LMFDB - Embedded newform 115.3.d.b.91.4

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			91.4
Root			$-2.67869 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	115.91
Dual form			115.3.d.b.91.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.67869 q^{2} +1.23330 q^{3} +3.17536 q^{4} +2.23607i q^{5} -3.30362 q^{6} -0.521669i q^{7} +2.20895 q^{8} -7.47898 q^{9} -5.98972i q^{10} +10.5914i q^{11} +3.91616 q^{12} +14.3029 q^{13} +1.39739i q^{14} +2.75774i q^{15} -18.6185 q^{16} +33.4342i q^{17} +20.0338 q^{18} +23.1053i q^{19} +7.10032i q^{20} -0.643373i q^{21} -28.3711i q^{22} +(22.5772 + 4.39000i) q^{23} +2.72429 q^{24} -5.00000 q^{25} -38.3131 q^{26} -20.3235 q^{27} -1.65649i q^{28} +11.7613 q^{29} -7.38711i q^{30} -17.8286 q^{31} +41.0374 q^{32} +13.0624i q^{33} -89.5597i q^{34} +1.16649 q^{35} -23.7485 q^{36} -57.2590i q^{37} -61.8920i q^{38} +17.6398 q^{39} +4.93936i q^{40} -33.7426 q^{41} +1.72339i q^{42} -53.7180i q^{43} +33.6316i q^{44} -16.7235i q^{45} +(-60.4771 - 11.7594i) q^{46} +14.0973 q^{47} -22.9622 q^{48} +48.7279 q^{49} +13.3934 q^{50} +41.2343i q^{51} +45.4170 q^{52} +85.7672i q^{53} +54.4402 q^{54} -23.6831 q^{55} -1.15234i q^{56} +28.4958i q^{57} -31.5049 q^{58} -70.7106 q^{59} +8.75681i q^{60} -31.8109i q^{61} +47.7571 q^{62} +3.90155i q^{63} -35.4522 q^{64} +31.9824i q^{65} -34.9900i q^{66} +39.4556i q^{67} +106.166i q^{68} +(27.8443 + 5.41418i) q^{69} -3.12465 q^{70} +68.9236 q^{71} -16.5207 q^{72} +30.3374 q^{73} +153.379i q^{74} -6.16649 q^{75} +73.3678i q^{76} +5.52521 q^{77} -47.2514 q^{78} -49.0126i q^{79} -41.6323i q^{80} +42.2459 q^{81} +90.3860 q^{82} -96.7624i q^{83} -2.04294i q^{84} -74.7611 q^{85} +143.894i q^{86} +14.5052 q^{87} +23.3959i q^{88} -56.7850i q^{89} +44.7970i q^{90} -7.46140i q^{91} +(71.6906 + 13.9398i) q^{92} -21.9879 q^{93} -37.7621 q^{94} -51.6651 q^{95} +50.6113 q^{96} +80.0997i q^{97} -130.527 q^{98} -79.2129i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67869			−1.33934			−0.669672	−	0.742657i	$-0.733565\pi$
$2$	−2.67869			−1.33934			−0.669672	+	0.742657i	$0.733565\pi$
$3$	1.23330			0.411099			0.205550	−	0.978647i	$-0.434102\pi$
$3$	1.23330			0.411099			0.205550	+	0.978647i	$0.434102\pi$
$4$	3.17536			0.793840
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−3.30362			−0.550603
$7$		−	0.521669i		−	0.0745241i	−0.999306	−	0.0372620i	$-0.988136\pi$
$7$		−	0.521669i		−	0.0745241i	0.999306	−	0.0372620i	$-0.0118636\pi$
$8$	2.20895			0.276119
$9$	−7.47898			−0.830998
$10$		−	5.98972i		−	0.598972i
$11$			10.5914i			0.962856i	0.876486	+	0.481428i	$0.159882\pi$
$11$			10.5914i			0.962856i	−0.876486	+	0.481428i	$0.840118\pi$
$12$	3.91616			0.326347
$13$	14.3029			1.10023			0.550113	−	0.835090i	$-0.314585\pi$
$13$	14.3029			1.10023			0.550113	+	0.835090i	$0.314585\pi$
$14$			1.39739i			0.0998133i
$15$			2.75774i			0.183849i
$16$	−18.6185			−1.16366
$17$			33.4342i			1.96672i	0.181676	+	0.983358i	$0.441848\pi$
$17$			33.4342i			1.96672i	−0.181676	+	0.983358i	$0.558152\pi$
$18$	20.0338			1.11299
$19$			23.1053i			1.21607i	0.793910	+	0.608035i	$0.208042\pi$
$19$			23.1053i			1.21607i	−0.793910	+	0.608035i	$0.791958\pi$
$20$			7.10032i			0.355016i
$21$		−	0.643373i		−	0.0306368i
$22$		−	28.3711i		−	1.28959i
$23$	22.5772	+	4.39000i	0.981615	+	0.190870i
$23$	22.5772	+	4.39000i	0.981615	+	0.190870i
$24$	2.72429			0.113512
$25$	−5.00000			−0.200000
$26$	−38.3131			−1.47358
$27$	−20.3235			−0.752721
$28$		−	1.65649i		−	0.0591602i
$29$	11.7613			0.405563			0.202782	−	0.979224i	$-0.435002\pi$
$29$	11.7613			0.405563			0.202782	+	0.979224i	$0.435002\pi$
$30$		−	7.38711i		−	0.246237i
$31$	−17.8286			−0.575115			−0.287558	−	0.957763i	$-0.592843\pi$
$31$	−17.8286			−0.575115			−0.287558	+	0.957763i	$0.592843\pi$
$32$	41.0374			1.28242
$33$			13.0624i			0.395829i
$34$		−	89.5597i		−	2.63411i
$35$	1.16649			0.0333282
$36$	−23.7485			−0.659679
$37$		−	57.2590i		−	1.54754i	−0.633466	−	0.773771i	$-0.718368\pi$
$37$		−	57.2590i		−	1.54754i	0.633466	−	0.773771i	$-0.281632\pi$
$38$		−	61.8920i		−	1.62874i
$39$	17.6398			0.452302
$40$			4.93936i			0.123484i
$41$	−33.7426			−0.822991			−0.411496	−	0.911412i	$-0.634993\pi$
$41$	−33.7426			−0.822991			−0.411496	+	0.911412i	$0.634993\pi$
$42$			1.72339i			0.0410332i
$43$		−	53.7180i		−	1.24926i	−0.780922	−	0.624628i	$-0.785251\pi$
$43$		−	53.7180i		−	1.24926i	0.780922	−	0.624628i	$-0.214749\pi$
$44$			33.6316i			0.764353i
$45$		−	16.7235i		−	0.371633i
$46$	−60.4771	−	11.7594i	−1.31472	−	0.255640i
$47$	14.0973			0.299942			0.149971	−	0.988690i	$-0.452082\pi$
$47$	14.0973			0.299942			0.149971	+	0.988690i	$0.452082\pi$
$48$	−22.9622			−0.478379
$49$	48.7279			0.994446
$50$	13.3934			0.267869
$51$			41.2343i			0.808516i
$52$	45.4170			0.873404
$53$			85.7672i			1.61825i	0.587638	+	0.809124i	$0.300058\pi$
$53$			85.7672i			1.61825i	−0.587638	+	0.809124i	$0.699942\pi$
$54$	54.4402			1.00815
$55$	−23.6831			−0.430602
$56$		−	1.15234i		−	0.0205775i
$57$			28.4958i			0.499926i
$58$	−31.5049			−0.543189
$59$	−70.7106			−1.19848			−0.599242	−	0.800568i	$-0.704531\pi$
$59$	−70.7106			−1.19848			−0.599242	+	0.800568i	$0.704531\pi$
$60$			8.75681i			0.145947i
$61$		−	31.8109i		−	0.521490i	−0.965408	−	0.260745i	$-0.916032\pi$
$61$		−	31.8109i		−	0.521490i	0.965408	−	0.260745i	$-0.0839682\pi$
$62$	47.7571			0.770276
$63$			3.90155i			0.0619293i
$64$	−35.4522			−0.553941
$65$			31.9824i			0.492036i
$66$		−	34.9900i		−	0.530151i
$67$			39.4556i			0.588890i	0.955668	+	0.294445i	$0.0951348\pi$
$67$			39.4556i			0.588890i	−0.955668	+	0.294445i	$0.904865\pi$
$68$			106.166i			1.56126i
$69$	27.8443	+	5.41418i	0.403541	+	0.0784664i
$70$	−3.12465			−0.0446379
$71$	68.9236			0.970754			0.485377	−	0.874305i	$-0.338682\pi$
$71$	68.9236			0.970754			0.485377	+	0.874305i	$0.338682\pi$
$72$	−16.5207			−0.229454
$73$	30.3374			0.415580			0.207790	−	0.978173i	$-0.433373\pi$
$73$	30.3374			0.415580			0.207790	+	0.978173i	$0.433373\pi$
$74$			153.379i			2.07269i
$75$	−6.16649			−0.0822198
$76$			73.3678i			0.965366i
$77$	5.52521			0.0717559
$78$	−47.2514			−0.605788
$79$		−	49.0126i		−	0.620412i	−0.950669	−	0.310206i	$-0.899602\pi$
$79$		−	49.0126i		−	0.620412i	0.950669	−	0.310206i	$-0.100398\pi$
$80$		−	41.6323i		−	0.520404i
$81$	42.2459			0.521554
$82$	90.3860			1.10227
$83$		−	96.7624i		−	1.16581i	−0.812540	−	0.582906i	$-0.801916\pi$
$83$		−	96.7624i		−	1.16581i	0.812540	−	0.582906i	$-0.198084\pi$
$84$		−	2.04294i		−	0.0243207i
$85$	−74.7611			−0.879543
$86$			143.894i			1.67318i
$87$	14.5052			0.166727
$88$			23.3959i			0.265862i
$89$		−	56.7850i		−	0.638034i	−0.947749	−	0.319017i	$-0.896647\pi$
$89$		−	56.7850i		−	0.638034i	0.947749	−	0.319017i	$-0.103353\pi$
$90$			44.7970i			0.497745i
$91$		−	7.46140i		−	0.0819934i
$92$	71.6906	+	13.9398i	0.779246	+	0.151520i
$93$	−21.9879			−0.236429
$94$	−37.7621			−0.401725
$95$	−51.6651			−0.543843
$96$	50.6113			0.527201
$97$			80.0997i			0.825770i	0.910783	+	0.412885i	$0.135479\pi$
$97$			80.0997i			0.825770i	−0.910783	+	0.412885i	$0.864521\pi$
$98$	−130.527			−1.33190
$99$		−	79.2129i		−	0.800131i
$100$	−15.8768			−0.158768
$101$	−20.8975			−0.206906			−0.103453	−	0.994634i	$-0.532989\pi$
$101$	−20.8975			−0.206906			−0.103453	+	0.994634i	$0.532989\pi$
$102$		−	110.454i		−	1.08288i
$103$		−	8.78760i		−	0.0853165i	−0.999090	−	0.0426582i	$-0.986417\pi$
$103$		−	8.78760i		−	0.0853165i	0.999090	−	0.0426582i	$-0.0135827\pi$
$104$	31.5945			0.303793
$105$	1.43862			0.0137012
$106$		−	229.743i		−	2.16739i
$107$		−	198.899i		−	1.85887i	−0.368992	−	0.929433i	$-0.620297\pi$
$107$		−	198.899i		−	1.85887i	0.368992	−	0.929433i	$-0.379703\pi$
$108$	−64.5344			−0.597541
$109$			142.315i			1.30564i	0.757512	+	0.652821i	$0.226415\pi$
$109$			142.315i			1.30564i	−0.757512	+	0.652821i	$0.773585\pi$
$110$	63.4396			0.576724
$111$		−	70.6174i		−	0.636193i
$112$			9.71270i			0.0867206i
$113$			22.9994i			0.203534i	0.994808	+	0.101767i	$0.0324497\pi$
$113$			22.9994i			0.203534i	−0.994808	+	0.101767i	$0.967550\pi$
$114$		−	76.3312i		−	0.669572i
$115$	−9.81635	+	50.4841i	−0.0853595	+	0.438992i
$116$	37.3465			0.321953
$117$	−106.971			−0.914286
$118$	189.411			1.60518
$119$	17.4416			0.146568
$120$			6.09170i			0.0507642i
$121$	8.82202			0.0729093
$122$			85.2115i			0.698455i
$123$	−41.6147			−0.338331
$124$	−56.6121			−0.456549
$125$		−	11.1803i		−	0.0894427i
$126$		−	10.4510i		−	0.0829446i
$127$	−59.8833			−0.471522			−0.235761	−	0.971811i	$-0.575758\pi$
$127$	−59.8833			−0.471522			−0.235761	+	0.971811i	$0.575758\pi$
$128$	−69.1842			−0.540502
$129$		−	66.2503i		−	0.513568i
$130$		−	85.6707i		−	0.659005i
$131$	158.280			1.20824			0.604121	−	0.796892i	$-0.293524\pi$
$131$	158.280			1.20824			0.604121	+	0.796892i	$0.293524\pi$
$132$			41.4777i			0.314225i
$133$	12.0533			0.0906266
$134$		−	105.689i		−	0.788726i
$135$		−	45.4447i		−	0.336627i
$136$			73.8544i			0.543047i
$137$			92.0533i			0.671922i	0.941876	+	0.335961i	$0.109061\pi$
$137$			92.0533i			0.671922i	−0.941876	+	0.335961i	$0.890939\pi$
$138$	−74.5863	−	14.5029i	−0.540480	−	0.105093i
$139$	3.03747			0.0218523			0.0109262	−	0.999940i	$-0.496522\pi$
$139$	3.03747			0.0218523			0.0109262	+	0.999940i	$0.496522\pi$
$140$	3.70402			0.0264573
$141$	17.3861			0.123306
$142$	−184.625			−1.30017
$143$			151.488i			1.05936i
$144$	139.248			0.966997
$145$			26.2991i			0.181373i
$146$	−81.2643			−0.556605
$147$	60.0959			0.408816
$148$		−	181.818i		−	1.22850i
$149$			127.915i			0.858493i	0.903187	+	0.429247i	$0.141221\pi$
$149$			127.915i			0.858493i	−0.903187	+	0.429247i	$0.858779\pi$
$150$	16.5181			0.110121
$151$	45.2103			0.299406			0.149703	−	0.988731i	$-0.452168\pi$
$151$	45.2103			0.299406			0.149703	+	0.988731i	$0.452168\pi$
$152$			51.0385i			0.335780i
$153$		−	250.054i		−	1.63434i
$154$	−14.8003			−0.0961058
$155$		−	39.8659i		−	0.257199i
$156$	56.0127			0.359056
$157$			19.3773i			0.123422i	0.998094	+	0.0617110i	$0.0196557\pi$
$157$			19.3773i			0.123422i	−0.998094	+	0.0617110i	$0.980344\pi$
$158$			131.289i			0.830945i
$159$			105.776i			0.665260i
$160$			91.7624i			0.573515i
$161$	2.29013	−	11.7778i	0.0142244	−	0.0731540i
$162$	−113.164			−0.698540
$163$	293.153			1.79849			0.899243	−	0.437450i	$-0.144118\pi$
$163$	293.153			1.79849			0.899243	+	0.437450i	$0.144118\pi$
$164$	−107.145			−0.653324
$165$	−29.2083			−0.177020
$166$			259.196i			1.56142i
$167$	−158.029			−0.946282			−0.473141	−	0.880987i	$-0.656880\pi$
$167$	−158.029			−0.946282			−0.473141	+	0.880987i	$0.656880\pi$
$168$		−	1.42118i		−	0.00845939i
$169$	35.5742			0.210498
$170$	200.262			1.17801
$171$		−	172.804i		−	1.01055i
$172$		−	170.574i		−	0.991710i
$173$	−114.157			−0.659868			−0.329934	−	0.944004i	$-0.607027\pi$
$173$	−114.157			−0.659868			−0.329934	+	0.944004i	$0.607027\pi$
$174$	−38.8550			−0.223304
$175$			2.60834i			0.0149048i
$176$		−	197.196i		−	1.12043i
$177$	−87.2071			−0.492696
$178$			152.109i			0.854546i
$179$	−172.889			−0.965862			−0.482931	−	0.875659i	$-0.660428\pi$
$179$	−172.889			−0.965862			−0.482931	+	0.875659i	$0.660428\pi$
$180$		−	53.1032i		−	0.295018i
$181$			173.085i			0.956270i	0.878286	+	0.478135i	$0.158687\pi$
$181$			173.085i			0.956270i	−0.878286	+	0.478135i	$0.841313\pi$
$182$			19.9867i			0.109817i
$183$		−	39.2323i		−	0.214384i
$184$	49.8718	+	9.69730i	0.271042	+	0.0527027i
$185$	128.035			0.692082
$186$	58.8988			0.316660
$187$	−354.115			−1.89366
$188$	44.7639			0.238106
$189$			10.6021i			0.0560959i
$190$	138.395			0.728393
$191$		−	213.863i		−	1.11970i	−0.828594	−	0.559850i	$-0.810859\pi$
$191$		−	213.863i		−	1.11970i	0.828594	−	0.559850i	$-0.189141\pi$
$192$	−43.7231			−0.227725
$193$	232.186			1.20303			0.601517	−	0.798860i	$-0.294563\pi$
$193$	232.186			1.20303			0.601517	+	0.798860i	$0.294563\pi$
$194$		−	214.562i		−	1.10599i
$195$			39.4438i			0.202276i
$196$	154.729			0.789431
$197$	301.664			1.53129			0.765646	−	0.643262i	$-0.222420\pi$
$197$	301.664			1.53129			0.765646	+	0.643262i	$0.222420\pi$
$198$			212.187i			1.07165i
$199$		−	349.041i		−	1.75397i	−0.480515	−	0.876986i	$-0.659550\pi$
$199$		−	349.041i		−	1.75397i	0.480515	−	0.876986i	$-0.340450\pi$
$200$	−11.0447			−0.0552237
$201$			48.6605i			0.242092i
$202$	55.9779			0.277118
$203$		−	6.13552i		−	0.0302242i
$204$			130.934i			0.641832i
$205$		−	75.4508i		−	0.368053i
$206$			23.5392i			0.114268i
$207$	−168.854	−	32.8327i	−0.815720	−	0.158612i
$208$	−266.300			−1.28029
$209$	−244.718			−1.17090
$210$	−3.85362			−0.0183506
$211$	−178.918			−0.847952			−0.423976	−	0.905673i	$-0.639366\pi$
$211$	−178.918			−0.847952			−0.423976	+	0.905673i	$0.639366\pi$
$212$			272.342i			1.28463i
$213$	85.0032			0.399076
$214$			532.787i			2.48966i
$215$	120.117			0.558684
$216$	−44.8935			−0.207840
$217$			9.30060i			0.0428599i
$218$		−	381.217i		−	1.74870i
$219$	37.4150			0.170845
$220$	−75.2024			−0.341829
$221$			478.207i			2.16383i
$222$			189.162i			0.852081i
$223$	131.985			0.591862			0.295931	−	0.955209i	$-0.404370\pi$
$223$	131.985			0.591862			0.295931	+	0.955209i	$0.404370\pi$
$224$		−	21.4079i		−	0.0955711i
$225$	37.3949			0.166200
$226$		−	61.6082i		−	0.272603i
$227$		−	91.7919i		−	0.404369i	−0.979347	−	0.202185i	$-0.935196\pi$
$227$		−	91.7919i		−	0.404369i	0.979347	−	0.202185i	$-0.0648041\pi$
$228$			90.4843i			0.396861i
$229$			304.840i			1.33118i	0.746318	+	0.665589i	$0.231820\pi$
$229$			304.840i			1.33118i	−0.746318	+	0.665589i	$0.768180\pi$
$230$	26.2949	−	135.231i	0.114326	−	0.587961i
$231$	6.81422			0.0294988
$232$	25.9802			0.111984
$233$	239.908			1.02965			0.514824	−	0.857296i	$-0.327857\pi$
$233$	239.908			1.02965			0.514824	+	0.857296i	$0.327857\pi$
$234$	286.543			1.22454
$235$			31.5224i			0.134138i
$236$	−224.532			−0.951405
$237$		−	60.4471i		−	0.255051i
$238$	−46.7205			−0.196305
$239$	−324.673			−1.35846			−0.679232	−	0.733923i	$-0.737687\pi$
$239$	−324.673			−1.35846			−0.679232	+	0.733923i	$0.737687\pi$
$240$		−	51.3450i		−	0.213937i
$241$		−	133.840i		−	0.555353i	−0.960675	−	0.277676i	$-0.910436\pi$
$241$		−	133.840i		−	0.555353i	0.960675	−	0.277676i	$-0.0895643\pi$
$242$	−23.6314			−0.0976505
$243$	235.013			0.967132
$244$		−	101.011i		−	0.413980i
$245$			108.959i			0.444730i
$246$	111.473			0.453141
$247$			330.475i			1.33795i
$248$	−39.3824			−0.158800
$249$		−	119.337i		−	0.479264i
$250$			29.9486i			0.119794i
$251$		−	134.518i		−	0.535929i	−0.963429	−	0.267964i	$-0.913649\pi$
$251$		−	134.518i		−	0.535929i	0.963429	−	0.267964i	$-0.0863509\pi$
$252$			12.3888i			0.0491620i
$253$	−46.4963	+	239.124i	−0.183780	+	0.945154i
$254$	160.409			0.631530
$255$	−92.2027			−0.361579
$256$	327.132			1.27786
$257$	186.968			0.727503			0.363752	−	0.931496i	$-0.381496\pi$
$257$	186.968			0.727503			0.363752	+	0.931496i	$0.381496\pi$
$258$			177.464i			0.687844i
$259$	−29.8703			−0.115329
$260$			101.556i			0.390598i
$261$	−87.9628			−0.337022
$262$	−423.982			−1.61825
$263$		−	188.537i		−	0.716871i	−0.933555	−	0.358435i	$-0.883310\pi$
$263$		−	188.537i		−	0.716871i	0.933555	−	0.358435i	$-0.116690\pi$
$264$			28.8541i			0.109296i
$265$	−191.781			−0.723703
$266$	−32.2871			−0.121380
$267$		−	70.0328i		−	0.262295i
$268$			125.286i			0.467485i
$269$	−238.007			−0.884786			−0.442393	−	0.896821i	$-0.645870\pi$
$269$	−238.007			−0.884786			−0.442393	+	0.896821i	$0.645870\pi$
$270$			121.732i			0.450859i
$271$	134.114			0.494885			0.247442	−	0.968903i	$-0.420410\pi$
$271$	134.114			0.494885			0.247442	+	0.968903i	$0.420410\pi$
$272$		−	622.495i		−	2.28859i
$273$		−	9.20212i		−	0.0337074i
$274$		−	246.582i		−	0.899934i
$275$		−	52.9571i		−	0.192571i
$276$	88.4158	+	17.1920i	0.320347	+	0.0622898i
$277$	389.169			1.40494			0.702471	−	0.711713i	$-0.252080\pi$
$277$	389.169			1.40494			0.702471	+	0.711713i	$0.252080\pi$
$278$	−8.13644			−0.0292678
$279$	133.339			0.477919
$280$	2.57671			0.00920254
$281$		−	76.2923i		−	0.271503i	−0.990743	−	0.135751i	$-0.956655\pi$
$281$		−	76.2923i		−	0.271503i	0.990743	−	0.135751i	$-0.0433449\pi$
$282$	−46.5719			−0.165149
$283$		−	263.833i		−	0.932271i	−0.884713	−	0.466136i	$-0.845646\pi$
$283$		−	263.833i		−	0.932271i	0.884713	−	0.466136i	$-0.154354\pi$
$284$	218.857			0.770624
$285$	−63.7185			−0.223574
$286$		−	405.790i		−	1.41885i
$287$			17.6025i			0.0613327i
$288$	−306.918			−1.06569
$289$	−828.845			−2.86798
$290$		−	70.4472i		−	0.242921i
$291$			98.7868i			0.339473i
$292$	96.3321			0.329904
$293$		−	66.4738i		−	0.226873i	−0.993545	−	0.113437i	$-0.963814\pi$
$293$		−	66.4738i		−	0.226873i	0.993545	−	0.113437i	$-0.0361859\pi$
$294$	−160.978			−0.547545
$295$		−	158.114i		−	0.535978i
$296$		−	126.482i		−	0.427305i
$297$		−	215.254i		−	0.724762i
$298$		−	342.645i		−	1.14982i
$299$	322.920	+	62.7900i	1.08000	+	0.210000i
$300$	−19.5808			−0.0652694
$301$	−28.0230			−0.0930997
$302$	−121.104			−0.401008
$303$	−25.7728			−0.0850589
$304$		−	430.188i		−	1.41509i
$305$	71.1314			0.233218
$306$			669.815i			2.18894i
$307$	76.2175			0.248266			0.124133	−	0.992266i	$-0.460385\pi$
$307$	76.2175			0.248266			0.124133	+	0.992266i	$0.460385\pi$
$308$	17.5445			0.0569628
$309$		−	10.8377i		−	0.0350735i
$310$			106.788i			0.344478i
$311$	378.675			1.21761			0.608803	−	0.793321i	$-0.291650\pi$
$311$	378.675			1.21761			0.608803	+	0.793321i	$0.291650\pi$
$312$	38.9654			0.124889
$313$			226.302i			0.723010i	0.932370	+	0.361505i	$0.117737\pi$
$313$			226.302i			0.723010i	−0.932370	+	0.361505i	$0.882263\pi$
$314$		−	51.9056i		−	0.165305i
$315$	−8.72413			−0.0276956
$316$		−	155.633i		−	0.492508i
$317$	431.012			1.35966			0.679830	−	0.733370i	$-0.262054\pi$
$317$	431.012			1.35966			0.679830	+	0.733370i	$0.262054\pi$
$318$		−	283.342i		−	0.891012i
$319$			124.569i			0.390499i
$320$		−	79.2736i		−	0.247730i
$321$		−	245.301i		−	0.764178i
$322$	−6.13453	+	31.5490i	−0.0190513	+	0.0979783i
$323$	−772.508			−2.39167
$324$	134.146			0.414031
$325$	−71.5147			−0.220045
$326$	−785.265			−2.40879
$327$			175.517i			0.536748i
$328$	−74.5358			−0.227243
$329$		−	7.35410i		−	0.0223529i
$330$	78.2399			0.237091
$331$	385.002			1.16315			0.581574	−	0.813493i	$-0.302437\pi$
$331$	385.002			1.16315			0.581574	+	0.813493i	$0.302437\pi$
$332$		−	307.255i		−	0.925468i
$333$			428.239i			1.28600i
$334$	423.310			1.26740
$335$	−88.2255			−0.263360
$336$			11.9786i			0.0356507i
$337$		−	203.770i		−	0.604658i	−0.953204	−	0.302329i	$-0.902236\pi$
$337$		−	203.770i		−	0.604658i	0.953204	−	0.302329i	$-0.0977642\pi$
$338$	−95.2922			−0.281930
$339$			28.3651i			0.0836728i
$340$	−237.394			−0.698216
$341$		−	188.830i		−	0.553753i
$342$			462.889i			1.35348i
$343$		−	50.9816i		−	0.148634i
$344$		−	118.660i		−	0.344943i
$345$	−12.1065	+	62.2618i	−0.0350912	+	0.180469i
$346$	305.791			0.883790
$347$	55.5063			0.159961			0.0799803	−	0.996796i	$-0.474514\pi$
$347$	55.5063			0.159961			0.0799803	+	0.996796i	$0.474514\pi$
$348$	46.0593			0.132354
$349$	588.423			1.68603			0.843013	−	0.537893i	$-0.180780\pi$
$349$	588.423			1.68603			0.843013	+	0.537893i	$0.180780\pi$
$350$		−	6.98693i		−	0.0199627i
$351$	−290.686			−0.828164
$352$			434.644i			1.23478i
$353$	−447.976			−1.26905			−0.634527	−	0.772900i	$-0.718805\pi$
$353$	−447.976			−1.26905			−0.634527	+	0.772900i	$0.718805\pi$
$354$	233.601			0.659889
$355$			154.118i			0.434135i
$356$		−	180.313i		−	0.506497i
$357$	21.5106			0.0602539
$358$	463.116			1.29362
$359$			563.019i			1.56830i	0.620573	+	0.784149i	$0.286900\pi$
$359$			563.019i			1.56830i	−0.620573	+	0.784149i	$0.713100\pi$
$360$		−	36.9414i		−	0.102615i
$361$	−172.857			−0.478828
$362$		−	463.640i		−	1.28077i
$363$	10.8802			0.0299729
$364$		−	23.6926i		−	0.0650897i
$365$			67.8364i			0.185853i
$366$			105.091i			0.287134i
$367$		−	306.018i		−	0.833836i	−0.908944	−	0.416918i	$-0.863110\pi$
$367$		−	306.018i		−	0.833836i	0.908944	−	0.416918i	$-0.136890\pi$
$368$	−420.353	−	81.7354i	−1.14226	−	0.222107i
$369$	252.360			0.683904
$370$	−342.966			−0.926935
$371$	44.7420			0.120598
$372$	−69.8196			−0.187687
$373$		−	80.0977i		−	0.214739i	−0.994219	−	0.107370i	$-0.965757\pi$
$373$		−	80.0977i		−	0.214739i	0.994219	−	0.107370i	$-0.0342428\pi$
$374$	948.564			2.53627
$375$		−	13.7887i		−	0.0367698i
$376$	31.1401			0.0828195
$377$	168.222			0.446212
$378$		−	28.3998i		−	0.0751316i
$379$		−	5.99870i		−	0.0158277i	−0.999969	−	0.00791385i	$-0.997481\pi$
$379$		−	5.99870i		−	0.0158277i	0.999969	−	0.00791385i	$-0.00251908\pi$
$380$	−164.055			−0.431725
$381$	−73.8539			−0.193842
$382$			572.871i			1.49966i
$383$			490.051i			1.27951i	0.768580	+	0.639753i	$0.220963\pi$
$383$			490.051i			1.27951i	−0.768580	+	0.639753i	$0.779037\pi$
$384$	−85.3247			−0.222200
$385$			12.3547i			0.0320902i
$386$	−621.953			−1.61128
$387$			401.756i			1.03813i
$388$			254.345i			0.655530i
$389$		−	536.332i		−	1.37874i	−0.724407	−	0.689372i	$-0.757886\pi$
$389$		−	536.332i		−	1.37874i	0.724407	−	0.689372i	$-0.242114\pi$
$390$		−	105.657i		−	0.270917i
$391$	−146.776	+	754.849i	−0.375387	+	1.93056i
$392$	107.637			0.274585
$393$	195.206			0.496707
$394$	−808.064			−2.05092
$395$	109.595			0.277457
$396$		−	251.530i		−	0.635176i
$397$	97.6151			0.245882			0.122941	−	0.992414i	$-0.460767\pi$
$397$	97.6151			0.245882			0.122941	+	0.992414i	$0.460767\pi$
$398$			934.970i			2.34917i
$399$	14.8653			0.0372565
$400$	93.0926			0.232732
$401$			756.313i			1.88607i	0.332696	+	0.943034i	$0.392042\pi$
$401$			756.313i			1.88607i	−0.332696	+	0.943034i	$0.607958\pi$
$402$		−	130.346i		−	0.324244i
$403$	−255.001			−0.632757
$404$	−66.3571			−0.164250
$405$			94.4647i			0.233246i
$406$			16.4351i			0.0404806i
$407$	606.454			1.49006
$408$			91.0845i			0.223246i
$409$	−425.609			−1.04061			−0.520304	−	0.853981i	$-0.674181\pi$
$409$	−425.609			−1.04061			−0.520304	+	0.853981i	$0.674181\pi$
$410$			202.109i			0.492949i
$411$			113.529i			0.276226i
$412$		−	27.9038i		−	0.0677277i
$413$			36.8875i			0.0893159i
$414$	452.307	+	87.9486i	1.09253	+	0.212436i
$415$	216.367			0.521367
$416$	586.956			1.41095
$417$	3.74611			0.00898347
$418$	655.523			1.56824
$419$			663.073i			1.58251i	0.611484	+	0.791257i	$0.290573\pi$
$419$			663.073i			1.58251i	−0.611484	+	0.791257i	$0.709427\pi$
$420$	4.56815			0.0108766
$421$		−	163.431i		−	0.388197i	−0.980982	−	0.194098i	$-0.937822\pi$
$421$		−	163.431i		−	0.388197i	0.980982	−	0.194098i	$-0.0621781\pi$
$422$	479.265			1.13570
$423$	−105.433			−0.249251
$424$			189.455i			0.446829i
$425$		−	167.171i		−	0.393343i
$426$	−227.697			−0.534500
$427$	−16.5948			−0.0388636
$428$		−	631.575i		−	1.47564i
$429$			186.830i			0.435502i
$430$	−321.756			−0.748270
$431$		−	213.125i		−	0.494490i	−0.968953	−	0.247245i	$-0.920475\pi$
$431$		−	213.125i		−	0.494490i	0.968953	−	0.247245i	$-0.0795252\pi$
$432$	378.393			0.875910
$433$		−	769.179i		−	1.77640i	−0.459461	−	0.888198i	$-0.651957\pi$
$433$		−	769.179i		−	1.77640i	0.459461	−	0.888198i	$-0.348043\pi$
$434$		−	24.9134i		−	0.0574042i
$435$			32.4347i			0.0745625i
$436$			451.901i			1.03647i
$437$	−101.433	+	521.653i	−0.232111	+	1.19371i
$438$	−100.223			−0.228820
$439$	−615.630			−1.40235			−0.701173	−	0.712991i	$-0.747340\pi$
$439$	−615.630			−1.40235			−0.701173	+	0.712991i	$0.747340\pi$
$440$	−52.3148			−0.118897
$441$	−364.435			−0.826382
$442$		−	1280.97i		−	2.89812i
$443$	−34.9484			−0.0788904			−0.0394452	−	0.999222i	$-0.512559\pi$
$443$	−34.9484			−0.0788904			−0.0394452	+	0.999222i	$0.512559\pi$
$444$		−	224.236i		−	0.505036i
$445$	126.975			0.285337
$446$	−353.547			−0.792706
$447$			157.758i			0.352926i
$448$			18.4943i			0.0412819i
$449$	259.106			0.577074			0.288537	−	0.957469i	$-0.406831\pi$
$449$	259.106			0.577074			0.288537	+	0.957469i	$0.406831\pi$
$450$	−100.169			−0.222598
$451$		−	357.382i		−	0.792422i
$452$			73.0314i			0.161574i
$453$	55.7578			0.123086
$454$			245.882i			0.541590i
$455$	16.6842			0.0366686
$456$			62.9457i			0.138039i
$457$		−	362.602i		−	0.793440i	−0.917940	−	0.396720i	$-0.870148\pi$
$457$		−	362.602i		−	0.793440i	0.917940	−	0.396720i	$-0.129852\pi$
$458$		−	816.570i		−	1.78290i
$459$		−	679.499i		−	1.48039i
$460$	−31.1704	+	160.305i	−0.0677618	+	0.348489i
$461$	−703.013			−1.52497			−0.762487	−	0.647003i	$-0.776022\pi$
$461$	−703.013			−1.52497			−0.762487	+	0.647003i	$0.776022\pi$
$462$	−18.2532			−0.0395090
$463$	775.327			1.67457			0.837286	−	0.546765i	$-0.184141\pi$
$463$	775.327			1.67457			0.837286	+	0.546765i	$0.184141\pi$
$464$	−218.979			−0.471937
$465$		−	49.1665i		−	0.105734i
$466$	−642.638			−1.37905
$467$			154.199i			0.330190i	0.986278	+	0.165095i	$0.0527931\pi$
$467$			154.199i			0.330190i	−0.986278	+	0.165095i	$0.947207\pi$
$468$	−339.673			−0.725797
$469$	20.5828			0.0438865
$470$		−	84.4387i		−	0.179657i
$471$			23.8979i			0.0507387i
$472$	−156.196			−0.330924
$473$	568.949			1.20285
$474$			161.919i			0.341601i
$475$		−	115.527i		−	0.243214i
$476$	55.3833			0.116351
$477$		−	641.451i		−	1.34476i
$478$	869.697			1.81945
$479$		−	496.640i		−	1.03683i	−0.855130	−	0.518413i	$-0.826523\pi$
$479$		−	496.640i		−	1.03683i	0.855130	−	0.518413i	$-0.173477\pi$
$480$			113.170i			0.235772i
$481$		−	818.973i		−	1.70265i
$482$			358.515i			0.743808i
$483$	2.82441	−	14.5255i	0.00584764	−	0.0300735i
$484$	28.0131			0.0578783
$485$	−179.108			−0.369296
$486$	−629.526			−1.29532
$487$	−321.989			−0.661168			−0.330584	−	0.943777i	$-0.607246\pi$
$487$	−321.989			−0.661168			−0.330584	+	0.943777i	$0.607246\pi$
$488$		−	70.2687i		−	0.143993i
$489$	361.545			0.739356
$490$		−	291.866i		−	0.595646i
$491$	247.376			0.503820			0.251910	−	0.967751i	$-0.418941\pi$
$491$	247.376			0.503820			0.251910	+	0.967751i	$0.418941\pi$
$492$	−132.142			−0.268581
$493$			393.231i			0.797628i
$494$		−	885.238i		−	1.79198i
$495$	177.125			0.357829
$496$	331.942			0.669237
$497$		−	35.9553i		−	0.0723446i
$498$			319.666i			0.641899i
$499$	−463.163			−0.928183			−0.464091	−	0.885787i	$-0.653619\pi$
$499$	−463.163			−0.928183			−0.464091	+	0.885787i	$0.653619\pi$
$500$		−	35.5016i		−	0.0710032i
$501$	−194.897			−0.389016
$502$			360.332i			0.717792i
$503$		−	117.024i		−	0.232652i	−0.993211	−	0.116326i	$-0.962888\pi$
$503$		−	117.024i		−	0.232652i	0.993211	−	0.116326i	$-0.0371118\pi$
$504$			8.61832i			0.0170998i
$505$		−	46.7282i		−	0.0925312i
$506$	124.549	−	640.538i	0.246144	−	1.26589i
$507$	43.8736			0.0865357
$508$	−190.151			−0.374313
$509$	−547.729			−1.07609			−0.538044	−	0.842917i	$-0.680837\pi$
$509$	−547.729			−1.07609			−0.538044	+	0.842917i	$0.680837\pi$
$510$	246.982			0.484279
$511$		−	15.8261i		−	0.0309707i
$512$	−599.546			−1.17099
$513$		−	469.581i		−	0.915363i
$514$	−500.830			−0.974377
$515$	19.6497			0.0381547
$516$		−	210.369i		−	0.407691i
$517$			149.310i			0.288800i
$518$	80.0130			0.154465
$519$	−140.790			−0.271271
$520$			70.6474i			0.135860i
$521$			23.6219i			0.0453395i	0.999743	+	0.0226698i	$0.00721663\pi$
$521$			23.6219i			0.0453395i	−0.999743	+	0.0226698i	$0.992783\pi$
$522$	235.625			0.451388
$523$			151.625i			0.289914i	0.989438	+	0.144957i	$0.0463044\pi$
$523$			151.625i			0.289914i	−0.989438	+	0.144957i	$0.953696\pi$
$524$	502.595			0.959152
$525$			3.21686i			0.00612736i
$526$			505.032i			0.960136i
$527$		−	596.084i		−	1.13109i
$528$		−	243.202i		−	0.460610i
$529$	490.456	+	198.228i	0.927138	+	0.374721i
$530$	513.722			0.969286
$531$	528.843			0.995937
$532$	38.2737			0.0719430
$533$	−482.619			−0.905477
$534$			187.596i			0.351303i
$535$	444.751			0.831310
$536$			87.1555i			0.162604i
$537$	−213.224			−0.397065
$538$	637.547			1.18503
$539$			516.097i			0.957508i
$540$		−	144.303i		−	0.267228i
$541$	243.075			0.449308			0.224654	−	0.974439i	$-0.427875\pi$
$541$	243.075			0.449308			0.224654	+	0.974439i	$0.427875\pi$
$542$	−359.249			−0.662821
$543$			213.465i			0.393122i
$544$			1372.05i			2.52215i
$545$	−318.226			−0.583901
$546$			24.6496i			0.0451458i
$547$	66.6228			0.121797			0.0608983	−	0.998144i	$-0.480603\pi$
$547$	66.6228			0.121797			0.0608983	+	0.998144i	$0.480603\pi$
$548$			292.302i			0.533399i
$549$			237.913i			0.433357i
$550$			141.855i			0.257919i
$551$			271.750i			0.493194i
$552$	61.5067	+	11.9596i	0.111425	+	0.0216660i
$553$	−25.5683			−0.0462357
$554$	−1042.46			−1.88170
$555$	157.905			0.284514
$556$	9.64508			0.0173473
$557$			548.308i			0.984395i	0.870483	+	0.492198i	$0.163806\pi$
$557$			548.308i			0.984395i	−0.870483	+	0.492198i	$0.836194\pi$
$558$	−357.175			−0.640098
$559$		−	768.326i		−	1.37446i
$560$	−21.7183			−0.0387826
$561$	−436.729			−0.778484
$562$			204.363i			0.363636i
$563$			249.788i			0.443673i	0.975084	+	0.221837i	$0.0712052\pi$
$563$			249.788i			0.443673i	−0.975084	+	0.221837i	$0.928795\pi$
$564$	55.2072			0.0978851
$565$	−51.4282			−0.0910234
$566$			706.725i			1.24863i
$567$		−	22.0384i		−	0.0388684i
$568$	152.249			0.268043
$569$		−	771.295i		−	1.35553i	−0.735280	−	0.677763i	$-0.762949\pi$
$569$		−	771.295i		−	1.35553i	0.735280	−	0.677763i	$-0.237051\pi$
$570$	170.682			0.299442
$571$		−	34.8847i		−	0.0610940i	−0.999533	−	0.0305470i	$-0.990275\pi$
$571$		−	34.8847i		−	0.0610940i	0.999533	−	0.0305470i	$-0.00972492\pi$
$572$			481.030i			0.840962i
$573$		−	263.756i		−	0.460308i
$574$		−	47.1515i		−	0.0821455i
$575$	−112.886	−	21.9500i	−0.196323	−	0.0381739i
$576$	265.146			0.460323
$577$	472.936			0.819646			0.409823	−	0.912165i	$-0.365590\pi$
$577$	472.936			0.819646			0.409823	+	0.912165i	$0.365590\pi$
$578$	2220.22			3.84120
$579$	286.354			0.494567
$580$			83.5093i			0.143982i
$581$	−50.4779			−0.0868810
$582$		−	264.619i		−	0.454671i
$583$	−908.395			−1.55814
$584$	67.0137			0.114749
$585$		−	239.195i		−	0.408881i
$586$			178.063i			0.303861i
$587$	−737.792			−1.25689			−0.628443	−	0.777855i	$-0.716308\pi$
$587$	−737.792			−1.25689			−0.628443	+	0.777855i	$0.716308\pi$
$588$	190.826			0.324535
$589$		−	411.935i		−	0.699381i
$590$			423.537i			0.717859i
$591$	372.042			0.629513
$592$			1066.08i			1.80081i
$593$	−438.218			−0.738986			−0.369493	−	0.929234i	$-0.620469\pi$
$593$	−438.218			−0.738986			−0.369493	+	0.929234i	$0.620469\pi$
$594$			576.599i			0.970705i
$595$			39.0005i			0.0655471i
$596$			406.178i			0.681506i
$597$		−	430.471i		−	0.721057i
$598$	−865.001	−	168.195i	−1.44649	−	0.281262i
$599$	721.525			1.20455			0.602275	−	0.798289i	$-0.294261\pi$
$599$	721.525			1.20455			0.602275	+	0.798289i	$0.294261\pi$
$600$	−13.6215			−0.0227024
$601$	−152.892			−0.254395			−0.127198	−	0.991877i	$-0.540598\pi$
$601$	−152.892			−0.254395			−0.127198	+	0.991877i	$0.540598\pi$
$602$	75.0648			0.124692
$603$		−	295.088i		−	0.489366i
$604$	143.559			0.237681
$605$			19.7266i			0.0326060i
$606$	69.0373			0.113923
$607$	−694.250			−1.14374			−0.571870	−	0.820344i	$-0.693782\pi$
$607$	−694.250			−1.14374			−0.571870	+	0.820344i	$0.693782\pi$
$608$			948.183i			1.55951i
$609$		−	7.56692i		−	0.0124252i
$610$	−190.539			−0.312358
$611$	201.632			0.330004
$612$		−	794.010i		−	1.29740i
$613$		−	916.314i		−	1.49480i	−0.664373	−	0.747401i	$-0.731301\pi$
$613$		−	916.314i		−	1.49480i	0.664373	−	0.747401i	$-0.268699\pi$
$614$	−204.163			−0.332513
$615$		−	93.0533i		−	0.151306i
$616$	12.2049			0.0198132
$617$		−	414.587i		−	0.671941i	−0.941873	−	0.335970i	$-0.890936\pi$
$617$		−	414.587i		−	0.671941i	0.941873	−	0.335970i	$-0.109064\pi$
$618$			29.0309i			0.0469755i
$619$			904.936i			1.46193i	0.682414	+	0.730966i	$0.260930\pi$
$619$			904.936i			1.46193i	−0.682414	+	0.730966i	$0.739070\pi$
$620$		−	126.589i		−	0.204175i
$621$	−458.846	−	89.2201i	−0.738883	−	0.143672i
$622$	−1014.35			−1.63079
$623$	−29.6230			−0.0475489
$624$	−328.427			−0.526325
$625$	25.0000			0.0400000
$626$		−	606.193i		−	0.968359i
$627$	−301.810			−0.481356
$628$			61.5298i			0.0979774i
$629$	1914.41			3.04358
$630$	23.3692			0.0370940
$631$			190.276i			0.301547i	0.988568	+	0.150773i	$0.0481763\pi$
$631$			190.276i			0.301547i	−0.988568	+	0.150773i	$0.951824\pi$
$632$		−	108.266i		−	0.171307i
$633$	−220.659			−0.348592
$634$	−1154.55			−1.82105
$635$		−	133.903i		−	0.210871i
$636$			335.878i			0.528110i
$637$	696.952			1.09412
$638$		−	333.682i		−	0.523012i
$639$	−515.478			−0.806694
$640$		−	154.701i		−	0.241720i
$641$		−	915.056i		−	1.42755i	−0.700378	−	0.713773i	$-0.746985\pi$
$641$		−	915.056i		−	1.42755i	0.700378	−	0.713773i	$-0.253015\pi$
$642$			657.085i			1.02350i
$643$			998.723i			1.55322i	0.629979	+	0.776612i	$0.283064\pi$
$643$			998.723i			1.55322i	−0.629979	+	0.776612i	$0.716936\pi$
$644$	7.27198	−	37.3987i	0.0112919	−	0.0580726i
$645$	148.140			0.229675
$646$	2069.31			3.20326
$647$	−484.292			−0.748519			−0.374260	−	0.927324i	$-0.622103\pi$
$647$	−484.292			−0.748519			−0.374260	+	0.927324i	$0.622103\pi$
$648$	93.3191			0.144011
$649$		−	748.925i		−	1.15397i
$650$	191.566			0.294716
$651$			11.4704i			0.0176197i
$652$	930.867			1.42771
$653$	161.111			0.246724			0.123362	−	0.992362i	$-0.460632\pi$
$653$	161.111			0.246724			0.123362	+	0.992362i	$0.460632\pi$
$654$		−	470.154i		−	0.718890i
$655$			353.924i			0.540343i
$656$	628.238			0.957680
$657$	−226.892			−0.345346
$658$			19.6993i			0.0299382i
$659$		−	388.234i		−	0.589126i	−0.955632	−	0.294563i	$-0.904826\pi$
$659$		−	388.234i		−	0.589126i	0.955632	−	0.294563i	$-0.0951741\pi$
$660$	−92.7470			−0.140526
$661$		−	44.1368i		−	0.0667728i	−0.999443	−	0.0333864i	$-0.989371\pi$
$661$		−	44.1368i		−	0.0667728i	0.999443	−	0.0333864i	$-0.0106292\pi$
$662$	−1031.30			−1.55786
$663$			589.772i			0.889550i
$664$		−	213.743i		−	0.321902i
$665$			26.9521i			0.0405294i
$666$		−	1147.12i		−	1.72240i
$667$	265.538	+	51.6323i	0.398107	+	0.0774098i
$668$	−501.800			−0.751197
$669$	162.777			0.243314
$670$	236.328			0.352729
$671$	336.922			0.502120
$672$		−	26.4023i		−	0.0392892i
$673$	−549.707			−0.816801			−0.408401	−	0.912803i	$-0.633913\pi$
$673$	−549.707			−0.816801			−0.408401	+	0.912803i	$0.633913\pi$
$674$			545.835i			0.809845i
$675$	101.617			0.150544
$676$	112.961			0.167102
$677$			767.490i			1.13366i	0.823834	+	0.566832i	$0.191831\pi$
$677$			767.490i			1.13366i	−0.823834	+	0.566832i	$0.808169\pi$
$678$		−	75.9812i		−	0.112067i
$679$	41.7855			0.0615398
$680$	−165.144			−0.242858
$681$		−	113.207i		−	0.166236i
$682$			505.815i			0.741665i
$683$	−791.512			−1.15888			−0.579438	−	0.815017i	$-0.696728\pi$
$683$	−791.512			−1.15888			−0.579438	+	0.815017i	$0.696728\pi$
$684$		−	548.716i		−	0.802217i
$685$	−205.837			−0.300493
$686$			136.564i			0.199072i
$687$			375.958i			0.547246i
$688$			1000.15i			1.45371i
$689$			1226.72i			1.78044i
$690$	32.4294	−	166.780i	0.0469992	−	0.241710i
$691$	−464.599			−0.672357			−0.336179	−	0.941798i	$-0.609135\pi$
$691$	−464.599			−0.672357			−0.336179	+	0.941798i	$0.609135\pi$
$692$	−362.490			−0.523830
$693$	−41.3229			−0.0596290
$694$	−148.684			−0.214242
$695$			6.79200i			0.00977266i
$696$	32.0413			0.0460364
$697$		−	1128.16i		−	1.61859i
$698$	−1576.20			−2.25817
$699$	295.878			0.423287
$700$			8.28243i			0.0118320i
$701$			646.813i			0.922700i	0.887218	+	0.461350i	$0.152635\pi$
$701$			646.813i			0.922700i	−0.887218	+	0.461350i	$0.847365\pi$
$702$	778.656			1.10920
$703$	1322.99			1.88192
$704$		−	375.489i		−	0.533365i
$705$			38.8765i			0.0551440i
$706$	1199.99			1.69970
$707$			10.9016i			0.0154195i
$708$	−276.914			−0.391122
$709$			469.683i			0.662458i	0.943550	+	0.331229i	$0.107463\pi$
$709$			469.683i			0.662458i	−0.943550	+	0.331229i	$0.892537\pi$
$710$		−	412.833i		−	0.581455i
$711$			366.564i			0.515561i
$712$		−	125.435i		−	0.176173i
$713$	−402.518	−	78.2675i	−0.564542	−	0.109772i
$714$	−57.6203			−0.0807006
$715$	−338.738			−0.473760
$716$	−548.986			−0.766740
$717$	−400.418			−0.558464
$718$		−	1508.15i		−	2.10049i
$719$	661.292			0.919738			0.459869	−	0.887987i	$-0.347896\pi$
$719$	661.292			0.919738			0.459869	+	0.887987i	$0.347896\pi$
$720$			311.367i			0.432454i
$721$	−4.58422			−0.00635813
$722$	463.030			0.641315
$723$		−	165.065i		−	0.228305i
$724$			549.607i			0.759126i
$725$	−58.8067			−0.0811127
$726$	−29.1446			−0.0401440
$727$		−	20.5037i		−	0.0282032i	−0.999901	−	0.0141016i	$-0.995511\pi$
$727$		−	20.5037i		−	0.0282032i	0.999901	−	0.0141016i	$-0.00448882\pi$
$728$		−	16.4819i		−	0.0226399i
$729$	−90.3722			−0.123967
$730$		−	181.712i		−	0.248921i
$731$	1796.02			2.45693
$732$		−	124.577i		−	0.170187i
$733$			90.9287i			0.124050i	0.998075	+	0.0620250i	$0.0197559\pi$
$733$			90.9287i			0.124050i	−0.998075	+	0.0620250i	$0.980244\pi$
$734$			819.726i			1.11679i
$735$			134.379i			0.182828i
$736$	926.508	+	180.154i	1.25884	+	0.244775i
$737$	−417.891			−0.567016
$738$	−675.995			−0.915982
$739$	−679.537			−0.919537			−0.459768	−	0.888039i	$-0.652068\pi$
$739$	−679.537			−0.919537			−0.459768	+	0.888039i	$0.652068\pi$
$740$	406.558			0.549402
$741$			407.573i			0.550031i
$742$	−119.850			−0.161523
$743$		−	748.573i		−	1.00750i	−0.863849	−	0.503750i	$-0.831953\pi$
$743$		−	748.573i		−	1.00750i	0.863849	−	0.503750i	$-0.168047\pi$
$744$	−48.5702			−0.0652825
$745$	−286.028			−0.383930
$746$			214.557i			0.287609i
$747$			723.683i			0.968786i
$748$	−1124.44			−1.50327
$749$	−103.759			−0.138530
$750$			36.9356i			0.0492474i
$751$		−	765.774i		−	1.01967i	−0.860272	−	0.509836i	$-0.829706\pi$
$751$		−	765.774i		−	1.01967i	0.860272	−	0.509836i	$-0.170294\pi$
$752$	−262.470			−0.349029
$753$		−	165.901i		−	0.220320i
$754$	−450.613			−0.597630
$755$			101.093i			0.133899i
$756$			33.6656i			0.0445312i
$757$			665.274i			0.878830i	0.898284	+	0.439415i	$0.144814\pi$
$757$			665.274i			0.878830i	−0.898284	+	0.439415i	$0.855186\pi$
$758$			16.0686i			0.0211987i
$759$	−57.3438	+	294.911i	−0.0755518	+	0.388552i
$760$	−114.126			−0.150165
$761$	656.887			0.863189			0.431594	−	0.902068i	$-0.357951\pi$
$761$	656.887			0.863189			0.431594	+	0.902068i	$0.357951\pi$
$762$	197.831			0.259621
$763$	74.2413			0.0973018
$764$		−	679.091i		−	0.888863i
$765$	559.137			0.730898
$766$		−	1312.69i		−	1.71370i
$767$	−1011.37			−1.31860
$768$	403.451			0.525326
$769$		−	790.399i		−	1.02783i	−0.857842	−	0.513914i	$-0.828195\pi$
$769$		−	790.399i		−	1.02783i	0.857842	−	0.513914i	$-0.171805\pi$
$770$		−	33.0945i		−	0.0429798i
$771$	230.588			0.299076
$772$	737.273			0.955017
$773$			783.714i			1.01386i	0.861987	+	0.506930i	$0.169220\pi$
$773$			783.714i			1.01386i	−0.861987	+	0.506930i	$0.830780\pi$
$774$		−	1076.18i		−	1.39041i
$775$	89.1428			0.115023
$776$			176.936i			0.228011i
$777$	−36.8389			−0.0474117
$778$			1436.66i			1.84661i
$779$		−	779.635i		−	1.00082i
$780$			125.248i			0.160575i
$781$			729.998i			0.934696i
$782$	393.167	−	2022.00i	0.502772	−	2.58568i
$783$	−239.031			−0.305276
$784$	−907.241			−1.15720
$785$	−43.3289			−0.0551960
$786$	−522.896			−0.665262
$787$		−	131.079i		−	0.166556i	−0.996526	−	0.0832779i	$-0.973461\pi$
$787$		−	131.079i		−	0.166556i	0.996526	−	0.0832779i	$-0.0265389\pi$
$788$	957.893			1.21560
$789$		−	232.522i		−	0.294705i
$790$	−293.572			−0.371610
$791$	11.9981			0.0151682
$792$		−	174.977i		−	0.220931i
$793$		−	454.990i		−	0.573758i
$794$	−261.480			−0.329320
$795$	−236.523			−0.297514
$796$		−	1108.33i		−	1.39237i
$797$			627.924i			0.787859i	0.919141	+	0.393930i	$0.128885\pi$
$797$			627.924i			0.787859i	−0.919141	+	0.393930i	$0.871115\pi$
$798$	−39.8196			−0.0498993
$799$			471.330i			0.589900i
$800$	−205.187			−0.256484
$801$			424.694i			0.530204i
$802$		−	2025.93i		−	2.52609i
$803$			321.315i			0.400144i
$804$			154.515i			0.192182i
$805$	26.3359	+	5.12088i	0.0327155	+	0.00636134i
$806$	683.068			0.847479
$807$	−293.534			−0.363735
$808$	−46.1615			−0.0571306
$809$	125.748			0.155436			0.0777179	−	0.996975i	$-0.475237\pi$
$809$	125.748			0.155436			0.0777179	+	0.996975i	$0.475237\pi$
$810$		−	253.041i		−	0.312397i
$811$	−450.426			−0.555396			−0.277698	−	0.960668i	$-0.589571\pi$
$811$	−450.426			−0.555396			−0.277698	+	0.960668i	$0.589571\pi$
$812$		−	19.4825i		−	0.0239932i
$813$	165.402			0.203447
$814$	−1624.50			−1.99570
$815$			655.510i			0.804307i
$816$		−	767.722i		−	0.940836i
$817$	1241.17			1.51918
$818$	1140.07			1.39373
$819$			55.8036i			0.0681363i
$820$		−	239.584i		−	0.292175i
$821$	−47.5865			−0.0579616			−0.0289808	−	0.999580i	$-0.509226\pi$
$821$	−47.5865			−0.0579616			−0.0289808	+	0.999580i	$0.509226\pi$
$822$		−	304.109i		−	0.369962i
$823$	600.613			0.729784			0.364892	−	0.931050i	$-0.381106\pi$
$823$	600.613			0.729784			0.364892	+	0.931050i	$0.381106\pi$
$824$		−	19.4114i		−	0.0235575i
$825$		−	65.3118i		−	0.0791658i
$826$		−	98.8100i		−	0.119625i
$827$			1073.18i			1.29768i	0.760925	+	0.648840i	$0.224745\pi$
$827$			1073.18i			1.29768i	−0.760925	+	0.648840i	$0.775255\pi$
$828$	−536.172	−	104.256i	−0.647551	−	0.125913i
$829$	972.327			1.17289			0.586446	−	0.809988i	$-0.300527\pi$
$829$	972.327			1.17289			0.586446	+	0.809988i	$0.300527\pi$
$830$	−579.580			−0.698289
$831$	479.961			0.577570
$832$	−507.071			−0.609460
$833$			1629.18i			1.95579i
$834$	−10.0346			−0.0120320
$835$		−	353.364i		−	0.423190i
$836$	−777.069			−0.929508
$837$	362.338			0.432901
$838$		−	1776.16i		−	2.11953i
$839$			1524.09i			1.81656i	0.418364	+	0.908279i	$0.362604\pi$
$839$			1524.09i			1.81656i	−0.418364	+	0.908279i	$0.637396\pi$
$840$	3.17785			0.00378315
$841$	−702.671			−0.835518
$842$			437.780i			0.519929i
$843$		−	94.0911i		−	0.111615i
$844$	−568.129			−0.673138
$845$			79.5464i			0.0941378i
$846$	282.422			0.333832
$847$		−	4.60217i		−	0.00543350i
$848$		−	1596.86i		−	1.88309i
$849$		−	325.384i		−	0.383256i
$850$			447.799i			0.526822i
$851$	251.367	−	1292.75i	0.295379	−	1.51909i
$852$	269.916			0.316803
$853$	−485.965			−0.569713			−0.284857	−	0.958570i	$-0.591946\pi$
$853$	−485.965			−0.569713			−0.284857	+	0.958570i	$0.591946\pi$
$854$	44.4522			0.0520517
$855$	386.402			0.451933
$856$		−	439.357i		−	0.513267i
$857$	−1253.82			−1.46304			−0.731518	−	0.681822i	$-0.761188\pi$
$857$	−1253.82			−1.46304			−0.731518	+	0.681822i	$0.761188\pi$
$858$		−	500.460i		−	0.583286i
$859$	992.552			1.15547			0.577737	−	0.816223i	$-0.303936\pi$
$859$	992.552			1.15547			0.577737	+	0.816223i	$0.303936\pi$
$860$	381.415			0.443506
$861$			21.7091i			0.0252138i
$862$			570.895i			0.662291i
$863$	−1170.45			−1.35626			−0.678128	−	0.734944i	$-0.737208\pi$
$863$	−1170.45			−1.35626			−0.678128	+	0.734944i	$0.737208\pi$
$864$	−834.023			−0.965304
$865$		−	255.263i		−	0.295102i
$866$			2060.39i			2.37920i
$867$	−1022.21			−1.17902
$868$			29.5328i			0.0340239i
$869$	519.112			0.597367
$870$		−	86.8823i		−	0.0998647i
$871$			564.332i			0.647912i
$872$			314.367i			0.360512i
$873$		−	599.064i		−	0.686213i
$874$	271.706	−	1397.34i	0.310876	−	1.59879i
$875$	−5.83243			−0.00666564
$876$	118.806			0.135623
$877$	382.998			0.436714			0.218357	−	0.975869i	$-0.429930\pi$
$877$	382.998			0.436714			0.218357	+	0.975869i	$0.429930\pi$
$878$	1649.08			1.87822
$879$		−	81.9820i		−	0.0932673i
$880$	440.945			0.501074
$881$		−	514.592i		−	0.584100i	−0.956403	−	0.292050i	$-0.905663\pi$
$881$		−	514.592i		−	0.584100i	0.956403	−	0.292050i	$-0.0943373\pi$
$882$	976.206			1.10681
$883$	−28.1064			−0.0318306			−0.0159153	−	0.999873i	$-0.505066\pi$
$883$	−28.1064			−0.0318306			−0.0159153	+	0.999873i	$0.505066\pi$
$884$			1518.48i			1.71774i
$885$		−	195.001i		−	0.220340i
$886$	93.6159			0.105661
$887$	−651.934			−0.734988			−0.367494	−	0.930026i	$-0.619784\pi$
$887$	−651.934			−0.734988			−0.367494	+	0.930026i	$0.619784\pi$
$888$		−	155.990i		−	0.175665i
$889$			31.2392i			0.0351397i
$890$	−340.126			−0.382165
$891$			447.444i			0.502182i
$892$	419.101			0.469844
$893$			325.722i			0.364750i
$894$		−	422.584i		−	0.472689i
$895$		−	386.592i		−	0.431946i
$896$			36.0912i			0.0402804i
$897$	398.256	+	77.4387i	0.443987	+	0.0863308i
$898$	−694.064			−0.772900
$899$	−209.688			−0.233246
$900$	118.742			0.131936
$901$	−2867.56			−3.18264
$902$			957.315i			1.06132i
$903$	−34.5607			−0.0382732
$904$			50.8045i			0.0561997i
$905$	−387.030			−0.427657
$906$	−149.358			−0.164854
$907$		−	249.920i		−	0.275546i	−0.990464	−	0.137773i	$-0.956006\pi$
$907$		−	249.920i		−	0.275546i	0.990464	−	0.137773i	$-0.0439944\pi$
$908$		−	291.472i		−	0.321005i
$909$	156.292			0.171938
$910$	−44.6917			−0.0491118
$911$		−	1000.23i		−	1.09795i	−0.835839	−	0.548975i	$-0.815018\pi$
$911$		−	1000.23i		−	1.09795i	0.835839	−	0.548975i	$-0.184982\pi$
$912$		−	530.549i		−	0.581742i
$913$	1024.85			1.12251
$914$			971.298i			1.06269i
$915$	87.7261			0.0958755
$916$			967.977i			1.05674i
$917$		−	82.5696i		−	0.0900432i
$918$			1820.16i			1.98275i
$919$		−	759.452i		−	0.826389i	−0.910643	−	0.413195i	$-0.864413\pi$
$919$		−	759.452i		−	0.826389i	0.910643	−	0.413195i	$-0.135587\pi$
$920$	−21.6838	+	111.517i	−0.0235694	+	0.121214i
$921$	93.9989			0.102062
$922$	1883.15			2.04246
$923$	985.810			1.06805
$924$	21.6376			0.0234173
$925$			286.295i			0.309508i
$926$	−2076.86			−2.24283
$927$			65.7223i			0.0708978i
$928$	482.655			0.520102
$929$	1097.98			1.18190			0.590950	−	0.806708i	$-0.298753\pi$
$929$	1097.98			1.18190			0.590950	+	0.806708i	$0.298753\pi$
$930$			131.702i			0.141615i
$931$			1125.87i			1.20932i
$932$	761.794			0.817376
$933$	467.019			0.500557
$934$		−	413.050i		−	0.442238i
$935$		−	791.826i		−	0.846872i
$936$	−236.294			−0.252451
$937$		−	429.342i		−	0.458209i	−0.973402	−	0.229105i	$-0.926420\pi$
$937$		−	429.342i		−	0.458209i	0.973402	−	0.229105i	$-0.0735798\pi$
$938$	−55.1348			−0.0587791
$939$			279.098i			0.297229i
$940$			100.095i			0.106484i
$941$			1813.97i			1.92770i	0.266442	+	0.963851i	$0.414152\pi$
$941$			1813.97i			1.92770i	−0.266442	+	0.963851i	$0.585848\pi$
$942$		−	64.0151i		−	0.0679565i
$943$	−761.813	−	148.130i	−0.807861	−	0.157084i
$944$	1316.53			1.39463
$945$	−23.7071			−0.0250868
$946$	−1524.04			−1.61103
$947$	1020.51			1.07762			0.538810	−	0.842427i	$-0.318874\pi$
$947$	1020.51			1.07762			0.538810	+	0.842427i	$0.318874\pi$
$948$		−	191.941i		−	0.202470i
$949$	433.914			0.457233
$950$			309.460i			0.325747i
$951$	531.566			0.558955
$952$	38.5275			0.0404701
$953$			1222.97i			1.28328i	0.767006	+	0.641640i	$0.221746\pi$
$953$			1222.97i			1.28328i	−0.767006	+	0.641640i	$0.778254\pi$
$954$			1718.25i			1.80110i
$955$	478.211			0.500745
$956$	−1030.95			−1.07840
$957$			153.631i			0.160534i
$958$			1330.34i			1.38867i
$959$	48.0213			0.0500744
$960$		−	97.7679i		−	0.101842i
$961$	−643.142			−0.669243
$962$			2193.77i			2.28043i
$963$			1487.56i			1.54471i
$964$		−	424.990i		−	0.440861i
$965$			519.183i			0.538014i
$966$	−7.56570	+	38.9093i	−0.00783199	+	0.0402788i
$967$	604.850			0.625491			0.312745	−	0.949837i	$-0.398751\pi$
$967$	604.850			0.625491			0.312745	+	0.949837i	$0.398751\pi$
$968$	19.4874			0.0201316
$969$	−952.733			−0.983212
$970$	479.775			0.494614
$971$			1403.19i			1.44510i	0.691321	+	0.722548i	$0.257029\pi$
$971$			1403.19i			1.44510i	−0.691321	+	0.722548i	$0.742971\pi$
$972$	746.251			0.767748
$973$		−	1.58456i		−	0.00162853i
$974$	862.507			0.885531
$975$	−88.1989			−0.0904604
$976$			592.272i			0.606836i
$977$		−	1557.63i		−	1.59430i	−0.603780	−	0.797151i	$-0.706339\pi$
$977$		−	1557.63i		−	1.59430i	0.603780	−	0.797151i	$-0.293661\pi$
$978$	−968.466			−0.990251
$979$	601.433			0.614334
$980$			345.984i			0.353044i
$981$		−	1064.37i		−	1.08499i
$982$	−662.642			−0.674788
$983$		−	1074.26i		−	1.09284i	−0.837512	−	0.546418i	$-0.815991\pi$
$983$		−	1074.26i		−	1.09284i	0.837512	−	0.546418i	$-0.184009\pi$
$984$	−91.9248			−0.0934195
$985$			674.542i			0.684814i
$986$		−	1053.34i		−	1.06830i
$987$		−	9.06979i		−	0.00918925i
$988$			1049.38i			1.06212i
$989$	235.822	−	1212.80i	0.238445	−	1.22629i
$990$	−474.464			−0.479256
$991$	−974.643			−0.983494			−0.491747	−	0.870738i	$-0.663642\pi$
$991$	−974.643			−0.983494			−0.491747	+	0.870738i	$0.663642\pi$
$992$	−731.638			−0.737538
$993$	474.822			0.478169
$994$			96.3129i			0.0968942i
$995$	780.479			0.784401
$996$		−	378.937i		−	0.380459i
$997$	−1575.15			−1.57989			−0.789945	−	0.613178i	$-0.789891\pi$
$997$	−1575.15			−1.57989			−0.789945	+	0.613178i	$0.789891\pi$
$998$	1240.67			1.24316
$999$			1163.70i			1.16487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.d.b.91.4	yes	10
3.2	odd	2		1035.3.g.b.91.7		10
4.3	odd	2		1840.3.k.b.321.4		10
5.2	odd	4		575.3.c.d.574.6		20
5.3	odd	4		575.3.c.d.574.15		20
5.4	even	2		575.3.d.g.551.8		10
23.22	odd	2	inner	115.3.d.b.91.3	✓	10
69.68	even	2		1035.3.g.b.91.8		10
92.91	even	2		1840.3.k.b.321.3		10
115.22	even	4		575.3.c.d.574.5		20
115.68	even	4		575.3.c.d.574.16		20
115.114	odd	2		575.3.d.g.551.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.d.b.91.3	✓	10	23.22	odd	2	inner
115.3.d.b.91.4	yes	10	1.1	even	1	trivial
575.3.c.d.574.5		20	115.22	even	4
575.3.c.d.574.6		20	5.2	odd	4
575.3.c.d.574.15		20	5.3	odd	4
575.3.c.d.574.16		20	115.68	even	4
575.3.d.g.551.7		10	115.114	odd	2
575.3.d.g.551.8		10	5.4	even	2
1035.3.g.b.91.7		10	3.2	odd	2
1035.3.g.b.91.8		10	69.68	even	2
1840.3.k.b.321.3		10	92.91	even	2
1840.3.k.b.321.4		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)

\(f(q)\)	\(=\)	\(q-2.67869 q^{2} +1.23330 q^{3} +3.17536 q^{4} +2.23607i q^{5} -3.30362 q^{6} -0.521669i q^{7} +2.20895 q^{8} -7.47898 q^{9} -5.98972i q^{10} +10.5914i q^{11} +3.91616 q^{12} +14.3029 q^{13} +1.39739i q^{14} +2.75774i q^{15} -18.6185 q^{16} +33.4342i q^{17} +20.0338 q^{18} +23.1053i q^{19} +7.10032i q^{20} -0.643373i q^{21} -28.3711i q^{22} +(22.5772 + 4.39000i) q^{23} +2.72429 q^{24} -5.00000 q^{25} -38.3131 q^{26} -20.3235 q^{27} -1.65649i q^{28} +11.7613 q^{29} -7.38711i q^{30} -17.8286 q^{31} +41.0374 q^{32} +13.0624i q^{33} -89.5597i q^{34} +1.16649 q^{35} -23.7485 q^{36} -57.2590i q^{37} -61.8920i q^{38} +17.6398 q^{39} +4.93936i q^{40} -33.7426 q^{41} +1.72339i q^{42} -53.7180i q^{43} +33.6316i q^{44} -16.7235i q^{45} +(-60.4771 - 11.7594i) q^{46} +14.0973 q^{47} -22.9622 q^{48} +48.7279 q^{49} +13.3934 q^{50} +41.2343i q^{51} +45.4170 q^{52} +85.7672i q^{53} +54.4402 q^{54} -23.6831 q^{55} -1.15234i q^{56} +28.4958i q^{57} -31.5049 q^{58} -70.7106 q^{59} +8.75681i q^{60} -31.8109i q^{61} +47.7571 q^{62} +3.90155i q^{63} -35.4522 q^{64} +31.9824i q^{65} -34.9900i q^{66} +39.4556i q^{67} +106.166i q^{68} +(27.8443 + 5.41418i) q^{69} -3.12465 q^{70} +68.9236 q^{71} -16.5207 q^{72} +30.3374 q^{73} +153.379i q^{74} -6.16649 q^{75} +73.3678i q^{76} +5.52521 q^{77} -47.2514 q^{78} -49.0126i q^{79} -41.6323i q^{80} +42.2459 q^{81} +90.3860 q^{82} -96.7624i q^{83} -2.04294i q^{84} -74.7611 q^{85} +143.894i q^{86} +14.5052 q^{87} +23.3959i q^{88} -56.7850i q^{89} +44.7970i q^{90} -7.46140i q^{91} +(71.6906 + 13.9398i) q^{92} -21.9879 q^{93} -37.7621 q^{94} -51.6651 q^{95} +50.6113 q^{96} +80.0997i q^{97} -130.527 q^{98} -79.2129i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 2 q^{3} + 34 q^{4} + 28 q^{6} - 20 q^{8} - 16 q^{9} - 24 q^{12} - 2 q^{13} - 38 q^{16} - 22 q^{18} + 44 q^{23} + 70 q^{24} - 50 q^{25} - 72 q^{26} + 40 q^{27} - 46 q^{29} + 16 q^{31} + 142 q^{32}+ \cdots + 388 q^{98}+O(q^{100}) \) 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

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