LMFDB - Embedded newform 8470.2.a.cg.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.a (trivial)

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:	yes
Analytic conductor:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.289169 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.289169 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91638 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.289169 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.289169 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91638 q^{9} +1.00000 q^{10} +0.289169 q^{12} -0.289169 q^{13} +1.00000 q^{14} -0.289169 q^{15} +1.00000 q^{16} +0.916382 q^{17} +2.91638 q^{18} +3.20555 q^{19} -1.00000 q^{20} -0.289169 q^{21} -5.33804 q^{23} -0.289169 q^{24} +1.00000 q^{25} +0.289169 q^{26} -1.71083 q^{27} -1.00000 q^{28} -9.83276 q^{29} +0.289169 q^{30} -1.00000 q^{32} -0.916382 q^{34} +1.00000 q^{35} -2.91638 q^{36} -9.25443 q^{37} -3.20555 q^{38} -0.0836184 q^{39} +1.00000 q^{40} +0.578337 q^{41} +0.289169 q^{42} -5.75971 q^{43} +2.91638 q^{45} +5.33804 q^{46} +11.2544 q^{47} +0.289169 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.264989 q^{51} -0.289169 q^{52} +4.91638 q^{53} +1.71083 q^{54} +1.00000 q^{56} +0.926944 q^{57} +9.83276 q^{58} +7.20555 q^{59} -0.289169 q^{60} -9.49472 q^{61} +2.91638 q^{63} +1.00000 q^{64} +0.289169 q^{65} +10.7491 q^{67} +0.916382 q^{68} -1.54359 q^{69} -1.00000 q^{70} +1.66196 q^{71} +2.91638 q^{72} -10.3380 q^{73} +9.25443 q^{74} +0.289169 q^{75} +3.20555 q^{76} +0.0836184 q^{78} +2.42166 q^{79} -1.00000 q^{80} +8.25443 q^{81} -0.578337 q^{82} -2.28917 q^{83} -0.289169 q^{84} -0.916382 q^{85} +5.75971 q^{86} -2.84333 q^{87} +3.42166 q^{89} -2.91638 q^{90} +0.289169 q^{91} -5.33804 q^{92} -11.2544 q^{94} -3.20555 q^{95} -0.289169 q^{96} -6.33804 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9} + 3 q^{10} + 3 q^{14} + 3 q^{16} - 11 q^{17} - 5 q^{18} - 5 q^{19} - 3 q^{20} - 4 q^{23} + 3 q^{25} - 6 q^{27} - 3 q^{28} - 2 q^{29} - 3 q^{32} + 11 q^{34} + 3 q^{35} + 5 q^{36} - 2 q^{37} + 5 q^{38} - 14 q^{39} + 3 q^{40} - 7 q^{43} - 5 q^{45} + 4 q^{46} + 8 q^{47} + 3 q^{49} - 3 q^{50} + 6 q^{51} + q^{53} + 6 q^{54} + 3 q^{56} + 20 q^{57} + 2 q^{58} + 7 q^{59} - 13 q^{61} - 5 q^{63} + 3 q^{64} - 9 q^{67} - 11 q^{68} + 22 q^{69} - 3 q^{70} + 17 q^{71} - 5 q^{72} - 19 q^{73} + 2 q^{74} - 5 q^{76} + 14 q^{78} + 9 q^{79} - 3 q^{80} - q^{81} - 6 q^{83} + 11 q^{85} + 7 q^{86} - 12 q^{87} + 12 q^{89} + 5 q^{90} - 4 q^{92} - 8 q^{94} + 5 q^{95} - 7 q^{97} - 3 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9 + 3 * q^10 + 3 * q^14 + 3 * q^16 - 11 * q^17 - 5 * q^18 - 5 * q^19 - 3 * q^20 - 4 * q^23 + 3 * q^25 - 6 * q^27 - 3 * q^28 - 2 * q^29 - 3 * q^32 + 11 * q^34 + 3 * q^35 + 5 * q^36 - 2 * q^37 + 5 * q^38 - 14 * q^39 + 3 * q^40 - 7 * q^43 - 5 * q^45 + 4 * q^46 + 8 * q^47 + 3 * q^49 - 3 * q^50 + 6 * q^51 + q^53 + 6 * q^54 + 3 * q^56 + 20 * q^57 + 2 * q^58 + 7 * q^59 - 13 * q^61 - 5 * q^63 + 3 * q^64 - 9 * q^67 - 11 * q^68 + 22 * q^69 - 3 * q^70 + 17 * q^71 - 5 * q^72 - 19 * q^73 + 2 * q^74 - 5 * q^76 + 14 * q^78 + 9 * q^79 - 3 * q^80 - q^81 - 6 * q^83 + 11 * q^85 + 7 * q^86 - 12 * q^87 + 12 * q^89 + 5 * q^90 - 4 * q^92 - 8 * q^94 + 5 * q^95 - 7 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.289169	0.166952	0.0834758	−	0.996510i	$-0.473398\pi$
$3$	0.289169	0.166952	0.0834758	+	0.996510i	$0.473398\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.289169	−0.118053
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.91638	−0.972127
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	0.289169	0.0834758
$13$	−0.289169	−0.0802009	−0.0401005	−	0.999196i	$-0.512768\pi$
$13$	−0.289169	−0.0802009	−0.0401005	+	0.999196i	$0.512768\pi$
$14$	1.00000	0.267261
$15$	−0.289169	−0.0746630
$16$	1.00000	0.250000
$17$	0.916382	0.222255	0.111128	−	0.993806i	$-0.464554\pi$
$17$	0.916382	0.222255	0.111128	+	0.993806i	$0.464554\pi$
$18$	2.91638	0.687398
$19$	3.20555	0.735404	0.367702	−	0.929944i	$-0.380145\pi$
$19$	3.20555	0.735404	0.367702	+	0.929944i	$0.380145\pi$
$20$	−1.00000	−0.223607
$21$	−0.289169	−0.0631018
$22$	0	0
$23$	−5.33804	−1.11306	−0.556530	−	0.830828i	$-0.687867\pi$
$23$	−5.33804	−1.11306	−0.556530	+	0.830828i	$0.687867\pi$
$24$	−0.289169	−0.0590263
$25$	1.00000	0.200000
$26$	0.289169	0.0567106
$27$	−1.71083	−0.329250
$28$	−1.00000	−0.188982
$29$	−9.83276	−1.82590	−0.912949	−	0.408073i	$-0.866201\pi$
$29$	−9.83276	−1.82590	−0.912949	+	0.408073i	$0.866201\pi$
$30$	0.289169	0.0527947
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.916382	−0.157158
$35$	1.00000	0.169031
$36$	−2.91638	−0.486064
$37$	−9.25443	−1.52142	−0.760709	−	0.649093i	$-0.775149\pi$
$37$	−9.25443	−1.52142	−0.760709	+	0.649093i	$0.775149\pi$
$38$	−3.20555	−0.520009
$39$	−0.0836184	−0.0133897
$40$	1.00000	0.158114
$41$	0.578337	0.0903211	0.0451605	−	0.998980i	$-0.485620\pi$
$41$	0.578337	0.0903211	0.0451605	+	0.998980i	$0.485620\pi$
$42$	0.289169	0.0446197
$43$	−5.75971	−0.878347	−0.439174	−	0.898402i	$-0.644729\pi$
$43$	−5.75971	−0.878347	−0.439174	+	0.898402i	$0.644729\pi$
$44$	0	0
$45$	2.91638	0.434748
$46$	5.33804	0.787052
$47$	11.2544	1.64163	0.820813	−	0.571196i	$-0.193521\pi$
$47$	11.2544	1.64163	0.820813	+	0.571196i	$0.193521\pi$
$48$	0.289169	0.0417379
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0.264989	0.0371058
$52$	−0.289169	−0.0401005
$53$	4.91638	0.675317	0.337658	−	0.941269i	$-0.390365\pi$
$53$	4.91638	0.675317	0.337658	+	0.941269i	$0.390365\pi$
$54$	1.71083	0.232815
$55$	0	0
$56$	1.00000	0.133631
$57$	0.926944	0.122777
$58$	9.83276	1.29111
$59$	7.20555	0.938083	0.469041	−	0.883176i	$-0.344600\pi$
$59$	7.20555	0.938083	0.469041	+	0.883176i	$0.344600\pi$
$60$	−0.289169	−0.0373315
$61$	−9.49472	−1.21567	−0.607837	−	0.794062i	$-0.707963\pi$
$61$	−9.49472	−1.21567	−0.607837	+	0.794062i	$0.707963\pi$
$62$	0	0
$63$	2.91638	0.367430
$64$	1.00000	0.125000
$65$	0.289169	0.0358669
$66$	0	0
$67$	10.7491	1.31322	0.656609	−	0.754232i	$-0.271990\pi$
$67$	10.7491	1.31322	0.656609	+	0.754232i	$0.271990\pi$
$68$	0.916382	0.111128
$69$	−1.54359	−0.185827
$70$	−1.00000	−0.119523
$71$	1.66196	0.197238	0.0986189	−	0.995125i	$-0.468558\pi$
$71$	1.66196	0.197238	0.0986189	+	0.995125i	$0.468558\pi$
$72$	2.91638	0.343699
$73$	−10.3380	−1.20998	−0.604988	−	0.796234i	$-0.706822\pi$
$73$	−10.3380	−1.20998	−0.604988	+	0.796234i	$0.706822\pi$
$74$	9.25443	1.07581
$75$	0.289169	0.0333903
$76$	3.20555	0.367702
$77$	0	0
$78$	0.0836184	0.00946792
$79$	2.42166	0.272458	0.136229	−	0.990677i	$-0.456502\pi$
$79$	2.42166	0.272458	0.136229	+	0.990677i	$0.456502\pi$
$80$	−1.00000	−0.111803
$81$	8.25443	0.917158
$82$	−0.578337	−0.0638666
$83$	−2.28917	−0.251269	−0.125634	−	0.992077i	$-0.540097\pi$
$83$	−2.28917	−0.251269	−0.125634	+	0.992077i	$0.540097\pi$
$84$	−0.289169	−0.0315509
$85$	−0.916382	−0.0993955
$86$	5.75971	0.621085
$87$	−2.84333	−0.304837
$88$	0	0
$89$	3.42166	0.362696	0.181348	−	0.983419i	$-0.441954\pi$
$89$	3.42166	0.362696	0.181348	+	0.983419i	$0.441954\pi$
$90$	−2.91638	−0.307414
$91$	0.289169	0.0303131
$92$	−5.33804	−0.556530
$93$	0	0
$94$	−11.2544	−1.16081
$95$	−3.20555	−0.328883
$96$	−0.289169	−0.0295131
$97$	−6.33804	−0.643531	−0.321765	−	0.946819i	$-0.604276\pi$
$97$	−6.33804	−0.643531	−0.321765	+	0.946819i	$0.604276\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	4.28917	0.426788	0.213394	−	0.976966i	$-0.431548\pi$
$101$	4.28917	0.426788	0.213394	+	0.976966i	$0.431548\pi$
$102$	−0.264989	−0.0262378
$103$	5.49472	0.541411	0.270705	−	0.962662i	$-0.412743\pi$
$103$	5.49472	0.541411	0.270705	+	0.962662i	$0.412743\pi$
$104$	0.289169	0.0283553
$105$	0.289169	0.0282200
$106$	−4.91638	−0.477521
$107$	2.50528	0.242195	0.121097	−	0.992641i	$-0.461359\pi$
$107$	2.50528	0.242195	0.121097	+	0.992641i	$0.461359\pi$
$108$	−1.71083	−0.164625
$109$	−7.25443	−0.694848	−0.347424	−	0.937708i	$-0.612944\pi$
$109$	−7.25443	−0.694848	−0.347424	+	0.937708i	$0.612944\pi$
$110$	0	0
$111$	−2.67609	−0.254003
$112$	−1.00000	−0.0944911
$113$	−7.74914	−0.728978	−0.364489	−	0.931208i	$-0.618756\pi$
$113$	−7.74914	−0.728978	−0.364489	+	0.931208i	$0.618756\pi$
$114$	−0.926944	−0.0868163
$115$	5.33804	0.497775
$116$	−9.83276	−0.912949
$117$	0.843326	0.0779655
$118$	−7.20555	−0.663325
$119$	−0.916382	−0.0840046
$120$	0.289169	0.0263974
$121$	0	0
$122$	9.49472	0.859611
$123$	0.167237	0.0150792
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	−2.91638	−0.259812
$127$	−13.3380	−1.18356	−0.591780	−	0.806099i	$-0.701575\pi$
$127$	−13.3380	−1.18356	−0.591780	+	0.806099i	$0.701575\pi$
$128$	−1.00000	−0.0883883
$129$	−1.66553	−0.146641
$130$	−0.289169	−0.0253618
$131$	−11.8086	−1.03172	−0.515860	−	0.856673i	$-0.672528\pi$
$131$	−11.8086	−1.03172	−0.515860	+	0.856673i	$0.672528\pi$
$132$	0	0
$133$	−3.20555	−0.277956
$134$	−10.7491	−0.928585
$135$	1.71083	0.147245
$136$	−0.916382	−0.0785791
$137$	−2.18137	−0.186367	−0.0931835	−	0.995649i	$-0.529704\pi$
$137$	−2.18137	−0.186367	−0.0931835	+	0.995649i	$0.529704\pi$
$138$	1.54359	0.131399
$139$	16.2927	1.38193	0.690966	−	0.722887i	$-0.257185\pi$
$139$	16.2927	1.38193	0.690966	+	0.722887i	$0.257185\pi$
$140$	1.00000	0.0845154
$141$	3.25443	0.274072
$142$	−1.66196	−0.139468
$143$	0	0
$144$	−2.91638	−0.243032
$145$	9.83276	0.816567
$146$	10.3380	0.855583
$147$	0.289169	0.0238502
$148$	−9.25443	−0.760709
$149$	1.73501	0.142138	0.0710688	−	0.997471i	$-0.477359\pi$
$149$	1.73501	0.142138	0.0710688	+	0.997471i	$0.477359\pi$
$150$	−0.289169	−0.0236105
$151$	−6.18137	−0.503033	−0.251516	−	0.967853i	$-0.580929\pi$
$151$	−6.18137	−0.503033	−0.251516	+	0.967853i	$0.580929\pi$
$152$	−3.20555	−0.260004
$153$	−2.67252	−0.216060
$154$	0	0
$155$	0	0
$156$	−0.0836184	−0.00669483
$157$	5.54359	0.442427	0.221214	−	0.975225i	$-0.428998\pi$
$157$	5.54359	0.442427	0.221214	+	0.975225i	$0.428998\pi$
$158$	−2.42166	−0.192657
$159$	1.42166	0.112745
$160$	1.00000	0.0790569
$161$	5.33804	0.420697
$162$	−8.25443	−0.648529
$163$	−21.0141	−1.64595	−0.822977	−	0.568075i	$-0.807688\pi$
$163$	−21.0141	−1.64595	−0.822977	+	0.568075i	$0.807688\pi$
$164$	0.578337	0.0451605
$165$	0	0
$166$	2.28917	0.177674
$167$	9.01413	0.697535	0.348767	−	0.937209i	$-0.386600\pi$
$167$	9.01413	0.697535	0.348767	+	0.937209i	$0.386600\pi$
$168$	0.289169	0.0223098
$169$	−12.9164	−0.993568
$170$	0.916382	0.0702833
$171$	−9.34861	−0.714906
$172$	−5.75971	−0.439174
$173$	16.9894	1.29168	0.645841	−	0.763472i	$-0.276507\pi$
$173$	16.9894	1.29168	0.645841	+	0.763472i	$0.276507\pi$
$174$	2.84333	0.215552
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	2.08362	0.156614
$178$	−3.42166	−0.256464
$179$	5.32391	0.397928	0.198964	−	0.980007i	$-0.436242\pi$
$179$	5.32391	0.397928	0.198964	+	0.980007i	$0.436242\pi$
$180$	2.91638	0.217374
$181$	25.4494	1.89164	0.945820	−	0.324691i	$-0.105260\pi$
$181$	25.4494	1.89164	0.945820	+	0.324691i	$0.105260\pi$
$182$	−0.289169	−0.0214346
$183$	−2.74557	−0.202959
$184$	5.33804	0.393526
$185$	9.25443	0.680399
$186$	0	0
$187$	0	0
$188$	11.2544	0.820813
$189$	1.71083	0.124445
$190$	3.20555	0.232555
$191$	4.08362	0.295480	0.147740	−	0.989026i	$-0.452800\pi$
$191$	4.08362	0.295480	0.147740	+	0.989026i	$0.452800\pi$
$192$	0.289169	0.0208689
$193$	−19.5819	−1.40954	−0.704768	−	0.709438i	$-0.748949\pi$
$193$	−19.5819	−1.40954	−0.704768	+	0.709438i	$0.748949\pi$
$194$	6.33804	0.455045
$195$	0.0836184	0.00598804
$196$	1.00000	0.0714286
$197$	8.43580	0.601026	0.300513	−	0.953778i	$-0.402842\pi$
$197$	8.43580	0.601026	0.300513	+	0.953778i	$0.402842\pi$
$198$	0	0
$199$	10.9894	0.779021	0.389510	−	0.921022i	$-0.372644\pi$
$199$	10.9894	0.779021	0.389510	+	0.921022i	$0.372644\pi$
$200$	−1.00000	−0.0707107
$201$	3.10831	0.219244
$202$	−4.28917	−0.301785
$203$	9.83276	0.690125
$204$	0.264989	0.0185529
$205$	−0.578337	−0.0403928
$206$	−5.49472	−0.382835
$207$	15.5678	1.08204
$208$	−0.289169	−0.0200502
$209$	0	0
$210$	−0.289169	−0.0199545
$211$	−3.66553	−0.252345	−0.126173	−	0.992008i	$-0.540269\pi$
$211$	−3.66553	−0.252345	−0.126173	+	0.992008i	$0.540269\pi$
$212$	4.91638	0.337658
$213$	0.480585	0.0329292
$214$	−2.50528	−0.171258
$215$	5.75971	0.392809
$216$	1.71083	0.116407
$217$	0	0
$218$	7.25443	0.491332
$219$	−2.98944	−0.202007
$220$	0	0
$221$	−0.264989	−0.0178251
$222$	2.67609	0.179607
$223$	14.0731	0.942402	0.471201	−	0.882026i	$-0.343821\pi$
$223$	14.0731	0.942402	0.471201	+	0.882026i	$0.343821\pi$
$224$	1.00000	0.0668153
$225$	−2.91638	−0.194425
$226$	7.74914	0.515465
$227$	−3.25443	−0.216004	−0.108002	−	0.994151i	$-0.534445\pi$
$227$	−3.25443	−0.216004	−0.108002	+	0.994151i	$0.534445\pi$
$228$	0.926944	0.0613884
$229$	15.1814	1.00321	0.501607	−	0.865096i	$-0.332743\pi$
$229$	15.1814	1.00321	0.501607	+	0.865096i	$0.332743\pi$
$230$	−5.33804	−0.351980
$231$	0	0
$232$	9.83276	0.645553
$233$	−3.50528	−0.229639	−0.114819	−	0.993386i	$-0.536629\pi$
$233$	−3.50528	−0.229639	−0.114819	+	0.993386i	$0.536629\pi$
$234$	−0.843326	−0.0551299
$235$	−11.2544	−0.734158
$236$	7.20555	0.469041
$237$	0.700269	0.0454873
$238$	0.916382	0.0594002
$239$	26.6408	1.72325	0.861626	−	0.507544i	$-0.169446\pi$
$239$	26.6408	1.72325	0.861626	+	0.507544i	$0.169446\pi$
$240$	−0.289169	−0.0186657
$241$	−3.58890	−0.231181	−0.115591	−	0.993297i	$-0.536876\pi$
$241$	−3.58890	−0.231181	−0.115591	+	0.993297i	$0.536876\pi$
$242$	0	0
$243$	7.51941	0.482371
$244$	−9.49472	−0.607837
$245$	−1.00000	−0.0638877
$246$	−0.167237	−0.0106626
$247$	−0.926944	−0.0589801
$248$	0	0
$249$	−0.661956	−0.0419497
$250$	1.00000	0.0632456
$251$	−10.0731	−0.635806	−0.317903	−	0.948123i	$-0.602979\pi$
$251$	−10.0731	−0.635806	−0.317903	+	0.948123i	$0.602979\pi$
$252$	2.91638	0.183715
$253$	0	0
$254$	13.3380	0.836903
$255$	−0.264989	−0.0165942
$256$	1.00000	0.0625000
$257$	14.7491	0.920026	0.460013	−	0.887912i	$-0.347845\pi$
$257$	14.7491	0.920026	0.460013	+	0.887912i	$0.347845\pi$
$258$	1.66553	0.103691
$259$	9.25443	0.575042
$260$	0.289169	0.0179335
$261$	28.6761	1.77501
$262$	11.8086	0.729537
$263$	6.90582	0.425831	0.212916	−	0.977071i	$-0.431704\pi$
$263$	6.90582	0.425831	0.212916	+	0.977071i	$0.431704\pi$
$264$	0	0
$265$	−4.91638	−0.302011
$266$	3.20555	0.196545
$267$	0.989437	0.0605526
$268$	10.7491	0.656609
$269$	29.0383	1.77050	0.885249	−	0.465118i	$-0.153988\pi$
$269$	29.0383	1.77050	0.885249	+	0.465118i	$0.153988\pi$
$270$	−1.71083	−0.104118
$271$	−4.26499	−0.259080	−0.129540	−	0.991574i	$-0.541350\pi$
$271$	−4.26499	−0.259080	−0.129540	+	0.991574i	$0.541350\pi$
$272$	0.916382	0.0555638
$273$	0.0836184	0.00506082
$274$	2.18137	0.131781
$275$	0	0
$276$	−1.54359	−0.0929135
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	−16.2927	−0.977174
$279$	0	0
$280$	−1.00000	−0.0597614
$281$	−15.1461	−0.903541	−0.451771	−	0.892134i	$-0.649207\pi$
$281$	−15.1461	−0.903541	−0.451771	+	0.892134i	$0.649207\pi$
$282$	−3.25443	−0.193798
$283$	18.5330	1.10167	0.550837	−	0.834613i	$-0.314309\pi$
$283$	18.5330	1.10167	0.550837	+	0.834613i	$0.314309\pi$
$284$	1.66196	0.0986189
$285$	−0.926944	−0.0549074
$286$	0	0
$287$	−0.578337	−0.0341382
$288$	2.91638	0.171849
$289$	−16.1602	−0.950603
$290$	−9.83276	−0.577400
$291$	−1.83276	−0.107438
$292$	−10.3380	−0.604988
$293$	4.02418	0.235095	0.117548	−	0.993067i	$-0.462497\pi$
$293$	4.02418	0.235095	0.117548	+	0.993067i	$0.462497\pi$
$294$	−0.289169	−0.0168647
$295$	−7.20555	−0.419523
$296$	9.25443	0.537903
$297$	0	0
$298$	−1.73501	−0.100507
$299$	1.54359	0.0892684
$300$	0.289169	0.0166952
$301$	5.75971	0.331984
$302$	6.18137	0.355698
$303$	1.24029	0.0712530
$304$	3.20555	0.183851
$305$	9.49472	0.543666
$306$	2.67252	0.152778
$307$	−34.2439	−1.95440	−0.977200	−	0.212320i	$-0.931898\pi$
$307$	−34.2439	−1.95440	−0.977200	+	0.212320i	$0.931898\pi$
$308$	0	0
$309$	1.58890	0.0903894
$310$	0	0
$311$	−6.89169	−0.390792	−0.195396	−	0.980724i	$-0.562599\pi$
$311$	−6.89169	−0.390792	−0.195396	+	0.980724i	$0.562599\pi$
$312$	0.0836184	0.00473396
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−5.54359	−0.312843
$315$	−2.91638	−0.164319
$316$	2.42166	0.136229
$317$	29.7386	1.67029	0.835143	−	0.550034i	$-0.185385\pi$
$317$	29.7386	1.67029	0.835143	+	0.550034i	$0.185385\pi$
$318$	−1.42166	−0.0797229
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	0.724449	0.0404348
$322$	−5.33804	−0.297478
$323$	2.93751	0.163447
$324$	8.25443	0.458579
$325$	−0.289169	−0.0160402
$326$	21.0141	1.16387
$327$	−2.09775	−0.116006
$328$	−0.578337	−0.0319333
$329$	−11.2544	−0.620477
$330$	0	0
$331$	25.2544	1.38811	0.694054	−	0.719923i	$-0.255823\pi$
$331$	25.2544	1.38811	0.694054	+	0.719923i	$0.255823\pi$
$332$	−2.28917	−0.125634
$333$	26.9894	1.47901
$334$	−9.01413	−0.493231
$335$	−10.7491	−0.587289
$336$	−0.289169	−0.0157754
$337$	13.9164	0.758074	0.379037	−	0.925382i	$-0.376255\pi$
$337$	13.9164	0.758074	0.379037	+	0.925382i	$0.376255\pi$
$338$	12.9164	0.702559
$339$	−2.24081	−0.121704
$340$	−0.916382	−0.0496978
$341$	0	0
$342$	9.34861	0.505515
$343$	−1.00000	−0.0539949
$344$	5.75971	0.310543
$345$	1.54359	0.0831043
$346$	−16.9894	−0.913358
$347$	−21.0836	−1.13183	−0.565914	−	0.824464i	$-0.691477\pi$
$347$	−21.0836	−1.13183	−0.565914	+	0.824464i	$0.691477\pi$
$348$	−2.84333	−0.152418
$349$	29.2786	1.56725	0.783624	−	0.621236i	$-0.213369\pi$
$349$	29.2786	1.56725	0.783624	+	0.621236i	$0.213369\pi$
$350$	1.00000	0.0534522
$351$	0.494719	0.0264061
$352$	0	0
$353$	−19.0141	−1.01202	−0.506010	−	0.862528i	$-0.668880\pi$
$353$	−19.0141	−1.01202	−0.506010	+	0.862528i	$0.668880\pi$
$354$	−2.08362	−0.110743
$355$	−1.66196	−0.0882074
$356$	3.42166	0.181348
$357$	−0.264989	−0.0140247
$358$	−5.32391	−0.281377
$359$	26.4842	1.39778	0.698890	−	0.715229i	$-0.253678\pi$
$359$	26.4842	1.39778	0.698890	+	0.715229i	$0.253678\pi$
$360$	−2.91638	−0.153707
$361$	−8.72445	−0.459182
$362$	−25.4494	−1.33759
$363$	0	0
$364$	0.289169	0.0151566
$365$	10.3380	0.541118
$366$	2.74557	0.143513
$367$	13.2297	0.690586	0.345293	−	0.938495i	$-0.387779\pi$
$367$	13.2297	0.690586	0.345293	+	0.938495i	$0.387779\pi$
$368$	−5.33804	−0.278265
$369$	−1.68665	−0.0878036
$370$	−9.25443	−0.481115
$371$	−4.91638	−0.255246
$372$	0	0
$373$	−30.8469	−1.59719	−0.798596	−	0.601868i	$-0.794423\pi$
$373$	−30.8469	−1.59719	−0.798596	+	0.601868i	$0.794423\pi$
$374$	0	0
$375$	−0.289169	−0.0149326
$376$	−11.2544	−0.580403
$377$	2.84333	0.146439
$378$	−1.71083	−0.0879957
$379$	−34.0071	−1.74683	−0.873415	−	0.486977i	$-0.838100\pi$
$379$	−34.0071	−1.74683	−0.873415	+	0.486977i	$0.838100\pi$
$380$	−3.20555	−0.164441
$381$	−3.85694	−0.197597
$382$	−4.08362	−0.208936
$383$	2.09418	0.107008	0.0535038	−	0.998568i	$-0.482961\pi$
$383$	2.09418	0.107008	0.0535038	+	0.998568i	$0.482961\pi$
$384$	−0.289169	−0.0147566
$385$	0	0
$386$	19.5819	0.996693
$387$	16.7975	0.853865
$388$	−6.33804	−0.321765
$389$	8.94108	0.453331	0.226665	−	0.973973i	$-0.427218\pi$
$389$	8.94108	0.453331	0.226665	+	0.973973i	$0.427218\pi$
$390$	−0.0836184	−0.00423418
$391$	−4.89169	−0.247383
$392$	−1.00000	−0.0505076
$393$	−3.41467	−0.172247
$394$	−8.43580	−0.424989
$395$	−2.42166	−0.121847
$396$	0	0
$397$	−31.4983	−1.58085	−0.790427	−	0.612556i	$-0.790141\pi$
$397$	−31.4983	−1.58085	−0.790427	+	0.612556i	$0.790141\pi$
$398$	−10.9894	−0.550851
$399$	−0.926944	−0.0464053
$400$	1.00000	0.0500000
$401$	−0.508852	−0.0254109	−0.0127054	−	0.999919i	$-0.504044\pi$
$401$	−0.508852	−0.0254109	−0.0127054	+	0.999919i	$0.504044\pi$
$402$	−3.10831	−0.155029
$403$	0	0
$404$	4.28917	0.213394
$405$	−8.25443	−0.410166
$406$	−9.83276	−0.487992
$407$	0	0
$408$	−0.264989	−0.0131189
$409$	0.745574	0.0368663	0.0184331	−	0.999830i	$-0.494132\pi$
$409$	0.745574	0.0368663	0.0184331	+	0.999830i	$0.494132\pi$
$410$	0.578337	0.0285620
$411$	−0.630784	−0.0311143
$412$	5.49472	0.270705
$413$	−7.20555	−0.354562
$414$	−15.5678	−0.765114
$415$	2.28917	0.112371
$416$	0.289169	0.0141777
$417$	4.71135	0.230716
$418$	0	0
$419$	12.6272	0.616880	0.308440	−	0.951244i	$-0.400193\pi$
$419$	12.6272	0.616880	0.308440	+	0.951244i	$0.400193\pi$
$420$	0.289169	0.0141100
$421$	1.35218	0.0659011	0.0329506	−	0.999457i	$-0.489510\pi$
$421$	1.35218	0.0659011	0.0329506	+	0.999457i	$0.489510\pi$
$422$	3.66553	0.178435
$423$	−32.8222	−1.59587
$424$	−4.91638	−0.238761
$425$	0.916382	0.0444510
$426$	−0.480585	−0.0232844
$427$	9.49472	0.459482
$428$	2.50528	0.121097
$429$	0	0
$430$	−5.75971	−0.277758
$431$	7.33447	0.353289	0.176645	−	0.984275i	$-0.443476\pi$
$431$	7.33447	0.353289	0.176645	+	0.984275i	$0.443476\pi$
$432$	−1.71083	−0.0823124
$433$	30.6066	1.47086	0.735430	−	0.677601i	$-0.236980\pi$
$433$	30.6066	1.47086	0.735430	+	0.677601i	$0.236980\pi$
$434$	0	0
$435$	2.84333	0.136327
$436$	−7.25443	−0.347424
$437$	−17.1114	−0.818548
$438$	2.98944	0.142841
$439$	36.5855	1.74613	0.873065	−	0.487604i	$-0.162129\pi$
$439$	36.5855	1.74613	0.873065	+	0.487604i	$0.162129\pi$
$440$	0	0
$441$	−2.91638	−0.138875
$442$	0.264989	0.0126042
$443$	40.0766	1.90410	0.952049	−	0.305946i	$-0.0989726\pi$
$443$	40.0766	1.90410	0.952049	+	0.305946i	$0.0989726\pi$
$444$	−2.67609	−0.127002
$445$	−3.42166	−0.162202
$446$	−14.0731	−0.666379
$447$	0.501711	0.0237301
$448$	−1.00000	−0.0472456
$449$	12.6655	0.597723	0.298862	−	0.954296i	$-0.403393\pi$
$449$	12.6655	0.597723	0.298862	+	0.954296i	$0.403393\pi$
$450$	2.91638	0.137480
$451$	0	0
$452$	−7.74914	−0.364489
$453$	−1.78746	−0.0839821
$454$	3.25443	0.152738
$455$	−0.289169	−0.0135564
$456$	−0.926944	−0.0434081
$457$	6.39697	0.299237	0.149619	−	0.988744i	$-0.452195\pi$
$457$	6.39697	0.299237	0.149619	+	0.988744i	$0.452195\pi$
$458$	−15.1814	−0.709379
$459$	−1.56777	−0.0731774
$460$	5.33804	0.248888
$461$	−27.4736	−1.27957	−0.639786	−	0.768553i	$-0.720977\pi$
$461$	−27.4736	−1.27957	−0.639786	+	0.768553i	$0.720977\pi$
$462$	0	0
$463$	30.1119	1.39942	0.699709	−	0.714428i	$-0.253313\pi$
$463$	30.1119	1.39942	0.699709	+	0.714428i	$0.253313\pi$
$464$	−9.83276	−0.456475
$465$	0	0
$466$	3.50528	0.162379
$467$	37.5719	1.73862	0.869309	−	0.494269i	$-0.164564\pi$
$467$	37.5719	1.73862	0.869309	+	0.494269i	$0.164564\pi$
$468$	0.843326	0.0389827
$469$	−10.7491	−0.496349
$470$	11.2544	0.519128
$471$	1.60303	0.0738639
$472$	−7.20555	−0.331662
$473$	0	0
$474$	−0.700269	−0.0321644
$475$	3.20555	0.147081
$476$	−0.916382	−0.0420023
$477$	−14.3380	−0.656494
$478$	−26.6408	−1.21852
$479$	−20.3627	−0.930397	−0.465199	−	0.885206i	$-0.654017\pi$
$479$	−20.3627	−0.930397	−0.465199	+	0.885206i	$0.654017\pi$
$480$	0.289169	0.0131987
$481$	2.67609	0.122019
$482$	3.58890	0.163470
$483$	1.54359	0.0702360
$484$	0	0
$485$	6.33804	0.287796
$486$	−7.51941	−0.341088
$487$	−6.18137	−0.280105	−0.140052	−	0.990144i	$-0.544727\pi$
$487$	−6.18137	−0.280105	−0.140052	+	0.990144i	$0.544727\pi$
$488$	9.49472	0.429806
$489$	−6.07663	−0.274795
$490$	1.00000	0.0451754
$491$	11.5889	0.523000	0.261500	−	0.965204i	$-0.415783\pi$
$491$	11.5889	0.523000	0.261500	+	0.965204i	$0.415783\pi$
$492$	0.167237	0.00753962
$493$	−9.01056	−0.405815
$494$	0.926944	0.0417052
$495$	0	0
$496$	0	0
$497$	−1.66196	−0.0745489
$498$	0.661956	0.0296629
$499$	10.6761	0.477927	0.238964	−	0.971029i	$-0.423192\pi$
$499$	10.6761	0.477927	0.238964	+	0.971029i	$0.423192\pi$
$500$	−1.00000	−0.0447214
$501$	2.60660	0.116454
$502$	10.0731	0.449582
$503$	−6.02470	−0.268628	−0.134314	−	0.990939i	$-0.542883\pi$
$503$	−6.02470	−0.268628	−0.134314	+	0.990939i	$0.542883\pi$
$504$	−2.91638	−0.129906
$505$	−4.28917	−0.190865
$506$	0	0
$507$	−3.73501	−0.165878
$508$	−13.3380	−0.591780
$509$	14.1255	0.626102	0.313051	−	0.949736i	$-0.398649\pi$
$509$	14.1255	0.626102	0.313051	+	0.949736i	$0.398649\pi$
$510$	0.264989	0.0117339
$511$	10.3380	0.457328
$512$	−1.00000	−0.0441942
$513$	−5.48416	−0.242131
$514$	−14.7491	−0.650557
$515$	−5.49472	−0.242126
$516$	−1.66553	−0.0733207
$517$	0	0
$518$	−9.25443	−0.406616
$519$	4.91281	0.215648
$520$	−0.289169	−0.0126809
$521$	20.6761	0.905836	0.452918	−	0.891552i	$-0.350383\pi$
$521$	20.6761	0.905836	0.452918	+	0.891552i	$0.350383\pi$
$522$	−28.6761	−1.25512
$523$	19.0630	0.833567	0.416784	−	0.909006i	$-0.363157\pi$
$523$	19.0630	0.833567	0.416784	+	0.909006i	$0.363157\pi$
$524$	−11.8086	−0.515860
$525$	−0.289169	−0.0126204
$526$	−6.90582	−0.301108
$527$	0	0
$528$	0	0
$529$	5.49472	0.238901
$530$	4.91638	0.213554
$531$	−21.0141	−0.911936
$532$	−3.20555	−0.138978
$533$	−0.167237	−0.00724383
$534$	−0.989437	−0.0428171
$535$	−2.50528	−0.108313
$536$	−10.7491	−0.464292
$537$	1.53951	0.0664347
$538$	−29.0383	−1.25193
$539$	0	0
$540$	1.71083	0.0736225
$541$	23.2333	0.998878	0.499439	−	0.866349i	$-0.333540\pi$
$541$	23.2333	0.998878	0.499439	+	0.866349i	$0.333540\pi$
$542$	4.26499	0.183197
$543$	7.35917	0.315812
$544$	−0.916382	−0.0392895
$545$	7.25443	0.310745
$546$	−0.0836184	−0.00357854
$547$	11.8575	0.506988	0.253494	−	0.967337i	$-0.418420\pi$
$547$	11.8575	0.506988	0.253494	+	0.967337i	$0.418420\pi$
$548$	−2.18137	−0.0931835
$549$	27.6902	1.18179
$550$	0	0
$551$	−31.5194	−1.34277
$552$	1.54359	0.0656997
$553$	−2.42166	−0.102980
$554$	−10.0000	−0.424859
$555$	2.67609	0.113594
$556$	16.2927	0.690966
$557$	6.16724	0.261314	0.130657	−	0.991428i	$-0.458291\pi$
$557$	6.16724	0.261314	0.130657	+	0.991428i	$0.458291\pi$
$558$	0	0
$559$	1.66553	0.0704443
$560$	1.00000	0.0422577
$561$	0	0
$562$	15.1461	0.638900
$563$	9.44584	0.398095	0.199047	−	0.979990i	$-0.436215\pi$
$563$	9.44584	0.398095	0.199047	+	0.979990i	$0.436215\pi$
$564$	3.25443	0.137036
$565$	7.74914	0.326009
$566$	−18.5330	−0.779001
$567$	−8.25443	−0.346653
$568$	−1.66196	−0.0697341
$569$	33.0978	1.38753	0.693765	−	0.720201i	$-0.255951\pi$
$569$	33.0978	1.38753	0.693765	+	0.720201i	$0.255951\pi$
$570$	0.926944	0.0388254
$571$	11.4005	0.477098	0.238549	−	0.971131i	$-0.423328\pi$
$571$	11.4005	0.477098	0.238549	+	0.971131i	$0.423328\pi$
$572$	0	0
$573$	1.18085	0.0493309
$574$	0.578337	0.0241393
$575$	−5.33804	−0.222612
$576$	−2.91638	−0.121516
$577$	−7.73858	−0.322161	−0.161081	−	0.986941i	$-0.551498\pi$
$577$	−7.73858	−0.322161	−0.161081	+	0.986941i	$0.551498\pi$
$578$	16.1602	0.672178
$579$	−5.66247	−0.235324
$580$	9.83276	0.408283
$581$	2.28917	0.0949707
$582$	1.83276	0.0759705
$583$	0	0
$584$	10.3380	0.427791
$585$	−0.843326	−0.0348672
$586$	−4.02418	−0.166237
$587$	5.61308	0.231677	0.115838	−	0.993268i	$-0.463045\pi$
$587$	5.61308	0.231677	0.115838	+	0.993268i	$0.463045\pi$
$588$	0.289169	0.0119251
$589$	0	0
$590$	7.20555	0.296648
$591$	2.43937	0.100342
$592$	−9.25443	−0.380355
$593$	−40.3169	−1.65562	−0.827809	−	0.561010i	$-0.810413\pi$
$593$	−40.3169	−1.65562	−0.827809	+	0.561010i	$0.810413\pi$
$594$	0	0
$595$	0.916382	0.0375680
$596$	1.73501	0.0710688
$597$	3.17780	0.130059
$598$	−1.54359	−0.0631223
$599$	19.2439	0.786283	0.393141	−	0.919478i	$-0.371388\pi$
$599$	19.2439	0.786283	0.393141	+	0.919478i	$0.371388\pi$
$600$	−0.289169	−0.0118053
$601$	31.6655	1.29166	0.645832	−	0.763480i	$-0.276511\pi$
$601$	31.6655	1.29166	0.645832	+	0.763480i	$0.276511\pi$
$602$	−5.75971	−0.234748
$603$	−31.3486	−1.27661
$604$	−6.18137	−0.251516
$605$	0	0
$606$	−1.24029	−0.0503834
$607$	29.0141	1.17765	0.588824	−	0.808262i	$-0.299591\pi$
$607$	29.0141	1.17765	0.588824	+	0.808262i	$0.299591\pi$
$608$	−3.20555	−0.130002
$609$	2.84333	0.115217
$610$	−9.49472	−0.384430
$611$	−3.25443	−0.131660
$612$	−2.67252	−0.108030
$613$	2.91638	0.117792	0.0588958	−	0.998264i	$-0.481242\pi$
$613$	2.91638	0.117792	0.0588958	+	0.998264i	$0.481242\pi$
$614$	34.2439	1.38197
$615$	−0.167237	−0.00674364
$616$	0	0
$617$	14.1955	0.571489	0.285745	−	0.958306i	$-0.407759\pi$
$617$	14.1955	0.571489	0.285745	+	0.958306i	$0.407759\pi$
$618$	−1.58890	−0.0639149
$619$	−40.2680	−1.61851	−0.809255	−	0.587458i	$-0.800129\pi$
$619$	−40.2680	−1.61851	−0.809255	+	0.587458i	$0.800129\pi$
$620$	0	0
$621$	9.13249	0.366474
$622$	6.89169	0.276331
$623$	−3.42166	−0.137086
$624$	−0.0836184	−0.00334742
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	0	0
$628$	5.54359	0.221214
$629$	−8.48059	−0.338143
$630$	2.91638	0.116191
$631$	−10.9647	−0.436499	−0.218250	−	0.975893i	$-0.570035\pi$
$631$	−10.9647	−0.436499	−0.218250	+	0.975893i	$0.570035\pi$
$632$	−2.42166	−0.0963286
$633$	−1.05995	−0.0421294
$634$	−29.7386	−1.18107
$635$	13.3380	0.529304
$636$	1.42166	0.0563726
$637$	−0.289169	−0.0114573
$638$	0	0
$639$	−4.84690	−0.191740
$640$	1.00000	0.0395285
$641$	1.57834	0.0623406	0.0311703	−	0.999514i	$-0.490077\pi$
$641$	1.57834	0.0623406	0.0311703	+	0.999514i	$0.490077\pi$
$642$	−0.724449	−0.0285917
$643$	−24.7456	−0.975870	−0.487935	−	0.872880i	$-0.662250\pi$
$643$	−24.7456	−0.975870	−0.487935	+	0.872880i	$0.662250\pi$
$644$	5.33804	0.210348
$645$	1.66553	0.0655800
$646$	−2.93751	−0.115575
$647$	−18.1013	−0.711636	−0.355818	−	0.934555i	$-0.615798\pi$
$647$	−18.1013	−0.711636	−0.355818	+	0.934555i	$0.615798\pi$
$648$	−8.25443	−0.324264
$649$	0	0
$650$	0.289169	0.0113421
$651$	0	0
$652$	−21.0141	−0.822977
$653$	−45.0908	−1.76454	−0.882269	−	0.470746i	$-0.843985\pi$
$653$	−45.0908	−1.76454	−0.882269	+	0.470746i	$0.843985\pi$
$654$	2.09775	0.0820286
$655$	11.8086	0.461400
$656$	0.578337	0.0225803
$657$	30.1497	1.17625
$658$	11.2544	0.438743
$659$	6.31335	0.245933	0.122967	−	0.992411i	$-0.460759\pi$
$659$	6.31335	0.245933	0.122967	+	0.992411i	$0.460759\pi$
$660$	0	0
$661$	46.2680	1.79962	0.899809	−	0.436284i	$-0.143706\pi$
$661$	46.2680	1.79962	0.899809	+	0.436284i	$0.143706\pi$
$662$	−25.2544	−0.981541
$663$	−0.0766264	−0.00297592
$664$	2.28917	0.0888370
$665$	3.20555	0.124306
$666$	−26.9894	−1.04582
$667$	52.4877	2.03233
$668$	9.01413	0.348767
$669$	4.06949	0.157335
$670$	10.7491	0.415276
$671$	0	0
$672$	0.289169	0.0111549
$673$	6.01413	0.231828	0.115914	−	0.993259i	$-0.463020\pi$
$673$	6.01413	0.231828	0.115914	+	0.993259i	$0.463020\pi$
$674$	−13.9164	−0.536039
$675$	−1.71083	−0.0658499
$676$	−12.9164	−0.496784
$677$	3.03474	0.116635	0.0583173	−	0.998298i	$-0.481426\pi$
$677$	3.03474	0.116635	0.0583173	+	0.998298i	$0.481426\pi$
$678$	2.24081	0.0860577
$679$	6.33804	0.243232
$680$	0.916382	0.0351416
$681$	−0.941078	−0.0360622
$682$	0	0
$683$	−33.7386	−1.29097	−0.645485	−	0.763773i	$-0.723345\pi$
$683$	−33.7386	−1.29097	−0.645485	+	0.763773i	$0.723345\pi$
$684$	−9.34861	−0.357453
$685$	2.18137	0.0833459
$686$	1.00000	0.0381802
$687$	4.38997	0.167488
$688$	−5.75971	−0.219587
$689$	−1.42166	−0.0541610
$690$	−1.54359	−0.0587636
$691$	15.2791	0.581245	0.290623	−	0.956838i	$-0.406138\pi$
$691$	15.2791	0.581245	0.290623	+	0.956838i	$0.406138\pi$
$692$	16.9894	0.645841
$693$	0	0
$694$	21.0836	0.800323
$695$	−16.2927	−0.618019
$696$	2.84333	0.107776
$697$	0.529977	0.0200743
$698$	−29.2786	−1.10821
$699$	−1.01362	−0.0383385
$700$	−1.00000	−0.0377964
$701$	−16.4111	−0.619839	−0.309919	−	0.950763i	$-0.600302\pi$
$701$	−16.4111	−0.619839	−0.309919	+	0.950763i	$0.600302\pi$
$702$	−0.494719	−0.0186720
$703$	−29.6655	−1.11886
$704$	0	0
$705$	−3.25443	−0.122569
$706$	19.0141	0.715606
$707$	−4.28917	−0.161311
$708$	2.08362	0.0783072
$709$	23.3522	0.877009	0.438505	−	0.898729i	$-0.355508\pi$
$709$	23.3522	0.877009	0.438505	+	0.898729i	$0.355508\pi$
$710$	1.66196	0.0623721
$711$	−7.06249	−0.264864
$712$	−3.42166	−0.128232
$713$	0	0
$714$	0.264989	0.00991695
$715$	0	0
$716$	5.32391	0.198964
$717$	7.70369	0.287700
$718$	−26.4842	−0.988380
$719$	28.3416	1.05696	0.528482	−	0.848945i	$-0.322761\pi$
$719$	28.3416	1.05696	0.528482	+	0.848945i	$0.322761\pi$
$720$	2.91638	0.108687
$721$	−5.49472	−0.204634
$722$	8.72445	0.324690
$723$	−1.03780	−0.0385961
$724$	25.4494	0.945820
$725$	−9.83276	−0.365180
$726$	0	0
$727$	−0.411100	−0.0152469	−0.00762343	−	0.999971i	$-0.502427\pi$
$727$	−0.411100	−0.0152469	−0.00762343	+	0.999971i	$0.502427\pi$
$728$	−0.289169	−0.0107173
$729$	−22.5889	−0.836626
$730$	−10.3380	−0.382628
$731$	−5.27809	−0.195217
$732$	−2.74557	−0.101479
$733$	−34.1502	−1.26137	−0.630683	−	0.776040i	$-0.717225\pi$
$733$	−34.1502	−1.26137	−0.630683	+	0.776040i	$0.717225\pi$
$734$	−13.2297	−0.488318
$735$	−0.289169	−0.0106661
$736$	5.33804	0.196763
$737$	0	0
$738$	1.68665	0.0620865
$739$	42.9200	1.57884	0.789418	−	0.613856i	$-0.210382\pi$
$739$	42.9200	1.57884	0.789418	+	0.613856i	$0.210382\pi$
$740$	9.25443	0.340199
$741$	−0.268043	−0.00984681
$742$	4.91638	0.180486
$743$	−10.9894	−0.403163	−0.201582	−	0.979472i	$-0.564608\pi$
$743$	−10.9894	−0.403163	−0.201582	+	0.979472i	$0.564608\pi$
$744$	0	0
$745$	−1.73501	−0.0635659
$746$	30.8469	1.12939
$747$	6.67609	0.244265
$748$	0	0
$749$	−2.50528	−0.0915410
$750$	0.289169	0.0105589
$751$	23.0036	0.839412	0.419706	−	0.907660i	$-0.362133\pi$
$751$	23.0036	0.839412	0.419706	+	0.907660i	$0.362133\pi$
$752$	11.2544	0.410407
$753$	−2.91281	−0.106149
$754$	−2.84333	−0.103548
$755$	6.18137	0.224963
$756$	1.71083	0.0622223
$757$	−29.0836	−1.05706	−0.528531	−	0.848914i	$-0.677257\pi$
$757$	−29.0836	−1.05706	−0.528531	+	0.848914i	$0.677257\pi$
$758$	34.0071	1.23519
$759$	0	0
$760$	3.20555	0.116278
$761$	−1.90225	−0.0689564	−0.0344782	−	0.999405i	$-0.510977\pi$
$761$	−1.90225	−0.0689564	−0.0344782	+	0.999405i	$0.510977\pi$
$762$	3.85694	0.139722
$763$	7.25443	0.262628
$764$	4.08362	0.147740
$765$	2.67252	0.0966251
$766$	−2.09418	−0.0756658
$767$	−2.08362	−0.0752351
$768$	0.289169	0.0104345
$769$	−9.05892	−0.326673	−0.163337	−	0.986570i	$-0.552226\pi$
$769$	−9.05892	−0.326673	−0.163337	+	0.986570i	$0.552226\pi$
$770$	0	0
$771$	4.26499	0.153600
$772$	−19.5819	−0.704768
$773$	5.49523	0.197650	0.0988249	−	0.995105i	$-0.468492\pi$
$773$	5.49523	0.197650	0.0988249	+	0.995105i	$0.468492\pi$
$774$	−16.7975	−0.603774
$775$	0	0
$776$	6.33804	0.227523
$777$	2.67609	0.0960042
$778$	−8.94108	−0.320553
$779$	1.85389	0.0664224
$780$	0.0836184	0.00299402
$781$	0	0
$782$	4.89169	0.174926
$783$	16.8222	0.601176
$784$	1.00000	0.0357143
$785$	−5.54359	−0.197859
$786$	3.41467	0.121797
$787$	−1.42166	−0.0506768	−0.0253384	−	0.999679i	$-0.508066\pi$
$787$	−1.42166	−0.0506768	−0.0253384	+	0.999679i	$0.508066\pi$
$788$	8.43580	0.300513
$789$	1.99695	0.0710931
$790$	2.42166	0.0861589
$791$	7.74914	0.275528
$792$	0	0
$793$	2.74557	0.0974982
$794$	31.4983	1.11783
$795$	−1.42166	−0.0504212
$796$	10.9894	0.389510
$797$	−14.0524	−0.497763	−0.248882	−	0.968534i	$-0.580063\pi$
$797$	−14.0524	−0.497763	−0.248882	+	0.968534i	$0.580063\pi$
$798$	0.926944	0.0328135
$799$	10.3133	0.364860
$800$	−1.00000	−0.0353553
$801$	−9.97887	−0.352586
$802$	0.508852	0.0179682
$803$	0	0
$804$	3.10831	0.109622
$805$	−5.33804	−0.188141
$806$	0	0
$807$	8.39697	0.295587
$808$	−4.28917	−0.150892
$809$	17.8363	0.627092	0.313546	−	0.949573i	$-0.398483\pi$
$809$	17.8363	0.627092	0.313546	+	0.949573i	$0.398483\pi$
$810$	8.25443	0.290031
$811$	−45.4288	−1.59522	−0.797611	−	0.603173i	$-0.793903\pi$
$811$	−45.4288	−1.59522	−0.797611	+	0.603173i	$0.793903\pi$
$812$	9.83276	0.345062
$813$	−1.23330	−0.0432537
$814$	0	0
$815$	21.0141	0.736093
$816$	0.264989	0.00927646
$817$	−18.4630	−0.645940
$818$	−0.745574	−0.0260684
$819$	−0.843326	−0.0294682
$820$	−0.578337	−0.0201964
$821$	53.4005	1.86369	0.931846	−	0.362855i	$-0.118198\pi$
$821$	53.4005	1.86369	0.931846	+	0.362855i	$0.118198\pi$
$822$	0.630784	0.0220011
$823$	−30.1672	−1.05156	−0.525782	−	0.850619i	$-0.676227\pi$
$823$	−30.1672	−1.05156	−0.525782	+	0.850619i	$0.676227\pi$
$824$	−5.49472	−0.191418
$825$	0	0
$826$	7.20555	0.250713
$827$	3.54411	0.123241	0.0616204	−	0.998100i	$-0.480373\pi$
$827$	3.54411	0.123241	0.0616204	+	0.998100i	$0.480373\pi$
$828$	15.5678	0.541018
$829$	34.2680	1.19018	0.595089	−	0.803660i	$-0.297117\pi$
$829$	34.2680	1.19018	0.595089	+	0.803660i	$0.297117\pi$
$830$	−2.28917	−0.0794582
$831$	2.89169	0.100311
$832$	−0.289169	−0.0100251
$833$	0.916382	0.0317507
$834$	−4.71135	−0.163141
$835$	−9.01413	−0.311947
$836$	0	0
$837$	0	0
$838$	−12.6272	−0.436200
$839$	36.7244	1.26787	0.633934	−	0.773387i	$-0.281439\pi$
$839$	36.7244	1.26787	0.633934	+	0.773387i	$0.281439\pi$
$840$	−0.289169	−0.00997726
$841$	67.6832	2.33390
$842$	−1.35218	−0.0465991
$843$	−4.37978	−0.150848
$844$	−3.66553	−0.126173
$845$	12.9164	0.444337
$846$	32.8222	1.12845
$847$	0	0
$848$	4.91638	0.168829
$849$	5.35917	0.183926
$850$	−0.916382	−0.0314316
$851$	49.4005	1.69343
$852$	0.480585	0.0164646
$853$	34.5542	1.18311	0.591556	−	0.806264i	$-0.298514\pi$
$853$	34.5542	1.18311	0.591556	+	0.806264i	$0.298514\pi$
$854$	−9.49472	−0.324903
$855$	9.34861	0.319716
$856$	−2.50528	−0.0856288
$857$	−14.5783	−0.497987	−0.248993	−	0.968505i	$-0.580100\pi$
$857$	−14.5783	−0.497987	−0.248993	+	0.968505i	$0.580100\pi$
$858$	0	0
$859$	−17.0625	−0.582165	−0.291082	−	0.956698i	$-0.594015\pi$
$859$	−17.0625	−0.582165	−0.291082	+	0.956698i	$0.594015\pi$
$860$	5.75971	0.196404
$861$	−0.167237	−0.00569942
$862$	−7.33447	−0.249813
$863$	−8.48059	−0.288682	−0.144341	−	0.989528i	$-0.546106\pi$
$863$	−8.48059	−0.288682	−0.144341	+	0.989528i	$0.546106\pi$
$864$	1.71083	0.0582037
$865$	−16.9894	−0.577658
$866$	−30.6066	−1.04005
$867$	−4.67303	−0.158705
$868$	0	0
$869$	0	0
$870$	−2.84333	−0.0963978
$871$	−3.10831	−0.105321
$872$	7.25443	0.245666
$873$	18.4842	0.625594
$874$	17.1114	0.578801
$875$	1.00000	0.0338062
$876$	−2.98944	−0.101004
$877$	−19.8575	−0.670539	−0.335269	−	0.942122i	$-0.608827\pi$
$877$	−19.8575	−0.670539	−0.335269	+	0.942122i	$0.608827\pi$
$878$	−36.5855	−1.23470
$879$	1.16367	0.0392495
$880$	0	0
$881$	41.1849	1.38756	0.693778	−	0.720189i	$-0.255945\pi$
$881$	41.1849	1.38756	0.693778	+	0.720189i	$0.255945\pi$
$882$	2.91638	0.0981997
$883$	6.24029	0.210003	0.105001	−	0.994472i	$-0.466515\pi$
$883$	6.24029	0.210003	0.105001	+	0.994472i	$0.466515\pi$
$884$	−0.264989	−0.00891254
$885$	−2.08362	−0.0700401
$886$	−40.0766	−1.34640
$887$	33.8116	1.13528	0.567642	−	0.823276i	$-0.307856\pi$
$887$	33.8116	1.13528	0.567642	+	0.823276i	$0.307856\pi$
$888$	2.67609	0.0898037
$889$	13.3380	0.447344
$890$	3.42166	0.114694
$891$	0	0
$892$	14.0731	0.471201
$893$	36.0766	1.20726
$894$	−0.501711	−0.0167797
$895$	−5.32391	−0.177959
$896$	1.00000	0.0334077
$897$	0.446359	0.0149035
$898$	−12.6655	−0.422654
$899$	0	0
$900$	−2.91638	−0.0972127
$901$	4.50528	0.150093
$902$	0	0
$903$	1.66553	0.0554252
$904$	7.74914	0.257733
$905$	−25.4494	−0.845967
$906$	1.78746	0.0593843
$907$	−23.6408	−0.784981	−0.392490	−	0.919756i	$-0.628386\pi$
$907$	−23.6408	−0.784981	−0.392490	+	0.919756i	$0.628386\pi$
$908$	−3.25443	−0.108002
$909$	−12.5089	−0.414892
$910$	0.289169	0.00958584
$911$	−41.8222	−1.38563	−0.692816	−	0.721115i	$-0.743630\pi$
$911$	−41.8222	−1.38563	−0.692816	+	0.721115i	$0.743630\pi$
$912$	0.926944	0.0306942
$913$	0	0
$914$	−6.39697	−0.211593
$915$	2.74557	0.0907659
$916$	15.1814	0.501607
$917$	11.8086	0.389954
$918$	1.56777	0.0517443
$919$	45.9789	1.51670	0.758352	−	0.651846i	$-0.226005\pi$
$919$	45.9789	1.51670	0.758352	+	0.651846i	$0.226005\pi$
$920$	−5.33804	−0.175990
$921$	−9.90225	−0.326290
$922$	27.4736	0.904795
$923$	−0.480585	−0.0158187
$924$	0	0
$925$	−9.25443	−0.304284
$926$	−30.1119	−0.989538
$927$	−16.0247	−0.526320
$928$	9.83276	0.322776
$929$	−39.5266	−1.29682	−0.648412	−	0.761290i	$-0.724567\pi$
$929$	−39.5266	−1.29682	−0.648412	+	0.761290i	$0.724567\pi$
$930$	0	0
$931$	3.20555	0.105058
$932$	−3.50528	−0.114819
$933$	−1.99286	−0.0652433
$934$	−37.5719	−1.22939
$935$	0	0
$936$	−0.843326	−0.0275650
$937$	−39.0661	−1.27623	−0.638116	−	0.769940i	$-0.720286\pi$
$937$	−39.0661	−1.27623	−0.638116	+	0.769940i	$0.720286\pi$
$938$	10.7491	0.350972
$939$	−2.89169	−0.0943666
$940$	−11.2544	−0.367079
$941$	−47.8152	−1.55873	−0.779366	−	0.626569i	$-0.784458\pi$
$941$	−47.8152	−1.55873	−0.779366	+	0.626569i	$0.784458\pi$
$942$	−1.60303	−0.0522296
$943$	−3.08719	−0.100533
$944$	7.20555	0.234521
$945$	−1.71083	−0.0556534
$946$	0	0
$947$	19.7844	0.642907	0.321453	−	0.946925i	$-0.395829\pi$
$947$	19.7844	0.642907	0.321453	+	0.946925i	$0.395829\pi$
$948$	0.700269	0.0227437
$949$	2.98944	0.0970412
$950$	−3.20555	−0.104002
$951$	8.59946	0.278857
$952$	0.916382	0.0297001
$953$	−42.6902	−1.38287	−0.691436	−	0.722438i	$-0.743022\pi$
$953$	−42.6902	−1.38287	−0.691436	+	0.722438i	$0.743022\pi$
$954$	14.3380	0.464211
$955$	−4.08362	−0.132143
$956$	26.6408	0.861626
$957$	0	0
$958$	20.3627	0.657890
$959$	2.18137	0.0704401
$960$	−0.289169	−0.00933287
$961$	−31.0000	−1.00000
$962$	−2.67609	−0.0862806
$963$	−7.30636	−0.235444
$964$	−3.58890	−0.115591
$965$	19.5819	0.630364
$966$	−1.54359	−0.0496643
$967$	−8.34162	−0.268248	−0.134124	−	0.990965i	$-0.542822\pi$
$967$	−8.34162	−0.268248	−0.134124	+	0.990965i	$0.542822\pi$
$968$	0	0
$969$	0.849435	0.0272878
$970$	−6.33804	−0.203502
$971$	−24.9688	−0.801288	−0.400644	−	0.916234i	$-0.631214\pi$
$971$	−24.9688	−0.801288	−0.400644	+	0.916234i	$0.631214\pi$
$972$	7.51941	0.241185
$973$	−16.2927	−0.522321
$974$	6.18137	0.198064
$975$	−0.0836184	−0.00267793
$976$	−9.49472	−0.303919
$977$	29.6725	0.949308	0.474654	−	0.880172i	$-0.342573\pi$
$977$	29.6725	0.949308	0.474654	+	0.880172i	$0.342573\pi$
$978$	6.07663	0.194309
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	21.1567	0.675481
$982$	−11.5889	−0.369817
$983$	32.2439	1.02842	0.514210	−	0.857664i	$-0.328085\pi$
$983$	32.2439	1.02842	0.514210	+	0.857664i	$0.328085\pi$
$984$	−0.167237	−0.00533132
$985$	−8.43580	−0.268787
$986$	9.01056	0.286955
$987$	−3.25443	−0.103590
$988$	−0.926944	−0.0294900
$989$	30.7456	0.977652
$990$	0	0
$991$	5.74557	0.182514	0.0912571	−	0.995827i	$-0.470911\pi$
$991$	5.74557	0.182514	0.0912571	+	0.995827i	$0.470911\pi$
$992$	0	0
$993$	7.30279	0.231747
$994$	1.66196	0.0527140
$995$	−10.9894	−0.348389
$996$	−0.661956	−0.0209749
$997$	−12.6025	−0.399126	−0.199563	−	0.979885i	$-0.563952\pi$
$997$	−12.6025	−0.399126	−0.199563	+	0.979885i	$0.563952\pi$
$998$	−10.6761	−0.337946
$999$	15.8328	0.500926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cg.1.2	✓	3
11.10	odd	2		8470.2.a.ck.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cg.1.2	✓	3	1.1	even	1	trivial
8470.2.a.ck.1.2	yes	3	11.10	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.289169 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.289169 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91638 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.289169 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.289169 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91638 q^{9} +1.00000 q^{10} +0.289169 q^{12} -0.289169 q^{13} +1.00000 q^{14} -0.289169 q^{15} +1.00000 q^{16} +0.916382 q^{17} +2.91638 q^{18} +3.20555 q^{19} -1.00000 q^{20} -0.289169 q^{21} -5.33804 q^{23} -0.289169 q^{24} +1.00000 q^{25} +0.289169 q^{26} -1.71083 q^{27} -1.00000 q^{28} -9.83276 q^{29} +0.289169 q^{30} -1.00000 q^{32} -0.916382 q^{34} +1.00000 q^{35} -2.91638 q^{36} -9.25443 q^{37} -3.20555 q^{38} -0.0836184 q^{39} +1.00000 q^{40} +0.578337 q^{41} +0.289169 q^{42} -5.75971 q^{43} +2.91638 q^{45} +5.33804 q^{46} +11.2544 q^{47} +0.289169 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.264989 q^{51} -0.289169 q^{52} +4.91638 q^{53} +1.71083 q^{54} +1.00000 q^{56} +0.926944 q^{57} +9.83276 q^{58} +7.20555 q^{59} -0.289169 q^{60} -9.49472 q^{61} +2.91638 q^{63} +1.00000 q^{64} +0.289169 q^{65} +10.7491 q^{67} +0.916382 q^{68} -1.54359 q^{69} -1.00000 q^{70} +1.66196 q^{71} +2.91638 q^{72} -10.3380 q^{73} +9.25443 q^{74} +0.289169 q^{75} +3.20555 q^{76} +0.0836184 q^{78} +2.42166 q^{79} -1.00000 q^{80} +8.25443 q^{81} -0.578337 q^{82} -2.28917 q^{83} -0.289169 q^{84} -0.916382 q^{85} +5.75971 q^{86} -2.84333 q^{87} +3.42166 q^{89} -2.91638 q^{90} +0.289169 q^{91} -5.33804 q^{92} -11.2544 q^{94} -3.20555 q^{95} -0.289169 q^{96} -6.33804 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9} + 3 q^{10} + 3 q^{14} + 3 q^{16} - 11 q^{17} - 5 q^{18} - 5 q^{19} - 3 q^{20} - 4 q^{23} + 3 q^{25} - 6 q^{27} - 3 q^{28} - 2 q^{29} - 3 q^{32} + 11 q^{34} + 3 q^{35} + 5 q^{36} - 2 q^{37} + 5 q^{38} - 14 q^{39} + 3 q^{40} - 7 q^{43} - 5 q^{45} + 4 q^{46} + 8 q^{47} + 3 q^{49} - 3 q^{50} + 6 q^{51} + q^{53} + 6 q^{54} + 3 q^{56} + 20 q^{57} + 2 q^{58} + 7 q^{59} - 13 q^{61} - 5 q^{63} + 3 q^{64} - 9 q^{67} - 11 q^{68} + 22 q^{69} - 3 q^{70} + 17 q^{71} - 5 q^{72} - 19 q^{73} + 2 q^{74} - 5 q^{76} + 14 q^{78} + 9 q^{79} - 3 q^{80} - q^{81} - 6 q^{83} + 11 q^{85} + 7 q^{86} - 12 q^{87} + 12 q^{89} + 5 q^{90} - 4 q^{92} - 8 q^{94} + 5 q^{95} - 7 q^{97} - 3 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9 + 3 * q^10 + 3 * q^14 + 3 * q^16 - 11 * q^17 - 5 * q^18 - 5 * q^19 - 3 * q^20 - 4 * q^23 + 3 * q^25 - 6 * q^27 - 3 * q^28 - 2 * q^29 - 3 * q^32 + 11 * q^34 + 3 * q^35 + 5 * q^36 - 2 * q^37 + 5 * q^38 - 14 * q^39 + 3 * q^40 - 7 * q^43 - 5 * q^45 + 4 * q^46 + 8 * q^47 + 3 * q^49 - 3 * q^50 + 6 * q^51 + q^53 + 6 * q^54 + 3 * q^56 + 20 * q^57 + 2 * q^58 + 7 * q^59 - 13 * q^61 - 5 * q^63 + 3 * q^64 - 9 * q^67 - 11 * q^68 + 22 * q^69 - 3 * q^70 + 17 * q^71 - 5 * q^72 - 19 * q^73 + 2 * q^74 - 5 * q^76 + 14 * q^78 + 9 * q^79 - 3 * q^80 - q^81 - 6 * q^83 + 11 * q^85 + 7 * q^86 - 12 * q^87 + 12 * q^89 + 5 * q^90 - 4 * q^92 - 8 * q^94 + 5 * q^95 - 7 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more