LMFDB - Embedded newform 294.5.c.a.97.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,5,Mod(97,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.97"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	294.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,32,0,0,0,0,-108,0,324,0,0,0,396,256,0,0,0,0,0,-192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(22)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.3907691467$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.97
Dual form			294.5.c.a.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -23.9515i q^{5} -14.6969i q^{6} -22.6274 q^{8} -27.0000 q^{9} +67.7452i q^{10} +97.9706 q^{11} +41.5692i q^{12} -104.211i q^{13} +124.456 q^{15} +64.0000 q^{16} -107.676i q^{17} +76.3675 q^{18} +38.3935i q^{19} -191.612i q^{20} -277.103 q^{22} -1021.50 q^{23} -117.576i q^{24} +51.3238 q^{25} +294.755i q^{26} -140.296i q^{27} +621.603 q^{29} -352.014 q^{30} +1519.14i q^{31} -181.019 q^{32} +509.070i q^{33} +304.553i q^{34} -216.000 q^{36} -562.235 q^{37} -108.593i q^{38} +541.499 q^{39} +541.961i q^{40} -1023.20i q^{41} -3382.41 q^{43} +783.765 q^{44} +646.692i q^{45} +2889.23 q^{46} -3945.03i q^{47} +332.554i q^{48} -145.166 q^{50} +559.499 q^{51} -833.692i q^{52} +2190.60 q^{53} +396.817i q^{54} -2346.55i q^{55} -199.499 q^{57} -1758.16 q^{58} -2934.87i q^{59} +995.647 q^{60} +665.346i q^{61} -4296.76i q^{62} +512.000 q^{64} -2496.03 q^{65} -1439.87i q^{66} -5925.38 q^{67} -861.405i q^{68} -5307.86i q^{69} -4494.41 q^{71} +610.940 q^{72} -8968.93i q^{73} +1590.24 q^{74} +266.686i q^{75} +307.148i q^{76} -1531.59 q^{78} -10446.8 q^{79} -1532.90i q^{80} +729.000 q^{81} +2894.04i q^{82} +1269.28i q^{83} -2579.00 q^{85} +9566.89 q^{86} +3229.94i q^{87} -2216.82 q^{88} -3604.36i q^{89} -1829.12i q^{90} -8171.99 q^{92} -7893.66 q^{93} +11158.2i q^{94} +919.584 q^{95} -940.604i q^{96} -1950.53i q^{97} -2645.21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{4} - 108 q^{9} + 324 q^{11} + 396 q^{15} + 256 q^{16} - 192 q^{22} - 624 q^{23} + 952 q^{25} + 2724 q^{29} - 288 q^{30} - 864 q^{36} - 2792 q^{37} - 1296 q^{39} - 632 q^{43} + 2592 q^{44} + 9792 q^{46}+ \cdots - 8748 q^{99}+O(q^{100}) $ 4 * q + 32 * q^4 - 108 * q^9 + 324 * q^11 + 396 * q^15 + 256 * q^16 - 192 * q^22 - 624 * q^23 + 952 * q^25 + 2724 * q^29 - 288 * q^30 - 864 * q^36 - 2792 * q^37 - 1296 * q^39 - 632 * q^43 + 2592 * q^44 + 9792 * q^46 + 2112 * q^50 - 1224 * q^51 + 2076 * q^53 + 2664 * q^57 + 672 * q^58 + 3168 * q^60 + 2048 * q^64 + 1488 * q^65 - 29200 * q^67 - 9696 * q^71 - 1536 * q^74 - 9792 * q^78 - 7948 * q^79 + 2916 * q^81 + 1224 * q^85 + 36480 * q^86 - 1536 * q^88 - 4992 * q^92 - 22716 * q^93 - 6504 * q^95 - 8748 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.82843	−0.707107
$2$	−2.82843	−0.707107
$3$	5.19615i	0.577350i
$3$	5.19615i	0.577350i
$4$	8.00000	0.500000
$5$	− 23.9515i	− 0.958062i	−0.877798	−	0.479031i	$-0.840988\pi$
$5$	− 23.9515i	− 0.958062i	0.877798	−	0.479031i	$-0.159012\pi$
$6$	− 14.6969i	− 0.408248i
$7$	0	0
$7$	0	0
$8$	−22.6274	−0.353553
$9$	−27.0000	−0.333333
$10$	67.7452i	0.677452i
$11$	97.9706	0.809674	0.404837	−	0.914389i	$-0.367328\pi$
$11$	97.9706	0.809674	0.404837	+	0.914389i	$0.367328\pi$
$12$	41.5692i	0.288675i
$13$	− 104.211i	− 0.616636i	−0.951283	−	0.308318i	$-0.900234\pi$
$13$	− 104.211i	− 0.616636i	0.951283	−	0.308318i	$-0.0997661\pi$
$14$	0	0
$15$	124.456	0.553137
$16$	64.0000	0.250000
$17$	− 107.676i	− 0.372580i	−0.982495	−	0.186290i	$-0.940354\pi$
$17$	− 107.676i	− 0.372580i	0.982495	−	0.186290i	$-0.0596464\pi$
$18$	76.3675	0.235702
$19$	38.3935i	0.106353i	0.998585	+	0.0531767i	$0.0169346\pi$
$19$	38.3935i	0.106353i	−0.998585	+	0.0531767i	$0.983065\pi$
$20$	− 191.612i	− 0.479031i
$21$	0	0
$22$	−277.103	−0.572526
$23$	−1021.50	−1.93100	−0.965500	−	0.260404i	$-0.916144\pi$
$23$	−1021.50	−1.93100	−0.965500	+	0.260404i	$0.916144\pi$
$24$	− 117.576i	− 0.204124i
$25$	51.3238	0.0821181
$26$	294.755i	0.436027i
$27$	− 140.296i	− 0.192450i
$28$	0	0
$29$	621.603	0.739124	0.369562	−	0.929206i	$-0.379508\pi$
$29$	621.603	0.739124	0.369562	+	0.929206i	$0.379508\pi$
$30$	−352.014	−0.391127
$31$	1519.14i	1.58079i	0.612600	+	0.790393i	$0.290124\pi$
$31$	1519.14i	1.58079i	−0.612600	+	0.790393i	$0.709876\pi$
$32$	−181.019	−0.176777
$33$	509.070i	0.467466i
$34$	304.553i	0.263454i
$35$	0	0
$36$	−216.000	−0.166667
$37$	−562.235	−0.410691	−0.205345	−	0.978690i	$-0.565832\pi$
$37$	−562.235	−0.410691	−0.205345	+	0.978690i	$0.565832\pi$
$38$	− 108.593i	− 0.0752031i
$39$	541.499	0.356015
$40$	541.961i	0.338726i
$41$	− 1023.20i	− 0.608684i	−0.952563	−	0.304342i	$-0.901563\pi$
$41$	− 1023.20i	− 0.608684i	0.952563	−	0.304342i	$-0.0984365\pi$
$42$	0	0
$43$	−3382.41	−1.82932	−0.914658	−	0.404228i	$-0.867540\pi$
$43$	−3382.41	−1.82932	−0.914658	+	0.404228i	$0.867540\pi$
$44$	783.765	0.404837
$45$	646.692i	0.319354i
$46$	2889.23	1.36542
$47$	− 3945.03i	− 1.78589i	−0.450165	−	0.892945i	$-0.648635\pi$
$47$	− 3945.03i	− 1.78589i	0.450165	−	0.892945i	$-0.351365\pi$
$48$	332.554i	0.144338i
$49$	0	0
$50$	−145.166	−0.0580663
$51$	559.499	0.215109
$52$	− 833.692i	− 0.308318i
$53$	2190.60	0.779851	0.389925	−	0.920846i	$-0.372501\pi$
$53$	2190.60	0.779851	0.389925	+	0.920846i	$0.372501\pi$
$54$	396.817i	0.136083i
$55$	− 2346.55i	− 0.775718i
$56$	0	0
$57$	−199.499	−0.0614031
$58$	−1758.16	−0.522639
$59$	− 2934.87i	− 0.843111i	−0.906803	−	0.421556i	$-0.861484\pi$
$59$	− 2934.87i	− 0.843111i	0.906803	−	0.421556i	$-0.138516\pi$
$60$	995.647	0.276569
$61$	665.346i	0.178809i	0.995995	+	0.0894043i	$0.0284963\pi$
$61$	665.346i	0.178809i	−0.995995	+	0.0894043i	$0.971504\pi$
$62$	− 4296.76i	− 1.11778i
$63$	0	0
$64$	512.000	0.125000
$65$	−2496.03	−0.590775
$66$	− 1439.87i	− 0.330548i
$67$	−5925.38	−1.31998	−0.659989	−	0.751275i	$-0.729439\pi$
$67$	−5925.38	−1.31998	−0.659989	+	0.751275i	$0.729439\pi$
$68$	− 861.405i	− 0.186290i
$69$	− 5307.86i	− 1.11486i
$70$	0	0
$71$	−4494.41	−0.891571	−0.445785	−	0.895140i	$-0.647076\pi$
$71$	−4494.41	−0.891571	−0.445785	+	0.895140i	$0.647076\pi$
$72$	610.940	0.117851
$73$	− 8968.93i	− 1.68304i	−0.540225	−	0.841521i	$-0.681661\pi$
$73$	− 8968.93i	− 1.68304i	0.540225	−	0.841521i	$-0.318339\pi$
$74$	1590.24	0.290402
$75$	266.686i	0.0474109i
$76$	307.148i	0.0531767i
$77$	0	0
$78$	−1531.59	−0.251741
$79$	−10446.8	−1.67390	−0.836951	−	0.547277i	$-0.815664\pi$
$79$	−10446.8	−1.67390	−0.836951	+	0.547277i	$0.815664\pi$
$80$	− 1532.90i	− 0.239515i
$81$	729.000	0.111111
$82$	2894.04i	0.430405i
$83$	1269.28i	0.184247i	0.995748	+	0.0921234i	$0.0293654\pi$
$83$	1269.28i	0.184247i	−0.995748	+	0.0921234i	$0.970635\pi$
$84$	0	0
$85$	−2579.00	−0.356954
$86$	9566.89	1.29352
$87$	3229.94i	0.426733i
$88$	−2216.82	−0.286263
$89$	− 3604.36i	− 0.455038i	−0.973774	−	0.227519i	$-0.926939\pi$
$89$	− 3604.36i	− 0.455038i	0.973774	−	0.227519i	$-0.0730614\pi$
$90$	− 1829.12i	− 0.225817i
$91$	0	0
$92$	−8171.99	−0.965500
$93$	−7893.66	−0.912667
$94$	11158.2i	1.26282i
$95$	919.584	0.101893
$96$	− 940.604i	− 0.102062i
$97$	− 1950.53i	− 0.207304i	−0.994614	−	0.103652i	$-0.966947\pi$
$97$	− 1950.53i	− 0.207304i	0.994614	−	0.103652i	$-0.0330529\pi$
$98$	0	0
$99$	−2645.21	−0.269891
$100$	410.590	0.0410590
$101$	− 11326.2i	− 1.11031i	−0.831748	−	0.555153i	$-0.812660\pi$
$101$	− 11326.2i	− 1.11031i	0.831748	−	0.555153i	$-0.187340\pi$
$102$	−1582.50	−0.152105
$103$	− 16328.9i	− 1.53915i	−0.638555	−	0.769576i	$-0.720468\pi$
$103$	− 16328.9i	− 1.53915i	0.638555	−	0.769576i	$-0.279532\pi$
$104$	2358.04i	0.218014i
$105$	0	0
$106$	−6195.95	−0.551438
$107$	4396.46	0.384004	0.192002	−	0.981395i	$-0.438502\pi$
$107$	4396.46	0.384004	0.192002	+	0.981395i	$0.438502\pi$
$108$	− 1122.37i	− 0.0962250i
$109$	−14697.8	−1.23708	−0.618541	−	0.785753i	$-0.712276\pi$
$109$	−14697.8	−1.23708	−0.618541	+	0.785753i	$0.712276\pi$
$110$	6637.03i	0.548515i
$111$	− 2921.46i	− 0.237112i
$112$	0	0
$113$	2124.36	0.166368	0.0831842	−	0.996534i	$-0.473491\pi$
$113$	2124.36	0.166368	0.0831842	+	0.996534i	$0.473491\pi$
$114$	564.268	0.0434186
$115$	24466.5i	1.85002i
$116$	4972.82	0.369562
$117$	2813.71i	0.205545i
$118$	8301.07i	0.596170i
$119$	0	0
$120$	−2816.11	−0.195563
$121$	−5042.77	−0.344428
$122$	− 1881.88i	− 0.126437i
$123$	5316.69	0.351424
$124$	12153.1i	0.790393i
$125$	− 16199.0i	− 1.03674i
$126$	0	0
$127$	8498.07	0.526881	0.263441	−	0.964676i	$-0.415143\pi$
$127$	8498.07	0.526881	0.263441	+	0.964676i	$0.415143\pi$
$128$	−1448.15	−0.0883883
$129$	− 17575.5i	− 1.05616i
$130$	7059.83	0.417741
$131$	14472.3i	0.843324i	0.906753	+	0.421662i	$0.138553\pi$
$131$	14472.3i	0.843324i	−0.906753	+	0.421662i	$0.861447\pi$
$132$	4072.56i	0.233733i
$133$	0	0
$134$	16759.5	0.933366
$135$	−3360.31	−0.184379
$136$	2436.42i	0.131727i
$137$	12855.2	0.684915	0.342458	−	0.939533i	$-0.388741\pi$
$137$	12855.2	0.684915	0.342458	+	0.939533i	$0.388741\pi$
$138$	15012.9i	0.788327i
$139$	5009.46i	0.259275i	0.991561	+	0.129638i	$0.0413814\pi$
$139$	5009.46i	0.259275i	−0.991561	+	0.129638i	$0.958619\pi$
$140$	0	0
$141$	20499.0	1.03108
$142$	12712.1	0.630436
$143$	− 10209.7i	− 0.499274i
$144$	−1728.00	−0.0833333
$145$	− 14888.3i	− 0.708126i
$146$	25368.0i	1.19009i
$147$	0	0
$148$	−4497.88	−0.205345
$149$	25398.9	1.14404	0.572022	−	0.820238i	$-0.306159\pi$
$149$	25398.9	1.14404	0.572022	+	0.820238i	$0.306159\pi$
$150$	− 754.303i	− 0.0335246i
$151$	−18308.8	−0.802981	−0.401491	−	0.915863i	$-0.631508\pi$
$151$	−18308.8	−0.802981	−0.401491	+	0.915863i	$0.631508\pi$
$152$	− 868.747i	− 0.0376016i
$153$	2907.24i	0.124193i
$154$	0	0
$155$	36385.6	1.51449
$156$	4331.99	0.178007
$157$	35244.4i	1.42985i	0.699200	+	0.714926i	$0.253540\pi$
$157$	35244.4i	1.42985i	−0.699200	+	0.714926i	$0.746460\pi$
$158$	29548.1	1.18363
$159$	11382.7i	0.450247i
$160$	4335.69i	0.169363i
$161$	0	0
$162$	−2061.92	−0.0785674
$163$	145.939	0.00549281	0.00274641	−	0.999996i	$-0.499126\pi$
$163$	145.939	0.00549281	0.00274641	+	0.999996i	$0.499126\pi$
$164$	− 8185.58i	− 0.304342i
$165$	12193.0	0.447861
$166$	− 3590.05i	− 0.130282i
$167$	31314.1i	1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$167$	31314.1i	1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$168$	0	0
$169$	17701.0	0.619760
$170$	7294.50	0.252405
$171$	− 1036.63i	− 0.0354511i
$172$	−27059.3	−0.914658
$173$	− 40115.8i	− 1.34037i	−0.742196	−	0.670183i	$-0.766216\pi$
$173$	− 40115.8i	− 1.34037i	0.742196	−	0.670183i	$-0.233784\pi$
$174$	− 9135.66i	− 0.301746i
$175$	0	0
$176$	6270.12	0.202419
$177$	15250.0	0.486771
$178$	10194.7i	0.321760i
$179$	−50154.5	−1.56532	−0.782661	−	0.622448i	$-0.786138\pi$
$179$	−50154.5	−1.56532	−0.782661	+	0.622448i	$0.786138\pi$
$180$	5173.53i	0.159677i
$181$	63974.3i	1.95276i	0.216069	+	0.976378i	$0.430677\pi$
$181$	63974.3i	1.95276i	−0.216069	+	0.976378i	$0.569323\pi$
$182$	0	0
$183$	−3457.24	−0.103235
$184$	23113.9	0.682711
$185$	13466.4i	0.393467i
$186$	22326.6	0.645353
$187$	− 10549.0i	− 0.301668i
$188$	− 31560.3i	− 0.892945i
$189$	0	0
$190$	−2600.98	−0.0720492
$191$	−42768.9	−1.17236	−0.586180	−	0.810181i	$-0.699369\pi$
$191$	−42768.9	−1.17236	−0.586180	+	0.810181i	$0.699369\pi$
$192$	2660.43i	0.0721688i
$193$	−8772.58	−0.235512	−0.117756	−	0.993043i	$-0.537570\pi$
$193$	−8772.58	−0.235512	−0.117756	+	0.993043i	$0.537570\pi$
$194$	5516.92i	0.146586i
$195$	− 12969.7i	− 0.341084i
$196$	0	0
$197$	−32825.0	−0.845808	−0.422904	−	0.906174i	$-0.638989\pi$
$197$	−32825.0	−0.845808	−0.422904	+	0.906174i	$0.638989\pi$
$198$	7481.77	0.190842
$199$	26464.2i	0.668271i	0.942525	+	0.334136i	$0.108444\pi$
$199$	26464.2i	0.668271i	−0.942525	+	0.334136i	$0.891556\pi$
$200$	−1161.33	−0.0290331
$201$	− 30789.2i	− 0.762090i
$202$	32035.4i	0.785106i
$203$	0	0
$204$	4475.99	0.107555
$205$	−24507.2	−0.583157
$206$	46185.0i	1.08834i
$207$	27580.5	0.643666
$208$	− 6669.53i	− 0.154159i
$209$	3761.44i	0.0861115i
$210$	0	0
$211$	67056.3	1.50617	0.753087	−	0.657921i	$-0.228564\pi$
$211$	67056.3	1.50617	0.753087	+	0.657921i	$0.228564\pi$
$212$	17524.8	0.389925
$213$	− 23353.6i	− 0.514749i
$214$	−12435.1	−0.271532
$215$	81013.8i	1.75260i
$216$	3174.54i	0.0680414i
$217$	0	0
$218$	41571.6	0.874749
$219$	46603.9	0.971705
$220$	− 18772.4i	− 0.387859i
$221$	−11221.0	−0.229746
$222$	8263.14i	0.167664i
$223$	56260.1i	1.13133i	0.824634	+	0.565666i	$0.191381\pi$
$223$	56260.1i	1.13133i	−0.824634	+	0.565666i	$0.808619\pi$
$224$	0	0
$225$	−1385.74	−0.0273727
$226$	−6008.59	−0.117640
$227$	− 61148.1i	− 1.18667i	−0.804954	−	0.593337i	$-0.797810\pi$
$227$	− 61148.1i	− 1.18667i	0.804954	−	0.593337i	$-0.202190\pi$
$228$	−1595.99	−0.0307016
$229$	33803.7i	0.644605i	0.946637	+	0.322303i	$0.104457\pi$
$229$	33803.7i	0.644605i	−0.946637	+	0.322303i	$0.895543\pi$
$230$	− 69201.6i	− 1.30816i
$231$	0	0
$232$	−14065.3	−0.261320
$233$	8687.26	0.160019	0.0800094	−	0.996794i	$-0.474505\pi$
$233$	8687.26	0.160019	0.0800094	+	0.996794i	$0.474505\pi$
$234$	− 7958.37i	− 0.145342i
$235$	−94489.6	−1.71099
$236$	− 23479.0i	− 0.421556i
$237$	− 54283.3i	− 0.966428i
$238$	0	0
$239$	−15715.0	−0.275118	−0.137559	−	0.990494i	$-0.543926\pi$
$239$	−15715.0	−0.275118	−0.137559	+	0.990494i	$0.543926\pi$
$240$	7965.17	0.138284
$241$	5478.82i	0.0943307i	0.998887	+	0.0471654i	$0.0150188\pi$
$241$	5478.82i	0.0943307i	−0.998887	+	0.0471654i	$0.984981\pi$
$242$	14263.1	0.243547
$243$	3788.00i	0.0641500i
$244$	5322.77i	0.0894043i
$245$	0	0
$246$	−15037.9	−0.248494
$247$	4001.05	0.0655813
$248$	− 34374.1i	− 0.558892i
$249$	−6595.35	−0.106375
$250$	45817.7i	0.733083i
$251$	− 24350.9i	− 0.386516i	−0.981148	−	0.193258i	$-0.938095\pi$
$251$	− 24350.9i	− 0.386516i	0.981148	−	0.193258i	$-0.0619054\pi$
$252$	0	0
$253$	−100077.	−1.56348
$254$	−24036.2	−0.372561
$255$	− 13400.9i	− 0.206088i
$256$	4096.00	0.0625000
$257$	11606.7i	0.175729i	0.996132	+	0.0878647i	$0.0280043\pi$
$257$	11606.7i	0.175729i	−0.996132	+	0.0878647i	$0.971996\pi$
$258$	49711.0i	0.746815i
$259$	0	0
$260$	−19968.2	−0.295388
$261$	−16783.3	−0.246375
$262$	− 40933.8i	− 0.596320i
$263$	120668.	1.74453	0.872266	−	0.489031i	$-0.162649\pi$
$263$	120668.	1.74453	0.872266	+	0.489031i	$0.162649\pi$
$264$	− 11518.9i	− 0.165274i
$265$	− 52468.3i	− 0.747145i
$266$	0	0
$267$	18728.8	0.262716
$268$	−47403.1	−0.659989
$269$	27246.6i	0.376537i	0.982118	+	0.188269i	$0.0602876\pi$
$269$	27246.6i	0.376537i	−0.982118	+	0.188269i	$0.939712\pi$
$270$	9504.39	0.130376
$271$	− 97043.3i	− 1.32138i	−0.750660	−	0.660689i	$-0.770264\pi$
$271$	− 97043.3i	− 1.32138i	0.750660	−	0.660689i	$-0.229736\pi$
$272$	− 6891.24i	− 0.0931450i
$273$	0	0
$274$	−36359.9	−0.484308
$275$	5028.22	0.0664889
$276$	− 42462.9i	− 0.557432i
$277$	29752.8	0.387765	0.193882	−	0.981025i	$-0.437892\pi$
$277$	29752.8	0.387765	0.193882	+	0.981025i	$0.437892\pi$
$278$	− 14168.9i	− 0.183335i
$279$	− 41016.7i	− 0.526929i
$280$	0	0
$281$	−122275.	−1.54855	−0.774276	−	0.632849i	$-0.781886\pi$
$281$	−122275.	−1.54855	−0.774276	+	0.632849i	$0.781886\pi$
$282$	−57979.9	−0.729087
$283$	60700.7i	0.757916i	0.925414	+	0.378958i	$0.123718\pi$
$283$	60700.7i	0.757916i	−0.925414	+	0.378958i	$0.876282\pi$
$284$	−35955.3	−0.445785
$285$	4778.30i	0.0588280i
$286$	28877.3i	0.353040i
$287$	0	0
$288$	4887.52	0.0589256
$289$	71927.0	0.861184
$290$	42110.6i	0.500721i
$291$	10135.2	0.119687
$292$	− 71751.4i	− 0.841521i
$293$	− 29557.4i	− 0.344296i	−0.985071	−	0.172148i	$-0.944929\pi$
$293$	− 29557.4i	− 0.344296i	0.985071	−	0.172148i	$-0.0550707\pi$
$294$	0	0
$295$	−70294.7	−0.807752
$296$	12721.9	0.145201
$297$	− 13744.9i	− 0.155822i
$298$	−71839.0	−0.808961
$299$	106452.i	1.19072i
$300$	2133.49i	0.0237055i
$301$	0	0
$302$	51785.0	0.567794
$303$	58852.9	0.641036
$304$	2457.19i	0.0265883i
$305$	15936.1	0.171310
$306$	− 8222.92i	− 0.0878179i
$307$	− 107567.i	− 1.14131i	−0.821191	−	0.570654i	$-0.806690\pi$
$307$	− 107567.i	− 1.14131i	0.821191	−	0.570654i	$-0.193310\pi$
$308$	0	0
$309$	84847.3	0.888630
$310$	−102914.	−1.07091
$311$	− 43371.8i	− 0.448421i	−0.974541	−	0.224211i	$-0.928020\pi$
$311$	− 43371.8i	− 0.448421i	0.974541	−	0.224211i	$-0.0719804\pi$
$312$	−12252.7	−0.125870
$313$	− 107746.i	− 1.09980i	−0.835230	−	0.549900i	$-0.814666\pi$
$313$	− 107746.i	− 1.09980i	0.835230	−	0.549900i	$-0.185334\pi$
$314$	− 99686.3i	− 1.01106i
$315$	0	0
$316$	−83574.6	−0.836951
$317$	−155994.	−1.55235	−0.776174	−	0.630519i	$-0.782842\pi$
$317$	−155994.	−1.55235	−0.776174	+	0.630519i	$0.782842\pi$
$318$	− 32195.1i	− 0.318373i
$319$	60898.8	0.598449
$320$	− 12263.2i	− 0.119758i
$321$	22844.7i	0.221705i
$322$	0	0
$323$	4134.05	0.0396251
$324$	5832.00	0.0555556
$325$	− 5348.53i	− 0.0506370i
$326$	−412.776	−0.00388400
$327$	− 76371.9i	− 0.714230i
$328$	23152.3i	0.215202i
$329$	0	0
$330$	−34487.0	−0.316685
$331$	40218.7	0.367090	0.183545	−	0.983011i	$-0.441243\pi$
$331$	40218.7	0.367090	0.183545	+	0.983011i	$0.441243\pi$
$332$	10154.2i	0.0921234i
$333$	15180.4	0.136897
$334$	− 88569.6i	− 0.793947i
$335$	141922.i	1.26462i
$336$	0	0
$337$	90476.4	0.796665	0.398332	−	0.917241i	$-0.369589\pi$
$337$	90476.4	0.796665	0.398332	+	0.917241i	$0.369589\pi$
$338$	−50065.9	−0.438237
$339$	11038.5i	0.0960529i
$340$	−20632.0	−0.178477
$341$	148831.i	1.27992i
$342$	2932.02i	0.0250677i
$343$	0	0
$344$	76535.1	0.646761
$345$	−127131.	−1.06811
$346$	113465.i	0.947782i
$347$	32074.5	0.266379	0.133190	−	0.991091i	$-0.457478\pi$
$347$	32074.5	0.266379	0.133190	+	0.991091i	$0.457478\pi$
$348$	25839.6i	0.213367i
$349$	− 116783.i	− 0.958805i	−0.877595	−	0.479402i	$-0.840853\pi$
$349$	− 116783.i	− 0.958805i	0.877595	−	0.479402i	$-0.159147\pi$
$350$	0	0
$351$	−14620.5	−0.118672
$352$	−17734.6	−0.143132
$353$	− 124658.i	− 1.00039i	−0.865912	−	0.500197i	$-0.833261\pi$
$353$	− 124658.i	− 1.00039i	0.865912	−	0.500197i	$-0.166739\pi$
$354$	−43133.6	−0.344199
$355$	107648.i	0.854180i
$356$	− 28834.8i	− 0.227519i
$357$	0	0
$358$	141858.	1.10685
$359$	99442.1	0.771581	0.385790	−	0.922587i	$-0.373929\pi$
$359$	99442.1	0.771581	0.385790	+	0.922587i	$0.373929\pi$
$360$	− 14633.0i	− 0.112909i
$361$	128847.	0.988689
$362$	− 180947.i	− 1.38081i
$363$	− 26203.0i	− 0.198856i
$364$	0	0
$365$	−214820.	−1.61246
$366$	9778.56	0.0729983
$367$	− 88914.6i	− 0.660147i	−0.943955	−	0.330074i	$-0.892926\pi$
$367$	− 88914.6i	− 0.660147i	0.943955	−	0.330074i	$-0.107074\pi$
$368$	−65375.9	−0.482750
$369$	27626.3i	0.202895i
$370$	− 38088.7i	− 0.278223i
$371$	0	0
$372$	−63149.3	−0.456334
$373$	−91352.9	−0.656606	−0.328303	−	0.944573i	$-0.606477\pi$
$373$	−91352.9	−0.656606	−0.328303	+	0.944573i	$0.606477\pi$
$374$	29837.2i	0.213312i
$375$	84172.5	0.598560
$376$	89265.9i	0.631408i
$377$	− 64778.2i	− 0.455770i
$378$	0	0
$379$	6328.51	0.0440578	0.0220289	−	0.999757i	$-0.492987\pi$
$379$	6328.51	0.0440578	0.0220289	+	0.999757i	$0.492987\pi$
$380$	7356.68	0.0509465
$381$	44157.2i	0.304195i
$382$	120969.	0.828984
$383$	− 13436.0i	− 0.0915949i	−0.998951	−	0.0457974i	$-0.985417\pi$
$383$	− 13436.0i	− 0.0915949i	0.998951	−	0.0457974i	$-0.0145829\pi$
$384$	− 7524.83i	− 0.0510310i
$385$	0	0
$386$	24812.6	0.166532
$387$	91325.0	0.609772
$388$	− 15604.2i	− 0.103652i
$389$	88296.3	0.583503	0.291752	−	0.956494i	$-0.405762\pi$
$389$	88296.3	0.583503	0.291752	+	0.956494i	$0.405762\pi$
$390$	36683.9i	0.241183i
$391$	109990.i	0.719451i
$392$	0	0
$393$	−75200.2	−0.486894
$394$	92843.0	0.598077
$395$	250218.i	1.60370i
$396$	−21161.6	−0.134946
$397$	216587.i	1.37421i	0.726560	+	0.687103i	$0.241118\pi$
$397$	216587.i	1.37421i	−0.726560	+	0.687103i	$0.758882\pi$
$398$	− 74852.1i	− 0.472539i
$399$	0	0
$400$	3284.72	0.0205295
$401$	−5166.84	−0.0321319	−0.0160659	−	0.999871i	$-0.505114\pi$
$401$	−5166.84	−0.0321319	−0.0160659	+	0.999871i	$0.505114\pi$
$402$	87085.0i	0.538879i
$403$	158311.	0.974769
$404$	− 90609.9i	− 0.555153i
$405$	− 17460.7i	− 0.106451i
$406$	0	0
$407$	−55082.5	−0.332526
$408$	−12660.0	−0.0760525
$409$	− 38910.7i	− 0.232607i	−0.993214	−	0.116303i	$-0.962896\pi$
$409$	− 38910.7i	− 0.232607i	0.993214	−	0.116303i	$-0.0371045\pi$
$410$	69316.7	0.412354
$411$	66797.4i	0.395436i
$412$	− 130631.i	− 0.769576i
$413$	0	0
$414$	−78009.3	−0.455141
$415$	30401.1	0.176520
$416$	18864.3i	0.109007i
$417$	−26029.9	−0.149693
$418$	− 10639.0i	− 0.0608900i
$419$	263425.i	1.50048i	0.661167	+	0.750239i	$0.270062\pi$
$419$	263425.i	1.50048i	−0.661167	+	0.750239i	$0.729938\pi$
$420$	0	0
$421$	−16375.1	−0.0923889	−0.0461944	−	0.998932i	$-0.514709\pi$
$421$	−16375.1	−0.0923889	−0.0461944	+	0.998932i	$0.514709\pi$
$422$	−189664.	−1.06503
$423$	106516.i	0.595297i
$424$	−49567.6	−0.275719
$425$	− 5526.32i	− 0.0305955i
$426$	66054.0i	0.363982i
$427$	0	0
$428$	35171.7	0.192002
$429$	53050.9	0.288256
$430$	− 229142.i	− 1.23927i
$431$	−250416.	−1.34806	−0.674028	−	0.738705i	$-0.735437\pi$
$431$	−250416.	−1.34806	−0.674028	+	0.738705i	$0.735437\pi$
$432$	− 8978.95i	− 0.0481125i
$433$	− 91495.1i	− 0.488002i	−0.969775	−	0.244001i	$-0.921540\pi$
$433$	− 91495.1i	− 0.488002i	0.969775	−	0.244001i	$-0.0784601\pi$
$434$	0	0
$435$	77362.1	0.408837
$436$	−117582.	−0.618541
$437$	− 39219.0i	− 0.205368i
$438$	−131816.	−0.687099
$439$	8859.37i	0.0459699i	0.999736	+	0.0229850i	$0.00731699\pi$
$439$	8859.37i	0.0459699i	−0.999736	+	0.0229850i	$0.992683\pi$
$440$	53096.3i	0.274258i
$441$	0	0
$442$	31737.9	0.162455
$443$	300209.	1.52974	0.764868	−	0.644187i	$-0.222804\pi$
$443$	300209.	1.52974	0.764868	+	0.644187i	$0.222804\pi$
$444$	− 23371.7i	− 0.118556i
$445$	−86329.9	−0.435954
$446$	− 159127.i	− 0.799973i
$447$	131977.i	0.660514i
$448$	0	0
$449$	116866.	0.579691	0.289846	−	0.957073i	$-0.406396\pi$
$449$	116866.	0.579691	0.289846	+	0.957073i	$0.406396\pi$
$450$	3919.47	0.0193554
$451$	− 100243.i	− 0.492836i
$452$	16994.9	0.0831842
$453$	− 95135.2i	− 0.463601i
$454$	172953.i	0.839105i
$455$	0	0
$456$	4514.14	0.0217093
$457$	73745.8	0.353106	0.176553	−	0.984291i	$-0.443505\pi$
$457$	73745.8	0.353106	0.176553	+	0.984291i	$0.443505\pi$
$458$	− 95611.4i	− 0.455805i
$459$	−15106.5	−0.0717030
$460$	195732.i	0.925008i
$461$	− 88219.1i	− 0.415108i	−0.978224	−	0.207554i	$-0.933450\pi$
$461$	− 88219.1i	− 0.415108i	0.978224	−	0.207554i	$-0.0665502\pi$
$462$	0	0
$463$	297880.	1.38957	0.694784	−	0.719219i	$-0.255500\pi$
$463$	297880.	1.38957	0.694784	+	0.719219i	$0.255500\pi$
$464$	39782.6	0.184781
$465$	189065.i	0.874391i
$466$	−24571.3	−0.113150
$467$	− 187470.i	− 0.859601i	−0.902924	−	0.429801i	$-0.858584\pi$
$467$	− 187470.i	− 0.859601i	0.902924	−	0.429801i	$-0.141416\pi$
$468$	22509.7i	0.102773i
$469$	0	0
$470$	267257.	1.20985
$471$	−183135.	−0.825526
$472$	66408.5i	0.298085i
$473$	−331376.	−1.48115
$474$	153536.i	0.683368i
$475$	1970.50i	0.00873353i
$476$	0	0
$477$	−59146.2	−0.259950
$478$	44448.8	0.194538
$479$	120489.i	0.525142i	0.964913	+	0.262571i	$0.0845703\pi$
$479$	120489.i	0.525142i	−0.964913	+	0.262571i	$0.915430\pi$
$480$	−22528.9	−0.0977817
$481$	58591.4i	0.253247i
$482$	− 15496.4i	− 0.0667019i
$483$	0	0
$484$	−40342.2	−0.172214
$485$	−46718.1	−0.198610
$486$	− 10714.1i	− 0.0453609i
$487$	−267394.	−1.12744	−0.563721	−	0.825966i	$-0.690631\pi$
$487$	−267394.	−1.12744	−0.563721	+	0.825966i	$0.690631\pi$
$488$	− 15055.1i	− 0.0632184i
$489$	758.319i	0.00317128i
$490$	0	0
$491$	178364.	0.739851	0.369926	−	0.929061i	$-0.379383\pi$
$491$	178364.	0.739851	0.369926	+	0.929061i	$0.379383\pi$
$492$	42533.5	0.175712
$493$	− 66931.5i	− 0.275383i
$494$	−11316.7	−0.0463730
$495$	63356.7i	0.258573i
$496$	97224.7i	0.395196i
$497$	0	0
$498$	18654.5	0.0752184
$499$	263747.	1.05922	0.529610	−	0.848241i	$-0.322338\pi$
$499$	263747.	1.05922	0.529610	+	0.848241i	$0.322338\pi$
$500$	− 129592.i	− 0.518368i
$501$	−162713.	−0.648255
$502$	68874.7i	0.273308i
$503$	480056.i	1.89739i	0.316197	+	0.948694i	$0.397594\pi$
$503$	480056.i	1.89739i	−0.316197	+	0.948694i	$0.602406\pi$
$504$	0	0
$505$	−271281.	−1.06374
$506$	283060.	1.10555
$507$	91976.9i	0.357819i
$508$	67984.5	0.263441
$509$	− 60266.8i	− 0.232618i	−0.993213	−	0.116309i	$-0.962894\pi$
$509$	− 60266.8i	− 0.232618i	0.993213	−	0.116309i	$-0.0371062\pi$
$510$	37903.3i	0.145726i
$511$	0	0
$512$	−11585.2	−0.0441942
$513$	5386.46	0.0204677
$514$	− 32828.8i	− 0.124259i
$515$	−391101.	−1.47460
$516$	− 140604.i	− 0.528078i
$517$	− 386497.i	− 1.44599i
$518$	0	0
$519$	208448.	0.773861
$520$	56478.6	0.208871
$521$	− 287316.i	− 1.05848i	−0.848471	−	0.529242i	$-0.822476\pi$
$521$	− 287316.i	− 1.05848i	0.848471	−	0.529242i	$-0.177524\pi$
$522$	47470.3	0.174213
$523$	− 276444.i	− 1.01066i	−0.862927	−	0.505328i	$-0.831371\pi$
$523$	− 276444.i	− 1.01066i	0.862927	−	0.505328i	$-0.168629\pi$
$524$	115778.i	0.421662i
$525$	0	0
$526$	−341300.	−1.23357
$527$	163574.	0.588969
$528$	32580.5i	0.116866i
$529$	763619.	2.72876
$530$	148403.i	0.528311i
$531$	79241.5i	0.281037i
$532$	0	0
$533$	−106629.	−0.375336
$534$	−52973.0	−0.185768
$535$	− 105302.i	− 0.367900i
$536$	134076.	0.466683
$537$	− 260610.i	− 0.903739i
$538$	− 77065.1i	− 0.266252i
$539$	0	0
$540$	−26882.5	−0.0921895
$541$	−59664.0	−0.203853	−0.101927	−	0.994792i	$-0.532501\pi$
$541$	−59664.0	−0.203853	−0.101927	+	0.994792i	$0.532501\pi$
$542$	274480.i	0.934355i
$543$	−332420.	−1.12742
$544$	19491.4i	0.0658634i
$545$	352034.i	1.18520i
$546$	0	0
$547$	489585.	1.63627	0.818133	−	0.575030i	$-0.195010\pi$
$547$	489585.	1.63627	0.818133	+	0.575030i	$0.195010\pi$
$548$	102841.	0.342458
$549$	− 17964.4i	− 0.0596028i
$550$	−14222.0	−0.0470147
$551$	23865.5i	0.0786082i
$552$	120103.i	0.394164i
$553$	0	0
$554$	−84153.6	−0.274191
$555$	−69973.5	−0.227168
$556$	40075.7i	0.129638i
$557$	508534.	1.63912	0.819558	−	0.572996i	$-0.194219\pi$
$557$	508534.	1.63912	0.819558	+	0.572996i	$0.194219\pi$
$558$	116013.i	0.372595i
$559$	352486.i	1.12802i
$560$	0	0
$561$	54814.4	0.174168
$562$	345846.	1.09499
$563$	− 119817.i	− 0.378009i	−0.981976	−	0.189004i	$-0.939474\pi$
$563$	− 119817.i	− 0.378009i	0.981976	−	0.189004i	$-0.0605260\pi$
$564$	163992.	0.515542
$565$	− 50881.7i	− 0.159391i
$566$	− 171688.i	− 0.535927i
$567$	0	0
$568$	101697.	0.315218
$569$	−97659.4	−0.301640	−0.150820	−	0.988561i	$-0.548191\pi$
$569$	−97659.4	−0.301640	−0.150820	+	0.988561i	$0.548191\pi$
$570$	− 13515.1i	− 0.0415976i
$571$	47651.4	0.146151	0.0730757	−	0.997326i	$-0.476719\pi$
$571$	47651.4	0.146151	0.0730757	+	0.997326i	$0.476719\pi$
$572$	− 81677.3i	− 0.249637i
$573$	− 222234.i	− 0.676863i
$574$	0	0
$575$	−52427.2	−0.158570
$576$	−13824.0	−0.0416667
$577$	131457.i	0.394849i	0.980318	+	0.197425i	$0.0632578\pi$
$577$	131457.i	0.394849i	−0.980318	+	0.197425i	$0.936742\pi$
$578$	−203440.	−0.608949
$579$	− 45583.7i	− 0.135973i
$580$	− 119107.i	− 0.354063i
$581$	0	0
$582$	−28666.8	−0.0846316
$583$	214614.	0.631425
$584$	202944.i	0.595045i
$585$	67392.7	0.196925
$586$	83601.0i	0.243454i
$587$	− 135493.i	− 0.393224i	−0.980481	−	0.196612i	$-0.937006\pi$
$587$	− 135493.i	− 0.393224i	0.980481	−	0.196612i	$-0.0629940\pi$
$588$	0	0
$589$	−58325.0	−0.168122
$590$	198823.	0.571167
$591$	− 170564.i	− 0.488328i
$592$	−35983.1	−0.102673
$593$	188208.i	0.535216i	0.963528	+	0.267608i	$0.0862332\pi$
$593$	188208.i	0.535216i	−0.963528	+	0.267608i	$0.913767\pi$
$594$	38876.4i	0.110183i
$595$	0	0
$596$	203191.	0.572022
$597$	−137512.	−0.385827
$598$	− 301091.i	− 0.841969i
$599$	−78404.8	−0.218519	−0.109259	−	0.994013i	$-0.534848\pi$
$599$	−78404.8	−0.218519	−0.109259	+	0.994013i	$0.534848\pi$
$600$	− 6034.42i	− 0.0167623i
$601$	− 254898.i	− 0.705695i	−0.935681	−	0.352848i	$-0.885213\pi$
$601$	− 254898.i	− 0.705695i	0.935681	−	0.352848i	$-0.114787\pi$
$602$	0	0
$603$	159985.	0.439993
$604$	−146470.	−0.401491
$605$	120782.i	0.329983i
$606$	−166461.	−0.453281
$607$	565684.i	1.53531i	0.640863	+	0.767655i	$0.278577\pi$
$607$	565684.i	1.53531i	−0.640863	+	0.767655i	$0.721423\pi$
$608$	− 6949.97i	− 0.0188008i
$609$	0	0
$610$	−45074.0	−0.121134
$611$	−411118.	−1.10124
$612$	23257.9i	0.0620966i
$613$	−414221.	−1.10233	−0.551164	−	0.834397i	$-0.685816\pi$
$613$	−414221.	−1.10233	−0.551164	+	0.834397i	$0.685816\pi$
$614$	304246.i	0.807026i
$615$	− 127343.i	− 0.336686i
$616$	0	0
$617$	22896.0	0.0601435	0.0300717	−	0.999548i	$-0.490426\pi$
$617$	22896.0	0.0601435	0.0300717	+	0.999548i	$0.490426\pi$
$618$	−239984.	−0.628356
$619$	− 161155.i	− 0.420593i	−0.977638	−	0.210296i	$-0.932557\pi$
$619$	− 161155.i	− 0.420593i	0.977638	−	0.210296i	$-0.0674429\pi$
$620$	291085.	0.757245
$621$	143312.i	0.371621i
$622$	122674.i	0.317082i
$623$	0	0
$624$	34655.9	0.0890037
$625$	−355913.	−0.911139
$626$	304753.i	0.777676i
$627$	−19545.0	−0.0497165
$628$	281956.i	0.714926i
$629$	60539.0i	0.153015i
$630$	0	0
$631$	489038.	1.22824	0.614121	−	0.789212i	$-0.289511\pi$
$631$	489038.	1.22824	0.614121	+	0.789212i	$0.289511\pi$
$632$	236385.	0.591814
$633$	348435.i	0.869590i
$634$	441217.	1.09768
$635$	− 203542.i	− 0.504785i
$636$	91061.5i	0.225123i
$637$	0	0
$638$	−172248.	−0.423168
$639$	121349.	0.297190
$640$	34685.5i	0.0846815i
$641$	119340.	0.290448	0.145224	−	0.989399i	$-0.453610\pi$
$641$	119340.	0.290448	0.145224	+	0.989399i	$0.453610\pi$
$642$	− 64614.5i	− 0.156769i
$643$	− 324224.i	− 0.784194i	−0.919924	−	0.392097i	$-0.871750\pi$
$643$	− 324224.i	− 0.784194i	0.919924	−	0.392097i	$-0.128250\pi$
$644$	0	0
$645$	−420960.	−1.01186
$646$	−11692.9	−0.0280192
$647$	460781.i	1.10074i	0.834920	+	0.550372i	$0.185514\pi$
$647$	460781.i	1.10074i	−0.834920	+	0.550372i	$0.814486\pi$
$648$	−16495.4	−0.0392837
$649$	− 287531.i	− 0.682645i
$650$	15127.9i	0.0358057i
$651$	0	0
$652$	1167.51	0.00274641
$653$	−559124.	−1.31124	−0.655620	−	0.755091i	$-0.727593\pi$
$653$	−559124.	−1.31124	−0.655620	+	0.755091i	$0.727593\pi$
$654$	216012.i	0.505037i
$655$	346634.	0.807957
$656$	− 65484.6i	− 0.152171i
$657$	242161.i	0.561014i
$658$	0	0
$659$	−184372.	−0.424546	−0.212273	−	0.977210i	$-0.568087\pi$
$659$	−184372.	−0.424546	−0.212273	+	0.977210i	$0.568087\pi$
$660$	97544.1	0.223930
$661$	− 79226.4i	− 0.181329i	−0.995881	−	0.0906645i	$-0.971101\pi$
$661$	− 79226.4i	− 0.181329i	0.995881	−	0.0906645i	$-0.0288991\pi$
$662$	−113756.	−0.259572
$663$	− 58306.2i	− 0.132644i
$664$	− 28720.4i	− 0.0651411i
$665$	0	0
$666$	−42936.5	−0.0968007
$667$	−634967.	−1.42725
$668$	250513.i	0.561405i
$669$	−292336.	−0.653175
$670$	− 401416.i	− 0.894222i
$671$	65184.4i	0.144777i
$672$	0	0
$673$	−482896.	−1.06616	−0.533082	−	0.846064i	$-0.678966\pi$
$673$	−482896.	−1.06616	−0.533082	+	0.846064i	$0.678966\pi$
$674$	−255906.	−0.563327
$675$	− 7200.53i	− 0.0158036i
$676$	141608.	0.309880
$677$	− 380329.i	− 0.829817i	−0.909863	−	0.414908i	$-0.863814\pi$
$677$	− 380329.i	− 0.829817i	0.909863	−	0.414908i	$-0.136186\pi$
$678$	− 31221.6i	− 0.0679196i
$679$	0	0
$680$	58356.0	0.126202
$681$	317735.	0.685127
$682$	− 420956.i	− 0.905041i
$683$	−342069.	−0.733283	−0.366642	−	0.930362i	$-0.619493\pi$
$683$	−342069.	−0.733283	−0.366642	+	0.930362i	$0.619493\pi$
$684$	− 8293.01i	− 0.0177256i
$685$	− 307901.i	− 0.656191i
$686$	0	0
$687$	−175649.	−0.372163
$688$	−216474.	−0.457329
$689$	− 228286.i	− 0.480884i
$690$	359582.	0.755266
$691$	73062.6i	0.153017i	0.997069	+	0.0765084i	$0.0243772\pi$
$691$	73062.6i	0.153017i	−0.997069	+	0.0765084i	$0.975623\pi$
$692$	− 320927.i	− 0.670183i
$693$	0	0
$694$	−90720.3	−0.188359
$695$	119984.	0.248402
$696$	− 73085.3i	− 0.150873i
$697$	−110173.	−0.226783
$698$	330313.i	0.677977i
$699$	45140.3i	0.0923869i
$700$	0	0
$701$	−288287.	−0.586664	−0.293332	−	0.956011i	$-0.594764\pi$
$701$	−288287.	−0.586664	−0.293332	+	0.956011i	$0.594764\pi$
$702$	41352.9	0.0839135
$703$	− 21586.2i	− 0.0436783i
$704$	50160.9	0.101209
$705$	− 490982.i	− 0.987842i
$706$	352586.i	0.707386i
$707$	0	0
$708$	122000.	0.243385
$709$	−310512.	−0.617711	−0.308856	−	0.951109i	$-0.599946\pi$
$709$	−310512.	−0.617711	−0.308856	+	0.951109i	$0.599946\pi$
$710$	− 304475.i	− 0.603996i
$711$	282064.	0.557968
$712$	81557.3i	0.160880i
$713$	− 1.55179e6i	− 3.05250i
$714$	0	0
$715$	−244537.	−0.478335
$716$	−401236.	−0.782661
$717$	− 81657.7i	− 0.158840i
$718$	−281265.	−0.545590
$719$	10084.7i	0.0195077i	0.999952	+	0.00975383i	$0.00310479\pi$
$719$	10084.7i	0.0195077i	−0.999952	+	0.00975383i	$0.996895\pi$
$720$	41388.3i	0.0798385i
$721$	0	0
$722$	−364434.	−0.699109
$723$	−28468.8	−0.0544619
$724$	511794.i	0.976378i
$725$	31903.0	0.0606954
$726$	74113.3i	0.140612i
$727$	− 638552.i	− 1.20817i	−0.796921	−	0.604084i	$-0.793539\pi$
$727$	− 638552.i	− 1.20817i	0.796921	−	0.604084i	$-0.206461\pi$
$728$	0	0
$729$	−19683.0	−0.0370370
$730$	607602.	1.14018
$731$	364203.i	0.681567i
$732$	−27657.9	−0.0516176
$733$	− 826084.i	− 1.53750i	−0.639547	−	0.768752i	$-0.720878\pi$
$733$	− 826084.i	− 1.53750i	0.639547	−	0.768752i	$-0.279122\pi$
$734$	251488.i	0.466795i
$735$	0	0
$736$	184911.	0.341356
$737$	−580513.	−1.06875
$738$	− 78139.1i	− 0.143468i
$739$	769990.	1.40992	0.704962	−	0.709245i	$-0.250964\pi$
$739$	769990.	1.40992	0.704962	+	0.709245i	$0.250964\pi$
$740$	107731.i	0.196733i
$741$	20790.1i	0.0378634i
$742$	0	0
$743$	−611777.	−1.10819	−0.554097	−	0.832452i	$-0.686936\pi$
$743$	−611777.	−1.10819	−0.554097	+	0.832452i	$0.686936\pi$
$744$	178613.	0.322677
$745$	− 608343.i	− 1.09606i
$746$	258385.	0.464290
$747$	− 34270.4i	− 0.0614156i
$748$	− 84392.3i	− 0.150834i
$749$	0	0
$750$	−238076.	−0.423246
$751$	370622.	0.657129	0.328565	−	0.944481i	$-0.393435\pi$
$751$	370622.	0.657129	0.328565	+	0.944481i	$0.393435\pi$
$752$	− 252482.i	− 0.446473i
$753$	126531.	0.223155
$754$	183220.i	0.322278i
$755$	438523.i	0.769305i
$756$	0	0
$757$	298778.	0.521384	0.260692	−	0.965422i	$-0.416049\pi$
$757$	298778.	0.521384	0.260692	+	0.965422i	$0.416049\pi$
$758$	−17899.7	−0.0311536
$759$	− 520014.i	− 0.902676i
$760$	−20807.8	−0.0360246
$761$	803142.i	1.38683i	0.720539	+	0.693414i	$0.243894\pi$
$761$	803142.i	1.38683i	−0.720539	+	0.693414i	$0.756106\pi$
$762$	− 124896.i	− 0.215098i
$763$	0	0
$764$	−342151.	−0.586180
$765$	69632.9	0.118985
$766$	38002.6i	0.0647674i
$767$	−305847.	−0.519893
$768$	21283.4i	0.0360844i
$769$	452541.i	0.765253i	0.923903	+	0.382626i	$0.124980\pi$
$769$	452541.i	0.765253i	−0.923903	+	0.382626i	$0.875020\pi$
$770$	0	0
$771$	−60310.4	−0.101457
$772$	−70180.7	−0.117756
$773$	− 1.04853e6i	− 1.75478i	−0.479774	−	0.877392i	$-0.659281\pi$
$773$	− 1.04853e6i	− 1.75478i	0.479774	−	0.877392i	$-0.340719\pi$
$774$	−258306.	−0.431174
$775$	77967.8i	0.129811i
$776$	44135.4i	0.0732932i
$777$	0	0
$778$	−249740.	−0.412599
$779$	39284.2	0.0647355
$780$	− 103758.i	− 0.170542i
$781$	−440320.	−0.721882
$782$	− 311100.i	− 0.508729i
$783$	− 87208.5i	− 0.142244i
$784$	0	0
$785$	844159.	1.36989
$786$	212698.	0.344286
$787$	− 195967.i	− 0.316398i	−0.987407	−	0.158199i	$-0.949431\pi$
$787$	− 195967.i	− 0.316398i	0.987407	−	0.158199i	$-0.0505687\pi$
$788$	−262600.	−0.422904
$789$	627007.i	1.00721i
$790$	− 707722.i	− 1.13399i
$791$	0	0
$792$	59854.2	0.0954210
$793$	69336.7	0.110260
$794$	− 612601.i	− 0.971710i
$795$	272633.	0.431364
$796$	211714.i	0.334136i
$797$	66453.8i	0.104617i	0.998631	+	0.0523086i	$0.0166579\pi$
$797$	66453.8i	0.104617i	−0.998631	+	0.0523086i	$0.983342\pi$
$798$	0	0
$799$	−424784.	−0.665387
$800$	−9290.60	−0.0145166
$801$	97317.6i	0.151679i
$802$	14614.0	0.0227207
$803$	− 878691.i	− 1.36272i
$804$	− 246314.i	− 0.381045i
$805$	0	0
$806$	−447772.	−0.689266
$807$	−141578.	−0.217394
$808$	256284.i	0.392553i
$809$	82304.6	0.125755	0.0628777	−	0.998021i	$-0.479972\pi$
$809$	82304.6	0.125755	0.0628777	+	0.998021i	$0.479972\pi$
$810$	49386.2i	0.0752724i
$811$	469097.i	0.713215i	0.934254	+	0.356608i	$0.116067\pi$
$811$	469097.i	0.713215i	−0.934254	+	0.356608i	$0.883933\pi$
$812$	0	0
$813$	504252.	0.762898
$814$	155797.	0.235131
$815$	− 3495.45i	− 0.00526245i
$816$	35807.9	0.0537773
$817$	− 129863.i	− 0.194554i
$818$	110056.i	0.164478i
$819$	0	0
$820$	−196057.	−0.291578
$821$	−5379.52	−0.00798099	−0.00399050	−	0.999992i	$-0.501270\pi$
$821$	−5379.52	−0.00798099	−0.00399050	+	0.999992i	$0.501270\pi$
$822$	− 188932.i	− 0.279615i
$823$	−969806.	−1.43181	−0.715905	−	0.698198i	$-0.753986\pi$
$823$	−969806.	−1.43181	−0.715905	+	0.698198i	$0.753986\pi$
$824$	369480.i	0.544172i
$825$	26127.4i	0.0383874i
$826$	0	0
$827$	838747.	1.22637	0.613183	−	0.789941i	$-0.289889\pi$
$827$	838747.	1.22637	0.613183	+	0.789941i	$0.289889\pi$
$828$	220644.	0.321833
$829$	883703.i	1.28587i	0.765920	+	0.642935i	$0.222284\pi$
$829$	883703.i	1.28587i	−0.765920	+	0.642935i	$0.777716\pi$
$830$	−85987.3	−0.124818
$831$	154600.i	0.223876i
$832$	− 53356.3i	− 0.0770795i
$833$	0	0
$834$	73623.7	0.105849
$835$	750020.	1.07572
$836$	30091.5i	0.0430558i
$837$	213129.	0.304222
$838$	− 745080.i	− 1.06100i
$839$	− 1.12626e6i	− 1.59998i	−0.600011	−	0.799992i	$-0.704837\pi$
$839$	− 1.12626e6i	− 1.59998i	0.600011	−	0.799992i	$-0.295163\pi$
$840$	0	0
$841$	−320891.	−0.453696
$842$	46315.8	0.0653288
$843$	− 635360.i	− 0.894056i
$844$	536451.	0.753087
$845$	− 423965.i	− 0.593768i
$846$	− 301272.i	− 0.420938i
$847$	0	0
$848$	140198.	0.194963
$849$	−315410.	−0.437583
$850$	15630.8i	0.0216343i
$851$	574323.	0.793043
$852$	− 186829.i	− 0.257374i
$853$	805486.i	1.10703i	0.832839	+	0.553516i	$0.186714\pi$
$853$	805486.i	1.10703i	−0.832839	+	0.553516i	$0.813286\pi$
$854$	0	0
$855$	−24828.8	−0.0339643
$856$	−99480.6	−0.135766
$857$	980477.i	1.33498i	0.744618	+	0.667491i	$0.232632\pi$
$857$	980477.i	1.33498i	−0.744618	+	0.667491i	$0.767368\pi$
$858$	−150051.	−0.203828
$859$	− 433780.i	− 0.587873i	−0.955825	−	0.293936i	$-0.905035\pi$
$859$	− 433780.i	− 0.587873i	0.955825	−	0.293936i	$-0.0949654\pi$
$860$	648111.i	0.876299i
$861$	0	0
$862$	708284.	0.953220
$863$	−303157.	−0.407048	−0.203524	−	0.979070i	$-0.565240\pi$
$863$	−303157.	−0.407048	−0.203524	+	0.979070i	$0.565240\pi$
$864$	25396.3i	0.0340207i
$865$	−960836.	−1.28415
$866$	258787.i	0.345070i
$867$	373744.i	0.497205i
$868$	0	0
$869$	−1.02348e6	−1.35532
$870$	−218813.	−0.289091
$871$	617493.i	0.813946i
$872$	332573.	0.437375
$873$	52664.2i	0.0691015i
$874$	110928.i	0.145217i
$875$	0	0
$876$	372831.	0.485852
$877$	355000.	0.461562	0.230781	−	0.973006i	$-0.425872\pi$
$877$	355000.	0.461562	0.230781	+	0.973006i	$0.425872\pi$
$878$	− 25058.1i	− 0.0325057i
$879$	153585.	0.198779
$880$	− 150179.i	− 0.193929i
$881$	− 320002.i	− 0.412288i	−0.978522	−	0.206144i	$-0.933909\pi$
$881$	− 320002.i	− 0.412288i	0.978522	−	0.206144i	$-0.0660915\pi$
$882$	0	0
$883$	−1.08605e6	−1.39293	−0.696467	−	0.717589i	$-0.745246\pi$
$883$	−1.08605e6	−1.39293	−0.696467	+	0.717589i	$0.745246\pi$
$884$	−89768.2	−0.114873
$885$	− 365262.i	− 0.466356i
$886$	−849120.	−1.08169
$887$	1.28423e6i	1.63229i	0.577848	+	0.816144i	$0.303893\pi$
$887$	1.28423e6i	1.63229i	−0.577848	+	0.816144i	$0.696107\pi$
$888$	66105.1i	0.0838319i
$889$	0	0
$890$	244178.	0.308266
$891$	71420.5	0.0899638
$892$	450080.i	0.565666i
$893$	151464.	0.189935
$894$	− 373286.i	− 0.467054i
$895$	1.20128e6i	1.49967i
$896$	0	0
$897$	−553140.	−0.687465
$898$	−330548.	−0.409904
$899$	944299.i	1.16840i
$900$	−11085.9	−0.0136863
$901$	− 235874.i	− 0.290557i
$902$	283531.i	0.348487i
$903$	0	0
$904$	−48068.7	−0.0588201
$905$	1.53228e6	1.87086
$906$	269083.i	0.327816i
$907$	48435.5	0.0588775	0.0294388	−	0.999567i	$-0.490628\pi$
$907$	48435.5	0.0588775	0.0294388	+	0.999567i	$0.490628\pi$
$908$	− 489185.i	− 0.593337i
$909$	305808.i	0.370102i
$910$	0	0
$911$	727675.	0.876801	0.438400	−	0.898780i	$-0.355545\pi$
$911$	727675.	0.876801	0.438400	+	0.898780i	$0.355545\pi$
$912$	−12767.9	−0.0153508
$913$	124352.i	0.149180i
$914$	−208584.	−0.249683
$915$	82806.3i	0.0989056i
$916$	270430.i	0.322303i
$917$	0	0
$918$	42727.5	0.0507017
$919$	87715.9	0.103860	0.0519299	−	0.998651i	$-0.483463\pi$
$919$	87715.9	0.103860	0.0519299	+	0.998651i	$0.483463\pi$
$920$	− 553613.i	− 0.654080i
$921$	558935.	0.658934
$922$	249521.i	0.293526i
$923$	468369.i	0.549775i
$924$	0	0
$925$	−28856.1	−0.0337251
$926$	−842533.	−0.982573
$927$	440879.i	0.513051i
$928$	−112522.	−0.130660
$929$	901913.i	1.04504i	0.852627	+	0.522520i	$0.175008\pi$
$929$	901913.i	1.04504i	−0.852627	+	0.522520i	$0.824992\pi$
$930$	− 534757.i	− 0.618288i
$931$	0	0
$932$	69498.1	0.0800094
$933$	225366.	0.258896
$934$	530244.i	0.607830i
$935$	−252666.	−0.289017
$936$	− 63667.0i	− 0.0726712i
$937$	1.24186e6i	1.41447i	0.706978	+	0.707236i	$0.250058\pi$
$937$	1.24186e6i	1.41447i	−0.706978	+	0.707236i	$0.749942\pi$
$938$	0	0
$939$	559867.	0.634970
$940$	−755917.	−0.855496
$941$	− 426245.i	− 0.481371i	−0.970603	−	0.240685i	$-0.922628\pi$
$941$	− 426245.i	− 0.481371i	0.970603	−	0.240685i	$-0.0773722\pi$
$942$	517985.	0.583735
$943$	1.04520e6i	1.17537i
$944$	− 187832.i	− 0.210778i
$945$	0	0
$946$	937274.	1.04733
$947$	27330.4	0.0304752	0.0152376	−	0.999884i	$-0.495150\pi$
$947$	27330.4	0.0304752	0.0152376	+	0.999884i	$0.495150\pi$
$948$	− 434266.i	− 0.483214i
$949$	−934665.	−1.03782
$950$	− 5573.42i	− 0.00617554i
$951$	− 810568.i	− 0.896248i
$952$	0	0
$953$	1.30093e6	1.43242	0.716208	−	0.697887i	$-0.245876\pi$
$953$	1.30093e6	1.43242	0.716208	+	0.697887i	$0.245876\pi$
$954$	167291.	0.183813
$955$	1.02438e6i	1.12319i
$956$	−125720.	−0.137559
$957$	316439.i	0.345515i
$958$	− 340794.i	− 0.371331i
$959$	0	0
$960$	63721.4	0.0691421
$961$	−1.38425e6	−1.49888
$962$	− 165721.i	− 0.179072i
$963$	−118705.	−0.128001
$964$	43830.6i	0.0471654i
$965$	210117.i	0.225635i
$966$	0	0
$967$	463079.	0.495225	0.247612	−	0.968859i	$-0.420354\pi$
$967$	463079.	0.495225	0.247612	+	0.968859i	$0.420354\pi$
$968$	114105.	0.121774
$969$	21481.1i	0.0228776i
$970$	132139.	0.140439
$971$	63188.7i	0.0670195i	0.999438	+	0.0335098i	$0.0106685\pi$
$971$	63188.7i	0.0670195i	−0.999438	+	0.0335098i	$0.989332\pi$
$972$	30304.0i	0.0320750i
$973$	0	0
$974$	756305.	0.797221
$975$	27791.8	0.0292353
$976$	42582.2i	0.0447021i
$977$	1.43899e6	1.50754	0.753772	−	0.657136i	$-0.228232\pi$
$977$	1.43899e6	1.50754	0.753772	+	0.657136i	$0.228232\pi$
$978$	− 2144.85i	− 0.00224243i
$979$	− 353121.i	− 0.368432i
$980$	0	0
$981$	396840.	0.412361
$982$	−504490.	−0.523154
$983$	− 400596.i	− 0.414572i	−0.978280	−	0.207286i	$-0.933537\pi$
$983$	− 400596.i	− 0.414572i	0.978280	−	0.207286i	$-0.0664630\pi$
$984$	−120303.	−0.124247
$985$	786209.i	0.810336i
$986$	189311.i	0.194725i
$987$	0	0
$988$	32008.4	0.0327906
$989$	3.45512e6	3.53241
$990$	− 179200.i	− 0.182838i
$991$	198549.	0.202172	0.101086	−	0.994878i	$-0.467768\pi$
$991$	198549.	0.202172	0.101086	+	0.994878i	$0.467768\pi$
$992$	− 274993.i	− 0.279446i
$993$	208983.i	0.211939i
$994$	0	0
$995$	633858.	0.640245
$996$	−52762.8	−0.0531875
$997$	− 914786.i	− 0.920299i	−0.887841	−	0.460150i	$-0.847796\pi$
$997$	− 914786.i	− 0.920299i	0.887841	−	0.460150i	$-0.152204\pi$
$998$	−745988.	−0.748981
$999$	78879.5i	0.0790375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.5.c.a.97.2		4
3.2	odd	2		882.5.c.a.685.4		4
7.2	even	3		42.5.g.a.31.2	yes	4
7.3	odd	6		42.5.g.a.19.2	✓	4
7.4	even	3		294.5.g.c.19.2		4
7.5	odd	6		294.5.g.c.31.2		4
7.6	odd	2	inner	294.5.c.a.97.1		4
21.2	odd	6		126.5.n.b.73.1		4
21.17	even	6		126.5.n.b.19.1		4
21.20	even	2		882.5.c.a.685.3		4
28.3	even	6		336.5.bh.d.145.1		4
28.23	odd	6		336.5.bh.d.241.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.2	✓	4	7.3	odd	6
42.5.g.a.31.2	yes	4	7.2	even	3
126.5.n.b.19.1		4	21.17	even	6
126.5.n.b.73.1		4	21.2	odd	6
294.5.c.a.97.1		4	7.6	odd	2	inner
294.5.c.a.97.2		4	1.1	even	1	trivial
294.5.g.c.19.2		4	7.4	even	3
294.5.g.c.31.2		4	7.5	odd	6
336.5.bh.d.145.1		4	28.3	even	6
336.5.bh.d.241.1		4	28.23	odd	6
882.5.c.a.685.3		4	21.20	even	2
882.5.c.a.685.4		4	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	294.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -23.9515i q^{5} -14.6969i q^{6} -22.6274 q^{8} -27.0000 q^{9} +67.7452i q^{10} +97.9706 q^{11} +41.5692i q^{12} -104.211i q^{13} +124.456 q^{15} +64.0000 q^{16} -107.676i q^{17} +76.3675 q^{18} +38.3935i q^{19} -191.612i q^{20} -277.103 q^{22} -1021.50 q^{23} -117.576i q^{24} +51.3238 q^{25} +294.755i q^{26} -140.296i q^{27} +621.603 q^{29} -352.014 q^{30} +1519.14i q^{31} -181.019 q^{32} +509.070i q^{33} +304.553i q^{34} -216.000 q^{36} -562.235 q^{37} -108.593i q^{38} +541.499 q^{39} +541.961i q^{40} -1023.20i q^{41} -3382.41 q^{43} +783.765 q^{44} +646.692i q^{45} +2889.23 q^{46} -3945.03i q^{47} +332.554i q^{48} -145.166 q^{50} +559.499 q^{51} -833.692i q^{52} +2190.60 q^{53} +396.817i q^{54} -2346.55i q^{55} -199.499 q^{57} -1758.16 q^{58} -2934.87i q^{59} +995.647 q^{60} +665.346i q^{61} -4296.76i q^{62} +512.000 q^{64} -2496.03 q^{65} -1439.87i q^{66} -5925.38 q^{67} -861.405i q^{68} -5307.86i q^{69} -4494.41 q^{71} +610.940 q^{72} -8968.93i q^{73} +1590.24 q^{74} +266.686i q^{75} +307.148i q^{76} -1531.59 q^{78} -10446.8 q^{79} -1532.90i q^{80} +729.000 q^{81} +2894.04i q^{82} +1269.28i q^{83} -2579.00 q^{85} +9566.89 q^{86} +3229.94i q^{87} -2216.82 q^{88} -3604.36i q^{89} -1829.12i q^{90} -8171.99 q^{92} -7893.66 q^{93} +11158.2i q^{94} +919.584 q^{95} -940.604i q^{96} -1950.53i q^{97} -2645.21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{4} - 108 q^{9} + 324 q^{11} + 396 q^{15} + 256 q^{16} - 192 q^{22} - 624 q^{23} + 952 q^{25} + 2724 q^{29} - 288 q^{30} - 864 q^{36} - 2792 q^{37} - 1296 q^{39} - 632 q^{43} + 2592 q^{44} + 9792 q^{46}+ \cdots - 8748 q^{99}+O(q^{100}) \) 4 * q + 32 * q^4 - 108 * q^9 + 324 * q^11 + 396 * q^15 + 256 * q^16 - 192 * q^22 - 624 * q^23 + 952 * q^25 + 2724 * q^29 - 288 * q^30 - 864 * q^36 - 2792 * q^37 - 1296 * q^39 - 632 * q^43 + 2592 * q^44 + 9792 * q^46 + 2112 * q^50 - 1224 * q^51 + 2076 * q^53 + 2664 * q^57 + 672 * q^58 + 3168 * q^60 + 2048 * q^64 + 1488 * q^65 - 29200 * q^67 - 9696 * q^71 - 1536 * q^74 - 9792 * q^78 - 7948 * q^79 + 2916 * q^81 + 1224 * q^85 + 36480 * q^86 - 1536 * q^88 - 4992 * q^92 - 22716 * q^93 - 6504 * q^95 - 8748 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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