LMFDB - Embedded newform 1815.4.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} +7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} +7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} -12.8078 q^{10} -4.31534 q^{12} +49.1231 q^{13} -16.0000 q^{14} -15.0000 q^{15} -50.4233 q^{16} -82.7083 q^{17} +23.0540 q^{18} +130.354 q^{19} +7.19224 q^{20} -18.7386 q^{21} -185.693 q^{23} -72.5312 q^{24} +25.0000 q^{25} +125.831 q^{26} +27.0000 q^{27} +8.98485 q^{28} +8.90720 q^{29} -38.4233 q^{30} +5.26137 q^{31} +64.2547 q^{32} -211.862 q^{34} +31.2311 q^{35} -12.9460 q^{36} -416.894 q^{37} +333.909 q^{38} +147.369 q^{39} +120.885 q^{40} +298.479 q^{41} -48.0000 q^{42} +513.633 q^{43} -45.0000 q^{45} -475.663 q^{46} +557.295 q^{47} -151.270 q^{48} -303.985 q^{49} +64.0388 q^{50} -248.125 q^{51} -70.6610 q^{52} -168.064 q^{53} +69.1619 q^{54} +151.015 q^{56} +391.062 q^{57} +22.8163 q^{58} +618.773 q^{59} +21.5767 q^{60} -786.405 q^{61} +13.4773 q^{62} -56.2159 q^{63} +567.978 q^{64} -245.616 q^{65} -339.015 q^{67} +118.972 q^{68} -557.080 q^{69} +80.0000 q^{70} +1120.71 q^{71} -217.594 q^{72} +123.430 q^{73} -1067.90 q^{74} +75.0000 q^{75} -187.508 q^{76} +377.494 q^{78} +309.835 q^{79} +252.116 q^{80} +81.0000 q^{81} +764.570 q^{82} +1021.22 q^{83} +26.9545 q^{84} +413.542 q^{85} +1315.70 q^{86} +26.7216 q^{87} -141.879 q^{89} -115.270 q^{90} -306.833 q^{91} +267.110 q^{92} +15.7841 q^{93} +1427.54 q^{94} -651.771 q^{95} +192.764 q^{96} +798.345 q^{97} -778.673 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 + 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9	\( 2 q + q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9} - 5 q^{10} - 21 q^{12} + 90 q^{13} - 32 q^{14} - 30 q^{15} - 39 q^{16} + 16 q^{17} + 9 q^{18} + 170 q^{19} + 35 q^{20} + 12 q^{21} - 124 q^{23} - 9 q^{24} + 50 q^{25} + 62 q^{26} + 54 q^{27} - 48 q^{28} + 158 q^{29} - 15 q^{30} + 60 q^{31} - 123 q^{32} - 366 q^{34} - 20 q^{35} - 63 q^{36} - 372 q^{37} + 272 q^{38} + 270 q^{39} + 15 q^{40} - 38 q^{41} - 96 q^{42} + 516 q^{43} - 90 q^{45} - 572 q^{46} + 224 q^{47} - 117 q^{48} - 542 q^{49} + 25 q^{50} + 48 q^{51} - 298 q^{52} + 472 q^{53} + 27 q^{54} + 368 q^{56} + 510 q^{57} - 210 q^{58} + 248 q^{59} + 105 q^{60} - 72 q^{61} - 72 q^{62} + 36 q^{63} + 769 q^{64} - 450 q^{65} - 744 q^{67} - 430 q^{68} - 372 q^{69} + 160 q^{70} + 2060 q^{71} - 27 q^{72} + 486 q^{73} - 1138 q^{74} + 150 q^{75} - 408 q^{76} + 186 q^{78} - 642 q^{79} + 195 q^{80} + 162 q^{81} + 1290 q^{82} + 286 q^{83} - 144 q^{84} - 80 q^{85} + 1312 q^{86} + 474 q^{87} + 244 q^{89} - 45 q^{90} + 112 q^{91} - 76 q^{92} + 180 q^{93} + 1948 q^{94} - 850 q^{95} - 369 q^{96} - 168 q^{97} - 407 q^{98}+O(q^{100}) \) 2 * q + q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 + 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9 - 5 * q^10 - 21 * q^12 + 90 * q^13 - 32 * q^14 - 30 * q^15 - 39 * q^16 + 16 * q^17 + 9 * q^18 + 170 * q^19 + 35 * q^20 + 12 * q^21 - 124 * q^23 - 9 * q^24 + 50 * q^25 + 62 * q^26 + 54 * q^27 - 48 * q^28 + 158 * q^29 - 15 * q^30 + 60 * q^31 - 123 * q^32 - 366 * q^34 - 20 * q^35 - 63 * q^36 - 372 * q^37 + 272 * q^38 + 270 * q^39 + 15 * q^40 - 38 * q^41 - 96 * q^42 + 516 * q^43 - 90 * q^45 - 572 * q^46 + 224 * q^47 - 117 * q^48 - 542 * q^49 + 25 * q^50 + 48 * q^51 - 298 * q^52 + 472 * q^53 + 27 * q^54 + 368 * q^56 + 510 * q^57 - 210 * q^58 + 248 * q^59 + 105 * q^60 - 72 * q^61 - 72 * q^62 + 36 * q^63 + 769 * q^64 - 450 * q^65 - 744 * q^67 - 430 * q^68 - 372 * q^69 + 160 * q^70 + 2060 * q^71 - 27 * q^72 + 486 * q^73 - 1138 * q^74 + 150 * q^75 - 408 * q^76 + 186 * q^78 - 642 * q^79 + 195 * q^80 + 162 * q^81 + 1290 * q^82 + 286 * q^83 - 144 * q^84 - 80 * q^85 + 1312 * q^86 + 474 * q^87 + 244 * q^89 - 45 * q^90 + 112 * q^91 - 76 * q^92 + 180 * q^93 + 1948 * q^94 - 850 * q^95 - 369 * q^96 - 168 * q^97 - 407 * q^98

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 $

$2$	2.56155	0.905646	0.452823	−	0.891601i	$-0.350417\pi$
$2$	2.56155	0.905646	0.452823	+	0.891601i	$0.350417\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−1.43845	−0.179806
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	7.68466	0.522875
$7$	−6.24621	−0.337264	−0.168632	−	0.985679i	$-0.553935\pi$
$7$	−6.24621	−0.337264	−0.168632	+	0.985679i	$0.553935\pi$
$8$	−24.1771	−1.06849
$9$	9.00000	0.333333
$10$	−12.8078	−0.405017
$11$	0	0
$11$	0	0
$12$	−4.31534	−0.103811
$13$	49.1231	1.04802	0.524011	−	0.851711i	$-0.324435\pi$
$13$	49.1231	1.04802	0.524011	+	0.851711i	$0.324435\pi$
$14$	−16.0000	−0.305441
$15$	−15.0000	−0.258199
$16$	−50.4233	−0.787864
$17$	−82.7083	−1.17998	−0.589992	−	0.807409i	$-0.700869\pi$
$17$	−82.7083	−1.17998	−0.589992	+	0.807409i	$0.700869\pi$
$18$	23.0540	0.301882
$19$	130.354	1.57396	0.786981	−	0.616977i	$-0.211643\pi$
$19$	130.354	1.57396	0.786981	+	0.616977i	$0.211643\pi$
$20$	7.19224	0.0804116
$21$	−18.7386	−0.194719
$22$	0	0
$23$	−185.693	−1.68347	−0.841733	−	0.539895i	$-0.818464\pi$
$23$	−185.693	−1.68347	−0.841733	+	0.539895i	$0.818464\pi$
$24$	−72.5312	−0.616891
$25$	25.0000	0.200000
$26$	125.831	0.949137
$27$	27.0000	0.192450
$28$	8.98485	0.0606420
$29$	8.90720	0.0570354	0.0285177	−	0.999593i	$-0.490921\pi$
$29$	8.90720	0.0570354	0.0285177	+	0.999593i	$0.490921\pi$
$30$	−38.4233	−0.233837
$31$	5.26137	0.0304829	0.0152414	−	0.999884i	$-0.495148\pi$
$31$	5.26137	0.0304829	0.0152414	+	0.999884i	$0.495148\pi$
$32$	64.2547	0.354961
$33$	0	0
$34$	−211.862	−1.06865
$35$	31.2311	0.150829
$36$	−12.9460	−0.0599353
$37$	−416.894	−1.85235	−0.926175	−	0.377094i	$-0.876923\pi$
$37$	−416.894	−1.85235	−0.926175	+	0.377094i	$0.876923\pi$
$38$	333.909	1.42545
$39$	147.369	0.605076
$40$	120.885	0.477842
$41$	298.479	1.13694	0.568471	−	0.822703i	$-0.307535\pi$
$41$	298.479	1.13694	0.568471	+	0.822703i	$0.307535\pi$
$42$	−48.0000	−0.176347
$43$	513.633	1.82159	0.910793	−	0.412863i	$-0.135471\pi$
$43$	513.633	1.82159	0.910793	+	0.412863i	$0.135471\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	−475.663	−1.52462
$47$	557.295	1.72957	0.864786	−	0.502140i	$-0.167454\pi$
$47$	557.295	1.72957	0.864786	+	0.502140i	$0.167454\pi$
$48$	−151.270	−0.454873
$49$	−303.985	−0.886253
$50$	64.0388	0.181129
$51$	−248.125	−0.681264
$52$	−70.6610	−0.188441
$53$	−168.064	−0.435574	−0.217787	−	0.975996i	$-0.569884\pi$
$53$	−168.064	−0.435574	−0.217787	+	0.975996i	$0.569884\pi$
$54$	69.1619	0.174292
$55$	0	0
$56$	151.015	0.360362
$57$	391.062	0.908728
$58$	22.8163	0.0516539
$59$	618.773	1.36538	0.682689	−	0.730709i	$-0.260810\pi$
$59$	618.773	1.36538	0.682689	+	0.730709i	$0.260810\pi$
$60$	21.5767	0.0464257
$61$	−786.405	−1.65064	−0.825319	−	0.564667i	$-0.809004\pi$
$61$	−786.405	−1.65064	−0.825319	+	0.564667i	$0.809004\pi$
$62$	13.4773	0.0276067
$63$	−56.2159	−0.112421
$64$	567.978	1.10933
$65$	−245.616	−0.468690
$66$	0	0
$67$	−339.015	−0.618169	−0.309084	−	0.951035i	$-0.600023\pi$
$67$	−339.015	−0.618169	−0.309084	+	0.951035i	$0.600023\pi$
$68$	118.972	0.212168
$69$	−557.080	−0.971949
$70$	80.0000	0.136598
$71$	1120.71	1.87329	0.936645	−	0.350280i	$-0.113913\pi$
$71$	1120.71	1.87329	0.936645	+	0.350280i	$0.113913\pi$
$72$	−217.594	−0.356162
$73$	123.430	0.197896	0.0989478	−	0.995093i	$-0.468452\pi$
$73$	123.430	0.197896	0.0989478	+	0.995093i	$0.468452\pi$
$74$	−1067.90	−1.67757
$75$	75.0000	0.115470
$76$	−187.508	−0.283008
$77$	0	0
$78$	377.494	0.547985
$79$	309.835	0.441255	0.220628	−	0.975358i	$-0.429189\pi$
$79$	309.835	0.441255	0.220628	+	0.975358i	$0.429189\pi$
$80$	252.116	0.352343
$81$	81.0000	0.111111
$82$	764.570	1.02967
$83$	1021.22	1.35053	0.675263	−	0.737577i	$-0.264030\pi$
$83$	1021.22	1.35053	0.675263	+	0.737577i	$0.264030\pi$
$84$	26.9545	0.0350117
$85$	413.542	0.527705
$86$	1315.70	1.64971
$87$	26.7216	0.0329294
$88$	0	0
$89$	−141.879	−0.168979	−0.0844894	−	0.996424i	$-0.526926\pi$
$89$	−141.879	−0.168979	−0.0844894	+	0.996424i	$0.526926\pi$
$90$	−115.270	−0.135006
$91$	−306.833	−0.353460
$92$	267.110	0.302697
$93$	15.7841	0.0175993
$94$	1427.54	1.56638
$95$	−651.771	−0.703898
$96$	192.764	0.204937
$97$	798.345	0.835666	0.417833	−	0.908524i	$-0.362790\pi$
$97$	798.345	0.835666	0.417833	+	0.908524i	$0.362790\pi$
$98$	−778.673	−0.802631
$99$	0	0
$100$	−35.9612	−0.0359612
$101$	−241.400	−0.237823	−0.118912	−	0.992905i	$-0.537941\pi$
$101$	−241.400	−0.237823	−0.118912	+	0.992905i	$0.537941\pi$
$102$	−635.585	−0.616983
$103$	1168.38	1.11771	0.558853	−	0.829267i	$-0.311242\pi$
$103$	1168.38	1.11771	0.558853	+	0.829267i	$0.311242\pi$
$104$	−1187.65	−1.11980
$105$	93.6932	0.0870811
$106$	−430.506	−0.394476
$107$	2106.82	1.90350	0.951748	−	0.306882i	$-0.0992857\pi$
$107$	2106.82	1.90350	0.951748	+	0.306882i	$0.0992857\pi$
$108$	−38.8381	−0.0346037
$109$	−493.792	−0.433914	−0.216957	−	0.976181i	$-0.569613\pi$
$109$	−493.792	−0.433914	−0.216957	+	0.976181i	$0.569613\pi$
$110$	0	0
$111$	−1250.68	−1.06945
$112$	314.955	0.265718
$113$	170.000	0.141524	0.0707622	−	0.997493i	$-0.477457\pi$
$113$	170.000	0.141524	0.0707622	+	0.997493i	$0.477457\pi$
$114$	1001.73	0.822986
$115$	928.466	0.752869
$116$	−12.8125	−0.0102553
$117$	442.108	0.349341
$118$	1585.02	1.23655
$119$	516.614	0.397966
$120$	362.656	0.275882
$121$	0	0
$122$	−2014.42	−1.49489
$123$	895.437	0.656414
$124$	−7.56820	−0.00548100
$125$	−125.000	−0.0894427
$126$	−144.000	−0.101814
$127$	948.182	0.662500	0.331250	−	0.943543i	$-0.392530\pi$
$127$	948.182	0.662500	0.331250	+	0.943543i	$0.392530\pi$
$128$	940.868	0.649702
$129$	1540.90	1.05169
$130$	−629.157	−0.424467
$131$	1484.84	0.990312	0.495156	−	0.868804i	$-0.335111\pi$
$131$	1484.84	0.990312	0.495156	+	0.868804i	$0.335111\pi$
$132$	0	0
$133$	−814.220	−0.530841
$134$	−868.405	−0.559842
$135$	−135.000	−0.0860663
$136$	1999.65	1.26080
$137$	684.928	0.427134	0.213567	−	0.976928i	$-0.431492\pi$
$137$	684.928	0.427134	0.213567	+	0.976928i	$0.431492\pi$
$138$	−1426.99	−0.880242
$139$	−830.483	−0.506767	−0.253384	−	0.967366i	$-0.581543\pi$
$139$	−830.483	−0.506767	−0.253384	+	0.967366i	$0.581543\pi$
$140$	−44.9242	−0.0271199
$141$	1671.89	0.998569
$142$	2870.75	1.69654
$143$	0	0
$144$	−453.810	−0.262621
$145$	−44.5360	−0.0255070
$146$	316.172	0.179223
$147$	−911.955	−0.511679
$148$	599.680	0.333063
$149$	1213.64	0.667285	0.333642	−	0.942700i	$-0.391722\pi$
$149$	1213.64	0.667285	0.333642	+	0.942700i	$0.391722\pi$
$150$	192.116	0.104575
$151$	−30.8466	−0.0166242	−0.00831212	−	0.999965i	$-0.502646\pi$
$151$	−30.8466	−0.0166242	−0.00831212	+	0.999965i	$0.502646\pi$
$152$	−3151.58	−1.68176
$153$	−744.375	−0.393328
$154$	0	0
$155$	−26.3068	−0.0136324
$156$	−211.983	−0.108796
$157$	345.239	0.175497	0.0877485	−	0.996143i	$-0.472033\pi$
$157$	345.239	0.175497	0.0877485	+	0.996143i	$0.472033\pi$
$158$	793.659	0.399621
$159$	−504.193	−0.251479
$160$	−321.274	−0.158743
$161$	1159.88	0.567772
$162$	207.486	0.100627
$163$	1921.49	0.923331	0.461665	−	0.887054i	$-0.347252\pi$
$163$	1921.49	0.923331	0.461665	+	0.887054i	$0.347252\pi$
$164$	−429.346	−0.204429
$165$	0	0
$166$	2615.91	1.22310
$167$	−172.297	−0.0798369	−0.0399185	−	0.999203i	$-0.512710\pi$
$167$	−172.297	−0.0798369	−0.0399185	+	0.999203i	$0.512710\pi$
$168$	453.045	0.208055
$169$	216.080	0.0983521
$170$	1059.31	0.477913
$171$	1173.19	0.524654
$172$	−738.833	−0.327532
$173$	1025.29	0.450587	0.225293	−	0.974291i	$-0.427666\pi$
$173$	1025.29	0.450587	0.225293	+	0.974291i	$0.427666\pi$
$174$	68.4488	0.0298224
$175$	−156.155	−0.0674527
$176$	0	0
$177$	1856.32	0.788302
$178$	−363.430	−0.153035
$179$	1658.29	0.692437	0.346219	−	0.938154i	$-0.387466\pi$
$179$	1658.29	0.692437	0.346219	+	0.938154i	$0.387466\pi$
$180$	64.7301	0.0268039
$181$	−2021.81	−0.830275	−0.415137	−	0.909759i	$-0.636266\pi$
$181$	−2021.81	−0.830275	−0.415137	+	0.909759i	$0.636266\pi$
$182$	−785.970	−0.320110
$183$	−2359.22	−0.952996
$184$	4489.52	1.79876
$185$	2084.47	0.828396
$186$	40.4318	0.0159387
$187$	0	0
$188$	−801.640	−0.310987
$189$	−168.648	−0.0649064
$190$	−1669.55	−0.637482
$191$	1440.22	0.545607	0.272803	−	0.962070i	$-0.412049\pi$
$191$	1440.22	0.545607	0.272803	+	0.962070i	$0.412049\pi$
$192$	1703.93	0.640473
$193$	2798.05	1.04356	0.521782	−	0.853079i	$-0.325267\pi$
$193$	2798.05	1.04356	0.521782	+	0.853079i	$0.325267\pi$
$194$	2045.00	0.756817
$195$	−736.847	−0.270598
$196$	437.266	0.159354
$197$	−458.943	−0.165982	−0.0829908	−	0.996550i	$-0.526447\pi$
$197$	−458.943	−0.165982	−0.0829908	+	0.996550i	$0.526447\pi$
$198$	0	0
$199$	−2371.04	−0.844615	−0.422308	−	0.906453i	$-0.638780\pi$
$199$	−2371.04	−0.844615	−0.422308	+	0.906453i	$0.638780\pi$
$200$	−604.427	−0.213697
$201$	−1017.05	−0.356900
$202$	−618.358	−0.215384
$203$	−55.6363	−0.0192360
$204$	356.915	0.122495
$205$	−1492.40	−0.508456
$206$	2992.86	1.01225
$207$	−1671.24	−0.561155
$208$	−2476.95	−0.825699
$209$	0	0
$210$	240.000	0.0788646
$211$	−4319.87	−1.40944	−0.704721	−	0.709484i	$-0.748928\pi$
$211$	−4319.87	−1.40944	−0.704721	+	0.709484i	$0.748928\pi$
$212$	241.752	0.0783187
$213$	3362.12	1.08154
$214$	5396.73	1.72389
$215$	−2568.16	−0.814638
$216$	−652.781	−0.205630
$217$	−32.8636	−0.0102808
$218$	−1264.87	−0.392973
$219$	370.290	0.114255
$220$	0	0
$221$	−4062.89	−1.23665
$222$	−3203.69	−0.968547
$223$	−3837.73	−1.15244	−0.576219	−	0.817295i	$-0.695473\pi$
$223$	−3837.73	−1.15244	−0.576219	+	0.817295i	$0.695473\pi$
$224$	−401.349	−0.119715
$225$	225.000	0.0666667
$226$	435.464	0.128171
$227$	5003.71	1.46303	0.731515	−	0.681825i	$-0.238813\pi$
$227$	5003.71	1.46303	0.731515	+	0.681825i	$0.238813\pi$
$228$	−562.523	−0.163395
$229$	−277.375	−0.0800412	−0.0400206	−	0.999199i	$-0.512742\pi$
$229$	−277.375	−0.0800412	−0.0400206	+	0.999199i	$0.512742\pi$
$230$	2378.31	0.681832
$231$	0	0
$232$	−215.350	−0.0609415
$233$	−2269.91	−0.638225	−0.319113	−	0.947717i	$-0.603385\pi$
$233$	−2269.91	−0.638225	−0.319113	+	0.947717i	$0.603385\pi$
$234$	1132.48	0.316379
$235$	−2786.48	−0.773488
$236$	−890.072	−0.245503
$237$	929.505	0.254759
$238$	1323.33	0.360416
$239$	1617.11	0.437665	0.218832	−	0.975762i	$-0.429775\pi$
$239$	1617.11	0.437665	0.218832	+	0.975762i	$0.429775\pi$
$240$	756.349	0.203426
$241$	−5646.63	−1.50926	−0.754629	−	0.656151i	$-0.772183\pi$
$241$	−5646.63	−1.50926	−0.754629	+	0.656151i	$0.772183\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	1131.20	0.296794
$245$	1519.92	0.396344
$246$	2293.71	0.594478
$247$	6403.40	1.64955
$248$	−127.204	−0.0325705
$249$	3063.66	0.779726
$250$	−320.194	−0.0810034
$251$	−6217.61	−1.56355	−0.781777	−	0.623558i	$-0.785687\pi$
$251$	−6217.61	−1.56355	−0.781777	+	0.623558i	$0.785687\pi$
$252$	80.8636	0.0202140
$253$	0	0
$254$	2428.82	0.599991
$255$	1240.62	0.304670
$256$	−2133.74	−0.520933
$257$	7712.75	1.87202	0.936008	−	0.351980i	$-0.114491\pi$
$257$	7712.75	1.87202	0.936008	+	0.351980i	$0.114491\pi$
$258$	3947.09	0.952462
$259$	2604.01	0.624730
$260$	353.305	0.0842732
$261$	80.1648	0.0190118
$262$	3803.49	0.896871
$263$	−206.347	−0.0483798	−0.0241899	−	0.999707i	$-0.507701\pi$
$263$	−206.347	−0.0483798	−0.0241899	+	0.999707i	$0.507701\pi$
$264$	0	0
$265$	840.322	0.194795
$266$	−2085.67	−0.480753
$267$	−425.636	−0.0975600
$268$	487.655	0.111150
$269$	1712.47	0.388146	0.194073	−	0.980987i	$-0.437830\pi$
$269$	1712.47	0.388146	0.194073	+	0.980987i	$0.437830\pi$
$270$	−345.810	−0.0779456
$271$	477.081	0.106940	0.0534698	−	0.998569i	$-0.482972\pi$
$271$	477.081	0.106940	0.0534698	+	0.998569i	$0.482972\pi$
$272$	4170.43	0.929666
$273$	−920.500	−0.204070
$274$	1754.48	0.386832
$275$	0	0
$276$	801.329	0.174762
$277$	−4283.48	−0.929130	−0.464565	−	0.885539i	$-0.653789\pi$
$277$	−4283.48	−0.929130	−0.464565	+	0.885539i	$0.653789\pi$
$278$	−2127.33	−0.458952
$279$	47.3523	0.0101610
$280$	−755.076	−0.161159
$281$	−3477.79	−0.738319	−0.369160	−	0.929366i	$-0.620354\pi$
$281$	−3477.79	−0.738319	−0.369160	+	0.929366i	$0.620354\pi$
$282$	4282.62	0.904350
$283$	6568.27	1.37966	0.689829	−	0.723973i	$-0.257686\pi$
$283$	6568.27	1.37966	0.689829	+	0.723973i	$0.257686\pi$
$284$	−1612.08	−0.336829
$285$	−1955.31	−0.406395
$286$	0	0
$287$	−1864.36	−0.383449
$288$	578.292	0.118320
$289$	1927.67	0.392360
$290$	−114.081	−0.0231003
$291$	2395.03	0.482472
$292$	−177.547	−0.0355828
$293$	−8352.29	−1.66534	−0.832672	−	0.553766i	$-0.813190\pi$
$293$	−8352.29	−1.66534	−0.832672	+	0.553766i	$0.813190\pi$
$294$	−2336.02	−0.463399
$295$	−3093.86	−0.610616
$296$	10079.3	1.97921
$297$	0	0
$298$	3108.81	0.604324
$299$	−9121.83	−1.76431
$300$	−107.884	−0.0207622
$301$	−3208.26	−0.614355
$302$	−79.0152	−0.0150557
$303$	−724.199	−0.137307
$304$	−6572.89	−1.24007
$305$	3932.03	0.738187
$306$	−1906.76	−0.356216
$307$	−5383.89	−1.00090	−0.500448	−	0.865767i	$-0.666831\pi$
$307$	−5383.89	−1.00090	−0.500448	+	0.865767i	$0.666831\pi$
$308$	0	0
$309$	3505.14	0.645308
$310$	−67.3863	−0.0123461
$311$	−1790.41	−0.326447	−0.163223	−	0.986589i	$-0.552189\pi$
$311$	−1790.41	−0.326447	−0.163223	+	0.986589i	$0.552189\pi$
$312$	−3562.96	−0.646516
$313$	−809.076	−0.146108	−0.0730538	−	0.997328i	$-0.523274\pi$
$313$	−809.076	−0.146108	−0.0730538	+	0.997328i	$0.523274\pi$
$314$	884.347	0.158938
$315$	281.080	0.0502763
$316$	−445.682	−0.0793403
$317$	10744.5	1.90370	0.951849	−	0.306567i	$-0.0991804\pi$
$317$	10744.5	1.90370	0.951849	+	0.306567i	$0.0991804\pi$
$318$	−1291.52	−0.227751
$319$	0	0
$320$	−2839.89	−0.496109
$321$	6320.46	1.09898
$322$	2971.09	0.514200
$323$	−10781.4	−1.85725
$324$	−116.514	−0.0199784
$325$	1228.08	0.209605
$326$	4922.00	0.836210
$327$	−1481.37	−0.250521
$328$	−7216.35	−1.21481
$329$	−3480.98	−0.583322
$330$	0	0
$331$	3399.12	0.564449	0.282224	−	0.959348i	$-0.408928\pi$
$331$	3399.12	0.564449	0.282224	+	0.959348i	$0.408928\pi$
$332$	−1468.97	−0.242832
$333$	−3752.05	−0.617450
$334$	−441.349	−0.0723039
$335$	1695.08	0.276453
$336$	944.864	0.153412
$337$	11840.0	1.91384	0.956919	−	0.290356i	$-0.0937736\pi$
$337$	11840.0	1.91384	0.956919	+	0.290356i	$0.0937736\pi$
$338$	553.499	0.0890721
$339$	510.000	0.0817091
$340$	−594.858	−0.0948844
$341$	0	0
$342$	3005.18	0.475151
$343$	4041.20	0.636165
$344$	−12418.1	−1.94634
$345$	2785.40	0.434669
$346$	2626.34	0.408072
$347$	2076.67	0.321272	0.160636	−	0.987014i	$-0.448645\pi$
$347$	2076.67	0.321272	0.160636	+	0.987014i	$0.448645\pi$
$348$	−38.4376	−0.00592090
$349$	−5837.37	−0.895322	−0.447661	−	0.894203i	$-0.647743\pi$
$349$	−5837.37	−0.895322	−0.447661	+	0.894203i	$0.647743\pi$
$350$	−400.000	−0.0610883
$351$	1326.32	0.201692
$352$	0	0
$353$	−2423.64	−0.365431	−0.182715	−	0.983166i	$-0.558489\pi$
$353$	−2423.64	−0.365431	−0.182715	+	0.983166i	$0.558489\pi$
$354$	4755.06	0.713922
$355$	−5603.54	−0.837761
$356$	204.085	0.0303834
$357$	1549.84	0.229765
$358$	4247.79	0.627103
$359$	3882.22	0.570740	0.285370	−	0.958417i	$-0.407884\pi$
$359$	3882.22	0.570740	0.285370	+	0.958417i	$0.407884\pi$
$360$	1087.97	0.159281
$361$	10133.2	1.47736
$362$	−5178.96	−0.751935
$363$	0	0
$364$	441.363	0.0635542
$365$	−617.150	−0.0885016
$366$	−6043.26	−0.863077
$367$	5666.65	0.805986	0.402993	−	0.915203i	$-0.367970\pi$
$367$	5666.65	0.805986	0.402993	+	0.915203i	$0.367970\pi$
$368$	9363.26	1.32634
$369$	2686.31	0.378981
$370$	5339.48	0.750233
$371$	1049.77	0.146903
$372$	−22.7046	−0.00316446
$373$	−174.771	−0.0242608	−0.0121304	−	0.999926i	$-0.503861\pi$
$373$	−174.771	−0.0242608	−0.0121304	+	0.999926i	$0.503861\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−13473.8	−1.84802
$377$	437.550	0.0597744
$378$	−432.000	−0.0587822
$379$	252.686	0.0342470	0.0171235	−	0.999853i	$-0.494549\pi$
$379$	252.686	0.0342470	0.0171235	+	0.999853i	$0.494549\pi$
$380$	937.538	0.126565
$381$	2844.55	0.382495
$382$	3689.21	0.494126
$383$	−11014.5	−1.46950	−0.734748	−	0.678340i	$-0.762700\pi$
$383$	−11014.5	−1.46950	−0.734748	+	0.678340i	$0.762700\pi$
$384$	2822.61	0.375105
$385$	0	0
$386$	7167.35	0.945099
$387$	4622.69	0.607196
$388$	−1148.38	−0.150258
$389$	8099.40	1.05567	0.527835	−	0.849347i	$-0.323004\pi$
$389$	8099.40	1.05567	0.527835	+	0.849347i	$0.323004\pi$
$390$	−1887.47	−0.245066
$391$	15358.4	1.98646
$392$	7349.47	0.946949
$393$	4454.51	0.571757
$394$	−1175.61	−0.150320
$395$	−1549.18	−0.197335
$396$	0	0
$397$	−424.353	−0.0536465	−0.0268232	−	0.999640i	$-0.508539\pi$
$397$	−424.353	−0.0536465	−0.0268232	+	0.999640i	$0.508539\pi$
$398$	−6073.54	−0.764922
$399$	−2442.66	−0.306481
$400$	−1260.58	−0.157573
$401$	−5904.18	−0.735263	−0.367632	−	0.929972i	$-0.619831\pi$
$401$	−5904.18	−0.735263	−0.367632	+	0.929972i	$0.619831\pi$
$402$	−2605.22	−0.323225
$403$	258.455	0.0319468
$404$	347.241	0.0427620
$405$	−405.000	−0.0496904
$406$	−142.515	−0.0174210
$407$	0	0
$408$	5998.94	0.727921
$409$	−1370.47	−0.165686	−0.0828430	−	0.996563i	$-0.526400\pi$
$409$	−1370.47	−0.165686	−0.0828430	+	0.996563i	$0.526400\pi$
$410$	−3822.85	−0.460481
$411$	2054.78	0.246606
$412$	−1680.65	−0.200970
$413$	−3864.98	−0.460493
$414$	−4280.97	−0.508208
$415$	−5106.11	−0.603973
$416$	3156.39	0.372007
$417$	−2491.45	−0.292582
$418$	0	0
$419$	1268.73	0.147927	0.0739635	−	0.997261i	$-0.476435\pi$
$419$	1268.73	0.147927	0.0739635	+	0.997261i	$0.476435\pi$
$420$	−134.773	−0.0156577
$421$	−12241.9	−1.41719	−0.708594	−	0.705617i	$-0.750670\pi$
$421$	−12241.9	−1.41719	−0.708594	+	0.705617i	$0.750670\pi$
$422$	−11065.6	−1.27646
$423$	5015.66	0.576524
$424$	4063.31	0.465405
$425$	−2067.71	−0.235997
$426$	8612.26	0.979496
$427$	4912.05	0.556700
$428$	−3030.55	−0.342260
$429$	0	0
$430$	−6578.48	−0.737774
$431$	−8050.11	−0.899675	−0.449838	−	0.893110i	$-0.648518\pi$
$431$	−8050.11	−0.899675	−0.449838	+	0.893110i	$0.648518\pi$
$432$	−1361.43	−0.151624
$433$	−16565.7	−1.83856	−0.919282	−	0.393600i	$-0.871230\pi$
$433$	−16565.7	−1.83856	−0.919282	+	0.393600i	$0.871230\pi$
$434$	−84.1819	−0.00931073
$435$	−133.608	−0.0147265
$436$	710.293	0.0780203
$437$	−24205.9	−2.64971
$438$	948.517	0.103475
$439$	−4705.80	−0.511607	−0.255804	−	0.966729i	$-0.582340\pi$
$439$	−4705.80	−0.511607	−0.255804	+	0.966729i	$0.582340\pi$
$440$	0	0
$441$	−2735.86	−0.295418
$442$	−10407.3	−1.11997
$443$	15094.0	1.61882	0.809408	−	0.587246i	$-0.199788\pi$
$443$	15094.0	1.61882	0.809408	+	0.587246i	$0.199788\pi$
$444$	1799.04	0.192294
$445$	709.394	0.0755696
$446$	−9830.56	−1.04370
$447$	3640.93	0.385257
$448$	−3547.71	−0.374138
$449$	973.478	0.102319	0.0511595	−	0.998690i	$-0.483708\pi$
$449$	973.478	0.102319	0.0511595	+	0.998690i	$0.483708\pi$
$450$	576.349	0.0603764
$451$	0	0
$452$	−244.536	−0.0254469
$453$	−92.5398	−0.00959801
$454$	12817.3	1.32499
$455$	1534.17	0.158072
$456$	−9454.75	−0.970963
$457$	−62.6577	−0.00641358	−0.00320679	−	0.999995i	$-0.501021\pi$
$457$	−62.6577	−0.00641358	−0.00320679	+	0.999995i	$0.501021\pi$
$458$	−710.510	−0.0724890
$459$	−2233.12	−0.227088
$460$	−1335.55	−0.135370
$461$	11866.2	1.19884	0.599419	−	0.800436i	$-0.295398\pi$
$461$	11866.2	1.19884	0.599419	+	0.800436i	$0.295398\pi$
$462$	0	0
$463$	−13144.8	−1.31942	−0.659711	−	0.751519i	$-0.729321\pi$
$463$	−13144.8	−1.31942	−0.659711	+	0.751519i	$0.729321\pi$
$464$	−449.131	−0.0449361
$465$	−78.9205	−0.00787065
$466$	−5814.48	−0.578006
$467$	−10176.8	−1.00840	−0.504201	−	0.863586i	$-0.668213\pi$
$467$	−10176.8	−1.00840	−0.504201	+	0.863586i	$0.668213\pi$
$468$	−635.949	−0.0628136
$469$	2117.56	0.208486
$470$	−7137.71	−0.700506
$471$	1035.72	0.101323
$472$	−14960.1	−1.45889
$473$	0	0
$474$	2380.98	0.230721
$475$	3258.85	0.314793
$476$	−743.121	−0.0715565
$477$	−1512.58	−0.145191
$478$	4142.30	0.396369
$479$	−3431.25	−0.327302	−0.163651	−	0.986518i	$-0.552327\pi$
$479$	−3431.25	−0.327302	−0.163651	+	0.986518i	$0.552327\pi$
$480$	−963.821	−0.0916504
$481$	−20479.1	−1.94130
$482$	−14464.1	−1.36685
$483$	3479.64	0.327803
$484$	0	0
$485$	−3991.72	−0.373721
$486$	622.457	0.0580972
$487$	−2833.20	−0.263624	−0.131812	−	0.991275i	$-0.542079\pi$
$487$	−2833.20	−0.263624	−0.131812	+	0.991275i	$0.542079\pi$
$488$	19013.0	1.76368
$489$	5764.48	0.533085
$490$	3893.37	0.358948
$491$	2667.29	0.245159	0.122580	−	0.992459i	$-0.460883\pi$
$491$	2667.29	0.245159	0.122580	+	0.992459i	$0.460883\pi$
$492$	−1288.04	−0.118027
$493$	−736.700	−0.0673008
$494$	16402.7	1.49391
$495$	0	0
$496$	−265.295	−0.0240164
$497$	−7000.18	−0.631793
$498$	7847.74	0.706156
$499$	−11137.0	−0.999120	−0.499560	−	0.866279i	$-0.666505\pi$
$499$	−11137.0	−0.999120	−0.499560	+	0.866279i	$0.666505\pi$
$500$	179.806	0.0160823
$501$	−516.892	−0.0460939
$502$	−15926.7	−1.41603
$503$	−8780.30	−0.778319	−0.389159	−	0.921170i	$-0.627234\pi$
$503$	−8780.30	−0.778319	−0.389159	+	0.921170i	$0.627234\pi$
$504$	1359.14	0.120121
$505$	1207.00	0.106358
$506$	0	0
$507$	648.239	0.0567836
$508$	−1363.91	−0.119121
$509$	13597.4	1.18408	0.592039	−	0.805910i	$-0.298323\pi$
$509$	13597.4	1.18408	0.592039	+	0.805910i	$0.298323\pi$
$510$	3177.93	0.275923
$511$	−770.969	−0.0667430
$512$	−12992.6	−1.12148
$513$	3519.56	0.302909
$514$	19756.6	1.69538
$515$	−5841.89	−0.499854
$516$	−2216.50	−0.189101
$517$	0	0
$518$	6670.30	0.565784
$519$	3075.88	0.260146
$520$	5938.27	0.500789
$521$	14001.3	1.17736	0.588682	−	0.808364i	$-0.299647\pi$
$521$	14001.3	1.17736	0.588682	+	0.808364i	$0.299647\pi$
$522$	205.346	0.0172180
$523$	14749.8	1.23320	0.616602	−	0.787275i	$-0.288509\pi$
$523$	14749.8	1.23320	0.616602	+	0.787275i	$0.288509\pi$
$524$	−2135.86	−0.178064
$525$	−468.466	−0.0389439
$526$	−528.568	−0.0438149
$527$	−435.159	−0.0359693
$528$	0	0
$529$	22315.0	1.83406
$530$	2152.53	0.176415
$531$	5568.95	0.455126
$532$	1171.21	0.0954483
$533$	14662.2	1.19154
$534$	−1090.29	−0.0883548
$535$	−10534.1	−0.851269
$536$	8196.40	0.660505
$537$	4974.86	0.399779
$538$	4386.59	0.351523
$539$	0	0
$540$	194.190	0.0154752
$541$	−1484.06	−0.117939	−0.0589694	−	0.998260i	$-0.518781\pi$
$541$	−1484.06	−0.117939	−0.0589694	+	0.998260i	$0.518781\pi$
$542$	1222.07	0.0968493
$543$	−6065.42	−0.479359
$544$	−5314.40	−0.418847
$545$	2468.96	0.194052
$546$	−2357.91	−0.184815
$547$	16562.2	1.29460	0.647302	−	0.762234i	$-0.275897\pi$
$547$	16562.2	1.29460	0.647302	+	0.762234i	$0.275897\pi$
$548$	−985.233	−0.0768012
$549$	−7077.65	−0.550212
$550$	0	0
$551$	1161.09	0.0897716
$552$	13468.6	1.03851
$553$	−1935.30	−0.148819
$554$	−10972.3	−0.841463
$555$	6253.41	0.478275
$556$	1194.61	0.0911197
$557$	8821.52	0.671059	0.335529	−	0.942030i	$-0.391085\pi$
$557$	8821.52	0.671059	0.335529	+	0.942030i	$0.391085\pi$
$558$	121.295	0.00920223
$559$	25231.2	1.90906
$560$	−1574.77	−0.118833
$561$	0	0
$562$	−8908.55	−0.668656
$563$	5985.53	0.448064	0.224032	−	0.974582i	$-0.428078\pi$
$563$	5985.53	0.448064	0.224032	+	0.974582i	$0.428078\pi$
$564$	−2404.92	−0.179549
$565$	−850.000	−0.0632916
$566$	16825.0	1.24948
$567$	−505.943	−0.0374737
$568$	−27095.5	−2.00158
$569$	3453.08	0.254413	0.127206	−	0.991876i	$-0.459399\pi$
$569$	3453.08	0.254413	0.127206	+	0.991876i	$0.459399\pi$
$570$	−5008.64	−0.368050
$571$	21484.5	1.57460	0.787302	−	0.616568i	$-0.211477\pi$
$571$	21484.5	1.57460	0.787302	+	0.616568i	$0.211477\pi$
$572$	0	0
$573$	4320.67	0.315006
$574$	−4775.67	−0.347269
$575$	−4642.33	−0.336693
$576$	5111.80	0.369777
$577$	−13294.4	−0.959189	−0.479594	−	0.877490i	$-0.659216\pi$
$577$	−13294.4	−0.959189	−0.479594	+	0.877490i	$0.659216\pi$
$578$	4937.82	0.355340
$579$	8394.14	0.602502
$580$	64.0627	0.00458631
$581$	−6378.77	−0.455483
$582$	6135.01	0.436949
$583$	0	0
$584$	−2984.18	−0.211449
$585$	−2210.54	−0.156230
$586$	−21394.8	−1.50821
$587$	6695.73	0.470805	0.235402	−	0.971898i	$-0.424359\pi$
$587$	6695.73	0.470805	0.235402	+	0.971898i	$0.424359\pi$
$588$	1311.80	0.0920028
$589$	685.841	0.0479789
$590$	−7925.09	−0.553002
$591$	−1376.83	−0.0958295
$592$	21021.2	1.45940
$593$	10239.6	0.709088	0.354544	−	0.935039i	$-0.384636\pi$
$593$	10239.6	0.709088	0.354544	+	0.935039i	$0.384636\pi$
$594$	0	0
$595$	−2583.07	−0.177976
$596$	−1745.76	−0.119982
$597$	−7113.11	−0.487639
$598$	−23366.0	−1.59784
$599$	−23890.8	−1.62963	−0.814817	−	0.579719i	$-0.803162\pi$
$599$	−23890.8	−1.62963	−0.814817	+	0.579719i	$0.803162\pi$
$600$	−1813.28	−0.123378
$601$	11343.8	0.769920	0.384960	−	0.922933i	$-0.374215\pi$
$601$	11343.8	0.769920	0.384960	+	0.922933i	$0.374215\pi$
$602$	−8218.12	−0.556388
$603$	−3051.14	−0.206056
$604$	44.3712	0.00298914
$605$	0	0
$606$	−1855.07	−0.124352
$607$	26032.5	1.74074	0.870369	−	0.492399i	$-0.163880\pi$
$607$	26032.5	1.74074	0.870369	+	0.492399i	$0.163880\pi$
$608$	8375.87	0.558695
$609$	−166.909	−0.0111059
$610$	10072.1	0.668536
$611$	27376.1	1.81263
$612$	1070.74	0.0707226
$613$	4568.13	0.300987	0.150493	−	0.988611i	$-0.451914\pi$
$613$	4568.13	0.300987	0.150493	+	0.988611i	$0.451914\pi$
$614$	−13791.1	−0.906457
$615$	−4477.19	−0.293557
$616$	0	0
$617$	−12755.9	−0.832308	−0.416154	−	0.909294i	$-0.636622\pi$
$617$	−12755.9	−0.832308	−0.416154	+	0.909294i	$0.636622\pi$
$618$	8978.59	0.584421
$619$	−1138.94	−0.0739545	−0.0369772	−	0.999316i	$-0.511773\pi$
$619$	−1138.94	−0.0739545	−0.0369772	+	0.999316i	$0.511773\pi$
$620$	37.8410	0.00245118
$621$	−5013.72	−0.323983
$622$	−4586.24	−0.295645
$623$	886.205	0.0569904
$624$	−7430.85	−0.476718
$625$	625.000	0.0400000
$626$	−2072.49	−0.132322
$627$	0	0
$628$	−496.607	−0.0315554
$629$	34480.6	2.18574
$630$	720.000	0.0455325
$631$	7997.36	0.504548	0.252274	−	0.967656i	$-0.418822\pi$
$631$	7997.36	0.504548	0.252274	+	0.967656i	$0.418822\pi$
$632$	−7490.91	−0.471475
$633$	−12959.6	−0.813742
$634$	27522.7	1.72408
$635$	−4740.91	−0.296279
$636$	725.255	0.0452173
$637$	−14932.7	−0.928814
$638$	0	0
$639$	10086.4	0.624430
$640$	−4704.34	−0.290555
$641$	−573.115	−0.0353146	−0.0176573	−	0.999844i	$-0.505621\pi$
$641$	−573.115	−0.0353146	−0.0176573	+	0.999844i	$0.505621\pi$
$642$	16190.2	0.995290
$643$	−16027.8	−0.983009	−0.491504	−	0.870875i	$-0.663553\pi$
$643$	−16027.8	−0.983009	−0.491504	+	0.870875i	$0.663553\pi$
$644$	−1668.42	−0.102089
$645$	−7704.49	−0.470332
$646$	−27617.1	−1.68201
$647$	−2622.74	−0.159367	−0.0796837	−	0.996820i	$-0.525391\pi$
$647$	−2622.74	−0.159367	−0.0796837	+	0.996820i	$0.525391\pi$
$648$	−1958.34	−0.118721
$649$	0	0
$650$	3145.79	0.189827
$651$	−98.5908	−0.00593560
$652$	−2763.97	−0.166020
$653$	3102.00	0.185897	0.0929484	−	0.995671i	$-0.470371\pi$
$653$	3102.00	0.185897	0.0929484	+	0.995671i	$0.470371\pi$
$654$	−3794.62	−0.226883
$655$	−7424.19	−0.442881
$656$	−15050.3	−0.895755
$657$	1110.87	0.0659652
$658$	−8916.73	−0.528283
$659$	20840.2	1.23190	0.615948	−	0.787787i	$-0.288773\pi$
$659$	20840.2	1.23190	0.615948	+	0.787787i	$0.288773\pi$
$660$	0	0
$661$	18242.9	1.07348	0.536738	−	0.843749i	$-0.319657\pi$
$661$	18242.9	1.07348	0.536738	+	0.843749i	$0.319657\pi$
$662$	8707.03	0.511191
$663$	−12188.7	−0.713980
$664$	−24690.2	−1.44302
$665$	4071.10	0.237399
$666$	−9611.06	−0.559191
$667$	−1654.01	−0.0960171
$668$	247.841	0.0143551
$669$	−11513.2	−0.665361
$670$	4342.03	0.250369
$671$	0	0
$672$	−1204.05	−0.0691177
$673$	12746.6	0.730084	0.365042	−	0.930991i	$-0.381055\pi$
$673$	12746.6	0.730084	0.365042	+	0.930991i	$0.381055\pi$
$674$	30328.7	1.73326
$675$	675.000	0.0384900
$676$	−310.819	−0.0176843
$677$	7683.11	0.436168	0.218084	−	0.975930i	$-0.430019\pi$
$677$	7683.11	0.436168	0.218084	+	0.975930i	$0.430019\pi$
$678$	1306.39	0.0739995
$679$	−4986.63	−0.281840
$680$	−9998.23	−0.563845
$681$	15011.1	0.844681
$682$	0	0
$683$	−21397.1	−1.19874	−0.599368	−	0.800473i	$-0.704582\pi$
$683$	−21397.1	−1.19874	−0.599368	+	0.800473i	$0.704582\pi$
$684$	−1687.57	−0.0943359
$685$	−3424.64	−0.191020
$686$	10351.8	0.576140
$687$	−832.124	−0.0462118
$688$	−25899.0	−1.43516
$689$	−8255.84	−0.456491
$690$	7134.94	0.393656
$691$	26137.5	1.43895	0.719477	−	0.694516i	$-0.244381\pi$
$691$	26137.5	1.43895	0.719477	+	0.694516i	$0.244381\pi$
$692$	−1474.83	−0.0810181
$693$	0	0
$694$	5319.50	0.290959
$695$	4152.41	0.226633
$696$	−646.051	−0.0351846
$697$	−24686.7	−1.34157
$698$	−14952.7	−0.810845
$699$	−6809.72	−0.368479
$700$	224.621	0.0121284
$701$	−13382.4	−0.721036	−0.360518	−	0.932752i	$-0.617400\pi$
$701$	−13382.4	−0.721036	−0.360518	+	0.932752i	$0.617400\pi$
$702$	3397.45	0.182662
$703$	−54343.9	−2.91553
$704$	0	0
$705$	−8359.43	−0.446574
$706$	−6208.27	−0.330951
$707$	1507.83	0.0802092
$708$	−2670.22	−0.141741
$709$	18164.6	0.962179	0.481090	−	0.876671i	$-0.340241\pi$
$709$	18164.6	0.962179	0.481090	+	0.876671i	$0.340241\pi$
$710$	−14353.8	−0.758715
$711$	2788.52	0.147085
$712$	3430.21	0.180552
$713$	−977.000	−0.0513169
$714$	3970.00	0.208086
$715$	0	0
$716$	−2385.36	−0.124504
$717$	4851.32	0.252686
$718$	9944.50	0.516888
$719$	9665.62	0.501344	0.250672	−	0.968072i	$-0.419348\pi$
$719$	9665.62	0.501344	0.250672	+	0.968072i	$0.419348\pi$
$720$	2269.05	0.117448
$721$	−7297.94	−0.376962
$722$	25956.7	1.33796
$723$	−16939.9	−0.871371
$724$	2908.26	0.149288
$725$	222.680	0.0114071
$726$	0	0
$727$	−29779.6	−1.51921	−0.759605	−	0.650385i	$-0.774608\pi$
$727$	−29779.6	−1.51921	−0.759605	+	0.650385i	$0.774608\pi$
$728$	7418.33	0.377667
$729$	729.000	0.0370370
$730$	−1580.86	−0.0801511
$731$	−42481.7	−2.14944
$732$	3393.61	0.171354
$733$	−35029.5	−1.76513	−0.882567	−	0.470187i	$-0.844186\pi$
$733$	−35029.5	−1.76513	−0.882567	+	0.470187i	$0.844186\pi$
$734$	14515.4	0.729937
$735$	4559.77	0.228830
$736$	−11931.7	−0.597564
$737$	0	0
$738$	6881.13	0.343222
$739$	−23297.3	−1.15968	−0.579842	−	0.814729i	$-0.696886\pi$
$739$	−23297.3	−1.15968	−0.579842	+	0.814729i	$0.696886\pi$
$740$	−2998.40	−0.148950
$741$	19210.2	0.952368
$742$	2689.03	0.133042
$743$	−21570.4	−1.06506	−0.532530	−	0.846411i	$-0.678759\pi$
$743$	−21570.4	−1.06506	−0.532530	+	0.846411i	$0.678759\pi$
$744$	−381.613	−0.0188046
$745$	−6068.21	−0.298419
$746$	−447.684	−0.0219717
$747$	9190.99	0.450175
$748$	0	0
$749$	−13159.6	−0.641980
$750$	−960.582	−0.0467673
$751$	28554.8	1.38746	0.693729	−	0.720236i	$-0.255966\pi$
$751$	28554.8	1.38746	0.693729	+	0.720236i	$0.255966\pi$
$752$	−28100.7	−1.36267
$753$	−18652.8	−0.902719
$754$	1120.81	0.0541344
$755$	154.233	0.00743458
$756$	242.591	0.0116706
$757$	7812.81	0.375114	0.187557	−	0.982254i	$-0.439943\pi$
$757$	7812.81	0.375114	0.187557	+	0.982254i	$0.439943\pi$
$758$	647.268	0.0310156
$759$	0	0
$760$	15757.9	0.752105
$761$	−2875.13	−0.136956	−0.0684778	−	0.997653i	$-0.521814\pi$
$761$	−2875.13	−0.136956	−0.0684778	+	0.997653i	$0.521814\pi$
$762$	7286.45	0.346405
$763$	3084.33	0.146344
$764$	−2071.69	−0.0981033
$765$	3721.87	0.175902
$766$	−28214.3	−1.33084
$767$	30396.0	1.43095
$768$	−6401.22	−0.300761
$769$	27657.7	1.29696	0.648479	−	0.761233i	$-0.275406\pi$
$769$	27657.7	1.29696	0.648479	+	0.761233i	$0.275406\pi$
$770$	0	0
$771$	23138.2	1.08081
$772$	−4024.84	−0.187639
$773$	−3929.35	−0.182832	−0.0914160	−	0.995813i	$-0.529139\pi$
$773$	−3929.35	−0.182832	−0.0914160	+	0.995813i	$0.529139\pi$
$774$	11841.3	0.549904
$775$	131.534	0.00609658
$776$	−19301.6	−0.892898
$777$	7812.02	0.360688
$778$	20747.0	0.956064
$779$	38908.0	1.78950
$780$	1059.91	0.0486552
$781$	0	0
$782$	39341.3	1.79903
$783$	240.495	0.0109765
$784$	15327.9	0.698247
$785$	−1726.19	−0.0784847
$786$	11410.5	0.517809
$787$	21125.7	0.956860	0.478430	−	0.878126i	$-0.341206\pi$
$787$	21125.7	0.956860	0.478430	+	0.878126i	$0.341206\pi$
$788$	660.166	0.0298445
$789$	−619.040	−0.0279321
$790$	−3968.30	−0.178716
$791$	−1061.86	−0.0477310
$792$	0	0
$793$	−38630.7	−1.72991
$794$	−1087.00	−0.0485847
$795$	2520.97	0.112465
$796$	3410.61	0.151867
$797$	11696.3	0.519828	0.259914	−	0.965632i	$-0.416306\pi$
$797$	11696.3	0.519828	0.259914	+	0.965632i	$0.416306\pi$
$798$	−6257.00	−0.277563
$799$	−46093.0	−2.04087
$800$	1606.37	0.0709921
$801$	−1276.91	−0.0563263
$802$	−15123.9	−0.665888
$803$	0	0
$804$	1462.97	0.0641727
$805$	−5799.39	−0.253915
$806$	662.045	0.0289324
$807$	5137.42	0.224096
$808$	5836.34	0.254111
$809$	−14310.2	−0.621902	−0.310951	−	0.950426i	$-0.600648\pi$
$809$	−14310.2	−0.621902	−0.310951	+	0.950426i	$0.600648\pi$
$810$	−1037.43	−0.0450019
$811$	−21697.9	−0.939477	−0.469739	−	0.882806i	$-0.655652\pi$
$811$	−21697.9	−0.939477	−0.469739	+	0.882806i	$0.655652\pi$
$812$	80.0299	0.00345874
$813$	1431.24	0.0617416
$814$	0	0
$815$	−9607.46	−0.412926
$816$	12511.3	0.536743
$817$	66954.1	2.86711
$818$	−3510.54	−0.150053
$819$	−2761.50	−0.117820
$820$	2146.73	0.0914233
$821$	−3613.00	−0.153587	−0.0767934	−	0.997047i	$-0.524468\pi$
$821$	−3613.00	−0.153587	−0.0767934	+	0.997047i	$0.524468\pi$
$822$	5263.44	0.223338
$823$	−4763.98	−0.201776	−0.100888	−	0.994898i	$-0.532168\pi$
$823$	−4763.98	−0.201776	−0.100888	+	0.994898i	$0.532168\pi$
$824$	−28248.0	−1.19425
$825$	0	0
$826$	−9900.36	−0.417043
$827$	33571.7	1.41161	0.705806	−	0.708405i	$-0.250585\pi$
$827$	33571.7	1.41161	0.705806	+	0.708405i	$0.250585\pi$
$828$	2403.99	0.100899
$829$	17980.5	0.753303	0.376652	−	0.926355i	$-0.377075\pi$
$829$	17980.5	0.753303	0.376652	+	0.926355i	$0.377075\pi$
$830$	−13079.6	−0.546986
$831$	−12850.4	−0.536434
$832$	27900.9	1.16261
$833$	25142.1	1.04576
$834$	−6381.98	−0.264976
$835$	861.486	0.0357041
$836$	0	0
$837$	142.057	0.00586643
$838$	3249.91	0.133969
$839$	−40139.5	−1.65169	−0.825847	−	0.563895i	$-0.809302\pi$
$839$	−40139.5	−1.65169	−0.825847	+	0.563895i	$0.809302\pi$
$840$	−2265.23	−0.0930450
$841$	−24309.7	−0.996747
$842$	−31358.4	−1.28347
$843$	−10433.4	−0.426269
$844$	6213.91	0.253426
$845$	−1080.40	−0.0439844
$846$	12847.9	0.522127
$847$	0	0
$848$	8474.36	0.343173
$849$	19704.8	0.796546
$850$	−5296.54	−0.213729
$851$	77414.4	3.11837
$852$	−4836.24	−0.194468
$853$	15369.2	0.616919	0.308459	−	0.951237i	$-0.400187\pi$
$853$	15369.2	0.616919	0.308459	+	0.951237i	$0.400187\pi$
$854$	12582.5	0.504173
$855$	−5865.94	−0.234633
$856$	−50936.8	−2.03386
$857$	−10324.9	−0.411541	−0.205770	−	0.978600i	$-0.565970\pi$
$857$	−10324.9	−0.411541	−0.205770	+	0.978600i	$0.565970\pi$
$858$	0	0
$859$	−27112.5	−1.07691	−0.538455	−	0.842655i	$-0.680992\pi$
$859$	−27112.5	−1.07691	−0.538455	+	0.842655i	$0.680992\pi$
$860$	3694.17	0.146477
$861$	−5593.09	−0.221384
$862$	−20620.8	−0.814787
$863$	30463.6	1.20161	0.600807	−	0.799394i	$-0.294846\pi$
$863$	30463.6	1.20161	0.600807	+	0.799394i	$0.294846\pi$
$864$	1734.88	0.0683122
$865$	−5126.46	−0.201508
$866$	−42434.0	−1.66509
$867$	5783.00	0.226529
$868$	47.2726	0.00184854
$869$	0	0
$870$	−342.244	−0.0133370
$871$	−16653.5	−0.647855
$872$	11938.4	0.463631
$873$	7185.10	0.278555
$874$	−62004.6	−2.39970
$875$	780.776	0.0301658
$876$	−532.642	−0.0205437
$877$	5086.12	0.195833	0.0979167	−	0.995195i	$-0.468782\pi$
$877$	5086.12	0.195833	0.0979167	+	0.995195i	$0.468782\pi$
$878$	−12054.2	−0.463335
$879$	−25056.9	−0.961487
$880$	0	0
$881$	−10625.5	−0.406338	−0.203169	−	0.979144i	$-0.565124\pi$
$881$	−10625.5	−0.406338	−0.203169	+	0.979144i	$0.565124\pi$
$882$	−7008.06	−0.267544
$883$	13112.2	0.499728	0.249864	−	0.968281i	$-0.419614\pi$
$883$	13112.2	0.499728	0.249864	+	0.968281i	$0.419614\pi$
$884$	5844.25	0.222357
$885$	−9281.59	−0.352539
$886$	38664.0	1.46607
$887$	14442.8	0.546719	0.273360	−	0.961912i	$-0.411865\pi$
$887$	14442.8	0.546719	0.273360	+	0.961912i	$0.411865\pi$
$888$	30237.8	1.14270
$889$	−5922.54	−0.223437
$890$	1817.15	0.0684393
$891$	0	0
$892$	5520.38	0.207215
$893$	72645.8	2.72228
$894$	9326.43	0.348906
$895$	−8291.44	−0.309667
$896$	−5876.86	−0.219121
$897$	−27365.5	−1.01863
$898$	2493.61	0.0926648
$899$	46.8641	0.00173860
$900$	−323.651	−0.0119871
$901$	13900.3	0.513970
$902$	0	0
$903$	−9624.77	−0.354698
$904$	−4110.10	−0.151217
$905$	10109.0	0.371310
$906$	−237.045	−0.00869239
$907$	−44981.9	−1.64675	−0.823374	−	0.567499i	$-0.807911\pi$
$907$	−44981.9	−1.64675	−0.823374	+	0.567499i	$0.807911\pi$
$908$	−7197.57	−0.263062
$909$	−2172.60	−0.0792745
$910$	3929.85	0.143157
$911$	6841.96	0.248830	0.124415	−	0.992230i	$-0.460295\pi$
$911$	6841.96	0.248830	0.124415	+	0.992230i	$0.460295\pi$
$912$	−19718.7	−0.715954
$913$	0	0
$914$	−160.501	−0.00580843
$915$	11796.1	0.426193
$916$	398.989	0.0143919
$917$	−9274.61	−0.333996
$918$	−5720.27	−0.205661
$919$	4753.54	0.170625	0.0853127	−	0.996354i	$-0.472811\pi$
$919$	4753.54	0.170625	0.0853127	+	0.996354i	$0.472811\pi$
$920$	−22447.6	−0.804430
$921$	−16151.7	−0.577868
$922$	30395.9	1.08572
$923$	55052.7	1.96325
$924$	0	0
$925$	−10422.3	−0.370470
$926$	−33671.2	−1.19493
$927$	10515.4	0.372569
$928$	572.330	0.0202453
$929$	−7507.93	−0.265153	−0.132576	−	0.991173i	$-0.542325\pi$
$929$	−7507.93	−0.265153	−0.132576	+	0.991173i	$0.542325\pi$
$930$	−202.159	−0.00712802
$931$	−39625.7	−1.39493
$932$	3265.14	0.114757
$933$	−5371.24	−0.188474
$934$	−26068.3	−0.913256
$935$	0	0
$936$	−10688.9	−0.373266
$937$	−8540.47	−0.297764	−0.148882	−	0.988855i	$-0.547567\pi$
$937$	−8540.47	−0.297764	−0.148882	+	0.988855i	$0.547567\pi$
$938$	5424.24	0.188814
$939$	−2427.23	−0.0843552
$940$	4008.20	0.139078
$941$	−9101.13	−0.315290	−0.157645	−	0.987496i	$-0.550390\pi$
$941$	−9101.13	−0.315290	−0.157645	+	0.987496i	$0.550390\pi$
$942$	2653.04	0.0917630
$943$	−55425.5	−1.91400
$944$	−31200.6	−1.07573
$945$	843.239	0.0290270
$946$	0	0
$947$	47540.0	1.63130	0.815650	−	0.578546i	$-0.196380\pi$
$947$	47540.0	1.63130	0.815650	+	0.578546i	$0.196380\pi$
$948$	−1337.04	−0.0458072
$949$	6063.26	0.207399
$950$	8347.73	0.285091
$951$	32233.6	1.09910
$952$	−12490.2	−0.425221
$953$	−47370.7	−1.61016	−0.805082	−	0.593164i	$-0.797879\pi$
$953$	−47370.7	−1.61016	−0.805082	+	0.593164i	$0.797879\pi$
$954$	−3874.55	−0.131492
$955$	−7201.12	−0.244003
$956$	−2326.12	−0.0786947
$957$	0	0
$958$	−8789.33	−0.296420
$959$	−4278.20	−0.144057
$960$	−8519.67	−0.286428
$961$	−29763.3	−0.999071
$962$	−52458.4	−1.75813
$963$	18961.4	0.634498
$964$	8122.38	0.271374
$965$	−13990.2	−0.466696
$966$	8913.27	0.296874
$967$	36171.6	1.20290	0.601448	−	0.798912i	$-0.294591\pi$
$967$	36171.6	1.20290	0.601448	+	0.798912i	$0.294591\pi$
$968$	0	0
$969$	−32344.1	−1.07228
$970$	−10225.0	−0.338459
$971$	−31713.2	−1.04812	−0.524060	−	0.851681i	$-0.675583\pi$
$971$	−31713.2	−1.04812	−0.524060	+	0.851681i	$0.675583\pi$
$972$	−349.543	−0.0115346
$973$	5187.37	0.170914
$974$	−7257.40	−0.238750
$975$	3684.23	0.121015
$976$	39653.1	1.30048
$977$	22800.5	0.746626	0.373313	−	0.927706i	$-0.378222\pi$
$977$	22800.5	0.746626	0.373313	+	0.927706i	$0.378222\pi$
$978$	14766.0	0.482786
$979$	0	0
$980$	−2186.33	−0.0712651
$981$	−4444.12	−0.144638
$982$	6832.41	0.222027
$983$	−44597.4	−1.44704	−0.723518	−	0.690305i	$-0.757476\pi$
$983$	−44597.4	−1.44704	−0.723518	+	0.690305i	$0.757476\pi$
$984$	−21649.1	−0.701369
$985$	2294.72	0.0742292
$986$	−1887.10	−0.0609507
$987$	−10443.0	−0.336781
$988$	−9210.95	−0.296599
$989$	−95378.1	−3.06658
$990$	0	0
$991$	−34788.1	−1.11512	−0.557558	−	0.830138i	$-0.688261\pi$
$991$	−34788.1	−1.11512	−0.557558	+	0.830138i	$0.688261\pi$
$992$	338.068	0.0108202
$993$	10197.4	0.325885
$994$	−17931.3	−0.572180
$995$	11855.2	0.377723
$996$	−4406.92	−0.140199
$997$	20360.5	0.646765	0.323383	−	0.946268i	$-0.395180\pi$
$997$	20360.5	0.646765	0.323383	+	0.946268i	$0.395180\pi$
$998$	−28528.0	−0.904849
$999$	−11256.1	−0.356485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.n.1.2		2
11.10	odd	2		165.4.a.c.1.1	✓	2
33.32	even	2		495.4.a.d.1.2		2
55.32	even	4		825.4.c.j.199.1		4
55.43	even	4		825.4.c.j.199.4		4
55.54	odd	2		825.4.a.m.1.2		2
165.164	even	2		2475.4.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.c.1.1	✓	2	11.10	odd	2
495.4.a.d.1.2		2	33.32	even	2
825.4.a.m.1.2		2	55.54	odd	2
825.4.c.j.199.1		4	55.32	even	4
825.4.c.j.199.4		4	55.43	even	4
1815.4.a.n.1.2		2	1.1	even	1	trivial
2475.4.a.n.1.1		2	165.164	even	2

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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} +7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} +7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} -12.8078 q^{10} -4.31534 q^{12} +49.1231 q^{13} -16.0000 q^{14} -15.0000 q^{15} -50.4233 q^{16} -82.7083 q^{17} +23.0540 q^{18} +130.354 q^{19} +7.19224 q^{20} -18.7386 q^{21} -185.693 q^{23} -72.5312 q^{24} +25.0000 q^{25} +125.831 q^{26} +27.0000 q^{27} +8.98485 q^{28} +8.90720 q^{29} -38.4233 q^{30} +5.26137 q^{31} +64.2547 q^{32} -211.862 q^{34} +31.2311 q^{35} -12.9460 q^{36} -416.894 q^{37} +333.909 q^{38} +147.369 q^{39} +120.885 q^{40} +298.479 q^{41} -48.0000 q^{42} +513.633 q^{43} -45.0000 q^{45} -475.663 q^{46} +557.295 q^{47} -151.270 q^{48} -303.985 q^{49} +64.0388 q^{50} -248.125 q^{51} -70.6610 q^{52} -168.064 q^{53} +69.1619 q^{54} +151.015 q^{56} +391.062 q^{57} +22.8163 q^{58} +618.773 q^{59} +21.5767 q^{60} -786.405 q^{61} +13.4773 q^{62} -56.2159 q^{63} +567.978 q^{64} -245.616 q^{65} -339.015 q^{67} +118.972 q^{68} -557.080 q^{69} +80.0000 q^{70} +1120.71 q^{71} -217.594 q^{72} +123.430 q^{73} -1067.90 q^{74} +75.0000 q^{75} -187.508 q^{76} +377.494 q^{78} +309.835 q^{79} +252.116 q^{80} +81.0000 q^{81} +764.570 q^{82} +1021.22 q^{83} +26.9545 q^{84} +413.542 q^{85} +1315.70 q^{86} +26.7216 q^{87} -141.879 q^{89} -115.270 q^{90} -306.833 q^{91} +267.110 q^{92} +15.7841 q^{93} +1427.54 q^{94} -651.771 q^{95} +192.764 q^{96} +798.345 q^{97} -778.673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 + 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9	\( 2 q + q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9} - 5 q^{10} - 21 q^{12} + 90 q^{13} - 32 q^{14} - 30 q^{15} - 39 q^{16} + 16 q^{17} + 9 q^{18} + 170 q^{19} + 35 q^{20} + 12 q^{21} - 124 q^{23} - 9 q^{24} + 50 q^{25} + 62 q^{26} + 54 q^{27} - 48 q^{28} + 158 q^{29} - 15 q^{30} + 60 q^{31} - 123 q^{32} - 366 q^{34} - 20 q^{35} - 63 q^{36} - 372 q^{37} + 272 q^{38} + 270 q^{39} + 15 q^{40} - 38 q^{41} - 96 q^{42} + 516 q^{43} - 90 q^{45} - 572 q^{46} + 224 q^{47} - 117 q^{48} - 542 q^{49} + 25 q^{50} + 48 q^{51} - 298 q^{52} + 472 q^{53} + 27 q^{54} + 368 q^{56} + 510 q^{57} - 210 q^{58} + 248 q^{59} + 105 q^{60} - 72 q^{61} - 72 q^{62} + 36 q^{63} + 769 q^{64} - 450 q^{65} - 744 q^{67} - 430 q^{68} - 372 q^{69} + 160 q^{70} + 2060 q^{71} - 27 q^{72} + 486 q^{73} - 1138 q^{74} + 150 q^{75} - 408 q^{76} + 186 q^{78} - 642 q^{79} + 195 q^{80} + 162 q^{81} + 1290 q^{82} + 286 q^{83} - 144 q^{84} - 80 q^{85} + 1312 q^{86} + 474 q^{87} + 244 q^{89} - 45 q^{90} + 112 q^{91} - 76 q^{92} + 180 q^{93} + 1948 q^{94} - 850 q^{95} - 369 q^{96} - 168 q^{97} - 407 q^{98}+O(q^{100}) \) 2 * q + q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 + 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9 - 5 * q^10 - 21 * q^12 + 90 * q^13 - 32 * q^14 - 30 * q^15 - 39 * q^16 + 16 * q^17 + 9 * q^18 + 170 * q^19 + 35 * q^20 + 12 * q^21 - 124 * q^23 - 9 * q^24 + 50 * q^25 + 62 * q^26 + 54 * q^27 - 48 * q^28 + 158 * q^29 - 15 * q^30 + 60 * q^31 - 123 * q^32 - 366 * q^34 - 20 * q^35 - 63 * q^36 - 372 * q^37 + 272 * q^38 + 270 * q^39 + 15 * q^40 - 38 * q^41 - 96 * q^42 + 516 * q^43 - 90 * q^45 - 572 * q^46 + 224 * q^47 - 117 * q^48 - 542 * q^49 + 25 * q^50 + 48 * q^51 - 298 * q^52 + 472 * q^53 + 27 * q^54 + 368 * q^56 + 510 * q^57 - 210 * q^58 + 248 * q^59 + 105 * q^60 - 72 * q^61 - 72 * q^62 + 36 * q^63 + 769 * q^64 - 450 * q^65 - 744 * q^67 - 430 * q^68 - 372 * q^69 + 160 * q^70 + 2060 * q^71 - 27 * q^72 + 486 * q^73 - 1138 * q^74 + 150 * q^75 - 408 * q^76 + 186 * q^78 - 642 * q^79 + 195 * q^80 + 162 * q^81 + 1290 * q^82 + 286 * q^83 - 144 * q^84 - 80 * q^85 + 1312 * q^86 + 474 * q^87 + 244 * q^89 - 45 * q^90 + 112 * q^91 - 76 * q^92 + 180 * q^93 + 1948 * q^94 - 850 * q^95 - 369 * q^96 - 168 * q^97 - 407 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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