LMFDB - Embedded newform 1150.3.c.c.1149.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(1149,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1150.1149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1149.15
Character	$\chi$	$=$	1150.1149
Dual form			1150.3.c.c.1149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -3.36596i q^{3} -2.00000 q^{4} -4.76019 q^{6} +1.16919 q^{7} +2.82843i q^{8} -2.32968 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -3.36596i q^{3} -2.00000 q^{4} -4.76019 q^{6} +1.16919 q^{7} +2.82843i q^{8} -2.32968 q^{9} +10.6148i q^{11} +6.73192i q^{12} -15.0913i q^{13} -1.65348i q^{14} +4.00000 q^{16} +20.0887 q^{17} +3.29467i q^{18} -22.5221i q^{19} -3.93543i q^{21} +15.0116 q^{22} +(-9.45142 - 20.9683i) q^{23} +9.52037 q^{24} -21.3424 q^{26} -22.4520i q^{27} -2.33837 q^{28} -32.5993 q^{29} -27.0975 q^{31} -5.65685i q^{32} +35.7289 q^{33} -28.4097i q^{34} +4.65936 q^{36} -53.0568 q^{37} -31.8510 q^{38} -50.7968 q^{39} +9.43720 q^{41} -5.56554 q^{42} -36.4382 q^{43} -21.2296i q^{44} +(-29.6537 + 13.3663i) q^{46} +49.1365i q^{47} -13.4638i q^{48} -47.6330 q^{49} -67.6176i q^{51} +30.1827i q^{52} +104.253 q^{53} -31.7520 q^{54} +3.30696i q^{56} -75.8083 q^{57} +46.1023i q^{58} -53.5457 q^{59} -23.5166i q^{61} +38.3217i q^{62} -2.72383 q^{63} -8.00000 q^{64} -50.5284i q^{66} +59.4754 q^{67} -40.1773 q^{68} +(-70.5785 + 31.8131i) q^{69} +55.2130 q^{71} -6.58933i q^{72} -8.77305i q^{73} +75.0337i q^{74} +45.0441i q^{76} +12.4107i q^{77} +71.8376i q^{78} -57.0848i q^{79} -96.5397 q^{81} -13.3462i q^{82} +55.1788 q^{83} +7.87086i q^{84} +51.5314i q^{86} +109.728i q^{87} -30.0232 q^{88} -139.825i q^{89} -17.6446i q^{91} +(18.9028 + 41.9366i) q^{92} +91.2091i q^{93} +69.4894 q^{94} -19.0407 q^{96} -19.8635 q^{97} +67.3632i q^{98} -24.7291i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		−	3.36596i		−	1.12199i	−0.827820	−	0.560993i	$-0.810419\pi$
$3$		−	3.36596i		−	1.12199i	0.827820	−	0.560993i	$-0.189581\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−4.76019			−0.793364
$7$	1.16919			0.167026			0.0835132	−	0.996507i	$-0.473386\pi$
$7$	1.16919			0.167026			0.0835132	+	0.996507i	$0.473386\pi$
$8$			2.82843i			0.353553i
$9$	−2.32968			−0.258853
$10$		0			0
$11$			10.6148i			0.964981i	0.875901	+	0.482490i	$0.160268\pi$
$11$			10.6148i			0.964981i	−0.875901	+	0.482490i	$0.839732\pi$
$12$			6.73192i			0.560993i
$13$		−	15.0913i		−	1.16087i	−0.814306	−	0.580436i	$-0.802882\pi$
$13$		−	15.0913i		−	1.16087i	0.814306	−	0.580436i	$-0.197118\pi$
$14$		−	1.65348i		−	0.118106i
$15$		0			0
$16$	4.00000			0.250000
$17$	20.0887			1.18169			0.590843	−	0.806787i	$-0.298795\pi$
$17$	20.0887			1.18169			0.590843	+	0.806787i	$0.298795\pi$
$18$			3.29467i			0.183037i
$19$		−	22.5221i		−	1.18537i	−0.805434	−	0.592686i	$-0.798068\pi$
$19$		−	22.5221i		−	1.18537i	0.805434	−	0.592686i	$-0.201932\pi$
$20$		0			0
$21$		−	3.93543i		−	0.187401i
$22$	15.0116			0.682344
$23$	−9.45142	−	20.9683i	−0.410931	−	0.911666i
$23$	−9.45142	−	20.9683i	−0.410931	−	0.911666i
$24$	9.52037			0.396682
$25$		0			0
$26$	−21.3424			−0.820860
$27$		−	22.4520i		−	0.831556i
$28$	−2.33837			−0.0835132
$29$	−32.5993			−1.12411			−0.562056	−	0.827099i	$-0.689990\pi$
$29$	−32.5993			−1.12411			−0.562056	+	0.827099i	$0.689990\pi$
$30$		0			0
$31$	−27.0975			−0.874113			−0.437056	−	0.899434i	$-0.643979\pi$
$31$	−27.0975			−0.874113			−0.437056	+	0.899434i	$0.643979\pi$
$32$		−	5.65685i		−	0.176777i
$33$	35.7289			1.08270
$34$		−	28.4097i		−	0.835578i
$35$		0			0
$36$	4.65936			0.129427
$37$	−53.0568			−1.43397			−0.716984	−	0.697089i	$-0.754478\pi$
$37$	−53.0568			−1.43397			−0.716984	+	0.697089i	$0.754478\pi$
$38$	−31.8510			−0.838184
$39$	−50.7968			−1.30248
$40$		0			0
$41$	9.43720			0.230176			0.115088	−	0.993355i	$-0.463285\pi$
$41$	9.43720			0.230176			0.115088	+	0.993355i	$0.463285\pi$
$42$	−5.56554			−0.132513
$43$	−36.4382			−0.847400			−0.423700	−	0.905802i	$-0.639269\pi$
$43$	−36.4382			−0.847400			−0.423700	+	0.905802i	$0.639269\pi$
$44$		−	21.2296i		−	0.482490i
$45$		0			0
$46$	−29.6537	+	13.3663i	−0.644645	+	0.290572i
$47$			49.1365i			1.04546i	0.852499	+	0.522728i	$0.175086\pi$
$47$			49.1365i			1.04546i	−0.852499	+	0.522728i	$0.824914\pi$
$48$		−	13.4638i		−	0.280497i
$49$	−47.6330			−0.972102
$50$		0			0
$51$		−	67.6176i		−	1.32584i
$52$			30.1827i			0.580436i
$53$	104.253			1.96703			0.983517	−	0.180815i	$-0.0578736\pi$
$53$	104.253			1.96703			0.983517	+	0.180815i	$0.0578736\pi$
$54$	−31.7520			−0.587999
$55$		0			0
$56$			3.30696i			0.0590528i
$57$	−75.8083			−1.32997
$58$			46.1023i			0.794868i
$59$	−53.5457			−0.907554			−0.453777	−	0.891115i	$-0.649924\pi$
$59$	−53.5457			−0.907554			−0.453777	+	0.891115i	$0.649924\pi$
$60$		0			0
$61$		−	23.5166i		−	0.385518i	−0.981246	−	0.192759i	$-0.938257\pi$
$61$		−	23.5166i		−	0.385518i	0.981246	−	0.192759i	$-0.0617435\pi$
$62$			38.3217i			0.618091i
$63$	−2.72383			−0.0432354
$64$	−8.00000			−0.125000
$65$		0			0
$66$		−	50.5284i		−	0.765581i
$67$	59.4754			0.887692			0.443846	−	0.896103i	$-0.353614\pi$
$67$	59.4754			0.887692			0.443846	+	0.896103i	$0.353614\pi$
$68$	−40.1773			−0.590843
$69$	−70.5785	+	31.8131i	−1.02288	+	0.461060i
$70$		0			0
$71$	55.2130			0.777648			0.388824	−	0.921312i	$-0.372881\pi$
$71$	55.2130			0.777648			0.388824	+	0.921312i	$0.372881\pi$
$72$		−	6.58933i		−	0.0915185i
$73$		−	8.77305i		−	0.120179i	−0.998193	−	0.0600894i	$-0.980861\pi$
$73$		−	8.77305i		−	0.120179i	0.998193	−	0.0600894i	$-0.0191386\pi$
$74$			75.0337i			1.01397i
$75$		0			0
$76$			45.0441i			0.592686i
$77$			12.4107i			0.161177i
$78$			71.8376i			0.920994i
$79$		−	57.0848i		−	0.722592i	−0.932451	−	0.361296i	$-0.882334\pi$
$79$		−	57.0848i		−	0.722592i	0.932451	−	0.361296i	$-0.117666\pi$
$80$		0			0
$81$	−96.5397			−1.19185
$82$		−	13.3462i		−	0.162759i
$83$	55.1788			0.664805			0.332403	−	0.943138i	$-0.392141\pi$
$83$	55.1788			0.664805			0.332403	+	0.943138i	$0.392141\pi$
$84$			7.87086i			0.0937007i
$85$		0			0
$86$			51.5314i			0.599203i
$87$			109.728i			1.26124i
$88$	−30.0232			−0.341172
$89$		−	139.825i		−	1.57107i	−0.618815	−	0.785536i	$-0.712387\pi$
$89$		−	139.825i		−	1.57107i	0.618815	−	0.785536i	$-0.287613\pi$
$90$		0			0
$91$		−	17.6446i		−	0.193896i
$92$	18.9028	+	41.9366i	0.205466	+	0.455833i
$93$			91.2091i			0.980743i
$94$	69.4894			0.739249
$95$		0			0
$96$	−19.0407			−0.198341
$97$	−19.8635			−0.204778			−0.102389	−	0.994744i	$-0.532649\pi$
$97$	−19.8635			−0.204778			−0.102389	+	0.994744i	$0.532649\pi$
$98$			67.3632i			0.687380i
$99$		−	24.7291i		−	0.249789i
$100$		0			0
$101$	86.5639			0.857068			0.428534	−	0.903526i	$-0.359030\pi$
$101$	86.5639			0.857068			0.428534	+	0.903526i	$0.359030\pi$
$102$	−95.6258			−0.937507
$103$	−144.118			−1.39920			−0.699600	−	0.714535i	$-0.746639\pi$
$103$	−144.118			−1.39920			−0.699600	+	0.714535i	$0.746639\pi$
$104$	42.6847			0.410430
$105$		0			0
$106$		−	147.436i		−	1.39090i
$107$	−10.4544			−0.0977050			−0.0488525	−	0.998806i	$-0.515556\pi$
$107$	−10.4544			−0.0977050			−0.0488525	+	0.998806i	$0.515556\pi$
$108$			44.9040i			0.415778i
$109$			69.1221i			0.634148i	0.948401	+	0.317074i	$0.102700\pi$
$109$			69.1221i			0.634148i	−0.948401	+	0.317074i	$0.897300\pi$
$110$		0			0
$111$			178.587i			1.60889i
$112$	4.67674			0.0417566
$113$	−137.264			−1.21473			−0.607364	−	0.794423i	$-0.707773\pi$
$113$	−137.264			−1.21473			−0.607364	+	0.794423i	$0.707773\pi$
$114$			107.209i			0.940431i
$115$		0			0
$116$	65.1985			0.562056
$117$			35.1580i			0.300496i
$118$			75.7250i			0.641738i
$119$	23.4874			0.197373
$120$		0			0
$121$	8.32629			0.0688123
$122$	−33.2575			−0.272602
$123$		−	31.7652i		−	0.258254i
$124$	54.1950			0.437056
$125$		0			0
$126$			3.85208i			0.0305720i
$127$		−	57.9697i		−	0.456455i	−0.973608	−	0.228227i	$-0.926707\pi$
$127$		−	57.9697i		−	0.456455i	0.973608	−	0.228227i	$-0.0732929\pi$
$128$			11.3137i			0.0883883i
$129$			122.650i			0.950772i
$130$		0			0
$131$	−95.0810			−0.725809			−0.362905	−	0.931826i	$-0.618215\pi$
$131$	−95.0810			−0.725809			−0.362905	+	0.931826i	$0.618215\pi$
$132$	−71.4579			−0.541348
$133$		−	26.3325i		−	0.197988i
$134$		−	84.1109i		−	0.627693i
$135$		0			0
$136$			56.8193i			0.417789i
$137$	−198.711			−1.45045			−0.725223	−	0.688514i	$-0.758263\pi$
$137$	−198.711			−1.45045			−0.725223	+	0.688514i	$0.758263\pi$
$138$	44.9905	+	99.8131i	0.326018	+	0.723283i
$139$	0.129480			0.000931508			0.000465754	−	1.00000i	$-0.499852\pi$
$139$	0.129480			0.000931508			0.000465754		1.00000i	$0.499852\pi$
$140$		0			0
$141$	165.391			1.17299
$142$		−	78.0830i		−	0.549880i
$143$	160.191			1.12022
$144$	−9.31873			−0.0647134
$145$		0			0
$146$	−12.4070			−0.0849792
$147$			160.331i			1.09069i
$148$	106.114			0.716984
$149$			63.8745i			0.428688i	0.976758	+	0.214344i	$0.0687613\pi$
$149$			63.8745i			0.428688i	−0.976758	+	0.214344i	$0.931239\pi$
$150$		0			0
$151$	−35.2673			−0.233558			−0.116779	−	0.993158i	$-0.537257\pi$
$151$	−35.2673			−0.233558			−0.116779	+	0.993158i	$0.537257\pi$
$152$	63.7020			0.419092
$153$	−46.8002			−0.305884
$154$	17.5513			0.113970
$155$		0			0
$156$	101.594			0.651241
$157$	289.136			1.84163			0.920814	−	0.390002i	$-0.127526\pi$
$157$	289.136			1.84163			0.920814	+	0.390002i	$0.127526\pi$
$158$	−80.7300			−0.510950
$159$		−	350.911i		−	2.20699i
$160$		0			0
$161$	−11.0505	−	24.5159i	−0.0686364	−	0.152272i
$162$			136.528i			0.842764i
$163$		−	46.2536i		−	0.283764i	−0.989884	−	0.141882i	$-0.954685\pi$
$163$		−	46.2536i		−	0.283764i	0.989884	−	0.141882i	$-0.0453154\pi$
$164$	−18.8744			−0.115088
$165$		0			0
$166$		−	78.0346i		−	0.470088i
$167$			90.8735i			0.544153i	0.962276	+	0.272076i	$0.0877103\pi$
$167$			90.8735i			0.544153i	−0.962276	+	0.272076i	$0.912290\pi$
$168$	11.1311			0.0662564
$169$	−58.7484			−0.347624
$170$		0			0
$171$			52.4692i			0.306837i
$172$	72.8764			0.423700
$173$		−	90.7893i		−	0.524794i	−0.964960	−	0.262397i	$-0.915487\pi$
$173$		−	90.7893i		−	0.524794i	0.964960	−	0.262397i	$-0.0845129\pi$
$174$	155.179			0.891831
$175$		0			0
$176$			42.4591i			0.241245i
$177$			180.233i			1.01826i
$178$	−197.743			−1.11092
$179$	−301.636			−1.68511			−0.842557	−	0.538607i	$-0.818951\pi$
$179$	−301.636			−1.68511			−0.842557	+	0.538607i	$0.818951\pi$
$180$		0			0
$181$			248.547i			1.37319i	0.727040	+	0.686595i	$0.240895\pi$
$181$			248.547i			1.37319i	−0.727040	+	0.686595i	$0.759105\pi$
$182$	−24.9532			−0.137105
$183$	−79.1558			−0.432546
$184$	59.3074	−	26.7327i	0.322323	−	0.145286i
$185$		0			0
$186$	128.989			0.693490
$187$			213.237i			1.14030i
$188$		−	98.2729i		−	0.522728i
$189$		−	26.2506i		−	0.138892i
$190$		0			0
$191$			146.382i			0.766397i	0.923666	+	0.383199i	$0.125178\pi$
$191$			146.382i			0.766397i	−0.923666	+	0.383199i	$0.874822\pi$
$192$			26.9277i			0.140248i
$193$		−	120.648i		−	0.625120i	−0.949898	−	0.312560i	$-0.898813\pi$
$193$		−	120.648i		−	0.625120i	0.949898	−	0.312560i	$-0.101187\pi$
$194$			28.0912i			0.144800i
$195$		0			0
$196$	95.2660			0.486051
$197$		−	31.6502i		−	0.160661i	−0.996768	−	0.0803305i	$-0.974402\pi$
$197$		−	31.6502i		−	0.160661i	0.996768	−	0.0803305i	$-0.0255976\pi$
$198$	−34.9722			−0.176627
$199$		−	37.4496i		−	0.188189i	−0.995563	−	0.0940944i	$-0.970004\pi$
$199$		−	37.4496i		−	0.188189i	0.995563	−	0.0940944i	$-0.0299955\pi$
$200$		0			0
$201$		−	200.192i		−	0.995979i
$202$		−	122.420i		−	0.606039i
$203$	−38.1146			−0.187757
$204$			135.235i			0.662918i
$205$		0			0
$206$			203.813i			0.989384i
$207$	22.0188	+	48.8495i	0.106371	+	0.235988i
$208$		−	60.3653i		−	0.290218i
$209$	239.067			1.14386
$210$		0			0
$211$	−43.6572			−0.206906			−0.103453	−	0.994634i	$-0.532989\pi$
$211$	−43.6572			−0.206906			−0.103453	+	0.994634i	$0.532989\pi$
$212$	−208.506			−0.983517
$213$		−	185.845i		−	0.872510i
$214$			14.7848i			0.0690879i
$215$		0			0
$216$	63.5039			0.294000
$217$	−31.6820			−0.146000
$218$	97.7535			0.448410
$219$	−29.5297			−0.134839
$220$		0			0
$221$		−	303.165i		−	1.37179i
$222$	252.560			1.13766
$223$			348.623i			1.56333i	0.623697	+	0.781666i	$0.285630\pi$
$223$			348.623i			1.56333i	−0.623697	+	0.781666i	$0.714370\pi$
$224$		−	6.61391i		−	0.0295264i
$225$		0			0
$226$			194.121i			0.858943i
$227$	175.793			0.774421			0.387210	−	0.921991i	$-0.373439\pi$
$227$	175.793			0.774421			0.387210	+	0.921991i	$0.373439\pi$
$228$	151.617			0.664985
$229$		−	1.44148i		−	0.00629466i	−0.999995	−	0.00314733i	$-0.998998\pi$
$229$		−	1.44148i		−	0.00629466i	0.999995	−	0.00314733i	$-0.00100183\pi$
$230$		0			0
$231$	41.7738			0.180839
$232$		−	92.2047i		−	0.397434i
$233$		−	113.416i		−	0.486763i	−0.969931	−	0.243381i	$-0.921743\pi$
$233$		−	113.416i		−	0.486763i	0.969931	−	0.243381i	$-0.0782567\pi$
$234$	49.7209			0.212483
$235$		0			0
$236$	107.091			0.453777
$237$	−192.145			−0.810738
$238$		−	33.2162i		−	0.139564i
$239$	−367.260			−1.53665			−0.768326	−	0.640059i	$-0.778910\pi$
$239$	−367.260			−1.53665			−0.768326	+	0.640059i	$0.778910\pi$
$240$		0			0
$241$			220.365i			0.914378i	0.889370	+	0.457189i	$0.151144\pi$
$241$			220.365i			0.914378i	−0.889370	+	0.457189i	$0.848856\pi$
$242$		−	11.7752i		−	0.0486577i
$243$			122.881i			0.505681i
$244$			47.0332i			0.192759i
$245$		0			0
$246$	−44.9228			−0.182613
$247$	−339.888			−1.37606
$248$		−	76.6433i		−	0.309046i
$249$		−	185.730i		−	0.745902i
$250$		0			0
$251$		−	440.210i		−	1.75382i	−0.480650	−	0.876912i	$-0.659599\pi$
$251$		−	440.210i		−	1.75382i	0.480650	−	0.876912i	$-0.340401\pi$
$252$	5.44766			0.0216177
$253$	222.574	−	100.325i	0.879740	−	0.396541i
$254$	−81.9816			−0.322762
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	491.519i		−	1.91252i	−0.292512	−	0.956262i	$-0.594491\pi$
$257$		−	491.519i		−	1.91252i	0.292512	−	0.956262i	$-0.405509\pi$
$258$	173.453			0.672297
$259$	−62.0333			−0.239511
$260$		0			0
$261$	75.9459			0.290980
$262$			134.465i			0.513225i
$263$	267.833			1.01838			0.509189	−	0.860655i	$-0.329946\pi$
$263$	267.833			1.01838			0.509189	+	0.860655i	$0.329946\pi$
$264$			101.057i			0.382791i
$265$		0			0
$266$	−37.2397			−0.139999
$267$	−470.647			−1.76272
$268$	−118.951			−0.443846
$269$	−95.6985			−0.355756			−0.177878	−	0.984053i	$-0.556923\pi$
$269$	−95.6985			−0.355756			−0.177878	+	0.984053i	$0.556923\pi$
$270$		0			0
$271$	−452.255			−1.66884			−0.834419	−	0.551131i	$-0.814197\pi$
$271$	−452.255			−1.66884			−0.834419	+	0.551131i	$0.814197\pi$
$272$	80.3547			0.295422
$273$	−59.3909			−0.217549
$274$			281.020i			1.02562i
$275$		0			0
$276$	141.157	−	63.6262i	0.511439	−	0.230530i
$277$			87.4783i			0.315806i	0.987455	+	0.157903i	$0.0504734\pi$
$277$			87.4783i			0.315806i	−0.987455	+	0.157903i	$0.949527\pi$
$278$		−	0.183112i		−	0.000658676i
$279$	63.1285			0.226267
$280$		0			0
$281$		−	232.157i		−	0.826183i	−0.910690	−	0.413091i	$-0.864449\pi$
$281$		−	232.157i		−	0.826183i	0.910690	−	0.413091i	$-0.135551\pi$
$282$		−	233.899i		−	0.829428i
$283$	−239.367			−0.845820			−0.422910	−	0.906172i	$-0.638991\pi$
$283$	−239.367			−0.845820			−0.422910	+	0.906172i	$0.638991\pi$
$284$	−110.426			−0.388824
$285$		0			0
$286$		−	226.545i		−	0.792114i
$287$	11.0338			0.0384454
$288$			13.1787i			0.0457593i
$289$	114.554			0.396382
$290$		0			0
$291$			66.8597i			0.229758i
$292$			17.5461i			0.0600894i
$293$	581.830			1.98577			0.992883	−	0.119092i	$-0.0379984\pi$
$293$	581.830			1.98577			0.992883	+	0.119092i	$0.0379984\pi$
$294$	226.742			0.771231
$295$		0			0
$296$		−	150.067i		−	0.506984i
$297$	238.323			0.802436
$298$	90.3322			0.303128
$299$	−316.440	+	142.635i	−1.05833	+	0.477039i
$300$		0			0
$301$	−42.6030			−0.141538
$302$			49.8755i			0.165151i
$303$		−	291.370i		−	0.961619i
$304$		−	90.0882i		−	0.296343i
$305$		0			0
$306$			66.1855i			0.216292i
$307$		−	110.134i		−	0.358742i	−0.983782	−	0.179371i	$-0.942594\pi$
$307$		−	110.134i		−	0.358742i	0.983782	−	0.179371i	$-0.0574062\pi$
$308$		−	24.8213i		−	0.0805887i
$309$			485.094i			1.56988i
$310$		0			0
$311$	−298.100			−0.958520			−0.479260	−	0.877673i	$-0.659095\pi$
$311$	−298.100			−0.958520			−0.479260	+	0.877673i	$0.659095\pi$
$312$		−	143.675i		−	0.460497i
$313$	109.474			0.349758			0.174879	−	0.984590i	$-0.444047\pi$
$313$	109.474			0.349758			0.174879	+	0.984590i	$0.444047\pi$
$314$		−	408.900i		−	1.30223i
$315$		0			0
$316$			114.170i			0.361296i
$317$		−	474.434i		−	1.49664i	−0.663340	−	0.748318i	$-0.730862\pi$
$317$		−	474.434i		−	1.49664i	0.663340	−	0.748318i	$-0.269138\pi$
$318$	−496.263			−1.56057
$319$		−	346.034i		−	1.08475i
$320$		0			0
$321$			35.1892i			0.109624i
$322$	−34.6707	+	15.6277i	−0.107673	+	0.0485333i
$323$		−	452.438i		−	1.40074i
$324$	193.079			0.595924
$325$		0			0
$326$	−65.4124			−0.200652
$327$	232.662			0.711506
$328$			26.6924i			0.0813794i
$329$			57.4496i			0.174619i
$330$		0			0
$331$	255.367			0.771503			0.385751	−	0.922603i	$-0.373942\pi$
$331$	255.367			0.771503			0.385751	+	0.922603i	$0.373942\pi$
$332$	−110.358			−0.332403
$333$	123.606			0.371188
$334$	128.515			0.384774
$335$		0			0
$336$		−	15.7417i		−	0.0468504i
$337$	458.486			1.36049			0.680247	−	0.732983i	$-0.261873\pi$
$337$	458.486			1.36049			0.680247	+	0.732983i	$0.261873\pi$
$338$			83.0828i			0.245807i
$339$			462.026i			1.36291i
$340$		0			0
$341$		−	287.634i		−	0.843502i
$342$	74.2027			0.216967
$343$	−112.982			−0.329393
$344$		−	103.063i		−	0.299601i
$345$		0			0
$346$	−128.395			−0.371085
$347$		−	510.676i		−	1.47169i	−0.677151	−	0.735845i	$-0.736785\pi$
$347$		−	510.676i		−	1.47169i	0.677151	−	0.735845i	$-0.263215\pi$
$348$		−	219.456i		−	0.630620i
$349$	591.870			1.69590			0.847951	−	0.530075i	$-0.177836\pi$
$349$	591.870			1.69590			0.847951	+	0.530075i	$0.177836\pi$
$350$		0			0
$351$	−338.831			−0.965330
$352$	60.0463			0.170586
$353$			168.334i			0.476866i	0.971159	+	0.238433i	$0.0766337\pi$
$353$			168.334i			0.476866i	−0.971159	+	0.238433i	$0.923366\pi$
$354$	254.887			0.720021
$355$		0			0
$356$			279.651i			0.785536i
$357$		−	79.0575i		−	0.221450i
$358$			426.577i			1.19156i
$359$		−	37.5719i		−	0.104657i	−0.998630	−	0.0523285i	$-0.983336\pi$
$359$		−	37.5719i		−	0.104657i	0.998630	−	0.0523285i	$-0.0166643\pi$
$360$		0			0
$361$	−146.243			−0.405105
$362$	351.499			0.970992
$363$		−	28.0260i		−	0.0772065i
$364$			35.2891i			0.0969482i
$365$		0			0
$366$			111.943i			0.305856i
$367$	427.036			1.16359			0.581793	−	0.813337i	$-0.302351\pi$
$367$	427.036			1.16359			0.581793	+	0.813337i	$0.302351\pi$
$368$	−37.8057	−	83.8733i	−0.102733	−	0.227917i
$369$	−21.9857			−0.0595818
$370$		0			0
$371$	121.891			0.328547
$372$		−	182.418i		−	0.490371i
$373$	−369.980			−0.991904			−0.495952	−	0.868350i	$-0.665181\pi$
$373$	−369.980			−0.991904			−0.495952	+	0.868350i	$0.665181\pi$
$374$	301.563			0.806317
$375$		0			0
$376$	−138.979			−0.369625
$377$			491.966i			1.30495i
$378$	−37.1239			−0.0982114
$379$		−	78.8009i		−	0.207918i	−0.994582	−	0.103959i	$-0.966849\pi$
$379$		−	78.8009i		−	0.207918i	0.994582	−	0.103959i	$-0.0331511\pi$
$380$		0			0
$381$	−195.124			−0.512136
$382$	207.015			0.541925
$383$	−254.083			−0.663403			−0.331702	−	0.943384i	$-0.607623\pi$
$383$	−254.083			−0.663403			−0.331702	+	0.943384i	$0.607623\pi$
$384$	38.0815			0.0991705
$385$		0			0
$386$	−170.622			−0.442027
$387$	84.8894			0.219353
$388$	39.7270			0.102389
$389$			322.363i			0.828698i	0.910118	+	0.414349i	$0.135991\pi$
$389$			322.363i			0.828698i	−0.910118	+	0.414349i	$0.864009\pi$
$390$		0			0
$391$	−189.866	−	421.226i	−0.485592	−	1.07730i
$392$		−	134.726i		−	0.343690i
$393$			320.039i			0.814348i
$394$	−44.7602			−0.113605
$395$		0			0
$396$			49.4581i			0.124894i
$397$		−	715.832i		−	1.80310i	−0.432671	−	0.901552i	$-0.642429\pi$
$397$		−	715.832i		−	1.80310i	0.432671	−	0.901552i	$-0.357571\pi$
$398$	−52.9617			−0.133070
$399$	−88.6340			−0.222140
$400$		0			0
$401$			441.435i			1.10083i	0.834890	+	0.550417i	$0.185531\pi$
$401$			441.435i			1.10083i	−0.834890	+	0.550417i	$0.814469\pi$
$402$	−283.114			−0.704263
$403$			408.937i			1.01473i
$404$	−173.128			−0.428534
$405$		0			0
$406$			53.9022i			0.132764i
$407$		−	563.187i		−	1.38375i
$408$	191.252			0.468754
$409$	608.727			1.48833			0.744164	−	0.667996i	$-0.232848\pi$
$409$	608.727			1.48833			0.744164	+	0.667996i	$0.232848\pi$
$410$		0			0
$411$			668.853i			1.62738i
$412$	288.235			0.699600
$413$	−62.6048			−0.151586
$414$	69.0836	−	31.1393i	0.166869	−	0.0752157i
$415$		0			0
$416$	−85.3695			−0.205215
$417$		−	0.435823i		−	0.00104514i
$418$		−	338.091i		−	0.808831i
$419$			287.454i			0.686047i	0.939327	+	0.343023i	$0.111451\pi$
$419$			287.454i			0.686047i	−0.939327	+	0.343023i	$0.888549\pi$
$420$		0			0
$421$		−	130.848i		−	0.310803i	−0.987851	−	0.155402i	$-0.950333\pi$
$421$		−	130.848i		−	0.310803i	0.987851	−	0.155402i	$-0.0496672\pi$
$422$			61.7406i			0.146305i
$423$		−	114.472i		−	0.270620i
$424$			294.871i			0.695452i
$425$		0			0
$426$	−262.824			−0.616958
$427$		−	27.4952i		−	0.0643917i
$428$	20.9089			0.0488525
$429$		−	539.197i		−	1.25687i
$430$		0			0
$431$		−	239.816i		−	0.556417i	−0.960521	−	0.278209i	$-0.910259\pi$
$431$		−	239.816i		−	0.556417i	0.960521	−	0.278209i	$-0.0897406\pi$
$432$		−	89.8081i		−	0.207889i
$433$	305.542			0.705640			0.352820	−	0.935691i	$-0.385223\pi$
$433$	305.542			0.705640			0.352820	+	0.935691i	$0.385223\pi$
$434$			44.8051i			0.103238i
$435$		0			0
$436$		−	138.244i		−	0.317074i
$437$	−472.250	+	212.865i	−1.08066	+	0.487106i
$438$			41.7613i			0.0953455i
$439$	579.018			1.31895			0.659474	−	0.751727i	$-0.270779\pi$
$439$	579.018			1.31895			0.659474	+	0.751727i	$0.270779\pi$
$440$		0			0
$441$	110.970			0.251632
$442$	−428.740			−0.969999
$443$		−	606.274i		−	1.36856i	−0.729217	−	0.684282i	$-0.760116\pi$
$443$		−	606.274i		−	1.36856i	0.729217	−	0.684282i	$-0.239884\pi$
$444$		−	357.174i		−	0.804446i
$445$		0			0
$446$	493.028			1.10544
$447$	214.999			0.480982
$448$	−9.35348			−0.0208783
$449$	202.580			0.451181			0.225590	−	0.974222i	$-0.427569\pi$
$449$	202.580			0.451181			0.225590	+	0.974222i	$0.427569\pi$
$450$		0			0
$451$			100.174i			0.222115i
$452$	274.529			0.607364
$453$			118.708i			0.262049i
$454$		−	248.609i		−	0.547598i
$455$		0			0
$456$		−	214.418i		−	0.470215i
$457$	373.760			0.817857			0.408928	−	0.912567i	$-0.365903\pi$
$457$	373.760			0.817857			0.408928	+	0.912567i	$0.365903\pi$
$458$	−2.03856			−0.00445100
$459$		−	451.031i		−	0.982639i
$460$		0			0
$461$	709.377			1.53878			0.769390	−	0.638780i	$-0.220561\pi$
$461$	709.377			1.53878			0.769390	+	0.638780i	$0.220561\pi$
$462$		−	59.0770i		−	0.127872i
$463$			266.488i			0.575569i	0.957695	+	0.287785i	$0.0929187\pi$
$463$			266.488i			0.575569i	−0.957695	+	0.287785i	$0.907081\pi$
$464$	−130.397			−0.281028
$465$		0			0
$466$	−160.394			−0.344193
$467$	686.135			1.46924			0.734620	−	0.678479i	$-0.237361\pi$
$467$	686.135			1.46924			0.734620	+	0.678479i	$0.237361\pi$
$468$		−	70.3160i		−	0.150248i
$469$	69.5378			0.148268
$470$		0			0
$471$		−	973.219i		−	2.06628i
$472$		−	151.450i		−	0.320869i
$473$		−	386.784i		−	0.817725i
$474$			271.734i			0.573279i
$475$		0			0
$476$	−46.9747			−0.0986864
$477$	−242.876			−0.509174
$478$			519.384i			1.08658i
$479$			176.517i			0.368511i	0.982878	+	0.184256i	$0.0589874\pi$
$479$			176.517i			0.368511i	−0.982878	+	0.184256i	$0.941013\pi$
$480$		0			0
$481$			800.698i			1.66465i
$482$	311.643			0.646563
$483$	−82.5194	+	37.1954i	−0.170848	+	0.0770091i
$484$	−16.6526			−0.0344062
$485$		0			0
$486$	173.779			0.357571
$487$		−	524.802i		−	1.07762i	−0.842427	−	0.538811i	$-0.818874\pi$
$487$		−	524.802i		−	1.07762i	0.842427	−	0.538811i	$-0.181126\pi$
$488$	66.5149			0.136301
$489$	−155.688			−0.318380
$490$		0			0
$491$	−551.047			−1.12229			−0.561147	−	0.827716i	$-0.689640\pi$
$491$	−551.047			−1.12229			−0.561147	+	0.827716i	$0.689640\pi$
$492$			63.5304i			0.129127i
$493$	−654.876			−1.32835
$494$			480.674i			0.973024i
$495$		0			0
$496$	−108.390			−0.218528
$497$	64.5542			0.129888
$498$	−262.661			−0.527433
$499$	736.739			1.47643			0.738216	−	0.674565i	$-0.235669\pi$
$499$	736.739			1.47643			0.738216	+	0.674565i	$0.235669\pi$
$500$		0			0
$501$	305.876			0.610532
$502$	−622.551			−1.24014
$503$	−699.308			−1.39027			−0.695137	−	0.718877i	$-0.744656\pi$
$503$	−699.308			−1.39027			−0.695137	+	0.718877i	$0.744656\pi$
$504$		−	7.70415i		−	0.0152860i
$505$		0			0
$506$	−141.881	−	314.768i	−0.280397	−	0.622070i
$507$			197.745i			0.390029i
$508$			115.939i			0.228227i
$509$	316.428			0.621666			0.310833	−	0.950464i	$-0.399392\pi$
$509$	316.428			0.621666			0.310833	+	0.950464i	$0.399392\pi$
$510$		0			0
$511$		−	10.2573i		−	0.0200730i
$512$		−	22.6274i		−	0.0441942i
$513$	−505.666			−0.985703
$514$	−695.112			−1.35236
$515$		0			0
$516$		−	245.299i		−	0.475386i
$517$	−521.573			−1.00885
$518$			87.7283i			0.169360i
$519$	−305.593			−0.588811
$520$		0			0
$521$			798.875i			1.53335i	0.642035	+	0.766675i	$0.278090\pi$
$521$			798.875i			1.53335i	−0.642035	+	0.766675i	$0.721910\pi$
$522$		−	107.404i		−	0.205754i
$523$	819.091			1.56614			0.783070	−	0.621934i	$-0.213653\pi$
$523$	819.091			1.56614			0.783070	+	0.621934i	$0.213653\pi$
$524$	190.162			0.362905
$525$		0			0
$526$		−	378.773i		−	0.720101i
$527$	−544.353			−1.03293
$528$	142.916			0.270674
$529$	−350.341	+	396.361i	−0.662271	+	0.749265i
$530$		0			0
$531$	124.744			0.234924
$532$			52.6649i			0.0989942i
$533$		−	142.420i		−	0.267204i
$534$			665.595i			1.24643i
$535$		0			0
$536$			168.222i			0.313847i
$537$			1015.29i			1.89068i
$538$			135.338i			0.251558i
$539$		−	505.614i		−	0.938060i
$540$		0			0
$541$	289.616			0.535335			0.267668	−	0.963511i	$-0.413747\pi$
$541$	289.616			0.535335			0.267668	+	0.963511i	$0.413747\pi$
$542$			639.585i			1.18005i
$543$	836.600			1.54070
$544$		−	113.639i		−	0.208895i
$545$		0			0
$546$			83.9914i			0.153830i
$547$		−	996.117i		−	1.82106i	−0.413448	−	0.910528i	$-0.635676\pi$
$547$		−	996.117i		−	1.82106i	0.413448	−	0.910528i	$-0.364324\pi$
$548$	397.422			0.725223
$549$			54.7861i			0.0997926i
$550$		0			0
$551$			734.202i			1.33249i
$552$	−89.9811	−	199.626i	−0.163009	−	0.361642i
$553$		−	66.7427i		−	0.120692i
$554$	123.713			0.223309
$555$		0			0
$556$	−0.258959			−0.000465754
$557$	937.756			1.68358			0.841792	−	0.539802i	$-0.181501\pi$
$557$	937.756			1.68358			0.841792	+	0.539802i	$0.181501\pi$
$558$		−	89.2772i		−	0.159995i
$559$			549.901i			0.983723i
$560$		0			0
$561$	717.747			1.27941
$562$	−328.320			−0.584200
$563$	785.252			1.39476			0.697382	−	0.716700i	$-0.254348\pi$
$563$	785.252			1.39476			0.697382	+	0.716700i	$0.254348\pi$
$564$	−330.783			−0.586494
$565$		0			0
$566$			338.516i			0.598085i
$567$	−112.873			−0.199070
$568$			156.166i			0.274940i
$569$		−	403.851i		−	0.709755i	−0.934913	−	0.354877i	$-0.884523\pi$
$569$		−	403.851i		−	0.709755i	0.934913	−	0.354877i	$-0.115477\pi$
$570$		0			0
$571$		−	335.474i		−	0.587519i	−0.955879	−	0.293760i	$-0.905093\pi$
$571$		−	335.474i		−	0.587519i	0.955879	−	0.293760i	$-0.0949065\pi$
$572$	−320.383			−0.560110
$573$	492.715			0.859887
$574$		−	15.6042i		−	0.0271850i
$575$		0			0
$576$	18.6375			0.0323567
$577$			152.703i			0.264649i	0.991206	+	0.132325i	$0.0422441\pi$
$577$			152.703i			0.264649i	−0.991206	+	0.132325i	$0.957756\pi$
$578$		−	162.004i		−	0.280284i
$579$	−406.097			−0.701376
$580$		0			0
$581$	64.5143			0.111040
$582$	94.5538			0.162464
$583$			1106.62i			1.89815i
$584$	24.8139			0.0424896
$585$		0			0
$586$		−	822.831i		−	1.40415i
$587$		−	129.262i		−	0.220207i	−0.993920	−	0.110104i	$-0.964882\pi$
$587$		−	129.262i		−	0.220207i	0.993920	−	0.110104i	$-0.0351183\pi$
$588$		−	320.662i		−	0.545343i
$589$			610.291i			1.03615i
$590$		0			0
$591$	−106.533			−0.180260
$592$	−212.227			−0.358492
$593$		−	879.853i		−	1.48373i	−0.670548	−	0.741866i	$-0.733941\pi$
$593$		−	879.853i		−	1.48373i	0.670548	−	0.741866i	$-0.266059\pi$
$594$		−	337.040i		−	0.567408i
$595$		0			0
$596$		−	127.749i		−	0.214344i
$597$	−126.054			−0.211145
$598$	201.716	+	447.514i	0.337317	+	0.748351i
$599$	709.708			1.18482			0.592411	−	0.805636i	$-0.298176\pi$
$599$	709.708			1.18482			0.592411	+	0.805636i	$0.298176\pi$
$600$		0			0
$601$	238.861			0.397439			0.198719	−	0.980056i	$-0.436322\pi$
$601$	238.861			0.397439			0.198719	+	0.980056i	$0.436322\pi$
$602$			60.2498i			0.100083i
$603$	−138.559			−0.229782
$604$	70.5346			0.116779
$605$		0			0
$606$	−412.060			−0.679967
$607$			1082.53i			1.78341i	0.452621	+	0.891703i	$0.350489\pi$
$607$			1082.53i			1.78341i	−0.452621	+	0.891703i	$0.649511\pi$
$608$	−127.404			−0.209546
$609$			128.292i			0.210660i
$610$		0			0
$611$	741.535			1.21364
$612$	93.6004			0.152942
$613$	−54.0902			−0.0882384			−0.0441192	−	0.999026i	$-0.514048\pi$
$613$	−54.0902			−0.0882384			−0.0441192	+	0.999026i	$0.514048\pi$
$614$	−155.753			−0.253669
$615$		0			0
$616$	−35.1026			−0.0569848
$617$	−454.342			−0.736373			−0.368186	−	0.929752i	$-0.620021\pi$
$617$	−454.342			−0.736373			−0.368186	+	0.929752i	$0.620021\pi$
$618$	686.027			1.11008
$619$			153.676i			0.248264i	0.992266	+	0.124132i	$0.0396147\pi$
$619$			153.676i			0.248264i	−0.992266	+	0.124132i	$0.960385\pi$
$620$		0			0
$621$	−470.781	+	212.204i	−0.758102	+	0.341713i
$622$			421.577i			0.677776i
$623$		−	163.482i		−	0.262411i
$624$	−203.187			−0.325621
$625$		0			0
$626$		−	154.820i		−	0.247316i
$627$		−	804.689i		−	1.28340i
$628$	−578.271			−0.920814
$629$	−1065.84			−1.69450
$630$		0			0
$631$		−	1241.15i		−	1.96696i	−0.181027	−	0.983478i	$-0.557942\pi$
$631$		−	1241.15i		−	1.96696i	0.181027	−	0.983478i	$-0.442058\pi$
$632$	161.460			0.255475
$633$			146.948i			0.232146i
$634$	−670.950			−1.05828
$635$		0			0
$636$			701.821i			1.10349i
$637$			718.846i			1.12849i
$638$	−489.366			−0.767032
$639$	−128.629			−0.201297
$640$		0			0
$641$			545.978i			0.851759i	0.904780	+	0.425880i	$0.140035\pi$
$641$			545.978i			0.851759i	−0.904780	+	0.425880i	$0.859965\pi$
$642$	49.7651			0.0775157
$643$	−539.118			−0.838441			−0.419221	−	0.907884i	$-0.637697\pi$
$643$	−539.118			−0.838441			−0.419221	+	0.907884i	$0.637697\pi$
$644$	22.1009	+	49.0317i	0.0343182	+	0.0761362i
$645$		0			0
$646$	−639.844			−0.990470
$647$		−	652.715i		−	1.00883i	−0.863460	−	0.504417i	$-0.831708\pi$
$647$		−	652.715i		−	1.00883i	0.863460	−	0.504417i	$-0.168292\pi$
$648$		−	273.056i		−	0.421382i
$649$		−	568.376i		−	0.875772i
$650$		0			0
$651$			106.640i			0.163810i
$652$			92.5071i			0.141882i
$653$			374.815i			0.573989i	0.957932	+	0.286995i	$0.0926562\pi$
$653$			374.815i			0.573989i	−0.957932	+	0.286995i	$0.907344\pi$
$654$		−	329.034i		−	0.503110i
$655$		0			0
$656$	37.7488			0.0575439
$657$			20.4384i			0.0311087i
$658$	81.2460			0.123474
$659$			440.090i			0.667815i	0.942606	+	0.333907i	$0.108367\pi$
$659$			440.090i			0.667815i	−0.942606	+	0.333907i	$0.891633\pi$
$660$		0			0
$661$		−	72.6725i		−	0.109943i	−0.998488	−	0.0549716i	$-0.982493\pi$
$661$		−	72.6725i		−	0.109943i	0.998488	−	0.0549716i	$-0.0175068\pi$
$662$		−	361.144i		−	0.545535i
$663$	−1020.44			−1.53913
$664$			156.069i			0.235044i
$665$		0			0
$666$		−	174.805i		−	0.262469i
$667$	308.110	+	683.552i	0.461933	+	1.02482i
$668$		−	181.747i		−	0.272076i
$669$	1173.45			1.75404
$670$		0			0
$671$	249.623			0.372017
$672$	−22.2622			−0.0331282
$673$		−	1052.88i		−	1.56445i	−0.622993	−	0.782227i	$-0.714084\pi$
$673$		−	1052.88i		−	1.56445i	0.622993	−	0.782227i	$-0.285916\pi$
$674$		−	648.398i		−	0.962014i
$675$		0			0
$676$	117.497			0.173812
$677$	−393.587			−0.581369			−0.290684	−	0.956819i	$-0.593883\pi$
$677$	−393.587			−0.581369			−0.290684	+	0.956819i	$0.593883\pi$
$678$	653.404			0.963722
$679$	−23.2241			−0.0342034
$680$		0			0
$681$		−	591.714i		−	0.868889i
$682$	−406.776			−0.596446
$683$		−	645.240i		−	0.944714i	−0.881407	−	0.472357i	$-0.843403\pi$
$683$		−	645.240i		−	0.944714i	0.881407	−	0.472357i	$-0.156597\pi$
$684$		−	104.938i		−	0.153419i
$685$		0			0
$686$			159.781i			0.232916i
$687$	−4.85195			−0.00706252
$688$	−145.753			−0.211850
$689$		−	1573.31i		−	2.28347i
$690$		0			0
$691$	548.216			0.793366			0.396683	−	0.917956i	$-0.370161\pi$
$691$	548.216			0.793366			0.396683	+	0.917956i	$0.370161\pi$
$692$			181.579i			0.262397i
$693$		−	28.9129i		−	0.0417213i
$694$	−722.205			−1.04064
$695$		0			0
$696$	−310.357			−0.445915
$697$	189.581			0.271995
$698$		−	837.030i		−	1.19918i
$699$	−381.753			−0.546141
$700$		0			0
$701$		−	92.2064i		−	0.131536i	−0.997835	−	0.0657678i	$-0.979050\pi$
$701$		−	92.2064i		−	0.131536i	0.997835	−	0.0657678i	$-0.0209496\pi$
$702$			479.179i			0.682592i
$703$			1194.95i			1.69978i
$704$		−	84.9183i		−	0.120623i
$705$		0			0
$706$	238.060			0.337195
$707$	101.209			0.143153
$708$		−	360.465i		−	0.509132i
$709$			922.612i			1.30129i	0.759384	+	0.650643i	$0.225501\pi$
$709$			922.612i			1.30129i	−0.759384	+	0.650643i	$0.774499\pi$
$710$		0			0
$711$			132.989i			0.187045i
$712$	395.486			0.555458
$713$	256.110	+	568.189i	0.359201	+	0.796899i
$714$	−111.804			−0.156589
$715$		0			0
$716$	603.271			0.842557
$717$			1236.18i			1.72410i
$718$	−53.1347			−0.0740037
$719$	−606.887			−0.844071			−0.422035	−	0.906579i	$-0.638684\pi$
$719$	−606.887			−0.844071			−0.422035	+	0.906579i	$0.638684\pi$
$720$		0			0
$721$	−168.500			−0.233704
$722$			206.819i			0.286452i
$723$	741.740			1.02592
$724$		−	497.095i		−	0.686595i
$725$		0			0
$726$	−39.6347			−0.0545932
$727$	−787.544			−1.08328			−0.541640	−	0.840611i	$-0.682196\pi$
$727$	−787.544			−1.08328			−0.541640	+	0.840611i	$0.682196\pi$
$728$	49.9064			0.0685527
$729$	−455.246			−0.624481
$730$		0			0
$731$	−731.995			−1.00136
$732$	158.312			0.216273
$733$	−415.085			−0.566282			−0.283141	−	0.959078i	$-0.591376\pi$
$733$	−415.085			−0.566282			−0.283141	+	0.959078i	$0.591376\pi$
$734$		−	603.921i		−	0.822780i
$735$		0			0
$736$	−118.615	+	53.4653i	−0.161161	+	0.0726431i
$737$			631.319i			0.856606i
$738$			31.0924i			0.0421307i
$739$	−639.964			−0.865987			−0.432993	−	0.901397i	$-0.642543\pi$
$739$	−639.964			−0.865987			−0.432993	+	0.901397i	$0.642543\pi$
$740$		0			0
$741$			1144.05i			1.54393i
$742$		−	172.380i		−	0.232318i
$743$	743.739			1.00099			0.500497	−	0.865738i	$-0.333151\pi$
$743$	743.739			1.00099			0.500497	+	0.865738i	$0.333151\pi$
$744$	−257.978			−0.346745
$745$		0			0
$746$			523.231i			0.701382i
$747$	−128.549			−0.172087
$748$		−	426.474i		−	0.570152i
$749$	−12.2232			−0.0163193
$750$		0			0
$751$		−	517.047i		−	0.688478i	−0.938882	−	0.344239i	$-0.888137\pi$
$751$		−	517.047i		−	0.688478i	0.938882	−	0.344239i	$-0.111863\pi$
$752$			196.546i			0.261364i
$753$	−1481.73			−1.96777
$754$	695.746			0.922740
$755$		0			0
$756$			52.5011i			0.0694460i
$757$	−911.823			−1.20452			−0.602261	−	0.798299i	$-0.705733\pi$
$757$	−911.823			−1.20452			−0.602261	+	0.798299i	$0.705733\pi$
$758$	−111.441			−0.147020
$759$	−337.689	−	749.176i	−0.444914	−	0.987057i
$760$		0			0
$761$	954.073			1.25371			0.626855	−	0.779136i	$-0.284342\pi$
$761$	954.073			1.25371			0.626855	+	0.779136i	$0.284342\pi$
$762$			275.947i			0.362135i
$763$			80.8166i			0.105920i
$764$		−	292.764i		−	0.383199i
$765$		0			0
$766$			359.328i			0.469097i
$767$			808.076i			1.05355i
$768$		−	53.8553i		−	0.0701242i
$769$			276.277i			0.359268i	0.983734	+	0.179634i	$0.0574913\pi$
$769$			276.277i			0.359268i	−0.983734	+	0.179634i	$0.942509\pi$
$770$		0			0
$771$	−1654.43			−2.14583
$772$			241.296i			0.312560i
$773$	40.8440			0.0528383			0.0264192	−	0.999651i	$-0.491590\pi$
$773$	40.8440			0.0528383			0.0264192	+	0.999651i	$0.491590\pi$
$774$		−	120.052i		−	0.155106i
$775$		0			0
$776$		−	56.1824i		−	0.0724000i
$777$			208.801i			0.268728i
$778$	455.891			0.585978
$779$		−	212.545i		−	0.272843i
$780$		0			0
$781$			586.074i			0.750415i
$782$	−595.703	+	268.512i	−0.761768	+	0.343365i
$783$			731.919i			0.934763i
$784$	−190.532			−0.243026
$785$		0			0
$786$	452.603			0.575831
$787$	−1364.69			−1.73404			−0.867019	−	0.498274i	$-0.833967\pi$
$787$	−1364.69			−1.73404			−0.867019	+	0.498274i	$0.833967\pi$
$788$			63.3005i			0.0803305i
$789$		−	901.515i		−	1.14261i
$790$		0			0
$791$	−160.487			−0.202892
$792$	69.9444			0.0883136
$793$	−354.897			−0.447537
$794$	−1012.34			−1.27499
$795$		0			0
$796$			74.8991i			0.0940944i
$797$	20.2192			0.0253692			0.0126846	−	0.999920i	$-0.495962\pi$
$797$	20.2192			0.0253692			0.0126846	+	0.999920i	$0.495962\pi$
$798$			125.347i			0.157077i
$799$			987.086i			1.23540i
$800$		0			0
$801$			325.749i			0.406678i
$802$	624.283			0.778407
$803$	93.1240			0.115970
$804$			400.384i			0.497989i
$805$		0			0
$806$	578.325			0.717525
$807$			322.117i			0.399154i
$808$			244.840i			0.303019i
$809$	1032.11			1.27579			0.637894	−	0.770124i	$-0.279806\pi$
$809$	1032.11			1.27579			0.637894	+	0.770124i	$0.279806\pi$
$810$		0			0
$811$	−70.2781			−0.0866561			−0.0433281	−	0.999061i	$-0.513796\pi$
$811$	−70.2781			−0.0866561			−0.0433281	+	0.999061i	$0.513796\pi$
$812$	76.2292			0.0938783
$813$			1522.27i			1.87241i
$814$	−796.467			−0.978460
$815$		0			0
$816$		−	270.470i		−	0.331459i
$817$			820.663i			1.00448i
$818$		−	860.869i		−	1.05241i
$819$			41.1062i			0.0501907i
$820$		0			0
$821$	84.7400			0.103216			0.0516078	−	0.998667i	$-0.483565\pi$
$821$	84.7400			0.103216			0.0516078	+	0.998667i	$0.483565\pi$
$822$	945.901			1.15073
$823$			46.0292i			0.0559286i	0.999609	+	0.0279643i	$0.00890247\pi$
$823$			46.0292i			0.0559286i	−0.999609	+	0.0279643i	$0.991098\pi$
$824$		−	407.626i		−	0.494692i
$825$		0			0
$826$			88.5366i			0.107187i
$827$	1283.77			1.55232			0.776160	−	0.630536i	$-0.217165\pi$
$827$	1283.77			1.55232			0.776160	+	0.630536i	$0.217165\pi$
$828$	−44.0376	−	97.6990i	−0.0531855	−	0.117994i
$829$	483.453			0.583177			0.291588	−	0.956544i	$-0.405816\pi$
$829$	483.453			0.583177			0.291588	+	0.956544i	$0.405816\pi$
$830$		0			0
$831$	294.449			0.354330
$832$			120.731i			0.145109i
$833$	−956.883			−1.14872
$834$	−0.616347			−0.000739025
$835$		0			0
$836$	−478.134			−0.571930
$837$			608.394i			0.726874i
$838$	406.521			0.485108
$839$			1060.74i			1.26429i	0.774852	+	0.632143i	$0.217824\pi$
$839$			1060.74i			1.26429i	−0.774852	+	0.632143i	$0.782176\pi$
$840$		0			0
$841$	221.712			0.263629
$842$	−185.047			−0.219771
$843$	−781.432			−0.926966
$844$	87.3144			0.103453
$845$		0			0
$846$	−161.888			−0.191357
$847$	9.73498			0.0114935
$848$	417.011			0.491759
$849$			805.700i			0.948999i
$850$		0			0
$851$	501.463	+	1112.51i	0.589263	+	1.30730i
$852$			371.689i			0.436255i
$853$			1653.13i			1.93802i	0.247023	+	0.969010i	$0.420548\pi$
$853$			1653.13i			1.93802i	−0.247023	+	0.969010i	$0.579452\pi$
$854$	−38.8841			−0.0455318
$855$		0			0
$856$		−	29.5696i		−	0.0345439i
$857$		−	1453.42i		−	1.69593i	−0.530048	−	0.847967i	$-0.677826\pi$
$857$		−	1453.42i		−	1.69593i	0.530048	−	0.847967i	$-0.322174\pi$
$858$	−762.540			−0.888742
$859$	−936.399			−1.09010			−0.545052	−	0.838402i	$-0.683490\pi$
$859$	−936.399			−1.09010			−0.545052	+	0.838402i	$0.683490\pi$
$860$		0			0
$861$		−	37.1394i		−	0.0431352i
$862$	−339.151			−0.393446
$863$			961.830i			1.11452i	0.830339	+	0.557259i	$0.188147\pi$
$863$			961.830i			1.11452i	−0.830339	+	0.557259i	$0.811853\pi$
$864$	−127.008			−0.147000
$865$		0			0
$866$		−	432.102i		−	0.498963i
$867$		−	385.585i		−	0.444735i
$868$	63.3640			0.0730000
$869$	605.943			0.697287
$870$		0			0
$871$		−	897.563i		−	1.03050i
$872$	−195.507			−0.224205
$873$	46.2756			0.0530075
$874$	301.037	+	667.862i	0.344436	+	0.764144i
$875$		0			0
$876$	59.0594			0.0674194
$877$			1244.55i			1.41910i	0.704657	+	0.709549i	$0.251101\pi$
$877$			1244.55i			1.41910i	−0.704657	+	0.709549i	$0.748899\pi$
$878$		−	818.855i		−	0.932637i
$879$		−	1958.41i		−	2.22800i
$880$		0			0
$881$		−	961.719i		−	1.09162i	−0.837908	−	0.545811i	$-0.816222\pi$
$881$		−	961.719i		−	1.09162i	0.837908	−	0.545811i	$-0.183778\pi$
$882$		−	156.935i		−	0.177931i
$883$			42.4945i			0.0481251i	0.999710	+	0.0240626i	$0.00766009\pi$
$883$			42.4945i			0.0481251i	−0.999710	+	0.0240626i	$0.992340\pi$
$884$			606.330i			0.685893i
$885$		0			0
$886$	−857.401			−0.967722
$887$			551.962i			0.622279i	0.950364	+	0.311140i	$0.100711\pi$
$887$			551.962i			0.622279i	−0.950364	+	0.311140i	$0.899289\pi$
$888$	−505.121			−0.568830
$889$		−	67.7774i		−	0.0762400i
$890$		0			0
$891$		−	1024.75i		−	1.15011i
$892$		−	697.246i		−	0.781666i
$893$	1106.65			1.23925
$894$		−	304.054i		−	0.340106i
$895$		0			0
$896$			13.2278i			0.0147632i
$897$	480.102	+	1065.12i	0.535231	+	1.18743i
$898$		−	286.492i		−	0.319033i
$899$	883.359			0.982601
$900$		0			0
$901$	2094.30			2.32442
$902$	141.667			0.157059
$903$			143.400i			0.158804i
$904$		−	388.242i		−	0.429472i
$905$		0			0
$906$	167.879			0.185297
$907$	237.524			0.261878			0.130939	−	0.991390i	$-0.458201\pi$
$907$	237.524			0.261878			0.130939	+	0.991390i	$0.458201\pi$
$908$	−351.587			−0.387210
$909$	−201.666			−0.221855
$910$		0			0
$911$		−	402.885i		−	0.442245i	−0.975246	−	0.221122i	$-0.929028\pi$
$911$		−	402.885i		−	0.442245i	0.975246	−	0.221122i	$-0.0709720\pi$
$912$	−303.233			−0.332493
$913$			585.712i			0.641524i
$914$		−	528.577i		−	0.578312i
$915$		0			0
$916$			2.88295i			0.00314733i
$917$	−111.167			−0.121229
$918$	−637.854			−0.694830
$919$			1338.53i			1.45650i	0.685310	+	0.728251i	$0.259667\pi$
$919$			1338.53i			1.45650i	−0.685310	+	0.728251i	$0.740333\pi$
$920$		0			0
$921$	−370.706			−0.402503
$922$		−	1003.21i		−	1.08808i
$923$		−	833.238i		−	0.902750i
$924$	−83.5475			−0.0904194
$925$		0			0
$926$	376.872			0.406989
$927$	335.748			0.362188
$928$			184.409i			0.198717i
$929$	−621.771			−0.669291			−0.334646	−	0.942344i	$-0.608617\pi$
$929$	−621.771			−0.669291			−0.334646	+	0.942344i	$0.608617\pi$
$930$		0			0
$931$			1072.79i			1.15230i
$932$			226.831i			0.243381i
$933$			1003.39i			1.07545i
$934$		−	970.341i		−	1.03891i
$935$		0			0
$936$	−99.4419			−0.106241
$937$	−915.580			−0.977140			−0.488570	−	0.872525i	$-0.662481\pi$
$937$	−915.580			−0.977140			−0.488570	+	0.872525i	$0.662481\pi$
$938$		−	98.3412i		−	0.104841i
$939$		−	368.486i		−	0.392424i
$940$		0			0
$941$		−	834.255i		−	0.886563i	−0.896383	−	0.443281i	$-0.853814\pi$
$941$		−	834.255i		−	0.886563i	0.896383	−	0.443281i	$-0.146186\pi$
$942$	−1376.34			−1.46108
$943$	−89.1950	−	197.882i	−0.0945864	−	0.209843i
$944$	−214.183			−0.226889
$945$		0			0
$946$	−546.995			−0.578219
$947$		−	918.683i		−	0.970099i	−0.874487	−	0.485049i	$-0.838802\pi$
$947$		−	918.683i		−	0.970099i	0.874487	−	0.485049i	$-0.161198\pi$
$948$	384.290			0.405369
$949$	−132.397			−0.139512
$950$		0			0
$951$	−1596.92			−1.67921
$952$			66.4323i			0.0697818i
$953$	789.341			0.828270			0.414135	−	0.910215i	$-0.364084\pi$
$953$	789.341			0.828270			0.414135	+	0.910215i	$0.364084\pi$
$954$			343.478i			0.360040i
$955$		0			0
$956$	734.519			0.768326
$957$	−1164.74			−1.21707
$958$	249.632			0.260577
$959$	−232.330			−0.242263
$960$		0			0
$961$	−226.725			−0.235927
$962$	1132.36			1.17709
$963$	24.3555			0.0252913
$964$		−	440.730i		−	0.457189i
$965$		0			0
$966$	52.6023	+	116.700i	0.0544537	+	0.120807i
$967$		−	875.476i		−	0.905353i	−0.891675	−	0.452677i	$-0.850469\pi$
$967$		−	875.476i		−	0.905353i	0.891675	−	0.452677i	$-0.149531\pi$
$968$			23.5503i			0.0243288i
$969$	−1522.89			−1.57161
$970$		0			0
$971$			1232.49i			1.26930i	0.772801	+	0.634648i	$0.218855\pi$
$971$			1232.49i			1.26930i	−0.772801	+	0.634648i	$0.781145\pi$
$972$		−	245.761i		−	0.252841i
$973$	0.151386			0.000155587
$974$	−742.182			−0.761994
$975$		0			0
$976$		−	94.0663i		−	0.0963794i
$977$	879.183			0.899880			0.449940	−	0.893059i	$-0.351445\pi$
$977$	879.183			0.899880			0.449940	+	0.893059i	$0.351445\pi$
$978$			220.176i			0.225128i
$979$	1484.22			1.51606
$980$		0			0
$981$		−	161.033i		−	0.164151i
$982$			779.298i			0.793582i
$983$	−247.090			−0.251363			−0.125682	−	0.992071i	$-0.540112\pi$
$983$	−247.090			−0.251363			−0.125682	+	0.992071i	$0.540112\pi$
$984$	89.8456			0.0913065
$985$		0			0
$986$			926.134i			0.939284i
$987$	193.373			0.195920
$988$	679.776			0.688032
$989$	344.393	+	764.048i	0.348223	+	0.772546i
$990$		0			0
$991$	−1750.79			−1.76669			−0.883347	−	0.468721i	$-0.844715\pi$
$991$	−1750.79			−1.76669			−0.883347	+	0.468721i	$0.844715\pi$
$992$			153.287i			0.154523i
$993$		−	859.556i		−	0.865615i
$994$		−	91.2935i		−	0.0918445i
$995$		0			0
$996$			371.459i			0.372951i
$997$			456.156i			0.457529i	0.973482	+	0.228765i	$0.0734686\pi$
$997$			456.156i			0.457529i	−0.973482	+	0.228765i	$0.926531\pi$
$998$		−	1041.91i		−	1.04399i
$999$			1191.23i			1.19243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.c.c.1149.15		32
5.2	odd	4		230.3.d.a.91.12	yes	16
5.3	odd	4		1150.3.d.b.551.5		16
5.4	even	2	inner	1150.3.c.c.1149.18		32
15.2	even	4		2070.3.c.a.91.3		16
20.7	even	4		1840.3.k.d.321.12		16
23.22	odd	2	inner	1150.3.c.c.1149.17		32
115.22	even	4		230.3.d.a.91.11	✓	16
115.68	even	4		1150.3.d.b.551.6		16
115.114	odd	2	inner	1150.3.c.c.1149.16		32
345.137	odd	4		2070.3.c.a.91.6		16
460.367	odd	4		1840.3.k.d.321.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.11	✓	16	115.22	even	4
230.3.d.a.91.12	yes	16	5.2	odd	4
1150.3.c.c.1149.15		32	1.1	even	1	trivial
1150.3.c.c.1149.16		32	115.114	odd	2	inner
1150.3.c.c.1149.17		32	23.22	odd	2	inner
1150.3.c.c.1149.18		32	5.4	even	2	inner
1150.3.d.b.551.5		16	5.3	odd	4
1150.3.d.b.551.6		16	115.68	even	4
1840.3.k.d.321.11		16	460.367	odd	4
1840.3.k.d.321.12		16	20.7	even	4
2070.3.c.a.91.3		16	15.2	even	4
2070.3.c.a.91.6		16	345.137	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -3.36596i q^{3} -2.00000 q^{4} -4.76019 q^{6} +1.16919 q^{7} +2.82843i q^{8} -2.32968 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -3.36596i q^{3} -2.00000 q^{4} -4.76019 q^{6} +1.16919 q^{7} +2.82843i q^{8} -2.32968 q^{9} +10.6148i q^{11} +6.73192i q^{12} -15.0913i q^{13} -1.65348i q^{14} +4.00000 q^{16} +20.0887 q^{17} +3.29467i q^{18} -22.5221i q^{19} -3.93543i q^{21} +15.0116 q^{22} +(-9.45142 - 20.9683i) q^{23} +9.52037 q^{24} -21.3424 q^{26} -22.4520i q^{27} -2.33837 q^{28} -32.5993 q^{29} -27.0975 q^{31} -5.65685i q^{32} +35.7289 q^{33} -28.4097i q^{34} +4.65936 q^{36} -53.0568 q^{37} -31.8510 q^{38} -50.7968 q^{39} +9.43720 q^{41} -5.56554 q^{42} -36.4382 q^{43} -21.2296i q^{44} +(-29.6537 + 13.3663i) q^{46} +49.1365i q^{47} -13.4638i q^{48} -47.6330 q^{49} -67.6176i q^{51} +30.1827i q^{52} +104.253 q^{53} -31.7520 q^{54} +3.30696i q^{56} -75.8083 q^{57} +46.1023i q^{58} -53.5457 q^{59} -23.5166i q^{61} +38.3217i q^{62} -2.72383 q^{63} -8.00000 q^{64} -50.5284i q^{66} +59.4754 q^{67} -40.1773 q^{68} +(-70.5785 + 31.8131i) q^{69} +55.2130 q^{71} -6.58933i q^{72} -8.77305i q^{73} +75.0337i q^{74} +45.0441i q^{76} +12.4107i q^{77} +71.8376i q^{78} -57.0848i q^{79} -96.5397 q^{81} -13.3462i q^{82} +55.1788 q^{83} +7.87086i q^{84} +51.5314i q^{86} +109.728i q^{87} -30.0232 q^{88} -139.825i q^{89} -17.6446i q^{91} +(18.9028 + 41.9366i) q^{92} +91.2091i q^{93} +69.4894 q^{94} -19.0407 q^{96} -19.8635 q^{97} +67.3632i q^{98} -24.7291i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

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