LMFDB - Embedded newform 637.6.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,6,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	637.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:	$102.164493221$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 250x^{6} + 210x^{5} + 20076x^{4} - 12252x^{3} - 544784x^{2} + 65648x + 2393792 $ x^8 - x^7 - 250x^6 + 210x^5 + 20076x^4 - 12252x^3 - 544784x^2 + 65648x + 2393792
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.33047$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.33047 q^{2} -3.45560 q^{3} -26.5689 q^{4} -94.0769 q^{5} +8.05316 q^{6} +136.493 q^{8} -231.059 q^{9} +219.243 q^{10} -141.785 q^{11} +91.8115 q^{12} +169.000 q^{13} +325.092 q^{15} +532.113 q^{16} -1287.76 q^{17} +538.475 q^{18} -1912.62 q^{19} +2499.52 q^{20} +330.426 q^{22} +1069.34 q^{23} -471.665 q^{24} +5725.47 q^{25} -393.849 q^{26} +1638.16 q^{27} +3439.24 q^{29} -757.616 q^{30} -4842.73 q^{31} -5607.85 q^{32} +489.953 q^{33} +3001.09 q^{34} +6138.98 q^{36} +9538.53 q^{37} +4457.30 q^{38} -583.996 q^{39} -12840.8 q^{40} +14570.9 q^{41} +11985.1 q^{43} +3767.09 q^{44} +21737.3 q^{45} -2492.06 q^{46} -12145.7 q^{47} -1838.77 q^{48} -13343.0 q^{50} +4449.99 q^{51} -4490.15 q^{52} +32750.2 q^{53} -3817.67 q^{54} +13338.7 q^{55} +6609.25 q^{57} -8015.04 q^{58} +48082.8 q^{59} -8637.34 q^{60} +37581.5 q^{61} +11285.8 q^{62} -3958.69 q^{64} -15899.0 q^{65} -1141.82 q^{66} -12664.7 q^{67} +34214.5 q^{68} -3695.20 q^{69} -71435.7 q^{71} -31537.9 q^{72} -53368.5 q^{73} -22229.2 q^{74} -19784.9 q^{75} +50816.3 q^{76} +1360.98 q^{78} -14516.6 q^{79} -50059.5 q^{80} +50486.5 q^{81} -33957.1 q^{82} -78340.8 q^{83} +121149. q^{85} -27930.9 q^{86} -11884.6 q^{87} -19352.7 q^{88} +24546.1 q^{89} -50658.1 q^{90} -28411.2 q^{92} +16734.5 q^{93} +28305.2 q^{94} +179934. q^{95} +19378.5 q^{96} +80624.4 q^{97} +32760.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 28 q^{3} + 245 q^{4} - 219 q^{5} - 435 q^{6} - 57 q^{8} + 930 q^{9} + 948 q^{10} + 184 q^{11} - 463 q^{12} + 1352 q^{13} - 256 q^{15} + 4953 q^{16} - 2278 q^{17} - 5308 q^{18} - 4959 q^{19}+ \cdots + 90754 q^{99}+O(q^{100}) $ 8 * q - q^2 - 28 * q^3 + 245 * q^4 - 219 * q^5 - 435 * q^6 - 57 * q^8 + 930 * q^9 + 948 * q^10 + 184 * q^11 - 463 * q^12 + 1352 * q^13 - 256 * q^15 + 4953 * q^16 - 2278 * q^17 - 5308 * q^18 - 4959 * q^19 - 6684 * q^20 - 2009 * q^22 + 1889 * q^23 - 26021 * q^24 + 4505 * q^25 - 169 * q^26 - 9016 * q^27 + 15265 * q^29 + 24204 * q^30 - 6805 * q^31 + 1335 * q^32 + 12892 * q^33 - 5828 * q^34 + 58838 * q^36 + 5534 * q^37 - 506 * q^38 - 4732 * q^39 + 56256 * q^40 - 31176 * q^41 - 391 * q^43 + 14047 * q^44 - 29403 * q^45 - 30027 * q^46 - 1539 * q^47 + 106629 * q^48 - 24367 * q^50 - 71892 * q^51 + 41405 * q^52 + 19553 * q^53 + 8155 * q^54 - 69414 * q^55 + 54432 * q^57 - 148020 * q^58 - 90596 * q^59 - 299448 * q^60 + 58218 * q^61 - 7697 * q^62 + 61681 * q^64 - 37011 * q^65 + 145411 * q^66 - 89884 * q^67 - 120612 * q^68 - 24278 * q^69 + 2308 * q^71 - 317742 * q^72 + 69187 * q^73 + 52027 * q^74 + 154856 * q^75 + 47258 * q^76 - 73515 * q^78 - 167799 * q^79 - 173400 * q^80 + 163984 * q^81 + 49553 * q^82 - 101449 * q^83 + 24684 * q^85 - 357720 * q^86 - 61908 * q^87 - 270819 * q^88 - 51833 * q^89 + 567124 * q^90 - 542963 * q^92 + 132644 * q^93 + 122399 * q^94 + 188103 * q^95 - 871725 * q^96 - 295025 * q^97 + 90754 * q^99

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 $

$2$	−2.33047	−0.411972	−0.205986	−	0.978555i	$-0.566040\pi$
$2$	−2.33047	−0.411972	−0.205986	+	0.978555i	$0.566040\pi$
$3$	−3.45560	−0.221677	−0.110838	−	0.993838i	$-0.535354\pi$
$3$	−3.45560	−0.221677	−0.110838	+	0.993838i	$0.535354\pi$
$4$	−26.5689	−0.830279
$5$	−94.0769	−1.68290	−0.841450	−	0.540336i	$-0.818297\pi$
$5$	−94.0769	−1.68290	−0.841450	+	0.540336i	$0.818297\pi$
$6$	8.05316	0.0913247
$7$	0	0
$7$	0	0
$8$	136.493	0.754024
$9$	−231.059	−0.950859
$10$	219.243	0.693308
$11$	−141.785	−0.353305	−0.176653	−	0.984273i	$-0.556527\pi$
$11$	−141.785	−0.353305	−0.176653	+	0.984273i	$0.556527\pi$
$12$	91.8115	0.184053
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	0	0
$15$	325.092	0.373059
$16$	532.113	0.519641
$17$	−1287.76	−1.08072	−0.540361	−	0.841434i	$-0.681712\pi$
$17$	−1287.76	−1.08072	−0.540361	+	0.841434i	$0.681712\pi$
$18$	538.475	0.391728
$19$	−1912.62	−1.21547	−0.607736	−	0.794139i	$-0.707922\pi$
$19$	−1912.62	−1.21547	−0.607736	+	0.794139i	$0.707922\pi$
$20$	2499.52	1.39728
$21$	0	0
$22$	330.426	0.145552
$23$	1069.34	0.421498	0.210749	−	0.977540i	$-0.432410\pi$
$23$	1069.34	0.421498	0.210749	+	0.977540i	$0.432410\pi$
$24$	−471.665	−0.167150
$25$	5725.47	1.83215
$26$	−393.849	−0.114261
$27$	1638.16	0.432460
$28$	0	0
$29$	3439.24	0.759395	0.379697	−	0.925111i	$-0.376028\pi$
$29$	3439.24	0.759395	0.379697	+	0.925111i	$0.376028\pi$
$30$	−757.616	−0.153690
$31$	−4842.73	−0.905079	−0.452539	−	0.891744i	$-0.649482\pi$
$31$	−4842.73	−0.905079	−0.452539	+	0.891744i	$0.649482\pi$
$32$	−5607.85	−0.968102
$33$	489.953	0.0783195
$34$	3001.09	0.445227
$35$	0	0
$36$	6138.98	0.789478
$37$	9538.53	1.14545	0.572726	−	0.819747i	$-0.305886\pi$
$37$	9538.53	1.14545	0.572726	+	0.819747i	$0.305886\pi$
$38$	4457.30	0.500741
$39$	−583.996	−0.0614820
$40$	−12840.8	−1.26895
$41$	14570.9	1.35372	0.676859	−	0.736113i	$-0.263341\pi$
$41$	14570.9	1.35372	0.676859	+	0.736113i	$0.263341\pi$
$42$	0	0
$43$	11985.1	0.988487	0.494243	−	0.869324i	$-0.335445\pi$
$43$	11985.1	0.988487	0.494243	+	0.869324i	$0.335445\pi$
$44$	3767.09	0.293342
$45$	21737.3	1.60020
$46$	−2492.06	−0.173646
$47$	−12145.7	−0.802007	−0.401003	−	0.916077i	$-0.631338\pi$
$47$	−12145.7	−0.802007	−0.401003	+	0.916077i	$0.631338\pi$
$48$	−1838.77	−0.115192
$49$	0	0
$50$	−13343.0	−0.754795
$51$	4449.99	0.239571
$52$	−4490.15	−0.230278
$53$	32750.2	1.60149	0.800745	−	0.599006i	$-0.204437\pi$
$53$	32750.2	1.60149	0.800745	+	0.599006i	$0.204437\pi$
$54$	−3817.67	−0.178162
$55$	13338.7	0.594577
$56$	0	0
$57$	6609.25	0.269442
$58$	−8015.04	−0.312850
$59$	48082.8	1.79829	0.899145	−	0.437651i	$-0.144190\pi$
$59$	48082.8	1.79829	0.899145	+	0.437651i	$0.144190\pi$
$60$	−8637.34	−0.309743
$61$	37581.5	1.29315	0.646577	−	0.762849i	$-0.276200\pi$
$61$	37581.5	1.29315	0.646577	+	0.762849i	$0.276200\pi$
$62$	11285.8	0.372867
$63$	0	0
$64$	−3958.69	−0.120810
$65$	−15899.0	−0.466752
$66$	−1141.82	−0.0322655
$67$	−12664.7	−0.344674	−0.172337	−	0.985038i	$-0.555132\pi$
$67$	−12664.7	−0.344674	−0.172337	+	0.985038i	$0.555132\pi$
$68$	34214.5	0.897300
$69$	−3695.20	−0.0934362
$70$	0	0
$71$	−71435.7	−1.68178	−0.840891	−	0.541205i	$-0.817968\pi$
$71$	−71435.7	−1.68178	−0.840891	+	0.541205i	$0.817968\pi$
$72$	−31537.9	−0.716971
$73$	−53368.5	−1.17214	−0.586068	−	0.810262i	$-0.699325\pi$
$73$	−53368.5	−1.17214	−0.586068	+	0.810262i	$0.699325\pi$
$74$	−22229.2	−0.471895
$75$	−19784.9	−0.406145
$76$	50816.3	1.00918
$77$	0	0
$78$	1360.98	0.0253289
$79$	−14516.6	−0.261696	−0.130848	−	0.991402i	$-0.541770\pi$
$79$	−14516.6	−0.261696	−0.130848	+	0.991402i	$0.541770\pi$
$80$	−50059.5	−0.874504
$81$	50486.5	0.854993
$82$	−33957.1	−0.557694
$83$	−78340.8	−1.24823	−0.624113	−	0.781334i	$-0.714539\pi$
$83$	−78340.8	−1.24823	−0.624113	+	0.781334i	$0.714539\pi$
$84$	0	0
$85$	121149.	1.81874
$86$	−27930.9	−0.407229
$87$	−11884.6	−0.168340
$88$	−19352.7	−0.266401
$89$	24546.1	0.328479	0.164240	−	0.986420i	$-0.447483\pi$
$89$	24546.1	0.328479	0.164240	+	0.986420i	$0.447483\pi$
$90$	−50658.1	−0.659239
$91$	0	0
$92$	−28411.2	−0.349961
$93$	16734.5	0.200635
$94$	28305.2	0.330405
$95$	179934.	2.04552
$96$	19378.5	0.214606
$97$	80624.4	0.870035	0.435018	−	0.900422i	$-0.356742\pi$
$97$	80624.4	0.870035	0.435018	+	0.900422i	$0.356742\pi$
$98$	0	0
$99$	32760.8	0.335943
$100$	−152120.	−1.52120
$101$	−137332.	−1.33958	−0.669789	−	0.742551i	$-0.733616\pi$
$101$	−137332.	−1.33958	−0.669789	+	0.742551i	$0.733616\pi$
$102$	−10370.6	−0.0986965
$103$	62513.9	0.580609	0.290304	−	0.956934i	$-0.406243\pi$
$103$	62513.9	0.580609	0.290304	+	0.956934i	$0.406243\pi$
$104$	23067.3	0.209129
$105$	0	0
$106$	−76323.3	−0.659769
$107$	−210684.	−1.77899	−0.889494	−	0.456947i	$-0.848943\pi$
$107$	−210684.	−1.77899	−0.889494	+	0.456947i	$0.848943\pi$
$108$	−43524.0	−0.359062
$109$	−14943.2	−0.120470	−0.0602348	−	0.998184i	$-0.519185\pi$
$109$	−14943.2	−0.120470	−0.0602348	+	0.998184i	$0.519185\pi$
$110$	−31085.5	−0.244949
$111$	−32961.3	−0.253920
$112$	0	0
$113$	93907.9	0.691841	0.345920	−	0.938264i	$-0.387567\pi$
$113$	93907.9	0.691841	0.345920	+	0.938264i	$0.387567\pi$
$114$	−15402.6	−0.111003
$115$	−100600.	−0.709339
$116$	−91376.9	−0.630509
$117$	−39048.9	−0.263721
$118$	−112055.	−0.740846
$119$	0	0
$120$	44372.8	0.281296
$121$	−140948.	−0.875176
$122$	−87582.6	−0.532744
$123$	−50351.3	−0.300087
$124$	128666.	0.751467
$125$	−244644.	−1.40042
$126$	0	0
$127$	−114137.	−0.627941	−0.313970	−	0.949433i	$-0.601659\pi$
$127$	−114137.	−0.627941	−0.313970	+	0.949433i	$0.601659\pi$
$128$	188677.	1.01787
$129$	−41415.7	−0.219124
$130$	37052.1	0.192289
$131$	−180702.	−0.919994	−0.459997	−	0.887920i	$-0.652150\pi$
$131$	−180702.	−0.919994	−0.459997	+	0.887920i	$0.652150\pi$
$132$	−13017.5	−0.0650270
$133$	0	0
$134$	29514.7	0.141996
$135$	−154113.	−0.727787
$136$	−175771.	−0.814890
$137$	324600.	1.47757	0.738783	−	0.673944i	$-0.235401\pi$
$137$	324600.	1.47757	0.738783	+	0.673944i	$0.235401\pi$
$138$	8611.55	0.0384932
$139$	247720.	1.08749	0.543745	−	0.839251i	$-0.317006\pi$
$139$	247720.	1.08749	0.543745	+	0.839251i	$0.317006\pi$
$140$	0	0
$141$	41970.6	0.177786
$142$	166479.	0.692848
$143$	−23961.7	−0.0979892
$144$	−122949.	−0.494106
$145$	−323553.	−1.27798
$146$	124374.	0.482888
$147$	0	0
$148$	−253428.	−0.951044
$149$	−277701.	−1.02474	−0.512368	−	0.858766i	$-0.671232\pi$
$149$	−277701.	−1.02474	−0.512368	+	0.858766i	$0.671232\pi$
$150$	46108.1	0.167321
$151$	−317691.	−1.13387	−0.566934	−	0.823763i	$-0.691870\pi$
$151$	−317691.	−1.13387	−0.566934	+	0.823763i	$0.691870\pi$
$152$	−261059.	−0.916496
$153$	297549.	1.02761
$154$	0	0
$155$	455589.	1.52316
$156$	15516.1	0.0510472
$157$	361097.	1.16916	0.584581	−	0.811336i	$-0.301259\pi$
$157$	361097.	1.16916	0.584581	+	0.811336i	$0.301259\pi$
$158$	33830.5	0.107812
$159$	−113171.	−0.355013
$160$	527569.	1.62922
$161$	0	0
$162$	−117657.	−0.352234
$163$	189986.	0.560084	0.280042	−	0.959988i	$-0.409652\pi$
$163$	189986.	0.560084	0.280042	+	0.959988i	$0.409652\pi$
$164$	−387134.	−1.12396
$165$	−46093.3	−0.131804
$166$	182571.	0.514235
$167$	173782.	0.482184	0.241092	−	0.970502i	$-0.422494\pi$
$167$	173782.	0.482184	0.241092	+	0.970502i	$0.422494\pi$
$168$	0	0
$169$	28561.0	0.0769231
$170$	−282333.	−0.749273
$171$	441928.	1.15574
$172$	−318431.	−0.820719
$173$	310587.	0.788984	0.394492	−	0.918899i	$-0.370921\pi$
$173$	310587.	0.788984	0.394492	+	0.918899i	$0.370921\pi$
$174$	27696.7	0.0693515
$175$	0	0
$176$	−75445.8	−0.183592
$177$	−166155.	−0.398639
$178$	−57204.0	−0.135324
$179$	−66623.4	−0.155415	−0.0777077	−	0.996976i	$-0.524760\pi$
$179$	−66623.4	−0.155415	−0.0777077	+	0.996976i	$0.524760\pi$
$180$	−577537.	−1.32861
$181$	169918.	0.385516	0.192758	−	0.981246i	$-0.438257\pi$
$181$	169918.	0.385516	0.192758	+	0.981246i	$0.438257\pi$
$182$	0	0
$183$	−129867.	−0.286662
$184$	145957.	0.317820
$185$	−897355.	−1.92768
$186$	−38999.3	−0.0826560
$187$	182586.	0.381824
$188$	322698.	0.665889
$189$	0	0
$190$	−419329.	−0.842697
$191$	181518.	0.360029	0.180014	−	0.983664i	$-0.442386\pi$
$191$	181518.	0.360029	0.180014	+	0.983664i	$0.442386\pi$
$192$	13679.6	0.0267807
$193$	751561.	1.45235	0.726174	−	0.687511i	$-0.241297\pi$
$193$	751561.	1.45235	0.726174	+	0.687511i	$0.241297\pi$
$194$	−187893.	−0.358431
$195$	54940.5	0.103468
$196$	0	0
$197$	−250963.	−0.460727	−0.230364	−	0.973105i	$-0.573992\pi$
$197$	−250963.	−0.460727	−0.230364	+	0.973105i	$0.573992\pi$
$198$	−76348.0	−0.138399
$199$	−9.51204	−1.70271e−5 0	−8.51355e−6	−	1.00000i	$-0.500003\pi$
$199$	−9.51204	−1.70271e−5 0	−8.51355e−6		1.00000i	$0.500003\pi$
$200$	781486.	1.38149
$201$	43764.2	0.0764062
$202$	320048.	0.551870
$203$	0	0
$204$	−118231.	−0.198910
$205$	−1.37079e6	−2.27817
$206$	−145687.	−0.239195
$207$	−247080.	−0.400785
$208$	89927.0	0.144123
$209$	271182.	0.429432
$210$	0	0
$211$	225993.	0.349454	0.174727	−	0.984617i	$-0.444096\pi$
$211$	225993.	0.349454	0.174727	+	0.984617i	$0.444096\pi$
$212$	−870137.	−1.32968
$213$	246853.	0.372812
$214$	490993.	0.732894
$215$	−1.12752e6	−1.66352
$216$	223597.	0.326085
$217$	0	0
$218$	34824.6	0.0496301
$219$	184420.	0.259835
$220$	−354396.	−0.493665
$221$	−217632.	−0.299738
$222$	76815.3	0.104608
$223$	−207052.	−0.278816	−0.139408	−	0.990235i	$-0.544520\pi$
$223$	−207052.	−0.278816	−0.139408	+	0.990235i	$0.544520\pi$
$224$	0	0
$225$	−1.32292e6	−1.74212
$226$	−218849.	−0.285019
$227$	860357.	1.10819	0.554095	−	0.832453i	$-0.313064\pi$
$227$	860357.	1.10819	0.554095	+	0.832453i	$0.313064\pi$
$228$	−175601.	−0.223712
$229$	235104.	0.296259	0.148130	−	0.988968i	$-0.452675\pi$
$229$	235104.	0.296259	0.148130	+	0.988968i	$0.452675\pi$
$230$	234445.	0.292228
$231$	0	0
$232$	469432.	0.572602
$233$	−735958.	−0.888103	−0.444051	−	0.896001i	$-0.646459\pi$
$233$	−735958.	−0.888103	−0.444051	+	0.896001i	$0.646459\pi$
$234$	91002.3	0.108646
$235$	1.14263e6	1.34970
$236$	−1.27751e6	−1.49308
$237$	50163.5	0.0580119
$238$	0	0
$239$	−557974.	−0.631857	−0.315929	−	0.948783i	$-0.602316\pi$
$239$	−557974.	−0.631857	−0.315929	+	0.948783i	$0.602316\pi$
$240$	172986.	0.193857
$241$	−1.76415e6	−1.95656	−0.978279	−	0.207291i	$-0.933535\pi$
$241$	−1.76415e6	−1.95656	−0.978279	+	0.207291i	$0.933535\pi$
$242$	328475.	0.360548
$243$	−572533.	−0.621992
$244$	−998501.	−1.07368
$245$	0	0
$246$	117342.	0.123628
$247$	−323233.	−0.337111
$248$	−660999.	−0.682451
$249$	270714.	0.276702
$250$	570135.	0.576936
$251$	−881828.	−0.883486	−0.441743	−	0.897142i	$-0.645640\pi$
$251$	−881828.	−0.883486	−0.441743	+	0.897142i	$0.645640\pi$
$252$	0	0
$253$	−151617.	−0.148917
$254$	265994.	0.258694
$255$	−418641.	−0.403173
$256$	−313027.	−0.298526
$257$	−949971.	−0.897176	−0.448588	−	0.893739i	$-0.648073\pi$
$257$	−949971.	−0.897176	−0.448588	+	0.893739i	$0.648073\pi$
$258$	96518.0	0.0902732
$259$	0	0
$260$	422419.	0.387534
$261$	−794667.	−0.722078
$262$	421121.	0.379012
$263$	−94646.4	−0.0843752	−0.0421876	−	0.999110i	$-0.513433\pi$
$263$	−94646.4	−0.0843752	−0.0421876	+	0.999110i	$0.513433\pi$
$264$	66875.2	0.0590548
$265$	−3.08104e6	−2.69514
$266$	0	0
$267$	−84821.5	−0.0728162
$268$	336488.	0.286176
$269$	1.25855e6	1.06045	0.530226	−	0.847857i	$-0.322107\pi$
$269$	1.25855e6	1.06045	0.530226	+	0.847857i	$0.322107\pi$
$270$	359155.	0.299828
$271$	1.79951e6	1.48844	0.744221	−	0.667933i	$-0.232821\pi$
$271$	1.79951e6	1.48844	0.744221	+	0.667933i	$0.232821\pi$
$272$	−685235.	−0.561587
$273$	0	0
$274$	−756470.	−0.608716
$275$	−811788.	−0.647308
$276$	98177.5	0.0775781
$277$	277895.	0.217612	0.108806	−	0.994063i	$-0.465297\pi$
$277$	277895.	0.217612	0.108806	+	0.994063i	$0.465297\pi$
$278$	−577305.	−0.448016
$279$	1.11896e6	0.860603
$280$	0	0
$281$	−28661.2	−0.0216535	−0.0108267	−	0.999941i	$-0.503446\pi$
$281$	−28661.2	−0.0216535	−0.0108267	+	0.999941i	$0.503446\pi$
$282$	−97811.3	−0.0732430
$283$	128237.	0.0951803	0.0475901	−	0.998867i	$-0.484846\pi$
$283$	128237.	0.0951803	0.0475901	+	0.998867i	$0.484846\pi$
$284$	1.89797e6	1.39635
$285$	−621778.	−0.453443
$286$	55842.1	0.0403689
$287$	0	0
$288$	1.29574e6	0.920529
$289$	238476.	0.167958
$290$	754030.	0.526495
$291$	−278605.	−0.192867
$292$	1.41794e6	0.973199
$293$	−633549.	−0.431133	−0.215566	−	0.976489i	$-0.569160\pi$
$293$	−633549.	−0.431133	−0.215566	+	0.976489i	$0.569160\pi$
$294$	0	0
$295$	−4.52348e6	−3.02634
$296$	1.30194e6	0.863699
$297$	−232267.	−0.152790
$298$	647174.	0.422163
$299$	180718.	0.116903
$300$	525664.	0.337213
$301$	0	0
$302$	740368.	0.467122
$303$	474564.	0.296953
$304$	−1.01773e6	−0.631609
$305$	−3.53556e6	−2.17625
$306$	−693429.	−0.423349
$307$	1.69354e6	1.02554	0.512768	−	0.858527i	$-0.328620\pi$
$307$	1.69354e6	1.02554	0.512768	+	0.858527i	$0.328620\pi$
$308$	0	0
$309$	−216023.	−0.128707
$310$	−1.06174e6	−0.627498
$311$	−3.22139e6	−1.88861	−0.944306	−	0.329068i	$-0.893265\pi$
$311$	−3.22139e6	−1.88861	−0.944306	+	0.329068i	$0.893265\pi$
$312$	−79711.3	−0.0463590
$313$	−1.27603e6	−0.736205	−0.368103	−	0.929785i	$-0.619992\pi$
$313$	−1.27603e6	−0.736205	−0.368103	+	0.929785i	$0.619992\pi$
$314$	−841524.	−0.481662
$315$	0	0
$316$	385691.	0.217281
$317$	−274374.	−0.153354	−0.0766769	−	0.997056i	$-0.524431\pi$
$317$	−274374.	−0.153354	−0.0766769	+	0.997056i	$0.524431\pi$
$318$	263742.	0.146255
$319$	−487634.	−0.268298
$320$	372422.	0.203311
$321$	728041.	0.394360
$322$	0	0
$323$	2.46300e6	1.31359
$324$	−1.34137e6	−0.709883
$325$	967604.	0.508147
$326$	−442757.	−0.230739
$327$	51637.6	0.0267053
$328$	1.98883e6	1.02074
$329$	0	0
$330$	107419.	0.0542995
$331$	84209.9	0.0422468	0.0211234	−	0.999777i	$-0.493276\pi$
$331$	84209.9	0.0422468	0.0211234	+	0.999777i	$0.493276\pi$
$332$	2.08143e6	1.03637
$333$	−2.20396e6	−1.08916
$334$	−404993.	−0.198647
$335$	1.19146e6	0.580052
$336$	0	0
$337$	2.76043e6	1.32404	0.662022	−	0.749484i	$-0.269698\pi$
$337$	2.76043e6	1.32404	0.662022	+	0.749484i	$0.269698\pi$
$338$	−66560.5	−0.0316902
$339$	−324508.	−0.153365
$340$	−3.21879e6	−1.51006
$341$	686629.	0.319769
$342$	−1.02990e6	−0.476134
$343$	0	0
$344$	1.63588e6	0.745343
$345$	347633.	0.157244
$346$	−723813.	−0.325040
$347$	−2.36067e6	−1.05248	−0.526238	−	0.850337i	$-0.676398\pi$
$347$	−2.36067e6	−1.05248	−0.526238	+	0.850337i	$0.676398\pi$
$348$	315762.	0.139769
$349$	3.35029e6	1.47238	0.736188	−	0.676777i	$-0.236624\pi$
$349$	3.35029e6	1.47238	0.736188	+	0.676777i	$0.236624\pi$
$350$	0	0
$351$	276848.	0.119943
$352$	795111.	0.342036
$353$	−364538.	−0.155706	−0.0778532	−	0.996965i	$-0.524807\pi$
$353$	−364538.	−0.155706	−0.0778532	+	0.996965i	$0.524807\pi$
$354$	387218.	0.164228
$355$	6.72045e6	2.83027
$356$	−652164.	−0.272729
$357$	0	0
$358$	155264.	0.0640269
$359$	2.05925e6	0.843283	0.421642	−	0.906763i	$-0.361454\pi$
$359$	2.05925e6	0.843283	0.421642	+	0.906763i	$0.361454\pi$
$360$	2.96699e6	1.20659
$361$	1.18202e6	0.477372
$362$	−395988.	−0.158822
$363$	487059.	0.194006
$364$	0	0
$365$	5.02075e6	1.97259
$366$	302650.	0.118097
$367$	1.51741e6	0.588083	0.294041	−	0.955793i	$-0.405000\pi$
$367$	1.51741e6	0.588083	0.294041	+	0.955793i	$0.405000\pi$
$368$	569008.	0.219028
$369$	−3.36674e6	−1.28719
$370$	2.09126e6	0.794151
$371$	0	0
$372$	−444618.	−0.166583
$373$	4.91745e6	1.83007	0.915035	−	0.403374i	$-0.132163\pi$
$373$	4.91745e6	1.83007	0.915035	+	0.403374i	$0.132163\pi$
$374$	−425511.	−0.157301
$375$	845391.	0.310441
$376$	−1.65780e6	−0.604733
$377$	581232.	0.210618
$378$	0	0
$379$	−5.22913e6	−1.86996	−0.934978	−	0.354707i	$-0.884581\pi$
$379$	−5.22913e6	−1.86996	−0.934978	+	0.354707i	$0.884581\pi$
$380$	−4.78064e6	−1.69835
$381$	394413.	0.139200
$382$	−423023.	−0.148322
$383$	4.17641e6	1.45481	0.727405	−	0.686209i	$-0.240726\pi$
$383$	4.17641e6	1.45481	0.727405	+	0.686209i	$0.240726\pi$
$384$	−651991.	−0.225639
$385$	0	0
$386$	−1.75149e6	−0.598328
$387$	−2.76927e6	−0.939912
$388$	−2.14210e6	−0.722372
$389$	5.06273e6	1.69633	0.848166	−	0.529731i	$-0.177707\pi$
$389$	5.06273e6	1.69633	0.848166	+	0.529731i	$0.177707\pi$
$390$	−128037.	−0.0426260
$391$	−1.37705e6	−0.455522
$392$	0	0
$393$	624434.	0.203941
$394$	584861.	0.189807
$395$	1.36568e6	0.440408
$396$	−870418.	−0.278927
$397$	−3.67149e6	−1.16914	−0.584569	−	0.811344i	$-0.698736\pi$
$397$	−3.67149e6	−1.16914	−0.584569	+	0.811344i	$0.698736\pi$
$398$	22.1675	7.01470e−6 0
$399$	0	0
$400$	3.04659e6	0.952061
$401$	2.79607e6	0.868336	0.434168	−	0.900832i	$-0.357042\pi$
$401$	2.79607e6	0.868336	0.434168	+	0.900832i	$0.357042\pi$
$402$	−101991.	−0.0314772
$403$	−818422.	−0.251024
$404$	3.64876e6	1.11222
$405$	−4.74961e6	−1.43887
$406$	0	0
$407$	−1.35242e6	−0.404694
$408$	607392.	0.180642
$409$	74975.7	0.0221622	0.0110811	−	0.999939i	$-0.496473\pi$
$409$	74975.7	0.0221622	0.0110811	+	0.999939i	$0.496473\pi$
$410$	3.19458e6	0.938543
$411$	−1.12169e6	−0.327542
$412$	−1.66093e6	−0.482067
$413$	0	0
$414$	575812.	0.165113
$415$	7.37007e6	2.10064
$416$	−947726.	−0.268503
$417$	−856022.	−0.241071
$418$	−631981.	−0.176914
$419$	1.62459e6	0.452072	0.226036	−	0.974119i	$-0.427423\pi$
$419$	1.62459e6	0.452072	0.226036	+	0.974119i	$0.427423\pi$
$420$	0	0
$421$	−6.21952e6	−1.71022	−0.855109	−	0.518448i	$-0.826510\pi$
$421$	−6.21952e6	−1.71022	−0.855109	+	0.518448i	$0.826510\pi$
$422$	−526671.	−0.143965
$423$	2.80637e6	0.762596
$424$	4.47017e6	1.20756
$425$	−7.37305e6	−1.98004
$426$	−575283.	−0.153588
$427$	0	0
$428$	5.59766e6	1.47706
$429$	82802.1	0.0217219
$430$	2.62765e6	0.685326
$431$	−1.19072e6	−0.308758	−0.154379	−	0.988012i	$-0.549338\pi$
$431$	−1.19072e6	−0.308758	−0.154379	+	0.988012i	$0.549338\pi$
$432$	871684.	0.224724
$433$	−477391.	−0.122364	−0.0611821	−	0.998127i	$-0.519487\pi$
$433$	−477391.	−0.122364	−0.0611821	+	0.998127i	$0.519487\pi$
$434$	0	0
$435$	1.11807e6	0.283299
$436$	397024.	0.100023
$437$	−2.04524e6	−0.512319
$438$	−429785.	−0.107045
$439$	1.84753e6	0.457541	0.228770	−	0.973480i	$-0.426529\pi$
$439$	1.84753e6	0.457541	0.228770	+	0.973480i	$0.426529\pi$
$440$	1.82064e6	0.448326
$441$	0	0
$442$	507184.	0.123484
$443$	1.60951e6	0.389658	0.194829	−	0.980837i	$-0.437585\pi$
$443$	1.60951e6	0.389658	0.194829	+	0.980837i	$0.437585\pi$
$444$	875746.	0.210824
$445$	−2.30923e6	−0.552798
$446$	482529.	0.114865
$447$	959623.	0.227160
$448$	0	0
$449$	4.13027e6	0.966858	0.483429	−	0.875383i	$-0.339391\pi$
$449$	4.13027e6	0.966858	0.483429	+	0.875383i	$0.339391\pi$
$450$	3.08302e6	0.717704
$451$	−2.06595e6	−0.478275
$452$	−2.49503e6	−0.574421
$453$	1.09781e6	0.251352
$454$	−2.00504e6	−0.456544
$455$	0	0
$456$	902116.	0.203166
$457$	5.55845e6	1.24498	0.622491	−	0.782627i	$-0.286121\pi$
$457$	5.55845e6	1.24498	0.622491	+	0.782627i	$0.286121\pi$
$458$	−547904.	−0.122051
$459$	−2.10956e6	−0.467369
$460$	2.67283e6	0.588949
$461$	−4.47320e6	−0.980316	−0.490158	−	0.871634i	$-0.663061\pi$
$461$	−4.47320e6	−0.980316	−0.490158	+	0.871634i	$0.663061\pi$
$462$	0	0
$463$	−6.29324e6	−1.36434	−0.682169	−	0.731195i	$-0.738963\pi$
$463$	−6.29324e6	−1.36434	−0.682169	+	0.731195i	$0.738963\pi$
$464$	1.83006e6	0.394613
$465$	−1.57433e6	−0.337648
$466$	1.71513e6	0.365874
$467$	8.50258e6	1.80409	0.902046	−	0.431641i	$-0.142065\pi$
$467$	8.50258e6	1.80409	0.902046	+	0.431641i	$0.142065\pi$
$468$	1.03749e6	0.218962
$469$	0	0
$470$	−2.66286e6	−0.556038
$471$	−1.24780e6	−0.259176
$472$	6.56296e6	1.35595
$473$	−1.69931e6	−0.349237
$474$	−116905.	−0.0238993
$475$	−1.09507e7	−2.22693
$476$	0	0
$477$	−7.56722e6	−1.52279
$478$	1.30034e6	0.260308
$479$	−5.85017e6	−1.16501	−0.582505	−	0.812827i	$-0.697927\pi$
$479$	−5.85017e6	−1.16501	−0.582505	+	0.812827i	$0.697927\pi$
$480$	−1.82307e6	−0.361160
$481$	1.61201e6	0.317691
$482$	4.11130e6	0.806048
$483$	0	0
$484$	3.74483e6	0.726640
$485$	−7.58489e6	−1.46418
$486$	1.33427e6	0.256244
$487$	9.56841e6	1.82817	0.914086	−	0.405519i	$-0.132909\pi$
$487$	9.56841e6	1.82817	0.914086	+	0.405519i	$0.132909\pi$
$488$	5.12962e6	0.975069
$489$	−656515.	−0.124157
$490$	0	0
$491$	4.18960e6	0.784277	0.392138	−	0.919906i	$-0.371735\pi$
$491$	4.18960e6	0.784277	0.392138	+	0.919906i	$0.371735\pi$
$492$	1.33778e6	0.249156
$493$	−4.42893e6	−0.820694
$494$	753284.	0.138881
$495$	−3.08203e6	−0.565359
$496$	−2.57688e6	−0.470316
$497$	0	0
$498$	−630891.	−0.113994
$499$	5.76516e6	1.03648	0.518239	−	0.855236i	$-0.326588\pi$
$499$	5.76516e6	1.03648	0.518239	+	0.855236i	$0.326588\pi$
$500$	6.49993e6	1.16274
$501$	−600520.	−0.106889
$502$	2.05507e6	0.363972
$503$	−1.14664e6	−0.202073	−0.101036	−	0.994883i	$-0.532216\pi$
$503$	−1.14664e6	−0.202073	−0.101036	+	0.994883i	$0.532216\pi$
$504$	0	0
$505$	1.29198e7	2.25438
$506$	353338.	0.0613499
$507$	−98695.3	−0.0170520
$508$	3.03251e6	0.521366
$509$	−6.36053e6	−1.08817	−0.544087	−	0.839029i	$-0.683124\pi$
$509$	−6.36053e6	−1.08817	−0.544087	+	0.839029i	$0.683124\pi$
$510$	975630.	0.166096
$511$	0	0
$512$	−5.30816e6	−0.894888
$513$	−3.13317e6	−0.525643
$514$	2.21388e6	0.369612
$515$	−5.88112e6	−0.977106
$516$	1.10037e6	0.181934
$517$	1.72208e6	0.283353
$518$	0	0
$519$	−1.07326e6	−0.174899
$520$	−2.17010e6	−0.351943
$521$	7.39468e6	1.19351	0.596754	−	0.802424i	$-0.296457\pi$
$521$	7.39468e6	1.19351	0.596754	+	0.802424i	$0.296457\pi$
$522$	1.85195e6	0.297476
$523$	1.05734e7	1.69029	0.845144	−	0.534538i	$-0.179515\pi$
$523$	1.05734e7	1.69029	0.845144	+	0.534538i	$0.179515\pi$
$524$	4.80106e6	0.763852
$525$	0	0
$526$	220570.	0.0347603
$527$	6.23629e6	0.978138
$528$	260710.	0.0406980
$529$	−5.29286e6	−0.822339
$530$	7.18026e6	1.11033
$531$	−1.11100e7	−1.70992
$532$	0	0
$533$	2.46249e6	0.375454
$534$	197674.	0.0299983
$535$	1.98205e7	2.99386
$536$	−1.72865e6	−0.259893
$537$	230224.	0.0344520
$538$	−2.93302e6	−0.436877
$539$	0	0
$540$	4.09461e6	0.604266
$541$	2.20343e6	0.323672	0.161836	−	0.986818i	$-0.448258\pi$
$541$	2.20343e6	0.323672	0.161836	+	0.986818i	$0.448258\pi$
$542$	−4.19371e6	−0.613197
$543$	−587167.	−0.0854599
$544$	7.22158e6	1.04625
$545$	1.40581e6	0.202738
$546$	0	0
$547$	−6.87903e6	−0.983012	−0.491506	−	0.870874i	$-0.663553\pi$
$547$	−6.87903e6	−0.983012	−0.491506	+	0.870874i	$0.663553\pi$
$548$	−8.62426e6	−1.22679
$549$	−8.68355e6	−1.22961
$550$	1.89185e6	0.266673
$551$	−6.57796e6	−0.923023
$552$	−504369.	−0.0704532
$553$	0	0
$554$	−647626.	−0.0896500
$555$	3.10090e6	0.427322
$556$	−6.58167e6	−0.902919
$557$	−8.29313e6	−1.13261	−0.566305	−	0.824196i	$-0.691628\pi$
$557$	−8.29313e6	−1.13261	−0.566305	+	0.824196i	$0.691628\pi$
$558$	−2.60769e6	−0.354545
$559$	2.02548e6	0.274157
$560$	0	0
$561$	−630944.	−0.0846415
$562$	66793.9	0.00892064
$563$	−2.02389e6	−0.269102	−0.134551	−	0.990907i	$-0.542959\pi$
$563$	−2.02389e6	−0.269102	−0.134551	+	0.990907i	$0.542959\pi$
$564$	−1.11511e6	−0.147612
$565$	−8.83457e6	−1.16430
$566$	−298852.	−0.0392117
$567$	0	0
$568$	−9.75048e6	−1.26810
$569$	557196.	0.0721486	0.0360743	−	0.999349i	$-0.488515\pi$
$569$	557196.	0.0721486	0.0360743	+	0.999349i	$0.488515\pi$
$570$	1.44903e6	0.186806
$571$	−7.28586e6	−0.935170	−0.467585	−	0.883948i	$-0.654876\pi$
$571$	−7.28586e6	−0.935170	−0.467585	+	0.883948i	$0.654876\pi$
$572$	636637.	0.0813583
$573$	−627254.	−0.0798099
$574$	0	0
$575$	6.12246e6	0.772248
$576$	914691.	0.114873
$577$	1.11109e7	1.38935	0.694675	−	0.719324i	$-0.255548\pi$
$577$	1.11109e7	1.38935	0.694675	+	0.719324i	$0.255548\pi$
$578$	−555762.	−0.0691941
$579$	−2.59709e6	−0.321952
$580$	8.59646e6	1.06108
$581$	0	0
$582$	649281.	0.0794557
$583$	−4.64350e6	−0.565814
$584$	−7.28443e6	−0.883819
$585$	3.67361e6	0.443816
$586$	1.47646e6	0.177615
$587$	−7.21001e6	−0.863656	−0.431828	−	0.901956i	$-0.642131\pi$
$587$	−7.21001e6	−0.863656	−0.431828	+	0.901956i	$0.642131\pi$
$588$	0	0
$589$	9.26231e6	1.10010
$590$	1.05418e7	1.24677
$591$	867226.	0.102132
$592$	5.07557e6	0.595224
$593$	−2.44935e6	−0.286031	−0.143016	−	0.989720i	$-0.545680\pi$
$593$	−2.44935e6	−0.286031	−0.143016	+	0.989720i	$0.545680\pi$
$594$	541290.	0.0629454
$595$	0	0
$596$	7.37822e6	0.850817
$597$	32.8698	3.77451e−6 0
$598$	−421158.	−0.0481606
$599$	−1.01766e7	−1.15887	−0.579434	−	0.815019i	$-0.696726\pi$
$599$	−1.01766e7	−1.15887	−0.579434	+	0.815019i	$0.696726\pi$
$600$	−2.70050e6	−0.306243
$601$	6.77189e6	0.764757	0.382379	−	0.924006i	$-0.375105\pi$
$601$	6.77189e6	0.764757	0.382379	+	0.924006i	$0.375105\pi$
$602$	0	0
$603$	2.92630e6	0.327737
$604$	8.44070e6	0.941426
$605$	1.32599e7	1.47283
$606$	−1.10596e6	−0.122337
$607$	1.65271e6	0.182065	0.0910323	−	0.995848i	$-0.470983\pi$
$607$	1.65271e6	0.182065	0.0910323	+	0.995848i	$0.470983\pi$
$608$	1.07257e7	1.17670
$609$	0	0
$610$	8.23950e6	0.896554
$611$	−2.05262e6	−0.222437
$612$	−7.90556e6	−0.853206
$613$	−4.28409e6	−0.460476	−0.230238	−	0.973134i	$-0.573950\pi$
$613$	−4.28409e6	−0.460476	−0.230238	+	0.973134i	$0.573950\pi$
$614$	−3.94675e6	−0.422492
$615$	4.73690e6	0.505017
$616$	0	0
$617$	−1.62812e7	−1.72176	−0.860882	−	0.508805i	$-0.830087\pi$
$617$	−1.62812e7	−1.72176	−0.860882	+	0.508805i	$0.830087\pi$
$618$	503434.	0.0530239
$619$	3.98727e6	0.418262	0.209131	−	0.977888i	$-0.432936\pi$
$619$	3.98727e6	0.418262	0.209131	+	0.977888i	$0.432936\pi$
$620$	−1.21045e7	−1.26464
$621$	1.75174e6	0.182281
$622$	7.50736e6	0.778056
$623$	0	0
$624$	−310752.	−0.0319486
$625$	5.12328e6	0.524624
$626$	2.97374e6	0.303296
$627$	−937095.	−0.0951951
$628$	−9.59395e6	−0.970730
$629$	−1.22834e7	−1.23791
$630$	0	0
$631$	−1.74367e7	−1.74337	−0.871687	−	0.490064i	$-0.836973\pi$
$631$	−1.74367e7	−1.74337	−0.871687	+	0.490064i	$0.836973\pi$
$632$	−1.98142e6	−0.197325
$633$	−780942.	−0.0774657
$634$	639420.	0.0631776
$635$	1.07377e7	1.05676
$636$	3.00684e6	0.294759
$637$	0	0
$638$	1.13642e6	0.110531
$639$	1.65059e7	1.59914
$640$	−1.77501e7	−1.71298
$641$	−1.70605e6	−0.164001	−0.0820005	−	0.996632i	$-0.526131\pi$
$641$	−1.70605e6	−0.164001	−0.0820005	+	0.996632i	$0.526131\pi$
$642$	−1.69668e6	−0.162466
$643$	−5.82462e6	−0.555572	−0.277786	−	0.960643i	$-0.589601\pi$
$643$	−5.82462e6	−0.555572	−0.277786	+	0.960643i	$0.589601\pi$
$644$	0	0
$645$	3.89626e6	0.368764
$646$	−5.73995e6	−0.541161
$647$	4.68507e6	0.440003	0.220002	−	0.975500i	$-0.429394\pi$
$647$	4.68507e6	0.440003	0.220002	+	0.975500i	$0.429394\pi$
$648$	6.89105e6	0.644686
$649$	−6.81744e6	−0.635345
$650$	−2.25497e6	−0.209343
$651$	0	0
$652$	−5.04773e6	−0.465026
$653$	5.58318e6	0.512387	0.256194	−	0.966625i	$-0.417531\pi$
$653$	5.58318e6	0.512387	0.256194	+	0.966625i	$0.417531\pi$
$654$	−120340.	−0.0110018
$655$	1.69999e7	1.54826
$656$	7.75338e6	0.703447
$657$	1.23313e7	1.11454
$658$	0	0
$659$	−1.28185e7	−1.14980	−0.574901	−	0.818223i	$-0.694959\pi$
$659$	−1.28185e7	−1.14980	−0.574901	+	0.818223i	$0.694959\pi$
$660$	1.22465e6	0.109434
$661$	6.69964e6	0.596414	0.298207	−	0.954501i	$-0.403611\pi$
$661$	6.69964e6	0.596414	0.298207	+	0.954501i	$0.403611\pi$
$662$	−196249.	−0.0174045
$663$	752048.	0.0664449
$664$	−1.06930e7	−0.941193
$665$	0	0
$666$	5.13626e6	0.448706
$667$	3.67771e6	0.320083
$668$	−4.61719e6	−0.400347
$669$	715489.	0.0618070
$670$	−2.77666e6	−0.238965
$671$	−5.32852e6	−0.456878
$672$	0	0
$673$	1.93713e7	1.64862	0.824310	−	0.566139i	$-0.191563\pi$
$673$	1.93713e7	1.64862	0.824310	+	0.566139i	$0.191563\pi$
$674$	−6.43310e6	−0.545470
$675$	9.37921e6	0.792332
$676$	−758835.	−0.0638676
$677$	3.25613e6	0.273043	0.136521	−	0.990637i	$-0.456408\pi$
$677$	3.25613e6	0.273043	0.136521	+	0.990637i	$0.456408\pi$
$678$	756255.	0.0631821
$679$	0	0
$680$	1.65360e7	1.37138
$681$	−2.97305e6	−0.245660
$682$	−1.60017e6	−0.131736
$683$	1.13168e7	0.928265	0.464133	−	0.885766i	$-0.346366\pi$
$683$	1.13168e7	0.928265	0.464133	+	0.885766i	$0.346366\pi$
$684$	−1.17415e7	−0.959589
$685$	−3.05374e7	−2.48659
$686$	0	0
$687$	−812426.	−0.0656738
$688$	6.37743e6	0.513658
$689$	5.53478e6	0.444173
$690$	−810148.	−0.0647801
$691$	2.03184e6	0.161881	0.0809404	−	0.996719i	$-0.474208\pi$
$691$	2.03184e6	0.161881	0.0809404	+	0.996719i	$0.474208\pi$
$692$	−8.25196e6	−0.655077
$693$	0	0
$694$	5.50148e6	0.433591
$695$	−2.33048e7	−1.83013
$696$	−1.62217e6	−0.126933
$697$	−1.87639e7	−1.46299
$698$	−7.80774e6	−0.606578
$699$	2.54317e6	0.196872
$700$	0	0
$701$	−1.12608e7	−0.865511	−0.432755	−	0.901511i	$-0.642459\pi$
$701$	−1.12608e7	−0.865511	−0.432755	+	0.901511i	$0.642459\pi$
$702$	−645186.	−0.0494131
$703$	−1.82436e7	−1.39226
$704$	561285.	0.0426827
$705$	−3.94847e6	−0.299196
$706$	849545.	0.0641467
$707$	0	0
$708$	4.41455e6	0.330981
$709$	−1.07065e7	−0.799892	−0.399946	−	0.916539i	$-0.630971\pi$
$709$	−1.07065e7	−0.799892	−0.399946	+	0.916539i	$0.630971\pi$
$710$	−1.56618e7	−1.16599
$711$	3.35419e6	0.248836
$712$	3.35038e6	0.247681
$713$	−5.17852e6	−0.381489
$714$	0	0
$715$	2.25425e6	0.164906
$716$	1.77011e6	0.129038
$717$	1.92813e6	0.140068
$718$	−4.79902e6	−0.347410
$719$	−1.34883e7	−0.973053	−0.486526	−	0.873666i	$-0.661736\pi$
$719$	−1.34883e7	−0.973053	−0.486526	+	0.873666i	$0.661736\pi$
$720$	1.15667e7	0.831530
$721$	0	0
$722$	−2.75466e6	−0.196664
$723$	6.09619e6	0.433723
$724$	−4.51453e6	−0.320086
$725$	1.96913e7	1.39132
$726$	−1.13508e6	−0.0799251
$727$	2.80788e7	1.97034	0.985172	−	0.171567i	$-0.0548831\pi$
$727$	2.80788e7	1.97034	0.985172	+	0.171567i	$0.0548831\pi$
$728$	0	0
$729$	−1.02898e7	−0.717112
$730$	−1.17007e7	−0.812651
$731$	−1.54340e7	−1.06828
$732$	3.45042e6	0.238009
$733$	−1.59894e7	−1.09919	−0.549593	−	0.835432i	$-0.685217\pi$
$733$	−1.59894e7	−1.09919	−0.549593	+	0.835432i	$0.685217\pi$
$734$	−3.53628e6	−0.242274
$735$	0	0
$736$	−5.99669e6	−0.408053
$737$	1.79567e6	0.121775
$738$	7.84609e6	0.530289
$739$	7.00735e6	0.472001	0.236001	−	0.971753i	$-0.424163\pi$
$739$	7.00735e6	0.472001	0.236001	+	0.971753i	$0.424163\pi$
$740$	2.38418e7	1.60051
$741$	1.11696e6	0.0747297
$742$	0	0
$743$	−9.29455e6	−0.617670	−0.308835	−	0.951116i	$-0.599939\pi$
$743$	−9.29455e6	−0.617670	−0.308835	+	0.951116i	$0.599939\pi$
$744$	2.28415e6	0.151284
$745$	2.61253e7	1.72453
$746$	−1.14600e7	−0.753939
$747$	1.81013e7	1.18689
$748$	−4.85111e6	−0.317021
$749$	0	0
$750$	−1.97016e6	−0.127893
$751$	−6.36984e6	−0.412125	−0.206062	−	0.978539i	$-0.566065\pi$
$751$	−6.36984e6	−0.412125	−0.206062	+	0.978539i	$0.566065\pi$
$752$	−6.46288e6	−0.416756
$753$	3.04724e6	0.195848
$754$	−1.35454e6	−0.0867689
$755$	2.98874e7	1.90818
$756$	0	0
$757$	−2.35253e7	−1.49209	−0.746047	−	0.665894i	$-0.768050\pi$
$757$	−2.35253e7	−1.49209	−0.746047	+	0.665894i	$0.768050\pi$
$758$	1.21863e7	0.770370
$759$	523926.	0.0330115
$760$	2.45597e7	1.54237
$761$	8.29811e6	0.519419	0.259709	−	0.965687i	$-0.416373\pi$
$761$	8.29811e6	0.519419	0.259709	+	0.965687i	$0.416373\pi$
$762$	−919166.	−0.0573465
$763$	0	0
$764$	−4.82275e6	−0.298924
$765$	−2.79925e7	−1.72937
$766$	−9.73299e6	−0.599341
$767$	8.12599e6	0.498756
$768$	1.08170e6	0.0661762
$769$	−1.77597e7	−1.08298	−0.541490	−	0.840707i	$-0.682139\pi$
$769$	−1.77597e7	−1.08298	−0.541490	+	0.840707i	$0.682139\pi$
$770$	0	0
$771$	3.28272e6	0.198883
$772$	−1.99682e7	−1.20585
$773$	1.72118e6	0.103604	0.0518022	−	0.998657i	$-0.483503\pi$
$773$	1.72118e6	0.103604	0.0518022	+	0.998657i	$0.483503\pi$
$774$	6.45368e6	0.387218
$775$	−2.77269e7	−1.65824
$776$	1.10047e7	0.656028
$777$	0	0
$778$	−1.17985e7	−0.698842
$779$	−2.78687e7	−1.64541
$780$	−1.45971e6	−0.0859073
$781$	1.01285e7	0.594182
$782$	3.20918e6	0.187662
$783$	5.63401e6	0.328408
$784$	0	0
$785$	−3.39709e7	−1.96758
$786$	−1.45522e6	−0.0840182
$787$	1.13760e7	0.654717	0.327358	−	0.944900i	$-0.393842\pi$
$787$	1.13760e7	0.654717	0.327358	+	0.944900i	$0.393842\pi$
$788$	6.66781e6	0.382532
$789$	327060.	0.0187040
$790$	−3.18267e6	−0.181436
$791$	0	0
$792$	4.47162e6	0.253310
$793$	6.35128e6	0.358656
$794$	8.55628e6	0.481653
$795$	1.06468e7	0.597451
$796$	252.725	1.41372e−5 0
$797$	−1.06288e7	−0.592705	−0.296352	−	0.955079i	$-0.595770\pi$
$797$	−1.06288e7	−0.592705	−0.296352	+	0.955079i	$0.595770\pi$
$798$	0	0
$799$	1.56408e7	0.866745
$800$	−3.21076e7	−1.77371
$801$	−5.67160e6	−0.312338
$802$	−6.51616e6	−0.357730
$803$	7.56688e6	0.414122
$804$	−1.16277e6	−0.0634384
$805$	0	0
$806$	1.90731e6	0.103415
$807$	−4.34905e6	−0.235077
$808$	−1.87449e7	−1.01007
$809$	1.20321e7	0.646351	0.323176	−	0.946339i	$-0.395250\pi$
$809$	1.20321e7	0.646351	0.323176	+	0.946339i	$0.395250\pi$
$810$	1.10688e7	0.592774
$811$	2.01295e7	1.07468	0.537341	−	0.843365i	$-0.319429\pi$
$811$	2.01295e7	1.07468	0.537341	+	0.843365i	$0.319429\pi$
$812$	0	0
$813$	−6.21840e6	−0.329953
$814$	3.15178e6	0.166723
$815$	−1.78733e7	−0.942564
$816$	2.36790e6	0.124491
$817$	−2.29230e7	−1.20148
$818$	−174729.	−0.00913021
$819$	0	0
$820$	3.64204e7	1.89152
$821$	−5.15933e6	−0.267138	−0.133569	−	0.991040i	$-0.542644\pi$
$821$	−5.15933e6	−0.267138	−0.133569	+	0.991040i	$0.542644\pi$
$822$	2.61405e6	0.134938
$823$	−8.50866e6	−0.437887	−0.218943	−	0.975738i	$-0.570261\pi$
$823$	−8.50866e6	−0.437887	−0.218943	+	0.975738i	$0.570261\pi$
$824$	8.53271e6	0.437793
$825$	2.80521e6	0.143493
$826$	0	0
$827$	−258054.	−0.0131204	−0.00656020	−	0.999978i	$-0.502088\pi$
$827$	−258054.	−0.0131204	−0.00656020	+	0.999978i	$0.502088\pi$
$828$	6.56465e6	0.332764
$829$	−2.00650e7	−1.01404	−0.507018	−	0.861936i	$-0.669252\pi$
$829$	−2.00650e7	−1.01404	−0.507018	+	0.861936i	$0.669252\pi$
$830$	−1.71757e7	−0.865405
$831$	−960294.	−0.0482394
$832$	−669019.	−0.0335066
$833$	0	0
$834$	1.99493e6	0.0993146
$835$	−1.63489e7	−0.811468
$836$	−7.20501e6	−0.356549
$837$	−7.93315e6	−0.391410
$838$	−3.78605e6	−0.186241
$839$	−1.61723e7	−0.793169	−0.396585	−	0.917998i	$-0.629805\pi$
$839$	−1.61723e7	−0.793169	−0.396585	+	0.917998i	$0.629805\pi$
$840$	0	0
$841$	−8.68278e6	−0.423320
$842$	1.44944e7	0.704563
$843$	99041.4	0.00480007
$844$	−6.00440e6	−0.290144
$845$	−2.68693e6	−0.129454
$846$	−6.54016e6	−0.314168
$847$	0	0
$848$	1.74268e7	0.832200
$849$	−443135.	−0.0210992
$850$	1.71827e7	0.815723
$851$	1.01999e7	0.482806
$852$	−6.55862e6	−0.309538
$853$	1.30290e7	0.613109	0.306555	−	0.951853i	$-0.400824\pi$
$853$	1.30290e7	0.613109	0.306555	+	0.951853i	$0.400824\pi$
$854$	0	0
$855$	−4.15752e7	−1.94500
$856$	−2.87570e7	−1.34140
$857$	−9.33250e6	−0.434056	−0.217028	−	0.976165i	$-0.569636\pi$
$857$	−9.33250e6	−0.434056	−0.217028	+	0.976165i	$0.569636\pi$
$858$	−192968.	−0.00894883
$859$	−2.41317e7	−1.11585	−0.557925	−	0.829892i	$-0.688402\pi$
$859$	−2.41317e7	−1.11585	−0.557925	+	0.829892i	$0.688402\pi$
$860$	2.99570e7	1.38119
$861$	0	0
$862$	2.77495e6	0.127200
$863$	−1.35663e7	−0.620059	−0.310029	−	0.950727i	$-0.600339\pi$
$863$	−1.35663e7	−0.620059	−0.310029	+	0.950727i	$0.600339\pi$
$864$	−9.18653e6	−0.418666
$865$	−2.92191e7	−1.32778
$866$	1.11255e6	0.0504107
$867$	−824078.	−0.0372324
$868$	0	0
$869$	2.05824e6	0.0924586
$870$	−2.60562e6	−0.116712
$871$	−2.14034e6	−0.0955954
$872$	−2.03964e6	−0.0908370
$873$	−1.86290e7	−0.827281
$874$	4.76636e6	0.211061
$875$	0	0
$876$	−4.89984e6	−0.215736
$877$	3.45398e7	1.51642	0.758212	−	0.652008i	$-0.226073\pi$
$877$	3.45398e7	1.51642	0.758212	+	0.652008i	$0.226073\pi$
$878$	−4.30561e6	−0.188494
$879$	2.18929e6	0.0955720
$880$	7.09771e6	0.308967
$881$	1.05351e7	0.457296	0.228648	−	0.973509i	$-0.426570\pi$
$881$	1.05351e7	0.457296	0.228648	+	0.973509i	$0.426570\pi$
$882$	0	0
$883$	−1.67328e7	−0.722215	−0.361108	−	0.932524i	$-0.617601\pi$
$883$	−1.67328e7	−0.722215	−0.361108	+	0.932524i	$0.617601\pi$
$884$	5.78224e6	0.248866
$885$	1.56313e7	0.670869
$886$	−3.75091e6	−0.160529
$887$	8.35618e6	0.356614	0.178307	−	0.983975i	$-0.442938\pi$
$887$	8.35618e6	0.356614	0.178307	+	0.983975i	$0.442938\pi$
$888$	−4.49899e6	−0.191462
$889$	0	0
$890$	5.38158e6	0.227737
$891$	−7.15825e6	−0.302073
$892$	5.50115e6	0.231495
$893$	2.32301e7	0.974817
$894$	−2.23637e6	−0.0935837
$895$	6.26772e6	0.261549
$896$	0	0
$897$	−624489.	−0.0259146
$898$	−9.62547e6	−0.398319
$899$	−1.66553e7	−0.687312
$900$	3.51486e7	1.44644
$901$	−4.21745e7	−1.73076
$902$	4.81462e6	0.197036
$903$	0	0
$904$	1.28178e7	0.521665
$905$	−1.59853e7	−0.648785
$906$	−2.55841e6	−0.103550
$907$	−2.67901e7	−1.08133	−0.540663	−	0.841239i	$-0.681827\pi$
$907$	−2.67901e7	−1.08133	−0.540663	+	0.841239i	$0.681827\pi$
$908$	−2.28588e7	−0.920107
$909$	3.17318e7	1.27375
$910$	0	0
$911$	1.30483e7	0.520903	0.260451	−	0.965487i	$-0.416129\pi$
$911$	1.30483e7	0.520903	0.260451	+	0.965487i	$0.416129\pi$
$912$	3.51686e6	0.140013
$913$	1.11076e7	0.441004
$914$	−1.29538e7	−0.512898
$915$	1.22175e7	0.482423
$916$	−6.24647e6	−0.245978
$917$	0	0
$918$	4.91626e6	0.192543
$919$	4.76756e7	1.86212	0.931059	−	0.364868i	$-0.118886\pi$
$919$	4.76756e7	1.86212	0.931059	+	0.364868i	$0.118886\pi$
$920$	−1.37312e7	−0.534859
$921$	−5.85221e6	−0.227337
$922$	1.04246e7	0.403863
$923$	−1.20726e7	−0.466442
$924$	0	0
$925$	5.46125e7	2.09864
$926$	1.46662e7	0.562070
$927$	−1.44444e7	−0.552077
$928$	−1.92867e7	−0.735172
$929$	−4.29575e6	−0.163305	−0.0816525	−	0.996661i	$-0.526020\pi$
$929$	−4.29575e6	−0.163305	−0.0816525	+	0.996661i	$0.526020\pi$
$930$	3.66893e6	0.139102
$931$	0	0
$932$	1.95536e7	0.737373
$933$	1.11318e7	0.418661
$934$	−1.98150e7	−0.743236
$935$	−1.71771e7	−0.642572
$936$	−5.32991e6	−0.198852
$937$	2.72511e7	1.01399	0.506996	−	0.861948i	$-0.330756\pi$
$937$	2.72511e7	1.01399	0.506996	+	0.861948i	$0.330756\pi$
$938$	0	0
$939$	4.40943e6	0.163200
$940$	−3.03584e7	−1.12062
$941$	−1.96932e7	−0.725006	−0.362503	−	0.931983i	$-0.618078\pi$
$941$	−1.96932e7	−0.725006	−0.362503	+	0.931983i	$0.618078\pi$
$942$	2.90797e6	0.106773
$943$	1.55813e7	0.570589
$944$	2.55855e7	0.934466
$945$	0	0
$946$	3.96020e6	0.143876
$947$	2.86451e7	1.03795	0.518974	−	0.854790i	$-0.326314\pi$
$947$	2.86451e7	1.03795	0.518974	+	0.854790i	$0.326314\pi$
$948$	−1.33279e6	−0.0481661
$949$	−9.01928e6	−0.325092
$950$	2.55201e7	0.917433
$951$	948126.	0.0339950
$952$	0	0
$953$	3.29296e7	1.17450	0.587252	−	0.809404i	$-0.300210\pi$
$953$	3.29296e7	1.17450	0.587252	+	0.809404i	$0.300210\pi$
$954$	1.76352e7	0.627348
$955$	−1.70767e7	−0.605892
$956$	1.48248e7	0.524617
$957$	1.68507e6	0.0594754
$958$	1.36336e7	0.479952
$959$	0	0
$960$	−1.28694e6	−0.0450692
$961$	−5.17709e6	−0.180833
$962$	−3.75674e6	−0.130880
$963$	4.86805e7	1.69157
$964$	4.68716e7	1.62449
$965$	−7.07045e7	−2.44416
$966$	0	0
$967$	3.09880e7	1.06568	0.532841	−	0.846216i	$-0.321125\pi$
$967$	3.09880e7	1.06568	0.532841	+	0.846216i	$0.321125\pi$
$968$	−1.92384e7	−0.659904
$969$	−8.51114e6	−0.291191
$970$	1.76764e7	0.603203
$971$	−4.87466e7	−1.65919	−0.829594	−	0.558366i	$-0.811428\pi$
$971$	−4.87466e7	−1.65919	−0.829594	+	0.558366i	$0.811428\pi$
$972$	1.52116e7	0.516427
$973$	0	0
$974$	−2.22989e7	−0.753157
$975$	−3.34365e6	−0.112644
$976$	1.99976e7	0.671976
$977$	−1.70428e7	−0.571223	−0.285612	−	0.958345i	$-0.592197\pi$
$977$	−1.70428e7	−0.571223	−0.285612	+	0.958345i	$0.592197\pi$
$978$	1.52999e6	0.0511495
$979$	−3.48028e6	−0.116053
$980$	0	0
$981$	3.45276e6	0.114550
$982$	−9.76374e6	−0.323100
$983$	−2.82661e7	−0.933001	−0.466501	−	0.884521i	$-0.654485\pi$
$983$	−2.82661e7	−0.933001	−0.466501	+	0.884521i	$0.654485\pi$
$984$	−6.87260e6	−0.226273
$985$	2.36098e7	0.775357
$986$	1.03215e7	0.338103
$987$	0	0
$988$	8.58795e6	0.279896
$989$	1.28161e7	0.416645
$990$	7.18258e6	0.232912
$991$	−3.72185e7	−1.20386	−0.601929	−	0.798550i	$-0.705601\pi$
$991$	−3.72185e7	−1.20386	−0.601929	+	0.798550i	$0.705601\pi$
$992$	2.71573e7	0.876209
$993$	−290996.	−0.00936512
$994$	0	0
$995$	894.863	2.86549e−5 0
$996$	−7.19259e6	−0.229740
$997$	−2.01775e7	−0.642880	−0.321440	−	0.946930i	$-0.604167\pi$
$997$	−2.01775e7	−0.642880	−0.321440	+	0.946930i	$0.604167\pi$
$998$	−1.34355e7	−0.427000
$999$	1.56256e7	0.495362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.6.a.e.1.4		8
7.6	odd	2		91.6.a.c.1.4	✓	8
21.20	even	2		819.6.a.j.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.6.a.c.1.4	✓	8	7.6	odd	2
637.6.a.e.1.4		8	1.1	even	1	trivial
819.6.a.j.1.5		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33047 q^{2} -3.45560 q^{3} -26.5689 q^{4} -94.0769 q^{5} +8.05316 q^{6} +136.493 q^{8} -231.059 q^{9} +219.243 q^{10} -141.785 q^{11} +91.8115 q^{12} +169.000 q^{13} +325.092 q^{15} +532.113 q^{16} -1287.76 q^{17} +538.475 q^{18} -1912.62 q^{19} +2499.52 q^{20} +330.426 q^{22} +1069.34 q^{23} -471.665 q^{24} +5725.47 q^{25} -393.849 q^{26} +1638.16 q^{27} +3439.24 q^{29} -757.616 q^{30} -4842.73 q^{31} -5607.85 q^{32} +489.953 q^{33} +3001.09 q^{34} +6138.98 q^{36} +9538.53 q^{37} +4457.30 q^{38} -583.996 q^{39} -12840.8 q^{40} +14570.9 q^{41} +11985.1 q^{43} +3767.09 q^{44} +21737.3 q^{45} -2492.06 q^{46} -12145.7 q^{47} -1838.77 q^{48} -13343.0 q^{50} +4449.99 q^{51} -4490.15 q^{52} +32750.2 q^{53} -3817.67 q^{54} +13338.7 q^{55} +6609.25 q^{57} -8015.04 q^{58} +48082.8 q^{59} -8637.34 q^{60} +37581.5 q^{61} +11285.8 q^{62} -3958.69 q^{64} -15899.0 q^{65} -1141.82 q^{66} -12664.7 q^{67} +34214.5 q^{68} -3695.20 q^{69} -71435.7 q^{71} -31537.9 q^{72} -53368.5 q^{73} -22229.2 q^{74} -19784.9 q^{75} +50816.3 q^{76} +1360.98 q^{78} -14516.6 q^{79} -50059.5 q^{80} +50486.5 q^{81} -33957.1 q^{82} -78340.8 q^{83} +121149. q^{85} -27930.9 q^{86} -11884.6 q^{87} -19352.7 q^{88} +24546.1 q^{89} -50658.1 q^{90} -28411.2 q^{92} +16734.5 q^{93} +28305.2 q^{94} +179934. q^{95} +19378.5 q^{96} +80624.4 q^{97} +32760.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 28 q^{3} + 245 q^{4} - 219 q^{5} - 435 q^{6} - 57 q^{8} + 930 q^{9} + 948 q^{10} + 184 q^{11} - 463 q^{12} + 1352 q^{13} - 256 q^{15} + 4953 q^{16} - 2278 q^{17} - 5308 q^{18} - 4959 q^{19}+ \cdots + 90754 q^{99}+O(q^{100}) \) 8 * q - q^2 - 28 * q^3 + 245 * q^4 - 219 * q^5 - 435 * q^6 - 57 * q^8 + 930 * q^9 + 948 * q^10 + 184 * q^11 - 463 * q^12 + 1352 * q^13 - 256 * q^15 + 4953 * q^16 - 2278 * q^17 - 5308 * q^18 - 4959 * q^19 - 6684 * q^20 - 2009 * q^22 + 1889 * q^23 - 26021 * q^24 + 4505 * q^25 - 169 * q^26 - 9016 * q^27 + 15265 * q^29 + 24204 * q^30 - 6805 * q^31 + 1335 * q^32 + 12892 * q^33 - 5828 * q^34 + 58838 * q^36 + 5534 * q^37 - 506 * q^38 - 4732 * q^39 + 56256 * q^40 - 31176 * q^41 - 391 * q^43 + 14047 * q^44 - 29403 * q^45 - 30027 * q^46 - 1539 * q^47 + 106629 * q^48 - 24367 * q^50 - 71892 * q^51 + 41405 * q^52 + 19553 * q^53 + 8155 * q^54 - 69414 * q^55 + 54432 * q^57 - 148020 * q^58 - 90596 * q^59 - 299448 * q^60 + 58218 * q^61 - 7697 * q^62 + 61681 * q^64 - 37011 * q^65 + 145411 * q^66 - 89884 * q^67 - 120612 * q^68 - 24278 * q^69 + 2308 * q^71 - 317742 * q^72 + 69187 * q^73 + 52027 * q^74 + 154856 * q^75 + 47258 * q^76 - 73515 * q^78 - 167799 * q^79 - 173400 * q^80 + 163984 * q^81 + 49553 * q^82 - 101449 * q^83 + 24684 * q^85 - 357720 * q^86 - 61908 * q^87 - 270819 * q^88 - 51833 * q^89 + 567124 * q^90 - 542963 * q^92 + 132644 * q^93 + 122399 * q^94 + 188103 * q^95 - 871725 * q^96 - 295025 * q^97 + 90754 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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