LMFDB - Embedded newform 7935.2.a.bi.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.963105$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.963105 q^{2} +1.00000 q^{3} -1.07243 q^{4} +1.00000 q^{5} +0.963105 q^{6} +2.92900 q^{7} -2.95907 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.963105 q^{2} +1.00000 q^{3} -1.07243 q^{4} +1.00000 q^{5} +0.963105 q^{6} +2.92900 q^{7} -2.95907 q^{8} +1.00000 q^{9} +0.963105 q^{10} +0.188701 q^{11} -1.07243 q^{12} +0.702304 q^{13} +2.82093 q^{14} +1.00000 q^{15} -0.705042 q^{16} -6.37136 q^{17} +0.963105 q^{18} -0.665410 q^{19} -1.07243 q^{20} +2.92900 q^{21} +0.181739 q^{22} -2.95907 q^{24} +1.00000 q^{25} +0.676393 q^{26} +1.00000 q^{27} -3.14114 q^{28} +3.25013 q^{29} +0.963105 q^{30} -3.44612 q^{31} +5.23911 q^{32} +0.188701 q^{33} -6.13629 q^{34} +2.92900 q^{35} -1.07243 q^{36} +5.25139 q^{37} -0.640860 q^{38} +0.702304 q^{39} -2.95907 q^{40} +5.37012 q^{41} +2.82093 q^{42} +4.14564 q^{43} -0.202368 q^{44} +1.00000 q^{45} +6.27949 q^{47} -0.705042 q^{48} +1.57903 q^{49} +0.963105 q^{50} -6.37136 q^{51} -0.753171 q^{52} -2.27115 q^{53} +0.963105 q^{54} +0.188701 q^{55} -8.66711 q^{56} -0.665410 q^{57} +3.13022 q^{58} -0.830770 q^{59} -1.07243 q^{60} +9.81589 q^{61} -3.31898 q^{62} +2.92900 q^{63} +6.45590 q^{64} +0.702304 q^{65} +0.181739 q^{66} +15.3645 q^{67} +6.83283 q^{68} +2.82093 q^{70} +9.65169 q^{71} -2.95907 q^{72} -3.27928 q^{73} +5.05764 q^{74} +1.00000 q^{75} +0.713604 q^{76} +0.552705 q^{77} +0.676393 q^{78} +0.749250 q^{79} -0.705042 q^{80} +1.00000 q^{81} +5.17200 q^{82} +11.4918 q^{83} -3.14114 q^{84} -6.37136 q^{85} +3.99269 q^{86} +3.25013 q^{87} -0.558380 q^{88} +8.28110 q^{89} +0.963105 q^{90} +2.05705 q^{91} -3.44612 q^{93} +6.04781 q^{94} -0.665410 q^{95} +5.23911 q^{96} -16.7493 q^{97} +1.52077 q^{98} +0.188701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * 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 $

$2$	0.963105	0.681018	0.340509	−	0.940241i	$-0.389401\pi$
$2$	0.963105	0.681018	0.340509	+	0.940241i	$0.389401\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.07243	−0.536214
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.963105	0.393186
$7$	2.92900	1.10706	0.553528	−	0.832830i	$-0.313281\pi$
$7$	2.92900	1.10706	0.553528	+	0.832830i	$0.313281\pi$
$8$	−2.95907	−1.04619
$9$	1.00000	0.333333
$10$	0.963105	0.304561
$11$	0.188701	0.0568955	0.0284478	−	0.999595i	$-0.490944\pi$
$11$	0.188701	0.0568955	0.0284478	+	0.999595i	$0.490944\pi$
$12$	−1.07243	−0.309583
$13$	0.702304	0.194784	0.0973921	−	0.995246i	$-0.468950\pi$
$13$	0.702304	0.194784	0.0973921	+	0.995246i	$0.468950\pi$
$14$	2.82093	0.753926
$15$	1.00000	0.258199
$16$	−0.705042	−0.176261
$17$	−6.37136	−1.54528	−0.772641	−	0.634843i	$-0.781065\pi$
$17$	−6.37136	−1.54528	−0.772641	+	0.634843i	$0.781065\pi$
$18$	0.963105	0.227006
$19$	−0.665410	−0.152655	−0.0763277	−	0.997083i	$-0.524320\pi$
$19$	−0.665410	−0.152655	−0.0763277	+	0.997083i	$0.524320\pi$
$20$	−1.07243	−0.239802
$21$	2.92900	0.639160
$22$	0.181739	0.0387469
$23$	0	0
$23$	0	0
$24$	−2.95907	−0.604018
$25$	1.00000	0.200000
$26$	0.676393	0.132652
$27$	1.00000	0.192450
$28$	−3.14114	−0.593619
$29$	3.25013	0.603535	0.301767	−	0.953382i	$-0.402423\pi$
$29$	3.25013	0.603535	0.301767	+	0.953382i	$0.402423\pi$
$30$	0.963105	0.175838
$31$	−3.44612	−0.618941	−0.309471	−	0.950909i	$-0.600152\pi$
$31$	−3.44612	−0.618941	−0.309471	+	0.950909i	$0.600152\pi$
$32$	5.23911	0.926153
$33$	0.188701	0.0328486
$34$	−6.13629	−1.05237
$35$	2.92900	0.495091
$36$	−1.07243	−0.178738
$37$	5.25139	0.863324	0.431662	−	0.902036i	$-0.357927\pi$
$37$	5.25139	0.863324	0.431662	+	0.902036i	$0.357927\pi$
$38$	−0.640860	−0.103961
$39$	0.702304	0.112459
$40$	−2.95907	−0.467870
$41$	5.37012	0.838672	0.419336	−	0.907831i	$-0.362263\pi$
$41$	5.37012	0.838672	0.419336	+	0.907831i	$0.362263\pi$
$42$	2.82093	0.435279
$43$	4.14564	0.632204	0.316102	−	0.948725i	$-0.397626\pi$
$43$	4.14564	0.632204	0.316102	+	0.948725i	$0.397626\pi$
$44$	−0.202368	−0.0305082
$45$	1.00000	0.149071
$46$	0	0
$47$	6.27949	0.915958	0.457979	−	0.888963i	$-0.348574\pi$
$47$	6.27949	0.915958	0.457979	+	0.888963i	$0.348574\pi$
$48$	−0.705042	−0.101764
$49$	1.57903	0.225575
$50$	0.963105	0.136204
$51$	−6.37136	−0.892169
$52$	−0.753171	−0.104446
$53$	−2.27115	−0.311967	−0.155983	−	0.987760i	$-0.549855\pi$
$53$	−2.27115	−0.311967	−0.155983	+	0.987760i	$0.549855\pi$
$54$	0.963105	0.131062
$55$	0.188701	0.0254444
$56$	−8.66711	−1.15819
$57$	−0.665410	−0.0881357
$58$	3.13022	0.411018
$59$	−0.830770	−0.108157	−0.0540785	−	0.998537i	$-0.517222\pi$
$59$	−0.830770	−0.108157	−0.0540785	+	0.998537i	$0.517222\pi$
$60$	−1.07243	−0.138450
$61$	9.81589	1.25680	0.628398	−	0.777892i	$-0.283711\pi$
$61$	9.81589	1.25680	0.628398	+	0.777892i	$0.283711\pi$
$62$	−3.31898	−0.421510
$63$	2.92900	0.369019
$64$	6.45590	0.806988
$65$	0.702304	0.0871101
$66$	0.181739	0.0223705
$67$	15.3645	1.87708	0.938539	−	0.345174i	$-0.112180\pi$
$67$	15.3645	1.87708	0.938539	+	0.345174i	$0.112180\pi$
$68$	6.83283	0.828602
$69$	0	0
$70$	2.82093	0.337166
$71$	9.65169	1.14545	0.572723	−	0.819749i	$-0.305887\pi$
$71$	9.65169	1.14545	0.572723	+	0.819749i	$0.305887\pi$
$72$	−2.95907	−0.348730
$73$	−3.27928	−0.383810	−0.191905	−	0.981413i	$-0.561467\pi$
$73$	−3.27928	−0.383810	−0.191905	+	0.981413i	$0.561467\pi$
$74$	5.05764	0.587939
$75$	1.00000	0.115470
$76$	0.713604	0.0818560
$77$	0.552705	0.0629866
$78$	0.676393	0.0765864
$79$	0.749250	0.0842972	0.0421486	−	0.999111i	$-0.486580\pi$
$79$	0.749250	0.0842972	0.0421486	+	0.999111i	$0.486580\pi$
$80$	−0.705042	−0.0788261
$81$	1.00000	0.111111
$82$	5.17200	0.571151
$83$	11.4918	1.26139	0.630694	−	0.776032i	$-0.282770\pi$
$83$	11.4918	1.26139	0.630694	+	0.776032i	$0.282770\pi$
$84$	−3.14114	−0.342726
$85$	−6.37136	−0.691071
$86$	3.99269	0.430542
$87$	3.25013	0.348451
$88$	−0.558380	−0.0595235
$89$	8.28110	0.877794	0.438897	−	0.898537i	$-0.355369\pi$
$89$	8.28110	0.877794	0.438897	+	0.898537i	$0.355369\pi$
$90$	0.963105	0.101520
$91$	2.05705	0.215637
$92$	0	0
$93$	−3.44612	−0.357346
$94$	6.04781	0.623784
$95$	−0.665410	−0.0682696
$96$	5.23911	0.534715
$97$	−16.7493	−1.70063	−0.850317	−	0.526271i	$-0.823590\pi$
$97$	−16.7493	−1.70063	−0.850317	+	0.526271i	$0.823590\pi$
$98$	1.52077	0.153621
$99$	0.188701	0.0189652
$100$	−1.07243	−0.107243
$101$	−7.94947	−0.791002	−0.395501	−	0.918466i	$-0.629429\pi$
$101$	−7.94947	−0.791002	−0.395501	+	0.918466i	$0.629429\pi$
$102$	−6.13629	−0.607584
$103$	−9.98752	−0.984099	−0.492050	−	0.870567i	$-0.663752\pi$
$103$	−9.98752	−0.984099	−0.492050	+	0.870567i	$0.663752\pi$
$104$	−2.07817	−0.203781
$105$	2.92900	0.285841
$106$	−2.18736	−0.212455
$107$	9.69746	0.937489	0.468744	−	0.883334i	$-0.344707\pi$
$107$	9.69746	0.937489	0.468744	+	0.883334i	$0.344707\pi$
$108$	−1.07243	−0.103194
$109$	13.2093	1.26522	0.632609	−	0.774471i	$-0.281984\pi$
$109$	13.2093	1.26522	0.632609	+	0.774471i	$0.281984\pi$
$110$	0.181739	0.0173281
$111$	5.25139	0.498440
$112$	−2.06507	−0.195130
$113$	−1.40358	−0.132038	−0.0660189	−	0.997818i	$-0.521030\pi$
$113$	−1.40358	−0.132038	−0.0660189	+	0.997818i	$0.521030\pi$
$114$	−0.640860	−0.0600220
$115$	0	0
$116$	−3.48553	−0.323624
$117$	0.702304	0.0649281
$118$	−0.800119	−0.0736569
$119$	−18.6617	−1.71072
$120$	−2.95907	−0.270125
$121$	−10.9644	−0.996763
$122$	9.45374	0.855901
$123$	5.37012	0.484208
$124$	3.69572	0.331885
$125$	1.00000	0.0894427
$126$	2.82093	0.251309
$127$	−7.82113	−0.694014	−0.347007	−	0.937863i	$-0.612802\pi$
$127$	−7.82113	−0.694014	−0.347007	+	0.937863i	$0.612802\pi$
$128$	−4.26051	−0.376580
$129$	4.14564	0.365003
$130$	0.676393	0.0593236
$131$	−0.0233176	−0.00203727	−0.00101863	−	0.999999i	$-0.500324\pi$
$131$	−0.0233176	−0.00203727	−0.00101863	+	0.999999i	$0.500324\pi$
$132$	−0.202368	−0.0176139
$133$	−1.94898	−0.168998
$134$	14.7977	1.27832
$135$	1.00000	0.0860663
$136$	18.8533	1.61666
$137$	22.6715	1.93696	0.968479	−	0.249095i	$-0.0801330\pi$
$137$	22.6715	1.93696	0.968479	+	0.249095i	$0.0801330\pi$
$138$	0	0
$139$	7.67887	0.651313	0.325657	−	0.945488i	$-0.394415\pi$
$139$	7.67887	0.651313	0.325657	+	0.945488i	$0.394415\pi$
$140$	−3.14114	−0.265475
$141$	6.27949	0.528829
$142$	9.29560	0.780069
$143$	0.132526	0.0110823
$144$	−0.705042	−0.0587535
$145$	3.25013	0.269909
$146$	−3.15829	−0.261382
$147$	1.57903	0.130236
$148$	−5.63174	−0.462926
$149$	11.9953	0.982697	0.491349	−	0.870963i	$-0.336504\pi$
$149$	11.9953	0.982697	0.491349	+	0.870963i	$0.336504\pi$
$150$	0.963105	0.0786372
$151$	−7.18738	−0.584901	−0.292450	−	0.956281i	$-0.594471\pi$
$151$	−7.18738	−0.584901	−0.292450	+	0.956281i	$0.594471\pi$
$152$	1.96900	0.159707
$153$	−6.37136	−0.515094
$154$	0.532313	0.0428950
$155$	−3.44612	−0.276799
$156$	−0.753171	−0.0603019
$157$	−14.5025	−1.15743	−0.578714	−	0.815530i	$-0.696445\pi$
$157$	−14.5025	−1.15743	−0.578714	+	0.815530i	$0.696445\pi$
$158$	0.721606	0.0574079
$159$	−2.27115	−0.180114
$160$	5.23911	0.414188
$161$	0	0
$162$	0.963105	0.0756687
$163$	2.19245	0.171726	0.0858630	−	0.996307i	$-0.472635\pi$
$163$	2.19245	0.171726	0.0858630	+	0.996307i	$0.472635\pi$
$164$	−5.75907	−0.449708
$165$	0.188701	0.0146904
$166$	11.0678	0.859028
$167$	16.1031	1.24609	0.623047	−	0.782184i	$-0.285894\pi$
$167$	16.1031	1.24609	0.623047	+	0.782184i	$0.285894\pi$
$168$	−8.66711	−0.668682
$169$	−12.5068	−0.962059
$170$	−6.13629	−0.470632
$171$	−0.665410	−0.0508851
$172$	−4.44590	−0.338997
$173$	19.1841	1.45854	0.729268	−	0.684228i	$-0.239861\pi$
$173$	19.1841	1.45854	0.729268	+	0.684228i	$0.239861\pi$
$174$	3.13022	0.237301
$175$	2.92900	0.221411
$176$	−0.133042	−0.0100284
$177$	−0.830770	−0.0624445
$178$	7.97557	0.597794
$179$	22.1900	1.65856	0.829278	−	0.558837i	$-0.188752\pi$
$179$	22.1900	1.65856	0.829278	+	0.558837i	$0.188752\pi$
$180$	−1.07243	−0.0799341
$181$	19.6503	1.46059	0.730297	−	0.683130i	$-0.239382\pi$
$181$	19.6503	1.46059	0.730297	+	0.683130i	$0.239382\pi$
$182$	1.98115	0.146853
$183$	9.81589	0.725612
$184$	0	0
$185$	5.25139	0.386090
$186$	−3.31898	−0.243359
$187$	−1.20228	−0.0879196
$188$	−6.73430	−0.491149
$189$	2.92900	0.213053
$190$	−0.640860	−0.0464928
$191$	−7.15708	−0.517868	−0.258934	−	0.965895i	$-0.583371\pi$
$191$	−7.15708	−0.517868	−0.258934	+	0.965895i	$0.583371\pi$
$192$	6.45590	0.465915
$193$	−22.0158	−1.58473	−0.792364	−	0.610048i	$-0.791150\pi$
$193$	−22.0158	−1.58473	−0.792364	+	0.610048i	$0.791150\pi$
$194$	−16.1313	−1.15816
$195$	0.702304	0.0502931
$196$	−1.69339	−0.120957
$197$	−17.4241	−1.24142	−0.620708	−	0.784042i	$-0.713155\pi$
$197$	−17.4241	−1.24142	−0.620708	+	0.784042i	$0.713155\pi$
$198$	0.181739	0.0129156
$199$	−17.8328	−1.26413	−0.632066	−	0.774915i	$-0.717793\pi$
$199$	−17.8328	−1.26413	−0.632066	+	0.774915i	$0.717793\pi$
$200$	−2.95907	−0.209238
$201$	15.3645	1.08373
$202$	−7.65618	−0.538687
$203$	9.51963	0.668147
$204$	6.83283	0.478394
$205$	5.37012	0.375066
$206$	−9.61903	−0.670190
$207$	0	0
$208$	−0.495154	−0.0343328
$209$	−0.125564	−0.00868541
$210$	2.82093	0.194663
$211$	−13.0850	−0.900810	−0.450405	−	0.892824i	$-0.648720\pi$
$211$	−13.0850	−0.900810	−0.450405	+	0.892824i	$0.648720\pi$
$212$	2.43565	0.167281
$213$	9.65169	0.661323
$214$	9.33967	0.638447
$215$	4.14564	0.282730
$216$	−2.95907	−0.201339
$217$	−10.0937	−0.685203
$218$	12.7219	0.861637
$219$	−3.27928	−0.221593
$220$	−0.202368	−0.0136437
$221$	−4.47464	−0.300997
$222$	5.05764	0.339447
$223$	−21.6004	−1.44647	−0.723237	−	0.690600i	$-0.757346\pi$
$223$	−21.6004	−1.44647	−0.723237	+	0.690600i	$0.757346\pi$
$224$	15.3454	1.02530
$225$	1.00000	0.0666667
$226$	−1.35180	−0.0899201
$227$	−4.61934	−0.306596	−0.153298	−	0.988180i	$-0.548989\pi$
$227$	−4.61934	−0.306596	−0.153298	+	0.988180i	$0.548989\pi$
$228$	0.713604	0.0472596
$229$	−5.26854	−0.348155	−0.174077	−	0.984732i	$-0.555694\pi$
$229$	−5.26854	−0.348155	−0.174077	+	0.984732i	$0.555694\pi$
$230$	0	0
$231$	0.552705	0.0363653
$232$	−9.61738	−0.631412
$233$	−26.2636	−1.72059	−0.860293	−	0.509800i	$-0.829719\pi$
$233$	−26.2636	−1.72059	−0.860293	+	0.509800i	$0.829719\pi$
$234$	0.676393	0.0442172
$235$	6.27949	0.409629
$236$	0.890941	0.0579953
$237$	0.749250	0.0486690
$238$	−17.9732	−1.16503
$239$	−1.49050	−0.0964122	−0.0482061	−	0.998837i	$-0.515350\pi$
$239$	−1.49050	−0.0964122	−0.0482061	+	0.998837i	$0.515350\pi$
$240$	−0.705042	−0.0455103
$241$	23.4835	1.51270	0.756352	−	0.654164i	$-0.226980\pi$
$241$	23.4835	1.51270	0.756352	+	0.654164i	$0.226980\pi$
$242$	−10.5599	−0.678814
$243$	1.00000	0.0641500
$244$	−10.5268	−0.673912
$245$	1.57903	0.100880
$246$	5.17200	0.329754
$247$	−0.467320	−0.0297349
$248$	10.1973	0.647530
$249$	11.4918	0.728263
$250$	0.963105	0.0609121
$251$	17.3489	1.09506	0.547528	−	0.836788i	$-0.315569\pi$
$251$	17.3489	1.09506	0.547528	+	0.836788i	$0.315569\pi$
$252$	−3.14114	−0.197873
$253$	0	0
$254$	−7.53258	−0.472636
$255$	−6.37136	−0.398990
$256$	−17.0151	−1.06345
$257$	−20.9810	−1.30876	−0.654379	−	0.756167i	$-0.727070\pi$
$257$	−20.9810	−1.30876	−0.654379	+	0.756167i	$0.727070\pi$
$258$	3.99269	0.248574
$259$	15.3813	0.955748
$260$	−0.753171	−0.0467097
$261$	3.25013	0.201178
$262$	−0.0224573	−0.00138742
$263$	5.39846	0.332883	0.166442	−	0.986051i	$-0.446772\pi$
$263$	5.39846	0.332883	0.166442	+	0.986051i	$0.446772\pi$
$264$	−0.558380	−0.0343659
$265$	−2.27115	−0.139516
$266$	−1.87708	−0.115091
$267$	8.28110	0.506795
$268$	−16.4774	−1.00652
$269$	18.8584	1.14982	0.574908	−	0.818218i	$-0.305038\pi$
$269$	18.8584	1.14982	0.574908	+	0.818218i	$0.305038\pi$
$270$	0.963105	0.0586127
$271$	7.14670	0.434131	0.217066	−	0.976157i	$-0.430351\pi$
$271$	7.14670	0.434131	0.217066	+	0.976157i	$0.430351\pi$
$272$	4.49208	0.272372
$273$	2.05705	0.124498
$274$	21.8351	1.31910
$275$	0.188701	0.0113791
$276$	0	0
$277$	9.74788	0.585694	0.292847	−	0.956159i	$-0.405397\pi$
$277$	9.74788	0.585694	0.292847	+	0.956159i	$0.405397\pi$
$278$	7.39556	0.443556
$279$	−3.44612	−0.206314
$280$	−8.66711	−0.517959
$281$	−9.68720	−0.577890	−0.288945	−	0.957346i	$-0.593304\pi$
$281$	−9.68720	−0.577890	−0.288945	+	0.957346i	$0.593304\pi$
$282$	6.04781	0.360142
$283$	3.87371	0.230268	0.115134	−	0.993350i	$-0.463270\pi$
$283$	3.87371	0.230268	0.115134	+	0.993350i	$0.463270\pi$
$284$	−10.3507	−0.614204
$285$	−0.665410	−0.0394155
$286$	0.127636	0.00754728
$287$	15.7291	0.928458
$288$	5.23911	0.308718
$289$	23.5943	1.38790
$290$	3.13022	0.183813
$291$	−16.7493	−0.981861
$292$	3.51679	0.205805
$293$	18.5915	1.08613	0.543064	−	0.839691i	$-0.317264\pi$
$293$	18.5915	1.08613	0.543064	+	0.839691i	$0.317264\pi$
$294$	1.52077	0.0886930
$295$	−0.830770	−0.0483693
$296$	−15.5392	−0.903200
$297$	0.188701	0.0109495
$298$	11.5528	0.669235
$299$	0	0
$300$	−1.07243	−0.0619167
$301$	12.1426	0.699886
$302$	−6.92220	−0.398328
$303$	−7.94947	−0.456685
$304$	0.469142	0.0269071
$305$	9.81589	0.562056
$306$	−6.13629	−0.350789
$307$	5.91016	0.337310	0.168655	−	0.985675i	$-0.446058\pi$
$307$	5.91016	0.337310	0.168655	+	0.985675i	$0.446058\pi$
$308$	−0.592736	−0.0337743
$309$	−9.98752	−0.568170
$310$	−3.31898	−0.188505
$311$	−23.8395	−1.35181	−0.675906	−	0.736988i	$-0.736248\pi$
$311$	−23.8395	−1.35181	−0.675906	+	0.736988i	$0.736248\pi$
$312$	−2.07817	−0.117653
$313$	31.8810	1.80202	0.901011	−	0.433796i	$-0.142826\pi$
$313$	31.8810	1.80202	0.901011	+	0.433796i	$0.142826\pi$
$314$	−13.9675	−0.788230
$315$	2.92900	0.165030
$316$	−0.803516	−0.0452013
$317$	31.8319	1.78786	0.893928	−	0.448211i	$-0.147939\pi$
$317$	31.8319	1.78786	0.893928	+	0.448211i	$0.147939\pi$
$318$	−2.18736	−0.122661
$319$	0.613304	0.0343384
$320$	6.45590	0.360896
$321$	9.69746	0.541259
$322$	0	0
$323$	4.23957	0.235896
$324$	−1.07243	−0.0595793
$325$	0.702304	0.0389568
$326$	2.11156	0.116948
$327$	13.2093	0.730474
$328$	−15.8906	−0.877411
$329$	18.3926	1.01402
$330$	0.181739	0.0100044
$331$	21.9788	1.20807	0.604033	−	0.796959i	$-0.293560\pi$
$331$	21.9788	1.20807	0.604033	+	0.796959i	$0.293560\pi$
$332$	−12.3241	−0.676374
$333$	5.25139	0.287775
$334$	15.5090	0.848613
$335$	15.3645	0.839455
$336$	−2.06507	−0.112659
$337$	27.3295	1.48873	0.744367	−	0.667770i	$-0.232751\pi$
$337$	27.3295	1.48873	0.744367	+	0.667770i	$0.232751\pi$
$338$	−12.0453	−0.655180
$339$	−1.40358	−0.0762320
$340$	6.83283	0.370562
$341$	−0.650287	−0.0352150
$342$	−0.640860	−0.0346537
$343$	−15.8780	−0.857332
$344$	−12.2672	−0.661405
$345$	0	0
$346$	18.4763	0.993290
$347$	−10.5541	−0.566574	−0.283287	−	0.959035i	$-0.591425\pi$
$347$	−10.5541	−0.566574	−0.283287	+	0.959035i	$0.591425\pi$
$348$	−3.48553	−0.186844
$349$	9.63406	0.515700	0.257850	−	0.966185i	$-0.416986\pi$
$349$	9.63406	0.515700	0.257850	+	0.966185i	$0.416986\pi$
$350$	2.82093	0.150785
$351$	0.702304	0.0374862
$352$	0.988626	0.0526940
$353$	−13.9381	−0.741852	−0.370926	−	0.928662i	$-0.620960\pi$
$353$	−13.9381	−0.741852	−0.370926	+	0.928662i	$0.620960\pi$
$354$	−0.800119	−0.0425259
$355$	9.65169	0.512259
$356$	−8.88088	−0.470686
$357$	−18.6617	−0.987682
$358$	21.3713	1.12951
$359$	−26.5411	−1.40078	−0.700392	−	0.713758i	$-0.746992\pi$
$359$	−26.5411	−1.40078	−0.700392	+	0.713758i	$0.746992\pi$
$360$	−2.95907	−0.155957
$361$	−18.5572	−0.976696
$362$	18.9253	0.994691
$363$	−10.9644	−0.575481
$364$	−2.20604	−0.115628
$365$	−3.27928	−0.171645
$366$	9.45374	0.494155
$367$	31.2284	1.63011	0.815054	−	0.579385i	$-0.196707\pi$
$367$	31.2284	1.63011	0.815054	+	0.579385i	$0.196707\pi$
$368$	0	0
$369$	5.37012	0.279557
$370$	5.05764	0.262934
$371$	−6.65220	−0.345365
$372$	3.69572	0.191614
$373$	−27.8772	−1.44343	−0.721714	−	0.692191i	$-0.756645\pi$
$373$	−27.8772	−1.44343	−0.721714	+	0.692191i	$0.756645\pi$
$374$	−1.15793	−0.0598749
$375$	1.00000	0.0516398
$376$	−18.5815	−0.958266
$377$	2.28258	0.117559
$378$	2.82093	0.145093
$379$	−14.0953	−0.724026	−0.362013	−	0.932173i	$-0.617910\pi$
$379$	−14.0953	−0.724026	−0.362013	+	0.932173i	$0.617910\pi$
$380$	0.713604	0.0366071
$381$	−7.82113	−0.400689
$382$	−6.89302	−0.352677
$383$	12.5235	0.639922	0.319961	−	0.947431i	$-0.396330\pi$
$383$	12.5235	0.639922	0.319961	+	0.947431i	$0.396330\pi$
$384$	−4.26051	−0.217418
$385$	0.552705	0.0281685
$386$	−21.2035	−1.07923
$387$	4.14564	0.210735
$388$	17.9624	0.911903
$389$	−9.77693	−0.495710	−0.247855	−	0.968797i	$-0.579726\pi$
$389$	−9.77693	−0.495710	−0.247855	+	0.968797i	$0.579726\pi$
$390$	0.676393	0.0342505
$391$	0	0
$392$	−4.67245	−0.235994
$393$	−0.0233176	−0.00117622
$394$	−16.7813	−0.845427
$395$	0.749250	0.0376988
$396$	−0.202368	−0.0101694
$397$	9.93796	0.498772	0.249386	−	0.968404i	$-0.419771\pi$
$397$	9.93796	0.498772	0.249386	+	0.968404i	$0.419771\pi$
$398$	−17.1748	−0.860897
$399$	−1.94898	−0.0975712
$400$	−0.705042	−0.0352521
$401$	−6.15592	−0.307412	−0.153706	−	0.988117i	$-0.549121\pi$
$401$	−6.15592	−0.307412	−0.153706	+	0.988117i	$0.549121\pi$
$402$	14.7977	0.738041
$403$	−2.42022	−0.120560
$404$	8.52524	0.424146
$405$	1.00000	0.0496904
$406$	9.16841	0.455021
$407$	0.990943	0.0491192
$408$	18.8533	0.933379
$409$	−30.7353	−1.51976	−0.759882	−	0.650061i	$-0.774743\pi$
$409$	−30.7353	−1.51976	−0.759882	+	0.650061i	$0.774743\pi$
$410$	5.17200	0.255427
$411$	22.6715	1.11830
$412$	10.7109	0.527688
$413$	−2.43332	−0.119736
$414$	0	0
$415$	11.4918	0.564110
$416$	3.67945	0.180400
$417$	7.67887	0.376036
$418$	−0.120931	−0.00591492
$419$	−19.4419	−0.949798	−0.474899	−	0.880040i	$-0.657515\pi$
$419$	−19.4419	−0.949798	−0.474899	+	0.880040i	$0.657515\pi$
$420$	−3.14114	−0.153272
$421$	10.9493	0.533637	0.266819	−	0.963747i	$-0.414028\pi$
$421$	10.9493	0.533637	0.266819	+	0.963747i	$0.414028\pi$
$422$	−12.6023	−0.613468
$423$	6.27949	0.305319
$424$	6.72050	0.326376
$425$	−6.37136	−0.309057
$426$	9.29560	0.450373
$427$	28.7507	1.39134
$428$	−10.3998	−0.502695
$429$	0.132526	0.00639839
$430$	3.99269	0.192544
$431$	9.94436	0.479003	0.239502	−	0.970896i	$-0.423016\pi$
$431$	9.94436	0.479003	0.239502	+	0.970896i	$0.423016\pi$
$432$	−0.705042	−0.0339214
$433$	−12.3029	−0.591240	−0.295620	−	0.955306i	$-0.595526\pi$
$433$	−12.3029	−0.591240	−0.295620	+	0.955306i	$0.595526\pi$
$434$	−9.72127	−0.466636
$435$	3.25013	0.155832
$436$	−14.1660	−0.678428
$437$	0	0
$438$	−3.15829	−0.150909
$439$	34.7288	1.65751	0.828757	−	0.559608i	$-0.189048\pi$
$439$	34.7288	1.65751	0.828757	+	0.559608i	$0.189048\pi$
$440$	−0.558380	−0.0266197
$441$	1.57903	0.0751917
$442$	−4.30955	−0.204984
$443$	18.7990	0.893169	0.446585	−	0.894741i	$-0.352640\pi$
$443$	18.7990	0.893169	0.446585	+	0.894741i	$0.352640\pi$
$444$	−5.63174	−0.267271
$445$	8.28110	0.392562
$446$	−20.8035	−0.985075
$447$	11.9953	0.567361
$448$	18.9093	0.893382
$449$	−21.9055	−1.03379	−0.516893	−	0.856050i	$-0.672912\pi$
$449$	−21.9055	−1.03379	−0.516893	+	0.856050i	$0.672912\pi$
$450$	0.963105	0.0454012
$451$	1.01335	0.0477167
$452$	1.50524	0.0708005
$453$	−7.18738	−0.337693
$454$	−4.44891	−0.208798
$455$	2.05705	0.0964359
$456$	1.96900	0.0922066
$457$	−8.38356	−0.392166	−0.196083	−	0.980587i	$-0.562822\pi$
$457$	−8.38356	−0.392166	−0.196083	+	0.980587i	$0.562822\pi$
$458$	−5.07416	−0.237100
$459$	−6.37136	−0.297390
$460$	0	0
$461$	7.75287	0.361087	0.180544	−	0.983567i	$-0.442214\pi$
$461$	7.75287	0.361087	0.180544	+	0.983567i	$0.442214\pi$
$462$	0.532313	0.0247654
$463$	−38.7726	−1.80191	−0.900957	−	0.433908i	$-0.857134\pi$
$463$	−38.7726	−1.80191	−0.900957	+	0.433908i	$0.857134\pi$
$464$	−2.29148	−0.106379
$465$	−3.44612	−0.159810
$466$	−25.2946	−1.17175
$467$	−28.6215	−1.32445	−0.662223	−	0.749307i	$-0.730387\pi$
$467$	−28.6215	−1.32445	−0.662223	+	0.749307i	$0.730387\pi$
$468$	−0.753171	−0.0348153
$469$	45.0027	2.07803
$470$	6.04781	0.278965
$471$	−14.5025	−0.668242
$472$	2.45831	0.113153
$473$	0.782286	0.0359696
$474$	0.721606	0.0331445
$475$	−0.665410	−0.0305311
$476$	20.0133	0.917310
$477$	−2.27115	−0.103989
$478$	−1.43550	−0.0656585
$479$	9.54313	0.436037	0.218018	−	0.975945i	$-0.430041\pi$
$479$	9.54313	0.436037	0.218018	+	0.975945i	$0.430041\pi$
$480$	5.23911	0.239132
$481$	3.68808	0.168162
$482$	22.6171	1.03018
$483$	0	0
$484$	11.7585	0.534478
$485$	−16.7493	−0.760546
$486$	0.963105	0.0436873
$487$	39.4415	1.78727	0.893633	−	0.448797i	$-0.148148\pi$
$487$	39.4415	1.78727	0.893633	+	0.448797i	$0.148148\pi$
$488$	−29.0459	−1.31485
$489$	2.19245	0.0991460
$490$	1.52077	0.0687013
$491$	−11.0874	−0.500367	−0.250183	−	0.968198i	$-0.580491\pi$
$491$	−11.0874	−0.500367	−0.250183	+	0.968198i	$0.580491\pi$
$492$	−5.75907	−0.259639
$493$	−20.7078	−0.932632
$494$	−0.450078	−0.0202500
$495$	0.188701	0.00848148
$496$	2.42966	0.109095
$497$	28.2698	1.26807
$498$	11.0678	0.495960
$499$	−31.3704	−1.40433	−0.702166	−	0.712013i	$-0.747784\pi$
$499$	−31.3704	−1.40433	−0.702166	+	0.712013i	$0.747784\pi$
$500$	−1.07243	−0.0479604
$501$	16.1031	0.719433
$502$	16.7089	0.745753
$503$	−3.37891	−0.150658	−0.0753291	−	0.997159i	$-0.524001\pi$
$503$	−3.37891	−0.150658	−0.0753291	+	0.997159i	$0.524001\pi$
$504$	−8.66711	−0.386064
$505$	−7.94947	−0.353747
$506$	0	0
$507$	−12.5068	−0.555445
$508$	8.38760	0.372140
$509$	0.878960	0.0389592	0.0194796	−	0.999810i	$-0.493799\pi$
$509$	0.878960	0.0389592	0.0194796	+	0.999810i	$0.493799\pi$
$510$	−6.13629	−0.271720
$511$	−9.60500	−0.424900
$512$	−7.86634	−0.347646
$513$	−0.665410	−0.0293786
$514$	−20.2069	−0.891288
$515$	−9.98752	−0.440103
$516$	−4.44590	−0.195720
$517$	1.18495	0.0521139
$518$	14.8138	0.650882
$519$	19.1841	0.842086
$520$	−2.07817	−0.0911337
$521$	36.3151	1.59099	0.795496	−	0.605959i	$-0.207210\pi$
$521$	36.3151	1.59099	0.795496	+	0.605959i	$0.207210\pi$
$522$	3.13022	0.137006
$523$	−18.0522	−0.789369	−0.394684	−	0.918817i	$-0.629146\pi$
$523$	−18.0522	−0.789369	−0.394684	+	0.918817i	$0.629146\pi$
$524$	0.0250065	0.00109241
$525$	2.92900	0.127832
$526$	5.19928	0.226699
$527$	21.9565	0.956439
$528$	−0.133042	−0.00578992
$529$	0	0
$530$	−2.18736	−0.0950128
$531$	−0.830770	−0.0360524
$532$	2.09014	0.0906192
$533$	3.77146	0.163360
$534$	7.97557	0.345137
$535$	9.69746	0.419258
$536$	−45.4648	−1.96378
$537$	22.1900	0.957567
$538$	18.1626	0.783046
$539$	0.297964	0.0128342
$540$	−1.07243	−0.0461500
$541$	−17.4298	−0.749365	−0.374683	−	0.927153i	$-0.622248\pi$
$541$	−17.4298	−0.749365	−0.374683	+	0.927153i	$0.622248\pi$
$542$	6.88303	0.295651
$543$	19.6503	0.843274
$544$	−33.3803	−1.43117
$545$	13.2093	0.565823
$546$	1.98115	0.0847855
$547$	2.37029	0.101346	0.0506731	−	0.998715i	$-0.483863\pi$
$547$	2.37029	0.101346	0.0506731	+	0.998715i	$0.483863\pi$
$548$	−24.3136	−1.03862
$549$	9.81589	0.418932
$550$	0.181739	0.00774938
$551$	−2.16267	−0.0921329
$552$	0	0
$553$	2.19455	0.0933218
$554$	9.38824	0.398868
$555$	5.25139	0.222909
$556$	−8.23503	−0.349243
$557$	13.5671	0.574856	0.287428	−	0.957802i	$-0.407200\pi$
$557$	13.5671	0.574856	0.287428	+	0.957802i	$0.407200\pi$
$558$	−3.31898	−0.140503
$559$	2.91150	0.123143
$560$	−2.06507	−0.0872650
$561$	−1.20228	−0.0507604
$562$	−9.32979	−0.393553
$563$	24.6343	1.03821	0.519107	−	0.854709i	$-0.326265\pi$
$563$	24.6343	1.03821	0.519107	+	0.854709i	$0.326265\pi$
$564$	−6.73430	−0.283565
$565$	−1.40358	−0.0590491
$566$	3.73079	0.156817
$567$	2.92900	0.123006
$568$	−28.5601	−1.19835
$569$	−3.82942	−0.160538	−0.0802688	−	0.996773i	$-0.525578\pi$
$569$	−3.82942	−0.160538	−0.0802688	+	0.996773i	$0.525578\pi$
$570$	−0.640860	−0.0268427
$571$	−30.2969	−1.26789	−0.633944	−	0.773379i	$-0.718565\pi$
$571$	−30.2969	−1.26789	−0.633944	+	0.773379i	$0.718565\pi$
$572$	−0.142124	−0.00594251
$573$	−7.15708	−0.298991
$574$	15.1488	0.632297
$575$	0	0
$576$	6.45590	0.268996
$577$	9.67800	0.402900	0.201450	−	0.979499i	$-0.435435\pi$
$577$	9.67800	0.402900	0.201450	+	0.979499i	$0.435435\pi$
$578$	22.7238	0.945184
$579$	−22.0158	−0.914944
$580$	−3.48553	−0.144729
$581$	33.6594	1.39643
$582$	−16.1313	−0.668665
$583$	−0.428569	−0.0177495
$584$	9.70362	0.401539
$585$	0.702304	0.0290367
$586$	17.9056	0.739673
$587$	25.4887	1.05203	0.526017	−	0.850474i	$-0.323685\pi$
$587$	25.4887	1.05203	0.526017	+	0.850474i	$0.323685\pi$
$588$	−1.69339	−0.0698343
$589$	2.29308	0.0944848
$590$	−0.800119	−0.0329404
$591$	−17.4241	−0.716732
$592$	−3.70245	−0.152170
$593$	−19.5634	−0.803373	−0.401686	−	0.915777i	$-0.631576\pi$
$593$	−19.5634	−0.803373	−0.401686	+	0.915777i	$0.631576\pi$
$594$	0.181739	0.00745684
$595$	−18.6617	−0.765055
$596$	−12.8641	−0.526936
$597$	−17.8328	−0.729847
$598$	0	0
$599$	43.3468	1.77110	0.885552	−	0.464540i	$-0.153780\pi$
$599$	43.3468	1.77110	0.885552	+	0.464540i	$0.153780\pi$
$600$	−2.95907	−0.120804
$601$	−15.1133	−0.616485	−0.308242	−	0.951308i	$-0.599741\pi$
$601$	−15.1133	−0.616485	−0.308242	+	0.951308i	$0.599741\pi$
$602$	11.6946	0.476635
$603$	15.3645	0.625693
$604$	7.70795	0.313632
$605$	−10.9644	−0.445766
$606$	−7.65618	−0.311011
$607$	23.9527	0.972210	0.486105	−	0.873900i	$-0.338417\pi$
$607$	23.9527	0.972210	0.486105	+	0.873900i	$0.338417\pi$
$608$	−3.48616	−0.141382
$609$	9.51963	0.385755
$610$	9.45374	0.382771
$611$	4.41011	0.178414
$612$	6.83283	0.276201
$613$	43.7314	1.76629	0.883147	−	0.469096i	$-0.155420\pi$
$613$	43.7314	1.76629	0.883147	+	0.469096i	$0.155420\pi$
$614$	5.69210	0.229715
$615$	5.37012	0.216544
$616$	−1.63549	−0.0658959
$617$	11.9710	0.481935	0.240968	−	0.970533i	$-0.422535\pi$
$617$	11.9710	0.481935	0.240968	+	0.970533i	$0.422535\pi$
$618$	−9.61903	−0.386934
$619$	4.41133	0.177306	0.0886532	−	0.996063i	$-0.471744\pi$
$619$	4.41133	0.177306	0.0886532	+	0.996063i	$0.471744\pi$
$620$	3.69572	0.148424
$621$	0	0
$622$	−22.9599	−0.920609
$623$	24.2553	0.971768
$624$	−0.495154	−0.0198220
$625$	1.00000	0.0400000
$626$	30.7048	1.22721
$627$	−0.125564	−0.00501452
$628$	15.5529	0.620630
$629$	−33.4585	−1.33408
$630$	2.82093	0.112389
$631$	−5.45874	−0.217309	−0.108655	−	0.994080i	$-0.534654\pi$
$631$	−5.45874	−0.217309	−0.108655	+	0.994080i	$0.534654\pi$
$632$	−2.21708	−0.0881908
$633$	−13.0850	−0.520083
$634$	30.6574	1.21756
$635$	−7.82113	−0.310372
$636$	2.43565	0.0965797
$637$	1.10896	0.0439385
$638$	0.590676	0.0233851
$639$	9.65169	0.381815
$640$	−4.26051	−0.168412
$641$	−2.45266	−0.0968741	−0.0484370	−	0.998826i	$-0.515424\pi$
$641$	−2.45266	−0.0968741	−0.0484370	+	0.998826i	$0.515424\pi$
$642$	9.33967	0.368608
$643$	−29.2975	−1.15538	−0.577691	−	0.816256i	$-0.696046\pi$
$643$	−29.2975	−1.15538	−0.577691	+	0.816256i	$0.696046\pi$
$644$	0	0
$645$	4.14564	0.163234
$646$	4.08315	0.160649
$647$	27.1930	1.06907	0.534534	−	0.845147i	$-0.320487\pi$
$647$	27.1930	1.06907	0.534534	+	0.845147i	$0.320487\pi$
$648$	−2.95907	−0.116243
$649$	−0.156767	−0.00615365
$650$	0.676393	0.0265303
$651$	−10.0937	−0.395602
$652$	−2.35124	−0.0920818
$653$	−38.0073	−1.48734	−0.743670	−	0.668546i	$-0.766917\pi$
$653$	−38.0073	−1.48734	−0.743670	+	0.668546i	$0.766917\pi$
$654$	12.7219	0.497466
$655$	−0.0233176	−0.000911095 0
$656$	−3.78616	−0.147825
$657$	−3.27928	−0.127937
$658$	17.7140	0.690565
$659$	−7.03381	−0.273998	−0.136999	−	0.990571i	$-0.543746\pi$
$659$	−7.03381	−0.273998	−0.136999	+	0.990571i	$0.543746\pi$
$660$	−0.202368	−0.00787718
$661$	−40.2648	−1.56612	−0.783059	−	0.621947i	$-0.786342\pi$
$661$	−40.2648	−1.56612	−0.783059	+	0.621947i	$0.786342\pi$
$662$	21.1679	0.822715
$663$	−4.47464	−0.173780
$664$	−34.0050	−1.31965
$665$	−1.94898	−0.0755783
$666$	5.05764	0.195980
$667$	0	0
$668$	−17.2694	−0.668173
$669$	−21.6004	−0.835122
$670$	14.7977	0.571684
$671$	1.85227	0.0715061
$672$	15.3454	0.591960
$673$	−19.1475	−0.738082	−0.369041	−	0.929413i	$-0.620314\pi$
$673$	−19.1475	−0.738082	−0.369041	+	0.929413i	$0.620314\pi$
$674$	26.3212	1.01386
$675$	1.00000	0.0384900
$676$	13.4126	0.515870
$677$	−0.150330	−0.00577767	−0.00288883	−	0.999996i	$-0.500920\pi$
$677$	−0.150330	−0.00577767	−0.00288883	+	0.999996i	$0.500920\pi$
$678$	−1.35180	−0.0519154
$679$	−49.0586	−1.88270
$680$	18.8533	0.722992
$681$	−4.61934	−0.177013
$682$	−0.626294	−0.0239821
$683$	10.3817	0.397243	0.198622	−	0.980076i	$-0.436354\pi$
$683$	10.3817	0.397243	0.198622	+	0.980076i	$0.436354\pi$
$684$	0.713604	0.0272853
$685$	22.6715	0.866234
$686$	−15.2922	−0.583859
$687$	−5.26854	−0.201007
$688$	−2.92285	−0.111433
$689$	−1.59504	−0.0607662
$690$	0	0
$691$	−14.6952	−0.559031	−0.279515	−	0.960141i	$-0.590174\pi$
$691$	−14.6952	−0.559031	−0.279515	+	0.960141i	$0.590174\pi$
$692$	−20.5735	−0.782088
$693$	0.552705	0.0209955
$694$	−10.1647	−0.385847
$695$	7.67887	0.291276
$696$	−9.61738	−0.364546
$697$	−34.2150	−1.29599
$698$	9.27862	0.351201
$699$	−26.2636	−0.993381
$700$	−3.14114	−0.118724
$701$	−40.6214	−1.53425	−0.767124	−	0.641498i	$-0.778313\pi$
$701$	−40.6214	−1.53425	−0.767124	+	0.641498i	$0.778313\pi$
$702$	0.676393	0.0255288
$703$	−3.49433	−0.131791
$704$	1.21824	0.0459140
$705$	6.27949	0.236499
$706$	−13.4239	−0.505215
$707$	−23.2840	−0.875684
$708$	0.890941	0.0334836
$709$	46.2323	1.73629	0.868145	−	0.496311i	$-0.165312\pi$
$709$	46.2323	1.73629	0.868145	+	0.496311i	$0.165312\pi$
$710$	9.29560	0.348858
$711$	0.749250	0.0280991
$712$	−24.5044	−0.918340
$713$	0	0
$714$	−17.9732	−0.672630
$715$	0.132526	0.00495617
$716$	−23.7971	−0.889340
$717$	−1.49050	−0.0556636
$718$	−25.5619	−0.953960
$719$	14.4570	0.539156	0.269578	−	0.962979i	$-0.413116\pi$
$719$	14.4570	0.539156	0.269578	+	0.962979i	$0.413116\pi$
$720$	−0.705042	−0.0262754
$721$	−29.2534	−1.08945
$722$	−17.8726	−0.665148
$723$	23.4835	0.873360
$724$	−21.0735	−0.783191
$725$	3.25013	0.120707
$726$	−10.5599	−0.391913
$727$	−2.39540	−0.0888406	−0.0444203	−	0.999013i	$-0.514144\pi$
$727$	−2.39540	−0.0888406	−0.0444203	+	0.999013i	$0.514144\pi$
$728$	−6.08695	−0.225597
$729$	1.00000	0.0370370
$730$	−3.15829	−0.116894
$731$	−26.4134	−0.976934
$732$	−10.5268	−0.389083
$733$	−28.8537	−1.06574	−0.532868	−	0.846199i	$-0.678886\pi$
$733$	−28.8537	−1.06574	−0.532868	+	0.846199i	$0.678886\pi$
$734$	30.0762	1.11013
$735$	1.57903	0.0582433
$736$	0	0
$737$	2.89931	0.106797
$738$	5.17200	0.190384
$739$	−11.6916	−0.430084	−0.215042	−	0.976605i	$-0.568989\pi$
$739$	−11.6916	−0.430084	−0.215042	+	0.976605i	$0.568989\pi$
$740$	−5.63174	−0.207027
$741$	−0.467320	−0.0171674
$742$	−6.40677	−0.235200
$743$	−20.2577	−0.743184	−0.371592	−	0.928396i	$-0.621188\pi$
$743$	−20.2577	−0.743184	−0.371592	+	0.928396i	$0.621188\pi$
$744$	10.1973	0.373852
$745$	11.9953	0.439476
$746$	−26.8487	−0.983001
$747$	11.4918	0.420463
$748$	1.28936	0.0471437
$749$	28.4038	1.03785
$750$	0.963105	0.0351676
$751$	18.6449	0.680363	0.340181	−	0.940360i	$-0.389512\pi$
$751$	18.6449	0.680363	0.340181	+	0.940360i	$0.389512\pi$
$752$	−4.42731	−0.161447
$753$	17.3489	0.632230
$754$	2.19837	0.0800598
$755$	−7.18738	−0.261576
$756$	−3.14114	−0.114242
$757$	9.01171	0.327536	0.163768	−	0.986499i	$-0.447635\pi$
$757$	9.01171	0.327536	0.163768	+	0.986499i	$0.447635\pi$
$758$	−13.5752	−0.493075
$759$	0	0
$760$	1.96900	0.0714230
$761$	−30.1297	−1.09220	−0.546100	−	0.837720i	$-0.683888\pi$
$761$	−30.1297	−1.09220	−0.546100	+	0.837720i	$0.683888\pi$
$762$	−7.53258	−0.272876
$763$	38.6899	1.40067
$764$	7.67545	0.277688
$765$	−6.37136	−0.230357
$766$	12.0615	0.435798
$767$	−0.583453	−0.0210673
$768$	−17.0151	−0.613981
$769$	20.7427	0.748001	0.374000	−	0.927429i	$-0.377986\pi$
$769$	20.7427	0.748001	0.374000	+	0.927429i	$0.377986\pi$
$770$	0.532313	0.0191832
$771$	−20.9810	−0.755612
$772$	23.6103	0.849754
$773$	−9.18883	−0.330499	−0.165250	−	0.986252i	$-0.552843\pi$
$773$	−9.18883	−0.330499	−0.165250	+	0.986252i	$0.552843\pi$
$774$	3.99269	0.143514
$775$	−3.44612	−0.123788
$776$	49.5624	1.77919
$777$	15.3813	0.551802
$778$	−9.41621	−0.337588
$779$	−3.57333	−0.128028
$780$	−0.753171	−0.0269678
$781$	1.82128	0.0651707
$782$	0	0
$783$	3.25013	0.116150
$784$	−1.11328	−0.0397600
$785$	−14.5025	−0.517618
$786$	−0.0224573	−0.000801026 0
$787$	23.0600	0.822001	0.411000	−	0.911635i	$-0.365179\pi$
$787$	23.0600	0.822001	0.411000	+	0.911635i	$0.365179\pi$
$788$	18.6861	0.665665
$789$	5.39846	0.192190
$790$	0.721606	0.0256736
$791$	−4.11108	−0.146173
$792$	−0.558380	−0.0198412
$793$	6.89374	0.244804
$794$	9.57130	0.339673
$795$	−2.27115	−0.0805495
$796$	19.1244	0.677845
$797$	5.64107	0.199817	0.0999085	−	0.994997i	$-0.468145\pi$
$797$	5.64107	0.199817	0.0999085	+	0.994997i	$0.468145\pi$
$798$	−1.87708	−0.0664478
$799$	−40.0089	−1.41541
$800$	5.23911	0.185231
$801$	8.28110	0.292598
$802$	−5.92880	−0.209353
$803$	−0.618803	−0.0218371
$804$	−16.4774	−0.581112
$805$	0	0
$806$	−2.33093	−0.0821036
$807$	18.8584	0.663847
$808$	23.5231	0.827538
$809$	−27.3567	−0.961811	−0.480905	−	0.876773i	$-0.659692\pi$
$809$	−27.3567	−0.961811	−0.480905	+	0.876773i	$0.659692\pi$
$810$	0.963105	0.0338401
$811$	51.5374	1.80972	0.904861	−	0.425707i	$-0.139975\pi$
$811$	51.5374	1.80972	0.904861	+	0.425707i	$0.139975\pi$
$812$	−10.2091	−0.358270
$813$	7.14670	0.250646
$814$	0.954383	0.0334511
$815$	2.19245	0.0767982
$816$	4.49208	0.157254
$817$	−2.75855	−0.0965094
$818$	−29.6014	−1.03499
$819$	2.05705	0.0718791
$820$	−5.75907	−0.201115
$821$	−11.6117	−0.405250	−0.202625	−	0.979256i	$-0.564947\pi$
$821$	−11.6117	−0.405250	−0.202625	+	0.979256i	$0.564947\pi$
$822$	21.8351	0.761585
$823$	−45.8637	−1.59871	−0.799353	−	0.600861i	$-0.794824\pi$
$823$	−45.8637	−1.59871	−0.799353	+	0.600861i	$0.794824\pi$
$824$	29.5538	1.02955
$825$	0.188701	0.00656973
$826$	−2.34355	−0.0815424
$827$	47.8722	1.66468	0.832339	−	0.554266i	$-0.187001\pi$
$827$	47.8722	1.66468	0.832339	+	0.554266i	$0.187001\pi$
$828$	0	0
$829$	38.2600	1.32883	0.664413	−	0.747366i	$-0.268682\pi$
$829$	38.2600	1.32883	0.664413	+	0.747366i	$0.268682\pi$
$830$	11.0678	0.384169
$831$	9.74788	0.338150
$832$	4.53401	0.157188
$833$	−10.0605	−0.348577
$834$	7.39556	0.256087
$835$	16.1031	0.557270
$836$	0.134658	0.00465724
$837$	−3.44612	−0.119115
$838$	−18.7246	−0.646830
$839$	−7.77970	−0.268585	−0.134293	−	0.990942i	$-0.542876\pi$
$839$	−7.77970	−0.268585	−0.134293	+	0.990942i	$0.542876\pi$
$840$	−8.66711	−0.299044
$841$	−18.4366	−0.635746
$842$	10.5454	0.363417
$843$	−9.68720	−0.333645
$844$	14.0327	0.483027
$845$	−12.5068	−0.430246
$846$	6.04781	0.207928
$847$	−32.1147	−1.10347
$848$	1.60126	0.0549874
$849$	3.87371	0.132945
$850$	−6.13629	−0.210473
$851$	0	0
$852$	−10.3507	−0.354611
$853$	−23.2460	−0.795928	−0.397964	−	0.917401i	$-0.630283\pi$
$853$	−23.2460	−0.795928	−0.397964	+	0.917401i	$0.630283\pi$
$854$	27.6900	0.947531
$855$	−0.665410	−0.0227565
$856$	−28.6955	−0.980791
$857$	−8.19070	−0.279789	−0.139895	−	0.990166i	$-0.544676\pi$
$857$	−8.19070	−0.279789	−0.139895	+	0.990166i	$0.544676\pi$
$858$	0.127636	0.00435742
$859$	49.5205	1.68962	0.844809	−	0.535069i	$-0.179714\pi$
$859$	49.5205	1.68962	0.844809	+	0.535069i	$0.179714\pi$
$860$	−4.44590	−0.151604
$861$	15.7291	0.536046
$862$	9.57747	0.326210
$863$	−26.0635	−0.887210	−0.443605	−	0.896222i	$-0.646301\pi$
$863$	−26.0635	−0.887210	−0.443605	+	0.896222i	$0.646301\pi$
$864$	5.23911	0.178238
$865$	19.1841	0.652277
$866$	−11.8490	−0.402645
$867$	23.5943	0.801303
$868$	10.8247	0.367416
$869$	0.141384	0.00479613
$870$	3.13022	0.106124
$871$	10.7906	0.365625
$872$	−39.0872	−1.32366
$873$	−16.7493	−0.566878
$874$	0	0
$875$	2.92900	0.0990182
$876$	3.51679	0.118821
$877$	−52.2177	−1.76327	−0.881633	−	0.471936i	$-0.843555\pi$
$877$	−52.2177	−1.76327	−0.881633	+	0.471936i	$0.843555\pi$
$878$	33.4475	1.12880
$879$	18.5915	0.627076
$880$	−0.133042	−0.00448485
$881$	−36.5549	−1.23157	−0.615783	−	0.787916i	$-0.711160\pi$
$881$	−36.5549	−1.23157	−0.615783	+	0.787916i	$0.711160\pi$
$882$	1.52077	0.0512069
$883$	−1.53240	−0.0515693	−0.0257846	−	0.999668i	$-0.508208\pi$
$883$	−1.53240	−0.0515693	−0.0257846	+	0.999668i	$0.508208\pi$
$884$	4.79872	0.161399
$885$	−0.830770	−0.0279260
$886$	18.1055	0.608265
$887$	−14.2659	−0.479002	−0.239501	−	0.970896i	$-0.576984\pi$
$887$	−14.2659	−0.479002	−0.239501	+	0.970896i	$0.576984\pi$
$888$	−15.5392	−0.521463
$889$	−22.9081	−0.768312
$890$	7.97557	0.267342
$891$	0.188701	0.00632172
$892$	23.1649	0.775619
$893$	−4.17843	−0.139826
$894$	11.5528	0.386383
$895$	22.1900	0.741728
$896$	−12.4790	−0.416895
$897$	0	0
$898$	−21.0973	−0.704028
$899$	−11.2004	−0.373553
$900$	−1.07243	−0.0357476
$901$	14.4703	0.482077
$902$	0.975961	0.0324959
$903$	12.1426	0.404079
$904$	4.15330	0.138137
$905$	19.6503	0.653197
$906$	−6.92220	−0.229975
$907$	−30.9158	−1.02654	−0.513270	−	0.858227i	$-0.671566\pi$
$907$	−30.9158	−1.02654	−0.513270	+	0.858227i	$0.671566\pi$
$908$	4.95391	0.164401
$909$	−7.94947	−0.263667
$910$	1.98115	0.0656746
$911$	−22.7316	−0.753132	−0.376566	−	0.926390i	$-0.622895\pi$
$911$	−22.7316	−0.753132	−0.376566	+	0.926390i	$0.622895\pi$
$912$	0.469142	0.0155348
$913$	2.16851	0.0717673
$914$	−8.07425	−0.267073
$915$	9.81589	0.324503
$916$	5.65013	0.186685
$917$	−0.0682972	−0.00225537
$918$	−6.13629	−0.202528
$919$	−14.1077	−0.465370	−0.232685	−	0.972552i	$-0.574751\pi$
$919$	−14.1077	−0.465370	−0.232685	+	0.972552i	$0.574751\pi$
$920$	0	0
$921$	5.91016	0.194746
$922$	7.46683	0.245907
$923$	6.77843	0.223115
$924$	−0.592736	−0.0194996
$925$	5.25139	0.172665
$926$	−37.3421	−1.22714
$927$	−9.98752	−0.328033
$928$	17.0278	0.558966
$929$	−52.6183	−1.72635	−0.863175	−	0.504905i	$-0.831528\pi$
$929$	−52.6183	−1.72635	−0.863175	+	0.504905i	$0.831528\pi$
$930$	−3.31898	−0.108834
$931$	−1.05070	−0.0344353
$932$	28.1658	0.922602
$933$	−23.8395	−0.780469
$934$	−27.5656	−0.901972
$935$	−1.20228	−0.0393189
$936$	−2.07817	−0.0679271
$937$	−37.7919	−1.23461	−0.617304	−	0.786725i	$-0.711775\pi$
$937$	−37.7919	−1.23461	−0.617304	+	0.786725i	$0.711775\pi$
$938$	43.3423	1.41518
$939$	31.8810	1.04040
$940$	−6.73430	−0.219649
$941$	−24.8542	−0.810222	−0.405111	−	0.914267i	$-0.632767\pi$
$941$	−24.8542	−0.810222	−0.405111	+	0.914267i	$0.632767\pi$
$942$	−13.9675	−0.455085
$943$	0	0
$944$	0.585728	0.0190638
$945$	2.92900	0.0952803
$946$	0.753424	0.0244959
$947$	−18.8450	−0.612379	−0.306190	−	0.951971i	$-0.599054\pi$
$947$	−18.8450	−0.612379	−0.306190	+	0.951971i	$0.599054\pi$
$948$	−0.803516	−0.0260970
$949$	−2.30305	−0.0747602
$950$	−0.640860	−0.0207922
$951$	31.8319	1.03222
$952$	55.2213	1.78973
$953$	13.6632	0.442594	0.221297	−	0.975206i	$-0.428971\pi$
$953$	13.6632	0.442594	0.221297	+	0.975206i	$0.428971\pi$
$954$	−2.18736	−0.0708184
$955$	−7.15708	−0.231598
$956$	1.59845	0.0516976
$957$	0.613304	0.0198253
$958$	9.19104	0.296949
$959$	66.4048	2.14432
$960$	6.45590	0.208363
$961$	−19.1243	−0.616912
$962$	3.55200	0.114521
$963$	9.69746	0.312496
$964$	−25.1844	−0.811133
$965$	−22.0158	−0.708712
$966$	0	0
$967$	4.53421	0.145810	0.0729051	−	0.997339i	$-0.476773\pi$
$967$	4.53421	0.145810	0.0729051	+	0.997339i	$0.476773\pi$
$968$	32.4444	1.04280
$969$	4.23957	0.136195
$970$	−16.1313	−0.517946
$971$	56.4799	1.81253	0.906263	−	0.422715i	$-0.138923\pi$
$971$	56.4799	1.81253	0.906263	+	0.422715i	$0.138923\pi$
$972$	−1.07243	−0.0343981
$973$	22.4914	0.721041
$974$	37.9864	1.21716
$975$	0.702304	0.0224917
$976$	−6.92062	−0.221524
$977$	−49.5573	−1.58548	−0.792739	−	0.609561i	$-0.791346\pi$
$977$	−49.5573	−1.58548	−0.792739	+	0.609561i	$0.791346\pi$
$978$	2.11156	0.0675202
$979$	1.56265	0.0499426
$980$	−1.69339	−0.0540934
$981$	13.2093	0.421739
$982$	−10.6783	−0.340759
$983$	58.4021	1.86274	0.931369	−	0.364077i	$-0.118616\pi$
$983$	58.4021	1.86274	0.931369	+	0.364077i	$0.118616\pi$
$984$	−15.8906	−0.506573
$985$	−17.4241	−0.555178
$986$	−19.9438	−0.635139
$987$	18.3926	0.585443
$988$	0.501167	0.0159443
$989$	0	0
$990$	0.181739	0.00577604
$991$	−19.1233	−0.607471	−0.303735	−	0.952756i	$-0.598234\pi$
$991$	−19.1233	−0.607471	−0.303735	+	0.952756i	$0.598234\pi$
$992$	−18.0546	−0.573235
$993$	21.9788	0.697477
$994$	27.2268	0.863581
$995$	−17.8328	−0.565337
$996$	−12.3241	−0.390505
$997$	45.9606	1.45559	0.727793	−	0.685797i	$-0.240546\pi$
$997$	45.9606	1.45559	0.727793	+	0.685797i	$0.240546\pi$
$998$	−30.2130	−0.956376
$999$	5.25139	0.166147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bi.1.6	yes	8
23.22	odd	2		7935.2.a.bh.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.6	✓	8	23.22	odd	2
7935.2.a.bi.1.6	yes	8	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.963105 q^{2} +1.00000 q^{3} -1.07243 q^{4} +1.00000 q^{5} +0.963105 q^{6} +2.92900 q^{7} -2.95907 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.963105 q^{2} +1.00000 q^{3} -1.07243 q^{4} +1.00000 q^{5} +0.963105 q^{6} +2.92900 q^{7} -2.95907 q^{8} +1.00000 q^{9} +0.963105 q^{10} +0.188701 q^{11} -1.07243 q^{12} +0.702304 q^{13} +2.82093 q^{14} +1.00000 q^{15} -0.705042 q^{16} -6.37136 q^{17} +0.963105 q^{18} -0.665410 q^{19} -1.07243 q^{20} +2.92900 q^{21} +0.181739 q^{22} -2.95907 q^{24} +1.00000 q^{25} +0.676393 q^{26} +1.00000 q^{27} -3.14114 q^{28} +3.25013 q^{29} +0.963105 q^{30} -3.44612 q^{31} +5.23911 q^{32} +0.188701 q^{33} -6.13629 q^{34} +2.92900 q^{35} -1.07243 q^{36} +5.25139 q^{37} -0.640860 q^{38} +0.702304 q^{39} -2.95907 q^{40} +5.37012 q^{41} +2.82093 q^{42} +4.14564 q^{43} -0.202368 q^{44} +1.00000 q^{45} +6.27949 q^{47} -0.705042 q^{48} +1.57903 q^{49} +0.963105 q^{50} -6.37136 q^{51} -0.753171 q^{52} -2.27115 q^{53} +0.963105 q^{54} +0.188701 q^{55} -8.66711 q^{56} -0.665410 q^{57} +3.13022 q^{58} -0.830770 q^{59} -1.07243 q^{60} +9.81589 q^{61} -3.31898 q^{62} +2.92900 q^{63} +6.45590 q^{64} +0.702304 q^{65} +0.181739 q^{66} +15.3645 q^{67} +6.83283 q^{68} +2.82093 q^{70} +9.65169 q^{71} -2.95907 q^{72} -3.27928 q^{73} +5.05764 q^{74} +1.00000 q^{75} +0.713604 q^{76} +0.552705 q^{77} +0.676393 q^{78} +0.749250 q^{79} -0.705042 q^{80} +1.00000 q^{81} +5.17200 q^{82} +11.4918 q^{83} -3.14114 q^{84} -6.37136 q^{85} +3.99269 q^{86} +3.25013 q^{87} -0.558380 q^{88} +8.28110 q^{89} +0.963105 q^{90} +2.05705 q^{91} -3.44612 q^{93} +6.04781 q^{94} -0.665410 q^{95} +5.23911 q^{96} -16.7493 q^{97} +1.52077 q^{98} +0.188701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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