LMFDB - Embedded newform 1815.4.a.i.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:	$1$
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			1.2
Root			$-2.70156$ 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)

$f(q)$	$=$	$q+2.70156 q^{2} +3.00000 q^{3} -0.701562 q^{4} +5.00000 q^{5} +8.10469 q^{6} -10.1047 q^{7} -23.5078 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.70156 q^{2} +3.00000 q^{3} -0.701562 q^{4} +5.00000 q^{5} +8.10469 q^{6} -10.1047 q^{7} -23.5078 q^{8} +9.00000 q^{9} +13.5078 q^{10} -2.10469 q^{12} -26.7016 q^{13} -27.2984 q^{14} +15.0000 q^{15} -57.8953 q^{16} +36.1938 q^{17} +24.3141 q^{18} +66.3141 q^{19} -3.50781 q^{20} -30.3141 q^{21} +70.7484 q^{23} -70.5234 q^{24} +25.0000 q^{25} -72.1359 q^{26} +27.0000 q^{27} +7.08907 q^{28} +41.0891 q^{29} +40.5234 q^{30} -24.2672 q^{31} +31.6547 q^{32} +97.7797 q^{34} -50.5234 q^{35} -6.31406 q^{36} -367.423 q^{37} +179.152 q^{38} -80.1047 q^{39} -117.539 q^{40} +10.2094 q^{41} -81.8953 q^{42} +79.8844 q^{43} +45.0000 q^{45} +191.131 q^{46} -99.3985 q^{47} -173.686 q^{48} -240.895 q^{49} +67.5391 q^{50} +108.581 q^{51} +18.7328 q^{52} -460.298 q^{53} +72.9422 q^{54} +237.539 q^{56} +198.942 q^{57} +111.005 q^{58} -753.475 q^{59} -10.5234 q^{60} -424.183 q^{61} -65.5593 q^{62} -90.9422 q^{63} +548.680 q^{64} -133.508 q^{65} -1049.23 q^{67} -25.3922 q^{68} +212.245 q^{69} -136.492 q^{70} +263.695 q^{71} -211.570 q^{72} -117.550 q^{73} -992.617 q^{74} +75.0000 q^{75} -46.5234 q^{76} -216.408 q^{78} -707.408 q^{79} -289.477 q^{80} +81.0000 q^{81} +27.5813 q^{82} -535.758 q^{83} +21.2672 q^{84} +180.969 q^{85} +215.813 q^{86} +123.267 q^{87} -823.287 q^{89} +121.570 q^{90} +269.811 q^{91} -49.6344 q^{92} -72.8016 q^{93} -268.531 q^{94} +331.570 q^{95} +94.9641 q^{96} +128.481 q^{97} -650.794 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.70156	0.955146	0.477573	−	0.878592i	$-0.341517\pi$
$2$	2.70156	0.955146	0.477573	+	0.878592i	$0.341517\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−0.701562	−0.0876953
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	8.10469	0.551454
$7$	−10.1047	−0.545602	−0.272801	−	0.962071i	$-0.587950\pi$
$7$	−10.1047	−0.545602	−0.272801	+	0.962071i	$0.587950\pi$
$8$	−23.5078	−1.03891
$9$	9.00000	0.333333
$10$	13.5078	0.427154
$11$	0	0
$11$	0	0
$12$	−2.10469	−0.0506309
$13$	−26.7016	−0.569668	−0.284834	−	0.958577i	$-0.591938\pi$
$13$	−26.7016	−0.569668	−0.284834	+	0.958577i	$0.591938\pi$
$14$	−27.2984	−0.521130
$15$	15.0000	0.258199
$16$	−57.8953	−0.904614
$17$	36.1938	0.516369	0.258185	−	0.966096i	$-0.416876\pi$
$17$	36.1938	0.516369	0.258185	+	0.966096i	$0.416876\pi$
$18$	24.3141	0.318382
$19$	66.3141	0.800710	0.400355	−	0.916360i	$-0.368887\pi$
$19$	66.3141	0.800710	0.400355	+	0.916360i	$0.368887\pi$
$20$	−3.50781	−0.0392185
$21$	−30.3141	−0.315003
$22$	0	0
$23$	70.7484	0.641394	0.320697	−	0.947182i	$-0.396083\pi$
$23$	70.7484	0.641394	0.320697	+	0.947182i	$0.396083\pi$
$24$	−70.5234	−0.599814
$25$	25.0000	0.200000
$26$	−72.1359	−0.544116
$27$	27.0000	0.192450
$28$	7.08907	0.0478467
$29$	41.0891	0.263105	0.131553	−	0.991309i	$-0.458004\pi$
$29$	41.0891	0.263105	0.131553	+	0.991309i	$0.458004\pi$
$30$	40.5234	0.246618
$31$	−24.2672	−0.140597	−0.0702987	−	0.997526i	$-0.522395\pi$
$31$	−24.2672	−0.140597	−0.0702987	+	0.997526i	$0.522395\pi$
$32$	31.6547	0.174869
$33$	0	0
$34$	97.7797	0.493208
$35$	−50.5234	−0.244001
$36$	−6.31406	−0.0292318
$37$	−367.423	−1.63254	−0.816271	−	0.577669i	$-0.803962\pi$
$37$	−367.423	−1.63254	−0.816271	+	0.577669i	$0.803962\pi$
$38$	179.152	0.764795
$39$	−80.1047	−0.328898
$40$	−117.539	−0.464614
$41$	10.2094	0.0388887	0.0194443	−	0.999811i	$-0.493810\pi$
$41$	10.2094	0.0388887	0.0194443	+	0.999811i	$0.493810\pi$
$42$	−81.8953	−0.300874
$43$	79.8844	0.283308	0.141654	−	0.989916i	$-0.454758\pi$
$43$	79.8844	0.283308	0.141654	+	0.989916i	$0.454758\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	191.131	0.612625
$47$	−99.3985	−0.308484	−0.154242	−	0.988033i	$-0.549294\pi$
$47$	−99.3985	−0.308484	−0.154242	+	0.988033i	$0.549294\pi$
$48$	−173.686	−0.522279
$49$	−240.895	−0.702319
$50$	67.5391	0.191029
$51$	108.581	0.298126
$52$	18.7328	0.0499572
$53$	−460.298	−1.19296	−0.596480	−	0.802628i	$-0.703434\pi$
$53$	−460.298	−1.19296	−0.596480	+	0.802628i	$0.703434\pi$
$54$	72.9422	0.183818
$55$	0	0
$56$	237.539	0.566830
$57$	198.942	0.462290
$58$	111.005	0.251304
$59$	−753.475	−1.66261	−0.831306	−	0.555815i	$-0.812406\pi$
$59$	−753.475	−1.66261	−0.831306	+	0.555815i	$0.812406\pi$
$60$	−10.5234	−0.0226428
$61$	−424.183	−0.890345	−0.445172	−	0.895445i	$-0.646858\pi$
$61$	−424.183	−0.890345	−0.445172	+	0.895445i	$0.646858\pi$
$62$	−65.5593	−0.134291
$63$	−90.9422	−0.181867
$64$	548.680	1.07164
$65$	−133.508	−0.254763
$66$	0	0
$67$	−1049.23	−1.91320	−0.956600	−	0.291405i	$-0.905877\pi$
$67$	−1049.23	−1.91320	−0.956600	+	0.291405i	$0.905877\pi$
$68$	−25.3922	−0.0452831
$69$	212.245	0.370309
$70$	−136.492	−0.233056
$71$	263.695	0.440773	0.220386	−	0.975413i	$-0.429268\pi$
$71$	263.695	0.440773	0.220386	+	0.975413i	$0.429268\pi$
$72$	−211.570	−0.346303
$73$	−117.550	−0.188468	−0.0942342	−	0.995550i	$-0.530040\pi$
$73$	−117.550	−0.188468	−0.0942342	+	0.995550i	$0.530040\pi$
$74$	−992.617	−1.55932
$75$	75.0000	0.115470
$76$	−46.5234	−0.0702185
$77$	0	0
$78$	−216.408	−0.314146
$79$	−707.408	−1.00746	−0.503732	−	0.863860i	$-0.668040\pi$
$79$	−707.408	−1.00746	−0.503732	+	0.863860i	$0.668040\pi$
$80$	−289.477	−0.404556
$81$	81.0000	0.111111
$82$	27.5813	0.0371444
$83$	−535.758	−0.708519	−0.354259	−	0.935147i	$-0.615267\pi$
$83$	−535.758	−0.708519	−0.354259	+	0.935147i	$0.615267\pi$
$84$	21.2672	0.0276243
$85$	180.969	0.230927
$86$	215.813	0.270601
$87$	123.267	0.151904
$88$	0	0
$89$	−823.287	−0.980543	−0.490271	−	0.871570i	$-0.663102\pi$
$89$	−823.287	−0.980543	−0.490271	+	0.871570i	$0.663102\pi$
$90$	121.570	0.142385
$91$	269.811	0.310812
$92$	−49.6344	−0.0562472
$93$	−72.8016	−0.0811739
$94$	−268.531	−0.294648
$95$	331.570	0.358088
$96$	94.9641	0.100961
$97$	128.481	0.134488	0.0672438	−	0.997737i	$-0.478579\pi$
$97$	128.481	0.134488	0.0672438	+	0.997737i	$0.478579\pi$
$98$	−650.794	−0.670817
$99$	0	0
$100$	−17.5391	−0.0175391
$101$	−225.748	−0.222404	−0.111202	−	0.993798i	$-0.535470\pi$
$101$	−225.748	−0.222404	−0.111202	+	0.993798i	$0.535470\pi$
$102$	293.339	0.284754
$103$	−979.798	−0.937305	−0.468652	−	0.883383i	$-0.655260\pi$
$103$	−979.798	−0.937305	−0.468652	+	0.883383i	$0.655260\pi$
$104$	627.695	0.591833
$105$	−151.570	−0.140874
$106$	−1243.52	−1.13945
$107$	185.961	0.168014	0.0840071	−	0.996465i	$-0.473228\pi$
$107$	185.961	0.168014	0.0840071	+	0.996465i	$0.473228\pi$
$108$	−18.9422	−0.0168770
$109$	−5.66566	−0.00497864	−0.00248932	−	0.999997i	$-0.500792\pi$
$109$	−5.66566	−0.00497864	−0.00248932	+	0.999997i	$0.500792\pi$
$110$	0	0
$111$	−1102.27	−0.942548
$112$	585.014	0.493559
$113$	415.311	0.345745	0.172872	−	0.984944i	$-0.444695\pi$
$113$	415.311	0.345745	0.172872	+	0.984944i	$0.444695\pi$
$114$	537.455	0.441555
$115$	353.742	0.286840
$116$	−28.8265	−0.0230731
$117$	−240.314	−0.189889
$118$	−2035.56	−1.58804
$119$	−365.727	−0.281732
$120$	−352.617	−0.268245
$121$	0	0
$122$	−1145.96	−0.850410
$123$	30.6281	0.0224524
$124$	17.0249	0.0123297
$125$	125.000	0.0894427
$126$	−245.686	−0.173710
$127$	−113.159	−0.0790650	−0.0395325	−	0.999218i	$-0.512587\pi$
$127$	−113.159	−0.0790650	−0.0395325	+	0.999218i	$0.512587\pi$
$128$	1229.05	0.848704
$129$	239.653	0.163568
$130$	−360.680	−0.243336
$131$	−943.106	−0.629004	−0.314502	−	0.949257i	$-0.601838\pi$
$131$	−943.106	−0.629004	−0.314502	+	0.949257i	$0.601838\pi$
$132$	0	0
$133$	−670.083	−0.436869
$134$	−2834.57	−1.82739
$135$	135.000	0.0860663
$136$	−850.836	−0.536460
$137$	2767.42	1.72582	0.862909	−	0.505359i	$-0.168640\pi$
$137$	2767.42	1.72582	0.862909	+	0.505359i	$0.168640\pi$
$138$	573.394	0.353699
$139$	363.369	0.221731	0.110865	−	0.993835i	$-0.464638\pi$
$139$	363.369	0.221731	0.110865	+	0.993835i	$0.464638\pi$
$140$	35.4453	0.0213977
$141$	−298.195	−0.178103
$142$	712.389	0.421003
$143$	0	0
$144$	−521.058	−0.301538
$145$	205.445	0.117664
$146$	−317.569	−0.180015
$147$	−722.686	−0.405484
$148$	257.770	0.143166
$149$	161.100	0.0885760	0.0442880	−	0.999019i	$-0.485898\pi$
$149$	161.100	0.0885760	0.0442880	+	0.999019i	$0.485898\pi$
$150$	202.617	0.110291
$151$	−176.217	−0.0949693	−0.0474846	−	0.998872i	$-0.515121\pi$
$151$	−176.217	−0.0949693	−0.0474846	+	0.998872i	$0.515121\pi$
$152$	−1558.90	−0.831864
$153$	325.744	0.172123
$154$	0	0
$155$	−121.336	−0.0628770
$156$	56.1984	0.0288428
$157$	−137.895	−0.0700971	−0.0350485	−	0.999386i	$-0.511159\pi$
$157$	−137.895	−0.0700971	−0.0350485	+	0.999386i	$0.511159\pi$
$158$	−1911.11	−0.962275
$159$	−1380.90	−0.688755
$160$	158.273	0.0782039
$161$	−714.891	−0.349946
$162$	218.827	0.106127
$163$	−952.656	−0.457778	−0.228889	−	0.973453i	$-0.573509\pi$
$163$	−952.656	−0.457778	−0.228889	+	0.973453i	$0.573509\pi$
$164$	−7.16251	−0.00341035
$165$	0	0
$166$	−1447.38	−0.676739
$167$	2100.45	0.973282	0.486641	−	0.873602i	$-0.338222\pi$
$167$	2100.45	0.973282	0.486641	+	0.873602i	$0.338222\pi$
$168$	712.617	0.327260
$169$	−1484.03	−0.675479
$170$	488.898	0.220569
$171$	596.827	0.266903
$172$	−56.0438	−0.0248448
$173$	1040.22	0.457147	0.228573	−	0.973527i	$-0.426594\pi$
$173$	1040.22	0.457147	0.228573	+	0.973527i	$0.426594\pi$
$174$	333.014	0.145090
$175$	−252.617	−0.109120
$176$	0	0
$177$	−2260.42	−0.959909
$178$	−2224.16	−0.936562
$179$	1570.93	0.655959	0.327980	−	0.944685i	$-0.393632\pi$
$179$	1570.93	0.655959	0.327980	+	0.944685i	$0.393632\pi$
$180$	−31.5703	−0.0130728
$181$	2883.25	1.18403	0.592017	−	0.805925i	$-0.298332\pi$
$181$	2883.25	1.18403	0.592017	+	0.805925i	$0.298332\pi$
$182$	728.911	0.296871
$183$	−1272.55	−0.514041
$184$	−1663.14	−0.666350
$185$	−1837.12	−0.730095
$186$	−196.678	−0.0775330
$187$	0	0
$188$	69.7342	0.0270526
$189$	−272.827	−0.105001
$190$	895.758	0.342027
$191$	−4176.94	−1.58237	−0.791186	−	0.611575i	$-0.790536\pi$
$191$	−4176.94	−1.58237	−0.791186	+	0.611575i	$0.790536\pi$
$192$	1646.04	0.618712
$193$	1346.96	0.502363	0.251181	−	0.967940i	$-0.419181\pi$
$193$	1346.96	0.502363	0.251181	+	0.967940i	$0.419181\pi$
$194$	347.100	0.128455
$195$	−400.523	−0.147088
$196$	169.003	0.0615900
$197$	3488.00	1.26147	0.630736	−	0.775998i	$-0.282753\pi$
$197$	3488.00	1.26147	0.630736	+	0.775998i	$0.282753\pi$
$198$	0	0
$199$	−1969.15	−0.701454	−0.350727	−	0.936478i	$-0.614066\pi$
$199$	−1969.15	−0.701454	−0.350727	+	0.936478i	$0.614066\pi$
$200$	−587.695	−0.207782
$201$	−3147.70	−1.10459
$202$	−609.873	−0.212428
$203$	−415.192	−0.143551
$204$	−76.1765	−0.0261442
$205$	51.0469	0.0173915
$206$	−2646.99	−0.895263
$207$	636.736	0.213798
$208$	1545.90	0.515330
$209$	0	0
$210$	−409.477	−0.134555
$211$	−3829.56	−1.24947	−0.624734	−	0.780837i	$-0.714793\pi$
$211$	−3829.56	−1.24947	−0.624734	+	0.780837i	$0.714793\pi$
$212$	322.928	0.104617
$213$	791.086	0.254480
$214$	502.385	0.160478
$215$	399.422	0.126699
$216$	−634.711	−0.199938
$217$	245.212	0.0767101
$218$	−15.3061	−0.00475533
$219$	−352.650	−0.108812
$220$	0	0
$221$	−966.430	−0.294159
$222$	−2977.85	−0.900272
$223$	3783.58	1.13618	0.568088	−	0.822968i	$-0.307683\pi$
$223$	3783.58	1.13618	0.568088	+	0.822968i	$0.307683\pi$
$224$	−319.861	−0.0954089
$225$	225.000	0.0666667
$226$	1121.99	0.330237
$227$	3305.66	0.966539	0.483270	−	0.875472i	$-0.339449\pi$
$227$	3305.66	0.966539	0.483270	+	0.875472i	$0.339449\pi$
$228$	−139.570	−0.0405407
$229$	1881.69	0.542994	0.271497	−	0.962439i	$-0.412481\pi$
$229$	1881.69	0.542994	0.271497	+	0.962439i	$0.412481\pi$
$230$	955.656	0.273974
$231$	0	0
$232$	−965.914	−0.273342
$233$	−6167.54	−1.73412	−0.867058	−	0.498207i	$-0.833992\pi$
$233$	−6167.54	−1.73412	−0.867058	+	0.498207i	$0.833992\pi$
$234$	−649.223	−0.181372
$235$	−496.992	−0.137958
$236$	528.609	0.145803
$237$	−2122.22	−0.581659
$238$	−988.033	−0.269095
$239$	2574.48	0.696776	0.348388	−	0.937350i	$-0.386729\pi$
$239$	2574.48	0.696776	0.348388	+	0.937350i	$0.386729\pi$
$240$	−868.430	−0.233570
$241$	−1125.12	−0.300728	−0.150364	−	0.988631i	$-0.548045\pi$
$241$	−1125.12	−0.300728	−0.150364	+	0.988631i	$0.548045\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	297.591	0.0780790
$245$	−1204.48	−0.314086
$246$	82.7438	0.0214453
$247$	−1770.69	−0.456139
$248$	570.469	0.146068
$249$	−1607.27	−0.409063
$250$	337.695	0.0854309
$251$	558.309	0.140399	0.0701995	−	0.997533i	$-0.477636\pi$
$251$	558.309	0.140399	0.0701995	+	0.997533i	$0.477636\pi$
$252$	63.8016	0.0159489
$253$	0	0
$254$	−305.707	−0.0755187
$255$	542.906	0.133326
$256$	−1069.07	−0.261003
$257$	−166.553	−0.0404252	−0.0202126	−	0.999796i	$-0.506434\pi$
$257$	−166.553	−0.0404252	−0.0202126	+	0.999796i	$0.506434\pi$
$258$	647.438	0.156231
$259$	3712.70	0.890718
$260$	93.6640	0.0223415
$261$	369.802	0.0877017
$262$	−2547.86	−0.600791
$263$	5678.97	1.33148	0.665742	−	0.746182i	$-0.268115\pi$
$263$	5678.97	1.33148	0.665742	+	0.746182i	$0.268115\pi$
$264$	0	0
$265$	−2301.49	−0.533508
$266$	−1810.27	−0.417274
$267$	−2469.86	−0.566117
$268$	736.103	0.167779
$269$	2056.03	0.466015	0.233008	−	0.972475i	$-0.425143\pi$
$269$	2056.03	0.466015	0.233008	+	0.972475i	$0.425143\pi$
$270$	364.711	0.0822059
$271$	−6349.58	−1.42328	−0.711641	−	0.702544i	$-0.752048\pi$
$271$	−6349.58	−1.42328	−0.711641	+	0.702544i	$0.752048\pi$
$272$	−2095.45	−0.467115
$273$	809.433	0.179447
$274$	7476.37	1.64841
$275$	0	0
$276$	−148.903	−0.0324744
$277$	5318.77	1.15370	0.576848	−	0.816851i	$-0.304282\pi$
$277$	5318.77	1.15370	0.576848	+	0.816851i	$0.304282\pi$
$278$	981.664	0.211785
$279$	−218.405	−0.0468658
$280$	1187.70	0.253494
$281$	8731.32	1.85362	0.926810	−	0.375532i	$-0.122540\pi$
$281$	8731.32	1.85362	0.926810	+	0.375532i	$0.122540\pi$
$282$	−805.593	−0.170115
$283$	−8899.43	−1.86931	−0.934657	−	0.355550i	$-0.884294\pi$
$283$	−8899.43	−1.86931	−0.934657	+	0.355550i	$0.884294\pi$
$284$	−184.999	−0.0386537
$285$	994.711	0.206742
$286$	0	0
$287$	−103.163	−0.0212177
$288$	284.892	0.0582897
$289$	−3603.01	−0.733363
$290$	555.023	0.112387
$291$	385.444	0.0776464
$292$	82.4686	0.0165278
$293$	8071.93	1.60944	0.804722	−	0.593652i	$-0.202314\pi$
$293$	8071.93	1.60944	0.804722	+	0.593652i	$0.202314\pi$
$294$	−1952.38	−0.387296
$295$	−3767.37	−0.743542
$296$	8637.32	1.69606
$297$	0	0
$298$	435.222	0.0846031
$299$	−1889.09	−0.365382
$300$	−52.6172	−0.0101262
$301$	−807.206	−0.154573
$302$	−476.062	−0.0907096
$303$	−677.245	−0.128405
$304$	−3839.27	−0.724334
$305$	−2120.91	−0.398174
$306$	880.017	0.164403
$307$	2698.56	0.501677	0.250839	−	0.968029i	$-0.419294\pi$
$307$	2698.56	0.501677	0.250839	+	0.968029i	$0.419294\pi$
$308$	0	0
$309$	−2939.39	−0.541153
$310$	−327.797	−0.0600568
$311$	−2955.76	−0.538926	−0.269463	−	0.963011i	$-0.586846\pi$
$311$	−2955.76	−0.538926	−0.269463	+	0.963011i	$0.586846\pi$
$312$	1883.09	0.341695
$313$	−2124.40	−0.383636	−0.191818	−	0.981431i	$-0.561438\pi$
$313$	−2124.40	−0.383636	−0.191818	+	0.981431i	$0.561438\pi$
$314$	−372.533	−0.0669530
$315$	−454.711	−0.0813335
$316$	496.291	0.0883498
$317$	−2404.95	−0.426105	−0.213053	−	0.977041i	$-0.568341\pi$
$317$	−2404.95	−0.426105	−0.213053	+	0.977041i	$0.568341\pi$
$318$	−3730.57	−0.657862
$319$	0	0
$320$	2743.40	0.479252
$321$	557.882	0.0970030
$322$	−1931.32	−0.334250
$323$	2400.15	0.413462
$324$	−56.8265	−0.00974392
$325$	−667.539	−0.113934
$326$	−2573.66	−0.437245
$327$	−16.9970	−0.00287442
$328$	−240.000	−0.0404018
$329$	1004.39	0.168310
$330$	0	0
$331$	−6375.50	−1.05870	−0.529349	−	0.848404i	$-0.677564\pi$
$331$	−6375.50	−1.05870	−0.529349	+	0.848404i	$0.677564\pi$
$332$	375.867	0.0621337
$333$	−3306.81	−0.544181
$334$	5674.51	0.929627
$335$	−5246.17	−0.855609
$336$	1755.04	0.284957
$337$	−8482.64	−1.37115	−0.685577	−	0.728000i	$-0.740450\pi$
$337$	−8482.64	−1.37115	−0.685577	+	0.728000i	$0.740450\pi$
$338$	−4009.19	−0.645181
$339$	1245.93	0.199616
$340$	−126.961	−0.0202512
$341$	0	0
$342$	1612.36	0.254932
$343$	5900.08	0.928788
$344$	−1877.91	−0.294331
$345$	1061.23	0.165607
$346$	2810.22	0.436642
$347$	1062.72	0.164409	0.0822044	−	0.996615i	$-0.473804\pi$
$347$	1062.72	0.164409	0.0822044	+	0.996615i	$0.473804\pi$
$348$	−86.4796	−0.0133212
$349$	−5284.62	−0.810542	−0.405271	−	0.914197i	$-0.632823\pi$
$349$	−5284.62	−0.810542	−0.405271	+	0.914197i	$0.632823\pi$
$350$	−682.461	−0.104226
$351$	−720.942	−0.109633
$352$	0	0
$353$	−12074.0	−1.82049	−0.910244	−	0.414072i	$-0.864106\pi$
$353$	−12074.0	−1.82049	−0.910244	+	0.414072i	$0.864106\pi$
$354$	−6106.68	−0.916854
$355$	1318.48	0.197120
$356$	577.587	0.0859889
$357$	−1097.18	−0.162658
$358$	4243.96	0.626537
$359$	6002.96	0.882519	0.441259	−	0.897380i	$-0.354532\pi$
$359$	6002.96	0.882519	0.441259	+	0.897380i	$0.354532\pi$
$360$	−1057.85	−0.154871
$361$	−2461.45	−0.358864
$362$	7789.28	1.13093
$363$	0	0
$364$	−189.289	−0.0272567
$365$	−587.750	−0.0842856
$366$	−3437.87	−0.490984
$367$	2684.43	0.381815	0.190908	−	0.981608i	$-0.438857\pi$
$367$	2684.43	0.381815	0.190908	+	0.981608i	$0.438857\pi$
$368$	−4096.00	−0.580214
$369$	91.8844	0.0129629
$370$	−4963.09	−0.697347
$371$	4651.17	0.650881
$372$	51.0748	0.00711857
$373$	−9694.41	−1.34573	−0.672866	−	0.739765i	$-0.734937\pi$
$373$	−9694.41	−1.34573	−0.672866	+	0.739765i	$0.734937\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	2336.64	0.320487
$377$	−1097.14	−0.149882
$378$	−737.058	−0.100291
$379$	8409.86	1.13980	0.569902	−	0.821713i	$-0.306981\pi$
$379$	8409.86	1.13980	0.569902	+	0.821713i	$0.306981\pi$
$380$	−232.617	−0.0314027
$381$	−339.478	−0.0456482
$382$	−11284.3	−1.51140
$383$	−13673.0	−1.82417	−0.912085	−	0.410001i	$-0.865528\pi$
$383$	−13673.0	−1.82417	−0.912085	+	0.410001i	$0.865528\pi$
$384$	3687.16	0.489999
$385$	0	0
$386$	3638.89	0.479830
$387$	718.959	0.0944360
$388$	−90.1376	−0.0117939
$389$	−6628.44	−0.863946	−0.431973	−	0.901886i	$-0.642182\pi$
$389$	−6628.44	−0.863946	−0.431973	+	0.901886i	$0.642182\pi$
$390$	−1082.04	−0.140490
$391$	2560.65	0.331196
$392$	5662.92	0.729645
$393$	−2829.32	−0.363156
$394$	9423.06	1.20489
$395$	−3537.04	−0.450551
$396$	0	0
$397$	1787.98	0.226036	0.113018	−	0.993593i	$-0.463948\pi$
$397$	1787.98	0.226036	0.113018	+	0.993593i	$0.463948\pi$
$398$	−5319.78	−0.669992
$399$	−2010.25	−0.252226
$400$	−1447.38	−0.180923
$401$	−5846.25	−0.728049	−0.364025	−	0.931389i	$-0.618598\pi$
$401$	−5846.25	−0.728049	−0.364025	+	0.931389i	$0.618598\pi$
$402$	−8503.72	−1.05504
$403$	647.972	0.0800938
$404$	158.377	0.0195038
$405$	405.000	0.0496904
$406$	−1121.67	−0.137112
$407$	0	0
$408$	−2552.51	−0.309725
$409$	12683.5	1.53339	0.766695	−	0.642011i	$-0.221900\pi$
$409$	12683.5	1.53339	0.766695	+	0.642011i	$0.221900\pi$
$410$	137.906	0.0166115
$411$	8302.27	0.996401
$412$	687.389	0.0821972
$413$	7613.63	0.907124
$414$	1720.18	0.204208
$415$	−2678.79	−0.316859
$416$	−845.230	−0.0996173
$417$	1090.11	0.128016
$418$	0	0
$419$	6841.28	0.797657	0.398829	−	0.917025i	$-0.369417\pi$
$419$	6841.28	0.797657	0.398829	+	0.917025i	$0.369417\pi$
$420$	106.336	0.0123540
$421$	−1807.76	−0.209275	−0.104637	−	0.994510i	$-0.533368\pi$
$421$	−1807.76	−0.209275	−0.104637	+	0.994510i	$0.533368\pi$
$422$	−10345.8	−1.19343
$423$	−894.586	−0.102828
$424$	10820.6	1.23938
$425$	904.844	0.103274
$426$	2137.17	0.243066
$427$	4286.23	0.485774
$428$	−130.463	−0.0147340
$429$	0	0
$430$	1079.06	0.121016
$431$	1777.64	0.198667	0.0993337	−	0.995054i	$-0.468329\pi$
$431$	1777.64	0.198667	0.0993337	+	0.995054i	$0.468329\pi$
$432$	−1563.17	−0.174093
$433$	12979.4	1.44053	0.720264	−	0.693700i	$-0.244021\pi$
$433$	12979.4	1.44053	0.720264	+	0.693700i	$0.244021\pi$
$434$	662.457	0.0732694
$435$	616.336	0.0679334
$436$	3.97481	0.000436603 0
$437$	4691.62	0.513571
$438$	−952.706	−0.103932
$439$	−4471.38	−0.486121	−0.243061	−	0.970011i	$-0.578151\pi$
$439$	−4471.38	−0.486121	−0.243061	+	0.970011i	$0.578151\pi$
$440$	0	0
$441$	−2168.06	−0.234106
$442$	−2610.87	−0.280965
$443$	5115.99	0.548686	0.274343	−	0.961632i	$-0.411540\pi$
$443$	5115.99	0.548686	0.274343	+	0.961632i	$0.411540\pi$
$444$	773.311	0.0826570
$445$	−4116.44	−0.438512
$446$	10221.6	1.08522
$447$	483.300	0.0511394
$448$	−5544.24	−0.584689
$449$	−5834.81	−0.613278	−0.306639	−	0.951826i	$-0.599204\pi$
$449$	−5834.81	−0.613278	−0.306639	+	0.951826i	$0.599204\pi$
$450$	607.851	0.0636764
$451$	0	0
$452$	−291.366	−0.0303202
$453$	−528.652	−0.0548305
$454$	8930.45	0.923186
$455$	1349.05	0.138999
$456$	−4676.70	−0.480277
$457$	15429.8	1.57938	0.789691	−	0.613504i	$-0.210241\pi$
$457$	15429.8	1.57938	0.789691	+	0.613504i	$0.210241\pi$
$458$	5083.51	0.518639
$459$	977.231	0.0993753
$460$	−248.172	−0.0251545
$461$	−1187.92	−0.120015	−0.0600074	−	0.998198i	$-0.519112\pi$
$461$	−1187.92	−0.120015	−0.0600074	+	0.998198i	$0.519112\pi$
$462$	0	0
$463$	3781.30	0.379550	0.189775	−	0.981828i	$-0.439224\pi$
$463$	3781.30	0.379550	0.189775	+	0.981828i	$0.439224\pi$
$464$	−2378.86	−0.238009
$465$	−364.008	−0.0363021
$466$	−16662.0	−1.65634
$467$	590.287	0.0584908	0.0292454	−	0.999572i	$-0.490690\pi$
$467$	590.287	0.0584908	0.0292454	+	0.999572i	$0.490690\pi$
$468$	168.595	0.0166524
$469$	10602.2	1.04385
$470$	−1342.66	−0.131770
$471$	−413.686	−0.0404706
$472$	17712.5	1.72730
$473$	0	0
$474$	−5733.32	−0.555570
$475$	1657.85	0.160142
$476$	256.580	0.0247066
$477$	−4142.69	−0.397653
$478$	6955.12	0.665523
$479$	17061.5	1.62747	0.813735	−	0.581236i	$-0.197431\pi$
$479$	17061.5	1.62747	0.813735	+	0.581236i	$0.197431\pi$
$480$	474.820	0.0451510
$481$	9810.78	0.930006
$482$	−3039.59	−0.287239
$483$	−2144.67	−0.202041
$484$	0	0
$485$	642.406	0.0601447
$486$	656.480	0.0612727
$487$	−12480.6	−1.16129	−0.580646	−	0.814156i	$-0.697200\pi$
$487$	−12480.6	−1.16129	−0.580646	+	0.814156i	$0.697200\pi$
$488$	9971.61	0.924987
$489$	−2857.97	−0.264298
$490$	−3253.97	−0.299999
$491$	12257.3	1.12661	0.563303	−	0.826250i	$-0.309530\pi$
$491$	12257.3	1.12661	0.563303	+	0.826250i	$0.309530\pi$
$492$	−21.4875	−0.00196897
$493$	1487.17	0.135859
$494$	−4783.63	−0.435679
$495$	0	0
$496$	1404.96	0.127186
$497$	−2664.56	−0.240486
$498$	−4342.15	−0.390716
$499$	2873.79	0.257813	0.128907	−	0.991657i	$-0.458853\pi$
$499$	2873.79	0.257813	0.128907	+	0.991657i	$0.458853\pi$
$500$	−87.6953	−0.00784370
$501$	6301.36	0.561925
$502$	1508.31	0.134102
$503$	−1150.72	−0.102004	−0.0510020	−	0.998699i	$-0.516241\pi$
$503$	−1150.72	−0.102004	−0.0510020	+	0.998699i	$0.516241\pi$
$504$	2137.85	0.188943
$505$	−1128.74	−0.0994621
$506$	0	0
$507$	−4452.08	−0.389988
$508$	79.3882	0.00693363
$509$	1002.22	0.0872745	0.0436372	−	0.999047i	$-0.486105\pi$
$509$	1002.22	0.0872745	0.0436372	+	0.999047i	$0.486105\pi$
$510$	1466.70	0.127346
$511$	1187.81	0.102829
$512$	−12720.6	−1.09800
$513$	1790.48	0.154097
$514$	−449.953	−0.0386120
$515$	−4898.99	−0.419175
$516$	−168.132	−0.0143441
$517$	0	0
$518$	10030.1	0.850766
$519$	3120.66	0.263934
$520$	3138.48	0.264676
$521$	−14545.1	−1.22310	−0.611549	−	0.791207i	$-0.709453\pi$
$521$	−14545.1	−1.22310	−0.611549	+	0.791207i	$0.709453\pi$
$522$	999.042	0.0837680
$523$	−8685.21	−0.726152	−0.363076	−	0.931759i	$-0.618274\pi$
$523$	−8685.21	−0.726152	−0.363076	+	0.931759i	$0.618274\pi$
$524$	661.647	0.0551607
$525$	−757.851	−0.0630007
$526$	15342.1	1.27176
$527$	−878.321	−0.0726001
$528$	0	0
$529$	−7161.66	−0.588613
$530$	−6217.62	−0.509578
$531$	−6781.27	−0.554204
$532$	470.105	0.0383113
$533$	−272.606	−0.0221536
$534$	−6672.49	−0.540724
$535$	929.804	0.0751382
$536$	24665.2	1.98764
$537$	4712.78	0.378718
$538$	5554.48	0.445113
$539$	0	0
$540$	−94.7109	−0.00754761
$541$	21517.2	1.70998	0.854988	−	0.518648i	$-0.173564\pi$
$541$	21517.2	1.70998	0.854988	+	0.518648i	$0.173564\pi$
$542$	−17153.8	−1.35944
$543$	8649.75	0.683603
$544$	1145.70	0.0902970
$545$	−28.3283	−0.00222651
$546$	2186.73	0.171398
$547$	−12053.4	−0.942170	−0.471085	−	0.882088i	$-0.656138\pi$
$547$	−12053.4	−0.942170	−0.471085	+	0.882088i	$0.656138\pi$
$548$	−1941.52	−0.151346
$549$	−3817.65	−0.296782
$550$	0	0
$551$	2724.78	0.210671
$552$	−4989.42	−0.384717
$553$	7148.13	0.549674
$554$	14369.0	1.10195
$555$	−5511.35	−0.421520
$556$	−254.926	−0.0194447
$557$	4454.51	0.338857	0.169429	−	0.985542i	$-0.445808\pi$
$557$	4454.51	0.338857	0.169429	+	0.985542i	$0.445808\pi$
$558$	−590.034	−0.0447637
$559$	−2133.04	−0.161392
$560$	2925.07	0.220726
$561$	0	0
$562$	23588.2	1.77048
$563$	13628.5	1.02020	0.510102	−	0.860114i	$-0.329608\pi$
$563$	13628.5	1.02020	0.510102	+	0.860114i	$0.329608\pi$
$564$	209.203	0.0156188
$565$	2076.55	0.154622
$566$	−24042.4	−1.78547
$567$	−818.480	−0.0606224
$568$	−6198.90	−0.457923
$569$	−2064.07	−0.152075	−0.0760373	−	0.997105i	$-0.524227\pi$
$569$	−2064.07	−0.152075	−0.0760373	+	0.997105i	$0.524227\pi$
$570$	2687.27	0.197469
$571$	666.014	0.0488123	0.0244061	−	0.999702i	$-0.492231\pi$
$571$	666.014	0.0488123	0.0244061	+	0.999702i	$0.492231\pi$
$572$	0	0
$573$	−12530.8	−0.913583
$574$	−278.700	−0.0202660
$575$	1768.71	0.128279
$576$	4938.12	0.357213
$577$	2115.23	0.152614	0.0763068	−	0.997084i	$-0.475687\pi$
$577$	2115.23	0.152614	0.0763068	+	0.997084i	$0.475687\pi$
$578$	−9733.76	−0.700469
$579$	4040.87	0.290039
$580$	−144.133	−0.0103186
$581$	5413.66	0.386569
$582$	1041.30	0.0741637
$583$	0	0
$584$	2763.34	0.195801
$585$	−1201.57	−0.0849211
$586$	21806.8	1.53725
$587$	−16525.0	−1.16194	−0.580969	−	0.813926i	$-0.697326\pi$
$587$	−16525.0	−1.16194	−0.580969	+	0.813926i	$0.697326\pi$
$588$	507.009	0.0355590
$589$	−1609.26	−0.112578
$590$	−10177.8	−0.710192
$591$	10464.0	0.728311
$592$	21272.1	1.47682
$593$	−26736.2	−1.85147	−0.925736	−	0.378171i	$-0.876553\pi$
$593$	−26736.2	−1.85147	−0.925736	+	0.378171i	$0.876553\pi$
$594$	0	0
$595$	−1828.63	−0.125994
$596$	−113.022	−0.00776770
$597$	−5907.45	−0.404985
$598$	−5103.50	−0.348993
$599$	15220.7	1.03823	0.519117	−	0.854703i	$-0.326261\pi$
$599$	15220.7	1.03823	0.519117	+	0.854703i	$0.326261\pi$
$600$	−1763.09	−0.119963
$601$	−24398.7	−1.65598	−0.827989	−	0.560744i	$-0.810515\pi$
$601$	−24398.7	−1.65598	−0.827989	+	0.560744i	$0.810515\pi$
$602$	−2180.72	−0.147640
$603$	−9443.11	−0.637733
$604$	123.627	0.00832836
$605$	0	0
$606$	−1829.62	−0.122646
$607$	23619.4	1.57938	0.789688	−	0.613509i	$-0.210242\pi$
$607$	23619.4	1.57938	0.789688	+	0.613509i	$0.210242\pi$
$608$	2099.15	0.140019
$609$	−1245.58	−0.0828790
$610$	−5729.78	−0.380315
$611$	2654.09	0.175733
$612$	−228.529	−0.0150944
$613$	−23250.9	−1.53197	−0.765984	−	0.642859i	$-0.777748\pi$
$613$	−23250.9	−1.53197	−0.765984	+	0.642859i	$0.777748\pi$
$614$	7290.33	0.479175
$615$	153.141	0.0100410
$616$	0	0
$617$	15687.9	1.02362	0.511809	−	0.859099i	$-0.328976\pi$
$617$	15687.9	1.02362	0.511809	+	0.859099i	$0.328976\pi$
$618$	−7940.96	−0.516881
$619$	15447.8	1.00307	0.501534	−	0.865138i	$-0.332769\pi$
$619$	15447.8	1.00307	0.501534	+	0.865138i	$0.332769\pi$
$620$	85.1247	0.00551402
$621$	1910.21	0.123436
$622$	−7985.18	−0.514753
$623$	8319.06	0.534986
$624$	4637.69	0.297526
$625$	625.000	0.0400000
$626$	−5739.19	−0.366428
$627$	0	0
$628$	96.7421	0.00614718
$629$	−13298.4	−0.842994
$630$	−1228.43	−0.0776854
$631$	−26681.2	−1.68330	−0.841648	−	0.540026i	$-0.818414\pi$
$631$	−26681.2	−1.68330	−0.841648	+	0.540026i	$0.818414\pi$
$632$	16629.6	1.04666
$633$	−11488.7	−0.721381
$634$	−6497.12	−0.406993
$635$	−565.796	−0.0353590
$636$	968.784	0.0604006
$637$	6432.28	0.400088
$638$	0	0
$639$	2373.26	0.146924
$640$	6145.27	0.379552
$641$	−15244.1	−0.939321	−0.469661	−	0.882847i	$-0.655624\pi$
$641$	−15244.1	−0.939321	−0.469661	+	0.882847i	$0.655624\pi$
$642$	1507.15	0.0926521
$643$	−24128.9	−1.47986	−0.739929	−	0.672684i	$-0.765141\pi$
$643$	−24128.9	−1.47986	−0.739929	+	0.672684i	$0.765141\pi$
$644$	501.540	0.0306886
$645$	1198.27	0.0731498
$646$	6484.17	0.394917
$647$	5415.41	0.329060	0.164530	−	0.986372i	$-0.447389\pi$
$647$	5415.41	0.329060	0.164530	+	0.986372i	$0.447389\pi$
$648$	−1904.13	−0.115434
$649$	0	0
$650$	−1803.40	−0.108823
$651$	735.637	0.0442886
$652$	668.347	0.0401449
$653$	11335.3	0.679303	0.339651	−	0.940551i	$-0.389691\pi$
$653$	11335.3	0.679303	0.339651	+	0.940551i	$0.389691\pi$
$654$	−45.9184	−0.00274549
$655$	−4715.53	−0.281299
$656$	−591.075	−0.0351793
$657$	−1057.95	−0.0628228
$658$	2713.42	0.160760
$659$	−25441.6	−1.50389	−0.751945	−	0.659226i	$-0.770884\pi$
$659$	−25441.6	−1.50389	−0.751945	+	0.659226i	$0.770884\pi$
$660$	0	0
$661$	312.429	0.0183844	0.00919219	−	0.999958i	$-0.497074\pi$
$661$	312.429	0.0183844	0.00919219	+	0.999958i	$0.497074\pi$
$662$	−17223.8	−1.01121
$663$	−2899.29	−0.169833
$664$	12594.5	0.736086
$665$	−3350.41	−0.195374
$666$	−8933.55	−0.519772
$667$	2906.99	0.168754
$668$	−1473.60	−0.0853522
$669$	11350.7	0.655972
$670$	−14172.9	−0.817232
$671$	0	0
$672$	−959.582	−0.0550844
$673$	−13815.1	−0.791280	−0.395640	−	0.918406i	$-0.629477\pi$
$673$	−13815.1	−0.791280	−0.395640	+	0.918406i	$0.629477\pi$
$674$	−22916.4	−1.30965
$675$	675.000	0.0384900
$676$	1041.14	0.0592363
$677$	−23931.4	−1.35858	−0.679290	−	0.733870i	$-0.737712\pi$
$677$	−23931.4	−1.35858	−0.679290	+	0.733870i	$0.737712\pi$
$678$	3365.96	0.190662
$679$	−1298.26	−0.0733766
$680$	−4254.18	−0.239912
$681$	9916.98	0.558032
$682$	0	0
$683$	−6301.98	−0.353058	−0.176529	−	0.984295i	$-0.556487\pi$
$683$	−6301.98	−0.353058	−0.176529	+	0.984295i	$0.556487\pi$
$684$	−418.711	−0.0234062
$685$	13837.1	0.771809
$686$	15939.4	0.887129
$687$	5645.08	0.313498
$688$	−4624.93	−0.256285
$689$	12290.7	0.679591
$690$	2866.97	0.158179
$691$	8554.84	0.470972	0.235486	−	0.971878i	$-0.424332\pi$
$691$	8554.84	0.470972	0.235486	+	0.971878i	$0.424332\pi$
$692$	−729.778	−0.0400896
$693$	0	0
$694$	2871.01	0.157034
$695$	1816.84	0.0991609
$696$	−2897.74	−0.157814
$697$	369.515	0.0200809
$698$	−14276.7	−0.774187
$699$	−18502.6	−1.00119
$700$	177.227	0.00956934
$701$	29410.3	1.58461	0.792306	−	0.610124i	$-0.208880\pi$
$701$	29410.3	1.58461	0.792306	+	0.610124i	$0.208880\pi$
$702$	−1947.67	−0.104715
$703$	−24365.3	−1.30719
$704$	0	0
$705$	−1490.98	−0.0796503
$706$	−32618.6	−1.73883
$707$	2281.12	0.121344
$708$	1585.83	0.0841795
$709$	15207.4	0.805537	0.402768	−	0.915302i	$-0.368048\pi$
$709$	15207.4	0.805537	0.402768	+	0.915302i	$0.368048\pi$
$710$	3561.95	0.188278
$711$	−6366.67	−0.335821
$712$	19353.7	1.01869
$713$	−1716.87	−0.0901783
$714$	−2964.10	−0.155362
$715$	0	0
$716$	−1102.10	−0.0575245
$717$	7723.45	0.402284
$718$	16217.4	0.842935
$719$	−13773.8	−0.714431	−0.357215	−	0.934022i	$-0.616274\pi$
$719$	−13773.8	−0.714431	−0.357215	+	0.934022i	$0.616274\pi$
$720$	−2605.29	−0.134852
$721$	9900.55	0.511395
$722$	−6649.75	−0.342767
$723$	−3375.37	−0.173625
$724$	−2022.78	−0.103834
$725$	1027.23	0.0526210
$726$	0	0
$727$	33429.1	1.70539	0.852694	−	0.522410i	$-0.174967\pi$
$727$	33429.1	1.70539	0.852694	+	0.522410i	$0.174967\pi$
$728$	−6342.66	−0.322905
$729$	729.000	0.0370370
$730$	−1587.84	−0.0805051
$731$	2891.31	0.146292
$732$	892.772	0.0450790
$733$	−7774.73	−0.391768	−0.195884	−	0.980627i	$-0.562758\pi$
$733$	−7774.73	−0.391768	−0.195884	+	0.980627i	$0.562758\pi$
$734$	7252.16	0.364690
$735$	−3613.43	−0.181338
$736$	2239.52	0.112160
$737$	0	0
$738$	248.231	0.0123815
$739$	37474.1	1.86537	0.932684	−	0.360693i	$-0.117460\pi$
$739$	37474.1	1.86537	0.932684	+	0.360693i	$0.117460\pi$
$740$	1288.85	0.0640259
$741$	−5312.07	−0.263352
$742$	12565.4	0.621687
$743$	−30510.7	−1.50650	−0.753250	−	0.657735i	$-0.771515\pi$
$743$	−30510.7	−1.50650	−0.753250	+	0.657735i	$0.771515\pi$
$744$	1711.41	0.0843322
$745$	805.500	0.0396124
$746$	−26190.1	−1.28537
$747$	−4821.82	−0.236173
$748$	0	0
$749$	−1879.08	−0.0916688
$750$	1013.09	0.0493236
$751$	34091.1	1.65646	0.828229	−	0.560389i	$-0.189348\pi$
$751$	34091.1	1.65646	0.828229	+	0.560389i	$0.189348\pi$
$752$	5754.71	0.279059
$753$	1674.93	0.0810594
$754$	−2964.00	−0.143160
$755$	−881.087	−0.0424716
$756$	191.405	0.00920810
$757$	901.287	0.0432733	0.0216366	−	0.999766i	$-0.493112\pi$
$757$	901.287	0.0432733	0.0216366	+	0.999766i	$0.493112\pi$
$758$	22719.8	1.08868
$759$	0	0
$760$	−7794.49	−0.372021
$761$	5030.20	0.239612	0.119806	−	0.992797i	$-0.461773\pi$
$761$	5030.20	0.239612	0.119806	+	0.992797i	$0.461773\pi$
$762$	−917.120	−0.0436007
$763$	57.2497	0.00271635
$764$	2930.39	0.138767
$765$	1628.72	0.0769758
$766$	−36938.4	−1.74235
$767$	20119.0	0.947136
$768$	−3207.21	−0.150690
$769$	−13447.0	−0.630574	−0.315287	−	0.948996i	$-0.602101\pi$
$769$	−13447.0	−0.630574	−0.315287	+	0.948996i	$0.602101\pi$
$770$	0	0
$771$	−499.658	−0.0233395
$772$	−944.974	−0.0440548
$773$	35885.7	1.66975	0.834876	−	0.550438i	$-0.185539\pi$
$773$	35885.7	1.66975	0.834876	+	0.550438i	$0.185539\pi$
$774$	1942.31	0.0902003
$775$	−606.680	−0.0281195
$776$	−3020.31	−0.139720
$777$	11138.1	0.514256
$778$	−17907.1	−0.825195
$779$	677.025	0.0311386
$780$	280.992	0.0128989
$781$	0	0
$782$	6917.76	0.316341
$783$	1109.40	0.0506346
$784$	13946.7	0.635328
$785$	−689.477	−0.0313484
$786$	−7643.58	−0.346867
$787$	−29894.2	−1.35402	−0.677010	−	0.735974i	$-0.736725\pi$
$787$	−29894.2	−1.35402	−0.677010	+	0.735974i	$0.736725\pi$
$788$	−2447.05	−0.110625
$789$	17036.9	0.768732
$790$	−9555.53	−0.430342
$791$	−4196.59	−0.188639
$792$	0	0
$793$	11326.3	0.507201
$794$	4830.34	0.215897
$795$	−6904.48	−0.308021
$796$	1381.48	0.0615142
$797$	14033.8	0.623716	0.311858	−	0.950129i	$-0.399049\pi$
$797$	14033.8	0.623716	0.311858	+	0.950129i	$0.399049\pi$
$798$	−5430.81	−0.240913
$799$	−3597.60	−0.159292
$800$	791.367	0.0349738
$801$	−7409.59	−0.326848
$802$	−15794.0	−0.695394
$803$	0	0
$804$	2208.31	0.0968670
$805$	−3574.45	−0.156501
$806$	1750.54	0.0765013
$807$	6168.08	0.269054
$808$	5306.85	0.231057
$809$	−45008.7	−1.95602	−0.978011	−	0.208552i	$-0.933125\pi$
$809$	−45008.7	−1.95602	−0.978011	+	0.208552i	$0.933125\pi$
$810$	1094.13	0.0474616
$811$	26921.1	1.16563	0.582816	−	0.812604i	$-0.301951\pi$
$811$	26921.1	1.16563	0.582816	+	0.812604i	$0.301951\pi$
$812$	291.283	0.0125887
$813$	−19048.7	−0.821732
$814$	0	0
$815$	−4763.28	−0.204724
$816$	−6286.35	−0.269689
$817$	5297.46	0.226848
$818$	34265.2	1.46461
$819$	2428.30	0.103604
$820$	−35.8125	−0.00152516
$821$	−11197.0	−0.475976	−0.237988	−	0.971268i	$-0.576488\pi$
$821$	−11197.0	−0.475976	−0.237988	+	0.971268i	$0.576488\pi$
$822$	22429.1	0.951709
$823$	1247.54	0.0528392	0.0264196	−	0.999651i	$-0.491589\pi$
$823$	1247.54	0.0528392	0.0264196	+	0.999651i	$0.491589\pi$
$824$	23032.9	0.973774
$825$	0	0
$826$	20568.7	0.866436
$827$	11594.1	0.487504	0.243752	−	0.969838i	$-0.421622\pi$
$827$	11594.1	0.487504	0.243752	+	0.969838i	$0.421622\pi$
$828$	−446.710	−0.0187491
$829$	1658.14	0.0694689	0.0347344	−	0.999397i	$-0.488941\pi$
$829$	1658.14	0.0694689	0.0347344	+	0.999397i	$0.488941\pi$
$830$	−7236.91	−0.302647
$831$	15956.3	0.666087
$832$	−14650.6	−0.610479
$833$	−8718.91	−0.362656
$834$	2944.99	0.122274
$835$	10502.3	0.435265
$836$	0	0
$837$	−655.214	−0.0270580
$838$	18482.1	0.761880
$839$	−15906.9	−0.654549	−0.327275	−	0.944929i	$-0.606130\pi$
$839$	−15906.9	−0.654549	−0.327275	+	0.944929i	$0.606130\pi$
$840$	3563.09	0.146355
$841$	−22700.7	−0.930776
$842$	−4883.77	−0.199888
$843$	26194.0	1.07019
$844$	2686.68	0.109573
$845$	−7420.13	−0.302083
$846$	−2416.78	−0.0982159
$847$	0	0
$848$	26649.1	1.07917
$849$	−26698.3	−1.07925
$850$	2444.49	0.0986416
$851$	−25994.6	−1.04710
$852$	−554.996	−0.0223167
$853$	−9055.06	−0.363469	−0.181735	−	0.983348i	$-0.558171\pi$
$853$	−9055.06	−0.363469	−0.181735	+	0.983348i	$0.558171\pi$
$854$	11579.5	0.463985
$855$	2984.13	0.119363
$856$	−4371.53	−0.174551
$857$	−8173.52	−0.325790	−0.162895	−	0.986643i	$-0.552083\pi$
$857$	−8173.52	−0.325790	−0.162895	+	0.986643i	$0.552083\pi$
$858$	0	0
$859$	41286.0	1.63988	0.819941	−	0.572447i	$-0.194006\pi$
$859$	41286.0	1.63988	0.819941	+	0.572447i	$0.194006\pi$
$860$	−280.219	−0.0111109
$861$	−309.488	−0.0122501
$862$	4802.39	0.189757
$863$	18537.1	0.731182	0.365591	−	0.930776i	$-0.380867\pi$
$863$	18537.1	0.731182	0.365591	+	0.930776i	$0.380867\pi$
$864$	854.677	0.0336536
$865$	5201.09	0.204442
$866$	35064.6	1.37591
$867$	−10809.0	−0.423407
$868$	−172.032	−0.00672712
$869$	0	0
$870$	1665.07	0.0648864
$871$	28016.2	1.08989
$872$	133.187	0.00517235
$873$	1156.33	0.0448292
$874$	12674.7	0.490535
$875$	−1263.09	−0.0488001
$876$	247.406	0.00954232
$877$	−22220.2	−0.855558	−0.427779	−	0.903883i	$-0.640704\pi$
$877$	−22220.2	−0.855558	−0.427779	+	0.903883i	$0.640704\pi$
$878$	−12079.7	−0.464317
$879$	24215.8	0.929213
$880$	0	0
$881$	−50496.5	−1.93107	−0.965534	−	0.260275i	$-0.916187\pi$
$881$	−50496.5	−1.93107	−0.965534	+	0.260275i	$0.916187\pi$
$882$	−5857.14	−0.223606
$883$	22313.1	0.850391	0.425196	−	0.905102i	$-0.360205\pi$
$883$	22313.1	0.850391	0.425196	+	0.905102i	$0.360205\pi$
$884$	678.010	0.0257963
$885$	−11302.1	−0.429284
$886$	13821.2	0.524076
$887$	41393.3	1.56691	0.783456	−	0.621447i	$-0.213455\pi$
$887$	41393.3	1.56691	0.783456	+	0.621447i	$0.213455\pi$
$888$	25912.0	0.979221
$889$	1143.44	0.0431380
$890$	−11120.8	−0.418843
$891$	0	0
$892$	−2654.42	−0.0996373
$893$	−6591.52	−0.247006
$894$	1305.67	0.0488456
$895$	7854.64	0.293354
$896$	−12419.2	−0.463054
$897$	−5667.28	−0.210953
$898$	−15763.1	−0.585770
$899$	−997.116	−0.0369919
$900$	−157.851	−0.00584635
$901$	−16659.9	−0.616007
$902$	0	0
$903$	−2421.62	−0.0892430
$904$	−9763.05	−0.359197
$905$	14416.2	0.529516
$906$	−1428.19	−0.0523712
$907$	47821.8	1.75071	0.875356	−	0.483479i	$-0.160627\pi$
$907$	47821.8	1.75071	0.875356	+	0.483479i	$0.160627\pi$
$908$	−2319.13	−0.0847609
$909$	−2031.74	−0.0741347
$910$	3644.55	0.132765
$911$	32560.8	1.18418	0.592091	−	0.805871i	$-0.298303\pi$
$911$	32560.8	1.18418	0.592091	+	0.805871i	$0.298303\pi$
$912$	−11517.8	−0.418194
$913$	0	0
$914$	41684.7	1.50854
$915$	−6362.74	−0.229886
$916$	−1320.12	−0.0476180
$917$	9529.79	0.343186
$918$	2640.05	0.0949179
$919$	−13638.7	−0.489554	−0.244777	−	0.969579i	$-0.578715\pi$
$919$	−13638.7	−0.489554	−0.244777	+	0.969579i	$0.578715\pi$
$920$	−8315.70	−0.298001
$921$	8095.68	0.289643
$922$	−3209.23	−0.114632
$923$	−7041.08	−0.251094
$924$	0	0
$925$	−9185.59	−0.326508
$926$	10215.4	0.362526
$927$	−8818.18	−0.312435
$928$	1300.66	0.0460090
$929$	−17716.2	−0.625672	−0.312836	−	0.949807i	$-0.601279\pi$
$929$	−17716.2	−0.625672	−0.312836	+	0.949807i	$0.601279\pi$
$930$	−983.390	−0.0346738
$931$	−15974.7	−0.562354
$932$	4326.91	0.152074
$933$	−8867.29	−0.311149
$934$	1594.70	0.0558673
$935$	0	0
$936$	5649.26	0.197278
$937$	46320.5	1.61497	0.807483	−	0.589890i	$-0.200829\pi$
$937$	46320.5	1.61497	0.807483	+	0.589890i	$0.200829\pi$
$938$	28642.5	0.997025
$939$	−6373.19	−0.221492
$940$	348.671	0.0120983
$941$	7828.97	0.271219	0.135609	−	0.990762i	$-0.456701\pi$
$941$	7828.97	0.271219	0.135609	+	0.990762i	$0.456701\pi$
$942$	−1117.60	−0.0386553
$943$	722.297	0.0249430
$944$	43622.7	1.50402
$945$	−1364.13	−0.0469579
$946$	0	0
$947$	−23815.7	−0.817219	−0.408610	−	0.912709i	$-0.633986\pi$
$947$	−23815.7	−0.817219	−0.408610	+	0.912709i	$0.633986\pi$
$948$	1488.87	0.0510088
$949$	3138.77	0.107364
$950$	4478.79	0.152959
$951$	−7214.85	−0.246012
$952$	8597.43	0.292694
$953$	−2187.90	−0.0743685	−0.0371842	−	0.999308i	$-0.511839\pi$
$953$	−2187.90	−0.0743685	−0.0371842	+	0.999308i	$0.511839\pi$
$954$	−11191.7	−0.379817
$955$	−20884.7	−0.707658
$956$	−1806.16	−0.0611039
$957$	0	0
$958$	46092.6	1.55447
$959$	−27964.0	−0.941609
$960$	8230.19	0.276696
$961$	−29202.1	−0.980232
$962$	26504.4	0.888292
$963$	1673.65	0.0560047
$964$	789.343	0.0263724
$965$	6734.78	0.224664
$966$	−5793.96	−0.192979
$967$	14139.2	0.470201	0.235101	−	0.971971i	$-0.424458\pi$
$967$	14139.2	0.470201	0.235101	+	0.971971i	$0.424458\pi$
$968$	0	0
$969$	7200.46	0.238712
$970$	1735.50	0.0574470
$971$	−6358.97	−0.210164	−0.105082	−	0.994464i	$-0.533510\pi$
$971$	−6358.97	−0.210164	−0.105082	+	0.994464i	$0.533510\pi$
$972$	−170.480	−0.00562565
$973$	−3671.73	−0.120977
$974$	−33717.1	−1.10920
$975$	−2002.62	−0.0657796
$976$	24558.2	0.805419
$977$	46153.9	1.51136	0.755678	−	0.654944i	$-0.227308\pi$
$977$	46153.9	1.51136	0.755678	+	0.654944i	$0.227308\pi$
$978$	−7720.98	−0.252443
$979$	0	0
$980$	845.015	0.0275439
$981$	−50.9909	−0.00165955
$982$	33113.8	1.07607
$983$	20863.0	0.676935	0.338467	−	0.940978i	$-0.390091\pi$
$983$	20863.0	0.676935	0.338467	+	0.940978i	$0.390091\pi$
$984$	−720.000	−0.0233260
$985$	17440.0	0.564147
$986$	4017.68	0.129766
$987$	3013.17	0.0971735
$988$	1242.25	0.0400012
$989$	5651.69	0.181712
$990$	0	0
$991$	21394.4	0.685788	0.342894	−	0.939374i	$-0.388593\pi$
$991$	21394.4	0.685788	0.342894	+	0.939374i	$0.388593\pi$
$992$	−768.171	−0.0245861
$993$	−19126.5	−0.611240
$994$	−7198.47	−0.229700
$995$	−9845.76	−0.313700
$996$	1127.60	0.0358729
$997$	46133.4	1.46546	0.732728	−	0.680521i	$-0.238247\pi$
$997$	46133.4	1.46546	0.732728	+	0.680521i	$0.238247\pi$
$998$	7763.73	0.246249
$999$	−9920.43	−0.314183

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.70156 q^{2} +3.00000 q^{3} -0.701562 q^{4} +5.00000 q^{5} +8.10469 q^{6} -10.1047 q^{7} -23.5078 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.70156 q^{2} +3.00000 q^{3} -0.701562 q^{4} +5.00000 q^{5} +8.10469 q^{6} -10.1047 q^{7} -23.5078 q^{8} +9.00000 q^{9} +13.5078 q^{10} -2.10469 q^{12} -26.7016 q^{13} -27.2984 q^{14} +15.0000 q^{15} -57.8953 q^{16} +36.1938 q^{17} +24.3141 q^{18} +66.3141 q^{19} -3.50781 q^{20} -30.3141 q^{21} +70.7484 q^{23} -70.5234 q^{24} +25.0000 q^{25} -72.1359 q^{26} +27.0000 q^{27} +7.08907 q^{28} +41.0891 q^{29} +40.5234 q^{30} -24.2672 q^{31} +31.6547 q^{32} +97.7797 q^{34} -50.5234 q^{35} -6.31406 q^{36} -367.423 q^{37} +179.152 q^{38} -80.1047 q^{39} -117.539 q^{40} +10.2094 q^{41} -81.8953 q^{42} +79.8844 q^{43} +45.0000 q^{45} +191.131 q^{46} -99.3985 q^{47} -173.686 q^{48} -240.895 q^{49} +67.5391 q^{50} +108.581 q^{51} +18.7328 q^{52} -460.298 q^{53} +72.9422 q^{54} +237.539 q^{56} +198.942 q^{57} +111.005 q^{58} -753.475 q^{59} -10.5234 q^{60} -424.183 q^{61} -65.5593 q^{62} -90.9422 q^{63} +548.680 q^{64} -133.508 q^{65} -1049.23 q^{67} -25.3922 q^{68} +212.245 q^{69} -136.492 q^{70} +263.695 q^{71} -211.570 q^{72} -117.550 q^{73} -992.617 q^{74} +75.0000 q^{75} -46.5234 q^{76} -216.408 q^{78} -707.408 q^{79} -289.477 q^{80} +81.0000 q^{81} +27.5813 q^{82} -535.758 q^{83} +21.2672 q^{84} +180.969 q^{85} +215.813 q^{86} +123.267 q^{87} -823.287 q^{89} +121.570 q^{90} +269.811 q^{91} -49.6344 q^{92} -72.8016 q^{93} -268.531 q^{94} +331.570 q^{95} +94.9641 q^{96} +128.481 q^{97} -650.794 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 15 q^{8} + 18 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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