LMFDB - Embedded newform 325.6.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,6,Mod(1,325)]

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([0, 0]))

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

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	325.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$52.1247414392$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 $ x^11 - 5x^10 - 257x^9 + 1165x^8 + 22234x^7 - 90282x^6 - 751180x^5 + 2564400x^4 + 9571584x^3 - 23191072x^2 - 33154496x + 44115200
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$11.2252$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+11.2252 q^{2} +19.1897 q^{3} +94.0044 q^{4} +215.408 q^{6} +70.9909 q^{7} +696.009 q^{8} +125.246 q^{9} -161.025 q^{11} +1803.92 q^{12} +169.000 q^{13} +796.885 q^{14} +4804.68 q^{16} -121.397 q^{17} +1405.90 q^{18} -3111.76 q^{19} +1362.30 q^{21} -1807.53 q^{22} -3100.00 q^{23} +13356.2 q^{24} +1897.05 q^{26} -2259.68 q^{27} +6673.46 q^{28} +3172.08 q^{29} -3515.11 q^{31} +31661.0 q^{32} -3090.02 q^{33} -1362.70 q^{34} +11773.6 q^{36} +6991.30 q^{37} -34930.1 q^{38} +3243.06 q^{39} -19551.6 q^{41} +15292.0 q^{42} +13398.3 q^{43} -15137.0 q^{44} -34798.0 q^{46} +7637.52 q^{47} +92200.5 q^{48} -11767.3 q^{49} -2329.57 q^{51} +15886.7 q^{52} +27750.4 q^{53} -25365.2 q^{54} +49410.3 q^{56} -59713.9 q^{57} +35607.1 q^{58} +33042.3 q^{59} -33195.2 q^{61} -39457.6 q^{62} +8891.30 q^{63} +201651. q^{64} -34686.0 q^{66} +24591.9 q^{67} -11411.8 q^{68} -59488.1 q^{69} +16641.4 q^{71} +87172.0 q^{72} -5252.97 q^{73} +78478.5 q^{74} -292519. q^{76} -11431.3 q^{77} +36403.9 q^{78} -3121.54 q^{79} -73797.2 q^{81} -219470. q^{82} -25125.8 q^{83} +128062. q^{84} +150399. q^{86} +60871.3 q^{87} -112075. q^{88} +634.739 q^{89} +11997.5 q^{91} -291413. q^{92} -67453.9 q^{93} +85732.5 q^{94} +607566. q^{96} +156159. q^{97} -132090. q^{98} -20167.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 5 q^{2} + 11 q^{3} + 187 q^{4} + 351 q^{6} + 208 q^{7} + 165 q^{8} + 1372 q^{9} + 1276 q^{11} + 1533 q^{12} + 1859 q^{13} + 578 q^{14} + 5707 q^{16} + 2218 q^{17} - 6776 q^{18} + 3520 q^{19} + 1706 q^{21}+ \cdots + 426698 q^{99}+O(q^{100}) $ 11 * q + 5 * q^2 + 11 * q^3 + 187 * q^4 + 351 * q^6 + 208 * q^7 + 165 * q^8 + 1372 * q^9 + 1276 * q^11 + 1533 * q^12 + 1859 * q^13 + 578 * q^14 + 5707 * q^16 + 2218 * q^17 - 6776 * q^18 + 3520 * q^19 + 1706 * q^21 - 6785 * q^22 - 1215 * q^23 + 7723 * q^24 + 845 * q^26 + 161 * q^27 + 12746 * q^28 + 18425 * q^29 + 9068 * q^31 + 21165 * q^32 + 19748 * q^33 - 14455 * q^34 + 37684 * q^36 - 2280 * q^37 - 23783 * q^38 + 1859 * q^39 - 10010 * q^41 - 44184 * q^42 + 6763 * q^43 + 60651 * q^44 - 9858 * q^46 + 4110 * q^47 + 63289 * q^48 + 73313 * q^49 + 36606 * q^51 + 31603 * q^52 + 15633 * q^53 + 48013 * q^54 - 1262 * q^56 - 205974 * q^57 + 77652 * q^58 + 131642 * q^59 - 43365 * q^61 - 115940 * q^62 + 218466 * q^63 + 180071 * q^64 - 58607 * q^66 - 100904 * q^67 + 371277 * q^68 + 59345 * q^69 + 68420 * q^71 - 210708 * q^72 + 124436 * q^73 + 371396 * q^74 + 22517 * q^76 - 150978 * q^77 + 59319 * q^78 + 52239 * q^79 + 107507 * q^81 - 351137 * q^82 + 211538 * q^83 + 852716 * q^84 + 202246 * q^86 - 28273 * q^87 - 28107 * q^88 + 327712 * q^89 + 35152 * q^91 - 413252 * q^92 + 243338 * q^93 + 649974 * q^94 + 899663 * q^96 - 110796 * q^97 + 27143 * q^98 + 426698 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	11.2252	1.98435	0.992174	−	0.124864i	$-0.0398494\pi$
$2$	11.2252	1.98435	0.992174	+	0.124864i	$0.0398494\pi$
$3$	19.1897	1.23102	0.615511	−	0.788129i	$-0.288950\pi$
$3$	19.1897	1.23102	0.615511	+	0.788129i	$0.288950\pi$
$4$	94.0044	2.93764
$5$	0	0
$5$	0	0
$6$	215.408	2.44277
$7$	70.9909	0.547593	0.273796	−	0.961788i	$-0.411721\pi$
$7$	70.9909	0.547593	0.273796	+	0.961788i	$0.411721\pi$
$8$	696.009	3.84494
$9$	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	$0.564297\pi$
$12$	1803.92	3.61629
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	796.885	1.08661
$15$	0	0
$16$	4804.68	4.69207
$17$	−121.397	−0.101879	−0.0509396	−	0.998702i	$-0.516222\pi$
$17$	−121.397	−0.101879	−0.0509396	+	0.998702i	$0.516222\pi$
$18$	1405.90	1.02276
$19$	−3111.76	−1.97753	−0.988764	−	0.149485i	$-0.952238\pi$
$19$	−3111.76	−1.97753	−0.988764	+	0.149485i	$0.952238\pi$
$20$	0	0
$21$	1362.30	0.674099
$22$	−1807.53	−0.796211
$23$	−3100.00	−1.22192	−0.610959	−	0.791662i	$-0.709216\pi$
$23$	−3100.00	−1.22192	−0.610959	+	0.791662i	$0.709216\pi$
$24$	13356.2	4.73321
$25$	0	0
$26$	1897.05	0.550359
$27$	−2259.68	−0.596536
$28$	6673.46	1.60863
$29$	3172.08	0.700404	0.350202	−	0.936674i	$-0.386113\pi$
$29$	3172.08	0.700404	0.350202	+	0.936674i	$0.386113\pi$
$30$	0	0
$31$	−3515.11	−0.656953	−0.328476	−	0.944512i	$-0.606535\pi$
$31$	−3515.11	−0.656953	−0.328476	+	0.944512i	$0.606535\pi$
$32$	31661.0	5.46575
$33$	−3090.02	−0.493942
$34$	−1362.70	−0.202164
$35$	0	0
$36$	11773.6	1.51410
$37$	6991.30	0.839563	0.419782	−	0.907625i	$-0.362107\pi$
$37$	6991.30	0.839563	0.419782	+	0.907625i	$0.362107\pi$
$38$	−34930.1	−3.92410
$39$	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	$0.862560\pi$
$42$	15292.0	1.33765
$43$	13398.3	1.10504	0.552522	−	0.833498i	$-0.313665\pi$
$43$	13398.3	1.10504	0.552522	+	0.833498i	$0.313665\pi$
$44$	−15137.0	−1.17871
$45$	0	0
$46$	−34798.0	−2.42471
$47$	7637.52	0.504322	0.252161	−	0.967685i	$-0.418859\pi$
$47$	7637.52	0.504322	0.252161	+	0.967685i	$0.418859\pi$
$48$	92200.5	5.77604
$49$	−11767.3	−0.700142
$50$	0	0
$51$	−2329.57	−0.125415
$52$	15886.7	0.814754
$53$	27750.4	1.35700	0.678500	−	0.734600i	$-0.262630\pi$
$53$	27750.4	1.35700	0.678500	+	0.734600i	$0.262630\pi$
$54$	−25365.2	−1.18374
$55$	0	0
$56$	49410.3	2.10546
$57$	−59713.9	−2.43438
$58$	35607.1	1.38985
$59$	33042.3	1.23578	0.617889	−	0.786265i	$-0.287988\pi$
$59$	33042.3	1.23578	0.617889	+	0.786265i	$0.287988\pi$
$60$	0	0
$61$	−33195.2	−1.14222	−0.571110	−	0.820873i	$-0.693487\pi$
$61$	−33195.2	−1.14222	−0.571110	+	0.820873i	$0.693487\pi$
$62$	−39457.6	−1.30362
$63$	8891.30	0.282237
$64$	201651.	6.15389
$65$	0	0
$66$	−34686.0	−0.980153
$67$	24591.9	0.669275	0.334637	−	0.942347i	$-0.391386\pi$
$67$	24591.9	0.669275	0.334637	+	0.942347i	$0.391386\pi$
$68$	−11411.8	−0.299284
$69$	−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	$0.437240\pi$
$72$	87172.0	1.98174
$73$	−5252.97	−0.115371	−0.0576856	−	0.998335i	$-0.518372\pi$
$73$	−5252.97	−0.115371	−0.0576856	+	0.998335i	$0.518372\pi$
$74$	78478.5	1.66599
$75$	0	0
$76$	−292519.	−5.80926
$77$	−11431.3	−0.219719
$78$	36403.9	0.677504
$79$	−3121.54	−0.0562731	−0.0281366	−	0.999604i	$-0.508957\pi$
$79$	−3121.54	−0.0562731	−0.0281366	+	0.999604i	$0.508957\pi$
$80$	0	0
$81$	−73797.2	−1.24976
$82$	−219470.	−3.60446
$83$	−25125.8	−0.400336	−0.200168	−	0.979762i	$-0.564149\pi$
$83$	−25125.8	−0.400336	−0.200168	+	0.979762i	$0.564149\pi$
$84$	128062.	1.98026
$85$	0	0
$86$	150399.	2.19279
$87$	60871.3	0.862213
$88$	−112075.	−1.54277
$89$	634.739	0.00849416	0.00424708	−	0.999991i	$-0.498648\pi$
$89$	634.739	0.00849416	0.00424708	+	0.999991i	$0.498648\pi$
$90$	0	0
$91$	11997.5	0.151875
$92$	−291413.	−3.58955
$93$	−67453.9	−0.808723
$94$	85732.5	1.00075
$95$	0	0
$96$	607566.	6.72846
$97$	156159.	1.68514	0.842572	−	0.538584i	$-0.181041\pi$
$97$	156159.	1.68514	0.842572	+	0.538584i	$0.181041\pi$
$98$	−132090.	−1.38933
$99$	−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	$0.797903\pi$
$102$	−26149.9	−0.248868
$103$	75861.6	0.704578	0.352289	−	0.935891i	$-0.385403\pi$
$103$	75861.6	0.704578	0.352289	+	0.935891i	$0.385403\pi$
$104$	117626.	1.06640
$105$	0	0
$106$	311503.	2.69276
$107$	−141728.	−1.19673	−0.598366	−	0.801223i	$-0.704183\pi$
$107$	−141728.	−1.19673	−0.598366	+	0.801223i	$0.704183\pi$
$108$	−212419.	−1.75241
$109$	11820.9	0.0952981	0.0476490	−	0.998864i	$-0.484827\pi$
$109$	11820.9	0.0952981	0.0476490	+	0.998864i	$0.484827\pi$
$110$	0	0
$111$	134161.	1.03352
$112$	341089.	2.56934
$113$	−43552.7	−0.320862	−0.160431	−	0.987047i	$-0.551288\pi$
$113$	−43552.7	−0.320862	−0.160431	+	0.987047i	$0.551288\pi$
$114$	−670298.	−4.83065
$115$	0	0
$116$	298189.	2.05753
$117$	21166.5	0.142950
$118$	370906.	2.45222
$119$	−8618.08	−0.0557883
$120$	0	0
$121$	−135122.	−0.839002
$122$	−372621.	−2.26656
$123$	−375189.	−2.23608
$124$	−330435.	−1.92989
$125$	0	0
$126$	99806.3	0.560056
$127$	229412.	1.26214	0.631068	−	0.775727i	$-0.282617\pi$
$127$	229412.	1.26214	0.631068	+	0.775727i	$0.282617\pi$
$128$	1.25041e6	6.74570
$129$	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.	−1.45102
$133$	−220907.	−1.08288
$134$	276048.	1.32807
$135$	0	0
$136$	−84493.4	−0.391720
$137$	233597.	1.06332	0.531662	−	0.846956i	$-0.321567\pi$
$137$	233597.	1.06332	0.531662	+	0.846956i	$0.321567\pi$
$138$	−667764.	−2.98487
$139$	97992.9	0.430187	0.215094	−	0.976593i	$-0.430994\pi$
$139$	97992.9	0.430187	0.215094	+	0.976593i	$0.430994\pi$
$140$	0	0
$141$	146562.	0.620831
$142$	186802.	0.777430
$143$	−27213.1	−0.111286
$144$	601765.	2.41836
$145$	0	0
$146$	−58965.4	−0.228937
$147$	−225811.	−0.861890
$148$	657212.	2.46633
$149$	267805.	0.988219	0.494110	−	0.869400i	$-0.335494\pi$
$149$	267805.	0.988219	0.494110	+	0.869400i	$0.335494\pi$
$150$	0	0
$151$	−125041.	−0.446283	−0.223141	−	0.974786i	$-0.571631\pi$
$151$	−125041.	−0.446283	−0.223141	+	0.974786i	$0.571631\pi$
$152$	−2.16582e6	−7.60348
$153$	−15204.4	−0.0525099
$154$	−128318.	−0.436000
$155$	0	0
$156$	304862.	1.00298
$157$	−323793.	−1.04838	−0.524189	−	0.851602i	$-0.675632\pi$
$157$	−323793.	−1.04838	−0.524189	+	0.851602i	$0.675632\pi$
$158$	−35039.8	−0.111665
$159$	532523.	1.67050
$160$	0	0
$161$	−220072.	−0.669113
$162$	−828386.	−2.47996
$163$	−483015.	−1.42394	−0.711970	−	0.702210i	$-0.752197\pi$
$163$	−483015.	−1.42394	−0.711970	+	0.702210i	$0.752197\pi$
$164$	−1.83793e6	−5.33605
$165$	0	0
$166$	−282041.	−0.794406
$167$	272660.	0.756538	0.378269	−	0.925696i	$-0.376520\pi$
$167$	272660.	0.756538	0.378269	+	0.925696i	$0.376520\pi$
$168$	948171.	2.59187
$169$	28561.0	0.0769231
$170$	0	0
$171$	−389734.	−1.01924
$172$	1.25950e6	3.24622
$173$	248584.	0.631477	0.315738	−	0.948846i	$-0.397748\pi$
$173$	248584.	0.631477	0.315738	+	0.948846i	$0.397748\pi$
$174$	683290.	1.71093
$175$	0	0
$176$	−773671.	−1.88267
$177$	634073.	1.52127
$178$	7125.05	0.0168554
$179$	29132.9	0.0679597	0.0339798	−	0.999423i	$-0.489182\pi$
$179$	29132.9	0.0679597	0.0339798	+	0.999423i	$0.489182\pi$
$180$	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.	0.301373
$183$	−637006.	−1.40610
$184$	−2.15763e6	−4.69820
$185$	0	0
$186$	−757181.	−1.60479
$187$	19547.9	0.0408786
$188$	717960.	1.48151
$189$	−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	$0.252130\pi$
$192$	3.86962e6	7.57557
$193$	−596277.	−1.15227	−0.576136	−	0.817354i	$-0.695440\pi$
$193$	−596277.	−1.15227	−0.576136	+	0.817354i	$0.695440\pi$
$194$	1.75291e6	3.34391
$195$	0	0
$196$	−1.10618e6	−2.05676
$197$	−23822.5	−0.0437342	−0.0218671	−	0.999761i	$-0.506961\pi$
$197$	−23822.5	−0.0437342	−0.0218671	+	0.999761i	$0.506961\pi$
$198$	−226385.	−0.410378
$199$	470656.	0.842503	0.421251	−	0.906944i	$-0.361591\pi$
$199$	470656.	0.842503	0.421251	+	0.906944i	$0.361591\pi$
$200$	0	0
$201$	471911.	0.823892
$202$	−1.85307e6	−3.19531
$203$	225189.	0.383536
$204$	−218990.	−0.368425
$205$	0	0
$206$	851560.	1.39813
$207$	−388261.	−0.629793
$208$	811991.	1.30135
$209$	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	$0.659074\pi$
$212$	2.60866e6	3.98637
$213$	319344.	0.482291
$214$	−1.59092e6	−2.37473
$215$	0	0
$216$	−1.57276e6	−2.29365
$217$	−249541.	−0.359743
$218$	132692.	0.189105
$219$	−100803.	−0.142024
$220$	0	0
$221$	−20516.1	−0.0282562
$222$	1.50598e6	2.05086
$223$	−310997.	−0.418787	−0.209394	−	0.977831i	$-0.567149\pi$
$223$	−310997.	−0.418787	−0.209394	+	0.977831i	$0.567149\pi$
$224$	2.24765e6	2.99301
$225$	0	0
$226$	−488886.	−0.636702
$227$	−450336.	−0.580059	−0.290030	−	0.957018i	$-0.593665\pi$
$227$	−450336.	−0.580059	−0.290030	+	0.957018i	$0.593665\pi$
$228$	−5.61337e6	−7.15132
$229$	855126.	1.07756	0.538780	−	0.842447i	$-0.318886\pi$
$229$	855126.	1.07756	0.538780	+	0.842447i	$0.318886\pi$
$230$	0	0
$231$	−219363.	−0.270479
$232$	2.20779e6	2.69301
$233$	−1.09514e6	−1.32153	−0.660767	−	0.750591i	$-0.729769\pi$
$233$	−1.09514e6	−1.32153	−0.660767	+	0.750591i	$0.729769\pi$
$234$	237597.	0.283663
$235$	0	0
$236$	3.10612e6	3.63027
$237$	−59901.4	−0.0692734
$238$	−96739.4	−0.110703
$239$	917921.	1.03947	0.519733	−	0.854329i	$-0.326031\pi$
$239$	917921.	1.03947	0.519733	+	0.854329i	$0.326031\pi$
$240$	0	0
$241$	−642632.	−0.712721	−0.356361	−	0.934349i	$-0.615982\pi$
$241$	−642632.	−0.712721	−0.356361	+	0.934349i	$0.615982\pi$
$242$	−1.51677e6	−1.66487
$243$	−867047.	−0.941948
$244$	−3.12049e6	−3.35543
$245$	0	0
$246$	−4.21156e6	−4.43717
$247$	−525888.	−0.548468
$248$	−2.44655e6	−2.52595
$249$	−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.	0.829109
$253$	499176.	0.490289
$254$	2.57518e6	2.50452
$255$	0	0
$256$	7.58322e6	7.23192
$257$	1.06681e6	1.00752	0.503759	−	0.863844i	$-0.331950\pi$
$257$	1.06681e6	1.00752	0.503759	+	0.863844i	$0.331950\pi$
$258$	2.88611e6	2.69937
$259$	496319.	0.459739
$260$	0	0
$261$	397288.	0.360998
$262$	−1.81532e6	−1.63381
$263$	503116.	0.448517	0.224258	−	0.974530i	$-0.428004\pi$
$263$	503116.	0.448517	0.224258	+	0.974530i	$0.428004\pi$
$264$	−2.15068e6	−1.89918
$265$	0	0
$266$	−2.47972e6	−2.14881
$267$	12180.5	0.0104565
$268$	2.31174e6	1.96609
$269$	−104820.	−0.0883212	−0.0441606	−	0.999024i	$-0.514061\pi$
$269$	−104820.	−0.0883212	−0.0441606	+	0.999024i	$0.514061\pi$
$270$	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.	−0.478024
$273$	230228.	0.186961
$274$	2.62217e6	2.11001
$275$	0	0
$276$	−5.59214e6	−4.41881
$277$	−863313.	−0.676034	−0.338017	−	0.941140i	$-0.609756\pi$
$277$	−863313.	−0.676034	−0.338017	+	0.941140i	$0.609756\pi$
$278$	1.09999e6	0.853641
$279$	−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	$0.702010\pi$
$282$	1.64518e6	1.23194
$283$	1.10553e6	0.820546	0.410273	−	0.911963i	$-0.365433\pi$
$283$	1.10553e6	0.820546	0.410273	+	0.911963i	$0.365433\pi$
$284$	1.56436e6	1.15091
$285$	0	0
$286$	−305472.	−0.220829
$287$	−1.38799e6	−0.994672
$288$	3.96540e6	2.81712
$289$	−1.40512e6	−0.989621
$290$	0	0
$291$	2.99664e6	2.07445
$292$	−493802.	−0.338919
$293$	−116407.	−0.0792155	−0.0396077	−	0.999215i	$-0.512611\pi$
$293$	−116407.	−0.0792155	−0.0396077	+	0.999215i	$0.512611\pi$
$294$	−2.53477e6	−1.71029
$295$	0	0
$296$	4.86601e6	3.22807
$297$	363863.	0.239358
$298$	3.00616e6	1.96097
$299$	−523900.	−0.338899
$300$	0	0
$301$	951161.	0.605115
$302$	−1.40361e6	−0.885580
$303$	−3.16787e6	−1.98226
$304$	−1.49510e7	−9.27870
$305$	0	0
$306$	−170672.	−0.104198
$307$	−830234.	−0.502753	−0.251376	−	0.967889i	$-0.580883\pi$
$307$	−830234.	−0.502753	−0.251376	+	0.967889i	$0.580883\pi$
$308$	−1.07459e6	−0.645455
$309$	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	$0.480873\pi$
$312$	2.25720e6	1.31276
$313$	−1.96760e6	−1.13521	−0.567604	−	0.823302i	$-0.692129\pi$
$313$	−1.96760e6	−1.13521	−0.567604	+	0.823302i	$0.692129\pi$
$314$	−3.63463e6	−2.08035
$315$	0	0
$316$	−293438.	−0.165310
$317$	−2.47859e6	−1.38534	−0.692670	−	0.721255i	$-0.743566\pi$
$317$	−2.47859e6	−1.38534	−0.692670	+	0.721255i	$0.743566\pi$
$318$	5.97766e6	3.31485
$319$	−510782.	−0.281034
$320$	0	0
$321$	−2.71973e6	−1.47320
$322$	−2.47034e6	−1.32775
$323$	377759.	0.201469
$324$	−6.93726e6	−3.67135
$325$	0	0
$326$	−5.42193e6	−2.82559
$327$	226840.	0.117314
$328$	−1.36081e7	−6.98413
$329$	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	$0.793567\pi$
$332$	−2.36193e6	−1.17604
$333$	875629.	0.432722
$334$	3.06066e6	1.50123
$335$	0	0
$336$	6.54540e6	3.16292
$337$	1.04972e6	0.503500	0.251750	−	0.967792i	$-0.418994\pi$
$337$	1.04972e6	0.503500	0.251750	+	0.967792i	$0.418994\pi$
$338$	320602.	0.152642
$339$	−835764.	−0.394988
$340$	0	0
$341$	566018.	0.263599
$342$	−4.37483e6	−2.02254
$343$	−2.02852e6	−0.930986
$344$	9.32537e6	4.24883
$345$	0	0
$346$	2.79039e6	1.25307
$347$	502238.	0.223916	0.111958	−	0.993713i	$-0.464288\pi$
$347$	502238.	0.223916	0.111958	+	0.993713i	$0.464288\pi$
$348$	5.72217e6	2.53287
$349$	−1.28824e6	−0.566152	−0.283076	−	0.959098i	$-0.591355\pi$
$349$	−1.28824e6	−0.566152	−0.283076	+	0.959098i	$0.591355\pi$
$350$	0	0
$351$	−381885.	−0.165449
$352$	−5.09820e6	−2.19311
$353$	3.80443e6	1.62500	0.812499	−	0.582962i	$-0.198107\pi$
$353$	3.80443e6	1.62500	0.812499	+	0.582962i	$0.198107\pi$
$354$	7.11758e6	3.01873
$355$	0	0
$356$	59668.2	0.0249527
$357$	−165379.	−0.0686766
$358$	327022.	0.134856
$359$	3.18303e6	1.30348	0.651740	−	0.758442i	$-0.274039\pi$
$359$	3.18303e6	1.30348	0.651740	+	0.758442i	$0.274039\pi$
$360$	0	0
$361$	7.20697e6	2.91062
$362$	6.55472e6	2.62895
$363$	−2.59296e6	−1.03283
$364$	1.12781e6	0.446153
$365$	0	0
$366$	−7.15050e6	−2.79019
$367$	1.51403e6	0.586770	0.293385	−	0.955994i	$-0.405218\pi$
$367$	1.51403e6	0.586770	0.293385	+	0.955994i	$0.405218\pi$
$368$	−1.48945e7	−5.73332
$369$	−2.44875e6	−0.936221
$370$	0	0
$371$	1.97003e6	0.743084
$372$	−6.34096e6	−2.37573
$373$	1.59920e6	0.595156	0.297578	−	0.954698i	$-0.403821\pi$
$373$	1.59920e6	0.595156	0.297578	+	0.954698i	$0.403821\pi$
$374$	219428.	0.0811173
$375$	0	0
$376$	5.31579e6	1.93909
$377$	536081.	0.194257
$378$	−1.80070e6	−0.648205
$379$	2.52547e6	0.903116	0.451558	−	0.892242i	$-0.350868\pi$
$379$	2.52547e6	0.903116	0.451558	+	0.892242i	$0.350868\pi$
$380$	0	0
$381$	4.40235e6	1.55372
$382$	7.94997e6	2.78745
$383$	−3.16883e6	−1.10383	−0.551915	−	0.833900i	$-0.686103\pi$
$383$	−3.16883e6	−1.10383	−0.551915	+	0.833900i	$0.686103\pi$
$384$	2.39950e7	8.30410
$385$	0	0
$386$	−6.69331e6	−2.28651
$387$	1.67808e6	0.569555
$388$	1.46796e7	4.95034
$389$	1.03129e6	0.345545	0.172773	−	0.984962i	$-0.444727\pi$
$389$	1.03129e6	0.345545	0.172773	+	0.984962i	$0.444727\pi$
$390$	0	0
$391$	376330.	0.124488
$392$	−8.19014e6	−2.69201
$393$	−3.10334e6	−1.01356
$394$	−267411.	−0.0867838
$395$	0	0
$396$	−1.89584e6	−0.607525
$397$	634862.	0.202164	0.101082	−	0.994878i	$-0.467770\pi$
$397$	634862.	0.202164	0.101082	+	0.994878i	$0.467770\pi$
$398$	5.28320e6	1.67182
$399$	−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	$0.389073\pi$
$402$	5.29728e6	1.63489
$403$	−594053.	−0.182206
$404$	−1.55184e7	−4.73035
$405$	0	0
$406$	2.52778e6	0.761070
$407$	−1.12577e6	−0.336871
$408$	−1.62140e6	−0.482215
$409$	−4.25223e6	−1.25692	−0.628461	−	0.777841i	$-0.716315\pi$
$409$	−4.25223e6	−1.25692	−0.628461	+	0.777841i	$0.716315\pi$
$410$	0	0
$411$	4.48266e6	1.30898
$412$	7.13132e6	2.06979
$413$	2.34571e6	0.676704
$414$	−4.35829e6	−1.24973
$415$	0	0
$416$	5.35071e6	1.51593
$417$	1.88046e6	0.529570
$418$	5.62460e6	1.57453
$419$	3.54751e6	0.987161	0.493581	−	0.869700i	$-0.335688\pi$
$419$	3.54751e6	0.987161	0.493581	+	0.869700i	$0.335688\pi$
$420$	0	0
$421$	1.40038e6	0.385071	0.192535	−	0.981290i	$-0.438329\pi$
$421$	1.40038e6	0.385071	0.192535	+	0.981290i	$0.438329\pi$
$422$	−6.95742e6	−1.90181
$423$	956565.	0.259934
$424$	1.93146e7	5.21759
$425$	0	0
$426$	3.58469e6	0.957033
$427$	−2.35656e6	−0.625472
$428$	−1.33231e7	−3.51556
$429$	−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	$0.252167\pi$
$432$	−1.08570e7	−2.79899
$433$	5.58069e6	1.43043	0.715217	−	0.698902i	$-0.246328\pi$
$433$	5.58069e6	1.43043	0.715217	+	0.698902i	$0.246328\pi$
$434$	−2.80113e6	−0.713854
$435$	0	0
$436$	1.11122e6	0.279951
$437$	9.64646e6	2.41638
$438$	−1.13153e6	−0.281826
$439$	−1.76748e6	−0.437716	−0.218858	−	0.975757i	$-0.570233\pi$
$439$	−1.76748e6	−0.437716	−0.218858	+	0.975757i	$0.570233\pi$
$440$	0	0
$441$	−1.47380e6	−0.360863
$442$	−230296.	−0.0560701
$443$	−2.11511e6	−0.512062	−0.256031	−	0.966669i	$-0.582415\pi$
$443$	−2.11511e6	−0.512062	−0.256031	+	0.966669i	$0.582415\pi$
$444$	1.26117e7	3.03611
$445$	0	0
$446$	−3.49099e6	−0.831019
$447$	5.13911e6	1.21652
$448$	1.43154e7	3.36982
$449$	2.74804e6	0.643290	0.321645	−	0.946860i	$-0.395764\pi$
$449$	2.74804e6	0.643290	0.321645	+	0.946860i	$0.395764\pi$
$450$	0	0
$451$	3.14828e6	0.728841
$452$	−4.09414e6	−0.942577
$453$	−2.39950e6	−0.549384
$454$	−5.05510e6	−1.15104
$455$	0	0
$456$	−4.15614e7	−9.36005
$457$	3.46825e6	0.776820	0.388410	−	0.921487i	$-0.373024\pi$
$457$	3.46825e6	0.776820	0.388410	+	0.921487i	$0.373024\pi$
$458$	9.59893e6	2.13825
$459$	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	$0.308496\pi$
$462$	−2.46239e6	−0.536725
$463$	6.87934e6	1.49140	0.745700	−	0.666282i	$-0.232115\pi$
$463$	6.87934e6	1.49140	0.745700	+	0.666282i	$0.232115\pi$
$464$	1.52408e7	3.28634
$465$	0	0
$466$	−1.22931e7	−2.62238
$467$	569700.	0.120880	0.0604400	−	0.998172i	$-0.480750\pi$
$467$	569700.	0.120880	0.0604400	+	0.998172i	$0.480750\pi$
$468$	1.98974e6	0.419935
$469$	1.74580e6	0.366490
$470$	0	0
$471$	−6.21350e6	−1.29058
$472$	2.29978e7	4.75150
$473$	−2.15746e6	−0.443394
$474$	−672404.	−0.137463
$475$	0	0
$476$	−810137.	−0.163886
$477$	3.47562e6	0.699417
$478$	1.03038e7	2.06266
$479$	−3.33256e6	−0.663649	−0.331825	−	0.943341i	$-0.607664\pi$
$479$	−3.33256e6	−0.663649	−0.331825	+	0.943341i	$0.607664\pi$
$480$	0	0
$481$	1.18153e6	0.232853
$482$	−7.21365e6	−1.41429
$483$	−4.22312e6	−0.823693
$484$	−1.27021e7	−2.46468
$485$	0	0
$486$	−9.73275e6	−1.86915
$487$	5.24387e6	1.00191	0.500956	−	0.865473i	$-0.332982\pi$
$487$	5.24387e6	1.00191	0.500956	+	0.865473i	$0.332982\pi$
$488$	−2.31041e7	−4.39177
$489$	−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	$0.639277\pi$
$492$	−3.52694e7	−6.56880
$493$	−385080.	−0.0713566
$494$	−5.90318e6	−1.08835
$495$	0	0
$496$	−1.68890e7	−3.08247
$497$	1.18139e6	0.214537
$498$	−5.41229e6	−0.977930
$499$	8.06232e6	1.44947	0.724734	−	0.689029i	$-0.241963\pi$
$499$	8.06232e6	1.44947	0.724734	+	0.689029i	$0.241963\pi$
$500$	0	0
$501$	5.23227e6	0.931314
$502$	−1.08597e6	−0.192335
$503$	−3.91235e6	−0.689474	−0.344737	−	0.938699i	$-0.612032\pi$
$503$	−3.91235e6	−0.689474	−0.344737	+	0.938699i	$0.612032\pi$
$504$	6.18842e6	1.08518
$505$	0	0
$506$	5.60333e6	0.972904
$507$	548078.	0.0946940
$508$	2.15657e7	3.70770
$509$	−1.01584e7	−1.73792	−0.868959	−	0.494884i	$-0.835210\pi$
$509$	−1.01584e7	−1.73792	−0.868959	+	0.494884i	$0.835210\pi$
$510$	0	0
$511$	−372913.	−0.0631765
$512$	4.51098e7	7.60495
$513$	7.03158e6	1.17967
$514$	1.19751e7	1.99927
$515$	0	0
$516$	2.41695e7	3.99616
$517$	−1.22983e6	−0.202357
$518$	5.57126e6	0.912282
$519$	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	$0.462678\pi$
$522$	4.45963e6	0.716345
$523$	−203871.	−0.0325912	−0.0162956	−	0.999867i	$-0.505187\pi$
$523$	−203871.	−0.0325912	−0.0162956	+	0.999867i	$0.505187\pi$
$524$	−1.52023e7	−2.41869
$525$	0	0
$526$	5.64756e6	0.890013
$527$	426723.	0.0669298
$528$	−1.48465e7	−2.31761
$529$	3.17365e6	0.493082
$530$	0	0
$531$	4.13841e6	0.636937
$532$	−2.07662e7	−3.18111
$533$	−3.30422e6	−0.503791
$534$	136728.	0.0207493
$535$	0	0
$536$	1.71162e7	2.57332
$537$	559052.	0.0836598
$538$	−1.17663e6	−0.175260
$539$	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	$0.320181\pi$
$542$	−1.89472e6	−0.277042
$543$	1.12055e7	1.63091
$544$	−3.84355e6	−0.556846
$545$	0	0
$546$	2.58435e6	0.370996
$547$	−5.64096e6	−0.806092	−0.403046	−	0.915180i	$-0.632049\pi$
$547$	−5.64096e6	−0.806092	−0.403046	+	0.915180i	$0.632049\pi$
$548$	2.19591e7	3.12366
$549$	−4.15754e6	−0.588716
$550$	0	0
$551$	−9.87075e6	−1.38507
$552$	−4.14043e7	−5.78359
$553$	−221601.	−0.0308148
$554$	−9.69083e6	−1.34149
$555$	0	0
$556$	9.21176e6	1.26373
$557$	910831.	0.124394	0.0621971	−	0.998064i	$-0.480189\pi$
$557$	910831.	0.124394	0.0621971	+	0.998064i	$0.480189\pi$
$558$	−4.94189e6	−0.671905
$559$	2.26432e6	0.306484
$560$	0	0
$561$	375119.	0.0503224
$562$	−1.76180e7	−2.35297
$563$	7.96586e6	1.05916	0.529580	−	0.848260i	$-0.322349\pi$
$563$	7.96586e6	1.05916	0.529580	+	0.848260i	$0.322349\pi$
$564$	1.37775e7	1.82378
$565$	0	0
$566$	1.24097e7	1.62825
$567$	−5.23893e6	−0.684361
$568$	1.15826e7	1.50638
$569$	−3.26286e6	−0.422492	−0.211246	−	0.977433i	$-0.567752\pi$
$569$	−3.26286e6	−0.422492	−0.211246	+	0.977433i	$0.567752\pi$
$570$	0	0
$571$	−7.89949e6	−1.01393	−0.506966	−	0.861966i	$-0.669233\pi$
$571$	−7.89949e6	−1.01393	−0.506966	+	0.861966i	$0.669233\pi$
$572$	−2.55815e6	−0.326916
$573$	1.35907e7	1.72924
$574$	−1.55804e7	−1.97378
$575$	0	0
$576$	2.52558e7	3.17180
$577$	−1.91866e6	−0.239916	−0.119958	−	0.992779i	$-0.538276\pi$
$577$	−1.91866e6	−0.239916	−0.119958	+	0.992779i	$0.538276\pi$
$578$	−1.57727e7	−1.96375
$579$	−1.14424e7	−1.41847
$580$	0	0
$581$	−1.78370e6	−0.219221
$582$	3.36378e7	4.11642
$583$	−4.46850e6	−0.544491
$584$	−3.65611e6	−0.443596
$585$	0	0
$586$	−1.30669e6	−0.157191
$587$	1.98302e6	0.237537	0.118769	−	0.992922i	$-0.462105\pi$
$587$	1.98302e6	0.237537	0.118769	+	0.992922i	$0.462105\pi$
$588$	−2.12272e7	−2.53192
$589$	1.09382e7	1.29914
$590$	0	0
$591$	−457146.	−0.0538377
$592$	3.35909e7	3.93929
$593$	9.43563e6	1.10188	0.550940	−	0.834545i	$-0.314269\pi$
$593$	9.43563e6	1.10188	0.550940	+	0.834545i	$0.314269\pi$
$594$	4.08443e6	0.474969
$595$	0	0
$596$	2.51749e7	2.90303
$597$	9.03177e6	1.03714
$598$	−5.88086e6	−0.672493
$599$	6.57359e6	0.748576	0.374288	−	0.927313i	$-0.377887\pi$
$599$	6.57359e6	0.748576	0.374288	+	0.927313i	$0.377887\pi$
$600$	0	0
$601$	9.04817e6	1.02182	0.510910	−	0.859634i	$-0.329308\pi$
$601$	9.04817e6	1.02182	0.510910	+	0.859634i	$0.329308\pi$
$602$	1.06769e7	1.20076
$603$	3.08002e6	0.344953
$604$	−1.17544e7	−1.31102
$605$	0	0
$606$	−3.55598e7	−3.93349
$607$	2.54414e6	0.280266	0.140133	−	0.990133i	$-0.455247\pi$
$607$	2.54414e6	0.280266	0.140133	+	0.990133i	$0.455247\pi$
$608$	−9.85216e7	−10.8087
$609$	4.32131e6	0.472141
$610$	0	0
$611$	1.29074e6	0.139874
$612$	−1.42928e6	−0.154255
$613$	7.53921e6	0.810354	0.405177	−	0.914238i	$-0.367210\pi$
$613$	7.53921e6	0.810354	0.405177	+	0.914238i	$0.367210\pi$
$614$	−9.31951e6	−0.997636
$615$	0	0
$616$	−7.95628e6	−0.844808
$617$	1.44546e6	0.152860	0.0764300	−	0.997075i	$-0.475648\pi$
$617$	1.44546e6	0.152860	0.0764300	+	0.997075i	$0.475648\pi$
$618$	1.63412e7	1.72113
$619$	832032.	0.0872797	0.0436399	−	0.999047i	$-0.486105\pi$
$619$	832032.	0.0872797	0.0436399	+	0.999047i	$0.486105\pi$
$620$	0	0
$621$	7.00499e6	0.728918
$622$	2.29962e6	0.238330
$623$	45060.7	0.00465134
$624$	1.55819e7	1.60198
$625$	0	0
$626$	−2.20866e7	−2.25265
$627$	9.61540e6	0.976784
$628$	−3.04379e7	−3.07975
$629$	−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	$0.477235\pi$
$632$	−2.17262e6	−0.216367
$633$	−1.18939e7	−1.17982
$634$	−2.78226e7	−2.74900
$635$	0	0
$636$	5.00595e7	4.90731
$637$	−1.98867e6	−0.194184
$638$	−5.73362e6	−0.557669
$639$	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	$0.765429\pi$
$642$	−3.05294e7	−2.92335
$643$	−3.71125e6	−0.353992	−0.176996	−	0.984212i	$-0.556638\pi$
$643$	−3.71125e6	−0.353992	−0.176996	+	0.984212i	$0.556638\pi$
$644$	−2.06877e7	−1.96561
$645$	0	0
$646$	4.24040e6	0.399784
$647$	−8.31438e6	−0.780853	−0.390426	−	0.920634i	$-0.627672\pi$
$647$	−8.31438e6	−0.780853	−0.390426	+	0.920634i	$0.627672\pi$
$648$	−5.13635e7	−4.80527
$649$	−5.32063e6	−0.495851
$650$	0	0
$651$	−4.78862e6	−0.442851
$652$	−4.54055e7	−4.18302
$653$	2.58516e6	0.237249	0.118624	−	0.992939i	$-0.462152\pi$
$653$	2.58516e6	0.237249	0.118624	+	0.992939i	$0.462152\pi$
$654$	2.54631e6	0.232792
$655$	0	0
$656$	−9.39391e7	−8.52289
$657$	−657911.	−0.0594639
$658$	6.08623e6	0.548004
$659$	1.77052e7	1.58813	0.794065	−	0.607833i	$-0.207961\pi$
$659$	1.77052e7	1.58813	0.794065	+	0.607833i	$0.207961\pi$
$660$	0	0
$661$	2.01104e6	0.179027	0.0895134	−	0.995986i	$-0.471469\pi$
$661$	2.01104e6	0.179027	0.0895134	+	0.995986i	$0.471469\pi$
$662$	−3.56646e7	−3.16295
$663$	−393698.	−0.0347840
$664$	−1.74878e7	−1.53927
$665$	0	0
$666$	9.82908e6	0.858672
$667$	−9.83343e6	−0.855836
$668$	2.56312e7	2.22243
$669$	−5.96794e6	−0.515536
$670$	0	0
$671$	5.34523e6	0.458311
$672$	4.31317e7	3.68446
$673$	−5.48300e6	−0.466639	−0.233319	−	0.972400i	$-0.574959\pi$
$673$	−5.48300e6	−0.466639	−0.233319	+	0.972400i	$0.574959\pi$
$674$	1.17833e7	0.999119
$675$	0	0
$676$	2.68486e6	0.225972
$677$	−1.58127e7	−1.32597	−0.662987	−	0.748631i	$-0.730712\pi$
$677$	−1.58127e7	−1.32597	−0.662987	+	0.748631i	$0.730712\pi$
$678$	−9.38159e6	−0.783794
$679$	1.10859e7	0.922772
$680$	0	0
$681$	−8.64183e6	−0.714065
$682$	6.35365e6	0.523073
$683$	2.24599e7	1.84229	0.921143	−	0.389225i	$-0.127257\pi$
$683$	2.24599e7	1.84229	0.921143	+	0.389225i	$0.127257\pi$
$684$	−3.66367e7	−2.99417
$685$	0	0
$686$	−2.27704e7	−1.84740
$687$	1.64096e7	1.32650
$688$	6.43747e7	5.18495
$689$	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	$0.615424\pi$
$692$	2.33679e7	1.85505
$693$	−1.43172e6	−0.113246
$694$	5.63770e6	0.444328
$695$	0	0
$696$	4.23670e7	3.31516
$697$	2.37350e6	0.185058
$698$	−1.44607e7	−1.12344
$699$	−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	$0.749229\pi$
$702$	−4.28673e6	−0.328309
$703$	−2.17553e7	−1.66026
$704$	−3.24707e7	−2.46922
$705$	0	0
$706$	4.27054e7	3.22456
$707$	−1.17193e7	−0.881765
$708$	5.96057e7	4.46894
$709$	−2.57581e7	−1.92441	−0.962207	−	0.272318i	$-0.912210\pi$
$709$	−2.57581e7	−1.92441	−0.962207	+	0.272318i	$0.912210\pi$
$710$	0	0
$711$	−390959.	−0.0290039
$712$	441784.	0.0326596
$713$	1.08968e7	0.802742
$714$	−1.85640e6	−0.136278
$715$	0	0
$716$	2.73862e6	0.199641
$717$	1.76146e7	1.27961
$718$	3.57300e7	2.58656
$719$	1.69710e6	0.122429	0.0612146	−	0.998125i	$-0.480503\pi$
$719$	1.69710e6	0.122429	0.0612146	+	0.998125i	$0.480503\pi$
$720$	0	0
$721$	5.38549e6	0.385822
$722$	8.08995e7	5.77568
$723$	−1.23319e7	−0.877375
$724$	5.48921e7	3.89191
$725$	0	0
$726$	−2.91064e7	−2.04949
$727$	−1.84315e7	−1.29338	−0.646689	−	0.762754i	$-0.723847\pi$
$727$	−1.84315e7	−1.29338	−0.646689	+	0.762754i	$0.723847\pi$
$728$	8.35035e6	0.583951
$729$	1.29433e6	0.0902041
$730$	0	0
$731$	−1.62652e6	−0.112581
$732$	−5.98813e7	−4.13060
$733$	−1.79395e7	−1.23325	−0.616624	−	0.787258i	$-0.711500\pi$
$733$	−1.79395e7	−1.23325	−0.616624	+	0.787258i	$0.711500\pi$
$734$	1.69952e7	1.16436
$735$	0	0
$736$	−9.81491e7	−6.67870
$737$	−3.95989e6	−0.268544
$738$	−2.74876e7	−1.85779
$739$	1.84597e7	1.24341	0.621703	−	0.783253i	$-0.286441\pi$
$739$	1.84597e7	1.24341	0.621703	+	0.783253i	$0.286441\pi$
$740$	0	0
$741$	−1.00916e7	−0.675175
$742$	2.21139e7	1.47454
$743$	−3.97606e6	−0.264229	−0.132115	−	0.991234i	$-0.542177\pi$
$743$	−3.97606e6	−0.264229	−0.132115	+	0.991234i	$0.542177\pi$
$744$	−4.69485e7	−3.10949
$745$	0	0
$746$	1.79513e7	1.18100
$747$	−3.14689e6	−0.206339
$748$	1.83759e6	0.120086
$749$	−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	$0.239089\pi$
$752$	3.66958e7	2.36631
$753$	−1.85649e6	−0.119318
$754$	6.01760e6	0.385474
$755$	0	0
$756$	−1.50799e7	−0.959605
$757$	−1.40367e7	−0.890279	−0.445139	−	0.895461i	$-0.646846\pi$
$757$	−1.40367e7	−0.890279	−0.445139	+	0.895461i	$0.646846\pi$
$758$	2.83488e7	1.79210
$759$	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	$0.560712\pi$
$762$	4.94171e7	3.08311
$763$	839177.	0.0521846
$764$	6.65765e7	4.12655
$765$	0	0
$766$	−3.55707e7	−2.19038
$767$	5.58416e6	0.342743
$768$	1.45520e8	8.90265
$769$	1.07705e7	0.656778	0.328389	−	0.944543i	$-0.393494\pi$
$769$	1.07705e7	0.656778	0.328389	+	0.944543i	$0.393494\pi$
$770$	0	0
$771$	2.04717e7	1.24028
$772$	−5.60527e7	−3.38496
$773$	−8.92164e6	−0.537027	−0.268514	−	0.963276i	$-0.586532\pi$
$773$	−8.92164e6	−0.537027	−0.268514	+	0.963276i	$0.586532\pi$
$774$	1.88367e7	1.13020
$775$	0	0
$776$	1.08688e8	6.47928
$777$	9.52422e6	0.565949
$778$	1.15764e7	0.685682
$779$	6.08399e7	3.59207
$780$	0	0
$781$	−2.67967e6	−0.157201
$782$	4.22437e6	0.247027
$783$	−7.16787e6	−0.417816
$784$	−5.65380e7	−3.28511
$785$	0	0
$786$	−3.48356e7	−2.01125
$787$	−542225.	−0.0312063	−0.0156032	−	0.999878i	$-0.504967\pi$
$787$	−542225.	−0.0312063	−0.0156032	+	0.999878i	$0.504967\pi$
$788$	−2.23941e6	−0.128475
$789$	9.65466e6	0.552134
$790$	0	0
$791$	−3.09185e6	−0.175702
$792$	−1.40368e7	−0.795163
$793$	−5.60998e6	−0.316795
$794$	7.12643e6	0.401163
$795$	0	0
$796$	4.42437e7	2.47497
$797$	1.82250e7	1.01630	0.508149	−	0.861269i	$-0.330330\pi$
$797$	1.82250e7	1.01630	0.508149	+	0.861269i	$0.330330\pi$
$798$	−4.75851e7	−2.64523
$799$	−927172.	−0.0513799
$800$	0	0
$801$	79498.2	0.00437800
$802$	2.46856e7	1.35522
$803$	845857.	0.0462922
$804$	4.43617e7	2.42029
$805$	0	0
$806$	−6.66834e6	−0.361560
$807$	−2.01147e6	−0.108725
$808$	−1.14898e8	−6.19134
$809$	−3.56238e7	−1.91368	−0.956840	−	0.290615i	$-0.906140\pi$
$809$	−3.56238e7	−1.91368	−0.956840	+	0.290615i	$0.906140\pi$
$810$	0	0
$811$	9.68050e6	0.516828	0.258414	−	0.966034i	$-0.416800\pi$
$811$	9.68050e6	0.516828	0.258414	+	0.966034i	$0.416800\pi$
$812$	2.11687e7	1.12669
$813$	−3.23907e6	−0.171868
$814$	−1.26370e7	−0.668470
$815$	0	0
$816$	−1.11929e7	−0.588458
$817$	−4.16925e7	−2.18526
$818$	−4.77320e7	−2.49417
$819$	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	$0.311229\pi$
$822$	5.03186e7	2.59746
$823$	−2.95621e7	−1.52137	−0.760686	−	0.649120i	$-0.775137\pi$
$823$	−2.95621e7	−1.52137	−0.760686	+	0.649120i	$0.775137\pi$
$824$	5.28004e7	2.70906
$825$	0	0
$826$	2.63309e7	1.34282
$827$	−2.85332e7	−1.45073	−0.725364	−	0.688365i	$-0.758329\pi$
$827$	−2.85332e7	−1.45073	−0.725364	+	0.688365i	$0.758329\pi$
$828$	−3.64982e7	−1.85010
$829$	−2.02156e7	−1.02165	−0.510823	−	0.859686i	$-0.670659\pi$
$829$	−2.02156e7	−1.02165	−0.510823	+	0.859686i	$0.670659\pi$
$830$	0	0
$831$	−1.65667e7	−0.832213
$832$	3.40789e7	1.70678
$833$	1.42851e6	0.0713299
$834$	2.11084e7	1.05085
$835$	0	0
$836$	4.71028e7	2.33094
$837$	7.94300e6	0.391896
$838$	3.98214e7	1.95887
$839$	−6.64057e6	−0.325687	−0.162843	−	0.986652i	$-0.552067\pi$
$839$	−6.64057e6	−0.325687	−0.162843	+	0.986652i	$0.552067\pi$
$840$	0	0
$841$	−1.04491e7	−0.509434
$842$	1.57195e7	0.764114
$843$	−3.01185e7	−1.45970
$844$	−5.82644e7	−2.81544
$845$	0	0
$846$	1.07376e7	0.515800
$847$	−9.59244e6	−0.459432
$848$	1.33332e8	6.36714
$849$	2.12148e7	1.01011
$850$	0	0
$851$	−2.16730e7	−1.02588
$852$	3.00197e7	1.41680
$853$	1.92258e7	0.904716	0.452358	−	0.891836i	$-0.350583\pi$
$853$	1.92258e7	0.904716	0.452358	+	0.891836i	$0.350583\pi$
$854$	−2.64527e7	−1.24115
$855$	0	0
$856$	−9.86442e7	−4.60137
$857$	1.98896e6	0.0925068	0.0462534	−	0.998930i	$-0.485272\pi$
$857$	1.98896e6	0.0925068	0.0462534	+	0.998930i	$0.485272\pi$
$858$	−5.86193e6	−0.271845
$859$	−7.32029e6	−0.338490	−0.169245	−	0.985574i	$-0.554133\pi$
$859$	−7.32029e6	−0.338490	−0.169245	+	0.985574i	$0.554133\pi$
$860$	0	0
$861$	−2.66351e7	−1.22446
$862$	6.08028e7	2.78712
$863$	−3.13431e7	−1.43257	−0.716283	−	0.697809i	$-0.754158\pi$
$863$	−3.13431e7	−1.43257	−0.716283	+	0.697809i	$0.754158\pi$
$864$	−7.15437e7	−3.26052
$865$	0	0
$866$	6.26441e7	2.83848
$867$	−2.69639e7	−1.21824
$868$	−2.34579e7	−1.05679
$869$	502644.	0.0225793
$870$	0	0
$871$	4.15603e6	0.185623
$872$	8.22745e6	0.366416
$873$	1.95582e7	0.868546
$874$	1.08283e8	4.79493
$875$	0	0
$876$	−9.47592e6	−0.417216
$877$	2.47672e7	1.08737	0.543686	−	0.839289i	$-0.317028\pi$
$877$	2.47672e7	1.08737	0.543686	+	0.839289i	$0.317028\pi$
$878$	−1.98402e7	−0.868581
$879$	−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	$0.414161\pi$
$882$	−1.65436e7	−0.716077
$883$	−2.56013e7	−1.10500	−0.552498	−	0.833514i	$-0.686325\pi$
$883$	−2.56013e7	−1.10500	−0.552498	+	0.833514i	$0.686325\pi$
$884$	−1.92860e6	−0.0830064
$885$	0	0
$886$	−2.37424e7	−1.01611
$887$	5.01026e6	0.213821	0.106911	−	0.994269i	$-0.465904\pi$
$887$	5.01026e6	0.213821	0.106911	+	0.994269i	$0.465904\pi$
$888$	9.33773e7	3.97383
$889$	1.62862e7	0.691137
$890$	0	0
$891$	1.18832e7	0.501462
$892$	−2.92350e7	−1.23024
$893$	−2.37662e7	−0.997311
$894$	5.76873e7	2.41400
$895$	0	0
$896$	8.87676e7	3.69390
$897$	−1.00535e7	−0.417192
$898$	3.08472e7	1.27651
$899$	−1.11502e7	−0.460132
$900$	0	0
$901$	−3.36882e6	−0.138250
$902$	3.53400e7	1.44627
$903$	1.82525e7	0.744909
$904$	−3.03131e7	−1.23370
$905$	0	0
$906$	−2.69348e7	−1.09017
$907$	4.85441e7	1.95938	0.979688	−	0.200527i	$-0.0642656\pi$
$907$	4.85441e7	1.95938	0.979688	+	0.200527i	$0.0642656\pi$
$908$	−4.23336e7	−1.70400
$909$	−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	$0.707392\pi$
$912$	−2.86906e8	−11.4223
$913$	4.04587e6	0.160633
$914$	3.89317e7	1.54148
$915$	0	0
$916$	8.03855e7	3.16548
$917$	−1.14806e7	−0.450859
$918$	3.07926e6	0.120598
$919$	−3.70802e7	−1.44828	−0.724141	−	0.689652i	$-0.757764\pi$
$919$	−3.70802e7	−1.44828	−0.724141	+	0.689652i	$0.757764\pi$
$920$	0	0
$921$	−1.59320e7	−0.618899
$922$	5.79803e7	2.24623
$923$	2.81239e6	0.108661
$924$	−2.06211e7	−0.794569
$925$	0	0
$926$	7.72217e7	2.95946
$927$	9.50133e6	0.363149
$928$	1.00431e8	3.82824
$929$	2.82561e6	0.107417	0.0537084	−	0.998557i	$-0.482896\pi$
$929$	2.82561e6	0.107417	0.0537084	+	0.998557i	$0.482896\pi$
$930$	0	0
$931$	3.66170e7	1.38455
$932$	−1.02948e8	−3.88219
$933$	3.93126e6	0.147852
$934$	6.39498e6	0.239868
$935$	0	0
$936$	1.47321e7	0.549635
$937$	−3.19406e6	−0.118849	−0.0594243	−	0.998233i	$-0.518926\pi$
$937$	−3.19406e6	−0.118849	−0.0594243	+	0.998233i	$0.518926\pi$
$938$	1.95969e7	0.727244
$939$	−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	$0.634077\pi$
$942$	−6.97475e7	−2.56095
$943$	6.06099e7	2.21955
$944$	1.58758e8	5.79836
$945$	0	0
$946$	−2.42179e7	−0.879849
$947$	−2.24064e7	−0.811889	−0.405945	−	0.913898i	$-0.633057\pi$
$947$	−2.24064e7	−0.811889	−0.405945	+	0.913898i	$0.633057\pi$
$948$	−5.63100e6	−0.203500
$949$	−887751.	−0.0319982
$950$	0	0
$951$	−4.75634e7	−1.70538
$952$	−5.99826e6	−0.214503
$953$	−1.48416e7	−0.529358	−0.264679	−	0.964337i	$-0.585266\pi$
$953$	−1.48416e7	−0.529358	−0.264679	+	0.964337i	$0.585266\pi$
$954$	3.90144e7	1.38789
$955$	0	0
$956$	8.62886e7	3.05357
$957$	−9.80177e6	−0.345959
$958$	−3.74085e7	−1.31691
$959$	1.65833e7	0.582269
$960$	0	0
$961$	−1.62732e7	−0.568413
$962$	1.32629e7	0.462061
$963$	−1.77508e7	−0.616812
$964$	−6.04102e7	−2.09371
$965$	0	0
$966$	−4.74052e7	−1.63449
$967$	−3.06919e7	−1.05550	−0.527749	−	0.849401i	$-0.676964\pi$
$967$	−3.06919e7	−1.05550	−0.527749	+	0.849401i	$0.676964\pi$
$968$	−9.40462e7	−3.22591
$969$	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	$0.752646\pi$
$972$	−8.15062e7	−2.76710
$973$	6.95661e6	0.235568
$974$	5.88633e7	1.98814
$975$	0	0
$976$	−1.59492e8	−5.35938
$977$	2.54822e7	0.854084	0.427042	−	0.904232i	$-0.359556\pi$
$977$	2.54822e7	0.854084	0.427042	+	0.904232i	$0.359556\pi$
$978$	−1.04045e8	−3.47837
$979$	−102209.	−0.00340824
$980$	0	0
$981$	1.48051e6	0.0491179
$982$	−5.08170e7	−1.68163
$983$	5.91830e7	1.95350	0.976749	−	0.214388i	$-0.0687756\pi$
$983$	5.91830e7	1.95350	0.976749	+	0.214388i	$0.0687756\pi$
$984$	−2.61135e8	−8.59761
$985$	0	0
$986$	−4.32259e6	−0.141596
$987$	1.04046e7	0.339963
$988$	−4.94358e7	−1.61120
$989$	−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	$0.503220\pi$
$992$	−1.11292e8	−3.59074
$993$	−6.09695e7	−1.96218
$994$	1.32613e7	0.425715
$995$	0	0
$996$	−4.53249e7	−1.44773
$997$	−5.76822e7	−1.83783	−0.918913	−	0.394461i	$-0.870931\pi$
$997$	−5.76822e7	−1.83783	−0.918913	+	0.394461i	$0.870931\pi$
$998$	9.05009e7	2.87625
$999$	−1.57981e7	−0.500830

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.6.a.j.1.1	✓	11	5.4	even	2
325.6.a.k.1.11	yes	11	1.1	even	1	trivial
325.6.b.i.274.1		22	5.3	odd	4
325.6.b.i.274.22		22	5.2	odd	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q+11.2252 q^{2} +19.1897 q^{3} +94.0044 q^{4} +215.408 q^{6} +70.9909 q^{7} +696.009 q^{8} +125.246 q^{9} -161.025 q^{11} +1803.92 q^{12} +169.000 q^{13} +796.885 q^{14} +4804.68 q^{16} -121.397 q^{17} +1405.90 q^{18} -3111.76 q^{19} +1362.30 q^{21} -1807.53 q^{22} -3100.00 q^{23} +13356.2 q^{24} +1897.05 q^{26} -2259.68 q^{27} +6673.46 q^{28} +3172.08 q^{29} -3515.11 q^{31} +31661.0 q^{32} -3090.02 q^{33} -1362.70 q^{34} +11773.6 q^{36} +6991.30 q^{37} -34930.1 q^{38} +3243.06 q^{39} -19551.6 q^{41} +15292.0 q^{42} +13398.3 q^{43} -15137.0 q^{44} -34798.0 q^{46} +7637.52 q^{47} +92200.5 q^{48} -11767.3 q^{49} -2329.57 q^{51} +15886.7 q^{52} +27750.4 q^{53} -25365.2 q^{54} +49410.3 q^{56} -59713.9 q^{57} +35607.1 q^{58} +33042.3 q^{59} -33195.2 q^{61} -39457.6 q^{62} +8891.30 q^{63} +201651. q^{64} -34686.0 q^{66} +24591.9 q^{67} -11411.8 q^{68} -59488.1 q^{69} +16641.4 q^{71} +87172.0 q^{72} -5252.97 q^{73} +78478.5 q^{74} -292519. q^{76} -11431.3 q^{77} +36403.9 q^{78} -3121.54 q^{79} -73797.2 q^{81} -219470. q^{82} -25125.8 q^{83} +128062. q^{84} +150399. q^{86} +60871.3 q^{87} -112075. q^{88} +634.739 q^{89} +11997.5 q^{91} -291413. q^{92} -67453.9 q^{93} +85732.5 q^{94} +607566. q^{96} +156159. q^{97} -132090. q^{98} -20167.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 5 q^{2} + 11 q^{3} + 187 q^{4} + 351 q^{6} + 208 q^{7} + 165 q^{8} + 1372 q^{9} + 1276 q^{11} + 1533 q^{12} + 1859 q^{13} + 578 q^{14} + 5707 q^{16} + 2218 q^{17} - 6776 q^{18} + 3520 q^{19} + 1706 q^{21}+ \cdots + 426698 q^{99}+O(q^{100}) \) 11 * q + 5 * q^2 + 11 * q^3 + 187 * q^4 + 351 * q^6 + 208 * q^7 + 165 * q^8 + 1372 * q^9 + 1276 * q^11 + 1533 * q^12 + 1859 * q^13 + 578 * q^14 + 5707 * q^16 + 2218 * q^17 - 6776 * q^18 + 3520 * q^19 + 1706 * q^21 - 6785 * q^22 - 1215 * q^23 + 7723 * q^24 + 845 * q^26 + 161 * q^27 + 12746 * q^28 + 18425 * q^29 + 9068 * q^31 + 21165 * q^32 + 19748 * q^33 - 14455 * q^34 + 37684 * q^36 - 2280 * q^37 - 23783 * q^38 + 1859 * q^39 - 10010 * q^41 - 44184 * q^42 + 6763 * q^43 + 60651 * q^44 - 9858 * q^46 + 4110 * q^47 + 63289 * q^48 + 73313 * q^49 + 36606 * q^51 + 31603 * q^52 + 15633 * q^53 + 48013 * q^54 - 1262 * q^56 - 205974 * q^57 + 77652 * q^58 + 131642 * q^59 - 43365 * q^61 - 115940 * q^62 + 218466 * q^63 + 180071 * q^64 - 58607 * q^66 - 100904 * q^67 + 371277 * q^68 + 59345 * q^69 + 68420 * q^71 - 210708 * q^72 + 124436 * q^73 + 371396 * q^74 + 22517 * q^76 - 150978 * q^77 + 59319 * q^78 + 52239 * q^79 + 107507 * q^81 - 351137 * q^82 + 211538 * q^83 + 852716 * q^84 + 202246 * q^86 - 28273 * q^87 - 28107 * q^88 + 327712 * q^89 + 35152 * q^91 - 413252 * q^92 + 243338 * q^93 + 649974 * q^94 + 899663 * q^96 - 110796 * q^97 + 27143 * q^98 + 426698 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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