LMFDB - Embedded newform 315.2.bq.a.194.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(164,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.164"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bq (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			194.3
Character	$\chi$	$=$	315.194
Dual form			315.2.bq.a.164.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.53172 q^{2} +(1.70470 + 0.306605i) q^{3} +4.40959 q^{4} +(-1.09270 + 1.95090i) q^{5} +(-4.31581 - 0.776236i) q^{6} +(2.57916 - 0.589845i) q^{7} -6.10041 q^{8} +(2.81199 + 1.04534i) q^{9} +(2.76640 - 4.93913i) q^{10} +(1.23377 + 0.712319i) q^{11} +(7.51702 + 1.35200i) q^{12} +(-2.08746 + 3.61559i) q^{13} +(-6.52971 + 1.49332i) q^{14} +(-2.46088 + 2.99067i) q^{15} +6.62532 q^{16} +(4.27416 - 2.46769i) q^{17} +(-7.11916 - 2.64650i) q^{18} +(-4.54377 - 2.62335i) q^{19} +(-4.81835 + 8.60267i) q^{20} +(4.57754 - 0.214725i) q^{21} +(-3.12356 - 1.80339i) q^{22} +(0.238847 + 0.413696i) q^{23} +(-10.3993 - 1.87041i) q^{24} +(-2.61202 - 4.26349i) q^{25} +(5.28486 - 9.15364i) q^{26} +(4.47308 + 2.64415i) q^{27} +(11.3731 - 2.60098i) q^{28} +(-1.74963 + 1.01015i) q^{29} +(6.23024 - 7.57152i) q^{30} +10.6444i q^{31} -4.57262 q^{32} +(1.88481 + 1.59257i) q^{33} +(-10.8210 + 6.24749i) q^{34} +(-1.66752 + 5.67621i) q^{35} +(12.3997 + 4.60951i) q^{36} +(7.03282 + 4.06040i) q^{37} +(11.5035 + 6.64157i) q^{38} +(-4.66704 + 5.52345i) q^{39} +(6.66590 - 11.9013i) q^{40} +(0.421048 - 0.729276i) q^{41} +(-11.5890 + 0.543622i) q^{42} +(3.70789 - 2.14075i) q^{43} +(5.44044 + 3.14104i) q^{44} +(-5.11200 + 4.34367i) q^{45} +(-0.604694 - 1.04736i) q^{46} +4.94304i q^{47} +(11.2942 + 2.03135i) q^{48} +(6.30416 - 3.04261i) q^{49} +(6.61290 + 10.7940i) q^{50} +(8.04276 - 2.89618i) q^{51} +(-9.20484 + 15.9433i) q^{52} +(-2.33122 - 4.03778i) q^{53} +(-11.3246 - 6.69424i) q^{54} +(-2.73781 + 1.62862i) q^{55} +(-15.7339 + 3.59830i) q^{56} +(-6.94142 - 5.86515i) q^{57} +(4.42958 - 2.55742i) q^{58} +0.202459 q^{59} +(-10.8515 + 13.1876i) q^{60} -1.78370i q^{61} -26.9486i q^{62} +(7.86916 + 1.03745i) q^{63} -1.67406 q^{64} +(-4.77268 - 8.02317i) q^{65} +(-4.77180 - 4.03193i) q^{66} +2.38316i q^{67} +(18.8473 - 10.8815i) q^{68} +(0.280322 + 0.778458i) q^{69} +(4.22169 - 14.3706i) q^{70} -11.7260i q^{71} +(-17.1543 - 6.37697i) q^{72} +(-4.52420 - 7.83614i) q^{73} +(-17.8051 - 10.2798i) q^{74} +(-3.14550 - 8.06882i) q^{75} +(-20.0362 - 11.5679i) q^{76} +(3.60226 + 1.10945i) q^{77} +(11.8156 - 13.9838i) q^{78} +0.452236 q^{79} +(-7.23947 + 12.9253i) q^{80} +(6.81454 + 5.87894i) q^{81} +(-1.06597 + 1.84632i) q^{82} +(-10.6524 + 6.15019i) q^{83} +(20.1851 - 0.946848i) q^{84} +(0.143843 + 11.0349i) q^{85} +(-9.38732 + 5.41977i) q^{86} +(-3.29231 + 1.18556i) q^{87} +(-7.52652 - 4.34544i) q^{88} +(-1.33067 + 2.30479i) q^{89} +(12.9421 - 10.9969i) q^{90} +(-3.25126 + 10.5565i) q^{91} +(1.05322 + 1.82423i) q^{92} +(-3.26363 + 18.1455i) q^{93} -12.5144i q^{94} +(10.0829 - 5.99791i) q^{95} +(-7.79493 - 1.40199i) q^{96} +(-4.69437 - 8.13089i) q^{97} +(-15.9604 + 7.70304i) q^{98} +(2.72474 + 3.29274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36}+ \cdots + 30 q^{99}+O(q^{100}) $ 88 * q + 76 * q^4 - 3 * q^5 - 12 * q^6 - 6 * q^10 - 12 * q^11 - 12 * q^14 - 6 * q^15 + 52 * q^16 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 48 * q^24 + q^25 - 12 * q^26 + 6 * q^29 + 33 * q^30 - 12 * q^34 - 36 * q^36 + 12 * q^39 - 30 * q^40 + 6 * q^41 - 84 * q^44 + 21 * q^45 - 18 * q^46 - 8 * q^49 + 30 * q^50 - 24 * q^51 - 60 * q^54 - 78 * q^56 - 12 * q^59 - 45 * q^60 - 8 * q^64 - 24 * q^66 + 60 * q^69 + 15 * q^70 - 30 * q^74 - 48 * q^75 - 48 * q^76 - 16 * q^79 - 69 * q^80 + 36 * q^81 - 90 * q^84 - 7 * q^85 - 12 * q^86 + 72 * q^89 + 33 * q^90 + 20 * q^91 - 60 * q^96 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.53172			−1.79019			−0.895097	−	0.445871i	$-0.852894\pi$
$2$	−2.53172			−1.79019			−0.895097	+	0.445871i	$0.852894\pi$
$3$	1.70470	+	0.306605i	0.984208	+	0.177018i
$3$	1.70470	+	0.306605i	0.984208	+	0.177018i
$4$	4.40959			2.20480
$5$	−1.09270	+	1.95090i	−0.488670	+	0.872469i
$5$	−1.09270	+	1.95090i	−0.488670	+	0.872469i
$6$	−4.31581	−	0.776236i	−1.76192	−	0.316897i
$7$	2.57916	−	0.589845i	0.974832	−	0.222941i
$7$	2.57916	−	0.589845i	0.974832	−	0.222941i
$8$	−6.10041			−2.15682
$9$	2.81199	+	1.04534i	0.937329	+	0.348445i
$10$	2.76640	−	4.93913i	0.874814	−	1.56189i
$11$	1.23377	+	0.712319i	0.371997	+	0.214772i	0.674330	−	0.738430i	$-0.264432\pi$
$11$	1.23377	+	0.712319i	0.371997	+	0.214772i	−0.302334	+	0.953202i	$0.597766\pi$
$12$	7.51702	+	1.35200i	2.16998	+	0.390289i
$13$	−2.08746	+	3.61559i	−0.578957	+	1.00278i	0.416642	+	0.909071i	$0.363207\pi$
$13$	−2.08746	+	3.61559i	−0.578957	+	1.00278i	−0.995599	+	0.0937125i	$0.970127\pi$
$14$	−6.52971	+	1.49332i	−1.74514	+	0.399107i
$15$	−2.46088	+	2.99067i	−0.635395	+	0.772187i
$16$	6.62532			1.65633
$17$	4.27416	−	2.46769i	1.03664	−	0.598502i	0.117758	−	0.993042i	$-0.462429\pi$
$17$	4.27416	−	2.46769i	1.03664	−	0.598502i	0.918879	+	0.394540i	$0.129096\pi$
$18$	−7.11916	−	2.64650i	−1.67800	−	0.623785i
$19$	−4.54377	−	2.62335i	−1.04241	−	0.601837i	−0.121896	−	0.992543i	$-0.538898\pi$
$19$	−4.54377	−	2.62335i	−1.04241	−	0.601837i	−0.920515	+	0.390706i	$0.872231\pi$
$20$	−4.81835	+	8.60267i	−1.07742	+	1.92362i
$21$	4.57754	−	0.214725i	0.998902	−	0.0468568i
$22$	−3.12356	−	1.80339i	−0.665946	−	0.384484i
$23$	0.238847	+	0.413696i	0.0498031	+	0.0862616i	0.889852	−	0.456249i	$-0.150807\pi$
$23$	0.238847	+	0.413696i	0.0498031	+	0.0862616i	−0.840049	+	0.542510i	$0.817474\pi$
$24$	−10.3993	−	1.87041i	−2.12276	−	0.381796i
$25$	−2.61202	−	4.26349i	−0.522404	−	0.852698i
$26$	5.28486	−	9.15364i	1.03645	−	1.79518i
$27$	4.47308	+	2.64415i	0.860845	+	0.508867i
$28$	11.3731	−	2.60098i	2.14931	−	0.491539i
$29$	−1.74963	+	1.01015i	−0.324899	+	0.187580i	−0.653574	−	0.756863i	$-0.726731\pi$
$29$	−1.74963	+	1.01015i	−0.324899	+	0.187580i	0.328675	+	0.944443i	$0.393398\pi$
$30$	6.23024	−	7.57152i	1.13748	−	1.38236i
$31$			10.6444i			1.91179i	0.293703	+	0.955897i	$0.405112\pi$
$31$			10.6444i			1.91179i	−0.293703	+	0.955897i	$0.594888\pi$
$32$	−4.57262			−0.808333
$33$	1.88481	+	1.59257i	0.328103	+	0.277231i
$34$	−10.8210	+	6.24749i	−1.85578	+	1.07144i
$35$	−1.66752	+	5.67621i	−0.281862	+	0.959455i
$36$	12.3997	+	4.60951i	2.06662	+	0.768251i
$37$	7.03282	+	4.06040i	1.15619	+	0.667526i	0.950388	−	0.311068i	$-0.100687\pi$
$37$	7.03282	+	4.06040i	1.15619	+	0.667526i	0.205801	+	0.978594i	$0.434020\pi$
$38$	11.5035	+	6.64157i	1.86612	+	1.07740i
$39$	−4.66704	+	5.52345i	−0.747325	+	0.884461i
$40$	6.66590	−	11.9013i	1.05397	−	1.88176i
$41$	0.421048	−	0.729276i	0.0657566	−	0.113894i	−0.831273	−	0.555865i	$-0.812387\pi$
$41$	0.421048	−	0.729276i	0.0657566	−	0.113894i	0.897029	+	0.441971i	$0.145721\pi$
$42$	−11.5890	+	0.543622i	−1.78823	+	0.0838827i
$43$	3.70789	−	2.14075i	0.565447	−	0.326461i	−0.189882	−	0.981807i	$-0.560810\pi$
$43$	3.70789	−	2.14075i	0.565447	−	0.326461i	0.755329	+	0.655346i	$0.227477\pi$
$44$	5.44044	+	3.14104i	0.820176	+	0.473529i
$45$	−5.11200	+	4.34367i	−0.762052	+	0.647516i
$46$	−0.604694	−	1.04736i	−0.0891573	−	0.154425i
$47$			4.94304i			0.721016i	0.932756	+	0.360508i	$0.117397\pi$
$47$			4.94304i			0.721016i	−0.932756	+	0.360508i	$0.882603\pi$
$48$	11.2942	+	2.03135i	1.63017	+	0.293201i
$49$	6.30416	−	3.04261i	0.900595	−	0.434659i
$50$	6.61290	+	10.7940i	0.935205	+	1.52650i
$51$	8.04276	−	2.89618i	1.12621	−	0.405547i
$52$	−9.20484	+	15.9433i	−1.27648	+	2.21093i
$53$	−2.33122	−	4.03778i	−0.320217	−	0.554632i	0.660316	−	0.750988i	$-0.270423\pi$
$53$	−2.33122	−	4.03778i	−0.320217	−	0.554632i	−0.980533	+	0.196356i	$0.937089\pi$
$54$	−11.3246	−	6.69424i	−1.54108	−	0.910971i
$55$	−2.73781	+	1.62862i	−0.369166	+	0.219603i
$56$	−15.7339	+	3.59830i	−2.10254	+	0.480843i
$57$	−6.94142	−	5.86515i	−0.919413	−	0.776858i
$58$	4.42958	−	2.55742i	0.581632	−	0.335805i
$59$	0.202459			0.0263579			0.0131790	−	0.999913i	$-0.495805\pi$
$59$	0.202459			0.0263579			0.0131790	+	0.999913i	$0.495805\pi$
$60$	−10.8515	+	13.1876i	−1.40092	+	1.70251i
$61$		−	1.78370i		−	0.228379i	−0.993459	−	0.114189i	$-0.963573\pi$
$61$		−	1.78370i		−	0.228379i	0.993459	−	0.114189i	$-0.0364271\pi$
$62$		−	26.9486i		−	3.42248i
$63$	7.86916	+	1.03745i	0.991421	+	0.130707i
$64$	−1.67406			−0.209257
$65$	−4.77268	−	8.02317i	−0.591978	−	0.995152i
$66$	−4.77180	−	4.03193i	−0.587368	−	0.496297i
$67$			2.38316i			0.291150i	0.989347	+	0.145575i	$0.0465032\pi$
$67$			2.38316i			0.291150i	−0.989347	+	0.145575i	$0.953497\pi$
$68$	18.8473	−	10.8815i	2.28557	−	1.31958i
$69$	0.280322	+	0.778458i	0.0337468	+	0.0937154i
$70$	4.22169	−	14.3706i	0.504588	−	1.71761i
$71$		−	11.7260i		−	1.39162i	−0.718223	−	0.695812i	$-0.755044\pi$
$71$		−	11.7260i		−	1.39162i	0.718223	−	0.695812i	$-0.244956\pi$
$72$	−17.1543	−	6.37697i	−2.02165	−	0.751534i
$73$	−4.52420	−	7.83614i	−0.529517	−	0.917150i	−0.999407	−	0.0344256i	$-0.989040\pi$
$73$	−4.52420	−	7.83614i	−0.529517	−	0.917150i	0.469890	−	0.882725i	$-0.344293\pi$
$74$	−17.8051	−	10.2798i	−2.06980	−	1.19500i
$75$	−3.14550	−	8.06882i	−0.363211	−	0.931707i
$76$	−20.0362	−	11.5679i	−2.29831	−	1.32693i
$77$	3.60226	+	1.10945i	0.410516	+	0.126434i
$78$	11.8156	−	13.9838i	1.33786	−	1.58336i
$79$	0.452236			0.0508806			0.0254403	−	0.999676i	$-0.491901\pi$
$79$	0.452236			0.0508806			0.0254403	+	0.999676i	$0.491901\pi$
$80$	−7.23947	+	12.9253i	−0.809398	+	1.44510i
$81$	6.81454	+	5.87894i	0.757172	+	0.653216i
$82$	−1.06597	+	1.84632i	−0.117717	+	0.203892i
$83$	−10.6524	+	6.15019i	−1.16926	+	0.675071i	−0.953505	−	0.301378i	$-0.902553\pi$
$83$	−10.6524	+	6.15019i	−1.16926	+	0.675071i	−0.215752	+	0.976448i	$0.569220\pi$
$84$	20.1851	−	0.946848i	2.20237	−	0.103310i
$85$	0.143843	+	11.0349i	0.0156019	+	1.19690i
$86$	−9.38732	+	5.41977i	−1.01226	+	0.584429i
$87$	−3.29231	+	1.18556i	−0.352973	+	0.127105i
$88$	−7.52652	−	4.34544i	−0.802329	−	0.463225i
$89$	−1.33067	+	2.30479i	−0.141051	+	0.244307i	−0.927893	−	0.372848i	$-0.878381\pi$
$89$	−1.33067	+	2.30479i	−0.141051	+	0.244307i	0.786842	+	0.617155i	$0.211715\pi$
$90$	12.9421	−	10.9969i	1.36422	−	1.15918i
$91$	−3.25126	+	10.5565i	−0.340825	+	1.10662i
$92$	1.05322	+	1.82423i	0.109806	+	0.190189i
$93$	−3.26363	+	18.1455i	−0.338422	+	1.88160i
$94$		−	12.5144i		−	1.29076i
$95$	10.0829	−	5.99791i	1.03448	−	0.615372i
$96$	−7.79493	−	1.40199i	−0.795567	−	0.143090i
$97$	−4.69437	−	8.13089i	−0.476641	−	0.825567i	0.523001	−	0.852332i	$-0.324813\pi$
$97$	−4.69437	−	8.13089i	−0.476641	−	0.825567i	−0.999642	+	0.0267656i	$0.991479\pi$
$98$	−15.9604	+	7.70304i	−1.61224	+	0.778125i
$99$	2.72474	+	3.29274i	0.273847	+	0.330933i
$100$	−11.5179	−	18.8003i	−1.15179	−	1.88003i
$101$	9.22577	−	15.9795i	0.917998	−	1.59002i	0.115546	−	0.993302i	$-0.463138\pi$
$101$	9.22577	−	15.9795i	0.917998	−	1.59002i	0.802452	−	0.596717i	$-0.203529\pi$
$102$	−20.3620	+	7.33232i	−2.01614	+	0.726008i
$103$	−9.34498	−	16.1860i	−0.920789	−	1.59485i	−0.798198	−	0.602396i	$-0.794213\pi$
$103$	−9.34498	−	16.1860i	−0.920789	−	1.59485i	−0.122591	−	0.992457i	$-0.539120\pi$
$104$	12.7343	−	22.0565i	1.24871	−	2.16282i
$105$	−4.58297	+	9.16496i	−0.447252	+	0.894408i
$106$	5.90198	+	10.2225i	0.573251	+	0.992900i
$107$	0.440832	−	0.763543i	0.0426168	−	0.0738145i	−0.843930	−	0.536453i	$-0.819764\pi$
$107$	0.440832	−	0.763543i	0.0426168	−	0.0738145i	0.886547	+	0.462639i	$0.153097\pi$
$108$	19.7245	+	11.6596i	1.89799	+	1.12195i
$109$	2.17023	+	3.75895i	0.207870	+	0.360042i	0.951043	−	0.309057i	$-0.100013\pi$
$109$	2.17023	+	3.75895i	0.207870	+	0.360042i	−0.743173	+	0.669099i	$0.766680\pi$
$110$	6.93135	−	4.12320i	0.660878	−	0.393132i
$111$	10.7439	+	9.07805i	1.01977	+	0.861650i
$112$	17.0878	−	3.90791i	1.61464	−	0.369263i
$113$	−4.60460	+	7.97540i	−0.433164	+	0.750262i	−0.997144	−	0.0755263i	$-0.975936\pi$
$113$	−4.60460	+	7.97540i	−0.433164	+	0.750262i	0.563980	+	0.825789i	$0.309270\pi$
$114$	17.5737	+	14.8489i	1.64593	+	1.39073i
$115$	−1.06807	+	0.0139225i	−0.0995978	+	0.00129828i
$116$	−7.71517	+	4.45436i	−0.716336	+	0.413577i
$117$	−9.64941	+	7.98488i	−0.892088	+	0.738203i
$118$	−0.512569			−0.0471858
$119$	9.56821	−	8.88566i	0.877116	−	0.814548i
$120$	15.0123	−	18.2443i	1.37043	−	1.66547i
$121$	−4.48520	−	7.76860i	−0.407746	−	0.706236i
$122$			4.51581i			0.408843i
$123$	0.941358	−	1.11410i	0.0848794	−	0.100455i
$124$			46.9375i			4.21511i
$125$	11.1718	−	0.437080i	0.999236	−	0.0390936i
$126$	−19.9225	−	2.62654i	−1.77484	−	0.233991i
$127$		−	8.82849i		−	0.783401i	−0.920093	−	0.391701i	$-0.871887\pi$
$127$		−	8.82849i		−	0.783401i	0.920093	−	0.391701i	$-0.128113\pi$
$128$	13.3835			1.18294
$129$	6.97719	−	2.51247i	0.614307	−	0.221211i
$130$	12.0831	+	20.3124i	1.05976	+	1.78151i
$131$	−1.10536	−	1.91453i	−0.0965753	−	0.167273i	0.813690	−	0.581300i	$-0.197456\pi$
$131$	−1.10536	−	1.91453i	−0.0965753	−	0.167273i	−0.910265	+	0.414026i	$0.864122\pi$
$132$	8.31124	+	7.02258i	0.723401	+	0.611237i
$133$	−13.2665	−	4.08591i	−1.15035	−	0.354294i
$134$		−	6.03350i		−	0.521215i
$135$	−10.0462	+	5.83728i	−0.864639	+	0.502393i
$136$	−26.0741	+	15.0539i	−2.23584	+	1.29086i
$137$	2.41786	−	4.18786i	0.206572	−	0.357793i	−0.744061	−	0.668112i	$-0.767103\pi$
$137$	2.41786	−	4.18786i	0.206572	−	0.357793i	0.950632	+	0.310319i	$0.100436\pi$
$138$	−0.709695	−	1.97084i	−0.0604133	−	0.167769i
$139$	1.08200	+	0.624695i	0.0917743	+	0.0529859i	0.545185	−	0.838316i	$-0.316459\pi$
$139$	1.08200	+	0.624695i	0.0917743	+	0.0529859i	−0.453410	+	0.891302i	$0.649793\pi$
$140$	−7.35308	+	25.0298i	−0.621448	+	2.11540i
$141$	−1.51556	+	8.42638i	−0.127633	+	0.709630i
$142$			29.6870i			2.49128i
$143$	−5.15090	+	2.97387i	−0.430740	+	0.248688i
$144$	18.6303	+	6.92568i	1.55253	+	0.577140i
$145$	−0.0588822	−	4.51715i	−0.00488990	−	0.375129i
$146$	11.4540	+	19.8389i	0.947938	+	1.64188i
$147$	11.6796	−	3.25385i	0.963315	−	0.268373i
$148$	31.0119	+	17.9047i	2.54916	+	1.47176i
$149$	2.98242	−	1.72190i	0.244329	−	0.141063i	−0.372836	−	0.927897i	$-0.621615\pi$
$149$	2.98242	−	1.72190i	0.244329	−	0.141063i	0.617165	+	0.786834i	$0.288281\pi$
$150$	7.96351	+	20.4280i	0.650218	+	1.66794i
$151$	8.51168	−	14.7427i	0.692671	−	1.19974i	−0.278288	−	0.960498i	$-0.589767\pi$
$151$	8.51168	−	14.7427i	0.692671	−	1.19974i	0.970960	−	0.239244i	$-0.0768995\pi$
$152$	27.7188	+	16.0035i	2.24829	+	1.29805i
$153$	14.5985	−	2.47117i	1.18021	−	0.199782i
$154$	−9.11990	−	2.80882i	−0.734903	−	0.226341i
$155$	−20.7662	−	11.6311i	−1.66798	−	0.934235i
$156$	−20.5797	+	24.3562i	−1.64770	+	1.95006i
$157$	4.68164			0.373636			0.186818	−	0.982395i	$-0.440183\pi$
$157$	4.68164			0.373636			0.186818	+	0.982395i	$0.440183\pi$
$158$	−1.14493			−0.0910861
$159$	−2.73601	−	7.59796i	−0.216980	−	0.602558i
$160$	4.99649	−	8.92072i	0.395008	−	0.705245i
$161$	0.860043	+	0.926106i	0.0677809	+	0.0729874i
$162$	−17.2525	−	14.8838i	−1.35548	−	1.16938i
$163$	−13.9563	−	8.05767i	−1.09314	−	0.631125i	−0.158730	−	0.987322i	$-0.550740\pi$
$163$	−13.9563	−	8.05767i	−1.09314	−	0.631125i	−0.934411	+	0.356197i	$0.884073\pi$
$164$	1.85665	−	3.21581i	0.144980	−	0.251112i
$165$	−5.16647	+	1.93688i	−0.402209	+	0.150786i
$166$	26.9689	−	15.5705i	2.09320	−	1.20851i
$167$	−9.83837	−	5.68018i	−0.761316	−	0.439546i	0.0684521	−	0.997654i	$-0.478194\pi$
$167$	−9.83837	−	5.68018i	−0.761316	−	0.439546i	−0.829768	+	0.558108i	$0.811527\pi$
$168$	−27.9249	+	1.30991i	−2.15445	+	0.101062i
$169$	−2.21497	−	3.83644i	−0.170382	−	0.295111i
$170$	−0.364169	−	27.9372i	−0.0279305	−	2.14269i
$171$	−10.0347	−	12.1266i	−0.767376	−	0.927343i
$172$	16.3503	−	9.43983i	1.24670	−	0.719780i
$173$			13.5586i			1.03084i	0.856938	+	0.515420i	$0.172364\pi$
$173$			13.5586i			1.03084i	−0.856938	+	0.515420i	$0.827636\pi$
$174$	8.33521	−	3.00149i	0.631890	−	0.227543i
$175$	−9.25163	−	9.45555i	−0.699357	−	0.714772i
$176$	8.17414	+	4.71934i	0.616149	+	0.355734i
$177$	0.345132	+	0.0620749i	0.0259417	+	0.00466584i
$178$	3.36888	−	5.83507i	0.252508	−	0.437357i
$179$	−0.777342	+	0.448799i	−0.0581013	+	0.0335448i	−0.528769	−	0.848766i	$-0.677346\pi$
$179$	−0.777342	+	0.448799i	−0.0581013	+	0.0335448i	0.470668	+	0.882310i	$0.344013\pi$
$180$	−22.5418	+	19.1538i	−1.68017	+	1.42764i
$181$			13.4784i			1.00184i	0.865493	+	0.500921i	$0.167005\pi$
$181$			13.4784i			1.00184i	−0.865493	+	0.500921i	$0.832995\pi$
$182$	8.23127	−	26.7260i	0.610143	−	1.98106i
$183$	0.546889	−	3.04066i	0.0404272	−	0.224772i
$184$	−1.45707	−	2.52371i	−0.107416	−	0.186051i
$185$	−15.6062	+	9.28353i	−1.14739	+	0.682539i
$186$	8.26258	−	45.9393i	0.605842	−	3.36843i
$187$	7.03113			0.514167
$188$			21.7968i			1.58969i
$189$	13.0964	+	4.18127i	0.952627	+	0.304142i
$190$	−25.5269	+	15.1850i	−1.85192	+	1.10164i
$191$		−	1.97538i		−	0.142934i	−0.997443	−	0.0714668i	$-0.977232\pi$
$191$		−	1.97538i		−	0.142934i	0.997443	−	0.0714668i	$-0.0227680\pi$
$192$	−2.85376	−	0.513273i	−0.205952	−	0.0370423i
$193$		−	16.5768i		−	1.19322i	−0.802531	−	0.596611i	$-0.796514\pi$
$193$		−	16.5768i		−	1.19322i	0.802531	−	0.596611i	$-0.203486\pi$
$194$	11.8848	+	20.5851i	0.853280	+	1.47792i
$195$	−5.67604	−	15.1404i	−0.406470	−	1.08423i
$196$	27.7988	−	13.4167i	1.98563	−	0.958335i
$197$	24.5924			1.75214			0.876069	−	0.482186i	$-0.160157\pi$
$197$	24.5924			1.75214			0.876069	+	0.482186i	$0.160157\pi$
$198$	−6.89827	−	8.33629i	−0.490239	−	0.592434i
$199$	0.627348	−	0.362200i	0.0444715	−	0.0256757i	−0.477599	−	0.878578i	$-0.658493\pi$
$199$	0.627348	−	0.362200i	0.0444715	−	0.0256757i	0.522071	+	0.852902i	$0.325160\pi$
$200$	15.9344	+	26.0090i	1.12673	+	1.83912i
$201$	−0.730689	+	4.06257i	−0.0515388	+	0.286552i
$202$	−23.3570	+	40.4556i	−1.64339	+	2.84644i
$203$	−3.91676	+	3.63736i	−0.274902	+	0.255293i
$204$	35.4653	−	12.7710i	2.48307	−	0.894148i
$205$	0.962666	+	1.61830i	0.0672355	+	0.113027i
$206$	23.6589	+	40.9783i	1.64839	+	2.85510i
$207$	0.239185	+	1.41298i	0.0166245	+	0.0982092i
$208$	−13.8301	+	23.9544i	−0.958944	+	1.66094i
$209$	−3.73732	−	6.47322i	−0.258516	−	0.447762i
$210$	11.6028	−	23.2031i	0.800668	−	1.60116i
$211$	5.83962	−	10.1145i	0.402016	−	0.696312i	−0.591953	−	0.805972i	$-0.701643\pi$
$211$	5.83962	−	10.1145i	0.402016	−	0.696312i	0.993969	+	0.109660i	$0.0349763\pi$
$212$	−10.2797	−	17.8050i	−0.706013	−	1.22285i
$213$	3.59526	−	19.9894i	0.246343	−	1.36965i
$214$	−1.11606	+	1.93307i	−0.0762924	+	0.132142i
$215$	0.124785	+	9.57291i	0.00851029	+	0.652867i
$216$	−27.2876	−	16.1304i	−1.85669	−	1.09753i
$217$	6.27856	+	27.4537i	0.426216	+	1.86368i
$218$	−5.49441	−	9.51659i	−0.372128	−	0.644545i
$219$	−5.30979	−	14.7454i	−0.358802	−	0.996401i
$220$	−12.0726	+	7.18154i	−0.813935	+	0.484179i
$221$			20.6048i			1.38603i
$222$	−27.2005	−	22.9831i	−1.82558	−	1.54252i
$223$	13.2349	+	22.9235i	0.886275	+	1.53507i	0.844245	+	0.535957i	$0.180049\pi$
$223$	13.2349	+	22.9235i	0.886275	+	1.53507i	0.0420295	+	0.999116i	$0.486618\pi$
$224$	−11.7935	+	2.69714i	−0.787989	+	0.180210i
$225$	−2.88819	−	14.7193i	−0.192546	−	0.981288i
$226$	11.6575	−	20.1915i	0.775448	−	1.34312i
$227$	−6.71384	−	3.87624i	−0.445613	−	0.257275i	0.260363	−	0.965511i	$-0.416158\pi$
$227$	−6.71384	−	3.87624i	−0.445613	−	0.257275i	−0.705976	+	0.708236i	$0.749491\pi$
$228$	−30.6088	−	25.8629i	−2.02712	−	1.71281i
$229$	−16.0456	+	9.26392i	−1.06032	+	0.612177i	−0.925521	−	0.378696i	$-0.876373\pi$
$229$	−16.0456	+	9.26392i	−1.06032	+	0.612177i	−0.134800	+	0.990873i	$0.543039\pi$
$230$	2.70405	−	0.0352479i	0.178299	−	0.00232418i
$231$	5.80060	+	2.99575i	0.381651	+	0.197106i
$232$	10.6735	−	6.16233i	0.700748	−	0.404577i
$233$	4.75564	−	8.23700i	0.311552	−	0.539624i	−0.667146	−	0.744927i	$-0.732484\pi$
$233$	4.75564	−	8.23700i	0.311552	−	0.539624i	0.978699	+	0.205302i	$0.0658178\pi$
$234$	24.4296	−	20.2155i	1.59701	−	1.32153i
$235$	−9.64337	−	5.40125i	−0.629064	−	0.352339i
$236$	0.892762			0.0581139
$237$	0.770926	+	0.138658i	0.0500770	+	0.00900679i
$238$	−24.2240	+	22.4960i	−1.57021	+	1.45820i
$239$	−17.6506	−	10.1906i	−1.14173	−	0.659175i	−0.194868	−	0.980829i	$-0.562428\pi$
$239$	−17.6506	−	10.1906i	−1.14173	−	0.659175i	−0.946857	+	0.321654i	$0.895761\pi$
$240$	−16.3041	+	19.8141i	−1.05242	+	1.27900i
$241$	−7.82942	−	4.52032i	−0.504337	−	0.291179i	0.226166	−	0.974089i	$-0.427381\pi$
$241$	−7.82942	−	4.52032i	−0.504337	−	0.291179i	−0.730503	+	0.682910i	$0.760714\pi$
$242$	11.3553	+	19.6679i	0.729944	+	1.26430i
$243$	9.81423	+	12.1112i	0.629583	+	0.776933i
$244$		−	7.86537i		−	0.503529i
$245$	−0.952715	+	15.6235i	−0.0608667	+	0.998146i
$246$	−2.38325	+	2.82058i	−0.151951	+	0.179834i
$247$	18.9699	−	10.9523i	1.20702	−	0.696875i
$248$		−	64.9352i		−	4.12339i
$249$	−20.0449	+	7.21812i	−1.27029	+	0.457430i
$250$	−28.2838	+	1.10656i	−1.78883	+	0.0699852i
$251$	−4.81421			−0.303871			−0.151935	−	0.988390i	$-0.548551\pi$
$251$	−4.81421			−0.303871			−0.151935	+	0.988390i	$0.548551\pi$
$252$	34.6998	+	4.57475i	2.18588	+	0.288182i
$253$			0.680543i			0.0427853i
$254$			22.3512i			1.40244i
$255$	−3.13814	+	18.8553i	−0.196518	+	1.18076i
$256$	−30.5351			−1.90844
$257$	−0.228355	+	0.131841i	−0.0142444	+	0.00822401i	−0.507105	−	0.861884i	$-0.669284\pi$
$257$	−0.228355	+	0.131841i	−0.0142444	+	0.00822401i	0.492861	+	0.870108i	$0.335951\pi$
$258$	−17.6643	+	6.36088i	−1.09973	+	0.396011i
$259$	20.5338	+	6.32416i	1.27591	+	0.392964i
$260$	−21.0456	−	35.3789i	−1.30519	−	2.19411i
$261$	−5.97589	+	1.01158i	−0.369899	+	0.0626151i
$262$	2.79845	+	4.84705i	0.172889	+	0.299452i
$263$	4.69057	−	8.12431i	0.289233	−	0.500966i	−0.684394	−	0.729113i	$-0.739933\pi$
$263$	4.69057	−	8.12431i	0.289233	−	0.500966i	0.973627	+	0.228146i	$0.0732664\pi$
$264$	−11.4981	−	9.71532i	−0.707659	−	0.597936i
$265$	10.4246	−	0.135888i	0.640380	−	0.00834752i
$266$	33.5870	+	10.3444i	2.05935	+	0.634255i
$267$	−2.97505	+	3.52097i	−0.182070	+	0.215480i
$268$			10.5088i			0.641926i
$269$	5.85382	+	10.1391i	0.356914	+	0.618192i	0.987444	−	0.157972i	$-0.0504957\pi$
$269$	5.85382	+	10.1391i	0.356914	+	0.618192i	−0.630530	+	0.776165i	$0.717162\pi$
$270$	25.4341	−	14.7783i	1.54787	−	0.899381i
$271$	9.67252	+	5.58443i	0.587564	+	0.339230i	0.764134	−	0.645058i	$-0.223167\pi$
$271$	9.67252	+	5.58443i	0.587564	+	0.339230i	−0.176570	+	0.984288i	$0.556500\pi$
$272$	28.3177	−	16.3492i	1.71701	−	0.991317i
$273$	−8.77908	+	16.9987i	−0.531334	+	1.02881i
$274$	−6.12134	+	10.6025i	−0.369804	+	0.640519i
$275$	−0.185674	−	7.12077i	−0.0111966	−	0.429399i
$276$	1.23610	+	3.43268i	0.0744047	+	0.206623i
$277$	−8.68920	−	5.01671i	−0.522083	−	0.301425i	0.215703	−	0.976459i	$-0.430796\pi$
$277$	−8.68920	−	5.01671i	−0.522083	−	0.301425i	−0.737787	+	0.675034i	$0.764129\pi$
$278$	−2.73933	−	1.58155i	−0.164294	−	0.0948551i
$279$	−11.1270	+	29.9320i	−0.666156	+	1.79198i
$280$	10.1725	−	34.6272i	0.607925	−	2.06937i
$281$	−11.3034	+	6.52601i	−0.674303	+	0.389309i	−0.797705	−	0.603048i	$-0.793953\pi$
$281$	−11.3034	+	6.52601i	−0.674303	+	0.389309i	0.123402	+	0.992357i	$0.460620\pi$
$282$	3.83696	−	21.3332i	0.228488	−	1.27037i
$283$	13.3399			0.792974			0.396487	−	0.918040i	$-0.370229\pi$
$283$	13.3399			0.792974			0.396487	+	0.918040i	$0.370229\pi$
$284$		−	51.7071i		−	3.06825i
$285$	19.0272	−	7.13317i	1.12707	−	0.422533i
$286$	13.0406	−	7.52901i	0.771108	−	0.445200i
$287$	0.655790	−	2.12927i	0.0387101	−	0.125687i
$288$	−12.8581	−	4.77993i	−0.757674	−	0.281660i
$289$	3.67897	−	6.37216i	0.216410	−	0.374833i
$290$	0.149073	+	11.4361i	0.00875388	+	0.671554i
$291$	−5.50951	−	15.3000i	−0.322973	−	0.896903i
$292$	−19.9499	−	34.5542i	−1.16748	−	2.02213i
$293$	3.97741	+	2.29636i	0.232363	+	0.134155i	0.611662	−	0.791120i	$-0.290501\pi$
$293$	3.97741	+	2.29636i	0.232363	+	0.134155i	−0.379299	+	0.925274i	$0.623835\pi$
$294$	−29.5694	+	8.23783i	−1.72452	+	0.480440i
$295$	−0.221227	+	0.394978i	−0.0128803	+	0.0229965i
$296$	−42.9031	−	24.7701i	−2.49369	−	1.43973i
$297$	3.63529	+	6.44854i	0.210941	+	0.374182i
$298$	−7.55063	+	4.35936i	−0.437396	+	0.252531i
$299$	−1.99434			−0.115336
$300$	−13.8704	−	35.5802i	−0.800806	−	2.05422i
$301$	8.30053	−	7.70842i	0.478435	−	0.444306i
$302$	−21.5492	+	37.3243i	−1.24002	+	2.14777i
$303$	20.6265	−	24.4115i	1.18496	−	1.40241i
$304$	−30.1039	−	17.3805i	−1.72658	−	0.996840i
$305$	3.47981	+	1.94904i	0.199253	+	0.111602i
$306$	−36.9592	+	6.25631i	−2.11281	+	0.357649i
$307$	−20.6137			−1.17649			−0.588244	−	0.808683i	$-0.700181\pi$
$307$	−20.6137			−1.17649			−0.588244	+	0.808683i	$0.700181\pi$
$308$	15.8845	+	4.89223i	0.905103	+	0.278761i
$309$	−10.9677	−	30.4574i	−0.623929	−	1.73266i
$310$	52.5741	+	29.4467i	2.98601	+	1.67246i
$311$	−11.5614			−0.655584			−0.327792	−	0.944750i	$-0.606305\pi$
$311$	−11.5614			−0.655584			−0.327792	+	0.944750i	$0.606305\pi$
$312$	28.4708	−	33.6953i	1.61184	−	1.90762i
$313$	29.0404			1.64146			0.820731	−	0.571315i	$-0.193566\pi$
$313$	29.0404			1.64146			0.820731	+	0.571315i	$0.193566\pi$
$314$	−11.8526			−0.668881
$315$	−10.6226	+	14.2183i	−0.598515	+	0.801111i
$316$	1.99418			0.112181
$317$	−21.6855			−1.21798			−0.608988	−	0.793179i	$-0.708424\pi$
$317$	−21.6855			−1.21798			−0.608988	+	0.793179i	$0.708424\pi$
$318$	6.92682	+	19.2359i	0.388437	+	1.07870i
$319$	−2.87820			−0.161148
$320$	1.82924	−	3.26591i	0.102257	−	0.182570i
$321$	0.985590	−	1.16645i	0.0550103	−	0.0651048i
$322$	−2.17739	−	2.34464i	−0.121341	−	0.130662i
$323$	−25.8944			−1.44080
$324$	30.0494	+	25.9237i	1.66941	+	1.44021i
$325$	20.8675	−	0.544119i	1.15752	−	0.0301823i
$326$	35.3334	+	20.3997i	1.95693	+	1.12984i
$327$	2.54707	+	7.07327i	0.140854	+	0.391153i
$328$	−2.56856	+	4.44888i	−0.141825	+	0.245648i
$329$	2.91563	+	12.7489i	0.160744	+	0.702870i
$330$	13.0800	−	4.90362i	0.720033	−	0.269936i
$331$	5.95239			0.327173			0.163587	−	0.986529i	$-0.447694\pi$
$331$	5.95239			0.327173			0.163587	+	0.986529i	$0.447694\pi$
$332$	−46.9729	+	27.1198i	−2.57797	+	1.48839i
$333$	15.5317	+	18.7695i	0.851133	+	1.02856i
$334$	24.9080	+	14.3806i	1.36290	+	0.786873i
$335$	−4.64931	−	2.60408i	−0.254019	−	0.142276i
$336$	30.3277	−	1.42262i	1.65451	−	0.0776102i
$337$	2.43132	+	1.40373i	0.132443	+	0.0764658i	0.564757	−	0.825257i	$-0.308970\pi$
$337$	2.43132	+	1.40373i	0.132443	+	0.0764658i	−0.432315	+	0.901723i	$0.642303\pi$
$338$	5.60768	+	9.71279i	0.305018	+	0.528306i
$339$	−10.2947	+	12.1839i	−0.559134	+	0.661736i
$340$	0.634288	+	48.6594i	0.0343991	+	2.63893i
$341$	−7.58222	+	13.1328i	−0.410600	+	0.711181i
$342$	25.4051	+	30.7011i	1.37375	+	1.66012i
$343$	14.4648	−	11.5659i	0.781026	−	0.624499i
$344$	−22.6196	+	13.0594i	−1.21957	+	0.704118i
$345$	−1.82500	−	0.303741i	−0.0982548	−	0.0163529i
$346$		−	34.3265i		−	1.84540i
$347$	9.89128			0.530992			0.265496	−	0.964112i	$-0.414464\pi$
$347$	9.89128			0.530992			0.265496	+	0.964112i	$0.414464\pi$
$348$	−14.5178	+	5.22782i	−0.778233	+	0.280241i
$349$	0.279669	−	0.161467i	0.0149703	−	0.00864312i	−0.492496	−	0.870315i	$-0.663915\pi$
$349$	0.279669	−	0.161467i	0.0149703	−	0.00864312i	0.507466	+	0.861671i	$0.330582\pi$
$350$	23.4225	+	23.9388i	1.25199	+	1.27958i
$351$	−18.8975	+	10.6533i	−1.00868	+	0.568629i
$352$	−5.64157	−	3.25716i	−0.300697	−	0.173607i
$353$	14.7971	+	8.54312i	0.787571	+	0.454704i	0.839107	−	0.543967i	$-0.183078\pi$
$353$	14.7971	+	8.54312i	0.787571	+	0.454704i	−0.0515356	+	0.998671i	$0.516412\pi$
$354$	−0.873776	−	0.157156i	−0.0464407	−	0.00835275i
$355$	22.8763	+	12.8130i	1.21415	+	0.680045i
$356$	−5.86771	+	10.1632i	−0.310988	+	0.538647i
$357$	19.0353	−	12.2137i	1.00745	−	0.646418i
$358$	1.96801	−	1.13623i	0.104013	−	0.0600517i
$359$	−17.2188	−	9.94126i	−0.908772	−	0.524680i	−0.0287362	−	0.999587i	$-0.509148\pi$
$359$	−17.2188	−	9.94126i	−0.908772	−	0.524680i	−0.880036	+	0.474907i	$0.842482\pi$
$360$	31.1853	−	26.4981i	1.64361	−	1.39657i
$361$	4.26388	+	7.38525i	0.224415	+	0.388698i
$362$		−	34.1235i		−	1.79349i
$363$	−5.26403	−	14.6183i	−0.276290	−	0.767262i
$364$	−14.3367	+	46.5497i	−0.751449	+	2.43987i
$365$	20.2311	−	0.263718i	1.05894	−	0.0138036i
$366$	−1.38457	+	7.69810i	−0.0723726	+	0.402386i
$367$	15.6841	−	27.1656i	0.818702	−	1.41803i	−0.0879374	−	0.996126i	$-0.528028\pi$
$367$	15.6841	−	27.1656i	0.818702	−	1.41803i	0.906639	−	0.421907i	$-0.138639\pi$
$368$	1.58244	+	2.74087i	0.0824904	+	0.142878i
$369$	1.94632	−	1.61058i	0.101321	−	0.0838433i
$370$	39.5104	−	23.5033i	2.05405	−	1.22188i
$371$	−8.39425	−	9.03905i	−0.435808	−	0.469284i
$372$	−14.3913	+	80.0143i	−0.746152	+	4.14855i
$373$	−22.1887	+	12.8107i	−1.14889	+	0.663312i	−0.948616	−	0.316428i	$-0.897516\pi$
$373$	−22.1887	+	12.8107i	−1.14889	+	0.663312i	−0.200273	+	0.979740i	$0.564183\pi$
$374$	−17.8008			−0.920459
$375$	19.1785	+	2.68023i	0.990375	+	0.138407i
$376$		−	30.1545i		−	1.55510i
$377$		−	8.43460i		−	0.434404i
$378$	−33.1565	−	10.5858i	−1.70539	−	0.544474i
$379$	−5.00587			−0.257134			−0.128567	−	0.991701i	$-0.541038\pi$
$379$	−5.00587			−0.257134			−0.128567	+	0.991701i	$0.541038\pi$
$380$	44.4613	−	26.4483i	2.28081	−	1.35677i
$381$	2.70685	−	15.0499i	0.138676	−	0.771030i
$382$			5.00111i			0.255879i
$383$	−19.9749	+	11.5325i	−1.02067	+	0.589284i	−0.914298	−	0.405043i	$-0.867257\pi$
$383$	−19.9749	+	11.5325i	−1.02067	+	0.589284i	−0.106372	+	0.994326i	$0.533923\pi$
$384$	22.8148	+	4.10343i	1.16426	+	0.209403i
$385$	−6.10061	+	5.81535i	−0.310916	+	0.296378i
$386$			41.9677i			2.13610i
$387$	12.6643	−	2.14377i	0.643764	−	0.108974i
$388$	−20.7003	−	35.8539i	−1.05090	−	1.82021i
$389$	14.5687	+	8.41123i	0.738661	+	0.426466i	0.821582	−	0.570090i	$-0.193092\pi$
$389$	14.5687	+	8.41123i	0.738661	+	0.426466i	−0.0829213	+	0.996556i	$0.526425\pi$
$390$	14.3701	+	38.3312i	0.727659	+	1.94098i
$391$	2.04175	+	1.17880i	0.103256	+	0.0596146i
$392$	−38.4580	+	18.5612i	−1.94242	+	0.937481i
$393$	−1.29729	−	3.60260i	−0.0654397	−	0.181727i
$394$	−62.2611			−3.13667
$395$	−0.494158	+	0.882268i	−0.0248638	+	0.0443917i
$396$	12.0150	+	14.5196i	0.603776	+	0.729639i
$397$	−13.0997	+	22.6893i	−0.657453	+	1.13874i	0.323820	+	0.946119i	$0.395033\pi$
$397$	−13.0997	+	22.6893i	−0.657453	+	1.13874i	−0.981273	+	0.192623i	$0.938301\pi$
$398$	−1.58827	+	0.916987i	−0.0796127	+	0.0459644i
$399$	−21.3626	−	11.0328i	−1.06947	−	0.552332i
$400$	−17.3055	−	28.2470i	−0.865273	−	1.41235i
$401$	31.4306	−	18.1465i	1.56957	−	0.906192i	0.573352	−	0.819309i	$-0.305643\pi$
$401$	31.4306	−	18.1465i	1.56957	−	0.906192i	0.996219	−	0.0868828i	$-0.0276906\pi$
$402$	1.84990	−	10.2853i	0.0922645	−	0.512983i
$403$	−38.4858	−	22.2198i	−1.91711	−	1.10685i
$404$	40.6819	−	70.4631i	2.02400	−	3.50567i
$405$	−18.9155	+	6.87058i	−0.939917	+	0.341402i
$406$	9.91612	−	9.20876i	0.492129	−	0.457023i
$407$	5.78460	+	10.0192i	0.286732	+	0.496634i
$408$	−49.0641	+	17.6679i	−2.42903	+	0.874691i
$409$		−	2.42575i		−	0.119945i	−0.998200	−	0.0599727i	$-0.980899\pi$
$409$		−	2.42575i		−	0.119945i	0.998200	−	0.0599727i	$-0.0191014\pi$
$410$	−2.43720	−	4.09708i	−0.120365	−	0.202340i
$411$	5.40574	−	6.39770i	0.266645	−	0.315575i
$412$	−41.2076	−	71.3736i	−2.03015	−	3.51633i
$413$	0.522175	−	0.119420i	0.0256946	−	0.00587626i
$414$	−0.605548	−	3.57728i	−0.0297611	−	0.175813i
$415$	−0.358497	−	27.5021i	−0.0175979	−	1.35003i
$416$	9.54516	−	16.5327i	0.467990	−	0.810582i
$417$	1.65295	+	1.39666i	0.0809455	+	0.0683949i
$418$	9.46183	+	16.3884i	0.462793	+	0.801582i
$419$	7.51552	−	13.0173i	0.367157	−	0.635935i	−0.621963	−	0.783047i	$-0.713664\pi$
$419$	7.51552	−	13.0173i	0.367157	−	0.635935i	0.989120	+	0.147112i	$0.0469978\pi$
$420$	−20.2090	+	40.4137i	−0.986099	+	1.97199i
$421$	11.1388	+	19.2929i	0.542871	+	0.940281i	0.998738	+	0.0502323i	$0.0159962\pi$
$421$	11.1388	+	19.2929i	0.542871	+	0.940281i	−0.455866	+	0.890048i	$0.650671\pi$
$422$	−14.7843	+	25.6071i	−0.719687	+	1.24653i
$423$	−5.16714	+	13.8998i	−0.251235	+	0.675829i
$424$	14.2214	+	24.6321i	0.690650	+	1.19624i
$425$	−21.6852	−	11.7772i	−1.05188	−	0.571278i
$426$	−9.10218	+	50.6074i	−0.441002	+	2.45194i
$427$	−1.05210	−	4.60044i	−0.0509149	−	0.222631i
$428$	1.94389	−	3.36691i	0.0939614	−	0.162746i
$429$	−9.69253	+	3.49027i	−0.467960	+	0.168512i
$430$	−0.315921	−	24.2359i	−0.0152351	−	1.16876i
$431$	16.8829	−	9.74735i	0.813221	−	0.469514i	−0.0348520	−	0.999392i	$-0.511096\pi$
$431$	16.8829	−	9.74735i	0.813221	−	0.469514i	0.848073	+	0.529879i	$0.177763\pi$
$432$	29.6356	+	17.5183i	1.42584	+	0.842851i
$433$	16.9416			0.814161			0.407080	−	0.913392i	$-0.366547\pi$
$433$	16.9416			0.814161			0.407080	+	0.913392i	$0.366547\pi$
$434$	−15.8955	−	69.5050i	−0.763010	−	3.33634i
$435$	1.28460	−	7.71843i	0.0615920	−	0.370070i
$436$	9.56983	+	16.5754i	0.458312	+	0.793819i
$437$		−	2.50632i		−	0.119893i
$438$	13.4429	+	37.3311i	0.642326	+	1.78375i
$439$			1.65776i			0.0791207i	0.999217	+	0.0395604i	$0.0125957\pi$
$439$			1.65776i			0.0791207i	−0.999217	+	0.0395604i	$0.987404\pi$
$440$	16.7017	−	9.93523i	0.796223	−	0.473643i
$441$	20.9078	−	1.96582i	0.995609	−	0.0936106i
$442$		−	52.1655i		−	2.48126i
$443$	−36.0899			−1.71468			−0.857341	−	0.514749i	$-0.827885\pi$
$443$	−36.0899			−1.71468			−0.857341	+	0.514749i	$0.827885\pi$
$444$	47.3762	+	40.0305i	2.24837	+	1.89976i
$445$	−3.04239	−	5.11444i	−0.144223	−	0.242448i
$446$	−33.5070	−	58.0359i	−1.58660	−	2.74808i
$447$	5.61206	−	2.02089i	0.265441	−	0.0955850i
$448$	−4.31766	+	0.987434i	−0.203990	+	0.0466519i
$449$			26.4059i			1.24617i	0.782154	+	0.623086i	$0.214121\pi$
$449$			26.4059i			1.24617i	−0.782154	+	0.623086i	$0.785879\pi$
$450$	7.31207	+	37.2652i	0.344694	+	1.75670i
$451$	1.03895	−	0.599840i	0.0489224	−	0.0282454i
$452$	−20.3044	+	35.1683i	−0.955039	+	1.65418i
$453$	19.0300	−	22.5221i	0.894108	−	1.05818i
$454$	16.9975	+	9.81354i	0.797734	+	0.460572i
$455$	−17.0420	−	17.8779i	−0.798939	−	0.838130i
$456$	42.3455	+	35.7798i	1.98301	+	1.67554i
$457$			31.7898i			1.48706i	0.668700	+	0.743532i	$0.266851\pi$
$457$			31.7898i			1.48706i	−0.668700	+	0.743532i	$0.733149\pi$
$458$	40.6229	−	23.4536i	1.89818	−	1.09592i
$459$	25.6436	+	0.263351i	1.19694	+	0.0122922i
$460$	−4.70974	+	0.0613927i	−0.219593	+	0.00286245i
$461$	−5.79487	−	10.0370i	−0.269894	−	0.467470i	0.698940	−	0.715180i	$-0.253655\pi$
$461$	−5.79487	−	10.0370i	−0.269894	−	0.467470i	−0.968834	+	0.247710i	$0.920322\pi$
$462$	−14.6855	−	7.58439i	−0.683230	−	0.352858i
$463$	−25.9642	−	14.9904i	−1.20666	−	0.696664i	−0.244630	−	0.969616i	$-0.578667\pi$
$463$	−25.9642	−	14.9904i	−1.20666	−	0.696664i	−0.962028	+	0.272952i	$0.912000\pi$
$464$	−11.5919	+	6.69257i	−0.538139	+	0.310695i
$465$	−31.8339	−	26.1946i	−1.47626	−	1.21474i
$466$	−12.0399	+	20.8538i	−0.557739	+	0.966032i
$467$	2.17113	+	1.25350i	0.100468	+	0.0580052i	0.549392	−	0.835565i	$-0.314859\pi$
$467$	2.17113	+	1.25350i	0.100468	+	0.0580052i	−0.448924	+	0.893570i	$0.648193\pi$
$468$	−42.5500	+	35.2101i	−1.96687	+	1.62759i
$469$	1.40570	+	6.14657i	0.0649091	+	0.283822i
$470$	24.4143	+	13.6744i	1.12615	+	0.630755i
$471$	7.98079	+	1.43541i	0.367735	+	0.0661404i
$472$	−1.23508			−0.0568493
$473$	6.09959			0.280459
$474$	−1.95177	−	0.351042i	−0.0896476	−	0.0161239i
$475$	0.683804	+	26.2245i	0.0313751	+	1.20326i
$476$	42.1919	−	39.1822i	1.93386	−	1.79591i
$477$	−2.33451	−	13.7911i	−0.106890	−	0.631451i
$478$	44.6864	+	25.7997i	2.04391	+	1.18005i
$479$	−17.7777	+	30.7920i	−0.812286	+	1.40692i	0.0989748	+	0.995090i	$0.468444\pi$
$479$	−17.7777	+	30.7920i	−0.812286	+	1.40692i	−0.911261	+	0.411830i	$0.864890\pi$
$480$	11.2526	−	13.6752i	0.513611	−	0.624184i
$481$	−29.3614	+	16.9518i	−1.33877	+	0.772937i
$482$	19.8219	+	11.4442i	0.902862	+	0.521267i
$483$	1.18217	+	1.84242i	0.0537904	+	0.0838332i
$484$	−19.7779	−	34.2564i	−0.898996	−	1.55711i
$485$	20.9921	−	0.273637i	0.953201	−	0.0124252i
$486$	−24.8468	−	30.6621i	−1.12708	−	1.39086i
$487$	15.4460	−	8.91776i	0.699926	−	0.404102i	−0.107394	−	0.994217i	$-0.534251\pi$
$487$	15.4460	−	8.91776i	0.699926	−	0.404102i	0.807320	+	0.590114i	$0.200917\pi$
$488$			10.8813i			0.492572i
$489$	−21.3207	−	18.0149i	−0.964157	−	0.814664i
$490$	2.41200	−	39.5542i	0.108963	−	1.78688i
$491$	−6.13294	−	3.54085i	−0.276776	−	0.159796i	0.355187	−	0.934795i	$-0.384417\pi$
$491$	−6.13294	−	3.54085i	−0.276776	−	0.159796i	−0.631963	+	0.774999i	$0.717750\pi$
$492$	4.15100	−	4.91272i	0.187142	−	0.221483i
$493$	−4.98548	+	8.63510i	−0.224535	+	0.388905i
$494$	−48.0263	+	27.7280i	−2.16081	+	1.24754i
$495$	−9.40113	+	1.71772i	−0.422549	+	0.0772060i
$496$			70.5226i			3.16656i
$497$	−6.91655	−	30.2434i	−0.310250	−	1.35660i
$498$	50.7479	−	18.2742i	2.27407	−	0.818888i
$499$	−11.4852	−	19.8930i	−0.514149	−	0.890533i	−0.999865	−	0.0164161i	$-0.994774\pi$
$499$	−11.4852	−	19.8930i	−0.514149	−	0.890533i	0.485716	−	0.874117i	$-0.338559\pi$
$500$	49.2630	−	1.92734i	2.20311	−	0.0861934i
$501$	−15.0299	−	12.6995i	−0.671485	−	0.567371i
$502$	12.1882			0.543987
$503$			5.23692i			0.233503i	0.993161	+	0.116751i	$0.0372481\pi$
$503$			5.23692i			0.233503i	−0.993161	+	0.116751i	$0.962752\pi$
$504$	−48.0051	−	6.32890i	−2.13832	−	0.281911i
$505$	21.0934	+	35.4593i	0.938645	+	1.57792i
$506$		−	1.72294i		−	0.0765941i
$507$	−2.59959	−	7.21910i	−0.115452	−	0.320611i
$508$		−	38.9300i		−	1.72724i
$509$	−4.85855	−	8.41525i	−0.215351	−	0.373000i	0.738030	−	0.674768i	$-0.235756\pi$
$509$	−4.85855	−	8.41525i	−0.215351	−	0.373000i	−0.953381	+	0.301769i	$0.902423\pi$
$510$	7.94489	−	47.7362i	0.351806	−	2.11379i
$511$	−16.2907	−	17.5421i	−0.720660	−	0.776017i
$512$	50.5392			2.23354
$513$	−13.3881	−	23.7488i	−0.591100	−	1.04854i
$514$	0.578131	−	0.333784i	0.0255003	−	0.0147226i
$515$	41.7885	−	0.544724i	1.84142	−	0.0240034i
$516$	30.7666	−	11.0790i	1.35442	−	0.487725i
$517$	−3.52102	+	6.09859i	−0.154854	+	0.268216i
$518$	−51.9858	−	16.0110i	−2.28412	−	0.703482i
$519$	−4.15712	+	23.1133i	−0.182477	+	1.01456i
$520$	29.1153	+	48.9446i	1.27679	+	2.14636i
$521$	2.77492	+	4.80630i	0.121571	+	0.210568i	0.920387	−	0.391007i	$-0.127873\pi$
$521$	2.77492	+	4.80630i	0.121571	+	0.210568i	−0.798816	+	0.601575i	$0.794540\pi$
$522$	15.1293	−	2.56103i	0.662190	−	0.112093i
$523$	−3.79740	+	6.57728i	−0.166049	+	0.287605i	−0.937027	−	0.349257i	$-0.886434\pi$
$523$	−3.79740	+	6.57728i	−0.166049	+	0.287605i	0.770979	+	0.636861i	$0.219768\pi$
$524$	−4.87417	−	8.44230i	−0.212929	−	0.368804i
$525$	−12.8721	−	18.9554i	−0.561785	−	0.827283i
$526$	−11.8752	+	20.5685i	−0.517784	+	0.896827i
$527$	26.2671	+	45.4959i	1.14421	+	1.98183i
$528$	12.4875	+	10.5513i	0.543447	+	0.459185i
$529$	11.3859	−	19.7210i	0.495039	−	0.857433i
$530$	−26.3922	+	0.344029i	−1.14640	+	0.0149437i
$531$	0.569313	+	0.211638i	0.0247061	+	0.00918430i
$532$	−58.4998	−	18.0172i	−2.53629	−	0.781145i
$533$	1.75784	+	3.04467i	0.0761405	+	0.131879i
$534$	7.53198	−	8.91411i	0.325940	−	0.385751i
$535$	1.00790	+	1.69434i	0.0435753	+	0.0732527i
$536$		−	14.5383i		−	0.627957i
$537$	−1.46274	+	0.526729i	−0.0631218	+	0.0227301i
$538$	−14.8202	−	25.6694i	−0.638945	−	1.10668i
$539$	9.94522	+	0.736681i	0.428371	+	0.0317311i
$540$	−44.2997	+	25.7400i	−1.90635	+	1.10767i
$541$	−16.8986	+	29.2693i	−0.726530	+	1.25839i	0.231812	+	0.972761i	$0.425535\pi$
$541$	−16.8986	+	29.2693i	−0.726530	+	1.25839i	−0.958341	+	0.285626i	$0.907799\pi$
$542$	−24.4881	−	14.1382i	−1.05185	−	0.607288i
$543$	−4.13254	+	22.9766i	−0.177344	+	0.986021i
$544$	−19.5441	+	11.2838i	−0.837947	+	0.483789i
$545$	−9.70474	+	0.126504i	−0.415705	+	0.00541883i
$546$	22.2261	−	43.0360i	0.951191	−	1.84177i
$547$	14.5277	−	8.38754i	0.621158	−	0.358626i	−0.156162	−	0.987731i	$-0.549912\pi$
$547$	14.5277	−	8.38754i	0.621158	−	0.358626i	0.777320	+	0.629106i	$0.216579\pi$
$548$	10.6618	−	18.4667i	0.455449	−	0.788860i
$549$	1.86456	−	5.01573i	0.0795776	−	0.214066i
$550$	0.470074	+	18.0278i	0.0200440	+	0.768707i
$551$	10.5999			0.451571
$552$	−1.71008	−	4.74891i	−0.0727857	−	0.202127i
$553$	1.16639	−	0.266749i	0.0496000	−	0.0113433i
$554$	21.9986	+	12.7009i	0.934631	+	0.539609i
$555$	−29.4502	+	11.0407i	−1.25009	+	0.468651i
$556$	4.77119	+	2.75465i	0.202344	+	0.116823i
$557$	−3.36711	−	5.83201i	−0.142669	−	0.247110i	0.785832	−	0.618440i	$-0.212235\pi$
$557$	−3.36711	−	5.83201i	−0.142669	−	0.247110i	−0.928501	+	0.371330i	$0.878902\pi$
$558$	28.1704	−	75.7793i	1.19255	−	3.20799i
$559$			17.8749i			0.756028i
$560$	−11.0478	+	37.6067i	−0.466856	+	1.58917i
$561$	11.9859	+	2.15578i	0.506047	+	0.0910169i
$562$	28.6170	−	16.5220i	1.20713	−	0.696939i
$563$			45.8890i			1.93399i	0.254795	+	0.966995i	$0.417992\pi$
$563$			45.8890i			1.93399i	−0.254795	+	0.966995i	$0.582008\pi$
$564$	−6.68299	+	37.1569i	−0.281405	+	1.56459i
$565$	−10.5278	−	17.6978i	−0.442906	−	0.744553i
$566$	−33.7728			−1.41958
$567$	21.0435	+	11.1432i	0.883744	+	0.467972i
$568$			71.5336i			3.00148i
$569$			25.9763i			1.08898i	0.838767	+	0.544491i	$0.183277\pi$
$569$			25.9763i			1.08898i	−0.838767	+	0.544491i	$0.816723\pi$
$570$	−48.1715	+	18.0592i	−2.01768	+	0.756416i
$571$	−27.1543			−1.13637			−0.568187	−	0.822900i	$-0.692355\pi$
$571$	−27.1543			−1.13637			−0.568187	+	0.822900i	$0.692355\pi$
$572$	−22.7134	+	13.1136i	−0.949694	+	0.548306i
$573$	0.605661	−	3.36743i	0.0253019	−	0.140676i
$574$	−1.66028	+	5.39072i	−0.0692986	+	0.225004i
$575$	1.13991	−	2.09891i	0.0475377	−	0.0875304i
$576$	−4.70742	−	1.74995i	−0.196143	−	0.0729146i
$577$	−6.23651	−	10.8020i	−0.259629	−	0.449691i	0.706513	−	0.707700i	$-0.250267\pi$
$577$	−6.23651	−	10.8020i	−0.259629	−	0.449691i	−0.966143	+	0.258008i	$0.916934\pi$
$578$	−9.31411	+	16.1325i	−0.387416	+	0.671024i
$579$	5.08251	−	28.2584i	0.211222	−	1.17438i
$580$	−0.259647	−	19.9188i	−0.0107812	−	0.827083i
$581$	−23.8467	+	22.1456i	−0.989328	+	0.918755i
$582$	13.9485	+	38.7353i	0.578185	+	1.60563i
$583$		−	6.64228i		−	0.275095i
$584$	27.5994	+	47.8036i	1.14207	+	1.97813i
$585$	−5.03381	−	27.5501i	−0.208122	−	1.13906i
$586$	−10.0697	−	5.81373i	−0.415974	−	0.240163i
$587$	14.4358	−	8.33452i	0.595830	−	0.344002i	−0.171569	−	0.985172i	$-0.554884\pi$
$587$	14.4358	−	8.33452i	0.595830	−	0.344002i	0.767399	+	0.641170i	$0.221550\pi$
$588$	51.5022	−	14.3482i	2.12391	−	0.591708i
$589$	27.9240	−	48.3657i	1.15059	−	1.99288i
$590$	0.560084	−	0.999972i	0.0230583	−	0.0411682i
$591$	41.9227	+	7.54015i	1.72447	+	0.310160i
$592$	46.5947	+	26.9014i	1.91503	+	1.10564i
$593$	0.329806	+	0.190413i	0.0135435	+	0.00781934i	0.506756	−	0.862089i	$-0.330844\pi$
$593$	0.329806	+	0.190413i	0.0135435	+	0.00781934i	−0.493213	+	0.869909i	$0.664178\pi$
$594$	−9.20353	−	16.3259i	−0.377625	−	0.669859i
$595$	6.87988	+	28.3760i	0.282048	+	1.16330i
$596$	13.1512	−	7.59287i	0.538696	−	0.311016i
$597$	1.18049	−	0.425093i	0.0483143	−	0.0173979i
$598$	5.04910			0.206473
$599$			21.0025i			0.858137i	0.903272	+	0.429069i	$0.141158\pi$
$599$			21.0025i			0.858137i	−0.903272	+	0.429069i	$0.858842\pi$
$600$	19.1888	+	49.2231i	0.783380	+	2.00952i
$601$	−3.49714	+	2.01907i	−0.142651	+	0.0823597i	−0.569627	−	0.821903i	$-0.692912\pi$
$601$	−3.49714	+	2.01907i	−0.142651	+	0.0823597i	0.426976	+	0.904263i	$0.359579\pi$
$602$	−21.0146	+	19.5155i	−0.856491	+	0.795394i
$603$	−2.49121	+	6.70143i	−0.101450	+	0.272903i
$604$	37.5331	−	65.0092i	1.52720	−	2.64519i
$605$	20.0567	−	0.261445i	0.815422	−	0.0106292i
$606$	−52.2205	+	61.8031i	−2.12131	+	2.51058i
$607$	8.88367	+	15.3870i	0.360577	+	0.624538i	0.988056	−	0.154096i	$-0.0492465\pi$
$607$	8.88367	+	15.3870i	0.360577	+	0.624538i	−0.627479	+	0.778634i	$0.715913\pi$
$608$	20.7769	+	11.9956i	0.842615	+	0.486484i
$609$	−7.79212	+	4.99970i	−0.315753	+	0.202598i
$610$	−8.80990	−	4.93442i	−0.356702	−	0.199789i
$611$	−17.8720	−	10.3184i	−0.723023	−	0.417437i
$612$	64.3732	−	10.8969i	2.60213	−	0.440480i
$613$	12.3044	−	7.10394i	0.496969	−	0.286925i	−0.230492	−	0.973074i	$-0.574034\pi$
$613$	12.3044	−	7.10394i	0.496969	−	0.286925i	0.727461	+	0.686149i	$0.240700\pi$
$614$	52.1881			2.10614
$615$	1.14488	+	3.05387i	0.0461659	+	0.123144i
$616$	−21.9752	−	6.76811i	−0.885408	−	0.272695i
$617$	16.5509	−	28.6670i	0.666314	−	1.15409i	−0.312614	−	0.949880i	$-0.601205\pi$
$617$	16.5509	−	28.6670i	0.666314	−	1.15409i	0.978927	−	0.204209i	$-0.0654622\pi$
$618$	27.7670	+	77.1096i	1.11695	+	3.10180i
$619$	35.6504	+	20.5828i	1.43291	+	0.827291i	0.997342	−	0.0728641i	$-0.0232139\pi$
$619$	35.6504	+	20.5828i	1.43291	+	0.827291i	0.435569	+	0.900155i	$0.356547\pi$
$620$	−91.5704	−	51.2886i	−3.67756	−	2.05980i
$621$	−0.0254898	+	2.48205i	−0.00102287	+	0.0996010i
$622$	29.2701			1.17362
$623$	−2.07254	+	6.72931i	−0.0830348	+	0.269604i
$624$	−30.9206	+	36.5946i	−1.23782	+	1.46496i
$625$	−11.3547	+	22.2726i	−0.454188	+	0.890906i
$626$	−73.5222			−2.93854
$627$	−4.38628	−	12.1808i	−0.175171	−	0.486453i
$628$	20.6441			0.823791
$629$	40.0792			1.59806
$630$	26.8934	−	35.9968i	1.07146	−	1.43415i
$631$	10.0626			0.400586			0.200293	−	0.979736i	$-0.435811\pi$
$631$	10.0626			0.400586			0.200293	+	0.979736i	$0.435811\pi$
$632$	−2.75882			−0.109740
$633$	13.0559	−	15.4517i	0.518927	−	0.614151i
$634$	54.9015			2.18042
$635$	17.2235	+	9.64687i	0.683493	+	0.382824i
$636$	−12.0647	−	33.5039i	−0.478397	−	1.32852i
$637$	−2.15885	+	29.1446i	−0.0855369	+	1.15475i
$638$	7.28679			0.288487
$639$	12.2577	−	32.9735i	0.484905	−	1.30441i
$640$	−14.6241	+	26.1098i	−0.578068	+	1.03208i
$641$	−33.9181	−	19.5826i	−1.33968	−	0.773466i	−0.352923	−	0.935652i	$-0.614812\pi$
$641$	−33.9181	−	19.5826i	−1.33968	−	0.773466i	−0.986760	+	0.162186i	$0.948145\pi$
$642$	−2.49524	+	2.95312i	−0.0984791	+	0.116550i
$643$	7.40682	−	12.8290i	0.292097	−	0.505926i	−0.682209	−	0.731157i	$-0.738980\pi$
$643$	7.40682	−	12.8290i	0.292097	−	0.505926i	0.974305	+	0.225231i	$0.0723138\pi$
$644$	3.79244	+	4.08375i	0.149443	+	0.160922i
$645$	−2.72238	+	16.3572i	−0.107193	+	0.644063i
$646$	65.5573			2.57932
$647$	−23.0628	+	13.3153i	−0.906691	+	0.523478i	−0.879365	−	0.476148i	$-0.842033\pi$
$647$	−23.0628	+	13.3153i	−0.906691	+	0.523478i	−0.0273261	+	0.999627i	$0.508699\pi$
$648$	−41.5715	−	35.8639i	−1.63308	−	1.40887i
$649$	0.249789	+	0.144216i	0.00980506	+	0.00566096i
$650$	−52.8306	+	1.37756i	−2.07219	+	0.0540322i
$651$	2.28562	+	48.7253i	0.0895804	+	1.90969i
$652$	−61.5415	−	35.5310i	−2.41015	−	1.39150i
$653$	10.6651	+	18.4725i	0.417358	+	0.722885i	0.995673	−	0.0929286i	$-0.0296228\pi$
$653$	10.6651	+	18.4725i	0.417358	+	0.722885i	−0.578315	+	0.815814i	$0.696289\pi$
$654$	−6.44847	−	17.9075i	−0.252155	−	0.700240i
$655$	4.94288	−	0.0644317i	0.193134	−	0.00251756i
$656$	2.78957	−	4.83168i	0.108915	−	0.188646i
$657$	−4.53058	−	26.7644i	−0.176755	−	1.04418i
$658$	−7.38155	−	32.2766i	−0.287763	−	1.25827i
$659$	−3.91124	+	2.25816i	−0.152360	+	0.0879653i	−0.574242	−	0.818686i	$-0.694703\pi$
$659$	−3.91124	+	2.25816i	−0.152360	+	0.0879653i	0.421882	+	0.906651i	$0.361370\pi$
$660$	−22.7820	+	8.54083i	−0.886789	+	0.332452i
$661$			33.8778i			1.31770i	0.752276	+	0.658848i	$0.228956\pi$
$661$			33.8778i			1.31770i	−0.752276	+	0.658848i	$0.771044\pi$
$662$	−15.0698			−0.585703
$663$	−6.31752	+	35.1249i	−0.245352	+	1.36414i
$664$	64.9842	−	37.5186i	2.52187	−	1.45601i
$665$	22.4675	−	21.4169i	0.871251	−	0.830512i
$666$	−39.3219	−	47.5190i	−1.52369	−	1.84132i
$667$	−0.835791	−	0.482544i	−0.0323620	−	0.0186842i
$668$	−43.3832	−	25.0473i	−1.67855	−	0.969109i
$669$	15.5331	+	43.1356i	0.600543	+	1.66772i
$670$	11.7707	+	6.59279i	0.454744	+	0.254702i
$671$	1.27056	−	2.20068i	0.0490495	−	0.0849561i
$672$	−20.9314	+	0.981854i	−0.807445	+	0.0378758i
$673$	−0.00944408	+	0.00545254i	−0.000364043	+	0.000210180i	−0.500182	−	0.865920i	$-0.666734\pi$
$673$	−0.00944408	+	0.00545254i	−0.000364043	+	0.000210180i	0.499818	+	0.866130i	$0.333400\pi$
$674$	−6.15542	−	3.55384i	−0.237098	−	0.136889i
$675$	−0.410472	−	25.9775i	−0.0157991	−	0.999875i
$676$	−9.76712	−	16.9172i	−0.375659	−	0.650660i
$677$			35.1941i			1.35262i	0.736618	+	0.676309i	$0.236422\pi$
$677$			35.1941i			1.35262i	−0.736618	+	0.676309i	$0.763578\pi$
$678$	26.0634	−	30.8461i	1.00096	−	1.18464i
$679$	−16.9035	−	18.2019i	−0.648697	−	0.698526i
$680$	−0.877499	−	67.3174i	−0.0336506	−	2.58150i
$681$	−10.2566	−	8.66631i	−0.393034	−	0.332094i
$682$	19.1960	−	33.2485i	0.735054	−	1.27315i
$683$	−13.2893	−	23.0177i	−0.508499	−	0.880746i	−0.999952	−	0.00984199i	$-0.996867\pi$
$683$	−13.2893	−	23.0177i	−0.508499	−	0.880746i	0.491452	−	0.870904i	$-0.336466\pi$
$684$	−44.2491	−	53.4733i	−1.69191	−	2.04460i
$685$	5.52810	+	9.29307i	0.211218	+	0.355070i
$686$	−36.6208	+	29.2815i	−1.39819	+	1.11797i
$687$	−30.1932	+	10.8725i	−1.15194	+	0.414813i
$688$	24.5659	−	14.1831i	0.936567	−	0.540727i
$689$	19.4653			0.741568
$690$	4.62039	+	0.768986i	0.175895	+	0.0292748i
$691$			3.28870i			0.125108i	0.998042	+	0.0625540i	$0.0199246\pi$
$691$			3.28870i			0.125108i	−0.998042	+	0.0625540i	$0.980075\pi$
$692$			59.7878i			2.27279i
$693$	8.96976	+	6.88534i	0.340733	+	0.261552i
$694$	−25.0419			−0.950578
$695$	−2.40102	+	1.42828i	−0.0910759	+	0.0541776i
$696$	20.0844	−	7.23238i	0.761299	−	0.274143i
$697$		−	4.15606i		−	0.157422i
$698$	−0.708042	+	0.408788i	−0.0267998	+	0.0154729i
$699$	10.6324	−	12.5835i	0.402155	−	0.475952i
$700$	−40.7959	−	41.6951i	−1.54194	−	1.57593i
$701$		−	39.7933i		−	1.50297i	−0.659749	−	0.751486i	$-0.729337\pi$
$701$		−	39.7933i		−	1.50297i	0.659749	−	0.751486i	$-0.270663\pi$
$702$	47.8432	−	26.9710i	1.80573	−	1.01796i
$703$	−21.3037	−	36.8990i	−0.803483	−	1.39167i
$704$	−2.06540	−	1.19246i	−0.0778428	−	0.0449426i
$705$	−14.7830	−	12.1642i	−0.556759	−	0.458130i
$706$	−37.4621	−	21.6288i	−1.40991	−	0.814009i
$707$	14.3693	−	46.6555i	0.540414	−	1.75466i
$708$	1.52189	+	0.273725i	0.0571961	+	0.0102872i
$709$	−3.08929			−0.116021			−0.0580103	−	0.998316i	$-0.518476\pi$
$709$	−3.08929			−0.116021			−0.0580103	+	0.998316i	$0.518476\pi$
$710$	−57.9164	−	32.4390i	−2.17356	−	1.21741i
$711$	1.27168	+	0.472739i	0.0476918	+	0.0177291i
$712$	8.11762	−	14.0601i	0.304221	−	0.526926i
$713$	−4.40355	+	2.54239i	−0.164914	+	0.0952133i
$714$	−48.1919	+	30.9217i	−1.80354	+	1.15721i
$715$	−0.173349	−	13.2984i	−0.00648287	−	0.497333i
$716$	−3.42776	+	1.97902i	−0.128101	+	0.0739594i
$717$	−26.9645	−	22.7837i	−1.00701	−	0.850872i
$718$	43.5931	+	25.1685i	1.62688	+	0.939279i
$719$	10.5791	−	18.3235i	0.394532	−	0.683350i	−0.598509	−	0.801116i	$-0.704240\pi$
$719$	10.5791	−	18.3235i	0.394532	−	0.683350i	0.993041	+	0.117766i	$0.0375734\pi$
$720$	−33.8686	+	28.7782i	−1.26221	+	1.07250i
$721$	−33.6495	−	36.2342i	−1.25317	−	1.34943i
$722$	−10.7949	−	18.6974i	−0.401746	−	0.695844i
$723$	−11.9608	−	10.1063i	−0.444829	−	0.375858i
$724$			59.4343i			2.20886i
$725$	8.87685	+	4.82101i	0.329678	+	0.179048i
$726$	13.3270	+	37.0094i	0.494612	+	1.37355i
$727$	4.31669	+	7.47672i	0.160097	+	0.277296i	0.934903	−	0.354903i	$-0.115486\pi$
$727$	4.31669	+	7.47672i	0.160097	+	0.277296i	−0.774806	+	0.632199i	$0.782153\pi$
$728$	19.8340	−	64.3987i	0.735097	−	2.38677i
$729$	13.0169	+	23.6550i	0.482109	+	0.876111i
$730$	−51.2194	+	0.667659i	−1.89572	+	0.0247112i
$731$	10.5654	−	18.2998i	0.390776	−	0.676843i
$732$	2.41156	−	13.4081i	0.0891338	−	0.495577i
$733$	−2.57990	−	4.46851i	−0.0952907	−	0.165048i	0.814439	−	0.580249i	$-0.197045\pi$
$733$	−2.57990	−	4.46851i	−0.0952907	−	0.165048i	−0.909730	+	0.415201i	$0.863711\pi$
$734$	−39.7076	+	68.7756i	−1.46564	+	2.53855i
$735$	−6.41431	+	26.3412i	−0.236596	+	0.971608i
$736$	−1.09216	−	1.89167i	−0.0402575	−	0.0697280i
$737$	−1.69757	+	2.94028i	−0.0625309	+	0.108307i
$738$	−4.92753	+	4.07753i	−0.181385	+	0.150096i
$739$	−7.92896	−	13.7334i	−0.291671	−	0.505190i	0.682534	−	0.730854i	$-0.260878\pi$
$739$	−7.92896	−	13.7334i	−0.291671	−	0.505190i	−0.974205	+	0.225664i	$0.927545\pi$
$740$	−68.8169	+	40.9366i	−2.52976	+	1.50486i
$741$	35.6959	−	12.8540i	1.31132	−	0.472205i
$742$	21.2519	+	22.8843i	0.780181	+	0.840110i
$743$	−14.5897	+	25.2701i	−0.535243	+	0.927069i	0.463908	+	0.885883i	$0.346447\pi$
$743$	−14.5897	+	25.2701i	−0.535243	+	0.927069i	−0.999152	+	0.0411854i	$0.986887\pi$
$744$	19.9094	−	110.695i	0.729916	−	4.05827i
$745$	0.100370	+	7.69991i	0.00367729	+	0.282103i
$746$	56.1756	−	32.4330i	2.05674	−	1.18746i
$747$	−36.3835	+	6.15887i	−1.33120	+	0.225341i
$748$	31.0044			1.13363
$749$	0.686605	−	2.22932i	0.0250880	−	0.0814577i
$750$	−48.5546	−	6.78560i	−1.77296	−	0.247775i
$751$	13.9911	+	24.2333i	0.510543	+	0.884287i	0.999925	+	0.0122173i	$0.00388898\pi$
$751$	13.9911	+	24.2333i	0.510543	+	0.884287i	−0.489382	+	0.872069i	$0.662778\pi$
$752$			32.7492i			1.19424i
$753$	−8.20678	−	1.47606i	−0.299072	−	0.0537906i
$754$			21.3540i			0.777668i
$755$	19.4608	+	32.7147i	0.708250	+	1.19061i
$756$	57.7500	+	18.4377i	2.10035	+	0.670572i
$757$		−	12.4434i		−	0.452263i	−0.974097	−	0.226132i	$-0.927392\pi$
$757$		−	12.4434i		−	0.452263i	0.974097	−	0.226132i	$-0.0726079\pi$
$758$	12.6734			0.460320
$759$	−0.208657	+	1.16012i	−0.00757379	+	0.0421097i
$760$	−61.5095	+	36.5897i	−2.23118	+	1.32725i
$761$	−10.5154	−	18.2131i	−0.381181	−	0.660225i	0.610050	−	0.792363i	$-0.291149\pi$
$761$	−10.5154	−	18.2131i	−0.381181	−	0.660225i	−0.991231	+	0.132138i	$0.957816\pi$
$762$	−6.85299	+	38.1021i	−0.248258	+	1.38029i
$763$	7.81457	+	8.41484i	0.282907	+	0.304638i
$764$		−	8.71063i		−	0.315140i
$765$	−11.1307	+	31.1804i	−0.402431	+	1.12733i
$766$	50.5708	−	29.1971i	1.82720	−	1.05493i
$767$	−0.422625	+	0.732009i	−0.0152601	+	0.0264313i
$768$	−52.0530	−	9.36219i	−1.87830	−	0.337829i
$769$	−11.8574	−	6.84585i	−0.427588	−	0.246868i	0.270731	−	0.962655i	$-0.412735\pi$
$769$	−11.8574	−	6.84585i	−0.427588	−	0.246868i	−0.698318	+	0.715787i	$0.746068\pi$
$770$	15.4450	−	14.7228i	0.556600	−	0.530574i
$771$	−0.429700	+	0.154734i	−0.0154753	+	0.00557262i
$772$		−	73.0967i		−	2.63081i
$773$	0.308779	−	0.178273i	0.0111060	−	0.00641205i	−0.494437	−	0.869214i	$-0.664626\pi$
$773$	0.308779	−	0.178273i	0.0111060	−	0.00641205i	0.505543	+	0.862802i	$0.331292\pi$
$774$	−32.0625	+	5.42742i	−1.15246	+	0.195085i
$775$	45.3824	−	27.8034i	1.63018	−	0.998729i
$776$	28.6376	+	49.6017i	1.02803	+	1.78060i
$777$	33.0649	+	17.0765i	1.18620	+	0.612617i
$778$	−36.8838	−	21.2948i	−1.32235	−	0.763457i
$779$	−3.82628	+	2.20911i	−0.137091	+	0.0791494i
$780$	−25.0290	−	66.7630i	−0.896182	−	2.39050i
$781$	8.35268	−	14.4673i	0.298882	−	0.517680i
$782$	−5.16912	−	2.98439i	−0.184847	−	0.106722i
$783$	−10.4972	−	0.107803i	−0.375141	−	0.00385257i
$784$	41.7671	−	20.1583i	1.49168	−	0.719939i
$785$	−5.11562	+	9.13342i	−0.182584	+	0.325986i
$786$	3.28438	+	9.12077i	0.117150	+	0.325327i
$787$	10.5853			0.377324			0.188662	−	0.982042i	$-0.439585\pi$
$787$	10.5853			0.377324			0.188662	+	0.982042i	$0.439585\pi$
$788$	108.443			3.86311
$789$	10.4870	−	12.4113i	0.373346	−	0.441855i
$790$	1.25107	−	2.23365i	0.0445110	−	0.0794698i
$791$	−7.17176	+	23.2859i	−0.254998	+	0.827950i
$792$	−16.6220	−	20.0870i	−0.590638	−	0.713762i
$793$	6.44910	+	3.72339i	0.229014	+	0.132222i
$794$	33.1646	−	57.4428i	1.17697	−	2.03857i
$795$	17.8125	+	2.96459i	0.631744	+	0.105143i
$796$	2.76635	−	1.59715i	0.0980507	−	0.0566096i
$797$	−32.2113	−	18.5972i	−1.14098	−	0.658747i	−0.194309	−	0.980940i	$-0.562247\pi$
$797$	−32.2113	−	18.5972i	−1.14098	−	0.658747i	−0.946674	+	0.322193i	$0.895580\pi$
$798$	54.0840	+	27.9320i	1.91455	+	0.988781i
$799$	12.1979	+	21.1273i	0.431530	+	0.747432i
$800$	11.9438	+	19.4953i	0.422276	+	0.689264i
$801$	−6.15110	+	5.09003i	−0.217338	+	0.179847i
$802$	−79.5735	+	45.9418i	−2.80984	+	1.62226i
$803$		−	12.8907i		−	0.454902i
$804$	−3.22204	+	17.9143i	−0.113633	+	0.631788i
$805$	−2.74651	+	0.665903i	−0.0968017	+	0.0234700i
$806$	97.4351	+	56.2542i	3.43201	+	1.98147i
$807$	6.87029	+	19.0789i	0.241846	+	0.671610i
$808$	−56.2809	+	97.4814i	−1.97996	+	3.42938i
$809$	−27.2837	+	15.7522i	−0.959243	+	0.553819i	−0.895940	−	0.444175i	$-0.853497\pi$
$809$	−27.2837	+	15.7522i	−0.959243	+	0.553819i	−0.0633032	+	0.997994i	$0.520164\pi$
$810$	47.8886	−	17.3944i	1.68263	−	0.611176i
$811$			1.59210i			0.0559062i	0.999609	+	0.0279531i	$0.00889891\pi$
$811$			1.59210i			0.0559062i	−0.999609	+	0.0279531i	$0.991101\pi$
$812$	−17.2713	+	16.0393i	−0.606104	+	0.562868i
$813$	14.7765	+	12.4854i	0.518235	+	0.437882i
$814$	−14.6450	−	25.3658i	−0.513306	−	0.889072i
$815$	30.9697	−	18.4227i	1.08482	−	0.645320i
$816$	53.2858	−	19.1881i	1.86538	−	0.671719i
$817$	−22.4637			−0.785905
$818$			6.14130i			0.214726i
$819$	−20.1776	+	26.2860i	−0.705061	+	0.918506i
$820$	4.24496	+	7.13604i	0.148241	+	0.249201i
$821$			25.4155i			0.887006i	0.896273	+	0.443503i	$0.146264\pi$
$821$			25.4155i			0.887006i	−0.896273	+	0.443503i	$0.853736\pi$
$822$	−13.6858	+	16.1972i	−0.477347	+	0.564941i
$823$			19.7366i			0.687973i	0.938975	+	0.343986i	$0.111777\pi$
$823$			19.7366i			0.687973i	−0.938975	+	0.343986i	$0.888223\pi$
$824$	57.0082	+	98.7411i	1.98597	+	3.43981i
$825$	1.86674	−	12.1957i	0.0649917	−	0.424599i
$826$	−1.32200	+	0.302337i	−0.0459983	+	0.0105196i
$827$	−11.0429			−0.383998			−0.191999	−	0.981395i	$-0.561497\pi$
$827$	−11.0429			−0.383998			−0.191999	+	0.981395i	$0.561497\pi$
$828$	1.05471	+	6.23068i	0.0366536	+	0.216531i
$829$	−18.4118	+	10.6300i	−0.639467	+	0.369196i	−0.784409	−	0.620244i	$-0.787034\pi$
$829$	−18.4118	+	10.6300i	−0.639467	+	0.369196i	0.144942	+	0.989440i	$0.453700\pi$
$830$	0.907614	+	69.6276i	0.0315037	+	2.41681i
$831$	−13.2743	−	11.2161i	−0.460481	−	0.389083i
$832$	3.49452	−	6.05269i	0.121151	−	0.209839i
$833$	19.4368	−	28.5613i	0.673445	−	0.989592i
$834$	−4.18481	−	3.53596i	−0.144908	−	0.122440i
$835$	21.8318	−	12.9869i	0.755522	−	0.449432i
$836$	−16.4800	−	28.5443i	−0.569974	−	0.987225i
$837$	−28.1454	+	47.6133i	−0.972848	+	1.64576i
$838$	−19.0272	+	32.9560i	−0.657283	+	1.13845i
$839$	−17.8301	−	30.8827i	−0.615564	−	1.06619i	−0.990285	−	0.139051i	$-0.955595\pi$
$839$	−17.8301	−	30.8827i	−0.615564	−	1.06619i	0.374721	−	0.927137i	$-0.377738\pi$
$840$	27.9580	−	55.9099i	0.964641	−	1.92908i
$841$	−12.4592	+	21.5799i	−0.429627	+	0.744136i
$842$	−28.2003	−	48.8443i	−0.971845	−	1.68328i
$843$	−21.2698	+	7.65921i	−0.732569	+	0.263797i
$844$	25.7503	−	44.6009i	0.886363	−	1.53523i
$845$	9.90481	−	0.129112i	0.340736	−	0.00444158i
$846$	13.0817	−	35.1903i	0.449759	−	1.20987i
$847$	−16.1503	−	17.3909i	−0.554932	−	0.597559i
$848$	−15.4450	−	26.7516i	−0.530385	−	0.918654i
$849$	22.7405	+	4.09007i	0.780451	+	0.140371i
$850$	54.9007	+	29.8165i	1.88308	+	1.02270i
$851$			3.87927i			0.132980i
$852$	15.8536	−	88.1449i	0.543136	−	3.01979i
$853$	12.0777	+	20.9192i	0.413534	+	0.716261i	0.995273	−	0.0971139i	$-0.0309611\pi$
$853$	12.0777	+	20.9192i	0.413534	+	0.716261i	−0.581740	+	0.813375i	$0.697628\pi$
$854$	2.66363	+	11.6470i	0.0911476	+	0.398553i
$855$	34.6227	−	6.32607i	1.18407	−	0.216347i
$856$	−2.68925	+	4.65792i	−0.0919167	+	0.159204i
$857$	46.6132	+	26.9122i	1.59228	+	0.919302i	0.992915	+	0.118824i	$0.0379123\pi$
$857$	46.6132	+	26.9122i	1.59228	+	0.919302i	0.599362	+	0.800478i	$0.295421\pi$
$858$	24.5388	−	8.83637i	0.837739	−	0.301669i
$859$	−14.8971	+	8.60083i	−0.508282	+	0.293457i	−0.732127	−	0.681168i	$-0.761472\pi$
$859$	−14.8971	+	8.60083i	−0.508282	+	0.293457i	0.223845	+	0.974625i	$0.428139\pi$
$860$	0.550253	+	42.2126i	0.0187635	+	1.43944i
$861$	1.77077	−	3.42870i	0.0603477	−	0.116850i
$862$	−42.7428	+	24.6775i	−1.45582	+	0.840521i
$863$	14.6092	−	25.3039i	0.497304	−	0.861356i	−0.502691	−	0.864466i	$-0.667657\pi$
$863$	14.6092	−	25.3039i	0.497304	−	0.861356i	0.999995	+	0.00310991i	$0.000989916\pi$
$864$	−20.4537	−	12.0907i	−0.695849	−	0.411334i
$865$	−26.4514	−	14.8154i	−0.899375	−	0.503740i
$866$	−42.8913			−1.45751
$867$	8.22527	−	9.73462i	0.279345	−	0.330605i
$868$	27.6859	+	121.060i	0.939720	+	4.10903i
$869$	0.557957	+	0.322137i	0.0189274	+	0.0109277i
$870$	−3.25225	+	19.5409i	−0.110262	+	0.662498i
$871$	−8.61653	−	4.97476i	−0.291960	−	0.168563i
$872$	−13.2393	−	22.9311i	−0.448339	−	0.776545i
$873$	−4.70100	−	27.7712i	−0.159105	−	0.939911i
$874$			6.34529i			0.214633i
$875$	28.5561	−	7.71693i	0.965371	−	0.260880i
$876$	−23.4140	−	65.0211i	−0.791086	−	2.19686i
$877$	−28.2956	+	16.3364i	−0.955473	+	0.551643i	−0.894777	−	0.446514i	$-0.852665\pi$
$877$	−28.2956	+	16.3364i	−0.955473	+	0.551643i	−0.0606963	+	0.998156i	$0.519332\pi$
$878$		−	4.19699i		−	0.141641i
$879$	6.07621	+	5.13409i	0.204945	+	0.173168i
$880$	−18.1388	+	10.7901i	−0.611460	+	0.363734i
$881$	−51.6741			−1.74094			−0.870472	−	0.492217i	$-0.836186\pi$
$881$	−51.6741			−1.74094			−0.870472	+	0.492217i	$0.836186\pi$
$882$	−52.9326	+	4.97691i	−1.78233	+	0.167581i
$883$			18.8576i			0.634610i	0.948324	+	0.317305i	$0.102778\pi$
$883$			18.8576i			0.634610i	−0.948324	+	0.317305i	$0.897222\pi$
$884$			90.8587i			3.05591i
$885$	−0.498227	+	0.605488i	−0.0167477	+	0.0203533i
$886$	91.3693			3.06961
$887$	−33.3082	+	19.2305i	−1.11838	+	0.645697i	−0.940987	−	0.338443i	$-0.890100\pi$
$887$	−33.3082	+	19.2305i	−1.11838	+	0.645697i	−0.177393	+	0.984140i	$0.556766\pi$
$888$	−65.5421	−	55.3798i	−2.19945	−	1.85842i
$889$	−5.20744	−	22.7701i	−0.174652	−	0.763685i
$890$	7.70246	+	12.9483i	0.258187	+	0.434028i
$891$	4.21992	+	12.1074i	0.141373	+	0.405614i
$892$	58.3605	+	101.083i	1.95406	+	3.38452i
$893$	12.9673	−	22.4600i	0.433934	−	0.751596i
$894$	−14.2081	+	5.11633i	−0.475192	+	0.171116i
$895$	−0.0261607	−	2.00692i	−0.000874456	−	0.0670839i
$896$	34.5182	−	7.89418i	1.15317	−	0.263726i
$897$	−3.39974	−	0.611473i	−0.113514	−	0.0204165i
$898$		−	66.8523i		−	2.23089i
$899$	−10.7525	−	18.6238i	−0.358615	−	0.621139i
$900$	−12.7357	−	64.9062i	−0.424524	−	2.16354i
$901$	−19.9280	−	11.5054i	−0.663897	−	0.383301i
$902$	−2.63034	+	1.51863i	−0.0875807	+	0.0505647i
$903$	16.5133	−	10.5955i	0.549529	−	0.352598i
$904$	28.0899	−	48.6532i	0.934257	−	1.61818i
$905$	−26.2950	−	14.7278i	−0.874076	−	0.489570i
$906$	−48.1786	+	57.0195i	−1.60063	+	1.89435i
$907$	5.68017	+	3.27945i	0.188607	+	0.108892i	0.591330	−	0.806430i	$-0.298603\pi$
$907$	5.68017	+	3.27945i	0.188607	+	0.108892i	−0.402723	+	0.915322i	$0.631936\pi$
$908$	−29.6053	−	17.0926i	−0.982486	−	0.567239i
$909$	42.6467	−	35.2901i	1.41450	−	1.17050i
$910$	43.1454	+	45.2618i	1.43026	+	1.50042i
$911$	40.3423	−	23.2916i	1.33660	−	0.771686i	0.350298	−	0.936638i	$-0.386080\pi$
$911$	40.3423	−	23.2916i	1.33660	−	0.771686i	0.986302	+	0.164952i	$0.0527469\pi$
$912$	−45.9891	−	38.8585i	−1.52285	−	1.28673i
$913$	−17.5236			−0.579946
$914$		−	80.4828i		−	2.66213i
$915$	5.33444	+	4.38945i	0.176351	+	0.145111i
$916$	−70.7544	+	40.8501i	−2.33779	+	1.34972i
$917$	−3.98017	−	4.28590i	−0.131437	−	0.141533i
$918$	−64.9224	−	0.666731i	−2.14276	−	0.0220054i
$919$	−25.8448	+	44.7644i	−0.852540	+	1.47664i	0.0263686	+	0.999652i	$0.491606\pi$
$919$	−25.8448	+	44.7644i	−0.852540	+	1.47664i	−0.878909	+	0.476990i	$0.841728\pi$
$920$	6.51565	−	0.0849332i	0.214814	−	0.00280016i
$921$	−35.1402	−	6.32027i	−1.15791	−	0.208260i
$922$	14.6710	+	25.4109i	0.483163	+	0.836863i
$923$	42.3965	+	24.4776i	1.39550	+	0.805691i
$924$	25.5783	+	13.2100i	0.841464	+	0.434578i
$925$	−1.05839	−	40.5902i	−0.0347996	−	1.33460i
$926$	65.7340	+	37.9515i	2.16015	+	1.24716i
$927$	−9.35818	−	55.2834i	−0.307363	−	1.81575i
$928$	8.00041	−	4.61904i	0.262626	−	0.151627i
$929$	45.2591			1.48490			0.742452	−	0.669899i	$-0.233663\pi$
$929$	45.2591			1.48490			0.742452	+	0.669899i	$0.233663\pi$
$930$	80.5945	+	66.3173i	2.64280	+	2.17463i
$931$	−36.6265	−	2.71307i	−1.20038	−	0.0889172i
$932$	20.9704	−	36.3218i	0.686909	−	1.18976i
$933$	−19.7086	−	3.54476i	−0.645231	−	0.116050i
$934$	−5.49669	−	3.17352i	−0.179857	−	0.103841i
$935$	−7.68290	+	13.7170i	−0.251258	+	0.448595i
$936$	58.8653	−	48.7110i	1.92407	−	1.59217i
$937$	16.0761			0.525184			0.262592	−	0.964907i	$-0.415423\pi$
$937$	16.0761			0.525184			0.262592	+	0.964907i	$0.415423\pi$
$938$	−3.55883	−	15.5614i	−0.116200	−	0.508097i
$939$	49.5052	+	8.90393i	1.61554	+	0.290569i
$940$	−42.5233	−	23.8173i	−1.38696	−	0.776835i
$941$	−23.6483			−0.770912			−0.385456	−	0.922726i	$-0.625956\pi$
$941$	−23.6483			−0.770912			−0.385456	+	0.922726i	$0.625956\pi$
$942$	−20.2051	−	3.63406i	−0.658318	−	0.118404i
$943$	0.402265			0.0130995
$944$	1.34136			0.0436574
$945$	−22.4677	+	20.9810i	−0.730875	+	0.682512i
$946$	−15.4424			−0.502077
$947$	28.5396			0.927413			0.463707	−	0.885989i	$-0.346519\pi$
$947$	28.5396			0.927413			0.463707	+	0.885989i	$0.346519\pi$
$948$	3.39947	+	0.611424i	0.110410	+	0.0198581i
$949$	37.7763			1.22627
$950$	−1.73120	−	66.3931i	−0.0561675	−	2.15408i
$951$	−36.9672	−	6.64886i	−1.19874	−	0.215604i
$952$	−58.3699	+	54.2062i	−1.89178	+	1.75683i
$953$	60.3601			1.95525			0.977627	−	0.210346i	$-0.0674590\pi$
$953$	60.3601			1.95525			0.977627	+	0.210346i	$0.0674590\pi$
$954$	5.91031	+	34.9152i	0.191353	+	1.13042i
$955$	3.85377	+	2.15850i	0.124705	+	0.0698473i
$956$	−77.8321	−	44.9364i	−2.51727	−	1.45335i
$957$	−4.90646	−	0.882470i	−0.158603	−	0.0285262i
$958$	45.0082	−	77.9565i	1.45415	−	2.51866i
$959$	3.76587	−	12.2273i	0.121606	−	0.394841i
$960$	4.11964	−	5.00654i	0.132961	−	0.161585i
$961$	−82.3036			−2.65495
$962$	74.3349	−	42.9173i	2.39665	−	1.38371i
$963$	2.03777	−	1.68626i	0.0656663	−	0.0543388i
$964$	−34.5245	−	19.9328i	−1.11196	−	0.641991i
$965$	32.3396	+	18.1134i	1.04105	+	0.583091i
$966$	−2.99291	−	4.66450i	−0.0962952	−	0.150078i
$967$	20.6715	+	11.9347i	0.664752	+	0.383795i	0.794085	−	0.607807i	$-0.207950\pi$
$967$	20.6715	+	11.9347i	0.664752	+	0.383795i	−0.129333	+	0.991601i	$0.541284\pi$
$968$	27.3616	+	47.3916i	0.879434	+	1.52322i
$969$	−44.1421	−	7.93934i	−1.41805	−	0.255048i
$970$	−53.1460	+	0.692772i	−1.70642	+	0.0222436i
$971$	−21.2234	+	36.7601i	−0.681092	+	1.17969i	0.293555	+	0.955942i	$0.405161\pi$
$971$	−21.2234	+	36.7601i	−0.681092	+	1.17969i	−0.974648	+	0.223745i	$0.928172\pi$
$972$	43.2767	+	53.4054i	1.38810	+	1.71298i
$973$	3.15914	+	0.972975i	0.101277	+	0.0311922i
$974$	−39.1049	+	22.5772i	−1.25300	+	0.723422i
$975$	35.7396	+	5.47051i	1.14458	+	0.175197i
$976$		−	11.8176i		−	0.378271i
$977$	7.00412			0.224082			0.112041	−	0.993704i	$-0.464261\pi$
$977$	7.00412			0.224082			0.112041	+	0.993704i	$0.464261\pi$
$978$	53.9781	+	45.6087i	1.72603	+	1.45841i
$979$	−3.28349	+	1.89572i	−0.104941	+	0.0605875i
$980$	−4.20108	+	68.8931i	−0.134199	+	2.20071i
$981$	2.17329	+	12.8387i	0.0693879	+	0.409909i
$982$	15.5269	+	8.96444i	0.495482	+	0.286067i
$983$	24.7050	+	14.2634i	0.787967	+	0.454933i	0.839246	−	0.543751i	$-0.182997\pi$
$983$	24.7050	+	14.2634i	0.787967	+	0.454933i	−0.0512794	+	0.998684i	$0.516330\pi$
$984$	−5.74267	+	6.79646i	−0.183069	+	0.216663i
$985$	−26.8721	+	47.9774i	−0.856217	+	1.52869i
$986$	12.6218	−	21.8616i	0.401961	−	0.696216i
$987$	1.06139	+	22.6270i	0.0337845	+	0.720224i
$988$	83.6493	−	48.2950i	2.66124	−	1.53647i
$989$	1.77124	+	1.02263i	0.0563221	+	0.0325176i
$990$	23.8010	−	4.34879i	0.756445	−	0.138214i
$991$	28.9247	+	50.0991i	0.918824	+	1.59145i	0.801204	+	0.598391i	$0.204193\pi$
$991$	28.9247	+	50.0991i	0.918824	+	1.59145i	0.117620	+	0.993059i	$0.462474\pi$
$992$		−	48.6729i		−	1.54536i
$993$	10.1470	+	1.82503i	0.322006	+	0.0579156i
$994$	17.5108	+	76.5677i	0.555407	+	2.42858i
$995$	0.0211128	+	1.61967i	0.000669321	+	0.0513469i
$996$	−88.3896	+	31.8290i	−2.80073	+	1.00854i
$997$	−1.10662	+	1.91671i	−0.0350469	+	0.0607030i	−0.883017	−	0.469341i	$-0.844491\pi$
$997$	−1.10662	+	1.91671i	−0.0350469	+	0.0607030i	0.847970	+	0.530044i	$0.177825\pi$
$998$	29.0773	+	50.3634i	0.920427	+	1.59423i
$999$	20.7221	+	36.7583i	0.655617	+	1.16298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bq.a.194.3	yes	88
3.2	odd	2		945.2.bq.a.719.42		88
5.4	even	2	inner	315.2.bq.a.194.42	yes	88
7.3	odd	6		315.2.u.a.59.42	yes	88
9.2	odd	6		315.2.u.a.299.3	yes	88
9.7	even	3		945.2.u.a.89.42		88
15.14	odd	2		945.2.bq.a.719.3		88
21.17	even	6		945.2.u.a.584.3		88
35.24	odd	6		315.2.u.a.59.3	✓	88
45.29	odd	6		315.2.u.a.299.42	yes	88
45.34	even	6		945.2.u.a.89.3		88
63.38	even	6	inner	315.2.bq.a.164.42	yes	88
63.52	odd	6		945.2.bq.a.899.3		88
105.59	even	6		945.2.u.a.584.42		88
315.164	even	6	inner	315.2.bq.a.164.3	yes	88
315.304	odd	6		945.2.bq.a.899.42		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.u.a.59.3	✓	88	35.24	odd	6
315.2.u.a.59.42	yes	88	7.3	odd	6
315.2.u.a.299.3	yes	88	9.2	odd	6
315.2.u.a.299.42	yes	88	45.29	odd	6
315.2.bq.a.164.3	yes	88	315.164	even	6	inner
315.2.bq.a.164.42	yes	88	63.38	even	6	inner
315.2.bq.a.194.3	yes	88	1.1	even	1	trivial
315.2.bq.a.194.42	yes	88	5.4	even	2	inner
945.2.u.a.89.3		88	45.34	even	6
945.2.u.a.89.42		88	9.7	even	3
945.2.u.a.584.3		88	21.17	even	6
945.2.u.a.584.42		88	105.59	even	6
945.2.bq.a.719.3		88	15.14	odd	2
945.2.bq.a.719.42		88	3.2	odd	2
945.2.bq.a.899.3		88	63.52	odd	6
945.2.bq.a.899.42		88	315.304	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.53172 q^{2} +(1.70470 + 0.306605i) q^{3} +4.40959 q^{4} +(-1.09270 + 1.95090i) q^{5} +(-4.31581 - 0.776236i) q^{6} +(2.57916 - 0.589845i) q^{7} -6.10041 q^{8} +(2.81199 + 1.04534i) q^{9} +(2.76640 - 4.93913i) q^{10} +(1.23377 + 0.712319i) q^{11} +(7.51702 + 1.35200i) q^{12} +(-2.08746 + 3.61559i) q^{13} +(-6.52971 + 1.49332i) q^{14} +(-2.46088 + 2.99067i) q^{15} +6.62532 q^{16} +(4.27416 - 2.46769i) q^{17} +(-7.11916 - 2.64650i) q^{18} +(-4.54377 - 2.62335i) q^{19} +(-4.81835 + 8.60267i) q^{20} +(4.57754 - 0.214725i) q^{21} +(-3.12356 - 1.80339i) q^{22} +(0.238847 + 0.413696i) q^{23} +(-10.3993 - 1.87041i) q^{24} +(-2.61202 - 4.26349i) q^{25} +(5.28486 - 9.15364i) q^{26} +(4.47308 + 2.64415i) q^{27} +(11.3731 - 2.60098i) q^{28} +(-1.74963 + 1.01015i) q^{29} +(6.23024 - 7.57152i) q^{30} +10.6444i q^{31} -4.57262 q^{32} +(1.88481 + 1.59257i) q^{33} +(-10.8210 + 6.24749i) q^{34} +(-1.66752 + 5.67621i) q^{35} +(12.3997 + 4.60951i) q^{36} +(7.03282 + 4.06040i) q^{37} +(11.5035 + 6.64157i) q^{38} +(-4.66704 + 5.52345i) q^{39} +(6.66590 - 11.9013i) q^{40} +(0.421048 - 0.729276i) q^{41} +(-11.5890 + 0.543622i) q^{42} +(3.70789 - 2.14075i) q^{43} +(5.44044 + 3.14104i) q^{44} +(-5.11200 + 4.34367i) q^{45} +(-0.604694 - 1.04736i) q^{46} +4.94304i q^{47} +(11.2942 + 2.03135i) q^{48} +(6.30416 - 3.04261i) q^{49} +(6.61290 + 10.7940i) q^{50} +(8.04276 - 2.89618i) q^{51} +(-9.20484 + 15.9433i) q^{52} +(-2.33122 - 4.03778i) q^{53} +(-11.3246 - 6.69424i) q^{54} +(-2.73781 + 1.62862i) q^{55} +(-15.7339 + 3.59830i) q^{56} +(-6.94142 - 5.86515i) q^{57} +(4.42958 - 2.55742i) q^{58} +0.202459 q^{59} +(-10.8515 + 13.1876i) q^{60} -1.78370i q^{61} -26.9486i q^{62} +(7.86916 + 1.03745i) q^{63} -1.67406 q^{64} +(-4.77268 - 8.02317i) q^{65} +(-4.77180 - 4.03193i) q^{66} +2.38316i q^{67} +(18.8473 - 10.8815i) q^{68} +(0.280322 + 0.778458i) q^{69} +(4.22169 - 14.3706i) q^{70} -11.7260i q^{71} +(-17.1543 - 6.37697i) q^{72} +(-4.52420 - 7.83614i) q^{73} +(-17.8051 - 10.2798i) q^{74} +(-3.14550 - 8.06882i) q^{75} +(-20.0362 - 11.5679i) q^{76} +(3.60226 + 1.10945i) q^{77} +(11.8156 - 13.9838i) q^{78} +0.452236 q^{79} +(-7.23947 + 12.9253i) q^{80} +(6.81454 + 5.87894i) q^{81} +(-1.06597 + 1.84632i) q^{82} +(-10.6524 + 6.15019i) q^{83} +(20.1851 - 0.946848i) q^{84} +(0.143843 + 11.0349i) q^{85} +(-9.38732 + 5.41977i) q^{86} +(-3.29231 + 1.18556i) q^{87} +(-7.52652 - 4.34544i) q^{88} +(-1.33067 + 2.30479i) q^{89} +(12.9421 - 10.9969i) q^{90} +(-3.25126 + 10.5565i) q^{91} +(1.05322 + 1.82423i) q^{92} +(-3.26363 + 18.1455i) q^{93} -12.5144i q^{94} +(10.0829 - 5.99791i) q^{95} +(-7.79493 - 1.40199i) q^{96} +(-4.69437 - 8.13089i) q^{97} +(-15.9604 + 7.70304i) q^{98} +(2.72474 + 3.29274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36}+ \cdots + 30 q^{99}+O(q^{100}) \) 88 * q + 76 * q^4 - 3 * q^5 - 12 * q^6 - 6 * q^10 - 12 * q^11 - 12 * q^14 - 6 * q^15 + 52 * q^16 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 48 * q^24 + q^25 - 12 * q^26 + 6 * q^29 + 33 * q^30 - 12 * q^34 - 36 * q^36 + 12 * q^39 - 30 * q^40 + 6 * q^41 - 84 * q^44 + 21 * q^45 - 18 * q^46 - 8 * q^49 + 30 * q^50 - 24 * q^51 - 60 * q^54 - 78 * q^56 - 12 * q^59 - 45 * q^60 - 8 * q^64 - 24 * q^66 + 60 * q^69 + 15 * q^70 - 30 * q^74 - 48 * q^75 - 48 * q^76 - 16 * q^79 - 69 * q^80 + 36 * q^81 - 90 * q^84 - 7 * q^85 - 12 * q^86 + 72 * q^89 + 33 * q^90 + 20 * q^91 - 60 * q^96 + 30 * q^99

Introduction

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