LMFDB - Embedded newform 2401.4.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34370 q^{2} +8.19575 q^{3} -2.50708 q^{4} -0.508590 q^{5} -19.2083 q^{6} +24.6254 q^{8} +40.1702 q^{9} +O(q^{10})$	\(q-2.34370 q^{2} +8.19575 q^{3} -2.50708 q^{4} -0.508590 q^{5} -19.2083 q^{6} +24.6254 q^{8} +40.1702 q^{9} +1.19198 q^{10} -37.4267 q^{11} -20.5474 q^{12} +12.9443 q^{13} -4.16827 q^{15} -37.6579 q^{16} +125.064 q^{17} -94.1469 q^{18} -59.9098 q^{19} +1.27508 q^{20} +87.7169 q^{22} -13.4377 q^{23} +201.824 q^{24} -124.741 q^{25} -30.3376 q^{26} +107.940 q^{27} +105.198 q^{29} +9.76917 q^{30} -217.007 q^{31} -108.745 q^{32} -306.740 q^{33} -293.113 q^{34} -100.710 q^{36} +97.3538 q^{37} +140.410 q^{38} +106.088 q^{39} -12.5242 q^{40} -178.443 q^{41} -420.660 q^{43} +93.8319 q^{44} -20.4302 q^{45} +31.4939 q^{46} +621.744 q^{47} -308.634 q^{48} +292.356 q^{50} +1025.00 q^{51} -32.4525 q^{52} +97.4805 q^{53} -252.979 q^{54} +19.0349 q^{55} -491.006 q^{57} -246.552 q^{58} -647.664 q^{59} +10.4502 q^{60} -380.887 q^{61} +508.600 q^{62} +556.128 q^{64} -6.58335 q^{65} +718.906 q^{66} -418.726 q^{67} -313.547 q^{68} -110.132 q^{69} +678.546 q^{71} +989.209 q^{72} -125.623 q^{73} -228.168 q^{74} -1022.35 q^{75} +150.199 q^{76} -248.639 q^{78} -952.335 q^{79} +19.1524 q^{80} -199.948 q^{81} +418.217 q^{82} +358.744 q^{83} -63.6065 q^{85} +985.900 q^{86} +862.174 q^{87} -921.649 q^{88} -174.344 q^{89} +47.8822 q^{90} +33.6894 q^{92} -1778.54 q^{93} -1457.18 q^{94} +30.4695 q^{95} -891.244 q^{96} +1351.05 q^{97} -1503.44 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * 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 $

$2$	−2.34370	−0.828622	−0.414311	−	0.910135i	$-0.635977\pi$
$2$	−2.34370	−0.828622	−0.414311	+	0.910135i	$0.635977\pi$
$3$	8.19575	1.57727	0.788636	−	0.614860i	$-0.210788\pi$
$3$	8.19575	1.57727	0.788636	+	0.614860i	$0.210788\pi$
$4$	−2.50708	−0.313385
$5$	−0.508590	−0.0454897	−0.0227448	−	0.999741i	$-0.507241\pi$
$5$	−0.508590	−0.0454897	−0.0227448	+	0.999741i	$0.507241\pi$
$6$	−19.2083	−1.30696
$7$	0	0
$7$	0	0
$8$	24.6254	1.08830
$9$	40.1702	1.48779
$10$	1.19198	0.0376937
$11$	−37.4267	−1.02587	−0.512936	−	0.858427i	$-0.671442\pi$
$11$	−37.4267	−1.02587	−0.512936	+	0.858427i	$0.671442\pi$
$12$	−20.5474	−0.494294
$13$	12.9443	0.276162	0.138081	−	0.990421i	$-0.455907\pi$
$13$	12.9443	0.276162	0.138081	+	0.990421i	$0.455907\pi$
$14$	0	0
$15$	−4.16827	−0.0717496
$16$	−37.6579	−0.588404
$17$	125.064	1.78427	0.892134	−	0.451771i	$-0.149208\pi$
$17$	125.064	1.78427	0.892134	+	0.451771i	$0.149208\pi$
$18$	−94.1469	−1.23281
$19$	−59.9098	−0.723382	−0.361691	−	0.932298i	$-0.617800\pi$
$19$	−59.9098	−0.723382	−0.361691	+	0.932298i	$0.617800\pi$
$20$	1.27508	0.0142558
$21$	0	0
$22$	87.7169	0.850060
$23$	−13.4377	−0.121824	−0.0609120	−	0.998143i	$-0.519401\pi$
$23$	−13.4377	−0.121824	−0.0609120	+	0.998143i	$0.519401\pi$
$24$	201.824	1.71655
$25$	−124.741	−0.997931
$26$	−30.3376	−0.228834
$27$	107.940	0.769373
$28$	0	0
$29$	105.198	0.673611	0.336806	−	0.941574i	$-0.390653\pi$
$29$	105.198	0.673611	0.336806	+	0.941574i	$0.390653\pi$
$30$	9.76917	0.0594533
$31$	−217.007	−1.25728	−0.628640	−	0.777696i	$-0.716388\pi$
$31$	−217.007	−1.25728	−0.628640	+	0.777696i	$0.716388\pi$
$32$	−108.745	−0.600736
$33$	−306.740	−1.61808
$34$	−293.113	−1.47848
$35$	0	0
$36$	−100.710	−0.466251
$37$	97.3538	0.432564	0.216282	−	0.976331i	$-0.430607\pi$
$37$	97.3538	0.432564	0.216282	+	0.976331i	$0.430607\pi$
$38$	140.410	0.599410
$39$	106.088	0.435583
$40$	−12.5242	−0.0495064
$41$	−178.443	−0.679711	−0.339855	−	0.940478i	$-0.610378\pi$
$41$	−178.443	−0.679711	−0.339855	+	0.940478i	$0.610378\pi$
$42$	0	0
$43$	−420.660	−1.49186	−0.745931	−	0.666023i	$-0.767995\pi$
$43$	−420.660	−1.49186	−0.745931	+	0.666023i	$0.767995\pi$
$44$	93.8319	0.321493
$45$	−20.4302	−0.0676789
$46$	31.4939	0.100946
$47$	621.744	1.92959	0.964794	−	0.263006i	$-0.0847139\pi$
$47$	621.744	1.92959	0.964794	+	0.263006i	$0.0847139\pi$
$48$	−308.634	−0.928073
$49$	0	0
$50$	292.356	0.826907
$51$	1025.00	2.81428
$52$	−32.4525	−0.0865452
$53$	97.4805	0.252641	0.126320	−	0.991989i	$-0.459683\pi$
$53$	97.4805	0.252641	0.126320	+	0.991989i	$0.459683\pi$
$54$	−252.979	−0.637519
$55$	19.0349	0.0466665
$56$	0	0
$57$	−491.006	−1.14097
$58$	−246.552	−0.558169
$59$	−647.664	−1.42913	−0.714565	−	0.699569i	$-0.753375\pi$
$59$	−647.664	−1.42913	−0.714565	+	0.699569i	$0.753375\pi$
$60$	10.4502	0.0224853
$61$	−380.887	−0.799469	−0.399735	−	0.916631i	$-0.630898\pi$
$61$	−380.887	−0.799469	−0.399735	+	0.916631i	$0.630898\pi$
$62$	508.600	1.04181
$63$	0	0
$64$	556.128	1.08619
$65$	−6.58335	−0.0125625
$66$	718.906	1.34078
$67$	−418.726	−0.763515	−0.381757	−	0.924263i	$-0.624681\pi$
$67$	−418.726	−0.763515	−0.381757	+	0.924263i	$0.624681\pi$
$68$	−313.547	−0.559164
$69$	−110.132	−0.192150
$70$	0	0
$71$	678.546	1.13420	0.567102	−	0.823647i	$-0.308064\pi$
$71$	678.546	1.13420	0.567102	+	0.823647i	$0.308064\pi$
$72$	989.209	1.61916
$73$	−125.623	−0.201412	−0.100706	−	0.994916i	$-0.532110\pi$
$73$	−125.623	−0.201412	−0.100706	+	0.994916i	$0.532110\pi$
$74$	−228.168	−0.358432
$75$	−1022.35	−1.57401
$76$	150.199	0.226697
$77$	0	0
$78$	−248.639	−0.360933
$79$	−952.335	−1.35628	−0.678140	−	0.734933i	$-0.737214\pi$
$79$	−952.335	−1.35628	−0.678140	+	0.734933i	$0.737214\pi$
$80$	19.1524	0.0267663
$81$	−199.948	−0.274277
$82$	418.217	0.563224
$83$	358.744	0.474425	0.237213	−	0.971458i	$-0.423766\pi$
$83$	358.744	0.474425	0.237213	+	0.971458i	$0.423766\pi$
$84$	0	0
$85$	−63.6065	−0.0811657
$86$	985.900	1.23619
$87$	862.174	1.06247
$88$	−921.649	−1.11646
$89$	−174.344	−0.207646	−0.103823	−	0.994596i	$-0.533107\pi$
$89$	−174.344	−0.207646	−0.103823	+	0.994596i	$0.533107\pi$
$90$	47.8822	0.0560803
$91$	0	0
$92$	33.6894	0.0381779
$93$	−1778.54	−1.98307
$94$	−1457.18	−1.59890
$95$	30.4695	0.0329064
$96$	−891.244	−0.947523
$97$	1351.05	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$97$	1351.05	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$98$	0	0
$99$	−1503.44	−1.52628
$100$	312.737	0.312737
$101$	936.371	0.922499	0.461250	−	0.887270i	$-0.347401\pi$
$101$	936.371	0.922499	0.461250	+	0.887270i	$0.347401\pi$
$102$	−2402.28	−2.33197
$103$	920.129	0.880223	0.440112	−	0.897943i	$-0.354939\pi$
$103$	920.129	0.880223	0.440112	+	0.897943i	$0.354939\pi$
$104$	318.759	0.300547
$105$	0	0
$106$	−228.465	−0.209344
$107$	686.236	0.620009	0.310004	−	0.950735i	$-0.399669\pi$
$107$	686.236	0.620009	0.310004	+	0.950735i	$0.399669\pi$
$108$	−270.615	−0.241110
$109$	−1808.80	−1.58947	−0.794733	−	0.606959i	$-0.792389\pi$
$109$	−1808.80	−1.58947	−0.794733	+	0.606959i	$0.792389\pi$
$110$	−44.6119	−0.0386689
$111$	797.887	0.682271
$112$	0	0
$113$	615.264	0.512205	0.256103	−	0.966650i	$-0.417562\pi$
$113$	615.264	0.512205	0.256103	+	0.966650i	$0.417562\pi$
$114$	1150.77	0.945433
$115$	6.83427	0.00554173
$116$	−263.739	−0.211100
$117$	519.976	0.410870
$118$	1517.93	1.18421
$119$	0	0
$120$	−102.646	−0.0780851
$121$	69.7601	0.0524118
$122$	892.685	0.662458
$123$	−1462.48	−1.07209
$124$	544.056	0.394013
$125$	127.016	0.0908852
$126$	0	0
$127$	−2348.58	−1.64096	−0.820482	−	0.571673i	$-0.806295\pi$
$127$	−2348.58	−1.64096	−0.820482	+	0.571673i	$0.806295\pi$
$128$	−433.437	−0.299303
$129$	−3447.62	−2.35307
$130$	15.4294	0.0104096
$131$	65.4858	0.0436757	0.0218379	−	0.999762i	$-0.493048\pi$
$131$	65.4858	0.0436757	0.0218379	+	0.999762i	$0.493048\pi$
$132$	769.023	0.507082
$133$	0	0
$134$	981.366	0.632665
$135$	−54.8972	−0.0349985
$136$	3079.76	1.94182
$137$	−2756.83	−1.71921	−0.859606	−	0.510957i	$-0.829291\pi$
$137$	−2756.83	−1.71921	−0.859606	+	0.510957i	$0.829291\pi$
$138$	258.116	0.159219
$139$	1593.71	0.972496	0.486248	−	0.873821i	$-0.338365\pi$
$139$	1593.71	0.972496	0.486248	+	0.873821i	$0.338365\pi$
$140$	0	0
$141$	5095.65	3.04349
$142$	−1590.31	−0.939827
$143$	−484.463	−0.283307
$144$	−1512.73	−0.875420
$145$	−53.5025	−0.0306424
$146$	294.423	0.166895
$147$	0	0
$148$	−244.074	−0.135559
$149$	−1640.84	−0.902166	−0.451083	−	0.892482i	$-0.648962\pi$
$149$	−1640.84	−0.902166	−0.451083	+	0.892482i	$0.648962\pi$
$150$	2396.07	1.30426
$151$	2270.49	1.22364	0.611820	−	0.790997i	$-0.290438\pi$
$151$	2270.49	1.22364	0.611820	+	0.790997i	$0.290438\pi$
$152$	−1475.30	−0.787257
$153$	5023.86	2.65461
$154$	0	0
$155$	110.368	0.0571933
$156$	−265.972	−0.136505
$157$	−1322.55	−0.672297	−0.336148	−	0.941809i	$-0.609124\pi$
$157$	−1322.55	−0.672297	−0.336148	+	0.941809i	$0.609124\pi$
$158$	2231.99	1.12384
$159$	798.925	0.398484
$160$	55.3065	0.0273273
$161$	0	0
$162$	468.617	0.227272
$163$	1520.50	0.730644	0.365322	−	0.930881i	$-0.380959\pi$
$163$	1520.50	0.730644	0.365322	+	0.930881i	$0.380959\pi$
$164$	447.372	0.213012
$165$	156.005	0.0736058
$166$	−840.788	−0.393119
$167$	882.155	0.408762	0.204381	−	0.978891i	$-0.434482\pi$
$167$	882.155	0.408762	0.204381	+	0.978891i	$0.434482\pi$
$168$	0	0
$169$	−2029.44	−0.923734
$170$	149.074	0.0672557
$171$	−2406.59	−1.07624
$172$	1054.63	0.467528
$173$	1546.73	0.679743	0.339871	−	0.940472i	$-0.389616\pi$
$173$	1546.73	0.679743	0.339871	+	0.940472i	$0.389616\pi$
$174$	−2020.67	−0.880384
$175$	0	0
$176$	1409.41	0.603627
$177$	−5308.09	−2.25413
$178$	408.610	0.172060
$179$	−2932.20	−1.22437	−0.612187	−	0.790713i	$-0.709710\pi$
$179$	−2932.20	−1.22437	−0.612187	+	0.790713i	$0.709710\pi$
$180$	51.2202	0.0212096
$181$	−2408.68	−0.989149	−0.494575	−	0.869135i	$-0.664676\pi$
$181$	−2408.68	−0.989149	−0.494575	+	0.869135i	$0.664676\pi$
$182$	0	0
$183$	−3121.66	−1.26098
$184$	−330.909	−0.132581
$185$	−49.5132	−0.0196772
$186$	4168.35	1.64322
$187$	−4680.75	−1.83043
$188$	−1558.76	−0.604705
$189$	0	0
$190$	−71.4114	−0.0272670
$191$	−4645.61	−1.75992	−0.879959	−	0.475050i	$-0.842430\pi$
$191$	−4645.61	−1.75992	−0.879959	+	0.475050i	$0.842430\pi$
$192$	4557.88	1.71321
$193$	−2664.50	−0.993754	−0.496877	−	0.867821i	$-0.665520\pi$
$193$	−2664.50	−0.993754	−0.496877	+	0.867821i	$0.665520\pi$
$194$	−3166.46	−1.17185
$195$	−53.9555	−0.0198145
$196$	0	0
$197$	1234.85	0.446598	0.223299	−	0.974750i	$-0.428317\pi$
$197$	1234.85	0.446598	0.223299	+	0.974750i	$0.428317\pi$
$198$	3523.61	1.26471
$199$	−2468.71	−0.879407	−0.439703	−	0.898143i	$-0.644916\pi$
$199$	−2468.71	−0.879407	−0.439703	+	0.898143i	$0.644916\pi$
$200$	−3071.81	−1.08605
$201$	−3431.77	−1.20427
$202$	−2194.57	−0.764403
$203$	0	0
$204$	−2569.75	−0.881953
$205$	90.7544	0.0309198
$206$	−2156.50	−0.729372
$207$	−539.795	−0.181248
$208$	−487.455	−0.162495
$209$	2242.23	0.742097
$210$	0	0
$211$	−3247.66	−1.05961	−0.529806	−	0.848119i	$-0.677735\pi$
$211$	−3247.66	−1.05961	−0.529806	+	0.848119i	$0.677735\pi$
$212$	−244.392	−0.0791740
$213$	5561.19	1.78895
$214$	−1608.33	−0.513753
$215$	213.944	0.0678643
$216$	2658.07	0.837308
$217$	0	0
$218$	4239.28	1.31707
$219$	−1029.58	−0.317682
$220$	−47.7220	−0.0146246
$221$	1618.87	0.492747
$222$	−1870.01	−0.565345
$223$	2375.53	0.713350	0.356675	−	0.934228i	$-0.383910\pi$
$223$	2375.53	0.713350	0.356675	+	0.934228i	$0.383910\pi$
$224$	0	0
$225$	−5010.89	−1.48471
$226$	−1441.99	−0.424424
$227$	−2838.00	−0.829799	−0.414900	−	0.909867i	$-0.636183\pi$
$227$	−2838.00	−0.829799	−0.414900	+	0.909867i	$0.636183\pi$
$228$	1230.99	0.357563
$229$	−1785.24	−0.515163	−0.257581	−	0.966257i	$-0.582926\pi$
$229$	−1785.24	−0.515163	−0.257581	+	0.966257i	$0.582926\pi$
$230$	−16.0175	−0.00459200
$231$	0	0
$232$	2590.54	0.733091
$233$	−2402.85	−0.675604	−0.337802	−	0.941217i	$-0.609683\pi$
$233$	−2402.85	−0.675604	−0.337802	+	0.941217i	$0.609683\pi$
$234$	−1218.67	−0.340456
$235$	−316.213	−0.0877763
$236$	1623.75	0.447868
$237$	−7805.10	−2.13922
$238$	0	0
$239$	1443.87	0.390779	0.195389	−	0.980726i	$-0.437403\pi$
$239$	1443.87	0.390779	0.195389	+	0.980726i	$0.437403\pi$
$240$	156.968	0.0422177
$241$	313.200	0.0837138	0.0418569	−	0.999124i	$-0.486673\pi$
$241$	313.200	0.0837138	0.0418569	+	0.999124i	$0.486673\pi$
$242$	−163.497	−0.0434296
$243$	−4553.10	−1.20198
$244$	954.917	0.250542
$245$	0	0
$246$	3427.60	0.888357
$247$	−775.492	−0.199771
$248$	−5343.90	−1.36830
$249$	2940.18	0.748298
$250$	−297.687	−0.0753095
$251$	1600.70	0.402532	0.201266	−	0.979537i	$-0.435494\pi$
$251$	1600.70	0.402532	0.201266	+	0.979537i	$0.435494\pi$
$252$	0	0
$253$	502.929	0.124976
$254$	5504.35	1.35974
$255$	−521.302	−0.128020
$256$	−3433.18	−0.838178
$257$	−1626.74	−0.394838	−0.197419	−	0.980319i	$-0.563256\pi$
$257$	−1626.74	−0.394838	−0.197419	+	0.980319i	$0.563256\pi$
$258$	8080.19	1.94981
$259$	0	0
$260$	16.5050	0.00393691
$261$	4225.82	1.00219
$262$	−153.479	−0.0361907
$263$	2602.75	0.610236	0.305118	−	0.952314i	$-0.401304\pi$
$263$	2602.75	0.610236	0.305118	+	0.952314i	$0.401304\pi$
$264$	−7553.60	−1.76095
$265$	−49.5776	−0.0114926
$266$	0	0
$267$	−1428.88	−0.327514
$268$	1049.78	0.239274
$269$	6969.38	1.57967	0.789833	−	0.613321i	$-0.210167\pi$
$269$	6969.38	1.57967	0.789833	+	0.613321i	$0.210167\pi$
$270$	128.662	0.0290005
$271$	−4161.30	−0.932771	−0.466386	−	0.884581i	$-0.654444\pi$
$271$	−4161.30	−0.932771	−0.466386	+	0.884581i	$0.654444\pi$
$272$	−4709.65	−1.04987
$273$	0	0
$274$	6461.18	1.42458
$275$	4668.66	1.02375
$276$	276.110	0.0602169
$277$	5858.66	1.27080	0.635402	−	0.772181i	$-0.280834\pi$
$277$	5858.66	1.27080	0.635402	+	0.772181i	$0.280834\pi$
$278$	−3735.18	−0.805832
$279$	−8717.24	−1.87057
$280$	0	0
$281$	−556.114	−0.118060	−0.0590302	−	0.998256i	$-0.518801\pi$
$281$	−556.114	−0.118060	−0.0590302	+	0.998256i	$0.518801\pi$
$282$	−11942.7	−2.52190
$283$	−2149.55	−0.451512	−0.225756	−	0.974184i	$-0.572485\pi$
$283$	−2149.55	−0.451512	−0.225756	+	0.974184i	$0.572485\pi$
$284$	−1701.17	−0.355443
$285$	249.721	0.0519023
$286$	1135.44	0.234754
$287$	0	0
$288$	−4368.30	−0.893767
$289$	10728.1	2.18361
$290$	125.394	0.0253909
$291$	11072.9	2.23060
$292$	314.948	0.0631197
$293$	−5583.29	−1.11324	−0.556620	−	0.830767i	$-0.687902\pi$
$293$	−5583.29	−1.11324	−0.556620	+	0.830767i	$0.687902\pi$
$294$	0	0
$295$	329.395	0.0650106
$296$	2397.38	0.470760
$297$	−4039.84	−0.789277
$298$	3845.63	0.747555
$299$	−173.942	−0.0336432
$300$	2563.11	0.493271
$301$	0	0
$302$	−5321.33	−1.01393
$303$	7674.26	1.45503
$304$	2256.08	0.425641
$305$	193.716	0.0363676
$306$	−11774.4	−2.19967
$307$	7444.93	1.38405	0.692027	−	0.721872i	$-0.256718\pi$
$307$	7444.93	1.38405	0.692027	+	0.721872i	$0.256718\pi$
$308$	0	0
$309$	7541.14	1.38835
$310$	−258.669	−0.0473916
$311$	−5298.53	−0.966085	−0.483042	−	0.875597i	$-0.660468\pi$
$311$	−5298.53	−0.966085	−0.483042	+	0.875597i	$0.660468\pi$
$312$	2612.47	0.474045
$313$	3197.95	0.577504	0.288752	−	0.957404i	$-0.406760\pi$
$313$	3197.95	0.577504	0.288752	+	0.957404i	$0.406760\pi$
$314$	3099.65	0.557080
$315$	0	0
$316$	2387.58	0.425038
$317$	−3783.19	−0.670301	−0.335150	−	0.942165i	$-0.608787\pi$
$317$	−3783.19	−0.670301	−0.335150	+	0.942165i	$0.608787\pi$
$318$	−1872.44	−0.330192
$319$	−3937.21	−0.691038
$320$	−282.841	−0.0494103
$321$	5624.22	0.977922
$322$	0	0
$323$	−7492.58	−1.29071
$324$	501.286	0.0859544
$325$	−1614.69	−0.275591
$326$	−3563.60	−0.605428
$327$	−14824.5	−2.50702
$328$	−4394.24	−0.739730
$329$	0	0
$330$	−365.628	−0.0609914
$331$	−11576.3	−1.92233	−0.961166	−	0.275970i	$-0.911001\pi$
$331$	−11576.3	−1.92233	−0.961166	+	0.275970i	$0.911001\pi$
$332$	−899.402	−0.148678
$333$	3910.73	0.643563
$334$	−2067.51	−0.338709
$335$	212.960	0.0347320
$336$	0	0
$337$	−7808.77	−1.26223	−0.631114	−	0.775690i	$-0.717402\pi$
$337$	−7808.77	−1.26223	−0.631114	+	0.775690i	$0.717402\pi$
$338$	4756.40	0.765427
$339$	5042.55	0.807887
$340$	159.467	0.0254362
$341$	8121.88	1.28981
$342$	5640.32	0.891795
$343$	0	0
$344$	−10358.9	−1.62359
$345$	56.0120	0.00874082
$346$	−3625.06	−0.563250
$347$	1193.26	0.184604	0.0923022	−	0.995731i	$-0.470577\pi$
$347$	1193.26	0.184604	0.0923022	+	0.995731i	$0.470577\pi$
$348$	−2161.54	−0.332962
$349$	10373.7	1.59109	0.795546	−	0.605893i	$-0.207184\pi$
$349$	10373.7	1.59109	0.795546	+	0.605893i	$0.207184\pi$
$350$	0	0
$351$	1397.21	0.212472
$352$	4069.96	0.616277
$353$	6609.50	0.996568	0.498284	−	0.867014i	$-0.333964\pi$
$353$	6609.50	0.996568	0.498284	+	0.867014i	$0.333964\pi$
$354$	12440.5	1.86782
$355$	−345.101	−0.0515946
$356$	437.096	0.0650731
$357$	0	0
$358$	6872.19	1.01454
$359$	728.925	0.107162	0.0535811	−	0.998564i	$-0.482936\pi$
$359$	728.925	0.107162	0.0535811	+	0.998564i	$0.482936\pi$
$360$	−503.102	−0.0736550
$361$	−3269.81	−0.476719
$362$	5645.22	0.819631
$363$	571.736	0.0826677
$364$	0	0
$365$	63.8908	0.00916218
$366$	7316.22	1.04488
$367$	−9515.25	−1.35338	−0.676692	−	0.736266i	$-0.736587\pi$
$367$	−9515.25	−1.35338	−0.676692	+	0.736266i	$0.736587\pi$
$368$	506.035	0.0716817
$369$	−7168.11	−1.01127
$370$	116.044	0.0163050
$371$	0	0
$372$	4458.94	0.621466
$373$	−353.047	−0.0490083	−0.0245041	−	0.999700i	$-0.507801\pi$
$373$	−353.047	−0.0490083	−0.0245041	+	0.999700i	$0.507801\pi$
$374$	10970.3	1.51673
$375$	1040.99	0.143351
$376$	15310.7	2.09997
$377$	1361.71	0.186026
$378$	0	0
$379$	1341.74	0.181848	0.0909240	−	0.995858i	$-0.471018\pi$
$379$	1341.74	0.181848	0.0909240	+	0.995858i	$0.471018\pi$
$380$	−76.3897	−0.0103124
$381$	−19248.3	−2.58825
$382$	10887.9	1.45831
$383$	−1656.99	−0.221065	−0.110533	−	0.993872i	$-0.535256\pi$
$383$	−1656.99	−0.221065	−0.110533	+	0.993872i	$0.535256\pi$
$384$	−3552.34	−0.472082
$385$	0	0
$386$	6244.77	0.823447
$387$	−16898.0	−2.21957
$388$	−3387.20	−0.443194
$389$	−2795.87	−0.364413	−0.182206	−	0.983260i	$-0.558324\pi$
$389$	−2795.87	−0.364413	−0.182206	+	0.983260i	$0.558324\pi$
$390$	126.455	0.0164187
$391$	−1680.58	−0.217367
$392$	0	0
$393$	536.705	0.0688885
$394$	−2894.12	−0.370061
$395$	484.348	0.0616967
$396$	3769.25	0.478313
$397$	2974.65	0.376054	0.188027	−	0.982164i	$-0.439791\pi$
$397$	2974.65	0.376054	0.188027	+	0.982164i	$0.439791\pi$
$398$	5785.90	0.728696
$399$	0	0
$400$	4697.49	0.587186
$401$	8068.75	1.00482	0.502412	−	0.864629i	$-0.332446\pi$
$401$	8068.75	1.00482	0.502412	+	0.864629i	$0.332446\pi$
$402$	8043.03	0.997885
$403$	−2809.01	−0.347213
$404$	−2347.56	−0.289098
$405$	101.692	0.0124768
$406$	0	0
$407$	−3643.64	−0.443755
$408$	25240.9	3.06278
$409$	−7629.71	−0.922408	−0.461204	−	0.887294i	$-0.652582\pi$
$409$	−7629.71	−0.922408	−0.461204	+	0.887294i	$0.652582\pi$
$410$	−212.701	−0.0256209
$411$	−22594.3	−2.71167
$412$	−2306.84	−0.275849
$413$	0	0
$414$	1265.12	0.150186
$415$	−182.454	−0.0215814
$416$	−1407.63	−0.165900
$417$	13061.7	1.53389
$418$	−5255.10	−0.614918
$419$	−11599.3	−1.35241	−0.676207	−	0.736712i	$-0.736377\pi$
$419$	−11599.3	−1.35241	−0.676207	+	0.736712i	$0.736377\pi$
$420$	0	0
$421$	2003.90	0.231981	0.115990	−	0.993250i	$-0.462996\pi$
$421$	2003.90	0.231981	0.115990	+	0.993250i	$0.462996\pi$
$422$	7611.53	0.878018
$423$	24975.6	2.87082
$424$	2400.50	0.274949
$425$	−15600.7	−1.78058
$426$	−13033.7	−1.48236
$427$	0	0
$428$	−1720.45	−0.194302
$429$	−3970.54	−0.446852
$430$	−501.419	−0.0562339
$431$	−3181.56	−0.355569	−0.177784	−	0.984069i	$-0.556893\pi$
$431$	−3181.56	−0.355569	−0.177784	+	0.984069i	$0.556893\pi$
$432$	−4064.79	−0.452702
$433$	−6197.27	−0.687810	−0.343905	−	0.939004i	$-0.611750\pi$
$433$	−6197.27	−0.687810	−0.343905	+	0.939004i	$0.611750\pi$
$434$	0	0
$435$	−438.493	−0.0483313
$436$	4534.82	0.498116
$437$	805.049	0.0881253
$438$	2413.02	0.263238
$439$	−4665.45	−0.507221	−0.253610	−	0.967306i	$-0.581618\pi$
$439$	−4665.45	−0.507221	−0.253610	+	0.967306i	$0.581618\pi$
$440$	468.741	0.0507872
$441$	0	0
$442$	−3794.15	−0.408301
$443$	−13054.2	−1.40006	−0.700028	−	0.714115i	$-0.746829\pi$
$443$	−13054.2	−1.40006	−0.700028	+	0.714115i	$0.746829\pi$
$444$	−2000.37	−0.213814
$445$	88.6698	0.00944573
$446$	−5567.52	−0.591098
$447$	−13447.9	−1.42296
$448$	0	0
$449$	13783.4	1.44873	0.724366	−	0.689416i	$-0.242133\pi$
$449$	13783.4	1.44873	0.724366	+	0.689416i	$0.242133\pi$
$450$	11744.0	1.23026
$451$	6678.55	0.697296
$452$	−1542.52	−0.160518
$453$	18608.3	1.93001
$454$	6651.40	0.687590
$455$	0	0
$456$	−12091.2	−1.24172
$457$	−1110.99	−0.113720	−0.0568600	−	0.998382i	$-0.518109\pi$
$457$	−1110.99	−0.113720	−0.0568600	+	0.998382i	$0.518109\pi$
$458$	4184.07	0.426875
$459$	13499.4	1.37277
$460$	−17.1341	−0.00173670
$461$	5176.45	0.522975	0.261487	−	0.965207i	$-0.415787\pi$
$461$	5176.45	0.522975	0.261487	+	0.965207i	$0.415787\pi$
$462$	0	0
$463$	−5875.17	−0.589725	−0.294862	−	0.955540i	$-0.595274\pi$
$463$	−5875.17	−0.589725	−0.294862	+	0.955540i	$0.595274\pi$
$464$	−3961.52	−0.396356
$465$	904.547	0.0902093
$466$	5631.54	0.559820
$467$	1998.27	0.198006	0.0990030	−	0.995087i	$-0.468435\pi$
$467$	1998.27	0.198006	0.0990030	+	0.995087i	$0.468435\pi$
$468$	−1303.62	−0.128761
$469$	0	0
$470$	741.107	0.0727334
$471$	−10839.2	−1.06040
$472$	−15949.0	−1.55532
$473$	15743.9	1.53046
$474$	18292.8	1.77261
$475$	7473.23	0.721885
$476$	0	0
$477$	3915.81	0.375876
$478$	−3383.99	−0.323808
$479$	11530.9	1.09992	0.549960	−	0.835191i	$-0.314643\pi$
$479$	11530.9	1.09992	0.549960	+	0.835191i	$0.314643\pi$
$480$	453.278	0.0431025
$481$	1260.18	0.119458
$482$	−734.047	−0.0693671
$483$	0	0
$484$	−174.894	−0.0164251
$485$	−687.132	−0.0643321
$486$	10671.1	0.995989
$487$	−1741.59	−0.162051	−0.0810255	−	0.996712i	$-0.525820\pi$
$487$	−1741.59	−0.162051	−0.0810255	+	0.996712i	$0.525820\pi$
$488$	−9379.51	−0.870063
$489$	12461.7	1.15242
$490$	0	0
$491$	12623.9	1.16030	0.580152	−	0.814508i	$-0.302993\pi$
$491$	12623.9	1.16030	0.580152	+	0.814508i	$0.302993\pi$
$492$	3666.55	0.335977
$493$	13156.5	1.20190
$494$	1817.52	0.165534
$495$	764.635	0.0694299
$496$	8172.04	0.739789
$497$	0	0
$498$	−6890.88	−0.620056
$499$	−9578.75	−0.859326	−0.429663	−	0.902989i	$-0.641368\pi$
$499$	−9578.75	−0.859326	−0.429663	+	0.902989i	$0.641368\pi$
$500$	−318.440	−0.0284821
$501$	7229.92	0.644729
$502$	−3751.56	−0.333547
$503$	−15577.2	−1.38082	−0.690410	−	0.723418i	$-0.742570\pi$
$503$	−15577.2	−1.38082	−0.690410	+	0.723418i	$0.742570\pi$
$504$	0	0
$505$	−476.229	−0.0419642
$506$	−1178.71	−0.103558
$507$	−16632.8	−1.45698
$508$	5888.08	0.514254
$509$	−3010.35	−0.262144	−0.131072	−	0.991373i	$-0.541842\pi$
$509$	−3010.35	−0.262144	−0.131072	+	0.991373i	$0.541842\pi$
$510$	1221.77	0.106081
$511$	0	0
$512$	11513.8	0.993836
$513$	−6466.66	−0.556550
$514$	3812.59	0.327171
$515$	−467.968	−0.0400411
$516$	8643.48	0.737419
$517$	−23269.8	−1.97951
$518$	0	0
$519$	12676.6	1.07214
$520$	−162.118	−0.0136718
$521$	−1065.01	−0.0895567	−0.0447784	−	0.998997i	$-0.514258\pi$
$521$	−1065.01	−0.0895567	−0.0447784	+	0.998997i	$0.514258\pi$
$522$	−9904.04	−0.830437
$523$	−4664.44	−0.389985	−0.194992	−	0.980805i	$-0.562468\pi$
$523$	−4664.44	−0.389985	−0.194992	+	0.980805i	$0.562468\pi$
$524$	−164.178	−0.0136873
$525$	0	0
$526$	−6100.05	−0.505655
$527$	−27139.9	−2.24332
$528$	11551.2	0.952084
$529$	−11986.4	−0.985159
$530$	116.195	0.00952298
$531$	−26016.8	−2.12624
$532$	0	0
$533$	−2309.83	−0.187710
$534$	3348.87	0.271385
$535$	−349.013	−0.0282040
$536$	−10311.3	−0.830933
$537$	−24031.6	−1.93117
$538$	−16334.1	−1.30895
$539$	0	0
$540$	137.632	0.0109680
$541$	−1126.88	−0.0895533	−0.0447767	−	0.998997i	$-0.514258\pi$
$541$	−1126.88	−0.0895533	−0.0447767	+	0.998997i	$0.514258\pi$
$542$	9752.83	0.772915
$543$	−19741.0	−1.56016
$544$	−13600.1	−1.07187
$545$	919.938	0.0723043
$546$	0	0
$547$	8414.57	0.657735	0.328867	−	0.944376i	$-0.393333\pi$
$547$	8414.57	0.657735	0.328867	+	0.944376i	$0.393333\pi$
$548$	6911.61	0.538776
$549$	−15300.3	−1.18944
$550$	−10941.9	−0.848301
$551$	−6302.38	−0.487278
$552$	−2712.04	−0.209116
$553$	0	0
$554$	−13730.9	−1.05302
$555$	−405.798	−0.0310363
$556$	−3995.57	−0.304766
$557$	−7064.06	−0.537367	−0.268684	−	0.963228i	$-0.586589\pi$
$557$	−7064.06	−0.537367	−0.268684	+	0.963228i	$0.586589\pi$
$558$	20430.6	1.54999
$559$	−5445.16	−0.411996
$560$	0	0
$561$	−38362.2	−2.88708
$562$	1303.36	0.0978275
$563$	13378.4	1.00148	0.500741	−	0.865597i	$-0.333061\pi$
$563$	13378.4	1.00148	0.500741	+	0.865597i	$0.333061\pi$
$564$	−12775.2	−0.953784
$565$	−312.917	−0.0233000
$566$	5037.91	0.374132
$567$	0	0
$568$	16709.5	1.23436
$569$	−18967.1	−1.39744	−0.698718	−	0.715397i	$-0.746246\pi$
$569$	−18967.1	−1.39744	−0.698718	+	0.715397i	$0.746246\pi$
$570$	−585.269	−0.0430074
$571$	−20797.3	−1.52424	−0.762121	−	0.647435i	$-0.775842\pi$
$571$	−20797.3	−1.52424	−0.762121	+	0.647435i	$0.775842\pi$
$572$	1214.59	0.0887842
$573$	−38074.2	−2.77587
$574$	0	0
$575$	1676.24	0.121572
$576$	22339.8	1.61601
$577$	2534.23	0.182845	0.0914223	−	0.995812i	$-0.470859\pi$
$577$	2534.23	0.182845	0.0914223	+	0.995812i	$0.470859\pi$
$578$	−25143.4	−1.80939
$579$	−21837.5	−1.56742
$580$	134.135	0.00960287
$581$	0	0
$582$	−25951.5	−1.84832
$583$	−3648.38	−0.259177
$584$	−3093.53	−0.219197
$585$	−264.455	−0.0186904
$586$	13085.5	0.922455
$587$	−24973.2	−1.75597	−0.877985	−	0.478687i	$-0.841113\pi$
$587$	−24973.2	−1.75597	−0.877985	+	0.478687i	$0.841113\pi$
$588$	0	0
$589$	13000.9	0.909494
$590$	−772.003	−0.0538692
$591$	10120.6	0.704406
$592$	−3666.14	−0.254523
$593$	4060.88	0.281215	0.140607	−	0.990065i	$-0.455094\pi$
$593$	4060.88	0.281215	0.140607	+	0.990065i	$0.455094\pi$
$594$	9468.16	0.654013
$595$	0	0
$596$	4113.72	0.282726
$597$	−20232.9	−1.38706
$598$	407.667	0.0278775
$599$	6512.09	0.444202	0.222101	−	0.975024i	$-0.428709\pi$
$599$	6512.09	0.444202	0.222101	+	0.975024i	$0.428709\pi$
$600$	−25175.8	−1.71299
$601$	20863.3	1.41603	0.708014	−	0.706198i	$-0.249591\pi$
$601$	20863.3	1.41603	0.708014	+	0.706198i	$0.249591\pi$
$602$	0	0
$603$	−16820.3	−1.13595
$604$	−5692.30	−0.383471
$605$	−35.4793	−0.00238420
$606$	−17986.1	−1.20567
$607$	−2087.96	−0.139617	−0.0698087	−	0.997560i	$-0.522239\pi$
$607$	−2087.96	−0.139617	−0.0698087	+	0.997560i	$0.522239\pi$
$608$	6514.88	0.434561
$609$	0	0
$610$	−454.010	−0.0301350
$611$	8048.05	0.532879
$612$	−12595.2	−0.831916
$613$	−20208.6	−1.33151	−0.665755	−	0.746170i	$-0.731891\pi$
$613$	−20208.6	−1.33151	−0.665755	+	0.746170i	$0.731891\pi$
$614$	−17448.7	−1.14686
$615$	743.800	0.0487690
$616$	0	0
$617$	−10137.2	−0.661441	−0.330720	−	0.943729i	$-0.607292\pi$
$617$	−10137.2	−0.661441	−0.330720	+	0.943729i	$0.607292\pi$
$618$	−17674.2	−1.15042
$619$	−8513.93	−0.552833	−0.276416	−	0.961038i	$-0.589147\pi$
$619$	−8513.93	−0.552833	−0.276416	+	0.961038i	$0.589147\pi$
$620$	−276.701	−0.0179235
$621$	−1450.46	−0.0937280
$622$	12418.2	0.800519
$623$	0	0
$624$	−3995.06	−0.256299
$625$	15528.1	0.993796
$626$	−7495.02	−0.478532
$627$	18376.7	1.17049
$628$	3315.73	0.210688
$629$	12175.5	0.771810
$630$	0	0
$631$	30427.4	1.91964	0.959821	−	0.280613i	$-0.0905377\pi$
$631$	30427.4	1.91964	0.959821	+	0.280613i	$0.0905377\pi$
$632$	−23451.7	−1.47604
$633$	−26617.0	−1.67130
$634$	8866.66	0.555426
$635$	1194.46	0.0746469
$636$	−2002.97	−0.124879
$637$	0	0
$638$	9227.62	0.572610
$639$	27257.3	1.68746
$640$	220.442	0.0136152
$641$	5174.03	0.318817	0.159409	−	0.987213i	$-0.449041\pi$
$641$	5174.03	0.318817	0.159409	+	0.987213i	$0.449041\pi$
$642$	−13181.5	−0.810328
$643$	−20900.6	−1.28186	−0.640931	−	0.767598i	$-0.721452\pi$
$643$	−20900.6	−1.28186	−0.640931	+	0.767598i	$0.721452\pi$
$644$	0	0
$645$	1753.43	0.107040
$646$	17560.3	1.06951
$647$	−23053.3	−1.40080	−0.700400	−	0.713751i	$-0.746995\pi$
$647$	−23053.3	−1.40080	−0.700400	+	0.713751i	$0.746995\pi$
$648$	−4923.80	−0.298496
$649$	24239.9	1.46610
$650$	3784.35	0.228360
$651$	0	0
$652$	−3812.03	−0.228973
$653$	−11976.9	−0.717749	−0.358875	−	0.933386i	$-0.616839\pi$
$653$	−11976.9	−0.717749	−0.358875	+	0.933386i	$0.616839\pi$
$654$	34744.1	2.07737
$655$	−33.3054	−0.00198680
$656$	6719.79	0.399945
$657$	−5046.32	−0.299659
$658$	0	0
$659$	3838.55	0.226903	0.113451	−	0.993544i	$-0.463809\pi$
$659$	3838.55	0.226903	0.113451	+	0.993544i	$0.463809\pi$
$660$	−391.117	−0.0230670
$661$	−6.24944	−0.000367738 0	−0.000183869	−	1.00000i	$-0.500059\pi$
$661$	−6.24944	−0.000367738 0	−0.000183869		1.00000i	$0.500059\pi$
$662$	27131.4	1.59289
$663$	13267.9	0.777196
$664$	8834.23	0.516317
$665$	0	0
$666$	−9165.56	−0.533271
$667$	−1413.61	−0.0820620
$668$	−2211.64	−0.128100
$669$	19469.2	1.12515
$670$	−499.113	−0.0287797
$671$	14255.4	0.820153
$672$	0	0
$673$	15336.5	0.878423	0.439211	−	0.898384i	$-0.355258\pi$
$673$	15336.5	0.878423	0.439211	+	0.898384i	$0.355258\pi$
$674$	18301.4	1.04591
$675$	−13464.6	−0.767781
$676$	5087.99	0.289485
$677$	−7578.05	−0.430204	−0.215102	−	0.976592i	$-0.569008\pi$
$677$	−7578.05	−0.430204	−0.215102	+	0.976592i	$0.569008\pi$
$678$	−11818.2	−0.669433
$679$	0	0
$680$	−1566.34	−0.0883327
$681$	−23259.5	−1.30882
$682$	−19035.2	−1.06876
$683$	3334.75	0.186824	0.0934119	−	0.995628i	$-0.470223\pi$
$683$	3334.75	0.186824	0.0934119	+	0.995628i	$0.470223\pi$
$684$	6033.53	0.337277
$685$	1402.10	0.0782064
$686$	0	0
$687$	−14631.4	−0.812552
$688$	15841.2	0.877818
$689$	1261.82	0.0697699
$690$	−131.275	−0.00724284
$691$	4768.66	0.262530	0.131265	−	0.991347i	$-0.458096\pi$
$691$	4768.66	0.262530	0.131265	+	0.991347i	$0.458096\pi$
$692$	−3877.77	−0.213021
$693$	0	0
$694$	−2796.65	−0.152967
$695$	−810.547	−0.0442385
$696$	21231.4	1.15628
$697$	−22316.9	−1.21279
$698$	−24312.8	−1.31841
$699$	−19693.1	−1.06561
$700$	0	0
$701$	9995.75	0.538565	0.269283	−	0.963061i	$-0.413213\pi$
$701$	9995.75	0.538565	0.269283	+	0.963061i	$0.413213\pi$
$702$	−3274.64	−0.176059
$703$	−5832.45	−0.312909
$704$	−20814.0	−1.11429
$705$	−2591.60	−0.138447
$706$	−15490.7	−0.825778
$707$	0	0
$708$	13307.8	0.706410
$709$	−9879.25	−0.523305	−0.261652	−	0.965162i	$-0.584267\pi$
$709$	−9879.25	−0.523305	−0.261652	+	0.965162i	$0.584267\pi$
$710$	808.813	0.0427524
$711$	−38255.5	−2.01786
$712$	−4293.30	−0.225981
$713$	2916.08	0.153167
$714$	0	0
$715$	246.393	0.0128875
$716$	7351.27	0.383701
$717$	11833.6	0.616364
$718$	−1708.38	−0.0887969
$719$	−8121.77	−0.421267	−0.210634	−	0.977565i	$-0.567553\pi$
$719$	−8121.77	−0.421267	−0.210634	+	0.977565i	$0.567553\pi$
$720$	769.357	0.0398226
$721$	0	0
$722$	7663.45	0.395020
$723$	2566.91	0.132039
$724$	6038.77	0.309985
$725$	−13122.5	−0.672217
$726$	−1339.98	−0.0685003
$727$	−7996.92	−0.407963	−0.203982	−	0.978975i	$-0.565388\pi$
$727$	−7996.92	−0.407963	−0.203982	+	0.978975i	$0.565388\pi$
$728$	0	0
$729$	−31917.5	−1.62158
$730$	−149.741	−0.00759199
$731$	−52609.6	−2.66188
$732$	7826.25	0.395173
$733$	−588.393	−0.0296491	−0.0148246	−	0.999890i	$-0.504719\pi$
$733$	−588.393	−0.0296491	−0.0148246	+	0.999890i	$0.504719\pi$
$734$	22300.9	1.12144
$735$	0	0
$736$	1461.28	0.0731840
$737$	15671.5	0.783268
$738$	16799.9	0.837957
$739$	3591.55	0.178779	0.0893894	−	0.995997i	$-0.471508\pi$
$739$	3591.55	0.178779	0.0893894	+	0.995997i	$0.471508\pi$
$740$	124.134	0.00616655
$741$	−6355.73	−0.315093
$742$	0	0
$743$	16072.8	0.793612	0.396806	−	0.917903i	$-0.370119\pi$
$743$	16072.8	0.793612	0.396806	+	0.917903i	$0.370119\pi$
$744$	−43797.3	−2.15818
$745$	834.514	0.0410392
$746$	827.435	0.0406093
$747$	14410.8	0.705844
$748$	11735.0	0.573630
$749$	0	0
$750$	−2439.77	−0.118784
$751$	−4982.31	−0.242087	−0.121043	−	0.992647i	$-0.538624\pi$
$751$	−4982.31	−0.242087	−0.121043	+	0.992647i	$0.538624\pi$
$752$	−23413.5	−1.13538
$753$	13119.0	0.634902
$754$	−3191.44	−0.154145
$755$	−1154.75	−0.0556630
$756$	0	0
$757$	1393.49	0.0669051	0.0334526	−	0.999440i	$-0.489350\pi$
$757$	1393.49	0.0669051	0.0334526	+	0.999440i	$0.489350\pi$
$758$	−3144.62	−0.150683
$759$	4121.88	0.197121
$760$	750.325	0.0358120
$761$	10532.2	0.501696	0.250848	−	0.968026i	$-0.419291\pi$
$761$	10532.2	0.501696	0.250848	+	0.968026i	$0.419291\pi$
$762$	45112.2	2.14468
$763$	0	0
$764$	11646.9	0.551533
$765$	−2555.09	−0.120757
$766$	3883.47	0.183180
$767$	−8383.56	−0.394671
$768$	−28137.4	−1.32203
$769$	−35798.6	−1.67871	−0.839357	−	0.543581i	$-0.817068\pi$
$769$	−35798.6	−1.67871	−0.839357	+	0.543581i	$0.817068\pi$
$770$	0	0
$771$	−13332.4	−0.622767
$772$	6680.11	0.311428
$773$	17861.0	0.831069	0.415535	−	0.909577i	$-0.363594\pi$
$773$	17861.0	0.831069	0.415535	+	0.909577i	$0.363594\pi$
$774$	39603.8	1.83919
$775$	27069.8	1.25468
$776$	33270.3	1.53909
$777$	0	0
$778$	6552.68	0.301960
$779$	10690.5	0.491691
$780$	135.271	0.00620958
$781$	−25395.7	−1.16355
$782$	3938.76	0.180115
$783$	11355.0	0.518258
$784$	0	0
$785$	672.633	0.0305826
$786$	−1257.87	−0.0570826
$787$	13418.6	0.607780	0.303890	−	0.952707i	$-0.401714\pi$
$787$	13418.6	0.607780	0.303890	+	0.952707i	$0.401714\pi$
$788$	−3095.88	−0.139957
$789$	21331.4	0.962509
$790$	−1135.17	−0.0511233
$791$	0	0
$792$	−37022.9	−1.66105
$793$	−4930.33	−0.220783
$794$	−6971.68	−0.311607
$795$	−406.325	−0.0181269
$796$	6189.25	0.275593
$797$	15119.1	0.671953	0.335977	−	0.941870i	$-0.390934\pi$
$797$	15119.1	0.671953	0.335977	+	0.941870i	$0.390934\pi$
$798$	0	0
$799$	77758.0	3.44290
$800$	13565.0	0.599492
$801$	−7003.45	−0.308932
$802$	−18910.7	−0.832619
$803$	4701.67	0.206623
$804$	8603.73	0.377401
$805$	0	0
$806$	6583.48	0.287709
$807$	57119.2	2.49156
$808$	23058.5	1.00396
$809$	−9802.12	−0.425988	−0.212994	−	0.977054i	$-0.568321\pi$
$809$	−9802.12	−0.425988	−0.212994	+	0.977054i	$0.568321\pi$
$810$	−238.334	−0.0103385
$811$	−38160.7	−1.65228	−0.826142	−	0.563462i	$-0.809469\pi$
$811$	−38160.7	−1.65228	−0.826142	+	0.563462i	$0.809469\pi$
$812$	0	0
$813$	−34105.0	−1.47123
$814$	8539.58	0.367705
$815$	−773.312	−0.0332368
$816$	−38599.1	−1.65593
$817$	25201.7	1.07919
$818$	17881.7	0.764328
$819$	0	0
$820$	−227.529	−0.00968983
$821$	19720.5	0.838308	0.419154	−	0.907915i	$-0.362327\pi$
$821$	19720.5	0.838308	0.419154	+	0.907915i	$0.362327\pi$
$822$	52954.2	2.24695
$823$	−37375.3	−1.58302	−0.791508	−	0.611159i	$-0.790704\pi$
$823$	−37375.3	−1.58302	−0.791508	+	0.611159i	$0.790704\pi$
$824$	22658.6	0.957947
$825$	38263.2	1.61473
$826$	0	0
$827$	1377.74	0.0579308	0.0289654	−	0.999580i	$-0.490779\pi$
$827$	1377.74	0.0579308	0.0289654	+	0.999580i	$0.490779\pi$
$828$	1353.31	0.0568005
$829$	22041.5	0.923441	0.461720	−	0.887026i	$-0.347232\pi$
$829$	22041.5	0.923441	0.461720	+	0.887026i	$0.347232\pi$
$830$	427.616	0.0178829
$831$	48016.1	2.00440
$832$	7198.69	0.299964
$833$	0	0
$834$	−30612.6	−1.27102
$835$	−448.655	−0.0185944
$836$	−5621.45	−0.232562
$837$	−23423.8	−0.967317
$838$	27185.2	1.12064
$839$	−2189.78	−0.0901069	−0.0450534	−	0.998985i	$-0.514346\pi$
$839$	−2189.78	−0.0901069	−0.0450534	+	0.998985i	$0.514346\pi$
$840$	0	0
$841$	−13322.4	−0.546248
$842$	−4696.53	−0.192224
$843$	−4557.77	−0.186213
$844$	8142.16	0.332067
$845$	1032.16	0.0420204
$846$	−58535.2	−2.37882
$847$	0	0
$848$	−3670.91	−0.148655
$849$	−17617.2	−0.712157
$850$	36563.3	1.47542
$851$	−1308.21	−0.0526967
$852$	−13942.4	−0.560631
$853$	5374.29	0.215724	0.107862	−	0.994166i	$-0.465600\pi$
$853$	5374.29	0.215724	0.107862	+	0.994166i	$0.465600\pi$
$854$	0	0
$855$	1223.97	0.0489577
$856$	16898.9	0.674756
$857$	6904.19	0.275196	0.137598	−	0.990488i	$-0.456062\pi$
$857$	6904.19	0.275196	0.137598	+	0.990488i	$0.456062\pi$
$858$	9305.74	0.370271
$859$	14509.1	0.576304	0.288152	−	0.957585i	$-0.406959\pi$
$859$	14509.1	0.576304	0.288152	+	0.957585i	$0.406959\pi$
$860$	−536.374	−0.0212677
$861$	0	0
$862$	7456.60	0.294632
$863$	19735.6	0.778455	0.389228	−	0.921142i	$-0.372742\pi$
$863$	19735.6	0.778455	0.389228	+	0.921142i	$0.372742\pi$
$864$	−11737.9	−0.462189
$865$	−786.650	−0.0309213
$866$	14524.5	0.569934
$867$	87924.6	3.44415
$868$	0	0
$869$	35642.8	1.39137
$870$	1027.69	0.0400484
$871$	−5420.12	−0.210854
$872$	−44542.5	−1.72982
$873$	54272.2	2.10405
$874$	−1886.79	−0.0730225
$875$	0	0
$876$	2581.24	0.0995569
$877$	36449.6	1.40344	0.701719	−	0.712454i	$-0.252416\pi$
$877$	36449.6	1.40344	0.701719	+	0.712454i	$0.252416\pi$
$878$	10934.4	0.420294
$879$	−45759.2	−1.75588
$880$	−716.812	−0.0274588
$881$	−840.638	−0.0321474	−0.0160737	−	0.999871i	$-0.505117\pi$
$881$	−840.638	−0.0321474	−0.0160737	+	0.999871i	$0.505117\pi$
$882$	0	0
$883$	19961.4	0.760763	0.380382	−	0.924830i	$-0.375793\pi$
$883$	19961.4	0.760763	0.380382	+	0.924830i	$0.375793\pi$
$884$	−4058.65	−0.154420
$885$	2699.64	0.102539
$886$	30595.2	1.16012
$887$	−8697.67	−0.329244	−0.164622	−	0.986357i	$-0.552640\pi$
$887$	−8697.67	−0.329244	−0.164622	+	0.986357i	$0.552640\pi$
$888$	19648.3	0.742516
$889$	0	0
$890$	−207.815	−0.00782694
$891$	7483.40	0.281373
$892$	−5955.65	−0.223554
$893$	−37248.6	−1.39583
$894$	31517.8	1.17910
$895$	1491.29	0.0556964
$896$	0	0
$897$	−1425.58	−0.0530644
$898$	−32304.2	−1.20045
$899$	−22828.7	−0.846918
$900$	12562.7	0.465286
$901$	12191.3	0.450779
$902$	−15652.5	−0.577795
$903$	0	0
$904$	15151.1	0.557433
$905$	1225.03	0.0449961
$906$	−43612.3	−1.59925
$907$	27678.6	1.01329	0.506644	−	0.862155i	$-0.330886\pi$
$907$	27678.6	1.01329	0.506644	+	0.862155i	$0.330886\pi$
$908$	7115.10	0.260047
$909$	37614.3	1.37248
$910$	0	0
$911$	16329.3	0.593867	0.296933	−	0.954898i	$-0.404036\pi$
$911$	16329.3	0.593867	0.296933	+	0.954898i	$0.404036\pi$
$912$	18490.2	0.671351
$913$	−13426.6	−0.486699
$914$	2603.83	0.0942309
$915$	1587.64	0.0573616
$916$	4475.76	0.161444
$917$	0	0
$918$	−31638.6	−1.13750
$919$	31346.0	1.12515	0.562574	−	0.826747i	$-0.309811\pi$
$919$	31346.0	1.12515	0.562574	+	0.826747i	$0.309811\pi$
$920$	168.297	0.00603107
$921$	61016.7	2.18303
$922$	−12132.0	−0.433348
$923$	8783.31	0.313224
$924$	0	0
$925$	−12144.0	−0.431669
$926$	13769.6	0.488659
$927$	36961.8	1.30958
$928$	−11439.7	−0.404662
$929$	20810.3	0.734946	0.367473	−	0.930034i	$-0.380223\pi$
$929$	20810.3	0.734946	0.367473	+	0.930034i	$0.380223\pi$
$930$	−2119.98	−0.0747495
$931$	0	0
$932$	6024.14	0.211724
$933$	−43425.4	−1.52378
$934$	−4683.33	−0.164072
$935$	2380.58	0.0832656
$936$	12804.6	0.447150
$937$	−18200.0	−0.634546	−0.317273	−	0.948334i	$-0.602767\pi$
$937$	−18200.0	−0.634546	−0.317273	+	0.948334i	$0.602767\pi$
$938$	0	0
$939$	26209.6	0.910881
$940$	792.772	0.0275078
$941$	−19327.1	−0.669551	−0.334775	−	0.942298i	$-0.608660\pi$
$941$	−19327.1	−0.669551	−0.334775	+	0.942298i	$0.608660\pi$
$942$	25403.9	0.878667
$943$	2397.86	0.0828051
$944$	24389.6	0.840906
$945$	0	0
$946$	−36899.0	−1.26817
$947$	41623.8	1.42829	0.714145	−	0.699997i	$-0.246816\pi$
$947$	41623.8	1.42829	0.714145	+	0.699997i	$0.246816\pi$
$948$	19568.0	0.670401
$949$	−1626.11	−0.0556225
$950$	−17515.0	−0.598170
$951$	−31006.1	−1.05725
$952$	0	0
$953$	19450.5	0.661137	0.330569	−	0.943782i	$-0.392759\pi$
$953$	19450.5	0.661137	0.330569	+	0.943782i	$0.392759\pi$
$954$	−9177.48	−0.311459
$955$	2362.71	0.0800581
$956$	−3619.90	−0.122464
$957$	−32268.3	−1.08996
$958$	−27025.0	−0.911418
$959$	0	0
$960$	−2318.09	−0.0779335
$961$	17301.2	0.580754
$962$	−2953.48	−0.0989854
$963$	27566.3	0.922441
$964$	−785.220	−0.0262347
$965$	1355.14	0.0452056
$966$	0	0
$967$	−15673.2	−0.521217	−0.260608	−	0.965445i	$-0.583923\pi$
$967$	−15673.2	−0.521217	−0.260608	+	0.965445i	$0.583923\pi$
$968$	1717.87	0.0570398
$969$	−61407.3	−2.03580
$970$	1610.43	0.0533070
$971$	−47000.7	−1.55337	−0.776686	−	0.629888i	$-0.783101\pi$
$971$	−47000.7	−1.55337	−0.776686	+	0.629888i	$0.783101\pi$
$972$	11415.0	0.376684
$973$	0	0
$974$	4081.75	0.134279
$975$	−13233.6	−0.434681
$976$	14343.4	0.470411
$977$	43424.2	1.42197	0.710985	−	0.703207i	$-0.248249\pi$
$977$	43424.2	1.42197	0.710985	+	0.703207i	$0.248249\pi$
$978$	−29206.3	−0.954924
$979$	6525.14	0.213018
$980$	0	0
$981$	−72660.0	−2.36479
$982$	−29586.6	−0.961453
$983$	−28244.0	−0.916421	−0.458211	−	0.888844i	$-0.651509\pi$
$983$	−28244.0	−0.916421	−0.458211	+	0.888844i	$0.651509\pi$
$984$	−36014.1	−1.16675
$985$	−628.035	−0.0203156
$986$	−30834.8	−0.995923
$987$	0	0
$988$	1944.22	0.0626052
$989$	5652.70	0.181745
$990$	−1792.07	−0.0575311
$991$	25441.0	0.815499	0.407750	−	0.913094i	$-0.366314\pi$
$991$	25441.0	0.815499	0.407750	+	0.913094i	$0.366314\pi$
$992$	23598.4	0.755293
$993$	−94876.6	−3.03204
$994$	0	0
$995$	1255.56	0.0400039
$996$	−7371.27	−0.234506
$997$	14210.9	0.451418	0.225709	−	0.974195i	$-0.427530\pi$
$997$	14210.9	0.451418	0.225709	+	0.974195i	$0.427530\pi$
$998$	22449.7	0.712056
$999$	10508.4	0.332803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.12		39
7.6	odd	2		2401.4.a.d.1.12		39
49.20	odd	14		49.4.e.a.8.5	✓	78
49.27	odd	14		49.4.e.a.43.5	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.5	✓	78	49.20	odd	14
49.4.e.a.43.5	yes	78	49.27	odd	14
2401.4.a.c.1.12		39	1.1	even	1	trivial
2401.4.a.d.1.12		39	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34370 q^{2} +8.19575 q^{3} -2.50708 q^{4} -0.508590 q^{5} -19.2083 q^{6} +24.6254 q^{8} +40.1702 q^{9} +O(q^{10})\)	\(q-2.34370 q^{2} +8.19575 q^{3} -2.50708 q^{4} -0.508590 q^{5} -19.2083 q^{6} +24.6254 q^{8} +40.1702 q^{9} +1.19198 q^{10} -37.4267 q^{11} -20.5474 q^{12} +12.9443 q^{13} -4.16827 q^{15} -37.6579 q^{16} +125.064 q^{17} -94.1469 q^{18} -59.9098 q^{19} +1.27508 q^{20} +87.7169 q^{22} -13.4377 q^{23} +201.824 q^{24} -124.741 q^{25} -30.3376 q^{26} +107.940 q^{27} +105.198 q^{29} +9.76917 q^{30} -217.007 q^{31} -108.745 q^{32} -306.740 q^{33} -293.113 q^{34} -100.710 q^{36} +97.3538 q^{37} +140.410 q^{38} +106.088 q^{39} -12.5242 q^{40} -178.443 q^{41} -420.660 q^{43} +93.8319 q^{44} -20.4302 q^{45} +31.4939 q^{46} +621.744 q^{47} -308.634 q^{48} +292.356 q^{50} +1025.00 q^{51} -32.4525 q^{52} +97.4805 q^{53} -252.979 q^{54} +19.0349 q^{55} -491.006 q^{57} -246.552 q^{58} -647.664 q^{59} +10.4502 q^{60} -380.887 q^{61} +508.600 q^{62} +556.128 q^{64} -6.58335 q^{65} +718.906 q^{66} -418.726 q^{67} -313.547 q^{68} -110.132 q^{69} +678.546 q^{71} +989.209 q^{72} -125.623 q^{73} -228.168 q^{74} -1022.35 q^{75} +150.199 q^{76} -248.639 q^{78} -952.335 q^{79} +19.1524 q^{80} -199.948 q^{81} +418.217 q^{82} +358.744 q^{83} -63.6065 q^{85} +985.900 q^{86} +862.174 q^{87} -921.649 q^{88} -174.344 q^{89} +47.8822 q^{90} +33.6894 q^{92} -1778.54 q^{93} -1457.18 q^{94} +30.4695 q^{95} -891.244 q^{96} +1351.05 q^{97} -1503.44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Introduction

L-functions

Modular forms

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