LMFDB - Embedded newform 336.2.s.c.155.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.14
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.724332 + 1.21464i) q^{2} +(-0.119805 + 1.72790i) q^{3} +(-0.950686 + 1.75960i) q^{4} +(-0.793669 + 0.793669i) q^{5} +(-2.18555 + 1.10606i) q^{6} -1.00000 q^{7} +(-2.82589 + 0.119796i) q^{8} +(-2.97129 - 0.414021i) q^{9} +O(q^{10})$	\(q+(0.724332 + 1.21464i) q^{2} +(-0.119805 + 1.72790i) q^{3} +(-0.950686 + 1.75960i) q^{4} +(-0.793669 + 0.793669i) q^{5} +(-2.18555 + 1.10606i) q^{6} -1.00000 q^{7} +(-2.82589 + 0.119796i) q^{8} +(-2.97129 - 0.414021i) q^{9} +(-1.53890 - 0.389140i) q^{10} +(0.687038 + 0.687038i) q^{11} +(-2.92652 - 1.85350i) q^{12} +(2.91110 - 2.91110i) q^{13} +(-0.724332 - 1.21464i) q^{14} +(-1.27630 - 1.46647i) q^{15} +(-2.19239 - 3.34566i) q^{16} +1.81984i q^{17} +(-1.64932 - 3.90893i) q^{18} +(3.24223 + 3.24223i) q^{19} +(-0.642010 - 2.15107i) q^{20} +(0.119805 - 1.72790i) q^{21} +(-0.336858 + 1.33215i) q^{22} +5.92103i q^{23} +(0.131558 - 4.89721i) q^{24} +3.74018i q^{25} +(5.64454 + 1.42733i) q^{26} +(1.07136 - 5.08450i) q^{27} +(0.950686 - 1.75960i) q^{28} +(-1.54834 - 1.54834i) q^{29} +(0.856763 - 2.61245i) q^{30} +3.60999i q^{31} +(2.47574 - 5.08633i) q^{32} +(-1.26945 + 1.10482i) q^{33} +(-2.21044 + 1.31817i) q^{34} +(0.793669 - 0.793669i) q^{35} +(3.55328 - 4.83469i) q^{36} +(-5.10312 - 5.10312i) q^{37} +(-1.58968 + 6.28658i) q^{38} +(4.68134 + 5.37887i) q^{39} +(2.14774 - 2.33790i) q^{40} -1.19627 q^{41} +(2.18555 - 1.10606i) q^{42} +(-7.00779 + 7.00779i) q^{43} +(-1.86207 + 0.555755i) q^{44} +(2.68682 - 2.02963i) q^{45} +(-7.19190 + 4.28879i) q^{46} +13.1565 q^{47} +(6.04363 - 3.38741i) q^{48} +1.00000 q^{49} +(-4.54296 + 2.70913i) q^{50} +(-3.14450 - 0.218025i) q^{51} +(2.35483 + 7.88993i) q^{52} +(2.08667 - 2.08667i) q^{53} +(6.95185 - 2.38155i) q^{54} -1.09056 q^{55} +(2.82589 - 0.119796i) q^{56} +(-5.99069 + 5.21382i) q^{57} +(0.759161 - 3.00219i) q^{58} +(0.919177 + 0.919177i) q^{59} +(3.79376 - 0.851623i) q^{60} +(4.21756 - 4.21756i) q^{61} +(-4.38483 + 2.61483i) q^{62} +(2.97129 + 0.414021i) q^{63} +(7.97130 - 0.677063i) q^{64} +4.62091i q^{65} +(-2.26146 - 0.741655i) q^{66} +(7.87889 + 7.87889i) q^{67} +(-3.20219 - 1.73009i) q^{68} +(-10.2310 - 0.709366i) q^{69} +(1.53890 + 0.389140i) q^{70} -7.99444i q^{71} +(8.44614 + 0.814027i) q^{72} +4.19057i q^{73} +(2.50208 - 9.89478i) q^{74} +(-6.46266 - 0.448090i) q^{75} +(-8.78737 + 2.62269i) q^{76} +(-0.687038 - 0.687038i) q^{77} +(-3.14253 + 9.58221i) q^{78} +8.07689i q^{79} +(4.39538 + 0.915312i) q^{80} +(8.65717 + 2.46036i) q^{81} +(-0.866499 - 1.45304i) q^{82} +(11.0241 - 11.0241i) q^{83} +(2.92652 + 1.85350i) q^{84} +(-1.44435 - 1.44435i) q^{85} +(-13.5879 - 3.43595i) q^{86} +(2.86089 - 2.48989i) q^{87} +(-2.02380 - 1.85919i) q^{88} -7.73403 q^{89} +(4.41141 + 1.79339i) q^{90} +(-2.91110 + 2.91110i) q^{91} +(-10.4186 - 5.62904i) q^{92} +(-6.23771 - 0.432493i) q^{93} +(9.52970 + 15.9804i) q^{94} -5.14651 q^{95} +(8.49207 + 4.88720i) q^{96} +6.61707 q^{97} +(0.724332 + 1.21464i) q^{98} +(-1.75694 - 2.32584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.724332	+	1.21464i	0.512180	+	0.858878i
$2$	0.724332	+	1.21464i	0.512180	+	0.858878i
$3$	−0.119805	+	1.72790i	−0.0691692	+	0.997605i
$3$	−0.119805	+	1.72790i	−0.0691692	+	0.997605i
$4$	−0.950686	+	1.75960i	−0.475343	+	0.879800i
$5$	−0.793669	+	0.793669i	−0.354940	+	0.354940i	−0.861944	−	0.507004i	$-0.830753\pi$
$5$	−0.793669	+	0.793669i	−0.354940	+	0.354940i	0.507004	+	0.861944i	$0.330753\pi$
$6$	−2.18555	+	1.10606i	−0.892248	+	0.451545i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.82589	+	0.119796i	−0.999103	+	0.0423544i
$9$	−2.97129	−	0.414021i	−0.990431	−	0.138007i
$10$	−1.53890	−	0.389140i	−0.486643	−	0.123057i
$11$	0.687038	+	0.687038i	0.207150	+	0.207150i	0.803055	−	0.595905i	$-0.203207\pi$
$11$	0.687038	+	0.687038i	0.207150	+	0.207150i	−0.595905	+	0.803055i	$0.703207\pi$
$12$	−2.92652	−	1.85350i	−0.844814	−	0.535060i
$13$	2.91110	−	2.91110i	0.807395	−	0.807395i	−0.176844	−	0.984239i	$-0.556589\pi$
$13$	2.91110	−	2.91110i	0.807395	−	0.807395i	0.984239	+	0.176844i	$0.0565888\pi$
$14$	−0.724332	−	1.21464i	−0.193586	−	0.324625i
$15$	−1.27630	−	1.46647i	−0.329539	−	0.378640i
$16$	−2.19239	−	3.34566i	−0.548098	−	0.836414i
$17$			1.81984i			0.441375i	0.975345	+	0.220688i	$0.0708302\pi$
$17$			1.81984i			0.441375i	−0.975345	+	0.220688i	$0.929170\pi$
$18$	−1.64932	−	3.90893i	−0.388748	−	0.921344i
$19$	3.24223	+	3.24223i	0.743818	+	0.743818i	0.973310	−	0.229492i	$-0.0737066\pi$
$19$	3.24223	+	3.24223i	0.743818	+	0.743818i	−0.229492	+	0.973310i	$0.573707\pi$
$20$	−0.642010	−	2.15107i	−0.143558	−	0.480994i
$21$	0.119805	−	1.72790i	0.0261435	−	0.377059i
$22$	−0.336858	+	1.33215i	−0.0718184	+	0.284014i
$23$			5.92103i			1.23462i	0.786720	+	0.617310i	$0.211778\pi$
$23$			5.92103i			1.23462i	−0.786720	+	0.617310i	$0.788222\pi$
$24$	0.131558	−	4.89721i	0.0268541	−	0.999639i
$25$			3.74018i			0.748036i
$26$	5.64454	+	1.42733i	1.10699	+	0.279922i
$27$	1.07136	−	5.08450i	0.206184	−	0.978513i
$28$	0.950686	−	1.75960i	0.179663	−	0.332533i
$29$	−1.54834	−	1.54834i	−0.287520	−	0.287520i	0.548579	−	0.836099i	$-0.315169\pi$
$29$	−1.54834	−	1.54834i	−0.287520	−	0.287520i	−0.836099	+	0.548579i	$0.815169\pi$
$30$	0.856763	−	2.61245i	0.156423	−	0.476965i
$31$			3.60999i			0.648373i	0.945993	+	0.324187i	$0.105091\pi$
$31$			3.60999i			0.648373i	−0.945993	+	0.324187i	$0.894909\pi$
$32$	2.47574	−	5.08633i	0.437653	−	0.899144i
$33$	−1.26945	+	1.10482i	−0.220982	+	0.192325i
$34$	−2.21044	+	1.31817i	−0.379088	+	0.226064i
$35$	0.793669	−	0.793669i	0.134155	−	0.134155i
$36$	3.55328	−	4.83469i	0.592213	−	0.805781i
$37$	−5.10312	−	5.10312i	−0.838947	−	0.838947i	0.149773	−	0.988720i	$-0.452146\pi$
$37$	−5.10312	−	5.10312i	−0.838947	−	0.838947i	−0.988720	+	0.149773i	$0.952146\pi$
$38$	−1.58968	+	6.28658i	−0.257880	+	1.01982i
$39$	4.68134	+	5.37887i	0.749614	+	0.861308i
$40$	2.14774	−	2.33790i	0.339588	−	0.369654i
$41$	−1.19627			−0.186826			−0.0934132	−	0.995627i	$-0.529778\pi$
$41$	−1.19627			−0.186826			−0.0934132	+	0.995627i	$0.529778\pi$
$42$	2.18555	−	1.10606i	0.337238	−	0.170668i
$43$	−7.00779	+	7.00779i	−1.06868	+	1.06868i	−0.0712169	+	0.997461i	$0.522688\pi$
$43$	−7.00779	+	7.00779i	−1.06868	+	1.06868i	−0.997461	+	0.0712169i	$0.977312\pi$
$44$	−1.86207	+	0.555755i	−0.280718	+	0.0837832i
$45$	2.68682	−	2.02963i	0.400527	−	0.302559i
$46$	−7.19190	+	4.28879i	−1.06039	+	0.632348i
$47$	13.1565			1.91908			0.959539	−	0.281577i	$-0.0908574\pi$
$47$	13.1565			1.91908			0.959539	+	0.281577i	$0.0908574\pi$
$48$	6.04363	−	3.38741i	0.872322	−	0.488931i
$49$	1.00000			0.142857
$50$	−4.54296	+	2.70913i	−0.642472	+	0.383129i
$51$	−3.14450	−	0.218025i	−0.440318	−	0.0305296i
$52$	2.35483	+	7.88993i	0.326557	+	1.09414i
$53$	2.08667	−	2.08667i	0.286627	−	0.286627i	−0.549118	−	0.835745i	$-0.685036\pi$
$53$	2.08667	−	2.08667i	0.286627	−	0.286627i	0.835745	+	0.549118i	$0.185036\pi$
$54$	6.95185	−	2.38155i	0.946027	−	0.324088i
$55$	−1.09056			−0.147051
$56$	2.82589	−	0.119796i	0.377625	−	0.0160085i
$57$	−5.99069	+	5.21382i	−0.793486	+	0.690587i
$58$	0.759161	−	3.00219i	0.0996827	−	0.394207i
$59$	0.919177	+	0.919177i	0.119667	+	0.119667i	0.764404	−	0.644737i	$-0.223033\pi$
$59$	0.919177	+	0.919177i	0.119667	+	0.119667i	−0.644737	+	0.764404i	$0.723033\pi$
$60$	3.79376	−	0.851623i	0.489772	−	0.109944i
$61$	4.21756	−	4.21756i	0.540003	−	0.540003i	−0.383527	−	0.923530i	$-0.625291\pi$
$61$	4.21756	−	4.21756i	0.540003	−	0.540003i	0.923530	+	0.383527i	$0.125291\pi$
$62$	−4.38483	+	2.61483i	−0.556874	+	0.332084i
$63$	2.97129	+	0.414021i	0.374348	+	0.0521618i
$64$	7.97130	−	0.677063i	0.996412	−	0.0846329i
$65$			4.62091i			0.573153i
$66$	−2.26146	−	0.741655i	−0.278367	−	0.0912915i
$67$	7.87889	+	7.87889i	0.962560	+	0.962560i	0.999324	−	0.0367640i	$-0.0117050\pi$
$67$	7.87889	+	7.87889i	0.962560	+	0.962560i	−0.0367640	+	0.999324i	$0.511705\pi$
$68$	−3.20219	−	1.73009i	−0.388322	−	0.209805i
$69$	−10.2310	−	0.709366i	−1.23166	−	0.0853977i
$70$	1.53890	+	0.389140i	0.183934	+	0.0465111i
$71$		−	7.99444i		−	0.948765i	−0.880319	−	0.474383i	$-0.842671\pi$
$71$		−	7.99444i		−	0.948765i	0.880319	−	0.474383i	$-0.157329\pi$
$72$	8.44614	+	0.814027i	0.995388	+	0.0959340i
$73$			4.19057i			0.490469i	0.969464	+	0.245235i	$0.0788650\pi$
$73$			4.19057i			0.490469i	−0.969464	+	0.245235i	$0.921135\pi$
$74$	2.50208	−	9.89478i	0.290861	−	1.15025i
$75$	−6.46266	−	0.448090i	−0.746244	−	0.0517410i
$76$	−8.78737	+	2.62269i	−1.00798	+	0.300843i
$77$	−0.687038	−	0.687038i	−0.0782953	−	0.0782953i
$78$	−3.14253	+	9.58221i	−0.355821	+	1.08497i
$79$			8.07689i			0.908721i	0.890818	+	0.454361i	$0.150132\pi$
$79$			8.07689i			0.908721i	−0.890818	+	0.454361i	$0.849868\pi$
$80$	4.39538	+	0.915312i	0.491418	+	0.102335i
$81$	8.65717	+	2.46036i	0.961908	+	0.273373i
$82$	−0.866499	−	1.45304i	−0.0956888	−	0.160461i
$83$	11.0241	−	11.0241i	1.21005	−	1.21005i	0.239045	−	0.971008i	$-0.423166\pi$
$83$	11.0241	−	11.0241i	1.21005	−	1.21005i	0.971008	−	0.239045i	$-0.0768344\pi$
$84$	2.92652	+	1.85350i	0.319310	+	0.202234i
$85$	−1.44435	−	1.44435i	−0.156662	−	0.156662i
$86$	−13.5879	−	3.43595i	−1.46522	−	0.370508i
$87$	2.86089	−	2.48989i	0.306719	−	0.266944i
$88$	−2.02380	−	1.85919i	−0.215738	−	0.198190i
$89$	−7.73403			−0.819806			−0.409903	−	0.912129i	$-0.634437\pi$
$89$	−7.73403			−0.819806			−0.409903	+	0.912129i	$0.634437\pi$
$90$	4.41141	+	1.79339i	0.465003	+	0.189039i
$91$	−2.91110	+	2.91110i	−0.305167	+	0.305167i
$92$	−10.4186	−	5.62904i	−1.08622	−	0.586868i
$93$	−6.23771	−	0.432493i	−0.646820	−	0.0448474i
$94$	9.52970	+	15.9804i	0.982913	+	1.64825i
$95$	−5.14651			−0.528021
$96$	8.49207	+	4.88720i	0.866718	+	0.498798i
$97$	6.61707			0.671862			0.335931	−	0.941887i	$-0.390949\pi$
$97$	6.61707			0.671862			0.335931	+	0.941887i	$0.390949\pi$
$98$	0.724332	+	1.21464i	0.0731686	+	0.122697i
$99$	−1.75694	−	2.32584i	−0.176579	−	0.233756i
$100$	−6.58122	−	3.55574i	−0.658122	−	0.355574i
$101$	11.9768	−	11.9768i	1.19174	−	1.19174i	0.215159	−	0.976579i	$-0.430973\pi$
$101$	11.9768	−	11.9768i	1.19174	−	1.19174i	0.976579	−	0.215159i	$-0.0690271\pi$
$102$	−2.01284	−	3.97735i	−0.199301	−	0.393816i
$103$	4.02452			0.396548			0.198274	−	0.980147i	$-0.436466\pi$
$103$	4.02452			0.396548			0.198274	+	0.980147i	$0.436466\pi$
$104$	−7.87772	+	8.57520i	−0.772474	+	0.840867i
$105$	1.27630	+	1.46647i	0.124554	+	0.143113i
$106$	4.04599	+	1.02311i	0.392982	+	0.0993729i
$107$	1.46112	+	1.46112i	0.141252	+	0.141252i	0.774197	−	0.632945i	$-0.218154\pi$
$107$	1.46112	+	1.46112i	0.141252	+	0.141252i	−0.632945	+	0.774197i	$0.718154\pi$
$108$	7.92817	+	6.71894i	0.762888	+	0.646530i
$109$	1.82675	−	1.82675i	0.174971	−	0.174971i	−0.614189	−	0.789159i	$-0.710517\pi$
$109$	1.82675	−	1.82675i	0.174971	−	0.174971i	0.789159	+	0.614189i	$0.210517\pi$
$110$	−0.789929	−	1.32464i	−0.0753167	−	0.126299i
$111$	9.42906	−	8.20631i	0.894967	−	0.778908i
$112$	2.19239	+	3.34566i	0.207161	+	0.316135i
$113$			10.8842i			1.02390i	0.859016	+	0.511949i	$0.171076\pi$
$113$			10.8842i			1.02390i	−0.859016	+	0.511949i	$0.828924\pi$
$114$	−10.6721	−	3.49997i	−0.999538	−	0.327803i
$115$	−4.69934	−	4.69934i	−0.438215	−	0.438215i
$116$	4.19646	−	1.25248i	0.389631	−	0.116290i
$117$	−9.85500	+	7.44449i	−0.911095	+	0.688243i
$118$	−0.450677	+	1.78226i	−0.0414882	+	0.164070i
$119$		−	1.81984i		−	0.166824i
$120$	3.78235	+	3.99118i	0.345280	+	0.364343i
$121$		−	10.0560i		−	0.914178i
$122$	8.17771	+	2.06789i	0.740375	+	0.187218i
$123$	0.143319	−	2.06704i	0.0129226	−	0.186379i
$124$	−6.35214	−	3.43197i	−0.570439	−	0.308200i
$125$	−6.93681	−	6.93681i	−0.620447	−	0.620447i
$126$	1.64932	+	3.90893i	0.146933	+	0.348235i
$127$		−	19.1621i		−	1.70036i	−0.526489	−	0.850182i	$-0.676492\pi$
$127$		−	19.1621i		−	1.70036i	0.526489	−	0.850182i	$-0.323508\pi$
$128$	6.59625	+	9.19182i	0.583032	+	0.812449i
$129$	−11.2692	−	12.9483i	−0.992199	−	1.14004i
$130$	−5.61272	+	3.34707i	−0.492268	+	0.293557i
$131$	10.9053	−	10.9053i	0.952803	−	0.952803i	−0.0461322	−	0.998935i	$-0.514690\pi$
$131$	10.9053	−	10.9053i	0.952803	−	0.952803i	0.998935	+	0.0461322i	$0.0146895\pi$
$132$	−0.737206	−	3.28406i	−0.0641656	−	0.285841i
$133$	−3.24223	−	3.24223i	−0.281137	−	0.281137i
$134$	−3.86306	+	15.2769i	−0.333718	+	1.31973i
$135$	3.18511	+	4.88572i	0.274130	+	0.420496i
$136$	−0.218010	−	5.14266i	−0.0186942	−	0.440979i
$137$	−8.23506			−0.703569			−0.351784	−	0.936081i	$-0.614425\pi$
$137$	−8.23506			−0.703569			−0.351784	+	0.936081i	$0.614425\pi$
$138$	−6.54899	−	12.9407i	−0.557487	−	1.10159i
$139$	−13.8449	+	13.8449i	−1.17431	+	1.17431i	−0.193133	+	0.981173i	$0.561865\pi$
$139$	−13.8449	+	13.8449i	−1.17431	+	1.17431i	−0.981173	+	0.193133i	$0.938135\pi$
$140$	0.642010	+	2.15107i	0.0542598	+	0.181799i
$141$	−1.57621	+	22.7332i	−0.132741	+	1.91448i
$142$	9.71034	−	5.79063i	0.814874	−	0.485939i
$143$	4.00008			0.334503
$144$	5.12906	+	10.8486i	0.427422	+	0.904052i
$145$	2.45775			0.204105
$146$	−5.09002	+	3.03536i	−0.421253	+	0.251208i
$147$	−0.119805	+	1.72790i	−0.00988131	+	0.142515i
$148$	13.8309	−	4.12798i	1.13689	−	0.339318i
$149$	1.63533	−	1.63533i	0.133972	−	0.133972i	−0.636941	−	0.770913i	$-0.719801\pi$
$149$	1.63533	−	1.63533i	0.133972	−	0.133972i	0.770913	+	0.636941i	$0.219801\pi$
$150$	−4.13685	−	8.17436i	−0.337772	−	0.667434i
$151$	3.55689			0.289456			0.144728	−	0.989472i	$-0.453769\pi$
$151$	3.55689			0.289456			0.144728	+	0.989472i	$0.453769\pi$
$152$	−9.55058	−	8.77377i	−0.774655	−	0.711647i
$153$	0.753451	−	5.40727i	0.0609129	−	0.437152i
$154$	0.336858	−	1.33215i	0.0271448	−	0.107347i
$155$	−2.86514	−	2.86514i	−0.230133	−	0.230133i
$156$	−13.9151	+	3.12368i	−1.11410	+	0.250094i
$157$	3.03338	−	3.03338i	0.242090	−	0.242090i	−0.575624	−	0.817714i	$-0.695241\pi$
$157$	3.03338	−	3.03338i	0.242090	−	0.242090i	0.817714	+	0.575624i	$0.195241\pi$
$158$	−9.81049	+	5.85035i	−0.780481	+	0.465429i
$159$	3.35557	+	3.85556i	0.266114	+	0.305766i
$160$	2.07194	+	6.00178i	0.163801	+	0.474482i
$161$		−	5.92103i		−	0.466643i
$162$	3.28223	+	12.2974i	0.257876	+	0.966178i
$163$	−11.1463	−	11.1463i	−0.873046	−	0.873046i	0.119758	−	0.992803i	$-0.461788\pi$
$163$	−11.1463	−	11.1463i	−0.873046	−	0.873046i	−0.992803	+	0.119758i	$0.961788\pi$
$164$	1.13728	−	2.10496i	0.0888067	−	0.164370i
$165$	0.130654	−	1.88438i	0.0101714	−	0.146699i
$166$	21.3754	+	5.40518i	1.65905	+	0.419523i
$167$			11.0498i			0.855061i	0.904001	+	0.427530i	$0.140616\pi$
$167$			11.0498i			0.855061i	−0.904001	+	0.427530i	$0.859384\pi$
$168$	−0.131558	+	4.89721i	−0.0101499	+	0.377828i
$169$		−	3.94905i		−	0.303773i
$170$	0.708171	−	2.80055i	0.0543143	−	0.214792i
$171$	−8.29126	−	10.9760i	−0.634049	−	0.839353i
$172$	−5.66870	−	18.9931i	−0.432235	−	1.44821i
$173$	7.29280	+	7.29280i	0.554461	+	0.554461i	0.927725	−	0.373264i	$-0.121761\pi$
$173$	7.29280	+	7.29280i	0.554461	+	0.554461i	−0.373264	+	0.927725i	$0.621761\pi$
$174$	5.09654	+	1.67143i	0.386368	+	0.126711i
$175$		−	3.74018i		−	0.282731i
$176$	0.792338	−	3.80485i	0.0597247	−	0.286801i
$177$	−1.69837	+	1.47813i	−0.127657	+	0.111103i
$178$	−5.60201	−	9.39404i	−0.419888	−	0.704113i
$179$	−12.1608	+	12.1608i	−0.908941	+	0.908941i	−0.996187	−	0.0872455i	$-0.972194\pi$
$179$	−12.1608	+	12.1608i	−0.908941	+	0.908941i	0.0872455	+	0.996187i	$0.472194\pi$
$180$	1.01701	+	6.65727i	0.0758037	+	0.496204i
$181$	−13.8880	−	13.8880i	−1.03229	−	1.03229i	−0.999461	−	0.0328291i	$-0.989548\pi$
$181$	−13.8880	−	13.8880i	−1.03229	−	1.03229i	−0.0328291	−	0.999461i	$-0.510452\pi$
$182$	−5.64454	−	1.42733i	−0.418401	−	0.105801i
$183$	6.78224	+	7.79281i	0.501358	+	0.576061i
$184$	−0.709318	−	16.7322i	−0.0522916	−	1.23351i
$185$	8.10037			0.595551
$186$	−3.99285	−	7.88982i	−0.292770	−	0.578510i
$187$	−1.25030	+	1.25030i	−0.0914308	+	0.0914308i
$188$	−12.5077	+	23.1502i	−0.912220	+	1.68841i
$189$	−1.07136	+	5.08450i	−0.0779302	+	0.369843i
$190$	−3.72778	−	6.25114i	−0.270442	−	0.453506i
$191$	−20.4639			−1.48072			−0.740360	−	0.672211i	$-0.765345\pi$
$191$	−20.4639			−1.48072			−0.740360	+	0.672211i	$0.765345\pi$
$192$	0.214901	+	13.8547i	0.0155091	+	0.999880i
$193$	16.2138			1.16709			0.583546	−	0.812080i	$-0.301665\pi$
$193$	16.2138			1.16709			0.583546	+	0.812080i	$0.301665\pi$
$194$	4.79296	+	8.03734i	0.344114	+	0.577048i
$195$	−7.98447	−	0.553606i	−0.571780	−	0.0396445i
$196$	−0.950686	+	1.75960i	−0.0679062	+	0.125686i
$197$	18.0133	−	18.0133i	1.28340	−	1.28340i	0.344676	−	0.938722i	$-0.387989\pi$
$197$	18.0133	−	18.0133i	1.28340	−	1.28340i	0.938722	−	0.344676i	$-0.112011\pi$
$198$	1.55244	−	3.81873i	0.110327	−	0.271385i
$199$	−8.64711			−0.612977			−0.306489	−	0.951874i	$-0.599154\pi$
$199$	−8.64711			−0.612977			−0.306489	+	0.951874i	$0.599154\pi$
$200$	−0.448060	−	10.5693i	−0.0316826	−	0.747365i
$201$	−14.5579	+	12.6700i	−1.02683	+	0.893675i
$202$	23.2227	+	5.87230i	1.63394	+	0.413173i
$203$	1.54834	+	1.54834i	0.108672	+	0.108672i
$204$	3.37307	−	5.32580i	0.236162	−	0.372880i
$205$	0.949445	−	0.949445i	0.0663121	−	0.0663121i
$206$	2.91509	+	4.88834i	0.203104	+	0.340586i
$207$	2.45143	−	17.5931i	0.170386	−	1.22281i
$208$	−16.1218	−	3.35728i	−1.11785	−	0.232785i
$209$			4.45507i			0.308164i
$210$	−0.856763	+	2.61245i	−0.0591223	+	0.180276i
$211$	−15.1424	−	15.1424i	−1.04245	−	1.04245i	−0.999058	−	0.0433902i	$-0.986184\pi$
$211$	−15.1424	−	15.1424i	−1.04245	−	1.04245i	−0.0433902	−	0.999058i	$-0.513816\pi$
$212$	1.68794	+	5.65548i	0.115928	+	0.388420i
$213$	13.8136	+	0.957770i	0.946493	+	0.0656253i
$214$	−0.716393	+	2.83306i	−0.0489716	+	0.193664i
$215$		−	11.1237i		−	0.758632i
$216$	−2.41845	+	14.4966i	−0.164554	+	0.986368i
$217$		−	3.60999i		−	0.245062i
$218$	3.54201	+	0.895664i	0.239895	+	0.0606620i
$219$	−7.24089	−	0.502049i	−0.489294	−	0.0339253i
$220$	1.03678	−	1.91895i	0.0698998	−	0.129376i
$221$	5.29774	+	5.29774i	0.356364	+	0.356364i
$222$	16.7975	+	5.50880i	1.12737	+	0.369726i
$223$			9.38004i			0.628134i	0.949401	+	0.314067i	$0.101692\pi$
$223$			9.38004i			0.628134i	−0.949401	+	0.314067i	$0.898308\pi$
$224$	−2.47574	+	5.08633i	−0.165417	+	0.339844i
$225$	1.54851	−	11.1132i	0.103234	−	0.740878i
$226$	−13.2203	+	7.88377i	−0.879404	+	0.524420i
$227$	−2.75222	+	2.75222i	−0.182671	+	0.182671i	−0.792519	−	0.609848i	$-0.791231\pi$
$227$	−2.75222	+	2.75222i	−0.182671	+	0.182671i	0.609848	+	0.792519i	$0.291231\pi$
$228$	−3.47898	−	15.4979i	−0.230401	−	1.02638i
$229$	5.83239	+	5.83239i	0.385415	+	0.385415i	0.873049	−	0.487633i	$-0.162140\pi$
$229$	5.83239	+	5.83239i	0.385415	+	0.385415i	−0.487633	+	0.873049i	$0.662140\pi$
$230$	2.30411	−	9.11187i	0.151928	−	0.600819i
$231$	1.26945	−	1.10482i	0.0835234	−	0.0726921i
$232$	4.56094	+	4.18996i	0.299440	+	0.275085i
$233$	−1.59095			−0.104227			−0.0521134	−	0.998641i	$-0.516596\pi$
$233$	−1.59095			−0.104227			−0.0521134	+	0.998641i	$0.516596\pi$
$234$	−16.1806	−	6.57797i	−1.05776	−	0.430016i
$235$	−10.4419	+	10.4419i	−0.681157	+	0.681157i
$236$	−2.49123	+	0.743536i	−0.162166	+	0.0484001i
$237$	−13.9561	−	0.967648i	−0.906545	−	0.0628555i
$238$	2.21044	−	1.31817i	0.143282	−	0.0854441i
$239$	−14.6487			−0.947548			−0.473774	−	0.880646i	$-0.657109\pi$
$239$	−14.6487			−0.947548			−0.473774	+	0.880646i	$0.657109\pi$
$240$	−2.10816	+	7.48512i	−0.136081	+	0.483163i
$241$	−28.4135			−1.83027			−0.915136	−	0.403146i	$-0.867917\pi$
$241$	−28.4135			−1.83027			−0.915136	+	0.403146i	$0.867917\pi$
$242$	12.2143	−	7.28385i	0.785167	−	0.468224i
$243$	−5.28843	+	14.6640i	−0.339253	+	0.940695i
$244$	3.41164	+	11.4308i	0.218408	+	0.731781i
$245$	−0.793669	+	0.793669i	−0.0507057	+	0.0507057i
$246$	2.61452	−	1.32314i	0.166696	−	0.0843606i
$247$	18.8769			1.20111
$248$	−0.432464	−	10.2014i	−0.0274615	−	0.647791i
$249$	17.7279	+	20.3693i	1.12346	+	1.29085i
$250$	3.40115	−	13.4503i	0.215108	−	0.850669i
$251$	−4.85544	−	4.85544i	−0.306473	−	0.306473i	0.537067	−	0.843540i	$-0.319532\pi$
$251$	−4.85544	−	4.85544i	−0.306473	−	0.306473i	−0.843540	+	0.537067i	$0.819532\pi$
$252$	−3.55328	+	4.83469i	−0.223836	+	0.304557i
$253$	−4.06797	+	4.06797i	−0.255751	+	0.255751i
$254$	23.2750	−	13.8797i	1.46040	−	0.870892i
$255$	2.66873	−	2.32265i	0.167123	−	0.145450i
$256$	−6.38684	+	14.6700i	−0.399178	+	0.916874i
$257$			13.3855i			0.834967i	0.908685	+	0.417483i	$0.137088\pi$
$257$			13.3855i			0.834967i	−0.908685	+	0.417483i	$0.862912\pi$
$258$	7.56488	−	23.0669i	0.470969	−	1.43608i
$259$	5.10312	+	5.10312i	0.317092	+	0.317092i
$260$	−8.13095	−	4.39303i	−0.504260	−	0.272444i
$261$	3.95954	+	5.24163i	0.245089	+	0.324449i
$262$	21.1451	+	5.34694i	1.30635	+	0.330335i
$263$			17.9546i			1.10713i	0.832806	+	0.553565i	$0.186733\pi$
$263$			17.9546i			1.10713i	−0.832806	+	0.553565i	$0.813267\pi$
$264$	3.45496	−	3.27419i	0.212638	−	0.201512i
$265$			3.31226i			0.203470i
$266$	1.58968	−	6.28658i	0.0974696	−	0.385455i
$267$	0.926572	−	13.3637i	0.0567053	−	0.817842i
$268$	−21.3541	+	6.37335i	−1.30441	+	0.389314i
$269$	2.45104	+	2.45104i	0.149442	+	0.149442i	0.777869	−	0.628427i	$-0.216301\pi$
$269$	2.45104	+	2.45104i	0.149442	+	0.149442i	−0.628427	+	0.777869i	$0.716301\pi$
$270$	−3.62730	+	7.40763i	−0.220751	+	0.450814i
$271$			12.0677i			0.733063i	0.930406	+	0.366531i	$0.119455\pi$
$271$			12.0677i			0.733063i	−0.930406	+	0.366531i	$0.880545\pi$
$272$	6.08855	−	3.98980i	0.369173	−	0.241917i
$273$	−4.68134	−	5.37887i	−0.283328	−	0.325544i
$274$	−5.96492	−	10.0026i	−0.360354	−	0.604280i
$275$	−2.56965	+	2.56965i	−0.154955	+	0.154955i
$276$	10.9746	−	17.3280i	0.660596	−	1.04302i
$277$	9.70343	+	9.70343i	0.583023	+	0.583023i	0.935733	−	0.352710i	$-0.114740\pi$
$277$	9.70343	+	9.70343i	0.583023	+	0.583023i	−0.352710	+	0.935733i	$0.614740\pi$
$278$	−26.8447	−	6.78820i	−1.61004	−	0.407129i
$279$	1.49461	−	10.7263i	0.0894801	−	0.642169i
$280$	−2.14774	+	2.33790i	−0.128352	+	0.139716i
$281$	29.4216			1.75515			0.877574	−	0.479442i	$-0.159161\pi$
$281$	29.4216			1.75515			0.877574	+	0.479442i	$0.159161\pi$
$282$	−28.7543	+	14.5519i	−1.71229	+	0.866551i
$283$	14.9400	−	14.9400i	0.888090	−	0.888090i	−0.106250	−	0.994339i	$-0.533884\pi$
$283$	14.9400	−	14.9400i	0.888090	−	0.888090i	0.994339	+	0.106250i	$0.0338843\pi$
$284$	14.0670	+	7.60020i	0.834724	+	0.450989i
$285$	0.616576	−	8.89267i	0.0365228	−	0.526756i
$286$	2.89738	+	4.85864i	0.171326	+	0.287298i
$287$	1.19627			0.0706137
$288$	−9.46200	+	14.0880i	−0.557554	+	0.830141i
$289$	13.6882			0.805188
$290$	1.78022	+	2.98527i	0.104538	+	0.175301i
$291$	−0.792755	+	11.4337i	−0.0464721	+	0.670253i
$292$	−7.37373	−	3.98392i	−0.431515	−	0.233141i
$293$	9.23001	−	9.23001i	0.539223	−	0.539223i	−0.384078	−	0.923301i	$-0.625481\pi$
$293$	9.23001	−	9.23001i	0.539223	−	0.539223i	0.923301	+	0.384078i	$0.125481\pi$
$294$	−2.18555	+	1.10606i	−0.127464	+	0.0645065i
$295$	−1.45904			−0.0849489
$296$	15.0322	+	13.8095i	0.873727	+	0.802661i
$297$	4.22931	−	2.75718i	0.245410	−	0.159988i
$298$	3.17086	+	0.801811i	0.183683	+	0.0464477i
$299$	17.2367	+	17.2367i	0.996826	+	0.996826i
$300$	6.93243	−	10.9457i	0.400244	−	0.631951i
$301$	7.00779	−	7.00779i	0.403922	−	0.403922i
$302$	2.57637	+	4.32033i	0.148253	+	0.248607i
$303$	19.2599	+	22.1297i	1.10645	+	1.27132i
$304$	3.73915	−	17.9556i	0.214455	−	1.02983i
$305$			6.69469i			0.383337i
$306$	7.11362	−	3.00149i	0.406659	−	0.171584i
$307$	4.11606	+	4.11606i	0.234916	+	0.234916i	0.814741	−	0.579825i	$-0.196879\pi$
$307$	4.11606	+	4.11606i	0.234916	+	0.234916i	−0.579825	+	0.814741i	$0.696879\pi$
$308$	1.86207	−	0.555755i	0.106101	−	0.0316671i
$309$	−0.482156	+	6.95398i	−0.0274289	+	0.395598i
$310$	1.40479	−	5.55541i	0.0797868	−	0.315526i
$311$			2.62720i			0.148975i	0.997222	+	0.0744875i	$0.0237321\pi$
$311$			2.62720i			0.148975i	−0.997222	+	0.0744875i	$0.976268\pi$
$312$	−13.8733	−	14.6393i	−0.785422	−	0.828786i
$313$		−	13.7108i		−	0.774979i	−0.921874	−	0.387490i	$-0.873342\pi$
$313$		−	13.7108i		−	0.774979i	0.921874	−	0.387490i	$-0.126658\pi$
$314$	5.88162	+	1.48728i	0.331919	+	0.0839320i
$315$	−2.68682	+	2.02963i	−0.151385	+	0.114357i
$316$	−14.2121	−	7.67859i	−0.799493	−	0.431954i
$317$	−17.8313	−	17.8313i	−1.00151	−	1.00151i	−0.999999	−	0.00150927i	$-0.999520\pi$
$317$	−17.8313	−	17.8313i	−1.00151	−	1.00151i	−0.00150927	−	0.999999i	$-0.500480\pi$
$318$	−2.25256	+	6.86851i	−0.126317	+	0.385167i
$319$		−	2.12754i		−	0.119120i
$320$	−5.78921	+	6.86394i	−0.323627	+	0.383706i
$321$	−2.69972	+	2.34962i	−0.150684	+	0.131143i
$322$	7.19190	−	4.28879i	0.400789	−	0.239005i
$323$	−5.90033	+	5.90033i	−0.328303	+	0.328303i
$324$	−12.5595	+	12.8941i	−0.697750	+	0.716341i
$325$	10.8881	+	10.8881i	0.603960	+	0.603960i
$326$	5.46509	−	21.6123i	0.302683	−	1.19700i
$327$	2.93759	+	3.37529i	0.162449	+	0.186654i
$328$	3.38053	−	0.143309i	0.186659	−	0.00791293i
$329$	−13.1565			−0.725343
$330$	2.38348	−	1.20622i	0.131206	−	0.0664003i
$331$	14.0930	−	14.0930i	0.774621	−	0.774621i	−0.204289	−	0.978911i	$-0.565488\pi$
$331$	14.0930	−	14.0930i	0.774621	−	0.774621i	0.978911	+	0.204289i	$0.0654883\pi$
$332$	8.91757	+	29.8785i	0.489415	+	1.63980i
$333$	13.0501	+	17.2757i	0.715139	+	0.946700i
$334$	−13.4215	+	8.00374i	−0.734393	+	0.437945i
$335$	−12.5065			−0.683301
$336$	−6.04363	+	3.38741i	−0.329707	+	0.184799i
$337$	32.8017			1.78682			0.893412	−	0.449237i	$-0.148304\pi$
$337$	32.8017			1.78682			0.893412	+	0.449237i	$0.148304\pi$
$338$	4.79667	−	2.86043i	0.260904	−	0.155587i
$339$	−18.8068	−	1.30398i	−1.02145	−	0.0708222i
$340$	3.91460	−	1.16835i	0.212299	−	0.0633629i
$341$	−2.48020	+	2.48020i	−0.134310	+	0.134310i
$342$	7.32619	−	18.0211i	0.396155	−	0.974470i
$343$	−1.00000			−0.0539949
$344$	18.9637	−	20.6427i	1.02246	−	1.11298i
$345$	8.68300	−	7.55699i	0.467477	−	0.406855i
$346$	−3.57569	+	14.1405i	−0.192231	+	0.760198i
$347$	−8.47003	−	8.47003i	−0.454695	−	0.454695i	0.442214	−	0.896909i	$-0.354193\pi$
$347$	−8.47003	−	8.47003i	−0.454695	−	0.454695i	−0.896909	+	0.442214i	$0.854193\pi$
$348$	1.66141	+	7.40112i	0.0890607	+	0.396742i
$349$	−19.6664	+	19.6664i	−1.05272	+	1.05272i	−0.0541874	+	0.998531i	$0.517257\pi$
$349$	−19.6664	+	19.6664i	−1.05272	+	1.05272i	−0.998531	+	0.0541874i	$0.982743\pi$
$350$	4.54296	−	2.70913i	0.242831	−	0.144809i
$351$	−11.6827	−	17.9204i	−0.623575	−	0.956519i
$352$	5.19543	−	1.79357i	0.276917	−	0.0955977i
$353$			0.437771i			0.0233002i	0.999932	+	0.0116501i	$0.00370843\pi$
$353$			0.437771i			0.0233002i	−0.999932	+	0.0116501i	$0.996292\pi$
$354$	−3.02557	−	0.992249i	−0.160807	−	0.0527374i
$355$	6.34494	+	6.34494i	0.336754	+	0.336754i
$356$	7.35264	−	13.6088i	0.389689	−	0.721266i
$357$	3.14450	+	0.218025i	0.166425	+	0.0115391i
$358$	−23.5794	−	5.96250i	−1.24621	−	0.315128i
$359$			1.40232i			0.0740117i	0.999315	+	0.0370059i	$0.0117820\pi$
$359$			1.40232i			0.0740117i	−0.999315	+	0.0370059i	$0.988218\pi$
$360$	−7.34951	+	6.05737i	−0.387353	+	0.319252i
$361$			2.02409i			0.106531i
$362$	6.80938	−	26.9285i	0.357893	−	1.41533i
$363$	17.3757	+	1.20475i	0.911988	+	0.0632329i
$364$	−2.35483	−	7.88993i	−0.123427	−	0.413545i
$365$	−3.32592	−	3.32592i	−0.174087	−	0.174087i
$366$	−4.55284	+	13.8825i	−0.237981	+	0.725652i
$367$		−	16.9905i		−	0.886896i	−0.896300	−	0.443448i	$-0.853755\pi$
$367$		−	16.9905i		−	0.886896i	0.896300	−	0.443448i	$-0.146245\pi$
$368$	19.8097	−	12.9812i	1.03265	−	0.676692i
$369$	3.55448	+	0.495282i	0.185039	+	0.0257834i
$370$	5.86736	+	9.83901i	0.305029	+	0.511506i
$371$	−2.08667	+	2.08667i	−0.108335	+	0.108335i
$372$	6.69112	−	10.5647i	0.346918	−	0.547755i
$373$	18.2390	+	18.2390i	0.944378	+	0.944378i	0.998533	−	0.0541550i	$-0.0172465\pi$
$373$	18.2390	+	18.2390i	0.944378	+	0.944378i	−0.0541550	+	0.998533i	$0.517247\pi$
$374$	−2.42429	−	0.613027i	−0.125357	−	0.0316989i
$375$	12.8172	−	11.1551i	0.661877	−	0.576045i
$376$	−37.1789	+	1.57611i	−1.91736	+	0.0812814i
$377$	−9.01478			−0.464285
$378$	−6.95185	+	2.38155i	−0.357565	+	0.122494i
$379$	10.0196	−	10.0196i	0.514671	−	0.514671i	−0.401283	−	0.915954i	$-0.631436\pi$
$379$	10.0196	−	10.0196i	0.514671	−	0.514671i	0.915954	+	0.401283i	$0.131436\pi$
$380$	4.89272	−	9.05581i	0.250991	−	0.464553i
$381$	33.1103	+	2.29571i	1.69629	+	0.117613i
$382$	−14.8227	−	24.8563i	−0.758395	−	1.27176i
$383$	−3.40774			−0.174127			−0.0870637	−	0.996203i	$-0.527748\pi$
$383$	−3.40774			−0.174127			−0.0870637	+	0.996203i	$0.527748\pi$
$384$	−16.6728	+	10.2965i	−0.850831	+	0.525439i
$385$	1.09056			0.0555802
$386$	11.7441	+	19.6938i	0.597761	+	1.00239i
$387$	23.7236	−	17.9208i	1.20594	−	0.910967i
$388$	−6.29076	+	11.6434i	−0.319365	+	0.591104i
$389$	−12.5187	+	12.5187i	−0.634726	+	0.634726i	−0.949250	−	0.314524i	$-0.898155\pi$
$389$	−12.5187	+	12.5187i	−0.634726	+	0.634726i	0.314524	+	0.949250i	$0.398155\pi$
$390$	−5.11098	−	10.0992i	−0.258805	−	0.511395i
$391$	−10.7753			−0.544931
$392$	−2.82589	+	0.119796i	−0.142729	+	0.00605063i
$393$	17.5368	+	20.1499i	0.884617	+	1.01643i
$394$	34.9273	+	8.83203i	1.75961	+	0.444951i
$395$	−6.41038	−	6.41038i	−0.322541	−	0.322541i
$396$	5.76285	−	0.880375i	0.289594	−	0.0442405i
$397$	14.5696	−	14.5696i	0.731227	−	0.731227i	−0.239636	−	0.970863i	$-0.577028\pi$
$397$	14.5696	−	14.5696i	0.731227	−	0.731227i	0.970863	+	0.239636i	$0.0770280\pi$
$398$	−6.26338	−	10.5031i	−0.313955	−	0.526473i
$399$	5.99069	−	5.21382i	0.299910	−	0.261018i
$400$	12.5134	−	8.19994i	0.625668	−	0.409997i
$401$			33.0155i			1.64871i	0.566071	+	0.824357i	$0.308463\pi$
$401$			33.0155i			1.64871i	−0.566071	+	0.824357i	$0.691537\pi$
$402$	−25.9342	−	8.50524i	−1.29348	−	0.424203i
$403$	10.5091	+	10.5091i	0.523493	+	0.523493i
$404$	9.68823	+	32.4606i	0.482007	+	1.61498i
$405$	−8.82364	+	4.91822i	−0.438450	+	0.244388i
$406$	−0.759161	+	3.00219i	−0.0376765	+	0.148996i
$407$		−	7.01207i		−	0.347575i
$408$	8.91213	+	0.239414i	0.441216	+	0.0118528i
$409$			32.8186i			1.62278i	0.584507	+	0.811389i	$0.301288\pi$
$409$			32.8186i			1.62278i	−0.584507	+	0.811389i	$0.698712\pi$
$410$	1.84094	+	0.465517i	0.0909177	+	0.0229903i
$411$	0.986598	−	14.2294i	0.0486653	−	0.701884i
$412$	−3.82606	+	7.08156i	−0.188496	+	0.348883i
$413$	−0.919177	−	0.919177i	−0.0452297	−	0.0452297i
$414$	23.1449	−	9.76566i	1.13751	−	0.479956i
$415$			17.4990i			0.858992i
$416$	−7.59969	−	22.0140i	−0.372605	−	1.07932i
$417$	−22.2639	−	25.5812i	−1.09027	−	1.25272i
$418$	−5.41129	+	3.22695i	−0.264675	+	0.157835i
$419$	26.1424	−	26.1424i	1.27714	−	1.27714i	0.334878	−	0.942261i	$-0.391305\pi$
$419$	26.1424	−	26.1424i	1.27714	−	1.27714i	0.942261	−	0.334878i	$-0.108695\pi$
$420$	−3.79376	+	0.851623i	−0.185116	+	0.0415550i
$421$	−10.8258	−	10.8258i	−0.527619	−	0.527619i	0.392243	−	0.919862i	$-0.371699\pi$
$421$	−10.8258	−	10.8258i	−0.527619	−	0.527619i	−0.919862	+	0.392243i	$0.871699\pi$
$422$	7.42441	−	29.3607i	0.361415	−	1.42926i
$423$	−39.0919	−	5.44708i	−1.90071	−	0.264846i
$424$	−5.64673	+	6.14668i	−0.274229	+	0.298509i
$425$	−6.80652			−0.330165
$426$	8.84230	+	17.4723i	0.428411	+	0.846534i
$427$	−4.21756	+	4.21756i	−0.204102	+	0.204102i
$428$	−3.96005	+	1.18192i	−0.191416	+	0.0571302i
$429$	−0.479228	+	6.91175i	−0.0231373	+	0.333702i
$430$	13.5113	−	8.05727i	0.651572	−	0.388556i
$431$	−23.9053			−1.15148			−0.575739	−	0.817633i	$-0.695286\pi$
$431$	−23.9053			−1.15148			−0.575739	+	0.817633i	$0.695286\pi$
$432$	−19.3599	+	7.56281i	−0.931451	+	0.363866i
$433$	−1.75665			−0.0844192			−0.0422096	−	0.999109i	$-0.513440\pi$
$433$	−1.75665			−0.0844192			−0.0422096	+	0.999109i	$0.513440\pi$
$434$	4.38483	−	2.61483i	0.210478	−	0.125516i
$435$	−0.294449	+	4.24675i	−0.0141178	+	0.203616i
$436$	1.47768	+	4.95101i	0.0707682	+	0.237110i
$437$	−19.1973	+	19.1973i	−0.918333	+	0.918333i
$438$	−4.63500	−	9.15871i	−0.221469	−	0.437620i
$439$	−14.0251			−0.669383			−0.334692	−	0.942328i	$-0.608632\pi$
$439$	−14.0251			−0.669383			−0.334692	+	0.942328i	$0.608632\pi$
$440$	3.08181	−	0.130645i	0.146919	−	0.00622827i
$441$	−2.97129	−	0.414021i	−0.141490	−	0.0197153i
$442$	−2.59751	+	10.2721i	−0.123551	+	0.488596i
$443$	16.6535	+	16.6535i	0.791232	+	0.791232i	0.981694	−	0.190463i	$-0.0609988\pi$
$443$	16.6535	+	16.6535i	0.791232	+	0.791232i	−0.190463	+	0.981694i	$0.560999\pi$
$444$	5.47575	+	24.3930i	0.259868	+	1.15764i
$445$	6.13826	−	6.13826i	0.290982	−	0.290982i
$446$	−11.3933	+	6.79426i	−0.539490	+	0.321718i
$447$	2.62977	+	3.02161i	0.124384	+	0.142917i
$448$	−7.97130	+	0.677063i	−0.376608	+	0.0319882i
$449$		−	15.4487i		−	0.729069i	−0.931190	−	0.364535i	$-0.881228\pi$
$449$		−	15.4487i		−	0.729069i	0.931190	−	0.364535i	$-0.118772\pi$
$450$	14.6201	−	6.16874i	0.689198	−	0.290797i
$451$	−0.821885	−	0.821885i	−0.0387010	−	0.0387010i
$452$	−19.1518	−	10.3475i	−0.900826	−	0.486703i
$453$	−0.426132	+	6.14596i	−0.0200214	+	0.288762i
$454$	−5.33647	−	1.34943i	−0.250453	−	0.0633317i
$455$		−	4.62091i		−	0.216631i
$456$	16.3044	−	15.4513i	0.763525	−	0.723575i
$457$		−	14.8875i		−	0.696410i	−0.937418	−	0.348205i	$-0.886791\pi$
$457$		−	14.8875i		−	0.696410i	0.937418	−	0.348205i	$-0.113209\pi$
$458$	−2.85965	+	11.3088i	−0.133623	+	0.528427i
$459$	9.25297	+	1.94971i	0.431892	+	0.0910045i
$460$	12.7366	−	3.80136i	0.593845	−	0.177239i
$461$	6.75343	+	6.75343i	0.314539	+	0.314539i	0.846665	−	0.532126i	$-0.178607\pi$
$461$	6.75343	+	6.75343i	0.314539	+	0.314539i	−0.532126	+	0.846665i	$0.678607\pi$
$462$	2.26146	+	0.741655i	0.105213	+	0.0345049i
$463$			3.04014i			0.141287i	0.997502	+	0.0706437i	$0.0225053\pi$
$463$			3.04014i			0.141287i	−0.997502	+	0.0706437i	$0.977495\pi$
$464$	−1.78565	+	8.57481i	−0.0828969	+	0.398075i
$465$	5.29393	−	4.60742i	0.245500	−	0.213664i
$466$	−1.15238	−	1.93243i	−0.0533829	−	0.0895181i
$467$	−6.49283	+	6.49283i	−0.300452	+	0.300452i	−0.841191	−	0.540739i	$-0.818145\pi$
$467$	−6.49283	+	6.49283i	−0.300452	+	0.300452i	0.540739	+	0.841191i	$0.318145\pi$
$468$	−3.73031	−	24.4182i	−0.172434	−	1.12873i
$469$	−7.87889	−	7.87889i	−0.363813	−	0.363813i
$470$	−20.2466	−	5.11973i	−0.933905	−	0.236156i
$471$	4.87796	+	5.60479i	0.224765	+	0.258255i
$472$	−2.70761	−	2.48738i	−0.124628	−	0.114491i
$473$	−9.62924			−0.442753
$474$	−8.93349	−	17.6525i	−0.410329	−	0.810805i
$475$	−12.1265	+	12.1265i	−0.556403	+	0.556403i
$476$	3.20219	+	1.73009i	0.146772	+	0.0792988i
$477$	−7.06404	+	5.33619i	−0.323440	+	0.244327i
$478$	−10.6106	−	17.7929i	−0.485315	−	0.813828i
$479$	−22.2658			−1.01735			−0.508674	−	0.860959i	$-0.669864\pi$
$479$	−22.2658			−1.01735			−0.508674	+	0.860959i	$0.669864\pi$
$480$	−10.6187	+	2.86107i	−0.484676	+	0.130589i
$481$	−29.7114			−1.35472
$482$	−20.5808	−	34.5120i	−0.937429	−	1.57198i
$483$	10.2310	+	0.709366i	0.465525	+	0.0322773i
$484$	17.6945	+	9.56006i	0.804294	+	0.434548i
$485$	−5.25177	+	5.25177i	−0.238470	+	0.238470i
$486$	−21.6420	+	4.19808i	−0.981701	+	0.190429i
$487$	−33.2574			−1.50704			−0.753518	−	0.657428i	$-0.771644\pi$
$487$	−33.2574			−1.50704			−0.753518	+	0.657428i	$0.771644\pi$
$488$	−11.4131	+	12.4236i	−0.516647	+	0.562390i
$489$	20.5951	−	17.9243i	0.931343	−	0.810567i
$490$	−1.53890	−	0.389140i	−0.0695204	−	0.0175795i
$491$	3.40809	+	3.40809i	0.153805	+	0.153805i	0.779815	−	0.626010i	$-0.215313\pi$
$491$	3.40809	+	3.40809i	0.153805	+	0.153805i	−0.626010	+	0.779815i	$0.715313\pi$
$492$	3.50092	+	2.21729i	0.157834	+	0.0999633i
$493$	2.81774	−	2.81774i	0.126904	−	0.126904i
$494$	13.6732	+	22.9286i	0.615185	+	1.03161i
$495$	3.24038	+	0.451516i	0.145644	+	0.0202941i
$496$	12.0778	−	7.91451i	0.542309	−	0.355372i
$497$			7.99444i			0.358600i
$498$	−11.9005	+	36.2871i	−0.533274	+	1.62606i
$499$	−8.47025	−	8.47025i	−0.379180	−	0.379180i	0.491626	−	0.870806i	$-0.336403\pi$
$499$	−8.47025	−	8.47025i	−0.379180	−	0.379180i	−0.870806	+	0.491626i	$0.836403\pi$
$500$	18.8007	−	5.61129i	0.840795	−	0.250944i
$501$	−19.0930	−	1.32382i	−0.853013	−	0.0591439i
$502$	2.38065	−	9.41455i	0.106254	−	0.420192i
$503$		−	8.10503i		−	0.361385i	−0.983540	−	0.180693i	$-0.942166\pi$
$503$		−	8.10503i		−	0.361385i	0.983540	−	0.180693i	$-0.0578339\pi$
$504$	−8.44614	−	0.814027i	−0.376221	−	0.0362597i
$505$			19.0113i			0.845990i
$506$	−7.88767	−	1.99455i	−0.350650	−	0.0886685i
$507$	6.82358	+	0.473115i	0.303046	+	0.0210118i
$508$	33.7177	+	18.2172i	1.49598	+	0.808256i
$509$	−13.3365	−	13.3365i	−0.591128	−	0.591128i	0.346808	−	0.937936i	$-0.387266\pi$
$509$	−13.3365	−	13.3365i	−0.591128	−	0.591128i	−0.937936	+	0.346808i	$0.887266\pi$
$510$	4.75423	+	1.55917i	0.210521	+	0.0690412i
$511$		−	4.19057i		−	0.185380i
$512$	−22.4449	+	2.86824i	−0.991933	+	0.126759i
$513$	19.9587	−	13.0115i	0.881199	−	0.574473i
$514$	−16.2586	+	9.69557i	−0.717135	+	0.427653i
$515$	−3.19414	+	3.19414i	−0.140751	+	0.140751i
$516$	33.4974	−	7.51950i	1.47464	−	0.331028i
$517$	9.03904	+	9.03904i	0.397536	+	0.397536i
$518$	−2.50208	+	9.89478i	−0.109935	+	0.434752i
$519$	−13.4749	+	11.7275i	−0.591485	+	0.514781i
$520$	−0.553568	−	13.0582i	−0.0242756	−	0.572639i
$521$	−27.8638			−1.22073			−0.610367	−	0.792118i	$-0.708978\pi$
$521$	−27.8638			−1.22073			−0.610367	+	0.792118i	$0.708978\pi$
$522$	−3.49866	+	8.60609i	−0.153132	+	0.376678i
$523$	5.47159	−	5.47159i	0.239256	−	0.239256i	−0.577286	−	0.816542i	$-0.695888\pi$
$523$	5.47159	−	5.47159i	0.239256	−	0.239256i	0.816542	+	0.577286i	$0.195888\pi$
$524$	8.82148	+	29.5566i	0.385368	+	1.29119i
$525$	6.46266	+	0.448090i	0.282054	+	0.0195563i
$526$	−21.8084	+	13.0051i	−0.950889	+	0.567050i
$527$	−6.56959			−0.286176
$528$	6.47948	+	1.82492i	0.281983	+	0.0794195i
$529$	−12.0586			−0.524287
$530$	−4.02319	+	2.39917i	−0.174756	+	0.104213i
$531$	−2.35059	−	3.11170i	−0.102007	−	0.135036i
$532$	8.78737	−	2.62269i	0.380981	−	0.113708i
$533$	−3.48247	+	3.48247i	−0.150843	+	0.150843i
$534$	16.9031	−	8.55427i	0.731470	−	0.370180i
$535$	−2.31929			−0.100272
$536$	−23.2087	−	21.3210i	−1.00246	−	0.920928i
$537$	−19.5558	−	22.4696i	−0.843894	−	0.969635i
$538$	−1.20176	+	4.75248i	−0.0518114	+	0.204894i
$539$	0.687038	+	0.687038i	0.0295928	+	0.0295928i
$540$	−11.6250	+	0.959728i	−0.500258	+	0.0413001i
$541$	−20.1581	+	20.1581i	−0.866666	+	0.866666i	−0.992102	−	0.125436i	$-0.959967\pi$
$541$	−20.1581	+	20.1581i	−0.866666	+	0.866666i	0.125436	+	0.992102i	$0.459967\pi$
$542$	−14.6579	+	8.74105i	−0.629611	+	0.375460i
$543$	25.6610	−	22.3333i	1.10122	−	0.958415i
$544$	9.25629	+	4.50545i	0.396860	+	0.193169i
$545$			2.89967i			0.124208i
$546$	3.14253	−	9.58221i	0.134488	−	0.410081i
$547$	13.7420	+	13.7420i	0.587566	+	0.587566i	0.936972	−	0.349405i	$-0.113616\pi$
$547$	13.7420	+	13.7420i	0.587566	+	0.587566i	−0.349405	+	0.936972i	$0.613616\pi$
$548$	7.82896	−	14.4904i	0.334437	−	0.619000i
$549$	−14.2778	+	10.7854i	−0.609360	+	0.460311i
$550$	−4.98246	−	1.25991i	−0.212453	−	0.0537228i
$551$		−	10.0402i		−	0.427726i
$552$	28.9965	+	0.778958i	1.23417	+	0.0331546i
$553$		−	8.07689i		−	0.343464i
$554$	−4.75764	+	18.8147i	−0.202133	+	0.799358i
$555$	−0.970461	+	13.9966i	−0.0411938	+	0.594125i
$556$	−11.1993	−	37.5235i	−0.474956	−	1.59135i
$557$	−13.2012	−	13.2012i	−0.559354	−	0.559354i	0.369770	−	0.929123i	$-0.379437\pi$
$557$	−13.2012	−	13.2012i	−0.559354	−	0.559354i	−0.929123	+	0.369770i	$0.879437\pi$
$558$	14.1112	−	5.95402i	0.597375	−	0.252054i
$559$			40.8008i			1.72569i
$560$	−4.39538	−	0.915312i	−0.185739	−	0.0386790i
$561$	−2.01060	−	2.31018i	−0.0848876	−	0.0975360i
$562$	21.3110	+	35.7366i	0.898951	+	1.50746i
$563$	−24.9115	+	24.9115i	−1.04990	+	1.04990i	−0.0512070	+	0.998688i	$0.516307\pi$
$563$	−24.9115	+	24.9115i	−1.04990	+	1.04990i	−0.998688	+	0.0512070i	$0.983693\pi$
$564$	−38.5029	−	24.3857i	−1.62126	−	1.02682i
$565$	−8.63844	−	8.63844i	−0.363422	−	0.363422i
$566$	28.9682	+	7.32515i	1.21762	+	0.307899i
$567$	−8.65717	−	2.46036i	−0.363567	−	0.103325i
$568$	0.957705	+	22.5914i	0.0401844	+	0.947914i
$569$	18.3196			0.767996			0.383998	−	0.923334i	$-0.374547\pi$
$569$	18.3196			0.767996			0.383998	+	0.923334i	$0.374547\pi$
$570$	11.2480	−	5.69233i	0.471126	−	0.238425i
$571$	16.5968	−	16.5968i	0.694552	−	0.694552i	−0.268678	−	0.963230i	$-0.586587\pi$
$571$	16.5968	−	16.5968i	0.694552	−	0.694552i	0.963230	+	0.268678i	$0.0865867\pi$
$572$	−3.80282	+	7.03854i	−0.159004	+	0.294296i
$573$	2.45167	−	35.3597i	0.102420	−	1.47717i
$574$	0.866499	+	1.45304i	0.0361670	+	0.0606486i
$575$	−22.1457			−0.923540
$576$	−23.9654	−	1.28853i	−0.998558	−	0.0536889i
$577$	−34.1660			−1.42235			−0.711174	−	0.703016i	$-0.751836\pi$
$577$	−34.1660			−1.42235			−0.711174	+	0.703016i	$0.751836\pi$
$578$	9.91479	+	16.6262i	0.412401	+	0.691558i
$579$	−1.94248	+	28.0158i	−0.0807268	+	1.16430i
$580$	−2.33655	+	4.32465i	−0.0970198	+	0.179571i
$581$	−11.0241	+	11.0241i	−0.457357	+	0.457357i
$582$	−14.4620	+	7.31885i	−0.599468	+	0.303376i
$583$	2.86725			0.118749
$584$	−0.502015	−	11.8421i	−0.0207735	−	0.490029i
$585$	1.91315	−	13.7301i	0.0790991	−	0.567668i
$586$	17.8967	+	4.52552i	0.739306	+	0.186948i
$587$	32.1989	+	32.1989i	1.32899	+	1.32899i	0.906252	+	0.422739i	$0.138931\pi$
$587$	32.1989	+	32.1989i	1.32899	+	1.32899i	0.422739	+	0.906252i	$0.361069\pi$
$588$	−2.92652	−	1.85350i	−0.120688	−	0.0764371i
$589$	−11.7044	+	11.7044i	−0.482272	+	0.482272i
$590$	−1.05683	−	1.77221i	−0.0435091	−	0.0729607i
$591$	28.9672	+	33.2834i	1.19155	+	1.36910i
$592$	−5.88525	+	28.2613i	−0.241882	+	1.16153i
$593$		−	44.2672i		−	1.81783i	−0.416977	−	0.908917i	$-0.636910\pi$
$593$		−	44.2672i		−	1.81783i	0.416977	−	0.908917i	$-0.363090\pi$
$594$	6.41240	+	3.13997i	0.263104	+	0.128834i
$595$	1.44435	+	1.44435i	0.0592125	+	0.0592125i
$596$	1.32284	+	4.43222i	0.0541858	+	0.181551i
$597$	1.03596	−	14.9414i	0.0423991	−	0.611509i
$598$	−8.45126	+	33.4215i	−0.345598	+	1.36671i
$599$		−	20.2525i		−	0.827493i	−0.910392	−	0.413747i	$-0.864220\pi$
$599$		−	20.2525i		−	0.827493i	0.910392	−	0.413747i	$-0.135780\pi$
$600$	18.3165	+	0.492050i	0.747766	+	0.0200878i
$601$		−	32.5467i		−	1.32761i	−0.747906	−	0.663805i	$-0.768941\pi$
$601$		−	32.5467i		−	1.32761i	0.747906	−	0.663805i	$-0.231059\pi$
$602$	13.5879	+	3.43595i	0.553801	+	0.140039i
$603$	−20.1485	−	26.6725i	−0.820509	−	1.08619i
$604$	−3.38149	+	6.25871i	−0.137591	+	0.254663i
$605$	7.98110	+	7.98110i	0.324478	+	0.324478i
$606$	−12.9289	+	39.4230i	−0.525202	+	1.60145i
$607$		−	30.3618i		−	1.23235i	−0.787611	−	0.616173i	$-0.788682\pi$
$607$		−	30.3618i		−	1.23235i	0.787611	−	0.616173i	$-0.211318\pi$
$608$	24.5179	−	8.46411i	0.994334	−	0.343265i
$609$	−2.86089	+	2.48989i	−0.115929	+	0.100895i
$610$	−8.13162	+	4.84918i	−0.329239	+	0.196337i
$611$	38.3000	−	38.3000i	1.54945	−	1.54945i
$612$	8.79835	+	6.46639i	0.355652	+	0.261388i
$613$	−4.99303	−	4.99303i	−0.201667	−	0.201667i	0.599047	−	0.800714i	$-0.295546\pi$
$613$	−4.99303	−	4.99303i	−0.201667	−	0.201667i	−0.800714	+	0.599047i	$0.795546\pi$
$614$	−2.01812	+	7.98090i	−0.0814448	+	0.322083i
$615$	1.52680	+	1.75430i	0.0615665	+	0.0707400i
$616$	2.02380	+	1.85919i	0.0815411	+	0.0749088i
$617$	42.8610			1.72552			0.862760	−	0.505613i	$-0.168734\pi$
$617$	42.8610			1.72552			0.862760	+	0.505613i	$0.168734\pi$
$618$	−8.79581	+	4.45135i	−0.353819	+	0.179059i
$619$	10.7162	−	10.7162i	0.430720	−	0.430720i	−0.458154	−	0.888873i	$-0.651489\pi$
$619$	10.7162	−	10.7162i	0.430720	−	0.430720i	0.888873	+	0.458154i	$0.151489\pi$
$620$	7.76534	−	2.31765i	0.311864	−	0.0930791i
$621$	30.1055	+	6.34357i	1.20809	+	0.254559i
$622$	−3.19110	+	1.90297i	−0.127951	+	0.0763020i
$623$	7.73403			0.309857
$624$	7.73252	−	27.4547i	0.309548	−	1.09907i
$625$	−7.68984			−0.307593
$626$	16.6536	−	9.93116i	0.665613	−	0.396929i
$627$	−7.69792	−	0.533737i	−0.307425	−	0.0213154i
$628$	2.45374	+	8.22132i	0.0979149	+	0.328066i
$629$	9.28684	−	9.28684i	0.370291	−	0.370291i
$630$	−4.41141	−	1.79339i	−0.175755	−	0.0714502i
$631$	−2.23257			−0.0888772			−0.0444386	−	0.999012i	$-0.514150\pi$
$631$	−2.23257			−0.0888772			−0.0444386	+	0.999012i	$0.514150\pi$
$632$	−0.967583	−	22.8244i	−0.0384884	−	0.907906i
$633$	27.9788	−	24.3505i	1.11206	−	0.967846i
$634$	8.74280	−	34.5744i	0.347221	−	1.37313i
$635$	15.2084	+	15.2084i	0.603526	+	0.603526i
$636$	−9.97435	+	2.23904i	−0.395509	+	0.0887839i
$637$	2.91110	−	2.91110i	0.115342	−	0.115342i
$638$	2.58419	−	1.54105i	0.102309	−	0.0610107i
$639$	−3.30987	+	23.7538i	−0.130936	+	0.939687i
$640$	−12.5305	−	2.06002i	−0.495311	−	0.0814294i
$641$			15.4714i			0.611084i	0.952179	+	0.305542i	$0.0988376\pi$
$641$			15.4714i			0.611084i	−0.952179	+	0.305542i	$0.901162\pi$
$642$	−4.80943	−	1.57727i	−0.189813	−	0.0622499i
$643$	−5.09054	−	5.09054i	−0.200751	−	0.200751i	0.599571	−	0.800322i	$-0.295338\pi$
$643$	−5.09054	−	5.09054i	−0.200751	−	0.200751i	−0.800322	+	0.599571i	$0.795338\pi$
$644$	10.4186	+	5.62904i	0.410552	+	0.221815i
$645$	19.2207	+	1.33267i	0.756815	+	0.0524740i
$646$	−11.4406	−	2.89296i	−0.450123	−	0.113822i
$647$		−	30.5094i		−	1.19945i	−0.800207	−	0.599723i	$-0.795277\pi$
$647$		−	30.5094i		−	1.19945i	0.800207	−	0.599723i	$-0.204723\pi$
$648$	−24.7590	−	5.91560i	−0.972623	−	0.232387i
$649$			1.26302i			0.0495778i
$650$	−5.33847	+	21.1116i	−0.209392	+	0.828065i
$651$	6.23771	+	0.432493i	0.244475	+	0.0169507i
$652$	30.2097	−	9.01641i	1.18310	−	0.353110i
$653$	−31.0832	−	31.0832i	−1.21638	−	1.21638i	−0.968891	−	0.247489i	$-0.920395\pi$
$653$	−31.0832	−	31.0832i	−1.21638	−	1.21638i	−0.247489	−	0.968891i	$-0.579605\pi$
$654$	−1.97197	+	6.01294i	−0.0771100	+	0.235124i
$655$			17.3104i			0.676375i
$656$	2.62270	+	4.00232i	0.102399	+	0.156264i
$657$	1.73498	−	12.4514i	0.0676882	−	0.485776i
$658$	−9.52970	−	15.9804i	−0.371506	−	0.622981i
$659$	−2.29783	+	2.29783i	−0.0895109	+	0.0895109i	−0.750444	−	0.660934i	$-0.770161\pi$
$659$	−2.29783	+	2.29783i	−0.0895109	+	0.0895109i	0.660934	+	0.750444i	$0.270161\pi$
$660$	3.19155	+	2.02136i	0.124231	+	0.0786812i
$661$	17.7096	+	17.7096i	0.688823	+	0.688823i	0.961972	−	0.273149i	$-0.0880650\pi$
$661$	17.7096	+	17.7096i	0.688823	+	0.688823i	−0.273149	+	0.961972i	$0.588065\pi$
$662$	27.3259	+	6.90987i	1.06205	+	0.268560i
$663$	−9.78867	+	8.51928i	−0.380160	+	0.330861i
$664$	−29.8323	+	32.4736i	−1.15772	+	1.26022i
$665$	5.14651			0.199573
$666$	−11.5311	+	28.3644i	−0.446820	+	1.09910i
$667$	9.16779	−	9.16779i	0.354978	−	0.354978i
$668$	−19.4433	−	10.5049i	−0.752283	−	0.406447i
$669$	−16.2078	−	1.12377i	−0.626629	−	0.0434475i
$670$	−9.05883	−	15.1908i	−0.349973	−	0.586872i
$671$	5.79524			0.223723
$672$	−8.49207	−	4.88720i	−0.327589	−	0.188528i
$673$	−13.2746			−0.511700			−0.255850	−	0.966717i	$-0.582355\pi$
$673$	−13.2746			−0.511700			−0.255850	+	0.966717i	$0.582355\pi$
$674$	23.7594	+	39.8422i	0.915176	+	1.53466i
$675$	19.0170	+	4.00709i	0.731963	+	0.154233i
$676$	6.94876	+	3.75431i	0.267260	+	0.144397i
$677$	16.7445	−	16.7445i	0.643543	−	0.643543i	−0.307882	−	0.951425i	$-0.599620\pi$
$677$	16.7445	−	16.7445i	0.643543	−	0.643543i	0.951425	+	0.307882i	$0.0996202\pi$
$678$	−12.0385	−	23.7880i	−0.462337	−	0.913572i
$679$	−6.61707			−0.253940
$680$	4.25460	+	3.90854i	0.163156	+	0.149886i
$681$	−4.42584	−	5.08529i	−0.169598	−	0.194869i
$682$	−4.80903	−	1.21605i	−0.184147	−	0.0465651i
$683$	17.3241	+	17.3241i	0.662887	+	0.662887i	0.956060	−	0.293173i	$-0.0947110\pi$
$683$	17.3241	+	17.3241i	0.662887	+	0.662887i	−0.293173	+	0.956060i	$0.594711\pi$
$684$	27.1957	−	4.15461i	1.03985	−	0.158856i
$685$	6.53591	−	6.53591i	0.249724	−	0.249724i
$686$	−0.724332	−	1.21464i	−0.0276551	−	0.0463751i
$687$	−10.7765	+	9.37905i	−0.411151	+	0.357833i
$688$	38.8095	+	8.08185i	1.47960	+	0.308117i
$689$		−	12.1490i		−	0.462842i
$690$	15.4684	+	5.07292i	0.588871	+	0.193123i
$691$	8.73989	+	8.73989i	0.332481	+	0.332481i	0.853528	−	0.521047i	$-0.174458\pi$
$691$	8.73989	+	8.73989i	0.332481	+	0.332481i	−0.521047	+	0.853528i	$0.674458\pi$
$692$	−19.7656	+	5.89925i	−0.751374	+	0.224256i
$693$	1.75694	+	2.32584i	0.0667408	+	0.0883514i
$694$	4.15290	−	16.4231i	0.157642	−	0.623414i
$695$		−	21.9765i		−	0.833615i
$696$	−7.78627	+	7.37888i	−0.295138	+	0.279696i
$697$		−	2.17702i		−	0.0824606i
$698$	−38.1325	−	9.64253i	−1.44334	−	0.364975i
$699$	0.190603	−	2.74901i	0.00720928	−	0.103977i
$700$	6.58122	+	3.55574i	0.248747	+	0.134394i
$701$	6.71385	+	6.71385i	0.253579	+	0.253579i	0.822436	−	0.568857i	$-0.192614\pi$
$701$	6.71385	+	6.71385i	0.253579	+	0.253579i	−0.568857	+	0.822436i	$0.692614\pi$
$702$	13.3046	−	27.1705i	0.502150	−	1.02548i
$703$		−	33.0909i		−	1.24805i
$704$	5.94175	+	5.01142i	0.223938	+	0.188875i
$705$	−16.7916	−	19.2936i	−0.632410	−	0.726640i
$706$	−0.531733	+	0.317092i	−0.0200120	+	0.0119339i
$707$	−11.9768	+	11.9768i	−0.450435	+	0.450435i
$708$	−0.986296	−	4.39369i	−0.0370673	−	0.165125i
$709$	−21.5025	−	21.5025i	−0.807542	−	0.807542i	0.176719	−	0.984261i	$-0.443451\pi$
$709$	−21.5025	−	21.5025i	−0.807542	−	0.807542i	−0.984261	+	0.176719i	$0.943451\pi$
$710$	−3.11096	+	12.3026i	−0.116752	+	0.461710i
$711$	3.34400	−	23.9988i	0.125410	−	0.900026i
$712$	21.8555	−	0.926510i	0.819070	−	0.0347224i
$713$	−21.3749			−0.800495
$714$	2.01284	+	3.97735i	0.0753287	+	0.148849i
$715$	−3.17474	+	3.17474i	−0.118728	+	0.118728i
$716$	−9.83705	−	32.9593i	−0.367628	−	1.23175i
$717$	1.75499	−	25.3116i	0.0655411	−	0.945279i
$718$	−1.70331	+	1.01575i	−0.0635670	+	0.0379073i
$719$	41.4285			1.54502			0.772511	−	0.635001i	$-0.219000\pi$
$719$	41.4285			1.54502			0.772511	+	0.635001i	$0.219000\pi$
$720$	−12.6810	−	4.53944i	−0.472593	−	0.169175i
$721$	−4.02452			−0.149881
$722$	−2.45853	+	1.46611i	−0.0914971	+	0.0545631i
$723$	3.40406	−	49.0957i	0.126598	−	1.82589i
$724$	37.6406	−	11.2342i	1.39890	−	0.417517i
$725$	5.79109	−	5.79109i	0.215076	−	0.215076i
$726$	11.1225	+	21.9778i	0.412793	+	0.815674i
$727$	46.8176			1.73637			0.868185	−	0.496240i	$-0.165286\pi$
$727$	46.8176			1.73637			0.868185	+	0.496240i	$0.165286\pi$
$728$	7.87772	−	8.57520i	0.291968	−	0.317818i
$729$	−24.7044	−	10.8947i	−0.914976	−	0.403507i
$730$	1.63072	−	6.44886i	0.0603556	−	0.238683i
$731$	−12.7530	−	12.7530i	−0.471688	−	0.471688i
$732$	−20.1600	+	4.52553i	−0.745136	+	0.167268i
$733$	4.53750	−	4.53750i	0.167596	−	0.167596i	−0.618326	−	0.785922i	$-0.712189\pi$
$733$	4.53750	−	4.53750i	0.167596	−	0.167596i	0.785922	+	0.618326i	$0.212189\pi$
$734$	20.6373	−	12.3067i	0.761735	−	0.454250i
$735$	−1.27630	−	1.46647i	−0.0470769	−	0.0540915i
$736$	30.1163	+	14.6589i	1.11010	+	0.540335i
$737$			10.8262i			0.398788i
$738$	1.97303	+	4.67615i	0.0726284	+	0.172131i
$739$	−7.62556	−	7.62556i	−0.280511	−	0.280511i	0.552802	−	0.833313i	$-0.313559\pi$
$739$	−7.62556	−	7.62556i	−0.280511	−	0.280511i	−0.833313	+	0.552802i	$0.813559\pi$
$740$	−7.70091	+	14.2534i	−0.283091	+	0.523966i
$741$	−2.26154	+	32.6175i	−0.0830798	+	1.19823i
$742$	−4.04599	−	1.02311i	−0.148533	−	0.0375594i
$743$			39.5962i			1.45264i	0.687354	+	0.726322i	$0.258772\pi$
$743$			39.5962i			1.45264i	−0.687354	+	0.726322i	$0.741228\pi$
$744$	17.6789	+	0.474922i	0.648139	+	0.0174115i
$745$			2.59582i			0.0951036i
$746$	−8.94265	+	35.3648i	−0.327414	+	1.29480i
$747$	−37.3201	+	28.1917i	−1.36547	+	1.03148i
$748$	−1.01138	−	3.38867i	−0.0369799	−	0.123902i
$749$	−1.46112	−	1.46112i	−0.0533881	−	0.0533881i
$750$	22.8333	+	7.48826i	0.833753	+	0.273433i
$751$			28.0916i			1.02508i	0.858664	+	0.512539i	$0.171295\pi$
$751$			28.0916i			1.02508i	−0.858664	+	0.512539i	$0.828705\pi$
$752$	−28.8443	−	44.0172i	−1.05184	−	1.60514i
$753$	8.97143	−	7.80803i	0.326937	−	0.284540i
$754$	−6.52970	−	10.9497i	−0.237798	−	0.398764i
$755$	−2.82299	+	2.82299i	−0.102739	+	0.102739i
$756$	−7.92817	−	6.71894i	−0.288345	−	0.244365i
$757$	33.6575	+	33.6575i	1.22330	+	1.22330i	0.966451	+	0.256850i	$0.0826847\pi$
$757$	33.6575	+	33.6575i	1.22330	+	1.22330i	0.256850	+	0.966451i	$0.417315\pi$
$758$	19.4276	+	4.91264i	0.705643	+	0.178435i
$759$	−6.54170	−	7.51642i	−0.237449	−	0.272829i
$760$	14.5435	−	0.616534i	0.527547	−	0.0223640i
$761$	45.4670			1.64818			0.824089	−	0.566460i	$-0.191687\pi$
$761$	45.4670			1.64818			0.824089	+	0.566460i	$0.191687\pi$
$762$	21.1944	+	41.8798i	0.767791	+	1.51715i
$763$	−1.82675	+	1.82675i	−0.0661327	+	0.0661327i
$764$	19.4548	−	36.0084i	0.703850	−	1.30274i
$765$	3.69359	+	4.88958i	0.133542	+	0.176783i
$766$	−2.46833	−	4.13917i	−0.0891846	−	0.149554i
$767$	5.35164			0.193237
$768$	−24.5831	−	12.7934i	−0.887067	−	0.461641i
$769$	41.5500			1.49833			0.749165	−	0.662383i	$-0.230455\pi$
$769$	41.5500			1.49833			0.749165	+	0.662383i	$0.230455\pi$
$770$	0.789929	+	1.32464i	0.0284671	+	0.0477366i
$771$	−23.1289	−	1.60365i	−0.832967	−	0.0577540i
$772$	−15.4142	+	28.5298i	−0.554769	+	1.02681i
$773$	7.34561	−	7.34561i	0.264203	−	0.264203i	−0.562556	−	0.826759i	$-0.690182\pi$
$773$	7.34561	−	7.34561i	0.264203	−	0.264203i	0.826759	+	0.562556i	$0.190182\pi$
$774$	38.9510	+	15.8349i	1.40007	+	0.569174i
$775$	−13.5020			−0.485006
$776$	−18.6991	+	0.792702i	−0.671259	+	0.0284563i
$777$	−9.42906	+	8.20631i	−0.338266	+	0.294400i
$778$	−24.2735	−	6.13801i	−0.870246	−	0.220058i
$779$	−3.87859	−	3.87859i	−0.138965	−	0.138965i
$780$	8.56486	−	13.5232i	0.306671	−	0.484208i
$781$	5.49248	−	5.49248i	0.196537	−	0.196537i
$782$	−7.80490	−	13.0881i	−0.279103	−	0.468029i
$783$	−9.53140	+	6.21373i	−0.340625	+	0.222060i
$784$	−2.19239	−	3.34566i	−0.0782997	−	0.119488i
$785$			4.81499i			0.171854i
$786$	−11.7723	+	35.8961i	−0.419903	+	1.28037i
$787$	15.6277	+	15.6277i	0.557067	+	0.557067i	0.928471	−	0.371404i	$-0.121124\pi$
$787$	15.6277	+	15.6277i	0.557067	+	0.557067i	−0.371404	+	0.928471i	$0.621124\pi$
$788$	14.5713	+	48.8213i	0.519080	+	1.73919i
$789$	−31.0238	−	2.15105i	−1.10448	−	0.0765793i
$790$	3.14304	−	12.4295i	0.111824	−	0.442223i
$791$		−	10.8842i		−	0.386997i
$792$	5.24356	+	6.36209i	0.186322	+	0.226067i
$793$		−	24.5555i		−	0.871991i
$794$	28.2500	+	7.14355i	1.00256	+	0.253515i
$795$	−5.72325	−	0.396823i	−0.202983	−	0.0140739i
$796$	8.22069	−	15.2155i	0.291375	−	0.539298i
$797$	1.27149	+	1.27149i	0.0450386	+	0.0450386i	0.729267	−	0.684229i	$-0.239861\pi$
$797$	1.27149	+	1.27149i	0.0450386	+	0.0450386i	−0.684229	+	0.729267i	$0.739861\pi$
$798$	10.6721	+	3.49997i	0.377790	+	0.123898i
$799$			23.9428i			0.847034i
$800$	19.0238	+	9.25971i	0.672592	+	0.327380i
$801$	22.9801	+	3.20205i	0.811961	+	0.113139i
$802$	−40.1018	+	23.9142i	−1.41604	+	0.844438i
$803$	−2.87908	+	2.87908i	−0.101601	+	0.101601i
$804$	−8.45422	−	37.6613i	−0.298157	−	1.32821i
$805$	4.69934	+	4.69934i	0.165630	+	0.165630i
$806$	−5.15264	+	20.3767i	−0.181494	+	0.717740i
$807$	−4.52880	+	3.94151i	−0.159421	+	0.138748i
$808$	−32.4104	+	35.2800i	−1.14019	+	1.24114i
$809$	−22.1723			−0.779536			−0.389768	−	0.920913i	$-0.627445\pi$
$809$	−22.1723			−0.779536			−0.389768	+	0.920913i	$0.627445\pi$
$810$	−12.3651	−	7.15509i	−0.434465	−	0.251404i
$811$	12.7466	−	12.7466i	0.447592	−	0.447592i	−0.446961	−	0.894553i	$-0.647494\pi$
$811$	12.7466	−	12.7466i	0.447592	−	0.447592i	0.894553	+	0.446961i	$0.147494\pi$
$812$	−4.19646	+	1.25248i	−0.147267	+	0.0439534i
$813$	−20.8519	−	1.44577i	−0.731307	−	0.0507054i
$814$	8.51712	−	5.07907i	0.298525	−	0.178021i
$815$	17.6929			0.619757
$816$	6.16454	+	10.9984i	0.215802	+	0.385022i
$817$	−45.4417			−1.58980
$818$	−39.8627	+	23.7716i	−1.39377	+	0.831154i
$819$	9.85500	−	7.44449i	0.344362	−	0.260131i
$820$	0.768020	+	2.57327i	0.0268204	+	0.0898624i
$821$	−17.2846	+	17.2846i	−0.603237	+	0.603237i	−0.941170	−	0.337933i	$-0.890272\pi$
$821$	−17.2846	+	17.2846i	−0.603237	+	0.603237i	0.337933	+	0.941170i	$0.390272\pi$
$822$	17.9982	−	9.10844i	0.627758	−	0.317693i
$823$	−20.8242			−0.725885			−0.362943	−	0.931811i	$-0.618228\pi$
$823$	−20.8242			−0.725885			−0.362943	+	0.931811i	$0.618228\pi$
$824$	−11.3729	+	0.482124i	−0.396192	+	0.0167956i
$825$	−4.13224	−	4.74795i	−0.143866	−	0.165302i
$826$	0.450677	−	1.78226i	0.0156811	−	0.0620126i
$827$	8.47227	+	8.47227i	0.294610	+	0.294610i	0.838898	−	0.544288i	$-0.183200\pi$
$827$	8.47227	+	8.47227i	0.294610	+	0.294610i	−0.544288	+	0.838898i	$0.683200\pi$
$828$	28.6263	+	21.0391i	0.994834	+	0.731159i
$829$	−22.1752	+	22.1752i	−0.770175	+	0.770175i	−0.978137	−	0.207962i	$-0.933317\pi$
$829$	−22.1752	+	22.1752i	−0.770175	+	0.770175i	0.207962	+	0.978137i	$0.433317\pi$
$830$	−21.2549	+	12.6751i	−0.737769	+	0.439958i
$831$	−17.9291	+	15.6041i	−0.621953	+	0.541299i
$832$	21.2343	−	25.1763i	0.736166	−	0.872830i
$833$			1.81984i			0.0630536i
$834$	14.9455	−	45.5719i	0.517520	−	1.57802i
$835$	−8.76990	−	8.76990i	−0.303495	−	0.303495i
$836$	−7.83914	−	4.23537i	−0.271122	−	0.146483i
$837$	18.3550	+	3.86761i	0.634442	+	0.133684i
$838$	50.6893	+	12.8177i	1.75103	+	0.442782i
$839$			32.9450i			1.13739i	0.822550	+	0.568693i	$0.192551\pi$
$839$			32.9450i			1.13739i	−0.822550	+	0.568693i	$0.807449\pi$
$840$	−3.78235	−	3.99118i	−0.130504	−	0.137709i
$841$		−	24.2053i		−	0.834664i
$842$	5.30796	−	20.9910i	0.182924	−	0.723396i
$843$	−3.52484	+	50.8377i	−0.121402	+	1.75094i
$844$	41.0404	−	12.2489i	1.41267	−	0.421626i
$845$	3.13424	+	3.13424i	0.107821	+	0.107821i
$846$	−21.6993	−	51.4280i	−0.746037	−	1.76813i
$847$			10.0560i			0.345527i
$848$	−11.5561	−	2.40649i	−0.396838	−	0.0826392i
$849$	24.0250	+	27.6047i	0.824534	+	0.947391i
$850$	−4.93018	−	8.26745i	−0.169104	−	0.283571i
$851$	30.2157	−	30.2157i	1.03578	−	1.03578i
$852$	−14.8177	+	23.3959i	−0.507646	+	0.801530i
$853$	−1.85899	−	1.85899i	−0.0636505	−	0.0636505i	0.674565	−	0.738215i	$-0.264331\pi$
$853$	−1.85899	−	1.85899i	−0.0636505	−	0.0636505i	−0.738215	+	0.674565i	$0.764331\pi$
$854$	−8.17771	−	2.06789i	−0.279836	−	0.0707617i
$855$	15.2918	+	2.13076i	0.522968	+	0.0728706i
$856$	−4.30399	−	3.95392i	−0.147107	−	0.135142i
$857$	−42.9571			−1.46739			−0.733693	−	0.679481i	$-0.762205\pi$
$857$	−42.9571			−1.46739			−0.733693	+	0.679481i	$0.762205\pi$
$858$	−8.74238	+	4.42431i	−0.298460	+	0.151043i
$859$	2.45763	−	2.45763i	0.0838532	−	0.0838532i	−0.663936	−	0.747789i	$-0.731115\pi$
$859$	2.45763	−	2.45763i	0.0838532	−	0.0838532i	0.747789	+	0.663936i	$0.231115\pi$
$860$	19.5733	+	10.5752i	0.667445	+	0.360611i
$861$	−0.143319	+	2.06704i	−0.00488430	+	0.0704446i
$862$	−17.3154	−	29.0363i	−0.589764	−	0.988979i
$863$	−24.3220			−0.827931			−0.413965	−	0.910293i	$-0.635857\pi$
$863$	−24.3220			−0.827931			−0.413965	+	0.910293i	$0.635857\pi$
$864$	−23.2090	−	18.0372i	−0.789587	−	0.613638i
$865$	−11.5761			−0.393600
$866$	−1.27240	−	2.13369i	−0.0432379	−	0.0725058i
$867$	−1.63991	+	23.6519i	−0.0556942	+	0.803259i
$868$	6.35214	+	3.43197i	0.215606	+	0.116489i
$869$	−5.54913	+	5.54913i	−0.188241	+	0.188241i
$870$	−5.37153	+	2.71840i	−0.182112	+	0.0921626i
$871$	45.8726			1.55433
$872$	−4.94335	+	5.38102i	−0.167403	+	0.182224i
$873$	−19.6613	−	2.73961i	−0.665433	−	0.0927217i
$874$	−37.2230	−	9.41255i	−1.25909	−	0.318384i
$875$	6.93681	+	6.93681i	0.234507	+	0.234507i
$876$	7.76723	−	12.2638i	0.262430	−	0.414355i
$877$	−37.4633	+	37.4633i	−1.26505	+	1.26505i	−0.316429	+	0.948616i	$0.602484\pi$
$877$	−37.4633	+	37.4633i	−1.26505	+	1.26505i	−0.948616	+	0.316429i	$0.897516\pi$
$878$	−10.1589	−	17.0355i	−0.342845	−	0.574919i
$879$	14.8428	+	17.0544i	0.500634	+	0.575229i
$880$	2.39094	+	3.64865i	0.0805985	+	0.122996i
$881$			13.6767i			0.460778i	0.973099	+	0.230389i	$0.0739999\pi$
$881$			13.6767i			0.460778i	−0.973099	+	0.230389i	$0.926000\pi$
$882$	−1.64932	−	3.90893i	−0.0555354	−	0.131621i
$883$	−25.0213	−	25.0213i	−0.842035	−	0.842035i	0.147088	−	0.989123i	$-0.453010\pi$
$883$	−25.0213	−	25.0213i	−0.842035	−	0.842035i	−0.989123	+	0.147088i	$0.953010\pi$
$884$	−14.3584	+	4.28542i	−0.482925	+	0.144134i
$885$	0.174800	−	2.52109i	0.00587584	−	0.0847454i
$886$	−8.16530	+	32.2906i	−0.274319	+	1.08483i
$887$		−	11.3258i		−	0.380283i	−0.981757	−	0.190142i	$-0.939105\pi$
$887$		−	11.3258i		−	0.380283i	0.981757	−	0.190142i	$-0.0608947\pi$
$888$	−25.6624	+	24.3197i	−0.861174	+	0.816115i
$889$			19.1621i			0.642677i
$890$	11.9019	+	3.00962i	0.398953	+	0.100883i
$891$	4.25745	+	7.63817i	0.142630	+	0.255888i
$892$	−16.5051	−	8.91748i	−0.552632	−	0.298579i
$893$	42.6565	+	42.6565i	1.42744	+	1.42744i
$894$	−1.76533	+	5.38287i	−0.0590416	+	0.180030i
$895$		−	19.3033i		−	0.645238i
$896$	−6.59625	−	9.19182i	−0.220365	−	0.307077i
$897$	−31.8484	+	27.7184i	−1.06339	+	0.925489i
$898$	18.7646	−	11.1900i	0.626182	−	0.373415i
$899$	5.58951	−	5.58951i	0.186420	−	0.186420i
$900$	18.0826	+	13.2899i	0.602753	+	0.442997i
$901$	3.79741	+	3.79741i	0.126510	+	0.126510i
$902$	0.402974	−	1.59361i	0.0134176	−	0.0530614i
$903$	11.2692	+	12.9483i	0.375016	+	0.430894i
$904$	−1.30389	−	30.7575i	−0.0433666	−	1.02298i
$905$	22.0450			0.732801
$906$	−7.77377	+	3.93412i	−0.258266	+	0.130702i
$907$	−15.7617	+	15.7617i	−0.523359	+	0.523359i	−0.918584	−	0.395225i	$-0.870667\pi$
$907$	−15.7617	+	15.7617i	−0.523359	+	0.523359i	0.395225	+	0.918584i	$0.370667\pi$
$908$	−2.22631	−	7.45930i	−0.0738827	−	0.247546i
$909$	−40.5453	+	30.6280i	−1.34480	+	1.01587i
$910$	5.61272	−	3.34707i	0.186060	−	0.110954i
$911$	1.71533			0.0568314			0.0284157	−	0.999596i	$-0.490954\pi$
$911$	1.71533			0.0568314			0.0284157	+	0.999596i	$0.490954\pi$
$912$	30.5776	+	8.61205i	1.01253	+	0.285174i
$913$	15.1480			0.501325
$914$	18.0830	−	10.7835i	0.598131	−	0.356687i
$915$	−11.5678	−	0.802054i	−0.382419	−	0.0265151i
$916$	−15.8075	+	4.71791i	−0.522293	+	0.155884i
$917$	−10.9053	+	10.9053i	−0.360126	+	0.360126i
$918$	4.33404	+	12.6512i	0.143045	+	0.417553i
$919$	11.9819			0.395245			0.197623	−	0.980278i	$-0.436678\pi$
$919$	11.9819			0.395245			0.197623	+	0.980278i	$0.436678\pi$
$920$	13.8428	+	12.7168i	0.456383	+	0.419262i
$921$	−7.60526	+	6.61902i	−0.250602	+	0.218104i
$922$	−3.31124	+	13.0947i	−0.109050	+	0.431251i
$923$	−23.2726	−	23.2726i	−0.766028	−	0.766028i
$924$	0.737206	+	3.28406i	0.0242523	+	0.108038i
$925$	19.0866	−	19.0866i	0.627562	−	0.627562i
$926$	−3.69267	+	2.20207i	−0.121349	+	0.0723646i
$927$	−11.9580	−	1.66624i	−0.392754	−	0.0547264i
$928$	−11.7087	+	4.04209i	−0.384356	+	0.132688i
$929$		−	3.91557i		−	0.128466i	−0.997935	−	0.0642329i	$-0.979540\pi$
$929$		−	3.91557i		−	0.128466i	0.997935	−	0.0642329i	$-0.0204600\pi$
$930$	9.43091	+	3.09290i	0.309252	+	0.101420i
$931$	3.24223	+	3.24223i	0.106260	+	0.106260i
$932$	1.51250	−	2.79944i	0.0495435	−	0.0916987i
$933$	−4.53955	−	0.314751i	−0.148618	−	0.0103045i
$934$	−12.5894	−	3.18347i	−0.411937	−	0.104166i
$935$		−	1.98465i		−	0.0649048i
$936$	26.9573	−	22.2179i	0.881128	−	0.726214i
$937$		−	18.0568i		−	0.589889i	−0.955514	−	0.294944i	$-0.904699\pi$
$937$		−	18.0568i		−	0.589889i	0.955514	−	0.294944i	$-0.0953011\pi$
$938$	3.86306	−	15.2769i	0.126133	−	0.498809i
$939$	23.6909	+	1.64261i	0.773123	+	0.0536047i
$940$	−8.44663	−	28.3006i	−0.275499	−	0.923065i
$941$	16.2020	+	16.2020i	0.528171	+	0.528171i	0.920027	−	0.391856i	$-0.128167\pi$
$941$	16.2020	+	16.2020i	0.528171	+	0.528171i	−0.391856	+	0.920027i	$0.628167\pi$
$942$	−3.27452	+	9.98468i	−0.106690	+	0.325319i
$943$		−	7.08317i		−	0.230660i
$944$	1.06006	−	5.09045i	0.0345019	−	0.165680i
$945$	−3.18511	−	4.88572i	−0.103612	−	0.158932i
$946$	−6.97476	−	11.6960i	−0.226769	−	0.380271i
$947$	−5.87730	+	5.87730i	−0.190987	+	0.190987i	−0.796122	−	0.605136i	$-0.793119\pi$
$947$	−5.87730	+	5.87730i	−0.190987	+	0.190987i	0.605136	+	0.796122i	$0.293119\pi$
$948$	14.9705	−	23.6372i	0.486220	−	0.767701i
$949$	12.1992	+	12.1992i	0.396002	+	0.396002i
$950$	−23.5129	−	5.94569i	−0.762860	−	0.192904i
$951$	32.9471	−	28.6745i	1.06838	−	0.929836i
$952$	0.218010	+	5.14266i	0.00706575	+	0.166675i
$953$	−3.56742			−0.115560			−0.0577800	−	0.998329i	$-0.518402\pi$
$953$	−3.56742			−0.115560			−0.0577800	+	0.998329i	$0.518402\pi$
$954$	−11.5982	−	4.71508i	−0.375507	−	0.152656i
$955$	16.2416	−	16.2416i	0.525566	−	0.525566i
$956$	13.9264	−	25.7759i	0.450411	−	0.833653i
$957$	3.67619	+	0.254889i	0.118834	+	0.00823940i
$958$	−16.1278	−	27.0448i	−0.521065	−	0.873778i
$959$	8.23506			0.265924
$960$	−11.1666	−	10.8255i	−0.360402	−	0.349392i
$961$	17.9680			0.579612
$962$	−21.5209	−	36.0886i	−0.693862	−	1.16354i
$963$	−3.73648	−	4.94634i	−0.120406	−	0.159394i
$964$	27.0123	−	49.9963i	0.870007	−	1.61027i
$965$	−12.8684	+	12.8684i	−0.414247	+	0.414247i
$966$	6.54899	+	12.9407i	0.210710	+	0.416361i
$967$	0.0190295			0.000611946			0.000305973	−	1.00000i	$-0.499903\pi$
$967$	0.0190295			0.000611946			0.000305973		1.00000i	$0.499903\pi$
$968$	1.20467	+	28.4170i	0.0387195	+	0.913358i
$969$	−9.48831	−	10.9021i	−0.304808	−	0.350225i
$970$	−10.1830	−	2.57497i	−0.326957	−	0.0826772i
$971$	−14.4569	−	14.4569i	−0.463942	−	0.463942i	0.436003	−	0.899945i	$-0.356394\pi$
$971$	−14.4569	−	14.4569i	−0.463942	−	0.463942i	−0.899945	+	0.436003i	$0.856394\pi$
$972$	−20.7751	−	23.2464i	−0.666363	−	0.745628i
$973$	13.8449	−	13.8449i	0.443846	−	0.443846i
$974$	−24.0894	−	40.3956i	−0.771873	−	1.29436i
$975$	−20.1179	+	17.5091i	−0.644289	+	0.560738i
$976$	−23.3570	−	4.86397i	−0.747640	−	0.155692i
$977$		−	27.0977i		−	0.866932i	−0.901170	−	0.433466i	$-0.857290\pi$
$977$		−	27.0977i		−	0.866932i	0.901170	−	0.433466i	$-0.142710\pi$
$978$	36.6893	+	12.0324i	1.17319	+	0.384754i
$979$	−5.31357	−	5.31357i	−0.169823	−	0.169823i
$980$	−0.642010	−	2.15107i	−0.0205083	−	0.0687134i
$981$	−6.18412	+	4.67149i	−0.197444	+	0.149149i
$982$	−1.67100	+	6.60818i	−0.0533239	+	0.210876i
$983$			27.2678i			0.869708i	0.900501	+	0.434854i	$0.143200\pi$
$983$			27.2678i			0.869708i	−0.900501	+	0.434854i	$0.856800\pi$
$984$	−0.157379	+	5.85840i	−0.00501706	+	0.186759i
$985$			28.5933i			0.911057i
$986$	5.46350	+	1.38155i	0.173993	+	0.0439975i
$987$	1.57621	−	22.7332i	0.0501714	−	0.723606i
$988$	−17.9460	+	33.2159i	−0.570939	+	1.05674i
$989$	−41.4933	−	41.4933i	−1.31941	−	1.31941i
$990$	1.79868	+	4.26293i	0.0571659	+	0.135485i
$991$		−	33.7498i		−	1.07210i	−0.844187	−	0.536050i	$-0.819916\pi$
$991$		−	33.7498i		−	1.07210i	0.844187	−	0.536050i	$-0.180084\pi$
$992$	18.3616	+	8.93739i	0.582981	+	0.283763i
$993$	22.6629	+	26.0397i	0.719186	+	0.826346i
$994$	−9.71034	+	5.79063i	−0.307993	+	0.183668i
$995$	6.86294	−	6.86294i	0.217570	−	0.217570i
$996$	−52.6955	+	11.8291i	−1.66972	+	0.374819i
$997$	−20.2763	−	20.2763i	−0.642157	−	0.642157i	0.308928	−	0.951085i	$-0.400030\pi$
$997$	−20.2763	−	20.2763i	−0.642157	−	0.642157i	−0.951085	+	0.308928i	$0.900030\pi$
$998$	4.15301	−	16.4236i	0.131461	−	0.519878i
$999$	−31.4141	+	20.4795i	−0.993898	+	0.647943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.14	yes	40
3.2	odd	2	inner	336.2.s.c.155.7	✓	40
4.3	odd	2		1344.2.s.c.911.13		40
12.11	even	2		1344.2.s.c.911.2		40
16.3	odd	4	inner	336.2.s.c.323.7	yes	40
16.13	even	4		1344.2.s.c.239.2		40
48.29	odd	4		1344.2.s.c.239.13		40
48.35	even	4	inner	336.2.s.c.323.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.7	✓	40	3.2	odd	2	inner
336.2.s.c.155.14	yes	40	1.1	even	1	trivial
336.2.s.c.323.7	yes	40	16.3	odd	4	inner
336.2.s.c.323.14	yes	40	48.35	even	4	inner
1344.2.s.c.239.2		40	16.13	even	4
1344.2.s.c.239.13		40	48.29	odd	4
1344.2.s.c.911.2		40	12.11	even	2
1344.2.s.c.911.13		40	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.724332 + 1.21464i) q^{2} +(-0.119805 + 1.72790i) q^{3} +(-0.950686 + 1.75960i) q^{4} +(-0.793669 + 0.793669i) q^{5} +(-2.18555 + 1.10606i) q^{6} -1.00000 q^{7} +(-2.82589 + 0.119796i) q^{8} +(-2.97129 - 0.414021i) q^{9} +O(q^{10})\)	\(q+(0.724332 + 1.21464i) q^{2} +(-0.119805 + 1.72790i) q^{3} +(-0.950686 + 1.75960i) q^{4} +(-0.793669 + 0.793669i) q^{5} +(-2.18555 + 1.10606i) q^{6} -1.00000 q^{7} +(-2.82589 + 0.119796i) q^{8} +(-2.97129 - 0.414021i) q^{9} +(-1.53890 - 0.389140i) q^{10} +(0.687038 + 0.687038i) q^{11} +(-2.92652 - 1.85350i) q^{12} +(2.91110 - 2.91110i) q^{13} +(-0.724332 - 1.21464i) q^{14} +(-1.27630 - 1.46647i) q^{15} +(-2.19239 - 3.34566i) q^{16} +1.81984i q^{17} +(-1.64932 - 3.90893i) q^{18} +(3.24223 + 3.24223i) q^{19} +(-0.642010 - 2.15107i) q^{20} +(0.119805 - 1.72790i) q^{21} +(-0.336858 + 1.33215i) q^{22} +5.92103i q^{23} +(0.131558 - 4.89721i) q^{24} +3.74018i q^{25} +(5.64454 + 1.42733i) q^{26} +(1.07136 - 5.08450i) q^{27} +(0.950686 - 1.75960i) q^{28} +(-1.54834 - 1.54834i) q^{29} +(0.856763 - 2.61245i) q^{30} +3.60999i q^{31} +(2.47574 - 5.08633i) q^{32} +(-1.26945 + 1.10482i) q^{33} +(-2.21044 + 1.31817i) q^{34} +(0.793669 - 0.793669i) q^{35} +(3.55328 - 4.83469i) q^{36} +(-5.10312 - 5.10312i) q^{37} +(-1.58968 + 6.28658i) q^{38} +(4.68134 + 5.37887i) q^{39} +(2.14774 - 2.33790i) q^{40} -1.19627 q^{41} +(2.18555 - 1.10606i) q^{42} +(-7.00779 + 7.00779i) q^{43} +(-1.86207 + 0.555755i) q^{44} +(2.68682 - 2.02963i) q^{45} +(-7.19190 + 4.28879i) q^{46} +13.1565 q^{47} +(6.04363 - 3.38741i) q^{48} +1.00000 q^{49} +(-4.54296 + 2.70913i) q^{50} +(-3.14450 - 0.218025i) q^{51} +(2.35483 + 7.88993i) q^{52} +(2.08667 - 2.08667i) q^{53} +(6.95185 - 2.38155i) q^{54} -1.09056 q^{55} +(2.82589 - 0.119796i) q^{56} +(-5.99069 + 5.21382i) q^{57} +(0.759161 - 3.00219i) q^{58} +(0.919177 + 0.919177i) q^{59} +(3.79376 - 0.851623i) q^{60} +(4.21756 - 4.21756i) q^{61} +(-4.38483 + 2.61483i) q^{62} +(2.97129 + 0.414021i) q^{63} +(7.97130 - 0.677063i) q^{64} +4.62091i q^{65} +(-2.26146 - 0.741655i) q^{66} +(7.87889 + 7.87889i) q^{67} +(-3.20219 - 1.73009i) q^{68} +(-10.2310 - 0.709366i) q^{69} +(1.53890 + 0.389140i) q^{70} -7.99444i q^{71} +(8.44614 + 0.814027i) q^{72} +4.19057i q^{73} +(2.50208 - 9.89478i) q^{74} +(-6.46266 - 0.448090i) q^{75} +(-8.78737 + 2.62269i) q^{76} +(-0.687038 - 0.687038i) q^{77} +(-3.14253 + 9.58221i) q^{78} +8.07689i q^{79} +(4.39538 + 0.915312i) q^{80} +(8.65717 + 2.46036i) q^{81} +(-0.866499 - 1.45304i) q^{82} +(11.0241 - 11.0241i) q^{83} +(2.92652 + 1.85350i) q^{84} +(-1.44435 - 1.44435i) q^{85} +(-13.5879 - 3.43595i) q^{86} +(2.86089 - 2.48989i) q^{87} +(-2.02380 - 1.85919i) q^{88} -7.73403 q^{89} +(4.41141 + 1.79339i) q^{90} +(-2.91110 + 2.91110i) q^{91} +(-10.4186 - 5.62904i) q^{92} +(-6.23771 - 0.432493i) q^{93} +(9.52970 + 15.9804i) q^{94} -5.14651 q^{95} +(8.49207 + 4.88720i) q^{96} +6.61707 q^{97} +(0.724332 + 1.21464i) q^{98} +(-1.75694 - 2.32584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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