LMFDB - Embedded newform 1075.6.a.k.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$1$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.93825 q^{2} -29.9925 q^{3} +16.1393 q^{4} +208.095 q^{6} -148.275 q^{7} +110.045 q^{8} +656.549 q^{9} +O(q^{10})$	\(q-6.93825 q^{2} -29.9925 q^{3} +16.1393 q^{4} +208.095 q^{6} -148.275 q^{7} +110.045 q^{8} +656.549 q^{9} +48.2690 q^{11} -484.058 q^{12} +448.915 q^{13} +1028.77 q^{14} -1279.98 q^{16} -657.403 q^{17} -4555.30 q^{18} +2110.04 q^{19} +4447.14 q^{21} -334.902 q^{22} +1052.27 q^{23} -3300.54 q^{24} -3114.69 q^{26} -12403.4 q^{27} -2393.06 q^{28} +3728.07 q^{29} -960.834 q^{31} +5359.37 q^{32} -1447.71 q^{33} +4561.23 q^{34} +10596.3 q^{36} -7299.37 q^{37} -14640.0 q^{38} -13464.1 q^{39} -9308.06 q^{41} -30855.4 q^{42} +1849.00 q^{43} +779.028 q^{44} -7300.88 q^{46} -28298.2 q^{47} +38389.8 q^{48} +5178.49 q^{49} +19717.2 q^{51} +7245.19 q^{52} +5716.81 q^{53} +86057.7 q^{54} -16317.0 q^{56} -63285.3 q^{57} -25866.3 q^{58} -26936.3 q^{59} -15608.8 q^{61} +6666.51 q^{62} -97349.9 q^{63} +3774.72 q^{64} +10044.6 q^{66} +43835.7 q^{67} -10610.0 q^{68} -31560.1 q^{69} +80205.4 q^{71} +72250.3 q^{72} -62178.7 q^{73} +50644.9 q^{74} +34054.5 q^{76} -7157.09 q^{77} +93417.2 q^{78} +56823.9 q^{79} +212467. q^{81} +64581.7 q^{82} -14908.9 q^{83} +71773.8 q^{84} -12828.8 q^{86} -111814. q^{87} +5311.78 q^{88} +2900.75 q^{89} -66563.0 q^{91} +16982.8 q^{92} +28817.8 q^{93} +196340. q^{94} -160741. q^{96} -107179. q^{97} -35929.7 q^{98} +31691.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{2} - 54 q^{3} + 826 q^{4} - 162 q^{6} - 196 q^{7} - 960 q^{8} + 4098 q^{9}+O(q^{10}) $ 52 * q - 20 * q^2 - 54 * q^3 + 826 * q^4 - 162 * q^6 - 196 * q^7 - 960 * q^8 + 4098 * q^9	\( 52 q - 20 q^{2} - 54 q^{3} + 826 q^{4} - 162 q^{6} - 196 q^{7} - 960 q^{8} + 4098 q^{9} - 664 q^{11} + 523 q^{12} - 2704 q^{13} + 150 q^{14} + 13474 q^{16} - 7266 q^{17} - 4860 q^{18} - 1970 q^{19} + 800 q^{21} - 14477 q^{22} - 9522 q^{23} + 314 q^{24} + 5514 q^{26} - 22926 q^{27} - 9408 q^{28} - 7188 q^{29} - 11556 q^{31} - 48390 q^{32} - 26136 q^{33} + 16774 q^{34} + 51872 q^{36} - 42558 q^{37} - 46208 q^{38} + 4682 q^{39} - 7746 q^{41} - 174265 q^{42} + 96148 q^{43} - 48600 q^{44} + 16182 q^{46} - 87136 q^{47} + 2912 q^{48} + 142286 q^{49} - 3710 q^{51} - 146868 q^{52} - 127034 q^{53} - 49563 q^{54} - 2849 q^{56} - 101594 q^{57} - 9480 q^{58} - 55924 q^{59} + 73702 q^{61} - 186016 q^{62} - 50120 q^{63} + 157750 q^{64} + 58211 q^{66} - 131996 q^{67} - 298560 q^{68} + 128436 q^{69} - 56284 q^{71} - 343775 q^{72} - 128620 q^{73} - 17721 q^{74} - 170410 q^{76} - 448438 q^{77} - 237616 q^{78} + 106204 q^{79} + 478568 q^{81} - 249596 q^{82} - 348616 q^{83} - 131855 q^{84} - 36980 q^{86} - 267478 q^{87} - 525216 q^{88} + 80410 q^{89} + 226376 q^{91} - 581456 q^{92} - 902902 q^{93} + 180980 q^{94} + 38543 q^{96} - 316148 q^{97} - 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q - 20 * q^2 - 54 * q^3 + 826 * q^4 - 162 * q^6 - 196 * q^7 - 960 * q^8 + 4098 * q^9 - 664 * q^11 + 523 * q^12 - 2704 * q^13 + 150 * q^14 + 13474 * q^16 - 7266 * q^17 - 4860 * q^18 - 1970 * q^19 + 800 * q^21 - 14477 * q^22 - 9522 * q^23 + 314 * q^24 + 5514 * q^26 - 22926 * q^27 - 9408 * q^28 - 7188 * q^29 - 11556 * q^31 - 48390 * q^32 - 26136 * q^33 + 16774 * q^34 + 51872 * q^36 - 42558 * q^37 - 46208 * q^38 + 4682 * q^39 - 7746 * q^41 - 174265 * q^42 + 96148 * q^43 - 48600 * q^44 + 16182 * q^46 - 87136 * q^47 + 2912 * q^48 + 142286 * q^49 - 3710 * q^51 - 146868 * q^52 - 127034 * q^53 - 49563 * q^54 - 2849 * q^56 - 101594 * q^57 - 9480 * q^58 - 55924 * q^59 + 73702 * q^61 - 186016 * q^62 - 50120 * q^63 + 157750 * q^64 + 58211 * q^66 - 131996 * q^67 - 298560 * q^68 + 128436 * q^69 - 56284 * q^71 - 343775 * q^72 - 128620 * q^73 - 17721 * q^74 - 170410 * q^76 - 448438 * q^77 - 237616 * q^78 + 106204 * q^79 + 478568 * q^81 - 249596 * q^82 - 348616 * q^83 - 131855 * q^84 - 36980 * q^86 - 267478 * q^87 - 525216 * q^88 + 80410 * q^89 + 226376 * q^91 - 581456 * q^92 - 902902 * q^93 + 180980 * q^94 + 38543 * q^96 - 316148 * q^97 - 295095 * q^98 + 68428 * 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 $

$2$	−6.93825	−1.22652	−0.613260	−	0.789881i	$-0.710142\pi$
$2$	−6.93825	−1.22652	−0.613260	+	0.789881i	$0.710142\pi$
$3$	−29.9925	−1.92402	−0.962010	−	0.273016i	$-0.911979\pi$
$3$	−29.9925	−1.92402	−0.962010	+	0.273016i	$0.911979\pi$
$4$	16.1393	0.504353
$5$	0	0
$5$	0	0
$6$	208.095	2.35985
$7$	−148.275	−1.14373	−0.571864	−	0.820348i	$-0.693780\pi$
$7$	−148.275	−1.14373	−0.571864	+	0.820348i	$0.693780\pi$
$8$	110.045	0.607921
$9$	656.549	2.70185
$10$	0	0
$11$	48.2690	0.120278	0.0601390	−	0.998190i	$-0.480846\pi$
$11$	48.2690	0.120278	0.0601390	+	0.998190i	$0.480846\pi$
$12$	−484.058	−0.970386
$13$	448.915	0.736726	0.368363	−	0.929682i	$-0.379918\pi$
$13$	448.915	0.736726	0.368363	+	0.929682i	$0.379918\pi$
$14$	1028.77	1.40281
$15$	0	0
$16$	−1279.98	−1.24998
$17$	−657.403	−0.551708	−0.275854	−	0.961200i	$-0.588961\pi$
$17$	−657.403	−0.551708	−0.275854	+	0.961200i	$0.588961\pi$
$18$	−4555.30	−3.31388
$19$	2110.04	1.34093	0.670465	−	0.741941i	$-0.266095\pi$
$19$	2110.04	1.34093	0.670465	+	0.741941i	$0.266095\pi$
$20$	0	0
$21$	4447.14	2.20056
$22$	−334.902	−0.147524
$23$	1052.27	0.414768	0.207384	−	0.978260i	$-0.433505\pi$
$23$	1052.27	0.414768	0.207384	+	0.978260i	$0.433505\pi$
$24$	−3300.54	−1.16965
$25$	0	0
$26$	−3114.69	−0.903610
$27$	−12403.4	−3.27439
$28$	−2393.06	−0.576844
$29$	3728.07	0.823169	0.411584	−	0.911372i	$-0.364976\pi$
$29$	3728.07	0.823169	0.411584	+	0.911372i	$0.364976\pi$
$30$	0	0
$31$	−960.834	−0.179574	−0.0897872	−	0.995961i	$-0.528619\pi$
$31$	−960.834	−0.179574	−0.0897872	+	0.995961i	$0.528619\pi$
$32$	5359.37	0.925207
$33$	−1447.71	−0.231417
$34$	4561.23	0.676682
$35$	0	0
$36$	10596.3	1.36269
$37$	−7299.37	−0.876559	−0.438280	−	0.898839i	$-0.644412\pi$
$37$	−7299.37	−0.876559	−0.438280	+	0.898839i	$0.644412\pi$
$38$	−14640.0	−1.64468
$39$	−13464.1	−1.41748
$40$	0	0
$41$	−9308.06	−0.864768	−0.432384	−	0.901690i	$-0.642327\pi$
$41$	−9308.06	−0.864768	−0.432384	+	0.901690i	$0.642327\pi$
$42$	−30855.4	−2.69903
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	779.028	0.0606627
$45$	0	0
$46$	−7300.88	−0.508722
$47$	−28298.2	−1.86859	−0.934295	−	0.356500i	$-0.883970\pi$
$47$	−28298.2	−1.86859	−0.934295	+	0.356500i	$0.883970\pi$
$48$	38389.8	2.40499
$49$	5178.49	0.308115
$50$	0	0
$51$	19717.2	1.06150
$52$	7245.19	0.371570
$53$	5716.81	0.279553	0.139776	−	0.990183i	$-0.455362\pi$
$53$	5716.81	0.279553	0.139776	+	0.990183i	$0.455362\pi$
$54$	86057.7	4.01611
$55$	0	0
$56$	−16317.0	−0.695296
$57$	−63285.3	−2.57997
$58$	−25866.3	−1.00963
$59$	−26936.3	−1.00741	−0.503706	−	0.863875i	$-0.668031\pi$
$59$	−26936.3	−1.00741	−0.503706	+	0.863875i	$0.668031\pi$
$60$	0	0
$61$	−15608.8	−0.537086	−0.268543	−	0.963268i	$-0.586542\pi$
$61$	−15608.8	−0.537086	−0.268543	+	0.963268i	$0.586542\pi$
$62$	6666.51	0.220252
$63$	−97349.9	−3.09018
$64$	3774.72	0.115195
$65$	0	0
$66$	10044.6	0.283838
$67$	43835.7	1.19300	0.596500	−	0.802613i	$-0.296558\pi$
$67$	43835.7	1.19300	0.596500	+	0.802613i	$0.296558\pi$
$68$	−10610.0	−0.278256
$69$	−31560.1	−0.798022
$70$	0	0
$71$	80205.4	1.88824	0.944121	−	0.329598i	$-0.106913\pi$
$71$	80205.4	1.88824	0.944121	+	0.329598i	$0.106913\pi$
$72$	72250.3	1.64251
$73$	−62178.7	−1.36563	−0.682817	−	0.730589i	$-0.739245\pi$
$73$	−62178.7	−1.36563	−0.682817	+	0.730589i	$0.739245\pi$
$74$	50644.9	1.07512
$75$	0	0
$76$	34054.5	0.676303
$77$	−7157.09	−0.137565
$78$	93417.2	1.73856
$79$	56823.9	1.02439	0.512193	−	0.858870i	$-0.328833\pi$
$79$	56823.9	1.02439	0.512193	+	0.858870i	$0.328833\pi$
$80$	0	0
$81$	212467.	3.59814
$82$	64581.7	1.06066
$83$	−14908.9	−0.237547	−0.118773	−	0.992921i	$-0.537896\pi$
$83$	−14908.9	−0.237547	−0.118773	+	0.992921i	$0.537896\pi$
$84$	71773.8	1.10986
$85$	0	0
$86$	−12828.8	−0.187043
$87$	−111814.	−1.58379
$88$	5311.78	0.0731195
$89$	2900.75	0.0388183	0.0194091	−	0.999812i	$-0.493821\pi$
$89$	2900.75	0.0388183	0.0194091	+	0.999812i	$0.493821\pi$
$90$	0	0
$91$	−66563.0	−0.842615
$92$	16982.8	0.209190
$93$	28817.8	0.345505
$94$	196340.	2.29187
$95$	0	0
$96$	−160741.	−1.78012
$97$	−107179.	−1.15660	−0.578298	−	0.815825i	$-0.696283\pi$
$97$	−107179.	−1.15660	−0.578298	+	0.815825i	$0.696283\pi$
$98$	−35929.7	−0.377910
$99$	31691.0	0.324973
$100$	0	0
$101$	−57811.6	−0.563912	−0.281956	−	0.959427i	$-0.590983\pi$
$101$	−57811.6	−0.563912	−0.281956	+	0.959427i	$0.590983\pi$
$102$	−136803.	−1.30195
$103$	165688.	1.53885	0.769426	−	0.638735i	$-0.220542\pi$
$103$	165688.	1.53885	0.769426	+	0.638735i	$0.220542\pi$
$104$	49401.1	0.447871
$105$	0	0
$106$	−39664.7	−0.342878
$107$	196333.	1.65780	0.828902	−	0.559393i	$-0.188966\pi$
$107$	196333.	1.65780	0.828902	+	0.559393i	$0.188966\pi$
$108$	−200182.	−1.65145
$109$	−228369.	−1.84107	−0.920535	−	0.390659i	$-0.872247\pi$
$109$	−228369.	−1.84107	−0.920535	+	0.390659i	$0.872247\pi$
$110$	0	0
$111$	218926.	1.68652
$112$	189789.	1.42964
$113$	196317.	1.44631	0.723157	−	0.690684i	$-0.242690\pi$
$113$	196317.	1.44631	0.723157	+	0.690684i	$0.242690\pi$
$114$	439089.	3.16439
$115$	0	0
$116$	60168.5	0.415168
$117$	294735.	1.99052
$118$	186891.	1.23561
$119$	97476.5	0.631004
$120$	0	0
$121$	−158721.	−0.985533
$122$	108297.	0.658747
$123$	279172.	1.66383
$124$	−15507.2	−0.0905690
$125$	0	0
$126$	675438.	3.79017
$127$	−103787.	−0.570997	−0.285499	−	0.958379i	$-0.592159\pi$
$127$	−103787.	−0.570997	−0.285499	+	0.958379i	$0.592159\pi$
$128$	−197690.	−1.06650
$129$	−55456.1	−0.293410
$130$	0	0
$131$	−51481.2	−0.262102	−0.131051	−	0.991376i	$-0.541835\pi$
$131$	−51481.2	−0.262102	−0.131051	+	0.991376i	$0.541835\pi$
$132$	−23365.0	−0.116716
$133$	−312866.	−1.53366
$134$	−304143.	−1.46324
$135$	0	0
$136$	−72344.2	−0.335395
$137$	−301851.	−1.37401	−0.687007	−	0.726650i	$-0.741076\pi$
$137$	−301851.	−1.37401	−0.687007	+	0.726650i	$0.741076\pi$
$138$	218972.	0.978791
$139$	358425.	1.57348	0.786741	−	0.617283i	$-0.211767\pi$
$139$	358425.	1.57348	0.786741	+	0.617283i	$0.211767\pi$
$140$	0	0
$141$	848733.	3.59520
$142$	−556485.	−2.31597
$143$	21668.7	0.0886120
$144$	−840371.	−3.37726
$145$	0	0
$146$	431411.	1.67498
$147$	−155316.	−0.592820
$148$	−117807.	−0.442096
$149$	63390.2	0.233914	0.116957	−	0.993137i	$-0.462686\pi$
$149$	63390.2	0.233914	0.116957	+	0.993137i	$0.462686\pi$
$150$	0	0
$151$	−142358.	−0.508088	−0.254044	−	0.967193i	$-0.581761\pi$
$151$	−142358.	−0.508088	−0.254044	+	0.967193i	$0.581761\pi$
$152$	232200.	0.815179
$153$	−431618.	−1.49063
$154$	49657.7	0.168727
$155$	0	0
$156$	−217301.	−0.714909
$157$	256118.	0.829260	0.414630	−	0.909990i	$-0.363911\pi$
$157$	256118.	0.829260	0.414630	+	0.909990i	$0.363911\pi$
$158$	−394259.	−1.25643
$159$	−171461.	−0.537865
$160$	0	0
$161$	−156025.	−0.474383
$162$	−1.47415e6	−4.41320
$163$	102714.	0.302803	0.151401	−	0.988472i	$-0.451621\pi$
$163$	102714.	0.302803	0.151401	+	0.988472i	$0.451621\pi$
$164$	−150226.	−0.436149
$165$	0	0
$166$	103441.	0.291356
$167$	447395.	1.24137	0.620683	−	0.784062i	$-0.286855\pi$
$167$	447395.	1.24137	0.620683	+	0.784062i	$0.286855\pi$
$168$	489387.	1.33776
$169$	−169768.	−0.457234
$170$	0	0
$171$	1.38534e6	3.62299
$172$	29841.6	0.0769132
$173$	−51929.1	−0.131915	−0.0659577	−	0.997822i	$-0.521010\pi$
$173$	−51929.1	−0.131915	−0.0659577	+	0.997822i	$0.521010\pi$
$174$	775794.	1.94255
$175$	0	0
$176$	−61783.4	−0.150345
$177$	807886.	1.93828
$178$	−20126.2	−0.0476114
$179$	801231.	1.86907	0.934534	−	0.355874i	$-0.115817\pi$
$179$	801231.	1.86907	0.934534	+	0.355874i	$0.115817\pi$
$180$	0	0
$181$	365598.	0.829482	0.414741	−	0.909940i	$-0.363872\pi$
$181$	365598.	0.829482	0.414741	+	0.909940i	$0.363872\pi$
$182$	461830.	1.03348
$183$	468145.	1.03336
$184$	115797.	0.252146
$185$	0	0
$186$	−199945.	−0.423769
$187$	−31732.2	−0.0663584
$188$	−456713.	−0.942430
$189$	1.83911e6	3.74502
$190$	0	0
$191$	−71022.8	−0.140869	−0.0704343	−	0.997516i	$-0.522439\pi$
$191$	−71022.8	−0.140869	−0.0704343	+	0.997516i	$0.522439\pi$
$192$	−113213.	−0.221638
$193$	−45689.6	−0.0882926	−0.0441463	−	0.999025i	$-0.514057\pi$
$193$	−45689.6	−0.0882926	−0.0441463	+	0.999025i	$0.514057\pi$
$194$	743638.	1.41859
$195$	0	0
$196$	83577.3	0.155399
$197$	473769.	0.869764	0.434882	−	0.900488i	$-0.356790\pi$
$197$	473769.	0.869764	0.434882	+	0.900488i	$0.356790\pi$
$198$	−219880.	−0.398587
$199$	−327581.	−0.586389	−0.293195	−	0.956053i	$-0.594718\pi$
$199$	−327581.	−0.586389	−0.293195	+	0.956053i	$0.594718\pi$
$200$	0	0
$201$	−1.31474e6	−2.29536
$202$	401111.	0.691650
$203$	−552780.	−0.941482
$204$	318221.	0.535370
$205$	0	0
$206$	−1.14958e6	−1.88744
$207$	690864.	1.12064
$208$	−574603.	−0.920894
$209$	101849.	0.161284
$210$	0	0
$211$	575032.	0.889173	0.444586	−	0.895736i	$-0.353351\pi$
$211$	575032.	0.889173	0.444586	+	0.895736i	$0.353351\pi$
$212$	92265.4	0.140994
$213$	−2.40556e6	−3.63302
$214$	−1.36221e6	−2.03333
$215$	0	0
$216$	−1.36494e6	−1.99057
$217$	142468.	0.205384
$218$	1.58448e6	2.25811
$219$	1.86489e6	2.62751
$220$	0	0
$221$	−295118.	−0.406458
$222$	−1.51897e6	−2.06855
$223$	−389452.	−0.524435	−0.262218	−	0.965009i	$-0.584454\pi$
$223$	−389452.	−0.524435	−0.262218	+	0.965009i	$0.584454\pi$
$224$	−794661.	−1.05819
$225$	0	0
$226$	−1.36210e6	−1.77393
$227$	1.25857e6	1.62112	0.810558	−	0.585658i	$-0.199164\pi$
$227$	1.25857e6	1.62112	0.810558	+	0.585658i	$0.199164\pi$
$228$	−1.02138e6	−1.30122
$229$	−558389.	−0.703636	−0.351818	−	0.936068i	$-0.614436\pi$
$229$	−558389.	−0.703636	−0.351818	+	0.936068i	$0.614436\pi$
$230$	0	0
$231$	214659.	0.264679
$232$	410257.	0.500421
$233$	505939.	0.610532	0.305266	−	0.952267i	$-0.401255\pi$
$233$	505939.	0.610532	0.305266	+	0.952267i	$0.401255\pi$
$234$	−2.04495e6	−2.44142
$235$	0	0
$236$	−434733.	−0.508092
$237$	−1.70429e6	−1.97094
$238$	−676316.	−0.773940
$239$	−261377.	−0.295987	−0.147993	−	0.988988i	$-0.547281\pi$
$239$	−261377.	−0.295987	−0.147993	+	0.988988i	$0.547281\pi$
$240$	0	0
$241$	797767.	0.884776	0.442388	−	0.896824i	$-0.354131\pi$
$241$	797767.	0.884776	0.442388	+	0.896824i	$0.354131\pi$
$242$	1.10125e6	1.20878
$243$	−3.35838e6	−3.64850
$244$	−251915.	−0.270881
$245$	0	0
$246$	−1.93696e6	−2.04072
$247$	947228.	0.987898
$248$	−105735.	−0.109167
$249$	447154.	0.457044
$250$	0	0
$251$	−1.81788e6	−1.82130	−0.910649	−	0.413180i	$-0.864418\pi$
$251$	−1.81788e6	−1.82130	−0.910649	+	0.413180i	$0.864418\pi$
$252$	−1.57116e6	−1.55854
$253$	50791.8	0.0498875
$254$	720101.	0.700340
$255$	0	0
$256$	1.25083e6	1.19288
$257$	−1.71618e6	−1.62081	−0.810403	−	0.585873i	$-0.800752\pi$
$257$	−1.71618e6	−1.62081	−0.810403	+	0.585873i	$0.800752\pi$
$258$	384768.	0.359874
$259$	1.08232e6	1.00255
$260$	0	0
$261$	2.44766e6	2.22408
$262$	357189.	0.321474
$263$	−161862.	−0.144296	−0.0721481	−	0.997394i	$-0.522985\pi$
$263$	−161862.	−0.144296	−0.0721481	+	0.997394i	$0.522985\pi$
$264$	−159314.	−0.140683
$265$	0	0
$266$	2.17074e6	1.88107
$267$	−87000.9	−0.0746871
$268$	707477.	0.601694
$269$	−1.27361e6	−1.07314	−0.536569	−	0.843856i	$-0.680280\pi$
$269$	−1.27361e6	−1.07314	−0.536569	+	0.843856i	$0.680280\pi$
$270$	0	0
$271$	−1.08613e6	−0.898381	−0.449190	−	0.893436i	$-0.648288\pi$
$271$	−1.08613e6	−0.898381	−0.449190	+	0.893436i	$0.648288\pi$
$272$	841463.	0.689625
$273$	1.99639e6	1.62121
$274$	2.09432e6	1.68526
$275$	0	0
$276$	−509358.	−0.402485
$277$	−1.51028e6	−1.18265	−0.591327	−	0.806432i	$-0.701396\pi$
$277$	−1.51028e6	−1.18265	−0.591327	+	0.806432i	$0.701396\pi$
$278$	−2.48685e6	−1.92991
$279$	−630835.	−0.485183
$280$	0	0
$281$	−2.14758e6	−1.62249	−0.811246	−	0.584705i	$-0.801210\pi$
$281$	−2.14758e6	−1.62249	−0.811246	+	0.584705i	$0.801210\pi$
$282$	−5.88872e6	−4.40959
$283$	−93710.0	−0.0695536	−0.0347768	−	0.999395i	$-0.511072\pi$
$283$	−93710.0	−0.0695536	−0.0347768	+	0.999395i	$0.511072\pi$
$284$	1.29446e6	0.952342
$285$	0	0
$286$	−150343.	−0.108684
$287$	1.38015e6	0.989060
$288$	3.51869e6	2.49977
$289$	−987678.	−0.695618
$290$	0	0
$291$	3.21458e6	2.22531
$292$	−1.00352e6	−0.688763
$293$	−598682.	−0.407406	−0.203703	−	0.979033i	$-0.565298\pi$
$293$	−598682.	−0.407406	−0.203703	+	0.979033i	$0.565298\pi$
$294$	1.07762e6	0.727106
$295$	0	0
$296$	−803263.	−0.532879
$297$	−598699.	−0.393837
$298$	−439817.	−0.286901
$299$	472378.	0.305571
$300$	0	0
$301$	−274161.	−0.174417
$302$	987714.	0.623180
$303$	1.73391e6	1.08498
$304$	−2.70081e6	−1.67614
$305$	0	0
$306$	2.99467e6	1.82829
$307$	475744.	0.288090	0.144045	−	0.989571i	$-0.453989\pi$
$307$	475744.	0.288090	0.144045	+	0.989571i	$0.453989\pi$
$308$	−115510.	−0.0693816
$309$	−4.96939e6	−2.96078
$310$	0	0
$311$	−1.07715e6	−0.631501	−0.315751	−	0.948842i	$-0.602256\pi$
$311$	−1.07715e6	−0.631501	−0.315751	+	0.948842i	$0.602256\pi$
$312$	−1.48166e6	−0.861713
$313$	505494.	0.291646	0.145823	−	0.989311i	$-0.453417\pi$
$313$	505494.	0.291646	0.145823	+	0.989311i	$0.453417\pi$
$314$	−1.77701e6	−1.01710
$315$	0	0
$316$	917099.	0.516653
$317$	115509.	0.0645608	0.0322804	−	0.999479i	$-0.489723\pi$
$317$	115509.	0.0645608	0.0322804	+	0.999479i	$0.489723\pi$
$318$	1.18964e6	0.659703
$319$	179950.	0.0990091
$320$	0	0
$321$	−5.88851e6	−3.18965
$322$	1.08254e6	0.581840
$323$	−1.38714e6	−0.739802
$324$	3.42907e6	1.81474
$325$	0	0
$326$	−712654.	−0.371394
$327$	6.84935e6	3.54225
$328$	−1.02431e6	−0.525710
$329$	4.19592e6	2.13716
$330$	0	0
$331$	−1.07607e6	−0.539845	−0.269922	−	0.962882i	$-0.586998\pi$
$331$	−1.07607e6	−0.539845	−0.269922	+	0.962882i	$0.586998\pi$
$332$	−240619.	−0.119807
$333$	−4.79240e6	−2.36833
$334$	−3.10414e6	−1.52256
$335$	0	0
$336$	−5.69225e6	−2.75065
$337$	2.76696e6	1.32718	0.663588	−	0.748098i	$-0.269033\pi$
$337$	2.76696e6	1.32718	0.663588	+	0.748098i	$0.269033\pi$
$338$	1.17789e6	0.560808
$339$	−5.88804e6	−2.78273
$340$	0	0
$341$	−46378.5	−0.0215989
$342$	−9.61186e6	−4.44367
$343$	1.72422e6	0.791328
$344$	203474.	0.0927071
$345$	0	0
$346$	360297.	0.161797
$347$	−1.13201e6	−0.504691	−0.252345	−	0.967637i	$-0.581202\pi$
$347$	−1.13201e6	−0.504691	−0.252345	+	0.967637i	$0.581202\pi$
$348$	−1.80460e6	−0.798791
$349$	1.42802e6	0.627583	0.313792	−	0.949492i	$-0.398401\pi$
$349$	1.42802e6	0.627583	0.313792	+	0.949492i	$0.398401\pi$
$350$	0	0
$351$	−5.56807e6	−2.41233
$352$	258691.	0.111282
$353$	3.42161e6	1.46148	0.730741	−	0.682655i	$-0.239175\pi$
$353$	3.42161e6	1.46148	0.730741	+	0.682655i	$0.239175\pi$
$354$	−5.60531e6	−2.37734
$355$	0	0
$356$	46816.2	0.0195781
$357$	−2.92356e6	−1.21406
$358$	−5.55914e6	−2.29245
$359$	−192404.	−0.0787911	−0.0393956	−	0.999224i	$-0.512543\pi$
$359$	−192404.	−0.0787911	−0.0393956	+	0.999224i	$0.512543\pi$
$360$	0	0
$361$	1.97616e6	0.798093
$362$	−2.53661e6	−1.01738
$363$	4.76044e6	1.89618
$364$	−1.07428e6	−0.424976
$365$	0	0
$366$	−3.24811e6	−1.26744
$367$	−4.51112e6	−1.74831	−0.874157	−	0.485643i	$-0.838585\pi$
$367$	−4.51112e6	−1.74831	−0.874157	+	0.485643i	$0.838585\pi$
$368$	−1.34688e6	−0.518453
$369$	−6.11120e6	−2.33647
$370$	0	0
$371$	−847660.	−0.319733
$372$	465100.	0.174256
$373$	2.04147e6	0.759752	0.379876	−	0.925037i	$-0.375967\pi$
$373$	2.04147e6	0.759752	0.379876	+	0.925037i	$0.375967\pi$
$374$	220166.	0.0813899
$375$	0	0
$376$	−3.11409e6	−1.13596
$377$	1.67359e6	0.606450
$378$	−1.27602e7	−4.59334
$379$	2.05997e6	0.736653	0.368327	−	0.929696i	$-0.379931\pi$
$379$	2.05997e6	0.736653	0.368327	+	0.929696i	$0.379931\pi$
$380$	0	0
$381$	3.11283e6	1.09861
$382$	492774.	0.172778
$383$	−1.51015e6	−0.526044	−0.263022	−	0.964790i	$-0.584719\pi$
$383$	−1.51015e6	−0.526044	−0.263022	+	0.964790i	$0.584719\pi$
$384$	5.92921e6	2.05196
$385$	0	0
$386$	317006.	0.108293
$387$	1.21396e6	0.412028
$388$	−1.72980e6	−0.583334
$389$	4.49440e6	1.50590	0.752952	−	0.658075i	$-0.228629\pi$
$389$	4.49440e6	1.50590	0.752952	+	0.658075i	$0.228629\pi$
$390$	0	0
$391$	−691762.	−0.228831
$392$	569869.	0.187310
$393$	1.54405e6	0.504289
$394$	−3.28713e6	−1.06678
$395$	0	0
$396$	511471.	0.163901
$397$	272359.	0.0867291	0.0433645	−	0.999059i	$-0.486192\pi$
$397$	272359.	0.0867291	0.0433645	+	0.999059i	$0.486192\pi$
$398$	2.27284e6	0.719219
$399$	9.38363e6	2.95079
$400$	0	0
$401$	2.35186e6	0.730383	0.365191	−	0.930933i	$-0.381004\pi$
$401$	2.35186e6	0.730383	0.365191	+	0.930933i	$0.381004\pi$
$402$	9.12200e6	2.81530
$403$	−431333.	−0.132297
$404$	−933040.	−0.284411
$405$	0	0
$406$	3.83532e6	1.15475
$407$	−352333.	−0.105431
$408$	2.16978e6	0.645306
$409$	−3.34536e6	−0.988858	−0.494429	−	0.869218i	$-0.664623\pi$
$409$	−3.34536e6	−0.988858	−0.494429	+	0.869218i	$0.664623\pi$
$410$	0	0
$411$	9.05327e6	2.64363
$412$	2.67408e6	0.776126
$413$	3.99398e6	1.15221
$414$	−4.79339e6	−1.37449
$415$	0	0
$416$	2.40590e6	0.681624
$417$	−1.07501e7	−3.02741
$418$	−706656.	−0.197819
$419$	−2.55258e6	−0.710304	−0.355152	−	0.934809i	$-0.615571\pi$
$419$	−2.55258e6	−0.710304	−0.355152	+	0.934809i	$0.615571\pi$
$420$	0	0
$421$	−46671.4	−0.0128335	−0.00641675	−	0.999979i	$-0.502043\pi$
$421$	−46671.4	−0.0128335	−0.00641675	+	0.999979i	$0.502043\pi$
$422$	−3.98972e6	−1.09059
$423$	−1.85792e7	−5.04865
$424$	629109.	0.169946
$425$	0	0
$426$	1.66904e7	4.45597
$427$	2.31439e6	0.614280
$428$	3.16868e6	0.836120
$429$	−649898.	−0.170491
$430$	0	0
$431$	2.74902e6	0.712827	0.356413	−	0.934328i	$-0.383999\pi$
$431$	2.74902e6	0.712827	0.356413	+	0.934328i	$0.383999\pi$
$432$	1.58761e7	4.09293
$433$	5.77965e6	1.48143	0.740716	−	0.671818i	$-0.234486\pi$
$433$	5.77965e6	1.48143	0.740716	+	0.671818i	$0.234486\pi$
$434$	−988477.	−0.251908
$435$	0	0
$436$	−3.68571e6	−0.928550
$437$	2.22032e6	0.556175
$438$	−1.29391e7	−3.22269
$439$	−2.47058e6	−0.611839	−0.305920	−	0.952057i	$-0.598964\pi$
$439$	−2.47058e6	−0.611839	−0.305920	+	0.952057i	$0.598964\pi$
$440$	0	0
$441$	3.39994e6	0.832481
$442$	2.04760e6	0.498529
$443$	1.78840e6	0.432967	0.216484	−	0.976286i	$-0.430541\pi$
$443$	1.78840e6	0.432967	0.216484	+	0.976286i	$0.430541\pi$
$444$	3.53332e6	0.850601
$445$	0	0
$446$	2.70212e6	0.643231
$447$	−1.90123e6	−0.450055
$448$	−559696.	−0.131752
$449$	7.65330e6	1.79157	0.895783	−	0.444491i	$-0.146616\pi$
$449$	7.65330e6	1.79157	0.895783	+	0.444491i	$0.146616\pi$
$450$	0	0
$451$	−449291.	−0.104013
$452$	3.16843e6	0.729453
$453$	4.26966e6	0.977571
$454$	−8.73230e6	−1.98833
$455$	0	0
$456$	−6.96425e6	−1.56842
$457$	1.78626e6	0.400088	0.200044	−	0.979787i	$-0.435892\pi$
$457$	1.78626e6	0.400088	0.200044	+	0.979787i	$0.435892\pi$
$458$	3.87424e6	0.863024
$459$	8.15402e6	1.80651
$460$	0	0
$461$	4.14391e6	0.908152	0.454076	−	0.890963i	$-0.349969\pi$
$461$	4.14391e6	0.908152	0.454076	+	0.890963i	$0.349969\pi$
$462$	−1.48936e6	−0.324634
$463$	8.26621e6	1.79207	0.896033	−	0.443988i	$-0.146437\pi$
$463$	8.26621e6	1.79207	0.896033	+	0.443988i	$0.146437\pi$
$464$	−4.77185e6	−1.02895
$465$	0	0
$466$	−3.51033e6	−0.748830
$467$	201695.	0.0427959	0.0213980	−	0.999771i	$-0.493188\pi$
$467$	201695.	0.0427959	0.0213980	+	0.999771i	$0.493188\pi$
$468$	4.75682e6	1.00393
$469$	−6.49973e6	−1.36447
$470$	0	0
$471$	−7.68161e6	−1.59551
$472$	−2.96421e6	−0.612427
$473$	89249.4	0.0183422
$474$	1.18248e7	2.41740
$475$	0	0
$476$	1.57320e6	0.318249
$477$	3.75337e6	0.755310
$478$	1.81350e6	0.363034
$479$	1.24790e6	0.248509	0.124255	−	0.992250i	$-0.460346\pi$
$479$	1.24790e6	0.248509	0.124255	+	0.992250i	$0.460346\pi$
$480$	0	0
$481$	−3.27680e6	−0.645784
$482$	−5.53510e6	−1.08520
$483$	4.67957e6	0.912721
$484$	−2.56165e6	−0.497057
$485$	0	0
$486$	2.33013e7	4.47497
$487$	7.15294e6	1.36667	0.683333	−	0.730107i	$-0.260530\pi$
$487$	7.15294e6	1.36667	0.683333	+	0.730107i	$0.260530\pi$
$488$	−1.71767e6	−0.326506
$489$	−3.08064e6	−0.582598
$490$	0	0
$491$	345058.	0.0645934	0.0322967	−	0.999478i	$-0.489718\pi$
$491$	345058.	0.0645934	0.0322967	+	0.999478i	$0.489718\pi$
$492$	4.50564e6	0.839159
$493$	−2.45084e6	−0.454149
$494$	−6.57211e6	−1.21168
$495$	0	0
$496$	1.22985e6	0.224465
$497$	−1.18925e7	−2.15964
$498$	−3.10246e6	−0.560574
$499$	−1.34098e6	−0.241086	−0.120543	−	0.992708i	$-0.538464\pi$
$499$	−1.34098e6	−0.241086	−0.120543	+	0.992708i	$0.538464\pi$
$500$	0	0
$501$	−1.34185e7	−2.38841
$502$	1.26129e7	2.23386
$503$	−5.81930e6	−1.02554	−0.512768	−	0.858527i	$-0.671380\pi$
$503$	−5.81930e6	−1.02554	−0.512768	+	0.858527i	$0.671380\pi$
$504$	−1.07129e7	−1.87859
$505$	0	0
$506$	−352406.	−0.0611881
$507$	5.09176e6	0.879728
$508$	−1.67505e6	−0.287984
$509$	5.16484e6	0.883614	0.441807	−	0.897110i	$-0.354338\pi$
$509$	5.16484e6	0.883614	0.441807	+	0.897110i	$0.354338\pi$
$510$	0	0
$511$	9.21955e6	1.56192
$512$	−2.35250e6	−0.396602
$513$	−2.61716e7	−4.39073
$514$	1.19073e7	1.98795
$515$	0	0
$516$	−895024.	−0.147982
$517$	−1.36593e6	−0.224750
$518$	−7.50937e6	−1.22964
$519$	1.55748e6	0.253808
$520$	0	0
$521$	777504.	0.125490	0.0627449	−	0.998030i	$-0.480015\pi$
$521$	777504.	0.125490	0.0627449	+	0.998030i	$0.480015\pi$
$522$	−1.69825e7	−2.72788
$523$	2.01656e6	0.322371	0.161186	−	0.986924i	$-0.448468\pi$
$523$	2.01656e6	0.322371	0.161186	+	0.986924i	$0.448468\pi$
$524$	−830871.	−0.132192
$525$	0	0
$526$	1.12304e6	0.176982
$527$	631655.	0.0990726
$528$	1.85304e6	0.289267
$529$	−5.32908e6	−0.827967
$530$	0	0
$531$	−1.76850e7	−2.72188
$532$	−5.04944e6	−0.773507
$533$	−4.17853e6	−0.637097
$534$	603634.	0.0916052
$535$	0	0
$536$	4.82391e6	0.725250
$537$	−2.40309e7	−3.59612
$538$	8.83662e6	1.31623
$539$	249961.	0.0370595
$540$	0	0
$541$	1.18468e7	1.74023	0.870117	−	0.492844i	$-0.164043\pi$
$541$	1.18468e7	1.74023	0.870117	+	0.492844i	$0.164043\pi$
$542$	7.53588e6	1.10188
$543$	−1.09652e7	−1.59594
$544$	−3.52327e6	−0.510444
$545$	0	0
$546$	−1.38514e7	−1.98844
$547$	2.44946e6	0.350028	0.175014	−	0.984566i	$-0.444003\pi$
$547$	2.44946e6	0.350028	0.175014	+	0.984566i	$0.444003\pi$
$548$	−4.87167e6	−0.692989
$549$	−1.02479e7	−1.45113
$550$	0	0
$551$	7.86636e6	1.10381
$552$	−3.47304e6	−0.485134
$553$	−8.42557e6	−1.17162
$554$	1.04787e7	1.45055
$555$	0	0
$556$	5.78474e6	0.793591
$557$	−317889.	−0.0434148	−0.0217074	−	0.999764i	$-0.506910\pi$
$557$	−317889.	−0.0434148	−0.0217074	+	0.999764i	$0.506910\pi$
$558$	4.37689e6	0.595087
$559$	830045.	0.112350
$560$	0	0
$561$	951727.	0.127675
$562$	1.49004e7	1.99002
$563$	−8.44002e6	−1.12221	−0.561103	−	0.827746i	$-0.689623\pi$
$563$	−8.44002e6	−1.12221	−0.561103	+	0.827746i	$0.689623\pi$
$564$	1.36980e7	1.81325
$565$	0	0
$566$	650183.	0.0853090
$567$	−3.15035e7	−4.11530
$568$	8.82624e6	1.14790
$569$	−602539.	−0.0780197	−0.0390098	−	0.999239i	$-0.512420\pi$
$569$	−602539.	−0.0780197	−0.0390098	+	0.999239i	$0.512420\pi$
$570$	0	0
$571$	1.93952e6	0.248946	0.124473	−	0.992223i	$-0.460276\pi$
$571$	1.93952e6	0.248946	0.124473	+	0.992223i	$0.460276\pi$
$572$	349718.	0.0446918
$573$	2.13015e6	0.271034
$574$	−9.57585e6	−1.21310
$575$	0	0
$576$	2.47829e6	0.311240
$577$	−9.36462e6	−1.17098	−0.585492	−	0.810678i	$-0.699098\pi$
$577$	−9.36462e6	−1.17098	−0.585492	+	0.810678i	$0.699098\pi$
$578$	6.85276e6	0.853190
$579$	1.37035e6	0.169877
$580$	0	0
$581$	2.21061e6	0.271689
$582$	−2.23035e7	−2.72939
$583$	275945.	0.0336241
$584$	−6.84248e6	−0.830198
$585$	0	0
$586$	4.15381e6	0.499692
$587$	1.46317e7	1.75267	0.876334	−	0.481705i	$-0.159982\pi$
$587$	1.46317e7	1.75267	0.876334	+	0.481705i	$0.159982\pi$
$588$	−2.50669e6	−0.298991
$589$	−2.02740e6	−0.240797
$590$	0	0
$591$	−1.42095e7	−1.67344
$592$	9.34306e6	1.09568
$593$	1.31436e7	1.53489	0.767445	−	0.641115i	$-0.221528\pi$
$593$	1.31436e7	1.53489	0.767445	+	0.641115i	$0.221528\pi$
$594$	4.15392e6	0.483050
$595$	0	0
$596$	1.02307e6	0.117975
$597$	9.82497e6	1.12822
$598$	−3.27748e6	−0.374789
$599$	−1.32449e7	−1.50828	−0.754139	−	0.656715i	$-0.771945\pi$
$599$	−1.32449e7	−1.50828	−0.754139	+	0.656715i	$0.771945\pi$
$600$	0	0
$601$	−9.14247e6	−1.03247	−0.516235	−	0.856447i	$-0.672667\pi$
$601$	−9.14247e6	−1.03247	−0.516235	+	0.856447i	$0.672667\pi$
$602$	1.90219e6	0.213926
$603$	2.87803e7	3.22331
$604$	−2.29756e6	−0.256256
$605$	0	0
$606$	−1.20303e7	−1.33075
$607$	7.79802e6	0.859038	0.429519	−	0.903058i	$-0.358683\pi$
$607$	7.79802e6	0.859038	0.429519	+	0.903058i	$0.358683\pi$
$608$	1.13085e7	1.24064
$609$	1.65792e7	1.81143
$610$	0	0
$611$	−1.27035e7	−1.37664
$612$	−6.96601e6	−0.751806
$613$	5.44870e6	0.585655	0.292828	−	0.956165i	$-0.405404\pi$
$613$	5.44870e6	0.585655	0.292828	+	0.956165i	$0.405404\pi$
$614$	−3.30083e6	−0.353348
$615$	0	0
$616$	−787605.	−0.0836289
$617$	−9.23639e6	−0.976763	−0.488382	−	0.872630i	$-0.662413\pi$
$617$	−9.23639e6	−0.976763	−0.488382	+	0.872630i	$0.662413\pi$
$618$	3.44788e7	3.63146
$619$	−428216.	−0.0449196	−0.0224598	−	0.999748i	$-0.507150\pi$
$619$	−428216.	−0.0449196	−0.0224598	+	0.999748i	$0.507150\pi$
$620$	0	0
$621$	−1.30516e7	−1.35811
$622$	7.47352e6	0.774550
$623$	−430110.	−0.0443975
$624$	1.72338e7	1.77182
$625$	0	0
$626$	−3.50725e6	−0.357709
$627$	−3.05472e6	−0.310314
$628$	4.13357e6	0.418240
$629$	4.79863e6	0.483605
$630$	0	0
$631$	1.39505e7	1.39481	0.697407	−	0.716675i	$-0.254337\pi$
$631$	1.39505e7	1.39481	0.697407	+	0.716675i	$0.254337\pi$
$632$	6.25321e6	0.622746
$633$	−1.72466e7	−1.71078
$634$	−801433.	−0.0791852
$635$	0	0
$636$	−2.76727e6	−0.271274
$637$	2.32470e6	0.226997
$638$	−1.24854e6	−0.121437
$639$	5.26588e7	5.10175
$640$	0	0
$641$	−1.50529e7	−1.44702	−0.723511	−	0.690313i	$-0.757473\pi$
$641$	−1.50529e7	−1.44702	−0.723511	+	0.690313i	$0.757473\pi$
$642$	4.08559e7	3.91217
$643$	−7.17089e6	−0.683983	−0.341992	−	0.939703i	$-0.611101\pi$
$643$	−7.17089e6	−0.683983	−0.341992	+	0.939703i	$0.611101\pi$
$644$	−2.51813e6	−0.239257
$645$	0	0
$646$	9.62436e6	0.907383
$647$	−9.37075e6	−0.880063	−0.440031	−	0.897982i	$-0.645033\pi$
$647$	−9.37075e6	−0.880063	−0.440031	+	0.897982i	$0.645033\pi$
$648$	2.33810e7	2.18739
$649$	−1.30019e6	−0.121170
$650$	0	0
$651$	−4.27296e6	−0.395163
$652$	1.65773e6	0.152720
$653$	−1.01477e7	−0.931287	−0.465644	−	0.884972i	$-0.654177\pi$
$653$	−1.01477e7	−0.931287	−0.465644	+	0.884972i	$0.654177\pi$
$654$	−4.75225e7	−4.34465
$655$	0	0
$656$	1.19141e7	1.08094
$657$	−4.08234e7	−3.68974
$658$	−2.91123e7	−2.62127
$659$	5.74065e6	0.514929	0.257465	−	0.966288i	$-0.417113\pi$
$659$	5.74065e6	0.514929	0.257465	+	0.966288i	$0.417113\pi$
$660$	0	0
$661$	8.09122e6	0.720295	0.360148	−	0.932895i	$-0.382726\pi$
$661$	8.09122e6	0.720295	0.360148	+	0.932895i	$0.382726\pi$
$662$	7.46601e6	0.662131
$663$	8.85133e6	0.782033
$664$	−1.64065e6	−0.144410
$665$	0	0
$666$	3.32509e7	2.90481
$667$	3.92292e6	0.341424
$668$	7.22065e6	0.626087
$669$	1.16806e7	1.00902
$670$	0	0
$671$	−753419.	−0.0645996
$672$	2.38339e7	2.03597
$673$	1.47592e7	1.25611	0.628053	−	0.778171i	$-0.283852\pi$
$673$	1.47592e7	1.25611	0.628053	+	0.778171i	$0.283852\pi$
$674$	−1.91979e7	−1.62781
$675$	0	0
$676$	−2.73994e6	−0.230608
$677$	−1.03968e7	−0.871826	−0.435913	−	0.899989i	$-0.643574\pi$
$677$	−1.03968e7	−0.871826	−0.435913	+	0.899989i	$0.643574\pi$
$678$	4.08527e7	3.41308
$679$	1.58920e7	1.32283
$680$	0	0
$681$	−3.77478e7	−3.11906
$682$	321786.	0.0264915
$683$	1.73910e7	1.42651	0.713254	−	0.700906i	$-0.247221\pi$
$683$	1.73910e7	1.42651	0.713254	+	0.700906i	$0.247221\pi$
$684$	2.23585e7	1.82727
$685$	0	0
$686$	−1.19631e7	−0.970581
$687$	1.67475e7	1.35381
$688$	−2.36668e6	−0.190620
$689$	2.56636e6	0.205954
$690$	0	0
$691$	1.01586e6	0.0809356	0.0404678	−	0.999181i	$-0.487115\pi$
$691$	1.01586e6	0.0809356	0.0404678	+	0.999181i	$0.487115\pi$
$692$	−838099.	−0.0665320
$693$	−4.69898e6	−0.371681
$694$	7.85415e6	0.619014
$695$	0	0
$696$	−1.23046e7	−0.962820
$697$	6.11915e6	0.477100
$698$	−9.90798e6	−0.769744
$699$	−1.51744e7	−1.17468
$700$	0	0
$701$	−3.68701e6	−0.283387	−0.141693	−	0.989911i	$-0.545255\pi$
$701$	−3.68701e6	−0.283387	−0.141693	+	0.989911i	$0.545255\pi$
$702$	3.86326e7	2.95877
$703$	−1.54019e7	−1.17540
$704$	182202.	0.0138555
$705$	0	0
$706$	−2.37400e7	−1.79254
$707$	8.57202e6	0.644963
$708$	1.30387e7	0.977579
$709$	−5.06094e6	−0.378108	−0.189054	−	0.981967i	$-0.560542\pi$
$709$	−5.06094e6	−0.378108	−0.189054	+	0.981967i	$0.560542\pi$
$710$	0	0
$711$	3.73077e7	2.76774
$712$	319215.	0.0235984
$713$	−1.01105e6	−0.0744818
$714$	2.02844e7	1.48908
$715$	0	0
$716$	1.29313e7	0.942671
$717$	7.83934e6	0.569484
$718$	1.33495e6	0.0966390
$719$	−1.70834e7	−1.23240	−0.616199	−	0.787591i	$-0.711328\pi$
$719$	−1.70834e7	−1.23240	−0.616199	+	0.787591i	$0.711328\pi$
$720$	0	0
$721$	−2.45673e7	−1.76003
$722$	−1.37111e7	−0.978878
$723$	−2.39270e7	−1.70233
$724$	5.90049e6	0.418352
$725$	0	0
$726$	−3.30291e7	−2.32571
$727$	2.51999e7	1.76833	0.884163	−	0.467178i	$-0.154729\pi$
$727$	2.51999e7	1.76833	0.884163	+	0.467178i	$0.154729\pi$
$728$	−7.32495e6	−0.512243
$729$	4.90969e7	3.42165
$730$	0	0
$731$	−1.21554e6	−0.0841347
$732$	7.55555e6	0.521180
$733$	2.45408e7	1.68705	0.843525	−	0.537090i	$-0.180476\pi$
$733$	2.45408e7	1.68705	0.843525	+	0.537090i	$0.180476\pi$
$734$	3.12993e7	2.14434
$735$	0	0
$736$	5.63948e6	0.383747
$737$	2.11590e6	0.143492
$738$	4.24011e7	2.86573
$739$	−2.37974e7	−1.60294	−0.801472	−	0.598033i	$-0.795949\pi$
$739$	−2.37974e7	−1.60294	−0.801472	+	0.598033i	$0.795949\pi$
$740$	0	0
$741$	−2.84097e7	−1.90074
$742$	5.88128e6	0.392159
$743$	−2.85354e7	−1.89632	−0.948160	−	0.317793i	$-0.897058\pi$
$743$	−2.85354e7	−1.89632	−0.948160	+	0.317793i	$0.897058\pi$
$744$	3.17127e6	0.210039
$745$	0	0
$746$	−1.41643e7	−0.931852
$747$	−9.78840e6	−0.641815
$748$	−512135.	−0.0334681
$749$	−2.91113e7	−1.89608
$750$	0	0
$751$	3.99347e6	0.258375	0.129188	−	0.991620i	$-0.458763\pi$
$751$	3.99347e6	0.258375	0.129188	+	0.991620i	$0.458763\pi$
$752$	3.62211e7	2.33570
$753$	5.45228e7	3.50421
$754$	−1.16118e7	−0.743824
$755$	0	0
$756$	2.96820e7	1.88881
$757$	5.01805e6	0.318270	0.159135	−	0.987257i	$-0.449130\pi$
$757$	5.01805e6	0.318270	0.159135	+	0.987257i	$0.449130\pi$
$758$	−1.42926e7	−0.903520
$759$	−1.52337e6	−0.0959846
$760$	0	0
$761$	1.71006e7	1.07041	0.535206	−	0.844722i	$-0.320234\pi$
$761$	1.71006e7	1.07041	0.535206	+	0.844722i	$0.320234\pi$
$762$	−2.15976e7	−1.34747
$763$	3.38614e7	2.10569
$764$	−1.14626e6	−0.0710476
$765$	0	0
$766$	1.04778e7	0.645204
$767$	−1.20921e7	−0.742187
$768$	−3.75155e7	−2.29513
$769$	−5.18999e6	−0.316483	−0.158242	−	0.987400i	$-0.550583\pi$
$769$	−5.18999e6	−0.316483	−0.158242	+	0.987400i	$0.550583\pi$
$770$	0	0
$771$	5.14726e7	3.11846
$772$	−737399.	−0.0445307
$773$	1.75483e7	1.05630	0.528149	−	0.849152i	$-0.322886\pi$
$773$	1.75483e7	1.05630	0.528149	+	0.849152i	$0.322886\pi$
$774$	−8.42276e6	−0.505361
$775$	0	0
$776$	−1.17946e7	−0.703119
$777$	−3.24613e7	−1.92892
$778$	−3.11833e7	−1.84702
$779$	−1.96404e7	−1.15959
$780$	0	0
$781$	3.87143e6	0.227114
$782$	4.79962e6	0.280666
$783$	−4.62406e7	−2.69538
$784$	−6.62837e6	−0.385138
$785$	0	0
$786$	−1.07130e7	−0.618521
$787$	−2.02524e7	−1.16558	−0.582788	−	0.812624i	$-0.698038\pi$
$787$	−2.02524e7	−1.16558	−0.582788	+	0.812624i	$0.698038\pi$
$788$	7.64631e6	0.438668
$789$	4.85464e6	0.277629
$790$	0	0
$791$	−2.91090e7	−1.65419
$792$	3.48745e6	0.197558
$793$	−7.00701e6	−0.395685
$794$	−1.88969e6	−0.106375
$795$	0	0
$796$	−5.28693e6	−0.295748
$797$	−1.88120e7	−1.04904	−0.524518	−	0.851400i	$-0.675754\pi$
$797$	−1.88120e7	−1.04904	−0.524518	+	0.851400i	$0.675754\pi$
$798$	−6.51059e7	−3.61921
$799$	1.86033e7	1.03092
$800$	0	0
$801$	1.90449e6	0.104881
$802$	−1.63178e7	−0.895829
$803$	−3.00130e6	−0.164256
$804$	−2.12190e7	−1.15767
$805$	0	0
$806$	2.99270e6	0.162265
$807$	3.81987e7	2.06474
$808$	−6.36190e6	−0.342814
$809$	−3.28928e7	−1.76697	−0.883486	−	0.468458i	$-0.844810\pi$
$809$	−3.28928e7	−1.76697	−0.883486	+	0.468458i	$0.844810\pi$
$810$	0	0
$811$	3.08398e7	1.64649	0.823247	−	0.567684i	$-0.192160\pi$
$811$	3.08398e7	1.64649	0.823247	+	0.567684i	$0.192160\pi$
$812$	−8.92148e6	−0.474840
$813$	3.25759e7	1.72850
$814$	2.44458e6	0.129313
$815$	0	0
$816$	−2.52376e7	−1.32685
$817$	3.90146e6	0.204490
$818$	2.32109e7	1.21286
$819$	−4.37019e7	−2.27662
$820$	0	0
$821$	1.00637e7	0.521074	0.260537	−	0.965464i	$-0.416100\pi$
$821$	1.00637e7	0.521074	0.260537	+	0.965464i	$0.416100\pi$
$822$	−6.28138e7	−3.24247
$823$	9.76803e6	0.502698	0.251349	−	0.967896i	$-0.419126\pi$
$823$	9.76803e6	0.502698	0.251349	+	0.967896i	$0.419126\pi$
$824$	1.82332e7	0.935501
$825$	0	0
$826$	−2.77112e7	−1.41321
$827$	−2.59060e7	−1.31715	−0.658577	−	0.752513i	$-0.728841\pi$
$827$	−2.59060e7	−1.31715	−0.658577	+	0.752513i	$0.728841\pi$
$828$	1.11501e7	0.565200
$829$	1.00227e7	0.506522	0.253261	−	0.967398i	$-0.418497\pi$
$829$	1.00227e7	0.506522	0.253261	+	0.967398i	$0.418497\pi$
$830$	0	0
$831$	4.52971e7	2.27545
$832$	1.69453e6	0.0848674
$833$	−3.40436e6	−0.169990
$834$	7.45867e7	3.71318
$835$	0	0
$836$	1.64378e6	0.0813444
$837$	1.19176e7	0.587997
$838$	1.77104e7	0.871203
$839$	4.32216e6	0.211981	0.105990	−	0.994367i	$-0.466199\pi$
$839$	4.32216e6	0.211981	0.105990	+	0.994367i	$0.466199\pi$
$840$	0	0
$841$	−6.61266e6	−0.322393
$842$	323818.	0.0157406
$843$	6.44111e7	3.12171
$844$	9.28062e6	0.448457
$845$	0	0
$846$	1.28907e8	6.19228
$847$	2.35344e7	1.12718
$848$	−7.31741e6	−0.349436
$849$	2.81060e6	0.133823
$850$	0	0
$851$	−7.68088e6	−0.363569
$852$	−3.88241e7	−1.83232
$853$	−4.00376e7	−1.88407	−0.942033	−	0.335521i	$-0.891088\pi$
$853$	−4.00376e7	−1.88407	−0.942033	+	0.335521i	$0.891088\pi$
$854$	−1.60578e7	−0.753428
$855$	0	0
$856$	2.16055e7	1.00781
$857$	−2.90678e6	−0.135195	−0.0675974	−	0.997713i	$-0.521533\pi$
$857$	−2.90678e6	−0.135195	−0.0675974	+	0.997713i	$0.521533\pi$
$858$	4.50915e6	0.209111
$859$	1.34540e7	0.622111	0.311055	−	0.950392i	$-0.399318\pi$
$859$	1.34540e7	0.622111	0.311055	+	0.950392i	$0.399318\pi$
$860$	0	0
$861$	−4.13942e7	−1.90297
$862$	−1.90734e7	−0.874297
$863$	3.35858e7	1.53507	0.767537	−	0.641005i	$-0.221482\pi$
$863$	3.35858e7	1.53507	0.767537	+	0.641005i	$0.221482\pi$
$864$	−6.64743e7	−3.02949
$865$	0	0
$866$	−4.01006e7	−1.81701
$867$	2.96229e7	1.33838
$868$	2.29933e6	0.103586
$869$	2.74283e6	0.123211
$870$	0	0
$871$	1.96785e7	0.878914
$872$	−2.51309e7	−1.11923
$873$	−7.03686e7	−3.12495
$874$	−1.54051e7	−0.682161
$875$	0	0
$876$	3.00981e7	1.32519
$877$	−3.14407e6	−0.138036	−0.0690180	−	0.997615i	$-0.521987\pi$
$877$	−3.14407e6	−0.138036	−0.0690180	+	0.997615i	$0.521987\pi$
$878$	1.71415e7	0.750434
$879$	1.79560e7	0.783857
$880$	0	0
$881$	−2.29804e7	−0.997511	−0.498755	−	0.866743i	$-0.666209\pi$
$881$	−2.29804e7	−0.997511	−0.498755	+	0.866743i	$0.666209\pi$
$882$	−2.35896e7	−1.02106
$883$	−3.60095e7	−1.55423	−0.777115	−	0.629358i	$-0.783318\pi$
$883$	−3.60095e7	−1.55423	−0.777115	+	0.629358i	$0.783318\pi$
$884$	−4.76301e6	−0.204998
$885$	0	0
$886$	−1.24084e7	−0.531043
$887$	1.58320e7	0.675656	0.337828	−	0.941208i	$-0.390308\pi$
$887$	1.58320e7	0.675656	0.337828	+	0.941208i	$0.390308\pi$
$888$	2.40918e7	1.02527
$889$	1.53890e7	0.653066
$890$	0	0
$891$	1.02556e7	0.432778
$892$	−6.28549e6	−0.264501
$893$	−5.97102e7	−2.50565
$894$	1.31912e7	0.552002
$895$	0	0
$896$	2.93125e7	1.21978
$897$	−1.41678e7	−0.587924
$898$	−5.31005e7	−2.19739
$899$	−3.58206e6	−0.147820
$900$	0	0
$901$	−3.75825e6	−0.154232
$902$	3.11729e6	0.127574
$903$	8.22276e6	0.335582
$904$	2.16038e7	0.879244
$905$	0	0
$906$	−2.96240e7	−1.19901
$907$	8.62301e6	0.348049	0.174025	−	0.984741i	$-0.444323\pi$
$907$	8.62301e6	0.348049	0.174025	+	0.984741i	$0.444323\pi$
$908$	2.03125e7	0.817616
$909$	−3.79562e7	−1.52361
$910$	0	0
$911$	3.94385e6	0.157443	0.0787217	−	0.996897i	$-0.474916\pi$
$911$	3.94385e6	0.157443	0.0787217	+	0.996897i	$0.474916\pi$
$912$	8.10039e7	3.22492
$913$	−719635.	−0.0285717
$914$	−1.23935e7	−0.490716
$915$	0	0
$916$	−9.01201e6	−0.354881
$917$	7.63338e6	0.299774
$918$	−5.65746e7	−2.21572
$919$	−2.13973e7	−0.835736	−0.417868	−	0.908508i	$-0.637223\pi$
$919$	−2.13973e7	−0.835736	−0.417868	+	0.908508i	$0.637223\pi$
$920$	0	0
$921$	−1.42688e7	−0.554290
$922$	−2.87515e7	−1.11387
$923$	3.60054e7	1.39112
$924$	3.46445e6	0.133492
$925$	0	0
$926$	−5.73530e7	−2.19801
$927$	1.08782e8	4.15775
$928$	1.99801e7	0.761602
$929$	1.12434e7	0.427422	0.213711	−	0.976897i	$-0.431445\pi$
$929$	1.12434e7	0.427422	0.213711	+	0.976897i	$0.431445\pi$
$930$	0	0
$931$	1.09268e7	0.413161
$932$	8.16551e6	0.307924
$933$	3.23063e7	1.21502
$934$	−1.39941e6	−0.0524901
$935$	0	0
$936$	3.24343e7	1.21008
$937$	1.91852e7	0.713866	0.356933	−	0.934130i	$-0.383822\pi$
$937$	1.91852e7	0.713866	0.356933	+	0.934130i	$0.383822\pi$
$938$	4.50968e7	1.67355
$939$	−1.51610e7	−0.561132
$940$	0	0
$941$	468237.	0.0172382	0.00861909	−	0.999963i	$-0.497256\pi$
$941$	468237.	0.0172382	0.00861909	+	0.999963i	$0.497256\pi$
$942$	5.32969e7	1.95693
$943$	−9.79455e6	−0.358678
$944$	3.44779e7	1.25925
$945$	0	0
$946$	−619234.	−0.0224971
$947$	1.78459e6	0.0646642	0.0323321	−	0.999477i	$-0.489707\pi$
$947$	1.78459e6	0.0646642	0.0323321	+	0.999477i	$0.489707\pi$
$948$	−2.75061e7	−0.994050
$949$	−2.79130e7	−1.00610
$950$	0	0
$951$	−3.46442e6	−0.124216
$952$	1.07268e7	0.383601
$953$	1.69694e7	0.605249	0.302625	−	0.953110i	$-0.402137\pi$
$953$	1.69694e7	0.605249	0.302625	+	0.953110i	$0.402137\pi$
$954$	−2.60418e7	−0.926404
$955$	0	0
$956$	−4.21844e6	−0.149282
$957$	−5.39715e6	−0.190495
$958$	−8.65826e6	−0.304801
$959$	4.47570e7	1.57150
$960$	0	0
$961$	−2.77059e7	−0.967753
$962$	2.27353e7	0.792068
$963$	1.28902e8	4.47914
$964$	1.28754e7	0.446240
$965$	0	0
$966$	−3.24680e7	−1.11947
$967$	−3.92714e7	−1.35055	−0.675274	−	0.737567i	$-0.735975\pi$
$967$	−3.92714e7	−1.35055	−0.675274	+	0.737567i	$0.735975\pi$
$968$	−1.74665e7	−0.599126
$969$	4.16039e7	1.42339
$970$	0	0
$971$	−3.89607e7	−1.32611	−0.663054	−	0.748572i	$-0.730740\pi$
$971$	−3.89607e7	−1.32611	−0.663054	+	0.748572i	$0.730740\pi$
$972$	−5.42020e7	−1.84014
$973$	−5.31456e7	−1.79964
$974$	−4.96289e7	−1.67624
$975$	0	0
$976$	1.99789e7	0.671347
$977$	−3.55661e7	−1.19207	−0.596033	−	0.802960i	$-0.703257\pi$
$977$	−3.55661e7	−1.19207	−0.596033	+	0.802960i	$0.703257\pi$
$978$	2.13743e7	0.714569
$979$	140016.	0.00466898
$980$	0	0
$981$	−1.49935e8	−4.97430
$982$	−2.39410e6	−0.0792251
$983$	−4.72860e7	−1.56080	−0.780402	−	0.625278i	$-0.784986\pi$
$983$	−4.72860e7	−1.56080	−0.780402	+	0.625278i	$0.784986\pi$
$984$	3.07216e7	1.01148
$985$	0	0
$986$	1.70046e7	0.557023
$987$	−1.25846e8	−4.11194
$988$	1.52876e7	0.498250
$989$	1.94564e6	0.0632516
$990$	0	0
$991$	5.69298e7	1.84143	0.920715	−	0.390236i	$-0.127607\pi$
$991$	5.69298e7	1.84143	0.920715	+	0.390236i	$0.127607\pi$
$992$	−5.14947e6	−0.166143
$993$	3.22739e7	1.03867
$994$	8.25129e7	2.64884
$995$	0	0
$996$	7.21675e6	0.230512
$997$	1.44999e7	0.461983	0.230991	−	0.972956i	$-0.425803\pi$
$997$	1.44999e7	0.461983	0.230991	+	0.972956i	$0.425803\pi$
$998$	9.30407e6	0.295697
$999$	9.05369e7	2.87020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.k.1.14		52
5.2	odd	4		215.6.b.a.44.24	✓	104
5.3	odd	4		215.6.b.a.44.81	yes	104
5.4	even	2		1075.6.a.l.1.39		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.6.b.a.44.24	✓	104	5.2	odd	4
215.6.b.a.44.81	yes	104	5.3	odd	4
1075.6.a.k.1.14		52	1.1	even	1	trivial
1075.6.a.l.1.39		52	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-6.93825 q^{2} -29.9925 q^{3} +16.1393 q^{4} +208.095 q^{6} -148.275 q^{7} +110.045 q^{8} +656.549 q^{9} +O(q^{10})\)	\(q-6.93825 q^{2} -29.9925 q^{3} +16.1393 q^{4} +208.095 q^{6} -148.275 q^{7} +110.045 q^{8} +656.549 q^{9} +48.2690 q^{11} -484.058 q^{12} +448.915 q^{13} +1028.77 q^{14} -1279.98 q^{16} -657.403 q^{17} -4555.30 q^{18} +2110.04 q^{19} +4447.14 q^{21} -334.902 q^{22} +1052.27 q^{23} -3300.54 q^{24} -3114.69 q^{26} -12403.4 q^{27} -2393.06 q^{28} +3728.07 q^{29} -960.834 q^{31} +5359.37 q^{32} -1447.71 q^{33} +4561.23 q^{34} +10596.3 q^{36} -7299.37 q^{37} -14640.0 q^{38} -13464.1 q^{39} -9308.06 q^{41} -30855.4 q^{42} +1849.00 q^{43} +779.028 q^{44} -7300.88 q^{46} -28298.2 q^{47} +38389.8 q^{48} +5178.49 q^{49} +19717.2 q^{51} +7245.19 q^{52} +5716.81 q^{53} +86057.7 q^{54} -16317.0 q^{56} -63285.3 q^{57} -25866.3 q^{58} -26936.3 q^{59} -15608.8 q^{61} +6666.51 q^{62} -97349.9 q^{63} +3774.72 q^{64} +10044.6 q^{66} +43835.7 q^{67} -10610.0 q^{68} -31560.1 q^{69} +80205.4 q^{71} +72250.3 q^{72} -62178.7 q^{73} +50644.9 q^{74} +34054.5 q^{76} -7157.09 q^{77} +93417.2 q^{78} +56823.9 q^{79} +212467. q^{81} +64581.7 q^{82} -14908.9 q^{83} +71773.8 q^{84} -12828.8 q^{86} -111814. q^{87} +5311.78 q^{88} +2900.75 q^{89} -66563.0 q^{91} +16982.8 q^{92} +28817.8 q^{93} +196340. q^{94} -160741. q^{96} -107179. q^{97} -35929.7 q^{98} +31691.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{2} - 54 q^{3} + 826 q^{4} - 162 q^{6} - 196 q^{7} - 960 q^{8} + 4098 q^{9}+O(q^{10}) \) 52 * q - 20 * q^2 - 54 * q^3 + 826 * q^4 - 162 * q^6 - 196 * q^7 - 960 * q^8 + 4098 * q^9	\( 52 q - 20 q^{2} - 54 q^{3} + 826 q^{4} - 162 q^{6} - 196 q^{7} - 960 q^{8} + 4098 q^{9} - 664 q^{11} + 523 q^{12} - 2704 q^{13} + 150 q^{14} + 13474 q^{16} - 7266 q^{17} - 4860 q^{18} - 1970 q^{19} + 800 q^{21} - 14477 q^{22} - 9522 q^{23} + 314 q^{24} + 5514 q^{26} - 22926 q^{27} - 9408 q^{28} - 7188 q^{29} - 11556 q^{31} - 48390 q^{32} - 26136 q^{33} + 16774 q^{34} + 51872 q^{36} - 42558 q^{37} - 46208 q^{38} + 4682 q^{39} - 7746 q^{41} - 174265 q^{42} + 96148 q^{43} - 48600 q^{44} + 16182 q^{46} - 87136 q^{47} + 2912 q^{48} + 142286 q^{49} - 3710 q^{51} - 146868 q^{52} - 127034 q^{53} - 49563 q^{54} - 2849 q^{56} - 101594 q^{57} - 9480 q^{58} - 55924 q^{59} + 73702 q^{61} - 186016 q^{62} - 50120 q^{63} + 157750 q^{64} + 58211 q^{66} - 131996 q^{67} - 298560 q^{68} + 128436 q^{69} - 56284 q^{71} - 343775 q^{72} - 128620 q^{73} - 17721 q^{74} - 170410 q^{76} - 448438 q^{77} - 237616 q^{78} + 106204 q^{79} + 478568 q^{81} - 249596 q^{82} - 348616 q^{83} - 131855 q^{84} - 36980 q^{86} - 267478 q^{87} - 525216 q^{88} + 80410 q^{89} + 226376 q^{91} - 581456 q^{92} - 902902 q^{93} + 180980 q^{94} + 38543 q^{96} - 316148 q^{97} - 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q - 20 * q^2 - 54 * q^3 + 826 * q^4 - 162 * q^6 - 196 * q^7 - 960 * q^8 + 4098 * q^9 - 664 * q^11 + 523 * q^12 - 2704 * q^13 + 150 * q^14 + 13474 * q^16 - 7266 * q^17 - 4860 * q^18 - 1970 * q^19 + 800 * q^21 - 14477 * q^22 - 9522 * q^23 + 314 * q^24 + 5514 * q^26 - 22926 * q^27 - 9408 * q^28 - 7188 * q^29 - 11556 * q^31 - 48390 * q^32 - 26136 * q^33 + 16774 * q^34 + 51872 * q^36 - 42558 * q^37 - 46208 * q^38 + 4682 * q^39 - 7746 * q^41 - 174265 * q^42 + 96148 * q^43 - 48600 * q^44 + 16182 * q^46 - 87136 * q^47 + 2912 * q^48 + 142286 * q^49 - 3710 * q^51 - 146868 * q^52 - 127034 * q^53 - 49563 * q^54 - 2849 * q^56 - 101594 * q^57 - 9480 * q^58 - 55924 * q^59 + 73702 * q^61 - 186016 * q^62 - 50120 * q^63 + 157750 * q^64 + 58211 * q^66 - 131996 * q^67 - 298560 * q^68 + 128436 * q^69 - 56284 * q^71 - 343775 * q^72 - 128620 * q^73 - 17721 * q^74 - 170410 * q^76 - 448438 * q^77 - 237616 * q^78 + 106204 * q^79 + 478568 * q^81 - 249596 * q^82 - 348616 * q^83 - 131855 * q^84 - 36980 * q^86 - 267478 * q^87 - 525216 * q^88 + 80410 * q^89 + 226376 * q^91 - 581456 * q^92 - 902902 * q^93 + 180980 * q^94 + 38543 * q^96 - 316148 * q^97 - 295095 * q^98 + 68428 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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