LMFDB - Embedded newform 7381.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.33240 q^{2} -1.95631 q^{3} -0.224702 q^{4} -2.95532 q^{5} +2.60660 q^{6} +3.88914 q^{7} +2.96420 q^{8} +0.827159 q^{9} +O(q^{10})$	\(q-1.33240 q^{2} -1.95631 q^{3} -0.224702 q^{4} -2.95532 q^{5} +2.60660 q^{6} +3.88914 q^{7} +2.96420 q^{8} +0.827159 q^{9} +3.93768 q^{10} +0.439588 q^{12} +2.81079 q^{13} -5.18191 q^{14} +5.78153 q^{15} -3.50010 q^{16} -2.46007 q^{17} -1.10211 q^{18} -6.39451 q^{19} +0.664067 q^{20} -7.60838 q^{21} +6.21549 q^{23} -5.79890 q^{24} +3.73393 q^{25} -3.74510 q^{26} +4.25076 q^{27} -0.873899 q^{28} +9.76132 q^{29} -7.70333 q^{30} +2.33316 q^{31} -1.26485 q^{32} +3.27780 q^{34} -11.4937 q^{35} -0.185864 q^{36} -0.734361 q^{37} +8.52007 q^{38} -5.49878 q^{39} -8.76017 q^{40} +4.87482 q^{41} +10.1374 q^{42} +4.95721 q^{43} -2.44452 q^{45} -8.28153 q^{46} -0.728720 q^{47} +6.84730 q^{48} +8.12544 q^{49} -4.97510 q^{50} +4.81266 q^{51} -0.631590 q^{52} +9.91867 q^{53} -5.66372 q^{54} +11.5282 q^{56} +12.5097 q^{57} -13.0060 q^{58} +6.07308 q^{59} -1.29912 q^{60} -1.00000 q^{61} -3.10871 q^{62} +3.21694 q^{63} +8.68550 q^{64} -8.30678 q^{65} +9.66809 q^{67} +0.552783 q^{68} -12.1594 q^{69} +15.3142 q^{70} -1.46268 q^{71} +2.45186 q^{72} +5.27410 q^{73} +0.978465 q^{74} -7.30473 q^{75} +1.43686 q^{76} +7.32659 q^{78} -14.1137 q^{79} +10.3439 q^{80} -10.7973 q^{81} -6.49522 q^{82} +4.53037 q^{83} +1.70962 q^{84} +7.27030 q^{85} -6.60500 q^{86} -19.0962 q^{87} -10.9203 q^{89} +3.25709 q^{90} +10.9316 q^{91} -1.39663 q^{92} -4.56438 q^{93} +0.970949 q^{94} +18.8978 q^{95} +2.47444 q^{96} -6.19390 q^{97} -10.8264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9} + 12 q^{10} + q^{12} + 3 q^{13} - q^{14} - 5 q^{15} + 17 q^{16} + 8 q^{17} + 20 q^{18} + 8 q^{19} + 16 q^{20} + 11 q^{21} + 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 13 q^{27} - 7 q^{28} + 43 q^{29} + 30 q^{30} - 4 q^{31} + 23 q^{32} + 31 q^{35} - 35 q^{36} - 4 q^{37} - 13 q^{38} + 11 q^{39} + 57 q^{40} + 29 q^{41} + 48 q^{42} + 10 q^{43} - 10 q^{45} - 14 q^{46} - 13 q^{47} + 42 q^{48} + 26 q^{49} - 6 q^{50} + 56 q^{51} + 25 q^{52} - 15 q^{53} + 35 q^{54} - 9 q^{56} - 3 q^{57} - 84 q^{58} - 13 q^{59} + 34 q^{60} - 24 q^{61} + 55 q^{62} + 22 q^{63} + 61 q^{64} + 41 q^{65} - q^{67} - 4 q^{68} - 27 q^{69} + 55 q^{70} - 6 q^{71} + 22 q^{72} + 18 q^{73} + 28 q^{74} + 47 q^{75} + 36 q^{76} - 10 q^{78} + 9 q^{79} - 40 q^{80} + 40 q^{81} + 15 q^{82} + 10 q^{83} + 93 q^{84} - 9 q^{85} + 38 q^{86} + 51 q^{87} - 17 q^{89} - 44 q^{90} - 22 q^{91} + 11 q^{92} + 32 q^{93} - 47 q^{94} + 54 q^{95} + 44 q^{96} - q^{97} + 45 q^{98}+O(q^{100}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9 + 12 * q^10 + q^12 + 3 * q^13 - q^14 - 5 * q^15 + 17 * q^16 + 8 * q^17 + 20 * q^18 + 8 * q^19 + 16 * q^20 + 11 * q^21 + 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 13 * q^27 - 7 * q^28 + 43 * q^29 + 30 * q^30 - 4 * q^31 + 23 * q^32 + 31 * q^35 - 35 * q^36 - 4 * q^37 - 13 * q^38 + 11 * q^39 + 57 * q^40 + 29 * q^41 + 48 * q^42 + 10 * q^43 - 10 * q^45 - 14 * q^46 - 13 * q^47 + 42 * q^48 + 26 * q^49 - 6 * q^50 + 56 * q^51 + 25 * q^52 - 15 * q^53 + 35 * q^54 - 9 * q^56 - 3 * q^57 - 84 * q^58 - 13 * q^59 + 34 * q^60 - 24 * q^61 + 55 * q^62 + 22 * q^63 + 61 * q^64 + 41 * q^65 - q^67 - 4 * q^68 - 27 * q^69 + 55 * q^70 - 6 * q^71 + 22 * q^72 + 18 * q^73 + 28 * q^74 + 47 * q^75 + 36 * q^76 - 10 * q^78 + 9 * q^79 - 40 * q^80 + 40 * q^81 + 15 * q^82 + 10 * q^83 + 93 * q^84 - 9 * q^85 + 38 * q^86 + 51 * q^87 - 17 * q^89 - 44 * q^90 - 22 * q^91 + 11 * q^92 + 32 * q^93 - 47 * q^94 + 54 * q^95 + 44 * q^96 - q^97 + 45 * q^98

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 $

$2$	−1.33240	−0.942151	−0.471076	−	0.882093i	$-0.656134\pi$
$2$	−1.33240	−0.942151	−0.471076	+	0.882093i	$0.656134\pi$
$3$	−1.95631	−1.12948	−0.564739	−	0.825270i	$-0.691023\pi$
$3$	−1.95631	−1.12948	−0.564739	+	0.825270i	$0.691023\pi$
$4$	−0.224702	−0.112351
$5$	−2.95532	−1.32166	−0.660830	−	0.750535i	$-0.729796\pi$
$5$	−2.95532	−1.32166	−0.660830	+	0.750535i	$0.729796\pi$
$6$	2.60660	1.06414
$7$	3.88914	1.46996	0.734979	−	0.678090i	$-0.237192\pi$
$7$	3.88914	1.46996	0.734979	+	0.678090i	$0.237192\pi$
$8$	2.96420	1.04800
$9$	0.827159	0.275720
$10$	3.93768	1.24520
$11$	0	0
$11$	0	0
$12$	0.439588	0.126898
$13$	2.81079	0.779572	0.389786	−	0.920905i	$-0.372549\pi$
$13$	2.81079	0.779572	0.389786	+	0.920905i	$0.372549\pi$
$14$	−5.18191	−1.38492
$15$	5.78153	1.49279
$16$	−3.50010	−0.875026
$17$	−2.46007	−0.596654	−0.298327	−	0.954464i	$-0.596429\pi$
$17$	−2.46007	−0.596654	−0.298327	+	0.954464i	$0.596429\pi$
$18$	−1.10211	−0.259770
$19$	−6.39451	−1.46700	−0.733501	−	0.679689i	$-0.762115\pi$
$19$	−6.39451	−1.46700	−0.733501	+	0.679689i	$0.762115\pi$
$20$	0.664067	0.148490
$21$	−7.60838	−1.66029
$22$	0	0
$23$	6.21549	1.29602	0.648009	−	0.761633i	$-0.275602\pi$
$23$	6.21549	1.29602	0.648009	+	0.761633i	$0.275602\pi$
$24$	−5.79890	−1.18370
$25$	3.73393	0.746786
$26$	−3.74510	−0.734475
$27$	4.25076	0.818058
$28$	−0.873899	−0.165151
$29$	9.76132	1.81263	0.906316	−	0.422601i	$-0.138883\pi$
$29$	9.76132	1.81263	0.906316	+	0.422601i	$0.138883\pi$
$30$	−7.70333	−1.40643
$31$	2.33316	0.419047	0.209524	−	0.977804i	$-0.432809\pi$
$31$	2.33316	0.419047	0.209524	+	0.977804i	$0.432809\pi$
$32$	−1.26485	−0.223596
$33$	0	0
$34$	3.27780	0.562139
$35$	−11.4937	−1.94279
$36$	−0.185864	−0.0309774
$37$	−0.734361	−0.120728	−0.0603641	−	0.998176i	$-0.519226\pi$
$37$	−0.734361	−0.120728	−0.0603641	+	0.998176i	$0.519226\pi$
$38$	8.52007	1.38214
$39$	−5.49878	−0.880509
$40$	−8.76017	−1.38510
$41$	4.87482	0.761319	0.380659	−	0.924715i	$-0.375697\pi$
$41$	4.87482	0.761319	0.380659	+	0.924715i	$0.375697\pi$
$42$	10.1374	1.56424
$43$	4.95721	0.755967	0.377983	−	0.925812i	$-0.376618\pi$
$43$	4.95721	0.755967	0.377983	+	0.925812i	$0.376618\pi$
$44$	0	0
$45$	−2.44452	−0.364408
$46$	−8.28153	−1.22105
$47$	−0.728720	−0.106295	−0.0531474	−	0.998587i	$-0.516925\pi$
$47$	−0.728720	−0.106295	−0.0531474	+	0.998587i	$0.516925\pi$
$48$	6.84730	0.988322
$49$	8.12544	1.16078
$50$	−4.97510	−0.703585
$51$	4.81266	0.673908
$52$	−0.631590	−0.0875858
$53$	9.91867	1.36243	0.681217	−	0.732081i	$-0.261451\pi$
$53$	9.91867	1.36243	0.681217	+	0.732081i	$0.261451\pi$
$54$	−5.66372	−0.770735
$55$	0	0
$56$	11.5282	1.54052
$57$	12.5097	1.65695
$58$	−13.0060	−1.70777
$59$	6.07308	0.790648	0.395324	−	0.918542i	$-0.370632\pi$
$59$	6.07308	0.790648	0.395324	+	0.918542i	$0.370632\pi$
$60$	−1.29912	−0.167716
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−3.10871	−0.394806
$63$	3.21694	0.405296
$64$	8.68550	1.08569
$65$	−8.30678	−1.03033
$66$	0	0
$67$	9.66809	1.18115	0.590573	−	0.806984i	$-0.298902\pi$
$67$	9.66809	1.18115	0.590573	+	0.806984i	$0.298902\pi$
$68$	0.552783	0.0670347
$69$	−12.1594	−1.46382
$70$	15.3142	1.83040
$71$	−1.46268	−0.173588	−0.0867939	−	0.996226i	$-0.527662\pi$
$71$	−1.46268	−0.173588	−0.0867939	+	0.996226i	$0.527662\pi$
$72$	2.45186	0.288955
$73$	5.27410	0.617286	0.308643	−	0.951178i	$-0.400125\pi$
$73$	5.27410	0.617286	0.308643	+	0.951178i	$0.400125\pi$
$74$	0.978465	0.113744
$75$	−7.30473	−0.843478
$76$	1.43686	0.164819
$77$	0	0
$78$	7.32659	0.829573
$79$	−14.1137	−1.58791	−0.793955	−	0.607976i	$-0.791982\pi$
$79$	−14.1137	−1.58791	−0.793955	+	0.607976i	$0.791982\pi$
$80$	10.3439	1.15649
$81$	−10.7973	−1.19970
$82$	−6.49522	−0.717278
$83$	4.53037	0.497273	0.248637	−	0.968597i	$-0.420018\pi$
$83$	4.53037	0.497273	0.248637	+	0.968597i	$0.420018\pi$
$84$	1.70962	0.186535
$85$	7.27030	0.788574
$86$	−6.60500	−0.712235
$87$	−19.0962	−2.04733
$88$	0	0
$89$	−10.9203	−1.15755	−0.578776	−	0.815487i	$-0.696469\pi$
$89$	−10.9203	−1.15755	−0.578776	+	0.815487i	$0.696469\pi$
$90$	3.25709	0.343327
$91$	10.9316	1.14594
$92$	−1.39663	−0.145609
$93$	−4.56438	−0.473305
$94$	0.970949	0.100146
$95$	18.8978	1.93888
$96$	2.47444	0.252547
$97$	−6.19390	−0.628895	−0.314448	−	0.949275i	$-0.601819\pi$
$97$	−6.19390	−0.628895	−0.314448	+	0.949275i	$0.601819\pi$
$98$	−10.8264	−1.09363
$99$	0	0
$100$	−0.839022	−0.0839022
$101$	1.46356	0.145629	0.0728146	−	0.997345i	$-0.476802\pi$
$101$	1.46356	0.145629	0.0728146	+	0.997345i	$0.476802\pi$
$102$	−6.41241	−0.634923
$103$	10.2860	1.01351	0.506753	−	0.862092i	$-0.330846\pi$
$103$	10.2860	1.01351	0.506753	+	0.862092i	$0.330846\pi$
$104$	8.33174	0.816994
$105$	22.4852	2.19433
$106$	−13.2157	−1.28362
$107$	7.10117	0.686496	0.343248	−	0.939245i	$-0.388473\pi$
$107$	7.10117	0.686496	0.343248	+	0.939245i	$0.388473\pi$
$108$	−0.955154	−0.0919097
$109$	−6.71428	−0.643112	−0.321556	−	0.946891i	$-0.604206\pi$
$109$	−6.71428	−0.643112	−0.321556	+	0.946891i	$0.604206\pi$
$110$	0	0
$111$	1.43664	0.136360
$112$	−13.6124	−1.28625
$113$	7.31000	0.687667	0.343834	−	0.939031i	$-0.388274\pi$
$113$	7.31000	0.687667	0.343834	+	0.939031i	$0.388274\pi$
$114$	−16.6679	−1.56109
$115$	−18.3688	−1.71290
$116$	−2.19339	−0.203651
$117$	2.32497	0.214943
$118$	−8.09179	−0.744910
$119$	−9.56756	−0.877057
$120$	17.1376	1.56444
$121$	0	0
$122$	1.33240	0.120630
$123$	−9.53667	−0.859893
$124$	−0.524265	−0.0470804
$125$	3.74164	0.334663
$126$	−4.28626	−0.381851
$127$	20.1861	1.79123	0.895615	−	0.444830i	$-0.146736\pi$
$127$	20.1861	1.79123	0.895615	+	0.444830i	$0.146736\pi$
$128$	−9.04289	−0.799286
$129$	−9.69785	−0.853848
$130$	11.0680	0.970726
$131$	−0.172988	−0.0151140	−0.00755702	−	0.999971i	$-0.502405\pi$
$131$	−0.172988	−0.0151140	−0.00755702	+	0.999971i	$0.502405\pi$
$132$	0	0
$133$	−24.8692	−2.15643
$134$	−12.8818	−1.11282
$135$	−12.5624	−1.08120
$136$	−7.29213	−0.625295
$137$	−2.09278	−0.178798	−0.0893992	−	0.995996i	$-0.528495\pi$
$137$	−2.09278	−0.178798	−0.0893992	+	0.995996i	$0.528495\pi$
$138$	16.2013	1.37914
$139$	14.1517	1.20033	0.600167	−	0.799875i	$-0.295101\pi$
$139$	14.1517	1.20033	0.600167	+	0.799875i	$0.295101\pi$
$140$	2.58265	0.218274
$141$	1.42560	0.120058
$142$	1.94887	0.163546
$143$	0	0
$144$	−2.89514	−0.241262
$145$	−28.8478	−2.39568
$146$	−7.02722	−0.581577
$147$	−15.8959	−1.31107
$148$	0.165013	0.0135639
$149$	−15.4550	−1.26612	−0.633061	−	0.774102i	$-0.718202\pi$
$149$	−15.4550	−1.26612	−0.633061	+	0.774102i	$0.718202\pi$
$150$	9.73285	0.794684
$151$	−15.0361	−1.22362	−0.611808	−	0.791006i	$-0.709558\pi$
$151$	−15.0361	−1.22362	−0.611808	+	0.791006i	$0.709558\pi$
$152$	−18.9546	−1.53742
$153$	−2.03487	−0.164509
$154$	0	0
$155$	−6.89523	−0.553838
$156$	1.23559	0.0989262
$157$	15.8050	1.26137	0.630687	−	0.776037i	$-0.282773\pi$
$157$	15.8050	1.26137	0.630687	+	0.776037i	$0.282773\pi$
$158$	18.8051	1.49605
$159$	−19.4040	−1.53884
$160$	3.73804	0.295518
$161$	24.1729	1.90509
$162$	14.3863	1.13030
$163$	−10.3512	−0.810768	−0.405384	−	0.914146i	$-0.632862\pi$
$163$	−10.3512	−0.810768	−0.405384	+	0.914146i	$0.632862\pi$
$164$	−1.09538	−0.0855350
$165$	0	0
$166$	−6.03628	−0.468507
$167$	−16.6330	−1.28710	−0.643549	−	0.765405i	$-0.722539\pi$
$167$	−16.6330	−1.28710	−0.643549	+	0.765405i	$0.722539\pi$
$168$	−22.5528	−1.73998
$169$	−5.09947	−0.392267
$170$	−9.68696	−0.742956
$171$	−5.28928	−0.404481
$172$	−1.11389	−0.0849337
$173$	0.252247	0.0191780	0.00958898	−	0.999954i	$-0.496948\pi$
$173$	0.252247	0.0191780	0.00958898	+	0.999954i	$0.496948\pi$
$174$	25.4438	1.92889
$175$	14.5218	1.09774
$176$	0	0
$177$	−11.8808	−0.893019
$178$	14.5503	1.09059
$179$	−8.43176	−0.630220	−0.315110	−	0.949055i	$-0.602041\pi$
$179$	−8.43176	−0.630220	−0.315110	+	0.949055i	$0.602041\pi$
$180$	0.549289	0.0409416
$181$	−21.4950	−1.59771	−0.798856	−	0.601523i	$-0.794561\pi$
$181$	−21.4950	−1.59771	−0.798856	+	0.601523i	$0.794561\pi$
$182$	−14.5652	−1.07965
$183$	1.95631	0.144615
$184$	18.4239	1.35823
$185$	2.17027	0.159562
$186$	6.08160	0.445925
$187$	0	0
$188$	0.163745	0.0119423
$189$	16.5318	1.20251
$190$	−25.1795	−1.82672
$191$	3.65700	0.264612	0.132306	−	0.991209i	$-0.457762\pi$
$191$	3.65700	0.264612	0.132306	+	0.991209i	$0.457762\pi$
$192$	−16.9916	−1.22626
$193$	−15.7880	−1.13644	−0.568222	−	0.822875i	$-0.692368\pi$
$193$	−15.7880	−1.13644	−0.568222	+	0.822875i	$0.692368\pi$
$194$	8.25277	0.592514
$195$	16.2507	1.16373
$196$	−1.82580	−0.130415
$197$	14.9436	1.06469	0.532344	−	0.846528i	$-0.321311\pi$
$197$	14.9436	1.06469	0.532344	+	0.846528i	$0.321311\pi$
$198$	0	0
$199$	−8.88035	−0.629511	−0.314756	−	0.949173i	$-0.601923\pi$
$199$	−8.88035	−0.629511	−0.314756	+	0.949173i	$0.601923\pi$
$200$	11.0681	0.782634
$201$	−18.9138	−1.33408
$202$	−1.95005	−0.137205
$203$	37.9632	2.66449
$204$	−1.08142	−0.0757142
$205$	−14.4067	−1.00620
$206$	−13.7050	−0.954875
$207$	5.14119	0.357338
$208$	−9.83805	−0.682146
$209$	0	0
$210$	−29.9594	−2.06739
$211$	−14.4115	−0.992128	−0.496064	−	0.868286i	$-0.665222\pi$
$211$	−14.4115	−0.992128	−0.496064	+	0.868286i	$0.665222\pi$
$212$	−2.22875	−0.153071
$213$	2.86145	0.196063
$214$	−9.46162	−0.646783
$215$	−14.6501	−0.999131
$216$	12.6001	0.857328
$217$	9.07398	0.615982
$218$	8.94613	0.605908
$219$	−10.3178	−0.697211
$220$	0	0
$221$	−6.91473	−0.465135
$222$	−1.91418	−0.128472
$223$	3.71357	0.248679	0.124339	−	0.992240i	$-0.460319\pi$
$223$	3.71357	0.248679	0.124339	+	0.992240i	$0.460319\pi$
$224$	−4.91918	−0.328677
$225$	3.08855	0.205904
$226$	−9.73987	−0.647886
$227$	−11.7245	−0.778183	−0.389091	−	0.921199i	$-0.627211\pi$
$227$	−11.7245	−0.778183	−0.389091	+	0.921199i	$0.627211\pi$
$228$	−2.81095	−0.186160
$229$	−10.4314	−0.689329	−0.344664	−	0.938726i	$-0.612007\pi$
$229$	−10.4314	−0.689329	−0.344664	+	0.938726i	$0.612007\pi$
$230$	24.4746	1.61381
$231$	0	0
$232$	28.9345	1.89964
$233$	22.4058	1.46785	0.733925	−	0.679230i	$-0.237686\pi$
$233$	22.4058	1.46785	0.733925	+	0.679230i	$0.237686\pi$
$234$	−3.09779	−0.202509
$235$	2.15360	0.140486
$236$	−1.36463	−0.0888302
$237$	27.6107	1.79351
$238$	12.7478	0.826320
$239$	16.3294	1.05626	0.528132	−	0.849163i	$-0.322893\pi$
$239$	16.3294	1.05626	0.528132	+	0.849163i	$0.322893\pi$
$240$	−20.2360	−1.30623
$241$	11.8419	0.762803	0.381401	−	0.924410i	$-0.375442\pi$
$241$	11.8419	0.762803	0.381401	+	0.924410i	$0.375442\pi$
$242$	0	0
$243$	8.37060	0.536974
$244$	0.224702	0.0143851
$245$	−24.0133	−1.53415
$246$	12.7067	0.810149
$247$	−17.9736	−1.14363
$248$	6.91594	0.439163
$249$	−8.86283	−0.561659
$250$	−4.98538	−0.315303
$251$	−22.0253	−1.39022	−0.695112	−	0.718901i	$-0.744645\pi$
$251$	−22.0253	−1.39022	−0.695112	+	0.718901i	$0.744645\pi$
$252$	−0.722854	−0.0455355
$253$	0	0
$254$	−26.8961	−1.68761
$255$	−14.2230	−0.890677
$256$	−5.32223	−0.332639
$257$	−13.9457	−0.869909	−0.434954	−	0.900452i	$-0.643236\pi$
$257$	−13.9457	−0.869909	−0.434954	+	0.900452i	$0.643236\pi$
$258$	12.9214	0.804454
$259$	−2.85604	−0.177465
$260$	1.86655	0.115759
$261$	8.07416	0.499778
$262$	0.230490	0.0142397
$263$	−26.7596	−1.65007	−0.825034	−	0.565083i	$-0.808844\pi$
$263$	−26.7596	−1.65007	−0.825034	+	0.565083i	$0.808844\pi$
$264$	0	0
$265$	−29.3129	−1.80068
$266$	33.1358	2.03168
$267$	21.3635	1.30743
$268$	−2.17244	−0.132703
$269$	16.6360	1.01432	0.507158	−	0.861853i	$-0.330696\pi$
$269$	16.6360	1.01432	0.507158	+	0.861853i	$0.330696\pi$
$270$	16.7381	1.01865
$271$	−16.3847	−0.995299	−0.497650	−	0.867378i	$-0.665803\pi$
$271$	−16.3847	−0.995299	−0.497650	+	0.867378i	$0.665803\pi$
$272$	8.61050	0.522088
$273$	−21.3855	−1.29431
$274$	2.78843	0.168455
$275$	0	0
$276$	2.73225	0.164462
$277$	6.41499	0.385439	0.192720	−	0.981254i	$-0.438269\pi$
$277$	6.41499	0.385439	0.192720	+	0.981254i	$0.438269\pi$
$278$	−18.8558	−1.13090
$279$	1.92989	0.115540
$280$	−34.0696	−2.03605
$281$	−26.1520	−1.56010	−0.780048	−	0.625720i	$-0.784805\pi$
$281$	−26.1520	−1.56010	−0.780048	+	0.625720i	$0.784805\pi$
$282$	−1.89948	−0.113112
$283$	−16.7135	−0.993516	−0.496758	−	0.867889i	$-0.665476\pi$
$283$	−16.7135	−0.993516	−0.496758	+	0.867889i	$0.665476\pi$
$284$	0.328667	0.0195028
$285$	−36.9701	−2.18992
$286$	0	0
$287$	18.9589	1.11911
$288$	−1.04623	−0.0616498
$289$	−10.9481	−0.644004
$290$	38.4370	2.25710
$291$	12.1172	0.710323
$292$	−1.18510	−0.0693528
$293$	33.8380	1.97684	0.988420	−	0.151744i	$-0.0484891\pi$
$293$	33.8380	1.97684	0.988420	+	0.151744i	$0.0484891\pi$
$294$	21.1798	1.23523
$295$	−17.9479	−1.04497
$296$	−2.17679	−0.126524
$297$	0	0
$298$	20.5923	1.19288
$299$	17.4704	1.01034
$300$	1.64139	0.0947657
$301$	19.2793	1.11124
$302$	20.0341	1.15283
$303$	−2.86317	−0.164485
$304$	22.3815	1.28366
$305$	2.95532	0.169221
$306$	2.71126	0.154993
$307$	−19.4125	−1.10793	−0.553965	−	0.832540i	$-0.686886\pi$
$307$	−19.4125	−1.10793	−0.553965	+	0.832540i	$0.686886\pi$
$308$	0	0
$309$	−20.1225	−1.14473
$310$	9.18723	0.521799
$311$	14.2725	0.809321	0.404660	−	0.914467i	$-0.367390\pi$
$311$	14.2725	0.809321	0.404660	+	0.914467i	$0.367390\pi$
$312$	−16.2995	−0.922776
$313$	27.8630	1.57491	0.787454	−	0.616374i	$-0.211399\pi$
$313$	27.8630	1.57491	0.787454	+	0.616374i	$0.211399\pi$
$314$	−21.0586	−1.18841
$315$	−9.50710	−0.535664
$316$	3.17137	0.178403
$317$	30.8857	1.73471	0.867356	−	0.497688i	$-0.165817\pi$
$317$	30.8857	1.73471	0.867356	+	0.497688i	$0.165817\pi$
$318$	25.8540	1.44982
$319$	0	0
$320$	−25.6684	−1.43491
$321$	−13.8921	−0.775382
$322$	−32.2081	−1.79489
$323$	15.7309	0.875293
$324$	2.42617	0.134787
$325$	10.4953	0.582174
$326$	13.7920	0.763866
$327$	13.1352	0.726380
$328$	14.4499	0.797864
$329$	−2.83410	−0.156249
$330$	0	0
$331$	8.02347	0.441010	0.220505	−	0.975386i	$-0.429230\pi$
$331$	8.02347	0.441010	0.220505	+	0.975386i	$0.429230\pi$
$332$	−1.01798	−0.0558692
$333$	−0.607434	−0.0332872
$334$	22.1618	1.21264
$335$	−28.5723	−1.56107
$336$	26.6301	1.45279
$337$	19.0294	1.03660	0.518298	−	0.855200i	$-0.326566\pi$
$337$	19.0294	1.03660	0.518298	+	0.855200i	$0.326566\pi$
$338$	6.79455	0.369575
$339$	−14.3006	−0.776705
$340$	−1.63365	−0.0885972
$341$	0	0
$342$	7.04745	0.381082
$343$	4.37701	0.236336
$344$	14.6942	0.792256
$345$	35.9350	1.93468
$346$	−0.336094	−0.0180685
$347$	23.7071	1.27267	0.636333	−	0.771415i	$-0.280451\pi$
$347$	23.7071	1.27267	0.636333	+	0.771415i	$0.280451\pi$
$348$	4.29096	0.230019
$349$	−25.7421	−1.37794	−0.688971	−	0.724789i	$-0.741937\pi$
$349$	−25.7421	−1.37794	−0.688971	+	0.724789i	$0.741937\pi$
$350$	−19.3489	−1.03424
$351$	11.9480	0.637736
$352$	0	0
$353$	−2.67544	−0.142399	−0.0711996	−	0.997462i	$-0.522683\pi$
$353$	−2.67544	−0.142399	−0.0711996	+	0.997462i	$0.522683\pi$
$354$	15.8301	0.841359
$355$	4.32268	0.229424
$356$	2.45382	0.130052
$357$	18.7171	0.990616
$358$	11.2345	0.593762
$359$	−16.0096	−0.844953	−0.422477	−	0.906374i	$-0.638839\pi$
$359$	−16.0096	−0.844953	−0.422477	+	0.906374i	$0.638839\pi$
$360$	−7.24605	−0.381900
$361$	21.8898	1.15209
$362$	28.6400	1.50529
$363$	0	0
$364$	−2.45634	−0.128747
$365$	−15.5867	−0.815843
$366$	−2.60660	−0.136249
$367$	14.3350	0.748283	0.374142	−	0.927372i	$-0.377937\pi$
$367$	14.3350	0.748283	0.374142	+	0.927372i	$0.377937\pi$
$368$	−21.7548	−1.13405
$369$	4.03225	0.209911
$370$	−2.89168	−0.150331
$371$	38.5751	2.00272
$372$	1.02563	0.0531763
$373$	20.6389	1.06864	0.534320	−	0.845282i	$-0.320568\pi$
$373$	20.6389	1.06864	0.534320	+	0.845282i	$0.320568\pi$
$374$	0	0
$375$	−7.31983	−0.377994
$376$	−2.16007	−0.111397
$377$	27.4370	1.41308
$378$	−22.0270	−1.13295
$379$	6.22962	0.319994	0.159997	−	0.987117i	$-0.448851\pi$
$379$	6.22962	0.319994	0.159997	+	0.987117i	$0.448851\pi$
$380$	−4.24639	−0.217835
$381$	−39.4904	−2.02315
$382$	−4.87260	−0.249304
$383$	32.7822	1.67509	0.837546	−	0.546367i	$-0.183989\pi$
$383$	32.7822	1.67509	0.837546	+	0.546367i	$0.183989\pi$
$384$	17.6907	0.902775
$385$	0	0
$386$	21.0360	1.07070
$387$	4.10040	0.208435
$388$	1.39178	0.0706570
$389$	14.8458	0.752712	0.376356	−	0.926475i	$-0.377177\pi$
$389$	14.8458	0.752712	0.376356	+	0.926475i	$0.377177\pi$
$390$	−21.6524	−1.09641
$391$	−15.2905	−0.773275
$392$	24.0854	1.21650
$393$	0.338419	0.0170710
$394$	−19.9109	−1.00310
$395$	41.7104	2.09868
$396$	0	0
$397$	−4.97813	−0.249845	−0.124923	−	0.992166i	$-0.539868\pi$
$397$	−4.97813	−0.249845	−0.124923	+	0.992166i	$0.539868\pi$
$398$	11.8322	0.593095
$399$	48.6519	2.43564
$400$	−13.0691	−0.653457
$401$	12.8437	0.641383	0.320691	−	0.947184i	$-0.396085\pi$
$401$	12.8437	0.641383	0.320691	+	0.947184i	$0.396085\pi$
$402$	25.2008	1.25690
$403$	6.55801	0.326678
$404$	−0.328864	−0.0163616
$405$	31.9095	1.58559
$406$	−50.5822	−2.51035
$407$	0	0
$408$	14.2657	0.706257
$409$	−39.3839	−1.94741	−0.973703	−	0.227820i	$-0.926840\pi$
$409$	−39.3839	−1.94741	−0.973703	+	0.227820i	$0.926840\pi$
$410$	19.1955	0.947997
$411$	4.09413	0.201949
$412$	−2.31128	−0.113868
$413$	23.6191	1.16222
$414$	−6.85014	−0.336666
$415$	−13.3887	−0.657226
$416$	−3.55522	−0.174309
$417$	−27.6852	−1.35575
$418$	0	0
$419$	−23.6384	−1.15481	−0.577407	−	0.816457i	$-0.695935\pi$
$419$	−23.6384	−1.15481	−0.577407	+	0.816457i	$0.695935\pi$
$420$	−5.05248	−0.246536
$421$	3.79061	0.184743	0.0923715	−	0.995725i	$-0.470555\pi$
$421$	3.79061	0.184743	0.0923715	+	0.995725i	$0.470555\pi$
$422$	19.2019	0.934734
$423$	−0.602768	−0.0293076
$424$	29.4009	1.42784
$425$	−9.18572	−0.445573
$426$	−3.81261	−0.184721
$427$	−3.88914	−0.188209
$428$	−1.59565	−0.0771286
$429$	0	0
$430$	19.5199	0.941333
$431$	35.3357	1.70206	0.851030	−	0.525117i	$-0.175979\pi$
$431$	35.3357	1.70206	0.851030	+	0.525117i	$0.175979\pi$
$432$	−14.8781	−0.715823
$433$	30.1537	1.44909	0.724546	−	0.689226i	$-0.242049\pi$
$433$	30.1537	1.44909	0.724546	+	0.689226i	$0.242049\pi$
$434$	−12.0902	−0.580348
$435$	56.4354	2.70587
$436$	1.50871	0.0722543
$437$	−39.7450	−1.90126
$438$	13.7474	0.656878
$439$	12.5088	0.597012	0.298506	−	0.954408i	$-0.403512\pi$
$439$	12.5088	0.597012	0.298506	+	0.954408i	$0.403512\pi$
$440$	0	0
$441$	6.72103	0.320049
$442$	9.21321	0.438228
$443$	26.9963	1.28263	0.641316	−	0.767277i	$-0.278389\pi$
$443$	26.9963	1.28263	0.641316	+	0.767277i	$0.278389\pi$
$444$	−0.322816	−0.0153202
$445$	32.2730	1.52989
$446$	−4.94797	−0.234293
$447$	30.2348	1.43006
$448$	33.7792	1.59592
$449$	40.6274	1.91733	0.958663	−	0.284543i	$-0.0918419\pi$
$449$	40.6274	1.91733	0.958663	+	0.284543i	$0.0918419\pi$
$450$	−4.11520	−0.193992
$451$	0	0
$452$	−1.64257	−0.0772601
$453$	29.4152	1.38205
$454$	15.6218	0.733166
$455$	−32.3063	−1.51454
$456$	37.0811	1.73648
$457$	22.6981	1.06177	0.530886	−	0.847443i	$-0.321859\pi$
$457$	22.6981	1.06177	0.530886	+	0.847443i	$0.321859\pi$
$458$	13.8989	0.649452
$459$	−10.4572	−0.488098
$460$	4.12750	0.192446
$461$	20.9626	0.976325	0.488162	−	0.872753i	$-0.337667\pi$
$461$	20.9626	0.976325	0.488162	+	0.872753i	$0.337667\pi$
$462$	0	0
$463$	−41.8050	−1.94284	−0.971421	−	0.237361i	$-0.923717\pi$
$463$	−41.8050	−1.94284	−0.971421	+	0.237361i	$0.923717\pi$
$464$	−34.1656	−1.58610
$465$	13.4892	0.625548
$466$	−29.8535	−1.38294
$467$	−4.10418	−0.189919	−0.0949594	−	0.995481i	$-0.530272\pi$
$467$	−4.10418	−0.189919	−0.0949594	+	0.995481i	$0.530272\pi$
$468$	−0.522425	−0.0241491
$469$	37.6006	1.73623
$470$	−2.86947	−0.132359
$471$	−30.9195	−1.42469
$472$	18.0018	0.828602
$473$	0	0
$474$	−36.7886	−1.68976
$475$	−23.8767	−1.09554
$476$	2.14985	0.0985383
$477$	8.20432	0.375650
$478$	−21.7574	−0.995160
$479$	12.7055	0.580530	0.290265	−	0.956946i	$-0.406257\pi$
$479$	12.7055	0.580530	0.290265	+	0.956946i	$0.406257\pi$
$480$	−7.31277	−0.333781
$481$	−2.06413	−0.0941164
$482$	−15.7782	−0.718675
$483$	−47.2898	−2.15176
$484$	0	0
$485$	18.3050	0.831186
$486$	−11.1530	−0.505911
$487$	−24.2029	−1.09674	−0.548369	−	0.836236i	$-0.684751\pi$
$487$	−24.2029	−1.09674	−0.548369	+	0.836236i	$0.684751\pi$
$488$	−2.96420	−0.134183
$489$	20.2502	0.915745
$490$	31.9954	1.44540
$491$	−25.7771	−1.16330	−0.581652	−	0.813438i	$-0.697593\pi$
$491$	−25.7771	−1.16330	−0.581652	+	0.813438i	$0.697593\pi$
$492$	2.14291	0.0966099
$493$	−24.0135	−1.08151
$494$	23.9481	1.07748
$495$	0	0
$496$	−8.16629	−0.366677
$497$	−5.68856	−0.255167
$498$	11.8089	0.529168
$499$	−34.8533	−1.56025	−0.780125	−	0.625624i	$-0.784844\pi$
$499$	−34.8533	−1.56025	−0.780125	+	0.625624i	$0.784844\pi$
$500$	−0.840756	−0.0375997
$501$	32.5393	1.45375
$502$	29.3466	1.30980
$503$	19.4998	0.869455	0.434727	−	0.900562i	$-0.356845\pi$
$503$	19.4998	0.869455	0.434727	+	0.900562i	$0.356845\pi$
$504$	9.53566	0.424752
$505$	−4.32528	−0.192472
$506$	0	0
$507$	9.97617	0.443057
$508$	−4.53587	−0.201247
$509$	34.4886	1.52868	0.764339	−	0.644814i	$-0.223065\pi$
$509$	34.4886	1.52868	0.764339	+	0.644814i	$0.223065\pi$
$510$	18.9507	0.839152
$511$	20.5117	0.907385
$512$	25.1771	1.11268
$513$	−27.1815	−1.20009
$514$	18.5813	0.819586
$515$	−30.3983	−1.33951
$516$	2.17913	0.0959307
$517$	0	0
$518$	3.80539	0.167199
$519$	−0.493473	−0.0216611
$520$	−24.6230	−1.07979
$521$	−18.7284	−0.820507	−0.410253	−	0.911972i	$-0.634560\pi$
$521$	−18.7284	−0.820507	−0.410253	+	0.911972i	$0.634560\pi$
$522$	−10.7580	−0.470867
$523$	−27.9756	−1.22329	−0.611644	−	0.791133i	$-0.709492\pi$
$523$	−27.9756	−1.22329	−0.611644	+	0.791133i	$0.709492\pi$
$524$	0.0388708	0.00169808
$525$	−28.4092	−1.23988
$526$	35.6546	1.55461
$527$	−5.73973	−0.250026
$528$	0	0
$529$	15.6323	0.679663
$530$	39.0566	1.69651
$531$	5.02341	0.217997
$532$	5.58816	0.242277
$533$	13.7021	0.593503
$534$	−28.4649	−1.23179
$535$	−20.9862	−0.907314
$536$	28.6582	1.23784
$537$	16.4952	0.711819
$538$	−22.1659	−0.955640
$539$	0	0
$540$	2.82279	0.121473
$541$	22.6404	0.973385	0.486692	−	0.873573i	$-0.338203\pi$
$541$	22.6404	0.973385	0.486692	+	0.873573i	$0.338203\pi$
$542$	21.8310	0.937723
$543$	42.0509	1.80458
$544$	3.11162	0.133409
$545$	19.8429	0.849975
$546$	28.4942	1.21944
$547$	39.1961	1.67590	0.837952	−	0.545744i	$-0.183753\pi$
$547$	39.1961	1.67590	0.837952	+	0.545744i	$0.183753\pi$
$548$	0.470252	0.0200882
$549$	−0.827159	−0.0353023
$550$	0	0
$551$	−62.4189	−2.65913
$552$	−36.0430	−1.53409
$553$	−54.8901	−2.33416
$554$	−8.54735	−0.363142
$555$	−4.24573	−0.180221
$556$	−3.17992	−0.134859
$557$	−0.220852	−0.00935781	−0.00467891	−	0.999989i	$-0.501489\pi$
$557$	−0.220852	−0.00935781	−0.00467891	+	0.999989i	$0.501489\pi$
$558$	−2.57139	−0.108856
$559$	13.9337	0.589331
$560$	40.2291	1.69999
$561$	0	0
$562$	34.8450	1.46985
$563$	9.07227	0.382351	0.191175	−	0.981556i	$-0.438770\pi$
$563$	9.07227	0.382351	0.191175	+	0.981556i	$0.438770\pi$
$564$	−0.320337	−0.0134886
$565$	−21.6034	−0.908862
$566$	22.2692	0.936042
$567$	−41.9922	−1.76351
$568$	−4.33567	−0.181920
$569$	12.7009	0.532449	0.266225	−	0.963911i	$-0.414224\pi$
$569$	12.7009	0.532449	0.266225	+	0.963911i	$0.414224\pi$
$570$	49.2591	2.06324
$571$	43.8240	1.83398	0.916988	−	0.398914i	$-0.130613\pi$
$571$	43.8240	1.83398	0.916988	+	0.398914i	$0.130613\pi$
$572$	0	0
$573$	−7.15424	−0.298873
$574$	−25.2609	−1.05437
$575$	23.2082	0.967848
$576$	7.18429	0.299345
$577$	−23.2110	−0.966285	−0.483142	−	0.875542i	$-0.660505\pi$
$577$	−23.2110	−0.966285	−0.483142	+	0.875542i	$0.660505\pi$
$578$	14.5872	0.606749
$579$	30.8862	1.28359
$580$	6.48217	0.269158
$581$	17.6193	0.730971
$582$	−16.1450	−0.669232
$583$	0	0
$584$	15.6335	0.646918
$585$	−6.87103	−0.284082
$586$	−45.0859	−1.86248
$587$	−27.2582	−1.12506	−0.562532	−	0.826775i	$-0.690173\pi$
$587$	−27.2582	−1.12506	−0.562532	+	0.826775i	$0.690173\pi$
$588$	3.57184	0.147300
$589$	−14.9194	−0.614743
$590$	23.9139	0.984518
$591$	−29.2344	−1.20254
$592$	2.57034	0.105640
$593$	2.23942	0.0919620	0.0459810	−	0.998942i	$-0.485359\pi$
$593$	2.23942	0.0919620	0.0459810	+	0.998942i	$0.485359\pi$
$594$	0	0
$595$	28.2752	1.15917
$596$	3.47277	0.142250
$597$	17.3727	0.711019
$598$	−23.2776	−0.951893
$599$	20.0780	0.820364	0.410182	−	0.912004i	$-0.365465\pi$
$599$	20.0780	0.820364	0.410182	+	0.912004i	$0.365465\pi$
$600$	−21.6527	−0.883968
$601$	−26.1450	−1.06648	−0.533238	−	0.845965i	$-0.679025\pi$
$601$	−26.1450	−1.06648	−0.533238	+	0.845965i	$0.679025\pi$
$602$	−25.6878	−1.04696
$603$	7.99705	0.325665
$604$	3.37863	0.137475
$605$	0	0
$606$	3.81490	0.154970
$607$	−4.63652	−0.188191	−0.0940953	−	0.995563i	$-0.529996\pi$
$607$	−4.63652	−0.188191	−0.0940953	+	0.995563i	$0.529996\pi$
$608$	8.08810	0.328016
$609$	−74.2678	−3.00948
$610$	−3.93768	−0.159432
$611$	−2.04828	−0.0828645
$612$	0.457239	0.0184828
$613$	−0.430468	−0.0173865	−0.00869323	−	0.999962i	$-0.502767\pi$
$613$	−0.430468	−0.0173865	−0.00869323	+	0.999962i	$0.502767\pi$
$614$	25.8653	1.04384
$615$	28.1839	1.13649
$616$	0	0
$617$	−44.1235	−1.77634	−0.888172	−	0.459511i	$-0.848025\pi$
$617$	−44.1235	−1.77634	−0.888172	+	0.459511i	$0.848025\pi$
$618$	26.8113	1.07851
$619$	−14.5488	−0.584765	−0.292383	−	0.956301i	$-0.594448\pi$
$619$	−14.5488	−0.584765	−0.292383	+	0.956301i	$0.594448\pi$
$620$	1.54937	0.0622243
$621$	26.4205	1.06022
$622$	−19.0168	−0.762503
$623$	−42.4707	−1.70155
$624$	19.2463	0.770469
$625$	−29.7274	−1.18910
$626$	−37.1247	−1.48380
$627$	0	0
$628$	−3.55141	−0.141717
$629$	1.80658	0.0720330
$630$	12.6673	0.504677
$631$	−23.9849	−0.954823	−0.477412	−	0.878680i	$-0.658425\pi$
$631$	−23.9849	−0.954823	−0.477412	+	0.878680i	$0.658425\pi$
$632$	−41.8357	−1.66414
$633$	28.1934	1.12059
$634$	−41.1522	−1.63436
$635$	−59.6566	−2.36740
$636$	4.36013	0.172890
$637$	22.8389	0.904910
$638$	0	0
$639$	−1.20987	−0.0478616
$640$	26.7246	1.05638
$641$	27.8316	1.09928	0.549641	−	0.835401i	$-0.314765\pi$
$641$	27.8316	1.09928	0.549641	+	0.835401i	$0.314765\pi$
$642$	18.5099	0.730527
$643$	−32.6118	−1.28609	−0.643043	−	0.765830i	$-0.722328\pi$
$643$	−32.6118	−1.28609	−0.643043	+	0.765830i	$0.722328\pi$
$644$	−5.43171	−0.214039
$645$	28.6603	1.12850
$646$	−20.9600	−0.824658
$647$	24.7095	0.971429	0.485714	−	0.874118i	$-0.338559\pi$
$647$	24.7095	0.971429	0.485714	+	0.874118i	$0.338559\pi$
$648$	−32.0053	−1.25729
$649$	0	0
$650$	−13.9839	−0.548496
$651$	−17.7515	−0.695738
$652$	2.32594	0.0910907
$653$	17.5477	0.686693	0.343346	−	0.939209i	$-0.388440\pi$
$653$	17.5477	0.686693	0.343346	+	0.939209i	$0.388440\pi$
$654$	−17.5014	−0.684360
$655$	0.511235	0.0199756
$656$	−17.0624	−0.666174
$657$	4.36252	0.170198
$658$	3.77616	0.147210
$659$	44.1227	1.71878	0.859388	−	0.511323i	$-0.170845\pi$
$659$	44.1227	1.71878	0.859388	+	0.511323i	$0.170845\pi$
$660$	0	0
$661$	−2.00922	−0.0781496	−0.0390748	−	0.999236i	$-0.512441\pi$
$661$	−2.00922	−0.0781496	−0.0390748	+	0.999236i	$0.512441\pi$
$662$	−10.6905	−0.415498
$663$	13.5274	0.525360
$664$	13.4289	0.521144
$665$	73.4964	2.85007
$666$	0.809346	0.0313615
$667$	60.6713	2.34920
$668$	3.73746	0.144607
$669$	−7.26490	−0.280877
$670$	38.0699	1.47077
$671$	0	0
$672$	9.62346	0.371233
$673$	−50.7277	−1.95541	−0.977705	−	0.209984i	$-0.932659\pi$
$673$	−50.7277	−1.95541	−0.977705	+	0.209984i	$0.932659\pi$
$674$	−25.3548	−0.976631
$675$	15.8720	0.610915
$676$	1.14586	0.0440716
$677$	−17.8557	−0.686249	−0.343125	−	0.939290i	$-0.611485\pi$
$677$	−17.8557	−0.686249	−0.343125	+	0.939290i	$0.611485\pi$
$678$	19.0542	0.731773
$679$	−24.0890	−0.924450
$680$	21.5506	0.826428
$681$	22.9368	0.878940
$682$	0	0
$683$	11.2781	0.431544	0.215772	−	0.976444i	$-0.430773\pi$
$683$	11.2781	0.431544	0.215772	+	0.976444i	$0.430773\pi$
$684$	1.18851	0.0454439
$685$	6.18484	0.236311
$686$	−5.83194	−0.222665
$687$	20.4072	0.778581
$688$	−17.3507	−0.661491
$689$	27.8793	1.06212
$690$	−47.8800	−1.82276
$691$	21.7867	0.828805	0.414403	−	0.910094i	$-0.363991\pi$
$691$	21.7867	0.828805	0.414403	+	0.910094i	$0.363991\pi$
$692$	−0.0566804	−0.00215466
$693$	0	0
$694$	−31.5874	−1.19904
$695$	−41.8229	−1.58643
$696$	−56.6049	−2.14560
$697$	−11.9924	−0.454244
$698$	34.2988	1.29823
$699$	−43.8327	−1.65790
$700$	−3.26308	−0.123333
$701$	15.4921	0.585129	0.292565	−	0.956246i	$-0.405491\pi$
$701$	15.4921	0.585129	0.292565	+	0.956246i	$0.405491\pi$
$702$	−15.9195	−0.600843
$703$	4.69588	0.177109
$704$	0	0
$705$	−4.21312	−0.158675
$706$	3.56476	0.134162
$707$	5.69198	0.214069
$708$	2.66965	0.100332
$709$	−42.6061	−1.60011	−0.800053	−	0.599930i	$-0.795195\pi$
$709$	−42.6061	−1.60011	−0.800053	+	0.599930i	$0.795195\pi$
$710$	−5.75955	−0.216152
$711$	−11.6742	−0.437818
$712$	−32.3700	−1.21312
$713$	14.5017	0.543093
$714$	−24.9388	−0.933310
$715$	0	0
$716$	1.89464	0.0708059
$717$	−31.9455	−1.19303
$718$	21.3312	0.796074
$719$	−11.1914	−0.417370	−0.208685	−	0.977983i	$-0.566918\pi$
$719$	−11.1914	−0.417370	−0.208685	+	0.977983i	$0.566918\pi$
$720$	8.55608	0.318866
$721$	40.0036	1.48981
$722$	−29.1660	−1.08545
$723$	−23.1664	−0.861569
$724$	4.82997	0.179505
$725$	36.4481	1.35365
$726$	0	0
$727$	39.7809	1.47539	0.737695	−	0.675134i	$-0.235914\pi$
$727$	39.7809	1.47539	0.737695	+	0.675134i	$0.235914\pi$
$728$	32.4033	1.20095
$729$	16.0164	0.593198
$730$	20.7677	0.768647
$731$	−12.1951	−0.451051
$732$	−0.439588	−0.0162476
$733$	34.8864	1.28856	0.644279	−	0.764791i	$-0.277158\pi$
$733$	34.8864	1.28856	0.644279	+	0.764791i	$0.277158\pi$
$734$	−19.1001	−0.704996
$735$	46.9775	1.73279
$736$	−7.86165	−0.289784
$737$	0	0
$738$	−5.37258	−0.197768
$739$	45.8860	1.68794	0.843972	−	0.536388i	$-0.180211\pi$
$739$	45.8860	1.68794	0.843972	+	0.536388i	$0.180211\pi$
$740$	−0.487665	−0.0179269
$741$	35.1620	1.29171
$742$	−51.3976	−1.88687
$743$	−20.2330	−0.742278	−0.371139	−	0.928577i	$-0.621033\pi$
$743$	−20.2330	−0.742278	−0.371139	+	0.928577i	$0.621033\pi$
$744$	−13.5297	−0.496025
$745$	45.6745	1.67338
$746$	−27.4993	−1.00682
$747$	3.74734	0.137108
$748$	0	0
$749$	27.6175	1.00912
$750$	9.75296	0.356128
$751$	−22.5585	−0.823173	−0.411586	−	0.911371i	$-0.635025\pi$
$751$	−22.5585	−0.823173	−0.411586	+	0.911371i	$0.635025\pi$
$752$	2.55060	0.0930107
$753$	43.0884	1.57023
$754$	−36.5571	−1.33133
$755$	44.4364	1.61721
$756$	−3.71473	−0.135103
$757$	20.8797	0.758884	0.379442	−	0.925215i	$-0.376116\pi$
$757$	20.8797	0.758884	0.379442	+	0.925215i	$0.376116\pi$
$758$	−8.30037	−0.301483
$759$	0	0
$760$	56.0170	2.03195
$761$	3.28606	0.119120	0.0595599	−	0.998225i	$-0.481030\pi$
$761$	3.28606	0.119120	0.0595599	+	0.998225i	$0.481030\pi$
$762$	52.6171	1.90612
$763$	−26.1128	−0.945347
$764$	−0.821737	−0.0297294
$765$	6.01369	0.217425
$766$	−43.6791	−1.57819
$767$	17.0701	0.616367
$768$	10.4119	0.375709
$769$	−7.43132	−0.267980	−0.133990	−	0.990983i	$-0.542779\pi$
$769$	−7.43132	−0.267980	−0.133990	+	0.990983i	$0.542779\pi$
$770$	0	0
$771$	27.2822	0.982543
$772$	3.54759	0.127681
$773$	−9.59852	−0.345235	−0.172617	−	0.984989i	$-0.555222\pi$
$773$	−9.59852	−0.345235	−0.172617	+	0.984989i	$0.555222\pi$
$774$	−5.46338	−0.196377
$775$	8.71185	0.312939
$776$	−18.3600	−0.659084
$777$	5.58730	0.200443
$778$	−19.7806	−0.709169
$779$	−31.1721	−1.11686
$780$	−3.65156	−0.130747
$781$	0	0
$782$	20.3731	0.728542
$783$	41.4930	1.48284
$784$	−28.4399	−1.01571
$785$	−46.7088	−1.66711
$786$	−0.450910	−0.0160834
$787$	−43.7311	−1.55885	−0.779423	−	0.626498i	$-0.784488\pi$
$787$	−43.7311	−1.55885	−0.779423	+	0.626498i	$0.784488\pi$
$788$	−3.35786	−0.119619
$789$	52.3502	1.86371
$790$	−55.5751	−1.97727
$791$	28.4296	1.01084
$792$	0	0
$793$	−2.81079	−0.0998140
$794$	6.63288	0.235392
$795$	57.3451	2.03382
$796$	1.99543	0.0707263
$797$	−14.2501	−0.504764	−0.252382	−	0.967628i	$-0.581214\pi$
$797$	−14.2501	−0.504764	−0.252382	+	0.967628i	$0.581214\pi$
$798$	−64.8239	−2.29474
$799$	1.79270	0.0634212
$800$	−4.72286	−0.166978
$801$	−9.03284	−0.319160
$802$	−17.1130	−0.604280
$803$	0	0
$804$	4.24997	0.149885
$805$	−71.4388	−2.51789
$806$	−8.73791	−0.307780
$807$	−32.5453	−1.14565
$808$	4.33827	0.152620
$809$	27.6299	0.971417	0.485708	−	0.874121i	$-0.338562\pi$
$809$	27.6299	0.971417	0.485708	+	0.874121i	$0.338562\pi$
$810$	−42.5163	−1.49387
$811$	−50.2312	−1.76386	−0.881929	−	0.471383i	$-0.843755\pi$
$811$	−50.2312	−1.76386	−0.881929	+	0.471383i	$0.843755\pi$
$812$	−8.53041	−0.299359
$813$	32.0536	1.12417
$814$	0	0
$815$	30.5911	1.07156
$816$	−16.8448	−0.589687
$817$	−31.6989	−1.10900
$818$	52.4752	1.83475
$819$	9.04214	0.315958
$820$	3.23721	0.113048
$821$	−34.2119	−1.19400	−0.597002	−	0.802240i	$-0.703642\pi$
$821$	−34.2119	−1.19400	−0.597002	+	0.802240i	$0.703642\pi$
$822$	−5.45504	−0.190266
$823$	29.3504	1.02309	0.511546	−	0.859256i	$-0.329073\pi$
$823$	29.3504	1.02309	0.511546	+	0.859256i	$0.329073\pi$
$824$	30.4896	1.06216
$825$	0	0
$826$	−31.4702	−1.09499
$827$	5.82170	0.202440	0.101220	−	0.994864i	$-0.467725\pi$
$827$	5.82170	0.202440	0.101220	+	0.994864i	$0.467725\pi$
$828$	−1.15524	−0.0401473
$829$	26.8335	0.931965	0.465982	−	0.884794i	$-0.345701\pi$
$829$	26.8335	0.931965	0.465982	+	0.884794i	$0.345701\pi$
$830$	17.8392	0.619207
$831$	−12.5497	−0.435345
$832$	24.4131	0.846372
$833$	−19.9891	−0.692583
$834$	36.8878	1.27732
$835$	49.1558	1.70111
$836$	0	0
$837$	9.91768	0.342805
$838$	31.4959	1.08801
$839$	4.91432	0.169661	0.0848306	−	0.996395i	$-0.472965\pi$
$839$	4.91432	0.169661	0.0848306	+	0.996395i	$0.472965\pi$
$840$	66.6507	2.29967
$841$	66.2833	2.28563
$842$	−5.05062	−0.174056
$843$	51.1614	1.76209
$844$	3.23829	0.111467
$845$	15.0706	0.518444
$846$	0.803129	0.0276122
$847$	0	0
$848$	−34.7164	−1.19217
$849$	32.6969	1.12215
$850$	12.2391	0.419797
$851$	−4.56441	−0.156466
$852$	−0.642975	−0.0220279
$853$	8.73167	0.298967	0.149483	−	0.988764i	$-0.452239\pi$
$853$	8.73167	0.298967	0.149483	+	0.988764i	$0.452239\pi$
$854$	5.18191	0.177321
$855$	15.6315	0.534587
$856$	21.0493	0.719450
$857$	−49.8942	−1.70435	−0.852176	−	0.523255i	$-0.824717\pi$
$857$	−49.8942	−1.70435	−0.852176	+	0.523255i	$0.824717\pi$
$858$	0	0
$859$	22.3212	0.761590	0.380795	−	0.924660i	$-0.375650\pi$
$859$	22.3212	0.761590	0.380795	+	0.924660i	$0.375650\pi$
$860$	3.29192	0.112253
$861$	−37.0895	−1.26401
$862$	−47.0814	−1.60360
$863$	−40.2505	−1.37014	−0.685072	−	0.728475i	$-0.740229\pi$
$863$	−40.2505	−1.37014	−0.685072	+	0.728475i	$0.740229\pi$
$864$	−5.37657	−0.182915
$865$	−0.745470	−0.0253468
$866$	−40.1768	−1.36526
$867$	21.4178	0.727388
$868$	−2.03894	−0.0692063
$869$	0	0
$870$	−75.1947	−2.54934
$871$	27.1749	0.920788
$872$	−19.9025	−0.673983
$873$	−5.12334	−0.173399
$874$	52.9564	1.79128
$875$	14.5518	0.491940
$876$	2.31843	0.0783324
$877$	−13.8067	−0.466220	−0.233110	−	0.972450i	$-0.574890\pi$
$877$	−13.8067	−0.466220	−0.233110	+	0.972450i	$0.574890\pi$
$878$	−16.6668	−0.562476
$879$	−66.1978	−2.23280
$880$	0	0
$881$	−45.9863	−1.54932	−0.774658	−	0.632380i	$-0.782078\pi$
$881$	−45.9863	−1.54932	−0.774658	+	0.632380i	$0.782078\pi$
$882$	−8.95513	−0.301535
$883$	30.2131	1.01675	0.508376	−	0.861135i	$-0.330246\pi$
$883$	30.2131	1.01675	0.508376	+	0.861135i	$0.330246\pi$
$884$	1.55375	0.0522584
$885$	35.1117	1.18027
$886$	−35.9699	−1.20843
$887$	−29.3933	−0.986932	−0.493466	−	0.869765i	$-0.664270\pi$
$887$	−29.3933	−0.986932	−0.493466	+	0.869765i	$0.664270\pi$
$888$	4.25849	0.142906
$889$	78.5068	2.63303
$890$	−43.0007	−1.44139
$891$	0	0
$892$	−0.834446	−0.0279393
$893$	4.65981	0.155935
$894$	−40.2849	−1.34733
$895$	24.9186	0.832936
$896$	−35.1691	−1.17492
$897$	−34.1776	−1.14116
$898$	−54.1321	−1.80641
$899$	22.7747	0.759578
$900$	−0.694005	−0.0231335
$901$	−24.4006	−0.812902
$902$	0	0
$903$	−37.7163	−1.25512
$904$	21.6683	0.720677
$905$	63.5247	2.11163
$906$	−39.1929	−1.30210
$907$	−20.8845	−0.693459	−0.346729	−	0.937965i	$-0.612708\pi$
$907$	−20.8845	−0.693459	−0.346729	+	0.937965i	$0.612708\pi$
$908$	2.63452	0.0874297
$909$	1.21059	0.0401528
$910$	43.0450	1.42693
$911$	−12.2472	−0.405766	−0.202883	−	0.979203i	$-0.565031\pi$
$911$	−12.2472	−0.405766	−0.202883	+	0.979203i	$0.565031\pi$
$912$	−43.7851	−1.44987
$913$	0	0
$914$	−30.2430	−1.00035
$915$	−5.78153	−0.191132
$916$	2.34397	0.0774468
$917$	−0.672775	−0.0222170
$918$	13.9331	0.459862
$919$	35.7554	1.17946	0.589731	−	0.807600i	$-0.299234\pi$
$919$	35.7554	1.17946	0.589731	+	0.807600i	$0.299234\pi$
$920$	−54.4487	−1.79512
$921$	37.9769	1.25138
$922$	−27.9306	−0.919845
$923$	−4.11127	−0.135324
$924$	0	0
$925$	−2.74205	−0.0901582
$926$	55.7011	1.83045
$927$	8.50812	0.279443
$928$	−12.3466	−0.405297
$929$	−49.0945	−1.61074	−0.805370	−	0.592772i	$-0.798033\pi$
$929$	−49.0945	−1.61074	−0.805370	+	0.592772i	$0.798033\pi$
$930$	−17.9731	−0.589361
$931$	−51.9582	−1.70286
$932$	−5.03462	−0.164915
$933$	−27.9215	−0.914110
$934$	5.46842	0.178932
$935$	0	0
$936$	6.89167	0.225261
$937$	−19.5996	−0.640290	−0.320145	−	0.947369i	$-0.603732\pi$
$937$	−19.5996	−0.640290	−0.320145	+	0.947369i	$0.603732\pi$
$938$	−50.0992	−1.63580
$939$	−54.5086	−1.77882
$940$	−0.483919	−0.0157837
$941$	32.4492	1.05781	0.528907	−	0.848680i	$-0.322602\pi$
$941$	32.4492	1.05781	0.528907	+	0.848680i	$0.322602\pi$
$942$	41.1972	1.34228
$943$	30.2994	0.986683
$944$	−21.2564	−0.691838
$945$	−48.8568	−1.58931
$946$	0	0
$947$	−0.860626	−0.0279666	−0.0139833	−	0.999902i	$-0.504451\pi$
$947$	−0.860626	−0.0279666	−0.0139833	+	0.999902i	$0.504451\pi$
$948$	−6.20419	−0.201503
$949$	14.8244	0.481219
$950$	31.8133	1.03216
$951$	−60.4220	−1.95932
$952$	−28.3602	−0.919158
$953$	31.0225	1.00492	0.502459	−	0.864601i	$-0.332429\pi$
$953$	31.0225	1.00492	0.502459	+	0.864601i	$0.332429\pi$
$954$	−10.9315	−0.353919
$955$	−10.8076	−0.349727
$956$	−3.66926	−0.118672
$957$	0	0
$958$	−16.9289	−0.546947
$959$	−8.13913	−0.262826
$960$	50.2155	1.62070
$961$	−25.5564	−0.824399
$962$	2.75026	0.0886719
$963$	5.87380	0.189280
$964$	−2.66090	−0.0857017
$965$	46.6586	1.50199
$966$	63.0091	2.02728
$967$	31.5866	1.01576	0.507879	−	0.861429i	$-0.330430\pi$
$967$	31.5866	1.01576	0.507879	+	0.861429i	$0.330430\pi$
$968$	0	0
$969$	−30.7746	−0.988624
$970$	−24.3896	−0.783103
$971$	−15.3987	−0.494167	−0.247084	−	0.968994i	$-0.579472\pi$
$971$	−15.3987	−0.494167	−0.247084	+	0.968994i	$0.579472\pi$
$972$	−1.88089	−0.0603296
$973$	55.0381	1.76444
$974$	32.2480	1.03329
$975$	−20.5321	−0.657552
$976$	3.50010	0.112036
$977$	−38.1762	−1.22136	−0.610682	−	0.791876i	$-0.709105\pi$
$977$	−38.1762	−1.22136	−0.610682	+	0.791876i	$0.709105\pi$
$978$	−26.9814	−0.862770
$979$	0	0
$980$	5.39584	0.172364
$981$	−5.55378	−0.177318
$982$	34.3455	1.09601
$983$	16.6089	0.529742	0.264871	−	0.964284i	$-0.414671\pi$
$983$	16.6089	0.529742	0.264871	+	0.964284i	$0.414671\pi$
$984$	−28.2686	−0.901170
$985$	−44.1632	−1.40716
$986$	31.9957	1.01895
$987$	5.54438	0.176480
$988$	4.03871	0.128488
$989$	30.8114	0.979747
$990$	0	0
$991$	18.1537	0.576673	0.288336	−	0.957529i	$-0.406898\pi$
$991$	18.1537	0.576673	0.288336	+	0.957529i	$0.406898\pi$
$992$	−2.95109	−0.0936973
$993$	−15.6964	−0.498111
$994$	7.57945	0.240406
$995$	26.2443	0.832000
$996$	1.99150	0.0631030
$997$	11.7252	0.371342	0.185671	−	0.982612i	$-0.440554\pi$
$997$	11.7252	0.371342	0.185671	+	0.982612i	$0.440554\pi$
$998$	46.4387	1.46999
$999$	−3.12159	−0.0987628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.l.1.6	yes	24
11.10	odd	2		7381.2.a.k.1.19	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.k.1.19	✓	24	11.10	odd	2
7381.2.a.l.1.6	yes	24	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.33240 q^{2} -1.95631 q^{3} -0.224702 q^{4} -2.95532 q^{5} +2.60660 q^{6} +3.88914 q^{7} +2.96420 q^{8} +0.827159 q^{9} +O(q^{10})\)	\(q-1.33240 q^{2} -1.95631 q^{3} -0.224702 q^{4} -2.95532 q^{5} +2.60660 q^{6} +3.88914 q^{7} +2.96420 q^{8} +0.827159 q^{9} +3.93768 q^{10} +0.439588 q^{12} +2.81079 q^{13} -5.18191 q^{14} +5.78153 q^{15} -3.50010 q^{16} -2.46007 q^{17} -1.10211 q^{18} -6.39451 q^{19} +0.664067 q^{20} -7.60838 q^{21} +6.21549 q^{23} -5.79890 q^{24} +3.73393 q^{25} -3.74510 q^{26} +4.25076 q^{27} -0.873899 q^{28} +9.76132 q^{29} -7.70333 q^{30} +2.33316 q^{31} -1.26485 q^{32} +3.27780 q^{34} -11.4937 q^{35} -0.185864 q^{36} -0.734361 q^{37} +8.52007 q^{38} -5.49878 q^{39} -8.76017 q^{40} +4.87482 q^{41} +10.1374 q^{42} +4.95721 q^{43} -2.44452 q^{45} -8.28153 q^{46} -0.728720 q^{47} +6.84730 q^{48} +8.12544 q^{49} -4.97510 q^{50} +4.81266 q^{51} -0.631590 q^{52} +9.91867 q^{53} -5.66372 q^{54} +11.5282 q^{56} +12.5097 q^{57} -13.0060 q^{58} +6.07308 q^{59} -1.29912 q^{60} -1.00000 q^{61} -3.10871 q^{62} +3.21694 q^{63} +8.68550 q^{64} -8.30678 q^{65} +9.66809 q^{67} +0.552783 q^{68} -12.1594 q^{69} +15.3142 q^{70} -1.46268 q^{71} +2.45186 q^{72} +5.27410 q^{73} +0.978465 q^{74} -7.30473 q^{75} +1.43686 q^{76} +7.32659 q^{78} -14.1137 q^{79} +10.3439 q^{80} -10.7973 q^{81} -6.49522 q^{82} +4.53037 q^{83} +1.70962 q^{84} +7.27030 q^{85} -6.60500 q^{86} -19.0962 q^{87} -10.9203 q^{89} +3.25709 q^{90} +10.9316 q^{91} -1.39663 q^{92} -4.56438 q^{93} +0.970949 q^{94} +18.8978 q^{95} +2.47444 q^{96} -6.19390 q^{97} -10.8264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9} + 12 q^{10} + q^{12} + 3 q^{13} - q^{14} - 5 q^{15} + 17 q^{16} + 8 q^{17} + 20 q^{18} + 8 q^{19} + 16 q^{20} + 11 q^{21} + 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 13 q^{27} - 7 q^{28} + 43 q^{29} + 30 q^{30} - 4 q^{31} + 23 q^{32} + 31 q^{35} - 35 q^{36} - 4 q^{37} - 13 q^{38} + 11 q^{39} + 57 q^{40} + 29 q^{41} + 48 q^{42} + 10 q^{43} - 10 q^{45} - 14 q^{46} - 13 q^{47} + 42 q^{48} + 26 q^{49} - 6 q^{50} + 56 q^{51} + 25 q^{52} - 15 q^{53} + 35 q^{54} - 9 q^{56} - 3 q^{57} - 84 q^{58} - 13 q^{59} + 34 q^{60} - 24 q^{61} + 55 q^{62} + 22 q^{63} + 61 q^{64} + 41 q^{65} - q^{67} - 4 q^{68} - 27 q^{69} + 55 q^{70} - 6 q^{71} + 22 q^{72} + 18 q^{73} + 28 q^{74} + 47 q^{75} + 36 q^{76} - 10 q^{78} + 9 q^{79} - 40 q^{80} + 40 q^{81} + 15 q^{82} + 10 q^{83} + 93 q^{84} - 9 q^{85} + 38 q^{86} + 51 q^{87} - 17 q^{89} - 44 q^{90} - 22 q^{91} + 11 q^{92} + 32 q^{93} - 47 q^{94} + 54 q^{95} + 44 q^{96} - q^{97} + 45 q^{98}+O(q^{100}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9 + 12 * q^10 + q^12 + 3 * q^13 - q^14 - 5 * q^15 + 17 * q^16 + 8 * q^17 + 20 * q^18 + 8 * q^19 + 16 * q^20 + 11 * q^21 + 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 13 * q^27 - 7 * q^28 + 43 * q^29 + 30 * q^30 - 4 * q^31 + 23 * q^32 + 31 * q^35 - 35 * q^36 - 4 * q^37 - 13 * q^38 + 11 * q^39 + 57 * q^40 + 29 * q^41 + 48 * q^42 + 10 * q^43 - 10 * q^45 - 14 * q^46 - 13 * q^47 + 42 * q^48 + 26 * q^49 - 6 * q^50 + 56 * q^51 + 25 * q^52 - 15 * q^53 + 35 * q^54 - 9 * q^56 - 3 * q^57 - 84 * q^58 - 13 * q^59 + 34 * q^60 - 24 * q^61 + 55 * q^62 + 22 * q^63 + 61 * q^64 + 41 * q^65 - q^67 - 4 * q^68 - 27 * q^69 + 55 * q^70 - 6 * q^71 + 22 * q^72 + 18 * q^73 + 28 * q^74 + 47 * q^75 + 36 * q^76 - 10 * q^78 + 9 * q^79 - 40 * q^80 + 40 * q^81 + 15 * q^82 + 10 * q^83 + 93 * q^84 - 9 * q^85 + 38 * q^86 + 51 * q^87 - 17 * q^89 - 44 * q^90 - 22 * q^91 + 11 * q^92 + 32 * q^93 - 47 * q^94 + 54 * q^95 + 44 * q^96 - q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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