LMFDB - Embedded newform 231.2.e.a.188.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(188,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, 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("231.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.e (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.17
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.776672i q^{2} +(-0.233960 + 1.71618i) q^{3} +1.39678 q^{4} -3.58495 q^{5} +(-1.33291 - 0.181710i) q^{6} +(-2.64177 - 0.145081i) q^{7} +2.63818i q^{8} +(-2.89053 - 0.803035i) q^{9} +O(q^{10})$	\(q+0.776672i q^{2} +(-0.233960 + 1.71618i) q^{3} +1.39678 q^{4} -3.58495 q^{5} +(-1.33291 - 0.181710i) q^{6} +(-2.64177 - 0.145081i) q^{7} +2.63818i q^{8} +(-2.89053 - 0.803035i) q^{9} -2.78433i q^{10} +1.00000i q^{11} +(-0.326791 + 2.39712i) q^{12} +4.05287i q^{13} +(0.112680 - 2.05179i) q^{14} +(0.838736 - 6.15240i) q^{15} +0.744557 q^{16} +4.26370 q^{17} +(0.623695 - 2.24499i) q^{18} -2.75361i q^{19} -5.00739 q^{20} +(0.867054 - 4.49980i) q^{21} -0.776672 q^{22} +7.51125i q^{23} +(-4.52759 - 0.617231i) q^{24} +7.85185 q^{25} -3.14775 q^{26} +(2.05442 - 4.77277i) q^{27} +(-3.68997 - 0.202646i) q^{28} -5.24578i q^{29} +(4.77840 + 0.651423i) q^{30} +6.53209i q^{31} +5.85465i q^{32} +(-1.71618 - 0.233960i) q^{33} +3.31149i q^{34} +(9.47061 + 0.520107i) q^{35} +(-4.03743 - 1.12166i) q^{36} -2.71212 q^{37} +2.13865 q^{38} +(-6.95544 - 0.948211i) q^{39} -9.45775i q^{40} -4.19889 q^{41} +(3.49487 + 0.673417i) q^{42} +0.621637 q^{43} +1.39678i q^{44} +(10.3624 + 2.87884i) q^{45} -5.83378 q^{46} +7.15260 q^{47} +(-0.174197 + 1.27779i) q^{48} +(6.95790 + 0.766541i) q^{49} +6.09831i q^{50} +(-0.997536 + 7.31725i) q^{51} +5.66097i q^{52} +1.37425i q^{53} +(3.70688 + 1.59561i) q^{54} -3.58495i q^{55} +(0.382750 - 6.96948i) q^{56} +(4.72567 + 0.644235i) q^{57} +4.07425 q^{58} +11.1032 q^{59} +(1.17153 - 8.59356i) q^{60} -0.588781i q^{61} -5.07329 q^{62} +(7.51960 + 2.54079i) q^{63} -3.05803 q^{64} -14.5293i q^{65} +(0.181710 - 1.33291i) q^{66} -7.60926 q^{67} +5.95545 q^{68} +(-12.8906 - 1.75733i) q^{69} +(-0.403953 + 7.35556i) q^{70} +8.94987i q^{71} +(2.11855 - 7.62574i) q^{72} -9.68633i q^{73} -2.10643i q^{74} +(-1.83702 + 13.4752i) q^{75} -3.84618i q^{76} +(0.145081 - 2.64177i) q^{77} +(0.736449 - 5.40209i) q^{78} +5.10669 q^{79} -2.66920 q^{80} +(7.71027 + 4.64238i) q^{81} -3.26116i q^{82} -1.24236 q^{83} +(1.21108 - 6.28524i) q^{84} -15.2851 q^{85} +0.482808i q^{86} +(9.00269 + 1.22731i) q^{87} -2.63818 q^{88} -10.3591 q^{89} +(-2.23591 + 8.04817i) q^{90} +(0.587994 - 10.7067i) q^{91} +10.4916i q^{92} +(-11.2102 - 1.52825i) q^{93} +5.55523i q^{94} +9.87153i q^{95} +(-10.0476 - 1.36976i) q^{96} +13.9249i q^{97} +(-0.595351 + 5.40401i) q^{98} +(0.803035 - 2.89053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			0.776672i			0.549190i	0.961560	+	0.274595i	$0.0885438\pi$
$2$			0.776672i			0.549190i	−0.961560	+	0.274595i	$0.911456\pi$
$3$	−0.233960	+	1.71618i	−0.135077	+	0.990835i
$3$	−0.233960	+	1.71618i	−0.135077	+	0.990835i
$4$	1.39678			0.698390
$5$	−3.58495			−1.60324			−0.801619	−	0.597836i	$-0.796028\pi$
$5$	−3.58495			−1.60324			−0.801619	+	0.597836i	$0.796028\pi$
$6$	−1.33291	−	0.181710i	−0.544157	−	0.0741830i
$7$	−2.64177	−	0.145081i	−0.998495	−	0.0548354i
$7$	−2.64177	−	0.145081i	−0.998495	−	0.0548354i
$8$			2.63818i			0.932739i
$9$	−2.89053	−	0.803035i	−0.963508	−	0.267678i
$10$		−	2.78433i		−	0.880482i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−0.326791	+	2.39712i	−0.0943365	+	0.691990i
$13$			4.05287i			1.12406i	0.827116	+	0.562032i	$0.189980\pi$
$13$			4.05287i			1.12406i	−0.827116	+	0.562032i	$0.810020\pi$
$14$	0.112680	−	2.05179i	0.0301151	−	0.548364i
$15$	0.838736	−	6.15240i	0.216561	−	1.58854i
$16$	0.744557			0.186139
$17$	4.26370			1.03410			0.517049	−	0.855956i	$-0.327030\pi$
$17$	4.26370			1.03410			0.517049	+	0.855956i	$0.327030\pi$
$18$	0.623695	−	2.24499i	0.147006	−	0.529149i
$19$		−	2.75361i		−	0.631721i	−0.948806	−	0.315860i	$-0.897707\pi$
$19$		−	2.75361i		−	0.631721i	0.948806	−	0.315860i	$-0.102293\pi$
$20$	−5.00739			−1.11969
$21$	0.867054	−	4.49980i	0.189207	−	0.981937i
$22$	−0.776672			−0.165587
$23$			7.51125i			1.56620i	0.621894	+	0.783102i	$0.286364\pi$
$23$			7.51125i			1.56620i	−0.621894	+	0.783102i	$0.713636\pi$
$24$	−4.52759	−	0.617231i	−0.924191	−	0.125992i
$25$	7.85185			1.57037
$26$	−3.14775			−0.617325
$27$	2.05442	−	4.77277i	0.395373	−	0.918521i
$28$	−3.68997	−	0.202646i	−0.697339	−	0.0382965i
$29$		−	5.24578i		−	0.974117i	−0.873369	−	0.487059i	$-0.838070\pi$
$29$		−	5.24578i		−	0.974117i	0.873369	−	0.487059i	$-0.161930\pi$
$30$	4.77840	+	0.651423i	0.872413	+	0.118933i
$31$			6.53209i			1.17320i	0.809878	+	0.586599i	$0.199533\pi$
$31$			6.53209i			1.17320i	−0.809878	+	0.586599i	$0.800467\pi$
$32$			5.85465i			1.03496i
$33$	−1.71618	−	0.233960i	−0.298748	−	0.0407273i
$34$			3.31149i			0.567916i
$35$	9.47061	+	0.520107i	1.60083	+	0.0879142i
$36$	−4.03743	−	1.12166i	−0.672905	−	0.186944i
$37$	−2.71212			−0.445870			−0.222935	−	0.974833i	$-0.571564\pi$
$37$	−2.71212			−0.445870			−0.222935	+	0.974833i	$0.571564\pi$
$38$	2.13865			0.346935
$39$	−6.95544	−	0.948211i	−1.11376	−	0.151835i
$40$		−	9.45775i		−	1.49540i
$41$	−4.19889			−0.655757			−0.327879	−	0.944720i	$-0.606334\pi$
$41$	−4.19889			−0.655757			−0.327879	+	0.944720i	$0.606334\pi$
$42$	3.49487	+	0.673417i	0.539270	+	0.103910i
$43$	0.621637			0.0947987			0.0473993	−	0.998876i	$-0.484907\pi$
$43$	0.621637			0.0947987			0.0473993	+	0.998876i	$0.484907\pi$
$44$			1.39678i			0.210573i
$45$	10.3624	+	2.87884i	1.54473	+	0.429152i
$46$	−5.83378			−0.860143
$47$	7.15260			1.04331			0.521657	−	0.853155i	$-0.325314\pi$
$47$	7.15260			1.04331			0.521657	+	0.853155i	$0.325314\pi$
$48$	−0.174197	+	1.27779i	−0.0251432	+	0.184433i
$49$	6.95790	+	0.766541i	0.993986	+	0.109506i
$50$			6.09831i			0.862432i
$51$	−0.997536	+	7.31725i	−0.139683	+	1.02462i
$52$			5.66097i			0.785035i
$53$			1.37425i			0.188767i	0.995536	+	0.0943837i	$0.0300880\pi$
$53$			1.37425i			0.188767i	−0.995536	+	0.0943837i	$0.969912\pi$
$54$	3.70688	+	1.59561i	0.504442	+	0.217135i
$55$		−	3.58495i		−	0.483394i
$56$	0.382750	−	6.96948i	0.0511471	−	0.931336i
$57$	4.72567	+	0.644235i	0.625931	+	0.0853310i
$58$	4.07425			0.534976
$59$	11.1032			1.44552			0.722759	−	0.691100i	$-0.242874\pi$
$59$	11.1032			1.44552			0.722759	+	0.691100i	$0.242874\pi$
$60$	1.17153	−	8.59356i	0.151244	−	1.10942i
$61$		−	0.588781i		−	0.0753857i	−0.999289	−	0.0376929i	$-0.987999\pi$
$61$		−	0.588781i		−	0.0753857i	0.999289	−	0.0376929i	$-0.0120009\pi$
$62$	−5.07329			−0.644309
$63$	7.51960	+	2.54079i	0.947380	+	0.320110i
$64$	−3.05803			−0.382253
$65$		−	14.5293i		−	1.80214i
$66$	0.181710	−	1.33291i	0.0223670	−	0.164069i
$67$	−7.60926			−0.929619			−0.464810	−	0.885411i	$-0.653877\pi$
$67$	−7.60926			−0.929619			−0.464810	+	0.885411i	$0.653877\pi$
$68$	5.95545			0.722204
$69$	−12.8906	−	1.75733i	−1.55185	−	0.211558i
$70$	−0.403953	+	7.35556i	−0.0482816	+	0.879157i
$71$			8.94987i			1.06215i	0.847324	+	0.531077i	$0.178212\pi$
$71$			8.94987i			1.06215i	−0.847324	+	0.531077i	$0.821788\pi$
$72$	2.11855	−	7.62574i	0.249674	−	0.898702i
$73$		−	9.68633i		−	1.13370i	−0.823821	−	0.566849i	$-0.808162\pi$
$73$		−	9.68633i		−	1.13370i	0.823821	−	0.566849i	$-0.191838\pi$
$74$		−	2.10643i		−	0.244867i
$75$	−1.83702	+	13.4752i	−0.212121	+	1.55598i
$76$		−	3.84618i		−	0.441188i
$77$	0.145081	−	2.64177i	0.0165335	−	0.301058i
$78$	0.736449	−	5.40209i	0.0833864	−	0.611667i
$79$	5.10669			0.574547			0.287274	−	0.957849i	$-0.407251\pi$
$79$	5.10669			0.574547			0.287274	+	0.957849i	$0.407251\pi$
$80$	−2.66920			−0.298425
$81$	7.71027	+	4.64238i	0.856697	+	0.515820i
$82$		−	3.26116i		−	0.360135i
$83$	−1.24236			−0.136367			−0.0681836	−	0.997673i	$-0.521720\pi$
$83$	−1.24236			−0.136367			−0.0681836	+	0.997673i	$0.521720\pi$
$84$	1.21108	−	6.28524i	0.132140	−	0.685775i
$85$	−15.2851			−1.65790
$86$			0.482808i			0.0520625i
$87$	9.00269	+	1.22731i	0.965190	+	0.131581i
$88$	−2.63818			−0.281231
$89$	−10.3591			−1.09806			−0.549031	−	0.835802i	$-0.685003\pi$
$89$	−10.3591			−1.09806			−0.549031	+	0.835802i	$0.685003\pi$
$90$	−2.23591	+	8.04817i	−0.235686	+	0.848352i
$91$	0.587994	−	10.7067i	0.0616385	−	1.12237i
$92$			10.4916i			1.09382i
$93$	−11.2102	−	1.52825i	−1.16245	−	0.158472i
$94$			5.55523i			0.572978i
$95$			9.87153i			1.01280i
$96$	−10.0476	−	1.36976i	−1.02548	−	0.139800i
$97$			13.9249i			1.41386i	0.707286	+	0.706928i	$0.249919\pi$
$97$			13.9249i			1.41386i	−0.707286	+	0.706928i	$0.750081\pi$
$98$	−0.595351	+	5.40401i	−0.0601395	+	0.545887i
$99$	0.803035	−	2.89053i	0.0807080	−	0.290509i
$100$	10.9673			1.09673
$101$	−3.61277			−0.359484			−0.179742	−	0.983714i	$-0.557526\pi$
$101$	−3.61277			−0.359484			−0.179742	+	0.983714i	$0.557526\pi$
$102$	−5.68311	−	0.774758i	−0.562711	−	0.0767125i
$103$			2.22913i			0.219643i	0.993951	+	0.109821i	$0.0350279\pi$
$103$			2.22913i			0.219643i	−0.993951	+	0.109821i	$0.964972\pi$
$104$	−10.6922			−1.04846
$105$	−3.10834	+	16.1316i	−0.303343	+	1.57428i
$106$	−1.06734			−0.103669
$107$		−	19.3229i		−	1.86801i	−0.357255	−	0.934007i	$-0.616287\pi$
$107$		−	19.3229i		−	1.86801i	0.357255	−	0.934007i	$-0.383713\pi$
$108$	2.86957	−	6.66652i	0.276125	−	0.641486i
$109$	−8.69394			−0.832728			−0.416364	−	0.909198i	$-0.636696\pi$
$109$	−8.69394			−0.832728			−0.416364	+	0.909198i	$0.636696\pi$
$110$	2.78433			0.265475
$111$	0.634529	−	4.65448i	0.0602268	−	0.441784i
$112$	−1.96695	−	0.108021i	−0.185859	−	0.0102070i
$113$		−	0.681534i		−	0.0641133i	−0.999486	−	0.0320567i	$-0.989794\pi$
$113$		−	0.681534i		−	0.0641133i	0.999486	−	0.0320567i	$-0.0102057\pi$
$114$	−0.500359	+	3.67030i	−0.0468629	+	0.343755i
$115$		−	26.9274i		−	2.51100i
$116$		−	7.32721i		−	0.680314i
$117$	3.25459	−	11.7149i	0.300887	−	1.08304i
$118$			8.62357i			0.793864i
$119$	−11.2637	−	0.618580i	−1.03254	−	0.0567052i
$120$	16.2312	+	2.21274i	1.48170	+	0.201995i
$121$	−1.00000			−0.0909091
$122$	0.457290			0.0414011
$123$	0.982375	−	7.20604i	0.0885778	−	0.649747i
$124$			9.12389i			0.819350i
$125$	−10.2237			−0.914439
$126$	−1.97336	+	5.84026i	−0.175801	+	0.520292i
$127$	20.5687			1.82517			0.912587	−	0.408883i	$-0.134081\pi$
$127$	20.5687			1.82517			0.912587	+	0.408883i	$0.134081\pi$
$128$			9.33421i			0.825035i
$129$	−0.145438	+	1.06684i	−0.0128051	+	0.0939299i
$130$	11.2845			0.989718
$131$	−6.13786			−0.536268			−0.268134	−	0.963382i	$-0.586407\pi$
$131$	−6.13786			−0.536268			−0.268134	+	0.963382i	$0.586407\pi$
$132$	−2.39712	−	0.326791i	−0.208643	−	0.0284435i
$133$	−0.399495	+	7.27440i	−0.0346407	+	0.630770i
$134$		−	5.90990i		−	0.510538i
$135$	−7.36498	+	17.1101i	−0.633877	+	1.47261i
$136$			11.2484i			0.964544i
$137$			0.903085i			0.0771557i	0.999256	+	0.0385779i	$0.0122828\pi$
$137$			0.903085i			0.0771557i	−0.999256	+	0.0385779i	$0.987717\pi$
$138$	1.36487	−	10.0118i	0.116186	−	0.852260i
$139$		−	1.84234i		−	0.156266i	−0.996943	−	0.0781328i	$-0.975104\pi$
$139$		−	1.84234i		−	0.156266i	0.996943	−	0.0781328i	$-0.0248958\pi$
$140$	13.2284	+	0.726476i	1.11800	+	0.0613984i
$141$	−1.67343	+	12.2751i	−0.140928	+	1.03375i
$142$	−6.95111			−0.583324
$143$	−4.05287			−0.338918
$144$	−2.15216	−	0.597905i	−0.179347	−	0.0498254i
$145$			18.8059i			1.56174i
$146$	7.52310			0.622616
$147$	−2.94339	+	11.7617i	−0.242767	+	0.970085i
$148$	−3.78824			−0.311391
$149$		−	14.9075i		−	1.22127i	−0.791912	−	0.610635i	$-0.790914\pi$
$149$		−	14.9075i		−	1.22127i	0.791912	−	0.610635i	$-0.209086\pi$
$150$	−10.4658	−	1.42676i	−0.854528	−	0.116495i
$151$	11.2490			0.915428			0.457714	−	0.889099i	$-0.348668\pi$
$151$	11.2490			0.915428			0.457714	+	0.889099i	$0.348668\pi$
$152$	7.26452			0.589230
$153$	−12.3243	−	3.42390i	−0.996362	−	0.276806i
$154$	2.05179	+	0.112680i	0.165338	+	0.00908003i
$155$		−	23.4172i		−	1.88091i
$156$	−9.71522	−	1.32444i	−0.777840	−	0.106040i
$157$			7.34109i			0.585882i	0.956130	+	0.292941i	$0.0946340\pi$
$157$			7.34109i			0.585882i	−0.956130	+	0.292941i	$0.905366\pi$
$158$			3.96622i			0.315536i
$159$	−2.35845	−	0.321519i	−0.187037	−	0.0254982i
$160$		−	20.9886i		−	1.65929i
$161$	1.08974	−	19.8430i	0.0858834	−	1.56385i
$162$	−3.60561	+	5.98835i	−0.283283	+	0.470489i
$163$	2.33654			0.183012			0.0915060	−	0.995805i	$-0.470832\pi$
$163$	2.33654			0.183012			0.0915060	+	0.995805i	$0.470832\pi$
$164$	−5.86493			−0.457974
$165$	6.15240	+	0.838736i	0.478964	+	0.0652955i
$166$		−	0.964909i		−	0.0748915i
$167$	−0.595906			−0.0461126			−0.0230563	−	0.999734i	$-0.507340\pi$
$167$	−0.595906			−0.0461126			−0.0230563	+	0.999734i	$0.507340\pi$
$168$	11.8713	+	2.28745i	0.915891	+	0.176480i
$169$	−3.42574			−0.263519
$170$		−	11.8715i		−	0.910505i
$171$	−2.21124	+	7.95937i	−0.169098	+	0.608668i
$172$	0.868290			0.0662065
$173$	−8.15611			−0.620097			−0.310049	−	0.950721i	$-0.600345\pi$
$173$	−8.15611			−0.620097			−0.310049	+	0.950721i	$0.600345\pi$
$174$	−0.953214	+	6.99214i	−0.0722629	+	0.530073i
$175$	−20.7428	−	1.13915i	−1.56801	−	0.0861119i
$176$			0.744557i			0.0561231i
$177$	−2.59772	+	19.0551i	−0.195256	+	1.43227i
$178$		−	8.04563i		−	0.603045i
$179$		−	4.50558i		−	0.336763i	−0.985722	−	0.168382i	$-0.946146\pi$
$179$		−	4.50558i		−	0.336763i	0.985722	−	0.168382i	$-0.0538541\pi$
$180$	14.4740	+	4.02110i	1.07883	+	0.299715i
$181$		−	13.2642i		−	0.985917i	−0.870053	−	0.492958i	$-0.835916\pi$
$181$		−	13.2642i		−	0.985917i	0.870053	−	0.492958i	$-0.164084\pi$
$182$	8.31563	+	0.456678i	0.616396	+	0.0338512i
$183$	1.01045	+	0.137752i	0.0746948	+	0.0101829i
$184$	−19.8161			−1.46086
$185$	9.72281			0.714835
$186$	1.18695	−	8.70666i	0.0870313	−	0.638403i
$187$			4.26370i			0.311792i
$188$	9.99062			0.728641
$189$	−6.11974	+	12.3105i	−0.445145	+	0.895458i
$190$	−7.66694			−0.556219
$191$		−	9.98530i		−	0.722511i	−0.932467	−	0.361255i	$-0.882348\pi$
$191$		−	9.98530i		−	0.722511i	0.932467	−	0.361255i	$-0.117652\pi$
$192$	0.715457	−	5.24811i	0.0516336	−	0.378750i
$193$	7.00164			0.503989			0.251994	−	0.967729i	$-0.418914\pi$
$193$	7.00164			0.503989			0.251994	+	0.967729i	$0.418914\pi$
$194$	−10.8150			−0.776475
$195$	24.9349	+	3.39929i	1.78562	+	0.243428i
$196$	9.71866	+	1.07069i	0.694190	+	0.0764778i
$197$			10.3799i			0.739538i	0.929124	+	0.369769i	$0.120563\pi$
$197$			10.3799i			0.739538i	−0.929124	+	0.369769i	$0.879437\pi$
$198$	2.24499	+	0.623695i	0.159544	+	0.0443240i
$199$			15.8410i			1.12294i	0.827496	+	0.561471i	$0.189764\pi$
$199$			15.8410i			1.12294i	−0.827496	+	0.561471i	$0.810236\pi$
$200$			20.7146i			1.46475i
$201$	1.78027	−	13.0588i	0.125570	−	0.921099i
$202$		−	2.80594i		−	0.197425i
$203$	−0.761062	+	13.8582i	−0.0534161	+	0.972652i
$204$	−1.39334	+	10.2206i	−0.0975532	+	0.715585i
$205$	15.0528			1.05133
$206$	−1.73130			−0.120626
$207$	6.03179	−	21.7114i	0.419239	−	1.50905i
$208$			3.01759i			0.209232i
$209$	2.75361			0.190471
$210$	−12.5289	−	2.41416i	−0.864578	−	0.166593i
$211$	12.8456			0.884330			0.442165	−	0.896934i	$-0.354210\pi$
$211$	12.8456			0.884330			0.442165	+	0.896934i	$0.354210\pi$
$212$			1.91952i			0.131833i
$213$	−15.3596	−	2.09391i	−1.05242	−	0.143473i
$214$	15.0075			1.02589
$215$	−2.22853			−0.151985
$216$	12.5915	+	5.41993i	0.856740	+	0.368780i
$217$	0.947681	−	17.2563i	0.0643328	−	1.17143i
$218$		−	6.75234i		−	0.457326i
$219$	16.6234	+	2.26622i	1.12331	+	0.153137i
$220$		−	5.00739i		−	0.337598i
$221$			17.2802i			1.16239i
$222$	3.61500	+	0.492821i	0.242623	+	0.0330760i
$223$		−	3.77096i		−	0.252522i	−0.991997	−	0.126261i	$-0.959702\pi$
$223$		−	3.77096i		−	0.252522i	0.991997	−	0.126261i	$-0.0402977\pi$
$224$	0.849397	−	15.4666i	0.0567527	−	1.03341i
$225$	−22.6960	−	6.30531i	−1.51306	−	0.420354i
$226$	0.529329			0.0352104
$227$	26.2910			1.74500			0.872499	−	0.488616i	$-0.162498\pi$
$227$	26.2910			1.74500			0.872499	+	0.488616i	$0.162498\pi$
$228$	6.60073	+	0.899855i	0.437144	+	0.0595943i
$229$			7.26272i			0.479934i	0.970781	+	0.239967i	$0.0771367\pi$
$229$			7.26272i			0.479934i	−0.970781	+	0.239967i	$0.922863\pi$
$230$	20.9138			1.37901
$231$	4.49980	+	0.867054i	0.296065	+	0.0570480i
$232$	13.8393			0.908597
$233$			1.20802i			0.0791402i	0.999217	+	0.0395701i	$0.0125988\pi$
$233$			1.20802i			0.0791402i	−0.999217	+	0.0395701i	$0.987401\pi$
$234$	9.09865	+	2.52775i	0.594797	+	0.165244i
$235$	−25.6417			−1.67268
$236$	15.5088			1.00954
$237$	−1.19476	+	8.76398i	−0.0776082	+	0.569282i
$238$	0.480434	−	8.74820i	0.0311419	−	0.567062i
$239$			19.6508i			1.27110i	0.772059	+	0.635551i	$0.219227\pi$
$239$			19.6508i			1.27110i	−0.772059	+	0.635551i	$0.780773\pi$
$240$	0.624487	−	4.58082i	0.0403104	−	0.295690i
$241$		−	17.8123i		−	1.14739i	−0.819068	−	0.573697i	$-0.805509\pi$
$241$		−	17.8123i		−	1.14739i	0.819068	−	0.573697i	$-0.194491\pi$
$242$		−	0.776672i		−	0.0499264i
$243$	−9.77105	+	12.1461i	−0.626813	+	0.779170i
$244$		−	0.822398i		−	0.0526487i
$245$	−24.9437	−	2.74801i	−1.59360	−	0.175564i
$246$	5.59673	+	0.762983i	0.356835	+	0.0486460i
$247$	11.1600			0.710094
$248$	−17.2329			−1.09429
$249$	0.290664	−	2.13212i	0.0184201	−	0.135117i
$250$		−	7.94049i		−	0.502201i
$251$	19.8062			1.25016			0.625079	−	0.780562i	$-0.285067\pi$
$251$	19.8062			1.25016			0.625079	+	0.780562i	$0.285067\pi$
$252$	10.5032	+	3.54893i	0.661641	+	0.223562i
$253$	−7.51125			−0.472228
$254$			15.9751i			1.00237i
$255$	3.57611	−	26.2320i	0.223945	−	1.64271i
$256$	−13.3657			−0.835354
$257$	20.2115			1.26076			0.630380	−	0.776287i	$-0.282899\pi$
$257$	20.2115			1.26076			0.630380	+	0.776287i	$0.282899\pi$
$258$	−0.828583	−	0.112958i	−0.0515854	−	0.00703245i
$259$	7.16480	+	0.393477i	0.445199	+	0.0244495i
$260$		−	20.2943i		−	1.25860i
$261$	−4.21255	+	15.1631i	−0.260750	+	0.938570i
$262$		−	4.76711i		−	0.294513i
$263$			6.33654i			0.390728i	0.980731	+	0.195364i	$0.0625888\pi$
$263$			6.33654i			0.390728i	−0.980731	+	0.195364i	$0.937411\pi$
$264$	0.617231	−	4.52759i	0.0379879	−	0.278654i
$265$		−	4.92661i		−	0.302639i
$266$	−5.64982	−	0.310277i	−0.346413	−	0.0190243i
$267$	2.42362	−	17.7781i	0.148323	−	1.08800i
$268$	−10.6285			−0.649237
$269$	−2.93713			−0.179080			−0.0895399	−	0.995983i	$-0.528540\pi$
$269$	−2.93713			−0.179080			−0.0895399	+	0.995983i	$0.528540\pi$
$270$	−13.2890	−	5.72017i	−0.808741	−	0.348119i
$271$			6.48266i			0.393794i	0.980424	+	0.196897i	$0.0630864\pi$
$271$			6.48266i			0.393794i	−0.980424	+	0.196897i	$0.936914\pi$
$272$	3.17456			0.192486
$273$	18.2371	+	3.51406i	1.10376	+	0.212680i
$274$	−0.701401			−0.0423732
$275$			7.85185i			0.473484i
$276$	−18.0054	−	2.45461i	−1.08380	−	0.147750i
$277$	−0.00529989			−0.000318440			−0.000159220	−	1.00000i	$-0.500051\pi$
$277$	−0.00529989			−0.000318440			−0.000159220		1.00000i	$0.500051\pi$
$278$	1.43090			0.0858195
$279$	5.24549	−	18.8812i	0.314040	−	1.13039i
$280$	−1.37214	+	24.9852i	−0.0820010	+	1.49315i
$281$		−	11.0139i		−	0.657033i	−0.944498	−	0.328516i	$-0.893451\pi$
$281$		−	11.0139i		−	0.657033i	0.944498	−	0.328516i	$-0.106549\pi$
$282$	−9.53375	−	1.29970i	−0.567727	−	0.0773962i
$283$			22.7314i			1.35124i	0.737250	+	0.675620i	$0.236124\pi$
$283$			22.7314i			1.35124i	−0.737250	+	0.675620i	$0.763876\pi$
$284$			12.5010i			0.741798i
$285$	−16.9413	−	2.30955i	−1.00352	−	0.136806i
$286$		−	3.14775i		−	0.186130i
$287$	11.0925	+	0.609179i	0.654770	+	0.0359587i
$288$	4.70148	−	16.9230i	0.277038	−	0.997197i
$289$	1.17910			0.0693586
$290$	−14.6060			−0.857693
$291$	−23.8975	−	3.25787i	−1.40090	−	0.190979i
$292$		−	13.5297i		−	0.791764i
$293$	−23.5606			−1.37642			−0.688212	−	0.725509i	$-0.741604\pi$
$293$	−23.5606			−1.37642			−0.688212	+	0.725509i	$0.741604\pi$
$294$	−9.13495	−	2.28605i	−0.532761	−	0.133325i
$295$	−39.8045			−2.31751
$296$		−	7.15508i		−	0.415880i
$297$	4.77277	+	2.05442i	0.276944	+	0.119209i
$298$	11.5782			0.670709
$299$	−30.4421			−1.76051
$300$	−2.56592	+	18.8218i	−0.148143	+	1.08668i
$301$	−1.64222	−	0.0901876i	−0.0946561	−	0.00519832i
$302$			8.73676i			0.502744i
$303$	0.845245	−	6.20015i	0.0485581	−	0.356189i
$304$		−	2.05022i		−	0.117588i
$305$			2.11075i			0.120861i
$306$	2.65924	−	9.57195i	0.152019	−	0.547192i
$307$			25.0808i			1.43144i	0.698388	+	0.715720i	$0.253901\pi$
$307$			25.0808i			1.43144i	−0.698388	+	0.715720i	$0.746099\pi$
$308$	0.202646	−	3.68997i	0.0115468	−	0.210256i
$309$	−3.82559	−	0.521529i	−0.217630	−	0.0296687i
$310$	18.1875			1.03298
$311$	−13.4661			−0.763592			−0.381796	−	0.924247i	$-0.624694\pi$
$311$	−13.4661			−0.763592			−0.381796	+	0.924247i	$0.624694\pi$
$312$	2.50155	−	18.3497i	0.141623	−	1.03885i
$313$			31.5157i			1.78137i	0.454617	+	0.890687i	$0.349776\pi$
$313$			31.5157i			1.78137i	−0.454617	+	0.890687i	$0.650224\pi$
$314$	−5.70162			−0.321761
$315$	−26.9574	−	9.10861i	−1.51888	−	0.513212i
$316$	7.13292			0.401258
$317$			3.77958i			0.212282i	0.994351	+	0.106141i	$0.0338495\pi$
$317$			3.77958i			0.212282i	−0.994351	+	0.106141i	$0.966150\pi$
$318$	0.249715	−	1.83174i	0.0140033	−	0.102719i
$319$	5.24578			0.293707
$320$	10.9629			0.612843
$321$	33.1615	+	4.52079i	1.85089	+	0.252326i
$322$	15.4115	+	0.846369i	0.858849	+	0.0471663i
$323$		−	11.7405i		−	0.653261i
$324$	10.7696	+	6.48439i	0.598309	+	0.360244i
$325$			31.8225i			1.76520i
$326$			1.81473i			0.100508i
$327$	2.03404	−	14.9203i	0.112483	−	0.825097i
$328$		−	11.0775i		−	0.611650i
$329$	−18.8955	−	1.03771i	−1.04174	−	0.0572106i
$330$	−0.651423	+	4.77840i	−0.0358596	+	0.263042i
$331$	1.94580			0.106951			0.0534755	−	0.998569i	$-0.482970\pi$
$331$	1.94580			0.106951			0.0534755	+	0.998569i	$0.482970\pi$
$332$	−1.73531			−0.0952375
$333$	7.83945	+	2.17793i	0.429599	+	0.119350i
$334$		−	0.462823i		−	0.0253246i
$335$	27.2788			1.49040
$336$	0.645571	−	3.35036i	0.0352188	−	0.182777i
$337$	−13.3183			−0.725493			−0.362746	−	0.931888i	$-0.618161\pi$
$337$	−13.3183			−0.725493			−0.362746	+	0.931888i	$0.618161\pi$
$338$		−	2.66068i		−	0.144722i
$339$	1.16963	+	0.159452i	0.0635258	+	0.00866024i
$340$	−21.3500			−1.15786
$341$	−6.53209			−0.353732
$342$	−6.18182	−	1.71741i	−0.334274	−	0.0928669i
$343$	−18.2700	−	3.03448i	−0.986486	−	0.163847i
$344$			1.63999i			0.0884224i
$345$	46.2122	+	6.29995i	2.48798	+	0.339178i
$346$		−	6.33462i		−	0.340551i
$347$			19.3391i			1.03818i	0.854720	+	0.519089i	$0.173729\pi$
$347$			19.3391i			1.03818i	−0.854720	+	0.519089i	$0.826271\pi$
$348$	12.5748	+	1.71428i	0.674079	+	0.0918948i
$349$		−	16.0970i		−	0.861650i	−0.902435	−	0.430825i	$-0.858223\pi$
$349$		−	16.0970i		−	0.861650i	0.902435	−	0.430825i	$-0.141777\pi$
$350$	0.884748	−	16.1103i	0.0472918	−	0.861134i
$351$	19.3434	+	8.32629i	1.03248	+	0.444424i
$352$	−5.85465			−0.312054
$353$	−22.9802			−1.22311			−0.611557	−	0.791200i	$-0.709457\pi$
$353$	−22.9802			−1.22311			−0.611557	+	0.791200i	$0.709457\pi$
$354$	−14.7996	−	2.01757i	−0.786589	−	0.107233i
$355$		−	32.0848i		−	1.70288i
$356$	−14.4694			−0.766876
$357$	3.69685	−	19.1858i	0.195658	−	1.01542i
$358$	3.49936			0.184947
$359$			12.4746i			0.658386i	0.944263	+	0.329193i	$0.106777\pi$
$359$			12.4746i			0.658386i	−0.944263	+	0.329193i	$0.893223\pi$
$360$	−7.59490	+	27.3379i	−0.400287	+	1.44083i
$361$	11.4177			0.600929
$362$	10.3019			0.541456
$363$	0.233960	−	1.71618i	0.0122797	−	0.0900759i
$364$	0.821298	−	14.9550i	0.0430477	−	0.783854i
$365$			34.7250i			1.81759i
$366$	−0.106988	+	0.784791i	−0.00559234	+	0.0410217i
$367$		−	17.6135i		−	0.919416i	−0.888070	−	0.459708i	$-0.847954\pi$
$367$		−	17.6135i		−	0.919416i	0.888070	−	0.459708i	$-0.152046\pi$
$368$			5.59255i			0.291532i
$369$	12.1370	+	3.37186i	0.631827	+	0.175532i
$370$			7.55144i			0.392581i
$371$	0.199377	−	3.63045i	0.0103511	−	0.188483i
$372$	−15.6582	−	2.13463i	−0.811841	−	0.110675i
$373$	−12.0833			−0.625650			−0.312825	−	0.949811i	$-0.601275\pi$
$373$	−12.0833			−0.625650			−0.312825	+	0.949811i	$0.601275\pi$
$374$	−3.31149			−0.171233
$375$	2.39195	−	17.5457i	0.123520	−	0.906058i
$376$			18.8699i			0.973140i
$377$	21.2605			1.09497
$378$	−9.56123	−	4.75303i	−0.491777	−	0.244469i
$379$	26.0759			1.33943			0.669715	−	0.742618i	$-0.266416\pi$
$379$	26.0759			1.33943			0.669715	+	0.742618i	$0.266416\pi$
$380$			13.7884i			0.707328i
$381$	−4.81225	+	35.2995i	−0.246539	+	1.80845i
$382$	7.75530			0.396796
$383$	16.1774			0.826624			0.413312	−	0.910589i	$-0.364372\pi$
$383$	16.1774			0.826624			0.413312	+	0.910589i	$0.364372\pi$
$384$	−16.0192	−	2.18383i	−0.817474	−	0.111443i
$385$	−0.520107	+	9.47061i	−0.0265071	+	0.482667i
$386$			5.43798i			0.276786i
$387$	−1.79686	−	0.499196i	−0.0913393	−	0.0253755i
$388$			19.4500i			0.987423i
$389$			21.9974i			1.11531i	0.830072	+	0.557656i	$0.188299\pi$
$389$			21.9974i			1.11531i	−0.830072	+	0.557656i	$0.811701\pi$
$390$	−2.64013	+	19.3662i	−0.133688	+	0.980647i
$391$			32.0257i			1.61961i
$392$	−2.02228	+	18.3562i	−0.102140	+	0.927130i
$393$	1.43602	−	10.5337i	0.0724375	−	0.531353i
$394$	−8.06179			−0.406147
$395$	−18.3072			−0.921136
$396$	1.12166	−	4.03743i	0.0563657	−	0.202888i
$397$		−	31.4114i		−	1.57649i	−0.615361	−	0.788245i	$-0.710990\pi$
$397$		−	31.4114i		−	1.57649i	0.615361	−	0.788245i	$-0.289010\pi$
$398$	−12.3033			−0.616709
$399$	−12.3907	−	2.38753i	−0.620310	−	0.119526i
$400$	5.84615			0.292308
$401$		−	11.8859i		−	0.593554i	−0.954947	−	0.296777i	$-0.904088\pi$
$401$		−	11.8859i		−	0.593554i	0.954947	−	0.296777i	$-0.0959118\pi$
$402$	10.1424	+	1.38268i	0.505859	+	0.0689619i
$403$	−26.4737			−1.31875
$404$	−5.04625			−0.251060
$405$	−27.6409	−	16.6427i	−1.37349	−	0.826983i
$406$	−10.7632	−	0.591096i	−0.534171	−	0.0293356i
$407$		−	2.71212i		−	0.134435i
$408$	−19.3043	−	2.63168i	−0.955704	−	0.130288i
$409$		−	28.7226i		−	1.42024i	−0.704079	−	0.710121i	$-0.748640\pi$
$409$		−	28.7226i		−	1.42024i	0.704079	−	0.710121i	$-0.251360\pi$
$410$			11.6911i			0.577382i
$411$	−1.54985	−	0.211286i	−0.0764486	−	0.0104220i
$412$			3.11361i			0.153397i
$413$	−29.3322	−	1.61087i	−1.44334	−	0.0792656i
$414$	16.8627	+	4.68472i	0.828755	+	0.230242i
$415$	4.45381			0.218629
$416$	−23.7281			−1.16337
$417$	3.16179	+	0.431035i	0.154833	+	0.0211079i
$418$			2.13865i			0.104605i
$419$	17.3987			0.849984			0.424992	−	0.905197i	$-0.360277\pi$
$419$	17.3987			0.849984			0.424992	+	0.905197i	$0.360277\pi$
$420$	−4.34167	+	22.5322i	−0.211852	+	1.09946i
$421$	24.4121			1.18977			0.594887	−	0.803809i	$-0.297197\pi$
$421$	24.4121			1.18977			0.594887	+	0.803809i	$0.297197\pi$
$422$			9.97685i			0.485665i
$423$	−20.6748	−	5.74379i	−1.00524	−	0.279273i
$424$	−3.62552			−0.176071
$425$	33.4779			1.62392
$426$	1.62628	−	11.9293i	0.0787937	−	0.577978i
$427$	−0.0854209	+	1.55543i	−0.00413381	+	0.0752723i
$428$		−	26.9898i		−	1.30460i
$429$	0.948211	−	6.95544i	0.0457800	−	0.335812i
$430$		−	1.73084i		−	0.0834686i
$431$		−	37.2639i		−	1.79494i	−0.441075	−	0.897470i	$-0.645403\pi$
$431$		−	37.2639i		−	1.79494i	0.441075	−	0.897470i	$-0.354597\pi$
$432$	1.52963	−	3.55360i	0.0735944	−	0.170973i
$433$		−	17.8993i		−	0.860184i	−0.902785	−	0.430092i	$-0.858481\pi$
$433$		−	17.8993i		−	0.860184i	0.902785	−	0.430092i	$-0.141519\pi$
$434$	13.4025	+	0.736037i	0.643339	+	0.0353309i
$435$	−32.2742	−	4.39983i	−1.54743	−	0.210955i
$436$	−12.1435			−0.581569
$437$	20.6830			0.989403
$438$	−1.76011	+	12.9110i	−0.0841012	+	0.616910i
$439$		−	13.6094i		−	0.649539i	−0.945793	−	0.324770i	$-0.894713\pi$
$439$		−	13.6094i		−	0.649539i	0.945793	−	0.324770i	$-0.105287\pi$
$440$	9.45775			0.450881
$441$	−19.4964	−	7.80314i	−0.928402	−	0.371578i
$442$	−13.4210			−0.638374
$443$		−	25.4575i		−	1.20952i	−0.796407	−	0.604761i	$-0.793269\pi$
$443$		−	25.4575i		−	1.20952i	0.796407	−	0.604761i	$-0.206731\pi$
$444$	0.886298	−	6.50129i	0.0420618	−	0.308537i
$445$	37.1368			1.76046
$446$	2.92880			0.138682
$447$	25.5839	+	3.48777i	1.21008	+	0.164966i
$448$	8.07860	+	0.443661i	0.381678	+	0.0209610i
$449$			23.2375i			1.09664i	0.836267	+	0.548322i	$0.184733\pi$
$449$			23.2375i			1.09664i	−0.836267	+	0.548322i	$0.815267\pi$
$450$	4.89716	−	17.6273i	0.230854	−	0.830960i
$451$		−	4.19889i		−	0.197718i
$452$		−	0.951954i		−	0.0447761i
$453$	−2.63181	+	19.3052i	−0.123653	+	0.907039i
$454$			20.4195i			0.958336i
$455$	−2.10793	+	38.3831i	−0.0988211	+	1.79943i
$456$	−1.69961	+	12.4672i	−0.0795915	+	0.583830i
$457$	−25.7638			−1.20518			−0.602591	−	0.798051i	$-0.705865\pi$
$457$	−25.7638			−1.20518			−0.602591	+	0.798051i	$0.705865\pi$
$458$	−5.64075			−0.263575
$459$	8.75941	−	20.3497i	0.408854	−	0.949840i
$460$		−	37.6117i		−	1.75366i
$461$	29.5305			1.37537			0.687686	−	0.726009i	$-0.258627\pi$
$461$	29.5305			1.37537			0.687686	+	0.726009i	$0.258627\pi$
$462$	−0.673417	+	3.49487i	−0.0313302	+	0.162596i
$463$	28.3142			1.31587			0.657936	−	0.753074i	$-0.271430\pi$
$463$	28.3142			1.31587			0.657936	+	0.753074i	$0.271430\pi$
$464$		−	3.90578i		−	0.181321i
$465$	40.1880	+	5.47870i	1.86368	+	0.254068i
$466$	−0.938238			−0.0434630
$467$	−13.9998			−0.647832			−0.323916	−	0.946086i	$-0.605000\pi$
$467$	−13.9998			−0.647832			−0.323916	+	0.946086i	$0.605000\pi$
$468$	4.54595	−	16.3632i	0.210137	−	0.756388i
$469$	20.1019	+	1.10396i	0.928220	+	0.0509760i
$470$		−	19.9152i		−	0.918620i
$471$	−12.5986	−	1.71752i	−0.580513	−	0.0791393i
$472$			29.2924i			1.34829i
$473$			0.621637i			0.0285829i
$474$	−6.80674	−	0.927939i	−0.312644	−	0.0426216i
$475$		−	21.6209i		−	0.992035i
$476$	−15.7329	−	0.864021i	−0.721117	−	0.0396023i
$477$	1.10357	−	3.97230i	0.0505289	−	0.181879i
$478$	−15.2622			−0.698076
$479$	22.9754			1.04977			0.524886	−	0.851173i	$-0.324108\pi$
$479$	22.9754			1.04977			0.524886	+	0.851173i	$0.324108\pi$
$480$	36.0201	+	4.91050i	1.64409	+	0.224133i
$481$		−	10.9919i		−	0.501186i
$482$	13.8343			0.630137
$483$	33.7991	+	6.51266i	1.53791	+	0.296336i
$484$	−1.39678			−0.0634900
$485$		−	49.9199i		−	2.26675i
$486$	−9.43350	−	7.58890i	−0.427912	−	0.344240i
$487$	7.85833			0.356095			0.178048	−	0.984022i	$-0.443022\pi$
$487$	7.85833			0.356095			0.178048	+	0.984022i	$0.443022\pi$
$488$	1.55331			0.0703152
$489$	−0.546658	+	4.00992i	−0.0247207	+	0.181335i
$490$	2.13430	−	19.3731i	0.0964179	−	0.875187i
$491$			31.7886i			1.43460i	0.696764	+	0.717301i	$0.254623\pi$
$491$			31.7886i			1.43460i	−0.696764	+	0.717301i	$0.745377\pi$
$492$	1.37216	−	10.0653i	0.0618618	−	0.453777i
$493$		−	22.3664i		−	1.00733i
$494$			8.66766i			0.389977i
$495$	−2.87884	+	10.3624i	−0.129394	+	0.465754i
$496$			4.86351i			0.218378i
$497$	1.29845	−	23.6435i	0.0582436	−	1.06056i
$498$	1.65596	+	0.225751i	0.0742051	+	0.0101161i
$499$	−35.6336			−1.59518			−0.797589	−	0.603201i	$-0.793892\pi$
$499$	−35.6336			−1.59518			−0.797589	+	0.603201i	$0.793892\pi$
$500$	−14.2803			−0.638635
$501$	0.139418	−	1.02268i	0.00622875	−	0.0456900i
$502$			15.3829i			0.686574i
$503$	1.35331			0.0603412			0.0301706	−	0.999545i	$-0.490395\pi$
$503$	1.35331			0.0603412			0.0301706	+	0.999545i	$0.490395\pi$
$504$	−6.70308	+	19.8381i	−0.298579	+	0.883659i
$505$	12.9516			0.576338
$506$		−	5.83378i		−	0.259343i
$507$	0.801489	−	5.87918i	0.0355954	−	0.261104i
$508$	28.7299			1.27468
$509$	−1.84366			−0.0817186			−0.0408593	−	0.999165i	$-0.513010\pi$
$509$	−1.84366			−0.0817186			−0.0408593	+	0.999165i	$0.513010\pi$
$510$	20.3736	+	2.77747i	0.902160	+	0.122988i
$511$	−1.40530	+	25.5891i	−0.0621668	+	1.13199i
$512$			8.28768i			0.366267i
$513$	−13.1423	−	5.65706i	−0.580248	−	0.249765i
$514$			15.6977i			0.692397i
$515$		−	7.99132i		−	0.352140i
$516$	−0.203145	+	1.49014i	−0.00894298	+	0.0655997i
$517$			7.15260i			0.314571i
$518$	−0.305602	+	5.56470i	−0.0134274	+	0.244499i
$519$	1.90821	−	13.9973i	0.0837610	−	0.614414i
$520$	38.3310			1.68093
$521$	36.0480			1.57929			0.789646	−	0.613563i	$-0.210264\pi$
$521$	36.0480			1.57929			0.789646	+	0.613563i	$0.210264\pi$
$522$	−11.7767	−	3.27177i	−0.515453	−	0.143201i
$523$		−	17.6572i		−	0.772097i	−0.922479	−	0.386048i	$-0.873840\pi$
$523$		−	17.6572i		−	0.772097i	0.922479	−	0.386048i	$-0.126160\pi$
$524$	−8.57325			−0.374524
$525$	6.80798	−	35.3318i	0.297125	−	1.54201i
$526$	−4.92141			−0.214584
$527$			27.8508i			1.21320i
$528$	−1.27779	−	0.174197i	−0.0556087	−	0.00758095i
$529$	−33.4188			−1.45299
$530$	3.82636			0.166206
$531$	−32.0942	−	8.91629i	−1.39277	−	0.386934i
$532$	−0.558008	+	10.1607i	−0.0241927	+	0.440524i
$533$		−	17.0176i		−	0.737113i
$534$	13.8077	+	1.88236i	0.597518	+	0.0814576i
$535$			69.2715i			2.99487i
$536$		−	20.0746i		−	0.867092i
$537$	7.73238	+	1.05413i	0.333677	+	0.0454890i
$538$		−	2.28118i		−	0.0983488i
$539$	−0.766541	+	6.95790i	−0.0330172	+	0.299698i
$540$	−10.2873	+	23.8991i	−0.442693	+	1.02845i
$541$	−5.93517			−0.255173			−0.127586	−	0.991827i	$-0.540723\pi$
$541$	−5.93517			−0.255173			−0.127586	+	0.991827i	$0.540723\pi$
$542$	−5.03490			−0.216268
$543$	22.7636	+	3.10329i	0.976881	+	0.133175i
$544$			24.9624i			1.07026i
$545$	31.1673			1.33506
$546$	−2.72927	+	14.1643i	−0.116802	+	0.606174i
$547$	−14.5720			−0.623054			−0.311527	−	0.950237i	$-0.600840\pi$
$547$	−14.5720			−0.623054			−0.311527	+	0.950237i	$0.600840\pi$
$548$			1.26141i			0.0538848i
$549$	−0.472812	+	1.70189i	−0.0201791	+	0.0726348i
$550$	−6.09831			−0.260033
$551$	−14.4448			−0.615370
$552$	4.63617	−	34.0079i	0.197329	−	1.44747i
$553$	−13.4907	−	0.740883i	−0.573683	−	0.0315055i
$554$		−	0.00411628i		−	0.000174884i
$555$	−2.27475	+	16.6861i	−0.0965579	+	0.708284i
$556$		−	2.57335i		−	0.109134i
$557$		−	28.2875i		−	1.19858i	−0.800533	−	0.599289i	$-0.795450\pi$
$557$		−	28.2875i		−	1.19858i	0.800533	−	0.599289i	$-0.204550\pi$
$558$	14.6645	+	4.07403i	0.620797	+	0.172467i
$559$			2.51941i			0.106560i
$560$	7.05141	+	0.387250i	0.297976	+	0.0163643i
$561$	−7.31725	−	0.997536i	−0.308935	−	0.0421160i
$562$	8.55417			0.360836
$563$	23.3507			0.984116			0.492058	−	0.870563i	$-0.336245\pi$
$563$	23.3507			0.984116			0.492058	+	0.870563i	$0.336245\pi$
$564$	−2.33741	+	17.1457i	−0.0984227	+	0.721963i
$565$			2.44326i			0.102789i
$566$	−17.6548			−0.742088
$567$	−19.6952	−	13.3827i	−0.827123	−	0.562022i
$568$	−23.6114			−0.990712
$569$			21.4971i			0.901205i	0.892725	+	0.450602i	$0.148791\pi$
$569$			21.4971i			0.901205i	−0.892725	+	0.450602i	$0.851209\pi$
$570$	1.79376	−	13.1578i	0.0751324	−	0.551121i
$571$	9.85025			0.412220			0.206110	−	0.978529i	$-0.433919\pi$
$571$	9.85025			0.412220			0.206110	+	0.978529i	$0.433919\pi$
$572$	−5.66097			−0.236697
$573$	17.1365	+	2.33616i	0.715889	+	0.0975947i
$574$	−0.473132	+	8.61525i	−0.0197482	+	0.359593i
$575$			58.9772i			2.45952i
$576$	8.83930	+	2.45570i	0.368304	+	0.102321i
$577$		−	45.8262i		−	1.90777i	−0.300172	−	0.953885i	$-0.597044\pi$
$577$		−	45.8262i		−	1.90777i	0.300172	−	0.953885i	$-0.402956\pi$
$578$			0.915771i			0.0380911i
$579$	−1.63811	+	12.0160i	−0.0680774	+	0.499370i
$580$			26.2677i			1.09070i
$581$	3.28204	+	0.180243i	0.136162	+	0.00747775i
$582$	2.53029	−	18.5605i	0.104884	−	0.769359i
$583$	−1.37425			−0.0569155
$584$	25.5543			1.05745
$585$	−11.6676	+	41.9974i	−0.482394	+	1.73638i
$586$		−	18.2989i		−	0.755919i
$587$	−37.9222			−1.56522			−0.782608	−	0.622515i	$-0.786111\pi$
$587$	−37.9222			−1.56522			−0.782608	+	0.622515i	$0.786111\pi$
$588$	−4.11127	+	16.4284i	−0.169546	+	0.677498i
$589$	17.9868			0.741133
$590$		−	30.9151i		−	1.27275i
$591$	−17.8138	−	2.42849i	−0.732760	−	0.0998947i
$592$	−2.01933			−0.0829939
$593$	26.4380			1.08568			0.542840	−	0.839836i	$-0.317349\pi$
$593$	26.4380			1.08568			0.542840	+	0.839836i	$0.317349\pi$
$594$	−1.59561	+	3.70688i	−0.0654686	+	0.152095i
$595$	40.3798	+	2.21758i	1.65541	+	0.0909119i
$596$		−	20.8225i		−	0.852923i
$597$	−27.1860	−	3.70618i	−1.11265	−	0.151684i
$598$		−	23.6435i		−	0.966856i
$599$			0.314176i			0.0128369i	0.999979	+	0.00641844i	$0.00204307\pi$
$599$			0.314176i			0.0128369i	−0.999979	+	0.00641844i	$0.997957\pi$
$600$	−35.5500	−	4.84640i	−1.45132	−	0.197854i
$601$			32.2641i			1.31608i	0.752984	+	0.658039i	$0.228614\pi$
$601$			32.2641i			1.31608i	−0.752984	+	0.658039i	$0.771386\pi$
$602$	0.0700462	−	1.27547i	0.00285487	−	0.0519842i
$603$	21.9948	+	6.11050i	0.895696	+	0.248839i
$604$	15.7123			0.639326
$605$	3.58495			0.145749
$606$	4.81548	+	0.656478i	0.195616	+	0.0266676i
$607$		−	17.2421i		−	0.699835i	−0.936780	−	0.349918i	$-0.886210\pi$
$607$		−	17.2421i		−	0.699835i	0.936780	−	0.349918i	$-0.113790\pi$
$608$	16.1214			0.653809
$609$	−23.6050	−	4.54838i	−0.956522	−	0.184310i
$610$	−1.63936			−0.0663758
$611$			28.9886i			1.17275i
$612$	−17.2144	−	4.78243i	−0.695850	−	0.193318i
$613$	−31.3089			−1.26455			−0.632276	−	0.774743i	$-0.717879\pi$
$613$	−31.3089			−1.26455			−0.632276	+	0.774743i	$0.717879\pi$
$614$	−19.4796			−0.786132
$615$	−3.52176	+	25.8333i	−0.142011	+	1.04170i
$616$	6.96948	+	0.382750i	0.280808	+	0.0154214i
$617$			13.5329i			0.544814i	0.962182	+	0.272407i	$0.0878196\pi$
$617$			13.5329i			0.544814i	−0.962182	+	0.272407i	$0.912180\pi$
$618$	0.405057	−	2.97123i	0.0162938	−	0.119520i
$619$			1.91653i			0.0770320i	0.999258	+	0.0385160i	$0.0122631\pi$
$619$			1.91653i			0.0770320i	−0.999258	+	0.0385160i	$0.987737\pi$
$620$		−	32.7087i		−	1.31361i
$621$	35.8495	+	15.4312i	1.43859	+	0.619234i
$622$		−	10.4587i		−	0.419357i
$623$	27.3664	+	1.50291i	1.09641	+	0.0602127i
$624$	−5.17872	−	0.705997i	−0.207315	−	0.0282625i
$625$	−2.60769			−0.104307
$626$	−24.4774			−0.978313
$627$	−0.644235	+	4.72567i	−0.0257283	+	0.188725i
$628$			10.2539i			0.409175i
$629$	−11.5637			−0.461073
$630$	7.07440	−	20.9370i	0.281851	−	0.834151i
$631$	−2.28071			−0.0907935			−0.0453967	−	0.998969i	$-0.514455\pi$
$631$	−2.28071			−0.0907935			−0.0453967	+	0.998969i	$0.514455\pi$
$632$			13.4724i			0.535903i
$633$	−3.00537	+	22.0454i	−0.119453	+	0.876226i
$634$	−2.93549			−0.116583
$635$	−73.7376			−2.92619
$636$	−3.29424	−	0.449092i	−0.130625	−	0.0178077i
$637$	−3.10669	+	28.1995i	−0.123091	+	1.11730i
$638$			4.07425i			0.161301i
$639$	7.18705	−	25.8698i	0.284315	−	1.02339i
$640$		−	33.4627i		−	1.32273i
$641$		−	26.3779i		−	1.04186i	−0.853598	−	0.520932i	$-0.825585\pi$
$641$		−	26.3779i		−	1.04186i	0.853598	−	0.520932i	$-0.174415\pi$
$642$	−3.51117	+	25.7556i	−0.138575	+	1.01649i
$643$		−	2.23702i		−	0.0882196i	−0.999027	−	0.0441098i	$-0.985955\pi$
$643$		−	2.23702i		−	0.0882196i	0.999027	−	0.0441098i	$-0.0140451\pi$
$644$	1.52212	−	27.7163i	0.0599801	−	1.09218i
$645$	0.521389	−	3.82456i	0.0205297	−	0.150592i
$646$	9.11855			0.358764
$647$	−35.8748			−1.41038			−0.705191	−	0.709017i	$-0.749139\pi$
$647$	−35.8748			−1.41038			−0.705191	+	0.709017i	$0.749139\pi$
$648$	−12.2475	+	20.3411i	−0.481126	+	0.799074i
$649$			11.1032i			0.435840i
$650$	−24.7157			−0.969428
$651$	29.3931	+	5.66367i	1.15201	+	0.221977i
$652$	3.26364			0.127814
$653$		−	22.8406i		−	0.893824i	−0.894578	−	0.446912i	$-0.852524\pi$
$653$		−	22.8406i		−	0.893824i	0.894578	−	0.446912i	$-0.147476\pi$
$654$	11.5882	+	1.57978i	0.453135	+	0.0617743i
$655$	22.0039			0.859765
$656$	−3.12632			−0.122062
$657$	−7.77846	+	27.9986i	−0.303467	+	1.09233i
$658$	0.805957	−	14.6756i	0.0314195	−	0.572116i
$659$		−	20.8656i		−	0.812808i	−0.913693	−	0.406404i	$-0.866782\pi$
$659$		−	20.8656i		−	0.812808i	0.913693	−	0.406404i	$-0.133218\pi$
$660$	8.59356	+	1.17153i	0.334504	+	0.0456017i
$661$		−	17.7851i		−	0.691761i	−0.938278	−	0.345881i	$-0.887580\pi$
$661$		−	17.7851i		−	0.691761i	0.938278	−	0.345881i	$-0.112420\pi$
$662$			1.51125i			0.0587364i
$663$	−29.6559	−	4.04288i	−1.15174	−	0.157013i
$664$		−	3.27759i		−	0.127195i
$665$	1.43217	−	26.0783i	0.0555372	−	1.01127i
$666$	−1.69154	+	6.08868i	−0.0655457	+	0.235932i
$667$	39.4024			1.52567
$668$	−0.832350			−0.0322046
$669$	6.47163	+	0.882254i	0.250208	+	0.0341099i
$670$			21.1867i			0.818513i
$671$	0.588781			0.0227297
$672$	26.3447	+	5.07629i	1.01627	+	0.195822i
$673$	−5.30111			−0.204343			−0.102171	−	0.994767i	$-0.532579\pi$
$673$	−5.30111			−0.204343			−0.102171	+	0.994767i	$0.532579\pi$
$674$		−	10.3439i		−	0.398433i
$675$	16.1310	−	37.4751i	0.620882	−	1.44242i
$676$	−4.78501			−0.184039
$677$	−8.41956			−0.323590			−0.161795	−	0.986824i	$-0.551728\pi$
$677$	−8.41956			−0.323590			−0.161795	+	0.986824i	$0.551728\pi$
$678$	−0.123842	+	0.908421i	−0.00475612	+	0.0348877i
$679$	2.02023	−	36.7863i	0.0775293	−	1.41173i
$680$		−	40.3250i		−	1.54639i
$681$	−6.15106	+	45.1201i	−0.235709	+	1.72901i
$682$		−	5.07329i		−	0.194266i
$683$			12.3075i			0.470932i	0.971883	+	0.235466i	$0.0756616\pi$
$683$			12.3075i			0.470932i	−0.971883	+	0.235466i	$0.924338\pi$
$684$	−3.08862	+	11.1175i	−0.118096	+	0.425088i
$685$		−	3.23751i		−	0.123699i
$686$	2.35680	−	14.1898i	0.0899830	−	0.541768i
$687$	−12.4641	−	1.69919i	−0.475536	−	0.0648281i
$688$	0.462844			0.0176458
$689$	−5.56964			−0.212187
$690$	−4.89300	+	35.8917i	−0.186273	+	1.36638i
$691$			19.3086i			0.734533i	0.930116	+	0.367267i	$0.119706\pi$
$691$			19.3086i			0.734533i	−0.930116	+	0.367267i	$0.880294\pi$
$692$	−11.3923			−0.433070
$693$	−2.54079	+	7.51960i	−0.0965168	+	0.285646i
$694$	−15.0201			−0.570157
$695$			6.60471i			0.250531i
$696$	−3.23786	+	23.7508i	−0.122731	+	0.900270i
$697$	−17.9028			−0.678117
$698$	12.5021			0.473210
$699$	−2.07318	−	0.282630i	−0.0784149	−	0.0106900i
$700$	−28.9731	−	1.59115i	−1.09508	−	0.0601397i
$701$			0.851863i			0.0321744i	0.999871	+	0.0160872i	$0.00512094\pi$
$701$			0.851863i			0.0321744i	−0.999871	+	0.0160872i	$0.994879\pi$
$702$	−6.46679	+	15.0235i	−0.244073	+	0.567025i
$703$			7.46811i			0.281665i
$704$		−	3.05803i		−	0.115254i
$705$	5.99914	−	44.0057i	0.225941	−	1.65735i
$706$		−	17.8481i		−	0.671723i
$707$	9.54411	+	0.524144i	0.358943	+	0.0197125i
$708$	−3.62844	+	26.6158i	−0.136365	+	1.00028i
$709$	0.198680			0.00746160			0.00373080	−	0.999993i	$-0.498812\pi$
$709$	0.198680			0.00746160			0.00373080	+	0.999993i	$0.498812\pi$
$710$	24.9194			0.935207
$711$	−14.7610	−	4.10085i	−0.553581	−	0.153794i
$712$		−	27.3292i		−	1.02421i
$713$	−49.0641			−1.83747
$714$	14.9011	+	2.87124i	0.557658	+	0.107454i
$715$	14.5293			0.543366
$716$		−	6.29331i		−	0.235192i
$717$	−33.7242	−	4.59750i	−1.25945	−	0.171697i
$718$	−9.68870			−0.361579
$719$	−4.64935			−0.173392			−0.0866958	−	0.996235i	$-0.527631\pi$
$719$	−4.64935			−0.173392			−0.0866958	+	0.996235i	$0.527631\pi$
$720$	7.71538	+	2.14346i	0.287535	+	0.0798820i
$721$	0.323404	−	5.88886i	0.0120442	−	0.219312i
$722$			8.86777i			0.330024i
$723$	30.5691	+	4.16738i	1.13688	+	0.154987i
$724$		−	18.5271i		−	0.688555i
$725$		−	41.1891i		−	1.52972i
$726$	1.33291	+	0.181710i	0.0494688	+	0.00674391i
$727$		−	23.9838i		−	0.889511i	−0.895652	−	0.444756i	$-0.853290\pi$
$727$		−	23.9838i		−	0.889511i	0.895652	−	0.444756i	$-0.146710\pi$
$728$	28.2464	+	1.55124i	1.04688	+	0.0574926i
$729$	−18.5587	−	19.6105i	−0.687361	−	0.726316i
$730$	−26.9699			−0.998202
$731$	2.65047			0.0980311
$732$	1.41138	+	0.192409i	0.0521661	+	0.00711163i
$733$		−	24.5974i		−	0.908527i	−0.890867	−	0.454264i	$-0.849902\pi$
$733$		−	24.5974i		−	0.908527i	0.890867	−	0.454264i	$-0.150098\pi$
$734$	13.6799			0.504934
$735$	10.5519	−	42.1649i	0.389213	−	1.55528i
$736$	−43.9757			−1.62097
$737$		−	7.60926i		−	0.280291i
$738$	−2.61883	+	9.42647i	−0.0964004	+	0.346993i
$739$	−37.5371			−1.38083			−0.690413	−	0.723416i	$-0.742571\pi$
$739$	−37.5371			−1.38083			−0.690413	+	0.723416i	$0.742571\pi$
$740$	13.5806			0.499234
$741$	−2.61100	+	19.1525i	−0.0959174	+	0.703586i
$742$	2.81967	+	0.154851i	0.103513	+	0.00568474i
$743$		−	39.2980i		−	1.44170i	−0.693089	−	0.720852i	$-0.743751\pi$
$743$		−	39.2980i		−	1.44170i	0.693089	−	0.720852i	$-0.256249\pi$
$744$	4.03181	−	29.5746i	0.147813	−	1.08426i
$745$			53.4426i			1.95799i
$746$		−	9.38476i		−	0.343601i
$747$	3.59108	+	0.997661i	0.131391	+	0.0365025i
$748$			5.95545i			0.217753i
$749$	−2.80338	+	51.0466i	−0.102433	+	1.86520i
$750$	13.6273	+	1.85776i	0.497598	+	0.0678358i
$751$	−34.7758			−1.26899			−0.634494	−	0.772928i	$-0.718792\pi$
$751$	−34.7758			−1.26899			−0.634494	+	0.772928i	$0.718792\pi$
$752$	5.32552			0.194202
$753$	−4.63387	+	33.9910i	−0.168868	+	1.23870i
$754$			16.5124i			0.601346i
$755$	−40.3270			−1.46765
$756$	−8.54793	+	17.1951i	−0.310885	+	0.625379i
$757$	37.6288			1.36764			0.683820	−	0.729650i	$-0.260317\pi$
$757$	37.6288			1.36764			0.683820	+	0.729650i	$0.260317\pi$
$758$			20.2524i			0.735601i
$759$	1.75733	−	12.8906i	0.0637872	−	0.467900i
$760$	−26.0429			−0.944676
$761$	46.7976			1.69641			0.848206	−	0.529667i	$-0.177683\pi$
$761$	46.7976			1.69641			0.848206	+	0.529667i	$0.177683\pi$
$762$	−27.4161	−	3.73754i	−0.993181	−	0.135397i
$763$	22.9674	+	1.26132i	0.831476	+	0.0456630i
$764$		−	13.9473i		−	0.504595i
$765$	44.1820	+	12.2745i	1.59740	+	0.443785i
$766$			12.5645i			0.453974i
$767$			45.0000i			1.62485i
$768$	3.12704	−	22.9379i	0.112837	−	0.827698i
$769$		−	36.1869i		−	1.30493i	−0.757818	−	0.652466i	$-0.773734\pi$
$769$		−	36.1869i		−	1.30493i	0.757818	−	0.652466i	$-0.226266\pi$
$770$	−7.35556	−	0.403953i	−0.265076	−	0.0145574i
$771$	−4.72869	+	34.6865i	−0.170300	+	1.24921i
$772$	9.77975			0.351981
$773$	−9.92555			−0.356997			−0.178499	−	0.983940i	$-0.557124\pi$
$773$	−9.92555			−0.356997			−0.178499	+	0.983940i	$0.557124\pi$
$774$	0.387711	−	1.39557i	0.0139360	−	0.0501627i
$775$			51.2890i			1.84235i
$776$	−36.7363			−1.31876
$777$	−2.35156	+	12.2040i	−0.0843616	+	0.437816i
$778$	−17.0848			−0.612518
$779$			11.5621i			0.414255i
$780$	34.8286	+	4.74806i	1.24706	+	0.170008i
$781$	−8.94987			−0.320251
$782$	−24.8734			−0.889472
$783$	−25.0369	−	10.7770i	−0.894747	−	0.385140i
$784$	5.18056	+	0.570733i	0.185020	+	0.0203833i
$785$		−	26.3174i		−	0.939309i
$786$	8.18120	+	1.11531i	0.291814	+	0.0397819i
$787$		−	2.12178i		−	0.0756334i	−0.999285	−	0.0378167i	$-0.987960\pi$
$787$		−	2.12178i		−	0.0756334i	0.999285	−	0.0378167i	$-0.0120403\pi$
$788$			14.4985i			0.516486i
$789$	−10.8746	−	1.48250i	−0.387147	−	0.0527784i
$790$		−	14.2187i		−	0.505879i
$791$	−0.0988775	+	1.80046i	−0.00351568	+	0.0640169i
$792$	7.62574	+	2.11855i	0.270969	+	0.0752795i
$793$	2.38625			0.0847384
$794$	24.3963			0.865793
$795$	8.45493	+	1.15263i	0.299865	+	0.0408796i
$796$			22.1265i			0.784252i
$797$	−44.4216			−1.57349			−0.786747	−	0.617275i	$-0.788236\pi$
$797$	−44.4216			−1.57349			−0.786747	+	0.617275i	$0.788236\pi$
$798$	1.85432	−	9.62350i	0.0656424	−	0.340668i
$799$	30.4965			1.07889
$800$			45.9698i			1.62528i
$801$	29.9432	+	8.31872i	1.05799	+	0.293928i
$802$	9.23145			0.325974
$803$	9.68633			0.341823
$804$	2.48664	−	18.2403i	0.0876970	−	0.643287i
$805$	−3.90665	+	71.1361i	−0.137691	+	2.50722i
$806$		−	20.5614i		−	0.724244i
$807$	0.687171	−	5.04063i	0.0241896	−	0.177439i
$808$		−	9.53115i		−	0.335305i
$809$		−	0.749307i		−	0.0263442i	−0.999913	−	0.0131721i	$-0.995807\pi$
$809$		−	0.749307i		−	0.0263442i	0.999913	−	0.0131721i	$-0.00419294\pi$
$810$	12.9259	−	21.4679i	0.454171	−	0.754306i
$811$		−	17.9030i		−	0.628659i	−0.949314	−	0.314330i	$-0.898220\pi$
$811$		−	17.9030i		−	0.628659i	0.949314	−	0.314330i	$-0.101780\pi$
$812$	−1.06304	+	19.3568i	−0.0373053	+	0.679290i
$813$	−11.1254	−	1.51669i	−0.390184	−	0.0531925i
$814$	2.10643			0.0738303
$815$	−8.37638			−0.293412
$816$	−0.742722	+	5.44811i	−0.0260005	+	0.190722i
$817$		−	1.71174i		−	0.0598863i
$818$	22.3081			0.779983
$819$	−10.2975	+	30.4759i	−0.359824	+	1.06492i
$820$	21.0255			0.734242
$821$		−	25.4041i		−	0.886609i	−0.896371	−	0.443304i	$-0.853806\pi$
$821$		−	25.4041i		−	0.886609i	0.896371	−	0.443304i	$-0.146194\pi$
$822$	0.164100	−	1.20373i	0.00572364	−	0.0419848i
$823$	7.47961			0.260723			0.130361	−	0.991467i	$-0.458386\pi$
$823$	7.47961			0.260723			0.130361	+	0.991467i	$0.458386\pi$
$824$	−5.88086			−0.204870
$825$	−13.4752	−	1.83702i	−0.469145	−	0.0639569i
$826$	1.25112	−	22.7815i	0.0435319	−	0.792670i
$827$			34.8389i			1.21147i	0.795667	+	0.605734i	$0.207121\pi$
$827$			34.8389i			1.21147i	−0.795667	+	0.605734i	$0.792879\pi$
$828$	8.42509	−	30.3261i	0.292792	−	1.05391i
$829$		−	36.7416i		−	1.27609i	−0.770000	−	0.638043i	$-0.779744\pi$
$829$		−	36.7416i		−	1.27609i	0.770000	−	0.638043i	$-0.220256\pi$
$830$			3.45915i			0.120069i
$831$	0.00123997	−	0.00909556i	4.30139e−5	−	0.000315521i
$832$		−	12.3938i		−	0.429677i
$833$	29.6664	+	3.26830i	1.02788	+	0.113240i
$834$	−0.334773	+	2.45567i	−0.0115922	+	0.0850330i
$835$	2.13629			0.0739294
$836$	3.84618			0.133023
$837$	31.1762	+	13.4196i	1.07761	+	0.463851i
$838$			13.5131i			0.466803i
$839$	28.4173			0.981076			0.490538	−	0.871420i	$-0.336800\pi$
$839$	28.4173			0.981076			0.490538	+	0.871420i	$0.336800\pi$
$840$	−42.5580	−	8.20038i	−1.46839	−	0.282940i
$841$	1.48177			0.0510956
$842$			18.9602i			0.653412i
$843$	18.9018	+	2.57681i	0.651011	+	0.0887501i
$844$	17.9425			0.617608
$845$	12.2811			0.422483
$846$	4.46104	−	16.0575i	0.153374	−	0.552069i
$847$	2.64177	+	0.145081i	0.0907723	+	0.00498504i
$848$			1.02321i			0.0351370i
$849$	−39.0111	−	5.31824i	−1.33886	−	0.182522i
$850$			26.0013i			0.891839i
$851$		−	20.3714i		−	0.698323i
$852$	−21.4539	−	2.92474i	−0.734999	−	0.100200i
$853$			49.5453i			1.69640i	0.529677	+	0.848200i	$0.322313\pi$
$853$			49.5453i			1.69640i	−0.529677	+	0.848200i	$0.677687\pi$
$854$	−1.20806	−	0.0663440i	−0.0413388	−	0.00227025i
$855$	7.92719	−	28.5339i	0.271104	−	0.975839i
$856$	50.9773			1.74237
$857$	32.9971			1.12716			0.563580	−	0.826061i	$-0.309424\pi$
$857$	32.9971			1.12716			0.563580	+	0.826061i	$0.309424\pi$
$858$	5.40209	+	0.736449i	0.184424	+	0.0251419i
$859$			44.6867i			1.52469i	0.647170	+	0.762345i	$0.275952\pi$
$859$			44.6867i			1.52469i	−0.647170	+	0.762345i	$0.724048\pi$
$860$	−3.11277			−0.106145
$861$	−3.64067	+	18.8942i	−0.124074	+	0.643912i
$862$	28.9418			0.985763
$863$			31.3339i			1.06662i	0.845921	+	0.533309i	$0.179052\pi$
$863$			31.3339i			1.06662i	−0.845921	+	0.533309i	$0.820948\pi$
$864$	27.9429	+	12.0279i	0.950637	+	0.409197i
$865$	29.2392			0.994164
$866$	13.9019			0.472405
$867$	−0.275862	+	2.02354i	−0.00936876	+	0.0687230i
$868$	1.32370	−	24.1032i	0.0449294	−	0.818117i
$869$			5.10669i			0.173233i
$870$	3.41722	−	25.0664i	0.115855	−	0.849832i
$871$		−	30.8393i		−	1.04495i
$872$		−	22.9362i		−	0.776718i
$873$	11.1821	−	40.2502i	0.378458	−	1.36226i
$874$			16.0639i			0.543370i
$875$	27.0088	+	1.48327i	0.913063	+	0.0501436i
$876$	23.2193	+	3.16541i	0.784508	+	0.106949i
$877$	−11.3430			−0.383025			−0.191512	−	0.981490i	$-0.561339\pi$
$877$	−11.3430			−0.383025			−0.191512	+	0.981490i	$0.561339\pi$
$878$	10.5700			0.356721
$879$	5.51225	−	40.4341i	0.185923	−	1.36381i
$880$		−	2.66920i		−	0.0899787i
$881$	7.00533			0.236016			0.118008	−	0.993013i	$-0.462349\pi$
$881$	7.00533			0.236016			0.118008	+	0.993013i	$0.462349\pi$
$882$	6.06048	−	15.1423i	0.204067	−	0.509869i
$883$	−49.7964			−1.67578			−0.837892	−	0.545836i	$-0.816212\pi$
$883$	−49.7964			−1.67578			−0.837892	+	0.545836i	$0.816212\pi$
$884$			24.1366i			0.811803i
$885$	9.31268	−	68.3116i	0.313042	−	2.29627i
$886$	19.7721			0.664258
$887$	−41.7434			−1.40161			−0.700803	−	0.713355i	$-0.747175\pi$
$887$	−41.7434			−1.40161			−0.700803	+	0.713355i	$0.747175\pi$
$888$	12.2794	+	1.67400i	0.412069	+	0.0561759i
$889$	−54.3377	−	2.98412i	−1.82243	−	0.100084i
$890$			28.8431i			0.966825i
$891$	−4.64238	+	7.71027i	−0.155526	+	0.258304i
$892$		−	5.26720i		−	0.176359i
$893$		−	19.6955i		−	0.659083i
$894$	−2.70885	+	19.8703i	−0.0905975	+	0.664562i
$895$			16.1523i			0.539911i
$896$	1.35421	−	24.6588i	0.0452411	−	0.823794i
$897$	7.12225	−	52.2440i	0.237805	−	1.74438i
$898$	−18.0479			−0.602266
$899$	34.2659			1.14283
$900$	−31.7013	−	8.80713i	−1.05671	−	0.293571i
$901$			5.85937i			0.195204i
$902$	3.26116			0.108585
$903$	0.538993	−	2.79724i	0.0179365	−	0.0930864i
$904$	1.79801			0.0598010
$905$			47.5513i			1.58066i
$906$	−14.9938	−	2.04406i	−0.498137	−	0.0679092i
$907$	−23.7772			−0.789509			−0.394755	−	0.918787i	$-0.629170\pi$
$907$	−23.7772			−0.789509			−0.394755	+	0.918787i	$0.629170\pi$
$908$	36.7228			1.21869
$909$	10.4428	+	2.90118i	0.346366	+	0.0962261i
$910$	−29.8111	−	1.63717i	−0.988229	−	0.0542716i
$911$		−	15.3652i		−	0.509071i	−0.967063	−	0.254535i	$-0.918078\pi$
$911$		−	15.3652i		−	0.509071i	0.967063	−	0.254535i	$-0.0819225\pi$
$912$	3.51853	+	0.479670i	0.116510	+	0.0158834i
$913$		−	1.24236i		−	0.0411162i
$914$		−	20.0100i		−	0.661873i
$915$	−3.62242	−	0.493832i	−0.119754	−	0.0163256i
$916$			10.1444i			0.335181i
$917$	16.2148	+	0.890487i	0.535461	+	0.0294065i
$918$	15.8050	+	6.80319i	0.521643	+	0.224539i
$919$	−11.7471			−0.387503			−0.193751	−	0.981051i	$-0.562065\pi$
$919$	−11.7471			−0.387503			−0.193751	+	0.981051i	$0.562065\pi$
$920$	71.0395			2.34210
$921$	−43.0432	−	5.86793i	−1.41832	−	0.193355i
$922$			22.9355i			0.755340i
$923$	−36.2726			−1.19393
$924$	6.28524	+	1.21108i	0.206769	+	0.0398417i
$925$	−21.2952			−0.700181
$926$			21.9908i			0.722664i
$927$	1.79007	−	6.44336i	0.0587936	−	0.211628i
$928$	30.7122			1.00818
$929$	−1.43274			−0.0470068			−0.0235034	−	0.999724i	$-0.507482\pi$
$929$	−1.43274			−0.0470068			−0.0235034	+	0.999724i	$0.507482\pi$
$930$	−4.25515	+	31.2129i	−0.139532	+	1.02351i
$931$	2.11075	−	19.1593i	0.0691771	−	0.627922i
$932$			1.68734i			0.0552708i
$933$	3.15053	−	23.1102i	0.103144	−	0.756594i
$934$		−	10.8732i		−	0.355783i
$935$		−	15.2851i		−	0.499877i
$936$	30.9061	+	8.58622i	1.01020	+	0.280649i
$937$			17.9657i			0.586914i	0.955972	+	0.293457i	$0.0948057\pi$
$937$			17.9657i			0.586914i	−0.955972	+	0.293457i	$0.905194\pi$
$938$	−0.857413	+	15.6126i	−0.0279955	+	0.509769i
$939$	−54.0865	−	7.37343i	−1.76505	−	0.240623i
$940$	−35.8158			−1.16818
$941$	−22.2404			−0.725015			−0.362507	−	0.931981i	$-0.618079\pi$
$941$	−22.2404			−0.725015			−0.362507	+	0.931981i	$0.618079\pi$
$942$	1.33395	−	9.78498i	0.0434625	−	0.318812i
$943$		−	31.5389i		−	1.02705i
$944$	8.26699			0.269068
$945$	21.9389	−	44.1326i	0.713674	−	1.43563i
$946$	−0.482808			−0.0156974
$947$		−	27.7647i		−	0.902231i	−0.892466	−	0.451115i	$-0.851026\pi$
$947$		−	27.7647i		−	0.902231i	0.892466	−	0.451115i	$-0.148974\pi$
$948$	−1.66882	+	12.2414i	−0.0542008	+	0.397581i
$949$	39.2574			1.27435
$950$	16.7924			0.544816
$951$	−6.48642	−	0.884272i	−0.210337	−	0.0286745i
$952$	1.63193	−	29.7157i	0.0528911	−	0.963092i
$953$			28.8005i			0.932940i	0.884537	+	0.466470i	$0.154474\pi$
$953$			28.8005i			0.932940i	−0.884537	+	0.466470i	$0.845526\pi$
$954$	3.08517	+	0.857111i	0.0998861	+	0.0277500i
$955$			35.7968i			1.15836i
$956$			27.4478i			0.887725i
$957$	−1.22731	+	9.00269i	−0.0396731	+	0.291016i
$958$			17.8443i			0.576524i
$959$	0.131020	−	2.38574i	0.00423087	−	0.0770396i
$960$	−2.56488	+	18.8142i	−0.0827810	+	0.607226i
$961$	−11.6682			−0.376393
$962$	8.53708			0.275246
$963$	−15.5169	+	55.8533i	−0.500027	+	1.79985i
$964$		−	24.8799i		−	0.801328i
$965$	−25.1005			−0.808014
$966$	−5.05820	+	26.2508i	−0.162745	+	0.844607i
$967$	−22.5367			−0.724730			−0.362365	−	0.932036i	$-0.618031\pi$
$967$	−22.5367			−0.724730			−0.362365	+	0.932036i	$0.618031\pi$
$968$		−	2.63818i		−	0.0847945i
$969$	20.1488	+	2.74682i	0.647274	+	0.0882406i
$970$	38.7714			1.24487
$971$	34.6079			1.11062			0.555311	−	0.831643i	$-0.312599\pi$
$971$	34.6079			1.11062			0.555311	+	0.831643i	$0.312599\pi$
$972$	−13.6480	+	16.9654i	−0.437760	+	0.544165i
$973$	−0.267289	+	4.86705i	−0.00856888	+	0.156030i
$974$			6.10335i			0.195564i
$975$	−54.6131	−	7.44521i	−1.74902	−	0.238438i
$976$		−	0.438381i		−	0.0140322i
$977$			1.83007i			0.0585493i	0.999571	+	0.0292746i	$0.00931974\pi$
$977$			1.83007i			0.0585493i	−0.999571	+	0.0292746i	$0.990680\pi$
$978$	−3.11439	−	0.424574i	−0.0995873	−	0.0135764i
$979$		−	10.3591i		−	0.331078i
$980$	−34.8409	−	3.83836i	−1.11295	−	0.122612i
$981$	25.1301	+	6.98154i	0.802341	+	0.222903i
$982$	−24.6893			−0.787869
$983$	−60.1655			−1.91898			−0.959491	−	0.281738i	$-0.909089\pi$
$983$	−60.1655			−1.91898			−0.959491	+	0.281738i	$0.909089\pi$
$984$	19.0109	+	2.59169i	0.606045	+	0.0826199i
$985$		−	37.2114i		−	1.18566i
$986$	17.3714			0.553217
$987$	6.20169	−	32.1853i	0.197402	−	1.02447i
$988$	15.5881			0.495923
$989$			4.66927i			0.148474i
$990$	−8.04817	−	2.23591i	−0.255788	−	0.0710620i
$991$	42.5231			1.35079			0.675396	−	0.737455i	$-0.263973\pi$
$991$	42.5231			1.35079			0.675396	+	0.737455i	$0.263973\pi$
$992$	−38.2431			−1.21422
$993$	−0.455241	+	3.33934i	−0.0144466	+	0.105971i
$994$	18.3632	+	1.00847i	0.582447	+	0.0319868i
$995$		−	56.7893i		−	1.80034i
$996$	0.405994	−	2.97810i	0.0128644	−	0.0943647i
$997$		−	12.7983i		−	0.405325i	−0.979249	−	0.202662i	$-0.935041\pi$
$997$		−	12.7983i		−	0.405325i	0.979249	−	0.202662i	$-0.0649594\pi$
$998$		−	27.6756i		−	0.876056i
$999$	−5.57183	+	12.9443i	−0.176285	+	0.409541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.e.a.188.17	yes	28
3.2	odd	2	inner	231.2.e.a.188.12	yes	28
7.6	odd	2	inner	231.2.e.a.188.18	yes	28
21.20	even	2	inner	231.2.e.a.188.11	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.e.a.188.11	✓	28	21.20	even	2	inner
231.2.e.a.188.12	yes	28	3.2	odd	2	inner
231.2.e.a.188.17	yes	28	1.1	even	1	trivial
231.2.e.a.188.18	yes	28	7.6	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.776672i q^{2} +(-0.233960 + 1.71618i) q^{3} +1.39678 q^{4} -3.58495 q^{5} +(-1.33291 - 0.181710i) q^{6} +(-2.64177 - 0.145081i) q^{7} +2.63818i q^{8} +(-2.89053 - 0.803035i) q^{9} +O(q^{10})\)	\(q+0.776672i q^{2} +(-0.233960 + 1.71618i) q^{3} +1.39678 q^{4} -3.58495 q^{5} +(-1.33291 - 0.181710i) q^{6} +(-2.64177 - 0.145081i) q^{7} +2.63818i q^{8} +(-2.89053 - 0.803035i) q^{9} -2.78433i q^{10} +1.00000i q^{11} +(-0.326791 + 2.39712i) q^{12} +4.05287i q^{13} +(0.112680 - 2.05179i) q^{14} +(0.838736 - 6.15240i) q^{15} +0.744557 q^{16} +4.26370 q^{17} +(0.623695 - 2.24499i) q^{18} -2.75361i q^{19} -5.00739 q^{20} +(0.867054 - 4.49980i) q^{21} -0.776672 q^{22} +7.51125i q^{23} +(-4.52759 - 0.617231i) q^{24} +7.85185 q^{25} -3.14775 q^{26} +(2.05442 - 4.77277i) q^{27} +(-3.68997 - 0.202646i) q^{28} -5.24578i q^{29} +(4.77840 + 0.651423i) q^{30} +6.53209i q^{31} +5.85465i q^{32} +(-1.71618 - 0.233960i) q^{33} +3.31149i q^{34} +(9.47061 + 0.520107i) q^{35} +(-4.03743 - 1.12166i) q^{36} -2.71212 q^{37} +2.13865 q^{38} +(-6.95544 - 0.948211i) q^{39} -9.45775i q^{40} -4.19889 q^{41} +(3.49487 + 0.673417i) q^{42} +0.621637 q^{43} +1.39678i q^{44} +(10.3624 + 2.87884i) q^{45} -5.83378 q^{46} +7.15260 q^{47} +(-0.174197 + 1.27779i) q^{48} +(6.95790 + 0.766541i) q^{49} +6.09831i q^{50} +(-0.997536 + 7.31725i) q^{51} +5.66097i q^{52} +1.37425i q^{53} +(3.70688 + 1.59561i) q^{54} -3.58495i q^{55} +(0.382750 - 6.96948i) q^{56} +(4.72567 + 0.644235i) q^{57} +4.07425 q^{58} +11.1032 q^{59} +(1.17153 - 8.59356i) q^{60} -0.588781i q^{61} -5.07329 q^{62} +(7.51960 + 2.54079i) q^{63} -3.05803 q^{64} -14.5293i q^{65} +(0.181710 - 1.33291i) q^{66} -7.60926 q^{67} +5.95545 q^{68} +(-12.8906 - 1.75733i) q^{69} +(-0.403953 + 7.35556i) q^{70} +8.94987i q^{71} +(2.11855 - 7.62574i) q^{72} -9.68633i q^{73} -2.10643i q^{74} +(-1.83702 + 13.4752i) q^{75} -3.84618i q^{76} +(0.145081 - 2.64177i) q^{77} +(0.736449 - 5.40209i) q^{78} +5.10669 q^{79} -2.66920 q^{80} +(7.71027 + 4.64238i) q^{81} -3.26116i q^{82} -1.24236 q^{83} +(1.21108 - 6.28524i) q^{84} -15.2851 q^{85} +0.482808i q^{86} +(9.00269 + 1.22731i) q^{87} -2.63818 q^{88} -10.3591 q^{89} +(-2.23591 + 8.04817i) q^{90} +(0.587994 - 10.7067i) q^{91} +10.4916i q^{92} +(-11.2102 - 1.52825i) q^{93} +5.55523i q^{94} +9.87153i q^{95} +(-10.0476 - 1.36976i) q^{96} +13.9249i q^{97} +(-0.595351 + 5.40401i) q^{98} +(0.803035 - 2.89053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

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