LMFDB - Embedded newform 350.6.c.b.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,6,Mod(99,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, 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("350.99");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	350.c (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:	$56.1343369345$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.6.c.b.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000i q^{2} +11.0000i q^{3} -16.0000 q^{4} -44.0000 q^{6} +49.0000i q^{7} -64.0000i q^{8} +122.000 q^{9} -267.000 q^{11} -176.000i q^{12} +1087.00i q^{13} -196.000 q^{14} +256.000 q^{16} -513.000i q^{17} +488.000i q^{18} +802.000 q^{19} -539.000 q^{21} -1068.00i q^{22} +1290.00i q^{23} +704.000 q^{24} -4348.00 q^{26} +4015.00i q^{27} -784.000i q^{28} -1779.00 q^{29} -2584.00 q^{31} +1024.00i q^{32} -2937.00i q^{33} +2052.00 q^{34} -1952.00 q^{36} +13862.0i q^{37} +3208.00i q^{38} -11957.0 q^{39} -11904.0 q^{41} -2156.00i q^{42} +598.000i q^{43} +4272.00 q^{44} -5160.00 q^{46} -17019.0i q^{47} +2816.00i q^{48} -2401.00 q^{49} +5643.00 q^{51} -17392.0i q^{52} -27852.0i q^{53} -16060.0 q^{54} +3136.00 q^{56} +8822.00i q^{57} -7116.00i q^{58} -30912.0 q^{59} -1780.00 q^{61} -10336.0i q^{62} +5978.00i q^{63} -4096.00 q^{64} +11748.0 q^{66} +25052.0i q^{67} +8208.00i q^{68} -14190.0 q^{69} -51984.0 q^{71} -7808.00i q^{72} -47690.0i q^{73} -55448.0 q^{74} -12832.0 q^{76} -13083.0i q^{77} -47828.0i q^{78} +102121. q^{79} -14519.0 q^{81} -47616.0i q^{82} +83676.0i q^{83} +8624.00 q^{84} -2392.00 q^{86} -19569.0i q^{87} +17088.0i q^{88} +32400.0 q^{89} -53263.0 q^{91} -20640.0i q^{92} -28424.0i q^{93} +68076.0 q^{94} -11264.0 q^{96} -148645. i q^{97} -9604.00i q^{98} -32574.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 88 q^{6} + 244 q^{9} - 534 q^{11} - 392 q^{14} + 512 q^{16} + 1604 q^{19} - 1078 q^{21} + 1408 q^{24} - 8696 q^{26} - 3558 q^{29} - 5168 q^{31} + 4104 q^{34} - 3904 q^{36} - 23914 q^{39}+ \cdots - 65148 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 - 88 * q^6 + 244 * q^9 - 534 * q^11 - 392 * q^14 + 512 * q^16 + 1604 * q^19 - 1078 * q^21 + 1408 * q^24 - 8696 * q^26 - 3558 * q^29 - 5168 * q^31 + 4104 * q^34 - 3904 * q^36 - 23914 * q^39 - 23808 * q^41 + 8544 * q^44 - 10320 * q^46 - 4802 * q^49 + 11286 * q^51 - 32120 * q^54 + 6272 * q^56 - 61824 * q^59 - 3560 * q^61 - 8192 * q^64 + 23496 * q^66 - 28380 * q^69 - 103968 * q^71 - 110896 * q^74 - 25664 * q^76 + 204242 * q^79 - 29038 * q^81 + 17248 * q^84 - 4784 * q^86 + 64800 * q^89 - 106526 * q^91 + 136152 * q^94 - 22528 * q^96 - 65148 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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
$3$	11.0000i	0.705650i	0.935689	+	0.352825i	$0.114779\pi$
$3$	11.0000i	0.705650i	−0.935689	+	0.352825i	$0.885221\pi$
$4$	−16.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	−44.0000	−0.498970
$7$	49.0000i	0.377964i
$7$	49.0000i	0.377964i
$8$	− 64.0000i	− 0.353553i
$9$	122.000	0.502058
$10$	0	0
$11$	−267.000	−0.665318	−0.332659	−	0.943047i	$-0.607946\pi$
$11$	−267.000	−0.665318	−0.332659	+	0.943047i	$0.607946\pi$
$12$	− 176.000i	− 0.352825i
$13$	1087.00i	1.78390i	0.452131	+	0.891951i	$0.350664\pi$
$13$	1087.00i	1.78390i	−0.452131	+	0.891951i	$0.649336\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	− 513.000i	− 0.430522i	−0.976557	−	0.215261i	$-0.930940\pi$
$17$	− 513.000i	− 0.430522i	0.976557	−	0.215261i	$-0.0690602\pi$
$18$	488.000i	0.355008i
$19$	802.000	0.509672	0.254836	−	0.966984i	$-0.417979\pi$
$19$	802.000	0.509672	0.254836	+	0.966984i	$0.417979\pi$
$20$	0	0
$21$	−539.000	−0.266711
$22$	− 1068.00i	− 0.470451i
$23$	1290.00i	0.508476i	0.967142	+	0.254238i	$0.0818246\pi$
$23$	1290.00i	0.508476i	−0.967142	+	0.254238i	$0.918175\pi$
$24$	704.000	0.249485
$25$	0	0
$26$	−4348.00	−1.26141
$27$	4015.00i	1.05993i
$28$	− 784.000i	− 0.188982i
$29$	−1779.00	−0.392809	−0.196404	−	0.980523i	$-0.562926\pi$
$29$	−1779.00	−0.392809	−0.196404	+	0.980523i	$0.562926\pi$
$30$	0	0
$31$	−2584.00	−0.482935	−0.241467	−	0.970409i	$-0.577629\pi$
$31$	−2584.00	−0.482935	−0.241467	+	0.970409i	$0.577629\pi$
$32$	1024.00i	0.176777i
$33$	− 2937.00i	− 0.469482i
$34$	2052.00	0.304425
$35$	0	0
$36$	−1952.00	−0.251029
$37$	13862.0i	1.66464i	0.554292	+	0.832322i	$0.312989\pi$
$37$	13862.0i	1.66464i	−0.554292	+	0.832322i	$0.687011\pi$
$38$	3208.00i	0.360392i
$39$	−11957.0	−1.25881
$40$	0	0
$41$	−11904.0	−1.10594	−0.552972	−	0.833200i	$-0.686506\pi$
$41$	−11904.0	−1.10594	−0.552972	+	0.833200i	$0.686506\pi$
$42$	− 2156.00i	− 0.188593i
$43$	598.000i	0.0493208i	0.999696	+	0.0246604i	$0.00785044\pi$
$43$	598.000i	0.0493208i	−0.999696	+	0.0246604i	$0.992150\pi$
$44$	4272.00	0.332659
$45$	0	0
$46$	−5160.00	−0.359547
$47$	− 17019.0i	− 1.12380i	−0.827205	−	0.561900i	$-0.810070\pi$
$47$	− 17019.0i	− 1.12380i	0.827205	−	0.561900i	$-0.189930\pi$
$48$	2816.00i	0.176413i
$49$	−2401.00	−0.142857
$50$	0	0
$51$	5643.00	0.303798
$52$	− 17392.0i	− 0.891951i
$53$	− 27852.0i	− 1.36197i	−0.732299	−	0.680984i	$-0.761552\pi$
$53$	− 27852.0i	− 1.36197i	0.732299	−	0.680984i	$-0.238448\pi$
$54$	−16060.0	−0.749482
$55$	0	0
$56$	3136.00	0.133631
$57$	8822.00i	0.359650i
$58$	− 7116.00i	− 0.277758i
$59$	−30912.0	−1.15610	−0.578052	−	0.816000i	$-0.696187\pi$
$59$	−30912.0	−1.15610	−0.578052	+	0.816000i	$0.696187\pi$
$60$	0	0
$61$	−1780.00	−0.0612485	−0.0306242	−	0.999531i	$-0.509750\pi$
$61$	−1780.00	−0.0612485	−0.0306242	+	0.999531i	$0.509750\pi$
$62$	− 10336.0i	− 0.341486i
$63$	5978.00i	0.189760i
$64$	−4096.00	−0.125000
$65$	0	0
$66$	11748.0	0.331974
$67$	25052.0i	0.681797i	0.940100	+	0.340899i	$0.110731\pi$
$67$	25052.0i	0.681797i	−0.940100	+	0.340899i	$0.889269\pi$
$68$	8208.00i	0.215261i
$69$	−14190.0	−0.358806
$70$	0	0
$71$	−51984.0	−1.22384	−0.611919	−	0.790921i	$-0.709602\pi$
$71$	−51984.0	−1.22384	−0.611919	+	0.790921i	$0.709602\pi$
$72$	− 7808.00i	− 0.177504i
$73$	− 47690.0i	− 1.04742i	−0.851897	−	0.523709i	$-0.824548\pi$
$73$	− 47690.0i	− 1.04742i	0.851897	−	0.523709i	$-0.175452\pi$
$74$	−55448.0	−1.17708
$75$	0	0
$76$	−12832.0	−0.254836
$77$	− 13083.0i	− 0.251467i
$78$	− 47828.0i	− 0.890114i
$79$	102121.	1.84097	0.920486	−	0.390775i	$-0.127793\pi$
$79$	102121.	1.84097	0.920486	+	0.390775i	$0.127793\pi$
$80$	0	0
$81$	−14519.0	−0.245881
$82$	− 47616.0i	− 0.782021i
$83$	83676.0i	1.33323i	0.745401	+	0.666616i	$0.232258\pi$
$83$	83676.0i	1.33323i	−0.745401	+	0.666616i	$0.767742\pi$
$84$	8624.00	0.133355
$85$	0	0
$86$	−2392.00	−0.0348751
$87$	− 19569.0i	− 0.277185i
$88$	17088.0i	0.235226i
$89$	32400.0	0.433581	0.216790	−	0.976218i	$-0.430441\pi$
$89$	32400.0	0.433581	0.216790	+	0.976218i	$0.430441\pi$
$90$	0	0
$91$	−53263.0	−0.674252
$92$	− 20640.0i	− 0.254238i
$93$	− 28424.0i	− 0.340783i
$94$	68076.0	0.794647
$95$	0	0
$96$	−11264.0	−0.124743
$97$	− 148645.i	− 1.60406i	−0.597283	−	0.802031i	$-0.703753\pi$
$97$	− 148645.i	− 1.60406i	0.597283	−	0.802031i	$-0.296247\pi$
$98$	− 9604.00i	− 0.101015i
$99$	−32574.0	−0.334028
$100$	0	0
$101$	−41310.0	−0.402951	−0.201475	−	0.979494i	$-0.564574\pi$
$101$	−41310.0	−0.402951	−0.201475	+	0.979494i	$0.564574\pi$
$102$	22572.0i	0.214817i
$103$	− 108785.i	− 1.01036i	−0.863014	−	0.505180i	$-0.831426\pi$
$103$	− 108785.i	− 1.01036i	0.863014	−	0.505180i	$-0.168574\pi$
$104$	69568.0	0.630705
$105$	0	0
$106$	111408.	0.963056
$107$	− 106098.i	− 0.895876i	−0.894065	−	0.447938i	$-0.852159\pi$
$107$	− 106098.i	− 0.895876i	0.894065	−	0.447938i	$-0.147841\pi$
$108$	− 64240.0i	− 0.529964i
$109$	124111.	1.00056	0.500281	−	0.865863i	$-0.333230\pi$
$109$	124111.	1.00056	0.500281	+	0.865863i	$0.333230\pi$
$110$	0	0
$111$	−152482.	−1.17466
$112$	12544.0i	0.0944911i
$113$	− 192834.i	− 1.42065i	−0.703873	−	0.710326i	$-0.748548\pi$
$113$	− 192834.i	− 1.42065i	0.703873	−	0.710326i	$-0.251452\pi$
$114$	−35288.0	−0.254311
$115$	0	0
$116$	28464.0	0.196404
$117$	132614.i	0.895622i
$118$	− 123648.i	− 0.817489i
$119$	25137.0	0.162722
$120$	0	0
$121$	−89762.0	−0.557351
$122$	− 7120.00i	− 0.0433092i
$123$	− 130944.i	− 0.780410i
$124$	41344.0	0.241467
$125$	0	0
$126$	−23912.0	−0.134181
$127$	99248.0i	0.546025i	0.962010	+	0.273012i	$0.0880200\pi$
$127$	99248.0i	0.546025i	−0.962010	+	0.273012i	$0.911980\pi$
$128$	− 16384.0i	− 0.0883883i
$129$	−6578.00	−0.0348032
$130$	0	0
$131$	−276810.	−1.40930	−0.704650	−	0.709555i	$-0.748896\pi$
$131$	−276810.	−1.40930	−0.704650	+	0.709555i	$0.748896\pi$
$132$	46992.0i	0.234741i
$133$	39298.0i	0.192638i
$134$	−100208.	−0.482104
$135$	0	0
$136$	−32832.0	−0.152212
$137$	237744.i	1.08220i	0.840958	+	0.541101i	$0.181992\pi$
$137$	237744.i	1.08220i	−0.840958	+	0.541101i	$0.818008\pi$
$138$	− 56760.0i	− 0.253714i
$139$	−160478.	−0.704496	−0.352248	−	0.935907i	$-0.614583\pi$
$139$	−160478.	−0.704496	−0.352248	+	0.935907i	$0.614583\pi$
$140$	0	0
$141$	187209.	0.793011
$142$	− 207936.i	− 0.865384i
$143$	− 290229.i	− 1.18686i
$144$	31232.0	0.125514
$145$	0	0
$146$	190760.	0.740637
$147$	− 26411.0i	− 0.100807i
$148$	− 221792.i	− 0.832322i
$149$	99678.0	0.367819	0.183909	−	0.982943i	$-0.441125\pi$
$149$	99678.0	0.367819	0.183909	+	0.982943i	$0.441125\pi$
$150$	0	0
$151$	−206017.	−0.735293	−0.367647	−	0.929966i	$-0.619836\pi$
$151$	−206017.	−0.735293	−0.367647	+	0.929966i	$0.619836\pi$
$152$	− 51328.0i	− 0.180196i
$153$	− 62586.0i	− 0.216147i
$154$	52332.0	0.177814
$155$	0	0
$156$	191312.	0.629406
$157$	581150.i	1.88165i	0.338891	+	0.940826i	$0.389948\pi$
$157$	581150.i	1.88165i	−0.338891	+	0.940826i	$0.610052\pi$
$158$	408484.i	1.30176i
$159$	306372.	0.961073
$160$	0	0
$161$	−63210.0	−0.192186
$162$	− 58076.0i	− 0.173864i
$163$	− 346610.i	− 1.02181i	−0.859636	−	0.510907i	$-0.829310\pi$
$163$	− 346610.i	− 1.02181i	0.859636	−	0.510907i	$-0.170690\pi$
$164$	190464.	0.552972
$165$	0	0
$166$	−334704.	−0.942737
$167$	− 448887.i	− 1.24551i	−0.782418	−	0.622753i	$-0.786014\pi$
$167$	− 448887.i	− 1.24551i	0.782418	−	0.622753i	$-0.213986\pi$
$168$	34496.0i	0.0942965i
$169$	−810276.	−2.18231
$170$	0	0
$171$	97844.0	0.255884
$172$	− 9568.00i	− 0.0246604i
$173$	262509.i	0.666851i	0.942776	+	0.333426i	$0.108205\pi$
$173$	262509.i	0.666851i	−0.942776	+	0.333426i	$0.891795\pi$
$174$	78276.0	0.196000
$175$	0	0
$176$	−68352.0	−0.166330
$177$	− 340032.i	− 0.815805i
$178$	129600.i	0.306588i
$179$	111012.	0.258963	0.129481	−	0.991582i	$-0.458669\pi$
$179$	111012.	0.258963	0.129481	+	0.991582i	$0.458669\pi$
$180$	0	0
$181$	112772.	0.255861	0.127931	−	0.991783i	$-0.459166\pi$
$181$	112772.	0.255861	0.127931	+	0.991783i	$0.459166\pi$
$182$	− 213052.i	− 0.476768i
$183$	− 19580.0i	− 0.0432200i
$184$	82560.0	0.179773
$185$	0	0
$186$	113696.	0.240970
$187$	136971.i	0.286434i
$188$	272304.i	0.561900i
$189$	−196735.	−0.400615
$190$	0	0
$191$	−731991.	−1.45185	−0.725926	−	0.687773i	$-0.758589\pi$
$191$	−731991.	−1.45185	−0.725926	+	0.687773i	$0.758589\pi$
$192$	− 45056.0i	− 0.0882063i
$193$	186040.i	0.359512i	0.983711	+	0.179756i	$0.0575308\pi$
$193$	186040.i	0.359512i	−0.983711	+	0.179756i	$0.942469\pi$
$194$	594580.	1.13424
$195$	0	0
$196$	38416.0	0.0714286
$197$	121356.i	0.222790i	0.993776	+	0.111395i	$0.0355319\pi$
$197$	121356.i	0.222790i	−0.993776	+	0.111395i	$0.964468\pi$
$198$	− 130296.i	− 0.236194i
$199$	−648584.	−1.16100	−0.580502	−	0.814259i	$-0.697144\pi$
$199$	−648584.	−1.16100	−0.580502	+	0.814259i	$0.697144\pi$
$200$	0	0
$201$	−275572.	−0.481111
$202$	− 165240.i	− 0.284929i
$203$	− 87171.0i	− 0.148468i
$204$	−90288.0	−0.151899
$205$	0	0
$206$	435140.	0.714432
$207$	157380.i	0.255284i
$208$	278272.i	0.445976i
$209$	−214134.	−0.339094
$210$	0	0
$211$	−149773.	−0.231594	−0.115797	−	0.993273i	$-0.536942\pi$
$211$	−149773.	−0.231594	−0.115797	+	0.993273i	$0.536942\pi$
$212$	445632.i	0.680984i
$213$	− 571824.i	− 0.863601i
$214$	424392.	0.633480
$215$	0	0
$216$	256960.	0.374741
$217$	− 126616.i	− 0.182532i
$218$	496444.i	0.707504i
$219$	524590.	0.739111
$220$	0	0
$221$	557631.	0.768009
$222$	− 609928.i	− 0.830608i
$223$	1.10096e6i	1.48255i	0.671202	+	0.741274i	$0.265778\pi$
$223$	1.10096e6i	1.48255i	−0.671202	+	0.741274i	$0.734222\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	771336.	1.00455
$227$	− 695127.i	− 0.895364i	−0.894193	−	0.447682i	$-0.852250\pi$
$227$	− 695127.i	− 0.895364i	0.894193	−	0.447682i	$-0.147750\pi$
$228$	− 141152.i	− 0.179825i
$229$	−463736.	−0.584362	−0.292181	−	0.956363i	$-0.594381\pi$
$229$	−463736.	−0.584362	−0.292181	+	0.956363i	$0.594381\pi$
$230$	0	0
$231$	143913.	0.177448
$232$	113856.i	0.138879i
$233$	1.57654e6i	1.90245i	0.308492	+	0.951227i	$0.400176\pi$
$233$	1.57654e6i	1.90245i	−0.308492	+	0.951227i	$0.599824\pi$
$234$	−530456.	−0.633300
$235$	0	0
$236$	494592.	0.578052
$237$	1.12333e6i	1.29908i
$238$	100548.i	0.115062i
$239$	512037.	0.579838	0.289919	−	0.957051i	$-0.406372\pi$
$239$	512037.	0.579838	0.289919	+	0.957051i	$0.406372\pi$
$240$	0	0
$241$	989330.	1.09723	0.548616	−	0.836074i	$-0.315155\pi$
$241$	989330.	1.09723	0.548616	+	0.836074i	$0.315155\pi$
$242$	− 359048.i	− 0.394107i
$243$	815936.i	0.886422i
$244$	28480.0	0.0306242
$245$	0	0
$246$	523776.	0.551833
$247$	871774.i	0.909204i
$248$	165376.i	0.170743i
$249$	−920436.	−0.940795
$250$	0	0
$251$	−61230.0	−0.0613451	−0.0306726	−	0.999529i	$-0.509765\pi$
$251$	−61230.0	−0.0613451	−0.0306726	+	0.999529i	$0.509765\pi$
$252$	− 95648.0i	− 0.0948800i
$253$	− 344430.i	− 0.338298i
$254$	−396992.	−0.386098
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.33887e6i	1.26446i	0.774780	+	0.632231i	$0.217861\pi$
$257$	1.33887e6i	1.26446i	−0.774780	+	0.632231i	$0.782139\pi$
$258$	− 26312.0i	− 0.0246096i
$259$	−679238.	−0.629177
$260$	0	0
$261$	−217038.	−0.197213
$262$	− 1.10724e6i	− 0.996526i
$263$	1.65619e6i	1.47645i	0.674553	+	0.738227i	$0.264337\pi$
$263$	1.65619e6i	1.47645i	−0.674553	+	0.738227i	$0.735663\pi$
$264$	−187968.	−0.165987
$265$	0	0
$266$	−157192.	−0.136215
$267$	356400.i	0.305956i
$268$	− 400832.i	− 0.340899i
$269$	750606.	0.632457	0.316229	−	0.948683i	$-0.397583\pi$
$269$	750606.	0.632457	0.316229	+	0.948683i	$0.397583\pi$
$270$	0	0
$271$	−557908.	−0.461466	−0.230733	−	0.973017i	$-0.574112\pi$
$271$	−557908.	−0.461466	−0.230733	+	0.973017i	$0.574112\pi$
$272$	− 131328.i	− 0.107630i
$273$	− 585893.i	− 0.475786i
$274$	−950976.	−0.765232
$275$	0	0
$276$	227040.	0.179403
$277$	1.77256e6i	1.38804i	0.719957	+	0.694018i	$0.244161\pi$
$277$	1.77256e6i	1.38804i	−0.719957	+	0.694018i	$0.755839\pi$
$278$	− 641912.i	− 0.498154i
$279$	−315248.	−0.242461
$280$	0	0
$281$	−1.09893e6	−0.830243	−0.415122	−	0.909766i	$-0.636261\pi$
$281$	−1.09893e6	−0.830243	−0.415122	+	0.909766i	$0.636261\pi$
$282$	748836.i	0.560743i
$283$	320569.i	0.237933i	0.992898	+	0.118967i	$0.0379582\pi$
$283$	320569.i	0.237933i	−0.992898	+	0.118967i	$0.962042\pi$
$284$	831744.	0.611919
$285$	0	0
$286$	1.16092e6	0.839239
$287$	− 583296.i	− 0.418008i
$288$	124928.i	0.0887521i
$289$	1.15669e6	0.814651
$290$	0	0
$291$	1.63510e6	1.13191
$292$	763040.i	0.523709i
$293$	1.62337e6i	1.10471i	0.833609	+	0.552355i	$0.186271\pi$
$293$	1.62337e6i	1.10471i	−0.833609	+	0.552355i	$0.813729\pi$
$294$	105644.	0.0712814
$295$	0	0
$296$	887168.	0.588541
$297$	− 1.07200e6i	− 0.705189i
$298$	398712.i	0.260087i
$299$	−1.40223e6	−0.907071
$300$	0	0
$301$	−29302.0	−0.0186415
$302$	− 824068.i	− 0.519931i
$303$	− 454410.i	− 0.284342i
$304$	205312.	0.127418
$305$	0	0
$306$	250344.	0.152839
$307$	995087.i	0.602581i	0.953532	+	0.301290i	$0.0974173\pi$
$307$	995087.i	0.602581i	−0.953532	+	0.301290i	$0.902583\pi$
$308$	209328.i	0.125733i
$309$	1.19664e6	0.712961
$310$	0	0
$311$	1.34398e6	0.787939	0.393969	−	0.919124i	$-0.371102\pi$
$311$	1.34398e6	0.787939	0.393969	+	0.919124i	$0.371102\pi$
$312$	765248.i	0.445057i
$313$	− 1.91971e6i	− 1.10758i	−0.832658	−	0.553788i	$-0.813182\pi$
$313$	− 1.91971e6i	− 1.10758i	0.832658	−	0.553788i	$-0.186818\pi$
$314$	−2.32460e6	−1.33053
$315$	0	0
$316$	−1.63394e6	−0.920486
$317$	− 1.91366e6i	− 1.06959i	−0.844983	−	0.534794i	$-0.820389\pi$
$317$	− 1.91366e6i	− 1.06959i	0.844983	−	0.534794i	$-0.179611\pi$
$318$	1.22549e6i	0.679581i
$319$	474993.	0.261343
$320$	0	0
$321$	1.16708e6	0.632175
$322$	− 252840.i	− 0.135896i
$323$	− 411426.i	− 0.219425i
$324$	232304.	0.122940
$325$	0	0
$326$	1.38644e6	0.722532
$327$	1.36522e6i	0.706047i
$328$	761856.i	0.391010i
$329$	833931.	0.424757
$330$	0	0
$331$	−2.25694e6	−1.13227	−0.566135	−	0.824313i	$-0.691562\pi$
$331$	−2.25694e6	−1.13227	−0.566135	+	0.824313i	$0.691562\pi$
$332$	− 1.33882e6i	− 0.666616i
$333$	1.69116e6i	0.835748i
$334$	1.79555e6	0.880706
$335$	0	0
$336$	−137984.	−0.0666777
$337$	− 1.45016e6i	− 0.695571i	−0.937574	−	0.347786i	$-0.886934\pi$
$337$	− 1.45016e6i	− 0.695571i	0.937574	−	0.347786i	$-0.113066\pi$
$338$	− 3.24110e6i	− 1.54313i
$339$	2.12117e6	1.00248
$340$	0	0
$341$	689928.	0.321305
$342$	391376.i	0.180938i
$343$	− 117649.i	− 0.0539949i
$344$	38272.0	0.0174375
$345$	0	0
$346$	−1.05004e6	−0.471535
$347$	856386.i	0.381809i	0.981609	+	0.190904i	$0.0611420\pi$
$347$	856386.i	0.381809i	−0.981609	+	0.190904i	$0.938858\pi$
$348$	313104.i	0.138593i
$349$	347602.	0.152763	0.0763816	−	0.997079i	$-0.475663\pi$
$349$	347602.	0.152763	0.0763816	+	0.997079i	$0.475663\pi$
$350$	0	0
$351$	−4.36430e6	−1.89081
$352$	− 273408.i	− 0.117613i
$353$	2.21860e6i	0.947640i	0.880622	+	0.473820i	$0.157125\pi$
$353$	2.21860e6i	0.947640i	−0.880622	+	0.473820i	$0.842875\pi$
$354$	1.36013e6	0.576862
$355$	0	0
$356$	−518400.	−0.216790
$357$	276507.i	0.114825i
$358$	444048.i	0.183114i
$359$	−2.94338e6	−1.20534	−0.602672	−	0.797989i	$-0.705897\pi$
$359$	−2.94338e6	−1.20534	−0.602672	+	0.797989i	$0.705897\pi$
$360$	0	0
$361$	−1.83290e6	−0.740235
$362$	451088.i	0.180921i
$363$	− 987382.i	− 0.393295i
$364$	852208.	0.337126
$365$	0	0
$366$	78320.0	0.0305612
$367$	2.33000e6i	0.903005i	0.892270	+	0.451503i	$0.149112\pi$
$367$	2.33000e6i	0.903005i	−0.892270	+	0.451503i	$0.850888\pi$
$368$	330240.i	0.127119i
$369$	−1.45229e6	−0.555248
$370$	0	0
$371$	1.36475e6	0.514775
$372$	454784.i	0.170391i
$373$	− 1.69246e6i	− 0.629865i	−0.949114	−	0.314932i	$-0.898018\pi$
$373$	− 1.69246e6i	− 0.629865i	0.949114	−	0.314932i	$-0.101982\pi$
$374$	−547884.	−0.202539
$375$	0	0
$376$	−1.08922e6	−0.397324
$377$	− 1.93377e6i	− 0.700732i
$378$	− 786940.i	− 0.283278i
$379$	1.50075e6	0.536673	0.268337	−	0.963325i	$-0.413526\pi$
$379$	1.50075e6	0.536673	0.268337	+	0.963325i	$0.413526\pi$
$380$	0	0
$381$	−1.09173e6	−0.385303
$382$	− 2.92796e6i	− 1.02661i
$383$	− 3.48522e6i	− 1.21404i	−0.794686	−	0.607020i	$-0.792365\pi$
$383$	− 3.48522e6i	− 1.21404i	0.794686	−	0.607020i	$-0.207635\pi$
$384$	180224.	0.0623713
$385$	0	0
$386$	−744160.	−0.254213
$387$	72956.0i	0.0247619i
$388$	2.37832e6i	0.802031i
$389$	3.60598e6	1.20823	0.604114	−	0.796898i	$-0.293527\pi$
$389$	3.60598e6	1.20823	0.604114	+	0.796898i	$0.293527\pi$
$390$	0	0
$391$	661770.	0.218910
$392$	153664.i	0.0505076i
$393$	− 3.04491e6i	− 0.994473i
$394$	−485424.	−0.157536
$395$	0	0
$396$	521184.	0.167014
$397$	4.74380e6i	1.51060i	0.655377	+	0.755302i	$0.272510\pi$
$397$	4.74380e6i	1.51060i	−0.655377	+	0.755302i	$0.727490\pi$
$398$	− 2.59434e6i	− 0.820953i
$399$	−432278.	−0.135935
$400$	0	0
$401$	5.26539e6	1.63520	0.817598	−	0.575789i	$-0.195305\pi$
$401$	5.26539e6	1.63520	0.817598	+	0.575789i	$0.195305\pi$
$402$	− 1.10229e6i	− 0.340197i
$403$	− 2.80881e6i	− 0.861508i
$404$	660960.	0.201475
$405$	0	0
$406$	348684.	0.104983
$407$	− 3.70115e6i	− 1.10752i
$408$	− 361152.i	− 0.107409i
$409$	−1.37015e6	−0.405004	−0.202502	−	0.979282i	$-0.564907\pi$
$409$	−1.37015e6	−0.405004	−0.202502	+	0.979282i	$0.564907\pi$
$410$	0	0
$411$	−2.61518e6	−0.763656
$412$	1.74056e6i	0.505180i
$413$	− 1.51469e6i	− 0.436966i
$414$	−629520.	−0.180513
$415$	0	0
$416$	−1.11309e6	−0.315352
$417$	− 1.76526e6i	− 0.497128i
$418$	− 856536.i	− 0.239776i
$419$	−6.16429e6	−1.71533	−0.857666	−	0.514207i	$-0.828086\pi$
$419$	−6.16429e6	−1.71533	−0.857666	+	0.514207i	$0.828086\pi$
$420$	0	0
$421$	2.45358e6	0.674677	0.337338	−	0.941383i	$-0.390473\pi$
$421$	2.45358e6	0.674677	0.337338	+	0.941383i	$0.390473\pi$
$422$	− 599092.i	− 0.163762i
$423$	− 2.07632e6i	− 0.564213i
$424$	−1.78253e6	−0.481528
$425$	0	0
$426$	2.28730e6	0.610658
$427$	− 87220.0i	− 0.0231498i
$428$	1.69757e6i	0.447938i
$429$	3.19252e6	0.837510
$430$	0	0
$431$	7.66771e6	1.98826	0.994128	−	0.108207i	$-0.0345111\pi$
$431$	7.66771e6	1.98826	0.994128	+	0.108207i	$0.0345111\pi$
$432$	1.02784e6i	0.264982i
$433$	5.00285e6i	1.28232i	0.767406	+	0.641161i	$0.221547\pi$
$433$	5.00285e6i	1.28232i	−0.767406	+	0.641161i	$0.778453\pi$
$434$	506464.	0.129070
$435$	0	0
$436$	−1.98578e6	−0.500281
$437$	1.03458e6i	0.259156i
$438$	2.09836e6i	0.522630i
$439$	−1.86363e6	−0.461527	−0.230764	−	0.973010i	$-0.574122\pi$
$439$	−1.86363e6	−0.461527	−0.230764	+	0.973010i	$0.574122\pi$
$440$	0	0
$441$	−292922.	−0.0717225
$442$	2.23052e6i	0.543064i
$443$	− 2.60747e6i	− 0.631263i	−0.948882	−	0.315632i	$-0.897784\pi$
$443$	− 2.60747e6i	− 0.631263i	0.948882	−	0.315632i	$-0.102216\pi$
$444$	2.43971e6	0.587329
$445$	0	0
$446$	−4.40384e6	−1.04832
$447$	1.09646e6i	0.259551i
$448$	− 200704.i	− 0.0472456i
$449$	4.78007e6	1.11897	0.559484	−	0.828841i	$-0.310999\pi$
$449$	4.78007e6	1.11897	0.559484	+	0.828841i	$0.310999\pi$
$450$	0	0
$451$	3.17837e6	0.735805
$452$	3.08534e6i	0.710326i
$453$	− 2.26619e6i	− 0.518860i
$454$	2.78051e6	0.633118
$455$	0	0
$456$	564608.	0.127155
$457$	− 7.96757e6i	− 1.78458i	−0.451465	−	0.892289i	$-0.649098\pi$
$457$	− 7.96757e6i	− 1.78458i	0.451465	−	0.892289i	$-0.350902\pi$
$458$	− 1.85494e6i	− 0.413206i
$459$	2.05969e6	0.456322
$460$	0	0
$461$	1.77665e6	0.389358	0.194679	−	0.980867i	$-0.437633\pi$
$461$	1.77665e6	0.389358	0.194679	+	0.980867i	$0.437633\pi$
$462$	575652.i	0.125474i
$463$	998548.i	0.216479i	0.994125	+	0.108240i	$0.0345214\pi$
$463$	998548.i	0.216479i	−0.994125	+	0.108240i	$0.965479\pi$
$464$	−455424.	−0.0982021
$465$	0	0
$466$	−6.30614e6	−1.34524
$467$	− 5.08478e6i	− 1.07890i	−0.842019	−	0.539449i	$-0.818633\pi$
$467$	− 5.08478e6i	− 1.07890i	0.842019	−	0.539449i	$-0.181367\pi$
$468$	− 2.12182e6i	− 0.447811i
$469$	−1.22755e6	−0.257695
$470$	0	0
$471$	−6.39265e6	−1.32779
$472$	1.97837e6i	0.408745i
$473$	− 159666.i	− 0.0328140i
$474$	−4.49332e6	−0.918590
$475$	0	0
$476$	−402192.	−0.0813610
$477$	− 3.39794e6i	− 0.683786i
$478$	2.04815e6i	0.410007i
$479$	−3.71936e6	−0.740678	−0.370339	−	0.928897i	$-0.620758\pi$
$479$	−3.71936e6	−0.740678	−0.370339	+	0.928897i	$0.620758\pi$
$480$	0	0
$481$	−1.50680e7	−2.96956
$482$	3.95732e6i	0.775860i
$483$	− 695310.i	− 0.135616i
$484$	1.43619e6	0.278676
$485$	0	0
$486$	−3.26374e6	−0.626795
$487$	− 9.12035e6i	− 1.74256i	−0.490782	−	0.871282i	$-0.663289\pi$
$487$	− 9.12035e6i	− 1.74256i	0.490782	−	0.871282i	$-0.336711\pi$
$488$	113920.i	0.0216546i
$489$	3.81271e6	0.721044
$490$	0	0
$491$	−7.83774e6	−1.46719	−0.733596	−	0.679586i	$-0.762160\pi$
$491$	−7.83774e6	−1.46719	−0.733596	+	0.679586i	$0.762160\pi$
$492$	2.09510e6i	0.390205i
$493$	912627.i	0.169113i
$494$	−3.48710e6	−0.642905
$495$	0	0
$496$	−661504.	−0.120734
$497$	− 2.54722e6i	− 0.462567i
$498$	− 3.68174e6i	− 0.665243i
$499$	96103.0	0.0172777	0.00863884	−	0.999963i	$-0.497250\pi$
$499$	96103.0	0.0172777	0.00863884	+	0.999963i	$0.497250\pi$
$500$	0	0
$501$	4.93776e6	0.878892
$502$	− 244920.i	− 0.0433775i
$503$	2.37577e6i	0.418682i	0.977843	+	0.209341i	$0.0671319\pi$
$503$	2.37577e6i	0.418682i	−0.977843	+	0.209341i	$0.932868\pi$
$504$	382592.	0.0670903
$505$	0	0
$506$	1.37772e6	0.239213
$507$	− 8.91304e6i	− 1.53995i
$508$	− 1.58797e6i	− 0.273012i
$509$	−5.91484e6	−1.01193	−0.505963	−	0.862555i	$-0.668863\pi$
$509$	−5.91484e6	−1.01193	−0.505963	+	0.862555i	$0.668863\pi$
$510$	0	0
$511$	2.33681e6	0.395887
$512$	262144.i	0.0441942i
$513$	3.22003e6i	0.540215i
$514$	−5.35548e6	−0.894109
$515$	0	0
$516$	105248.	0.0174016
$517$	4.54407e6i	0.747685i
$518$	− 2.71695e6i	− 0.444895i
$519$	−2.88760e6	−0.470564
$520$	0	0
$521$	1.46099e6	0.235806	0.117903	−	0.993025i	$-0.462383\pi$
$521$	1.46099e6	0.235806	0.117903	+	0.993025i	$0.462383\pi$
$522$	− 868152.i	− 0.139450i
$523$	2.90691e6i	0.464705i	0.972632	+	0.232352i	$0.0746422\pi$
$523$	2.90691e6i	0.464705i	−0.972632	+	0.232352i	$0.925358\pi$
$524$	4.42896e6	0.704650
$525$	0	0
$526$	−6.62474e6	−1.04401
$527$	1.32559e6i	0.207914i
$528$	− 751872.i	− 0.117371i
$529$	4.77224e6	0.741453
$530$	0	0
$531$	−3.77126e6	−0.580431
$532$	− 628768.i	− 0.0963189i
$533$	− 1.29396e7i	− 1.97290i
$534$	−1.42560e6	−0.216344
$535$	0	0
$536$	1.60333e6	0.241052
$537$	1.22113e6i	0.182737i
$538$	3.00242e6i	0.447215i
$539$	641067.	0.0950455
$540$	0	0
$541$	5.28092e6	0.775741	0.387870	−	0.921714i	$-0.373211\pi$
$541$	5.28092e6	0.775741	0.387870	+	0.921714i	$0.373211\pi$
$542$	− 2.23163e6i	− 0.326305i
$543$	1.24049e6i	0.180549i
$544$	525312.	0.0761062
$545$	0	0
$546$	2.34357e6	0.336432
$547$	1.31999e7i	1.88626i	0.332419	+	0.943132i	$0.392135\pi$
$547$	1.31999e7i	1.88626i	−0.332419	+	0.943132i	$0.607865\pi$
$548$	− 3.80390e6i	− 0.541101i
$549$	−217160.	−0.0307503
$550$	0	0
$551$	−1.42676e6	−0.200203
$552$	908160.i	0.126857i
$553$	5.00393e6i	0.695822i
$554$	−7.09023e6	−0.981490
$555$	0	0
$556$	2.56765e6	0.352248
$557$	− 1.39920e7i	− 1.91091i	−0.295131	−	0.955457i	$-0.595363\pi$
$557$	− 1.39920e7i	− 1.91091i	0.295131	−	0.955457i	$-0.404637\pi$
$558$	− 1.26099e6i	− 0.171446i
$559$	−650026.	−0.0879835
$560$	0	0
$561$	−1.50668e6	−0.202122
$562$	− 4.39573e6i	− 0.587071i
$563$	5.12689e6i	0.681684i	0.940121	+	0.340842i	$0.110712\pi$
$563$	5.12689e6i	0.681684i	−0.940121	+	0.340842i	$0.889288\pi$
$564$	−2.99534e6	−0.396505
$565$	0	0
$566$	−1.28228e6	−0.168244
$567$	− 711431.i	− 0.0929341i
$568$	3.32698e6i	0.432692i
$569$	8.29102e6	1.07356	0.536781	−	0.843721i	$-0.319640\pi$
$569$	8.29102e6	1.07356	0.536781	+	0.843721i	$0.319640\pi$
$570$	0	0
$571$	6.21372e6	0.797556	0.398778	−	0.917048i	$-0.369434\pi$
$571$	6.21372e6	0.797556	0.398778	+	0.917048i	$0.369434\pi$
$572$	4.64366e6i	0.593432i
$573$	− 8.05190e6i	− 1.02450i
$574$	2.33318e6	0.295576
$575$	0	0
$576$	−499712.	−0.0627572
$577$	1.14818e7i	1.43572i	0.696186	+	0.717861i	$0.254879\pi$
$577$	1.14818e7i	1.43572i	−0.696186	+	0.717861i	$0.745121\pi$
$578$	4.62675e6i	0.576045i
$579$	−2.04644e6	−0.253690
$580$	0	0
$581$	−4.10012e6	−0.503914
$582$	6.54038e6i	0.800379i
$583$	7.43648e6i	0.906142i
$584$	−3.05216e6	−0.370318
$585$	0	0
$586$	−6.49348e6	−0.781148
$587$	641856.i	0.0768851i	0.999261	+	0.0384426i	$0.0122397\pi$
$587$	641856.i	0.0768851i	−0.999261	+	0.0384426i	$0.987760\pi$
$588$	422576.i	0.0504036i
$589$	−2.07237e6	−0.246138
$590$	0	0
$591$	−1.33492e6	−0.157212
$592$	3.54867e6i	0.416161i
$593$	2.80572e6i	0.327648i	0.986490	+	0.163824i	$0.0523830\pi$
$593$	2.80572e6i	0.327648i	−0.986490	+	0.163824i	$0.947617\pi$
$594$	4.28802e6	0.498644
$595$	0	0
$596$	−1.59485e6	−0.183909
$597$	− 7.13442e6i	− 0.819263i
$598$	− 5.60892e6i	− 0.641396i
$599$	−7.74415e6	−0.881874	−0.440937	−	0.897538i	$-0.645354\pi$
$599$	−7.74415e6	−0.881874	−0.440937	+	0.897538i	$0.645354\pi$
$600$	0	0
$601$	2.88868e6	0.326222	0.163111	−	0.986608i	$-0.447847\pi$
$601$	2.88868e6	0.326222	0.163111	+	0.986608i	$0.447847\pi$
$602$	− 117208.i	− 0.0131815i
$603$	3.05634e6i	0.342302i
$604$	3.29627e6	0.367647
$605$	0	0
$606$	1.81764e6	0.201060
$607$	1.22095e7i	1.34501i	0.740093	+	0.672504i	$0.234781\pi$
$607$	1.22095e7i	1.34501i	−0.740093	+	0.672504i	$0.765219\pi$
$608$	821248.i	0.0900980i
$609$	958881.	0.104766
$610$	0	0
$611$	1.84997e7	2.00475
$612$	1.00138e6i	0.108073i
$613$	− 1.51667e7i	− 1.63019i	−0.579326	−	0.815096i	$-0.696684\pi$
$613$	− 1.51667e7i	− 1.63019i	0.579326	−	0.815096i	$-0.303316\pi$
$614$	−3.98035e6	−0.426089
$615$	0	0
$616$	−837312.	−0.0889069
$617$	1.53927e7i	1.62780i	0.581006	+	0.813899i	$0.302659\pi$
$617$	1.53927e7i	1.62780i	−0.581006	+	0.813899i	$0.697341\pi$
$618$	4.78654e6i	0.504139i
$619$	1.40843e7	1.47744	0.738720	−	0.674013i	$-0.235431\pi$
$619$	1.40843e7	1.47744	0.738720	+	0.674013i	$0.235431\pi$
$620$	0	0
$621$	−5.17935e6	−0.538947
$622$	5.37593e6i	0.557157i
$623$	1.58760e6i	0.163878i
$624$	−3.06099e6	−0.314703
$625$	0	0
$626$	7.67882e6	0.783175
$627$	− 2.35547e6i	− 0.239282i
$628$	− 9.29840e6i	− 0.940826i
$629$	7.11121e6	0.716666
$630$	0	0
$631$	1.56178e7	1.56152	0.780760	−	0.624831i	$-0.214832\pi$
$631$	1.56178e7	1.56152	0.780760	+	0.624831i	$0.214832\pi$
$632$	− 6.53574e6i	− 0.650882i
$633$	− 1.64750e6i	− 0.163424i
$634$	7.65463e6	0.756312
$635$	0	0
$636$	−4.90195e6	−0.480536
$637$	− 2.60989e6i	− 0.254843i
$638$	1.89997e6i	0.184797i
$639$	−6.34205e6	−0.614437
$640$	0	0
$641$	4.04157e6	0.388513	0.194256	−	0.980951i	$-0.437771\pi$
$641$	4.04157e6	0.388513	0.194256	+	0.980951i	$0.437771\pi$
$642$	4.66831e6i	0.447015i
$643$	1.71035e7i	1.63139i	0.578485	+	0.815693i	$0.303644\pi$
$643$	1.71035e7i	1.63139i	−0.578485	+	0.815693i	$0.696356\pi$
$644$	1.01136e6	0.0960929
$645$	0	0
$646$	1.64570e6	0.155157
$647$	− 8.83546e6i	− 0.829790i	−0.909869	−	0.414895i	$-0.863818\pi$
$647$	− 8.83546e6i	− 0.829790i	0.909869	−	0.414895i	$-0.136182\pi$
$648$	929216.i	0.0869319i
$649$	8.25350e6	0.769178
$650$	0	0
$651$	1.39278e6	0.128804
$652$	5.54576e6i	0.510907i
$653$	− 9.36125e6i	− 0.859115i	−0.903040	−	0.429557i	$-0.858670\pi$
$653$	− 9.36125e6i	− 0.859115i	0.903040	−	0.429557i	$-0.141330\pi$
$654$	−5.46088e6	−0.499251
$655$	0	0
$656$	−3.04742e6	−0.276486
$657$	− 5.81818e6i	− 0.525864i
$658$	3.33572e6i	0.300348i
$659$	366111.	0.0328397	0.0164199	−	0.999865i	$-0.494773\pi$
$659$	366111.	0.0328397	0.0164199	+	0.999865i	$0.494773\pi$
$660$	0	0
$661$	2.05164e7	1.82640	0.913202	−	0.407508i	$-0.133602\pi$
$661$	2.05164e7	1.82640	0.913202	+	0.407508i	$0.133602\pi$
$662$	− 9.02776e6i	− 0.800636i
$663$	6.13394e6i	0.541946i
$664$	5.35526e6	0.471369
$665$	0	0
$666$	−6.76466e6	−0.590963
$667$	− 2.29491e6i	− 0.199734i
$668$	7.18219e6i	0.622753i
$669$	−1.21105e7	−1.04616
$670$	0	0
$671$	475260.	0.0407498
$672$	− 551936.i	− 0.0471482i
$673$	− 7.48189e6i	− 0.636757i	−0.947964	−	0.318378i	$-0.896862\pi$
$673$	− 7.48189e6i	− 0.636757i	0.947964	−	0.318378i	$-0.103138\pi$
$674$	5.80065e6	0.491843
$675$	0	0
$676$	1.29644e7	1.09115
$677$	1.21459e7i	1.01849i	0.860621	+	0.509247i	$0.170076\pi$
$677$	1.21459e7i	1.01849i	−0.860621	+	0.509247i	$0.829924\pi$
$678$	8.48470e6i	0.708863i
$679$	7.28360e6	0.606278
$680$	0	0
$681$	7.64640e6	0.631814
$682$	2.75971e6i	0.227197i
$683$	1.15232e7i	0.945197i	0.881278	+	0.472599i	$0.156684\pi$
$683$	1.15232e7i	0.945197i	−0.881278	+	0.472599i	$0.843316\pi$
$684$	−1.56550e6	−0.127942
$685$	0	0
$686$	470596.	0.0381802
$687$	− 5.10110e6i	− 0.412355i
$688$	153088.i	0.0123302i
$689$	3.02751e7	2.42962
$690$	0	0
$691$	−1.71185e7	−1.36386	−0.681931	−	0.731417i	$-0.738859\pi$
$691$	−1.71185e7	−1.36386	−0.681931	+	0.731417i	$0.738859\pi$
$692$	− 4.20014e6i	− 0.333426i
$693$	− 1.59613e6i	− 0.126251i
$694$	−3.42554e6	−0.269980
$695$	0	0
$696$	−1.25242e6	−0.0979999
$697$	6.10675e6i	0.476133i
$698$	1.39041e6i	0.108020i
$699$	−1.73419e7	−1.34247
$700$	0	0
$701$	9.72758e6	0.747669	0.373835	−	0.927495i	$-0.378043\pi$
$701$	9.72758e6	0.747669	0.373835	+	0.927495i	$0.378043\pi$
$702$	− 1.74572e7i	− 1.33700i
$703$	1.11173e7i	0.848422i
$704$	1.09363e6	0.0831648
$705$	0	0
$706$	−8.87442e6	−0.670082
$707$	− 2.02419e6i	− 0.152301i
$708$	5.44051e6i	0.407903i
$709$	673813.	0.0503412	0.0251706	−	0.999683i	$-0.491987\pi$
$709$	673813.	0.0503412	0.0251706	+	0.999683i	$0.491987\pi$
$710$	0	0
$711$	1.24588e7	0.924274
$712$	− 2.07360e6i	− 0.153294i
$713$	− 3.33336e6i	− 0.245560i
$714$	−1.10603e6	−0.0811934
$715$	0	0
$716$	−1.77619e6	−0.129481
$717$	5.63241e6i	0.409163i
$718$	− 1.17735e7i	− 0.852307i
$719$	−2.77719e6	−0.200347	−0.100174	−	0.994970i	$-0.531940\pi$
$719$	−2.77719e6	−0.200347	−0.100174	+	0.994970i	$0.531940\pi$
$720$	0	0
$721$	5.33046e6	0.381880
$722$	− 7.33158e6i	− 0.523425i
$723$	1.08826e7i	0.774262i
$724$	−1.80435e6	−0.127931
$725$	0	0
$726$	3.94953e6	0.278102
$727$	1.16385e7i	0.816700i	0.912825	+	0.408350i	$0.133896\pi$
$727$	1.16385e7i	0.816700i	−0.912825	+	0.408350i	$0.866104\pi$
$728$	3.40883e6i	0.238384i
$729$	−1.25034e7	−0.871384
$730$	0	0
$731$	306774.	0.0212337
$732$	313280.i	0.0216100i
$733$	1.32013e7i	0.907522i	0.891123	+	0.453761i	$0.149918\pi$
$733$	1.32013e7i	0.907522i	−0.891123	+	0.453761i	$0.850082\pi$
$734$	−9.31999e6	−0.638521
$735$	0	0
$736$	−1.32096e6	−0.0898866
$737$	− 6.68888e6i	− 0.453612i
$738$	− 5.80915e6i	− 0.392619i
$739$	−3.25476e6	−0.219234	−0.109617	−	0.993974i	$-0.534962\pi$
$739$	−3.25476e6	−0.219234	−0.109617	+	0.993974i	$0.534962\pi$
$740$	0	0
$741$	−9.58951e6	−0.641580
$742$	5.45899e6i	0.364001i
$743$	7.61596e6i	0.506119i	0.967451	+	0.253059i	$0.0814368\pi$
$743$	7.61596e6i	0.506119i	−0.967451	+	0.253059i	$0.918563\pi$
$744$	−1.81914e6	−0.120485
$745$	0	0
$746$	6.76986e6	0.445382
$747$	1.02085e7i	0.669359i
$748$	− 2.19154e6i	− 0.143217i
$749$	5.19880e6	0.338609
$750$	0	0
$751$	655199.	0.0423910	0.0211955	−	0.999775i	$-0.493253\pi$
$751$	655199.	0.0423910	0.0211955	+	0.999775i	$0.493253\pi$
$752$	− 4.35686e6i	− 0.280950i
$753$	− 673530.i	− 0.0432882i
$754$	7.73509e6	0.495493
$755$	0	0
$756$	3.14776e6	0.200307
$757$	1.85111e7i	1.17406i	0.809564	+	0.587032i	$0.199704\pi$
$757$	1.85111e7i	1.17406i	−0.809564	+	0.587032i	$0.800296\pi$
$758$	6.00299e6i	0.379485i
$759$	3.78873e6	0.238720
$760$	0	0
$761$	−1.85291e7	−1.15983	−0.579914	−	0.814678i	$-0.696914\pi$
$761$	−1.85291e7	−1.15983	−0.579914	+	0.814678i	$0.696914\pi$
$762$	− 4.36691e6i	− 0.272450i
$763$	6.08144e6i	0.378177i
$764$	1.17119e7	0.725926
$765$	0	0
$766$	1.39409e7	0.858456
$767$	− 3.36013e7i	− 2.06238i
$768$	720896.i	0.0441031i
$769$	1.48414e7	0.905024	0.452512	−	0.891758i	$-0.350528\pi$
$769$	1.48414e7	0.905024	0.452512	+	0.891758i	$0.350528\pi$
$770$	0	0
$771$	−1.47276e7	−0.892268
$772$	− 2.97664e6i	− 0.179756i
$773$	− 3.93042e6i	− 0.236586i	−0.992979	−	0.118293i	$-0.962258\pi$
$773$	− 3.93042e6i	− 0.236586i	0.992979	−	0.118293i	$-0.0377423\pi$
$774$	−291824.	−0.0175093
$775$	0	0
$776$	−9.51328e6	−0.567121
$777$	− 7.47162e6i	− 0.443979i
$778$	1.44239e7i	0.854347i
$779$	−9.54701e6	−0.563668
$780$	0	0
$781$	1.38797e7	0.814242
$782$	2.64708e6i	0.154793i
$783$	− 7.14269e6i	− 0.416349i
$784$	−614656.	−0.0357143
$785$	0	0
$786$	1.21796e7	0.703199
$787$	1.17824e7i	0.678105i	0.940767	+	0.339053i	$0.110107\pi$
$787$	1.17824e7i	0.678105i	−0.940767	+	0.339053i	$0.889893\pi$
$788$	− 1.94170e6i	− 0.111395i
$789$	−1.82180e7	−1.04186
$790$	0	0
$791$	9.44887e6	0.536956
$792$	2.08474e6i	0.118097i
$793$	− 1.93486e6i	− 0.109261i
$794$	−1.89752e7	−1.06816
$795$	0	0
$796$	1.03773e7	0.580502
$797$	− 5.40952e6i	− 0.301657i	−0.988560	−	0.150828i	$-0.951806\pi$
$797$	− 5.40952e6i	− 0.301657i	0.988560	−	0.150828i	$-0.0481941\pi$
$798$	− 1.72911e6i	− 0.0961205i
$799$	−8.73075e6	−0.483821
$800$	0	0
$801$	3.95280e6	0.217683
$802$	2.10616e7i	1.15626i
$803$	1.27332e7i	0.696867i
$804$	4.40915e6	0.240555
$805$	0	0
$806$	1.12352e7	0.609178
$807$	8.25667e6i	0.446294i
$808$	2.64384e6i	0.142465i
$809$	7.12264e6	0.382622	0.191311	−	0.981529i	$-0.438726\pi$
$809$	7.12264e6	0.382622	0.191311	+	0.981529i	$0.438726\pi$
$810$	0	0
$811$	−3.03045e7	−1.61791	−0.808956	−	0.587869i	$-0.799967\pi$
$811$	−3.03045e7	−1.61791	−0.808956	+	0.587869i	$0.799967\pi$
$812$	1.39474e6i	0.0742338i
$813$	− 6.13699e6i	− 0.325633i
$814$	1.48046e7	0.783134
$815$	0	0
$816$	1.44461e6	0.0759494
$817$	479596.i	0.0251374i
$818$	− 5.48060e6i	− 0.286381i
$819$	−6.49809e6	−0.338513
$820$	0	0
$821$	2.82181e7	1.46106	0.730532	−	0.682878i	$-0.239272\pi$
$821$	2.82181e7	1.46106	0.730532	+	0.682878i	$0.239272\pi$
$822$	− 1.04607e7i	− 0.539986i
$823$	2.64534e7i	1.36139i	0.732567	+	0.680694i	$0.238322\pi$
$823$	2.64534e7i	1.36139i	−0.732567	+	0.680694i	$0.761678\pi$
$824$	−6.96224e6	−0.357216
$825$	0	0
$826$	6.05875e6	0.308982
$827$	4.44481e6i	0.225990i	0.993596	+	0.112995i	$0.0360444\pi$
$827$	4.44481e6i	0.225990i	−0.993596	+	0.112995i	$0.963956\pi$
$828$	− 2.51808e6i	− 0.127642i
$829$	2.80386e6	0.141700	0.0708501	−	0.997487i	$-0.477429\pi$
$829$	2.80386e6	0.141700	0.0708501	+	0.997487i	$0.477429\pi$
$830$	0	0
$831$	−1.94981e7	−0.979469
$832$	− 4.45235e6i	− 0.222988i
$833$	1.23171e6i	0.0615031i
$834$	7.06103e6	0.351522
$835$	0	0
$836$	3.42614e6	0.169547
$837$	− 1.03748e7i	− 0.511876i
$838$	− 2.46572e7i	− 1.21292i
$839$	−2.59804e7	−1.27421	−0.637104	−	0.770778i	$-0.719868\pi$
$839$	−2.59804e7	−1.27421	−0.637104	+	0.770778i	$0.719868\pi$
$840$	0	0
$841$	−1.73463e7	−0.845701
$842$	9.81434e6i	0.477069i
$843$	− 1.20883e7i	− 0.585862i
$844$	2.39637e6	0.115797
$845$	0	0
$846$	8.30527e6	0.398959
$847$	− 4.39834e6i	− 0.210659i
$848$	− 7.13011e6i	− 0.340492i
$849$	−3.52626e6	−0.167898
$850$	0	0
$851$	−1.78820e7	−0.846431
$852$	9.14918e6i	0.431801i
$853$	− 1.18392e7i	− 0.557121i	−0.960419	−	0.278560i	$-0.910143\pi$
$853$	− 1.18392e7i	− 0.557121i	0.960419	−	0.278560i	$-0.0898573\pi$
$854$	348880.	0.0163693
$855$	0	0
$856$	−6.79027e6	−0.316740
$857$	− 2.99283e6i	− 0.139197i	−0.997575	−	0.0695985i	$-0.977828\pi$
$857$	− 2.99283e6i	− 0.139197i	0.997575	−	0.0695985i	$-0.0221718\pi$
$858$	1.27701e7i	0.592209i
$859$	−2.80980e7	−1.29925	−0.649626	−	0.760254i	$-0.725074\pi$
$859$	−2.80980e7	−1.29925	−0.649626	+	0.760254i	$0.725074\pi$
$860$	0	0
$861$	6.41626e6	0.294967
$862$	3.06708e7i	1.40591i
$863$	− 1.15833e7i	− 0.529424i	−0.964328	−	0.264712i	$-0.914723\pi$
$863$	− 1.15833e7i	− 0.529424i	0.964328	−	0.264712i	$-0.0852769\pi$
$864$	−4.11136e6	−0.187370
$865$	0	0
$866$	−2.00114e7	−0.906739
$867$	1.27236e7i	0.574859i
$868$	2.02586e6i	0.0912661i
$869$	−2.72663e7	−1.22483
$870$	0	0
$871$	−2.72315e7	−1.21626
$872$	− 7.94310e6i	− 0.353752i
$873$	− 1.81347e7i	− 0.805331i
$874$	−4.13832e6	−0.183251
$875$	0	0
$876$	−8.39344e6	−0.369556
$877$	4.12538e7i	1.81119i	0.424141	+	0.905596i	$0.360576\pi$
$877$	4.12538e7i	1.81119i	−0.424141	+	0.905596i	$0.639424\pi$
$878$	− 7.45450e6i	− 0.326349i
$879$	−1.78571e7	−0.779539
$880$	0	0
$881$	−1.32541e7	−0.575321	−0.287661	−	0.957732i	$-0.592877\pi$
$881$	−1.32541e7	−0.575321	−0.287661	+	0.957732i	$0.592877\pi$
$882$	− 1.17169e6i	− 0.0507155i
$883$	3.19208e7i	1.37776i	0.724877	+	0.688878i	$0.241897\pi$
$883$	3.19208e7i	1.37776i	−0.724877	+	0.688878i	$0.758103\pi$
$884$	−8.92210e6	−0.384004
$885$	0	0
$886$	1.04299e7	0.446371
$887$	1.74303e7i	0.743866i	0.928260	+	0.371933i	$0.121305\pi$
$887$	1.74303e7i	0.743866i	−0.928260	+	0.371933i	$0.878695\pi$
$888$	9.75885e6i	0.415304i
$889$	−4.86315e6	−0.206378
$890$	0	0
$891$	3.87657e6	0.163589
$892$	− 1.76153e7i	− 0.741274i
$893$	− 1.36492e7i	− 0.572769i
$894$	−4.38583e6	−0.183530
$895$	0	0
$896$	802816.	0.0334077
$897$	− 1.54245e7i	− 0.640075i
$898$	1.91203e7i	0.791230i
$899$	4.59694e6	0.189701
$900$	0	0
$901$	−1.42881e7	−0.586357
$902$	1.27135e7i	0.520293i
$903$	− 322322.i	− 0.0131544i
$904$	−1.23414e7	−0.502276
$905$	0	0
$906$	9.06475e6	0.366889
$907$	− 3.15066e7i	− 1.27170i	−0.771815	−	0.635848i	$-0.780651\pi$
$907$	− 3.15066e7i	− 1.27170i	0.771815	−	0.635848i	$-0.219349\pi$
$908$	1.11220e7i	0.447682i
$909$	−5.03982e6	−0.202304
$910$	0	0
$911$	−4.91214e7	−1.96099	−0.980494	−	0.196548i	$-0.937027\pi$
$911$	−4.91214e7	−1.96099	−0.980494	+	0.196548i	$0.937027\pi$
$912$	2.25843e6i	0.0899125i
$913$	− 2.23415e7i	− 0.887024i
$914$	3.18703e7	1.26189
$915$	0	0
$916$	7.41978e6	0.292181
$917$	− 1.35637e7i	− 0.532665i
$918$	8.23878e6i	0.322668i
$919$	4.51238e7	1.76245	0.881226	−	0.472696i	$-0.156719\pi$
$919$	4.51238e7	1.76245	0.881226	+	0.472696i	$0.156719\pi$
$920$	0	0
$921$	−1.09460e7	−0.425211
$922$	7.10659e6i	0.275318i
$923$	− 5.65066e7i	− 2.18321i
$924$	−2.30261e6	−0.0887238
$925$	0	0
$926$	−3.99419e6	−0.153074
$927$	− 1.32718e7i	− 0.507259i
$928$	− 1.82170e6i	− 0.0694394i
$929$	3.68196e7	1.39972	0.699858	−	0.714282i	$-0.253247\pi$
$929$	3.68196e7	1.39972	0.699858	+	0.714282i	$0.253247\pi$
$930$	0	0
$931$	−1.92560e6	−0.0728102
$932$	− 2.52246e7i	− 0.951227i
$933$	1.47838e7i	0.556009i
$934$	2.03391e7	0.762896
$935$	0	0
$936$	8.48730e6	0.316650
$937$	1.71904e7i	0.639641i	0.947478	+	0.319820i	$0.103623\pi$
$937$	1.71904e7i	0.639641i	−0.947478	+	0.319820i	$0.896377\pi$
$938$	− 4.91019e6i	− 0.182218i
$939$	2.11168e7	0.781562
$940$	0	0
$941$	−8.10352e6	−0.298332	−0.149166	−	0.988812i	$-0.547659\pi$
$941$	−8.10352e6	−0.298332	−0.149166	+	0.988812i	$0.547659\pi$
$942$	− 2.55706e7i	− 0.938888i
$943$	− 1.53562e7i	− 0.562346i
$944$	−7.91347e6	−0.289026
$945$	0	0
$946$	638664.	0.0232030
$947$	1.83337e7i	0.664317i	0.943224	+	0.332158i	$0.107777\pi$
$947$	1.83337e7i	0.664317i	−0.943224	+	0.332158i	$0.892223\pi$
$948$	− 1.79733e7i	− 0.649541i
$949$	5.18390e7	1.86849
$950$	0	0
$951$	2.10502e7	0.754755
$952$	− 1.60877e6i	− 0.0575309i
$953$	− 6.03035e6i	− 0.215085i	−0.994200	−	0.107542i	$-0.965702\pi$
$953$	− 6.03035e6i	− 0.215085i	0.994200	−	0.107542i	$-0.0342982\pi$
$954$	1.35918e7	0.483510
$955$	0	0
$956$	−8.19259e6	−0.289919
$957$	5.22492e6i	0.184417i
$958$	− 1.48774e7i	− 0.523738i
$959$	−1.16495e7	−0.409034
$960$	0	0
$961$	−2.19521e7	−0.766774
$962$	− 6.02720e7i	− 2.09980i
$963$	− 1.29440e7i	− 0.449781i
$964$	−1.58293e7	−0.548616
$965$	0	0
$966$	2.78124e6	0.0958949
$967$	− 3.09228e7i	− 1.06344i	−0.846920	−	0.531720i	$-0.821546\pi$
$967$	− 3.09228e7i	− 1.06344i	0.846920	−	0.531720i	$-0.178454\pi$
$968$	5.74477e6i	0.197053i
$969$	4.52569e6	0.154837
$970$	0	0
$971$	−2.47924e6	−0.0843859	−0.0421929	−	0.999109i	$-0.513434\pi$
$971$	−2.47924e6	−0.0843859	−0.0421929	+	0.999109i	$0.513434\pi$
$972$	− 1.30550e7i	− 0.443211i
$973$	− 7.86342e6i	− 0.266274i
$974$	3.64814e7	1.23218
$975$	0	0
$976$	−455680.	−0.0153121
$977$	− 2.09758e6i	− 0.0703044i	−0.999382	−	0.0351522i	$-0.988808\pi$
$977$	− 2.09758e6i	− 0.0703044i	0.999382	−	0.0351522i	$-0.0111916\pi$
$978$	1.52508e7i	0.509855i
$979$	−8.65080e6	−0.288469
$980$	0	0
$981$	1.51415e7	0.502340
$982$	− 3.13509e7i	− 1.03746i
$983$	4.45491e7i	1.47047i	0.677814	+	0.735233i	$0.262927\pi$
$983$	4.45491e7i	1.47047i	−0.677814	+	0.735233i	$0.737073\pi$
$984$	−8.38042e6	−0.275917
$985$	0	0
$986$	−3.65051e6	−0.119581
$987$	9.17324e6i	0.299730i
$988$	− 1.39484e7i	− 0.454602i
$989$	−771420.	−0.0250784
$990$	0	0
$991$	−1.95104e7	−0.631075	−0.315538	−	0.948913i	$-0.602185\pi$
$991$	−1.95104e7	−0.631075	−0.315538	+	0.948913i	$0.602185\pi$
$992$	− 2.64602e6i	− 0.0853716i
$993$	− 2.48263e7i	− 0.798987i
$994$	1.01889e7	0.327084
$995$	0	0
$996$	1.47270e7	0.470398
$997$	− 2.00678e7i	− 0.639385i	−0.947521	−	0.319692i	$-0.896420\pi$
$997$	− 2.00678e7i	− 0.639385i	0.947521	−	0.319692i	$-0.103580\pi$
$998$	384412.i	0.0122172i
$999$	−5.56559e7	−1.76440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.6.c.b.99.2		2
5.2	odd	4		350.6.a.d.1.1		1
5.3	odd	4		70.6.a.f.1.1	✓	1
5.4	even	2	inner	350.6.c.b.99.1		2
15.8	even	4		630.6.a.e.1.1		1
20.3	even	4		560.6.a.f.1.1		1
35.13	even	4		490.6.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.f.1.1	✓	1	5.3	odd	4
350.6.a.d.1.1		1	5.2	odd	4
350.6.c.b.99.1		2	5.4	even	2	inner
350.6.c.b.99.2		2	1.1	even	1	trivial
490.6.a.l.1.1		1	35.13	even	4
560.6.a.f.1.1		1	20.3	even	4
630.6.a.e.1.1		1	15.8	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} +11.0000i q^{3} -16.0000 q^{4} -44.0000 q^{6} +49.0000i q^{7} -64.0000i q^{8} +122.000 q^{9} -267.000 q^{11} -176.000i q^{12} +1087.00i q^{13} -196.000 q^{14} +256.000 q^{16} -513.000i q^{17} +488.000i q^{18} +802.000 q^{19} -539.000 q^{21} -1068.00i q^{22} +1290.00i q^{23} +704.000 q^{24} -4348.00 q^{26} +4015.00i q^{27} -784.000i q^{28} -1779.00 q^{29} -2584.00 q^{31} +1024.00i q^{32} -2937.00i q^{33} +2052.00 q^{34} -1952.00 q^{36} +13862.0i q^{37} +3208.00i q^{38} -11957.0 q^{39} -11904.0 q^{41} -2156.00i q^{42} +598.000i q^{43} +4272.00 q^{44} -5160.00 q^{46} -17019.0i q^{47} +2816.00i q^{48} -2401.00 q^{49} +5643.00 q^{51} -17392.0i q^{52} -27852.0i q^{53} -16060.0 q^{54} +3136.00 q^{56} +8822.00i q^{57} -7116.00i q^{58} -30912.0 q^{59} -1780.00 q^{61} -10336.0i q^{62} +5978.00i q^{63} -4096.00 q^{64} +11748.0 q^{66} +25052.0i q^{67} +8208.00i q^{68} -14190.0 q^{69} -51984.0 q^{71} -7808.00i q^{72} -47690.0i q^{73} -55448.0 q^{74} -12832.0 q^{76} -13083.0i q^{77} -47828.0i q^{78} +102121. q^{79} -14519.0 q^{81} -47616.0i q^{82} +83676.0i q^{83} +8624.00 q^{84} -2392.00 q^{86} -19569.0i q^{87} +17088.0i q^{88} +32400.0 q^{89} -53263.0 q^{91} -20640.0i q^{92} -28424.0i q^{93} +68076.0 q^{94} -11264.0 q^{96} -148645. i q^{97} -9604.00i q^{98} -32574.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 88 q^{6} + 244 q^{9} - 534 q^{11} - 392 q^{14} + 512 q^{16} + 1604 q^{19} - 1078 q^{21} + 1408 q^{24} - 8696 q^{26} - 3558 q^{29} - 5168 q^{31} + 4104 q^{34} - 3904 q^{36} - 23914 q^{39}+ \cdots - 65148 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 - 88 * q^6 + 244 * q^9 - 534 * q^11 - 392 * q^14 + 512 * q^16 + 1604 * q^19 - 1078 * q^21 + 1408 * q^24 - 8696 * q^26 - 3558 * q^29 - 5168 * q^31 + 4104 * q^34 - 3904 * q^36 - 23914 * q^39 - 23808 * q^41 + 8544 * q^44 - 10320 * q^46 - 4802 * q^49 + 11286 * q^51 - 32120 * q^54 + 6272 * q^56 - 61824 * q^59 - 3560 * q^61 - 8192 * q^64 + 23496 * q^66 - 28380 * q^69 - 103968 * q^71 - 110896 * q^74 - 25664 * q^76 + 204242 * q^79 - 29038 * q^81 + 17248 * q^84 - 4784 * q^86 + 64800 * q^89 - 106526 * q^91 + 136152 * q^94 - 22528 * q^96 - 65148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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