LMFDB - Embedded newform 325.6.a.j.1.10

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			1.10
Root			$-9.60154$ 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)

$f(q)$	$=$	\(q+9.60154 q^{2} -25.9222 q^{3} +60.1895 q^{4} -248.893 q^{6} -181.554 q^{7} +270.662 q^{8} +428.963 q^{9} +512.944 q^{11} -1560.25 q^{12} -169.000 q^{13} -1743.19 q^{14} +672.710 q^{16} -1668.15 q^{17} +4118.70 q^{18} -464.071 q^{19} +4706.28 q^{21} +4925.05 q^{22} +2095.04 q^{23} -7016.17 q^{24} -1622.66 q^{26} -4820.57 q^{27} -10927.6 q^{28} +5935.75 q^{29} +8397.76 q^{31} -2202.14 q^{32} -13296.7 q^{33} -16016.8 q^{34} +25819.0 q^{36} +8909.35 q^{37} -4455.79 q^{38} +4380.86 q^{39} +3256.85 q^{41} +45187.5 q^{42} +5951.12 q^{43} +30873.8 q^{44} +20115.6 q^{46} +10741.1 q^{47} -17438.1 q^{48} +16154.7 q^{49} +43242.3 q^{51} -10172.0 q^{52} +39344.1 q^{53} -46284.9 q^{54} -49139.7 q^{56} +12029.8 q^{57} +56992.4 q^{58} -3940.20 q^{59} -41477.5 q^{61} +80631.4 q^{62} -77879.7 q^{63} -42670.7 q^{64} -127668. q^{66} -18589.7 q^{67} -100405. q^{68} -54308.1 q^{69} +70348.8 q^{71} +116104. q^{72} +78602.6 q^{73} +85543.4 q^{74} -27932.2 q^{76} -93126.8 q^{77} +42063.0 q^{78} -71703.3 q^{79} +20722.1 q^{81} +31270.8 q^{82} -208.877 q^{83} +283268. q^{84} +57139.9 q^{86} -153868. q^{87} +138835. q^{88} -43537.5 q^{89} +30682.6 q^{91} +126099. q^{92} -217689. q^{93} +103131. q^{94} +57084.5 q^{96} -15298.0 q^{97} +155110. q^{98} +220034. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.60154	1.69733	0.848664	−	0.528933i	$-0.177408\pi$
$2$	9.60154	1.69733	0.848664	+	0.528933i	$0.177408\pi$
$3$	−25.9222	−1.66291	−0.831456	−	0.555590i	$-0.812492\pi$
$3$	−25.9222	−1.66291	−0.831456	+	0.555590i	$0.812492\pi$
$4$	60.1895	1.88092
$5$	0	0
$5$	0	0
$6$	−248.893	−2.82251
$7$	−181.554	−1.40042	−0.700212	−	0.713935i	$-0.746911\pi$
$7$	−181.554	−1.40042	−0.700212	+	0.713935i	$0.746911\pi$
$8$	270.662	1.49521
$9$	428.963	1.76528
$10$	0	0
$11$	512.944	1.27817	0.639084	−	0.769137i	$-0.279313\pi$
$11$	512.944	1.27817	0.639084	+	0.769137i	$0.279313\pi$
$12$	−1560.25	−3.12781
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	−1743.19	−2.37698
$15$	0	0
$16$	672.710	0.656943
$17$	−1668.15	−1.39995	−0.699977	−	0.714165i	$-0.746807\pi$
$17$	−1668.15	−1.39995	−0.699977	+	0.714165i	$0.746807\pi$
$18$	4118.70	2.99626
$19$	−464.071	−0.294917	−0.147459	−	0.989068i	$-0.547109\pi$
$19$	−464.071	−0.294917	−0.147459	+	0.989068i	$0.547109\pi$
$20$	0	0
$21$	4706.28	2.32878
$22$	4925.05	2.16947
$23$	2095.04	0.825795	0.412897	−	0.910778i	$-0.364517\pi$
$23$	2095.04	0.825795	0.412897	+	0.910778i	$0.364517\pi$
$24$	−7016.17	−2.48641
$25$	0	0
$26$	−1622.66	−0.470754
$27$	−4820.57	−1.27259
$28$	−10927.6	−2.63409
$29$	5935.75	1.31063	0.655316	−	0.755355i	$-0.272535\pi$
$29$	5935.75	1.31063	0.655316	+	0.755355i	$0.272535\pi$
$30$	0	0
$31$	8397.76	1.56949	0.784746	−	0.619817i	$-0.212793\pi$
$31$	8397.76	1.56949	0.784746	+	0.619817i	$0.212793\pi$
$32$	−2202.14	−0.380164
$33$	−13296.7	−2.12548
$34$	−16016.8	−2.37618
$35$	0	0
$36$	25819.0	3.32035
$37$	8909.35	1.06990	0.534948	−	0.844885i	$-0.320331\pi$
$37$	8909.35	1.06990	0.534948	+	0.844885i	$0.320331\pi$
$38$	−4455.79	−0.500571
$39$	4380.86	0.461209
$40$	0	0
$41$	3256.85	0.302579	0.151289	−	0.988490i	$-0.451657\pi$
$41$	3256.85	0.302579	0.151289	+	0.988490i	$0.451657\pi$
$42$	45187.5	3.95271
$43$	5951.12	0.490826	0.245413	−	0.969419i	$-0.421076\pi$
$43$	5951.12	0.490826	0.245413	+	0.969419i	$0.421076\pi$
$44$	30873.8	2.40413
$45$	0	0
$46$	20115.6	1.40164
$47$	10741.1	0.709255	0.354628	−	0.935008i	$-0.384608\pi$
$47$	10741.1	0.709255	0.354628	+	0.935008i	$0.384608\pi$
$48$	−17438.1	−1.09244
$49$	16154.7	0.961190
$50$	0	0
$51$	43242.3	2.32800
$52$	−10172.0	−0.521674
$53$	39344.1	1.92393	0.961967	−	0.273167i	$-0.0880710\pi$
$53$	39344.1	1.92393	0.961967	+	0.273167i	$0.0880710\pi$
$54$	−46284.9	−2.16001
$55$	0	0
$56$	−49139.7	−2.09393
$57$	12029.8	0.490422
$58$	56992.4	2.22457
$59$	−3940.20	−0.147363	−0.0736815	−	0.997282i	$-0.523475\pi$
$59$	−3940.20	−0.147363	−0.0736815	+	0.997282i	$0.523475\pi$
$60$	0	0
$61$	−41477.5	−1.42721	−0.713605	−	0.700548i	$-0.752939\pi$
$61$	−41477.5	−1.42721	−0.713605	+	0.700548i	$0.752939\pi$
$62$	80631.4	2.66394
$63$	−77879.7	−2.47214
$64$	−42670.7	−1.30221
$65$	0	0
$66$	−127668.	−3.60764
$67$	−18589.7	−0.505923	−0.252961	−	0.967476i	$-0.581405\pi$
$67$	−18589.7	−0.505923	−0.252961	+	0.967476i	$0.581405\pi$
$68$	−100405.	−2.63320
$69$	−54308.1	−1.37322
$70$	0	0
$71$	70348.8	1.65619	0.828096	−	0.560586i	$-0.189424\pi$
$71$	70348.8	1.65619	0.828096	+	0.560586i	$0.189424\pi$
$72$	116104.	2.63947
$73$	78602.6	1.72635	0.863176	−	0.504902i	$-0.168471\pi$
$73$	78602.6	1.72635	0.863176	+	0.504902i	$0.168471\pi$
$74$	85543.4	1.81596
$75$	0	0
$76$	−27932.2	−0.554716
$77$	−93126.8	−1.78998
$78$	42063.0	0.782823
$79$	−71703.3	−1.29262	−0.646310	−	0.763075i	$-0.723689\pi$
$79$	−71703.3	−1.29262	−0.646310	+	0.763075i	$0.723689\pi$
$80$	0	0
$81$	20722.1	0.350931
$82$	31270.8	0.513575
$83$	−208.877	−0.00332808	−0.00166404	−	0.999999i	$-0.500530\pi$
$83$	−208.877	−0.00332808	−0.00166404	+	0.999999i	$0.500530\pi$
$84$	283268.	4.38026
$85$	0	0
$86$	57139.9	0.833093
$87$	−153868.	−2.17947
$88$	138835.	1.91113
$89$	−43537.5	−0.582624	−0.291312	−	0.956628i	$-0.594092\pi$
$89$	−43537.5	−0.582624	−0.291312	+	0.956628i	$0.594092\pi$
$90$	0	0
$91$	30682.6	0.388408
$92$	126099.	1.55325
$93$	−217689.	−2.60993
$94$	103131.	1.20384
$95$	0	0
$96$	57084.5	0.632179
$97$	−15298.0	−0.165084	−0.0825419	−	0.996588i	$-0.526304\pi$
$97$	−15298.0	−0.165084	−0.0825419	+	0.996588i	$0.526304\pi$
$98$	155110.	1.63145
$99$	220034.	2.25632
$100$	0	0
$101$	2600.25	0.0253636	0.0126818	−	0.999920i	$-0.495963\pi$
$101$	2600.25	0.0253636	0.0126818	+	0.999920i	$0.495963\pi$
$102$	415193.	3.95138
$103$	210878.	1.95857	0.979283	−	0.202497i	$-0.0649056\pi$
$103$	210878.	1.95857	0.979283	+	0.202497i	$0.0649056\pi$
$104$	−45741.9	−0.414697
$105$	0	0
$106$	377764.	3.26555
$107$	−107005.	−0.903531	−0.451765	−	0.892137i	$-0.649206\pi$
$107$	−107005.	−0.903531	−0.451765	+	0.892137i	$0.649206\pi$
$108$	−290148.	−2.39365
$109$	151212.	1.21904	0.609522	−	0.792769i	$-0.291362\pi$
$109$	151212.	1.21904	0.609522	+	0.792769i	$0.291362\pi$
$110$	0	0
$111$	−230950.	−1.77914
$112$	−122133.	−0.920000
$113$	−176779.	−1.30237	−0.651186	−	0.758918i	$-0.725728\pi$
$113$	−176779.	−1.30237	−0.651186	+	0.758918i	$0.725728\pi$
$114$	115504.	0.832407
$115$	0	0
$116$	357270.	2.46520
$117$	−72494.7	−0.489600
$118$	−37832.0	−0.250123
$119$	302860.	1.96053
$120$	0	0
$121$	102060.	0.633715
$122$	−398248.	−2.42244
$123$	−84424.9	−0.503162
$124$	505457.	2.95209
$125$	0	0
$126$	−747765.	−4.19603
$127$	3379.52	0.0185929	0.00929643	−	0.999957i	$-0.497041\pi$
$127$	3379.52	0.0185929	0.00929643	+	0.999957i	$0.497041\pi$
$128$	−339235.	−1.83011
$129$	−154266.	−0.816201
$130$	0	0
$131$	−165563.	−0.842915	−0.421458	−	0.906848i	$-0.638481\pi$
$131$	−165563.	−0.842915	−0.421458	+	0.906848i	$0.638481\pi$
$132$	−800319.	−3.99787
$133$	84253.8	0.413010
$134$	−178489.	−0.858717
$135$	0	0
$136$	−451507.	−2.09323
$137$	−54105.0	−0.246284	−0.123142	−	0.992389i	$-0.539297\pi$
$137$	−54105.0	−0.246284	−0.123142	+	0.992389i	$0.539297\pi$
$138$	−521441.	−2.33081
$139$	−248178.	−1.08950	−0.544749	−	0.838599i	$-0.683375\pi$
$139$	−248178.	−1.08950	−0.544749	+	0.838599i	$0.683375\pi$
$140$	0	0
$141$	−278432.	−1.17943
$142$	675457.	2.81110
$143$	−86687.5	−0.354500
$144$	288567.	1.15969
$145$	0	0
$146$	754705.	2.93019
$147$	−418767.	−1.59838
$148$	536249.	2.01239
$149$	102637.	0.378736	0.189368	−	0.981906i	$-0.439356\pi$
$149$	102637.	0.378736	0.189368	+	0.981906i	$0.439356\pi$
$150$	0	0
$151$	513812.	1.83384	0.916921	−	0.399068i	$-0.130666\pi$
$151$	513812.	1.83384	0.916921	+	0.399068i	$0.130666\pi$
$152$	−125606.	−0.440964
$153$	−715576.	−2.47131
$154$	−894161.	−3.03818
$155$	0	0
$156$	263682.	0.867498
$157$	276514.	0.895300	0.447650	−	0.894209i	$-0.352261\pi$
$157$	276514.	0.895300	0.447650	+	0.894209i	$0.352261\pi$
$158$	−688461.	−2.19400
$159$	−1.01989e6	−3.19933
$160$	0	0
$161$	−380362.	−1.15646
$162$	198964.	0.595644
$163$	−278424.	−0.820801	−0.410401	−	0.911905i	$-0.634611\pi$
$163$	−278424.	−0.820801	−0.410401	+	0.911905i	$0.634611\pi$
$164$	196028.	0.569127
$165$	0	0
$166$	−2005.54	−0.00564885
$167$	407177.	1.12978	0.564888	−	0.825167i	$-0.308919\pi$
$167$	407177.	1.12978	0.564888	+	0.825167i	$0.308919\pi$
$168$	1.27381e6	3.48203
$169$	28561.0	0.0769231
$170$	0	0
$171$	−199069.	−0.520611
$172$	358195.	0.923206
$173$	−49123.8	−0.124789	−0.0623946	−	0.998052i	$-0.519874\pi$
$173$	−49123.8	−0.124789	−0.0623946	+	0.998052i	$0.519874\pi$
$174$	−1.47737e6	−3.69927
$175$	0	0
$176$	345062.	0.839684
$177$	102139.	0.245052
$178$	−418026.	−0.988903
$179$	386317.	0.901179	0.450590	−	0.892731i	$-0.351214\pi$
$179$	386317.	0.901179	0.450590	+	0.892731i	$0.351214\pi$
$180$	0	0
$181$	−218966.	−0.496799	−0.248400	−	0.968658i	$-0.579905\pi$
$181$	−218966.	−0.496799	−0.248400	+	0.968658i	$0.579905\pi$
$182$	294600.	0.659256
$183$	1.07519e6	2.37333
$184$	567047.	1.23474
$185$	0	0
$186$	−2.09015e6	−4.42991
$187$	−855670.	−1.78938
$188$	646499.	1.33405
$189$	875192.	1.78217
$190$	0	0
$191$	277244.	0.549894	0.274947	−	0.961459i	$-0.411340\pi$
$191$	277244.	0.549894	0.274947	+	0.961459i	$0.411340\pi$
$192$	1.10612e6	2.16545
$193$	−310407.	−0.599844	−0.299922	−	0.953964i	$-0.596961\pi$
$193$	−310407.	−0.599844	−0.299922	+	0.953964i	$0.596961\pi$
$194$	−146884.	−0.280201
$195$	0	0
$196$	972344.	1.80792
$197$	−516120.	−0.947513	−0.473757	−	0.880656i	$-0.657102\pi$
$197$	−516120.	−0.947513	−0.473757	+	0.880656i	$0.657102\pi$
$198$	2.11266e6	3.82972
$199$	647020.	1.15820	0.579102	−	0.815255i	$-0.303403\pi$
$199$	647020.	1.15820	0.579102	+	0.815255i	$0.303403\pi$
$200$	0	0
$201$	481886.	0.841306
$202$	24966.4	0.0430504
$203$	−1.07766e6	−1.83544
$204$	2.60273e6	4.37879
$205$	0	0
$206$	2.02475e6	3.32433
$207$	898693.	1.45776
$208$	−113688.	−0.182203
$209$	−238042.	−0.376954
$210$	0	0
$211$	132130.	0.204312	0.102156	−	0.994768i	$-0.467426\pi$
$211$	132130.	0.204312	0.102156	+	0.994768i	$0.467426\pi$
$212$	2.36810e6	3.61877
$213$	−1.82360e6	−2.75410
$214$	−1.02741e6	−1.53359
$215$	0	0
$216$	−1.30475e6	−1.90279
$217$	−1.52464e6	−2.19796
$218$	1.45186e6	2.06912
$219$	−2.03756e6	−2.87077
$220$	0	0
$221$	281918.	0.388278
$222$	−2.21748e6	−3.01979
$223$	919984.	1.23885	0.619424	−	0.785057i	$-0.287366\pi$
$223$	919984.	1.23885	0.619424	+	0.785057i	$0.287366\pi$
$224$	399807.	0.532391
$225$	0	0
$226$	−1.69735e6	−2.21055
$227$	30962.8	0.0398819	0.0199409	−	0.999801i	$-0.493652\pi$
$227$	30962.8	0.0398819	0.0199409	+	0.999801i	$0.493652\pi$
$228$	724065.	0.922445
$229$	163086.	0.205508	0.102754	−	0.994707i	$-0.467235\pi$
$229$	163086.	0.205508	0.102754	+	0.994707i	$0.467235\pi$
$230$	0	0
$231$	2.41406e6	2.97658
$232$	1.60658e6	1.95967
$233$	−1.19712e6	−1.44460	−0.722298	−	0.691582i	$-0.756914\pi$
$233$	−1.19712e6	−1.44460	−0.722298	+	0.691582i	$0.756914\pi$
$234$	−696060.	−0.831012
$235$	0	0
$236$	−237159.	−0.277178
$237$	1.85871e6	2.14952
$238$	2.90792e6	3.32766
$239$	−769561.	−0.871462	−0.435731	−	0.900077i	$-0.643510\pi$
$239$	−769561.	−0.871462	−0.435731	+	0.900077i	$0.643510\pi$
$240$	0	0
$241$	−850451.	−0.943206	−0.471603	−	0.881811i	$-0.656324\pi$
$241$	−850451.	−0.943206	−0.471603	+	0.881811i	$0.656324\pi$
$242$	979937.	1.07562
$243$	634236.	0.689025
$244$	−2.49651e6	−2.68447
$245$	0	0
$246$	−810609.	−0.854031
$247$	78428.0	0.0817954
$248$	2.27296e6	2.34672
$249$	5414.55	0.00553431
$250$	0	0
$251$	992979.	0.994846	0.497423	−	0.867508i	$-0.334280\pi$
$251$	992979.	0.994846	0.497423	+	0.867508i	$0.334280\pi$
$252$	−4.68754e6	−4.64990
$253$	1.07464e6	1.05550
$254$	32448.6	0.0315582
$255$	0	0
$256$	−1.89172e6	−1.80408
$257$	−1.29318e6	−1.22131	−0.610655	−	0.791897i	$-0.709094\pi$
$257$	−1.29318e6	−1.22131	−0.610655	+	0.791897i	$0.709094\pi$
$258$	−1.48120e6	−1.38536
$259$	−1.61752e6	−1.49831
$260$	0	0
$261$	2.54622e6	2.31363
$262$	−1.58965e6	−1.43070
$263$	1.69375e6	1.50994	0.754972	−	0.655757i	$-0.227650\pi$
$263$	1.69375e6	1.50994	0.754972	+	0.655757i	$0.227650\pi$
$264$	−3.59890e6	−3.17805
$265$	0	0
$266$	808966.	0.701013
$267$	1.12859e6	0.968852
$268$	−1.11890e6	−0.951601
$269$	−857080.	−0.722172	−0.361086	−	0.932532i	$-0.617594\pi$
$269$	−857080.	−0.722172	−0.361086	+	0.932532i	$0.617594\pi$
$270$	0	0
$271$	1.66147e6	1.37426	0.687130	−	0.726534i	$-0.258870\pi$
$271$	1.66147e6	1.37426	0.687130	+	0.726534i	$0.258870\pi$
$272$	−1.12218e6	−0.919691
$273$	−795361.	−0.645889
$274$	−519491.	−0.418024
$275$	0	0
$276$	−3.26877e6	−2.58293
$277$	−2.15375e6	−1.68654	−0.843269	−	0.537491i	$-0.819372\pi$
$277$	−2.15375e6	−1.68654	−0.843269	+	0.537491i	$0.819372\pi$
$278$	−2.38289e6	−1.84924
$279$	3.60233e6	2.77059
$280$	0	0
$281$	−547631.	−0.413735	−0.206868	−	0.978369i	$-0.566327\pi$
$281$	−547631.	−0.413735	−0.206868	+	0.978369i	$0.566327\pi$
$282$	−2.67338e6	−2.00188
$283$	609080.	0.452073	0.226036	−	0.974119i	$-0.427423\pi$
$283$	609080.	0.452073	0.226036	+	0.974119i	$0.427423\pi$
$284$	4.23426e6	3.11517
$285$	0	0
$286$	−832333.	−0.601703
$287$	−591293.	−0.423739
$288$	−944638.	−0.671095
$289$	1.36288e6	0.959874
$290$	0	0
$291$	396558.	0.274520
$292$	4.73105e6	3.24713
$293$	−927787.	−0.631363	−0.315682	−	0.948865i	$-0.602233\pi$
$293$	−927787.	−0.631363	−0.315682	+	0.948865i	$0.602233\pi$
$294$	−4.02080e6	−2.71297
$295$	0	0
$296$	2.41142e6	1.59972
$297$	−2.47268e6	−1.62659
$298$	985469.	0.642839
$299$	−354061.	−0.229034
$300$	0	0
$301$	−1.08045e6	−0.687365
$302$	4.93339e6	3.11263
$303$	−67404.3	−0.0421775
$304$	−312185.	−0.193744
$305$	0	0
$306$	−6.87063e6	−4.19462
$307$	2.39073e6	1.44772	0.723859	−	0.689948i	$-0.242367\pi$
$307$	2.39073e6	1.44772	0.723859	+	0.689948i	$0.242367\pi$
$308$	−5.60526e6	−3.36681
$309$	−5.46643e6	−3.25692
$310$	0	0
$311$	−1.27080e6	−0.745032	−0.372516	−	0.928026i	$-0.621505\pi$
$311$	−1.27080e6	−0.745032	−0.372516	+	0.928026i	$0.621505\pi$
$312$	1.18573e6	0.689605
$313$	1.69293e6	0.976738	0.488369	−	0.872637i	$-0.337592\pi$
$313$	1.69293e6	0.976738	0.488369	+	0.872637i	$0.337592\pi$
$314$	2.65496e6	1.51962
$315$	0	0
$316$	−4.31578e6	−2.43132
$317$	958135.	0.535523	0.267762	−	0.963485i	$-0.413716\pi$
$317$	958135.	0.535523	0.267762	+	0.963485i	$0.413716\pi$
$318$	−9.79249e6	−5.43032
$319$	3.04471e6	1.67521
$320$	0	0
$321$	2.77380e6	1.50249
$322$	−3.65205e6	−1.96290
$323$	774142.	0.412871
$324$	1.24725e6	0.660073
$325$	0	0
$326$	−2.67330e6	−1.39317
$327$	−3.91975e6	−2.02716
$328$	881507.	0.452419
$329$	−1.95008e6	−0.993259
$330$	0	0
$331$	2.29139e6	1.14955	0.574777	−	0.818310i	$-0.305089\pi$
$331$	2.29139e6	1.14955	0.574777	+	0.818310i	$0.305089\pi$
$332$	−12572.2	−0.00625986
$333$	3.82178e6	1.88866
$334$	3.90953e6	1.91760
$335$	0	0
$336$	3.16596e6	1.52988
$337$	1.20806e6	0.579446	0.289723	−	0.957110i	$-0.406437\pi$
$337$	1.20806e6	0.579446	0.289723	+	0.957110i	$0.406437\pi$
$338$	274229.	0.130564
$339$	4.58251e6	2.16573
$340$	0	0
$341$	4.30758e6	2.00608
$342$	−1.91137e6	−0.883648
$343$	118424.	0.0543505
$344$	1.61074e6	0.733889
$345$	0	0
$346$	−471664.	−0.211808
$347$	4.27369e6	1.90537	0.952684	−	0.303962i	$-0.0983097\pi$
$347$	4.27369e6	1.90537	0.952684	+	0.303962i	$0.0983097\pi$
$348$	−9.26124e6	−4.09941
$349$	−1.49638e6	−0.657625	−0.328812	−	0.944395i	$-0.606648\pi$
$349$	−1.49638e6	−0.657625	−0.328812	+	0.944395i	$0.606648\pi$
$350$	0	0
$351$	814677.	0.352954
$352$	−1.12958e6	−0.485914
$353$	−730249.	−0.311914	−0.155957	−	0.987764i	$-0.549846\pi$
$353$	−730249.	−0.311914	−0.155957	+	0.987764i	$0.549846\pi$
$354$	980690.	0.415933
$355$	0	0
$356$	−2.62050e6	−1.09587
$357$	−7.85080e6	−3.26019
$358$	3.70924e6	1.52960
$359$	1.04399e6	0.427522	0.213761	−	0.976886i	$-0.431429\pi$
$359$	1.04399e6	0.427522	0.213761	+	0.976886i	$0.431429\pi$
$360$	0	0
$361$	−2.26074e6	−0.913024
$362$	−2.10241e6	−0.843231
$363$	−2.64564e6	−1.05381
$364$	1.84677e6	0.730565
$365$	0	0
$366$	1.03235e7	4.02831
$367$	75157.4	0.0291277	0.0145639	−	0.999894i	$-0.495364\pi$
$367$	75157.4	0.0291277	0.0145639	+	0.999894i	$0.495364\pi$
$368$	1.40935e6	0.542500
$369$	1.39707e6	0.534136
$370$	0	0
$371$	−7.14307e6	−2.69432
$372$	−1.31026e7	−4.90907
$373$	1.44619e6	0.538212	0.269106	−	0.963111i	$-0.413272\pi$
$373$	1.44619e6	0.538212	0.269106	+	0.963111i	$0.413272\pi$
$374$	−8.21574e6	−3.03716
$375$	0	0
$376$	2.90720e6	1.06049
$377$	−1.00314e6	−0.363504
$378$	8.40319e6	3.02493
$379$	291357.	0.104190	0.0520951	−	0.998642i	$-0.483410\pi$
$379$	291357.	0.104190	0.0520951	+	0.998642i	$0.483410\pi$
$380$	0	0
$381$	−87604.8	−0.0309183
$382$	2.66197e6	0.933350
$383$	3.40227e6	1.18515	0.592573	−	0.805517i	$-0.298112\pi$
$383$	3.40227e6	1.18515	0.592573	+	0.805517i	$0.298112\pi$
$384$	8.79374e6	3.04331
$385$	0	0
$386$	−2.98038e6	−1.01813
$387$	2.55281e6	0.866445
$388$	−920777.	−0.310510
$389$	1.64309e6	0.550537	0.275268	−	0.961367i	$-0.411233\pi$
$389$	1.64309e6	0.550537	0.275268	+	0.961367i	$0.411233\pi$
$390$	0	0
$391$	−3.49485e6	−1.15608
$392$	4.37247e6	1.43718
$393$	4.29175e6	1.40169
$394$	−4.95555e6	−1.60824
$395$	0	0
$396$	1.32437e7	4.24397
$397$	2.47328e6	0.787585	0.393792	−	0.919199i	$-0.371163\pi$
$397$	2.47328e6	0.787585	0.393792	+	0.919199i	$0.371163\pi$
$398$	6.21239e6	1.96585
$399$	−2.18405e6	−0.686799
$400$	0	0
$401$	4.41469e6	1.37100	0.685502	−	0.728071i	$-0.259583\pi$
$401$	4.41469e6	1.37100	0.685502	+	0.728071i	$0.259583\pi$
$402$	4.62684e6	1.42797
$403$	−1.41922e6	−0.435299
$404$	156508.	0.0477070
$405$	0	0
$406$	−1.03472e7	−3.11535
$407$	4.56999e6	1.36751
$408$	1.17041e7	3.48086
$409$	−2.67344e6	−0.790244	−0.395122	−	0.918629i	$-0.629298\pi$
$409$	−2.67344e6	−0.790244	−0.395122	+	0.918629i	$0.629298\pi$
$410$	0	0
$411$	1.40252e6	0.409549
$412$	1.26926e7	3.68391
$413$	715358.	0.206371
$414$	8.62883e6	2.47429
$415$	0	0
$416$	372162.	0.105439
$417$	6.43334e6	1.81174
$418$	−2.28557e6	−0.639815
$419$	2.27577e6	0.633277	0.316639	−	0.948546i	$-0.397446\pi$
$419$	2.27577e6	0.633277	0.316639	+	0.948546i	$0.397446\pi$
$420$	0	0
$421$	4.79147e6	1.31754	0.658770	−	0.752345i	$-0.271077\pi$
$421$	4.79147e6	1.31754	0.658770	+	0.752345i	$0.271077\pi$
$422$	1.26865e6	0.346785
$423$	4.60751e6	1.25203
$424$	1.06490e7	2.87669
$425$	0	0
$426$	−1.75093e7	−4.67462
$427$	7.53039e6	1.99870
$428$	−6.44055e6	−1.69947
$429$	2.24714e6	0.589503
$430$	0	0
$431$	−2.09885e6	−0.544238	−0.272119	−	0.962264i	$-0.587725\pi$
$431$	−2.09885e6	−0.544238	−0.272119	+	0.962264i	$0.587725\pi$
$432$	−3.24285e6	−0.836021
$433$	2.53735e6	0.650370	0.325185	−	0.945650i	$-0.394573\pi$
$433$	2.53735e6	0.650370	0.325185	+	0.945650i	$0.394573\pi$
$434$	−1.46389e7	−3.73065
$435$	0	0
$436$	9.10135e6	2.29292
$437$	−972246.	−0.243541
$438$	−1.95637e7	−4.87264
$439$	3.67042e6	0.908979	0.454490	−	0.890752i	$-0.349822\pi$
$439$	3.67042e6	0.908979	0.454490	+	0.890752i	$0.349822\pi$
$440$	0	0
$441$	6.92977e6	1.69677
$442$	2.70685e6	0.659034
$443$	−2.32270e6	−0.562321	−0.281161	−	0.959661i	$-0.590719\pi$
$443$	−2.32270e6	−0.562321	−0.281161	+	0.959661i	$0.590719\pi$
$444$	−1.39008e7	−3.34643
$445$	0	0
$446$	8.83325e6	2.10273
$447$	−2.66057e6	−0.629805
$448$	7.74702e6	1.82364
$449$	−4.30759e6	−1.00837	−0.504183	−	0.863597i	$-0.668206\pi$
$449$	−4.30759e6	−1.00837	−0.504183	+	0.863597i	$0.668206\pi$
$450$	0	0
$451$	1.67058e6	0.386747
$452$	−1.06403e7	−2.44966
$453$	−1.33192e7	−3.04952
$454$	297290.	0.0676926
$455$	0	0
$456$	3.25600e6	0.733285
$457$	1.14361e6	0.256145	0.128073	−	0.991765i	$-0.459121\pi$
$457$	1.14361e6	0.256145	0.128073	+	0.991765i	$0.459121\pi$
$458$	1.56588e6	0.348814
$459$	8.04146e6	1.78157
$460$	0	0
$461$	−3.73288e6	−0.818071	−0.409036	−	0.912518i	$-0.634135\pi$
$461$	−3.73288e6	−0.818071	−0.409036	+	0.912518i	$0.634135\pi$
$462$	2.31786e7	5.05223
$463$	4.46756e6	0.968540	0.484270	−	0.874919i	$-0.339085\pi$
$463$	4.46756e6	0.968540	0.484270	+	0.874919i	$0.339085\pi$
$464$	3.99304e6	0.861011
$465$	0	0
$466$	−1.14942e7	−2.45195
$467$	−5.73689e6	−1.21726	−0.608632	−	0.793453i	$-0.708281\pi$
$467$	−5.73689e6	−1.21726	−0.608632	+	0.793453i	$0.708281\pi$
$468$	−4.36342e6	−0.920900
$469$	3.37502e6	0.708507
$470$	0	0
$471$	−7.16787e6	−1.48881
$472$	−1.06646e6	−0.220339
$473$	3.05259e6	0.627359
$474$	1.78465e7	3.64843
$475$	0	0
$476$	1.82290e7	3.68761
$477$	1.68772e7	3.39628
$478$	−7.38897e6	−1.47916
$479$	−8.44282e6	−1.68131	−0.840657	−	0.541567i	$-0.817831\pi$
$479$	−8.44282e6	−1.68131	−0.840657	+	0.541567i	$0.817831\pi$
$480$	0	0
$481$	−1.50568e6	−0.296736
$482$	−8.16563e6	−1.60093
$483$	9.85982e6	1.92310
$484$	6.14297e6	1.19197
$485$	0	0
$486$	6.08964e6	1.16950
$487$	−2.30080e6	−0.439599	−0.219799	−	0.975545i	$-0.570540\pi$
$487$	−2.30080e6	−0.439599	−0.219799	+	0.975545i	$0.570540\pi$
$488$	−1.12264e7	−2.13398
$489$	7.21738e6	1.36492
$490$	0	0
$491$	−1.83374e6	−0.343269	−0.171635	−	0.985161i	$-0.554905\pi$
$491$	−1.83374e6	−0.343269	−0.171635	+	0.985161i	$0.554905\pi$
$492$	−5.08149e6	−0.946408
$493$	−9.90176e6	−1.83483
$494$	753029.	0.138834
$495$	0	0
$496$	5.64926e6	1.03107
$497$	−1.27721e7	−2.31937
$498$	51988.0	0.00939354
$499$	−1.65708e6	−0.297916	−0.148958	−	0.988844i	$-0.547592\pi$
$499$	−1.65708e6	−0.297916	−0.148958	+	0.988844i	$0.547592\pi$
$500$	0	0
$501$	−1.05550e7	−1.87872
$502$	9.53412e6	1.68858
$503$	674839.	0.118927	0.0594634	−	0.998230i	$-0.481061\pi$
$503$	674839.	0.118927	0.0594634	+	0.998230i	$0.481061\pi$
$504$	−2.10791e7	−3.69637
$505$	0	0
$506$	1.03182e7	1.79154
$507$	−740365.	−0.127916
$508$	203412.	0.0349717
$509$	214603.	0.0367148	0.0183574	−	0.999831i	$-0.494156\pi$
$509$	214603.	0.0367148	0.0183574	+	0.999831i	$0.494156\pi$
$510$	0	0
$511$	−1.42706e7	−2.41763
$512$	−7.30787e6	−1.23202
$513$	2.23709e6	0.375310
$514$	−1.24165e7	−2.07296
$515$	0	0
$516$	−9.28522e6	−1.53521
$517$	5.50956e6	0.906548
$518$	−1.55307e7	−2.54312
$519$	1.27340e6	0.207513
$520$	0	0
$521$	9.75675e6	1.57475	0.787373	−	0.616476i	$-0.211440\pi$
$521$	9.75675e6	1.57475	0.787373	+	0.616476i	$0.211440\pi$
$522$	2.44476e7	3.92699
$523$	−1.41439e6	−0.226107	−0.113054	−	0.993589i	$-0.536063\pi$
$523$	−1.41439e6	−0.226107	−0.113054	+	0.993589i	$0.536063\pi$
$524$	−9.96512e6	−1.58546
$525$	0	0
$526$	1.62626e7	2.56287
$527$	−1.40088e7	−2.19722
$528$	−8.94479e6	−1.39632
$529$	−2.04716e6	−0.318063
$530$	0	0
$531$	−1.69020e6	−0.260137
$532$	5.07119e6	0.776839
$533$	−550408.	−0.0839203
$534$	1.08362e7	1.64446
$535$	0	0
$536$	−5.03152e6	−0.756462
$537$	−1.00142e7	−1.49858
$538$	−8.22929e6	−1.22576
$539$	8.28647e6	1.22856
$540$	0	0
$541$	6.38226e6	0.937522	0.468761	−	0.883325i	$-0.344700\pi$
$541$	6.38226e6	0.937522	0.468761	+	0.883325i	$0.344700\pi$
$542$	1.59527e7	2.33257
$543$	5.67610e6	0.826134
$544$	3.67352e6	0.532212
$545$	0	0
$546$	−7.63669e6	−1.09628
$547$	−6.98550e6	−0.998227	−0.499113	−	0.866537i	$-0.666341\pi$
$547$	−6.98550e6	−0.998227	−0.499113	+	0.866537i	$0.666341\pi$
$548$	−3.25655e6	−0.463241
$549$	−1.77923e7	−2.51943
$550$	0	0
$551$	−2.75461e6	−0.386528
$552$	−1.46991e7	−2.05326
$553$	1.30180e7	1.81022
$554$	−2.06793e7	−2.86261
$555$	0	0
$556$	−1.49377e7	−2.04926
$557$	−8.50622e6	−1.16171	−0.580856	−	0.814006i	$-0.697282\pi$
$557$	−8.50622e6	−1.16171	−0.580856	+	0.814006i	$0.697282\pi$
$558$	3.45879e7	4.70260
$559$	−1.00574e6	−0.136131
$560$	0	0
$561$	2.21809e7	2.97558
$562$	−5.25810e6	−0.702244
$563$	5.22994e6	0.695386	0.347693	−	0.937608i	$-0.386965\pi$
$563$	5.22994e6	0.695386	0.347693	+	0.937608i	$0.386965\pi$
$564$	−1.67587e7	−2.21841
$565$	0	0
$566$	5.84810e6	0.767315
$567$	−3.76217e6	−0.491452
$568$	1.90408e7	2.47636
$569$	1.12412e7	1.45556	0.727781	−	0.685809i	$-0.240552\pi$
$569$	1.12412e7	1.45556	0.727781	+	0.685809i	$0.240552\pi$
$570$	0	0
$571$	−3.42903e6	−0.440130	−0.220065	−	0.975485i	$-0.570627\pi$
$571$	−3.42903e6	−0.440130	−0.220065	+	0.975485i	$0.570627\pi$
$572$	−5.21768e6	−0.666787
$573$	−7.18679e6	−0.914426
$574$	−5.67732e6	−0.719224
$575$	0	0
$576$	−1.83041e7	−2.29876
$577$	−1.39888e7	−1.74920	−0.874600	−	0.484845i	$-0.838876\pi$
$577$	−1.39888e7	−1.74920	−0.874600	+	0.484845i	$0.838876\pi$
$578$	1.30858e7	1.62922
$579$	8.04645e6	0.997488
$580$	0	0
$581$	37922.3	0.00466073
$582$	3.80756e6	0.465950
$583$	2.01813e7	2.45911
$584$	2.12747e7	2.58126
$585$	0	0
$586$	−8.90818e6	−1.07163
$587$	2.19504e6	0.262934	0.131467	−	0.991321i	$-0.458031\pi$
$587$	2.19504e6	0.262934	0.131467	+	0.991321i	$0.458031\pi$
$588$	−2.52053e7	−3.00642
$589$	−3.89716e6	−0.462871
$590$	0	0
$591$	1.33790e7	1.57563
$592$	5.99340e6	0.702861
$593$	1.41425e6	0.165154	0.0825772	−	0.996585i	$-0.473685\pi$
$593$	1.41425e6	0.165154	0.0825772	+	0.996585i	$0.473685\pi$
$594$	−2.37416e7	−2.76085
$595$	0	0
$596$	6.17765e6	0.712373
$597$	−1.67722e7	−1.92599
$598$	−3.39953e6	−0.388746
$599$	−9.66661e6	−1.10080	−0.550398	−	0.834902i	$-0.685524\pi$
$599$	−9.66661e6	−1.10080	−0.550398	+	0.834902i	$0.685524\pi$
$600$	0	0
$601$	−8.23263e6	−0.929721	−0.464860	−	0.885384i	$-0.653895\pi$
$601$	−8.23263e6	−0.929721	−0.464860	+	0.885384i	$0.653895\pi$
$602$	−1.03740e7	−1.16668
$603$	−7.97427e6	−0.893095
$604$	3.09261e7	3.44931
$605$	0	0
$606$	−647185.	−0.0715891
$607$	7.61203e6	0.838549	0.419275	−	0.907859i	$-0.362284\pi$
$607$	7.61203e6	0.838549	0.419275	+	0.907859i	$0.362284\pi$
$608$	1.02195e6	0.112117
$609$	2.79353e7	3.05218
$610$	0	0
$611$	−1.81524e6	−0.196712
$612$	−4.30702e7	−4.64834
$613$	1.04544e7	1.12369	0.561844	−	0.827243i	$-0.310092\pi$
$613$	1.04544e7	1.12369	0.561844	+	0.827243i	$0.310092\pi$
$614$	2.29546e7	2.45725
$615$	0	0
$616$	−2.52059e7	−2.67640
$617$	−8.78600e6	−0.929134	−0.464567	−	0.885538i	$-0.653790\pi$
$617$	−8.78600e6	−0.929134	−0.464567	+	0.885538i	$0.653790\pi$
$618$	−5.24861e7	−5.52807
$619$	8.05994e6	0.845484	0.422742	−	0.906250i	$-0.361068\pi$
$619$	8.05994e6	0.845484	0.422742	+	0.906250i	$0.361068\pi$
$620$	0	0
$621$	−1.00993e7	−1.05090
$622$	−1.22016e7	−1.26456
$623$	7.90438e6	0.815921
$624$	2.94705e6	0.302988
$625$	0	0
$626$	1.62547e7	1.65784
$627$	6.17059e6	0.626842
$628$	1.66433e7	1.68399
$629$	−1.48622e7	−1.49781
$630$	0	0
$631$	1.42505e6	0.142481	0.0712404	−	0.997459i	$-0.477304\pi$
$631$	1.42505e6	0.142481	0.0712404	+	0.997459i	$0.477304\pi$
$632$	−1.94074e7	−1.93274
$633$	−3.42510e6	−0.339754
$634$	9.19956e6	0.908959
$635$	0	0
$636$	−6.13865e7	−6.01769
$637$	−2.73015e6	−0.266586
$638$	2.92339e7	2.84338
$639$	3.01770e7	2.92364
$640$	0	0
$641$	1.11250e6	0.106944	0.0534718	−	0.998569i	$-0.482971\pi$
$641$	1.11250e6	0.106944	0.0534718	+	0.998569i	$0.482971\pi$
$642$	2.66327e7	2.55022
$643$	−9.07113e6	−0.865235	−0.432617	−	0.901578i	$-0.642410\pi$
$643$	−9.07113e6	−0.865235	−0.432617	+	0.901578i	$0.642410\pi$
$644$	−2.28938e7	−2.17522
$645$	0	0
$646$	7.43295e6	0.700777
$647$	2.19842e6	0.206467	0.103234	−	0.994657i	$-0.467081\pi$
$647$	2.19842e6	0.206467	0.103234	+	0.994657i	$0.467081\pi$
$648$	5.60869e6	0.524716
$649$	−2.02110e6	−0.188355
$650$	0	0
$651$	3.95222e7	3.65501
$652$	−1.67582e7	−1.54386
$653$	−1.42857e7	−1.31105	−0.655525	−	0.755173i	$-0.727553\pi$
$653$	−1.42857e7	−1.31105	−0.655525	+	0.755173i	$0.727553\pi$
$654$	−3.76356e7	−3.44076
$655$	0	0
$656$	2.19092e6	0.198777
$657$	3.37176e7	3.04749
$658$	−1.87237e7	−1.68589
$659$	1.54265e7	1.38374	0.691869	−	0.722023i	$-0.256787\pi$
$659$	1.54265e7	1.38374	0.691869	+	0.722023i	$0.256787\pi$
$660$	0	0
$661$	1.65514e7	1.47344	0.736719	−	0.676199i	$-0.236374\pi$
$661$	1.65514e7	1.47344	0.736719	+	0.676199i	$0.236374\pi$
$662$	2.20009e7	1.95117
$663$	−7.30795e6	−0.645672
$664$	−56535.0	−0.00497619
$665$	0	0
$666$	3.66949e7	3.20568
$667$	1.24356e7	1.08231
$668$	2.45078e7	2.12502
$669$	−2.38480e7	−2.06010
$670$	0	0
$671$	−2.12756e7	−1.82422
$672$	−1.03639e7	−0.885320
$673$	8.91603e6	0.758811	0.379406	−	0.925230i	$-0.376129\pi$
$673$	8.91603e6	0.758811	0.379406	+	0.925230i	$0.376129\pi$
$674$	1.15992e7	0.983510
$675$	0	0
$676$	1.71907e6	0.144686
$677$	−8.15442e6	−0.683788	−0.341894	−	0.939739i	$-0.611068\pi$
$677$	−8.15442e6	−0.683788	−0.341894	+	0.939739i	$0.611068\pi$
$678$	4.39992e7	3.67596
$679$	2.77740e6	0.231187
$680$	0	0
$681$	−802625.	−0.0663200
$682$	4.13594e7	3.40497
$683$	2.02314e6	0.165948	0.0829742	−	0.996552i	$-0.473558\pi$
$683$	2.02314e6	0.165948	0.0829742	+	0.996552i	$0.473558\pi$
$684$	−1.19819e7	−0.979229
$685$	0	0
$686$	1.13705e6	0.0922507
$687$	−4.22756e6	−0.341742
$688$	4.00338e6	0.322445
$689$	−6.64915e6	−0.533603
$690$	0	0
$691$	−5.61163e6	−0.447089	−0.223545	−	0.974694i	$-0.571763\pi$
$691$	−5.61163e6	−0.447089	−0.223545	+	0.974694i	$0.571763\pi$
$692$	−2.95674e6	−0.234719
$693$	−3.99479e7	−3.15981
$694$	4.10339e7	3.23403
$695$	0	0
$696$	−4.16463e7	−3.25877
$697$	−5.43293e6	−0.423597
$698$	−1.43675e7	−1.11620
$699$	3.10319e7	2.40224
$700$	0	0
$701$	−5.09127e6	−0.391319	−0.195660	−	0.980672i	$-0.562685\pi$
$701$	−5.09127e6	−0.391319	−0.195660	+	0.980672i	$0.562685\pi$
$702$	7.82215e6	0.599078
$703$	−4.13457e6	−0.315531
$704$	−2.18877e7	−1.66444
$705$	0	0
$706$	−7.01152e6	−0.529420
$707$	−472085.	−0.0355199
$708$	6.14769e6	0.460923
$709$	1.54906e7	1.15732	0.578658	−	0.815570i	$-0.303577\pi$
$709$	1.54906e7	1.15732	0.578658	+	0.815570i	$0.303577\pi$
$710$	0	0
$711$	−3.07580e7	−2.28184
$712$	−1.17839e7	−0.871146
$713$	1.75936e7	1.29608
$714$	−7.53797e7	−5.53362
$715$	0	0
$716$	2.32522e7	1.69505
$717$	1.99488e7	1.44916
$718$	1.00239e7	0.725645
$719$	−1.12604e7	−0.812328	−0.406164	−	0.913800i	$-0.633134\pi$
$719$	−1.12604e7	−0.812328	−0.406164	+	0.913800i	$0.633134\pi$
$720$	0	0
$721$	−3.82857e7	−2.74282
$722$	−2.17065e7	−1.54970
$723$	2.20456e7	1.56847
$724$	−1.31795e7	−0.934440
$725$	0	0
$726$	−2.54022e7	−1.78867
$727$	−8.14136e6	−0.571296	−0.285648	−	0.958335i	$-0.592209\pi$
$727$	−8.14136e6	−0.571296	−0.285648	+	0.958335i	$0.592209\pi$
$728$	8.30461e6	0.580752
$729$	−2.14763e7	−1.49672
$730$	0	0
$731$	−9.92740e6	−0.687135
$732$	6.47151e7	4.46404
$733$	1.30341e7	0.896025	0.448013	−	0.894027i	$-0.352132\pi$
$733$	1.30341e7	0.896025	0.448013	+	0.894027i	$0.352132\pi$
$734$	721626.	0.0494393
$735$	0	0
$736$	−4.61357e6	−0.313937
$737$	−9.53545e6	−0.646655
$738$	1.34140e7	0.906604
$739$	−1.95666e7	−1.31796	−0.658981	−	0.752159i	$-0.729012\pi$
$739$	−1.95666e7	−1.31796	−0.658981	+	0.752159i	$0.729012\pi$
$740$	0	0
$741$	−2.03303e6	−0.136019
$742$	−6.85844e7	−4.57315
$743$	1.78971e6	0.118935	0.0594675	−	0.998230i	$-0.481060\pi$
$743$	1.78971e6	0.118935	0.0594675	+	0.998230i	$0.481060\pi$
$744$	−5.89201e7	−3.90240
$745$	0	0
$746$	1.38857e7	0.913523
$747$	−89600.2	−0.00587500
$748$	−5.15023e7	−3.36568
$749$	1.94271e7	1.26533
$750$	0	0
$751$	−2.13528e7	−1.38151	−0.690755	−	0.723089i	$-0.742722\pi$
$751$	−2.13528e7	−1.38151	−0.690755	+	0.723089i	$0.742722\pi$
$752$	7.22562e6	0.465940
$753$	−2.57402e7	−1.65434
$754$	−9.63171e6	−0.616985
$755$	0	0
$756$	5.26774e7	3.35212
$757$	7.21618e6	0.457686	0.228843	−	0.973463i	$-0.426506\pi$
$757$	7.21618e6	0.457686	0.228843	+	0.973463i	$0.426506\pi$
$758$	2.79747e6	0.176845
$759$	−2.78570e7	−1.75521
$760$	0	0
$761$	−1.18696e7	−0.742974	−0.371487	−	0.928438i	$-0.621152\pi$
$761$	−1.18696e7	−0.742974	−0.371487	+	0.928438i	$0.621152\pi$
$762$	−841141.	−0.0524785
$763$	−2.74530e7	−1.70718
$764$	1.66872e7	1.03431
$765$	0	0
$766$	3.26670e7	2.01158
$767$	665894.	0.0408711
$768$	4.90376e7	3.00003
$769$	−2.02111e7	−1.23247	−0.616233	−	0.787564i	$-0.711342\pi$
$769$	−2.02111e7	−1.23247	−0.616233	+	0.787564i	$0.711342\pi$
$770$	0	0
$771$	3.35221e7	2.03093
$772$	−1.86832e7	−1.12826
$773$	4.38847e6	0.264158	0.132079	−	0.991239i	$-0.457835\pi$
$773$	4.38847e6	0.264158	0.132079	+	0.991239i	$0.457835\pi$
$774$	2.45109e7	1.47064
$775$	0	0
$776$	−4.14058e6	−0.246835
$777$	4.19299e7	2.49156
$778$	1.57762e7	0.934442
$779$	−1.51141e6	−0.0892357
$780$	0	0
$781$	3.60850e7	2.11689
$782$	−3.35559e7	−1.96224
$783$	−2.86137e7	−1.66790
$784$	1.08674e7	0.631447
$785$	0	0
$786$	4.12074e7	2.37913
$787$	−4.56154e6	−0.262527	−0.131264	−	0.991347i	$-0.541903\pi$
$787$	−4.56154e6	−0.262527	−0.131264	+	0.991347i	$0.541903\pi$
$788$	−3.10650e7	−1.78220
$789$	−4.39059e7	−2.51090
$790$	0	0
$791$	3.20949e7	1.82387
$792$	5.95549e7	3.37368
$793$	7.00970e6	0.395837
$794$	2.37473e7	1.33679
$795$	0	0
$796$	3.89438e7	2.17849
$797$	1.86077e7	1.03764	0.518820	−	0.854883i	$-0.326371\pi$
$797$	1.86077e7	1.03764	0.518820	+	0.854883i	$0.326371\pi$
$798$	−2.09702e7	−1.16572
$799$	−1.79177e7	−0.992925
$800$	0	0
$801$	−1.86759e7	−1.02849
$802$	4.23878e7	2.32704
$803$	4.03187e7	2.20657
$804$	2.90044e7	1.58243
$805$	0	0
$806$	−1.36267e7	−0.738845
$807$	2.22175e7	1.20091
$808$	703789.	0.0379240
$809$	−1.95576e7	−1.05062	−0.525309	−	0.850911i	$-0.676050\pi$
$809$	−1.95576e7	−1.05062	−0.525309	+	0.850911i	$0.676050\pi$
$810$	0	0
$811$	−1.88885e7	−1.00843	−0.504214	−	0.863579i	$-0.668218\pi$
$811$	−1.88885e7	−1.00843	−0.504214	+	0.863579i	$0.668218\pi$
$812$	−6.48637e7	−3.45232
$813$	−4.30690e7	−2.28528
$814$	4.38790e7	2.32111
$815$	0	0
$816$	2.90895e7	1.52937
$817$	−2.76174e6	−0.144753
$818$	−2.56691e7	−1.34130
$819$	1.31617e7	0.685648
$820$	0	0
$821$	7.00926e6	0.362923	0.181461	−	0.983398i	$-0.441917\pi$
$821$	7.00926e6	0.362923	0.181461	+	0.983398i	$0.441917\pi$
$822$	1.34664e7	0.695138
$823$	−2.33685e7	−1.20263	−0.601313	−	0.799014i	$-0.705355\pi$
$823$	−2.33685e7	−1.20263	−0.601313	+	0.799014i	$0.705355\pi$
$824$	5.70767e7	2.92847
$825$	0	0
$826$	6.86853e6	0.350279
$827$	2.84662e7	1.44732	0.723662	−	0.690155i	$-0.242458\pi$
$827$	2.84662e7	1.44732	0.723662	+	0.690155i	$0.242458\pi$
$828$	5.40918e7	2.74193
$829$	−1.37621e7	−0.695503	−0.347752	−	0.937587i	$-0.613055\pi$
$829$	−1.37621e7	−0.695503	−0.347752	+	0.937587i	$0.613055\pi$
$830$	0	0
$831$	5.58301e7	2.80457
$832$	7.21135e6	0.361167
$833$	−2.69486e7	−1.34562
$834$	6.17699e7	3.07512
$835$	0	0
$836$	−1.43276e7	−0.709021
$837$	−4.04820e7	−1.99732
$838$	2.18509e7	1.07488
$839$	−3.18392e7	−1.56155	−0.780776	−	0.624811i	$-0.785176\pi$
$839$	−3.18392e7	−1.56155	−0.780776	+	0.624811i	$0.785176\pi$
$840$	0	0
$841$	1.47220e7	0.717757
$842$	4.60055e7	2.23630
$843$	1.41958e7	0.688006
$844$	7.95282e6	0.384295
$845$	0	0
$846$	4.42392e7	2.12511
$847$	−1.85294e7	−0.887471
$848$	2.64672e7	1.26392
$849$	−1.57887e7	−0.751757
$850$	0	0
$851$	1.86654e7	0.883514
$852$	−1.09761e8	−5.18025
$853$	2.97955e6	0.140210	0.0701049	−	0.997540i	$-0.477667\pi$
$853$	2.97955e6	0.140210	0.0701049	+	0.997540i	$0.477667\pi$
$854$	7.23033e7	3.39245
$855$	0	0
$856$	−2.89621e7	−1.35097
$857$	−1.00599e7	−0.467886	−0.233943	−	0.972250i	$-0.575163\pi$
$857$	−1.00599e7	−0.467886	−0.233943	+	0.972250i	$0.575163\pi$
$858$	2.15759e7	1.00058
$859$	1.59873e7	0.739252	0.369626	−	0.929181i	$-0.379486\pi$
$859$	1.59873e7	0.739252	0.369626	+	0.929181i	$0.379486\pi$
$860$	0	0
$861$	1.53277e7	0.704641
$862$	−2.01522e7	−0.923751
$863$	9.59580e6	0.438586	0.219293	−	0.975659i	$-0.429625\pi$
$863$	9.59580e6	0.438586	0.219293	+	0.975659i	$0.429625\pi$
$864$	1.06156e7	0.483794
$865$	0	0
$866$	2.43624e7	1.10389
$867$	−3.53290e7	−1.59619
$868$	−9.17675e7	−4.13418
$869$	−3.67797e7	−1.65219
$870$	0	0
$871$	3.14165e6	0.140318
$872$	4.09273e7	1.82273
$873$	−6.56226e6	−0.291419
$874$	−9.33505e6	−0.413369
$875$	0	0
$876$	−1.22639e8	−5.39970
$877$	1.09080e7	0.478902	0.239451	−	0.970908i	$-0.423033\pi$
$877$	1.09080e7	0.478902	0.239451	+	0.970908i	$0.423033\pi$
$878$	3.52416e7	1.54284
$879$	2.40503e7	1.04990
$880$	0	0
$881$	−897407.	−0.0389538	−0.0194769	−	0.999810i	$-0.506200\pi$
$881$	−897407.	−0.0389538	−0.0194769	+	0.999810i	$0.506200\pi$
$882$	6.65365e7	2.87997
$883$	−3.37890e7	−1.45839	−0.729195	−	0.684306i	$-0.760105\pi$
$883$	−3.37890e7	−1.45839	−0.729195	+	0.684306i	$0.760105\pi$
$884$	1.69685e7	0.730320
$885$	0	0
$886$	−2.23015e7	−0.954443
$887$	2.26350e7	0.965989	0.482994	−	0.875623i	$-0.339549\pi$
$887$	2.26350e7	0.965989	0.482994	+	0.875623i	$0.339549\pi$
$888$	−6.25095e7	−2.66020
$889$	−613565.	−0.0260379
$890$	0	0
$891$	1.06293e7	0.448549
$892$	5.53733e7	2.33017
$893$	−4.98461e6	−0.209172
$894$	−2.55456e7	−1.06899
$895$	0	0
$896$	6.15894e7	2.56293
$897$	9.17806e6	0.380864
$898$	−4.13594e7	−1.71153
$899$	4.98470e7	2.05703
$900$	0	0
$901$	−6.56321e7	−2.69342
$902$	1.60402e7	0.656436
$903$	2.80076e7	1.14303
$904$	−4.78475e7	−1.94732
$905$	0	0
$906$	−1.27884e8	−5.17604
$907$	−3.13826e7	−1.26669	−0.633345	−	0.773870i	$-0.718319\pi$
$907$	−3.13826e7	−1.26669	−0.633345	+	0.773870i	$0.718319\pi$
$908$	1.86363e6	0.0750146
$909$	1.11541e6	0.0447739
$910$	0	0
$911$	−2.54672e7	−1.01668	−0.508341	−	0.861156i	$-0.669741\pi$
$911$	−2.54672e7	−1.01668	−0.508341	+	0.861156i	$0.669741\pi$
$912$	8.09254e6	0.322179
$913$	−107142.	−0.00425385
$914$	1.09804e7	0.434763
$915$	0	0
$916$	9.81608e6	0.386544
$917$	3.00585e7	1.18044
$918$	7.72104e7	3.02391
$919$	−2.19820e7	−0.858577	−0.429288	−	0.903167i	$-0.641236\pi$
$919$	−2.19820e7	−0.858577	−0.429288	+	0.903167i	$0.641236\pi$
$920$	0	0
$921$	−6.19730e7	−2.40743
$922$	−3.58413e7	−1.38854
$923$	−1.18889e7	−0.459345
$924$	1.45301e8	5.59871
$925$	0	0
$926$	4.28954e7	1.64393
$927$	9.04588e7	3.45741
$928$	−1.30714e7	−0.498255
$929$	2.75340e7	1.04672	0.523359	−	0.852112i	$-0.324679\pi$
$929$	2.75340e7	1.04672	0.523359	+	0.852112i	$0.324679\pi$
$930$	0	0
$931$	−7.49694e6	−0.283472
$932$	−7.20538e7	−2.71717
$933$	3.29419e7	1.23892
$934$	−5.50830e7	−2.06610
$935$	0	0
$936$	−1.96216e7	−0.732056
$937$	−117742.	−0.00438111	−0.00219055	−	0.999998i	$-0.500697\pi$
$937$	−117742.	−0.00438111	−0.00219055	+	0.999998i	$0.500697\pi$
$938$	3.24054e7	1.20257
$939$	−4.38845e7	−1.62423
$940$	0	0
$941$	1.19282e7	0.439136	0.219568	−	0.975597i	$-0.429535\pi$
$941$	1.19282e7	0.439136	0.219568	+	0.975597i	$0.429535\pi$
$942$	−6.88226e7	−2.52699
$943$	6.82323e6	0.249868
$944$	−2.65061e6	−0.0968091
$945$	0	0
$946$	2.93096e7	1.06483
$947$	4.67856e7	1.69526	0.847632	−	0.530585i	$-0.178028\pi$
$947$	4.67856e7	1.69526	0.847632	+	0.530585i	$0.178028\pi$
$948$	1.11875e8	4.04307
$949$	−1.32838e7	−0.478804
$950$	0	0
$951$	−2.48370e7	−0.890529
$952$	8.19727e7	2.93141
$953$	1.84653e6	0.0658603	0.0329301	−	0.999458i	$-0.489516\pi$
$953$	1.84653e6	0.0658603	0.0329301	+	0.999458i	$0.489516\pi$
$954$	1.62047e8	5.76460
$955$	0	0
$956$	−4.63195e7	−1.63915
$957$	−7.89257e7	−2.78573
$958$	−8.10641e7	−2.85374
$959$	9.82296e6	0.344902
$960$	0	0
$961$	4.18932e7	1.46331
$962$	−1.44568e7	−0.503658
$963$	−4.59010e7	−1.59498
$964$	−5.11882e7	−1.77410
$965$	0	0
$966$	9.46694e7	3.26413
$967$	−3.47395e7	−1.19470	−0.597349	−	0.801982i	$-0.703779\pi$
$967$	−3.47395e7	−1.19470	−0.597349	+	0.801982i	$0.703779\pi$
$968$	2.76239e7	0.947538
$969$	−2.00675e7	−0.686569
$970$	0	0
$971$	1.02513e7	0.348923	0.174462	−	0.984664i	$-0.444182\pi$
$971$	1.02513e7	0.348923	0.174462	+	0.984664i	$0.444182\pi$
$972$	3.81743e7	1.29600
$973$	4.50577e7	1.52576
$974$	−2.20912e7	−0.746143
$975$	0	0
$976$	−2.79023e7	−0.937597
$977$	1.54408e6	0.0517528	0.0258764	−	0.999665i	$-0.491762\pi$
$977$	1.54408e6	0.0517528	0.0258764	+	0.999665i	$0.491762\pi$
$978$	6.92980e7	2.31672
$979$	−2.23323e7	−0.744691
$980$	0	0
$981$	6.48642e7	2.15195
$982$	−1.76068e7	−0.582640
$983$	−3.24347e7	−1.07060	−0.535299	−	0.844663i	$-0.679801\pi$
$983$	−3.24347e7	−1.07060	−0.535299	+	0.844663i	$0.679801\pi$
$984$	−2.28506e7	−0.752334
$985$	0	0
$986$	−9.50721e7	−3.11430
$987$	5.05504e7	1.65170
$988$	4.72054e6	0.153851
$989$	1.24678e7	0.405322
$990$	0	0
$991$	−3.76595e7	−1.21812	−0.609060	−	0.793124i	$-0.708453\pi$
$991$	−3.76595e7	−1.21812	−0.609060	+	0.793124i	$0.708453\pi$
$992$	−1.84931e7	−0.596664
$993$	−5.93980e7	−1.91161
$994$	−1.22632e8	−3.93674
$995$	0	0
$996$	325899.	0.0104096
$997$	−3.72285e7	−1.18614	−0.593072	−	0.805149i	$-0.702085\pi$
$997$	−3.72285e7	−1.18614	−0.593072	+	0.805149i	$0.702085\pi$
$998$	−1.59106e7	−0.505661
$999$	−4.29481e7	−1.36154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.6.a.j.1.10	✓	11
5.2	odd	4		325.6.b.i.274.20		22
5.3	odd	4		325.6.b.i.274.3		22
5.4	even	2		325.6.a.k.1.2	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.6.a.j.1.10	✓	11	1.1	even	1	trivial
325.6.a.k.1.2	yes	11	5.4	even	2
325.6.b.i.274.3		22	5.3	odd	4
325.6.b.i.274.20		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)

\(f(q)\)	\(=\)	\(q+9.60154 q^{2} -25.9222 q^{3} +60.1895 q^{4} -248.893 q^{6} -181.554 q^{7} +270.662 q^{8} +428.963 q^{9} +512.944 q^{11} -1560.25 q^{12} -169.000 q^{13} -1743.19 q^{14} +672.710 q^{16} -1668.15 q^{17} +4118.70 q^{18} -464.071 q^{19} +4706.28 q^{21} +4925.05 q^{22} +2095.04 q^{23} -7016.17 q^{24} -1622.66 q^{26} -4820.57 q^{27} -10927.6 q^{28} +5935.75 q^{29} +8397.76 q^{31} -2202.14 q^{32} -13296.7 q^{33} -16016.8 q^{34} +25819.0 q^{36} +8909.35 q^{37} -4455.79 q^{38} +4380.86 q^{39} +3256.85 q^{41} +45187.5 q^{42} +5951.12 q^{43} +30873.8 q^{44} +20115.6 q^{46} +10741.1 q^{47} -17438.1 q^{48} +16154.7 q^{49} +43242.3 q^{51} -10172.0 q^{52} +39344.1 q^{53} -46284.9 q^{54} -49139.7 q^{56} +12029.8 q^{57} +56992.4 q^{58} -3940.20 q^{59} -41477.5 q^{61} +80631.4 q^{62} -77879.7 q^{63} -42670.7 q^{64} -127668. q^{66} -18589.7 q^{67} -100405. q^{68} -54308.1 q^{69} +70348.8 q^{71} +116104. q^{72} +78602.6 q^{73} +85543.4 q^{74} -27932.2 q^{76} -93126.8 q^{77} +42063.0 q^{78} -71703.3 q^{79} +20722.1 q^{81} +31270.8 q^{82} -208.877 q^{83} +283268. q^{84} +57139.9 q^{86} -153868. q^{87} +138835. q^{88} -43537.5 q^{89} +30682.6 q^{91} +126099. q^{92} -217689. q^{93} +103131. q^{94} +57084.5 q^{96} -15298.0 q^{97} +155110. q^{98} +220034. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 5 q^{2} - 11 q^{3} + 187 q^{4} + 351 q^{6} - 208 q^{7} - 165 q^{8} + 1372 q^{9} + 1276 q^{11} - 1533 q^{12} - 1859 q^{13} + 578 q^{14} + 5707 q^{16} - 2218 q^{17} + 6776 q^{18} + 3520 q^{19} + 1706 q^{21}+ \cdots + 426698 q^{99}+O(q^{100}) \) 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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