LMFDB - Embedded newform 1859.4.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.84193 q^{2} +8.79911 q^{3} +6.76044 q^{4} +17.0951 q^{5} -33.8056 q^{6} -10.3600 q^{7} +4.76230 q^{8} +50.4244 q^{9} +O(q^{10})$	\(q-3.84193 q^{2} +8.79911 q^{3} +6.76044 q^{4} +17.0951 q^{5} -33.8056 q^{6} -10.3600 q^{7} +4.76230 q^{8} +50.4244 q^{9} -65.6783 q^{10} +11.0000 q^{11} +59.4859 q^{12} +39.8025 q^{14} +150.422 q^{15} -72.3800 q^{16} -58.2591 q^{17} -193.727 q^{18} +45.1598 q^{19} +115.571 q^{20} -91.1591 q^{21} -42.2613 q^{22} -141.303 q^{23} +41.9041 q^{24} +167.243 q^{25} +206.114 q^{27} -70.0383 q^{28} +9.06810 q^{29} -577.911 q^{30} +234.539 q^{31} +239.980 q^{32} +96.7903 q^{33} +223.827 q^{34} -177.106 q^{35} +340.891 q^{36} -86.4659 q^{37} -173.501 q^{38} +81.4122 q^{40} -219.580 q^{41} +350.227 q^{42} +211.984 q^{43} +74.3648 q^{44} +862.012 q^{45} +542.878 q^{46} +477.830 q^{47} -636.880 q^{48} -235.670 q^{49} -642.537 q^{50} -512.628 q^{51} +575.189 q^{53} -791.876 q^{54} +188.046 q^{55} -49.3376 q^{56} +397.366 q^{57} -34.8390 q^{58} -252.681 q^{59} +1016.92 q^{60} -0.301006 q^{61} -901.084 q^{62} -522.398 q^{63} -342.949 q^{64} -371.862 q^{66} +862.823 q^{67} -393.857 q^{68} -1243.35 q^{69} +680.429 q^{70} +789.791 q^{71} +240.136 q^{72} -367.931 q^{73} +332.196 q^{74} +1471.59 q^{75} +305.300 q^{76} -113.960 q^{77} -681.873 q^{79} -1237.34 q^{80} +452.163 q^{81} +843.612 q^{82} +511.155 q^{83} -616.275 q^{84} -995.947 q^{85} -814.429 q^{86} +79.7913 q^{87} +52.3853 q^{88} +1181.53 q^{89} -3311.79 q^{90} -955.273 q^{92} +2063.74 q^{93} -1835.79 q^{94} +772.012 q^{95} +2111.62 q^{96} +1671.49 q^{97} +905.427 q^{98} +554.669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{2} + 12 q^{3} + 152 q^{4} + 40 q^{5} + 98 q^{6} + 56 q^{7} + 84 q^{8} + 360 q^{9}+O(q^{10}) $ 36 * q + 4 * q^2 + 12 * q^3 + 152 * q^4 + 40 * q^5 + 98 * q^6 + 56 * q^7 + 84 * q^8 + 360 * q^9	\( 36 q + 4 q^{2} + 12 q^{3} + 152 q^{4} + 40 q^{5} + 98 q^{6} + 56 q^{7} + 84 q^{8} + 360 q^{9} - 56 q^{10} + 396 q^{11} + 66 q^{12} + 164 q^{14} + 120 q^{15} + 644 q^{16} + 138 q^{17} - 28 q^{18} + 498 q^{19} + 320 q^{20} + 404 q^{21} + 44 q^{22} + 46 q^{23} + 1340 q^{24} + 818 q^{25} + 24 q^{27} + 1382 q^{28} + 262 q^{29} + 104 q^{30} + 660 q^{31} + 106 q^{32} + 132 q^{33} - 640 q^{34} + 68 q^{35} + 1960 q^{36} + 1372 q^{37} + 224 q^{38} + 108 q^{40} + 1216 q^{41} + 82 q^{42} + 436 q^{43} + 1672 q^{44} + 820 q^{45} + 2512 q^{46} - 140 q^{47} - 1944 q^{48} + 1192 q^{49} + 3484 q^{50} + 712 q^{51} + 146 q^{53} + 3078 q^{54} + 440 q^{55} - 102 q^{56} + 3656 q^{57} - 324 q^{58} + 404 q^{59} - 2944 q^{60} - 590 q^{61} + 1776 q^{62} + 4364 q^{63} + 2514 q^{64} + 1078 q^{66} + 2236 q^{67} - 1530 q^{68} + 12 q^{69} + 4852 q^{70} + 292 q^{71} + 2990 q^{72} + 1936 q^{73} + 1568 q^{74} + 4688 q^{75} + 7398 q^{76} + 616 q^{77} - 1464 q^{79} - 808 q^{80} + 3780 q^{81} - 4072 q^{82} + 4422 q^{83} - 2678 q^{84} + 3700 q^{85} - 2588 q^{86} - 1832 q^{87} + 924 q^{88} + 6856 q^{89} - 3422 q^{90} - 668 q^{92} + 840 q^{93} - 4166 q^{94} - 256 q^{95} + 18290 q^{96} + 2776 q^{97} + 4608 q^{98} + 3960 q^{99}+O(q^{100}) \) 36 * q + 4 * q^2 + 12 * q^3 + 152 * q^4 + 40 * q^5 + 98 * q^6 + 56 * q^7 + 84 * q^8 + 360 * q^9 - 56 * q^10 + 396 * q^11 + 66 * q^12 + 164 * q^14 + 120 * q^15 + 644 * q^16 + 138 * q^17 - 28 * q^18 + 498 * q^19 + 320 * q^20 + 404 * q^21 + 44 * q^22 + 46 * q^23 + 1340 * q^24 + 818 * q^25 + 24 * q^27 + 1382 * q^28 + 262 * q^29 + 104 * q^30 + 660 * q^31 + 106 * q^32 + 132 * q^33 - 640 * q^34 + 68 * q^35 + 1960 * q^36 + 1372 * q^37 + 224 * q^38 + 108 * q^40 + 1216 * q^41 + 82 * q^42 + 436 * q^43 + 1672 * q^44 + 820 * q^45 + 2512 * q^46 - 140 * q^47 - 1944 * q^48 + 1192 * q^49 + 3484 * q^50 + 712 * q^51 + 146 * q^53 + 3078 * q^54 + 440 * q^55 - 102 * q^56 + 3656 * q^57 - 324 * q^58 + 404 * q^59 - 2944 * q^60 - 590 * q^61 + 1776 * q^62 + 4364 * q^63 + 2514 * q^64 + 1078 * q^66 + 2236 * q^67 - 1530 * q^68 + 12 * q^69 + 4852 * q^70 + 292 * q^71 + 2990 * q^72 + 1936 * q^73 + 1568 * q^74 + 4688 * q^75 + 7398 * q^76 + 616 * q^77 - 1464 * q^79 - 808 * q^80 + 3780 * q^81 - 4072 * q^82 + 4422 * q^83 - 2678 * q^84 + 3700 * q^85 - 2588 * q^86 - 1832 * q^87 + 924 * q^88 + 6856 * q^89 - 3422 * q^90 - 668 * q^92 + 840 * q^93 - 4166 * q^94 - 256 * q^95 + 18290 * q^96 + 2776 * q^97 + 4608 * q^98 + 3960 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.84193	−1.35833	−0.679164	−	0.733987i	$-0.737658\pi$
$2$	−3.84193	−1.35833	−0.679164	+	0.733987i	$0.737658\pi$
$3$	8.79911	1.69339	0.846695	−	0.532078i	$-0.178589\pi$
$3$	8.79911	1.69339	0.846695	+	0.532078i	$0.178589\pi$
$4$	6.76044	0.845055
$5$	17.0951	1.52903	0.764517	−	0.644603i	$-0.222977\pi$
$5$	17.0951	1.52903	0.764517	+	0.644603i	$0.222977\pi$
$6$	−33.8056	−2.30018
$7$	−10.3600	−0.559389	−0.279694	−	0.960089i	$-0.590233\pi$
$7$	−10.3600	−0.559389	−0.279694	+	0.960089i	$0.590233\pi$
$8$	4.76230	0.210466
$9$	50.4244	1.86757
$10$	−65.6783	−2.07693
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	59.4859	1.43101
$13$	0	0
$13$	0	0
$14$	39.8025	0.759834
$15$	150.422	2.58925
$16$	−72.3800	−1.13094
$17$	−58.2591	−0.831171	−0.415585	−	0.909554i	$-0.636423\pi$
$17$	−58.2591	−0.831171	−0.415585	+	0.909554i	$0.636423\pi$
$18$	−193.727	−2.53677
$19$	45.1598	0.545282	0.272641	−	0.962116i	$-0.412103\pi$
$19$	45.1598	0.545282	0.272641	+	0.962116i	$0.412103\pi$
$20$	115.571	1.29212
$21$	−91.1591	−0.947264
$22$	−42.2613	−0.409551
$23$	−141.303	−1.28103	−0.640517	−	0.767944i	$-0.721280\pi$
$23$	−141.303	−1.28103	−0.640517	+	0.767944i	$0.721280\pi$
$24$	41.9041	0.356401
$25$	167.243	1.33795
$26$	0	0
$27$	206.114	1.46914
$28$	−70.0383	−0.472714
$29$	9.06810	0.0580657	0.0290328	−	0.999578i	$-0.490757\pi$
$29$	9.06810	0.0580657	0.0290328	+	0.999578i	$0.490757\pi$
$30$	−577.911	−3.51705
$31$	234.539	1.35885	0.679427	−	0.733743i	$-0.262228\pi$
$31$	234.539	1.35885	0.679427	+	0.733743i	$0.262228\pi$
$32$	239.980	1.32572
$33$	96.7903	0.510576
$34$	223.827	1.12900
$35$	−177.106	−0.855325
$36$	340.891	1.57820
$37$	−86.4659	−0.384186	−0.192093	−	0.981377i	$-0.561528\pi$
$37$	−86.4659	−0.384186	−0.192093	+	0.981377i	$0.561528\pi$
$38$	−173.501	−0.740672
$39$	0	0
$40$	81.4122	0.321810
$41$	−219.580	−0.836406	−0.418203	−	0.908354i	$-0.637340\pi$
$41$	−219.580	−0.836406	−0.418203	+	0.908354i	$0.637340\pi$
$42$	350.227	1.28669
$43$	211.984	0.751797	0.375899	−	0.926661i	$-0.377334\pi$
$43$	211.984	0.751797	0.375899	+	0.926661i	$0.377334\pi$
$44$	74.3648	0.254794
$45$	862.012	2.85558
$46$	542.878	1.74007
$47$	477.830	1.48295	0.741475	−	0.670981i	$-0.234127\pi$
$47$	477.830	1.48295	0.741475	+	0.670981i	$0.234127\pi$
$48$	−636.880	−1.91512
$49$	−235.670	−0.687084
$50$	−642.537	−1.81737
$51$	−512.628	−1.40750
$52$	0	0
$53$	575.189	1.49072	0.745361	−	0.666661i	$-0.232277\pi$
$53$	575.189	1.49072	0.745361	+	0.666661i	$0.232277\pi$
$54$	−791.876	−1.99557
$55$	188.046	0.461021
$56$	−49.3376	−0.117732
$57$	397.366	0.923376
$58$	−34.8390	−0.0788722
$59$	−252.681	−0.557563	−0.278782	−	0.960354i	$-0.589931\pi$
$59$	−252.681	−0.557563	−0.278782	+	0.960354i	$0.589931\pi$
$60$	1016.92	2.18806
$61$	−0.301006	−0.000631801 0	−0.000315901	−	1.00000i	$-0.500101\pi$
$61$	−0.301006	−0.000631801 0	−0.000315901		1.00000i	$0.500101\pi$
$62$	−901.084	−1.84577
$63$	−522.398	−1.04470
$64$	−342.949	−0.669822
$65$	0	0
$66$	−371.862	−0.693530
$67$	862.823	1.57329	0.786646	−	0.617404i	$-0.211816\pi$
$67$	862.823	1.57329	0.786646	+	0.617404i	$0.211816\pi$
$68$	−393.857	−0.702385
$69$	−1243.35	−2.16929
$70$	680.429	1.16181
$71$	789.791	1.32015	0.660077	−	0.751198i	$-0.270524\pi$
$71$	789.791	1.32015	0.660077	+	0.751198i	$0.270524\pi$
$72$	240.136	0.393060
$73$	−367.931	−0.589905	−0.294953	−	0.955512i	$-0.595304\pi$
$73$	−367.931	−0.589905	−0.294953	+	0.955512i	$0.595304\pi$
$74$	332.196	0.521851
$75$	1471.59	2.26567
$76$	305.300	0.460793
$77$	−113.960	−0.168662
$78$	0	0
$79$	−681.873	−0.971097	−0.485549	−	0.874210i	$-0.661380\pi$
$79$	−681.873	−0.971097	−0.485549	+	0.874210i	$0.661380\pi$
$80$	−1237.34	−1.72924
$81$	452.163	0.620250
$82$	843.612	1.13611
$83$	511.155	0.675983	0.337991	−	0.941149i	$-0.390253\pi$
$83$	511.155	0.675983	0.337991	+	0.941149i	$0.390253\pi$
$84$	−616.275	−0.800490
$85$	−995.947	−1.27089
$86$	−814.429	−1.02119
$87$	79.7913	0.0983278
$88$	52.3853	0.0634579
$89$	1181.53	1.40722	0.703609	−	0.710587i	$-0.251571\pi$
$89$	1181.53	1.40722	0.703609	+	0.710587i	$0.251571\pi$
$90$	−3311.79	−3.87882
$91$	0	0
$92$	−955.273	−1.08254
$93$	2063.74	2.30107
$94$	−1835.79	−2.01433
$95$	772.012	0.833755
$96$	2111.62	2.24496
$97$	1671.49	1.74963	0.874813	−	0.484461i	$-0.160984\pi$
$97$	1671.49	1.74963	0.874813	+	0.484461i	$0.160984\pi$
$98$	905.427	0.933286
$99$	554.669	0.563094
$100$	1130.64	1.13064
$101$	1753.65	1.72767	0.863833	−	0.503779i	$-0.168057\pi$
$101$	1753.65	1.72767	0.863833	+	0.503779i	$0.168057\pi$
$102$	1969.48	1.91184
$103$	1564.67	1.49681	0.748406	−	0.663241i	$-0.230819\pi$
$103$	1564.67	1.49681	0.748406	+	0.663241i	$0.230819\pi$
$104$	0	0
$105$	−1558.38	−1.44840
$106$	−2209.84	−2.02489
$107$	1894.91	1.71203	0.856017	−	0.516948i	$-0.172932\pi$
$107$	1894.91	1.71203	0.856017	+	0.516948i	$0.172932\pi$
$108$	1393.42	1.24150
$109$	−639.509	−0.561962	−0.280981	−	0.959713i	$-0.590660\pi$
$109$	−639.509	−0.561962	−0.280981	+	0.959713i	$0.590660\pi$
$110$	−722.461	−0.626218
$111$	−760.823	−0.650578
$112$	749.858	0.632634
$113$	865.856	0.720822	0.360411	−	0.932794i	$-0.382636\pi$
$113$	865.856	0.720822	0.360411	+	0.932794i	$0.382636\pi$
$114$	−1526.65	−1.25425
$115$	−2415.60	−1.95875
$116$	61.3044	0.0490687
$117$	0	0
$118$	970.783	0.757354
$119$	603.566	0.464948
$120$	716.355	0.544950
$121$	121.000	0.0909091
$122$	1.15644	0.000858193 0
$123$	−1932.11	−1.41636
$124$	1585.59	1.14831
$125$	722.155	0.516732
$126$	2007.02	1.41904
$127$	−2497.90	−1.74530	−0.872650	−	0.488347i	$-0.837600\pi$
$127$	−2497.90	−1.74530	−0.872650	+	0.488347i	$0.837600\pi$
$128$	−602.258	−0.415879
$129$	1865.27	1.27309
$130$	0	0
$131$	2144.18	1.43006	0.715029	−	0.699095i	$-0.246414\pi$
$131$	2144.18	1.43006	0.715029	+	0.699095i	$0.246414\pi$
$132$	654.345	0.431465
$133$	−467.856	−0.305025
$134$	−3314.91	−2.13705
$135$	3523.55	2.24636
$136$	−277.448	−0.174933
$137$	−1952.85	−1.21784	−0.608918	−	0.793233i	$-0.708396\pi$
$137$	−1952.85	−1.21784	−0.608918	+	0.793233i	$0.708396\pi$
$138$	4776.85	2.94661
$139$	−486.491	−0.296861	−0.148430	−	0.988923i	$-0.547422\pi$
$139$	−486.491	−0.296861	−0.148430	+	0.988923i	$0.547422\pi$
$140$	−1197.31	−0.722797
$141$	4204.48	2.51121
$142$	−3034.32	−1.79320
$143$	0	0
$144$	−3649.72	−2.11211
$145$	155.020	0.0887844
$146$	1413.57	0.801285
$147$	−2073.69	−1.16350
$148$	−584.547	−0.324659
$149$	1546.08	0.850066	0.425033	−	0.905178i	$-0.360263\pi$
$149$	1546.08	0.850066	0.425033	+	0.905178i	$0.360263\pi$
$150$	−5653.76	−3.07752
$151$	2742.11	1.47781	0.738907	−	0.673808i	$-0.235342\pi$
$151$	2742.11	1.47781	0.738907	+	0.673808i	$0.235342\pi$
$152$	215.065	0.114763
$153$	−2937.68	−1.55227
$154$	437.828	0.229098
$155$	4009.48	2.07774
$156$	0	0
$157$	−542.648	−0.275847	−0.137924	−	0.990443i	$-0.544043\pi$
$157$	−542.648	−0.275847	−0.137924	+	0.990443i	$0.544043\pi$
$158$	2619.71	1.31907
$159$	5061.15	2.52437
$160$	4102.50	2.02707
$161$	1463.91	0.716597
$162$	−1737.18	−0.842503
$163$	−479.016	−0.230180	−0.115090	−	0.993355i	$-0.536716\pi$
$163$	−479.016	−0.230180	−0.115090	+	0.993355i	$0.536716\pi$
$164$	−1484.46	−0.706809
$165$	1654.64	0.780689
$166$	−1963.82	−0.918207
$167$	1732.95	0.802993	0.401496	−	0.915861i	$-0.368490\pi$
$167$	1732.95	0.802993	0.401496	+	0.915861i	$0.368490\pi$
$168$	−434.127	−0.199367
$169$	0	0
$170$	3826.36	1.72628
$171$	2277.16	1.01835
$172$	1433.11	0.635310
$173$	−3660.66	−1.60876	−0.804378	−	0.594118i	$-0.797501\pi$
$173$	−3660.66	−1.60876	−0.804378	+	0.594118i	$0.797501\pi$
$174$	−306.553	−0.133561
$175$	−1732.65	−0.748433
$176$	−796.180	−0.340990
$177$	−2223.37	−0.944173
$178$	−4539.38	−1.91146
$179$	1698.30	0.709144	0.354572	−	0.935029i	$-0.384627\pi$
$179$	1698.30	0.709144	0.354572	+	0.935029i	$0.384627\pi$
$180$	5827.58	2.41312
$181$	−1993.50	−0.818649	−0.409325	−	0.912389i	$-0.634236\pi$
$181$	−1993.50	−0.818649	−0.409325	+	0.912389i	$0.634236\pi$
$182$	0	0
$183$	−2.64859	−0.00106989
$184$	−672.930	−0.269614
$185$	−1478.14	−0.587434
$186$	−7928.74	−3.12561
$187$	−640.850	−0.250607
$188$	3230.34	1.25317
$189$	−2135.35	−0.821819
$190$	−2966.02	−1.13251
$191$	−990.916	−0.375394	−0.187697	−	0.982227i	$-0.560102\pi$
$191$	−990.916	−0.375394	−0.187697	+	0.982227i	$0.560102\pi$
$192$	−3017.65	−1.13427
$193$	−406.422	−0.151580	−0.0757899	−	0.997124i	$-0.524148\pi$
$193$	−406.422	−0.151580	−0.0757899	+	0.997124i	$0.524148\pi$
$194$	−6421.73	−2.37656
$195$	0	0
$196$	−1593.23	−0.580624
$197$	−3124.56	−1.13003	−0.565014	−	0.825081i	$-0.691129\pi$
$197$	−3124.56	−1.13003	−0.565014	+	0.825081i	$0.691129\pi$
$198$	−2131.00	−0.764866
$199$	−1246.81	−0.444140	−0.222070	−	0.975031i	$-0.571281\pi$
$199$	−1246.81	−0.444140	−0.222070	+	0.975031i	$0.571281\pi$
$200$	796.464	0.281592
$201$	7592.08	2.66420
$202$	−6737.38	−2.34674
$203$	−93.9458	−0.0324813
$204$	−3465.59	−1.18941
$205$	−3753.75	−1.27889
$206$	−6011.36	−2.03316
$207$	−7125.14	−2.39242
$208$	0	0
$209$	496.757	0.164409
$210$	5987.17	1.96740
$211$	1847.90	0.602914	0.301457	−	0.953480i	$-0.402527\pi$
$211$	1847.90	0.602914	0.301457	+	0.953480i	$0.402527\pi$
$212$	3888.53	1.25974
$213$	6949.46	2.23554
$214$	−7280.10	−2.32550
$215$	3623.90	1.14952
$216$	981.578	0.309203
$217$	−2429.83	−0.760128
$218$	2456.95	0.763329
$219$	−3237.47	−0.998940
$220$	1271.28	0.389588
$221$	0	0
$222$	2923.03	0.883698
$223$	−754.954	−0.226706	−0.113353	−	0.993555i	$-0.536159\pi$
$223$	−754.954	−0.226706	−0.113353	+	0.993555i	$0.536159\pi$
$224$	−2486.20	−0.741592
$225$	8433.15	2.49871
$226$	−3326.56	−0.979113
$227$	−4976.76	−1.45515	−0.727575	−	0.686028i	$-0.759353\pi$
$227$	−4976.76	−1.45515	−0.727575	+	0.686028i	$0.759353\pi$
$228$	2686.37	0.780303
$229$	889.436	0.256662	0.128331	−	0.991731i	$-0.459038\pi$
$229$	889.436	0.256662	0.128331	+	0.991731i	$0.459038\pi$
$230$	9280.57	2.66062
$231$	−1002.75	−0.285611
$232$	43.1851	0.0122209
$233$	−3310.07	−0.930687	−0.465343	−	0.885130i	$-0.654069\pi$
$233$	−3310.07	−0.930687	−0.465343	+	0.885130i	$0.654069\pi$
$234$	0	0
$235$	8168.56	2.26748
$236$	−1708.23	−0.471172
$237$	−5999.88	−1.64445
$238$	−2318.86	−0.631552
$239$	−5416.15	−1.46586	−0.732932	−	0.680302i	$-0.761849\pi$
$239$	−5416.15	−1.46586	−0.732932	+	0.680302i	$0.761849\pi$
$240$	−10887.5	−2.92828
$241$	−2041.12	−0.545561	−0.272781	−	0.962076i	$-0.587943\pi$
$241$	−2041.12	−0.545561	−0.272781	+	0.962076i	$0.587943\pi$
$242$	−464.874	−0.123484
$243$	−1586.45	−0.418810
$244$	−2.03493	−0.000533907 0
$245$	−4028.81	−1.05058
$246$	7423.04	1.92388
$247$	0	0
$248$	1116.95	0.285993
$249$	4497.71	1.14470
$250$	−2774.47	−0.701892
$251$	−2921.21	−0.734603	−0.367301	−	0.930102i	$-0.619718\pi$
$251$	−2921.21	−0.734603	−0.367301	+	0.930102i	$0.619718\pi$
$252$	−3531.64	−0.882828
$253$	−1554.34	−0.386247
$254$	9596.77	2.37069
$255$	−8763.45	−2.15211
$256$	5057.42	1.23472
$257$	178.594	0.0433477	0.0216739	−	0.999765i	$-0.493100\pi$
$257$	178.594	0.0433477	0.0216739	+	0.999765i	$0.493100\pi$
$258$	−7166.25	−1.72927
$259$	895.789	0.214910
$260$	0	0
$261$	457.254	0.108442
$262$	−8237.78	−1.94249
$263$	−5629.40	−1.31986	−0.659931	−	0.751327i	$-0.729414\pi$
$263$	−5629.40	−1.31986	−0.659931	+	0.751327i	$0.729414\pi$
$264$	460.945	0.107459
$265$	9832.93	2.27937
$266$	1797.47	0.414324
$267$	10396.5	2.38297
$268$	5833.06	1.32952
$269$	−2981.32	−0.675741	−0.337871	−	0.941193i	$-0.609707\pi$
$269$	−2981.32	−0.675741	−0.337871	+	0.941193i	$0.609707\pi$
$270$	−13537.2	−3.05129
$271$	−2546.63	−0.570836	−0.285418	−	0.958403i	$-0.592132\pi$
$271$	−2546.63	−0.570836	−0.285418	+	0.958403i	$0.592132\pi$
$272$	4216.79	0.940002
$273$	0	0
$274$	7502.73	1.65422
$275$	1839.68	0.403406
$276$	−8405.56	−1.83317
$277$	2203.41	0.477943	0.238971	−	0.971027i	$-0.423190\pi$
$277$	2203.41	0.477943	0.238971	+	0.971027i	$0.423190\pi$
$278$	1869.06	0.403234
$279$	11826.5	2.53776
$280$	−843.433	−0.180017
$281$	−1100.32	−0.233593	−0.116797	−	0.993156i	$-0.537263\pi$
$281$	−1100.32	−0.233593	−0.116797	+	0.993156i	$0.537263\pi$
$282$	−16153.3	−3.41105
$283$	1944.27	0.408391	0.204196	−	0.978930i	$-0.434542\pi$
$283$	1944.27	0.408391	0.204196	+	0.978930i	$0.434542\pi$
$284$	5339.34	1.11560
$285$	6793.02	1.41187
$286$	0	0
$287$	2274.86	0.467876
$288$	12100.9	2.47587
$289$	−1518.88	−0.309155
$290$	−595.578	−0.120598
$291$	14707.6	2.96280
$292$	−2487.38	−0.498502
$293$	6441.80	1.28442	0.642208	−	0.766530i	$-0.278018\pi$
$293$	6441.80	1.28442	0.642208	+	0.766530i	$0.278018\pi$
$294$	7966.96	1.58042
$295$	−4319.61	−0.852534
$296$	−411.777	−0.0808582
$297$	2267.26	0.442961
$298$	−5939.93	−1.15467
$299$	0	0
$300$	9948.62	1.91461
$301$	−2196.16	−0.420547
$302$	−10535.0	−2.00736
$303$	15430.5	2.92561
$304$	−3268.66	−0.616680
$305$	−5.14574	−0.000966046 0
$306$	11286.4	2.10849
$307$	−1494.25	−0.277790	−0.138895	−	0.990307i	$-0.544355\pi$
$307$	−1494.25	−0.277790	−0.138895	+	0.990307i	$0.544355\pi$
$308$	−770.422	−0.142529
$309$	13767.7	2.53469
$310$	−15404.1	−2.82225
$311$	10501.1	1.91467	0.957337	−	0.288974i	$-0.0933142\pi$
$311$	10501.1	1.91467	0.957337	+	0.288974i	$0.0933142\pi$
$312$	0	0
$313$	−2436.03	−0.439912	−0.219956	−	0.975510i	$-0.570591\pi$
$313$	−2436.03	−0.439912	−0.219956	+	0.975510i	$0.570591\pi$
$314$	2084.82	0.374691
$315$	−8930.47	−1.59738
$316$	−4609.76	−0.820631
$317$	−8684.65	−1.53873	−0.769367	−	0.638807i	$-0.779428\pi$
$317$	−8684.65	−1.53873	−0.769367	+	0.638807i	$0.779428\pi$
$318$	−19444.6	−3.42893
$319$	99.7491	0.0175075
$320$	−5862.75	−1.02418
$321$	16673.5	2.89914
$322$	−5624.23	−0.973373
$323$	−2630.97	−0.453223
$324$	3056.82	0.524146
$325$	0	0
$326$	1840.35	0.312661
$327$	−5627.12	−0.951622
$328$	−1045.71	−0.176035
$329$	−4950.33	−0.829546
$330$	−6357.02	−1.06043
$331$	−4350.00	−0.722349	−0.361175	−	0.932498i	$-0.617624\pi$
$331$	−4350.00	−0.722349	−0.361175	+	0.932498i	$0.617624\pi$
$332$	3455.63	0.571243
$333$	−4359.99	−0.717496
$334$	−6657.88	−1.09073
$335$	14750.1	2.40562
$336$	6598.09	1.07130
$337$	−2231.42	−0.360693	−0.180346	−	0.983603i	$-0.557722\pi$
$337$	−2231.42	−0.360693	−0.180346	+	0.983603i	$0.557722\pi$
$338$	0	0
$339$	7618.77	1.22063
$340$	−6733.04	−1.07397
$341$	2579.93	0.409710
$342$	−8748.67	−1.38326
$343$	5995.04	0.943736
$344$	1009.53	0.158228
$345$	−21255.1	−3.31692
$346$	14064.0	2.18522
$347$	448.745	0.0694234	0.0347117	−	0.999397i	$-0.488949\pi$
$347$	448.745	0.0694234	0.0347117	+	0.999397i	$0.488949\pi$
$348$	539.424	0.0830924
$349$	4239.52	0.650248	0.325124	−	0.945671i	$-0.394594\pi$
$349$	4239.52	0.650248	0.325124	+	0.945671i	$0.394594\pi$
$350$	6656.71	1.01662
$351$	0	0
$352$	2639.79	0.399719
$353$	6580.07	0.992129	0.496065	−	0.868286i	$-0.334778\pi$
$353$	6580.07	0.992129	0.496065	+	0.868286i	$0.334778\pi$
$354$	8542.03	1.28250
$355$	13501.6	2.01856
$356$	7987.70	1.18918
$357$	5310.84	0.787338
$358$	−6524.74	−0.963250
$359$	−6599.99	−0.970290	−0.485145	−	0.874434i	$-0.661233\pi$
$359$	−6599.99	−0.970290	−0.485145	+	0.874434i	$0.661233\pi$
$360$	4105.16	0.601003
$361$	−4819.60	−0.702667
$362$	7658.88	1.11199
$363$	1064.69	0.153945
$364$	0	0
$365$	−6289.83	−0.901985
$366$	10.1757	0.00145326
$367$	165.979	0.0236077	0.0118039	−	0.999930i	$-0.496243\pi$
$367$	165.979	0.0236077	0.0118039	+	0.999930i	$0.496243\pi$
$368$	10227.5	1.44877
$369$	−11072.2	−1.56205
$370$	5678.93	0.797929
$371$	−5958.97	−0.833893
$372$	13951.8	1.94453
$373$	7075.45	0.982179	0.491089	−	0.871109i	$-0.336599\pi$
$373$	7075.45	0.982179	0.491089	+	0.871109i	$0.336599\pi$
$374$	2462.10	0.340407
$375$	6354.33	0.875029
$376$	2275.57	0.312111
$377$	0	0
$378$	8203.86	1.11630
$379$	4485.41	0.607915	0.303958	−	0.952686i	$-0.401692\pi$
$379$	4485.41	0.607915	0.303958	+	0.952686i	$0.401692\pi$
$380$	5219.14	0.704569
$381$	−21979.3	−2.95547
$382$	3807.03	0.509908
$383$	−9405.78	−1.25486	−0.627432	−	0.778671i	$-0.715894\pi$
$383$	−9405.78	−1.25486	−0.627432	+	0.778671i	$0.715894\pi$
$384$	−5299.33	−0.704246
$385$	−1948.17	−0.257890
$386$	1561.45	0.205895
$387$	10689.2	1.40403
$388$	11300.0	1.47853
$389$	693.715	0.0904184	0.0452092	−	0.998978i	$-0.485605\pi$
$389$	693.715	0.0904184	0.0452092	+	0.998978i	$0.485605\pi$
$390$	0	0
$391$	8232.21	1.06476
$392$	−1122.33	−0.144608
$393$	18866.9	2.42165
$394$	12004.3	1.53495
$395$	−11656.7	−1.48484
$396$	3749.80	0.475845
$397$	3002.55	0.379581	0.189791	−	0.981825i	$-0.439219\pi$
$397$	3002.55	0.379581	0.189791	+	0.981825i	$0.439219\pi$
$398$	4790.15	0.603288
$399$	−4116.72	−0.516526
$400$	−12105.1	−1.51313
$401$	−5139.69	−0.640060	−0.320030	−	0.947407i	$-0.603693\pi$
$401$	−5139.69	−0.640060	−0.320030	+	0.947407i	$0.603693\pi$
$402$	−29168.2	−3.61885
$403$	0	0
$404$	11855.4	1.45997
$405$	7729.78	0.948384
$406$	360.933	0.0441202
$407$	−951.124	−0.115837
$408$	−2441.29	−0.296230
$409$	−5972.85	−0.722099	−0.361050	−	0.932547i	$-0.617581\pi$
$409$	−5972.85	−0.722099	−0.361050	+	0.932547i	$0.617581\pi$
$410$	14421.7	1.73716
$411$	−17183.4	−2.06227
$412$	10577.9	1.26489
$413$	2617.78	0.311895
$414$	27374.3	3.24970
$415$	8738.26	1.03360
$416$	0	0
$417$	−4280.69	−0.502701
$418$	−1908.51	−0.223321
$419$	−5663.34	−0.660316	−0.330158	−	0.943926i	$-0.607102\pi$
$419$	−5663.34	−0.660316	−0.330158	+	0.943926i	$0.607102\pi$
$420$	−10535.3	−1.22398
$421$	−3837.92	−0.444297	−0.222148	−	0.975013i	$-0.571307\pi$
$421$	−3837.92	−0.444297	−0.222148	+	0.975013i	$0.571307\pi$
$422$	−7099.51	−0.818955
$423$	24094.3	2.76951
$424$	2739.22	0.313746
$425$	−9743.45	−1.11206
$426$	−26699.4	−3.03659
$427$	3.11843	0.000353423 0
$428$	12810.4	1.44676
$429$	0	0
$430$	−13922.8	−1.56143
$431$	−2386.48	−0.266711	−0.133356	−	0.991068i	$-0.542575\pi$
$431$	−2386.48	−0.266711	−0.133356	+	0.991068i	$0.542575\pi$
$432$	−14918.5	−1.66150
$433$	−3054.98	−0.339060	−0.169530	−	0.985525i	$-0.554225\pi$
$433$	−3054.98	−0.339060	−0.169530	+	0.985525i	$0.554225\pi$
$434$	9335.25	1.03250
$435$	1364.04	0.150347
$436$	−4323.37	−0.474889
$437$	−6381.23	−0.698526
$438$	12438.1	1.35689
$439$	−882.767	−0.0959730	−0.0479865	−	0.998848i	$-0.515280\pi$
$439$	−882.767	−0.0959730	−0.0479865	+	0.998848i	$0.515280\pi$
$440$	895.534	0.0970293
$441$	−11883.5	−1.28318
$442$	0	0
$443$	5197.06	0.557381	0.278691	−	0.960381i	$-0.410100\pi$
$443$	5197.06	0.557381	0.278691	+	0.960381i	$0.410100\pi$
$444$	−5143.50	−0.549774
$445$	20198.5	2.15169
$446$	2900.48	0.307941
$447$	13604.1	1.43949
$448$	3552.96	0.374691
$449$	8429.65	0.886013	0.443006	−	0.896518i	$-0.353912\pi$
$449$	8429.65	0.886013	0.443006	+	0.896518i	$0.353912\pi$
$450$	−32399.6	−3.39407
$451$	−2415.38	−0.252186
$452$	5853.57	0.609134
$453$	24128.2	2.50252
$454$	19120.4	1.97657
$455$	0	0
$456$	1892.38	0.194339
$457$	17378.3	1.77882	0.889410	−	0.457110i	$-0.151116\pi$
$457$	17378.3	1.77882	0.889410	+	0.457110i	$0.151116\pi$
$458$	−3417.15	−0.348631
$459$	−12008.0	−1.22110
$460$	−16330.5	−1.65525
$461$	−9466.64	−0.956411	−0.478206	−	0.878248i	$-0.658713\pi$
$461$	−9466.64	−0.956411	−0.478206	+	0.878248i	$0.658713\pi$
$462$	3852.50	0.387953
$463$	10717.2	1.07574	0.537871	−	0.843027i	$-0.319229\pi$
$463$	10717.2	1.07574	0.537871	+	0.843027i	$0.319229\pi$
$464$	−656.349	−0.0656686
$465$	35279.9	3.51842
$466$	12717.1	1.26418
$467$	−4227.22	−0.418870	−0.209435	−	0.977823i	$-0.567163\pi$
$467$	−4227.22	−0.418870	−0.209435	+	0.977823i	$0.567163\pi$
$468$	0	0
$469$	−8938.87	−0.880082
$470$	−31383.1	−3.07998
$471$	−4774.82	−0.467117
$472$	−1203.34	−0.117348
$473$	2331.83	0.226675
$474$	23051.1	2.23370
$475$	7552.67	0.729559
$476$	4080.37	0.392906
$477$	29003.6	2.78403
$478$	20808.5	1.99112
$479$	2199.03	0.209763	0.104881	−	0.994485i	$-0.466554\pi$
$479$	2199.03	0.209763	0.104881	+	0.994485i	$0.466554\pi$
$480$	36098.3	3.43262
$481$	0	0
$482$	7841.85	0.741051
$483$	12881.1	1.21348
$484$	818.013	0.0768232
$485$	28574.3	2.67524
$486$	6095.04	0.568882
$487$	−18020.8	−1.67679	−0.838397	−	0.545060i	$-0.816507\pi$
$487$	−18020.8	−1.67679	−0.838397	+	0.545060i	$0.816507\pi$
$488$	−1.43348	−0.000132973 0
$489$	−4214.92	−0.389785
$490$	15478.4	1.42703
$491$	14260.1	1.31069	0.655345	−	0.755330i	$-0.272523\pi$
$491$	14260.1	1.31069	0.655345	+	0.755330i	$0.272523\pi$
$492$	−13061.9	−1.19690
$493$	−528.299	−0.0482625
$494$	0	0
$495$	9482.13	0.860990
$496$	−16975.9	−1.53678
$497$	−8182.26	−0.738480
$498$	−17279.9	−1.55488
$499$	−8958.99	−0.803727	−0.401863	−	0.915700i	$-0.631637\pi$
$499$	−8958.99	−0.803727	−0.401863	+	0.915700i	$0.631637\pi$
$500$	4882.09	0.436667
$501$	15248.4	1.35978
$502$	11223.1	0.997831
$503$	6801.88	0.602944	0.301472	−	0.953475i	$-0.402522\pi$
$503$	6801.88	0.602944	0.301472	+	0.953475i	$0.402522\pi$
$504$	−2487.82	−0.219874
$505$	29978.8	2.64166
$506$	5971.66	0.524650
$507$	0	0
$508$	−16886.9	−1.47487
$509$	−445.479	−0.0387927	−0.0193964	−	0.999812i	$-0.506174\pi$
$509$	−445.479	−0.0387927	−0.0193964	+	0.999812i	$0.506174\pi$
$510$	33668.6	2.92327
$511$	3811.78	0.329986
$512$	−14612.2	−1.26128
$513$	9308.07	0.801094
$514$	−686.145	−0.0588804
$515$	26748.3	2.28868
$516$	12610.1	1.07583
$517$	5256.13	0.447126
$518$	−3441.56	−0.291918
$519$	−32210.6	−2.72425
$520$	0	0
$521$	3283.84	0.276138	0.138069	−	0.990423i	$-0.455910\pi$
$521$	3283.84	0.276138	0.138069	+	0.990423i	$0.455910\pi$
$522$	−1756.74	−0.147299
$523$	−14926.7	−1.24799	−0.623996	−	0.781427i	$-0.714492\pi$
$523$	−14926.7	−1.24799	−0.623996	+	0.781427i	$0.714492\pi$
$524$	14495.6	1.20848
$525$	−15245.7	−1.26739
$526$	21627.8	1.79280
$527$	−13664.0	−1.12944
$528$	−7005.68	−0.577430
$529$	7799.66	0.641050
$530$	−37777.4	−3.09613
$531$	−12741.3	−1.04129
$532$	−3162.92	−0.257763
$533$	0	0
$534$	−39942.5	−3.23686
$535$	32393.7	2.61776
$536$	4109.02	0.331125
$537$	14943.5	1.20086
$538$	11454.0	0.917878
$539$	−2592.37	−0.207164
$540$	23820.7	1.89830
$541$	24978.7	1.98506	0.992531	−	0.121994i	$-0.0389289\pi$
$541$	24978.7	1.98506	0.992531	+	0.121994i	$0.0389289\pi$
$542$	9783.96	0.775382
$543$	−17541.0	−1.38629
$544$	−13981.0	−1.10190
$545$	−10932.5	−0.859260
$546$	0	0
$547$	−3154.72	−0.246592	−0.123296	−	0.992370i	$-0.539347\pi$
$547$	−3154.72	−0.246592	−0.123296	+	0.992370i	$0.539347\pi$
$548$	−13202.2	−1.02914
$549$	−15.1781	−0.00117993
$550$	−7067.91	−0.547958
$551$	409.513	0.0316622
$552$	−5921.19	−0.456562
$553$	7064.22	0.543221
$554$	−8465.35	−0.649203
$555$	−13006.4	−0.994756
$556$	−3288.89	−0.250864
$557$	7091.87	0.539483	0.269742	−	0.962933i	$-0.413062\pi$
$557$	7091.87	0.539483	0.269742	+	0.962933i	$0.413062\pi$
$558$	−45436.6	−3.44711
$559$	0	0
$560$	12818.9	0.967319
$561$	−5638.91	−0.424376
$562$	4227.36	0.317296
$563$	248.292	0.0185866	0.00929331	−	0.999957i	$-0.497042\pi$
$563$	248.292	0.0185866	0.00929331	+	0.999957i	$0.497042\pi$
$564$	28424.1	2.12211
$565$	14801.9	1.10216
$566$	−7469.75	−0.554729
$567$	−4684.42	−0.346961
$568$	3761.23	0.277848
$569$	21642.6	1.59456	0.797279	−	0.603611i	$-0.206272\pi$
$569$	21642.6	1.59456	0.797279	+	0.603611i	$0.206272\pi$
$570$	−26098.3	−1.91779
$571$	6397.75	0.468892	0.234446	−	0.972129i	$-0.424672\pi$
$571$	6397.75	0.468892	0.234446	+	0.972129i	$0.424672\pi$
$572$	0	0
$573$	−8719.18	−0.635688
$574$	−8739.84	−0.635530
$575$	−23632.1	−1.71396
$576$	−17293.0	−1.25094
$577$	2877.93	0.207643	0.103821	−	0.994596i	$-0.466893\pi$
$577$	2877.93	0.207643	0.103821	+	0.994596i	$0.466893\pi$
$578$	5835.43	0.419934
$579$	−3576.15	−0.256684
$580$	1048.01	0.0750277
$581$	−5295.58	−0.378137
$582$	−56505.6	−4.02445
$583$	6327.08	0.449470
$584$	−1752.20	−0.124155
$585$	0	0
$586$	−24749.0	−1.74466
$587$	−17888.8	−1.25783	−0.628917	−	0.777473i	$-0.716501\pi$
$587$	−17888.8	−1.25783	−0.628917	+	0.777473i	$0.716501\pi$
$588$	−14019.0	−0.983223
$589$	10591.7	0.740959
$590$	16595.6	1.15802
$591$	−27493.4	−1.91358
$592$	6258.40	0.434491
$593$	−4674.75	−0.323725	−0.161863	−	0.986813i	$-0.551750\pi$
$593$	−4674.75	−0.323725	−0.161863	+	0.986813i	$0.551750\pi$
$594$	−8710.64	−0.601687
$595$	10318.0	0.710921
$596$	10452.2	0.718352
$597$	−10970.8	−0.752103
$598$	0	0
$599$	−24797.7	−1.69150	−0.845748	−	0.533583i	$-0.820845\pi$
$599$	−24797.7	−1.69150	−0.845748	+	0.533583i	$0.820845\pi$
$600$	7008.17	0.476846
$601$	−12110.5	−0.821962	−0.410981	−	0.911644i	$-0.634814\pi$
$601$	−12110.5	−0.821962	−0.410981	+	0.911644i	$0.634814\pi$
$602$	8437.51	0.571241
$603$	43507.3	2.93823
$604$	18537.9	1.24883
$605$	2068.51	0.139003
$606$	−59283.0	−3.97394
$607$	−14655.8	−0.980003	−0.490001	−	0.871722i	$-0.663004\pi$
$607$	−14655.8	−0.980003	−0.490001	+	0.871722i	$0.663004\pi$
$608$	10837.5	0.722890
$609$	−826.640	−0.0550035
$610$	19.7696	0.00131221
$611$	0	0
$612$	−19860.0	−1.31175
$613$	2189.50	0.144263	0.0721314	−	0.997395i	$-0.477020\pi$
$613$	2189.50	0.144263	0.0721314	+	0.997395i	$0.477020\pi$
$614$	5740.82	0.377330
$615$	−33029.7	−2.16567
$616$	−542.714	−0.0354977
$617$	11517.1	0.751478	0.375739	−	0.926726i	$-0.377389\pi$
$617$	11517.1	0.751478	0.375739	+	0.926726i	$0.377389\pi$
$618$	−52894.7	−3.44294
$619$	−1332.07	−0.0864949	−0.0432474	−	0.999064i	$-0.513770\pi$
$619$	−1332.07	−0.0864949	−0.0432474	+	0.999064i	$0.513770\pi$
$620$	27105.8	1.75580
$621$	−29124.6	−1.88201
$622$	−40344.6	−2.60076
$623$	−12240.7	−0.787182
$624$	0	0
$625$	−8560.08	−0.547845
$626$	9359.05	0.597544
$627$	4371.03	0.278408
$628$	−3668.54	−0.233106
$629$	5037.42	0.319325
$630$	34310.2	2.16977
$631$	12234.4	0.771862	0.385931	−	0.922528i	$-0.373880\pi$
$631$	12234.4	0.771862	0.385931	+	0.922528i	$0.373880\pi$
$632$	−3247.29	−0.204383
$633$	16259.9	1.02097
$634$	33365.9	2.09011
$635$	−42702.0	−2.66862
$636$	34215.6	2.13324
$637$	0	0
$638$	−383.229	−0.0237809
$639$	39824.8	2.46548
$640$	−10295.7	−0.635894
$641$	3096.77	0.190819	0.0954096	−	0.995438i	$-0.469584\pi$
$641$	3096.77	0.190819	0.0954096	+	0.995438i	$0.469584\pi$
$642$	−64058.5	−3.93798
$643$	25007.6	1.53375	0.766875	−	0.641796i	$-0.221810\pi$
$643$	25007.6	1.53375	0.766875	+	0.641796i	$0.221810\pi$
$644$	9896.66	0.605564
$645$	31887.1	1.94659
$646$	10108.0	0.615625
$647$	−20599.9	−1.25172	−0.625862	−	0.779934i	$-0.715253\pi$
$647$	−20599.9	−1.25172	−0.625862	+	0.779934i	$0.715253\pi$
$648$	2153.34	0.130542
$649$	−2779.49	−0.168112
$650$	0	0
$651$	−21380.4	−1.28719
$652$	−3238.36	−0.194515
$653$	−5663.28	−0.339389	−0.169695	−	0.985497i	$-0.554278\pi$
$653$	−5663.28	−0.339389	−0.169695	+	0.985497i	$0.554278\pi$
$654$	21619.0	1.29261
$655$	36655.0	2.18661
$656$	15893.2	0.945923
$657$	−18552.7	−1.10169
$658$	19018.8	1.12680
$659$	−940.171	−0.0555749	−0.0277874	−	0.999614i	$-0.508846\pi$
$659$	−940.171	−0.0555749	−0.0277874	+	0.999614i	$0.508846\pi$
$660$	11186.1	0.659725
$661$	7280.03	0.428382	0.214191	−	0.976792i	$-0.431289\pi$
$661$	7280.03	0.428382	0.214191	+	0.976792i	$0.431289\pi$
$662$	16712.4	0.981187
$663$	0	0
$664$	2434.28	0.142271
$665$	−7998.07	−0.466393
$666$	16750.8	0.974594
$667$	−1281.35	−0.0743841
$668$	11715.5	0.678573
$669$	−6642.93	−0.383902
$670$	−56668.7	−3.26762
$671$	−3.31107	−0.000190495 0
$672$	−21876.4	−1.25580
$673$	756.620	0.0433366	0.0216683	−	0.999765i	$-0.493102\pi$
$673$	756.620	0.0433366	0.0216683	+	0.999765i	$0.493102\pi$
$674$	8572.98	0.489939
$675$	34471.2	1.96563
$676$	0	0
$677$	3938.64	0.223595	0.111798	−	0.993731i	$-0.464339\pi$
$677$	3938.64	0.223595	0.111798	+	0.993731i	$0.464339\pi$
$678$	−29270.8	−1.65802
$679$	−17316.6	−0.978721
$680$	−4743.00	−0.267479
$681$	−43791.1	−2.46414
$682$	−9911.92	−0.556521
$683$	2656.83	0.148845	0.0744223	−	0.997227i	$-0.476289\pi$
$683$	2656.83	0.148845	0.0744223	+	0.997227i	$0.476289\pi$
$684$	15394.6	0.860565
$685$	−33384.3	−1.86211
$686$	−23032.5	−1.28190
$687$	7826.25	0.434629
$688$	−15343.4	−0.850235
$689$	0	0
$690$	81660.8	4.50547
$691$	−22262.9	−1.22564	−0.612821	−	0.790222i	$-0.709965\pi$
$691$	−22262.9	−1.22564	−0.612821	+	0.790222i	$0.709965\pi$
$692$	−24747.7	−1.35949
$693$	−5746.38	−0.314988
$694$	−1724.05	−0.0942997
$695$	−8316.62	−0.453910
$696$	379.990	0.0206947
$697$	12792.5	0.695197
$698$	−16288.0	−0.883250
$699$	−29125.7	−1.57602
$700$	−11713.4	−0.632467
$701$	−20966.9	−1.12968	−0.564841	−	0.825200i	$-0.691063\pi$
$701$	−20966.9	−1.12968	−0.564841	+	0.825200i	$0.691063\pi$
$702$	0	0
$703$	−3904.78	−0.209490
$704$	−3772.44	−0.201959
$705$	71876.1	3.83973
$706$	−25280.2	−1.34764
$707$	−18167.8	−0.966437
$708$	−15030.9	−0.797878
$709$	10689.4	0.566220	0.283110	−	0.959087i	$-0.408634\pi$
$709$	10689.4	0.566220	0.283110	+	0.959087i	$0.408634\pi$
$710$	−51872.2	−2.74187
$711$	−34383.0	−1.81359
$712$	5626.83	0.296172
$713$	−33141.2	−1.74074
$714$	−20403.9	−1.06946
$715$	0	0
$716$	11481.2	0.599265
$717$	−47657.3	−2.48228
$718$	25356.7	1.31797
$719$	−22622.3	−1.17339	−0.586696	−	0.809807i	$-0.699572\pi$
$719$	−22622.3	−1.17339	−0.586696	+	0.809807i	$0.699572\pi$
$720$	−62392.4	−3.22948
$721$	−16210.0	−0.837300
$722$	18516.6	0.954453
$723$	−17960.1	−0.923848
$724$	−13476.9	−0.691804
$725$	1516.58	0.0776888
$726$	−4090.48	−0.209107
$727$	−23532.2	−1.20050	−0.600249	−	0.799813i	$-0.704932\pi$
$727$	−23532.2	−1.20050	−0.600249	+	0.799813i	$0.704932\pi$
$728$	0	0
$729$	−26167.8	−1.32946
$730$	24165.1	1.22519
$731$	−12350.0	−0.624872
$732$	−17.9056	−0.000904112 0
$733$	9658.63	0.486698	0.243349	−	0.969939i	$-0.421754\pi$
$733$	9658.63	0.486698	0.243349	+	0.969939i	$0.421754\pi$
$734$	−637.681	−0.0320671
$735$	−35449.9	−1.77903
$736$	−33910.1	−1.69829
$737$	9491.05	0.474365
$738$	42538.6	2.12177
$739$	14278.5	0.710749	0.355375	−	0.934724i	$-0.384353\pi$
$739$	14278.5	0.710749	0.355375	+	0.934724i	$0.384353\pi$
$740$	−9992.91	−0.496414
$741$	0	0
$742$	22894.0	1.13270
$743$	−14645.1	−0.723119	−0.361560	−	0.932349i	$-0.617756\pi$
$743$	−14645.1	−0.723119	−0.361560	+	0.932349i	$0.617756\pi$
$744$	9828.15	0.484298
$745$	26430.4	1.29978
$746$	−27183.4	−1.33412
$747$	25774.7	1.26245
$748$	−4332.43	−0.211777
$749$	−19631.3	−0.957692
$750$	−24412.9	−1.18858
$751$	−3645.29	−0.177122	−0.0885609	−	0.996071i	$-0.528227\pi$
$751$	−3645.29	−0.177122	−0.0885609	+	0.996071i	$0.528227\pi$
$752$	−34585.3	−1.67712
$753$	−25704.1	−1.24397
$754$	0	0
$755$	46876.7	2.25963
$756$	−14435.9	−0.694482
$757$	−13899.2	−0.667338	−0.333669	−	0.942690i	$-0.608287\pi$
$757$	−13899.2	−0.667338	−0.333669	+	0.942690i	$0.608287\pi$
$758$	−17232.6	−0.825749
$759$	−13676.8	−0.654066
$760$	3676.56	0.175477
$761$	38750.4	1.84586	0.922930	−	0.384968i	$-0.125788\pi$
$761$	38750.4	1.84586	0.922930	+	0.384968i	$0.125788\pi$
$762$	84443.1	4.01450
$763$	6625.34	0.314355
$764$	−6699.03	−0.317228
$765$	−50220.0	−2.37348
$766$	36136.4	1.70452
$767$	0	0
$768$	44500.9	2.09087
$769$	−29446.0	−1.38082	−0.690410	−	0.723418i	$-0.742570\pi$
$769$	−29446.0	−1.38082	−0.690410	+	0.723418i	$0.742570\pi$
$770$	7484.72	0.350299
$771$	1571.47	0.0734046
$772$	−2747.59	−0.128093
$773$	−12683.7	−0.590171	−0.295085	−	0.955471i	$-0.595348\pi$
$773$	−12683.7	−0.590171	−0.295085	+	0.955471i	$0.595348\pi$
$774$	−41067.1	−1.90714
$775$	39225.1	1.81808
$776$	7960.12	0.368237
$777$	7882.15	0.363926
$778$	−2665.21	−0.122818
$779$	−9916.19	−0.456077
$780$	0	0
$781$	8687.70	0.398042
$782$	−31627.6	−1.44629
$783$	1869.06	0.0853064
$784$	17057.8	0.777049
$785$	−9276.64	−0.421780
$786$	−72485.2	−3.28939
$787$	1560.85	0.0706967	0.0353483	−	0.999375i	$-0.488746\pi$
$787$	1560.85	0.0706967	0.0353483	+	0.999375i	$0.488746\pi$
$788$	−21123.4	−0.954936
$789$	−49533.7	−2.23504
$790$	44784.2	2.01690
$791$	−8970.30	−0.403220
$792$	2641.50	0.118512
$793$	0	0
$794$	−11535.6	−0.515596
$795$	86521.1	3.85986
$796$	−8428.98	−0.375323
$797$	35970.5	1.59867	0.799336	−	0.600884i	$-0.205185\pi$
$797$	35970.5	1.59867	0.799336	+	0.600884i	$0.205185\pi$
$798$	15816.2	0.701612
$799$	−27837.9	−1.23258
$800$	40135.1	1.77374
$801$	59578.2	2.62808
$802$	19746.3	0.869411
$803$	−4047.24	−0.177863
$804$	51325.8	2.25139
$805$	25025.7	1.09570
$806$	0	0
$807$	−26233.0	−1.14429
$808$	8351.39	0.363615
$809$	39842.3	1.73149	0.865747	−	0.500481i	$-0.166844\pi$
$809$	39842.3	1.73149	0.865747	+	0.500481i	$0.166844\pi$
$810$	−29697.3	−1.28822
$811$	−22291.8	−0.965194	−0.482597	−	0.875843i	$-0.660306\pi$
$811$	−22291.8	−0.965194	−0.482597	+	0.875843i	$0.660306\pi$
$812$	−635.115	−0.0274485
$813$	−22408.1	−0.966648
$814$	3654.16	0.157344
$815$	−8188.84	−0.351954
$816$	37104.0	1.59179
$817$	9573.16	0.409942
$818$	22947.3	0.980847
$819$	0	0
$820$	−25377.0	−1.08074
$821$	42576.2	1.80989	0.904944	−	0.425530i	$-0.139912\pi$
$821$	42576.2	1.80989	0.904944	+	0.425530i	$0.139912\pi$
$822$	66017.4	2.80124
$823$	13433.1	0.568955	0.284478	−	0.958683i	$-0.408180\pi$
$823$	13433.1	0.568955	0.284478	+	0.958683i	$0.408180\pi$
$824$	7451.44	0.315028
$825$	16187.5	0.683124
$826$	−10057.3	−0.423655
$827$	−45020.9	−1.89302	−0.946511	−	0.322670i	$-0.895420\pi$
$827$	−45020.9	−1.89302	−0.946511	+	0.322670i	$0.895420\pi$
$828$	−48169.1	−2.02173
$829$	28815.0	1.20722	0.603611	−	0.797279i	$-0.293728\pi$
$829$	28815.0	1.20722	0.603611	+	0.797279i	$0.293728\pi$
$830$	−33571.8	−1.40397
$831$	19388.1	0.809344
$832$	0	0
$833$	13729.9	0.571084
$834$	16446.1	0.682833
$835$	29625.0	1.22780
$836$	3358.30	0.138934
$837$	48341.9	1.99634
$838$	21758.2	0.896925
$839$	−25705.0	−1.05773	−0.528864	−	0.848706i	$-0.677382\pi$
$839$	−25705.0	−1.05773	−0.528864	+	0.848706i	$0.677382\pi$
$840$	−7421.46	−0.304839
$841$	−24306.8	−0.996628
$842$	14745.0	0.603501
$843$	−9681.85	−0.395564
$844$	12492.6	0.509495
$845$	0	0
$846$	−92568.6	−3.76191
$847$	−1253.56	−0.0508535
$848$	−41632.2	−1.68591
$849$	17107.8	0.691566
$850$	37433.7	1.51055
$851$	12217.9	0.492156
$852$	46981.4	1.88915
$853$	−12858.6	−0.516143	−0.258072	−	0.966126i	$-0.583087\pi$
$853$	−12858.6	−0.516143	−0.258072	+	0.966126i	$0.583087\pi$
$854$	−11.9808	−0.000480064 0
$855$	38928.3	1.55710
$856$	9024.12	0.360325
$857$	−38021.3	−1.51550	−0.757750	−	0.652545i	$-0.773701\pi$
$857$	−38021.3	−1.51550	−0.757750	+	0.652545i	$0.773701\pi$
$858$	0	0
$859$	−20844.9	−0.827960	−0.413980	−	0.910286i	$-0.635862\pi$
$859$	−20844.9	−0.827960	−0.413980	+	0.910286i	$0.635862\pi$
$860$	24499.1	0.971411
$861$	20016.7	0.792297
$862$	9168.69	0.362282
$863$	8084.29	0.318879	0.159439	−	0.987208i	$-0.449031\pi$
$863$	8084.29	0.318879	0.159439	+	0.987208i	$0.449031\pi$
$864$	49463.4	1.94766
$865$	−62579.4	−2.45984
$866$	11737.0	0.460555
$867$	−13364.8	−0.523520
$868$	−16426.7	−0.642350
$869$	−7500.60	−0.292797
$870$	−5240.55	−0.204220
$871$	0	0
$872$	−3045.54	−0.118274
$873$	84283.7	3.26755
$874$	24516.3	0.948827
$875$	−7481.55	−0.289054
$876$	−21886.7	−0.844159
$877$	5820.06	0.224093	0.112046	−	0.993703i	$-0.464259\pi$
$877$	5820.06	0.224093	0.112046	+	0.993703i	$0.464259\pi$
$878$	3391.53	0.130363
$879$	56682.1	2.17502
$880$	−13610.8	−0.521386
$881$	−5160.84	−0.197359	−0.0986793	−	0.995119i	$-0.531462\pi$
$881$	−5160.84	−0.197359	−0.0986793	+	0.995119i	$0.531462\pi$
$882$	45655.6	1.74298
$883$	4260.82	0.162387	0.0811937	−	0.996698i	$-0.474127\pi$
$883$	4260.82	0.162387	0.0811937	+	0.996698i	$0.474127\pi$
$884$	0	0
$885$	−38008.7	−1.44367
$886$	−19966.8	−0.757107
$887$	−9375.28	−0.354894	−0.177447	−	0.984130i	$-0.556784\pi$
$887$	−9375.28	−0.354894	−0.177447	+	0.984130i	$0.556784\pi$
$888$	−3623.27	−0.136925
$889$	25878.3	0.976301
$890$	−77601.2	−2.92270
$891$	4973.79	0.187013
$892$	−5103.82	−0.191579
$893$	21578.7	0.808626
$894$	−52266.1	−1.95530
$895$	29032.6	1.08430
$896$	6239.41	0.232638
$897$	0	0
$898$	−32386.1	−1.20350
$899$	2126.83	0.0789028
$900$	57011.8	2.11155
$901$	−33510.0	−1.23904
$902$	9279.73	0.342551
$903$	−19324.3	−0.712150
$904$	4123.47	0.151709
$905$	−34079.1	−1.25174
$906$	−92698.7	−3.39924
$907$	−44700.8	−1.63646	−0.818229	−	0.574893i	$-0.805044\pi$
$907$	−44700.8	−1.63646	−0.818229	+	0.574893i	$0.805044\pi$
$908$	−33645.1	−1.22968
$909$	88426.5	3.22654
$910$	0	0
$911$	−26711.0	−0.971432	−0.485716	−	0.874117i	$-0.661441\pi$
$911$	−26711.0	−0.971432	−0.485716	+	0.874117i	$0.661441\pi$
$912$	−28761.3	−1.04428
$913$	5622.71	0.203817
$914$	−66766.1	−2.41622
$915$	−45.2779	−0.00163589
$916$	6012.98	0.216893
$917$	−22213.7	−0.799958
$918$	46134.0	1.65866
$919$	24920.3	0.894499	0.447250	−	0.894409i	$-0.352404\pi$
$919$	24920.3	0.894499	0.447250	+	0.894409i	$0.352404\pi$
$920$	−11503.8	−0.412250
$921$	−13148.1	−0.470407
$922$	36370.2	1.29912
$923$	0	0
$924$	−6779.03	−0.241357
$925$	−14460.8	−0.514021
$926$	−41174.6	−1.46121
$927$	78897.7	2.79540
$928$	2176.17	0.0769787
$929$	41532.0	1.46676	0.733381	−	0.679818i	$-0.237941\pi$
$929$	41532.0	1.46676	0.733381	+	0.679818i	$0.237941\pi$
$930$	−135543.	−4.77917
$931$	−10642.8	−0.374655
$932$	−22377.5	−0.786481
$933$	92400.5	3.24229
$934$	16240.7	0.568963
$935$	−10955.4	−0.383187
$936$	0	0
$937$	−45942.9	−1.60180	−0.800902	−	0.598795i	$-0.795646\pi$
$937$	−45942.9	−1.60180	−0.800902	+	0.598795i	$0.795646\pi$
$938$	34342.5	1.19544
$939$	−21434.9	−0.744942
$940$	55223.1	1.91615
$941$	20544.3	0.711716	0.355858	−	0.934540i	$-0.384189\pi$
$941$	20544.3	0.711716	0.355858	+	0.934540i	$0.384189\pi$
$942$	18344.5	0.634498
$943$	31027.4	1.07147
$944$	18289.0	0.630569
$945$	−36504.0	−1.25659
$946$	−8958.72	−0.307900
$947$	−27035.8	−0.927716	−0.463858	−	0.885910i	$-0.653535\pi$
$947$	−27035.8	−0.927716	−0.463858	+	0.885910i	$0.653535\pi$
$948$	−40561.8	−1.38965
$949$	0	0
$950$	−29016.8	−0.990980
$951$	−76417.3	−2.60568
$952$	2874.36	0.0978557
$953$	7192.23	0.244469	0.122235	−	0.992501i	$-0.460994\pi$
$953$	7192.23	0.244469	0.122235	+	0.992501i	$0.460994\pi$
$954$	−111430.	−3.78163
$955$	−16939.8	−0.573990
$956$	−36615.5	−1.23874
$957$	877.704	0.0296470
$958$	−8448.53	−0.284926
$959$	20231.6	0.681244
$960$	−51587.0	−1.73434
$961$	25217.7	0.846486
$962$	0	0
$963$	95549.6	3.19734
$964$	−13798.9	−0.461029
$965$	−6947.83	−0.231771
$966$	−49488.3	−1.64830
$967$	51459.2	1.71129	0.855645	−	0.517564i	$-0.173161\pi$
$967$	51459.2	1.71129	0.855645	+	0.517564i	$0.173161\pi$
$968$	576.239	0.0191333
$969$	−23150.2	−0.767483
$970$	−109780.	−3.63385
$971$	22904.9	0.757005	0.378503	−	0.925600i	$-0.376439\pi$
$971$	22904.9	0.757005	0.378503	+	0.925600i	$0.376439\pi$
$972$	−10725.1	−0.353918
$973$	5040.06	0.166061
$974$	69234.6	2.27764
$975$	0	0
$976$	21.7868	0.000714527 0
$977$	−53517.2	−1.75248	−0.876238	−	0.481879i	$-0.839954\pi$
$977$	−53517.2	−1.75248	−0.876238	+	0.481879i	$0.839954\pi$
$978$	16193.4	0.529456
$979$	12996.9	0.424292
$980$	−27236.5	−0.887794
$981$	−32246.9	−1.04950
$982$	−54786.3	−1.78035
$983$	8324.54	0.270103	0.135052	−	0.990839i	$-0.456880\pi$
$983$	8324.54	0.270103	0.135052	+	0.990839i	$0.456880\pi$
$984$	−9201.30	−0.298096
$985$	−53414.7	−1.72785
$986$	2029.69	0.0655563
$987$	−43558.5	−1.40474
$988$	0	0
$989$	−29954.1	−0.963079
$990$	−36429.7	−1.16951
$991$	−45847.9	−1.46963	−0.734817	−	0.678265i	$-0.762732\pi$
$991$	−45847.9	−1.46963	−0.734817	+	0.678265i	$0.762732\pi$
$992$	56284.8	1.80146
$993$	−38276.1	−1.22322
$994$	31435.7	1.00310
$995$	−21314.4	−0.679106
$996$	30406.5	0.967337
$997$	53699.2	1.70579	0.852895	−	0.522083i	$-0.174845\pi$
$997$	53699.2	1.70579	0.852895	+	0.522083i	$0.174845\pi$
$998$	34419.8	1.09172
$999$	−17821.8	−0.564422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.m.1.7		36
13.6	odd	12		143.4.j.a.23.30	✓	72
13.11	odd	12		143.4.j.a.56.30	yes	72
13.12	even	2		1859.4.a.l.1.30		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.30	✓	72	13.6	odd	12
143.4.j.a.56.30	yes	72	13.11	odd	12
1859.4.a.l.1.30		36	13.12	even	2
1859.4.a.m.1.7		36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-3.84193 q^{2} +8.79911 q^{3} +6.76044 q^{4} +17.0951 q^{5} -33.8056 q^{6} -10.3600 q^{7} +4.76230 q^{8} +50.4244 q^{9} +O(q^{10})\)	\(q-3.84193 q^{2} +8.79911 q^{3} +6.76044 q^{4} +17.0951 q^{5} -33.8056 q^{6} -10.3600 q^{7} +4.76230 q^{8} +50.4244 q^{9} -65.6783 q^{10} +11.0000 q^{11} +59.4859 q^{12} +39.8025 q^{14} +150.422 q^{15} -72.3800 q^{16} -58.2591 q^{17} -193.727 q^{18} +45.1598 q^{19} +115.571 q^{20} -91.1591 q^{21} -42.2613 q^{22} -141.303 q^{23} +41.9041 q^{24} +167.243 q^{25} +206.114 q^{27} -70.0383 q^{28} +9.06810 q^{29} -577.911 q^{30} +234.539 q^{31} +239.980 q^{32} +96.7903 q^{33} +223.827 q^{34} -177.106 q^{35} +340.891 q^{36} -86.4659 q^{37} -173.501 q^{38} +81.4122 q^{40} -219.580 q^{41} +350.227 q^{42} +211.984 q^{43} +74.3648 q^{44} +862.012 q^{45} +542.878 q^{46} +477.830 q^{47} -636.880 q^{48} -235.670 q^{49} -642.537 q^{50} -512.628 q^{51} +575.189 q^{53} -791.876 q^{54} +188.046 q^{55} -49.3376 q^{56} +397.366 q^{57} -34.8390 q^{58} -252.681 q^{59} +1016.92 q^{60} -0.301006 q^{61} -901.084 q^{62} -522.398 q^{63} -342.949 q^{64} -371.862 q^{66} +862.823 q^{67} -393.857 q^{68} -1243.35 q^{69} +680.429 q^{70} +789.791 q^{71} +240.136 q^{72} -367.931 q^{73} +332.196 q^{74} +1471.59 q^{75} +305.300 q^{76} -113.960 q^{77} -681.873 q^{79} -1237.34 q^{80} +452.163 q^{81} +843.612 q^{82} +511.155 q^{83} -616.275 q^{84} -995.947 q^{85} -814.429 q^{86} +79.7913 q^{87} +52.3853 q^{88} +1181.53 q^{89} -3311.79 q^{90} -955.273 q^{92} +2063.74 q^{93} -1835.79 q^{94} +772.012 q^{95} +2111.62 q^{96} +1671.49 q^{97} +905.427 q^{98} +554.669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{2} + 12 q^{3} + 152 q^{4} + 40 q^{5} + 98 q^{6} + 56 q^{7} + 84 q^{8} + 360 q^{9}+O(q^{10}) \) 36 * q + 4 * q^2 + 12 * q^3 + 152 * q^4 + 40 * q^5 + 98 * q^6 + 56 * q^7 + 84 * q^8 + 360 * q^9	\( 36 q + 4 q^{2} + 12 q^{3} + 152 q^{4} + 40 q^{5} + 98 q^{6} + 56 q^{7} + 84 q^{8} + 360 q^{9} - 56 q^{10} + 396 q^{11} + 66 q^{12} + 164 q^{14} + 120 q^{15} + 644 q^{16} + 138 q^{17} - 28 q^{18} + 498 q^{19} + 320 q^{20} + 404 q^{21} + 44 q^{22} + 46 q^{23} + 1340 q^{24} + 818 q^{25} + 24 q^{27} + 1382 q^{28} + 262 q^{29} + 104 q^{30} + 660 q^{31} + 106 q^{32} + 132 q^{33} - 640 q^{34} + 68 q^{35} + 1960 q^{36} + 1372 q^{37} + 224 q^{38} + 108 q^{40} + 1216 q^{41} + 82 q^{42} + 436 q^{43} + 1672 q^{44} + 820 q^{45} + 2512 q^{46} - 140 q^{47} - 1944 q^{48} + 1192 q^{49} + 3484 q^{50} + 712 q^{51} + 146 q^{53} + 3078 q^{54} + 440 q^{55} - 102 q^{56} + 3656 q^{57} - 324 q^{58} + 404 q^{59} - 2944 q^{60} - 590 q^{61} + 1776 q^{62} + 4364 q^{63} + 2514 q^{64} + 1078 q^{66} + 2236 q^{67} - 1530 q^{68} + 12 q^{69} + 4852 q^{70} + 292 q^{71} + 2990 q^{72} + 1936 q^{73} + 1568 q^{74} + 4688 q^{75} + 7398 q^{76} + 616 q^{77} - 1464 q^{79} - 808 q^{80} + 3780 q^{81} - 4072 q^{82} + 4422 q^{83} - 2678 q^{84} + 3700 q^{85} - 2588 q^{86} - 1832 q^{87} + 924 q^{88} + 6856 q^{89} - 3422 q^{90} - 668 q^{92} + 840 q^{93} - 4166 q^{94} - 256 q^{95} + 18290 q^{96} + 2776 q^{97} + 4608 q^{98} + 3960 q^{99}+O(q^{100}) \) 36 * q + 4 * q^2 + 12 * q^3 + 152 * q^4 + 40 * q^5 + 98 * q^6 + 56 * q^7 + 84 * q^8 + 360 * q^9 - 56 * q^10 + 396 * q^11 + 66 * q^12 + 164 * q^14 + 120 * q^15 + 644 * q^16 + 138 * q^17 - 28 * q^18 + 498 * q^19 + 320 * q^20 + 404 * q^21 + 44 * q^22 + 46 * q^23 + 1340 * q^24 + 818 * q^25 + 24 * q^27 + 1382 * q^28 + 262 * q^29 + 104 * q^30 + 660 * q^31 + 106 * q^32 + 132 * q^33 - 640 * q^34 + 68 * q^35 + 1960 * q^36 + 1372 * q^37 + 224 * q^38 + 108 * q^40 + 1216 * q^41 + 82 * q^42 + 436 * q^43 + 1672 * q^44 + 820 * q^45 + 2512 * q^46 - 140 * q^47 - 1944 * q^48 + 1192 * q^49 + 3484 * q^50 + 712 * q^51 + 146 * q^53 + 3078 * q^54 + 440 * q^55 - 102 * q^56 + 3656 * q^57 - 324 * q^58 + 404 * q^59 - 2944 * q^60 - 590 * q^61 + 1776 * q^62 + 4364 * q^63 + 2514 * q^64 + 1078 * q^66 + 2236 * q^67 - 1530 * q^68 + 12 * q^69 + 4852 * q^70 + 292 * q^71 + 2990 * q^72 + 1936 * q^73 + 1568 * q^74 + 4688 * q^75 + 7398 * q^76 + 616 * q^77 - 1464 * q^79 - 808 * q^80 + 3780 * q^81 - 4072 * q^82 + 4422 * q^83 - 2678 * q^84 + 3700 * q^85 - 2588 * q^86 - 1832 * q^87 + 924 * q^88 + 6856 * q^89 - 3422 * q^90 - 668 * q^92 + 840 * q^93 - 4166 * q^94 - 256 * q^95 + 18290 * q^96 + 2776 * q^97 + 4608 * q^98 + 3960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more