LMFDB - Embedded newform 336.2.s.d.155.10

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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.10
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.641365 - 1.26042i) q^{2} +(-1.71202 - 0.262630i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(2.76208 - 2.76208i) q^{5} +(0.767010 + 2.32631i) q^{6} +1.00000 q^{7} +(2.79289 + 0.446945i) q^{8} +(2.86205 + 0.899256i) q^{9} +O(q^{10})$	\(q+(-0.641365 - 1.26042i) q^{2} +(-1.71202 - 0.262630i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(2.76208 - 2.76208i) q^{5} +(0.767010 + 2.32631i) q^{6} +1.00000 q^{7} +(2.79289 + 0.446945i) q^{8} +(2.86205 + 0.899256i) q^{9} +(-5.25287 - 1.70987i) q^{10} +(3.92989 + 3.92989i) q^{11} +(2.44018 - 2.45876i) q^{12} +(-1.26876 + 1.26876i) q^{13} +(-0.641365 - 1.26042i) q^{14} +(-5.45415 + 4.00334i) q^{15} +(-1.22793 - 3.80686i) q^{16} -7.10884i q^{17} +(-0.702183 - 4.18413i) q^{18} +(-0.652997 - 0.652997i) q^{19} +(1.21386 + 7.71746i) q^{20} +(-1.71202 - 0.262630i) q^{21} +(2.43280 - 7.47379i) q^{22} -3.98276i q^{23} +(-4.66411 - 1.49868i) q^{24} -10.2582i q^{25} +(2.41291 + 0.785428i) q^{26} +(-4.66373 - 2.29121i) q^{27} +(-1.17730 + 1.61678i) q^{28} +(0.280064 + 0.280064i) q^{29} +(8.54398 + 4.30690i) q^{30} +2.51952i q^{31} +(-4.01068 + 3.98929i) q^{32} +(-5.69595 - 7.76016i) q^{33} +(-8.96010 + 4.55937i) q^{34} +(2.76208 - 2.76208i) q^{35} +(-4.82339 + 3.56860i) q^{36} +(2.94433 + 2.94433i) q^{37} +(-0.404238 + 1.24186i) q^{38} +(2.50536 - 1.83893i) q^{39} +(8.94869 - 6.47969i) q^{40} +5.39610 q^{41} +(0.767010 + 2.32631i) q^{42} +(-1.15575 + 1.15575i) q^{43} +(-10.9804 + 1.72709i) q^{44} +(10.3890 - 5.42140i) q^{45} +(-5.01994 + 2.55441i) q^{46} -5.00105 q^{47} +(1.10245 + 6.83993i) q^{48} +1.00000 q^{49} +(-12.9296 + 6.57924i) q^{50} +(-1.86699 + 12.1705i) q^{51} +(-0.557588 - 3.54501i) q^{52} +(-6.25168 + 6.25168i) q^{53} +(0.103279 + 7.34774i) q^{54} +21.7093 q^{55} +(2.79289 + 0.446945i) q^{56} +(0.946449 + 1.28944i) q^{57} +(0.173374 - 0.532620i) q^{58} +(-1.75981 - 1.75981i) q^{59} +(-0.0513320 - 13.5313i) q^{60} +(-2.02736 + 2.02736i) q^{61} +(3.17564 - 1.61593i) q^{62} +(2.86205 + 0.899256i) q^{63} +(7.60048 + 2.49654i) q^{64} +7.00883i q^{65} +(-6.12785 + 12.1564i) q^{66} +(-0.986955 - 0.986955i) q^{67} +(11.4934 + 8.36924i) q^{68} +(-1.04599 + 6.81859i) q^{69} +(-5.25287 - 1.70987i) q^{70} -5.74760i q^{71} +(7.59148 + 3.79071i) q^{72} +0.913402i q^{73} +(1.82269 - 5.59948i) q^{74} +(-2.69410 + 17.5622i) q^{75} +(1.82452 - 0.286976i) q^{76} +(3.92989 + 3.92989i) q^{77} +(-3.92468 - 1.97837i) q^{78} -3.77043i q^{79} +(-13.9065 - 7.12323i) q^{80} +(7.38268 + 5.14744i) q^{81} +(-3.46087 - 6.80133i) q^{82} +(9.11508 - 9.11508i) q^{83} +(2.44018 - 2.45876i) q^{84} +(-19.6352 - 19.6352i) q^{85} +(2.19799 + 0.715470i) q^{86} +(-0.405923 - 0.553029i) q^{87} +(9.21930 + 12.7322i) q^{88} +2.10538 q^{89} +(-13.4964 - 9.61741i) q^{90} +(-1.26876 + 1.26876i) q^{91} +(6.43923 + 4.68891i) q^{92} +(0.661699 - 4.31347i) q^{93} +(3.20750 + 6.30340i) q^{94} -3.60726 q^{95} +(7.91409 - 5.77643i) q^{96} +11.0425 q^{97} +(-0.641365 - 1.26042i) q^{98} +(7.71356 + 14.7815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * 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 $

$2$	−0.641365	−	1.26042i	−0.453514	−	0.891249i
$2$	−0.641365	−	1.26042i	−0.453514	−	0.891249i
$3$	−1.71202	−	0.262630i	−0.988437	−	0.151629i
$3$	−1.71202	−	0.262630i	−0.988437	−	0.151629i
$4$	−1.17730	+	1.61678i	−0.588650	+	0.808388i
$5$	2.76208	−	2.76208i	1.23524	−	1.23524i	0.273315	−	0.961925i	$-0.411880\pi$
$5$	2.76208	−	2.76208i	1.23524	−	1.23524i	0.961925	−	0.273315i	$-0.0881202\pi$
$6$	0.767010	+	2.32631i	0.313131	+	0.949710i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.79289	+	0.446945i	0.987436	+	0.158019i
$9$	2.86205	+	0.899256i	0.954017	+	0.299752i
$10$	−5.25287	−	1.70987i	−1.66110	−	0.540708i
$11$	3.92989	+	3.92989i	1.18491	+	1.18491i	0.978458	+	0.206448i	$0.0661903\pi$
$11$	3.92989	+	3.92989i	1.18491	+	1.18491i	0.206448	+	0.978458i	$0.433810\pi$
$12$	2.44018	−	2.45876i	0.704419	−	0.709784i
$13$	−1.26876	+	1.26876i	−0.351891	+	0.351891i	−0.860813	−	0.508922i	$-0.830044\pi$
$13$	−1.26876	+	1.26876i	−0.351891	+	0.351891i	0.508922	+	0.860813i	$0.330044\pi$
$14$	−0.641365	−	1.26042i	−0.171412	−	0.336861i
$15$	−5.45415	+	4.00334i	−1.40826	+	1.03366i
$16$	−1.22793	−	3.80686i	−0.306982	−	0.951715i
$17$		−	7.10884i		−	1.72415i	−0.506783	−	0.862074i	$-0.669165\pi$
$17$		−	7.10884i		−	1.72415i	0.506783	−	0.862074i	$-0.330835\pi$
$18$	−0.702183	−	4.18413i	−0.165506	−	0.986209i
$19$	−0.652997	−	0.652997i	−0.149808	−	0.149808i	0.628224	−	0.778032i	$-0.283782\pi$
$19$	−0.652997	−	0.652997i	−0.149808	−	0.149808i	−0.778032	+	0.628224i	$0.783782\pi$
$20$	1.21386	+	7.71746i	0.271428	+	1.72568i
$21$	−1.71202	−	0.262630i	−0.373594	−	0.0573105i
$22$	2.43280	−	7.47379i	0.518675	−	1.59342i
$23$		−	3.98276i		−	0.830464i	−0.909716	−	0.415232i	$-0.863700\pi$
$23$		−	3.98276i		−	0.830464i	0.909716	−	0.415232i	$-0.136300\pi$
$24$	−4.66411	−	1.49868i	−0.952058	−	0.305916i
$25$		−	10.2582i		−	2.05163i
$26$	2.41291	+	0.785428i	0.473210	+	0.154035i
$27$	−4.66373	−	2.29121i	−0.897535	−	0.440943i
$28$	−1.17730	+	1.61678i	−0.222489	+	0.305542i
$29$	0.280064	+	0.280064i	0.0520065	+	0.0520065i	0.732632	−	0.680625i	$-0.238292\pi$
$29$	0.280064	+	0.280064i	0.0520065	+	0.0520065i	−0.680625	+	0.732632i	$0.738292\pi$
$30$	8.54398	+	4.30690i	1.55991	+	0.786328i
$31$			2.51952i			0.452518i	0.974067	+	0.226259i	$0.0726496\pi$
$31$			2.51952i			0.452518i	−0.974067	+	0.226259i	$0.927350\pi$
$32$	−4.01068	+	3.98929i	−0.708995	+	0.705213i
$33$	−5.69595	−	7.76016i	−0.991538	−	1.35087i
$34$	−8.96010	+	4.55937i	−1.53665	+	0.781925i
$35$	2.76208	−	2.76208i	0.466877	−	0.466877i
$36$	−4.82339	+	3.56860i	−0.803898	+	0.594767i
$37$	2.94433	+	2.94433i	0.484045	+	0.484045i	0.906421	−	0.422376i	$-0.138804\pi$
$37$	2.94433	+	2.94433i	0.484045	+	0.484045i	−0.422376	+	0.906421i	$0.638804\pi$
$38$	−0.404238	+	1.24186i	−0.0655761	+	0.201456i
$39$	2.50536	−	1.83893i	0.401179	−	0.294465i
$40$	8.94869	−	6.47969i	1.41491	−	1.02453i
$41$	5.39610			0.842729			0.421365	−	0.906891i	$-0.361551\pi$
$41$	5.39610			0.842729			0.421365	+	0.906891i	$0.361551\pi$
$42$	0.767010	+	2.32631i	0.118352	+	0.358957i
$43$	−1.15575	+	1.15575i	−0.176251	+	0.176251i	−0.789719	−	0.613469i	$-0.789774\pi$
$43$	−1.15575	+	1.15575i	−0.176251	+	0.176251i	0.613469	+	0.789719i	$0.289774\pi$
$44$	−10.9804	+	1.72709i	−1.65536	+	0.260368i
$45$	10.3890	−	5.42140i	1.54871	−	0.808174i
$46$	−5.01994	+	2.55441i	−0.740150	+	0.376627i
$47$	−5.00105			−0.729477			−0.364739	−	0.931110i	$-0.618842\pi$
$47$	−5.00105			−0.729477			−0.364739	+	0.931110i	$0.618842\pi$
$48$	1.10245	+	6.83993i	0.159124	+	0.987259i
$49$	1.00000			0.142857
$50$	−12.9296	+	6.57924i	−1.82852	+	0.930445i
$51$	−1.86699	+	12.1705i	−0.261431	+	1.70421i
$52$	−0.557588	−	3.54501i	−0.0773236	−	0.491605i
$53$	−6.25168	+	6.25168i	−0.858734	+	0.858734i	−0.991189	−	0.132455i	$-0.957714\pi$
$53$	−6.25168	+	6.25168i	−0.858734	+	0.858734i	0.132455	+	0.991189i	$0.457714\pi$
$54$	0.103279	+	7.34774i	0.0140544	+	0.999901i
$55$	21.7093			2.92728
$56$	2.79289	+	0.446945i	0.373216	+	0.0597256i
$57$	0.946449	+	1.28944i	0.125360	+	0.170791i
$58$	0.173374	−	0.532620i	0.0227651	−	0.0699365i
$59$	−1.75981	−	1.75981i	−0.229108	−	0.229108i	0.583212	−	0.812320i	$-0.301796\pi$
$59$	−1.75981	−	1.75981i	−0.229108	−	0.229108i	−0.812320	+	0.583212i	$0.801796\pi$
$60$	−0.0513320	−	13.5313i	−0.00662693	−	1.74688i
$61$	−2.02736	+	2.02736i	−0.259577	+	0.259577i	−0.824882	−	0.565305i	$-0.808759\pi$
$61$	−2.02736	+	2.02736i	−0.259577	+	0.259577i	0.565305	+	0.824882i	$0.308759\pi$
$62$	3.17564	−	1.61593i	0.403307	−	0.205223i
$63$	2.86205	+	0.899256i	0.360585	+	0.113296i
$64$	7.60048	+	2.49654i	0.950060	+	0.312067i
$65$			7.00883i			0.869339i
$66$	−6.12785	+	12.1564i	−0.754286	+	1.49635i
$67$	−0.986955	−	0.986955i	−0.120576	−	0.120576i	0.644244	−	0.764820i	$-0.277172\pi$
$67$	−0.986955	−	0.986955i	−0.120576	−	0.120576i	−0.764820	+	0.644244i	$0.777172\pi$
$68$	11.4934	+	8.36924i	1.39378	+	1.01492i
$69$	−1.04599	+	6.81859i	−0.125923	+	0.820861i
$70$	−5.25287	−	1.70987i	−0.627839	−	0.204368i
$71$		−	5.74760i		−	0.682115i	−0.940042	−	0.341057i	$-0.889215\pi$
$71$		−	5.74760i		−	0.682115i	0.940042	−	0.341057i	$-0.110785\pi$
$72$	7.59148	+	3.79071i	0.894664	+	0.446739i
$73$			0.913402i			0.106906i	0.998570	+	0.0534528i	$0.0170227\pi$
$73$			0.913402i			0.106906i	−0.998570	+	0.0534528i	$0.982977\pi$
$74$	1.82269	−	5.59948i	0.211884	−	0.650926i
$75$	−2.69410	+	17.5622i	−0.311088	+	2.02791i
$76$	1.82452	−	0.286976i	0.209287	−	0.0329184i
$77$	3.92989	+	3.92989i	0.447852	+	0.447852i
$78$	−3.92468	−	1.97837i	−0.444382	−	0.224006i
$79$		−	3.77043i		−	0.424206i	−0.977247	−	0.212103i	$-0.931969\pi$
$79$		−	3.77043i		−	0.424206i	0.977247	−	0.212103i	$-0.0680313\pi$
$80$	−13.9065	−	7.12323i	−1.55479	−	0.796401i
$81$	7.38268	+	5.14744i	0.820297	+	0.571937i
$82$	−3.46087	−	6.80133i	−0.382189	−	0.751082i
$83$	9.11508	−	9.11508i	1.00051	−	1.00051i	0.000510506	−	1.00000i	$-0.499838\pi$
$83$	9.11508	−	9.11508i	1.00051	−	1.00051i	1.00000		0.000510506i	$-0.000162499\pi$
$84$	2.44018	−	2.45876i	0.266245	−	0.268273i
$85$	−19.6352	−	19.6352i	−2.12974	−	2.12974i
$86$	2.19799	+	0.715470i	0.237015	+	0.0771511i
$87$	−0.405923	−	0.553029i	−0.0435195	−	0.0592909i
$88$	9.21930	+	12.7322i	0.982781	+	1.35726i
$89$	2.10538			0.223170			0.111585	−	0.993755i	$-0.464407\pi$
$89$	2.10538			0.223170			0.111585	+	0.993755i	$0.464407\pi$
$90$	−13.4964	−	9.61741i	−1.42264	−	1.01376i
$91$	−1.26876	+	1.26876i	−0.133002	+	0.133002i
$92$	6.43923	+	4.68891i	0.671337	+	0.488853i
$93$	0.661699	−	4.31347i	0.0686150	−	0.447286i
$94$	3.20750	+	6.30340i	0.330828	+	0.650146i
$95$	−3.60726			−0.370097
$96$	7.91409	−	5.77643i	0.807728	−	0.589555i
$97$	11.0425			1.12120			0.560599	−	0.828087i	$-0.310571\pi$
$97$	11.0425			1.12120			0.560599	+	0.828087i	$0.310571\pi$
$98$	−0.641365	−	1.26042i	−0.0647877	−	0.127321i
$99$	7.71356	+	14.7815i	0.775242	+	1.48560i
$100$	16.5852	+	12.0770i	1.65852	+	1.20770i
$101$	9.78409	−	9.78409i	0.973553	−	0.973553i	−0.0261061	−	0.999659i	$-0.508311\pi$
$101$	9.78409	−	9.78409i	0.973553	−	0.973553i	0.999659	+	0.0261061i	$0.00831078\pi$
$102$	16.5373	−	5.45256i	1.63744	−	0.539883i
$103$	−8.98633			−0.885449			−0.442725	−	0.896658i	$-0.645988\pi$
$103$	−8.98633			−0.885449			−0.442725	+	0.896658i	$0.645988\pi$
$104$	−4.11058	+	2.97644i	−0.403075	+	0.291864i
$105$	−5.45415	+	4.00334i	−0.532271	+	0.390686i
$106$	11.8893	+	3.87011i	1.15479	+	0.375898i
$107$	7.72822	+	7.72822i	0.747116	+	0.747116i	0.973936	−	0.226821i	$-0.0728332\pi$
$107$	7.72822	+	7.72822i	0.747116	+	0.747116i	−0.226821	+	0.973936i	$0.572833\pi$
$108$	9.19498	−	4.84276i	0.884787	−	0.465995i
$109$	−11.7747	+	11.7747i	−1.12781	+	1.12781i	−0.137276	+	0.990533i	$0.543835\pi$
$109$	−11.7747	+	11.7747i	−1.12781	+	1.12781i	−0.990533	+	0.137276i	$0.956165\pi$
$110$	−13.9236	−	27.3628i	−1.32756	−	2.60894i
$111$	−4.26750	−	5.81404i	−0.405053	−	0.551844i
$112$	−1.22793	−	3.80686i	−0.116028	−	0.359715i
$113$			5.06042i			0.476044i	0.971260	+	0.238022i	$0.0764990\pi$
$113$			5.06042i			0.476044i	−0.971260	+	0.238022i	$0.923501\pi$
$114$	1.01821	−	2.01992i	0.0953645	−	0.189183i
$115$	−11.0007	−	11.0007i	−1.02582	−	1.02582i
$116$	−0.782519	+	0.123081i	−0.0726551	+	0.0114278i
$117$	−4.77220	+	2.49032i	−0.441190	+	0.230230i
$118$	−1.08941	+	3.34677i	−0.100288	+	0.308095i
$119$		−	7.10884i		−	0.651667i
$120$	−17.0221	+	8.74319i	−1.55390	+	0.798141i
$121$			19.8880i			1.80800i
$122$	3.85561	+	1.25504i	0.349070	+	0.113626i
$123$	−9.23825	−	1.41718i	−0.832985	−	0.127782i
$124$	−4.07349	−	2.96623i	−0.365810	−	0.266375i
$125$	−14.5235	−	14.5235i	−1.29902	−	1.29902i
$126$	−0.702183	−	4.18413i	−0.0625555	−	0.372752i
$127$		−	0.811521i		−	0.0720108i	−0.999352	−	0.0360054i	$-0.988537\pi$
$127$		−	0.811521i		−	0.0720108i	0.999352	−	0.0360054i	$-0.0114634\pi$
$128$	−1.72801	−	11.1810i	−0.152736	−	0.988267i
$129$	2.28221	−	1.67514i	0.200937	−	0.147488i
$130$	8.83405	−	4.49522i	0.774798	−	0.394257i
$131$	−14.6635	+	14.6635i	−1.28115	+	1.28115i	−0.341142	+	0.940012i	$0.610814\pi$
$131$	−14.6635	+	14.6635i	−1.28115	+	1.28115i	−0.940012	+	0.341142i	$0.889186\pi$
$132$	19.2523	−	0.0730352i	1.67570	−	0.00635690i
$133$	−0.652997	−	0.652997i	−0.0566220	−	0.0566220i
$134$	−0.610975	+	1.87697i	−0.0527802	+	0.162146i
$135$	−19.2101	+	6.55309i	−1.65334	+	0.564001i
$136$	3.17726	−	19.8542i	0.272448	−	1.70249i
$137$	14.1272			1.20697			0.603483	−	0.797376i	$-0.293779\pi$
$137$	14.1272			1.20697			0.603483	+	0.797376i	$0.293779\pi$
$138$	9.26512	−	3.05482i	0.788700	−	0.260044i
$139$	−11.6721	+	11.6721i	−0.990011	+	0.990011i	−0.999951	−	0.00993974i	$-0.996836\pi$
$139$	−11.6721	+	11.6721i	−0.990011	+	0.990011i	0.00993974	+	0.999951i	$0.496836\pi$
$140$	1.21386	+	7.71746i	0.102590	+	0.652245i
$141$	8.56191	+	1.31342i	0.721043	+	0.110610i
$142$	−7.24437	+	3.68631i	−0.607934	+	0.309349i
$143$	−9.97217			−0.833914
$144$	−0.0910447	−	11.9997i	−0.00758706	−	0.999971i
$145$	1.54712			0.128481
$146$	1.15127	−	0.585825i	0.0952796	−	0.0484832i
$147$	−1.71202	−	0.262630i	−0.141205	−	0.0216613i
$148$	−8.22669	+	1.29396i	−0.676230	+	0.106363i
$149$	−9.48788	+	9.48788i	−0.777278	+	0.777278i	−0.979367	−	0.202089i	$-0.935227\pi$
$149$	−9.48788	+	9.48788i	−0.777278	+	0.777278i	0.202089	+	0.979367i	$0.435227\pi$
$150$	23.8636	−	7.86812i	1.94846	−	0.642430i
$151$	−8.56314			−0.696858			−0.348429	−	0.937335i	$-0.613285\pi$
$151$	−8.56314			−0.696858			−0.348429	+	0.937335i	$0.613285\pi$
$152$	−1.53189	−	2.11560i	−0.124253	−	0.171598i
$153$	6.39267	−	20.3459i	0.516817	−	1.64487i
$154$	2.43280	−	7.47379i	0.196041	−	0.602255i
$155$	6.95910	+	6.95910i	0.558969	+	0.558969i
$156$	0.0235793	+	6.21559i	0.00188786	+	0.497645i
$157$	−7.19844	+	7.19844i	−0.574498	+	0.574498i	−0.933382	−	0.358884i	$-0.883157\pi$
$157$	−7.19844	+	7.19844i	−0.574498	+	0.574498i	0.358884	+	0.933382i	$0.383157\pi$
$158$	−4.75231	+	2.41822i	−0.378074	+	0.192383i
$159$	12.3449	−	9.06114i	0.979014	−	0.718595i
$160$	−0.0590908	+	22.0966i	−0.00467153	+	1.74689i
$161$		−	3.98276i		−	0.313886i
$162$	1.75292	−	12.6066i	0.137722	−	0.990471i
$163$	−2.47226	−	2.47226i	−0.193643	−	0.193643i	0.603625	−	0.797268i	$-0.293722\pi$
$163$	−2.47226	−	2.47226i	−0.193643	−	0.193643i	−0.797268	+	0.603625i	$0.793722\pi$
$164$	−6.35283	+	8.72428i	−0.496073	+	0.681252i
$165$	−37.1669	−	5.70151i	−2.89344	−	0.443862i
$166$	−17.3349	−	5.64270i	−1.34545	−	0.437959i
$167$			8.81314i			0.681981i	0.940067	+	0.340990i	$0.110762\pi$
$167$			8.81314i			0.681981i	−0.940067	+	0.340990i	$0.889238\pi$
$168$	−4.66411	−	1.49868i	−0.359844	−	0.115625i
$169$			9.78050i			0.752346i
$170$	−12.1552	+	37.3419i	−0.932260	+	2.86399i
$171$	−1.28170	−	2.45612i	−0.0980139	−	0.187824i
$172$	−0.507924	−	3.22926i	−0.0387288	−	0.246229i
$173$	3.61856	+	3.61856i	0.275114	+	0.275114i	0.831155	−	0.556041i	$-0.187680\pi$
$173$	3.61856	+	3.61856i	0.275114	+	0.275114i	−0.556041	+	0.831155i	$0.687680\pi$
$174$	−0.436702	+	0.866325i	−0.0331063	+	0.0656760i
$175$		−	10.2582i		−	0.775445i
$176$	10.1349	−	19.7861i	0.763948	−	1.49144i
$177$	2.55066	+	3.47501i	0.191719	+	0.261198i
$178$	−1.35032	−	2.65366i	−0.101211	−	0.198900i
$179$	1.44438	−	1.44438i	0.107958	−	0.107958i	−0.651064	−	0.759023i	$-0.725677\pi$
$179$	1.44438	−	1.44438i	0.107958	−	0.107958i	0.759023	+	0.651064i	$0.225677\pi$
$180$	−3.46583	+	23.1793i	−0.258328	+	1.72769i
$181$	9.19999	+	9.19999i	0.683830	+	0.683830i	0.960861	−	0.277031i	$-0.0893506\pi$
$181$	9.19999	+	9.19999i	0.683830	+	0.683830i	−0.277031	+	0.960861i	$0.589351\pi$
$182$	2.41291	+	0.785428i	0.178856	+	0.0582198i
$183$	4.00334	−	2.93845i	0.295936	−	0.217217i
$184$	1.78008	−	11.1234i	0.131229	−	0.820030i
$185$	16.2650			1.19582
$186$	−5.86116	+	1.93249i	−0.429761	+	0.141697i
$187$	27.9369	−	27.9369i	2.04295	−	2.04295i
$188$	5.88773	−	8.08557i	0.429407	−	0.589701i
$189$	−4.66373	−	2.29121i	−0.339236	−	0.166661i
$190$	2.31357	+	4.54665i	0.167844	+	0.329848i
$191$	−2.75575			−0.199399			−0.0996995	−	0.995018i	$-0.531788\pi$
$191$	−2.75575			−0.199399			−0.0996995	+	0.995018i	$0.531788\pi$
$192$	−12.3565	−	6.27025i	−0.891756	−	0.452516i
$193$	−12.7111			−0.914965			−0.457483	−	0.889219i	$-0.651249\pi$
$193$	−12.7111			−0.914965			−0.457483	+	0.889219i	$0.651249\pi$
$194$	−7.08229	−	13.9182i	−0.508479	−	0.999267i
$195$	1.84073	−	11.9993i	0.131817	−	0.859287i
$196$	−1.17730	+	1.61678i	−0.0840929	+	0.115484i
$197$	12.4779	−	12.4779i	0.889010	−	0.889010i	−0.105418	−	0.994428i	$-0.533618\pi$
$197$	12.4779	−	12.4779i	0.889010	−	0.889010i	0.994428	+	0.105418i	$0.0336180\pi$
$198$	13.6837	−	19.2027i	0.972455	−	1.36467i
$199$	16.2474			1.15175			0.575876	−	0.817537i	$-0.304661\pi$
$199$	16.2474			1.15175			0.575876	+	0.817537i	$0.304661\pi$
$200$	4.58484	−	28.6500i	0.324197	−	2.02586i
$201$	1.43049	+	1.94889i	0.100899	+	0.137464i
$202$	−18.6072	−	6.05685i	−1.30920	−	0.426159i
$203$	0.280064	+	0.280064i	0.0196566	+	0.0196566i
$204$	−17.4790	−	17.3469i	−1.22377	−	1.21452i
$205$	14.9045	−	14.9045i	1.04097	−	1.04097i
$206$	5.76352	+	11.3265i	0.401564	+	0.789156i
$207$	3.58152	−	11.3989i	0.248933	−	0.792276i
$208$	6.38794	+	3.27205i	0.442924	+	0.226876i
$209$		−	5.13240i		−	0.355016i
$210$	8.54398	+	4.30690i	0.589591	+	0.297204i
$211$	18.8613	+	18.8613i	1.29846	+	1.29846i	0.929408	+	0.369055i	$0.120319\pi$
$211$	18.8613	+	18.8613i	1.29846	+	1.29846i	0.369055	+	0.929408i	$0.379681\pi$
$212$	−2.74745	−	17.4677i	−0.188696	−	1.19968i
$213$	−1.50949	+	9.84003i	−0.103429	+	0.674228i
$214$	4.78417	−	14.6974i	0.327039	−	1.00469i
$215$			6.38456i			0.435423i
$216$	−12.0012	−	8.48352i	−0.816581	−	0.577231i
$217$			2.51952i			0.171036i
$218$	22.3929	+	7.28912i	1.51664	+	0.493682i
$219$	0.239886	−	1.56377i	0.0162100	−	0.105670i
$220$	−25.5584	+	35.0991i	−1.72315	+	2.36638i
$221$	9.01942	+	9.01942i	0.606712	+	0.606712i
$222$	−4.59108	+	9.10775i	−0.308133	+	0.611272i
$223$		−	14.1500i		−	0.947552i	−0.880645	−	0.473776i	$-0.842891\pi$
$223$		−	14.1500i		−	0.947552i	0.880645	−	0.473776i	$-0.157109\pi$
$224$	−4.01068	+	3.98929i	−0.267975	+	0.266546i
$225$	9.22472	−	29.3594i	0.614982	−	1.95729i
$226$	6.37823	−	3.24558i	0.424274	−	0.215893i
$227$	−6.21650	+	6.21650i	−0.412603	+	0.412603i	−0.882645	−	0.470041i	$-0.844239\pi$
$227$	−6.21650	+	6.21650i	−0.412603	+	0.412603i	0.470041	+	0.882645i	$0.344239\pi$
$228$	−3.19899	+	0.0121356i	−0.211859	+	0.000803703i
$229$	−2.04458	−	2.04458i	−0.135110	−	0.135110i	0.636318	−	0.771427i	$-0.280457\pi$
$229$	−2.04458	−	2.04458i	−0.135110	−	0.135110i	−0.771427	+	0.636318i	$0.780457\pi$
$230$	−6.81000	+	20.9210i	−0.449038	+	1.37949i
$231$	−5.69595	−	7.76016i	−0.374766	−	0.510581i
$232$	0.657014	+	0.907361i	0.0431351	+	0.0595711i
$233$	−25.5534			−1.67406			−0.837030	−	0.547157i	$-0.815710\pi$
$233$	−25.5534			−1.67406			−0.837030	+	0.547157i	$0.815710\pi$
$234$	6.19956	+	4.41775i	0.405278	+	0.288798i
$235$	−13.8133	+	13.8133i	−0.901079	+	0.901079i
$236$	4.91704	−	0.773392i	0.320072	−	0.0503435i
$237$	−0.990226	+	6.45506i	−0.0643221	+	0.419301i
$238$	−8.96010	+	4.55937i	−0.580797	+	0.295540i
$239$	−20.4220			−1.32099			−0.660493	−	0.750832i	$-0.729653\pi$
$239$	−20.4220			−1.32099			−0.660493	+	0.750832i	$0.729653\pi$
$240$	21.9375	+	15.8474i	1.41606	+	1.02294i
$241$	−9.12556			−0.587829			−0.293914	−	0.955832i	$-0.594958\pi$
$241$	−9.12556			−0.587829			−0.293914	+	0.955832i	$0.594958\pi$
$242$	25.0672	−	12.7555i	1.61138	−	0.819954i
$243$	−11.2874	−	10.7514i	−0.724090	−	0.689705i
$244$	−0.890976	−	5.66461i	−0.0570389	−	0.362640i
$245$	2.76208	−	2.76208i	0.176463	−	0.176463i
$246$	4.13886	+	12.5530i	0.263884	+	0.800348i
$247$	1.65699			0.105432
$248$	−1.12609	+	7.03673i	−0.0715065	+	0.446833i
$249$	−17.9991	+	13.2113i	−1.14065	+	0.837235i
$250$	−8.99078	+	27.6205i	−0.568627	+	1.74687i
$251$	13.0159	+	13.0159i	0.821554	+	0.821554i	0.986331	−	0.164777i	$-0.0526905\pi$
$251$	13.0159	+	13.0159i	0.821554	+	0.821554i	−0.164777	+	0.986331i	$0.552691\pi$
$252$	−4.82339	+	3.56860i	−0.303845	+	0.224801i
$253$	15.6518	−	15.6518i	0.984021	−	0.984021i
$254$	−1.02285	+	0.520481i	−0.0641796	+	0.0326579i
$255$	28.4591	+	38.7727i	1.78218	+	2.42804i
$256$	−12.9844	+	9.34909i	−0.811525	+	0.584318i
$257$			4.90026i			0.305670i	0.988252	+	0.152835i	$0.0488402\pi$
$257$			4.90026i			0.305670i	−0.988252	+	0.152835i	$0.951160\pi$
$258$	−3.57511	−	1.80216i	−0.222576	−	0.112197i
$259$	2.94433	+	2.94433i	0.182952	+	0.182952i
$260$	−11.3317	−	8.25150i	−0.702763	−	0.511737i
$261$	0.549708	+	1.05341i	0.0340261	+	0.0652042i
$262$	27.8867	+	9.07744i	1.72285	+	0.560806i
$263$		−	3.50904i		−	0.216377i	−0.994130	−	0.108188i	$-0.965495\pi$
$263$		−	3.50904i		−	0.216377i	0.994130	−	0.108188i	$-0.0345050\pi$
$264$	−12.4398	−	24.2191i	−0.765617	−	1.49058i
$265$			34.5353i			2.12148i
$266$	−0.404238	+	1.24186i	−0.0247854	+	0.0761432i
$267$	−3.60446	−	0.552935i	−0.220590	−	0.0338391i
$268$	2.75763	−	0.433742i	0.168449	−	0.0264950i
$269$	−9.49745	−	9.49745i	−0.579070	−	0.579070i	0.355577	−	0.934647i	$-0.384284\pi$
$269$	−9.49745	−	9.49745i	−0.579070	−	0.579070i	−0.934647	+	0.355577i	$0.884284\pi$
$270$	20.5803	+	20.0098i	1.25248	+	1.21776i
$271$		−	0.198651i		−	0.0120672i	−0.999982	−	0.00603358i	$-0.998079\pi$
$271$		−	0.198651i		−	0.0120672i	0.999982	−	0.00603358i	$-0.00192056\pi$
$272$	−27.0624	+	8.72914i	−1.64090	+	0.529282i
$273$	2.50536	−	1.83893i	0.151631	−	0.111297i
$274$	−9.06068	−	17.8061i	−0.547375	−	1.07571i
$275$	40.3134	−	40.3134i	2.43099	−	2.43099i
$276$	−9.79268	−	9.71866i	−0.589450	−	0.584995i
$277$	15.9895	+	15.9895i	0.960714	+	0.960714i	0.999257	−	0.0385425i	$-0.0122715\pi$
$277$	15.9895	+	15.9895i	0.960714	+	0.960714i	−0.0385425	+	0.999257i	$0.512271\pi$
$278$	22.1977	+	7.22560i	1.33133	+	0.433363i
$279$	−2.26569	+	7.21098i	−0.135643	+	0.431710i
$280$	8.94869	−	6.47969i	0.534786	−	0.387236i
$281$	9.46558			0.564669			0.282335	−	0.959316i	$-0.408891\pi$
$281$	9.46558			0.564669			0.282335	+	0.959316i	$0.408891\pi$
$282$	−3.83585	−	11.6340i	−0.228422	−	0.692792i
$283$	8.84357	−	8.84357i	0.525696	−	0.525696i	−0.393590	−	0.919286i	$-0.628767\pi$
$283$	8.84357	−	8.84357i	0.525696	−	0.525696i	0.919286	+	0.393590i	$0.128767\pi$
$284$	9.29258	+	6.76666i	0.551413	+	0.401527i
$285$	6.17571	+	0.947372i	0.365818	+	0.0561175i
$286$	6.39580	+	12.5691i	0.378192	+	0.743226i
$287$	5.39610			0.318522
$288$	−15.0662	+	7.81092i	−0.887783	+	0.460263i
$289$	−33.5356			−1.97268
$290$	−0.992267	−	1.95001i	−0.0582679	−	0.114509i
$291$	−18.9051	−	2.90009i	−1.10823	−	0.170006i
$292$	−1.47677	−	1.07535i	−0.0864212	−	0.0629300i
$293$	−18.8459	+	18.8459i	−1.10099	+	1.10099i	−0.106696	+	0.994292i	$0.534027\pi$
$293$	−18.8459	+	18.8459i	−1.10099	+	1.10099i	−0.994292	+	0.106696i	$0.965973\pi$
$294$	0.767010	+	2.32631i	0.0447329	+	0.135673i
$295$	−9.72146			−0.566005
$296$	6.90725	+	9.53916i	0.401476	+	0.554452i
$297$	−9.32374	−	27.3321i	−0.541018	−	1.58597i
$298$	18.0439	+	5.87348i	1.04525	+	0.340242i
$299$	5.05317	+	5.05317i	0.292232	+	0.292232i
$300$	−25.2224	−	25.0318i	−1.45622	−	1.44521i
$301$	−1.15575	+	1.15575i	−0.0666164	+	0.0666164i
$302$	5.49210	+	10.7931i	0.316035	+	0.621074i
$303$	−19.3202	+	14.1810i	−1.10992	+	0.814677i
$304$	−1.68404	+	3.28770i	−0.0965861	+	0.188562i
$305$			11.1995i			0.641281i
$306$	−29.7443	+	4.99171i	−1.70037	+	0.285357i
$307$	2.17003	+	2.17003i	0.123850	+	0.123850i	0.766315	−	0.642465i	$-0.222088\pi$
$307$	2.17003	+	2.17003i	0.123850	+	0.123850i	−0.642465	+	0.766315i	$0.722088\pi$
$308$	−10.9804	+	1.72709i	−0.625666	+	0.0984099i
$309$	15.3848	+	2.36008i	0.875211	+	0.134260i
$310$	4.30804	−	13.2347i	0.244680	−	0.751680i
$311$		−	30.2350i		−	1.71447i	−0.514926	−	0.857235i	$-0.672181\pi$
$311$		−	30.2350i		−	1.71447i	0.514926	−	0.857235i	$-0.327819\pi$
$312$	7.81910	−	4.01618i	0.442670	−	0.227372i
$313$			18.5885i			1.05069i	0.850891	+	0.525343i	$0.176063\pi$
$313$			18.5885i			1.05069i	−0.850891	+	0.525343i	$0.823937\pi$
$314$	13.6899	+	4.45620i	0.772564	+	0.251478i
$315$	10.3890	−	5.42140i	0.585356	−	0.305461i
$316$	6.09594	+	4.43893i	0.342923	+	0.249709i
$317$	−19.3130	−	19.3130i	−1.08473	−	1.08473i	−0.996061	−	0.0886652i	$-0.971740\pi$
$317$	−19.3130	−	19.3130i	−1.08473	−	1.08473i	−0.0886652	−	0.996061i	$-0.528260\pi$
$318$	−19.3384	−	9.74820i	−1.08444	−	0.546652i
$319$			2.20124i			0.123246i
$320$	27.8888	−	14.0975i	1.55903	−	0.788074i
$321$	−11.2012	−	15.2606i	−0.625192	−	0.851762i
$322$	−5.01994	+	2.55441i	−0.279750	+	0.142352i
$323$	−4.64205	+	4.64205i	−0.258291	+	0.258291i
$324$	−17.0139	+	5.87605i	−0.945215	+	0.326447i
$325$	13.0152	+	13.0152i	0.721951	+	0.721951i
$326$	−1.53046	+	4.70171i	−0.0847642	+	0.260403i
$327$	23.2509	−	17.0661i	1.28578	−	0.943760i
$328$	15.0707	+	2.41176i	0.832141	+	0.133167i
$329$	−5.00105			−0.275717
$330$	16.6513	+	50.5025i	0.916622	+	2.78007i
$331$	21.6694	−	21.6694i	1.19106	−	1.19106i	0.214284	−	0.976771i	$-0.431258\pi$
$331$	21.6694	−	21.6694i	1.19106	−	1.19106i	0.976771	−	0.214284i	$-0.0687419\pi$
$332$	4.00585	+	25.4682i	0.219850	+	1.39775i
$333$	5.77912	+	11.0745i	0.316694	+	0.606881i
$334$	11.1082	−	5.65244i	0.607815	−	0.309288i
$335$	−5.45209			−0.297880
$336$	1.10245	+	6.83993i	0.0601433	+	0.373149i
$337$	13.1246			0.714944			0.357472	−	0.933924i	$-0.383639\pi$
$337$	13.1246			0.714944			0.357472	+	0.933924i	$0.383639\pi$
$338$	12.3275	−	6.27287i	0.670528	−	0.341199i
$339$	1.32902	−	8.66355i	0.0721822	−	0.470540i
$340$	54.8622	−	8.62917i	2.97532	−	0.467983i
$341$	−9.90141	+	9.90141i	−0.536191	+	0.536191i
$342$	−2.27370	+	3.19075i	−0.122948	+	0.172536i
$343$	1.00000			0.0539949
$344$	−3.74445	+	2.71133i	−0.201887	+	0.146185i
$345$	15.9444	+	21.7226i	0.858416	+	1.16950i
$346$	2.24007	−	6.88171i	0.120427	−	0.369963i
$347$	5.82438	+	5.82438i	0.312669	+	0.312669i	0.845943	−	0.533274i	$-0.179038\pi$
$347$	5.82438	+	5.82438i	0.312669	+	0.312669i	−0.533274	+	0.845943i	$0.679038\pi$
$348$	1.37202	−	0.00520486i	0.0735478	−	0.000279010i
$349$	−16.4941	+	16.4941i	−0.882909	+	0.882909i	−0.993829	−	0.110920i	$-0.964620\pi$
$349$	−16.4941	+	16.4941i	−0.882909	+	0.882909i	0.110920	+	0.993829i	$0.464620\pi$
$350$	−12.9296	+	6.57924i	−0.691115	+	0.351675i
$351$	8.82415	−	3.01016i	0.470998	−	0.160670i
$352$	−31.4390	−	0.0840743i	−1.67570	−	0.00448118i
$353$			15.6060i			0.830625i	0.909679	+	0.415313i	$0.136328\pi$
$353$			15.6060i			0.830625i	−0.909679	+	0.415313i	$0.863672\pi$
$354$	2.74406	−	5.44364i	0.145845	−	0.289326i
$355$	−15.8753	−	15.8753i	−0.842575	−	0.842575i
$356$	−2.47867	+	3.40393i	−0.131369	+	0.180408i
$357$	−1.86699	+	12.1705i	−0.0988117	+	0.644132i
$358$	−2.74690	−	0.894147i	−0.145178	−	0.0472571i
$359$			9.53840i			0.503417i	0.967803	+	0.251709i	$0.0809925\pi$
$359$			9.53840i			0.503417i	−0.967803	+	0.251709i	$0.919008\pi$
$360$	31.4385	−	10.4980i	1.65695	−	0.553295i
$361$		−	18.1472i		−	0.955115i
$362$	5.69526	−	17.4964i	0.299336	−	0.919589i
$363$	5.22318	−	34.0487i	0.274146	−	1.78710i
$364$	−0.557588	−	3.54501i	−0.0292256	−	0.185809i
$365$	2.52289	+	2.52289i	0.132054	+	0.132054i
$366$	−6.27128	−	3.16126i	−0.327805	−	0.165242i
$367$			12.3806i			0.646260i	0.946355	+	0.323130i	$0.104735\pi$
$367$			12.3806i			0.646260i	−0.946355	+	0.323130i	$0.895265\pi$
$368$	−15.1618	+	4.89054i	−0.790365	+	0.254937i
$369$	15.4439	+	4.85248i	0.803978	+	0.252610i
$370$	−10.4318	−	20.5006i	−0.542323	−	1.06578i
$371$	−6.25168	+	6.25168i	−0.324571	+	0.324571i
$372$	6.19489	+	6.14807i	0.321190	+	0.318763i
$373$	3.59111	+	3.59111i	0.185941	+	0.185941i	0.793939	−	0.607998i	$-0.208027\pi$
$373$	3.59111	+	3.59111i	0.185941	+	0.185941i	−0.607998	+	0.793939i	$0.708027\pi$
$374$	−53.1300	−	17.2944i	−2.74729	−	0.894272i
$375$	21.0503	+	28.6789i	1.08703	+	1.48097i
$376$	−13.9674	−	2.23519i	−0.720312	−	0.115271i
$377$	−0.710667			−0.0366012
$378$	0.103279	+	7.34774i	0.00531208	+	0.377927i
$379$	−15.3273	+	15.3273i	−0.787313	+	0.787313i	−0.981053	−	0.193740i	$-0.937938\pi$
$379$	−15.3273	+	15.3273i	−0.787313	+	0.787313i	0.193740	+	0.981053i	$0.437938\pi$
$380$	4.24683	−	5.83213i	0.217858	−	0.299182i
$381$	−0.213129	+	1.38934i	−0.0109189	+	0.0711782i
$382$	1.76744	+	3.47339i	0.0904302	+	0.177714i
$383$	−4.41723			−0.225710			−0.112855	−	0.993611i	$-0.536000\pi$
$383$	−4.41723			−0.225710			−0.112855	+	0.993611i	$0.536000\pi$
$384$	0.0219350	+	19.5959i	0.00111936	+	0.999999i
$385$	21.7093			1.10641
$386$	8.15246	+	16.0213i	0.414949	+	0.815462i
$387$	−4.34714	+	2.26850i	−0.220977	+	0.115315i
$388$	−13.0004	+	17.8533i	−0.659994	+	0.906363i
$389$	23.4765	−	23.4765i	1.19031	−	1.19031i	0.213325	−	0.976981i	$-0.431571\pi$
$389$	23.4765	−	23.4765i	1.19031	−	1.19031i	0.976981	−	0.213325i	$-0.0684294\pi$
$390$	−16.3047	+	5.37585i	−0.825620	+	0.272217i
$391$	−28.3128			−1.43184
$392$	2.79289	+	0.446945i	0.141062	+	0.0225741i
$393$	28.9553	−	21.2532i	1.46060	−	1.07208i
$394$	−23.7302	−	7.72443i	−1.19551	−	0.389151i
$395$	−10.4142	−	10.4142i	−0.523997	−	0.523997i
$396$	−32.9796	−	4.93118i	−1.65729	−	0.247801i
$397$	−14.2331	+	14.2331i	−0.714340	+	0.714340i	−0.967440	−	0.253100i	$-0.918550\pi$
$397$	−14.2331	+	14.2331i	−0.714340	+	0.714340i	0.253100	+	0.967440i	$0.418550\pi$
$398$	−10.4206	−	20.4786i	−0.522335	−	1.02650i
$399$	0.946449	+	1.28944i	0.0473817	+	0.0645528i
$400$	−39.0514	+	12.5963i	−1.95257	+	0.629814i
$401$			35.8009i			1.78781i	0.448257	+	0.893905i	$0.352045\pi$
$401$			35.8009i			1.78781i	−0.448257	+	0.893905i	$0.647955\pi$
$402$	1.53895	−	3.05296i	0.0767560	−	0.152268i
$403$	−3.19666	−	3.19666i	−0.159237	−	0.159237i
$404$	4.29986	+	27.3375i	0.213926	+	1.36009i
$405$	34.6092	−	6.17391i	1.71974	−	0.306784i
$406$	0.173374	−	0.532620i	0.00860440	−	0.0264335i
$407$			23.1418i			1.14710i
$408$	−10.6539	+	33.1565i	−0.527445	+	1.64149i
$409$		−	11.6596i		−	0.576532i	−0.957550	−	0.288266i	$-0.906921\pi$
$409$		−	11.6596i		−	0.576532i	0.957550	−	0.288266i	$-0.0930787\pi$
$410$	−28.3450	−	9.22662i	−1.39986	−	0.455670i
$411$	−24.1860	−	3.71021i	−1.19301	−	0.183011i
$412$	10.5796	−	14.5289i	0.521220	−	0.715787i
$413$	−1.75981	−	1.75981i	−0.0865945	−	0.0865945i
$414$	−16.6644	+	2.79663i	−0.819010	+	0.137447i
$415$		−	50.3532i		−	2.47174i
$416$	0.0271433	−	10.1500i	0.00133081	−	0.497647i
$417$	23.0483	−	16.9174i	1.12868	−	0.828449i
$418$	−6.46897	+	3.29175i	−0.316408	+	0.161005i
$419$	14.9672	−	14.9672i	0.731196	−	0.731196i	−0.239661	−	0.970857i	$-0.577036\pi$
$419$	14.9672	−	14.9672i	0.731196	−	0.731196i	0.970857	+	0.239661i	$0.0770363\pi$
$420$	−0.0513320	−	13.5313i	−0.00250475	−	0.660259i
$421$	−3.24667	−	3.24667i	−0.158233	−	0.158233i	0.623550	−	0.781783i	$-0.285690\pi$
$421$	−3.24667	−	3.24667i	−0.158233	−	0.158233i	−0.781783	+	0.623550i	$0.785690\pi$
$422$	11.6761	−	35.8700i	0.568383	−	1.74612i
$423$	−14.3132	−	4.49722i	−0.695934	−	0.218662i
$424$	−20.2544	+	14.6661i	−0.983641	+	0.712248i
$425$	−72.9237			−3.53732
$426$	13.3707	−	4.40847i	0.647811	−	0.213591i
$427$	−2.02736	+	2.02736i	−0.0981111	+	0.0981111i
$428$	−21.5932	+	3.39636i	−1.04375	+	0.164169i
$429$	17.0726	+	2.61899i	0.824272	+	0.126446i
$430$	8.04720	−	4.09484i	0.388071	−	0.197470i
$431$	−0.423649			−0.0204065			−0.0102032	−	0.999948i	$-0.503248\pi$
$431$	−0.423649			−0.0204065			−0.0102032	+	0.999948i	$0.503248\pi$
$432$	−2.99559	+	20.5676i	−0.144126	+	0.989559i
$433$	16.1430			0.775783			0.387891	−	0.921705i	$-0.373204\pi$
$433$	16.1430			0.775783			0.387891	+	0.921705i	$0.373204\pi$
$434$	3.17564	−	1.61593i	0.152436	−	0.0775671i
$435$	−2.64870	−	0.406319i	−0.126995	−	0.0194815i
$436$	−5.17467	−	32.8993i	−0.247822	−	1.57559i
$437$	−2.60073	+	2.60073i	−0.124410	+	0.124410i
$438$	−2.12485	+	0.700589i	−0.101529	+	0.0334754i
$439$	−16.3312			−0.779444			−0.389722	−	0.920933i	$-0.627429\pi$
$439$	−16.3312			−0.779444			−0.389722	+	0.920933i	$0.627429\pi$
$440$	60.6318	+	9.70288i	2.89051	+	0.462567i
$441$	2.86205	+	0.899256i	0.136288	+	0.0428217i
$442$	5.58348	−	17.1530i	0.265579	−	0.815883i
$443$	1.31668	+	1.31668i	0.0625575	+	0.0625575i	0.737693	−	0.675136i	$-0.235915\pi$
$443$	1.31668	+	1.31668i	0.0625575	+	0.0625575i	−0.675136	+	0.737693i	$0.735915\pi$
$444$	14.4241	−	0.0547191i	0.684539	−	0.00259685i
$445$	5.81523	−	5.81523i	0.275668	−	0.275668i
$446$	−17.8349	+	9.07530i	−0.844505	+	0.429728i
$447$	18.7353	−	13.7517i	0.886148	−	0.650432i
$448$	7.60048	+	2.49654i	0.359089	+	0.117950i
$449$		−	10.5577i		−	0.498249i	−0.968471	−	0.249124i	$-0.919857\pi$
$449$		−	10.5577i		−	0.498249i	0.968471	−	0.249124i	$-0.0801428\pi$
$450$	−42.9215	+	7.20312i	−2.02334	+	0.339558i
$451$	21.2061	+	21.2061i	0.998554	+	0.998554i
$452$	−8.18156	−	5.95763i	−0.384828	−	0.280223i
$453$	14.6603	+	2.24893i	0.688801	+	0.105664i
$454$	11.8224	+	3.84833i	0.554854	+	0.180611i
$455$			7.00883i			0.328579i
$456$	2.06702	+	4.02428i	0.0967971	+	0.188454i
$457$		−	16.5719i		−	0.775201i	−0.921827	−	0.387600i	$-0.873304\pi$
$457$		−	16.5719i		−	0.775201i	0.921827	−	0.387600i	$-0.126696\pi$
$458$	−1.26570	+	3.88835i	−0.0591423	+	0.181691i
$459$	−16.2878	+	33.1537i	−0.760251	+	1.54748i
$460$	30.7368	−	4.83454i	1.43311	−	0.225411i
$461$	−19.2689	−	19.2689i	−0.897444	−	0.897444i	0.0977653	−	0.995209i	$-0.468831\pi$
$461$	−19.2689	−	19.2689i	−0.897444	−	0.897444i	−0.995209	+	0.0977653i	$0.968831\pi$
$462$	−6.12785	+	12.1564i	−0.285093	+	0.565566i
$463$			0.0613759i			0.00285238i	0.999999	+	0.00142619i	$0.000453971\pi$
$463$			0.0613759i			0.00285238i	−0.999999	+	0.00142619i	$0.999546\pi$
$464$	0.722266	−	1.41006i	0.0335304	−	0.0654605i
$465$	−10.0865	−	13.7418i	−0.467749	−	0.637261i
$466$	16.3891	+	32.2080i	0.759209	+	1.49200i
$467$	6.97512	−	6.97512i	0.322770	−	0.322770i	−0.527059	−	0.849829i	$-0.676705\pi$
$467$	6.97512	−	6.97512i	0.322770	−	0.322770i	0.849829	+	0.527059i	$0.176705\pi$
$468$	1.59203	−	10.6474i	0.0735915	−	0.492177i
$469$	−0.986955	−	0.986955i	−0.0455733	−	0.0455733i
$470$	26.2699	+	8.55113i	1.21174	+	0.394434i
$471$	14.2144	−	10.4334i	0.654966	−	0.480745i
$472$	−4.12841	−	5.70149i	−0.190026	−	0.262432i
$473$	−9.08395			−0.417680
$474$	8.77117	−	2.89196i	0.402873	−	0.132832i
$475$	−6.69855	+	6.69855i	−0.307351	+	0.307351i
$476$	11.4934	+	8.36924i	0.526799	+	0.383604i
$477$	−23.5145	+	12.2708i	−1.07665	+	0.561839i
$478$	13.0979	+	25.7402i	0.599086	+	1.17733i
$479$	28.9163			1.32122			0.660610	−	0.750729i	$-0.270298\pi$
$479$	28.9163			1.32122			0.660610	+	0.750729i	$0.270298\pi$
$480$	5.90438	−	37.8143i	0.269497	−	1.72598i
$481$	−7.47131			−0.340662
$482$	5.85282	+	11.5020i	0.266589	+	0.523902i
$483$	−1.04599	+	6.81859i	−0.0475943	+	0.310256i
$484$	−32.1544	−	23.4142i	−1.46157	−	1.06428i
$485$	30.5003	−	30.5003i	1.38495	−	1.38495i
$486$	−6.31192	+	21.1225i	−0.286314	+	0.958136i
$487$	5.49646			0.249068			0.124534	−	0.992215i	$-0.460256\pi$
$487$	5.49646			0.249068			0.124534	+	0.992215i	$0.460256\pi$
$488$	−6.56833	+	4.75609i	−0.297334	+	0.215298i
$489$	3.58328	+	4.88186i	0.162042	+	0.220766i
$490$	−5.25287	−	1.70987i	−0.237301	−	0.0772440i
$491$	−25.5668	−	25.5668i	−1.15381	−	1.15381i	−0.985782	−	0.168032i	$-0.946259\pi$
$491$	−25.5668	−	25.5668i	−1.15381	−	1.15381i	−0.168032	−	0.985782i	$-0.553741\pi$
$492$	13.1675	−	13.2677i	0.593635	−	0.598156i
$493$	1.99093	−	1.99093i	0.0896669	−	0.0896669i
$494$	−1.06274	−	2.08850i	−0.0478148	−	0.0939661i
$495$	62.1332	+	19.5222i	2.79268	+	0.877459i
$496$	9.59145	−	3.09378i	0.430669	−	0.138915i
$497$		−	5.74760i		−	0.257815i
$498$	28.1958	+	14.2131i	1.26349	+	0.636904i
$499$	2.47543	+	2.47543i	0.110815	+	0.110815i	0.760340	−	0.649525i	$-0.225032\pi$
$499$	2.47543	+	2.47543i	0.110815	+	0.110815i	−0.649525	+	0.760340i	$0.725032\pi$
$500$	40.5797	−	6.38271i	1.81478	−	0.285443i
$501$	2.31459	−	15.0883i	0.103408	−	0.674095i
$502$	8.05748	−	24.7533i	0.359623	−	1.10479i
$503$		−	28.0431i		−	1.25038i	−0.780472	−	0.625191i	$-0.785021\pi$
$503$		−	28.0431i		−	1.25038i	0.780472	−	0.625191i	$-0.214979\pi$
$504$	7.59148	+	3.79071i	0.338151	+	0.168851i
$505$		−	54.0489i		−	2.40514i
$506$	−29.7663	−	9.68927i	−1.32327	−	0.430741i
$507$	2.56865	−	16.7444i	0.114078	−	0.743647i
$508$	1.31205	+	0.955404i	0.0582127	+	0.0423892i
$509$	2.29808	+	2.29808i	0.101861	+	0.101861i	0.756201	−	0.654340i	$-0.227053\pi$
$509$	2.29808	+	2.29808i	0.101861	+	0.101861i	−0.654340	+	0.756201i	$0.727053\pi$
$510$	30.6170	−	60.7378i	1.35575	−	2.68952i
$511$			0.913402i			0.0404065i
$512$	20.1115	+	10.3696i	0.888811	+	0.458274i
$513$	1.54925	+	4.54155i	0.0684010	+	0.200514i
$514$	6.17636	−	3.14285i	0.272428	−	0.138625i
$515$	−24.8210	+	24.8210i	−1.09374	+	1.09374i
$516$	0.0214791	+	5.66196i	0.000945566	+	0.249254i
$517$	−19.6535	−	19.6535i	−0.864362	−	0.864362i
$518$	1.82269	−	5.59948i	0.0800845	−	0.246027i
$519$	−5.24471	−	7.14539i	−0.230217	−	0.313648i
$520$	−3.13257	+	19.5749i	−0.137372	+	0.858417i
$521$	−19.1601			−0.839420			−0.419710	−	0.907658i	$-0.637868\pi$
$521$	−19.1601			−0.839420			−0.419710	+	0.907658i	$0.637868\pi$
$522$	0.975167	−	1.36848i	0.0426819	−	0.0598967i
$523$	−6.72307	+	6.72307i	−0.293979	+	0.293979i	−0.838650	−	0.544671i	$-0.816655\pi$
$523$	−6.72307	+	6.72307i	−0.293979	+	0.293979i	0.544671	+	0.838650i	$0.316655\pi$
$524$	−6.44423	−	40.9709i	−0.281517	−	1.78982i
$525$	−2.69410	+	17.5622i	−0.117580	+	0.766479i
$526$	−4.42286	+	2.25058i	−0.192846	+	0.0981299i
$527$	17.9108			0.780208
$528$	−22.5477	+	31.2126i	−0.981261	+	1.35836i
$529$	7.13760			0.310330
$530$	43.5288	−	22.1497i	1.89077	−	0.962122i
$531$	−3.45414	−	6.61918i	−0.149897	−	0.287248i
$532$	1.82452	−	0.286976i	0.0791031	−	0.0124420i
$533$	−6.84636	+	6.84636i	−0.296549	+	0.296549i
$534$	1.61485	+	4.89776i	0.0698814	+	0.211947i
$535$	42.6919			1.84573
$536$	−2.31534	−	3.19757i	−0.100008	−	0.138114i
$537$	−2.85215	+	2.09348i	−0.123080	+	0.0903403i
$538$	−5.87941	+	18.0621i	−0.253479	+	0.778712i
$539$	3.92989	+	3.92989i	0.169272	+	0.169272i
$540$	12.0212	−	38.7734i	0.517309	−	1.66854i
$541$	0.396767	−	0.396767i	0.0170584	−	0.0170584i	−0.698526	−	0.715585i	$-0.746160\pi$
$541$	0.396767	−	0.396767i	0.0170584	−	0.0170584i	0.715585	+	0.698526i	$0.246160\pi$
$542$	−0.250382	+	0.127408i	−0.0107548	+	0.00547262i
$543$	−13.3344	−	18.1668i	−0.572234	−	0.779611i
$544$	28.3592	+	28.5113i	1.21589	+	1.22241i
$545$			65.0452i			2.78623i
$546$	−3.92468	−	1.97837i	−0.167961	−	0.0846665i
$547$	1.62002	+	1.62002i	0.0692672	+	0.0692672i	0.740892	−	0.671624i	$-0.234403\pi$
$547$	1.62002	+	1.62002i	0.0692672	+	0.0692672i	−0.671624	+	0.740892i	$0.734403\pi$
$548$	−16.6319	+	22.8405i	−0.710480	+	0.975696i
$549$	−7.62554	+	3.97930i	−0.325450	+	0.169832i
$550$	−76.6674	−	24.9561i	−3.26911	−	1.06413i
$551$		−	0.365761i		−	0.0155820i
$552$	−5.96888	+	18.5761i	−0.254052	+	0.790650i
$553$		−	3.77043i		−	0.160335i
$554$	9.89830	−	30.4085i	0.420539	−	1.29193i
$555$	−27.8460	−	4.27166i	−1.18200	−	0.181322i
$556$	−5.12958	−	32.6126i	−0.217542	−	1.38308i
$557$	−3.91321	−	3.91321i	−0.165808	−	0.165808i	0.619326	−	0.785134i	$-0.287406\pi$
$557$	−3.91321	−	3.91321i	−0.165808	−	0.165808i	−0.785134	+	0.619326i	$0.787406\pi$
$558$	10.5420	−	1.76916i	0.446277	−	0.0748946i
$559$		−	2.93274i		−	0.124042i
$560$	−13.9065	−	7.12323i	−0.587656	−	0.301011i
$561$	−55.1658	+	40.4916i	−2.32910	+	1.70956i
$562$	−6.07090	−	11.9306i	−0.256085	−	0.503261i
$563$	−21.9917	+	21.9917i	−0.926839	+	0.926839i	−0.997500	−	0.0706616i	$-0.977489\pi$
$563$	−21.9917	+	21.9917i	−0.926839	+	0.926839i	0.0706616	+	0.997500i	$0.477489\pi$
$564$	−12.2034	+	12.2964i	−0.513858	+	0.517771i
$565$	13.9773	+	13.9773i	0.588028	+	0.588028i
$566$	−16.8185	−	5.47462i	−0.706936	−	0.230116i
$567$	7.38268	+	5.14744i	0.310043	+	0.216172i
$568$	2.56886	−	16.0524i	0.107787	−	0.673545i
$569$	38.8292			1.62781			0.813903	−	0.581001i	$-0.197339\pi$
$569$	38.8292			1.62781			0.813903	+	0.581001i	$0.197339\pi$
$570$	−2.76680	−	8.39158i	−0.115889	−	0.351485i
$571$	28.6026	−	28.6026i	1.19698	−	1.19698i	0.221918	−	0.975065i	$-0.428768\pi$
$571$	28.6026	−	28.6026i	1.19698	−	1.19698i	0.975065	−	0.221918i	$-0.0712318\pi$
$572$	11.7402	−	16.1228i	0.490884	−	0.674126i
$573$	4.71791	+	0.723741i	0.197094	+	0.0302347i
$574$	−3.46087	−	6.80133i	−0.144454	−	0.283882i
$575$	−40.8559			−1.70381
$576$	19.5079	+	13.9800i	0.812831	+	0.582500i
$577$	−23.0517			−0.959655			−0.479828	−	0.877363i	$-0.659301\pi$
$577$	−23.0517			−0.959655			−0.479828	+	0.877363i	$0.659301\pi$
$578$	21.5086	+	42.2689i	0.894640	+	1.75815i
$579$	21.7617	+	3.33831i	0.904386	+	0.138735i
$580$	−1.82142	+	2.50134i	−0.0756304	+	0.103863i
$581$	9.11508	−	9.11508i	0.378157	−	0.378157i
$582$	8.46973	+	25.6883i	0.351082	+	1.06481i
$583$	−49.1367			−2.03504
$584$	−0.408241	+	2.55103i	−0.0168931	+	0.105562i
$585$	−6.30274	+	20.0596i	−0.260586	+	0.829364i
$586$	35.8407	+	11.6666i	1.48057	+	0.481941i
$587$	−0.0987095	−	0.0987095i	−0.00407418	−	0.00407418i	0.705067	−	0.709141i	$-0.250917\pi$
$587$	−0.0987095	−	0.0987095i	−0.00407418	−	0.00407418i	−0.709141	+	0.705067i	$0.750917\pi$
$588$	2.44018	−	2.45876i	0.100631	−	0.101398i
$589$	1.64523	−	1.64523i	0.0677907	−	0.0677907i
$590$	6.23501	+	12.2531i	0.256691	+	0.504452i
$591$	−24.6394	+	18.0853i	−1.01353	+	0.743931i
$592$	7.59324	−	14.8241i	0.312080	−	0.609267i
$593$			1.95818i			0.0804128i	0.999191	+	0.0402064i	$0.0128015\pi$
$593$			1.95818i			0.0804128i	−0.999191	+	0.0402064i	$0.987198\pi$
$594$	−28.4699	+	29.2817i	−1.16814	+	1.20144i
$595$	−19.6352	−	19.6352i	−0.804964	−	0.804964i
$596$	−4.16969	−	26.5099i	−0.170797	−	1.08589i
$597$	−27.8160	−	4.26706i	−1.13843	−	0.174639i
$598$	3.12817	−	9.61003i	0.127920	−	0.392983i
$599$			28.3381i			1.15786i	0.815377	+	0.578931i	$0.196530\pi$
$599$			28.3381i			1.15786i	−0.815377	+	0.578931i	$0.803470\pi$
$600$	−15.3737	+	47.8453i	−0.627628	+	1.95328i
$601$		−	1.19282i		−	0.0486562i	−0.999704	−	0.0243281i	$-0.992255\pi$
$601$		−	1.19282i		−	0.0486562i	0.999704	−	0.0243281i	$-0.00774464\pi$
$602$	2.19799	+	0.715470i	0.0895833	+	0.0291604i
$603$	−1.93719	−	3.71224i	−0.0788885	−	0.151174i
$604$	10.0814	−	13.8447i	0.410206	−	0.563332i
$605$	54.9323	+	54.9323i	2.23331	+	2.23331i
$606$	30.2653	+	15.2563i	1.22944	+	0.619744i
$607$			22.0892i			0.896571i	0.893890	+	0.448285i	$0.147965\pi$
$607$			22.0892i			0.896571i	−0.893890	+	0.448285i	$0.852035\pi$
$608$	5.22395	+	0.0139699i	0.211859	+	0.000566555i
$609$	−0.405923	−	0.553029i	−0.0164488	−	0.0224099i
$610$	14.1160	−	7.18296i	0.571541	−	0.290830i
$611$	6.34513	−	6.34513i	0.256696	−	0.256696i
$612$	25.3686	+	34.2887i	1.02547	+	1.38604i
$613$	−1.62425	−	1.62425i	−0.0656027	−	0.0656027i	0.673544	−	0.739147i	$-0.264771\pi$
$613$	−1.62425	−	1.62425i	−0.0656027	−	0.0656027i	−0.739147	+	0.673544i	$0.764771\pi$
$614$	1.34336	−	4.12693i	0.0542137	−	0.166549i
$615$	−29.4311	+	21.6024i	−1.18678	+	0.871094i
$616$	9.21930	+	12.7322i	0.371456	+	0.512994i
$617$	−7.82504			−0.315024			−0.157512	−	0.987517i	$-0.550347\pi$
$617$	−7.82504			−0.315024			−0.157512	+	0.987517i	$0.550347\pi$
$618$	−6.89261	−	20.9049i	−0.277261	−	0.840920i
$619$	−5.36556	+	5.36556i	−0.215660	+	0.215660i	−0.806667	−	0.591007i	$-0.798731\pi$
$619$	−5.36556	+	5.36556i	−0.215660	+	0.215660i	0.591007	+	0.806667i	$0.298731\pi$
$620$	−19.4443	+	3.05835i	−0.780900	+	0.122826i
$621$	−9.12534	+	18.5745i	−0.366187	+	0.745370i
$622$	−38.1087	+	19.3917i	−1.52802	+	0.777536i
$623$	2.10538			0.0843503
$624$	−10.0770	−	7.27949i	−0.403401	−	0.291413i
$625$	−28.9392			−1.15757
$626$	23.4293	−	11.9220i	0.936423	−	0.476501i
$627$	−1.34792	+	8.78680i	−0.0538308	+	0.350911i
$628$	−3.16353	−	20.1130i	−0.126239	−	0.802595i
$629$	20.9308	−	20.9308i	0.834566	−	0.834566i
$630$	−13.4964	−	9.61741i	−0.537709	−	0.383167i
$631$	38.0571			1.51503			0.757514	−	0.652819i	$-0.226414\pi$
$631$	38.0571			1.51503			0.757514	+	0.652819i	$0.226414\pi$
$632$	1.68518	−	10.5304i	0.0670327	−	0.418877i
$633$	−27.3374	−	37.2444i	−1.08656	−	1.48033i
$634$	−11.9557	+	36.7291i	−0.474823	+	1.45870i
$635$	−2.24148	−	2.24148i	−0.0889506	−	0.0889506i
$636$	0.116185	+	30.6266i	0.00460702	+	1.21442i
$637$	−1.26876	+	1.26876i	−0.0502701	+	0.0502701i
$638$	2.77448	−	1.41180i	0.109843	−	0.0558936i
$639$	5.16857	−	16.4499i	0.204465	−	0.650749i
$640$	−35.6556	−	26.1098i	−1.40941	−	1.03208i
$641$		−	19.4732i		−	0.769144i	−0.923095	−	0.384572i	$-0.874349\pi$
$641$		−	19.4732i		−	0.769144i	0.923095	−	0.384572i	$-0.125651\pi$
$642$	−12.0506	+	23.9058i	−0.475598	+	0.943488i
$643$	13.0510	+	13.0510i	0.514680	+	0.514680i	0.915957	−	0.401277i	$-0.131433\pi$
$643$	13.0510	+	13.0510i	0.514680	+	0.514680i	−0.401277	+	0.915957i	$0.631433\pi$
$644$	6.43923	+	4.68891i	0.253741	+	0.184769i
$645$	1.67677	−	10.9305i	0.0660229	−	0.430389i
$646$	8.82817	+	2.87367i	0.347340	+	0.113063i
$647$			24.7212i			0.971891i	0.873989	+	0.485945i	$0.161525\pi$
$647$			24.7212i			0.971891i	−0.873989	+	0.485945i	$0.838475\pi$
$648$	18.3184	+	17.6759i	0.719614	+	0.694374i
$649$		−	13.8317i		−	0.542941i
$650$	8.05705	−	24.7520i	0.316023	−	0.970853i
$651$	0.661699	−	4.31347i	0.0259340	−	0.169058i
$652$	6.90769	−	1.08650i	0.270526	−	0.0425505i
$653$	−29.4389	−	29.4389i	−1.15203	−	1.15203i	−0.986145	−	0.165888i	$-0.946951\pi$
$653$	−29.4389	−	29.4389i	−1.15203	−	1.15203i	−0.165888	−	0.986145i	$-0.553049\pi$
$654$	−36.4228	−	18.3602i	−1.42424	−	0.717940i
$655$			81.0034i			3.16506i
$656$	−6.62601	−	20.5422i	−0.258702	−	0.802038i
$657$	−0.821383	+	2.61420i	−0.0320452	+	0.101990i
$658$	3.20750	+	6.30340i	0.125041	+	0.245732i
$659$	2.12621	−	2.12621i	0.0828252	−	0.0828252i	−0.664480	−	0.747306i	$-0.731347\pi$
$659$	2.12621	−	2.12621i	0.0828252	−	0.0828252i	0.747306	+	0.664480i	$0.231347\pi$
$660$	52.9746	−	53.3781i	2.06204	−	2.07774i
$661$	−19.0840	−	19.0840i	−0.742282	−	0.742282i	0.230735	−	0.973017i	$-0.425887\pi$
$661$	−19.0840	−	19.0840i	−0.742282	−	0.742282i	−0.973017	+	0.230735i	$0.925887\pi$
$662$	−41.2104	−	13.4144i	−1.60169	−	0.521367i
$663$	−13.0727	−	17.8102i	−0.507701	−	0.691692i
$664$	29.5314	−	21.3835i	1.14604	−	0.829840i
$665$	−3.60726			−0.139883
$666$	10.2520	−	14.3869i	0.397257	−	0.557482i
$667$	1.11543	−	1.11543i	0.0431895	−	0.0431895i
$668$	−14.2489	−	10.3757i	−0.551305	−	0.401448i
$669$	−3.71620	+	24.2251i	−0.143677	+	0.936596i
$670$	3.49679	+	6.87191i	0.135093	+	0.265485i
$671$	−15.9346			−0.615149
$672$	7.91409	−	5.77643i	0.305293	−	0.222831i
$673$	18.1038			0.697851			0.348925	−	0.937150i	$-0.386547\pi$
$673$	18.1038			0.697851			0.348925	+	0.937150i	$0.386547\pi$
$674$	−8.41768	−	16.5425i	−0.324237	−	0.637193i
$675$	−23.5036	+	47.8413i	−0.904654	+	1.84141i
$676$	−15.8129	−	11.5146i	−0.608187	−	0.442869i
$677$	−21.8857	+	21.8857i	−0.841136	+	0.841136i	−0.989007	−	0.147871i	$-0.952758\pi$
$677$	−21.8857	+	21.8857i	−0.841136	+	0.841136i	0.147871	+	0.989007i	$0.452758\pi$
$678$	−11.7721	+	3.88139i	−0.452104	+	0.149064i
$679$	11.0425			0.423773
$680$	−46.0631	−	63.6148i	−1.76644	−	2.43952i
$681$	12.2754	−	9.01016i	0.470395	−	0.345270i
$682$	18.8303	+	6.12948i	0.721050	+	0.234710i
$683$	−21.1021	−	21.1021i	−0.807449	−	0.807449i	0.176798	−	0.984247i	$-0.443426\pi$
$683$	−21.1021	−	21.1021i	−0.807449	−	0.807449i	−0.984247	+	0.176798i	$0.943426\pi$
$684$	5.47994	+	0.819374i	0.209531	+	0.0313295i
$685$	39.0204	−	39.0204i	1.49089	−	1.49089i
$686$	−0.641365	−	1.26042i	−0.0244874	−	0.0481229i
$687$	2.96341	+	4.03734i	0.113061	+	0.154034i
$688$	5.81897	+	2.98061i	0.221846	+	0.113635i
$689$		−	15.8638i		−	0.604361i
$690$	17.1534	−	34.0287i	0.653017	−	1.29545i
$691$	−22.6731	−	22.6731i	−0.862526	−	0.862526i	0.129105	−	0.991631i	$-0.458790\pi$
$691$	−22.6731	−	22.6731i	−0.862526	−	0.862526i	−0.991631	+	0.129105i	$0.958790\pi$
$692$	−10.1105	+	1.59026i	−0.384344	+	0.0604528i
$693$	7.71356	+	14.7815i	0.293014	+	0.561503i
$694$	3.60559	−	11.0767i	0.136866	−	0.420466i
$695$			64.4783i			2.44580i
$696$	−0.886524	−	1.72597i	−0.0336036	−	0.0654229i
$697$		−	38.3600i		−	1.45299i
$698$	31.3682	+	10.2107i	1.18730	+	0.386480i
$699$	43.7481	+	6.71108i	1.65470	+	0.253836i
$700$	16.5852	+	12.0770i	0.626860	+	0.456466i
$701$	−13.6997	−	13.6997i	−0.517431	−	0.517431i	0.399362	−	0.916793i	$-0.369232\pi$
$701$	−13.6997	−	13.6997i	−0.517431	−	0.517431i	−0.916793	+	0.399362i	$0.869232\pi$
$702$	−9.45356	−	9.19149i	−0.356802	−	0.346910i
$703$		−	3.84528i		−	0.145027i
$704$	20.0579	+	39.6801i	0.755961	+	1.49550i
$705$	27.2765	−	20.0209i	1.02729	−	0.754031i
$706$	19.6701	−	10.0092i	0.740294	−	0.376700i
$707$	9.78409	−	9.78409i	0.367968	−	0.367968i
$708$	−8.62120	+	0.0327052i	−0.324005	+	0.00122914i
$709$	24.7783	+	24.7783i	0.930567	+	0.930567i	0.997741	−	0.0671741i	$-0.0213983\pi$
$709$	24.7783	+	24.7783i	0.930567	+	0.930567i	−0.0671741	+	0.997741i	$0.521398\pi$
$710$	−9.82765	+	30.1914i	−0.368825	+	1.13306i
$711$	3.39058	−	10.7912i	0.127157	−	0.404700i
$712$	5.88010	+	0.940990i	0.220366	+	0.0352651i
$713$	10.0346			0.375800
$714$	16.5373	−	5.45256i	0.618894	−	0.204057i
$715$	−27.5439	+	27.5439i	−1.03008	+	1.03008i
$716$	0.634770	+	4.03571i	0.0237225	+	0.150822i
$717$	34.9629	+	5.36341i	1.30571	+	0.200300i
$718$	12.0224	−	6.11760i	0.448670	−	0.228307i
$719$	−20.2382			−0.754759			−0.377379	−	0.926059i	$-0.623175\pi$
$719$	−20.2382			−0.754759			−0.377379	+	0.926059i	$0.623175\pi$
$720$	−33.3955	−	32.8925i	−1.24458	−	1.22583i
$721$	−8.98633			−0.334668
$722$	−22.8730	+	11.6390i	−0.851246	+	0.433158i
$723$	15.6232	+	2.39664i	0.581032	+	0.0891321i
$724$	−25.7055	+	4.04316i	−0.955336	+	0.150263i
$725$	2.87294	−	2.87294i	0.106698	−	0.106698i
$726$	−46.2656	+	15.2543i	−1.71708	+	0.566141i
$727$	−31.6117			−1.17241			−0.586206	−	0.810162i	$-0.699379\pi$
$727$	−31.6117			−1.17241			−0.586206	+	0.810162i	$0.699379\pi$
$728$	−4.11058	+	2.97644i	−0.152348	+	0.110314i
$729$	16.5007	+	21.3711i	0.611138	+	0.791524i
$730$	1.56180	−	4.79799i	0.0578047	−	0.177581i
$731$	8.21606	+	8.21606i	0.303882	+	0.303882i
$732$	0.0376777	+	9.93195i	0.00139261	+	0.367095i
$733$	4.40384	−	4.40384i	0.162660	−	0.162660i	−0.621084	−	0.783744i	$-0.713308\pi$
$733$	4.40384	−	4.40384i	0.162660	−	0.162660i	0.783744	+	0.621084i	$0.213308\pi$
$734$	15.6047	−	7.94047i	0.575979	−	0.293088i
$735$	−5.45415	+	4.00334i	−0.201179	+	0.147666i
$736$	15.8884	+	15.9736i	0.585654	+	0.588795i
$737$		−	7.75724i		−	0.285742i
$738$	−3.78905	−	22.5780i	−0.139477	−	0.831107i
$739$	25.7232	+	25.7232i	0.946243	+	0.946243i	0.998627	−	0.0523842i	$-0.0166820\pi$
$739$	25.7232	+	25.7232i	0.946243	+	0.946243i	−0.0523842	+	0.998627i	$0.516682\pi$
$740$	−19.1488	+	26.2968i	−0.703922	+	0.966690i
$741$	−2.83681	−	0.435175i	−0.104213	−	0.0159866i
$742$	11.8893	+	3.87011i	0.436471	+	0.142076i
$743$			34.9069i			1.28061i	0.768121	+	0.640305i	$0.221192\pi$
$743$			34.9069i			1.28061i	−0.768121	+	0.640305i	$0.778808\pi$
$744$	3.77594	−	11.7513i	0.138433	−	0.430824i
$745$			52.4126i			1.92025i
$746$	2.22308	−	6.82951i	0.0813928	−	0.250046i
$747$	34.2846	−	17.8910i	1.25441	−	0.654599i
$748$	12.2776	+	78.0579i	0.448913	+	2.85408i
$749$	7.72822	+	7.72822i	0.282383	+	0.282383i
$750$	22.6464	−	44.9257i	0.826930	−	1.64046i
$751$			47.1826i			1.72172i	0.508845	+	0.860858i	$0.330072\pi$
$751$			47.1826i			1.72172i	−0.508845	+	0.860858i	$0.669928\pi$
$752$	6.14092	+	19.0383i	0.223936	+	0.694255i
$753$	−18.8651	−	25.7018i	−0.687483	−	0.936626i
$754$	0.455798	+	0.895737i	0.0165992	+	0.0326208i
$755$	−23.6521	+	23.6521i	−0.860787	+	0.860787i
$756$	9.19498	−	4.84276i	0.334418	−	0.176130i
$757$	−7.03526	−	7.03526i	−0.255701	−	0.255701i	0.567602	−	0.823303i	$-0.307871\pi$
$757$	−7.03526	−	7.03526i	−0.255701	−	0.255701i	−0.823303	+	0.567602i	$0.807871\pi$
$758$	29.1493	+	9.48841i	1.05875	+	0.344635i
$759$	−30.9069	+	22.6856i	−1.12185	+	0.823437i
$760$	−10.0747	−	1.61225i	−0.365447	−	0.0584823i
$761$	35.0753			1.27148			0.635739	−	0.771904i	$-0.280695\pi$
$761$	35.0753			1.27148			0.635739	+	0.771904i	$0.280695\pi$
$762$	1.88784	−	0.622445i	0.0683894	−	0.0225488i
$763$	−11.7747	+	11.7747i	−0.426272	+	0.426272i
$764$	3.24435	−	4.45543i	0.117376	−	0.161192i
$765$	−38.5399	−	73.8540i	−1.39341	−	2.67020i
$766$	2.83306	+	5.56756i	0.102363	+	0.201164i
$767$	4.46555			0.161242
$768$	24.6849	−	12.5958i	0.890741	−	0.454511i
$769$	−38.8510			−1.40100			−0.700502	−	0.713650i	$-0.747041\pi$
$769$	−38.8510			−1.40100			−0.700502	+	0.713650i	$0.747041\pi$
$770$	−13.9236	−	27.3628i	−0.501772	−	0.986086i
$771$	1.28695	−	8.38935i	0.0463484	−	0.302135i
$772$	14.9648	−	20.5510i	0.538595	−	0.739647i
$773$	34.2875	−	34.2875i	1.23324	−	1.23324i	0.270523	−	0.962713i	$-0.412803\pi$
$773$	34.2875	−	34.2875i	1.23324	−	1.23324i	0.962713	−	0.270523i	$-0.0871968\pi$
$774$	5.64737	+	4.02427i	0.202990	+	0.144649i
$775$	25.8456			0.928402
$776$	30.8406	+	4.93540i	1.10711	+	0.177171i
$777$	−4.26750	−	5.81404i	−0.153096	−	0.208577i
$778$	−44.6472	−	14.5332i	−1.60068	−	0.521039i
$779$	−3.52363	−	3.52363i	−0.126247	−	0.126247i
$780$	17.2331	+	17.1028i	0.617043	+	0.612379i
$781$	22.5874	−	22.5874i	0.808241	−	0.808241i
$782$	18.1589	+	35.6860i	0.649360	+	1.27613i
$783$	−0.664457	−	1.94783i	−0.0237458	−	0.0696096i
$784$	−1.22793	−	3.80686i	−0.0438545	−	0.135959i
$785$			39.7653i			1.41929i
$786$	−45.3588	−	22.8647i	−1.61789	−	0.815556i
$787$	−36.3051	−	36.3051i	−1.29414	−	1.29414i	−0.932205	−	0.361931i	$-0.882118\pi$
$787$	−36.3051	−	36.3051i	−1.29414	−	1.29414i	−0.361931	−	0.932205i	$-0.617882\pi$
$788$	5.48370	+	34.8641i	0.195349	+	1.24198i
$789$	−0.921578	+	6.00756i	−0.0328091	+	0.213875i
$790$	−6.44694	+	19.8056i	−0.229372	+	0.704651i
$791$			5.06042i			0.179928i
$792$	14.9366	+	44.7307i	0.530749	+	1.58944i
$793$		−	5.14448i		−	0.182686i
$794$	27.0683	+	8.81103i	0.960618	+	0.312692i
$795$	9.06998	−	59.1252i	0.321679	−	2.09695i
$796$	−19.1281	+	26.2685i	−0.677979	+	0.931062i
$797$	17.0156	+	17.0156i	0.602723	+	0.602723i	0.941034	−	0.338312i	$-0.109856\pi$
$797$	17.0156	+	17.0156i	0.602723	+	0.602723i	−0.338312	+	0.941034i	$0.609856\pi$
$798$	1.01821	−	2.01992i	0.0360444	−	0.0715045i
$799$			35.5516i			1.25773i
$800$	40.9228	+	41.1423i	1.44684	+	1.45460i
$801$	6.02571	+	1.89328i	0.212908	+	0.0668957i
$802$	45.1240	−	22.9614i	1.59338	−	0.810796i
$803$	−3.58957	+	3.58957i	−0.126673	+	0.126673i
$804$	−4.83504	+	0.0183421i	−0.170519	+	0.000646876i
$805$	−11.0007	−	11.0007i	−0.387724	−	0.387724i
$806$	−1.97890	+	6.07935i	−0.0697037	+	0.214136i
$807$	13.7656	+	18.7542i	0.484570	+	0.660178i
$808$	31.6988	−	22.9529i	1.11516	−	0.807481i
$809$	19.0095			0.668337			0.334168	−	0.942513i	$-0.391545\pi$
$809$	19.0095			0.668337			0.334168	+	0.942513i	$0.391545\pi$
$810$	−29.9788	−	39.6622i	−1.05335	−	1.39359i
$811$	7.33718	−	7.33718i	0.257643	−	0.257643i	−0.566452	−	0.824095i	$-0.691684\pi$
$811$	7.33718	−	7.33718i	0.257643	−	0.257643i	0.824095	+	0.566452i	$0.191684\pi$
$812$	−0.782519	+	0.123081i	−0.0274610	+	0.00431930i
$813$	−0.0521715	+	0.340094i	−0.00182973	+	0.0119276i
$814$	29.1683	−	14.8423i	1.02235	−	0.520224i
$815$	−13.6572			−0.478390
$816$	48.6240	−	7.83711i	1.70218	−	0.274354i
$817$	1.50940			0.0528074
$818$	−14.6960	+	7.47809i	−0.513834	+	0.261465i
$819$	−4.77220	+	2.49032i	−0.166754	+	0.0870187i
$820$	6.55014	+	41.6442i	0.228741	+	1.45428i
$821$	19.4973	−	19.4973i	0.680460	−	0.680460i	−0.279644	−	0.960104i	$-0.590216\pi$
$821$	19.4973	−	19.4973i	0.680460	−	0.680460i	0.960104	+	0.279644i	$0.0902164\pi$
$822$	10.8357	+	32.8641i	0.377938	+	1.14627i
$823$	−48.4184			−1.68776			−0.843879	−	0.536534i	$-0.819733\pi$
$823$	−48.4184			−1.68776			−0.843879	+	0.536534i	$0.819733\pi$
$824$	−25.0978	−	4.01640i	−0.874325	−	0.139918i
$825$	−79.6051	+	58.4301i	−2.77149	+	2.03427i
$826$	−1.08941	+	3.34677i	−0.0379055	+	0.116449i
$827$	10.0314	+	10.0314i	0.348826	+	0.348826i	0.859672	−	0.510846i	$-0.170668\pi$
$827$	10.0314	+	10.0314i	0.348826	+	0.348826i	−0.510846	+	0.859672i	$0.670668\pi$
$828$	14.2129	+	19.2104i	0.493932	+	0.667608i
$829$	−9.00803	+	9.00803i	−0.312862	+	0.312862i	−0.846017	−	0.533156i	$-0.821006\pi$
$829$	−9.00803	+	9.00803i	−0.312862	+	0.312862i	0.533156	+	0.846017i	$0.321006\pi$
$830$	−63.4660	+	32.2948i	−2.20294	+	1.12097i
$831$	−23.1751	−	31.5737i	−0.803934	−	1.09528i
$832$	−12.8107	+	6.47568i	−0.444131	+	0.224504i
$833$		−	7.10884i		−	0.246307i
$834$	−36.1053	−	18.2002i	−1.25023	−	0.630221i
$835$	24.3426	+	24.3426i	0.842410	+	0.842410i
$836$	8.29795	+	6.04238i	0.286990	+	0.208980i
$837$	5.77273	−	11.7503i	0.199535	−	0.406151i
$838$	−28.4644	−	9.26546i	−0.983285	−	0.320070i
$839$		−	45.7743i		−	1.58030i	−0.612911	−	0.790152i	$-0.710002\pi$
$839$		−	45.7743i		−	1.58030i	0.612911	−	0.790152i	$-0.289998\pi$
$840$	−17.0221	+	8.74319i	−0.587319	+	0.301669i
$841$		−	28.8431i		−	0.994591i
$842$	−2.00985	+	6.17446i	−0.0692642	+	0.212786i
$843$	−16.2053	−	2.48594i	−0.558140	−	0.0856204i
$844$	−52.6998	+	8.28905i	−1.81400	+	0.285321i
$845$	27.0145	+	27.0145i	0.929327	+	0.929327i
$846$	3.51165	+	20.9250i	0.120733	+	0.719417i
$847$			19.8880i			0.683360i
$848$	31.4759	+	16.1227i	1.08089	+	0.553655i
$849$	−17.4630	+	12.8178i	−0.599328	+	0.439907i
$850$	46.7708	+	91.9143i	1.60422	+	3.15263i
$851$	11.7266	−	11.7266i	0.401982	−	0.401982i
$852$	−14.1320	−	14.0252i	−0.484154	−	0.480495i
$853$	−13.8350	−	13.8350i	−0.473700	−	0.473700i	0.429410	−	0.903110i	$-0.358722\pi$
$853$	−13.8350	−	13.8350i	−0.473700	−	0.473700i	−0.903110	+	0.429410i	$0.858722\pi$
$854$	3.85561	+	1.25504i	0.131936	+	0.0429467i
$855$	−10.3242	−	3.24385i	−0.353079	−	0.110937i
$856$	18.1300	+	25.0382i	0.619670	+	0.855787i
$857$	0.198042			0.00676499			0.00338250	−	0.999994i	$-0.498923\pi$
$857$	0.198042			0.00676499			0.00338250	+	0.999994i	$0.498923\pi$
$858$	−7.64875	−	23.1983i	−0.261124	−	0.791977i
$859$	9.93654	−	9.93654i	0.339030	−	0.339030i	−0.516972	−	0.856002i	$-0.672941\pi$
$859$	9.93654	−	9.93654i	0.339030	−	0.339030i	0.856002	+	0.516972i	$0.172941\pi$
$860$	−10.3224	−	7.51654i	−0.351991	−	0.256312i
$861$	−9.23825	−	1.41718i	−0.314839	−	0.0482972i
$862$	0.271714	+	0.533975i	0.00925462	+	0.0181873i
$863$	−41.3690			−1.40822			−0.704108	−	0.710093i	$-0.748653\pi$
$863$	−41.3690			−1.40822			−0.704108	+	0.710093i	$0.748653\pi$
$864$	27.8450	−	9.41566i	0.947307	−	0.320327i
$865$	19.9895			0.679663
$866$	−10.3536	−	20.3469i	−0.351828	−	0.691416i
$867$	57.4138	+	8.80745i	1.94988	+	0.299117i
$868$	−4.07349	−	2.96623i	−0.138263	−	0.100680i
$869$	14.8174	−	14.8174i	0.502644	−	0.502644i
$870$	1.18665	+	3.59907i	0.0402314	+	0.122020i
$871$	2.50442			0.0848589
$872$	−38.1480	+	27.6227i	−1.29185	+	0.935424i
$873$	31.6043	+	9.93006i	1.06964	+	0.336082i
$874$	4.94602	+	1.60999i	0.167302	+	0.0544586i
$875$	−14.5235	−	14.5235i	−0.490984	−	0.490984i
$876$	2.24584	+	2.22887i	0.0758799	+	0.0753064i
$877$	−35.0042	+	35.0042i	−1.18201	+	1.18201i	−0.202784	+	0.979223i	$0.564999\pi$
$877$	−35.0042	+	35.0042i	−1.18201	+	1.18201i	−0.979223	+	0.202784i	$0.935001\pi$
$878$	10.4742	+	20.5841i	0.353489	+	0.694679i
$879$	37.2141	−	27.3151i	1.25520	−	0.921315i
$880$	−26.6574	−	82.6444i	−0.898622	−	2.78594i
$881$		−	36.6416i		−	1.23449i	−0.786772	−	0.617244i	$-0.788249\pi$
$881$		−	36.6416i		−	1.23449i	0.786772	−	0.617244i	$-0.211751\pi$
$882$	−0.702183	−	4.18413i	−0.0236437	−	0.140887i
$883$	−0.637898	−	0.637898i	−0.0214670	−	0.0214670i	0.696292	−	0.717759i	$-0.254832\pi$
$883$	−0.637898	−	0.637898i	−0.0214670	−	0.0214670i	−0.717759	+	0.696292i	$0.754832\pi$
$884$	−25.2009	+	3.96381i	−0.847599	+	0.133317i
$885$	16.6434	+	2.55314i	0.559461	+	0.0858230i
$886$	0.815094	−	2.50404i	0.0273836	−	0.0841250i
$887$			8.74783i			0.293723i	0.989157	+	0.146862i	$0.0469172\pi$
$887$			8.74783i			0.293723i	−0.989157	+	0.146862i	$0.953083\pi$
$888$	−9.32010	−	18.1453i	−0.312762	−	0.608917i
$889$		−	0.811521i		−	0.0272175i
$890$	−11.0593	−	3.59993i	−0.370709	−	0.120670i
$891$	8.78424	+	49.2419i	0.294283	+	1.64967i
$892$	22.8773	+	16.6588i	0.765990	+	0.557777i
$893$	3.26567	+	3.26567i	0.109281	+	0.109281i
$894$	−29.3490	−	14.7944i	−0.981578	−	0.494799i
$895$		−	7.97900i		−	0.266709i
$896$	−1.72801	−	11.1810i	−0.0577286	−	0.373530i
$897$	−7.32404	−	9.97826i	−0.244542	−	0.333164i
$898$	−13.3071	+	6.77135i	−0.444064	+	0.225963i
$899$	−0.705625	+	0.705625i	−0.0235339	+	0.0235339i
$900$	36.6073	+	49.4792i	1.22024	+	1.64931i
$901$	44.4422	+	44.4422i	1.48058	+	1.48058i
$902$	13.1276	−	40.3293i	0.437102	−	1.34282i
$903$	2.28221	−	1.67514i	0.0759472	−	0.0557452i
$904$	−2.26173	+	14.1332i	−0.0752240	+	0.470063i
$905$	50.8222			1.68939
$906$	−6.56802	−	19.9205i	−0.218208	−	0.661813i
$907$	19.7335	−	19.7335i	0.655241	−	0.655241i	−0.299009	−	0.954250i	$-0.596656\pi$
$907$	19.7335	−	19.7335i	0.655241	−	0.655241i	0.954250	+	0.299009i	$0.0966562\pi$
$908$	−2.73200	−	17.3694i	−0.0906644	−	0.576423i
$909$	36.8010	−	19.2042i	1.22061	−	0.636962i
$910$	8.83405	−	4.49522i	0.292846	−	0.149015i
$911$	21.9542			0.727374			0.363687	−	0.931521i	$-0.381518\pi$
$911$	21.9542			0.727374			0.363687	+	0.931521i	$0.381518\pi$
$912$	3.74656	−	5.18634i	0.124061	−	0.171737i
$913$	71.6425			2.37102
$914$	−20.8875	+	10.6286i	−0.690897	+	0.351564i
$915$	2.94132	−	19.1738i	0.0972369	−	0.633866i
$916$	5.71272	−	0.898542i	0.188753	−	0.0296887i
$917$	−14.6635	+	14.6635i	−0.484231	+	0.484231i
$918$	52.2339	−	0.734191i	1.72398	−	0.0242319i
$919$	−8.20968			−0.270812			−0.135406	−	0.990790i	$-0.543234\pi$
$919$	−8.20968			−0.270812			−0.135406	+	0.990790i	$0.543234\pi$
$920$	−25.8071	−	35.6405i	−0.850834	−	1.17503i
$921$	−3.14523	−	4.28506i	−0.103639	−	0.141198i
$922$	−11.9285	+	36.6453i	−0.392843	+	1.20685i
$923$	7.29233	+	7.29233i	0.240030	+	0.240030i
$924$	19.2523	−	0.0730352i	0.633354	−	0.00240268i
$925$	30.2035	−	30.2035i	0.993084	−	0.993084i
$926$	0.0773592	−	0.0393644i	0.00254218	−	0.00129359i
$927$	−25.7193	−	8.08101i	−0.844734	−	0.265415i
$928$	−2.24050	−	0.00599156i	−0.0735481	−	0.000196683i
$929$			38.0207i			1.24742i	0.781657	+	0.623709i	$0.214375\pi$
$929$			38.0207i			1.24742i	−0.781657	+	0.623709i	$0.785625\pi$
$930$	−10.8513	+	21.5267i	−0.355828	+	0.705888i
$931$	−0.652997	−	0.652997i	−0.0214011	−	0.0214011i
$932$	30.0841	−	41.3141i	0.985436	−	1.35329i
$933$	−7.94060	+	51.7630i	−0.259964	+	1.69465i
$934$	−13.2652	−	4.31796i	−0.434049	−	0.141288i
$935$		−	154.328i		−	5.04707i
$936$	−14.4413	+	4.82227i	−0.472027	+	0.157621i
$937$			11.5227i			0.376430i	0.982128	+	0.188215i	$0.0602701\pi$
$937$			11.5227i			0.376430i	−0.982128	+	0.188215i	$0.939730\pi$
$938$	−0.610975	+	1.87697i	−0.0199491	+	0.0612853i
$939$	4.88190	−	31.8240i	0.159315	−	1.03854i
$940$	−6.07059	−	38.5954i	−0.198001	−	1.25884i
$941$	−32.1285	−	32.1285i	−1.04736	−	1.04736i	−0.998821	−	0.0485386i	$-0.984544\pi$
$941$	−32.1285	−	32.1285i	−1.04736	−	1.04736i	−0.0485386	−	0.998821i	$-0.515456\pi$
$942$	−22.2670	−	11.2245i	−0.725499	−	0.365714i
$943$		−	21.4914i		−	0.699856i
$944$	−4.53843	+	8.86026i	−0.147713	+	0.288377i
$945$	−19.2101	+	6.55309i	−0.624904	+	0.213172i
$946$	5.82613	+	11.4496i	0.189424	+	0.372257i
$947$	31.1625	−	31.1625i	1.01265	−	1.01265i	0.0127273	−	0.999919i	$-0.495949\pi$
$947$	31.1625	−	31.1625i	1.01265	−	1.01265i	0.999919	−	0.0127273i	$-0.00405133\pi$
$948$	−9.27060	−	9.20052i	−0.301095	−	0.298819i
$949$	−1.15889	−	1.15889i	−0.0376191	−	0.0376191i
$950$	12.7392	+	4.14675i	0.413314	+	0.134538i
$951$	27.9922	+	38.1365i	0.907708	+	1.23666i
$952$	3.17726	−	19.8542i	0.102976	−	0.643479i
$953$	−23.9408			−0.775520			−0.387760	−	0.921760i	$-0.626751\pi$
$953$	−23.9408			−0.775520			−0.387760	+	0.921760i	$0.626751\pi$
$954$	30.5476	+	21.7680i	0.989016	+	0.704765i
$955$	−7.61160	+	7.61160i	−0.246306	+	0.246306i
$956$	24.0428	−	33.0177i	0.777599	−	1.06787i
$957$	0.578110	−	3.76857i	0.0186876	−	0.121821i
$958$	−18.5459	−	36.4466i	−0.599191	−	1.17754i
$959$	14.1272			0.456190
$960$	−51.4487	+	16.8108i	−1.66050	+	0.542567i
$961$	24.6520			0.795227
$962$	4.79184	+	9.41696i	0.154495	+	0.303615i
$963$	15.1689	+	29.0682i	0.488812	+	0.936711i
$964$	10.7435	−	14.7540i	0.346026	−	0.475194i
$965$	−35.1091	+	35.1091i	−1.13020	+	1.13020i
$966$	9.26512	−	3.05482i	0.298100	−	0.0982872i
$967$	−35.6844			−1.14753			−0.573767	−	0.819019i	$-0.694519\pi$
$967$	−35.6844			−1.14753			−0.573767	+	0.819019i	$0.694519\pi$
$968$	−8.88885	+	55.5450i	−0.285699	+	1.78529i
$969$	9.16644	−	6.72816i	0.294468	−	0.216140i
$970$	−58.0050	−	18.8813i	−1.86243	−	0.606241i
$971$	−33.2472	−	33.2472i	−1.06695	−	1.06695i	−0.997592	−	0.0693607i	$-0.977904\pi$
$971$	−33.2472	−	33.2472i	−1.06695	−	1.06695i	−0.0693607	−	0.997592i	$-0.522096\pi$
$972$	30.6714	−	5.59159i	0.983785	−	0.179350i
$973$	−11.6721	+	11.6721i	−0.374189	+	0.374189i
$974$	−3.52524	−	6.92783i	−0.112956	−	0.221982i
$975$	−18.8641	−	25.7004i	−0.604135	−	0.823072i
$976$	10.2074	+	5.22844i	0.326729	+	0.167358i
$977$		−	51.7092i		−	1.65432i	−0.561963	−	0.827162i	$-0.689954\pi$
$977$		−	51.7092i		−	1.65432i	0.561963	−	0.827162i	$-0.310046\pi$
$978$	3.85499	−	7.64749i	0.123269	−	0.244540i
$979$	8.27391	+	8.27391i	0.264435	+	0.264435i
$980$	1.21386	+	7.71746i	0.0387755	+	0.246525i
$981$	−44.2882	+	23.1113i	−1.41401	+	0.737886i
$982$	−15.8272	+	48.6225i	−0.505065	+	1.55161i
$983$		−	11.7952i		−	0.376209i	−0.982149	−	0.188105i	$-0.939766\pi$
$983$		−	11.7952i		−	0.376209i	0.982149	−	0.188105i	$-0.0602344\pi$
$984$	−25.1680	−	8.08701i	−0.802327	−	0.257804i
$985$		−	68.9296i		−	2.19628i
$986$	−3.78631	−	1.23249i	−0.120581	−	0.0392504i
$987$	8.56191	+	1.31342i	0.272529	+	0.0418067i
$988$	−1.95078	+	2.67898i	−0.0620625	+	0.0852298i
$989$	4.60309	+	4.60309i	0.146370	+	0.146370i
$990$	−15.2439	−	90.8346i	−0.484484	−	2.88691i
$991$			4.96971i			0.157868i	0.996880	+	0.0789341i	$0.0251517\pi$
$991$			4.96971i			0.157868i	−0.996880	+	0.0789341i	$0.974848\pi$
$992$	−10.0511	−	10.1050i	−0.319122	−	0.320833i
$993$	−42.7895	+	31.4074i	−1.35788	+	0.996685i
$994$	−7.24437	+	3.68631i	−0.229778	+	0.116923i
$995$	44.8768	−	44.8768i	1.42269	−	1.42269i
$996$	−0.169400	−	44.6543i	−0.00536764	−	1.41493i
$997$	−37.4527	−	37.4527i	−1.18614	−	1.18614i	−0.978126	−	0.208015i	$-0.933300\pi$
$997$	−37.4527	−	37.4527i	−1.18614	−	1.18614i	−0.208015	−	0.978126i	$-0.566700\pi$
$998$	1.53242	−	4.70773i	0.0485078	−	0.149021i
$999$	−6.98549	−	20.4777i	−0.221011	−	0.647884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.10	✓	48
3.2	odd	2	inner	336.2.s.d.155.15	yes	48
4.3	odd	2		1344.2.s.d.911.24		48
12.11	even	2		1344.2.s.d.911.14		48
16.3	odd	4	inner	336.2.s.d.323.15	yes	48
16.13	even	4		1344.2.s.d.239.14		48
48.29	odd	4		1344.2.s.d.239.24		48
48.35	even	4	inner	336.2.s.d.323.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.10	✓	48	1.1	even	1	trivial
336.2.s.d.155.15	yes	48	3.2	odd	2	inner
336.2.s.d.323.10	yes	48	48.35	even	4	inner
336.2.s.d.323.15	yes	48	16.3	odd	4	inner
1344.2.s.d.239.14		48	16.13	even	4
1344.2.s.d.239.24		48	48.29	odd	4
1344.2.s.d.911.14		48	12.11	even	2
1344.2.s.d.911.24		48	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)

\(f(q)\)	\(=\)	\(q+(-0.641365 - 1.26042i) q^{2} +(-1.71202 - 0.262630i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(2.76208 - 2.76208i) q^{5} +(0.767010 + 2.32631i) q^{6} +1.00000 q^{7} +(2.79289 + 0.446945i) q^{8} +(2.86205 + 0.899256i) q^{9} +O(q^{10})\)	\(q+(-0.641365 - 1.26042i) q^{2} +(-1.71202 - 0.262630i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(2.76208 - 2.76208i) q^{5} +(0.767010 + 2.32631i) q^{6} +1.00000 q^{7} +(2.79289 + 0.446945i) q^{8} +(2.86205 + 0.899256i) q^{9} +(-5.25287 - 1.70987i) q^{10} +(3.92989 + 3.92989i) q^{11} +(2.44018 - 2.45876i) q^{12} +(-1.26876 + 1.26876i) q^{13} +(-0.641365 - 1.26042i) q^{14} +(-5.45415 + 4.00334i) q^{15} +(-1.22793 - 3.80686i) q^{16} -7.10884i q^{17} +(-0.702183 - 4.18413i) q^{18} +(-0.652997 - 0.652997i) q^{19} +(1.21386 + 7.71746i) q^{20} +(-1.71202 - 0.262630i) q^{21} +(2.43280 - 7.47379i) q^{22} -3.98276i q^{23} +(-4.66411 - 1.49868i) q^{24} -10.2582i q^{25} +(2.41291 + 0.785428i) q^{26} +(-4.66373 - 2.29121i) q^{27} +(-1.17730 + 1.61678i) q^{28} +(0.280064 + 0.280064i) q^{29} +(8.54398 + 4.30690i) q^{30} +2.51952i q^{31} +(-4.01068 + 3.98929i) q^{32} +(-5.69595 - 7.76016i) q^{33} +(-8.96010 + 4.55937i) q^{34} +(2.76208 - 2.76208i) q^{35} +(-4.82339 + 3.56860i) q^{36} +(2.94433 + 2.94433i) q^{37} +(-0.404238 + 1.24186i) q^{38} +(2.50536 - 1.83893i) q^{39} +(8.94869 - 6.47969i) q^{40} +5.39610 q^{41} +(0.767010 + 2.32631i) q^{42} +(-1.15575 + 1.15575i) q^{43} +(-10.9804 + 1.72709i) q^{44} +(10.3890 - 5.42140i) q^{45} +(-5.01994 + 2.55441i) q^{46} -5.00105 q^{47} +(1.10245 + 6.83993i) q^{48} +1.00000 q^{49} +(-12.9296 + 6.57924i) q^{50} +(-1.86699 + 12.1705i) q^{51} +(-0.557588 - 3.54501i) q^{52} +(-6.25168 + 6.25168i) q^{53} +(0.103279 + 7.34774i) q^{54} +21.7093 q^{55} +(2.79289 + 0.446945i) q^{56} +(0.946449 + 1.28944i) q^{57} +(0.173374 - 0.532620i) q^{58} +(-1.75981 - 1.75981i) q^{59} +(-0.0513320 - 13.5313i) q^{60} +(-2.02736 + 2.02736i) q^{61} +(3.17564 - 1.61593i) q^{62} +(2.86205 + 0.899256i) q^{63} +(7.60048 + 2.49654i) q^{64} +7.00883i q^{65} +(-6.12785 + 12.1564i) q^{66} +(-0.986955 - 0.986955i) q^{67} +(11.4934 + 8.36924i) q^{68} +(-1.04599 + 6.81859i) q^{69} +(-5.25287 - 1.70987i) q^{70} -5.74760i q^{71} +(7.59148 + 3.79071i) q^{72} +0.913402i q^{73} +(1.82269 - 5.59948i) q^{74} +(-2.69410 + 17.5622i) q^{75} +(1.82452 - 0.286976i) q^{76} +(3.92989 + 3.92989i) q^{77} +(-3.92468 - 1.97837i) q^{78} -3.77043i q^{79} +(-13.9065 - 7.12323i) q^{80} +(7.38268 + 5.14744i) q^{81} +(-3.46087 - 6.80133i) q^{82} +(9.11508 - 9.11508i) q^{83} +(2.44018 - 2.45876i) q^{84} +(-19.6352 - 19.6352i) q^{85} +(2.19799 + 0.715470i) q^{86} +(-0.405923 - 0.553029i) q^{87} +(9.21930 + 12.7322i) q^{88} +2.10538 q^{89} +(-13.4964 - 9.61741i) q^{90} +(-1.26876 + 1.26876i) q^{91} +(6.43923 + 4.68891i) q^{92} +(0.661699 - 4.31347i) q^{93} +(3.20750 + 6.30340i) q^{94} -3.60726 q^{95} +(7.91409 - 5.77643i) q^{96} +11.0425 q^{97} +(-0.641365 - 1.26042i) q^{98} +(7.71356 + 14.7815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

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