LMFDB - Embedded newform 231.2.e.a.188.18

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			188.18
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.776672i q^{2} +(0.233960 - 1.71618i) q^{3} +1.39678 q^{4} +3.58495 q^{5} +(1.33291 + 0.181710i) q^{6} +(-2.64177 + 0.145081i) q^{7} +2.63818i q^{8} +(-2.89053 - 0.803035i) q^{9} +O(q^{10})$	\(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} +(-0.369085 + 4.56769i) 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} +(-3.54760 - 0.286658i) 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} +(7.75261 + 1.70207i) 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} +(-0.515531 + 6.38006i) 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	$-0.203972\pi$
$5$	3.58495			1.60324			0.801619	+	0.597836i	$0.203972\pi$
$6$	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	$-0.810020\pi$
$13$		−	4.05287i		−	1.12406i	0.827116	−	0.562032i	$-0.189980\pi$
$14$	−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	$-0.672970\pi$
$17$	−4.26370			−1.03410			−0.517049	+	0.855956i	$0.672970\pi$
$18$	0.623695	−	2.24499i	0.147006	−	0.529149i
$19$			2.75361i			0.631721i	0.948806	+	0.315860i	$0.102293\pi$
$19$			2.75361i			0.631721i	−0.948806	+	0.315860i	$0.897707\pi$
$20$	5.00739			1.11969
$21$	−0.369085	+	4.56769i	−0.0805410	+	0.996751i
$22$	−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	$-0.800467\pi$
$31$		−	6.53209i		−	1.17320i	0.809878	−	0.586599i	$-0.199533\pi$
$32$			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	$-0.393666\pi$
$41$	4.19889			0.655757			0.327879	+	0.944720i	$0.393666\pi$
$42$	−3.54760	−	0.286658i	−0.547406	−	0.0442323i
$43$	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	$-0.674686\pi$
$47$	−7.15260			−1.04331			−0.521657	+	0.853155i	$0.674686\pi$
$48$	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	$-0.757126\pi$
$59$	−11.1032			−1.44552			−0.722759	+	0.691100i	$0.757126\pi$
$60$	1.17153	−	8.59356i	0.151244	−	1.10942i
$61$			0.588781i			0.0753857i	0.999289	+	0.0376929i	$0.0120009\pi$
$61$			0.588781i			0.0753857i	−0.999289	+	0.0376929i	$0.987999\pi$
$62$	5.07329			0.644309
$63$	7.75261	+	1.70207i	0.976737	+	0.214441i
$64$	−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	$0.191838\pi$
$73$			9.68633i			1.13370i	−0.823821	+	0.566849i	$0.808162\pi$
$74$		−	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	$-0.478280\pi$
$83$	1.24236			0.136367			0.0681836	+	0.997673i	$0.478280\pi$
$84$	−0.515531	+	6.38006i	−0.0562491	+	0.696121i
$85$	−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	$-0.314997\pi$
$89$	10.3591			1.09806			0.549031	+	0.835802i	$0.314997\pi$
$90$	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	$-0.750081\pi$
$97$		−	13.9249i		−	1.41386i	0.707286	−	0.706928i	$-0.249919\pi$
$98$	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	$-0.442474\pi$
$101$	3.61277			0.359484			0.179742	+	0.983714i	$0.442474\pi$
$102$	−5.68311	−	0.774758i	−0.562711	−	0.0767125i
$103$		−	2.22913i		−	0.219643i	−0.993951	−	0.109821i	$-0.964972\pi$
$103$		−	2.22913i		−	0.219643i	0.993951	−	0.109821i	$-0.0350279\pi$
$104$	10.6922			1.04846
$105$	−1.32315	+	16.3749i	−0.129126	+	1.59803i
$106$	−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
$126$	−1.32195	+	6.02123i	−0.117769	+	0.536414i
$127$	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	$-0.413593\pi$
$131$	6.13786			0.536268			0.268134	+	0.963382i	$0.413593\pi$
$132$	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	$0.0248958\pi$
$139$			1.84234i			0.156266i	−0.996943	+	0.0781328i	$0.975104\pi$
$140$	−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
$147$	0.312355	−	12.1203i	0.0257626	−	0.999668i
$148$	−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	$-0.905366\pi$
$157$		−	7.34109i		−	0.585882i	0.956130	−	0.292941i	$-0.0946340\pi$
$158$			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	$-0.492660\pi$
$167$	0.595906			0.0461126			0.0230563	+	0.999734i	$0.492660\pi$
$168$	−12.0504	−	0.973715i	−0.929709	−	0.0751238i
$169$	−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	$-0.399655\pi$
$173$	8.15611			0.620097			0.310049	+	0.950721i	$0.399655\pi$
$174$	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	$0.164084\pi$
$181$			13.2642i			0.985917i	−0.870053	+	0.492958i	$0.835916\pi$
$182$	−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
$189$	4.73486	−	12.9066i	0.344411	−	0.938819i
$190$	−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	$-0.810236\pi$
$199$		−	15.8410i		−	1.12294i	0.827496	−	0.561471i	$-0.189764\pi$
$200$			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
$210$	−12.7179	−	1.02765i	−0.877622	−	0.0709149i
$211$	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	$0.0402977\pi$
$223$			3.77096i			0.252522i	−0.991997	+	0.126261i	$0.959702\pi$
$224$	−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	$-0.837502\pi$
$227$	−26.2910			−1.74500			−0.872499	+	0.488616i	$0.837502\pi$
$228$	6.60073	+	0.899855i	0.437144	+	0.0595943i
$229$		−	7.26272i		−	0.479934i	−0.970781	−	0.239967i	$-0.922863\pi$
$229$		−	7.26272i		−	0.479934i	0.970781	−	0.239967i	$-0.0771367\pi$
$230$	−20.9138			−1.37901
$231$	−4.56769	−	0.369085i	−0.300532	−	0.0242840i
$232$	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	$0.194491\pi$
$241$			17.8123i			1.14739i	−0.819068	+	0.573697i	$0.805509\pi$
$242$		−	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	$-0.714933\pi$
$251$	−19.8062			−1.25016			−0.625079	+	0.780562i	$0.714933\pi$
$252$	10.8287	+	2.37742i	0.682144	+	0.149764i
$253$	−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	$-0.717101\pi$
$257$	−20.2115			−1.26076			−0.630380	+	0.776287i	$0.717101\pi$
$258$	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	$-0.471460\pi$
$269$	2.93713			0.179080			0.0895399	+	0.995983i	$0.471460\pi$
$270$	−13.2890	−	5.72017i	−0.808741	−	0.348119i
$271$		−	6.48266i		−	0.393794i	−0.980424	−	0.196897i	$-0.936914\pi$
$271$		−	6.48266i		−	0.393794i	0.980424	−	0.196897i	$-0.0630864\pi$
$272$	−3.17456			−0.192486
$273$	18.5122	+	1.49585i	1.12041	+	0.0905332i
$274$	−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	$-0.763876\pi$
$283$		−	22.7314i		−	1.35124i	0.737250	−	0.675620i	$-0.236124\pi$
$284$			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	$-0.258396\pi$
$293$	23.5606			1.37642			0.688212	+	0.725509i	$0.258396\pi$
$294$	9.41352	+	0.242597i	0.549008	+	0.0141486i
$295$	−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	$-0.746099\pi$
$307$		−	25.0808i		−	1.43144i	0.698388	−	0.715720i	$-0.253901\pi$
$308$	−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	$-0.375306\pi$
$311$	13.4661			0.763592			0.381796	+	0.924247i	$0.375306\pi$
$312$	2.50155	−	18.3497i	0.141623	−	1.03885i
$313$		−	31.5157i		−	1.78137i	−0.454617	−	0.890687i	$-0.650224\pi$
$313$		−	31.5157i		−	1.78137i	0.454617	−	0.890687i	$-0.349776\pi$
$314$	5.70162			0.321761
$315$	27.7927	+	6.10185i	1.56594	+	0.343800i
$316$	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
$336$	−0.274805	+	3.40090i	−0.0149918	+	0.185535i
$337$	−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	$0.141777\pi$
$349$			16.0970i			0.861650i	−0.902435	+	0.430825i	$0.858223\pi$
$350$	−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	$-0.290543\pi$
$353$	22.9802			1.22311			0.611557	+	0.791200i	$0.290543\pi$
$354$	−14.7996	−	2.01757i	−0.786589	−	0.107233i
$355$			32.0848i			1.70288i
$356$	14.4694			0.766876
$357$	1.57367	−	19.4752i	0.0832873	−	1.03074i
$358$	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	$0.152046\pi$
$367$			17.6135i			0.919416i	−0.888070	+	0.459708i	$0.847954\pi$
$368$			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
$378$	10.0242	+	3.67744i	0.515590	+	0.189147i
$379$	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	$-0.635628\pi$
$383$	−16.1774			−0.826624			−0.413312	+	0.910589i	$0.635628\pi$
$384$	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	$0.289010\pi$
$397$			31.4114i			1.57649i	−0.615361	+	0.788245i	$0.710990\pi$
$398$	12.3033			0.616709
$399$	−12.5776	−	1.01632i	−0.629668	−	0.0508794i
$400$	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	$0.251360\pi$
$409$			28.7226i			1.42024i	−0.704079	+	0.710121i	$0.748640\pi$
$410$			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	$-0.639723\pi$
$419$	−17.3987			−0.849984			−0.424992	+	0.905197i	$0.639723\pi$
$420$	−1.84815	+	22.8722i	−0.0901806	+	1.11605i
$421$	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	$0.141519\pi$
$433$			17.8993i			0.860184i	−0.902785	+	0.430092i	$0.858481\pi$
$434$	−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	$0.105287\pi$
$439$			13.6094i			0.649539i	−0.945793	+	0.324770i	$0.894713\pi$
$440$	−9.45775			−0.450881
$441$	−20.7276	−	3.37173i	−0.987026	−	0.160559i
$442$	−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	$-0.741373\pi$
$461$	−29.5305			−1.37537			−0.687686	+	0.726009i	$0.741373\pi$
$462$	0.286658	−	3.54760i	0.0133365	−	0.165049i
$463$	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	$-0.395000\pi$
$467$	13.9998			0.647832			0.323916	+	0.946086i	$0.395000\pi$
$468$	−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	$-0.675892\pi$
$479$	−22.9754			−1.04977			−0.524886	+	0.851173i	$0.675892\pi$
$480$	36.0201	+	4.91050i	1.64409	+	0.224133i
$481$			10.9919i			0.501186i
$482$	−13.8343			−0.630137
$483$	−34.3090	−	2.77229i	−1.56112	−	0.126144i
$484$	−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	$-0.509605\pi$
$503$	−1.35331			−0.0603412			−0.0301706	+	0.999545i	$0.509605\pi$
$504$	−4.49038	+	20.4528i	−0.200018	+	0.911041i
$505$	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	$-0.486990\pi$
$509$	1.84366			0.0817186			0.0408593	+	0.999165i	$0.486990\pi$
$510$	−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	$-0.789736\pi$
$521$	−36.0480			−1.57929			−0.789646	+	0.613563i	$0.789736\pi$
$522$	−11.7767	−	3.27177i	−0.515453	−	0.143201i
$523$			17.6572i			0.772097i	0.922479	+	0.386048i	$0.126160\pi$
$523$			17.6572i			0.772097i	−0.922479	+	0.386048i	$0.873840\pi$
$524$	8.57325			0.374524
$525$	−2.89800	+	35.8648i	−0.126479	+	1.56527i
$526$	−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
$546$	−1.16179	+	14.3779i	−0.0497199	+	0.615319i
$547$	−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	$-0.663755\pi$
$563$	−23.3507			−0.984116			−0.492058	+	0.870563i	$0.663755\pi$
$564$	−2.33741	+	17.1457i	−0.0984227	+	0.721963i
$565$		−	2.44326i		−	0.102789i
$566$	17.6548			0.742088
$567$	−21.0423	−	11.1455i	−0.883693	−	0.468067i
$568$	−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	$0.402956\pi$
$577$			45.8262i			1.90777i	−0.300172	+	0.953885i	$0.597044\pi$
$578$			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	$-0.213889\pi$
$587$	37.9222			1.56522			0.782608	+	0.622515i	$0.213889\pi$
$588$	0.436291	−	16.9294i	0.0179923	−	0.698158i
$589$	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	$-0.682651\pi$
$593$	−26.4380			−1.08568			−0.542840	+	0.839836i	$0.682651\pi$
$594$	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	$-0.771386\pi$
$601$		−	32.2641i		−	1.31608i	0.752984	−	0.658039i	$-0.228614\pi$
$602$	−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	$0.113790\pi$
$607$			17.2421i			0.699835i	−0.936780	+	0.349918i	$0.886210\pi$
$608$	−16.1214			−0.653809
$609$	23.9611	+	1.93614i	0.970953	+	0.0784564i
$610$	−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	$-0.987737\pi$
$619$		−	1.91653i		−	0.0770320i	0.999258	−	0.0385160i	$-0.0122631\pi$
$620$		−	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
$630$	−4.73913	+	21.5858i	−0.188812	+	0.859999i
$631$	−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	$0.0140451\pi$
$643$			2.23702i			0.0882196i	−0.999027	+	0.0441098i	$0.985955\pi$
$644$	−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	$-0.250861\pi$
$647$	35.8748			1.41038			0.705191	+	0.709017i	$0.250861\pi$
$648$	−12.2475	+	20.3411i	−0.481126	+	0.799074i
$649$		−	11.1032i		−	0.435840i
$650$	24.7157			0.969428
$651$	29.8365	+	2.41090i	1.16939	+	0.0944905i
$652$	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	$0.112420\pi$
$661$			17.7851i			0.691761i	−0.938278	+	0.345881i	$0.887580\pi$
$662$			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
$672$	−26.7422	−	2.16086i	−1.03160	−	0.0833571i
$673$	−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	$-0.448272\pi$
$677$	8.41956			0.323590			0.161795	+	0.986824i	$0.448272\pi$
$678$	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	$-0.880294\pi$
$691$		−	19.3086i		−	0.734533i	0.930116	−	0.367267i	$-0.119706\pi$
$692$	11.3923			0.433070
$693$	−1.70207	+	7.75261i	−0.0646564	+	0.294497i
$694$	−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
$714$	15.1259	+	1.22222i	0.566071	+	0.0457406i
$715$	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	$-0.472369\pi$
$719$	4.64935			0.173392			0.0866958	+	0.996235i	$0.472369\pi$
$720$	−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	$0.146710\pi$
$727$			23.9838i			0.889511i	−0.895652	+	0.444756i	$0.853290\pi$
$728$	−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	$0.150098\pi$
$733$			24.5974i			0.908527i	−0.890867	+	0.454264i	$0.849902\pi$
$734$	−13.6799			−0.504934
$735$	1.11978	−	43.4508i	0.0413035	−	1.60271i
$736$	−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
$756$	6.61356	−	18.0277i	0.240533	−	0.655662i
$757$	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	$-0.822317\pi$
$761$	−46.7976			−1.69641			−0.848206	+	0.529667i	$0.822317\pi$
$762$	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	$0.226266\pi$
$769$			36.1869i			1.30493i	−0.757818	+	0.652466i	$0.773734\pi$
$770$	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	$-0.442876\pi$
$773$	9.92555			0.356997			0.178499	+	0.983940i	$0.442876\pi$
$774$	0.387711	−	1.39557i	0.0139360	−	0.0501627i
$775$		−	51.2890i		−	1.84235i
$776$	36.7363			1.31876
$777$	1.00100	−	12.3881i	0.0359108	−	0.444421i
$778$	−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	$0.0120403\pi$
$787$			2.12178i			0.0756334i	−0.999285	+	0.0378167i	$0.987960\pi$
$788$			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	$-0.211764\pi$
$797$	44.4216			1.57349			0.786747	+	0.617275i	$0.211764\pi$
$798$	0.789344	−	9.76868i	0.0279425	−	0.345808i
$799$	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	$0.101780\pi$
$811$			17.9030i			0.628659i	−0.949314	+	0.314330i	$0.898220\pi$
$812$	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
$819$	6.89828	−	31.4203i	0.241045	−	1.09791i
$820$	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	$0.220256\pi$
$829$			36.7416i			1.27609i	−0.770000	+	0.638043i	$0.779744\pi$
$830$			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	$-0.663200\pi$
$839$	−28.4173			−0.981076			−0.490538	+	0.871420i	$0.663200\pi$
$840$	−43.2001	−	3.49072i	−1.49054	−	0.120441i
$841$	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	$-0.677687\pi$
$853$		−	49.5453i		−	1.69640i	0.529677	−	0.848200i	$-0.322313\pi$
$854$	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	$-0.690576\pi$
$857$	−32.9971			−1.12716			−0.563580	+	0.826061i	$0.690576\pi$
$858$	5.40209	+	0.736449i	0.184424	+	0.0251419i
$859$		−	44.6867i		−	1.52469i	−0.647170	−	0.762345i	$-0.724048\pi$
$859$		−	44.6867i		−	1.52469i	0.647170	−	0.762345i	$-0.275952\pi$
$860$	3.11277			0.106145
$861$	−1.54975	+	19.1792i	−0.0528153	+	0.653627i
$862$	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	$-0.537651\pi$
$881$	−7.00533			−0.236016			−0.118008	+	0.993013i	$0.537651\pi$
$882$	2.61873	−	16.0985i	0.0881773	−	0.542065i
$883$	−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	$-0.252825\pi$
$887$	41.7434			1.40161			0.700803	+	0.713355i	$0.252825\pi$
$888$	−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
$903$	−0.229437	+	2.83944i	−0.00763518	+	0.0944907i
$904$	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
$924$	−6.38006	−	0.515531i	−0.209889	−	0.0169597i
$925$	−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	$-0.492518\pi$
$929$	1.43274			0.0470068			0.0235034	+	0.999724i	$0.492518\pi$
$930$	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	$-0.905194\pi$
$937$		−	17.9657i		−	0.586914i	0.955972	−	0.293457i	$-0.0948057\pi$
$938$	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	$-0.381921\pi$
$941$	22.2404			0.725015			0.362507	+	0.931981i	$0.381921\pi$
$942$	1.33395	−	9.78498i	0.0434625	−	0.318812i
$943$			31.5389i			1.02705i
$944$	−8.26699			−0.269068
$945$	16.9742	−	46.2696i	0.552172	−	1.50515i
$946$	−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
$966$	2.15316	−	26.6469i	0.0692768	−	0.857349i
$967$	−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	$-0.687401\pi$
$971$	−34.6079			−1.11062			−0.555311	+	0.831643i	$0.687401\pi$
$972$	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	$-0.0909110\pi$
$983$	60.1655			1.91898			0.959491	+	0.281738i	$0.0909110\pi$
$984$	19.0109	+	2.59169i	0.606045	+	0.0826199i
$985$			37.2114i			1.18566i
$986$	−17.3714			−0.553217
$987$	2.63992	−	32.6709i	0.0840296	−	1.03993i
$988$	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	$0.0649594\pi$
$997$			12.7983i			0.405325i	−0.979249	+	0.202662i	$0.935041\pi$
$998$		−	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.188.18	yes	28
3.2	odd	2	inner	231.2.e.a.188.11	✓	28
7.6	odd	2	inner	231.2.e.a.188.17	yes	28
21.20	even	2	inner	231.2.e.a.188.12	yes	28

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
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} +(-0.369085 + 4.56769i) 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} +(-3.54760 - 0.286658i) 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} +(7.75261 + 1.70207i) 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} +(-0.515531 + 6.38006i) 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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