LMFDB - Embedded newform 231.2.e.a.188.1

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			188.1
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73839i q^{2} +(-0.280799 - 1.70914i) q^{3} -5.49880 q^{4} +2.40492 q^{5} +(-4.68029 + 0.768937i) q^{6} +(-1.28455 - 2.31299i) q^{7} +9.58108i q^{8} +(-2.84230 + 0.959847i) q^{9} +O(q^{10})$	\(q-2.73839i q^{2} +(-0.280799 - 1.70914i) q^{3} -5.49880 q^{4} +2.40492 q^{5} +(-4.68029 + 0.768937i) q^{6} +(-1.28455 - 2.31299i) q^{7} +9.58108i q^{8} +(-2.84230 + 0.959847i) q^{9} -6.58561i q^{10} -1.00000i q^{11} +(1.54405 + 9.39820i) q^{12} +1.84332i q^{13} +(-6.33388 + 3.51760i) q^{14} +(-0.675298 - 4.11034i) q^{15} +15.2392 q^{16} +5.51775 q^{17} +(2.62844 + 7.78335i) q^{18} -4.50439i q^{19} -13.2242 q^{20} +(-3.59252 + 2.84496i) q^{21} -2.73839 q^{22} -0.776922i q^{23} +(16.3754 - 2.69035i) q^{24} +0.783628 q^{25} +5.04773 q^{26} +(2.43863 + 4.58837i) q^{27} +(7.06348 + 12.7187i) q^{28} -2.13607i q^{29} +(-11.2557 + 1.84923i) q^{30} -1.00848i q^{31} -22.5687i q^{32} +(-1.70914 + 0.280799i) q^{33} -15.1098i q^{34} +(-3.08924 - 5.56255i) q^{35} +(15.6293 - 5.27800i) q^{36} +0.563797 q^{37} -12.3348 q^{38} +(3.15049 - 0.517602i) q^{39} +23.0417i q^{40} +2.52403 q^{41} +(7.79061 + 9.83774i) q^{42} -3.71187 q^{43} +5.49880i q^{44} +(-6.83551 + 2.30835i) q^{45} -2.12752 q^{46} -4.25312 q^{47} +(-4.27914 - 26.0458i) q^{48} +(-3.69986 + 5.94231i) q^{49} -2.14588i q^{50} +(-1.54938 - 9.43059i) q^{51} -10.1360i q^{52} +6.96875i q^{53} +(12.5647 - 6.67792i) q^{54} -2.40492i q^{55} +(22.1610 - 12.3074i) q^{56} +(-7.69862 + 1.26483i) q^{57} -5.84939 q^{58} +1.34352 q^{59} +(3.71332 + 22.6019i) q^{60} -11.1299i q^{61} -2.76160 q^{62} +(5.87120 + 5.34126i) q^{63} -31.3236 q^{64} +4.43303i q^{65} +(0.768937 + 4.68029i) q^{66} +6.52619 q^{67} -30.3410 q^{68} +(-1.32787 + 0.218159i) q^{69} +(-15.2325 + 8.45954i) q^{70} +5.51948i q^{71} +(-9.19637 - 27.2323i) q^{72} -6.97276i q^{73} -1.54390i q^{74} +(-0.220042 - 1.33933i) q^{75} +24.7687i q^{76} +(-2.31299 + 1.28455i) q^{77} +(-1.41740 - 8.62727i) q^{78} +12.9536 q^{79} +36.6489 q^{80} +(7.15739 - 5.45636i) q^{81} -6.91179i q^{82} +14.2180 q^{83} +(19.7545 - 15.6438i) q^{84} +13.2697 q^{85} +10.1646i q^{86} +(-3.65083 + 0.599805i) q^{87} +9.58108 q^{88} +1.17551 q^{89} +(6.32118 + 18.7183i) q^{90} +(4.26358 - 2.36784i) q^{91} +4.27213i q^{92} +(-1.72362 + 0.283179i) q^{93} +11.6467i q^{94} -10.8327i q^{95} +(-38.5730 + 6.33725i) q^{96} +12.4658i q^{97} +(16.2724 + 10.1317i) q^{98} +(0.959847 + 2.84230i) 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 $

$2$		−	2.73839i		−	1.93634i	−0.250301	−	0.968168i	$-0.580530\pi$
$2$		−	2.73839i		−	1.93634i	0.250301	−	0.968168i	$-0.419470\pi$
$3$	−0.280799	−	1.70914i	−0.162119	−	0.986771i
$3$	−0.280799	−	1.70914i	−0.162119	−	0.986771i
$4$	−5.49880			−2.74940
$5$	2.40492			1.07551			0.537756	−	0.843101i	$-0.319272\pi$
$5$	2.40492			1.07551			0.537756	+	0.843101i	$0.319272\pi$
$6$	−4.68029	+	0.768937i	−1.91072	+	0.313917i
$7$	−1.28455	−	2.31299i	−0.485514	−	0.874229i
$7$	−1.28455	−	2.31299i	−0.485514	−	0.874229i
$8$			9.58108i			3.38742i
$9$	−2.84230	+	0.959847i	−0.947435	+	0.319949i
$10$		−	6.58561i		−	2.08255i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	1.54405	+	9.39820i	0.445730	+	2.71303i
$13$			1.84332i			0.511245i	0.966777	+	0.255622i	$0.0822804\pi$
$13$			1.84332i			0.511245i	−0.966777	+	0.255622i	$0.917720\pi$
$14$	−6.33388	+	3.51760i	−1.69280	+	0.940119i
$15$	−0.675298	−	4.11034i	−0.174361	−	1.06128i
$16$	15.2392			3.80979
$17$	5.51775			1.33825			0.669125	−	0.743150i	$-0.266669\pi$
$17$	5.51775			1.33825			0.669125	+	0.743150i	$0.266669\pi$
$18$	2.62844	+	7.78335i	0.619529	+	1.83455i
$19$		−	4.50439i		−	1.03338i	−0.856173	−	0.516689i	$-0.827164\pi$
$19$		−	4.50439i		−	1.03338i	0.856173	−	0.516689i	$-0.172836\pi$
$20$	−13.2242			−2.95701
$21$	−3.59252	+	2.84496i	−0.783953	+	0.620821i
$22$	−2.73839			−0.583827
$23$		−	0.776922i		−	0.161999i	−0.996714	−	0.0809997i	$-0.974189\pi$
$23$		−	0.776922i		−	0.161999i	0.996714	−	0.0809997i	$-0.0258113\pi$
$24$	16.3754	−	2.69035i	3.34261	−	0.549166i
$25$	0.783628			0.156726
$26$	5.04773			0.989942
$27$	2.43863	+	4.58837i	0.469314	+	0.883031i
$28$	7.06348	+	12.7187i	1.33487	+	2.40360i
$29$		−	2.13607i		−	0.396658i	−0.980136	−	0.198329i	$-0.936449\pi$
$29$		−	2.13607i		−	0.396658i	0.980136	−	0.198329i	$-0.0635514\pi$
$30$	−11.2557	+	1.84923i	−2.05500	+	0.337622i
$31$		−	1.00848i		−	0.181128i	−0.995891	−	0.0905638i	$-0.971133\pi$
$31$		−	1.00848i		−	0.181128i	0.995891	−	0.0905638i	$-0.0288669\pi$
$32$		−	22.5687i		−	3.98961i
$33$	−1.70914	+	0.280799i	−0.297523	+	0.0488808i
$34$		−	15.1098i		−	2.59130i
$35$	−3.08924	−	5.56255i	−0.522176	−	0.940243i
$36$	15.6293	−	5.27800i	2.60488	−	0.879667i
$37$	0.563797			0.0926877			0.0463438	−	0.998926i	$-0.485243\pi$
$37$	0.563797			0.0926877			0.0463438	+	0.998926i	$0.485243\pi$
$38$	−12.3348			−2.00097
$39$	3.15049	−	0.517602i	0.504482	−	0.0828826i
$40$			23.0417i			3.64321i
$41$	2.52403			0.394187			0.197094	−	0.980385i	$-0.436850\pi$
$41$	2.52403			0.394187			0.197094	+	0.980385i	$0.436850\pi$
$42$	7.79061	+	9.83774i	1.20212	+	1.51800i
$43$	−3.71187			−0.566055			−0.283028	−	0.959112i	$-0.591339\pi$
$43$	−3.71187			−0.566055			−0.283028	+	0.959112i	$0.591339\pi$
$44$			5.49880i			0.828975i
$45$	−6.83551	+	2.30835i	−1.01898	+	0.344109i
$46$	−2.12752			−0.313685
$47$	−4.25312			−0.620381			−0.310191	−	0.950674i	$-0.600393\pi$
$47$	−4.25312			−0.620381			−0.310191	+	0.950674i	$0.600393\pi$
$48$	−4.27914	−	26.0458i	−0.617640	−	3.75939i
$49$	−3.69986	+	5.94231i	−0.528552	+	0.848901i
$50$		−	2.14588i		−	0.303473i
$51$	−1.54938	−	9.43059i	−0.216956	−	1.32055i
$52$		−	10.1360i		−	1.40562i
$53$			6.96875i			0.957232i	0.878024	+	0.478616i	$0.158861\pi$
$53$			6.96875i			0.957232i	−0.878024	+	0.478616i	$0.841139\pi$
$54$	12.5647	−	6.67792i	1.70985	−	0.908750i
$55$		−	2.40492i		−	0.324279i
$56$	22.1610	−	12.3074i	2.96138	−	1.64464i
$57$	−7.69862	+	1.26483i	−1.01971	+	0.167530i
$58$	−5.84939			−0.768063
$59$	1.34352			0.174912			0.0874560	−	0.996168i	$-0.472126\pi$
$59$	1.34352			0.174912			0.0874560	+	0.996168i	$0.472126\pi$
$60$	3.71332	+	22.6019i	0.479388	+	2.91789i
$61$		−	11.1299i		−	1.42504i	−0.701654	−	0.712518i	$-0.747555\pi$
$61$		−	11.1299i		−	1.42504i	0.701654	−	0.712518i	$-0.252445\pi$
$62$	−2.76160			−0.350724
$63$	5.87120	+	5.34126i	0.739702	+	0.672935i
$64$	−31.3236			−3.91544
$65$			4.43303i			0.549850i
$66$	0.768937	+	4.68029i	0.0946496	+	0.576104i
$67$	6.52619			0.797300			0.398650	−	0.917103i	$-0.369479\pi$
$67$	6.52619			0.797300			0.398650	+	0.917103i	$0.369479\pi$
$68$	−30.3410			−3.67938
$69$	−1.32787	+	0.218159i	−0.159856	+	0.0262632i
$70$	−15.2325	+	8.45954i	−1.82063	+	1.01111i
$71$			5.51948i			0.655042i	0.944844	+	0.327521i	$0.106213\pi$
$71$			5.51948i			0.655042i	−0.944844	+	0.327521i	$0.893787\pi$
$72$	−9.19637	−	27.2323i	−1.08380	−	3.20936i
$73$		−	6.97276i		−	0.816100i	−0.912960	−	0.408050i	$-0.866209\pi$
$73$		−	6.97276i		−	0.816100i	0.912960	−	0.408050i	$-0.133791\pi$
$74$		−	1.54390i		−	0.179474i
$75$	−0.220042	−	1.33933i	−0.0254082	−	0.154652i
$76$			24.7687i			2.84117i
$77$	−2.31299	+	1.28455i	−0.263590	+	0.146388i
$78$	−1.41740	−	8.62727i	−0.160489	−	0.976846i
$79$	12.9536			1.45739			0.728695	−	0.684838i	$-0.240127\pi$
$79$	12.9536			1.45739			0.728695	+	0.684838i	$0.240127\pi$
$80$	36.6489			4.09748
$81$	7.15739	−	5.45636i	0.795265	−	0.606262i
$82$		−	6.91179i		−	0.763279i
$83$	14.2180			1.56063			0.780314	−	0.625388i	$-0.215059\pi$
$83$	14.2180			1.56063			0.780314	+	0.625388i	$0.215059\pi$
$84$	19.7545	−	15.6438i	2.15540	−	1.70688i
$85$	13.2697			1.43930
$86$			10.1646i			1.09607i
$87$	−3.65083	+	0.599805i	−0.391410	+	0.0643058i
$88$	9.58108			1.02135
$89$	1.17551			0.124604			0.0623019	−	0.998057i	$-0.480156\pi$
$89$	1.17551			0.124604			0.0623019	+	0.998057i	$0.480156\pi$
$90$	6.32118	+	18.7183i	0.666311	+	1.97308i
$91$	4.26358	−	2.36784i	0.446945	−	0.248217i
$92$			4.27213i			0.445401i
$93$	−1.72362	+	0.283179i	−0.178732	+	0.0293643i
$94$			11.6467i			1.20127i
$95$		−	10.8327i		−	1.11141i
$96$	−38.5730	+	6.33725i	−3.93684	+	0.646793i
$97$			12.4658i			1.26571i	0.774271	+	0.632854i	$0.218117\pi$
$97$			12.4658i			1.26571i	−0.774271	+	0.632854i	$0.781883\pi$
$98$	16.2724	+	10.1317i	1.64376	+	1.02345i
$99$	0.959847	+	2.84230i	0.0964683	+	0.285662i
$100$	−4.30901			−0.430901
$101$	15.7002			1.56223			0.781115	−	0.624388i	$-0.214651\pi$
$101$	15.7002			1.56223			0.781115	+	0.624388i	$0.214651\pi$
$102$	−25.8247	+	4.24280i	−2.55702	+	0.420100i
$103$		−	1.65885i		−	0.163451i	−0.996655	−	0.0817256i	$-0.973957\pi$
$103$		−	1.65885i		−	0.163451i	0.996655	−	0.0817256i	$-0.0260431\pi$
$104$	−17.6610			−1.73180
$105$	−8.63972	+	6.84189i	−0.843150	+	0.667700i
$106$	19.0832			1.85352
$107$		−	4.56456i		−	0.441273i	−0.975356	−	0.220636i	$-0.929187\pi$
$107$		−	4.56456i		−	0.441273i	0.975356	−	0.220636i	$-0.0708134\pi$
$108$	−13.4095	−	25.2305i	−1.29033	−	2.42780i
$109$	9.08743			0.870418			0.435209	−	0.900329i	$-0.356674\pi$
$109$	9.08743			0.870418			0.435209	+	0.900329i	$0.356674\pi$
$110$	−6.58561			−0.627913
$111$	−0.158313	−	0.963607i	−0.0150264	−	0.0914615i
$112$	−19.5755	−	35.2481i	−1.84971	−	3.33063i
$113$			14.4623i			1.36050i	0.732981	+	0.680249i	$0.238128\pi$
$113$			14.4623i			1.36050i	−0.732981	+	0.680249i	$0.761872\pi$
$114$	3.46359	+	21.0819i	0.324395	+	1.97450i
$115$		−	1.86843i		−	0.174232i
$116$			11.7458i			1.09057i
$117$	−1.76931	−	5.23928i	−0.163572	−	0.484371i
$118$		−	3.67910i		−	0.338688i
$119$	−7.08782	−	12.7625i	−0.649739	−	1.16994i
$120$	39.3814	−	6.47008i	3.59502	−	0.590635i
$121$	−1.00000			−0.0909091
$122$	−30.4780			−2.75935
$123$	−0.708745	−	4.31392i	−0.0639053	−	0.388973i
$124$			5.54540i			0.497992i
$125$	−10.1400			−0.906952
$126$	14.6265	−	16.0777i	1.30303	−	1.43231i
$127$	−10.7006			−0.949527			−0.474764	−	0.880113i	$-0.657466\pi$
$127$	−10.7006			−0.949527			−0.474764	+	0.880113i	$0.657466\pi$
$128$			40.6389i			3.59200i
$129$	1.04229	+	6.34410i	0.0917684	+	0.558567i
$130$	12.1394			1.06469
$131$	−3.76080			−0.328583			−0.164291	−	0.986412i	$-0.552534\pi$
$131$	−3.76080			−0.328583			−0.164291	+	0.986412i	$0.552534\pi$
$132$	9.39820	−	1.54405i	0.818008	−	0.134393i
$133$	−10.4186	+	5.78611i	−0.903409	+	0.501720i
$134$		−	17.8713i		−	1.54384i
$135$	5.86470	+	11.0346i	0.504753	+	0.949711i
$136$			52.8660i			4.53322i
$137$		−	7.42525i		−	0.634382i	−0.948362	−	0.317191i	$-0.897260\pi$
$137$		−	7.42525i		−	0.634382i	0.948362	−	0.317191i	$-0.102740\pi$
$138$	0.597404	+	3.63622i	0.0508544	+	0.309536i
$139$			18.8286i			1.59702i	0.601981	+	0.798510i	$0.294378\pi$
$139$			18.8286i			1.59702i	−0.601981	+	0.798510i	$0.705622\pi$
$140$	16.9871	+	30.5874i	1.43567	+	2.58510i
$141$	1.19427	+	7.26917i	0.100576	+	0.612174i
$142$	15.1145			1.26838
$143$	1.84332			0.154146
$144$	−43.3143	+	14.6273i	−3.60953	+	1.21894i
$145$		−	5.13707i		−	0.426610i
$146$	−19.0942			−1.58024
$147$	11.1951	+	4.65499i	0.923359	+	0.383937i
$148$	−3.10020			−0.254835
$149$			11.3230i			0.927615i	0.885936	+	0.463808i	$0.153517\pi$
$149$			11.3230i			0.927615i	−0.885936	+	0.463808i	$0.846483\pi$
$150$	−3.66760	+	0.602560i	−0.299459	+	0.0491988i
$151$	−10.5819			−0.861147			−0.430573	−	0.902556i	$-0.641689\pi$
$151$	−10.5819			−0.861147			−0.430573	+	0.902556i	$0.641689\pi$
$152$	43.1569			3.50049
$153$	−15.6831	+	5.29620i	−1.26790	+	0.428172i
$154$	3.51760	+	6.33388i	0.283456	+	0.510399i
$155$		−	2.42530i		−	0.194805i
$156$	−17.3239	+	2.84619i	−1.38702	+	0.227877i
$157$		−	5.52023i		−	0.440562i	−0.975436	−	0.220281i	$-0.929303\pi$
$157$		−	5.52023i		−	0.440562i	0.975436	−	0.220281i	$-0.0706975\pi$
$158$		−	35.4720i		−	2.82200i
$159$	11.9106	−	1.95682i	0.944569	−	0.155186i
$160$		−	54.2758i		−	4.29088i
$161$	−1.79701	+	0.997995i	−0.141625	+	0.0786530i
$162$	−14.9416	−	19.5997i	−1.17393	−	1.53990i
$163$	−14.8062			−1.15971			−0.579855	−	0.814720i	$-0.696891\pi$
$163$	−14.8062			−1.15971			−0.579855	+	0.814720i	$0.696891\pi$
$164$	−13.8791			−1.08378
$165$	−4.11034	+	0.675298i	−0.319989	+	0.0525719i
$166$		−	38.9345i		−	3.02190i
$167$	9.31300			0.720662			0.360331	−	0.932825i	$-0.382664\pi$
$167$	9.31300			0.720662			0.360331	+	0.932825i	$0.382664\pi$
$168$	−27.2578	−	34.4202i	−2.10298	−	2.65558i
$169$	9.60217			0.738629
$170$		−	36.3377i		−	2.78698i
$171$	4.32353	+	12.8028i	0.330628	+	0.979058i
$172$	20.4108			1.55631
$173$	−4.10764			−0.312298			−0.156149	−	0.987733i	$-0.549908\pi$
$173$	−4.10764			−0.312298			−0.156149	+	0.987733i	$0.549908\pi$
$174$	1.64250	+	9.99742i	0.124518	+	0.757902i
$175$	−1.00661	−	1.81252i	−0.0760924	−	0.137014i
$176$		−	15.2392i		−	1.14870i
$177$	−0.377260	−	2.29627i	−0.0283566	−	0.172598i
$178$		−	3.21901i		−	0.241275i
$179$			18.7415i			1.40081i	0.713748	+	0.700403i	$0.246996\pi$
$179$			18.7415i			1.40081i	−0.713748	+	0.700403i	$0.753004\pi$
$180$	37.5871	−	12.6932i	2.80157	−	0.946093i
$181$		−	11.1946i		−	0.832085i	−0.909345	−	0.416043i	$-0.863417\pi$
$181$		−	11.1946i		−	0.832085i	0.909345	−	0.416043i	$-0.136583\pi$
$182$	−6.48407	−	11.6754i	−0.480631	−	0.865436i
$183$	−19.0225	+	3.12526i	−1.40618	+	0.231026i
$184$	7.44375			0.548760
$185$	1.35589			0.0996867
$186$	0.775455	+	4.71996i	0.0568591	+	0.346084i
$187$		−	5.51775i		−	0.403498i
$188$	23.3870			1.70568
$189$	7.48032	−	11.5345i	0.544113	−	0.839012i
$190$	−29.6641			−2.15206
$191$		−	3.28007i		−	0.237338i	−0.992934	−	0.118669i	$-0.962137\pi$
$191$		−	3.28007i		−	0.237338i	0.992934	−	0.118669i	$-0.0378627\pi$
$192$	8.79561	+	53.5363i	0.634769	+	3.86365i
$193$	−22.9711			−1.65350			−0.826748	−	0.562573i	$-0.809812\pi$
$193$	−22.9711			−1.65350			−0.826748	+	0.562573i	$0.809812\pi$
$194$	34.1362			2.45084
$195$	7.57666	−	1.24479i	0.542576	−	0.0891412i
$196$	20.3448	−	32.6755i	1.45320	−	2.33397i
$197$			18.9333i			1.34894i	0.738301	+	0.674472i	$0.235629\pi$
$197$			18.9333i			1.34894i	−0.738301	+	0.674472i	$0.764371\pi$
$198$	7.78335	−	2.62844i	0.553138	−	0.186795i
$199$			0.918738i			0.0651276i	0.999470	+	0.0325638i	$0.0103672\pi$
$199$			0.918738i			0.0651276i	−0.999470	+	0.0325638i	$0.989633\pi$
$200$			7.50800i			0.530896i
$201$	−1.83254	−	11.1542i	−0.129258	−	0.786753i
$202$		−	42.9933i		−	3.02500i
$203$	−4.94071	+	2.74388i	−0.346770	+	0.192583i
$204$	8.51970	+	51.8569i	0.596499	+	3.63071i
$205$	6.07009			0.423953
$206$	−4.54258			−0.316497
$207$	0.745726	+	2.20825i	0.0518316	+	0.153484i
$208$			28.0907i			1.94774i
$209$	−4.50439			−0.311575
$210$	18.7358	+	23.6589i	1.29289	+	1.63262i
$211$	9.93832			0.684182			0.342091	−	0.939667i	$-0.388865\pi$
$211$	9.93832			0.684182			0.342091	+	0.939667i	$0.388865\pi$
$212$		−	38.3197i		−	2.63181i
$213$	9.43355	−	1.54986i	0.646376	−	0.106195i
$214$	−12.4996			−0.854452
$215$	−8.92675			−0.608799
$216$	−43.9615	+	23.3647i	−2.99120	+	1.58976i
$217$	−2.33260	+	1.29544i	−0.158347	+	0.0879400i
$218$		−	24.8850i		−	1.68542i
$219$	−11.9174	+	1.95794i	−0.805304	+	0.132305i
$220$			13.2242i			0.891572i
$221$			10.1710i			0.684174i
$222$	−2.63873	+	0.433524i	−0.177100	+	0.0290963i
$223$			17.5493i			1.17519i	0.809156	+	0.587593i	$0.199924\pi$
$223$			17.5493i			1.17519i	−0.809156	+	0.587593i	$0.800076\pi$
$224$	−52.2012	+	28.9906i	−3.48784	+	1.93701i
$225$	−2.22731	+	0.752163i	−0.148487	+	0.0501442i
$226$	39.6034			2.63438
$227$	27.1168			1.79981			0.899903	−	0.436091i	$-0.143637\pi$
$227$	27.1168			1.79981			0.899903	+	0.436091i	$0.143637\pi$
$228$	42.3332	−	6.95502i	2.80358	−	0.460608i
$229$		−	13.4385i		−	0.888042i	−0.896016	−	0.444021i	$-0.853552\pi$
$229$		−	13.4385i		−	0.888042i	0.896016	−	0.444021i	$-0.146448\pi$
$230$	−5.11650			−0.337372
$231$	2.84496	+	3.59252i	0.187184	+	0.236371i
$232$	20.4658			1.34365
$233$			10.8412i			0.710233i	0.934822	+	0.355116i	$0.115559\pi$
$233$			10.8412i			0.710233i	−0.934822	+	0.355116i	$0.884441\pi$
$234$	−14.3472	+	4.84505i	−0.937906	+	0.316731i
$235$	−10.2284			−0.667227
$236$	−7.38777			−0.480903
$237$	−3.63735	−	22.1394i	−0.236271	−	1.43811i
$238$	−34.9488	+	19.4092i	−2.26539	+	1.25811i
$239$		−	15.8103i		−	1.02268i	−0.859378	−	0.511341i	$-0.829149\pi$
$239$		−	15.8103i		−	1.02268i	0.859378	−	0.511341i	$-0.170851\pi$
$240$	−10.2910	−	62.6381i	−0.664279	−	4.04327i
$241$		−	2.21102i		−	0.142424i	−0.997461	−	0.0712122i	$-0.977313\pi$
$241$		−	2.21102i		−	0.142424i	0.997461	−	0.0712122i	$-0.0226868\pi$
$242$			2.73839i			0.176031i
$243$	−11.3354	−	10.7008i	−0.727169	−	0.686458i
$244$			61.2010i			3.91799i
$245$	−8.89787	+	14.2908i	−0.568464	+	0.913003i
$246$	−11.8132	+	1.94082i	−0.753182	+	0.123742i
$247$	8.30303			0.528309
$248$	9.66229			0.613556
$249$	−3.99240	−	24.3005i	−0.253008	−	1.53998i
$250$			27.7674i			1.75616i
$251$	−15.3509			−0.968942			−0.484471	−	0.874807i	$-0.660988\pi$
$251$	−15.3509			−0.968942			−0.484471	+	0.874807i	$0.660988\pi$
$252$	−32.2845	−	29.3705i	−2.03373	−	1.85017i
$253$	−0.776922			−0.0488447
$254$			29.3025i			1.83860i
$255$	−3.72612	−	22.6798i	−0.233339	−	1.42026i
$256$	48.6381			3.03988
$257$	16.2639			1.01452			0.507258	−	0.861794i	$-0.330659\pi$
$257$	16.2639			1.01452			0.507258	+	0.861794i	$0.330659\pi$
$258$	17.3726	−	2.85420i	1.08157	−	0.177695i
$259$	−0.724225	−	1.30406i	−0.0450012	−	0.0810302i
$260$		−	24.3763i		−	1.51176i
$261$	2.05030	+	6.07135i	0.126910	+	0.375807i
$262$			10.2986i			0.636247i
$263$			10.8062i			0.666338i	0.942867	+	0.333169i	$0.108118\pi$
$263$			10.8062i			0.666338i	−0.942867	+	0.333169i	$0.891882\pi$
$264$	−2.69035	−	16.3754i	−0.165580	−	1.00784i
$265$			16.7593i			1.02951i
$266$	15.8446	+	28.5303i	0.971498	+	1.74930i
$267$	−0.330082	−	2.00911i	−0.0202007	−	0.122955i
$268$	−35.8862			−2.19210
$269$	−19.4531			−1.18608			−0.593039	−	0.805173i	$-0.702072\pi$
$269$	−19.4531			−1.18608			−0.593039	+	0.805173i	$0.702072\pi$
$270$	30.2172	−	16.0598i	1.83896	−	0.977371i
$271$		−	9.55020i		−	0.580133i	−0.957006	−	0.290067i	$-0.906323\pi$
$271$		−	9.55020i		−	0.580133i	0.957006	−	0.290067i	$-0.0936775\pi$
$272$	84.0859			5.09845
$273$	−5.24417	−	6.62217i	−0.317391	−	0.400792i
$274$	−20.3333			−1.22838
$275$		−	0.783628i		−	0.0472545i
$276$	7.30167	−	1.19961i	0.439509	−	0.0722080i
$277$	−31.8806			−1.91552			−0.957761	−	0.287565i	$-0.907154\pi$
$277$	−31.8806			−1.91552			−0.957761	+	0.287565i	$0.907154\pi$
$278$	51.5601			3.09237
$279$	0.967983	+	2.86640i	0.0579516	+	0.171607i
$280$	53.2953	−	29.5982i	3.18500	−	1.76883i
$281$		−	21.8351i		−	1.30257i	−0.758832	−	0.651286i	$-0.774230\pi$
$281$		−	21.8351i		−	1.30257i	0.758832	−	0.651286i	$-0.225770\pi$
$282$	19.9058	−	3.27038i	1.18538	−	0.194748i
$283$			6.32612i			0.376049i	0.982164	+	0.188025i	$0.0602084\pi$
$283$			6.32612i			0.376049i	−0.982164	+	0.188025i	$0.939792\pi$
$284$		−	30.3505i		−	1.80097i
$285$	−18.5145	+	3.04180i	−1.09671	+	0.180181i
$286$		−	5.04773i		−	0.298479i
$287$	−3.24224	−	5.83806i	−0.191384	−	0.344610i
$288$	21.6625	+	64.1470i	1.27647	+	3.77990i
$289$	13.4455			0.790914
$290$	−14.0673			−0.826060
$291$	21.3057	−	3.50038i	1.24897	−	0.205196i
$292$			38.3418i			2.24378i
$293$	−5.29648			−0.309423			−0.154712	−	0.987960i	$-0.549445\pi$
$293$	−5.29648			−0.309423			−0.154712	+	0.987960i	$0.549445\pi$
$294$	12.7472	−	30.6567i	0.743431	−	1.78793i
$295$	3.23106			0.188120
$296$			5.40178i			0.313972i
$297$	4.58837	−	2.43863i	0.266244	−	0.141503i
$298$	31.0068			1.79618
$299$	1.43212			0.0828214
$300$	1.20996	+	7.36469i	0.0698573	+	0.425200i
$301$	4.76808	+	8.58553i	0.274828	+	0.494862i
$302$			28.9775i			1.66747i
$303$	−4.40860	−	26.8338i	−0.253267	−	1.54156i
$304$		−	68.6431i		−	3.93695i
$305$		−	26.7665i		−	1.53264i
$306$	14.5031	+	42.9465i	0.829085	+	2.45509i
$307$		−	12.9450i		−	0.738811i	−0.929268	−	0.369405i	$-0.879561\pi$
$307$		−	12.9450i		−	0.738811i	0.929268	−	0.369405i	$-0.120439\pi$
$308$	12.7187	−	7.06348i	0.724714	−	0.402479i
$309$	−2.83520	+	0.465803i	−0.161289	+	0.0264986i
$310$	−6.64143			−0.377208
$311$	−21.6050			−1.22511			−0.612553	−	0.790429i	$-0.709857\pi$
$311$	−21.6050			−1.22511			−0.612553	+	0.790429i	$0.709857\pi$
$312$	4.95918	+	30.1851i	0.280759	+	1.70889i
$313$			15.7562i			0.890596i	0.895383	+	0.445298i	$0.146902\pi$
$313$			15.7562i			0.890596i	−0.895383	+	0.445298i	$0.853098\pi$
$314$	−15.1166			−0.853077
$315$	14.1198	+	12.8453i	0.795558	+	0.723749i
$316$	−71.2291			−4.00695
$317$			31.2049i			1.75264i	0.481730	+	0.876320i	$0.340008\pi$
$317$			31.2049i			1.75264i	−0.481730	+	0.876320i	$0.659992\pi$
$318$	−5.35853	−	32.6158i	−0.300492	−	1.82900i
$319$	−2.13607			−0.119597
$320$	−75.3306			−4.21111
$321$	−7.80146	+	1.28172i	−0.435435	+	0.0715388i
$322$	2.73290	+	4.92093i	0.152299	+	0.274233i
$323$		−	24.8541i		−	1.38292i
$324$	−39.3570	+	30.0034i	−2.18650	+	1.66686i
$325$			1.44448i			0.0801251i
$326$			40.5451i			2.24559i
$327$	−2.55174	−	15.5317i	−0.141111	−	0.858903i
$328$			24.1829i			1.33528i
$329$	5.46334	+	9.83743i	0.301204	+	0.542355i
$330$	1.84923	+	11.2557i	0.101797	+	0.619607i
$331$	−29.3324			−1.61225			−0.806126	−	0.591743i	$-0.798440\pi$
$331$	−29.3324			−1.61225			−0.806126	+	0.591743i	$0.798440\pi$
$332$	−78.1819			−4.29079
$333$	−1.60248	+	0.541159i	−0.0878155	+	0.0296553i
$334$		−	25.5027i		−	1.39544i
$335$	15.6949			0.857506
$336$	−54.7470	+	43.3548i	−2.98670	+	2.36520i
$337$	9.00835			0.490716			0.245358	−	0.969433i	$-0.421094\pi$
$337$	9.00835			0.490716			0.245358	+	0.969433i	$0.421094\pi$
$338$		−	26.2945i		−	1.43023i
$339$	24.7181	−	4.06099i	1.34250	−	0.220563i
$340$	−72.9675			−3.95722
$341$	−1.00848			−0.0546120
$342$	35.0592	−	11.8395i	1.89579	−	0.640208i
$343$	18.4972	+	0.924569i	0.998753	+	0.0499220i
$344$		−	35.5637i		−	1.91747i
$345$	−3.19341	+	0.524653i	−0.171927	+	0.0282464i
$346$			11.2483i			0.604715i
$347$			20.4218i			1.09630i	0.836379	+	0.548151i	$0.184668\pi$
$347$			20.4218i			1.09630i	−0.836379	+	0.548151i	$0.815332\pi$
$348$	20.0752	−	3.29820i	1.07614	−	0.176802i
$349$			12.9951i			0.695612i	0.937567	+	0.347806i	$0.113073\pi$
$349$			12.9951i			0.695612i	−0.937567	+	0.347806i	$0.886927\pi$
$350$	−4.96340	+	2.75649i	−0.265305	+	0.147341i
$351$	−8.45783	+	4.49517i	−0.451445	+	0.239934i
$352$	−22.5687			−1.20291
$353$	21.7147			1.15576			0.577878	−	0.816123i	$-0.303881\pi$
$353$	21.7147			1.15576			0.577878	+	0.816123i	$0.303881\pi$
$354$	−6.28808	+	1.03309i	−0.334208	+	0.0549079i
$355$			13.2739i			0.704505i
$356$	−6.46389			−0.342585
$357$	−19.8226	+	15.6978i	−1.04912	+	0.830813i
$358$	51.3216			2.71243
$359$		−	24.7796i		−	1.30782i	−0.756573	−	0.653909i	$-0.773128\pi$
$359$		−	24.7796i		−	1.30782i	0.756573	−	0.653909i	$-0.226872\pi$
$360$	−22.1165	−	65.4915i	−1.16564	−	3.45171i
$361$	−1.28952			−0.0678696
$362$	−30.6551			−1.61120
$363$	0.280799	+	1.70914i	0.0147381	+	0.0897065i
$364$	−23.4446	+	13.0202i	−1.22883	+	0.682446i
$365$		−	16.7689i		−	0.877725i
$366$	8.55818	+	52.0911i	0.447343	+	2.72285i
$367$			17.7727i			0.927728i	0.885906	+	0.463864i	$0.153537\pi$
$367$			17.7727i			0.927728i	−0.885906	+	0.463864i	$0.846463\pi$
$368$		−	11.8396i		−	0.617184i
$369$	−7.17406	+	2.42268i	−0.373467	+	0.126120i
$370$		−	3.71295i		−	0.193027i
$371$	16.1187	−	8.95171i	0.836839	−	0.464749i
$372$	9.47786	−	1.55714i	0.491404	−	0.0807341i
$373$	−17.3469			−0.898187			−0.449094	−	0.893485i	$-0.648253\pi$
$373$	−17.3469			−0.898187			−0.449094	+	0.893485i	$0.648253\pi$
$374$	−15.1098			−0.781307
$375$	2.84731	+	17.3307i	0.147034	+	0.894954i
$376$		−	40.7495i		−	2.10149i
$377$	3.93746			0.202789
$378$	−31.5860	−	20.4840i	−1.62461	−	1.05359i
$379$	16.3016			0.837354			0.418677	−	0.908135i	$-0.362494\pi$
$379$	16.3016			0.837354			0.418677	+	0.908135i	$0.362494\pi$
$380$			59.5667i			3.05571i
$381$	3.00472	+	18.2888i	0.153937	+	0.936966i
$382$	−8.98213			−0.459566
$383$	−29.5146			−1.50812			−0.754062	−	0.656803i	$-0.771908\pi$
$383$	−29.5146			−1.50812			−0.754062	+	0.656803i	$0.771908\pi$
$384$	69.4574	−	11.4113i	3.54448	−	0.582332i
$385$	−5.56255	+	3.08924i	−0.283494	+	0.157442i
$386$			62.9039i			3.20172i
$387$	10.5503	−	3.56283i	0.536300	−	0.181109i
$388$		−	68.5468i		−	3.47994i
$389$			33.3300i			1.68990i	0.534845	+	0.844950i	$0.320370\pi$
$389$			33.3300i			1.68990i	−0.534845	+	0.844950i	$0.679630\pi$
$390$	−3.40872	−	20.7479i	−0.172607	−	1.05061i
$391$		−	4.28686i		−	0.216796i
$392$	−56.9337	−	35.4487i	−2.87559	−	1.79043i
$393$	1.05603	+	6.42773i	0.0532696	+	0.324236i
$394$	51.8469			2.61201
$395$	31.1523			1.56744
$396$	−5.27800	−	15.6293i	−0.265230	−	0.785399i
$397$			25.4685i			1.27823i	0.769113	+	0.639113i	$0.220698\pi$
$397$			25.4685i			1.27823i	−0.769113	+	0.639113i	$0.779302\pi$
$398$	2.51586			0.126109
$399$	12.8148	+	16.1821i	0.641542	+	0.810119i
$400$	11.9418			0.597092
$401$		−	37.5065i		−	1.87299i	−0.350685	−	0.936493i	$-0.614051\pi$
$401$		−	37.5065i		−	1.87299i	0.350685	−	0.936493i	$-0.385949\pi$
$402$	−30.5444	+	5.01823i	−1.52342	+	0.250286i
$403$	1.85894			0.0926006
$404$	−86.3323			−4.29519
$405$	17.2129	−	13.1221i	0.855317	−	0.652042i
$406$	7.51383	+	13.5296i	0.372905	+	0.671463i
$407$		−	0.563797i		−	0.0279464i
$408$	90.3552	−	14.8447i	4.47325	−	0.734922i
$409$			5.38329i			0.266186i	0.991104	+	0.133093i	$0.0424910\pi$
$409$			5.38329i			0.266186i	−0.991104	+	0.133093i	$0.957509\pi$
$410$		−	16.6223i		−	0.820916i
$411$	−12.6908	+	2.08500i	−0.625990	+	0.102846i
$412$			9.12167i			0.449393i
$413$	−1.72582	−	3.10756i	−0.0849222	−	0.152913i
$414$	6.04705	−	2.04209i	0.297196	−	0.100363i
$415$	34.1931			1.67847
$416$	41.6013			2.03967
$417$	32.1807	−	5.28705i	1.57589	−	0.258908i
$418$			12.3348i			0.603314i
$419$	31.3944			1.53372			0.766860	−	0.641815i	$-0.221818\pi$
$419$	31.3944			1.53372			0.766860	+	0.641815i	$0.221818\pi$
$420$	47.5081	−	37.6221i	2.31816	−	1.83577i
$421$	12.4458			0.606572			0.303286	−	0.952900i	$-0.401916\pi$
$421$	12.4458			0.606572			0.303286	+	0.952900i	$0.401916\pi$
$422$		−	27.2150i		−	1.32481i
$423$	12.0887	−	4.08235i	0.587771	−	0.198490i
$424$	−66.7682			−3.24255
$425$	4.32386			0.209738
$426$	−4.24413	−	25.8328i	−0.205629	−	1.25160i
$427$	−25.7433	+	14.2969i	−1.24581	+	0.691875i
$428$			25.0996i			1.21323i
$429$	−0.517602	−	3.15049i	−0.0249901	−	0.152107i
$430$			24.4449i			1.17884i
$431$		−	16.0846i		−	0.774766i	−0.921919	−	0.387383i	$-0.873379\pi$
$431$		−	16.0846i		−	0.774766i	0.921919	−	0.387383i	$-0.126621\pi$
$432$	37.1626	+	69.9229i	1.78799	+	3.36417i
$433$		−	26.1060i		−	1.25458i	−0.778787	−	0.627288i	$-0.784165\pi$
$433$		−	26.1060i		−	1.25458i	0.778787	−	0.627288i	$-0.215835\pi$
$434$	3.54742	+	6.38757i	0.170281	+	0.306613i
$435$	−8.77995	+	1.44248i	−0.420966	+	0.0691617i
$436$	−49.9699			−2.39313
$437$	−3.49956			−0.167407
$438$	5.36161	+	32.6345i	0.256188	+	1.55934i
$439$			1.45216i			0.0693077i	0.999399	+	0.0346538i	$0.0110329\pi$
$439$			1.45216i			0.0693077i	−0.999399	+	0.0346538i	$0.988967\pi$
$440$	23.0417			1.09847
$441$	4.81243	−	20.4411i	0.229163	−	0.973388i
$442$	27.8521			1.32479
$443$			3.84762i			0.182806i	0.995814	+	0.0914029i	$0.0291351\pi$
$443$			3.84762i			0.182806i	−0.995814	+	0.0914029i	$0.970865\pi$
$444$	0.870533	+	5.29868i	0.0413137	+	0.251464i
$445$	2.82700			0.134013
$446$	48.0568			2.27556
$447$	19.3525	−	3.17948i	0.915344	−	0.150384i
$448$	40.2367	+	72.4511i	1.90100	+	3.42299i
$449$		−	22.8625i		−	1.07895i	−0.842002	−	0.539474i	$-0.818623\pi$
$449$		−	22.8625i		−	1.07895i	0.842002	−	0.539474i	$-0.181377\pi$
$450$	2.05972	+	6.09924i	0.0970960	+	0.287521i
$451$		−	2.52403i		−	0.118852i
$452$		−	79.5252i		−	3.74055i
$453$	2.97140	+	18.0860i	0.139608	+	0.849755i
$454$		−	74.2565i		−	3.48503i
$455$	10.2536	−	5.69445i	0.480695	−	0.266960i
$456$	−12.1184	−	73.7611i	−0.567496	−	3.45418i
$457$	2.39520			0.112043			0.0560214	−	0.998430i	$-0.482159\pi$
$457$	2.39520			0.112043			0.0560214	+	0.998430i	$0.482159\pi$
$458$	−36.7999			−1.71955
$459$	13.4557	+	25.3174i	0.628060	+	1.18172i
$460$			10.2741i			0.479034i
$461$	−24.7970			−1.15491			−0.577456	−	0.816422i	$-0.695954\pi$
$461$	−24.7970			−1.15491			−0.577456	+	0.816422i	$0.695954\pi$
$462$	9.83774	−	7.79061i	0.457693	−	0.362452i
$463$	15.1088			0.702167			0.351083	−	0.936344i	$-0.385813\pi$
$463$	15.1088			0.702167			0.351083	+	0.936344i	$0.385813\pi$
$464$		−	32.5519i		−	1.51118i
$465$	−4.14517	+	0.681021i	−0.192228	+	0.0315816i
$466$	29.6876			1.37525
$467$	−23.3144			−1.07886			−0.539432	−	0.842029i	$-0.681361\pi$
$467$	−23.3144			−1.07886			−0.539432	+	0.842029i	$0.681361\pi$
$468$	9.72905	+	28.8097i	0.449726	+	1.33173i
$469$	−8.38321	−	15.0950i	−0.387101	−	0.697023i
$470$			28.0094i			1.29198i
$471$	−9.43483	+	1.55007i	−0.434734	+	0.0714236i
$472$			12.8724i			0.592501i
$473$			3.71187i			0.170672i
$474$	−60.6265	+	9.96048i	−2.78467	+	0.457500i
$475$		−	3.52976i		−	0.161957i
$476$	38.9745	+	70.1784i	1.78639	+	3.21662i
$477$	−6.68894	−	19.8073i	−0.306265	−	0.906914i
$478$	−43.2947			−1.98026
$479$	−40.1619			−1.83504			−0.917521	−	0.397687i	$-0.869813\pi$
$479$	−40.1619			−1.83504			−0.917521	+	0.397687i	$0.869813\pi$
$480$	−92.7648	+	15.2406i	−4.23411	+	0.695634i
$481$			1.03926i			0.0473861i
$482$	−6.05465			−0.275782
$483$	2.21031	+	2.79111i	0.100573	+	0.127000i
$484$	5.49880			0.249945
$485$			29.9792i			1.36128i
$486$	−29.3031	+	31.0409i	−1.32921	+	1.40804i
$487$	15.2101			0.689235			0.344617	−	0.938743i	$-0.388009\pi$
$487$	15.2101			0.689235			0.344617	+	0.938743i	$0.388009\pi$
$488$	106.636			4.82720
$489$	4.15756	+	25.3058i	0.188011	+	1.14437i
$490$	39.1337	+	24.3659i	1.76788	+	1.10074i
$491$			30.0953i			1.35818i	0.734054	+	0.679091i	$0.237626\pi$
$491$			30.0953i			1.35818i	−0.734054	+	0.679091i	$0.762374\pi$
$492$	3.89724	+	23.7213i	0.175701	+	1.06944i
$493$		−	11.7863i		−	0.530827i
$494$		−	22.7370i		−	1.02298i
$495$	2.30835	+	6.83551i	0.103753	+	0.307233i
$496$		−	15.3683i		−	0.690058i
$497$	12.7665	−	7.09005i	0.572656	−	0.318032i
$498$	−66.5444	+	10.9327i	−2.98192	+	0.489908i
$499$	13.3974			0.599749			0.299874	−	0.953979i	$-0.403055\pi$
$499$	13.3974			0.599749			0.299874	+	0.953979i	$0.403055\pi$
$500$	55.7579			2.49357
$501$	−2.61508	−	15.9172i	−0.116833	−	0.711128i
$502$			42.0369i			1.87620i
$503$	−26.7937			−1.19467			−0.597336	−	0.801991i	$-0.703774\pi$
$503$	−26.7937			−1.19467			−0.597336	+	0.801991i	$0.703774\pi$
$504$	−51.1750	+	56.2524i	−2.27952	+	2.50568i
$505$	37.7577			1.68020
$506$			2.12752i			0.0945797i
$507$	−2.69628	−	16.4114i	−0.119746	−	0.728857i
$508$	58.8406			2.61063
$509$	7.96017			0.352829			0.176414	−	0.984316i	$-0.443550\pi$
$509$	7.96017			0.352829			0.176414	+	0.984316i	$0.443550\pi$
$510$	−62.1062	+	10.2036i	−2.75011	+	0.451822i
$511$	−16.1279	+	8.95686i	−0.713458	+	0.396228i
$512$		−	51.9124i		−	2.29423i
$513$	20.6678	−	10.9845i	0.912505	−	0.484979i
$514$		−	44.5370i		−	1.96444i
$515$		−	3.98940i		−	0.175794i
$516$	−5.73133	−	34.8849i	−0.252308	−	1.53572i
$517$			4.25312i			0.187052i
$518$	−3.57102	+	1.98321i	−0.156902	+	0.0871374i
$519$	1.15342	+	7.02053i	0.0506296	+	0.308167i
$520$	−42.4732			−1.86257
$521$	39.7391			1.74100			0.870500	−	0.492169i	$-0.163796\pi$
$521$	39.7391			1.74100			0.870500	+	0.492169i	$0.163796\pi$
$522$	16.6257	−	5.61452i	0.727689	−	0.245741i
$523$		−	25.2953i		−	1.10609i	−0.833153	−	0.553043i	$-0.813467\pi$
$523$		−	25.2953i		−	1.10609i	0.833153	−	0.553043i	$-0.186533\pi$
$524$	20.6799			0.903405
$525$	−2.81520	+	2.22939i	−0.122865	+	0.0972984i
$526$	29.5916			1.29025
$527$		−	5.56452i		−	0.242394i
$528$	−26.0458	+	4.27914i	−1.13350	+	0.186226i
$529$	22.3964			0.973756
$530$	45.8935			1.99348
$531$	−3.81870	+	1.28958i	−0.165718	+	0.0559629i
$532$	57.2898	−	31.8166i	2.48383	−	1.37943i
$533$			4.65260i			0.201526i
$534$	−5.50173	+	0.903893i	−0.238083	+	0.0391153i
$535$		−	10.9774i		−	0.474594i
$536$			62.5279i			2.70079i
$537$	32.0318	−	5.26259i	1.38227	−	0.227097i
$538$			53.2703i			2.29665i
$539$	5.94231	+	3.69986i	0.255953	+	0.159364i
$540$	−32.2488	−	60.6772i	−1.38777	−	2.61113i
$541$	−30.6381			−1.31724			−0.658618	−	0.752477i	$-0.728859\pi$
$541$	−30.6381			−1.31724			−0.658618	+	0.752477i	$0.728859\pi$
$542$	−26.1522			−1.12333
$543$	−19.1331	+	3.14342i	−0.821078	+	0.134897i
$544$		−	124.528i		−	5.33910i
$545$	21.8545			0.936145
$546$	−18.1341	+	14.3606i	−0.776068	+	0.614577i
$547$	−8.03945			−0.343742			−0.171871	−	0.985119i	$-0.554981\pi$
$547$	−8.03945			−0.343742			−0.171871	+	0.985119i	$0.554981\pi$
$548$			40.8300i			1.74417i
$549$	10.6830	+	31.6345i	0.455939	+	1.35013i
$550$	−2.14588			−0.0915006
$551$	−9.62168			−0.409897
$552$	−2.09019	−	12.7224i	−0.0889646	−	0.541501i
$553$	−16.6395	−	29.9615i	−0.707584	−	1.27409i
$554$			87.3017i			3.70910i
$555$	−0.380731	−	2.31739i	−0.0161611	−	0.0983679i
$556$		−	103.535i		−	4.39085i
$557$		−	8.74260i		−	0.370436i	−0.982697	−	0.185218i	$-0.940701\pi$
$557$		−	8.74260i		−	0.370436i	0.982697	−	0.185218i	$-0.0592991\pi$
$558$	7.84932	−	2.65072i	0.332288	−	0.112214i
$559$		−	6.84217i		−	0.289393i
$560$	−47.0774	−	84.7687i	−1.98938	−	3.58213i
$561$	−9.43059	+	1.54938i	−0.398160	+	0.0654147i
$562$	−59.7931			−2.52222
$563$	−8.95852			−0.377557			−0.188778	−	0.982020i	$-0.560453\pi$
$563$	−8.95852			−0.377557			−0.188778	+	0.982020i	$0.560453\pi$
$564$	−6.56705	−	39.9717i	−0.276523	−	1.68311i
$565$			34.7806i			1.46323i
$566$	17.3234			0.728157
$567$	−21.8145	−	9.54602i	−0.916124	−	0.400895i
$568$	−52.8826			−2.21890
$569$			4.25225i			0.178264i	0.996020	+	0.0891319i	$0.0284093\pi$
$569$			4.25225i			0.178264i	−0.996020	+	0.0891319i	$0.971591\pi$
$570$	8.32965	+	50.7001i	0.348891	+	2.12359i
$571$	2.11482			0.0885026			0.0442513	−	0.999020i	$-0.485910\pi$
$571$	2.11482			0.0885026			0.0442513	+	0.999020i	$0.485910\pi$
$572$	−10.1360			−0.423809
$573$	−5.60610	+	0.921041i	−0.234198	+	0.0384770i
$574$	−15.9869	+	8.87854i	−0.667281	+	0.370583i
$575$		−	0.608817i		−	0.0253894i
$576$	89.0311	−	30.0658i	3.70963	−	1.25274i
$577$		−	4.93686i		−	0.205524i	−0.994706	−	0.102762i	$-0.967232\pi$
$577$		−	4.93686i		−	0.205524i	0.994706	−	0.102762i	$-0.0327680\pi$
$578$		−	36.8192i		−	1.53148i
$579$	6.45025	+	39.2608i	0.268063	+	1.63162i
$580$			28.2477i			1.17292i
$581$	−18.2637	−	32.8861i	−0.757707	−	1.36435i
$582$	−9.58541	−	58.3435i	−0.397328	−	2.41842i
$583$	6.96875			0.288616
$584$	66.8066			2.76447
$585$	−4.25503	−	12.6000i	−0.175924	−	0.520947i
$586$			14.5038i			0.599148i
$587$	−34.6298			−1.42932			−0.714661	−	0.699470i	$-0.753419\pi$
$587$	−34.6298			−1.42932			−0.714661	+	0.699470i	$0.753419\pi$
$588$	−61.5598	−	25.5968i	−2.53868	−	1.05559i
$589$	−4.54257			−0.187173
$590$		−	8.84793i		−	0.364263i
$591$	32.3597	−	5.31645i	1.33110	−	0.218690i
$592$	8.59180			0.353121
$593$	19.5422			0.802500			0.401250	−	0.915969i	$-0.368576\pi$
$593$	19.5422			0.802500			0.401250	+	0.915969i	$0.368576\pi$
$594$	−6.67792	−	12.5647i	−0.273998	−	0.515538i
$595$	−17.0456	−	30.6928i	−0.698802	−	1.25828i
$596$		−	62.2628i		−	2.55038i
$597$	1.57025	−	0.257980i	0.0642660	−	0.0105584i
$598$		−	3.92169i		−	0.160370i
$599$		−	1.86144i		−	0.0760564i	−0.999277	−	0.0380282i	$-0.987892\pi$
$599$		−	1.86144i		−	0.0760564i	0.999277	−	0.0380282i	$-0.0121077\pi$
$600$	12.8322	−	2.10824i	0.523872	−	0.0860684i
$601$		−	29.2244i		−	1.19209i	−0.802951	−	0.596045i	$-0.796738\pi$
$601$		−	29.2244i		−	1.19209i	0.802951	−	0.596045i	$-0.203262\pi$
$602$	23.5106	−	13.0569i	0.958219	−	0.532159i
$603$	−18.5494	+	6.26414i	−0.755390	+	0.255096i
$604$	58.1880			2.36763
$605$	−2.40492			−0.0977738
$606$	−73.4816	+	12.0725i	−2.98498	+	0.490411i
$607$			37.2987i			1.51391i	0.653469	+	0.756954i	$0.273313\pi$
$607$			37.2987i			1.51391i	−0.653469	+	0.756954i	$0.726687\pi$
$608$	−101.658			−4.12278
$609$	6.07702	+	7.67387i	0.246253	+	0.310961i
$610$	−73.2971			−2.96771
$611$		−	7.83986i		−	0.317167i
$612$	86.2383	−	29.1227i	3.48598	−	1.17722i
$613$	−4.35187			−0.175770			−0.0878852	−	0.996131i	$-0.528011\pi$
$613$	−4.35187			−0.175770			−0.0878852	+	0.996131i	$0.528011\pi$
$614$	−35.4485			−1.43059
$615$	−1.70447	−	10.3746i	−0.0687309	−	0.418345i
$616$	−12.3074	−	22.1610i	−0.495878	−	0.892890i
$617$		−	34.4828i		−	1.38822i	−0.719867	−	0.694112i	$-0.755797\pi$
$617$		−	34.4828i		−	1.38822i	0.719867	−	0.694112i	$-0.244203\pi$
$618$	1.27555	+	7.76390i	0.0513102	+	0.312310i
$619$			45.7786i			1.84000i	0.391922	+	0.919998i	$0.371810\pi$
$619$			45.7786i			1.84000i	−0.391922	+	0.919998i	$0.628190\pi$
$620$			13.3362i			0.535596i
$621$	3.56480	−	1.89462i	0.143051	−	0.0760286i
$622$			59.1629i			2.37222i
$623$	−1.51000	−	2.71894i	−0.0604969	−	0.108932i
$624$	48.0108	−	7.88782i	1.92197	−	0.315766i
$625$	−28.3041			−1.13216
$626$	43.1468			1.72449
$627$	1.26483	+	7.69862i	0.0505123	+	0.307453i
$628$			30.3546i			1.21128i
$629$	3.11089			0.124039
$630$	35.1754	−	38.6654i	1.40142	−	1.54047i
$631$	12.9002			0.513548			0.256774	−	0.966471i	$-0.417340\pi$
$631$	12.9002			0.513548			0.256774	+	0.966471i	$0.417340\pi$
$632$			124.109i			4.93680i
$633$	−2.79067	−	16.9860i	−0.110919	−	0.675131i
$634$	85.4511			3.39370
$635$	−25.7341			−1.02123
$636$	−65.4937	+	10.7601i	−2.59699	+	0.426667i
$637$	−10.9536	−	6.82003i	−0.433996	−	0.270220i
$638$			5.84939i			0.231580i
$639$	−5.29786	−	15.6880i	−0.209580	−	0.620609i
$640$			97.7331i			3.86324i
$641$		−	19.6557i		−	0.776353i	−0.921585	−	0.388176i	$-0.873105\pi$
$641$		−	19.6557i		−	0.776353i	0.921585	−	0.388176i	$-0.126895\pi$
$642$	3.50986	+	21.3635i	0.138523	+	0.843149i
$643$		−	13.3560i		−	0.526707i	−0.964699	−	0.263354i	$-0.915171\pi$
$643$		−	13.3560i		−	0.526707i	0.964699	−	0.263354i	$-0.0848286\pi$
$644$	9.88141	−	5.48777i	0.389382	−	0.216248i
$645$	2.50662	+	15.2570i	0.0986980	+	0.600745i
$646$	−68.0602			−2.67779
$647$	−24.3849			−0.958669			−0.479334	−	0.877632i	$-0.659122\pi$
$647$	−24.3849			−0.958669			−0.479334	+	0.877632i	$0.659122\pi$
$648$	52.2778	+	68.5755i	2.05367	+	2.69390i
$649$		−	1.34352i		−	0.0527379i
$650$	3.95554			0.155149
$651$	2.86907	+	3.62297i	0.112448	+	0.141995i
$652$	81.4162			3.18850
$653$			14.4452i			0.565284i	0.959225	+	0.282642i	$0.0912109\pi$
$653$			14.4452i			0.565284i	−0.959225	+	0.282642i	$0.908789\pi$
$654$	−42.5318	+	6.98766i	−1.66313	+	0.273239i
$655$	−9.04442			−0.353395
$656$	38.4641			1.50177
$657$	6.69278	+	19.8187i	0.261110	+	0.773201i
$658$	26.9388	−	14.9608i	1.05018	−	0.583232i
$659$			15.1692i			0.590907i	0.955357	+	0.295454i	$0.0954708\pi$
$659$			15.1692i			0.590907i	−0.955357	+	0.295454i	$0.904529\pi$
$660$	22.6019	−	3.71332i	0.879778	−	0.144541i
$661$		−	2.53853i		−	0.0987373i	−0.998781	−	0.0493687i	$-0.984279\pi$
$661$		−	2.53853i		−	0.0987373i	0.998781	−	0.0493687i	$-0.0157209\pi$
$662$			80.3236i			3.12186i
$663$	17.3836	−	2.85600i	0.675123	−	0.110918i
$664$			136.224i			5.28651i
$665$	−25.0559	+	13.9151i	−0.971627	+	0.539605i
$666$	1.48191	+	4.38823i	0.0574227	+	0.170040i
$667$	−1.65956			−0.0642583
$668$	−51.2103			−1.98139
$669$	29.9941	−	4.92781i	1.15964	−	0.190520i
$670$		−	42.9789i		−	1.66042i
$671$	−11.1299			−0.429665
$672$	64.2069	+	81.0784i	2.47684	+	3.12767i
$673$	−36.1248			−1.39251			−0.696255	−	0.717795i	$-0.745152\pi$
$673$	−36.1248			−1.39251			−0.696255	+	0.717795i	$0.745152\pi$
$674$		−	24.6684i		−	0.950191i
$675$	1.91098	+	3.59557i	0.0735535	+	0.138394i
$676$	−52.8004			−2.03078
$677$	37.5137			1.44177			0.720884	−	0.693056i	$-0.243736\pi$
$677$	37.5137			1.44177			0.720884	+	0.693056i	$0.243736\pi$
$678$	−11.1206	−	67.6877i	−0.427084	−	2.59953i
$679$	28.8333	−	16.0129i	1.10652	−	0.614520i
$680$			127.138i			4.87553i
$681$	−7.61436	−	46.3463i	−0.291783	−	1.77600i
$682$			2.76160i			0.105747i
$683$		−	9.01261i		−	0.344858i	−0.985022	−	0.172429i	$-0.944838\pi$
$683$		−	9.01261i		−	0.344858i	0.985022	−	0.172429i	$-0.0551615\pi$
$684$	−23.7742	−	70.4002i	−0.909029	−	2.69182i
$685$		−	17.8571i		−	0.682286i
$686$	2.53183	−	50.6525i	0.0966658	−	1.93392i
$687$	−22.9683	+	3.77352i	−0.876294	+	0.143969i
$688$	−56.5658			−2.15655
$689$	−12.8456			−0.489380
$690$	1.43671	+	8.74481i	0.0546945	+	0.332909i
$691$		−	21.7322i		−	0.826731i	−0.910565	−	0.413366i	$-0.864353\pi$
$691$		−	21.7322i		−	0.826731i	0.910565	−	0.413366i	$-0.135647\pi$
$692$	22.5871			0.858632
$693$	5.34126	−	5.87120i	0.202898	−	0.223028i
$694$	55.9230			2.12281
$695$			45.2812i			1.71761i
$696$	−5.74678	−	34.9789i	−0.217831	−	1.32587i
$697$	13.9270			0.527521
$698$	35.5857			1.34694
$699$	18.5292	−	3.04420i	0.700837	−	0.115142i
$700$	5.53513	+	9.96670i	0.209208	+	0.376706i
$701$		−	1.24048i		−	0.0468525i	−0.999726	−	0.0234262i	$-0.992543\pi$
$701$		−	1.24048i		−	0.0468525i	0.999726	−	0.0234262i	$-0.00745748\pi$
$702$	12.3095	+	23.1609i	0.464594	+	0.874150i
$703$		−	2.53956i		−	0.0957814i
$704$			31.3236i			1.18055i
$705$	2.87212	+	17.4817i	0.108170	+	0.658401i
$706$		−	59.4634i		−	2.23793i
$707$	−20.1677	−	36.3145i	−0.758484	−	1.36575i
$708$	2.07448	+	12.6267i	0.0779635	+	0.474541i
$709$	51.7975			1.94530			0.972648	−	0.232286i	$-0.0746204\pi$
$709$	51.7975			1.94530			0.972648	+	0.232286i	$0.0746204\pi$
$710$	36.3491			1.36416
$711$	−36.8180	+	12.4335i	−1.38078	+	0.466291i
$712$			11.2626i			0.422086i
$713$	−0.783507			−0.0293426
$714$	42.9866	+	54.2822i	1.60873	+	2.03146i
$715$	4.43303			0.165786
$716$		−	103.056i		−	3.85137i
$717$	−27.0219	+	4.43950i	−1.00915	+	0.165796i
$718$	−67.8563			−2.53238
$719$	−18.8970			−0.704740			−0.352370	−	0.935861i	$-0.614624\pi$
$719$	−18.8970			−0.704740			−0.352370	+	0.935861i	$0.614624\pi$
$720$	−104.167	+	35.1774i	−3.88209	+	1.31098i
$721$	−3.83690	+	2.13087i	−0.142894	+	0.0793579i
$722$			3.53122i			0.131418i
$723$	−3.77894	+	0.620852i	−0.140540	+	0.0230897i
$724$			61.5566i			2.28773i
$725$		−	1.67388i		−	0.0621664i
$726$	4.68029	−	0.768937i	0.173702	−	0.0285379i
$727$		−	23.2862i		−	0.863639i	−0.901960	−	0.431819i	$-0.857872\pi$
$727$		−	23.2862i		−	0.863639i	0.901960	−	0.431819i	$-0.142128\pi$
$728$	22.6864	+	40.8497i	0.840815	+	1.51399i
$729$	−15.1062	+	22.3786i	−0.559489	+	0.828838i
$730$	−45.9199			−1.69957
$731$	−20.4812			−0.757524
$732$	104.601	−	17.1852i	3.86616	−	0.635182i
$733$		−	22.7476i		−	0.840203i	−0.907477	−	0.420102i	$-0.861994\pi$
$733$		−	22.7476i		−	0.840203i	0.907477	−	0.420102i	$-0.138006\pi$
$734$	48.6687			1.79639
$735$	26.9234	+	11.1949i	0.993084	+	0.412928i
$736$	−17.5341			−0.646315
$737$		−	6.52619i		−	0.240395i
$738$	6.63426	+	19.6454i	0.244211	+	0.723157i
$739$	−14.6982			−0.540683			−0.270342	−	0.962764i	$-0.587137\pi$
$739$	−14.6982			−0.540683			−0.270342	+	0.962764i	$0.587137\pi$
$740$	−7.45574			−0.274078
$741$	−2.33148	−	14.1910i	−0.0856491	−	0.521320i
$742$	−24.5133	−	44.1392i	−0.899911	−	1.62040i
$743$			4.07134i			0.149363i	0.997207	+	0.0746816i	$0.0237940\pi$
$743$			4.07134i			0.149363i	−0.997207	+	0.0746816i	$0.976206\pi$
$744$	−2.71316	−	16.5142i	−0.0994692	−	0.605439i
$745$			27.2309i			0.997661i
$746$			47.5026i			1.73919i
$747$	−40.4119	+	13.6471i	−1.47859	+	0.499322i
$748$			30.3410i			1.10938i
$749$	−10.5578	+	5.86340i	−0.385773	+	0.214244i
$750$	47.4583	−	7.79704i	1.73293	−	0.284708i
$751$	−23.3612			−0.852462			−0.426231	−	0.904614i	$-0.640159\pi$
$751$	−23.3612			−0.852462			−0.426231	+	0.904614i	$0.640159\pi$
$752$	−64.8140			−2.36352
$753$	4.31052	+	26.2368i	0.157084	+	0.956124i
$754$		−	10.7823i		−	0.392668i
$755$	−25.4487			−0.926173
$756$	−41.1327	+	63.4259i	−1.49598	+	2.30678i
$757$	7.54284			0.274149			0.137075	−	0.990561i	$-0.456230\pi$
$757$	7.54284			0.274149			0.137075	+	0.990561i	$0.456230\pi$
$758$		−	44.6401i		−	1.62140i
$759$	0.218159	+	1.32787i	0.00791866	+	0.0481985i
$760$	103.789			3.76482
$761$	7.52566			0.272805			0.136402	−	0.990654i	$-0.456446\pi$
$761$	7.52566			0.272805			0.136402	+	0.990654i	$0.456446\pi$
$762$	50.0820	−	8.22811i	1.81428	−	0.298073i
$763$	−11.6733	−	21.0192i	−0.422600	−	0.760944i
$764$			18.0365i			0.652536i
$765$	−37.7166	+	12.7369i	−1.36365	+	0.460504i
$766$			80.8225i			2.92023i
$767$			2.47655i			0.0894229i
$768$	−13.6575	−	83.1291i	−0.492823	−	2.99966i
$769$		−	43.5521i		−	1.57053i	−0.619160	−	0.785265i	$-0.712527\pi$
$769$		−	43.5521i		−	1.57053i	0.619160	−	0.785265i	$-0.287473\pi$
$770$	8.45954	+	15.2325i	0.304861	+	0.548940i
$771$	−4.56689	−	27.7973i	−0.164473	−	1.00110i
$772$	126.313			4.54612
$773$	10.4676			0.376494			0.188247	−	0.982122i	$-0.439719\pi$
$773$	10.4676			0.376494			0.188247	+	0.982122i	$0.439719\pi$
$774$	−9.75643	−	28.8908i	−0.350688	−	1.03846i
$775$		−	0.790269i		−	0.0283873i
$776$	−119.436			−4.28749
$777$	−2.02545	+	1.60398i	−0.0726627	+	0.0575424i
$778$	91.2707			3.27221
$779$		−	11.3692i		−	0.407344i
$780$	−41.6625	+	6.84484i	−1.49176	+	0.245085i
$781$	5.51948			0.197503
$782$	−11.7391			−0.419789
$783$	9.80106	−	5.20907i	0.350261	−	0.186157i
$784$	−56.3828	+	90.5558i	−2.01367	+	3.23414i
$785$		−	13.2757i		−	0.473830i
$786$	17.6017	−	2.89182i	0.627830	−	0.103148i
$787$			9.61685i			0.342804i	0.985201	+	0.171402i	$0.0548296\pi$
$787$			9.61685i			0.342804i	−0.985201	+	0.171402i	$0.945170\pi$
$788$		−	104.111i		−	3.70878i
$789$	18.4693	−	3.03436i	0.657523	−	0.108026i
$790$		−	85.3072i		−	3.03509i
$791$	33.4512	−	18.5775i	1.18939	−	0.660541i
$792$	−27.2323	+	9.19637i	−0.967659	+	0.326779i
$793$	20.5159			0.728543
$794$	69.7427			2.47507
$795$	28.6439	−	4.70598i	1.01589	−	0.166904i
$796$		−	5.05195i		−	0.179062i
$797$	51.9722			1.84095			0.920475	−	0.390800i	$-0.127802\pi$
$797$	51.9722			1.84095			0.920475	+	0.390800i	$0.127802\pi$
$798$	44.3130	−	35.0919i	1.56866	−	1.24224i
$799$	−23.4676			−0.830225
$800$		−	17.6854i		−	0.625274i
$801$	−3.34116	+	1.12831i	−0.118054	+	0.0398669i
$802$	−102.708			−3.62673
$803$	−6.97276			−0.246063
$804$	10.0768	+	61.3344i	0.355381	+	2.16310i
$805$	−4.32167	+	2.40009i	−0.152319	+	0.0845922i
$806$		−	5.09052i		−	0.179306i
$807$	5.46242	+	33.2481i	0.192286	+	1.17039i
$808$			150.425i			5.29193i
$809$		−	2.70382i		−	0.0950612i	−0.998870	−	0.0475306i	$-0.984865\pi$
$809$		−	2.70382i		−	0.0950612i	0.998870	−	0.0475306i	$-0.0151352\pi$
$810$	−35.9334	−	47.1357i	−1.26257	−	1.65618i
$811$		−	16.8802i		−	0.592744i	−0.955073	−	0.296372i	$-0.904223\pi$
$811$		−	16.8802i		−	0.592744i	0.955073	−	0.296372i	$-0.0957768\pi$
$812$	27.1679	−	15.0881i	0.953408	−	0.529487i
$813$	−16.3226	+	2.68168i	−0.572459	+	0.0940507i
$814$	−1.54390			−0.0541136
$815$	−35.6076			−1.24728
$816$	−23.6112	−	143.714i	−0.826557	−	5.03101i
$817$			16.7197i			0.584949i
$818$	14.7416			0.515426
$819$	−9.84564	+	10.8225i	−0.344035	+	0.378169i
$820$	−33.3782			−1.16562
$821$			9.62621i			0.335957i	0.985791	+	0.167978i	$0.0537239\pi$
$821$			9.62621i			0.335957i	−0.985791	+	0.167978i	$0.946276\pi$
$822$	5.70955	+	34.7524i	0.199144	+	1.21213i
$823$	−40.6770			−1.41791			−0.708956	−	0.705253i	$-0.750833\pi$
$823$	−40.6770			−1.41791			−0.708956	+	0.705253i	$0.750833\pi$
$824$	15.8936			0.553679
$825$	−1.33933	+	0.220042i	−0.0466294	+	0.00766086i
$826$	−8.50972	+	4.72598i	−0.296091	+	0.164438i
$827$			14.2485i			0.495468i	0.968828	+	0.247734i	$0.0796860\pi$
$827$			14.2485i			0.495468i	−0.968828	+	0.247734i	$0.920314\pi$
$828$	−4.10060	−	12.1427i	−0.142506	−	0.421988i
$829$		−	28.6535i		−	0.995179i	−0.867413	−	0.497589i	$-0.834219\pi$
$829$		−	28.6535i		−	0.995179i	0.867413	−	0.497589i	$-0.165781\pi$
$830$		−	93.6342i		−	3.25009i
$831$	8.95204	+	54.4884i	0.310543	+	1.89018i
$832$		−	57.7393i		−	2.00175i
$833$	−20.4149	+	32.7881i	−0.707335	+	1.13604i
$834$	−14.4780	−	88.1233i	−0.501333	−	3.05146i
$835$	22.3970			0.775080
$836$	24.7687			0.856644
$837$	4.62726	−	2.45930i	0.159941	−	0.0850057i
$838$		−	85.9703i		−	2.96980i
$839$	43.4835			1.50122			0.750609	−	0.660747i	$-0.229760\pi$
$839$	43.4835			1.50122			0.750609	+	0.660747i	$0.229760\pi$
$840$	−65.5527	−	82.7778i	−2.26178	−	2.85611i
$841$	24.4372			0.842663
$842$		−	34.0816i		−	1.17453i
$843$	−37.3192	+	6.13127i	−1.28534	+	0.211172i
$844$	−54.6488			−1.88109
$845$	23.0924			0.794404
$846$	−11.1791	−	33.1035i	−0.384344	−	1.13812i
$847$	1.28455	+	2.31299i	0.0441376	+	0.0794753i
$848$			106.198i			3.64685i
$849$	10.8122	−	1.77637i	0.371074	−	0.0609648i
$850$		−	11.8404i		−	0.406123i
$851$		−	0.438026i		−	0.0150153i
$852$	−51.8732	+	8.52238i	−1.77715	+	0.291972i
$853$			21.0380i			0.720327i	0.932889	+	0.360163i	$0.117279\pi$
$853$			21.0380i			0.720327i	−0.932889	+	0.360163i	$0.882721\pi$
$854$	39.1505	+	70.4954i	1.33970	+	2.41230i
$855$	10.3977	+	30.7898i	0.355595	+	1.05299i
$856$	43.7334			1.49478
$857$	43.7002			1.49277			0.746385	−	0.665514i	$-0.231788\pi$
$857$	43.7002			1.49277			0.746385	+	0.665514i	$0.231788\pi$
$858$	−8.62727	+	1.41740i	−0.294530	+	0.0483891i
$859$		−	14.9516i		−	0.510143i	−0.966922	−	0.255072i	$-0.917901\pi$
$859$		−	14.9516i		−	0.510143i	0.966922	−	0.255072i	$-0.0820991\pi$
$860$	49.0864			1.67383
$861$	−9.06764	+	7.18076i	−0.309024	+	0.244720i
$862$	−44.0458			−1.50021
$863$			23.0125i			0.783356i	0.920102	+	0.391678i	$0.128105\pi$
$863$			23.0125i			0.783356i	−0.920102	+	0.391678i	$0.871895\pi$
$864$	103.553	−	55.0366i	3.52295	−	1.87238i
$865$	−9.87854			−0.335881
$866$	−71.4886			−2.42928
$867$	−3.77549	−	22.9803i	−0.128222	−	0.780451i
$868$	12.8265	−	7.12335i	0.435359	−	0.241782i
$869$		−	12.9536i		−	0.439420i
$870$	3.95008	+	24.0430i	0.133920	+	0.815133i
$871$			12.0298i			0.407616i
$872$			87.0674i			2.94847i
$873$	−11.9653	−	35.4316i	−0.404962	−	1.19918i
$874$			9.58317i			0.324155i
$875$	13.0254	+	23.4538i	0.440338	+	0.792883i
$876$	65.5314	−	10.7663i	2.21410	−	0.363760i
$877$	−22.2788			−0.752303			−0.376151	−	0.926558i	$-0.622753\pi$
$877$	−22.2788			−0.752303			−0.376151	+	0.926558i	$0.622753\pi$
$878$	3.97658			0.134203
$879$	1.48724	+	9.05241i	0.0501635	+	0.305330i
$880$		−	36.6489i		−	1.23544i
$881$	23.1900			0.781289			0.390645	−	0.920542i	$-0.372252\pi$
$881$	23.1900			0.781289			0.390645	+	0.920542i	$0.372252\pi$
$882$	−55.9759	−	13.1783i	−1.88481	−	0.443737i
$883$	41.7132			1.40376			0.701881	−	0.712294i	$-0.252344\pi$
$883$	41.7132			1.40376			0.701881	+	0.712294i	$0.252344\pi$
$884$		−	55.9281i		−	1.88107i
$885$	−0.907279	−	5.52234i	−0.0304978	−	0.185631i
$886$	10.5363			0.353973
$887$	−40.1032			−1.34654			−0.673268	−	0.739399i	$-0.735110\pi$
$887$	−40.1032			−1.34654			−0.673268	+	0.739399i	$0.735110\pi$
$888$	9.23239	−	1.51681i	0.309819	−	0.0509009i
$889$	13.7455	+	24.7505i	0.461009	+	0.830104i
$890$		−	7.74145i		−	0.259494i
$891$	−5.45636	−	7.15739i	−0.182795	−	0.239781i
$892$		−	96.4999i		−	3.23106i
$893$			19.1577i			0.641088i
$894$	−8.70667	−	52.9949i	−0.291194	−	1.77241i
$895$			45.0718i			1.50658i
$896$	93.9974	−	52.2026i	3.14023	−	1.74397i
$897$	−0.402136	−	2.44768i	−0.0134269	−	0.0817257i
$898$	−62.6065			−2.08921
$899$	−2.15417			−0.0718457
$900$	12.2475	−	4.13599i	0.408250	−	0.137866i
$901$			38.4518i			1.28102i
$902$	−6.91179			−0.230137
$903$	13.3350	−	10.5601i	0.443760	−	0.351419i
$904$	−138.564			−4.60858
$905$		−	26.9220i		−	0.894918i
$906$	49.5266	−	8.13685i	1.64541	−	0.270329i
$907$	−3.45308			−0.114658			−0.0573288	−	0.998355i	$-0.518258\pi$
$907$	−3.45308			−0.114658			−0.0573288	+	0.998355i	$0.518258\pi$
$908$	−149.110			−4.94838
$909$	−44.6248	+	15.0698i	−1.48011	+	0.499834i
$910$	−15.5936	−	28.0783i	−0.516924	−	0.930787i
$911$		−	2.83070i		−	0.0937851i	−0.998900	−	0.0468926i	$-0.985068\pi$
$911$		−	2.83070i		−	0.0937851i	0.998900	−	0.0468926i	$-0.0149318\pi$
$912$	−117.321	+	19.2749i	−3.88487	+	0.638256i
$913$		−	14.2180i		−	0.470547i
$914$		−	6.55900i		−	0.216952i
$915$	−45.7476	+	7.51599i	−1.51237	+	0.248471i
$916$			73.8956i			2.44158i
$917$	4.83094	+	8.69871i	0.159532	+	0.287257i
$918$	69.3291	−	36.8471i	2.28820	−	1.21613i
$919$	33.8981			1.11819			0.559097	−	0.829102i	$-0.311148\pi$
$919$	33.8981			1.11819			0.559097	+	0.829102i	$0.311148\pi$
$920$	17.9016			0.590198
$921$	−22.1248	+	3.63494i	−0.729037	+	0.119775i
$922$			67.9039i			2.23630i
$923$	−10.1742			−0.334887
$924$	−15.6438	−	19.7545i	−0.514645	−	0.649877i
$925$	0.441807			0.0145265
$926$		−	41.3739i		−	1.35963i
$927$	1.59224	+	4.71495i	0.0522961	+	0.154859i
$928$	−48.2082			−1.58251
$929$	22.6165			0.742025			0.371012	−	0.928628i	$-0.379011\pi$
$929$	22.6165			0.742025			0.371012	+	0.928628i	$0.379011\pi$
$930$	1.86490	+	11.3511i	0.0611526	+	0.372218i
$931$	26.7665	+	16.6656i	0.877235	+	0.546194i
$932$		−	59.6137i		−	1.95271i
$933$	6.06665	+	36.9259i	0.198613	+	1.20890i
$934$			63.8441i			2.08904i
$935$		−	13.2697i		−	0.433966i
$936$	50.1979	−	16.9519i	1.64077	−	0.554089i
$937$		−	35.5079i		−	1.15999i	−0.814619	−	0.579996i	$-0.803054\pi$
$937$		−	35.5079i		−	1.15999i	0.814619	−	0.579996i	$-0.196946\pi$
$938$	−41.3361	+	22.9565i	−1.34967	+	0.749557i
$939$	26.9296	−	4.42433i	0.878814	−	0.144383i
$940$	56.2439			1.83447
$941$	−8.56208			−0.279116			−0.139558	−	0.990214i	$-0.544568\pi$
$941$	−8.56208			−0.279116			−0.139558	+	0.990214i	$0.544568\pi$
$942$	4.24471	+	25.8363i	0.138300	+	0.841791i
$943$		−	1.96097i		−	0.0638581i
$944$	20.4742			0.666378
$945$	17.9895	−	27.7395i	0.585200	−	0.902367i
$946$	10.1646			0.330479
$947$			37.0486i			1.20392i	0.798527	+	0.601959i	$0.205613\pi$
$947$			37.0486i			1.20392i	−0.798527	+	0.601959i	$0.794387\pi$
$948$	20.0010	+	121.740i	0.649603	+	3.95394i
$949$	12.8530			0.417227
$950$	−9.66588			−0.313603
$951$	53.3334	−	8.76228i	1.72945	−	0.284136i
$952$	122.279	−	67.9090i	3.96307	−	2.20094i
$953$			19.7422i			0.639514i	0.947500	+	0.319757i	$0.103601\pi$
$953$			19.7422i			0.639514i	−0.947500	+	0.319757i	$0.896399\pi$
$954$	−54.2402	+	18.3169i	−1.75609	+	0.593033i
$955$		−	7.88831i		−	0.255260i
$956$			86.9375i			2.81176i
$957$	0.599805	+	3.65083i	0.0193889	+	0.118015i
$958$			109.979i			3.55326i
$959$	−17.1746	+	9.53811i	−0.554595	+	0.308002i
$960$	21.1527	+	128.750i	0.682701	+	4.15540i
$961$	29.9830			0.967193
$962$	2.84590			0.0917554
$963$	4.38128	+	12.9739i	0.141185	+	0.418077i
$964$			12.1580i			0.391581i
$965$	−55.2436			−1.77835
$966$	7.64315	−	6.05270i	0.245914	−	0.194742i
$967$	−20.8865			−0.671664			−0.335832	−	0.941922i	$-0.609017\pi$
$967$	−20.8865			−0.671664			−0.335832	+	0.941922i	$0.609017\pi$
$968$		−	9.58108i		−	0.307948i
$969$	−42.4791	+	6.97899i	−1.36462	+	0.224198i
$970$	82.0948			2.63590
$971$	−40.0985			−1.28682			−0.643411	−	0.765521i	$-0.722481\pi$
$971$	−40.0985			−1.28682			−0.643411	+	0.765521i	$0.722481\pi$
$972$	62.3313	+	58.8416i	1.99928	+	1.88735i
$973$	43.5504	−	24.1863i	1.39616	−	0.775376i
$974$		−	41.6512i		−	1.33459i
$975$	2.46881	−	0.405607i	0.0790652	−	0.0129898i
$976$		−	169.610i		−	5.42909i
$977$		−	3.56988i		−	0.114211i	−0.998368	−	0.0571053i	$-0.981813\pi$
$977$		−	3.56988i		−	0.114211i	0.998368	−	0.0571053i	$-0.0181871\pi$
$978$	69.2972	−	11.3850i	2.21588	−	0.364053i
$979$		−	1.17551i		−	0.0375694i
$980$	48.9276	−	78.5820i	1.56293	−	2.51021i
$981$	−25.8292	+	8.72255i	−0.824664	+	0.278489i
$982$	82.4128			2.62990
$983$	3.83424			0.122293			0.0611466	−	0.998129i	$-0.480524\pi$
$983$	3.83424			0.122293			0.0611466	+	0.998129i	$0.480524\pi$
$984$	41.3320	−	6.79054i	1.31762	−	0.216474i
$985$			45.5331i			1.45080i
$986$	−32.2755			−1.02786
$987$	15.2794	−	12.0999i	0.486350	−	0.385145i
$988$	−45.6567			−1.45253
$989$			2.88383i			0.0917006i
$990$	18.7183	−	6.32118i	0.594907	−	0.200900i
$991$	−15.5005			−0.492388			−0.246194	−	0.969221i	$-0.579180\pi$
$991$	−15.5005			−0.492388			−0.246194	+	0.969221i	$0.579180\pi$
$992$	−22.7600			−0.722629
$993$	8.23649	+	50.1331i	0.261377	+	1.59092i
$994$	−19.4153	−	34.9597i	−0.615817	−	1.10886i
$995$			2.20949i			0.0700455i
$996$	21.9534	+	133.624i	0.695619	+	4.23403i
$997$			4.14286i			0.131206i	0.997846	+	0.0656029i	$0.0208971\pi$
$997$			4.14286i			0.131206i	−0.997846	+	0.0656029i	$0.979103\pi$
$998$		−	36.6873i		−	1.16132i
$999$	1.37489	+	2.58691i	0.0434996	+	0.0818461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.e.a.188.1	✓	28
3.2	odd	2	inner	231.2.e.a.188.28	yes	28
7.6	odd	2	inner	231.2.e.a.188.2	yes	28
21.20	even	2	inner	231.2.e.a.188.27	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.e.a.188.1	✓	28	1.1	even	1	trivial
231.2.e.a.188.2	yes	28	7.6	odd	2	inner
231.2.e.a.188.27	yes	28	21.20	even	2	inner
231.2.e.a.188.28	yes	28	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.73839i q^{2} +(-0.280799 - 1.70914i) q^{3} -5.49880 q^{4} +2.40492 q^{5} +(-4.68029 + 0.768937i) q^{6} +(-1.28455 - 2.31299i) q^{7} +9.58108i q^{8} +(-2.84230 + 0.959847i) q^{9} +O(q^{10})\)	\(q-2.73839i q^{2} +(-0.280799 - 1.70914i) q^{3} -5.49880 q^{4} +2.40492 q^{5} +(-4.68029 + 0.768937i) q^{6} +(-1.28455 - 2.31299i) q^{7} +9.58108i q^{8} +(-2.84230 + 0.959847i) q^{9} -6.58561i q^{10} -1.00000i q^{11} +(1.54405 + 9.39820i) q^{12} +1.84332i q^{13} +(-6.33388 + 3.51760i) q^{14} +(-0.675298 - 4.11034i) q^{15} +15.2392 q^{16} +5.51775 q^{17} +(2.62844 + 7.78335i) q^{18} -4.50439i q^{19} -13.2242 q^{20} +(-3.59252 + 2.84496i) q^{21} -2.73839 q^{22} -0.776922i q^{23} +(16.3754 - 2.69035i) q^{24} +0.783628 q^{25} +5.04773 q^{26} +(2.43863 + 4.58837i) q^{27} +(7.06348 + 12.7187i) q^{28} -2.13607i q^{29} +(-11.2557 + 1.84923i) q^{30} -1.00848i q^{31} -22.5687i q^{32} +(-1.70914 + 0.280799i) q^{33} -15.1098i q^{34} +(-3.08924 - 5.56255i) q^{35} +(15.6293 - 5.27800i) q^{36} +0.563797 q^{37} -12.3348 q^{38} +(3.15049 - 0.517602i) q^{39} +23.0417i q^{40} +2.52403 q^{41} +(7.79061 + 9.83774i) q^{42} -3.71187 q^{43} +5.49880i q^{44} +(-6.83551 + 2.30835i) q^{45} -2.12752 q^{46} -4.25312 q^{47} +(-4.27914 - 26.0458i) q^{48} +(-3.69986 + 5.94231i) q^{49} -2.14588i q^{50} +(-1.54938 - 9.43059i) q^{51} -10.1360i q^{52} +6.96875i q^{53} +(12.5647 - 6.67792i) q^{54} -2.40492i q^{55} +(22.1610 - 12.3074i) q^{56} +(-7.69862 + 1.26483i) q^{57} -5.84939 q^{58} +1.34352 q^{59} +(3.71332 + 22.6019i) q^{60} -11.1299i q^{61} -2.76160 q^{62} +(5.87120 + 5.34126i) q^{63} -31.3236 q^{64} +4.43303i q^{65} +(0.768937 + 4.68029i) q^{66} +6.52619 q^{67} -30.3410 q^{68} +(-1.32787 + 0.218159i) q^{69} +(-15.2325 + 8.45954i) q^{70} +5.51948i q^{71} +(-9.19637 - 27.2323i) q^{72} -6.97276i q^{73} -1.54390i q^{74} +(-0.220042 - 1.33933i) q^{75} +24.7687i q^{76} +(-2.31299 + 1.28455i) q^{77} +(-1.41740 - 8.62727i) q^{78} +12.9536 q^{79} +36.6489 q^{80} +(7.15739 - 5.45636i) q^{81} -6.91179i q^{82} +14.2180 q^{83} +(19.7545 - 15.6438i) q^{84} +13.2697 q^{85} +10.1646i q^{86} +(-3.65083 + 0.599805i) q^{87} +9.58108 q^{88} +1.17551 q^{89} +(6.32118 + 18.7183i) q^{90} +(4.26358 - 2.36784i) q^{91} +4.27213i q^{92} +(-1.72362 + 0.283179i) q^{93} +11.6467i q^{94} -10.8327i q^{95} +(-38.5730 + 6.33725i) q^{96} +12.4658i q^{97} +(16.2724 + 10.1317i) q^{98} +(0.959847 + 2.84230i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more