LMFDB - Embedded newform 8034.2.a.z.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 $ x^14 - 3x^13 - 36x^12 + 108x^11 + 434x^10 - 1239x^9 - 2404x^8 + 6204x^7 + 6361x^6 - 14618x^5 - 7015x^4 + 15763x^3 + 1118x^2 - 6316*x + 1552
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.664239$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.664239 q^{5} +1.00000 q^{6} +2.36162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.664239 q^{5} +1.00000 q^{6} +2.36162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.664239 q^{10} -3.14397 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.36162 q^{14} +0.664239 q^{15} +1.00000 q^{16} -7.53535 q^{17} -1.00000 q^{18} +5.47817 q^{19} -0.664239 q^{20} -2.36162 q^{21} +3.14397 q^{22} +1.27876 q^{23} +1.00000 q^{24} -4.55879 q^{25} -1.00000 q^{26} -1.00000 q^{27} +2.36162 q^{28} -5.06863 q^{29} -0.664239 q^{30} +6.27777 q^{31} -1.00000 q^{32} +3.14397 q^{33} +7.53535 q^{34} -1.56868 q^{35} +1.00000 q^{36} +10.8042 q^{37} -5.47817 q^{38} -1.00000 q^{39} +0.664239 q^{40} +11.1801 q^{41} +2.36162 q^{42} -6.25237 q^{43} -3.14397 q^{44} -0.664239 q^{45} -1.27876 q^{46} -8.67811 q^{47} -1.00000 q^{48} -1.42277 q^{49} +4.55879 q^{50} +7.53535 q^{51} +1.00000 q^{52} -9.70904 q^{53} +1.00000 q^{54} +2.08835 q^{55} -2.36162 q^{56} -5.47817 q^{57} +5.06863 q^{58} -10.6905 q^{59} +0.664239 q^{60} -2.60711 q^{61} -6.27777 q^{62} +2.36162 q^{63} +1.00000 q^{64} -0.664239 q^{65} -3.14397 q^{66} -6.78514 q^{67} -7.53535 q^{68} -1.27876 q^{69} +1.56868 q^{70} +1.70711 q^{71} -1.00000 q^{72} +0.395522 q^{73} -10.8042 q^{74} +4.55879 q^{75} +5.47817 q^{76} -7.42484 q^{77} +1.00000 q^{78} +2.79959 q^{79} -0.664239 q^{80} +1.00000 q^{81} -11.1801 q^{82} +11.4961 q^{83} -2.36162 q^{84} +5.00528 q^{85} +6.25237 q^{86} +5.06863 q^{87} +3.14397 q^{88} +17.4900 q^{89} +0.664239 q^{90} +2.36162 q^{91} +1.27876 q^{92} -6.27777 q^{93} +8.67811 q^{94} -3.63882 q^{95} +1.00000 q^{96} +9.21361 q^{97} +1.42277 q^{98} -3.14397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.664239	−0.297057	−0.148528	−	0.988908i	$-0.547454\pi$
$5$	−0.664239	−0.297057	−0.148528	+	0.988908i	$0.547454\pi$
$6$	1.00000	0.408248
$7$	2.36162	0.892607	0.446304	−	0.894882i	$-0.352740\pi$
$7$	2.36162	0.892607	0.446304	+	0.894882i	$0.352740\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.664239	0.210051
$11$	−3.14397	−0.947941	−0.473971	−	0.880541i	$-0.657180\pi$
$11$	−3.14397	−0.947941	−0.473971	+	0.880541i	$0.657180\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.36162	−0.631169
$15$	0.664239	0.171506
$16$	1.00000	0.250000
$17$	−7.53535	−1.82759	−0.913796	−	0.406174i	$-0.866863\pi$
$17$	−7.53535	−1.82759	−0.913796	+	0.406174i	$0.866863\pi$
$18$	−1.00000	−0.235702
$19$	5.47817	1.25678	0.628389	−	0.777899i	$-0.283714\pi$
$19$	5.47817	1.25678	0.628389	+	0.777899i	$0.283714\pi$
$20$	−0.664239	−0.148528
$21$	−2.36162	−0.515347
$22$	3.14397	0.670296
$23$	1.27876	0.266641	0.133320	−	0.991073i	$-0.457436\pi$
$23$	1.27876	0.266641	0.133320	+	0.991073i	$0.457436\pi$
$24$	1.00000	0.204124
$25$	−4.55879	−0.911757
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	2.36162	0.446304
$29$	−5.06863	−0.941221	−0.470610	−	0.882341i	$-0.655966\pi$
$29$	−5.06863	−0.941221	−0.470610	+	0.882341i	$0.655966\pi$
$30$	−0.664239	−0.121273
$31$	6.27777	1.12752	0.563760	−	0.825938i	$-0.309354\pi$
$31$	6.27777	1.12752	0.563760	+	0.825938i	$0.309354\pi$
$32$	−1.00000	−0.176777
$33$	3.14397	0.547294
$34$	7.53535	1.29230
$35$	−1.56868	−0.265155
$36$	1.00000	0.166667
$37$	10.8042	1.77620	0.888102	−	0.459647i	$-0.152024\pi$
$37$	10.8042	1.77620	0.888102	+	0.459647i	$0.152024\pi$
$38$	−5.47817	−0.888677
$39$	−1.00000	−0.160128
$40$	0.664239	0.105025
$41$	11.1801	1.74604	0.873022	−	0.487681i	$-0.162157\pi$
$41$	11.1801	1.74604	0.873022	+	0.487681i	$0.162157\pi$
$42$	2.36162	0.364405
$43$	−6.25237	−0.953478	−0.476739	−	0.879045i	$-0.658181\pi$
$43$	−6.25237	−0.953478	−0.476739	+	0.879045i	$0.658181\pi$
$44$	−3.14397	−0.473971
$45$	−0.664239	−0.0990189
$46$	−1.27876	−0.188543
$47$	−8.67811	−1.26583	−0.632916	−	0.774220i	$-0.718142\pi$
$47$	−8.67811	−1.26583	−0.632916	+	0.774220i	$0.718142\pi$
$48$	−1.00000	−0.144338
$49$	−1.42277	−0.203252
$50$	4.55879	0.644710
$51$	7.53535	1.05516
$52$	1.00000	0.138675
$53$	−9.70904	−1.33364	−0.666819	−	0.745219i	$-0.732345\pi$
$53$	−9.70904	−1.33364	−0.666819	+	0.745219i	$0.732345\pi$
$54$	1.00000	0.136083
$55$	2.08835	0.281592
$56$	−2.36162	−0.315584
$57$	−5.47817	−0.725602
$58$	5.06863	0.665543
$59$	−10.6905	−1.39179	−0.695893	−	0.718145i	$-0.744991\pi$
$59$	−10.6905	−1.39179	−0.695893	+	0.718145i	$0.744991\pi$
$60$	0.664239	0.0857529
$61$	−2.60711	−0.333807	−0.166903	−	0.985973i	$-0.553377\pi$
$61$	−2.60711	−0.333807	−0.166903	+	0.985973i	$0.553377\pi$
$62$	−6.27777	−0.797277
$63$	2.36162	0.297536
$64$	1.00000	0.125000
$65$	−0.664239	−0.0823887
$66$	−3.14397	−0.386995
$67$	−6.78514	−0.828937	−0.414469	−	0.910064i	$-0.636033\pi$
$67$	−6.78514	−0.828937	−0.414469	+	0.910064i	$0.636033\pi$
$68$	−7.53535	−0.913796
$69$	−1.27876	−0.153945
$70$	1.56868	0.187493
$71$	1.70711	0.202596	0.101298	−	0.994856i	$-0.467700\pi$
$71$	1.70711	0.202596	0.101298	+	0.994856i	$0.467700\pi$
$72$	−1.00000	−0.117851
$73$	0.395522	0.0462923	0.0231462	−	0.999732i	$-0.492632\pi$
$73$	0.395522	0.0462923	0.0231462	+	0.999732i	$0.492632\pi$
$74$	−10.8042	−1.25597
$75$	4.55879	0.526403
$76$	5.47817	0.628389
$77$	−7.42484	−0.846139
$78$	1.00000	0.113228
$79$	2.79959	0.314979	0.157489	−	0.987521i	$-0.449660\pi$
$79$	2.79959	0.314979	0.157489	+	0.987521i	$0.449660\pi$
$80$	−0.664239	−0.0742642
$81$	1.00000	0.111111
$82$	−11.1801	−1.23464
$83$	11.4961	1.26186	0.630929	−	0.775841i	$-0.282674\pi$
$83$	11.4961	1.26186	0.630929	+	0.775841i	$0.282674\pi$
$84$	−2.36162	−0.257674
$85$	5.00528	0.542899
$86$	6.25237	0.674211
$87$	5.06863	0.543414
$88$	3.14397	0.335148
$89$	17.4900	1.85393	0.926967	−	0.375142i	$-0.122406\pi$
$89$	17.4900	1.85393	0.926967	+	0.375142i	$0.122406\pi$
$90$	0.664239	0.0700170
$91$	2.36162	0.247565
$92$	1.27876	0.133320
$93$	−6.27777	−0.650974
$94$	8.67811	0.895079
$95$	−3.63882	−0.373335
$96$	1.00000	0.102062
$97$	9.21361	0.935501	0.467750	−	0.883861i	$-0.345065\pi$
$97$	9.21361	0.935501	0.467750	+	0.883861i	$0.345065\pi$
$98$	1.42277	0.143721
$99$	−3.14397	−0.315980
$100$	−4.55879	−0.455879
$101$	14.3771	1.43057	0.715285	−	0.698832i	$-0.246297\pi$
$101$	14.3771	1.43057	0.715285	+	0.698832i	$0.246297\pi$
$102$	−7.53535	−0.746111
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	1.56868	0.153087
$106$	9.70904	0.943025
$107$	12.2751	1.18668	0.593341	−	0.804952i	$-0.297809\pi$
$107$	12.2751	1.18668	0.593341	+	0.804952i	$0.297809\pi$
$108$	−1.00000	−0.0962250
$109$	19.6836	1.88534	0.942672	−	0.333721i	$-0.108304\pi$
$109$	19.6836	1.88534	0.942672	+	0.333721i	$0.108304\pi$
$110$	−2.08835	−0.199116
$111$	−10.8042	−1.02549
$112$	2.36162	0.223152
$113$	−12.4526	−1.17144	−0.585721	−	0.810513i	$-0.699188\pi$
$113$	−12.4526	−1.17144	−0.585721	+	0.810513i	$0.699188\pi$
$114$	5.47817	0.513078
$115$	−0.849405	−0.0792074
$116$	−5.06863	−0.470610
$117$	1.00000	0.0924500
$118$	10.6905	0.984142
$119$	−17.7956	−1.63132
$120$	−0.664239	−0.0606365
$121$	−1.11548	−0.101407
$122$	2.60711	0.236037
$123$	−11.1801	−1.00808
$124$	6.27777	0.563760
$125$	6.34932	0.567901
$126$	−2.36162	−0.210390
$127$	−12.7497	−1.13135	−0.565676	−	0.824627i	$-0.691385\pi$
$127$	−12.7497	−1.13135	−0.565676	+	0.824627i	$0.691385\pi$
$128$	−1.00000	−0.0883883
$129$	6.25237	0.550491
$130$	0.664239	0.0582576
$131$	−6.54233	−0.571606	−0.285803	−	0.958288i	$-0.592260\pi$
$131$	−6.54233	−0.571606	−0.285803	+	0.958288i	$0.592260\pi$
$132$	3.14397	0.273647
$133$	12.9373	1.12181
$134$	6.78514	0.586147
$135$	0.664239	0.0571686
$136$	7.53535	0.646151
$137$	18.3434	1.56718	0.783592	−	0.621276i	$-0.213386\pi$
$137$	18.3434	1.56718	0.783592	+	0.621276i	$0.213386\pi$
$138$	1.27876	0.108856
$139$	4.49746	0.381470	0.190735	−	0.981642i	$-0.438913\pi$
$139$	4.49746	0.381470	0.190735	+	0.981642i	$0.438913\pi$
$140$	−1.56868	−0.132578
$141$	8.67811	0.730829
$142$	−1.70711	−0.143257
$143$	−3.14397	−0.262912
$144$	1.00000	0.0833333
$145$	3.36678	0.279596
$146$	−0.395522	−0.0327336
$147$	1.42277	0.117348
$148$	10.8042	0.888102
$149$	10.5024	0.860392	0.430196	−	0.902736i	$-0.358444\pi$
$149$	10.5024	0.860392	0.430196	+	0.902736i	$0.358444\pi$
$150$	−4.55879	−0.372223
$151$	−0.330883	−0.0269269	−0.0134635	−	0.999909i	$-0.504286\pi$
$151$	−0.330883	−0.0269269	−0.0134635	+	0.999909i	$0.504286\pi$
$152$	−5.47817	−0.444338
$153$	−7.53535	−0.609197
$154$	7.42484	0.598311
$155$	−4.16994	−0.334938
$156$	−1.00000	−0.0800641
$157$	6.48802	0.517800	0.258900	−	0.965904i	$-0.416640\pi$
$157$	6.48802	0.517800	0.258900	+	0.965904i	$0.416640\pi$
$158$	−2.79959	−0.222724
$159$	9.70904	0.769977
$160$	0.664239	0.0525127
$161$	3.01995	0.238005
$162$	−1.00000	−0.0785674
$163$	−10.2456	−0.802499	−0.401249	−	0.915969i	$-0.631424\pi$
$163$	−10.2456	−0.802499	−0.401249	+	0.915969i	$0.631424\pi$
$164$	11.1801	0.873022
$165$	−2.08835	−0.162577
$166$	−11.4961	−0.892268
$167$	1.93544	0.149769	0.0748846	−	0.997192i	$-0.476141\pi$
$167$	1.93544	0.149769	0.0748846	+	0.997192i	$0.476141\pi$
$168$	2.36162	0.182203
$169$	1.00000	0.0769231
$170$	−5.00528	−0.383887
$171$	5.47817	0.418926
$172$	−6.25237	−0.476739
$173$	−2.22848	−0.169428	−0.0847142	−	0.996405i	$-0.526998\pi$
$173$	−2.22848	−0.169428	−0.0847142	+	0.996405i	$0.526998\pi$
$174$	−5.06863	−0.384252
$175$	−10.7661	−0.813841
$176$	−3.14397	−0.236985
$177$	10.6905	0.803548
$178$	−17.4900	−1.31093
$179$	−5.40080	−0.403675	−0.201838	−	0.979419i	$-0.564691\pi$
$179$	−5.40080	−0.403675	−0.201838	+	0.979419i	$0.564691\pi$
$180$	−0.664239	−0.0495095
$181$	−14.4182	−1.07170	−0.535848	−	0.844314i	$-0.680008\pi$
$181$	−14.4182	−1.07170	−0.535848	+	0.844314i	$0.680008\pi$
$182$	−2.36162	−0.175055
$183$	2.60711	0.192723
$184$	−1.27876	−0.0942717
$185$	−7.17659	−0.527633
$186$	6.27777	0.460308
$187$	23.6909	1.73245
$188$	−8.67811	−0.632916
$189$	−2.36162	−0.171782
$190$	3.63882	0.263988
$191$	10.8810	0.787324	0.393662	−	0.919255i	$-0.371208\pi$
$191$	10.8810	0.787324	0.393662	+	0.919255i	$0.371208\pi$
$192$	−1.00000	−0.0721688
$193$	−27.6749	−1.99209	−0.996043	−	0.0888700i	$-0.971674\pi$
$193$	−27.6749	−1.99209	−0.996043	+	0.0888700i	$0.971674\pi$
$194$	−9.21361	−0.661499
$195$	0.664239	0.0475672
$196$	−1.42277	−0.101626
$197$	−22.7122	−1.61817	−0.809087	−	0.587689i	$-0.800038\pi$
$197$	−22.7122	−1.61817	−0.809087	+	0.587689i	$0.800038\pi$
$198$	3.14397	0.223432
$199$	−10.5958	−0.751118	−0.375559	−	0.926799i	$-0.622549\pi$
$199$	−10.5958	−0.751118	−0.375559	+	0.926799i	$0.622549\pi$
$200$	4.55879	0.322355
$201$	6.78514	0.478587
$202$	−14.3771	−1.01157
$203$	−11.9702	−0.840140
$204$	7.53535	0.527580
$205$	−7.42629	−0.518674
$206$	1.00000	0.0696733
$207$	1.27876	0.0888802
$208$	1.00000	0.0693375
$209$	−17.2232	−1.19135
$210$	−1.56868	−0.108249
$211$	−23.9450	−1.64844	−0.824220	−	0.566269i	$-0.808386\pi$
$211$	−23.9450	−1.64844	−0.824220	+	0.566269i	$0.808386\pi$
$212$	−9.70904	−0.666819
$213$	−1.70711	−0.116969
$214$	−12.2751	−0.839110
$215$	4.15307	0.283237
$216$	1.00000	0.0680414
$217$	14.8257	1.00643
$218$	−19.6836	−1.33314
$219$	−0.395522	−0.0267269
$220$	2.08835	0.140796
$221$	−7.53535	−0.506883
$222$	10.8042	0.725132
$223$	9.14462	0.612369	0.306185	−	0.951972i	$-0.400948\pi$
$223$	9.14462	0.612369	0.306185	+	0.951972i	$0.400948\pi$
$224$	−2.36162	−0.157792
$225$	−4.55879	−0.303919
$226$	12.4526	0.828334
$227$	−0.990850	−0.0657650	−0.0328825	−	0.999459i	$-0.510469\pi$
$227$	−0.990850	−0.0657650	−0.0328825	+	0.999459i	$0.510469\pi$
$228$	−5.47817	−0.362801
$229$	−0.230645	−0.0152414	−0.00762072	−	0.999971i	$-0.502426\pi$
$229$	−0.230645	−0.0152414	−0.00762072	+	0.999971i	$0.502426\pi$
$230$	0.849405	0.0560081
$231$	7.42484	0.488519
$232$	5.06863	0.332772
$233$	29.6243	1.94075	0.970377	−	0.241598i	$-0.0776714\pi$
$233$	29.6243	1.94075	0.970377	+	0.241598i	$0.0776714\pi$
$234$	−1.00000	−0.0653720
$235$	5.76434	0.376024
$236$	−10.6905	−0.695893
$237$	−2.79959	−0.181853
$238$	17.7956	1.15352
$239$	−12.1630	−0.786760	−0.393380	−	0.919376i	$-0.628694\pi$
$239$	−12.1630	−0.786760	−0.393380	+	0.919376i	$0.628694\pi$
$240$	0.664239	0.0428765
$241$	−9.36359	−0.603162	−0.301581	−	0.953441i	$-0.597514\pi$
$241$	−9.36359	−0.603162	−0.301581	+	0.953441i	$0.597514\pi$
$242$	1.11548	0.0717057
$243$	−1.00000	−0.0641500
$244$	−2.60711	−0.166903
$245$	0.945057	0.0603775
$246$	11.1801	0.712820
$247$	5.47817	0.348568
$248$	−6.27777	−0.398639
$249$	−11.4961	−0.728534
$250$	−6.34932	−0.401566
$251$	24.7530	1.56239	0.781196	−	0.624286i	$-0.214610\pi$
$251$	24.7530	1.56239	0.781196	+	0.624286i	$0.214610\pi$
$252$	2.36162	0.148768
$253$	−4.02039	−0.252760
$254$	12.7497	0.799987
$255$	−5.00528	−0.313443
$256$	1.00000	0.0625000
$257$	−9.92601	−0.619167	−0.309584	−	0.950872i	$-0.600190\pi$
$257$	−9.92601	−0.619167	−0.309584	+	0.950872i	$0.600190\pi$
$258$	−6.25237	−0.389256
$259$	25.5154	1.58545
$260$	−0.664239	−0.0411944
$261$	−5.06863	−0.313740
$262$	6.54233	0.404186
$263$	23.0280	1.41997	0.709983	−	0.704219i	$-0.248703\pi$
$263$	23.0280	1.41997	0.709983	+	0.704219i	$0.248703\pi$
$264$	−3.14397	−0.193498
$265$	6.44912	0.396166
$266$	−12.9373	−0.793239
$267$	−17.4900	−1.07037
$268$	−6.78514	−0.414469
$269$	11.0757	0.675296	0.337648	−	0.941273i	$-0.390369\pi$
$269$	11.0757	0.675296	0.337648	+	0.941273i	$0.390369\pi$
$270$	−0.664239	−0.0404243
$271$	13.7124	0.832970	0.416485	−	0.909143i	$-0.363262\pi$
$271$	13.7124	0.832970	0.416485	+	0.909143i	$0.363262\pi$
$272$	−7.53535	−0.456898
$273$	−2.36162	−0.142932
$274$	−18.3434	−1.10817
$275$	14.3327	0.864292
$276$	−1.27876	−0.0769725
$277$	25.1561	1.51148	0.755742	−	0.654869i	$-0.227276\pi$
$277$	25.1561	1.51148	0.755742	+	0.654869i	$0.227276\pi$
$278$	−4.49746	−0.269740
$279$	6.27777	0.375840
$280$	1.56868	0.0937465
$281$	−19.4460	−1.16005	−0.580026	−	0.814598i	$-0.696957\pi$
$281$	−19.4460	−1.16005	−0.580026	+	0.814598i	$0.696957\pi$
$282$	−8.67811	−0.516774
$283$	−16.6056	−0.987100	−0.493550	−	0.869717i	$-0.664301\pi$
$283$	−16.6056	−0.987100	−0.493550	+	0.869717i	$0.664301\pi$
$284$	1.70711	0.101298
$285$	3.63882	0.215545
$286$	3.14397	0.185907
$287$	26.4032	1.55853
$288$	−1.00000	−0.0589256
$289$	39.7815	2.34009
$290$	−3.36678	−0.197704
$291$	−9.21361	−0.540112
$292$	0.395522	0.0231462
$293$	22.3887	1.30796	0.653982	−	0.756511i	$-0.273097\pi$
$293$	22.3887	1.30796	0.653982	+	0.756511i	$0.273097\pi$
$294$	−1.42277	−0.0829774
$295$	7.10106	0.413440
$296$	−10.8042	−0.627983
$297$	3.14397	0.182431
$298$	−10.5024	−0.608389
$299$	1.27876	0.0739528
$300$	4.55879	0.263202
$301$	−14.7657	−0.851081
$302$	0.330883	0.0190402
$303$	−14.3771	−0.825940
$304$	5.47817	0.314195
$305$	1.73175	0.0991596
$306$	7.53535	0.430767
$307$	8.75392	0.499612	0.249806	−	0.968296i	$-0.419633\pi$
$307$	8.75392	0.499612	0.249806	+	0.968296i	$0.419633\pi$
$308$	−7.42484	−0.423070
$309$	1.00000	0.0568880
$310$	4.16994	0.236837
$311$	3.32236	0.188394	0.0941968	−	0.995554i	$-0.469972\pi$
$311$	3.32236	0.188394	0.0941968	+	0.995554i	$0.469972\pi$
$312$	1.00000	0.0566139
$313$	13.9039	0.785894	0.392947	−	0.919561i	$-0.371456\pi$
$313$	13.9039	0.785894	0.392947	+	0.919561i	$0.371456\pi$
$314$	−6.48802	−0.366140
$315$	−1.56868	−0.0883850
$316$	2.79959	0.157489
$317$	−12.9648	−0.728177	−0.364089	−	0.931364i	$-0.618619\pi$
$317$	−12.9648	−0.728177	−0.364089	+	0.931364i	$0.618619\pi$
$318$	−9.70904	−0.544456
$319$	15.9356	0.892222
$320$	−0.664239	−0.0371321
$321$	−12.2751	−0.685131
$322$	−3.01995	−0.168295
$323$	−41.2800	−2.29688
$324$	1.00000	0.0555556
$325$	−4.55879	−0.252876
$326$	10.2456	0.567452
$327$	−19.6836	−1.08850
$328$	−11.1801	−0.617320
$329$	−20.4944	−1.12989
$330$	2.08835	0.114960
$331$	28.9193	1.58955	0.794773	−	0.606906i	$-0.207590\pi$
$331$	28.9193	1.58955	0.794773	+	0.606906i	$0.207590\pi$
$332$	11.4961	0.630929
$333$	10.8042	0.592068
$334$	−1.93544	−0.105903
$335$	4.50696	0.246242
$336$	−2.36162	−0.128837
$337$	−24.6699	−1.34386	−0.671929	−	0.740616i	$-0.734534\pi$
$337$	−24.6699	−1.34386	−0.671929	+	0.740616i	$0.734534\pi$
$338$	−1.00000	−0.0543928
$339$	12.4526	0.676332
$340$	5.00528	0.271449
$341$	−19.7371	−1.06882
$342$	−5.47817	−0.296226
$343$	−19.8913	−1.07403
$344$	6.25237	0.337105
$345$	0.849405	0.0457304
$346$	2.22848	0.119804
$347$	−3.17151	−0.170255	−0.0851277	−	0.996370i	$-0.527130\pi$
$347$	−3.17151	−0.170255	−0.0851277	+	0.996370i	$0.527130\pi$
$348$	5.06863	0.271707
$349$	−31.3835	−1.67992	−0.839961	−	0.542646i	$-0.817422\pi$
$349$	−31.3835	−1.67992	−0.839961	+	0.542646i	$0.817422\pi$
$350$	10.7661	0.575473
$351$	−1.00000	−0.0533761
$352$	3.14397	0.167574
$353$	17.0417	0.907037	0.453519	−	0.891247i	$-0.350169\pi$
$353$	17.0417	0.907037	0.453519	+	0.891247i	$0.350169\pi$
$354$	−10.6905	−0.568194
$355$	−1.13393	−0.0601826
$356$	17.4900	0.926967
$357$	17.7956	0.941844
$358$	5.40080	0.285441
$359$	25.2917	1.33484	0.667422	−	0.744680i	$-0.267398\pi$
$359$	25.2917	1.33484	0.667422	+	0.744680i	$0.267398\pi$
$360$	0.664239	0.0350085
$361$	11.0104	0.579493
$362$	14.4182	0.757804
$363$	1.11548	0.0585475
$364$	2.36162	0.123782
$365$	−0.262721	−0.0137515
$366$	−2.60711	−0.136276
$367$	13.0779	0.682662	0.341331	−	0.939943i	$-0.389122\pi$
$367$	13.0779	0.682662	0.341331	+	0.939943i	$0.389122\pi$
$368$	1.27876	0.0666601
$369$	11.1801	0.582015
$370$	7.17659	0.373093
$371$	−22.9290	−1.19042
$372$	−6.27777	−0.325487
$373$	−25.9846	−1.34543	−0.672717	−	0.739900i	$-0.734873\pi$
$373$	−25.9846	−1.34543	−0.672717	+	0.739900i	$0.734873\pi$
$374$	−23.6909	−1.22503
$375$	−6.34932	−0.327878
$376$	8.67811	0.447539
$377$	−5.06863	−0.261048
$378$	2.36162	0.121468
$379$	−14.4762	−0.743590	−0.371795	−	0.928315i	$-0.621258\pi$
$379$	−14.4762	−0.743590	−0.371795	+	0.928315i	$0.621258\pi$
$380$	−3.63882	−0.186667
$381$	12.7497	0.653187
$382$	−10.8810	−0.556722
$383$	29.6314	1.51409	0.757046	−	0.653362i	$-0.226642\pi$
$383$	29.6314	1.51409	0.757046	+	0.653362i	$0.226642\pi$
$384$	1.00000	0.0510310
$385$	4.93187	0.251351
$386$	27.6749	1.40862
$387$	−6.25237	−0.317826
$388$	9.21361	0.467750
$389$	−31.9402	−1.61943	−0.809716	−	0.586822i	$-0.800379\pi$
$389$	−31.9402	−1.61943	−0.809716	+	0.586822i	$0.800379\pi$
$390$	−0.664239	−0.0336351
$391$	−9.63593	−0.487310
$392$	1.42277	0.0718605
$393$	6.54233	0.330017
$394$	22.7122	1.14422
$395$	−1.85960	−0.0935666
$396$	−3.14397	−0.157990
$397$	−1.91074	−0.0958973	−0.0479486	−	0.998850i	$-0.515268\pi$
$397$	−1.91074	−0.0958973	−0.0479486	+	0.998850i	$0.515268\pi$
$398$	10.5958	0.531120
$399$	−12.9373	−0.647677
$400$	−4.55879	−0.227939
$401$	24.2814	1.21255	0.606277	−	0.795254i	$-0.292662\pi$
$401$	24.2814	1.21255	0.606277	+	0.795254i	$0.292662\pi$
$402$	−6.78514	−0.338412
$403$	6.27777	0.312718
$404$	14.3771	0.715285
$405$	−0.664239	−0.0330063
$406$	11.9702	0.594069
$407$	−33.9681	−1.68374
$408$	−7.53535	−0.373056
$409$	8.85686	0.437944	0.218972	−	0.975731i	$-0.429730\pi$
$409$	8.85686	0.437944	0.218972	+	0.975731i	$0.429730\pi$
$410$	7.42629	0.366758
$411$	−18.3434	−0.904814
$412$	−1.00000	−0.0492665
$413$	−25.2469	−1.24232
$414$	−1.27876	−0.0628478
$415$	−7.63614	−0.374844
$416$	−1.00000	−0.0490290
$417$	−4.49746	−0.220242
$418$	17.2232	0.842414
$419$	24.4543	1.19467	0.597334	−	0.801992i	$-0.296227\pi$
$419$	24.4543	1.19467	0.597334	+	0.801992i	$0.296227\pi$
$420$	1.56868	0.0765437
$421$	28.6102	1.39437	0.697187	−	0.716889i	$-0.254435\pi$
$421$	28.6102	1.39437	0.697187	+	0.716889i	$0.254435\pi$
$422$	23.9450	1.16562
$423$	−8.67811	−0.421944
$424$	9.70904	0.471512
$425$	34.3521	1.66632
$426$	1.70711	0.0827095
$427$	−6.15701	−0.297958
$428$	12.2751	0.593341
$429$	3.14397	0.151792
$430$	−4.15307	−0.200279
$431$	−0.310658	−0.0149639	−0.00748193	−	0.999972i	$-0.502382\pi$
$431$	−0.310658	−0.0149639	−0.00748193	+	0.999972i	$0.502382\pi$
$432$	−1.00000	−0.0481125
$433$	−7.72676	−0.371324	−0.185662	−	0.982614i	$-0.559443\pi$
$433$	−7.72676	−0.371324	−0.185662	+	0.982614i	$0.559443\pi$
$434$	−14.8257	−0.711656
$435$	−3.36678	−0.161425
$436$	19.6836	0.942672
$437$	7.00528	0.335108
$438$	0.395522	0.0188988
$439$	22.7682	1.08667	0.543333	−	0.839517i	$-0.317162\pi$
$439$	22.7682	1.08667	0.543333	+	0.839517i	$0.317162\pi$
$440$	−2.08835	−0.0995580
$441$	−1.42277	−0.0677508
$442$	7.53535	0.358420
$443$	16.7094	0.793888	0.396944	−	0.917843i	$-0.370071\pi$
$443$	16.7094	0.793888	0.396944	+	0.917843i	$0.370071\pi$
$444$	−10.8042	−0.512746
$445$	−11.6175	−0.550724
$446$	−9.14462	−0.433010
$447$	−10.5024	−0.496748
$448$	2.36162	0.111576
$449$	28.7189	1.35533	0.677664	−	0.735372i	$-0.262992\pi$
$449$	28.7189	1.35533	0.677664	+	0.735372i	$0.262992\pi$
$450$	4.55879	0.214903
$451$	−35.1500	−1.65515
$452$	−12.4526	−0.585721
$453$	0.330883	0.0155463
$454$	0.990850	0.0465029
$455$	−1.56868	−0.0735408
$456$	5.47817	0.256539
$457$	1.32877	0.0621571	0.0310786	−	0.999517i	$-0.490106\pi$
$457$	1.32877	0.0621571	0.0310786	+	0.999517i	$0.490106\pi$
$458$	0.230645	0.0107773
$459$	7.53535	0.351720
$460$	−0.849405	−0.0396037
$461$	7.92563	0.369133	0.184567	−	0.982820i	$-0.440912\pi$
$461$	7.92563	0.369133	0.184567	+	0.982820i	$0.440912\pi$
$462$	−7.42484	−0.345435
$463$	13.7247	0.637840	0.318920	−	0.947782i	$-0.396680\pi$
$463$	13.7247	0.637840	0.318920	+	0.947782i	$0.396680\pi$
$464$	−5.06863	−0.235305
$465$	4.16994	0.193376
$466$	−29.6243	−1.37232
$467$	23.7417	1.09863	0.549317	−	0.835614i	$-0.314888\pi$
$467$	23.7417	1.09863	0.549317	+	0.835614i	$0.314888\pi$
$468$	1.00000	0.0462250
$469$	−16.0239	−0.739915
$470$	−5.76434	−0.265889
$471$	−6.48802	−0.298952
$472$	10.6905	0.492071
$473$	19.6572	0.903841
$474$	2.79959	0.128589
$475$	−24.9738	−1.14588
$476$	−17.7956	−0.815661
$477$	−9.70904	−0.444546
$478$	12.1630	0.556323
$479$	−37.4668	−1.71190	−0.855951	−	0.517057i	$-0.827028\pi$
$479$	−37.4668	−1.71190	−0.855951	+	0.517057i	$0.827028\pi$
$480$	−0.664239	−0.0303182
$481$	10.8042	0.492630
$482$	9.36359	0.426500
$483$	−3.01995	−0.137412
$484$	−1.11548	−0.0507036
$485$	−6.12004	−0.277897
$486$	1.00000	0.0453609
$487$	38.2613	1.73379	0.866893	−	0.498494i	$-0.166113\pi$
$487$	38.2613	1.73379	0.866893	+	0.498494i	$0.166113\pi$
$488$	2.60711	0.118019
$489$	10.2456	0.463323
$490$	−0.945057	−0.0426933
$491$	33.2072	1.49862	0.749311	−	0.662218i	$-0.230385\pi$
$491$	33.2072	1.49862	0.749311	+	0.662218i	$0.230385\pi$
$492$	−11.1801	−0.504040
$493$	38.1939	1.72017
$494$	−5.47817	−0.246475
$495$	2.08835	0.0938642
$496$	6.27777	0.281880
$497$	4.03153	0.180839
$498$	11.4961	0.515151
$499$	17.9832	0.805039	0.402520	−	0.915411i	$-0.368135\pi$
$499$	17.9832	0.805039	0.402520	+	0.915411i	$0.368135\pi$
$500$	6.34932	0.283950
$501$	−1.93544	−0.0864693
$502$	−24.7530	−1.10478
$503$	10.8923	0.485663	0.242832	−	0.970068i	$-0.421924\pi$
$503$	10.8923	0.485663	0.242832	+	0.970068i	$0.421924\pi$
$504$	−2.36162	−0.105195
$505$	−9.54981	−0.424961
$506$	4.02039	0.178728
$507$	−1.00000	−0.0444116
$508$	−12.7497	−0.565676
$509$	−44.1708	−1.95784	−0.978918	−	0.204256i	$-0.934523\pi$
$509$	−44.1708	−1.95784	−0.978918	+	0.204256i	$0.934523\pi$
$510$	5.00528	0.221637
$511$	0.934071	0.0413209
$512$	−1.00000	−0.0441942
$513$	−5.47817	−0.241867
$514$	9.92601	0.437817
$515$	0.664239	0.0292699
$516$	6.25237	0.275245
$517$	27.2837	1.19993
$518$	−25.5154	−1.12108
$519$	2.22848	0.0978195
$520$	0.664239	0.0291288
$521$	15.4635	0.677470	0.338735	−	0.940882i	$-0.390001\pi$
$521$	15.4635	0.677470	0.338735	+	0.940882i	$0.390001\pi$
$522$	5.06863	0.221848
$523$	24.4856	1.07068	0.535341	−	0.844636i	$-0.320183\pi$
$523$	24.4856	1.07068	0.535341	+	0.844636i	$0.320183\pi$
$524$	−6.54233	−0.285803
$525$	10.7661	0.469871
$526$	−23.0280	−1.00407
$527$	−47.3052	−2.06065
$528$	3.14397	0.136824
$529$	−21.3648	−0.928903
$530$	−6.44912	−0.280132
$531$	−10.6905	−0.463929
$532$	12.9373	0.560905
$533$	11.1801	0.484266
$534$	17.4900	0.756866
$535$	−8.15362	−0.352512
$536$	6.78514	0.293074
$537$	5.40080	0.233062
$538$	−11.0757	−0.477506
$539$	4.47313	0.192671
$540$	0.664239	0.0285843
$541$	12.8639	0.553063	0.276531	−	0.961005i	$-0.410815\pi$
$541$	12.8639	0.553063	0.276531	+	0.961005i	$0.410815\pi$
$542$	−13.7124	−0.588999
$543$	14.4182	0.618744
$544$	7.53535	0.323076
$545$	−13.0746	−0.560054
$546$	2.36162	0.101068
$547$	31.9973	1.36810	0.684052	−	0.729433i	$-0.260216\pi$
$547$	31.9973	1.36810	0.684052	+	0.729433i	$0.260216\pi$
$548$	18.3434	0.783592
$549$	−2.60711	−0.111269
$550$	−14.3327	−0.611147
$551$	−27.7668	−1.18291
$552$	1.27876	0.0544278
$553$	6.61156	0.281152
$554$	−25.1561	−1.06878
$555$	7.17659	0.304629
$556$	4.49746	0.190735
$557$	−33.3350	−1.41245	−0.706225	−	0.707987i	$-0.749603\pi$
$557$	−33.3350	−1.41245	−0.706225	+	0.707987i	$0.749603\pi$
$558$	−6.27777	−0.265759
$559$	−6.25237	−0.264447
$560$	−1.56868	−0.0662888
$561$	−23.6909	−1.00023
$562$	19.4460	0.820280
$563$	13.5663	0.571753	0.285877	−	0.958266i	$-0.407715\pi$
$563$	13.5663	0.571753	0.285877	+	0.958266i	$0.407715\pi$
$564$	8.67811	0.365414
$565$	8.27150	0.347985
$566$	16.6056	0.697985
$567$	2.36162	0.0991786
$568$	−1.70711	−0.0716286
$569$	8.42617	0.353244	0.176622	−	0.984279i	$-0.443483\pi$
$569$	8.42617	0.353244	0.176622	+	0.984279i	$0.443483\pi$
$570$	−3.63882	−0.152413
$571$	2.49998	0.104621	0.0523105	−	0.998631i	$-0.483341\pi$
$571$	2.49998	0.104621	0.0523105	+	0.998631i	$0.483341\pi$
$572$	−3.14397	−0.131456
$573$	−10.8810	−0.454561
$574$	−26.4032	−1.10205
$575$	−5.82961	−0.243111
$576$	1.00000	0.0416667
$577$	−8.45831	−0.352124	−0.176062	−	0.984379i	$-0.556336\pi$
$577$	−8.45831	−0.352124	−0.176062	+	0.984379i	$0.556336\pi$
$578$	−39.7815	−1.65469
$579$	27.6749	1.15013
$580$	3.36678	0.139798
$581$	27.1493	1.12634
$582$	9.21361	0.381917
$583$	30.5249	1.26421
$584$	−0.395522	−0.0163668
$585$	−0.664239	−0.0274629
$586$	−22.3887	−0.924870
$587$	12.8004	0.528327	0.264164	−	0.964478i	$-0.414904\pi$
$587$	12.8004	0.528327	0.264164	+	0.964478i	$0.414904\pi$
$588$	1.42277	0.0586739
$589$	34.3907	1.41704
$590$	−7.10106	−0.292346
$591$	22.7122	0.934253
$592$	10.8042	0.444051
$593$	45.6065	1.87284	0.936418	−	0.350887i	$-0.114120\pi$
$593$	45.6065	1.87284	0.936418	+	0.350887i	$0.114120\pi$
$594$	−3.14397	−0.128998
$595$	11.8205	0.484595
$596$	10.5024	0.430196
$597$	10.5958	0.433658
$598$	−1.27876	−0.0522925
$599$	20.6359	0.843162	0.421581	−	0.906791i	$-0.361475\pi$
$599$	20.6359	0.843162	0.421581	+	0.906791i	$0.361475\pi$
$600$	−4.55879	−0.186112
$601$	42.0920	1.71697	0.858483	−	0.512842i	$-0.171407\pi$
$601$	42.0920	1.71697	0.858483	+	0.512842i	$0.171407\pi$
$602$	14.7657	0.601805
$603$	−6.78514	−0.276312
$604$	−0.330883	−0.0134635
$605$	0.740945	0.0301237
$606$	14.3771	0.584028
$607$	5.21766	0.211778	0.105889	−	0.994378i	$-0.466231\pi$
$607$	5.21766	0.211778	0.105889	+	0.994378i	$0.466231\pi$
$608$	−5.47817	−0.222169
$609$	11.9702	0.485055
$610$	−1.73175	−0.0701164
$611$	−8.67811	−0.351079
$612$	−7.53535	−0.304599
$613$	7.11873	0.287523	0.143761	−	0.989612i	$-0.454080\pi$
$613$	7.11873	0.287523	0.143761	+	0.989612i	$0.454080\pi$
$614$	−8.75392	−0.353279
$615$	7.42629	0.299457
$616$	7.42484	0.299155
$617$	20.5398	0.826900	0.413450	−	0.910527i	$-0.364324\pi$
$617$	20.5398	0.826900	0.413450	+	0.910527i	$0.364324\pi$
$618$	−1.00000	−0.0402259
$619$	14.3158	0.575400	0.287700	−	0.957721i	$-0.407109\pi$
$619$	14.3158	0.575400	0.287700	+	0.957721i	$0.407109\pi$
$620$	−4.16994	−0.167469
$621$	−1.27876	−0.0513150
$622$	−3.32236	−0.133214
$623$	41.3046	1.65484
$624$	−1.00000	−0.0400320
$625$	18.5765	0.743058
$626$	−13.9039	−0.555711
$627$	17.2232	0.687828
$628$	6.48802	0.258900
$629$	−81.4136	−3.24617
$630$	1.56868	0.0624977
$631$	−3.55289	−0.141438	−0.0707191	−	0.997496i	$-0.522529\pi$
$631$	−3.55289	−0.141438	−0.0707191	+	0.997496i	$0.522529\pi$
$632$	−2.79959	−0.111362
$633$	23.9450	0.951728
$634$	12.9648	0.514899
$635$	8.46885	0.336076
$636$	9.70904	0.384988
$637$	−1.42277	−0.0563720
$638$	−15.9356	−0.630896
$639$	1.70711	0.0675321
$640$	0.664239	0.0262564
$641$	−3.75222	−0.148204	−0.0741018	−	0.997251i	$-0.523609\pi$
$641$	−3.75222	−0.148204	−0.0741018	+	0.997251i	$0.523609\pi$
$642$	12.2751	0.484461
$643$	−8.72343	−0.344018	−0.172009	−	0.985095i	$-0.555026\pi$
$643$	−8.72343	−0.344018	−0.172009	+	0.985095i	$0.555026\pi$
$644$	3.01995	0.119003
$645$	−4.15307	−0.163527
$646$	41.2800	1.62414
$647$	45.6646	1.79526	0.897630	−	0.440749i	$-0.145287\pi$
$647$	45.6646	1.79526	0.897630	+	0.440749i	$0.145287\pi$
$648$	−1.00000	−0.0392837
$649$	33.6106	1.31933
$650$	4.55879	0.178810
$651$	−14.8257	−0.581064
$652$	−10.2456	−0.401249
$653$	−41.8437	−1.63747	−0.818734	−	0.574173i	$-0.805324\pi$
$653$	−41.8437	−1.63747	−0.818734	+	0.574173i	$0.805324\pi$
$654$	19.6836	0.769689
$655$	4.34567	0.169799
$656$	11.1801	0.436511
$657$	0.395522	0.0154308
$658$	20.4944	0.798954
$659$	27.0576	1.05402	0.527008	−	0.849860i	$-0.323314\pi$
$659$	27.0576	1.05402	0.527008	+	0.849860i	$0.323314\pi$
$660$	−2.08835	−0.0812887
$661$	−22.9241	−0.891643	−0.445822	−	0.895122i	$-0.647088\pi$
$661$	−22.9241	−0.891643	−0.445822	+	0.895122i	$0.647088\pi$
$662$	−28.9193	−1.12398
$663$	7.53535	0.292649
$664$	−11.4961	−0.446134
$665$	−8.59349	−0.333241
$666$	−10.8042	−0.418655
$667$	−6.48157	−0.250968
$668$	1.93544	0.0748846
$669$	−9.14462	−0.353552
$670$	−4.50696	−0.174119
$671$	8.19668	0.316429
$672$	2.36162	0.0911013
$673$	−20.6263	−0.795084	−0.397542	−	0.917584i	$-0.630137\pi$
$673$	−20.6263	−0.795084	−0.397542	+	0.917584i	$0.630137\pi$
$674$	24.6699	0.950251
$675$	4.55879	0.175468
$676$	1.00000	0.0384615
$677$	−32.8317	−1.26183	−0.630913	−	0.775854i	$-0.717320\pi$
$677$	−32.8317	−1.26183	−0.630913	+	0.775854i	$0.717320\pi$
$678$	−12.4526	−0.478239
$679$	21.7590	0.835035
$680$	−5.00528	−0.191944
$681$	0.990850	0.0379694
$682$	19.7371	0.755772
$683$	9.15816	0.350427	0.175214	−	0.984530i	$-0.443938\pi$
$683$	9.15816	0.350427	0.175214	+	0.984530i	$0.443938\pi$
$684$	5.47817	0.209463
$685$	−12.1844	−0.465543
$686$	19.8913	0.759455
$687$	0.230645	0.00879965
$688$	−6.25237	−0.238370
$689$	−9.70904	−0.369885
$690$	−0.849405	−0.0323363
$691$	−38.4791	−1.46381	−0.731907	−	0.681404i	$-0.761370\pi$
$691$	−38.4791	−1.46381	−0.731907	+	0.681404i	$0.761370\pi$
$692$	−2.22848	−0.0847142
$693$	−7.42484	−0.282046
$694$	3.17151	0.120389
$695$	−2.98739	−0.113318
$696$	−5.06863	−0.192126
$697$	−84.2463	−3.19106
$698$	31.3835	1.18788
$699$	−29.6243	−1.12049
$700$	−10.7661	−0.406921
$701$	13.1508	0.496699	0.248350	−	0.968670i	$-0.420112\pi$
$701$	13.1508	0.496699	0.248350	+	0.968670i	$0.420112\pi$
$702$	1.00000	0.0377426
$703$	59.1874	2.23229
$704$	−3.14397	−0.118493
$705$	−5.76434	−0.217098
$706$	−17.0417	−0.641372
$707$	33.9531	1.27694
$708$	10.6905	0.401774
$709$	25.9875	0.975981	0.487991	−	0.872849i	$-0.337730\pi$
$709$	25.9875	0.975981	0.487991	+	0.872849i	$0.337730\pi$
$710$	1.13393	0.0425555
$711$	2.79959	0.104993
$712$	−17.4900	−0.655465
$713$	8.02778	0.300643
$714$	−17.7956	−0.665984
$715$	2.08835	0.0780997
$716$	−5.40080	−0.201838
$717$	12.1630	0.454236
$718$	−25.2917	−0.943877
$719$	19.2146	0.716585	0.358293	−	0.933609i	$-0.383359\pi$
$719$	19.2146	0.716585	0.358293	+	0.933609i	$0.383359\pi$
$720$	−0.664239	−0.0247547
$721$	−2.36162	−0.0879512
$722$	−11.0104	−0.409763
$723$	9.36359	0.348236
$724$	−14.4182	−0.535848
$725$	23.1068	0.858165
$726$	−1.11548	−0.0413993
$727$	45.1083	1.67297	0.836487	−	0.547986i	$-0.184605\pi$
$727$	45.1083	1.67297	0.836487	+	0.547986i	$0.184605\pi$
$728$	−2.36162	−0.0875273
$729$	1.00000	0.0370370
$730$	0.262721	0.00972375
$731$	47.1138	1.74257
$732$	2.60711	0.0963617
$733$	39.0830	1.44356	0.721782	−	0.692120i	$-0.243323\pi$
$733$	39.0830	1.44356	0.721782	+	0.692120i	$0.243323\pi$
$734$	−13.0779	−0.482715
$735$	−0.945057	−0.0348590
$736$	−1.27876	−0.0471358
$737$	21.3323	0.785784
$738$	−11.1801	−0.411547
$739$	38.5615	1.41851	0.709254	−	0.704954i	$-0.249032\pi$
$739$	38.5615	1.41851	0.709254	+	0.704954i	$0.249032\pi$
$740$	−7.17659	−0.263817
$741$	−5.47817	−0.201246
$742$	22.9290	0.841751
$743$	−11.8727	−0.435568	−0.217784	−	0.975997i	$-0.569883\pi$
$743$	−11.8727	−0.435568	−0.217784	+	0.975997i	$0.569883\pi$
$744$	6.27777	0.230154
$745$	−6.97612	−0.255585
$746$	25.9846	0.951365
$747$	11.4961	0.420619
$748$	23.6909	0.866225
$749$	28.9891	1.05924
$750$	6.34932	0.231844
$751$	12.6541	0.461755	0.230878	−	0.972983i	$-0.425840\pi$
$751$	12.6541	0.461755	0.230878	+	0.972983i	$0.425840\pi$
$752$	−8.67811	−0.316458
$753$	−24.7530	−0.902048
$754$	5.06863	0.184589
$755$	0.219786	0.00799882
$756$	−2.36162	−0.0858912
$757$	−38.6113	−1.40335	−0.701675	−	0.712497i	$-0.747564\pi$
$757$	−38.6113	−1.40335	−0.701675	+	0.712497i	$0.747564\pi$
$758$	14.4762	0.525798
$759$	4.02039	0.145931
$760$	3.63882	0.131994
$761$	−27.9940	−1.01478	−0.507392	−	0.861716i	$-0.669390\pi$
$761$	−27.9940	−1.01478	−0.507392	+	0.861716i	$0.669390\pi$
$762$	−12.7497	−0.461873
$763$	46.4851	1.68287
$764$	10.8810	0.393662
$765$	5.00528	0.180966
$766$	−29.6314	−1.07062
$767$	−10.6905	−0.386012
$768$	−1.00000	−0.0360844
$769$	0.756287	0.0272724	0.0136362	−	0.999907i	$-0.495659\pi$
$769$	0.756287	0.0272724	0.0136362	+	0.999907i	$0.495659\pi$
$770$	−4.93187	−0.177732
$771$	9.92601	0.357476
$772$	−27.6749	−0.996043
$773$	−47.1362	−1.69537	−0.847686	−	0.530498i	$-0.822005\pi$
$773$	−47.1362	−1.69537	−0.847686	+	0.530498i	$0.822005\pi$
$774$	6.25237	0.224737
$775$	−28.6190	−1.02802
$776$	−9.21361	−0.330749
$777$	−25.5154	−0.915361
$778$	31.9402	1.14511
$779$	61.2467	2.19439
$780$	0.664239	0.0237836
$781$	−5.36708	−0.192049
$782$	9.63593	0.344580
$783$	5.06863	0.181138
$784$	−1.42277	−0.0508131
$785$	−4.30960	−0.153816
$786$	−6.54233	−0.233357
$787$	−32.8581	−1.17127	−0.585633	−	0.810577i	$-0.699154\pi$
$787$	−32.8581	−1.17127	−0.585633	+	0.810577i	$0.699154\pi$
$788$	−22.7122	−0.809087
$789$	−23.0280	−0.819818
$790$	1.85960	0.0661615
$791$	−29.4083	−1.04564
$792$	3.14397	0.111716
$793$	−2.60711	−0.0925814
$794$	1.91074	0.0678096
$795$	−6.44912	−0.228727
$796$	−10.5958	−0.375559
$797$	30.1082	1.06649	0.533243	−	0.845962i	$-0.320973\pi$
$797$	30.1082	1.06649	0.533243	+	0.845962i	$0.320973\pi$
$798$	12.9373	0.457977
$799$	65.3926	2.31342
$800$	4.55879	0.161177
$801$	17.4900	0.617978
$802$	−24.2814	−0.857405
$803$	−1.24351	−0.0438824
$804$	6.78514	0.239294
$805$	−2.00597	−0.0707011
$806$	−6.27777	−0.221125
$807$	−11.0757	−0.389882
$808$	−14.3771	−0.505783
$809$	−42.1891	−1.48329	−0.741645	−	0.670792i	$-0.765954\pi$
$809$	−42.1891	−1.48329	−0.741645	+	0.670792i	$0.765954\pi$
$810$	0.664239	0.0233390
$811$	49.6828	1.74460	0.872300	−	0.488971i	$-0.162628\pi$
$811$	49.6828	1.74460	0.872300	+	0.488971i	$0.162628\pi$
$812$	−11.9702	−0.420070
$813$	−13.7124	−0.480915
$814$	33.9681	1.19058
$815$	6.80554	0.238388
$816$	7.53535	0.263790
$817$	−34.2516	−1.19831
$818$	−8.85686	−0.309673
$819$	2.36162	0.0825216
$820$	−7.42629	−0.259337
$821$	7.94747	0.277369	0.138684	−	0.990337i	$-0.455713\pi$
$821$	7.94747	0.277369	0.138684	+	0.990337i	$0.455713\pi$
$822$	18.3434	0.639800
$823$	−4.62944	−0.161372	−0.0806860	−	0.996740i	$-0.525711\pi$
$823$	−4.62944	−0.161372	−0.0806860	+	0.996740i	$0.525711\pi$
$824$	1.00000	0.0348367
$825$	−14.3327	−0.498999
$826$	25.2469	0.878452
$827$	5.49732	0.191161	0.0955804	−	0.995422i	$-0.469529\pi$
$827$	5.49732	0.191161	0.0955804	+	0.995422i	$0.469529\pi$
$828$	1.27876	0.0444401
$829$	−19.6703	−0.683179	−0.341589	−	0.939849i	$-0.610965\pi$
$829$	−19.6703	−0.683179	−0.341589	+	0.939849i	$0.610965\pi$
$830$	7.63614	0.265054
$831$	−25.1561	−0.872656
$832$	1.00000	0.0346688
$833$	10.7210	0.371462
$834$	4.49746	0.155734
$835$	−1.28560	−0.0444900
$836$	−17.2232	−0.595676
$837$	−6.27777	−0.216991
$838$	−24.4543	−0.844758
$839$	8.90073	0.307287	0.153644	−	0.988126i	$-0.450899\pi$
$839$	8.90073	0.307287	0.153644	+	0.988126i	$0.450899\pi$
$840$	−1.56868	−0.0541246
$841$	−3.30901	−0.114104
$842$	−28.6102	−0.985972
$843$	19.4460	0.669756
$844$	−23.9450	−0.824220
$845$	−0.664239	−0.0228505
$846$	8.67811	0.298360
$847$	−2.63433	−0.0905168
$848$	−9.70904	−0.333410
$849$	16.6056	0.569903
$850$	−34.3521	−1.17827
$851$	13.8160	0.473608
$852$	−1.70711	−0.0584845
$853$	36.4129	1.24675	0.623376	−	0.781922i	$-0.285760\pi$
$853$	36.4129	1.24675	0.623376	+	0.781922i	$0.285760\pi$
$854$	6.15701	0.210688
$855$	−3.63882	−0.124445
$856$	−12.2751	−0.419555
$857$	−24.7991	−0.847121	−0.423561	−	0.905868i	$-0.639220\pi$
$857$	−24.7991	−0.847121	−0.423561	+	0.905868i	$0.639220\pi$
$858$	−3.14397	−0.107333
$859$	36.7409	1.25358	0.626792	−	0.779187i	$-0.284368\pi$
$859$	36.7409	1.25358	0.626792	+	0.779187i	$0.284368\pi$
$860$	4.15307	0.141619
$861$	−26.4032	−0.899819
$862$	0.310658	0.0105810
$863$	−15.9874	−0.544217	−0.272109	−	0.962267i	$-0.587721\pi$
$863$	−15.9874	−0.544217	−0.272109	+	0.962267i	$0.587721\pi$
$864$	1.00000	0.0340207
$865$	1.48025	0.0503299
$866$	7.72676	0.262566
$867$	−39.7815	−1.35105
$868$	14.8257	0.503216
$869$	−8.80182	−0.298581
$870$	3.36678	0.114145
$871$	−6.78514	−0.229906
$872$	−19.6836	−0.666570
$873$	9.21361	0.311834
$874$	−7.00528	−0.236957
$875$	14.9947	0.506912
$876$	−0.395522	−0.0133634
$877$	6.44711	0.217703	0.108852	−	0.994058i	$-0.465283\pi$
$877$	6.44711	0.217703	0.108852	+	0.994058i	$0.465283\pi$
$878$	−22.7682	−0.768389
$879$	−22.3887	−0.755153
$880$	2.08835	0.0703981
$881$	−0.521288	−0.0175627	−0.00878133	−	0.999961i	$-0.502795\pi$
$881$	−0.521288	−0.0175627	−0.00878133	+	0.999961i	$0.502795\pi$
$882$	1.42277	0.0479070
$883$	−5.73123	−0.192871	−0.0964355	−	0.995339i	$-0.530744\pi$
$883$	−5.73123	−0.192871	−0.0964355	+	0.995339i	$0.530744\pi$
$884$	−7.53535	−0.253441
$885$	−7.10106	−0.238700
$886$	−16.7094	−0.561363
$887$	−21.9178	−0.735927	−0.367963	−	0.929840i	$-0.619945\pi$
$887$	−21.9178	−0.735927	−0.367963	+	0.929840i	$0.619945\pi$
$888$	10.8042	0.362566
$889$	−30.1099	−1.00985
$890$	11.6175	0.389421
$891$	−3.14397	−0.105327
$892$	9.14462	0.306185
$893$	−47.5402	−1.59087
$894$	10.5024	0.351254
$895$	3.58743	0.119914
$896$	−2.36162	−0.0788961
$897$	−1.27876	−0.0426967
$898$	−28.7189	−0.958362
$899$	−31.8197	−1.06125
$900$	−4.55879	−0.151960
$901$	73.1610	2.43735
$902$	35.1500	1.17037
$903$	14.7657	0.491372
$904$	12.4526	0.414167
$905$	9.57714	0.318355
$906$	−0.330883	−0.0109929
$907$	28.4556	0.944851	0.472426	−	0.881370i	$-0.343378\pi$
$907$	28.4556	0.944851	0.472426	+	0.881370i	$0.343378\pi$
$908$	−0.990850	−0.0328825
$909$	14.3771	0.476857
$910$	1.56868	0.0520012
$911$	18.7391	0.620853	0.310427	−	0.950597i	$-0.399528\pi$
$911$	18.7391	0.620853	0.310427	+	0.950597i	$0.399528\pi$
$912$	−5.47817	−0.181400
$913$	−36.1433	−1.19617
$914$	−1.32877	−0.0439517
$915$	−1.73175	−0.0572498
$916$	−0.230645	−0.00762072
$917$	−15.4505	−0.510220
$918$	−7.53535	−0.248704
$919$	−47.2334	−1.55809	−0.779044	−	0.626970i	$-0.784295\pi$
$919$	−47.2334	−1.55809	−0.779044	+	0.626970i	$0.784295\pi$
$920$	0.849405	0.0280040
$921$	−8.75392	−0.288451
$922$	−7.92563	−0.261017
$923$	1.70711	0.0561901
$924$	7.42484	0.244259
$925$	−49.2541	−1.61947
$926$	−13.7247	−0.451021
$927$	−1.00000	−0.0328443
$928$	5.06863	0.166386
$929$	−10.0189	−0.328709	−0.164354	−	0.986401i	$-0.552554\pi$
$929$	−10.0189	−0.328709	−0.164354	+	0.986401i	$0.552554\pi$
$930$	−4.16994	−0.136738
$931$	−7.79416	−0.255443
$932$	29.6243	0.970377
$933$	−3.32236	−0.108769
$934$	−23.7417	−0.776851
$935$	−15.7364	−0.514636
$936$	−1.00000	−0.0326860
$937$	−43.2306	−1.41228	−0.706140	−	0.708072i	$-0.749565\pi$
$937$	−43.2306	−1.41228	−0.706140	+	0.708072i	$0.749565\pi$
$938$	16.0239	0.523199
$939$	−13.9039	−0.453736
$940$	5.76434	0.188012
$941$	6.82721	0.222561	0.111280	−	0.993789i	$-0.464505\pi$
$941$	6.82721	0.222561	0.111280	+	0.993789i	$0.464505\pi$
$942$	6.48802	0.211391
$943$	14.2967	0.465566
$944$	−10.6905	−0.347947
$945$	1.56868	0.0510291
$946$	−19.6572	−0.639112
$947$	−26.7614	−0.869630	−0.434815	−	0.900520i	$-0.643186\pi$
$947$	−26.7614	−0.869630	−0.434815	+	0.900520i	$0.643186\pi$
$948$	−2.79959	−0.0909265
$949$	0.395522	0.0128392
$950$	24.9738	0.810258
$951$	12.9648	0.420413
$952$	17.7956	0.576759
$953$	38.6543	1.25213	0.626067	−	0.779769i	$-0.284663\pi$
$953$	38.6543	1.25213	0.626067	+	0.779769i	$0.284663\pi$
$954$	9.70904	0.314342
$955$	−7.22761	−0.233880
$956$	−12.1630	−0.393380
$957$	−15.9356	−0.515125
$958$	37.4668	1.21050
$959$	43.3201	1.39888
$960$	0.664239	0.0214382
$961$	8.41038	0.271302
$962$	−10.8042	−0.348342
$963$	12.2751	0.395560
$964$	−9.36359	−0.301581
$965$	18.3828	0.591763
$966$	3.01995	0.0971653
$967$	−4.22906	−0.135997	−0.0679986	−	0.997685i	$-0.521661\pi$
$967$	−4.22906	−0.135997	−0.0679986	+	0.997685i	$0.521661\pi$
$968$	1.11548	0.0358529
$969$	41.2800	1.32610
$970$	6.12004	0.196503
$971$	−17.2273	−0.552851	−0.276426	−	0.961035i	$-0.589150\pi$
$971$	−17.2273	−0.552851	−0.276426	+	0.961035i	$0.589150\pi$
$972$	−1.00000	−0.0320750
$973$	10.6213	0.340503
$974$	−38.2613	−1.22597
$975$	4.55879	0.145998
$976$	−2.60711	−0.0834517
$977$	25.4933	0.815604	0.407802	−	0.913070i	$-0.366295\pi$
$977$	25.4933	0.815604	0.407802	+	0.913070i	$0.366295\pi$
$978$	−10.2456	−0.327619
$979$	−54.9879	−1.75742
$980$	0.945057	0.0301887
$981$	19.6836	0.628448
$982$	−33.2072	−1.05969
$983$	13.7769	0.439414	0.219707	−	0.975566i	$-0.429490\pi$
$983$	13.7769	0.439414	0.219707	+	0.975566i	$0.429490\pi$
$984$	11.1801	0.356410
$985$	15.0863	0.480690
$986$	−38.1939	−1.21634
$987$	20.4944	0.652343
$988$	5.47817	0.174284
$989$	−7.99531	−0.254236
$990$	−2.08835	−0.0663720
$991$	14.8256	0.470952	0.235476	−	0.971880i	$-0.424335\pi$
$991$	14.8256	0.470952	0.235476	+	0.971880i	$0.424335\pi$
$992$	−6.27777	−0.199319
$993$	−28.9193	−0.917725
$994$	−4.03153	−0.127872
$995$	7.03816	0.223125
$996$	−11.4961	−0.364267
$997$	−18.5990	−0.589036	−0.294518	−	0.955646i	$-0.595159\pi$
$997$	−18.5990	−0.589036	−0.294518	+	0.955646i	$0.595159\pi$
$998$	−17.9832	−0.569249
$999$	−10.8042	−0.341830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.7	✓	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.664239 q^{5} +1.00000 q^{6} +2.36162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.664239 q^{5} +1.00000 q^{6} +2.36162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.664239 q^{10} -3.14397 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.36162 q^{14} +0.664239 q^{15} +1.00000 q^{16} -7.53535 q^{17} -1.00000 q^{18} +5.47817 q^{19} -0.664239 q^{20} -2.36162 q^{21} +3.14397 q^{22} +1.27876 q^{23} +1.00000 q^{24} -4.55879 q^{25} -1.00000 q^{26} -1.00000 q^{27} +2.36162 q^{28} -5.06863 q^{29} -0.664239 q^{30} +6.27777 q^{31} -1.00000 q^{32} +3.14397 q^{33} +7.53535 q^{34} -1.56868 q^{35} +1.00000 q^{36} +10.8042 q^{37} -5.47817 q^{38} -1.00000 q^{39} +0.664239 q^{40} +11.1801 q^{41} +2.36162 q^{42} -6.25237 q^{43} -3.14397 q^{44} -0.664239 q^{45} -1.27876 q^{46} -8.67811 q^{47} -1.00000 q^{48} -1.42277 q^{49} +4.55879 q^{50} +7.53535 q^{51} +1.00000 q^{52} -9.70904 q^{53} +1.00000 q^{54} +2.08835 q^{55} -2.36162 q^{56} -5.47817 q^{57} +5.06863 q^{58} -10.6905 q^{59} +0.664239 q^{60} -2.60711 q^{61} -6.27777 q^{62} +2.36162 q^{63} +1.00000 q^{64} -0.664239 q^{65} -3.14397 q^{66} -6.78514 q^{67} -7.53535 q^{68} -1.27876 q^{69} +1.56868 q^{70} +1.70711 q^{71} -1.00000 q^{72} +0.395522 q^{73} -10.8042 q^{74} +4.55879 q^{75} +5.47817 q^{76} -7.42484 q^{77} +1.00000 q^{78} +2.79959 q^{79} -0.664239 q^{80} +1.00000 q^{81} -11.1801 q^{82} +11.4961 q^{83} -2.36162 q^{84} +5.00528 q^{85} +6.25237 q^{86} +5.06863 q^{87} +3.14397 q^{88} +17.4900 q^{89} +0.664239 q^{90} +2.36162 q^{91} +1.27876 q^{92} -6.27777 q^{93} +8.67811 q^{94} -3.63882 q^{95} +1.00000 q^{96} +9.21361 q^{97} +1.42277 q^{98} -3.14397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more