LMFDB - Embedded newform 6013.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99923 q^{2} +0.235231 q^{3} +1.99692 q^{4} +2.61420 q^{5} -0.470281 q^{6} -1.00000 q^{7} +0.00615784 q^{8} -2.94467 q^{9} +O(q^{10})$	\(q-1.99923 q^{2} +0.235231 q^{3} +1.99692 q^{4} +2.61420 q^{5} -0.470281 q^{6} -1.00000 q^{7} +0.00615784 q^{8} -2.94467 q^{9} -5.22639 q^{10} -5.09945 q^{11} +0.469738 q^{12} -3.10205 q^{13} +1.99923 q^{14} +0.614942 q^{15} -4.00615 q^{16} -3.20766 q^{17} +5.88706 q^{18} -4.09012 q^{19} +5.22035 q^{20} -0.235231 q^{21} +10.1950 q^{22} +0.198977 q^{23} +0.00144852 q^{24} +1.83405 q^{25} +6.20171 q^{26} -1.39837 q^{27} -1.99692 q^{28} +0.346086 q^{29} -1.22941 q^{30} +2.19804 q^{31} +7.99690 q^{32} -1.19955 q^{33} +6.41284 q^{34} -2.61420 q^{35} -5.88026 q^{36} -0.0864061 q^{37} +8.17710 q^{38} -0.729698 q^{39} +0.0160978 q^{40} -9.52978 q^{41} +0.470281 q^{42} -4.56380 q^{43} -10.1832 q^{44} -7.69795 q^{45} -0.397801 q^{46} -3.35958 q^{47} -0.942372 q^{48} +1.00000 q^{49} -3.66669 q^{50} -0.754541 q^{51} -6.19454 q^{52} -12.7654 q^{53} +2.79566 q^{54} -13.3310 q^{55} -0.00615784 q^{56} -0.962124 q^{57} -0.691906 q^{58} +12.3969 q^{59} +1.22799 q^{60} -5.86950 q^{61} -4.39438 q^{62} +2.94467 q^{63} -7.97534 q^{64} -8.10938 q^{65} +2.39818 q^{66} +9.92707 q^{67} -6.40543 q^{68} +0.0468057 q^{69} +5.22639 q^{70} +12.7351 q^{71} -0.0181328 q^{72} +7.65691 q^{73} +0.172746 q^{74} +0.431426 q^{75} -8.16765 q^{76} +5.09945 q^{77} +1.45883 q^{78} -5.22707 q^{79} -10.4729 q^{80} +8.50506 q^{81} +19.0522 q^{82} -17.2939 q^{83} -0.469738 q^{84} -8.38546 q^{85} +9.12409 q^{86} +0.0814103 q^{87} -0.0314016 q^{88} +5.42620 q^{89} +15.3900 q^{90} +3.10205 q^{91} +0.397342 q^{92} +0.517047 q^{93} +6.71658 q^{94} -10.6924 q^{95} +1.88112 q^{96} +10.9300 q^{97} -1.99923 q^{98} +15.0162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−1.99923	−1.41367	−0.706834	−	0.707379i	$-0.749877\pi$
$2$	−1.99923	−1.41367	−0.706834	+	0.707379i	$0.749877\pi$
$3$	0.235231	0.135811	0.0679054	−	0.997692i	$-0.478368\pi$
$3$	0.235231	0.135811	0.0679054	+	0.997692i	$0.478368\pi$
$4$	1.99692	0.998460
$5$	2.61420	1.16911	0.584553	−	0.811355i	$-0.301270\pi$
$5$	2.61420	1.16911	0.584553	+	0.811355i	$0.301270\pi$
$6$	−0.470281	−0.191992
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.00615784	0.00217713
$9$	−2.94467	−0.981555
$10$	−5.22639	−1.65273
$11$	−5.09945	−1.53754	−0.768771	−	0.639524i	$-0.779131\pi$
$11$	−5.09945	−1.53754	−0.768771	+	0.639524i	$0.779131\pi$
$12$	0.469738	0.135602
$13$	−3.10205	−0.860353	−0.430177	−	0.902745i	$-0.641549\pi$
$13$	−3.10205	−0.860353	−0.430177	+	0.902745i	$0.641549\pi$
$14$	1.99923	0.534317
$15$	0.614942	0.158777
$16$	−4.00615	−1.00154
$17$	−3.20766	−0.777971	−0.388985	−	0.921244i	$-0.627174\pi$
$17$	−3.20766	−0.777971	−0.388985	+	0.921244i	$0.627174\pi$
$18$	5.88706	1.38759
$19$	−4.09012	−0.938339	−0.469169	−	0.883108i	$-0.655447\pi$
$19$	−4.09012	−0.938339	−0.469169	+	0.883108i	$0.655447\pi$
$20$	5.22035	1.16731
$21$	−0.235231	−0.0513317
$22$	10.1950	2.17358
$23$	0.198977	0.0414896	0.0207448	−	0.999785i	$-0.493396\pi$
$23$	0.198977	0.0414896	0.0207448	+	0.999785i	$0.493396\pi$
$24$	0.00144852	0.000295677 0
$25$	1.83405	0.366811
$26$	6.20171	1.21625
$27$	−1.39837	−0.269117
$28$	−1.99692	−0.377382
$29$	0.346086	0.0642666	0.0321333	−	0.999484i	$-0.489770\pi$
$29$	0.346086	0.0642666	0.0321333	+	0.999484i	$0.489770\pi$
$30$	−1.22941	−0.224459
$31$	2.19804	0.394779	0.197390	−	0.980325i	$-0.436754\pi$
$31$	2.19804	0.394779	0.197390	+	0.980325i	$0.436754\pi$
$32$	7.99690	1.41367
$33$	−1.19955	−0.208815
$34$	6.41284	1.09979
$35$	−2.61420	−0.441881
$36$	−5.88026	−0.980044
$37$	−0.0864061	−0.0142051	−0.00710254	−	0.999975i	$-0.502261\pi$
$37$	−0.0864061	−0.0142051	−0.00710254	+	0.999975i	$0.502261\pi$
$38$	8.17710	1.32650
$39$	−0.729698	−0.116845
$40$	0.0160978	0.00254529
$41$	−9.52978	−1.48830	−0.744151	−	0.668011i	$-0.767146\pi$
$41$	−9.52978	−1.48830	−0.744151	+	0.668011i	$0.767146\pi$
$42$	0.470281	0.0725660
$43$	−4.56380	−0.695974	−0.347987	−	0.937499i	$-0.613135\pi$
$43$	−4.56380	−0.695974	−0.347987	+	0.937499i	$0.613135\pi$
$44$	−10.1832	−1.53517
$45$	−7.69795	−1.14754
$46$	−0.397801	−0.0586526
$47$	−3.35958	−0.490046	−0.245023	−	0.969517i	$-0.578795\pi$
$47$	−3.35958	−0.490046	−0.245023	+	0.969517i	$0.578795\pi$
$48$	−0.942372	−0.136020
$49$	1.00000	0.142857
$50$	−3.66669	−0.518549
$51$	−0.754541	−0.105657
$52$	−6.19454	−0.859028
$53$	−12.7654	−1.75346	−0.876728	−	0.480987i	$-0.840279\pi$
$53$	−12.7654	−1.75346	−0.876728	+	0.480987i	$0.840279\pi$
$54$	2.79566	0.380442
$55$	−13.3310	−1.79755
$56$	−0.00615784	−0.000822876 0
$57$	−0.962124	−0.127436
$58$	−0.691906	−0.0908517
$59$	12.3969	1.61394	0.806969	−	0.590594i	$-0.201107\pi$
$59$	12.3969	1.61394	0.806969	+	0.590594i	$0.201107\pi$
$60$	1.22799	0.158533
$61$	−5.86950	−0.751512	−0.375756	−	0.926719i	$-0.622617\pi$
$61$	−5.86950	−0.751512	−0.375756	+	0.926719i	$0.622617\pi$
$62$	−4.39438	−0.558087
$63$	2.94467	0.370993
$64$	−7.97534	−0.996918
$65$	−8.10938	−1.00584
$66$	2.39818	0.295195
$67$	9.92707	1.21278	0.606392	−	0.795166i	$-0.292616\pi$
$67$	9.92707	1.21278	0.606392	+	0.795166i	$0.292616\pi$
$68$	−6.40543	−0.776773
$69$	0.0468057	0.00563474
$70$	5.22639	0.624673
$71$	12.7351	1.51137	0.755687	−	0.654933i	$-0.227303\pi$
$71$	12.7351	1.51137	0.755687	+	0.654933i	$0.227303\pi$
$72$	−0.0181328	−0.00213697
$73$	7.65691	0.896174	0.448087	−	0.893990i	$-0.352106\pi$
$73$	7.65691	0.896174	0.448087	+	0.893990i	$0.352106\pi$
$74$	0.172746	0.0200813
$75$	0.431426	0.0498168
$76$	−8.16765	−0.936893
$77$	5.09945	0.581136
$78$	1.45883	0.165180
$79$	−5.22707	−0.588091	−0.294046	−	0.955791i	$-0.595002\pi$
$79$	−5.22707	−0.588091	−0.294046	+	0.955791i	$0.595002\pi$
$80$	−10.4729	−1.17090
$81$	8.50506	0.945006
$82$	19.0522	2.10397
$83$	−17.2939	−1.89825	−0.949125	−	0.314899i	$-0.898029\pi$
$83$	−17.2939	−1.89825	−0.949125	+	0.314899i	$0.898029\pi$
$84$	−0.469738	−0.0512526
$85$	−8.38546	−0.909531
$86$	9.12409	0.983876
$87$	0.0814103	0.00872810
$88$	−0.0314016	−0.00334742
$89$	5.42620	0.575176	0.287588	−	0.957754i	$-0.407147\pi$
$89$	5.42620	0.575176	0.287588	+	0.957754i	$0.407147\pi$
$90$	15.3900	1.62225
$91$	3.10205	0.325183
$92$	0.397342	0.0414257
$93$	0.517047	0.0536153
$94$	6.71658	0.692762
$95$	−10.6924	−1.09702
$96$	1.88112	0.191991
$97$	10.9300	1.10977	0.554887	−	0.831925i	$-0.312761\pi$
$97$	10.9300	1.10977	0.554887	+	0.831925i	$0.312761\pi$
$98$	−1.99923	−0.201953
$99$	15.0162	1.50918
$100$	3.66246	0.366246
$101$	16.2111	1.61306	0.806531	−	0.591192i	$-0.201342\pi$
$101$	16.2111	1.61306	0.806531	+	0.591192i	$0.201342\pi$
$102$	1.50850	0.149364
$103$	9.26290	0.912701	0.456350	−	0.889800i	$-0.349156\pi$
$103$	9.26290	0.912701	0.456350	+	0.889800i	$0.349156\pi$
$104$	−0.0191019	−0.00187310
$105$	−0.614942	−0.0600122
$106$	25.5209	2.47881
$107$	14.8116	1.43189	0.715947	−	0.698155i	$-0.245995\pi$
$107$	14.8116	1.43189	0.715947	+	0.698155i	$0.245995\pi$
$108$	−2.79243	−0.268702
$109$	5.46322	0.523281	0.261641	−	0.965165i	$-0.415736\pi$
$109$	5.46322	0.523281	0.261641	+	0.965165i	$0.415736\pi$
$110$	26.6517	2.54114
$111$	−0.0203254	−0.00192920
$112$	4.00615	0.378546
$113$	5.81349	0.546887	0.273444	−	0.961888i	$-0.411837\pi$
$113$	5.81349	0.546887	0.273444	+	0.961888i	$0.411837\pi$
$114$	1.92351	0.180153
$115$	0.520167	0.0485058
$116$	0.691106	0.0641676
$117$	9.13449	0.844484
$118$	−24.7842	−2.28157
$119$	3.20766	0.294045
$120$	0.00378672	0.000345678 0
$121$	15.0044	1.36404
$122$	11.7345	1.06239
$123$	−2.24170	−0.202128
$124$	4.38931	0.394171
$125$	−8.27643	−0.740266
$126$	−5.88706	−0.524461
$127$	4.23361	0.375672	0.187836	−	0.982200i	$-0.439853\pi$
$127$	4.23361	0.375672	0.187836	+	0.982200i	$0.439853\pi$
$128$	−0.0492627	−0.00435425
$129$	−1.07355	−0.0945207
$130$	16.2125	1.42193
$131$	−9.72934	−0.850056	−0.425028	−	0.905180i	$-0.639736\pi$
$131$	−9.72934	−0.850056	−0.425028	+	0.905180i	$0.639736\pi$
$132$	−2.39540	−0.208493
$133$	4.09012	0.354659
$134$	−19.8465	−1.71448
$135$	−3.65562	−0.314626
$136$	−0.0197522	−0.00169374
$137$	3.24779	0.277478	0.138739	−	0.990329i	$-0.455695\pi$
$137$	3.24779	0.277478	0.138739	+	0.990329i	$0.455695\pi$
$138$	−0.0935753	−0.00796566
$139$	−13.2093	−1.12040	−0.560201	−	0.828357i	$-0.689276\pi$
$139$	−13.2093	−1.12040	−0.560201	+	0.828357i	$0.689276\pi$
$140$	−5.22035	−0.441200
$141$	−0.790279	−0.0665535
$142$	−25.4603	−2.13658
$143$	15.8187	1.32283
$144$	11.7968	0.983065
$145$	0.904739	0.0751345
$146$	−15.3079	−1.26689
$147$	0.235231	0.0194015
$148$	−0.172546	−0.0141832
$149$	16.5938	1.35941	0.679707	−	0.733483i	$-0.262107\pi$
$149$	16.5938	1.35941	0.679707	+	0.733483i	$0.262107\pi$
$150$	−0.862521	−0.0704245
$151$	−5.18377	−0.421849	−0.210925	−	0.977502i	$-0.567647\pi$
$151$	−5.18377	−0.421849	−0.210925	+	0.977502i	$0.567647\pi$
$152$	−0.0251863	−0.00204288
$153$	9.44547	0.763621
$154$	−10.1950	−0.821534
$155$	5.74612	0.461539
$156$	−1.45715	−0.116665
$157$	21.6261	1.72595	0.862975	−	0.505247i	$-0.168599\pi$
$157$	21.6261	1.72595	0.862975	+	0.505247i	$0.168599\pi$
$158$	10.4501	0.831367
$159$	−3.00281	−0.238138
$160$	20.9055	1.65273
$161$	−0.198977	−0.0156816
$162$	−17.0036	−1.33593
$163$	7.70252	0.603308	0.301654	−	0.953417i	$-0.402461\pi$
$163$	7.70252	0.603308	0.301654	+	0.953417i	$0.402461\pi$
$164$	−19.0302	−1.48601
$165$	−3.13587	−0.244127
$166$	34.5745	2.68350
$167$	−13.5669	−1.04984	−0.524918	−	0.851153i	$-0.675904\pi$
$167$	−13.5669	−1.04984	−0.524918	+	0.851153i	$0.675904\pi$
$168$	−0.00144852	−0.000111755 0
$169$	−3.37730	−0.259792
$170$	16.7645	1.28578
$171$	12.0440	0.921031
$172$	−9.11355	−0.694902
$173$	−7.73909	−0.588392	−0.294196	−	0.955745i	$-0.595052\pi$
$173$	−7.73909	−0.588392	−0.294196	+	0.955745i	$0.595052\pi$
$174$	−0.162758	−0.0123386
$175$	−1.83405	−0.138641
$176$	20.4292	1.53991
$177$	2.91614	0.219190
$178$	−10.8482	−0.813108
$179$	17.2416	1.28869	0.644347	−	0.764733i	$-0.277129\pi$
$179$	17.2416	1.28869	0.644347	+	0.764733i	$0.277129\pi$
$180$	−15.3722	−1.14578
$181$	21.6677	1.61054	0.805272	−	0.592905i	$-0.202019\pi$
$181$	21.6677	1.61054	0.805272	+	0.592905i	$0.202019\pi$
$182$	−6.20171	−0.459701
$183$	−1.38069	−0.102063
$184$	0.00122527	9.03282e−5 0
$185$	−0.225883	−0.0166073
$186$	−1.03370	−0.0757943
$187$	16.3573	1.19616
$188$	−6.70882	−0.489291
$189$	1.39837	0.101717
$190$	21.3766	1.55082
$191$	−12.6700	−0.916769	−0.458385	−	0.888754i	$-0.651572\pi$
$191$	−12.6700	−0.916769	−0.458385	+	0.888754i	$0.651572\pi$
$192$	−1.87605	−0.135392
$193$	−1.13151	−0.0814481	−0.0407241	−	0.999170i	$-0.512966\pi$
$193$	−1.13151	−0.0814481	−0.0407241	+	0.999170i	$0.512966\pi$
$194$	−21.8516	−1.56885
$195$	−1.90758	−0.136605
$196$	1.99692	0.142637
$197$	−8.19927	−0.584173	−0.292087	−	0.956392i	$-0.594350\pi$
$197$	−8.19927	−0.584173	−0.292087	+	0.956392i	$0.594350\pi$
$198$	−30.0208	−2.13348
$199$	−27.7206	−1.96506	−0.982531	−	0.186099i	$-0.940416\pi$
$199$	−27.7206	−1.96506	−0.982531	+	0.186099i	$0.940416\pi$
$200$	0.0112938	0.000798593 0
$201$	2.33516	0.164709
$202$	−32.4097	−2.28034
$203$	−0.346086	−0.0242905
$204$	−1.50676	−0.105494
$205$	−24.9128	−1.73998
$206$	−18.5187	−1.29026
$207$	−0.585922	−0.0407244
$208$	12.4273	0.861676
$209$	20.8574	1.44273
$210$	1.22941	0.0848374
$211$	−5.91802	−0.407413	−0.203707	−	0.979032i	$-0.565299\pi$
$211$	−5.91802	−0.407413	−0.203707	+	0.979032i	$0.565299\pi$
$212$	−25.4914	−1.75076
$213$	2.99568	0.205261
$214$	−29.6118	−2.02422
$215$	−11.9307	−0.813667
$216$	−0.00861095	−0.000585901 0
$217$	−2.19804	−0.149213
$218$	−10.9222	−0.739746
$219$	1.80114	0.121710
$220$	−26.6209	−1.79478
$221$	9.95030	0.669330
$222$	0.0406352	0.00272725
$223$	3.89027	0.260512	0.130256	−	0.991480i	$-0.458420\pi$
$223$	3.89027	0.260512	0.130256	+	0.991480i	$0.458420\pi$
$224$	−7.99690	−0.534315
$225$	−5.40067	−0.360045
$226$	−11.6225	−0.773117
$227$	−22.8510	−1.51667	−0.758336	−	0.651864i	$-0.773987\pi$
$227$	−22.8510	−1.51667	−0.758336	+	0.651864i	$0.773987\pi$
$228$	−1.92129	−0.127240
$229$	4.08694	0.270073	0.135036	−	0.990841i	$-0.456885\pi$
$229$	4.08694	0.270073	0.135036	+	0.990841i	$0.456885\pi$
$230$	−1.03993	−0.0685712
$231$	1.19955	0.0789246
$232$	0.00213114	0.000139916 0
$233$	27.4991	1.80153	0.900763	−	0.434312i	$-0.143008\pi$
$233$	27.4991	1.80153	0.900763	+	0.434312i	$0.143008\pi$
$234$	−18.2620	−1.19382
$235$	−8.78263	−0.572916
$236$	24.7556	1.61145
$237$	−1.22957	−0.0798692
$238$	−6.41284	−0.415683
$239$	27.8418	1.80093	0.900467	−	0.434924i	$-0.143225\pi$
$239$	27.8418	1.80093	0.900467	+	0.434924i	$0.143225\pi$
$240$	−2.46355	−0.159021
$241$	−17.6450	−1.13661	−0.568306	−	0.822818i	$-0.692401\pi$
$241$	−17.6450	−1.13661	−0.568306	+	0.822818i	$0.692401\pi$
$242$	−29.9972	−1.92829
$243$	6.19577	0.397459
$244$	−11.7209	−0.750355
$245$	2.61420	0.167015
$246$	4.48168	0.285741
$247$	12.6878	0.807303
$248$	0.0135352	0.000859484 0
$249$	−4.06806	−0.257803
$250$	16.5465	1.04649
$251$	19.5858	1.23624	0.618122	−	0.786083i	$-0.287894\pi$
$251$	19.5858	1.23624	0.618122	+	0.786083i	$0.287894\pi$
$252$	5.88026	0.370422
$253$	−1.01467	−0.0637921
$254$	−8.46396	−0.531076
$255$	−1.97252	−0.123524
$256$	16.0492	1.00307
$257$	3.40485	0.212389	0.106194	−	0.994345i	$-0.466133\pi$
$257$	3.40485	0.212389	0.106194	+	0.994345i	$0.466133\pi$
$258$	2.14627	0.133621
$259$	0.0864061	0.00536902
$260$	−16.1938	−1.00430
$261$	−1.01911	−0.0630812
$262$	19.4512	1.20170
$263$	22.4723	1.38570	0.692852	−	0.721080i	$-0.256354\pi$
$263$	22.4723	1.38570	0.692852	+	0.721080i	$0.256354\pi$
$264$	−0.00738664	−0.000454616 0
$265$	−33.3712	−2.04998
$266$	−8.17710	−0.501370
$267$	1.27641	0.0781151
$268$	19.8236	1.21092
$269$	−8.55770	−0.521772	−0.260886	−	0.965370i	$-0.584015\pi$
$269$	−8.55770	−0.521772	−0.260886	+	0.965370i	$0.584015\pi$
$270$	7.30843	0.444777
$271$	6.87641	0.417712	0.208856	−	0.977946i	$-0.433026\pi$
$271$	6.87641	0.417712	0.208856	+	0.977946i	$0.433026\pi$
$272$	12.8504	0.779167
$273$	0.729698	0.0441634
$274$	−6.49308	−0.392261
$275$	−9.35266	−0.563987
$276$	0.0934672	0.00562606
$277$	7.80614	0.469026	0.234513	−	0.972113i	$-0.424651\pi$
$277$	7.80614	0.469026	0.234513	+	0.972113i	$0.424651\pi$
$278$	26.4085	1.58388
$279$	−6.47249	−0.387498
$280$	−0.0160978	−0.000962030 0
$281$	−31.2273	−1.86286	−0.931432	−	0.363916i	$-0.881439\pi$
$281$	−31.2273	−1.86286	−0.931432	+	0.363916i	$0.881439\pi$
$282$	1.57995	0.0940846
$283$	25.5322	1.51773	0.758867	−	0.651246i	$-0.225753\pi$
$283$	25.5322	1.51773	0.758867	+	0.651246i	$0.225753\pi$
$284$	25.4309	1.50905
$285$	−2.51519	−0.148987
$286$	−31.6253	−1.87004
$287$	9.52978	0.562525
$288$	−23.5482	−1.38759
$289$	−6.71095	−0.394762
$290$	−1.80878	−0.106215
$291$	2.57108	0.150719
$292$	15.2902	0.894794
$293$	−32.4025	−1.89297	−0.946487	−	0.322741i	$-0.895396\pi$
$293$	−32.4025	−1.89297	−0.946487	+	0.322741i	$0.895396\pi$
$294$	−0.470281	−0.0274274
$295$	32.4080	1.88687
$296$	−0.000532075 0	−3.09263e−5 0
$297$	7.13092	0.413778
$298$	−33.1748	−1.92176
$299$	−0.617237	−0.0356957
$300$	0.861524	0.0497401
$301$	4.56380	0.263053
$302$	10.3635	0.596355
$303$	3.81335	0.219071
$304$	16.3856	0.939781
$305$	−15.3441	−0.878598
$306$	−18.8837	−1.07951
$307$	−23.5976	−1.34679	−0.673393	−	0.739285i	$-0.735164\pi$
$307$	−23.5976	−1.34679	−0.673393	+	0.739285i	$0.735164\pi$
$308$	10.1832	0.580241
$309$	2.17892	0.123955
$310$	−11.4878	−0.652464
$311$	26.6951	1.51374	0.756869	−	0.653567i	$-0.226728\pi$
$311$	26.6951	1.51374	0.756869	+	0.653567i	$0.226728\pi$
$312$	−0.00449337	−0.000254387 0
$313$	−9.77387	−0.552452	−0.276226	−	0.961093i	$-0.589084\pi$
$313$	−9.77387	−0.552452	−0.276226	+	0.961093i	$0.589084\pi$
$314$	−43.2355	−2.43992
$315$	7.69795	0.433731
$316$	−10.4380	−0.587186
$317$	−29.4794	−1.65573	−0.827865	−	0.560928i	$-0.810445\pi$
$317$	−29.4794	−1.65573	−0.827865	+	0.560928i	$0.810445\pi$
$318$	6.00330	0.336649
$319$	−1.76485	−0.0988126
$320$	−20.8492	−1.16550
$321$	3.48416	0.194467
$322$	0.397801	0.0221686
$323$	13.1197	0.730000
$324$	16.9839	0.943551
$325$	−5.68932	−0.315587
$326$	−15.3991	−0.852878
$327$	1.28512	0.0710672
$328$	−0.0586829	−0.00324022
$329$	3.35958	0.185220
$330$	6.26932	0.345114
$331$	−17.9669	−0.987548	−0.493774	−	0.869590i	$-0.664383\pi$
$331$	−17.9669	−0.987548	−0.493774	+	0.869590i	$0.664383\pi$
$332$	−34.5345	−1.89533
$333$	0.254437	0.0139431
$334$	27.1233	1.48412
$335$	25.9514	1.41787
$336$	0.942372	0.0514106
$337$	−31.5394	−1.71806	−0.859031	−	0.511923i	$-0.828933\pi$
$337$	−31.5394	−1.71806	−0.859031	+	0.511923i	$0.828933\pi$
$338$	6.75200	0.367261
$339$	1.36751	0.0742732
$340$	−16.7451	−0.908130
$341$	−11.2088	−0.606990
$342$	−24.0788	−1.30203
$343$	−1.00000	−0.0539949
$344$	−0.0281032	−0.00151522
$345$	0.122359	0.00658761
$346$	15.4722	0.831792
$347$	0.821453	0.0440979	0.0220490	−	0.999757i	$-0.492981\pi$
$347$	0.821453	0.0440979	0.0220490	+	0.999757i	$0.492981\pi$
$348$	0.162570	0.00871465
$349$	34.5762	1.85082	0.925412	−	0.378963i	$-0.123719\pi$
$349$	34.5762	1.85082	0.925412	+	0.378963i	$0.123719\pi$
$350$	3.66669	0.195993
$351$	4.33781	0.231535
$352$	−40.7798	−2.17357
$353$	13.3004	0.707908	0.353954	−	0.935263i	$-0.384837\pi$
$353$	13.3004	0.707908	0.353954	+	0.935263i	$0.384837\pi$
$354$	−5.83002	−0.309862
$355$	33.2920	1.76696
$356$	10.8357	0.574290
$357$	0.754541	0.0399345
$358$	−34.4698	−1.82179
$359$	9.51405	0.502132	0.251066	−	0.967970i	$-0.419219\pi$
$359$	9.51405	0.502132	0.251066	+	0.967970i	$0.419219\pi$
$360$	−0.0474028	−0.00249835
$361$	−2.27090	−0.119521
$362$	−43.3186	−2.27678
$363$	3.52950	0.185251
$364$	6.19454	0.324682
$365$	20.0167	1.04772
$366$	2.76031	0.144284
$367$	−23.6726	−1.23570	−0.617849	−	0.786297i	$-0.711996\pi$
$367$	−23.6726	−1.23570	−0.617849	+	0.786297i	$0.711996\pi$
$368$	−0.797133	−0.0415534
$369$	28.0620	1.46085
$370$	0.451592	0.0234772
$371$	12.7654	0.662744
$372$	1.03250	0.0535327
$373$	−25.1487	−1.30215	−0.651075	−	0.759014i	$-0.725682\pi$
$373$	−25.1487	−1.30215	−0.651075	+	0.759014i	$0.725682\pi$
$374$	−32.7020	−1.69098
$375$	−1.94687	−0.100536
$376$	−0.0206878	−0.00106689
$377$	−1.07358	−0.0552920
$378$	−2.79566	−0.143793
$379$	11.4202	0.586614	0.293307	−	0.956018i	$-0.405244\pi$
$379$	11.4202	0.586614	0.293307	+	0.956018i	$0.405244\pi$
$380$	−21.3519	−1.09533
$381$	0.995878	0.0510204
$382$	25.3302	1.29601
$383$	−29.9149	−1.52858	−0.764289	−	0.644874i	$-0.776910\pi$
$383$	−29.9149	−1.52858	−0.764289	+	0.644874i	$0.776910\pi$
$384$	−0.0115881	−0.000591354 0
$385$	13.3310	0.679410
$386$	2.26216	0.115141
$387$	13.4389	0.683137
$388$	21.8264	1.10807
$389$	−16.2879	−0.825828	−0.412914	−	0.910770i	$-0.635489\pi$
$389$	−16.2879	−0.825828	−0.412914	+	0.910770i	$0.635489\pi$
$390$	3.81369	0.193114
$391$	−0.638251	−0.0322777
$392$	0.00615784	0.000311018 0
$393$	−2.28864	−0.115447
$394$	16.3922	0.825828
$395$	−13.6646	−0.687542
$396$	29.9861	1.50686
$397$	−30.1548	−1.51343	−0.756714	−	0.653747i	$-0.773196\pi$
$397$	−30.1548	−1.51343	−0.756714	+	0.653747i	$0.773196\pi$
$398$	55.4199	2.77795
$399$	0.962124	0.0481665
$400$	−7.34749	−0.367375
$401$	−17.1173	−0.854799	−0.427399	−	0.904063i	$-0.640570\pi$
$401$	−17.1173	−0.854799	−0.427399	+	0.904063i	$0.640570\pi$
$402$	−4.66851	−0.232844
$403$	−6.81842	−0.339650
$404$	32.3722	1.61058
$405$	22.2339	1.10481
$406$	0.691906	0.0343387
$407$	0.440624	0.0218409
$408$	−0.00464634	−0.000230028 0
$409$	32.0511	1.58483	0.792413	−	0.609985i	$-0.208825\pi$
$409$	32.0511	1.58483	0.792413	+	0.609985i	$0.208825\pi$
$410$	49.8064	2.45976
$411$	0.763982	0.0376844
$412$	18.4973	0.911295
$413$	−12.3969	−0.610011
$414$	1.17139	0.0575708
$415$	−45.2097	−2.21926
$416$	−24.8068	−1.21625
$417$	−3.10725	−0.152163
$418$	−41.6987	−2.03955
$419$	3.65026	0.178327	0.0891635	−	0.996017i	$-0.471581\pi$
$419$	3.65026	0.178327	0.0891635	+	0.996017i	$0.471581\pi$
$420$	−1.22799	−0.0599198
$421$	0.0542094	0.00264200	0.00132100	−	0.999999i	$-0.499580\pi$
$421$	0.0542094	0.00264200	0.00132100	+	0.999999i	$0.499580\pi$
$422$	11.8315	0.575948
$423$	9.89285	0.481007
$424$	−0.0786070	−0.00381749
$425$	−5.88301	−0.285368
$426$	−5.98906	−0.290171
$427$	5.86950	0.284045
$428$	29.5776	1.42969
$429$	3.72106	0.179654
$430$	23.8522	1.15026
$431$	21.6416	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$431$	21.6416	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$432$	5.60208	0.269530
$433$	−15.7349	−0.756170	−0.378085	−	0.925771i	$-0.623417\pi$
$433$	−15.7349	−0.756170	−0.378085	+	0.925771i	$0.623417\pi$
$434$	4.39438	0.210937
$435$	0.212823	0.0102041
$436$	10.9096	0.522475
$437$	−0.813842	−0.0389313
$438$	−3.60090	−0.172058
$439$	4.84634	0.231303	0.115652	−	0.993290i	$-0.463104\pi$
$439$	4.84634	0.231303	0.115652	+	0.993290i	$0.463104\pi$
$440$	−0.0820902	−0.00391349
$441$	−2.94467	−0.140222
$442$	−19.8929	−0.946210
$443$	−4.77792	−0.227006	−0.113503	−	0.993538i	$-0.536207\pi$
$443$	−4.77792	−0.227006	−0.113503	+	0.993538i	$0.536207\pi$
$444$	−0.0405882	−0.00192623
$445$	14.1852	0.672442
$446$	−7.77754	−0.368277
$447$	3.90337	0.184623
$448$	7.97534	0.376799
$449$	11.6347	0.549077	0.274538	−	0.961576i	$-0.411475\pi$
$449$	11.6347	0.549077	0.274538	+	0.961576i	$0.411475\pi$
$450$	10.7972	0.508984
$451$	48.5967	2.28833
$452$	11.6091	0.546045
$453$	−1.21938	−0.0572917
$454$	45.6843	2.14407
$455$	8.10938	0.380174
$456$	−0.00592461	−0.000277445 0
$457$	−23.1418	−1.08253	−0.541263	−	0.840853i	$-0.682054\pi$
$457$	−23.1418	−1.08253	−0.541263	+	0.840853i	$0.682054\pi$
$458$	−8.17074	−0.381793
$459$	4.48549	0.209365
$460$	1.03873	0.0484311
$461$	−5.12891	−0.238877	−0.119438	−	0.992842i	$-0.538109\pi$
$461$	−5.12891	−0.238877	−0.119438	+	0.992842i	$0.538109\pi$
$462$	−2.39818	−0.111573
$463$	−6.60329	−0.306881	−0.153441	−	0.988158i	$-0.549035\pi$
$463$	−6.60329	−0.306881	−0.153441	+	0.988158i	$0.549035\pi$
$464$	−1.38647	−0.0643654
$465$	1.35167	0.0626820
$466$	−54.9770	−2.54676
$467$	16.5748	0.766988	0.383494	−	0.923543i	$-0.374721\pi$
$467$	16.5748	0.766988	0.383494	+	0.923543i	$0.374721\pi$
$468$	18.2409	0.843184
$469$	−9.92707	−0.458389
$470$	17.5585	0.809913
$471$	5.08713	0.234403
$472$	0.0763381	0.00351375
$473$	23.2729	1.07009
$474$	2.45819	0.112909
$475$	−7.50150	−0.344193
$476$	6.40543	0.293592
$477$	37.5897	1.72111
$478$	−55.6621	−2.54592
$479$	−2.51037	−0.114702	−0.0573509	−	0.998354i	$-0.518265\pi$
$479$	−2.51037	−0.114702	−0.0573509	+	0.998354i	$0.518265\pi$
$480$	4.91763	0.224458
$481$	0.268036	0.0122214
$482$	35.2763	1.60679
$483$	−0.0468057	−0.00212973
$484$	29.9626	1.36193
$485$	28.5733	1.29745
$486$	−12.3868	−0.561875
$487$	13.1024	0.593728	0.296864	−	0.954920i	$-0.404059\pi$
$487$	13.1024	0.593728	0.296864	+	0.954920i	$0.404059\pi$
$488$	−0.0361434	−0.00163614
$489$	1.81187	0.0819357
$490$	−5.22639	−0.236104
$491$	36.4016	1.64278	0.821391	−	0.570365i	$-0.193198\pi$
$491$	36.4016	1.64278	0.821391	+	0.570365i	$0.193198\pi$
$492$	−4.47650	−0.201816
$493$	−1.11013	−0.0499975
$494$	−25.3657	−1.14126
$495$	39.2553	1.76440
$496$	−8.80567	−0.395386
$497$	−12.7351	−0.571246
$498$	8.13299	0.364448
$499$	−33.2591	−1.48888	−0.744442	−	0.667687i	$-0.767284\pi$
$499$	−33.2591	−1.48888	−0.744442	+	0.667687i	$0.767284\pi$
$500$	−16.5274	−0.739126
$501$	−3.19135	−0.142579
$502$	−39.1565	−1.74764
$503$	28.0828	1.25215	0.626076	−	0.779762i	$-0.284660\pi$
$503$	28.0828	1.25215	0.626076	+	0.779762i	$0.284660\pi$
$504$	0.0181328	0.000807699 0
$505$	42.3790	1.88584
$506$	2.02857	0.0901809
$507$	−0.794447	−0.0352826
$508$	8.45419	0.375094
$509$	7.78566	0.345093	0.172547	−	0.985001i	$-0.444800\pi$
$509$	7.78566	0.345093	0.172547	+	0.985001i	$0.444800\pi$
$510$	3.94352	0.174622
$511$	−7.65691	−0.338722
$512$	−31.9874	−1.41366
$513$	5.71951	0.252522
$514$	−6.80709	−0.300248
$515$	24.2151	1.06704
$516$	−2.14379	−0.0943752
$517$	17.1320	0.753466
$518$	−0.172746	−0.00759001
$519$	−1.82048	−0.0799100
$520$	−0.0499363	−0.00218985
$521$	10.2188	0.447695	0.223848	−	0.974624i	$-0.428138\pi$
$521$	10.2188	0.447695	0.223848	+	0.974624i	$0.428138\pi$
$522$	2.03743	0.0891760
$523$	−15.4940	−0.677504	−0.338752	−	0.940876i	$-0.610005\pi$
$523$	−15.4940	−0.677504	−0.338752	+	0.940876i	$0.610005\pi$
$524$	−19.4287	−0.848747
$525$	−0.431426	−0.0188290
$526$	−44.9274	−1.95893
$527$	−7.05055	−0.307127
$528$	4.80558	0.209136
$529$	−22.9604	−0.998279
$530$	66.7167	2.89799
$531$	−36.5047	−1.58417
$532$	8.16765	0.354112
$533$	29.5618	1.28047
$534$	−2.55184	−0.110429
$535$	38.7206	1.67404
$536$	0.0611293	0.00264038
$537$	4.05575	0.175019
$538$	17.1088	0.737613
$539$	−5.09945	−0.219649
$540$	−7.29999	−0.314142
$541$	33.5853	1.44395	0.721973	−	0.691921i	$-0.243235\pi$
$541$	33.5853	1.44395	0.721973	+	0.691921i	$0.243235\pi$
$542$	−13.7475	−0.590506
$543$	5.09691	0.218729
$544$	−25.6513	−1.09979
$545$	14.2820	0.611772
$546$	−1.45883	−0.0624324
$547$	4.82590	0.206341	0.103170	−	0.994664i	$-0.467101\pi$
$547$	4.82590	0.206341	0.103170	+	0.994664i	$0.467101\pi$
$548$	6.48558	0.277050
$549$	17.2837	0.737651
$550$	18.6981	0.797291
$551$	−1.41553	−0.0603038
$552$	0.000288222 0	1.22675e−5 0
$553$	5.22707	0.222278
$554$	−15.6063	−0.663047
$555$	−0.0531348	−0.00225544
$556$	−26.3780	−1.11868
$557$	−27.4533	−1.16323	−0.581617	−	0.813463i	$-0.697580\pi$
$557$	−27.4533	−1.16323	−0.581617	+	0.813463i	$0.697580\pi$
$558$	12.9400	0.547794
$559$	14.1571	0.598783
$560$	10.4729	0.442560
$561$	3.84774	0.162452
$562$	62.4305	2.63347
$563$	40.8805	1.72291	0.861454	−	0.507835i	$-0.169554\pi$
$563$	40.8805	1.72291	0.861454	+	0.507835i	$0.169554\pi$
$564$	−1.57812	−0.0664510
$565$	15.1976	0.639369
$566$	−51.0448	−2.14557
$567$	−8.50506	−0.357179
$568$	0.0784205	0.00329045
$569$	−22.9551	−0.962330	−0.481165	−	0.876630i	$-0.659786\pi$
$569$	−22.9551	−0.962330	−0.481165	+	0.876630i	$0.659786\pi$
$570$	5.02844	0.210618
$571$	−29.3269	−1.22729	−0.613646	−	0.789581i	$-0.710298\pi$
$571$	−29.3269	−1.22729	−0.613646	+	0.789581i	$0.710298\pi$
$572$	31.5887	1.32079
$573$	−2.98038	−0.124507
$574$	−19.0522	−0.795225
$575$	0.364935	0.0152188
$576$	23.4847	0.978530
$577$	−12.4327	−0.517580	−0.258790	−	0.965934i	$-0.583324\pi$
$577$	−12.4327	−0.517580	−0.258790	+	0.965934i	$0.583324\pi$
$578$	13.4167	0.558062
$579$	−0.266167	−0.0110615
$580$	1.80669	0.0750188
$581$	17.2939	0.717471
$582$	−5.14018	−0.213067
$583$	65.0963	2.69601
$584$	0.0471501	0.00195108
$585$	23.8794	0.987292
$586$	64.7800	2.67604
$587$	43.3160	1.78784	0.893922	−	0.448222i	$-0.147943\pi$
$587$	43.3160	1.78784	0.893922	+	0.448222i	$0.147943\pi$
$588$	0.469738	0.0193717
$589$	−8.99025	−0.370437
$590$	−64.7910	−2.66740
$591$	−1.92872	−0.0793371
$592$	0.346156	0.0142269
$593$	−32.7369	−1.34434	−0.672172	−	0.740395i	$-0.734638\pi$
$593$	−32.7369	−1.34434	−0.672172	+	0.740395i	$0.734638\pi$
$594$	−14.2564	−0.584945
$595$	8.38546	0.343770
$596$	33.1364	1.35732
$597$	−6.52075	−0.266877
$598$	1.23400	0.0504620
$599$	−25.0818	−1.02481	−0.512406	−	0.858743i	$-0.671246\pi$
$599$	−25.0818	−1.02481	−0.512406	+	0.858743i	$0.671246\pi$
$600$	0.00265666	0.000108458 0
$601$	8.05613	0.328616	0.164308	−	0.986409i	$-0.447461\pi$
$601$	8.05613	0.328616	0.164308	+	0.986409i	$0.447461\pi$
$602$	−9.12409	−0.371870
$603$	−29.2319	−1.19042
$604$	−10.3516	−0.421199
$605$	39.2245	1.59470
$606$	−7.62376	−0.309694
$607$	45.5618	1.84930	0.924649	−	0.380821i	$-0.124359\pi$
$607$	45.5618	1.84930	0.924649	+	0.380821i	$0.124359\pi$
$608$	−32.7083	−1.32650
$609$	−0.0814103	−0.00329891
$610$	30.6763	1.24205
$611$	10.4216	0.421612
$612$	18.8619	0.762445
$613$	40.4634	1.63430	0.817150	−	0.576425i	$-0.195553\pi$
$613$	40.4634	1.63430	0.817150	+	0.576425i	$0.195553\pi$
$614$	47.1770	1.90391
$615$	−5.86026	−0.236309
$616$	0.0314016	0.00126521
$617$	−17.3650	−0.699087	−0.349544	−	0.936920i	$-0.613663\pi$
$617$	−17.3650	−0.699087	−0.349544	+	0.936920i	$0.613663\pi$
$618$	−4.35617	−0.175231
$619$	−46.0936	−1.85266	−0.926330	−	0.376714i	$-0.877054\pi$
$619$	−46.0936	−1.85266	−0.926330	+	0.376714i	$0.877054\pi$
$620$	11.4745	0.460828
$621$	−0.278244	−0.0111656
$622$	−53.3695	−2.13992
$623$	−5.42620	−0.217396
$624$	2.92328	0.117025
$625$	−30.8065	−1.23226
$626$	19.5402	0.780984
$627$	4.90631	0.195939
$628$	43.1855	1.72329
$629$	0.277161	0.0110511
$630$	−15.3900	−0.613151
$631$	−35.4443	−1.41102	−0.705508	−	0.708702i	$-0.749281\pi$
$631$	−35.4443	−1.41102	−0.705508	+	0.708702i	$0.749281\pi$
$632$	−0.0321875	−0.00128035
$633$	−1.39210	−0.0553311
$634$	58.9362	2.34065
$635$	11.0675	0.439201
$636$	−5.99637	−0.237771
$637$	−3.10205	−0.122908
$638$	3.52834	0.139688
$639$	−37.5005	−1.48350
$640$	−0.128783	−0.00509058
$641$	−31.2727	−1.23520	−0.617599	−	0.786493i	$-0.711895\pi$
$641$	−31.2727	−1.23520	−0.617599	+	0.786493i	$0.711895\pi$
$642$	−6.96563	−0.274911
$643$	37.2808	1.47021	0.735105	−	0.677953i	$-0.237133\pi$
$643$	37.2808	1.47021	0.735105	+	0.677953i	$0.237133\pi$
$644$	−0.397342	−0.0156575
$645$	−2.80647	−0.110505
$646$	−26.2293	−1.03198
$647$	37.5275	1.47536	0.737679	−	0.675152i	$-0.235922\pi$
$647$	37.5275	1.47536	0.737679	+	0.675152i	$0.235922\pi$
$648$	0.0523728	0.00205740
$649$	−63.2173	−2.48150
$650$	11.3743	0.446135
$651$	−0.517047	−0.0202647
$652$	15.3813	0.602379
$653$	45.8607	1.79467	0.897333	−	0.441354i	$-0.145502\pi$
$653$	45.8607	1.79467	0.897333	+	0.441354i	$0.145502\pi$
$654$	−2.56925	−0.100466
$655$	−25.4345	−0.993806
$656$	38.1778	1.49059
$657$	−22.5471	−0.879644
$658$	−6.71658	−0.261839
$659$	−23.5058	−0.915657	−0.457828	−	0.889041i	$-0.651373\pi$
$659$	−23.5058	−0.915657	−0.457828	+	0.889041i	$0.651373\pi$
$660$	−6.26207	−0.243751
$661$	−0.143142	−0.00556759	−0.00278380	−	0.999996i	$-0.500886\pi$
$661$	−0.143142	−0.00556759	−0.00278380	+	0.999996i	$0.500886\pi$
$662$	35.9199	1.39607
$663$	2.34062	0.0909022
$664$	−0.106493	−0.00413273
$665$	10.6924	0.414634
$666$	−0.508678	−0.0197109
$667$	0.0688633	0.00266640
$668$	−27.0920	−1.04822
$669$	0.915113	0.0353803
$670$	−51.8827	−2.00441
$671$	29.9312	1.15548
$672$	−1.88112	−0.0725658
$673$	−10.2666	−0.395749	−0.197874	−	0.980227i	$-0.563404\pi$
$673$	−10.2666	−0.395749	−0.197874	+	0.980227i	$0.563404\pi$
$674$	63.0546	2.42877
$675$	−2.56469	−0.0987148
$676$	−6.74420	−0.259392
$677$	20.4734	0.786857	0.393428	−	0.919355i	$-0.371289\pi$
$677$	20.4734	0.786857	0.393428	+	0.919355i	$0.371289\pi$
$678$	−2.73397	−0.104998
$679$	−10.9300	−0.419455
$680$	−0.0516363	−0.00198016
$681$	−5.37526	−0.205980
$682$	22.4089	0.858083
$683$	16.2914	0.623373	0.311687	−	0.950185i	$-0.399106\pi$
$683$	16.2914	0.623373	0.311687	+	0.950185i	$0.399106\pi$
$684$	24.0510	0.919613
$685$	8.49038	0.324401
$686$	1.99923	0.0763309
$687$	0.961376	0.0366788
$688$	18.2833	0.697044
$689$	39.5987	1.50859
$690$	−0.244625	−0.00931270
$691$	41.3696	1.57378	0.786888	−	0.617096i	$-0.211691\pi$
$691$	41.3696	1.57378	0.786888	+	0.617096i	$0.211691\pi$
$692$	−15.4543	−0.587486
$693$	−15.0162	−0.570417
$694$	−1.64227	−0.0623399
$695$	−34.5319	−1.30987
$696$	0.000501312 0	1.90022e−5 0
$697$	30.5683	1.15786
$698$	−69.1258	−2.61645
$699$	6.46864	0.244667
$700$	−3.66246	−0.138428
$701$	13.0898	0.494395	0.247197	−	0.968965i	$-0.420490\pi$
$701$	13.0898	0.494395	0.247197	+	0.968965i	$0.420490\pi$
$702$	−8.67229	−0.327314
$703$	0.353412	0.0133292
$704$	40.6698	1.53280
$705$	−2.06595	−0.0778081
$706$	−26.5905	−1.00075
$707$	−16.2111	−0.609680
$708$	5.82329	0.218853
$709$	−30.7312	−1.15414	−0.577068	−	0.816696i	$-0.695803\pi$
$709$	−30.7312	−1.15414	−0.577068	+	0.816696i	$0.695803\pi$
$710$	−66.5584	−2.49789
$711$	15.3920	0.577244
$712$	0.0334137	0.00125223
$713$	0.437360	0.0163793
$714$	−1.50850	−0.0564542
$715$	41.3534	1.54653
$716$	34.4300	1.28671
$717$	6.54925	0.244586
$718$	−19.0208	−0.709849
$719$	−23.6416	−0.881682	−0.440841	−	0.897585i	$-0.645320\pi$
$719$	−23.6416	−0.881682	−0.440841	+	0.897585i	$0.645320\pi$
$720$	30.8392	1.14931
$721$	−9.26290	−0.344968
$722$	4.54004	0.168963
$723$	−4.15064	−0.154364
$724$	43.2686	1.60806
$725$	0.634740	0.0235737
$726$	−7.05628	−0.261883
$727$	−11.4677	−0.425314	−0.212657	−	0.977127i	$-0.568212\pi$
$727$	−11.4677	−0.425314	−0.212657	+	0.977127i	$0.568212\pi$
$728$	0.0191019	0.000707964 0
$729$	−24.0577	−0.891027
$730$	−40.0180	−1.48113
$731$	14.6391	0.541447
$732$	−2.75713	−0.101906
$733$	−15.8426	−0.585160	−0.292580	−	0.956241i	$-0.594514\pi$
$733$	−15.8426	−0.585160	−0.292580	+	0.956241i	$0.594514\pi$
$734$	47.3269	1.74687
$735$	0.614942	0.0226825
$736$	1.59120	0.0586525
$737$	−50.6226	−1.86471
$738$	−56.1025	−2.06516
$739$	27.1447	0.998534	0.499267	−	0.866448i	$-0.333603\pi$
$739$	27.1447	0.998534	0.499267	+	0.866448i	$0.333603\pi$
$740$	−0.451070	−0.0165817
$741$	2.98456	0.109640
$742$	−25.5209	−0.936901
$743$	41.3731	1.51783	0.758915	−	0.651189i	$-0.225730\pi$
$743$	41.3731	1.51783	0.758915	+	0.651189i	$0.225730\pi$
$744$	0.00318390	0.000116727 0
$745$	43.3795	1.58930
$746$	50.2780	1.84081
$747$	50.9247	1.86324
$748$	32.6642	1.19432
$749$	−14.8116	−0.541205
$750$	3.89225	0.142125
$751$	−11.0704	−0.403965	−0.201983	−	0.979389i	$-0.564738\pi$
$751$	−11.0704	−0.403965	−0.201983	+	0.979389i	$0.564738\pi$
$752$	13.4590	0.490799
$753$	4.60718	0.167895
$754$	2.14632	0.0781645
$755$	−13.5514	−0.493187
$756$	2.79243	0.101560
$757$	−25.2672	−0.918353	−0.459177	−	0.888345i	$-0.651855\pi$
$757$	−25.2672	−0.918353	−0.459177	+	0.888345i	$0.651855\pi$
$758$	−22.8315	−0.829278
$759$	−0.238683	−0.00866365
$760$	−0.0658422	−0.00238835
$761$	−0.368705	−0.0133655	−0.00668277	−	0.999978i	$-0.502127\pi$
$761$	−0.368705	−0.0133655	−0.00668277	+	0.999978i	$0.502127\pi$
$762$	−1.99099	−0.0721259
$763$	−5.46322	−0.197782
$764$	−25.3010	−0.915357
$765$	24.6924	0.892755
$766$	59.8067	2.16090
$767$	−38.4557	−1.38856
$768$	3.77526	0.136228
$769$	−19.6173	−0.707417	−0.353708	−	0.935356i	$-0.615080\pi$
$769$	−19.6173	−0.707417	−0.353708	+	0.935356i	$0.615080\pi$
$770$	−26.6517	−0.960461
$771$	0.800928	0.0288447
$772$	−2.25954	−0.0813227
$773$	26.3231	0.946777	0.473388	−	0.880854i	$-0.343031\pi$
$773$	26.3231	0.946777	0.473388	+	0.880854i	$0.343031\pi$
$774$	−26.8674	−0.965729
$775$	4.03132	0.144809
$776$	0.0673053	0.00241612
$777$	0.0203254	0.000729170 0
$778$	32.5632	1.16745
$779$	38.9780	1.39653
$780$	−3.80928	−0.136394
$781$	−64.9418	−2.32380
$782$	1.27601	0.0456300
$783$	−0.483957	−0.0172952
$784$	−4.00615	−0.143077
$785$	56.5349	2.01782
$786$	4.57552	0.163204
$787$	−11.9167	−0.424784	−0.212392	−	0.977185i	$-0.568125\pi$
$787$	−11.9167	−0.424784	−0.212392	+	0.977185i	$0.568125\pi$
$788$	−16.3733	−0.583274
$789$	5.28620	0.188194
$790$	27.3187	0.971956
$791$	−5.81349	−0.206704
$792$	0.0924673	0.00328568
$793$	18.2075	0.646566
$794$	60.2864	2.13948
$795$	−7.84995	−0.278409
$796$	−55.3558	−1.96204
$797$	−9.69780	−0.343514	−0.171757	−	0.985139i	$-0.554944\pi$
$797$	−9.69780	−0.343514	−0.171757	+	0.985139i	$0.554944\pi$
$798$	−1.92351	−0.0680914
$799$	10.7764	0.381241
$800$	14.6667	0.518548
$801$	−15.9783	−0.564567
$802$	34.2215	1.20840
$803$	−39.0460	−1.37790
$804$	4.66312	0.164456
$805$	−0.520167	−0.0183335
$806$	13.6316	0.480152
$807$	−2.01304	−0.0708623
$808$	0.0998252	0.00351184
$809$	29.2075	1.02688	0.513440	−	0.858125i	$-0.328371\pi$
$809$	29.2075	1.02688	0.513440	+	0.858125i	$0.328371\pi$
$810$	−44.4508	−1.56184
$811$	−20.5813	−0.722707	−0.361353	−	0.932429i	$-0.617685\pi$
$811$	−20.5813	−0.722707	−0.361353	+	0.932429i	$0.617685\pi$
$812$	−0.691106	−0.0242531
$813$	1.61755	0.0567298
$814$	−0.880908	−0.0308758
$815$	20.1359	0.705331
$816$	3.02280	0.105819
$817$	18.6665	0.653059
$818$	−64.0776	−2.24042
$819$	−9.13449	−0.319185
$820$	−49.7488	−1.73730
$821$	−7.23375	−0.252460	−0.126230	−	0.992001i	$-0.540288\pi$
$821$	−7.23375	−0.252460	−0.126230	+	0.992001i	$0.540288\pi$
$822$	−1.52738	−0.0532733
$823$	16.9895	0.592216	0.296108	−	0.955154i	$-0.404311\pi$
$823$	16.9895	0.592216	0.296108	+	0.955154i	$0.404311\pi$
$824$	0.0570395	0.00198706
$825$	−2.20004	−0.0765955
$826$	24.7842	0.862354
$827$	21.1835	0.736621	0.368310	−	0.929703i	$-0.379936\pi$
$827$	21.1835	0.736621	0.368310	+	0.929703i	$0.379936\pi$
$828$	−1.17004	−0.0406617
$829$	−3.80092	−0.132012	−0.0660058	−	0.997819i	$-0.521026\pi$
$829$	−3.80092	−0.132012	−0.0660058	+	0.997819i	$0.521026\pi$
$830$	90.3846	3.13730
$831$	1.83625	0.0636987
$832$	24.7399	0.857701
$833$	−3.20766	−0.111139
$834$	6.21210	0.215107
$835$	−35.4666	−1.22737
$836$	41.6505	1.44051
$837$	−3.07367	−0.106242
$838$	−7.29771	−0.252095
$839$	28.2132	0.974029	0.487014	−	0.873394i	$-0.338086\pi$
$839$	28.2132	0.974029	0.487014	+	0.873394i	$0.338086\pi$
$840$	−0.00378672	−0.000130654 0
$841$	−28.8802	−0.995870
$842$	−0.108377	−0.00373492
$843$	−7.34563	−0.252997
$844$	−11.8178	−0.406786
$845$	−8.82895	−0.303725
$846$	−19.7781	−0.679984
$847$	−15.0044	−0.515557
$848$	51.1399	1.75615
$849$	6.00598	0.206125
$850$	11.7615	0.403416
$851$	−0.0171929	−0.000589364 0
$852$	5.98214	0.204945
$853$	−8.88461	−0.304203	−0.152102	−	0.988365i	$-0.548604\pi$
$853$	−8.88461	−0.304203	−0.152102	+	0.988365i	$0.548604\pi$
$854$	−11.7345	−0.401545
$855$	31.4856	1.07678
$856$	0.0912077	0.00311741
$857$	−12.5698	−0.429376	−0.214688	−	0.976683i	$-0.568873\pi$
$857$	−12.5698	−0.429376	−0.214688	+	0.976683i	$0.568873\pi$
$858$	−7.43925	−0.253972
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−23.8247	−0.812414
$861$	2.24170	0.0763970
$862$	−43.2666	−1.47367
$863$	3.49843	0.119088	0.0595439	−	0.998226i	$-0.481035\pi$
$863$	3.49843	0.119088	0.0595439	+	0.998226i	$0.481035\pi$
$864$	−11.1826	−0.380441
$865$	−20.2315	−0.687893
$866$	31.4577	1.06897
$867$	−1.57862	−0.0536129
$868$	−4.38931	−0.148983
$869$	26.6552	0.904215
$870$	−0.425482	−0.0144252
$871$	−30.7942	−1.04342
$872$	0.0336416	0.00113925
$873$	−32.1852	−1.08931
$874$	1.62706	0.0550360
$875$	8.27643	0.279794
$876$	3.59674	0.121523
$877$	21.5763	0.728578	0.364289	−	0.931286i	$-0.381312\pi$
$877$	21.5763	0.728578	0.364289	+	0.931286i	$0.381312\pi$
$878$	−9.68895	−0.326986
$879$	−7.62208	−0.257086
$880$	53.4060	1.80031
$881$	10.8784	0.366504	0.183252	−	0.983066i	$-0.441338\pi$
$881$	10.8784	0.366504	0.183252	+	0.983066i	$0.441338\pi$
$882$	5.88706	0.198228
$883$	−27.5809	−0.928172	−0.464086	−	0.885790i	$-0.653617\pi$
$883$	−27.5809	−0.928172	−0.464086	+	0.885790i	$0.653617\pi$
$884$	19.8700	0.668299
$885$	7.62337	0.256257
$886$	9.55216	0.320911
$887$	41.9488	1.40850	0.704251	−	0.709951i	$-0.251283\pi$
$887$	41.9488	1.40850	0.704251	+	0.709951i	$0.251283\pi$
$888$	−0.000125161 0	−4.20012e−6 0
$889$	−4.23361	−0.141991
$890$	−28.3594	−0.950610
$891$	−43.3711	−1.45299
$892$	7.76856	0.260111
$893$	13.7411	0.459829
$894$	−7.80374	−0.260996
$895$	45.0729	1.50662
$896$	0.0492627	0.00164575
$897$	−0.145193	−0.00484787
$898$	−23.2605	−0.776213
$899$	0.760711	0.0253711
$900$	−10.7847	−0.359490
$901$	40.9468	1.36414
$902$	−97.1559	−3.23494
$903$	1.07355	0.0357255
$904$	0.0357985	0.00119064
$905$	56.6437	1.88290
$906$	2.43783	0.0809914
$907$	15.2319	0.505765	0.252883	−	0.967497i	$-0.418621\pi$
$907$	15.2319	0.505765	0.252883	+	0.967497i	$0.418621\pi$
$908$	−45.6315	−1.51434
$909$	−47.7362	−1.58331
$910$	−16.2125	−0.537440
$911$	−8.35730	−0.276890	−0.138445	−	0.990370i	$-0.544210\pi$
$911$	−8.35730	−0.276890	−0.138445	+	0.990370i	$0.544210\pi$
$912$	3.85442	0.127632
$913$	88.1893	2.91864
$914$	46.2657	1.53033
$915$	−3.60940	−0.119323
$916$	8.16130	0.269657
$917$	9.72934	0.321291
$918$	−8.96753	−0.295973
$919$	−5.69897	−0.187992	−0.0939958	−	0.995573i	$-0.529964\pi$
$919$	−5.69897	−0.187992	−0.0939958	+	0.995573i	$0.529964\pi$
$920$	0.00320311	0.000105603 0
$921$	−5.55089	−0.182908
$922$	10.2539	0.337693
$923$	−39.5048	−1.30032
$924$	2.39540	0.0788030
$925$	−0.158473	−0.00521057
$926$	13.2015	0.433828
$927$	−27.2761	−0.895866
$928$	2.76762	0.0908515
$929$	−39.8982	−1.30902	−0.654508	−	0.756055i	$-0.727124\pi$
$929$	−39.8982	−1.30902	−0.654508	+	0.756055i	$0.727124\pi$
$930$	−2.70229	−0.0886116
$931$	−4.09012	−0.134048
$932$	54.9135	1.79875
$933$	6.27951	0.205582
$934$	−33.1367	−1.08427
$935$	42.7612	1.39844
$936$	0.0562488	0.00183855
$937$	0.183175	0.00598408	0.00299204	−	0.999996i	$-0.499048\pi$
$937$	0.183175	0.00598408	0.00299204	+	0.999996i	$0.499048\pi$
$938$	19.8465	0.648011
$939$	−2.29912	−0.0750289
$940$	−17.5382	−0.572033
$941$	10.1310	0.330261	0.165131	−	0.986272i	$-0.447195\pi$
$941$	10.1310	0.330261	0.165131	+	0.986272i	$0.447195\pi$
$942$	−10.1703	−0.331368
$943$	−1.89621	−0.0617491
$944$	−49.6638	−1.61642
$945$	3.65562	0.118917
$946$	−46.5279	−1.51275
$947$	−8.99572	−0.292322	−0.146161	−	0.989261i	$-0.546692\pi$
$947$	−8.99572	−0.292322	−0.146161	+	0.989261i	$0.546692\pi$
$948$	−2.45535	−0.0797462
$949$	−23.7521	−0.771026
$950$	14.9972	0.486574
$951$	−6.93448	−0.224866
$952$	0.0197522	0.000640174 0
$953$	16.0622	0.520307	0.260153	−	0.965567i	$-0.416227\pi$
$953$	16.0622	0.520307	0.260153	+	0.965567i	$0.416227\pi$
$954$	−75.1504	−2.43309
$955$	−33.1220	−1.07180
$956$	55.5978	1.79816
$957$	−0.415148	−0.0134198
$958$	5.01881	0.162150
$959$	−3.24779	−0.104877
$960$	−4.90437	−0.158288
$961$	−26.1686	−0.844149
$962$	−0.535865	−0.0172770
$963$	−43.6153	−1.40548
$964$	−35.2356	−1.13486
$965$	−2.95801	−0.0952216
$966$	0.0935753	0.00301074
$967$	−8.55267	−0.275035	−0.137518	−	0.990499i	$-0.543912\pi$
$967$	−8.55267	−0.275035	−0.137518	+	0.990499i	$0.543912\pi$
$968$	0.0923947	0.00296968
$969$	3.08616	0.0991419
$970$	−57.1245	−1.83416
$971$	−14.1568	−0.454315	−0.227157	−	0.973858i	$-0.572943\pi$
$971$	−14.1568	−0.454315	−0.227157	+	0.973858i	$0.572943\pi$
$972$	12.3725	0.396847
$973$	13.2093	0.423472
$974$	−26.1948	−0.839335
$975$	−1.33831	−0.0428601
$976$	23.5141	0.752668
$977$	52.6654	1.68492	0.842458	−	0.538761i	$-0.181108\pi$
$977$	52.6654	1.68492	0.842458	+	0.538761i	$0.181108\pi$
$978$	−3.62235	−0.115830
$979$	−27.6706	−0.884357
$980$	5.22035	0.166758
$981$	−16.0874	−0.513630
$982$	−72.7752	−2.32235
$983$	21.7387	0.693356	0.346678	−	0.937984i	$-0.387310\pi$
$983$	21.7387	0.693356	0.346678	+	0.937984i	$0.387310\pi$
$984$	−0.0138041	−0.000440057 0
$985$	−21.4345	−0.682961
$986$	2.21940	0.0706799
$987$	0.790279	0.0251548
$988$	25.3364	0.806059
$989$	−0.908093	−0.0288757
$990$	−78.4804	−2.49427
$991$	41.4484	1.31665	0.658326	−	0.752733i	$-0.271265\pi$
$991$	41.4484	1.31665	0.658326	+	0.752733i	$0.271265\pi$
$992$	17.5775	0.558086
$993$	−4.22636	−0.134120
$994$	25.4603	0.807552
$995$	−72.4673	−2.29737
$996$	−8.12359	−0.257406
$997$	−24.3639	−0.771613	−0.385807	−	0.922580i	$-0.626077\pi$
$997$	−24.3639	−0.771613	−0.385807	+	0.922580i	$0.626077\pi$
$998$	66.4927	2.10479
$999$	0.120828	0.00382282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.17	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.17	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99923 q^{2} +0.235231 q^{3} +1.99692 q^{4} +2.61420 q^{5} -0.470281 q^{6} -1.00000 q^{7} +0.00615784 q^{8} -2.94467 q^{9} +O(q^{10})\)	\(q-1.99923 q^{2} +0.235231 q^{3} +1.99692 q^{4} +2.61420 q^{5} -0.470281 q^{6} -1.00000 q^{7} +0.00615784 q^{8} -2.94467 q^{9} -5.22639 q^{10} -5.09945 q^{11} +0.469738 q^{12} -3.10205 q^{13} +1.99923 q^{14} +0.614942 q^{15} -4.00615 q^{16} -3.20766 q^{17} +5.88706 q^{18} -4.09012 q^{19} +5.22035 q^{20} -0.235231 q^{21} +10.1950 q^{22} +0.198977 q^{23} +0.00144852 q^{24} +1.83405 q^{25} +6.20171 q^{26} -1.39837 q^{27} -1.99692 q^{28} +0.346086 q^{29} -1.22941 q^{30} +2.19804 q^{31} +7.99690 q^{32} -1.19955 q^{33} +6.41284 q^{34} -2.61420 q^{35} -5.88026 q^{36} -0.0864061 q^{37} +8.17710 q^{38} -0.729698 q^{39} +0.0160978 q^{40} -9.52978 q^{41} +0.470281 q^{42} -4.56380 q^{43} -10.1832 q^{44} -7.69795 q^{45} -0.397801 q^{46} -3.35958 q^{47} -0.942372 q^{48} +1.00000 q^{49} -3.66669 q^{50} -0.754541 q^{51} -6.19454 q^{52} -12.7654 q^{53} +2.79566 q^{54} -13.3310 q^{55} -0.00615784 q^{56} -0.962124 q^{57} -0.691906 q^{58} +12.3969 q^{59} +1.22799 q^{60} -5.86950 q^{61} -4.39438 q^{62} +2.94467 q^{63} -7.97534 q^{64} -8.10938 q^{65} +2.39818 q^{66} +9.92707 q^{67} -6.40543 q^{68} +0.0468057 q^{69} +5.22639 q^{70} +12.7351 q^{71} -0.0181328 q^{72} +7.65691 q^{73} +0.172746 q^{74} +0.431426 q^{75} -8.16765 q^{76} +5.09945 q^{77} +1.45883 q^{78} -5.22707 q^{79} -10.4729 q^{80} +8.50506 q^{81} +19.0522 q^{82} -17.2939 q^{83} -0.469738 q^{84} -8.38546 q^{85} +9.12409 q^{86} +0.0814103 q^{87} -0.0314016 q^{88} +5.42620 q^{89} +15.3900 q^{90} +3.10205 q^{91} +0.397342 q^{92} +0.517047 q^{93} +6.71658 q^{94} -10.6924 q^{95} +1.88112 q^{96} +10.9300 q^{97} -1.99923 q^{98} +15.0162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more