LMFDB - Embedded newform 228.2.c.a.191.7

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			191.7
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13655 - 0.841583i) q^{2} +(0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} +1.36832i q^{5} +(1.37923 - 2.02429i) q^{6} +1.12940i q^{7} +(0.946798 - 2.66525i) q^{8} +(-2.99075 + 0.235461i) q^{9} +O(q^{10})$	\(q+(-1.13655 - 0.841583i) q^{2} +(0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} +1.36832i q^{5} +(1.37923 - 2.02429i) 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} +(-3.27116 + 1.13996i) 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} +(3.59728 + 2.24935i) 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} +(4.67720 + 1.45734i) 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} +(2.76988 + 1.88723i) 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} +(-2.19546 - 5.58390i) 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} +(2.28622 + 1.55770i) 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} +(-4.08938 - 5.59258i) 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} +(-3.64828 + 6.37888i) 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} +(-1.55983 - 4.47601i) 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} +(-4.74308 + 6.96139i) 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} +(-2.20407 + 8.19403i) 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} +(-1.10667 + 1.62426i) 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} +(-1.28747 - 3.69444i) 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} +(-3.07784 + 4.92225i) 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} +(-0.0588464 + 9.79778i) 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	$0.0989796\pi$
$5$			1.36832i			0.611933i	−0.952042	+	0.305966i	$0.901020\pi$
$6$	1.37923	−	2.02429i	0.563067	−	0.826411i
$7$			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	$-0.673487\pi$
$11$	−3.43894			−1.03688			−0.518440	+	0.855114i	$0.673487\pi$
$12$	−3.27116	+	1.13996i	−0.944303	+	0.329078i
$13$	−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	$0.209688\pi$
$17$			5.04776i			1.22426i	−0.790756	+	0.612131i	$0.790312\pi$
$18$	3.59728	+	2.24935i	0.847887	+	0.530176i
$19$		−	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	$-0.503565\pi$
$23$	−0.107423			−0.0223993			−0.0111997	+	0.999937i	$0.503565\pi$
$24$	4.67720	+	1.45734i	0.954729	+	0.297477i
$25$	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	$0.0679215\pi$
$29$			2.28079i			0.423532i	−0.977320	+	0.211766i	$0.932078\pi$
$30$	2.76988	+	1.88723i	0.505708	+	0.344559i
$31$			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
$36$	−2.19546	−	5.58390i	−0.365911	−	0.930650i
$37$	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	$0.208766\pi$
$41$			7.80977i			1.21968i	−0.792524	+	0.609840i	$0.791234\pi$
$42$	2.28622	+	1.55770i	0.352772	+	0.240358i
$43$		−	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	$-0.642222\pi$
$47$	−5.92447			−0.864172			−0.432086	+	0.901832i	$0.642222\pi$
$48$	−4.08938	−	5.59258i	−0.590252	−	0.807219i
$49$	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	$-0.815987\pi$
$53$		−	7.95610i		−	1.09285i	0.837507	−	0.546427i	$-0.184013\pi$
$54$	−3.64828	+	6.37888i	−0.496468	+	0.868055i
$55$		−	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	$-0.0724108\pi$
$59$	14.9665			1.94847			0.974237	+	0.225528i	$0.0724108\pi$
$60$	−1.55983	−	4.47601i	−0.201374	−	0.577850i
$61$	−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
$66$	−4.74308	+	6.96139i	−0.583833	+	0.856888i
$67$		−	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	$-0.132522\pi$
$71$	15.4128			1.82916			0.914579	+	0.404407i	$0.132522\pi$
$72$	−2.20407	+	8.19403i	−0.259752	+	0.965675i
$73$	−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
$78$	−1.10667	+	1.62426i	−0.125306	+	0.183911i
$79$			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	$-0.383121\pi$
$83$	6.54111			0.717981			0.358990	+	0.933341i	$0.383121\pi$
$84$	−1.28747	−	3.69444i	−0.140474	−	0.403097i
$85$	−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	$0.0781876\pi$
$89$			4.58814i			0.486342i	−0.969983	+	0.243171i	$0.921812\pi$
$90$	−3.07784	+	4.92225i	−0.324432	+	0.518850i
$91$		−	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
$96$	−0.0588464	+	9.79778i	−0.00600599	+	0.999982i
$97$	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	$0.238881\pi$
$101$			13.7076i			1.36396i	−0.731370	+	0.681980i	$0.761119\pi$
$102$	10.2181	+	6.96201i	1.01174	+	0.689342i
$103$			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	$-0.367192\pi$
$107$	8.38344			0.810458			0.405229	+	0.914215i	$0.367192\pi$
$108$	9.51479	−	4.17956i	0.915561	−	0.402179i
$109$	−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	$-0.679081\pi$
$113$		−	17.9835i		−	1.69174i	0.533387	−	0.845871i	$-0.320919\pi$
$114$	−2.02429	−	1.37923i	−0.189592	−	0.129176i
$115$		−	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
$120$	−1.99411	+	6.39992i	−0.182036	+	0.584230i
$121$	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
$126$	−2.54041	+	4.06276i	−0.226318	+	0.361940i
$127$			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	$-0.474969\pi$
$131$	1.79824			0.157113			0.0785565	+	0.996910i	$0.474969\pi$
$132$	11.2493	−	3.92025i	0.979128	−	0.341214i
$133$	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	$-0.924921\pi$
$137$		−	5.47046i		−	0.467373i	0.972312	−	0.233686i	$-0.0750789\pi$
$138$	−0.148161	+	0.217456i	−0.0126123	+	0.0185110i
$139$		−	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
$144$	9.40098	−	7.45799i	0.783415	−	0.621499i
$145$	−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	$-0.873820\pi$
$149$		−	9.42605i		−	0.772212i	0.922454	−	0.386106i	$-0.126180\pi$
$150$	4.31380	−	6.33134i	0.352220	−	0.516952i
$151$		−	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
$156$	2.62474	−	0.914690i	0.210147	−	0.0732338i
$157$	−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
$162$	−11.2882	−	5.88021i	−0.886884	−	0.461993i
$163$			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	$-0.713572\pi$
$167$	−16.0692			−1.24347			−0.621736	+	0.783227i	$0.713572\pi$
$168$	−1.64591	+	5.28242i	−0.126985	+	0.407547i
$169$	−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	$-0.761882\pi$
$173$		−	17.8939i		−	1.36045i	0.733004	−	0.680225i	$-0.238118\pi$
$174$	4.61697	+	3.14573i	0.350012	+	0.238477i
$175$			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	$-0.697880\pi$
$179$	−15.5836			−1.16477			−0.582385	+	0.812913i	$0.697880\pi$
$180$	7.64058	−	3.00411i	0.569495	−	0.223913i
$181$	−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
$186$	12.7950	+	8.71774i	0.938174	+	0.639216i
$187$		−	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	$-0.640368\pi$
$191$	−11.7977			−0.853653			−0.426826	+	0.904334i	$0.640368\pi$
$192$	8.31253	−	11.0861i	0.599905	−	0.800071i
$193$	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	$0.231273\pi$
$197$			18.6480i			1.32861i	−0.747461	+	0.664306i	$0.768727\pi$
$198$	−12.3708	−	7.73537i	−0.879157	−	0.549729i
$199$		−	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
$204$	−5.75425	−	16.5120i	−0.402878	−	1.15607i
$205$	−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
$210$	−2.13143	+	3.12830i	−0.147083	+	0.215873i
$211$			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
$216$	−14.3315	−	3.25722i	−0.975132	−	0.221626i
$217$	−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
$222$	6.70875	−	9.84640i	0.450262	−	0.660847i
$223$		−	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	$-0.651964\pi$
$227$	−13.8455			−0.918961			−0.459480	+	0.888188i	$0.651964\pi$
$228$	1.13996	+	3.27116i	0.0754957	+	0.216638i
$229$	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	$0.0908722\pi$
$233$			8.59752i			0.563243i	−0.959526	+	0.281621i	$0.909128\pi$
$234$	−2.88641	−	1.80485i	−0.188691	−	0.117987i
$235$		−	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	$-0.347232\pi$
$239$	14.2761			0.923443			0.461721	+	0.887025i	$0.347232\pi$
$240$	7.65246	−	5.59560i	0.493964	−	0.361194i
$241$	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
$246$	15.8092	+	10.7714i	1.00796	+	0.686762i
$247$			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	$-0.359652\pi$
$251$	13.5225			0.853535			0.426768	+	0.904361i	$0.359652\pi$
$252$	6.30645	−	2.47955i	0.397269	−	0.156197i
$253$	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	$0.0296096\pi$
$257$			2.97819i			0.185774i	−0.995677	+	0.0928872i	$0.970390\pi$
$258$	−8.91534	−	6.07438i	−0.555045	−	0.378174i
$259$			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	$-0.729689\pi$
$263$	−21.4255			−1.32116			−0.660578	+	0.750758i	$0.729689\pi$
$264$	−16.0846	−	5.01169i	−0.989938	−	0.308448i
$265$	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	$0.287291\pi$
$269$			25.7470i			1.56982i	−0.619610	+	0.784910i	$0.712709\pi$
$270$	−8.72837	−	4.99202i	−0.531192	−	0.303805i
$271$			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
$276$	0.351399	−	0.122458i	0.0211517	−	0.00737113i
$277$	−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	$-0.749556\pi$
$281$		−	23.7396i		−	1.41618i	0.706120	−	0.708092i	$-0.250444\pi$
$282$	−8.17119	+	11.9928i	−0.486587	+	0.714162i
$283$			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
$288$	−16.9612	+	0.564641i	−0.999446	+	0.0332718i
$289$	−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	$-0.831304\pi$
$293$		−	17.3059i		−	1.01102i	0.862820	−	0.505511i	$-0.168696\pi$
$294$	7.89533	−	11.5879i	0.460465	−	0.675822i
$295$			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
$300$	−10.2312	+	3.56544i	−0.590697	+	0.205851i
$301$	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
$306$	−11.3542	+	18.1582i	−0.649075	+	1.03804i
$307$		−	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	$-0.595195\pi$
$311$	−10.3915			−0.589249			−0.294625	+	0.955613i	$0.595195\pi$
$312$	−3.75292	−	1.16935i	−0.212467	−	0.0662013i
$313$	−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	$-0.850568\pi$
$317$		−	16.1095i		−	0.904801i	0.891815	−	0.452400i	$-0.149432\pi$
$318$	−16.1054	−	10.9733i	−0.903147	−	0.615351i
$319$		−	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
$324$	7.88087	+	16.1831i	0.437826	+	0.899060i
$325$	−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
$330$	−9.52544	−	6.49007i	−0.524358	−	0.357266i
$331$			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
$336$	6.31625	−	4.61854i	0.344580	−	0.251962i
$337$	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
$342$	2.24935	−	3.59728i	0.121631	−	0.194519i
$343$			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	$-0.702725\pi$
$347$	−22.1557			−1.18938			−0.594689	+	0.803955i	$0.702725\pi$
$348$	−2.60001	−	7.46083i	−0.139375	−	0.399943i
$349$	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	$-0.897056\pi$
$353$		−	11.9419i		−	0.635602i	0.948158	−	0.317801i	$-0.102944\pi$
$354$	20.6422	−	30.2965i	1.09712	−	1.61024i
$355$			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	$-0.265851\pi$
$359$	25.4285			1.34207			0.671033	+	0.741428i	$0.265851\pi$
$360$	−11.2121	−	3.01588i	−0.590929	−	0.158951i
$361$	−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
$366$	−16.4512	+	24.1454i	−0.859919	+	1.26210i
$367$		−	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
$372$	−7.20539	−	20.6762i	−0.373582	−	1.07201i
$373$	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
$378$	−7.20429	−	4.12036i	−0.370549	−	0.211928i
$379$			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	$-0.273272\pi$
$383$	25.5811			1.30713			0.653565	+	0.756870i	$0.273272\pi$
$384$	−18.7775	+	5.60420i	−0.958233	+	0.285988i
$385$	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	$-0.680202\pi$
$389$		−	33.2921i		−	1.68798i	0.536362	−	0.843988i	$-0.319798\pi$
$390$	−2.22252	−	1.51429i	−0.112541	−	0.0766790i
$391$		−	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
$396$	7.55007	+	19.2027i	0.379405	+	0.964971i
$397$	−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	$0.212708\pi$
$401$			24.8153i			1.23921i	−0.784912	+	0.619607i	$0.787292\pi$
$402$	−16.2739	−	11.0880i	−0.811667	−	0.553022i
$403$		−	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
$408$	−7.35628	+	23.6094i	−0.364190	+	1.16884i
$409$	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
$414$	−0.386432	−	0.241632i	−0.0189921	−	0.0118756i
$415$			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	$-0.451190\pi$
$419$	6.25303			0.305481			0.152740	+	0.988266i	$0.451190\pi$
$420$	5.05519	−	1.76167i	0.246668	−	0.0859609i
$421$	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
$426$	21.2577	−	31.1998i	1.02994	−	1.51164i
$427$		−	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	$-0.422864\pi$
$431$	9.96360			0.479930			0.239965	+	0.970782i	$0.422864\pi$
$432$	13.5471	+	15.7631i	0.651787	+	0.758402i
$433$	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
$438$	−1.17568	+	1.72554i	−0.0561762	+	0.0824495i
$439$		−	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	$-0.289017\pi$
$443$	25.9029			1.23069			0.615343	+	0.788259i	$0.289017\pi$
$444$	−15.9114	+	5.54492i	−0.755120	+	0.263150i
$445$	−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	$-0.958846\pi$
$449$		−	5.46392i		−	0.257858i	0.991654	−	0.128929i	$-0.0411540\pi$
$450$	11.2512	+	7.03526i	0.530386	+	0.331646i
$451$		−	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
$456$	1.45734	−	4.67720i	0.0682460	−	0.219030i
$457$	−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	$-0.922259\pi$
$461$		−	10.3838i		−	0.483621i	0.970323	−	0.241810i	$-0.0777412\pi$
$462$	−7.86219	−	5.35682i	−0.365782	−	0.249222i
$463$			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	$-0.368804\pi$
$467$	17.3138			0.801189			0.400595	+	0.916255i	$0.368804\pi$
$468$	1.76161	+	4.48045i	0.0814306	+	0.207109i
$469$	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
$474$	19.3645	+	13.1938i	0.889443	+	0.606013i
$475$		−	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	$-0.505095\pi$
$479$	−0.700592			−0.0320109			−0.0160054	+	0.999872i	$0.505095\pi$
$480$	−13.4065	−	0.0805209i	−0.611922	−	0.00367526i
$481$	−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
$486$	9.40909	−	19.9366i	0.426805	−	0.904344i
$487$			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	$-0.700149\pi$
$491$	−26.0657			−1.17633			−0.588165	+	0.808741i	$0.700149\pi$
$492$	−8.90282	−	25.5470i	−0.401370	−	1.15175i
$493$	−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
$498$	9.02168	−	13.2411i	0.404271	−	0.593347i
$499$		−	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	$-0.131702\pi$
$503$	41.0703			1.83124			0.915618	+	0.402050i	$0.131702\pi$
$504$	−9.25432	−	2.48927i	−0.412220	−	0.110881i
$505$	−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	$-0.721617\pi$
$509$		−	34.6206i		−	1.53453i	0.641331	−	0.767265i	$-0.278383\pi$
$510$	−9.52629	+	13.9817i	−0.421831	+	0.619120i
$511$		−	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
$516$	5.02060	+	14.4068i	0.221020	+	0.634225i
$517$	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	$0.0881697\pi$
$521$			12.4839i			0.546929i	−0.961882	+	0.273465i	$0.911830\pi$
$522$	−5.13029	+	8.20465i	−0.224547	+	0.359108i
$523$		−	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
$528$	14.0631	+	19.2325i	0.612020	+	0.836989i
$529$	−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
$534$	9.28770	+	6.32808i	0.401918	+	0.273843i
$535$			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
$540$	5.71900	+	13.0193i	0.246106	+	0.560262i
$541$	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
$546$	−1.83444	−	1.24988i	−0.0785067	−	0.0534898i
$547$		−	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
$552$	−0.502440	−	0.156552i	−0.0213853	−	0.00666329i
$553$	−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	$0.114279\pi$
$557$			16.5845i			0.702710i	−0.936242	+	0.351355i	$0.885721\pi$
$558$	−14.2175	+	22.7375i	−0.601877	+	0.962554i
$559$			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	$-0.517469\pi$
$563$	−2.60303			−0.109704			−0.0548522	+	0.998494i	$0.517469\pi$
$564$	19.3799	−	6.75366i	0.816040	−	0.284380i
$565$	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	$-0.698643\pi$
$569$		−	38.7153i		−	1.62303i	0.584332	−	0.811515i	$-0.301357\pi$
$570$	1.88723	−	2.76988i	0.0790473	−	0.116017i
$571$		−	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
$576$	19.7523	+	13.6325i	0.823014	+	0.568020i
$577$	−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
$582$	21.8080	−	32.0075i	0.903970	−	1.32675i
$583$			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	$-0.335853\pi$
$587$	23.8952			0.986260			0.493130	+	0.869956i	$0.335853\pi$
$588$	−18.7256	+	6.52566i	−0.772232	+	0.269114i
$589$	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	$0.165370\pi$
$593$			24.1796i			0.992939i	−0.868054	+	0.496469i	$0.834630\pi$
$594$	12.5462	−	21.9366i	0.514777	−	0.900068i
$595$		−	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	$-0.696101\pi$
$599$	−28.2842			−1.15566			−0.577831	+	0.816157i	$0.696101\pi$
$600$	14.6288	+	4.55809i	0.597219	+	0.186083i
$601$	−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
$606$	27.7482	+	18.9059i	1.12719	+	0.768002i
$607$		−	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
$612$	28.1862	−	11.0822i	1.13936	−	0.447971i
$613$	−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	$-0.928036\pi$
$617$		−	11.1361i		−	0.448323i	0.974552	−	0.224162i	$-0.0719644\pi$
$618$	14.3182	+	9.75556i	0.575962	+	0.392426i
$619$			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
$624$	3.28127	+	4.48742i	0.131356	+	0.179640i
$625$	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
$630$	−5.55918	−	3.47610i	−0.221483	−	0.138491i
$631$			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
$636$	9.06964	+	26.0257i	0.359635	+	1.03199i
$637$	−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	$0.0358999\pi$
$641$			5.69877i			0.225088i	−0.993647	+	0.112544i	$0.964100\pi$
$642$	11.5627	−	16.9705i	0.456342	−	0.669771i
$643$		−	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	$-0.796035\pi$
$647$	−40.7809			−1.60326			−0.801632	+	0.597818i	$0.796035\pi$
$648$	4.66243	−	25.0252i	0.183158	−	0.983084i
$649$	−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	$0.280771\pi$
$653$			39.4580i			1.54411i	−0.635556	+	0.772055i	$0.719229\pi$
$654$	−15.5196	+	22.7781i	−0.606865	+	0.890693i
$655$			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	$-0.455854\pi$
$659$	7.09777			0.276490			0.138245	+	0.990398i	$0.455854\pi$
$660$	5.36418	+	15.3927i	0.208800	+	0.599160i
$661$	−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
$666$	17.4977	+	10.9411i	0.678021	+	0.423960i
$667$		−	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
$672$	−11.0656	−	0.0664610i	−0.426865	−	0.00256379i
$673$	−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	$0.222039\pi$
$677$			33.4267i			1.28469i	−0.766415	+	0.642346i	$0.777961\pi$
$678$	−36.4037	−	24.8033i	−1.39807	−	0.952564i
$679$			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	$-0.383269\pi$
$683$	18.7412			0.717113			0.358556	+	0.933508i	$0.383269\pi$
$684$	−5.58390	+	2.19546i	−0.213506	+	0.0839457i
$685$	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
$690$	−0.297550	−	0.202732i	−0.0113275	−	0.00771789i
$691$			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
$696$	−3.32388	+	10.6677i	−0.125991	+	0.404359i
$697$	−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	$0.0715903\pi$
$701$			11.8093i			0.446033i	−0.974815	+	0.223016i	$0.928410\pi$
$702$	2.92733	−	5.11833i	0.110485	−	0.193179i
$703$		−	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
$708$	−48.9578	+	17.0612i	−1.83995	+	0.641200i
$709$	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
$714$	−7.86288	+	11.5403i	−0.294261	+	0.431886i
$715$			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	$-0.435346\pi$
$719$	10.8180			0.403444			0.201722	+	0.979443i	$0.435346\pi$
$720$	10.2049	+	12.8636i	0.380316	+	0.479398i
$721$	−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
$726$	1.13965	−	1.67267i	0.0422965	−	0.0620784i
$727$			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
$732$	39.0179	−	13.5973i	1.44214	−	0.502570i
$733$	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
$738$	−17.5669	+	28.0939i	−0.646646	+	1.03415i
$739$		−	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	$-0.503544\pi$
$743$	−0.606961			−0.0222672			−0.0111336	+	0.999938i	$0.503544\pi$
$744$	−9.21144	+	29.5634i	−0.337708	+	1.08385i
$745$	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
$750$	22.5127	+	15.3388i	0.822048	+	0.560094i
$751$			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
$756$	4.72039	+	10.7460i	0.171679	+	0.390828i
$757$	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	$0.0457269\pi$
$761$			7.89858i			0.286323i	−0.989699	+	0.143162i	$0.954273\pi$
$762$	10.1859	+	6.94005i	0.368995	+	0.251411i
$763$		−	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
$768$	26.0579	+	9.43336i	0.940282	+	0.340397i
$769$	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	$-0.845013\pi$
$773$		−	26.0176i		−	0.935789i	0.883784	−	0.467895i	$-0.154987\pi$
$774$	9.90656	−	15.8431i	0.356084	−	0.569469i
$775$			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
$780$	1.25159	+	3.59149i	0.0448142	+	0.128596i
$781$	−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
$786$	2.48018	−	3.64015i	0.0884652	−	0.129840i
$787$			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
$792$	7.57966	−	28.1788i	0.269331	−	1.00129i
$793$	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	$-0.918009\pi$
$797$		−	14.3835i		−	0.509489i	0.967008	−	0.254745i	$-0.0819914\pi$
$798$	1.55770	−	2.28622i	0.0551419	−	0.0809315i
$799$		−	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
$804$	9.16451	+	26.2979i	0.323207	+	0.927456i
$805$	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	$0.168084\pi$
$809$			28.6620i			1.00770i	−0.863790	+	0.503851i	$0.831916\pi$
$810$	8.04603	−	15.4459i	0.282709	−	0.542713i
$811$		−	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
$816$	28.2300	−	20.6422i	0.988248	−	0.722623i
$817$	−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	$0.106970\pi$
$821$			18.8977i			0.659535i	−0.944062	+	0.329767i	$0.893030\pi$
$822$	−11.0738	−	7.54501i	−0.386242	−	0.263162i
$823$		−	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	$-0.416255\pi$
$827$	14.9579			0.520137			0.260069	+	0.965590i	$0.416255\pi$
$828$	0.235844	+	0.599841i	0.00819615	+	0.0208459i
$829$	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
$834$	−3.63974	−	2.47990i	−0.126034	−	0.0858719i
$835$		−	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	$-0.634558\pi$
$839$	−23.7661			−0.820499			−0.410249	+	0.911973i	$0.634558\pi$
$840$	−7.22806	−	2.25214i	−0.249392	−	0.0777062i
$841$	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
$846$	−21.3120	−	13.3262i	−0.732721	−	0.458164i
$847$			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
$852$	−50.4176	+	17.5699i	−1.72728	+	0.601936i
$853$	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	$-0.779890\pi$
$857$		−	37.3362i		−	1.27538i	0.770293	−	0.637690i	$-0.220110\pi$
$858$	3.80579	−	5.58573i	0.129927	−	0.190694i
$859$			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	$-0.579780\pi$
$863$	−14.5721			−0.496040			−0.248020	+	0.968755i	$0.579780\pi$
$864$	−2.13100	−	29.3165i	−0.0724983	−	0.997369i
$865$	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
$870$	−4.30438	+	6.31751i	−0.145932	+	0.214184i
$871$			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
$876$	2.78840	−	0.971725i	0.0942114	−	0.0328315i
$877$	−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	$0.0368894\pi$
$881$			6.86432i			0.231265i	−0.993292	+	0.115632i	$0.963111\pi$
$882$	20.5925	+	12.8763i	0.693385	+	0.433568i
$883$		−	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	$-0.240786\pi$
$887$	43.3203			1.45455			0.727276	+	0.686345i	$0.240786\pi$
$888$	22.7505	+	7.08868i	0.763458	+	0.237880i
$889$	−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
$894$	−19.0810	−	13.0007i	−0.638165	−	0.434807i
$895$		−	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
$900$	−6.86673	−	17.4647i	−0.228891	−	0.582157i
$901$	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
$906$	−10.6564	−	7.26066i	−0.354036	−	0.241219i
$907$			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	$-0.342547\pi$
$911$	28.6571			0.949453			0.474726	+	0.880134i	$0.342547\pi$
$912$	−5.59258	+	4.08938i	−0.185189	+	0.135413i
$913$	−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
$918$	−32.1991	−	18.4156i	−1.06273	−	0.607807i
$919$		−	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
$924$	4.42753	+	12.7050i	0.145655	+	0.417963i
$925$	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	$-0.611921\pi$
$929$		−	57.2295i		−	1.87764i	0.344410	−	0.938819i	$-0.388079\pi$
$930$	−11.9287	+	17.5077i	−0.391157	+	0.574100i
$931$		−	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
$936$	1.76852	−	6.57478i	0.0578058	−	0.214904i
$937$	−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	$0.0651475\pi$
$941$			12.4691i			0.406482i	−0.979129	+	0.203241i	$0.934853\pi$
$942$	−2.92959	+	4.29975i	−0.0954513	+	0.140093i
$943$		−	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	$-0.726085\pi$
$947$	−40.1306			−1.30407			−0.652035	+	0.758189i	$0.726085\pi$
$948$	−10.9050	−	31.2923i	−0.354177	−	1.01633i
$949$	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	$-0.945930\pi$
$953$		−	10.4373i		−	0.338098i	0.985608	−	0.169049i	$-0.0540696\pi$
$954$	17.8960	−	28.6203i	0.579406	−	0.926618i
$955$		−	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
$960$	15.1694	+	11.3742i	0.489590	+	0.367102i
$961$	−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
$966$	−0.245594	−	0.167333i	−0.00790185	−	0.00538385i
$967$			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	$-0.340100\pi$
$971$	30.0066			0.962959			0.481479	+	0.876457i	$0.340100\pi$
$972$	−27.4722	+	14.7404i	−0.881171	+	0.472798i
$973$	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	$-0.927349\pi$
$977$		−	14.1446i		−	0.452527i	0.974066	−	0.226263i	$-0.0726510\pi$
$978$	13.3094	+	9.06820i	0.425586	+	0.289969i
$979$		−	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	$-0.368237\pi$
$983$	25.2217			0.804448			0.402224	+	0.915541i	$0.368237\pi$
$984$	−11.3814	+	36.5278i	−0.362827	+	1.16446i
$985$	−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
$990$	10.5845	−	16.9273i	0.336397	−	0.537985i
$991$		−	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
$996$	−21.3970	+	7.45661i	−0.677991	+	0.236272i
$997$	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.191.7	✓	36
3.2	odd	2	inner	228.2.c.a.191.30	yes	36
4.3	odd	2	inner	228.2.c.a.191.29	yes	36
12.11	even	2	inner	228.2.c.a.191.8	yes	36

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.13655 - 0.841583i) q^{2} +(0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} +1.36832i q^{5} +(1.37923 - 2.02429i) q^{6} +1.12940i q^{7} +(0.946798 - 2.66525i) q^{8} +(-2.99075 + 0.235461i) q^{9} +O(q^{10})\)	\(q+(-1.13655 - 0.841583i) q^{2} +(0.0680243 + 1.73071i) q^{3} +(0.583476 + 1.91300i) q^{4} +1.36832i q^{5} +(1.37923 - 2.02429i) 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} +(-3.27116 + 1.13996i) 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} +(3.59728 + 2.24935i) 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} +(4.67720 + 1.45734i) 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} +(2.76988 + 1.88723i) 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} +(-2.19546 - 5.58390i) 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} +(2.28622 + 1.55770i) 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} +(-4.08938 - 5.59258i) 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} +(-3.64828 + 6.37888i) 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} +(-1.55983 - 4.47601i) 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} +(-4.74308 + 6.96139i) 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} +(-2.20407 + 8.19403i) 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} +(-1.10667 + 1.62426i) 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} +(-1.28747 - 3.69444i) 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} +(-3.07784 + 4.92225i) 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} +(-0.0588464 + 9.79778i) 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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