LMFDB - Embedded newform 1815.4.a.r.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:	$3$
Coefficient field:	3.3.47528.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x - 22 $ x^3 - x^2 - 26*x - 22
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			$-0.906392$ 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)

$f(q)$	$=$	$q+1.90639 q^{2} +3.00000 q^{3} -4.36567 q^{4} -5.00000 q^{5} +5.71918 q^{6} +22.9186 q^{7} -23.5738 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.90639 q^{2} +3.00000 q^{3} -4.36567 q^{4} -5.00000 q^{5} +5.71918 q^{6} +22.9186 q^{7} -23.5738 q^{8} +9.00000 q^{9} -9.53196 q^{10} -13.0970 q^{12} -66.7313 q^{13} +43.6917 q^{14} -15.0000 q^{15} -10.0156 q^{16} +3.45588 q^{17} +17.1575 q^{18} -78.2359 q^{19} +21.8283 q^{20} +68.7557 q^{21} +12.2907 q^{23} -70.7214 q^{24} +25.0000 q^{25} -127.216 q^{26} +27.0000 q^{27} -100.055 q^{28} +31.1827 q^{29} -28.5959 q^{30} +247.181 q^{31} +169.497 q^{32} +6.58825 q^{34} -114.593 q^{35} -39.2910 q^{36} +304.128 q^{37} -149.148 q^{38} -200.194 q^{39} +117.869 q^{40} +29.8219 q^{41} +131.075 q^{42} -269.060 q^{43} -45.0000 q^{45} +23.4309 q^{46} +225.463 q^{47} -30.0467 q^{48} +182.260 q^{49} +47.6598 q^{50} +10.3676 q^{51} +291.327 q^{52} -16.8371 q^{53} +51.4726 q^{54} -540.278 q^{56} -234.708 q^{57} +59.4464 q^{58} +28.0701 q^{59} +65.4850 q^{60} +853.742 q^{61} +471.224 q^{62} +206.267 q^{63} +403.252 q^{64} +333.657 q^{65} -36.7885 q^{67} -15.0872 q^{68} +36.8722 q^{69} -218.459 q^{70} +23.8552 q^{71} -212.164 q^{72} -707.265 q^{73} +579.787 q^{74} +75.0000 q^{75} +341.552 q^{76} -381.648 q^{78} +412.126 q^{79} +50.0778 q^{80} +81.0000 q^{81} +56.8522 q^{82} +552.596 q^{83} -300.165 q^{84} -17.2794 q^{85} -512.934 q^{86} +93.5480 q^{87} -1495.26 q^{89} -85.7876 q^{90} -1529.39 q^{91} -53.6573 q^{92} +741.543 q^{93} +429.820 q^{94} +391.179 q^{95} +508.491 q^{96} +1199.45 q^{97} +347.459 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 - 10 * q^10 + 90 * q^12 - 114 * q^13 - 68 * q^14 - 45 * q^15 + 178 * q^16 + 104 * q^17 + 18 * q^18 + 58 * q^19 - 150 * q^20 - 30 * q^21 + 120 * q^23 - 54 * q^24 + 75 * q^25 - 120 * q^26 + 81 * q^27 - 676 * q^28 + 220 * q^29 - 30 * q^30 + 248 * q^31 + 258 * q^32 - 80 * q^34 + 50 * q^35 + 270 * q^36 + 838 * q^37 + 600 * q^38 - 342 * q^39 + 90 * q^40 - 156 * q^41 - 204 * q^42 - 122 * q^43 - 135 * q^45 + 1256 * q^46 + 504 * q^47 + 534 * q^48 + 279 * q^49 + 50 * q^50 + 312 * q^51 - 520 * q^52 + 282 * q^53 + 54 * q^54 - 1644 * q^56 + 174 * q^57 - 1644 * q^58 + 548 * q^59 - 450 * q^60 - 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 + 570 * q^65 - 428 * q^67 + 1704 * q^68 + 360 * q^69 + 340 * q^70 - 912 * q^71 - 162 * q^72 - 618 * q^73 + 1612 * q^74 + 225 * q^75 + 2752 * q^76 - 360 * q^78 + 542 * q^79 - 890 * q^80 + 243 * q^81 + 3372 * q^82 - 2028 * q^84 - 520 * q^85 - 1548 * q^86 + 660 * q^87 + 790 * q^89 - 90 * q^90 - 772 * q^91 + 1912 * q^92 + 744 * q^93 + 424 * q^94 - 290 * q^95 + 774 * q^96 + 2074 * q^97 + 3978 * 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 $

$2$	1.90639	0.674011	0.337006	−	0.941503i	$-0.390586\pi$
$2$	1.90639	0.674011	0.337006	+	0.941503i	$0.390586\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−4.36567	−0.545709
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	5.71918	0.389141
$7$	22.9186	1.23749	0.618743	−	0.785594i	$-0.287642\pi$
$7$	22.9186	1.23749	0.618743	+	0.785594i	$0.287642\pi$
$8$	−23.5738	−1.04183
$9$	9.00000	0.333333
$10$	−9.53196	−0.301427
$11$	0	0
$11$	0	0
$12$	−13.0970	−0.315065
$13$	−66.7313	−1.42369	−0.711844	−	0.702338i	$-0.752140\pi$
$13$	−66.7313	−1.42369	−0.711844	+	0.702338i	$0.752140\pi$
$14$	43.6917	0.834079
$15$	−15.0000	−0.258199
$16$	−10.0156	−0.156493
$17$	3.45588	0.0493043	0.0246522	−	0.999696i	$-0.492152\pi$
$17$	3.45588	0.0493043	0.0246522	+	0.999696i	$0.492152\pi$
$18$	17.1575	0.224670
$19$	−78.2359	−0.944660	−0.472330	−	0.881422i	$-0.656587\pi$
$19$	−78.2359	−0.944660	−0.472330	+	0.881422i	$0.656587\pi$
$20$	21.8283	0.244048
$21$	68.7557	0.714463
$22$	0	0
$23$	12.2907	0.111426	0.0557129	−	0.998447i	$-0.482257\pi$
$23$	12.2907	0.111426	0.0557129	+	0.998447i	$0.482257\pi$
$24$	−70.7214	−0.601498
$25$	25.0000	0.200000
$26$	−127.216	−0.959582
$27$	27.0000	0.192450
$28$	−100.055	−0.675307
$29$	31.1827	0.199672	0.0998358	−	0.995004i	$-0.468168\pi$
$29$	31.1827	0.199672	0.0998358	+	0.995004i	$0.468168\pi$
$30$	−28.5959	−0.174029
$31$	247.181	1.43210	0.716049	−	0.698050i	$-0.245949\pi$
$31$	247.181	1.43210	0.716049	+	0.698050i	$0.245949\pi$
$32$	169.497	0.936347
$33$	0	0
$34$	6.58825	0.0332317
$35$	−114.593	−0.553420
$36$	−39.2910	−0.181903
$37$	304.128	1.35131	0.675653	−	0.737220i	$-0.263862\pi$
$37$	304.128	1.35131	0.675653	+	0.737220i	$0.263862\pi$
$38$	−149.148	−0.636712
$39$	−200.194	−0.821967
$40$	117.869	0.465918
$41$	29.8219	0.113595	0.0567975	−	0.998386i	$-0.481911\pi$
$41$	29.8219	0.113595	0.0567975	+	0.998386i	$0.481911\pi$
$42$	131.075	0.481556
$43$	−269.060	−0.954215	−0.477108	−	0.878845i	$-0.658315\pi$
$43$	−269.060	−0.954215	−0.477108	+	0.878845i	$0.658315\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	23.4309	0.0751023
$47$	225.463	0.699726	0.349863	−	0.936801i	$-0.386228\pi$
$47$	225.463	0.699726	0.349863	+	0.936801i	$0.386228\pi$
$48$	−30.0467	−0.0903514
$49$	182.260	0.531371
$50$	47.6598	0.134802
$51$	10.3676	0.0284659
$52$	291.327	0.776919
$53$	−16.8371	−0.0436369	−0.0218184	−	0.999762i	$-0.506946\pi$
$53$	−16.8371	−0.0436369	−0.0218184	+	0.999762i	$0.506946\pi$
$54$	51.4726	0.129714
$55$	0	0
$56$	−540.278	−1.28924
$57$	−234.708	−0.545400
$58$	59.4464	0.134581
$59$	28.0701	0.0619392	0.0309696	−	0.999520i	$-0.490140\pi$
$59$	28.0701	0.0619392	0.0309696	+	0.999520i	$0.490140\pi$
$60$	65.4850	0.140901
$61$	853.742	1.79198	0.895988	−	0.444079i	$-0.146469\pi$
$61$	853.742	1.79198	0.895988	+	0.444079i	$0.146469\pi$
$62$	471.224	0.965250
$63$	206.267	0.412495
$64$	403.252	0.787602
$65$	333.657	0.636693
$66$	0	0
$67$	−36.7885	−0.0670810	−0.0335405	−	0.999437i	$-0.510678\pi$
$67$	−36.7885	−0.0670810	−0.0335405	+	0.999437i	$0.510678\pi$
$68$	−15.0872	−0.0269058
$69$	36.8722	0.0643317
$70$	−218.459	−0.373012
$71$	23.8552	0.0398746	0.0199373	−	0.999801i	$-0.493653\pi$
$71$	23.8552	0.0398746	0.0199373	+	0.999801i	$0.493653\pi$
$72$	−212.164	−0.347275
$73$	−707.265	−1.13396	−0.566980	−	0.823731i	$-0.691889\pi$
$73$	−707.265	−1.13396	−0.566980	+	0.823731i	$0.691889\pi$
$74$	579.787	0.910795
$75$	75.0000	0.115470
$76$	341.552	0.515509
$77$	0	0
$78$	−381.648	−0.554015
$79$	412.126	0.586934	0.293467	−	0.955969i	$-0.405191\pi$
$79$	412.126	0.586934	0.293467	+	0.955969i	$0.405191\pi$
$80$	50.0778	0.0699859
$81$	81.0000	0.111111
$82$	56.8522	0.0765643
$83$	552.596	0.730786	0.365393	−	0.930853i	$-0.380935\pi$
$83$	552.596	0.730786	0.365393	+	0.930853i	$0.380935\pi$
$84$	−300.165	−0.389889
$85$	−17.2794	−0.0220496
$86$	−512.934	−0.643152
$87$	93.5480	0.115280
$88$	0	0
$89$	−1495.26	−1.78087	−0.890434	−	0.455113i	$-0.849599\pi$
$89$	−1495.26	−1.78087	−0.890434	+	0.455113i	$0.849599\pi$
$90$	−85.7876	−0.100476
$91$	−1529.39	−1.76179
$92$	−53.6573	−0.0608060
$93$	741.543	0.826822
$94$	429.820	0.471623
$95$	391.179	0.422465
$96$	508.491	0.540600
$97$	1199.45	1.25552	0.627761	−	0.778406i	$-0.283971\pi$
$97$	1199.45	1.25552	0.627761	+	0.778406i	$0.283971\pi$
$98$	347.459	0.358150
$99$	0	0
$100$	−109.142	−0.109142
$101$	1009.66	0.994701	0.497351	−	0.867550i	$-0.334306\pi$
$101$	1009.66	0.994701	0.497351	+	0.867550i	$0.334306\pi$
$102$	19.7648	0.0191863
$103$	1156.70	1.10653	0.553266	−	0.833004i	$-0.313381\pi$
$103$	1156.70	1.10653	0.553266	+	0.833004i	$0.313381\pi$
$104$	1573.11	1.48323
$105$	−343.778	−0.319517
$106$	−32.0981	−0.0294117
$107$	−491.857	−0.444389	−0.222194	−	0.975002i	$-0.571322\pi$
$107$	−491.857	−0.444389	−0.222194	+	0.975002i	$0.571322\pi$
$108$	−117.873	−0.105022
$109$	−1340.77	−1.17819	−0.589093	−	0.808066i	$-0.700515\pi$
$109$	−1340.77	−1.17819	−0.589093	+	0.808066i	$0.700515\pi$
$110$	0	0
$111$	912.384	0.780177
$112$	−229.542	−0.193658
$113$	1849.21	1.53946	0.769729	−	0.638371i	$-0.220391\pi$
$113$	1849.21	1.53946	0.769729	+	0.638371i	$0.220391\pi$
$114$	−447.445	−0.367606
$115$	−61.4536	−0.0498311
$116$	−136.133	−0.108963
$117$	−600.582	−0.474563
$118$	53.5126	0.0417478
$119$	79.2037	0.0610134
$120$	353.607	0.268998
$121$	0	0
$122$	1627.57	1.20781
$123$	89.4656	0.0655841
$124$	−1079.11	−0.781508
$125$	−125.000	−0.0894427
$126$	393.226	0.278026
$127$	1020.24	0.712850	0.356425	−	0.934324i	$-0.383995\pi$
$127$	1020.24	0.712850	0.356425	+	0.934324i	$0.383995\pi$
$128$	−587.219	−0.405495
$129$	−807.180	−0.550917
$130$	636.080	0.429138
$131$	−1003.30	−0.669147	−0.334574	−	0.942370i	$-0.608592\pi$
$131$	−1003.30	−0.669147	−0.334574	+	0.942370i	$0.608592\pi$
$132$	0	0
$133$	−1793.05	−1.16900
$134$	−70.1332	−0.0452134
$135$	−135.000	−0.0860663
$136$	−81.4682	−0.0513665
$137$	2665.14	1.66203	0.831016	−	0.556249i	$-0.187760\pi$
$137$	2665.14	1.66203	0.831016	+	0.556249i	$0.187760\pi$
$138$	70.2928	0.0433603
$139$	−2557.64	−1.56069	−0.780347	−	0.625347i	$-0.784957\pi$
$139$	−2557.64	−1.56069	−0.780347	+	0.625347i	$0.784957\pi$
$140$	500.274	0.302006
$141$	676.388	0.403987
$142$	45.4774	0.0268759
$143$	0	0
$144$	−90.1401	−0.0521644
$145$	−155.913	−0.0892959
$146$	−1348.32	−0.764303
$147$	546.781	0.306787
$148$	−1327.72	−0.737419
$149$	2644.66	1.45409	0.727044	−	0.686591i	$-0.240894\pi$
$149$	2644.66	1.45409	0.727044	+	0.686591i	$0.240894\pi$
$150$	142.979	0.0778281
$151$	2871.44	1.54751	0.773757	−	0.633482i	$-0.218375\pi$
$151$	2871.44	1.54751	0.773757	+	0.633482i	$0.218375\pi$
$152$	1844.32	0.984171
$153$	31.1029	0.0164348
$154$	0	0
$155$	−1235.91	−0.640454
$156$	873.981	0.448554
$157$	1048.51	0.532996	0.266498	−	0.963835i	$-0.414133\pi$
$157$	1048.51	0.532996	0.266498	+	0.963835i	$0.414133\pi$
$158$	785.674	0.395600
$159$	−50.5113	−0.0251937
$160$	−847.485	−0.418747
$161$	281.686	0.137888
$162$	154.418	0.0748901
$163$	−1953.90	−0.938905	−0.469452	−	0.882958i	$-0.655549\pi$
$163$	−1953.90	−0.938905	−0.469452	+	0.882958i	$0.655549\pi$
$164$	−130.192	−0.0619898
$165$	0	0
$166$	1053.46	0.492558
$167$	−2085.79	−0.966488	−0.483244	−	0.875486i	$-0.660542\pi$
$167$	−2085.79	−0.966488	−0.483244	+	0.875486i	$0.660542\pi$
$168$	−1620.83	−0.744345
$169$	2256.07	1.02689
$170$	−32.9413	−0.0148616
$171$	−704.123	−0.314887
$172$	1174.63	0.520724
$173$	3999.28	1.75757	0.878785	−	0.477218i	$-0.158355\pi$
$173$	3999.28	1.75757	0.878785	+	0.477218i	$0.158355\pi$
$174$	178.339	0.0777003
$175$	572.964	0.247497
$176$	0	0
$177$	84.2103	0.0357606
$178$	−2850.55	−1.20032
$179$	2046.60	0.854580	0.427290	−	0.904115i	$-0.359468\pi$
$179$	2046.60	0.854580	0.427290	+	0.904115i	$0.359468\pi$
$180$	196.455	0.0813495
$181$	64.2973	0.0264043	0.0132022	−	0.999913i	$-0.495797\pi$
$181$	64.2973	0.0264043	0.0132022	+	0.999913i	$0.495797\pi$
$182$	−2915.61	−1.18747
$183$	2561.23	1.03460
$184$	−289.739	−0.116086
$185$	−1520.64	−0.604322
$186$	1413.67	0.557287
$187$	0	0
$188$	−984.296	−0.381846
$189$	618.801	0.238154
$190$	745.741	0.284746
$191$	4816.60	1.82470	0.912348	−	0.409416i	$-0.134268\pi$
$191$	4816.60	1.82470	0.912348	+	0.409416i	$0.134268\pi$
$192$	1209.76	0.454722
$193$	295.804	0.110323	0.0551617	−	0.998477i	$-0.482433\pi$
$193$	295.804	0.110323	0.0551617	+	0.998477i	$0.482433\pi$
$194$	2286.62	0.846237
$195$	1000.97	0.367595
$196$	−795.688	−0.289974
$197$	2147.97	0.776835	0.388418	−	0.921483i	$-0.373022\pi$
$197$	2147.97	0.776835	0.388418	+	0.921483i	$0.373022\pi$
$198$	0	0
$199$	−876.260	−0.312143	−0.156071	−	0.987746i	$-0.549883\pi$
$199$	−876.260	−0.312143	−0.156071	+	0.987746i	$0.549883\pi$
$200$	−589.345	−0.208365
$201$	−110.365	−0.0387292
$202$	1924.81	0.670440
$203$	714.662	0.247091
$204$	−45.2616	−0.0155341
$205$	−149.109	−0.0508012
$206$	2205.12	0.745815
$207$	110.617	0.0371419
$208$	668.352	0.222798
$209$	0	0
$210$	−655.376	−0.215358
$211$	−1413.99	−0.461341	−0.230670	−	0.973032i	$-0.574092\pi$
$211$	−1413.99	−0.461341	−0.230670	+	0.973032i	$0.574092\pi$
$212$	73.5052	0.0238130
$213$	71.5657	0.0230216
$214$	−937.672	−0.299523
$215$	1345.30	0.426738
$216$	−636.493	−0.200499
$217$	5665.03	1.77220
$218$	−2556.03	−0.794110
$219$	−2121.80	−0.654693
$220$	0	0
$221$	−230.615	−0.0701939
$222$	1739.36	0.525848
$223$	3365.53	1.01064	0.505320	−	0.862932i	$-0.331374\pi$
$223$	3365.53	1.01064	0.505320	+	0.862932i	$0.331374\pi$
$224$	3884.62	1.15872
$225$	225.000	0.0666667
$226$	3525.31	1.03761
$227$	5724.31	1.67373	0.836864	−	0.547411i	$-0.184387\pi$
$227$	5724.31	1.67373	0.836864	+	0.547411i	$0.184387\pi$
$228$	1024.66	0.297629
$229$	2586.74	0.746447	0.373224	−	0.927741i	$-0.378252\pi$
$229$	2586.74	0.746447	0.373224	+	0.927741i	$0.378252\pi$
$230$	−117.155	−0.0335867
$231$	0	0
$232$	−735.095	−0.208023
$233$	−5571.63	−1.56656	−0.783282	−	0.621666i	$-0.786456\pi$
$233$	−5571.63	−1.56656	−0.783282	+	0.621666i	$0.786456\pi$
$234$	−1144.94	−0.319861
$235$	−1127.31	−0.312927
$236$	−122.545	−0.0338008
$237$	1236.38	0.338867
$238$	150.993	0.0411237
$239$	1822.92	0.493369	0.246685	−	0.969096i	$-0.420659\pi$
$239$	1822.92	0.493369	0.246685	+	0.969096i	$0.420659\pi$
$240$	150.233	0.0404064
$241$	2226.66	0.595152	0.297576	−	0.954698i	$-0.403822\pi$
$241$	2226.66	0.595152	0.297576	+	0.954698i	$0.403822\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−3727.16	−0.977897
$245$	−911.301	−0.237636
$246$	170.556	0.0442044
$247$	5220.78	1.34490
$248$	−5827.00	−1.49200
$249$	1657.79	0.421920
$250$	−238.299	−0.0602854
$251$	7888.22	1.98367	0.991833	−	0.127543i	$-0.0407092\pi$
$251$	7888.22	1.98367	0.991833	+	0.127543i	$0.0407092\pi$
$252$	−900.494	−0.225102
$253$	0	0
$254$	1944.98	0.480469
$255$	−51.8381	−0.0127303
$256$	−4345.49	−1.06091
$257$	−4755.32	−1.15420	−0.577099	−	0.816674i	$-0.695815\pi$
$257$	−4755.32	−1.15420	−0.577099	+	0.816674i	$0.695815\pi$
$258$	−1538.80	−0.371324
$259$	6970.17	1.67222
$260$	−1456.64	−0.347449
$261$	280.644	0.0665572
$262$	−1912.67	−0.451013
$263$	103.437	0.0242517	0.0121258	−	0.999926i	$-0.496140\pi$
$263$	103.437	0.0242517	0.0121258	+	0.999926i	$0.496140\pi$
$264$	0	0
$265$	84.1855	0.0195150
$266$	−3418.26	−0.787921
$267$	−4485.78	−1.02818
$268$	160.606	0.0366067
$269$	−2179.50	−0.494002	−0.247001	−	0.969015i	$-0.579445\pi$
$269$	−2179.50	−0.494002	−0.247001	+	0.969015i	$0.579445\pi$
$270$	−257.363	−0.0580097
$271$	3688.54	0.826800	0.413400	−	0.910550i	$-0.364341\pi$
$271$	3688.54	0.826800	0.413400	+	0.910550i	$0.364341\pi$
$272$	−34.6126	−0.00771579
$273$	−4588.16	−1.01717
$274$	5080.80	1.12023
$275$	0	0
$276$	−160.972	−0.0351064
$277$	3087.18	0.669641	0.334821	−	0.942282i	$-0.391324\pi$
$277$	3087.18	0.669641	0.334821	+	0.942282i	$0.391324\pi$
$278$	−4875.87	−1.05193
$279$	2224.63	0.477366
$280$	2701.39	0.576567
$281$	−3338.91	−0.708836	−0.354418	−	0.935087i	$-0.615321\pi$
$281$	−3338.91	−0.708836	−0.354418	+	0.935087i	$0.615321\pi$
$282$	1289.46	0.272292
$283$	−1483.75	−0.311661	−0.155830	−	0.987784i	$-0.549805\pi$
$283$	−1483.75	−0.311661	−0.155830	+	0.987784i	$0.549805\pi$
$284$	−104.144	−0.0217599
$285$	1173.54	0.243910
$286$	0	0
$287$	683.474	0.140572
$288$	1525.47	0.312116
$289$	−4901.06	−0.997569
$290$	−297.232	−0.0601864
$291$	3598.35	0.724877
$292$	3087.69	0.618812
$293$	1590.55	0.317137	0.158569	−	0.987348i	$-0.449312\pi$
$293$	1590.55	0.317137	0.158569	+	0.987348i	$0.449312\pi$
$294$	1042.38	0.206778
$295$	−140.350	−0.0277001
$296$	−7169.45	−1.40782
$297$	0	0
$298$	5041.76	0.980071
$299$	−820.177	−0.158636
$300$	−327.425	−0.0630130
$301$	−6166.47	−1.18083
$302$	5474.10	1.04304
$303$	3028.98	0.574291
$304$	783.577	0.147833
$305$	−4268.71	−0.801396
$306$	59.2943	0.0110772
$307$	−10175.3	−1.89164	−0.945818	−	0.324697i	$-0.894738\pi$
$307$	−10175.3	−1.89164	−0.945818	+	0.324697i	$0.894738\pi$
$308$	0	0
$309$	3470.09	0.638857
$310$	−2356.12	−0.431673
$311$	−6258.24	−1.14107	−0.570535	−	0.821274i	$-0.693264\pi$
$311$	−6258.24	−1.14107	−0.570535	+	0.821274i	$0.693264\pi$
$312$	4719.34	0.856346
$313$	9592.24	1.73222	0.866111	−	0.499852i	$-0.166612\pi$
$313$	9592.24	1.73222	0.866111	+	0.499852i	$0.166612\pi$
$314$	1998.88	0.359245
$315$	−1031.34	−0.184473
$316$	−1799.21	−0.320295
$317$	−10632.3	−1.88381	−0.941907	−	0.335874i	$-0.890969\pi$
$317$	−10632.3	−1.88381	−0.941907	+	0.335874i	$0.890969\pi$
$318$	−96.2943	−0.0169809
$319$	0	0
$320$	−2016.26	−0.352226
$321$	−1475.57	−0.256568
$322$	537.003	0.0929380
$323$	−270.373	−0.0465758
$324$	−353.619	−0.0606343
$325$	−1668.28	−0.284738
$326$	−3724.90	−0.632832
$327$	−4022.30	−0.680226
$328$	−703.015	−0.118346
$329$	5167.28	0.865901
$330$	0	0
$331$	8222.61	1.36542	0.682712	−	0.730687i	$-0.260800\pi$
$331$	8222.61	1.36542	0.682712	+	0.730687i	$0.260800\pi$
$332$	−2412.45	−0.398796
$333$	2737.15	0.450435
$334$	−3976.34	−0.651424
$335$	183.942	0.0299995
$336$	−688.627	−0.111809
$337$	2947.77	0.476484	0.238242	−	0.971206i	$-0.423429\pi$
$337$	2947.77	0.476484	0.238242	+	0.971206i	$0.423429\pi$
$338$	4300.96	0.692134
$339$	5547.62	0.888806
$340$	75.4361	0.0120326
$341$	0	0
$342$	−1342.33	−0.212237
$343$	−3683.92	−0.579922
$344$	6342.77	0.994126
$345$	−184.361	−0.0287700
$346$	7624.20	1.18462
$347$	−3322.43	−0.513999	−0.256999	−	0.966412i	$-0.582734\pi$
$347$	−3322.43	−0.513999	−0.256999	+	0.966412i	$0.582734\pi$
$348$	−408.400	−0.0629096
$349$	9199.67	1.41102	0.705511	−	0.708699i	$-0.250717\pi$
$349$	9199.67	1.41102	0.705511	+	0.708699i	$0.250717\pi$
$350$	1092.29	0.166816
$351$	−1801.75	−0.273989
$352$	0	0
$353$	−10105.2	−1.52363	−0.761817	−	0.647792i	$-0.775693\pi$
$353$	−10105.2	−1.52363	−0.761817	+	0.647792i	$0.775693\pi$
$354$	160.538	0.0241031
$355$	−119.276	−0.0178325
$356$	6527.81	0.971835
$357$	237.611	0.0352261
$358$	3901.62	0.575997
$359$	5236.42	0.769826	0.384913	−	0.922953i	$-0.374231\pi$
$359$	5236.42	0.769826	0.384913	+	0.922953i	$0.374231\pi$
$360$	1060.82	0.155306
$361$	−738.148	−0.107617
$362$	122.576	0.0177968
$363$	0	0
$364$	6676.79	0.961426
$365$	3536.33	0.507123
$366$	4882.70	0.697330
$367$	−9337.95	−1.32817	−0.664083	−	0.747659i	$-0.731178\pi$
$367$	−9337.95	−1.32817	−0.664083	+	0.747659i	$0.731178\pi$
$368$	−123.099	−0.0174374
$369$	268.397	0.0378650
$370$	−2898.93	−0.407320
$371$	−385.882	−0.0540000
$372$	−3237.33	−0.451204
$373$	−14256.1	−1.97896	−0.989482	−	0.144659i	$-0.953791\pi$
$373$	−14256.1	−1.97896	−0.989482	+	0.144659i	$0.953791\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−5315.02	−0.728992
$377$	−2080.86	−0.284270
$378$	1179.68	0.160519
$379$	1911.19	0.259027	0.129514	−	0.991578i	$-0.458658\pi$
$379$	1911.19	0.259027	0.129514	+	0.991578i	$0.458658\pi$
$380$	−1707.76	−0.230543
$381$	3060.73	0.411564
$382$	9182.32	1.22987
$383$	1743.91	0.232662	0.116331	−	0.993210i	$-0.462887\pi$
$383$	1743.91	0.232662	0.116331	+	0.993210i	$0.462887\pi$
$384$	−1761.66	−0.234112
$385$	0	0
$386$	563.917	0.0743592
$387$	−2421.54	−0.318072
$388$	−5236.40	−0.685150
$389$	−2734.88	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$389$	−2734.88	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$390$	1908.24	0.247763
$391$	42.4752	0.00549377
$392$	−4296.57	−0.553596
$393$	−3009.89	−0.386332
$394$	4094.87	0.523596
$395$	−2060.63	−0.262485
$396$	0	0
$397$	−14879.5	−1.88106	−0.940530	−	0.339709i	$-0.889671\pi$
$397$	−14879.5	−1.88106	−0.940530	+	0.339709i	$0.889671\pi$
$398$	−1670.50	−0.210388
$399$	−5379.16	−0.674924
$400$	−250.389	−0.0312986
$401$	−11638.2	−1.44934	−0.724668	−	0.689098i	$-0.758007\pi$
$401$	−11638.2	−1.44934	−0.724668	+	0.689098i	$0.758007\pi$
$402$	−210.400	−0.0261039
$403$	−16494.7	−2.03886
$404$	−4407.84	−0.542817
$405$	−405.000	−0.0496904
$406$	1362.43	0.166542
$407$	0	0
$408$	−244.405	−0.0296564
$409$	−936.594	−0.113231	−0.0566157	−	0.998396i	$-0.518031\pi$
$409$	−936.594	−0.113231	−0.0566157	+	0.998396i	$0.518031\pi$
$410$	−284.261	−0.0342406
$411$	7995.42	0.959574
$412$	−5049.76	−0.603845
$413$	643.326	0.0766489
$414$	210.878	0.0250341
$415$	−2762.98	−0.326818
$416$	−11310.8	−1.33307
$417$	−7672.93	−0.901067
$418$	0	0
$419$	128.037	0.0149285	0.00746425	−	0.999972i	$-0.497624\pi$
$419$	128.037	0.0149285	0.00746425	+	0.999972i	$0.497624\pi$
$420$	1500.82	0.174363
$421$	−6628.97	−0.767402	−0.383701	−	0.923457i	$-0.625351\pi$
$421$	−6628.97	−0.767402	−0.383701	+	0.923457i	$0.625351\pi$
$422$	−2695.61	−0.310949
$423$	2029.16	0.233242
$424$	396.915	0.0454620
$425$	86.3969	0.00986086
$426$	136.432	0.0155168
$427$	19566.5	2.21754
$428$	2147.29	0.242507
$429$	0	0
$430$	2564.67	0.287626
$431$	−14677.8	−1.64038	−0.820192	−	0.572089i	$-0.806133\pi$
$431$	−14677.8	−1.64038	−0.820192	+	0.572089i	$0.806133\pi$
$432$	−270.420	−0.0301171
$433$	−1150.36	−0.127674	−0.0638369	−	0.997960i	$-0.520334\pi$
$433$	−1150.36	−0.127674	−0.0638369	+	0.997960i	$0.520334\pi$
$434$	10799.8	1.19448
$435$	−467.740	−0.0515550
$436$	5853.35	0.642946
$437$	−961.576	−0.105259
$438$	−4044.97	−0.441270
$439$	9308.30	1.01198	0.505992	−	0.862538i	$-0.331127\pi$
$439$	9308.30	1.01198	0.505992	+	0.862538i	$0.331127\pi$
$440$	0	0
$441$	1640.34	0.177124
$442$	−439.643	−0.0473115
$443$	−5689.21	−0.610164	−0.305082	−	0.952326i	$-0.598684\pi$
$443$	−5689.21	−0.610164	−0.305082	+	0.952326i	$0.598684\pi$
$444$	−3983.17	−0.425749
$445$	7476.30	0.796428
$446$	6416.02	0.681183
$447$	7933.98	0.839518
$448$	9241.96	0.974646
$449$	−6644.91	−0.698425	−0.349212	−	0.937044i	$-0.613551\pi$
$449$	−6644.91	−0.698425	−0.349212	+	0.937044i	$0.613551\pi$
$450$	428.938	0.0449341
$451$	0	0
$452$	−8073.02	−0.840095
$453$	8614.33	0.893458
$454$	10912.8	1.12811
$455$	7646.93	0.787898
$456$	5532.95	0.568211
$457$	8355.11	0.855220	0.427610	−	0.903963i	$-0.359356\pi$
$457$	8355.11	0.855220	0.427610	+	0.903963i	$0.359356\pi$
$458$	4931.33	0.503114
$459$	93.3087	0.00948862
$460$	268.286	0.0271933
$461$	15580.5	1.57409	0.787044	−	0.616897i	$-0.211611\pi$
$461$	15580.5	1.57409	0.787044	+	0.616897i	$0.211611\pi$
$462$	0	0
$463$	7139.16	0.716598	0.358299	−	0.933607i	$-0.383357\pi$
$463$	7139.16	0.716598	0.358299	+	0.933607i	$0.383357\pi$
$464$	−312.312	−0.0312473
$465$	−3707.72	−0.369766
$466$	−10621.7	−1.05588
$467$	−12415.1	−1.23019	−0.615097	−	0.788451i	$-0.710883\pi$
$467$	−12415.1	−1.23019	−0.615097	+	0.788451i	$0.710883\pi$
$468$	2621.94	0.258973
$469$	−843.139	−0.0830118
$470$	−2149.10	−0.210916
$471$	3145.54	0.307726
$472$	−661.719	−0.0645299
$473$	0	0
$474$	2357.02	0.228400
$475$	−1955.90	−0.188932
$476$	−345.777	−0.0332955
$477$	−151.534	−0.0145456
$478$	3475.21	0.332536
$479$	14151.0	1.34985	0.674925	−	0.737887i	$-0.264176\pi$
$479$	14151.0	1.34985	0.674925	+	0.737887i	$0.264176\pi$
$480$	−2542.45	−0.241764
$481$	−20294.9	−1.92384
$482$	4244.88	0.401139
$483$	845.057	0.0796096
$484$	0	0
$485$	−5997.25	−0.561487
$486$	463.253	0.0432378
$487$	−76.6358	−0.00713080	−0.00356540	−	0.999994i	$-0.501135\pi$
$487$	−76.6358	−0.00713080	−0.00356540	+	0.999994i	$0.501135\pi$
$488$	−20126.0	−1.86693
$489$	−5861.71	−0.542077
$490$	−1737.30	−0.160170
$491$	1707.54	0.156945	0.0784725	−	0.996916i	$-0.474996\pi$
$491$	1707.54	0.156945	0.0784725	+	0.996916i	$0.474996\pi$
$492$	−390.577	−0.0357898
$493$	107.763	0.00984467
$494$	9952.86	0.906479
$495$	0	0
$496$	−2475.66	−0.224114
$497$	546.728	0.0493443
$498$	3160.39	0.284379
$499$	−13168.5	−1.18137	−0.590686	−	0.806902i	$-0.701143\pi$
$499$	−13168.5	−1.18137	−0.590686	+	0.806902i	$0.701143\pi$
$500$	545.709	0.0488097
$501$	−6257.38	−0.558002
$502$	15038.0	1.33701
$503$	1525.32	0.135210	0.0676052	−	0.997712i	$-0.478464\pi$
$503$	1525.32	0.135210	0.0676052	+	0.997712i	$0.478464\pi$
$504$	−4862.50	−0.429748
$505$	−5048.29	−0.444844
$506$	0	0
$507$	6768.22	0.592874
$508$	−4454.05	−0.389009
$509$	9006.01	0.784253	0.392126	−	0.919911i	$-0.371740\pi$
$509$	9006.01	0.784253	0.392126	+	0.919911i	$0.371740\pi$
$510$	−98.8238	−0.00858038
$511$	−16209.5	−1.40326
$512$	−3586.45	−0.309571
$513$	−2112.37	−0.181800
$514$	−9065.51	−0.777942
$515$	−5783.49	−0.494856
$516$	3523.88	0.300640
$517$	0	0
$518$	13287.9	1.12710
$519$	11997.8	1.01473
$520$	−7865.56	−0.663322
$521$	21707.8	1.82541	0.912703	−	0.408623i	$-0.133991\pi$
$521$	21707.8	1.82541	0.912703	+	0.408623i	$0.133991\pi$
$522$	535.018	0.0448603
$523$	14015.0	1.17177	0.585883	−	0.810396i	$-0.300748\pi$
$523$	14015.0	1.17177	0.585883	+	0.810396i	$0.300748\pi$
$524$	4380.06	0.365160
$525$	1718.89	0.142893
$526$	197.191	0.0163459
$527$	854.227	0.0706086
$528$	0	0
$529$	−12015.9	−0.987584
$530$	160.491	0.0131533
$531$	252.631	0.0206464
$532$	7827.88	0.637935
$533$	−1990.05	−0.161724
$534$	−8551.65	−0.693008
$535$	2459.29	0.198737
$536$	867.244	0.0698867
$537$	6139.79	0.493392
$538$	−4154.98	−0.332963
$539$	0	0
$540$	589.365	0.0469671
$541$	−14444.9	−1.14793	−0.573967	−	0.818878i	$-0.694596\pi$
$541$	−14444.9	−1.14793	−0.573967	+	0.818878i	$0.694596\pi$
$542$	7031.80	0.557273
$543$	192.892	0.0152445
$544$	585.760	0.0461659
$545$	6703.83	0.526900
$546$	−8746.83	−0.685585
$547$	−20286.4	−1.58571	−0.792854	−	0.609412i	$-0.791406\pi$
$547$	−20286.4	−1.58571	−0.792854	+	0.609412i	$0.791406\pi$
$548$	−11635.1	−0.906985
$549$	7683.68	0.597325
$550$	0	0
$551$	−2439.60	−0.188622
$552$	−869.218	−0.0670224
$553$	9445.34	0.726323
$554$	5885.38	0.451346
$555$	−4561.92	−0.348906
$556$	11165.8	0.851684
$557$	24482.4	1.86239	0.931196	−	0.364520i	$-0.118767\pi$
$557$	24482.4	1.86239	0.931196	+	0.364520i	$0.118767\pi$
$558$	4241.02	0.321750
$559$	17954.7	1.35851
$560$	1147.71	0.0866065
$561$	0	0
$562$	−6365.27	−0.477763
$563$	20383.5	1.52587	0.762933	−	0.646478i	$-0.223759\pi$
$563$	20383.5	1.52587	0.762933	+	0.646478i	$0.223759\pi$
$564$	−2952.89	−0.220459
$565$	−9246.03	−0.688466
$566$	−2828.62	−0.210063
$567$	1856.40	0.137498
$568$	−562.359	−0.0415424
$569$	−3297.74	−0.242967	−0.121484	−	0.992593i	$-0.538765\pi$
$569$	−3297.74	−0.242967	−0.121484	+	0.992593i	$0.538765\pi$
$570$	2237.22	0.164398
$571$	7213.03	0.528644	0.264322	−	0.964434i	$-0.414852\pi$
$571$	7213.03	0.528644	0.264322	+	0.964434i	$0.414852\pi$
$572$	0	0
$573$	14449.8	1.05349
$574$	1302.97	0.0947472
$575$	307.268	0.0222852
$576$	3629.27	0.262534
$577$	−18080.4	−1.30450	−0.652251	−	0.758003i	$-0.726175\pi$
$577$	−18080.4	−1.30450	−0.652251	+	0.758003i	$0.726175\pi$
$578$	−9343.34	−0.672373
$579$	887.411	0.0636952
$580$	680.666	0.0487295
$581$	12664.7	0.904337
$582$	6859.87	0.488575
$583$	0	0
$584$	16672.9	1.18139
$585$	3002.91	0.212231
$586$	3032.22	0.213754
$587$	13457.5	0.946250	0.473125	−	0.880995i	$-0.343126\pi$
$587$	13457.5	0.946250	0.473125	+	0.880995i	$0.343126\pi$
$588$	−2387.06	−0.167416
$589$	−19338.4	−1.35285
$590$	−267.563	−0.0186702
$591$	6443.91	0.448506
$592$	−3046.01	−0.211470
$593$	10262.3	0.710665	0.355332	−	0.934740i	$-0.384368\pi$
$593$	10262.3	0.710665	0.355332	+	0.934740i	$0.384368\pi$
$594$	0	0
$595$	−396.018	−0.0272860
$596$	−11545.7	−0.793508
$597$	−2628.78	−0.180216
$598$	−1563.58	−0.106922
$599$	23153.3	1.57933	0.789665	−	0.613538i	$-0.210254\pi$
$599$	23153.3	1.57933	0.789665	+	0.613538i	$0.210254\pi$
$600$	−1768.04	−0.120300
$601$	−14414.8	−0.978357	−0.489178	−	0.872184i	$-0.662703\pi$
$601$	−14414.8	−0.978357	−0.489178	+	0.872184i	$0.662703\pi$
$602$	−11755.7	−0.795891
$603$	−331.096	−0.0223603
$604$	−12535.8	−0.844492
$605$	0	0
$606$	5774.42	0.387079
$607$	−10808.8	−0.722757	−0.361379	−	0.932419i	$-0.617694\pi$
$607$	−10808.8	−0.722757	−0.361379	+	0.932419i	$0.617694\pi$
$608$	−13260.7	−0.884530
$609$	2143.99	0.142658
$610$	−8137.84	−0.540150
$611$	−15045.4	−0.996191
$612$	−135.785	−0.00896860
$613$	−12072.8	−0.795455	−0.397727	−	0.917504i	$-0.630201\pi$
$613$	−12072.8	−0.795455	−0.397727	+	0.917504i	$0.630201\pi$
$614$	−19398.0	−1.27498
$615$	−447.328	−0.0293301
$616$	0	0
$617$	11593.5	0.756462	0.378231	−	0.925711i	$-0.376532\pi$
$617$	11593.5	0.756462	0.378231	+	0.925711i	$0.376532\pi$
$618$	6615.36	0.430597
$619$	4037.96	0.262196	0.131098	−	0.991369i	$-0.458150\pi$
$619$	4037.96	0.262196	0.131098	+	0.991369i	$0.458150\pi$
$620$	5395.55	0.349501
$621$	331.850	0.0214439
$622$	−11930.7	−0.769094
$623$	−34269.2	−2.20380
$624$	2005.06	0.128632
$625$	625.000	0.0400000
$626$	18286.6	1.16754
$627$	0	0
$628$	−4577.46	−0.290861
$629$	1051.03	0.0666252
$630$	−1966.13	−0.124337
$631$	2896.22	0.182721	0.0913604	−	0.995818i	$-0.470878\pi$
$631$	2896.22	0.182721	0.0913604	+	0.995818i	$0.470878\pi$
$632$	−9715.39	−0.611483
$633$	−4241.96	−0.266355
$634$	−20269.3	−1.26971
$635$	−5101.22	−0.318796
$636$	220.516	0.0137484
$637$	−12162.5	−0.756506
$638$	0	0
$639$	214.697	0.0132915
$640$	2936.09	0.181343
$641$	13371.2	0.823916	0.411958	−	0.911203i	$-0.364845\pi$
$641$	13371.2	0.823916	0.411958	+	0.911203i	$0.364845\pi$
$642$	−2813.02	−0.172930
$643$	14063.6	0.862544	0.431272	−	0.902222i	$-0.358065\pi$
$643$	14063.6	0.862544	0.431272	+	0.902222i	$0.358065\pi$
$644$	−1229.75	−0.0752466
$645$	4035.90	0.246377
$646$	−515.438	−0.0313926
$647$	20899.7	1.26994	0.634971	−	0.772536i	$-0.281012\pi$
$647$	20899.7	1.26994	0.634971	+	0.772536i	$0.281012\pi$
$648$	−1909.48	−0.115758
$649$	0	0
$650$	−3180.40	−0.191916
$651$	16995.1	1.02318
$652$	8530.09	0.512368
$653$	−1607.80	−0.0963523	−0.0481761	−	0.998839i	$-0.515341\pi$
$653$	−1607.80	−0.0963523	−0.0481761	+	0.998839i	$0.515341\pi$
$654$	−7668.08	−0.458480
$655$	5016.48	0.299252
$656$	−298.683	−0.0177768
$657$	−6365.39	−0.377987
$658$	9850.86	0.583627
$659$	−14733.1	−0.870896	−0.435448	−	0.900214i	$-0.643410\pi$
$659$	−14733.1	−0.870896	−0.435448	+	0.900214i	$0.643410\pi$
$660$	0	0
$661$	−16442.2	−0.967518	−0.483759	−	0.875201i	$-0.660729\pi$
$661$	−16442.2	−0.967518	−0.483759	+	0.875201i	$0.660729\pi$
$662$	15675.5	0.920312
$663$	−691.846	−0.0405265
$664$	−13026.8	−0.761351
$665$	8965.27	0.522794
$666$	5218.08	0.303598
$667$	383.258	0.0222486
$668$	9105.88	0.527421
$669$	10096.6	0.583493
$670$	350.666	0.0202200
$671$	0	0
$672$	11653.9	0.668985
$673$	25246.6	1.44604	0.723021	−	0.690826i	$-0.242753\pi$
$673$	25246.6	1.44604	0.723021	+	0.690826i	$0.242753\pi$
$674$	5619.60	0.321156
$675$	675.000	0.0384900
$676$	−9849.26	−0.560381
$677$	−24582.6	−1.39555	−0.697774	−	0.716318i	$-0.745826\pi$
$677$	−24582.6	−1.39555	−0.697774	+	0.716318i	$0.745826\pi$
$678$	10575.9	0.599065
$679$	27489.7	1.55369
$680$	407.341	0.0229718
$681$	17172.9	0.966327
$682$	0	0
$683$	11459.5	0.642000	0.321000	−	0.947079i	$-0.395981\pi$
$683$	11459.5	0.642000	0.321000	+	0.947079i	$0.395981\pi$
$684$	3073.97	0.171836
$685$	−13325.7	−0.743283
$686$	−7023.00	−0.390874
$687$	7760.21	0.430961
$688$	2694.79	0.149328
$689$	1123.56	0.0621253
$690$	−351.464	−0.0193913
$691$	−15683.8	−0.863445	−0.431723	−	0.902006i	$-0.642094\pi$
$691$	−15683.8	−0.863445	−0.431723	+	0.902006i	$0.642094\pi$
$692$	−17459.5	−0.959121
$693$	0	0
$694$	−6333.86	−0.346441
$695$	12788.2	0.697963
$696$	−2205.28	−0.120102
$697$	103.061	0.00560072
$698$	17538.2	0.951045
$699$	−16714.9	−0.904457
$700$	−2501.37	−0.135061
$701$	−6185.65	−0.333279	−0.166640	−	0.986018i	$-0.553292\pi$
$701$	−6185.65	−0.333279	−0.166640	+	0.986018i	$0.553292\pi$
$702$	−3434.83	−0.184672
$703$	−23793.7	−1.27652
$704$	0	0
$705$	−3381.94	−0.180668
$706$	−19264.4	−1.02695
$707$	23139.9	1.23093
$708$	−367.634	−0.0195149
$709$	−28031.2	−1.48481	−0.742407	−	0.669950i	$-0.766316\pi$
$709$	−28031.2	−1.48481	−0.742407	+	0.669950i	$0.766316\pi$
$710$	−227.387	−0.0120193
$711$	3709.14	0.195645
$712$	35249.0	1.85535
$713$	3038.03	0.159573
$714$	452.980	0.0237428
$715$	0	0
$716$	−8934.77	−0.466352
$717$	5468.77	0.284847
$718$	9982.67	0.518872
$719$	23313.0	1.20922	0.604610	−	0.796522i	$-0.293329\pi$
$719$	23313.0	1.20922	0.604610	+	0.796522i	$0.293329\pi$
$720$	450.700	0.0233286
$721$	26509.9	1.36932
$722$	−1407.20	−0.0725354
$723$	6679.98	0.343611
$724$	−280.701	−0.0144091
$725$	779.567	0.0399343
$726$	0	0
$727$	−69.6810	−0.00355478	−0.00177739	−	0.999998i	$-0.500566\pi$
$727$	−69.6810	−0.00355478	−0.00177739	+	0.999998i	$0.500566\pi$
$728$	36053.5	1.83548
$729$	729.000	0.0370370
$730$	6741.62	0.341806
$731$	−929.838	−0.0470469
$732$	−11181.5	−0.564589
$733$	−15152.9	−0.763552	−0.381776	−	0.924255i	$-0.624687\pi$
$733$	−15152.9	−0.763552	−0.381776	+	0.924255i	$0.624687\pi$
$734$	−17801.8	−0.895199
$735$	−2733.90	−0.137199
$736$	2083.24	0.104333
$737$	0	0
$738$	511.669	0.0255214
$739$	31557.9	1.57087	0.785437	−	0.618941i	$-0.212438\pi$
$739$	31557.9	1.57087	0.785437	+	0.618941i	$0.212438\pi$
$740$	6638.61	0.329784
$741$	15662.4	0.776479
$742$	−735.642	−0.0363966
$743$	−6925.00	−0.341929	−0.170965	−	0.985277i	$-0.554688\pi$
$743$	−6925.00	−0.341929	−0.170965	+	0.985277i	$0.554688\pi$
$744$	−17481.0	−0.861404
$745$	−13223.3	−0.650288
$746$	−27177.7	−1.33384
$747$	4973.36	0.243595
$748$	0	0
$749$	−11272.7	−0.549925
$750$	−714.897	−0.0348058
$751$	−22202.1	−1.07878	−0.539392	−	0.842055i	$-0.681346\pi$
$751$	−22202.1	−1.07878	−0.539392	+	0.842055i	$0.681346\pi$
$752$	−2258.14	−0.109502
$753$	23664.7	1.14527
$754$	−3966.94	−0.191601
$755$	−14357.2	−0.692070
$756$	−2701.48	−0.129963
$757$	18928.6	0.908813	0.454406	−	0.890795i	$-0.349851\pi$
$757$	18928.6	0.908813	0.454406	+	0.890795i	$0.349851\pi$
$758$	3643.48	0.174587
$759$	0	0
$760$	−9221.59	−0.440134
$761$	22883.3	1.09004	0.545019	−	0.838423i	$-0.316522\pi$
$761$	22883.3	1.09004	0.545019	+	0.838423i	$0.316522\pi$
$762$	5834.95	0.277399
$763$	−30728.4	−1.45799
$764$	−21027.7	−0.995752
$765$	−155.514	−0.00734985
$766$	3324.57	0.156817
$767$	−1873.16	−0.0881822
$768$	−13036.5	−0.612516
$769$	−8903.82	−0.417529	−0.208765	−	0.977966i	$-0.566944\pi$
$769$	−8903.82	−0.417529	−0.208765	+	0.977966i	$0.566944\pi$
$770$	0	0
$771$	−14266.0	−0.666376
$772$	−1291.38	−0.0602044
$773$	24691.9	1.14891	0.574454	−	0.818537i	$-0.305214\pi$
$773$	24691.9	1.14891	0.574454	+	0.818537i	$0.305214\pi$
$774$	−4616.40	−0.214384
$775$	6179.53	0.286420
$776$	−28275.6	−1.30804
$777$	20910.5	0.965457
$778$	−5213.75	−0.240259
$779$	−2333.14	−0.107309
$780$	−4369.91	−0.200600
$781$	0	0
$782$	80.9744	0.00370286
$783$	841.932	0.0384268
$784$	−1825.44	−0.0831559
$785$	−5242.56	−0.238363
$786$	−5738.02	−0.260392
$787$	7418.83	0.336026	0.168013	−	0.985785i	$-0.446265\pi$
$787$	7418.83	0.336026	0.168013	+	0.985785i	$0.446265\pi$
$788$	−9377.33	−0.423926
$789$	310.311	0.0140017
$790$	−3928.37	−0.176918
$791$	42381.1	1.90506
$792$	0	0
$793$	−56971.4	−2.55121
$794$	−28366.2	−1.26786
$795$	252.556	0.0112670
$796$	3825.46	0.170339
$797$	−27971.2	−1.24315	−0.621576	−	0.783354i	$-0.713507\pi$
$797$	−27971.2	−1.24315	−0.621576	+	0.783354i	$0.713507\pi$
$798$	−10254.8	−0.454907
$799$	779.171	0.0344995
$800$	4237.42	0.187269
$801$	−13457.3	−0.593622
$802$	−22187.0	−0.976869
$803$	0	0
$804$	481.819	0.0211349
$805$	−1408.43	−0.0616653
$806$	−31445.4	−1.37421
$807$	−6538.51	−0.285212
$808$	−23801.5	−1.03630
$809$	10670.0	0.463704	0.231852	−	0.972751i	$-0.425521\pi$
$809$	10670.0	0.463704	0.231852	+	0.972751i	$0.425521\pi$
$810$	−772.089	−0.0334919
$811$	−40618.3	−1.75869	−0.879346	−	0.476182i	$-0.842020\pi$
$811$	−40618.3	−1.75869	−0.879346	+	0.476182i	$0.842020\pi$
$812$	−3119.98	−0.134840
$813$	11065.6	0.477353
$814$	0	0
$815$	9769.51	0.419891
$816$	−103.838	−0.00445471
$817$	21050.1	0.901409
$818$	−1785.52	−0.0763192
$819$	−13764.5	−0.587265
$820$	650.962	0.0277227
$821$	−16710.5	−0.710355	−0.355178	−	0.934799i	$-0.615580\pi$
$821$	−16710.5	−0.710355	−0.355178	+	0.934799i	$0.615580\pi$
$822$	15242.4	0.646764
$823$	−16920.5	−0.716661	−0.358331	−	0.933595i	$-0.616654\pi$
$823$	−16920.5	−0.716661	−0.358331	+	0.933595i	$0.616654\pi$
$824$	−27267.8	−1.15281
$825$	0	0
$826$	1226.43	0.0516623
$827$	9478.39	0.398544	0.199272	−	0.979944i	$-0.436142\pi$
$827$	9478.39	0.398544	0.199272	+	0.979944i	$0.436142\pi$
$828$	−482.915	−0.0202687
$829$	−31908.1	−1.33681	−0.668405	−	0.743798i	$-0.733023\pi$
$829$	−31908.1	−1.33681	−0.668405	+	0.743798i	$0.733023\pi$
$830$	−5267.32	−0.220279
$831$	9261.54	0.386618
$832$	−26909.6	−1.12130
$833$	629.869	0.0261989
$834$	−14627.6	−0.607329
$835$	10429.0	0.432226
$836$	0	0
$837$	6673.89	0.275607
$838$	244.090	0.0100620
$839$	25195.7	1.03677	0.518386	−	0.855147i	$-0.326533\pi$
$839$	25195.7	1.03677	0.518386	+	0.855147i	$0.326533\pi$
$840$	8104.17	0.332881
$841$	−23416.6	−0.960131
$842$	−12637.4	−0.517238
$843$	−10016.7	−0.409246
$844$	6173.00	0.251758
$845$	−11280.4	−0.459238
$846$	3868.38	0.157208
$847$	0	0
$848$	168.633	0.00682887
$849$	−4451.26	−0.179938
$850$	164.706	0.00664633
$851$	3737.95	0.150570
$852$	−312.432	−0.0125631
$853$	−8239.19	−0.330720	−0.165360	−	0.986233i	$-0.552879\pi$
$853$	−8239.19	−0.330720	−0.165360	+	0.986233i	$0.552879\pi$
$854$	37301.5	1.49465
$855$	3520.61	0.140822
$856$	11594.9	0.462976
$857$	−12912.8	−0.514694	−0.257347	−	0.966319i	$-0.582848\pi$
$857$	−12912.8	−0.514694	−0.257347	+	0.966319i	$0.582848\pi$
$858$	0	0
$859$	18534.6	0.736196	0.368098	−	0.929787i	$-0.380009\pi$
$859$	18534.6	0.736196	0.368098	+	0.929787i	$0.380009\pi$
$860$	−5873.14	−0.232875
$861$	2050.42	0.0811594
$862$	−27981.7	−1.10564
$863$	−18743.4	−0.739318	−0.369659	−	0.929168i	$-0.620525\pi$
$863$	−18743.4	−0.739318	−0.369659	+	0.929168i	$0.620525\pi$
$864$	4576.42	0.180200
$865$	−19996.4	−0.786009
$866$	−2193.04	−0.0860536
$867$	−14703.2	−0.575947
$868$	−24731.7	−0.967105
$869$	0	0
$870$	−891.696	−0.0347487
$871$	2454.94	0.0955024
$872$	31607.0	1.22746
$873$	10795.1	0.418508
$874$	−1833.14	−0.0709461
$875$	−2864.82	−0.110684
$876$	9263.06	0.357272
$877$	−25629.7	−0.986833	−0.493417	−	0.869793i	$-0.664252\pi$
$877$	−25629.7	−0.986833	−0.493417	+	0.869793i	$0.664252\pi$
$878$	17745.3	0.682088
$879$	4771.66	0.183099
$880$	0	0
$881$	14336.5	0.548250	0.274125	−	0.961694i	$-0.411612\pi$
$881$	14336.5	0.548250	0.274125	+	0.961694i	$0.411612\pi$
$882$	3127.13	0.119383
$883$	1012.36	0.0385827	0.0192914	−	0.999814i	$-0.493859\pi$
$883$	1012.36	0.0385827	0.0192914	+	0.999814i	$0.493859\pi$
$884$	1006.79	0.0383054
$885$	−421.051	−0.0159926
$886$	−10845.9	−0.411258
$887$	2586.40	0.0979061	0.0489530	−	0.998801i	$-0.484412\pi$
$887$	2586.40	0.0979061	0.0489530	+	0.998801i	$0.484412\pi$
$888$	−21508.4	−0.812808
$889$	23382.5	0.882142
$890$	14252.8	0.536801
$891$	0	0
$892$	−14692.8	−0.551515
$893$	−17639.3	−0.661003
$894$	15125.3	0.565844
$895$	−10233.0	−0.382180
$896$	−13458.2	−0.501794
$897$	−2460.53	−0.0915883
$898$	−12667.8	−0.470746
$899$	7707.77	0.285949
$900$	−982.276	−0.0363806
$901$	−58.1869	−0.00215148
$902$	0	0
$903$	−18499.4	−0.681751
$904$	−43592.8	−1.60385
$905$	−321.487	−0.0118084
$906$	16422.3	0.602201
$907$	43346.1	1.58686	0.793431	−	0.608660i	$-0.208293\pi$
$907$	43346.1	1.58686	0.793431	+	0.608660i	$0.208293\pi$
$908$	−24990.5	−0.913368
$909$	9086.93	0.331567
$910$	14578.0	0.531052
$911$	−5218.71	−0.189796	−0.0948978	−	0.995487i	$-0.530252\pi$
$911$	−5218.71	−0.189796	−0.0948978	+	0.995487i	$0.530252\pi$
$912$	2350.73	0.0853514
$913$	0	0
$914$	15928.1	0.576428
$915$	−12806.1	−0.462686
$916$	−11292.8	−0.407343
$917$	−22994.1	−0.828060
$918$	177.883	0.00639544
$919$	29209.5	1.04846	0.524230	−	0.851577i	$-0.324353\pi$
$919$	29209.5	1.04846	0.524230	+	0.851577i	$0.324353\pi$
$920$	1448.70	0.0519153
$921$	−30525.8	−1.09214
$922$	29702.5	1.06095
$923$	−1591.89	−0.0567690
$924$	0	0
$925$	7603.20	0.270261
$926$	13610.0	0.482995
$927$	10410.3	0.368844
$928$	5285.37	0.186962
$929$	−39401.0	−1.39150	−0.695751	−	0.718283i	$-0.744928\pi$
$929$	−39401.0	−1.39150	−0.695751	+	0.718283i	$0.744928\pi$
$930$	−7068.36	−0.249226
$931$	−14259.3	−0.501965
$932$	24323.9	0.854888
$933$	−18774.7	−0.658797
$934$	−23668.0	−0.829165
$935$	0	0
$936$	14158.0	0.494411
$937$	−6099.66	−0.212665	−0.106332	−	0.994331i	$-0.533911\pi$
$937$	−6099.66	−0.212665	−0.106332	+	0.994331i	$0.533911\pi$
$938$	−1607.35	−0.0559509
$939$	28776.7	1.00010
$940$	4921.48	0.170767
$941$	−11534.4	−0.399587	−0.199793	−	0.979838i	$-0.564027\pi$
$941$	−11534.4	−0.399587	−0.199793	+	0.979838i	$0.564027\pi$
$942$	5996.63	0.207410
$943$	366.532	0.0126574
$944$	−281.138	−0.00969307
$945$	−3094.01	−0.106506
$946$	0	0
$947$	−16680.4	−0.572376	−0.286188	−	0.958174i	$-0.592388\pi$
$947$	−16680.4	−0.572376	−0.286188	+	0.958174i	$0.592388\pi$
$948$	−5397.62	−0.184923
$949$	47196.8	1.61441
$950$	−3728.71	−0.127342
$951$	−31896.9	−1.08762
$952$	−1867.13	−0.0635653
$953$	17114.4	0.581733	0.290866	−	0.956764i	$-0.406057\pi$
$953$	17114.4	0.581733	0.290866	+	0.956764i	$0.406057\pi$
$954$	−288.883	−0.00980391
$955$	−24083.0	−0.816029
$956$	−7958.29	−0.269236
$957$	0	0
$958$	26977.4	0.909814
$959$	61081.2	2.05674
$960$	−6048.78	−0.203358
$961$	31307.5	1.05090
$962$	−38690.0	−1.29669
$963$	−4426.71	−0.148130
$964$	−9720.86	−0.324780
$965$	−1479.02	−0.0493381
$966$	1611.01	0.0536578
$967$	35200.4	1.17060	0.585299	−	0.810817i	$-0.300977\pi$
$967$	35200.4	1.17060	0.585299	+	0.810817i	$0.300977\pi$
$968$	0	0
$969$	−811.120	−0.0268906
$970$	−11433.1	−0.378449
$971$	−43502.6	−1.43776	−0.718881	−	0.695134i	$-0.755345\pi$
$971$	−43502.6	−1.43776	−0.718881	+	0.695134i	$0.755345\pi$
$972$	−1060.86	−0.0350072
$973$	−58617.5	−1.93134
$974$	−146.098	−0.00480624
$975$	−5004.85	−0.164393
$976$	−8550.71	−0.280432
$977$	−5365.50	−0.175699	−0.0878494	−	0.996134i	$-0.527999\pi$
$977$	−5365.50	−0.175699	−0.0878494	+	0.996134i	$0.527999\pi$
$978$	−11174.7	−0.365366
$979$	0	0
$980$	3978.44	0.129680
$981$	−12066.9	−0.392728
$982$	3255.23	0.105783
$983$	42459.0	1.37765	0.688826	−	0.724926i	$-0.258126\pi$
$983$	42459.0	1.37765	0.688826	+	0.724926i	$0.258126\pi$
$984$	−2109.05	−0.0683271
$985$	−10739.8	−0.347411
$986$	205.439	0.00663542
$987$	15501.8	0.499928
$988$	−22792.2	−0.733924
$989$	−3306.94	−0.106324
$990$	0	0
$991$	−6881.29	−0.220576	−0.110288	−	0.993900i	$-0.535177\pi$
$991$	−6881.29	−0.220576	−0.110288	+	0.993900i	$0.535177\pi$
$992$	41896.4	1.34094
$993$	24667.8	0.788328
$994$	1042.28	0.0332586
$995$	4381.30	0.139595
$996$	−7237.35	−0.230245
$997$	3166.87	0.100597	0.0502987	−	0.998734i	$-0.483983\pi$
$997$	3166.87	0.100597	0.0502987	+	0.998734i	$0.483983\pi$
$998$	−25104.4	−0.796258
$999$	8211.45	0.260059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.r.1.2		3
11.10	odd	2		165.4.a.e.1.2	✓	3
33.32	even	2		495.4.a.k.1.2		3
55.32	even	4		825.4.c.k.199.3		6
55.43	even	4		825.4.c.k.199.4		6
55.54	odd	2		825.4.a.r.1.2		3
165.164	even	2		2475.4.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.2	✓	3	11.10	odd	2
495.4.a.k.1.2		3	33.32	even	2
825.4.a.r.1.2		3	55.54	odd	2
825.4.c.k.199.3		6	55.32	even	4
825.4.c.k.199.4		6	55.43	even	4
1815.4.a.r.1.2		3	1.1	even	1	trivial
2475.4.a.t.1.2		3	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)

\(f(q)\)	\(=\)	\(q+1.90639 q^{2} +3.00000 q^{3} -4.36567 q^{4} -5.00000 q^{5} +5.71918 q^{6} +22.9186 q^{7} -23.5738 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.90639 q^{2} +3.00000 q^{3} -4.36567 q^{4} -5.00000 q^{5} +5.71918 q^{6} +22.9186 q^{7} -23.5738 q^{8} +9.00000 q^{9} -9.53196 q^{10} -13.0970 q^{12} -66.7313 q^{13} +43.6917 q^{14} -15.0000 q^{15} -10.0156 q^{16} +3.45588 q^{17} +17.1575 q^{18} -78.2359 q^{19} +21.8283 q^{20} +68.7557 q^{21} +12.2907 q^{23} -70.7214 q^{24} +25.0000 q^{25} -127.216 q^{26} +27.0000 q^{27} -100.055 q^{28} +31.1827 q^{29} -28.5959 q^{30} +247.181 q^{31} +169.497 q^{32} +6.58825 q^{34} -114.593 q^{35} -39.2910 q^{36} +304.128 q^{37} -149.148 q^{38} -200.194 q^{39} +117.869 q^{40} +29.8219 q^{41} +131.075 q^{42} -269.060 q^{43} -45.0000 q^{45} +23.4309 q^{46} +225.463 q^{47} -30.0467 q^{48} +182.260 q^{49} +47.6598 q^{50} +10.3676 q^{51} +291.327 q^{52} -16.8371 q^{53} +51.4726 q^{54} -540.278 q^{56} -234.708 q^{57} +59.4464 q^{58} +28.0701 q^{59} +65.4850 q^{60} +853.742 q^{61} +471.224 q^{62} +206.267 q^{63} +403.252 q^{64} +333.657 q^{65} -36.7885 q^{67} -15.0872 q^{68} +36.8722 q^{69} -218.459 q^{70} +23.8552 q^{71} -212.164 q^{72} -707.265 q^{73} +579.787 q^{74} +75.0000 q^{75} +341.552 q^{76} -381.648 q^{78} +412.126 q^{79} +50.0778 q^{80} +81.0000 q^{81} +56.8522 q^{82} +552.596 q^{83} -300.165 q^{84} -17.2794 q^{85} -512.934 q^{86} +93.5480 q^{87} -1495.26 q^{89} -85.7876 q^{90} -1529.39 q^{91} -53.6573 q^{92} +741.543 q^{93} +429.820 q^{94} +391.179 q^{95} +508.491 q^{96} +1199.45 q^{97} +347.459 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 - 10 * q^10 + 90 * q^12 - 114 * q^13 - 68 * q^14 - 45 * q^15 + 178 * q^16 + 104 * q^17 + 18 * q^18 + 58 * q^19 - 150 * q^20 - 30 * q^21 + 120 * q^23 - 54 * q^24 + 75 * q^25 - 120 * q^26 + 81 * q^27 - 676 * q^28 + 220 * q^29 - 30 * q^30 + 248 * q^31 + 258 * q^32 - 80 * q^34 + 50 * q^35 + 270 * q^36 + 838 * q^37 + 600 * q^38 - 342 * q^39 + 90 * q^40 - 156 * q^41 - 204 * q^42 - 122 * q^43 - 135 * q^45 + 1256 * q^46 + 504 * q^47 + 534 * q^48 + 279 * q^49 + 50 * q^50 + 312 * q^51 - 520 * q^52 + 282 * q^53 + 54 * q^54 - 1644 * q^56 + 174 * q^57 - 1644 * q^58 + 548 * q^59 - 450 * q^60 - 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 + 570 * q^65 - 428 * q^67 + 1704 * q^68 + 360 * q^69 + 340 * q^70 - 912 * q^71 - 162 * q^72 - 618 * q^73 + 1612 * q^74 + 225 * q^75 + 2752 * q^76 - 360 * q^78 + 542 * q^79 - 890 * q^80 + 243 * q^81 + 3372 * q^82 - 2028 * q^84 - 520 * q^85 - 1548 * q^86 + 660 * q^87 + 790 * q^89 - 90 * q^90 - 772 * q^91 + 1912 * q^92 + 744 * q^93 + 424 * q^94 - 290 * q^95 + 774 * q^96 + 2074 * q^97 + 3978 * q^98

Introduction

L-functions

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