LMFDB - Embedded newform 475.3.c.f.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("475.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.9428125571$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 42x^{6} + 771x^{4} - 7098x^{2} + 28561 $ x^8 - 42x^6 + 771x^4 - 7098*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.6
Root			$3.52946 - 0.736813i$ of defining polynomial
Character	$\chi$	$=$	475.151
Dual form			475.3.c.f.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.47363i q^{2} +3.55765i q^{3} +1.82843 q^{4} -5.24264 q^{6} +7.05893 q^{7} +8.58892i q^{8} -3.65685 q^{9} +O(q^{10})$	\(q+1.47363i q^{2} +3.55765i q^{3} +1.82843 q^{4} -5.24264 q^{6} +7.05893 q^{7} +8.58892i q^{8} -3.65685 q^{9} +2.24264 q^{11} +6.50490i q^{12} +6.86246i q^{13} +10.4022i q^{14} -5.34315 q^{16} +11.1939 q^{17} -5.38883i q^{18} +(-15.8995 - 10.4022i) q^{19} +25.1132i q^{21} +3.30481i q^{22} +21.1768 q^{23} -30.5563 q^{24} -10.1127 q^{26} +19.0090i q^{27} +12.9067 q^{28} +45.9176i q^{29} -14.7110i q^{31} +26.4819i q^{32} +7.97852i q^{33} +16.4957i q^{34} -6.68629 q^{36} -25.0083i q^{37} +(15.3290 - 23.4299i) q^{38} -24.4142 q^{39} -64.9373i q^{41} -37.0074 q^{42} -44.0663 q^{43} +4.10051 q^{44} +31.2066i q^{46} -34.0835 q^{47} -19.0090i q^{48} +0.828427 q^{49} +39.8241i q^{51} +12.5475i q^{52} -20.8836i q^{53} -28.0122 q^{54} +60.6285i q^{56} +(37.0074 - 56.5648i) q^{57} -67.6654 q^{58} -69.2460i q^{59} +23.4142 q^{61} +21.6784 q^{62} -25.8135 q^{63} -60.3970 q^{64} -11.7574 q^{66} -79.3843i q^{67} +20.4673 q^{68} +75.3395i q^{69} -26.8979i q^{71} -31.4084i q^{72} -99.3266 q^{73} +36.8528 q^{74} +(-29.0711 - 19.0197i) q^{76} +15.8306 q^{77} -35.9774i q^{78} +109.070i q^{79} -100.539 q^{81} +95.6933 q^{82} +124.638 q^{83} +45.9176i q^{84} -64.9373i q^{86} -163.359 q^{87} +19.2619i q^{88} -85.7417i q^{89} +48.4416i q^{91} +38.7202 q^{92} +52.3364 q^{93} -50.2263i q^{94} -94.2132 q^{96} -35.5765i q^{97} +1.22079i q^{98} -8.20101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	$ 8 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 16 q^{11} - 88 q^{16} - 48 q^{19} - 120 q^{24} + 168 q^{26} - 144 q^{36} - 184 q^{39} + 112 q^{44} - 16 q^{49} + 104 q^{54} + 176 q^{61} - 8 q^{64} - 128 q^{66} - 384 q^{74} - 176 q^{76} - 216 q^{81} - 584 q^{96} - 224 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 16 * q^11 - 88 * q^16 - 48 * q^19 - 120 * q^24 + 168 * q^26 - 144 * q^36 - 184 * q^39 + 112 * q^44 - 16 * q^49 + 104 * q^54 + 176 * q^61 - 8 * q^64 - 128 * q^66 - 384 * q^74 - 176 * q^76 - 216 * q^81 - 584 * q^96 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.47363i			0.736813i	0.929665	+	0.368406i	$0.120097\pi$
$2$			1.47363i			0.736813i	−0.929665	+	0.368406i	$0.879903\pi$
$3$			3.55765i			1.18588i	0.805246	+	0.592941i	$0.202033\pi$
$3$			3.55765i			1.18588i	−0.805246	+	0.592941i	$0.797967\pi$
$4$	1.82843			0.457107
$5$		0			0
$5$		0			0
$6$	−5.24264			−0.873773
$7$	7.05893			1.00842			0.504209	−	0.863582i	$-0.331784\pi$
$7$	7.05893			1.00842			0.504209	+	0.863582i	$0.331784\pi$
$8$			8.58892i			1.07362i
$9$	−3.65685			−0.406317
$10$		0			0
$11$	2.24264			0.203876			0.101938	−	0.994791i	$-0.467496\pi$
$11$	2.24264			0.203876			0.101938	+	0.994791i	$0.467496\pi$
$12$			6.50490i			0.542075i
$13$			6.86246i			0.527882i	0.964539	+	0.263941i	$0.0850224\pi$
$13$			6.86246i			0.527882i	−0.964539	+	0.263941i	$0.914978\pi$
$14$			10.4022i			0.743015i
$15$		0			0
$16$	−5.34315			−0.333947
$17$	11.1939			0.658468			0.329234	−	0.944248i	$-0.393210\pi$
$17$	11.1939			0.658468			0.329234	+	0.944248i	$0.393210\pi$
$18$		−	5.38883i		−	0.299380i
$19$	−15.8995	−	10.4022i	−0.836816	−	0.547485i
$19$	−15.8995	−	10.4022i	−0.836816	−	0.547485i
$20$		0			0
$21$			25.1132i			1.19587i
$22$			3.30481i			0.150219i
$23$	21.1768			0.920729			0.460365	−	0.887730i	$-0.347719\pi$
$23$	21.1768			0.920729			0.460365	+	0.887730i	$0.347719\pi$
$24$	−30.5563			−1.27318
$25$		0			0
$26$	−10.1127			−0.388950
$27$			19.0090i			0.704038i
$28$	12.9067			0.460955
$29$			45.9176i			1.58337i	0.610933	+	0.791683i	$0.290795\pi$
$29$			45.9176i			1.58337i	−0.610933	+	0.791683i	$0.709205\pi$
$30$		0			0
$31$		−	14.7110i		−	0.474547i	−0.971443	−	0.237273i	$-0.923746\pi$
$31$		−	14.7110i		−	0.474547i	0.971443	−	0.237273i	$-0.0762537\pi$
$32$			26.4819i			0.827559i
$33$			7.97852i			0.241773i
$34$			16.4957i			0.485167i
$35$		0			0
$36$	−6.68629			−0.185730
$37$		−	25.0083i		−	0.675899i	−0.941164	−	0.337949i	$-0.890267\pi$
$37$		−	25.0083i		−	0.675899i	0.941164	−	0.337949i	$-0.109733\pi$
$38$	15.3290	−	23.4299i	0.403394	−	0.616576i
$39$	−24.4142			−0.626005
$40$		0			0
$41$		−	64.9373i		−	1.58384i	−0.610627	−	0.791918i	$-0.709083\pi$
$41$		−	64.9373i		−	1.58384i	0.610627	−	0.791918i	$-0.290917\pi$
$42$	−37.0074			−0.881129
$43$	−44.0663			−1.02480			−0.512399	−	0.858747i	$-0.671243\pi$
$43$	−44.0663			−1.02480			−0.512399	+	0.858747i	$0.671243\pi$
$44$	4.10051			0.0931933
$45$		0			0
$46$			31.2066i			0.678405i
$47$	−34.0835			−0.725181			−0.362590	−	0.931949i	$-0.618108\pi$
$47$	−34.0835			−0.725181			−0.362590	+	0.931949i	$0.618108\pi$
$48$		−	19.0090i		−	0.396021i
$49$	0.828427			0.0169067
$50$		0			0
$51$			39.8241i			0.780865i
$52$			12.5475i			0.241298i
$53$		−	20.8836i		−	0.394030i	−0.980400	−	0.197015i	$-0.936875\pi$
$53$		−	20.8836i		−	0.394030i	0.980400	−	0.197015i	$-0.0631248\pi$
$54$	−28.0122			−0.518744
$55$		0			0
$56$			60.6285i			1.08265i
$57$	37.0074	−	56.5648i	0.649253	−	0.992365i
$58$	−67.6654			−1.16664
$59$		−	69.2460i		−	1.17366i	−0.809710	−	0.586831i	$-0.800375\pi$
$59$		−	69.2460i		−	1.17366i	0.809710	−	0.586831i	$-0.199625\pi$
$60$		0			0
$61$	23.4142			0.383840			0.191920	−	0.981411i	$-0.438529\pi$
$61$	23.4142			0.383840			0.191920	+	0.981411i	$0.438529\pi$
$62$	21.6784			0.349652
$63$	−25.8135			−0.409737
$64$	−60.3970			−0.943703
$65$		0			0
$66$	−11.7574			−0.178142
$67$		−	79.3843i		−	1.18484i	−0.805629	−	0.592420i	$-0.798173\pi$
$67$		−	79.3843i		−	1.18484i	0.805629	−	0.592420i	$-0.201827\pi$
$68$	20.4673			0.300990
$69$			75.3395i			1.09188i
$70$		0			0
$71$		−	26.8979i		−	0.378844i	−0.981896	−	0.189422i	$-0.939339\pi$
$71$		−	26.8979i		−	0.378844i	0.981896	−	0.189422i	$-0.0606614\pi$
$72$		−	31.4084i		−	0.436228i
$73$	−99.3266			−1.36064			−0.680319	−	0.732916i	$-0.738159\pi$
$73$	−99.3266			−1.36064			−0.680319	+	0.732916i	$0.738159\pi$
$74$	36.8528			0.498011
$75$		0			0
$76$	−29.0711	−	19.0197i	−0.382514	−	0.250259i
$77$	15.8306			0.205593
$78$		−	35.9774i		−	0.461249i
$79$			109.070i			1.38063i	0.723507	+	0.690317i	$0.242529\pi$
$79$			109.070i			1.38063i	−0.723507	+	0.690317i	$0.757471\pi$
$80$		0			0
$81$	−100.539			−1.24122
$82$	95.6933			1.16699
$83$	124.638			1.50167			0.750834	−	0.660491i	$-0.229652\pi$
$83$	124.638			1.50167			0.750834	+	0.660491i	$0.229652\pi$
$84$			45.9176i			0.546638i
$85$		0			0
$86$		−	64.9373i		−	0.755085i
$87$	−163.359			−1.87769
$88$			19.2619i			0.218885i
$89$		−	85.7417i		−	0.963390i	−0.876339	−	0.481695i	$-0.840021\pi$
$89$		−	85.7417i		−	0.963390i	0.876339	−	0.481695i	$-0.159979\pi$
$90$		0			0
$91$			48.4416i			0.532325i
$92$	38.7202			0.420872
$93$	52.3364			0.562757
$94$		−	50.2263i		−	0.534323i
$95$		0			0
$96$	−94.2132			−0.981388
$97$		−	35.5765i		−	0.366768i	−0.983041	−	0.183384i	$-0.941295\pi$
$97$		−	35.5765i		−	0.366768i	0.983041	−	0.183384i	$-0.0587051\pi$
$98$			1.22079i			0.0124571i
$99$	−8.20101			−0.0828385
$100$		0			0
$101$	200.492			1.98507			0.992537	−	0.121946i	$-0.0389134\pi$
$101$	200.492			1.98507			0.992537	+	0.121946i	$0.0389134\pi$
$102$	−58.6858			−0.575351
$103$			48.5249i			0.471116i	0.971860	+	0.235558i	$0.0756917\pi$
$103$			48.5249i			0.471116i	−0.971860	+	0.235558i	$0.924308\pi$
$104$	−58.9411			−0.566742
$105$		0			0
$106$	30.7746			0.290326
$107$			173.104i			1.61779i	0.587951	+	0.808897i	$0.299935\pi$
$107$			173.104i			1.61779i	−0.587951	+	0.808897i	$0.700065\pi$
$108$			34.7566i			0.321821i
$109$		−	96.1439i		−	0.882054i	−0.897494	−	0.441027i	$-0.854614\pi$
$109$		−	96.1439i		−	0.882054i	0.897494	−	0.441027i	$-0.145386\pi$
$110$		0			0
$111$	88.9706			0.801537
$112$	−37.7169			−0.336758
$113$			112.057i			0.991654i	0.868421	+	0.495827i	$0.165135\pi$
$113$			112.057i			0.991654i	−0.868421	+	0.495827i	$0.834865\pi$
$114$	83.3553	+	54.5351i	0.731187	+	0.478378i
$115$		0			0
$116$			83.9570i			0.723767i
$117$		−	25.0950i		−	0.214487i
$118$	102.043			0.864769
$119$	79.0172			0.664010
$120$		0			0
$121$	−115.971			−0.958434
$122$			34.5038i			0.282818i
$123$	231.024			1.87824
$124$		−	26.8979i		−	0.216919i
$125$		0			0
$126$		−	38.0394i		−	0.301900i
$127$			162.727i			1.28132i	0.767826	+	0.640658i	$0.221338\pi$
$127$			162.727i			1.28132i	−0.767826	+	0.640658i	$0.778662\pi$
$128$			16.9250i			0.132227i
$129$		−	156.772i		−	1.21529i
$130$		0			0
$131$	122.593			0.935824			0.467912	−	0.883775i	$-0.345006\pi$
$131$	122.593			0.935824			0.467912	+	0.883775i	$0.345006\pi$
$132$			14.5882i			0.110516i
$133$	−112.233	−	73.4285i	−0.843860	−	0.552094i
$134$	116.983			0.873006
$135$		0			0
$136$			96.1439i			0.706941i
$137$	−66.2464			−0.483551			−0.241775	−	0.970332i	$-0.577730\pi$
$137$	−66.2464			−0.483551			−0.241775	+	0.970332i	$0.577730\pi$
$138$	−111.022			−0.804509
$139$	176.191			1.26756			0.633780	−	0.773513i	$-0.281502\pi$
$139$	176.191			1.26756			0.633780	+	0.773513i	$0.281502\pi$
$140$		0			0
$141$		−	121.257i		−	0.859979i
$142$	39.6374			0.279137
$143$			15.3900i			0.107623i
$144$	19.5391			0.135688
$145$		0			0
$146$		−	146.370i		−	1.00254i
$147$			2.94725i			0.0200493i
$148$		−	45.7258i		−	0.308958i
$149$	8.94618			0.0600415			0.0300207	−	0.999549i	$-0.490443\pi$
$149$	8.94618			0.0600415			0.0300207	+	0.999549i	$0.490443\pi$
$150$		0			0
$151$		−	263.319i		−	1.74383i	−0.489656	−	0.871916i	$-0.662877\pi$
$151$		−	263.319i		−	1.74383i	0.489656	−	0.871916i	$-0.337123\pi$
$152$	89.3438	−	136.559i	0.587788	−	0.898418i
$153$	−40.9346			−0.267547
$154$			23.3284i			0.151483i
$155$		0			0
$156$	−44.6396			−0.286151
$157$	218.619			1.39248			0.696239	−	0.717811i	$-0.254856\pi$
$157$	218.619			1.39248			0.696239	+	0.717811i	$0.254856\pi$
$158$	−160.729			−1.01727
$159$	74.2965			0.467273
$160$		0			0
$161$	149.485			0.928480
$162$		−	148.157i		−	0.914549i
$163$	56.7653			0.348253			0.174127	−	0.984723i	$-0.444290\pi$
$163$	56.7653			0.348253			0.174127	+	0.984723i	$0.444290\pi$
$164$		−	118.733i		−	0.723982i
$165$		0			0
$166$			183.670i			1.10645i
$167$			89.4035i			0.535350i	0.963509	+	0.267675i	$0.0862554\pi$
$167$			89.4035i			0.535350i	−0.963509	+	0.267675i	$0.913745\pi$
$168$	−215.695			−1.28390
$169$	121.907			0.721341
$170$		0			0
$171$	58.1421	+	38.0394i	0.340012	+	0.222453i
$172$	−80.5721			−0.468442
$173$		−	105.090i		−	0.607455i	−0.952759	−	0.303728i	$-0.901769\pi$
$173$		−	105.090i		−	0.607455i	0.952759	−	0.303728i	$-0.0982312\pi$
$174$		−	240.729i		−	1.38350i
$175$		0			0
$176$	−11.9828			−0.0680838
$177$	246.353			1.39182
$178$	126.351			0.709838
$179$		−	65.9828i		−	0.368619i	−0.982868	−	0.184309i	$-0.940995\pi$
$179$		−	65.9828i		−	0.368619i	0.982868	−	0.184309i	$-0.0590048\pi$
$180$		0			0
$181$			129.875i			0.717539i	0.933426	+	0.358770i	$0.116804\pi$
$181$			129.875i			0.717539i	−0.933426	+	0.358770i	$0.883196\pi$
$182$	−71.3848			−0.392224
$183$			83.2995i			0.455189i
$184$			181.886i			0.988509i
$185$		0			0
$186$			77.1242i			0.414646i
$187$	25.1040			0.134246
$188$	−62.3192			−0.331485
$189$			134.183i			0.709965i
$190$		0			0
$191$	−172.012			−0.900587			−0.450294	−	0.892880i	$-0.648681\pi$
$191$	−172.012			−0.900587			−0.450294	+	0.892880i	$0.648681\pi$
$192$		−	214.871i		−	1.11912i
$193$		−	230.810i		−	1.19591i	−0.801531	−	0.597954i	$-0.795981\pi$
$193$		−	230.810i		−	1.19591i	0.801531	−	0.597954i	$-0.204019\pi$
$194$	52.4264			0.270239
$195$		0			0
$196$	1.51472			0.00772816
$197$	44.0663			0.223687			0.111843	−	0.993726i	$-0.464324\pi$
$197$	44.0663			0.223687			0.111843	+	0.993726i	$0.464324\pi$
$198$		−	12.0852i		−	0.0610365i
$199$	−15.1493			−0.0761270			−0.0380635	−	0.999275i	$-0.512119\pi$
$199$	−15.1493			−0.0761270			−0.0380635	+	0.999275i	$0.512119\pi$
$200$		0			0
$201$	282.421			1.40508
$202$			295.451i			1.46263i
$203$			324.129i			1.59669i
$204$			72.8155i			0.356939i
$205$		0			0
$206$	−71.5076			−0.347124
$207$	−77.4404			−0.374108
$208$		−	36.6671i		−	0.176284i
$209$	−35.6569	−	23.3284i	−0.170607	−	0.111619i
$210$		0			0
$211$		−	332.565i		−	1.57614i	−0.615588	−	0.788068i	$-0.711082\pi$
$211$		−	332.565i		−	1.57614i	0.615588	−	0.788068i	$-0.288918\pi$
$212$		−	38.1841i		−	0.180114i
$213$	95.6933			0.449264
$214$	−255.090			−1.19201
$215$		0			0
$216$	−163.267			−0.755866
$217$		−	103.844i		−	0.478542i
$218$	141.680			0.649909
$219$		−	353.369i		−	1.61356i
$220$		0			0
$221$			76.8180i			0.347593i
$222$			131.109i			0.590582i
$223$		−	135.400i		−	0.607175i	−0.952804	−	0.303588i	$-0.901816\pi$
$223$		−	135.400i		−	0.607175i	0.952804	−	0.303588i	$-0.0981845\pi$
$224$			186.934i			0.834525i
$225$		0			0
$226$	−165.130			−0.730663
$227$			313.683i			1.38187i	0.722919	+	0.690933i	$0.242800\pi$
$227$			313.683i			1.38187i	−0.722919	+	0.690933i	$0.757200\pi$
$228$	67.6654	−	103.425i	0.296778	−	0.453617i
$229$	−221.373			−0.966693			−0.483346	−	0.875429i	$-0.660579\pi$
$229$	−221.373			−0.966693			−0.483346	+	0.875429i	$0.660579\pi$
$230$		0			0
$231$			56.3198i			0.243809i
$232$	−394.383			−1.69992
$233$	−344.261			−1.47751			−0.738757	−	0.673972i	$-0.764587\pi$
$233$	−344.261			−1.47751			−0.738757	+	0.673972i	$0.764587\pi$
$234$	36.9807			0.158037
$235$		0			0
$236$		−	126.611i		−	0.536489i
$237$	−388.033			−1.63727
$238$			116.442i			0.489251i
$239$	403.825			1.68965			0.844823	−	0.535046i	$-0.179706\pi$
$239$	403.825			1.68965			0.844823	+	0.535046i	$0.179706\pi$
$240$		0			0
$241$			233.897i			0.970526i	0.874368	+	0.485263i	$0.161276\pi$
$241$			233.897i			0.970526i	−0.874368	+	0.485263i	$0.838724\pi$
$242$		−	170.897i		−	0.706187i
$243$		−	186.601i		−	0.767907i
$244$	42.8112			0.175456
$245$		0			0
$246$			340.443i			1.38391i
$247$	71.3848	−	109.110i	0.289007	−	0.441739i
$248$	126.351			0.509481
$249$			443.420i			1.78080i
$250$		0			0
$251$	183.816			0.732336			0.366168	−	0.930549i	$-0.380670\pi$
$251$	183.816			0.732336			0.366168	+	0.930549i	$0.380670\pi$
$252$	−47.1980			−0.187294
$253$	47.4919			0.187715
$254$	−239.799			−0.944091
$255$		0			0
$256$	−266.529			−1.04113
$257$		−	190.867i		−	0.742672i	−0.928499	−	0.371336i	$-0.878900\pi$
$257$		−	190.867i		−	0.742672i	0.928499	−	0.371336i	$-0.121100\pi$
$258$	231.024			0.895442
$259$		−	176.531i		−	0.681589i
$260$		0			0
$261$		−	167.914i		−	0.643348i
$262$			180.656i			0.689527i
$263$	123.220			0.468515			0.234258	−	0.972175i	$-0.424734\pi$
$263$	123.220			0.468515			0.234258	+	0.972175i	$0.424734\pi$
$264$	−68.5269			−0.259572
$265$		0			0
$266$	108.206	−	165.390i	0.406790	−	0.621767i
$267$	305.039			1.14247
$268$		−	145.148i		−	0.541599i
$269$			3.56948i			0.0132694i	0.999978	+	0.00663471i	$0.00211191\pi$
$269$			3.56948i			0.0132694i	−0.999978	+	0.00663471i	$0.997888\pi$
$270$		0			0
$271$	122.983			0.453811			0.226905	−	0.973917i	$-0.427139\pi$
$271$	122.983			0.453811			0.226905	+	0.973917i	$0.427139\pi$
$272$	−59.8109			−0.219893
$273$	−172.338			−0.631275
$274$		−	97.6225i		−	0.356286i
$275$		0			0
$276$			137.753i			0.499104i
$277$	−103.669			−0.374258			−0.187129	−	0.982335i	$-0.559918\pi$
$277$	−103.669			−0.374258			−0.187129	+	0.982335i	$0.559918\pi$
$278$			259.639i			0.933955i
$279$			53.7958i			0.192817i
$280$		0			0
$281$		−	362.726i		−	1.29084i	−0.763828	−	0.645420i	$-0.776683\pi$
$281$		−	362.726i		−	1.29084i	0.763828	−	0.645420i	$-0.223317\pi$
$282$	178.688			0.633644
$283$	123.220			0.435405			0.217702	−	0.976015i	$-0.430144\pi$
$283$	123.220			0.435405			0.217702	+	0.976015i	$0.430144\pi$
$284$		−	49.1809i		−	0.173172i
$285$		0			0
$286$	−22.6791			−0.0792977
$287$		−	458.387i		−	1.59717i
$288$		−	96.8404i		−	0.336251i
$289$	−163.696			−0.566421
$290$		0			0
$291$	126.569			0.434943
$292$	−181.611			−0.621957
$293$		−	30.4764i		−	0.104015i	−0.998647	−	0.0520075i	$-0.983438\pi$
$293$		−	30.4764i		−	0.104015i	0.998647	−	0.0520075i	$-0.0165620\pi$
$294$	−4.34315			−0.0147726
$295$		0			0
$296$	214.794			0.725655
$297$			42.6304i			0.143537i
$298$			13.1833i			0.0442393i
$299$			145.325i			0.486036i
$300$		0			0
$301$	−311.061			−1.03343
$302$	388.033			1.28488
$303$			713.281i			2.35406i
$304$	84.9533	+	55.5805i	0.279452	+	0.182831i
$305$		0			0
$306$		−	60.3223i		−	0.197132i
$307$		−	214.557i		−	0.698883i	−0.936958	−	0.349441i	$-0.886371\pi$
$307$		−	214.557i		−	0.698883i	0.936958	−	0.349441i	$-0.113629\pi$
$308$	28.9452			0.0939778
$309$	−172.635			−0.558688
$310$		0			0
$311$	178.345			0.573457			0.286729	−	0.958012i	$-0.407432\pi$
$311$	178.345			0.573457			0.286729	+	0.958012i	$0.407432\pi$
$312$		−	209.692i		−	0.672089i
$313$	−377.255			−1.20529			−0.602643	−	0.798011i	$-0.705886\pi$
$313$	−377.255			−1.20529			−0.602643	+	0.798011i	$0.705886\pi$
$314$			322.162i			1.02599i
$315$		0			0
$316$			199.427i			0.631097i
$317$			448.813i			1.41581i	0.706306	+	0.707906i	$0.250360\pi$
$317$			448.813i			1.41581i	−0.706306	+	0.707906i	$0.749640\pi$
$318$			109.485i			0.344293i
$319$			102.977i			0.322811i
$320$		0			0
$321$	−615.843			−1.91851
$322$			220.285i			0.684116i
$323$	−177.978	−	116.442i	−0.551016	−	0.360501i
$324$	−183.828			−0.567372
$325$		0			0
$326$			83.6508i			0.256597i
$327$	342.046			1.04601
$328$	557.741			1.70043
$329$	−240.593			−0.731285
$330$		0			0
$331$			590.835i			1.78500i	0.451047	+	0.892500i	$0.351051\pi$
$331$			590.835i			1.78500i	−0.451047	+	0.892500i	$0.648949\pi$
$332$	227.892			0.686422
$333$			91.4516i			0.274629i
$334$	−131.747			−0.394453
$335$		0			0
$336$		−	134.183i		−	0.399355i
$337$		−	515.902i		−	1.53087i	−0.643515	−	0.765434i	$-0.722525\pi$
$337$		−	515.902i		−	1.53087i	0.643515	−	0.765434i	$-0.277475\pi$
$338$			179.645i			0.531493i
$339$	−398.659			−1.17599
$340$		0			0
$341$		−	32.9914i		−	0.0967489i
$342$	−56.0558	+	85.6797i	−0.163906	+	0.250526i
$343$	−340.040			−0.991369
$344$		−	378.482i		−	1.10024i
$345$		0			0
$346$	154.863			0.447581
$347$	−114.362			−0.329573			−0.164786	−	0.986329i	$-0.552693\pi$
$347$	−114.362			−0.329573			−0.164786	+	0.986329i	$0.552693\pi$
$348$	−298.689			−0.858303
$349$	37.5980			0.107731			0.0538653	−	0.998548i	$-0.482846\pi$
$349$	37.5980			0.107731			0.0538653	+	0.998548i	$0.482846\pi$
$350$		0			0
$351$	−130.449			−0.371649
$352$			59.3894i			0.168720i
$353$	207.841			0.588783			0.294392	−	0.955685i	$-0.404883\pi$
$353$	207.841			0.588783			0.294392	+	0.955685i	$0.404883\pi$
$354$			363.032i			1.02551i
$355$		0			0
$356$		−	156.772i		−	0.440372i
$357$			281.115i			0.787438i
$358$	97.2339			0.271603
$359$	−355.444			−0.990094			−0.495047	−	0.868866i	$-0.664849\pi$
$359$	−355.444			−0.990094			−0.495047	+	0.868866i	$0.664849\pi$
$360$		0			0
$361$	144.588	+	330.780i	0.400520	+	0.916288i
$362$	−191.387			−0.528692
$363$		−	412.582i		−	1.13659i
$364$			88.5719i			0.243329i
$365$		0			0
$366$	−122.752			−0.335389
$367$	−288.793			−0.786901			−0.393450	−	0.919346i	$-0.628719\pi$
$367$	−288.793			−0.786901			−0.393450	+	0.919346i	$0.628719\pi$
$368$	−113.151			−0.307474
$369$			237.466i			0.643540i
$370$		0			0
$371$		−	147.416i		−	0.397347i
$372$	95.6933			0.257240
$373$		−	480.221i		−	1.28746i	−0.765254	−	0.643728i	$-0.777387\pi$
$373$		−	480.221i		−	1.28746i	0.765254	−	0.643728i	$-0.222613\pi$
$374$			36.9939i			0.0989142i
$375$		0			0
$376$		−	292.741i		−	0.778565i
$377$	−315.108			−0.835829
$378$	−197.736			−0.523111
$379$			186.934i			0.493229i	0.969114	+	0.246614i	$0.0793181\pi$
$379$			186.934i			0.493229i	−0.969114	+	0.246614i	$0.920682\pi$
$380$		0			0
$381$	−578.926			−1.51949
$382$		−	253.482i		−	0.663564i
$383$		−	424.292i		−	1.10781i	−0.832579	−	0.553906i	$-0.813137\pi$
$383$		−	424.292i		−	1.10781i	0.832579	−	0.553906i	$-0.186863\pi$
$384$	−60.2132			−0.156805
$385$		0			0
$386$	340.128			0.881160
$387$	161.144			0.416393
$388$		−	65.0490i		−	0.167652i
$389$	−283.757			−0.729453			−0.364727	−	0.931115i	$-0.618838\pi$
$389$	−283.757			−0.729453			−0.364727	+	0.931115i	$0.618838\pi$
$390$		0			0
$391$	237.052			0.606270
$392$			7.11529i			0.0181513i
$393$			436.142i			1.10978i
$394$			64.9373i			0.164815i
$395$		0			0
$396$	−14.9949			−0.0378660
$397$	−569.143			−1.43361			−0.716805	−	0.697274i	$-0.754396\pi$
$397$	−569.143			−1.43361			−0.716805	+	0.697274i	$0.754396\pi$
$398$		−	22.3244i		−	0.0560914i
$399$	261.233	−	399.287i	0.654718	−	1.00072i
$400$		0			0
$401$			475.365i			1.18545i	0.805405	+	0.592725i	$0.201948\pi$
$401$			475.365i			1.18545i	−0.805405	+	0.592725i	$0.798052\pi$
$402$			416.183i			1.03528i
$403$	100.953			0.250505
$404$	366.586			0.907391
$405$		0			0
$406$	−477.645			−1.17646
$407$		−	56.0845i		−	0.137800i
$408$	−342.046			−0.838348
$409$			581.479i			1.42171i	0.703340	+	0.710854i	$0.251691\pi$
$409$			581.479i			1.42171i	−0.703340	+	0.710854i	$0.748309\pi$
$410$		0			0
$411$		−	235.681i		−	0.573434i
$412$			88.7243i			0.215350i
$413$		−	488.803i		−	1.18354i
$414$		−	114.118i		−	0.275648i
$415$		0			0
$416$	−181.731			−0.436853
$417$			626.825i			1.50318i
$418$	34.3774	−	52.5449i	0.0822425	−	0.125705i
$419$	227.508			0.542978			0.271489	−	0.962442i	$-0.412484\pi$
$419$	227.508			0.542978			0.271489	+	0.962442i	$0.412484\pi$
$420$		0			0
$421$		−	106.240i		−	0.252351i	−0.992008	−	0.126176i	$-0.959730\pi$
$421$		−	106.240i		−	0.252351i	0.992008	−	0.126176i	$-0.0402703\pi$
$422$	490.076			1.16132
$423$	124.638			0.294653
$424$	179.368			0.423037
$425$		0			0
$426$			141.016i			0.331024i
$427$	165.279			0.387071
$428$			316.508i			0.739504i
$429$	−54.7523			−0.127628
$430$		0			0
$431$		−	236.421i		−	0.548540i	−0.961653	−	0.274270i	$-0.911564\pi$
$431$		−	236.421i		−	0.548540i	0.961653	−	0.274270i	$-0.0884362\pi$
$432$		−	101.568i		−	0.235111i
$433$		−	405.561i		−	0.936631i	−0.883561	−	0.468316i	$-0.844861\pi$
$433$		−	405.561i		−	0.936631i	0.883561	−	0.468316i	$-0.155139\pi$
$434$	153.026			0.352596
$435$		0			0
$436$		−	175.792i		−	0.403193i
$437$	−336.700	−	220.285i	−0.770481	−	0.504085i
$438$	520.734			1.18889
$439$		−	415.043i		−	0.945428i	−0.881216	−	0.472714i	$-0.843274\pi$
$439$		−	415.043i		−	0.945428i	0.881216	−	0.472714i	$-0.156726\pi$
$440$		0			0
$441$	−3.02944			−0.00686947
$442$	−113.201			−0.256111
$443$	372.790			0.841513			0.420756	−	0.907174i	$-0.361765\pi$
$443$	372.790			0.841513			0.420756	+	0.907174i	$0.361765\pi$
$444$	162.676			0.366388
$445$		0			0
$446$	199.529			0.447374
$447$			31.8273i			0.0712021i
$448$	−426.338			−0.951647
$449$		−	297.789i		−	0.663226i	−0.943415	−	0.331613i	$-0.892407\pi$
$449$		−	297.789i		−	0.663226i	0.943415	−	0.331613i	$-0.107593\pi$
$450$		0			0
$451$		−	145.631i		−	0.322907i
$452$			204.888i			0.453292i
$453$	936.795			2.06798
$454$	−462.252			−1.01818
$455$		0			0
$456$	485.831	+	317.854i	1.06542	+	0.697048i
$457$	111.022			0.242937			0.121469	−	0.992595i	$-0.461240\pi$
$457$	111.022			0.242937			0.121469	+	0.992595i	$0.461240\pi$
$458$		−	326.220i		−	0.712271i
$459$			212.786i			0.463586i
$460$		0			0
$461$	692.531			1.50224			0.751118	−	0.660168i	$-0.229515\pi$
$461$	692.531			1.50224			0.751118	+	0.660168i	$0.229515\pi$
$462$	−82.9943			−0.179641
$463$	−460.213			−0.993981			−0.496991	−	0.867756i	$-0.665562\pi$
$463$	−460.213			−0.993981			−0.496991	+	0.867756i	$0.665562\pi$
$464$		−	245.344i		−	0.528759i
$465$		0			0
$466$		−	507.311i		−	1.08865i
$467$	581.548			1.24528			0.622642	−	0.782507i	$-0.286059\pi$
$467$	581.548			1.24528			0.622642	+	0.782507i	$0.286059\pi$
$468$		−	45.8844i		−	0.0980436i
$469$		−	560.368i		−	1.19481i
$470$		0			0
$471$			777.769i			1.65131i
$472$	594.749			1.26006
$473$	−98.8250			−0.208932
$474$		−	571.816i		−	1.20636i
$475$		0			0
$476$	144.477			0.303524
$477$			76.3683i			0.160101i
$478$			595.088i			1.24495i
$479$	290.686			0.606861			0.303430	−	0.952854i	$-0.401868\pi$
$479$	290.686			0.606861			0.303430	+	0.952854i	$0.401868\pi$
$480$		0			0
$481$	171.618			0.356795
$482$	−344.676			−0.715096
$483$			531.816i			1.10107i
$484$	−212.044			−0.438107
$485$		0			0
$486$	274.981			0.565804
$487$		−	402.206i		−	0.825884i	−0.910757	−	0.412942i	$-0.864501\pi$
$487$		−	402.206i		−	0.825884i	0.910757	−	0.412942i	$-0.135499\pi$
$488$			201.103i			0.412096i
$489$			201.951i			0.412987i
$490$		0			0
$491$	−568.222			−1.15728			−0.578638	−	0.815585i	$-0.696416\pi$
$491$	−568.222			−1.15728			−0.578638	+	0.815585i	$0.696416\pi$
$492$	422.410			0.858558
$493$			513.999i			1.04259i
$494$	160.787	+	105.194i	0.325479	+	0.212944i
$495$		0			0
$496$			78.6028i			0.158473i
$497$		−	189.870i		−	0.382033i
$498$	−653.434			−1.31212
$499$	536.237			1.07462			0.537311	−	0.843384i	$-0.319440\pi$
$499$	536.237			1.07462			0.537311	+	0.843384i	$0.319440\pi$
$500$		0			0
$501$	−318.066			−0.634862
$502$			270.876i			0.539594i
$503$	−167.787			−0.333574			−0.166787	−	0.985993i	$-0.553339\pi$
$503$	−167.787			−0.333574			−0.166787	+	0.985993i	$0.553339\pi$
$504$		−	221.710i		−	0.439900i
$505$		0			0
$506$			69.9853i			0.138311i
$507$			433.701i			0.855426i
$508$			297.535i			0.585698i
$509$			622.042i			1.22209i	0.791597	+	0.611043i	$0.209250\pi$
$509$			622.042i			1.22209i	−0.791597	+	0.611043i	$0.790750\pi$
$510$		0			0
$511$	−701.139			−1.37209
$512$		−	325.064i		−	0.634891i
$513$	197.736	−	302.234i	0.385450	−	0.589150i
$514$	281.266			0.547210
$515$		0			0
$516$		−	286.647i		−	0.555518i
$517$	−76.4371			−0.147847
$518$	260.141			0.502203
$519$	373.872			0.720370
$520$		0			0
$521$		−	805.100i		−	1.54530i	−0.634834	−	0.772649i	$-0.718931\pi$
$521$		−	805.100i		−	1.54530i	0.634834	−	0.772649i	$-0.281069\pi$
$522$	247.442			0.474027
$523$			283.164i			0.541422i	0.962661	+	0.270711i	$0.0872587\pi$
$523$			283.164i			0.541422i	−0.962661	+	0.270711i	$0.912741\pi$
$524$	224.152			0.427771
$525$		0			0
$526$			181.579i			0.345208i
$527$		−	164.674i		−	0.312474i
$528$		−	42.6304i		−	0.0807394i
$529$	−80.5442			−0.152257
$530$		0			0
$531$			253.223i			0.476879i
$532$	−205.210	−	134.259i	−0.385734	−	0.252366i
$533$	445.630			0.836078
$534$			449.513i			0.841785i
$535$		0			0
$536$	681.825			1.27206
$537$	234.743			0.437139
$538$	−5.26007			−0.00977708
$539$	1.85786			0.00344687
$540$		0			0
$541$	−296.551			−0.548154			−0.274077	−	0.961708i	$-0.588372\pi$
$541$	−296.551			−0.548154			−0.274077	+	0.961708i	$0.588372\pi$
$542$			181.231i			0.334374i
$543$	−462.048			−0.850917
$544$			296.437i			0.544921i
$545$		0			0
$546$		−	253.962i		−	0.465132i
$547$		−	368.218i		−	0.673159i	−0.941655	−	0.336580i	$-0.890730\pi$
$547$		−	368.218i		−	0.673159i	0.941655	−	0.336580i	$-0.109270\pi$
$548$	−121.127			−0.221034
$549$	−85.6224			−0.155961
$550$		0			0
$551$	477.645	−	730.067i	0.866869	−	1.32498i
$552$	−647.085			−1.17226
$553$			769.918i			1.39226i
$554$		−	152.770i		−	0.275758i
$555$		0			0
$556$	322.152			0.579410
$557$	−718.764			−1.29042			−0.645210	−	0.764006i	$-0.723230\pi$
$557$	−718.764			−1.29042			−0.645210	+	0.764006i	$0.723230\pi$
$558$	−79.2749			−0.142070
$559$		−	302.403i		−	0.540972i
$560$		0			0
$561$			89.3112i			0.159200i
$562$	534.522			0.951107
$563$			50.1751i			0.0891210i	0.999007	+	0.0445605i	$0.0141888\pi$
$563$			50.1751i			0.0891210i	−0.999007	+	0.0445605i	$0.985811\pi$
$564$		−	221.710i		−	0.393102i
$565$		0			0
$566$			181.579i			0.320812i
$567$	−709.698			−1.25167
$568$	231.024			0.406732
$569$		−	356.632i		−	0.626770i	−0.949626	−	0.313385i	$-0.898537\pi$
$569$		−	356.632i		−	0.626770i	0.949626	−	0.313385i	$-0.101463\pi$
$570$		0			0
$571$	−434.831			−0.761526			−0.380763	−	0.924673i	$-0.624339\pi$
$571$	−434.831			−0.761526			−0.380763	+	0.924673i	$0.624339\pi$
$572$			28.1396i			0.0491950i
$573$		−	611.959i		−	1.06799i
$574$	675.492			1.17681
$575$		0			0
$576$	220.863			0.383443
$577$	1000.20			1.73345			0.866727	−	0.498782i	$-0.166219\pi$
$577$	1000.20			1.73345			0.866727	+	0.498782i	$0.166219\pi$
$578$		−	241.226i		−	0.417346i
$579$	821.141			1.41821
$580$		0			0
$581$	879.813			1.51431
$582$			186.515i			0.320472i
$583$		−	46.8344i		−	0.0803334i
$584$		−	853.108i		−	1.46080i
$585$		0			0
$586$	44.9108			0.0766396
$587$	−402.860			−0.686304			−0.343152	−	0.939280i	$-0.611495\pi$
$587$	−402.860			−0.686304			−0.343152	+	0.939280i	$0.611495\pi$
$588$			5.38883i			0.00916468i
$589$	−153.026	+	233.897i	−0.259807	+	0.397108i
$590$		0			0
$591$			156.772i			0.265266i
$592$			133.623i			0.225714i
$593$	−640.735			−1.08050			−0.540249	−	0.841505i	$-0.681670\pi$
$593$	−640.735			−1.08050			−0.540249	+	0.841505i	$0.681670\pi$
$594$	−62.8213			−0.105760
$595$		0			0
$596$	16.3574			0.0274454
$597$		−	53.8958i		−	0.0902777i
$598$	−214.154			−0.358118
$599$		−	735.727i		−	1.22826i	−0.789205	−	0.614129i	$-0.789507\pi$
$599$		−	735.727i		−	1.22826i	0.789205	−	0.614129i	$-0.210493\pi$
$600$		0			0
$601$			204.042i			0.339504i	0.985487	+	0.169752i	$0.0542966\pi$
$601$			204.042i			0.339504i	−0.985487	+	0.169752i	$0.945703\pi$
$602$		−	458.387i		−	0.761441i
$603$			290.297i			0.481421i
$604$		−	481.459i		−	0.797117i
$605$		0			0
$606$	−1051.11			−1.73450
$607$		−	169.424i		−	0.279116i	−0.990214	−	0.139558i	$-0.955432\pi$
$607$		−	169.424i		−	0.279116i	0.990214	−	0.139558i	$-0.0445682\pi$
$608$	275.470	−	421.049i	0.453076	−	0.692514i
$609$	−1153.14			−1.89349
$610$		0			0
$611$		−	233.897i		−	0.382810i
$612$	−74.8460			−0.122297
$613$	132.615			0.216337			0.108169	−	0.994133i	$-0.465501\pi$
$613$	132.615			0.216337			0.108169	+	0.994133i	$0.465501\pi$
$614$	316.177			0.514946
$615$		0			0
$616$			135.968i			0.220727i
$617$	−109.517			−0.177500			−0.0887498	−	0.996054i	$-0.528287\pi$
$617$	−109.517			−0.177500			−0.0887498	+	0.996054i	$0.528287\pi$
$618$		−	254.399i		−	0.411648i
$619$	841.414			1.35931			0.679656	−	0.733531i	$-0.262129\pi$
$619$	841.414			1.35931			0.679656	+	0.733531i	$0.262129\pi$
$620$		0			0
$621$			402.550i			0.648229i
$622$			262.814i			0.422531i
$623$		−	605.244i		−	0.971500i
$624$	130.449			0.209052
$625$		0			0
$626$		−	555.932i		−	0.888071i
$627$	82.9943	−	126.855i	0.132367	−	0.202320i
$628$	399.729			0.636511
$629$		−	279.941i		−	0.445057i
$630$		0			0
$631$	699.661			1.10881			0.554407	−	0.832246i	$-0.312945\pi$
$631$	699.661			1.10881			0.554407	+	0.832246i	$0.312945\pi$
$632$	−936.795			−1.48227
$633$	1183.15			1.86911
$634$	−661.382			−1.04319
$635$		0			0
$636$	135.846			0.213594
$637$			5.68505i			0.00892472i
$638$	−151.749			−0.237851
$639$			98.3617i			0.153931i
$640$		0			0
$641$			1163.39i			1.81496i	0.420094	+	0.907481i	$0.361997\pi$
$641$			1163.39i			1.81496i	−0.420094	+	0.907481i	$0.638003\pi$
$642$		−	907.522i		−	1.41359i
$643$	−32.0769			−0.0498862			−0.0249431	−	0.999689i	$-0.507940\pi$
$643$	−32.0769			−0.0498862			−0.0249431	+	0.999689i	$0.507940\pi$
$644$	273.323			0.424415
$645$		0			0
$646$	171.592	−	262.273i	0.265622	−	0.405996i
$647$	324.087			0.500908			0.250454	−	0.968129i	$-0.419420\pi$
$647$	324.087			0.500908			0.250454	+	0.968129i	$0.419420\pi$
$648$		−	863.522i		−	1.33260i
$649$		−	155.294i		−	0.239282i
$650$		0			0
$651$	369.439			0.567494
$652$	103.791			0.159189
$653$	−245.436			−0.375859			−0.187929	−	0.982183i	$-0.560178\pi$
$653$	−245.436			−0.375859			−0.187929	+	0.982183i	$0.560178\pi$
$654$			504.048i			0.770716i
$655$		0			0
$656$			346.969i			0.528917i
$657$	363.223			0.552851
$658$		−	354.544i		−	0.538821i
$659$			959.655i			1.45623i	0.685456	+	0.728114i	$0.259603\pi$
$659$			959.655i			1.45623i	−0.685456	+	0.728114i	$0.740397\pi$
$660$		0			0
$661$		−	172.835i		−	0.261475i	−0.991417	−	0.130738i	$-0.958265\pi$
$661$		−	172.835i		−	0.261475i	0.991417	−	0.130738i	$-0.0417345\pi$
$662$	−870.670			−1.31521
$663$	−273.291			−0.412204
$664$			1070.51i			1.61221i
$665$		0			0
$666$	−134.765			−0.202350
$667$			972.387i			1.45785i
$668$			163.468i			0.244712i
$669$	481.706			0.720038
$670$		0			0
$671$	52.5097			0.0782558
$672$	−665.044			−0.989649
$673$			866.672i			1.28777i	0.765121	+	0.643887i	$0.222679\pi$
$673$			866.672i			1.28777i	−0.765121	+	0.643887i	$0.777321\pi$
$674$	760.247			1.12796
$675$		0			0
$676$	222.897			0.329730
$677$			232.811i			0.343886i	0.985107	+	0.171943i	$0.0550044\pi$
$677$			232.811i			0.343886i	−0.985107	+	0.171943i	$0.944996\pi$
$678$		−	587.474i		−	0.866481i
$679$		−	251.132i		−	0.369855i
$680$		0			0
$681$	−1115.97			−1.63873
$682$	48.6169			0.0712858
$683$			1.51701i			0.00222109i	0.999999	+	0.00111055i	$0.000353498\pi$
$683$			1.51701i			0.00222109i	−0.999999	+	0.00111055i	$0.999647\pi$
$684$	106.309	+	69.5522i	0.155422	+	0.101685i
$685$		0			0
$686$		−	501.091i		−	0.730453i
$687$		−	787.566i		−	1.14638i
$688$	235.453			0.342228
$689$	143.313			0.208001
$690$		0			0
$691$	−584.049			−0.845223			−0.422611	−	0.906311i	$-0.638886\pi$
$691$	−584.049			−0.845223			−0.422611	+	0.906311i	$0.638886\pi$
$692$		−	192.149i		−	0.277672i
$693$	−57.8903			−0.0835358
$694$		−	168.526i		−	0.242833i
$695$		0			0
$696$		−	1403.07i		−	2.01591i
$697$		−	726.905i		−	1.04290i
$698$			55.4054i			0.0793773i
$699$		−	1224.76i		−	1.75216i
$700$		0			0
$701$	−861.671			−1.22920			−0.614601	−	0.788838i	$-0.710683\pi$
$701$	−861.671			−1.22920			−0.614601	+	0.788838i	$0.710683\pi$
$702$		−	192.233i		−	0.273836i
$703$	−260.141	+	397.619i	−0.370044	+	0.565603i
$704$	−135.449			−0.192399
$705$		0			0
$706$			306.279i			0.433823i
$707$	1415.26			2.00178
$708$	450.438			0.636212
$709$	−808.916			−1.14093			−0.570463	−	0.821324i	$-0.693236\pi$
$709$	−808.916			−1.14093			−0.570463	+	0.821324i	$0.693236\pi$
$710$		0			0
$711$		−	398.854i		−	0.560976i
$712$	736.429			1.03431
$713$		−	311.531i		−	0.436929i
$714$	−414.259			−0.580195
$715$		0			0
$716$		−	120.645i		−	0.168498i
$717$			1436.67i			2.00372i
$718$		−	523.791i		−	0.729514i
$719$	−364.836			−0.507422			−0.253711	−	0.967280i	$-0.581651\pi$
$719$	−364.836			−0.507422			−0.253711	+	0.967280i	$0.581651\pi$
$720$		0			0
$721$			342.534i			0.475082i
$722$	−487.446	+	213.068i	−0.675133	+	0.295109i
$723$	−832.122			−1.15093
$724$			237.466i			0.327992i
$725$		0			0
$726$	607.992			0.837455
$727$	−786.551			−1.08191			−0.540956	−	0.841051i	$-0.681938\pi$
$727$	−786.551			−1.08191			−0.540956	+	0.841051i	$0.681938\pi$
$728$	−416.061			−0.571512
$729$	−240.990			−0.330576
$730$		0			0
$731$	−493.276			−0.674797
$732$			152.307i			0.208070i
$733$	−471.493			−0.643238			−0.321619	−	0.946869i	$-0.604227\pi$
$733$	−471.493			−0.643238			−0.321619	+	0.946869i	$0.604227\pi$
$734$		−	425.572i		−	0.579799i
$735$		0			0
$736$			560.801i			0.761958i
$737$		−	178.030i		−	0.241561i
$738$	−349.936			−0.474168
$739$	−492.673			−0.666676			−0.333338	−	0.942807i	$-0.608175\pi$
$739$	−492.673			−0.666676			−0.333338	+	0.942807i	$0.608175\pi$
$740$		0			0
$741$	388.174	+	253.962i	0.523851	+	0.342729i
$742$	217.236			0.292770
$743$			437.843i			0.589291i	0.955607	+	0.294646i	$0.0952016\pi$
$743$			437.843i			0.589291i	−0.955607	+	0.294646i	$0.904798\pi$
$744$			449.513i			0.604184i
$745$		0			0
$746$	707.666			0.948614
$747$	−455.785			−0.610153
$748$	45.9008			0.0613648
$749$			1221.93i			1.63141i
$750$		0			0
$751$			690.549i			0.919506i	0.888047	+	0.459753i	$0.152062\pi$
$751$			690.549i			0.919506i	−0.888047	+	0.459753i	$0.847938\pi$
$752$	182.113			0.242172
$753$			653.953i			0.868464i
$754$		−	464.351i		−	0.615850i
$755$		0			0
$756$			245.344i			0.324530i
$757$	386.442			0.510491			0.255246	−	0.966876i	$-0.417844\pi$
$757$	386.442			0.510491			0.255246	+	0.966876i	$0.417844\pi$
$758$	−275.470			−0.363417
$759$			168.959i			0.222608i
$760$		0			0
$761$	−1032.01			−1.35613			−0.678064	−	0.735003i	$-0.737181\pi$
$761$	−1032.01			−1.35613			−0.678064	+	0.735003i	$0.737181\pi$
$762$		−	853.120i		−	1.11958i
$763$		−	678.673i		−	0.889479i
$764$	−314.512			−0.411665
$765$		0			0
$766$	625.248			0.816250
$767$	475.198			0.619554
$768$		−	948.216i		−	1.23466i
$769$	−562.421			−0.731367			−0.365684	−	0.930739i	$-0.619165\pi$
$769$	−562.421			−0.731367			−0.365684	+	0.930739i	$0.619165\pi$
$770$		0			0
$771$	679.037			0.880722
$772$		−	422.020i		−	0.546658i
$773$			503.048i			0.650774i	0.945581	+	0.325387i	$0.105495\pi$
$773$			503.048i			0.650774i	−0.945581	+	0.325387i	$0.894505\pi$
$774$			237.466i			0.306804i
$775$		0			0
$776$	305.563			0.393767
$777$	628.037			0.808284
$778$		−	418.152i		−	0.537471i
$779$	−675.492	+	1032.47i	−0.867127	+	1.32538i
$780$		0			0
$781$		−	60.3223i		−	0.0772373i
$782$			349.326i			0.446708i
$783$	−872.849			−1.11475
$784$	−4.42641			−0.00564593
$785$		0			0
$786$	−642.711			−0.817698
$787$			1453.47i			1.84685i	0.383774	+	0.923427i	$0.374624\pi$
$787$			1453.47i			1.84685i	−0.383774	+	0.923427i	$0.625376\pi$
$788$	80.5721			0.102249
$789$			438.372i			0.555604i
$790$		0			0
$791$			791.001i			1.00000i
$792$		−	70.4378i		−	0.0889366i
$793$			160.679i			0.202622i
$794$		−	838.704i		−	1.05630i
$795$		0			0
$796$	−27.6994			−0.0347982
$797$		−	754.127i		−	0.946207i	−0.881007	−	0.473104i	$-0.843134\pi$
$797$		−	754.127i		−	0.946207i	0.881007	−	0.473104i	$-0.156866\pi$
$798$	588.399	+	384.959i	0.737342	+	0.482405i
$799$	−381.529			−0.477508
$800$		0			0
$801$			313.545i			0.391442i
$802$	−700.511			−0.873455
$803$	−222.754			−0.277402
$804$	516.387			0.642272
$805$		0			0
$806$			148.767i			0.184575i
$807$	−12.6989			−0.0157360
$808$			1722.01i			2.13120i
$809$	57.1136			0.0705977			0.0352989	−	0.999377i	$-0.488762\pi$
$809$	57.1136			0.0705977			0.0352989	+	0.999377i	$0.488762\pi$
$810$		0			0
$811$		−	899.332i		−	1.10892i	−0.832211	−	0.554459i	$-0.812925\pi$
$811$		−	899.332i		−	1.10892i	0.832211	−	0.554459i	$-0.187075\pi$
$812$			592.646i			0.729860i
$813$			437.529i			0.538166i
$814$	82.6476			0.101533
$815$		0			0
$816$		−	212.786i		−	0.260767i
$817$	700.632	+	458.387i	0.857567	+	0.561062i
$818$	−856.882			−1.04753
$819$		−	177.144i		−	0.216293i
$820$		0			0
$821$	−524.303			−0.638615			−0.319307	−	0.947651i	$-0.603450\pi$
$821$	−524.303			−0.638615			−0.319307	+	0.947651i	$0.603450\pi$
$822$	347.306			0.422514
$823$	1107.42			1.34559			0.672795	−	0.739829i	$-0.265094\pi$
$823$	1107.42			1.34559			0.672795	+	0.739829i	$0.265094\pi$
$824$	−416.777			−0.505797
$825$		0			0
$826$	720.312			0.872048
$827$			549.290i			0.664196i	0.943245	+	0.332098i	$0.107756\pi$
$827$			549.290i			0.664196i	−0.943245	+	0.332098i	$0.892244\pi$
$828$	−141.594			−0.171007
$829$			676.577i			0.816136i	0.912951	+	0.408068i	$0.133797\pi$
$829$			676.577i			0.816136i	−0.912951	+	0.408068i	$0.866203\pi$
$830$		0			0
$831$		−	368.819i		−	0.443826i
$832$		−	414.472i		−	0.498163i
$833$	9.27337			0.0111325
$834$	−923.706			−1.10756
$835$		0			0
$836$	−65.1960	−	42.6543i	−0.0779856	−	0.0510219i
$837$	279.641			0.334099
$838$			335.261i			0.400073i
$839$		−	196.723i		−	0.234474i	−0.993104	−	0.117237i	$-0.962596\pi$
$839$		−	196.723i		−	0.234474i	0.993104	−	0.117237i	$-0.0374037\pi$
$840$		0			0
$841$	−1267.43			−1.50705
$842$	156.558			0.185936
$843$	1290.45			1.53078
$844$		−	608.070i		−	0.720462i
$845$		0			0
$846$			183.670i			0.217104i
$847$	−818.628			−0.966502
$848$			111.584i			0.131585i
$849$			438.372i			0.516339i
$850$		0			0
$851$		−	529.594i		−	0.622320i
$852$	174.968			0.205362
$853$	1124.34			1.31810			0.659050	−	0.752099i	$-0.270958\pi$
$853$	1124.34			1.31810			0.659050	+	0.752099i	$0.270958\pi$
$854$			243.560i			0.285199i
$855$		0			0
$856$	−1486.78			−1.73689
$857$			1634.72i			1.90749i	0.300616	+	0.953745i	$0.402808\pi$
$857$			1634.72i			1.90749i	−0.300616	+	0.953745i	$0.597192\pi$
$858$		−	80.6844i		−	0.0940378i
$859$	325.977			0.379484			0.189742	−	0.981834i	$-0.439235\pi$
$859$	325.977			0.379484			0.189742	+	0.981834i	$0.439235\pi$
$860$		0			0
$861$	1630.78			1.89405
$862$	348.396			0.404171
$863$			330.052i			0.382447i	0.981547	+	0.191224i	$0.0612455\pi$
$863$			330.052i			0.382447i	−0.981547	+	0.191224i	$0.938754\pi$
$864$	−503.395			−0.582633
$865$		0			0
$866$	597.646			0.690122
$867$		−	582.371i		−	0.671708i
$868$		−	189.870i		−	0.218745i
$869$			244.605i			0.281479i
$870$		0			0
$871$	544.772			0.625455
$872$	825.773			0.946987
$873$			130.098i			0.149024i
$874$	324.618	−	496.170i	0.371417	−	0.567700i
$875$		0			0
$876$		−	646.110i		−	0.737568i
$877$		−	415.606i		−	0.473895i	−0.971522	−	0.236947i	$-0.923853\pi$
$877$		−	415.606i		−	0.473895i	0.971522	−	0.236947i	$-0.0761469\pi$
$878$	611.618			0.696604
$879$	108.424			0.123350
$880$		0			0
$881$	−1411.11			−1.60172			−0.800859	−	0.598854i	$-0.795623\pi$
$881$	−1411.11			−1.60172			−0.800859	+	0.598854i	$0.795623\pi$
$882$		−	4.46426i		−	0.00506152i
$883$	811.984			0.919574			0.459787	−	0.888029i	$-0.347926\pi$
$883$	811.984			0.919574			0.459787	+	0.888029i	$0.347926\pi$
$884$			140.456i			0.158887i
$885$		0			0
$886$			549.353i			0.620038i
$887$		−	534.735i		−	0.602858i	−0.953489	−	0.301429i	$-0.902536\pi$
$887$		−	534.735i		−	0.602858i	0.953489	−	0.301429i	$-0.0974636\pi$
$888$			764.161i			0.860542i
$889$			1148.68i			1.29210i
$890$		0			0
$891$	−225.473			−0.253056
$892$		−	247.569i		−	0.277544i
$893$	541.911	+	354.544i	0.606843	+	0.397026i
$894$	−46.9016			−0.0524626
$895$		0			0
$896$			119.472i			0.133340i
$897$	−517.014			−0.576382
$898$	438.829			0.488674
$899$	675.492			0.751381
$900$		0			0
$901$		−	233.770i		−	0.259456i
$902$	214.606			0.237922
$903$		−	1106.65i		−	1.22552i
$904$	−962.448			−1.06465
$905$		0			0
$906$			1380.48i			1.52371i
$907$			634.240i			0.699272i	0.936886	+	0.349636i	$0.113695\pi$
$907$			634.240i			0.699272i	−0.936886	+	0.349636i	$0.886305\pi$
$908$			573.547i			0.631660i
$909$	−733.172			−0.806569
$910$		0			0
$911$			931.405i			1.02240i	0.859462	+	0.511199i	$0.170799\pi$
$911$			931.405i			1.02240i	−0.859462	+	0.511199i	$0.829201\pi$
$912$	−197.736	+	302.234i	−0.216816	+	0.331397i
$913$	279.519			0.306155
$914$			163.605i			0.178999i
$915$		0			0
$916$	−404.764			−0.441882
$917$	865.374			0.943702
$918$	−313.567			−0.341576
$919$	596.055			0.648591			0.324295	−	0.945956i	$-0.394873\pi$
$919$	596.055			0.648591			0.324295	+	0.945956i	$0.394873\pi$
$920$		0			0
$921$	763.318			0.828793
$922$			1020.53i			1.10687i
$923$	184.586			0.199985
$924$			102.977i			0.111447i
$925$		0			0
$926$		−	678.182i		−	0.732378i
$927$		−	177.449i		−	0.191422i
$928$	−1215.98			−1.31033
$929$	−953.514			−1.02639			−0.513194	−	0.858273i	$-0.671538\pi$
$929$	−953.514			−1.02639			−0.513194	+	0.858273i	$0.671538\pi$
$930$		0			0
$931$	−13.1716	−	8.61748i	−0.0141478	−	0.00925615i
$932$	−629.455			−0.675381
$933$			634.489i			0.680053i
$934$			856.984i			0.917542i
$935$		0			0
$936$	215.539			0.230277
$937$	248.360			0.265058			0.132529	−	0.991179i	$-0.457690\pi$
$937$	248.360			0.265058			0.132529	+	0.991179i	$0.457690\pi$
$938$	825.773			0.880355
$939$		−	1342.14i		−	1.42933i
$940$		0			0
$941$		−	736.899i		−	0.783102i	−0.920156	−	0.391551i	$-0.871939\pi$
$941$		−	736.899i		−	0.783102i	0.920156	−	0.391551i	$-0.128061\pi$
$942$	−1146.14			−1.21671
$943$		−	1375.16i		−	1.45828i
$944$			369.992i			0.391940i
$945$		0			0
$946$		−	145.631i		−	0.153944i
$947$	−257.547			−0.271961			−0.135980	−	0.990712i	$-0.543418\pi$
$947$	−257.547			−0.271961			−0.135980	+	0.990712i	$0.543418\pi$
$948$	−709.490			−0.748407
$949$		−	681.625i		−	0.718256i
$950$		0			0
$951$	−1596.72			−1.67899
$952$			678.673i			0.712892i
$953$			251.242i			0.263633i	0.991274	+	0.131816i	$0.0420809\pi$
$953$			251.242i			0.263633i	−0.991274	+	0.131816i	$0.957919\pi$
$954$	−112.538			−0.117965
$955$		0			0
$956$	738.365			0.772349
$957$	−366.355			−0.382816
$958$			428.363i			0.447143i
$959$	−467.629			−0.487621
$960$		0			0
$961$	744.588			0.774805
$962$			252.901i			0.262891i
$963$		−	633.016i		−	0.657337i
$964$			427.663i			0.443634i
$965$		0			0
$966$	−783.698			−0.811281
$967$	−1508.95			−1.56044			−0.780221	−	0.625504i	$-0.784893\pi$
$967$	−1508.95			−1.56044			−0.780221	+	0.625504i	$0.784893\pi$
$968$		−	996.062i		−	1.02899i
$969$	414.259	−	633.183i	0.427512	−	0.653440i
$970$		0			0
$971$			701.690i			0.722647i	0.932441	+	0.361323i	$0.117675\pi$
$971$			701.690i			0.722647i	−0.932441	+	0.361323i	$0.882325\pi$
$972$		−	341.187i		−	0.351016i
$973$	1243.72			1.27823
$974$	592.701			0.608522
$975$		0			0
$976$	−125.106			−0.128182
$977$		−	485.382i		−	0.496809i	−0.968656	−	0.248405i	$-0.920094\pi$
$977$		−	485.382i		−	0.496809i	0.968656	−	0.248405i	$-0.0799062\pi$
$978$	−297.600			−0.304294
$979$		−	192.288i		−	0.196413i
$980$		0			0
$981$			351.584i			0.358394i
$982$		−	837.347i		−	0.852696i
$983$		−	1015.25i		−	1.03281i	−0.856344	−	0.516406i	$-0.827269\pi$
$983$		−	1015.25i		−	1.03281i	0.856344	−	0.516406i	$-0.172731\pi$
$984$			1984.25i			2.01651i
$985$		0			0
$986$	−757.442			−0.768197
$987$		−	855.945i		−	0.867219i
$988$	130.522	−	199.499i	0.132107	−	0.201922i
$989$	−933.183			−0.943562
$990$		0			0
$991$		−	93.4931i		−	0.0943422i	−0.998887	−	0.0471711i	$-0.984979\pi$
$991$		−	93.4931i		−	0.0943422i	0.998887	−	0.0471711i	$-0.0150206\pi$
$992$	389.574			0.392715
$993$	−2101.98			−2.11680
$994$	279.798			0.281487
$995$		0			0
$996$			810.760i			0.814016i
$997$	−1088.79			−1.09206			−0.546032	−	0.837764i	$-0.683862\pi$
$997$	−1088.79			−1.09206			−0.546032	+	0.837764i	$0.683862\pi$
$998$			790.212i			0.791796i
$999$	475.383			0.475859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.c.f.151.6		8
5.2	odd	4		95.3.d.d.94.4	yes	8
5.3	odd	4		95.3.d.d.94.5	yes	8
5.4	even	2	inner	475.3.c.f.151.3		8
15.2	even	4		855.3.g.g.379.5		8
15.8	even	4		855.3.g.g.379.4		8
19.18	odd	2	inner	475.3.c.f.151.4		8
95.18	even	4		95.3.d.d.94.3	✓	8
95.37	even	4		95.3.d.d.94.6	yes	8
95.94	odd	2	inner	475.3.c.f.151.5		8
285.113	odd	4		855.3.g.g.379.6		8
285.227	odd	4		855.3.g.g.379.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.d.d.94.3	✓	8	95.18	even	4
95.3.d.d.94.4	yes	8	5.2	odd	4
95.3.d.d.94.5	yes	8	5.3	odd	4
95.3.d.d.94.6	yes	8	95.37	even	4
475.3.c.f.151.3		8	5.4	even	2	inner
475.3.c.f.151.4		8	19.18	odd	2	inner
475.3.c.f.151.5		8	95.94	odd	2	inner
475.3.c.f.151.6		8	1.1	even	1	trivial
855.3.g.g.379.3		8	285.227	odd	4
855.3.g.g.379.4		8	15.8	even	4
855.3.g.g.379.5		8	15.2	even	4
855.3.g.g.379.6		8	285.113	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.47363i q^{2} +3.55765i q^{3} +1.82843 q^{4} -5.24264 q^{6} +7.05893 q^{7} +8.58892i q^{8} -3.65685 q^{9} +O(q^{10})\)	\(q+1.47363i q^{2} +3.55765i q^{3} +1.82843 q^{4} -5.24264 q^{6} +7.05893 q^{7} +8.58892i q^{8} -3.65685 q^{9} +2.24264 q^{11} +6.50490i q^{12} +6.86246i q^{13} +10.4022i q^{14} -5.34315 q^{16} +11.1939 q^{17} -5.38883i q^{18} +(-15.8995 - 10.4022i) q^{19} +25.1132i q^{21} +3.30481i q^{22} +21.1768 q^{23} -30.5563 q^{24} -10.1127 q^{26} +19.0090i q^{27} +12.9067 q^{28} +45.9176i q^{29} -14.7110i q^{31} +26.4819i q^{32} +7.97852i q^{33} +16.4957i q^{34} -6.68629 q^{36} -25.0083i q^{37} +(15.3290 - 23.4299i) q^{38} -24.4142 q^{39} -64.9373i q^{41} -37.0074 q^{42} -44.0663 q^{43} +4.10051 q^{44} +31.2066i q^{46} -34.0835 q^{47} -19.0090i q^{48} +0.828427 q^{49} +39.8241i q^{51} +12.5475i q^{52} -20.8836i q^{53} -28.0122 q^{54} +60.6285i q^{56} +(37.0074 - 56.5648i) q^{57} -67.6654 q^{58} -69.2460i q^{59} +23.4142 q^{61} +21.6784 q^{62} -25.8135 q^{63} -60.3970 q^{64} -11.7574 q^{66} -79.3843i q^{67} +20.4673 q^{68} +75.3395i q^{69} -26.8979i q^{71} -31.4084i q^{72} -99.3266 q^{73} +36.8528 q^{74} +(-29.0711 - 19.0197i) q^{76} +15.8306 q^{77} -35.9774i q^{78} +109.070i q^{79} -100.539 q^{81} +95.6933 q^{82} +124.638 q^{83} +45.9176i q^{84} -64.9373i q^{86} -163.359 q^{87} +19.2619i q^{88} -85.7417i q^{89} +48.4416i q^{91} +38.7202 q^{92} +52.3364 q^{93} -50.2263i q^{94} -94.2132 q^{96} -35.5765i q^{97} +1.22079i q^{98} -8.20101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	\( 8 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 16 q^{11} - 88 q^{16} - 48 q^{19} - 120 q^{24} + 168 q^{26} - 144 q^{36} - 184 q^{39} + 112 q^{44} - 16 q^{49} + 104 q^{54} + 176 q^{61} - 8 q^{64} - 128 q^{66} - 384 q^{74} - 176 q^{76} - 216 q^{81} - 584 q^{96} - 224 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 16 * q^11 - 88 * q^16 - 48 * q^19 - 120 * q^24 + 168 * q^26 - 144 * q^36 - 184 * q^39 + 112 * q^44 - 16 * q^49 + 104 * q^54 + 176 * q^61 - 8 * q^64 - 128 * q^66 - 384 * q^74 - 176 * q^76 - 216 * q^81 - 584 * q^96 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more