.107138	+	0.561637i
$340$	6.68088	−	20.5616i	0.362321	−	1.11511i
$341$	0.0164444	−	0.261377i	0.000890516	−	0.0141543i
$342$	−2.89141	+	45.9576i	−0.156349	+	2.48510i
$343$	−11.6896	−	6.42640i	−0.631178	−	0.346993i
$344$	−70.4397	+	27.8891i	−3.79785	+	1.50368i
$345$	−2.03268	−	2.45709i	−0.109436	−	0.132285i
$346$	1.38429	+	7.25669i	0.0744197	+	0.390122i
$347$	−13.8503	+	7.61425i	−0.743522	+	0.408755i	−0.808014	−	0.589164i	$-0.799457\pi$
$347$	−13.8503	+	7.61425i	−0.743522	+	0.408755i	0.0644919	+	0.997918i	$0.479457\pi$
$348$	−1.05416	+	3.24436i	−0.0565087	+	0.173916i
$349$	28.5577	+	15.6998i	1.52866	+	0.840389i	0.999965	−	0.00842218i	$-0.00268089\pi$
$349$	28.5577	+	15.6998i	1.52866	+	0.840389i	0.528697	+	0.848811i	$0.322681\pi$
$350$	2.08117	−	1.95435i	0.111243	−	0.104465i
$351$	0.339651	+	1.78051i	0.0181292	+	0.0950368i
$352$	−40.9218	−	5.16962i	−2.18114	−	0.275542i
$353$	25.3549	+	23.8099i	1.34951	+	1.26727i	0.933810	+	0.357769i	$0.116462\pi$
$353$	25.3549	+	23.8099i	1.34951	+	1.26727i	0.415697	+	0.909503i	$0.363538\pi$
$354$	11.4297	−	1.44391i	0.607481	−	0.0767427i
$355$	−2.28454	+	4.85488i	−0.121251	+	0.257671i
$356$	−1.66302	−	0.426991i	−0.0881398	−	0.0226305i
$357$	2.53335	−	0.320036i	0.134079	−	0.0169381i
$358$	−10.9356	−	17.2317i	−0.577963	−	0.910725i
$359$	8.15222	+	17.3243i	0.430257	+	0.914344i	0.995965	+	0.0897380i	$0.0286030\pi$
$359$	8.15222	+	17.3243i	0.430257	+	0.914344i	−0.565708	+	0.824606i	$0.691397\pi$
$360$	−4.90470	−	25.7113i	−0.258500	−	1.35511i
$361$	−18.2784	+	13.2801i	−0.962022	+	0.698950i
$362$	−36.9912	−	44.7146i	−1.94421	−	2.35015i
$363$	5.47868	+	0.692119i	0.287556	+	0.0363268i
$364$	1.56726	−	2.46961i	0.0821469	−	0.129443i
$365$	−1.83311	+	3.89557i	−0.0959496	+	0.203903i
$366$	5.48501	+	3.98509i	0.286706	+	0.208304i
$367$	−1.24762	−	19.8303i	−0.0651250	−	1.03513i	−0.885899	−	0.463879i	$-0.846457\pi$
$367$	−1.24762	−	19.8303i	−0.0651250	−	1.03513i	0.820774	−	0.571254i	$-0.193543\pi$
$368$	66.6680	+	48.4371i	3.47531	+	2.52496i
$369$	25.7821	+	6.61973i	1.34216	+	0.344609i
$370$	9.85159	−	15.5236i	0.512160	−	0.807034i
$371$	3.65829	+	7.77427i	0.189929	+	0.403620i
$372$	0.534688	−	0.293947i	0.0277223	−	0.0152405i
$373$	14.3222	−	17.3126i	0.741575	−	0.896410i	−0.255952	−	0.966689i	$-0.582389\pi$
$373$	14.3222	−	17.3126i	0.741575	−	0.896410i	0.997527	+	0.0702790i	$0.0223889\pi$
$374$	−1.04699	+	16.6414i	−0.0541385	+	0.860507i
$375$	0.413679	−	0.500052i	0.0213623	−	0.0258226i
$376$	25.8329	−	24.2587i	1.33223	−	1.25105i
$377$	0.375755	−	0.273002i	0.0193524	−	0.0140603i
$378$	8.36246	−	6.07569i	0.430119	−	0.312500i
$379$	4.39456	−	4.12677i	0.225733	−	0.211978i	−0.563425	−	0.826167i	$-0.690517\pi$
$379$	4.39456	−	4.12677i	0.225733	−	0.211978i	0.789159	+	0.614189i	$0.210517\pi$
$380$	23.2922	−	28.1555i	1.19487	−	1.44434i
$381$	−0.512725	+	8.14952i	−0.0262677	+	0.417513i
$382$	−23.9662	+	28.9701i	−1.22622	+	1.48224i
$383$	−17.4440	+	9.58991i	−0.891346	+	0.490022i	−0.860470	−	0.509501i	$-0.829830\pi$
$383$	−17.4440	+	9.58991i	−0.891346	+	0.490022i	−0.0308764	+	0.999523i	$0.509830\pi$
$384$	−15.2546	−	32.4178i	−0.778460	−	1.65431i
$385$	−0.872022	+	1.37409i	−0.0444423	+	0.0700299i
$386$	−27.1089	−	6.96039i	−1.37981	−	0.354275i
$387$	15.5723	+	11.3139i	0.791583	+	0.575119i
$388$	−1.98881	−	31.6112i	−0.100967	−	1.60482i
$389$	−7.60411	−	5.52471i	−0.385544	−	0.280114i	0.378083	−	0.925772i	$-0.376583\pi$
$389$	−7.60411	−	5.52471i	−0.385544	−	0.280114i	−0.763627	+	0.645658i	$0.776583\pi$
$390$	0.383029	−	0.813977i	0.0193954	−	0.0412173i
$391$	10.0464	−	15.8306i	0.508068	−	0.800588i
$392$	59.7828	+	7.55232i	3.01949	+	0.381450i
$393$	3.45247	+	4.17333i	0.174154	+	0.210516i
$394$	−15.4031	+	11.1910i	−0.775998	+	0.563796i
$395$	2.34297	+	12.2823i	0.117888	+	0.617989i
$396$	9.81886	+	20.8661i	0.493416	+	1.04856i
$397$	15.5203	+	24.4561i	0.778941	+	1.22741i	0.969344	+	0.245709i	$0.0790207\pi$
$397$	15.5203	+	24.4561i	0.778941	+	1.22741i	−0.190403	+	0.981706i	$0.560979\pi$
$398$	22.3571	−	2.82436i	1.12066	−	0.141572i
$399$	4.18024	+	1.07330i	0.209274	+	0.0537324i
$400$	−7.14067	+	15.1747i	−0.357033	+	0.758734i
$401$	−25.0719	+	3.16732i	−1.25203	+	0.158168i	−0.723248	−	0.690589i	$-0.757352\pi$
$401$	−25.0719	+	3.16732i	−1.25203	+	0.158168i	−0.528783	+	0.848757i	$0.677352\pi$
$402$	−16.9709	−	15.9367i	−0.846432	−	0.794853i
$403$	−0.0824196	−	0.0104120i	−0.00410561	−	0.000518660i
$404$	−10.3381	−	54.1944i	−0.514341	−	2.69627i
$405$	−3.92678	+	3.68749i	−0.195123	+	0.183233i
$406$	−2.32099	−	1.27597i	−0.115189	−	0.0633255i
$407$	−3.23868	+	9.96762i	−0.160535	+	0.494076i
$408$	−22.0261	+	12.1089i	−1.09045	+	0.599481i
$409$	−0.297192	−	1.55793i	−0.0146952	−	0.0770349i	0.974184	−	0.225755i	$-0.0724848\pi$
$409$	−0.297192	−	1.55793i	−0.0146952	−	0.0770349i	−0.988879	+	0.148720i	$0.952485\pi$
$410$	−18.2168	−	22.0203i	−0.899663	−	1.08751i
$411$	5.35073	−	2.11850i	0.263932	−	0.104498i
$412$	−90.7907	−	49.9126i	−4.47294	−	2.45902i
$413$	−0.415114	+	6.59804i	−0.0204264	+	0.324668i
$414$	2.20294	−	35.0147i	0.108269	−	1.72088i
$415$	3.86064	−	11.8818i	0.189511	−	0.583256i
$416$	−2.45167	+	12.8521i	−0.120203	+	0.630127i
$417$	3.86356	+	6.08800i	0.189200	+	0.298131i
$418$	−11.9995	+	25.5003i	−0.586916	+	1.24726i
$419$	0.0649362	+	1.03213i	0.00317234	+	0.0504229i	0.999294	−	0.0375590i	$-0.0119582\pi$
$419$	0.0649362	+	1.03213i	0.00317234	+	0.0504229i	−0.996122	+	0.0879819i	$0.971958\pi$
$420$	−3.79160			−0.185011
$421$	−20.4379			−0.996082			−0.498041	−	0.867153i	$-0.665947\pi$
$421$	−20.4379			−0.996082			−0.498041	+	0.867153i	$0.665947\pi$
$422$	−3.00902	−	47.8271i	−0.146477	−	2.32819i
$423$	−8.72081	−	2.23912i	−0.424020	−	0.108870i
$424$	−61.6525	−	57.8955i	−2.99411	−	2.81166i
$425$	3.54780	+	1.40467i	0.172094	+	0.0681367i
$426$	8.96415	−	3.54916i	0.434314	−	0.171957i
$427$	−2.83615	+	2.66332i	−0.137251	+	0.128887i
$428$	28.6940	−	15.7747i	1.38698	−	0.762497i
$429$	−0.0960896	+	0.503719i	−0.00463925	+	0.0243198i
$430$	−6.38614	−	19.6545i	−0.307967	−	0.947825i
$431$	−17.7967	−	16.7122i	−0.857235	−	0.804998i	0.125097	−	0.992145i	$-0.460076\pi$
$431$	−17.7967	−	16.7122i	−0.857235	−	0.804998i	−0.982332	+	0.187147i	$0.940076\pi$
$432$	−32.5354	+	51.2675i	−1.56536	+	2.46661i
$433$	−8.07940	−	12.7311i	−0.388271	−	0.611817i	0.592827	−	0.805330i	$-0.298012\pi$
$433$	−8.07940	−	12.7311i	−0.388271	−	0.611817i	−0.981098	+	0.193513i	$0.938012\pi$
$434$	0.146393	+	0.450552i	0.00702710	+	0.0216272i
$435$	−0.559797	−	0.221639i	−0.0268402	−	0.0106268i
$436$	54.2933	+	65.6294i	2.60018	+	3.14308i
$437$	25.6375	−	18.6267i	1.22641	−	0.891037i
$438$	7.19285	−	2.84785i	0.343687	−	0.136075i
$439$	−25.6439	+	6.58424i	−1.22392	+	0.314249i	−0.804725	−	0.593648i	$-0.797687\pi$
$439$	−25.6439	+	6.58424i	−1.22392	+	0.314249i	−0.419194	+	0.907897i	$0.637687\pi$
$440$	3.00177	−	15.7358i	0.143104	−	0.750176i
$441$	−6.51860	−	13.8527i	−0.310409	−	0.659653i
$442$	5.24752	+	0.662916i	0.249599	+	0.0315317i
$443$	0.449889	+	0.178124i	0.0213749	+	0.00846291i	0.378788	−	0.925484i	$-0.376341\pi$
$443$	0.449889	+	0.178124i	0.0213749	+	0.00846291i	−0.357413	+	0.933947i	$0.616341\pi$
$444$	−23.6506	+	6.07244i	−1.12241	+	0.288185i
$445$	0.0936423	−	0.288201i	0.00443907	−	0.0136621i
$446$	8.92756	−	10.7916i	0.422732	−	0.510995i
$447$	−7.99177	−	4.39351i	−0.377998	−	0.207806i
$448$	38.7680	−	9.95394i	1.83162	−	0.470280i
$449$	−8.66182	−	26.6583i	−0.408776	−	1.25808i	−0.917700	−	0.397273i	$-0.869957\pi$
$449$	−8.66182	−	26.6583i	−0.408776	−	1.25808i	0.508924	−	0.860811i	$-0.330043\pi$
$450$	7.08377	−	0.894889i	0.333932	−	0.0421855i
$451$	13.1797	+	9.57559i	0.620606	+	0.450897i
$452$	91.9078			4.32298
$453$	−7.62735	+	2.32851i	−0.358364	+	0.109403i
$454$	68.1586			3.19884
$455$	0.417642	+	0.303435i	0.0195794	+	0.0142252i
$456$	−42.1477	+	5.32450i	−1.97375	+	0.249342i
$457$	10.8799	+	33.4849i	0.508941	+	1.56636i	0.794043	+	0.607862i	$0.207973\pi$
$457$	10.8799	+	33.4849i	0.508941	+	1.56636i	−0.285102	+	0.958497i	$0.592027\pi$
$458$	49.0809	−	12.6018i	2.29340	−	0.588846i
$459$	12.1064	+	6.65553i	0.565077	+	0.310654i
$460$	−17.7462	+	21.4514i	−0.827419	+	1.00018i
$461$	11.1572	−	34.3385i	0.519645	−	1.59930i	−0.255025	−	0.966935i	$-0.582084\pi$
$461$	11.1572	−	34.3385i	0.519645	−	1.59930i	0.774669	−	0.632367i	$-0.217916\pi$
$462$	2.83241	−	0.727241i	0.131776	−	0.0338343i
$463$	−26.2905	−	10.4092i	−1.22183	−	0.483755i	−0.333404	−	0.942784i	$-0.608197\pi$
$463$	−26.2905	−	10.4092i	−1.22183	−	0.483755i	−0.888421	+	0.459029i	$0.848197\pi$
$464$	15.4359	+	1.95001i	0.716596	+	0.0905271i
$465$	0.0458520	+	0.0974405i	0.00212634	+	0.00451870i
$466$	−7.15922	+	37.5299i	−0.331644	+	1.73854i
$467$	31.5428	−	8.09880i	1.45962	−	0.374768i	0.566307	−	0.824194i	$-0.308372\pi$
$467$	31.5428	−	8.09880i	1.45962	−	0.374768i	0.893317	+	0.449426i	$0.148372\pi$
$468$	6.80141	−	2.69287i	0.314396	−	0.124478i
$469$	10.8082	−	7.85263i	0.499077	−	0.362601i
$470$	6.16183	+	7.44837i	0.284224	+	0.343568i
$471$	0.751940	+	0.297714i	0.0346475	+	0.0137179i
$472$	−20.1096	−	61.8909i	−0.925619	−	2.84876i
$473$	6.31224	+	9.94650i	0.290237	+	0.457341i
$474$	12.0388	−	18.9701i	0.552960	−	0.871325i
$475$	4.70133	+	4.41484i	0.215712	+	0.202567i
$476$	−6.88891	−	21.2019i	−0.315753	−	0.971787i
$477$	−4.02646	+	21.1074i	−0.184359	+	0.966444i
$478$	61.1265	−	33.6046i	2.79586	−	1.53704i
$479$	−19.8906	+	18.6785i	−0.908823	+	0.853442i	−0.989682	−	0.143284i	$-0.954234\pi$
$479$	−19.8906	+	18.6785i	−0.908823	+	0.853442i	0.0808585	+	0.996726i	$0.474234\pi$
$480$	15.7696	−	6.24362i	0.719780	−	0.284981i
$481$	3.09106	+	1.22384i	0.140940	+	0.0558022i
$482$	9.92646	+	9.32157i	0.452138	+	0.424586i
$483$	−3.18489	−	0.817742i	−0.144918	−	0.0372085i
$484$	−3.02722	−	48.1163i	−0.137601	−	2.18710i
$485$	5.59022			0.253839
$486$	39.7526			1.80321
$487$	1.20350	+	19.1290i	0.0545356	+	0.866818i	0.926275	+	0.376848i	$0.122992\pi$
$487$	1.20350	+	19.1290i	0.0545356	+	0.866818i	−0.871739	+	0.489970i	$0.837008\pi$
$488$	16.3062	−	34.6524i	0.738146	−	1.56864i
$489$	1.26826	+	1.99845i	0.0573526	+	0.0903732i
$490$	−3.08005	+	16.1462i	−0.139142	+	0.729410i
$491$	−6.80063	+	20.9302i	−0.306908	+	0.944566i	0.672050	+	0.740506i	$0.265414\pi$
$491$	−6.80063	+	20.9302i	−0.306908	+	0.944566i	−0.978958	+	0.204061i	$0.934586\pi$
$492$	−2.38320	+	37.8799i	−0.107443	+	1.70776i
$493$	0.222276	−	3.53297i	0.0100108	−	0.159117i
$494$	7.83393	+	4.30674i	0.352465	+	0.193769i
$495$	−3.78429	+	1.49831i	−0.170091	+	0.0673439i
$496$	−1.77387	−	2.14424i	−0.0796491	−	0.0962792i
$497$	1.03671	+	5.43462i	0.0465028	+	0.243776i
$498$	−19.6721	+	10.8148i	−0.881527	+	0.484623i
$499$	−2.65398	+	8.16811i	−0.118808	+	0.365655i	−0.992722	−	0.120426i	$-0.961574\pi$
$499$	−2.65398	+	8.16811i	−0.118808	+	0.365655i	0.873914	+	0.486081i	$0.161574\pi$
$500$	−4.96508	−	2.72958i	−0.222045	−	0.122070i
$501$	−3.92318	+	3.68411i	−0.175275	+	0.164594i
$502$	9.62974	+	50.4808i	0.429796	+	2.25307i
$503$	−15.5341	−	1.96241i	−0.692631	−	0.0874997i	−0.228866	−	0.973458i	$-0.573502\pi$
$503$	−15.5341	−	1.96241i	−0.692631	−	0.0874997i	−0.463765	+	0.885958i	$0.653502\pi$
$504$	−19.6749	−	18.4759i	−0.876389	−	0.822984i
$505$	9.66066	−	1.22043i	0.429894	−	0.0543082i
$506$	9.14235	−	19.4285i	0.406427	−	0.863701i
$507$	−8.01420	−	2.05770i	−0.355923	−	0.0913855i
$508$	70.7274	−	8.93494i	3.13802	−	0.396424i
$509$	17.3928	+	27.4067i	0.770922	+	1.21478i	0.971949	+	0.235193i	$0.0755724\pi$
$509$	17.3928	+	27.4067i	0.770922	+	1.21478i	−0.201026	+	0.979586i	$0.564428\pi$
$510$	−2.91932	−	6.20388i	−0.129270	−	0.274712i
$511$	0.831857	+	4.36075i	0.0367992	+	0.192908i
$512$	−79.1564	+	57.5105i	−3.49825	+	2.54163i
$513$	14.8839	+	17.9916i	0.657142	+	0.794348i
$514$	−30.3580	−	3.83511i	−1.33903	−	0.169159i
$515$	9.79804	−	15.4392i	0.431753	−	0.680334i
$516$	−11.6859	+	24.8339i	−0.514445	+	1.09325i
$517$	−4.45802	−	3.23894i	−0.196064	−	0.142449i
$518$	−1.19040	−	18.9209i	−0.0523032	−	0.831335i
$519$	1.40091	+	1.01782i	0.0614931	+	0.0446774i
$520$	−4.92189	−	1.26373i	−0.215839	−	0.0554181i
$521$	19.6858	−	31.0199i	0.862450	−	1.35900i	−0.0699397	−	0.997551i	$-0.522281\pi$
$521$	19.6858	−	31.0199i	0.862450	−	1.35900i	0.932390	−	0.361453i	$-0.117719\pi$
$522$	−2.82036	−	5.99357i	−0.123444	−	0.262331i
$523$	−2.45670	+	1.35058i	−0.107424	+	0.0590570i	−0.534560	−	0.845131i	$-0.679523\pi$
$523$	−2.45670	+	1.35058i	−0.107424	+	0.0590570i	0.427136	+	0.904187i	$0.359523\pi$
$524$	30.1416	−	36.4349i	1.31674	−	1.59167i
$525$	0.0420191	−	0.667874i	0.00183386	−	0.0291484i
$526$	−18.1836	+	21.9803i	−0.792845	+	0.958385i
$527$	−0.461560	+	0.433434i	−0.0201059	+	0.0188807i
$528$	−13.8974	+	10.0970i	−0.604805	+	0.439417i
$529$	−0.925609	+	0.672494i	−0.0402439	+	0.0292389i
$530$	16.8177	−	15.7929i	0.730516	−	0.686000i
$531$	−10.5391	+	12.7396i	−0.457359	+	0.552852i
$532$	2.36589	−	37.6047i	0.102574	−	1.63037i
$533$	3.29397	−	3.98172i	0.142678	−	0.172468i
$534$	−0.477159	+	0.262320i	−0.0206487	+	0.0113517i
$535$	2.46065	+	5.22914i	0.106383	+	0.226075i
$536$	−70.4643	+	111.034i	−3.04359	+	4.79593i
$537$	−4.63348	−	1.18968i	−0.199949	−	0.0513383i
$538$	−28.0075	−	20.3487i	−1.20749	−	0.877293i
$539$	−0.588340	−	9.35140i	−0.0253416	−	0.402793i
$540$	−16.5961	−	12.0578i	−0.714181	−	0.518883i
$541$	3.31060	−	7.03538i	0.142334	−	0.302474i	−0.820931	−	0.571027i	$-0.806545\pi$
$541$	3.31060	−	7.03538i	0.142334	−	0.302474i	0.963265	+	0.268552i	$0.0865452\pi$
$542$	−36.1098	+	56.9000i	−1.55105	+	2.44406i
$543$	−13.4954	−	1.70486i	−0.579141	−	0.0731625i
$544$	63.5647	+	76.8365i	2.72531	+	3.29434i
$545$	−12.1620	+	8.83622i	−0.520963	+	0.378502i
$546$	−0.173816	−	0.911176i	−0.00743865	−	0.0389948i
$547$	−10.5021	−	22.3182i	−0.449039	−	0.954256i	−0.993324	−	0.115356i	$-0.963199\pi$
$547$	−10.5021	−	22.3182i	−0.449039	−	0.954256i	0.544285	−	0.838900i	$-0.316801\pi$
$548$	−26.9212	−	42.4210i	−1.15002	−	1.81213i
$549$	−9.65350	+	1.21952i	−0.412002	+	0.0520479i
$550$	4.23257	+	1.08674i	0.180478	+	0.0463388i
$551$	2.54750	−	5.41371i	0.108527	−	0.230632i
$552$	32.1120	−	4.05669i	1.36678	−	0.172664i
$553$	9.39869	+	8.82595i	0.399673	+	0.375318i
$554$	3.29944	+	0.416816i	0.140180	+	0.0177088i
$555$	−0.807534	−	4.23324i	−0.0342779	−	0.179691i
$556$	45.8889	−	43.0926i	1.94612	−	1.82753i
$557$	−30.2919	−	16.6531i	−1.28351	−	0.705616i	−0.313711	−	0.949518i	$-0.601572\pi$
$557$	−30.2919	−	16.6531i	−1.28351	−	0.705616i	−0.969800	+	0.243902i	$0.921572\pi$
$558$	−0.366121	+	1.12680i	−0.0154991	+	0.0477014i
$559$	3.27461	−	1.80023i	0.138501	−	0.0761417i
$560$	3.24039	+	16.9867i	0.136932	+	0.717821i
$561$	2.49132	+	3.01149i	0.105184	+	0.127145i
$562$	−59.5309	+	23.5699i	−2.51116	+	0.994238i
$563$	−21.7636	−	11.9646i	−0.917226	−	0.504249i	−0.0481011	−	0.998842i	$-0.515317\pi$
$563$	−21.7636	−	11.9646i	−0.917226	−	0.504249i	−0.869124	+	0.494593i	$0.835317\pi$
$564$	0.806118	−	12.8129i	0.0339437	−	0.539520i
$565$	−1.01854	+	16.1892i	−0.0428501	+	0.681083i
$566$	−2.26320	+	6.96542i	−0.0951294	+	0.292778i
$567$	−1.04081	+	5.45611i	−0.0437098	+	0.229135i
$568$	−29.1812	−	45.9822i	−1.22442	−	1.92937i
$569$	−9.16085	+	19.4678i	−0.384043	+	0.816133i	0.615564	+	0.788087i	$0.288928\pi$
$569$	−9.16085	+	19.4678i	−0.384043	+	0.816133i	−0.999607	+	0.0280455i	$0.991072\pi$
$570$	−0.727651	−	11.5657i	−0.0304780	−	0.484433i
$571$	37.1970			1.55665			0.778324	−	0.627863i	$-0.216070\pi$
$571$	37.1970			1.55665			0.778324	+	0.627863i	$0.216070\pi$
$572$	4.47698			0.187192
$573$	0.553372	+	8.79560i	0.0231175	+	0.367441i
$574$	−28.5429	−	7.32856i	−1.19136	−	0.305888i
$575$	−3.58191	−	3.36364i	−0.149376	−	0.140273i
$576$	93.0720	+	36.8498i	3.87800	+	1.53541i
$577$	−31.3342	+	12.4061i	−1.30446	+	0.516473i	−0.914585	−	0.404394i	$-0.867482\pi$
$577$	−31.3342	+	12.4061i	−1.30446	+	0.516473i	−0.389877	+	0.920867i	$0.627482\pi$
$578$	−4.92474	+	4.62464i	−0.204842	+	0.192359i
$579$	−5.74890	+	3.16048i	−0.238916	+	0.131345i
$580$	−0.984950	+	5.16329i	−0.0408978	+	0.214394i
$581$	−3.98086	−	12.2518i	−0.165154	−	0.508291i
$582$	−7.32242	−	6.87621i	−0.303524	−	0.285028i
$583$	−7.04671	+	11.1038i	−0.291845	+	0.459874i
$584$	−23.4150	−	36.8962i	−0.968921	−	1.52677i
$585$	0.398963	+	1.22788i	0.0164951	+	0.0507667i
$586$	0.868367	+	0.343811i	0.0358719	+	0.0142027i
$587$	−7.83946	−	9.47627i	−0.323569	−	0.391128i	0.583498	−	0.812115i	$-0.301684\pi$
$587$	−7.83946	−	9.47627i	−0.323569	−	0.391128i	−0.907067	+	0.420987i	$0.861684\pi$
$588$	17.6609	−	12.8314i	0.728322	−	0.529157i
$589$	−0.995015	+	0.393954i	−0.0409989	+	0.0162326i
$590$	17.1939	−	4.41465i	0.707862	−	0.181748i
$591$	−0.836239	+	4.38372i	−0.0343983	+	0.180322i
$592$	47.4175	+	100.767i	1.94885	+	4.14151i
$593$	−10.9326	−	1.38111i	−0.448950	−	0.0567156i	−0.102392	−	0.994744i	$-0.532650\pi$
$593$	−10.9326	−	1.38111i	−0.448950	−	0.0567156i	−0.346558	+	0.938029i	$0.612650\pi$
$594$	14.7104	+	5.82424i	0.603574	+	0.238972i
$595$	3.81096	−	0.978489i	0.156234	−	0.0401141i
$596$	−24.6039	+	75.7231i	−1.00782	+	3.10174i
$597$	3.36694	−	4.06993i	0.137800	−	0.166571i
$598$	−5.96861	−	3.28127i	−0.244075	−	0.134181i
$599$	−30.3901	+	7.80286i	−1.24171	+	0.318816i	−0.811735	−	0.584026i	$-0.801477\pi$
$599$	−30.3901	+	7.80286i	−1.24171	+	0.318816i	−0.429972	+	0.902842i	$0.641477\pi$
$600$	2.03555	+	6.26479i	0.0831011	+	0.255759i
$601$	27.5603	−	3.48167i	1.12421	−	0.142020i	0.458827	−	0.888526i	$-0.348270\pi$
$601$	27.5603	−	3.48167i	1.12421	−	0.142020i	0.665380	+	0.746505i	$0.268270\pi$
$602$	−17.2397	−	12.5254i	−0.702640	−	0.510498i
$603$	33.4118			1.36063
$604$	32.4466	+	61.6013i	1.32023	+	2.50652i
$605$	8.50902			0.345941
$606$	−14.1553	−	10.2844i	−0.575021	−	0.417777i
$607$	9.63504	−	1.21719i	0.391074	−	0.0494042i	0.0726623	−	0.997357i	$-0.476850\pi$
$607$	9.63504	−	1.21719i	0.391074	−	0.0494042i	0.318412	+	0.947952i	$0.396850\pi$
$608$	52.0837	+	160.297i	2.11227	+	6.50090i
$609$	−0.601321	+	0.154393i	−0.0243668	+	0.00625632i
$610$	9.15463	+	5.03280i	0.370660	+	0.203772i
$611$	−1.11418	+	1.34682i	−0.0450751	+	0.0544864i
$612$	17.2288	−	53.0247i	0.696431	−	2.14340i
$613$	−9.14867	+	2.34898i	−0.369511	+	0.0948744i	−0.428879	−	0.903362i	$-0.641091\pi$
$613$	−9.14867	+	2.34898i	−0.369511	+	0.0948744i	0.0593680	+	0.998236i	$0.481091\pi$
$614$	−34.1364	−	13.5156i	−1.37763	−	0.545444i
$615$	−6.64597	−	0.839581i	−0.267991	−	0.0338552i
$616$	−7.03319	−	14.9463i	−0.283375	−	0.602203i
$617$	7.99011	−	41.8856i	0.321670	−	1.68625i	−0.343176	−	0.939271i	$-0.611503\pi$
$617$	7.99011	−	41.8856i	0.321670	−	1.68625i	0.664846	−	0.746980i	$-0.268497\pi$
$618$	−31.8250	+	8.17128i	−1.28019	+	0.328697i
$619$	−3.53516	+	1.39967i	−0.142090	+	0.0562574i	−0.438093	−	0.898930i	$-0.644346\pi$
$619$	−3.53516	+	1.39967i	−0.142090	+	0.0562574i	0.296003	+	0.955187i	$0.404346\pi$
$620$	0.760619	−	0.552622i	0.0305472	−	0.0221938i
$621$	−11.3400	−	13.7076i	−0.455057	−	0.550069i
$622$	66.1278	+	26.1818i	2.65148	+	1.04980i
$623$	−0.0965582	−	0.297176i	−0.00386852	−	0.0119061i
$624$	2.91973	+	4.60076i	0.116883	+	0.184178i
$625$	0.535827	−	0.844328i	0.0214331	−	0.0337731i
$626$	−61.1808	−	57.4526i	−2.44527	−	2.29627i
$627$	2.04134	+	6.28259i	0.0815232	+	0.250903i
$628$	1.32302	−	6.93551i	0.0527942	−	0.276757i
$629$	22.2043	−	12.2069i	0.885342	−	0.486721i
$630$	5.36697	−	5.03992i	0.213825	−	0.200795i
$631$	−32.4678	+	12.8549i	−1.29252	+	0.511745i	−0.910921	−	0.412582i	$-0.864627\pi$
$631$	−32.4678	+	12.8549i	−1.29252	+	0.511745i	−0.381601	+	0.924327i	$0.624627\pi$
$632$	−118.001	−	46.7198i	−4.69382	−	1.85841i
$633$	−8.18829	−	7.68932i	−0.325455	−	0.305623i
$634$	60.2298	+	15.4644i	2.39203	+	0.614169i
$635$	0.790040	+	12.5573i	0.0313518	+	0.498322i
$636$	−30.6395			−1.21494
$637$	−2.97220			−0.117763
$638$	−0.254553	−	4.04601i	−0.0100779	−	0.160183i
$639$	−5.89140	+	12.5199i	−0.233060	+	0.495278i
$640$	−29.5806	−	46.6115i	−1.16928	−	1.84248i
$641$	−1.14266	+	5.99003i	−0.0451323	+	0.236592i	−0.997704	−	0.0677217i	$-0.978427\pi$
$641$	−1.14266	+	5.99003i	−0.0451323	+	0.236592i	0.952572	+	0.304313i	$0.0984270\pi$
$642$	3.20896	−	9.87616i	0.126648	−	0.389781i
$643$	1.20187	−	19.1031i	0.0473970	−	0.753354i	−0.900516	−	0.434824i	$-0.856811\pi$
$643$	1.20187	−	19.1031i	0.0473970	−	0.753354i	0.947913	−	0.318530i	$-0.103189\pi$
$644$	−1.80255	+	28.6507i	−0.0710305	+	1.12900i
$645$	−4.24488	−	2.33364i	−0.167142	−	0.0918870i
$646$	63.3510	−	25.0824i	2.49251	−	0.986855i
$647$	−6.54211	−	7.90805i	−0.257197	−	0.310898i	0.626071	−	0.779766i	$-0.284662\pi$
$647$	−6.54211	−	7.90805i	−0.257197	−	0.310898i	−0.883268	+	0.468868i	$0.844662\pi$
$648$	−10.2452	−	53.7070i	−0.402468	−	2.10981i
$649$	−8.86742	+	4.87490i	−0.348077	+	0.191357i
$650$	0.428345	−	1.31831i	0.0168011	−	0.0517084i
$651$	0.0973078	+	0.0534954i	0.00381379	+	0.00209665i
$652$	15.0635	−	14.1456i	0.589934	−	0.553985i
$653$	5.10298	+	26.7508i	0.199695	+	1.04684i	0.931064	+	0.364856i	$0.118882\pi$
$653$	5.10298	+	26.7508i	0.199695	+	1.04684i	−0.731369	+	0.681982i	$0.761118\pi$
$654$	26.7995	+	3.38556i	1.04794	+	0.132386i
$655$	6.08381	+	5.71308i	0.237714	+	0.223229i
$656$	171.742	−	21.6961i	6.70541	−	0.847091i
$657$	−4.72727	+	10.0460i	−0.184428	+	0.391930i
$658$	9.65463	+	2.47889i	0.376377	+	0.0966371i
$659$	16.0791	−	2.03126i	0.626352	−	0.0791266i	0.194251	−	0.980952i	$-0.437772\pi$
$659$	16.0791	−	2.03126i	0.626352	−	0.0791266i	0.432101	+	0.901825i	$0.357772\pi$
$660$	−3.10968	−	4.90007i	−0.121044	−	0.190735i
$661$	2.57561	+	5.47344i	0.100180	+	0.212892i	0.948634	−	0.316377i	$-0.102466\pi$
$661$	2.57561	+	5.47344i	0.100180	+	0.212892i	−0.848454	+	0.529269i	$0.822466\pi$
$662$	−1.00233	−	5.25441i	−0.0389568	−	0.204219i
$663$	1.00300	−	0.728725i	0.0389535	−	0.0283013i
$664$	80.8296	+	97.7062i	3.13680	+	3.79174i
$665$	6.59768	+	0.833481i	0.255847	+	0.0323210i
$666$	25.4054	−	40.0326i	0.984441	−	1.55123i
$667$	−1.94092	+	4.12466i	−0.0751527	+	0.159708i
$668$	38.0122	+	27.6175i	1.47074	+	1.06855i
$669$	−0.206135	−	3.27642i	−0.00796963	−	0.126674i
$670$	−29.0214	−	21.0853i	−1.12120	−	0.814597i
$671$	−5.76800	−	1.48097i	−0.222671	−	0.0571722i
$672$	9.37095	−	14.7663i	0.361492	−	0.569621i
$673$	−13.5915	−	28.8835i	−0.523915	−	1.11338i	−0.975267	−	0.221030i	$-0.929058\pi$
$673$	−13.5915	−	28.8835i	−0.523915	−	1.11338i	0.451352	−	0.892346i	$-0.350942\pi$
$674$	−43.0737	+	23.6800i	−1.65914	+	0.912118i
$675$	2.30784	−	2.78970i	0.0888288	−	0.107376i
$676$	−4.53579	+	72.0943i	−0.174453	+	2.77286i
$677$	−4.83923	+	5.84962i	−0.185987	+	0.224819i	−0.855263	−	0.518194i	$-0.826604\pi$
$677$	−4.83923	+	5.84962i	−0.185987	+	0.224819i	0.669276	+	0.743014i	$0.266604\pi$
$678$	21.2475	−	19.9527i	0.816005	−	0.766280i
$679$	4.66341	−	3.38817i	0.178965	−	0.130026i
$680$	−31.3331	+	22.7648i	−1.20157	+	0.872991i
$681$	11.6461	−	10.9365i	0.446281	−	0.419086i
$682$	−0.462206	+	0.558711i	−0.0176988	+	0.0213941i
$683$	−1.08490	+	17.2439i	−0.0415124	+	0.659821i	0.921166	+	0.389171i	$0.127238\pi$
$683$	−1.08490	+	17.2439i	−0.0415124	+	0.659821i	−0.962678	+	0.270650i	$0.912762\pi$
$684$	60.0664	−	72.6078i	2.29670	−	2.77623i
$685$	7.77061	−	4.27193i	0.296900	−	0.163222i
$686$	15.7257	+	33.4188i	0.600409	+	1.27593i
$687$	6.36434	−	10.0286i	0.242815	−	0.382615i
$688$	121.245	+	31.1305i	4.62243	+	1.18684i
$689$	3.37492	+	2.45202i	0.128574	+	0.0934147i
$690$	0.554392	+	8.81181i	0.0211053	+	0.335460i
$691$	−36.4616	−	26.4909i	−1.38706	−	1.00776i	−0.996180	−	0.0873211i	$-0.972169\pi$
$691$	−36.4616	−	26.4909i	−1.38706	−	1.00776i	−0.390884	−	0.920440i	$-0.627831\pi$
$692$	6.43684	−	13.6790i	0.244692	−	0.519997i
$693$	−2.24878	+	3.54352i	−0.0854243	+	0.134607i
$694$	43.4157	+	5.48467i	1.64804	+	0.208195i
$695$	7.08202	+	8.56069i	0.268636	+	0.324725i
$696$	4.94396	−	3.59200i	0.187400	−	0.136154i
$697$	−7.38020	−	38.6884i	−0.279545	−	1.46543i
$698$	−38.4180	−	81.6424i	−1.45414	−	3.09021i
$699$	4.79862	+	7.56142i	0.181501	+	0.285999i
$700$	−5.79628	+	0.732241i	−0.219079	+	0.0276761i
$701$	−29.9199	−	7.68213i	−1.13006	−	0.290150i	−0.363040	−	0.931774i	$-0.618261\pi$
$701$	−29.9199	−	7.68213i	−1.13006	−	0.290150i	−0.767020	+	0.641624i	$0.778261\pi$
$702$	2.13685	−	4.54103i	0.0806501	−	0.171390i
$703$	42.4887	−	5.36757i	1.60249	−	0.202442i
$704$	44.6595	+	41.9381i	1.68317	+	1.58060i
$705$	2.24800	+	0.283988i	0.0846645	+	0.0106956i
$706$	−18.0452	−	94.5964i	−0.679141	−	3.56018i
$707$	7.31933	−	6.87331i	0.275272	−	0.258497i
$708$	−20.6594	−	11.3576i	−0.776427	−	0.426844i
$709$	4.83856	−	14.8916i	0.181716	−	0.559265i	−0.818160	−	0.574990i	$-0.805006\pi$
$709$	4.83856	−	14.8916i	0.181716	−	0.559265i	0.999876	+	0.0157256i	$0.00500582\pi$
$710$	13.0182	−	7.15683i	0.488565	−	0.268591i
$711$	6.04210	+	31.6738i	0.226596	+	1.18786i
$712$	1.96057	+	2.36993i	0.0734756	+	0.0888168i
$713$	0.758094	−	0.300151i	0.0283909	−	0.0112407i
$714$	−6.19542	−	3.40596i	−0.231858	−	0.127465i
$715$	−0.0496146	+	0.788601i	−0.00185548	+	0.0294920i
$716$	−2.62241	+	41.6819i	−0.0980039	+	1.55773i
$717$	5.05253	−	15.5501i	0.188690	−	0.580728i
$718$	9.93344	−	52.0729i	0.370713	−	1.94334i
$719$	1.69189	+	2.66599i	0.0630967	+	0.0994246i	0.874412	−	0.485185i	$-0.161248\pi$
$719$	1.69189	+	2.66599i	0.0630967	+	0.0994246i	−0.811315	+	0.584610i	$0.801248\pi$
$720$	−18.4145	+	39.1328i	−0.686267	+	1.45839i
$721$	−1.18393	−	18.8180i	−0.0440919	−	0.700820i
$722$	62.5552			2.32806
$723$	3.19182			0.118705
$724$	7.45679	+	118.522i	0.277129	+	4.40485i
$725$	−0.898575	−	0.230715i	−0.0333722	−	0.00856853i
$726$	−11.1456	−	10.4665i	−0.413654	−	0.388447i
$727$	−24.1518	−	9.56238i	−0.895741	−	0.354649i	−0.125269	−	0.992123i	$-0.539979\pi$
$727$	−24.1518	−	9.56238i	−0.895741	−	0.354649i	−0.770472	+	0.637474i	$0.779979\pi$
$728$	−4.87181	+	1.92889i	−0.180561	+	0.0714893i
$729$	−4.98787	+	4.68392i	−0.184736	+	0.173479i
$730$	10.4458	−	5.74265i	0.386618	−	0.212545i
$731$	5.33680	−	27.9765i	0.197389	−	1.03475i
$732$	−4.28736	−	13.1951i	−0.158466	−	0.487707i
$733$	19.7577	+	18.5537i	0.729768	+	0.685298i	0.957502	−	0.288426i	$-0.0931318\pi$
$733$	19.7577	+	18.5537i	0.729768	+	0.685298i	−0.227734	+	0.973723i	$0.573132\pi$
$734$	−29.4777	+	46.4494i	−1.08804	+	1.71448i
$735$	2.06447	+	3.25308i	0.0761491	+	0.119992i
$736$	−39.6821	−	122.129i	−1.46270	−	4.50174i
$737$	19.0127	+	7.52765i	0.700341	+	0.277285i
$738$	−46.9778	−	56.7864i	−1.72928	−	2.09034i
$739$	−18.9243	+	13.7493i	−0.696143	+	0.505778i	−0.878674	−	0.477423i	$-0.841571\pi$
$739$	−18.9243	+	13.7493i	−0.696143	+	0.505778i	0.182531	+	0.983200i	$0.441571\pi$
$740$	−34.9823	+	13.8505i	−1.28598	+	0.509154i
$741$	2.02961	−	0.521116i	0.0745598	−	0.0191437i
$742$	4.45761	−	23.3676i	0.163644	−	0.857852i
$743$	−17.5026	−	37.1950i	−0.642109	−	1.36455i	−0.915371	−	0.402612i	$-0.868102\pi$
$743$	−17.5026	−	37.1950i	−0.642109	−	1.36455i	0.273262	−	0.961940i	$-0.411898\pi$
$744$	−1.08443	−	0.136995i	−0.0397571	−	0.00502249i
$745$	−13.0656	−	5.17305i	−0.478688	−	0.189526i
$746$	−60.2560	+	15.4711i	−2.20613	+	0.566438i
$747$	9.95588	−	30.6411i	0.364267	−	1.12110i
$748$	21.7503	−	26.2916i	0.795269	−	0.961315i
$749$	5.22201	+	2.87083i	0.190808	+	0.104898i
$750$	−1.74042	+	0.446864i	−0.0635512	+	0.0163172i
$751$	4.53207	+	13.9483i	0.165377	+	0.508979i	0.999064	−	0.0432587i	$-0.0137740\pi$
$751$	4.53207	+	13.9483i	0.165377	+	0.508979i	−0.833686	+	0.552238i	$0.813774\pi$
$752$	−58.0919	+	7.33871i	−2.11839	+	0.267615i
$753$	9.74538	+	7.08043i	0.355141	+	0.258025i
$754$	−1.28596			−0.0468321
$755$	−11.2104	+	5.03264i	−0.407987	+	0.183157i
$756$	−21.1527			−0.769315
$757$	25.5644	+	18.5736i	0.929153	+	0.675069i	0.945785	−	0.324792i	$-0.105294\pi$
$757$	25.5644	+	18.5736i	0.929153	+	0.675069i	−0.0166322	+	0.999862i	$0.505294\pi$
$758$	−16.5596	+	2.09197i	−0.601473	+	0.0759837i
$759$	−1.55528	−	4.78666i	−0.0564531	−	0.173745i
$760$	−63.4036	+	16.2793i	−2.29989	+	0.590512i
$761$	−19.6912	−	10.8253i	−0.713806	−	0.392418i	0.0830842	−	0.996543i	$-0.473523\pi$
$761$	−19.6912	−	10.8253i	−0.713806	−	0.392418i	−0.796890	+	0.604124i	$0.793523\pi$
$762$	14.4112	−	17.4202i	0.522063	−	0.631066i
$763$	−4.79013	+	14.7425i	−0.173414	+	0.533715i
$764$	74.5239	−	19.1345i	2.69618	−	0.692261i
$765$	9.14913	+	3.62240i	0.330787	+	0.130968i
$766$	54.6807	+	6.90777i	1.97569	+	0.249588i
$767$	1.36669	+	2.90436i	0.0493483	+	0.104870i
$768$	−9.14686	+	47.9495i	−0.330059	+	1.73023i
$769$	−19.5393	+	5.01683i	−0.704605	+	0.180912i	−0.583958	−	0.811784i	$-0.698497\pi$
$769$	−19.5393	+	5.01683i	−0.704605	+	0.180912i	−0.120646	+	0.992696i	$0.538497\pi$
$770$	4.18951	−	1.65875i	0.150980	−	0.0597770i
$771$	−5.80259	+	4.21583i	−0.208975	+	0.151829i
$772$	36.5084	+	44.1310i	1.31396	+	1.58831i
$773$	−14.5079	−	5.74407i	−0.521812	−	0.206600i	0.0924281	−	0.995719i	$-0.470537\pi$
$773$	−14.5079	−	5.74407i	−0.521812	−	0.206600i	−0.614240	+	0.789120i	$0.710537\pi$
$774$	−16.4687	−	50.6854i	−0.591955	−	1.82185i
$775$	0.0889126	+	0.140104i	0.00319384	+	0.00503268i
$776$	−30.4031	+	47.9077i	−1.09141	+	1.71979i
$777$	−3.23937	−	3.04197i	−0.116212	−	0.109130i
$778$	8.04184	+	24.7502i	0.288314	+	0.887339i
$779$	12.4738	−	65.3901i	0.446921	−	2.34284i
$780$	−1.61321	+	0.886870i	−0.0577622	+	0.0317550i
$781$	−6.17316	+	5.79698i	−0.220893	+	0.207432i
$782$	−48.2666	+	19.1101i	−1.72601	+	0.683376i
$783$	−3.12301	−	1.23649i	−0.111607	−	0.0441884i
$784$	−72.5792	−	68.1564i	−2.59211	−	2.43416i
$785$	1.20700	+	0.309904i	0.0430796	+	0.0110610i
$786$	−0.941626	−	14.9667i	−0.0335867	−	0.533845i
$787$	−54.7921			−1.95313			−0.976565	−	0.215225i	$-0.930952\pi$
$787$	−54.7921			−1.95313			−0.976565	+	0.215225i	$0.930952\pi$
$788$	38.9618			1.38796
$789$	0.419855	+	6.67341i	0.0149472	+	0.237580i
$790$	14.7403	−	31.3248i	0.524438	−	1.11449i
$791$	8.96238	+	14.1225i	0.318666	+	0.502137i
$792$	7.74101	−	40.5798i	0.275065	−	1.44194i
$793$	−0.583733	+	1.79655i	−0.0207290	+	0.0637972i
$794$	5.03561	−	80.0387i	0.178707	−	2.84047i
$795$	0.339551	−	5.39702i	0.0120427	−	0.191412i
$796$	−40.4109	−	22.2161i	−1.43233	−	0.787428i
$797$	−12.5435	+	4.96633i	−0.444314	+	0.175916i	−0.579619	−	0.814888i	$-0.696799\pi$
$797$	−12.5435	+	4.96633i	−0.444314	+	0.175916i	0.135305	+	0.990804i	$0.456799\pi$
$798$	−7.61684	−	9.20718i	−0.269633	−	0.325931i
$799$	2.49635	+	13.0863i	0.0883146	+	0.462961i
$800$	22.9015	−	12.5902i	0.809689	−	0.445130i
$801$	0.241486	−	0.743219i	0.00853250	−	0.0262603i
$802$	61.3146	+	33.7080i	2.16509	+	1.19027i
$803$	−4.95335	+	4.65151i	−0.174800	+	0.164148i
$804$	8.92711	+	46.7976i	0.314835	+	1.65042i
$805$	−5.02672	−	0.635023i	−0.177169	−	0.0223816i
$806$	0.167672	+	0.157454i	0.00590598	+	0.00554609i
$807$	−8.05067	+	1.01704i	−0.283397	+	0.0358014i
$808$	−42.0819	+	89.4285i	−1.48043	+	3.14608i
$809$	−47.0319	−	12.0757i	−1.65355	−	0.424560i	−0.697224	−	0.716853i	$-0.745582\pi$
$809$	−47.0319	−	12.0757i	−1.65355	−	0.424560i	−0.956329	+	0.292293i	$0.905582\pi$
$810$	14.7969	−	1.86929i	0.519911	−	0.0656800i
$811$	1.25878	+	1.98352i	0.0442017	+	0.0696508i	0.865710	−	0.500545i	$-0.166867\pi$
$811$	1.25878	+	1.98352i	0.0442017	+	0.0696508i	−0.821509	+	0.570196i	$0.806867\pi$
$812$	2.30775	+	4.90423i	0.0809863	+	0.172105i
$813$	2.95992	+	15.5164i	0.103809	+	0.544186i
$814$	23.4760	−	17.0563i	0.822835	−	0.597824i
$815$	2.32475	+	2.81014i	0.0814324	+	0.0984349i
$816$	41.2033	+	5.20518i	1.44240	+	0.182218i
$817$	25.7935	−	40.6441i	0.902400	−	1.42196i
$818$	−1.86972	+	3.97336i	−0.0653733	+	0.138925i
$819$	1.07702	+	0.782503i	0.0376342	+	0.0273429i
$820$	3.67220	+	58.3679i	0.128239	+	2.03830i
$821$	44.6058	+	32.4080i	1.55675	+	1.13105i	0.938609	+	0.344984i	$0.112116\pi$
$821$	44.6058	+	32.4080i	1.55675	+	1.13105i	0.618145	+	0.786064i	$0.287884\pi$
$822$	−15.4331	−	3.96255i	−0.538291	−	0.138210i
$823$	−12.8424	+	20.2365i	−0.447659	+	0.705398i	−0.990963	−	0.134138i	$-0.957173\pi$
$823$	−12.8424	+	20.2365i	−0.447659	+	0.705398i	0.543303	+	0.839537i	$0.317173\pi$
$824$	79.0250	+	167.937i	2.75297	+	5.85035i
$825$	0.897587	−	0.493453i	0.0312500	−	0.0171798i
$826$	11.6676	−	14.1038i	0.405969	−	0.490733i
$827$	−1.29965	+	20.6574i	−0.0451934	+	0.718328i	0.908563	+	0.417748i	$0.137180\pi$
$827$	−1.29965	+	20.6574i	−0.0451934	+	0.718328i	−0.953756	+	0.300580i	$0.902820\pi$
$828$	−45.7641	+	55.3193i	−1.59041	+	1.92248i
$829$	−18.6584	+	17.5214i	−0.648032	+	0.608542i	−0.937224	−	0.348729i	$-0.886613\pi$
$829$	−18.6584	+	17.5214i	−0.648032	+	0.608542i	0.289192	+	0.957271i	$0.406613\pi$
$830$	−27.9844	+	20.3319i	−0.971354	+	0.705730i
$831$	0.630651	−	0.458194i	0.0218770	−	0.0158946i
$832$	14.1664	−	13.3031i	0.491130	−	0.461202i
$833$	−14.4397	+	17.4546i	−0.500306	+	0.604766i
$834$	1.25354	−	19.9245i	0.0434067	−	0.689930i
$835$	−5.28595	+	6.38962i	−0.182928	+	0.221122i
$836$	50.5387	−	27.7839i	1.74792	−	0.960926i
$837$	0.255800	+	0.543603i	0.00884175	+	0.0187897i
$838$	1.53426	−	2.41761i	0.0530002	−	0.0835149i
$839$	41.5308	+	10.6633i	1.43380	+	0.368138i	0.884129	−	0.467242i	$-0.154752\pi$
$839$	41.5308	+	10.6633i	1.43380	+	0.368138i	0.549673	+	0.835380i	$0.314752\pi$
$840$	5.49509	+	3.99242i	0.189599	+	0.137752i
$841$	−1.76688	−	28.0838i	−0.0609270	−	0.968407i
$842$	45.7800	+	33.2611i	1.57768	+	1.14625i
$843$	−6.39000	+	13.5794i	−0.220083	+	0.467701i
$844$	−52.5466	+	82.8002i	−1.80873	+	2.85010i
$845$	−12.6488	−	1.59792i	−0.435133	−	0.0549700i
$846$	15.8902	+	19.2080i	0.546318	+	0.660385i
$847$	7.09830	−	5.15722i	0.243900	−	0.177204i
$848$	26.1853	+	137.268i	0.899206	+	4.71380i
$849$	0.730934	+	1.55331i	0.0250856	+	0.0533096i
$850$	−5.66092	−	8.92018i	−0.194168	−	0.305960i
$851$	−32.3718	+	4.08951i	−1.10969	+	0.140187i
$852$	−19.1098	−	4.90656i	−0.654690	−	0.168096i
$853$	0.634278	−	1.34791i	0.0217173	−	0.0461515i	−0.893674	−	0.448717i	$-0.851881\pi$
$853$	0.634278	−	1.34791i	0.0217173	−	0.0461515i	0.915391	+	0.402565i	$0.131881\pi$
$854$	10.6872	−	1.35011i	0.365708	−	0.0461997i
$855$	12.1239	+	11.3851i	0.414628	+	0.389362i
$856$	−58.1958	−	7.35184i	−1.98909	−	0.251281i
$857$	7.51257	+	39.3823i	0.256625	+	1.34527i	0.844167	+	0.536080i	$0.180095\pi$
$857$	7.51257	+	39.3823i	0.256625	+	1.34527i	−0.587543	+	0.809193i	$0.699905\pi$
$858$	1.03500	−	0.971931i	0.0353344	−	0.0331812i
$859$	−33.0916	−	18.1923i	−1.12907	−	0.620712i	−0.196071	−	0.980590i	$-0.562818\pi$
$859$	−33.0916	−	18.1923i	−1.12907	−	0.620712i	−0.932999	+	0.359878i	$0.882818\pi$
$860$	−13.0685	+	40.2208i	−0.445633	+	1.37152i
$861$	−6.05299	+	3.32766i	−0.206285	+	0.113406i
$862$	12.6660	+	66.3973i	0.431404	+	2.26150i
$863$	−33.8092	−	40.8683i	−1.15088	−	1.39117i	−0.906875	−	0.421399i	$-0.861539\pi$
$863$	−33.8092	−	40.8683i	−1.15088	−	1.39117i	−0.244003	−	0.969774i	$-0.578461\pi$
$864$	87.9757	−	34.8320i	2.99299	−	1.18501i
$865$	2.33816	+	1.28541i	0.0794998	+	0.0437054i
$866$	−2.62138	+	41.6657i	−0.0890783	+	1.41586i
$867$	−0.0994308	+	1.58041i	−0.00337685	+	0.0536735i
$868$	0.299578	−	0.922005i	0.0101683	−	0.0312949i
$869$	−3.69788	+	19.3850i	−0.125442	+	0.657590i
$870$	0.893221	+	1.40749i	0.0302830	+	0.0477184i
$871$	2.76181	−	5.86914i	0.0935803	−	0.198868i
$872$	−9.58092	−	152.284i	−0.324451	−	5.15700i
$873$	14.4162			0.487913
$874$	−87.7405			−2.96787
$875$	−0.0647458	−	1.02910i	−0.00218881	−	0.0347901i
$876$	−15.3337	−	3.93703i	−0.518078	−	0.133020i
$877$	−33.4965	−	31.4553i	−1.13110	−	1.06217i	−0.997466	−	0.0711393i	$-0.977337\pi$
$877$	−33.4965	−	31.4553i	−1.13110	−	1.06217i	−0.133630	−	0.991031i	$-0.542663\pi$
$878$	68.1567	+	26.9851i	2.30018	+	0.910705i
$879$	0.203543	−	0.0805884i	0.00686534	−	0.00271818i
$880$	−19.2952	+	18.1194i	−0.650440	+	0.610804i
$881$	19.1831	−	10.5460i	0.646294	−	0.355303i	−0.124655	−	0.992200i	$-0.539782\pi$
$881$	19.1831	−	10.5460i	0.646294	−	0.355303i	0.770949	+	0.636897i	$0.219782\pi$
$882$	−7.94288	+	41.6380i	−0.267451	+	1.40203i
$883$	2.30110	+	7.08207i	0.0774383	+	0.238331i	0.982281	−	0.187416i	$-0.0600114\pi$
$883$	2.30110	+	7.08207i	0.0774383	+	0.238331i	−0.904842	+	0.425747i	$0.860011\pi$
$884$	−7.89023	−	7.40941i	−0.265377	−	0.249206i
$885$	2.22954	−	3.51319i	0.0749451	−	0.118095i
$886$	−0.717849	−	1.13115i	−0.0241166	−	0.0380017i
$887$	−5.02642	−	15.4697i	−0.168771	−	0.519422i	0.830524	−	0.556983i	$-0.188041\pi$
$887$	−5.02642	−	15.4697i	−0.168771	−	0.519422i	−0.999294	+	0.0375609i	$0.988041\pi$
$888$	40.6704	+	16.1025i	1.36481	+	0.540366i
$889$	8.26991	+	9.99660i	0.277364	+	0.335275i
$890$	−0.678781	+	0.493163i	−0.0227528	+	0.0165309i
$891$	−7.90481	+	3.12973i	−0.264821	+	0.104850i
$892$	−27.7606	+	7.12772i	−0.929495	+	0.238654i
$893$	−4.21927	+	22.1182i	−0.141193	+	0.740157i
$894$	10.7511	+	22.8473i	0.359571	+	0.764127i
$895$	−7.31303	−	0.923850i	−0.244448	−	0.0308809i
$896$	−52.9271	−	20.9553i	−1.76817	−	0.700068i
$897$	−1.54635	+	0.397035i	−0.0516310	+	0.0132566i
$898$	−23.9823	+	73.8100i	−0.800300	+	2.46307i
$899$	0.0981261	−	0.118614i	0.00327269	−	0.00395600i
$900$	−12.8040	−	7.03908i	−0.426802	−	0.234636i
$901$	30.7960	−	7.90706i	1.02596	−	0.263422i
$902$	−13.9384	−	42.8978i	−0.464096	−	1.42834i
$903$	−4.95551	+	0.626026i	−0.164909	+	0.0208328i
$904$	−133.200	−	96.7756i	−4.43017	−	3.21871i
$905$	−20.9598			−0.696728
$906$	20.8744	+	7.19717i	0.693506	+	0.239110i
$907$	51.2585			1.70201			0.851005	−	0.525157i	$-0.175993\pi$
$907$	51.2585			1.70201			0.851005	+	0.525157i	$0.175993\pi$
$908$	−112.841	−	81.9837i	−3.74476	−	2.72073i
$909$	24.9131	−	3.14726i	0.826315	−	0.104388i
$910$	−0.441684	−	1.35936i	−0.0146417	−	0.0450624i
$911$	−4.82939	+	1.23998i	−0.160005	+	0.0410822i	−0.327842	−	0.944732i	$-0.606322\pi$
$911$	−4.82939	+	1.23998i	−0.160005	+	0.0410822i	0.167838	+	0.985815i	$0.446322\pi$
$912$	61.5117	+	33.8163i	2.03685	+	1.11977i
$913$	12.5687	−	15.1930i	0.415964	−	0.502814i
$914$	30.1236	−	92.7111i	0.996402	−	3.06661i
$915$	2.37178	−	0.608970i	0.0784086	−	0.0201319i
$916$	−96.4146	−	38.1732i	−3.18563	−	1.26128i
$917$	8.53781	+	1.07858i	0.281943	+	0.0356177i
$918$	−16.2864	−	34.6103i	−0.537530	−	1.14231i
$919$	10.9685	−	57.4987i	0.361816	−	1.89671i	−0.0750489	−	0.997180i	$-0.523911\pi$
$919$	10.9685	−	57.4987i	0.361816	−	1.89671i	0.436865	−	0.899527i	$-0.356089\pi$
$920$	48.3067	−	12.4031i	1.59263	−	0.408917i
$921$	−8.00149	+	3.16801i	−0.263658	+	0.104390i
$922$	−80.8750	+	58.7591i	−2.66348	+	1.93513i
$923$	1.71227	+	2.06977i	0.0563599	+	0.0681274i
$924$	−5.56400	−	2.20294i	−0.183042	−	0.0724715i
$925$	−2.05202	−	6.31547i	−0.0674701	−	0.207651i
$926$	41.9496	+	66.1020i	1.37855	+	2.17224i
$927$	25.2674	−	39.8150i	0.829889	−	1.30770i
$928$	−17.6739	−	16.5969i	−0.580175	−	0.544821i
$929$	−18.0964	−	55.6951i	−0.593725	−	1.82730i	−0.560974	−	0.827833i	$-0.689573\pi$
$929$	−18.0964	−	55.6951i	−0.593725	−	1.82730i	−0.0327509	−	0.999464i	$-0.510427\pi$
$930$	0.0558705	−	0.292883i	0.00183207	−	0.00960403i
$931$	−33.5519	+	18.4453i	−1.09962	+	0.604521i
$932$	56.9950	−	53.5218i	1.86693	−	1.75317i
$933$	15.5002	−	6.13696i	0.507453	−	0.200915i
$934$	−83.8346	−	33.1925i	−2.74315	−	1.08609i
$935$	4.39010	+	4.12258i	0.143572	+	0.134823i
$936$	−12.6927	−	3.25892i	−0.414872	−	0.106521i
$937$	−1.01849	−	16.1884i	−0.0332726	−	0.528852i	−0.978996	−	0.203880i	$-0.934645\pi$
$937$	−1.01849	−	16.1884i	−0.0332726	−	0.528852i	0.945723	−	0.324973i	$-0.105355\pi$
$938$	−36.9895			−1.20775
$939$	−19.6725			−0.641987
$940$	−1.24212	−	19.7429i	−0.0405135	−	0.643944i
$941$	−7.69219	+	16.3467i	−0.250758	+	0.532888i	−0.990087	−	0.140456i	$-0.955143\pi$
$941$	−7.69219	+	16.3467i	−0.250758	+	0.532888i	0.739329	+	0.673345i	$0.235143\pi$
$942$	−1.19981	−	1.89059i	−0.0390918	−	0.0615988i
$943$	−9.50371	+	49.8202i	−0.309483	+	1.62237i
$944$	−33.2271	+	102.262i	−1.08145	+	3.32836i
$945$	0.234417	−	3.72595i	0.00762558	−	0.121205i
$946$	2.04803	−	32.5524i	0.0665871	−	1.05837i
$947$	18.7829	+	10.3260i	0.610363	+	0.335550i	0.756777	−	0.653673i	$-0.226773\pi$
$947$	18.7829	+	10.3260i	0.610363	+	0.335550i	−0.146413	+	0.989223i	$0.546773\pi$
$948$	−42.7489	+	16.9255i	−1.38842	+	0.549714i
$949$	1.37392	+	1.66079i	0.0445995	+	0.0539115i
$950$	−3.34596	−	17.5401i	−0.108557	−	0.569077i
$951$	12.7727	−	7.02186i	0.414184	−	0.227700i
$952$	−12.3409	+	37.9813i	−0.399970	+	1.23098i
$953$	−42.2955	−	23.2522i	−1.37009	−	0.753211i	−0.384618	−	0.923076i	$-0.625667\pi$
$953$	−42.2955	−	23.2522i	−1.37009	−	0.753211i	−0.985467	+	0.169865i	$0.945667\pi$
$954$	43.3699	−	40.7270i	1.40415	−	1.31859i
$955$	2.54457	+	13.3391i	0.0823404	+	0.431643i
$956$	−141.620	−	17.8907i	−4.58031	−	0.578627i
$957$	−0.692702	−	0.650491i	−0.0223919	−	0.0210274i
$958$	74.9519	−	9.46862i	2.42158	−	0.305917i
$959$	3.89315	−	8.27336i	0.125716	−	0.267161i
$960$	−24.4001	−	6.26488i	−0.787510	−	0.202198i
$961$	30.7282	−	3.88188i	0.991233	−	0.125222i
$962$	−4.93214	−	7.77181i	−0.159019	−	0.250573i
$963$	6.34556	+	13.4850i	0.204483	+	0.434548i
$964$	−5.22156	−	27.3724i	−0.168175	−	0.881605i
$965$	−8.17807	+	5.94172i	−0.263262	+	0.191271i
$966$	5.80321	+	7.01488i	0.186715	+	0.225700i
$967$	21.2175	+	2.68039i	0.682308	+	0.0861956i	0.458844	−	0.888517i	$-0.348264\pi$
$967$	21.2175	+	2.68039i	0.682308	+	0.0861956i	0.223464	+	0.974712i	$0.428264\pi$
$968$	−46.2774	+	72.9215i	−1.48741	+	2.34379i
$969$	6.80005	−	14.4508i	0.218449	−	0.464228i
$970$	−12.5218	−	9.09766i	−0.402052	−	0.292108i
$971$	2.30777	+	36.6810i	0.0740599	+	1.17715i	0.843031	+	0.537865i	$0.180769\pi$
$971$	2.30777	+	36.6810i	0.0740599	+	1.17715i	−0.768971	+	0.639284i	$0.779231\pi$
$972$	−65.8129	−	47.8159i	−2.11095	−	1.53370i
$973$	11.0964	+	2.84908i	0.355735	+	0.0913372i
$974$	28.4352	−	44.8068i	0.911124	−	1.43570i
$975$	−0.138340	−	0.293988i	−0.00443044	−	0.00941516i
$976$	−55.4514	+	30.4847i	−1.77496	+	0.975791i
$977$	−13.8509	+	16.7428i	−0.443129	+	0.535650i	−0.944033	−	0.329852i	$-0.893001\pi$
$977$	−13.8509	+	16.7428i	−0.443129	+	0.535650i	0.500904	+	0.865503i	$0.333001\pi$
$978$	0.411490	−	6.54044i	0.0131580	−	0.209140i
$979$	0.304862	−	0.368515i	0.00974344	−	0.0117778i
$980$	24.5204	−	23.0262i	0.783277	−	0.735546i
$981$	−31.3636	+	22.7870i	−1.00136	+	0.727533i
$982$	49.2954	−	35.8152i	1.57308	−	1.14291i
$983$	4.77272	−	4.48188i	0.152226	−	0.142950i	−0.604692	−	0.796459i	$-0.706704\pi$
$983$	4.77272	−	4.48188i	0.152226	−	0.142950i	0.756919	+	0.653509i	$0.226704\pi$
$984$	43.3401	−	52.3892i	1.38163	−	1.67011i
$985$	−0.431781	+	6.86296i	−0.0137577	+	0.218672i
$986$	−6.24753	+	7.55197i	−0.198962	+	0.240504i
$987$	2.04742	−	1.12558i	0.0651702	−	0.0358276i
$988$	−7.78927	−	16.5530i	−0.247810	−	0.526622i
$989$	−19.6519	+	30.9664i	−0.624893	+	0.984674i
$990$	10.9150	+	2.80251i	0.346903	+	0.0890695i
$991$	−19.3153	−	14.0334i	−0.613570	−	0.445784i	0.237100	−	0.971485i	$-0.423803\pi$
$991$	−19.3153	−	14.0334i	−0.613570	−	0.445784i	−0.850669	+	0.525701i	$0.823803\pi$
$992$	0.272295	+	4.32801i	0.00864539	+	0.137414i
$993$	−1.01437	−	0.736982i	−0.0321900	−	0.0233874i
$994$	6.52225	−	13.8605i	0.206873	−	0.439628i
$995$	4.36110	−	6.87200i	0.138256	−	0.217857i
$996$	45.5768	+	5.75769i	1.44416	+	0.182439i
$997$	18.4528	+	22.3055i	0.584405	+	0.706424i	0.976988	−	0.213293i	$-0.0684187\pi$
$997$	18.4528	+	22.3055i	0.584405	+	0.706424i	−0.392584	+	0.919716i	$0.628419\pi$
$998$	19.2378	−	13.9771i	0.608961	−	0.442436i
$999$	−4.50509	−	23.6165i	−0.142535	−	0.747192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.t.b.81.1	✓	520
151.110	even	25	inner	755.2.t.b.261.1	yes	520

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.t.b.81.1	✓	520	1.1	even	1	trivial
755.2.t.b.261.1	yes	520	151.110	even	25	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.t (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23996 - 1.62742i) q^{2} +(-0.643868 + 0.0813395i) q^{3} +(1.75087 + 5.38861i) q^{4} +(-0.968583 + 0.248690i) q^{5} +(1.57461 + 0.865650i) q^{6} +(-0.657273 + 0.794506i) q^{7} +(3.13652 - 9.65321i) q^{8} +(-2.49780 + 0.641326i) q^{9} +(2.57431 + 1.01924i) q^{10} +(-1.56584 - 0.197812i) q^{11} +(-1.56563 - 3.32714i) q^{12} +(-0.0938114 + 0.491777i) q^{13} +(2.76526 - 0.709999i) q^{14} +(0.603411 - 0.238908i) q^{15} +(-13.5679 + 9.85764i) q^{16} +(2.43225 + 2.94009i) q^{17} +(6.63867 + 2.62844i) q^{18} +(1.99294 + 6.13364i) q^{19} +(-3.03595 - 4.78390i) q^{20} +(0.358572 - 0.565019i) q^{21} +(3.18549 + 2.99138i) q^{22} +(-1.51841 - 4.67317i) q^{23} +(-1.23432 + 6.47051i) q^{24} +(0.876307 - 0.481754i) q^{25} +(1.01046 - 0.948888i) q^{26} +(3.36632 - 1.33282i) q^{27} +(-5.43208 - 2.15071i) q^{28} +(-0.676279 - 0.635068i) q^{29} +(-1.74042 - 0.446864i) q^{30} +(0.0104192 + 0.165608i) q^{31} +26.1341 q^{32} +1.02428 q^{33} +(-0.663371 - 10.5440i) q^{34} +(0.439038 - 0.933003i) q^{35} +(-7.82917 - 12.3368i) q^{36} +(1.24430 - 6.52286i) q^{37} +(5.51794 - 16.9825i) q^{38} +(0.0204013 - 0.324270i) q^{39} +(-0.637323 + 10.1300i) q^{40} +(-9.04519 - 4.97263i) q^{41} +(-1.72271 + 0.682070i) q^{42} +(-4.75776 - 5.75114i) q^{43} +(-1.67565 - 8.78404i) q^{44} +(2.25984 - 1.24235i) q^{45} +(-4.20407 + 12.9388i) q^{46} +(3.05953 + 1.68199i) q^{47} +(7.93411 - 7.45062i) q^{48} +(1.11244 + 5.83160i) q^{49} +(-2.74691 - 0.347015i) q^{50} +(-1.80520 - 1.69519i) q^{51} +(-2.81425 + 0.355522i) q^{52} +(3.54782 - 7.53949i) q^{53} +(-9.70949 - 2.49297i) q^{54} +(1.56584 - 0.197812i) q^{55} +(5.60799 + 8.83677i) q^{56} +(-1.78210 - 3.78715i) q^{57} +(0.481311 + 2.52312i) q^{58} +(5.18696 - 3.76855i) q^{59} +(2.34387 + 2.83325i) q^{60} +(3.74338 + 0.472899i) q^{61} +(0.246176 - 0.387911i) q^{62} +(1.13220 - 2.40604i) q^{63} +(-31.4035 - 22.8159i) q^{64} +(-0.0314357 - 0.499657i) q^{65} +(-2.29435 - 1.66695i) q^{66} +(-12.5492 - 3.22209i) q^{67} +(-11.5845 + 18.2542i) q^{68} +(1.35777 + 2.88540i) q^{69} +(-2.50182 + 1.37539i) q^{70} +(3.42012 - 4.13422i) q^{71} +(-1.64354 + 26.1233i) q^{72} +(2.74431 - 3.31730i) q^{73} +(-13.4026 + 12.5859i) q^{74} +(-0.525040 + 0.381464i) q^{75} +(-29.5624 + 21.4784i) q^{76} +(1.18635 - 1.11405i) q^{77} +(-0.573423 + 0.693149i) q^{78} +(0.785118 - 12.4791i) q^{79} +(10.6901 - 12.9221i) q^{80} +(4.72045 - 2.59509i) q^{81} +(12.1682 + 25.8588i) q^{82} +(-6.69424 + 10.5484i) q^{83} +(3.67248 + 0.942933i) q^{84} +(-3.08701 - 2.24284i) q^{85} +(1.29763 + 20.6252i) q^{86} +(0.487091 + 0.353892i) q^{87} +(-6.82080 + 14.4949i) q^{88} +(-0.162373 + 0.255859i) q^{89} +(-7.08377 - 0.894889i) q^{90} +(-0.329060 - 0.397765i) q^{91} +(22.5234 - 16.3642i) q^{92} +(-0.0201790 - 0.105782i) q^{93} +(-4.11591 - 8.74675i) q^{94} +(-3.45570 - 5.44532i) q^{95} +(-16.8269 + 2.12573i) q^{96} +(-5.41459 - 1.39023i) q^{97} +(6.99867 - 14.8729i) q^{98} +(4.03802 - 0.510120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 520 q - 140 q^{4} - 5 q^{6} + 5 q^{10} + 5 q^{11} - 20 q^{13} - 15 q^{14} - 160 q^{16} + 25 q^{17} + 25 q^{18} + 5 q^{20} - 30 q^{23} + 20 q^{24} - 15 q^{26} - 45 q^{27} - 145 q^{28} - 25 q^{29} - 30 q^{31}+ \cdots - 60 q^{99}+O(q^{100}) \) 520 * q - 140 * q^4 - 5 * q^6 + 5 * q^10 + 5 * q^11 - 20 * q^13 - 15 * q^14 - 160 * q^16 + 25 * q^17 + 25 * q^18 + 5 * q^20 - 30 * q^23 + 20 * q^24 - 15 * q^26 - 45 * q^27 - 145 * q^28 - 25 * q^29 - 30 * q^31 + 45 * q^34 + 10 * q^35 - 20 * q^36 - 30 * q^37 - 65 * q^38 + 30 * q^39 - 45 * q^40 + 5 * q^41 + 245 * q^42 + 50 * q^46 + 95 * q^47 + 290 * q^48 - 10 * q^49 + 5 * q^50 - 5 * q^51 - 55 * q^52 + 135 * q^53 - 390 * q^54 - 5 * q^55 + 150 * q^56 + 30 * q^58 + 20 * q^59 + 35 * q^60 + 10 * q^61 - 60 * q^62 - 30 * q^63 - 200 * q^64 + 25 * q^65 + 200 * q^66 - 60 * q^67 - 130 * q^68 + 10 * q^69 - 30 * q^70 - 30 * q^71 + 425 * q^72 + 30 * q^73 + 120 * q^74 - 15 * q^75 + 15 * q^76 + 40 * q^77 - 5 * q^78 + 215 * q^79 - 15 * q^80 - 100 * q^81 - 100 * q^82 - 5 * q^83 - 45 * q^84 - 15 * q^85 + 140 * q^86 - 20 * q^87 + 135 * q^88 - 15 * q^89 - 20 * q^90 - 10 * q^91 + 180 * q^92 + 100 * q^93 - 65 * q^94 - 55 * q^95 + 35 * q^96 + 15 * q^97 - 160 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more