LMFDB - Embedded newform 230.2.b.a.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("230.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.b (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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.3
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.2.b.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.618034i q^{3} -1.00000 q^{4} +2.23607 q^{5} +0.618034 q^{6} -4.85410i q^{7} -1.00000i q^{8} +2.61803 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.618034i q^{3} -1.00000 q^{4} +2.23607 q^{5} +0.618034 q^{6} -4.85410i q^{7} -1.00000i q^{8} +2.61803 q^{9} +2.23607i q^{10} -3.38197 q^{11} +0.618034i q^{12} +0.381966i q^{13} +4.85410 q^{14} -1.38197i q^{15} +1.00000 q^{16} +5.85410i q^{17} +2.61803i q^{18} +6.85410 q^{19} -2.23607 q^{20} -3.00000 q^{21} -3.38197i q^{22} +1.00000i q^{23} -0.618034 q^{24} +5.00000 q^{25} -0.381966 q^{26} -3.47214i q^{27} +4.85410i q^{28} -3.70820 q^{29} +1.38197 q^{30} -8.85410 q^{31} +1.00000i q^{32} +2.09017i q^{33} -5.85410 q^{34} -10.8541i q^{35} -2.61803 q^{36} -3.70820i q^{37} +6.85410i q^{38} +0.236068 q^{39} -2.23607i q^{40} -3.38197 q^{41} -3.00000i q^{42} +6.76393i q^{43} +3.38197 q^{44} +5.85410 q^{45} -1.00000 q^{46} +11.7082i q^{47} -0.618034i q^{48} -16.5623 q^{49} +5.00000i q^{50} +3.61803 q^{51} -0.381966i q^{52} -2.00000i q^{53} +3.47214 q^{54} -7.56231 q^{55} -4.85410 q^{56} -4.23607i q^{57} -3.70820i q^{58} +6.00000 q^{59} +1.38197i q^{60} -3.85410 q^{61} -8.85410i q^{62} -12.7082i q^{63} -1.00000 q^{64} +0.854102i q^{65} -2.09017 q^{66} -0.763932i q^{67} -5.85410i q^{68} +0.618034 q^{69} +10.8541 q^{70} +2.61803 q^{71} -2.61803i q^{72} -7.52786i q^{73} +3.70820 q^{74} -3.09017i q^{75} -6.85410 q^{76} +16.4164i q^{77} +0.236068i q^{78} -5.70820 q^{79} +2.23607 q^{80} +5.70820 q^{81} -3.38197i q^{82} -5.70820i q^{83} +3.00000 q^{84} +13.0902i q^{85} -6.76393 q^{86} +2.29180i q^{87} +3.38197i q^{88} +9.70820 q^{89} +5.85410i q^{90} +1.85410 q^{91} -1.00000i q^{92} +5.47214i q^{93} -11.7082 q^{94} +15.3262 q^{95} +0.618034 q^{96} +16.0344i q^{97} -16.5623i q^{98} -8.85410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9} - 18 q^{11} + 6 q^{14} + 4 q^{16} + 14 q^{19} - 12 q^{21} + 2 q^{24} + 20 q^{25} - 6 q^{26} + 12 q^{29} + 10 q^{30} - 22 q^{31} - 10 q^{34} - 6 q^{36} - 8 q^{39} - 18 q^{41} + 18 q^{44} + 10 q^{45} - 4 q^{46} - 26 q^{49} + 10 q^{51} - 4 q^{54} + 10 q^{55} - 6 q^{56} + 24 q^{59} - 2 q^{61} - 4 q^{64} + 14 q^{66} - 2 q^{69} + 30 q^{70} + 6 q^{71} - 12 q^{74} - 14 q^{76} + 4 q^{79} - 4 q^{81} + 12 q^{84} - 36 q^{86} + 12 q^{89} - 6 q^{91} - 20 q^{94} + 30 q^{95} - 2 q^{96} - 22 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9 - 18 * q^11 + 6 * q^14 + 4 * q^16 + 14 * q^19 - 12 * q^21 + 2 * q^24 + 20 * q^25 - 6 * q^26 + 12 * q^29 + 10 * q^30 - 22 * q^31 - 10 * q^34 - 6 * q^36 - 8 * q^39 - 18 * q^41 + 18 * q^44 + 10 * q^45 - 4 * q^46 - 26 * q^49 + 10 * q^51 - 4 * q^54 + 10 * q^55 - 6 * q^56 + 24 * q^59 - 2 * q^61 - 4 * q^64 + 14 * q^66 - 2 * q^69 + 30 * q^70 + 6 * q^71 - 12 * q^74 - 14 * q^76 + 4 * q^79 - 4 * q^81 + 12 * q^84 - 36 * q^86 + 12 * q^89 - 6 * q^91 - 20 * q^94 + 30 * q^95 - 2 * q^96 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 0.618034i	− 0.356822i	−0.983956	−	0.178411i	$-0.942904\pi$
$3$	− 0.618034i	− 0.356822i	0.983956	−	0.178411i	$-0.0570957\pi$
$4$	−1.00000	−0.500000
$5$	2.23607	1.00000
$5$	2.23607	1.00000
$6$	0.618034	0.252311
$7$	− 4.85410i	− 1.83468i	−0.398107	−	0.917339i	$-0.630333\pi$
$7$	− 4.85410i	− 1.83468i	0.398107	−	0.917339i	$-0.369667\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.61803	0.872678
$10$	2.23607i	0.707107i
$11$	−3.38197	−1.01970	−0.509851	−	0.860263i	$-0.670299\pi$
$11$	−3.38197	−1.01970	−0.509851	+	0.860263i	$0.670299\pi$
$12$	0.618034i	0.178411i
$13$	0.381966i	0.105938i	0.998596	+	0.0529692i	$0.0168685\pi$
$13$	0.381966i	0.105938i	−0.998596	+	0.0529692i	$0.983131\pi$
$14$	4.85410	1.29731
$15$	− 1.38197i	− 0.356822i
$16$	1.00000	0.250000
$17$	5.85410i	1.41983i	0.704288	+	0.709914i	$0.251266\pi$
$17$	5.85410i	1.41983i	−0.704288	+	0.709914i	$0.748734\pi$
$18$	2.61803i	0.617077i
$19$	6.85410	1.57244	0.786219	−	0.617947i	$-0.212036\pi$
$19$	6.85410	1.57244	0.786219	+	0.617947i	$0.212036\pi$
$20$	−2.23607	−0.500000
$21$	−3.00000	−0.654654
$22$	− 3.38197i	− 0.721038i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	−0.618034	−0.126156
$25$	5.00000	1.00000
$26$	−0.381966	−0.0749097
$27$	− 3.47214i	− 0.668213i
$28$	4.85410i	0.917339i
$29$	−3.70820	−0.688596	−0.344298	−	0.938860i	$-0.611883\pi$
$29$	−3.70820	−0.688596	−0.344298	+	0.938860i	$0.611883\pi$
$30$	1.38197	0.252311
$31$	−8.85410	−1.59024	−0.795122	−	0.606450i	$-0.792593\pi$
$31$	−8.85410	−1.59024	−0.795122	+	0.606450i	$0.792593\pi$
$32$	1.00000i	0.176777i
$33$	2.09017i	0.363852i
$34$	−5.85410	−1.00397
$35$	− 10.8541i	− 1.83468i
$36$	−2.61803	−0.436339
$37$	− 3.70820i	− 0.609625i	−0.952412	−	0.304812i	$-0.901406\pi$
$37$	− 3.70820i	− 0.609625i	0.952412	−	0.304812i	$-0.0985938\pi$
$38$	6.85410i	1.11188i
$39$	0.236068	0.0378011
$40$	− 2.23607i	− 0.353553i
$41$	−3.38197	−0.528174	−0.264087	−	0.964499i	$-0.585071\pi$
$41$	−3.38197	−0.528174	−0.264087	+	0.964499i	$0.585071\pi$
$42$	− 3.00000i	− 0.462910i
$43$	6.76393i	1.03149i	0.856742	+	0.515745i	$0.172485\pi$
$43$	6.76393i	1.03149i	−0.856742	+	0.515745i	$0.827515\pi$
$44$	3.38197	0.509851
$45$	5.85410	0.872678
$46$	−1.00000	−0.147442
$47$	11.7082i	1.70782i	0.520423	+	0.853909i	$0.325774\pi$
$47$	11.7082i	1.70782i	−0.520423	+	0.853909i	$0.674226\pi$
$48$	− 0.618034i	− 0.0892055i
$49$	−16.5623	−2.36604
$50$	5.00000i	0.707107i
$51$	3.61803	0.506626
$52$	− 0.381966i	− 0.0529692i
$53$	− 2.00000i	− 0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$	− 2.00000i	− 0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	3.47214	0.472498
$55$	−7.56231	−1.01970
$56$	−4.85410	−0.648657
$57$	− 4.23607i	− 0.561081i
$58$	− 3.70820i	− 0.486911i
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	1.38197i	0.178411i
$61$	−3.85410	−0.493467	−0.246734	−	0.969083i	$-0.579357\pi$
$61$	−3.85410	−0.493467	−0.246734	+	0.969083i	$0.579357\pi$
$62$	− 8.85410i	− 1.12447i
$63$	− 12.7082i	− 1.60108i
$64$	−1.00000	−0.125000
$65$	0.854102i	0.105938i
$66$	−2.09017	−0.257282
$67$	− 0.763932i	− 0.0933292i	−0.998911	−	0.0466646i	$-0.985141\pi$
$67$	− 0.763932i	− 0.0933292i	0.998911	−	0.0466646i	$-0.0148592\pi$
$68$	− 5.85410i	− 0.709914i
$69$	0.618034	0.0744025
$70$	10.8541	1.29731
$71$	2.61803	0.310703	0.155352	−	0.987859i	$-0.450349\pi$
$71$	2.61803	0.310703	0.155352	+	0.987859i	$0.450349\pi$
$72$	− 2.61803i	− 0.308538i
$73$	− 7.52786i	− 0.881070i	−0.897735	−	0.440535i	$-0.854789\pi$
$73$	− 7.52786i	− 0.881070i	0.897735	−	0.440535i	$-0.145211\pi$
$74$	3.70820	0.431070
$75$	− 3.09017i	− 0.356822i
$76$	−6.85410	−0.786219
$77$	16.4164i	1.87082i
$78$	0.236068i	0.0267294i
$79$	−5.70820	−0.642223	−0.321112	−	0.947041i	$-0.604056\pi$
$79$	−5.70820	−0.642223	−0.321112	+	0.947041i	$0.604056\pi$
$80$	2.23607	0.250000
$81$	5.70820	0.634245
$82$	− 3.38197i	− 0.373476i
$83$	− 5.70820i	− 0.626557i	−0.949661	−	0.313278i	$-0.898573\pi$
$83$	− 5.70820i	− 0.626557i	0.949661	−	0.313278i	$-0.101427\pi$
$84$	3.00000	0.327327
$85$	13.0902i	1.41983i
$86$	−6.76393	−0.729374
$87$	2.29180i	0.245706i
$88$	3.38197i	0.360519i
$89$	9.70820	1.02907	0.514534	−	0.857470i	$-0.327965\pi$
$89$	9.70820	1.02907	0.514534	+	0.857470i	$0.327965\pi$
$90$	5.85410i	0.617077i
$91$	1.85410	0.194363
$92$	− 1.00000i	− 0.104257i
$93$	5.47214i	0.567434i
$94$	−11.7082	−1.20761
$95$	15.3262	1.57244
$96$	0.618034	0.0630778
$97$	16.0344i	1.62805i	0.580829	+	0.814025i	$0.302728\pi$
$97$	16.0344i	1.62805i	−0.580829	+	0.814025i	$0.697272\pi$
$98$	− 16.5623i	− 1.67305i
$99$	−8.85410	−0.889871
$100$	−5.00000	−0.500000
$101$	−10.4721	−1.04202	−0.521008	−	0.853552i	$-0.674444\pi$
$101$	−10.4721	−1.04202	−0.521008	+	0.853552i	$0.674444\pi$
$102$	3.61803i	0.358239i
$103$	4.14590i	0.408507i	0.978918	+	0.204254i	$0.0654768\pi$
$103$	4.14590i	0.408507i	−0.978918	+	0.204254i	$0.934523\pi$
$104$	0.381966	0.0374548
$105$	−6.70820	−0.654654
$106$	2.00000	0.194257
$107$	1.70820i	0.165138i	0.996585	+	0.0825692i	$0.0263125\pi$
$107$	1.70820i	0.165138i	−0.996585	+	0.0825692i	$0.973687\pi$
$108$	3.47214i	0.334106i
$109$	12.5623	1.20325	0.601625	−	0.798778i	$-0.294520\pi$
$109$	12.5623	1.20325	0.601625	+	0.798778i	$0.294520\pi$
$110$	− 7.56231i	− 0.721038i
$111$	−2.29180	−0.217528
$112$	− 4.85410i	− 0.458670i
$113$	13.4164i	1.26211i	0.775738	+	0.631055i	$0.217378\pi$
$113$	13.4164i	1.26211i	−0.775738	+	0.631055i	$0.782622\pi$
$114$	4.23607	0.396744
$115$	2.23607i	0.208514i
$116$	3.70820	0.344298
$117$	1.00000i	0.0924500i
$118$	6.00000i	0.552345i
$119$	28.4164	2.60493
$120$	−1.38197	−0.126156
$121$	0.437694	0.0397904
$122$	− 3.85410i	− 0.348934i
$123$	2.09017i	0.188464i
$124$	8.85410	0.795122
$125$	11.1803	1.00000
$126$	12.7082	1.13214
$127$	− 3.70820i	− 0.329050i	−0.986373	−	0.164525i	$-0.947391\pi$
$127$	− 3.70820i	− 0.329050i	0.986373	−	0.164525i	$-0.0526091\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	4.18034	0.368058
$130$	−0.854102	−0.0749097
$131$	8.18034	0.714720	0.357360	−	0.933967i	$-0.383677\pi$
$131$	8.18034	0.714720	0.357360	+	0.933967i	$0.383677\pi$
$132$	− 2.09017i	− 0.181926i
$133$	− 33.2705i	− 2.88492i
$134$	0.763932	0.0659937
$135$	− 7.76393i	− 0.668213i
$136$	5.85410	0.501985
$137$	7.14590i	0.610515i	0.952270	+	0.305258i	$0.0987426\pi$
$137$	7.14590i	0.610515i	−0.952270	+	0.305258i	$0.901257\pi$
$138$	0.618034i	0.0526105i
$139$	−17.7082	−1.50199	−0.750995	−	0.660308i	$-0.770426\pi$
$139$	−17.7082	−1.50199	−0.750995	+	0.660308i	$0.770426\pi$
$140$	10.8541i	0.917339i
$141$	7.23607	0.609387
$142$	2.61803i	0.219701i
$143$	− 1.29180i	− 0.108025i
$144$	2.61803	0.218169
$145$	−8.29180	−0.688596
$146$	7.52786	0.623010
$147$	10.2361i	0.844257i
$148$	3.70820i	0.304812i
$149$	0.381966	0.0312919	0.0156459	−	0.999878i	$-0.495020\pi$
$149$	0.381966	0.0312919	0.0156459	+	0.999878i	$0.495020\pi$
$150$	3.09017	0.252311
$151$	−19.2705	−1.56821	−0.784106	−	0.620627i	$-0.786878\pi$
$151$	−19.2705	−1.56821	−0.784106	+	0.620627i	$0.786878\pi$
$152$	− 6.85410i	− 0.555941i
$153$	15.3262i	1.23905i
$154$	−16.4164	−1.32287
$155$	−19.7984	−1.59024
$156$	−0.236068	−0.0189006
$157$	− 15.7082i	− 1.25365i	−0.779160	−	0.626826i	$-0.784354\pi$
$157$	− 15.7082i	− 1.25365i	0.779160	−	0.626826i	$-0.215646\pi$
$158$	− 5.70820i	− 0.454120i
$159$	−1.23607	−0.0980266
$160$	2.23607i	0.176777i
$161$	4.85410	0.382557
$162$	5.70820i	0.448479i
$163$	7.03444i	0.550980i	0.961304	+	0.275490i	$0.0888401\pi$
$163$	7.03444i	0.550980i	−0.961304	+	0.275490i	$0.911160\pi$
$164$	3.38197	0.264087
$165$	4.67376i	0.363852i
$166$	5.70820	0.443043
$167$	− 3.70820i	− 0.286949i	−0.989654	−	0.143475i	$-0.954172\pi$
$167$	− 3.70820i	− 0.286949i	0.989654	−	0.143475i	$-0.0458276\pi$
$168$	3.00000i	0.231455i
$169$	12.8541	0.988777
$170$	−13.0902	−1.00397
$171$	17.9443	1.37223
$172$	− 6.76393i	− 0.515745i
$173$	− 3.56231i	− 0.270837i	−0.990788	−	0.135419i	$-0.956762\pi$
$173$	− 3.56231i	− 0.270837i	0.990788	−	0.135419i	$-0.0432379\pi$
$174$	−2.29180	−0.173741
$175$	− 24.2705i	− 1.83468i
$176$	−3.38197	−0.254925
$177$	− 3.70820i	− 0.278726i
$178$	9.70820i	0.727661i
$179$	−16.4721	−1.23119	−0.615593	−	0.788065i	$-0.711083\pi$
$179$	−16.4721	−1.23119	−0.615593	+	0.788065i	$0.711083\pi$
$180$	−5.85410	−0.436339
$181$	−4.56231	−0.339114	−0.169557	−	0.985520i	$-0.554234\pi$
$181$	−4.56231	−0.339114	−0.169557	+	0.985520i	$0.554234\pi$
$182$	1.85410i	0.137435i
$183$	2.38197i	0.176080i
$184$	1.00000	0.0737210
$185$	− 8.29180i	− 0.609625i
$186$	−5.47214	−0.401236
$187$	− 19.7984i	− 1.44780i
$188$	− 11.7082i	− 0.853909i
$189$	−16.8541	−1.22596
$190$	15.3262i	1.11188i
$191$	−1.41641	−0.102488	−0.0512438	−	0.998686i	$-0.516319\pi$
$191$	−1.41641	−0.102488	−0.0512438	+	0.998686i	$0.516319\pi$
$192$	0.618034i	0.0446028i
$193$	− 2.29180i	− 0.164967i	−0.996592	−	0.0824835i	$-0.973715\pi$
$193$	− 2.29180i	− 0.164967i	0.996592	−	0.0824835i	$-0.0262852\pi$
$194$	−16.0344	−1.15121
$195$	0.527864	0.0378011
$196$	16.5623	1.18302
$197$	0.437694i	0.0311844i	0.999878	+	0.0155922i	$0.00496335\pi$
$197$	0.437694i	0.0311844i	−0.999878	+	0.0155922i	$0.995037\pi$
$198$	− 8.85410i	− 0.629234i
$199$	15.4164	1.09284	0.546420	−	0.837511i	$-0.315990\pi$
$199$	15.4164	1.09284	0.546420	+	0.837511i	$0.315990\pi$
$200$	− 5.00000i	− 0.353553i
$201$	−0.472136	−0.0333019
$202$	− 10.4721i	− 0.736817i
$203$	18.0000i	1.26335i
$204$	−3.61803	−0.253313
$205$	−7.56231	−0.528174
$206$	−4.14590	−0.288858
$207$	2.61803i	0.181966i
$208$	0.381966i	0.0264846i
$209$	−23.1803	−1.60342
$210$	− 6.70820i	− 0.462910i
$211$	5.70820	0.392969	0.196484	−	0.980507i	$-0.437047\pi$
$211$	5.70820	0.392969	0.196484	+	0.980507i	$0.437047\pi$
$212$	2.00000i	0.137361i
$213$	− 1.61803i	− 0.110866i
$214$	−1.70820	−0.116770
$215$	15.1246i	1.03149i
$216$	−3.47214	−0.236249
$217$	42.9787i	2.91759i
$218$	12.5623i	0.850827i
$219$	−4.65248	−0.314385
$220$	7.56231	0.509851
$221$	−2.23607	−0.150414
$222$	− 2.29180i	− 0.153815i
$223$	− 22.3607i	− 1.49738i	−0.662919	−	0.748691i	$-0.730683\pi$
$223$	− 22.3607i	− 1.49738i	0.662919	−	0.748691i	$-0.269317\pi$
$224$	4.85410	0.324328
$225$	13.0902	0.872678
$226$	−13.4164	−0.892446
$227$	− 23.7082i	− 1.57357i	−0.617228	−	0.786784i	$-0.711744\pi$
$227$	− 23.7082i	− 1.57357i	0.617228	−	0.786784i	$-0.288256\pi$
$228$	4.23607i	0.280540i
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−2.23607	−0.147442
$231$	10.1459	0.667551
$232$	3.70820i	0.243456i
$233$	− 19.1246i	− 1.25289i	−0.779464	−	0.626447i	$-0.784508\pi$
$233$	− 19.1246i	− 1.25289i	0.779464	−	0.626447i	$-0.215492\pi$
$234$	−1.00000	−0.0653720
$235$	26.1803i	1.70782i
$236$	−6.00000	−0.390567
$237$	3.52786i	0.229159i
$238$	28.4164i	1.84196i
$239$	1.52786	0.0988293	0.0494147	−	0.998778i	$-0.484264\pi$
$239$	1.52786	0.0988293	0.0494147	+	0.998778i	$0.484264\pi$
$240$	− 1.38197i	− 0.0892055i
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	0.437694i	0.0281360i
$243$	− 13.9443i	− 0.894525i
$244$	3.85410	0.246734
$245$	−37.0344	−2.36604
$246$	−2.09017	−0.133264
$247$	2.61803i	0.166582i
$248$	8.85410i	0.562236i
$249$	−3.52786	−0.223569
$250$	11.1803i	0.707107i
$251$	7.79837	0.492229	0.246114	−	0.969241i	$-0.420846\pi$
$251$	7.79837	0.492229	0.246114	+	0.969241i	$0.420846\pi$
$252$	12.7082i	0.800542i
$253$	− 3.38197i	− 0.212622i
$254$	3.70820	0.232673
$255$	8.09017	0.506626
$256$	1.00000	0.0625000
$257$	− 15.4164i	− 0.961649i	−0.876817	−	0.480825i	$-0.840337\pi$
$257$	− 15.4164i	− 0.961649i	0.876817	−	0.480825i	$-0.159663\pi$
$258$	4.18034i	0.260257i
$259$	−18.0000	−1.11847
$260$	− 0.854102i	− 0.0529692i
$261$	−9.70820	−0.600923
$262$	8.18034i	0.505383i
$263$	15.2705i	0.941620i	0.882235	+	0.470810i	$0.156038\pi$
$263$	15.2705i	0.941620i	−0.882235	+	0.470810i	$0.843962\pi$
$264$	2.09017	0.128641
$265$	− 4.47214i	− 0.274721i
$266$	33.2705	2.03995
$267$	− 6.00000i	− 0.367194i
$268$	0.763932i	0.0466646i
$269$	10.4721	0.638497	0.319249	−	0.947671i	$-0.396569\pi$
$269$	10.4721	0.638497	0.319249	+	0.947671i	$0.396569\pi$
$270$	7.76393	0.472498
$271$	19.1459	1.16303	0.581515	−	0.813536i	$-0.302460\pi$
$271$	19.1459	1.16303	0.581515	+	0.813536i	$0.302460\pi$
$272$	5.85410i	0.354957i
$273$	− 1.14590i	− 0.0693529i
$274$	−7.14590	−0.431699
$275$	−16.9098	−1.01970
$276$	−0.618034	−0.0372013
$277$	− 16.4721i	− 0.989715i	−0.868974	−	0.494857i	$-0.835220\pi$
$277$	− 16.4721i	− 0.989715i	0.868974	−	0.494857i	$-0.164780\pi$
$278$	− 17.7082i	− 1.06207i
$279$	−23.1803	−1.38777
$280$	−10.8541	−0.648657
$281$	−0.652476	−0.0389234	−0.0194617	−	0.999811i	$-0.506195\pi$
$281$	−0.652476	−0.0389234	−0.0194617	+	0.999811i	$0.506195\pi$
$282$	7.23607i	0.430902i
$283$	3.05573i	0.181644i	0.995867	+	0.0908221i	$0.0289495\pi$
$283$	3.05573i	0.181644i	−0.995867	+	0.0908221i	$0.971051\pi$
$284$	−2.61803	−0.155352
$285$	− 9.47214i	− 0.561081i
$286$	1.29180	0.0763855
$287$	16.4164i	0.969030i
$288$	2.61803i	0.154269i
$289$	−17.2705	−1.01591
$290$	− 8.29180i	− 0.486911i
$291$	9.90983	0.580925
$292$	7.52786i	0.440535i
$293$	− 27.7082i	− 1.61873i	−0.587306	−	0.809365i	$-0.699811\pi$
$293$	− 27.7082i	− 1.61873i	0.587306	−	0.809365i	$-0.300189\pi$
$294$	−10.2361	−0.596980
$295$	13.4164	0.781133
$296$	−3.70820	−0.215535
$297$	11.7426i	0.681377i
$298$	0.381966i	0.0221267i
$299$	−0.381966	−0.0220897
$300$	3.09017i	0.178411i
$301$	32.8328	1.89245
$302$	− 19.2705i	− 1.10889i
$303$	6.47214i	0.371814i
$304$	6.85410	0.393110
$305$	−8.61803	−0.493467
$306$	−15.3262	−0.876143
$307$	− 10.1459i	− 0.579057i	−0.957169	−	0.289528i	$-0.906502\pi$
$307$	− 10.1459i	− 0.579057i	0.957169	−	0.289528i	$-0.0934985\pi$
$308$	− 16.4164i	− 0.935412i
$309$	2.56231	0.145764
$310$	− 19.7984i	− 1.12447i
$311$	−13.5279	−0.767095	−0.383547	−	0.923521i	$-0.625298\pi$
$311$	−13.5279	−0.767095	−0.383547	+	0.923521i	$0.625298\pi$
$312$	− 0.236068i	− 0.0133647i
$313$	19.1459i	1.08219i	0.840961	+	0.541095i	$0.181990\pi$
$313$	19.1459i	1.08219i	−0.840961	+	0.541095i	$0.818010\pi$
$314$	15.7082	0.886465
$315$	− 28.4164i	− 1.60108i
$316$	5.70820	0.321112
$317$	− 26.2705i	− 1.47550i	−0.675075	−	0.737749i	$-0.735889\pi$
$317$	− 26.2705i	− 1.47550i	0.675075	−	0.737749i	$-0.264111\pi$
$318$	− 1.23607i	− 0.0693153i
$319$	12.5410	0.702162
$320$	−2.23607	−0.125000
$321$	1.05573	0.0589250
$322$	4.85410i	0.270509i
$323$	40.1246i	2.23259i
$324$	−5.70820	−0.317122
$325$	1.90983i	0.105938i
$326$	−7.03444	−0.389602
$327$	− 7.76393i	− 0.429346i
$328$	3.38197i	0.186738i
$329$	56.8328	3.13329
$330$	−4.67376	−0.257282
$331$	15.1246	0.831324	0.415662	−	0.909519i	$-0.363550\pi$
$331$	15.1246	0.831324	0.415662	+	0.909519i	$0.363550\pi$
$332$	5.70820i	0.313278i
$333$	− 9.70820i	− 0.532006i
$334$	3.70820	0.202904
$335$	− 1.70820i	− 0.0933292i
$336$	−3.00000	−0.163663
$337$	5.61803i	0.306034i	0.988224	+	0.153017i	$0.0488989\pi$
$337$	5.61803i	0.306034i	−0.988224	+	0.153017i	$0.951101\pi$
$338$	12.8541i	0.699171i
$339$	8.29180	0.450349
$340$	− 13.0902i	− 0.709914i
$341$	29.9443	1.62157
$342$	17.9443i	0.970315i
$343$	46.4164i	2.50625i
$344$	6.76393	0.364687
$345$	1.38197	0.0744025
$346$	3.56231	0.191511
$347$	5.56231i	0.298600i	0.988792	+	0.149300i	$0.0477021\pi$
$347$	5.56231i	0.298600i	−0.988792	+	0.149300i	$0.952298\pi$
$348$	− 2.29180i	− 0.122853i
$349$	−14.2918	−0.765022	−0.382511	−	0.923951i	$-0.624941\pi$
$349$	−14.2918	−0.765022	−0.382511	+	0.923951i	$0.624941\pi$
$350$	24.2705	1.29731
$351$	1.32624	0.0707893
$352$	− 3.38197i	− 0.180259i
$353$	8.00000i	0.425797i	0.977074	+	0.212899i	$0.0682904\pi$
$353$	8.00000i	0.425797i	−0.977074	+	0.212899i	$0.931710\pi$
$354$	3.70820	0.197089
$355$	5.85410	0.310703
$356$	−9.70820	−0.514534
$357$	− 17.5623i	− 0.929496i
$358$	− 16.4721i	− 0.870579i
$359$	−13.4164	−0.708091	−0.354045	−	0.935228i	$-0.615194\pi$
$359$	−13.4164	−0.708091	−0.354045	+	0.935228i	$0.615194\pi$
$360$	− 5.85410i	− 0.308538i
$361$	27.9787	1.47256
$362$	− 4.56231i	− 0.239789i
$363$	− 0.270510i	− 0.0141981i
$364$	−1.85410	−0.0971813
$365$	− 16.8328i	− 0.881070i
$366$	−2.38197	−0.124507
$367$	− 12.0000i	− 0.626395i	−0.949688	−	0.313197i	$-0.898600\pi$
$367$	− 12.0000i	− 0.626395i	0.949688	−	0.313197i	$-0.101400\pi$
$368$	1.00000i	0.0521286i
$369$	−8.85410	−0.460926
$370$	8.29180	0.431070
$371$	−9.70820	−0.504025
$372$	− 5.47214i	− 0.283717i
$373$	− 3.05573i	− 0.158220i	−0.996866	−	0.0791098i	$-0.974792\pi$
$373$	− 3.05573i	− 0.158220i	0.996866	−	0.0791098i	$-0.0252078\pi$
$374$	19.7984	1.02375
$375$	− 6.90983i	− 0.356822i
$376$	11.7082	0.603805
$377$	− 1.41641i	− 0.0729487i
$378$	− 16.8541i	− 0.866881i
$379$	−9.27051	−0.476194	−0.238097	−	0.971241i	$-0.576524\pi$
$379$	−9.27051	−0.476194	−0.238097	+	0.971241i	$0.576524\pi$
$380$	−15.3262	−0.786219
$381$	−2.29180	−0.117412
$382$	− 1.41641i	− 0.0724697i
$383$	27.4164i	1.40091i	0.713695	+	0.700456i	$0.247020\pi$
$383$	27.4164i	1.40091i	−0.713695	+	0.700456i	$0.752980\pi$
$384$	−0.618034	−0.0315389
$385$	36.7082i	1.87082i
$386$	2.29180	0.116649
$387$	17.7082i	0.900159i
$388$	− 16.0344i	− 0.814025i
$389$	5.67376	0.287671	0.143836	−	0.989602i	$-0.454056\pi$
$389$	5.67376	0.287671	0.143836	+	0.989602i	$0.454056\pi$
$390$	0.527864i	0.0267294i
$391$	−5.85410	−0.296055
$392$	16.5623i	0.836523i
$393$	− 5.05573i	− 0.255028i
$394$	−0.437694	−0.0220507
$395$	−12.7639	−0.642223
$396$	8.85410	0.444935
$397$	− 35.5623i	− 1.78482i	−0.451224	−	0.892410i	$-0.649013\pi$
$397$	− 35.5623i	− 1.78482i	0.451224	−	0.892410i	$-0.350987\pi$
$398$	15.4164i	0.772755i
$399$	−20.5623	−1.02940
$400$	5.00000	0.250000
$401$	−34.4721	−1.72146	−0.860728	−	0.509065i	$-0.829991\pi$
$401$	−34.4721	−1.72146	−0.860728	+	0.509065i	$0.829991\pi$
$402$	− 0.472136i	− 0.0235480i
$403$	− 3.38197i	− 0.168468i
$404$	10.4721	0.521008
$405$	12.7639	0.634245
$406$	−18.0000	−0.893325
$407$	12.5410i	0.621635i
$408$	− 3.61803i	− 0.179119i
$409$	6.56231	0.324485	0.162243	−	0.986751i	$-0.448127\pi$
$409$	6.56231	0.324485	0.162243	+	0.986751i	$0.448127\pi$
$410$	− 7.56231i	− 0.373476i
$411$	4.41641	0.217845
$412$	− 4.14590i	− 0.204254i
$413$	− 29.1246i	− 1.43313i
$414$	−2.61803	−0.128669
$415$	− 12.7639i	− 0.626557i
$416$	−0.381966	−0.0187274
$417$	10.9443i	0.535943i
$418$	− 23.1803i	− 1.13379i
$419$	−5.88854	−0.287674	−0.143837	−	0.989601i	$-0.545944\pi$
$419$	−5.88854	−0.287674	−0.143837	+	0.989601i	$0.545944\pi$
$420$	6.70820	0.327327
$421$	6.85410	0.334048	0.167024	−	0.985953i	$-0.446584\pi$
$421$	6.85410	0.334048	0.167024	+	0.985953i	$0.446584\pi$
$422$	5.70820i	0.277871i
$423$	30.6525i	1.49037i
$424$	−2.00000	−0.0971286
$425$	29.2705i	1.41983i
$426$	1.61803	0.0783940
$427$	18.7082i	0.905353i
$428$	− 1.70820i	− 0.0825692i
$429$	−0.798374	−0.0385459
$430$	−15.1246	−0.729374
$431$	−6.76393	−0.325807	−0.162904	−	0.986642i	$-0.552086\pi$
$431$	−6.76393	−0.325807	−0.162904	+	0.986642i	$0.552086\pi$
$432$	− 3.47214i	− 0.167053i
$433$	− 29.6180i	− 1.42335i	−0.702508	−	0.711676i	$-0.747936\pi$
$433$	− 29.6180i	− 1.42335i	0.702508	−	0.711676i	$-0.252064\pi$
$434$	−42.9787	−2.06304
$435$	5.12461i	0.245706i
$436$	−12.5623	−0.601625
$437$	6.85410i	0.327876i
$438$	− 4.65248i	− 0.222304i
$439$	0.270510	0.0129107	0.00645536	−	0.999979i	$-0.497945\pi$
$439$	0.270510	0.0129107	0.00645536	+	0.999979i	$0.497945\pi$
$440$	7.56231i	0.360519i
$441$	−43.3607	−2.06479
$442$	− 2.23607i	− 0.106359i
$443$	6.85410i	0.325648i	0.986655	+	0.162824i	$0.0520603\pi$
$443$	6.85410i	0.325648i	−0.986655	+	0.162824i	$0.947940\pi$
$444$	2.29180	0.108764
$445$	21.7082	1.02907
$446$	22.3607	1.05881
$447$	− 0.236068i	− 0.0111656i
$448$	4.85410i	0.229335i
$449$	−2.56231	−0.120923	−0.0604613	−	0.998171i	$-0.519257\pi$
$449$	−2.56231	−0.120923	−0.0604613	+	0.998171i	$0.519257\pi$
$450$	13.0902i	0.617077i
$451$	11.4377	0.538580
$452$	− 13.4164i	− 0.631055i
$453$	11.9098i	0.559573i
$454$	23.7082	1.11268
$455$	4.14590	0.194363
$456$	−4.23607	−0.198372
$457$	25.4164i	1.18893i	0.804122	+	0.594465i	$0.202636\pi$
$457$	25.4164i	1.18893i	−0.804122	+	0.594465i	$0.797364\pi$
$458$	10.0000i	0.467269i
$459$	20.3262	0.948748
$460$	− 2.23607i	− 0.104257i
$461$	−25.3050	−1.17857	−0.589285	−	0.807926i	$-0.700590\pi$
$461$	−25.3050	−1.17857	−0.589285	+	0.807926i	$0.700590\pi$
$462$	10.1459i	0.472030i
$463$	− 2.29180i	− 0.106509i	−0.998581	−	0.0532544i	$-0.983041\pi$
$463$	− 2.29180i	− 0.106509i	0.998581	−	0.0532544i	$-0.0169594\pi$
$464$	−3.70820	−0.172149
$465$	12.2361i	0.567434i
$466$	19.1246	0.885931
$467$	17.1246i	0.792433i	0.918157	+	0.396216i	$0.129677\pi$
$467$	17.1246i	0.792433i	−0.918157	+	0.396216i	$0.870323\pi$
$468$	− 1.00000i	− 0.0462250i
$469$	−3.70820	−0.171229
$470$	−26.1803	−1.20761
$471$	−9.70820	−0.447330
$472$	− 6.00000i	− 0.276172i
$473$	− 22.8754i	− 1.05181i
$474$	−3.52786	−0.162040
$475$	34.2705	1.57244
$476$	−28.4164	−1.30246
$477$	− 5.23607i	− 0.239743i
$478$	1.52786i	0.0698829i
$479$	19.5279	0.892251	0.446125	−	0.894970i	$-0.352804\pi$
$479$	19.5279	0.892251	0.446125	+	0.894970i	$0.352804\pi$
$480$	1.38197	0.0630778
$481$	1.41641	0.0645826
$482$	− 2.00000i	− 0.0910975i
$483$	− 3.00000i	− 0.136505i
$484$	−0.437694	−0.0198952
$485$	35.8541i	1.62805i
$486$	13.9443	0.632525
$487$	21.7082i	0.983693i	0.870682	+	0.491846i	$0.163678\pi$
$487$	21.7082i	0.983693i	−0.870682	+	0.491846i	$0.836322\pi$
$488$	3.85410i	0.174467i
$489$	4.34752	0.196602
$490$	− 37.0344i	− 1.67305i
$491$	−26.8328	−1.21095	−0.605474	−	0.795865i	$-0.707016\pi$
$491$	−26.8328	−1.21095	−0.605474	+	0.795865i	$0.707016\pi$
$492$	− 2.09017i	− 0.0942321i
$493$	− 21.7082i	− 0.977688i
$494$	−2.61803	−0.117791
$495$	−19.7984	−0.889871
$496$	−8.85410	−0.397561
$497$	− 12.7082i	− 0.570041i
$498$	− 3.52786i	− 0.158087i
$499$	−11.4164	−0.511069	−0.255534	−	0.966800i	$-0.582251\pi$
$499$	−11.4164	−0.511069	−0.255534	+	0.966800i	$0.582251\pi$
$500$	−11.1803	−0.500000
$501$	−2.29180	−0.102390
$502$	7.79837i	0.348058i
$503$	16.8541i	0.751487i	0.926724	+	0.375744i	$0.122613\pi$
$503$	16.8541i	0.751487i	−0.926724	+	0.375744i	$0.877387\pi$
$504$	−12.7082	−0.566068
$505$	−23.4164	−1.04202
$506$	3.38197	0.150347
$507$	− 7.94427i	− 0.352818i
$508$	3.70820i	0.164525i
$509$	24.6525	1.09270	0.546351	−	0.837556i	$-0.316017\pi$
$509$	24.6525	1.09270	0.546351	+	0.837556i	$0.316017\pi$
$510$	8.09017i	0.358239i
$511$	−36.5410	−1.61648
$512$	1.00000i	0.0441942i
$513$	− 23.7984i	− 1.05072i
$514$	15.4164	0.679989
$515$	9.27051i	0.408507i
$516$	−4.18034	−0.184029
$517$	− 39.5967i	− 1.74146i
$518$	− 18.0000i	− 0.790875i
$519$	−2.20163	−0.0966407
$520$	0.854102	0.0374548
$521$	20.0689	0.879234	0.439617	−	0.898185i	$-0.355114\pi$
$521$	20.0689	0.879234	0.439617	+	0.898185i	$0.355114\pi$
$522$	− 9.70820i	− 0.424917i
$523$	− 40.3607i	− 1.76485i	−0.470454	−	0.882425i	$-0.655910\pi$
$523$	− 40.3607i	− 1.76485i	0.470454	−	0.882425i	$-0.344090\pi$
$524$	−8.18034	−0.357360
$525$	−15.0000	−0.654654
$526$	−15.2705	−0.665826
$527$	− 51.8328i	− 2.25787i
$528$	2.09017i	0.0909630i
$529$	−1.00000	−0.0434783
$530$	4.47214	0.194257
$531$	15.7082	0.681678
$532$	33.2705i	1.44246i
$533$	− 1.29180i	− 0.0559539i
$534$	6.00000	0.259645
$535$	3.81966i	0.165138i
$536$	−0.763932	−0.0329968
$537$	10.1803i	0.439314i
$538$	10.4721i	0.451486i
$539$	56.0132	2.41266
$540$	7.76393i	0.334106i
$541$	−27.4164	−1.17872	−0.589362	−	0.807869i	$-0.700621\pi$
$541$	−27.4164	−1.17872	−0.589362	+	0.807869i	$0.700621\pi$
$542$	19.1459i	0.822387i
$543$	2.81966i	0.121003i
$544$	−5.85410	−0.250993
$545$	28.0902	1.20325
$546$	1.14590	0.0490399
$547$	1.14590i	0.0489951i	0.999700	+	0.0244975i	$0.00779859\pi$
$547$	1.14590i	0.0489951i	−0.999700	+	0.0244975i	$0.992201\pi$
$548$	− 7.14590i	− 0.305258i
$549$	−10.0902	−0.430638
$550$	− 16.9098i	− 0.721038i
$551$	−25.4164	−1.08278
$552$	− 0.618034i	− 0.0263053i
$553$	27.7082i	1.17827i
$554$	16.4721	0.699834
$555$	−5.12461	−0.217528
$556$	17.7082	0.750995
$557$	30.0000i	1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$	30.0000i	1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$	− 23.1803i	− 0.981302i
$559$	−2.58359	−0.109274
$560$	− 10.8541i	− 0.458670i
$561$	−12.2361	−0.516607
$562$	− 0.652476i	− 0.0275230i
$563$	− 2.29180i	− 0.0965877i	−0.998833	−	0.0482938i	$-0.984622\pi$
$563$	− 2.29180i	− 0.0965877i	0.998833	−	0.0482938i	$-0.0153784\pi$
$564$	−7.23607	−0.304693
$565$	30.0000i	1.26211i
$566$	−3.05573	−0.128442
$567$	− 27.7082i	− 1.16364i
$568$	− 2.61803i	− 0.109850i
$569$	−28.3607	−1.18894	−0.594471	−	0.804117i	$-0.702638\pi$
$569$	−28.3607	−1.18894	−0.594471	+	0.804117i	$0.702638\pi$
$570$	9.47214	0.396744
$571$	−25.2705	−1.05754	−0.528769	−	0.848766i	$-0.677346\pi$
$571$	−25.2705	−1.05754	−0.528769	+	0.848766i	$0.677346\pi$
$572$	1.29180i	0.0540127i
$573$	0.875388i	0.0365699i
$574$	−16.4164	−0.685208
$575$	5.00000i	0.208514i
$576$	−2.61803	−0.109085
$577$	26.2918i	1.09454i	0.836956	+	0.547271i	$0.184333\pi$
$577$	26.2918i	1.09454i	−0.836956	+	0.547271i	$0.815667\pi$
$578$	− 17.2705i	− 0.718359i
$579$	−1.41641	−0.0588639
$580$	8.29180	0.344298
$581$	−27.7082	−1.14953
$582$	9.90983i	0.410776i
$583$	6.76393i	0.280133i
$584$	−7.52786	−0.311505
$585$	2.23607i	0.0924500i
$586$	27.7082	1.14462
$587$	2.14590i	0.0885707i	0.999019	+	0.0442853i	$0.0141011\pi$
$587$	2.14590i	0.0885707i	−0.999019	+	0.0442853i	$0.985899\pi$
$588$	− 10.2361i	− 0.422128i
$589$	−60.6869	−2.50056
$590$	13.4164i	0.552345i
$591$	0.270510	0.0111273
$592$	− 3.70820i	− 0.152406i
$593$	33.4164i	1.37225i	0.727485	+	0.686124i	$0.240689\pi$
$593$	33.4164i	1.37225i	−0.727485	+	0.686124i	$0.759311\pi$
$594$	−11.7426	−0.481807
$595$	63.5410	2.60493
$596$	−0.381966	−0.0156459
$597$	− 9.52786i	− 0.389950i
$598$	− 0.381966i	− 0.0156198i
$599$	−21.3820	−0.873643	−0.436822	−	0.899548i	$-0.643896\pi$
$599$	−21.3820	−0.873643	−0.436822	+	0.899548i	$0.643896\pi$
$600$	−3.09017	−0.126156
$601$	−3.14590	−0.128324	−0.0641619	−	0.997940i	$-0.520437\pi$
$601$	−3.14590	−0.128324	−0.0641619	+	0.997940i	$0.520437\pi$
$602$	32.8328i	1.33817i
$603$	− 2.00000i	− 0.0814463i
$604$	19.2705	0.784106
$605$	0.978714	0.0397904
$606$	−6.47214	−0.262913
$607$	− 38.9443i	− 1.58070i	−0.612656	−	0.790350i	$-0.709899\pi$
$607$	− 38.9443i	− 1.58070i	0.612656	−	0.790350i	$-0.290101\pi$
$608$	6.85410i	0.277971i
$609$	11.1246	0.450792
$610$	− 8.61803i	− 0.348934i
$611$	−4.47214	−0.180923
$612$	− 15.3262i	− 0.619526i
$613$	− 5.23607i	− 0.211483i	−0.994394	−	0.105741i	$-0.966278\pi$
$613$	− 5.23607i	− 0.211483i	0.994394	−	0.105741i	$-0.0337216\pi$
$614$	10.1459	0.409455
$615$	4.67376i	0.188464i
$616$	16.4164	0.661436
$617$	− 17.5623i	− 0.707032i	−0.935429	−	0.353516i	$-0.884986\pi$
$617$	− 17.5623i	− 0.707032i	0.935429	−	0.353516i	$-0.115014\pi$
$618$	2.56231i	0.103071i
$619$	21.1459	0.849925	0.424963	−	0.905211i	$-0.360287\pi$
$619$	21.1459	0.849925	0.424963	+	0.905211i	$0.360287\pi$
$620$	19.7984	0.795122
$621$	3.47214	0.139332
$622$	− 13.5279i	− 0.542418i
$623$	− 47.1246i	− 1.88801i
$624$	0.236068	0.00945028
$625$	25.0000	1.00000
$626$	−19.1459	−0.765224
$627$	14.3262i	0.572135i
$628$	15.7082i	0.626826i
$629$	21.7082	0.865563
$630$	28.4164	1.13214
$631$	3.41641	0.136005	0.0680025	−	0.997685i	$-0.478337\pi$
$631$	3.41641	0.136005	0.0680025	+	0.997685i	$0.478337\pi$
$632$	5.70820i	0.227060i
$633$	− 3.52786i	− 0.140220i
$634$	26.2705	1.04334
$635$	− 8.29180i	− 0.329050i
$636$	1.23607	0.0490133
$637$	− 6.32624i	− 0.250655i
$638$	12.5410i	0.496504i
$639$	6.85410	0.271144
$640$	− 2.23607i	− 0.0883883i
$641$	30.6525	1.21070	0.605350	−	0.795959i	$-0.293033\pi$
$641$	30.6525	1.21070	0.605350	+	0.795959i	$0.293033\pi$
$642$	1.05573i	0.0416663i
$643$	35.0132i	1.38078i	0.723435	+	0.690392i	$0.242562\pi$
$643$	35.0132i	1.38078i	−0.723435	+	0.690392i	$0.757438\pi$
$644$	−4.85410	−0.191278
$645$	9.34752	0.368058
$646$	−40.1246	−1.57868
$647$	0.291796i	0.0114717i	0.999984	+	0.00573584i	$0.00182579\pi$
$647$	0.291796i	0.0114717i	−0.999984	+	0.00573584i	$0.998174\pi$
$648$	− 5.70820i	− 0.224239i
$649$	−20.2918	−0.796523
$650$	−1.90983	−0.0749097
$651$	26.5623	1.04106
$652$	− 7.03444i	− 0.275490i
$653$	− 11.9787i	− 0.468763i	−0.972145	−	0.234382i	$-0.924693\pi$
$653$	− 11.9787i	− 0.468763i	0.972145	−	0.234382i	$-0.0753065\pi$
$654$	7.76393	0.303594
$655$	18.2918	0.714720
$656$	−3.38197	−0.132044
$657$	− 19.7082i	− 0.768890i
$658$	56.8328i	2.21557i
$659$	−17.8885	−0.696839	−0.348419	−	0.937339i	$-0.613281\pi$
$659$	−17.8885	−0.696839	−0.348419	+	0.937339i	$0.613281\pi$
$660$	− 4.67376i	− 0.181926i
$661$	34.3951	1.33782	0.668908	−	0.743346i	$-0.266762\pi$
$661$	34.3951	1.33782	0.668908	+	0.743346i	$0.266762\pi$
$662$	15.1246i	0.587835i
$663$	1.38197i	0.0536711i
$664$	−5.70820	−0.221521
$665$	− 74.3951i	− 2.88492i
$666$	9.70820	0.376185
$667$	− 3.70820i	− 0.143582i
$668$	3.70820i	0.143475i
$669$	−13.8197	−0.534299
$670$	1.70820	0.0659937
$671$	13.0344	0.503189
$672$	− 3.00000i	− 0.115728i
$673$	− 14.2918i	− 0.550908i	−0.961314	−	0.275454i	$-0.911172\pi$
$673$	− 14.2918i	− 0.550908i	0.961314	−	0.275454i	$-0.0888282\pi$
$674$	−5.61803	−0.216399
$675$	− 17.3607i	− 0.668213i
$676$	−12.8541	−0.494389
$677$	− 42.0000i	− 1.61419i	−0.590421	−	0.807096i	$-0.701038\pi$
$677$	− 42.0000i	− 1.61419i	0.590421	−	0.807096i	$-0.298962\pi$
$678$	8.29180i	0.318445i
$679$	77.8328	2.98695
$680$	13.0902	0.501985
$681$	−14.6525	−0.561484
$682$	29.9443i	1.14663i
$683$	35.9787i	1.37669i	0.725385	+	0.688344i	$0.241662\pi$
$683$	35.9787i	1.37669i	−0.725385	+	0.688344i	$0.758338\pi$
$684$	−17.9443	−0.686116
$685$	15.9787i	0.610515i
$686$	−46.4164	−1.77219
$687$	− 6.18034i	− 0.235795i
$688$	6.76393i	0.257872i
$689$	0.763932	0.0291035
$690$	1.38197i	0.0526105i
$691$	19.1246	0.727535	0.363767	−	0.931490i	$-0.381490\pi$
$691$	19.1246	0.727535	0.363767	+	0.931490i	$0.381490\pi$
$692$	3.56231i	0.135419i
$693$	42.9787i	1.63263i
$694$	−5.56231	−0.211142
$695$	−39.5967	−1.50199
$696$	2.29180	0.0868703
$697$	− 19.7984i	− 0.749917i
$698$	− 14.2918i	− 0.540952i
$699$	−11.8197	−0.447061
$700$	24.2705i	0.917339i
$701$	36.9230	1.39456	0.697281	−	0.716798i	$-0.254393\pi$
$701$	36.9230	1.39456	0.697281	+	0.716798i	$0.254393\pi$
$702$	1.32624i	0.0500556i
$703$	− 25.4164i	− 0.958598i
$704$	3.38197	0.127463
$705$	16.1803	0.609387
$706$	−8.00000	−0.301084
$707$	50.8328i	1.91176i
$708$	3.70820i	0.139363i
$709$	11.5623	0.434232	0.217116	−	0.976146i	$-0.430335\pi$
$709$	11.5623	0.434232	0.217116	+	0.976146i	$0.430335\pi$
$710$	5.85410i	0.219701i
$711$	−14.9443	−0.560454
$712$	− 9.70820i	− 0.363830i
$713$	− 8.85410i	− 0.331589i
$714$	17.5623	0.657253
$715$	− 2.88854i	− 0.108025i
$716$	16.4721	0.615593
$717$	− 0.944272i	− 0.0352645i
$718$	− 13.4164i	− 0.500696i
$719$	32.4508	1.21021	0.605106	−	0.796145i	$-0.293131\pi$
$719$	32.4508	1.21021	0.605106	+	0.796145i	$0.293131\pi$
$720$	5.85410	0.218169
$721$	20.1246	0.749480
$722$	27.9787i	1.04126i
$723$	1.23607i	0.0459699i
$724$	4.56231	0.169557
$725$	−18.5410	−0.688596
$726$	0.270510	0.0100396
$727$	1.74265i	0.0646312i	0.999478	+	0.0323156i	$0.0102882\pi$
$727$	1.74265i	0.0646312i	−0.999478	+	0.0323156i	$0.989712\pi$
$728$	− 1.85410i	− 0.0687176i
$729$	8.50658	0.315058
$730$	16.8328	0.623010
$731$	−39.5967	−1.46454
$732$	− 2.38197i	− 0.0880400i
$733$	35.8885i	1.32557i	0.748808	+	0.662787i	$0.230626\pi$
$733$	35.8885i	1.32557i	−0.748808	+	0.662787i	$0.769374\pi$
$734$	12.0000	0.442928
$735$	22.8885i	0.844257i
$736$	−1.00000	−0.0368605
$737$	2.58359i	0.0951678i
$738$	− 8.85410i	− 0.325924i
$739$	32.5410	1.19704	0.598520	−	0.801108i	$-0.295756\pi$
$739$	32.5410	1.19704	0.598520	+	0.801108i	$0.295756\pi$
$740$	8.29180i	0.304812i
$741$	1.61803	0.0594400
$742$	− 9.70820i	− 0.356399i
$743$	− 9.97871i	− 0.366084i	−0.983105	−	0.183042i	$-0.941406\pi$
$743$	− 9.97871i	− 0.366084i	0.983105	−	0.183042i	$-0.0585944\pi$
$744$	5.47214	0.200618
$745$	0.854102	0.0312919
$746$	3.05573	0.111878
$747$	− 14.9443i	− 0.546782i
$748$	19.7984i	0.723900i
$749$	8.29180	0.302976
$750$	6.90983	0.252311
$751$	−41.1246	−1.50066	−0.750329	−	0.661064i	$-0.770105\pi$
$751$	−41.1246	−1.50066	−0.750329	+	0.661064i	$0.770105\pi$
$752$	11.7082i	0.426954i
$753$	− 4.81966i	− 0.175638i
$754$	1.41641	0.0515825
$755$	−43.0902	−1.56821
$756$	16.8541	0.612978
$757$	47.0132i	1.70872i	0.519680	+	0.854361i	$0.326051\pi$
$757$	47.0132i	1.70872i	−0.519680	+	0.854361i	$0.673949\pi$
$758$	− 9.27051i	− 0.336720i
$759$	−2.09017	−0.0758684
$760$	− 15.3262i	− 0.555941i
$761$	−11.5066	−0.417113	−0.208557	−	0.978010i	$-0.566877\pi$
$761$	−11.5066	−0.417113	−0.208557	+	0.978010i	$0.566877\pi$
$762$	− 2.29180i	− 0.0830230i
$763$	− 60.9787i	− 2.20758i
$764$	1.41641	0.0512438
$765$	34.2705i	1.23905i
$766$	−27.4164	−0.990595
$767$	2.29180i	0.0827520i
$768$	− 0.618034i	− 0.0223014i
$769$	34.2918	1.23659	0.618297	−	0.785945i	$-0.287823\pi$
$769$	34.2918	1.23659	0.618297	+	0.785945i	$0.287823\pi$
$770$	−36.7082	−1.32287
$771$	−9.52786	−0.343138
$772$	2.29180i	0.0824835i
$773$	14.0000i	0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$	14.0000i	0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$	−17.7082	−0.636508
$775$	−44.2705	−1.59024
$776$	16.0344	0.575603
$777$	11.1246i	0.399093i
$778$	5.67376i	0.203414i
$779$	−23.1803	−0.830522
$780$	−0.527864	−0.0189006
$781$	−8.85410	−0.316825
$782$	− 5.85410i	− 0.209342i
$783$	12.8754i	0.460129i
$784$	−16.5623	−0.591511
$785$	− 35.1246i	− 1.25365i
$786$	5.05573	0.180332
$787$	− 31.4164i	− 1.11987i	−0.828535	−	0.559937i	$-0.810825\pi$
$787$	− 31.4164i	− 1.11987i	0.828535	−	0.559937i	$-0.189175\pi$
$788$	− 0.437694i	− 0.0155922i
$789$	9.43769	0.335991
$790$	− 12.7639i	− 0.454120i
$791$	65.1246	2.31556
$792$	8.85410i	0.314617i
$793$	− 1.47214i	− 0.0522771i
$794$	35.5623	1.26206
$795$	−2.76393	−0.0980266
$796$	−15.4164	−0.546420
$797$	− 18.5836i	− 0.658265i	−0.944284	−	0.329132i	$-0.893244\pi$
$797$	− 18.5836i	− 0.658265i	0.944284	−	0.329132i	$-0.106756\pi$
$798$	− 20.5623i	− 0.727898i
$799$	−68.5410	−2.42481
$800$	5.00000i	0.176777i
$801$	25.4164	0.898045
$802$	− 34.4721i	− 1.21725i
$803$	25.4590i	0.898428i
$804$	0.472136	0.0166510
$805$	10.8541	0.382557
$806$	3.38197	0.119125
$807$	− 6.47214i	− 0.227830i
$808$	10.4721i	0.368408i
$809$	−27.1591	−0.954861	−0.477431	−	0.878669i	$-0.658432\pi$
$809$	−27.1591	−0.954861	−0.477431	+	0.878669i	$0.658432\pi$
$810$	12.7639i	0.448479i
$811$	−7.70820	−0.270672	−0.135336	−	0.990800i	$-0.543211\pi$
$811$	−7.70820	−0.270672	−0.135336	+	0.990800i	$0.543211\pi$
$812$	− 18.0000i	− 0.631676i
$813$	− 11.8328i	− 0.414995i
$814$	−12.5410	−0.439563
$815$	15.7295i	0.550980i
$816$	3.61803	0.126657
$817$	46.3607i	1.62195i
$818$	6.56231i	0.229446i
$819$	4.85410	0.169616
$820$	7.56231	0.264087
$821$	−2.94427	−0.102756	−0.0513779	−	0.998679i	$-0.516361\pi$
$821$	−2.94427	−0.102756	−0.0513779	+	0.998679i	$0.516361\pi$
$822$	4.41641i	0.154040i
$823$	20.8328i	0.726186i	0.931753	+	0.363093i	$0.118279\pi$
$823$	20.8328i	0.726186i	−0.931753	+	0.363093i	$0.881721\pi$
$824$	4.14590	0.144429
$825$	10.4508i	0.363852i
$826$	29.1246	1.01337
$827$	− 48.2492i	− 1.67779i	−0.544293	−	0.838895i	$-0.683202\pi$
$827$	− 48.2492i	− 1.67779i	0.544293	−	0.838895i	$-0.316798\pi$
$828$	− 2.61803i	− 0.0909830i
$829$	−32.5410	−1.13020	−0.565098	−	0.825024i	$-0.691162\pi$
$829$	−32.5410	−1.13020	−0.565098	+	0.825024i	$0.691162\pi$
$830$	12.7639	0.443043
$831$	−10.1803	−0.353152
$832$	− 0.381966i	− 0.0132423i
$833$	− 96.9574i	− 3.35938i
$834$	−10.9443	−0.378969
$835$	− 8.29180i	− 0.286949i
$836$	23.1803	0.801709
$837$	30.7426i	1.06262i
$838$	− 5.88854i	− 0.203416i
$839$	6.76393	0.233517	0.116758	−	0.993160i	$-0.462750\pi$
$839$	6.76393	0.233517	0.116758	+	0.993160i	$0.462750\pi$
$840$	6.70820i	0.231455i
$841$	−15.2492	−0.525835
$842$	6.85410i	0.236208i
$843$	0.403252i	0.0138887i
$844$	−5.70820	−0.196484
$845$	28.7426	0.988777
$846$	−30.6525	−1.05385
$847$	− 2.12461i	− 0.0730025i
$848$	− 2.00000i	− 0.0686803i
$849$	1.88854	0.0648147
$850$	−29.2705	−1.00397
$851$	3.70820	0.127116
$852$	1.61803i	0.0554329i
$853$	− 51.2148i	− 1.75356i	−0.480891	−	0.876780i	$-0.659687\pi$
$853$	− 51.2148i	− 1.75356i	0.480891	−	0.876780i	$-0.340313\pi$
$854$	−18.7082	−0.640182
$855$	40.1246	1.37223
$856$	1.70820	0.0583852
$857$	36.0000i	1.22974i	0.788630	+	0.614868i	$0.210791\pi$
$857$	36.0000i	1.22974i	−0.788630	+	0.614868i	$0.789209\pi$
$858$	− 0.798374i	− 0.0272560i
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	− 15.1246i	− 0.515745i
$861$	10.1459	0.345771
$862$	− 6.76393i	− 0.230380i
$863$	24.0000i	0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$	24.0000i	0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	3.47214	0.118124
$865$	− 7.96556i	− 0.270837i
$866$	29.6180	1.00646
$867$	10.6738i	0.362500i
$868$	− 42.9787i	− 1.45879i
$869$	19.3050	0.654876
$870$	−5.12461	−0.173741
$871$	0.291796	0.00988713
$872$	− 12.5623i	− 0.425413i
$873$	41.9787i	1.42076i
$874$	−6.85410	−0.231843
$875$	− 54.2705i	− 1.83468i
$876$	4.65248	0.157193
$877$	34.6869i	1.17129i	0.810566	+	0.585647i	$0.199160\pi$
$877$	34.6869i	1.17129i	−0.810566	+	0.585647i	$0.800840\pi$
$878$	0.270510i	0.00912926i
$879$	−17.1246	−0.577599
$880$	−7.56231	−0.254925
$881$	−38.2918	−1.29008	−0.645042	−	0.764147i	$-0.723160\pi$
$881$	−38.2918	−1.29008	−0.645042	+	0.764147i	$0.723160\pi$
$882$	− 43.3607i	− 1.46003i
$883$	− 17.7295i	− 0.596645i	−0.954465	−	0.298322i	$-0.903573\pi$
$883$	− 17.7295i	− 0.596645i	0.954465	−	0.298322i	$-0.0964271\pi$
$884$	2.23607	0.0752071
$885$	− 8.29180i	− 0.278726i
$886$	−6.85410	−0.230268
$887$	36.5410i	1.22693i	0.789723	+	0.613464i	$0.210224\pi$
$887$	36.5410i	1.22693i	−0.789723	+	0.613464i	$0.789776\pi$
$888$	2.29180i	0.0769076i
$889$	−18.0000	−0.603701
$890$	21.7082i	0.727661i
$891$	−19.3050	−0.646740
$892$	22.3607i	0.748691i
$893$	80.2492i	2.68544i
$894$	0.236068	0.00789529
$895$	−36.8328	−1.23119
$896$	−4.85410	−0.162164
$897$	0.236068i	0.00788208i
$898$	− 2.56231i	− 0.0855053i
$899$	32.8328	1.09504
$900$	−13.0902	−0.436339
$901$	11.7082	0.390057
$902$	11.4377i	0.380834i
$903$	− 20.2918i	− 0.675269i
$904$	13.4164	0.446223
$905$	−10.2016	−0.339114
$906$	−11.9098	−0.395678
$907$	− 30.5410i	− 1.01410i	−0.861917	−	0.507049i	$-0.830736\pi$
$907$	− 30.5410i	− 1.01410i	0.861917	−	0.507049i	$-0.169264\pi$
$908$	23.7082i	0.786784i
$909$	−27.4164	−0.909345
$910$	4.14590i	0.137435i
$911$	22.3607	0.740842	0.370421	−	0.928864i	$-0.379213\pi$
$911$	22.3607	0.740842	0.370421	+	0.928864i	$0.379213\pi$
$912$	− 4.23607i	− 0.140270i
$913$	19.3050i	0.638901i
$914$	−25.4164	−0.840700
$915$	5.32624i	0.176080i
$916$	−10.0000	−0.330409
$917$	− 39.7082i	− 1.31128i
$918$	20.3262i	0.670866i
$919$	14.5836	0.481068	0.240534	−	0.970641i	$-0.422677\pi$
$919$	14.5836	0.481068	0.240534	+	0.970641i	$0.422677\pi$
$920$	2.23607	0.0737210
$921$	−6.27051	−0.206620
$922$	− 25.3050i	− 0.833374i
$923$	1.00000i	0.0329154i
$924$	−10.1459	−0.333776
$925$	− 18.5410i	− 0.609625i
$926$	2.29180	0.0753131
$927$	10.8541i	0.356495i
$928$	− 3.70820i	− 0.121728i
$929$	−19.3050	−0.633375	−0.316687	−	0.948530i	$-0.602571\pi$
$929$	−19.3050	−0.633375	−0.316687	+	0.948530i	$0.602571\pi$
$930$	−12.2361	−0.401236
$931$	−113.520	−3.72046
$932$	19.1246i	0.626447i
$933$	8.36068i	0.273716i
$934$	−17.1246	−0.560334
$935$	− 44.2705i	− 1.44780i
$936$	1.00000	0.0326860
$937$	8.67376i	0.283359i	0.989913	+	0.141680i	$0.0452503\pi$
$937$	8.67376i	0.283359i	−0.989913	+	0.141680i	$0.954750\pi$
$938$	− 3.70820i	− 0.121077i
$939$	11.8328	0.386149
$940$	− 26.1803i	− 0.853909i
$941$	−24.2148	−0.789379	−0.394690	−	0.918814i	$-0.629148\pi$
$941$	−24.2148	−0.789379	−0.394690	+	0.918814i	$0.629148\pi$
$942$	− 9.70820i	− 0.316310i
$943$	− 3.38197i	− 0.110132i
$944$	6.00000	0.195283
$945$	−37.6869	−1.22596
$946$	22.8754	0.743743
$947$	47.3951i	1.54013i	0.637963	+	0.770067i	$0.279777\pi$
$947$	47.3951i	1.54013i	−0.637963	+	0.770067i	$0.720223\pi$
$948$	− 3.52786i	− 0.114580i
$949$	2.87539	0.0933391
$950$	34.2705i	1.11188i
$951$	−16.2361	−0.526491
$952$	− 28.4164i	− 0.920981i
$953$	− 36.3951i	− 1.17895i	−0.807785	−	0.589477i	$-0.799334\pi$
$953$	− 36.3951i	− 1.17895i	0.807785	−	0.589477i	$-0.200666\pi$
$954$	5.23607	0.169524
$955$	−3.16718	−0.102488
$956$	−1.52786	−0.0494147
$957$	− 7.75078i	− 0.250547i
$958$	19.5279i	0.630917i
$959$	34.6869	1.12010
$960$	1.38197i	0.0446028i
$961$	47.3951	1.52887
$962$	1.41641i	0.0456668i
$963$	4.47214i	0.144113i
$964$	2.00000	0.0644157
$965$	− 5.12461i	− 0.164967i
$966$	3.00000	0.0965234
$967$	− 24.7639i	− 0.796354i	−0.917309	−	0.398177i	$-0.869643\pi$
$967$	− 24.7639i	− 0.796354i	0.917309	−	0.398177i	$-0.130357\pi$
$968$	− 0.437694i	− 0.0140680i
$969$	24.7984	0.796639
$970$	−35.8541	−1.15121
$971$	25.8541	0.829698	0.414849	−	0.909890i	$-0.363834\pi$
$971$	25.8541	0.829698	0.414849	+	0.909890i	$0.363834\pi$
$972$	13.9443i	0.447263i
$973$	85.9574i	2.75567i
$974$	−21.7082	−0.695576
$975$	1.18034	0.0378011
$976$	−3.85410	−0.123367
$977$	32.2705i	1.03243i	0.856461	+	0.516213i	$0.172659\pi$
$977$	32.2705i	1.03243i	−0.856461	+	0.516213i	$0.827341\pi$
$978$	4.34752i	0.139018i
$979$	−32.8328	−1.04934
$980$	37.0344	1.18302
$981$	32.8885	1.05005
$982$	− 26.8328i	− 0.856270i
$983$	26.3951i	0.841874i	0.907090	+	0.420937i	$0.138299\pi$
$983$	26.3951i	0.841874i	−0.907090	+	0.420937i	$0.861701\pi$
$984$	2.09017	0.0666322
$985$	0.978714i	0.0311844i
$986$	21.7082	0.691330
$987$	− 35.1246i	− 1.11803i
$988$	− 2.61803i	− 0.0832908i
$989$	−6.76393	−0.215081
$990$	− 19.7984i	− 0.629234i
$991$	51.2705	1.62866	0.814331	−	0.580401i	$-0.197104\pi$
$991$	51.2705	1.62866	0.814331	+	0.580401i	$0.197104\pi$
$992$	− 8.85410i	− 0.281118i
$993$	− 9.34752i	− 0.296635i
$994$	12.7082	0.403080
$995$	34.4721	1.09284
$996$	3.52786	0.111785
$997$	− 26.7214i	− 0.846274i	−0.906066	−	0.423137i	$-0.860929\pi$
$997$	− 26.7214i	− 0.846274i	0.906066	−	0.423137i	$-0.139071\pi$
$998$	− 11.4164i	− 0.361380i
$999$	−12.8754	−0.407359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.b.a.139.3	yes	4
3.2	odd	2		2070.2.d.c.829.1		4
4.3	odd	2		1840.2.e.c.369.3		4
5.2	odd	4		1150.2.a.l.1.1		2
5.3	odd	4		1150.2.a.n.1.2		2
5.4	even	2	inner	230.2.b.a.139.2	✓	4
15.14	odd	2		2070.2.d.c.829.3		4
20.3	even	4		9200.2.a.by.1.1		2
20.7	even	4		9200.2.a.bo.1.2		2
20.19	odd	2		1840.2.e.c.369.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.a.139.2	✓	4	5.4	even	2	inner
230.2.b.a.139.3	yes	4	1.1	even	1	trivial
1150.2.a.l.1.1		2	5.2	odd	4
1150.2.a.n.1.2		2	5.3	odd	4
1840.2.e.c.369.2		4	20.19	odd	2
1840.2.e.c.369.3		4	4.3	odd	2
2070.2.d.c.829.1		4	3.2	odd	2
2070.2.d.c.829.3		4	15.14	odd	2
9200.2.a.bo.1.2		2	20.7	even	4
9200.2.a.by.1.1		2	20.3	even	4

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.618034i q^{3} -1.00000 q^{4} +2.23607 q^{5} +0.618034 q^{6} -4.85410i q^{7} -1.00000i q^{8} +2.61803 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.618034i q^{3} -1.00000 q^{4} +2.23607 q^{5} +0.618034 q^{6} -4.85410i q^{7} -1.00000i q^{8} +2.61803 q^{9} +2.23607i q^{10} -3.38197 q^{11} +0.618034i q^{12} +0.381966i q^{13} +4.85410 q^{14} -1.38197i q^{15} +1.00000 q^{16} +5.85410i q^{17} +2.61803i q^{18} +6.85410 q^{19} -2.23607 q^{20} -3.00000 q^{21} -3.38197i q^{22} +1.00000i q^{23} -0.618034 q^{24} +5.00000 q^{25} -0.381966 q^{26} -3.47214i q^{27} +4.85410i q^{28} -3.70820 q^{29} +1.38197 q^{30} -8.85410 q^{31} +1.00000i q^{32} +2.09017i q^{33} -5.85410 q^{34} -10.8541i q^{35} -2.61803 q^{36} -3.70820i q^{37} +6.85410i q^{38} +0.236068 q^{39} -2.23607i q^{40} -3.38197 q^{41} -3.00000i q^{42} +6.76393i q^{43} +3.38197 q^{44} +5.85410 q^{45} -1.00000 q^{46} +11.7082i q^{47} -0.618034i q^{48} -16.5623 q^{49} +5.00000i q^{50} +3.61803 q^{51} -0.381966i q^{52} -2.00000i q^{53} +3.47214 q^{54} -7.56231 q^{55} -4.85410 q^{56} -4.23607i q^{57} -3.70820i q^{58} +6.00000 q^{59} +1.38197i q^{60} -3.85410 q^{61} -8.85410i q^{62} -12.7082i q^{63} -1.00000 q^{64} +0.854102i q^{65} -2.09017 q^{66} -0.763932i q^{67} -5.85410i q^{68} +0.618034 q^{69} +10.8541 q^{70} +2.61803 q^{71} -2.61803i q^{72} -7.52786i q^{73} +3.70820 q^{74} -3.09017i q^{75} -6.85410 q^{76} +16.4164i q^{77} +0.236068i q^{78} -5.70820 q^{79} +2.23607 q^{80} +5.70820 q^{81} -3.38197i q^{82} -5.70820i q^{83} +3.00000 q^{84} +13.0902i q^{85} -6.76393 q^{86} +2.29180i q^{87} +3.38197i q^{88} +9.70820 q^{89} +5.85410i q^{90} +1.85410 q^{91} -1.00000i q^{92} +5.47214i q^{93} -11.7082 q^{94} +15.3262 q^{95} +0.618034 q^{96} +16.0344i q^{97} -16.5623i q^{98} -8.85410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9} - 18 q^{11} + 6 q^{14} + 4 q^{16} + 14 q^{19} - 12 q^{21} + 2 q^{24} + 20 q^{25} - 6 q^{26} + 12 q^{29} + 10 q^{30} - 22 q^{31} - 10 q^{34} - 6 q^{36} - 8 q^{39} - 18 q^{41} + 18 q^{44} + 10 q^{45} - 4 q^{46} - 26 q^{49} + 10 q^{51} - 4 q^{54} + 10 q^{55} - 6 q^{56} + 24 q^{59} - 2 q^{61} - 4 q^{64} + 14 q^{66} - 2 q^{69} + 30 q^{70} + 6 q^{71} - 12 q^{74} - 14 q^{76} + 4 q^{79} - 4 q^{81} + 12 q^{84} - 36 q^{86} + 12 q^{89} - 6 q^{91} - 20 q^{94} + 30 q^{95} - 2 q^{96} - 22 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9 - 18 * q^11 + 6 * q^14 + 4 * q^16 + 14 * q^19 - 12 * q^21 + 2 * q^24 + 20 * q^25 - 6 * q^26 + 12 * q^29 + 10 * q^30 - 22 * q^31 - 10 * q^34 - 6 * q^36 - 8 * q^39 - 18 * q^41 + 18 * q^44 + 10 * q^45 - 4 * q^46 - 26 * q^49 + 10 * q^51 - 4 * q^54 + 10 * q^55 - 6 * q^56 + 24 * q^59 - 2 * q^61 - 4 * q^64 + 14 * q^66 - 2 * q^69 + 30 * q^70 + 6 * q^71 - 12 * q^74 - 14 * q^76 + 4 * q^79 - 4 * q^81 + 12 * q^84 - 36 * q^86 + 12 * q^89 - 6 * q^91 - 20 * q^94 + 30 * q^95 - 2 * q^96 - 22 * q^99

Introduction

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