LMFDB - Embedded newform 115.3.d.b.91.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(91,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.91"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 10 x^{8} + 34 x^{7} + 346 x^{6} - 968 x^{5} + 165 x^{4} + 6972 x^{3} + 19344 x^{2} + \cdots + 225444 $ x^10 - 2x^9 - 10x^8 + 34x^7 + 346x^6 - 968x^5 + 165x^4 + 6972x^3 + 19344x^2 - 89080*x + 225444
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.6
Root			$1.32878 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	115.91
Dual form			115.3.d.b.91.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.32878 q^{2} -2.60299 q^{3} -2.23434 q^{4} +2.23607i q^{5} -3.45880 q^{6} +8.05652i q^{7} -8.28408 q^{8} -2.22446 q^{9} +2.97125i q^{10} +5.14870i q^{11} +5.81595 q^{12} -6.63907 q^{13} +10.7054i q^{14} -5.82045i q^{15} -2.07038 q^{16} +10.7993i q^{17} -2.95583 q^{18} -9.70153i q^{19} -4.99613i q^{20} -20.9710i q^{21} +6.84150i q^{22} +(16.6172 - 15.9019i) q^{23} +21.5633 q^{24} -5.00000 q^{25} -8.82188 q^{26} +29.2171 q^{27} -18.0010i q^{28} -9.52776 q^{29} -7.73412i q^{30} -10.0640 q^{31} +30.3852 q^{32} -13.4020i q^{33} +14.3499i q^{34} -18.0149 q^{35} +4.97020 q^{36} +54.9767i q^{37} -12.8912i q^{38} +17.2814 q^{39} -18.5238i q^{40} -47.4339 q^{41} -27.8659i q^{42} +29.8177i q^{43} -11.5039i q^{44} -4.97405i q^{45} +(22.0806 - 21.1301i) q^{46} +10.2009 q^{47} +5.38918 q^{48} -15.9075 q^{49} -6.64391 q^{50} -28.1105i q^{51} +14.8339 q^{52} +86.4254i q^{53} +38.8232 q^{54} -11.5128 q^{55} -66.7408i q^{56} +25.2529i q^{57} -12.6603 q^{58} -4.11297 q^{59} +13.0049i q^{60} +17.2778i q^{61} -13.3728 q^{62} -17.9214i q^{63} +48.6569 q^{64} -14.8454i q^{65} -17.8083i q^{66} -49.4243i q^{67} -24.1293i q^{68} +(-43.2543 + 41.3923i) q^{69} -23.9379 q^{70} -42.0951 q^{71} +18.4276 q^{72} +52.2218 q^{73} +73.0520i q^{74} +13.0149 q^{75} +21.6765i q^{76} -41.4806 q^{77} +22.9632 q^{78} -110.634i q^{79} -4.62952i q^{80} -56.0316 q^{81} -63.0293 q^{82} +138.133i q^{83} +46.8563i q^{84} -24.1480 q^{85} +39.6212i q^{86} +24.8006 q^{87} -42.6522i q^{88} +163.641i q^{89} -6.60943i q^{90} -53.4878i q^{91} +(-37.1284 + 35.5301i) q^{92} +26.1964 q^{93} +13.5548 q^{94} +21.6933 q^{95} -79.0923 q^{96} +90.4792i q^{97} -21.1377 q^{98} -11.4531i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 2 q^{3} + 34 q^{4} + 28 q^{6} - 20 q^{8} - 16 q^{9} - 24 q^{12} - 2 q^{13} - 38 q^{16} - 22 q^{18} + 44 q^{23} + 70 q^{24} - 50 q^{25} - 72 q^{26} + 40 q^{27} - 46 q^{29} + 16 q^{31} + 142 q^{32}+ \cdots + 388 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 2 * q^3 + 34 * q^4 + 28 * q^6 - 20 * q^8 - 16 * q^9 - 24 * q^12 - 2 * q^13 - 38 * q^16 - 22 * q^18 + 44 * q^23 + 70 * q^24 - 50 * q^25 - 72 * q^26 + 40 * q^27 - 46 * q^29 + 16 * q^31 + 142 * q^32 - 60 * q^35 - 110 * q^36 + 72 * q^39 - 84 * q^41 + 86 * q^46 + 112 * q^47 - 236 * q^48 + 50 * q^49 - 10 * q^50 + 52 * q^52 + 30 * q^54 - 10 * q^55 + 246 * q^58 - 262 * q^59 - 136 * q^62 - 224 * q^64 + 124 * q^69 + 130 * q^70 + 236 * q^71 - 406 * q^72 + 168 * q^73 + 10 * q^75 + 300 * q^77 - 254 * q^78 - 258 * q^81 + 140 * q^82 + 540 * q^87 - 182 * q^92 + 100 * q^93 + 262 * q^94 - 90 * q^95 - 332 * q^96 + 388 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.32878			0.664391			0.332196	−	0.943211i	$-0.392211\pi$
$2$	1.32878			0.664391			0.332196	+	0.943211i	$0.392211\pi$
$3$	−2.60299			−0.867662			−0.433831	−	0.900994i	$-0.642839\pi$
$3$	−2.60299			−0.867662			−0.433831	+	0.900994i	$0.642839\pi$
$4$	−2.23434			−0.558584
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−3.45880			−0.576467
$7$			8.05652i			1.15093i	0.817826	+	0.575466i	$0.195179\pi$
$7$			8.05652i			1.15093i	−0.817826	+	0.575466i	$0.804821\pi$
$8$	−8.28408			−1.03551
$9$	−2.22446			−0.247163
$10$			2.97125i			0.297125i
$11$			5.14870i			0.468064i	0.972229	+	0.234032i	$0.0751920\pi$
$11$			5.14870i			0.468064i	−0.972229	+	0.234032i	$0.924808\pi$
$12$	5.81595			0.484662
$13$	−6.63907			−0.510698			−0.255349	−	0.966849i	$-0.582190\pi$
$13$	−6.63907			−0.510698			−0.255349	+	0.966849i	$0.582190\pi$
$14$			10.7054i			0.764669i
$15$		−	5.82045i		−	0.388030i
$16$	−2.07038			−0.129399
$17$			10.7993i			0.635254i	0.948216	+	0.317627i	$0.102886\pi$
$17$			10.7993i			0.635254i	−0.948216	+	0.317627i	$0.897114\pi$
$18$	−2.95583			−0.164213
$19$		−	9.70153i		−	0.510607i	−0.966861	−	0.255303i	$-0.917825\pi$
$19$		−	9.70153i		−	0.510607i	0.966861	−	0.255303i	$-0.0821754\pi$
$20$		−	4.99613i		−	0.249807i
$21$		−	20.9710i		−	0.998620i
$22$			6.84150i			0.310977i
$23$	16.6172	−	15.9019i	0.722486	−	0.691385i
$23$	16.6172	−	15.9019i	0.722486	−	0.691385i
$24$	21.5633			0.898472
$25$	−5.00000			−0.200000
$26$	−8.82188			−0.339303
$27$	29.2171			1.08212
$28$		−	18.0010i		−	0.642892i
$29$	−9.52776			−0.328544			−0.164272	−	0.986415i	$-0.552527\pi$
$29$	−9.52776			−0.328544			−0.164272	+	0.986415i	$0.552527\pi$
$30$		−	7.73412i		−	0.257804i
$31$	−10.0640			−0.324644			−0.162322	−	0.986738i	$-0.551898\pi$
$31$	−10.0640			−0.324644			−0.162322	+	0.986738i	$0.551898\pi$
$32$	30.3852			0.949538
$33$		−	13.4020i		−	0.406121i
$34$			14.3499i			0.422057i
$35$	−18.0149			−0.514712
$36$	4.97020			0.138061
$37$			54.9767i			1.48586i	0.669371	+	0.742928i	$0.266564\pi$
$37$			54.9767i			1.48586i	−0.669371	+	0.742928i	$0.733436\pi$
$38$		−	12.8912i		−	0.339243i
$39$	17.2814			0.443113
$40$		−	18.5238i		−	0.463094i
$41$	−47.4339			−1.15692			−0.578462	−	0.815710i	$-0.696347\pi$
$41$	−47.4339			−1.15692			−0.578462	+	0.815710i	$0.696347\pi$
$42$		−	27.8659i		−	0.663474i
$43$			29.8177i			0.693435i	0.937970	+	0.346717i	$0.112704\pi$
$43$			29.8177i			0.693435i	−0.937970	+	0.346717i	$0.887296\pi$
$44$		−	11.5039i		−	0.261453i
$45$		−	4.97405i		−	0.110535i
$46$	22.0806	−	21.1301i	0.480014	−	0.459350i
$47$	10.2009			0.217041			0.108521	−	0.994094i	$-0.465389\pi$
$47$	10.2009			0.217041			0.108521	+	0.994094i	$0.465389\pi$
$48$	5.38918			0.112275
$49$	−15.9075			−0.324644
$50$	−6.64391			−0.132878
$51$		−	28.1105i		−	0.551186i
$52$	14.8339			0.285268
$53$			86.4254i			1.63067i	0.578991	+	0.815334i	$0.303447\pi$
$53$			86.4254i			1.63067i	−0.578991	+	0.815334i	$0.696553\pi$
$54$	38.8232			0.718948
$55$	−11.5128			−0.209324
$56$		−	66.7408i		−	1.19180i
$57$			25.2529i			0.443034i
$58$	−12.6603			−0.218281
$59$	−4.11297			−0.0697114			−0.0348557	−	0.999392i	$-0.511097\pi$
$59$	−4.11297			−0.0697114			−0.0348557	+	0.999392i	$0.511097\pi$
$60$			13.0049i			0.216748i
$61$			17.2778i			0.283242i	0.989921	+	0.141621i	$0.0452315\pi$
$61$			17.2778i			0.283242i	−0.989921	+	0.141621i	$0.954769\pi$
$62$	−13.3728			−0.215691
$63$		−	17.9214i		−	0.284467i
$64$	48.6569			0.760264
$65$		−	14.8454i		−	0.228391i
$66$		−	17.8083i		−	0.269823i
$67$		−	49.4243i		−	0.737676i	−0.929494	−	0.368838i	$-0.879756\pi$
$67$		−	49.4243i		−	0.737676i	0.929494	−	0.368838i	$-0.120244\pi$
$68$		−	24.1293i		−	0.354843i
$69$	−43.2543	+	41.3923i	−0.626874	+	0.599889i
$70$	−23.9379			−0.341970
$71$	−42.0951			−0.592889			−0.296444	−	0.955050i	$-0.595801\pi$
$71$	−42.0951			−0.592889			−0.296444	+	0.955050i	$0.595801\pi$
$72$	18.4276			0.255939
$73$	52.2218			0.715367			0.357683	−	0.933843i	$-0.383567\pi$
$73$	52.2218			0.715367			0.357683	+	0.933843i	$0.383567\pi$
$74$			73.0520i			0.987190i
$75$	13.0149			0.173532
$76$			21.6765i			0.285217i
$77$	−41.4806			−0.538709
$78$	22.9632			0.294400
$79$		−	110.634i		−	1.40043i	−0.713930	−	0.700217i	$-0.753086\pi$
$79$		−	110.634i		−	1.40043i	0.713930	−	0.700217i	$-0.246914\pi$
$80$		−	4.62952i		−	0.0578690i
$81$	−56.0316			−0.691748
$82$	−63.0293			−0.768650
$83$			138.133i			1.66426i	0.554584	+	0.832128i	$0.312877\pi$
$83$			138.133i			1.66426i	−0.554584	+	0.832128i	$0.687123\pi$
$84$			46.8563i			0.557813i
$85$	−24.1480			−0.284094
$86$			39.6212i			0.460712i
$87$	24.8006			0.285065
$88$		−	42.6522i		−	0.484685i
$89$			163.641i			1.83866i	0.393489	+	0.919329i	$0.371268\pi$
$89$			163.641i			1.83866i	−0.393489	+	0.919329i	$0.628732\pi$
$90$		−	6.60943i		−	0.0734381i
$91$		−	53.4878i		−	0.587778i
$92$	−37.1284	+	35.5301i	−0.403570	+	0.386197i
$93$	26.1964			0.281681
$94$	13.5548			0.144200
$95$	21.6933			0.228350
$96$	−79.0923			−0.823878
$97$			90.4792i			0.932775i	0.884581	+	0.466388i	$0.154445\pi$
$97$			90.4792i			0.932775i	−0.884581	+	0.466388i	$0.845555\pi$
$98$	−21.1377			−0.215690
$99$		−	11.4531i		−	0.115688i
$100$	11.1717			0.111717
$101$	−136.457			−1.35105			−0.675527	−	0.737335i	$-0.736084\pi$
$101$	−136.457			−1.35105			−0.675527	+	0.737335i	$0.736084\pi$
$102$		−	37.3527i		−	0.366203i
$103$		−	51.1083i		−	0.496197i	−0.968735	−	0.248098i	$-0.920194\pi$
$103$		−	51.1083i		−	0.496197i	0.968735	−	0.248098i	$-0.0798056\pi$
$104$	54.9986			0.528833
$105$	46.8926			0.446596
$106$			114.841i			1.08340i
$107$		−	5.13765i		−	0.0480154i	−0.999712	−	0.0240077i	$-0.992357\pi$
$107$		−	5.13765i		−	0.0480154i	0.999712	−	0.0240077i	$-0.00764262\pi$
$108$	−65.2809			−0.604453
$109$		−	169.516i		−	1.55519i	−0.628765	−	0.777595i	$-0.716439\pi$
$109$		−	169.516i		−	1.55519i	0.628765	−	0.777595i	$-0.283561\pi$
$110$	−15.2981			−0.139073
$111$		−	143.104i		−	1.28922i
$112$		−	16.6801i		−	0.148929i
$113$		−	28.2160i		−	0.249699i	−0.992176	−	0.124849i	$-0.960155\pi$
$113$		−	28.2160i		−	0.249699i	0.992176	−	0.124849i	$-0.0398448\pi$
$114$			33.5557i			0.294348i
$115$	35.5576	+	37.1572i	0.309197	+	0.323106i
$116$	21.2882			0.183519
$117$	14.7684			0.126225
$118$	−5.46524			−0.0463156
$119$	−87.0050			−0.731134
$120$			48.2171i			0.401809i
$121$	94.4909			0.780916
$122$			22.9584i			0.188184i
$123$	123.470			1.00382
$124$	22.4863			0.181341
$125$		−	11.1803i		−	0.0894427i
$126$		−	23.8137i		−	0.188998i
$127$	238.395			1.87713			0.938563	−	0.345109i	$-0.112158\pi$
$127$	238.395			1.87713			0.938563	+	0.345109i	$0.112158\pi$
$128$	−56.8865			−0.444426
$129$		−	77.6150i		−	0.601667i
$130$		−	19.7263i		−	0.151741i
$131$	143.887			1.09838			0.549188	−	0.835699i	$-0.314937\pi$
$131$	143.887			1.09838			0.549188	+	0.835699i	$0.314937\pi$
$132$			29.9446i			0.226853i
$133$	78.1606			0.587674
$134$		−	65.6742i		−	0.490106i
$135$			65.3315i			0.483937i
$136$		−	89.4624i		−	0.657812i
$137$		−	128.956i		−	0.941282i	−0.882325	−	0.470641i	$-0.844023\pi$
$137$		−	128.956i		−	0.941282i	0.882325	−	0.470641i	$-0.155977\pi$
$138$	−57.4756	+	55.0014i	−0.416490	+	0.398561i
$139$	−133.982			−0.963899			−0.481949	−	0.876199i	$-0.660071\pi$
$139$	−133.982			−0.963899			−0.481949	+	0.876199i	$0.660071\pi$
$140$	40.2514			0.287510
$141$	−26.5529			−0.188318
$142$	−55.9352			−0.393910
$143$		−	34.1826i		−	0.239039i
$144$	4.60550			0.0319826
$145$		−	21.3047i		−	0.146929i
$146$	69.3914			0.475283
$147$	41.4071			0.281681
$148$		−	122.836i		−	0.829976i
$149$		−	69.7376i		−	0.468038i	−0.972232	−	0.234019i	$-0.924812\pi$
$149$		−	69.7376i		−	0.468038i	0.972232	−	0.234019i	$-0.0751878\pi$
$150$	17.2940			0.115293
$151$	276.903			1.83379			0.916897	−	0.399123i	$-0.130686\pi$
$151$	276.903			1.83379			0.916897	+	0.399123i	$0.130686\pi$
$152$			80.3682i			0.528738i
$153$		−	24.0227i		−	0.157011i
$154$	−55.1187			−0.357914
$155$		−	22.5037i		−	0.145185i
$156$	−38.6125			−0.247516
$157$		−	164.782i		−	1.04957i	−0.851236	−	0.524783i	$-0.824146\pi$
$157$		−	164.782i		−	1.04957i	0.851236	−	0.524783i	$-0.175854\pi$
$158$		−	147.009i		−	0.930436i
$159$		−	224.964i		−	1.41487i
$160$			67.9434i			0.424646i
$161$	128.114	+	133.877i	0.795737	+	0.831532i
$162$	−74.4538			−0.459591
$163$	−40.7616			−0.250071			−0.125036	−	0.992152i	$-0.539905\pi$
$163$	−40.7616			−0.250071			−0.125036	+	0.992152i	$0.539905\pi$
$164$	105.983			0.646239
$165$	29.9678			0.181623
$166$			183.549i			1.10572i
$167$	−132.027			−0.790578			−0.395289	−	0.918557i	$-0.629356\pi$
$167$	−132.027			−0.790578			−0.395289	+	0.918557i	$0.629356\pi$
$168$			173.725i			1.03408i
$169$	−124.923			−0.739188
$170$	−32.0875			−0.188750
$171$			21.5807i			0.126203i
$172$		−	66.6228i		−	0.387342i
$173$	−262.356			−1.51651			−0.758255	−	0.651958i	$-0.773948\pi$
$173$	−262.356			−1.51651			−0.758255	+	0.651958i	$0.773948\pi$
$174$	32.9546			0.189394
$175$		−	40.2826i		−	0.230186i
$176$		−	10.6598i		−	0.0605670i
$177$	10.7060			0.0604859
$178$			217.443i			1.22159i
$179$	50.6552			0.282990			0.141495	−	0.989939i	$-0.454809\pi$
$179$	50.6552			0.282990			0.141495	+	0.989939i	$0.454809\pi$
$180$			11.1137i			0.0617429i
$181$			255.326i			1.41064i	0.708890	+	0.705319i	$0.249196\pi$
$181$			255.326i			1.41064i	−0.708890	+	0.705319i	$0.750804\pi$
$182$		−	71.0737i		−	0.390515i
$183$		−	44.9738i		−	0.245758i
$184$	−137.658	+	131.732i	−0.748142	+	0.715936i
$185$	−122.932			−0.664495
$186$	34.8092			0.187146
$187$	−55.6025			−0.297339
$188$	−22.7923			−0.121236
$189$			235.388i			1.24544i
$190$	28.8256			0.151714
$191$			370.197i			1.93820i	0.246665	+	0.969101i	$0.420665\pi$
$191$			370.197i			1.93820i	−0.246665	+	0.969101i	$0.579335\pi$
$192$	−126.653			−0.659652
$193$	171.758			0.889940			0.444970	−	0.895545i	$-0.353214\pi$
$193$	171.758			0.889940			0.444970	+	0.895545i	$0.353214\pi$
$194$			120.227i			0.619727i
$195$			38.6424i			0.198166i
$196$	35.5428			0.181341
$197$	−265.313			−1.34677			−0.673384	−	0.739293i	$-0.735160\pi$
$197$	−265.313			−1.34677			−0.673384	+	0.739293i	$0.735160\pi$
$198$		−	15.2187i		−	0.0768620i
$199$		−	289.040i		−	1.45246i	−0.687451	−	0.726231i	$-0.741270\pi$
$199$		−	289.040i		−	1.45246i	0.687451	−	0.726231i	$-0.258730\pi$
$200$	41.4204			0.207102
$201$			128.651i			0.640054i
$202$	−181.321			−0.897629
$203$		−	76.7606i		−	0.378131i
$204$			62.8083i			0.307884i
$205$		−	106.065i		−	0.517392i
$206$		−	67.9117i		−	0.329669i
$207$	−36.9643	+	35.3731i	−0.178572	+	0.170885i
$208$	13.7454			0.0660838
$209$	49.9503			0.238997
$210$	62.3101			0.296715
$211$	235.268			1.11501			0.557507	−	0.830172i	$-0.311758\pi$
$211$	235.268			1.11501			0.557507	+	0.830172i	$0.311758\pi$
$212$		−	193.103i		−	0.910866i
$213$	109.573			0.514427
$214$		−	6.82681i		−	0.0319010i
$215$	−66.6744			−0.310113
$216$	−242.037			−1.12054
$217$		−	81.0805i		−	0.373643i
$218$		−	225.250i		−	1.03326i
$219$	−135.933			−0.620697
$220$	25.7236			0.116925
$221$		−	71.6975i		−	0.324423i
$222$		−	190.153i		−	0.856547i
$223$	−221.630			−0.993855			−0.496928	−	0.867792i	$-0.665539\pi$
$223$	−221.630			−0.993855			−0.496928	+	0.867792i	$0.665539\pi$
$224$			244.799i			1.09285i
$225$	11.1223			0.0494325
$226$		−	37.4929i		−	0.165898i
$227$			223.695i			0.985441i	0.870188	+	0.492720i	$0.163997\pi$
$227$			223.695i			0.985441i	−0.870188	+	0.492720i	$0.836003\pi$
$228$		−	56.4236i		−	0.247472i
$229$			170.011i			0.742406i	0.928552	+	0.371203i	$0.121055\pi$
$229$			170.011i			0.742406i	−0.928552	+	0.371203i	$0.878945\pi$
$230$	47.2484	+	49.3738i	0.205428	+	0.214669i
$231$	107.973			0.467418
$232$	78.9287			0.340210
$233$	29.9648			0.128604			0.0643020	−	0.997930i	$-0.479518\pi$
$233$	29.9648			0.128604			0.0643020	+	0.997930i	$0.479518\pi$
$234$	19.6240			0.0838631
$235$			22.8100i			0.0970638i
$236$	9.18977			0.0389397
$237$			287.980i			1.21510i
$238$	−115.611			−0.485759
$239$	181.416			0.759061			0.379530	−	0.925179i	$-0.376086\pi$
$239$	181.416			0.759061			0.379530	+	0.925179i	$0.376086\pi$
$240$			12.0506i			0.0502107i
$241$		−	156.298i		−	0.648538i	−0.945965	−	0.324269i	$-0.894882\pi$
$241$		−	156.298i		−	0.648538i	0.945965	−	0.324269i	$-0.105118\pi$
$242$	125.558			0.518834
$243$	−117.105			−0.481912
$244$		−	38.6044i		−	0.158215i
$245$		−	35.5703i		−	0.145185i
$246$	164.064			0.666928
$247$			64.4092i			0.260766i
$248$	83.3706			0.336172
$249$		−	359.559i		−	1.44401i
$250$		−	14.8562i		−	0.0594249i
$251$			250.907i			0.999628i	0.866133	+	0.499814i	$0.166598\pi$
$251$			250.907i			0.999628i	−0.866133	+	0.499814i	$0.833402\pi$
$252$			40.0426i			0.158899i
$253$	81.8739	+	85.5569i	0.323612	+	0.338170i
$254$	316.775			1.24715
$255$	62.8569			0.246498
$256$	−270.217			−1.05554
$257$	−134.881			−0.524831			−0.262415	−	0.964955i	$-0.584519\pi$
$257$	−134.881			−0.524831			−0.262415	+	0.964955i	$0.584519\pi$
$258$		−	103.133i		−	0.399742i
$259$	−442.921			−1.71012
$260$			33.1697i			0.127576i
$261$	21.1942			0.0812037
$262$	191.195			0.729752
$263$		−	191.244i		−	0.727164i	−0.931562	−	0.363582i	$-0.881554\pi$
$263$		−	191.244i		−	0.727164i	0.931562	−	0.363582i	$-0.118446\pi$
$264$			111.023i			0.420542i
$265$	−193.253			−0.729257
$266$	103.858			0.390445
$267$		−	425.954i		−	1.59533i
$268$			110.431i			0.412054i
$269$	211.957			0.787946			0.393973	−	0.919122i	$-0.371100\pi$
$269$	211.957			0.787946			0.393973	+	0.919122i	$0.371100\pi$
$270$			86.8113i			0.321523i
$271$	41.3602			0.152621			0.0763104	−	0.997084i	$-0.475686\pi$
$271$	41.3602			0.152621			0.0763104	+	0.997084i	$0.475686\pi$
$272$		−	22.3587i		−	0.0822013i
$273$			139.228i			0.509993i
$274$		−	171.354i		−	0.625379i
$275$		−	25.7435i		−	0.0936128i
$276$	96.6447	−	92.4844i	0.350162	−	0.335088i
$277$	209.778			0.757323			0.378662	−	0.925535i	$-0.376384\pi$
$277$	209.778			0.757323			0.378662	+	0.925535i	$0.376384\pi$
$278$	−178.033			−0.640406
$279$	22.3869			0.0802399
$280$	149.237			0.532990
$281$		−	132.745i		−	0.472402i	−0.971704	−	0.236201i	$-0.924098\pi$
$281$		−	132.745i		−	0.472402i	0.971704	−	0.236201i	$-0.0759023\pi$
$282$	−35.2830			−0.125117
$283$			218.496i			0.772071i	0.922484	+	0.386036i	$0.126156\pi$
$283$			218.496i			0.772071i	−0.922484	+	0.386036i	$0.873844\pi$
$284$	94.0546			0.331178
$285$	−56.4673			−0.198131
$286$		−	45.4212i		−	0.158816i
$287$		−	382.152i		−	1.33154i
$288$	−67.5908			−0.234690
$289$	172.375			0.596452
$290$		−	28.3093i		−	0.0976184i
$291$		−	235.516i		−	0.809333i
$292$	−116.681			−0.399593
$293$			257.693i			0.879497i	0.898121	+	0.439748i	$0.144932\pi$
$293$			257.693i			0.879497i	−0.898121	+	0.439748i	$0.855068\pi$
$294$	55.0210			0.187146
$295$		−	9.19688i		−	0.0311759i
$296$		−	455.431i		−	1.53862i
$297$			150.430i			0.506499i
$298$		−	92.6661i		−	0.310960i
$299$	−110.323	+	105.574i	−0.368972	+	0.353089i
$300$	−29.0797			−0.0969325
$301$	−240.227			−0.798096
$302$	367.944			1.21836
$303$	355.194			1.17226
$304$			20.0859i			0.0660720i
$305$	−38.6343			−0.126670
$306$		−	31.9209i		−	0.104317i
$307$	−12.9089			−0.0420485			−0.0210243	−	0.999779i	$-0.506693\pi$
$307$	−12.9089			−0.0420485			−0.0210243	+	0.999779i	$0.506693\pi$
$308$	92.6817			0.300915
$309$			133.034i			0.430531i
$310$		−	29.9025i		−	0.0964597i
$311$	212.171			0.682221			0.341110	−	0.940023i	$-0.389197\pi$
$311$	212.171			0.682221			0.341110	+	0.940023i	$0.389197\pi$
$312$	−143.161			−0.458848
$313$		−	12.5955i		−	0.0402414i	−0.999798	−	0.0201207i	$-0.993595\pi$
$313$		−	12.5955i		−	0.0402414i	0.999798	−	0.0201207i	$-0.00640504\pi$
$314$		−	218.959i		−	0.697323i
$315$	40.0736			0.127218
$316$			247.194i			0.782261i
$317$	−313.064			−0.987584			−0.493792	−	0.869580i	$-0.664390\pi$
$317$	−313.064			−0.987584			−0.493792	+	0.869580i	$0.664390\pi$
$318$		−	298.928i		−	0.940026i
$319$		−	49.0556i		−	0.153779i
$320$			108.800i			0.340000i
$321$			13.3732i			0.0416611i
$322$	170.235	+	177.893i	0.528681	+	0.552463i
$323$	104.770			0.324365
$324$	125.193			0.386400
$325$	33.1954			0.102140
$326$	−54.1633			−0.166145
$327$			441.247i			1.34938i
$328$	392.946			1.19801
$329$			82.1841i			0.249800i
$330$	39.8207			0.120669
$331$	−382.892			−1.15677			−0.578386	−	0.815763i	$-0.696317\pi$
$331$	−382.892			−1.15677			−0.578386	+	0.815763i	$0.696317\pi$
$332$		−	308.636i		−	0.929627i
$333$		−	122.294i		−	0.367248i
$334$	−175.435			−0.525253
$335$	110.516			0.329899
$336$			43.4181i			0.129220i
$337$			61.1020i			0.181311i	0.995882	+	0.0906557i	$0.0288963\pi$
$337$			61.1020i			0.181311i	−0.995882	+	0.0906557i	$0.971104\pi$
$338$	−165.995			−0.491110
$339$			73.4458i			0.216654i
$340$	53.9548			0.158691
$341$		−	51.8163i		−	0.151954i
$342$			28.6761i			0.0838481i
$343$			266.610i			0.777289i
$344$		−	247.012i		−	0.718058i
$345$	−92.5560	−	96.7196i	−0.268278	−	0.280347i
$346$	−348.614			−1.00756
$347$	287.399			0.828238			0.414119	−	0.910223i	$-0.364090\pi$
$347$	287.399			0.828238			0.414119	+	0.910223i	$0.364090\pi$
$348$	−55.4130			−0.159233
$349$	−660.469			−1.89246			−0.946231	−	0.323492i	$-0.895143\pi$
$349$	−660.469			−1.89246			−0.946231	+	0.323492i	$0.895143\pi$
$350$		−	53.5268i		−	0.152934i
$351$	−193.975			−0.552634
$352$			156.444i			0.444444i
$353$	386.196			1.09404			0.547020	−	0.837119i	$-0.315762\pi$
$353$	386.196			1.09404			0.547020	+	0.837119i	$0.315762\pi$
$354$	14.2259			0.0401863
$355$		−	94.1275i		−	0.265148i
$356$		−	365.628i		−	1.02705i
$357$	226.473			0.634377
$358$	67.3098			0.188016
$359$		−	91.2104i		−	0.254068i	−0.991898	−	0.127034i	$-0.959454\pi$
$359$		−	91.2104i		−	0.254068i	0.991898	−	0.127034i	$-0.0405457\pi$
$360$			41.2054i			0.114460i
$361$	266.880			0.739281
$362$			339.272i			0.937216i
$363$	−245.958			−0.677571
$364$			119.510i			0.328324i
$365$			116.771i			0.319922i
$366$		−	59.7604i		−	0.163280i
$367$			336.449i			0.916755i	0.888758	+	0.458378i	$0.151569\pi$
$367$			336.449i			0.916755i	−0.888758	+	0.458378i	$0.848431\pi$
$368$	−34.4040	+	32.9230i	−0.0934890	+	0.0894646i
$369$	105.515			0.285948
$370$	−163.349			−0.441485
$371$	−696.288			−1.87679
$372$	−58.5315			−0.157343
$373$			706.033i			1.89285i	0.322926	+	0.946424i	$0.395334\pi$
$373$			706.033i			1.89285i	−0.322926	+	0.946424i	$0.604666\pi$
$374$	−73.8836			−0.197550
$375$			29.1023i			0.0776060i
$376$	−84.5054			−0.224748
$377$	63.2555			0.167786
$378$			312.780i			0.827460i
$379$		−	293.798i		−	0.775193i	−0.921829	−	0.387597i	$-0.873305\pi$
$379$		−	293.798i		−	0.775193i	0.921829	−	0.387597i	$-0.126695\pi$
$380$	−48.4701			−0.127553
$381$	−620.539			−1.62871
$382$			491.911i			1.28772i
$383$		−	405.545i		−	1.05886i	−0.848352	−	0.529432i	$-0.822405\pi$
$383$		−	405.545i		−	1.05886i	0.848352	−	0.529432i	$-0.177595\pi$
$384$	148.075			0.385611
$385$		−	92.7535i		−	0.240918i
$386$	228.230			0.591268
$387$		−	66.3284i		−	0.171391i
$388$		−	202.161i		−	0.521034i
$389$			671.711i			1.72676i	0.504551	+	0.863382i	$0.331658\pi$
$389$			671.711i			1.72676i	−0.504551	+	0.863382i	$0.668342\pi$
$390$			51.3474i			0.131660i
$391$	171.729	+	179.454i	0.439205	+	0.458962i
$392$	131.779			0.336172
$393$	−374.537			−0.953020
$394$	−352.544			−0.894781
$395$	247.386			0.626293
$396$			25.5901i			0.0646215i
$397$	461.838			1.16332			0.581661	−	0.813432i	$-0.302403\pi$
$397$	461.838			1.16332			0.581661	+	0.813432i	$0.302403\pi$
$398$		−	384.071i		−	0.965003i
$399$	−203.451			−0.509902
$400$	10.3519			0.0258798
$401$		−	422.085i		−	1.05258i	−0.850305	−	0.526290i	$-0.823583\pi$
$401$		−	422.085i		−	1.05258i	0.850305	−	0.526290i	$-0.176417\pi$
$402$			170.949i			0.425246i
$403$	66.8154			0.165795
$404$	304.890			0.754678
$405$		−	125.290i		−	0.309359i
$406$		−	101.998i		−	0.251227i
$407$	−283.059			−0.695475
$408$			232.869i			0.570758i
$409$	227.299			0.555743			0.277872	−	0.960618i	$-0.410371\pi$
$409$	227.299			0.555743			0.277872	+	0.960618i	$0.410371\pi$
$410$		−	140.938i		−	0.343751i
$411$			335.670i			0.816715i
$412$			114.193i			0.277168i
$413$		−	33.1362i		−	0.0802330i
$414$	−49.1176	+	47.0032i	−0.118641	+	0.113534i
$415$	−308.875			−0.744278
$416$	−201.730			−0.484927
$417$	348.753			0.836338
$418$	66.3730			0.158787
$419$			135.807i			0.324121i	0.986781	+	0.162060i	$0.0518139\pi$
$419$			135.807i			0.324121i	−0.986781	+	0.162060i	$0.948186\pi$
$420$	−104.774			−0.249462
$421$		−	600.720i		−	1.42689i	−0.700713	−	0.713444i	$-0.747134\pi$
$421$		−	600.720i		−	1.42689i	0.700713	−	0.713444i	$-0.252866\pi$
$422$	312.620			0.740805
$423$	−22.6916			−0.0536445
$424$		−	715.955i		−	1.68857i
$425$		−	53.9966i		−	0.127051i
$426$	145.599			0.341781
$427$	−139.199			−0.325992
$428$			11.4792i			0.0268207i
$429$			88.9768i			0.207405i
$430$	−88.5957			−0.206037
$431$		−	375.319i		−	0.870810i	−0.900235	−	0.435405i	$-0.856605\pi$
$431$		−	375.319i		−	0.870810i	0.900235	−	0.435405i	$-0.143395\pi$
$432$	−60.4907			−0.140025
$433$			33.4009i			0.0771382i	0.999256	+	0.0385691i	$0.0122800\pi$
$433$			33.4009i			0.0771382i	−0.999256	+	0.0385691i	$0.987720\pi$
$434$		−	107.738i		−	0.248245i
$435$			55.4559i			0.127485i
$436$			378.756i			0.868705i
$437$	−154.272	−	161.212i	−0.353026	−	0.368906i
$438$	−180.625			−0.412385
$439$	600.923			1.36885			0.684423	−	0.729085i	$-0.260054\pi$
$439$	600.923			1.36885			0.684423	+	0.729085i	$0.260054\pi$
$440$	95.3733			0.216758
$441$	35.3857			0.0802398
$442$		−	95.2703i		−	0.215544i
$443$	666.130			1.50368			0.751839	−	0.659347i	$-0.229167\pi$
$443$	666.130			1.50368			0.751839	+	0.659347i	$0.229167\pi$
$444$			319.742i			0.720139i
$445$	−365.912			−0.822273
$446$	−294.498			−0.660309
$447$			181.526i			0.406099i
$448$			392.005i			0.875012i
$449$	194.665			0.433551			0.216776	−	0.976221i	$-0.430446\pi$
$449$	194.665			0.433551			0.216776	+	0.976221i	$0.430446\pi$
$450$	14.7791			0.0328425
$451$		−	244.223i		−	0.541514i
$452$			63.0440i			0.139478i
$453$	−720.775			−1.59111
$454$			297.242i			0.654718i
$455$	119.602			0.262862
$456$		−	209.197i		−	0.458766i
$457$		−	271.646i		−	0.594411i	−0.954814	−	0.297206i	$-0.903945\pi$
$457$		−	271.646i		−	0.594411i	0.954814	−	0.297206i	$-0.0960547\pi$
$458$			225.907i			0.493248i
$459$			315.525i			0.687418i
$460$	−79.4478	−	83.0216i	−0.172713	−	0.180482i
$461$	−325.220			−0.705466			−0.352733	−	0.935724i	$-0.614748\pi$
$461$	−325.220			−0.705466			−0.352733	+	0.935724i	$0.614748\pi$
$462$	143.473			0.310548
$463$	403.699			0.871920			0.435960	−	0.899966i	$-0.356409\pi$
$463$	403.699			0.871920			0.435960	+	0.899966i	$0.356409\pi$
$464$	19.7261			0.0425132
$465$			58.5768i			0.125972i
$466$	39.8166			0.0854434
$467$		−	284.878i		−	0.610017i	−0.952350	−	0.305009i	$-0.901341\pi$
$467$		−	284.878i		−	0.610017i	0.952350	−	0.305009i	$-0.0986594\pi$
$468$	−32.9975			−0.0705076
$469$	398.188			0.849015
$470$			30.3095i			0.0644883i
$471$			428.925i			0.910669i
$472$	34.0722			0.0721868
$473$	−153.522			−0.324572
$474$			382.662i			0.807304i
$475$			48.5076i			0.102121i
$476$	194.398			0.408400
$477$		−	192.250i		−	0.403040i
$478$	241.062			0.504313
$479$			296.818i			0.619662i	0.950792	+	0.309831i	$0.100273\pi$
$479$			296.818i			0.619662i	−0.950792	+	0.309831i	$0.899727\pi$
$480$		−	176.856i		−	0.368449i
$481$		−	364.994i		−	0.758824i
$482$		−	207.686i		−	0.430883i
$483$	−333.478	−	348.479i	−0.690431	−	0.721489i
$484$	−211.125			−0.436208
$485$	−202.318			−0.417150
$486$	−155.607			−0.320178
$487$	−498.378			−1.02336			−0.511682	−	0.859175i	$-0.670977\pi$
$487$	−498.378			−1.02336			−0.511682	+	0.859175i	$0.670977\pi$
$488$		−	143.130i		−	0.293300i
$489$	106.102			0.216977
$490$		−	47.2652i		−	0.0964597i
$491$	756.668			1.54108			0.770538	−	0.637394i	$-0.219988\pi$
$491$	756.668			1.54108			0.770538	+	0.637394i	$0.219988\pi$
$492$	−275.873			−0.560717
$493$		−	102.893i		−	0.208709i
$494$			85.5857i			0.173251i
$495$	25.6099			0.0517372
$496$	20.8363			0.0420086
$497$		−	339.140i		−	0.682374i
$498$		−	477.775i		−	0.959388i
$499$	−337.955			−0.677264			−0.338632	−	0.940919i	$-0.609964\pi$
$499$	−337.955			−0.677264			−0.338632	+	0.940919i	$0.609964\pi$
$500$			24.9807i			0.0499613i
$501$	343.663			0.685955
$502$			333.400i			0.664144i
$503$			727.880i			1.44708i	0.690283	+	0.723539i	$0.257486\pi$
$503$			727.880i			1.44708i	−0.690283	+	0.723539i	$0.742514\pi$
$504$			148.463i			0.294569i
$505$		−	305.126i		−	0.604210i
$506$	108.793	+	113.687i	0.215005	+	0.224677i
$507$	325.172			0.641365
$508$	−532.655			−1.04853
$509$	811.883			1.59505			0.797527	−	0.603283i	$-0.206141\pi$
$509$	811.883			1.59505			0.797527	+	0.603283i	$0.206141\pi$
$510$	83.5232			0.163771
$511$			420.726i			0.823338i
$512$	−131.514			−0.256863
$513$		−	283.451i		−	0.552536i
$514$	−179.228			−0.348693
$515$	114.282			0.221906
$516$			173.418i			0.336082i
$517$			52.5216i			0.101589i
$518$	−588.545			−1.13619
$519$	682.910			1.31582
$520$			122.981i			0.236501i
$521$		−	410.451i		−	0.787813i	−0.919150	−	0.393907i	$-0.871123\pi$
$521$		−	410.451i		−	0.787813i	0.919150	−	0.393907i	$-0.128877\pi$
$522$	28.1624			0.0539510
$523$		−	1011.33i		−	1.93372i	−0.255316	−	0.966858i	$-0.582179\pi$
$523$		−	1011.33i		−	1.93372i	0.255316	−	0.966858i	$-0.417821\pi$
$524$	−321.493			−0.613536
$525$			104.855i			0.199724i
$526$		−	254.122i		−	0.483121i
$527$		−	108.684i		−	0.206231i
$528$			27.7473i			0.0525517i
$529$	23.2618	−	528.488i	0.0439731	−	0.999033i
$530$	−256.791			−0.484512
$531$	9.14916			0.0172300
$532$	−174.637			−0.328265
$533$	314.917			0.590838
$534$		−	566.000i		−	1.05993i
$535$	11.4881			0.0214731
$536$			409.435i			0.763871i
$537$	−131.855			−0.245540
$538$	281.645			0.523504
$539$		−	81.9032i		−	0.151954i
$540$		−	145.973i		−	0.270320i
$541$	618.852			1.14390			0.571952	−	0.820287i	$-0.306186\pi$
$541$	618.852			1.14390			0.571952	+	0.820287i	$0.306186\pi$
$542$	54.9588			0.101400
$543$		−	664.609i		−	1.22396i
$544$			328.140i			0.603198i
$545$	379.049			0.695503
$546$			185.004i			0.338835i
$547$	−423.226			−0.773723			−0.386861	−	0.922138i	$-0.626441\pi$
$547$	−423.226			−0.773723			−0.386861	+	0.922138i	$0.626441\pi$
$548$			288.130i			0.525785i
$549$		−	38.4338i		−	0.0700069i
$550$		−	34.2075i		−	0.0621955i
$551$			92.4339i			0.167757i
$552$	358.322	−	342.897i	0.649134	−	0.621190i
$553$	891.328			1.61180
$554$	278.750			0.503159
$555$	319.989			0.576557
$556$	299.361			0.538419
$557$			461.268i			0.828130i	0.910247	+	0.414065i	$0.135891\pi$
$557$			461.268i			0.828130i	−0.910247	+	0.414065i	$0.864109\pi$
$558$	29.7473			0.0533107
$559$		−	197.962i		−	0.354136i
$560$	37.2978			0.0666033
$561$	144.732			0.257990
$562$		−	176.389i		−	0.313860i
$563$			510.695i			0.907096i	0.891232	+	0.453548i	$0.149842\pi$
$563$			510.695i			0.907096i	−0.891232	+	0.453548i	$0.850158\pi$
$564$	59.3281			0.105192
$565$	63.0928			0.111669
$566$			290.334i			0.512957i
$567$		−	451.420i		−	0.796155i
$568$	348.719			0.613942
$569$		−	186.632i		−	0.328001i	−0.986460	−	0.164000i	$-0.947560\pi$
$569$		−	186.632i		−	0.328001i	0.986460	−	0.164000i	$-0.0524398\pi$
$570$	−75.0328			−0.131636
$571$			730.831i			1.27991i	0.768411	+	0.639957i	$0.221048\pi$
$571$			730.831i			1.27991i	−0.768411	+	0.639957i	$0.778952\pi$
$572$			76.3755i			0.133524i
$573$		−	963.616i		−	1.68170i
$574$		−	507.797i		−	0.884663i
$575$	−83.0859	+	79.5093i	−0.144497	+	0.138277i
$576$	−108.235			−0.187909
$577$	920.204			1.59481			0.797404	−	0.603446i	$-0.206206\pi$
$577$	920.204			1.59481			0.797404	+	0.603446i	$0.206206\pi$
$578$	229.048			0.396278
$579$	−447.085			−0.772167
$580$			47.6019i			0.0820723i
$581$	−1112.87			−1.91544
$582$		−	312.950i		−	0.537714i
$583$	−444.979			−0.763257
$584$	−432.609			−0.740769
$585$			33.0231i			0.0564497i
$586$			342.417i			0.584330i
$587$	−50.4562			−0.0859561			−0.0429781	−	0.999076i	$-0.513685\pi$
$587$	−50.4562			−0.0859561			−0.0429781	+	0.999076i	$0.513685\pi$
$588$	−92.5175			−0.157343
$589$			97.6358i			0.165765i
$590$		−	12.2207i		−	0.0207130i
$591$	690.607			1.16854
$592$		−	113.823i		−	0.192268i
$593$	−192.419			−0.324485			−0.162242	−	0.986751i	$-0.551873\pi$
$593$	−192.419			−0.324485			−0.162242	+	0.986751i	$0.551873\pi$
$594$			199.889i			0.336514i
$595$		−	194.549i		−	0.326973i
$596$			155.817i			0.261439i
$597$			752.367i			1.26025i
$598$	−146.595	+	140.284i	−0.245142	+	0.234589i
$599$	−769.203			−1.28415			−0.642073	−	0.766644i	$-0.721925\pi$
$599$	−769.203			−1.28415			−0.642073	+	0.766644i	$0.721925\pi$
$600$	−107.817			−0.179694
$601$	−965.858			−1.60709			−0.803543	−	0.595247i	$-0.797054\pi$
$601$	−965.858			−1.60709			−0.803543	+	0.595247i	$0.797054\pi$
$602$	−319.209			−0.530248
$603$			109.943i			0.182326i
$604$	−618.695			−1.02433
$605$			211.288i			0.349236i
$606$	471.976			0.778838
$607$	−609.221			−1.00366			−0.501830	−	0.864966i	$-0.667340\pi$
$607$	−609.221			−1.00366			−0.501830	+	0.864966i	$0.667340\pi$
$608$		−	294.783i		−	0.484841i
$609$			199.807i			0.328090i
$610$	−51.3365			−0.0841583
$611$	−67.7248			−0.110842
$612$			53.6748i			0.0877040i
$613$			686.597i			1.12006i	0.828472	+	0.560030i	$0.189211\pi$
$613$			686.597i			1.12006i	−0.828472	+	0.560030i	$0.810789\pi$
$614$	−17.1531			−0.0279367
$615$			276.087i			0.448921i
$616$	343.629			0.557839
$617$		−	53.0755i		−	0.0860219i	−0.999075	−	0.0430109i	$-0.986305\pi$
$617$		−	53.0755i		−	0.0860219i	0.999075	−	0.0430109i	$-0.0136950\pi$
$618$			176.773i			0.286041i
$619$		−	263.514i		−	0.425709i	−0.977084	−	0.212855i	$-0.931724\pi$
$619$		−	263.514i		−	0.425709i	0.977084	−	0.212855i	$-0.0682761\pi$
$620$			50.2809i			0.0810982i
$621$	485.506	−	464.607i	0.781814	−	0.748159i
$622$	281.929			0.453262
$623$	−1318.37			−2.11617
$624$	−35.7792			−0.0573384
$625$	25.0000			0.0400000
$626$		−	16.7367i		−	0.0267360i
$627$	−130.020			−0.207368
$628$			368.179i			0.586272i
$629$	−593.711			−0.943896
$630$	53.2490			0.0845223
$631$		−	124.292i		−	0.196976i	−0.995138	−	0.0984879i	$-0.968599\pi$
$631$		−	124.292i		−	0.196976i	0.995138	−	0.0984879i	$-0.0314006\pi$
$632$			916.503i			1.45016i
$633$	−612.399			−0.967455
$634$	−415.994			−0.656142
$635$			533.067i			0.839476i
$636$			502.646i			0.790323i
$637$	105.611			0.165795
$638$		−	65.1842i		−	0.102170i
$639$	93.6390			0.146540
$640$		−	127.202i		−	0.198753i
$641$			603.832i			0.942015i	0.882129	+	0.471008i	$0.156110\pi$
$641$			603.832i			0.942015i	−0.882129	+	0.471008i	$0.843890\pi$
$642$			17.7701i			0.0276793i
$643$			1112.73i			1.73053i	0.501319	+	0.865263i	$0.332848\pi$
$643$			1112.73i			1.73053i	−0.501319	+	0.865263i	$0.667152\pi$
$644$	−286.249	−	299.126i	−0.444486	−	0.464481i
$645$	173.552			0.269074
$646$	139.216			0.215505
$647$	−695.666			−1.07522			−0.537609	−	0.843194i	$-0.680672\pi$
$647$	−695.666			−1.07522			−0.537609	+	0.843194i	$0.680672\pi$
$648$	464.170			0.716312
$649$		−	21.1765i		−	0.0326294i
$650$	44.1094			0.0678606
$651$			211.051i			0.324196i
$652$	91.0752			0.139686
$653$	357.346			0.547237			0.273618	−	0.961838i	$-0.411779\pi$
$653$	357.346			0.547237			0.273618	+	0.961838i	$0.411779\pi$
$654$			586.322i			0.896516i
$655$			321.742i			0.491209i
$656$	98.2063			0.149705
$657$	−116.165			−0.176812
$658$			109.205i			0.165965i
$659$			367.276i			0.557324i	0.960389	+	0.278662i	$0.0898908\pi$
$659$			367.276i			0.557324i	−0.960389	+	0.278662i	$0.910109\pi$
$660$	−66.9581			−0.101452
$661$		−	443.045i		−	0.670265i	−0.942171	−	0.335132i	$-0.891219\pi$
$661$		−	443.045i		−	0.670265i	0.942171	−	0.335132i	$-0.108781\pi$
$662$	−508.780			−0.768549
$663$			186.628i			0.281489i
$664$		−	1144.31i		−	1.72335i
$665$			174.772i			0.262816i
$666$		−	162.502i		−	0.243996i
$667$	−158.325	+	151.509i	−0.237368	+	0.227150i
$668$	294.992			0.441605
$669$	576.899			0.862331
$670$	146.852			0.219182
$671$	−88.9581			−0.132575
$672$		−	637.209i		−	0.948227i
$673$	1093.39			1.62465			0.812324	−	0.583206i	$-0.198202\pi$
$673$	1093.39			1.62465			0.812324	+	0.583206i	$0.198202\pi$
$674$			81.1912i			0.120462i
$675$	−146.086			−0.216423
$676$	279.120			0.412899
$677$			842.558i			1.24455i	0.782800	+	0.622273i	$0.213791\pi$
$677$			842.558i			1.24455i	−0.782800	+	0.622273i	$0.786209\pi$
$678$			97.5934i			0.143943i
$679$	−728.947			−1.07356
$680$	200.044			0.294182
$681$		−	582.275i		−	0.855029i
$682$		−	68.8526i		−	0.100957i
$683$	−858.398			−1.25681			−0.628403	−	0.777888i	$-0.716291\pi$
$683$	−858.398			−1.25681			−0.628403	+	0.777888i	$0.716291\pi$
$684$		−	48.2186i		−	0.0704950i
$685$	288.354			0.420954
$686$			354.267i			0.516424i
$687$		−	442.536i		−	0.644157i
$688$		−	61.7341i		−	0.0897298i
$689$		−	573.784i		−	0.832779i
$690$	−122.987	−	128.519i	−0.178242	−	0.186260i
$691$	206.282			0.298527			0.149264	−	0.988797i	$-0.452310\pi$
$691$	206.282			0.298527			0.149264	+	0.988797i	$0.452310\pi$
$692$	586.192			0.847099
$693$	92.2722			0.133149
$694$	381.890			0.550274
$695$		−	299.593i		−	0.431069i
$696$	−205.450			−0.295187
$697$		−	512.253i		−	0.734940i
$698$	−877.620			−1.25733
$699$	−77.9978			−0.111585
$700$			90.0049i			0.128578i
$701$			374.399i			0.534093i	0.963684	+	0.267047i	$0.0860478\pi$
$701$			374.399i			0.534093i	−0.963684	+	0.267047i	$0.913952\pi$
$702$	−257.750			−0.367165
$703$	533.358			0.758688
$704$			250.520i			0.355852i
$705$		−	59.3741i		−	0.0842186i
$706$	513.171			0.726871
$707$		−	1099.36i		−	1.55497i
$708$	−23.9208			−0.0337865
$709$			179.348i			0.252959i	0.991969	+	0.126480i	$0.0403678\pi$
$709$			179.348i			0.252959i	−0.991969	+	0.126480i	$0.959632\pi$
$710$		−	125.075i		−	0.176162i
$711$			246.102i			0.346135i
$712$		−	1355.61i		−	1.90395i
$713$	−167.235	+	160.036i	−0.234551	+	0.224454i
$714$	300.933			0.421475
$715$	76.4346			0.106902
$716$	−113.181			−0.158074
$717$	−472.222			−0.658608
$718$		−	121.199i		−	0.168801i
$719$	−324.519			−0.451347			−0.225674	−	0.974203i	$-0.572458\pi$
$719$	−324.519			−0.451347			−0.225674	+	0.974203i	$0.572458\pi$
$720$			10.2982i			0.0143031i
$721$	411.755			0.571088
$722$	354.626			0.491172
$723$			406.841i			0.562712i
$724$		−	570.484i		−	0.787961i
$725$	47.6388			0.0657087
$726$	−326.825			−0.450172
$727$			666.947i			0.917396i	0.888592	+	0.458698i	$0.151684\pi$
$727$			666.947i			0.917396i	−0.888592	+	0.458698i	$0.848316\pi$
$728$			443.097i			0.608650i
$729$	809.106			1.10988
$730$			155.164i			0.212553i
$731$	−322.011			−0.440507
$732$			100.487i			0.137277i
$733$		−	854.699i		−	1.16603i	−0.812462	−	0.583014i	$-0.801873\pi$
$733$		−	854.699i		−	1.16603i	0.812462	−	0.583014i	$-0.198127\pi$
$734$			447.068i			0.609084i
$735$			92.5891i			0.125972i
$736$	504.917	−	483.181i	0.686028	−	0.656497i
$737$	254.471			0.345280
$738$	140.206			0.189981
$739$	713.025			0.964851			0.482426	−	0.875937i	$-0.339756\pi$
$739$	713.025			0.964851			0.482426	+	0.875937i	$0.339756\pi$
$740$	274.671			0.371177
$741$		−	167.656i		−	0.226257i
$742$	−925.215			−1.24692
$743$		−	1115.52i		−	1.50137i	−0.660662	−	0.750683i	$-0.729724\pi$
$743$		−	1115.52i		−	1.50137i	0.660662	−	0.750683i	$-0.270276\pi$
$744$	−217.013			−0.291684
$745$	155.938			0.209313
$746$			938.164i			1.25759i
$747$		−	307.272i		−	0.411342i
$748$	124.235			0.166089
$749$	41.3916			0.0552624
$750$			38.6706i			0.0515608i
$751$			928.797i			1.23675i	0.785885	+	0.618373i	$0.212208\pi$
$751$			928.797i			1.23675i	−0.785885	+	0.618373i	$0.787792\pi$
$752$	−21.1199			−0.0280849
$753$		−	653.107i		−	0.867339i
$754$	84.0528			0.111476
$755$			619.174i			0.820098i
$756$		−	525.937i		−	0.695684i
$757$		−	930.052i		−	1.22860i	−0.789071	−	0.614301i	$-0.789438\pi$
$757$		−	930.052i		−	1.22860i	0.789071	−	0.614301i	$-0.210562\pi$
$758$		−	390.394i		−	0.515032i
$759$	−213.117	−	222.704i	−0.280786	−	0.293417i
$760$	−179.709			−0.236459
$761$	660.941			0.868517			0.434258	−	0.900788i	$-0.357011\pi$
$761$	660.941			0.868517			0.434258	+	0.900788i	$0.357011\pi$
$762$	−824.561			−1.08210
$763$	1365.71			1.78992
$764$		−	827.144i		−	1.08265i
$765$	53.7164			0.0702175
$766$		−	538.881i		−	0.703500i
$767$	27.3063			0.0356014
$768$	703.372			0.915849
$769$		−	15.1066i		−	0.0196445i	−0.999952	−	0.00982226i	$-0.996873\pi$
$769$		−	15.1066i		−	0.0196445i	0.999952	−	0.00982226i	$-0.00312657\pi$
$770$		−	123.249i		−	0.160064i
$771$	351.095			0.455376
$772$	−383.766			−0.497107
$773$		−	450.498i		−	0.582792i	−0.956602	−	0.291396i	$-0.905880\pi$
$773$		−	450.498i		−	0.582792i	0.956602	−	0.291396i	$-0.0941198\pi$
$774$		−	88.1360i		−	0.113871i
$775$	50.3198			0.0649288
$776$		−	749.537i		−	0.965898i
$777$	1152.92			1.48381
$778$			892.558i			1.14725i
$779$			460.181i			0.590733i
$780$		−	86.3402i		−	0.110693i
$781$		−	216.735i		−	0.277510i
$782$	228.191	+	238.456i	0.291804	+	0.304931i
$783$	−278.374			−0.355522
$784$	32.9347			0.0420086
$785$	368.464			0.469381
$786$	−497.678			−0.633178
$787$		−	602.812i		−	0.765963i	−0.923756	−	0.382981i	$-0.874897\pi$
$787$		−	602.812i		−	0.765963i	0.923756	−	0.382981i	$-0.125103\pi$
$788$	592.800			0.752284
$789$			497.806i			0.630932i
$790$	328.722			0.416104
$791$	227.323			0.287386
$792$			94.8784i			0.119796i
$793$		−	114.708i		−	0.144651i
$794$	613.683			0.772900
$795$	503.035			0.632748
$796$			645.813i			0.811323i
$797$			1169.49i			1.46736i	0.679494	+	0.733681i	$0.262199\pi$
$797$			1169.49i			1.46736i	−0.679494	+	0.733681i	$0.737801\pi$
$798$	−270.342			−0.338774
$799$			110.163i			0.137876i
$800$	−151.926			−0.189908
$801$		−	364.013i		−	0.454448i
$802$		−	560.859i		−	0.699325i
$803$			268.874i			0.334837i
$804$		−	287.449i		−	0.357524i
$805$	−299.357	+	286.471i	−0.371873	+	0.355864i
$806$	88.7831			0.110153
$807$	−551.722			−0.683670
$808$	1130.42			1.39903
$809$	−696.820			−0.861335			−0.430668	−	0.902511i	$-0.641722\pi$
$809$	−696.820			−0.861335			−0.430668	+	0.902511i	$0.641722\pi$
$810$		−	166.484i		−	0.205535i
$811$	−384.936			−0.474643			−0.237322	−	0.971431i	$-0.576269\pi$
$811$	−384.936			−0.474643			−0.237322	+	0.971431i	$0.576269\pi$
$812$			171.509i			0.211218i
$813$	−107.660			−0.132423
$814$	−376.123			−0.462068
$815$		−	91.1458i		−	0.111835i
$816$			58.1995i			0.0713229i
$817$	289.277			0.354072
$818$	302.031			0.369231
$819$			118.982i			0.145277i
$820$			236.986i			0.289007i
$821$	−506.372			−0.616775			−0.308388	−	0.951261i	$-0.599789\pi$
$821$	−506.372			−0.616775			−0.308388	+	0.951261i	$0.599789\pi$
$822$			446.032i			0.542618i
$823$	−1449.62			−1.76139			−0.880695	−	0.473684i	$-0.842924\pi$
$823$	−1449.62			−1.76139			−0.880695	+	0.473684i	$0.842924\pi$
$824$			423.385i			0.513816i
$825$			67.0100i			0.0812242i
$826$		−	44.0308i		−	0.0533061i
$827$		−	801.629i		−	0.969322i	−0.874702	−	0.484661i	$-0.838943\pi$
$827$		−	801.629i		−	0.969322i	0.874702	−	0.484661i	$-0.161057\pi$
$828$	82.5908	−	79.0355i	0.0997473	−	0.0954535i
$829$	−643.431			−0.776153			−0.388076	−	0.921627i	$-0.626860\pi$
$829$	−643.431			−0.776153			−0.388076	+	0.921627i	$0.626860\pi$
$830$	−410.428			−0.494492
$831$	−546.050			−0.657100
$832$	−323.037			−0.388265
$833$		−	171.791i		−	0.206231i
$834$	463.417			0.555656
$835$		−	295.220i		−	0.353557i
$836$	−111.606			−0.133500
$837$	−294.040			−0.351302
$838$			180.457i			0.215343i
$839$			460.853i			0.549288i	0.961546	+	0.274644i	$0.0885600\pi$
$839$			460.853i			0.549288i	−0.961546	+	0.274644i	$0.911440\pi$
$840$	−388.462			−0.462455
$841$	−750.222			−0.892059
$842$		−	798.226i		−	0.948011i
$843$			345.533i			0.409885i
$844$	−525.668			−0.622829
$845$		−	279.336i		−	0.330575i
$846$	−30.1522			−0.0356409
$847$			761.268i			0.898781i
$848$		−	178.934i		−	0.211007i
$849$		−	568.742i		−	0.669897i
$850$		−	71.7497i		−	0.0844114i
$851$	874.231	+	913.558i	1.02730	+	1.07351i
$852$	−244.823			−0.287351
$853$	−1399.59			−1.64079			−0.820393	−	0.571799i	$-0.806246\pi$
$853$	−1399.59			−1.64079			−0.820393	+	0.571799i	$0.806246\pi$
$854$	−184.965			−0.216586
$855$	−48.2559			−0.0564397
$856$			42.5607i			0.0497204i
$857$	477.360			0.557012			0.278506	−	0.960434i	$-0.410161\pi$
$857$	477.360			0.557012			0.278506	+	0.960434i	$0.410161\pi$
$858$			118.231i			0.137798i
$859$	1176.53			1.36965			0.684826	−	0.728707i	$-0.259878\pi$
$859$	1176.53			1.36965			0.684826	+	0.728707i	$0.259878\pi$
$860$	148.973			0.173225
$861$			994.736i			1.15533i
$862$		−	498.717i		−	0.578558i
$863$	−687.885			−0.797086			−0.398543	−	0.917150i	$-0.630484\pi$
$863$	−687.885			−0.797086			−0.398543	+	0.917150i	$0.630484\pi$
$864$	887.769			1.02751
$865$		−	586.646i		−	0.678204i
$866$			44.3825i			0.0512500i
$867$	−448.689			−0.517519
$868$			181.161i			0.208711i
$869$	569.623			0.655493
$870$			73.6888i			0.0846998i
$871$			328.132i			0.376730i
$872$			1404.28i			1.61042i
$873$		−	201.268i		−	0.230547i
$874$	−204.994	−	214.216i	−0.234547	−	0.245098i
$875$	90.0746			0.102942
$876$	303.719			0.346711
$877$	51.0202			0.0581758			0.0290879	−	0.999577i	$-0.490740\pi$
$877$	51.0202			0.0581758			0.0290879	+	0.999577i	$0.490740\pi$
$878$	798.496			0.909449
$879$		−	670.770i		−	0.763106i
$880$	23.8360			0.0270864
$881$		−	1644.35i		−	1.86646i	−0.359276	−	0.933231i	$-0.616976\pi$
$881$		−	1644.35i		−	1.86646i	0.359276	−	0.933231i	$-0.383024\pi$
$882$	47.0200			0.0533106
$883$	−351.562			−0.398145			−0.199073	−	0.979985i	$-0.563793\pi$
$883$	−351.562			−0.398145			−0.199073	+	0.979985i	$0.563793\pi$
$884$			160.196i			0.181218i
$885$			23.9394i			0.0270501i
$886$	885.141			0.999031
$887$	−116.003			−0.130781			−0.0653906	−	0.997860i	$-0.520829\pi$
$887$	−116.003			−0.130781			−0.0653906	+	0.997860i	$0.520829\pi$
$888$			1185.48i			1.33500i
$889$			1920.63i			2.16044i
$890$	−486.217			−0.546311
$891$		−	288.490i		−	0.323782i
$892$	495.196			0.555152
$893$		−	98.9647i		−	0.110823i
$894$			241.209i			0.269808i
$895$			113.269i			0.126557i
$896$		−	458.307i		−	0.511504i
$897$	287.168	−	274.807i	0.320143	−	0.306362i
$898$	258.667			0.288048
$899$	95.8870			0.106660
$900$	−24.8510			−0.0276122
$901$	−933.335			−1.03589
$902$		−	324.519i		−	0.359777i
$903$	625.307			0.692477
$904$			233.743i			0.258566i
$905$	−570.925			−0.630857
$906$	−957.752			−1.05712
$907$			13.8397i			0.0152587i	0.999971	+	0.00762936i	$0.00242852\pi$
$907$			13.8397i			0.0152587i	−0.999971	+	0.00762936i	$0.997571\pi$
$908$		−	499.810i		−	0.550452i
$909$	303.543			0.333930
$910$	158.926			0.174643
$911$		−	446.848i		−	0.490503i	−0.969460	−	0.245251i	$-0.921129\pi$
$911$		−	446.848i		−	0.490503i	0.969460	−	0.245251i	$-0.0788705\pi$
$912$		−	52.2833i		−	0.0573282i
$913$	−711.207			−0.778978
$914$		−	360.958i		−	0.394922i
$915$	100.564			0.109907
$916$		−	379.862i		−	0.414696i
$917$			1159.23i			1.26416i
$918$			419.264i			0.456715i
$919$			1164.24i			1.26686i	0.773800	+	0.633430i	$0.218354\pi$
$919$			1164.24i			1.26686i	−0.773800	+	0.633430i	$0.781646\pi$
$920$	−294.562	−	307.813i	−0.320176	−	0.334579i
$921$	33.6017			0.0364839
$922$	−432.146			−0.468705
$923$	279.472			0.302787
$924$	−241.249			−0.261092
$925$		−	274.883i		−	0.297171i
$926$	536.428			0.579296
$927$			113.688i			0.122641i
$928$	−289.503			−0.311965
$929$	15.7379			0.0169407			0.00847035	−	0.999964i	$-0.497304\pi$
$929$	15.7379			0.0169407			0.00847035	+	0.999964i	$0.497304\pi$
$930$			77.8358i			0.0836945i
$931$			154.327i			0.165765i
$932$	−66.9514			−0.0718362
$933$	−552.277			−0.591937
$934$		−	378.541i		−	0.405290i
$935$		−	124.331i		−	0.132974i
$936$	−122.342			−0.130708
$937$			282.231i			0.301207i	0.988594	+	0.150604i	$0.0481217\pi$
$937$			282.231i			0.301207i	−0.988594	+	0.150604i	$0.951878\pi$
$938$	529.105			0.564078
$939$			32.7860i			0.0349159i
$940$		−	50.9652i		−	0.0542183i
$941$			241.059i			0.256174i	0.991763	+	0.128087i	$0.0408836\pi$
$941$			241.059i			0.256174i	−0.991763	+	0.128087i	$0.959116\pi$
$942$			569.948i			0.605041i
$943$	−788.217	+	754.287i	−0.835861	+	0.799880i
$944$	8.51543			0.00902058
$945$	−526.344			−0.556978
$946$	−203.998			−0.215643
$947$	568.623			0.600447			0.300223	−	0.953869i	$-0.402939\pi$
$947$	568.623			0.600447			0.300223	+	0.953869i	$0.402939\pi$
$948$		−	643.444i		−	0.678738i
$949$	−346.704			−0.365336
$950$			64.4561i			0.0678485i
$951$	814.901			0.856889
$952$	720.756			0.757096
$953$			1106.49i			1.16106i	0.814240	+	0.580528i	$0.197154\pi$
$953$			1106.49i			1.16106i	−0.814240	+	0.580528i	$0.802846\pi$
$954$		−	255.459i		−	0.267776i
$955$	−827.785			−0.866790
$956$	−405.344			−0.424000
$957$			127.691i			0.133428i
$958$			394.407i			0.411698i
$959$	1038.93			1.08335
$960$		−	283.205i		−	0.295005i
$961$	−859.717			−0.894606
$962$		−	484.998i		−	0.504156i
$963$			11.4285i			0.0118676i
$964$			349.222i			0.362263i
$965$			384.063i			0.397993i
$966$	−443.120	−	463.053i	−0.458716	−	0.479351i
$967$	−409.424			−0.423396			−0.211698	−	0.977335i	$-0.567899\pi$
$967$	−409.424			−0.423396			−0.211698	+	0.977335i	$0.567899\pi$
$968$	−782.770			−0.808646
$969$	−272.715			−0.281439
$970$	−268.836			−0.277151
$971$		−	1540.49i		−	1.58650i	−0.608899	−	0.793248i	$-0.708388\pi$
$971$		−	1540.49i		−	1.58650i	0.608899	−	0.793248i	$-0.291612\pi$
$972$	261.651			0.269189
$973$		−	1079.43i		−	1.10938i
$974$	−662.236			−0.679914
$975$	−86.4071			−0.0886226
$976$		−	35.7716i		−	0.0366513i
$977$			1116.89i			1.14318i	0.820539	+	0.571590i	$0.193673\pi$
$977$			1116.89i			1.14318i	−0.820539	+	0.571590i	$0.806327\pi$
$978$	140.986			0.144158
$979$	−842.537			−0.860610
$980$			79.4762i			0.0810981i
$981$			377.082i			0.384385i
$982$	1005.45			1.02388
$983$		−	752.534i		−	0.765549i	−0.923842	−	0.382774i	$-0.874969\pi$
$983$		−	752.534i		−	0.765549i	0.923842	−	0.382774i	$-0.125031\pi$
$984$	−1022.83			−1.03946
$985$		−	593.259i		−	0.602293i
$986$		−	136.723i		−	0.138664i
$987$		−	213.924i		−	0.216742i
$988$		−	143.912i		−	0.145660i
$989$	474.157	+	495.486i	0.479430	+	0.500997i
$990$	34.0300			0.0343737
$991$	1678.60			1.69385			0.846923	−	0.531716i	$-0.178453\pi$
$991$	1678.60			1.69385			0.846923	+	0.531716i	$0.178453\pi$
$992$	−305.796			−0.308262
$993$	996.662			1.00369
$994$		−	450.643i		−	0.453363i
$995$	646.313			0.649561
$996$			803.376i			0.806602i
$997$	1062.89			1.06609			0.533045	−	0.846087i	$-0.321048\pi$
$997$	1062.89			1.06609			0.533045	+	0.846087i	$0.321048\pi$
$998$	−449.068			−0.449968
$999$			1606.26i			1.60787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.d.b.91.6	yes	10
3.2	odd	2		1035.3.g.b.91.5		10
4.3	odd	2		1840.3.k.b.321.8		10
5.2	odd	4		575.3.c.d.574.11		20
5.3	odd	4		575.3.c.d.574.10		20
5.4	even	2		575.3.d.g.551.5		10
23.22	odd	2	inner	115.3.d.b.91.5	✓	10
69.68	even	2		1035.3.g.b.91.6		10
92.91	even	2		1840.3.k.b.321.7		10
115.22	even	4		575.3.c.d.574.12		20
115.68	even	4		575.3.c.d.574.9		20
115.114	odd	2		575.3.d.g.551.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.d.b.91.5	✓	10	23.22	odd	2	inner
115.3.d.b.91.6	yes	10	1.1	even	1	trivial
575.3.c.d.574.9		20	115.68	even	4
575.3.c.d.574.10		20	5.3	odd	4
575.3.c.d.574.11		20	5.2	odd	4
575.3.c.d.574.12		20	115.22	even	4
575.3.d.g.551.5		10	5.4	even	2
575.3.d.g.551.6		10	115.114	odd	2
1035.3.g.b.91.5		10	3.2	odd	2
1035.3.g.b.91.6		10	69.68	even	2
1840.3.k.b.321.7		10	92.91	even	2
1840.3.k.b.321.8		10	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.32878 q^{2} -2.60299 q^{3} -2.23434 q^{4} +2.23607i q^{5} -3.45880 q^{6} +8.05652i q^{7} -8.28408 q^{8} -2.22446 q^{9} +2.97125i q^{10} +5.14870i q^{11} +5.81595 q^{12} -6.63907 q^{13} +10.7054i q^{14} -5.82045i q^{15} -2.07038 q^{16} +10.7993i q^{17} -2.95583 q^{18} -9.70153i q^{19} -4.99613i q^{20} -20.9710i q^{21} +6.84150i q^{22} +(16.6172 - 15.9019i) q^{23} +21.5633 q^{24} -5.00000 q^{25} -8.82188 q^{26} +29.2171 q^{27} -18.0010i q^{28} -9.52776 q^{29} -7.73412i q^{30} -10.0640 q^{31} +30.3852 q^{32} -13.4020i q^{33} +14.3499i q^{34} -18.0149 q^{35} +4.97020 q^{36} +54.9767i q^{37} -12.8912i q^{38} +17.2814 q^{39} -18.5238i q^{40} -47.4339 q^{41} -27.8659i q^{42} +29.8177i q^{43} -11.5039i q^{44} -4.97405i q^{45} +(22.0806 - 21.1301i) q^{46} +10.2009 q^{47} +5.38918 q^{48} -15.9075 q^{49} -6.64391 q^{50} -28.1105i q^{51} +14.8339 q^{52} +86.4254i q^{53} +38.8232 q^{54} -11.5128 q^{55} -66.7408i q^{56} +25.2529i q^{57} -12.6603 q^{58} -4.11297 q^{59} +13.0049i q^{60} +17.2778i q^{61} -13.3728 q^{62} -17.9214i q^{63} +48.6569 q^{64} -14.8454i q^{65} -17.8083i q^{66} -49.4243i q^{67} -24.1293i q^{68} +(-43.2543 + 41.3923i) q^{69} -23.9379 q^{70} -42.0951 q^{71} +18.4276 q^{72} +52.2218 q^{73} +73.0520i q^{74} +13.0149 q^{75} +21.6765i q^{76} -41.4806 q^{77} +22.9632 q^{78} -110.634i q^{79} -4.62952i q^{80} -56.0316 q^{81} -63.0293 q^{82} +138.133i q^{83} +46.8563i q^{84} -24.1480 q^{85} +39.6212i q^{86} +24.8006 q^{87} -42.6522i q^{88} +163.641i q^{89} -6.60943i q^{90} -53.4878i q^{91} +(-37.1284 + 35.5301i) q^{92} +26.1964 q^{93} +13.5548 q^{94} +21.6933 q^{95} -79.0923 q^{96} +90.4792i q^{97} -21.1377 q^{98} -11.4531i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 2 q^{3} + 34 q^{4} + 28 q^{6} - 20 q^{8} - 16 q^{9} - 24 q^{12} - 2 q^{13} - 38 q^{16} - 22 q^{18} + 44 q^{23} + 70 q^{24} - 50 q^{25} - 72 q^{26} + 40 q^{27} - 46 q^{29} + 16 q^{31} + 142 q^{32}+ \cdots + 388 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 2 * q^3 + 34 * q^4 + 28 * q^6 - 20 * q^8 - 16 * q^9 - 24 * q^12 - 2 * q^13 - 38 * q^16 - 22 * q^18 + 44 * q^23 + 70 * q^24 - 50 * q^25 - 72 * q^26 + 40 * q^27 - 46 * q^29 + 16 * q^31 + 142 * q^32 - 60 * q^35 - 110 * q^36 + 72 * q^39 - 84 * q^41 + 86 * q^46 + 112 * q^47 - 236 * q^48 + 50 * q^49 - 10 * q^50 + 52 * q^52 + 30 * q^54 - 10 * q^55 + 246 * q^58 - 262 * q^59 - 136 * q^62 - 224 * q^64 + 124 * q^69 + 130 * q^70 + 236 * q^71 - 406 * q^72 + 168 * q^73 + 10 * q^75 + 300 * q^77 - 254 * q^78 - 258 * q^81 + 140 * q^82 + 540 * q^87 - 182 * q^92 + 100 * q^93 + 262 * q^94 - 90 * q^95 - 332 * q^96 + 388 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more