LMFDB - Embedded newform 2366.4.a.bg.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,4,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2366.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2366.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:	$139.598519074$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 219 x^{10} + 1022 x^{9} + 17084 x^{8} - 65540 x^{7} - 566763 x^{6} + 1871300 x^{5} + \cdots + 543166 $ x^12 - 6x^11 - 219x^10 + 1022x^9 + 17084x^8 - 65540x^7 - 566763x^6 + 1871300x^5 + 6589295x^4 - 20167176x^3 + 8073768x^2 + 5594524*x + 543166
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 13 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-8.14920$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -6.41715 q^{3} +4.00000 q^{4} +16.3154 q^{5} -12.8343 q^{6} -7.00000 q^{7} +8.00000 q^{8} +14.1798 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -6.41715 q^{3} +4.00000 q^{4} +16.3154 q^{5} -12.8343 q^{6} -7.00000 q^{7} +8.00000 q^{8} +14.1798 q^{9} +32.6307 q^{10} -23.5348 q^{11} -25.6686 q^{12} -14.0000 q^{14} -104.698 q^{15} +16.0000 q^{16} -121.532 q^{17} +28.3595 q^{18} +13.5737 q^{19} +65.2615 q^{20} +44.9200 q^{21} -47.0695 q^{22} -71.0422 q^{23} -51.3372 q^{24} +141.191 q^{25} +82.2693 q^{27} -28.0000 q^{28} -36.2852 q^{29} -209.396 q^{30} -18.9989 q^{31} +32.0000 q^{32} +151.026 q^{33} -243.064 q^{34} -114.208 q^{35} +56.7190 q^{36} -137.121 q^{37} +27.1474 q^{38} +130.523 q^{40} +171.775 q^{41} +89.8400 q^{42} +547.149 q^{43} -94.1391 q^{44} +231.348 q^{45} -142.084 q^{46} -133.257 q^{47} -102.674 q^{48} +49.0000 q^{49} +282.382 q^{50} +779.889 q^{51} +235.455 q^{53} +164.539 q^{54} -383.978 q^{55} -56.0000 q^{56} -87.1044 q^{57} -72.5704 q^{58} +272.286 q^{59} -418.792 q^{60} -437.288 q^{61} -37.9977 q^{62} -99.2583 q^{63} +64.0000 q^{64} +302.052 q^{66} +650.852 q^{67} -486.128 q^{68} +455.888 q^{69} -228.415 q^{70} +194.031 q^{71} +113.438 q^{72} +961.250 q^{73} -274.243 q^{74} -906.045 q^{75} +54.2948 q^{76} +164.743 q^{77} +150.933 q^{79} +261.046 q^{80} -910.788 q^{81} +343.550 q^{82} +915.555 q^{83} +179.680 q^{84} -1982.84 q^{85} +1094.30 q^{86} +232.847 q^{87} -188.278 q^{88} +492.130 q^{89} +462.696 q^{90} -284.169 q^{92} +121.919 q^{93} -266.514 q^{94} +221.460 q^{95} -205.349 q^{96} +972.937 q^{97} +98.0000 q^{98} -333.717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{2} + 6 q^{3} + 48 q^{4} + 28 q^{5} + 12 q^{6} - 84 q^{7} + 96 q^{8} + 162 q^{9}+O(q^{10}) $ 12 * q + 24 * q^2 + 6 * q^3 + 48 * q^4 + 28 * q^5 + 12 * q^6 - 84 * q^7 + 96 * q^8 + 162 * q^9	\( 12 q + 24 q^{2} + 6 q^{3} + 48 q^{4} + 28 q^{5} + 12 q^{6} - 84 q^{7} + 96 q^{8} + 162 q^{9} + 56 q^{10} + 6 q^{11} + 24 q^{12} - 168 q^{14} - 138 q^{15} + 192 q^{16} - 56 q^{17} + 324 q^{18} + 158 q^{19} + 112 q^{20} - 42 q^{21} + 12 q^{22} + 414 q^{23} + 48 q^{24} + 478 q^{25} + 390 q^{27} - 336 q^{28} + 222 q^{29} - 276 q^{30} - 200 q^{31} + 384 q^{32} + 844 q^{33} - 112 q^{34} - 196 q^{35} + 648 q^{36} - 560 q^{37} + 316 q^{38} + 224 q^{40} - 66 q^{41} - 84 q^{42} + 484 q^{43} + 24 q^{44} + 542 q^{45} + 828 q^{46} + 618 q^{47} + 96 q^{48} + 588 q^{49} + 956 q^{50} + 992 q^{51} + 504 q^{53} + 780 q^{54} + 2584 q^{55} - 672 q^{56} - 1164 q^{57} + 444 q^{58} + 1460 q^{59} - 552 q^{60} - 2 q^{61} - 400 q^{62} - 1134 q^{63} + 768 q^{64} + 1688 q^{66} + 334 q^{67} - 224 q^{68} + 4660 q^{69} - 392 q^{70} - 196 q^{71} + 1296 q^{72} + 490 q^{73} - 1120 q^{74} - 338 q^{75} + 632 q^{76} - 42 q^{77} + 2942 q^{79} + 448 q^{80} + 2824 q^{81} - 132 q^{82} + 236 q^{83} - 168 q^{84} + 1352 q^{85} + 968 q^{86} + 1456 q^{87} + 48 q^{88} + 3566 q^{89} + 1084 q^{90} + 1656 q^{92} + 1884 q^{93} + 1236 q^{94} + 5754 q^{95} + 192 q^{96} + 3032 q^{97} + 1176 q^{98} + 3670 q^{99}+O(q^{100}) \) 12 * q + 24 * q^2 + 6 * q^3 + 48 * q^4 + 28 * q^5 + 12 * q^6 - 84 * q^7 + 96 * q^8 + 162 * q^9 + 56 * q^10 + 6 * q^11 + 24 * q^12 - 168 * q^14 - 138 * q^15 + 192 * q^16 - 56 * q^17 + 324 * q^18 + 158 * q^19 + 112 * q^20 - 42 * q^21 + 12 * q^22 + 414 * q^23 + 48 * q^24 + 478 * q^25 + 390 * q^27 - 336 * q^28 + 222 * q^29 - 276 * q^30 - 200 * q^31 + 384 * q^32 + 844 * q^33 - 112 * q^34 - 196 * q^35 + 648 * q^36 - 560 * q^37 + 316 * q^38 + 224 * q^40 - 66 * q^41 - 84 * q^42 + 484 * q^43 + 24 * q^44 + 542 * q^45 + 828 * q^46 + 618 * q^47 + 96 * q^48 + 588 * q^49 + 956 * q^50 + 992 * q^51 + 504 * q^53 + 780 * q^54 + 2584 * q^55 - 672 * q^56 - 1164 * q^57 + 444 * q^58 + 1460 * q^59 - 552 * q^60 - 2 * q^61 - 400 * q^62 - 1134 * q^63 + 768 * q^64 + 1688 * q^66 + 334 * q^67 - 224 * q^68 + 4660 * q^69 - 392 * q^70 - 196 * q^71 + 1296 * q^72 + 490 * q^73 - 1120 * q^74 - 338 * q^75 + 632 * q^76 - 42 * q^77 + 2942 * q^79 + 448 * q^80 + 2824 * q^81 - 132 * q^82 + 236 * q^83 - 168 * q^84 + 1352 * q^85 + 968 * q^86 + 1456 * q^87 + 48 * q^88 + 3566 * q^89 + 1084 * q^90 + 1656 * q^92 + 1884 * q^93 + 1236 * q^94 + 5754 * q^95 + 192 * q^96 + 3032 * q^97 + 1176 * q^98 + 3670 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−6.41715	−1.23498	−0.617490	−	0.786579i	$-0.711850\pi$
$3$	−6.41715	−1.23498	−0.617490	+	0.786579i	$0.711850\pi$
$4$	4.00000	0.500000
$5$	16.3154	1.45929	0.729645	−	0.683826i	$-0.239685\pi$
$5$	16.3154	1.45929	0.729645	+	0.683826i	$0.239685\pi$
$6$	−12.8343	−0.873263
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	14.1798	0.525176
$10$	32.6307	1.03187
$11$	−23.5348	−0.645091	−0.322545	−	0.946554i	$-0.604538\pi$
$11$	−23.5348	−0.645091	−0.322545	+	0.946554i	$0.604538\pi$
$12$	−25.6686	−0.617490
$13$	0	0
$13$	0	0
$14$	−14.0000	−0.267261
$15$	−104.698	−1.80220
$16$	16.0000	0.250000
$17$	−121.532	−1.73387	−0.866937	−	0.498418i	$-0.833914\pi$
$17$	−121.532	−1.73387	−0.866937	+	0.498418i	$0.833914\pi$
$18$	28.3595	0.371356
$19$	13.5737	0.163896	0.0819479	−	0.996637i	$-0.473886\pi$
$19$	13.5737	0.163896	0.0819479	+	0.996637i	$0.473886\pi$
$20$	65.2615	0.729645
$21$	44.9200	0.466779
$22$	−47.0695	−0.456148
$23$	−71.0422	−0.644058	−0.322029	−	0.946730i	$-0.604365\pi$
$23$	−71.0422	−0.644058	−0.322029	+	0.946730i	$0.604365\pi$
$24$	−51.3372	−0.436631
$25$	141.191	1.12953
$26$	0	0
$27$	82.2693	0.586398
$28$	−28.0000	−0.188982
$29$	−36.2852	−0.232345	−0.116172	−	0.993229i	$-0.537062\pi$
$29$	−36.2852	−0.232345	−0.116172	+	0.993229i	$0.537062\pi$
$30$	−209.396	−1.27434
$31$	−18.9989	−0.110074	−0.0550371	−	0.998484i	$-0.517528\pi$
$31$	−18.9989	−0.110074	−0.0550371	+	0.998484i	$0.517528\pi$
$32$	32.0000	0.176777
$33$	151.026	0.796674
$34$	−243.064	−1.22603
$35$	−114.208	−0.551560
$36$	56.7190	0.262588
$37$	−137.121	−0.609260	−0.304630	−	0.952471i	$-0.598533\pi$
$37$	−137.121	−0.609260	−0.304630	+	0.952471i	$0.598533\pi$
$38$	27.1474	0.115892
$39$	0	0
$40$	130.523	0.515937
$41$	171.775	0.654310	0.327155	−	0.944971i	$-0.393910\pi$
$41$	171.775	0.654310	0.327155	+	0.944971i	$0.393910\pi$
$42$	89.8400	0.330062
$43$	547.149	1.94045	0.970227	−	0.242199i	$-0.0778685\pi$
$43$	547.149	1.94045	0.970227	+	0.242199i	$0.0778685\pi$
$44$	−94.1391	−0.322545
$45$	231.348	0.766385
$46$	−142.084	−0.455418
$47$	−133.257	−0.413564	−0.206782	−	0.978387i	$-0.566299\pi$
$47$	−133.257	−0.413564	−0.206782	+	0.978387i	$0.566299\pi$
$48$	−102.674	−0.308745
$49$	49.0000	0.142857
$50$	282.382	0.798698
$51$	779.889	2.14130
$52$	0	0
$53$	235.455	0.610232	0.305116	−	0.952315i	$-0.401305\pi$
$53$	235.455	0.610232	0.305116	+	0.952315i	$0.401305\pi$
$54$	164.539	0.414646
$55$	−383.978	−0.941375
$56$	−56.0000	−0.133631
$57$	−87.1044	−0.202408
$58$	−72.5704	−0.164292
$59$	272.286	0.600825	0.300412	−	0.953809i	$-0.402876\pi$
$59$	272.286	0.600825	0.300412	+	0.953809i	$0.402876\pi$
$60$	−418.792	−0.901098
$61$	−437.288	−0.917853	−0.458927	−	0.888474i	$-0.651766\pi$
$61$	−437.288	−0.917853	−0.458927	+	0.888474i	$0.651766\pi$
$62$	−37.9977	−0.0778342
$63$	−99.2583	−0.198498
$64$	64.0000	0.125000
$65$	0	0
$66$	302.052	0.563334
$67$	650.852	1.18678	0.593389	−	0.804916i	$-0.297789\pi$
$67$	650.852	1.18678	0.593389	+	0.804916i	$0.297789\pi$
$68$	−486.128	−0.866937
$69$	455.888	0.795399
$70$	−228.415	−0.390012
$71$	194.031	0.324327	0.162163	−	0.986764i	$-0.448153\pi$
$71$	194.031	0.324327	0.162163	+	0.986764i	$0.448153\pi$
$72$	113.438	0.185678
$73$	961.250	1.54117	0.770587	−	0.637334i	$-0.219963\pi$
$73$	961.250	1.54117	0.770587	+	0.637334i	$0.219963\pi$
$74$	−274.243	−0.430812
$75$	−906.045	−1.39495
$76$	54.2948	0.0819479
$77$	164.743	0.243821
$78$	0	0
$79$	150.933	0.214953	0.107477	−	0.994208i	$-0.465723\pi$
$79$	150.933	0.214953	0.107477	+	0.994208i	$0.465723\pi$
$80$	261.046	0.364823
$81$	−910.788	−1.24937
$82$	343.550	0.462667
$83$	915.555	1.21079	0.605393	−	0.795927i	$-0.293016\pi$
$83$	915.555	1.21079	0.605393	+	0.795927i	$0.293016\pi$
$84$	179.680	0.233389
$85$	−1982.84	−2.53023
$86$	1094.30	1.37211
$87$	232.847	0.286941
$88$	−188.278	−0.228074
$89$	492.130	0.586131	0.293065	−	0.956092i	$-0.405325\pi$
$89$	492.130	0.586131	0.293065	+	0.956092i	$0.405325\pi$
$90$	462.696	0.541916
$91$	0	0
$92$	−284.169	−0.322029
$93$	121.919	0.135939
$94$	−266.514	−0.292434
$95$	221.460	0.239172
$96$	−205.349	−0.218316
$97$	972.937	1.01842	0.509210	−	0.860642i	$-0.329938\pi$
$97$	972.937	1.01842	0.509210	+	0.860642i	$0.329938\pi$
$98$	98.0000	0.101015
$99$	−333.717	−0.338786
$100$	564.765	0.564765
$101$	−1516.94	−1.49447	−0.747235	−	0.664559i	$-0.768619\pi$
$101$	−1516.94	−1.49447	−0.747235	+	0.664559i	$0.768619\pi$
$102$	1559.78	1.51413
$103$	1666.87	1.59458	0.797290	−	0.603597i	$-0.206266\pi$
$103$	1666.87	1.59458	0.797290	+	0.603597i	$0.206266\pi$
$104$	0	0
$105$	732.887	0.681166
$106$	470.911	0.431499
$107$	−233.747	−0.211189	−0.105594	−	0.994409i	$-0.533675\pi$
$107$	−233.747	−0.211189	−0.105594	+	0.994409i	$0.533675\pi$
$108$	329.077	0.293199
$109$	1797.31	1.57937	0.789684	−	0.613514i	$-0.210245\pi$
$109$	1797.31	1.57937	0.789684	+	0.613514i	$0.210245\pi$
$110$	−767.957	−0.665653
$111$	879.928	0.752424
$112$	−112.000	−0.0944911
$113$	−2338.03	−1.94640	−0.973201	−	0.229957i	$-0.926142\pi$
$113$	−2338.03	−1.94640	−0.973201	+	0.229957i	$0.926142\pi$
$114$	−174.209	−0.143124
$115$	−1159.08	−0.939868
$116$	−145.141	−0.116172
$117$	0	0
$118$	544.573	0.424847
$119$	850.724	0.655343
$120$	−837.585	−0.637172
$121$	−777.115	−0.583858
$122$	−874.577	−0.649020
$123$	−1102.30	−0.808060
$124$	−75.9955	−0.0550371
$125$	264.166	0.189022
$126$	−198.517	−0.140359
$127$	1303.14	0.910513	0.455257	−	0.890360i	$-0.349547\pi$
$127$	1303.14	0.910513	0.455257	+	0.890360i	$0.349547\pi$
$128$	128.000	0.0883883
$129$	−3511.14	−2.39642
$130$	0	0
$131$	−1237.31	−0.825226	−0.412613	−	0.910907i	$-0.635384\pi$
$131$	−1237.31	−0.825226	−0.412613	+	0.910907i	$0.635384\pi$
$132$	604.104	0.398337
$133$	−95.0159	−0.0619468
$134$	1301.70	0.839179
$135$	1342.25	0.855725
$136$	−972.256	−0.613017
$137$	829.400	0.517230	0.258615	−	0.965981i	$-0.416734\pi$
$137$	829.400	0.517230	0.258615	+	0.965981i	$0.416734\pi$
$138$	911.777	0.562432
$139$	−286.298	−0.174701	−0.0873506	−	0.996178i	$-0.527840\pi$
$139$	−286.298	−0.174701	−0.0873506	+	0.996178i	$0.527840\pi$
$140$	−456.830	−0.275780
$141$	855.129	0.510744
$142$	388.061	0.229334
$143$	0	0
$144$	226.876	0.131294
$145$	−592.007	−0.339058
$146$	1922.50	1.08978
$147$	−314.440	−0.176426
$148$	−548.485	−0.304630
$149$	−1750.60	−0.962515	−0.481257	−	0.876579i	$-0.659820\pi$
$149$	−1750.60	−0.962515	−0.481257	+	0.876579i	$0.659820\pi$
$150$	−1812.09	−0.986377
$151$	−1025.20	−0.552512	−0.276256	−	0.961084i	$-0.589094\pi$
$151$	−1025.20	−0.552512	−0.276256	+	0.961084i	$0.589094\pi$
$152$	108.590	0.0579459
$153$	−1723.30	−0.910589
$154$	329.487	0.172408
$155$	−309.974	−0.160630
$156$	0	0
$157$	−3168.21	−1.61051	−0.805256	−	0.592927i	$-0.797972\pi$
$157$	−3168.21	−1.61051	−0.805256	+	0.592927i	$0.797972\pi$
$158$	301.866	0.151995
$159$	−1510.95	−0.753624
$160$	522.092	0.257969
$161$	497.296	0.243431
$162$	−1821.58	−0.883435
$163$	1647.99	0.791904	0.395952	−	0.918271i	$-0.370415\pi$
$163$	1647.99	0.791904	0.395952	+	0.918271i	$0.370415\pi$
$164$	687.099	0.327155
$165$	2464.04	1.16258
$166$	1831.11	0.856155
$167$	−2769.69	−1.28338	−0.641691	−	0.766963i	$-0.721767\pi$
$167$	−2769.69	−1.28338	−0.641691	+	0.766963i	$0.721767\pi$
$168$	359.360	0.165031
$169$	0	0
$170$	−3965.68	−1.78914
$171$	192.472	0.0860742
$172$	2188.60	0.970227
$173$	−1638.30	−0.719987	−0.359994	−	0.932955i	$-0.617221\pi$
$173$	−1638.30	−0.719987	−0.359994	+	0.932955i	$0.617221\pi$
$174$	465.695	0.202898
$175$	−988.339	−0.426922
$176$	−376.556	−0.161273
$177$	−1747.30	−0.742007
$178$	984.260	0.414457
$179$	−1877.64	−0.784031	−0.392015	−	0.919959i	$-0.628222\pi$
$179$	−1877.64	−0.784031	−0.392015	+	0.919959i	$0.628222\pi$
$180$	925.392	0.383193
$181$	4657.89	1.91281	0.956405	−	0.292045i	$-0.0943358\pi$
$181$	4657.89	1.91281	0.956405	+	0.292045i	$0.0943358\pi$
$182$	0	0
$183$	2806.14	1.13353
$184$	−568.338	−0.227709
$185$	−2237.18	−0.889087
$186$	243.837	0.0961237
$187$	2860.23	1.11851
$188$	−533.028	−0.206782
$189$	−575.885	−0.221638
$190$	442.920	0.169120
$191$	3083.96	1.16831	0.584156	−	0.811642i	$-0.301426\pi$
$191$	3083.96	1.16831	0.584156	+	0.811642i	$0.301426\pi$
$192$	−410.697	−0.154373
$193$	2773.01	1.03423	0.517113	−	0.855917i	$-0.327007\pi$
$193$	2773.01	1.03423	0.517113	+	0.855917i	$0.327007\pi$
$194$	1945.87	0.720132
$195$	0	0
$196$	196.000	0.0714286
$197$	4216.12	1.52480	0.762401	−	0.647105i	$-0.224020\pi$
$197$	4216.12	1.52480	0.762401	+	0.647105i	$0.224020\pi$
$198$	−667.435	−0.239558
$199$	4167.88	1.48469	0.742344	−	0.670018i	$-0.233714\pi$
$199$	4167.88	1.48469	0.742344	+	0.670018i	$0.233714\pi$
$200$	1129.53	0.399349
$201$	−4176.61	−1.46565
$202$	−3033.89	−1.05675
$203$	253.996	0.0878180
$204$	3119.56	1.07065
$205$	2802.57	0.954829
$206$	3333.74	1.12754
$207$	−1007.36	−0.338244
$208$	0	0
$209$	−319.454	−0.105728
$210$	1465.77	0.481657
$211$	4250.49	1.38680	0.693402	−	0.720551i	$-0.256111\pi$
$211$	4250.49	1.38680	0.693402	+	0.720551i	$0.256111\pi$
$212$	941.821	0.305116
$213$	−1245.12	−0.400537
$214$	−467.495	−0.149333
$215$	8926.94	2.83169
$216$	658.155	0.207323
$217$	132.992	0.0416041
$218$	3594.62	1.11678
$219$	−6168.48	−1.90332
$220$	−1535.91	−0.470688
$221$	0	0
$222$	1759.86	0.532044
$223$	6142.65	1.84458	0.922292	−	0.386495i	$-0.126314\pi$
$223$	6142.65	1.84458	0.922292	+	0.386495i	$0.126314\pi$
$224$	−224.000	−0.0668153
$225$	2002.06	0.593202
$226$	−4676.06	−1.37631
$227$	−1808.02	−0.528646	−0.264323	−	0.964434i	$-0.585148\pi$
$227$	−1808.02	−0.528646	−0.264323	+	0.964434i	$0.585148\pi$
$228$	−348.418	−0.101204
$229$	290.478	0.0838223	0.0419112	−	0.999121i	$-0.486655\pi$
$229$	290.478	0.0838223	0.0419112	+	0.999121i	$0.486655\pi$
$230$	−2318.16	−0.664587
$231$	−1057.18	−0.301115
$232$	−290.282	−0.0821462
$233$	2100.84	0.590690	0.295345	−	0.955391i	$-0.404565\pi$
$233$	2100.84	0.590690	0.295345	+	0.955391i	$0.404565\pi$
$234$	0	0
$235$	−2174.14	−0.603511
$236$	1089.15	0.300412
$237$	−968.560	−0.265463
$238$	1701.45	0.463397
$239$	−1653.50	−0.447514	−0.223757	−	0.974645i	$-0.571832\pi$
$239$	−1653.50	−0.447514	−0.223757	+	0.974645i	$0.571832\pi$
$240$	−1675.17	−0.450549
$241$	−441.227	−0.117933	−0.0589667	−	0.998260i	$-0.518781\pi$
$241$	−441.227	−0.117933	−0.0589667	+	0.998260i	$0.518781\pi$
$242$	−1554.23	−0.412850
$243$	3623.39	0.956545
$244$	−1749.15	−0.458927
$245$	799.453	0.208470
$246$	−2204.61	−0.571385
$247$	0	0
$248$	−151.991	−0.0389171
$249$	−5875.25	−1.49530
$250$	528.332	0.133658
$251$	5646.84	1.42002	0.710010	−	0.704191i	$-0.248690\pi$
$251$	5646.84	1.42002	0.710010	+	0.704191i	$0.248690\pi$
$252$	−397.033	−0.0992490
$253$	1671.96	0.415476
$254$	2606.29	0.643830
$255$	12724.2	3.12478
$256$	256.000	0.0625000
$257$	−6829.96	−1.65775	−0.828874	−	0.559435i	$-0.811018\pi$
$257$	−6829.96	−1.65775	−0.828874	+	0.559435i	$0.811018\pi$
$258$	−7022.27	−1.69453
$259$	959.849	0.230279
$260$	0	0
$261$	−514.516	−0.122022
$262$	−2474.63	−0.583523
$263$	−2007.51	−0.470679	−0.235339	−	0.971913i	$-0.575620\pi$
$263$	−2007.51	−0.470679	−0.235339	+	0.971913i	$0.575620\pi$
$264$	1208.21	0.281667
$265$	3841.54	0.890505
$266$	−190.032	−0.0438030
$267$	−3158.07	−0.723860
$268$	2603.41	0.593389
$269$	6960.04	1.57755	0.788775	−	0.614682i	$-0.210716\pi$
$269$	6960.04	1.57755	0.788775	+	0.614682i	$0.210716\pi$
$270$	2684.51	0.605089
$271$	8534.11	1.91295	0.956476	−	0.291810i	$-0.0942576\pi$
$271$	8534.11	1.91295	0.956476	+	0.291810i	$0.0942576\pi$
$272$	−1944.51	−0.433468
$273$	0	0
$274$	1658.80	0.365737
$275$	−3322.90	−0.728649
$276$	1823.55	0.397699
$277$	−5230.79	−1.13461	−0.567306	−	0.823507i	$-0.692014\pi$
$277$	−5230.79	−1.13461	−0.567306	+	0.823507i	$0.692014\pi$
$278$	−572.596	−0.123532
$279$	−269.399	−0.0578083
$280$	−913.661	−0.195006
$281$	4253.41	0.902979	0.451490	−	0.892276i	$-0.350893\pi$
$281$	4253.41	0.902979	0.451490	+	0.892276i	$0.350893\pi$
$282$	1710.26	0.361150
$283$	−4833.82	−1.01534	−0.507669	−	0.861552i	$-0.669493\pi$
$283$	−4833.82	−1.01534	−0.507669	+	0.861552i	$0.669493\pi$
$284$	776.122	0.162163
$285$	−1421.14	−0.295372
$286$	0	0
$287$	−1202.42	−0.247306
$288$	453.752	0.0928389
$289$	9857.04	2.00632
$290$	−1184.01	−0.239750
$291$	−6243.48	−1.25773
$292$	3845.00	0.770587
$293$	8383.43	1.67155	0.835777	−	0.549069i	$-0.185018\pi$
$293$	8383.43	1.67155	0.835777	+	0.549069i	$0.185018\pi$
$294$	−628.880	−0.124752
$295$	4442.45	0.876778
$296$	−1096.97	−0.215406
$297$	−1936.19	−0.378280
$298$	−3501.20	−0.680601
$299$	0	0
$300$	−3624.18	−0.697474
$301$	−3830.05	−0.733422
$302$	−2050.39	−0.390685
$303$	9734.45	1.84564
$304$	217.179	0.0409740
$305$	−7134.52	−1.33941
$306$	−3446.59	−0.643884
$307$	2837.23	0.527457	0.263728	−	0.964597i	$-0.415048\pi$
$307$	2837.23	0.527457	0.263728	+	0.964597i	$0.415048\pi$
$308$	658.973	0.121911
$309$	−10696.6	−1.96927
$310$	−619.947	−0.113583
$311$	7213.35	1.31521	0.657607	−	0.753361i	$-0.271569\pi$
$311$	7213.35	1.31521	0.657607	+	0.753361i	$0.271569\pi$
$312$	0	0
$313$	5499.82	0.993189	0.496594	−	0.867983i	$-0.334584\pi$
$313$	5499.82	0.993189	0.496594	+	0.867983i	$0.334584\pi$
$314$	−6336.41	−1.13880
$315$	−1619.44	−0.289666
$316$	603.732	0.107477
$317$	−460.392	−0.0815715	−0.0407858	−	0.999168i	$-0.512986\pi$
$317$	−460.392	−0.0815715	−0.0407858	+	0.999168i	$0.512986\pi$
$318$	−3021.90	−0.532893
$319$	853.964	0.149883
$320$	1044.18	0.182411
$321$	1499.99	0.260814
$322$	994.591	0.172132
$323$	−1649.64	−0.284175
$324$	−3643.15	−0.624683
$325$	0	0
$326$	3295.98	0.559961
$327$	−11533.6	−1.95049
$328$	1374.20	0.231334
$329$	932.799	0.156313
$330$	4928.09	0.822068
$331$	−920.049	−0.152781	−0.0763904	−	0.997078i	$-0.524340\pi$
$331$	−920.049	−0.152781	−0.0763904	+	0.997078i	$0.524340\pi$
$332$	3662.22	0.605393
$333$	−1944.35	−0.319969
$334$	−5539.37	−0.907488
$335$	10618.9	1.73186
$336$	718.720	0.116695
$337$	2443.87	0.395033	0.197516	−	0.980300i	$-0.436712\pi$
$337$	2443.87	0.395033	0.197516	+	0.980300i	$0.436712\pi$
$338$	0	0
$339$	15003.5	2.40377
$340$	−7931.36	−1.26511
$341$	447.134	0.0710078
$342$	384.944	0.0608637
$343$	−343.000	−0.0539949
$344$	4377.19	0.686054
$345$	7437.99	1.16072
$346$	−3276.60	−0.509108
$347$	752.680	0.116444	0.0582219	−	0.998304i	$-0.481457\pi$
$347$	752.680	0.116444	0.0582219	+	0.998304i	$0.481457\pi$
$348$	931.390	0.143471
$349$	2002.59	0.307153	0.153577	−	0.988137i	$-0.450921\pi$
$349$	2002.59	0.307153	0.153577	+	0.988137i	$0.450921\pi$
$350$	−1976.68	−0.301880
$351$	0	0
$352$	−753.112	−0.114037
$353$	−6877.57	−1.03699	−0.518493	−	0.855082i	$-0.673507\pi$
$353$	−6877.57	−1.03699	−0.518493	+	0.855082i	$0.673507\pi$
$354$	−3494.60	−0.524678
$355$	3165.68	0.473287
$356$	1968.52	0.293065
$357$	−5459.22	−0.809335
$358$	−3755.28	−0.554393
$359$	−6920.28	−1.01738	−0.508689	−	0.860950i	$-0.669870\pi$
$359$	−6920.28	−1.01738	−0.508689	+	0.860950i	$0.669870\pi$
$360$	1850.78	0.270958
$361$	−6674.75	−0.973138
$362$	9315.79	1.35256
$363$	4986.86	0.721053
$364$	0	0
$365$	15683.1	2.24902
$366$	5612.29	0.801527
$367$	−9700.62	−1.37975	−0.689875	−	0.723928i	$-0.742335\pi$
$367$	−9700.62	−1.37975	−0.689875	+	0.723928i	$0.742335\pi$
$368$	−1136.68	−0.161014
$369$	2435.73	0.343628
$370$	−4474.37	−0.628679
$371$	−1648.19	−0.230646
$372$	487.674	0.0679697
$373$	−3291.67	−0.456934	−0.228467	−	0.973552i	$-0.573371\pi$
$373$	−3291.67	−0.456934	−0.228467	+	0.973552i	$0.573371\pi$
$374$	5720.46	0.790903
$375$	−1695.19	−0.233438
$376$	−1066.06	−0.146217
$377$	0	0
$378$	−1151.77	−0.156721
$379$	−9923.73	−1.34498	−0.672491	−	0.740106i	$-0.734776\pi$
$379$	−9923.73	−1.34498	−0.672491	+	0.740106i	$0.734776\pi$
$380$	885.840	0.119586
$381$	−8362.46	−1.12447
$382$	6167.92	0.826121
$383$	−3826.46	−0.510504	−0.255252	−	0.966875i	$-0.582158\pi$
$383$	−3826.46	−0.510504	−0.255252	+	0.966875i	$0.582158\pi$
$384$	−821.395	−0.109158
$385$	2687.85	0.355806
$386$	5546.02	0.731308
$387$	7758.45	1.01908
$388$	3891.75	0.509210
$389$	−3619.68	−0.471786	−0.235893	−	0.971779i	$-0.575802\pi$
$389$	−3619.68	−0.471786	−0.235893	+	0.971779i	$0.575802\pi$
$390$	0	0
$391$	8633.91	1.11671
$392$	392.000	0.0505076
$393$	7940.02	1.01914
$394$	8432.24	1.07820
$395$	2462.53	0.313679
$396$	−1334.87	−0.169393
$397$	−7567.95	−0.956736	−0.478368	−	0.878159i	$-0.658772\pi$
$397$	−7567.95	−0.956736	−0.478368	+	0.878159i	$0.658772\pi$
$398$	8335.76	1.04983
$399$	609.731	0.0765031
$400$	2259.06	0.282382
$401$	−1281.65	−0.159607	−0.0798034	−	0.996811i	$-0.525429\pi$
$401$	−1281.65	−0.159607	−0.0798034	+	0.996811i	$0.525429\pi$
$402$	−8353.22	−1.03637
$403$	0	0
$404$	−6067.78	−0.747235
$405$	−14859.8	−1.82319
$406$	507.993	0.0620967
$407$	3227.12	0.393028
$408$	6239.11	0.757064
$409$	8990.40	1.08691	0.543456	−	0.839438i	$-0.317116\pi$
$409$	8990.40	1.08691	0.543456	+	0.839438i	$0.317116\pi$
$410$	5605.14	0.675166
$411$	−5322.38	−0.638768
$412$	6667.48	0.797290
$413$	−1906.00	−0.227090
$414$	−2014.72	−0.239175
$415$	14937.6	1.76689
$416$	0	0
$417$	1837.22	0.215753
$418$	−638.908	−0.0747608
$419$	−5786.55	−0.674681	−0.337340	−	0.941383i	$-0.609527\pi$
$419$	−5786.55	−0.674681	−0.337340	+	0.941383i	$0.609527\pi$
$420$	2931.55	0.340583
$421$	−8420.66	−0.974817	−0.487409	−	0.873174i	$-0.662058\pi$
$421$	−8420.66	−0.974817	−0.487409	+	0.873174i	$0.662058\pi$
$422$	8500.97	0.980618
$423$	−1889.55	−0.217194
$424$	1883.64	0.215749
$425$	−17159.3	−1.95846
$426$	−2490.25	−0.283222
$427$	3061.02	0.346916
$428$	−934.990	−0.105594
$429$	0	0
$430$	17853.9	2.00230
$431$	12133.6	1.35605	0.678024	−	0.735040i	$-0.262837\pi$
$431$	12133.6	1.35605	0.678024	+	0.735040i	$0.262837\pi$
$432$	1316.31	0.146599
$433$	11131.9	1.23549	0.617744	−	0.786379i	$-0.288047\pi$
$433$	11131.9	1.23549	0.617744	+	0.786379i	$0.288047\pi$
$434$	265.984	0.0294186
$435$	3798.99	0.418730
$436$	7189.24	0.789684
$437$	−964.306	−0.105558
$438$	−12337.0	−1.34585
$439$	15842.3	1.72235	0.861175	−	0.508308i	$-0.169729\pi$
$439$	15842.3	1.72235	0.861175	+	0.508308i	$0.169729\pi$
$440$	−3071.83	−0.332826
$441$	694.808	0.0750252
$442$	0	0
$443$	−10539.2	−1.13032	−0.565161	−	0.824981i	$-0.691186\pi$
$443$	−10539.2	−1.13032	−0.565161	+	0.824981i	$0.691186\pi$
$444$	3519.71	0.376212
$445$	8029.28	0.855336
$446$	12285.3	1.30432
$447$	11233.9	1.18869
$448$	−448.000	−0.0472456
$449$	7859.50	0.826087	0.413043	−	0.910711i	$-0.364466\pi$
$449$	7859.50	0.826087	0.413043	+	0.910711i	$0.364466\pi$
$450$	4004.12	0.419457
$451$	−4042.68	−0.422089
$452$	−9352.12	−0.973201
$453$	6578.83	0.682341
$454$	−3616.04	−0.373809
$455$	0	0
$456$	−696.836	−0.0715621
$457$	−8879.79	−0.908925	−0.454463	−	0.890766i	$-0.650169\pi$
$457$	−8879.79	−0.908925	−0.454463	+	0.890766i	$0.650169\pi$
$458$	580.955	0.0592713
$459$	−9998.36	−1.01674
$460$	−4636.32	−0.469934
$461$	−5840.78	−0.590091	−0.295046	−	0.955483i	$-0.595335\pi$
$461$	−5840.78	−0.590091	−0.295046	+	0.955483i	$0.595335\pi$
$462$	−2114.36	−0.212920
$463$	7376.73	0.740444	0.370222	−	0.928943i	$-0.379282\pi$
$463$	7376.73	0.740444	0.370222	+	0.928943i	$0.379282\pi$
$464$	−580.563	−0.0580862
$465$	1989.15	0.198375
$466$	4201.69	0.417681
$467$	−1872.98	−0.185591	−0.0927957	−	0.995685i	$-0.529580\pi$
$467$	−1872.98	−0.185591	−0.0927957	+	0.995685i	$0.529580\pi$
$468$	0	0
$469$	−4555.96	−0.448560
$470$	−4348.27	−0.426746
$471$	20330.8	1.98895
$472$	2178.29	0.212424
$473$	−12877.0	−1.25177
$474$	−1937.12	−0.187711
$475$	1916.49	0.185125
$476$	3402.90	0.327671
$477$	3338.70	0.320479
$478$	−3307.00	−0.316440
$479$	15317.0	1.46107	0.730534	−	0.682876i	$-0.239271\pi$
$479$	15317.0	1.46107	0.730534	+	0.682876i	$0.239271\pi$
$480$	−3350.34	−0.318586
$481$	0	0
$482$	−882.455	−0.0833915
$483$	−3191.22	−0.300632
$484$	−3108.46	−0.291929
$485$	15873.8	1.48617
$486$	7246.77	0.676379
$487$	−6215.37	−0.578327	−0.289163	−	0.957280i	$-0.593377\pi$
$487$	−6215.37	−0.578327	−0.289163	+	0.957280i	$0.593377\pi$
$488$	−3498.31	−0.324510
$489$	−10575.4	−0.977986
$490$	1598.91	0.147411
$491$	570.831	0.0524669	0.0262335	−	0.999656i	$-0.491649\pi$
$491$	570.831	0.0524669	0.0262335	+	0.999656i	$0.491649\pi$
$492$	−4409.22	−0.404030
$493$	4409.82	0.402856
$494$	0	0
$495$	−5444.72	−0.494388
$496$	−303.982	−0.0275185
$497$	−1358.21	−0.122584
$498$	−11750.5	−1.05733
$499$	2965.89	0.266075	0.133038	−	0.991111i	$-0.457527\pi$
$499$	2965.89	0.266075	0.133038	+	0.991111i	$0.457527\pi$
$500$	1056.66	0.0945108
$501$	17773.5	1.58495
$502$	11293.7	1.00411
$503$	8979.27	0.795956	0.397978	−	0.917395i	$-0.369712\pi$
$503$	8979.27	0.795956	0.397978	+	0.917395i	$0.369712\pi$
$504$	−794.067	−0.0701796
$505$	−24749.5	−2.18087
$506$	3343.92	0.293786
$507$	0	0
$508$	5212.57	0.455257
$509$	16197.1	1.41046	0.705228	−	0.708981i	$-0.250845\pi$
$509$	16197.1	1.41046	0.705228	+	0.708981i	$0.250845\pi$
$510$	25448.3	2.20955
$511$	−6728.75	−0.582509
$512$	512.000	0.0441942
$513$	1116.70	0.0961082
$514$	−13659.9	−1.17221
$515$	27195.6	2.32695
$516$	−14044.5	−1.19821
$517$	3136.17	0.266787
$518$	1919.70	0.162831
$519$	10513.2	0.889170
$520$	0	0
$521$	9033.69	0.759641	0.379821	−	0.925060i	$-0.375986\pi$
$521$	9033.69	0.759641	0.379821	+	0.925060i	$0.375986\pi$
$522$	−1029.03	−0.0862825
$523$	−2699.17	−0.225672	−0.112836	−	0.993614i	$-0.535994\pi$
$523$	−2699.17	−0.225672	−0.112836	+	0.993614i	$0.535994\pi$
$524$	−4949.25	−0.412613
$525$	6342.31	0.527240
$526$	−4015.02	−0.332820
$527$	2308.97	0.190855
$528$	2416.42	0.199169
$529$	−7120.00	−0.585190
$530$	7683.08	0.629682
$531$	3860.96	0.315539
$532$	−380.064	−0.0309734
$533$	0	0
$534$	−6316.14	−0.511846
$535$	−3813.68	−0.308186
$536$	5206.81	0.419590
$537$	12049.1	0.968262
$538$	13920.1	1.11550
$539$	−1153.20	−0.0921558
$540$	5369.02	0.427863
$541$	−15298.2	−1.21575	−0.607875	−	0.794033i	$-0.707978\pi$
$541$	−15298.2	−1.21575	−0.607875	+	0.794033i	$0.707978\pi$
$542$	17068.2	1.35266
$543$	−29890.4	−2.36228
$544$	−3889.03	−0.306508
$545$	29323.8	2.30476
$546$	0	0
$547$	15393.5	1.20325	0.601626	−	0.798778i	$-0.294520\pi$
$547$	15393.5	1.20325	0.601626	+	0.798778i	$0.294520\pi$
$548$	3317.60	0.258615
$549$	−6200.64	−0.482035
$550$	−6645.80	−0.515233
$551$	−492.525	−0.0380803
$552$	3647.11	0.281216
$553$	−1056.53	−0.0812447
$554$	−10461.6	−0.802292
$555$	14356.3	1.09800
$556$	−1145.19	−0.0873506
$557$	−8011.34	−0.609428	−0.304714	−	0.952444i	$-0.598561\pi$
$557$	−8011.34	−0.609428	−0.304714	+	0.952444i	$0.598561\pi$
$558$	−538.799	−0.0408767
$559$	0	0
$560$	−1827.32	−0.137890
$561$	−18354.5	−1.38133
$562$	8506.82	0.638503
$563$	18410.1	1.37814	0.689069	−	0.724696i	$-0.258020\pi$
$563$	18410.1	1.37814	0.689069	+	0.724696i	$0.258020\pi$
$564$	3420.52	0.255372
$565$	−38145.8	−2.84037
$566$	−9667.64	−0.717953
$567$	6375.52	0.472216
$568$	1552.24	0.114667
$569$	10443.5	0.769448	0.384724	−	0.923032i	$-0.374297\pi$
$569$	10443.5	0.769448	0.384724	+	0.923032i	$0.374297\pi$
$570$	−2842.28	−0.208860
$571$	3218.86	0.235911	0.117955	−	0.993019i	$-0.462366\pi$
$571$	3218.86	0.235911	0.117955	+	0.993019i	$0.462366\pi$
$572$	0	0
$573$	−19790.2	−1.44284
$574$	−2404.85	−0.174872
$575$	−10030.5	−0.727482
$576$	907.505	0.0656470
$577$	−6872.73	−0.495867	−0.247934	−	0.968777i	$-0.579751\pi$
$577$	−6872.73	−0.495867	−0.247934	+	0.968777i	$0.579751\pi$
$578$	19714.1	1.41868
$579$	−17794.8	−1.27725
$580$	−2368.03	−0.169529
$581$	−6408.89	−0.457634
$582$	−12487.0	−0.889349
$583$	−5541.38	−0.393655
$584$	7690.00	0.544888
$585$	0	0
$586$	16766.9	1.18197
$587$	23211.7	1.63211	0.816055	−	0.577974i	$-0.196156\pi$
$587$	23211.7	1.63211	0.816055	+	0.577974i	$0.196156\pi$
$588$	−1257.76	−0.0882129
$589$	−257.885	−0.0180407
$590$	8884.90	0.619976
$591$	−27055.4	−1.88310
$592$	−2193.94	−0.152315
$593$	−13544.9	−0.937984	−0.468992	−	0.883203i	$-0.655383\pi$
$593$	−13544.9	−0.937984	−0.468992	+	0.883203i	$0.655383\pi$
$594$	−3872.38	−0.267484
$595$	13879.9	0.956336
$596$	−7002.40	−0.481257
$597$	−26745.9	−1.83356
$598$	0	0
$599$	−3740.74	−0.255163	−0.127581	−	0.991828i	$-0.540721\pi$
$599$	−3740.74	−0.255163	−0.127581	+	0.991828i	$0.540721\pi$
$600$	−7248.36	−0.493188
$601$	28183.7	1.91287	0.956436	−	0.291943i	$-0.0943018\pi$
$601$	28183.7	1.91287	0.956436	+	0.291943i	$0.0943018\pi$
$602$	−7660.09	−0.518608
$603$	9228.92	0.623268
$604$	−4100.78	−0.276256
$605$	−12678.9	−0.852019
$606$	19468.9	1.30507
$607$	−5887.64	−0.393694	−0.196847	−	0.980434i	$-0.563070\pi$
$607$	−5887.64	−0.393694	−0.196847	+	0.980434i	$0.563070\pi$
$608$	434.359	0.0289730
$609$	−1629.93	−0.108454
$610$	−14269.0	−0.947109
$611$	0	0
$612$	−6893.18	−0.455295
$613$	−11916.1	−0.785135	−0.392567	−	0.919723i	$-0.628413\pi$
$613$	−11916.1	−0.785135	−0.392567	+	0.919723i	$0.628413\pi$
$614$	5674.46	0.372968
$615$	−17984.5	−1.17919
$616$	1317.95	0.0862039
$617$	740.324	0.0483052	0.0241526	−	0.999708i	$-0.492311\pi$
$617$	740.324	0.0483052	0.0241526	+	0.999708i	$0.492311\pi$
$618$	−21393.1	−1.39249
$619$	−18224.8	−1.18339	−0.591693	−	0.806164i	$-0.701540\pi$
$619$	−18224.8	−1.18339	−0.591693	+	0.806164i	$0.701540\pi$
$620$	−1239.89	−0.0803151
$621$	−5844.60	−0.377674
$622$	14426.7	0.929997
$623$	−3444.91	−0.221537
$624$	0	0
$625$	−13338.9	−0.853692
$626$	10999.6	0.702290
$627$	2049.98	0.130572
$628$	−12672.8	−0.805256
$629$	16664.6	1.05638
$630$	−3238.87	−0.204825
$631$	−23620.2	−1.49018	−0.745091	−	0.666963i	$-0.767594\pi$
$631$	−23620.2	−1.49018	−0.745091	+	0.666963i	$0.767594\pi$
$632$	1207.46	0.0759974
$633$	−27276.0	−1.71267
$634$	−920.783	−0.0576798
$635$	21261.2	1.32870
$636$	−6043.80	−0.376812
$637$	0	0
$638$	1707.93	0.105984
$639$	2751.31	0.170329
$640$	2088.37	0.128984
$641$	860.082	0.0529972	0.0264986	−	0.999649i	$-0.491564\pi$
$641$	860.082	0.0529972	0.0264986	+	0.999649i	$0.491564\pi$
$642$	2999.98	0.184423
$643$	17289.2	1.06037	0.530187	−	0.847881i	$-0.322122\pi$
$643$	17289.2	1.06037	0.530187	+	0.847881i	$0.322122\pi$
$644$	1989.18	0.121715
$645$	−57285.5	−3.49708
$646$	−3299.28	−0.200942
$647$	−23330.9	−1.41767	−0.708835	−	0.705374i	$-0.750779\pi$
$647$	−23330.9	−1.41767	−0.708835	+	0.705374i	$0.750779\pi$
$648$	−7286.30	−0.441718
$649$	−6408.20	−0.387587
$650$	0	0
$651$	−853.430	−0.0513803
$652$	6591.95	0.395952
$653$	6657.73	0.398985	0.199492	−	0.979899i	$-0.436071\pi$
$653$	6657.73	0.398985	0.199492	+	0.979899i	$0.436071\pi$
$654$	−23067.2	−1.37920
$655$	−20187.2	−1.20424
$656$	2748.40	0.163578
$657$	13630.3	0.809389
$658$	1865.60	0.110530
$659$	13291.7	0.785690	0.392845	−	0.919605i	$-0.371491\pi$
$659$	13291.7	0.785690	0.392845	+	0.919605i	$0.371491\pi$
$660$	9856.18	0.581290
$661$	−1371.40	−0.0806980	−0.0403490	−	0.999186i	$-0.512847\pi$
$661$	−1371.40	−0.0806980	−0.0403490	+	0.999186i	$0.512847\pi$
$662$	−1840.10	−0.108032
$663$	0	0
$664$	7324.44	0.428077
$665$	−1550.22	−0.0903984
$666$	−3888.70	−0.226252
$667$	2577.78	0.149643
$668$	−11078.7	−0.641691
$669$	−39418.3	−2.27802
$670$	21237.8	1.22461
$671$	10291.5	0.592099
$672$	1437.44	0.0825156
$673$	−29099.0	−1.66669	−0.833346	−	0.552751i	$-0.813578\pi$
$673$	−29099.0	−1.66669	−0.833346	+	0.552751i	$0.813578\pi$
$674$	4887.74	0.279330
$675$	11615.7	0.662354
$676$	0	0
$677$	−7140.05	−0.405339	−0.202669	−	0.979247i	$-0.564962\pi$
$677$	−7140.05	−0.405339	−0.202669	+	0.979247i	$0.564962\pi$
$678$	30007.0	1.69972
$679$	−6810.56	−0.384927
$680$	−15862.7	−0.894570
$681$	11602.3	0.652867
$682$	894.268	0.0502101
$683$	−19997.6	−1.12033	−0.560165	−	0.828381i	$-0.689262\pi$
$683$	−19997.6	−1.12033	−0.560165	+	0.828381i	$0.689262\pi$
$684$	769.888	0.0430371
$685$	13532.0	0.754788
$686$	−686.000	−0.0381802
$687$	−1864.04	−0.103519
$688$	8754.39	0.485113
$689$	0	0
$690$	14876.0	0.820751
$691$	29266.3	1.61120	0.805602	−	0.592458i	$-0.201842\pi$
$691$	29266.3	1.61120	0.805602	+	0.592458i	$0.201842\pi$
$692$	−6553.21	−0.359994
$693$	2336.02	0.128049
$694$	1505.36	0.0823382
$695$	−4671.06	−0.254940
$696$	1862.78	0.101449
$697$	−20876.1	−1.13449
$698$	4005.19	0.217190
$699$	−13481.4	−0.729491
$700$	−3953.35	−0.213461
$701$	18808.2	1.01337	0.506686	−	0.862131i	$-0.330870\pi$
$701$	18808.2	1.01337	0.506686	+	0.862131i	$0.330870\pi$
$702$	0	0
$703$	−1861.24	−0.0998551
$704$	−1506.22	−0.0806363
$705$	13951.7	0.745324
$706$	−13755.1	−0.733260
$707$	10618.6	0.564857
$708$	−6989.21	−0.371003
$709$	24950.9	1.32165	0.660825	−	0.750540i	$-0.270206\pi$
$709$	24950.9	1.32165	0.660825	+	0.750540i	$0.270206\pi$
$710$	6331.36	0.334664
$711$	2140.20	0.112888
$712$	3937.04	0.207229
$713$	1349.72	0.0708941
$714$	−10918.4	−0.572286
$715$	0	0
$716$	−7510.56	−0.392015
$717$	10610.7	0.552671
$718$	−13840.6	−0.719395
$719$	12437.0	0.645093	0.322546	−	0.946554i	$-0.395461\pi$
$719$	12437.0	0.645093	0.322546	+	0.946554i	$0.395461\pi$
$720$	3701.57	0.191596
$721$	−11668.1	−0.602694
$722$	−13349.5	−0.688113
$723$	2831.42	0.145645
$724$	18631.6	0.956405
$725$	−5123.15	−0.262440
$726$	9973.72	0.509861
$727$	−2361.02	−0.120447	−0.0602237	−	0.998185i	$-0.519181\pi$
$727$	−2361.02	−0.120447	−0.0602237	+	0.998185i	$0.519181\pi$
$728$	0	0
$729$	1339.47	0.0680523
$730$	31366.3	1.59030
$731$	−66496.2	−3.36450
$732$	11224.6	0.566765
$733$	11501.4	0.579555	0.289777	−	0.957094i	$-0.406419\pi$
$733$	11501.4	0.579555	0.289777	+	0.957094i	$0.406419\pi$
$734$	−19401.2	−0.975631
$735$	−5130.21	−0.257456
$736$	−2273.35	−0.113854
$737$	−15317.6	−0.765580
$738$	4871.45	0.242982
$739$	−24047.5	−1.19703	−0.598514	−	0.801112i	$-0.704242\pi$
$739$	−24047.5	−1.19703	−0.598514	+	0.801112i	$0.704242\pi$
$740$	−8948.74	−0.444544
$741$	0	0
$742$	−3296.37	−0.163091
$743$	−22130.1	−1.09270	−0.546349	−	0.837558i	$-0.683983\pi$
$743$	−22130.1	−1.09270	−0.546349	+	0.837558i	$0.683983\pi$
$744$	975.348	0.0480618
$745$	−28561.7	−1.40459
$746$	−6583.34	−0.323101
$747$	12982.4	0.635876
$748$	11440.9	0.559253
$749$	1636.23	0.0798219
$750$	−3390.38	−0.165066
$751$	2976.06	0.144604	0.0723022	−	0.997383i	$-0.476965\pi$
$751$	2976.06	0.144604	0.0723022	+	0.997383i	$0.476965\pi$
$752$	−2132.11	−0.103391
$753$	−36236.6	−1.75370
$754$	0	0
$755$	−16726.4	−0.806275
$756$	−2303.54	−0.110819
$757$	−20416.3	−0.980241	−0.490120	−	0.871655i	$-0.663047\pi$
$757$	−20416.3	−0.980241	−0.490120	+	0.871655i	$0.663047\pi$
$758$	−19847.5	−0.951046
$759$	−10729.2	−0.513104
$760$	1771.68	0.0845600
$761$	−4983.91	−0.237407	−0.118703	−	0.992930i	$-0.537874\pi$
$761$	−4983.91	−0.237407	−0.118703	+	0.992930i	$0.537874\pi$
$762$	−16724.9	−0.795118
$763$	−12581.2	−0.596945
$764$	12335.8	0.584156
$765$	−28116.2	−1.32881
$766$	−7652.93	−0.360981
$767$	0	0
$768$	−1642.79	−0.0771863
$769$	−21101.4	−0.989514	−0.494757	−	0.869031i	$-0.664743\pi$
$769$	−21101.4	−0.989514	−0.494757	+	0.869031i	$0.664743\pi$
$770$	5375.70	0.251593
$771$	43828.9	2.04729
$772$	11092.0	0.517113
$773$	10943.5	0.509200	0.254600	−	0.967047i	$-0.418056\pi$
$773$	10943.5	0.509200	0.254600	+	0.967047i	$0.418056\pi$
$774$	15516.9	0.720599
$775$	−2682.47	−0.124332
$776$	7783.50	0.360066
$777$	−6159.49	−0.284389
$778$	−7239.36	−0.333603
$779$	2331.62	0.107239
$780$	0	0
$781$	−4566.46	−0.209220
$782$	17267.8	0.789637
$783$	−2985.16	−0.136246
$784$	784.000	0.0357143
$785$	−51690.5	−2.35021
$786$	15880.0	0.720639
$787$	−357.980	−0.0162142	−0.00810711	−	0.999967i	$-0.502581\pi$
$787$	−357.980	−0.0162142	−0.00810711	+	0.999967i	$0.502581\pi$
$788$	16864.5	0.762401
$789$	12882.5	0.581279
$790$	4925.06	0.221805
$791$	16366.2	0.735671
$792$	−2669.74	−0.119779
$793$	0	0
$794$	−15135.9	−0.676515
$795$	−24651.7	−1.09976
$796$	16671.5	0.742344
$797$	−23299.0	−1.03550	−0.517749	−	0.855533i	$-0.673230\pi$
$797$	−23299.0	−1.03550	−0.517749	+	0.855533i	$0.673230\pi$
$798$	1219.46	0.0540959
$799$	16195.0	0.717068
$800$	4518.12	0.199675
$801$	6978.28	0.307822
$802$	−2563.29	−0.112859
$803$	−22622.8	−0.994198
$804$	−16706.4	−0.732824
$805$	8113.56	0.355237
$806$	0	0
$807$	−44663.6	−1.94824
$808$	−12135.6	−0.528375
$809$	7262.47	0.315618	0.157809	−	0.987470i	$-0.449557\pi$
$809$	7262.47	0.315618	0.157809	+	0.987470i	$0.449557\pi$
$810$	−29719.7	−1.28919
$811$	−387.987	−0.0167991	−0.00839956	−	0.999965i	$-0.502674\pi$
$811$	−387.987	−0.0167991	−0.00839956	+	0.999965i	$0.502674\pi$
$812$	1015.99	0.0439090
$813$	−54764.6	−2.36246
$814$	6454.24	0.277913
$815$	26887.5	1.15562
$816$	12478.2	0.535325
$817$	7426.84	0.318032
$818$	17980.8	0.768562
$819$	0	0
$820$	11210.3	0.477414
$821$	4848.60	0.206111	0.103056	−	0.994676i	$-0.467138\pi$
$821$	4848.60	0.206111	0.103056	+	0.994676i	$0.467138\pi$
$822$	−10644.8	−0.451677
$823$	8220.08	0.348158	0.174079	−	0.984732i	$-0.444305\pi$
$823$	8220.08	0.348158	0.174079	+	0.984732i	$0.444305\pi$
$824$	13335.0	0.563769
$825$	21323.5	0.899867
$826$	−3812.01	−0.160577
$827$	−20734.4	−0.871833	−0.435916	−	0.899987i	$-0.643576\pi$
$827$	−20734.4	−0.871833	−0.435916	+	0.899987i	$0.643576\pi$
$828$	−4029.45	−0.169122
$829$	−11455.2	−0.479923	−0.239961	−	0.970782i	$-0.577135\pi$
$829$	−11455.2	−0.479923	−0.239961	+	0.970782i	$0.577135\pi$
$830$	29875.2	1.24938
$831$	33566.7	1.40122
$832$	0	0
$833$	−5955.07	−0.247696
$834$	3674.43	0.152560
$835$	−45188.5	−1.87283
$836$	−1277.82	−0.0528639
$837$	−1563.02	−0.0645472
$838$	−11573.1	−0.477071
$839$	10891.4	0.448167	0.224084	−	0.974570i	$-0.428061\pi$
$839$	10891.4	0.448167	0.224084	+	0.974570i	$0.428061\pi$
$840$	5863.09	0.240828
$841$	−23072.4	−0.946016
$842$	−16841.3	−0.689300
$843$	−27294.7	−1.11516
$844$	17001.9	0.693402
$845$	0	0
$846$	−3779.10	−0.153579
$847$	5439.80	0.220678
$848$	3767.28	0.152558
$849$	31019.3	1.25392
$850$	−34318.5	−1.38484
$851$	9741.40	0.392398
$852$	−4980.49	−0.200269
$853$	7628.62	0.306212	0.153106	−	0.988210i	$-0.451072\pi$
$853$	7628.62	0.306212	0.153106	+	0.988210i	$0.451072\pi$
$854$	6122.04	0.245307
$855$	3140.25	0.125607
$856$	−1869.98	−0.0746666
$857$	−24694.8	−0.984317	−0.492158	−	0.870506i	$-0.663792\pi$
$857$	−24694.8	−0.984317	−0.492158	+	0.870506i	$0.663792\pi$
$858$	0	0
$859$	−26236.8	−1.04213	−0.521064	−	0.853517i	$-0.674465\pi$
$859$	−26236.8	−1.04213	−0.521064	+	0.853517i	$0.674465\pi$
$860$	35707.8	1.41584
$861$	7716.13	0.305418
$862$	24267.3	0.958870
$863$	−29948.3	−1.18129	−0.590645	−	0.806932i	$-0.701126\pi$
$863$	−29948.3	−1.18129	−0.590645	+	0.806932i	$0.701126\pi$
$864$	2632.62	0.103661
$865$	−26729.5	−1.05067
$866$	22263.8	0.873622
$867$	−63254.1	−2.47776
$868$	531.968	0.0208021
$869$	−3552.18	−0.138664
$870$	7597.98	0.296087
$871$	0	0
$872$	14378.5	0.558391
$873$	13796.0	0.534850
$874$	−1928.61	−0.0746411
$875$	−1849.16	−0.0714435
$876$	−24673.9	−0.951660
$877$	24044.2	0.925786	0.462893	−	0.886414i	$-0.346811\pi$
$877$	24044.2	0.925786	0.462893	+	0.886414i	$0.346811\pi$
$878$	31684.6	1.21789
$879$	−53797.7	−2.06434
$880$	−6143.65	−0.235344
$881$	47105.2	1.80138	0.900689	−	0.434463i	$-0.143062\pi$
$881$	47105.2	1.80138	0.900689	+	0.434463i	$0.143062\pi$
$882$	1389.62	0.0530508
$883$	−28738.5	−1.09527	−0.547637	−	0.836716i	$-0.684472\pi$
$883$	−28738.5	−1.09527	−0.547637	+	0.836716i	$0.684472\pi$
$884$	0	0
$885$	−28507.9	−1.08280
$886$	−21078.4	−0.799258
$887$	−3119.14	−0.118073	−0.0590364	−	0.998256i	$-0.518803\pi$
$887$	−3119.14	−0.118073	−0.0590364	+	0.998256i	$0.518803\pi$
$888$	7039.42	0.266022
$889$	−9122.00	−0.344142
$890$	16058.6	0.604814
$891$	21435.2	0.805955
$892$	24570.6	0.922292
$893$	−1808.79	−0.0677815
$894$	22467.7	0.840528
$895$	−30634.4	−1.14413
$896$	−896.000	−0.0334077
$897$	0	0
$898$	15719.0	0.584131
$899$	689.378	0.0255751
$900$	8008.23	0.296601
$901$	−28615.4	−1.05806
$902$	−8085.36	−0.298462
$903$	24578.0	0.905762
$904$	−18704.2	−0.688157
$905$	75995.2	2.79134
$906$	13157.7	0.482488
$907$	21860.8	0.800305	0.400152	−	0.916449i	$-0.368957\pi$
$907$	21860.8	0.800305	0.400152	+	0.916449i	$0.368957\pi$
$908$	−7232.08	−0.264323
$909$	−21509.9	−0.784861
$910$	0	0
$911$	26945.0	0.979942	0.489971	−	0.871739i	$-0.337007\pi$
$911$	26945.0	0.979942	0.489971	+	0.871739i	$0.337007\pi$
$912$	−1393.67	−0.0506020
$913$	−21547.4	−0.781067
$914$	−17759.6	−0.642707
$915$	45783.3	1.65415
$916$	1161.91	0.0419112
$917$	8661.19	0.311906
$918$	−19996.7	−0.718944
$919$	41391.2	1.48571	0.742856	−	0.669452i	$-0.233471\pi$
$919$	41391.2	1.48571	0.742856	+	0.669452i	$0.233471\pi$
$920$	−9272.64	−0.332293
$921$	−18206.9	−0.651399
$922$	−11681.6	−0.417258
$923$	0	0
$924$	−4228.73	−0.150557
$925$	−19360.3	−0.688177
$926$	14753.5	0.523573
$927$	23635.8	0.837435
$928$	−1161.13	−0.0410731
$929$	−1155.34	−0.0408026	−0.0204013	−	0.999792i	$-0.506494\pi$
$929$	−1155.34	−0.0408026	−0.0204013	+	0.999792i	$0.506494\pi$
$930$	3978.29	0.140272
$931$	665.112	0.0234137
$932$	8403.38	0.295345
$933$	−46289.1	−1.62426
$934$	−3745.96	−0.131233
$935$	46665.7	1.63223
$936$	0	0
$937$	45962.5	1.60249	0.801243	−	0.598339i	$-0.204172\pi$
$937$	45962.5	1.60249	0.801243	+	0.598339i	$0.204172\pi$
$938$	−9111.92	−0.317180
$939$	−35293.1	−1.22657
$940$	−8696.54	−0.301755
$941$	−10558.8	−0.365789	−0.182895	−	0.983133i	$-0.558547\pi$
$941$	−10558.8	−0.365789	−0.182895	+	0.983133i	$0.558547\pi$
$942$	40661.7	1.40640
$943$	−12203.3	−0.421414
$944$	4356.58	0.150206
$945$	−9395.78	−0.323434
$946$	−25754.1	−0.885134
$947$	19038.8	0.653303	0.326651	−	0.945145i	$-0.394080\pi$
$947$	19038.8	0.653303	0.326651	+	0.945145i	$0.394080\pi$
$948$	−3874.24	−0.132731
$949$	0	0
$950$	3832.98	0.130903
$951$	2954.40	0.100739
$952$	6805.80	0.231699
$953$	−8723.69	−0.296525	−0.148262	−	0.988948i	$-0.547368\pi$
$953$	−8723.69	−0.296525	−0.148262	+	0.988948i	$0.547368\pi$
$954$	6677.40	0.226613
$955$	50315.9	1.70491
$956$	−6613.99	−0.223757
$957$	−5480.01	−0.185103
$958$	30634.0	1.03313
$959$	−5805.80	−0.195494
$960$	−6700.68	−0.225274
$961$	−29430.0	−0.987884
$962$	0	0
$963$	−3314.48	−0.110911
$964$	−1764.91	−0.0589667
$965$	45242.6	1.50924
$966$	−6382.44	−0.212579
$967$	−54728.4	−1.82001	−0.910004	−	0.414599i	$-0.863922\pi$
$967$	−54728.4	−1.82001	−0.910004	+	0.414599i	$0.863922\pi$
$968$	−6216.92	−0.206425
$969$	10586.0	0.350950
$970$	31747.6	1.05088
$971$	−47162.0	−1.55870	−0.779351	−	0.626588i	$-0.784451\pi$
$971$	−47162.0	−1.55870	−0.779351	+	0.626588i	$0.784451\pi$
$972$	14493.5	0.478272
$973$	2004.09	0.0660309
$974$	−12430.7	−0.408939
$975$	0	0
$976$	−6996.61	−0.229463
$977$	20259.6	0.663422	0.331711	−	0.943381i	$-0.392374\pi$
$977$	20259.6	0.663422	0.331711	+	0.943381i	$0.392374\pi$
$978$	−21150.8	−0.691540
$979$	−11582.2	−0.378108
$980$	3197.81	0.104235
$981$	25485.4	0.829446
$982$	1141.66	0.0370997
$983$	15282.9	0.495879	0.247939	−	0.968776i	$-0.420247\pi$
$983$	15282.9	0.495879	0.247939	+	0.968776i	$0.420247\pi$
$984$	−8818.43	−0.285692
$985$	68787.5	2.22513
$986$	8819.63	0.284862
$987$	−5985.90	−0.193043
$988$	0	0
$989$	−38870.7	−1.24976
$990$	−10889.4	−0.349585
$991$	−19966.4	−0.640014	−0.320007	−	0.947415i	$-0.603685\pi$
$991$	−19966.4	−0.640014	−0.320007	+	0.947415i	$0.603685\pi$
$992$	−607.964	−0.0194585
$993$	5904.09	0.188681
$994$	−2716.43	−0.0866800
$995$	68000.5	2.16659
$996$	−23501.0	−0.747648
$997$	−12890.1	−0.409462	−0.204731	−	0.978818i	$-0.565632\pi$
$997$	−12890.1	−0.409462	−0.204731	+	0.978818i	$0.565632\pi$
$998$	5931.78	0.188144
$999$	−11280.9	−0.357269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.4.a.bg.1.3		12
13.2	odd	12		182.4.m.b.43.12	✓	24
13.7	odd	12		182.4.m.b.127.12	yes	24
13.12	even	2		2366.4.a.bd.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.m.b.43.12	✓	24	13.2	odd	12
182.4.m.b.127.12	yes	24	13.7	odd	12
2366.4.a.bd.1.3		12	13.12	even	2
2366.4.a.bg.1.3		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -6.41715 q^{3} +4.00000 q^{4} +16.3154 q^{5} -12.8343 q^{6} -7.00000 q^{7} +8.00000 q^{8} +14.1798 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -6.41715 q^{3} +4.00000 q^{4} +16.3154 q^{5} -12.8343 q^{6} -7.00000 q^{7} +8.00000 q^{8} +14.1798 q^{9} +32.6307 q^{10} -23.5348 q^{11} -25.6686 q^{12} -14.0000 q^{14} -104.698 q^{15} +16.0000 q^{16} -121.532 q^{17} +28.3595 q^{18} +13.5737 q^{19} +65.2615 q^{20} +44.9200 q^{21} -47.0695 q^{22} -71.0422 q^{23} -51.3372 q^{24} +141.191 q^{25} +82.2693 q^{27} -28.0000 q^{28} -36.2852 q^{29} -209.396 q^{30} -18.9989 q^{31} +32.0000 q^{32} +151.026 q^{33} -243.064 q^{34} -114.208 q^{35} +56.7190 q^{36} -137.121 q^{37} +27.1474 q^{38} +130.523 q^{40} +171.775 q^{41} +89.8400 q^{42} +547.149 q^{43} -94.1391 q^{44} +231.348 q^{45} -142.084 q^{46} -133.257 q^{47} -102.674 q^{48} +49.0000 q^{49} +282.382 q^{50} +779.889 q^{51} +235.455 q^{53} +164.539 q^{54} -383.978 q^{55} -56.0000 q^{56} -87.1044 q^{57} -72.5704 q^{58} +272.286 q^{59} -418.792 q^{60} -437.288 q^{61} -37.9977 q^{62} -99.2583 q^{63} +64.0000 q^{64} +302.052 q^{66} +650.852 q^{67} -486.128 q^{68} +455.888 q^{69} -228.415 q^{70} +194.031 q^{71} +113.438 q^{72} +961.250 q^{73} -274.243 q^{74} -906.045 q^{75} +54.2948 q^{76} +164.743 q^{77} +150.933 q^{79} +261.046 q^{80} -910.788 q^{81} +343.550 q^{82} +915.555 q^{83} +179.680 q^{84} -1982.84 q^{85} +1094.30 q^{86} +232.847 q^{87} -188.278 q^{88} +492.130 q^{89} +462.696 q^{90} -284.169 q^{92} +121.919 q^{93} -266.514 q^{94} +221.460 q^{95} -205.349 q^{96} +972.937 q^{97} +98.0000 q^{98} -333.717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{2} + 6 q^{3} + 48 q^{4} + 28 q^{5} + 12 q^{6} - 84 q^{7} + 96 q^{8} + 162 q^{9}+O(q^{10}) \) 12 * q + 24 * q^2 + 6 * q^3 + 48 * q^4 + 28 * q^5 + 12 * q^6 - 84 * q^7 + 96 * q^8 + 162 * q^9	\( 12 q + 24 q^{2} + 6 q^{3} + 48 q^{4} + 28 q^{5} + 12 q^{6} - 84 q^{7} + 96 q^{8} + 162 q^{9} + 56 q^{10} + 6 q^{11} + 24 q^{12} - 168 q^{14} - 138 q^{15} + 192 q^{16} - 56 q^{17} + 324 q^{18} + 158 q^{19} + 112 q^{20} - 42 q^{21} + 12 q^{22} + 414 q^{23} + 48 q^{24} + 478 q^{25} + 390 q^{27} - 336 q^{28} + 222 q^{29} - 276 q^{30} - 200 q^{31} + 384 q^{32} + 844 q^{33} - 112 q^{34} - 196 q^{35} + 648 q^{36} - 560 q^{37} + 316 q^{38} + 224 q^{40} - 66 q^{41} - 84 q^{42} + 484 q^{43} + 24 q^{44} + 542 q^{45} + 828 q^{46} + 618 q^{47} + 96 q^{48} + 588 q^{49} + 956 q^{50} + 992 q^{51} + 504 q^{53} + 780 q^{54} + 2584 q^{55} - 672 q^{56} - 1164 q^{57} + 444 q^{58} + 1460 q^{59} - 552 q^{60} - 2 q^{61} - 400 q^{62} - 1134 q^{63} + 768 q^{64} + 1688 q^{66} + 334 q^{67} - 224 q^{68} + 4660 q^{69} - 392 q^{70} - 196 q^{71} + 1296 q^{72} + 490 q^{73} - 1120 q^{74} - 338 q^{75} + 632 q^{76} - 42 q^{77} + 2942 q^{79} + 448 q^{80} + 2824 q^{81} - 132 q^{82} + 236 q^{83} - 168 q^{84} + 1352 q^{85} + 968 q^{86} + 1456 q^{87} + 48 q^{88} + 3566 q^{89} + 1084 q^{90} + 1656 q^{92} + 1884 q^{93} + 1236 q^{94} + 5754 q^{95} + 192 q^{96} + 3032 q^{97} + 1176 q^{98} + 3670 q^{99}+O(q^{100}) \) 12 * q + 24 * q^2 + 6 * q^3 + 48 * q^4 + 28 * q^5 + 12 * q^6 - 84 * q^7 + 96 * q^8 + 162 * q^9 + 56 * q^10 + 6 * q^11 + 24 * q^12 - 168 * q^14 - 138 * q^15 + 192 * q^16 - 56 * q^17 + 324 * q^18 + 158 * q^19 + 112 * q^20 - 42 * q^21 + 12 * q^22 + 414 * q^23 + 48 * q^24 + 478 * q^25 + 390 * q^27 - 336 * q^28 + 222 * q^29 - 276 * q^30 - 200 * q^31 + 384 * q^32 + 844 * q^33 - 112 * q^34 - 196 * q^35 + 648 * q^36 - 560 * q^37 + 316 * q^38 + 224 * q^40 - 66 * q^41 - 84 * q^42 + 484 * q^43 + 24 * q^44 + 542 * q^45 + 828 * q^46 + 618 * q^47 + 96 * q^48 + 588 * q^49 + 956 * q^50 + 992 * q^51 + 504 * q^53 + 780 * q^54 + 2584 * q^55 - 672 * q^56 - 1164 * q^57 + 444 * q^58 + 1460 * q^59 - 552 * q^60 - 2 * q^61 - 400 * q^62 - 1134 * q^63 + 768 * q^64 + 1688 * q^66 + 334 * q^67 - 224 * q^68 + 4660 * q^69 - 392 * q^70 - 196 * q^71 + 1296 * q^72 + 490 * q^73 - 1120 * q^74 - 338 * q^75 + 632 * q^76 - 42 * q^77 + 2942 * q^79 + 448 * q^80 + 2824 * q^81 - 132 * q^82 + 236 * q^83 - 168 * q^84 + 1352 * q^85 + 968 * q^86 + 1456 * q^87 + 48 * q^88 + 3566 * q^89 + 1084 * q^90 + 1656 * q^92 + 1884 * q^93 + 1236 * q^94 + 5754 * q^95 + 192 * q^96 + 3032 * q^97 + 1176 * q^98 + 3670 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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