LMFDB - Embedded newform 7935.2.a.bl.1.2

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.85426$ 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)

$f(q)$	$=$	$q-1.85426 q^{2} +1.00000 q^{3} +1.43827 q^{4} -1.00000 q^{5} -1.85426 q^{6} -4.25122 q^{7} +1.04159 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.85426 q^{2} +1.00000 q^{3} +1.43827 q^{4} -1.00000 q^{5} -1.85426 q^{6} -4.25122 q^{7} +1.04159 q^{8} +1.00000 q^{9} +1.85426 q^{10} +1.39317 q^{11} +1.43827 q^{12} +2.97139 q^{13} +7.88285 q^{14} -1.00000 q^{15} -4.80792 q^{16} +5.65269 q^{17} -1.85426 q^{18} +7.04912 q^{19} -1.43827 q^{20} -4.25122 q^{21} -2.58330 q^{22} +1.04159 q^{24} +1.00000 q^{25} -5.50973 q^{26} +1.00000 q^{27} -6.11441 q^{28} +1.32492 q^{29} +1.85426 q^{30} +3.56980 q^{31} +6.83195 q^{32} +1.39317 q^{33} -10.4816 q^{34} +4.25122 q^{35} +1.43827 q^{36} +3.67112 q^{37} -13.0709 q^{38} +2.97139 q^{39} -1.04159 q^{40} -9.81542 q^{41} +7.88285 q^{42} +10.7813 q^{43} +2.00376 q^{44} -1.00000 q^{45} -7.10309 q^{47} -4.80792 q^{48} +11.0728 q^{49} -1.85426 q^{50} +5.65269 q^{51} +4.27368 q^{52} +8.09711 q^{53} -1.85426 q^{54} -1.39317 q^{55} -4.42800 q^{56} +7.04912 q^{57} -2.45675 q^{58} -0.141998 q^{59} -1.43827 q^{60} -3.62912 q^{61} -6.61934 q^{62} -4.25122 q^{63} -3.05236 q^{64} -2.97139 q^{65} -2.58330 q^{66} -12.0240 q^{67} +8.13012 q^{68} -7.88285 q^{70} +10.1535 q^{71} +1.04159 q^{72} -9.15769 q^{73} -6.80721 q^{74} +1.00000 q^{75} +10.1386 q^{76} -5.92267 q^{77} -5.50973 q^{78} +6.16073 q^{79} +4.80792 q^{80} +1.00000 q^{81} +18.2003 q^{82} +16.6390 q^{83} -6.11441 q^{84} -5.65269 q^{85} -19.9913 q^{86} +1.32492 q^{87} +1.45110 q^{88} +8.30577 q^{89} +1.85426 q^{90} -12.6320 q^{91} +3.56980 q^{93} +13.1710 q^{94} -7.04912 q^{95} +6.83195 q^{96} -0.605707 q^{97} -20.5319 q^{98} +1.39317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * 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 $

$2$	−1.85426	−1.31116	−0.655579	−	0.755126i	$-0.727576\pi$
$2$	−1.85426	−1.31116	−0.655579	+	0.755126i	$0.727576\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.43827	0.719137
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.85426	−0.756998
$7$	−4.25122	−1.60681	−0.803404	−	0.595434i	$-0.796980\pi$
$7$	−4.25122	−1.60681	−0.803404	+	0.595434i	$0.796980\pi$
$8$	1.04159	0.368256
$9$	1.00000	0.333333
$10$	1.85426	0.586368
$11$	1.39317	0.420056	0.210028	−	0.977695i	$-0.432644\pi$
$11$	1.39317	0.420056	0.210028	+	0.977695i	$0.432644\pi$
$12$	1.43827	0.415194
$13$	2.97139	0.824116	0.412058	−	0.911158i	$-0.364810\pi$
$13$	2.97139	0.824116	0.412058	+	0.911158i	$0.364810\pi$
$14$	7.88285	2.10678
$15$	−1.00000	−0.258199
$16$	−4.80792	−1.20198
$17$	5.65269	1.37098	0.685490	−	0.728082i	$-0.259588\pi$
$17$	5.65269	1.37098	0.685490	+	0.728082i	$0.259588\pi$
$18$	−1.85426	−0.437053
$19$	7.04912	1.61718	0.808589	−	0.588374i	$-0.200232\pi$
$19$	7.04912	1.61718	0.808589	+	0.588374i	$0.200232\pi$
$20$	−1.43827	−0.321608
$21$	−4.25122	−0.927692
$22$	−2.58330	−0.550761
$23$	0	0
$23$	0	0
$24$	1.04159	0.212613
$25$	1.00000	0.200000
$26$	−5.50973	−1.08055
$27$	1.00000	0.192450
$28$	−6.11441	−1.15552
$29$	1.32492	0.246032	0.123016	−	0.992405i	$-0.460743\pi$
$29$	1.32492	0.246032	0.123016	+	0.992405i	$0.460743\pi$
$30$	1.85426	0.338540
$31$	3.56980	0.641156	0.320578	−	0.947222i	$-0.396123\pi$
$31$	3.56980	0.641156	0.320578	+	0.947222i	$0.396123\pi$
$32$	6.83195	1.20773
$33$	1.39317	0.242520
$34$	−10.4816	−1.79757
$35$	4.25122	0.718587
$36$	1.43827	0.239712
$37$	3.67112	0.603529	0.301764	−	0.953383i	$-0.402424\pi$
$37$	3.67112	0.603529	0.301764	+	0.953383i	$0.402424\pi$
$38$	−13.0709	−2.12038
$39$	2.97139	0.475804
$40$	−1.04159	−0.164689
$41$	−9.81542	−1.53291	−0.766455	−	0.642298i	$-0.777981\pi$
$41$	−9.81542	−1.53291	−0.766455	+	0.642298i	$0.777981\pi$
$42$	7.88285	1.21635
$43$	10.7813	1.64413	0.822066	−	0.569392i	$-0.192821\pi$
$43$	10.7813	1.64413	0.822066	+	0.569392i	$0.192821\pi$
$44$	2.00376	0.302078
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−7.10309	−1.03609	−0.518046	−	0.855353i	$-0.673341\pi$
$47$	−7.10309	−1.03609	−0.518046	+	0.855353i	$0.673341\pi$
$48$	−4.80792	−0.693963
$49$	11.0728	1.58184
$50$	−1.85426	−0.262232
$51$	5.65269	0.791535
$52$	4.27368	0.592652
$53$	8.09711	1.11222	0.556112	−	0.831107i	$-0.312293\pi$
$53$	8.09711	1.11222	0.556112	+	0.831107i	$0.312293\pi$
$54$	−1.85426	−0.252333
$55$	−1.39317	−0.187855
$56$	−4.42800	−0.591717
$57$	7.04912	0.933678
$58$	−2.45675	−0.322587
$59$	−0.141998	−0.0184866	−0.00924330	−	0.999957i	$-0.502942\pi$
$59$	−0.141998	−0.0184866	−0.00924330	+	0.999957i	$0.502942\pi$
$60$	−1.43827	−0.185680
$61$	−3.62912	−0.464662	−0.232331	−	0.972637i	$-0.574635\pi$
$61$	−3.62912	−0.464662	−0.232331	+	0.972637i	$0.574635\pi$
$62$	−6.61934	−0.840657
$63$	−4.25122	−0.535603
$64$	−3.05236	−0.381546
$65$	−2.97139	−0.368556
$66$	−2.58330	−0.317982
$67$	−12.0240	−1.46896	−0.734481	−	0.678629i	$-0.762574\pi$
$67$	−12.0240	−1.46896	−0.734481	+	0.678629i	$0.762574\pi$
$68$	8.13012	0.985922
$69$	0	0
$70$	−7.88285	−0.942181
$71$	10.1535	1.20500	0.602501	−	0.798118i	$-0.294171\pi$
$71$	10.1535	1.20500	0.602501	+	0.798118i	$0.294171\pi$
$72$	1.04159	0.122752
$73$	−9.15769	−1.07183	−0.535913	−	0.844273i	$-0.680033\pi$
$73$	−9.15769	−1.07183	−0.535913	+	0.844273i	$0.680033\pi$
$74$	−6.80721	−0.791322
$75$	1.00000	0.115470
$76$	10.1386	1.16297
$77$	−5.92267	−0.674950
$78$	−5.50973	−0.623854
$79$	6.16073	0.693137	0.346568	−	0.938025i	$-0.387347\pi$
$79$	6.16073	0.693137	0.346568	+	0.938025i	$0.387347\pi$
$80$	4.80792	0.537541
$81$	1.00000	0.111111
$82$	18.2003	2.00989
$83$	16.6390	1.82637	0.913186	−	0.407543i	$-0.133614\pi$
$83$	16.6390	1.82637	0.913186	+	0.407543i	$0.133614\pi$
$84$	−6.11441	−0.667137
$85$	−5.65269	−0.613121
$86$	−19.9913	−2.15572
$87$	1.32492	0.142047
$88$	1.45110	0.154688
$89$	8.30577	0.880409	0.440205	−	0.897897i	$-0.354906\pi$
$89$	8.30577	0.880409	0.440205	+	0.897897i	$0.354906\pi$
$90$	1.85426	0.195456
$91$	−12.6320	−1.32420
$92$	0	0
$93$	3.56980	0.370171
$94$	13.1710	1.35848
$95$	−7.04912	−0.723224
$96$	6.83195	0.697283
$97$	−0.605707	−0.0615002	−0.0307501	−	0.999527i	$-0.509790\pi$
$97$	−0.605707	−0.0615002	−0.0307501	+	0.999527i	$0.509790\pi$
$98$	−20.5319	−2.07404
$99$	1.39317	0.140019
$100$	1.43827	0.143827
$101$	−15.0063	−1.49318	−0.746591	−	0.665283i	$-0.768311\pi$
$101$	−15.0063	−1.49318	−0.746591	+	0.665283i	$0.768311\pi$
$102$	−10.4816	−1.03783
$103$	12.4958	1.23125	0.615623	−	0.788041i	$-0.288904\pi$
$103$	12.4958	1.23125	0.615623	+	0.788041i	$0.288904\pi$
$104$	3.09496	0.303486
$105$	4.25122	0.414876
$106$	−15.0141	−1.45830
$107$	6.49186	0.627592	0.313796	−	0.949490i	$-0.398399\pi$
$107$	6.49186	0.627592	0.313796	+	0.949490i	$0.398399\pi$
$108$	1.43827	0.138398
$109$	−2.43055	−0.232804	−0.116402	−	0.993202i	$-0.537136\pi$
$109$	−2.43055	−0.232804	−0.116402	+	0.993202i	$0.537136\pi$
$110$	2.58330	0.246308
$111$	3.67112	0.348448
$112$	20.4395	1.93135
$113$	−6.75955	−0.635885	−0.317943	−	0.948110i	$-0.602992\pi$
$113$	−6.75955	−0.635885	−0.317943	+	0.948110i	$0.602992\pi$
$114$	−13.0709	−1.22420
$115$	0	0
$116$	1.90560	0.176931
$117$	2.97139	0.274705
$118$	0.263301	0.0242389
$119$	−24.0308	−2.20290
$120$	−1.04159	−0.0950833
$121$	−9.05908	−0.823553
$122$	6.72933	0.609245
$123$	−9.81542	−0.885026
$124$	5.13436	0.461079
$125$	−1.00000	−0.0894427
$126$	7.88285	0.702260
$127$	−17.5591	−1.55812	−0.779061	−	0.626948i	$-0.784304\pi$
$127$	−17.5591	−1.55812	−0.779061	+	0.626948i	$0.784304\pi$
$128$	−8.00402	−0.707462
$129$	10.7813	0.949240
$130$	5.50973	0.483235
$131$	−14.5126	−1.26797	−0.633985	−	0.773346i	$-0.718582\pi$
$131$	−14.5126	−1.26797	−0.633985	+	0.773346i	$0.718582\pi$
$132$	2.00376	0.174405
$133$	−29.9673	−2.59850
$134$	22.2956	1.92604
$135$	−1.00000	−0.0860663
$136$	5.88776	0.504871
$137$	13.0774	1.11728	0.558639	−	0.829411i	$-0.311324\pi$
$137$	13.0774	1.11728	0.558639	+	0.829411i	$0.311324\pi$
$138$	0	0
$139$	1.79484	0.152236	0.0761181	−	0.997099i	$-0.475747\pi$
$139$	1.79484	0.152236	0.0761181	+	0.997099i	$0.475747\pi$
$140$	6.11441	0.516762
$141$	−7.10309	−0.598188
$142$	−18.8273	−1.57995
$143$	4.13965	0.346175
$144$	−4.80792	−0.400660
$145$	−1.32492	−0.110029
$146$	16.9807	1.40533
$147$	11.0728	0.913273
$148$	5.28008	0.434020
$149$	−5.41867	−0.443914	−0.221957	−	0.975056i	$-0.571245\pi$
$149$	−5.41867	−0.443914	−0.221957	+	0.975056i	$0.571245\pi$
$150$	−1.85426	−0.151400
$151$	−1.11296	−0.0905714	−0.0452857	−	0.998974i	$-0.514420\pi$
$151$	−1.11296	−0.0905714	−0.0452857	+	0.998974i	$0.514420\pi$
$152$	7.34226	0.595536
$153$	5.65269	0.456993
$154$	10.9822	0.884967
$155$	−3.56980	−0.286734
$156$	4.27368	0.342168
$157$	−18.2796	−1.45887	−0.729435	−	0.684050i	$-0.760217\pi$
$157$	−18.2796	−1.45887	−0.729435	+	0.684050i	$0.760217\pi$
$158$	−11.4236	−0.908812
$159$	8.09711	0.642143
$160$	−6.83195	−0.540113
$161$	0	0
$162$	−1.85426	−0.145684
$163$	8.87311	0.694996	0.347498	−	0.937681i	$-0.387031\pi$
$163$	8.87311	0.694996	0.347498	+	0.937681i	$0.387031\pi$
$164$	−14.1173	−1.10237
$165$	−1.39317	−0.108458
$166$	−30.8531	−2.39466
$167$	2.08119	0.161047	0.0805236	−	0.996753i	$-0.474341\pi$
$167$	2.08119	0.161047	0.0805236	+	0.996753i	$0.474341\pi$
$168$	−4.42800	−0.341628
$169$	−4.17083	−0.320833
$170$	10.4816	0.803899
$171$	7.04912	0.539059
$172$	15.5065	1.18236
$173$	0.314083	0.0238793	0.0119396	−	0.999929i	$-0.496199\pi$
$173$	0.314083	0.0238793	0.0119396	+	0.999929i	$0.496199\pi$
$174$	−2.45675	−0.186246
$175$	−4.25122	−0.321362
$176$	−6.69824	−0.504899
$177$	−0.141998	−0.0106732
$178$	−15.4010	−1.15436
$179$	10.2580	0.766718	0.383359	−	0.923599i	$-0.374767\pi$
$179$	10.2580	0.766718	0.383359	+	0.923599i	$0.374767\pi$
$180$	−1.43827	−0.107203
$181$	−13.0194	−0.967726	−0.483863	−	0.875144i	$-0.660767\pi$
$181$	−13.0194	−0.967726	−0.483863	+	0.875144i	$0.660767\pi$
$182$	23.4231	1.73623
$183$	−3.62912	−0.268273
$184$	0	0
$185$	−3.67112	−0.269906
$186$	−6.61934	−0.485353
$187$	7.87516	0.575889
$188$	−10.2162	−0.745093
$189$	−4.25122	−0.309231
$190$	13.0709	0.948262
$191$	−4.88188	−0.353240	−0.176620	−	0.984279i	$-0.556516\pi$
$191$	−4.88188	−0.353240	−0.176620	+	0.984279i	$0.556516\pi$
$192$	−3.05236	−0.220285
$193$	23.6143	1.69980	0.849898	−	0.526948i	$-0.176664\pi$
$193$	23.6143	1.69980	0.849898	+	0.526948i	$0.176664\pi$
$194$	1.12314	0.0806365
$195$	−2.97139	−0.212786
$196$	15.9258	1.13756
$197$	15.2682	1.08781	0.543906	−	0.839146i	$-0.316945\pi$
$197$	15.2682	1.08781	0.543906	+	0.839146i	$0.316945\pi$
$198$	−2.58330	−0.183587
$199$	−25.2987	−1.79338	−0.896688	−	0.442664i	$-0.854034\pi$
$199$	−25.2987	−1.79338	−0.896688	+	0.442664i	$0.854034\pi$
$200$	1.04159	0.0736512
$201$	−12.0240	−0.848106
$202$	27.8255	1.95780
$203$	−5.63253	−0.395326
$204$	8.13012	0.569222
$205$	9.81542	0.685539
$206$	−23.1704	−1.61436
$207$	0	0
$208$	−14.2862	−0.990570
$209$	9.82062	0.679306
$210$	−7.88285	−0.543969
$211$	−21.8846	−1.50660	−0.753299	−	0.657678i	$-0.771539\pi$
$211$	−21.8846	−1.50660	−0.753299	+	0.657678i	$0.771539\pi$
$212$	11.6459	0.799841
$213$	10.1535	0.695708
$214$	−12.0376	−0.822872
$215$	−10.7813	−0.735278
$216$	1.04159	0.0708709
$217$	−15.1760	−1.03021
$218$	4.50686	0.305243
$219$	−9.15769	−0.618819
$220$	−2.00376	−0.135093
$221$	16.7964	1.12985
$222$	−6.80721	−0.456870
$223$	−7.25441	−0.485792	−0.242896	−	0.970052i	$-0.578097\pi$
$223$	−7.25441	−0.485792	−0.242896	+	0.970052i	$0.578097\pi$
$224$	−29.0441	−1.94059
$225$	1.00000	0.0666667
$226$	12.5340	0.833747
$227$	24.3482	1.61605	0.808025	−	0.589149i	$-0.200537\pi$
$227$	24.3482	1.61605	0.808025	+	0.589149i	$0.200537\pi$
$228$	10.1386	0.671443
$229$	6.29607	0.416056	0.208028	−	0.978123i	$-0.433295\pi$
$229$	6.29607	0.416056	0.208028	+	0.978123i	$0.433295\pi$
$230$	0	0
$231$	−5.92267	−0.389683
$232$	1.38002	0.0906027
$233$	0.805160	0.0527478	0.0263739	−	0.999652i	$-0.491604\pi$
$233$	0.805160	0.0527478	0.0263739	+	0.999652i	$0.491604\pi$
$234$	−5.50973	−0.360182
$235$	7.10309	0.463355
$236$	−0.204232	−0.0132944
$237$	6.16073	0.400183
$238$	44.5594	2.88835
$239$	−5.11824	−0.331071	−0.165536	−	0.986204i	$-0.552935\pi$
$239$	−5.11824	−0.331071	−0.165536	+	0.986204i	$0.552935\pi$
$240$	4.80792	0.310350
$241$	22.8101	1.46933	0.734663	−	0.678432i	$-0.237340\pi$
$241$	22.8101	1.46933	0.734663	+	0.678432i	$0.237340\pi$
$242$	16.7979	1.07981
$243$	1.00000	0.0641500
$244$	−5.21967	−0.334155
$245$	−11.0728	−0.707418
$246$	18.2003	1.16041
$247$	20.9457	1.33274
$248$	3.71825	0.236109
$249$	16.6390	1.05446
$250$	1.85426	0.117274
$251$	24.2557	1.53100	0.765502	−	0.643433i	$-0.222490\pi$
$251$	24.2557	1.53100	0.765502	+	0.643433i	$0.222490\pi$
$252$	−6.11441	−0.385172
$253$	0	0
$254$	32.5592	2.04294
$255$	−5.65269	−0.353985
$256$	20.9463	1.30914
$257$	16.1288	1.00609	0.503043	−	0.864261i	$-0.332214\pi$
$257$	16.1288	1.00609	0.503043	+	0.864261i	$0.332214\pi$
$258$	−19.9913	−1.24460
$259$	−15.6067	−0.969755
$260$	−4.27368	−0.265042
$261$	1.32492	0.0820106
$262$	26.9101	1.66251
$263$	−20.2298	−1.24742	−0.623711	−	0.781655i	$-0.714376\pi$
$263$	−20.2298	−1.24742	−0.623711	+	0.781655i	$0.714376\pi$
$264$	1.45110	0.0893093
$265$	−8.09711	−0.497402
$266$	55.5672	3.40704
$267$	8.30577	0.508305
$268$	−17.2938	−1.05639
$269$	10.4228	0.635488	0.317744	−	0.948177i	$-0.397075\pi$
$269$	10.4228	0.635488	0.317744	+	0.948177i	$0.397075\pi$
$270$	1.85426	0.112847
$271$	19.8990	1.20878	0.604391	−	0.796688i	$-0.293417\pi$
$271$	19.8990	1.20878	0.604391	+	0.796688i	$0.293417\pi$
$272$	−27.1777	−1.64789
$273$	−12.6320	−0.764525
$274$	−24.2489	−1.46493
$275$	1.39317	0.0840113
$276$	0	0
$277$	−5.79251	−0.348038	−0.174019	−	0.984742i	$-0.555675\pi$
$277$	−5.79251	−0.348038	−0.174019	+	0.984742i	$0.555675\pi$
$278$	−3.32809	−0.199606
$279$	3.56980	0.213719
$280$	4.42800	0.264624
$281$	2.83200	0.168943	0.0844713	−	0.996426i	$-0.473080\pi$
$281$	2.83200	0.168943	0.0844713	+	0.996426i	$0.473080\pi$
$282$	13.1710	0.784320
$283$	−30.7865	−1.83007	−0.915035	−	0.403376i	$-0.867837\pi$
$283$	−30.7865	−1.83007	−0.915035	+	0.403376i	$0.867837\pi$
$284$	14.6035	0.866561
$285$	−7.04912	−0.417554
$286$	−7.67599	−0.453891
$287$	41.7275	2.46309
$288$	6.83195	0.402576
$289$	14.9529	0.879585
$290$	2.45675	0.144265
$291$	−0.605707	−0.0355072
$292$	−13.1713	−0.770790
$293$	27.6214	1.61366	0.806829	−	0.590784i	$-0.201182\pi$
$293$	27.6214	1.61366	0.806829	+	0.590784i	$0.201182\pi$
$294$	−20.5319	−1.19745
$295$	0.141998	0.00826746
$296$	3.82379	0.222253
$297$	1.39317	0.0808399
$298$	10.0476	0.582042
$299$	0	0
$300$	1.43827	0.0830388
$301$	−45.8336	−2.64181
$302$	2.06372	0.118754
$303$	−15.0063	−0.862089
$304$	−33.8916	−1.94381
$305$	3.62912	0.207803
$306$	−10.4816	−0.599191
$307$	8.39750	0.479270	0.239635	−	0.970863i	$-0.422972\pi$
$307$	8.39750	0.479270	0.239635	+	0.970863i	$0.422972\pi$
$308$	−8.51842	−0.485382
$309$	12.4958	0.710860
$310$	6.61934	0.375953
$311$	15.8068	0.896319	0.448160	−	0.893954i	$-0.352080\pi$
$311$	15.8068	0.896319	0.448160	+	0.893954i	$0.352080\pi$
$312$	3.09496	0.175217
$313$	9.67365	0.546787	0.273394	−	0.961902i	$-0.411854\pi$
$313$	9.67365	0.546787	0.273394	+	0.961902i	$0.411854\pi$
$314$	33.8951	1.91281
$315$	4.25122	0.239529
$316$	8.86082	0.498460
$317$	15.3176	0.860323	0.430161	−	0.902752i	$-0.358457\pi$
$317$	15.3176	0.860323	0.430161	+	0.902752i	$0.358457\pi$
$318$	−15.0141	−0.841951
$319$	1.84584	0.103347
$320$	3.05236	0.170632
$321$	6.49186	0.362340
$322$	0	0
$323$	39.8465	2.21712
$324$	1.43827	0.0799041
$325$	2.97139	0.164823
$326$	−16.4530	−0.911250
$327$	−2.43055	−0.134409
$328$	−10.2236	−0.564504
$329$	30.1968	1.66480
$330$	2.58330	0.142206
$331$	28.5783	1.57081	0.785403	−	0.618985i	$-0.212456\pi$
$331$	28.5783	1.57081	0.785403	+	0.618985i	$0.212456\pi$
$332$	23.9315	1.31341
$333$	3.67112	0.201176
$334$	−3.85906	−0.211158
$335$	12.0240	0.656940
$336$	20.4395	1.11507
$337$	−19.0615	−1.03835	−0.519173	−	0.854669i	$-0.673760\pi$
$337$	−19.0615	−1.03835	−0.519173	+	0.854669i	$0.673760\pi$
$338$	7.73379	0.420663
$339$	−6.75955	−0.367129
$340$	−8.13012	−0.440918
$341$	4.97334	0.269322
$342$	−13.0709	−0.706792
$343$	−17.3145	−0.934898
$344$	11.2296	0.605461
$345$	0	0
$346$	−0.582391	−0.0313095
$347$	28.3518	1.52200	0.761002	−	0.648749i	$-0.224708\pi$
$347$	28.3518	1.52200	0.761002	+	0.648749i	$0.224708\pi$
$348$	1.90560	0.102151
$349$	−30.7164	−1.64421	−0.822106	−	0.569334i	$-0.807201\pi$
$349$	−30.7164	−1.64421	−0.822106	+	0.569334i	$0.807201\pi$
$350$	7.88285	0.421356
$351$	2.97139	0.158601
$352$	9.51806	0.507314
$353$	−17.2355	−0.917354	−0.458677	−	0.888603i	$-0.651677\pi$
$353$	−17.2355	−0.917354	−0.458677	+	0.888603i	$0.651677\pi$
$354$	0.263301	0.0139943
$355$	−10.1535	−0.538893
$356$	11.9460	0.633135
$357$	−24.0308	−1.27185
$358$	−19.0210	−1.00529
$359$	−24.8169	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$359$	−24.8169	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$360$	−1.04159	−0.0548964
$361$	30.6901	1.61527
$362$	24.1414	1.26884
$363$	−9.05908	−0.475478
$364$	−18.1683	−0.952279
$365$	9.15769	0.479335
$366$	6.72933	0.351748
$367$	−18.3101	−0.955778	−0.477889	−	0.878420i	$-0.658598\pi$
$367$	−18.3101	−0.955778	−0.477889	+	0.878420i	$0.658598\pi$
$368$	0	0
$369$	−9.81542	−0.510970
$370$	6.80721	0.353890
$371$	−34.4226	−1.78713
$372$	5.13436	0.266204
$373$	11.8267	0.612362	0.306181	−	0.951973i	$-0.400949\pi$
$373$	11.8267	0.612362	0.306181	+	0.951973i	$0.400949\pi$
$374$	−14.6026	−0.755082
$375$	−1.00000	−0.0516398
$376$	−7.39848	−0.381547
$377$	3.93686	0.202759
$378$	7.88285	0.405450
$379$	−28.5489	−1.46646	−0.733230	−	0.679981i	$-0.761988\pi$
$379$	−28.5489	−1.46646	−0.733230	+	0.679981i	$0.761988\pi$
$380$	−10.1386	−0.520097
$381$	−17.5591	−0.899582
$382$	9.05226	0.463154
$383$	−1.42176	−0.0726486	−0.0363243	−	0.999340i	$-0.511565\pi$
$383$	−1.42176	−0.0726486	−0.0363243	+	0.999340i	$0.511565\pi$
$384$	−8.00402	−0.408454
$385$	5.92267	0.301847
$386$	−43.7870	−2.22870
$387$	10.7813	0.548044
$388$	−0.871172	−0.0442271
$389$	0.0272669	0.00138249	0.000691244	−	1.00000i	$-0.499780\pi$
$389$	0.0272669	0.00138249	0.000691244		1.00000i	$0.499780\pi$
$390$	5.50973	0.278996
$391$	0	0
$392$	11.5333	0.582520
$393$	−14.5126	−0.732062
$394$	−28.3111	−1.42629
$395$	−6.16073	−0.309980
$396$	2.00376	0.100693
$397$	31.6029	1.58610	0.793052	−	0.609154i	$-0.208491\pi$
$397$	31.6029	1.58610	0.793052	+	0.609154i	$0.208491\pi$
$398$	46.9103	2.35140
$399$	−29.9673	−1.50024
$400$	−4.80792	−0.240396
$401$	−15.5880	−0.778427	−0.389213	−	0.921148i	$-0.627253\pi$
$401$	−15.5880	−0.778427	−0.389213	+	0.921148i	$0.627253\pi$
$402$	22.2956	1.11200
$403$	10.6073	0.528387
$404$	−21.5832	−1.07380
$405$	−1.00000	−0.0496904
$406$	10.4442	0.518335
$407$	5.11450	0.253516
$408$	5.88776	0.291488
$409$	1.44531	0.0714661	0.0357330	−	0.999361i	$-0.488623\pi$
$409$	1.44531	0.0714661	0.0357330	+	0.999361i	$0.488623\pi$
$410$	−18.2003	−0.898850
$411$	13.0774	0.645061
$412$	17.9724	0.885435
$413$	0.603665	0.0297044
$414$	0	0
$415$	−16.6390	−0.816779
$416$	20.3004	0.995309
$417$	1.79484	0.0878936
$418$	−18.2100	−0.890678
$419$	2.03085	0.0992137	0.0496068	−	0.998769i	$-0.484203\pi$
$419$	2.03085	0.0992137	0.0496068	+	0.998769i	$0.484203\pi$
$420$	6.11441	0.298353
$421$	20.8011	1.01378	0.506892	−	0.862010i	$-0.330794\pi$
$421$	20.8011	1.01378	0.506892	+	0.862010i	$0.330794\pi$
$422$	40.5797	1.97539
$423$	−7.10309	−0.345364
$424$	8.43383	0.409583
$425$	5.65269	0.274196
$426$	−18.8273	−0.912184
$427$	15.4282	0.746623
$428$	9.33707	0.451324
$429$	4.13965	0.199864
$430$	19.9913	0.964066
$431$	21.7967	1.04991	0.524954	−	0.851131i	$-0.324082\pi$
$431$	21.7967	1.04991	0.524954	+	0.851131i	$0.324082\pi$
$432$	−4.80792	−0.231321
$433$	29.7112	1.42783	0.713915	−	0.700232i	$-0.246920\pi$
$433$	29.7112	1.42783	0.713915	+	0.700232i	$0.246920\pi$
$434$	28.1402	1.35077
$435$	−1.32492	−0.0635252
$436$	−3.49579	−0.167418
$437$	0	0
$438$	16.9807	0.811370
$439$	−11.7444	−0.560528	−0.280264	−	0.959923i	$-0.590422\pi$
$439$	−11.7444	−0.560528	−0.280264	+	0.959923i	$0.590422\pi$
$440$	−1.45110	−0.0691787
$441$	11.0728	0.527278
$442$	−31.1448	−1.48141
$443$	5.43364	0.258160	0.129080	−	0.991634i	$-0.458798\pi$
$443$	5.43364	0.258160	0.129080	+	0.991634i	$0.458798\pi$
$444$	5.28008	0.250581
$445$	−8.30577	−0.393731
$446$	13.4516	0.636950
$447$	−5.41867	−0.256294
$448$	12.9763	0.613071
$449$	−18.5452	−0.875202	−0.437601	−	0.899169i	$-0.644172\pi$
$449$	−18.5452	−0.875202	−0.437601	+	0.899169i	$0.644172\pi$
$450$	−1.85426	−0.0874106
$451$	−13.6745	−0.643909
$452$	−9.72209	−0.457289
$453$	−1.11296	−0.0522914
$454$	−45.1479	−2.11890
$455$	12.6320	0.592199
$456$	7.34226	0.343833
$457$	−15.5338	−0.726640	−0.363320	−	0.931664i	$-0.618357\pi$
$457$	−15.5338	−0.726640	−0.363320	+	0.931664i	$0.618357\pi$
$458$	−11.6745	−0.545516
$459$	5.65269	0.263845
$460$	0	0
$461$	27.2456	1.26896	0.634478	−	0.772941i	$-0.281215\pi$
$461$	27.2456	1.26896	0.634478	+	0.772941i	$0.281215\pi$
$462$	10.9822	0.510936
$463$	−12.3876	−0.575700	−0.287850	−	0.957676i	$-0.592940\pi$
$463$	−12.3876	−0.575700	−0.287850	+	0.957676i	$0.592940\pi$
$464$	−6.37012	−0.295725
$465$	−3.56980	−0.165546
$466$	−1.49298	−0.0691607
$467$	30.9384	1.43166	0.715828	−	0.698276i	$-0.246049\pi$
$467$	30.9384	1.43166	0.715828	+	0.698276i	$0.246049\pi$
$468$	4.27368	0.197551
$469$	51.1165	2.36034
$470$	−13.1710	−0.607532
$471$	−18.2796	−0.842279
$472$	−0.147903	−0.00680780
$473$	15.0202	0.690628
$474$	−11.4236	−0.524703
$475$	7.04912	0.323436
$476$	−34.5629	−1.58419
$477$	8.09711	0.370741
$478$	9.49054	0.434087
$479$	−11.2174	−0.512535	−0.256268	−	0.966606i	$-0.582493\pi$
$479$	−11.2174	−0.512535	−0.256268	+	0.966606i	$0.582493\pi$
$480$	−6.83195	−0.311834
$481$	10.9083	0.497378
$482$	−42.2958	−1.92652
$483$	0	0
$484$	−13.0294	−0.592247
$485$	0.605707	0.0275037
$486$	−1.85426	−0.0841109
$487$	18.8663	0.854916	0.427458	−	0.904035i	$-0.359409\pi$
$487$	18.8663	0.854916	0.427458	+	0.904035i	$0.359409\pi$
$488$	−3.78004	−0.171114
$489$	8.87311	0.401256
$490$	20.5319	0.927537
$491$	−11.0118	−0.496956	−0.248478	−	0.968638i	$-0.579930\pi$
$491$	−11.0118	−0.496956	−0.248478	+	0.968638i	$0.579930\pi$
$492$	−14.1173	−0.636455
$493$	7.48938	0.337305
$494$	−38.8387	−1.74744
$495$	−1.39317	−0.0626183
$496$	−17.1633	−0.770656
$497$	−43.1648	−1.93621
$498$	−30.8531	−1.38256
$499$	−11.9591	−0.535363	−0.267682	−	0.963507i	$-0.586258\pi$
$499$	−11.9591	−0.535363	−0.267682	+	0.963507i	$0.586258\pi$
$500$	−1.43827	−0.0643216
$501$	2.08119	0.0929806
$502$	−44.9763	−2.00739
$503$	28.3704	1.26497	0.632486	−	0.774572i	$-0.282035\pi$
$503$	28.3704	1.26497	0.632486	+	0.774572i	$0.282035\pi$
$504$	−4.42800	−0.197239
$505$	15.0063	0.667771
$506$	0	0
$507$	−4.17083	−0.185233
$508$	−25.2548	−1.12050
$509$	24.3425	1.07896	0.539480	−	0.841998i	$-0.318621\pi$
$509$	24.3425	1.07896	0.539480	+	0.841998i	$0.318621\pi$
$510$	10.4816	0.464131
$511$	38.9313	1.72222
$512$	−22.8317	−1.00903
$513$	7.04912	0.311226
$514$	−29.9070	−1.31914
$515$	−12.4958	−0.550630
$516$	15.5065	0.682634
$517$	−9.89581	−0.435217
$518$	28.9389	1.27150
$519$	0.314083	0.0137867
$520$	−3.09496	−0.135723
$521$	16.4075	0.718827	0.359414	−	0.933178i	$-0.382977\pi$
$521$	16.4075	0.718827	0.359414	+	0.933178i	$0.382977\pi$
$522$	−2.45675	−0.107529
$523$	13.7353	0.600601	0.300301	−	0.953845i	$-0.402913\pi$
$523$	13.7353	0.600601	0.300301	+	0.953845i	$0.402913\pi$
$524$	−20.8731	−0.911843
$525$	−4.25122	−0.185538
$526$	37.5112	1.63557
$527$	20.1790	0.879011
$528$	−6.69824	−0.291504
$529$	0	0
$530$	15.0141	0.652172
$531$	−0.141998	−0.00616220
$532$	−43.1012	−1.86868
$533$	−29.1655	−1.26330
$534$	−15.4010	−0.666468
$535$	−6.49186	−0.280668
$536$	−12.5240	−0.540954
$537$	10.2580	0.442665
$538$	−19.3265	−0.833225
$539$	15.4264	0.664460
$540$	−1.43827	−0.0618935
$541$	2.16873	0.0932410	0.0466205	−	0.998913i	$-0.485155\pi$
$541$	2.16873	0.0932410	0.0466205	+	0.998913i	$0.485155\pi$
$542$	−36.8980	−1.58490
$543$	−13.0194	−0.558717
$544$	38.6189	1.65577
$545$	2.43055	0.104113
$546$	23.4231	1.00241
$547$	29.7021	1.26997	0.634986	−	0.772524i	$-0.281006\pi$
$547$	29.7021	1.26997	0.634986	+	0.772524i	$0.281006\pi$
$548$	18.8089	0.803476
$549$	−3.62912	−0.154887
$550$	−2.58330	−0.110152
$551$	9.33953	0.397877
$552$	0	0
$553$	−26.1906	−1.11374
$554$	10.7408	0.456333
$555$	−3.67112	−0.155830
$556$	2.58147	0.109479
$557$	−23.4072	−0.991794	−0.495897	−	0.868381i	$-0.665161\pi$
$557$	−23.4072	−0.991794	−0.495897	+	0.868381i	$0.665161\pi$
$558$	−6.61934	−0.280219
$559$	32.0355	1.35496
$560$	−20.4395	−0.863726
$561$	7.87516	0.332490
$562$	−5.25125	−0.221511
$563$	−37.5688	−1.58334	−0.791669	−	0.610951i	$-0.790787\pi$
$563$	−37.5688	−1.58334	−0.791669	+	0.610951i	$0.790787\pi$
$564$	−10.2162	−0.430179
$565$	6.75955	0.284377
$566$	57.0862	2.39951
$567$	−4.25122	−0.178534
$568$	10.5758	0.443749
$569$	−2.94288	−0.123372	−0.0616860	−	0.998096i	$-0.519648\pi$
$569$	−2.94288	−0.123372	−0.0616860	+	0.998096i	$0.519648\pi$
$570$	13.0709	0.547479
$571$	−20.8623	−0.873058	−0.436529	−	0.899690i	$-0.643792\pi$
$571$	−20.8623	−0.873058	−0.436529	+	0.899690i	$0.643792\pi$
$572$	5.95396	0.248947
$573$	−4.88188	−0.203943
$574$	−77.3735	−3.22951
$575$	0	0
$576$	−3.05236	−0.127182
$577$	25.3020	1.05334	0.526669	−	0.850071i	$-0.323441\pi$
$577$	25.3020	1.05334	0.526669	+	0.850071i	$0.323441\pi$
$578$	−27.7266	−1.15328
$579$	23.6143	0.981377
$580$	−1.90560	−0.0791258
$581$	−70.7362	−2.93463
$582$	1.12314	0.0465555
$583$	11.2806	0.467197
$584$	−9.53851	−0.394706
$585$	−2.97139	−0.122852
$586$	−51.2172	−2.11576
$587$	9.68936	0.399923	0.199961	−	0.979804i	$-0.435918\pi$
$587$	9.68936	0.399923	0.199961	+	0.979804i	$0.435918\pi$
$588$	15.9258	0.656768
$589$	25.1640	1.03686
$590$	−0.263301	−0.0108400
$591$	15.2682	0.628048
$592$	−17.6504	−0.725429
$593$	1.46234	0.0600510	0.0300255	−	0.999549i	$-0.490441\pi$
$593$	1.46234	0.0600510	0.0300255	+	0.999549i	$0.490441\pi$
$594$	−2.58330	−0.105994
$595$	24.0308	0.985168
$596$	−7.79353	−0.319235
$597$	−25.2987	−1.03541
$598$	0	0
$599$	−21.6389	−0.884143	−0.442071	−	0.896980i	$-0.645756\pi$
$599$	−21.6389	−0.884143	−0.442071	+	0.896980i	$0.645756\pi$
$600$	1.04159	0.0425225
$601$	5.78041	0.235788	0.117894	−	0.993026i	$-0.462386\pi$
$601$	5.78041	0.235788	0.117894	+	0.993026i	$0.462386\pi$
$602$	84.9874	3.46383
$603$	−12.0240	−0.489654
$604$	−1.60074	−0.0651333
$605$	9.05908	0.368304
$606$	27.8255	1.13034
$607$	−15.5294	−0.630317	−0.315159	−	0.949039i	$-0.602058\pi$
$607$	−15.5294	−0.630317	−0.315159	+	0.949039i	$0.602058\pi$
$608$	48.1592	1.95311
$609$	−5.63253	−0.228242
$610$	−6.72933	−0.272463
$611$	−21.1061	−0.853860
$612$	8.13012	0.328641
$613$	−0.679102	−0.0274287	−0.0137143	−	0.999906i	$-0.504366\pi$
$613$	−0.679102	−0.0274287	−0.0137143	+	0.999906i	$0.504366\pi$
$614$	−15.5711	−0.628400
$615$	9.81542	0.395796
$616$	−6.16896	−0.248555
$617$	−25.0527	−1.00858	−0.504292	−	0.863533i	$-0.668247\pi$
$617$	−25.0527	−1.00858	−0.504292	+	0.863533i	$0.668247\pi$
$618$	−23.1704	−0.932051
$619$	−20.9578	−0.842364	−0.421182	−	0.906976i	$-0.638385\pi$
$619$	−20.9578	−0.842364	−0.421182	+	0.906976i	$0.638385\pi$
$620$	−5.13436	−0.206201
$621$	0	0
$622$	−29.3098	−1.17522
$623$	−35.3096	−1.41465
$624$	−14.2862	−0.571906
$625$	1.00000	0.0400000
$626$	−17.9375	−0.716925
$627$	9.82062	0.392198
$628$	−26.2911	−1.04913
$629$	20.7517	0.827426
$630$	−7.88285	−0.314060
$631$	−40.7809	−1.62346	−0.811731	−	0.584031i	$-0.801475\pi$
$631$	−40.7809	−1.62346	−0.811731	+	0.584031i	$0.801475\pi$
$632$	6.41693	0.255252
$633$	−21.8846	−0.869835
$634$	−28.4028	−1.12802
$635$	17.5591	0.696813
$636$	11.6459	0.461788
$637$	32.9018	1.30362
$638$	−3.42267	−0.135505
$639$	10.1535	0.401667
$640$	8.00402	0.316387
$641$	−31.2458	−1.23413	−0.617067	−	0.786910i	$-0.711679\pi$
$641$	−31.2458	−1.23413	−0.617067	+	0.786910i	$0.711679\pi$
$642$	−12.0376	−0.475085
$643$	−12.7000	−0.500841	−0.250420	−	0.968137i	$-0.580569\pi$
$643$	−12.7000	−0.500841	−0.250420	+	0.968137i	$0.580569\pi$
$644$	0	0
$645$	−10.7813	−0.424513
$646$	−73.8857	−2.90699
$647$	−36.9130	−1.45120	−0.725599	−	0.688117i	$-0.758437\pi$
$647$	−36.9130	−1.45120	−0.725599	+	0.688117i	$0.758437\pi$
$648$	1.04159	0.0409173
$649$	−0.197828	−0.00776542
$650$	−5.50973	−0.216109
$651$	−15.1760	−0.594795
$652$	12.7620	0.499797
$653$	29.4553	1.15267	0.576337	−	0.817212i	$-0.304482\pi$
$653$	29.4553	1.15267	0.576337	+	0.817212i	$0.304482\pi$
$654$	4.50686	0.176232
$655$	14.5126	0.567053
$656$	47.1917	1.84253
$657$	−9.15769	−0.357275
$658$	−55.9927	−2.18282
$659$	20.4157	0.795284	0.397642	−	0.917541i	$-0.369829\pi$
$659$	20.4157	0.795284	0.397642	+	0.917541i	$0.369829\pi$
$660$	−2.00376	−0.0779962
$661$	24.5671	0.955549	0.477774	−	0.878483i	$-0.341444\pi$
$661$	24.5671	0.955549	0.477774	+	0.878483i	$0.341444\pi$
$662$	−52.9916	−2.05958
$663$	16.7964	0.652317
$664$	17.3310	0.672573
$665$	29.9673	1.16208
$666$	−6.80721	−0.263774
$667$	0	0
$668$	2.99332	0.115815
$669$	−7.25441	−0.280472
$670$	−22.2956	−0.861353
$671$	−5.05598	−0.195184
$672$	−29.0441	−1.12040
$673$	16.3296	0.629459	0.314730	−	0.949181i	$-0.398086\pi$
$673$	16.3296	0.629459	0.314730	+	0.949181i	$0.398086\pi$
$674$	35.3450	1.36144
$675$	1.00000	0.0384900
$676$	−5.99879	−0.230723
$677$	35.0814	1.34829	0.674145	−	0.738599i	$-0.264512\pi$
$677$	35.0814	1.34829	0.674145	+	0.738599i	$0.264512\pi$
$678$	12.5340	0.481364
$679$	2.57499	0.0988191
$680$	−5.88776	−0.225785
$681$	24.3482	0.933027
$682$	−9.22186	−0.353123
$683$	−24.4947	−0.937262	−0.468631	−	0.883394i	$-0.655253\pi$
$683$	−24.4947	−0.937262	−0.468631	+	0.883394i	$0.655253\pi$
$684$	10.1386	0.387658
$685$	−13.0774	−0.499662
$686$	32.1056	1.22580
$687$	6.29607	0.240210
$688$	−51.8356	−1.97621
$689$	24.0597	0.916601
$690$	0	0
$691$	−6.42675	−0.244485	−0.122242	−	0.992500i	$-0.539009\pi$
$691$	−6.42675	−0.244485	−0.122242	+	0.992500i	$0.539009\pi$
$692$	0.451737	0.0171725
$693$	−5.92267	−0.224983
$694$	−52.5716	−1.99559
$695$	−1.79484	−0.0680821
$696$	1.38002	0.0523095
$697$	−55.4835	−2.10159
$698$	56.9562	2.15582
$699$	0.805160	0.0304540
$700$	−6.11441	−0.231103
$701$	13.9361	0.526358	0.263179	−	0.964747i	$-0.415229\pi$
$701$	13.9361	0.526358	0.263179	+	0.964747i	$0.415229\pi$
$702$	−5.50973	−0.207951
$703$	25.8782	0.976014
$704$	−4.25246	−0.160271
$705$	7.10309	0.267518
$706$	31.9591	1.20280
$707$	63.7950	2.39926
$708$	−0.204232	−0.00767552
$709$	34.5931	1.29917	0.649586	−	0.760288i	$-0.274942\pi$
$709$	34.5931	1.29917	0.649586	+	0.760288i	$0.274942\pi$
$710$	18.8273	0.706574
$711$	6.16073	0.231046
$712$	8.65116	0.324216
$713$	0	0
$714$	44.5594	1.66759
$715$	−4.13965	−0.154814
$716$	14.7538	0.551375
$717$	−5.11824	−0.191144
$718$	46.0169	1.71733
$719$	−28.2432	−1.05329	−0.526647	−	0.850084i	$-0.676551\pi$
$719$	−28.2432	−1.05329	−0.526647	+	0.850084i	$0.676551\pi$
$720$	4.80792	0.179180
$721$	−53.1223	−1.97838
$722$	−56.9073	−2.11787
$723$	22.8101	0.848316
$724$	−18.7255	−0.695928
$725$	1.32492	0.0492064
$726$	16.7979	0.623427
$727$	−9.46297	−0.350962	−0.175481	−	0.984483i	$-0.556148\pi$
$727$	−9.46297	−0.350962	−0.175481	+	0.984483i	$0.556148\pi$
$728$	−13.1573	−0.487643
$729$	1.00000	0.0370370
$730$	−16.9807	−0.628484
$731$	60.9434	2.25407
$732$	−5.21967	−0.192925
$733$	−32.6884	−1.20737	−0.603686	−	0.797222i	$-0.706302\pi$
$733$	−32.6884	−1.20737	−0.603686	+	0.797222i	$0.706302\pi$
$734$	33.9516	1.25318
$735$	−11.0728	−0.408428
$736$	0	0
$737$	−16.7514	−0.617047
$738$	18.2003	0.669963
$739$	0.857460	0.0315422	0.0157711	−	0.999876i	$-0.494980\pi$
$739$	0.857460	0.0315422	0.0157711	+	0.999876i	$0.494980\pi$
$740$	−5.28008	−0.194100
$741$	20.9457	0.769459
$742$	63.8283	2.34321
$743$	24.8546	0.911828	0.455914	−	0.890024i	$-0.349312\pi$
$743$	24.8546	0.911828	0.455914	+	0.890024i	$0.349312\pi$
$744$	3.71825	0.136318
$745$	5.41867	0.198525
$746$	−21.9297	−0.802904
$747$	16.6390	0.608791
$748$	11.3266	0.414143
$749$	−27.5983	−1.00842
$750$	1.85426	0.0677079
$751$	18.6559	0.680764	0.340382	−	0.940287i	$-0.389444\pi$
$751$	18.6559	0.680764	0.340382	+	0.940287i	$0.389444\pi$
$752$	34.1511	1.24536
$753$	24.2557	0.883926
$754$	−7.29996	−0.265849
$755$	1.11296	0.0405048
$756$	−6.11441	−0.222379
$757$	17.9776	0.653408	0.326704	−	0.945127i	$-0.394062\pi$
$757$	17.9776	0.653408	0.326704	+	0.945127i	$0.394062\pi$
$758$	52.9371	1.92276
$759$	0	0
$760$	−7.34226	−0.266332
$761$	20.8296	0.755072	0.377536	−	0.925995i	$-0.376771\pi$
$761$	20.8296	0.755072	0.377536	+	0.925995i	$0.376771\pi$
$762$	32.5592	1.17949
$763$	10.3328	0.374072
$764$	−7.02148	−0.254028
$765$	−5.65269	−0.204374
$766$	2.63631	0.0952538
$767$	−0.421933	−0.0152351
$768$	20.9463	0.755833
$769$	45.5899	1.64401	0.822006	−	0.569478i	$-0.192855\pi$
$769$	45.5899	1.64401	0.822006	+	0.569478i	$0.192855\pi$
$770$	−10.9822	−0.395769
$771$	16.1288	0.580864
$772$	33.9638	1.22239
$773$	35.0873	1.26200	0.631000	−	0.775782i	$-0.282645\pi$
$773$	35.0873	1.26200	0.631000	+	0.775782i	$0.282645\pi$
$774$	−19.9913	−0.718573
$775$	3.56980	0.128231
$776$	−0.630895	−0.0226478
$777$	−15.6067	−0.559889
$778$	−0.0505600	−0.00181266
$779$	−69.1900	−2.47899
$780$	−4.27368	−0.153022
$781$	14.1456	0.506169
$782$	0	0
$783$	1.32492	0.0473489
$784$	−53.2373	−1.90133
$785$	18.2796	0.652426
$786$	26.9101	0.959850
$787$	−11.2816	−0.402146	−0.201073	−	0.979576i	$-0.564443\pi$
$787$	−11.2816	−0.402146	−0.201073	+	0.979576i	$0.564443\pi$
$788$	21.9598	0.782285
$789$	−20.2298	−0.720199
$790$	11.4236	0.406433
$791$	28.7363	1.02175
$792$	1.45110	0.0515628
$793$	−10.7835	−0.382935
$794$	−58.5999	−2.07963
$795$	−8.09711	−0.287175
$796$	−36.3864	−1.28968
$797$	41.2567	1.46139	0.730693	−	0.682706i	$-0.239197\pi$
$797$	41.2567	1.46139	0.730693	+	0.682706i	$0.239197\pi$
$798$	55.5672	1.96706
$799$	−40.1516	−1.42046
$800$	6.83195	0.241546
$801$	8.30577	0.293470
$802$	28.9042	1.02064
$803$	−12.7582	−0.450227
$804$	−17.2938	−0.609904
$805$	0	0
$806$	−19.6686	−0.692799
$807$	10.4228	0.366899
$808$	−15.6303	−0.549873
$809$	7.17448	0.252241	0.126121	−	0.992015i	$-0.459747\pi$
$809$	7.17448	0.252241	0.126121	+	0.992015i	$0.459747\pi$
$810$	1.85426	0.0651520
$811$	−23.2660	−0.816981	−0.408490	−	0.912763i	$-0.633945\pi$
$811$	−23.2660	−0.816981	−0.408490	+	0.912763i	$0.633945\pi$
$812$	−8.10112	−0.284294
$813$	19.8990	0.697890
$814$	−9.48360	−0.332400
$815$	−8.87311	−0.310812
$816$	−27.1777	−0.951409
$817$	75.9986	2.65885
$818$	−2.67998	−0.0937034
$819$	−12.6320	−0.441399
$820$	14.1173	0.492996
$821$	23.3620	0.815339	0.407670	−	0.913130i	$-0.366342\pi$
$821$	23.3620	0.815339	0.407670	+	0.913130i	$0.366342\pi$
$822$	−24.2489	−0.845777
$823$	−44.7202	−1.55885	−0.779425	−	0.626496i	$-0.784489\pi$
$823$	−44.7202	−1.55885	−0.779425	+	0.626496i	$0.784489\pi$
$824$	13.0154	0.453414
$825$	1.39317	0.0485039
$826$	−1.11935	−0.0389472
$827$	45.9014	1.59615	0.798074	−	0.602559i	$-0.205852\pi$
$827$	45.9014	1.59615	0.798074	+	0.602559i	$0.205852\pi$
$828$	0	0
$829$	−14.9654	−0.519771	−0.259886	−	0.965639i	$-0.583685\pi$
$829$	−14.9654	−0.519771	−0.259886	+	0.965639i	$0.583685\pi$
$830$	30.8531	1.07093
$831$	−5.79251	−0.200940
$832$	−9.06977	−0.314438
$833$	62.5914	2.16866
$834$	−3.32809	−0.115242
$835$	−2.08119	−0.0720225
$836$	14.1247	0.488514
$837$	3.56980	0.123390
$838$	−3.76573	−0.130085
$839$	−42.7113	−1.47456	−0.737279	−	0.675588i	$-0.763890\pi$
$839$	−42.7113	−1.47456	−0.737279	+	0.675588i	$0.763890\pi$
$840$	4.42800	0.152781
$841$	−27.2446	−0.939468
$842$	−38.5706	−1.32923
$843$	2.83200	0.0975391
$844$	−31.4761	−1.08345
$845$	4.17083	0.143481
$846$	13.1710	0.452827
$847$	38.5121	1.32329
$848$	−38.9302	−1.33687
$849$	−30.7865	−1.05659
$850$	−10.4816	−0.359514
$851$	0	0
$852$	14.6035	0.500309
$853$	−36.6497	−1.25486	−0.627430	−	0.778673i	$-0.715893\pi$
$853$	−36.6497	−1.25486	−0.627430	+	0.778673i	$0.715893\pi$
$854$	−28.6079	−0.978941
$855$	−7.04912	−0.241075
$856$	6.76182	0.231114
$857$	9.51730	0.325105	0.162552	−	0.986700i	$-0.448027\pi$
$857$	9.51730	0.325105	0.162552	+	0.986700i	$0.448027\pi$
$858$	−7.67599	−0.262054
$859$	39.5028	1.34782	0.673910	−	0.738814i	$-0.264614\pi$
$859$	39.5028	1.34782	0.673910	+	0.738814i	$0.264614\pi$
$860$	−15.5065	−0.528766
$861$	41.7275	1.42207
$862$	−40.4166	−1.37660
$863$	−22.5176	−0.766506	−0.383253	−	0.923643i	$-0.625196\pi$
$863$	−22.5176	−0.766506	−0.383253	+	0.923643i	$0.625196\pi$
$864$	6.83195	0.232428
$865$	−0.314083	−0.0106791
$866$	−55.0923	−1.87211
$867$	14.9529	0.507829
$868$	−21.8273	−0.740865
$869$	8.58295	0.291157
$870$	2.45675	0.0832916
$871$	−35.7279	−1.21060
$872$	−2.53162	−0.0857315
$873$	−0.605707	−0.0205001
$874$	0	0
$875$	4.25122	0.143717
$876$	−13.1713	−0.445016
$877$	12.6736	0.427956	0.213978	−	0.976838i	$-0.431358\pi$
$877$	12.6736	0.427956	0.213978	+	0.976838i	$0.431358\pi$
$878$	21.7771	0.734941
$879$	27.6214	0.931646
$880$	6.69824	0.225798
$881$	−3.71042	−0.125007	−0.0625037	−	0.998045i	$-0.519909\pi$
$881$	−3.71042	−0.125007	−0.0625037	+	0.998045i	$0.519909\pi$
$882$	−20.5319	−0.691346
$883$	49.3332	1.66019	0.830097	−	0.557618i	$-0.188285\pi$
$883$	49.3332	1.66019	0.830097	+	0.557618i	$0.188285\pi$
$884$	24.1578	0.812514
$885$	0.141998	0.00477322
$886$	−10.0754	−0.338489
$887$	−49.1707	−1.65099	−0.825495	−	0.564409i	$-0.809104\pi$
$887$	−49.1707	−1.65099	−0.825495	+	0.564409i	$0.809104\pi$
$888$	3.82379	0.128318
$889$	74.6477	2.50360
$890$	15.4010	0.516244
$891$	1.39317	0.0466729
$892$	−10.4338	−0.349351
$893$	−50.0705	−1.67555
$894$	10.0476	0.336042
$895$	−10.2580	−0.342887
$896$	34.0268	1.13676
$897$	0	0
$898$	34.3876	1.14753
$899$	4.72971	0.157745
$900$	1.43827	0.0479425
$901$	45.7705	1.52484
$902$	25.3561	0.844267
$903$	−45.8336	−1.52525
$904$	−7.04065	−0.234169
$905$	13.0194	0.432780
$906$	2.06372	0.0685624
$907$	−44.3413	−1.47233	−0.736164	−	0.676803i	$-0.763365\pi$
$907$	−44.3413	−1.47233	−0.736164	+	0.676803i	$0.763365\pi$
$908$	35.0194	1.16216
$909$	−15.0063	−0.497727
$910$	−23.4231	−0.776467
$911$	1.43828	0.0476522	0.0238261	−	0.999716i	$-0.492415\pi$
$911$	1.43828	0.0476522	0.0238261	+	0.999716i	$0.492415\pi$
$912$	−33.8916	−1.12226
$913$	23.1810	0.767179
$914$	28.8037	0.952740
$915$	3.62912	0.119975
$916$	9.05548	0.299201
$917$	61.6961	2.03738
$918$	−10.4816	−0.345943
$919$	6.54051	0.215751	0.107876	−	0.994164i	$-0.465595\pi$
$919$	6.54051	0.215751	0.107876	+	0.994164i	$0.465595\pi$
$920$	0	0
$921$	8.39750	0.276707
$922$	−50.5204	−1.66380
$923$	30.1701	0.993061
$924$	−8.51842	−0.280235
$925$	3.67112	0.120706
$926$	22.9698	0.754834
$927$	12.4958	0.410415
$928$	9.05180	0.297140
$929$	−1.30347	−0.0427653	−0.0213827	−	0.999771i	$-0.506807\pi$
$929$	−1.30347	−0.0427653	−0.0213827	+	0.999771i	$0.506807\pi$
$930$	6.61934	0.217057
$931$	78.0538	2.55811
$932$	1.15804	0.0379329
$933$	15.8068	0.517490
$934$	−57.3677	−1.87713
$935$	−7.87516	−0.257545
$936$	3.09496	0.101162
$937$	13.2941	0.434298	0.217149	−	0.976138i	$-0.430324\pi$
$937$	13.2941	0.434298	0.217149	+	0.976138i	$0.430324\pi$
$938$	−94.7833	−3.09478
$939$	9.67365	0.315688
$940$	10.2162	0.333216
$941$	−8.92964	−0.291098	−0.145549	−	0.989351i	$-0.546495\pi$
$941$	−8.92964	−0.291098	−0.145549	+	0.989351i	$0.546495\pi$
$942$	33.8951	1.10436
$943$	0	0
$944$	0.682716	0.0222205
$945$	4.25122	0.138292
$946$	−27.8513	−0.905523
$947$	10.1450	0.329667	0.164834	−	0.986321i	$-0.447291\pi$
$947$	10.1450	0.329667	0.164834	+	0.986321i	$0.447291\pi$
$948$	8.86082	0.287786
$949$	−27.2111	−0.883309
$950$	−13.0709	−0.424075
$951$	15.3176	0.496707
$952$	−25.0302	−0.811232
$953$	−24.5953	−0.796720	−0.398360	−	0.917229i	$-0.630421\pi$
$953$	−24.5953	−0.796720	−0.398360	+	0.917229i	$0.630421\pi$
$954$	−15.0141	−0.486101
$955$	4.88188	0.157974
$956$	−7.36143	−0.238086
$957$	1.84584	0.0596676
$958$	20.7999	0.672015
$959$	−55.5949	−1.79525
$960$	3.05236	0.0985146
$961$	−18.2565	−0.588919
$962$	−20.2269	−0.652141
$963$	6.49186	0.209197
$964$	32.8071	1.05665
$965$	−23.6143	−0.760171
$966$	0	0
$967$	17.6489	0.567551	0.283776	−	0.958891i	$-0.408413\pi$
$967$	17.6489	0.567551	0.283776	+	0.958891i	$0.408413\pi$
$968$	−9.43580	−0.303278
$969$	39.8465	1.28005
$970$	−1.12314	−0.0360618
$971$	−31.3835	−1.00714	−0.503572	−	0.863953i	$-0.667981\pi$
$971$	−31.3835	−1.00714	−0.503572	+	0.863953i	$0.667981\pi$
$972$	1.43827	0.0461327
$973$	−7.63025	−0.244615
$974$	−34.9831	−1.12093
$975$	2.97139	0.0951607
$976$	17.4485	0.558514
$977$	19.3981	0.620601	0.310300	−	0.950639i	$-0.399570\pi$
$977$	19.3981	0.620601	0.310300	+	0.950639i	$0.399570\pi$
$978$	−16.4530	−0.526110
$979$	11.5713	0.369822
$980$	−15.9258	−0.508731
$981$	−2.43055	−0.0776013
$982$	20.4187	0.651588
$983$	33.2323	1.05994	0.529972	−	0.848015i	$-0.322202\pi$
$983$	33.2323	1.05994	0.529972	+	0.848015i	$0.322202\pi$
$984$	−10.2236	−0.325916
$985$	−15.2682	−0.486484
$986$	−13.8872	−0.442260
$987$	30.1968	0.961174
$988$	30.1256	0.958424
$989$	0	0
$990$	2.58330	0.0821025
$991$	−35.3281	−1.12223	−0.561117	−	0.827736i	$-0.689628\pi$
$991$	−35.3281	−1.12223	−0.561117	+	0.827736i	$0.689628\pi$
$992$	24.3887	0.774342
$993$	28.5783	0.906905
$994$	80.0388	2.53868
$995$	25.2987	0.802022
$996$	23.9315	0.758299
$997$	55.3859	1.75409	0.877044	−	0.480409i	$-0.159512\pi$
$997$	55.3859	1.75409	0.877044	+	0.480409i	$0.159512\pi$
$998$	22.1753	0.701946
$999$	3.67112	0.116149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bl.1.2	✓	12
23.22	odd	2		7935.2.a.bm.1.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.2	✓	12	1.1	even	1	trivial
7935.2.a.bm.1.2	yes	12	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85426 q^{2} +1.00000 q^{3} +1.43827 q^{4} -1.00000 q^{5} -1.85426 q^{6} -4.25122 q^{7} +1.04159 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.85426 q^{2} +1.00000 q^{3} +1.43827 q^{4} -1.00000 q^{5} -1.85426 q^{6} -4.25122 q^{7} +1.04159 q^{8} +1.00000 q^{9} +1.85426 q^{10} +1.39317 q^{11} +1.43827 q^{12} +2.97139 q^{13} +7.88285 q^{14} -1.00000 q^{15} -4.80792 q^{16} +5.65269 q^{17} -1.85426 q^{18} +7.04912 q^{19} -1.43827 q^{20} -4.25122 q^{21} -2.58330 q^{22} +1.04159 q^{24} +1.00000 q^{25} -5.50973 q^{26} +1.00000 q^{27} -6.11441 q^{28} +1.32492 q^{29} +1.85426 q^{30} +3.56980 q^{31} +6.83195 q^{32} +1.39317 q^{33} -10.4816 q^{34} +4.25122 q^{35} +1.43827 q^{36} +3.67112 q^{37} -13.0709 q^{38} +2.97139 q^{39} -1.04159 q^{40} -9.81542 q^{41} +7.88285 q^{42} +10.7813 q^{43} +2.00376 q^{44} -1.00000 q^{45} -7.10309 q^{47} -4.80792 q^{48} +11.0728 q^{49} -1.85426 q^{50} +5.65269 q^{51} +4.27368 q^{52} +8.09711 q^{53} -1.85426 q^{54} -1.39317 q^{55} -4.42800 q^{56} +7.04912 q^{57} -2.45675 q^{58} -0.141998 q^{59} -1.43827 q^{60} -3.62912 q^{61} -6.61934 q^{62} -4.25122 q^{63} -3.05236 q^{64} -2.97139 q^{65} -2.58330 q^{66} -12.0240 q^{67} +8.13012 q^{68} -7.88285 q^{70} +10.1535 q^{71} +1.04159 q^{72} -9.15769 q^{73} -6.80721 q^{74} +1.00000 q^{75} +10.1386 q^{76} -5.92267 q^{77} -5.50973 q^{78} +6.16073 q^{79} +4.80792 q^{80} +1.00000 q^{81} +18.2003 q^{82} +16.6390 q^{83} -6.11441 q^{84} -5.65269 q^{85} -19.9913 q^{86} +1.32492 q^{87} +1.45110 q^{88} +8.30577 q^{89} +1.85426 q^{90} -12.6320 q^{91} +3.56980 q^{93} +13.1710 q^{94} -7.04912 q^{95} +6.83195 q^{96} -0.605707 q^{97} -20.5319 q^{98} +1.39317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Introduction

L-functions

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Database

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