LMFDB - Embedded newform 2401.4.a.d.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:	$0$
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	$-0.789212\pi$
$3$	−8.19575	−1.57727	−0.788636	+	0.614860i	$0.789212\pi$
$4$	−2.50708	−0.313385
$5$	0.508590	0.0454897	0.0227448	−	0.999741i	$-0.492759\pi$
$5$	0.508590	0.0454897	0.0227448	+	0.999741i	$0.492759\pi$
$6$	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	$-0.544093\pi$
$13$	−12.9443	−0.276162	−0.138081	+	0.990421i	$0.544093\pi$
$14$	0	0
$15$	−4.16827	−0.0717496
$16$	−37.6579	−0.588404
$17$	−125.064	−1.78427	−0.892134	−	0.451771i	$-0.850792\pi$
$17$	−125.064	−1.78427	−0.892134	+	0.451771i	$0.850792\pi$
$18$	−94.1469	−1.23281
$19$	59.9098	0.723382	0.361691	−	0.932298i	$-0.382200\pi$
$19$	59.9098	0.723382	0.361691	+	0.932298i	$0.382200\pi$
$20$	−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	$-0.283612\pi$
$31$	217.007	1.25728	0.628640	+	0.777696i	$0.283612\pi$
$32$	−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	$-0.389622\pi$
$41$	178.443	0.679711	0.339855	+	0.940478i	$0.389622\pi$
$42$	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	$-0.915286\pi$
$47$	−621.744	−1.92959	−0.964794	+	0.263006i	$0.915286\pi$
$48$	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	$-0.246625\pi$
$59$	647.664	1.42913	0.714565	+	0.699569i	$0.246625\pi$
$60$	10.4502	0.0224853
$61$	380.887	0.799469	0.399735	−	0.916631i	$-0.369102\pi$
$61$	380.887	0.799469	0.399735	+	0.916631i	$0.369102\pi$
$62$	−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	$-0.467890\pi$
$73$	125.623	0.201412	0.100706	+	0.994916i	$0.467890\pi$
$74$	−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	$-0.576234\pi$
$83$	−358.744	−0.474425	−0.237213	+	0.971458i	$0.576234\pi$
$84$	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	$-0.466893\pi$
$89$	174.344	0.207646	0.103823	+	0.994596i	$0.466893\pi$
$90$	−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	$-0.750000\pi$
$97$	−1351.05	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$98$	0	0
$99$	−1503.44	−1.52628
$100$	312.737	0.312737
$101$	−936.371	−0.922499	−0.461250	−	0.887270i	$-0.652599\pi$
$101$	−936.371	−0.922499	−0.461250	+	0.887270i	$0.652599\pi$
$102$	−2402.28	−2.33197
$103$	−920.129	−0.880223	−0.440112	−	0.897943i	$-0.645061\pi$
$103$	−920.129	−0.880223	−0.440112	+	0.897943i	$0.645061\pi$
$104$	−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	$-0.506952\pi$
$131$	−65.4858	−0.0436757	−0.0218379	+	0.999762i	$0.506952\pi$
$132$	−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	$-0.661635\pi$
$139$	−1593.71	−0.972496	−0.486248	+	0.873821i	$0.661635\pi$
$140$	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	$-0.390876\pi$
$157$	1322.55	0.672297	0.336148	+	0.941809i	$0.390876\pi$
$158$	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	$-0.565518\pi$
$167$	−882.155	−0.408762	−0.204381	+	0.978891i	$0.565518\pi$
$168$	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	$-0.610384\pi$
$173$	−1546.73	−0.679743	−0.339871	+	0.940472i	$0.610384\pi$
$174$	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	$-0.335324\pi$
$181$	2408.68	0.989149	0.494575	+	0.869135i	$0.335324\pi$
$182$	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	$-0.355084\pi$
$199$	2468.71	0.879407	0.439703	+	0.898143i	$0.355084\pi$
$200$	−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	$-0.616090\pi$
$223$	−2375.53	−0.713350	−0.356675	+	0.934228i	$0.616090\pi$
$224$	0	0
$225$	−5010.89	−1.48471
$226$	−1441.99	−0.424424
$227$	2838.00	0.829799	0.414900	−	0.909867i	$-0.363817\pi$
$227$	2838.00	0.829799	0.414900	+	0.909867i	$0.363817\pi$
$228$	1230.99	0.357563
$229$	1785.24	0.515163	0.257581	−	0.966257i	$-0.417074\pi$
$229$	1785.24	0.515163	0.257581	+	0.966257i	$0.417074\pi$
$230$	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	$-0.513327\pi$
$241$	−313.200	−0.0837138	−0.0418569	+	0.999124i	$0.513327\pi$
$242$	−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	$-0.564506\pi$
$251$	−1600.70	−0.402532	−0.201266	+	0.979537i	$0.564506\pi$
$252$	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	$-0.436744\pi$
$257$	1626.74	0.394838	0.197419	+	0.980319i	$0.436744\pi$
$258$	−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	$-0.789833\pi$
$269$	−6969.38	−1.57967	−0.789833	+	0.613321i	$0.789833\pi$
$270$	128.662	0.0290005
$271$	4161.30	0.932771	0.466386	−	0.884581i	$-0.345556\pi$
$271$	4161.30	0.932771	0.466386	+	0.884581i	$0.345556\pi$
$272$	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	$-0.427515\pi$
$283$	2149.55	0.451512	0.225756	+	0.974184i	$0.427515\pi$
$284$	−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	$-0.312098\pi$
$293$	5583.29	1.11324	0.556620	+	0.830767i	$0.312098\pi$
$294$	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	$-0.743282\pi$
$307$	−7444.93	−1.38405	−0.692027	+	0.721872i	$0.743282\pi$
$308$	0	0
$309$	7541.14	1.38835
$310$	−258.669	−0.0473916
$311$	5298.53	0.966085	0.483042	−	0.875597i	$-0.339532\pi$
$311$	5298.53	0.966085	0.483042	+	0.875597i	$0.339532\pi$
$312$	2612.47	0.474045
$313$	−3197.95	−0.577504	−0.288752	−	0.957404i	$-0.593240\pi$
$313$	−3197.95	−0.577504	−0.288752	+	0.957404i	$0.593240\pi$
$314$	−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	$-0.792816\pi$
$349$	−10373.7	−1.59109	−0.795546	+	0.605893i	$0.792816\pi$
$350$	0	0
$351$	1397.21	0.212472
$352$	4069.96	0.616277
$353$	−6609.50	−0.996568	−0.498284	−	0.867014i	$-0.666036\pi$
$353$	−6609.50	−0.996568	−0.498284	+	0.867014i	$0.666036\pi$
$354$	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	$-0.263413\pi$
$367$	9515.25	1.35338	0.676692	+	0.736266i	$0.263413\pi$
$368$	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	$-0.464744\pi$
$383$	1656.99	0.221065	0.110533	+	0.993872i	$0.464744\pi$
$384$	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	$-0.560209\pi$
$397$	−2974.65	−0.376054	−0.188027	+	0.982164i	$0.560209\pi$
$398$	−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	$-0.347418\pi$
$409$	7629.71	0.922408	0.461204	+	0.887294i	$0.347418\pi$
$410$	−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	$-0.263623\pi$
$419$	11599.3	1.35241	0.676207	+	0.736712i	$0.263623\pi$
$420$	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	$-0.388250\pi$
$433$	6197.27	0.687810	0.343905	+	0.939004i	$0.388250\pi$
$434$	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	$-0.418382\pi$
$439$	4665.45	0.507221	0.253610	+	0.967306i	$0.418382\pi$
$440$	−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	$-0.584213\pi$
$461$	−5176.45	−0.522975	−0.261487	+	0.965207i	$0.584213\pi$
$462$	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	$-0.531565\pi$
$467$	−1998.27	−0.198006	−0.0990030	+	0.995087i	$0.531565\pi$
$468$	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	$-0.685357\pi$
$479$	−11530.9	−1.09992	−0.549960	+	0.835191i	$0.685357\pi$
$480$	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	$-0.257430\pi$
$503$	15577.2	1.38082	0.690410	+	0.723418i	$0.257430\pi$
$504$	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	$-0.458158\pi$
$509$	3010.35	0.262144	0.131072	+	0.991373i	$0.458158\pi$
$510$	−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	$-0.485742\pi$
$521$	1065.01	0.0895567	0.0447784	+	0.998997i	$0.485742\pi$
$522$	−9904.04	−0.830437
$523$	4664.44	0.389985	0.194992	−	0.980805i	$-0.437532\pi$
$523$	4664.44	0.389985	0.194992	+	0.980805i	$0.437532\pi$
$524$	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	$-0.666939\pi$
$563$	−13378.4	−1.00148	−0.500741	+	0.865597i	$0.666939\pi$
$564$	−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	$-0.529141\pi$
$577$	−2534.23	−0.182845	−0.0914223	+	0.995812i	$0.529141\pi$
$578$	−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	$-0.158887\pi$
$587$	24973.2	1.75597	0.877985	+	0.478687i	$0.158887\pi$
$588$	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	$-0.544906\pi$
$593$	−4060.88	−0.281215	−0.140607	+	0.990065i	$0.544906\pi$
$594$	−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	$-0.750409\pi$
$601$	−20863.3	−1.41603	−0.708014	+	0.706198i	$0.750409\pi$
$602$	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	$-0.477761\pi$
$607$	2087.96	0.139617	0.0698087	+	0.997560i	$0.477761\pi$
$608$	−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	$-0.410853\pi$
$619$	8513.93	0.552833	0.276416	+	0.961038i	$0.410853\pi$
$620$	−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	$-0.278548\pi$
$643$	20900.6	1.28186	0.640931	+	0.767598i	$0.278548\pi$
$644$	0	0
$645$	1753.43	0.107040
$646$	17560.3	1.06951
$647$	23053.3	1.40080	0.700400	−	0.713751i	$-0.253005\pi$
$647$	23053.3	1.40080	0.700400	+	0.713751i	$0.253005\pi$
$648$	−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	$-0.499941\pi$
$661$	6.24944	0.000367738 0	0.000183869		1.00000i	$0.499941\pi$
$662$	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	$-0.430992\pi$
$677$	7578.05	0.430204	0.215102	+	0.976592i	$0.430992\pi$
$678$	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	$-0.541904\pi$
$691$	−4768.66	−0.262530	−0.131265	+	0.991347i	$0.541904\pi$
$692$	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	$-0.432447\pi$
$719$	8121.77	0.421267	0.210634	+	0.977565i	$0.432447\pi$
$720$	−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	$-0.434612\pi$
$727$	7996.92	0.407963	0.203982	+	0.978975i	$0.434612\pi$
$728$	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	$-0.495281\pi$
$733$	588.393	0.0296491	0.0148246	+	0.999890i	$0.495281\pi$
$734$	−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	$-0.580709\pi$
$761$	−10532.2	−0.501696	−0.250848	+	0.968026i	$0.580709\pi$
$762$	−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	$-0.182932\pi$
$769$	35798.6	1.67871	0.839357	+	0.543581i	$0.182932\pi$
$770$	0	0
$771$	−13332.4	−0.622767
$772$	6680.11	0.311428
$773$	−17861.0	−0.831069	−0.415535	−	0.909577i	$-0.636406\pi$
$773$	−17861.0	−0.831069	−0.415535	+	0.909577i	$0.636406\pi$
$774$	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	$-0.598286\pi$
$787$	−13418.6	−0.607780	−0.303890	+	0.952707i	$0.598286\pi$
$788$	−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	$-0.609066\pi$
$797$	−15119.1	−0.671953	−0.335977	+	0.941870i	$0.609066\pi$
$798$	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	$-0.190531\pi$
$811$	38160.7	1.65228	0.826142	+	0.563462i	$0.190531\pi$
$812$	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	$-0.652768\pi$
$829$	−22041.5	−0.923441	−0.461720	+	0.887026i	$0.652768\pi$
$830$	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	$-0.485654\pi$
$839$	2189.78	0.0901069	0.0450534	+	0.998985i	$0.485654\pi$
$840$	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	$-0.534400\pi$
$853$	−5374.29	−0.215724	−0.107862	+	0.994166i	$0.534400\pi$
$854$	0	0
$855$	1223.97	0.0489577
$856$	16898.9	0.674756
$857$	−6904.19	−0.275196	−0.137598	−	0.990488i	$-0.543938\pi$
$857$	−6904.19	−0.275196	−0.137598	+	0.990488i	$0.543938\pi$
$858$	9305.74	0.370271
$859$	−14509.1	−0.576304	−0.288152	−	0.957585i	$-0.593041\pi$
$859$	−14509.1	−0.576304	−0.288152	+	0.957585i	$0.593041\pi$
$860$	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	$-0.494883\pi$
$881$	840.638	0.0321474	0.0160737	+	0.999871i	$0.494883\pi$
$882$	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	$-0.447360\pi$
$887$	8697.67	0.329244	0.164622	+	0.986357i	$0.447360\pi$
$888$	−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	$-0.619777\pi$
$929$	−20810.3	−0.734946	−0.367473	+	0.930034i	$0.619777\pi$
$930$	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	$-0.397233\pi$
$937$	18200.0	0.634546	0.317273	+	0.948334i	$0.397233\pi$
$938$	0	0
$939$	26209.6	0.910881
$940$	792.772	0.0275078
$941$	19327.1	0.669551	0.334775	−	0.942298i	$-0.391340\pi$
$941$	19327.1	0.669551	0.334775	+	0.942298i	$0.391340\pi$
$942$	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	$-0.216899\pi$
$971$	47000.7	1.55337	0.776686	+	0.629888i	$0.216899\pi$
$972$	−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	$-0.348491\pi$
$983$	28244.0	0.916421	0.458211	+	0.888844i	$0.348491\pi$
$984$	−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	$-0.572470\pi$
$997$	−14210.9	−0.451418	−0.225709	+	0.974195i	$0.572470\pi$
$998$	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.d.1.12		39
7.6	odd	2		2401.4.a.c.1.12		39
49.22	even	7		49.4.e.a.43.5	yes	78
49.29	even	7		49.4.e.a.8.5	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.5	✓	78	49.29	even	7
49.4.e.a.43.5	yes	78	49.22	even	7
2401.4.a.c.1.12		39	7.6	odd	2
2401.4.a.d.1.12		39	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:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
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

Varieties

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Database

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