LMFDB - Embedded newform 798.2.cc.b.317.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			317.16
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.b.725.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.291399 + 1.70736i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.687483 + 1.88884i) q^{5} +(1.63082 - 0.583453i) q^{6} +(-0.708845 - 2.54903i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.83017 + 0.995048i) q^{9} +(1.97953 + 0.349044i) q^{10} +(-2.31917 - 1.33898i) q^{11} +(-0.857778 - 1.50473i) q^{12} +(-1.33096 - 3.65679i) q^{13} +(-2.38721 + 1.14071i) q^{14} +(-3.42527 - 0.623375i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.101924 - 0.280033i) q^{17} +(1.47139 + 2.61439i) q^{18} +(-4.27840 + 0.833861i) q^{19} -2.01007i q^{20} +(4.14556 - 1.95304i) q^{21} +(-0.915914 + 2.51645i) q^{22} +(4.01905 - 4.78972i) q^{23} +(-1.33292 + 1.10604i) q^{24} +(0.735125 + 0.616843i) q^{25} +(-3.37011 + 1.94573i) q^{26} +(-2.52362 - 4.54217i) q^{27} +(1.53792 + 2.15286i) q^{28} +(3.13515 + 2.63071i) q^{29} +(-0.0191119 + 3.48148i) q^{30} -9.25250i q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.61031 - 4.34985i) q^{33} +(-0.293478 - 0.0517481i) q^{34} +(5.30203 + 0.413514i) q^{35} +(2.31917 - 1.90302i) q^{36} +(-4.07083 - 2.35029i) q^{37} +(1.56413 + 4.06860i) q^{38} +(5.85562 - 3.33802i) q^{39} +(-1.97953 + 0.349044i) q^{40} +(-1.17992 - 0.429457i) q^{41} +(-2.64324 - 3.74343i) q^{42} +(0.132594 + 0.751977i) q^{43} +(2.63727 + 0.465022i) q^{44} +(0.0662044 - 6.02983i) q^{45} +(-5.41486 - 3.12627i) q^{46} +(-0.0211634 - 0.0581460i) q^{47} +(1.32070 + 1.12061i) q^{48} +(-5.99508 + 3.61373i) q^{49} +(0.479819 - 0.831071i) q^{50} +(0.507819 + 0.0924194i) q^{51} +(2.50139 + 2.98104i) q^{52} +(2.28482 - 0.831607i) q^{53} +(-4.03495 + 3.27402i) q^{54} +(4.12351 - 3.46003i) q^{55} +(1.85310 - 1.88839i) q^{56} +(-2.67042 - 7.06179i) q^{57} +(2.04633 - 3.54434i) q^{58} +(-10.5731 - 3.84831i) q^{59} +(3.43191 - 0.585732i) q^{60} +(-10.4248 - 8.74743i) q^{61} +(-9.11193 + 1.60668i) q^{62} +(4.54256 + 6.50885i) q^{63} +(-0.500000 + 0.866025i) q^{64} +7.82211 q^{65} +(-4.56339 - 0.830504i) q^{66} +(-0.484461 - 0.0854235i) q^{67} +0.298005i q^{68} +(9.34894 + 5.46626i) q^{69} +(-0.513456 - 5.29329i) q^{70} +(2.31924 + 13.1531i) q^{71} +(-2.27682 - 1.95348i) q^{72} +(-2.26946 - 12.8707i) q^{73} +(-1.60769 + 4.41711i) q^{74} +(-0.838960 + 1.43487i) q^{75} +(3.73518 - 2.24687i) q^{76} +(-1.76915 + 6.86077i) q^{77} +(-4.30412 - 5.18702i) q^{78} +(5.44027 + 6.48346i) q^{79} +(0.687483 + 1.88884i) q^{80} +(7.01976 - 5.63232i) q^{81} +(-0.218041 + 1.23657i) q^{82} +(-7.99484 - 4.61582i) q^{83} +(-3.22757 + 3.25312i) q^{84} +(0.458868 + 0.385036i) q^{85} +(0.717528 - 0.261159i) q^{86} +(-3.57799 + 6.11943i) q^{87} -2.67795i q^{88} +(-2.38216 + 13.5099i) q^{89} +(-5.94972 + 0.981871i) q^{90} +(-8.37780 + 5.98475i) q^{91} +(-2.13849 + 5.87546i) q^{92} +(15.7974 - 2.69617i) q^{93} +(-0.0535876 + 0.0309388i) q^{94} +(1.36629 - 8.65449i) q^{95} +(0.874247 - 1.49522i) q^{96} +(12.3055 + 14.6652i) q^{97} +(4.59986 + 5.27648i) q^{98} +(7.89601 + 1.48184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	0.291399	+	1.70736i	0.168239	+	0.985746i
$3$	0.291399	+	1.70736i	0.168239	+	0.985746i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.687483	+	1.88884i	−0.307452	+	0.844716i	0.685700	+	0.727884i	$0.259496\pi$
$5$	−0.687483	+	1.88884i	−0.307452	+	0.844716i	−0.993152	+	0.116832i	$0.962726\pi$
$6$	1.63082	−	0.583453i	0.665781	−	0.238194i
$7$	−0.708845	−	2.54903i	−0.267918	−	0.963442i
$7$	−0.708845	−	2.54903i	−0.267918	−	0.963442i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.83017	+	0.995048i	−0.943391	+	0.331683i
$10$	1.97953	+	0.349044i	0.625982	+	0.110377i
$11$	−2.31917	−	1.33898i	−0.699257	−	0.403716i	0.107813	−	0.994171i	$-0.465615\pi$
$11$	−2.31917	−	1.33898i	−0.699257	−	0.403716i	−0.807071	+	0.590455i	$0.798948\pi$
$12$	−0.857778	−	1.50473i	−0.247619	−	0.434379i
$13$	−1.33096	−	3.65679i	−0.369142	−	1.01421i	−0.975689	−	0.219162i	$-0.929668\pi$
$13$	−1.33096	−	3.65679i	−0.369142	−	1.01421i	0.606546	−	0.795048i	$-0.292554\pi$
$14$	−2.38721	+	1.14071i	−0.638009	+	0.304868i
$15$	−3.42527	−	0.623375i	−0.884402	−	0.160955i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.101924	−	0.280033i	0.0247202	−	0.0679181i	−0.926719	−	0.375756i	$-0.877383\pi$
$17$	0.101924	−	0.280033i	0.0247202	−	0.0679181i	0.951439	+	0.307838i	$0.0996054\pi$
$18$	1.47139	+	2.61439i	0.346809	+	0.616217i
$19$	−4.27840	+	0.833861i	−0.981531	+	0.191301i
$19$	−4.27840	+	0.833861i	−0.981531	+	0.191301i
$20$		−	2.01007i		−	0.449464i
$21$	4.14556	−	1.95304i	0.904634	−	0.426188i
$22$	−0.915914	+	2.51645i	−0.195273	+	0.536509i
$23$	4.01905	−	4.78972i	0.838031	−	0.998726i	−0.161898	−	0.986807i	$-0.551762\pi$
$23$	4.01905	−	4.78972i	0.838031	−	0.998726i	0.999929	−	0.0119185i	$-0.00379387\pi$
$24$	−1.33292	+	1.10604i	−0.272081	+	0.225770i
$25$	0.735125	+	0.616843i	0.147025	+	0.123369i
$26$	−3.37011	+	1.94573i	−0.660933	+	0.381590i
$27$	−2.52362	−	4.54217i	−0.485671	−	0.874142i
$28$	1.53792	+	2.15286i	0.290639	+	0.406853i
$29$	3.13515	+	2.63071i	0.582184	+	0.488510i	0.885663	−	0.464328i	$-0.153704\pi$
$29$	3.13515	+	2.63071i	0.582184	+	0.488510i	−0.303480	+	0.952838i	$0.598149\pi$
$30$	−0.0191119	+	3.48148i	−0.00348933	+	0.635629i
$31$		−	9.25250i		−	1.66180i	−0.556424	−	0.830899i	$-0.687827\pi$
$31$		−	9.25250i		−	1.66180i	0.556424	−	0.830899i	$-0.312173\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	1.61031	−	4.34985i	0.280319	−	0.757211i
$34$	−0.293478	−	0.0517481i	−0.0503310	−	0.00887472i
$35$	5.30203	+	0.413514i	0.896207	+	0.0698967i
$36$	2.31917	−	1.90302i	0.386528	−	0.317169i
$37$	−4.07083	−	2.35029i	−0.669240	−	0.386386i	0.126549	−	0.991960i	$-0.459610\pi$
$37$	−4.07083	−	2.35029i	−0.669240	−	0.386386i	−0.795788	+	0.605575i	$0.792943\pi$
$38$	1.56413	+	4.06860i	0.253735	+	0.660014i
$39$	5.85562	−	3.33802i	0.937649	−	0.534511i
$40$	−1.97953	+	0.349044i	−0.312991	+	0.0551887i
$41$	−1.17992	−	0.429457i	−0.184273	−	0.0670699i	0.248236	−	0.968700i	$-0.420149\pi$
$41$	−1.17992	−	0.429457i	−0.184273	−	0.0670699i	−0.432509	+	0.901630i	$0.642372\pi$
$42$	−2.64324	−	3.74343i	−0.407860	−	0.577624i
$43$	0.132594	+	0.751977i	0.0202204	+	0.114675i	0.993247	−	0.116016i	$-0.0370124\pi$
$43$	0.132594	+	0.751977i	0.0202204	+	0.114675i	−0.973027	+	0.230691i	$0.925901\pi$
$44$	2.63727	+	0.465022i	0.397583	+	0.0701046i
$45$	0.0662044	−	6.02983i	0.00986917	−	0.898874i
$46$	−5.41486	−	3.12627i	−0.798377	−	0.460943i
$47$	−0.0211634	−	0.0581460i	−0.00308700	−	0.00848146i	0.938140	−	0.346257i	$-0.112548\pi$
$47$	−0.0211634	−	0.0581460i	−0.00308700	−	0.00848146i	−0.941227	+	0.337776i	$0.890325\pi$
$48$	1.32070	+	1.12061i	0.190626	+	0.161746i
$49$	−5.99508	+	3.61373i	−0.856440	+	0.516247i
$50$	0.479819	−	0.831071i	0.0678566	−	0.117531i
$51$	0.507819	+	0.0924194i	0.0711089	+	0.0129413i
$52$	2.50139	+	2.98104i	0.346880	+	0.413396i
$53$	2.28482	−	0.831607i	0.313845	−	0.114230i	−0.180295	−	0.983613i	$-0.557705\pi$
$53$	2.28482	−	0.831607i	0.313845	−	0.114230i	0.494140	+	0.869382i	$0.335483\pi$
$54$	−4.03495	+	3.27402i	−0.549087	+	0.445538i
$55$	4.12351	−	3.46003i	0.556014	−	0.466551i
$56$	1.85310	−	1.88839i	0.247631	−	0.252347i
$57$	−2.67042	−	7.06179i	−0.353706	−	0.935357i
$58$	2.04633	−	3.54434i	0.268696	−	0.465395i
$59$	−10.5731	−	3.84831i	−1.37650	−	0.501007i	−0.455388	−	0.890293i	$-0.650499\pi$
$59$	−10.5731	−	3.84831i	−1.37650	−	0.501007i	−0.921117	+	0.389287i	$0.872722\pi$
$60$	3.43191	−	0.585732i	0.443058	−	0.0756176i
$61$	−10.4248	−	8.74743i	−1.33476	−	1.11999i	−0.982940	−	0.183924i	$-0.941120\pi$
$61$	−10.4248	−	8.74743i	−1.33476	−	1.11999i	−0.351816	−	0.936069i	$-0.614436\pi$
$62$	−9.11193	+	1.60668i	−1.15722	+	0.204048i
$63$	4.54256	+	6.50885i	0.572309	+	0.820038i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	7.82211			0.970213
$66$	−4.56339	−	0.830504i	−0.561715	−	0.102228i
$67$	−0.484461	−	0.0854235i	−0.0591863	−	0.0104361i	0.143977	−	0.989581i	$-0.454011\pi$
$67$	−0.484461	−	0.0854235i	−0.0591863	−	0.0104361i	−0.203163	+	0.979145i	$0.565122\pi$
$68$			0.298005i			0.0361385i
$69$	9.34894	+	5.46626i	1.12548	+	0.658060i
$70$	−0.513456	−	5.29329i	−0.0613697	−	0.632669i
$71$	2.31924	+	13.1531i	0.275243	+	1.56098i	0.738189	+	0.674594i	$0.235681\pi$
$71$	2.31924	+	13.1531i	0.275243	+	1.56098i	−0.462946	+	0.886387i	$0.653208\pi$
$72$	−2.27682	−	1.95348i	−0.268326	−	0.230220i
$73$	−2.26946	−	12.8707i	−0.265620	−	1.50640i	−0.767265	−	0.641331i	$-0.778383\pi$
$73$	−2.26946	−	12.8707i	−0.265620	−	1.50640i	0.501645	−	0.865074i	$-0.332728\pi$
$74$	−1.60769	+	4.41711i	−0.186891	+	0.513478i
$75$	−0.838960	+	1.43487i	−0.0968748	+	0.165685i
$76$	3.73518	−	2.24687i	0.428455	−	0.257734i
$77$	−1.76915	+	6.86077i	−0.201613	+	0.781857i
$78$	−4.30412	−	5.18702i	−0.487346	−	0.587314i
$79$	5.44027	+	6.48346i	0.612078	+	0.729447i	0.979687	−	0.200534i	$-0.0642678\pi$
$79$	5.44027	+	6.48346i	0.612078	+	0.729447i	−0.367608	+	0.929981i	$0.619823\pi$
$80$	0.687483	+	1.88884i	0.0768629	+	0.211179i
$81$	7.01976	−	5.63232i	0.779973	−	0.625813i
$82$	−0.218041	+	1.23657i	−0.0240786	+	0.136557i
$83$	−7.99484	−	4.61582i	−0.877547	−	0.506652i	−0.00769833	−	0.999970i	$-0.502450\pi$
$83$	−7.99484	−	4.61582i	−0.877547	−	0.506652i	−0.869849	+	0.493318i	$0.835784\pi$
$84$	−3.22757	+	3.25312i	−0.352157	+	0.354945i
$85$	0.458868	+	0.385036i	0.0497713	+	0.0417630i
$86$	0.717528	−	0.261159i	0.0773730	−	0.0281615i
$87$	−3.57799	+	6.11943i	−0.383601	+	0.656072i
$88$		−	2.67795i		−	0.285471i
$89$	−2.38216	+	13.5099i	−0.252509	+	1.43205i	0.549878	+	0.835245i	$0.314674\pi$
$89$	−2.38216	+	13.5099i	−0.252509	+	1.43205i	−0.802387	+	0.596804i	$0.796437\pi$
$90$	−5.94972	+	0.981871i	−0.627156	+	0.103498i
$91$	−8.37780	+	5.98475i	−0.878232	+	0.627372i
$92$	−2.13849	+	5.87546i	−0.222953	+	0.612559i
$93$	15.7974	−	2.69617i	1.63811	−	0.279580i
$94$	−0.0535876	+	0.0309388i	−0.00552714	+	0.00319110i
$95$	1.36629	−	8.65449i	0.140179	−	0.887932i
$96$	0.874247	−	1.49522i	0.0892274	−	0.152606i
$97$	12.3055	+	14.6652i	1.24944	+	1.48902i	0.805075	+	0.593173i	$0.202125\pi$
$97$	12.3055	+	14.6652i	1.24944	+	1.48902i	0.444362	+	0.895847i	$0.353430\pi$
$98$	4.59986	+	5.27648i	0.464657	+	0.533005i
$99$	7.89601	+	1.48184i	0.793579	+	0.148931i
$100$	−0.901764	−	0.328215i	−0.0901764	−	0.0328215i
$101$	−3.58537	+	4.27288i	−0.356758	+	0.425167i	−0.914336	−	0.404957i	$-0.867286\pi$
$101$	−3.58537	+	4.27288i	−0.356758	+	0.425167i	0.557578	+	0.830125i	$0.311731\pi$
$102$	0.00283346	−	0.516153i	0.000280554	−	0.0511067i
$103$		−	3.08671i		−	0.304142i	−0.988370	−	0.152071i	$-0.951406\pi$
$103$		−	3.08671i		−	0.304142i	0.988370	−	0.152071i	$-0.0485943\pi$
$104$	2.50139	−	2.98104i	0.245281	−	0.292315i
$105$	0.838989	+	9.17299i	0.0818770	+	0.895192i
$106$	−1.21573	−	2.10570i	−0.118082	−	0.204524i
$107$	−6.54878	−	11.3428i	−0.633095	−	1.09655i	−0.986915	−	0.161239i	$-0.948451\pi$
$107$	−6.54878	−	11.3428i	−0.633095	−	1.09655i	0.353820	−	0.935313i	$-0.384882\pi$
$108$	3.92494	+	3.40512i	0.377678	+	0.327658i
$109$	−9.32885	−	11.1177i	−0.893542	−	1.06488i	−0.997526	−	0.0703027i	$-0.977603\pi$
$109$	−9.32885	−	11.1177i	−0.893542	−	1.06488i	0.103984	−	0.994579i	$-0.466841\pi$
$110$	−4.12351	−	3.46003i	−0.393161	−	0.329901i
$111$	2.82657	−	7.63525i	0.268286	−	0.724706i
$112$	−2.18149	−	1.49703i	−0.206131	−	0.141456i
$113$	−18.7624			−1.76502			−0.882509	−	0.470295i	$-0.844147\pi$
$113$	−18.7624			−1.76502			−0.882509	+	0.470295i	$0.844147\pi$
$114$	−6.49079	+	3.85612i	−0.607918	+	0.361159i
$115$	6.28400	+	10.8842i	0.585986	+	1.01496i
$116$	−3.84584	−	1.39977i	−0.357077	−	0.129965i
$117$	7.40553	+	9.02496i	0.684641	+	0.834358i
$118$	−1.95384	+	11.0808i	−0.179865	+	1.02007i
$119$	−0.786061	−	0.0613062i	−0.0720581	−	0.00561993i
$120$	−1.17278	−	3.27806i	−0.107059	−	0.299245i
$121$	−1.91429	−	3.31564i	−0.174026	−	0.301422i
$122$	−6.80429	+	11.7854i	−0.616032	+	1.06700i
$123$	0.389410	−	2.13970i	0.0351119	−	0.192930i
$124$	3.16454	+	8.69450i	0.284184	+	0.780789i
$125$	−10.3743	+	5.98963i	−0.927910	+	0.535729i
$126$	5.62116	−	5.60380i	0.500773	−	0.499226i
$127$	2.75904	+	7.58040i	0.244825	+	0.672652i	0.999856	+	0.0169625i	$0.00539960\pi$
$127$	2.75904	+	7.58040i	0.244825	+	0.672652i	−0.755031	+	0.655689i	$0.772378\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−1.24526	+	0.445511i	−0.109639	+	0.0392251i
$130$	−1.35829	−	7.70327i	−0.119130	−	0.675622i
$131$	8.31632	−	1.46639i	0.726600	−	0.128119i	0.201900	−	0.979406i	$-0.435288\pi$
$131$	8.31632	−	1.46639i	0.726600	−	0.128119i	0.524700	+	0.851287i	$0.324177\pi$
$132$	−0.0254622	+	4.63828i	−0.00221620	+	0.403710i
$133$	5.15826	+	10.3147i	0.447277	+	0.894395i
$134$			0.491934i			0.0424966i
$135$	10.3144	−	1.64405i	0.887722	−	0.141498i
$136$	0.293478	−	0.0517481i	0.0251655	−	0.00443736i
$137$	4.29331	+	11.7958i	0.366803	+	1.00778i	0.976570	+	0.215201i	$0.0690408\pi$
$137$	4.29331	+	11.7958i	0.366803	+	1.00778i	−0.609767	+	0.792581i	$0.708737\pi$
$138$	3.75979	−	10.1561i	0.320054	−	0.864546i
$139$	−4.89477	+	1.78155i	−0.415169	+	0.151109i	−0.541155	−	0.840923i	$-0.682013\pi$
$139$	−4.89477	+	1.78155i	−0.415169	+	0.151109i	0.125986	+	0.992032i	$0.459791\pi$
$140$	−5.12371	+	1.42483i	−0.433033	+	0.120420i
$141$	0.0931092	−	0.0530773i	0.00784121	−	0.00446991i
$142$	12.5505	−	4.56801i	1.05321	−	0.383339i
$143$	−1.80962	+	10.2628i	−0.151328	+	0.858223i
$144$	−1.52843	+	2.58145i	−0.127369	+	0.215121i
$145$	−7.12436	+	4.11325i	−0.591646	+	0.341587i
$146$	−12.2811	+	4.46995i	−1.01639	+	0.369936i
$147$	−7.91691	−	9.18273i	−0.652976	−	0.757379i
$148$	4.62917	+	0.816248i	0.380516	+	0.0670952i
$149$	0.813483	+	0.969471i	0.0666431	+	0.0794222i	0.798336	−	0.602212i	$-0.205714\pi$
$149$	0.813483	+	0.969471i	0.0666431	+	0.0794222i	−0.731693	+	0.681634i	$0.761269\pi$
$150$	1.55876	+	0.577051i	0.127272	+	0.0471160i
$151$	0.0720732	−	0.0416115i	0.00586523	−	0.00338629i	−0.497065	−	0.867714i	$-0.665589\pi$
$151$	0.0720732	−	0.0416115i	0.00586523	−	0.00338629i	0.502930	+	0.864327i	$0.332255\pi$
$152$	−2.86134	−	3.28827i	−0.232086	−	0.266714i
$153$	−0.00981524	+	0.893962i	−0.000793515	+	0.0722725i
$154$	7.06374	+	0.550913i	0.569213	+	0.0443939i
$155$	17.4765	+	6.36093i	1.40375	+	0.510922i
$156$	−4.36081	+	5.13945i	−0.349144	+	0.411485i
$157$	−8.76005	+	7.35056i	−0.699128	+	0.586638i	−0.921526	−	0.388318i	$-0.873056\pi$
$157$	−8.76005	+	7.35056i	−0.699128	+	0.586638i	0.222397	+	0.974956i	$0.428612\pi$
$158$	5.44027	−	6.48346i	0.432805	−	0.515797i
$159$	2.08565	+	3.65869i	0.165403	+	0.290153i
$160$	1.74077	−	1.00503i	0.137620	−	0.0794548i
$161$	−15.0580	−	6.84950i	−1.18674	−	0.539817i
$162$	−6.76572	−	5.93507i	−0.531565	−	0.466303i
$163$	12.9016			1.01053			0.505266	−	0.862964i	$-0.331395\pi$
$163$	12.9016			1.01053			0.505266	+	0.862964i	$0.331395\pi$
$164$	1.25565			0.0980497
$165$	7.10912	+	6.03207i	0.553444	+	0.469596i
$166$	−3.15741	+	8.67491i	−0.245062	+	0.673303i
$167$	3.38885	−	19.2191i	0.262237	−	1.48722i	−0.514553	−	0.857459i	$-0.672042\pi$
$167$	3.38885	−	19.2191i	0.262237	−	1.48722i	0.776790	−	0.629760i	$-0.216847\pi$
$168$	3.76416	+	2.61364i	0.290411	+	0.201646i
$169$	−1.64204	+	1.37784i	−0.126311	+	0.105988i
$170$	0.299505	−	0.518758i	0.0229710	−	0.0397869i
$171$	11.2789	−	6.61718i	0.862517	−	0.506029i
$172$	−0.381789	−	0.661278i	−0.0291111	−	0.0504219i
$173$	0.244066	+	1.38417i	0.0185560	+	0.105236i	0.992679	−	0.120782i	$-0.0385402\pi$
$173$	0.244066	+	1.38417i	0.0185560	+	0.105236i	−0.974123	+	0.226018i	$0.927429\pi$
$174$	6.64777	+	2.46100i	0.503966	+	0.186568i
$175$	1.05126	−	2.31110i	0.0794678	−	0.174703i
$176$	−2.63727	+	0.465022i	−0.198792	+	0.0350523i
$177$	3.48945	−	19.1736i	0.262283	−	1.44117i
$178$	13.7183			1.02823
$179$	0.390714	−	0.676737i	0.0292034	−	0.0505817i	−0.851054	−	0.525078i	$-0.824036\pi$
$179$	0.390714	−	0.676737i	0.0292034	−	0.0505817i	0.880258	+	0.474496i	$0.157370\pi$
$180$	2.00011	+	5.68883i	0.149080	+	0.424021i
$181$	−2.47749	+	2.95256i	−0.184150	+	0.219462i	−0.850220	−	0.526428i	$-0.823531\pi$
$181$	−2.47749	+	2.95256i	−0.184150	+	0.219462i	0.666069	+	0.745890i	$0.267975\pi$
$182$	7.34862	+	7.21128i	0.544716	+	0.534536i
$183$	11.8973	−	20.3479i	0.879471	−	1.50416i
$184$	6.15755	+	1.08574i	0.453940	+	0.0800419i
$185$	7.23796	−	6.07337i	0.532145	−	0.446523i
$186$	−5.39839	−	15.0892i	−0.395829	−	1.10639i
$187$	−0.611337	+	0.512973i	−0.0447054	+	0.0375123i
$188$	0.0397742	+	0.0474010i	0.00290083	+	0.00345707i
$189$	−9.78927	+	9.65247i	−0.712065	+	0.702114i
$190$	−8.76026	+	0.157302i	−0.635536	+	0.0114119i
$191$	7.63961	+	4.41073i	0.552783	+	0.319149i	0.750244	−	0.661161i	$-0.229936\pi$
$191$	7.63961	+	4.41073i	0.552783	+	0.319149i	−0.197461	+	0.980311i	$0.563269\pi$
$192$	−1.62432	−	0.601322i	−0.117225	−	0.0433967i
$193$	25.4697	−	4.49100i	1.83335	−	0.323269i	0.853208	−	0.521570i	$-0.174654\pi$
$193$	25.4697	−	4.49100i	1.83335	−	0.323269i	0.980141	+	0.198301i	$0.0635425\pi$
$194$	12.3055	−	14.6652i	0.883485	−	1.05290i
$195$	2.27936	+	13.3552i	0.163228	+	0.956384i
$196$	4.39756	−	5.44623i	0.314111	−	0.389017i
$197$	−4.18467	−	2.41602i	−0.298145	−	0.172134i	0.343464	−	0.939166i	$-0.388400\pi$
$197$	−4.18467	−	2.41602i	−0.298145	−	0.172134i	−0.641609	+	0.767032i	$0.721733\pi$
$198$	0.0882023	−	8.03337i	0.00626826	−	0.570907i
$199$	0.369990	−	2.09832i	0.0262279	−	0.148746i	−0.968881	−	0.247525i	$-0.920383\pi$
$199$	0.369990	−	2.09832i	0.0262279	−	0.148746i	0.995109	+	0.0987793i	$0.0314938\pi$
$200$	−0.166639	+	0.945059i	−0.0117832	+	0.0668257i
$201$	0.00467735	−	0.852042i	0.000329915	−	0.0600984i
$202$	4.83055	+	2.78892i	0.339877	+	0.196228i
$203$	4.48340	−	9.85636i	0.314673	−	0.691781i
$204$	−0.508803	+	0.0868385i	−0.0356233	+	0.00607991i
$205$	1.62235	−	1.93345i	0.113310	−	0.135038i
$206$	−3.03981	+	0.536001i	−0.211794	+	0.0373450i
$207$	−6.60861	+	17.5549i	−0.459330	+	1.22015i
$208$	−3.37011	−	1.94573i	−0.233675	−	0.134912i
$209$	11.0389	+	3.79480i	0.763574	+	0.262492i
$210$	8.88794	−	2.41912i	0.613326	−	0.166935i
$211$	−8.33462	−	9.93281i	−0.573779	−	0.683803i	0.398623	−	0.917115i	$-0.369488\pi$
$211$	−8.33462	−	9.93281i	−0.573779	−	0.683803i	−0.972402	+	0.233312i	$0.925044\pi$
$212$	−1.86260	+	1.56291i	−0.127924	+	0.107341i
$213$	−21.7812	+	7.79257i	−1.49242	+	0.533938i
$214$	−10.0333	+	8.41896i	−0.685864	+	0.575508i
$215$	−1.51152	−	0.266522i	−0.103085	−	0.0181767i
$216$	2.67183	−	4.45661i	0.181795	−	0.303234i
$217$	−23.5849	+	6.55859i	−1.60104	+	0.445226i
$218$	−9.32885	+	11.1177i	−0.631830	+	0.752985i
$219$	21.3137	−	7.62530i	1.44024	−	0.515270i
$220$	−2.69143	+	4.66169i	−0.181456	+	0.314291i
$221$	−1.15968			−0.0780084
$222$	−8.01008	−	1.45778i	−0.537601	−	0.0978395i
$223$	19.1270	−	3.37261i	1.28084	−	0.225847i	0.508504	−	0.861060i	$-0.330199\pi$
$223$	19.1270	−	3.37261i	1.28084	−	0.225847i	0.772337	+	0.635213i	$0.219088\pi$
$224$	−1.09548	+	2.40830i	−0.0731946	+	0.160912i
$225$	−2.69432	−	1.01429i	−0.179621	−	0.0676192i
$226$	3.25806	+	18.4774i	0.216723	+	1.22910i
$227$	−8.87531	−	15.3725i	−0.589075	−	1.02031i	−0.994354	−	0.106115i	$-0.966159\pi$
$227$	−8.87531	−	15.3725i	−0.589075	−	1.02031i	0.405279	−	0.914193i	$-0.367174\pi$
$228$	4.92465	+	5.72257i	0.326143	+	0.378986i
$229$	−0.957176	+	1.65788i	−0.0632520	+	0.109556i	−0.895917	−	0.444221i	$-0.853481\pi$
$229$	−0.957176	+	1.65788i	−0.0632520	+	0.109556i	0.832665	+	0.553777i	$0.186814\pi$
$230$	9.62765	−	8.07856i	0.634829	−	0.532684i
$231$	−12.2293	−	1.02136i	−0.804632	−	0.0672004i
$232$	−0.710682	+	4.03048i	−0.0466585	+	0.264614i
$233$	−7.97199	+	21.9029i	−0.522263	+	1.43491i	0.345733	+	0.938333i	$0.387630\pi$
$233$	−7.97199	+	21.9029i	−0.522263	+	1.43491i	−0.867996	+	0.496572i	$0.834592\pi$
$234$	7.60190	−	8.86019i	0.496952	−	0.579209i
$235$	0.124378			0.00811353
$236$	11.2517			0.732423
$237$	−9.48433	+	11.1778i	−0.616073	+	0.726076i
$238$	0.0761232	+	0.784765i	0.00493433	+	0.0508687i
$239$	8.39001	−	4.84398i	0.542705	−	0.313331i	−0.203470	−	0.979081i	$-0.565222\pi$
$239$	8.39001	−	4.84398i	0.542705	−	0.313331i	0.746174	+	0.665751i	$0.231889\pi$
$240$	−3.02461	+	1.72419i	−0.195238	+	0.111296i
$241$	11.0882	−	13.2144i	0.714255	−	0.851216i	−0.279804	−	0.960057i	$-0.590269\pi$
$241$	11.0882	−	13.2144i	0.714255	−	0.851216i	0.994059	+	0.108841i	$0.0347139\pi$
$242$	−2.93286	+	2.46096i	−0.188531	+	0.158196i
$243$	11.6620	+	10.3440i	0.748115	+	0.663569i
$244$	12.7879	+	4.65441i	0.818660	+	0.297968i
$245$	−2.70426	−	13.8081i	−0.172769	−	0.882170i
$246$	−2.17481	−	0.0119388i	−0.138661	−	0.000761191i
$247$	8.74363	+	14.5353i	0.556344	+	0.924862i
$248$	8.01290	−	4.62625i	0.508820	−	0.293767i
$249$	5.55119	−	14.9951i	0.351792	−	0.950278i
$250$	7.70012	+	9.17665i	0.486998	+	0.580382i
$251$	13.2827	+	2.34209i	0.838393	+	0.147831i	0.576328	−	0.817219i	$-0.304485\pi$
$251$	13.2827	+	2.34209i	0.838393	+	0.147831i	0.262066	+	0.965050i	$0.415596\pi$
$252$	−6.49477	−	4.56267i	−0.409132	−	0.287421i
$253$	−15.7342	+	5.72678i	−0.989201	+	0.360040i
$254$	6.98613	−	4.03345i	0.438349	−	0.253081i
$255$	−0.523683	+	0.895654i	−0.0327943	+	0.0560880i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−18.0011	+	6.55186i	−1.12288	+	0.408694i	−0.835701	−	0.549185i	$-0.814938\pi$
$257$	−18.0011	+	6.55186i	−1.12288	+	0.408694i	−0.287175	+	0.957878i	$0.592716\pi$
$258$	0.654980	+	1.14898i	0.0407773	+	0.0715323i
$259$	−3.10537	+	12.0426i	−0.192959	+	0.748293i
$260$	−7.35038	+	2.67532i	−0.455851	+	0.165916i
$261$	−11.4907	−	4.32572i	−0.711257	−	0.267756i
$262$	−2.88823	−	7.93534i	−0.178435	−	0.490247i
$263$	1.09181	−	0.192515i	0.0673238	−	0.0118710i	−0.139885	−	0.990168i	$-0.544673\pi$
$263$	1.09181	−	0.192515i	0.0673238	−	0.0118710i	0.207209	+	0.978297i	$0.433562\pi$
$264$	4.57223	−	0.780353i	0.281402	−	0.0480274i
$265$			4.88739i			0.300230i
$266$	9.26224	−	6.87101i	0.567905	−	0.421289i
$267$	−23.7605	−	0.130435i	−1.45412	−	0.00798250i
$268$	0.484461	−	0.0854235i	0.0295931	−	0.00521807i
$269$	−1.26462	−	7.17203i	−0.0771053	−	0.437286i	−0.998783	−	0.0493286i	$-0.984292\pi$
$269$	−1.26462	−	7.17203i	−0.0771053	−	0.437286i	0.921677	−	0.387958i	$-0.126819\pi$
$270$	−3.41015	−	9.87222i	−0.207535	−	0.600804i
$271$	−3.12088	−	1.13591i	−0.189580	−	0.0690014i	0.245486	−	0.969400i	$-0.421053\pi$
$271$	−3.12088	−	1.13591i	−0.189580	−	0.0690014i	−0.435066	+	0.900399i	$0.643275\pi$
$272$	−0.101924	−	0.280033i	−0.00618004	−	0.0169795i
$273$	−12.6594	−	12.5600i	−0.766183	−	0.760165i
$274$	10.8711	−	6.27641i	0.656744	−	0.379172i
$275$	−0.878945	−	2.41488i	−0.0530024	−	0.145623i
$276$	−10.6547	−	1.93908i	−0.641338	−	0.116719i
$277$	−4.33210	+	7.50342i	−0.260291	+	0.450837i	−0.966319	−	0.257347i	$-0.917152\pi$
$277$	−4.33210	+	7.50342i	−0.260291	+	0.450837i	0.706028	+	0.708184i	$0.250485\pi$
$278$	2.60445	+	4.51105i	0.156205	+	0.270555i
$279$	9.20668	+	26.1862i	0.551190	+	1.56772i
$280$	2.29290	+	4.79845i	0.137027	+	0.286762i
$281$	0.271101	−	1.53749i	0.0161725	−	0.0917189i	−0.975653	−	0.219319i	$-0.929616\pi$
$281$	0.271101	−	1.53749i	0.0161725	−	0.0917189i	0.991826	+	0.127600i	$0.0407275\pi$
$282$	−0.0684392	−	0.0824779i	−0.00407549	−	0.00491149i
$283$	5.29231	+	1.92624i	0.314595	+	0.114503i	0.494492	−	0.869182i	$-0.335354\pi$
$283$	5.29231	+	1.92624i	0.314595	+	0.114503i	−0.179897	+	0.983685i	$0.557576\pi$
$284$	−6.67798	−	11.5666i	−0.396265	−	0.686352i
$285$	15.1745	−	0.189157i	0.898859	−	0.0112047i
$286$	10.4212			0.616217
$287$	−0.258314	+	3.31208i	−0.0152478	+	0.195506i
$288$	2.80764	+	1.05695i	0.165442	+	0.0622813i
$289$	12.9547	+	10.8703i	0.762043	+	0.639430i
$290$	5.28789	+	6.30186i	0.310516	+	0.370058i
$291$	−21.4529	+	25.2834i	−1.25759	+	1.48214i
$292$	6.53464	+	11.3183i	0.382411	+	0.662355i
$293$	13.5475	+	23.4650i	0.791454	+	1.37084i	0.925067	+	0.379805i	$0.124009\pi$
$293$	13.5475	+	23.4650i	0.791454	+	1.37084i	−0.133613	+	0.991034i	$0.542658\pi$
$294$	−7.66847	+	9.39120i	−0.447234	+	0.547706i
$295$	14.5377	−	17.3253i	0.846417	−	1.00872i
$296$		−	4.70059i		−	0.273216i
$297$	−0.229150	+	13.9132i	−0.0132967	+	0.807323i
$298$	0.813483	−	0.969471i	0.0471238	−	0.0561600i
$299$	−22.8642	−	8.32188i	−1.32227	−	0.481267i
$300$	0.297609	−	1.63528i	0.0171825	−	0.0944130i
$301$	1.82282	−	0.871021i	0.105066	−	0.0502048i
$302$	−0.0534947	−	0.0637525i	−0.00307827	−	0.00366854i
$303$	−8.34012	−	4.87641i	−0.479128	−	0.280143i
$304$	−2.74145	+	3.38887i	−0.157233	+	0.194365i
$305$	23.6894	−	13.6771i	1.35645	−	0.783147i
$306$	0.882085	−	0.145569i	0.0504255	−	0.00832161i
$307$	8.82093	−	24.2353i	0.503437	−	1.38318i	−0.384461	−	0.923141i	$-0.625613\pi$
$307$	8.82093	−	24.2353i	0.503437	−	1.38318i	0.887898	−	0.460041i	$-0.152165\pi$
$308$	−0.684063	−	7.05210i	−0.0389781	−	0.401830i
$309$	5.27013	−	0.899464i	0.299807	−	0.0511687i
$310$	3.22953	−	18.3156i	0.183425	−	1.04025i
$311$			10.5195i			0.596509i	0.954486	+	0.298254i	$0.0964044\pi$
$311$			10.5195i			0.596509i	−0.954486	+	0.298254i	$0.903596\pi$
$312$	5.81862	+	3.40210i	0.329414	+	0.192606i
$313$	−29.2567	+	10.6486i	−1.65369	+	0.601893i	−0.989352	−	0.145543i	$-0.953507\pi$
$313$	−29.2567	+	10.6486i	−1.65369	+	0.601893i	−0.664334	+	0.747436i	$0.731285\pi$
$314$	8.76005	+	7.35056i	0.494358	+	0.414816i
$315$	−15.4171	+	4.10546i	−0.868657	+	0.231317i
$316$	−7.32966	−	4.23178i	−0.412325	−	0.238056i
$317$	−1.57073	+	8.90805i	−0.0882210	+	0.500326i	0.908394	+	0.418115i	$0.137309\pi$
$317$	−1.57073	+	8.90805i	−0.0882210	+	0.500326i	−0.996615	+	0.0822107i	$0.973802\pi$
$318$	3.24094	−	2.68929i	0.181743	−	0.150808i
$319$	−3.74852	−	10.2990i	−0.209877	−	0.576631i
$320$	−1.29205	−	1.53980i	−0.0722275	−	0.0860774i
$321$	17.4580	−	14.4864i	0.974411	−	0.808554i
$322$	−4.13065	+	16.0187i	−0.230192	+	0.892685i
$323$	−0.202562	+	1.28308i	−0.0112708	+	0.0713927i
$324$	−4.67005	+	7.69355i	−0.259447	+	0.427419i
$325$	1.27724	−	3.50919i	0.0708485	−	0.194655i
$326$	−2.24034	−	12.7056i	−0.124081	−	0.703698i
$327$	16.2635	−	19.1674i	0.899374	−	1.05996i
$328$	−0.218041	−	1.23657i	−0.0120393	−	0.0682783i
$329$	−0.133214	+	0.0951626i	−0.00734433	+	0.00524648i
$330$	4.70595	−	8.04858i	0.259054	−	0.443060i
$331$		−	20.7232i		−	1.13905i	−0.821973	−	0.569526i	$-0.807127\pi$
$331$		−	20.7232i		−	1.13905i	0.821973	−	0.569526i	$-0.192873\pi$
$332$	9.09139	+	1.60306i	0.498955	+	0.0879792i
$333$	13.8598	+	2.60107i	0.759512	+	0.142537i
$334$	−19.5156			−1.06785
$335$	0.494410	−	0.856343i	0.0270125	−	0.0467870i
$336$	1.92029	−	4.16083i	0.104760	−	0.226992i
$337$	−7.19199	+	1.26814i	−0.391773	+	0.0690801i	−0.366065	−	0.930589i	$-0.619295\pi$
$337$	−7.19199	+	1.26814i	−0.391773	+	0.0690801i	−0.0257080	+	0.999669i	$0.508184\pi$
$338$	1.64204	+	1.37784i	0.0893154	+	0.0749445i
$339$	−5.46735	−	32.0342i	−0.296946	−	1.73986i
$340$	−0.562885	−	0.204874i	−0.0305267	−	0.0111108i
$341$	−12.3889	+	21.4582i	−0.670895	+	1.16202i
$342$	−8.47521	−	9.95846i	−0.458287	−	0.538492i
$343$	13.4611	+	12.7200i	0.726830	+	0.686817i
$344$	−0.584934	+	0.490818i	−0.0315375	+	0.0264631i
$345$	−16.7521	+	13.9007i	−0.901905	+	0.748390i
$346$	1.32076	−	0.480717i	0.0710044	−	0.0258435i
$347$	−2.29750	−	2.73805i	−0.123336	−	0.146986i	0.700843	−	0.713316i	$-0.252807\pi$
$347$	−2.29750	−	2.73805i	−0.123336	−	0.146986i	−0.824179	+	0.566329i	$0.808363\pi$
$348$	1.26924	−	6.97413i	0.0680384	−	0.373852i
$349$	2.44139	−	4.22861i	0.130685	−	0.226352i	−0.793256	−	0.608888i	$-0.791616\pi$
$349$	2.44139	−	4.22861i	0.130685	−	0.226352i	0.923941	+	0.382536i	$0.124949\pi$
$350$	−2.45854	−	0.633971i	−0.131414	−	0.0338872i
$351$	−13.2509	+	15.2738i	−0.707282	+	0.815255i
$352$	0.915914	+	2.51645i	0.0488184	+	0.134127i
$353$	10.8875	+	6.28592i	0.579485	+	0.334566i	0.760929	−	0.648836i	$-0.224744\pi$
$353$	10.8875	+	6.28592i	0.579485	+	0.334566i	−0.181444	+	0.983401i	$0.558077\pi$
$354$	−19.4882	−	0.106982i	−1.03579	−	0.00568603i
$355$	−26.4385	−	4.66182i	−1.40321	−	0.247424i
$356$	−2.38216	−	13.5099i	−0.126254	−	0.716025i
$357$	−0.124386	−	1.35996i	−0.00658319	−	0.0719765i
$358$	−0.734303	−	0.267264i	−0.0388091	−	0.0141254i
$359$	−9.44175	+	1.66483i	−0.498316	+	0.0878666i	−0.417157	−	0.908835i	$-0.636973\pi$
$359$	−9.44175	+	1.66483i	−0.498316	+	0.0878666i	−0.0811595	+	0.996701i	$0.525862\pi$
$360$	5.25509	−	2.95758i	0.276968	−	0.155878i
$361$	17.6094	−	7.13518i	0.926808	−	0.375536i
$362$	3.33791	+	1.92714i	0.175437	+	0.101288i
$363$	5.10318	−	4.23456i	0.267847	−	0.222257i
$364$	5.82565	−	8.48920i	0.305347	−	0.444955i
$365$	25.8710	+	4.56175i	1.35415	+	0.238773i
$366$	−22.1047	−	8.18314i	−1.15543	−	0.427740i
$367$	−7.64344	−	6.41361i	−0.398984	−	0.334788i	0.421117	−	0.907007i	$-0.361638\pi$
$367$	−7.64344	−	6.41361i	−0.398984	−	0.334788i	−0.820101	+	0.572219i	$0.806083\pi$
$368$		−	6.25254i		−	0.325936i
$369$	3.76672	+	0.0413566i	0.196088	+	0.00215294i
$370$	−7.23796	−	6.07337i	−0.376284	−	0.315739i
$371$	−3.73938	−	5.23459i	−0.194139	−	0.271767i
$372$	−13.9225	+	7.93659i	−0.721849	+	0.411493i
$373$	−14.2524	+	8.22863i	−0.737962	+	0.426063i	−0.821328	−	0.570456i	$-0.806766\pi$
$373$	−14.2524	+	8.22863i	−0.737962	+	0.426063i	0.0833658	+	0.996519i	$0.473433\pi$
$374$	0.611337	+	0.512973i	0.0316115	+	0.0265252i
$375$	−13.2495	−	15.9674i	−0.684204	−	0.824553i
$376$	0.0397742	−	0.0474010i	0.00205120	−	0.00244452i
$377$	5.44716	−	14.9660i	0.280543	−	0.770786i
$378$	11.2057	+	7.96441i	0.576360	+	0.409645i
$379$		−	23.7387i		−	1.21937i	−0.792642	−	0.609687i	$-0.791295\pi$
$379$		−	23.7387i		−	1.21937i	0.792642	−	0.609687i	$-0.208705\pi$
$380$	1.67611	+	8.59986i	0.0859829	+	0.441163i
$381$	−12.1385	+	6.91960i	−0.621875	+	0.354502i
$382$	3.01712	−	8.28947i	0.154369	−	0.424126i
$383$	1.11150	−	0.932659i	0.0567950	−	0.0476566i	−0.613948	−	0.789346i	$-0.710420\pi$
$383$	1.11150	−	0.932659i	0.0567950	−	0.0476566i	0.670743	+	0.741690i	$0.265975\pi$
$384$	−0.310127	+	1.70406i	−0.0158261	+	0.0869600i
$385$	−11.7427	−	8.05831i	−0.598461	−	0.410689i
$386$	−8.84554	−	24.3029i	−0.450226	−	1.23699i
$387$	−1.12352	−	1.99629i	−0.0571116	−	0.101477i
$388$	−16.5792	−	9.57200i	−0.841681	−	0.485945i
$389$	−7.22662	−	1.27425i	−0.366404	−	0.0646069i	−0.0125850	−	0.999921i	$-0.504006\pi$
$389$	−7.22662	−	1.27425i	−0.366404	−	0.0646069i	−0.353819	+	0.935314i	$0.615117\pi$
$390$	12.7565	−	4.56383i	0.645949	−	0.231099i
$391$	−0.931645	−	1.61366i	−0.0471153	−	0.0816061i
$392$	−6.12712	−	3.38502i	−0.309466	−	0.170969i
$393$	4.92703	+	13.7717i	0.248536	+	0.694689i
$394$	−1.65265	+	4.54063i	−0.0832596	+	0.228754i
$395$	−15.9863	+	5.81855i	−0.804360	+	0.292763i
$396$	−7.92664	+	1.30812i	−0.398329	+	0.0657354i
$397$	−0.251586	−	1.42682i	−0.0126267	−	0.0716098i	0.977843	−	0.209338i	$-0.0671310\pi$
$397$	−0.251586	−	1.42682i	−0.0126267	−	0.0716098i	−0.990470	+	0.137728i	$0.956020\pi$
$398$	−2.13069			−0.106802
$399$	−16.1078	+	11.8127i	−0.806397	+	0.591375i
$400$	0.959638			0.0479819
$401$	−3.65395	−	20.7226i	−0.182470	−	1.03484i	−0.929164	−	0.369669i	$-0.879471\pi$
$401$	−3.65395	−	20.7226i	−0.182470	−	1.03484i	0.746694	−	0.665168i	$-0.231640\pi$
$402$	−0.839910	+	0.143349i	−0.0418909	+	0.00714961i
$403$	−33.8344	+	12.3147i	−1.68541	+	0.613440i
$404$	1.90774	−	5.24146i	0.0949134	−	0.260772i
$405$	5.81261	+	17.1313i	0.288831	+	0.851263i
$406$	−10.4852	−	2.70375i	−0.520369	−	0.134185i
$407$	6.29397	+	10.9015i	0.311981	+	0.540366i
$408$	0.173872	+	0.485994i	0.00860795	+	0.0240603i
$409$	−21.9677	−	3.87349i	−1.08623	−	0.191532i	−0.398262	−	0.917272i	$-0.630386\pi$
$409$	−21.9677	−	3.87349i	−1.08623	−	0.191532i	−0.687969	+	0.725740i	$0.741498\pi$
$410$	−2.18579	−	1.26197i	−0.107949	−	0.0623241i
$411$	−18.8886	+	10.7675i	−0.931707	+	0.531123i
$412$	1.05572	+	2.90056i	0.0520114	+	0.142900i
$413$	−2.31472	+	29.6791i	−0.113900	+	1.46041i
$414$	18.4358	+	3.45984i	0.906069	+	0.170042i
$415$	14.2149	−	11.9277i	0.697781	−	0.585508i
$416$	−1.33096	+	3.65679i	−0.0652557	+	0.179289i
$417$	−4.46809	−	7.83801i	−0.218803	−	0.383829i
$418$	1.82027	−	11.5301i	0.0890323	−	0.563957i
$419$			6.85190i			0.334737i	0.985894	+	0.167369i	$0.0535270\pi$
$419$			6.85190i			0.334737i	−0.985894	+	0.167369i	$0.946473\pi$
$420$	−3.92574	−	8.33284i	−0.191556	−	0.406601i
$421$	9.74119	−	26.7637i	0.474757	−	1.30438i	−0.439134	−	0.898422i	$-0.644714\pi$
$421$	9.74119	−	26.7637i	0.474757	−	1.30438i	0.913890	−	0.405961i	$-0.133063\pi$
$422$	−8.33462	+	9.93281i	−0.405723	+	0.483522i
$423$	0.117754	+	0.143505i	0.00572540	+	0.00697743i
$424$	1.86260	+	1.56291i	0.0904561	+	0.0759017i
$425$	0.247663	−	0.142989i	0.0120134	−	0.00693596i
$426$	11.4565	+	20.0971i	0.555067	+	0.973710i
$427$	−14.9079	+	32.7736i	−0.721443	+	1.58603i
$428$	10.0333	+	8.41896i	0.484979	+	0.406946i
$429$	−18.0497	−	0.0990853i	−0.871449	−	0.00478388i
$430$			1.53484i			0.0740166i
$431$	0.377672	+	0.316904i	0.0181918	+	0.0152647i	0.651838	−	0.758358i	$-0.273998\pi$
$431$	0.377672	+	0.316904i	0.0181918	+	0.0152647i	−0.633646	+	0.773623i	$0.718443\pi$
$432$	−4.85286	−	1.85736i	−0.233483	−	0.0893621i
$433$	19.0575	+	3.36035i	0.915845	+	0.161488i	0.611656	−	0.791124i	$-0.290504\pi$
$433$	19.0575	+	3.36035i	0.915845	+	0.161488i	0.304189	+	0.952612i	$0.401615\pi$
$434$	10.5544	+	22.0877i	0.506628	+	1.06024i
$435$	−9.09884	−	10.9653i	−0.436256	−	0.525744i
$436$	12.5687	+	7.25656i	0.601933	+	0.347526i
$437$	−13.2011	+	23.8437i	−0.631496	+	1.14060i
$438$	−11.2105	−	19.6657i	−0.535660	−	0.939666i
$439$	27.4309	−	4.83681i	1.30920	−	0.230848i	0.524868	−	0.851183i	$-0.324115\pi$
$439$	27.4309	−	4.83681i	1.30920	−	0.230848i	0.784337	+	0.620335i	$0.213003\pi$
$440$	5.05823	+	1.84105i	0.241142	+	0.0877684i
$441$	13.3713	−	16.1929i	0.636727	−	0.771089i
$442$	0.201376	+	1.14206i	0.00957848	+	0.0543223i
$443$	−26.8527	−	4.73485i	−1.27581	−	0.224959i	−0.505609	−	0.862763i	$-0.668732\pi$
$443$	−26.8527	−	4.73485i	−1.27581	−	0.224959i	−0.770199	+	0.637803i	$0.779843\pi$
$444$	−0.0446935	+	8.14153i	−0.00212106	+	0.386380i
$445$	−23.8804	−	13.7874i	−1.13204	−	0.653584i
$446$	−6.64275	−	18.2508i	−0.314543	−	0.864201i
$447$	−1.41819	+	1.67141i	−0.0670781	+	0.0790551i
$448$	2.56194	+	0.660635i	0.121041	+	0.0312121i
$449$	−0.561837	+	0.973130i	−0.0265147	+	0.0459248i	−0.878978	−	0.476862i	$-0.841774\pi$
$449$	−0.561837	+	0.973130i	−0.0265147	+	0.0459248i	0.852464	+	0.522787i	$0.175108\pi$
$450$	−0.531015	+	2.82952i	−0.0250323	+	0.133385i
$451$	2.16142	+	2.57588i	0.101777	+	0.121293i
$452$	17.6309	−	6.41712i	0.829287	−	0.301836i
$453$	0.0920479	+	0.110929i	0.00432479	+	0.00521192i
$454$	−13.5978	+	11.4099i	−0.638175	+	0.535492i
$455$	−5.54466	−	19.9388i	−0.259938	−	0.934744i
$456$	4.78047	−	5.84355i	0.223866	−	0.273649i
$457$	4.27104	−	7.39766i	0.199791	−	0.346048i	−0.748670	−	0.662943i	$-0.769307\pi$
$457$	4.27104	−	7.39766i	0.199791	−	0.346048i	0.948461	+	0.316895i	$0.102640\pi$
$458$	1.79890	+	0.654747i	0.0840572	+	0.0305943i
$459$	−1.52918	+	0.243742i	−0.0713759	+	0.0113769i
$460$	−9.62765	−	8.07856i	−0.448892	−	0.376665i
$461$	−25.5592	+	4.50677i	−1.19041	+	0.209901i	−0.733548	−	0.679637i	$-0.762137\pi$
$461$	−25.5592	+	4.50677i	−1.19041	+	0.209901i	−0.456860	+	0.889538i	$0.651026\pi$
$462$	1.11776	+	12.2209i	0.0520030	+	0.568568i
$463$	−8.18339	+	14.1741i	−0.380314	+	0.658724i	−0.991107	−	0.133067i	$-0.957518\pi$
$463$	−8.18339	+	14.1741i	−0.380314	+	0.658724i	0.610793	+	0.791791i	$0.290851\pi$
$464$	4.09265			0.189997
$465$	−5.76777	+	31.6923i	−0.267474	+	1.46970i
$466$	22.9544	+	4.04749i	1.06334	+	0.187496i
$467$			22.7394i			1.05225i	0.850407	+	0.526126i	$0.176356\pi$
$467$			22.7394i			1.05225i	−0.850407	+	0.526126i	$0.823644\pi$
$468$	−10.0456	−	5.94785i	−0.464360	−	0.274940i
$469$	0.125661	+	1.29546i	0.00580248	+	0.0598186i
$470$	−0.0215980	−	0.122488i	−0.000996243	−	0.00564997i
$471$	−15.1027	−	12.8146i	−0.695898	−	0.590467i
$472$	−1.95384	−	11.0808i	−0.0899326	−	0.510033i
$473$	0.699371	−	1.92151i	0.0321571	−	0.0883509i
$474$	12.6549	+	7.39924i	0.581259	+	0.339858i
$475$	−3.65952	−	2.02611i	−0.167910	−	0.0929642i
$476$	0.759624	−	0.211240i	0.0348173	−	0.00968215i
$477$	−5.63895	+	4.62710i	−0.258190	+	0.211860i
$478$	−6.22729	−	7.42140i	−0.284830	−	0.339447i
$479$	−4.70126	−	12.9166i	−0.214806	−	0.590174i	0.784755	−	0.619806i	$-0.212789\pi$
$479$	−4.70126	−	12.9166i	−0.214806	−	0.590174i	−0.999561	+	0.0296317i	$0.990567\pi$
$480$	2.22321	+	2.67926i	0.101475	+	0.122291i
$481$	−3.17640	+	18.0143i	−0.144832	+	0.821381i
$482$	−14.9391	−	8.62511i	−0.680459	−	0.392863i
$483$	7.30669	−	27.7054i	0.332466	−	1.26064i
$484$	2.93286	+	2.46096i	0.133312	+	0.111862i
$485$	−36.1600	+	13.1612i	−1.64194	+	0.597618i
$486$	8.16179	−	13.2810i	0.370226	−	0.602439i
$487$			3.91250i			0.177292i	0.996063	+	0.0886461i	$0.0282540\pi$
$487$			3.91250i			0.177292i	−0.996063	+	0.0886461i	$0.971746\pi$
$488$	2.36311	−	13.4018i	0.106973	−	0.606673i
$489$	3.75952	+	22.0277i	0.170011	+	0.996127i
$490$	−13.1288	+	5.06094i	−0.593098	+	0.228630i
$491$	9.38312	−	25.7799i	0.423454	−	1.16343i	−0.526263	−	0.850322i	$-0.676407\pi$
$491$	9.38312	−	25.7799i	0.423454	−	1.16343i	0.949717	−	0.313109i	$-0.101370\pi$
$492$	0.365895	+	2.14385i	0.0164958	+	0.0966521i
$493$	1.05623	−	0.609816i	0.0475703	−	0.0274647i
$494$	12.7962	−	11.1348i	0.575728	−	0.500980i
$495$	−8.22734	+	13.8956i	−0.369791	+	0.624560i
$496$	−5.94739	−	7.08782i	−0.267046	−	0.318253i
$497$	31.8835	−	15.2353i	1.43017	−	0.683396i
$498$	−15.7313	−	2.86298i	−0.704935	−	0.128293i
$499$	−20.2114	−	7.35634i	−0.904786	−	0.329315i	−0.152617	−	0.988285i	$-0.548770\pi$
$499$	−20.2114	−	7.35634i	−0.904786	−	0.329315i	−0.752169	+	0.658970i	$0.770992\pi$
$500$	7.70012	−	9.17665i	0.344360	−	0.410392i
$501$	33.8015	+	0.185556i	1.51014	+	0.00829002i
$502$		−	13.4876i		−	0.601979i
$503$	12.4332	−	14.8173i	0.554368	−	0.660670i	−0.413976	−	0.910288i	$-0.635860\pi$
$503$	12.4332	−	14.8173i	0.554368	−	0.660670i	0.968345	+	0.249617i	$0.0803048\pi$
$504$	−3.36555	+	7.18840i	−0.149914	+	0.320197i
$505$	−5.60592	−	9.70973i	−0.249460	−	0.432077i
$506$	8.37200	+	14.5007i	0.372181	+	0.644636i
$507$	−2.83096	−	2.40206i	−0.125727	−	0.106679i
$508$	−5.18530	−	6.17960i	−0.230060	−	0.274175i
$509$	−3.89761	−	3.27049i	−0.172759	−	0.144962i	0.552309	−	0.833640i	$-0.313747\pi$
$509$	−3.89761	−	3.27049i	−0.172759	−	0.144962i	−0.725067	+	0.688678i	$0.758191\pi$
$510$	0.972983	+	0.360198i	0.0430844	+	0.0159498i
$511$	−31.1991	+	14.9083i	−1.38017	+	0.659502i
$512$	−1.00000			−0.0441942
$513$	14.5846	+	17.3289i	0.643925	+	0.765089i
$514$	9.57817	+	16.5899i	0.422475	+	0.731748i
$515$	5.83031	+	2.12206i	0.256914	+	0.0935091i
$516$	1.01779	−	0.844548i	0.0448056	−	0.0371791i
$517$	−0.0287744	+	0.163188i	−0.00126550	+	0.00717700i
$518$	12.3989	+	0.967013i	0.544778	+	0.0424881i
$519$	−2.29216	+	0.820055i	−0.100614	+	0.0359964i
$520$	3.91105	+	6.77414i	0.171511	+	0.297066i
$521$	20.7735	−	35.9807i	0.910103	−	1.57634i	0.0961864	−	0.995363i	$-0.469336\pi$
$521$	20.7735	−	35.9807i	0.910103	−	1.57634i	0.813917	−	0.580982i	$-0.197331\pi$
$522$	−2.26467	+	12.0673i	−0.0991218	+	0.528171i
$523$	−4.36879	−	12.0031i	−0.191034	−	0.524861i	0.806787	−	0.590842i	$-0.201204\pi$
$523$	−4.36879	−	12.0031i	−0.191034	−	0.524861i	−0.997821	+	0.0659813i	$0.978982\pi$
$524$	−7.31325	+	4.22231i	−0.319481	+	0.184452i
$525$	4.25222	+	1.12143i	0.185582	+	0.0489432i
$526$	−0.379181	−	1.04179i	−0.0165331	−	0.0454243i
$527$	−2.59101	−	0.943050i	−0.112866	−	0.0410799i
$528$	−1.56246	−	4.36727i	−0.0679973	−	0.190061i
$529$	−2.79473	−	15.8497i	−0.121510	−	0.689118i
$530$	4.81314	−	0.848686i	0.209069	−	0.0368646i
$531$	33.7530	+	0.370591i	1.46476	+	0.0160823i
$532$	−8.37500	−	7.92839i	−0.363102	−	0.343739i
$533$			4.88632i			0.211650i
$534$	3.99751	+	23.4222i	0.172989	+	1.01358i
$535$	25.9270	−	4.57163i	1.12092	−	0.197649i
$536$	−0.168251	−	0.462267i	−0.00726735	−	0.0199669i
$537$	1.26929	+	0.469890i	0.0547739	+	0.0202773i
$538$	−6.84347	+	2.49082i	−0.295043	+	0.107387i
$539$	18.7423	−	0.353610i	0.807289	−	0.0152310i
$540$	−9.13007	+	5.07264i	−0.392896	+	0.218292i
$541$	−22.9699	+	8.36035i	−0.987552	+	0.359440i	−0.784772	−	0.619785i	$-0.787220\pi$
$541$	−22.9699	+	8.36035i	−0.987552	+	0.359440i	−0.202780	+	0.979224i	$0.564998\pi$
$542$	−0.576715	+	3.27071i	−0.0247720	+	0.140489i
$543$	−5.76302	−	3.36960i	−0.247315	−	0.144603i
$544$	−0.258080	+	0.149003i	−0.0110651	+	0.00638844i
$545$	27.4130	−	9.97752i	1.17424	−	0.427390i
$546$	−10.1709	+	14.6481i	−0.435274	+	0.626882i
$547$	28.8866	+	5.09349i	1.23510	+	0.217782i	0.752815	−	0.658232i	$-0.228695\pi$
$547$	28.8866	+	5.09349i	1.23510	+	0.217782i	0.482286	+	0.876014i	$0.339806\pi$
$548$	−8.06879	−	9.61601i	−0.344682	−	0.410776i
$549$	38.2080	+	14.3836i	1.63068	+	0.613876i
$550$	−2.22557	+	1.28493i	−0.0948985	+	0.0547897i
$551$	−15.6071	−	8.64092i	−0.664884	−	0.368116i
$552$	−0.0594496	+	10.8295i	−0.00253034	+	0.460936i
$553$	12.6702	−	18.4632i	0.538792	−	0.785134i
$554$	8.14169	+	2.96333i	0.345907	+	0.125900i
$555$	12.4786	+	10.5880i	0.529686	+	0.449437i
$556$	3.99025	−	3.34822i	0.169224	−	0.141996i
$557$	9.84707	−	11.7353i	0.417234	−	0.497240i	−0.515960	−	0.856612i	$-0.672565\pi$
$557$	9.84707	−	11.7353i	0.417234	−	0.497240i	0.933194	+	0.359373i	$0.117009\pi$
$558$	24.1896	−	13.6140i	1.02403	−	0.576326i
$559$	2.57334	−	1.48572i	0.108841	−	0.0628392i
$560$	4.32739	−	3.09131i	0.182866	−	0.130632i
$561$	−1.05397	−	0.894294i	−0.0444988	−	0.0377571i
$562$	−1.56121			−0.0658556
$563$	34.9415			1.47261			0.736305	−	0.676650i	$-0.236569\pi$
$563$	34.9415			1.47261			0.736305	+	0.676650i	$0.236569\pi$
$564$	−0.0693405	+	0.0817216i	−0.00291976	+	0.00344110i
$565$	12.8988	−	35.4392i	0.542658	−	1.49094i
$566$	0.977979	−	5.54640i	0.0411075	−	0.233132i
$567$	−19.3329	−	13.9011i	−0.811903	−	0.583792i
$568$	−10.2313	+	8.58505i	−0.429294	+	0.360221i
$569$	−4.17880	+	7.23789i	−0.175184	+	0.303428i	−0.940225	−	0.340554i	$-0.889385\pi$
$569$	−4.17880	+	7.23789i	−0.175184	+	0.303428i	0.765041	+	0.643982i	$0.222719\pi$
$570$	−2.82130	−	14.9111i	−0.118171	−	0.624557i
$571$	6.65930	+	11.5342i	0.278683	+	0.482693i	0.971058	−	0.238845i	$-0.0767687\pi$
$571$	6.65930	+	11.5342i	0.278683	+	0.482693i	−0.692375	+	0.721538i	$0.743435\pi$
$572$	−1.80962	−	10.2628i	−0.0756639	−	0.429111i
$573$	−5.30454	+	14.3289i	−0.221600	+	0.598597i
$574$	3.30661	−	0.320746i	0.138015	−	0.0133877i
$575$	5.90901	−	1.04192i	0.246423	−	0.0434510i
$576$	0.553349	−	2.94853i	0.0230562	−	0.122855i
$577$	5.78316			0.240756			0.120378	−	0.992728i	$-0.461589\pi$
$577$	5.78316			0.240756			0.120378	+	0.992728i	$0.461589\pi$
$578$	8.45560	−	14.6455i	0.351706	−	0.609173i
$579$	15.0896	+	42.1773i	0.627103	+	1.75283i
$580$	5.28789	−	6.30186i	0.219568	−	0.261671i
$581$	−6.09875	+	23.6510i	−0.253019	+	0.981207i
$582$	28.6246	+	16.7366i	1.18653	+	0.693753i
$583$	−6.41240	−	1.13068i	−0.265575	−	0.0468280i
$584$	10.0116	−	8.40077i	0.414285	−	0.347626i
$585$	−22.1379	+	7.78338i	−0.915290	+	0.321803i
$586$	20.7560	−	17.4163i	0.857422	−	0.719462i
$587$	−19.9057	−	23.7227i	−0.821595	−	0.979139i	0.178393	−	0.983959i	$-0.442910\pi$
$587$	−19.9057	−	23.7227i	−0.821595	−	0.979139i	−0.999988	+	0.00482049i	$0.998466\pi$
$588$	10.5801	+	5.92120i	0.436318	+	0.244186i
$589$	7.71530	+	39.5859i	0.317903	+	1.63111i
$590$	−19.5866	−	11.3083i	−0.806367	−	0.465556i
$591$	2.90561	−	7.84877i	0.119521	−	0.322855i
$592$	−4.62917	+	0.816248i	−0.190258	+	0.0335476i
$593$	−16.7793	+	19.9968i	−0.689043	+	0.821170i	−0.991240	−	0.132076i	$-0.957836\pi$
$593$	−16.7793	+	19.9968i	−0.689043	+	0.821170i	0.302196	+	0.953246i	$0.402280\pi$
$594$	13.7416	−	2.19033i	0.563824	−	0.0898702i
$595$	0.656201	−	1.44260i	0.0269016	−	0.0591408i
$596$	−1.09600	−	0.632777i	−0.0448940	−	0.0259196i
$597$	3.69041	+	0.0202588i	0.151038	+	0.000829136i
$598$	−4.22513	+	23.9619i	−0.172778	+	0.979875i
$599$	6.51720	−	36.9609i	0.266286	−	1.51018i	−0.499063	−	0.866565i	$-0.666323\pi$
$599$	6.51720	−	36.9609i	0.266286	−	1.51018i	0.765349	−	0.643615i	$-0.222566\pi$
$600$	−1.66212	−	0.00912431i	−0.0678556	−	0.000372498i
$601$	4.35784	+	2.51600i	0.177760	+	0.102630i	0.586240	−	0.810138i	$-0.300608\pi$
$601$	4.35784	+	2.51600i	0.177760	+	0.102630i	−0.408480	+	0.912767i	$0.633941\pi$
$602$	−1.17432	−	1.64388i	−0.0478616	−	0.0669994i
$603$	1.45611	−	0.240299i	0.0592973	−	0.00978571i
$604$	−0.0534947	+	0.0637525i	−0.00217667	+	0.00259405i
$605$	7.57877	−	1.33634i	0.308121	−	0.0543300i
$606$	−3.35408	+	9.06020i	−0.136250	+	0.368045i
$607$	5.49371	+	3.17180i	0.222983	+	0.128739i	0.607331	−	0.794449i	$-0.292240\pi$
$607$	5.49371	+	3.17180i	0.222983	+	0.128739i	−0.384348	+	0.923188i	$0.625574\pi$
$608$	3.81344	+	2.11133i	0.154655	+	0.0856256i
$609$	18.1348	+	4.78266i	0.734861	+	0.193803i
$610$	−17.5829	−	20.9545i	−0.711911	−	0.848422i
$611$	−0.184460	+	0.154780i	−0.00746244	+	0.00626173i
$612$	−0.296530	−	0.843407i	−0.0119865	−	0.0340927i
$613$	3.71444	−	3.11679i	0.150025	−	0.125886i	−0.564686	−	0.825306i	$-0.691003\pi$
$613$	3.71444	−	3.11679i	0.150025	−	0.125886i	0.714711	+	0.699420i	$0.246558\pi$
$614$	−25.3989	−	4.47850i	−1.02501	−	0.180738i
$615$	3.77385	+	2.20654i	0.152176	+	0.0889764i
$616$	−6.82617	+	1.89825i	−0.275034	+	0.0764828i
$617$	21.2275	−	25.2979i	0.854586	−	1.01846i	−0.144993	−	0.989433i	$-0.546316\pi$
$617$	21.2275	−	25.2979i	0.854586	−	1.01846i	0.999579	−	0.0290233i	$-0.00923970\pi$
$618$	−1.80095	−	5.03387i	−0.0724447	−	0.202492i
$619$	−9.04807	+	15.6717i	−0.363673	+	0.629900i	−0.988562	−	0.150814i	$-0.951811\pi$
$619$	−9.04807	+	15.6717i	−0.363673	+	0.629900i	0.624889	+	0.780713i	$0.285144\pi$
$620$	−18.5981			−0.746919
$621$	−31.8983	−	6.16781i	−1.28004	−	0.247506i
$622$	10.3597	−	1.82670i	0.415387	−	0.0732440i
$623$	36.1257	−	3.50425i	1.44735	−	0.140395i
$624$	2.34003	−	6.32099i	0.0936760	−	0.253042i
$625$	−3.34809	−	18.9880i	−0.133924	−	0.759519i
$626$	15.5672	+	26.9631i	0.622189	+	1.07766i
$627$	−3.26238	+	19.9532i	−0.130287	+	0.796852i
$628$	5.71772	−	9.90338i	0.228162	−	0.395188i
$629$	−1.07307	+	0.900416i	−0.0427863	+	0.0359020i
$630$	6.72025	+	14.4700i	0.267741	+	0.576499i
$631$	−1.33794	+	7.58782i	−0.0532625	+	0.302067i	−0.999789	−	0.0205606i	$-0.993455\pi$
$631$	−1.33794	+	7.58782i	−0.0532625	+	0.302067i	0.946526	+	0.322627i	$0.104566\pi$
$632$	−2.89471	+	7.95314i	−0.115145	+	0.316359i
$633$	14.5302	−	17.1246i	0.577524	−	0.680643i
$634$	9.04547			0.359242
$635$	−16.2150			−0.643472
$636$	−3.21122	−	2.72471i	−0.127333	−	0.108042i
$637$	21.1939	+	17.1130i	0.839731	+	0.678041i
$638$	−9.49158	+	5.47996i	−0.375775	+	0.216954i
$639$	−19.6518	−	34.9177i	−0.777412	−	1.38132i
$640$	−1.29205	+	1.53980i	−0.0510726	+	0.0608659i
$641$	28.2549	−	23.7086i	1.11600	−	0.936435i	0.117604	−	0.993061i	$-0.462479\pi$
$641$	28.2549	−	23.7086i	1.11600	−	0.936435i	0.998395	+	0.0566257i	$0.0180342\pi$
$642$	−17.2979	−	14.6772i	−0.682694	−	0.579264i
$643$	−29.8824	−	10.8763i	−1.17845	−	0.428920i	−0.322794	−	0.946469i	$-0.604622\pi$
$643$	−29.8824	−	10.8763i	−1.17845	−	0.428920i	−0.855653	+	0.517549i	$0.826844\pi$
$644$	16.4926	+	1.28628i	0.649898	+	0.0506867i
$645$	0.0145934	−	2.65838i	0.000574614	−	0.104674i
$646$	1.29877	−	0.0233210i	0.0510993	−	0.000917553i
$647$	5.95626	−	3.43885i	0.234165	−	0.135195i	−0.378327	−	0.925672i	$-0.623501\pi$
$647$	5.95626	−	3.43885i	0.234165	−	0.135195i	0.612492	+	0.790477i	$0.290167\pi$
$648$	8.38761	+	3.26313i	0.329496	+	0.128188i
$649$	19.3681	+	23.0821i	0.760266	+	0.906050i
$650$	−3.67767	−	0.648472i	−0.144250	−	0.0254352i
$651$	−18.0705	−	38.3567i	−0.708239	−	1.50332i
$652$	−12.1235	+	4.41261i	−0.474794	+	0.172811i
$653$	42.4268	−	24.4951i	1.66029	−	0.958569i	0.687714	−	0.725982i	$-0.258614\pi$
$653$	42.4268	−	24.4951i	1.66029	−	0.958569i	0.972576	−	0.232587i	$-0.0747190\pi$
$654$	−21.7003	−	12.6880i	−0.848551	−	0.496142i
$655$	−2.94754	+	16.7163i	−0.115170	+	0.653162i
$656$	−1.17992	+	0.429457i	−0.0460683	+	0.0167675i
$657$	19.2299	+	34.1682i	0.750232	+	1.33303i
$658$	0.116849	+	0.114665i	0.00455526	+	0.00447012i
$659$	29.3153	−	10.6699i	1.14196	−	0.415641i	0.299342	−	0.954146i	$-0.403233\pi$
$659$	29.3153	−	10.6699i	1.14196	−	0.415641i	0.842622	+	0.538505i	$0.181011\pi$
$660$	−8.74348	−	3.23683i	−0.340339	−	0.125993i
$661$	−4.50523	−	12.3780i	−0.175233	−	0.481449i	0.820719	−	0.571332i	$-0.193573\pi$
$661$	−4.50523	−	12.3780i	−0.175233	−	0.481449i	−0.995952	+	0.0898825i	$0.971351\pi$
$662$	−20.4084	+	3.59855i	−0.793196	+	0.139862i
$663$	−0.337930	−	1.97999i	−0.0131241	−	0.0768965i
$664$		−	9.23164i		−	0.358257i
$665$	−23.0290	+	2.65198i	−0.893027	+	0.102839i
$666$	0.154821	−	14.1009i	0.00599918	−	0.546399i
$667$	25.2007	−	4.44356i	0.975775	−	0.172055i
$668$	3.38885	+	19.2191i	0.131118	+	0.743609i
$669$	11.3319	+	31.6740i	0.438116	+	1.22459i
$670$	−0.929187	−	0.338196i	−0.0358976	−	0.0130657i
$671$	12.4643	+	34.2453i	0.481178	+	1.32203i
$672$	−4.43107	−	1.16860i	−0.170932	−	0.0450796i
$673$	−25.9486	+	14.9815i	−1.00025	+	0.577493i	−0.908321	−	0.418273i	$-0.862636\pi$
$673$	−25.9486	+	14.9815i	−1.00025	+	0.577493i	−0.0919256	+	0.995766i	$0.529302\pi$
$674$	2.49775	+	6.86252i	0.0962098	+	0.264334i
$675$	0.946634	−	4.89574i	0.0364360	−	0.188437i
$676$	1.07177	−	1.85636i	0.0412218	−	0.0713983i
$677$	9.81001	+	16.9914i	0.377029	+	0.653034i	0.990629	−	0.136584i	$-0.0436122\pi$
$677$	9.81001	+	16.9914i	0.377029	+	0.653034i	−0.613599	+	0.789618i	$0.710279\pi$
$678$	−30.5982	+	10.9470i	−1.17511	+	0.420416i
$679$	28.6592	−	41.7624i	1.09984	−	1.60270i
$680$	−0.104017	+	0.589910i	−0.00398887	+	0.0226220i
$681$	23.6602	−	19.6329i	0.906659	−	0.752335i
$682$	23.2835	+	8.47449i	0.891570	+	0.324505i
$683$	2.89110	+	5.00752i	0.110625	+	0.191608i	0.916022	−	0.401127i	$-0.131382\pi$
$683$	2.89110	+	5.00752i	0.110625	+	0.191608i	−0.805398	+	0.592735i	$0.798048\pi$
$684$	−8.33546	+	10.0757i	−0.318714	+	0.385255i
$685$	−25.2320			−0.964064
$686$	10.1893	−	15.4654i	0.389029	−	0.590471i
$687$	−3.10952	−	1.15114i	−0.118636	−	0.0439188i
$688$	0.584934	+	0.490818i	0.0223004	+	0.0187123i
$689$	−6.08202	−	7.24827i	−0.231706	−	0.276137i
$690$	16.5985	+	14.0838i	0.631895	+	0.536161i
$691$	23.7388	+	41.1168i	0.903065	+	1.56415i	0.823493	+	0.567326i	$0.192022\pi$
$691$	23.7388	+	41.1168i	0.903065	+	1.56415i	0.0795718	+	0.996829i	$0.474645\pi$
$692$	−0.702761	−	1.21722i	−0.0267149	−	0.0462716i
$693$	−1.81979	−	21.1775i	−0.0691282	−	0.804468i
$694$	−2.29750	+	2.73805i	−0.0872118	+	0.103935i
$695$		−	10.4702i		−	0.397159i
$696$	−7.08858	−	0.0389133i	−0.268692	−	0.00147500i
$697$	−0.240525	+	0.286646i	−0.00911052	+	0.0108575i
$698$	−4.58831	−	1.67001i	−0.173670	−	0.0632107i
$699$	−39.7192	−	7.22860i	−1.50232	−	0.273411i
$700$	−0.197418	+	2.53128i	−0.00746172	+	0.0956732i
$701$	32.8155	+	39.1080i	1.23942	+	1.47709i	0.823124	+	0.567862i	$0.192229\pi$
$701$	32.8155	+	39.1080i	1.23942	+	1.47709i	0.416301	+	0.909227i	$0.363326\pi$
$702$	17.3427	+	10.3973i	0.654560	+	0.392422i
$703$	19.3764	+	6.66098i	0.730796	+	0.251224i
$704$	2.31917	−	1.33898i	0.0874072	−	0.0504646i
$705$	0.0362437	+	0.212358i	0.00136502	+	0.00799788i
$706$	4.29982	−	11.8137i	0.161826	−	0.444613i
$707$	13.4331	+	6.11039i	0.505206	+	0.229805i
$708$	3.27874	+	19.2107i	0.123222	+	0.721983i
$709$	2.04462	−	11.5956i	0.0767875	−	0.435483i	−0.922041	−	0.387092i	$-0.873479\pi$
$709$	2.04462	−	11.5956i	0.0767875	−	0.435483i	0.998828	−	0.0483911i	$-0.0154094\pi$
$710$			26.8464i			1.00753i
$711$	−21.8483	−	12.9360i	−0.819374	−	0.485137i
$712$	−12.8910	+	4.69195i	−0.483111	+	0.175838i
$713$	−44.3169	−	37.1863i	−1.65968	−	1.39264i
$714$	−1.31770	+	0.358650i	−0.0493135	+	0.0134221i
$715$	−18.1408	−	10.4736i	−0.678429	−	0.391691i
$716$	−0.135694	+	0.769557i	−0.00507111	+	0.0287597i
$717$	10.7153	+	12.9133i	0.400169	+	0.482254i
$718$	3.27908	+	9.00921i	0.122374	+	0.336221i
$719$	−1.61118	−	1.92014i	−0.0600871	−	0.0716090i	0.735164	−	0.677890i	$-0.237105\pi$
$719$	−1.61118	−	1.92014i	−0.0600871	−	0.0716090i	−0.795251	+	0.606281i	$0.792661\pi$
$720$	−3.82519	−	4.66167i	−0.142556	−	0.173730i
$721$	−7.86810	+	2.18800i	−0.293023	+	0.0814853i
$722$	−10.0846	−	16.1028i	−0.375310	−	0.599285i
$723$	25.7929	+	15.0809i	0.959249	+	0.560866i
$724$	1.31824	−	3.62185i	0.0489922	−	0.134605i
$725$	0.681997	+	3.86780i	0.0253287	+	0.143646i
$726$	−5.05638	−	4.29033i	−0.187660	−	0.159229i
$727$	5.94241	+	33.7011i	0.220392	+	1.24990i	0.871301	+	0.490749i	$0.163277\pi$
$727$	5.94241	+	33.7011i	0.220392	+	1.24990i	−0.650909	+	0.759156i	$0.725612\pi$
$728$	−9.37185	−	4.26301i	−0.347344	−	0.157998i
$729$	−14.2627	+	22.9254i	−0.528248	+	0.849090i
$730$		−	26.2701i		−	0.972300i
$731$	0.224093	+	0.0395137i	0.00828838	+	0.00146147i
$732$	−4.22038	+	23.1898i	−0.155990	+	0.857121i
$733$	48.5087			1.79171			0.895854	−	0.444348i	$-0.146565\pi$
$733$	48.5087			1.79171			0.895854	+	0.444348i	$0.146565\pi$
$734$	−4.98890	+	8.64103i	−0.184144	+	0.318946i
$735$	22.7875	−	8.64084i	0.840529	−	0.318722i
$736$	−6.15755	+	1.08574i	−0.226970	+	0.0400210i
$737$	1.00917	+	0.846793i	0.0371732	+	0.0311920i
$738$	−0.613355	−	3.71667i	−0.0225779	−	0.136813i
$739$	−12.1058	−	4.40615i	−0.445319	−	0.162083i	0.109621	−	0.993973i	$-0.465036\pi$
$739$	−12.1058	−	4.40615i	−0.445319	−	0.162083i	−0.554939	+	0.831891i	$0.687259\pi$
$740$	−4.72424	+	8.18263i	−0.173667	+	0.300799i
$741$	−22.2692	+	19.1641i	−0.818080	+	0.704012i
$742$	−4.50573	+	4.59154i	−0.165411	+	0.168561i
$743$	−16.3878	+	13.7510i	−0.601211	+	0.504476i	−0.891835	−	0.452361i	$-0.850582\pi$
$743$	−16.3878	+	13.7510i	−0.601211	+	0.504476i	0.290623	+	0.956838i	$0.406137\pi$
$744$	10.2336	+	12.3328i	0.375183	+	0.452144i
$745$	−2.39043	+	0.870047i	−0.0875787	+	0.0318761i
$746$	10.5785	+	12.6070i	0.387307	+	0.461575i
$747$	27.2197	+	5.10832i	0.995918	+	0.186904i
$748$	0.399022	−	0.691126i	0.0145897	−	0.0252701i
$749$	−24.2711	+	24.7333i	−0.886847	+	0.903737i
$750$	−13.4241	+	15.8210i	−0.490177	+	0.577700i
$751$	14.9517	+	41.0795i	0.545595	+	1.49901i	0.839599	+	0.543207i	$0.182790\pi$
$751$	14.9517	+	41.0795i	0.545595	+	1.49901i	−0.294004	+	0.955804i	$0.594988\pi$
$752$	−0.0535876	−	0.0309388i	−0.00195414	−	0.00112822i
$753$	−0.128241	+	23.3608i	−0.00467335	+	0.851314i
$754$	−15.6845	−	2.76560i	−0.571195	−	0.100717i
$755$	0.0290485	+	0.164742i	0.00105718	+	0.00599558i
$756$	5.89757	−	12.4185i	0.214492	−	0.451656i
$757$	37.0813	+	13.4965i	1.34774	+	0.490538i	0.912242	−	0.409651i	$-0.134350\pi$
$757$	37.0813	+	13.4965i	1.34774	+	0.490538i	0.435499	+	0.900189i	$0.356572\pi$
$758$	−23.3780	+	4.12218i	−0.849129	+	0.149724i
$759$	−14.3626	−	25.1952i	−0.521331	−	0.914528i
$760$	8.17815	−	3.14400i	0.296653	−	0.114045i
$761$	−37.8134	−	21.8316i	−1.37074	−	0.791394i	−0.379715	−	0.925104i	$-0.623978\pi$
$761$	−37.8134	−	21.8316i	−1.37074	−	0.791394i	−0.991021	+	0.133709i	$0.957311\pi$
$762$	8.92231	+	10.7525i	0.323221	+	0.389523i
$763$	−21.7266	+	31.6602i	−0.786555	+	1.14618i
$764$	−8.68745	−	1.53183i	−0.314301	−	0.0554197i
$765$	−1.68181	−	0.633123i	−0.0608058	−	0.0228906i
$766$	−1.11150	−	0.932659i	−0.0401601	−	0.0336983i
$767$			43.7856i			1.58101i
$768$	1.73202	+	0.00950808i	0.0624991	+	0.000343093i
$769$	−9.02223	−	7.57055i	−0.325350	−	0.273001i	0.465452	−	0.885073i	$-0.345892\pi$
$769$	−9.02223	−	7.57055i	−0.325350	−	0.273001i	−0.790802	+	0.612072i	$0.790336\pi$
$770$	−5.89679	+	12.9636i	−0.212506	+	0.467174i
$771$	−16.4319	−	28.8252i	−0.591780	−	1.03811i
$772$	−22.3977	+	12.9313i	−0.806110	+	0.465408i
$773$	−27.3919	−	22.9846i	−0.985219	−	0.826697i	−0.000350809	−	1.00000i	$-0.500112\pi$
$773$	−27.3919	−	22.9846i	−0.985219	−	0.826697i	−0.984869	+	0.173303i	$0.944556\pi$
$774$	−1.77086	+	1.45310i	−0.0636524	+	0.0522306i
$775$	5.70734	−	6.80174i	0.205014	−	0.244326i
$776$	−6.54763	+	17.9895i	−0.235046	+	0.645784i
$777$	−21.4661	−	1.79278i	−0.770090	−	0.0643157i
$778$			7.33810i			0.263084i
$779$	5.40629	+	0.853495i	0.193700	+	0.0305796i
$780$	−6.70963	−	11.7702i	−0.240243	−	0.421440i
$781$	12.2329	−	33.6096i	0.437728	−	1.20265i
$782$	−1.42736	+	1.19770i	−0.0510424	+	0.0428296i
$783$	4.03719	−	20.8793i	0.144278	−	0.746166i
$784$	−2.26963	+	6.62184i	−0.0810583	+	0.236494i
$785$	−7.86167	−	21.5998i	−0.280595	−	0.770928i
$786$	12.7069	−	7.24360i	0.453239	−	0.258371i
$787$	−23.9508	−	13.8280i	−0.853755	−	0.492915i	0.00816131	−	0.999967i	$-0.497402\pi$
$787$	−23.9508	−	13.8280i	−0.853755	−	0.492915i	−0.861916	+	0.507051i	$0.830735\pi$
$788$	4.75863	+	0.839075i	0.169519	+	0.0298908i
$789$	0.646845	+	1.80801i	0.0230283	+	0.0643670i
$790$	8.50615	+	14.7331i	0.302635	+	0.524180i
$791$	13.2996	+	47.8259i	0.472881	+	1.70049i
$792$	2.66469	+	7.57907i	0.0946857	+	0.269310i
$793$	−18.1125	+	49.7637i	−0.643194	+	1.76716i
$794$	−1.36145	+	0.495528i	−0.0483161	+	0.0175856i
$795$	−8.34454	+	1.42418i	−0.295950	+	0.0505105i
$796$	0.369990	+	2.09832i	0.0131140	+	0.0743730i
$797$	36.7936			1.30330			0.651648	−	0.758522i	$-0.274078\pi$
$797$	36.7936			1.30330			0.651648	+	0.758522i	$0.274078\pi$
$798$	14.4303	+	13.8118i	0.510828	+	0.488932i
$799$	−0.0184399			−0.000652355
$800$	−0.166639	−	0.945059i	−0.00589159	−	0.0334129i
$801$	−6.70109	−	40.6058i	−0.236771	−	1.43474i
$802$	−19.7733	+	7.19688i	−0.698218	+	0.254131i
$803$	−11.9703	+	32.8882i	−0.422424	+	1.16060i
$804$	0.287020	+	0.802258i	0.0101224	+	0.0282934i
$805$	23.2898	−	23.7333i	0.820856	−	0.836490i
$806$	18.0029	+	31.1819i	0.634125	+	1.09834i
$807$	11.8767	−	4.24909i	0.418081	−	0.149575i
$808$	−5.49310	−	0.968583i	−0.193247	−	0.0340746i
$809$	−14.5410	−	8.39525i	−0.511234	−	0.295161i	0.222107	−	0.975022i	$-0.428707\pi$
$809$	−14.5410	−	8.39525i	−0.511234	−	0.295161i	−0.733341	+	0.679861i	$0.762040\pi$
$810$	15.8617	−	8.69913i	0.557324	−	0.305656i
$811$	−6.17774	−	16.9732i	−0.216930	−	0.596009i	0.782723	−	0.622370i	$-0.213830\pi$
$811$	−6.17774	−	16.9732i	−0.216930	−	0.596009i	−0.999652	+	0.0263611i	$0.991608\pi$
$812$	−0.841948	+	10.7954i	−0.0295466	+	0.378843i
$813$	1.02998	−	5.65947i	0.0361231	−	0.198486i
$814$	9.64292	−	8.09137i	0.337984	−	0.283602i
$815$	−8.86963	+	24.3691i	−0.310689	+	0.853612i
$816$	0.448418	−	0.255622i	0.0156978	−	0.00894857i
$817$	−1.19433	−	3.10669i	−0.0417844	−	0.108689i
$818$			22.3066i			0.779930i
$819$	17.7555	−	25.2742i	0.620427	−	0.883152i
$820$	−0.863237	+	2.37172i	−0.0301455	+	0.0828242i
$821$	17.3523	−	20.6796i	0.605598	−	0.721723i	−0.372925	−	0.927861i	$-0.621645\pi$
$821$	17.3523	−	20.6796i	0.605598	−	0.721723i	0.978523	+	0.206138i	$0.0660896\pi$
$822$	13.8839	+	16.7319i	0.484257	+	0.583592i
$823$	−8.79995	−	7.38404i	−0.306747	−	0.257391i	0.476399	−	0.879229i	$-0.341942\pi$
$823$	−8.79995	−	7.38404i	−0.306747	−	0.257391i	−0.783146	+	0.621838i	$0.786386\pi$
$824$	2.67317	−	1.54335i	0.0931242	−	0.0537653i
$825$	3.86695	−	2.20437i	0.134630	−	0.0767464i
$826$	29.6301	−	2.87416i	1.03096	−	0.100005i
$827$	11.9477	+	10.0253i	0.415463	+	0.348615i	0.826434	−	0.563033i	$-0.190366\pi$
$827$	11.9477	+	10.0253i	0.415463	+	0.348615i	−0.410971	+	0.911648i	$0.634810\pi$
$828$	0.205936	−	18.7565i	0.00715679	−	0.651833i
$829$		−	24.0909i		−	0.836713i	−0.908283	−	0.418357i	$-0.862606\pi$
$829$		−	24.0909i		−	0.836713i	0.908283	−	0.418357i	$-0.137394\pi$
$830$	−14.2149	−	11.9277i	−0.493406	−	0.414016i
$831$	−14.0734	−	5.20998i	−0.488202	−	0.180732i
$832$	3.83235	+	0.675747i	0.132863	+	0.0234273i
$833$	0.400924	+	2.04715i	0.0138912	+	0.0709294i
$834$	−6.94305	+	5.76126i	−0.240418	+	0.199496i
$835$	33.9721	+	19.6138i	1.17565	+	0.678764i
$836$	−11.6710	+	0.209569i	−0.403651	+	0.00724808i
$837$	−42.0265	+	23.3498i	−1.45265	+	0.807086i
$838$	6.74781	−	1.18982i	0.233099	−	0.0411017i
$839$	−36.3834	−	13.2425i	−1.25609	−	0.457181i	−0.373638	−	0.927575i	$-0.621890\pi$
$839$	−36.3834	−	13.2425i	−1.25609	−	0.457181i	−0.882457	+	0.470393i	$0.844112\pi$
$840$	−7.52455	+	5.31308i	−0.259621	+	0.183319i
$841$	−2.12722	−	12.0641i	−0.0733525	−	0.416003i
$842$	−28.0486	−	4.94573i	−0.966620	−	0.170441i
$843$	2.70405	+	0.0148441i	0.0931324	+	0.000511258i
$844$	11.2292	+	6.48318i	0.386525	+	0.223160i
$845$	−1.47364	−	4.04880i	−0.0506949	−	0.139283i
$846$	0.120877	−	0.140884i	0.00415582	−	0.00484371i
$847$	−7.09473	+	7.22984i	−0.243778	+	0.248420i
$848$	1.21573	−	2.10570i	0.0417483	−	0.0723102i
$849$	−1.74662	+	9.59720i	−0.0599438	+	0.329375i
$850$	−0.183823	−	0.219071i	−0.00630506	−	0.00751408i
$851$	−27.6181	+	10.0522i	−0.946737	+	0.344584i
$852$	17.8024	−	14.7722i	0.609901	−	0.506089i
$853$	2.85982	−	2.39967i	0.0979182	−	0.0821632i	−0.592514	−	0.805560i	$-0.701865\pi$
$853$	2.85982	−	2.39967i	0.0979182	−	0.0821632i	0.690433	+	0.723397i	$0.257420\pi$
$854$	34.8644	+	8.99031i	1.19304	+	0.307642i
$855$	4.74479	+	25.8532i	0.162268	+	0.884161i
$856$	6.54878	−	11.3428i	0.223833	−	0.387690i
$857$	−25.8801	−	9.41957i	−0.884046	−	0.321766i	−0.140205	−	0.990123i	$-0.544776\pi$
$857$	−25.8801	−	9.41957i	−0.884046	−	0.321766i	−0.743841	+	0.668356i	$0.766998\pi$
$858$	3.03672	+	17.7927i	0.103672	+	0.607433i
$859$	−18.2923	−	15.3490i	−0.624124	−	0.523702i	0.274973	−	0.961452i	$-0.411331\pi$
$859$	−18.2923	−	15.3490i	−0.624124	−	0.523702i	−0.899097	+	0.437750i	$0.855776\pi$
$860$	1.51152	−	0.266522i	0.0515425	−	0.00908833i
$861$	−5.73019	+	0.524100i	−0.195284	+	0.0178613i
$862$	0.246508	−	0.426964i	0.00839609	−	0.0145425i
$863$	26.6285			0.906446			0.453223	−	0.891397i	$-0.350274\pi$
$863$	26.6285			0.906446			0.453223	+	0.891397i	$0.350274\pi$
$864$	−0.986449	+	5.10166i	−0.0335597	+	0.173562i
$865$	−2.78227	−	0.490589i	−0.0946000	−	0.0166805i
$866$		−	19.3515i		−	0.657591i
$867$	−14.7846	+	25.2860i	−0.502110	+	0.858758i
$868$	19.9194	−	14.2296i	0.676107	−	0.482983i
$869$	−3.93574	−	22.3207i	−0.133511	−	0.757177i
$870$	−9.21868	+	10.8647i	−0.312542	+	0.368348i
$871$	0.332423	+	1.88526i	0.0112637	+	0.0638797i
$872$	4.96378	−	13.6379i	0.168095	−	0.461836i
$873$	−49.4193	−	29.2603i	−1.67259	−	0.990312i
$874$	25.7738	+	8.86018i	0.871811	+	0.299700i
$875$	22.6215	+	22.1988i	0.764747	+	0.750455i
$876$	−17.4203	+	14.4551i	−0.588577	+	0.488394i
$877$	24.3987	+	29.0772i	0.823884	+	0.981867i	0.999997	−	0.00250293i	$-0.000796707\pi$
$877$	24.3987	+	29.0772i	0.823884	+	0.981867i	−0.176113	+	0.984370i	$0.556352\pi$
$878$	−9.52665	−	26.1743i	−0.321509	−	0.883338i
$879$	−36.1155	+	29.9682i	−1.21814	+	1.01080i
$880$	0.934724	−	5.30108i	0.0315095	−	0.178699i
$881$	−16.7337	−	9.66119i	−0.563772	−	0.325494i	0.190886	−	0.981612i	$-0.438864\pi$
$881$	−16.7337	−	9.66119i	−0.563772	−	0.325494i	−0.754658	+	0.656119i	$0.772197\pi$
$882$	−18.2688	−	10.3563i	−0.615141	−	0.348714i
$883$	38.1264	+	31.9919i	1.28306	+	1.07661i	0.992815	+	0.119658i	$0.0381798\pi$
$883$	38.1264	+	31.9919i	1.28306	+	1.07661i	0.290241	+	0.956954i	$0.406265\pi$
$884$	1.08974	−	0.396633i	0.0366520	−	0.0133402i
$885$	33.8169	+	19.7725i	1.13674	+	0.664646i
$886$			27.2669i			0.916049i
$887$	7.45724	−	42.2921i	0.250390	−	1.42003i	−0.557246	−	0.830348i	$-0.688142\pi$
$887$	7.45724	−	42.2921i	0.250390	−	1.42003i	0.807635	−	0.589682i	$-0.200747\pi$
$888$	8.02560	−	1.36975i	0.269322	−	0.0459657i
$889$	17.3669	−	12.4062i	0.582468	−	0.416091i
$890$	−9.43112	+	25.9118i	−0.316132	+	0.868565i
$891$	−23.8216	+	3.66304i	−0.798053	+	0.122717i
$892$	−16.8200	+	9.71105i	−0.563177	+	0.325150i
$893$	0.139031	+	0.231124i	0.00465250	+	0.00773427i
$894$	1.89229	+	1.10641i	0.0632875	+	0.0370038i
$895$	1.00964	+	1.20324i	0.0337486	+	0.0402200i
$896$	0.205722	−	2.63774i	0.00687269	−	0.0881207i
$897$	7.54586	−	41.4624i	0.251949	−	1.38439i
$898$	1.05591	+	0.384319i	0.0352361	+	0.0128249i
$899$	24.3406	−	29.0080i	0.811805	−	0.967471i
$900$	2.87874	+	0.0316071i	0.0959580	+	0.00105357i
$901$		−	0.724587i		−	0.0241395i
$902$	2.16142	−	2.57588i	0.0719673	−	0.0857673i
$903$	2.01832	+	2.85840i	0.0671654	+	0.0951217i
$904$	−9.38120	−	16.2487i	−0.312014	−	0.540424i
$905$	−3.87368	−	6.70942i	−0.128766	−	0.223029i
$906$	0.0932602	−	0.109912i	0.00309836	−	0.00365159i
$907$	3.04703	+	3.63131i	0.101175	+	0.120576i	0.814256	−	0.580506i	$-0.197145\pi$
$907$	3.04703	+	3.63131i	0.101175	+	0.120576i	−0.713081	+	0.701082i	$0.752701\pi$
$908$	13.5978	+	11.4099i	0.451258	+	0.378650i
$909$	5.89550	−	15.6606i	0.195541	−	0.519429i
$910$	−18.6730	+	8.92276i	−0.619005	+	0.295787i
$911$	−59.3490			−1.96632			−0.983159	−	0.182751i	$-0.941500\pi$
$911$	−59.3490			−1.96632			−0.983159	+	0.182751i	$0.941500\pi$
$912$	−6.58489	−	3.69313i	−0.218048	−	0.122292i
$913$	12.3609	+	21.4098i	0.409088	+	0.708561i
$914$	−8.02693	−	2.92156i	−0.265507	−	0.0966367i
$915$	30.2548	+	36.4609i	1.00019	+	1.20536i
$916$	0.332424	−	1.88527i	0.0109836	−	0.0622910i
$917$	−9.63285	−	20.1591i	−0.318105	−	0.665711i
$918$	0.505578	+	1.46362i	0.0166865	+	0.0483067i
$919$	8.80702	+	15.2542i	0.290517	+	0.503190i	0.973932	−	0.226840i	$-0.0728395\pi$
$919$	8.80702	+	15.2542i	0.290517	+	0.503190i	−0.683415	+	0.730030i	$0.739506\pi$
$920$	−6.28400	+	10.8842i	−0.207177	+	0.358842i
$921$	43.9489	+	7.99837i	1.44816	+	0.263555i
$922$	8.87660	+	24.3883i	0.292335	+	0.803185i
$923$	45.0111	−	25.9872i	1.48156	−	0.855378i
$924$	11.8411	−	3.22292i	0.389545	−	0.106026i
$925$	−1.54280	−	4.23882i	−0.0507271	−	0.139372i
$926$	15.3797	+	5.59777i	0.505410	+	0.183954i
$927$	3.07142	+	8.73592i	0.100879	+	0.286925i
$928$	−0.710682	−	4.03048i	−0.0233293	−	0.132307i
$929$	28.5251	−	5.02975i	0.935878	−	0.165021i	0.315146	−	0.949043i	$-0.397946\pi$
$929$	28.5251	−	5.02975i	0.935878	−	0.165021i	0.620732	+	0.784023i	$0.286835\pi$
$930$	32.2124	+	0.176832i	1.05629	+	0.00579856i
$931$	22.6360	−	20.4600i	0.741864	−	0.670551i
$932$		−	23.3086i		−	0.763497i
$933$	−17.9607	+	3.06539i	−0.588006	+	0.100356i
$934$	22.3939	−	3.94865i	0.732751	−	0.129204i
$935$	−0.548641	−	1.50738i	−0.0179425	−	0.0492966i
$936$	−4.11308	+	10.9259i	−0.134440	+	0.357123i
$937$	−39.9908	+	14.5555i	−1.30644	+	0.475507i	−0.899090	−	0.437764i	$-0.855771\pi$
$937$	−39.9908	+	14.5555i	−1.30644	+	0.475507i	−0.407354	+	0.913270i	$0.633548\pi$
$938$	1.25395	−	0.348705i	0.0409430	−	0.0113856i
$939$	−26.7063	−	46.8488i	−0.871529	−	1.52885i
$940$	−0.116877	+	0.0425398i	−0.00381211	+	0.00138750i
$941$	3.64274	−	20.6590i	0.118750	−	0.673465i	−0.866075	−	0.499914i	$-0.833365\pi$
$941$	3.64274	−	20.6590i	0.118750	−	0.673465i	0.984825	−	0.173551i	$-0.0555241\pi$
$942$	−9.99739	+	17.0985i	−0.325733	+	0.557100i
$943$	−6.79916	+	3.92549i	−0.221411	+	0.127832i
$944$	−10.5731	+	3.84831i	−0.344126	+	0.125252i
$945$	−11.5021	−	25.1263i	−0.374162	−	0.817359i
$946$	−2.01376	−	0.355080i	−0.0654729	−	0.0115446i
$947$	−2.98200	−	3.55382i	−0.0969021	−	0.115483i	0.715414	−	0.698701i	$-0.246238\pi$
$947$	−2.98200	−	3.55382i	−0.0969021	−	0.115483i	−0.812316	+	0.583217i	$0.801794\pi$
$948$	5.08932	−	13.7475i	0.165294	−	0.446499i
$949$	−44.0449	+	25.4293i	−1.42976	+	0.825471i
$950$	−1.35986	+	3.95575i	−0.0441196	+	0.128342i
$951$	−15.6670	−	0.0860051i	−0.508037	−	0.00278891i
$952$	−0.339938	−	0.711402i	−0.0110174	−	0.0230567i
$953$	−8.75027	−	3.18484i	−0.283449	−	0.103167i	0.196383	−	0.980527i	$-0.437080\pi$
$953$	−8.75027	−	3.18484i	−0.283449	−	0.103167i	−0.479832	+	0.877360i	$0.659303\pi$
$954$	5.53600	+	4.74980i	0.179235	+	0.153780i
$955$	−13.5833	+	11.3977i	−0.439545	+	0.368822i
$956$	−6.22729	+	7.42140i	−0.201405	+	0.240025i
$957$	16.4917	−	9.40119i	0.533103	−	0.303897i
$958$	−11.9040	+	6.87278i	−0.384601	+	0.222049i
$959$	27.0245	−	19.3052i	0.872666	−	0.623396i
$960$	2.25249	−	2.65469i	0.0726989	−	0.0856796i
$961$	−54.6087			−1.76157
$962$	18.2922			0.589764
$963$	29.8209	+	25.5858i	0.960964	+	0.824491i
$964$	−5.89992	+	16.2099i	−0.190024	+	0.522086i
$965$	−9.02720	+	51.1958i	−0.290596	+	1.64805i
$966$	−28.5533	−	2.38469i	−0.918688	−	0.0767261i
$967$	19.1060	−	16.0318i	0.614406	−	0.515548i	−0.281634	−	0.959522i	$-0.590876\pi$
$967$	19.1060	−	16.0318i	0.614406	−	0.515548i	0.896040	+	0.443974i	$0.146432\pi$
$968$	1.91429	−	3.31564i	0.0615275	−	0.106569i
$969$	−2.24972	+	0.0280438i	−0.0722713	+	0.000900896i
$970$	19.2403	+	33.3253i	0.617770	+	1.07001i
$971$	5.62556	+	31.9041i	0.180533	+	1.02385i	0.931562	+	0.363583i	$0.118447\pi$
$971$	5.62556	+	31.9041i	0.180533	+	1.02385i	−0.751029	+	0.660269i	$0.770442\pi$
$972$	−14.4965	−	5.73157i	−0.464976	−	0.183840i
$973$	8.01086	+	11.2141i	0.256816	+	0.359506i
$974$	3.85306	−	0.679398i	0.123460	−	0.0217693i
$975$	6.36364	+	1.15814i	0.203800	+	0.0370901i
$976$	−13.6086			−0.435600
$977$	30.1845	−	52.2811i	0.965688	−	1.67262i	0.257934	−	0.966162i	$-0.416958\pi$
$977$	30.1845	−	52.2811i	0.965688	−	1.67262i	0.707754	−	0.706459i	$-0.249708\pi$
$978$	21.0402	−	7.52747i	0.672792	−	0.240702i
$979$	23.6141	−	28.1422i	0.754711	−	0.899429i
$980$	7.26384	+	12.0505i	0.232035	+	0.384939i
$981$	37.4649	+	22.1823i	1.19616	+	0.708227i
$982$	−27.0176	−	4.76393i	−0.862166	−	0.152023i
$983$	−20.4573	+	17.1657i	−0.652488	+	0.547502i	−0.907825	−	0.419350i	$-0.862258\pi$
$983$	−20.4573	+	17.1657i	−0.652488	+	0.547502i	0.255337	+	0.966852i	$0.417814\pi$
$984$	2.04774	−	0.732611i	0.0652796	−	0.0233548i
$985$	7.44037	−	6.24321i	0.237070	−	0.198925i
$986$	−0.783965	−	0.934293i	−0.0249665	−	0.0297539i
$987$	−0.201295	−	0.199714i	−0.00640730	−	0.00635698i
$988$	−13.1877	−	10.6683i	−0.419557	−	0.339402i
$989$	4.13466	+	2.38715i	0.131475	+	0.0759069i
$990$	15.1131	+	5.68941i	0.480327	+	0.180821i
$991$	49.3016	−	8.69320i	1.56612	−	0.276149i	0.677753	−	0.735289i	$-0.262954\pi$
$991$	49.3016	−	8.69320i	1.56612	−	0.276149i	0.888363	+	0.459141i	$0.151843\pi$
$992$	−5.94739	+	7.08782i	−0.188830	+	0.225039i
$993$	35.3821	−	6.03874i	1.12282	−	0.191634i
$994$	−20.5403	−	28.7536i	−0.651500	−	0.912007i
$995$	3.70903	+	2.14141i	0.117584	+	0.0678873i
$996$	−0.0877752	+	15.9894i	−0.00278126	+	0.506645i
$997$	2.06336	−	11.7019i	0.0653473	−	0.370603i	−0.934544	−	0.355848i	$-0.884192\pi$
$997$	2.06336	−	11.7019i	0.0653473	−	0.370603i	0.999891	−	0.0147549i	$-0.00469679\pi$
$998$	−3.73491	+	21.1817i	−0.118227	+	0.670496i
$999$	−0.402226	+	24.4216i	−0.0127259	+	0.772667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.b.317.16	yes	162
3.2	odd	2		798.2.cc.a.317.12	yes	162
7.4	even	3		798.2.bu.b.431.20	yes	162
19.3	odd	18		798.2.bu.a.611.6	yes	162
21.11	odd	6		798.2.bu.a.431.6	✓	162
57.41	even	18		798.2.bu.b.611.20	yes	162
133.60	odd	18		798.2.cc.a.725.12	yes	162
399.326	even	18	inner	798.2.cc.b.725.16	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.6	✓	162	21.11	odd	6
798.2.bu.a.611.6	yes	162	19.3	odd	18
798.2.bu.b.431.20	yes	162	7.4	even	3
798.2.bu.b.611.20	yes	162	57.41	even	18
798.2.cc.a.317.12	yes	162	3.2	odd	2
798.2.cc.a.725.12	yes	162	133.60	odd	18
798.2.cc.b.317.16	yes	162	1.1	even	1	trivial
798.2.cc.b.725.16	yes	162	399.326	even	18	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.291399 + 1.70736i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.687483 + 1.88884i) q^{5} +(1.63082 - 0.583453i) q^{6} +(-0.708845 - 2.54903i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.83017 + 0.995048i) q^{9} +(1.97953 + 0.349044i) q^{10} +(-2.31917 - 1.33898i) q^{11} +(-0.857778 - 1.50473i) q^{12} +(-1.33096 - 3.65679i) q^{13} +(-2.38721 + 1.14071i) q^{14} +(-3.42527 - 0.623375i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.101924 - 0.280033i) q^{17} +(1.47139 + 2.61439i) q^{18} +(-4.27840 + 0.833861i) q^{19} -2.01007i q^{20} +(4.14556 - 1.95304i) q^{21} +(-0.915914 + 2.51645i) q^{22} +(4.01905 - 4.78972i) q^{23} +(-1.33292 + 1.10604i) q^{24} +(0.735125 + 0.616843i) q^{25} +(-3.37011 + 1.94573i) q^{26} +(-2.52362 - 4.54217i) q^{27} +(1.53792 + 2.15286i) q^{28} +(3.13515 + 2.63071i) q^{29} +(-0.0191119 + 3.48148i) q^{30} -9.25250i q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.61031 - 4.34985i) q^{33} +(-0.293478 - 0.0517481i) q^{34} +(5.30203 + 0.413514i) q^{35} +(2.31917 - 1.90302i) q^{36} +(-4.07083 - 2.35029i) q^{37} +(1.56413 + 4.06860i) q^{38} +(5.85562 - 3.33802i) q^{39} +(-1.97953 + 0.349044i) q^{40} +(-1.17992 - 0.429457i) q^{41} +(-2.64324 - 3.74343i) q^{42} +(0.132594 + 0.751977i) q^{43} +(2.63727 + 0.465022i) q^{44} +(0.0662044 - 6.02983i) q^{45} +(-5.41486 - 3.12627i) q^{46} +(-0.0211634 - 0.0581460i) q^{47} +(1.32070 + 1.12061i) q^{48} +(-5.99508 + 3.61373i) q^{49} +(0.479819 - 0.831071i) q^{50} +(0.507819 + 0.0924194i) q^{51} +(2.50139 + 2.98104i) q^{52} +(2.28482 - 0.831607i) q^{53} +(-4.03495 + 3.27402i) q^{54} +(4.12351 - 3.46003i) q^{55} +(1.85310 - 1.88839i) q^{56} +(-2.67042 - 7.06179i) q^{57} +(2.04633 - 3.54434i) q^{58} +(-10.5731 - 3.84831i) q^{59} +(3.43191 - 0.585732i) q^{60} +(-10.4248 - 8.74743i) q^{61} +(-9.11193 + 1.60668i) q^{62} +(4.54256 + 6.50885i) q^{63} +(-0.500000 + 0.866025i) q^{64} +7.82211 q^{65} +(-4.56339 - 0.830504i) q^{66} +(-0.484461 - 0.0854235i) q^{67} +0.298005i q^{68} +(9.34894 + 5.46626i) q^{69} +(-0.513456 - 5.29329i) q^{70} +(2.31924 + 13.1531i) q^{71} +(-2.27682 - 1.95348i) q^{72} +(-2.26946 - 12.8707i) q^{73} +(-1.60769 + 4.41711i) q^{74} +(-0.838960 + 1.43487i) q^{75} +(3.73518 - 2.24687i) q^{76} +(-1.76915 + 6.86077i) q^{77} +(-4.30412 - 5.18702i) q^{78} +(5.44027 + 6.48346i) q^{79} +(0.687483 + 1.88884i) q^{80} +(7.01976 - 5.63232i) q^{81} +(-0.218041 + 1.23657i) q^{82} +(-7.99484 - 4.61582i) q^{83} +(-3.22757 + 3.25312i) q^{84} +(0.458868 + 0.385036i) q^{85} +(0.717528 - 0.261159i) q^{86} +(-3.57799 + 6.11943i) q^{87} -2.67795i q^{88} +(-2.38216 + 13.5099i) q^{89} +(-5.94972 + 0.981871i) q^{90} +(-8.37780 + 5.98475i) q^{91} +(-2.13849 + 5.87546i) q^{92} +(15.7974 - 2.69617i) q^{93} +(-0.0535876 + 0.0309388i) q^{94} +(1.36629 - 8.65449i) q^{95} +(0.874247 - 1.49522i) q^{96} +(12.3055 + 14.6652i) q^{97} +(4.59986 + 5.27648i) q^{98} +(7.89601 + 1.48184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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