LMFDB - Embedded newform 1815.4.a.i.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.70156$ 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)

$f(q)$	$=$	$q-3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} +5.00000 q^{5} -11.1047 q^{6} +9.10469 q^{7} +8.50781 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} +5.00000 q^{5} -11.1047 q^{6} +9.10469 q^{7} +8.50781 q^{8} +9.00000 q^{9} -18.5078 q^{10} +17.1047 q^{12} -20.2984 q^{13} -33.7016 q^{14} +15.0000 q^{15} -77.1047 q^{16} +61.8062 q^{17} -33.3141 q^{18} +8.68594 q^{19} +28.5078 q^{20} +27.3141 q^{21} -127.748 q^{23} +25.5234 q^{24} +25.0000 q^{25} +75.1359 q^{26} +27.0000 q^{27} +51.9109 q^{28} +85.9109 q^{29} -55.5234 q^{30} -158.733 q^{31} +217.345 q^{32} -228.780 q^{34} +45.5234 q^{35} +51.3141 q^{36} +138.423 q^{37} -32.1515 q^{38} -60.8953 q^{39} +42.5391 q^{40} -28.2094 q^{41} -101.105 q^{42} -265.884 q^{43} +45.0000 q^{45} +472.869 q^{46} -515.602 q^{47} -231.314 q^{48} -260.105 q^{49} -92.5391 q^{50} +185.419 q^{51} -115.733 q^{52} -466.702 q^{53} -99.9422 q^{54} +77.4609 q^{56} +26.0578 q^{57} -318.005 q^{58} +373.475 q^{59} +85.5234 q^{60} -84.8172 q^{61} +587.559 q^{62} +81.9422 q^{63} -187.680 q^{64} -101.492 q^{65} -88.7657 q^{67} +352.392 q^{68} -383.245 q^{69} -168.508 q^{70} -536.695 q^{71} +76.5703 q^{72} -322.450 q^{73} -512.383 q^{74} +75.0000 q^{75} +49.5234 q^{76} +225.408 q^{78} -265.592 q^{79} -385.523 q^{80} +81.0000 q^{81} +104.419 q^{82} +520.758 q^{83} +155.733 q^{84} +309.031 q^{85} +984.187 q^{86} +257.733 q^{87} -464.713 q^{89} -166.570 q^{90} -184.811 q^{91} -728.366 q^{92} -476.198 q^{93} +1908.53 q^{94} +43.4297 q^{95} +652.036 q^{96} -204.481 q^{97} +962.794 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 15 * q^8 + 18 * q^9	\( 2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9} - 5 q^{10} + 15 q^{12} - 47 q^{13} - 61 q^{14} + 30 q^{15} - 135 q^{16} + 98 q^{17} - 9 q^{18} + 75 q^{19} + 25 q^{20} - 3 q^{21} - 57 q^{23} - 45 q^{24} + 50 q^{25} + 3 q^{26} + 54 q^{27} + 59 q^{28} + 127 q^{29} - 15 q^{30} - 183 q^{31} + 249 q^{32} - 131 q^{34} - 5 q^{35} + 45 q^{36} - 229 q^{37} + 147 q^{38} - 141 q^{39} - 75 q^{40} - 18 q^{41} - 183 q^{42} - 186 q^{43} + 90 q^{45} + 664 q^{46} - 615 q^{47} - 405 q^{48} - 501 q^{49} - 25 q^{50} + 294 q^{51} - 97 q^{52} - 927 q^{53} - 27 q^{54} + 315 q^{56} + 225 q^{57} - 207 q^{58} - 380 q^{59} + 75 q^{60} - 509 q^{61} + 522 q^{62} - 9 q^{63} + 361 q^{64} - 235 q^{65} - 1138 q^{67} + 327 q^{68} - 171 q^{69} - 305 q^{70} - 273 q^{71} - 135 q^{72} - 440 q^{73} - 1505 q^{74} + 150 q^{75} + 3 q^{76} + 9 q^{78} - 973 q^{79} - 675 q^{80} + 162 q^{81} + 132 q^{82} - 15 q^{83} + 177 q^{84} + 490 q^{85} + 1200 q^{86} + 381 q^{87} - 1288 q^{89} - 45 q^{90} + 85 q^{91} - 778 q^{92} - 549 q^{93} + 1640 q^{94} + 375 q^{95} + 747 q^{96} - 76 q^{97} + 312 q^{98}+O(q^{100}) \) 2 * q - q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 15 * q^8 + 18 * q^9 - 5 * q^10 + 15 * q^12 - 47 * q^13 - 61 * q^14 + 30 * q^15 - 135 * q^16 + 98 * q^17 - 9 * q^18 + 75 * q^19 + 25 * q^20 - 3 * q^21 - 57 * q^23 - 45 * q^24 + 50 * q^25 + 3 * q^26 + 54 * q^27 + 59 * q^28 + 127 * q^29 - 15 * q^30 - 183 * q^31 + 249 * q^32 - 131 * q^34 - 5 * q^35 + 45 * q^36 - 229 * q^37 + 147 * q^38 - 141 * q^39 - 75 * q^40 - 18 * q^41 - 183 * q^42 - 186 * q^43 + 90 * q^45 + 664 * q^46 - 615 * q^47 - 405 * q^48 - 501 * q^49 - 25 * q^50 + 294 * q^51 - 97 * q^52 - 927 * q^53 - 27 * q^54 + 315 * q^56 + 225 * q^57 - 207 * q^58 - 380 * q^59 + 75 * q^60 - 509 * q^61 + 522 * q^62 - 9 * q^63 + 361 * q^64 - 235 * q^65 - 1138 * q^67 + 327 * q^68 - 171 * q^69 - 305 * q^70 - 273 * q^71 - 135 * q^72 - 440 * q^73 - 1505 * q^74 + 150 * q^75 + 3 * q^76 + 9 * q^78 - 973 * q^79 - 675 * q^80 + 162 * q^81 + 132 * q^82 - 15 * q^83 + 177 * q^84 + 490 * q^85 + 1200 * q^86 + 381 * q^87 - 1288 * q^89 - 45 * q^90 + 85 * q^91 - 778 * q^92 - 549 * q^93 + 1640 * q^94 + 375 * q^95 + 747 * q^96 - 76 * q^97 + 312 * 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 $

$2$	−3.70156	−1.30870	−0.654350	−	0.756192i	$-0.727058\pi$
$2$	−3.70156	−1.30870	−0.654350	+	0.756192i	$0.727058\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.70156	0.712695
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−11.1047	−0.755578
$7$	9.10469	0.491607	0.245803	−	0.969320i	$-0.420948\pi$
$7$	9.10469	0.491607	0.245803	+	0.969320i	$0.420948\pi$
$8$	8.50781	0.375996
$9$	9.00000	0.333333
$10$	−18.5078	−0.585268
$11$	0	0
$11$	0	0
$12$	17.1047	0.411475
$13$	−20.2984	−0.433060	−0.216530	−	0.976276i	$-0.569474\pi$
$13$	−20.2984	−0.433060	−0.216530	+	0.976276i	$0.569474\pi$
$14$	−33.7016	−0.643366
$15$	15.0000	0.258199
$16$	−77.1047	−1.20476
$17$	61.8062	0.881777	0.440889	−	0.897562i	$-0.354663\pi$
$17$	61.8062	0.881777	0.440889	+	0.897562i	$0.354663\pi$
$18$	−33.3141	−0.436233
$19$	8.68594	0.104879	0.0524393	−	0.998624i	$-0.483300\pi$
$19$	8.68594	0.104879	0.0524393	+	0.998624i	$0.483300\pi$
$20$	28.5078	0.318727
$21$	27.3141	0.283829
$22$	0	0
$23$	−127.748	−1.15815	−0.579074	−	0.815275i	$-0.696586\pi$
$23$	−127.748	−1.15815	−0.579074	+	0.815275i	$0.696586\pi$
$24$	25.5234	0.217081
$25$	25.0000	0.200000
$26$	75.1359	0.566745
$27$	27.0000	0.192450
$28$	51.9109	0.350366
$29$	85.9109	0.550112	0.275056	−	0.961428i	$-0.411304\pi$
$29$	85.9109	0.550112	0.275056	+	0.961428i	$0.411304\pi$
$30$	−55.5234	−0.337905
$31$	−158.733	−0.919653	−0.459827	−	0.888009i	$-0.652088\pi$
$31$	−158.733	−0.919653	−0.459827	+	0.888009i	$0.652088\pi$
$32$	217.345	1.20067
$33$	0	0
$34$	−228.780	−1.15398
$35$	45.5234	0.219853
$36$	51.3141	0.237565
$37$	138.423	0.615045	0.307523	−	0.951541i	$-0.400500\pi$
$37$	138.423	0.615045	0.307523	+	0.951541i	$0.400500\pi$
$38$	−32.1515	−0.137254
$39$	−60.8953	−0.250027
$40$	42.5391	0.168150
$41$	−28.2094	−0.107453	−0.0537264	−	0.998556i	$-0.517110\pi$
$41$	−28.2094	−0.107453	−0.0537264	+	0.998556i	$0.517110\pi$
$42$	−101.105	−0.371447
$43$	−265.884	−0.942953	−0.471477	−	0.881879i	$-0.656279\pi$
$43$	−265.884	−0.942953	−0.471477	+	0.881879i	$0.656279\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	472.869	1.51567
$47$	−515.602	−1.60017	−0.800087	−	0.599883i	$-0.795214\pi$
$47$	−515.602	−1.60017	−0.800087	+	0.599883i	$0.795214\pi$
$48$	−231.314	−0.695569
$49$	−260.105	−0.758323
$50$	−92.5391	−0.261740
$51$	185.419	0.509094
$52$	−115.733	−0.308639
$53$	−466.702	−1.20955	−0.604777	−	0.796395i	$-0.706738\pi$
$53$	−466.702	−1.20955	−0.604777	+	0.796395i	$0.706738\pi$
$54$	−99.9422	−0.251859
$55$	0	0
$56$	77.4609	0.184842
$57$	26.0578	0.0605516
$58$	−318.005	−0.719932
$59$	373.475	0.824107	0.412053	−	0.911160i	$-0.364812\pi$
$59$	373.475	0.824107	0.412053	+	0.911160i	$0.364812\pi$
$60$	85.5234	0.184017
$61$	−84.8172	−0.178028	−0.0890142	−	0.996030i	$-0.528372\pi$
$61$	−84.8172	−0.178028	−0.0890142	+	0.996030i	$0.528372\pi$
$62$	587.559	1.20355
$63$	81.9422	0.163869
$64$	−187.680	−0.366562
$65$	−101.492	−0.193670
$66$	0	0
$67$	−88.7657	−0.161858	−0.0809288	−	0.996720i	$-0.525789\pi$
$67$	−88.7657	−0.161858	−0.0809288	+	0.996720i	$0.525789\pi$
$68$	352.392	0.628439
$69$	−383.245	−0.668657
$70$	−168.508	−0.287722
$71$	−536.695	−0.897099	−0.448549	−	0.893758i	$-0.648059\pi$
$71$	−536.695	−0.897099	−0.448549	+	0.893758i	$0.648059\pi$
$72$	76.5703	0.125332
$73$	−322.450	−0.516985	−0.258493	−	0.966013i	$-0.583226\pi$
$73$	−322.450	−0.516985	−0.258493	+	0.966013i	$0.583226\pi$
$74$	−512.383	−0.804909
$75$	75.0000	0.115470
$76$	49.5234	0.0747464
$77$	0	0
$78$	225.408	0.327210
$79$	−265.592	−0.378246	−0.189123	−	0.981953i	$-0.560565\pi$
$79$	−265.592	−0.378246	−0.189123	+	0.981953i	$0.560565\pi$
$80$	−385.523	−0.538785
$81$	81.0000	0.111111
$82$	104.419	0.140623
$83$	520.758	0.688682	0.344341	−	0.938845i	$-0.388102\pi$
$83$	520.758	0.688682	0.344341	+	0.938845i	$0.388102\pi$
$84$	155.733	0.202284
$85$	309.031	0.394343
$86$	984.187	1.23404
$87$	257.733	0.317608
$88$	0	0
$89$	−464.713	−0.553477	−0.276738	−	0.960945i	$-0.589254\pi$
$89$	−464.713	−0.553477	−0.276738	+	0.960945i	$0.589254\pi$
$90$	−166.570	−0.195089
$91$	−184.811	−0.212895
$92$	−728.366	−0.825406
$93$	−476.198	−0.530962
$94$	1908.53	2.09415
$95$	43.4297	0.0469031
$96$	652.036	0.693210
$97$	−204.481	−0.214040	−0.107020	−	0.994257i	$-0.534131\pi$
$97$	−204.481	−0.214040	−0.107020	+	0.994257i	$0.534131\pi$
$98$	962.794	0.992417
$99$	0	0
$100$	142.539	0.142539
$101$	−27.2516	−0.0268479	−0.0134239	−	0.999910i	$-0.504273\pi$
$101$	−27.2516	−0.0268479	−0.0134239	+	0.999910i	$0.504273\pi$
$102$	−686.339	−0.666252
$103$	1062.80	1.01671	0.508353	−	0.861149i	$-0.330255\pi$
$103$	1062.80	1.01671	0.508353	+	0.861149i	$0.330255\pi$
$104$	−172.695	−0.162828
$105$	136.570	0.126932
$106$	1727.52	1.58294
$107$	−1702.96	−1.53861	−0.769306	−	0.638881i	$-0.779398\pi$
$107$	−1702.96	−1.53861	−0.769306	+	0.638881i	$0.779398\pi$
$108$	153.942	0.137158
$109$	−556.334	−0.488873	−0.244437	−	0.969665i	$-0.578603\pi$
$109$	−556.334	−0.488873	−0.244437	+	0.969665i	$0.578603\pi$
$110$	0	0
$111$	415.270	0.355096
$112$	−702.014	−0.592269
$113$	−2088.31	−1.73851	−0.869256	−	0.494363i	$-0.835401\pi$
$113$	−2088.31	−1.73851	−0.869256	+	0.494363i	$0.835401\pi$
$114$	−96.4546	−0.0792439
$115$	−638.742	−0.517939
$116$	489.827	0.392063
$117$	−182.686	−0.144353
$118$	−1382.44	−1.07851
$119$	562.727	0.433488
$120$	127.617	0.0970817
$121$	0	0
$122$	313.956	0.232986
$123$	−84.6281	−0.0620379
$124$	−905.025	−0.655433
$125$	125.000	0.0894427
$126$	−303.314	−0.214455
$127$	2179.16	1.52259	0.761296	−	0.648405i	$-0.224564\pi$
$127$	2179.16	1.52259	0.761296	+	0.648405i	$0.224564\pi$
$128$	−1044.05	−0.720955
$129$	−797.653	−0.544414
$130$	375.680	0.253456
$131$	1951.11	1.30129	0.650645	−	0.759382i	$-0.274499\pi$
$131$	1951.11	1.30129	0.650645	+	0.759382i	$0.274499\pi$
$132$	0	0
$133$	79.0828	0.0515590
$134$	328.572	0.211823
$135$	135.000	0.0860663
$136$	525.836	0.331545
$137$	−613.425	−0.382543	−0.191272	−	0.981537i	$-0.561261\pi$
$137$	−613.425	−0.382543	−0.191272	+	0.981537i	$0.561261\pi$
$138$	1418.61	0.875071
$139$	2130.63	1.30013	0.650064	−	0.759880i	$-0.274742\pi$
$139$	2130.63	1.30013	0.650064	+	0.759880i	$0.274742\pi$
$140$	259.555	0.156688
$141$	−1546.80	−0.923861
$142$	1986.61	1.17403
$143$	0	0
$144$	−693.942	−0.401587
$145$	429.555	0.246018
$146$	1193.57	0.676578
$147$	−780.314	−0.437818
$148$	789.230	0.438340
$149$	570.900	0.313892	0.156946	−	0.987607i	$-0.449835\pi$
$149$	570.900	0.313892	0.156946	+	0.987607i	$0.449835\pi$
$150$	−277.617	−0.151116
$151$	−2154.78	−1.16128	−0.580641	−	0.814159i	$-0.697198\pi$
$151$	−2154.78	−1.16128	−0.580641	+	0.814159i	$0.697198\pi$
$152$	73.8983	0.0394339
$153$	556.256	0.293926
$154$	0	0
$155$	−793.664	−0.411281
$156$	−347.198	−0.178193
$157$	−157.105	−0.0798619	−0.0399310	−	0.999202i	$-0.512714\pi$
$157$	−157.105	−0.0798619	−0.0399310	+	0.999202i	$0.512714\pi$
$158$	983.106	0.495011
$159$	−1400.10	−0.698337
$160$	1086.73	0.536958
$161$	−1163.11	−0.569353
$162$	−299.827	−0.145411
$163$	1736.66	0.834512	0.417256	−	0.908789i	$-0.362992\pi$
$163$	1736.66	0.834512	0.417256	+	0.908789i	$0.362992\pi$
$164$	−160.837	−0.0765811
$165$	0	0
$166$	−1927.62	−0.901278
$167$	1466.55	0.679549	0.339775	−	0.940507i	$-0.389649\pi$
$167$	1466.55	0.679549	0.339775	+	0.940507i	$0.389649\pi$
$168$	232.383	0.106719
$169$	−1784.97	−0.812459
$170$	−1143.90	−0.516076
$171$	78.1735	0.0349595
$172$	−1515.96	−0.672038
$173$	143.781	0.0631878	0.0315939	−	0.999501i	$-0.489942\pi$
$173$	143.781	0.0631878	0.0315939	+	0.999501i	$0.489942\pi$
$174$	−954.014	−0.415653
$175$	227.617	0.0983214
$176$	0	0
$177$	1120.42	0.475798
$178$	1720.16	0.724335
$179$	−1412.93	−0.589984	−0.294992	−	0.955500i	$-0.595317\pi$
$179$	−1412.93	−0.589984	−0.294992	+	0.955500i	$0.595317\pi$
$180$	256.570	0.106242
$181$	−2239.25	−0.919570	−0.459785	−	0.888030i	$-0.652073\pi$
$181$	−2239.25	−0.919570	−0.459785	+	0.888030i	$0.652073\pi$
$182$	684.089	0.278616
$183$	−254.452	−0.102785
$184$	−1086.86	−0.435458
$185$	692.117	0.275057
$186$	1762.68	0.694870
$187$	0	0
$188$	−2939.73	−1.14044
$189$	245.827	0.0946098
$190$	−160.758	−0.0613821
$191$	1745.94	0.661425	0.330712	−	0.943732i	$-0.392711\pi$
$191$	1745.94	0.661425	0.330712	+	0.943732i	$0.392711\pi$
$192$	−563.039	−0.211635
$193$	3985.04	1.48627	0.743134	−	0.669143i	$-0.233338\pi$
$193$	3985.04	1.48627	0.743134	+	0.669143i	$0.233338\pi$
$194$	756.900	0.280115
$195$	−304.477	−0.111815
$196$	−1483.00	−0.540453
$197$	−2262.00	−0.818076	−0.409038	−	0.912517i	$-0.634136\pi$
$197$	−2262.00	−0.818076	−0.409038	+	0.912517i	$0.634136\pi$
$198$	0	0
$199$	2340.15	0.833613	0.416806	−	0.908995i	$-0.363149\pi$
$199$	2340.15	0.833613	0.416806	+	0.908995i	$0.363149\pi$
$200$	212.695	0.0751991
$201$	−266.297	−0.0934485
$202$	100.873	0.0351358
$203$	782.192	0.270439
$204$	1057.18	0.362829
$205$	−141.047	−0.0480543
$206$	−3934.01	−1.33056
$207$	−1149.74	−0.386049
$208$	1565.10	0.521733
$209$	0	0
$210$	−505.523	−0.166116
$211$	−1524.44	−0.497377	−0.248689	−	0.968583i	$-0.580000\pi$
$211$	−1524.44	−0.497377	−0.248689	+	0.968583i	$0.580000\pi$
$212$	−2660.93	−0.862044
$213$	−1610.09	−0.517940
$214$	6303.62	2.01358
$215$	−1329.42	−0.421701
$216$	229.711	0.0723604
$217$	−1445.21	−0.452108
$218$	2059.31	0.639788
$219$	−967.350	−0.298482
$220$	0	0
$221$	−1254.57	−0.381862
$222$	−1537.15	−0.464715
$223$	5083.42	1.52651	0.763253	−	0.646100i	$-0.223601\pi$
$223$	5083.42	1.52651	0.763253	+	0.646100i	$0.223601\pi$
$224$	1978.86	0.590260
$225$	225.000	0.0666667
$226$	7730.01	2.27519
$227$	−3910.66	−1.14343	−0.571717	−	0.820451i	$-0.693723\pi$
$227$	−3910.66	−1.14343	−0.571717	+	0.820451i	$0.693723\pi$
$228$	148.570	0.0431549
$229$	2733.31	0.788743	0.394371	−	0.918951i	$-0.370962\pi$
$229$	2733.31	0.788743	0.394371	+	0.918951i	$0.370962\pi$
$230$	2364.34	0.677827
$231$	0	0
$232$	730.914	0.206840
$233$	−4355.46	−1.22462	−0.612308	−	0.790619i	$-0.709759\pi$
$233$	−4355.46	−1.22462	−0.612308	+	0.790619i	$0.709759\pi$
$234$	676.223	0.188915
$235$	−2578.01	−0.715620
$236$	2129.39	0.587337
$237$	−796.777	−0.218381
$238$	−2082.97	−0.567305
$239$	−4731.48	−1.28056	−0.640281	−	0.768141i	$-0.721182\pi$
$239$	−4731.48	−1.28056	−0.640281	+	0.768141i	$0.721182\pi$
$240$	−1156.57	−0.311068
$241$	1833.12	0.489966	0.244983	−	0.969527i	$-0.421218\pi$
$241$	1833.12	0.489966	0.244983	+	0.969527i	$0.421218\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−483.591	−0.126880
$245$	−1300.52	−0.339132
$246$	313.256	0.0811890
$247$	−176.311	−0.0454186
$248$	−1350.47	−0.345786
$249$	1562.27	0.397611
$250$	−462.695	−0.117054
$251$	−3168.31	−0.796741	−0.398370	−	0.917225i	$-0.630424\pi$
$251$	−3168.31	−0.796741	−0.398370	+	0.917225i	$0.630424\pi$
$252$	467.198	0.116789
$253$	0	0
$254$	−8066.29	−1.99262
$255$	927.094	0.227674
$256$	5366.07	1.31008
$257$	5378.55	1.30547	0.652733	−	0.757588i	$-0.273622\pi$
$257$	5378.55	1.30547	0.652733	+	0.757588i	$0.273622\pi$
$258$	2952.56	0.712475
$259$	1260.30	0.302360
$260$	−578.664	−0.138028
$261$	773.198	0.183371
$262$	−7222.14	−1.70300
$263$	4584.03	1.07477	0.537383	−	0.843338i	$-0.319413\pi$
$263$	4584.03	1.07477	0.537383	+	0.843338i	$0.319413\pi$
$264$	0	0
$265$	−2333.51	−0.540929
$266$	−292.730	−0.0674752
$267$	−1394.14	−0.319550
$268$	−506.103	−0.115355
$269$	−1741.03	−0.394618	−0.197309	−	0.980341i	$-0.563220\pi$
$269$	−1741.03	−0.394618	−0.197309	+	0.980341i	$0.563220\pi$
$270$	−499.711	−0.112635
$271$	1340.58	0.300495	0.150248	−	0.988648i	$-0.451993\pi$
$271$	1340.58	0.300495	0.150248	+	0.988648i	$0.451993\pi$
$272$	−4765.55	−1.06233
$273$	−554.433	−0.122915
$274$	2270.63	0.500634
$275$	0	0
$276$	−2185.10	−0.476548
$277$	−5220.77	−1.13244	−0.566220	−	0.824254i	$-0.691595\pi$
$277$	−5220.77	−1.13244	−0.566220	+	0.824254i	$0.691595\pi$
$278$	−7886.66	−1.70148
$279$	−1428.60	−0.306551
$280$	387.305	0.0826639
$281$	2494.68	0.529609	0.264804	−	0.964302i	$-0.414693\pi$
$281$	2494.68	0.529609	0.264804	+	0.964302i	$0.414693\pi$
$282$	5725.59	1.20906
$283$	4329.43	0.909391	0.454696	−	0.890647i	$-0.349748\pi$
$283$	4329.43	0.909391	0.454696	+	0.890647i	$0.349748\pi$
$284$	−3060.00	−0.639358
$285$	130.289	0.0270795
$286$	0	0
$287$	−256.837	−0.0528245
$288$	1956.11	0.400225
$289$	−1092.99	−0.222468
$290$	−1590.02	−0.321963
$291$	−613.444	−0.123576
$292$	−1838.47	−0.368453
$293$	−4330.93	−0.863534	−0.431767	−	0.901985i	$-0.642110\pi$
$293$	−4330.93	−0.863534	−0.431767	+	0.901985i	$0.642110\pi$
$294$	2888.38	0.572972
$295$	1867.37	0.368552
$296$	1177.68	0.231254
$297$	0	0
$298$	−2113.22	−0.410791
$299$	2593.09	0.501547
$300$	427.617	0.0822950
$301$	−2420.79	−0.463562
$302$	7976.06	1.51977
$303$	−81.7547	−0.0155006
$304$	−669.727	−0.126353
$305$	−424.086	−0.0796167
$306$	−2059.02	−0.384661
$307$	−2052.56	−0.381582	−0.190791	−	0.981631i	$-0.561105\pi$
$307$	−2052.56	−0.381582	−0.190791	+	0.981631i	$0.561105\pi$
$308$	0	0
$309$	3188.39	0.586995
$310$	2937.80	0.538244
$311$	2627.76	0.479121	0.239561	−	0.970881i	$-0.422997\pi$
$311$	2627.76	0.479121	0.239561	+	0.970881i	$0.422997\pi$
$312$	−518.086	−0.0940091
$313$	6878.40	1.24214	0.621070	−	0.783755i	$-0.286698\pi$
$313$	6878.40	1.24214	0.621070	+	0.783755i	$0.286698\pi$
$314$	581.533	0.104515
$315$	409.711	0.0732844
$316$	−1514.29	−0.269574
$317$	−3026.05	−0.536151	−0.268076	−	0.963398i	$-0.586388\pi$
$317$	−3026.05	−0.536151	−0.268076	+	0.963398i	$0.586388\pi$
$318$	5182.57	0.913913
$319$	0	0
$320$	−938.398	−0.163931
$321$	−5108.88	−0.888318
$322$	4305.32	0.745112
$323$	536.845	0.0924795
$324$	461.827	0.0791884
$325$	−507.461	−0.0866119
$326$	−6428.34	−1.09213
$327$	−1669.00	−0.282251
$328$	−240.000	−0.0404018
$329$	−4694.39	−0.786657
$330$	0	0
$331$	−4326.50	−0.718447	−0.359223	−	0.933252i	$-0.616958\pi$
$331$	−4326.50	−0.718447	−0.359223	+	0.933252i	$0.616958\pi$
$332$	2969.13	0.490820
$333$	1245.81	0.205015
$334$	−5428.51	−0.889326
$335$	−443.828	−0.0723849
$336$	−2106.04	−0.341946
$337$	−1759.36	−0.284387	−0.142194	−	0.989839i	$-0.545416\pi$
$337$	−1759.36	−0.284387	−0.142194	+	0.989839i	$0.545416\pi$
$338$	6607.19	1.06327
$339$	−6264.93	−1.00373
$340$	1761.96	0.281046
$341$	0	0
$342$	−289.364	−0.0457515
$343$	−5491.08	−0.864403
$344$	−2262.09	−0.354546
$345$	−1916.23	−0.299032
$346$	−532.215	−0.0826939
$347$	−11730.7	−1.81481	−0.907404	−	0.420260i	$-0.861939\pi$
$347$	−11730.7	−1.81481	−0.907404	+	0.420260i	$0.861939\pi$
$348$	1469.48	0.226357
$349$	−3152.38	−0.483504	−0.241752	−	0.970338i	$-0.577722\pi$
$349$	−3152.38	−0.483504	−0.241752	+	0.970338i	$0.577722\pi$
$350$	−842.539	−0.128673
$351$	−548.058	−0.0833423
$352$	0	0
$353$	−6881.03	−1.03751	−0.518754	−	0.854923i	$-0.673604\pi$
$353$	−6881.03	−1.03751	−0.518754	+	0.854923i	$0.673604\pi$
$354$	−4147.32	−0.622677
$355$	−2683.48	−0.401195
$356$	−2649.59	−0.394460
$357$	1688.18	0.250274
$358$	5230.04	0.772112
$359$	−2858.96	−0.420307	−0.210154	−	0.977668i	$-0.567396\pi$
$359$	−2858.96	−0.420307	−0.210154	+	0.977668i	$0.567396\pi$
$360$	382.851	0.0560501
$361$	−6783.55	−0.989001
$362$	8288.72	1.20344
$363$	0	0
$364$	−1053.71	−0.151729
$365$	−1612.25	−0.231203
$366$	941.868	0.134514
$367$	−10973.4	−1.56079	−0.780393	−	0.625289i	$-0.784981\pi$
$367$	−10973.4	−1.56079	−0.780393	+	0.625289i	$0.784981\pi$
$368$	9850.00	1.39529
$369$	−253.884	−0.0358176
$370$	−2561.91	−0.359966
$371$	−4249.17	−0.594625
$372$	−2715.07	−0.378414
$373$	10443.4	1.44970	0.724852	−	0.688905i	$-0.241908\pi$
$373$	10443.4	1.44970	0.724852	+	0.688905i	$0.241908\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	−4386.64	−0.601659
$377$	−1743.86	−0.238231
$378$	−909.942	−0.123816
$379$	−7405.86	−1.00373	−0.501865	−	0.864946i	$-0.667352\pi$
$379$	−7405.86	−1.00373	−0.501865	+	0.864946i	$0.667352\pi$
$380$	247.617	0.0334276
$381$	6537.48	0.879069
$382$	−6462.72	−0.865607
$383$	14155.0	1.88848	0.944238	−	0.329264i	$-0.106801\pi$
$383$	14155.0	1.88848	0.944238	+	0.329264i	$0.106801\pi$
$384$	−3132.16	−0.416244
$385$	0	0
$386$	−14750.9	−1.94508
$387$	−2392.96	−0.314318
$388$	−1165.86	−0.152546
$389$	−13031.6	−1.69853	−0.849263	−	0.527970i	$-0.822953\pi$
$389$	−13031.6	−1.69853	−0.849263	+	0.527970i	$0.822953\pi$
$390$	1127.04	0.146333
$391$	−7895.65	−1.02123
$392$	−2212.92	−0.285126
$393$	5853.32	0.751300
$394$	8372.94	1.07062
$395$	−1327.96	−0.169157
$396$	0	0
$397$	2281.02	0.288366	0.144183	−	0.989551i	$-0.453945\pi$
$397$	2281.02	0.288366	0.144183	+	0.989551i	$0.453945\pi$
$398$	−8662.22	−1.09095
$399$	237.248	0.0297676
$400$	−1927.62	−0.240952
$401$	−13017.7	−1.62114	−0.810568	−	0.585645i	$-0.800841\pi$
$401$	−13017.7	−1.62114	−0.810568	+	0.585645i	$0.800841\pi$
$402$	985.715	0.122296
$403$	3222.03	0.398265
$404$	−155.377	−0.0191343
$405$	405.000	0.0496904
$406$	−2895.33	−0.353924
$407$	0	0
$408$	1577.51	0.191417
$409$	−3548.46	−0.428998	−0.214499	−	0.976724i	$-0.568812\pi$
$409$	−3548.46	−0.428998	−0.214499	+	0.976724i	$0.568812\pi$
$410$	522.094	0.0628887
$411$	−1840.27	−0.220861
$412$	6059.61	0.724601
$413$	3400.37	0.405136
$414$	4255.82	0.505222
$415$	2603.79	0.307988
$416$	−4411.77	−0.519964
$417$	6391.89	0.750629
$418$	0	0
$419$	−14801.3	−1.72575	−0.862876	−	0.505416i	$-0.831339\pi$
$419$	−14801.3	−1.72575	−0.862876	+	0.505416i	$0.831339\pi$
$420$	778.664	0.0904641
$421$	11542.8	1.33625	0.668123	−	0.744051i	$-0.267098\pi$
$421$	11542.8	1.33625	0.668123	+	0.744051i	$0.267098\pi$
$422$	5642.80	0.650918
$423$	−4640.41	−0.533392
$424$	−3970.61	−0.454787
$425$	1545.16	0.176355
$426$	5959.83	0.677828
$427$	−772.234	−0.0875200
$428$	−9709.54	−1.09656
$429$	0	0
$430$	4920.94	0.551881
$431$	−12712.6	−1.42076	−0.710378	−	0.703820i	$-0.751476\pi$
$431$	−12712.6	−1.42076	−0.710378	+	0.703820i	$0.751476\pi$
$432$	−2081.83	−0.231856
$433$	−16385.4	−1.81855	−0.909273	−	0.416200i	$-0.863361\pi$
$433$	−16385.4	−1.81855	−0.909273	+	0.416200i	$0.863361\pi$
$434$	5349.54	0.591674
$435$	1288.66	0.142038
$436$	−3171.97	−0.348418
$437$	−1109.62	−0.121465
$438$	3580.71	0.390623
$439$	−6603.62	−0.717935	−0.358968	−	0.933350i	$-0.616871\pi$
$439$	−6603.62	−0.717935	−0.358968	+	0.933350i	$0.616871\pi$
$440$	0	0
$441$	−2340.94	−0.252774
$442$	4643.87	0.499743
$443$	−11641.0	−1.24849	−0.624244	−	0.781230i	$-0.714593\pi$
$443$	−11641.0	−1.24849	−0.624244	+	0.781230i	$0.714593\pi$
$444$	2367.69	0.253076
$445$	−2323.56	−0.247522
$446$	−18816.6	−1.99774
$447$	1712.70	0.181226
$448$	−1708.76	−0.180204
$449$	13886.8	1.45960	0.729799	−	0.683662i	$-0.239614\pi$
$449$	13886.8	1.45960	0.729799	+	0.683662i	$0.239614\pi$
$450$	−832.851	−0.0872467
$451$	0	0
$452$	−11906.6	−1.23903
$453$	−6464.35	−0.670467
$454$	14475.6	1.49641
$455$	−924.055	−0.0952096
$456$	221.695	0.0227672
$457$	−3625.85	−0.371138	−0.185569	−	0.982631i	$-0.559413\pi$
$457$	−3625.85	−0.371138	−0.185569	+	0.982631i	$0.559413\pi$
$458$	−10117.5	−1.03223
$459$	1668.77	0.169698
$460$	−3641.83	−0.369133
$461$	−18329.1	−1.85178	−0.925890	−	0.377794i	$-0.876683\pi$
$461$	−18329.1	−1.85178	−0.925890	+	0.377794i	$0.876683\pi$
$462$	0	0
$463$	10760.7	1.08011	0.540056	−	0.841629i	$-0.318403\pi$
$463$	10760.7	1.08011	0.540056	+	0.841629i	$0.318403\pi$
$464$	−6624.14	−0.662754
$465$	−2380.99	−0.237453
$466$	16122.0	1.60265
$467$	−7964.29	−0.789172	−0.394586	−	0.918859i	$-0.629112\pi$
$467$	−7964.29	−0.789172	−0.394586	+	0.918859i	$0.629112\pi$
$468$	−1041.60	−0.102880
$469$	−808.184	−0.0795703
$470$	9542.66	0.936532
$471$	−471.314	−0.0461083
$472$	3177.45	0.309861
$473$	0	0
$474$	2949.32	0.285795
$475$	217.149	0.0209757
$476$	3208.42	0.308945
$477$	−4200.31	−0.403185
$478$	17513.9	1.67587
$479$	−822.463	−0.0784536	−0.0392268	−	0.999230i	$-0.512489\pi$
$479$	−822.463	−0.0784536	−0.0392268	+	0.999230i	$0.512489\pi$
$480$	3260.18	0.310013
$481$	−2809.78	−0.266351
$482$	−6785.41	−0.641218
$483$	−3489.33	−0.328716
$484$	0	0
$485$	−1022.41	−0.0957218
$486$	−899.480	−0.0839531
$487$	6709.58	0.624312	0.312156	−	0.950031i	$-0.398949\pi$
$487$	6709.58	0.624312	0.312156	+	0.950031i	$0.398949\pi$
$488$	−721.609	−0.0669379
$489$	5209.97	0.481806
$490$	4813.97	0.443822
$491$	−12689.3	−1.16631	−0.583156	−	0.812360i	$-0.698182\pi$
$491$	−12689.3	−1.16631	−0.583156	+	0.812360i	$0.698182\pi$
$492$	−482.512	−0.0442141
$493$	5309.83	0.485077
$494$	652.626	0.0594394
$495$	0	0
$496$	12239.0	1.10796
$497$	−4886.44	−0.441020
$498$	−5782.85	−0.520353
$499$	−9810.79	−0.880143	−0.440072	−	0.897963i	$-0.645047\pi$
$499$	−9810.79	−0.880143	−0.440072	+	0.897963i	$0.645047\pi$
$500$	712.695	0.0637454
$501$	4399.64	0.392338
$502$	11727.7	1.04269
$503$	12865.7	1.14047	0.570233	−	0.821483i	$-0.306853\pi$
$503$	12865.7	1.14047	0.570233	+	0.821483i	$0.306853\pi$
$504$	697.149	0.0616140
$505$	−136.258	−0.0120067
$506$	0	0
$507$	−5354.92	−0.469074
$508$	12424.6	1.08514
$509$	2551.78	0.222211	0.111106	−	0.993809i	$-0.464561\pi$
$509$	2551.78	0.222211	0.111106	+	0.993809i	$0.464561\pi$
$510$	−3431.70	−0.297957
$511$	−2935.81	−0.254153
$512$	−11510.4	−0.993541
$513$	234.520	0.0201839
$514$	−19909.0	−1.70846
$515$	5313.99	0.454684
$516$	−4547.87	−0.388001
$517$	0	0
$518$	−4665.09	−0.395699
$519$	431.344	0.0364815
$520$	−863.476	−0.0728191
$521$	9761.13	0.820812	0.410406	−	0.911903i	$-0.365387\pi$
$521$	9761.13	0.820812	0.410406	+	0.911903i	$0.365387\pi$
$522$	−2862.04	−0.239977
$523$	−4548.79	−0.380315	−0.190157	−	0.981754i	$-0.560900\pi$
$523$	−4548.79	−0.380315	−0.190157	+	0.981754i	$0.560900\pi$
$524$	11124.4	0.927423
$525$	682.851	0.0567659
$526$	−16968.1	−1.40655
$527$	−9810.68	−0.810930
$528$	0	0
$529$	4152.66	0.341305
$530$	8637.62	0.707914
$531$	3361.27	0.274702
$532$	450.895	0.0367458
$533$	572.606	0.0465334
$534$	5160.49	0.418195
$535$	−8514.80	−0.688088
$536$	−755.202	−0.0608577
$537$	−4238.78	−0.340628
$538$	6444.52	0.516437
$539$	0	0
$540$	769.711	0.0613390
$541$	9184.79	0.729917	0.364958	−	0.931024i	$-0.381083\pi$
$541$	9184.79	0.729917	0.364958	+	0.931024i	$0.381083\pi$
$542$	−4962.23	−0.393258
$543$	−6717.75	−0.530914
$544$	13433.3	1.05873
$545$	−2781.67	−0.218631
$546$	2052.27	0.160859
$547$	−20966.6	−1.63888	−0.819439	−	0.573167i	$-0.805715\pi$
$547$	−20966.6	−1.63888	−0.819439	+	0.573167i	$0.805715\pi$
$548$	−3497.48	−0.272637
$549$	−763.355	−0.0593428
$550$	0	0
$551$	746.217	0.0576950
$552$	−3260.58	−0.251412
$553$	−2418.13	−0.185948
$554$	19325.0	1.48202
$555$	2076.35	0.158804
$556$	12147.9	0.926595
$557$	4422.49	0.336422	0.168211	−	0.985751i	$-0.446201\pi$
$557$	4422.49	0.336422	0.168211	+	0.985751i	$0.446201\pi$
$558$	5288.03	0.401183
$559$	5397.04	0.408355
$560$	−3510.07	−0.264871
$561$	0	0
$562$	−9234.21	−0.693099
$563$	6066.46	0.454122	0.227061	−	0.973881i	$-0.427088\pi$
$563$	6066.46	0.454122	0.227061	+	0.973881i	$0.427088\pi$
$564$	−8819.20	−0.658432
$565$	−10441.6	−0.777486
$566$	−16025.6	−1.19012
$567$	737.480	0.0546230
$568$	−4566.10	−0.337305
$569$	−17341.9	−1.27770	−0.638850	−	0.769331i	$-0.720590\pi$
$569$	−17341.9	−1.27770	−0.638850	+	0.769331i	$0.720590\pi$
$570$	−482.273	−0.0354390
$571$	−621.014	−0.0455142	−0.0227571	−	0.999741i	$-0.507244\pi$
$571$	−621.014	−0.0455142	−0.0227571	+	0.999741i	$0.507244\pi$
$572$	0	0
$573$	5237.83	0.381874
$574$	950.700	0.0691314
$575$	−3193.71	−0.231629
$576$	−1689.12	−0.122187
$577$	4458.77	0.321700	0.160850	−	0.986979i	$-0.448576\pi$
$577$	4458.77	0.321700	0.160850	+	0.986979i	$0.448576\pi$
$578$	4045.76	0.291144
$579$	11955.1	0.858097
$580$	2449.13	0.175336
$581$	4741.34	0.338561
$582$	2270.70	0.161724
$583$	0	0
$584$	−2743.34	−0.194384
$585$	−913.430	−0.0645567
$586$	16031.2	1.13011
$587$	1326.96	0.0933038	0.0466519	−	0.998911i	$-0.485145\pi$
$587$	1326.96	0.0933038	0.0466519	+	0.998911i	$0.485145\pi$
$588$	−4449.01	−0.312031
$589$	−1378.74	−0.0964519
$590$	−6912.20	−0.482324
$591$	−6786.01	−0.472317
$592$	−10673.1	−0.740982
$593$	13296.2	0.920756	0.460378	−	0.887723i	$-0.347714\pi$
$593$	13296.2	0.920756	0.460378	+	0.887723i	$0.347714\pi$
$594$	0	0
$595$	2813.63	0.193862
$596$	3255.02	0.223710
$597$	7020.45	0.481287
$598$	−9598.50	−0.656374
$599$	−7420.72	−0.506181	−0.253091	−	0.967443i	$-0.581447\pi$
$599$	−7420.72	−0.506181	−0.253091	+	0.967443i	$0.581447\pi$
$600$	638.086	0.0434162
$601$	−5189.31	−0.352207	−0.176104	−	0.984372i	$-0.556349\pi$
$601$	−5189.31	−0.352207	−0.176104	+	0.984372i	$0.556349\pi$
$602$	8960.72	0.606664
$603$	−798.891	−0.0539525
$604$	−12285.6	−0.827641
$605$	0	0
$606$	302.620	0.0202857
$607$	26545.6	1.77505	0.887523	−	0.460763i	$-0.152424\pi$
$607$	26545.6	1.77505	0.887523	+	0.460763i	$0.152424\pi$
$608$	1887.85	0.125925
$609$	2346.58	0.156138
$610$	1569.78	0.104194
$611$	10465.9	0.692971
$612$	3171.53	0.209480
$613$	26097.9	1.71955	0.859776	−	0.510671i	$-0.170603\pi$
$613$	26097.9	1.71955	0.859776	+	0.510671i	$0.170603\pi$
$614$	7597.67	0.499377
$615$	−423.141	−0.0277442
$616$	0	0
$617$	12275.1	0.800933	0.400466	−	0.916311i	$-0.368848\pi$
$617$	12275.1	0.800933	0.400466	+	0.916311i	$0.368848\pi$
$618$	−11802.0	−0.768200
$619$	6067.21	0.393961	0.196980	−	0.980407i	$-0.436886\pi$
$619$	6067.21	0.393961	0.196980	+	0.980407i	$0.436886\pi$
$620$	−4525.12	−0.293118
$621$	−3449.21	−0.222886
$622$	−9726.82	−0.627026
$623$	−4231.06	−0.272093
$624$	4695.31	0.301223
$625$	625.000	0.0400000
$626$	−25460.8	−1.62559
$627$	0	0
$628$	−895.742	−0.0569172
$629$	8555.43	0.542333
$630$	−1516.57	−0.0959073
$631$	3074.16	0.193947	0.0969733	−	0.995287i	$-0.469084\pi$
$631$	3074.16	0.193947	0.0969733	+	0.995287i	$0.469084\pi$
$632$	−2259.61	−0.142219
$633$	−4573.31	−0.287161
$634$	11201.1	0.701661
$635$	10895.8	0.680924
$636$	−7982.78	−0.497701
$637$	5279.72	0.328399
$638$	0	0
$639$	−4830.26	−0.299033
$640$	−5220.27	−0.322421
$641$	−10825.9	−0.667080	−0.333540	−	0.942736i	$-0.608243\pi$
$641$	−10825.9	−0.667080	−0.333540	+	0.942736i	$0.608243\pi$
$642$	18910.8	1.16254
$643$	−117.142	−0.00718450	−0.00359225	−	0.999994i	$-0.501143\pi$
$643$	−117.142	−0.00718450	−0.00359225	+	0.999994i	$0.501143\pi$
$644$	−6631.54	−0.405775
$645$	−3988.27	−0.243469
$646$	−1987.17	−0.121028
$647$	23811.6	1.44688	0.723439	−	0.690388i	$-0.242560\pi$
$647$	23811.6	1.44688	0.723439	+	0.690388i	$0.242560\pi$
$648$	689.133	0.0417773
$649$	0	0
$650$	1878.40	0.113349
$651$	−4335.64	−0.261025
$652$	9901.65	0.594753
$653$	−17773.3	−1.06512	−0.532560	−	0.846392i	$-0.678770\pi$
$653$	−17773.3	−1.06512	−0.532560	+	0.846392i	$0.678770\pi$
$654$	6177.92	0.369382
$655$	9755.53	0.581954
$656$	2175.07	0.129455
$657$	−2902.05	−0.172328
$658$	17376.6	1.02950
$659$	13015.6	0.769370	0.384685	−	0.923048i	$-0.374310\pi$
$659$	13015.6	0.769370	0.384685	+	0.923048i	$0.374310\pi$
$660$	0	0
$661$	15769.6	0.927935	0.463968	−	0.885852i	$-0.346425\pi$
$661$	15769.6	0.927935	0.463968	+	0.885852i	$0.346425\pi$
$662$	16014.8	0.940231
$663$	−3763.71	−0.220468
$664$	4430.51	0.258941
$665$	395.414	0.0230579
$666$	−4611.45	−0.268303
$667$	−10975.0	−0.637111
$668$	8361.60	0.484311
$669$	15250.3	0.881329
$670$	1642.86	0.0947301
$671$	0	0
$672$	5936.58	0.340787
$673$	31519.1	1.80531	0.902653	−	0.430370i	$-0.141617\pi$
$673$	31519.1	1.80531	0.902653	+	0.430370i	$0.141617\pi$
$674$	6512.38	0.372177
$675$	675.000	0.0384900
$676$	−10177.1	−0.579036
$677$	−12418.6	−0.705000	−0.352500	−	0.935812i	$-0.614668\pi$
$677$	−12418.6	−0.705000	−0.352500	+	0.935812i	$0.614668\pi$
$678$	23190.0	1.31358
$679$	−1861.74	−0.105224
$680$	2629.18	0.148271
$681$	−11732.0	−0.660162
$682$	0	0
$683$	23543.0	1.31896	0.659478	−	0.751724i	$-0.270777\pi$
$683$	23543.0	1.31896	0.659478	+	0.751724i	$0.270777\pi$
$684$	445.711	0.0249155
$685$	−3067.12	−0.171079
$686$	20325.6	1.13124
$687$	8199.92	0.455381
$688$	20500.9	1.13603
$689$	9473.31	0.523809
$690$	7093.03	0.391344
$691$	−9642.84	−0.530870	−0.265435	−	0.964129i	$-0.585516\pi$
$691$	−9642.84	−0.530870	−0.265435	+	0.964129i	$0.585516\pi$
$692$	819.778	0.0450336
$693$	0	0
$694$	43422.0	2.37504
$695$	10653.2	0.581435
$696$	2192.74	0.119419
$697$	−1743.52	−0.0947494
$698$	11668.7	0.632762
$699$	−13066.4	−0.707032
$700$	1297.77	0.0700732
$701$	−30593.3	−1.64835	−0.824176	−	0.566334i	$-0.808361\pi$
$701$	−30593.3	−1.64835	−0.824176	+	0.566334i	$0.808361\pi$
$702$	2028.67	0.109070
$703$	1202.34	0.0645050
$704$	0	0
$705$	−7734.02	−0.413163
$706$	25470.6	1.35779
$707$	−248.117	−0.0131986
$708$	6388.17	0.339099
$709$	−30248.4	−1.60226	−0.801130	−	0.598491i	$-0.795767\pi$
$709$	−30248.4	−1.60226	−0.801130	+	0.598491i	$0.795767\pi$
$710$	9933.05	0.525044
$711$	−2390.33	−0.126082
$712$	−3953.69	−0.208105
$713$	20277.9	1.06509
$714$	−6248.90	−0.327534
$715$	0	0
$716$	−8055.90	−0.420479
$717$	−14194.4	−0.739332
$718$	10582.6	0.550056
$719$	30471.8	1.58054	0.790269	−	0.612761i	$-0.209941\pi$
$719$	30471.8	1.58054	0.790269	+	0.612761i	$0.209941\pi$
$720$	−3469.71	−0.179595
$721$	9676.45	0.499819
$722$	25109.7	1.29430
$723$	5499.37	0.282882
$724$	−12767.2	−0.655373
$725$	2147.77	0.110022
$726$	0	0
$727$	25149.9	1.28302	0.641511	−	0.767114i	$-0.278308\pi$
$727$	25149.9	1.28302	0.641511	+	0.767114i	$0.278308\pi$
$728$	−1572.34	−0.0800476
$729$	729.000	0.0370370
$730$	5967.84	0.302575
$731$	−16433.3	−0.831475
$732$	−1450.77	−0.0732542
$733$	9974.73	0.502626	0.251313	−	0.967906i	$-0.419138\pi$
$733$	9974.73	0.502626	0.251313	+	0.967906i	$0.419138\pi$
$734$	40618.8	2.04260
$735$	−3901.57	−0.195798
$736$	−27765.5	−1.39056
$737$	0	0
$738$	939.769	0.0468745
$739$	11579.9	0.576418	0.288209	−	0.957568i	$-0.406940\pi$
$739$	11579.9	0.576418	0.288209	+	0.957568i	$0.406940\pi$
$740$	3946.15	0.196031
$741$	−528.933	−0.0262225
$742$	15728.6	0.778186
$743$	20323.7	1.00351	0.501753	−	0.865011i	$-0.332689\pi$
$743$	20323.7	1.00351	0.501753	+	0.865011i	$0.332689\pi$
$744$	−4051.41	−0.199639
$745$	2854.50	0.140377
$746$	−38656.9	−1.89723
$747$	4686.82	0.229561
$748$	0	0
$749$	−15504.9	−0.756392
$750$	−1388.09	−0.0675810
$751$	8023.94	0.389877	0.194939	−	0.980815i	$-0.437549\pi$
$751$	8023.94	0.389877	0.194939	+	0.980815i	$0.437549\pi$
$752$	39755.3	1.92783
$753$	−9504.93	−0.459998
$754$	6455.00	0.311773
$755$	−10773.9	−0.519342
$756$	1401.60	0.0674279
$757$	542.713	0.0260571	0.0130285	−	0.999915i	$-0.495853\pi$
$757$	542.713	0.0260571	0.0130285	+	0.999915i	$0.495853\pi$
$758$	27413.2	1.31358
$759$	0	0
$760$	369.492	0.0176354
$761$	−16292.2	−0.776073	−0.388037	−	0.921644i	$-0.626847\pi$
$761$	−16292.2	−0.776073	−0.388037	+	0.921644i	$0.626847\pi$
$762$	−24198.9	−1.15044
$763$	−5065.25	−0.240333
$764$	9954.61	0.471394
$765$	2781.28	0.131448
$766$	−52395.6	−2.47145
$767$	−7580.96	−0.356887
$768$	16098.2	0.756373
$769$	7107.01	0.333271	0.166636	−	0.986019i	$-0.446710\pi$
$769$	7107.01	0.333271	0.166636	+	0.986019i	$0.446710\pi$
$770$	0	0
$771$	16135.7	0.753711
$772$	22721.0	1.05926
$773$	−19776.7	−0.920204	−0.460102	−	0.887866i	$-0.652187\pi$
$773$	−19776.7	−0.920204	−0.460102	+	0.887866i	$0.652187\pi$
$774$	8857.69	0.411348
$775$	−3968.32	−0.183931
$776$	−1739.69	−0.0804783
$777$	3780.91	0.174568
$778$	48237.1	2.22286
$779$	−245.025	−0.0112695
$780$	−1735.99	−0.0796904
$781$	0	0
$782$	29226.2	1.33648
$783$	2319.60	0.105869
$784$	20055.3	0.913597
$785$	−785.523	−0.0357153
$786$	−21666.4	−0.983226
$787$	−19943.8	−0.903327	−0.451664	−	0.892188i	$-0.649169\pi$
$787$	−19943.8	−0.903327	−0.451664	+	0.892188i	$0.649169\pi$
$788$	−12896.9	−0.583039
$789$	13752.1	0.620517
$790$	4915.53	0.221376
$791$	−19013.4	−0.854664
$792$	0	0
$793$	1721.66	0.0770969
$794$	−8443.34	−0.377384
$795$	−7000.52	−0.312306
$796$	13342.5	0.594112
$797$	−24333.8	−1.08149	−0.540744	−	0.841187i	$-0.681857\pi$
$797$	−24333.8	−1.08149	−0.540744	+	0.841187i	$0.681857\pi$
$798$	−878.189	−0.0389568
$799$	−31867.4	−1.41100
$800$	5433.63	0.240135
$801$	−4182.41	−0.184492
$802$	48186.0	2.12158
$803$	0	0
$804$	−1518.31	−0.0666003
$805$	−5815.55	−0.254622
$806$	−11926.5	−0.521209
$807$	−5223.08	−0.227833
$808$	−231.851	−0.0100947
$809$	15308.7	0.665298	0.332649	−	0.943051i	$-0.392058\pi$
$809$	15308.7	0.665298	0.332649	+	0.943051i	$0.392058\pi$
$810$	−1499.13	−0.0650298
$811$	−22639.1	−0.980229	−0.490115	−	0.871658i	$-0.663045\pi$
$811$	−22639.1	−0.980229	−0.490115	+	0.871658i	$0.663045\pi$
$812$	4459.72	0.192741
$813$	4021.73	0.173491
$814$	0	0
$815$	8683.28	0.373205
$816$	−14296.7	−0.613337
$817$	−2309.46	−0.0988955
$818$	13134.8	0.561429
$819$	−1663.30	−0.0709650
$820$	−804.187	−0.0342481
$821$	35341.0	1.50232	0.751162	−	0.660118i	$-0.229494\pi$
$821$	35341.0	1.50232	0.751162	+	0.660118i	$0.229494\pi$
$822$	6811.89	0.289041
$823$	28121.5	1.19107	0.595536	−	0.803329i	$-0.296940\pi$
$823$	28121.5	1.19107	0.595536	+	0.803329i	$0.296940\pi$
$824$	9042.09	0.382277
$825$	0	0
$826$	−12586.7	−0.530202
$827$	5952.92	0.250306	0.125153	−	0.992137i	$-0.460058\pi$
$827$	5952.92	0.250306	0.125153	+	0.992137i	$0.460058\pi$
$828$	−6555.29	−0.275135
$829$	18696.9	0.783316	0.391658	−	0.920111i	$-0.371902\pi$
$829$	18696.9	0.783316	0.391658	+	0.920111i	$0.371902\pi$
$830$	−9638.09	−0.403064
$831$	−15662.3	−0.653814
$832$	3809.60	0.158743
$833$	−16076.1	−0.668672
$834$	−23660.0	−0.982348
$835$	7332.73	0.303904
$836$	0	0
$837$	−4285.79	−0.176987
$838$	54787.9	2.25849
$839$	−25774.1	−1.06057	−0.530287	−	0.847818i	$-0.677916\pi$
$839$	−25774.1	−1.06057	−0.530287	+	0.847818i	$0.677916\pi$
$840$	1161.91	0.0477260
$841$	−17008.3	−0.697376
$842$	−42726.2	−1.74874
$843$	7484.04	0.305770
$844$	−8691.68	−0.354478
$845$	−8924.87	−0.363343
$846$	17176.8	0.698049
$847$	0	0
$848$	35984.9	1.45722
$849$	12988.3	0.525037
$850$	−5719.49	−0.230796
$851$	−17683.4	−0.712313
$852$	−9180.00	−0.369134
$853$	18664.1	0.749174	0.374587	−	0.927192i	$-0.377785\pi$
$853$	18664.1	0.749174	0.374587	+	0.927192i	$0.377785\pi$
$854$	2858.47	0.114537
$855$	390.867	0.0156344
$856$	−14488.5	−0.578511
$857$	−37192.5	−1.48246	−0.741232	−	0.671249i	$-0.765758\pi$
$857$	−37192.5	−1.48246	−0.741232	+	0.671249i	$0.765758\pi$
$858$	0	0
$859$	46306.0	1.83928	0.919640	−	0.392763i	$-0.128481\pi$
$859$	46306.0	1.83928	0.919640	+	0.392763i	$0.128481\pi$
$860$	−7579.78	−0.300545
$861$	−770.512	−0.0304983
$862$	47056.6	1.85934
$863$	−19587.1	−0.772599	−0.386299	−	0.922373i	$-0.626247\pi$
$863$	−19587.1	−0.772599	−0.386299	+	0.922373i	$0.626247\pi$
$864$	5868.32	0.231070
$865$	718.907	0.0282584
$866$	60651.4	2.37993
$867$	−3278.96	−0.128442
$868$	−8239.97	−0.322215
$869$	0	0
$870$	−4770.07	−0.185886
$871$	1801.80	0.0700939
$872$	−4733.19	−0.183814
$873$	−1840.33	−0.0713468
$874$	4107.31	0.158961
$875$	1138.09	0.0439707
$876$	−5515.41	−0.212726
$877$	−26580.8	−1.02345	−0.511727	−	0.859148i	$-0.670994\pi$
$877$	−26580.8	−1.02345	−0.511727	+	0.859148i	$0.670994\pi$
$878$	24443.7	0.939562
$879$	−12992.8	−0.498561
$880$	0	0
$881$	−731.459	−0.0279722	−0.0139861	−	0.999902i	$-0.504452\pi$
$881$	−731.459	−0.0279722	−0.0139861	+	0.999902i	$0.504452\pi$
$882$	8665.14	0.330806
$883$	−45291.1	−1.72612	−0.863062	−	0.505099i	$-0.831456\pi$
$883$	−45291.1	−1.72612	−0.863062	+	0.505099i	$0.831456\pi$
$884$	−7153.01	−0.272151
$885$	5602.12	0.212783
$886$	43089.8	1.63390
$887$	37730.7	1.42827	0.714134	−	0.700009i	$-0.246821\pi$
$887$	37730.7	1.42827	0.714134	+	0.700009i	$0.246821\pi$
$888$	3533.04	0.133515
$889$	19840.6	0.748516
$890$	8600.81	0.323932
$891$	0	0
$892$	28983.4	1.08793
$893$	−4478.48	−0.167824
$894$	−6339.67	−0.237170
$895$	−7064.64	−0.263849
$896$	−9505.79	−0.354426
$897$	7779.28	0.289568
$898$	−51402.9	−1.91017
$899$	−13636.9	−0.505913
$900$	1282.85	0.0475130
$901$	−28845.1	−1.06656
$902$	0	0
$903$	−7262.38	−0.267638
$904$	−17767.0	−0.653673
$905$	−11196.2	−0.411244
$906$	23928.2	0.877440
$907$	25846.2	0.946208	0.473104	−	0.881007i	$-0.343134\pi$
$907$	25846.2	0.946208	0.473104	+	0.881007i	$0.343134\pi$
$908$	−22296.9	−0.814920
$909$	−245.264	−0.00894928
$910$	3420.45	0.124601
$911$	−30349.8	−1.10377	−0.551885	−	0.833920i	$-0.686091\pi$
$911$	−30349.8	−1.10377	−0.551885	+	0.833920i	$0.686091\pi$
$912$	−2009.18	−0.0729502
$913$	0	0
$914$	13421.3	0.485708
$915$	−1272.26	−0.0459667
$916$	15584.1	0.562133
$917$	17764.2	0.639723
$918$	−6177.05	−0.222084
$919$	−41031.3	−1.47279	−0.736397	−	0.676550i	$-0.763474\pi$
$919$	−41031.3	−1.47279	−0.736397	+	0.676550i	$0.763474\pi$
$920$	−5434.30	−0.194743
$921$	−6157.68	−0.220307
$922$	67846.2	2.42342
$923$	10894.1	0.388497
$924$	0	0
$925$	3460.59	0.123009
$926$	−39831.4	−1.41354
$927$	9565.18	0.338902
$928$	18672.3	0.660506
$929$	−3859.82	−0.136315	−0.0681575	−	0.997675i	$-0.521712\pi$
$929$	−3859.82	−0.136315	−0.0681575	+	0.997675i	$0.521712\pi$
$930$	8813.39	0.310755
$931$	−2259.25	−0.0795317
$932$	−24832.9	−0.872778
$933$	7883.29	0.276621
$934$	29480.3	1.03279
$935$	0	0
$936$	−1554.26	−0.0542762
$937$	−22026.5	−0.767955	−0.383977	−	0.923343i	$-0.625446\pi$
$937$	−22026.5	−0.767955	−0.383977	+	0.923343i	$0.625446\pi$
$938$	2991.54	0.104134
$939$	20635.2	0.717150
$940$	−14698.7	−0.510019
$941$	24778.0	0.858386	0.429193	−	0.903213i	$-0.358798\pi$
$941$	24778.0	0.858386	0.429193	+	0.903213i	$0.358798\pi$
$942$	1744.60	0.0603419
$943$	3603.70	0.124446
$944$	−28796.7	−0.992851
$945$	1229.13	0.0423108
$946$	0	0
$947$	34055.7	1.16860	0.584299	−	0.811539i	$-0.301370\pi$
$947$	34055.7	1.16860	0.584299	+	0.811539i	$0.301370\pi$
$948$	−4542.87	−0.155639
$949$	6545.23	0.223885
$950$	−803.789	−0.0274509
$951$	−9078.15	−0.309547
$952$	4787.57	0.162990
$953$	30211.9	1.02693	0.513463	−	0.858112i	$-0.328363\pi$
$953$	30211.9	1.02693	0.513463	+	0.858112i	$0.328363\pi$
$954$	15547.7	0.527648
$955$	8729.72	0.295798
$956$	−26976.8	−0.912650
$957$	0	0
$958$	3044.40	0.102672
$959$	−5585.04	−0.188061
$960$	−2815.19	−0.0946459
$961$	−4594.90	−0.154238
$962$	10400.6	0.348574
$963$	−15326.6	−0.512871
$964$	10451.7	0.349196
$965$	19925.2	0.664679
$966$	12916.0	0.430191
$967$	−34883.2	−1.16005	−0.580024	−	0.814599i	$-0.696957\pi$
$967$	−34883.2	−1.16005	−0.580024	+	0.814599i	$0.696957\pi$
$968$	0	0
$969$	1610.54	0.0533931
$970$	3784.50	0.125271
$971$	19753.0	0.652835	0.326418	−	0.945226i	$-0.394158\pi$
$971$	19753.0	0.652835	0.326418	+	0.945226i	$0.394158\pi$
$972$	1385.48	0.0457194
$973$	19398.7	0.639152
$974$	−24835.9	−0.817038
$975$	−1522.38	−0.0500054
$976$	6539.80	0.214482
$977$	−2208.90	−0.0723326	−0.0361663	−	0.999346i	$-0.511515\pi$
$977$	−2208.90	−0.0723326	−0.0361663	+	0.999346i	$0.511515\pi$
$978$	−19285.0	−0.630539
$979$	0	0
$980$	−7415.02	−0.241698
$981$	−5007.01	−0.162958
$982$	46970.2	1.52635
$983$	−40306.0	−1.30779	−0.653897	−	0.756583i	$-0.726867\pi$
$983$	−40306.0	−1.30779	−0.653897	+	0.756583i	$0.726867\pi$
$984$	−720.000	−0.0233260
$985$	−11310.0	−0.365855
$986$	−19654.7	−0.634820
$987$	−14083.2	−0.454177
$988$	−1005.25	−0.0323696
$989$	33966.3	1.09208
$990$	0	0
$991$	−15199.4	−0.487211	−0.243605	−	0.969874i	$-0.578330\pi$
$991$	−15199.4	−0.487211	−0.243605	+	0.969874i	$0.578330\pi$
$992$	−34499.8	−1.10420
$993$	−12979.5	−0.414796
$994$	18087.5	0.577163
$995$	11700.8	0.372803
$996$	8907.40	0.283375
$997$	48073.6	1.52709	0.763543	−	0.645757i	$-0.223458\pi$
$997$	48073.6	1.52709	0.763543	+	0.645757i	$0.223458\pi$
$998$	36315.3	1.15184
$999$	3737.43	0.118365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.i.1.1	✓	2
11.10	odd	2		1815.4.a.o.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.4.a.i.1.1	✓	2	1.1	even	1	trivial
1815.4.a.o.1.2	yes	2	11.10	odd	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)

\(f(q)\)	\(=\)	\(q-3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} +5.00000 q^{5} -11.1047 q^{6} +9.10469 q^{7} +8.50781 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} +5.00000 q^{5} -11.1047 q^{6} +9.10469 q^{7} +8.50781 q^{8} +9.00000 q^{9} -18.5078 q^{10} +17.1047 q^{12} -20.2984 q^{13} -33.7016 q^{14} +15.0000 q^{15} -77.1047 q^{16} +61.8062 q^{17} -33.3141 q^{18} +8.68594 q^{19} +28.5078 q^{20} +27.3141 q^{21} -127.748 q^{23} +25.5234 q^{24} +25.0000 q^{25} +75.1359 q^{26} +27.0000 q^{27} +51.9109 q^{28} +85.9109 q^{29} -55.5234 q^{30} -158.733 q^{31} +217.345 q^{32} -228.780 q^{34} +45.5234 q^{35} +51.3141 q^{36} +138.423 q^{37} -32.1515 q^{38} -60.8953 q^{39} +42.5391 q^{40} -28.2094 q^{41} -101.105 q^{42} -265.884 q^{43} +45.0000 q^{45} +472.869 q^{46} -515.602 q^{47} -231.314 q^{48} -260.105 q^{49} -92.5391 q^{50} +185.419 q^{51} -115.733 q^{52} -466.702 q^{53} -99.9422 q^{54} +77.4609 q^{56} +26.0578 q^{57} -318.005 q^{58} +373.475 q^{59} +85.5234 q^{60} -84.8172 q^{61} +587.559 q^{62} +81.9422 q^{63} -187.680 q^{64} -101.492 q^{65} -88.7657 q^{67} +352.392 q^{68} -383.245 q^{69} -168.508 q^{70} -536.695 q^{71} +76.5703 q^{72} -322.450 q^{73} -512.383 q^{74} +75.0000 q^{75} +49.5234 q^{76} +225.408 q^{78} -265.592 q^{79} -385.523 q^{80} +81.0000 q^{81} +104.419 q^{82} +520.758 q^{83} +155.733 q^{84} +309.031 q^{85} +984.187 q^{86} +257.733 q^{87} -464.713 q^{89} -166.570 q^{90} -184.811 q^{91} -728.366 q^{92} -476.198 q^{93} +1908.53 q^{94} +43.4297 q^{95} +652.036 q^{96} -204.481 q^{97} +962.794 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 15 * q^8 + 18 * q^9	\( 2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9} - 5 q^{10} + 15 q^{12} - 47 q^{13} - 61 q^{14} + 30 q^{15} - 135 q^{16} + 98 q^{17} - 9 q^{18} + 75 q^{19} + 25 q^{20} - 3 q^{21} - 57 q^{23} - 45 q^{24} + 50 q^{25} + 3 q^{26} + 54 q^{27} + 59 q^{28} + 127 q^{29} - 15 q^{30} - 183 q^{31} + 249 q^{32} - 131 q^{34} - 5 q^{35} + 45 q^{36} - 229 q^{37} + 147 q^{38} - 141 q^{39} - 75 q^{40} - 18 q^{41} - 183 q^{42} - 186 q^{43} + 90 q^{45} + 664 q^{46} - 615 q^{47} - 405 q^{48} - 501 q^{49} - 25 q^{50} + 294 q^{51} - 97 q^{52} - 927 q^{53} - 27 q^{54} + 315 q^{56} + 225 q^{57} - 207 q^{58} - 380 q^{59} + 75 q^{60} - 509 q^{61} + 522 q^{62} - 9 q^{63} + 361 q^{64} - 235 q^{65} - 1138 q^{67} + 327 q^{68} - 171 q^{69} - 305 q^{70} - 273 q^{71} - 135 q^{72} - 440 q^{73} - 1505 q^{74} + 150 q^{75} + 3 q^{76} + 9 q^{78} - 973 q^{79} - 675 q^{80} + 162 q^{81} + 132 q^{82} - 15 q^{83} + 177 q^{84} + 490 q^{85} + 1200 q^{86} + 381 q^{87} - 1288 q^{89} - 45 q^{90} + 85 q^{91} - 778 q^{92} - 549 q^{93} + 1640 q^{94} + 375 q^{95} + 747 q^{96} - 76 q^{97} + 312 q^{98}+O(q^{100}) \) 2 * q - q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 15 * q^8 + 18 * q^9 - 5 * q^10 + 15 * q^12 - 47 * q^13 - 61 * q^14 + 30 * q^15 - 135 * q^16 + 98 * q^17 - 9 * q^18 + 75 * q^19 + 25 * q^20 - 3 * q^21 - 57 * q^23 - 45 * q^24 + 50 * q^25 + 3 * q^26 + 54 * q^27 + 59 * q^28 + 127 * q^29 - 15 * q^30 - 183 * q^31 + 249 * q^32 - 131 * q^34 - 5 * q^35 + 45 * q^36 - 229 * q^37 + 147 * q^38 - 141 * q^39 - 75 * q^40 - 18 * q^41 - 183 * q^42 - 186 * q^43 + 90 * q^45 + 664 * q^46 - 615 * q^47 - 405 * q^48 - 501 * q^49 - 25 * q^50 + 294 * q^51 - 97 * q^52 - 927 * q^53 - 27 * q^54 + 315 * q^56 + 225 * q^57 - 207 * q^58 - 380 * q^59 + 75 * q^60 - 509 * q^61 + 522 * q^62 - 9 * q^63 + 361 * q^64 - 235 * q^65 - 1138 * q^67 + 327 * q^68 - 171 * q^69 - 305 * q^70 - 273 * q^71 - 135 * q^72 - 440 * q^73 - 1505 * q^74 + 150 * q^75 + 3 * q^76 + 9 * q^78 - 973 * q^79 - 675 * q^80 + 162 * q^81 + 132 * q^82 - 15 * q^83 + 177 * q^84 + 490 * q^85 + 1200 * q^86 + 381 * q^87 - 1288 * q^89 - 45 * q^90 + 85 * q^91 - 778 * q^92 - 549 * q^93 + 1640 * q^94 + 375 * q^95 + 747 * q^96 - 76 * q^97 + 312 * q^98

Introduction

L-functions

Modular forms

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Database

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