LMFDB - Embedded newform 325.6.a.j.1.1

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			1.1
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	$-0.960151\pi$
$2$	−11.2252	−1.98435	−0.992174	+	0.124864i	$0.960151\pi$
$3$	−19.1897	−1.23102	−0.615511	−	0.788129i	$-0.711050\pi$
$3$	−19.1897	−1.23102	−0.615511	+	0.788129i	$0.711050\pi$
$4$	94.0044	2.93764
$5$	0	0
$5$	0	0
$6$	215.408	2.44277
$7$	−70.9909	−0.547593	−0.273796	−	0.961788i	$-0.588279\pi$
$7$	−70.9909	−0.547593	−0.273796	+	0.961788i	$0.588279\pi$
$8$	−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	$-0.483778\pi$
$17$	121.397	0.101879	0.0509396	+	0.998702i	$0.483778\pi$
$18$	−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	$-0.290784\pi$
$23$	3100.00	1.22192	0.610959	+	0.791662i	$0.290784\pi$
$24$	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	$-0.637893\pi$
$37$	−6991.30	−0.839563	−0.419782	+	0.907625i	$0.637893\pi$
$38$	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	$-0.686335\pi$
$43$	−13398.3	−1.10504	−0.552522	+	0.833498i	$0.686335\pi$
$44$	−15137.0	−1.17871
$45$	0	0
$46$	−34798.0	−2.42471
$47$	−7637.52	−0.504322	−0.252161	−	0.967685i	$-0.581141\pi$
$47$	−7637.52	−0.504322	−0.252161	+	0.967685i	$0.581141\pi$
$48$	−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	$-0.737370\pi$
$53$	−27750.4	−1.35700	−0.678500	+	0.734600i	$0.737370\pi$
$54$	−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	$-0.608614\pi$
$67$	−24591.9	−0.669275	−0.334637	+	0.942347i	$0.608614\pi$
$68$	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	$-0.481628\pi$
$73$	5252.97	0.115371	0.0576856	+	0.998335i	$0.481628\pi$
$74$	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	$-0.435851\pi$
$83$	25125.8	0.400336	0.200168	+	0.979762i	$0.435851\pi$
$84$	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	$-0.818959\pi$
$97$	−156159.	−1.68514	−0.842572	+	0.538584i	$0.818959\pi$
$98$	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	$-0.614597\pi$
$103$	−75861.6	−0.704578	−0.352289	+	0.935891i	$0.614597\pi$
$104$	117626.	1.06640
$105$	0	0
$106$	311503.	2.69276
$107$	141728.	1.19673	0.598366	−	0.801223i	$-0.295817\pi$
$107$	141728.	1.19673	0.598366	+	0.801223i	$0.295817\pi$
$108$	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	$-0.448712\pi$
$113$	43552.7	0.320862	0.160431	+	0.987047i	$0.448712\pi$
$114$	−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	$-0.717383\pi$
$127$	−229412.	−1.26214	−0.631068	+	0.775727i	$0.717383\pi$
$128$	−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	$-0.678433\pi$
$137$	−233597.	−1.06332	−0.531662	+	0.846956i	$0.678433\pi$
$138$	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	$-0.324368\pi$
$157$	323793.	1.04838	0.524189	+	0.851602i	$0.324368\pi$
$158$	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	$-0.247803\pi$
$163$	483015.	1.42394	0.711970	+	0.702210i	$0.247803\pi$
$164$	−1.83793e6	−5.33605
$165$	0	0
$166$	−282041.	−0.794406
$167$	−272660.	−0.756538	−0.378269	−	0.925696i	$-0.623480\pi$
$167$	−272660.	−0.756538	−0.378269	+	0.925696i	$0.623480\pi$
$168$	−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	$-0.602252\pi$
$173$	−248584.	−0.631477	−0.315738	+	0.948846i	$0.602252\pi$
$174$	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	$-0.304560\pi$
$193$	596277.	1.15227	0.576136	+	0.817354i	$0.304560\pi$
$194$	1.75291e6	3.34391
$195$	0	0
$196$	−1.10618e6	−2.05676
$197$	23822.5	0.0437342	0.0218671	−	0.999761i	$-0.493039\pi$
$197$	23822.5	0.0437342	0.0218671	+	0.999761i	$0.493039\pi$
$198$	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	$-0.432851\pi$
$223$	310997.	0.418787	0.209394	+	0.977831i	$0.432851\pi$
$224$	2.24765e6	2.99301
$225$	0	0
$226$	−488886.	−0.636702
$227$	450336.	0.580059	0.290030	−	0.957018i	$-0.406335\pi$
$227$	450336.	0.580059	0.290030	+	0.957018i	$0.406335\pi$
$228$	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	$-0.270231\pi$
$233$	1.09514e6	1.32153	0.660767	+	0.750591i	$0.270231\pi$
$234$	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	$-0.668050\pi$
$257$	−1.06681e6	−1.00752	−0.503759	+	0.863844i	$0.668050\pi$
$258$	−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	$-0.571996\pi$
$263$	−503116.	−0.448517	−0.224258	+	0.974530i	$0.571996\pi$
$264$	−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	$-0.390244\pi$
$277$	863313.	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$278$	−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	$-0.634567\pi$
$283$	−1.10553e6	−0.820546	−0.410273	+	0.911963i	$0.634567\pi$
$284$	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	$-0.487389\pi$
$293$	116407.	0.0792155	0.0396077	+	0.999215i	$0.487389\pi$
$294$	−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	$-0.419117\pi$
$307$	830234.	0.502753	0.251376	+	0.967889i	$0.419117\pi$
$308$	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	$-0.307871\pi$
$313$	1.96760e6	1.13521	0.567604	+	0.823302i	$0.307871\pi$
$314$	−3.63463e6	−2.08035
$315$	0	0
$316$	−293438.	−0.165310
$317$	2.47859e6	1.38534	0.692670	−	0.721255i	$-0.256434\pi$
$317$	2.47859e6	1.38534	0.692670	+	0.721255i	$0.256434\pi$
$318$	−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	$-0.581006\pi$
$337$	−1.04972e6	−0.503500	−0.251750	+	0.967792i	$0.581006\pi$
$338$	−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	$-0.535712\pi$
$347$	−502238.	−0.223916	−0.111958	+	0.993713i	$0.535712\pi$
$348$	−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	$-0.801893\pi$
$353$	−3.80443e6	−1.62500	−0.812499	+	0.582962i	$0.801893\pi$
$354$	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	$-0.594782\pi$
$367$	−1.51403e6	−0.586770	−0.293385	+	0.955994i	$0.594782\pi$
$368$	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	$-0.596179\pi$
$373$	−1.59920e6	−0.595156	−0.297578	+	0.954698i	$0.596179\pi$
$374$	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	$-0.313897\pi$
$383$	3.16883e6	1.10383	0.551915	+	0.833900i	$0.313897\pi$
$384$	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	$-0.532230\pi$
$397$	−634862.	−0.202164	−0.101082	+	0.994878i	$0.532230\pi$
$398$	−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	$-0.753672\pi$
$433$	−5.58069e6	−1.43043	−0.715217	+	0.698902i	$0.753672\pi$
$434$	−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	$-0.417585\pi$
$443$	2.11511e6	0.512062	0.256031	+	0.966669i	$0.417585\pi$
$444$	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	$-0.626976\pi$
$457$	−3.46825e6	−0.776820	−0.388410	+	0.921487i	$0.626976\pi$
$458$	−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	$-0.767885\pi$
$463$	−6.87934e6	−1.49140	−0.745700	+	0.666282i	$0.767885\pi$
$464$	1.52408e7	3.28634
$465$	0	0
$466$	−1.22931e7	−2.62238
$467$	−569700.	−0.120880	−0.0604400	−	0.998172i	$-0.519250\pi$
$467$	−569700.	−0.120880	−0.0604400	+	0.998172i	$0.519250\pi$
$468$	−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	$-0.667018\pi$
$487$	−5.24387e6	−1.00191	−0.500956	+	0.865473i	$0.667018\pi$
$488$	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	$-0.387968\pi$
$503$	3.91235e6	0.689474	0.344737	+	0.938699i	$0.387968\pi$
$504$	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	$-0.494813\pi$
$523$	203871.	0.0325912	0.0162956	+	0.999867i	$0.494813\pi$
$524$	−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	$-0.367951\pi$
$547$	5.64096e6	0.806092	0.403046	+	0.915180i	$0.367951\pi$
$548$	−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	$-0.519811\pi$
$557$	−910831.	−0.124394	−0.0621971	+	0.998064i	$0.519811\pi$
$558$	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	$-0.677651\pi$
$563$	−7.96586e6	−1.05916	−0.529580	+	0.848260i	$0.677651\pi$
$564$	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	$-0.461724\pi$
$577$	1.91866e6	0.239916	0.119958	+	0.992779i	$0.461724\pi$
$578$	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	$-0.537895\pi$
$587$	−1.98302e6	−0.237537	−0.118769	+	0.992922i	$0.537895\pi$
$588$	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	$-0.685731\pi$
$593$	−9.43563e6	−1.10188	−0.550940	+	0.834545i	$0.685731\pi$
$594$	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	$-0.544753\pi$
$607$	−2.54414e6	−0.280266	−0.140133	+	0.990133i	$0.544753\pi$
$608$	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	$-0.632790\pi$
$613$	−7.53921e6	−0.810354	−0.405177	+	0.914238i	$0.632790\pi$
$614$	−9.31951e6	−0.997636
$615$	0	0
$616$	−7.95628e6	−0.844808
$617$	−1.44546e6	−0.152860	−0.0764300	−	0.997075i	$-0.524352\pi$
$617$	−1.44546e6	−0.152860	−0.0764300	+	0.997075i	$0.524352\pi$
$618$	−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	$-0.443362\pi$
$643$	3.71125e6	0.353992	0.176996	+	0.984212i	$0.443362\pi$
$644$	−2.06877e7	−1.96561
$645$	0	0
$646$	4.24040e6	0.399784
$647$	8.31438e6	0.780853	0.390426	−	0.920634i	$-0.372328\pi$
$647$	8.31438e6	0.780853	0.390426	+	0.920634i	$0.372328\pi$
$648$	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	$-0.537848\pi$
$653$	−2.58516e6	−0.237249	−0.118624	+	0.992939i	$0.537848\pi$
$654$	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	$-0.425041\pi$
$673$	5.48300e6	0.466639	0.233319	+	0.972400i	$0.425041\pi$
$674$	1.17833e7	0.999119
$675$	0	0
$676$	2.68486e6	0.225972
$677$	1.58127e7	1.32597	0.662987	−	0.748631i	$-0.269288\pi$
$677$	1.58127e7	1.32597	0.662987	+	0.748631i	$0.269288\pi$
$678$	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	$-0.872743\pi$
$683$	−2.24599e7	−1.84229	−0.921143	+	0.389225i	$0.872743\pi$
$684$	−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	$-0.276153\pi$
$727$	1.84315e7	1.29338	0.646689	+	0.762754i	$0.276153\pi$
$728$	−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	$-0.288500\pi$
$733$	1.79395e7	1.23325	0.616624	+	0.787258i	$0.288500\pi$
$734$	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	$-0.457823\pi$
$743$	3.97606e6	0.264229	0.132115	+	0.991234i	$0.457823\pi$
$744$	−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	$-0.353154\pi$
$757$	1.40367e7	0.890279	0.445139	+	0.895461i	$0.353154\pi$
$758$	−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	$-0.413468\pi$
$773$	8.92164e6	0.537027	0.268514	+	0.963276i	$0.413468\pi$
$774$	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	$-0.495033\pi$
$787$	542225.	0.0312063	0.0156032	+	0.999878i	$0.495033\pi$
$788$	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	$-0.669670\pi$
$797$	−1.82250e7	−1.01630	−0.508149	+	0.861269i	$0.669670\pi$
$798$	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	$-0.224863\pi$
$823$	2.95621e7	1.52137	0.760686	+	0.649120i	$0.224863\pi$
$824$	5.28004e7	2.70906
$825$	0	0
$826$	2.63309e7	1.34282
$827$	2.85332e7	1.45073	0.725364	−	0.688365i	$-0.241671\pi$
$827$	2.85332e7	1.45073	0.725364	+	0.688365i	$0.241671\pi$
$828$	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	$-0.649417\pi$
$853$	−1.92258e7	−0.904716	−0.452358	+	0.891836i	$0.649417\pi$
$854$	−2.64527e7	−1.24115
$855$	0	0
$856$	−9.86442e7	−4.60137
$857$	−1.98896e6	−0.0925068	−0.0462534	−	0.998930i	$-0.514728\pi$
$857$	−1.98896e6	−0.0925068	−0.0462534	+	0.998930i	$0.514728\pi$
$858$	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	$-0.245842\pi$
$863$	3.13431e7	1.43257	0.716283	+	0.697809i	$0.245842\pi$
$864$	−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	$-0.682972\pi$
$877$	−2.47672e7	−1.08737	−0.543686	+	0.839289i	$0.682972\pi$
$878$	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	$-0.313675\pi$
$883$	2.56013e7	1.10500	0.552498	+	0.833514i	$0.313675\pi$
$884$	−1.92860e6	−0.0830064
$885$	0	0
$886$	−2.37424e7	−1.01611
$887$	−5.01026e6	−0.213821	−0.106911	−	0.994269i	$-0.534096\pi$
$887$	−5.01026e6	−0.213821	−0.106911	+	0.994269i	$0.534096\pi$
$888$	−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	$-0.935734\pi$
$907$	−4.85441e7	−1.95938	−0.979688	+	0.200527i	$0.935734\pi$
$908$	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	$-0.481074\pi$
$937$	3.19406e6	0.118849	0.0594243	+	0.998233i	$0.481074\pi$
$938$	−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	$-0.366943\pi$
$947$	2.24064e7	0.811889	0.405945	+	0.913898i	$0.366943\pi$
$948$	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	$-0.414734\pi$
$953$	1.48416e7	0.529358	0.264679	+	0.964337i	$0.414734\pi$
$954$	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	$-0.323036\pi$
$967$	3.06919e7	1.05550	0.527749	+	0.849401i	$0.323036\pi$
$968$	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	$-0.640444\pi$
$977$	−2.54822e7	−0.854084	−0.427042	+	0.904232i	$0.640444\pi$
$978$	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	$-0.931224\pi$
$983$	−5.91830e7	−1.95350	−0.976749	+	0.214388i	$0.931224\pi$
$984$	−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	$-0.129069\pi$
$997$	5.76822e7	1.83783	0.918913	+	0.394461i	$0.129069\pi$
$998$	−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.j.1.1	✓	11
5.2	odd	4		325.6.b.i.274.1		22
5.3	odd	4		325.6.b.i.274.22		22
5.4	even	2		325.6.a.k.1.11	yes	11

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