LMFDB - Embedded newform 228.2.c.a.191.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(191,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("228.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.30
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13655 + 0.841583i) q^{2} +(-0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} -1.36832i q^{5} +(-1.53385 + 1.90979i) q^{6} +1.12940i q^{7} +(-0.946798 + 2.66525i) q^{8} +(-2.99075 - 0.235461i) q^{9} +O(q^{10})$	\(q+(1.13655 + 0.841583i) q^{2} +(-0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} -1.36832i q^{5} +(-1.53385 + 1.90979i) q^{6} +1.12940i q^{7} +(-0.946798 + 2.66525i) q^{8} +(-2.99075 - 0.235461i) q^{9} +(1.15156 - 1.55516i) q^{10} +3.43894 q^{11} +(-3.35054 + 0.879700i) q^{12} -0.802387 q^{13} +(-0.950482 + 1.28361i) q^{14} +(2.36818 + 0.0930793i) q^{15} +(-3.31911 + 2.23237i) q^{16} -5.04776i q^{17} +(-3.20096 - 2.78457i) q^{18} -1.00000i q^{19} +(2.61760 - 0.798384i) q^{20} +(-1.95467 - 0.0768266i) q^{21} +(3.90851 + 2.89415i) q^{22} +0.107423 q^{23} +(-4.54839 - 1.81994i) q^{24} +3.12769 q^{25} +(-0.911951 - 0.675276i) q^{26} +(0.610960 - 5.16011i) q^{27} +(-2.16053 + 0.658976i) q^{28} -2.28079i q^{29} +(2.61321 + 2.09881i) q^{30} +6.32074i q^{31} +(-5.65105 - 0.256111i) q^{32} +(-0.233931 + 5.95182i) q^{33} +(4.24811 - 5.73702i) q^{34} +1.54538 q^{35} +(-1.29459 - 5.85867i) q^{36} +4.86414 q^{37} +(0.841583 - 1.13655i) q^{38} +(0.0545819 - 1.38870i) q^{39} +(3.64693 + 1.29553i) q^{40} -7.80977i q^{41} +(-2.15691 - 1.73233i) q^{42} -4.40419i q^{43} +(2.00654 + 6.57868i) q^{44} +(-0.322187 + 4.09231i) q^{45} +(0.122092 + 0.0904057i) q^{46} +5.92447 q^{47} +(-3.63782 - 5.89629i) q^{48} +5.72446 q^{49} +(3.55477 + 2.63221i) q^{50} +(8.73624 + 0.343371i) q^{51} +(-0.468174 - 1.53496i) q^{52} +7.95610i q^{53} +(5.03705 - 5.35053i) q^{54} -4.70558i q^{55} +(-3.01013 - 1.06931i) q^{56} +(1.73071 + 0.0680243i) q^{57} +(1.91948 - 2.59223i) q^{58} -14.9665 q^{59} +(1.20371 + 4.58463i) q^{60} -11.9278 q^{61} +(-5.31943 + 7.18382i) q^{62} +(0.265930 - 3.37774i) q^{63} +(-6.20715 - 5.04691i) q^{64} +1.09793i q^{65} +(-5.27483 + 6.56765i) q^{66} -8.03932i q^{67} +(9.65635 - 2.94525i) q^{68} +(-0.00730740 + 0.185919i) q^{69} +(1.75640 + 1.30057i) q^{70} -15.4128 q^{71} +(3.45920 - 7.74816i) q^{72} -0.852420 q^{73} +(5.52832 + 4.09358i) q^{74} +(-0.212759 + 5.41314i) q^{75} +(1.91300 - 0.583476i) q^{76} +3.88393i q^{77} +(1.23074 - 1.53239i) q^{78} +9.56611i q^{79} +(3.05461 + 4.54162i) q^{80} +(8.88912 + 1.40841i) q^{81} +(6.57257 - 8.87616i) q^{82} -6.54111 q^{83} +(-0.993531 - 3.78410i) q^{84} -6.90697 q^{85} +(3.70649 - 5.00557i) q^{86} +(3.94740 + 0.155149i) q^{87} +(-3.25598 + 9.16564i) q^{88} -4.58814i q^{89} +(-3.81020 + 4.37995i) q^{90} -0.906215i q^{91} +(0.0626789 + 0.205500i) q^{92} +(-10.9394 - 0.429964i) q^{93} +(6.73343 + 4.98593i) q^{94} -1.36832 q^{95} +(0.827665 - 9.76294i) q^{96} +15.8117 q^{97} +(6.50611 + 4.81761i) q^{98} +(-10.2850 - 0.809737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6}+O(q^{10}) $ 36 * q - 6 * q^6	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.13655	+	0.841583i	0.803660	+	0.595089i
$2$	1.13655	+	0.841583i	0.803660	+	0.595089i
$3$	−0.0680243	+	1.73071i	−0.0392739	+	0.999228i
$3$	−0.0680243	+	1.73071i	−0.0392739	+	0.999228i
$4$	0.583476	+	1.91300i	0.291738	+	0.956498i
$5$		−	1.36832i		−	0.611933i	−0.952042	−	0.305966i	$-0.901020\pi$
$5$		−	1.36832i		−	0.611933i	0.952042	−	0.305966i	$-0.0989796\pi$
$6$	−1.53385	+	1.90979i	−0.626193	+	0.779668i
$7$			1.12940i			0.426872i	0.976957	+	0.213436i	$0.0684655\pi$
$7$			1.12940i			0.426872i	−0.976957	+	0.213436i	$0.931534\pi$
$8$	−0.946798	+	2.66525i	−0.334744	+	0.942309i
$9$	−2.99075	−	0.235461i	−0.996915	−	0.0784871i
$10$	1.15156	−	1.55516i	0.364155	−	0.491786i
$11$	3.43894			1.03688			0.518440	−	0.855114i	$-0.326513\pi$
$11$	3.43894			1.03688			0.518440	+	0.855114i	$0.326513\pi$
$12$	−3.35054	+	0.879700i	−0.967218	+	0.253947i
$13$	−0.802387			−0.222542			−0.111271	−	0.993790i	$-0.535492\pi$
$13$	−0.802387			−0.222542			−0.111271	+	0.993790i	$0.535492\pi$
$14$	−0.950482	+	1.28361i	−0.254027	+	0.343060i
$15$	2.36818	+	0.0930793i	0.611461	+	0.0240330i
$16$	−3.31911	+	2.23237i	−0.829778	+	0.558094i
$17$		−	5.04776i		−	1.22426i	−0.790756	−	0.612131i	$-0.790312\pi$
$17$		−	5.04776i		−	1.22426i	0.790756	−	0.612131i	$-0.209688\pi$
$18$	−3.20096	−	2.78457i	−0.754474	−	0.656330i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.61760	−	0.798384i	0.585313	−	0.178524i
$21$	−1.95467	−	0.0768266i	−0.426543	−	0.0167649i
$22$	3.90851	+	2.89415i	0.833298	+	0.617035i
$23$	0.107423			0.0223993			0.0111997	−	0.999937i	$-0.496435\pi$
$23$	0.107423			0.0223993			0.0111997	+	0.999937i	$0.496435\pi$
$24$	−4.54839	−	1.81994i	−0.928436	−	0.371494i
$25$	3.12769			0.625538
$26$	−0.911951	−	0.675276i	−0.178848	−	0.132432i
$27$	0.610960	−	5.16011i	0.117579	−	0.993063i
$28$	−2.16053	+	0.658976i	−0.408303	+	0.124535i
$29$		−	2.28079i		−	0.423532i	−0.977320	−	0.211766i	$-0.932078\pi$
$29$		−	2.28079i		−	0.423532i	0.977320	−	0.211766i	$-0.0679215\pi$
$30$	2.61321	+	2.09881i	0.477105	+	0.383188i
$31$			6.32074i			1.13524i	0.823291	+	0.567619i	$0.192135\pi$
$31$			6.32074i			1.13524i	−0.823291	+	0.567619i	$0.807865\pi$
$32$	−5.65105	−	0.256111i	−0.998975	−	0.0452745i
$33$	−0.233931	+	5.95182i	−0.0407222	+	1.03608i
$34$	4.24811	−	5.73702i	0.728545	−	0.983890i
$35$	1.54538			0.261217
$36$	−1.29459	−	5.85867i	−0.215765	−	0.976445i
$37$	4.86414			0.799659			0.399830	−	0.916589i	$-0.369069\pi$
$37$	4.86414			0.799659			0.399830	+	0.916589i	$0.369069\pi$
$38$	0.841583	−	1.13655i	0.136523	−	0.184372i
$39$	0.0545819	−	1.38870i	0.00874009	−	0.222371i
$40$	3.64693	+	1.29553i	0.576630	+	0.204841i
$41$		−	7.80977i		−	1.21968i	−0.792524	−	0.609840i	$-0.791234\pi$
$41$		−	7.80977i		−	1.21968i	0.792524	−	0.609840i	$-0.208766\pi$
$42$	−2.15691	−	1.73233i	−0.332819	−	0.267304i
$43$		−	4.40419i		−	0.671633i	−0.941927	−	0.335816i	$-0.890988\pi$
$43$		−	4.40419i		−	0.671633i	0.941927	−	0.335816i	$-0.109012\pi$
$44$	2.00654	+	6.57868i	0.302497	+	0.991773i
$45$	−0.322187	+	4.09231i	−0.0480289	+	0.610045i
$46$	0.122092	+	0.0904057i	0.0180014	+	0.0133296i
$47$	5.92447			0.864172			0.432086	−	0.901832i	$-0.357778\pi$
$47$	5.92447			0.864172			0.432086	+	0.901832i	$0.357778\pi$
$48$	−3.63782	−	5.89629i	−0.525074	−	0.851056i
$49$	5.72446			0.817780
$50$	3.55477	+	2.63221i	0.502720	+	0.372251i
$51$	8.73624	+	0.343371i	1.22332	+	0.0480815i
$52$	−0.468174	−	1.53496i	−0.0649240	−	0.212861i
$53$			7.95610i			1.09285i	0.837507	+	0.546427i	$0.184013\pi$
$53$			7.95610i			1.09285i	−0.837507	+	0.546427i	$0.815987\pi$
$54$	5.03705	−	5.35053i	0.685455	−	0.728115i
$55$		−	4.70558i		−	0.634500i
$56$	−3.01013	−	1.06931i	−0.402246	−	0.142893i
$57$	1.73071	+	0.0680243i	0.229239	+	0.00901004i
$58$	1.91948	−	2.59223i	0.252039	−	0.340376i
$59$	−14.9665			−1.94847			−0.974237	−	0.225528i	$-0.927589\pi$
$59$	−14.9665			−1.94847			−0.974237	+	0.225528i	$0.927589\pi$
$60$	1.20371	+	4.58463i	0.155399	+	0.591873i
$61$	−11.9278			−1.52720			−0.763602	−	0.645687i	$-0.776571\pi$
$61$	−11.9278			−1.52720			−0.763602	+	0.645687i	$0.776571\pi$
$62$	−5.31943	+	7.18382i	−0.675568	+	0.912346i
$63$	0.265930	−	3.37774i	0.0335040	−	0.425556i
$64$	−6.20715	−	5.04691i	−0.775893	−	0.630864i
$65$			1.09793i			0.136181i
$66$	−5.27483	+	6.56765i	−0.649286	+	0.808422i
$67$		−	8.03932i		−	0.982159i	−0.871115	−	0.491080i	$-0.836602\pi$
$67$		−	8.03932i		−	0.982159i	0.871115	−	0.491080i	$-0.163398\pi$
$68$	9.65635	−	2.94525i	1.17100	−	0.357164i
$69$	−0.00730740	+	0.185919i	−0.000879708	+	0.0223820i
$70$	1.75640	+	1.30057i	0.209930	+	0.155448i
$71$	−15.4128			−1.82916			−0.914579	−	0.404407i	$-0.867478\pi$
$71$	−15.4128			−1.82916			−0.914579	+	0.404407i	$0.867478\pi$
$72$	3.45920	−	7.74816i	0.407670	−	0.913129i
$73$	−0.852420			−0.0997682			−0.0498841	−	0.998755i	$-0.515885\pi$
$73$	−0.852420			−0.0997682			−0.0498841	+	0.998755i	$0.515885\pi$
$74$	5.52832	+	4.09358i	0.642654	+	0.475868i
$75$	−0.212759	+	5.41314i	−0.0245673	+	0.625055i
$76$	1.91300	−	0.583476i	0.219436	−	0.0669293i
$77$			3.88393i			0.442615i
$78$	1.23074	−	1.53239i	0.139354	−	0.173509i
$79$			9.56611i			1.07627i	0.842858	+	0.538136i	$0.180871\pi$
$79$			9.56611i			1.07627i	−0.842858	+	0.538136i	$0.819129\pi$
$80$	3.05461	+	4.54162i	0.341516	+	0.507769i
$81$	8.88912	+	1.40841i	0.987680	+	0.156490i
$82$	6.57257	−	8.87616i	0.725819	−	0.980208i
$83$	−6.54111			−0.717981			−0.358990	−	0.933341i	$-0.616879\pi$
$83$	−6.54111			−0.717981			−0.358990	+	0.933341i	$0.616879\pi$
$84$	−0.993531	−	3.78410i	−0.108403	−	0.412879i
$85$	−6.90697			−0.749167
$86$	3.70649	−	5.00557i	0.399681	−	0.539764i
$87$	3.94740	+	0.155149i	0.423206	+	0.0166338i
$88$	−3.25598	+	9.16564i	−0.347089	+	0.977061i
$89$		−	4.58814i		−	0.486342i	−0.969983	−	0.243171i	$-0.921812\pi$
$89$		−	4.58814i		−	0.486342i	0.969983	−	0.243171i	$-0.0781876\pi$
$90$	−3.81020	+	4.37995i	−0.401630	+	0.461687i
$91$		−	0.906215i		−	0.0949971i
$92$	0.0626789	+	0.205500i	0.00653473	+	0.0214249i
$93$	−10.9394	−	0.429964i	−1.13436	−	0.0445852i
$94$	6.73343	+	4.98593i	0.694501	+	0.514260i
$95$	−1.36832			−0.140387
$96$	0.827665	−	9.76294i	0.0844732	−	0.996426i
$97$	15.8117			1.60544			0.802720	−	0.596357i	$-0.203386\pi$
$97$	15.8117			1.60544			0.802720	+	0.596357i	$0.203386\pi$
$98$	6.50611	+	4.81761i	0.657217	+	0.486652i
$99$	−10.2850	−	0.809737i	−1.03368	−	0.0813817i
$100$	1.82493	+	5.98326i	0.182493	+	0.598326i
$101$		−	13.7076i		−	1.36396i	−0.731370	−	0.681980i	$-0.761119\pi$
$101$		−	13.7076i		−	1.36396i	0.731370	−	0.681980i	$-0.238881\pi$
$102$	9.64016	+	7.74253i	0.954519	+	0.766624i
$103$			7.07320i			0.696943i	0.937319	+	0.348472i	$0.113299\pi$
$103$			7.07320i			0.696943i	−0.937319	+	0.348472i	$0.886701\pi$
$104$	0.759699	−	2.13857i	0.0744946	−	0.209704i
$105$	−0.105124	+	2.67462i	−0.0102590	+	0.261016i
$106$	−6.69572	+	9.04248i	−0.650346	+	0.878283i
$107$	−8.38344			−0.810458			−0.405229	−	0.914215i	$-0.632808\pi$
$107$	−8.38344			−0.810458			−0.405229	+	0.914215i	$0.632808\pi$
$108$	10.2278	−	1.84203i	0.984166	−	0.177250i
$109$	−11.2524			−1.07778			−0.538892	−	0.842375i	$-0.681157\pi$
$109$	−11.2524			−1.07778			−0.538892	+	0.842375i	$0.681157\pi$
$110$	3.96014	−	5.34811i	0.377584	−	0.509922i
$111$	−0.330880	+	8.41843i	−0.0314057	+	0.799042i
$112$	−2.52124	−	3.74860i	−0.238235	−	0.354209i
$113$			17.9835i			1.69174i	0.533387	+	0.845871i	$0.320919\pi$
$113$			17.9835i			1.69174i	−0.533387	+	0.845871i	$0.679081\pi$
$114$	1.90979	+	1.53385i	0.178868	+	0.143658i
$115$		−	0.146990i		−	0.0137069i
$116$	4.36315	−	1.33079i	0.405108	−	0.123560i
$117$	2.39974	+	0.188931i	0.221856	+	0.0174667i
$118$	−17.0101	−	12.5956i	−1.56591	−	1.15952i
$119$	5.70093			0.522604
$120$	−2.49027	+	6.22367i	−0.227329	+	0.568140i
$121$	0.826299			0.0751181
$122$	−13.5566	−	10.0383i	−1.22735	−	0.908823i
$123$	13.5165	+	0.531254i	1.21874	+	0.0479016i
$124$	−12.0916	+	3.68800i	−1.08585	+	0.331192i
$125$		−	11.1213i		−	0.994720i
$126$	3.14489	−	3.61516i	0.280169	−	0.322064i
$127$			5.03184i			0.446503i	0.974761	+	0.223252i	$0.0716672\pi$
$127$			5.03184i			0.446503i	−0.974761	+	0.223252i	$0.928333\pi$
$128$	−2.80731	−	10.9599i	−0.248134	−	0.968726i
$129$	7.62240	+	0.299592i	0.671115	+	0.0263776i
$130$	−0.923996	+	1.24784i	−0.0810398	+	0.109443i
$131$	−1.79824			−0.157113			−0.0785565	−	0.996910i	$-0.525031\pi$
$131$	−1.79824			−0.157113			−0.0785565	+	0.996910i	$0.525031\pi$
$132$	−11.5223	+	3.02523i	−1.00289	+	0.263313i
$133$	1.12940			0.0979312
$134$	6.76576	−	9.13706i	0.584472	−	0.789322i
$135$	−7.06070	−	0.835991i	−0.607688	−	0.0719506i
$136$	13.4536	+	4.77921i	1.15363	+	0.409814i
$137$			5.47046i			0.467373i	0.972312	+	0.233686i	$0.0750789\pi$
$137$			5.47046i			0.467373i	−0.972312	+	0.233686i	$0.924921\pi$
$138$	−0.164772	+	0.205156i	−0.0140263	+	0.0174640i
$139$		−	1.79803i		−	0.152507i	−0.997088	−	0.0762537i	$-0.975704\pi$
$139$		−	1.79803i		−	0.152507i	0.997088	−	0.0762537i	$-0.0242959\pi$
$140$	0.901693	+	2.95631i	0.0762070	+	0.249854i
$141$	−0.403008	+	10.2536i	−0.0339394	+	0.863506i
$142$	−17.5173	−	12.9711i	−1.47002	−	1.08851i
$143$	−2.75936			−0.230749
$144$	10.4523	−	5.89494i	0.871021	−	0.491245i
$145$	−3.12086			−0.259173
$146$	−0.968815	−	0.717382i	−0.0801797	−	0.0593710i
$147$	−0.389403	+	9.90741i	−0.0321174	+	0.817149i
$148$	2.83811	+	9.30508i	0.233291	+	0.764873i
$149$			9.42605i			0.772212i	0.922454	+	0.386106i	$0.126180\pi$
$149$			9.42605i			0.772212i	−0.922454	+	0.386106i	$0.873820\pi$
$150$	−4.79742	+	5.97323i	−0.391707	+	0.487712i
$151$		−	5.26429i		−	0.428402i	−0.976790	−	0.214201i	$-0.931285\pi$
$151$		−	5.26429i		−	0.428402i	0.976790	−	0.214201i	$-0.0687148\pi$
$152$	2.66525	+	0.946798i	0.216181	+	0.0767955i
$153$	−1.18855	+	15.0966i	−0.0960888	+	1.22049i
$154$	−3.26865	+	4.41427i	−0.263395	+	0.355712i
$155$	8.64882			0.694690
$156$	2.68843	−	0.705860i	0.215247	−	0.0565140i
$157$	−2.12408			−0.169520			−0.0847601	−	0.996401i	$-0.527012\pi$
$157$	−2.12408			−0.169520			−0.0847601	+	0.996401i	$0.527012\pi$
$158$	−8.05068	+	10.8723i	−0.640477	+	0.864956i
$159$	−13.7697	−	0.541208i	−1.09201	−	0.0429206i
$160$	−0.350443	+	7.73247i	−0.0277050	+	0.611305i
$161$			0.121324i			0.00956165i
$162$	8.91760	+	9.08165i	0.700633	+	0.713522i
$163$			6.57484i			0.514982i	0.966281	+	0.257491i	$0.0828957\pi$
$163$			6.57484i			0.514982i	−0.966281	+	0.257491i	$0.917104\pi$
$164$	14.9401	−	4.55681i	1.16662	−	0.355827i
$165$	8.14402	+	0.320094i	0.634011	+	0.0249193i
$166$	−7.43428	−	5.50489i	−0.577012	−	0.427262i
$167$	16.0692			1.24347			0.621736	−	0.783227i	$-0.286428\pi$
$167$	16.0692			1.24347			0.621736	+	0.783227i	$0.286428\pi$
$168$	2.05544	−	5.13694i	0.158580	−	0.396323i
$169$	−12.3562			−0.950475
$170$	−7.85010	−	5.81279i	−0.602075	−	0.445821i
$171$	−0.235461	+	2.99075i	−0.0180062	+	0.228708i
$172$	8.42520	−	2.56974i	0.642416	−	0.195941i
$173$			17.8939i			1.36045i	0.733004	+	0.680225i	$0.238118\pi$
$173$			17.8939i			1.36045i	−0.733004	+	0.680225i	$0.761882\pi$
$174$	4.35583	+	3.49840i	0.330215	+	0.265213i
$175$			3.53241i			0.267025i
$176$	−11.4142	+	7.67700i	−0.860379	+	0.578676i
$177$	1.01809	−	25.9028i	0.0765241	−	1.94697i
$178$	3.86130	−	5.21463i	0.289417	−	0.390853i
$179$	15.5836			1.16477			0.582385	−	0.812913i	$-0.302120\pi$
$179$	15.5836			1.16477			0.582385	+	0.812913i	$0.302120\pi$
$180$	−8.01656	+	1.77142i	−0.597519	+	0.132034i
$181$	−21.9590			−1.63220			−0.816101	−	0.577909i	$-0.803869\pi$
$181$	−21.9590			−1.63220			−0.816101	+	0.577909i	$0.803869\pi$
$182$	0.762655	−	1.02996i	0.0565318	−	0.0763454i
$183$	0.811384	−	20.6437i	0.0599792	−	1.52603i
$184$	−0.101708	+	0.286310i	−0.00749803	+	0.0211071i
$185$		−	6.65571i		−	0.489338i
$186$	−12.0713	−	9.69509i	−0.885110	−	0.710878i
$187$		−	17.3589i		−	1.26941i
$188$	3.45678	+	11.3335i	0.252112	+	0.826579i
$189$	5.82782	+	0.690017i	0.423911	+	0.0501913i
$190$	−1.55516	−	1.15156i	−0.112823	−	0.0835428i
$191$	11.7977			0.853653			0.426826	−	0.904334i	$-0.359632\pi$
$191$	11.7977			0.853653			0.426826	+	0.904334i	$0.359632\pi$
$192$	9.15700	−	10.3995i	0.660850	−	0.750518i
$193$	25.8531			1.86094			0.930472	−	0.366362i	$-0.119397\pi$
$193$	25.8531			1.86094			0.930472	+	0.366362i	$0.119397\pi$
$194$	17.9708	+	13.3069i	1.29023	+	0.955379i
$195$	−1.90020	−	0.0746857i	−0.136076	−	0.00534835i
$196$	3.34008	+	10.9509i	0.238577	+	0.782205i
$197$		−	18.6480i		−	1.32861i	−0.747461	−	0.664306i	$-0.768727\pi$
$197$		−	18.6480i		−	1.32861i	0.747461	−	0.664306i	$-0.231273\pi$
$198$	−11.0079	−	9.57598i	−0.782298	−	0.680535i
$199$		−	15.8383i		−	1.12275i	−0.827562	−	0.561374i	$-0.810273\pi$
$199$		−	15.8383i		−	1.12275i	0.827562	−	0.561374i	$-0.189727\pi$
$200$	−2.96129	+	8.33609i	−0.209395	+	0.589450i
$201$	13.9138	+	0.546869i	0.981402	+	0.0385732i
$202$	11.5361	−	15.5794i	0.811678	−	1.09616i
$203$	2.57592			0.180794
$204$	4.44052	+	16.9127i	0.310898	+	1.18413i
$205$	−10.6863			−0.746363
$206$	−5.95269	+	8.03902i	−0.414743	+	0.560105i
$207$	−0.321276	−	0.0252940i	−0.0223302	−	0.00175806i
$208$	2.66321	−	1.79123i	0.184661	−	0.124199i
$209$		−	3.43894i		−	0.237876i
$210$	−2.37039	+	2.95135i	−0.163572	+	0.203663i
$211$			10.8704i			0.748348i	0.927359	+	0.374174i	$0.122074\pi$
$211$			10.8704i			0.748348i	−0.927359	+	0.374174i	$0.877926\pi$
$212$	−15.2200	+	4.64219i	−1.04531	+	0.318827i
$213$	1.04844	−	26.6751i	0.0718381	−	1.82775i
$214$	−9.52817	−	7.05536i	−0.651332	−	0.482295i
$215$	−6.02636			−0.410994
$216$	13.1745	+	6.51395i	0.896414	+	0.443218i
$217$	−7.13863			−0.484602
$218$	−12.7889	−	9.46983i	−0.866172	−	0.641378i
$219$	0.0579853	−	1.47530i	0.00391828	−	0.0996912i
$220$	9.00176	−	2.74559i	0.606899	−	0.185108i
$221$			4.05026i			0.272450i
$222$	−7.46087	+	9.28948i	−0.500741	+	0.623469i
$223$		−	15.3139i		−	1.02550i	−0.858539	−	0.512748i	$-0.828628\pi$
$223$		−	15.3139i		−	1.02550i	0.858539	−	0.512748i	$-0.171372\pi$
$224$	0.289252	−	6.38229i	0.0193264	−	0.426435i
$225$	−9.35413	−	0.736450i	−0.623608	−	0.0490967i
$226$	−15.1346	+	20.4390i	−1.00674	+	1.35959i
$227$	13.8455			0.918961			0.459480	−	0.888188i	$-0.348036\pi$
$227$	13.8455			0.918961			0.459480	+	0.888188i	$0.348036\pi$
$228$	0.879700	+	3.35054i	0.0582595	+	0.221895i
$229$	22.3746			1.47856			0.739278	−	0.673400i	$-0.235167\pi$
$229$	22.3746			1.47856			0.739278	+	0.673400i	$0.235167\pi$
$230$	0.123704	−	0.167061i	0.00815681	−	0.0110157i
$231$	−6.72198	−	0.264202i	−0.442274	−	0.0173832i
$232$	6.07889	+	2.15945i	0.399098	+	0.141775i
$233$		−	8.59752i		−	0.563243i	−0.959526	−	0.281621i	$-0.909128\pi$
$233$		−	8.59752i		−	0.563243i	0.959526	−	0.281621i	$-0.0908722\pi$
$234$	2.56841	+	2.23431i	0.167902	+	0.146061i
$235$		−	8.10659i		−	0.528816i
$236$	−8.73259	−	28.6309i	−0.568444	−	1.86371i
$237$	−16.5562	−	0.650728i	−1.07544	−	0.0422693i
$238$	6.47938	+	4.79781i	0.419996	+	0.310996i
$239$	−14.2761			−0.923443			−0.461721	−	0.887025i	$-0.652768\pi$
$239$	−14.2761			−0.923443			−0.461721	+	0.887025i	$0.652768\pi$
$240$	−8.06803	+	4.97772i	−0.520789	+	0.321310i
$241$	4.64138			0.298978			0.149489	−	0.988763i	$-0.452237\pi$
$241$	4.64138			0.298978			0.149489	+	0.988763i	$0.452237\pi$
$242$	0.939127	+	0.695399i	0.0603694	+	0.0447020i
$243$	−3.04223	+	15.2887i	−0.195159	+	0.980772i
$244$	−6.95961	−	22.8179i	−0.445543	−	1.46077i
$245$		−	7.83291i		−	0.500427i
$246$	14.9150	+	11.9790i	0.950946	+	0.763755i
$247$			0.802387i			0.0510547i
$248$	−16.8464	−	5.98447i	−1.06975	−	0.380014i
$249$	0.444955	−	11.3208i	0.0281979	−	0.717427i
$250$	9.35951	−	12.6399i	0.591947	−	0.799417i
$251$	−13.5225			−0.853535			−0.426768	−	0.904361i	$-0.640348\pi$
$251$	−13.5225			−0.853535			−0.426768	+	0.904361i	$0.640348\pi$
$252$	6.61677	−	1.46211i	0.416818	−	0.0921042i
$253$	0.369422			0.0232254
$254$	−4.23471	+	5.71892i	−0.265709	+	0.358837i
$255$	0.469842	−	11.9540i	0.0294227	−	0.748589i
$256$	6.03301	−	14.8190i	0.377063	−	0.926188i
$257$		−	2.97819i		−	0.185774i	−0.995677	−	0.0928872i	$-0.970390\pi$
$257$		−	2.97819i		−	0.185774i	0.995677	−	0.0928872i	$-0.0296096\pi$
$258$	8.41108	+	6.75538i	0.523651	+	0.420572i
$259$			5.49355i			0.341352i
$260$	−2.10033	+	0.640613i	−0.130257	+	0.0397291i
$261$	−0.537038	+	6.82127i	−0.0332418	+	0.422226i
$262$	−2.04379	−	1.51337i	−0.126265	−	0.0934963i
$263$	21.4255			1.32116			0.660578	−	0.750758i	$-0.270311\pi$
$263$	21.4255			1.32116			0.660578	+	0.750758i	$0.270311\pi$
$264$	−15.6416	−	6.25866i	−0.962675	−	0.385194i
$265$	10.8865			0.668754
$266$	1.28361	+	0.950482i	0.0787034	+	0.0582778i
$267$	7.94076	+	0.312105i	0.485966	+	0.0191005i
$268$	15.3792	−	4.69075i	0.939434	−	0.286533i
$269$		−	25.7470i		−	1.56982i	−0.619610	−	0.784910i	$-0.712709\pi$
$269$		−	25.7470i		−	1.56982i	0.619610	−	0.784910i	$-0.287291\pi$
$270$	−7.32126	−	6.89231i	−0.445558	−	0.419453i
$271$			20.6518i			1.25451i	0.778814	+	0.627255i	$0.215821\pi$
$271$			20.6518i			1.25451i	−0.778814	+	0.627255i	$0.784179\pi$
$272$	11.2685	+	16.7541i	0.683253	+	1.01587i
$273$	1.56840	+	0.0616447i	0.0949238	+	0.00373090i
$274$	−4.60385	+	6.21743i	−0.278128	+	0.375609i
$275$	10.7559			0.648607
$276$	−0.359926	+	0.0945003i	−0.0216650	+	0.00568825i
$277$	−2.00519			−0.120480			−0.0602401	−	0.998184i	$-0.519187\pi$
$277$	−2.00519			−0.120480			−0.0602401	+	0.998184i	$0.519187\pi$
$278$	1.51320	−	2.04355i	0.0907554	−	0.122564i
$279$	1.48829	−	18.9037i	0.0891016	−	1.13174i
$280$	−1.46317	+	4.11883i	−0.0874408	+	0.246147i
$281$			23.7396i			1.41618i	0.706120	+	0.708092i	$0.250444\pi$
$281$			23.7396i			1.41618i	−0.706120	+	0.708092i	$0.749556\pi$
$282$	−9.08726	+	11.3145i	−0.541139	+	0.673768i
$283$			5.21899i			0.310237i	0.987896	+	0.155118i	$0.0495759\pi$
$283$			5.21899i			0.310237i	−0.987896	+	0.155118i	$0.950424\pi$
$284$	−8.99297	−	29.4846i	−0.533635	−	1.74959i
$285$	0.0930793	−	2.36818i	0.00551354	−	0.140279i
$286$	−3.13614	−	2.32223i	−0.185444	−	0.137316i
$287$	8.82033			0.520648
$288$	16.8406	+	2.09657i	0.992339	+	0.123541i
$289$	−8.47991			−0.498819
$290$	−3.54700	−	2.62646i	−0.208287	−	0.154231i
$291$	−1.07558	+	27.3656i	−0.0630518	+	1.60420i
$292$	−0.497366	−	1.63068i	−0.0291062	−	0.0954281i
$293$			17.3059i			1.01102i	0.862820	+	0.505511i	$0.168696\pi$
$293$			17.3059i			1.01102i	−0.862820	+	0.505511i	$0.831304\pi$
$294$	−8.78048	+	10.9325i	−0.512088	+	0.637597i
$295$			20.4790i			1.19234i
$296$	−4.60536	+	12.9642i	−0.267681	+	0.753526i
$297$	2.10105	−	17.7453i	0.121915	−	1.02969i
$298$	−7.93281	+	10.7131i	−0.459535	+	0.620596i
$299$	−0.0861951			−0.00498479
$300$	−10.4795	+	2.75143i	−0.605032	+	0.158854i
$301$	4.97408			0.286701
$302$	4.43034	−	5.98311i	0.254937	−	0.344289i
$303$	23.7240	+	0.932453i	1.36291	+	0.0535680i
$304$	2.23237	+	3.31911i	0.128035	+	0.190364i
$305$			16.3212i			0.934547i
$306$	−14.0559	+	16.1577i	−0.803521	+	0.923674i
$307$		−	22.6546i		−	1.29297i	−0.762928	−	0.646484i	$-0.776239\pi$
$307$		−	22.6546i		−	1.29297i	0.762928	−	0.646484i	$-0.223761\pi$
$308$	−7.42995	+	2.26618i	−0.423361	+	0.129128i
$309$	−12.2417	−	0.481150i	−0.696406	−	0.0273717i
$310$	9.82979	+	7.27870i	0.558294	+	0.413402i
$311$	10.3915			0.589249			0.294625	−	0.955613i	$-0.404805\pi$
$311$	10.3915			0.589249			0.294625	+	0.955613i	$0.404805\pi$
$312$	3.64957	+	1.46030i	0.206616	+	0.0826730i
$313$	−3.09254			−0.174801			−0.0874005	−	0.996173i	$-0.527856\pi$
$313$	−3.09254			−0.174801			−0.0874005	+	0.996173i	$0.527856\pi$
$314$	−2.41412	−	1.78759i	−0.136237	−	0.100880i
$315$	−4.62184	−	0.363878i	−0.260411	−	0.0205022i
$316$	−18.2999	+	5.58159i	−1.02945	+	0.313989i
$317$			16.1095i			0.904801i	0.891815	+	0.452400i	$0.149432\pi$
$317$			16.1095i			0.904801i	−0.891815	+	0.452400i	$0.850568\pi$
$318$	−15.1945	−	12.2035i	−0.852064	−	0.684338i
$319$		−	7.84350i		−	0.439152i
$320$	−6.90581	+	8.49339i	−0.386047	+	0.474795i
$321$	0.570278	−	14.5093i	0.0318298	−	0.809833i
$322$	−0.102104	+	0.137890i	−0.00569003	+	0.00768431i
$323$	−5.04776			−0.280865
$324$	2.49230	+	17.8266i	0.138461	+	0.990368i
$325$	−2.50962			−0.139209
$326$	−5.53328	+	7.47262i	−0.306460	+	0.413870i
$327$	0.765437	−	19.4747i	0.0423287	−	1.07695i
$328$	20.8150	+	7.39427i	1.14932	+	0.408280i
$329$			6.69108i			0.368891i
$330$	8.98667	+	7.21767i	0.494700	+	0.397320i
$331$			11.6544i			0.640585i	0.947319	+	0.320292i	$0.103781\pi$
$331$			11.6544i			0.640585i	−0.947319	+	0.320292i	$0.896219\pi$
$332$	−3.81658	−	12.5131i	−0.209462	−	0.686747i
$333$	−14.5474	−	1.14532i	−0.797192	−	0.0627630i
$334$	18.2634	+	13.5236i	0.999328	+	0.739977i
$335$	−11.0004			−0.601016
$336$	6.65926	−	4.10855i	0.363292	−	0.224140i
$337$	0.524512			0.0285720			0.0142860	−	0.999898i	$-0.495452\pi$
$337$	0.524512			0.0285720			0.0142860	+	0.999898i	$0.495452\pi$
$338$	−14.0434	−	10.3987i	−0.763858	−	0.565617i
$339$	−31.1242	−	1.22331i	−1.69044	−	0.0664413i
$340$	−4.03005	−	13.2130i	−0.218560	−	0.716577i
$341$			21.7366i			1.17711i
$342$	−2.78457	+	3.20096i	−0.150572	+	0.173088i
$343$			14.3710i			0.775960i
$344$	11.7383	+	4.16988i	0.632886	+	0.224825i
$345$	0.254398	+	0.00999889i	0.0136963	+	0.000538322i
$346$	−15.0592	+	20.3373i	−0.809589	+	1.09334i
$347$	22.1557			1.18938			0.594689	−	0.803955i	$-0.297275\pi$
$347$	22.1557			1.18938			0.594689	+	0.803955i	$0.297275\pi$
$348$	2.00641	+	7.64189i	0.107555	+	0.409648i
$349$	5.40637			0.289397			0.144698	−	0.989476i	$-0.453779\pi$
$349$	5.40637			0.289397			0.144698	+	0.989476i	$0.453779\pi$
$350$	−2.97281	+	4.01475i	−0.158904	+	0.214597i
$351$	−0.490226	+	4.14041i	−0.0261664	+	0.220999i
$352$	−19.4336	−	0.880751i	−1.03582	−	0.0469442i
$353$			11.9419i			0.635602i	0.948158	+	0.317801i	$0.102944\pi$
$353$			11.9419i			0.635602i	−0.948158	+	0.317801i	$0.897056\pi$
$354$	22.9564	−	28.5829i	1.22012	−	1.51916i
$355$			21.0896i			1.11932i
$356$	8.77709	−	2.67707i	0.465185	−	0.141884i
$357$	−0.387802	+	9.86669i	−0.0205247	+	0.522201i
$358$	17.7114	+	13.1149i	0.936079	+	0.693142i
$359$	−25.4285			−1.34207			−0.671033	−	0.741428i	$-0.734149\pi$
$359$	−25.4285			−1.34207			−0.671033	+	0.741428i	$0.734149\pi$
$360$	−10.6020	−	4.73330i	−0.558774	−	0.249467i
$361$	−1.00000			−0.0526316
$362$	−24.9575	−	18.4804i	−1.31174	−	0.971306i
$363$	−0.0562084	+	1.43009i	−0.00295018	+	0.0750601i
$364$	1.73359	−	0.528754i	0.0908646	−	0.0277143i
$365$			1.16639i			0.0610514i
$366$	18.2956	−	22.7797i	0.956324	−	1.19071i
$367$		−	8.23574i		−	0.429902i	−0.976625	−	0.214951i	$-0.931041\pi$
$367$		−	8.23574i		−	0.429902i	0.976625	−	0.214951i	$-0.0689592\pi$
$368$	−0.356550	+	0.239809i	−0.0185865	+	0.0125009i
$369$	−1.83890	+	23.3570i	−0.0957292	+	1.21592i
$370$	5.60134	−	7.56453i	0.291200	−	0.393261i
$371$	−8.98561			−0.466509
$372$	−5.56035	−	21.1779i	−0.288291	−	1.09802i
$373$	5.41410			0.280331			0.140166	−	0.990128i	$-0.455236\pi$
$373$	5.41410			0.280331			0.140166	+	0.990128i	$0.455236\pi$
$374$	14.6090	−	19.7293i	0.755413	−	1.02018i
$375$	19.2478	+	0.756520i	0.993953	+	0.0390665i
$376$	−5.60928	+	15.7902i	−0.289276	+	0.814318i
$377$			1.83008i			0.0942538i
$378$	6.04288	+	5.68883i	0.310812	+	0.292602i
$379$			6.47709i			0.332706i	0.986066	+	0.166353i	$0.0531991\pi$
$379$			6.47709i			0.332706i	−0.986066	+	0.166353i	$0.946801\pi$
$380$	−0.798384	−	2.61760i	−0.0409562	−	0.134280i
$381$	−8.70867	−	0.342287i	−0.446159	−	0.0175359i
$382$	13.4087	+	9.92876i	0.686046	+	0.507999i
$383$	−25.5811			−1.30713			−0.653565	−	0.756870i	$-0.726728\pi$
$383$	−25.5811			−1.30713			−0.653565	+	0.756870i	$0.726728\pi$
$384$	19.1594	−	4.11312i	0.977724	−	0.209897i
$385$	5.31447			0.270851
$386$	29.3832	+	21.7575i	1.49557	+	1.10743i
$387$	−1.03702	+	13.1718i	−0.0527145	+	0.669561i
$388$	9.22577	+	30.2478i	0.468368	+	1.53560i
$389$			33.2921i			1.68798i	0.536362	+	0.843988i	$0.319798\pi$
$389$			33.2921i			1.68798i	−0.536362	+	0.843988i	$0.680202\pi$
$390$	−2.09681	−	1.68406i	−0.106176	−	0.0852755i
$391$		−	0.542248i		−	0.0274226i
$392$	−5.41991	+	15.2571i	−0.273747	+	0.770602i
$393$	0.122324	−	3.11224i	0.00617044	−	0.156992i
$394$	15.6938	−	21.1943i	0.790642	−	1.06775i
$395$	13.0895			0.658606
$396$	−4.45202	−	20.1476i	−0.223722	−	1.01246i
$397$	−10.2310			−0.513477			−0.256738	−	0.966481i	$-0.582648\pi$
$397$	−10.2310			−0.513477			−0.256738	+	0.966481i	$0.582648\pi$
$398$	13.3292	−	18.0010i	0.668135	−	0.902307i
$399$	−0.0768266	+	1.95467i	−0.00384614	+	0.0978557i
$400$	−10.3812	+	6.98218i	−0.519058	+	0.349109i
$401$		−	24.8153i		−	1.23921i	−0.784912	−	0.619607i	$-0.787292\pi$
$401$		−	24.8153i		−	1.23921i	0.784912	−	0.619607i	$-0.212708\pi$
$402$	15.3534	+	12.3311i	0.765758	+	0.615021i
$403$		−	5.07168i		−	0.252639i
$404$	26.2227	−	7.99807i	1.30463	−	0.397919i
$405$	1.92716	−	12.1632i	0.0957614	−	0.604394i
$406$	2.92765	+	2.16785i	0.145297	+	0.107589i
$407$	16.7275			0.829150
$408$	−9.18662	+	22.9592i	−0.454806	+	1.13665i
$409$	13.3037			0.657828			0.328914	−	0.944360i	$-0.393317\pi$
$409$	13.3037			0.657828			0.328914	+	0.944360i	$0.393317\pi$
$410$	−12.1455	−	8.99340i	−0.599822	−	0.444152i
$411$	−9.46780	−	0.372124i	−0.467012	−	0.0183555i
$412$	−13.5310	+	4.12704i	−0.666625	+	0.203325i
$413$		−	16.9031i		−	0.831749i
$414$	−0.343858	−	0.299128i	−0.0168997	−	0.0147013i
$415$			8.95036i			0.439356i
$416$	4.53433	+	0.205500i	0.222314	+	0.0100755i
$417$	3.11188	+	0.122310i	0.152390	+	0.00598955i
$418$	2.89415	−	3.90851i	0.141558	−	0.191172i
$419$	−6.25303			−0.305481			−0.152740	−	0.988266i	$-0.548810\pi$
$419$	−6.25303			−0.305481			−0.152740	+	0.988266i	$0.548810\pi$
$420$	−5.17787	+	1.35947i	−0.252654	+	0.0663355i
$421$	11.5310			0.561986			0.280993	−	0.959710i	$-0.409336\pi$
$421$	11.5310			0.561986			0.280993	+	0.959710i	$0.409336\pi$
$422$	−9.14833	+	12.3547i	−0.445334	+	0.601417i
$423$	−17.7186	−	1.39498i	−0.861506	−	0.0678264i
$424$	−21.2050	−	7.53282i	−1.02981	−	0.365826i
$425$		−	15.7878i		−	0.765823i
$426$	23.6409	−	29.4351i	1.14541	−	1.42614i
$427$		−	13.4713i		−	0.651921i
$428$	−4.89153	−	16.0375i	−0.236441	−	0.775202i
$429$	0.187704	−	4.77567i	0.00906242	−	0.230571i
$430$	−6.84924	−	5.07168i	−0.330299	−	0.244578i
$431$	−9.96360			−0.479930			−0.239965	−	0.970782i	$-0.577136\pi$
$431$	−9.96360			−0.479930			−0.239965	+	0.970782i	$0.577136\pi$
$432$	9.49145	+	18.4909i	0.456658	+	0.889642i
$433$	38.5044			1.85040			0.925201	−	0.379476i	$-0.123896\pi$
$433$	38.5044			1.85040			0.925201	+	0.379476i	$0.123896\pi$
$434$	−8.11339	−	6.00775i	−0.389455	−	0.288381i
$435$	0.212294	−	5.40132i	0.0101787	−	0.258973i
$436$	−6.56550	−	21.5258i	−0.314430	−	1.03090i
$437$		−	0.107423i		−	0.00513875i
$438$	1.30749	−	1.62794i	0.0624741	−	0.0777861i
$439$		−	10.1838i		−	0.486045i	−0.970021	−	0.243022i	$-0.921861\pi$
$439$		−	10.1838i		−	0.486045i	0.970021	−	0.243022i	$-0.0781388\pi$
$440$	12.5416	+	4.45524i	0.597896	+	0.212395i
$441$	−17.1204	−	1.34789i	−0.815257	−	0.0641852i
$442$	−3.40863	+	4.60331i	−0.162132	+	0.218957i
$443$	−25.9029			−1.23069			−0.615343	−	0.788259i	$-0.710983\pi$
$443$	−25.9029			−1.23069			−0.615343	+	0.788259i	$0.710983\pi$
$444$	−16.2975	+	4.27898i	−0.773445	+	0.203071i
$445$	−6.27806			−0.297608
$446$	12.8879	−	17.4050i	0.610261	−	0.824149i
$447$	−16.3138	−	0.641201i	−0.771617	−	0.0303278i
$448$	5.69997	−	7.01034i	0.269299	−	0.331207i
$449$			5.46392i			0.257858i	0.991654	+	0.128929i	$0.0411540\pi$
$449$			5.46392i			0.257858i	−0.991654	+	0.128929i	$0.958846\pi$
$450$	−10.0116	−	8.70928i	−0.471952	−	0.410560i
$451$		−	26.8573i		−	1.26466i
$452$	−34.4023	+	10.4929i	−1.61815	+	0.493545i
$453$	9.11099	+	0.358100i	0.428072	+	0.0168250i
$454$	15.7361	+	11.6522i	0.738532	+	0.546864i
$455$	−1.24000			−0.0581319
$456$	−1.81994	+	4.54839i	−0.0852265	+	0.212998i
$457$	−21.9539			−1.02696			−0.513480	−	0.858101i	$-0.671644\pi$
$457$	−21.9539			−1.02696			−0.513480	+	0.858101i	$0.671644\pi$
$458$	25.4298	+	18.8301i	1.18826	+	0.879873i
$459$	−26.0470	−	3.08398i	−1.21577	−	0.143948i
$460$	0.281191	−	0.0857650i	0.0131106	−	0.00399882i
$461$			10.3838i			0.483621i	0.970323	+	0.241810i	$0.0777412\pi$
$461$			10.3838i			0.483621i	−0.970323	+	0.241810i	$0.922259\pi$
$462$	−7.41749	−	5.95738i	−0.345093	−	0.277162i
$463$			14.5651i			0.676897i	0.940985	+	0.338449i	$0.109902\pi$
$463$			14.5651i			0.676897i	−0.940985	+	0.338449i	$0.890098\pi$
$464$	5.09158	+	7.57020i	0.236371	+	0.351438i
$465$	−0.588330	+	14.9686i	−0.0272832	+	0.694154i
$466$	7.23553	−	9.77149i	0.335180	−	0.452655i
$467$	−17.3138			−0.801189			−0.400595	−	0.916255i	$-0.631196\pi$
$467$	−17.3138			−0.801189			−0.400595	+	0.916255i	$0.631196\pi$
$468$	1.03876	+	4.70092i	0.0480168	+	0.217300i
$469$	9.07959			0.419257
$470$	6.82237	−	9.21352i	0.314692	−	0.424988i
$471$	0.144489	−	3.67618i	0.00665771	−	0.169389i
$472$	14.1703	−	39.8895i	0.652239	−	1.83606i
$473$		−	15.1457i		−	0.696402i
$474$	−18.2693	−	14.6730i	−0.839135	−	0.673953i
$475$		−	3.12769i		−	0.143508i
$476$	3.32636	+	10.9059i	0.152463	+	0.499870i
$477$	1.87335	−	23.7947i	0.0857750	−	1.08948i
$478$	−16.2254	−	12.0145i	−0.742134	−	0.549531i
$479$	0.700592			0.0320109			0.0160054	−	0.999872i	$-0.494905\pi$
$479$	0.700592			0.0320109			0.0160054	+	0.999872i	$0.494905\pi$
$480$	−13.3589	−	1.13251i	−0.609746	−	0.0516919i
$481$	−3.90292			−0.177958
$482$	5.27515	+	3.90611i	0.240276	+	0.177918i
$483$	−0.209977	−	0.00825296i	−0.00955427	−	0.000375523i
$484$	0.482125	+	1.58071i	0.0219148	+	0.0718503i
$485$		−	21.6356i		−	0.982421i
$486$	−16.3244	+	14.8160i	−0.740488	+	0.672069i
$487$			17.7674i			0.805116i	0.915395	+	0.402558i	$0.131879\pi$
$487$			17.7674i			0.805116i	−0.915395	+	0.402558i	$0.868121\pi$
$488$	11.2933	−	31.7907i	0.511222	−	1.43910i
$489$	−11.3792	−	0.447249i	−0.514584	−	0.0202253i
$490$	6.59205	−	8.90247i	0.297798	−	0.402173i
$491$	26.0657			1.17633			0.588165	−	0.808741i	$-0.299851\pi$
$491$	26.0657			1.17633			0.588165	+	0.808741i	$0.299851\pi$
$492$	6.87025	+	26.1669i	0.309735	+	1.17970i
$493$	−11.5129			−0.518515
$494$	−0.675276	+	0.911951i	−0.0303821	+	0.0410306i
$495$	−1.10798	+	14.0732i	−0.0498001	+	0.632543i
$496$	−14.1103	−	20.9792i	−0.633569	−	0.941996i
$497$		−	17.4071i		−	0.780817i
$498$	10.0331	−	12.4922i	0.449594	−	0.559787i
$499$		−	22.1045i		−	0.989535i	−0.869025	−	0.494768i	$-0.835253\pi$
$499$		−	22.1045i		−	0.989535i	0.869025	−	0.494768i	$-0.164747\pi$
$500$	21.2750	−	6.48902i	0.951448	−	0.290198i
$501$	−1.09310	+	27.8112i	−0.0488359	+	1.24251i
$502$	−15.3690	−	11.3803i	−0.685952	−	0.507929i
$503$	−41.0703			−1.83124			−0.915618	−	0.402050i	$-0.868298\pi$
$503$	−41.0703			−1.83124			−0.915618	+	0.402050i	$0.868298\pi$
$504$	8.75076	+	3.90681i	0.389790	+	0.174023i
$505$	−18.7565			−0.834653
$506$	0.419866	+	0.310900i	0.0186653	+	0.0138212i
$507$	0.840520	−	21.3850i	0.0373288	−	0.949742i
$508$	−9.62589	+	2.93596i	−0.427080	+	0.130262i
$509$			34.6206i			1.53453i	0.641331	+	0.767265i	$0.278383\pi$
$509$			34.6206i			1.53453i	−0.641331	+	0.767265i	$0.721617\pi$
$510$	10.5943	−	13.1909i	0.469123	−	0.584101i
$511$		−	0.962721i		−	0.0425883i
$512$	19.3282	−	11.7652i	0.854195	−	0.519954i
$513$	−5.16011	−	0.610960i	−0.227824	−	0.0269745i
$514$	2.50640	−	3.38485i	0.110552	−	0.149299i
$515$	9.67843			0.426483
$516$	3.87436	+	14.7564i	0.170559	+	0.649615i
$517$	20.3739			0.896042
$518$	−4.62328	+	6.24367i	−0.203135	+	0.274331i
$519$	−30.9693	−	1.21722i	−1.35940	−	0.0534301i
$520$	−2.92625	−	1.03951i	−0.128325	−	0.0455857i
$521$		−	12.4839i		−	0.546929i	−0.961882	−	0.273465i	$-0.911830\pi$
$521$		−	12.4839i		−	0.546929i	0.961882	−	0.273465i	$-0.0881697\pi$
$522$	−6.35103	+	7.30072i	−0.277977	+	0.319544i
$523$		−	12.5001i		−	0.546593i	−0.961930	−	0.273296i	$-0.911886\pi$
$523$		−	12.5001i		−	0.546593i	0.961930	−	0.273296i	$-0.0881139\pi$
$524$	−1.04923	−	3.44003i	−0.0458358	−	0.150278i
$525$	−6.11359	−	0.240290i	−0.266819	−	0.0104871i
$526$	24.3511	+	18.0314i	1.06176	+	0.786205i
$527$	31.9056			1.38983
$528$	−12.5102	−	20.2770i	−0.544439	−	0.882442i
$529$	−22.9885			−0.999498
$530$	12.3730	+	9.16191i	0.537450	+	0.397968i
$531$	44.7610	+	3.52403i	1.94246	+	0.152930i
$532$	0.658976	+	2.16053i	0.0285703	+	0.0936711i
$533$			6.26646i			0.271430i
$534$	8.76238	+	7.03753i	0.379185	+	0.304544i
$535$			11.4713i			0.495946i
$536$	21.4268	+	7.61161i	0.925498	+	0.328772i
$537$	−1.06006	+	26.9707i	−0.0457450	+	1.16387i
$538$	21.6682	−	29.2626i	0.934183	−	1.26160i
$539$	19.6861			0.847939
$540$	−2.52050	−	13.9949i	−0.108465	−	0.602244i
$541$	12.1887			0.524032			0.262016	−	0.965064i	$-0.415613\pi$
$541$	12.1887			0.524032			0.262016	+	0.965064i	$0.415613\pi$
$542$	−17.3802	+	23.4718i	−0.746545	+	1.00820i
$543$	1.49375	−	38.0048i	0.0641029	−	1.63094i
$544$	−1.29279	+	28.5252i	−0.0554279	+	1.22301i
$545$			15.3969i			0.659532i
$546$	1.73068	+	1.39000i	0.0740662	+	0.0594865i
$547$		−	29.6447i		−	1.26752i	−0.773531	−	0.633759i	$-0.781511\pi$
$547$		−	29.6447i		−	1.26752i	0.773531	−	0.633759i	$-0.218489\pi$
$548$	−10.4650	+	3.19188i	−0.447041	+	0.136350i
$549$	35.6732	+	2.80855i	1.52249	+	0.119866i
$550$	12.2246	+	9.05201i	0.521260	+	0.385979i
$551$	−2.28079			−0.0971650
$552$	−0.488603	−	0.195504i	−0.0207963	−	0.00832120i
$553$	−10.8039			−0.459431
$554$	−2.27899	−	1.68753i	−0.0968250	−	0.0716964i
$555$	11.5191	+	0.452750i	0.488960	+	0.0192182i
$556$	3.43963	−	1.04911i	0.145873	−	0.0444922i
$557$		−	16.5845i		−	0.702710i	−0.936242	−	0.351355i	$-0.885721\pi$
$557$		−	16.5845i		−	0.702710i	0.936242	−	0.351355i	$-0.114279\pi$
$558$	17.6006	−	20.2324i	0.745091	−	0.856508i
$559$			3.53387i			0.149467i
$560$	−5.12930	+	3.44987i	−0.216752	+	0.145784i
$561$	30.0434	+	1.18083i	1.26843	+	0.0498547i
$562$	−19.9788	+	26.9811i	−0.842756	+	1.13813i
$563$	2.60303			0.109704			0.0548522	−	0.998494i	$-0.482531\pi$
$563$	2.60303			0.109704			0.0548522	+	0.998494i	$0.482531\pi$
$564$	−19.8502	+	5.21175i	−0.835843	+	0.219454i
$565$	24.6072			1.03523
$566$	−4.39221	+	5.93162i	−0.184618	+	0.249325i
$567$	−1.59066	+	10.0394i	−0.0668013	+	0.421613i
$568$	14.5928	−	41.0789i	0.612299	−	1.72363i
$569$			38.7153i			1.62303i	0.584332	+	0.811515i	$0.301357\pi$
$569$			38.7153i			1.62303i	−0.584332	+	0.811515i	$0.698643\pi$
$570$	2.09881	−	2.61321i	0.0879094	−	0.109455i
$571$		−	30.3691i		−	1.27091i	−0.772139	−	0.635454i	$-0.780813\pi$
$571$		−	30.3691i		−	1.27091i	0.772139	−	0.635454i	$-0.219187\pi$
$572$	−1.61002	−	5.27865i	−0.0673183	−	0.220711i
$573$	−0.802532	+	20.4185i	−0.0335262	+	0.852994i
$574$	10.0247	+	7.42304i	0.418424	+	0.309832i
$575$	0.335987			0.0140116
$576$	17.3756	+	16.5556i	0.723985	+	0.689816i
$577$	−4.12264			−0.171628			−0.0858138	−	0.996311i	$-0.527349\pi$
$577$	−4.12264			−0.171628			−0.0858138	+	0.996311i	$0.527349\pi$
$578$	−9.63782	−	7.13655i	−0.400880	−	0.296841i
$579$	−1.75864	+	44.7443i	−0.0730865	+	1.85951i
$580$	−1.82095	−	5.97020i	−0.0756107	−	0.247899i
$581$		−	7.38752i		−	0.306486i
$582$	−24.2529	+	30.1971i	−1.00531	+	1.25171i
$583$			27.3605i			1.13316i
$584$	0.807070	−	2.27191i	0.0333968	−	0.0940125i
$585$	0.258519	−	3.28362i	0.0106884	−	0.135761i
$586$	−14.5644	+	19.6690i	−0.601649	+	0.812518i
$587$	−23.8952			−0.986260			−0.493130	−	0.869956i	$-0.664147\pi$
$587$	−23.8952			−0.986260			−0.493130	+	0.869956i	$0.664147\pi$
$588$	−19.1800	+	5.03581i	−0.790972	+	0.207673i
$589$	6.32074			0.260442
$590$	−17.2348	+	23.2754i	−0.709546	+	0.958232i
$591$	32.2743	+	1.26851i	1.32759	+	0.0521797i
$592$	−16.1446	+	10.8586i	−0.663540	+	0.446285i
$593$		−	24.1796i		−	0.992939i	−0.868054	−	0.496469i	$-0.834630\pi$
$593$		−	24.1796i		−	0.992939i	0.868054	−	0.496469i	$-0.165370\pi$
$594$	17.3221	−	18.4001i	0.710734	−	0.754967i
$595$		−	7.80072i		−	0.319799i
$596$	−18.0320	+	5.49987i	−0.738620	+	0.225284i
$597$	27.4116	+	1.07739i	1.12188	+	0.0440946i
$598$	−0.0979648	−	0.0725404i	−0.00400608	−	0.00296640i
$599$	28.2842			1.15566			0.577831	−	0.816157i	$-0.303899\pi$
$599$	28.2842			1.15566			0.577831	+	0.816157i	$0.303899\pi$
$600$	−14.2259	−	5.69221i	−0.580772	−	0.232383i
$601$	−19.0616			−0.777537			−0.388769	−	0.921335i	$-0.627099\pi$
$601$	−19.0616			−0.777537			−0.388769	+	0.921335i	$0.627099\pi$
$602$	5.65328	+	4.18611i	0.230410	+	0.170613i
$603$	−1.89295	+	24.0436i	−0.0770869	+	0.979129i
$604$	10.0706	−	3.07159i	0.409766	−	0.124981i
$605$		−	1.13064i		−	0.0459672i
$606$	26.1787	+	21.0255i	1.06344	+	0.854102i
$607$		−	15.7458i		−	0.639100i	−0.947569	−	0.319550i	$-0.896468\pi$
$607$		−	15.7458i		−	0.639100i	0.947569	−	0.319550i	$-0.103532\pi$
$608$	−0.256111	+	5.65105i	−0.0103867	+	0.229180i
$609$	−0.175225	+	4.45818i	−0.00710049	+	0.180655i
$610$	−13.7356	+	18.5498i	−0.556139	+	0.751058i
$611$	−4.75372			−0.192315
$612$	−29.5732	+	6.53479i	−1.19543	+	0.264153i
$613$	−11.9720			−0.483547			−0.241773	−	0.970333i	$-0.577729\pi$
$613$	−11.9720			−0.483547			−0.241773	+	0.970333i	$0.577729\pi$
$614$	19.0657	−	25.7480i	0.769431	−	1.03911i
$615$	0.726927	−	18.4949i	0.0293125	−	0.745787i
$616$	−10.3517	−	3.67730i	−0.417080	−	0.148163i
$617$			11.1361i			0.448323i	0.974552	+	0.224162i	$0.0719644\pi$
$617$			11.1361i			0.448323i	−0.974552	+	0.224162i	$0.928036\pi$
$618$	−13.5083	−	10.8493i	−0.543385	−	0.436421i
$619$			45.7557i			1.83907i	0.393002	+	0.919537i	$0.371436\pi$
$619$			45.7557i			1.83907i	−0.393002	+	0.919537i	$0.628564\pi$
$620$	5.04638	+	16.5452i	0.202667	+	0.664470i
$621$	0.0656313	−	0.554316i	0.00263370	−	0.0222439i
$622$	11.8104	+	8.74533i	0.473556	+	0.350656i
$623$	5.18183			0.207606
$624$	2.91894	+	4.73111i	0.116851	+	0.189396i
$625$	0.420897			0.0168359
$626$	−3.51482	−	2.60263i	−0.140481	−	0.104022i
$627$	5.95182	+	0.233931i	0.237693	+	0.00934232i
$628$	−1.23935	−	4.06336i	−0.0494555	−	0.162146i
$629$		−	24.5530i		−	0.978993i
$630$	−4.94671	−	4.30323i	−0.197082	−	0.171445i
$631$			35.6261i			1.41825i	0.705082	+	0.709126i	$0.250910\pi$
$631$			35.6261i			1.41825i	−0.705082	+	0.709126i	$0.749090\pi$
$632$	−25.4961	−	9.05718i	−1.01418	−	0.360275i
$633$	−18.8135	−	0.739450i	−0.747770	−	0.0293905i
$634$	−13.5575	+	18.3092i	−0.538437	+	0.727152i
$635$	6.88518			0.273230
$636$	−6.99898	−	26.6572i	−0.277528	−	1.05703i
$637$	−4.59323			−0.181991
$638$	6.60096	−	8.91450i	0.261334	−	0.352929i
$639$	46.0957	+	3.62911i	1.82352	+	0.143565i
$640$	−14.9967	+	3.84131i	−0.592795	+	0.151841i
$641$		−	5.69877i		−	0.225088i	−0.993647	−	0.112544i	$-0.964100\pi$
$641$		−	5.69877i		−	0.225088i	0.993647	−	0.112544i	$-0.0358999\pi$
$642$	12.8590	−	16.0106i	0.507503	−	0.631888i
$643$		−	17.4265i		−	0.687232i	−0.939110	−	0.343616i	$-0.888348\pi$
$643$		−	17.4265i		−	0.687232i	0.939110	−	0.343616i	$-0.111652\pi$
$644$	−0.232092	+	0.0707895i	−0.00914570	+	0.00278950i
$645$	0.409939	−	10.4299i	0.0161413	−	0.410677i
$646$	−5.73702	−	4.24811i	−0.225720	−	0.167140i
$647$	40.7809			1.60326			0.801632	−	0.597818i	$-0.203965\pi$
$647$	40.7809			1.60326			0.801632	+	0.597818i	$0.203965\pi$
$648$	−12.1700	+	22.3583i	−0.478082	+	0.878315i
$649$	−51.4689			−2.02033
$650$	−2.85230	−	2.11205i	−0.111876	−	0.0828415i
$651$	0.485601	−	12.3549i	0.0190322	−	0.484228i
$652$	−12.5777	+	3.83626i	−0.492579	+	0.150240i
$653$		−	39.4580i		−	1.54411i	−0.635556	−	0.772055i	$-0.719229\pi$
$653$		−	39.4580i		−	1.54411i	0.635556	−	0.772055i	$-0.280771\pi$
$654$	17.2595	−	21.4897i	0.674901	−	0.840314i
$655$			2.46058i			0.0961427i
$656$	17.4343	+	25.9215i	0.680696	+	1.01206i
$657$	2.54937	+	0.200712i	0.0994604	+	0.00783052i
$658$	−5.63110	+	7.60473i	−0.219523	+	0.296463i
$659$	−7.09777			−0.276490			−0.138245	−	0.990398i	$-0.544146\pi$
$659$	−7.09777			−0.276490			−0.138245	+	0.990398i	$0.544146\pi$
$660$	4.13950	+	15.7662i	0.161130	+	0.613700i
$661$	−28.2722			−1.09966			−0.549831	−	0.835276i	$-0.685308\pi$
$661$	−28.2722			−1.09966			−0.549831	+	0.835276i	$0.685308\pi$
$662$	−9.80816	+	13.2458i	−0.381205	+	0.514812i
$663$	−7.00985	−	0.275516i	−0.272240	−	0.0107002i
$664$	6.19312	−	17.4337i	0.240340	−	0.676560i
$665$		−	1.54538i		−	0.0599274i
$666$	−15.5699	−	13.5445i	−0.603322	−	0.524841i
$667$		−	0.245010i		−	0.00948683i
$668$	9.37599	+	30.7403i	0.362768	+	1.18938i
$669$	26.5040	+	1.04172i	1.02470	+	0.0402752i
$670$	−12.5025	−	9.25774i	−0.483012	−	0.357658i
$671$	−41.0191			−1.58353
$672$	11.0262	+	0.934763i	0.425347	+	0.0360593i
$673$	−10.0595			−0.387765			−0.193883	−	0.981025i	$-0.562108\pi$
$673$	−10.0595			−0.387765			−0.193883	+	0.981025i	$0.562108\pi$
$674$	0.596132	+	0.441420i	0.0229621	+	0.0170029i
$675$	1.91089	−	16.1392i	0.0735503	−	0.621199i
$676$	−7.20953	−	23.6373i	−0.277290	−	0.909128i
$677$		−	33.4267i		−	1.28469i	−0.766415	−	0.642346i	$-0.777961\pi$
$677$		−	33.4267i		−	1.28469i	0.766415	−	0.642346i	$-0.222039\pi$
$678$	−34.3446	−	27.5840i	−1.31900	−	1.05936i
$679$			17.8578i			0.685318i
$680$	6.53951	−	18.4088i	0.250779	−	0.705947i
$681$	−0.941834	+	23.9627i	−0.0360911	+	0.918252i
$682$	−18.2932	+	24.7047i	−0.700482	+	0.945992i
$683$	−18.7412			−0.717113			−0.358556	−	0.933508i	$-0.616731\pi$
$683$	−18.7412			−0.717113			−0.358556	+	0.933508i	$0.616731\pi$
$684$	−5.85867	+	1.29459i	−0.224012	+	0.0494999i
$685$	7.48536			0.286001
$686$	−12.0944	+	16.3333i	−0.461765	+	0.623608i
$687$	−1.52202	+	38.7241i	−0.0580686	+	1.47742i
$688$	9.83180	+	14.6180i	0.374834	+	0.557306i
$689$		−	6.38388i		−	0.243206i
$690$	0.280720	+	0.225461i	0.0106868	+	0.00858315i
$691$			2.19141i			0.0833651i	0.999131	+	0.0416825i	$0.0132718\pi$
$691$			2.19141i			0.0833651i	−0.999131	+	0.0416825i	$0.986728\pi$
$692$	−34.2310	+	10.4407i	−1.30127	+	0.396895i
$693$	0.914516	−	11.6158i	0.0347396	−	0.441250i
$694$	25.1810	+	18.6458i	0.955856	+	0.707786i
$695$	−2.46029			−0.0933242
$696$	−4.15090	+	10.3739i	−0.157340	+	0.393222i
$697$	−39.4218			−1.49321
$698$	6.14459	+	4.54991i	0.232576	+	0.172217i
$699$	14.8799	+	0.584841i	0.562808	+	0.0221207i
$700$	−6.75748	+	2.06107i	−0.255409	+	0.0779013i
$701$		−	11.8093i		−	0.446033i	−0.974815	−	0.223016i	$-0.928410\pi$
$701$		−	11.8093i		−	0.446033i	0.974815	−	0.223016i	$-0.0715903\pi$
$702$	−4.04166	+	4.29320i	−0.152543	+	0.162036i
$703$		−	4.86414i		−	0.183454i
$704$	−21.3460	−	17.3560i	−0.804507	−	0.654130i
$705$	14.0302	+	0.551445i	0.528408	+	0.0207686i
$706$	−10.0501	+	13.5725i	−0.378240	+	0.510807i
$707$	15.4814			0.582237
$708$	50.1459	−	13.1660i	1.88460	−	0.494810i
$709$	26.6332			1.00023			0.500116	−	0.865958i	$-0.333291\pi$
$709$	26.6332			1.00023			0.500116	+	0.865958i	$0.333291\pi$
$710$	−17.7487	+	23.9694i	−0.666097	+	0.899554i
$711$	2.25245	−	28.6098i	0.0844735	−	1.07295i
$712$	12.2285	+	4.34404i	0.458284	+	0.162800i
$713$			0.678995i			0.0254286i
$714$	−8.74440	+	10.8876i	−0.327251	+	0.407458i
$715$			3.77570i			0.141203i
$716$	9.09263	+	29.8113i	0.339807	+	1.11410i
$717$	0.971120	−	24.7078i	0.0362672	−	0.922730i
$718$	−28.9007	−	21.4002i	−1.07856	−	0.798648i
$719$	−10.8180			−0.403444			−0.201722	−	0.979443i	$-0.564654\pi$
$719$	−10.8180			−0.403444			−0.201722	+	0.979443i	$0.564654\pi$
$720$	−8.06619	−	14.3021i	−0.300609	−	0.533007i
$721$	−7.98846			−0.297506
$722$	−1.13655	−	0.841583i	−0.0422979	−	0.0313205i
$723$	−0.315727	+	8.03291i	−0.0117420	+	0.298747i
$724$	−12.8126	−	42.0076i	−0.476175	−	1.56120i
$725$		−	7.13361i		−	0.264936i
$726$	−1.26742	+	1.57806i	−0.0470384	+	0.0585672i
$727$			29.2470i			1.08471i	0.840149	+	0.542356i	$0.182467\pi$
$727$			29.2470i			1.08471i	−0.840149	+	0.542356i	$0.817533\pi$
$728$	2.41529	+	0.858003i	0.0895167	+	0.0317997i
$729$	−26.2535	−	6.30524i	−0.972350	−	0.233527i
$730$	−0.981611	+	1.32565i	−0.0363311	+	0.0490646i
$731$	−22.2313			−0.822255
$732$	39.9647	−	10.4929i	1.47714	−	0.387830i
$733$	6.48771			0.239629			0.119815	−	0.992796i	$-0.461770\pi$
$733$	6.48771			0.239629			0.119815	+	0.992796i	$0.461770\pi$
$734$	6.93106	−	9.36030i	0.255830	−	0.345495i
$735$	13.5565	+	0.532829i	0.500040	+	0.0196537i
$736$	−0.607055	−	0.0275123i	−0.0223763	−	0.00101412i
$737$		−	27.6467i		−	1.01838i
$738$	−21.7469	+	24.9988i	−0.800513	+	0.920217i
$739$		−	9.72923i		−	0.357896i	−0.983859	−	0.178948i	$-0.942731\pi$
$739$		−	9.72923i		−	0.357896i	0.983859	−	0.178948i	$-0.0572693\pi$
$740$	12.7324	−	3.88345i	0.468051	−	0.142758i
$741$	−1.38870	−	0.0545819i	−0.0510153	−	0.00200511i
$742$	−10.2126	−	7.56213i	−0.374915	−	0.277615i
$743$	0.606961			0.0222672			0.0111336	−	0.999938i	$-0.496456\pi$
$743$	0.606961			0.0222672			0.0111336	+	0.999938i	$0.496456\pi$
$744$	11.5034	−	28.7492i	0.421734	−	1.05400i
$745$	12.8979			0.472542
$746$	6.15337	+	4.55641i	0.225291	+	0.166822i
$747$	19.5628	+	1.54018i	0.715766	+	0.0563522i
$748$	33.2076	−	10.1285i	1.21419	−	0.370336i
$749$		−	9.46824i		−	0.345962i
$750$	21.2394	+	17.0585i	0.775552	+	0.622887i
$751$			5.25931i			0.191915i	0.995385	+	0.0959574i	$0.0305913\pi$
$751$			5.25931i			0.191915i	−0.995385	+	0.0959574i	$0.969409\pi$
$752$	−19.6640	+	13.2256i	−0.717071	+	0.482289i
$753$	0.919862	−	23.4037i	0.0335216	−	0.852877i
$754$	−1.54016	+	2.07997i	−0.0560894	+	0.0757480i
$755$	−7.20326			−0.262153
$756$	2.08039	+	11.5512i	0.0756631	+	0.420113i
$757$	47.8465			1.73901			0.869506	−	0.493923i	$-0.164438\pi$
$757$	47.8465			1.73901			0.869506	+	0.493923i	$0.164438\pi$
$758$	−5.45101	+	7.36152i	−0.197990	+	0.267382i
$759$	−0.0251297	+	0.639364i	−0.000912150	+	0.0232075i
$760$	1.29553	−	3.64693i	0.0469937	−	0.132288i
$761$		−	7.89858i		−	0.286323i	−0.989699	−	0.143162i	$-0.954273\pi$
$761$		−	7.89858i		−	0.286323i	0.989699	−	0.143162i	$-0.0457269\pi$
$762$	−9.60975	−	7.71810i	−0.348124	−	0.279597i
$763$		−	12.7084i		−	0.460076i
$764$	6.88368	+	22.5690i	0.249043	+	0.816517i
$765$	20.6570	+	1.62633i	0.746855	+	0.0587999i
$766$	−29.0741	−	21.5286i	−1.05049	−	0.777859i
$767$	12.0089			0.433618
$768$	25.2371	+	11.4495i	0.910664	+	0.413147i
$769$	33.1970			1.19712			0.598558	−	0.801080i	$-0.295741\pi$
$769$	33.1970			1.19712			0.598558	+	0.801080i	$0.295741\pi$
$770$	6.04015	+	4.47257i	0.217672	+	0.161180i
$771$	5.15440	+	0.202589i	0.185631	+	0.00729608i
$772$	15.0846	+	49.4568i	0.542908	+	1.77999i
$773$			26.0176i			0.935789i	0.883784	+	0.467895i	$0.154987\pi$
$773$			26.0176i			0.935789i	−0.883784	+	0.467895i	$0.845013\pi$
$774$	−12.2638	+	14.0976i	−0.440813	+	0.506729i
$775$			19.7693i			0.710135i
$776$	−14.9705	+	42.1423i	−0.537411	+	1.51282i
$777$	−9.50776	−	0.373695i	−0.341089	−	0.0134062i
$778$	−28.0181	+	37.8380i	−1.00450	+	1.35656i
$779$	−7.80977			−0.279814
$780$	−0.965845	−	3.67865i	−0.0345828	−	0.131717i
$781$	−53.0035			−1.89662
$782$	0.456346	−	0.616290i	0.0163189	−	0.0220385i
$783$	−11.7691	−	1.39347i	−0.420594	−	0.0497986i
$784$	−19.0001	+	12.7791i	−0.678576	+	0.456398i
$785$			2.90643i			0.103735i
$786$	2.75824	−	3.43426i	0.0983831	−	0.122496i
$787$			20.1466i			0.718148i	0.933309	+	0.359074i	$0.116907\pi$
$787$			20.1466i			0.718148i	−0.933309	+	0.359074i	$0.883093\pi$
$788$	35.6735	−	10.8806i	1.27081	−	0.387606i
$789$	−1.45746	+	37.0815i	−0.0518869	+	1.32014i
$790$	14.8769	+	11.0159i	0.529295	+	0.391929i
$791$	−20.3105			−0.722158
$792$	11.8960	−	26.6454i	0.422705	−	0.946805i
$793$	9.57075			0.339867
$794$	−11.6280	−	8.61020i	−0.412661	−	0.305564i
$795$	−0.740548	+	18.8415i	−0.0262645	+	0.668238i
$796$	30.2986	−	9.24127i	1.07391	−	0.327548i
$797$			14.3835i			0.509489i	0.967008	+	0.254745i	$0.0819914\pi$
$797$			14.3835i			0.509489i	−0.967008	+	0.254745i	$0.918009\pi$
$798$	−1.73233	+	2.15691i	−0.0613238	+	0.0763539i
$799$		−	29.9053i		−	1.05797i
$800$	−17.6747	−	0.801037i	−0.624897	−	0.0283209i
$801$	−1.08033	+	13.7220i	−0.0381716	+	0.484841i
$802$	20.8841	−	28.2037i	0.737443	−	0.995907i
$803$	−2.93142			−0.103448
$804$	7.07219	+	26.9361i	0.249417	+	0.949962i
$805$	0.166010			0.00585109
$806$	4.26824	−	5.76420i	0.150342	−	0.203035i
$807$	44.5606	+	1.75142i	1.56861	+	0.0616529i
$808$	36.5343	+	12.9784i	1.28527	+	0.456577i
$809$		−	28.6620i		−	1.00770i	−0.863790	−	0.503851i	$-0.831916\pi$
$809$		−	28.6620i		−	1.00770i	0.863790	−	0.503851i	$-0.168084\pi$
$810$	12.4266	−	12.2022i	0.436628	−	0.428740i
$811$		−	37.4566i		−	1.31528i	−0.753333	−	0.657639i	$-0.771555\pi$
$811$		−	37.4566i		−	1.31528i	0.753333	−	0.657639i	$-0.228445\pi$
$812$	1.50299	+	4.92773i	0.0527445	+	0.172929i
$813$	−35.7424	−	1.40483i	−1.25354	−	0.0492694i
$814$	19.0115	+	14.0776i	0.666354	+	0.493418i
$815$	8.99652			0.315134
$816$	−29.7631	+	18.3629i	−1.04192	+	0.642829i
$817$	−4.40419			−0.154083
$818$	15.1203	+	11.1962i	0.528670	+	0.391466i
$819$	−0.213379	+	2.71026i	−0.00745605	+	0.0947041i
$820$	−6.23519	−	20.4428i	−0.217742	−	0.713895i
$821$		−	18.8977i		−	0.659535i	−0.944062	−	0.329767i	$-0.893030\pi$
$821$		−	18.8977i		−	0.659535i	0.944062	−	0.329767i	$-0.106970\pi$
$822$	−10.4474	−	8.39088i	−0.364396	−	0.292666i
$823$		−	47.5398i		−	1.65713i	−0.559891	−	0.828566i	$-0.689157\pi$
$823$		−	47.5398i		−	1.65713i	0.559891	−	0.828566i	$-0.310843\pi$
$824$	−18.8519	−	6.69690i	−0.656736	−	0.233297i
$825$	−0.731665	+	18.6155i	−0.0254733	+	0.648107i
$826$	14.2254	−	19.2112i	0.494965	−	0.668444i
$827$	−14.9579			−0.520137			−0.260069	−	0.965590i	$-0.583745\pi$
$827$	−14.9579			−0.520137			−0.260069	+	0.965590i	$0.583745\pi$
$828$	−0.139069	−	0.629358i	−0.00483299	−	0.0218717i
$829$	8.42289			0.292539			0.146270	−	0.989245i	$-0.453273\pi$
$829$	8.42289			0.292539			0.146270	+	0.989245i	$0.453273\pi$
$830$	−7.53247	+	10.1725i	−0.261456	+	0.353093i
$831$	0.136402	−	3.47041i	0.00473172	−	0.120387i
$832$	4.98054	+	4.04958i	0.172669	+	0.140394i
$833$		−	28.8957i		−	1.00118i
$834$	3.43387	+	2.75792i	0.118905	+	0.0954990i
$835$		−	21.9879i		−	0.760921i
$836$	6.57868	−	2.00654i	0.227528	−	0.0693975i
$837$	32.6157	+	3.86172i	1.12736	+	0.133481i
$838$	−7.10686	−	5.26245i	−0.245502	−	0.181788i
$839$	23.7661			0.820499			0.410249	−	0.911973i	$-0.365442\pi$
$839$	23.7661			0.820499			0.410249	+	0.911973i	$0.365442\pi$
$840$	−7.02900	−	2.81250i	−0.242523	−	0.0970405i
$841$	23.7980			0.820620
$842$	13.1055	+	9.70428i	0.451645	+	0.334432i
$843$	−41.0864	−	1.61487i	−1.41509	−	0.0556191i
$844$	−20.7950	+	6.34260i	−0.715793	+	0.218321i
$845$			16.9072i			0.581627i
$846$	−18.9640	−	16.4971i	−0.651995	−	0.567182i
$847$			0.933221i			0.0320658i
$848$	−17.7610	−	26.4072i	−0.609915	−	0.906827i
$849$	−9.03258	−	0.355018i	−0.309997	−	0.0121842i
$850$	13.2868	−	17.9436i	0.455733	−	0.615461i
$851$	0.522522			0.0179118
$852$	51.6411	−	13.5586i	1.76920	−	0.464510i
$853$	47.2986			1.61947			0.809737	−	0.586794i	$-0.199610\pi$
$853$	47.2986			1.61947			0.809737	+	0.586794i	$0.199610\pi$
$854$	11.3372	−	15.3107i	0.387951	−	0.523923i
$855$	4.09231	+	0.322187i	0.139954	+	0.0110186i
$856$	7.93743	−	22.3440i	0.271296	−	0.763702i
$857$			37.3362i			1.27538i	0.770293	+	0.637690i	$0.220110\pi$
$857$			37.3362i			1.27538i	−0.770293	+	0.637690i	$0.779890\pi$
$858$	4.23245	−	5.26980i	0.144494	−	0.179908i
$859$			9.79430i			0.334177i	0.985942	+	0.167089i	$0.0534366\pi$
$859$			9.79430i			0.334177i	−0.985942	+	0.167089i	$0.946563\pi$
$860$	−3.51623	−	11.5284i	−0.119903	−	0.393115i
$861$	−0.599997	+	15.2655i	−0.0204479	+	0.520246i
$862$	−11.3241	−	8.38520i	−0.385700	−	0.285601i
$863$	14.5721			0.496040			0.248020	−	0.968755i	$-0.420220\pi$
$863$	14.5721			0.496040			0.248020	+	0.968755i	$0.420220\pi$
$864$	−4.77413	+	29.0036i	−0.162419	+	0.986722i
$865$	24.4847			0.832504
$866$	43.7620	+	32.4046i	1.48709	+	1.10115i
$867$	0.576841	−	14.6763i	0.0195905	−	0.498434i
$868$	−4.16522	−	13.6562i	−0.141377	−	0.463521i
$869$			32.8973i			1.11596i
$870$	4.78694	−	5.96019i	0.162293	−	0.202069i
$871$			6.45065i			0.218572i
$872$	10.6537	−	29.9905i	0.360781	−	1.01561i
$873$	−47.2889	−	3.72306i	−1.60049	−	0.126006i
$874$	0.0904057	−	0.122092i	0.00305802	−	0.00412981i
$875$	12.5604			0.424619
$876$	2.85607	−	0.749873i	0.0964976	−	0.0253359i
$877$	−50.0949			−1.69158			−0.845792	−	0.533513i	$-0.820871\pi$
$877$	−50.0949			−1.69158			−0.845792	+	0.533513i	$0.820871\pi$
$878$	8.57049	−	11.5743i	0.289240	−	0.390615i
$879$	−29.9516	−	1.17722i	−1.01024	−	0.0397068i
$880$	10.5046	+	15.6184i	0.354111	+	0.526495i
$881$		−	6.86432i		−	0.231265i	−0.993292	−	0.115632i	$-0.963111\pi$
$881$		−	6.86432i		−	0.231265i	0.993292	−	0.115632i	$-0.0368894\pi$
$882$	−18.3238	−	15.9402i	−0.616993	−	0.536734i
$883$		−	2.11192i		−	0.0710717i	−0.999368	−	0.0355359i	$-0.988686\pi$
$883$		−	2.11192i		−	0.0710717i	0.999368	−	0.0355359i	$-0.0113138\pi$
$884$	−7.74814	+	2.36323i	−0.260598	+	0.0794840i
$885$	−35.4433	−	1.39307i	−1.19142	−	0.0468276i
$886$	−29.4399	−	21.7995i	−0.989053	−	0.732368i
$887$	−43.3203			−1.45455			−0.727276	−	0.686345i	$-0.759214\pi$
$887$	−43.3203			−1.45455			−0.727276	+	0.686345i	$0.759214\pi$
$888$	−22.1240	−	8.85243i	−0.742432	−	0.297068i
$889$	−5.68295			−0.190600
$890$	−7.13530	−	5.28351i	−0.239176	−	0.177104i
$891$	30.5691	+	4.84344i	1.02410	+	0.162261i
$892$	29.2955	−	8.93530i	0.980885	−	0.299176i
$893$		−	5.92447i		−	0.198255i
$894$	−18.0018	−	14.4582i	−0.602070	−	0.483554i
$895$		−	21.3234i		−	0.712761i
$896$	12.3781	−	3.17057i	0.413522	−	0.105921i
$897$	0.00586337	−	0.149179i	0.000195772	−	0.00498095i
$898$	−4.59834	+	6.21000i	−0.153449	+	0.207230i
$899$	14.4163			0.480810
$900$	−4.04908	−	18.3241i	−0.134969	−	0.610804i
$901$	40.1605			1.33794
$902$	22.6027	−	30.5246i	0.752586	−	1.01636i
$903$	−0.338359	+	8.60872i	−0.0112599	+	0.286480i
$904$	−47.9305	−	17.0267i	−1.59414	−	0.566300i
$905$			30.0471i			0.998799i
$906$	10.0537	+	8.07465i	0.334011	+	0.268262i
$907$			32.1243i			1.06667i	0.845904	+	0.533335i	$0.179061\pi$
$907$			32.1243i			1.06667i	−0.845904	+	0.533335i	$0.820939\pi$
$908$	8.07854	+	26.4865i	0.268096	+	0.878984i
$909$	−3.22762	+	40.9961i	−0.107053	+	1.35975i
$910$	−1.40931	−	1.04356i	−0.0467182	−	0.0345936i
$911$	−28.6571			−0.949453			−0.474726	−	0.880134i	$-0.657453\pi$
$911$	−28.6571			−0.949453			−0.474726	+	0.880134i	$0.657453\pi$
$912$	−5.89629	+	3.63782i	−0.195246	+	0.120460i
$913$	−22.4945			−0.744459
$914$	−24.9516	−	18.4760i	−0.825327	−	0.611133i
$915$	−28.2473	−	1.11024i	−0.933826	−	0.0367033i
$916$	13.0550	+	42.8026i	0.431351	+	1.41424i
$917$		−	2.03093i		−	0.0670672i
$918$	−27.0082	−	25.4258i	−0.891404	−	0.839177i
$919$		−	43.7862i		−	1.44437i	−0.691698	−	0.722187i	$-0.743137\pi$
$919$		−	43.7862i		−	1.44437i	0.691698	−	0.722187i	$-0.256863\pi$
$920$	0.391765	+	0.139170i	0.0129161	+	0.00458829i
$921$	39.2087	+	1.54107i	1.29197	+	0.0507798i
$922$	−8.73882	+	11.8017i	−0.287798	+	0.388667i
$923$	12.3670			0.407065
$924$	−3.41669	−	13.0133i	−0.112401	−	0.428105i
$925$	15.2135			0.500217
$926$	−12.2577	+	16.5539i	−0.402814	+	0.543995i
$927$	1.66547	−	21.1542i	0.0547011	−	0.694793i
$928$	−0.584136	+	12.8889i	−0.0191752	+	0.423098i
$929$			57.2295i			1.87764i	0.344410	+	0.938819i	$0.388079\pi$
$929$			57.2295i			1.87764i	−0.344410	+	0.938819i	$0.611921\pi$
$930$	−13.2660	+	16.5174i	−0.435010	+	0.541628i
$931$		−	5.72446i		−	0.187612i
$932$	16.4470	−	5.01645i	0.538741	−	0.164319i
$933$	−0.706876	+	17.9848i	−0.0231421	+	0.588794i
$934$	−19.6780	−	14.5710i	−0.643883	−	0.476779i
$935$	−23.7527			−0.776795
$936$	−2.77562	+	6.21702i	−0.0907238	+	0.203210i
$937$	−30.7790			−1.00551			−0.502753	−	0.864430i	$-0.667680\pi$
$937$	−30.7790			−1.00551			−0.502753	+	0.864430i	$0.667680\pi$
$938$	10.3194	+	7.64123i	0.336940	+	0.249495i
$939$	0.210368	−	5.35231i	0.00686511	−	0.174666i
$940$	15.5079	−	4.73000i	0.505811	−	0.154276i
$941$		−	12.4691i		−	0.406482i	−0.979129	−	0.203241i	$-0.934853\pi$
$941$		−	12.4691i		−	0.406482i	0.979129	−	0.203241i	$-0.0651475\pi$
$942$	3.25803	−	4.05655i	0.106152	−	0.132170i
$943$		−	0.838951i		−	0.0273200i
$944$	49.6755	−	33.4108i	1.61680	−	1.08743i
$945$	0.944167	−	7.97434i	0.0307137	−	0.259405i
$946$	12.7464	−	17.2138i	0.414421	−	0.559670i
$947$	40.1306			1.30407			0.652035	−	0.758189i	$-0.273915\pi$
$947$	40.1306			1.30407			0.652035	+	0.758189i	$0.273915\pi$
$948$	−8.41530	−	32.0516i	−0.273316	−	1.04099i
$949$	0.683971			0.0222026
$950$	2.63221	−	3.55477i	0.0854002	−	0.115332i
$951$	−27.8810	−	1.09584i	−0.904103	−	0.0355350i
$952$	−5.39763	+	15.1944i	−0.174938	+	0.492454i
$953$			10.4373i			0.338098i	0.985608	+	0.169049i	$0.0540696\pi$
$953$			10.4373i			0.338098i	−0.985608	+	0.169049i	$0.945930\pi$
$954$	22.1544	−	25.4672i	0.717274	−	0.824530i
$955$		−	16.1431i		−	0.522378i
$956$	−8.32974	−	27.3101i	−0.269403	−	0.883271i
$957$	13.5749	+	0.533549i	0.438813	+	0.0172472i
$958$	0.796255	+	0.589606i	0.0257258	+	0.0190493i
$959$	−6.17833			−0.199509
$960$	−14.2299	−	12.5297i	−0.459267	−	0.404396i
$961$	−8.95177			−0.288767
$962$	−4.43585	−	3.28463i	−0.143018	−	0.105901i
$963$	25.0727	+	1.97398i	0.807958	+	0.0636105i
$964$	2.70814	+	8.87895i	0.0872232	+	0.285972i
$965$		−	35.3754i		−	1.13877i
$966$	−0.231703	−	0.186093i	−0.00745491	−	0.00598744i
$967$			37.7852i			1.21509i	0.794285	+	0.607545i	$0.207846\pi$
$967$			37.7852i			1.21509i	−0.794285	+	0.607545i	$0.792154\pi$
$968$	−0.782338	+	2.20230i	−0.0251453	+	0.0707845i
$969$	0.343371	−	8.73624i	0.0110307	−	0.280648i
$970$	18.2081	−	24.5898i	0.584628	−	0.789532i
$971$	−30.0066			−0.962959			−0.481479	−	0.876457i	$-0.659900\pi$
$971$	−30.0066			−0.962959			−0.481479	+	0.876457i	$0.659900\pi$
$972$	−31.0223	+	3.10082i	−0.995042	+	0.0994587i
$973$	2.03070			0.0651012
$974$	−14.9527	+	20.1934i	−0.479116	+	0.647039i
$975$	0.170715	−	4.34343i	0.00546726	−	0.139101i
$976$	39.5899	−	26.6274i	1.26724	−	0.852323i
$977$			14.1446i			0.452527i	0.974066	+	0.226263i	$0.0726510\pi$
$977$			14.1446i			0.452527i	−0.974066	+	0.226263i	$0.927349\pi$
$978$	−12.5566	−	10.0848i	−0.401515	−	0.322478i
$979$		−	15.7783i		−	0.504277i
$980$	14.9843	−	4.57032i	0.478657	−	0.145993i
$981$	33.6530	+	2.64950i	1.07446	+	0.0845922i
$982$	29.6249	+	21.9365i	0.945369	+	0.700021i
$983$	−25.2217			−0.804448			−0.402224	−	0.915541i	$-0.631763\pi$
$983$	−25.2217			−0.804448			−0.402224	+	0.915541i	$0.631763\pi$
$984$	−14.2133	+	35.5218i	−0.453103	+	1.13239i
$985$	−25.5164			−0.813021
$986$	−13.0849	−	9.68906i	−0.416709	−	0.308562i
$987$	−11.5804	−	0.455156i	−0.368607	−	0.0144878i
$988$	−1.53496	+	0.468174i	−0.0488337	+	0.0148946i
$989$		−	0.473113i		−	0.0150441i
$990$	−13.1030	+	15.0624i	−0.416442	+	0.478714i
$991$		−	20.7877i		−	0.660342i	−0.943921	−	0.330171i	$-0.892894\pi$
$991$		−	20.7877i		−	0.660342i	0.943921	−	0.330171i	$-0.107106\pi$
$992$	1.61881	−	35.7188i	0.0513974	−	1.13407i
$993$	−20.1705	−	0.792784i	−0.640091	−	0.0251582i
$994$	14.6496	−	19.7840i	0.464656	−	0.627511i
$995$	−21.6719			−0.687046
$996$	21.9163	−	5.75422i	0.694444	−	0.182329i
$997$	25.9123			0.820652			0.410326	−	0.911939i	$-0.365415\pi$
$997$	25.9123			0.820652			0.410326	+	0.911939i	$0.365415\pi$
$998$	18.6028	−	25.1228i	0.588862	−	0.795250i
$999$	2.97179	−	25.0995i	0.0940234	−	0.794112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.30	yes	36
3.2	odd	2	inner	228.2.c.a.191.7	✓	36
4.3	odd	2	inner	228.2.c.a.191.8	yes	36
12.11	even	2	inner	228.2.c.a.191.29	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.7	✓	36	3.2	odd	2	inner
228.2.c.a.191.8	yes	36	4.3	odd	2	inner
228.2.c.a.191.29	yes	36	12.11	even	2	inner
228.2.c.a.191.30	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13655 + 0.841583i) q^{2} +(-0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} -1.36832i q^{5} +(-1.53385 + 1.90979i) q^{6} +1.12940i q^{7} +(-0.946798 + 2.66525i) q^{8} +(-2.99075 - 0.235461i) q^{9} +O(q^{10})\)	\(q+(1.13655 + 0.841583i) q^{2} +(-0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} -1.36832i q^{5} +(-1.53385 + 1.90979i) q^{6} +1.12940i q^{7} +(-0.946798 + 2.66525i) q^{8} +(-2.99075 - 0.235461i) q^{9} +(1.15156 - 1.55516i) q^{10} +3.43894 q^{11} +(-3.35054 + 0.879700i) q^{12} -0.802387 q^{13} +(-0.950482 + 1.28361i) q^{14} +(2.36818 + 0.0930793i) q^{15} +(-3.31911 + 2.23237i) q^{16} -5.04776i q^{17} +(-3.20096 - 2.78457i) q^{18} -1.00000i q^{19} +(2.61760 - 0.798384i) q^{20} +(-1.95467 - 0.0768266i) q^{21} +(3.90851 + 2.89415i) q^{22} +0.107423 q^{23} +(-4.54839 - 1.81994i) q^{24} +3.12769 q^{25} +(-0.911951 - 0.675276i) q^{26} +(0.610960 - 5.16011i) q^{27} +(-2.16053 + 0.658976i) q^{28} -2.28079i q^{29} +(2.61321 + 2.09881i) q^{30} +6.32074i q^{31} +(-5.65105 - 0.256111i) q^{32} +(-0.233931 + 5.95182i) q^{33} +(4.24811 - 5.73702i) q^{34} +1.54538 q^{35} +(-1.29459 - 5.85867i) q^{36} +4.86414 q^{37} +(0.841583 - 1.13655i) q^{38} +(0.0545819 - 1.38870i) q^{39} +(3.64693 + 1.29553i) q^{40} -7.80977i q^{41} +(-2.15691 - 1.73233i) q^{42} -4.40419i q^{43} +(2.00654 + 6.57868i) q^{44} +(-0.322187 + 4.09231i) q^{45} +(0.122092 + 0.0904057i) q^{46} +5.92447 q^{47} +(-3.63782 - 5.89629i) q^{48} +5.72446 q^{49} +(3.55477 + 2.63221i) q^{50} +(8.73624 + 0.343371i) q^{51} +(-0.468174 - 1.53496i) q^{52} +7.95610i q^{53} +(5.03705 - 5.35053i) q^{54} -4.70558i q^{55} +(-3.01013 - 1.06931i) q^{56} +(1.73071 + 0.0680243i) q^{57} +(1.91948 - 2.59223i) q^{58} -14.9665 q^{59} +(1.20371 + 4.58463i) q^{60} -11.9278 q^{61} +(-5.31943 + 7.18382i) q^{62} +(0.265930 - 3.37774i) q^{63} +(-6.20715 - 5.04691i) q^{64} +1.09793i q^{65} +(-5.27483 + 6.56765i) q^{66} -8.03932i q^{67} +(9.65635 - 2.94525i) q^{68} +(-0.00730740 + 0.185919i) q^{69} +(1.75640 + 1.30057i) q^{70} -15.4128 q^{71} +(3.45920 - 7.74816i) q^{72} -0.852420 q^{73} +(5.52832 + 4.09358i) q^{74} +(-0.212759 + 5.41314i) q^{75} +(1.91300 - 0.583476i) q^{76} +3.88393i q^{77} +(1.23074 - 1.53239i) q^{78} +9.56611i q^{79} +(3.05461 + 4.54162i) q^{80} +(8.88912 + 1.40841i) q^{81} +(6.57257 - 8.87616i) q^{82} -6.54111 q^{83} +(-0.993531 - 3.78410i) q^{84} -6.90697 q^{85} +(3.70649 - 5.00557i) q^{86} +(3.94740 + 0.155149i) q^{87} +(-3.25598 + 9.16564i) q^{88} -4.58814i q^{89} +(-3.81020 + 4.37995i) q^{90} -0.906215i q^{91} +(0.0626789 + 0.205500i) q^{92} +(-10.9394 - 0.429964i) q^{93} +(6.73343 + 4.98593i) q^{94} -1.36832 q^{95} +(0.827665 - 9.76294i) q^{96} +15.8117 q^{97} +(6.50611 + 4.81761i) q^{98} +(-10.2850 - 0.809737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6}+O(q^{10}) \) 36 * q - 6 * q^6	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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