LMFDB - Embedded newform 525.3.h.d.76.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(76,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("525.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.h (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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.10
Root			$0.198184 + 0.343264i$ of defining polynomial
Character	$\chi$	$=$	525.76
Dual form			525.3.h.d.76.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79155 q^{2} +1.73205i q^{3} +3.79273 q^{4} +4.83510i q^{6} +(-4.15782 + 5.63139i) q^{7} -0.578591 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+2.79155 q^{2} +1.73205i q^{3} +3.79273 q^{4} +4.83510i q^{6} +(-4.15782 + 5.63139i) q^{7} -0.578591 q^{8} -3.00000 q^{9} -18.9690 q^{11} +6.56921i q^{12} +10.9807i q^{13} +(-11.6068 + 15.7203i) q^{14} -16.7861 q^{16} +22.3060i q^{17} -8.37464 q^{18} -19.6057i q^{19} +(-9.75385 - 7.20156i) q^{21} -52.9528 q^{22} +31.9991 q^{23} -1.00215i q^{24} +30.6530i q^{26} -5.19615i q^{27} +(-15.7695 + 21.3583i) q^{28} +39.9967 q^{29} +36.6641i q^{31} -44.5448 q^{32} -32.8553i q^{33} +62.2683i q^{34} -11.3782 q^{36} -8.94699 q^{37} -54.7302i q^{38} -19.0191 q^{39} -37.6320i q^{41} +(-27.2283 - 20.1035i) q^{42} +18.8702 q^{43} -71.9443 q^{44} +89.3269 q^{46} +49.3786i q^{47} -29.0744i q^{48} +(-14.4250 - 46.8286i) q^{49} -38.6352 q^{51} +41.6468i q^{52} -49.2398 q^{53} -14.5053i q^{54} +(2.40568 - 3.25827i) q^{56} +33.9580 q^{57} +111.653 q^{58} +35.2173i q^{59} +63.4723i q^{61} +102.349i q^{62} +(12.4735 - 16.8942i) q^{63} -57.2046 q^{64} -91.7170i q^{66} -21.3544 q^{67} +84.6008i q^{68} +55.4240i q^{69} +36.2998 q^{71} +1.73577 q^{72} +6.66818i q^{73} -24.9759 q^{74} -74.3591i q^{76} +(78.8697 - 106.822i) q^{77} -53.0926 q^{78} -16.2015 q^{79} +9.00000 q^{81} -105.052i q^{82} +36.7822i q^{83} +(-36.9937 - 27.3136i) q^{84} +52.6770 q^{86} +69.2763i q^{87} +10.9753 q^{88} -88.0954i q^{89} +(-61.8364 - 45.6557i) q^{91} +121.364 q^{92} -63.5040 q^{93} +137.843i q^{94} -77.1539i q^{96} -133.810i q^{97} +(-40.2681 - 130.724i) q^{98} +56.9070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9	$ 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} - 12 q^{18} + 36 q^{21} + 88 q^{22} + 64 q^{23} - 88 q^{28} + 104 q^{29} + 228 q^{32} - 132 q^{36} - 32 q^{37} - 24 q^{39} + 60 q^{42} - 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 24 q^{51} - 176 q^{53} - 368 q^{56} + 240 q^{57} + 400 q^{58} - 24 q^{63} - 20 q^{64} - 168 q^{67} + 32 q^{71} + 12 q^{72} + 184 q^{74} - 8 q^{77} - 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 400 q^{86} + 536 q^{88} + 24 q^{91} - 192 q^{92} - 48 q^{93} - 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 - 12 * q^18 + 36 * q^21 + 88 * q^22 + 64 * q^23 - 88 * q^28 + 104 * q^29 + 228 * q^32 - 132 * q^36 - 32 * q^37 - 24 * q^39 + 60 * q^42 - 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 24 * q^51 - 176 * q^53 - 368 * q^56 + 240 * q^57 + 400 * q^58 - 24 * q^63 - 20 * q^64 - 168 * q^67 + 32 * q^71 + 12 * q^72 + 184 * q^74 - 8 * q^77 - 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 400 * q^86 + 536 * q^88 + 24 * q^91 - 192 * q^92 - 48 * q^93 - 884 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	2.79155			1.39577			0.697887	−	0.716208i	$-0.254124\pi$
$2$	2.79155			1.39577			0.697887	+	0.716208i	$0.254124\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.79273			0.948184
$5$		0			0
$5$		0			0
$6$			4.83510i			0.805850i
$7$	−4.15782	+	5.63139i	−0.593975	+	0.804484i
$7$	−4.15782	+	5.63139i	−0.593975	+	0.804484i
$8$	−0.578591			−0.0723239
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−18.9690			−1.72445			−0.862227	−	0.506522i	$-0.830931\pi$
$11$	−18.9690			−1.72445			−0.862227	+	0.506522i	$0.830931\pi$
$12$			6.56921i			0.547434i
$13$			10.9807i			0.844667i	0.906441	+	0.422333i	$0.138789\pi$
$13$			10.9807i			0.844667i	−0.906441	+	0.422333i	$0.861211\pi$
$14$	−11.6068	+	15.7203i	−0.829054	+	1.12288i
$15$		0			0
$16$	−16.7861			−1.04913
$17$			22.3060i			1.31212i	0.754709	+	0.656060i	$0.227778\pi$
$17$			22.3060i			1.31212i	−0.754709	+	0.656060i	$0.772222\pi$
$18$	−8.37464			−0.465258
$19$		−	19.6057i		−	1.03188i	−0.856625	−	0.515939i	$-0.827443\pi$
$19$		−	19.6057i		−	1.03188i	0.856625	−	0.515939i	$-0.172557\pi$
$20$		0			0
$21$	−9.75385	−	7.20156i	−0.464469	−	0.342932i
$22$	−52.9528			−2.40695
$23$	31.9991			1.39126			0.695632	−	0.718399i	$-0.255125\pi$
$23$	31.9991			1.39126			0.695632	+	0.718399i	$0.255125\pi$
$24$		−	1.00215i		−	0.0417562i
$25$		0			0
$26$			30.6530i			1.17896i
$27$		−	5.19615i		−	0.192450i
$28$	−15.7695	+	21.3583i	−0.563197	+	0.762798i
$29$	39.9967			1.37920			0.689598	−	0.724192i	$-0.257787\pi$
$29$	39.9967			1.37920			0.689598	+	0.724192i	$0.257787\pi$
$30$		0			0
$31$			36.6641i			1.18271i	0.806411	+	0.591356i	$0.201407\pi$
$31$			36.6641i			1.18271i	−0.806411	+	0.591356i	$0.798593\pi$
$32$	−44.5448			−1.39203
$33$		−	32.8553i		−	0.995614i
$34$			62.2683i			1.83142i
$35$		0			0
$36$	−11.3782			−0.316061
$37$	−8.94699			−0.241810			−0.120905	−	0.992664i	$-0.538580\pi$
$37$	−8.94699			−0.241810			−0.120905	+	0.992664i	$0.538580\pi$
$38$		−	54.7302i		−	1.44027i
$39$	−19.0191			−0.487669
$40$		0			0
$41$		−	37.6320i		−	0.917854i	−0.888474	−	0.458927i	$-0.848234\pi$
$41$		−	37.6320i		−	0.917854i	0.888474	−	0.458927i	$-0.151766\pi$
$42$	−27.2283	−	20.1035i	−0.648293	−	0.478655i
$43$	18.8702			0.438841			0.219421	−	0.975630i	$-0.429583\pi$
$43$	18.8702			0.438841			0.219421	+	0.975630i	$0.429583\pi$
$44$	−71.9443			−1.63510
$45$		0			0
$46$	89.3269			1.94189
$47$			49.3786i			1.05061i	0.850914	+	0.525304i	$0.176048\pi$
$47$			49.3786i			1.05061i	−0.850914	+	0.525304i	$0.823952\pi$
$48$		−	29.0744i		−	0.605716i
$49$	−14.4250	−	46.8286i	−0.294388	−	0.955686i
$50$		0			0
$51$	−38.6352			−0.757552
$52$			41.6468i			0.800899i
$53$	−49.2398			−0.929052			−0.464526	−	0.885559i	$-0.653775\pi$
$53$	−49.2398			−0.929052			−0.464526	+	0.885559i	$0.653775\pi$
$54$		−	14.5053i		−	0.268617i
$55$		0			0
$56$	2.40568	−	3.25827i	0.0429586	−	0.0581834i
$57$	33.9580			0.595755
$58$	111.653			1.92505
$59$			35.2173i			0.596903i	0.954425	+	0.298452i	$0.0964701\pi$
$59$			35.2173i			0.596903i	−0.954425	+	0.298452i	$0.903530\pi$
$60$		0			0
$61$			63.4723i			1.04053i	0.854005	+	0.520265i	$0.174167\pi$
$61$			63.4723i			1.04053i	−0.854005	+	0.520265i	$0.825833\pi$
$62$			102.349i			1.65080i
$63$	12.4735	−	16.8942i	0.197992	−	0.268161i
$64$	−57.2046			−0.893821
$65$		0			0
$66$		−	91.7170i		−	1.38965i
$67$	−21.3544			−0.318723			−0.159361	−	0.987220i	$-0.550943\pi$
$67$	−21.3544			−0.318723			−0.159361	+	0.987220i	$0.550943\pi$
$68$			84.6008i			1.24413i
$69$			55.4240i			0.803246i
$70$		0			0
$71$	36.2998			0.511265			0.255632	−	0.966774i	$-0.417716\pi$
$71$	36.2998			0.511265			0.255632	+	0.966774i	$0.417716\pi$
$72$	1.73577			0.0241080
$73$			6.66818i			0.0913449i	0.998956	+	0.0456725i	$0.0145431\pi$
$73$			6.66818i			0.0913449i	−0.998956	+	0.0456725i	$0.985457\pi$
$74$	−24.9759			−0.337513
$75$		0			0
$76$		−	74.3591i		−	0.978409i
$77$	78.8697	−	106.822i	1.02428	−	1.38729i
$78$	−53.0926			−0.680675
$79$	−16.2015			−0.205082			−0.102541	−	0.994729i	$-0.532697\pi$
$79$	−16.2015			−0.205082			−0.102541	+	0.994729i	$0.532697\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	105.052i		−	1.28112i
$83$			36.7822i			0.443159i	0.975142	+	0.221579i	$0.0711212\pi$
$83$			36.7822i			0.443159i	−0.975142	+	0.221579i	$0.928879\pi$
$84$	−36.9937	−	27.3136i	−0.440402	−	0.325162i
$85$		0			0
$86$	52.6770			0.612523
$87$			69.2763i			0.796279i
$88$	10.9753			0.124719
$89$		−	88.0954i		−	0.989836i	−0.868940	−	0.494918i	$-0.835198\pi$
$89$		−	88.0954i		−	0.989836i	0.868940	−	0.494918i	$-0.164802\pi$
$90$		0			0
$91$	−61.8364	−	45.6557i	−0.679520	−	0.501711i
$92$	121.364			1.31917
$93$	−63.5040			−0.682839
$94$			137.843i			1.46641i
$95$		0			0
$96$		−	77.1539i		−	0.803687i
$97$		−	133.810i		−	1.37948i	−0.724055	−	0.689742i	$-0.757724\pi$
$97$		−	133.810i		−	1.37948i	0.724055	−	0.689742i	$-0.242276\pi$
$98$	−40.2681	−	130.724i	−0.410899	−	1.33392i
$99$	56.9070			0.574818
$100$		0			0
$101$			194.903i			1.92973i	0.262743	+	0.964866i	$0.415373\pi$
$101$			194.903i			1.92973i	−0.262743	+	0.964866i	$0.584627\pi$
$102$	−107.852			−1.05737
$103$			41.2629i			0.400610i	0.979734	+	0.200305i	$0.0641933\pi$
$103$			41.2629i			0.400610i	−0.979734	+	0.200305i	$0.935807\pi$
$104$		−	6.35332i		−	0.0610896i
$105$		0			0
$106$	−137.455			−1.29675
$107$	−29.7031			−0.277599			−0.138799	−	0.990321i	$-0.544324\pi$
$107$	−29.7031			−0.277599			−0.138799	+	0.990321i	$0.544324\pi$
$108$		−	19.7076i		−	0.182478i
$109$	91.7028			0.841310			0.420655	−	0.907221i	$-0.361800\pi$
$109$	91.7028			0.841310			0.420655	+	0.907221i	$0.361800\pi$
$110$		0			0
$111$		−	15.4966i		−	0.139609i
$112$	69.7937	−	94.5290i	0.623158	−	0.844009i
$113$	−2.98301			−0.0263983			−0.0131992	−	0.999913i	$-0.504202\pi$
$113$	−2.98301			−0.0263983			−0.0131992	+	0.999913i	$0.504202\pi$
$114$	94.7954			0.831539
$115$		0			0
$116$	151.697			1.30773
$117$		−	32.9420i		−	0.281556i
$118$			98.3107i			0.833142i
$119$	−125.614	−	92.7445i	−1.05558	−	0.779366i
$120$		0			0
$121$	238.823			1.97374
$122$			177.186i			1.45234i
$123$	65.1806			0.529923
$124$			139.057i			1.12143i
$125$		0			0
$126$	34.8203	−	47.1608i	0.276351	−	0.374292i
$127$	−104.651			−0.824023			−0.412012	−	0.911179i	$-0.635174\pi$
$127$	−104.651			−0.824023			−0.412012	+	0.911179i	$0.635174\pi$
$128$	18.4901			0.144454
$129$			32.6841i			0.253365i
$130$		0			0
$131$		−	70.8051i		−	0.540497i	−0.962791	−	0.270249i	$-0.912894\pi$
$131$		−	70.8051i		−	0.540497i	0.962791	−	0.270249i	$-0.0871059\pi$
$132$		−	124.611i		−	0.944025i
$133$	110.407	+	81.5169i	0.830129	+	0.612909i
$134$	−59.6118			−0.444864
$135$		0			0
$136$		−	12.9061i		−	0.0948976i
$137$	158.673			1.15820			0.579100	−	0.815256i	$-0.303404\pi$
$137$	158.673			1.15820			0.579100	+	0.815256i	$0.303404\pi$
$138$			154.719i			1.12115i
$139$			54.4253i			0.391549i	0.980649	+	0.195774i	$0.0627220\pi$
$139$			54.4253i			0.391549i	−0.980649	+	0.195774i	$0.937278\pi$
$140$		0			0
$141$	−85.5262			−0.606569
$142$	101.333			0.713610
$143$		−	208.292i		−	1.45659i
$144$	50.3583			0.349710
$145$		0			0
$146$			18.6145i			0.127497i
$147$	81.1095	−	24.9848i	0.551766	−	0.169965i
$148$	−33.9335			−0.229281
$149$	229.102			1.53760			0.768799	−	0.639490i	$-0.220854\pi$
$149$	229.102			1.53760			0.768799	+	0.639490i	$0.220854\pi$
$150$		0			0
$151$	−197.735			−1.30950			−0.654750	−	0.755845i	$-0.727226\pi$
$151$	−197.735			−1.30950			−0.654750	+	0.755845i	$0.727226\pi$
$152$			11.3437i			0.0746294i
$153$		−	66.9181i		−	0.437373i
$154$	220.169	−	298.198i	1.42967	−	1.93635i
$155$		0			0
$156$	−72.1343			−0.462399
$157$			211.036i			1.34418i	0.740470	+	0.672089i	$0.234603\pi$
$157$			211.036i			1.34418i	−0.740470	+	0.672089i	$0.765397\pi$
$158$	−45.2271			−0.286248
$159$		−	85.2858i		−	0.536389i
$160$		0			0
$161$	−133.046	+	180.199i	−0.826375	+	1.11925i
$162$	25.1239			0.155086
$163$	−181.823			−1.11548			−0.557741	−	0.830015i	$-0.688332\pi$
$163$	−181.823			−1.11548			−0.557741	+	0.830015i	$0.688332\pi$
$164$		−	142.728i		−	0.870295i
$165$		0			0
$166$			102.679i			0.618549i
$167$			101.160i			0.605751i	0.953030	+	0.302876i	$0.0979467\pi$
$167$			101.160i			0.605751i	−0.953030	+	0.302876i	$0.902053\pi$
$168$	5.64349	+	4.16676i	0.0335922	+	0.0248021i
$169$	48.4250			0.286538
$170$		0			0
$171$			58.8170i			0.343959i
$172$	71.5696			0.416102
$173$			109.976i			0.635702i	0.948141	+	0.317851i	$0.102961\pi$
$173$			109.976i			0.635702i	−0.948141	+	0.317851i	$0.897039\pi$
$174$			193.388i			1.11143i
$175$		0			0
$176$	318.415			1.80918
$177$	−60.9981			−0.344622
$178$		−	245.922i		−	1.38159i
$179$	91.8832			0.513314			0.256657	−	0.966503i	$-0.417379\pi$
$179$	91.8832			0.513314			0.256657	+	0.966503i	$0.417379\pi$
$180$		0			0
$181$		−	62.8649i		−	0.347320i	−0.984806	−	0.173660i	$-0.944441\pi$
$181$		−	62.8649i		−	0.347320i	0.984806	−	0.173660i	$-0.0555594\pi$
$182$	−172.619	−	127.450i	−0.948457	−	0.700275i
$183$	−109.937			−0.600750
$184$	−18.5144			−0.100622
$185$		0			0
$186$	−177.274			−0.953088
$187$		−	423.123i		−	2.26269i
$188$			187.280i			0.996170i
$189$	29.2615	+	21.6047i	0.154823	+	0.114311i
$190$		0			0
$191$	−75.9925			−0.397866			−0.198933	−	0.980013i	$-0.563748\pi$
$191$	−75.9925			−0.397866			−0.198933	+	0.980013i	$0.563748\pi$
$192$		−	99.0812i		−	0.516048i
$193$	−22.7530			−0.117891			−0.0589456	−	0.998261i	$-0.518774\pi$
$193$	−22.7530			−0.117891			−0.0589456	+	0.998261i	$0.518774\pi$
$194$		−	373.537i		−	1.92545i
$195$		0			0
$196$	−54.7102	−	177.609i	−0.279134	−	0.906166i
$197$	137.485			0.697891			0.348946	−	0.937143i	$-0.386540\pi$
$197$	137.485			0.697891			0.348946	+	0.937143i	$0.386540\pi$
$198$	158.858			0.802316
$199$		−	267.299i		−	1.34321i	−0.740909	−	0.671606i	$-0.765605\pi$
$199$		−	267.299i		−	1.34321i	0.740909	−	0.671606i	$-0.234395\pi$
$200$		0			0
$201$		−	36.9869i		−	0.184015i
$202$			544.081i			2.69347i
$203$	−166.299	+	225.237i	−0.819208	+	1.10954i
$204$	−146.533			−0.718299
$205$		0			0
$206$			115.187i			0.559161i
$207$	−95.9972			−0.463754
$208$		−	184.323i		−	0.886166i
$209$			371.900i			1.77943i
$210$		0			0
$211$	−366.610			−1.73749			−0.868744	−	0.495261i	$-0.835073\pi$
$211$	−366.610			−1.73749			−0.868744	+	0.495261i	$0.835073\pi$
$212$	−186.753			−0.880912
$213$			62.8731i			0.295179i
$214$	−82.9175			−0.387465
$215$		0			0
$216$			3.00645i			0.0139187i
$217$	−206.469	−	152.443i	−0.951472	−	0.702501i
$218$	255.993			1.17428
$219$	−11.5496			−0.0527380
$220$		0			0
$221$	−244.935			−1.10830
$222$		−	43.2596i		−	0.194863i
$223$			282.872i			1.26848i	0.773134	+	0.634242i	$0.218688\pi$
$223$			282.872i			1.26848i	−0.773134	+	0.634242i	$0.781312\pi$
$224$	185.210	−	250.849i	0.826828	−	1.11986i
$225$		0			0
$226$	−8.32722			−0.0368461
$227$			210.777i			0.928534i	0.885695	+	0.464267i	$0.153682\pi$
$227$			210.777i			0.928534i	−0.885695	+	0.464267i	$0.846318\pi$
$228$	128.794			0.564885
$229$		−	137.506i		−	0.600464i	−0.953866	−	0.300232i	$-0.902936\pi$
$229$		−	137.506i		−	0.600464i	0.953866	−	0.300232i	$-0.0970641\pi$
$230$		0			0
$231$	185.021	+	136.606i	0.800955	+	0.591370i
$232$	−23.1417			−0.0997488
$233$	77.7682			0.333769			0.166884	−	0.985976i	$-0.446629\pi$
$233$	77.7682			0.333769			0.166884	+	0.985976i	$0.446629\pi$
$234$		−	91.9591i		−	0.392988i
$235$		0			0
$236$			133.570i			0.565974i
$237$		−	28.0618i		−	0.118404i
$238$	−350.657	−	258.901i	−1.47335	−	1.08782i
$239$	−123.843			−0.518173			−0.259086	−	0.965854i	$-0.583421\pi$
$239$	−123.843			−0.518173			−0.259086	+	0.965854i	$0.583421\pi$
$240$		0			0
$241$		−	155.802i		−	0.646481i	−0.946317	−	0.323240i	$-0.895228\pi$
$241$		−	155.802i		−	0.646481i	0.946317	−	0.323240i	$-0.104772\pi$
$242$	666.684			2.75489
$243$			15.5885i			0.0641500i
$244$			240.734i			0.986613i
$245$		0			0
$246$	181.955			0.739653
$247$	215.283			0.871593
$248$		−	21.2135i		−	0.0855383i
$249$	−63.7086			−0.255858
$250$		0			0
$251$			278.340i			1.10892i	0.832210	+	0.554461i	$0.187076\pi$
$251$			278.340i			1.10892i	−0.832210	+	0.554461i	$0.812924\pi$
$252$	47.3086	−	64.0750i	0.187732	−	0.254266i
$253$	−606.990			−2.39917
$254$	−292.138			−1.15015
$255$		0			0
$256$	280.434			1.09545
$257$		−	220.802i		−	0.859151i	−0.903031	−	0.429575i	$-0.858663\pi$
$257$		−	220.802i		−	0.859151i	0.903031	−	0.429575i	$-0.141337\pi$
$258$			91.2392i			0.353640i
$259$	37.2000	−	50.3839i	0.143629	−	0.194533i
$260$		0			0
$261$	−119.990			−0.459732
$262$		−	197.656i		−	0.754412i
$263$	17.3477			0.0659609			0.0329804	−	0.999456i	$-0.489500\pi$
$263$	17.3477			0.0659609			0.0329804	+	0.999456i	$0.489500\pi$
$264$			19.0098i			0.0720067i
$265$		0			0
$266$	308.207	+	227.558i	1.15867	+	0.855483i
$267$	152.586			0.571482
$268$	−80.9916			−0.302207
$269$			499.213i			1.85581i	0.372816	+	0.927905i	$0.378392\pi$
$269$			499.213i			1.85581i	−0.372816	+	0.927905i	$0.621608\pi$
$270$		0			0
$271$		−	330.005i		−	1.21773i	−0.793273	−	0.608866i	$-0.791625\pi$
$271$		−	330.005i		−	1.21773i	0.793273	−	0.608866i	$-0.208375\pi$
$272$		−	374.431i		−	1.37659i
$273$	79.0780	−	107.104i	0.289663	−	0.392321i
$274$	442.944			1.61659
$275$		0			0
$276$			210.209i			0.761625i
$277$	−147.766			−0.533452			−0.266726	−	0.963772i	$-0.585942\pi$
$277$	−147.766			−0.533452			−0.266726	+	0.963772i	$0.585942\pi$
$278$			151.931i			0.546513i
$279$		−	109.992i		−	0.394237i
$280$		0			0
$281$	353.405			1.25767			0.628834	−	0.777540i	$-0.283533\pi$
$281$	353.405			1.25767			0.628834	+	0.777540i	$0.283533\pi$
$282$	−238.751			−0.846633
$283$		−	428.203i		−	1.51308i	−0.653945	−	0.756542i	$-0.726887\pi$
$283$		−	428.203i		−	1.51308i	0.653945	−	0.756542i	$-0.273113\pi$
$284$	137.675			0.484773
$285$		0			0
$286$		−	581.457i		−	2.03307i
$287$	211.920	+	156.467i	0.738399	+	0.545182i
$288$	133.634			0.464009
$289$	−208.559			−0.721657
$290$		0			0
$291$	231.766			0.796446
$292$			25.2906i			0.0866117i
$293$			402.632i			1.37417i	0.726577	+	0.687085i	$0.241110\pi$
$293$			402.632i			1.37417i	−0.726577	+	0.687085i	$0.758890\pi$
$294$	226.421	−	69.7463i	0.770140	−	0.237232i
$295$		0			0
$296$	5.17665			0.0174887
$297$			98.5658i			0.331871i
$298$	639.550			2.14614
$299$			351.371i			1.17515i
$300$		0			0
$301$	−78.4589	+	106.265i	−0.260661	+	0.353041i
$302$	−551.986			−1.82777
$303$	−337.582			−1.11413
$304$			329.103i			1.08258i
$305$		0			0
$306$		−	186.805i		−	0.610474i
$307$			92.7330i			0.302062i	0.988529	+	0.151031i	$0.0482593\pi$
$307$			92.7330i			0.302062i	−0.988529	+	0.151031i	$0.951741\pi$
$308$	299.132	−	405.146i	0.971207	−	1.31541i
$309$	−71.4694			−0.231292
$310$		0			0
$311$		−	218.118i		−	0.701343i	−0.936498	−	0.350672i	$-0.885953\pi$
$311$		−	218.118i		−	0.701343i	0.936498	−	0.350672i	$-0.114047\pi$
$312$	11.0043			0.0352701
$313$		−	293.684i		−	0.938288i	−0.883122	−	0.469144i	$-0.844562\pi$
$313$		−	293.684i		−	0.938288i	0.883122	−	0.469144i	$-0.155438\pi$
$314$			589.117i			1.87617i
$315$		0			0
$316$	−61.4479			−0.194455
$317$	−109.074			−0.344081			−0.172041	−	0.985090i	$-0.555036\pi$
$317$	−109.074			−0.344081			−0.172041	+	0.985090i	$0.555036\pi$
$318$		−	238.079i		−	0.748677i
$319$	−758.697			−2.37836
$320$		0			0
$321$		−	51.4472i		−	0.160272i
$322$	−371.405	+	503.034i	−1.15343	+	1.56222i
$323$	437.325			1.35395
$324$	34.1346			0.105354
$325$		0			0
$326$	−507.569			−1.55696
$327$			158.834i			0.485731i
$328$			21.7736i			0.0663828i
$329$	−278.070	−	205.308i	−0.845197	−	0.624035i
$330$		0			0
$331$	408.913			1.23539			0.617694	−	0.786419i	$-0.288067\pi$
$331$	408.913			1.23539			0.617694	+	0.786419i	$0.288067\pi$
$332$			139.505i			0.420196i
$333$	26.8410			0.0806035
$334$			282.394i			0.845492i
$335$		0			0
$336$	163.729	+	120.886i	0.487289	+	0.359780i
$337$	299.269			0.888040			0.444020	−	0.896017i	$-0.353552\pi$
$337$	299.269			0.888040			0.444020	+	0.896017i	$0.353552\pi$
$338$	135.181			0.399942
$339$		−	5.16673i		−	0.0152411i
$340$		0			0
$341$		−	695.480i		−	2.03953i
$342$			164.190i			0.480089i
$343$	323.687	+	113.472i	0.943693	+	0.330823i
$344$	−10.9181			−0.0317387
$345$		0			0
$346$			307.004i			0.887296i
$347$	−567.731			−1.63611			−0.818056	−	0.575138i	$-0.804948\pi$
$347$	−567.731			−1.63611			−0.818056	+	0.575138i	$0.804948\pi$
$348$			262.747i			0.755019i
$349$		−	141.703i		−	0.406025i	−0.979176	−	0.203012i	$-0.934927\pi$
$349$		−	141.703i		−	0.406025i	0.979176	−	0.203012i	$-0.0650732\pi$
$350$		0			0
$351$	57.0572			0.162556
$352$	844.970			2.40048
$353$			452.435i			1.28169i	0.767672	+	0.640843i	$0.221415\pi$
$353$			452.435i			1.28169i	−0.767672	+	0.640843i	$0.778585\pi$
$354$	−170.279			−0.481015
$355$		0			0
$356$		−	334.123i		−	0.938546i
$357$	160.638	−	217.570i	0.449967	−	0.609439i
$358$	256.496			0.716470
$359$	174.670			0.486546			0.243273	−	0.969958i	$-0.421779\pi$
$359$	174.670			0.486546			0.243273	+	0.969958i	$0.421779\pi$
$360$		0			0
$361$	−23.3825			−0.0647714
$362$		−	175.490i		−	0.484780i
$363$			413.653i			1.13954i
$364$	−234.529	−	173.160i	−0.644310	−	0.475714i
$365$		0			0
$366$	−306.895			−0.838511
$367$		−	121.147i		−	0.330101i	−0.986285	−	0.165051i	$-0.947221\pi$
$367$		−	121.147i		−	0.330101i	0.986285	−	0.165051i	$-0.0527788\pi$
$368$	−537.139			−1.45962
$369$			112.896i			0.305951i
$370$		0			0
$371$	204.730	−	277.288i	0.551834	−	0.747407i
$372$	−240.854			−0.647456
$373$	90.9075			0.243720			0.121860	−	0.992547i	$-0.461114\pi$
$373$	90.9075			0.243720			0.121860	+	0.992547i	$0.461114\pi$
$374$		−	1181.17i		−	3.15820i
$375$		0			0
$376$		−	28.5700i		−	0.0759841i
$377$			439.190i			1.16496i
$378$	81.6850	+	60.3105i	0.216098	+	0.159552i
$379$	−638.344			−1.68429			−0.842143	−	0.539254i	$-0.818706\pi$
$379$	−638.344			−1.68429			−0.842143	+	0.539254i	$0.818706\pi$
$380$		0			0
$381$		−	181.261i		−	0.475750i
$382$	−212.137			−0.555331
$383$		−	176.395i		−	0.460561i	−0.973124	−	0.230281i	$-0.926036\pi$
$383$		−	176.395i		−	0.460561i	0.973124	−	0.230281i	$-0.0739644\pi$
$384$			32.0257i			0.0834003i
$385$		0			0
$386$	−63.5160			−0.164549
$387$	−56.6105			−0.146280
$388$		−	507.506i		−	1.30800i
$389$	249.521			0.641442			0.320721	−	0.947174i	$-0.396075\pi$
$389$	249.521			0.641442			0.320721	+	0.947174i	$0.396075\pi$
$390$		0			0
$391$			713.772i			1.82550i
$392$	8.34618	+	27.0946i	0.0212913	+	0.0691189i
$393$	122.638			0.312056
$394$	383.795			0.974098
$395$		0			0
$396$	215.833			0.545033
$397$			186.071i			0.468694i	0.972153	+	0.234347i	$0.0752951\pi$
$397$			186.071i			0.468694i	−0.972153	+	0.234347i	$0.924705\pi$
$398$		−	746.178i		−	1.87482i
$399$	−141.191	+	191.231i	−0.353863	+	0.479275i
$400$		0			0
$401$	−188.067			−0.468996			−0.234498	−	0.972117i	$-0.575345\pi$
$401$	−188.067			−0.468996			−0.234498	+	0.972117i	$0.575345\pi$
$402$		−	103.251i		−	0.256843i
$403$	−402.596			−0.998997
$404$			739.215i			1.82974i
$405$		0			0
$406$	−464.232	+	628.759i	−1.14343	+	1.54867i
$407$	169.715			0.416991
$408$	22.3540			0.0547891
$409$		−	512.173i		−	1.25226i	−0.779720	−	0.626128i	$-0.784639\pi$
$409$		−	512.173i		−	1.25226i	0.779720	−	0.626128i	$-0.215361\pi$
$410$		0			0
$411$			274.831i			0.668687i
$412$			156.499i			0.379852i
$413$	−198.322	−	146.427i	−0.480199	−	0.354545i
$414$	−267.981			−0.647296
$415$		0			0
$416$		−	489.132i		−	1.17580i
$417$	−94.2673			−0.226061
$418$			1038.18i			2.48367i
$419$			323.661i			0.772461i	0.922402	+	0.386231i	$0.126223\pi$
$419$			323.661i			0.772461i	−0.922402	+	0.386231i	$0.873777\pi$
$420$		0			0
$421$	−503.872			−1.19685			−0.598423	−	0.801180i	$-0.704206\pi$
$421$	−503.872			−1.19685			−0.598423	+	0.801180i	$0.704206\pi$
$422$	−1023.41			−2.42514
$423$		−	148.136i		−	0.350203i
$424$	28.4897			0.0671927
$425$		0			0
$426$			175.513i			0.412003i
$427$	−357.437	−	263.907i	−0.837089	−	0.618049i
$428$	−112.656			−0.263215
$429$	360.773			0.840962
$430$		0			0
$431$	317.731			0.737195			0.368597	−	0.929589i	$-0.379838\pi$
$431$	317.731			0.737195			0.368597	+	0.929589i	$0.379838\pi$
$432$			87.2231i			0.201905i
$433$			261.387i			0.603665i	0.953361	+	0.301833i	$0.0975984\pi$
$433$			261.387i			0.603665i	−0.953361	+	0.301833i	$0.902402\pi$
$434$	−576.369	−	425.551i	−1.32804	−	0.980532i
$435$		0			0
$436$	347.805			0.797717
$437$		−	627.363i		−	1.43561i
$438$	−32.2413			−0.0736103
$439$			789.513i			1.79844i	0.437501	+	0.899218i	$0.355863\pi$
$439$			789.513i			1.79844i	−0.437501	+	0.899218i	$0.644137\pi$
$440$		0			0
$441$	43.2750	+	140.486i	0.0981293	+	0.318562i
$442$	−683.748			−1.54694
$443$	−585.242			−1.32109			−0.660544	−	0.750787i	$-0.729674\pi$
$443$	−585.242			−1.32109			−0.660544	+	0.750787i	$0.729674\pi$
$444$		−	58.7746i		−	0.132375i
$445$		0			0
$446$			789.651i			1.77052i
$447$			396.817i			0.887733i
$448$	237.847	−	322.141i	0.530907	−	0.719065i
$449$	528.147			1.17627			0.588137	−	0.808761i	$-0.299862\pi$
$449$	528.147			1.17627			0.588137	+	0.808761i	$0.299862\pi$
$450$		0			0
$451$			713.842i			1.58280i
$452$	−11.3138			−0.0250305
$453$		−	342.486i		−	0.756041i
$454$			588.395i			1.29602i
$455$		0			0
$456$	−19.6478			−0.0430873
$457$	164.041			0.358953			0.179476	−	0.983762i	$-0.442560\pi$
$457$	164.041			0.358953			0.179476	+	0.983762i	$0.442560\pi$
$458$		−	383.855i		−	0.838112i
$459$	115.906			0.252517
$460$		0			0
$461$			399.626i			0.866867i	0.901186	+	0.433434i	$0.142698\pi$
$461$			399.626i			0.866867i	−0.901186	+	0.433434i	$0.857302\pi$
$462$	516.494	+	381.343i	1.11795	+	0.825418i
$463$	680.267			1.46926			0.734630	−	0.678468i	$-0.237356\pi$
$463$	680.267			1.46926			0.734630	+	0.678468i	$0.237356\pi$
$464$	−671.388			−1.44696
$465$		0			0
$466$	217.093			0.465866
$467$			725.217i			1.55293i	0.630162	+	0.776464i	$0.282989\pi$
$467$			725.217i			1.55293i	−0.630162	+	0.776464i	$0.717011\pi$
$468$		−	124.940i		−	0.266966i
$469$	88.7879	−	120.255i	0.189313	−	0.256407i
$470$		0			0
$471$	−365.525			−0.776062
$472$		−	20.3764i		−	0.0431704i
$473$	−357.948			−0.756762
$474$		−	78.3357i		−	0.165265i
$475$		0			0
$476$	−476.420	−	351.755i	−1.00088	−	0.738982i
$477$	147.719			0.309684
$478$	−345.714			−0.723252
$479$		−	317.103i		−	0.662010i	−0.943629	−	0.331005i	$-0.892612\pi$
$479$		−	317.103i		−	0.662010i	0.943629	−	0.331005i	$-0.107388\pi$
$480$		0			0
$481$		−	98.2439i		−	0.204249i
$482$		−	434.928i		−	0.902341i
$483$	−312.114	−	230.443i	−0.646198	−	0.477108i
$484$	905.791			1.87147
$485$		0			0
$486$			43.5159i			0.0895389i
$487$	−353.125			−0.725103			−0.362551	−	0.931964i	$-0.618094\pi$
$487$	−353.125			−0.725103			−0.362551	+	0.931964i	$0.618094\pi$
$488$		−	36.7245i		−	0.0752552i
$489$		−	314.927i		−	0.644023i
$490$		0			0
$491$	−343.280			−0.699145			−0.349572	−	0.936909i	$-0.613673\pi$
$491$	−343.280			−0.699145			−0.349572	+	0.936909i	$0.613673\pi$
$492$	247.213			0.502465
$493$			892.167i			1.80967i
$494$	600.974			1.21655
$495$		0			0
$496$		−	615.447i		−	1.24082i
$497$	−150.928	+	204.418i	−0.303678	+	0.411304i
$498$	−177.846			−0.357120
$499$	−420.584			−0.842853			−0.421427	−	0.906863i	$-0.638470\pi$
$499$	−420.584			−0.842853			−0.421427	+	0.906863i	$0.638470\pi$
$500$		0			0
$501$	−175.215			−0.349731
$502$			776.998i			1.54780i
$503$			183.030i			0.363876i	0.983310	+	0.181938i	$0.0582370\pi$
$503$			183.030i			0.363876i	−0.983310	+	0.181938i	$0.941763\pi$
$504$	−7.21704	+	9.77481i	−0.0143195	+	0.0193945i
$505$		0			0
$506$	−1694.44			−3.34870
$507$			83.8745i			0.165433i
$508$	−396.913			−0.781326
$509$		−	261.854i		−	0.514448i	−0.966352	−	0.257224i	$-0.917192\pi$
$509$		−	261.854i		−	0.514448i	0.966352	−	0.257224i	$-0.0828079\pi$
$510$		0			0
$511$	−37.5511	−	27.7251i	−0.0734855	−	0.0542566i
$512$	708.885			1.38454
$513$	−101.874			−0.198585
$514$		−	616.378i		−	1.19918i
$515$		0			0
$516$			123.962i			0.240237i
$517$		−	936.662i		−	1.81173i
$518$	103.846	−	140.649i	0.200474	−	0.271523i
$519$	−190.485			−0.367023
$520$		0			0
$521$			477.677i			0.916846i	0.888734	+	0.458423i	$0.151586\pi$
$521$			477.677i			0.916846i	−0.888734	+	0.458423i	$0.848414\pi$
$522$	−334.958			−0.641682
$523$		−	770.784i		−	1.47377i	−0.676016	−	0.736887i	$-0.736295\pi$
$523$		−	770.784i		−	1.47377i	0.676016	−	0.736887i	$-0.263705\pi$
$524$		−	268.545i		−	0.512491i
$525$		0			0
$526$	48.4269			0.0920664
$527$	−817.829			−1.55186
$528$			551.512i			1.04453i
$529$	494.940			0.935614
$530$		0			0
$531$		−	105.652i		−	0.198968i
$532$	418.745	+	309.172i	0.787114	+	0.581151i
$533$	413.225			0.775281
$534$	425.950			0.797660
$535$		0			0
$536$	12.3555			0.0230513
$537$			159.146i			0.296362i
$538$			1393.58i			2.59029i
$539$	273.628	+	888.292i	0.507658	+	1.64804i
$540$		0			0
$541$	1054.53			1.94922			0.974609	−	0.223912i	$-0.0718828\pi$
$541$	1054.53			1.94922			0.974609	+	0.223912i	$0.0718828\pi$
$542$		−	921.225i		−	1.69968i
$543$	108.885			0.200525
$544$		−	993.618i		−	1.82650i
$545$		0			0
$546$	220.750	−	298.985i	0.404304	−	0.547592i
$547$	−697.821			−1.27572			−0.637862	−	0.770151i	$-0.720181\pi$
$547$	−697.821			−1.27572			−0.637862	+	0.770151i	$0.720181\pi$
$548$	601.806			1.09819
$549$		−	190.417i		−	0.346843i
$550$		0			0
$551$		−	784.162i		−	1.42316i
$552$		−	32.0678i		−	0.0580939i
$553$	67.3628	−	91.2367i	0.121813	−	0.164985i
$554$	−412.496			−0.744578
$555$		0			0
$556$			206.421i			0.371260i
$557$	941.244			1.68985			0.844923	−	0.534888i	$-0.179646\pi$
$557$	941.244			1.68985			0.844923	+	0.534888i	$0.179646\pi$
$558$		−	307.048i		−	0.550266i
$559$			207.207i			0.370675i
$560$		0			0
$561$	732.870			1.30636
$562$	986.545			1.75542
$563$		−	768.996i		−	1.36589i	−0.730470	−	0.682945i	$-0.760699\pi$
$563$		−	768.996i		−	1.36589i	0.730470	−	0.682945i	$-0.239301\pi$
$564$	−324.378			−0.575139
$565$		0			0
$566$		−	1195.35i		−	2.11192i
$567$	−37.4204	+	50.6825i	−0.0659972	+	0.0893871i
$568$	−21.0027			−0.0369766
$569$	−46.4935			−0.0817108			−0.0408554	−	0.999165i	$-0.513008\pi$
$569$	−46.4935			−0.0817108			−0.0408554	+	0.999165i	$0.513008\pi$
$570$		0			0
$571$	774.153			1.35578			0.677892	−	0.735161i	$-0.262894\pi$
$571$	774.153			1.35578			0.677892	+	0.735161i	$0.262894\pi$
$572$		−	789.997i		−	1.38111i
$573$		−	131.623i		−	0.229708i
$574$	591.586	+	436.786i	1.03064	+	0.760951i
$575$		0			0
$576$	171.614			0.297940
$577$			66.7246i			0.115641i	0.998327	+	0.0578203i	$0.0184150\pi$
$577$			66.7246i			0.115641i	−0.998327	+	0.0578203i	$0.981585\pi$
$578$	−582.202			−1.00727
$579$		−	39.4093i		−	0.0680645i
$580$		0			0
$581$	−207.135	−	152.934i	−0.356514	−	0.263225i
$582$	646.985			1.11166
$583$	934.029			1.60211
$584$		−	3.85815i		−	0.00660642i
$585$		0			0
$586$			1123.97i			1.91803i
$587$		−	678.789i		−	1.15637i	−0.815906	−	0.578185i	$-0.803761\pi$
$587$		−	678.789i		−	1.15637i	0.815906	−	0.578185i	$-0.196239\pi$
$588$	307.627	−	94.7608i	0.523175	−	0.161158i
$589$	718.823			1.22041
$590$		0			0
$591$			238.130i			0.402928i
$592$	150.185			0.253691
$593$		−	289.610i		−	0.488381i	−0.969727	−	0.244190i	$-0.921478\pi$
$593$		−	289.610i		−	0.488381i	0.969727	−	0.244190i	$-0.0785222\pi$
$594$			275.151i			0.463217i
$595$		0			0
$596$	868.924			1.45793
$597$	462.976			0.775503
$598$			980.869i			1.64025i
$599$	384.076			0.641195			0.320598	−	0.947216i	$-0.396116\pi$
$599$	384.076			0.641195			0.320598	+	0.947216i	$0.396116\pi$
$600$		0			0
$601$		−	37.4083i		−	0.0622434i	−0.999516	−	0.0311217i	$-0.990092\pi$
$601$		−	37.4083i		−	0.0622434i	0.999516	−	0.0311217i	$-0.00990794\pi$
$602$	−219.022	+	296.644i	−0.363823	+	0.492765i
$603$	64.0632			0.106241
$604$	−749.955			−1.24165
$605$		0			0
$606$	−942.375			−1.55507
$607$			876.691i			1.44430i	0.691736	+	0.722150i	$0.256846\pi$
$607$			876.691i			1.44430i	−0.691736	+	0.722150i	$0.743154\pi$
$608$			873.331i			1.43640i
$609$	−390.121	−	288.039i	−0.640594	−	0.472970i
$610$		0			0
$611$	−542.210			−0.887414
$612$		−	253.803i		−	0.414710i
$613$	591.071			0.964226			0.482113	−	0.876109i	$-0.339869\pi$
$613$	591.071			0.964226			0.482113	+	0.876109i	$0.339869\pi$
$614$			258.868i			0.421610i
$615$		0			0
$616$	−45.6333	+	61.8061i	−0.0740801	+	0.100335i
$617$	744.668			1.20692			0.603459	−	0.797394i	$-0.293789\pi$
$617$	744.668			1.20692			0.603459	+	0.797394i	$0.293789\pi$
$618$	−199.510			−0.322832
$619$		−	851.811i		−	1.37611i	−0.725659	−	0.688054i	$-0.758465\pi$
$619$		−	851.811i		−	1.37611i	0.725659	−	0.688054i	$-0.241535\pi$
$620$		0			0
$621$		−	166.272i		−	0.267749i
$622$		−	608.886i		−	0.978917i
$623$	496.099	+	366.285i	0.796307	+	0.587938i
$624$	319.256			0.511628
$625$		0			0
$626$		−	819.833i		−	1.30964i
$627$	−644.149			−1.02735
$628$			800.404i			1.27453i
$629$		−	199.572i		−	0.317284i
$630$		0			0
$631$	316.625			0.501783			0.250891	−	0.968015i	$-0.419276\pi$
$631$	316.625			0.501783			0.250891	+	0.968015i	$0.419276\pi$
$632$	9.37402			0.0148323
$633$		−	634.987i		−	1.00314i
$634$	−304.485			−0.480260
$635$		0			0
$636$		−	323.466i		−	0.508595i
$637$	514.209	−	158.396i	0.807236	−	0.248660i
$638$	−2117.94			−3.31965
$639$	−108.899			−0.170422
$640$		0			0
$641$	173.979			0.271418			0.135709	−	0.990749i	$-0.456669\pi$
$641$	173.979			0.271418			0.135709	+	0.990749i	$0.456669\pi$
$642$		−	143.617i		−	0.223703i
$643$		−	926.785i		−	1.44135i	−0.693275	−	0.720673i	$-0.743833\pi$
$643$		−	926.785i		−	1.44135i	0.693275	−	0.720673i	$-0.256167\pi$
$644$	−504.610	+	683.447i	−0.783556	+	1.06125i
$645$		0			0
$646$	1220.81			1.88980
$647$		−	429.625i		−	0.664027i	−0.943275	−	0.332013i	$-0.892272\pi$
$647$		−	429.625i		−	0.664027i	0.943275	−	0.332013i	$-0.107728\pi$
$648$	−5.20732			−0.00803599
$649$		−	668.036i		−	1.02933i
$650$		0			0
$651$	264.038	−	357.615i	0.405589	−	0.549333i
$652$	−689.608			−1.05768
$653$	927.100			1.41976			0.709878	−	0.704325i	$-0.248750\pi$
$653$	927.100			1.41976			0.709878	+	0.704325i	$0.248750\pi$
$654$			443.392i			0.677970i
$655$		0			0
$656$			631.695i			0.962950i
$657$		−	20.0045i		−	0.0304483i
$658$	−776.245	−	573.126i	−1.17970	−	0.871012i
$659$	692.153			1.05031			0.525154	−	0.851007i	$-0.324008\pi$
$659$	692.153			1.05031			0.525154	+	0.851007i	$0.324008\pi$
$660$		0			0
$661$		−	1101.42i		−	1.66629i	−0.553053	−	0.833146i	$-0.686537\pi$
$661$		−	1101.42i		−	1.66629i	0.553053	−	0.833146i	$-0.313463\pi$
$662$	1141.50			1.72432
$663$		−	424.240i		−	0.639879i
$664$		−	21.2818i		−	0.0320510i
$665$		0			0
$666$	74.9278			0.112504
$667$	1279.86			1.91882
$668$			383.675i			0.574364i
$669$	−489.949			−0.732360
$670$		0			0
$671$		−	1204.01i		−	1.79435i
$672$	434.483	+	320.792i	0.646553	+	0.477370i
$673$	−701.861			−1.04288			−0.521442	−	0.853287i	$-0.674606\pi$
$673$	−701.861			−1.04288			−0.521442	+	0.853287i	$0.674606\pi$
$674$	835.424			1.23950
$675$		0			0
$676$	183.663			0.271691
$677$			404.920i			0.598110i	0.954236	+	0.299055i	$0.0966714\pi$
$677$			404.920i			0.598110i	−0.954236	+	0.299055i	$0.903329\pi$
$678$		−	14.4232i		−	0.0212731i
$679$	753.535	+	556.358i	1.10977	+	0.819379i
$680$		0			0
$681$	−365.077			−0.536090
$682$		−	1941.47i		−	2.84672i
$683$	766.177			1.12178			0.560891	−	0.827890i	$-0.310459\pi$
$683$	766.177			1.12178			0.560891	+	0.827890i	$0.310459\pi$
$684$			223.077i			0.326136i
$685$		0			0
$686$	903.586	+	316.764i	1.31718	+	0.461754i
$687$	238.168			0.346678
$688$	−316.757			−0.460402
$689$		−	540.686i		−	0.784740i
$690$		0			0
$691$			162.333i			0.234925i	0.993077	+	0.117462i	$0.0374760\pi$
$691$			162.333i			0.234925i	−0.993077	+	0.117462i	$0.962524\pi$
$692$			417.111i			0.602762i
$693$	−236.609	+	320.465i	−0.341427	+	0.462432i
$694$	−1584.85			−2.28364
$695$		0			0
$696$		−	40.0826i		−	0.0575900i
$697$	839.421			1.20433
$698$		−	395.570i		−	0.566719i
$699$			134.698i			0.192702i
$700$		0			0
$701$	−69.5098			−0.0991581			−0.0495790	−	0.998770i	$-0.515788\pi$
$701$	−69.5098			−0.0991581			−0.0495790	+	0.998770i	$0.515788\pi$
$702$	159.278			0.226892
$703$			175.412i			0.249519i
$704$	1085.11			1.54135
$705$		0			0
$706$			1262.99i			1.78894i
$707$	−1097.57	−	810.372i	−1.55244	−	1.14621i
$708$	−231.350			−0.326765
$709$	134.839			0.190182			0.0950912	−	0.995469i	$-0.469686\pi$
$709$	134.839			0.190182			0.0950912	+	0.995469i	$0.469686\pi$
$710$		0			0
$711$	48.6044			0.0683606
$712$			50.9712i			0.0715888i
$713$			1173.22i			1.64546i
$714$	448.429	−	607.356i	0.628052	−	0.850638i
$715$		0			0
$716$	348.489			0.486716
$717$		−	214.503i		−	0.299167i
$718$	487.600			0.679109
$719$			638.863i			0.888544i	0.895892	+	0.444272i	$0.146538\pi$
$719$			638.863i			0.888544i	−0.895892	+	0.444272i	$0.853462\pi$
$720$		0			0
$721$	−232.367	−	171.564i	−0.322284	−	0.237952i
$722$	−65.2732			−0.0904062
$723$	269.857			0.373246
$724$		−	238.430i		−	0.329323i
$725$		0			0
$726$			1154.73i			1.59054i
$727$			704.430i			0.968955i	0.874804	+	0.484477i	$0.160990\pi$
$727$			704.430i			0.968955i	−0.874804	+	0.484477i	$0.839010\pi$
$728$	35.7780	+	26.4160i	0.0491456	+	0.0362857i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			420.919i			0.575812i
$732$	−416.963			−0.569622
$733$		−	275.472i		−	0.375815i	−0.982187	−	0.187907i	$-0.939830\pi$
$733$		−	275.472i		−	0.375815i	0.982187	−	0.187907i	$-0.0601705\pi$
$734$		−	338.188i		−	0.460747i
$735$		0			0
$736$	−1425.39			−1.93667
$737$	405.072			0.549622
$738$			315.155i			0.427039i
$739$	238.655			0.322943			0.161471	−	0.986877i	$-0.448376\pi$
$739$	238.655			0.322943			0.161471	+	0.986877i	$0.448376\pi$
$740$		0			0
$741$			372.882i			0.503214i
$742$	571.514	−	774.063i	0.770235	−	1.04321i
$743$	−221.162			−0.297661			−0.148831	−	0.988863i	$-0.547551\pi$
$743$	−221.162			−0.297661			−0.148831	+	0.988863i	$0.547551\pi$
$744$	36.7429			0.0493856
$745$		0			0
$746$	253.773			0.340178
$747$		−	110.347i		−	0.147720i
$748$		−	1604.79i		−	2.14544i
$749$	123.500	−	167.269i	0.164887	−	0.223324i
$750$		0			0
$751$	−496.682			−0.661361			−0.330680	−	0.943743i	$-0.607278\pi$
$751$	−496.682			−0.661361			−0.330680	+	0.943743i	$0.607278\pi$
$752$		−	828.874i		−	1.10223i
$753$	−482.098			−0.640237
$754$			1226.02i			1.62602i
$755$		0			0
$756$	110.981	+	81.9408i	0.146801	+	0.108387i
$757$	−866.706			−1.14492			−0.572461	−	0.819932i	$-0.694011\pi$
$757$	−866.706			−1.14492			−0.572461	+	0.819932i	$0.694011\pi$
$758$	−1781.97			−2.35088
$759$		−	1051.34i		−	1.38516i
$760$		0			0
$761$		−	621.621i		−	0.816847i	−0.912793	−	0.408424i	$-0.866079\pi$
$761$		−	621.621i		−	0.816847i	0.912793	−	0.408424i	$-0.133921\pi$
$762$		−	505.998i		−	0.664039i
$763$	−381.284	+	516.414i	−0.499717	+	0.676820i
$764$	−288.219			−0.377250
$765$		0			0
$766$		−	492.415i		−	0.642839i
$767$	−386.709			−0.504184
$768$			485.726i			0.632456i
$769$			316.574i			0.411669i	0.978587	+	0.205835i	$0.0659909\pi$
$769$			316.574i			0.411669i	−0.978587	+	0.205835i	$0.934009\pi$
$770$		0			0
$771$	382.440			0.496031
$772$	−86.2961			−0.111782
$773$		−	710.993i		−	0.919784i	−0.887975	−	0.459892i	$-0.847888\pi$
$773$		−	710.993i		−	0.919784i	0.887975	−	0.459892i	$-0.152112\pi$
$774$	−158.031			−0.204174
$775$		0			0
$776$			77.4213i			0.0997697i
$777$	87.2675	+	64.4323i	0.112313	+	0.0829244i
$778$	696.550			0.895308
$779$	−737.801			−0.947113
$780$		0			0
$781$	−688.570			−0.881652
$782$			1992.53i			2.54799i
$783$		−	207.829i		−	0.265426i
$784$	242.140	+	786.070i	0.308851	+	1.00264i
$785$		0			0
$786$	342.350			0.435560
$787$			845.181i			1.07393i	0.843605	+	0.536964i	$0.180429\pi$
$787$			845.181i			1.07393i	−0.843605	+	0.536964i	$0.819571\pi$
$788$	521.443			0.661729
$789$			30.0471i			0.0380825i
$790$		0			0
$791$	12.4028	−	16.7985i	0.0156799	−	0.0212370i
$792$	−32.9259			−0.0415731
$793$	−696.968			−0.878901
$794$			519.427i			0.654190i
$795$		0			0
$796$		−	1013.79i		−	1.27361i
$797$		−	541.537i		−	0.679469i	−0.940521	−	0.339734i	$-0.889663\pi$
$797$		−	541.537i		−	0.679469i	0.940521	−	0.339734i	$-0.110337\pi$
$798$	−394.143	+	533.830i	−0.493913	+	0.668959i
$799$	−1101.44			−1.37852
$800$		0			0
$801$			264.286i			0.329945i
$802$	−524.999			−0.654612
$803$		−	126.489i		−	0.157520i
$804$		−	140.282i		−	0.174480i
$805$		0			0
$806$	−1123.86			−1.39437
$807$	−864.662			−1.07145
$808$		−	112.769i		−	0.139566i
$809$	−363.991			−0.449927			−0.224963	−	0.974367i	$-0.572226\pi$
$809$	−363.991			−0.449927			−0.224963	+	0.974367i	$0.572226\pi$
$810$		0			0
$811$			882.216i			1.08781i	0.839146	+	0.543906i	$0.183055\pi$
$811$			882.216i			1.08781i	−0.839146	+	0.543906i	$0.816945\pi$
$812$	−630.729	+	854.263i	−0.776759	+	1.05205i
$813$	571.586			0.703057
$814$	473.768			0.582025
$815$		0			0
$816$	648.534			0.794772
$817$		−	369.963i		−	0.452831i
$818$		−	1429.76i		−	1.74787i
$819$	185.509	+	136.967i	0.226507	+	0.167237i
$820$		0			0
$821$	681.271			0.829806			0.414903	−	0.909866i	$-0.363815\pi$
$821$	681.271			0.829806			0.414903	+	0.909866i	$0.363815\pi$
$822$			767.202i			0.933336i
$823$	360.544			0.438085			0.219042	−	0.975715i	$-0.429707\pi$
$823$	360.544			0.438085			0.219042	+	0.975715i	$0.429707\pi$
$824$		−	23.8743i		−	0.0289737i
$825$		0			0
$826$	−553.626	−	408.759i	−0.670249	−	0.494865i
$827$	770.095			0.931191			0.465596	−	0.884998i	$-0.345840\pi$
$827$	770.095			0.931191			0.465596	+	0.884998i	$0.345840\pi$
$828$	−364.092			−0.439724
$829$		−	128.381i		−	0.154862i	−0.996998	−	0.0774312i	$-0.975328\pi$
$829$		−	128.381i		−	0.154862i	0.996998	−	0.0774312i	$-0.0246718\pi$
$830$		0			0
$831$		−	255.938i		−	0.307988i
$832$		−	628.144i		−	0.754981i
$833$	1044.56	−	321.764i	1.25397	−	0.386272i
$834$	−263.152			−0.315530
$835$		0			0
$836$			1410.52i			1.68722i
$837$	190.512			0.227613
$838$			903.515i			1.07818i
$839$		−	1367.14i		−	1.62949i	−0.579823	−	0.814743i	$-0.696878\pi$
$839$		−	1367.14i		−	1.62949i	0.579823	−	0.814743i	$-0.303122\pi$
$840$		0			0
$841$	758.735			0.902182
$842$	−1406.58			−1.67053
$843$			612.115i			0.726115i
$844$	−1390.46			−1.64746
$845$		0			0
$846$		−	413.528i		−	0.488804i
$847$	−992.982	+	1344.90i	−1.17235	+	1.58784i
$848$	826.544			0.974698
$849$	741.669			0.873580
$850$		0			0
$851$	−286.295			−0.336422
$852$			238.461i			0.279884i
$853$		−	797.415i		−	0.934836i	−0.884036	−	0.467418i	$-0.845184\pi$
$853$		−	797.415i		−	0.934836i	0.884036	−	0.467418i	$-0.154816\pi$
$854$	−997.803	−	736.708i	−1.16839	−	0.862656i
$855$		0			0
$856$	17.1859			0.0200770
$857$			898.781i			1.04875i	0.851486	+	0.524377i	$0.175702\pi$
$857$			898.781i			1.04875i	−0.851486	+	0.524377i	$0.824298\pi$
$858$	1007.11			1.17379
$859$		−	915.157i		−	1.06537i	−0.846312	−	0.532687i	$-0.821182\pi$
$859$		−	915.157i		−	1.06537i	0.846312	−	0.532687i	$-0.178818\pi$
$860$		0			0
$861$	−271.009	+	367.057i	−0.314761	+	0.426315i
$862$	886.961			1.02896
$863$	1357.85			1.57341			0.786703	−	0.617332i	$-0.211786\pi$
$863$	1357.85			1.57341			0.786703	+	0.617332i	$0.211786\pi$
$864$			231.462i			0.267896i
$865$		0			0
$866$			729.674i			0.842580i
$867$		−	361.235i		−	0.416649i
$868$	−783.084	−	578.175i	−0.902170	−	0.666100i
$869$	307.325			0.353654
$870$		0			0
$871$		−	234.486i		−	0.269214i
$872$	−53.0584			−0.0608468
$873$			401.430i			0.459828i
$874$		−	1751.31i		−	2.00379i
$875$		0			0
$876$	−43.8047			−0.0500053
$877$	−1513.27			−1.72550			−0.862752	−	0.505627i	$-0.831261\pi$
$877$	−1513.27			−1.72550			−0.862752	+	0.505627i	$0.831261\pi$
$878$			2203.96i			2.51021i
$879$	−697.379			−0.793377
$880$		0			0
$881$			677.970i			0.769546i	0.923011	+	0.384773i	$0.125720\pi$
$881$			677.970i			0.769546i	−0.923011	+	0.384773i	$0.874280\pi$
$882$	120.804	+	392.173i	0.136966	+	0.444640i
$883$	−155.548			−0.176159			−0.0880793	−	0.996113i	$-0.528073\pi$
$883$	−155.548			−0.176159			−0.0880793	+	0.996113i	$0.528073\pi$
$884$	−928.974			−1.05088
$885$		0			0
$886$	−1633.73			−1.84394
$887$		−	871.417i		−	0.982432i	−0.871038	−	0.491216i	$-0.836553\pi$
$887$		−	871.417i		−	0.982432i	0.871038	−	0.491216i	$-0.163447\pi$
$888$			8.96622i			0.0100971i
$889$	435.120	−	589.330i	0.489449	−	0.662913i
$890$		0			0
$891$	−170.721			−0.191606
$892$			1072.86i			1.20276i
$893$	968.101			1.08410
$894$			1107.73i			1.23907i
$895$		0			0
$896$	−76.8784	+	104.125i	−0.0858018	+	0.116211i
$897$	−608.592			−0.678475
$898$	1474.35			1.64181
$899$			1466.44i			1.63119i
$900$		0			0
$901$		−	1098.34i		−	1.21903i
$902$			1992.72i			2.20923i
$903$	−184.057	−	135.895i	−0.203828	−	0.150493i
$904$	1.72594			0.00190923
$905$		0			0
$906$		−	956.067i		−	1.05526i
$907$	473.129			0.521642			0.260821	−	0.965387i	$-0.416007\pi$
$907$	473.129			0.521642			0.260821	+	0.965387i	$0.416007\pi$
$908$			799.422i			0.880421i
$909$		−	584.709i		−	0.643244i
$910$		0			0
$911$	−676.153			−0.742210			−0.371105	−	0.928591i	$-0.621021\pi$
$911$	−676.153			−0.742210			−0.371105	+	0.928591i	$0.621021\pi$
$912$	−570.023			−0.625025
$913$		−	697.721i		−	0.764207i
$914$	457.929			0.501017
$915$		0			0
$916$		−	521.525i		−	0.569350i
$917$	398.731	+	294.395i	0.434821	+	0.321042i
$918$	323.556			0.352457
$919$	1204.50			1.31066			0.655331	−	0.755342i	$-0.272529\pi$
$919$	1204.50			1.31066			0.655331	+	0.755342i	$0.272529\pi$
$920$		0			0
$921$	−160.618			−0.174395
$922$			1115.57i			1.20995i
$923$			398.596i			0.431848i
$924$	701.734	+	518.112i	0.759452	+	0.560727i
$925$		0			0
$926$	1899.00			2.05075
$927$		−	123.789i		−	0.133537i
$928$	−1781.65			−1.91988
$929$			586.143i			0.630940i	0.948936	+	0.315470i	$0.102162\pi$
$929$			586.143i			0.630940i	−0.948936	+	0.315470i	$0.897838\pi$
$930$		0			0
$931$	−918.107	+	282.812i	−0.986151	+	0.303772i
$932$	294.954			0.316474
$933$	377.791			0.404921
$934$			2024.48i			2.16754i
$935$		0			0
$936$			19.0599i			0.0203632i
$937$		−	449.053i		−	0.479245i	−0.970866	−	0.239623i	$-0.922976\pi$
$937$		−	449.053i		−	0.479245i	0.970866	−	0.239623i	$-0.0770237\pi$
$938$	247.856	−	335.697i	0.264238	−	0.357886i
$939$	508.676			0.541721
$940$		0			0
$941$			904.538i			0.961252i	0.876926	+	0.480626i	$0.159591\pi$
$941$			904.538i			0.961252i	−0.876926	+	0.480626i	$0.840409\pi$
$942$	−1020.38			−1.08321
$943$		−	1204.19i		−	1.27698i
$944$		−	591.161i		−	0.626230i
$945$		0			0
$946$	−999.229			−1.05627
$947$	−1631.56			−1.72288			−0.861439	−	0.507861i	$-0.830436\pi$
$947$	−1631.56			−1.72288			−0.861439	+	0.507861i	$0.830436\pi$
$948$		−	106.431i		−	0.112269i
$949$	−73.2210			−0.0771560
$950$		0			0
$951$		−	188.921i		−	0.198656i
$952$	72.6791	+	53.6612i	0.0763435	+	0.0563668i
$953$	−1547.14			−1.62344			−0.811721	−	0.584046i	$-0.801469\pi$
$953$	−1547.14			−1.62344			−0.811721	+	0.584046i	$0.801469\pi$
$954$	412.365			0.432249
$955$		0			0
$956$	−469.705			−0.491323
$957$		−	1314.10i		−	1.37315i
$958$		−	885.207i		−	0.924015i
$959$	−659.736	+	893.552i	−0.687942	+	0.931753i
$960$		0			0
$961$	−383.253			−0.398806
$962$		−	274.252i		−	0.285086i
$963$	89.1092			0.0925329
$964$		−	590.915i		−	0.612982i
$965$		0			0
$966$	−871.281	−	643.293i	−0.901947	−	0.665935i
$967$	−282.618			−0.292263			−0.146131	−	0.989265i	$-0.546682\pi$
$967$	−282.618			−0.292263			−0.146131	+	0.989265i	$0.546682\pi$
$968$	−138.181			−0.142749
$969$			757.469i			0.781701i
$970$		0			0
$971$			586.935i			0.604465i	0.953234	+	0.302232i	$0.0977319\pi$
$971$			586.935i			0.604465i	−0.953234	+	0.302232i	$0.902268\pi$
$972$			59.1229i			0.0608260i
$973$	−306.490	−	226.291i	−0.314994	−	0.232570i
$974$	−985.765			−1.01208
$975$		0			0
$976$		−	1065.45i		−	1.09165i
$977$	651.703			0.667045			0.333523	−	0.942742i	$-0.391763\pi$
$977$	651.703			0.667045			0.333523	+	0.942742i	$0.391763\pi$
$978$		−	879.135i		−	0.898911i
$979$			1671.08i			1.70693i
$980$		0			0
$981$	−275.109			−0.280437
$982$	−958.283			−0.975848
$983$			583.048i			0.593131i	0.955013	+	0.296565i	$0.0958413\pi$
$983$			583.048i			0.593131i	−0.955013	+	0.296565i	$0.904159\pi$
$984$	−37.7129			−0.0383261
$985$		0			0
$986$			2490.53i			2.52589i
$987$	355.603	−	481.631i	0.360287	−	0.487975i
$988$	816.513			0.826430
$989$	603.828			0.610544
$990$		0			0
$991$	377.146			0.380572			0.190286	−	0.981729i	$-0.439059\pi$
$991$	377.146			0.380572			0.190286	+	0.981729i	$0.439059\pi$
$992$		−	1633.19i		−	1.64636i
$993$			708.259i			0.713251i
$994$	−421.323	+	570.643i	−0.423866	+	0.574087i
$995$		0			0
$996$	−241.630			−0.242600
$997$			1586.82i			1.59159i	0.605565	+	0.795795i	$0.292947\pi$
$997$			1586.82i			1.59159i	−0.605565	+	0.795795i	$0.707053\pi$
$998$	−1174.08			−1.17643
$999$			46.4899i			0.0465364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.h.d.76.10		12
5.2	odd	4		525.3.e.c.349.22		24
5.3	odd	4		525.3.e.c.349.7		24
5.4	even	2		105.3.h.a.76.3	✓	12
7.6	odd	2	inner	525.3.h.d.76.9		12
15.14	odd	2		315.3.h.d.181.9		12
20.19	odd	2		1680.3.s.c.1441.10		12
35.13	even	4		525.3.e.c.349.21		24
35.27	even	4		525.3.e.c.349.8		24
35.34	odd	2		105.3.h.a.76.4	yes	12
105.104	even	2		315.3.h.d.181.10		12
140.139	even	2		1680.3.s.c.1441.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.3	✓	12	5.4	even	2
105.3.h.a.76.4	yes	12	35.34	odd	2
315.3.h.d.181.9		12	15.14	odd	2
315.3.h.d.181.10		12	105.104	even	2
525.3.e.c.349.7		24	5.3	odd	4
525.3.e.c.349.8		24	35.27	even	4
525.3.e.c.349.21		24	35.13	even	4
525.3.e.c.349.22		24	5.2	odd	4
525.3.h.d.76.9		12	7.6	odd	2	inner
525.3.h.d.76.10		12	1.1	even	1	trivial
1680.3.s.c.1441.1		12	140.139	even	2
1680.3.s.c.1441.10		12	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.79155 q^{2} +1.73205i q^{3} +3.79273 q^{4} +4.83510i q^{6} +(-4.15782 + 5.63139i) q^{7} -0.578591 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+2.79155 q^{2} +1.73205i q^{3} +3.79273 q^{4} +4.83510i q^{6} +(-4.15782 + 5.63139i) q^{7} -0.578591 q^{8} -3.00000 q^{9} -18.9690 q^{11} +6.56921i q^{12} +10.9807i q^{13} +(-11.6068 + 15.7203i) q^{14} -16.7861 q^{16} +22.3060i q^{17} -8.37464 q^{18} -19.6057i q^{19} +(-9.75385 - 7.20156i) q^{21} -52.9528 q^{22} +31.9991 q^{23} -1.00215i q^{24} +30.6530i q^{26} -5.19615i q^{27} +(-15.7695 + 21.3583i) q^{28} +39.9967 q^{29} +36.6641i q^{31} -44.5448 q^{32} -32.8553i q^{33} +62.2683i q^{34} -11.3782 q^{36} -8.94699 q^{37} -54.7302i q^{38} -19.0191 q^{39} -37.6320i q^{41} +(-27.2283 - 20.1035i) q^{42} +18.8702 q^{43} -71.9443 q^{44} +89.3269 q^{46} +49.3786i q^{47} -29.0744i q^{48} +(-14.4250 - 46.8286i) q^{49} -38.6352 q^{51} +41.6468i q^{52} -49.2398 q^{53} -14.5053i q^{54} +(2.40568 - 3.25827i) q^{56} +33.9580 q^{57} +111.653 q^{58} +35.2173i q^{59} +63.4723i q^{61} +102.349i q^{62} +(12.4735 - 16.8942i) q^{63} -57.2046 q^{64} -91.7170i q^{66} -21.3544 q^{67} +84.6008i q^{68} +55.4240i q^{69} +36.2998 q^{71} +1.73577 q^{72} +6.66818i q^{73} -24.9759 q^{74} -74.3591i q^{76} +(78.8697 - 106.822i) q^{77} -53.0926 q^{78} -16.2015 q^{79} +9.00000 q^{81} -105.052i q^{82} +36.7822i q^{83} +(-36.9937 - 27.3136i) q^{84} +52.6770 q^{86} +69.2763i q^{87} +10.9753 q^{88} -88.0954i q^{89} +(-61.8364 - 45.6557i) q^{91} +121.364 q^{92} -63.5040 q^{93} +137.843i q^{94} -77.1539i q^{96} -133.810i q^{97} +(-40.2681 - 130.724i) q^{98} +56.9070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} - 12 q^{18} + 36 q^{21} + 88 q^{22} + 64 q^{23} - 88 q^{28} + 104 q^{29} + 228 q^{32} - 132 q^{36} - 32 q^{37} - 24 q^{39} + 60 q^{42} - 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 24 q^{51} - 176 q^{53} - 368 q^{56} + 240 q^{57} + 400 q^{58} - 24 q^{63} - 20 q^{64} - 168 q^{67} + 32 q^{71} + 12 q^{72} + 184 q^{74} - 8 q^{77} - 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 400 q^{86} + 536 q^{88} + 24 q^{91} - 192 q^{92} - 48 q^{93} - 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 - 12 * q^18 + 36 * q^21 + 88 * q^22 + 64 * q^23 - 88 * q^28 + 104 * q^29 + 228 * q^32 - 132 * q^36 - 32 * q^37 - 24 * q^39 + 60 * q^42 - 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 24 * q^51 - 176 * q^53 - 368 * q^56 + 240 * q^57 + 400 * q^58 - 24 * q^63 - 20 * q^64 - 168 * q^67 + 32 * q^71 + 12 * q^72 + 184 * q^74 - 8 * q^77 - 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 400 * q^86 + 536 * q^88 + 24 * q^91 - 192 * q^92 - 48 * q^93 - 884 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more