LMFDB - Embedded newform 650.6.b.g.599.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,6,Mod(599,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("650.599");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	650.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$104.249482878$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.4
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	650.599
Dual form			650.6.b.g.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000i q^{2} +13.8114i q^{3} -16.0000 q^{4} -55.2456 q^{6} -213.246i q^{7} -64.0000i q^{8} +52.2456 q^{9} +587.285 q^{11} -220.982i q^{12} -169.000i q^{13} +852.982 q^{14} +256.000 q^{16} -162.605i q^{17} +208.982i q^{18} +81.3914 q^{19} +2945.22 q^{21} +2349.14i q^{22} -2948.84i q^{23} +883.929 q^{24} +676.000 q^{26} +4077.75i q^{27} +3411.93i q^{28} -6254.43 q^{29} -4034.62 q^{31} +1024.00i q^{32} +8111.22i q^{33} +650.420 q^{34} -835.929 q^{36} -7617.22i q^{37} +325.566i q^{38} +2334.12 q^{39} +958.121 q^{41} +11780.9i q^{42} +169.655i q^{43} -9396.56 q^{44} +11795.4 q^{46} -21612.6i q^{47} +3535.72i q^{48} -28666.7 q^{49} +2245.80 q^{51} +2704.00i q^{52} +24789.1i q^{53} -16311.0 q^{54} -13647.7 q^{56} +1124.13i q^{57} -25017.7i q^{58} -40109.2 q^{59} -16343.0 q^{61} -16138.5i q^{62} -11141.1i q^{63} -4096.00 q^{64} -32444.9 q^{66} -18362.1i q^{67} +2601.68i q^{68} +40727.6 q^{69} -77846.0 q^{71} -3343.72i q^{72} -62130.2i q^{73} +30468.9 q^{74} -1302.26 q^{76} -125236. i q^{77} +9336.50i q^{78} +60599.1 q^{79} -43623.7 q^{81} +3832.48i q^{82} -2654.46i q^{83} -47123.5 q^{84} -678.619 q^{86} -86382.4i q^{87} -37586.2i q^{88} -8229.77 q^{89} -36038.5 q^{91} +47181.5i q^{92} -55723.7i q^{93} +86450.3 q^{94} -14142.9 q^{96} +53844.0i q^{97} -114667. i q^{98} +30683.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{4} + 32 q^{6} - 44 q^{9} + 768 q^{11} + 2400 q^{14} + 1024 q^{16} + 4816 q^{19} + 2800 q^{21} - 512 q^{24} + 2704 q^{26} - 7056 q^{29} + 1760 q^{31} - 1952 q^{34} + 704 q^{36} - 1352 q^{39}+ \cdots + 91552 q^{99}+O(q^{100}) $ 4 * q - 64 * q^4 + 32 * q^6 - 44 * q^9 + 768 * q^11 + 2400 * q^14 + 1024 * q^16 + 4816 * q^19 + 2800 * q^21 - 512 * q^24 + 2704 * q^26 - 7056 * q^29 + 1760 * q^31 - 1952 * q^34 + 704 * q^36 - 1352 * q^39 + 32040 * q^41 - 12288 * q^44 - 2656 * q^46 - 38772 * q^49 + 18976 * q^51 - 8576 * q^54 - 38400 * q^56 - 85744 * q^59 - 66384 * q^61 - 16384 * q^64 - 93856 * q^66 + 198328 * q^69 - 139040 * q^71 + 85952 * q^74 - 77056 * q^76 - 70416 * q^79 - 230404 * q^81 - 44800 * q^84 - 23712 * q^86 + 36904 * q^89 - 101400 * q^91 + 306336 * q^94 + 8192 * q^96 + 91552 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$1$

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 $

$2$	4.00000i	0.707107i
$2$	4.00000i	0.707107i
$3$	13.8114i	0.886001i	0.896521	+	0.443000i	$0.146086\pi$
$3$	13.8114i	0.886001i	−0.896521	+	0.443000i	$0.853914\pi$
$4$	−16.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	−55.2456	−0.626497
$7$	− 213.246i	− 1.64488i	−0.568850	−	0.822441i	$-0.692612\pi$
$7$	− 213.246i	− 1.64488i	0.568850	−	0.822441i	$-0.307388\pi$
$8$	− 64.0000i	− 0.353553i
$9$	52.2456	0.215002
$10$	0	0
$11$	587.285	1.46341	0.731707	−	0.681620i	$-0.238724\pi$
$11$	587.285	1.46341	0.731707	+	0.681620i	$0.238724\pi$
$12$	− 220.982i	− 0.443000i
$13$	− 169.000i	− 0.277350i
$13$	− 169.000i	− 0.277350i
$14$	852.982	1.16311
$15$	0	0
$16$	256.000	0.250000
$17$	− 162.605i	− 0.136462i	−0.997670	−	0.0682310i	$-0.978265\pi$
$17$	− 162.605i	− 0.136462i	0.997670	−	0.0682310i	$-0.0217355\pi$
$18$	208.982i	0.152030i
$19$	81.3914	0.0517243	0.0258622	−	0.999666i	$-0.491767\pi$
$19$	81.3914	0.0517243	0.0258622	+	0.999666i	$0.491767\pi$
$20$	0	0
$21$	2945.22	1.45737
$22$	2349.14i	1.03479i
$23$	− 2948.84i	− 1.16234i	−0.813783	−	0.581169i	$-0.802596\pi$
$23$	− 2948.84i	− 1.16234i	0.813783	−	0.581169i	$-0.197404\pi$
$24$	883.929	0.313249
$25$	0	0
$26$	676.000	0.196116
$27$	4077.75i	1.07649i
$28$	3411.93i	0.822441i
$29$	−6254.43	−1.38100	−0.690499	−	0.723333i	$-0.742609\pi$
$29$	−6254.43	−1.38100	−0.690499	+	0.723333i	$0.742609\pi$
$30$	0	0
$31$	−4034.62	−0.754048	−0.377024	−	0.926204i	$-0.623052\pi$
$31$	−4034.62	−0.754048	−0.377024	+	0.926204i	$0.623052\pi$
$32$	1024.00i	0.176777i
$33$	8111.22i	1.29659i
$34$	650.420	0.0964932
$35$	0	0
$36$	−835.929	−0.107501
$37$	− 7617.22i	− 0.914728i	−0.889280	−	0.457364i	$-0.848794\pi$
$37$	− 7617.22i	− 0.914728i	0.889280	−	0.457364i	$-0.151206\pi$
$38$	325.566i	0.0365746i
$39$	2334.12	0.245732
$40$	0	0
$41$	958.121	0.0890145	0.0445072	−	0.999009i	$-0.485828\pi$
$41$	958.121	0.0890145	0.0445072	+	0.999009i	$0.485828\pi$
$42$	11780.9i	1.03051i
$43$	169.655i	0.0139925i	0.999976	+	0.00699624i	$0.00222699\pi$
$43$	169.655i	0.0139925i	−0.999976	+	0.00699624i	$0.997773\pi$
$44$	−9396.56	−0.731707
$45$	0	0
$46$	11795.4	0.821897
$47$	− 21612.6i	− 1.42712i	−0.700592	−	0.713562i	$-0.747081\pi$
$47$	− 21612.6i	− 1.42712i	0.700592	−	0.713562i	$-0.252919\pi$
$48$	3535.72i	0.221500i
$49$	−28666.7	−1.70564
$50$	0	0
$51$	2245.80	0.120905
$52$	2704.00i	0.138675i
$53$	24789.1i	1.21219i	0.795392	+	0.606096i	$0.207265\pi$
$53$	24789.1i	1.21219i	−0.795392	+	0.606096i	$0.792735\pi$
$54$	−16311.0	−0.761196
$55$	0	0
$56$	−13647.7	−0.581554
$57$	1124.13i	0.0458278i
$58$	− 25017.7i	− 0.976513i
$59$	−40109.2	−1.50008	−0.750040	−	0.661392i	$-0.769966\pi$
$59$	−40109.2	−1.50008	−0.750040	+	0.661392i	$0.769966\pi$
$60$	0	0
$61$	−16343.0	−0.562351	−0.281176	−	0.959656i	$-0.590724\pi$
$61$	−16343.0	−0.562351	−0.281176	+	0.959656i	$0.590724\pi$
$62$	− 16138.5i	− 0.533192i
$63$	− 11141.1i	− 0.353653i
$64$	−4096.00	−0.125000
$65$	0	0
$66$	−32444.9	−0.916824
$67$	− 18362.1i	− 0.499731i	−0.968281	−	0.249866i	$-0.919614\pi$
$67$	− 18362.1i	− 0.499731i	0.968281	−	0.249866i	$-0.0803864\pi$
$68$	2601.68i	0.0682310i
$69$	40727.6	1.02983
$70$	0	0
$71$	−77846.0	−1.83270	−0.916348	−	0.400382i	$-0.868877\pi$
$71$	−77846.0	−1.83270	−0.916348	+	0.400382i	$0.868877\pi$
$72$	− 3343.72i	− 0.0760148i
$73$	− 62130.2i	− 1.36457i	−0.731087	−	0.682285i	$-0.760986\pi$
$73$	− 62130.2i	− 1.36457i	0.731087	−	0.682285i	$-0.239014\pi$
$74$	30468.9	0.646810
$75$	0	0
$76$	−1302.26	−0.0258622
$77$	− 125236.i	− 2.40714i
$78$	9336.50i	0.173759i
$79$	60599.1	1.09244	0.546221	−	0.837641i	$-0.316066\pi$
$79$	60599.1	1.09244	0.546221	+	0.837641i	$0.316066\pi$
$80$	0	0
$81$	−43623.7	−0.738772
$82$	3832.48i	0.0629427i
$83$	− 2654.46i	− 0.0422941i	−0.999776	−	0.0211471i	$-0.993268\pi$
$83$	− 2654.46i	− 0.0422941i	0.999776	−	0.0211471i	$-0.00673182\pi$
$84$	−47123.5	−0.728684
$85$	0	0
$86$	−678.619	−0.00989418
$87$	− 86382.4i	− 1.22357i
$88$	− 37586.2i	− 0.517395i
$89$	−8229.77	−0.110132	−0.0550659	−	0.998483i	$-0.517537\pi$
$89$	−8229.77	−0.110132	−0.0550659	+	0.998483i	$0.517537\pi$
$90$	0	0
$91$	−36038.5	−0.456208
$92$	47181.5i	0.581169i
$93$	− 55723.7i	− 0.668087i
$94$	86450.3	1.00913
$95$	0	0
$96$	−14142.9	−0.156624
$97$	53844.0i	0.581042i	0.956869	+	0.290521i	$0.0938287\pi$
$97$	53844.0i	0.581042i	−0.956869	+	0.290521i	$0.906171\pi$
$98$	− 114667.i	− 1.20607i
$99$	30683.0	0.314637
$100$	0	0
$101$	−167556.	−1.63439	−0.817196	−	0.576360i	$-0.804473\pi$
$101$	−167556.	−1.63439	−0.817196	+	0.576360i	$0.804473\pi$
$102$	8983.20i	0.0854930i
$103$	30973.8i	0.287675i	0.989601	+	0.143837i	$0.0459442\pi$
$103$	30973.8i	0.287675i	−0.989601	+	0.143837i	$0.954056\pi$
$104$	−10816.0	−0.0980581
$105$	0	0
$106$	−99156.4	−0.857149
$107$	97343.8i	0.821956i	0.911645	+	0.410978i	$0.134813\pi$
$107$	97343.8i	0.821956i	−0.911645	+	0.410978i	$0.865187\pi$
$108$	− 65244.0i	− 0.538247i
$109$	−16696.8	−0.134607	−0.0673035	−	0.997733i	$-0.521440\pi$
$109$	−16696.8	−0.134607	−0.0673035	+	0.997733i	$0.521440\pi$
$110$	0	0
$111$	105204.	0.810450
$112$	− 54590.9i	− 0.411221i
$113$	219357.i	1.61605i	0.589145	+	0.808027i	$0.299465\pi$
$113$	219357.i	1.61605i	−0.589145	+	0.808027i	$0.700535\pi$
$114$	−4496.51	−0.0324051
$115$	0	0
$116$	100071.	0.690499
$117$	− 8829.50i	− 0.0596309i
$118$	− 160437.i	− 1.06072i
$119$	−34674.8	−0.224464
$120$	0	0
$121$	183852.	1.14158
$122$	− 65372.1i	− 0.397642i
$123$	13233.0i	0.0788669i
$124$	64554.0	0.377024
$125$	0	0
$126$	44564.5	0.250071
$127$	− 158753.i	− 0.873399i	−0.899607	−	0.436700i	$-0.856147\pi$
$127$	− 158753.i	− 0.873399i	0.899607	−	0.436700i	$-0.143853\pi$
$128$	− 16384.0i	− 0.0883883i
$129$	−2343.17	−0.0123974
$130$	0	0
$131$	160566.	0.817477	0.408739	−	0.912651i	$-0.365969\pi$
$131$	160566.	0.817477	0.408739	+	0.912651i	$0.365969\pi$
$132$	− 129779.i	− 0.648293i
$133$	− 17356.4i	− 0.0850804i
$134$	73448.6	0.353363
$135$	0	0
$136$	−10406.7	−0.0482466
$137$	295668.i	1.34587i	0.739702	+	0.672934i	$0.234966\pi$
$137$	295668.i	1.34587i	−0.739702	+	0.672934i	$0.765034\pi$
$138$	162910.i	0.728201i
$139$	−6197.57	−0.0272072	−0.0136036	−	0.999907i	$-0.504330\pi$
$139$	−6197.57	−0.0272072	−0.0136036	+	0.999907i	$0.504330\pi$
$140$	0	0
$141$	298500.	1.26443
$142$	− 311384.i	− 1.29591i
$143$	− 99251.1i	− 0.405878i
$144$	13374.9	0.0537506
$145$	0	0
$146$	248521.	0.964896
$147$	− 395926.i	− 1.51120i
$148$	121875.i	0.457364i
$149$	371033.	1.36914	0.684569	−	0.728948i	$-0.259990\pi$
$149$	371033.	1.36914	0.684569	+	0.728948i	$0.259990\pi$
$150$	0	0
$151$	−508361.	−1.81439	−0.907193	−	0.420714i	$-0.861780\pi$
$151$	−508361.	−1.81439	−0.907193	+	0.420714i	$0.861780\pi$
$152$	− 5209.05i	− 0.0182873i
$153$	− 8495.39i	− 0.0293396i
$154$	500943.	1.70211
$155$	0	0
$156$	−37346.0	−0.122866
$157$	− 60014.9i	− 0.194317i	−0.995269	−	0.0971583i	$-0.969025\pi$
$157$	− 60014.9i	− 0.194317i	0.995269	−	0.0971583i	$-0.0309753\pi$
$158$	242397.i	0.772474i
$159$	−342372.	−1.07400
$160$	0	0
$161$	−628828.	−1.91191
$162$	− 174495.i	− 0.522391i
$163$	− 365913.i	− 1.07872i	−0.842075	−	0.539360i	$-0.818666\pi$
$163$	− 365913.i	− 1.07872i	0.842075	−	0.539360i	$-0.181334\pi$
$164$	−15329.9	−0.0445072
$165$	0	0
$166$	10617.8	0.0299065
$167$	− 67392.0i	− 0.186990i	−0.995620	−	0.0934948i	$-0.970196\pi$
$167$	− 67392.0i	− 0.186990i	0.995620	−	0.0934948i	$-0.0298038\pi$
$168$	− 188494.i	− 0.515257i
$169$	−28561.0	−0.0769231
$170$	0	0
$171$	4252.34	0.0111208
$172$	− 2714.48i	− 0.00699624i
$173$	518921.i	1.31821i	0.752049	+	0.659107i	$0.229066\pi$
$173$	518921.i	1.31821i	−0.752049	+	0.659107i	$0.770934\pi$
$174$	345530.	0.865191
$175$	0	0
$176$	150345.	0.365853
$177$	− 553964.i	− 1.32907i
$178$	− 32919.1i	− 0.0778750i
$179$	89728.6	0.209314	0.104657	−	0.994508i	$-0.466626\pi$
$179$	89728.6	0.209314	0.104657	+	0.994508i	$0.466626\pi$
$180$	0	0
$181$	−376272.	−0.853700	−0.426850	−	0.904322i	$-0.640377\pi$
$181$	−376272.	−0.853700	−0.426850	+	0.904322i	$0.640377\pi$
$182$	− 144154.i	− 0.322588i
$183$	− 225720.i	− 0.498244i
$184$	−188726.	−0.410948
$185$	0	0
$186$	222895.	0.472409
$187$	− 95495.4i	− 0.199700i
$188$	345801.i	0.713562i
$189$	869562.	1.77070
$190$	0	0
$191$	206748.	0.410070	0.205035	−	0.978755i	$-0.434269\pi$
$191$	206748.	0.410070	0.205035	+	0.978755i	$0.434269\pi$
$192$	− 56571.4i	− 0.110750i
$193$	− 413088.i	− 0.798269i	−0.916892	−	0.399135i	$-0.869311\pi$
$193$	− 413088.i	− 0.798269i	0.916892	−	0.399135i	$-0.130689\pi$
$194$	−215376.	−0.410859
$195$	0	0
$196$	458667.	0.852819
$197$	− 538825.i	− 0.989196i	−0.869122	−	0.494598i	$-0.835315\pi$
$197$	− 538825.i	− 0.989196i	0.869122	−	0.494598i	$-0.164685\pi$
$198$	122732.i	0.222482i
$199$	147336.	0.263740	0.131870	−	0.991267i	$-0.457902\pi$
$199$	147336.	0.263740	0.131870	+	0.991267i	$0.457902\pi$
$200$	0	0
$201$	253607.	0.442762
$202$	− 670223.i	− 1.15569i
$203$	1.33373e6i	2.27158i
$204$	−35932.8	−0.0604527
$205$	0	0
$206$	−123895.	−0.203417
$207$	− 154064.i	− 0.249905i
$208$	− 43264.0i	− 0.0693375i
$209$	47799.9	0.0756940
$210$	0	0
$211$	−1.14921e6	−1.77703	−0.888515	−	0.458847i	$-0.848262\pi$
$211$	−1.14921e6	−1.77703	−0.888515	+	0.458847i	$0.848262\pi$
$212$	− 396626.i	− 0.606096i
$213$	− 1.07516e6i	− 1.62377i
$214$	−389375.	−0.581211
$215$	0	0
$216$	260976.	0.380598
$217$	860365.i	1.24032i
$218$	− 66787.3i	− 0.0951815i
$219$	858104.	1.20901
$220$	0	0
$221$	−27480.2	−0.0378477
$222$	420817.i	0.573075i
$223$	− 1.39430e6i	− 1.87756i	−0.344513	−	0.938782i	$-0.611956\pi$
$223$	− 1.39430e6i	− 1.87756i	0.344513	−	0.938782i	$-0.388044\pi$
$224$	218363.	0.290777
$225$	0	0
$226$	−877429.	−1.14272
$227$	− 1.40291e6i	− 1.80703i	−0.428556	−	0.903515i	$-0.640977\pi$
$227$	− 1.40291e6i	− 1.80703i	0.428556	−	0.903515i	$-0.359023\pi$
$228$	− 17986.1i	− 0.0229139i
$229$	796626.	1.00384	0.501922	−	0.864913i	$-0.332627\pi$
$229$	796626.	1.00384	0.501922	+	0.864913i	$0.332627\pi$
$230$	0	0
$231$	1.72968e6	2.13273
$232$	400284.i	0.488257i
$233$	1.15975e6i	1.39951i	0.714385	+	0.699753i	$0.246707\pi$
$233$	1.15975e6i	1.39951i	−0.714385	+	0.699753i	$0.753293\pi$
$234$	35318.0	0.0421654
$235$	0	0
$236$	641748.	0.750040
$237$	836958.i	0.967905i
$238$	− 138699.i	− 0.158720i
$239$	687529.	0.778568	0.389284	−	0.921118i	$-0.372722\pi$
$239$	687529.	0.778568	0.389284	+	0.921118i	$0.372722\pi$
$240$	0	0
$241$	−391345.	−0.434028	−0.217014	−	0.976169i	$-0.569632\pi$
$241$	−391345.	−0.434028	−0.217014	+	0.976169i	$0.569632\pi$
$242$	735409.i	0.807218i
$243$	388389.i	0.421941i
$244$	261488.	0.281176
$245$	0	0
$246$	−52931.9	−0.0557673
$247$	− 13755.2i	− 0.0143457i
$248$	258216.i	0.266596i
$249$	36661.7	0.0374727
$250$	0	0
$251$	944723.	0.946499	0.473249	−	0.880928i	$-0.343081\pi$
$251$	944723.	0.946499	0.473249	+	0.880928i	$0.343081\pi$
$252$	178258.i	0.176827i
$253$	− 1.73181e6i	− 1.70098i
$254$	635012.	0.617587
$255$	0	0
$256$	65536.0	0.0625000
$257$	− 297219.i	− 0.280701i	−0.990102	−	0.140351i	$-0.955177\pi$
$257$	− 297219.i	− 0.280701i	0.990102	−	0.140351i	$-0.0448230\pi$
$258$	− 9372.67i	− 0.00876626i
$259$	−1.62434e6	−1.50462
$260$	0	0
$261$	−326766.	−0.296918
$262$	642264.i	0.578044i
$263$	− 1.53097e6i	− 1.36483i	−0.730966	−	0.682414i	$-0.760930\pi$
$263$	− 1.53097e6i	− 1.36483i	0.730966	−	0.682414i	$-0.239070\pi$
$264$	519118.	0.458412
$265$	0	0
$266$	69425.4	0.0601609
$267$	− 113665.i	− 0.0975769i
$268$	293794.i	0.249866i
$269$	1.00878e6	0.849994	0.424997	−	0.905195i	$-0.360275\pi$
$269$	1.00878e6	0.849994	0.424997	+	0.905195i	$0.360275\pi$
$270$	0	0
$271$	2.19122e6	1.81244	0.906220	−	0.422806i	$-0.138955\pi$
$271$	2.19122e6	1.81244	0.906220	+	0.422806i	$0.138955\pi$
$272$	− 41626.9i	− 0.0341155i
$273$	− 497742.i	− 0.404201i
$274$	−1.18267e6	−0.951673
$275$	0	0
$276$	−651642.	−0.514916
$277$	17924.0i	0.0140357i	0.999975	+	0.00701786i	$0.00223387\pi$
$277$	17924.0i	0.0140357i	−0.999975	+	0.00701786i	$0.997766\pi$
$278$	− 24790.3i	− 0.0192384i
$279$	−210791.	−0.162122
$280$	0	0
$281$	−2.40663e6	−1.81821	−0.909106	−	0.416566i	$-0.863234\pi$
$281$	−2.40663e6	−1.81821	−0.909106	+	0.416566i	$0.863234\pi$
$282$	1.19400e6i	0.894090i
$283$	− 1.36921e6i	− 1.01626i	−0.861281	−	0.508128i	$-0.830338\pi$
$283$	− 1.36921e6i	− 1.01626i	0.861281	−	0.508128i	$-0.169662\pi$
$284$	1.24554e6	0.916348
$285$	0	0
$286$	397004.	0.286999
$287$	− 204315.i	− 0.146418i
$288$	53499.4i	0.0380074i
$289$	1.39342e6	0.981378
$290$	0	0
$291$	−743660.	−0.514804
$292$	994083.i	0.682285i
$293$	− 390649.i	− 0.265838i	−0.991127	−	0.132919i	$-0.957565\pi$
$293$	− 390649.i	− 0.265838i	0.991127	−	0.132919i	$-0.0424351\pi$
$294$	1.58371e6	1.06858
$295$	0	0
$296$	−487502.	−0.323405
$297$	2.39480e6i	1.57535i
$298$	1.48413e6i	0.968127i
$299$	−498355.	−0.322374
$300$	0	0
$301$	36178.1	0.0230160
$302$	− 2.03344e6i	− 1.28297i
$303$	− 2.31418e6i	− 1.44807i
$304$	20836.2	0.0129311
$305$	0	0
$306$	33981.6	0.0207463
$307$	− 566546.i	− 0.343075i	−0.985178	−	0.171537i	$-0.945127\pi$
$307$	− 566546.i	− 0.343075i	0.985178	−	0.171537i	$-0.0548735\pi$
$308$	2.00377e6i	1.20357i
$309$	−427791.	−0.254880
$310$	0	0
$311$	881239.	0.516646	0.258323	−	0.966059i	$-0.416830\pi$
$311$	881239.	0.516646	0.258323	+	0.966059i	$0.416830\pi$
$312$	− 149384.i	− 0.0868795i
$313$	− 916421.i	− 0.528731i	−0.964423	−	0.264365i	$-0.914838\pi$
$313$	− 916421.i	− 0.528731i	0.964423	−	0.264365i	$-0.0851624\pi$
$314$	240060.	0.137403
$315$	0	0
$316$	−969586.	−0.546221
$317$	− 2.01084e6i	− 1.12390i	−0.827170	−	0.561951i	$-0.810051\pi$
$317$	− 2.01084e6i	− 1.12390i	0.827170	−	0.561951i	$-0.189949\pi$
$318$	− 1.36949e6i	− 0.759435i
$319$	−3.67313e6	−2.02097
$320$	0	0
$321$	−1.34445e6	−0.728254
$322$	− 2.51531e6i	− 1.35192i
$323$	− 13234.7i	− 0.00705840i
$324$	697980.	0.369386
$325$	0	0
$326$	1.46365e6	0.762770
$327$	− 230606.i	− 0.119262i
$328$	− 61319.7i	− 0.0314714i
$329$	−4.60879e6	−2.34745
$330$	0	0
$331$	2.47715e6	1.24275	0.621373	−	0.783515i	$-0.286575\pi$
$331$	2.47715e6	1.24275	0.621373	+	0.783515i	$0.286575\pi$
$332$	42471.3i	0.0211471i
$333$	− 397966.i	− 0.196669i
$334$	269568.	0.132222
$335$	0	0
$336$	753976.	0.364342
$337$	− 2.55550e6i	− 1.22575i	−0.790181	−	0.612873i	$-0.790014\pi$
$337$	− 2.55550e6i	− 1.22575i	0.790181	−	0.612873i	$-0.209986\pi$
$338$	− 114244.i	− 0.0543928i
$339$	−3.02963e6	−1.43183
$340$	0	0
$341$	−2.36947e6	−1.10348
$342$	17009.4i	0.00786362i
$343$	2.52902e6i	1.16069i
$344$	10857.9	0.00494709
$345$	0	0
$346$	−2.07568e6	−0.932118
$347$	475000.i	0.211773i	0.994378	+	0.105886i	$0.0337680\pi$
$347$	475000.i	0.211773i	−0.994378	+	0.105886i	$0.966232\pi$
$348$	1.38212e6i	0.611783i
$349$	−615277.	−0.270400	−0.135200	−	0.990818i	$-0.543168\pi$
$349$	−615277.	−0.270400	−0.135200	+	0.990818i	$0.543168\pi$
$350$	0	0
$351$	689140.	0.298565
$352$	601380.i	0.258697i
$353$	− 4.37400e6i	− 1.86828i	−0.356908	−	0.934140i	$-0.616169\pi$
$353$	− 4.37400e6i	− 1.86828i	0.356908	−	0.934140i	$-0.383831\pi$
$354$	2.21586e6	0.939796
$355$	0	0
$356$	131676.	0.0550659
$357$	− 478907.i	− 0.198875i
$358$	358914.i	0.148007i
$359$	−4.59562e6	−1.88195	−0.940975	−	0.338476i	$-0.890089\pi$
$359$	−4.59562e6	−1.88195	−0.940975	+	0.338476i	$0.890089\pi$
$360$	0	0
$361$	−2.46947e6	−0.997325
$362$	− 1.50509e6i	− 0.603657i
$363$	2.53926e6i	1.01144i
$364$	576616.	0.228104
$365$	0	0
$366$	902879.	0.352312
$367$	4.59362e6i	1.78029i	0.455681	+	0.890143i	$0.349396\pi$
$367$	4.59362e6i	1.78029i	−0.455681	+	0.890143i	$0.650604\pi$
$368$	− 754904.i	− 0.290584i
$369$	50057.6	0.0191383
$370$	0	0
$371$	5.28617e6	1.99391
$372$	891580.i	0.334043i
$373$	1.74314e6i	0.648724i	0.945933	+	0.324362i	$0.105150\pi$
$373$	1.74314e6i	0.648724i	−0.945933	+	0.324362i	$0.894850\pi$
$374$	381982.	0.141209
$375$	0	0
$376$	−1.38320e6	−0.504565
$377$	1.05700e6i	0.383020i
$378$	3.47825e6i	1.25208i
$379$	4.42529e6	1.58250	0.791250	−	0.611493i	$-0.209431\pi$
$379$	4.42529e6	1.58250	0.791250	+	0.611493i	$0.209431\pi$
$380$	0	0
$381$	2.19260e6	0.773833
$382$	826992.i	0.289963i
$383$	1.39773e6i	0.486884i	0.969915	+	0.243442i	$0.0782766\pi$
$383$	1.39773e6i	0.486884i	−0.969915	+	0.243442i	$0.921723\pi$
$384$	226286.	0.0783122
$385$	0	0
$386$	1.65235e6	0.564462
$387$	8863.71i	0.00300842i
$388$	− 861504.i	− 0.290521i
$389$	−1.63535e6	−0.547946	−0.273973	−	0.961737i	$-0.588338\pi$
$389$	−1.63535e6	−0.547946	−0.273973	+	0.961737i	$0.588338\pi$
$390$	0	0
$391$	−479497.	−0.158615
$392$	1.83467e6i	0.603034i
$393$	2.21764e6i	0.724286i
$394$	2.15530e6	0.699468
$395$	0	0
$396$	−490928.	−0.157319
$397$	− 4.90653e6i	− 1.56242i	−0.624268	−	0.781210i	$-0.714603\pi$
$397$	− 4.90653e6i	− 1.56242i	0.624268	−	0.781210i	$-0.285397\pi$
$398$	589344.i	0.186493i
$399$	239715.	0.0753813
$400$	0	0
$401$	−951184.	−0.295395	−0.147698	−	0.989033i	$-0.547186\pi$
$401$	−951184.	−0.295395	−0.147698	+	0.989033i	$0.547186\pi$
$402$	1.01443e6i	0.313080i
$403$	681851.i	0.209135i
$404$	2.68089e6	0.817196
$405$	0	0
$406$	−5.33492e6	−1.60625
$407$	− 4.47348e6i	− 1.33863i
$408$	− 143731.i	− 0.0427465i
$409$	−4.49464e6	−1.32858	−0.664289	−	0.747476i	$-0.731265\pi$
$409$	−4.49464e6	−1.32858	−0.664289	+	0.747476i	$0.731265\pi$
$410$	0	0
$411$	−4.08358e6	−1.19244
$412$	− 495581.i	− 0.143837i
$413$	8.55312e6i	2.46746i
$414$	616256.	0.176710
$415$	0	0
$416$	173056.	0.0490290
$417$	− 85597.0i	− 0.0241056i
$418$	191200.i	0.0535238i
$419$	828906.	0.230659	0.115329	−	0.993327i	$-0.463208\pi$
$419$	828906.	0.230659	0.115329	+	0.993327i	$0.463208\pi$
$420$	0	0
$421$	744813.	0.204806	0.102403	−	0.994743i	$-0.467347\pi$
$421$	744813.	0.204806	0.102403	+	0.994743i	$0.467347\pi$
$422$	− 4.59686e6i	− 1.25655i
$423$	− 1.12916e6i	− 0.306835i
$424$	1.58650e6	0.428574
$425$	0	0
$426$	4.30065e6	1.14818
$427$	3.48508e6i	0.925002i
$428$	− 1.55750e6i	− 0.410978i
$429$	1.37080e6	0.359608
$430$	0	0
$431$	−3.89529e6	−1.01006	−0.505030	−	0.863102i	$-0.668519\pi$
$431$	−3.89529e6	−1.01006	−0.505030	+	0.863102i	$0.668519\pi$
$432$	1.04390e6i	0.269123i
$433$	− 5.88297e6i	− 1.50792i	−0.656923	−	0.753958i	$-0.728142\pi$
$433$	− 5.88297e6i	− 1.50792i	0.656923	−	0.753958i	$-0.271858\pi$
$434$	−3.44146e6	−0.877038
$435$	0	0
$436$	267149.	0.0673035
$437$	− 240011.i	− 0.0601211i
$438$	3.43242e6i	0.854899i
$439$	−1.73024e6	−0.428495	−0.214248	−	0.976779i	$-0.568730\pi$
$439$	−1.73024e6	−0.428495	−0.214248	+	0.976779i	$0.568730\pi$
$440$	0	0
$441$	−1.49771e6	−0.366716
$442$	− 109921.i	− 0.0267624i
$443$	− 106432.i	− 0.0257670i	−0.999917	−	0.0128835i	$-0.995899\pi$
$443$	− 106432.i	− 0.0257670i	0.999917	−	0.0128835i	$-0.00410105\pi$
$444$	−1.68327e6	−0.405225
$445$	0	0
$446$	5.57721e6	1.32764
$447$	5.12449e6i	1.21306i
$448$	873454.i	0.205610i
$449$	4.89220e6	1.14522	0.572609	−	0.819828i	$-0.305931\pi$
$449$	4.89220e6	1.14522	0.572609	+	0.819828i	$0.305931\pi$
$450$	0	0
$451$	562690.	0.130265
$452$	− 3.50972e6i	− 0.808027i
$453$	− 7.02117e6i	− 1.60755i
$454$	5.61165e6	1.27776
$455$	0	0
$456$	71944.2	0.0162026
$457$	− 177252.i	− 0.0397008i	−0.999803	−	0.0198504i	$-0.993681\pi$
$457$	− 177252.i	− 0.0397008i	0.999803	−	0.0198504i	$-0.00631900\pi$
$458$	3.18651e6i	0.709824i
$459$	663063.	0.146900
$460$	0	0
$461$	7.15676e6	1.56843	0.784213	−	0.620491i	$-0.213067\pi$
$461$	7.15676e6	1.56843	0.784213	+	0.620491i	$0.213067\pi$
$462$	6.91872e6i	1.50807i
$463$	3.44228e6i	0.746267i	0.927778	+	0.373133i	$0.121717\pi$
$463$	3.44228e6i	0.746267i	−0.927778	+	0.373133i	$0.878283\pi$
$464$	−1.60114e6	−0.345249
$465$	0	0
$466$	−4.63900e6	−0.989600
$467$	9.22486e6i	1.95735i	0.205423	+	0.978673i	$0.434143\pi$
$467$	9.22486e6i	1.95735i	−0.205423	+	0.978673i	$0.565857\pi$
$468$	141272.i	0.0298155i
$469$	−3.91565e6	−0.821999
$470$	0	0
$471$	828889.	0.172165
$472$	2.56699e6i	0.530358i
$473$	99635.7i	0.0204768i
$474$	−3.34783e6	−0.684412
$475$	0	0
$476$	554797.	0.112232
$477$	1.29512e6i	0.260624i
$478$	2.75012e6i	0.550531i
$479$	−1.23331e6	−0.245602	−0.122801	−	0.992431i	$-0.539188\pi$
$479$	−1.23331e6	−0.245602	−0.122801	+	0.992431i	$0.539188\pi$
$480$	0	0
$481$	−1.28731e6	−0.253700
$482$	− 1.56538e6i	− 0.306904i
$483$	− 8.68498e6i	− 1.69395i
$484$	−2.94164e6	−0.570789
$485$	0	0
$486$	−1.55356e6	−0.298357
$487$	6.21276e6i	1.18703i	0.804823	+	0.593516i	$0.202260\pi$
$487$	6.21276e6i	1.18703i	−0.804823	+	0.593516i	$0.797740\pi$
$488$	1.04595e6i	0.198821i
$489$	5.05376e6	0.955747
$490$	0	0
$491$	−7.05221e6	−1.32014	−0.660072	−	0.751202i	$-0.729474\pi$
$491$	−7.05221e6	−1.32014	−0.660072	+	0.751202i	$0.729474\pi$
$492$	− 211728.i	− 0.0394335i
$493$	1.01700e6i	0.188454i
$494$	55020.6	0.0101440
$495$	0	0
$496$	−1.03286e6	−0.188512
$497$	1.66003e7i	3.01457i
$498$	146647.i	0.0264972i
$499$	−5.63009e6	−1.01220	−0.506098	−	0.862476i	$-0.668912\pi$
$499$	−5.63009e6	−1.01220	−0.506098	+	0.862476i	$0.668912\pi$
$500$	0	0
$501$	930778.	0.165673
$502$	3.77889e6i	0.669276i
$503$	9.65803e6i	1.70204i	0.525137	+	0.851018i	$0.324014\pi$
$503$	9.65803e6i	1.70204i	−0.525137	+	0.851018i	$0.675986\pi$
$504$	−713032.	−0.125035
$505$	0	0
$506$	6.92724e6	1.20277
$507$	− 394467.i	− 0.0681539i
$508$	2.54005e6i	0.436700i
$509$	4.39209e6	0.751409	0.375705	−	0.926739i	$-0.377401\pi$
$509$	4.39209e6	0.751409	0.375705	+	0.926739i	$0.377401\pi$
$510$	0	0
$511$	−1.32490e7	−2.24456
$512$	262144.i	0.0441942i
$513$	331894.i	0.0556809i
$514$	1.18888e6	0.198486
$515$	0	0
$516$	37490.7	0.00619868
$517$	− 1.26927e7i	− 2.08847i
$518$	− 6.49735e6i	− 1.06393i
$519$	−7.16702e6	−1.16794
$520$	0	0
$521$	−8.38443e6	−1.35325	−0.676627	−	0.736326i	$-0.736559\pi$
$521$	−8.38443e6	−1.35325	−0.676627	+	0.736326i	$0.736559\pi$
$522$	− 1.30707e6i	− 0.209953i
$523$	2.54489e6i	0.406831i	0.979092	+	0.203416i	$0.0652042\pi$
$523$	2.54489e6i	0.406831i	−0.979092	+	0.203416i	$0.934796\pi$
$524$	−2.56906e6	−0.408739
$525$	0	0
$526$	6.12389e6	0.965080
$527$	656050.i	0.102899i
$528$	2.07647e6i	0.324146i
$529$	−2.25933e6	−0.351028
$530$	0	0
$531$	−2.09553e6	−0.322521
$532$	277702.i	0.0425402i
$533$	− 161922.i	− 0.0246882i
$534$	454658.	0.0689973
$535$	0	0
$536$	−1.17518e6	−0.176682
$537$	1.23928e6i	0.185452i
$538$	4.03512e6i	0.601036i
$539$	−1.68355e7	−2.49605
$540$	0	0
$541$	−3.83465e6	−0.563290	−0.281645	−	0.959519i	$-0.590880\pi$
$541$	−3.83465e6	−0.563290	−0.281645	+	0.959519i	$0.590880\pi$
$542$	8.76490e6i	1.28159i
$543$	− 5.19684e6i	− 0.756379i
$544$	166508.	0.0241233
$545$	0	0
$546$	1.99097e6	0.285813
$547$	2.61787e6i	0.374093i	0.982351	+	0.187047i	$0.0598916\pi$
$547$	2.61787e6i	0.374093i	−0.982351	+	0.187047i	$0.940108\pi$
$548$	− 4.73068e6i	− 0.672934i
$549$	−853850.	−0.120907
$550$	0	0
$551$	−509057.	−0.0714312
$552$	− 2.60657e6i	− 0.364101i
$553$	− 1.29225e7i	− 1.79694i
$554$	−71695.9	−0.00992476
$555$	0	0
$556$	99161.1	0.0136036
$557$	− 5.40419e6i	− 0.738061i	−0.929417	−	0.369031i	$-0.879690\pi$
$557$	− 5.40419e6i	− 0.738061i	0.929417	−	0.369031i	$-0.120310\pi$
$558$	− 843164.i	− 0.114638i
$559$	28671.7	0.00388082
$560$	0	0
$561$	1.31892e6	0.176935
$562$	− 9.62654e6i	− 1.28567i
$563$	904604.i	0.120278i	0.998190	+	0.0601392i	$0.0191545\pi$
$563$	904604.i	0.120278i	−0.998190	+	0.0601392i	$0.980846\pi$
$564$	−4.77599e6	−0.632217
$565$	0	0
$566$	5.47683e6	0.718602
$567$	9.30257e6i	1.21519i
$568$	4.98215e6i	0.647956i
$569$	6.69355e6	0.866714	0.433357	−	0.901222i	$-0.357329\pi$
$569$	6.69355e6	0.866714	0.433357	+	0.901222i	$0.357329\pi$
$570$	0	0
$571$	8.22981e6	1.05633	0.528165	−	0.849142i	$-0.322880\pi$
$571$	8.22981e6	1.05633	0.528165	+	0.849142i	$0.322880\pi$
$572$	1.58802e6i	0.202939i
$573$	2.85548e6i	0.363322i
$574$	817260.	0.103533
$575$	0	0
$576$	−213998.	−0.0268753
$577$	− 3.07720e6i	− 0.384783i	−0.981318	−	0.192391i	$-0.938376\pi$
$577$	− 3.07720e6i	− 0.384783i	0.981318	−	0.192391i	$-0.0616243\pi$
$578$	5.57367e6i	0.693939i
$579$	5.70532e6	0.707267
$580$	0	0
$581$	−566051.	−0.0695689
$582$	− 2.97464e6i	− 0.364021i
$583$	1.45583e7i	1.77394i
$584$	−3.97633e6	−0.482448
$585$	0	0
$586$	1.56260e6	0.187976
$587$	− 2.64175e6i	− 0.316443i	−0.987404	−	0.158222i	$-0.949424\pi$
$587$	− 2.64175e6i	− 0.316443i	0.987404	−	0.158222i	$-0.0505761\pi$
$588$	6.33482e6i	0.755599i
$589$	−328384.	−0.0390026
$590$	0	0
$591$	7.44193e6	0.876429
$592$	− 1.95001e6i	− 0.228682i
$593$	− 5.06641e6i	− 0.591649i	−0.955242	−	0.295824i	$-0.904406\pi$
$593$	− 5.06641e6i	− 0.591649i	0.955242	−	0.295824i	$-0.0955943\pi$
$594$	−9.57920e6	−1.11394
$595$	0	0
$596$	−5.93654e6	−0.684569
$597$	2.03492e6i	0.233674i
$598$	− 1.99342e6i	− 0.227953i
$599$	−1.31136e7	−1.49332	−0.746662	−	0.665204i	$-0.768345\pi$
$599$	−1.31136e7	−1.49332	−0.746662	+	0.665204i	$0.768345\pi$
$600$	0	0
$601$	7.53425e6	0.850852	0.425426	−	0.904993i	$-0.360124\pi$
$601$	7.53425e6	0.850852	0.425426	+	0.904993i	$0.360124\pi$
$602$	144713.i	0.0162748i
$603$	− 959341.i	− 0.107443i
$604$	8.13378e6	0.907193
$605$	0	0
$606$	9.25672e6	1.02394
$607$	− 8.76101e6i	− 0.965123i	−0.875862	−	0.482561i	$-0.839707\pi$
$607$	− 8.76101e6i	− 0.965123i	0.875862	−	0.482561i	$-0.160293\pi$
$608$	83344.8i	0.00914365i
$609$	−1.84207e7	−2.01262
$610$	0	0
$611$	−3.65253e6	−0.395813
$612$	135926.i	0.0146698i
$613$	− 469316.i	− 0.0504445i	−0.999682	−	0.0252223i	$-0.991971\pi$
$613$	− 469316.i	− 0.0504445i	0.999682	−	0.0252223i	$-0.00802935\pi$
$614$	2.26618e6	0.242591
$615$	0	0
$616$	−8.01509e6	−0.851054
$617$	4.14114e6i	0.437933i	0.975732	+	0.218966i	$0.0702685\pi$
$617$	4.14114e6i	0.437933i	−0.975732	+	0.218966i	$0.929732\pi$
$618$	− 1.71116e6i	− 0.180227i
$619$	1.31422e7	1.37861	0.689304	−	0.724472i	$-0.257916\pi$
$619$	1.31422e7	1.37861	0.689304	+	0.724472i	$0.257916\pi$
$620$	0	0
$621$	1.20246e7	1.25125
$622$	3.52496e6i	0.365324i
$623$	1.75496e6i	0.181154i
$624$	597536.	0.0614331
$625$	0	0
$626$	3.66569e6	0.373869
$627$	660184.i	0.0670650i
$628$	960239.i	0.0971583i
$629$	−1.23860e6	−0.124826
$630$	0	0
$631$	9.79229e6	0.979063	0.489532	−	0.871986i	$-0.337168\pi$
$631$	9.79229e6	0.979063	0.489532	+	0.871986i	$0.337168\pi$
$632$	− 3.87834e6i	− 0.386237i
$633$	− 1.58722e7i	− 1.57445i
$634$	8.04335e6	0.794719
$635$	0	0
$636$	5.47795e6	0.537001
$637$	4.84467e6i	0.473059i
$638$	− 1.46925e7i	− 1.42904i
$639$	−4.06711e6	−0.394034
$640$	0	0
$641$	3.38154e6	0.325064	0.162532	−	0.986703i	$-0.448034\pi$
$641$	3.38154e6	0.325064	0.162532	+	0.986703i	$0.448034\pi$
$642$	− 5.37781e6i	− 0.514953i
$643$	− 3.04366e6i	− 0.290314i	−0.989409	−	0.145157i	$-0.953631\pi$
$643$	− 3.04366e6i	− 0.290314i	0.989409	−	0.145157i	$-0.0463687\pi$
$644$	1.00612e7	0.955954
$645$	0	0
$646$	52938.6	0.00499104
$647$	− 8.51735e6i	− 0.799915i	−0.916534	−	0.399957i	$-0.869025\pi$
$647$	− 8.51735e6i	− 0.799915i	0.916534	−	0.399957i	$-0.130975\pi$
$648$	2.79192e6i	0.261195i
$649$	−2.35555e7	−2.19524
$650$	0	0
$651$	−1.18828e7	−1.09892
$652$	5.85461e6i	0.539360i
$653$	− 8.83998e6i	− 0.811275i	−0.914034	−	0.405638i	$-0.867050\pi$
$653$	− 8.83998e6i	− 0.811275i	0.914034	−	0.405638i	$-0.132950\pi$
$654$	922425.	0.0843309
$655$	0	0
$656$	245279.	0.0222536
$657$	− 3.24603e6i	− 0.293386i
$658$	− 1.84351e7i	− 1.65990i
$659$	2.97807e6	0.267129	0.133564	−	0.991040i	$-0.457358\pi$
$659$	2.97807e6	0.267129	0.133564	+	0.991040i	$0.457358\pi$
$660$	0	0
$661$	−7.90309e6	−0.703548	−0.351774	−	0.936085i	$-0.614421\pi$
$661$	−7.90309e6	−0.703548	−0.351774	+	0.936085i	$0.614421\pi$
$662$	9.90860e6i	0.878754i
$663$	− 379540.i	− 0.0335331i
$664$	−169885.	−0.0149532
$665$	0	0
$666$	1.59186e6	0.139066
$667$	1.84433e7i	1.60519i
$668$	1.07827e6i	0.0934948i
$669$	1.92572e7	1.66352
$670$	0	0
$671$	−9.59800e6	−0.822952
$672$	3.01590e6i	0.257629i
$673$	1.82522e7i	1.55338i	0.629885	+	0.776688i	$0.283102\pi$
$673$	1.82522e7i	1.55338i	−0.629885	+	0.776688i	$0.716898\pi$
$674$	1.02220e7	0.866734
$675$	0	0
$676$	456976.	0.0384615
$677$	− 5.39380e6i	− 0.452296i	−0.974093	−	0.226148i	$-0.927387\pi$
$677$	− 5.39380e6i	− 0.452296i	0.974093	−	0.226148i	$-0.0726134\pi$
$678$	− 1.21185e7i	− 1.01245i
$679$	1.14820e7	0.955746
$680$	0	0
$681$	1.93762e7	1.60103
$682$	− 9.47789e6i	− 0.780280i
$683$	2.30171e7i	1.88799i	0.329963	+	0.943994i	$0.392964\pi$
$683$	2.30171e7i	1.88799i	−0.329963	+	0.943994i	$0.607036\pi$
$684$	−68037.4	−0.00556042
$685$	0	0
$686$	−1.01161e7	−0.820733
$687$	1.10025e7i	0.889406i
$688$	43431.6i	0.00349812i
$689$	4.18936e6	0.336201
$690$	0	0
$691$	4.87910e6	0.388727	0.194364	−	0.980930i	$-0.437736\pi$
$691$	4.87910e6	0.388727	0.194364	+	0.980930i	$0.437736\pi$
$692$	− 8.30274e6i	− 0.659107i
$693$	− 6.54302e6i	− 0.517541i
$694$	−1.90000e6	−0.149746
$695$	0	0
$696$	−5.52847e6	−0.432596
$697$	− 155795.i	− 0.0121471i
$698$	− 2.46111e6i	− 0.191202i
$699$	−1.60178e7	−1.23996
$700$	0	0
$701$	1.47820e7	1.13615	0.568077	−	0.822976i	$-0.307688\pi$
$701$	1.47820e7	1.13615	0.568077	+	0.822976i	$0.307688\pi$
$702$	2.75656e6i	0.211118i
$703$	− 619976.i	− 0.0473137i
$704$	−2.40552e6	−0.182927
$705$	0	0
$706$	1.74960e7	1.32107
$707$	3.57305e7i	2.68838i
$708$	8.86343e6i	0.664536i
$709$	2.75364e6	0.205727	0.102863	−	0.994695i	$-0.467200\pi$
$709$	2.75364e6	0.205727	0.102863	+	0.994695i	$0.467200\pi$
$710$	0	0
$711$	3.16603e6	0.234878
$712$	526705.i	0.0389375i
$713$	1.18975e7i	0.876457i
$714$	1.91563e6	0.140626
$715$	0	0
$716$	−1.43566e6	−0.104657
$717$	9.49574e6i	0.689812i
$718$	− 1.83825e7i	− 1.33074i
$719$	2.10250e7	1.51675	0.758373	−	0.651820i	$-0.225994\pi$
$719$	2.10250e7	1.51675	0.758373	+	0.651820i	$0.225994\pi$
$720$	0	0
$721$	6.60502e6	0.473191
$722$	− 9.87790e6i	− 0.705215i
$723$	− 5.40502e6i	− 0.384549i
$724$	6.02035e6	0.426850
$725$	0	0
$726$	−1.01570e7	−0.715196
$727$	− 2.21381e7i	− 1.55347i	−0.629825	−	0.776737i	$-0.716873\pi$
$727$	− 2.21381e7i	− 1.55347i	0.629825	−	0.776737i	$-0.283127\pi$
$728$	2.30646e6i	0.161294i
$729$	−1.59648e7	−1.11261
$730$	0	0
$731$	27586.7	0.00190944
$732$	3.61152e6i	0.249122i
$733$	1.23177e7i	0.846775i	0.905949	+	0.423388i	$0.139159\pi$
$733$	1.23177e7i	0.846775i	−0.905949	+	0.423388i	$0.860841\pi$
$734$	−1.83745e7	−1.25885
$735$	0	0
$736$	3.01962e6	0.205474
$737$	− 1.07838e7i	− 0.731313i
$738$	200230.i	0.0135328i
$739$	1.79039e7	1.20597	0.602986	−	0.797752i	$-0.293977\pi$
$739$	1.79039e7	1.20597	0.602986	+	0.797752i	$0.293977\pi$
$740$	0	0
$741$	189978.	0.0127103
$742$	2.11447e7i	1.40991i
$743$	− 9.82085e6i	− 0.652645i	−0.945258	−	0.326323i	$-0.894190\pi$
$743$	− 9.82085e6i	− 0.652645i	0.945258	−	0.326323i	$-0.105810\pi$
$744$	−3.56632e6	−0.236204
$745$	0	0
$746$	−6.97256e6	−0.458717
$747$	− 138684.i	− 0.00909334i
$748$	1.52793e6i	0.0998501i
$749$	2.07581e7	1.35202
$750$	0	0
$751$	1.04747e7	0.677705	0.338852	−	0.940840i	$-0.389961\pi$
$751$	1.04747e7	0.677705	0.338852	+	0.940840i	$0.389961\pi$
$752$	− 5.53282e6i	− 0.356781i
$753$	1.30479e7i	0.838599i
$754$	−4.22800e6	−0.270836
$755$	0	0
$756$	−1.39130e7	−0.885352
$757$	− 2.20487e7i	− 1.39844i	−0.714908	−	0.699219i	$-0.753531\pi$
$757$	− 2.20487e7i	− 1.39844i	0.714908	−	0.699219i	$-0.246469\pi$
$758$	1.77012e7i	1.11900i
$759$	2.39187e7	1.50707
$760$	0	0
$761$	−2.75293e7	−1.72319	−0.861596	−	0.507594i	$-0.830535\pi$
$761$	−2.75293e7	−1.72319	−0.861596	+	0.507594i	$0.830535\pi$
$762$	8.77040e6i	0.547182i
$763$	3.56052e6i	0.221413i
$764$	−3.30797e6	−0.205035
$765$	0	0
$766$	−5.59091e6	−0.344279
$767$	6.77846e6i	0.416047i
$768$	905143.i	0.0553751i
$769$	−1.50464e7	−0.917525	−0.458763	−	0.888559i	$-0.651707\pi$
$769$	−1.50464e7	−0.917525	−0.458763	+	0.888559i	$0.651707\pi$
$770$	0	0
$771$	4.10501e6	0.248701
$772$	6.60941e6i	0.399135i
$773$	2.28606e6i	0.137606i	0.997630	+	0.0688031i	$0.0219180\pi$
$773$	2.28606e6i	0.137606i	−0.997630	+	0.0688031i	$0.978082\pi$
$774$	−35454.8	−0.00212727
$775$	0	0
$776$	3.44601e6	0.205430
$777$	− 2.24344e7i	− 1.33310i
$778$	− 6.54142e6i	− 0.387456i
$779$	77982.8	0.00460421
$780$	0	0
$781$	−4.57178e7	−2.68199
$782$	− 1.91799e6i	− 0.112158i
$783$	− 2.55040e7i	− 1.48663i
$784$	−7.33867e6	−0.426410
$785$	0	0
$786$	−8.87056e6	−0.512147
$787$	− 9.89052e6i	− 0.569223i	−0.958643	−	0.284611i	$-0.908135\pi$
$787$	− 9.89052e6i	− 0.569223i	0.958643	−	0.284611i	$-0.0918646\pi$
$788$	8.62121e6i	0.494598i
$789$	2.11449e7	1.20924
$790$	0	0
$791$	4.67770e7	2.65822
$792$	− 1.96371e6i	− 0.111241i
$793$	2.76197e6i	0.155968i
$794$	1.96261e7	1.10480
$795$	0	0
$796$	−2.35738e6	−0.131870
$797$	− 2.93049e7i	− 1.63416i	−0.576525	−	0.817080i	$-0.695592\pi$
$797$	− 2.93049e7i	− 1.63416i	0.576525	−	0.817080i	$-0.304408\pi$
$798$	958862.i	0.0533026i
$799$	−3.51431e6	−0.194748
$800$	0	0
$801$	−429969.	−0.0236786
$802$	− 3.80474e6i	− 0.208876i
$803$	− 3.64881e7i	− 1.99693i
$804$	−4.05771e6	−0.221381
$805$	0	0
$806$	−2.72741e6	−0.147881
$807$	1.39327e7i	0.753095i
$808$	1.07236e7i	0.577845i
$809$	−1.02027e7	−0.548078	−0.274039	−	0.961719i	$-0.588360\pi$
$809$	−1.02027e7	−0.548078	−0.274039	+	0.961719i	$0.588360\pi$
$810$	0	0
$811$	−1.26432e7	−0.675001	−0.337501	−	0.941325i	$-0.609582\pi$
$811$	−1.26432e7	−0.675001	−0.337501	+	0.941325i	$0.609582\pi$
$812$	− 2.13397e7i	− 1.13579i
$813$	3.02639e7i	1.60582i
$814$	1.78939e7	0.946551
$815$	0	0
$816$	574925.	0.0302264
$817$	13808.4i	0 0.000723752i
$818$	− 1.79786e7i	− 0.939446i
$819$	−1.88285e6	−0.0980858
$820$	0	0
$821$	−1.56881e7	−0.812294	−0.406147	−	0.913808i	$-0.633128\pi$
$821$	−1.56881e7	−0.812294	−0.406147	+	0.913808i	$0.633128\pi$
$822$	− 1.63343e7i	− 0.843183i
$823$	2.45799e7i	1.26497i	0.774571	+	0.632487i	$0.217966\pi$
$823$	2.45799e7i	1.26497i	−0.774571	+	0.632487i	$0.782034\pi$
$824$	1.98232e6	0.101708
$825$	0	0
$826$	−3.42125e7	−1.74475
$827$	− 3.62365e7i	− 1.84239i	−0.389098	−	0.921197i	$-0.627213\pi$
$827$	− 3.62365e7i	− 1.84239i	0.389098	−	0.921197i	$-0.372787\pi$
$828$	2.46502e6i	0.124953i
$829$	2.81815e7	1.42422	0.712110	−	0.702068i	$-0.247740\pi$
$829$	2.81815e7	1.42422	0.712110	+	0.702068i	$0.247740\pi$
$830$	0	0
$831$	−247555.	−0.0124357
$832$	692224.i	0.0346688i
$833$	4.66134e6i	0.232755i
$834$	342388.	0.0170453
$835$	0	0
$836$	−764799.	−0.0378470
$837$	− 1.64522e7i	− 0.811727i
$838$	3.31562e6i	0.163100i
$839$	8.42806e6	0.413354	0.206677	−	0.978409i	$-0.433735\pi$
$839$	8.42806e6	0.413354	0.206677	+	0.978409i	$0.433735\pi$
$840$	0	0
$841$	1.86068e7	0.907155
$842$	2.97925e6i	0.144820i
$843$	− 3.32390e7i	− 1.61094i
$844$	1.83874e7	0.888515
$845$	0	0
$846$	4.51664e6	0.216965
$847$	− 3.92057e7i	− 1.87776i
$848$	6.34601e6i	0.303048i
$849$	1.89107e7	0.900404
$850$	0	0
$851$	−2.24620e7	−1.06322
$852$	1.72026e7i	0.811886i
$853$	− 3.10763e7i	− 1.46237i	−0.682180	−	0.731184i	$-0.738968\pi$
$853$	− 3.10763e7i	− 1.46237i	0.682180	−	0.731184i	$-0.261032\pi$
$854$	−1.39403e7	−0.654075
$855$	0	0
$856$	6.23000e6	0.290605
$857$	5.72064e6i	0.266068i	0.991111	+	0.133034i	$0.0424720\pi$
$857$	5.72064e6i	0.266068i	−0.991111	+	0.133034i	$0.957528\pi$
$858$	5.48318e6i	0.254281i
$859$	6.04140e6	0.279354	0.139677	−	0.990197i	$-0.455394\pi$
$859$	6.04140e6	0.279354	0.139677	+	0.990197i	$0.455394\pi$
$860$	0	0
$861$	2.82187e6	0.129727
$862$	− 1.55812e7i	− 0.714220i
$863$	2.09227e7i	0.956292i	0.878280	+	0.478146i	$0.158691\pi$
$863$	2.09227e7i	0.956292i	−0.878280	+	0.478146i	$0.841309\pi$
$864$	−4.17562e6	−0.190299
$865$	0	0
$866$	2.35319e7	1.06626
$867$	1.92450e7i	0.869502i
$868$	− 1.37658e7i	− 0.620160i
$869$	3.55889e7	1.59869
$870$	0	0
$871$	−3.10320e6	−0.138601
$872$	1.06860e6i	0.0475908i
$873$	2.81311e6i	0.124925i
$874$	960042.	0.0425120
$875$	0	0
$876$	−1.37297e7	−0.604505
$877$	5.01539e6i	0.220194i	0.993921	+	0.110097i	$0.0351162\pi$
$877$	5.01539e6i	0.220194i	−0.993921	+	0.110097i	$0.964884\pi$
$878$	− 6.92097e6i	− 0.302992i
$879$	5.39541e6	0.235533
$880$	0	0
$881$	−2.14791e7	−0.932346	−0.466173	−	0.884694i	$-0.654368\pi$
$881$	−2.14791e7	−0.932346	−0.466173	+	0.884694i	$0.654368\pi$
$882$	− 5.99082e6i	− 0.259307i
$883$	996549.i	0.0430127i	0.999769	+	0.0215064i	$0.00684621\pi$
$883$	996549.i	0.0430127i	−0.999769	+	0.0215064i	$0.993154\pi$
$884$	439684.	0.0189239
$885$	0	0
$886$	425728.	0.0182200
$887$	− 4.67336e6i	− 0.199444i	−0.995015	−	0.0997219i	$-0.968205\pi$
$887$	− 4.67336e6i	− 0.199444i	0.995015	−	0.0997219i	$-0.0317953\pi$
$888$	− 6.73308e6i	− 0.286537i
$889$	−3.38534e7	−1.43664
$890$	0	0
$891$	−2.56196e7	−1.08113
$892$	2.23088e7i	0.938782i
$893$	− 1.75908e6i	− 0.0738170i
$894$	−2.04980e7	−0.857762
$895$	0	0
$896$	−3.49382e6	−0.145388
$897$	− 6.88297e6i	− 0.285624i
$898$	1.95688e7i	0.809792i
$899$	2.52343e7	1.04134
$900$	0	0
$901$	4.03083e6	0.165418
$902$	2.25076e6i	0.0921112i
$903$	499670.i	0.0203922i
$904$	1.40389e7	0.571362
$905$	0	0
$906$	2.80847e7	1.13671
$907$	− 1.18130e7i	− 0.476807i	−0.971166	−	0.238403i	$-0.923376\pi$
$907$	− 1.18130e7i	− 0.476807i	0.971166	−	0.238403i	$-0.0766240\pi$
$908$	2.24466e7i	0.903515i
$909$	−8.75405e6	−0.351398
$910$	0	0
$911$	3.55560e7	1.41944	0.709721	−	0.704483i	$-0.248821\pi$
$911$	3.55560e7	1.41944	0.709721	+	0.704483i	$0.248821\pi$
$912$	287777.i	0.0114569i
$913$	− 1.55892e6i	− 0.0618938i
$914$	709006.	0.0280727
$915$	0	0
$916$	−1.27460e7	−0.501922
$917$	− 3.42400e7i	− 1.34465i
$918$	2.65225e6i	0.103874i
$919$	−2.66902e7	−1.04247	−0.521235	−	0.853413i	$-0.674528\pi$
$919$	−2.66902e7	−1.04247	−0.521235	+	0.853413i	$0.674528\pi$
$920$	0	0
$921$	7.82478e6	0.303965
$922$	2.86270e7i	1.10905i
$923$	1.31560e7i	0.508299i
$924$	−2.76749e7	−1.06637
$925$	0	0
$926$	−1.37691e7	−0.527690
$927$	1.61824e6i	0.0618507i
$928$	− 6.40454e6i	− 0.244128i
$929$	3.08229e7	1.17175	0.585874	−	0.810402i	$-0.300751\pi$
$929$	3.08229e7	1.17175	0.585874	+	0.810402i	$0.300751\pi$
$930$	0	0
$931$	−2.33322e6	−0.0882230
$932$	− 1.85560e7i	− 0.699753i
$933$	1.21711e7i	0.457749i
$934$	−3.68994e7	−1.38405
$935$	0	0
$936$	−565088.	−0.0210827
$937$	− 2.78462e7i	− 1.03613i	−0.855340	−	0.518067i	$-0.826652\pi$
$937$	− 2.78462e7i	− 1.03613i	0.855340	−	0.518067i	$-0.173348\pi$
$938$	− 1.56626e7i	− 0.581241i
$939$	1.26571e7	0.468456
$940$	0	0
$941$	2.80836e7	1.03390	0.516950	−	0.856016i	$-0.327067\pi$
$941$	2.80836e7	1.03390	0.516950	+	0.856016i	$0.327067\pi$
$942$	3.31556e6i	0.121739i
$943$	− 2.82535e6i	− 0.103465i
$944$	−1.02680e7	−0.375020
$945$	0	0
$946$	−398543.	−0.0144793
$947$	4.49006e7i	1.62696i	0.581592	+	0.813481i	$0.302430\pi$
$947$	4.49006e7i	1.62696i	−0.581592	+	0.813481i	$0.697570\pi$
$948$	− 1.33913e7i	− 0.483953i
$949$	−1.05000e7	−0.378463
$950$	0	0
$951$	2.77724e7	0.995779
$952$	2.21919e6i	0.0793600i
$953$	− 1.13992e7i	− 0.406577i	−0.979119	−	0.203289i	$-0.934837\pi$
$953$	− 1.13992e7i	− 0.406577i	0.979119	−	0.203289i	$-0.0651630\pi$
$954$	−5.18048e6	−0.184289
$955$	0	0
$956$	−1.10005e7	−0.389284
$957$	− 5.07311e7i	− 1.79058i
$958$	− 4.93322e6i	− 0.173667i
$959$	6.30498e7	2.21380
$960$	0	0
$961$	−1.23510e7	−0.431412
$962$	− 5.14924e6i	− 0.179393i
$963$	5.08578e6i	0.176722i
$964$	6.26152e6	0.217014
$965$	0	0
$966$	3.47399e7	1.19781
$967$	5.54751e7i	1.90780i	0.300130	+	0.953898i	$0.402970\pi$
$967$	5.54751e7i	1.90780i	−0.300130	+	0.953898i	$0.597030\pi$
$968$	− 1.17665e7i	− 0.403609i
$969$	182789.	0.00625375
$970$	0	0
$971$	−2.45562e6	−0.0835819	−0.0417910	−	0.999126i	$-0.513306\pi$
$971$	−2.45562e6	−0.0835819	−0.0417910	+	0.999126i	$0.513306\pi$
$972$	− 6.21423e6i	− 0.210970i
$973$	1.32160e6i	0.0447527i
$974$	−2.48510e7	−0.839358
$975$	0	0
$976$	−4.18381e6	−0.140588
$977$	− 3.31344e7i	− 1.11056i	−0.831663	−	0.555280i	$-0.812611\pi$
$977$	− 3.31344e7i	− 1.11056i	0.831663	−	0.555280i	$-0.187389\pi$
$978$	2.02151e7i	0.675815i
$979$	−4.83322e6	−0.161168
$980$	0	0
$981$	−872335.	−0.0289408
$982$	− 2.82088e7i	− 0.933483i
$983$	− 4.46461e7i	− 1.47367i	−0.676073	−	0.736834i	$-0.736320\pi$
$983$	− 4.46461e7i	− 1.47367i	0.676073	−	0.736834i	$-0.263680\pi$
$984$	846911.	0.0278837
$985$	0	0
$986$	−4.06801e6	−0.133257
$987$	− 6.36537e7i	− 2.07985i
$988$	220082.i	0.00717287i
$989$	500285.	0.0162640
$990$	0	0
$991$	4.99797e7	1.61662	0.808312	−	0.588754i	$-0.200381\pi$
$991$	4.99797e7	1.61662	0.808312	+	0.588754i	$0.200381\pi$
$992$	− 4.13145e6i	− 0.133298i
$993$	3.42129e7i	1.10107i
$994$	−6.64013e7	−2.13162
$995$	0	0
$996$	−586588.	−0.0187363
$997$	1.25647e7i	0.400326i	0.979763	+	0.200163i	$0.0641472\pi$
$997$	1.25647e7i	0.400326i	−0.979763	+	0.200163i	$0.935853\pi$
$998$	− 2.25204e7i	− 0.715730i
$999$	3.10611e7	0.984699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.6.b.g.599.4		4
5.2	odd	4		130.6.a.a.1.2	✓	2
5.3	odd	4		650.6.a.h.1.1		2
5.4	even	2	inner	650.6.b.g.599.1		4
20.7	even	4		1040.6.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.a.1.2	✓	2	5.2	odd	4
650.6.a.h.1.1		2	5.3	odd	4
650.6.b.g.599.1		4	5.4	even	2	inner
650.6.b.g.599.4		4	1.1	even	1	trivial
1040.6.a.e.1.1		2	20.7	even	4

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	650.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} +13.8114i q^{3} -16.0000 q^{4} -55.2456 q^{6} -213.246i q^{7} -64.0000i q^{8} +52.2456 q^{9} +587.285 q^{11} -220.982i q^{12} -169.000i q^{13} +852.982 q^{14} +256.000 q^{16} -162.605i q^{17} +208.982i q^{18} +81.3914 q^{19} +2945.22 q^{21} +2349.14i q^{22} -2948.84i q^{23} +883.929 q^{24} +676.000 q^{26} +4077.75i q^{27} +3411.93i q^{28} -6254.43 q^{29} -4034.62 q^{31} +1024.00i q^{32} +8111.22i q^{33} +650.420 q^{34} -835.929 q^{36} -7617.22i q^{37} +325.566i q^{38} +2334.12 q^{39} +958.121 q^{41} +11780.9i q^{42} +169.655i q^{43} -9396.56 q^{44} +11795.4 q^{46} -21612.6i q^{47} +3535.72i q^{48} -28666.7 q^{49} +2245.80 q^{51} +2704.00i q^{52} +24789.1i q^{53} -16311.0 q^{54} -13647.7 q^{56} +1124.13i q^{57} -25017.7i q^{58} -40109.2 q^{59} -16343.0 q^{61} -16138.5i q^{62} -11141.1i q^{63} -4096.00 q^{64} -32444.9 q^{66} -18362.1i q^{67} +2601.68i q^{68} +40727.6 q^{69} -77846.0 q^{71} -3343.72i q^{72} -62130.2i q^{73} +30468.9 q^{74} -1302.26 q^{76} -125236. i q^{77} +9336.50i q^{78} +60599.1 q^{79} -43623.7 q^{81} +3832.48i q^{82} -2654.46i q^{83} -47123.5 q^{84} -678.619 q^{86} -86382.4i q^{87} -37586.2i q^{88} -8229.77 q^{89} -36038.5 q^{91} +47181.5i q^{92} -55723.7i q^{93} +86450.3 q^{94} -14142.9 q^{96} +53844.0i q^{97} -114667. i q^{98} +30683.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{4} + 32 q^{6} - 44 q^{9} + 768 q^{11} + 2400 q^{14} + 1024 q^{16} + 4816 q^{19} + 2800 q^{21} - 512 q^{24} + 2704 q^{26} - 7056 q^{29} + 1760 q^{31} - 1952 q^{34} + 704 q^{36} - 1352 q^{39}+ \cdots + 91552 q^{99}+O(q^{100}) \) 4 * q - 64 * q^4 + 32 * q^6 - 44 * q^9 + 768 * q^11 + 2400 * q^14 + 1024 * q^16 + 4816 * q^19 + 2800 * q^21 - 512 * q^24 + 2704 * q^26 - 7056 * q^29 + 1760 * q^31 - 1952 * q^34 + 704 * q^36 - 1352 * q^39 + 32040 * q^41 - 12288 * q^44 - 2656 * q^46 - 38772 * q^49 + 18976 * q^51 - 8576 * q^54 - 38400 * q^56 - 85744 * q^59 - 66384 * q^61 - 16384 * q^64 - 93856 * q^66 + 198328 * q^69 - 139040 * q^71 + 85952 * q^74 - 77056 * q^76 - 70416 * q^79 - 230404 * q^81 - 44800 * q^84 - 23712 * q^86 + 36904 * q^89 - 101400 * q^91 + 306336 * q^94 + 8192 * q^96 + 91552 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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