LMFDB - Embedded newform 192.2.r.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	192.13
Dual form			192.2.r.a.133.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711584 + 1.22215i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.987297 + 1.73932i) q^{4} +(3.50591 - 0.697369i) q^{5} +(-1.27065 - 0.620845i) q^{6} +(0.519328 + 1.25377i) q^{7} +(-2.82826 + 0.0310494i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(0.711584 + 1.22215i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.987297 + 1.73932i) q^{4} +(3.50591 - 0.697369i) q^{5} +(-1.27065 - 0.620845i) q^{6} +(0.519328 + 1.25377i) q^{7} +(-2.82826 + 0.0310494i) q^{8} +(0.382683 - 0.923880i) q^{9} +(3.34704 + 3.78851i) q^{10} +(-1.86115 + 2.78540i) q^{11} +(-0.145408 - 1.99471i) q^{12} +(-0.501734 - 0.0998012i) q^{13} +(-1.16275 + 1.52686i) q^{14} +(-2.52762 + 2.52762i) q^{15} +(-2.05049 - 3.43446i) q^{16} +(-2.63840 - 2.63840i) q^{17} +(1.40143 - 0.189721i) q^{18} +(0.729057 - 3.66521i) q^{19} +(-2.24843 + 6.78643i) q^{20} +(-1.12836 - 0.753948i) q^{21} +(-4.72854 - 0.292552i) q^{22} +(4.20944 + 1.74361i) q^{23} +(2.33436 - 1.59711i) q^{24} +(7.18570 - 2.97642i) q^{25} +(-0.235054 - 0.684211i) q^{26} +(0.195090 + 0.980785i) q^{27} +(-2.69344 - 0.334564i) q^{28} +(3.53799 + 5.29497i) q^{29} +(-4.88775 - 1.29052i) q^{30} -8.97511i q^{31} +(2.73833 - 4.94991i) q^{32} -3.34998i q^{33} +(1.34707 - 5.10196i) q^{34} +(2.69506 + 4.03344i) q^{35} +(1.22910 + 1.57775i) q^{36} +(-1.56154 - 7.85041i) q^{37} +(4.99822 - 1.71709i) q^{38} +(0.472623 - 0.195767i) q^{39} +(-9.89397 + 2.08120i) q^{40} +(1.96746 + 0.814947i) q^{41} +(0.118512 - 1.91553i) q^{42} +(4.67449 + 3.12339i) q^{43} +(-3.00721 - 5.98716i) q^{44} +(0.697369 - 3.50591i) q^{45} +(0.864421 + 6.38528i) q^{46} +(-7.87997 - 7.87997i) q^{47} +(3.61300 + 1.71646i) q^{48} +(3.64751 - 3.64751i) q^{49} +(8.75085 + 6.66403i) q^{50} +(3.65956 + 0.727932i) q^{51} +(0.668947 - 0.774145i) q^{52} +(-7.79457 + 11.6654i) q^{53} +(-1.05984 + 0.936340i) q^{54} +(-4.58256 + 11.0633i) q^{55} +(-1.50772 - 3.52986i) q^{56} +(1.43010 + 3.45256i) q^{57} +(-3.95367 + 8.09177i) q^{58} +(-3.02073 + 0.600861i) q^{59} +(-1.90084 - 6.89187i) q^{60} +(-6.51828 + 4.35538i) q^{61} +(10.9689 - 6.38655i) q^{62} +1.35707 q^{63} +(7.99807 - 0.175631i) q^{64} -1.82864 q^{65} +(4.09417 - 2.38379i) q^{66} +(-2.18485 + 1.45987i) q^{67} +(7.19391 - 1.98414i) q^{68} +(-4.46872 + 0.888883i) q^{69} +(-3.01171 + 6.16390i) q^{70} +(-3.27206 - 7.89945i) q^{71} +(-1.05364 + 2.62485i) q^{72} +(4.96324 - 11.9823i) q^{73} +(8.48320 - 7.49466i) q^{74} +(-4.32109 + 6.46696i) q^{75} +(5.65520 + 4.88672i) q^{76} +(-4.45880 - 0.886911i) q^{77} +(0.575568 + 0.438312i) q^{78} +(-3.66395 + 3.66395i) q^{79} +(-9.58392 - 10.6110i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(0.404023 + 2.98443i) q^{82} +(-2.39008 + 12.0157i) q^{83} +(2.42539 - 1.21822i) q^{84} +(-11.0899 - 7.41006i) q^{85} +(-0.490963 + 7.93548i) q^{86} +(-5.88346 - 2.43701i) q^{87} +(5.17732 - 7.93562i) q^{88} +(11.4475 - 4.74172i) q^{89} +(4.78099 - 1.64246i) q^{90} +(-0.135437 - 0.680889i) q^{91} +(-7.18866 + 5.60011i) q^{92} +(4.98631 + 7.46254i) q^{93} +(4.02324 - 15.2378i) q^{94} -13.3583i q^{95} +(0.473187 + 5.63703i) q^{96} +7.84952i q^{97} +(7.05331 + 1.86229i) q^{98} +(1.86115 + 2.78540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	0.711584	+	1.22215i	0.503166	+	0.864190i
$2$	0.711584	+	1.22215i	0.503166	+	0.864190i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$4$	−0.987297	+	1.73932i	−0.493649	+	0.869661i
$5$	3.50591	−	0.697369i	1.56789	−	0.311873i	0.666711	−	0.745316i	$-0.267702\pi$
$5$	3.50591	−	0.697369i	1.56789	−	0.311873i	0.901181	+	0.433443i	$0.142702\pi$
$6$	−1.27065	−	0.620845i	−0.518741	−	0.253459i
$7$	0.519328	+	1.25377i	0.196288	+	0.473880i	0.991124	−	0.132944i	$-0.0424431\pi$
$7$	0.519328	+	1.25377i	0.196288	+	0.473880i	−0.794836	+	0.606825i	$0.792443\pi$
$8$	−2.82826	+	0.0310494i	−0.999940	+	0.0109776i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	3.34704	+	3.78851i	1.05843	+	1.19803i
$11$	−1.86115	+	2.78540i	−0.561157	+	0.839831i	−0.998222	−	0.0595991i	$-0.981018\pi$
$11$	−1.86115	+	2.78540i	−0.561157	+	0.839831i	0.437066	+	0.899430i	$0.356018\pi$
$12$	−0.145408	−	1.99471i	−0.0419758	−	0.575822i
$13$	−0.501734	−	0.0998012i	−0.139156	−	0.0276799i	0.125021	−	0.992154i	$-0.460100\pi$
$13$	−0.501734	−	0.0998012i	−0.139156	−	0.0276799i	−0.264177	+	0.964474i	$0.585100\pi$
$14$	−1.16275	+	1.52686i	−0.310757	+	0.408070i
$15$	−2.52762	+	2.52762i	−0.652629	+	0.652629i
$16$	−2.05049	−	3.43446i	−0.512622	−	0.858614i
$17$	−2.63840	−	2.63840i	−0.639906	−	0.639906i	0.310627	−	0.950532i	$-0.399461\pi$
$17$	−2.63840	−	2.63840i	−0.639906	−	0.639906i	−0.950532	+	0.310627i	$0.899461\pi$
$18$	1.40143	−	0.189721i	0.330320	−	0.0447178i
$19$	0.729057	−	3.66521i	0.167257	−	0.840858i	−0.802475	−	0.596686i	$-0.796484\pi$
$19$	0.729057	−	3.66521i	0.167257	−	0.840858i	0.969732	−	0.244172i	$-0.0785162\pi$
$20$	−2.24843	+	6.78643i	−0.502764	+	1.51749i
$21$	−1.12836	−	0.753948i	−0.246229	−	0.164525i
$22$	−4.72854	−	0.292552i	−1.00813	−	0.0623722i
$23$	4.20944	+	1.74361i	0.877728	+	0.363567i	0.775615	−	0.631206i	$-0.217440\pi$
$23$	4.20944	+	1.74361i	0.877728	+	0.363567i	0.102113	+	0.994773i	$0.467440\pi$
$24$	2.33436	−	1.59711i	0.476499	−	0.326009i
$25$	7.18570	−	2.97642i	1.43714	−	0.595283i
$26$	−0.235054	−	0.684211i	−0.0460979	−	0.134185i
$27$	0.195090	+	0.980785i	0.0375451	+	0.188752i
$28$	−2.69344	−	0.334564i	−0.509013	−	0.0632266i
$29$	3.53799	+	5.29497i	0.656988	+	0.983252i	0.999050	+	0.0435745i	$0.0138746\pi$
$29$	3.53799	+	5.29497i	0.656988	+	0.983252i	−0.342062	+	0.939677i	$0.611125\pi$
$30$	−4.88775	−	1.29052i	−0.892376	−	0.235615i
$31$		−	8.97511i		−	1.61198i	−0.591930	−	0.805989i	$-0.701634\pi$
$31$		−	8.97511i		−	1.61198i	0.591930	−	0.805989i	$-0.298366\pi$
$32$	2.73833	−	4.94991i	0.484072	−	0.875028i
$33$		−	3.34998i		−	0.583156i
$34$	1.34707	−	5.10196i	0.231021	−	0.874978i
$35$	2.69506	+	4.03344i	0.455548	+	0.681776i
$36$	1.22910	+	1.57775i	0.204850	+	0.262959i
$37$	−1.56154	−	7.85041i	−0.256716	−	1.29060i	−0.866957	−	0.498383i	$-0.833927\pi$
$37$	−1.56154	−	7.85041i	−0.256716	−	1.29060i	0.610241	−	0.792216i	$-0.291073\pi$
$38$	4.99822	−	1.71709i	0.810819	−	0.278549i
$39$	0.472623	−	0.195767i	0.0756803	−	0.0313478i
$40$	−9.89397	+	2.08120i	−1.56437	+	0.329066i
$41$	1.96746	+	0.814947i	0.307265	+	0.127273i	0.530988	−	0.847380i	$-0.321821\pi$
$41$	1.96746	+	0.814947i	0.307265	+	0.127273i	−0.223723	+	0.974653i	$0.571821\pi$
$42$	0.118512	−	1.91553i	0.0182868	−	0.295572i
$43$	4.67449	+	3.12339i	0.712853	+	0.476313i	0.858362	−	0.513044i	$-0.171482\pi$
$43$	4.67449	+	3.12339i	0.712853	+	0.476313i	−0.145510	+	0.989357i	$0.546482\pi$
$44$	−3.00721	−	5.98716i	−0.453354	−	0.902598i
$45$	0.697369	−	3.50591i	0.103958	−	0.522631i
$46$	0.864421	+	6.38528i	0.127452	+	0.941459i
$47$	−7.87997	−	7.87997i	−1.14941	−	1.14941i	−0.986668	−	0.162744i	$-0.947966\pi$
$47$	−7.87997	−	7.87997i	−1.14941	−	1.14941i	−0.162744	−	0.986668i	$-0.552034\pi$
$48$	3.61300	+	1.71646i	0.521492	+	0.247749i
$49$	3.64751	−	3.64751i	0.521073	−	0.521073i
$50$	8.75085	+	6.66403i	1.23756	+	0.942437i
$51$	3.65956	+	0.727932i	0.512441	+	0.101931i
$52$	0.668947	−	0.774145i	0.0927663	−	0.107355i
$53$	−7.79457	+	11.6654i	−1.07067	+	1.60237i	−0.312966	+	0.949764i	$0.601323\pi$
$53$	−7.79457	+	11.6654i	−1.07067	+	1.60237i	−0.757701	+	0.652602i	$0.773677\pi$
$54$	−1.05984	+	0.936340i	−0.144226	+	0.127420i
$55$	−4.58256	+	11.0633i	−0.617913	+	1.49177i
$56$	−1.50772	−	3.52986i	−0.201478	−	0.471697i
$57$	1.43010	+	3.45256i	0.189421	+	0.457302i
$58$	−3.95367	+	8.09177i	−0.519143	+	1.06250i
$59$	−3.02073	+	0.600861i	−0.393266	+	0.0782255i	−0.387762	−	0.921759i	$-0.626752\pi$
$59$	−3.02073	+	0.600861i	−0.393266	+	0.0782255i	−0.00550363	+	0.999985i	$0.501752\pi$
$60$	−1.90084	−	6.89187i	−0.245397	−	0.889736i
$61$	−6.51828	+	4.35538i	−0.834581	+	0.557649i	−0.897827	−	0.440349i	$-0.854855\pi$
$61$	−6.51828	+	4.35538i	−0.834581	+	0.557649i	0.0632459	+	0.997998i	$0.479855\pi$
$62$	10.9689	−	6.38655i	1.39306	−	0.811092i
$63$	1.35707			0.170975
$64$	7.99807	−	0.175631i	0.999759	−	0.0219539i
$65$	−1.82864			−0.226814
$66$	4.09417	−	2.38379i	0.503957	−	0.293424i
$67$	−2.18485	+	1.45987i	−0.266922	+	0.178352i	−0.681828	−	0.731513i	$-0.738815\pi$
$67$	−2.18485	+	1.45987i	−0.266922	+	0.178352i	0.414905	+	0.909865i	$0.363815\pi$
$68$	7.19391	−	1.98414i	0.872390	−	0.240613i
$69$	−4.46872	+	0.888883i	−0.537970	+	0.107009i
$70$	−3.01171	+	6.16390i	−0.359968	+	0.736727i
$71$	−3.27206	−	7.89945i	−0.388322	−	0.937492i	−0.990296	−	0.138976i	$-0.955619\pi$
$71$	−3.27206	−	7.89945i	−0.388322	−	0.937492i	0.601974	−	0.798516i	$-0.294381\pi$
$72$	−1.05364	+	2.62485i	−0.124173	+	0.309342i
$73$	4.96324	−	11.9823i	0.580903	−	1.40242i	−0.311092	−	0.950380i	$-0.600695\pi$
$73$	4.96324	−	11.9823i	0.580903	−	1.40242i	0.891995	−	0.452045i	$-0.149305\pi$
$74$	8.48320	−	7.49466i	0.986152	−	0.871237i
$75$	−4.32109	+	6.46696i	−0.498956	+	0.746741i
$76$	5.65520	+	4.88672i	0.648696	+	0.560545i
$77$	−4.45880	−	0.886911i	−0.508127	−	0.101073i
$78$	0.575568	+	0.438312i	0.0651702	+	0.0496290i
$79$	−3.66395	+	3.66395i	−0.412227	+	0.412227i	−0.882514	−	0.470287i	$-0.844150\pi$
$79$	−3.66395	+	3.66395i	−0.412227	+	0.412227i	0.470287	+	0.882514i	$0.344150\pi$
$80$	−9.58392	−	10.6110i	−1.07151	−	1.18634i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	0.404023	+	2.98443i	0.0446169	+	0.329575i
$83$	−2.39008	+	12.0157i	−0.262345	+	1.31890i	0.594820	+	0.803859i	$0.297223\pi$
$83$	−2.39008	+	12.0157i	−0.262345	+	1.31890i	−0.857166	+	0.515041i	$0.827777\pi$
$84$	2.42539	−	1.21822i	0.264632	−	0.132918i
$85$	−11.0899	−	7.41006i	−1.20287	−	0.803733i
$86$	−0.490963	+	7.93548i	−0.0529419	+	0.855704i
$87$	−5.88346	−	2.43701i	−0.630773	−	0.261275i
$88$	5.17732	−	7.93562i	0.551904	−	0.845940i
$89$	11.4475	−	4.74172i	1.21343	−	0.502621i	0.318118	−	0.948051i	$-0.396949\pi$
$89$	11.4475	−	4.74172i	1.21343	−	0.502621i	0.895317	+	0.445430i	$0.146949\pi$
$90$	4.78099	−	1.64246i	0.503960	−	0.173131i
$91$	−0.135437	−	0.680889i	−0.0141977	−	0.0713766i
$92$	−7.18866	+	5.60011i	−0.749470	+	0.583852i
$93$	4.98631	+	7.46254i	0.517056	+	0.773829i
$94$	4.02324	−	15.2378i	0.414966	−	1.57166i
$95$		−	13.3583i		−	1.37054i
$96$	0.473187	+	5.63703i	0.0482944	+	0.575327i
$97$			7.84952i			0.796998i	0.917169	+	0.398499i	$0.130469\pi$
$97$			7.84952i			0.796998i	−0.917169	+	0.398499i	$0.869531\pi$
$98$	7.05331	+	1.86229i	0.712492	+	0.188120i
$99$	1.86115	+	2.78540i	0.187052	+	0.279944i
$100$	−1.91748	+	15.4369i	−0.191748	+	1.54369i
$101$	1.78662	+	8.98194i	0.177775	+	0.893737i	0.961956	+	0.273204i	$0.0880835\pi$
$101$	1.78662	+	8.98194i	0.177775	+	0.893737i	−0.784181	+	0.620532i	$0.786917\pi$
$102$	1.71444	+	4.99052i	0.169755	+	0.494135i
$103$	−13.7112	+	5.67939i	−1.35101	+	0.559606i	−0.936573	−	0.350472i	$-0.886021\pi$
$103$	−13.7112	+	5.67939i	−1.35101	+	0.559606i	−0.414436	+	0.910078i	$0.636021\pi$
$104$	1.42213	+	0.266685i	0.139452	+	0.0261506i
$105$	−4.48172	−	1.85639i	−0.437371	−	0.181165i
$106$	−19.8034	−	1.22522i	−1.92347	−	0.119004i
$107$	−1.43350	−	0.957834i	−0.138582	−	0.0925973i	0.484347	−	0.874876i	$-0.339057\pi$
$107$	−1.43350	−	0.957834i	−0.138582	−	0.0925973i	−0.622929	+	0.782279i	$0.714057\pi$
$108$	−1.89851	−	0.629002i	−0.182685	−	0.0605257i
$109$	0.0612531	−	0.307940i	0.00586698	−	0.0294953i	−0.977741	−	0.209816i	$-0.932714\pi$
$109$	0.0612531	−	0.307940i	0.00586698	−	0.0294953i	0.983608	+	0.180321i	$0.0577135\pi$
$110$	−16.7819	+	2.27188i	−1.60009	+	0.216615i
$111$	5.65983	+	5.65983i	0.537207	+	0.537207i
$112$	3.24114	−	4.35445i	0.306259	−	0.411457i
$113$	−12.6145	+	12.6145i	−1.18667	+	1.18667i	−0.208688	+	0.977982i	$0.566919\pi$
$113$	−12.6145	+	12.6145i	−1.18667	+	1.18667i	−0.977982	+	0.208688i	$0.933081\pi$
$114$	−3.20191	+	4.20457i	−0.299886	+	0.393794i
$115$	15.9739	+	3.17740i	1.48957	+	0.296294i
$116$	−12.7027	+	0.925991i	−1.17942	+	0.0859761i
$117$	−0.284210	+	0.425350i	−0.0262752	+	0.0393236i
$118$	−2.88385	−	3.26422i	−0.265480	−	0.300496i
$119$	1.93775	−	4.67814i	0.177633	−	0.428844i
$120$	7.07028	−	7.22725i	0.645426	−	0.659754i
$121$	−0.0850846	−	0.205412i	−0.00773496	−	0.0186739i
$122$	−9.96123	−	4.86710i	−0.901847	−	0.440647i
$123$	−2.08864	+	0.415456i	−0.188326	+	0.0374604i
$124$	15.6106	+	8.86111i	1.40188	+	0.795751i
$125$	8.25595	−	5.51645i	0.738434	−	0.493406i
$126$	0.965669	+	1.65854i	0.0860287	+	0.147755i
$127$	6.40072			0.567972			0.283986	−	0.958828i	$-0.408343\pi$
$127$	6.40072			0.567972			0.283986	+	0.958828i	$0.408343\pi$
$128$	5.90595	+	9.64986i	0.522017	+	0.852935i
$129$	−5.62196			−0.494986
$130$	−1.30123	−	2.23487i	−0.114125	−	0.196011i
$131$	17.9945	−	12.0235i	1.57218	−	1.05050i	0.605064	−	0.796177i	$-0.293147\pi$
$131$	17.9945	−	12.0235i	1.57218	−	1.05050i	0.967119	−	0.254323i	$-0.0818526\pi$
$132$	5.82669	+	3.30742i	0.507148	+	0.287874i
$133$	4.97396	−	0.989381i	0.431297	−	0.0857902i
$134$	−3.33889	−	1.63140i	−0.288436	−	0.140931i
$135$	1.36794	+	3.30250i	0.117733	+	0.284234i
$136$	7.54399	+	7.38015i	0.646892	+	0.632842i
$137$	−5.09074	+	12.2901i	−0.434931	+	1.05002i	0.542745	+	0.839898i	$0.317385\pi$
$137$	−5.09074	+	12.2901i	−0.434931	+	1.05002i	−0.977676	+	0.210119i	$0.932615\pi$
$138$	−4.26621	−	4.82892i	−0.363164	−	0.411065i
$139$	−0.825852	+	1.23597i	−0.0700478	+	0.104834i	−0.864840	−	0.502048i	$-0.832580\pi$
$139$	−0.825852	+	1.23597i	−0.0700478	+	0.104834i	0.794792	+	0.606882i	$0.207580\pi$
$140$	−9.67629	+	0.705374i	−0.817796	+	0.0596149i
$141$	10.9298	+	2.17408i	0.920458	+	0.183091i
$142$	7.32596	−	9.62007i	0.614781	−	0.807298i
$143$	1.21179	−	1.21179i	0.101335	−	0.101335i
$144$	−3.95771	+	0.580094i	−0.329809	+	0.0483412i
$145$	16.0964	+	16.0964i	1.33674	+	1.33674i
$146$	18.1759	−	2.46061i	1.50425	−	0.203641i
$147$	−1.00635	+	5.05924i	−0.0830020	+	0.417279i
$148$	15.1961	+	5.03466i	1.24911	+	0.413846i
$149$	−13.4247	−	8.97011i	−1.09980	−	0.734860i	−0.133181	−	0.991092i	$-0.542519\pi$
$149$	−13.4247	−	8.97011i	−1.09980	−	0.734860i	−0.966615	+	0.256232i	$0.917519\pi$
$150$	−10.9784	−	0.679227i	−0.896383	−	0.0554586i
$151$	9.03007	+	3.74038i	0.734857	+	0.304388i	0.718546	−	0.695479i	$-0.244808\pi$
$151$	9.03007	+	3.74038i	0.734857	+	0.304388i	0.0163107	+	0.999867i	$0.494808\pi$
$152$	−1.94816	+	10.3888i	−0.158016	+	0.842643i
$153$	−3.44723	+	1.42789i	−0.278692	+	0.115438i
$154$	−2.08887	−	6.08043i	−0.168326	−	0.489975i
$155$	−6.25897	−	31.4660i	−0.502733	−	2.52741i
$156$	−0.126118	+	1.01532i	−0.0100975	+	0.0812911i
$157$	1.83057	+	2.73964i	0.146095	+	0.218647i	0.897299	−	0.441424i	$-0.145526\pi$
$157$	1.83057	+	2.73964i	0.146095	+	0.218647i	−0.751204	+	0.660071i	$0.770526\pi$
$158$	−7.08510	−	1.87069i	−0.563660	−	0.148824i
$159$		−	14.0299i		−	1.11264i
$160$	6.14842	−	19.2636i	0.486075	−	1.52292i
$161$			6.18317i			0.487302i
$162$	0.361024	−	1.36736i	0.0283647	−	0.107430i
$163$	−8.78802	−	13.1522i	−0.688331	−	1.03016i	−0.996878	−	0.0789511i	$-0.974843\pi$
$163$	−8.78802	−	13.1522i	−0.688331	−	1.03016i	0.308548	−	0.951209i	$-0.400157\pi$
$164$	−3.35992	+	2.61745i	−0.262366	+	0.204388i
$165$	−2.33617	−	11.7447i	−0.181871	−	0.914325i
$166$	−16.3858	+	5.62917i	−1.27178	+	0.436909i
$167$	−1.26201	+	0.522740i	−0.0976570	+	0.0404509i	−0.430977	−	0.902363i	$-0.641831\pi$
$167$	−1.26201	+	0.522740i	−0.0976570	+	0.0404509i	0.333320	+	0.942814i	$0.391831\pi$
$168$	3.21471	+	2.09732i	0.248020	+	0.161812i
$169$	−11.7687	−	4.87474i	−0.905281	−	0.374980i
$170$	1.16478	−	18.8264i	0.0893344	−	1.44392i
$171$	−3.10722	−	2.07618i	−0.237615	−	0.158769i
$172$	−10.0477	+	5.04673i	−0.766130	+	0.384809i
$173$	−1.55679	+	7.82653i	−0.118361	+	0.595040i	0.875390	+	0.483418i	$0.160605\pi$
$173$	−1.55679	+	7.82653i	−0.118361	+	0.595040i	−0.993751	+	0.111622i	$0.964395\pi$
$174$	−1.20819	−	8.92460i	−0.0915923	−	0.676572i
$175$	7.46348	+	7.46348i	0.564186	+	0.564186i
$176$	13.3826	+	0.680593i	1.00875	+	0.0513016i
$177$	2.17783	−	2.17783i	0.163696	−	0.163696i
$178$	13.9410	+	10.6164i	1.04492	+	0.795736i
$179$	4.84636	+	0.964001i	0.362234	+	0.0720528i	0.372852	−	0.927891i	$-0.378380\pi$
$179$	4.84636	+	0.964001i	0.362234	+	0.0720528i	−0.0106180	+	0.999944i	$0.503380\pi$
$180$	5.40940	+	4.67433i	0.403193	+	0.348404i
$181$	−6.88530	+	10.3046i	−0.511780	+	0.765933i	−0.993913	−	0.110165i	$-0.964862\pi$
$181$	−6.88530	+	10.3046i	−0.511780	+	0.765933i	0.482133	+	0.876098i	$0.339862\pi$
$182$	0.735773	−	0.650034i	0.0545391	−	0.0481837i
$183$	3.00004	−	7.24273i	0.221769	−	0.535398i
$184$	−11.9595	−	4.80067i	−0.881667	−	0.353910i
$185$	−10.9493	−	26.4339i	−0.805007	−	1.94346i
$186$	−5.57216	+	11.4042i	−0.408570	+	0.836199i
$187$	12.2594	−	2.43856i	0.896500	−	0.178325i
$188$	21.4857	−	5.92594i	1.56701	−	0.432194i
$189$	−1.12836	+	0.753948i	−0.0820763	+	0.0548417i
$190$	16.3259	−	9.50558i	1.18440	−	0.689607i
$191$	−3.34679			−0.242165			−0.121082	−	0.992642i	$-0.538637\pi$
$191$	−3.34679			−0.242165			−0.121082	+	0.992642i	$0.538637\pi$
$192$	−6.55258	+	4.58952i	−0.472892	+	0.331220i
$193$	−14.6773			−1.05649			−0.528247	−	0.849091i	$-0.677151\pi$
$193$	−14.6773			−1.05649			−0.528247	+	0.849091i	$0.677151\pi$
$194$	−9.59329	+	5.58559i	−0.688758	+	0.401022i
$195$	1.52045	−	1.01594i	0.108882	−	0.0727526i
$196$	2.74302	+	9.94538i	0.195930	+	0.710384i
$197$	8.99387	−	1.78899i	0.640787	−	0.127460i	0.136006	−	0.990708i	$-0.456573\pi$
$197$	8.99387	−	1.78899i	0.640787	−	0.127460i	0.504781	+	0.863248i	$0.331573\pi$
$198$	−2.07982	+	4.25665i	−0.147806	+	0.302507i
$199$	−0.154916	−	0.374001i	−0.0109817	−	0.0265122i	0.918294	−	0.395900i	$-0.129567\pi$
$199$	−0.154916	−	0.374001i	−0.0109817	−	0.0265122i	−0.929275	+	0.369388i	$0.879567\pi$
$200$	−20.2306	+	8.64118i	−1.43052	+	0.611024i
$201$	1.00558	−	2.42768i	0.0709280	−	0.171235i
$202$	−9.70594	+	8.57492i	−0.682908	+	0.603329i
$203$	−4.80130	+	7.18565i	−0.336985	+	0.504334i
$204$	−4.87919	+	5.64648i	−0.341611	+	0.395332i
$205$	7.46605	+	1.48509i	0.521451	+	0.103723i
$206$	−16.6978	−	12.7158i	−1.16339	−	0.885954i
$207$	3.22176	−	3.22176i	0.223928	−	0.223928i
$208$	0.686038	+	1.92783i	0.0475681	+	0.133671i
$209$	8.85222	+	8.85222i	0.612321	+	0.612321i
$210$	−0.920335	−	6.79831i	−0.0635092	−	0.469128i
$211$	1.34907	−	6.78224i	0.0928739	−	0.466909i	−0.906159	−	0.422937i	$-0.860999\pi$
$211$	1.34907	−	6.78224i	0.0928739	−	0.466909i	0.999033	−	0.0439713i	$-0.0140010\pi$
$212$	−12.5943	−	25.0745i	−0.864983	−	1.72212i
$213$	7.10932	+	4.75029i	0.487122	+	0.325485i
$214$	0.150561	−	2.43353i	0.0102921	−	0.166353i
$215$	18.5665	+	7.69050i	1.26623	+	0.524488i
$216$	−0.582218	−	2.76786i	−0.0396149	−	0.188329i
$217$	11.2527	−	4.66103i	0.763885	−	0.316411i
$218$	0.419935	−	0.144265i	0.0284416	−	0.00977084i
$219$	2.53024	+	12.7204i	0.170978	+	0.859563i
$220$	−14.7183	−	18.8933i	−0.992306	−	1.27379i
$221$	1.06046	+	1.58709i	0.0713342	+	0.106759i
$222$	−2.88971	+	10.9446i	−0.193945	+	0.734553i
$223$			0.254868i			0.0170672i	0.999964	+	0.00853361i	$0.00271636\pi$
$223$			0.254868i			0.0170672i	−0.999964	+	0.00853361i	$0.997284\pi$
$224$	7.62813	+	0.862602i	0.509676	+	0.0576350i
$225$		−	7.77775i		−	0.518517i
$226$	−24.3930	−	6.44052i	−1.62260	−	0.428417i
$227$	−5.08152	−	7.60503i	−0.337272	−	0.504764i	0.623604	−	0.781740i	$-0.285668\pi$
$227$	−5.08152	−	7.60503i	−0.337272	−	0.504764i	−0.960877	+	0.276976i	$0.910668\pi$
$228$	−7.41704	−	0.921301i	−0.491206	−	0.0610147i
$229$	−0.466345	−	2.34448i	−0.0308170	−	0.154927i	0.962313	−	0.271945i	$-0.0876667\pi$
$229$	−0.466345	−	2.34448i	−0.0308170	−	0.154927i	−0.993130	+	0.117017i	$0.962667\pi$
$230$	7.48348	+	21.7834i	0.493446	+	1.43636i
$231$	4.20010	−	1.73974i	0.276346	−	0.114466i
$232$	−10.1707	−	14.8657i	−0.667742	−	0.975980i
$233$	21.0009	+	8.69884i	1.37581	+	0.569880i	0.943358	−	0.331776i	$-0.107648\pi$
$233$	21.0009	+	8.69884i	1.37581	+	0.569880i	0.432454	+	0.901656i	$0.357648\pi$
$234$	−0.722080	−	0.0446746i	−0.0472038	−	0.00292047i
$235$	−33.1218	−	22.1312i	−2.16062	−	1.44368i
$236$	1.93727	−	5.84726i	0.126106	−	0.380624i
$237$	1.01088	−	5.08204i	0.0656638	−	0.330114i
$238$	7.09625	−	0.960670i	0.459982	−	0.0622710i
$239$	1.00431	+	1.00431i	0.0649637	+	0.0649637i	0.738842	−	0.673878i	$-0.235373\pi$
$239$	1.00431	+	1.00431i	0.0649637	+	0.0649637i	−0.673878	+	0.738842i	$0.735373\pi$
$240$	13.8639	+	3.49815i	0.894909	+	0.225805i
$241$	13.1720	−	13.1720i	0.848485	−	0.848485i	−0.141459	−	0.989944i	$-0.545179\pi$
$241$	13.1720	−	13.1720i	0.848485	−	0.848485i	0.989944	+	0.141459i	$0.0451794\pi$
$242$	0.190500	−	0.250154i	0.0122458	−	0.0160805i
$243$	0.980785	+	0.195090i	0.0629174	+	0.0125150i
$244$	−1.13993	−	15.6375i	−0.0729762	−	1.00109i
$245$	10.2442	−	15.3315i	0.654477	−	0.979495i
$246$	−1.99399	−	2.25700i	−0.127132	−	0.143901i
$247$	−0.731585	+	1.76620i	−0.0465497	+	0.112381i
$248$	0.278672	+	25.3839i	0.0176957	+	1.61188i
$249$	−4.68831	−	11.3186i	−0.297110	−	0.717286i
$250$	12.6167	+	6.16458i	0.797951	+	0.389882i
$251$	13.2796	−	2.64147i	0.838198	−	0.166728i	0.242717	−	0.970097i	$-0.421961\pi$
$251$	13.2796	−	2.64147i	0.838198	−	0.166728i	0.595481	+	0.803369i	$0.296961\pi$
$252$	−1.33983	+	2.36038i	−0.0844015	+	0.148690i
$253$	−12.6910	+	8.47987i	−0.797878	+	0.533125i
$254$	4.55465	+	7.82264i	0.285784	+	0.490836i
$255$	13.3377			0.835242
$256$	−7.59099	+	14.0846i	−0.474437	+	0.880289i
$257$	−19.2027			−1.19783			−0.598917	−	0.800811i	$-0.704402\pi$
$257$	−19.2027			−1.19783			−0.598917	+	0.800811i	$0.704402\pi$
$258$	−4.00049	−	6.87087i	−0.249060	−	0.427762i
$259$	9.03165	−	6.03476i	0.561200	−	0.374982i
$260$	1.80541	−	3.18059i	0.111967	−	0.197252i
$261$	6.24585	−	1.24238i	0.386608	−	0.0769011i
$262$	27.4991	+	13.4362i	1.69890	+	0.830090i
$263$	8.85565	+	21.3794i	0.546063	+	1.31831i	0.920385	+	0.391014i	$0.127875\pi$
$263$	8.85565	+	21.3794i	0.546063	+	1.31831i	−0.374322	+	0.927299i	$0.622125\pi$
$264$	0.104015	+	9.47459i	0.00640166	+	0.583121i
$265$	−19.1920	+	46.3336i	−1.17896	+	2.84625i
$266$	4.74856	+	5.37489i	0.291153	+	0.329556i
$267$	−6.88391	+	10.3025i	−0.421288	+	0.630502i
$268$	−0.382090	−	5.24150i	−0.0233399	−	0.320175i
$269$	−1.03618	−	0.206108i	−0.0631768	−	0.0125666i	0.163401	−	0.986560i	$-0.447754\pi$
$269$	−1.03618	−	0.206108i	−0.0631768	−	0.0125666i	−0.226577	+	0.973993i	$0.572754\pi$
$270$	−3.06274	+	4.02183i	−0.186393	+	0.244761i
$271$	1.68669	−	1.68669i	0.102459	−	0.102459i	−0.654019	−	0.756478i	$-0.726918\pi$
$271$	1.68669	−	1.68669i	0.102459	−	0.102459i	0.756478	+	0.654019i	$0.226918\pi$
$272$	−3.65146	+	14.4715i	−0.221402	+	0.877462i
$273$	0.490894	+	0.490894i	0.0297102	+	0.0297102i
$274$	−18.6429	+	2.52381i	−1.12626	+	0.152469i
$275$	−5.08313	+	25.5546i	−0.306524	+	1.54100i
$276$	2.86590	−	8.65013i	0.172507	−	0.520677i
$277$	−17.6283	−	11.7789i	−1.05918	−	0.707725i	−0.101294	−	0.994857i	$-0.532298\pi$
$277$	−17.6283	−	11.7789i	−1.05918	−	0.707725i	−0.957891	+	0.287132i	$0.907298\pi$
$278$	−2.09821	−	0.129815i	−0.125842	−	0.00778577i
$279$	−8.29192	−	3.43463i	−0.496425	−	0.205626i
$280$	−7.74756	−	11.3239i	−0.463005	−	0.676735i
$281$	14.3421	−	5.94069i	0.855578	−	0.354392i	0.0886016	−	0.996067i	$-0.471760\pi$
$281$	14.3421	−	5.94069i	0.855578	−	0.354392i	0.766977	+	0.641675i	$0.221760\pi$
$282$	5.12044	+	14.9049i	0.304918	+	0.887576i
$283$	5.70722	+	28.6922i	0.339259	+	1.70557i	0.654084	+	0.756422i	$0.273054\pi$
$283$	5.70722	+	28.6922i	0.339259	+	1.70557i	−0.314825	+	0.949150i	$0.601946\pi$
$284$	16.9702	+	2.10794i	1.00700	+	0.125083i
$285$	7.42150	+	11.1071i	0.439612	+	0.657925i
$286$	2.34327	+	0.618697i	0.138561	+	0.0365843i
$287$			2.88996i			0.170589i
$288$	−3.52521	−	4.42413i	−0.207725	−	0.260694i
$289$		−	3.07771i		−	0.181042i
$290$	−8.21828	+	31.1262i	−0.482594	+	1.82779i
$291$	−4.36096	−	6.52664i	−0.255644	−	0.382598i
$292$	15.9409	+	20.4628i	0.932873	+	1.19749i
$293$	1.49497	+	7.51572i	0.0873371	+	0.439073i	0.999568	+	0.0293964i	$0.00935852\pi$
$293$	1.49497	+	7.51572i	0.0873371	+	0.439073i	−0.912231	+	0.409677i	$0.865641\pi$
$294$	−6.89925	+	2.37017i	−0.402372	+	0.138231i
$295$	−10.1714	+	4.21313i	−0.592202	+	0.245298i
$296$	4.66020	+	22.1545i	0.270868	+	1.28770i
$297$	−3.09497	−	1.28198i	−0.179589	−	0.0743880i
$298$	1.41000	−	22.7900i	0.0816792	−	1.32019i
$299$	−1.93801	−	1.29493i	−0.112078	−	0.0748880i
$300$	−6.98194	−	13.9006i	−0.403103	−	0.802550i
$301$	−1.48842	+	7.48280i	−0.0857912	+	0.431301i
$302$	1.85435	+	13.6977i	0.106706	+	0.788213i
$303$	−6.47562	−	6.47562i	−0.372015	−	0.372015i
$304$	−14.0829	+	5.01157i	−0.807712	+	0.287433i
$305$	−19.8152	+	19.8152i	−1.13462	+	1.13462i
$306$	−4.19809	−	3.19697i	−0.239989	−	0.182759i
$307$	10.4849	+	2.08558i	0.598405	+	0.119030i	0.484993	−	0.874518i	$-0.338822\pi$
$307$	10.4849	+	2.08558i	0.598405	+	0.119030i	0.113412	+	0.993548i	$0.463822\pi$
$308$	5.94479	−	6.87965i	0.338736	−	0.392004i
$309$	8.24519	−	12.3398i	0.469052	−	0.701987i
$310$	34.0023	−	30.0401i	1.93120	−	1.70616i
$311$	5.94196	−	14.3452i	0.336938	−	0.813440i	−0.661068	−	0.750326i	$-0.729897\pi$
$311$	5.94196	−	14.3452i	0.336938	−	0.813440i	0.998006	−	0.0631143i	$-0.0201033\pi$
$312$	−1.33062	+	0.568354i	−0.0753316	+	0.0321767i
$313$	4.43824	+	10.7149i	0.250864	+	0.605640i	0.998274	−	0.0587229i	$-0.0187029\pi$
$313$	4.43824	+	10.7149i	0.250864	+	0.605640i	−0.747410	+	0.664363i	$0.768703\pi$
$314$	−2.04564	+	4.18671i	−0.115442	+	0.236270i
$315$	4.75777	−	0.946380i	0.268070	−	0.0533225i
$316$	−2.75538	−	9.99020i	−0.155002	−	0.561993i
$317$	−10.1882	+	6.80751i	−0.572224	+	0.382348i	−0.807754	−	0.589519i	$-0.799317\pi$
$317$	−10.1882	+	6.80751i	−0.572224	+	0.382348i	0.235531	+	0.971867i	$0.424317\pi$
$318$	17.1466	−	9.98342i	0.961533	−	0.559842i
$319$	−21.3333			−1.19444
$320$	27.9181	−	6.19336i	1.56067	−	0.346219i
$321$	1.72406			0.0962274
$322$	−7.55676	+	4.39984i	−0.421122	+	0.245194i
$323$	−11.5938	+	7.74675i	−0.645098	+	0.431041i
$324$	1.92801	−	0.531762i	0.107112	−	0.0295424i
$325$	−3.90236	+	0.776229i	−0.216464	+	0.0430574i
$326$	9.82054	−	20.0992i	0.543909	−	1.11319i
$327$	0.120152	+	0.290073i	0.00664444	+	0.0160411i
$328$	−5.58977	−	2.24379i	−0.308644	−	0.123893i
$329$	5.78738	−	13.9720i	0.319068	−	0.770299i
$330$	12.6914	−	11.2125i	0.698640	−	0.617228i
$331$	−3.10773	+	4.65104i	−0.170816	+	0.255644i	−0.906994	−	0.421144i	$-0.861629\pi$
$331$	−3.10773	+	4.65104i	−0.170816	+	0.255644i	0.736178	+	0.676788i	$0.236629\pi$
$332$	−18.5395	−	16.0202i	−1.01749	−	0.879224i
$333$	−7.85041	−	1.56154i	−0.430200	−	0.0855721i
$334$	−1.53689	−	1.17039i	−0.0840949	−	0.0640407i
$335$	−6.64184	+	6.64184i	−0.362882	+	0.362882i
$336$	−0.275707	+	5.42128i	−0.0150411	+	0.295755i
$337$	−5.22899	−	5.22899i	−0.284841	−	0.284841i	0.550195	−	0.835036i	$-0.314553\pi$
$337$	−5.22899	−	5.22899i	−0.284841	−	0.284841i	−0.835036	+	0.550195i	$0.814553\pi$
$338$	−2.41673	−	17.8518i	−0.131453	−	0.971012i
$339$	3.48033	−	17.4968i	0.189025	−	0.950295i
$340$	23.8375	−	11.9730i	1.29277	−	0.649330i
$341$	24.9993	+	16.7040i	1.35379	+	0.904573i
$342$	0.326352	−	5.27486i	0.0176471	−	0.285232i
$343$	15.2438	+	6.31418i	0.823087	+	0.340934i
$344$	−13.3176	−	8.68862i	−0.718038	−	0.468459i
$345$	−15.0470	+	6.23269i	−0.810106	+	0.335557i
$346$	−10.6730	+	3.66660i	−0.573783	+	0.197117i
$347$	−0.394569	−	1.98363i	−0.0211816	−	0.106487i	0.968748	−	0.248046i	$-0.0797885\pi$
$347$	−0.394569	−	1.98363i	−0.0211816	−	0.106487i	−0.989930	+	0.141559i	$0.954788\pi$
$348$	10.0475	−	7.82718i	0.538601	−	0.419581i
$349$	−2.53692	−	3.79677i	−0.135798	−	0.203236i	0.757337	−	0.653024i	$-0.226500\pi$
$349$	−2.53692	−	3.79677i	−0.135798	−	0.203236i	−0.893136	+	0.449787i	$0.851500\pi$
$350$	−3.81060	+	14.4324i	−0.203685	+	0.771443i
$351$		−	0.511564i		−	0.0273053i
$352$	8.69106	+	16.8398i	0.463235	+	0.897567i
$353$		−	24.0810i		−	1.28170i	−0.767665	−	0.640851i	$-0.778581\pi$
$353$		−	24.0810i		−	1.28170i	0.767665	−	0.640851i	$-0.221419\pi$
$354$	4.21134	+	1.11192i	0.223830	+	0.0590981i
$355$	−16.9804	−	25.4130i	−0.901226	−	1.34878i
$356$	−3.05473	+	24.5924i	−0.161900	+	1.30340i
$357$	0.987856	+	4.96629i	0.0522829	+	0.262844i
$358$	2.27044	+	6.60895i	0.119996	+	0.349294i
$359$	−9.78988	+	4.05510i	−0.516690	+	0.214020i	−0.625762	−	0.780014i	$-0.715212\pi$
$359$	−9.78988	+	4.05510i	−0.516690	+	0.214020i	0.109072	+	0.994034i	$0.465212\pi$
$360$	−1.86348	+	9.93727i	−0.0982142	+	0.523740i
$361$	4.65144	+	1.92669i	0.244812	+	0.101405i
$362$	−17.4932	−	1.08229i	−0.919422	−	0.0568840i
$363$	0.184866	+	0.123524i	0.00970296	+	0.00648331i
$364$	1.31800	+	0.436671i	0.0690821	+	0.0228878i
$365$	9.04458	−	45.4702i	0.473415	−	2.38002i
$366$	10.9865	−	1.48732i	0.574272	−	0.0777433i
$367$	14.7649	+	14.7649i	0.770722	+	0.770722i	0.978233	−	0.207511i	$-0.0665361\pi$
$367$	14.7649	+	14.7649i	0.770722	+	0.770722i	−0.207511	+	0.978233i	$0.566536\pi$
$368$	−2.64306	−	18.0324i	−0.137779	−	0.940003i
$369$	1.50583	−	1.50583i	0.0783901	−	0.0783901i
$370$	24.5148	−	32.1916i	1.27446	−	1.67356i
$371$	−18.6737	−	3.71442i	−0.969489	−	0.192843i
$372$	−17.9027	+	1.30506i	−0.928213	+	0.0676641i
$373$	1.20937	−	1.80995i	0.0626187	−	0.0937155i	−0.798839	−	0.601545i	$-0.794552\pi$
$373$	1.20937	−	1.80995i	0.0626187	−	0.0937155i	0.861458	+	0.507830i	$0.169552\pi$
$374$	11.7039	+	13.2476i	0.605194	+	0.685019i
$375$	−3.79979	+	9.17351i	−0.196221	+	0.473718i
$376$	22.5313	+	22.0419i	1.16196	+	1.13673i
$377$	−1.24669	−	3.00976i	−0.0642076	−	0.155011i
$378$	−1.72436	−	0.842531i	−0.0886916	−	0.0433351i
$379$	−23.5132	+	4.67708i	−1.20779	+	0.240245i	−0.757620	−	0.652696i	$-0.773638\pi$
$379$	−23.5132	+	4.67708i	−1.20779	+	0.240245i	−0.450174	+	0.892941i	$0.648638\pi$
$380$	23.2345	+	13.1887i	1.19190	+	0.676564i
$381$	−5.32201	+	3.55605i	−0.272655	+	0.182182i
$382$	−2.38152	−	4.09027i	−0.121849	−	0.209277i
$383$	−22.6499			−1.15736			−0.578678	−	0.815556i	$-0.696431\pi$
$383$	−22.6499			−1.15736			−0.578678	+	0.815556i	$0.696431\pi$
$384$	−10.2718	−	4.74240i	−0.524180	−	0.242010i
$385$	−16.2507			−0.828211
$386$	−10.4441	−	17.9378i	−0.531592	−	0.913012i
$387$	4.67449	−	3.12339i	0.237618	−	0.158771i
$388$	−13.6529	−	7.74981i	−0.693119	−	0.393437i
$389$	21.0516	−	4.18743i	1.06736	−	0.212311i	0.369999	−	0.929032i	$-0.379358\pi$
$389$	21.0516	−	4.18743i	1.06736	−	0.212311i	0.697360	+	0.716721i	$0.254358\pi$
$390$	2.32356	+	1.13530i	0.117658	+	0.0574881i
$391$	−6.50585	−	15.7065i	−0.329015	−	0.794312i
$392$	−10.2028	+	10.4293i	−0.515321	+	0.526762i
$393$	−8.28194	+	19.9944i	−0.417769	+	1.00858i
$394$	8.58631	+	9.71883i	0.432572	+	0.489628i
$395$	−10.2904	+	15.4006i	−0.517764	+	0.774889i
$396$	−6.68222	+	0.487115i	−0.335794	+	0.0244784i
$397$	13.1713	+	2.61993i	0.661047	+	0.131490i	0.514202	−	0.857669i	$-0.328088\pi$
$397$	13.1713	+	2.61993i	0.661047	+	0.131490i	0.146845	+	0.989159i	$0.453088\pi$
$398$	0.346849	−	0.455464i	0.0173860	−	0.0228303i
$399$	−3.58602	+	3.58602i	−0.179526	+	0.179526i
$400$	−24.9566	−	18.5759i	−1.24783	−	0.928794i
$401$	2.83444	+	2.83444i	0.141545	+	0.141545i	0.774329	−	0.632784i	$-0.218088\pi$
$401$	2.83444	+	2.83444i	0.141545	+	0.141545i	−0.632784	+	0.774329i	$0.718088\pi$
$402$	3.68254	−	0.498531i	0.183668	−	0.0248645i
$403$	−0.895727	+	4.50312i	−0.0446193	+	0.224317i
$404$	−17.3864	−	5.76034i	−0.865007	−	0.286588i
$405$	−2.97217	−	1.98594i	−0.147688	−	0.0986822i
$406$	−12.1985	−	0.754711i	−0.605400	−	0.0374557i
$407$	24.7728	+	10.2612i	1.22794	+	0.508631i
$408$	−10.3728	−	1.94515i	−0.513529	−	0.0962994i
$409$	15.1064	−	6.25728i	0.746963	−	0.309402i	0.0234614	−	0.999725i	$-0.492531\pi$
$409$	15.1064	−	6.25728i	0.746963	−	0.309402i	0.723502	+	0.690322i	$0.242531\pi$
$410$	3.49772	+	10.1814i	0.172740	+	0.502823i
$411$	−2.59524	−	13.0471i	−0.128014	−	0.643567i
$412$	3.65879	−	29.4555i	0.180256	−	1.45117i
$413$	−2.32209	−	3.47526i	−0.114263	−	0.171006i
$414$	6.23003	+	1.64492i	0.306189	+	0.0808435i
$415$			43.7929i			2.14971i
$416$	−1.86792	+	2.21025i	−0.0915822	+	0.108366i
$417$		−	1.48649i		−	0.0727939i
$418$	−4.51964	+	17.1178i	−0.221063	+	0.837260i
$419$	4.11537	+	6.15908i	0.201049	+	0.300891i	0.918270	−	0.395955i	$-0.129586\pi$
$419$	4.11537	+	6.15908i	0.201049	+	0.300891i	−0.717221	+	0.696846i	$0.754586\pi$
$420$	7.65365	−	5.96235i	0.373460	−	0.290933i
$421$	−5.64694	−	28.3891i	−0.275215	−	1.38360i	−0.832843	−	0.553509i	$-0.813289\pi$
$421$	−5.64694	−	28.3891i	−0.275215	−	1.38360i	0.557628	−	0.830091i	$-0.311711\pi$
$422$	9.24889	−	3.17737i	0.450229	−	0.154672i
$423$	−10.2957	+	4.26461i	−0.500593	+	0.207352i
$424$	21.6828	−	33.2348i	1.05301	−	1.61402i
$425$	−26.8117	−	11.1058i	−1.30056	−	0.538709i
$426$	−0.746693	+	12.0689i	−0.0361774	+	0.584739i
$427$	−8.84577	−	5.91056i	−0.428077	−	0.286032i
$428$	3.08127	−	1.54765i	0.148939	−	0.0748086i
$429$	−0.334331	+	1.68080i	−0.0161417	+	0.0811497i
$430$	3.81269	+	28.1635i	0.183864	+	1.35816i
$431$	3.01952	+	3.01952i	0.145445	+	0.145445i	0.776080	−	0.630635i	$-0.217205\pi$
$431$	3.01952	+	3.01952i	0.145445	+	0.145445i	−0.630635	+	0.776080i	$0.717205\pi$
$432$	2.96843	−	2.68112i	0.142819	−	0.128995i
$433$	15.4248	−	15.4248i	0.741270	−	0.741270i	−0.231552	−	0.972822i	$-0.574380\pi$
$433$	15.4248	−	15.4248i	0.741270	−	0.741270i	0.972822	+	0.231552i	$0.0743804\pi$
$434$	13.7037	+	10.4358i	0.657800	+	0.500934i
$435$	−22.3264	−	4.44099i	−1.07047	−	0.212929i
$436$	0.475132	+	0.410567i	0.0227547	+	0.0196626i
$437$	9.45961	−	14.1573i	0.452515	−	0.677236i
$438$	−13.7457	+	12.1439i	−0.656795	+	0.580260i
$439$	−4.49415	+	10.8498i	−0.214494	+	0.517835i	−0.994104	−	0.108431i	$-0.965417\pi$
$439$	−4.49415	+	10.8498i	−0.214494	+	0.517835i	0.779610	+	0.626266i	$0.215417\pi$
$440$	12.6172	−	31.4321i	0.601499	−	1.49847i
$441$	−1.97402	−	4.76570i	−0.0940009	−	0.226938i
$442$	−1.18506	+	2.42539i	−0.0563673	+	0.115364i
$443$	16.7968	−	3.34109i	0.798039	−	0.158740i	0.220804	−	0.975318i	$-0.429132\pi$
$443$	16.7968	−	3.34109i	0.798039	−	0.158740i	0.577235	+	0.816578i	$0.304132\pi$
$444$	−15.4322	+	4.25634i	−0.732380	+	0.201997i
$445$	36.8273	−	24.6072i	1.74578	−	1.16649i
$446$	−0.311487	+	0.181360i	−0.0147493	+	0.00858764i
$447$	16.1458			0.763669
$448$	4.37383	+	9.93653i	0.206644	+	0.469457i
$449$	−10.4595			−0.493614			−0.246807	−	0.969065i	$-0.579381\pi$
$449$	−10.4595			−0.493614			−0.246807	+	0.969065i	$0.579381\pi$
$450$	9.50557	−	5.53452i	0.448097	−	0.260900i
$451$	−5.93168	+	3.96342i	−0.279312	+	0.186630i
$452$	−9.48641	−	34.3949i	−0.446203	−	1.61780i
$453$	−9.58627	+	1.90683i	−0.450402	+	0.0895906i
$454$	5.67856	−	11.6220i	0.266508	−	0.545447i
$455$	−0.949662	−	2.29269i	−0.0445209	−	0.107483i
$456$	−4.15188	−	9.72031i	−0.194430	−	0.455195i
$457$	4.50892	−	10.8855i	0.210918	−	0.509202i	−0.782646	−	0.622467i	$-0.786131\pi$
$457$	4.50892	−	10.8855i	0.210918	−	0.509202i	0.993565	+	0.113264i	$0.0361307\pi$
$458$	2.53346	−	2.23824i	0.118381	−	0.104586i
$459$	2.07298	−	3.10243i	0.0967582	−	0.144809i
$460$	−21.2975	+	24.6467i	−0.993000	+	1.14916i
$461$	−22.8720	−	4.54952i	−1.06525	−	0.211892i	−0.368811	−	0.929504i	$-0.620235\pi$
$461$	−22.8720	−	4.54952i	−1.06525	−	0.211892i	−0.696443	+	0.717612i	$0.745235\pi$
$462$	5.11494	+	3.89518i	0.237969	+	0.181220i
$463$	−7.60277	+	7.60277i	−0.353331	+	0.353331i	−0.861347	−	0.508017i	$-0.830379\pi$
$463$	−7.60277	+	7.60277i	−0.353331	+	0.353331i	0.508017	+	0.861347i	$0.330379\pi$
$464$	10.9308	−	23.0083i	0.507448	−	1.06814i
$465$	22.6857	+	22.6857i	1.05202	+	1.05202i
$466$	4.31259	+	31.8561i	0.199777	+	1.47571i
$467$	−1.51066	+	7.59459i	−0.0699049	+	0.351436i	−0.999869	−	0.0162159i	$-0.994838\pi$
$467$	−1.51066	+	7.59459i	−0.0699049	+	0.351436i	0.929964	+	0.367652i	$0.119838\pi$
$468$	−0.459221	−	0.914279i	−0.0212275	−	0.0422626i
$469$	−2.96500	−	1.98115i	−0.136911	−	0.0914810i
$470$	3.47879	−	56.2280i	0.160464	−	2.59360i
$471$	−3.04412	−	1.26092i	−0.140266	−	0.0581000i
$472$	8.52475	−	1.79318i	0.392384	−	0.0825379i
$473$	−17.3998	+	7.20724i	−0.800044	+	0.331389i
$474$	6.93034	−	2.38085i	0.318321	−	0.109356i
$475$	−5.67042	−	28.5071i	−0.260177	−	1.30800i
$476$	6.22366	+	7.98908i	0.285261	+	0.366179i
$477$	7.79457	+	11.6654i	0.356889	+	0.534122i
$478$	−0.512768	+	1.94208i	−0.0234535	+	0.0888285i
$479$		−	14.6313i		−	0.668520i	−0.942481	−	0.334260i	$-0.891514\pi$
$479$		−	14.6313i		−	0.668520i	0.942481	−	0.334260i	$-0.108486\pi$
$480$	5.59004	+	19.4329i	0.255149	+	0.886989i
$481$			4.09466i			0.186701i
$482$	25.4712	+	6.72518i	1.16018	+	0.306324i
$483$	−3.43519	−	5.14112i	−0.156306	−	0.233929i
$484$	0.441282	+	0.0548135i	0.0200583	+	0.00249152i
$485$	5.47402	+	27.5197i	0.248562	+	1.24961i
$486$	0.459481	+	1.33749i	0.0208425	+	0.0606697i
$487$	1.56212	−	0.647049i	0.0707862	−	0.0293206i	−0.347009	−	0.937862i	$-0.612803\pi$
$487$	1.56212	−	0.647049i	0.0707862	−	0.0293206i	0.417796	+	0.908541i	$0.362803\pi$
$488$	18.3002	−	12.5205i	0.828409	−	0.566777i
$489$	14.6139	+	6.05329i	0.660865	+	0.273739i
$490$	26.0270	+	1.61027i	1.17578	+	0.0727447i
$491$	2.74418	+	1.83360i	0.123843	+	0.0827492i	0.615949	−	0.787786i	$-0.288773\pi$
$491$	2.74418	+	1.83360i	0.123843	+	0.0827492i	−0.492106	+	0.870535i	$0.663773\pi$
$492$	1.33950	−	4.04300i	0.0603891	−	0.182272i
$493$	4.63563	−	23.3049i	0.208778	−	1.04960i
$494$	−2.67915	+	0.362695i	−0.120541	+	0.0163184i
$495$	8.46747	+	8.46747i	0.380585	+	0.380585i
$496$	−30.8246	+	18.4034i	−1.38407	+	0.826336i
$497$	8.20482	−	8.20482i	0.368036	−	0.368036i
$498$	10.4969	−	13.7839i	0.470376	−	0.617673i
$499$	36.7613	+	7.31227i	1.64566	+	0.327342i	0.929000	−	0.370080i	$-0.120670\pi$
$499$	36.7613	+	7.31227i	1.64566	+	0.327342i	0.716660	+	0.697422i	$0.245670\pi$
$500$	1.44381	+	19.8061i	0.0645691	+	0.885757i
$501$	0.758902	−	1.13578i	0.0339052	−	0.0507427i
$502$	12.6778	+	14.3500i	0.565837	+	0.640470i
$503$	−4.40508	+	10.6348i	−0.196413	+	0.474183i	−0.991146	−	0.132776i	$-0.957611\pi$
$503$	−4.40508	+	10.6348i	−0.196413	+	0.474183i	0.794733	+	0.606959i	$0.207611\pi$
$504$	−3.83814	+	0.0421362i	−0.170965	+	0.00187690i
$505$	12.5275	+	30.2440i	0.557465	+	1.34584i
$506$	−19.3944	−	9.47619i	−0.862186	−	0.421268i
$507$	12.4935	−	2.48512i	0.554858	−	0.110368i
$508$	−6.31942	+	11.1329i	−0.280379	+	0.493944i
$509$	8.15940	−	5.45194i	0.361659	−	0.241653i	−0.361443	−	0.932394i	$-0.617716\pi$
$509$	8.15940	−	5.45194i	0.361659	−	0.241653i	0.723102	+	0.690741i	$0.242716\pi$
$510$	9.49092	+	16.3007i	0.420265	+	0.721808i
$511$	17.6006			0.778606
$512$	−22.6151	+	0.745066i	−0.999458	+	0.0329276i
$513$	3.73702			0.164993
$514$	−13.6644	−	23.4686i	−0.602709	−	1.03516i
$515$	−44.1098	+	29.4732i	−1.94371	+	1.29875i
$516$	5.55054	−	9.77840i	0.244349	−	0.430470i
$517$	36.6147	−	7.28311i	1.61031	−	0.320311i
$518$	13.8022	+	6.74379i	0.606432	+	0.296305i
$519$	−3.05376	−	7.37243i	−0.134045	−	0.323614i
$520$	5.17185	−	0.0567780i	0.226801	−	0.00248988i
$521$	−1.10991	+	2.67956i	−0.0486261	+	0.117394i	−0.946326	−	0.323213i	$-0.895237\pi$
$521$	−1.10991	+	2.67956i	−0.0486261	+	0.117394i	0.897700	+	0.440607i	$0.145237\pi$
$522$	5.96281	+	6.74930i	0.260985	+	0.295409i
$523$	18.7026	−	27.9905i	0.817809	−	1.22394i	−0.153977	−	0.988074i	$-0.549208\pi$
$523$	18.7026	−	27.9905i	0.817809	−	1.22394i	0.971786	−	0.235863i	$-0.0757918\pi$
$524$	3.14689	+	43.1690i	0.137473	+	1.88585i
$525$	−10.3521	−	2.05917i	−0.451805	−	0.0898695i
$526$	−19.8273	+	26.0362i	−0.864512	+	1.13523i
$527$	−23.6799	+	23.6799i	−1.03151	+	1.03151i
$528$	−11.5053	+	6.86909i	−0.500706	+	0.298939i
$529$	−1.58425	−	1.58425i	−0.0688805	−	0.0688805i
$530$	−70.2833	+	9.51474i	−3.05291	+	0.413294i
$531$	−0.600861	+	3.02073i	−0.0260752	+	0.131089i
$532$	−3.18992	+	9.62813i	−0.138301	+	0.417432i
$533$	−0.905807	−	0.605241i	−0.0392349	−	0.0262159i
$534$	−17.4897	−	1.08207i	−0.756852	−	0.0468259i
$535$	−5.69369	−	2.35840i	−0.246160	−	0.101963i
$536$	6.13400	−	4.19673i	0.264948	−	0.181271i
$537$	−4.56517	+	1.89096i	−0.197002	+	0.0816008i
$538$	−0.485431	−	1.41302i	−0.0209284	−	0.0609198i
$539$	3.37123	+	16.9483i	0.145209	+	0.730017i
$540$	−7.09467	−	0.881259i	−0.305306	−	0.0379233i
$541$	3.34490	+	5.00600i	0.143809	+	0.215225i	0.896381	−	0.443285i	$-0.146187\pi$
$541$	3.34490	+	5.00600i	0.143809	+	0.215225i	−0.752572	+	0.658510i	$0.771187\pi$
$542$	3.26162	+	0.861168i	0.140098	+	0.0369903i
$543$		−	12.3932i		−	0.531843i
$544$	−20.2846	+	5.83503i	−0.869696	+	0.250175i
$545$		−	1.12233i		−	0.0480752i
$546$	−0.250633	+	0.949257i	−0.0107261	+	0.0406245i
$547$	1.77372	+	2.65456i	0.0758389	+	0.113501i	0.867450	−	0.497524i	$-0.165757\pi$
$547$	1.77372	+	2.65456i	0.0758389	+	0.113501i	−0.791611	+	0.611025i	$0.790757\pi$
$548$	−16.3504	−	20.9884i	−0.698456	−	0.896582i
$549$	1.52941	+	7.68884i	0.0652734	+	0.328152i
$550$	−34.8486	+	11.9719i	−1.48595	+	0.510484i
$551$	21.9866	−	9.10715i	0.936661	−	0.387978i
$552$	12.6111	−	2.65274i	0.536763	−	0.112908i
$553$	−6.49654	−	2.69096i	−0.276261	−	0.114431i
$554$	1.85151	−	29.9261i	0.0786631	−	1.27144i
$555$	23.7899	+	15.8959i	1.00982	+	0.674743i
$556$	−1.33440	−	2.65670i	−0.0565910	−	0.112669i
$557$	6.63260	−	33.3443i	0.281032	−	1.41284i	−0.539857	−	0.841757i	$-0.681522\pi$
$557$	6.63260	−	33.3443i	0.281032	−	1.41284i	0.820889	−	0.571087i	$-0.193478\pi$
$558$	−1.70277	−	12.5780i	−0.0720841	−	0.532469i
$559$	−2.03363	−	2.03363i	−0.0860135	−	0.0860135i
$560$	8.32650	−	17.5266i	0.351859	−	0.740634i
$561$	−8.83857	+	8.83857i	−0.373165	+	0.373165i
$562$	17.4660	+	13.3009i	0.736760	+	0.561064i
$563$	1.89575	+	0.377088i	0.0798964	+	0.0158924i	0.234877	−	0.972025i	$-0.424531\pi$
$563$	1.89575	+	0.377088i	0.0798964	+	0.0158924i	−0.154980	+	0.987918i	$0.549531\pi$
$564$	−14.5724	+	16.8641i	−0.613610	+	0.710105i
$565$	−35.4283	+	53.0222i	−1.49048	+	2.23066i
$566$	−31.0049	+	27.3919i	−1.30323	+	1.15137i
$567$	0.519328	−	1.25377i	0.0218097	−	0.0526534i
$568$	9.49950	+	22.2401i	0.398590	+	0.933173i
$569$	−3.70688	−	8.94920i	−0.155400	−	0.375170i	0.826935	−	0.562297i	$-0.190082\pi$
$569$	−3.70688	−	8.94920i	−0.155400	−	0.375170i	−0.982336	+	0.187127i	$0.940082\pi$
$570$	−8.29346	+	16.9738i	−0.347375	+	0.710953i
$571$	31.2068	−	6.20743i	1.30597	−	0.259773i	0.507416	−	0.861701i	$-0.330601\pi$
$571$	31.2068	−	6.20743i	1.30597	−	0.259773i	0.798550	+	0.601928i	$0.205601\pi$
$572$	0.911295	+	3.30408i	0.0381032	+	0.138151i
$573$	2.78275	−	1.85938i	0.116251	−	0.0776765i
$574$	−3.53196	+	2.05645i	−0.147421	+	0.0858345i
$575$	35.4375			1.47784
$576$	2.89847	−	7.45647i	0.120769	−	0.310686i
$577$	31.2986			1.30298			0.651489	−	0.758658i	$-0.274144\pi$
$577$	31.2986			1.30298			0.651489	+	0.758658i	$0.274144\pi$
$578$	3.76142	−	2.19005i	0.156455	−	0.0910940i
$579$	12.2037	−	8.15427i	0.507169	−	0.338880i
$580$	−43.8888	+	12.1049i	−1.82239	+	0.502630i
$581$	−16.3062	+	3.24351i	−0.676496	+	0.134563i
$582$	4.87334	−	9.97400i	0.202006	−	0.413435i
$583$	−17.9860	−	43.4220i	−0.744904	−	1.79836i
$584$	−13.6653	+	34.0432i	−0.565473	+	1.40872i
$585$	−0.699788	+	1.68944i	−0.0289327	+	0.0698497i
$586$	−8.12154	+	7.17514i	−0.335498	+	0.296402i
$587$	19.8531	−	29.7122i	0.819424	−	1.22636i	−0.151853	−	0.988403i	$-0.548524\pi$
$587$	19.8531	−	29.7122i	0.819424	−	1.22636i	0.971277	−	0.237952i	$-0.0764761\pi$
$588$	−7.80609	−	6.74534i	−0.321918	−	0.278173i
$589$	−32.8957	−	6.54337i	−1.35544	−	0.269615i
$590$	−12.3869	−	9.43298i	−0.509960	−	0.388350i
$591$	−6.48422	+	6.48422i	−0.266725	+	0.266725i
$592$	−23.7600	+	21.4602i	−0.976529	+	0.882010i
$593$	−6.42998	−	6.42998i	−0.264048	−	0.264048i	0.562649	−	0.826696i	$-0.309782\pi$
$593$	−6.42998	−	6.42998i	−0.264048	−	0.264048i	−0.826696	+	0.562649i	$0.809782\pi$
$594$	−0.635562	−	4.69476i	−0.0260774	−	0.192628i
$595$	3.53119	−	17.7525i	0.144765	−	0.727781i
$596$	28.8561	−	14.4938i	1.18199	−	0.593688i
$597$	0.336592	+	0.224904i	0.0137758	+	0.00920469i
$598$	0.203549	−	3.28999i	0.00832375	−	0.134538i
$599$	−24.7715	−	10.2607i	−1.01214	−	0.419241i	−0.185903	−	0.982568i	$-0.559521\pi$
$599$	−24.7715	−	10.2607i	−1.01214	−	0.419241i	−0.826234	+	0.563328i	$0.809521\pi$
$600$	12.0203	−	18.4244i	0.490729	−	0.752173i
$601$	−37.1935	+	15.4060i	−1.51715	+	0.628426i	−0.977019	−	0.213152i	$-0.931627\pi$
$601$	−37.1935	+	15.4060i	−1.51715	+	0.628426i	−0.540135	+	0.841578i	$0.681627\pi$
$602$	−10.2042	+	3.50556i	−0.415893	+	0.142876i
$603$	0.512639	+	2.57721i	0.0208763	+	0.104952i
$604$	−15.4211	+	12.0133i	−0.627475	+	0.488816i
$605$	−0.441547	−	0.660822i	−0.0179515	−	0.0268663i
$606$	3.30623	−	12.5221i	0.134306	−	0.508676i
$607$		−	25.5319i		−	1.03631i	−0.855287	−	0.518155i	$-0.826619\pi$
$607$		−	25.5319i		−	1.03631i	0.855287	−	0.518155i	$-0.173381\pi$
$608$	−16.1461	−	13.6453i	−0.654810	−	0.553390i
$609$		−	8.64211i		−	0.350196i
$610$	−38.3174	−	10.1170i	−1.55142	−	0.409624i
$611$	3.16722	+	4.74008i	0.128132	+	0.191763i
$612$	0.919881	−	7.40560i	0.0371840	−	0.299354i
$613$	8.10097	+	40.7263i	0.327195	+	1.64492i	0.697918	+	0.716177i	$0.254110\pi$
$613$	8.10097	+	40.7263i	0.327195	+	1.64492i	−0.370723	+	0.928743i	$0.620890\pi$
$614$	4.91200	+	14.2982i	0.198232	+	0.577028i
$615$	−7.03286	+	2.91311i	−0.283592	+	0.117468i
$616$	12.6382	+	2.36997i	0.509206	+	0.0954887i
$617$	8.74584	+	3.62265i	0.352094	+	0.145842i	0.551719	−	0.834030i	$-0.313972\pi$
$617$	8.74584	+	3.62265i	0.352094	+	0.145842i	−0.199624	+	0.979872i	$0.563972\pi$
$618$	20.9482	+	1.29605i	0.842661	+	0.0521349i
$619$	32.9605	+	22.0235i	1.32480	+	0.885200i	0.998201	−	0.0599641i	$-0.0190986\pi$
$619$	32.9605	+	22.0235i	1.32480	+	0.885200i	0.326595	+	0.945164i	$0.394099\pi$
$620$	60.9089	+	20.1799i	2.44616	+	0.810444i
$621$	−0.888883	+	4.46872i	−0.0356696	+	0.179323i
$622$	21.7601	−	2.94582i	0.872502	−	0.118117i
$623$	11.8900	+	11.8900i	0.476365	+	0.476365i
$624$	−1.64146	−	1.22179i	−0.0657111	−	0.0489106i
$625$	−2.40088	+	2.40088i	−0.0960350	+	0.0960350i
$626$	−9.93699	+	13.0487i	−0.397162	+	0.521532i
$627$	−12.2784	−	2.44232i	−0.490351	−	0.0975369i
$628$	−6.57243	+	0.479111i	−0.262269	+	0.0191186i
$629$	−16.5925	+	24.8325i	−0.661588	+	0.990136i
$630$	4.54217	+	5.14128i	0.180964	+	0.204833i
$631$	9.26560	−	22.3691i	0.368858	−	0.890502i	−0.625080	−	0.780560i	$-0.714934\pi$
$631$	9.26560	−	22.3691i	0.368858	−	0.890502i	0.993938	−	0.109941i	$-0.0350662\pi$
$632$	10.2488	−	10.4764i	0.407676	−	0.416727i
$633$	2.64630	+	6.38873i	0.105181	+	0.253929i
$634$	−15.5695	−	7.60733i	−0.618344	−	0.302126i
$635$	22.4404	−	4.46367i	0.890519	−	0.177135i
$636$	24.4025	+	13.8516i	0.967620	+	0.549253i
$637$	−2.19411	+	1.46606i	−0.0869337	+	0.0580872i
$638$	−15.1805	−	26.0725i	−0.601000	−	1.03222i
$639$	−8.55030			−0.338245
$640$	27.4352	+	29.7129i	1.08447	+	1.17451i
$641$	21.8499			0.863020			0.431510	−	0.902108i	$-0.357981\pi$
$641$	21.8499			0.863020			0.431510	+	0.902108i	$0.357981\pi$
$642$	1.22681	+	2.10705i	0.0484183	+	0.0831588i
$643$	−31.4102	+	20.9876i	−1.23870	+	0.827671i	−0.990022	−	0.140916i	$-0.954995\pi$
$643$	−31.4102	+	20.9876i	−1.23870	+	0.827671i	−0.248676	+	0.968587i	$0.579995\pi$
$644$	−10.7545	−	6.10463i	−0.423788	−	0.240556i
$645$	−19.7101	+	3.92058i	−0.776084	+	0.154373i
$646$	−17.7177	−	8.65693i	−0.697093	−	0.340603i
$647$	−2.71530	−	6.55532i	−0.106749	−	0.257716i	0.861474	−	0.507801i	$-0.169541\pi$
$647$	−2.71530	−	6.55532i	−0.106749	−	0.257716i	−0.968224	+	0.250085i	$0.919541\pi$
$648$	2.02183	+	1.97792i	0.0794252	+	0.0777002i
$649$	3.94839	−	9.53225i	0.154988	−	0.374174i
$650$	−3.72553	−	4.21692i	−0.146127	−	0.165401i
$651$	−6.76677	+	10.1272i	−0.265211	+	0.396916i
$652$	31.5523	−	2.30007i	1.23568	−	0.0900778i
$653$	−6.37150	−	1.26737i	−0.249336	−	0.0495960i	0.0688399	−	0.997628i	$-0.478070\pi$
$653$	−6.37150	−	1.26737i	−0.249336	−	0.0495960i	−0.318176	+	0.948032i	$0.603070\pi$
$654$	−0.269014	+	0.353255i	−0.0105193	+	0.0138134i
$655$	54.7022	−	54.7022i	2.13739	−	2.13739i
$656$	−1.23534	−	8.42818i	−0.0482321	−	0.329065i
$657$	−9.17087	−	9.17087i	−0.357790	−	0.357790i
$658$	21.1940	−	2.86918i	0.826229	−	0.111852i
$659$	0.256785	−	1.29094i	0.0100029	−	0.0502880i	−0.975461	−	0.220170i	$-0.929339\pi$
$659$	0.256785	−	1.29094i	0.0100029	−	0.0502880i	0.985464	+	0.169882i	$0.0543387\pi$
$660$	22.7344	+	7.53218i	0.884934	+	0.293190i
$661$	−11.2985	−	7.54941i	−0.439460	−	0.293638i	0.316089	−	0.948729i	$-0.397630\pi$
$661$	−11.2985	−	7.54941i	−0.439460	−	0.293638i	−0.755550	+	0.655091i	$0.772630\pi$
$662$	−7.89568	−	0.488500i	−0.306874	−	0.0189861i
$663$	−1.76348	−	0.730457i	−0.0684879	−	0.0283686i
$664$	6.38668	−	34.0578i	0.247851	−	1.32170i
$665$	16.7483	−	6.93737i	0.649471	−	0.269020i
$666$	−3.67778	−	10.7055i	−0.142511	−	0.414831i
$667$	5.66059	+	28.4577i	0.219179	+	1.10189i
$668$	0.336762	−	2.71114i	0.0130297	−	0.104897i
$669$	−0.141597	−	0.211915i	−0.00547446	−	0.00819310i
$670$	−12.8435	−	3.39109i	−0.496189	−	0.131009i
$671$		−	26.2620i		−	1.01384i
$672$	−6.82180	+	3.52074i	−0.263157	+	0.135815i
$673$		−	14.2660i		−	0.549913i	−0.961457	−	0.274956i	$-0.911337\pi$
$673$		−	14.2660i		−	0.549913i	0.961457	−	0.274956i	$-0.0886634\pi$
$674$	2.66974	−	10.1115i	0.102835	−	0.389479i
$675$	4.32109	+	6.46696i	0.166319	+	0.248914i
$676$	20.0979	−	15.6567i	0.772996	−	0.602180i
$677$	−4.64782	−	23.3662i	−0.178630	−	0.898036i	−0.961280	−	0.275573i	$-0.911132\pi$
$677$	−4.64782	−	23.3662i	−0.178630	−	0.898036i	0.782650	−	0.622462i	$-0.213868\pi$
$678$	23.8602	−	8.19695i	0.916346	−	0.314802i
$679$	−9.84149	+	4.07648i	−0.377682	+	0.156441i
$680$	31.5953	+	20.6132i	1.21162	+	0.790480i
$681$	8.45026	+	3.50021i	0.323815	+	0.134128i
$682$	−2.62568	+	42.4392i	−0.100543	+	1.62508i
$683$	1.15577	+	0.772259i	0.0442242	+	0.0295497i	0.577486	−	0.816401i	$-0.304034\pi$
$683$	1.15577	+	0.772259i	0.0442242	+	0.0295497i	−0.533262	+	0.845950i	$0.679034\pi$
$684$	6.67889	−	3.35465i	0.255374	−	0.128268i
$685$	−9.27692	+	46.6382i	−0.354453	+	1.78196i
$686$	3.13036	+	23.1232i	0.119518	+	0.882850i
$687$	1.69027	+	1.69027i	0.0644880	+	0.0644880i
$688$	1.14218	−	22.4588i	0.0435451	−	0.856234i
$689$	5.07503	−	5.07503i	0.193343	−	0.193343i
$690$	−18.3245	−	13.9547i	−0.697602	−	0.531245i
$691$	−24.0289	−	4.77964i	−0.914102	−	0.181826i	−0.284439	−	0.958694i	$-0.591807\pi$
$691$	−24.0289	−	4.77964i	−0.914102	−	0.181826i	−0.629664	+	0.776868i	$0.716807\pi$
$692$	−12.0758	−	10.4349i	−0.459055	−	0.396674i
$693$	−2.52571	+	3.77999i	−0.0959437	+	0.143590i
$694$	2.14353	−	1.89374i	0.0813671	−	0.0718855i
$695$	−2.03343	+	4.90914i	−0.0771325	+	0.186214i
$696$	16.7156	+	6.70981i	0.633603	+	0.254335i
$697$	−3.04078	−	7.34109i	−0.115178	−	0.278063i
$698$	2.83499	−	5.80221i	0.107306	−	0.219617i
$699$	−22.2944	+	4.43463i	−0.843252	+	0.167733i
$700$	−20.3501	+	5.61273i	−0.769161	+	0.212141i
$701$	−31.2358	+	20.8711i	−1.17976	+	0.788291i	−0.981426	−	0.191844i	$-0.938553\pi$
$701$	−31.2358	+	20.8711i	−1.17976	+	0.788291i	−0.198335	+	0.980134i	$0.563553\pi$
$702$	0.625207	−	0.364021i	0.0235969	−	0.0137391i
$703$	−29.9119			−1.12815
$704$	−14.3964	+	22.6047i	−0.542584	+	0.851948i
$705$	39.8352			1.50028
$706$	29.4306	−	17.1357i	1.10763	−	0.644909i
$707$	−10.3334	+	6.90459i	−0.388629	+	0.259674i
$708$	1.63778	+	5.93811i	0.0615516	+	0.223168i
$709$	11.1298	−	2.21385i	0.417988	−	0.0831429i	0.0183841	−	0.999831i	$-0.494148\pi$
$709$	11.1298	−	2.21385i	0.417988	−	0.0831429i	0.399603	+	0.916688i	$0.369148\pi$
$710$	18.9755	−	38.8360i	0.712136	−	1.45749i
$711$	1.98292	+	4.78718i	0.0743651	+	0.179533i
$712$	−32.2293	+	13.7662i	−1.20784	+	0.515911i
$713$	15.6491	−	37.7802i	0.586062	−	1.41488i
$714$	−5.36660	+	4.74124i	−0.200840	+	0.177436i
$715$	3.40336	−	5.09349i	0.127278	−	0.190486i
$716$	−6.46151	+	7.47763i	−0.241478	+	0.279452i
$717$	−1.39302	−	0.277090i	−0.0520234	−	0.0103481i
$718$	−11.9223	−	9.07915i	−0.444935	−	0.338831i
$719$	−31.5753	+	31.5753i	−1.17756	+	1.17756i	−0.197197	+	0.980364i	$0.563184\pi$
$719$	−31.5753	+	31.5753i	−1.17756	+	1.17756i	−0.980364	+	0.197197i	$0.936816\pi$
$720$	−13.4709	+	4.79375i	−0.502029	+	0.178652i
$721$	−14.2413	−	14.2413i	−0.530373	−	0.530373i
$722$	0.955186	+	7.05575i	0.0355483	+	0.262588i
$723$	−3.63415	+	18.2701i	−0.135156	+	0.679473i
$724$	−11.1251	−	22.1494i	−0.413463	−	0.823177i
$725$	41.1830	+	27.5176i	1.52950	+	1.02198i
$726$	−0.0194165	+	0.313832i	−0.000720616	+	0.0116474i
$727$	34.4626	+	14.2749i	1.27815	+	0.529426i	0.915431	−	0.402474i	$-0.131850\pi$
$727$	34.4626	+	14.2749i	1.27815	+	0.529426i	0.362716	+	0.931900i	$0.381850\pi$
$728$	0.404192	+	1.92152i	0.0149804	+	0.0712164i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	62.0073	−	21.3020i	2.29499	−	0.788423i
$731$	−4.09241	−	20.5739i	−0.151363	−	0.760954i
$732$	9.63552	+	12.3688i	0.356139	+	0.457163i
$733$	−0.973371	−	1.45675i	−0.0359523	−	0.0538064i	0.813058	−	0.582183i	$-0.197801\pi$
$733$	−0.973371	−	1.45675i	−0.0359523	−	0.0538064i	−0.849010	+	0.528376i	$0.822801\pi$
$734$	−7.53846	+	28.5514i	−0.278249	+	1.05385i
$735$			18.4391i			0.680135i
$736$	20.1575	−	16.0618i	0.743015	−	0.592044i
$737$		−	8.80274i		−	0.324253i
$738$	2.91186	+	0.768822i	0.107187	+	0.0283007i
$739$	−4.20428	−	6.29215i	−0.154657	−	0.231460i	0.746048	−	0.665893i	$-0.231949\pi$
$739$	−4.20428	−	6.29215i	−0.154657	−	0.231460i	−0.900705	+	0.434432i	$0.856949\pi$
$740$	56.7872	+	7.05378i	2.08754	+	0.259302i
$741$	−0.372959	−	1.87499i	−0.0137010	−	0.0688795i
$742$	−8.74830	−	25.4651i	−0.321160	−	0.934855i
$743$	10.9003	−	4.51504i	0.399892	−	0.165641i	−0.173668	−	0.984804i	$-0.555562\pi$
$743$	10.9003	−	4.51504i	0.399892	−	0.165641i	0.573560	+	0.819164i	$0.305562\pi$
$744$	−14.3343	−	20.9511i	−0.525520	−	0.768106i
$745$	−53.3214	−	22.0864i	−1.95354	−	0.809185i
$746$	3.07259	+	0.190099i	0.112496	+	0.00696003i
$747$	10.1865	+	6.80637i	0.372703	+	0.249032i
$748$	−7.86228	+	23.7307i	−0.287474	+	0.867681i
$749$	0.456446	−	2.29471i	0.0166782	−	0.0838469i
$750$	−13.9153	+	1.88381i	−0.508114	+	0.0687870i
$751$	−19.7638	−	19.7638i	−0.721192	−	0.721192i	0.247656	−	0.968848i	$-0.420340\pi$
$751$	−19.7638	−	19.7638i	−0.721192	−	0.721192i	−0.968848	+	0.247656i	$0.920340\pi$
$752$	−10.9056	+	43.2212i	−0.397688	+	1.57612i
$753$	−9.57402	+	9.57402i	−0.348897	+	0.348897i
$754$	2.79126	−	3.66534i	0.101652	−	0.133484i
$755$	34.2671	+	6.81614i	1.24711	+	0.248065i
$756$	−0.197329	−	2.70696i	−0.00717680	−	0.0984511i
$757$	17.5761	−	26.3045i	0.638815	−	0.956055i	−0.360910	−	0.932601i	$-0.617534\pi$
$757$	17.5761	−	26.3045i	0.638815	−	0.956055i	0.999725	−	0.0234539i	$-0.00746629\pi$
$758$	−22.4477	−	25.4086i	−0.815338	−	0.922881i
$759$	5.84104	−	14.1015i	0.212016	−	0.511853i
$760$	0.414769	+	37.7808i	0.0150452	+	1.37045i
$761$	15.3213	+	36.9889i	0.555396	+	1.34084i	0.913377	+	0.407116i	$0.133465\pi$
$761$	15.3213	+	36.9889i	0.555396	+	1.34084i	−0.357980	+	0.933729i	$0.616535\pi$
$762$	−8.13308	−	3.97386i	−0.294630	−	0.143958i
$763$	0.417896	−	0.0831248i	0.0151289	−	0.00300932i
$764$	3.30427	−	5.82114i	0.119544	−	0.210602i
$765$	−11.0899	+	7.41006i	−0.400957	+	0.267911i
$766$	−16.1173	−	27.6815i	−0.582341	−	1.00017i
$767$	1.57557			0.0568906
$768$	−1.51332	−	15.9283i	−0.0546072	−	0.574762i
$769$	37.7915			1.36280			0.681398	−	0.731914i	$-0.261373\pi$
$769$	37.7915			1.36280			0.681398	+	0.731914i	$0.261373\pi$
$770$	−11.5637	−	19.8607i	−0.416727	−	0.715732i
$771$	15.9665	−	10.6685i	0.575020	−	0.384216i
$772$	14.4908	−	25.5285i	0.521537	−	0.918793i
$773$	−24.5621	+	4.88571i	−0.883438	+	0.175727i	−0.615904	−	0.787822i	$-0.711209\pi$
$773$	−24.5621	+	4.88571i	−0.883438	+	0.175727i	−0.267534	+	0.963548i	$0.586209\pi$
$774$	7.14354	+	3.49037i	0.256769	+	0.125459i
$775$	−26.7137	−	64.4925i	−0.959584	−	2.31664i
$776$	−0.243723	−	22.2005i	−0.00874914	−	0.796950i
$777$	−4.15681	+	10.0354i	−0.149125	+	0.360019i
$778$	20.0976	+	22.7485i	0.720536	+	0.815574i
$779$	4.42134	−	6.61701i	0.158411	−	0.237079i
$780$	0.265899	+	3.64759i	0.00952071	+	0.130605i
$781$	28.0929	+	5.58803i	1.00524	+	0.199956i
$782$	14.5662	−	19.1276i	0.520887	−	0.684002i
$783$	−4.50300	+	4.50300i	−0.160924	+	0.160924i
$784$	−20.0064	−	5.04804i	−0.714514	−	0.180287i
$785$	8.32835	+	8.32835i	0.297252	+	0.297252i
$786$	−30.3294	+	4.10590i	−1.08181	+	0.146453i
$787$	−0.891237	+	4.48055i	−0.0317692	+	0.159714i	−0.993413	−	0.114585i	$-0.963446\pi$
$787$	−0.891237	+	4.48055i	−0.0317692	+	0.159714i	0.961644	+	0.274300i	$0.0884460\pi$
$788$	−5.76799	+	17.4095i	−0.205476	+	0.620188i
$789$	−19.2410	−	12.8564i	−0.684997	−	0.457700i
$790$	−26.1443	−	1.61753i	−0.930173	−	0.0575492i
$791$	−22.3667	−	9.26459i	−0.795269	−	0.329411i
$792$	−5.35029	−	7.82005i	−0.190114	−	0.277873i
$793$	3.70512	−	1.53471i	0.131573	−	0.0544992i
$794$	6.17052	+	17.9616i	0.218984	+	0.637432i
$795$	−9.78400	−	49.1875i	−0.347003	−	1.74450i
$796$	0.803457	+	0.0998007i	0.0284778	+	0.00353734i
$797$	−14.4093	−	21.5650i	−0.510402	−	0.763871i	0.483357	−	0.875424i	$-0.339417\pi$
$797$	−14.4093	−	21.5650i	−0.510402	−	0.763871i	−0.993758	+	0.111553i	$0.964417\pi$
$798$	−6.93441	−	1.83090i	−0.245475	−	0.0648131i
$799$			41.5810i			1.47103i
$800$	4.94381	−	43.7190i	0.174790	−	1.54570i
$801$		−	12.3907i		−	0.437804i
$802$	−1.44717	+	5.48105i	−0.0511012	+	0.193543i
$803$	24.1383	+	36.1255i	0.851821	+	1.27484i
$804$	3.22972	+	4.14587i	0.113903	+	0.146213i
$805$	4.31195	+	21.6777i	0.151976	+	0.764037i
$806$	−6.14087	+	2.10964i	−0.216303	+	0.0743088i
$807$	0.976056	−	0.404296i	0.0343588	−	0.0142319i
$808$	−5.33190	−	25.3478i	−0.187576	−	0.891731i
$809$	43.9606	+	18.2091i	1.54557	+	0.640197i	0.982509	−	0.186217i	$-0.0596227\pi$
$809$	43.9606	+	18.2091i	1.54557	+	0.640197i	0.563063	+	0.826414i	$0.309623\pi$
$810$	0.312168	−	5.04560i	0.0109685	−	0.177284i
$811$	12.8226	+	8.56777i	0.450262	+	0.300855i	0.759948	−	0.649983i	$-0.225224\pi$
$811$	12.8226	+	8.56777i	0.450262	+	0.300855i	−0.309687	+	0.950839i	$0.600224\pi$
$812$	−7.75786	−	15.4454i	−0.272248	−	0.542027i
$813$	−0.465358	+	2.33951i	−0.0163208	+	0.0820503i
$814$	5.08717	+	37.5778i	0.178305	+	1.31710i
$815$	−39.9820	−	39.9820i	−1.40051	−	1.40051i
$816$	−5.00384	−	14.0612i	−0.175169	−	0.492242i
$817$	14.8559	−	14.8559i	0.519741	−	0.519741i
$818$	18.3968	+	14.0097i	0.643229	+	0.489838i
$819$	−0.680889	−	0.135437i	−0.0237922	−	0.00473256i
$820$	−9.95426	+	11.5196i	−0.347618	+	0.402283i
$821$	−13.0794	+	19.5747i	−0.456473	+	0.683160i	−0.986303	−	0.164944i	$-0.947256\pi$
$821$	−13.0794	+	19.5747i	−0.456473	+	0.683160i	0.529830	+	0.848104i	$0.322256\pi$
$822$	14.0988	−	12.4559i	0.491753	−	0.434449i
$823$	12.7634	−	30.8136i	0.444904	−	1.07409i	−0.529302	−	0.848433i	$-0.677546\pi$
$823$	12.7634	−	30.8136i	0.444904	−	1.07409i	0.974206	−	0.225660i	$-0.0724538\pi$
$824$	38.6026	−	16.4885i	1.34479	−	0.574404i
$825$	−9.97092	−	24.0719i	−0.347143	−	0.838077i
$826$	2.59492	−	5.31088i	0.0902889	−	0.184789i
$827$	−48.6203	+	9.67117i	−1.69069	+	0.336300i	−0.944270	−	0.329173i	$-0.893230\pi$
$827$	−48.6203	+	9.67117i	−1.69069	+	0.336300i	−0.746422	+	0.665472i	$0.768230\pi$
$828$	2.42285	+	8.78453i	0.0841998	+	0.305283i
$829$	−20.0461	+	13.3944i	−0.696231	+	0.465207i	−0.852649	−	0.522484i	$-0.825005\pi$
$829$	−20.0461	+	13.3944i	−0.696231	+	0.465207i	0.156418	+	0.987691i	$0.450005\pi$
$830$	−53.5215	+	31.1623i	−1.85776	+	1.08166i
$831$	21.2014			0.735470
$832$	−4.03044	−	0.710097i	−0.139730	−	0.0246182i
$833$	−19.2472			−0.666875
$834$	1.81672	−	1.05776i	0.0629078	−	0.0366274i
$835$	−4.05994	+	2.71277i	−0.140500	+	0.0938792i
$836$	−24.1366	+	6.65710i	−0.834783	+	0.230240i
$837$	8.80266	−	1.75096i	0.304264	−	0.0605220i
$838$	−4.59889	+	9.41230i	−0.158866	+	0.325142i
$839$	14.2054	+	34.2948i	0.490423	+	1.18399i	0.954505	+	0.298194i	$0.0963843\pi$
$839$	14.2054	+	34.2948i	0.490423	+	1.18399i	−0.464082	+	0.885792i	$0.653616\pi$
$840$	12.7331	+	5.11119i	0.439334	+	0.176353i
$841$	−4.42156	+	10.6746i	−0.152468	+	0.368089i
$842$	30.6774	−	27.1026i	1.05721	−	0.934018i
$843$	−8.62455	+	12.9076i	−0.297045	+	0.444560i
$844$	10.4646	+	9.04256i	0.360205	+	0.311258i
$845$	−44.6594	−	8.88330i	−1.53633	−	0.305595i
$846$	−12.5382	−	9.54823i	−0.431073	−	0.328275i
$847$	0.213353	−	0.213353i	0.00733089	−	0.00733089i
$848$	56.0470	+	2.85035i	1.92466	+	0.0978816i
$849$	−20.6859	−	20.6859i	−0.709938	−	0.709938i
$850$	−5.50587	−	40.6706i	−0.188850	−	1.39499i
$851$	7.11480	−	35.7685i	0.243892	−	1.22613i
$852$	−15.2813	+	7.67545i	−0.523529	+	0.262957i
$853$	9.25748	+	6.18565i	0.316970	+	0.211793i	0.703870	−	0.710329i	$-0.251454\pi$
$853$	9.25748	+	6.18565i	0.316970	+	0.211793i	−0.386899	+	0.922122i	$0.626454\pi$
$854$	0.929074	−	15.0167i	0.0317922	−	0.513861i
$855$	−12.3415	−	5.11202i	−0.422070	−	0.174827i
$856$	4.08405	+	2.66449i	0.139590	+	0.0910705i
$857$	−32.7748	+	13.5758i	−1.11957	+	0.463740i	−0.864222	−	0.503110i	$-0.832189\pi$
$857$	−32.7748	+	13.5758i	−1.11957	+	0.463740i	−0.255344	+	0.966850i	$0.582189\pi$
$858$	−2.29209	+	0.787425i	−0.0782507	+	0.0268823i
$859$	9.73858	+	48.9591i	0.332276	+	1.67046i	0.680265	+	0.732966i	$0.261865\pi$
$859$	9.73858	+	48.9591i	0.332276	+	1.67046i	−0.347989	+	0.937498i	$0.613135\pi$
$860$	−31.7069	+	24.7003i	−1.08120	+	0.842275i
$861$	−1.60558	−	2.40292i	−0.0547179	−	0.0818911i
$862$	−1.54166	+	5.83895i	−0.0525093	+	0.198875i
$863$			46.4319i			1.58056i	0.612746	+	0.790280i	$0.290065\pi$
$863$			46.4319i			1.58056i	−0.612746	+	0.790280i	$0.709935\pi$
$864$	5.38902	+	1.72003i	0.183338	+	0.0585166i
$865$			28.5248i			0.969872i
$866$	29.8275	+	7.87539i	1.01358	+	0.267617i
$867$	1.70988	+	2.55902i	0.0580707	+	0.0869090i
$868$	−3.00275	+	24.1740i	−0.101920	+	0.820517i
$869$	−3.38643	−	17.0247i	−0.114877	−	0.577524i
$870$	−10.4595	−	30.4463i	−0.354612	−	1.03223i
$871$	1.24191	−	0.514417i	0.0420806	−	0.0174304i
$872$	−0.163678	+	0.872836i	−0.00554284	+	0.0295579i
$873$	7.25201	+	3.00388i	0.245443	+	0.101666i
$874$	24.0336	+	1.48695i	0.812950	+	0.0502967i
$875$	11.2039	+	7.48621i	0.378761	+	0.253080i
$876$	−24.6229	−	8.15788i	−0.831931	−	0.275629i
$877$	−7.66367	+	38.5279i	−0.258784	+	1.30099i	0.604634	+	0.796504i	$0.293320\pi$
$877$	−7.66367	+	38.5279i	−0.258784	+	1.30099i	−0.863417	+	0.504490i	$0.831680\pi$
$878$	−16.4581	+	2.22805i	−0.555434	+	0.0751930i
$879$	−5.41853	−	5.41853i	−0.182763	−	0.182763i
$880$	47.3929	−	6.94652i	1.59761	−	0.234167i
$881$	15.3576	−	15.3576i	0.517411	−	0.517411i	−0.399376	−	0.916787i	$-0.630773\pi$
$881$	15.3576	−	15.3576i	0.517411	−	0.517411i	0.916787	+	0.399376i	$0.130773\pi$
$882$	4.41972	−	5.80374i	0.148820	−	0.195422i
$883$	−37.3239	−	7.42418i	−1.25605	−	0.249844i	−0.478175	−	0.878265i	$-0.658701\pi$
$883$	−37.3239	−	7.42418i	−1.25605	−	0.249844i	−0.777873	+	0.628421i	$0.783701\pi$
$884$	−3.80745	+	0.277552i	−0.128058	+	0.00933509i
$885$	6.11652	−	9.15402i	0.205605	−	0.307709i
$886$	16.0356	+	18.1507i	0.538727	+	0.609785i
$887$	4.44573	−	10.7329i	0.149273	−	0.360377i	−0.831501	−	0.555523i	$-0.812518\pi$
$887$	4.44573	−	10.7329i	0.149273	−	0.360377i	0.980774	+	0.195146i	$0.0625181\pi$
$888$	−16.1832	−	15.8317i	−0.543072	−	0.531278i
$889$	3.32408	+	8.02503i	0.111486	+	0.269151i
$890$	56.2794	+	27.4983i	1.88649	+	0.921747i
$891$	3.28561	−	0.653548i	0.110072	−	0.0218947i
$892$	−0.443298	−	0.251630i	−0.0148427	−	0.00842521i
$893$	−34.6267	+	23.1368i	−1.15874	+	0.774245i
$894$	11.4891	+	19.7325i	0.384252	+	0.659955i
$895$	17.6632			0.590415
$896$	−9.03158	+	12.4161i	−0.301724	+	0.414794i
$897$	2.33082			0.0778238
$898$	−7.44281	−	12.7831i	−0.248370	−	0.426577i
$899$	47.5230	−	31.7538i	1.58498	−	1.05905i
$900$	13.5280	+	7.67895i	0.450934	+	0.255965i
$901$	51.3432	−	10.2128i	1.71049	−	0.340237i
$902$	−9.06478	−	4.42909i	−0.301824	−	0.147473i
$903$	−2.91964	−	7.04864i	−0.0971596	−	0.234564i
$904$	35.2853	−	36.0687i	1.17357	−	1.19963i
$905$	−16.9532	+	40.9285i	−0.563542	+	1.36051i
$906$	−9.15186	−	10.3590i	−0.304050	−	0.344154i
$907$	−15.3468	+	22.9680i	−0.509581	+	0.762642i	−0.993665	−	0.112380i	$-0.964153\pi$
$907$	−15.3468	+	22.9680i	−0.509581	+	0.762642i	0.484085	+	0.875021i	$0.339153\pi$
$908$	18.2446	−	1.32998i	0.605467	−	0.0441368i
$909$	8.98194	+	1.78662i	0.297912	+	0.0592584i
$910$	2.12624	−	2.79207i	0.0704842	−	0.0925562i
$911$	−21.9043	+	21.9043i	−0.725720	+	0.725720i	−0.969764	−	0.244044i	$-0.921526\pi$
$911$	−21.9043	+	21.9043i	−0.725720	+	0.725720i	0.244044	+	0.969764i	$0.421526\pi$
$912$	8.92526	−	11.9910i	0.295545	−	0.397063i
$913$	−29.0204	−	29.0204i	−0.960435	−	0.960435i
$914$	16.5122	−	2.23537i	0.546174	−	0.0739395i
$915$	5.46701	−	27.4845i	0.180734	−	0.908610i
$916$	4.53822	+	1.50357i	0.149947	+	0.0496794i
$917$	24.4198	+	16.3168i	0.806411	+	0.538827i
$918$	5.26673	+	0.325849i	0.173828	+	0.0107546i
$919$	−13.0031	−	5.38605i	−0.428932	−	0.177670i	0.157764	−	0.987477i	$-0.449572\pi$
$919$	−13.0031	−	5.38605i	−0.428932	−	0.177670i	−0.586696	+	0.809807i	$0.699572\pi$
$920$	−45.2768	−	8.49052i	−1.49273	−	0.279924i
$921$	−9.87656	+	4.09101i	−0.325444	+	0.134803i
$922$	−10.7151	−	31.1903i	−0.352884	−	1.02720i
$923$	0.853330	+	4.28998i	0.0280877	+	0.141206i
$924$	−1.12078	+	9.02297i	−0.0368709	+	0.296834i
$925$	−34.5869	−	51.7629i	−1.13721	−	1.70195i
$926$	−14.7017	−	3.88171i	−0.483129	−	0.127561i
$927$			14.8409i			0.487441i
$928$	35.8978	−	3.01335i	1.17840	−	0.0989181i
$929$			12.1677i			0.399209i	0.979877	+	0.199604i	$0.0639657\pi$
$929$			12.1677i			0.399209i	−0.979877	+	0.199604i	$0.936034\pi$
$930$	−11.5825	+	43.8681i	−0.379806	+	1.43849i
$931$	−10.7097	−	16.0282i	−0.350995	−	0.525301i
$932$	−35.8642	+	27.9389i	−1.17477	+	0.915171i
$933$	3.02919	+	15.2288i	0.0991711	+	0.498567i
$934$	−10.3567	+	3.55794i	−0.338881	+	0.116419i
$935$	41.2800	−	17.0987i	1.35000	−	0.559188i
$936$	0.790611	−	1.21182i	0.0258419	−	0.0396097i
$937$	−33.7772	−	13.9910i	−1.10345	−	0.457066i	−0.244775	−	0.969580i	$-0.578714\pi$
$937$	−33.7772	−	13.9910i	−1.10345	−	0.457066i	−0.858679	+	0.512514i	$0.828714\pi$
$938$	0.311415	−	5.03343i	0.0101681	−	0.164347i
$939$	−9.64313	−	6.44333i	−0.314692	−	0.210270i
$940$	71.1944	−	35.7593i	2.32211	−	1.16634i
$941$	−5.92101	+	29.7669i	−0.193019	+	0.970374i	0.755860	+	0.654734i	$0.227219\pi$
$941$	−5.92101	+	29.7669i	−0.193019	+	0.970374i	−0.948879	+	0.315640i	$0.897781\pi$
$942$	−0.625120	−	4.61762i	−0.0203675	−	0.150450i
$943$	6.86094	+	6.86094i	0.223423	+	0.223423i
$944$	8.25761	+	9.14252i	0.268762	+	0.297564i
$945$	−3.43016	+	3.43016i	−0.111583	+	0.111583i
$946$	−21.1897	−	16.1366i	−0.688938	−	0.524647i
$947$	−60.0805	−	11.9508i	−1.95235	−	0.388348i	−0.995066	−	0.0992132i	$-0.968367\pi$
$947$	−60.0805	−	11.9508i	−1.95235	−	0.388348i	−0.957289	−	0.289134i	$-0.906633\pi$
$948$	7.84128	+	6.77574i	0.254673	+	0.220066i
$949$	−3.68608	+	5.51661i	−0.119655	+	0.179077i
$950$	30.8050	−	27.2153i	0.999446	−	0.882981i
$951$	4.68909	−	11.3205i	0.152054	−	0.367091i
$952$	−5.33520	+	13.2911i	−0.172915	+	0.430768i
$953$	8.37203	+	20.2119i	0.271197	+	0.654727i	0.999535	−	0.0304908i	$-0.00970703\pi$
$953$	8.37203	+	20.2119i	0.271197	+	0.654727i	−0.728338	+	0.685218i	$0.759707\pi$
$954$	−8.71037	+	17.8270i	−0.282009	+	0.577172i
$955$	−11.7335	+	2.33395i	−0.379689	+	0.0755247i
$956$	−2.73838	+	0.755270i	−0.0885657	+	0.0244272i
$957$	17.7380	−	11.8522i	0.573389	−	0.383126i
$958$	17.8816	−	10.4114i	0.577728	−	0.336376i
$959$	−18.0528			−0.582954
$960$	−19.7722	+	20.6600i	−0.638144	+	0.666800i
$961$	−49.5527			−1.59847
$962$	−5.00429	+	2.91370i	−0.161345	+	0.0939413i
$963$	−1.43350	+	0.957834i	−0.0461939	+	0.0308658i
$964$	9.90570	+	35.9151i	0.319041	+	1.15675i
$965$	−51.4573	+	10.2355i	−1.65647	+	0.329492i
$966$	3.83879	−	7.85665i	0.123511	−	0.252783i
$967$	23.1630	+	55.9204i	0.744871	+	1.79828i	0.584810	+	0.811170i	$0.301169\pi$
$967$	23.1630	+	55.9204i	0.744871	+	1.79828i	0.160061	+	0.987107i	$0.448831\pi$
$968$	0.247019	+	0.578317i	0.00793949	+	0.0185878i
$969$	5.33606	−	12.8824i	0.171419	−	0.413842i
$970$	−29.7380	+	26.2727i	−0.954830	+	0.843565i
$971$	10.5018	−	15.7170i	0.337018	−	0.504383i	−0.623792	−	0.781590i	$-0.714409\pi$
$971$	10.5018	−	15.7170i	0.337018	−	0.504383i	0.960810	+	0.277207i	$0.0894089\pi$
$972$	−1.30765	+	1.51329i	−0.0419429	+	0.0485388i
$973$	−1.97852	−	0.393551i	−0.0634283	−	0.0126167i
$974$	1.90237	+	1.44871i	0.0609558	+	0.0464196i
$975$	2.81345	−	2.81345i	0.0901024	−	0.0901024i
$976$	28.3240	+	13.4561i	0.906630	+	0.430720i
$977$	16.3640	+	16.3640i	0.523529	+	0.523529i	0.918635	−	0.395106i	$-0.129292\pi$
$977$	16.3640	+	16.3640i	0.523529	+	0.523529i	−0.395106	+	0.918635i	$0.629292\pi$
$978$	3.00102	+	22.1678i	0.0959619	+	0.708850i
$979$	−8.09792	+	40.7110i	−0.258811	+	1.30113i
$980$	16.5524	+	32.9547i	0.528747	+	1.05270i
$981$	−0.261059	−	0.174434i	−0.00833497	−	0.00556925i
$982$	−0.288222	+	4.65855i	−0.00919752	+	0.148660i
$983$	−32.3181	−	13.3866i	−1.03079	−	0.426966i	−0.197791	−	0.980244i	$-0.563377\pi$
$983$	−32.3181	−	13.3866i	−1.03079	−	0.426966i	−0.832997	+	0.553278i	$0.813377\pi$
$984$	5.89431	−	1.23987i	0.187904	−	0.0395256i
$985$	30.2841	−	12.5441i	0.964933	−	0.399688i
$986$	31.7807	−	10.9179i	1.01210	−	0.347698i
$987$	2.95038	+	14.8326i	0.0939116	+	0.472126i
$988$	−2.34971	−	3.01623i	−0.0747541	−	0.0959591i
$989$	14.2310	+	21.2982i	0.452519	+	0.677243i
$990$	−4.32320	+	16.3738i	−0.137400	+	0.520395i
$991$		−	5.47098i		−	0.173791i	−0.996217	−	0.0868957i	$-0.972305\pi$
$991$		−	5.47098i		−	0.173791i	0.996217	−	0.0868957i	$-0.0276947\pi$
$992$	−44.4260	−	24.5768i	−1.41053	−	0.780314i
$993$		−	5.59376i		−	0.177513i
$994$	15.8659	+	4.18910i	0.503237	+	0.132870i
$995$	−0.803940	−	1.20318i	−0.0254866	−	0.0381434i
$996$	24.3154	+	3.02032i	0.770464	+	0.0957025i
$997$	−8.26079	−	41.5298i	−0.261622	−	1.31526i	−0.858452	−	0.512894i	$-0.828573\pi$
$997$	−8.26079	−	41.5298i	−0.261622	−	1.31526i	0.596830	−	0.802368i	$-0.296427\pi$
$998$	17.2220	+	50.1310i	0.545154	+	1.58687i
$999$	7.39492	−	3.06308i	0.233965	−	0.0969115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.13.12	✓	128
3.2	odd	2		576.2.bd.b.397.5		128
4.3	odd	2		768.2.r.a.145.16		128
64.5	even	16	inner	192.2.r.a.133.12	yes	128
64.59	odd	16		768.2.r.a.625.16		128
192.5	odd	16		576.2.bd.b.325.5		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.13.12	✓	128	1.1	even	1	trivial
192.2.r.a.133.12	yes	128	64.5	even	16	inner
576.2.bd.b.325.5		128	192.5	odd	16
576.2.bd.b.397.5		128	3.2	odd	2
768.2.r.a.145.16		128	4.3	odd	2
768.2.r.a.625.16		128	64.59	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.711584 + 1.22215i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.987297 + 1.73932i) q^{4} +(3.50591 - 0.697369i) q^{5} +(-1.27065 - 0.620845i) q^{6} +(0.519328 + 1.25377i) q^{7} +(-2.82826 + 0.0310494i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(0.711584 + 1.22215i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.987297 + 1.73932i) q^{4} +(3.50591 - 0.697369i) q^{5} +(-1.27065 - 0.620845i) q^{6} +(0.519328 + 1.25377i) q^{7} +(-2.82826 + 0.0310494i) q^{8} +(0.382683 - 0.923880i) q^{9} +(3.34704 + 3.78851i) q^{10} +(-1.86115 + 2.78540i) q^{11} +(-0.145408 - 1.99471i) q^{12} +(-0.501734 - 0.0998012i) q^{13} +(-1.16275 + 1.52686i) q^{14} +(-2.52762 + 2.52762i) q^{15} +(-2.05049 - 3.43446i) q^{16} +(-2.63840 - 2.63840i) q^{17} +(1.40143 - 0.189721i) q^{18} +(0.729057 - 3.66521i) q^{19} +(-2.24843 + 6.78643i) q^{20} +(-1.12836 - 0.753948i) q^{21} +(-4.72854 - 0.292552i) q^{22} +(4.20944 + 1.74361i) q^{23} +(2.33436 - 1.59711i) q^{24} +(7.18570 - 2.97642i) q^{25} +(-0.235054 - 0.684211i) q^{26} +(0.195090 + 0.980785i) q^{27} +(-2.69344 - 0.334564i) q^{28} +(3.53799 + 5.29497i) q^{29} +(-4.88775 - 1.29052i) q^{30} -8.97511i q^{31} +(2.73833 - 4.94991i) q^{32} -3.34998i q^{33} +(1.34707 - 5.10196i) q^{34} +(2.69506 + 4.03344i) q^{35} +(1.22910 + 1.57775i) q^{36} +(-1.56154 - 7.85041i) q^{37} +(4.99822 - 1.71709i) q^{38} +(0.472623 - 0.195767i) q^{39} +(-9.89397 + 2.08120i) q^{40} +(1.96746 + 0.814947i) q^{41} +(0.118512 - 1.91553i) q^{42} +(4.67449 + 3.12339i) q^{43} +(-3.00721 - 5.98716i) q^{44} +(0.697369 - 3.50591i) q^{45} +(0.864421 + 6.38528i) q^{46} +(-7.87997 - 7.87997i) q^{47} +(3.61300 + 1.71646i) q^{48} +(3.64751 - 3.64751i) q^{49} +(8.75085 + 6.66403i) q^{50} +(3.65956 + 0.727932i) q^{51} +(0.668947 - 0.774145i) q^{52} +(-7.79457 + 11.6654i) q^{53} +(-1.05984 + 0.936340i) q^{54} +(-4.58256 + 11.0633i) q^{55} +(-1.50772 - 3.52986i) q^{56} +(1.43010 + 3.45256i) q^{57} +(-3.95367 + 8.09177i) q^{58} +(-3.02073 + 0.600861i) q^{59} +(-1.90084 - 6.89187i) q^{60} +(-6.51828 + 4.35538i) q^{61} +(10.9689 - 6.38655i) q^{62} +1.35707 q^{63} +(7.99807 - 0.175631i) q^{64} -1.82864 q^{65} +(4.09417 - 2.38379i) q^{66} +(-2.18485 + 1.45987i) q^{67} +(7.19391 - 1.98414i) q^{68} +(-4.46872 + 0.888883i) q^{69} +(-3.01171 + 6.16390i) q^{70} +(-3.27206 - 7.89945i) q^{71} +(-1.05364 + 2.62485i) q^{72} +(4.96324 - 11.9823i) q^{73} +(8.48320 - 7.49466i) q^{74} +(-4.32109 + 6.46696i) q^{75} +(5.65520 + 4.88672i) q^{76} +(-4.45880 - 0.886911i) q^{77} +(0.575568 + 0.438312i) q^{78} +(-3.66395 + 3.66395i) q^{79} +(-9.58392 - 10.6110i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(0.404023 + 2.98443i) q^{82} +(-2.39008 + 12.0157i) q^{83} +(2.42539 - 1.21822i) q^{84} +(-11.0899 - 7.41006i) q^{85} +(-0.490963 + 7.93548i) q^{86} +(-5.88346 - 2.43701i) q^{87} +(5.17732 - 7.93562i) q^{88} +(11.4475 - 4.74172i) q^{89} +(4.78099 - 1.64246i) q^{90} +(-0.135437 - 0.680889i) q^{91} +(-7.18866 + 5.60011i) q^{92} +(4.98631 + 7.46254i) q^{93} +(4.02324 - 15.2378i) q^{94} -13.3583i q^{95} +(0.473187 + 5.63703i) q^{96} +7.84952i q^{97} +(7.05331 + 1.86229i) q^{98} +(1.86115 + 2.78540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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