LMFDB - Embedded newform 7007.2.a.bi.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7007,2,Mod(1,7007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7007, 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("7007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7007 = 7^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7007.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:	$55.9511766963$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1001)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	7007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0484145 q^{2} +1.85996 q^{3} -1.99766 q^{4} +2.21431 q^{5} +0.0900488 q^{6} -0.193545 q^{8} +0.459434 q^{9} +O(q^{10})$	\(q+0.0484145 q^{2} +1.85996 q^{3} -1.99766 q^{4} +2.21431 q^{5} +0.0900488 q^{6} -0.193545 q^{8} +0.459434 q^{9} +0.107205 q^{10} +1.00000 q^{11} -3.71555 q^{12} +1.00000 q^{13} +4.11852 q^{15} +3.98594 q^{16} +3.35684 q^{17} +0.0222433 q^{18} -6.21406 q^{19} -4.42343 q^{20} +0.0484145 q^{22} -4.37712 q^{23} -0.359984 q^{24} -0.0968341 q^{25} +0.0484145 q^{26} -4.72534 q^{27} -4.39582 q^{29} +0.199396 q^{30} +7.65667 q^{31} +0.580067 q^{32} +1.85996 q^{33} +0.162520 q^{34} -0.917792 q^{36} +5.38300 q^{37} -0.300851 q^{38} +1.85996 q^{39} -0.428568 q^{40} +4.23985 q^{41} +9.47985 q^{43} -1.99766 q^{44} +1.01733 q^{45} -0.211916 q^{46} +13.4090 q^{47} +7.41367 q^{48} -0.00468817 q^{50} +6.24358 q^{51} -1.99766 q^{52} -6.76895 q^{53} -0.228775 q^{54} +2.21431 q^{55} -11.5579 q^{57} -0.212822 q^{58} -10.4648 q^{59} -8.22738 q^{60} +11.5831 q^{61} +0.370694 q^{62} -7.94380 q^{64} +2.21431 q^{65} +0.0900488 q^{66} +12.6071 q^{67} -6.70582 q^{68} -8.14125 q^{69} -1.24711 q^{71} -0.0889210 q^{72} +11.5448 q^{73} +0.260615 q^{74} -0.180107 q^{75} +12.4136 q^{76} +0.0900488 q^{78} +0.448193 q^{79} +8.82611 q^{80} -10.1672 q^{81} +0.205270 q^{82} +3.12782 q^{83} +7.43309 q^{85} +0.458962 q^{86} -8.17604 q^{87} -0.193545 q^{88} +17.1236 q^{89} +0.0492535 q^{90} +8.74398 q^{92} +14.2411 q^{93} +0.649191 q^{94} -13.7599 q^{95} +1.07890 q^{96} +12.9138 q^{97} +0.459434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9	$ 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9} + 3 q^{10} + 25 q^{11} - 9 q^{12} + 25 q^{13} + 32 q^{16} + q^{17} + 44 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{22} + 15 q^{23} + 4 q^{24} + 50 q^{25} + 6 q^{26} + 17 q^{27} + 24 q^{29} + q^{30} + 12 q^{31} + 48 q^{32} + 2 q^{33} + 8 q^{34} + 30 q^{36} + 33 q^{37} - 16 q^{38} + 2 q^{39} + 21 q^{40} - 12 q^{41} + 38 q^{43} + 30 q^{44} + 22 q^{45} + 39 q^{46} - 4 q^{47} - 82 q^{48} + 16 q^{50} + 51 q^{51} + 30 q^{52} + 2 q^{53} - 10 q^{54} + q^{55} + 38 q^{57} + 17 q^{58} + 4 q^{59} - 33 q^{60} + 22 q^{61} - 42 q^{62} + 41 q^{64} + q^{65} - 2 q^{66} + 24 q^{67} - 14 q^{68} + 30 q^{69} + 9 q^{71} + 102 q^{72} - 11 q^{73} + 39 q^{74} + 16 q^{75} - 58 q^{76} - 2 q^{78} + 19 q^{79} + 33 q^{80} + 73 q^{81} + 32 q^{82} - 16 q^{83} + 14 q^{85} + 27 q^{86} + 11 q^{87} + 21 q^{88} - 13 q^{89} - 40 q^{90} + 17 q^{93} + 56 q^{94} + 15 q^{95} - 55 q^{96} - 34 q^{97} + 37 q^{99}+O(q^{100}) $ 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9 + 3 * q^10 + 25 * q^11 - 9 * q^12 + 25 * q^13 + 32 * q^16 + q^17 + 44 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^22 + 15 * q^23 + 4 * q^24 + 50 * q^25 + 6 * q^26 + 17 * q^27 + 24 * q^29 + q^30 + 12 * q^31 + 48 * q^32 + 2 * q^33 + 8 * q^34 + 30 * q^36 + 33 * q^37 - 16 * q^38 + 2 * q^39 + 21 * q^40 - 12 * q^41 + 38 * q^43 + 30 * q^44 + 22 * q^45 + 39 * q^46 - 4 * q^47 - 82 * q^48 + 16 * q^50 + 51 * q^51 + 30 * q^52 + 2 * q^53 - 10 * q^54 + q^55 + 38 * q^57 + 17 * q^58 + 4 * q^59 - 33 * q^60 + 22 * q^61 - 42 * q^62 + 41 * q^64 + q^65 - 2 * q^66 + 24 * q^67 - 14 * q^68 + 30 * q^69 + 9 * q^71 + 102 * q^72 - 11 * q^73 + 39 * q^74 + 16 * q^75 - 58 * q^76 - 2 * q^78 + 19 * q^79 + 33 * q^80 + 73 * q^81 + 32 * q^82 - 16 * q^83 + 14 * q^85 + 27 * q^86 + 11 * q^87 + 21 * q^88 - 13 * q^89 - 40 * q^90 + 17 * q^93 + 56 * q^94 + 15 * q^95 - 55 * q^96 - 34 * q^97 + 37 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.0484145	0.0342342	0.0171171	−	0.999853i	$-0.494551\pi$
$2$	0.0484145	0.0342342	0.0171171	+	0.999853i	$0.494551\pi$
$3$	1.85996	1.07385	0.536923	−	0.843631i	$-0.319587\pi$
$3$	1.85996	1.07385	0.536923	+	0.843631i	$0.319587\pi$
$4$	−1.99766	−0.998828
$5$	2.21431	0.990269	0.495135	−	0.868816i	$-0.335119\pi$
$5$	2.21431	0.990269	0.495135	+	0.868816i	$0.335119\pi$
$6$	0.0900488	0.0367623
$7$	0	0
$7$	0	0
$8$	−0.193545	−0.0684283
$9$	0.459434	0.153145
$10$	0.107205	0.0339011
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.71555	−1.07259
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	4.11852	1.06340
$16$	3.98594	0.996485
$17$	3.35684	0.814154	0.407077	−	0.913394i	$-0.366548\pi$
$17$	3.35684	0.814154	0.407077	+	0.913394i	$0.366548\pi$
$18$	0.0222433	0.00524279
$19$	−6.21406	−1.42560	−0.712802	−	0.701366i	$-0.752574\pi$
$19$	−6.21406	−1.42560	−0.712802	+	0.701366i	$0.752574\pi$
$20$	−4.42343	−0.989109
$21$	0	0
$22$	0.0484145	0.0103220
$23$	−4.37712	−0.912693	−0.456346	−	0.889802i	$-0.650842\pi$
$23$	−4.37712	−0.912693	−0.456346	+	0.889802i	$0.650842\pi$
$24$	−0.359984	−0.0734815
$25$	−0.0968341	−0.0193668
$26$	0.0484145	0.00949487
$27$	−4.72534	−0.909392
$28$	0	0
$29$	−4.39582	−0.816284	−0.408142	−	0.912918i	$-0.633823\pi$
$29$	−4.39582	−0.816284	−0.408142	+	0.912918i	$0.633823\pi$
$30$	0.199396	0.0364046
$31$	7.65667	1.37518	0.687589	−	0.726100i	$-0.258669\pi$
$31$	7.65667	1.37518	0.687589	+	0.726100i	$0.258669\pi$
$32$	0.580067	0.102542
$33$	1.85996	0.323777
$34$	0.162520	0.0278719
$35$	0	0
$36$	−0.917792	−0.152965
$37$	5.38300	0.884960	0.442480	−	0.896778i	$-0.354099\pi$
$37$	5.38300	0.884960	0.442480	+	0.896778i	$0.354099\pi$
$38$	−0.300851	−0.0488044
$39$	1.85996	0.297831
$40$	−0.428568	−0.0677625
$41$	4.23985	0.662153	0.331077	−	0.943604i	$-0.392588\pi$
$41$	4.23985	0.662153	0.331077	+	0.943604i	$0.392588\pi$
$42$	0	0
$43$	9.47985	1.44566	0.722832	−	0.691024i	$-0.242840\pi$
$43$	9.47985	1.44566	0.722832	+	0.691024i	$0.242840\pi$
$44$	−1.99766	−0.301158
$45$	1.01733	0.151655
$46$	−0.211916	−0.0312453
$47$	13.4090	1.95591	0.977953	−	0.208824i	$-0.0669634\pi$
$47$	13.4090	1.95591	0.977953	+	0.208824i	$0.0669634\pi$
$48$	7.41367	1.07007
$49$	0	0
$50$	−0.00468817	−0.000663008 0
$51$	6.24358	0.874276
$52$	−1.99766	−0.277025
$53$	−6.76895	−0.929786	−0.464893	−	0.885367i	$-0.653907\pi$
$53$	−6.76895	−0.929786	−0.464893	+	0.885367i	$0.653907\pi$
$54$	−0.228775	−0.0311323
$55$	2.21431	0.298577
$56$	0	0
$57$	−11.5579	−1.53088
$58$	−0.212822	−0.0279449
$59$	−10.4648	−1.36240	−0.681202	−	0.732095i	$-0.738543\pi$
$59$	−10.4648	−1.36240	−0.681202	+	0.732095i	$0.738543\pi$
$60$	−8.22738	−1.06215
$61$	11.5831	1.48307	0.741535	−	0.670914i	$-0.234098\pi$
$61$	11.5831	1.48307	0.741535	+	0.670914i	$0.234098\pi$
$62$	0.370694	0.0470782
$63$	0	0
$64$	−7.94380	−0.992975
$65$	2.21431	0.274651
$66$	0.0900488	0.0110842
$67$	12.6071	1.54020	0.770099	−	0.637925i	$-0.220207\pi$
$67$	12.6071	1.54020	0.770099	+	0.637925i	$0.220207\pi$
$68$	−6.70582	−0.813200
$69$	−8.14125	−0.980091
$70$	0	0
$71$	−1.24711	−0.148004	−0.0740022	−	0.997258i	$-0.523577\pi$
$71$	−1.24711	−0.148004	−0.0740022	+	0.997258i	$0.523577\pi$
$72$	−0.0889210	−0.0104794
$73$	11.5448	1.35122	0.675608	−	0.737261i	$-0.263881\pi$
$73$	11.5448	1.35122	0.675608	+	0.737261i	$0.263881\pi$
$74$	0.260615	0.0302959
$75$	−0.180107	−0.0207970
$76$	12.4136	1.42393
$77$	0	0
$78$	0.0900488	0.0101960
$79$	0.448193	0.0504256	0.0252128	−	0.999682i	$-0.491974\pi$
$79$	0.448193	0.0504256	0.0252128	+	0.999682i	$0.491974\pi$
$80$	8.82611	0.986789
$81$	−10.1672	−1.12969
$82$	0.205270	0.0226683
$83$	3.12782	0.343323	0.171662	−	0.985156i	$-0.445086\pi$
$83$	3.12782	0.343323	0.171662	+	0.985156i	$0.445086\pi$
$84$	0	0
$85$	7.43309	0.806232
$86$	0.458962	0.0494912
$87$	−8.17604	−0.876563
$88$	−0.193545	−0.0206319
$89$	17.1236	1.81510	0.907549	−	0.419946i	$-0.137951\pi$
$89$	17.1236	1.81510	0.907549	+	0.419946i	$0.137951\pi$
$90$	0.0492535	0.00519178
$91$	0	0
$92$	8.74398	0.911623
$93$	14.2411	1.47673
$94$	0.649191	0.0669590
$95$	−13.7599	−1.41173
$96$	1.07890	0.110115
$97$	12.9138	1.31120	0.655599	−	0.755109i	$-0.272416\pi$
$97$	12.9138	1.31120	0.655599	+	0.755109i	$0.272416\pi$
$98$	0	0
$99$	0.459434	0.0461749
$100$	0.193441	0.0193441
$101$	12.2686	1.22078	0.610388	−	0.792103i	$-0.291014\pi$
$101$	12.2686	1.22078	0.610388	+	0.792103i	$0.291014\pi$
$102$	0.302280	0.0299302
$103$	6.74582	0.664686	0.332343	−	0.943159i	$-0.392161\pi$
$103$	6.74582	0.664686	0.332343	+	0.943159i	$0.392161\pi$
$104$	−0.193545	−0.0189786
$105$	0	0
$106$	−0.327715	−0.0318305
$107$	−5.84088	−0.564659	−0.282330	−	0.959317i	$-0.591107\pi$
$107$	−5.84088	−0.564659	−0.282330	+	0.959317i	$0.591107\pi$
$108$	9.43960	0.908326
$109$	−0.798060	−0.0764403	−0.0382202	−	0.999269i	$-0.512169\pi$
$109$	−0.798060	−0.0764403	−0.0382202	+	0.999269i	$0.512169\pi$
$110$	0.107205	0.0102216
$111$	10.0121	0.950310
$112$	0	0
$113$	−11.7737	−1.10757	−0.553787	−	0.832659i	$-0.686818\pi$
$113$	−11.7737	−1.10757	−0.553787	+	0.832659i	$0.686818\pi$
$114$	−0.559569	−0.0524084
$115$	−9.69230	−0.903812
$116$	8.78134	0.815327
$117$	0.459434	0.0424747
$118$	−0.506649	−0.0466409
$119$	0	0
$120$	−0.797117	−0.0727665
$121$	1.00000	0.0909091
$122$	0.560792	0.0507717
$123$	7.88593	0.711051
$124$	−15.2954	−1.37357
$125$	−11.2860	−1.00945
$126$	0	0
$127$	−5.69441	−0.505297	−0.252648	−	0.967558i	$-0.581302\pi$
$127$	−5.69441	−0.505297	−0.252648	+	0.967558i	$0.581302\pi$
$128$	−1.54473	−0.136536
$129$	17.6321	1.55242
$130$	0.107205	0.00940247
$131$	12.5054	1.09260	0.546300	−	0.837589i	$-0.316036\pi$
$131$	12.5054	1.09260	0.546300	+	0.837589i	$0.316036\pi$
$132$	−3.71555	−0.323397
$133$	0	0
$134$	0.610365	0.0527275
$135$	−10.4634	−0.900543
$136$	−0.649699	−0.0557112
$137$	−9.10867	−0.778206	−0.389103	−	0.921194i	$-0.627215\pi$
$137$	−9.10867	−0.778206	−0.389103	+	0.921194i	$0.627215\pi$
$138$	−0.394155	−0.0335527
$139$	−18.6605	−1.58276	−0.791381	−	0.611323i	$-0.790638\pi$
$139$	−18.6605	−1.58276	−0.791381	+	0.611323i	$0.790638\pi$
$140$	0	0
$141$	24.9402	2.10034
$142$	−0.0603781	−0.00506682
$143$	1.00000	0.0836242
$144$	1.83128	0.152607
$145$	−9.73371	−0.808341
$146$	0.558936	0.0462579
$147$	0	0
$148$	−10.7534	−0.883922
$149$	−6.31255	−0.517144	−0.258572	−	0.965992i	$-0.583252\pi$
$149$	−6.31255	−0.517144	−0.258572	+	0.965992i	$0.583252\pi$
$150$	−0.00871980	−0.000711968 0
$151$	−0.790302	−0.0643138	−0.0321569	−	0.999483i	$-0.510238\pi$
$151$	−0.790302	−0.0643138	−0.0321569	+	0.999483i	$0.510238\pi$
$152$	1.20270	0.0975517
$153$	1.54225	0.124683
$154$	0	0
$155$	16.9542	1.36180
$156$	−3.71555	−0.297482
$157$	−4.04145	−0.322542	−0.161271	−	0.986910i	$-0.551559\pi$
$157$	−4.04145	−0.322542	−0.161271	+	0.986910i	$0.551559\pi$
$158$	0.0216990	0.00172628
$159$	−12.5899	−0.998447
$160$	1.28445	0.101544
$161$	0	0
$162$	−0.492241	−0.0386741
$163$	−8.45918	−0.662574	−0.331287	−	0.943530i	$-0.607483\pi$
$163$	−8.45918	−0.662574	−0.331287	+	0.943530i	$0.607483\pi$
$164$	−8.46976	−0.661377
$165$	4.11852	0.320626
$166$	0.151432	0.0117534
$167$	5.76704	0.446267	0.223134	−	0.974788i	$-0.428371\pi$
$167$	5.76704	0.446267	0.223134	+	0.974788i	$0.428371\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0.359869	0.0276007
$171$	−2.85495	−0.218324
$172$	−18.9375	−1.44397
$173$	−8.34498	−0.634457	−0.317228	−	0.948349i	$-0.602752\pi$
$173$	−8.34498	−0.634457	−0.317228	+	0.948349i	$0.602752\pi$
$174$	−0.395839	−0.0300085
$175$	0	0
$176$	3.98594	0.300452
$177$	−19.4641	−1.46301
$178$	0.829031	0.0621385
$179$	1.57840	0.117975	0.0589875	−	0.998259i	$-0.481213\pi$
$179$	1.57840	0.117975	0.0589875	+	0.998259i	$0.481213\pi$
$180$	−2.03228	−0.151477
$181$	−19.3014	−1.43466	−0.717332	−	0.696732i	$-0.754637\pi$
$181$	−19.3014	−1.43466	−0.717332	+	0.696732i	$0.754637\pi$
$182$	0	0
$183$	21.5441	1.59259
$184$	0.847168	0.0624540
$185$	11.9196	0.876348
$186$	0.689474	0.0505547
$187$	3.35684	0.245477
$188$	−26.7866	−1.95361
$189$	0	0
$190$	−0.666177	−0.0483295
$191$	4.52893	0.327702	0.163851	−	0.986485i	$-0.447608\pi$
$191$	4.52893	0.327702	0.163851	+	0.986485i	$0.447608\pi$
$192$	−14.7751	−1.06630
$193$	27.2233	1.95958	0.979788	−	0.200037i	$-0.0641061\pi$
$193$	27.2233	1.95958	0.979788	+	0.200037i	$0.0641061\pi$
$194$	0.625216	0.0448879
$195$	4.11852	0.294933
$196$	0	0
$197$	−22.7438	−1.62043	−0.810214	−	0.586134i	$-0.800649\pi$
$197$	−22.7438	−1.62043	−0.810214	+	0.586134i	$0.800649\pi$
$198$	0.0222433	0.00158076
$199$	23.9650	1.69883	0.849416	−	0.527723i	$-0.176954\pi$
$199$	23.9650	1.69883	0.849416	+	0.527723i	$0.176954\pi$
$200$	0.0187417	0.00132524
$201$	23.4486	1.65393
$202$	0.593980	0.0417923
$203$	0	0
$204$	−12.4725	−0.873251
$205$	9.38834	0.655710
$206$	0.326596	0.0227550
$207$	−2.01100	−0.139774
$208$	3.98594	0.276375
$209$	−6.21406	−0.429836
$210$	0	0
$211$	4.65727	0.320619	0.160310	−	0.987067i	$-0.448751\pi$
$211$	4.65727	0.320619	0.160310	+	0.987067i	$0.448751\pi$
$212$	13.5220	0.928697
$213$	−2.31956	−0.158934
$214$	−0.282783	−0.0193307
$215$	20.9913	1.43160
$216$	0.914564	0.0622282
$217$	0	0
$218$	−0.0386377	−0.00261687
$219$	21.4728	1.45100
$220$	−4.42343	−0.298227
$221$	3.35684	0.225806
$222$	0.484733	0.0325331
$223$	−24.0322	−1.60931	−0.804657	−	0.593741i	$-0.797651\pi$
$223$	−24.0322	−1.60931	−0.804657	+	0.593741i	$0.797651\pi$
$224$	0	0
$225$	−0.0444889	−0.00296593
$226$	−0.570016	−0.0379169
$227$	−16.4603	−1.09251	−0.546255	−	0.837619i	$-0.683947\pi$
$227$	−16.4603	−1.09251	−0.546255	+	0.837619i	$0.683947\pi$
$228$	23.0887	1.52908
$229$	13.5040	0.892367	0.446184	−	0.894941i	$-0.352783\pi$
$229$	13.5040	0.892367	0.446184	+	0.894941i	$0.352783\pi$
$230$	−0.469248	−0.0309413
$231$	0	0
$232$	0.850788	0.0558570
$233$	21.1968	1.38865	0.694324	−	0.719663i	$-0.255704\pi$
$233$	21.1968	1.38865	0.694324	+	0.719663i	$0.255704\pi$
$234$	0.0222433	0.00145409
$235$	29.6917	1.93687
$236$	20.9051	1.36081
$237$	0.833619	0.0541494
$238$	0	0
$239$	23.1259	1.49589	0.747946	−	0.663760i	$-0.231040\pi$
$239$	23.1259	1.49589	0.747946	+	0.663760i	$0.231040\pi$
$240$	16.4162	1.05966
$241$	−4.07929	−0.262770	−0.131385	−	0.991331i	$-0.541942\pi$
$241$	−4.07929	−0.262770	−0.131385	+	0.991331i	$0.541942\pi$
$242$	0.0484145	0.00311220
$243$	−4.73457	−0.303723
$244$	−23.1391	−1.48133
$245$	0	0
$246$	0.381794	0.0243423
$247$	−6.21406	−0.395391
$248$	−1.48191	−0.0941011
$249$	5.81761	0.368676
$250$	−0.546405	−0.0345577
$251$	6.90416	0.435787	0.217893	−	0.975973i	$-0.430082\pi$
$251$	6.90416	0.435787	0.217893	+	0.975973i	$0.430082\pi$
$252$	0	0
$253$	−4.37712	−0.275187
$254$	−0.275692	−0.0172984
$255$	13.8252	0.865768
$256$	15.8128	0.988301
$257$	7.29099	0.454799	0.227400	−	0.973802i	$-0.426978\pi$
$257$	7.29099	0.454799	0.227400	+	0.973802i	$0.426978\pi$
$258$	0.853650	0.0531459
$259$	0	0
$260$	−4.42343	−0.274329
$261$	−2.01959	−0.125010
$262$	0.605442	0.0374044
$263$	25.7364	1.58697	0.793486	−	0.608589i	$-0.208264\pi$
$263$	25.7364	1.58697	0.793486	+	0.608589i	$0.208264\pi$
$264$	−0.359984	−0.0221555
$265$	−14.9885	−0.920739
$266$	0	0
$267$	31.8491	1.94914
$268$	−25.1846	−1.53839
$269$	2.78906	0.170052	0.0850260	−	0.996379i	$-0.472903\pi$
$269$	2.78906	0.170052	0.0850260	+	0.996379i	$0.472903\pi$
$270$	−0.506579	−0.0308294
$271$	5.51241	0.334855	0.167428	−	0.985884i	$-0.446454\pi$
$271$	5.51241	0.334855	0.167428	+	0.985884i	$0.446454\pi$
$272$	13.3802	0.811292
$273$	0	0
$274$	−0.440992	−0.0266413
$275$	−0.0968341	−0.00583931
$276$	16.2634	0.978943
$277$	24.8391	1.49244	0.746219	−	0.665700i	$-0.231867\pi$
$277$	24.8391	1.49244	0.746219	+	0.665700i	$0.231867\pi$
$278$	−0.903439	−0.0541846
$279$	3.51774	0.210601
$280$	0	0
$281$	−12.5947	−0.751338	−0.375669	−	0.926754i	$-0.622587\pi$
$281$	−12.5947	−0.751338	−0.375669	+	0.926754i	$0.622587\pi$
$282$	1.20747	0.0719036
$283$	5.44727	0.323807	0.161903	−	0.986807i	$-0.448237\pi$
$283$	5.44727	0.323807	0.161903	+	0.986807i	$0.448237\pi$
$284$	2.49129	0.147831
$285$	−25.5927	−1.51598
$286$	0.0484145	0.00286281
$287$	0	0
$288$	0.266503	0.0157038
$289$	−5.73161	−0.337153
$290$	−0.471253	−0.0276729
$291$	24.0191	1.40802
$292$	−23.0625	−1.34963
$293$	−1.25534	−0.0733375	−0.0366688	−	0.999327i	$-0.511675\pi$
$293$	−1.25534	−0.0733375	−0.0366688	+	0.999327i	$0.511675\pi$
$294$	0	0
$295$	−23.1724	−1.34915
$296$	−1.04185	−0.0605563
$297$	−4.72534	−0.274192
$298$	−0.305619	−0.0177040
$299$	−4.37712	−0.253135
$300$	0.359792	0.0207726
$301$	0	0
$302$	−0.0382621	−0.00220173
$303$	22.8191	1.31092
$304$	−24.7689	−1.42059
$305$	25.6487	1.46864
$306$	0.0746672	0.00426844
$307$	5.87422	0.335259	0.167630	−	0.985850i	$-0.446389\pi$
$307$	5.87422	0.335259	0.167630	+	0.985850i	$0.446389\pi$
$308$	0	0
$309$	12.5469	0.713770
$310$	0.820831	0.0466200
$311$	−3.17398	−0.179980	−0.0899900	−	0.995943i	$-0.528683\pi$
$311$	−3.17398	−0.179980	−0.0899900	+	0.995943i	$0.528683\pi$
$312$	−0.359984	−0.0203801
$313$	−22.1549	−1.25227	−0.626135	−	0.779715i	$-0.715364\pi$
$313$	−22.1549	−1.25227	−0.626135	+	0.779715i	$0.715364\pi$
$314$	−0.195665	−0.0110420
$315$	0	0
$316$	−0.895335	−0.0503665
$317$	25.5549	1.43531	0.717654	−	0.696400i	$-0.245216\pi$
$317$	25.5549	1.43531	0.717654	+	0.696400i	$0.245216\pi$
$318$	−0.609536	−0.0341811
$319$	−4.39582	−0.246119
$320$	−17.5900	−0.983313
$321$	−10.8638	−0.606357
$322$	0	0
$323$	−20.8596	−1.16066
$324$	20.3106	1.12837
$325$	−0.0968341	−0.00537139
$326$	−0.409547	−0.0226827
$327$	−1.48436	−0.0820851
$328$	−0.820600	−0.0453100
$329$	0	0
$330$	0.199396	0.0109764
$331$	−16.6475	−0.915027	−0.457514	−	0.889203i	$-0.651260\pi$
$331$	−16.6475	−0.915027	−0.457514	+	0.889203i	$0.651260\pi$
$332$	−6.24831	−0.342921
$333$	2.47313	0.135527
$334$	0.279209	0.0152776
$335$	27.9159	1.52521
$336$	0	0
$337$	−1.07011	−0.0582929	−0.0291464	−	0.999575i	$-0.509279\pi$
$337$	−1.07011	−0.0582929	−0.0291464	+	0.999575i	$0.509279\pi$
$338$	0.0484145	0.00263340
$339$	−21.8985	−1.18936
$340$	−14.8488	−0.805287
$341$	7.65667	0.414632
$342$	−0.138221	−0.00747414
$343$	0	0
$344$	−1.83477	−0.0989244
$345$	−18.0272	−0.970554
$346$	−0.404018	−0.0217201
$347$	−12.3516	−0.663067	−0.331533	−	0.943443i	$-0.607566\pi$
$347$	−12.3516	−0.663067	−0.331533	+	0.943443i	$0.607566\pi$
$348$	16.3329	0.875536
$349$	24.8116	1.32814	0.664068	−	0.747672i	$-0.268829\pi$
$349$	24.8116	1.32814	0.664068	+	0.747672i	$0.268829\pi$
$350$	0	0
$351$	−4.72534	−0.252220
$352$	0.580067	0.0309177
$353$	27.0846	1.44157	0.720785	−	0.693159i	$-0.243782\pi$
$353$	27.0846	1.44157	0.720785	+	0.693159i	$0.243782\pi$
$354$	−0.942345	−0.0500851
$355$	−2.76148	−0.146564
$356$	−34.2071	−1.81297
$357$	0	0
$358$	0.0764174	0.00403878
$359$	−3.82539	−0.201897	−0.100948	−	0.994892i	$-0.532188\pi$
$359$	−3.82539	−0.201897	−0.100948	+	0.994892i	$0.532188\pi$
$360$	−0.196899	−0.0103775
$361$	19.6145	1.03234
$362$	−0.934469	−0.0491146
$363$	1.85996	0.0976223
$364$	0	0
$365$	25.5638	1.33807
$366$	1.04305	0.0545210
$367$	2.40968	0.125784	0.0628921	−	0.998020i	$-0.479968\pi$
$367$	2.40968	0.125784	0.0628921	+	0.998020i	$0.479968\pi$
$368$	−17.4469	−0.909485
$369$	1.94793	0.101405
$370$	0.577083	0.0300011
$371$	0	0
$372$	−28.4487	−1.47500
$373$	−13.1174	−0.679193	−0.339596	−	0.940571i	$-0.610290\pi$
$373$	−13.1174	−0.679193	−0.339596	+	0.940571i	$0.610290\pi$
$374$	0.162520	0.00840370
$375$	−20.9914	−1.08399
$376$	−2.59524	−0.133839
$377$	−4.39582	−0.226396
$378$	0	0
$379$	4.55335	0.233890	0.116945	−	0.993138i	$-0.462690\pi$
$379$	4.55335	0.233890	0.116945	+	0.993138i	$0.462690\pi$
$380$	27.4875	1.41008
$381$	−10.5913	−0.542611
$382$	0.219266	0.0112186
$383$	−0.831661	−0.0424959	−0.0212480	−	0.999774i	$-0.506764\pi$
$383$	−0.831661	−0.0424959	−0.0212480	+	0.999774i	$0.506764\pi$
$384$	−2.87313	−0.146619
$385$	0	0
$386$	1.31800	0.0670846
$387$	4.35537	0.221396
$388$	−25.7973	−1.30966
$389$	−24.3852	−1.23638	−0.618190	−	0.786029i	$-0.712134\pi$
$389$	−24.3852	−1.23638	−0.618190	+	0.786029i	$0.712134\pi$
$390$	0.199396	0.0100968
$391$	−14.6933	−0.743072
$392$	0	0
$393$	23.2595	1.17328
$394$	−1.10113	−0.0554741
$395$	0.992438	0.0499350
$396$	−0.917792	−0.0461208
$397$	25.5322	1.28143	0.640713	−	0.767780i	$-0.278639\pi$
$397$	25.5322	1.28143	0.640713	+	0.767780i	$0.278639\pi$
$398$	1.16025	0.0581582
$399$	0	0
$400$	−0.385975	−0.0192987
$401$	25.7759	1.28719	0.643594	−	0.765367i	$-0.277443\pi$
$401$	25.7759	1.28719	0.643594	+	0.765367i	$0.277443\pi$
$402$	1.13525	0.0566212
$403$	7.65667	0.381406
$404$	−24.5085	−1.21934
$405$	−22.5134	−1.11870
$406$	0	0
$407$	5.38300	0.266825
$408$	−1.20841	−0.0598252
$409$	27.4384	1.35674	0.678370	−	0.734721i	$-0.262687\pi$
$409$	27.4384	1.35674	0.678370	+	0.734721i	$0.262687\pi$
$410$	0.454532	0.0224477
$411$	−16.9417	−0.835673
$412$	−13.4758	−0.663907
$413$	0	0
$414$	−0.0973616	−0.00478506
$415$	6.92597	0.339982
$416$	0.580067	0.0284401
$417$	−34.7077	−1.69964
$418$	−0.300851	−0.0147151
$419$	−28.5097	−1.39279	−0.696396	−	0.717658i	$-0.745214\pi$
$419$	−28.5097	−1.39279	−0.696396	+	0.717658i	$0.745214\pi$
$420$	0	0
$421$	7.12795	0.347395	0.173697	−	0.984799i	$-0.444429\pi$
$421$	7.12795	0.347395	0.173697	+	0.984799i	$0.444429\pi$
$422$	0.225479	0.0109762
$423$	6.16057	0.299537
$424$	1.31009	0.0636237
$425$	−0.325057	−0.0157676
$426$	−0.112301	−0.00544098
$427$	0	0
$428$	11.6681	0.563997
$429$	1.85996	0.0897995
$430$	1.01628	0.0490096
$431$	−18.4564	−0.889012	−0.444506	−	0.895776i	$-0.646621\pi$
$431$	−18.4564	−0.889012	−0.444506	+	0.895776i	$0.646621\pi$
$432$	−18.8349	−0.906196
$433$	8.19728	0.393936	0.196968	−	0.980410i	$-0.436890\pi$
$433$	8.19728	0.393936	0.196968	+	0.980410i	$0.436890\pi$
$434$	0	0
$435$	−18.1043	−0.868034
$436$	1.59425	0.0763507
$437$	27.1997	1.30114
$438$	1.03960	0.0496738
$439$	9.66944	0.461497	0.230749	−	0.973013i	$-0.425883\pi$
$439$	9.66944	0.461497	0.230749	+	0.973013i	$0.425883\pi$
$440$	−0.428568	−0.0204312
$441$	0	0
$442$	0.162520	0.00773028
$443$	3.54842	0.168590	0.0842952	−	0.996441i	$-0.473136\pi$
$443$	3.54842	0.168590	0.0842952	+	0.996441i	$0.473136\pi$
$444$	−20.0008	−0.949196
$445$	37.9170	1.79744
$446$	−1.16351	−0.0550936
$447$	−11.7411	−0.555333
$448$	0	0
$449$	−32.3016	−1.52441	−0.762203	−	0.647338i	$-0.775882\pi$
$449$	−32.3016	−1.52441	−0.762203	+	0.647338i	$0.775882\pi$
$450$	−0.00215391	−0.000101536 0
$451$	4.23985	0.199647
$452$	23.5197	1.10628
$453$	−1.46993	−0.0690631
$454$	−0.796919	−0.0374012
$455$	0	0
$456$	2.23696	0.104755
$457$	22.7354	1.06352	0.531758	−	0.846896i	$-0.321532\pi$
$457$	22.7354	1.06352	0.531758	+	0.846896i	$0.321532\pi$
$458$	0.653788	0.0305495
$459$	−15.8622	−0.740385
$460$	19.3619	0.902752
$461$	−0.814074	−0.0379152	−0.0189576	−	0.999820i	$-0.506035\pi$
$461$	−0.814074	−0.0379152	−0.0189576	+	0.999820i	$0.506035\pi$
$462$	0	0
$463$	−7.40272	−0.344034	−0.172017	−	0.985094i	$-0.555028\pi$
$463$	−7.40272	−0.344034	−0.172017	+	0.985094i	$0.555028\pi$
$464$	−17.5215	−0.813415
$465$	31.5341	1.46236
$466$	1.02623	0.0475393
$467$	−32.5712	−1.50721	−0.753607	−	0.657325i	$-0.771688\pi$
$467$	−32.5712	−1.50721	−0.753607	+	0.657325i	$0.771688\pi$
$468$	−0.917792	−0.0424249
$469$	0	0
$470$	1.43751	0.0663074
$471$	−7.51691	−0.346361
$472$	2.02541	0.0932271
$473$	9.47985	0.435884
$474$	0.0403593	0.00185376
$475$	0.601733	0.0276094
$476$	0	0
$477$	−3.10989	−0.142392
$478$	1.11963	0.0512107
$479$	18.1121	0.827565	0.413782	−	0.910376i	$-0.364207\pi$
$479$	18.1121	0.827565	0.413782	+	0.910376i	$0.364207\pi$
$480$	2.38901	0.109043
$481$	5.38300	0.245444
$482$	−0.197497	−0.00899574
$483$	0	0
$484$	−1.99766	−0.0908025
$485$	28.5952	1.29844
$486$	−0.229222	−0.0103977
$487$	−23.6978	−1.07385	−0.536924	−	0.843631i	$-0.680414\pi$
$487$	−23.6978	−1.07385	−0.536924	+	0.843631i	$0.680414\pi$
$488$	−2.24185	−0.101484
$489$	−15.7337	−0.711502
$490$	0	0
$491$	7.73959	0.349283	0.174641	−	0.984632i	$-0.444123\pi$
$491$	7.73959	0.349283	0.174641	+	0.984632i	$0.444123\pi$
$492$	−15.7534	−0.710217
$493$	−14.7561	−0.664581
$494$	−0.300851	−0.0135359
$495$	1.01733	0.0457256
$496$	30.5190	1.37034
$497$	0	0
$498$	0.281657	0.0126213
$499$	17.1746	0.768842	0.384421	−	0.923158i	$-0.374401\pi$
$499$	17.1746	0.768842	0.384421	+	0.923158i	$0.374401\pi$
$500$	22.5455	1.00826
$501$	10.7264	0.479222
$502$	0.334262	0.0149188
$503$	−3.88918	−0.173410	−0.0867051	−	0.996234i	$-0.527634\pi$
$503$	−3.88918	−0.173410	−0.0867051	+	0.996234i	$0.527634\pi$
$504$	0	0
$505$	27.1666	1.20890
$506$	−0.211916	−0.00942082
$507$	1.85996	0.0826035
$508$	11.3755	0.504705
$509$	−24.5165	−1.08668	−0.543338	−	0.839514i	$-0.682840\pi$
$509$	−24.5165	−1.08668	−0.543338	+	0.839514i	$0.682840\pi$
$510$	0.669341	0.0296389
$511$	0	0
$512$	3.85503	0.170370
$513$	29.3635	1.29643
$514$	0.352990	0.0155697
$515$	14.9373	0.658218
$516$	−35.2229	−1.55060
$517$	13.4090	0.589728
$518$	0	0
$519$	−15.5213	−0.681309
$520$	−0.428568	−0.0187939
$521$	−38.3723	−1.68112	−0.840560	−	0.541718i	$-0.817774\pi$
$521$	−38.3723	−1.68112	−0.840560	+	0.541718i	$0.817774\pi$
$522$	−0.0977776	−0.00427961
$523$	−39.6248	−1.73267	−0.866336	−	0.499462i	$-0.833531\pi$
$523$	−39.6248	−1.73267	−0.866336	+	0.499462i	$0.833531\pi$
$524$	−24.9815	−1.09132
$525$	0	0
$526$	1.24601	0.0543287
$527$	25.7022	1.11961
$528$	7.41367	0.322639
$529$	−3.84082	−0.166992
$530$	−0.725663	−0.0315208
$531$	−4.80790	−0.208645
$532$	0	0
$533$	4.23985	0.183648
$534$	1.54196	0.0667272
$535$	−12.9335	−0.559165
$536$	−2.44003	−0.105393
$537$	2.93575	0.126687
$538$	0.135031	0.00582160
$539$	0	0
$540$	20.9022	0.899487
$541$	5.70134	0.245120	0.122560	−	0.992461i	$-0.460890\pi$
$541$	5.70134	0.245120	0.122560	+	0.992461i	$0.460890\pi$
$542$	0.266881	0.0114635
$543$	−35.8998	−1.54061
$544$	1.94719	0.0834852
$545$	−1.76715	−0.0756965
$546$	0	0
$547$	−31.6995	−1.35537	−0.677686	−	0.735352i	$-0.737017\pi$
$547$	−31.6995	−1.35537	−0.677686	+	0.735352i	$0.737017\pi$
$548$	18.1960	0.777294
$549$	5.32169	0.227124
$550$	−0.00468817	−0.000199904 0
$551$	27.3159	1.16370
$552$	1.57569	0.0670660
$553$	0	0
$554$	1.20257	0.0510925
$555$	22.1700	0.941063
$556$	37.2772	1.58091
$557$	32.7853	1.38916	0.694578	−	0.719418i	$-0.255591\pi$
$557$	32.7853	1.38916	0.694578	+	0.719418i	$0.255591\pi$
$558$	0.170309	0.00720977
$559$	9.47985	0.400955
$560$	0	0
$561$	6.24358	0.263604
$562$	−0.609767	−0.0257215
$563$	−37.0578	−1.56180	−0.780900	−	0.624657i	$-0.785239\pi$
$563$	−37.0578	−1.56180	−0.780900	+	0.624657i	$0.785239\pi$
$564$	−49.8219	−2.09788
$565$	−26.0705	−1.09680
$566$	0.263727	0.0110853
$567$	0	0
$568$	0.241371	0.0101277
$569$	−10.1914	−0.427248	−0.213624	−	0.976916i	$-0.568527\pi$
$569$	−10.1914	−0.427248	−0.213624	+	0.976916i	$0.568527\pi$
$570$	−1.23906	−0.0518985
$571$	−1.14516	−0.0479233	−0.0239616	−	0.999713i	$-0.507628\pi$
$571$	−1.14516	−0.0479233	−0.0239616	+	0.999713i	$0.507628\pi$
$572$	−1.99766	−0.0835262
$573$	8.42361	0.351902
$574$	0	0
$575$	0.423854	0.0176760
$576$	−3.64965	−0.152069
$577$	−40.9075	−1.70300	−0.851500	−	0.524354i	$-0.824307\pi$
$577$	−40.9075	−1.70300	−0.851500	+	0.524354i	$0.824307\pi$
$578$	−0.277493	−0.0115422
$579$	50.6341	2.10428
$580$	19.4446	0.807394
$581$	0	0
$582$	1.16287	0.0482026
$583$	−6.76895	−0.280341
$584$	−2.23443	−0.0924615
$585$	1.01733	0.0420614
$586$	−0.0607765	−0.00251065
$587$	5.87326	0.242416	0.121208	−	0.992627i	$-0.461323\pi$
$587$	5.87326	0.242416	0.121208	+	0.992627i	$0.461323\pi$
$588$	0	0
$589$	−47.5790	−1.96046
$590$	−1.12188	−0.0461870
$591$	−42.3025	−1.74009
$592$	21.4563	0.881849
$593$	5.92263	0.243213	0.121607	−	0.992578i	$-0.461195\pi$
$593$	5.92263	0.243213	0.121607	+	0.992578i	$0.461195\pi$
$594$	−0.228775	−0.00938675
$595$	0	0
$596$	12.6103	0.516538
$597$	44.5738	1.82428
$598$	−0.211916	−0.00866590
$599$	10.5027	0.429128	0.214564	−	0.976710i	$-0.431167\pi$
$599$	10.5027	0.429128	0.214564	+	0.976710i	$0.431167\pi$
$600$	0.0348587	0.00142310
$601$	−25.6777	−1.04741	−0.523707	−	0.851899i	$-0.675451\pi$
$601$	−25.6777	−1.04741	−0.523707	+	0.851899i	$0.675451\pi$
$602$	0	0
$603$	5.79212	0.235873
$604$	1.57875	0.0642385
$605$	2.21431	0.0900245
$606$	1.10478	0.0448785
$607$	2.99202	0.121442	0.0607212	−	0.998155i	$-0.480660\pi$
$607$	2.99202	0.121442	0.0607212	+	0.998155i	$0.480660\pi$
$608$	−3.60457	−0.146185
$609$	0	0
$610$	1.24177	0.0502777
$611$	13.4090	0.542471
$612$	−3.08088	−0.124537
$613$	−48.2748	−1.94980	−0.974901	−	0.222640i	$-0.928532\pi$
$613$	−48.2748	−1.94980	−0.974901	+	0.222640i	$0.928532\pi$
$614$	0.284397	0.0114773
$615$	17.4619	0.704131
$616$	0	0
$617$	10.2633	0.413187	0.206593	−	0.978427i	$-0.433762\pi$
$617$	10.2633	0.413187	0.206593	+	0.978427i	$0.433762\pi$
$618$	0.607454	0.0244354
$619$	−14.9262	−0.599935	−0.299967	−	0.953949i	$-0.596976\pi$
$619$	−14.9262	−0.599935	−0.299967	+	0.953949i	$0.596976\pi$
$620$	−33.8687	−1.36020
$621$	20.6834	0.829995
$622$	−0.153667	−0.00616147
$623$	0	0
$624$	7.41367	0.296784
$625$	−24.5065	−0.980258
$626$	−1.07262	−0.0428705
$627$	−11.5579	−0.461577
$628$	8.07342	0.322164
$629$	18.0699	0.720493
$630$	0	0
$631$	−21.5214	−0.856752	−0.428376	−	0.903600i	$-0.640914\pi$
$631$	−21.5214	−0.856752	−0.428376	+	0.903600i	$0.640914\pi$
$632$	−0.0867453	−0.00345054
$633$	8.66231	0.344296
$634$	1.23723	0.0491366
$635$	−12.6092	−0.500380
$636$	25.1504	0.997277
$637$	0	0
$638$	−0.212822	−0.00842569
$639$	−0.572964	−0.0226661
$640$	−3.42051	−0.135207
$641$	40.2138	1.58835	0.794175	−	0.607689i	$-0.207903\pi$
$641$	40.2138	1.58835	0.794175	+	0.607689i	$0.207903\pi$
$642$	−0.525964	−0.0207582
$643$	−18.5528	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$643$	−18.5528	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$644$	0	0
$645$	39.0429	1.53731
$646$	−1.00991	−0.0397343
$647$	30.4668	1.19777	0.598886	−	0.800834i	$-0.295610\pi$
$647$	30.4668	1.19777	0.598886	+	0.800834i	$0.295610\pi$
$648$	1.96781	0.0773029
$649$	−10.4648	−0.410780
$650$	−0.00468817	−0.000183885 0
$651$	0	0
$652$	16.8985	0.661797
$653$	−3.16380	−0.123809	−0.0619046	−	0.998082i	$-0.519717\pi$
$653$	−3.16380	−0.123809	−0.0619046	+	0.998082i	$0.519717\pi$
$654$	−0.0718644	−0.00281012
$655$	27.6908	1.08197
$656$	16.8998	0.659826
$657$	5.30408	0.206932
$658$	0	0
$659$	−40.8508	−1.59132	−0.795661	−	0.605742i	$-0.792877\pi$
$659$	−40.8508	−1.59132	−0.795661	+	0.605742i	$0.792877\pi$
$660$	−8.22738	−0.320250
$661$	37.6418	1.46409	0.732047	−	0.681254i	$-0.238565\pi$
$661$	37.6418	1.46409	0.732047	+	0.681254i	$0.238565\pi$
$662$	−0.805979	−0.0313252
$663$	6.24358	0.242480
$664$	−0.605373	−0.0234930
$665$	0	0
$666$	0.119736	0.00463966
$667$	19.2411	0.745017
$668$	−11.5206	−0.445744
$669$	−44.6988	−1.72815
$670$	1.35154	0.0522144
$671$	11.5831	0.447162
$672$	0	0
$673$	−9.63478	−0.371394	−0.185697	−	0.982607i	$-0.559454\pi$
$673$	−9.63478	−0.371394	−0.185697	+	0.982607i	$0.559454\pi$
$674$	−0.0518091	−0.00199561
$675$	0.457574	0.0176120
$676$	−1.99766	−0.0768329
$677$	40.6868	1.56372	0.781861	−	0.623453i	$-0.214271\pi$
$677$	40.6868	1.56372	0.781861	+	0.623453i	$0.214271\pi$
$678$	−1.06020	−0.0407169
$679$	0	0
$680$	−1.43863	−0.0551691
$681$	−30.6155	−1.17319
$682$	0.370694	0.0141946
$683$	17.2132	0.658644	0.329322	−	0.944218i	$-0.393180\pi$
$683$	17.2132	0.658644	0.329322	+	0.944218i	$0.393180\pi$
$684$	5.70321	0.218068
$685$	−20.1694	−0.770633
$686$	0	0
$687$	25.1168	0.958265
$688$	37.7861	1.44058
$689$	−6.76895	−0.257876
$690$	−0.872780	−0.0332262
$691$	−23.1324	−0.879997	−0.439999	−	0.897998i	$-0.645021\pi$
$691$	−23.1324	−0.879997	−0.439999	+	0.897998i	$0.645021\pi$
$692$	16.6704	0.633713
$693$	0	0
$694$	−0.597995	−0.0226996
$695$	−41.3201	−1.56736
$696$	1.58243	0.0599818
$697$	14.2325	0.539095
$698$	1.20124	0.0454677
$699$	39.4251	1.49119
$700$	0	0
$701$	−39.8017	−1.50329	−0.751645	−	0.659567i	$-0.770739\pi$
$701$	−39.8017	−1.50329	−0.751645	+	0.659567i	$0.770739\pi$
$702$	−0.228775	−0.00863456
$703$	−33.4503	−1.26160
$704$	−7.94380	−0.299393
$705$	55.2253	2.07990
$706$	1.31129	0.0493510
$707$	0	0
$708$	38.8826	1.46130
$709$	24.9134	0.935642	0.467821	−	0.883823i	$-0.345039\pi$
$709$	24.9134	0.935642	0.467821	+	0.883823i	$0.345039\pi$
$710$	−0.133696	−0.00501751
$711$	0.205915	0.00772243
$712$	−3.31418	−0.124204
$713$	−33.5142	−1.25511
$714$	0	0
$715$	2.21431	0.0828105
$716$	−3.15310	−0.117837
$717$	43.0132	1.60636
$718$	−0.185205	−0.00691177
$719$	−1.53135	−0.0571098	−0.0285549	−	0.999592i	$-0.509091\pi$
$719$	−1.53135	−0.0571098	−0.0285549	+	0.999592i	$0.509091\pi$
$720$	4.05502	0.151122
$721$	0	0
$722$	0.949629	0.0353415
$723$	−7.58730	−0.282175
$724$	38.5576	1.43298
$725$	0.425666	0.0158088
$726$	0.0900488	0.00334203
$727$	0.163235	0.00605404	0.00302702	−	0.999995i	$-0.499036\pi$
$727$	0.163235	0.00605404	0.00302702	+	0.999995i	$0.499036\pi$
$728$	0	0
$729$	21.6956	0.803540
$730$	1.23766	0.0458077
$731$	31.8224	1.17699
$732$	−43.0378	−1.59072
$733$	5.51306	0.203630	0.101815	−	0.994803i	$-0.467535\pi$
$733$	5.51306	0.203630	0.101815	+	0.994803i	$0.467535\pi$
$734$	0.116663	0.00430612
$735$	0	0
$736$	−2.53902	−0.0935896
$737$	12.6071	0.464387
$738$	0.0943082	0.00347153
$739$	−9.54152	−0.350991	−0.175495	−	0.984480i	$-0.556153\pi$
$739$	−9.54152	−0.350991	−0.175495	+	0.984480i	$0.556153\pi$
$740$	−23.8113	−0.875321
$741$	−11.5579	−0.424589
$742$	0	0
$743$	32.4987	1.19226	0.596131	−	0.802887i	$-0.296704\pi$
$743$	32.4987	1.19226	0.596131	+	0.802887i	$0.296704\pi$
$744$	−2.75628	−0.101050
$745$	−13.9779	−0.512112
$746$	−0.635072	−0.0232516
$747$	1.43703	0.0525781
$748$	−6.70582	−0.245189
$749$	0	0
$750$	−1.01629	−0.0371096
$751$	23.8521	0.870377	0.435189	−	0.900339i	$-0.356682\pi$
$751$	23.8521	0.870377	0.435189	+	0.900339i	$0.356682\pi$
$752$	53.4476	1.94903
$753$	12.8414	0.467968
$754$	−0.212822	−0.00775051
$755$	−1.74997	−0.0636880
$756$	0	0
$757$	−44.1774	−1.60565	−0.802827	−	0.596213i	$-0.796672\pi$
$757$	−44.1774	−1.60565	−0.802827	+	0.596213i	$0.796672\pi$
$758$	0.220448	0.00800705
$759$	−8.14125	−0.295509
$760$	2.66314	0.0966024
$761$	47.7316	1.73027	0.865134	−	0.501540i	$-0.167233\pi$
$761$	47.7316	1.73027	0.865134	+	0.501540i	$0.167233\pi$
$762$	−0.512775	−0.0185759
$763$	0	0
$764$	−9.04725	−0.327318
$765$	3.41502	0.123470
$766$	−0.0402645	−0.00145481
$767$	−10.4648	−0.377863
$768$	29.4111	1.06128
$769$	42.2995	1.52536	0.762680	−	0.646776i	$-0.223883\pi$
$769$	42.2995	1.52536	0.762680	+	0.646776i	$0.223883\pi$
$770$	0	0
$771$	13.5609	0.488384
$772$	−54.3828	−1.95728
$773$	−52.0205	−1.87105	−0.935524	−	0.353264i	$-0.885072\pi$
$773$	−52.0205	−1.87105	−0.935524	+	0.353264i	$0.885072\pi$
$774$	0.210863	0.00757932
$775$	−0.741426	−0.0266328
$776$	−2.49940	−0.0897231
$777$	0	0
$778$	−1.18060	−0.0423265
$779$	−26.3467	−0.943968
$780$	−8.22738	−0.294587
$781$	−1.24711	−0.0446250
$782$	−0.711369	−0.0254385
$783$	20.7718	0.742322
$784$	0	0
$785$	−8.94901	−0.319404
$786$	1.12610	0.0401665
$787$	−49.4037	−1.76105	−0.880525	−	0.473999i	$-0.842810\pi$
$787$	−49.4037	−1.76105	−0.880525	+	0.473999i	$0.842810\pi$
$788$	45.4343	1.61853
$789$	47.8685	1.70416
$790$	0.0480484	0.00170949
$791$	0	0
$792$	−0.0889210	−0.00315967
$793$	11.5831	0.411329
$794$	1.23613	0.0438687
$795$	−27.8780	−0.988732
$796$	−47.8738	−1.69684
$797$	20.0260	0.709357	0.354679	−	0.934988i	$-0.384590\pi$
$797$	20.0260	0.709357	0.354679	+	0.934988i	$0.384590\pi$
$798$	0	0
$799$	45.0120	1.59241
$800$	−0.0561702	−0.00198592
$801$	7.86717	0.277973
$802$	1.24793	0.0440659
$803$	11.5448	0.407407
$804$	−46.8422	−1.65200
$805$	0	0
$806$	0.370694	0.0130571
$807$	5.18753	0.182610
$808$	−2.37453	−0.0835356
$809$	33.0959	1.16359	0.581795	−	0.813336i	$-0.302351\pi$
$809$	33.0959	1.16359	0.581795	+	0.813336i	$0.302351\pi$
$810$	−1.08997	−0.0382978
$811$	−25.4462	−0.893537	−0.446768	−	0.894650i	$-0.647425\pi$
$811$	−25.4462	−0.893537	−0.446768	+	0.894650i	$0.647425\pi$
$812$	0	0
$813$	10.2528	0.359583
$814$	0.260615	0.00913456
$815$	−18.7312	−0.656126
$816$	24.8865	0.871203
$817$	−58.9084	−2.06094
$818$	1.32841	0.0464469
$819$	0	0
$820$	−18.7547	−0.654942
$821$	12.1947	0.425597	0.212799	−	0.977096i	$-0.431742\pi$
$821$	12.1947	0.425597	0.212799	+	0.977096i	$0.431742\pi$
$822$	−0.820225	−0.0286086
$823$	−3.91038	−0.136307	−0.0681537	−	0.997675i	$-0.521711\pi$
$823$	−3.91038	−0.136307	−0.0681537	+	0.997675i	$0.521711\pi$
$824$	−1.30562	−0.0454833
$825$	−0.180107	−0.00627052
$826$	0	0
$827$	−7.80086	−0.271263	−0.135631	−	0.990759i	$-0.543306\pi$
$827$	−7.80086	−0.271263	−0.135631	+	0.990759i	$0.543306\pi$
$828$	4.01729	0.139610
$829$	−5.81422	−0.201936	−0.100968	−	0.994890i	$-0.532194\pi$
$829$	−5.81422	−0.201936	−0.100968	+	0.994890i	$0.532194\pi$
$830$	0.335317	0.0116390
$831$	46.1997	1.60265
$832$	−7.94380	−0.275402
$833$	0	0
$834$	−1.68036	−0.0581860
$835$	12.7700	0.441925
$836$	12.4136	0.429332
$837$	−36.1803	−1.25058
$838$	−1.38028	−0.0476811
$839$	−1.51066	−0.0521538	−0.0260769	−	0.999660i	$-0.508301\pi$
$839$	−1.51066	−0.0521538	−0.0260769	+	0.999660i	$0.508301\pi$
$840$	0	0
$841$	−9.67673	−0.333680
$842$	0.345096	0.0118928
$843$	−23.4256	−0.806821
$844$	−9.30362	−0.320244
$845$	2.21431	0.0761746
$846$	0.298261	0.0102544
$847$	0	0
$848$	−26.9806	−0.926519
$849$	10.1317	0.347718
$850$	−0.0157375	−0.000539791 0
$851$	−23.5620	−0.807696
$852$	4.63369	0.158748
$853$	7.81098	0.267443	0.133721	−	0.991019i	$-0.457307\pi$
$853$	7.81098	0.267443	0.133721	+	0.991019i	$0.457307\pi$
$854$	0	0
$855$	−6.32175	−0.216199
$856$	1.13047	0.0386387
$857$	−1.07580	−0.0367485	−0.0183742	−	0.999831i	$-0.505849\pi$
$857$	−1.07580	−0.0367485	−0.0183742	+	0.999831i	$0.505849\pi$
$858$	0.0900488	0.00307422
$859$	−15.3322	−0.523127	−0.261563	−	0.965186i	$-0.584238\pi$
$859$	−15.3322	−0.523127	−0.261563	+	0.965186i	$0.584238\pi$
$860$	−41.9334	−1.42992
$861$	0	0
$862$	−0.893556	−0.0304346
$863$	24.9872	0.850575	0.425287	−	0.905058i	$-0.360173\pi$
$863$	24.9872	0.850575	0.425287	+	0.905058i	$0.360173\pi$
$864$	−2.74101	−0.0932511
$865$	−18.4784	−0.628283
$866$	0.396867	0.0134861
$867$	−10.6605	−0.362051
$868$	0	0
$869$	0.448193	0.0152039
$870$	−0.876510	−0.0297165
$871$	12.6071	0.427174
$872$	0.154460	0.00523068
$873$	5.93305	0.200803
$874$	1.31686	0.0445434
$875$	0	0
$876$	−42.8953	−1.44930
$877$	−48.1407	−1.62559	−0.812797	−	0.582547i	$-0.802056\pi$
$877$	−48.1407	−1.62559	−0.812797	+	0.582547i	$0.802056\pi$
$878$	0.468141	0.0157990
$879$	−2.33487	−0.0787532
$880$	8.82611	0.297528
$881$	−27.7557	−0.935115	−0.467557	−	0.883963i	$-0.654866\pi$
$881$	−27.7557	−0.935115	−0.467557	+	0.883963i	$0.654866\pi$
$882$	0	0
$883$	35.6868	1.20096	0.600479	−	0.799641i	$-0.294977\pi$
$883$	35.6868	1.20096	0.600479	+	0.799641i	$0.294977\pi$
$884$	−6.70582	−0.225541
$885$	−43.0996	−1.44878
$886$	0.171795	0.00577156
$887$	−17.4631	−0.586353	−0.293176	−	0.956058i	$-0.594712\pi$
$887$	−17.4631	−0.586353	−0.293176	+	0.956058i	$0.594712\pi$
$888$	−1.93779	−0.0650281
$889$	0	0
$890$	1.83573	0.0615338
$891$	−10.1672	−0.340615
$892$	48.0080	1.60743
$893$	−83.3245	−2.78835
$894$	−0.568438	−0.0190114
$895$	3.49506	0.116827
$896$	0	0
$897$	−8.14125	−0.271828
$898$	−1.56387	−0.0521869
$899$	−33.6574	−1.12254
$900$	0.0888735	0.00296245
$901$	−22.7223	−0.756989
$902$	0.205270	0.00683475
$903$	0	0
$904$	2.27873	0.0757894
$905$	−42.7393	−1.42070
$906$	−0.0711657	−0.00236432
$907$	41.3454	1.37285	0.686426	−	0.727199i	$-0.259178\pi$
$907$	41.3454	1.37285	0.686426	+	0.727199i	$0.259178\pi$
$908$	32.8821	1.09123
$909$	5.63664	0.186955
$910$	0	0
$911$	−40.2268	−1.33277	−0.666386	−	0.745607i	$-0.732160\pi$
$911$	−40.2268	−1.33277	−0.666386	+	0.745607i	$0.732160\pi$
$912$	−46.0690	−1.52550
$913$	3.12782	0.103516
$914$	1.10072	0.0364087
$915$	47.7054	1.57709
$916$	−26.9763	−0.891321
$917$	0	0
$918$	−0.767962	−0.0253465
$919$	28.3982	0.936771	0.468386	−	0.883524i	$-0.344836\pi$
$919$	28.3982	0.936771	0.468386	+	0.883524i	$0.344836\pi$
$920$	1.87589	0.0618463
$921$	10.9258	0.360017
$922$	−0.0394130	−0.00129800
$923$	−1.24711	−0.0410490
$924$	0	0
$925$	−0.521258	−0.0171388
$926$	−0.358399	−0.0117777
$927$	3.09926	0.101793
$928$	−2.54987	−0.0837036
$929$	6.93362	0.227485	0.113742	−	0.993510i	$-0.463716\pi$
$929$	6.93362	0.227485	0.113742	+	0.993510i	$0.463716\pi$
$930$	1.52671	0.0500627
$931$	0	0
$932$	−42.3439	−1.38702
$933$	−5.90346	−0.193271
$934$	−1.57692	−0.0515983
$935$	7.43309	0.243088
$936$	−0.0889210	−0.00290647
$937$	47.6411	1.55637	0.778183	−	0.628037i	$-0.216141\pi$
$937$	47.6411	1.55637	0.778183	+	0.628037i	$0.216141\pi$
$938$	0	0
$939$	−41.2071	−1.34474
$940$	−59.3138	−1.93460
$941$	−4.95250	−0.161447	−0.0807234	−	0.996737i	$-0.525723\pi$
$941$	−4.95250	−0.161447	−0.0807234	+	0.996737i	$0.525723\pi$
$942$	−0.363927	−0.0118574
$943$	−18.5583	−0.604342
$944$	−41.7122	−1.35762
$945$	0	0
$946$	0.458962	0.0149222
$947$	−37.7613	−1.22708	−0.613539	−	0.789664i	$-0.710255\pi$
$947$	−37.7613	−1.22708	−0.613539	+	0.789664i	$0.710255\pi$
$948$	−1.66528	−0.0540859
$949$	11.5448	0.374760
$950$	0.0291326	0.000945186 0
$951$	47.5310	1.54130
$952$	0	0
$953$	19.0205	0.616134	0.308067	−	0.951365i	$-0.400318\pi$
$953$	19.0205	0.616134	0.308067	+	0.951365i	$0.400318\pi$
$954$	−0.150564	−0.00487468
$955$	10.0285	0.324513
$956$	−46.1976	−1.49414
$957$	−8.17604	−0.264294
$958$	0.876890	0.0283310
$959$	0	0
$960$	−32.7167	−1.05593
$961$	27.6245	0.891114
$962$	0.260615	0.00840257
$963$	−2.68350	−0.0864746
$964$	8.14902	0.262462
$965$	60.2808	1.94051
$966$	0	0
$967$	−48.6320	−1.56390	−0.781950	−	0.623341i	$-0.785775\pi$
$967$	−48.6320	−1.56390	−0.781950	+	0.623341i	$0.785775\pi$
$968$	−0.193545	−0.00622076
$969$	−38.7980	−1.24637
$970$	1.38442	0.0444511
$971$	40.6559	1.30471	0.652355	−	0.757913i	$-0.273781\pi$
$971$	40.6559	1.30471	0.652355	+	0.757913i	$0.273781\pi$
$972$	9.45803	0.303367
$973$	0	0
$974$	−1.14732	−0.0367624
$975$	−0.180107	−0.00576804
$976$	46.1697	1.47786
$977$	20.9959	0.671717	0.335859	−	0.941912i	$-0.390974\pi$
$977$	20.9959	0.671717	0.335859	+	0.941912i	$0.390974\pi$
$978$	−0.761739	−0.0243577
$979$	17.1236	0.547273
$980$	0	0
$981$	−0.366656	−0.0117064
$982$	0.374708	0.0119574
$983$	−28.1571	−0.898071	−0.449035	−	0.893514i	$-0.648232\pi$
$983$	−28.1571	−0.898071	−0.449035	+	0.893514i	$0.648232\pi$
$984$	−1.52628	−0.0486560
$985$	−50.3618	−1.60466
$986$	−0.714409	−0.0227514
$987$	0	0
$988$	12.4136	0.394928
$989$	−41.4945	−1.31945
$990$	0.0492535	0.00156538
$991$	27.4423	0.871734	0.435867	−	0.900011i	$-0.356442\pi$
$991$	27.4423	0.871734	0.435867	+	0.900011i	$0.356442\pi$
$992$	4.44138	0.141014
$993$	−30.9635	−0.982598
$994$	0	0
$995$	53.0659	1.68230
$996$	−11.6216	−0.368244
$997$	4.15495	0.131589	0.0657943	−	0.997833i	$-0.479042\pi$
$997$	4.15495	0.131589	0.0657943	+	0.997833i	$0.479042\pi$
$998$	0.831501	0.0263207
$999$	−25.4365	−0.804775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7007.2.a.bi.1.12		25
7.3	odd	6		1001.2.i.d.716.14	yes	50
7.5	odd	6		1001.2.i.d.144.14	✓	50
7.6	odd	2		7007.2.a.bh.1.12		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.14	✓	50	7.5	odd	6
1001.2.i.d.716.14	yes	50	7.3	odd	6
7007.2.a.bh.1.12		25	7.6	odd	2
7007.2.a.bi.1.12		25	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:	\( N \)	\(=\)	\( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7007.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0484145 q^{2} +1.85996 q^{3} -1.99766 q^{4} +2.21431 q^{5} +0.0900488 q^{6} -0.193545 q^{8} +0.459434 q^{9} +O(q^{10})\)	\(q+0.0484145 q^{2} +1.85996 q^{3} -1.99766 q^{4} +2.21431 q^{5} +0.0900488 q^{6} -0.193545 q^{8} +0.459434 q^{9} +0.107205 q^{10} +1.00000 q^{11} -3.71555 q^{12} +1.00000 q^{13} +4.11852 q^{15} +3.98594 q^{16} +3.35684 q^{17} +0.0222433 q^{18} -6.21406 q^{19} -4.42343 q^{20} +0.0484145 q^{22} -4.37712 q^{23} -0.359984 q^{24} -0.0968341 q^{25} +0.0484145 q^{26} -4.72534 q^{27} -4.39582 q^{29} +0.199396 q^{30} +7.65667 q^{31} +0.580067 q^{32} +1.85996 q^{33} +0.162520 q^{34} -0.917792 q^{36} +5.38300 q^{37} -0.300851 q^{38} +1.85996 q^{39} -0.428568 q^{40} +4.23985 q^{41} +9.47985 q^{43} -1.99766 q^{44} +1.01733 q^{45} -0.211916 q^{46} +13.4090 q^{47} +7.41367 q^{48} -0.00468817 q^{50} +6.24358 q^{51} -1.99766 q^{52} -6.76895 q^{53} -0.228775 q^{54} +2.21431 q^{55} -11.5579 q^{57} -0.212822 q^{58} -10.4648 q^{59} -8.22738 q^{60} +11.5831 q^{61} +0.370694 q^{62} -7.94380 q^{64} +2.21431 q^{65} +0.0900488 q^{66} +12.6071 q^{67} -6.70582 q^{68} -8.14125 q^{69} -1.24711 q^{71} -0.0889210 q^{72} +11.5448 q^{73} +0.260615 q^{74} -0.180107 q^{75} +12.4136 q^{76} +0.0900488 q^{78} +0.448193 q^{79} +8.82611 q^{80} -10.1672 q^{81} +0.205270 q^{82} +3.12782 q^{83} +7.43309 q^{85} +0.458962 q^{86} -8.17604 q^{87} -0.193545 q^{88} +17.1236 q^{89} +0.0492535 q^{90} +8.74398 q^{92} +14.2411 q^{93} +0.649191 q^{94} -13.7599 q^{95} +1.07890 q^{96} +12.9138 q^{97} +0.459434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9	\( 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9} + 3 q^{10} + 25 q^{11} - 9 q^{12} + 25 q^{13} + 32 q^{16} + q^{17} + 44 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{22} + 15 q^{23} + 4 q^{24} + 50 q^{25} + 6 q^{26} + 17 q^{27} + 24 q^{29} + q^{30} + 12 q^{31} + 48 q^{32} + 2 q^{33} + 8 q^{34} + 30 q^{36} + 33 q^{37} - 16 q^{38} + 2 q^{39} + 21 q^{40} - 12 q^{41} + 38 q^{43} + 30 q^{44} + 22 q^{45} + 39 q^{46} - 4 q^{47} - 82 q^{48} + 16 q^{50} + 51 q^{51} + 30 q^{52} + 2 q^{53} - 10 q^{54} + q^{55} + 38 q^{57} + 17 q^{58} + 4 q^{59} - 33 q^{60} + 22 q^{61} - 42 q^{62} + 41 q^{64} + q^{65} - 2 q^{66} + 24 q^{67} - 14 q^{68} + 30 q^{69} + 9 q^{71} + 102 q^{72} - 11 q^{73} + 39 q^{74} + 16 q^{75} - 58 q^{76} - 2 q^{78} + 19 q^{79} + 33 q^{80} + 73 q^{81} + 32 q^{82} - 16 q^{83} + 14 q^{85} + 27 q^{86} + 11 q^{87} + 21 q^{88} - 13 q^{89} - 40 q^{90} + 17 q^{93} + 56 q^{94} + 15 q^{95} - 55 q^{96} - 34 q^{97} + 37 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9 + 3 * q^10 + 25 * q^11 - 9 * q^12 + 25 * q^13 + 32 * q^16 + q^17 + 44 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^22 + 15 * q^23 + 4 * q^24 + 50 * q^25 + 6 * q^26 + 17 * q^27 + 24 * q^29 + q^30 + 12 * q^31 + 48 * q^32 + 2 * q^33 + 8 * q^34 + 30 * q^36 + 33 * q^37 - 16 * q^38 + 2 * q^39 + 21 * q^40 - 12 * q^41 + 38 * q^43 + 30 * q^44 + 22 * q^45 + 39 * q^46 - 4 * q^47 - 82 * q^48 + 16 * q^50 + 51 * q^51 + 30 * q^52 + 2 * q^53 - 10 * q^54 + q^55 + 38 * q^57 + 17 * q^58 + 4 * q^59 - 33 * q^60 + 22 * q^61 - 42 * q^62 + 41 * q^64 + q^65 - 2 * q^66 + 24 * q^67 - 14 * q^68 + 30 * q^69 + 9 * q^71 + 102 * q^72 - 11 * q^73 + 39 * q^74 + 16 * q^75 - 58 * q^76 - 2 * q^78 + 19 * q^79 + 33 * q^80 + 73 * q^81 + 32 * q^82 - 16 * q^83 + 14 * q^85 + 27 * q^86 + 11 * q^87 + 21 * q^88 - 13 * q^89 - 40 * q^90 + 17 * q^93 + 56 * q^94 + 15 * q^95 - 55 * q^96 - 34 * q^97 + 37 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more