LMFDB - Embedded newform 325.6.b.i.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,6,Mod(274,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, 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("325.274");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	325.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:	$52.1247414392$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.1
Character	$\chi$	$=$	325.274
Dual form			325.6.b.i.274.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.2252i q^{2} +19.1897i q^{3} -94.0044 q^{4} +215.408 q^{6} -70.9909i q^{7} +696.009i q^{8} -125.246 q^{9} +O(q^{10})$	\(q-11.2252i q^{2} +19.1897i q^{3} -94.0044 q^{4} +215.408 q^{6} -70.9909i q^{7} +696.009i q^{8} -125.246 q^{9} -161.025 q^{11} -1803.92i q^{12} +169.000i q^{13} -796.885 q^{14} +4804.68 q^{16} +121.397i q^{17} +1405.90i q^{18} +3111.76 q^{19} +1362.30 q^{21} +1807.53i q^{22} -3100.00i q^{23} -13356.2 q^{24} +1897.05 q^{26} +2259.68i q^{27} +6673.46i q^{28} -3172.08 q^{29} -3515.11 q^{31} -31661.0i q^{32} -3090.02i q^{33} +1362.70 q^{34} +11773.6 q^{36} -6991.30i q^{37} -34930.1i q^{38} -3243.06 q^{39} -19551.6 q^{41} -15292.0i q^{42} +13398.3i q^{43} +15137.0 q^{44} -34798.0 q^{46} -7637.52i q^{47} +92200.5i q^{48} +11767.3 q^{49} -2329.57 q^{51} -15886.7i q^{52} +27750.4i q^{53} +25365.2 q^{54} +49410.3 q^{56} +59713.9i q^{57} +35607.1i q^{58} -33042.3 q^{59} -33195.2 q^{61} +39457.6i q^{62} +8891.30i q^{63} -201651. q^{64} -34686.0 q^{66} -24591.9i q^{67} -11411.8i q^{68} +59488.1 q^{69} +16641.4 q^{71} -87172.0i q^{72} -5252.97i q^{73} -78478.5 q^{74} -292519. q^{76} +11431.3i q^{77} +36403.9i q^{78} +3121.54 q^{79} -73797.2 q^{81} +219470. i q^{82} -25125.8i q^{83} -128062. q^{84} +150399. q^{86} -60871.3i q^{87} -112075. i q^{88} -634.739 q^{89} +11997.5 q^{91} +291413. i q^{92} -67453.9i q^{93} -85732.5 q^{94} +607566. q^{96} -156159. i q^{97} -132090. i q^{98} +20167.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 374 q^{4} + 702 q^{6} - 2744 q^{9}+O(q^{10}) $ 22 * q - 374 * q^4 + 702 * q^6 - 2744 * q^9	$ 22 q - 374 q^{4} + 702 q^{6} - 2744 q^{9} + 2552 q^{11} - 1156 q^{14} + 11414 q^{16} - 7040 q^{19} + 3412 q^{21} - 15446 q^{24} + 1690 q^{26} - 36850 q^{29} + 18136 q^{31} + 28910 q^{34} + 75368 q^{36} - 3718 q^{39} - 20020 q^{41} - 121302 q^{44} - 19716 q^{46} - 146626 q^{49} + 73212 q^{51} - 96026 q^{54} - 2524 q^{56} - 263284 q^{59} - 86730 q^{61} - 360142 q^{64} - 117214 q^{66} - 118690 q^{69} + 136840 q^{71} - 742792 q^{74} + 45034 q^{76} - 104478 q^{79} + 215014 q^{81} - 1705432 q^{84} + 404492 q^{86} - 655424 q^{89} + 70304 q^{91} - 1299948 q^{94} + 1799326 q^{96} - 853396 q^{99}+O(q^{100}) $ 22 * q - 374 * q^4 + 702 * q^6 - 2744 * q^9 + 2552 * q^11 - 1156 * q^14 + 11414 * q^16 - 7040 * q^19 + 3412 * q^21 - 15446 * q^24 + 1690 * q^26 - 36850 * q^29 + 18136 * q^31 + 28910 * q^34 + 75368 * q^36 - 3718 * q^39 - 20020 * q^41 - 121302 * q^44 - 19716 * q^46 - 146626 * q^49 + 73212 * q^51 - 96026 * q^54 - 2524 * q^56 - 263284 * q^59 - 86730 * q^61 - 360142 * q^64 - 117214 * q^66 - 118690 * q^69 + 136840 * q^71 - 742792 * q^74 + 45034 * q^76 - 104478 * q^79 + 215014 * q^81 - 1705432 * q^84 + 404492 * q^86 - 655424 * q^89 + 70304 * q^91 - 1299948 * q^94 + 1799326 * q^96 - 853396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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 $

$2$	− 11.2252i	− 1.98435i	−0.124864	−	0.992174i	$-0.539849\pi$
$2$	− 11.2252i	− 1.98435i	0.124864	−	0.992174i	$-0.460151\pi$
$3$	19.1897i	1.23102i	0.788129	+	0.615511i	$0.211050\pi$
$3$	19.1897i	1.23102i	−0.788129	+	0.615511i	$0.788950\pi$
$4$	−94.0044	−2.93764
$5$	0	0
$5$	0	0
$6$	215.408	2.44277
$7$	− 70.9909i	− 0.547593i	−0.961788	−	0.273796i	$-0.911721\pi$
$7$	− 70.9909i	− 0.547593i	0.961788	−	0.273796i	$-0.0882795\pi$
$8$	696.009i	3.84494i
$9$	−125.246	−0.515414
$10$	0	0
$11$	−161.025	−0.401246	−0.200623	−	0.979669i	$-0.564297\pi$
$11$	−161.025	−0.401246	−0.200623	+	0.979669i	$0.564297\pi$
$12$	− 1803.92i	− 3.61629i
$13$	169.000i	0.277350i
$13$	169.000i	0.277350i
$14$	−796.885	−1.08661
$15$	0	0
$16$	4804.68	4.69207
$17$	121.397i	0.101879i	0.998702	+	0.0509396i	$0.0162216\pi$
$17$	121.397i	0.101879i	−0.998702	+	0.0509396i	$0.983778\pi$
$18$	1405.90i	1.02276i
$19$	3111.76	1.97753	0.988764	−	0.149485i	$-0.0477617\pi$
$19$	3111.76	1.97753	0.988764	+	0.149485i	$0.0477617\pi$
$20$	0	0
$21$	1362.30	0.674099
$22$	1807.53i	0.796211i
$23$	− 3100.00i	− 1.22192i	−0.791662	−	0.610959i	$-0.790784\pi$
$23$	− 3100.00i	− 1.22192i	0.791662	−	0.610959i	$-0.209216\pi$
$24$	−13356.2	−4.73321
$25$	0	0
$26$	1897.05	0.550359
$27$	2259.68i	0.596536i
$28$	6673.46i	1.60863i
$29$	−3172.08	−0.700404	−0.350202	−	0.936674i	$-0.613887\pi$
$29$	−3172.08	−0.700404	−0.350202	+	0.936674i	$0.613887\pi$
$30$	0	0
$31$	−3515.11	−0.656953	−0.328476	−	0.944512i	$-0.606535\pi$
$31$	−3515.11	−0.656953	−0.328476	+	0.944512i	$0.606535\pi$
$32$	− 31661.0i	− 5.46575i
$33$	− 3090.02i	− 0.493942i
$34$	1362.70	0.202164
$35$	0	0
$36$	11773.6	1.51410
$37$	− 6991.30i	− 0.839563i	−0.907625	−	0.419782i	$-0.862107\pi$
$37$	− 6991.30i	− 0.839563i	0.907625	−	0.419782i	$-0.137893\pi$
$38$	− 34930.1i	− 3.92410i
$39$	−3243.06	−0.341424
$40$	0	0
$41$	−19551.6	−1.81644	−0.908222	−	0.418488i	$-0.862560\pi$
$41$	−19551.6	−1.81644	−0.908222	+	0.418488i	$0.862560\pi$
$42$	− 15292.0i	− 1.33765i
$43$	13398.3i	1.10504i	0.833498	+	0.552522i	$0.186335\pi$
$43$	13398.3i	1.10504i	−0.833498	+	0.552522i	$0.813665\pi$
$44$	15137.0	1.17871
$45$	0	0
$46$	−34798.0	−2.42471
$47$	− 7637.52i	− 0.504322i	−0.967685	−	0.252161i	$-0.918859\pi$
$47$	− 7637.52i	− 0.504322i	0.967685	−	0.252161i	$-0.0811412\pi$
$48$	92200.5i	5.77604i
$49$	11767.3	0.700142
$50$	0	0
$51$	−2329.57	−0.125415
$52$	− 15886.7i	− 0.814754i
$53$	27750.4i	1.35700i	0.734600	+	0.678500i	$0.237370\pi$
$53$	27750.4i	1.35700i	−0.734600	+	0.678500i	$0.762630\pi$
$54$	25365.2	1.18374
$55$	0	0
$56$	49410.3	2.10546
$57$	59713.9i	2.43438i
$58$	35607.1i	1.38985i
$59$	−33042.3	−1.23578	−0.617889	−	0.786265i	$-0.712012\pi$
$59$	−33042.3	−1.23578	−0.617889	+	0.786265i	$0.712012\pi$
$60$	0	0
$61$	−33195.2	−1.14222	−0.571110	−	0.820873i	$-0.693487\pi$
$61$	−33195.2	−1.14222	−0.571110	+	0.820873i	$0.693487\pi$
$62$	39457.6i	1.30362i
$63$	8891.30i	0.282237i
$64$	−201651.	−6.15389
$65$	0	0
$66$	−34686.0	−0.980153
$67$	− 24591.9i	− 0.669275i	−0.942347	−	0.334637i	$-0.891386\pi$
$67$	− 24591.9i	− 0.669275i	0.942347	−	0.334637i	$-0.108614\pi$
$68$	− 11411.8i	− 0.299284i
$69$	59488.1	1.50421
$70$	0	0
$71$	16641.4	0.391781	0.195891	−	0.980626i	$-0.437240\pi$
$71$	16641.4	0.391781	0.195891	+	0.980626i	$0.437240\pi$
$72$	− 87172.0i	− 1.98174i
$73$	− 5252.97i	− 0.115371i	−0.998335	−	0.0576856i	$-0.981628\pi$
$73$	− 5252.97i	− 0.115371i	0.998335	−	0.0576856i	$-0.0183721\pi$
$74$	−78478.5	−1.66599
$75$	0	0
$76$	−292519.	−5.80926
$77$	11431.3i	0.219719i
$78$	36403.9i	0.677504i
$79$	3121.54	0.0562731	0.0281366	−	0.999604i	$-0.491043\pi$
$79$	3121.54	0.0562731	0.0281366	+	0.999604i	$0.491043\pi$
$80$	0	0
$81$	−73797.2	−1.24976
$82$	219470.i	3.60446i
$83$	− 25125.8i	− 0.400336i	−0.979762	−	0.200168i	$-0.935851\pi$
$83$	− 25125.8i	− 0.400336i	0.979762	−	0.200168i	$-0.0641488\pi$
$84$	−128062.	−1.98026
$85$	0	0
$86$	150399.	2.19279
$87$	− 60871.3i	− 0.862213i
$88$	− 112075.i	− 1.54277i
$89$	−634.739	−0.00849416	−0.00424708	−	0.999991i	$-0.501352\pi$
$89$	−634.739	−0.00849416	−0.00424708	+	0.999991i	$0.501352\pi$
$90$	0	0
$91$	11997.5	0.151875
$92$	291413.i	3.58955i
$93$	− 67453.9i	− 0.808723i
$94$	−85732.5	−1.00075
$95$	0	0
$96$	607566.	6.72846
$97$	− 156159.i	− 1.68514i	−0.538584	−	0.842572i	$-0.681041\pi$
$97$	− 156159.i	− 1.68514i	0.538584	−	0.842572i	$-0.318959\pi$
$98$	− 132090.i	− 1.38933i
$99$	20167.6	0.206808
$100$	0	0
$101$	−165081.	−1.61026	−0.805128	−	0.593101i	$-0.797903\pi$
$101$	−165081.	−1.61026	−0.805128	+	0.593101i	$0.797903\pi$
$102$	26149.9i	0.248868i
$103$	75861.6i	0.704578i	0.935891	+	0.352289i	$0.114597\pi$
$103$	75861.6i	0.704578i	−0.935891	+	0.352289i	$0.885403\pi$
$104$	−117626.	−1.06640
$105$	0	0
$106$	311503.	2.69276
$107$	141728.i	1.19673i	0.801223	+	0.598366i	$0.204183\pi$
$107$	141728.i	1.19673i	−0.801223	+	0.598366i	$0.795817\pi$
$108$	− 212419.i	− 1.75241i
$109$	−11820.9	−0.0952981	−0.0476490	−	0.998864i	$-0.515173\pi$
$109$	−11820.9	−0.0952981	−0.0476490	+	0.998864i	$0.515173\pi$
$110$	0	0
$111$	134161.	1.03352
$112$	− 341089.i	− 2.56934i
$113$	− 43552.7i	− 0.320862i	−0.987047	−	0.160431i	$-0.948712\pi$
$113$	− 43552.7i	− 0.320862i	0.987047	−	0.160431i	$-0.0512885\pi$
$114$	670298.	4.83065
$115$	0	0
$116$	298189.	2.05753
$117$	− 21166.5i	− 0.142950i
$118$	370906.i	2.45222i
$119$	8618.08	0.0557883
$120$	0	0
$121$	−135122.	−0.839002
$122$	372621.i	2.26656i
$123$	− 375189.i	− 2.23608i
$124$	330435.	1.92989
$125$	0	0
$126$	99806.3	0.560056
$127$	− 229412.i	− 1.26214i	−0.775727	−	0.631068i	$-0.782617\pi$
$127$	− 229412.i	− 1.26214i	0.775727	−	0.631068i	$-0.217383\pi$
$128$	1.25041e6i	6.74570i
$129$	−257110.	−1.36033
$130$	0	0
$131$	−161719.	−0.823347	−0.411674	−	0.911331i	$-0.635056\pi$
$131$	−161719.	−0.823347	−0.411674	+	0.911331i	$0.635056\pi$
$132$	290475.i	1.45102i
$133$	− 220907.i	− 1.08288i
$134$	−276048.	−1.32807
$135$	0	0
$136$	−84493.4	−0.391720
$137$	− 233597.i	− 1.06332i	−0.846956	−	0.531662i	$-0.821567\pi$
$137$	− 233597.i	− 1.06332i	0.846956	−	0.531662i	$-0.178433\pi$
$138$	− 667764.i	− 2.98487i
$139$	−97992.9	−0.430187	−0.215094	−	0.976593i	$-0.569006\pi$
$139$	−97992.9	−0.430187	−0.215094	+	0.976593i	$0.569006\pi$
$140$	0	0
$141$	146562.	0.620831
$142$	− 186802.i	− 0.777430i
$143$	− 27213.1i	− 0.111286i
$144$	−601765.	−2.41836
$145$	0	0
$146$	−58965.4	−0.228937
$147$	225811.i	0.861890i
$148$	657212.i	2.46633i
$149$	−267805.	−0.988219	−0.494110	−	0.869400i	$-0.664506\pi$
$149$	−267805.	−0.988219	−0.494110	+	0.869400i	$0.664506\pi$
$150$	0	0
$151$	−125041.	−0.446283	−0.223141	−	0.974786i	$-0.571631\pi$
$151$	−125041.	−0.446283	−0.223141	+	0.974786i	$0.571631\pi$
$152$	2.16582e6i	7.60348i
$153$	− 15204.4i	− 0.0525099i
$154$	128318.	0.436000
$155$	0	0
$156$	304862.	1.00298
$157$	323793.i	1.04838i	0.851602	+	0.524189i	$0.175632\pi$
$157$	323793.i	1.04838i	−0.851602	+	0.524189i	$0.824368\pi$
$158$	− 35039.8i	− 0.111665i
$159$	−532523.	−1.67050
$160$	0	0
$161$	−220072.	−0.669113
$162$	828386.i	2.47996i
$163$	− 483015.i	− 1.42394i	−0.702210	−	0.711970i	$-0.747803\pi$
$163$	− 483015.i	− 1.42394i	0.702210	−	0.711970i	$-0.252197\pi$
$164$	1.83793e6	5.33605
$165$	0	0
$166$	−282041.	−0.794406
$167$	− 272660.i	− 0.756538i	−0.925696	−	0.378269i	$-0.876520\pi$
$167$	− 272660.i	− 0.756538i	0.925696	−	0.378269i	$-0.123480\pi$
$168$	948171.i	2.59187i
$169$	−28561.0	−0.0769231
$170$	0	0
$171$	−389734.	−1.01924
$172$	− 1.25950e6i	− 3.24622i
$173$	248584.i	0.631477i	0.948846	+	0.315738i	$0.102252\pi$
$173$	248584.i	0.631477i	−0.948846	+	0.315738i	$0.897748\pi$
$174$	−683290.	−1.71093
$175$	0	0
$176$	−773671.	−1.88267
$177$	− 634073.i	− 1.52127i
$178$	7125.05i	0.0168554i
$179$	−29132.9	−0.0679597	−0.0339798	−	0.999423i	$-0.510818\pi$
$179$	−29132.9	−0.0679597	−0.0339798	+	0.999423i	$0.510818\pi$
$180$	0	0
$181$	583931.	1.32485	0.662423	−	0.749130i	$-0.269528\pi$
$181$	583931.	1.32485	0.662423	+	0.749130i	$0.269528\pi$
$182$	− 134674.i	− 0.301373i
$183$	− 637006.i	− 1.40610i
$184$	2.15763e6	4.69820
$185$	0	0
$186$	−757181.	−1.60479
$187$	− 19547.9i	− 0.0408786i
$188$	717960.i	1.48151i
$189$	160417.	0.326659
$190$	0	0
$191$	708228.	1.40472	0.702359	−	0.711822i	$-0.252130\pi$
$191$	708228.	1.40472	0.702359	+	0.711822i	$0.252130\pi$
$192$	− 3.86962e6i	− 7.57557i
$193$	− 596277.i	− 1.15227i	−0.817354	−	0.576136i	$-0.804560\pi$
$193$	− 596277.i	− 1.15227i	0.817354	−	0.576136i	$-0.195440\pi$
$194$	−1.75291e6	−3.34391
$195$	0	0
$196$	−1.10618e6	−2.05676
$197$	23822.5i	0.0437342i	0.999761	+	0.0218671i	$0.00696107\pi$
$197$	23822.5i	0.0437342i	−0.999761	+	0.0218671i	$0.993039\pi$
$198$	− 226385.i	− 0.410378i
$199$	−470656.	−0.842503	−0.421251	−	0.906944i	$-0.638409\pi$
$199$	−470656.	−0.842503	−0.421251	+	0.906944i	$0.638409\pi$
$200$	0	0
$201$	471911.	0.823892
$202$	1.85307e6i	3.19531i
$203$	225189.i	0.383536i
$204$	218990.	0.368425
$205$	0	0
$206$	851560.	1.39813
$207$	388261.i	0.629793i
$208$	811991.i	1.30135i
$209$	−501070.	−0.793475
$210$	0	0
$211$	−619805.	−0.958405	−0.479202	−	0.877704i	$-0.659074\pi$
$211$	−619805.	−0.958405	−0.479202	+	0.877704i	$0.659074\pi$
$212$	− 2.60866e6i	− 3.98637i
$213$	319344.i	0.482291i
$214$	1.59092e6	2.37473
$215$	0	0
$216$	−1.57276e6	−2.29365
$217$	249541.i	0.359743i
$218$	132692.i	0.189105i
$219$	100803.	0.142024
$220$	0	0
$221$	−20516.1	−0.0282562
$222$	− 1.50598e6i	− 2.05086i
$223$	− 310997.i	− 0.418787i	−0.977831	−	0.209394i	$-0.932851\pi$
$223$	− 310997.i	− 0.418787i	0.977831	−	0.209394i	$-0.0671490\pi$
$224$	−2.24765e6	−2.99301
$225$	0	0
$226$	−488886.	−0.636702
$227$	450336.i	0.580059i	0.957018	+	0.290030i	$0.0936651\pi$
$227$	450336.i	0.580059i	−0.957018	+	0.290030i	$0.906335\pi$
$228$	− 5.61337e6i	− 7.15132i
$229$	−855126.	−1.07756	−0.538780	−	0.842447i	$-0.681114\pi$
$229$	−855126.	−1.07756	−0.538780	+	0.842447i	$0.681114\pi$
$230$	0	0
$231$	−219363.	−0.270479
$232$	− 2.20779e6i	− 2.69301i
$233$	− 1.09514e6i	− 1.32153i	−0.750591	−	0.660767i	$-0.770231\pi$
$233$	− 1.09514e6i	− 1.32153i	0.750591	−	0.660767i	$-0.229769\pi$
$234$	−237597.	−0.283663
$235$	0	0
$236$	3.10612e6	3.63027
$237$	59901.4i	0.0692734i
$238$	− 96739.4i	− 0.110703i
$239$	−917921.	−1.03947	−0.519733	−	0.854329i	$-0.673969\pi$
$239$	−917921.	−1.03947	−0.519733	+	0.854329i	$0.673969\pi$
$240$	0	0
$241$	−642632.	−0.712721	−0.356361	−	0.934349i	$-0.615982\pi$
$241$	−642632.	−0.712721	−0.356361	+	0.934349i	$0.615982\pi$
$242$	1.51677e6i	1.66487i
$243$	− 867047.i	− 0.941948i
$244$	3.12049e6	3.35543
$245$	0	0
$246$	−4.21156e6	−4.43717
$247$	525888.i	0.548468i
$248$	− 2.44655e6i	− 2.52595i
$249$	482157.	0.492822
$250$	0	0
$251$	−96744.1	−0.0969260	−0.0484630	−	0.998825i	$-0.515432\pi$
$251$	−96744.1	−0.0969260	−0.0484630	+	0.998825i	$0.515432\pi$
$252$	− 835821.i	− 0.829109i
$253$	499176.i	0.490289i
$254$	−2.57518e6	−2.50452
$255$	0	0
$256$	7.58322e6	7.23192
$257$	− 1.06681e6i	− 1.00752i	−0.863844	−	0.503759i	$-0.831950\pi$
$257$	− 1.06681e6i	− 1.00752i	0.863844	−	0.503759i	$-0.168050\pi$
$258$	2.88611e6i	2.69937i
$259$	−496319.	−0.459739
$260$	0	0
$261$	397288.	0.360998
$262$	1.81532e6i	1.63381i
$263$	503116.i	0.448517i	0.974530	+	0.224258i	$0.0719960\pi$
$263$	503116.i	0.448517i	−0.974530	+	0.224258i	$0.928004\pi$
$264$	2.15068e6	1.89918
$265$	0	0
$266$	−2.47972e6	−2.14881
$267$	− 12180.5i	− 0.0104565i
$268$	2.31174e6i	1.96609i
$269$	104820.	0.0883212	0.0441606	−	0.999024i	$-0.485939\pi$
$269$	104820.	0.0883212	0.0441606	+	0.999024i	$0.485939\pi$
$270$	0	0
$271$	−168792.	−0.139614	−0.0698069	−	0.997561i	$-0.522238\pi$
$271$	−168792.	−0.139614	−0.0698069	+	0.997561i	$0.522238\pi$
$272$	583273.i	0.478024i
$273$	230228.i	0.186961i
$274$	−2.62217e6	−2.11001
$275$	0	0
$276$	−5.59214e6	−4.41881
$277$	863313.i	0.676034i	0.941140	+	0.338017i	$0.109756\pi$
$277$	863313.i	0.676034i	−0.941140	+	0.338017i	$0.890244\pi$
$278$	1.09999e6i	0.853641i
$279$	440251.	0.338602
$280$	0	0
$281$	−1.56951e6	−1.18577	−0.592883	−	0.805289i	$-0.702010\pi$
$281$	−1.56951e6	−1.18577	−0.592883	+	0.805289i	$0.702010\pi$
$282$	− 1.64518e6i	− 1.23194i
$283$	1.10553e6i	0.820546i	0.911963	+	0.410273i	$0.134567\pi$
$283$	1.10553e6i	0.820546i	−0.911963	+	0.410273i	$0.865433\pi$
$284$	−1.56436e6	−1.15091
$285$	0	0
$286$	−305472.	−0.220829
$287$	1.38799e6i	0.994672i
$288$	3.96540e6i	2.81712i
$289$	1.40512e6	0.989621
$290$	0	0
$291$	2.99664e6	2.07445
$292$	493802.i	0.338919i
$293$	− 116407.i	− 0.0792155i	−0.999215	−	0.0396077i	$-0.987389\pi$
$293$	− 116407.i	− 0.0792155i	0.999215	−	0.0396077i	$-0.0126108\pi$
$294$	2.53477e6	1.71029
$295$	0	0
$296$	4.86601e6	3.22807
$297$	− 363863.i	− 0.239358i
$298$	3.00616e6i	1.96097i
$299$	523900.	0.338899
$300$	0	0
$301$	951161.	0.605115
$302$	1.40361e6i	0.885580i
$303$	− 3.16787e6i	− 1.98226i
$304$	1.49510e7	9.27870
$305$	0	0
$306$	−170672.	−0.104198
$307$	830234.i	0.502753i	0.967889	+	0.251376i	$0.0808832\pi$
$307$	830234.i	0.502753i	−0.967889	+	0.251376i	$0.919117\pi$
$308$	− 1.07459e6i	− 0.645455i
$309$	−1.45576e6	−0.867351
$310$	0	0
$311$	204863.	0.120105	0.0600526	−	0.998195i	$-0.480873\pi$
$311$	204863.	0.120105	0.0600526	+	0.998195i	$0.480873\pi$
$312$	− 2.25720e6i	− 1.31276i
$313$	− 1.96760e6i	− 1.13521i	−0.823302	−	0.567604i	$-0.807871\pi$
$313$	− 1.96760e6i	− 1.13521i	0.823302	−	0.567604i	$-0.192129\pi$
$314$	3.63463e6	2.08035
$315$	0	0
$316$	−293438.	−0.165310
$317$	2.47859e6i	1.38534i	0.721255	+	0.692670i	$0.243566\pi$
$317$	2.47859e6i	1.38534i	−0.721255	+	0.692670i	$0.756434\pi$
$318$	5.97766e6i	3.31485i
$319$	510782.	0.281034
$320$	0	0
$321$	−2.71973e6	−1.47320
$322$	2.47034e6i	1.32775i
$323$	377759.i	0.201469i
$324$	6.93726e6	3.67135
$325$	0	0
$326$	−5.42193e6	−2.82559
$327$	− 226840.i	− 0.117314i
$328$	− 1.36081e7i	− 6.98413i
$329$	−542195.	−0.276163
$330$	0	0
$331$	−3.17720e6	−1.59395	−0.796974	−	0.604013i	$-0.793567\pi$
$331$	−3.17720e6	−1.59395	−0.796974	+	0.604013i	$0.793567\pi$
$332$	2.36193e6i	1.17604i
$333$	875629.i	0.432722i
$334$	−3.06066e6	−1.50123
$335$	0	0
$336$	6.54540e6	3.16292
$337$	− 1.04972e6i	− 0.503500i	−0.967792	−	0.251750i	$-0.918994\pi$
$337$	− 1.04972e6i	− 0.503500i	0.967792	−	0.251750i	$-0.0810061\pi$
$338$	320602.i	0.152642i
$339$	835764.	0.394988
$340$	0	0
$341$	566018.	0.263599
$342$	4.37483e6i	2.02254i
$343$	− 2.02852e6i	− 0.930986i
$344$	−9.32537e6	−4.24883
$345$	0	0
$346$	2.79039e6	1.25307
$347$	− 502238.i	− 0.223916i	−0.993713	−	0.111958i	$-0.964288\pi$
$347$	− 502238.i	− 0.223916i	0.993713	−	0.111958i	$-0.0357123\pi$
$348$	5.72217e6i	2.53287i
$349$	1.28824e6	0.566152	0.283076	−	0.959098i	$-0.408645\pi$
$349$	1.28824e6	0.566152	0.283076	+	0.959098i	$0.408645\pi$
$350$	0	0
$351$	−381885.	−0.165449
$352$	5.09820e6i	2.19311i
$353$	3.80443e6i	1.62500i	0.582962	+	0.812499i	$0.301893\pi$
$353$	3.80443e6i	1.62500i	−0.582962	+	0.812499i	$0.698107\pi$
$354$	−7.11758e6	−3.01873
$355$	0	0
$356$	59668.2	0.0249527
$357$	165379.i	0.0686766i
$358$	327022.i	0.134856i
$359$	−3.18303e6	−1.30348	−0.651740	−	0.758442i	$-0.725961\pi$
$359$	−3.18303e6	−1.30348	−0.651740	+	0.758442i	$0.725961\pi$
$360$	0	0
$361$	7.20697e6	2.91062
$362$	− 6.55472e6i	− 2.62895i
$363$	− 2.59296e6i	− 1.03283i
$364$	−1.12781e6	−0.446153
$365$	0	0
$366$	−7.15050e6	−2.79019
$367$	− 1.51403e6i	− 0.586770i	−0.955994	−	0.293385i	$-0.905218\pi$
$367$	− 1.51403e6i	− 0.586770i	0.955994	−	0.293385i	$-0.0947818\pi$
$368$	− 1.48945e7i	− 5.73332i
$369$	2.44875e6	0.936221
$370$	0	0
$371$	1.97003e6	0.743084
$372$	6.34096e6i	2.37573i
$373$	1.59920e6i	0.595156i	0.954698	+	0.297578i	$0.0961788\pi$
$373$	1.59920e6i	0.595156i	−0.954698	+	0.297578i	$0.903821\pi$
$374$	−219428.	−0.0811173
$375$	0	0
$376$	5.31579e6	1.93909
$377$	− 536081.i	− 0.194257i
$378$	− 1.80070e6i	− 0.648205i
$379$	−2.52547e6	−0.903116	−0.451558	−	0.892242i	$-0.649132\pi$
$379$	−2.52547e6	−0.903116	−0.451558	+	0.892242i	$0.649132\pi$
$380$	0	0
$381$	4.40235e6	1.55372
$382$	− 7.94997e6i	− 2.78745i
$383$	− 3.16883e6i	− 1.10383i	−0.833900	−	0.551915i	$-0.813897\pi$
$383$	− 3.16883e6i	− 1.10383i	0.833900	−	0.551915i	$-0.186103\pi$
$384$	−2.39950e7	−8.30410
$385$	0	0
$386$	−6.69331e6	−2.28651
$387$	− 1.67808e6i	− 0.569555i
$388$	1.46796e7i	4.95034i
$389$	−1.03129e6	−0.345545	−0.172773	−	0.984962i	$-0.555273\pi$
$389$	−1.03129e6	−0.345545	−0.172773	+	0.984962i	$0.555273\pi$
$390$	0	0
$391$	376330.	0.124488
$392$	8.19014e6i	2.69201i
$393$	− 3.10334e6i	− 1.01356i
$394$	267411.	0.0867838
$395$	0	0
$396$	−1.89584e6	−0.607525
$397$	− 634862.i	− 0.202164i	−0.994878	−	0.101082i	$-0.967770\pi$
$397$	− 634862.i	− 0.202164i	0.994878	−	0.101082i	$-0.0322304\pi$
$398$	5.28320e6i	1.67182i
$399$	4.23915e6	1.33305
$400$	0	0
$401$	2.19913e6	0.682952	0.341476	−	0.939890i	$-0.389073\pi$
$401$	2.19913e6	0.682952	0.341476	+	0.939890i	$0.389073\pi$
$402$	− 5.29728e6i	− 1.63489i
$403$	− 594053.i	− 0.182206i
$404$	1.55184e7	4.73035
$405$	0	0
$406$	2.52778e6	0.761070
$407$	1.12577e6i	0.336871i
$408$	− 1.62140e6i	− 0.482215i
$409$	4.25223e6	1.25692	0.628461	−	0.777841i	$-0.283685\pi$
$409$	4.25223e6	1.25692	0.628461	+	0.777841i	$0.283685\pi$
$410$	0	0
$411$	4.48266e6	1.30898
$412$	− 7.13132e6i	− 2.06979i
$413$	2.34571e6i	0.676704i
$414$	4.35829e6	1.24973
$415$	0	0
$416$	5.35071e6	1.51593
$417$	− 1.88046e6i	− 0.529570i
$418$	5.62460e6i	1.57453i
$419$	−3.54751e6	−0.987161	−0.493581	−	0.869700i	$-0.664312\pi$
$419$	−3.54751e6	−0.987161	−0.493581	+	0.869700i	$0.664312\pi$
$420$	0	0
$421$	1.40038e6	0.385071	0.192535	−	0.981290i	$-0.438329\pi$
$421$	1.40038e6	0.385071	0.192535	+	0.981290i	$0.438329\pi$
$422$	6.95742e6i	1.90181i
$423$	956565.i	0.259934i
$424$	−1.93146e7	−5.21759
$425$	0	0
$426$	3.58469e6	0.957033
$427$	2.35656e6i	0.625472i
$428$	− 1.33231e7i	− 3.51556i
$429$	522213.	0.136995
$430$	0	0
$431$	5.41665e6	1.40455	0.702276	−	0.711905i	$-0.252167\pi$
$431$	5.41665e6	1.40455	0.702276	+	0.711905i	$0.252167\pi$
$432$	1.08570e7i	2.79899i
$433$	5.58069e6i	1.43043i	0.698902	+	0.715217i	$0.253672\pi$
$433$	5.58069e6i	1.43043i	−0.698902	+	0.715217i	$0.746328\pi$
$434$	2.80113e6	0.713854
$435$	0	0
$436$	1.11122e6	0.279951
$437$	− 9.64646e6i	− 2.41638i
$438$	− 1.13153e6i	− 0.281826i
$439$	1.76748e6	0.437716	0.218858	−	0.975757i	$-0.429767\pi$
$439$	1.76748e6	0.437716	0.218858	+	0.975757i	$0.429767\pi$
$440$	0	0
$441$	−1.47380e6	−0.360863
$442$	230296.i	0.0560701i
$443$	− 2.11511e6i	− 0.512062i	−0.966669	−	0.256031i	$-0.917585\pi$
$443$	− 2.11511e6i	− 0.512062i	0.966669	−	0.256031i	$-0.0824150\pi$
$444$	−1.26117e7	−3.03611
$445$	0	0
$446$	−3.49099e6	−0.831019
$447$	− 5.13911e6i	− 1.21652i
$448$	1.43154e7i	3.36982i
$449$	−2.74804e6	−0.643290	−0.321645	−	0.946860i	$-0.604236\pi$
$449$	−2.74804e6	−0.643290	−0.321645	+	0.946860i	$0.604236\pi$
$450$	0	0
$451$	3.14828e6	0.728841
$452$	4.09414e6i	0.942577i
$453$	− 2.39950e6i	− 0.549384i
$454$	5.05510e6	1.15104
$455$	0	0
$456$	−4.15614e7	−9.36005
$457$	− 3.46825e6i	− 0.776820i	−0.921487	−	0.388410i	$-0.873024\pi$
$457$	− 3.46825e6i	− 0.776820i	0.921487	−	0.388410i	$-0.126976\pi$
$458$	9.59893e6i	2.13825i
$459$	−274318.	−0.0607746
$460$	0	0
$461$	5.16521e6	1.13197	0.565986	−	0.824415i	$-0.308496\pi$
$461$	5.16521e6	1.13197	0.565986	+	0.824415i	$0.308496\pi$
$462$	2.46239e6i	0.536725i
$463$	6.87934e6i	1.49140i	0.666282	+	0.745700i	$0.267885\pi$
$463$	6.87934e6i	1.49140i	−0.666282	+	0.745700i	$0.732115\pi$
$464$	−1.52408e7	−3.28634
$465$	0	0
$466$	−1.22931e7	−2.62238
$467$	− 569700.i	− 0.120880i	−0.998172	−	0.0604400i	$-0.980750\pi$
$467$	− 569700.i	− 0.120880i	0.998172	−	0.0604400i	$-0.0192504\pi$
$468$	1.98974e6i	0.419935i
$469$	−1.74580e6	−0.366490
$470$	0	0
$471$	−6.21350e6	−1.29058
$472$	− 2.29978e7i	− 4.75150i
$473$	− 2.15746e6i	− 0.443394i
$474$	672404.	0.137463
$475$	0	0
$476$	−810137.	−0.163886
$477$	− 3.47562e6i	− 0.699417i
$478$	1.03038e7i	2.06266i
$479$	3.33256e6	0.663649	0.331825	−	0.943341i	$-0.392336\pi$
$479$	3.33256e6	0.663649	0.331825	+	0.943341i	$0.392336\pi$
$480$	0	0
$481$	1.18153e6	0.232853
$482$	7.21365e6i	1.41429i
$483$	− 4.22312e6i	− 0.823693i
$484$	1.27021e7	2.46468
$485$	0	0
$486$	−9.73275e6	−1.86915
$487$	− 5.24387e6i	− 1.00191i	−0.865473	−	0.500956i	$-0.832982\pi$
$487$	− 5.24387e6i	− 1.00191i	0.865473	−	0.500956i	$-0.167018\pi$
$488$	− 2.31041e7i	− 4.39177i
$489$	9.26893e6	1.75290
$490$	0	0
$491$	−4.52706e6	−0.847447	−0.423724	−	0.905792i	$-0.639277\pi$
$491$	−4.52706e6	−0.847447	−0.423724	+	0.905792i	$0.639277\pi$
$492$	3.52694e7i	6.56880i
$493$	− 385080.i	− 0.0713566i
$494$	5.90318e6	1.08835
$495$	0	0
$496$	−1.68890e7	−3.08247
$497$	− 1.18139e6i	− 0.214537i
$498$	− 5.41229e6i	− 0.977930i
$499$	−8.06232e6	−1.44947	−0.724734	−	0.689029i	$-0.758037\pi$
$499$	−8.06232e6	−1.44947	−0.724734	+	0.689029i	$0.758037\pi$
$500$	0	0
$501$	5.23227e6	0.931314
$502$	1.08597e6i	0.192335i
$503$	− 3.91235e6i	− 0.689474i	−0.938699	−	0.344737i	$-0.887968\pi$
$503$	− 3.91235e6i	− 0.689474i	0.938699	−	0.344737i	$-0.112032\pi$
$504$	−6.18842e6	−1.08518
$505$	0	0
$506$	5.60333e6	0.972904
$507$	− 548078.i	− 0.0946940i
$508$	2.15657e7i	3.70770i
$509$	1.01584e7	1.73792	0.868959	−	0.494884i	$-0.164790\pi$
$509$	1.01584e7	1.73792	0.868959	+	0.494884i	$0.164790\pi$
$510$	0	0
$511$	−372913.	−0.0631765
$512$	− 4.51098e7i	− 7.60495i
$513$	7.03158e6i	1.17967i
$514$	−1.19751e7	−1.99927
$515$	0	0
$516$	2.41695e7	3.99616
$517$	1.22983e6i	0.202357i
$518$	5.57126e6i	0.912282i
$519$	−4.77025e6	−0.777361
$520$	0	0
$521$	1.44957e6	0.233962	0.116981	−	0.993134i	$-0.462678\pi$
$521$	1.44957e6	0.233962	0.116981	+	0.993134i	$0.462678\pi$
$522$	− 4.45963e6i	− 0.716345i
$523$	− 203871.i	− 0.0325912i	−0.999867	−	0.0162956i	$-0.994813\pi$
$523$	− 203871.i	− 0.0325912i	0.999867	−	0.0162956i	$-0.00518728\pi$
$524$	1.52023e7	2.41869
$525$	0	0
$526$	5.64756e6	0.890013
$527$	− 426723.i	− 0.0669298i
$528$	− 1.48465e7i	− 2.31761i
$529$	−3.17365e6	−0.493082
$530$	0	0
$531$	4.13841e6	0.636937
$532$	2.07662e7i	3.18111i
$533$	− 3.30422e6i	− 0.503791i
$534$	−136728.	−0.0207493
$535$	0	0
$536$	1.71162e7	2.57332
$537$	− 559052.i	− 0.0836598i
$538$	− 1.17663e6i	− 0.175260i
$539$	−1.89482e6	−0.280929
$540$	0	0
$541$	7.28883e6	1.07069	0.535346	−	0.844633i	$-0.320181\pi$
$541$	7.28883e6	1.07069	0.535346	+	0.844633i	$0.320181\pi$
$542$	1.89472e6i	0.277042i
$543$	1.12055e7i	1.63091i
$544$	3.84355e6	0.556846
$545$	0	0
$546$	2.58435e6	0.370996
$547$	5.64096e6i	0.806092i	0.915180	+	0.403046i	$0.132049\pi$
$547$	5.64096e6i	0.806092i	−0.915180	+	0.403046i	$0.867951\pi$
$548$	2.19591e7i	3.12366i
$549$	4.15754e6	0.588716
$550$	0	0
$551$	−9.87075e6	−1.38507
$552$	4.14043e7i	5.78359i
$553$	− 221601.i	− 0.0308148i
$554$	9.69083e6	1.34149
$555$	0	0
$556$	9.21176e6	1.26373
$557$	− 910831.i	− 0.124394i	−0.998064	−	0.0621971i	$-0.980189\pi$
$557$	− 910831.i	− 0.124394i	0.998064	−	0.0621971i	$-0.0198107\pi$
$558$	− 4.94189e6i	− 0.671905i
$559$	−2.26432e6	−0.306484
$560$	0	0
$561$	375119.	0.0503224
$562$	1.76180e7i	2.35297i
$563$	7.96586e6i	1.05916i	0.848260	+	0.529580i	$0.177651\pi$
$563$	7.96586e6i	1.05916i	−0.848260	+	0.529580i	$0.822349\pi$
$564$	−1.37775e7	−1.82378
$565$	0	0
$566$	1.24097e7	1.62825
$567$	5.23893e6i	0.684361i
$568$	1.15826e7i	1.50638i
$569$	3.26286e6	0.422492	0.211246	−	0.977433i	$-0.432248\pi$
$569$	3.26286e6	0.422492	0.211246	+	0.977433i	$0.432248\pi$
$570$	0	0
$571$	−7.89949e6	−1.01393	−0.506966	−	0.861966i	$-0.669233\pi$
$571$	−7.89949e6	−1.01393	−0.506966	+	0.861966i	$0.669233\pi$
$572$	2.55815e6i	0.326916i
$573$	1.35907e7i	1.72924i
$574$	1.55804e7	1.97378
$575$	0	0
$576$	2.52558e7	3.17180
$577$	1.91866e6i	0.239916i	0.992779	+	0.119958i	$0.0382760\pi$
$577$	1.91866e6i	0.239916i	−0.992779	+	0.119958i	$0.961724\pi$
$578$	− 1.57727e7i	− 1.96375i
$579$	1.14424e7	1.41847
$580$	0	0
$581$	−1.78370e6	−0.219221
$582$	− 3.36378e7i	− 4.11642i
$583$	− 4.46850e6i	− 0.544491i
$584$	3.65611e6	0.443596
$585$	0	0
$586$	−1.30669e6	−0.157191
$587$	− 1.98302e6i	− 0.237537i	−0.992922	−	0.118769i	$-0.962105\pi$
$587$	− 1.98302e6i	− 0.237537i	0.992922	−	0.118769i	$-0.0378947\pi$
$588$	− 2.12272e7i	− 2.53192i
$589$	−1.09382e7	−1.29914
$590$	0	0
$591$	−457146.	−0.0538377
$592$	− 3.35909e7i	− 3.93929i
$593$	9.43563e6i	1.10188i	0.834545	+	0.550940i	$0.185731\pi$
$593$	9.43563e6i	1.10188i	−0.834545	+	0.550940i	$0.814269\pi$
$594$	−4.08443e6	−0.474969
$595$	0	0
$596$	2.51749e7	2.90303
$597$	− 9.03177e6i	− 1.03714i
$598$	− 5.88086e6i	− 0.672493i
$599$	−6.57359e6	−0.748576	−0.374288	−	0.927313i	$-0.622113\pi$
$599$	−6.57359e6	−0.748576	−0.374288	+	0.927313i	$0.622113\pi$
$600$	0	0
$601$	9.04817e6	1.02182	0.510910	−	0.859634i	$-0.329308\pi$
$601$	9.04817e6	1.02182	0.510910	+	0.859634i	$0.329308\pi$
$602$	− 1.06769e7i	− 1.20076i
$603$	3.08002e6i	0.344953i
$604$	1.17544e7	1.31102
$605$	0	0
$606$	−3.55598e7	−3.93349
$607$	− 2.54414e6i	− 0.280266i	−0.990133	−	0.140133i	$-0.955247\pi$
$607$	− 2.54414e6i	− 0.280266i	0.990133	−	0.140133i	$-0.0447530\pi$
$608$	− 9.85216e7i	− 10.8087i
$609$	−4.32131e6	−0.472141
$610$	0	0
$611$	1.29074e6	0.139874
$612$	1.42928e6i	0.154255i
$613$	7.53921e6i	0.810354i	0.914238	+	0.405177i	$0.132790\pi$
$613$	7.53921e6i	0.810354i	−0.914238	+	0.405177i	$0.867210\pi$
$614$	9.31951e6	0.997636
$615$	0	0
$616$	−7.95628e6	−0.844808
$617$	− 1.44546e6i	− 0.152860i	−0.997075	−	0.0764300i	$-0.975648\pi$
$617$	− 1.44546e6i	− 0.152860i	0.997075	−	0.0764300i	$-0.0243522\pi$
$618$	1.63412e7i	1.72113i
$619$	−832032.	−0.0872797	−0.0436399	−	0.999047i	$-0.513895\pi$
$619$	−832032.	−0.0872797	−0.0436399	+	0.999047i	$0.513895\pi$
$620$	0	0
$621$	7.00499e6	0.728918
$622$	− 2.29962e6i	− 0.238330i
$623$	45060.7i	0.00465134i
$624$	−1.55819e7	−1.60198
$625$	0	0
$626$	−2.20866e7	−2.25265
$627$	− 9.61540e6i	− 0.976784i
$628$	− 3.04379e7i	− 3.07975i
$629$	848722.	0.0855340
$630$	0	0
$631$	1.42941e6	0.142916	0.0714582	−	0.997444i	$-0.477235\pi$
$631$	1.42941e6	0.142916	0.0714582	+	0.997444i	$0.477235\pi$
$632$	2.17262e6i	0.216367i
$633$	− 1.18939e7i	− 1.17982i
$634$	2.78226e7	2.74900
$635$	0	0
$636$	5.00595e7	4.90731
$637$	1.98867e6i	0.194184i
$638$	− 5.73362e6i	− 0.557669i
$639$	−2.08426e6	−0.201929
$640$	0	0
$641$	−1.54071e7	−1.48107	−0.740537	−	0.672015i	$-0.765429\pi$
$641$	−1.54071e7	−1.48107	−0.740537	+	0.672015i	$0.765429\pi$
$642$	3.05294e7i	2.92335i
$643$	− 3.71125e6i	− 0.353992i	−0.984212	−	0.176996i	$-0.943362\pi$
$643$	− 3.71125e6i	− 0.353992i	0.984212	−	0.176996i	$-0.0566379\pi$
$644$	2.06877e7	1.96561
$645$	0	0
$646$	4.24040e6	0.399784
$647$	8.31438e6i	0.780853i	0.920634	+	0.390426i	$0.127672\pi$
$647$	8.31438e6i	0.780853i	−0.920634	+	0.390426i	$0.872328\pi$
$648$	− 5.13635e7i	− 4.80527i
$649$	5.32063e6	0.495851
$650$	0	0
$651$	−4.78862e6	−0.442851
$652$	4.54055e7i	4.18302i
$653$	2.58516e6i	0.237249i	0.992939	+	0.118624i	$0.0378484\pi$
$653$	2.58516e6i	0.237249i	−0.992939	+	0.118624i	$0.962152\pi$
$654$	−2.54631e6	−0.232792
$655$	0	0
$656$	−9.39391e7	−8.52289
$657$	657911.i	0.0594639i
$658$	6.08623e6i	0.548004i
$659$	−1.77052e7	−1.58813	−0.794065	−	0.607833i	$-0.792039\pi$
$659$	−1.77052e7	−1.58813	−0.794065	+	0.607833i	$0.792039\pi$
$660$	0	0
$661$	2.01104e6	0.179027	0.0895134	−	0.995986i	$-0.471469\pi$
$661$	2.01104e6	0.179027	0.0895134	+	0.995986i	$0.471469\pi$
$662$	3.56646e7i	3.16295i
$663$	− 393698.i	− 0.0347840i
$664$	1.74878e7	1.53927
$665$	0	0
$666$	9.82908e6	0.858672
$667$	9.83343e6i	0.855836i
$668$	2.56312e7i	2.22243i
$669$	5.96794e6	0.515536
$670$	0	0
$671$	5.34523e6	0.458311
$672$	− 4.31317e7i	− 3.68446i
$673$	− 5.48300e6i	− 0.466639i	−0.972400	−	0.233319i	$-0.925041\pi$
$673$	− 5.48300e6i	− 0.466639i	0.972400	−	0.233319i	$-0.0749587\pi$
$674$	−1.17833e7	−0.999119
$675$	0	0
$676$	2.68486e6	0.225972
$677$	1.58127e7i	1.32597i	0.748631	+	0.662987i	$0.230712\pi$
$677$	1.58127e7i	1.32597i	−0.748631	+	0.662987i	$0.769288\pi$
$678$	− 9.38159e6i	− 0.783794i
$679$	−1.10859e7	−0.922772
$680$	0	0
$681$	−8.64183e6	−0.714065
$682$	− 6.35365e6i	− 0.523073i
$683$	2.24599e7i	1.84229i	0.389225	+	0.921143i	$0.372743\pi$
$683$	2.24599e7i	1.84229i	−0.389225	+	0.921143i	$0.627257\pi$
$684$	3.66367e7	2.99417
$685$	0	0
$686$	−2.27704e7	−1.84740
$687$	− 1.64096e7i	− 1.32650i
$688$	6.43747e7i	5.18495i
$689$	−4.68982e6	−0.376364
$690$	0	0
$691$	−8.90456e6	−0.709443	−0.354721	−	0.934972i	$-0.615424\pi$
$691$	−8.90456e6	−0.709443	−0.354721	+	0.934972i	$0.615424\pi$
$692$	− 2.33679e7i	− 1.85505i
$693$	− 1.43172e6i	− 0.113246i
$694$	−5.63770e6	−0.444328
$695$	0	0
$696$	4.23670e7	3.31516
$697$	− 2.37350e6i	− 0.185058i
$698$	− 1.44607e7i	− 1.12344i
$699$	2.10154e7	1.62684
$700$	0	0
$701$	−1.83550e7	−1.41078	−0.705392	−	0.708818i	$-0.749229\pi$
$701$	−1.83550e7	−1.41078	−0.705392	+	0.708818i	$0.749229\pi$
$702$	4.28673e6i	0.328309i
$703$	− 2.17553e7i	− 1.66026i
$704$	3.24707e7	2.46922
$705$	0	0
$706$	4.27054e7	3.22456
$707$	1.17193e7i	0.881765i
$708$	5.96057e7i	4.46894i
$709$	2.57581e7	1.92441	0.962207	−	0.272318i	$-0.0877902\pi$
$709$	2.57581e7	1.92441	0.962207	+	0.272318i	$0.0877902\pi$
$710$	0	0
$711$	−390959.	−0.0290039
$712$	− 441784.i	− 0.0326596i
$713$	1.08968e7i	0.802742i
$714$	1.85640e6	0.136278
$715$	0	0
$716$	2.73862e6	0.199641
$717$	− 1.76146e7i	− 1.27961i
$718$	3.57300e7i	2.58656i
$719$	−1.69710e6	−0.122429	−0.0612146	−	0.998125i	$-0.519497\pi$
$719$	−1.69710e6	−0.122429	−0.0612146	+	0.998125i	$0.519497\pi$
$720$	0	0
$721$	5.38549e6	0.385822
$722$	− 8.08995e7i	− 5.77568i
$723$	− 1.23319e7i	− 0.877375i
$724$	−5.48921e7	−3.89191
$725$	0	0
$726$	−2.91064e7	−2.04949
$727$	1.84315e7i	1.29338i	0.762754	+	0.646689i	$0.223847\pi$
$727$	1.84315e7i	1.29338i	−0.762754	+	0.646689i	$0.776153\pi$
$728$	8.35035e6i	0.583951i
$729$	−1.29433e6	−0.0902041
$730$	0	0
$731$	−1.62652e6	−0.112581
$732$	5.98813e7i	4.13060i
$733$	− 1.79395e7i	− 1.23325i	−0.787258	−	0.616624i	$-0.788500\pi$
$733$	− 1.79395e7i	− 1.23325i	0.787258	−	0.616624i	$-0.211500\pi$
$734$	−1.69952e7	−1.16436
$735$	0	0
$736$	−9.81491e7	−6.67870
$737$	3.95989e6i	0.268544i
$738$	− 2.74876e7i	− 1.85779i
$739$	−1.84597e7	−1.24341	−0.621703	−	0.783253i	$-0.713559\pi$
$739$	−1.84597e7	−1.24341	−0.621703	+	0.783253i	$0.713559\pi$
$740$	0	0
$741$	−1.00916e7	−0.675175
$742$	− 2.21139e7i	− 1.47454i
$743$	− 3.97606e6i	− 0.264229i	−0.991234	−	0.132115i	$-0.957823\pi$
$743$	− 3.97606e6i	− 0.264229i	0.991234	−	0.132115i	$-0.0421767\pi$
$744$	4.69485e7	3.10949
$745$	0	0
$746$	1.79513e7	1.18100
$747$	3.14689e6i	0.206339i
$748$	1.83759e6i	0.120086i
$749$	1.00614e7	0.655322
$750$	0	0
$751$	2.25945e7	1.46185	0.730925	−	0.682458i	$-0.239089\pi$
$751$	2.25945e7	1.46185	0.730925	+	0.682458i	$0.239089\pi$
$752$	− 3.66958e7i	− 2.36631i
$753$	− 1.85649e6i	− 0.119318i
$754$	−6.01760e6	−0.385474
$755$	0	0
$756$	−1.50799e7	−0.959605
$757$	1.40367e7i	0.890279i	0.895461	+	0.445139i	$0.146846\pi$
$757$	1.40367e7i	0.890279i	−0.895461	+	0.445139i	$0.853154\pi$
$758$	2.83488e7i	1.79210i
$759$	−9.57905e6	−0.603556
$760$	0	0
$761$	−6.05735e6	−0.379159	−0.189579	−	0.981865i	$-0.560712\pi$
$761$	−6.05735e6	−0.379159	−0.189579	+	0.981865i	$0.560712\pi$
$762$	− 4.94171e7i	− 3.08311i
$763$	839177.i	0.0521846i
$764$	−6.65765e7	−4.12655
$765$	0	0
$766$	−3.55707e7	−2.19038
$767$	− 5.58416e6i	− 0.342743i
$768$	1.45520e8i	8.90265i
$769$	−1.07705e7	−0.656778	−0.328389	−	0.944543i	$-0.606506\pi$
$769$	−1.07705e7	−0.656778	−0.328389	+	0.944543i	$0.606506\pi$
$770$	0	0
$771$	2.04717e7	1.24028
$772$	5.60527e7i	3.38496i
$773$	− 8.92164e6i	− 0.537027i	−0.963276	−	0.268514i	$-0.913468\pi$
$773$	− 8.92164e6i	− 0.537027i	0.963276	−	0.268514i	$-0.0865324\pi$
$774$	−1.88367e7	−1.13020
$775$	0	0
$776$	1.08688e8	6.47928
$777$	− 9.52422e6i	− 0.565949i
$778$	1.15764e7i	0.685682i
$779$	−6.08399e7	−3.59207
$780$	0	0
$781$	−2.67967e6	−0.157201
$782$	− 4.22437e6i	− 0.247027i
$783$	− 7.16787e6i	− 0.417816i
$784$	5.65380e7	3.28511
$785$	0	0
$786$	−3.48356e7	−2.01125
$787$	542225.i	0.0312063i	0.999878	+	0.0156032i	$0.00496684\pi$
$787$	542225.i	0.0312063i	−0.999878	+	0.0156032i	$0.995033\pi$
$788$	− 2.23941e6i	− 0.128475i
$789$	−9.65466e6	−0.552134
$790$	0	0
$791$	−3.09185e6	−0.175702
$792$	1.40368e7i	0.795163i
$793$	− 5.60998e6i	− 0.316795i
$794$	−7.12643e6	−0.401163
$795$	0	0
$796$	4.42437e7	2.47497
$797$	− 1.82250e7i	− 1.01630i	−0.861269	−	0.508149i	$-0.830330\pi$
$797$	− 1.82250e7i	− 1.01630i	0.861269	−	0.508149i	$-0.169670\pi$
$798$	− 4.75851e7i	− 2.64523i
$799$	927172.	0.0513799
$800$	0	0
$801$	79498.2	0.00437800
$802$	− 2.46856e7i	− 1.35522i
$803$	845857.i	0.0462922i
$804$	−4.43617e7	−2.42029
$805$	0	0
$806$	−6.66834e6	−0.361560
$807$	2.01147e6i	0.108725i
$808$	− 1.14898e8i	− 6.19134i
$809$	3.56238e7	1.91368	0.956840	−	0.290615i	$-0.0938599\pi$
$809$	3.56238e7	1.91368	0.956840	+	0.290615i	$0.0938599\pi$
$810$	0	0
$811$	9.68050e6	0.516828	0.258414	−	0.966034i	$-0.416800\pi$
$811$	9.68050e6	0.516828	0.258414	+	0.966034i	$0.416800\pi$
$812$	− 2.11687e7i	− 1.12669i
$813$	− 3.23907e6i	− 0.171868i
$814$	1.26370e7	0.668470
$815$	0	0
$816$	−1.11929e7	−0.588458
$817$	4.16925e7i	2.18526i
$818$	− 4.77320e7i	− 2.49417i
$819$	−1.50263e6	−0.0782784
$820$	0	0
$821$	2.15879e7	1.11777	0.558885	−	0.829245i	$-0.311229\pi$
$821$	2.15879e7	1.11777	0.558885	+	0.829245i	$0.311229\pi$
$822$	− 5.03186e7i	− 2.59746i
$823$	− 2.95621e7i	− 1.52137i	−0.649120	−	0.760686i	$-0.724863\pi$
$823$	− 2.95621e7i	− 1.52137i	0.649120	−	0.760686i	$-0.275137\pi$
$824$	−5.28004e7	−2.70906
$825$	0	0
$826$	2.63309e7	1.34282
$827$	2.85332e7i	1.45073i	0.688365	+	0.725364i	$0.258329\pi$
$827$	2.85332e7i	1.45073i	−0.688365	+	0.725364i	$0.741671\pi$
$828$	− 3.64982e7i	− 1.85010i
$829$	2.02156e7	1.02165	0.510823	−	0.859686i	$-0.329341\pi$
$829$	2.02156e7	1.02165	0.510823	+	0.859686i	$0.329341\pi$
$830$	0	0
$831$	−1.65667e7	−0.832213
$832$	− 3.40789e7i	− 1.70678i
$833$	1.42851e6i	0.0713299i
$834$	−2.11084e7	−1.05085
$835$	0	0
$836$	4.71028e7	2.33094
$837$	− 7.94300e6i	− 0.391896i
$838$	3.98214e7i	1.95887i
$839$	6.64057e6	0.325687	0.162843	−	0.986652i	$-0.447933\pi$
$839$	6.64057e6	0.325687	0.162843	+	0.986652i	$0.447933\pi$
$840$	0	0
$841$	−1.04491e7	−0.509434
$842$	− 1.57195e7i	− 0.764114i
$843$	− 3.01185e7i	− 1.45970i
$844$	5.82644e7	2.81544
$845$	0	0
$846$	1.07376e7	0.515800
$847$	9.59244e6i	0.459432i
$848$	1.33332e8i	6.36714i
$849$	−2.12148e7	−1.01011
$850$	0	0
$851$	−2.16730e7	−1.02588
$852$	− 3.00197e7i	− 1.41680i
$853$	1.92258e7i	0.904716i	0.891836	+	0.452358i	$0.149417\pi$
$853$	1.92258e7i	0.904716i	−0.891836	+	0.452358i	$0.850583\pi$
$854$	2.64527e7	1.24115
$855$	0	0
$856$	−9.86442e7	−4.60137
$857$	− 1.98896e6i	− 0.0925068i	−0.998930	−	0.0462534i	$-0.985272\pi$
$857$	− 1.98896e6i	− 0.0925068i	0.998930	−	0.0462534i	$-0.0147282\pi$
$858$	− 5.86193e6i	− 0.271845i
$859$	7.32029e6	0.338490	0.169245	−	0.985574i	$-0.445867\pi$
$859$	7.32029e6	0.338490	0.169245	+	0.985574i	$0.445867\pi$
$860$	0	0
$861$	−2.66351e7	−1.22446
$862$	− 6.08028e7i	− 2.78712i
$863$	− 3.13431e7i	− 1.43257i	−0.697809	−	0.716283i	$-0.745842\pi$
$863$	− 3.13431e7i	− 1.43257i	0.697809	−	0.716283i	$-0.254158\pi$
$864$	7.15437e7	3.26052
$865$	0	0
$866$	6.26441e7	2.83848
$867$	2.69639e7i	1.21824i
$868$	− 2.34579e7i	− 1.05679i
$869$	−502644.	−0.0225793
$870$	0	0
$871$	4.15603e6	0.185623
$872$	− 8.22745e6i	− 0.366416i
$873$	1.95582e7i	0.868546i
$874$	−1.08283e8	−4.79493
$875$	0	0
$876$	−9.47592e6	−0.417216
$877$	− 2.47672e7i	− 1.08737i	−0.839289	−	0.543686i	$-0.817028\pi$
$877$	− 2.47672e7i	− 1.08737i	0.839289	−	0.543686i	$-0.182972\pi$
$878$	− 1.98402e7i	− 0.868581i
$879$	2.23382e6	0.0975160
$880$	0	0
$881$	1.22752e7	0.532831	0.266415	−	0.963858i	$-0.414161\pi$
$881$	1.22752e7	0.532831	0.266415	+	0.963858i	$0.414161\pi$
$882$	1.65436e7i	0.716077i
$883$	− 2.56013e7i	− 1.10500i	−0.833514	−	0.552498i	$-0.813675\pi$
$883$	− 2.56013e7i	− 1.10500i	0.833514	−	0.552498i	$-0.186325\pi$
$884$	1.92860e6	0.0830064
$885$	0	0
$886$	−2.37424e7	−1.01611
$887$	− 5.01026e6i	− 0.213821i	−0.994269	−	0.106911i	$-0.965904\pi$
$887$	− 5.01026e6i	− 0.213821i	0.994269	−	0.106911i	$-0.0340959\pi$
$888$	9.33773e7i	3.97383i
$889$	−1.62862e7	−0.691137
$890$	0	0
$891$	1.18832e7	0.501462
$892$	2.92350e7i	1.23024i
$893$	− 2.37662e7i	− 0.997311i
$894$	−5.76873e7	−2.41400
$895$	0	0
$896$	8.87676e7	3.69390
$897$	1.00535e7i	0.417192i
$898$	3.08472e7i	1.27651i
$899$	1.11502e7	0.460132
$900$	0	0
$901$	−3.36882e6	−0.138250
$902$	− 3.53400e7i	− 1.44627i
$903$	1.82525e7i	0.744909i
$904$	3.03131e7	1.23370
$905$	0	0
$906$	−2.69348e7	−1.09017
$907$	− 4.85441e7i	− 1.95938i	−0.200527	−	0.979688i	$-0.564266\pi$
$907$	− 4.85441e7i	− 1.95938i	0.200527	−	0.979688i	$-0.435734\pi$
$908$	− 4.23336e7i	− 1.70400i
$909$	2.06757e7	0.829948
$910$	0	0
$911$	−3.03805e7	−1.21283	−0.606413	−	0.795150i	$-0.707392\pi$
$911$	−3.03805e7	−1.21283	−0.606413	+	0.795150i	$0.707392\pi$
$912$	2.86906e8i	11.4223i
$913$	4.04587e6i	0.160633i
$914$	−3.89317e7	−1.54148
$915$	0	0
$916$	8.03855e7	3.16548
$917$	1.14806e7i	0.450859i
$918$	3.07926e6i	0.120598i
$919$	3.70802e7	1.44828	0.724141	−	0.689652i	$-0.242236\pi$
$919$	3.70802e7	1.44828	0.724141	+	0.689652i	$0.242236\pi$
$920$	0	0
$921$	−1.59320e7	−0.618899
$922$	− 5.79803e7i	− 2.24623i
$923$	2.81239e6i	0.108661i
$924$	2.06211e7	0.794569
$925$	0	0
$926$	7.72217e7	2.95946
$927$	− 9.50133e6i	− 0.363149i
$928$	1.00431e8i	3.82824i
$929$	−2.82561e6	−0.107417	−0.0537084	−	0.998557i	$-0.517104\pi$
$929$	−2.82561e6	−0.107417	−0.0537084	+	0.998557i	$0.517104\pi$
$930$	0	0
$931$	3.66170e7	1.38455
$932$	1.02948e8i	3.88219i
$933$	3.93126e6i	0.147852i
$934$	−6.39498e6	−0.239868
$935$	0	0
$936$	1.47321e7	0.549635
$937$	3.19406e6i	0.118849i	0.998233	+	0.0594243i	$0.0189265\pi$
$937$	3.19406e6i	0.118849i	−0.998233	+	0.0594243i	$0.981074\pi$
$938$	1.95969e7i	0.727244i
$939$	3.77576e7	1.39746
$940$	0	0
$941$	−2.22120e7	−0.817738	−0.408869	−	0.912593i	$-0.634077\pi$
$941$	−2.22120e7	−0.817738	−0.408869	+	0.912593i	$0.634077\pi$
$942$	6.97475e7i	2.56095i
$943$	6.06099e7i	2.21955i
$944$	−1.58758e8	−5.79836
$945$	0	0
$946$	−2.42179e7	−0.879849
$947$	2.24064e7i	0.811889i	0.913898	+	0.405945i	$0.133057\pi$
$947$	2.24064e7i	0.811889i	−0.913898	+	0.405945i	$0.866943\pi$
$948$	− 5.63100e6i	− 0.203500i
$949$	887751.	0.0319982
$950$	0	0
$951$	−4.75634e7	−1.70538
$952$	5.99826e6i	0.214503i
$953$	− 1.48416e7i	− 0.529358i	−0.964337	−	0.264679i	$-0.914734\pi$
$953$	− 1.48416e7i	− 0.529358i	0.964337	−	0.264679i	$-0.0852660\pi$
$954$	−3.90144e7	−1.38789
$955$	0	0
$956$	8.62886e7	3.05357
$957$	9.80177e6i	0.345959i
$958$	− 3.74085e7i	− 1.31691i
$959$	−1.65833e7	−0.582269
$960$	0	0
$961$	−1.62732e7	−0.568413
$962$	− 1.32629e7i	− 0.462061i
$963$	− 1.77508e7i	− 0.616812i
$964$	6.04102e7	2.09371
$965$	0	0
$966$	−4.74052e7	−1.63449
$967$	3.06919e7i	1.05550i	0.849401	+	0.527749i	$0.176964\pi$
$967$	3.06919e7i	1.05550i	−0.849401	+	0.527749i	$0.823036\pi$
$968$	− 9.40462e7i	− 3.22591i
$969$	−7.24908e6	−0.248013
$970$	0	0
$971$	−4.18932e7	−1.42592	−0.712961	−	0.701203i	$-0.752646\pi$
$971$	−4.18932e7	−1.42592	−0.712961	+	0.701203i	$0.752646\pi$
$972$	8.15062e7i	2.76710i
$973$	6.95661e6i	0.235568i
$974$	−5.88633e7	−1.98814
$975$	0	0
$976$	−1.59492e8	−5.35938
$977$	− 2.54822e7i	− 0.854084i	−0.904232	−	0.427042i	$-0.859556\pi$
$977$	− 2.54822e7i	− 0.854084i	0.904232	−	0.427042i	$-0.140444\pi$
$978$	− 1.04045e8i	− 3.47837i
$979$	102209.	0.00340824
$980$	0	0
$981$	1.48051e6	0.0491179
$982$	5.08170e7i	1.68163i
$983$	5.91830e7i	1.95350i	0.214388	+	0.976749i	$0.431224\pi$
$983$	5.91830e7i	1.95350i	−0.214388	+	0.976749i	$0.568776\pi$
$984$	2.61135e8	8.59761
$985$	0	0
$986$	−4.32259e6	−0.141596
$987$	− 1.04046e7i	− 0.339963i
$988$	− 4.94358e7i	− 1.61120i
$989$	4.15348e7	1.35027
$990$	0	0
$991$	−625464.	−0.0202310	−0.0101155	−	0.999949i	$-0.503220\pi$
$991$	−625464.	−0.0202310	−0.0101155	+	0.999949i	$0.503220\pi$
$992$	1.11292e8i	3.59074i
$993$	− 6.09695e7i	− 1.96218i
$994$	−1.32613e7	−0.425715
$995$	0	0
$996$	−4.53249e7	−1.44773
$997$	5.76822e7i	1.83783i	0.394461	+	0.918913i	$0.370931\pi$
$997$	5.76822e7i	1.83783i	−0.394461	+	0.918913i	$0.629069\pi$
$998$	9.05009e7i	2.87625i
$999$	1.57981e7	0.500830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.6.b.i.274.1		22
5.2	odd	4		325.6.a.k.1.11	yes	11
5.3	odd	4		325.6.a.j.1.1	✓	11
5.4	even	2	inner	325.6.b.i.274.22		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.6.a.j.1.1	✓	11	5.3	odd	4
325.6.a.k.1.11	yes	11	5.2	odd	4
325.6.b.i.274.1		22	1.1	even	1	trivial
325.6.b.i.274.22		22	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	325.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-11.2252i q^{2} +19.1897i q^{3} -94.0044 q^{4} +215.408 q^{6} -70.9909i q^{7} +696.009i q^{8} -125.246 q^{9} +O(q^{10})\)	\(q-11.2252i q^{2} +19.1897i q^{3} -94.0044 q^{4} +215.408 q^{6} -70.9909i q^{7} +696.009i q^{8} -125.246 q^{9} -161.025 q^{11} -1803.92i q^{12} +169.000i q^{13} -796.885 q^{14} +4804.68 q^{16} +121.397i q^{17} +1405.90i q^{18} +3111.76 q^{19} +1362.30 q^{21} +1807.53i q^{22} -3100.00i q^{23} -13356.2 q^{24} +1897.05 q^{26} +2259.68i q^{27} +6673.46i q^{28} -3172.08 q^{29} -3515.11 q^{31} -31661.0i q^{32} -3090.02i q^{33} +1362.70 q^{34} +11773.6 q^{36} -6991.30i q^{37} -34930.1i q^{38} -3243.06 q^{39} -19551.6 q^{41} -15292.0i q^{42} +13398.3i q^{43} +15137.0 q^{44} -34798.0 q^{46} -7637.52i q^{47} +92200.5i q^{48} +11767.3 q^{49} -2329.57 q^{51} -15886.7i q^{52} +27750.4i q^{53} +25365.2 q^{54} +49410.3 q^{56} +59713.9i q^{57} +35607.1i q^{58} -33042.3 q^{59} -33195.2 q^{61} +39457.6i q^{62} +8891.30i q^{63} -201651. q^{64} -34686.0 q^{66} -24591.9i q^{67} -11411.8i q^{68} +59488.1 q^{69} +16641.4 q^{71} -87172.0i q^{72} -5252.97i q^{73} -78478.5 q^{74} -292519. q^{76} +11431.3i q^{77} +36403.9i q^{78} +3121.54 q^{79} -73797.2 q^{81} +219470. i q^{82} -25125.8i q^{83} -128062. q^{84} +150399. q^{86} -60871.3i q^{87} -112075. i q^{88} -634.739 q^{89} +11997.5 q^{91} +291413. i q^{92} -67453.9i q^{93} -85732.5 q^{94} +607566. q^{96} -156159. i q^{97} -132090. i q^{98} +20167.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 374 q^{4} + 702 q^{6} - 2744 q^{9}+O(q^{10}) \) 22 * q - 374 * q^4 + 702 * q^6 - 2744 * q^9	\( 22 q - 374 q^{4} + 702 q^{6} - 2744 q^{9} + 2552 q^{11} - 1156 q^{14} + 11414 q^{16} - 7040 q^{19} + 3412 q^{21} - 15446 q^{24} + 1690 q^{26} - 36850 q^{29} + 18136 q^{31} + 28910 q^{34} + 75368 q^{36} - 3718 q^{39} - 20020 q^{41} - 121302 q^{44} - 19716 q^{46} - 146626 q^{49} + 73212 q^{51} - 96026 q^{54} - 2524 q^{56} - 263284 q^{59} - 86730 q^{61} - 360142 q^{64} - 117214 q^{66} - 118690 q^{69} + 136840 q^{71} - 742792 q^{74} + 45034 q^{76} - 104478 q^{79} + 215014 q^{81} - 1705432 q^{84} + 404492 q^{86} - 655424 q^{89} + 70304 q^{91} - 1299948 q^{94} + 1799326 q^{96} - 853396 q^{99}+O(q^{100}) \) 22 * q - 374 * q^4 + 702 * q^6 - 2744 * q^9 + 2552 * q^11 - 1156 * q^14 + 11414 * q^16 - 7040 * q^19 + 3412 * q^21 - 15446 * q^24 + 1690 * q^26 - 36850 * q^29 + 18136 * q^31 + 28910 * q^34 + 75368 * q^36 - 3718 * q^39 - 20020 * q^41 - 121302 * q^44 - 19716 * q^46 - 146626 * q^49 + 73212 * q^51 - 96026 * q^54 - 2524 * q^56 - 263284 * q^59 - 86730 * q^61 - 360142 * q^64 - 117214 * q^66 - 118690 * q^69 + 136840 * q^71 - 742792 * q^74 + 45034 * q^76 - 104478 * q^79 + 215014 * q^81 - 1705432 * q^84 + 404492 * q^86 - 655424 * q^89 + 70304 * q^91 - 1299948 * q^94 + 1799326 * q^96 - 853396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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