LMFDB - Embedded newform 213.2.n.a.104.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(11,213)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("213.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(70)) chi = DirichletCharacter(H, H._module([35, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.n (of order $70$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$528$
Relative dimension:	$22$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			104.17
Character	$\chi$	$=$	213.104
Dual form			213.2.n.a.170.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.573316 + 1.52759i) q^{2} +(-1.09945 + 1.33836i) q^{3} +(-0.498711 + 0.435711i) q^{4} +(0.396042 + 0.545105i) q^{5} +(-2.67480 - 0.912219i) q^{6} +(-3.57354 + 2.35887i) q^{7} +(1.92211 + 1.03433i) q^{8} +(-0.582401 - 2.94293i) q^{9} +(-0.605643 + 0.917509i) q^{10} +(-2.03260 + 2.12593i) q^{11} +(-0.0348267 - 1.14650i) q^{12} +(2.52087 - 2.41020i) q^{13} +(-5.65217 - 4.10654i) q^{14} +(-1.16498 - 0.0692723i) q^{15} +(-0.655852 + 4.84170i) q^{16} +(0.438855 + 1.35066i) q^{17} +(4.16170 - 2.57690i) q^{18} +(3.40880 + 0.306797i) q^{19} +(-0.435019 - 0.0992902i) q^{20} +(0.771928 - 7.37614i) q^{21} +(-4.41288 - 1.88615i) q^{22} +(-0.962744 + 1.20724i) q^{23} +(-3.49759 + 1.43527i) q^{24} +(1.40479 - 4.32351i) q^{25} +(5.12707 + 2.46906i) q^{26} +(4.57901 + 2.45615i) q^{27} +(0.754377 - 2.73343i) q^{28} +(0.274123 - 0.117166i) q^{29} +(-0.562079 - 1.81933i) q^{30} +(1.65628 - 0.224359i) q^{31} +(-3.51612 + 0.802532i) q^{32} +(-0.610506 - 5.05770i) q^{33} +(-1.81165 + 1.44475i) q^{34} +(-2.70111 - 1.01374i) q^{35} +(1.57271 + 1.21391i) q^{36} +(4.35158 + 5.45671i) q^{37} +(1.48566 + 5.38315i) q^{38} +(0.454126 + 6.02373i) q^{39} +(0.197417 + 1.45739i) q^{40} +(-3.74309 + 1.80258i) q^{41} +(11.7103 - 3.04967i) q^{42} +(9.42641 + 2.60152i) q^{43} +(0.0873882 - 1.94585i) q^{44} +(1.37355 - 1.48299i) q^{45} +(-2.39613 - 0.778551i) q^{46} +(6.21944 - 3.71594i) q^{47} +(-5.75884 - 6.20099i) q^{48} +(4.45473 - 10.4224i) q^{49} +(7.40997 - 0.332782i) q^{50} +(-2.29016 - 0.897641i) q^{51} +(-0.207037 + 2.30036i) q^{52} +(8.31485 + 7.26447i) q^{53} +(-1.12678 + 8.40302i) q^{54} +(-1.96385 - 0.266021i) q^{55} +(-9.30861 + 0.837790i) q^{56} +(-4.15842 + 4.22488i) q^{57} +(0.336140 + 0.351575i) q^{58} +(-10.7053 + 1.94273i) q^{59} +(0.611169 - 0.473046i) q^{60} +(-4.81193 - 3.17633i) q^{61} +(1.29230 + 2.40150i) q^{62} +(9.02322 + 9.14285i) q^{63} +(2.14148 + 3.24420i) q^{64} +(2.31218 + 0.419600i) q^{65} +(7.37610 - 3.83227i) q^{66} +(-5.38253 - 6.16081i) q^{67} +(-0.807358 - 0.482374i) q^{68} +(-0.557229 - 2.61580i) q^{69} -4.70739i q^{70} +(-4.02325 - 7.40361i) q^{71} +(1.92453 - 6.25904i) q^{72} +(-8.24274 + 3.09355i) q^{73} +(-5.84081 + 9.77586i) q^{74} +(4.24190 + 6.63362i) q^{75} +(-1.83368 + 1.33225i) q^{76} +(2.24877 - 12.3917i) q^{77} +(-8.94146 + 4.14722i) q^{78} +(4.29605 - 7.98340i) q^{79} +(-2.89898 + 1.56001i) q^{80} +(-8.32162 + 3.42793i) q^{81} +(-4.89958 - 4.68448i) q^{82} +(-2.87525 - 15.8439i) q^{83} +(2.82890 + 4.01490i) q^{84} +(-0.562445 + 0.774139i) q^{85} +(1.43024 + 15.8912i) q^{86} +(-0.144576 + 0.495692i) q^{87} +(-6.10580 + 1.98390i) q^{88} +(2.94705 - 3.37317i) q^{89} +(3.05289 + 1.24800i) q^{90} +(-3.32308 + 14.5594i) q^{91} +(-0.0458775 - 1.02154i) q^{92} +(-1.52073 + 2.46337i) q^{93} +(9.24215 + 7.37037i) q^{94} +(1.18279 + 1.97966i) q^{95} +(2.79174 - 5.58818i) q^{96} +(7.01786 - 14.5727i) q^{97} +(18.4751 + 0.829717i) q^{98} +(7.44024 + 4.74364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) $ 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{57}{70}\right)$	$-1$

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 $

$2$	0.573316	+	1.52759i	0.405395	+	1.08017i	0.967448	+	0.253071i	$0.0814405\pi$
$2$	0.573316	+	1.52759i	0.405395	+	1.08017i	−0.562052	+	0.827102i	$0.689988\pi$
$3$	−1.09945	+	1.33836i	−0.634770	+	0.772701i
$3$	−1.09945	+	1.33836i	−0.634770	+	0.772701i
$4$	−0.498711	+	0.435711i	−0.249356	+	0.217855i
$5$	0.396042	+	0.545105i	0.177115	+	0.243778i	0.888340	−	0.459187i	$-0.151859\pi$
$5$	0.396042	+	0.545105i	0.177115	+	0.243778i	−0.711224	+	0.702965i	$0.751859\pi$
$6$	−2.67480	−	0.912219i	−1.09198	−	0.372412i
$7$	−3.57354	+	2.35887i	−1.35067	+	0.891570i	−0.999007	−	0.0445563i	$-0.985813\pi$
$7$	−3.57354	+	2.35887i	−1.35067	+	0.891570i	−0.351664	+	0.936126i	$0.614384\pi$
$8$	1.92211	+	1.03433i	0.679570	+	0.365692i
$9$	−0.582401	−	2.94293i	−0.194134	−	0.980975i
$10$	−0.605643	+	0.917509i	−0.191521	+	0.290142i
$11$	−2.03260	+	2.12593i	−0.612851	+	0.640992i	−0.954279	−	0.298916i	$-0.903375\pi$
$11$	−2.03260	+	2.12593i	−0.612851	+	0.640992i	0.341429	+	0.939908i	$0.389089\pi$
$12$	−0.0348267	−	1.14650i	−0.0100536	−	0.330965i
$13$	2.52087	−	2.41020i	0.699164	−	0.668469i	−0.255277	−	0.966868i	$-0.582167\pi$
$13$	2.52087	−	2.41020i	0.699164	−	0.668469i	0.954441	+	0.298399i	$0.0964524\pi$
$14$	−5.65217	−	4.10654i	−1.51061	−	1.09752i
$15$	−1.16498	−	0.0692723i	−0.300795	−	0.0178860i
$16$	−0.655852	+	4.84170i	−0.163963	+	1.21042i
$17$	0.438855	+	1.35066i	0.106438	+	0.327582i	0.990065	−	0.140609i	$-0.0449059\pi$
$17$	0.438855	+	1.35066i	0.106438	+	0.327582i	−0.883627	+	0.468191i	$0.844906\pi$
$18$	4.16170	−	2.57690i	0.980921	−	0.607381i
$19$	3.40880	+	0.306797i	0.782031	+	0.0703841i	0.473458	−	0.880816i	$-0.343006\pi$
$19$	3.40880	+	0.306797i	0.782031	+	0.0703841i	0.308573	+	0.951201i	$0.400148\pi$
$20$	−0.435019	−	0.0992902i	−0.0972732	−	0.0222020i
$21$	0.771928	−	7.37614i	0.168449	−	1.60961i
$22$	−4.41288	−	1.88615i	−0.940829	−	0.402129i
$23$	−0.962744	+	1.20724i	−0.200746	+	0.251727i	−0.872007	−	0.489494i	$-0.837182\pi$
$23$	−0.962744	+	1.20724i	−0.200746	+	0.251727i	0.671261	+	0.741221i	$0.265753\pi$
$24$	−3.49759	+	1.43527i	−0.713942	+	0.292974i
$25$	1.40479	−	4.32351i	0.280959	−	0.864703i
$26$	5.12707	+	2.46906i	1.00550	+	0.484223i
$27$	4.57901	+	2.45615i	0.881231	+	0.472686i
$28$	0.754377	−	2.73343i	0.142564	−	0.516569i
$29$	0.274123	−	0.117166i	0.0509033	−	0.0217571i	−0.367423	−	0.930054i	$-0.619760\pi$
$29$	0.274123	−	0.117166i	0.0509033	−	0.0217571i	0.418326	+	0.908297i	$0.362617\pi$
$30$	−0.562079	−	1.81933i	−0.102621	−	0.332162i
$31$	1.65628	−	0.224359i	0.297477	−	0.0402960i	0.0160259	−	0.999872i	$-0.494899\pi$
$31$	1.65628	−	0.224359i	0.297477	−	0.0402960i	0.281451	+	0.959576i	$0.409184\pi$
$32$	−3.51612	+	0.802532i	−0.621569	+	0.141869i
$33$	−0.610506	−	5.05770i	−0.106276	−	0.880433i
$34$	−1.81165	+	1.44475i	−0.310696	+	0.247772i
$35$	−2.70111	−	1.01374i	−0.456570	−	0.171354i
$36$	1.57271	+	1.21391i	0.262119	+	0.202319i
$37$	4.35158	+	5.45671i	0.715395	+	0.897077i	0.998067	−	0.0621394i	$-0.0197923\pi$
$37$	4.35158	+	5.45671i	0.715395	+	0.897077i	−0.282672	+	0.959217i	$0.591221\pi$
$38$	1.48566	+	5.38315i	0.241005	+	0.873262i
$39$	0.454126	+	6.02373i	0.0727184	+	0.964569i
$40$	0.197417	+	1.45739i	0.0312144	+	0.230434i
$41$	−3.74309	+	1.80258i	−0.584573	+	0.281515i	−0.702704	−	0.711483i	$-0.748024\pi$
$41$	−3.74309	+	1.80258i	−0.584573	+	0.281515i	0.118131	+	0.992998i	$0.462310\pi$
$42$	11.7103	−	3.04967i	1.80694	−	0.470574i
$43$	9.42641	+	2.60152i	1.43751	+	0.396728i	0.896034	−	0.443986i	$-0.146436\pi$
$43$	9.42641	+	2.60152i	1.43751	+	0.396728i	0.541479	+	0.840714i	$0.317864\pi$
$44$	0.0873882	−	1.94585i	0.0131743	−	0.293348i
$45$	1.37355	−	1.48299i	0.204757	−	0.221071i
$46$	−2.39613	−	0.778551i	−0.353291	−	0.114791i
$47$	6.21944	−	3.71594i	0.907198	−	0.542026i	0.0181478	−	0.999835i	$-0.494223\pi$
$47$	6.21944	−	3.71594i	0.907198	−	0.542026i	0.889050	+	0.457810i	$0.151366\pi$
$48$	−5.75884	−	6.20099i	−0.831217	−	0.895036i
$49$	4.45473	−	10.4224i	0.636390	−	1.48891i
$50$	7.40997	−	0.332782i	1.04793	−	0.0470625i
$51$	−2.29016	−	0.897641i	−0.320687	−	0.125695i
$52$	−0.207037	+	2.30036i	−0.0287108	+	0.319003i
$53$	8.31485	+	7.26447i	1.14213	+	0.997852i	0.999968	+	0.00800853i	$0.00254922\pi$
$53$	8.31485	+	7.26447i	1.14213	+	0.997852i	0.142165	+	0.989843i	$0.454594\pi$
$54$	−1.12678	+	8.40302i	−0.153336	+	1.14351i
$55$	−1.96385	−	0.266021i	−0.264805	−	0.0358703i
$56$	−9.30861	+	0.837790i	−1.24392	+	0.111954i
$57$	−4.15842	+	4.22488i	−0.550796	+	0.559599i
$58$	0.336140	+	0.351575i	0.0441374	+	0.0461641i
$59$	−10.7053	+	1.94273i	−1.39372	+	0.252922i	−0.822914	−	0.568165i	$-0.807653\pi$
$59$	−10.7053	+	1.94273i	−1.39372	+	0.252922i	−0.570802	+	0.821088i	$0.693368\pi$
$60$	0.611169	−	0.473046i	0.0789016	−	0.0610699i
$61$	−4.81193	−	3.17633i	−0.616105	−	0.406687i	0.203943	−	0.978983i	$-0.434624\pi$
$61$	−4.81193	−	3.17633i	−0.616105	−	0.406687i	−0.820047	+	0.572296i	$0.806053\pi$
$62$	1.29230	+	2.40150i	0.164122	+	0.304991i
$63$	9.02322	+	9.14285i	1.13682	+	1.15189i
$64$	2.14148	+	3.24420i	0.267685	+	0.405525i
$65$	2.31218	+	0.419600i	0.286791	+	0.0520449i
$66$	7.37610	−	3.83227i	0.907936	−	0.471719i
$67$	−5.38253	−	6.16081i	−0.657581	−	0.752662i	0.323507	−	0.946226i	$-0.395138\pi$
$67$	−5.38253	−	6.16081i	−0.657581	−	0.752662i	−0.981088	+	0.193564i	$0.937995\pi$
$68$	−0.807358	−	0.482374i	−0.0979065	−	0.0584964i
$69$	−0.557229	−	2.61580i	−0.0670825	−	0.314906i
$70$		−	4.70739i		−	0.562641i
$71$	−4.02325	−	7.40361i	−0.477472	−	0.878647i
$71$	−4.02325	−	7.40361i	−0.477472	−	0.878647i
$72$	1.92453	−	6.25904i	0.226808	−	0.737635i
$73$	−8.24274	+	3.09355i	−0.964740	+	0.362073i	−0.783518	−	0.621369i	$-0.786577\pi$
$73$	−8.24274	+	3.09355i	−0.964740	+	0.362073i	−0.181222	+	0.983442i	$0.558005\pi$
$74$	−5.84081	+	9.77586i	−0.678980	+	1.13642i
$75$	4.24190	+	6.63362i	0.489812	+	0.765985i
$76$	−1.83368	+	1.33225i	−0.210337	+	0.152819i
$77$	2.24877	−	12.3917i	0.256271	−	1.41217i
$78$	−8.94146	+	4.14722i	−1.01242	+	0.469580i
$79$	4.29605	−	7.98340i	0.483343	−	0.898203i	−0.515795	−	0.856712i	$-0.672504\pi$
$79$	4.29605	−	7.98340i	0.483343	−	0.898203i	0.999139	−	0.0414908i	$-0.0132107\pi$
$80$	−2.89898	+	1.56001i	−0.324116	+	0.174414i
$81$	−8.32162	+	3.42793i	−0.924624	+	0.380881i
$82$	−4.89958	−	4.68448i	−0.541068	−	0.517314i
$83$	−2.87525	−	15.8439i	−0.315600	−	1.73910i	−0.618237	−	0.785992i	$-0.712153\pi$
$83$	−2.87525	−	15.8439i	−0.315600	−	1.73910i	0.302637	−	0.953106i	$-0.402133\pi$
$84$	2.82890	+	4.01490i	0.308658	+	0.438062i
$85$	−0.562445	+	0.774139i	−0.0610057	+	0.0839672i
$86$	1.43024	+	15.8912i	0.154226	+	1.71359i
$87$	−0.144576	+	0.495692i	−0.0155002	+	0.0531438i
$88$	−6.10580	+	1.98390i	−0.650881	+	0.211484i
$89$	2.94705	−	3.37317i	0.312386	−	0.357555i	−0.575350	−	0.817907i	$-0.695134\pi$
$89$	2.94705	−	3.37317i	0.312386	−	0.357555i	0.887736	+	0.460352i	$0.152277\pi$
$90$	3.05289	+	1.24800i	0.321803	+	0.131551i
$91$	−3.32308	+	14.5594i	−0.348353	+	1.52624i
$92$	−0.0458775	−	1.02154i	−0.00478307	−	0.106503i
$93$	−1.52073	+	2.46337i	−0.157693	+	0.255439i
$94$	9.24215	+	7.37037i	0.953255	+	0.760196i
$95$	1.18279	+	1.97966i	0.121352	+	0.203109i
$96$	2.79174	−	5.58818i	0.284931	−	0.570341i
$97$	7.01786	−	14.5727i	0.712556	−	1.47964i	−0.157934	−	0.987450i	$-0.550483\pi$
$97$	7.01786	−	14.5727i	0.712556	−	1.47964i	0.870489	−	0.492187i	$-0.163802\pi$
$98$	18.4751	+	0.829717i	1.86627	+	0.0838141i
$99$	7.44024	+	4.74364i	0.747772	+	0.476753i
$100$	1.18321	+	2.76827i	0.118321	+	0.276827i
$101$	−7.00937	−	14.5551i	−0.697459	−	1.44829i	−0.884789	−	0.465991i	$-0.845698\pi$
$101$	−7.00937	−	14.5551i	−0.697459	−	1.44829i	0.187331	−	0.982297i	$-0.440016\pi$
$102$	0.0582442	−	4.01307i	0.00576704	−	0.397353i
$103$	−0.302124	−	1.32369i	−0.0297692	−	0.130427i	0.957860	−	0.287236i	$-0.0927365\pi$
$103$	−0.302124	−	1.32369i	−0.0297692	−	0.130427i	−0.987629	+	0.156809i	$0.949879\pi$
$104$	7.33836	−	2.02526i	0.719585	−	0.198593i
$105$	4.32649	−	2.50048i	0.422222	−	0.244022i
$106$	−6.33013	+	16.8666i	−0.614836	+	1.63823i
$107$	3.54234	−	9.43854i	0.342451	−	0.912458i	−0.646326	−	0.763061i	$-0.723695\pi$
$107$	3.54234	−	9.43854i	0.342451	−	0.912458i	0.988777	−	0.149397i	$-0.0477331\pi$
$108$	−3.35377	+	0.770214i	−0.322717	+	0.0741139i
$109$	−7.50619	+	2.07158i	−0.718963	+	0.198421i	−0.606327	−	0.795215i	$-0.707358\pi$
$109$	−7.50619	+	2.07158i	−0.718963	+	0.198421i	−0.112635	+	0.993636i	$0.535929\pi$
$110$	−0.719533	−	3.15248i	−0.0686048	−	0.300577i
$111$	−12.0874	−	0.175432i	−1.14728	−	0.0166513i
$112$	−9.07723	−	18.8491i	−0.857718	−	1.78107i
$113$	6.88078	+	16.0984i	0.647290	+	1.51441i	0.845346	+	0.534219i	$0.179394\pi$
$113$	6.88078	+	16.0984i	0.647290	+	1.51441i	−0.198057	+	0.980191i	$0.563463\pi$
$114$	−8.83799	−	3.93019i	−0.827753	−	0.368096i
$115$	−1.03936	−	0.0466778i	−0.0969209	−	0.00435272i
$116$	−0.0856577	+	0.177870i	−0.00795311	+	0.0165148i
$117$	−8.56120	−	6.01504i	−0.791483	−	0.556090i
$118$	−9.10525	−	15.2396i	−0.838206	−	1.40292i
$119$	−4.75429	−	3.79142i	−0.435825	−	0.347559i
$120$	−2.16757	−	1.33812i	−0.197871	−	0.122153i
$121$	0.105386	+	2.34661i	0.00958059	+	0.213328i
$122$	2.09339	−	9.17172i	0.189526	−	0.830368i
$123$	1.70286	−	6.99144i	0.153542	−	0.630397i
$124$	−0.728251	+	0.833550i	−0.0653988	+	0.0748550i
$125$	6.11718	−	1.98759i	0.547137	−	0.177776i
$126$	−8.79341	+	19.0256i	−0.783379	+	1.69493i
$127$	1.66619	+	18.5129i	0.147851	+	1.64276i	0.637221	+	0.770681i	$0.280084\pi$
$127$	1.66619	+	18.5129i	0.147851	+	1.64276i	−0.489370	+	0.872076i	$0.662773\pi$
$128$	−7.96783	+	10.9668i	−0.704263	+	0.969336i
$129$	−13.8457	+	9.75564i	−1.21904	+	0.858937i
$130$	0.684634	+	3.77264i	0.0600464	+	0.330883i
$131$	−1.71431	−	1.63905i	−0.149780	−	0.143204i	0.612453	−	0.790507i	$-0.290183\pi$
$131$	−1.71431	−	1.63905i	−0.149780	−	0.143204i	−0.762233	+	0.647302i	$0.775897\pi$
$132$	2.50816	+	2.25633i	0.218307	+	0.196388i
$133$	−12.9052	+	6.94456i	−1.11902	+	0.602170i
$134$	6.32532	−	11.7544i	0.546425	−	1.01543i
$135$	0.474620	+	3.46878i	0.0408488	+	0.298545i
$136$	−0.553501	+	3.05004i	−0.0474623	+	0.261539i
$137$	−5.90137	+	4.28760i	−0.504188	+	0.366314i	−0.810615	−	0.585580i	$-0.800867\pi$
$137$	−5.90137	+	4.28760i	−0.504188	+	0.366314i	0.306426	+	0.951894i	$0.400867\pi$
$138$	3.67642	−	2.35090i	0.312957	−	0.200122i
$139$	1.47125	−	2.46245i	0.124790	−	0.208863i	−0.789678	−	0.613521i	$-0.789752\pi$
$139$	1.47125	−	2.46245i	0.124790	−	0.208863i	0.914468	+	0.404659i	$0.132610\pi$
$140$	1.78877	−	0.671336i	0.151179	−	0.0567383i
$141$	−1.86473	+	12.4093i	−0.157039	+	1.04505i
$142$	9.00312	−	10.3905i	0.755525	−	0.871952i
$143$			10.2582i			0.857830i
$144$	14.6307	−	0.889685i	1.21923	−	0.0741404i
$145$	0.172432	+	0.103023i	0.0143197	+	0.00855561i
$146$	−9.45139	−	10.8180i	−0.782202	−	0.895303i
$147$	9.05106	+	17.4209i	0.746519	+	1.43685i
$148$	−4.54773	−	0.825291i	−0.373821	−	0.0678385i
$149$	−5.41056	−	8.19664i	−0.443250	−	0.671495i	0.542434	−	0.840098i	$-0.317503\pi$
$149$	−5.41056	−	8.19664i	−0.443250	−	0.671495i	−0.985684	+	0.168603i	$0.946074\pi$
$150$	−7.70154	+	10.2831i	−0.628828	+	0.839608i
$151$	9.70693	+	18.0385i	0.789939	+	1.46795i	0.881516	+	0.472154i	$0.156523\pi$
$151$	9.70693	+	18.0385i	0.789939	+	1.46795i	−0.0915775	+	0.995798i	$0.529191\pi$
$152$	6.23477	+	4.11553i	0.505706	+	0.333814i
$153$	3.71929	−	2.07814i	0.300687	−	0.168008i
$154$	20.2188	−	3.66917i	1.62928	−	0.295670i
$155$	0.778256	+	0.813992i	0.0625111	+	0.0653814i
$156$	−2.85108	−	2.80623i	−0.228269	−	0.224679i
$157$	4.99013	−	0.449120i	0.398255	−	0.0358436i	0.111298	−	0.993787i	$-0.464499\pi$
$157$	4.99013	−	0.449120i	0.398255	−	0.0358436i	0.286957	+	0.957943i	$0.407356\pi$
$158$	14.6584	+	1.98561i	1.16616	+	0.157967i
$159$	−18.8643	+	3.14130i	−1.49603	+	0.249121i
$160$	−1.83000	−	1.59882i	−0.144674	−	0.126398i
$161$	0.592671	−	6.58512i	0.0467090	−	0.518980i
$162$	−10.0074	−	10.7468i	−0.786255	−	0.844346i
$163$	−6.71851	+	0.301729i	−0.526235	+	0.0236332i	−0.306398	−	0.951903i	$-0.599124\pi$
$163$	−6.71851	+	0.301729i	−0.526235	+	0.0236332i	−0.219837	+	0.975537i	$0.570552\pi$
$164$	1.08132	−	2.52987i	0.0844368	−	0.197550i
$165$	2.51519	−	2.33585i	0.195808	−	0.181846i
$166$	22.5547	−	13.4758i	1.75058	−	1.04592i
$167$	−14.3080	−	4.64895i	−1.10719	−	0.359746i	−0.302322	−	0.953206i	$-0.597762\pi$
$167$	−14.3080	−	4.64895i	−1.10719	−	0.359746i	−0.804864	+	0.593460i	$0.797762\pi$
$168$	9.11313	−	13.3794i	0.703093	−	1.03224i
$169$	−0.0375131	+	0.835294i	−0.00288562	+	0.0642534i
$170$	−1.50503	−	0.415362i	−0.115431	−	0.0318568i
$171$	−1.08241	−	10.2105i	−0.0827736	−	0.780817i
$172$	−5.83456	+	2.80978i	−0.444881	+	0.214244i
$173$	1.94783	+	14.3794i	0.148091	+	1.09325i	0.900594	+	0.434661i	$0.143132\pi$
$173$	1.94783	+	14.3794i	0.148091	+	1.09325i	−0.752504	+	0.658588i	$0.771154\pi$
$174$	−0.840104	+	0.0633351i	−0.0636882	+	0.00480142i
$175$	5.17853	+	18.7640i	0.391460	+	1.41842i
$176$	−8.96002	−	11.2355i	−0.675387	−	0.846909i
$177$	9.16996	−	16.4635i	0.689256	−	1.23747i
$178$	6.84242	+	2.56800i	0.512861	+	0.192480i
$179$	−4.34894	+	3.46816i	−0.325055	+	0.259223i	−0.772397	−	0.635140i	$-0.780942\pi$
$179$	−4.34894	+	3.46816i	−0.325055	+	0.259223i	0.447342	+	0.894363i	$0.352371\pi$
$180$	−0.0388482	+	1.33805i	−0.00289558	+	0.0997327i
$181$	24.1081	−	5.50251i	1.79194	−	0.408998i	0.808244	−	0.588848i	$-0.200418\pi$
$181$	24.1081	−	5.50251i	1.79194	−	0.408998i	0.983694	+	0.179850i	$0.0575611\pi$
$182$	−24.1460	+	3.27079i	−1.78982	+	0.242447i
$183$	9.54156	−	2.94786i	0.705332	−	0.217912i
$184$	−3.09920	+	1.32466i	−0.228476	+	0.0976552i
$185$	−1.25107	+	4.53315i	−0.0919806	+	0.333284i
$186$	−4.63489	−	0.910776i	−0.339847	−	0.0667814i
$187$	−3.76342	−	1.81237i	−0.275208	−	0.132533i
$188$	−1.48263	+	4.56306i	−0.108132	+	0.332795i
$189$	−22.1570	+	2.02415i	−1.61169	+	0.147235i
$190$	−2.34600	+	2.94179i	−0.170197	+	0.213420i
$191$	22.8642	+	9.77265i	1.65440	+	0.707124i	0.998846	−	0.0480256i	$-0.0152929\pi$
$191$	22.8642	+	9.77265i	1.65440	+	0.707124i	0.655553	+	0.755150i	$0.272436\pi$
$192$	−6.69636	−	0.700787i	−0.483268	−	0.0505749i
$193$	−0.771169	−	0.176014i	−0.0555099	−	0.0126698i	0.194676	−	0.980868i	$-0.437635\pi$
$193$	−0.771169	−	0.176014i	−0.0555099	−	0.0126698i	−0.250186	+	0.968198i	$0.580492\pi$
$194$	26.2847	+	2.36566i	1.88713	+	0.169845i
$195$	−3.10372	+	2.63320i	−0.222262	+	0.188567i
$196$	2.31951	+	7.13872i	0.165679	+	0.509908i
$197$	1.58734	−	11.7182i	0.113094	−	0.834890i	−0.842186	−	0.539187i	$-0.818732\pi$
$197$	1.58734	−	11.7182i	0.113094	−	0.834890i	0.955280	−	0.295703i	$-0.0955539\pi$
$198$	−2.98075	+	14.0853i	−0.211832	+	1.00100i
$199$	−13.6726	−	9.93373i	−0.969226	−	0.704184i	−0.0139508	−	0.999903i	$-0.504441\pi$
$199$	−13.6726	−	9.93373i	−0.969226	−	0.704184i	−0.955275	+	0.295719i	$0.904441\pi$
$200$	7.17213	−	6.85726i	0.507146	−	0.484882i
$201$	14.1632	−	0.430230i	0.998996	−	0.0303461i
$202$	18.2157	−	19.0522i	1.28165	−	1.34051i
$203$	−0.703209	+	1.06532i	−0.0493556	+	0.0747706i
$204$	1.53324	−	0.550185i	0.107348	−	0.0385207i
$205$	−2.46502	−	1.32648i	−0.172164	−	0.0926455i
$206$	1.84885	−	1.22042i	0.128816	−	0.0850305i
$207$	4.11353	+	2.13018i	0.285910	+	0.148058i
$208$	10.0161	+	13.7860i	0.694494	+	0.955890i
$209$	−7.58094	+	6.62326i	−0.524384	+	0.458141i
$210$	6.30017	+	5.17556i	0.434753	+	0.357147i
$211$	−3.65461	−	9.73767i	−0.251594	−	0.670369i	−0.999975	−	0.00710001i	$-0.997740\pi$
$211$	−3.65461	−	9.73767i	−0.251594	−	0.670369i	0.748381	−	0.663269i	$-0.230831\pi$
$212$	−7.31192			−0.502184
$213$	14.3321	+	2.75538i	0.982016	+	0.188796i
$214$	16.4491			1.12444
$215$	2.31515	+	6.16870i	0.157892	+	0.420702i
$216$	6.26090	+	9.45723i	0.426000	+	0.643483i
$217$	−5.38955	+	4.70871i	−0.365867	+	0.319648i
$218$	−7.46795	−	10.2787i	−0.505793	−	0.696165i
$219$	4.92224	−	14.4330i	0.332614	−	0.975289i
$220$	1.09530	−	0.723002i	0.0738452	−	0.0487448i
$221$	4.36165	+	2.34711i	0.293396	+	0.157883i
$222$	−6.66190	−	18.5652i	−0.447117	−	1.24601i
$223$	−8.21779	+	12.4494i	−0.550304	+	0.833675i	−0.998173	−	0.0604243i	$-0.980755\pi$
$223$	−8.21779	+	12.4494i	−0.550304	+	0.833675i	0.447869	+	0.894099i	$0.352183\pi$
$224$	10.6719	−	11.1620i	0.713049	−	0.745791i
$225$	−13.5419	−	1.61619i	−0.902795	−	0.107746i
$226$	−20.6470	+	19.7405i	−1.37341	+	1.31312i
$227$	1.51075	+	1.09763i	0.100272	+	0.0728519i	0.636792	−	0.771036i	$-0.280261\pi$
$227$	1.51075	+	1.09763i	0.100272	+	0.0728519i	−0.536519	+	0.843888i	$0.680261\pi$
$228$	0.233025	−	3.91886i	0.0154325	−	0.259533i
$229$	3.76277	−	27.7779i	0.248651	−	1.83561i	−0.249322	−	0.968421i	$-0.580208\pi$
$229$	3.76277	−	27.7779i	0.248651	−	1.83561i	0.497973	−	0.867192i	$-0.334078\pi$
$230$	−0.524578	−	1.61448i	−0.0345896	−	0.106456i
$231$	14.1121	+	16.6338i	0.928511	+	1.09442i
$232$	0.648083	+	0.0583286i	0.0425488	+	0.00382946i
$233$	1.67948	+	0.383331i	0.110027	+	0.0251128i	0.277180	−	0.960818i	$-0.410600\pi$
$233$	1.67948	+	0.383331i	0.110027	+	0.0251128i	−0.167153	+	0.985931i	$0.553457\pi$
$234$	4.28026	−	16.5266i	0.279810	−	1.08037i
$235$	4.48874	+	1.91858i	0.292813	+	0.125154i
$236$	4.49240	−	5.63329i	0.292430	−	0.366696i
$237$	5.96133	+	14.5270i	0.387230	+	0.943632i
$238$	3.06605	−	9.43632i	0.198742	−	0.611666i
$239$	−19.3631	−	9.32477i	−1.25249	−	0.603169i	−0.314315	−	0.949319i	$-0.601775\pi$
$239$	−19.3631	−	9.32477i	−1.25249	−	0.603169i	−0.938179	+	0.346150i	$0.887489\pi$
$240$	1.09945	−	5.59503i	0.0709690	−	0.361157i
$241$	−2.15821	+	7.82010i	−0.139023	+	0.503737i	−0.999988	−	0.00492675i	$-0.998432\pi$
$241$	−2.15821	+	7.82010i	−0.139023	+	0.503737i	0.860965	+	0.508664i	$0.169860\pi$
$242$	−3.52425	+	1.50634i	−0.226548	+	0.0968311i
$243$	4.56145	−	14.9061i	0.292617	−	0.956230i
$244$	3.78372	−	0.512540i	0.242228	−	0.0328120i
$245$	7.44554	−	1.69940i	0.475678	−	0.108570i
$246$	11.6564	−	1.40702i	0.743183	−	0.0897083i
$247$	9.33258	−	7.44249i	0.593818	−	0.473554i
$248$	3.41562	+	1.28191i	0.216892	+	0.0814011i
$249$	24.3661	+	13.5716i	1.54414	+	0.860063i
$250$	6.54331	+	8.20505i	0.413835	+	0.518933i
$251$	−1.77836	−	6.44376i	−0.112249	−	0.406726i	0.886143	−	0.463412i	$-0.153375\pi$
$251$	−1.77836	−	6.44376i	−0.112249	−	0.406726i	−0.998392	+	0.0566861i	$0.981947\pi$
$252$	−8.48362	−	0.628127i	−0.534418	−	0.0395683i
$253$	−0.609643	−	4.50056i	−0.0383279	−	0.282948i
$254$	−27.3250	+	13.1590i	−1.71452	+	0.825671i
$255$	−0.417692	−	1.60388i	−0.0261569	−	0.100439i
$256$	−13.8265	−	3.81588i	−0.864158	−	0.238493i
$257$	−0.0839111	+	1.86843i	−0.00523423	+	0.116549i	0.994675	+	0.103063i	$0.0328643\pi$
$257$	−0.0839111	+	1.86843i	−0.00523423	+	0.116549i	−0.999909	+	0.0134862i	$0.995707\pi$
$258$	−22.8406	−	15.5575i	−1.42199	−	0.968568i
$259$	−28.4222	−	9.23494i	−1.76607	−	0.573831i
$260$	−1.33594	+	0.798185i	−0.0828512	+	0.0495013i
$261$	−0.504459	−	0.738485i	−0.0312252	−	0.0457111i
$262$	1.52096	−	3.55847i	0.0939653	−	0.219843i
$263$	25.6375	−	1.15138i	1.58088	−	0.0709973i	0.763004	−	0.646394i	$-0.223724\pi$
$263$	25.6375	−	1.15138i	1.58088	−	0.0709973i	0.817874	+	0.575397i	$0.195152\pi$
$264$	4.05789	−	10.3529i	0.249746	−	0.637180i
$265$	−0.666868	+	7.40951i	−0.0409653	+	0.455162i
$266$	−18.0072	−	15.7324i	−1.10409	−	0.964617i
$267$	1.27436	+	7.65285i	0.0779895	+	0.468347i
$268$	5.36866	+	0.727234i	0.327943	+	0.0444229i
$269$	10.0115	−	0.901055i	0.610415	−	0.0549383i	0.219881	−	0.975527i	$-0.429433\pi$
$269$	10.0115	−	0.901055i	0.610415	−	0.0549383i	0.390534	+	0.920589i	$0.372290\pi$
$270$	−5.02678	+	2.71373i	−0.305920	+	0.165153i
$271$	6.68644	+	6.99347i	0.406173	+	0.424823i	0.893965	−	0.448136i	$-0.147912\pi$
$271$	6.68644	+	6.99347i	0.406173	+	0.424823i	−0.487793	+	0.872960i	$0.662198\pi$
$272$	−6.82730	+	1.23897i	−0.413966	+	0.0751237i
$273$	−15.8321	−	20.4548i	−0.958200	−	1.23798i
$274$	−9.93306	−	6.55676i	−0.600078	−	0.396108i
$275$	6.33610	+	11.7745i	0.382081	+	0.710026i
$276$	1.41763	+	1.06174i	0.0853313	+	0.0639092i
$277$	−4.32205	−	6.54762i	−0.259687	−	0.393408i	0.681218	−	0.732081i	$-0.261451\pi$
$277$	−4.32205	−	6.54762i	−0.259687	−	0.393408i	−0.940904	+	0.338672i	$0.890022\pi$
$278$	4.60512	+	0.835706i	0.276197	+	0.0501223i
$279$	−1.62489	−	4.74365i	−0.0972797	−	0.283995i
$280$	−4.14329	−	4.74237i	−0.247609	−	0.283411i
$281$	4.16066	+	2.48588i	0.248204	+	0.148295i	0.631613	−	0.775283i	$-0.282393\pi$
$281$	4.16066	+	2.48588i	0.248204	+	0.148295i	−0.383409	+	0.923579i	$0.625250\pi$
$282$	−20.0255	+	4.26592i	−1.19250	+	0.254032i
$283$			21.5414i			1.28051i	0.768164	+	0.640253i	$0.221170\pi$
$283$			21.5414i			1.28051i	−0.768164	+	0.640253i	$0.778830\pi$
$284$	5.23227	+	1.93929i	0.310478	+	0.115076i
$285$	−3.94991	−	0.593546i	−0.233973	−	0.0351587i
$286$	−15.6703	+	5.88117i	−0.926605	+	0.347761i
$287$	9.12403	−	15.2711i	0.538575	−	0.901422i
$288$	4.40959	+	9.88030i	0.259837	+	0.582202i
$289$	12.1216	−	8.80686i	0.713036	−	0.518051i
$290$	−0.0585198	+	0.322471i	−0.00343640	+	0.0189361i
$291$	11.7877	+	25.4145i	0.691008	+	1.48982i
$292$	2.76285	−	5.13424i	0.161684	−	0.300459i
$293$	−16.2871	+	8.76444i	−0.951501	+	0.512024i	−0.874510	−	0.485008i	$-0.838817\pi$
$293$	−16.2871	+	8.76444i	−0.951501	+	0.512024i	−0.0769905	+	0.997032i	$0.524531\pi$
$294$	−21.4230	+	23.8140i	−1.24941	+	1.38886i
$295$	−5.29876	−	5.06613i	−0.308506	−	0.294962i
$296$	2.72018	+	14.9894i	0.158107	+	0.871241i
$297$	−14.5289	+	4.74229i	−0.843051	+	0.275175i
$298$	9.41919	−	12.9644i	0.545639	−	0.751007i
$299$	0.482743	+	5.36371i	0.0279177	+	0.310191i
$300$	−5.00582	−	1.46002i	−0.289011	−	0.0842943i
$301$	−39.8223	+	12.9390i	−2.29532	+	0.745794i
$302$	−21.9904	+	25.1700i	−1.26540	+	1.44837i
$303$	27.1864	+	6.62163i	1.56182	+	0.380403i
$304$	−3.72109	+	16.3031i	−0.213419	+	0.935049i
$305$	−0.174295	−	3.88097i	−0.00998007	−	0.222224i
$306$	5.30689	+	4.49014i	0.303375	+	0.256684i
$307$	−5.20267	−	4.14899i	−0.296932	−	0.236795i	0.463679	−	0.886003i	$-0.346529\pi$
$307$	−5.20267	−	4.14899i	−0.296932	−	0.236795i	−0.760611	+	0.649208i	$0.775100\pi$
$308$	4.27772	+	7.15970i	0.243746	+	0.407962i
$309$	2.10375	+	1.05099i	0.119678	+	0.0597887i
$310$	−0.797264	+	1.65553i	−0.0452815	+	0.0940281i
$311$	15.2317	+	0.684056i	0.863709	+	0.0387892i	0.472311	−	0.881432i	$-0.343420\pi$
$311$	15.2317	+	0.684056i	0.863709	+	0.0387892i	0.391399	+	0.920221i	$0.371991\pi$
$312$	−5.35767	+	12.0480i	−0.303318	+	0.682085i
$313$	−5.55773	−	13.0030i	−0.314141	−	0.734970i	−0.999974	−	0.00721103i	$-0.997705\pi$
$313$	−5.55773	−	13.0030i	−0.314141	−	0.734970i	0.685833	−	0.727759i	$-0.259438\pi$
$314$	3.54699	+	7.36540i	0.200168	+	0.415654i
$315$	−1.41024	+	8.53956i	−0.0794580	+	0.481150i
$316$	1.33596	+	5.85324i	0.0751539	+	0.329271i
$317$	−6.86085	+	1.89347i	−0.385344	+	0.106348i	−0.453340	−	0.891337i	$-0.649768\pi$
$317$	−6.86085	+	1.89347i	−0.385344	+	0.106348i	0.0679968	+	0.997686i	$0.478339\pi$
$318$	−15.6138	−	27.0160i	−0.875578	−	1.51498i
$319$	−0.308095	+	0.820916i	−0.0172500	+	0.0459625i
$320$	−0.920315	+	2.45217i	−0.0514472	+	0.137081i
$321$	8.73749	+	15.1182i	0.487679	+	0.843813i
$322$	10.3992	−	2.86999i	0.579524	−	0.159938i
$323$	1.08159	+	4.73875i	0.0601813	+	0.263671i
$324$	2.65650	−	5.33536i	0.147583	−	0.296409i
$325$	−6.87923	−	14.2849i	−0.381591	−	0.792382i
$326$	−4.31275	−	10.0902i	−0.238861	−	0.558843i
$327$	5.48020	−	12.3236i	0.303056	−	0.681495i
$328$	−9.05912	−	0.406845i	−0.500206	−	0.0224643i
$329$	−13.4600	+	27.9499i	−0.742072	+	1.54093i
$330$	5.01024	+	2.50301i	0.275804	+	0.137786i
$331$	−10.2112	−	17.0907i	−0.561260	−	0.939391i	−0.999184	−	0.0403789i	$-0.987143\pi$
$331$	−10.2112	−	17.0907i	−0.561260	−	0.939391i	0.437925	−	0.899012i	$-0.355714\pi$
$332$	8.33729	+	6.64877i	0.457568	+	0.364899i
$333$	13.5243	−	15.9844i	0.741128	−	0.875938i
$334$	−1.10129	−	24.5221i	−0.0602599	−	1.34179i
$335$	1.22658	−	5.37399i	0.0670151	−	0.293612i
$336$	35.2068	+	8.57510i	1.92069	+	0.467810i
$337$	−1.74233	+	1.99425i	−0.0949106	+	0.108634i	−0.798565	−	0.601908i	$-0.794407\pi$
$337$	−1.74233	+	1.99425i	−0.0949106	+	0.108634i	0.703655	+	0.710542i	$0.251550\pi$
$338$	−1.29750	+	0.421582i	−0.0705746	+	0.0229311i
$339$	−29.1105	−	8.49050i	−1.58107	−	0.461141i
$340$	−0.0568032	−	0.631135i	−0.00308059	−	0.0342281i
$341$	−2.88958	+	3.97717i	−0.156480	+	0.215376i
$342$	14.9770	−	7.50732i	0.809861	−	0.405950i
$343$	3.31395	+	18.2614i	0.178936	+	0.986021i
$344$	15.4278	+	14.7505i	0.831811	+	0.795292i
$345$	1.20520	−	1.33972i	0.0648859	−	0.0721279i
$346$	−20.8492	+	11.2195i	−1.12086	+	0.603162i
$347$	−0.388114	+	0.721236i	−0.0208350	+	0.0387180i	−0.890800	−	0.454395i	$-0.849855\pi$
$347$	−0.388114	+	0.721236i	−0.0208350	+	0.0387180i	0.869965	+	0.493113i	$0.164141\pi$
$348$	−0.143877	−	0.310200i	−0.00771261	−	0.0166285i
$349$	−1.19186	+	6.56769i	−0.0637988	+	0.351560i	0.936201	+	0.351465i	$0.114316\pi$
$349$	−1.19186	+	6.56769i	−0.0637988	+	0.351560i	−1.00000		9.57896e-5i	$0.999970\pi$
$350$	−25.6948	+	18.6684i	−1.37345	+	0.997867i
$351$	17.4629	−	4.84469i	0.932101	−	0.258590i
$352$	5.44073	−	9.10626i	0.289992	−	0.485365i
$353$	−24.5694	+	9.22103i	−1.30769	+	0.490786i	−0.905336	−	0.424696i	$-0.860381\pi$
$353$	−24.5694	+	9.22103i	−1.30769	+	0.490786i	−0.402359	+	0.915482i	$0.631810\pi$
$354$	30.4069	+	4.56919i	1.61611	+	0.242849i
$355$	2.44237	−	5.12524i	0.129628	−	0.272019i
$356$			2.96630i			0.157213i
$357$	10.3014	−	2.19445i	0.545208	−	0.116143i
$358$	−7.79126	−	4.65506i	−0.411781	−	0.246028i
$359$	9.37942	+	10.7356i	0.495027	+	0.566604i	0.945265	−	0.326305i	$-0.105804\pi$
$359$	9.37942	+	10.7356i	0.495027	+	0.566604i	−0.450238	+	0.892909i	$0.648661\pi$
$360$	4.17403	−	1.42977i	0.219991	−	0.0753556i
$361$	−7.16890	−	1.30096i	−0.377310	−	0.0684717i
$362$	22.2271	+	33.6727i	1.16823	+	1.76980i
$363$	−3.25647	−	2.43895i	−0.170921	−	0.128012i
$364$	−4.68641	−	8.70882i	−0.245635	−	0.456466i
$365$	−4.95078	−	3.26798i	−0.259136	−	0.171054i
$366$	9.97346	+	12.8856i	0.521321	+	0.673540i
$367$	13.6551	−	2.47804i	0.712793	−	0.129353i	0.189965	−	0.981791i	$-0.439163\pi$
$367$	13.6551	−	2.47804i	0.712793	−	0.129353i	0.522828	+	0.852438i	$0.324877\pi$
$368$	−5.21368	−	5.45309i	−0.271782	−	0.284262i
$369$	7.48483	+	9.96581i	0.389645	+	0.518800i
$370$	−7.64208	+	0.687800i	−0.397293	+	0.0357570i
$371$	−46.8494	−	6.34618i	−2.43230	−	0.329477i
$372$	−0.314909	−	1.89111i	−0.0163273	−	0.0980495i
$373$	4.73955	+	4.14082i	0.245405	+	0.214404i	0.771849	−	0.635806i	$-0.219332\pi$
$373$	4.73955	+	4.14082i	0.245405	+	0.214404i	−0.526444	+	0.850210i	$0.676475\pi$
$374$	0.610934	−	6.78803i	0.0315906	−	0.351001i
$375$	−4.06545	+	10.3722i	−0.209939	+	0.535620i
$376$	15.7980	−	0.709489i	0.814719	−	0.0365891i
$377$	0.408635	−	0.956050i	0.0210458	−	0.0492391i
$378$	−15.7950	−	32.6865i	−0.812409	−	1.68121i
$379$	−14.0812	+	8.41311i	−0.723301	+	0.432152i	−0.826814	−	0.562476i	$-0.809849\pi$
$379$	−14.0812	+	8.41311i	−0.723301	+	0.432152i	0.103513	+	0.994628i	$0.466992\pi$
$380$	−1.45243	−	0.471923i	−0.0745080	−	0.0242091i
$381$	−26.6088	−	18.1242i	−1.36321	−	0.928529i
$382$	−1.82021	+	40.5301i	−0.0931300	+	2.07370i
$383$	−8.65839	−	2.38956i	−0.442423	−	0.122101i	0.0377256	−	0.999288i	$-0.487989\pi$
$383$	−8.65839	−	2.38956i	−0.442423	−	0.122101i	−0.480149	+	0.877187i	$0.659417\pi$
$384$	−5.91720	−	22.7213i	−0.301961	−	1.15949i
$385$	7.64540	−	3.68183i	0.389646	−	0.187643i
$386$	−0.173245	−	1.27894i	−0.00881793	−	0.0650966i
$387$	2.16614	−	29.2563i	0.110111	−	1.48718i
$388$	2.84961	+	10.3253i	0.144667	+	0.524190i
$389$	−1.35916	−	1.70434i	−0.0689124	−	0.0864134i	0.746181	−	0.665744i	$-0.231886\pi$
$389$	−1.35916	−	1.70434i	−0.0689124	−	0.0864134i	−0.815093	+	0.579330i	$0.803314\pi$
$390$	−5.80187	−	3.23156i	−0.293789	−	0.163637i
$391$	−2.05308	−	0.770532i	−0.103829	−	0.0389675i
$392$	19.3427	−	15.4253i	0.976953	−	0.779094i
$393$	4.07844	−	0.492302i	0.205730	−	0.0248333i
$394$	18.8108	−	4.29343i	0.947673	−	0.216300i
$395$	6.05321	−	0.819963i	0.304570	−	0.0412568i
$396$	−5.77738	+	0.876087i	−0.290324	+	0.0440250i
$397$	7.83260	−	3.34781i	0.393107	−	0.168022i	−0.187388	−	0.982286i	$-0.560002\pi$
$397$	7.83260	−	3.34781i	0.393107	−	0.168022i	0.580495	+	0.814264i	$0.302859\pi$
$398$	7.33599	−	26.5814i	0.367720	−	1.33240i
$399$	4.89433	−	24.9069i	0.245023	−	1.24691i
$400$	20.0118	+	9.63718i	1.00059	+	0.481859i
$401$	7.66889	−	23.6024i	0.382966	−	1.17865i	−0.554979	−	0.831865i	$-0.687274\pi$
$401$	7.66889	−	23.6024i	0.382966	−	1.17865i	0.937945	−	0.346784i	$-0.112726\pi$
$402$	8.77721	+	21.3890i	0.437767	+	1.06679i
$403$	3.63453	−	4.55755i	0.181049	−	0.227028i
$404$	9.83747	+	4.20474i	0.489432	+	0.209193i
$405$	−5.16429	−	3.17855i	−0.256616	−	0.157944i
$406$	−2.03053	−	0.463456i	−0.100774	−	0.0230009i
$407$	−20.4456	−	1.84014i	−1.01345	−	0.0912121i
$408$	−3.47350	−	4.09416i	−0.171964	−	0.202691i
$409$	3.91088	+	12.0365i	0.193381	+	0.595164i	0.999992	+	0.00408175i	$0.00129926\pi$
$409$	3.91088	+	12.0365i	0.193381	+	0.595164i	−0.806611	+	0.591083i	$0.798701\pi$
$410$	0.613093	−	4.52604i	0.0302785	−	0.223525i
$411$	0.749950	−	12.6122i	0.0369923	−	0.622112i
$412$	0.727420	+	0.528501i	0.0358374	+	0.0260374i
$413$	33.6733	−	32.1950i	1.65695	−	1.58421i
$414$	−0.895707	+	7.50507i	−0.0440216	+	0.368854i
$415$	7.49789	−	7.84218i	0.368057	−	0.384957i
$416$	−6.92944	+	10.4976i	−0.339744	+	0.514689i
$417$	1.67807	+	4.67641i	0.0821757	+	0.229005i
$418$	−14.4639	−	7.78337i	−0.707454	−	0.380697i
$419$	4.47680	−	2.95511i	0.218706	−	0.144366i	−0.436795	−	0.899561i	$-0.643886\pi$
$419$	4.47680	−	2.95511i	0.218706	−	0.144366i	0.655500	+	0.755195i	$0.272458\pi$
$420$	−1.06818	+	3.13212i	−0.0521219	+	0.152832i
$421$	8.39894	+	11.5601i	0.409339	+	0.563407i	0.963057	−	0.269297i	$-0.0867914\pi$
$421$	8.39894	+	11.5601i	0.409339	+	0.563407i	−0.553718	+	0.832704i	$0.686791\pi$
$422$	12.7800	−	11.1655i	0.622119	−	0.543529i
$423$	−14.5579	−	16.1392i	−0.707831	−	0.784713i
$424$	8.46821	+	22.5635i	0.411253	+	1.09578i
$425$	6.45609			0.313166
$426$	4.00769	+	23.4733i	0.194173	+	1.13728i
$427$	24.6882			1.19474
$428$	2.34587	+	6.25054i	0.113392	+	0.302131i
$429$	−13.7291	−	11.2784i	−0.662846	−	0.544525i
$430$	−8.09595	+	7.07322i	−0.390422	+	0.341101i
$431$	8.07727	+	11.1174i	0.389068	+	0.535507i	0.957959	−	0.286907i	$-0.0926270\pi$
$431$	8.07727	+	11.1174i	0.389068	+	0.535507i	−0.568890	+	0.822414i	$0.692627\pi$
$432$	−14.8951	+	20.5593i	−0.716640	+	0.989160i
$433$	4.38550	−	2.89484i	0.210754	−	0.139117i	−0.441111	−	0.897453i	$-0.645416\pi$
$433$	4.38550	−	2.89484i	0.210754	−	0.139117i	0.651865	+	0.758335i	$0.273987\pi$
$434$	−10.2829	−	5.53347i	−0.493596	−	0.265615i
$435$	−0.327463	+	0.117506i	−0.0157006	+	0.00563398i
$436$	2.84081	−	4.30365i	0.136050	−	0.206107i
$437$	−3.65218	+	3.81988i	−0.174707	+	0.182729i
$438$	24.8697	−	0.755457i	1.18832	−	0.0360972i
$439$	23.7376	−	22.6955i	1.13293	−	1.08320i	0.137236	−	0.990538i	$-0.456178\pi$
$439$	23.7376	−	22.6955i	1.13293	−	1.08320i	0.995698	−	0.0926580i	$-0.0295363\pi$
$440$	−3.49959	−	2.54260i	−0.166836	−	0.121214i
$441$	−33.2666	−	7.03994i	−1.58413	−	0.335235i
$442$	−1.08482	+	8.00847i	−0.0515997	+	0.380924i
$443$	−5.66081	−	17.4222i	−0.268953	−	0.827753i	−0.990756	−	0.135654i	$-0.956686\pi$
$443$	−5.66081	−	17.4222i	−0.268953	−	0.827753i	0.721803	−	0.692098i	$-0.243314\pi$
$444$	6.10455	−	5.17911i	0.289709	−	0.245790i
$445$	3.00589	+	0.270535i	0.142493	+	0.0128246i
$446$	−23.7291	−	5.41600i	−1.12360	−	0.256455i
$447$	16.9187	+	1.77057i	0.800227	+	0.0837453i
$448$	−15.3053	−	6.54181i	−0.723108	−	0.309071i
$449$	22.6525	−	28.4053i	1.06904	−	1.34053i	0.132019	−	0.991247i	$-0.457854\pi$
$449$	22.6525	−	28.4053i	1.06904	−	1.34053i	0.937017	−	0.349283i	$-0.113575\pi$
$450$	−5.29492	−	21.6132i	−0.249605	−	1.01885i
$451$	3.77604	−	11.6215i	0.177807	−	0.547233i
$452$	−10.4458	−	5.03042i	−0.491327	−	0.236611i
$453$	−34.8143	−	6.84116i	−1.63572	−	0.321426i
$454$	−0.810589	+	2.93710i	−0.0380428	+	0.137845i
$455$	−9.25246	+	3.95469i	−0.433762	+	0.185399i
$456$	−12.3629	+	3.81951i	−0.578946	+	0.178865i
$457$	−23.7163	+	3.21260i	−1.10940	+	0.150279i	−0.665934	−	0.746011i	$-0.731967\pi$
$457$	−23.7163	+	3.21260i	−1.10940	+	0.150279i	−0.443469	+	0.896290i	$0.646252\pi$
$458$	44.5906	−	10.1775i	2.08358	−	0.475564i
$459$	−1.30790	+	7.26257i	−0.0610474	+	0.338988i
$460$	0.538679	−	0.429582i	0.0251160	−	0.0200294i
$461$	28.7453	+	10.7883i	1.33880	+	0.502461i	0.915058	−	0.403322i	$-0.132144\pi$
$461$	28.7453	+	10.7883i	1.33880	+	0.502461i	0.423743	+	0.905782i	$0.360716\pi$
$462$	−17.3190	+	31.0940i	−0.805751	+	1.44663i
$463$	19.1217	+	23.9778i	0.888659	+	1.11434i	0.992800	+	0.119781i	$0.0382192\pi$
$463$	19.1217	+	23.9778i	0.888659	+	1.11434i	−0.104141	+	0.994563i	$0.533209\pi$
$464$	0.387497	+	1.40406i	0.0179891	+	0.0651819i
$465$	−1.94507	+	0.146638i	−0.0902005	+	0.00680017i
$466$	0.377300	+	2.78534i	0.0174781	+	0.129028i
$467$	−37.1305	+	17.8811i	−1.71820	+	0.827439i	−0.728365	+	0.685189i	$0.759719\pi$
$467$	−37.1305	+	17.8811i	−1.71820	+	0.827439i	−0.989831	+	0.142250i	$0.954566\pi$
$468$	6.89038	−	0.730442i	0.318508	−	0.0337647i
$469$	33.7673	+	9.31917i	1.55923	+	0.430319i
$470$	−0.357346	+	7.95692i	−0.0164831	+	0.367025i
$471$	−4.88533	+	7.17236i	−0.225104	+	0.330485i
$472$	−22.5863	−	7.33874i	−1.03962	−	0.337793i
$473$	−24.6907	+	14.7520i	−1.13528	+	0.678299i
$474$	−18.7737	+	17.4351i	−0.862304	+	0.800819i
$475$	6.11510	−	14.3070i	0.280580	−	0.656450i
$476$	4.02298	−	0.180672i	0.184393	−	0.00828110i
$477$	16.5362	−	28.7008i	0.757141	−	1.31412i
$478$	3.14331	−	34.9250i	0.143771	−	1.59743i
$479$	−14.2779	−	12.4742i	−0.652373	−	0.569961i	0.266831	−	0.963743i	$-0.414023\pi$
$479$	−14.2779	−	12.4742i	−0.652373	−	0.569961i	−0.919204	+	0.393782i	$0.871166\pi$
$480$	4.15179	−	0.691361i	0.189503	−	0.0315562i
$481$	24.1215	+	3.26748i	1.09985	+	0.148984i
$482$	−13.1833	+	1.18652i	−0.600482	+	0.0540443i
$483$	8.16163	+	8.03324i	0.371367	+	0.365525i
$484$	−1.07500	−	1.12436i	−0.0488637	−	0.0511074i
$485$	10.7230	−	1.94595i	0.486908	−	0.0883608i
$486$	25.3857	−	1.57789i	1.15152	−	0.0715744i
$487$	−21.1378	−	13.9529i	−0.957845	−	0.632268i	−0.0277606	−	0.999615i	$-0.508838\pi$
$487$	−21.1378	−	13.9529i	−0.957845	−	0.632268i	−0.930084	+	0.367347i	$0.880266\pi$
$488$	−5.96370	−	11.0824i	−0.269964	−	0.501677i
$489$	6.98288	−	9.32351i	0.315777	−	0.421624i
$490$	6.86463	+	10.3995i	0.310112	+	0.469800i
$491$	−4.31476	−	0.783013i	−0.194722	−	0.0353369i	0.0803195	−	0.996769i	$-0.474406\pi$
$491$	−4.31476	−	0.783013i	−0.194722	−	0.0353369i	−0.275042	+	0.961432i	$0.588692\pi$
$492$	2.19701	+	4.22867i	0.0990489	+	0.190643i
$493$	0.278551	+	0.318827i	0.0125453	+	0.0143592i
$494$	16.7196	+	9.98951i	0.752251	+	0.449449i
$495$	0.360866	+	5.93439i	0.0162197	+	0.266731i
$496$			8.16636i			0.366680i
$497$	31.8414	+	16.9668i	1.42828	+	0.761063i
$498$	−6.76241	+	45.0022i	−0.303031	+	2.01660i
$499$	3.32199	−	1.24676i	0.148713	−	0.0558128i	−0.275909	−	0.961184i	$-0.588979\pi$
$499$	3.32199	−	1.24676i	0.148713	−	0.0558128i	0.424621	+	0.905371i	$0.360407\pi$
$500$	−2.18469	+	3.65655i	−0.0977022	+	0.163526i
$501$	21.9529	−	14.0379i	0.980785	−	0.627167i
$502$	8.82388	−	6.41093i	0.393829	−	0.286134i
$503$	−2.10741	+	11.6128i	−0.0939646	+	0.517787i	0.902276	+	0.431159i	$0.141895\pi$
$503$	−2.10741	+	11.6128i	−0.0939646	+	0.517787i	−0.996241	+	0.0866288i	$0.972391\pi$
$504$	7.88690	+	26.9066i	0.351310	+	1.19852i
$505$	5.15806	−	9.58528i	0.229531	−	0.426540i
$506$	6.52552	−	3.51153i	0.290095	−	0.156107i
$507$	−1.07668	−	0.968573i	−0.0478169	−	0.0430159i
$508$	−8.89724	−	8.50663i	−0.394751	−	0.377421i
$509$	−2.95380	−	16.2768i	−0.130925	−	0.721456i	−0.980882	−	0.194604i	$-0.937658\pi$
$509$	−2.95380	−	16.2768i	−0.130925	−	0.721456i	0.849957	−	0.526852i	$-0.176628\pi$
$510$	2.21061	−	1.55760i	0.0978876	−	0.0689715i
$511$	22.1585	−	30.4985i	0.980233	−	1.34917i
$512$	0.332393	+	3.69319i	0.0146898	+	0.163217i
$513$	14.8554	+	9.77734i	0.655881	+	0.431680i
$514$	−2.90230	+	0.943016i	−0.128015	+	0.0415946i
$515$	0.601898	−	0.688927i	0.0265228	−	0.0303578i
$516$	2.65435	−	10.8980i	0.116851	−	0.479756i
$517$	−4.74178	+	20.7751i	−0.208543	+	0.913687i
$518$	−2.18767	−	48.7122i	−0.0961205	−	2.14029i
$519$	−21.3864	−	13.2027i	−0.938758	−	0.579532i
$520$	4.01028	+	3.19809i	0.175862	+	0.140245i
$521$	15.1120	+	25.2932i	0.662068	+	1.10812i	0.986743	+	0.162290i	$0.0518879\pi$
$521$	15.1120	+	25.2932i	0.662068	+	1.10812i	−0.324675	+	0.945826i	$0.605255\pi$
$522$	0.838891	−	1.19399i	0.0367173	−	0.0522597i
$523$	7.32923	−	15.2193i	0.320485	−	0.665494i	−0.677029	−	0.735956i	$-0.736733\pi$
$523$	7.32923	−	15.2193i	0.320485	−	0.665494i	0.997514	+	0.0704619i	$0.0224473\pi$
$524$	1.56910	+	0.0704683i	0.0685464	+	0.00307842i
$525$	−30.8065	−	13.6994i	−1.34450	−	0.597891i
$526$	16.4572	+	38.5036i	0.717570	+	1.67884i
$527$	1.02990	+	2.13861i	0.0448631	+	0.0931592i
$528$	24.8883	+	0.361219i	1.08312	+	0.0157200i
$529$	4.58742	+	20.0988i	0.199453	+	0.873861i
$530$	−11.7010	+	3.22928i	−0.508261	+	0.140271i
$531$	11.9521	+	30.3736i	0.518678	+	1.31810i
$532$	3.41013	−	9.08625i	0.147848	−	0.393939i
$533$	−5.09128	+	13.5657i	−0.220528	+	0.587594i
$534$	−10.9598	+	6.33420i	−0.474278	+	0.274108i
$535$	6.54791	−	1.80711i	0.283091	−	0.0781281i
$536$	−3.97352	−	17.4091i	−0.171630	−	0.751959i
$537$	0.139817	−	9.63352i	0.00603356	−	0.415717i
$538$	7.11622	+	14.7770i	0.306802	+	0.637081i
$539$	13.1025	+	30.6549i	0.564366	+	1.32040i
$540$	−1.74808	−	1.52312i	−0.0752255	−	0.0655448i
$541$	−28.1244	−	1.26307i	−1.20916	−	0.0543035i	−0.568864	−	0.822431i	$-0.692617\pi$
$541$	−28.1244	−	1.26307i	−1.20916	−	0.0543035i	−0.640297	+	0.768128i	$0.721189\pi$
$542$	−6.84975	+	14.2236i	−0.294222	+	0.610958i
$543$	−19.1414	+	38.3150i	−0.821436	+	1.64425i
$544$	−2.62702	−	4.39688i	−0.112632	−	0.188515i
$545$	−4.10199	−	3.27123i	−0.175710	−	0.140124i
$546$	22.1699	−	35.9120i	0.948784	−	1.53689i
$547$	0.252222	+	5.61615i	0.0107842	+	0.240129i	0.997144	+	0.0755251i	$0.0240633\pi$
$547$	0.252222	+	5.61615i	0.0107842	+	0.240129i	−0.986360	+	0.164604i	$0.947365\pi$
$548$	1.07493	−	4.70956i	0.0459186	−	0.201183i
$549$	−6.54522	+	16.0111i	−0.279343	+	0.683335i
$550$	−14.3540	+	16.4295i	−0.612057	+	0.700555i
$551$	0.970374	−	0.315294i	0.0413393	−	0.0134320i
$552$	1.63456	−	5.60423i	0.0695713	−	0.238532i
$553$	3.47972	+	38.6628i	0.147973	+	1.64411i
$554$	7.52421	−	10.3562i	0.319673	−	0.439992i
$555$	−4.69148	−	6.65838i	−0.199142	−	0.282632i
$556$	0.339190	+	1.86909i	0.0143849	+	0.0792672i
$557$	14.3717	+	13.7408i	0.608950	+	0.582216i	0.931232	−	0.364428i	$-0.118736\pi$
$557$	14.3717	+	13.7408i	0.608950	+	0.582216i	−0.322282	+	0.946644i	$0.604450\pi$
$558$	6.31479	−	5.20178i	0.267327	−	0.220209i
$559$	30.0330	−	16.1614i	1.27026	−	0.683555i
$560$	6.67976	−	12.4131i	0.282271	−	0.524548i
$561$	6.56330	−	3.04418i	0.277103	−	0.128526i
$562$	−1.41204	+	7.78100i	−0.0595634	+	0.328222i
$563$	−25.9697	+	18.8681i	−1.09449	+	0.795196i	−0.980152	−	0.198246i	$-0.936476\pi$
$563$	−25.9697	+	18.8681i	−1.09449	+	0.795196i	−0.114341	+	0.993442i	$0.536476\pi$
$564$	−4.47692	−	7.00115i	−0.188512	−	0.294802i
$565$	−6.05024	+	10.1264i	−0.254535	+	0.426020i
$566$	−32.9066	+	12.3501i	−1.38317	+	0.519111i
$567$	21.6516	−	31.8795i	0.909281	−	1.33881i
$568$	−0.0753422	−	18.3920i	−0.00316129	−	0.771710i
$569$			13.6554i			0.572462i	0.958161	+	0.286231i	$0.0924025\pi$
$569$			13.6554i			0.572462i	−0.958161	+	0.286231i	$0.907598\pi$
$570$	−1.35785	−	6.37415i	−0.0568740	−	0.266984i
$571$	−38.1297	−	22.7814i	−1.59568	−	0.953374i	−0.987142	−	0.159849i	$-0.948899\pi$
$571$	−38.1297	−	22.7814i	−1.59568	−	0.953374i	−0.608537	−	0.793525i	$-0.708243\pi$
$572$	−4.46959	−	5.11586i	−0.186883	−	0.213905i
$573$	−38.2175	+	19.8560i	−1.59656	+	0.829494i
$574$	28.5589	+	5.18268i	1.19203	+	0.216321i
$575$	3.86707	+	5.85836i	0.161268	+	0.244311i
$576$	8.30024	−	8.19164i	0.345843	−	0.341318i
$577$	15.4818	+	28.7701i	0.644517	+	1.19771i	0.967874	+	0.251436i	$0.0809028\pi$
$577$	15.4818	+	28.7701i	0.644517	+	1.19771i	−0.323357	+	0.946277i	$0.604811\pi$
$578$	20.4028	+	13.4678i	0.848646	+	0.560186i
$579$	1.08343	−	0.838580i	0.0450260	−	0.0348502i
$580$	−0.130882	+	0.0237516i	−0.00543457	+	0.000986230i
$581$	47.6486	+	49.8366i	1.97680	+	2.06757i
$582$	−32.0649	+	32.5774i	−1.32913	+	1.35037i
$583$	−32.3445	+	2.91106i	−1.33957	+	0.120564i
$584$	−19.0433	−	2.57958i	−0.788016	−	0.106744i
$585$	−0.111768	−	7.04896i	−0.00462105	−	0.291439i
$586$	−22.7261	−	19.8552i	−0.938809	−	0.820212i
$587$	3.60081	−	40.0082i	0.148621	−	1.65132i	−0.482694	−	0.875789i	$-0.660342\pi$
$587$	3.60081	−	40.0082i	0.148621	−	1.65132i	0.631315	−	0.775527i	$-0.282516\pi$
$588$	−12.1043	−	4.74436i	−0.499175	−	0.195654i
$589$	5.71476	−	0.256650i	0.235473	−	0.0105751i
$590$	4.70113	−	10.9988i	0.193543	−	0.452815i
$591$	13.9380	+	15.0081i	0.573332	+	0.617351i
$592$	−29.2737	+	17.4902i	−1.20314	+	0.718844i
$593$	−10.2417	−	3.32774i	−0.420578	−	0.136654i	0.0910794	−	0.995844i	$-0.470968\pi$
$593$	−10.2417	−	3.32774i	−0.420578	−	0.136654i	−0.511657	+	0.859190i	$0.670968\pi$
$594$	−15.5739	−	19.4754i	−0.639006	−	0.799086i
$595$	0.183824	−	4.09315i	0.00753604	−	0.167803i
$596$	6.26967	+	1.73032i	0.256816	+	0.0708766i
$597$	28.3273	−	7.37716i	1.15936	−	0.301927i
$598$	−7.91681	+	3.81253i	−0.323742	+	0.155906i
$599$	−5.07784	−	37.4861i	−0.207475	−	1.53164i	−0.732625	−	0.680633i	$-0.761705\pi$
$599$	−5.07784	−	37.4861i	−0.207475	−	1.53164i	0.525150	−	0.851010i	$-0.324009\pi$
$600$	1.29203	+	17.1381i	0.0527471	+	0.699661i
$601$	−0.708635	−	2.56768i	−0.0289058	−	0.104738i	0.948086	−	0.318013i	$-0.103016\pi$
$601$	−0.708635	−	2.56768i	−0.0289058	−	0.104738i	−0.976992	+	0.213275i	$0.931587\pi$
$602$	−42.5964	−	53.4142i	−1.73610	−	2.17700i
$603$	−14.9960	+	19.4285i	−0.610684	+	0.791188i
$604$	−12.7005	−	4.76658i	−0.516777	−	0.193950i
$605$	−1.23741	+	0.986804i	−0.0503080	+	0.0401193i
$606$	5.47124	+	45.3261i	0.222254	+	1.84125i
$607$	−19.6170	+	4.47744i	−0.796228	+	0.181734i	−0.601237	−	0.799071i	$-0.705325\pi$
$607$	−19.6170	+	4.47744i	−0.796228	+	0.181734i	−0.194991	+	0.980805i	$0.562468\pi$
$608$	−12.2320	+	1.65693i	−0.496072	+	0.0671975i
$609$	−0.652628	−	2.11241i	−0.0264458	−	0.0855992i
$610$	5.82862	−	2.49127i	0.235994	−	0.100869i
$611$	6.72224	−	24.3575i	0.271953	−	0.985399i
$612$	−0.949384	+	2.65693i	−0.0383766	+	0.107400i
$613$	−11.0925	−	5.34185i	−0.448020	−	0.215755i	0.196249	−	0.980554i	$-0.437124\pi$
$613$	−11.0925	−	5.34185i	−0.448020	−	0.215755i	−0.644269	+	0.764799i	$0.722838\pi$
$614$	3.35520	−	10.3262i	0.135405	−	0.416733i
$615$	4.48548	−	1.84067i	0.180872	−	0.0742228i
$616$	17.1396	−	21.4923i	0.690573	−	0.865951i
$617$	−9.66404	−	4.13061i	−0.389060	−	0.166292i	0.189600	−	0.981862i	$-0.439281\pi$
$617$	−9.66404	−	4.13061i	−0.389060	−	0.166292i	−0.578659	+	0.815569i	$0.696424\pi$
$618$	−0.399375	+	3.81622i	−0.0160652	+	0.153511i
$619$	−31.8910	−	7.27892i	−1.28181	−	0.292564i	−0.473223	−	0.880943i	$-0.656909\pi$
$619$	−31.8910	−	7.27892i	−1.28181	−	0.292564i	−0.808586	+	0.588378i	$0.799767\pi$
$620$	−0.742790	−	0.0668523i	−0.0298312	−	0.00268485i
$621$	−7.37358	+	3.16333i	−0.295892	+	0.126940i
$622$	7.68760	+	23.6600i	0.308245	+	0.948680i
$623$	−2.57452	+	19.0059i	−0.103146	+	0.761453i
$624$	−29.4629	−	1.75194i	−1.17946	−	0.0701336i
$625$	−14.8829	−	10.8131i	−0.595316	−	0.432522i
$626$	16.6769	−	15.9448i	0.666543	−	0.637281i
$627$	−0.529403	−	17.4280i	−0.0211423	−	0.696006i
$628$	−2.29295	+	2.39823i	−0.0914985	+	0.0956999i
$629$	−5.46043	+	8.27219i	−0.217722	+	0.329834i
$630$	−13.8535	+	2.74159i	−0.551936	+	0.109227i
$631$	1.82071	+	0.979765i	0.0724813	+	0.0390038i	0.509708	−	0.860348i	$-0.329753\pi$
$631$	1.82071	+	0.979765i	0.0724813	+	0.0390038i	−0.437227	+	0.899351i	$0.644039\pi$
$632$	16.5150	−	10.9015i	0.656931	−	0.433637i
$633$	17.0506	+	5.81495i	0.677699	+	0.231124i
$634$	−6.82589	−	9.39503i	−0.271091	−	0.373124i
$635$	−9.43162	+	8.24016i	−0.374282	+	0.327001i
$636$	8.03912	−	9.78596i	0.318772	−	0.388038i
$637$	−13.8902	−	37.0102i	−0.550348	−	1.46640i
$638$	−1.43066			−0.0566405
$639$	−19.4451	+	16.1520i	−0.769237	+	0.638963i
$640$	−9.13365			−0.361039
$641$	−13.1949	−	35.1578i	−0.521169	−	1.38865i	−0.888636	−	0.458613i	$-0.848346\pi$
$641$	−13.1949	−	35.1578i	−0.521169	−	1.38865i	0.367467	−	0.930037i	$-0.380225\pi$
$642$	−18.0851	+	22.0148i	−0.713761	+	0.868856i
$643$	12.8277	−	11.2072i	0.505874	−	0.441969i	−0.366780	−	0.930308i	$-0.619540\pi$
$643$	12.8277	−	11.2072i	0.505874	−	0.441969i	0.872654	+	0.488339i	$0.162397\pi$
$644$	2.57364	+	3.54230i	0.101415	+	0.139586i
$645$	−10.8013	−	3.68370i	−0.425302	−	0.145046i
$646$	−6.61880	+	4.36903i	−0.260413	+	0.171897i
$647$	4.74009	+	2.55075i	0.186352	+	0.100280i	0.564385	−	0.825512i	$-0.309114\pi$
$647$	4.74009	+	2.55075i	0.186352	+	0.100280i	−0.378032	+	0.925792i	$0.623399\pi$
$648$	−19.5407	−	2.01847i	−0.767632	−	0.0792929i
$649$	17.6295	−	26.7076i	0.692019	−	1.04836i
$650$	17.8775	−	18.6984i	0.701214	−	0.733412i
$651$	−0.376371	−	12.3902i	−0.0147512	−	0.485609i
$652$	3.21913	−	3.07780i	0.126071	−	0.120536i
$653$	19.1284	+	13.8976i	0.748553	+	0.543856i	0.895378	−	0.445307i	$-0.146905\pi$
$653$	19.1284	+	13.8976i	0.748553	+	0.543856i	−0.146825	+	0.989162i	$0.546905\pi$
$654$	21.9673	+	1.30623i	0.858989	+	0.0510776i
$655$	0.214515	−	1.58361i	0.00838180	−	0.0618769i
$656$	−6.27262	−	19.3051i	−0.244905	−	0.753739i
$657$	13.9047	+	22.4561i	0.542473	+	0.876095i
$658$	−50.4129	−	4.53725i	−1.96530	−	0.176880i
$659$	1.90232	+	0.434193i	0.0741040	+	0.0169138i	0.259412	−	0.965767i	$-0.416471\pi$
$659$	1.90232	+	0.434193i	0.0741040	+	0.0169138i	−0.185308	+	0.982680i	$0.559328\pi$
$660$	−0.236598	+	2.26081i	−0.00920958	+	0.0880020i
$661$	15.6654	+	6.69572i	0.609314	+	0.260433i	0.675483	−	0.737375i	$-0.263935\pi$
$661$	15.6654	+	6.69572i	0.609314	+	0.260433i	−0.0661696	+	0.997808i	$0.521078\pi$
$662$	20.2534	−	25.3970i	0.787172	−	0.987082i
$663$	−7.93670	+	3.25692i	−0.308236	+	0.126488i
$664$	10.8614	−	33.4278i	0.421502	−	1.29725i
$665$	−8.89651	−	4.28433i	−0.344992	−	0.166139i
$666$	32.1713	+	11.4956i	1.24661	+	0.445445i
$667$	−0.122463	+	0.443733i	−0.00474177	+	0.0171814i
$668$	9.16115	−	3.91566i	0.354455	−	0.151502i
$669$	−7.62669	−	24.6859i	−0.294865	−	0.954413i
$670$	8.91249	−	1.20728i	0.344319	−	0.0466412i
$671$	16.5334	−	3.77363i	0.638263	−	0.145679i
$672$	3.20540	+	26.5549i	0.123651	+	1.02438i
$673$	−17.0897	+	13.6286i	−0.658761	+	0.525344i	−0.894838	−	0.446390i	$-0.852709\pi$
$673$	−17.0897	+	13.6286i	−0.658761	+	0.525344i	0.236078	+	0.971734i	$0.424138\pi$
$674$	−4.04532	−	1.51823i	−0.155820	−	0.0584801i
$675$	17.0518	−	16.3470i	0.656323	−	0.629197i
$676$	−0.345238	−	0.432915i	−0.0132784	−	0.0166506i
$677$	−7.37805	−	26.7338i	−0.283562	−	1.02746i	−0.957443	−	0.288623i	$-0.906803\pi$
$677$	−7.37805	−	26.7338i	−0.283562	−	1.02746i	0.673881	−	0.738840i	$-0.264626\pi$
$678$	−3.71948	−	49.3368i	−0.142846	−	1.89477i
$679$	9.29663	+	68.6305i	0.356772	+	2.63380i
$680$	−1.88180	+	0.906228i	−0.0721638	+	0.0347523i
$681$	−3.13002	+	0.815137i	−0.119943	+	0.0312361i
$682$	−7.73214	−	2.13394i	−0.296079	−	0.0817126i
$683$	1.43397	−	31.9299i	0.0548695	−	1.22176i	−0.763015	−	0.646381i	$-0.776282\pi$
$683$	1.43397	−	31.9299i	0.0548695	−	1.22176i	0.817884	−	0.575383i	$-0.195147\pi$
$684$	4.98864	+	4.62048i	0.190745	+	0.176668i
$685$	−4.67438	−	1.51880i	−0.178599	−	0.0580304i
$686$	−25.9960	+	15.5319i	−0.992533	+	0.593011i
$687$	33.0397	+	35.5764i	1.26054	+	1.35732i
$688$	−18.7781	+	43.9336i	−0.715909	+	1.67495i
$689$	38.4695	−	1.72767i	1.46557	−	0.0658189i
$690$	2.73751	+	1.07298i	0.104215	+	0.0408476i
$691$	−0.0346715	+	0.385232i	−0.00131896	+	0.0146549i	−0.996607	−	0.0823094i	$-0.973770\pi$
$691$	−0.0346715	+	0.385232i	−0.00131896	+	0.0146549i	0.995288	+	0.0969643i	$0.0309133\pi$
$692$	−7.23668	−	6.32250i	−0.275097	−	0.240345i
$693$	−37.7776	+	0.599002i	−1.43505	+	0.0227542i
$694$	−1.32427	−	0.179384i	−0.0502685	−	0.00680934i
$695$	1.92497	−	0.173251i	0.0730184	−	0.00657177i
$696$	−0.790603	+	0.803238i	−0.0299677	+	0.0304466i
$697$	−4.07734	−	4.26456i	−0.154440	−	0.161532i
$698$	−10.7161	+	1.94468i	−0.405609	+	0.0736073i
$699$	−2.35955	+	1.82629i	−0.0892463	+	0.0690768i
$700$	−10.7583	−	7.10146i	−0.406624	−	0.268410i
$701$	0.941871	+	1.75029i	0.0355740	+	0.0661075i	0.897762	−	0.440481i	$-0.145192\pi$
$701$	0.941871	+	1.75029i	0.0355740	+	0.0661075i	−0.862188	+	0.506588i	$0.830906\pi$
$702$	17.4125	+	23.8987i	0.657192	+	0.901999i
$703$	13.1595	+	19.9359i	0.496322	+	0.751895i
$704$	−11.2497	−	2.04152i	−0.423989	−	0.0769427i
$705$	−7.50290	+	3.89815i	−0.282576	+	0.146813i
$706$	−28.1720	−	32.2454i	−1.06027	−	1.21357i
$707$	59.3819	+	35.4790i	2.23329	+	1.33433i
$708$	2.60017	+	12.2060i	0.0977204	+	0.458729i
$709$		−	15.1472i		−	0.568866i	−0.958696	−	0.284433i	$-0.908195\pi$
$709$		−	15.1472i		−	0.568866i	0.958696	−	0.284433i	$-0.0918053\pi$
$710$	9.22953	+	0.792572i	0.346378	+	0.0297447i
$711$	−25.9966	−	7.99341i	−0.974948	−	0.299776i
$712$	9.15354	−	3.43538i	0.343044	−	0.128746i
$713$	−1.32372	+	2.21553i	−0.0495737	+	0.0829724i
$714$	9.25819	+	14.4783i	0.346479	+	0.541835i
$715$	−5.59178	+	4.06266i	−0.209121	+	0.151935i
$716$	0.657748	−	3.62449i	0.0245812	−	0.135454i
$717$	33.7687	−	15.6626i	1.26112	−	0.584930i
$718$	−11.0223	+	20.4829i	−0.411348	+	0.764413i
$719$	−9.63483	+	5.18472i	−0.359318	+	0.193358i	−0.643561	−	0.765395i	$-0.722544\pi$
$719$	−9.63483	+	5.18472i	−0.359318	+	0.193358i	0.284242	+	0.958752i	$0.408258\pi$
$720$	6.27935	+	7.62293i	0.234018	+	0.284090i
$721$	4.20207	+	4.01759i	0.156493	+	0.149623i
$722$	−2.12270	−	11.6970i	−0.0789986	−	0.435318i
$723$	−8.09324	−	11.4863i	−0.300991	−	0.427180i
$724$	−9.62546	+	13.2483i	−0.357727	+	0.492369i
$725$	−0.121481	−	1.34977i	−0.00451170	−	0.0501291i
$726$	1.85874	−	6.37286i	0.0689842	−	0.236519i
$727$	10.0989	−	3.28133i	0.374548	−	0.121698i	−0.115693	−	0.993285i	$-0.536909\pi$
$727$	10.0989	−	3.28133i	0.374548	−	0.121698i	0.490241	+	0.871587i	$0.336909\pi$
$728$	−21.4466	+	24.5476i	−0.794863	+	0.909794i
$729$	14.9346	+	22.4935i	0.553135	+	0.833092i
$730$	2.15379	−	9.43638i	0.0797154	−	0.349256i
$731$	0.623061	+	13.8735i	0.0230447	+	0.513131i
$732$	−3.47407	+	5.62749i	−0.128405	+	0.207998i
$733$	5.97771	+	4.76707i	0.220792	+	0.176076i	0.727639	−	0.685960i	$-0.240618\pi$
$733$	5.97771	+	4.76707i	0.220792	+	0.176076i	−0.506847	+	0.862036i	$0.669189\pi$
$734$	11.6142	+	19.4388i	0.428686	+	0.717500i
$735$	−5.91163	+	11.8332i	−0.218054	+	0.436474i
$736$	2.41628	−	5.01745i	0.0890651	−	0.184946i
$737$	24.0380	+	1.07955i	0.885449	+	0.0397656i
$738$	−10.9326	+	17.1473i	−0.402433	+	0.631203i
$739$	−10.2363	−	23.9491i	−0.376550	−	0.880983i	−0.995430	−	0.0954970i	$-0.969556\pi$
$739$	−10.2363	−	23.9491i	−0.376550	−	0.880983i	0.618880	−	0.785486i	$-0.287587\pi$
$740$	−1.35122	−	2.80584i	−0.0496719	−	0.103145i
$741$	−0.300040	+	20.6730i	−0.0110223	+	0.759442i
$742$	−17.1651	−	75.2053i	−0.630151	−	2.76087i
$743$	−12.6907	+	3.50240i	−0.465576	+	0.128491i	−0.490951	−	0.871187i	$-0.663351\pi$
$743$	−12.6907	+	3.50240i	−0.465576	+	0.128491i	0.0253751	+	0.999678i	$0.491922\pi$
$744$	−5.47097	+	3.16193i	−0.200576	+	0.115922i
$745$	2.32522	−	6.19554i	0.0851896	−	0.226987i
$746$	−3.60824	+	9.61411i	−0.132107	+	0.351998i
$747$	−44.9530	+	17.6892i	−1.64474	+	0.647213i
$748$	2.66652	−	0.735914i	0.0974978	−	0.0269077i
$749$	9.60561	+	42.0849i	0.350981	+	1.53775i
$750$	−18.1753	−	0.263790i	−0.663670	−	0.00963226i
$751$	14.3869	+	29.8746i	0.524984	+	1.09014i	0.979878	+	0.199596i	$0.0639629\pi$
$751$	14.3869	+	29.8746i	0.524984	+	1.09014i	−0.454894	+	0.890546i	$0.650323\pi$
$752$	13.9124	+	32.5497i	0.507334	+	1.18697i
$753$	10.5793	+	4.70453i	0.385530	+	0.171443i
$754$	1.69473	+	0.0761106i	0.0617186	+	0.00277178i
$755$	−5.98853	+	12.4353i	−0.217945	+	0.452567i
$756$	10.1680	−	10.6635i	0.369807	−	0.387828i
$757$	6.31639	+	10.5719i	0.229573	+	0.384241i	0.951461	−	0.307769i	$-0.0995825\pi$
$757$	6.31639	+	10.5719i	0.229573	+	0.384241i	−0.721888	+	0.692010i	$0.756725\pi$
$758$	−20.9248	−	16.6870i	−0.760022	−	0.606097i
$759$	6.69363	+	4.13224i	0.242964	+	0.149991i
$760$	0.225831	+	5.02853i	0.00819177	+	0.182404i
$761$	−6.73308	+	29.4996i	−0.244074	+	1.06936i	0.693195	+	0.720750i	$0.256203\pi$
$761$	−6.73308	+	29.4996i	−0.244074	+	1.06936i	−0.937269	+	0.348608i	$0.886655\pi$
$762$	12.4311	−	51.0384i	0.450332	−	1.84893i
$763$	21.9371	−	25.1090i	0.794176	−	0.909007i
$764$	−15.6607	+	5.08847i	−0.566584	+	0.184094i
$765$	2.60580	+	1.20437i	0.0942130	+	0.0435443i
$766$	−1.31371	−	14.5965i	−0.0474662	−	0.527392i
$767$	−22.3044	+	30.6994i	−0.805366	+	1.10849i
$768$	20.3087	−	14.3095i	0.732825	−	0.516348i
$769$	−2.37253	−	13.0737i	−0.0855555	−	0.471450i	−0.998053	−	0.0623679i	$-0.980135\pi$
$769$	−2.37253	−	13.0737i	−0.0855555	−	0.471450i	0.912498	−	0.409082i	$-0.134151\pi$
$770$	10.0076	+	9.56822i	0.360648	+	0.344815i
$771$	−2.40836	−	2.16655i	−0.0867351	−	0.0780264i
$772$	0.461282	−	0.248226i	0.0166019	−	0.00893386i
$773$	16.5576	−	30.7692i	0.595537	−	1.10669i	−0.387254	−	0.921973i	$-0.626577\pi$
$773$	16.5576	−	30.7692i	0.595537	−	1.10669i	0.982791	−	0.184720i	$-0.0591378\pi$
$774$	45.9337	−	13.4641i	1.65105	−	0.483958i
$775$	1.35672	−	7.47613i	0.0487348	−	0.268551i
$776$	28.5622	−	20.7517i	1.02532	−	0.744941i
$777$	43.6086	−	27.8857i	1.56445	−	1.00039i
$778$	1.82431	−	3.05338i	0.0654046	−	0.109469i
$779$	−13.3125	+	4.99625i	−0.476968	+	0.179009i
$780$	0.400544	−	2.66553i	0.0143418	−	0.0954412i
$781$	23.9172	+	6.49541i	0.855825	+	0.232424i
$782$		−	3.57803i		−	0.127950i
$783$	1.54299	+	0.136784i	0.0551418	+	0.00488826i
$784$	47.5402	+	28.4040i	1.69787	+	1.01443i
$785$	2.22112	+	2.54227i	0.0792751	+	0.0907376i
$786$	3.09027	+	5.94796i	0.110226	+	0.212157i
$787$	−27.1453	−	4.92615i	−0.967627	−	0.175598i	−0.328334	−	0.944562i	$-0.606487\pi$
$787$	−27.1453	−	4.92615i	−0.967627	−	0.175598i	−0.639293	+	0.768963i	$0.720773\pi$
$788$	4.31414	+	6.53564i	0.153685	+	0.232822i
$789$	−26.6463	+	35.5781i	−0.948634	+	1.26661i
$790$	4.72297	+	8.77675i	0.168036	+	0.312263i
$791$	−62.5628	−	41.2973i	−2.22448	−	1.46836i
$792$	9.39448	+	16.8135i	0.333818	+	0.597442i
$793$	−19.7859	+	3.59060i	−0.702616	+	0.127506i
$794$	9.60466	+	10.0457i	0.340857	+	0.356508i
$795$	−9.18338	−	9.03892i	−0.325701	−	0.320577i
$796$	11.1469	−	1.00324i	0.395092	−	0.0355589i
$797$	−7.18149	−	0.972798i	−0.254381	−	0.0344583i	0.00593233	−	0.999982i	$-0.498112\pi$
$797$	−7.18149	−	0.972798i	−0.254381	−	0.0344583i	−0.260314	+	0.965524i	$0.583826\pi$
$798$	40.8537	−	6.80300i	1.44621	−	0.240824i
$799$	7.74839	+	6.76957i	0.274118	+	0.239490i
$800$	−1.46967	+	16.3294i	−0.0519608	+	0.577332i
$801$	−11.6433	−	6.70840i	−0.411397	−	0.237030i
$802$	40.4516	−	1.81668i	1.42840	−	0.0641494i
$803$	10.1775	−	23.8114i	0.359156	−	0.840287i
$804$	−6.87589	+	6.38562i	−0.242494	+	0.225204i
$805$	3.82431	−	2.28492i	0.134789	−	0.0805327i
$806$	9.04582	+	2.93917i	0.318625	+	0.103528i
$807$	−9.80130	+	14.3897i	−0.345022	+	0.506541i
$808$	1.58203	−	35.2266i	0.0556556	−	1.23927i
$809$	−23.7093	−	6.54335i	−0.833574	−	0.230052i	−0.176902	−	0.984228i	$-0.556608\pi$
$809$	−23.7093	−	6.54335i	−0.833574	−	0.230052i	−0.656672	+	0.754177i	$0.728036\pi$
$810$	1.89477	−	9.71126i	0.0665755	−	0.341219i
$811$	1.70281	−	0.820028i	0.0597936	−	0.0287951i	−0.403748	−	0.914870i	$-0.632293\pi$
$811$	1.70281	−	0.820028i	0.0597936	−	0.0287951i	0.463542	+	0.886075i	$0.346578\pi$
$812$	−0.113472	−	0.837681i	−0.00398207	−	0.0293968i
$813$	−16.7112	+	1.25985i	−0.586088	+	0.0441849i
$814$	−8.91079	−	32.2875i	−0.312323	−	1.13168i
$815$	−2.82529	−	3.54280i	−0.0989655	−	0.124099i
$816$	5.84811	−	10.4996i	0.204725	−	0.367558i
$817$	31.3346	+	11.7601i	1.09626	+	0.411432i
$818$	−16.1447	+	12.8749i	−0.564484	+	0.450161i
$819$	44.7825	+	1.30019i	1.56483	+	0.0454322i
$820$	1.80729	−	0.412503i	0.0631134	−	0.0144052i
$821$	−6.63782	+	0.899154i	−0.231662	+	0.0313807i	−0.249144	−	0.968466i	$-0.580149\pi$
$821$	−6.63782	+	0.899154i	−0.231662	+	0.0313807i	0.0174823	+	0.999847i	$0.494435\pi$
$822$	19.6962	−	6.08513i	0.686985	−	0.212243i
$823$	2.24010	−	0.957463i	0.0780849	−	0.0333751i	−0.353628	−	0.935386i	$-0.615052\pi$
$823$	2.24010	−	0.957463i	0.0780849	−	0.0333751i	0.431713	+	0.902011i	$0.357909\pi$
$824$	0.788423	−	2.85679i	0.0274660	−	0.0995208i
$825$	−22.7247	−	4.46550i	−0.791172	−	0.155469i
$826$	68.4863	+	32.9813i	2.38294	+	1.14756i
$827$	11.2753	−	34.7019i	0.392082	−	1.20670i	−0.539130	−	0.842223i	$-0.681247\pi$
$827$	11.2753	−	34.7019i	0.392082	−	1.20670i	0.931211	−	0.364480i	$-0.118753\pi$
$828$	−2.97961	+	0.729962i	−0.103548	+	0.0253679i
$829$	−21.0473	+	26.3925i	−0.731004	+	0.916650i	−0.998904	−	0.0467968i	$-0.985099\pi$
$829$	−21.0473	+	26.3925i	−0.731004	+	0.916650i	0.267901	+	0.963447i	$0.413670\pi$
$830$	16.2783	+	6.95769i	0.565029	+	0.241505i
$831$	13.5150	+	1.41437i	0.468828	+	0.0490638i
$832$	13.2176	+	3.01682i	0.458237	+	0.104590i
$833$	16.0320	+	1.44291i	0.555476	+	0.0499938i
$834$	−6.18159	+	5.24448i	−0.214051	+	0.181601i
$835$	−3.13240	−	9.64054i	−0.108401	−	0.333625i
$836$	0.894869	−	6.60619i	0.0309497	−	0.228480i
$837$	8.13519	+	3.04074i	0.281193	+	0.105103i
$838$	7.08083	+	5.14452i	0.244603	+	0.177715i
$839$	−19.0009	+	18.1667i	−0.655983	+	0.627184i	−0.943806	−	0.330500i	$-0.892783\pi$
$839$	−19.0009	+	18.1667i	−0.655983	+	0.627184i	0.287823	+	0.957683i	$0.407068\pi$
$840$	10.9023	−	0.331176i	0.376167	−	0.0114267i
$841$	−19.9794	+	20.8968i	−0.688945	+	0.720580i
$842$	−12.8440	+	19.4578i	−0.442633	+	0.670560i
$843$	−7.90145	+	2.83534i	−0.272140	+	0.0976543i
$844$	6.06540	+	3.26393i	0.208780	+	0.112349i
$845$	−0.470180	+	0.310363i	−0.0161747	+	0.0106768i
$846$	16.3078	−	31.4915i	0.560674	−	1.08270i
$847$	−5.91196	−	8.13712i	−0.203137	−	0.279595i
$848$	−40.6257	+	35.4936i	−1.39509	+	1.21885i
$849$	−28.8302	−	23.6838i	−0.989448	−	0.812827i
$850$	3.70138	+	9.86228i	0.126956	+	0.338273i
$851$	−10.7770			−0.369432
$852$	−8.34811	+	4.87049i	−0.286001	+	0.166860i
$853$	27.4680			0.940487			0.470244	−	0.882537i	$-0.344166\pi$
$853$	27.4680			0.940487			0.470244	+	0.882537i	$0.344166\pi$
$854$	14.1541	+	37.7135i	0.484344	+	1.29053i
$855$	5.13712	−	4.63382i	0.175686	−	0.158473i
$856$	16.5714	−	14.4780i	0.566398	−	0.494847i
$857$	−32.8028	−	45.1492i	−1.12052	−	1.54227i	−0.804927	−	0.593374i	$-0.797795\pi$
$857$	−32.8028	−	45.1492i	−1.12052	−	1.54227i	−0.315596	−	0.948894i	$-0.602205\pi$
$858$	9.35769	−	27.4385i	0.319466	−	0.936737i
$859$	−12.6494	+	8.34979i	−0.431592	+	0.284891i	−0.747958	−	0.663746i	$-0.768966\pi$
$859$	−12.6494	+	8.34979i	−0.431592	+	0.284891i	0.316366	+	0.948637i	$0.397537\pi$
$860$	−3.84236	−	2.06766i	−0.131023	−	0.0705066i
$861$	10.4067	+	29.0010i	0.354659	+	0.988353i
$862$	−12.3521	+	18.7126i	−0.420713	+	0.637353i
$863$	16.2283	−	16.9734i	0.552416	−	0.577782i	−0.386343	−	0.922355i	$-0.626262\pi$
$863$	16.2283	−	16.9734i	0.552416	−	0.577782i	0.938760	+	0.344573i	$0.111976\pi$
$864$	−18.0715	−	4.96133i	−0.614805	−	0.168788i
$865$	−7.06689	+	6.75664i	−0.240281	+	0.229733i
$866$	6.93643	+	5.03961i	0.235709	+	0.171253i
$867$	−1.54042	+	25.9058i	−0.0523155	+	0.879807i
$868$	0.636194	−	4.69657i	0.0215938	−	0.159412i
$869$	8.24000	+	25.3601i	0.279523	+	0.860283i
$870$	−0.367241	−	0.432862i	−0.0124506	−	0.0146754i
$871$	−28.4175	−	2.55762i	−0.962889	−	0.0866616i
$872$	−16.5705	−	3.78210i	−0.561147	−	0.128078i
$873$	−46.9737	−	12.1659i	−1.58982	−	0.411752i
$874$	−7.92907	−	3.38905i	−0.268205	−	0.114636i
$875$	−17.1715	+	21.5324i	−0.580502	+	0.727927i
$876$	3.83382	+	9.34255i	0.129533	+	0.315655i
$877$	−11.3840	+	35.0363i	−0.384410	+	1.18309i	0.552497	+	0.833515i	$0.313675\pi$
$877$	−11.3840	+	35.0363i	−0.384410	+	1.18309i	−0.936907	+	0.349578i	$0.886325\pi$
$878$	48.2786	+	23.2498i	1.62933	+	0.784642i
$879$	6.17692	−	31.4340i	0.208342	−	1.06024i
$880$	2.57599	−	9.33389i	0.0868366	−	0.314645i
$881$	−38.4016	+	16.4136i	−1.29378	+	0.552989i	−0.926211	−	0.377006i	$-0.876954\pi$
$881$	−38.4016	+	16.4136i	−1.29378	+	0.552989i	−0.367572	+	0.929995i	$0.619811\pi$
$882$	−8.31812	−	54.8541i	−0.280086	−	1.84703i
$883$	−40.0427	+	5.42415i	−1.34754	+	0.182537i	−0.772202	−	0.635377i	$-0.780845\pi$
$883$	−40.0427	+	5.42415i	−1.34754	+	0.182537i	−0.575341	+	0.817914i	$0.695131\pi$
$884$	−3.19786	+	0.729891i	−0.107556	+	0.0245489i
$885$	12.6060	−	1.52165i	0.423747	−	0.0511498i
$886$	23.3686	−	18.6358i	0.785083	−	0.626083i
$887$	−5.28036	−	1.98175i	−0.177297	−	0.0665407i	0.261148	−	0.965299i	$-0.415899\pi$
$887$	−5.28036	−	1.98175i	−0.177297	−	0.0665407i	−0.438445	+	0.898758i	$0.644470\pi$
$888$	−23.0519	−	12.8396i	−0.773571	−	0.430869i
$889$	−49.6239	−	62.2264i	−1.66433	−	2.08701i
$890$	1.31005	+	4.74688i	0.0439131	+	0.159116i
$891$	9.62696	−	24.6588i	0.322515	−	0.826100i
$892$	−1.32604	−	9.78925i	−0.0443992	−	0.327768i
$893$	22.3408	−	10.7588i	0.747607	−	0.360029i
$894$	6.99503	+	26.8600i	0.233949	+	0.898333i
$895$	−3.61288	−	0.997091i	−0.120765	−	0.0333291i
$896$	2.60412	−	57.9853i	0.0869977	−	1.93715i
$897$	−7.70931	−	5.25107i	−0.257407	−	0.175328i
$898$	56.3788	+	18.3186i	1.88139	+	0.611299i
$899$	0.427737	−	0.255561i	0.0142658	−	0.00852344i
$900$	7.45770	−	5.09435i	0.248590	−	0.169812i
$901$	−6.16279	+	14.4186i	−0.205312	+	0.480352i
$902$	19.9177	−	0.894507i	0.663188	−	0.0297838i
$903$	26.4657	−	67.5223i	0.880724	−	2.24700i
$904$	−3.42546	+	38.0600i	−0.113929	+	1.26586i
$905$	12.5473	+	10.9622i	0.417085	+	0.364396i
$906$	−9.50906	−	57.1042i	−0.315917	−	1.89716i
$907$	12.3151	+	1.66819i	0.408915	+	0.0553912i	0.335802	−	0.941932i	$-0.390993\pi$
$907$	12.3151	+	1.66819i	0.408915	+	0.0553912i	0.0731122	+	0.997324i	$0.476707\pi$
$908$	−1.23168	+	0.110853i	−0.0408746	+	0.00367878i
$909$	−38.7523	+	29.1050i	−1.28533	+	0.965351i
$910$	−11.3458	−	11.8667i	−0.376108	−	0.393378i
$911$	44.5400	−	8.08282i	1.47568	−	0.267796i	0.619711	−	0.784830i	$-0.287250\pi$
$911$	44.5400	−	8.08282i	1.47568	−	0.267796i	0.855965	+	0.517034i	$0.172964\pi$
$912$	−17.7283	−	22.9047i	−0.587042	−	0.758451i
$913$	39.5273	+	26.0917i	1.30816	+	0.863511i
$914$	−18.5045	−	34.3871i	−0.612074	−	1.13742i
$915$	5.38575	+	4.03368i	0.178047	+	0.133349i
$916$	10.2266	+	15.4926i	0.337896	+	0.511890i
$917$	9.99247	+	1.81337i	0.329981	+	0.0598826i
$918$	−11.8441	+	2.16581i	−0.390913	+	0.0714823i
$919$	34.9063	+	39.9535i	1.15145	+	1.31794i	0.940244	+	0.340502i	$0.110597\pi$
$919$	34.9063	+	39.9535i	1.15145	+	1.31794i	0.211208	+	0.977441i	$0.432260\pi$
$920$	−1.94949	−	1.16477i	−0.0642728	−	0.0384012i
$921$	11.2729	−	2.40141i	0.371455	−	0.0791290i
$922$			50.0962i			1.64983i
$923$	−27.9863	−	8.96672i	−0.921180	−	0.295143i
$924$	−14.2854	−	2.14664i	−0.469955	−	0.0706194i
$925$	29.7052	−	11.1486i	0.976702	−	0.366562i
$926$	−25.6656	+	42.9570i	−0.843425	+	1.41165i
$927$	−3.71957	+	1.66005i	−0.122167	+	0.0545231i
$928$	−0.869820	+	0.631961i	−0.0285532	+	0.0207451i
$929$	6.33402	−	34.9033i	0.207812	−	1.14514i	−0.696269	−	0.717781i	$-0.745158\pi$
$929$	6.33402	−	34.9033i	0.207812	−	1.14514i	0.904082	−	0.427360i	$-0.140556\pi$
$930$	−1.33914	−	2.88721i	−0.0439122	−	0.0946753i
$931$	18.3828	−	34.1610i	0.602472	−	1.11958i
$932$	−1.00460	+	0.540597i	−0.0329067	+	0.0177079i
$933$	−17.6620	+	19.6333i	−0.578229	+	0.642767i
$934$	−48.6026	−	46.4689i	−1.59033	−	1.52051i
$935$	−0.502541	−	2.76923i	−0.0164349	−	0.0905635i
$936$	−10.2340	−	20.4167i	−0.334510	−	0.667342i
$937$	−2.29922	+	3.16460i	−0.0751122	+	0.103383i	−0.844920	−	0.534893i	$-0.820352\pi$
$937$	−2.29922	+	3.16460i	−0.0751122	+	0.103383i	0.769808	+	0.638276i	$0.220352\pi$
$938$	5.12339	+	56.9255i	0.167285	+	1.85868i
$939$	23.5131	+	6.85792i	0.767320	+	0.223800i
$940$	−3.07453	+	0.998975i	−0.100280	+	0.0325830i
$941$	14.2715	−	16.3350i	0.465237	−	0.532507i	−0.471814	−	0.881698i	$-0.656401\pi$
$941$	14.2715	−	16.3350i	0.465237	−	0.532507i	0.937052	+	0.349191i	$0.113544\pi$
$942$	−13.7573	−	3.35078i	−0.448237	−	0.109174i
$943$	1.42749	−	6.25424i	0.0464854	−	0.203666i
$944$	−2.38500	−	53.1061i	−0.0776251	−	1.72846i
$945$	−9.87848	−	11.2763i	−0.321347	−	0.366817i
$946$	−36.6907	−	29.2599i	−1.19292	−	0.951320i
$947$	6.59024	+	11.0302i	0.214154	+	0.358433i	0.946610	−	0.322381i	$-0.104483\pi$
$947$	6.59024	+	11.0302i	0.214154	+	0.358433i	−0.732456	+	0.680814i	$0.761626\pi$
$948$	−9.30257	−	4.64738i	−0.302133	−	0.150940i
$949$	−13.3228	+	27.6651i	−0.432477	+	0.898048i
$950$	25.3612	+	1.13897i	0.822825	+	0.0369531i
$951$	5.00904	−	11.2641i	0.162429	−	0.365262i
$952$	−5.21670	−	12.2051i	−0.169074	−	0.395569i
$953$	6.59359	+	13.6917i	0.213587	+	0.443519i	0.980045	−	0.198776i	$-0.0636967\pi$
$953$	6.59359	+	13.6917i	0.213587	+	0.443519i	−0.766457	+	0.642295i	$0.777982\pi$
$954$	53.3237	+	8.80598i	1.72642	+	0.285104i
$955$	3.72808	+	16.3338i	0.120638	+	0.528549i
$956$	13.7195	−	3.78634i	0.443720	−	0.122459i
$957$	−0.759943	−	1.31490i	−0.0245655	−	0.0425047i
$958$	10.8698	−	28.9625i	0.351187	−	0.935735i
$959$	10.9749	−	29.2425i	0.354398	−	0.944289i
$960$	−2.27004	−	3.92776i	−0.0732651	−	0.126768i
$961$	−27.1899	+	7.50394i	−0.877094	+	0.242063i
$962$	8.83787	+	38.7212i	0.284944	+	1.24842i
$963$	−29.8400	−	4.92783i	−0.961580	−	0.158797i
$964$	−2.33098	−	4.84033i	−0.0750758	−	0.155896i
$965$	−0.209469	−	0.490077i	−0.00674305	−	0.0157761i
$966$	−7.59235	+	17.0732i	−0.244280	+	0.549323i
$967$	11.7824	+	0.529147i	0.378896	+	0.0170162i	0.233499	−	0.972357i	$-0.424983\pi$
$967$	11.7824	+	0.529147i	0.378896	+	0.0170162i	0.145397	+	0.989373i	$0.453554\pi$
$968$	−2.22462	+	4.61946i	−0.0715019	+	0.148475i
$969$	−7.53131	−	3.76249i	−0.241940	−	0.120869i
$970$	9.12030	+	15.2648i	0.292835	+	0.490124i
$971$	−19.8265	−	15.8111i	−0.636262	−	0.507402i	0.251408	−	0.967881i	$-0.419106\pi$
$971$	−19.8265	−	15.8111i	−0.636262	−	0.507402i	−0.887671	+	0.460479i	$0.847678\pi$
$972$	4.21992	+	9.42133i	0.135354	+	0.302189i
$973$	0.551054	+	12.2702i	0.0176660	+	0.393363i
$974$	9.19579	−	40.2894i	0.294652	−	1.29096i
$975$	26.6816	+	6.49869i	0.854497	+	0.208125i
$976$	18.5347	−	21.2147i	0.593282	−	0.679066i
$977$	−42.8459	+	13.9215i	−1.37076	+	0.445387i	−0.899621	−	0.436671i	$-0.856157\pi$
$977$	−42.8459	+	13.9215i	−1.37076	+	0.445387i	−0.471140	+	0.882058i	$0.656157\pi$
$978$	18.2459	+	5.32169i	0.583441	+	0.170169i
$979$	1.18096	+	13.1215i	0.0377435	+	0.419365i
$980$	−2.97273	+	4.09161i	−0.0949603	+	0.130702i
$981$	10.4681	+	20.8837i	0.334221	+	0.666764i
$982$	−1.27759	−	7.04011i	−0.0407696	−	0.224659i
$983$	24.7302	+	23.6445i	0.788772	+	0.754143i	0.973510	−	0.228645i	$-0.0734294\pi$
$983$	24.7302	+	23.6445i	0.788772	+	0.754143i	−0.184738	+	0.982788i	$0.559144\pi$
$984$	10.5046	−	11.6770i	0.334874	−	0.372250i
$985$	7.01633	−	3.77565i	0.223559	−	0.120302i
$986$	−0.327341	+	0.608301i	−0.0104247	+	0.0193723i
$987$	−22.6084	−	48.7439i	−0.719632	−	1.55154i
$988$	−1.41149	+	7.77796i	−0.0449055	+	0.247450i
$989$	−12.2159	+	8.87536i	−0.388442	+	0.282220i
$990$	−8.85845	+	3.95354i	−0.281540	+	0.125652i
$991$	3.49791	−	5.85451i	0.111115	−	0.185975i	−0.797840	−	0.602869i	$-0.794024\pi$
$991$	3.49791	−	5.85451i	0.111115	−	0.185975i	0.908955	+	0.416894i	$0.136881\pi$
$992$	−5.64364	+	2.11809i	−0.179186	+	0.0672495i
$993$	34.1003	+	5.12419i	1.08214	+	0.162611i
$994$	−7.66314	+	58.3681i	−0.243060	+	1.85132i
$995$		−	11.3872i		−	0.360998i
$996$	−18.0649	+	3.84826i	−0.572408	+	0.121937i
$997$	34.5549	+	20.6456i	1.09437	+	0.653853i	0.942385	−	0.334530i	$-0.108578\pi$
$997$	34.5549	+	20.6456i	1.09437	+	0.653853i	0.151981	+	0.988383i	$0.451435\pi$
$998$	3.80910	+	4.35986i	0.120575	+	0.138009i
$999$	6.52342	+	35.6744i	0.206392	+	1.12869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.n.a.104.17	yes	528
3.2	odd	2	inner	213.2.n.a.104.6	✓	528
71.28	odd	70	inner	213.2.n.a.170.6	yes	528
213.170	even	70	inner	213.2.n.a.170.17	yes	528

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.n.a.104.6	✓	528	3.2	odd	2	inner
213.2.n.a.104.17	yes	528	1.1	even	1	trivial
213.2.n.a.170.6	yes	528	71.28	odd	70	inner
213.2.n.a.170.17	yes	528	213.170	even	70	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:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.n (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573316 + 1.52759i) q^{2} +(-1.09945 + 1.33836i) q^{3} +(-0.498711 + 0.435711i) q^{4} +(0.396042 + 0.545105i) q^{5} +(-2.67480 - 0.912219i) q^{6} +(-3.57354 + 2.35887i) q^{7} +(1.92211 + 1.03433i) q^{8} +(-0.582401 - 2.94293i) q^{9} +(-0.605643 + 0.917509i) q^{10} +(-2.03260 + 2.12593i) q^{11} +(-0.0348267 - 1.14650i) q^{12} +(2.52087 - 2.41020i) q^{13} +(-5.65217 - 4.10654i) q^{14} +(-1.16498 - 0.0692723i) q^{15} +(-0.655852 + 4.84170i) q^{16} +(0.438855 + 1.35066i) q^{17} +(4.16170 - 2.57690i) q^{18} +(3.40880 + 0.306797i) q^{19} +(-0.435019 - 0.0992902i) q^{20} +(0.771928 - 7.37614i) q^{21} +(-4.41288 - 1.88615i) q^{22} +(-0.962744 + 1.20724i) q^{23} +(-3.49759 + 1.43527i) q^{24} +(1.40479 - 4.32351i) q^{25} +(5.12707 + 2.46906i) q^{26} +(4.57901 + 2.45615i) q^{27} +(0.754377 - 2.73343i) q^{28} +(0.274123 - 0.117166i) q^{29} +(-0.562079 - 1.81933i) q^{30} +(1.65628 - 0.224359i) q^{31} +(-3.51612 + 0.802532i) q^{32} +(-0.610506 - 5.05770i) q^{33} +(-1.81165 + 1.44475i) q^{34} +(-2.70111 - 1.01374i) q^{35} +(1.57271 + 1.21391i) q^{36} +(4.35158 + 5.45671i) q^{37} +(1.48566 + 5.38315i) q^{38} +(0.454126 + 6.02373i) q^{39} +(0.197417 + 1.45739i) q^{40} +(-3.74309 + 1.80258i) q^{41} +(11.7103 - 3.04967i) q^{42} +(9.42641 + 2.60152i) q^{43} +(0.0873882 - 1.94585i) q^{44} +(1.37355 - 1.48299i) q^{45} +(-2.39613 - 0.778551i) q^{46} +(6.21944 - 3.71594i) q^{47} +(-5.75884 - 6.20099i) q^{48} +(4.45473 - 10.4224i) q^{49} +(7.40997 - 0.332782i) q^{50} +(-2.29016 - 0.897641i) q^{51} +(-0.207037 + 2.30036i) q^{52} +(8.31485 + 7.26447i) q^{53} +(-1.12678 + 8.40302i) q^{54} +(-1.96385 - 0.266021i) q^{55} +(-9.30861 + 0.837790i) q^{56} +(-4.15842 + 4.22488i) q^{57} +(0.336140 + 0.351575i) q^{58} +(-10.7053 + 1.94273i) q^{59} +(0.611169 - 0.473046i) q^{60} +(-4.81193 - 3.17633i) q^{61} +(1.29230 + 2.40150i) q^{62} +(9.02322 + 9.14285i) q^{63} +(2.14148 + 3.24420i) q^{64} +(2.31218 + 0.419600i) q^{65} +(7.37610 - 3.83227i) q^{66} +(-5.38253 - 6.16081i) q^{67} +(-0.807358 - 0.482374i) q^{68} +(-0.557229 - 2.61580i) q^{69} -4.70739i q^{70} +(-4.02325 - 7.40361i) q^{71} +(1.92453 - 6.25904i) q^{72} +(-8.24274 + 3.09355i) q^{73} +(-5.84081 + 9.77586i) q^{74} +(4.24190 + 6.63362i) q^{75} +(-1.83368 + 1.33225i) q^{76} +(2.24877 - 12.3917i) q^{77} +(-8.94146 + 4.14722i) q^{78} +(4.29605 - 7.98340i) q^{79} +(-2.89898 + 1.56001i) q^{80} +(-8.32162 + 3.42793i) q^{81} +(-4.89958 - 4.68448i) q^{82} +(-2.87525 - 15.8439i) q^{83} +(2.82890 + 4.01490i) q^{84} +(-0.562445 + 0.774139i) q^{85} +(1.43024 + 15.8912i) q^{86} +(-0.144576 + 0.495692i) q^{87} +(-6.10580 + 1.98390i) q^{88} +(2.94705 - 3.37317i) q^{89} +(3.05289 + 1.24800i) q^{90} +(-3.32308 + 14.5594i) q^{91} +(-0.0458775 - 1.02154i) q^{92} +(-1.52073 + 2.46337i) q^{93} +(9.24215 + 7.37037i) q^{94} +(1.18279 + 1.97966i) q^{95} +(2.79174 - 5.58818i) q^{96} +(7.01786 - 14.5727i) q^{97} +(18.4751 + 0.829717i) q^{98} +(7.44024 + 4.74364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) \) 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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