LMFDB - Embedded newform 525.4.d.j.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.1
Root			$-3.70156i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.j.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.70156i q^{2} +3.00000i q^{3} -14.1047 q^{4} +14.1047 q^{6} -7.00000i q^{7} +28.7016i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-4.70156i q^{2} +3.00000i q^{3} -14.1047 q^{4} +14.1047 q^{6} -7.00000i q^{7} +28.7016i q^{8} -9.00000 q^{9} +24.5969 q^{11} -42.3141i q^{12} -35.0156i q^{13} -32.9109 q^{14} +22.1047 q^{16} +18.4187i q^{17} +42.3141i q^{18} +67.4031 q^{19} +21.0000 q^{21} -115.644i q^{22} -145.675i q^{23} -86.1047 q^{24} -164.628 q^{26} -27.0000i q^{27} +98.7328i q^{28} -214.419 q^{29} -88.6594 q^{31} +125.686i q^{32} +73.7906i q^{33} +86.5969 q^{34} +126.942 q^{36} -162.125i q^{37} -316.900i q^{38} +105.047 q^{39} -337.769 q^{41} -98.7328i q^{42} +122.156i q^{43} -346.931 q^{44} -684.900 q^{46} -354.219i q^{47} +66.3141i q^{48} -49.0000 q^{49} -55.2562 q^{51} +493.884i q^{52} +676.691i q^{53} -126.942 q^{54} +200.911 q^{56} +202.209i q^{57} +1008.10i q^{58} -501.319 q^{59} -708.931 q^{61} +416.837i q^{62} +63.0000i q^{63} +767.758 q^{64} +346.931 q^{66} +907.956i q^{67} -259.791i q^{68} +437.025 q^{69} +430.334 q^{71} -258.314i q^{72} +41.3406i q^{73} -762.241 q^{74} -950.700 q^{76} -172.178i q^{77} -493.884i q^{78} -890.388 q^{79} +81.0000 q^{81} +1588.04i q^{82} -1057.15i q^{83} -296.198 q^{84} +574.325 q^{86} -643.256i q^{87} +705.969i q^{88} -1473.72 q^{89} -245.109 q^{91} +2054.70i q^{92} -265.978i q^{93} -1665.38 q^{94} -377.058 q^{96} -555.034i q^{97} +230.377i q^{98} -221.372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9	$ 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9} + 124 q^{11} - 42 q^{14} + 50 q^{16} + 244 q^{19} + 84 q^{21} - 306 q^{24} - 428 q^{26} - 704 q^{29} + 132 q^{31} + 372 q^{34} + 162 q^{36} + 36 q^{39} + 32 q^{41} - 312 q^{44} - 1920 q^{46} - 196 q^{49} + 240 q^{51} - 162 q^{54} + 714 q^{56} - 1032 q^{59} - 1760 q^{61} + 958 q^{64} + 312 q^{66} - 96 q^{69} + 620 q^{71} - 2716 q^{74} - 1344 q^{76} - 3664 q^{79} + 324 q^{81} - 378 q^{84} + 2912 q^{86} - 1592 q^{89} - 84 q^{91} - 5176 q^{94} - 1854 q^{96} - 1116 q^{99}+O(q^{100}) $ 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9 + 124 * q^11 - 42 * q^14 + 50 * q^16 + 244 * q^19 + 84 * q^21 - 306 * q^24 - 428 * q^26 - 704 * q^29 + 132 * q^31 + 372 * q^34 + 162 * q^36 + 36 * q^39 + 32 * q^41 - 312 * q^44 - 1920 * q^46 - 196 * q^49 + 240 * q^51 - 162 * q^54 + 714 * q^56 - 1032 * q^59 - 1760 * q^61 + 958 * q^64 + 312 * q^66 - 96 * q^69 + 620 * q^71 - 2716 * q^74 - 1344 * q^76 - 3664 * q^79 + 324 * q^81 - 378 * q^84 + 2912 * q^86 - 1592 * q^89 - 84 * q^91 - 5176 * q^94 - 1854 * q^96 - 1116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	− 4.70156i	− 1.66225i	−0.556083	−	0.831127i	$-0.687696\pi$
$2$	− 4.70156i	− 1.66225i	0.556083	−	0.831127i	$-0.312304\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−14.1047	−1.76309
$5$	0	0
$5$	0	0
$6$	14.1047	0.959702
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	28.7016i	1.26844i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	24.5969	0.674203	0.337102	−	0.941468i	$-0.390553\pi$
$11$	24.5969	0.674203	0.337102	+	0.941468i	$0.390553\pi$
$12$	− 42.3141i	− 1.01792i
$13$	− 35.0156i	− 0.747045i	−0.927621	−	0.373523i	$-0.878150\pi$
$13$	− 35.0156i	− 0.747045i	0.927621	−	0.373523i	$-0.121850\pi$
$14$	−32.9109	−0.628273
$15$	0	0
$16$	22.1047	0.345386
$17$	18.4187i	0.262777i	0.991331	+	0.131388i	$0.0419435\pi$
$17$	18.4187i	0.262777i	−0.991331	+	0.131388i	$0.958057\pi$
$18$	42.3141i	0.554084i
$19$	67.4031	0.813860	0.406930	−	0.913459i	$-0.366599\pi$
$19$	67.4031	0.813860	0.406930	+	0.913459i	$0.366599\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 115.644i	− 1.12070i
$23$	− 145.675i	− 1.32067i	−0.750973	−	0.660333i	$-0.770415\pi$
$23$	− 145.675i	− 1.32067i	0.750973	−	0.660333i	$-0.229585\pi$
$24$	−86.1047	−0.732335
$25$	0	0
$26$	−164.628	−1.24178
$27$	− 27.0000i	− 0.192450i
$28$	98.7328i	0.666384i
$29$	−214.419	−1.37298	−0.686492	−	0.727137i	$-0.740851\pi$
$29$	−214.419	−1.37298	−0.686492	+	0.727137i	$0.740851\pi$
$30$	0	0
$31$	−88.6594	−0.513667	−0.256834	−	0.966456i	$-0.582679\pi$
$31$	−88.6594	−0.513667	−0.256834	+	0.966456i	$0.582679\pi$
$32$	125.686i	0.694323i
$33$	73.7906i	0.389251i
$34$	86.5969	0.436801
$35$	0	0
$36$	126.942	0.587695
$37$	− 162.125i	− 0.720356i	−0.932884	−	0.360178i	$-0.882716\pi$
$37$	− 162.125i	− 0.720356i	0.932884	−	0.360178i	$-0.117284\pi$
$38$	− 316.900i	− 1.35284i
$39$	105.047	0.431307
$40$	0	0
$41$	−337.769	−1.28660	−0.643300	−	0.765614i	$-0.722435\pi$
$41$	−337.769	−1.28660	−0.643300	+	0.765614i	$0.722435\pi$
$42$	− 98.7328i	− 0.362733i
$43$	122.156i	0.433224i	0.976258	+	0.216612i	$0.0695007\pi$
$43$	122.156i	0.433224i	−0.976258	+	0.216612i	$0.930499\pi$
$44$	−346.931	−1.18868
$45$	0	0
$46$	−684.900	−2.19528
$47$	− 354.219i	− 1.09932i	−0.835388	−	0.549661i	$-0.814757\pi$
$47$	− 354.219i	− 1.09932i	0.835388	−	0.549661i	$-0.185243\pi$
$48$	66.3141i	0.199409i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−55.2562	−0.151714
$52$	493.884i	1.31710i
$53$	676.691i	1.75378i	0.480687	+	0.876892i	$0.340387\pi$
$53$	676.691i	1.75378i	−0.480687	+	0.876892i	$0.659613\pi$
$54$	−126.942	−0.319901
$55$	0	0
$56$	200.911	0.479426
$57$	202.209i	0.469882i
$58$	1008.10i	2.28225i
$59$	−501.319	−1.10621	−0.553103	−	0.833113i	$-0.686556\pi$
$59$	−501.319	−1.10621	−0.553103	+	0.833113i	$0.686556\pi$
$60$	0	0
$61$	−708.931	−1.48802	−0.744011	−	0.668167i	$-0.767079\pi$
$61$	−708.931	−1.48802	−0.744011	+	0.668167i	$0.767079\pi$
$62$	416.837i	0.853845i
$63$	63.0000i	0.125988i
$64$	767.758	1.49953
$65$	0	0
$66$	346.931	0.647035
$67$	907.956i	1.65559i	0.561031	+	0.827795i	$0.310405\pi$
$67$	907.956i	1.65559i	−0.561031	+	0.827795i	$0.689595\pi$
$68$	− 259.791i	− 0.463298i
$69$	437.025	0.762487
$70$	0	0
$71$	430.334	0.719314	0.359657	−	0.933085i	$-0.382894\pi$
$71$	430.334	0.719314	0.359657	+	0.933085i	$0.382894\pi$
$72$	− 258.314i	− 0.422814i
$73$	41.3406i	0.0662816i	0.999451	+	0.0331408i	$0.0105510\pi$
$73$	41.3406i	0.0662816i	−0.999451	+	0.0331408i	$0.989449\pi$
$74$	−762.241	−1.19741
$75$	0	0
$76$	−950.700	−1.43490
$77$	− 172.178i	− 0.254825i
$78$	− 493.884i	− 0.716941i
$79$	−890.388	−1.26806	−0.634028	−	0.773310i	$-0.718600\pi$
$79$	−890.388	−1.26806	−0.634028	+	0.773310i	$0.718600\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1588.04i	2.13866i
$83$	− 1057.15i	− 1.39804i	−0.715102	−	0.699020i	$-0.753620\pi$
$83$	− 1057.15i	− 1.39804i	0.715102	−	0.699020i	$-0.246380\pi$
$84$	−296.198	−0.384737
$85$	0	0
$86$	574.325	0.720129
$87$	− 643.256i	− 0.792693i
$88$	705.969i	0.855188i
$89$	−1473.72	−1.75522	−0.877610	−	0.479376i	$-0.840863\pi$
$89$	−1473.72	−1.75522	−0.877610	+	0.479376i	$0.840863\pi$
$90$	0	0
$91$	−245.109	−0.282356
$92$	2054.70i	2.32845i
$93$	− 265.978i	− 0.296566i
$94$	−1665.38	−1.82735
$95$	0	0
$96$	−377.058	−0.400868
$97$	− 555.034i	− 0.580981i	−0.956878	−	0.290491i	$-0.906181\pi$
$97$	− 555.034i	− 0.580981i	0.956878	−	0.290491i	$-0.0938185\pi$
$98$	230.377i	0.237465i
$99$	−221.372	−0.224734
$100$	0	0
$101$	1890.14	1.86214	0.931071	−	0.364838i	$-0.118876\pi$
$101$	1890.14	1.86214	0.931071	+	0.364838i	$0.118876\pi$
$102$	259.791i	0.252187i
$103$	662.700i	0.633959i	0.948432	+	0.316979i	$0.102669\pi$
$103$	662.700i	0.633959i	−0.948432	+	0.316979i	$0.897331\pi$
$104$	1005.00	0.947583
$105$	0	0
$106$	3181.50	2.91523
$107$	− 1614.53i	− 1.45872i	−0.684132	−	0.729358i	$-0.739819\pi$
$107$	− 1614.53i	− 1.45872i	0.684132	−	0.729358i	$-0.260181\pi$
$108$	380.827i	0.339306i
$109$	−217.206	−0.190868	−0.0954339	−	0.995436i	$-0.530424\pi$
$109$	−217.206	−0.190868	−0.0954339	+	0.995436i	$0.530424\pi$
$110$	0	0
$111$	486.375	0.415898
$112$	− 154.733i	− 0.130544i
$113$	− 1658.20i	− 1.38044i	−0.723598	−	0.690221i	$-0.757513\pi$
$113$	− 1658.20i	− 1.38044i	0.723598	−	0.690221i	$-0.242487\pi$
$114$	950.700	0.781063
$115$	0	0
$116$	3024.31	2.42069
$117$	315.141i	0.249015i
$118$	2356.98i	1.83879i
$119$	128.931	0.0993202
$120$	0	0
$121$	−725.994	−0.545450
$122$	3333.08i	2.47347i
$123$	− 1013.31i	− 0.742819i
$124$	1250.51	0.905640
$125$	0	0
$126$	296.198	0.209424
$127$	1108.81i	0.774734i	0.921926	+	0.387367i	$0.126615\pi$
$127$	1108.81i	0.774734i	−0.921926	+	0.387367i	$0.873385\pi$
$128$	− 2604.17i	− 1.79827i
$129$	−366.469	−0.250122
$130$	0	0
$131$	185.488	0.123711	0.0618554	−	0.998085i	$-0.480298\pi$
$131$	185.488	0.123711	0.0618554	+	0.998085i	$0.480298\pi$
$132$	− 1040.79i	− 0.686284i
$133$	− 471.822i	− 0.307610i
$134$	4268.81	2.75201
$135$	0	0
$136$	−528.647	−0.333317
$137$	37.9907i	0.0236917i	0.999930	+	0.0118458i	$0.00377074\pi$
$137$	37.9907i	0.0236917i	−0.999930	+	0.0118458i	$0.996229\pi$
$138$	− 2054.70i	− 1.26745i
$139$	−183.609	−0.112040	−0.0560199	−	0.998430i	$-0.517841\pi$
$139$	−183.609	−0.112040	−0.0560199	+	0.998430i	$0.517841\pi$
$140$	0	0
$141$	1062.66	0.634694
$142$	− 2023.24i	− 1.19568i
$143$	− 861.275i	− 0.503660i
$144$	−198.942	−0.115129
$145$	0	0
$146$	194.366	0.110177
$147$	− 147.000i	− 0.0824786i
$148$	2286.72i	1.27005i
$149$	1383.34	0.760587	0.380293	−	0.924866i	$-0.375823\pi$
$149$	1383.34	0.760587	0.380293	+	0.924866i	$0.375823\pi$
$150$	0	0
$151$	765.256	0.412422	0.206211	−	0.978508i	$-0.433887\pi$
$151$	765.256	0.412422	0.206211	+	0.978508i	$0.433887\pi$
$152$	1934.57i	1.03233i
$153$	− 165.769i	− 0.0875922i
$154$	−809.506	−0.423584
$155$	0	0
$156$	−1481.65	−0.760431
$157$	2366.76i	1.20311i	0.798832	+	0.601554i	$0.205452\pi$
$157$	2366.76i	1.20311i	−0.798832	+	0.601554i	$0.794548\pi$
$158$	4186.21i	2.10783i
$159$	−2030.07	−1.01255
$160$	0	0
$161$	−1019.72	−0.499165
$162$	− 380.827i	− 0.184695i
$163$	− 3137.69i	− 1.50775i	−0.657018	−	0.753875i	$-0.728183\pi$
$163$	− 3137.69i	− 1.50775i	0.657018	−	0.753875i	$-0.271817\pi$
$164$	4764.12	2.26839
$165$	0	0
$166$	−4970.26	−2.32390
$167$	− 146.469i	− 0.0678688i	−0.999424	−	0.0339344i	$-0.989196\pi$
$167$	− 146.469i	− 0.0678688i	0.999424	−	0.0339344i	$-0.0108037\pi$
$168$	602.733i	0.276797i
$169$	970.906	0.441924
$170$	0	0
$171$	−606.628	−0.271287
$172$	− 1722.98i	− 0.763812i
$173$	− 1424.12i	− 0.625860i	−0.949776	−	0.312930i	$-0.898689\pi$
$173$	− 1424.12i	− 0.625860i	0.949776	−	0.312930i	$-0.101311\pi$
$174$	−3024.31	−1.31766
$175$	0	0
$176$	543.706	0.232860
$177$	− 1503.96i	− 0.638668i
$178$	6928.81i	2.91762i
$179$	−1244.70	−0.519737	−0.259869	−	0.965644i	$-0.583679\pi$
$179$	−1244.70	−0.519737	−0.259869	+	0.965644i	$0.583679\pi$
$180$	0	0
$181$	−3879.09	−1.59299	−0.796493	−	0.604648i	$-0.793314\pi$
$181$	−3879.09	−1.59299	−0.796493	+	0.604648i	$0.793314\pi$
$182$	1152.40i	0.469348i
$183$	− 2126.79i	− 0.859110i
$184$	4181.10	1.67519
$185$	0	0
$186$	−1250.51	−0.492968
$187$	453.044i	0.177165i
$188$	4996.14i	1.93820i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	1574.90	0.596628	0.298314	−	0.954468i	$-0.403576\pi$
$191$	1574.90	0.596628	0.298314	+	0.954468i	$0.403576\pi$
$192$	2303.27i	0.865752i
$193$	− 4775.67i	− 1.78114i	−0.454843	−	0.890572i	$-0.650305\pi$
$193$	− 4775.67i	− 1.78114i	0.454843	−	0.890572i	$-0.349695\pi$
$194$	−2609.53	−0.965738
$195$	0	0
$196$	691.130	0.251869
$197$	2803.58i	1.01394i	0.861963	+	0.506971i	$0.169235\pi$
$197$	2803.58i	1.01394i	−0.861963	+	0.506971i	$0.830765\pi$
$198$	1040.79i	0.373566i
$199$	−4102.92	−1.46155	−0.730774	−	0.682620i	$-0.760841\pi$
$199$	−4102.92	−1.46155	−0.730774	+	0.682620i	$0.760841\pi$
$200$	0	0
$201$	−2723.87	−0.955855
$202$	− 8886.63i	− 3.09535i
$203$	1500.93i	0.518940i
$204$	779.372	0.267485
$205$	0	0
$206$	3115.72	1.05380
$207$	1311.07i	0.440222i
$208$	− 774.009i	− 0.258019i
$209$	1657.91	0.548707
$210$	0	0
$211$	−823.512	−0.268687	−0.134343	−	0.990935i	$-0.542893\pi$
$211$	−823.512	−0.268687	−0.134343	+	0.990935i	$0.542893\pi$
$212$	− 9544.51i	− 3.09207i
$213$	1291.00i	0.415296i
$214$	−7590.82	−2.42476
$215$	0	0
$216$	774.942	0.244112
$217$	620.616i	0.194148i
$218$	1021.21i	0.317271i
$219$	−124.022	−0.0382677
$220$	0	0
$221$	644.944	0.196306
$222$	− 2286.72i	− 0.691328i
$223$	817.194i	0.245396i	0.992444	+	0.122698i	$0.0391547\pi$
$223$	817.194i	0.245396i	−0.992444	+	0.122698i	$0.960845\pi$
$224$	879.802	0.262430
$225$	0	0
$226$	−7796.12	−2.29465
$227$	− 3655.85i	− 1.06893i	−0.845190	−	0.534465i	$-0.820513\pi$
$227$	− 3655.85i	− 1.06893i	0.845190	−	0.534465i	$-0.179487\pi$
$228$	− 2852.10i	− 0.828443i
$229$	−939.393	−0.271078	−0.135539	−	0.990772i	$-0.543277\pi$
$229$	−939.393	−0.271078	−0.135539	+	0.990772i	$0.543277\pi$
$230$	0	0
$231$	516.534	0.147123
$232$	− 6154.15i	− 1.74155i
$233$	− 7.64701i	− 0.00215010i	−0.999999	−	0.00107505i	$-0.999658\pi$
$233$	− 7.64701i	− 0.00215010i	0.999999	−	0.00107505i	$-0.000342198\pi$
$234$	1481.65	0.413926
$235$	0	0
$236$	7070.94	1.95034
$237$	− 2671.16i	− 0.732112i
$238$	− 606.178i	− 0.165095i
$239$	889.115	0.240636	0.120318	−	0.992735i	$-0.461609\pi$
$239$	889.115	0.240636	0.120318	+	0.992735i	$0.461609\pi$
$240$	0	0
$241$	2140.23	0.572051	0.286026	−	0.958222i	$-0.407666\pi$
$241$	2140.23	0.572051	0.286026	+	0.958222i	$0.407666\pi$
$242$	3413.30i	0.906676i
$243$	243.000i	0.0641500i
$244$	9999.25	2.62351
$245$	0	0
$246$	−4764.12	−1.23475
$247$	− 2360.16i	− 0.607990i
$248$	− 2544.66i	− 0.651557i
$249$	3171.45	0.807158
$250$	0	0
$251$	−6749.81	−1.69739	−0.848693	−	0.528886i	$-0.822610\pi$
$251$	−6749.81	−1.69739	−0.848693	+	0.528886i	$0.822610\pi$
$252$	− 888.595i	− 0.222128i
$253$	− 3583.15i	− 0.890398i
$254$	5213.15	1.28780
$255$	0	0
$256$	−6101.62	−1.48965
$257$	− 3068.64i	− 0.744811i	−0.928070	−	0.372405i	$-0.878533\pi$
$257$	− 3068.64i	− 0.744811i	0.928070	−	0.372405i	$-0.121467\pi$
$258$	1722.98i	0.415766i
$259$	−1134.87	−0.272269
$260$	0	0
$261$	1929.77	0.457662
$262$	− 872.081i	− 0.205639i
$263$	− 4674.12i	− 1.09589i	−0.836515	−	0.547944i	$-0.815411\pi$
$263$	− 4674.12i	− 1.09589i	0.836515	−	0.547944i	$-0.184589\pi$
$264$	−2117.91	−0.493743
$265$	0	0
$266$	−2218.30	−0.511326
$267$	− 4421.17i	− 1.01338i
$268$	− 12806.4i	− 2.91895i
$269$	−2417.38	−0.547919	−0.273960	−	0.961741i	$-0.588333\pi$
$269$	−2417.38	−0.547919	−0.273960	+	0.961741i	$0.588333\pi$
$270$	0	0
$271$	7724.30	1.73143	0.865715	−	0.500537i	$-0.166864\pi$
$271$	7724.30	1.73143	0.865715	+	0.500537i	$0.166864\pi$
$272$	407.141i	0.0907593i
$273$	− 735.328i	− 0.163019i
$274$	178.616	0.0393816
$275$	0	0
$276$	−6164.10	−1.34433
$277$	4576.17i	0.992620i	0.868145	+	0.496310i	$0.165312\pi$
$277$	4576.17i	0.992620i	−0.868145	+	0.496310i	$0.834688\pi$
$278$	863.250i	0.186239i
$279$	797.934	0.171222
$280$	0	0
$281$	−1358.56	−0.288415	−0.144208	−	0.989547i	$-0.546063\pi$
$281$	−1358.56	−0.288415	−0.144208	+	0.989547i	$0.546063\pi$
$282$	− 4996.14i	− 1.05502i
$283$	3885.04i	0.816048i	0.912971	+	0.408024i	$0.133782\pi$
$283$	3885.04i	0.816048i	−0.912971	+	0.408024i	$0.866218\pi$
$284$	−6069.73	−1.26821
$285$	0	0
$286$	−4049.34	−0.837211
$287$	2364.38i	0.486289i
$288$	− 1131.17i	− 0.231441i
$289$	4573.75	0.930948
$290$	0	0
$291$	1665.10	0.335430
$292$	− 583.097i	− 0.116860i
$293$	− 4033.91i	− 0.804312i	−0.915571	−	0.402156i	$-0.868261\pi$
$293$	− 4033.91i	− 0.804312i	0.915571	−	0.402156i	$-0.131739\pi$
$294$	−691.130	−0.137100
$295$	0	0
$296$	4653.24	0.913730
$297$	− 664.116i	− 0.129750i
$298$	− 6503.85i	− 1.26429i
$299$	−5100.90	−0.986598
$300$	0	0
$301$	855.093	0.163743
$302$	− 3597.90i	− 0.685549i
$303$	5670.43i	1.07511i
$304$	1489.92	0.281096
$305$	0	0
$306$	−779.372	−0.145600
$307$	4620.36i	0.858950i	0.903079	+	0.429475i	$0.141301\pi$
$307$	4620.36i	0.858950i	−0.903079	+	0.429475i	$0.858699\pi$
$308$	2428.52i	0.449278i
$309$	−1988.10	−0.366016
$310$	0	0
$311$	6675.89	1.21722	0.608609	−	0.793470i	$-0.291728\pi$
$311$	6675.89	1.21722	0.608609	+	0.793470i	$0.291728\pi$
$312$	3015.01i	0.547087i
$313$	2836.78i	0.512283i	0.966639	+	0.256141i	$0.0824513\pi$
$313$	2836.78i	0.512283i	−0.966639	+	0.256141i	$0.917549\pi$
$314$	11127.5	1.99987
$315$	0	0
$316$	12558.6	2.23569
$317$	− 4010.63i	− 0.710597i	−0.934753	−	0.355299i	$-0.884379\pi$
$317$	− 4010.63i	− 0.710597i	0.934753	−	0.355299i	$-0.115621\pi$
$318$	9544.51i	1.68311i
$319$	−5274.03	−0.925671
$320$	0	0
$321$	4843.59	0.842190
$322$	4794.30i	0.829739i
$323$	1241.48i	0.213863i
$324$	−1142.48	−0.195898
$325$	0	0
$326$	−14752.1	−2.50626
$327$	− 651.619i	− 0.110198i
$328$	− 9694.49i	− 1.63198i
$329$	−2479.53	−0.415504
$330$	0	0
$331$	11087.5	1.84117	0.920583	−	0.390546i	$-0.127714\pi$
$331$	11087.5	1.84117	0.920583	+	0.390546i	$0.127714\pi$
$332$	14910.8i	2.46486i
$333$	1459.12i	0.240119i
$334$	−688.631	−0.112815
$335$	0	0
$336$	464.198	0.0753693
$337$	− 12118.7i	− 1.95890i	−0.201689	−	0.979450i	$-0.564643\pi$
$337$	− 12118.7i	− 1.95890i	0.201689	−	0.979450i	$-0.435357\pi$
$338$	− 4564.78i	− 0.734589i
$339$	4974.59	0.796999
$340$	0	0
$341$	−2180.74	−0.346316
$342$	2852.10i	0.450947i
$343$	343.000i	0.0539949i
$344$	−3506.07	−0.549520
$345$	0	0
$346$	−6695.58	−1.04034
$347$	6361.22i	0.984116i	0.870562	+	0.492058i	$0.163755\pi$
$347$	6361.22i	0.984116i	−0.870562	+	0.492058i	$0.836245\pi$
$348$	9072.93i	1.39759i
$349$	3115.18	0.477799	0.238899	−	0.971044i	$-0.423213\pi$
$349$	3115.18	0.477799	0.238899	+	0.971044i	$0.423213\pi$
$350$	0	0
$351$	−945.422	−0.143769
$352$	3091.48i	0.468115i
$353$	− 11927.4i	− 1.79839i	−0.437550	−	0.899194i	$-0.644154\pi$
$353$	− 11927.4i	− 1.79839i	0.437550	−	0.899194i	$-0.355846\pi$
$354$	−7070.94	−1.06163
$355$	0	0
$356$	20786.4	3.09460
$357$	386.794i	0.0573426i
$358$	5852.02i	0.863935i
$359$	6143.95	0.903245	0.451623	−	0.892209i	$-0.350845\pi$
$359$	6143.95	0.903245	0.451623	+	0.892209i	$0.350845\pi$
$360$	0	0
$361$	−2315.82	−0.337632
$362$	18237.8i	2.64794i
$363$	− 2177.98i	− 0.314916i
$364$	3457.19	0.497819
$365$	0	0
$366$	−9999.25	−1.42806
$367$	1927.67i	0.274178i	0.990559	+	0.137089i	$0.0437747\pi$
$367$	1927.67i	0.274178i	−0.990559	+	0.137089i	$0.956225\pi$
$368$	− 3220.10i	− 0.456139i
$369$	3039.92	0.428867
$370$	0	0
$371$	4736.83	0.662868
$372$	3751.54i	0.522871i
$373$	10452.0i	1.45090i	0.688276	+	0.725449i	$0.258368\pi$
$373$	10452.0i	1.45090i	−0.688276	+	0.725449i	$0.741632\pi$
$374$	2130.01	0.294493
$375$	0	0
$376$	10166.6	1.39443
$377$	7508.01i	1.02568i
$378$	888.595i	0.120911i
$379$	−7066.43	−0.957726	−0.478863	−	0.877890i	$-0.658951\pi$
$379$	−7066.43	−0.957726	−0.478863	+	0.877890i	$0.658951\pi$
$380$	0	0
$381$	−3326.44	−0.447293
$382$	− 7404.51i	− 0.991747i
$383$	7168.04i	0.956318i	0.878273	+	0.478159i	$0.158696\pi$
$383$	7168.04i	0.956318i	−0.878273	+	0.478159i	$0.841304\pi$
$384$	7812.52	1.03823
$385$	0	0
$386$	−22453.1	−2.96071
$387$	− 1099.41i	− 0.144408i
$388$	7828.58i	1.02432i
$389$	7414.06	0.966344	0.483172	−	0.875525i	$-0.339485\pi$
$389$	7414.06	0.966344	0.483172	+	0.875525i	$0.339485\pi$
$390$	0	0
$391$	2683.15	0.347040
$392$	− 1406.38i	− 0.181206i
$393$	556.463i	0.0714245i
$394$	13181.2	1.68543
$395$	0	0
$396$	3122.38	0.396226
$397$	8936.01i	1.12969i	0.825198	+	0.564843i	$0.191063\pi$
$397$	8936.01i	1.12969i	−0.825198	+	0.564843i	$0.808937\pi$
$398$	19290.1i	2.42946i
$399$	1415.47	0.177599
$400$	0	0
$401$	1782.91	0.222031	0.111015	−	0.993819i	$-0.464590\pi$
$401$	1782.91	0.222031	0.111015	+	0.993819i	$0.464590\pi$
$402$	12806.4i	1.58887i
$403$	3104.46i	0.383733i
$404$	−26659.9	−3.28312
$405$	0	0
$406$	7056.72	0.862609
$407$	− 3987.77i	− 0.485667i
$408$	− 1585.94i	− 0.192441i
$409$	8759.92	1.05905	0.529524	−	0.848295i	$-0.322371\pi$
$409$	8759.92	1.05905	0.529524	+	0.848295i	$0.322371\pi$
$410$	0	0
$411$	−113.972	−0.0136784
$412$	− 9347.17i	− 1.11772i
$413$	3509.23i	0.418106i
$414$	6164.10	0.731761
$415$	0	0
$416$	4400.97	0.518691
$417$	− 550.828i	− 0.0646862i
$418$	− 7794.75i	− 0.912090i
$419$	3212.74	0.374588	0.187294	−	0.982304i	$-0.440028\pi$
$419$	3212.74	0.374588	0.187294	+	0.982304i	$0.440028\pi$
$420$	0	0
$421$	15757.8	1.82420	0.912101	−	0.409965i	$-0.134459\pi$
$421$	15757.8	1.82420	0.912101	+	0.409965i	$0.134459\pi$
$422$	3871.79i	0.446626i
$423$	3187.97i	0.366440i
$424$	−19422.1	−2.22457
$425$	0	0
$426$	6069.73	0.690327
$427$	4962.52i	0.562419i
$428$	22772.5i	2.57184i
$429$	2583.82	0.290788
$430$	0	0
$431$	−405.917	−0.0453650	−0.0226825	−	0.999743i	$-0.507221\pi$
$431$	−405.917	−0.0453650	−0.0226825	+	0.999743i	$0.507221\pi$
$432$	− 596.827i	− 0.0664695i
$433$	− 7845.25i	− 0.870713i	−0.900258	−	0.435357i	$-0.856622\pi$
$433$	− 7845.25i	− 0.870713i	0.900258	−	0.435357i	$-0.143378\pi$
$434$	2917.86	0.322723
$435$	0	0
$436$	3063.63	0.336516
$437$	− 9818.95i	− 1.07484i
$438$	583.097i	0.0636106i
$439$	−423.029	−0.0459911	−0.0229955	−	0.999736i	$-0.507320\pi$
$439$	−423.029	−0.0459911	−0.0229955	+	0.999736i	$0.507320\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 3032.24i	− 0.326310i
$443$	− 16058.7i	− 1.72229i	−0.508362	−	0.861143i	$-0.669749\pi$
$443$	− 16058.7i	− 1.72229i	0.508362	−	0.861143i	$-0.330251\pi$
$444$	−6860.17	−0.733264
$445$	0	0
$446$	3842.09	0.407911
$447$	4150.01i	0.439125i
$448$	− 5374.30i	− 0.566768i
$449$	−2186.75	−0.229842	−0.114921	−	0.993375i	$-0.536662\pi$
$449$	−2186.75	−0.229842	−0.114921	+	0.993375i	$0.536662\pi$
$450$	0	0
$451$	−8308.05	−0.867430
$452$	23388.3i	2.43384i
$453$	2295.77i	0.238112i
$454$	−17188.2	−1.77683
$455$	0	0
$456$	−5803.72	−0.596018
$457$	5799.22i	0.593602i	0.954939	+	0.296801i	$0.0959198\pi$
$457$	5799.22i	0.593602i	−0.954939	+	0.296801i	$0.904080\pi$
$458$	4416.62i	0.450600i
$459$	497.306	0.0505714
$460$	0	0
$461$	9873.35	0.997500	0.498750	−	0.866746i	$-0.333793\pi$
$461$	9873.35	0.997500	0.498750	+	0.866746i	$0.333793\pi$
$462$	− 2428.52i	− 0.244556i
$463$	− 6181.84i	− 0.620506i	−0.950654	−	0.310253i	$-0.899586\pi$
$463$	− 6181.84i	− 0.620506i	0.950654	−	0.310253i	$-0.100414\pi$
$464$	−4739.66	−0.474209
$465$	0	0
$466$	−35.9529	−0.00357400
$467$	− 6145.50i	− 0.608950i	−0.952520	−	0.304475i	$-0.901519\pi$
$467$	− 6145.50i	− 0.608950i	0.952520	−	0.304475i	$-0.0984810\pi$
$468$	− 4444.96i	− 0.439035i
$469$	6355.69	0.625754
$470$	0	0
$471$	−7100.28	−0.694615
$472$	− 14388.6i	− 1.40316i
$473$	3004.66i	0.292081i
$474$	−12558.6	−1.21696
$475$	0	0
$476$	−1818.53	−0.175110
$477$	− 6090.22i	− 0.584595i
$478$	− 4180.23i	− 0.399999i
$479$	−10879.4	−1.03777	−0.518887	−	0.854843i	$-0.673653\pi$
$479$	−10879.4	−1.03777	−0.518887	+	0.854843i	$0.673653\pi$
$480$	0	0
$481$	−5676.91	−0.538139
$482$	− 10062.4i	− 0.950894i
$483$	− 3059.17i	− 0.288193i
$484$	10239.9	0.961675
$485$	0	0
$486$	1142.48	0.106634
$487$	− 8087.51i	− 0.752526i	−0.926513	−	0.376263i	$-0.877209\pi$
$487$	− 8087.51i	− 0.752526i	0.926513	−	0.376263i	$-0.122791\pi$
$488$	− 20347.4i	− 1.88747i
$489$	9413.08	0.870499
$490$	0	0
$491$	−6959.90	−0.639707	−0.319853	−	0.947467i	$-0.603634\pi$
$491$	−6959.90	−0.639707	−0.319853	+	0.947467i	$0.603634\pi$
$492$	14292.4i	1.30965i
$493$	− 3949.32i	− 0.360788i
$494$	−11096.4	−1.01063
$495$	0	0
$496$	−1959.79	−0.177413
$497$	− 3012.34i	− 0.271875i
$498$	− 14910.8i	− 1.34170i
$499$	−18632.0	−1.67151	−0.835756	−	0.549101i	$-0.814970\pi$
$499$	−18632.0	−1.67151	−0.835756	+	0.549101i	$0.814970\pi$
$500$	0	0
$501$	439.406	0.0391840
$502$	31734.6i	2.82149i
$503$	4627.62i	0.410209i	0.978740	+	0.205105i	$0.0657535\pi$
$503$	4627.62i	0.410209i	−0.978740	+	0.205105i	$0.934247\pi$
$504$	−1808.20	−0.159809
$505$	0	0
$506$	−16846.4	−1.48007
$507$	2912.72i	0.255145i
$508$	− 15639.4i	− 1.36592i
$509$	11351.8	0.988528	0.494264	−	0.869312i	$-0.335438\pi$
$509$	11351.8	0.988528	0.494264	+	0.869312i	$0.335438\pi$
$510$	0	0
$511$	289.384	0.0250521
$512$	7853.76i	0.677911i
$513$	− 1819.88i	− 0.156627i
$514$	−14427.4	−1.23806
$515$	0	0
$516$	5168.93	0.440987
$517$	− 8712.67i	− 0.741166i
$518$	5335.68i	0.452580i
$519$	4272.36	0.361340
$520$	0	0
$521$	19096.1	1.60579	0.802893	−	0.596123i	$-0.203293\pi$
$521$	19096.1	1.60579	0.802893	+	0.596123i	$0.203293\pi$
$522$	− 9072.93i	− 0.760750i
$523$	− 3145.11i	− 0.262956i	−0.991319	−	0.131478i	$-0.958028\pi$
$523$	− 3145.11i	− 0.262956i	0.991319	−	0.131478i	$-0.0419723\pi$
$524$	−2616.24	−0.218113
$525$	0	0
$526$	−21975.7	−1.82164
$527$	− 1632.99i	− 0.134980i
$528$	1631.12i	0.134442i
$529$	−9054.20	−0.744160
$530$	0	0
$531$	4511.87	0.368735
$532$	6654.90i	0.542343i
$533$	11827.2i	0.961148i
$534$	−20786.4	−1.68449
$535$	0	0
$536$	−26059.8	−2.10002
$537$	− 3734.09i	− 0.300071i
$538$	11365.5i	0.910781i
$539$	−1205.25	−0.0963148
$540$	0	0
$541$	8776.12	0.697440	0.348720	−	0.937227i	$-0.386616\pi$
$541$	8776.12	0.697440	0.348720	+	0.937227i	$0.386616\pi$
$542$	− 36316.3i	− 2.87808i
$543$	− 11637.3i	− 0.919710i
$544$	−2314.98	−0.182452
$545$	0	0
$546$	−3457.19	−0.270978
$547$	13695.1i	1.07049i	0.844696	+	0.535247i	$0.179781\pi$
$547$	13695.1i	1.07049i	−0.844696	+	0.535247i	$0.820219\pi$
$548$	− 535.847i	− 0.0417705i
$549$	6380.38	0.496007
$550$	0	0
$551$	−14452.5	−1.11742
$552$	12543.3i	0.967171i
$553$	6232.71i	0.479280i
$554$	21515.2	1.64999
$555$	0	0
$556$	2589.75	0.197536
$557$	− 7850.44i	− 0.597188i	−0.954380	−	0.298594i	$-0.903482\pi$
$557$	− 7850.44i	− 0.597188i	0.954380	−	0.298594i	$-0.0965177\pi$
$558$	− 3751.54i	− 0.284615i
$559$	4277.38	0.323638
$560$	0	0
$561$	−1359.13	−0.102286
$562$	6387.33i	0.479419i
$563$	− 4948.81i	− 0.370457i	−0.982695	−	0.185229i	$-0.940697\pi$
$563$	− 4948.81i	− 0.370457i	0.982695	−	0.185229i	$-0.0593026\pi$
$564$	−14988.4	−1.11902
$565$	0	0
$566$	18265.7	1.35648
$567$	− 567.000i	− 0.0419961i
$568$	12351.3i	0.912408i
$569$	8115.76	0.597945	0.298972	−	0.954262i	$-0.403356\pi$
$569$	8115.76	0.597945	0.298972	+	0.954262i	$0.403356\pi$
$570$	0	0
$571$	5656.42	0.414560	0.207280	−	0.978282i	$-0.433539\pi$
$571$	5656.42	0.414560	0.207280	+	0.978282i	$0.433539\pi$
$572$	12148.0i	0.887996i
$573$	4724.71i	0.344463i
$574$	11116.3	0.808336
$575$	0	0
$576$	−6909.82	−0.499842
$577$	9536.77i	0.688078i	0.938955	+	0.344039i	$0.111795\pi$
$577$	9536.77i	0.688078i	−0.938955	+	0.344039i	$0.888205\pi$
$578$	− 21503.8i	− 1.54747i
$579$	14327.0	1.02834
$580$	0	0
$581$	−7400.05	−0.528409
$582$	− 7828.58i	− 0.557569i
$583$	16644.5i	1.18241i
$584$	−1186.54	−0.0840743
$585$	0	0
$586$	−18965.7	−1.33697
$587$	13089.6i	0.920383i	0.887820	+	0.460191i	$0.152219\pi$
$587$	13089.6i	0.920383i	−0.887820	+	0.460191i	$0.847781\pi$
$588$	2073.39i	0.145417i
$589$	−5975.92	−0.418053
$590$	0	0
$591$	−8410.73	−0.585400
$592$	− 3583.72i	− 0.248801i
$593$	4281.96i	0.296524i	0.988948	+	0.148262i	$0.0473679\pi$
$593$	4281.96i	0.296524i	−0.988948	+	0.148262i	$0.952632\pi$
$594$	−3122.38	−0.215678
$595$	0	0
$596$	−19511.5	−1.34098
$597$	− 12308.7i	− 0.843825i
$598$	23982.2i	1.63997i
$599$	−3699.92	−0.252378	−0.126189	−	0.992006i	$-0.540275\pi$
$599$	−3699.92	−0.252378	−0.126189	+	0.992006i	$0.540275\pi$
$600$	0	0
$601$	−17286.1	−1.17323	−0.586616	−	0.809865i	$-0.699540\pi$
$601$	−17286.1	−1.17323	−0.586616	+	0.809865i	$0.699540\pi$
$602$	− 4020.28i	− 0.272183i
$603$	− 8171.61i	− 0.551863i
$604$	−10793.7	−0.727135
$605$	0	0
$606$	26659.9	1.78710
$607$	− 14456.7i	− 0.966689i	−0.875430	−	0.483344i	$-0.839422\pi$
$607$	− 14456.7i	− 0.966689i	0.875430	−	0.483344i	$-0.160578\pi$
$608$	8471.63i	0.565082i
$609$	−4502.79	−0.299610
$610$	0	0
$611$	−12403.2	−0.821243
$612$	2338.12i	0.154433i
$613$	17981.9i	1.18480i	0.805644	+	0.592400i	$0.201819\pi$
$613$	17981.9i	1.18480i	−0.805644	+	0.592400i	$0.798181\pi$
$614$	21722.9	1.42779
$615$	0	0
$616$	4941.78	0.323231
$617$	− 19614.7i	− 1.27983i	−0.768445	−	0.639916i	$-0.778969\pi$
$617$	− 19614.7i	− 1.27983i	0.768445	−	0.639916i	$-0.221031\pi$
$618$	9347.17i	0.608412i
$619$	10462.9	0.679385	0.339692	−	0.940537i	$-0.389677\pi$
$619$	10462.9	0.679385	0.339692	+	0.940537i	$0.389677\pi$
$620$	0	0
$621$	−3933.22	−0.254162
$622$	− 31387.1i	− 2.02332i
$623$	10316.1i	0.663411i
$624$	2322.03	0.148967
$625$	0	0
$626$	13337.3	0.851544
$627$	4973.72i	0.316796i
$628$	− 33382.4i	− 2.12118i
$629$	2986.14	0.189293
$630$	0	0
$631$	24481.9	1.54454	0.772272	−	0.635292i	$-0.219120\pi$
$631$	24481.9	1.54454	0.772272	+	0.635292i	$0.219120\pi$
$632$	− 25555.5i	− 1.60846i
$633$	− 2470.54i	− 0.155126i
$634$	−18856.2	−1.18119
$635$	0	0
$636$	28633.5	1.78521
$637$	1715.77i	0.106721i
$638$	24796.2i	1.53870i
$639$	−3873.01	−0.239771
$640$	0	0
$641$	−1109.39	−0.0683595	−0.0341797	−	0.999416i	$-0.510882\pi$
$641$	−1109.39	−0.0683595	−0.0341797	+	0.999416i	$0.510882\pi$
$642$	− 22772.5i	− 1.39993i
$643$	30112.5i	1.84684i	0.383787	+	0.923422i	$0.374620\pi$
$643$	30112.5i	1.84684i	−0.383787	+	0.923422i	$0.625380\pi$
$644$	14382.9	0.880071
$645$	0	0
$646$	5836.90	0.355495
$647$	4260.27i	0.258869i	0.991588	+	0.129435i	$0.0413162\pi$
$647$	4260.27i	0.258869i	−0.991588	+	0.129435i	$0.958684\pi$
$648$	2324.83i	0.140938i
$649$	−12330.9	−0.745808
$650$	0	0
$651$	−1861.85	−0.112091
$652$	44256.2i	2.65829i
$653$	− 10576.8i	− 0.633844i	−0.948452	−	0.316922i	$-0.897351\pi$
$653$	− 10576.8i	− 0.633844i	0.948452	−	0.316922i	$-0.102649\pi$
$654$	−3063.63	−0.183176
$655$	0	0
$656$	−7466.27	−0.444373
$657$	− 372.066i	− 0.0220939i
$658$	11657.7i	0.690674i
$659$	−3394.70	−0.200666	−0.100333	−	0.994954i	$-0.531991\pi$
$659$	−3394.70	−0.200666	−0.100333	+	0.994954i	$0.531991\pi$
$660$	0	0
$661$	−33174.4	−1.95210	−0.976048	−	0.217554i	$-0.930192\pi$
$661$	−33174.4	−1.95210	−0.976048	+	0.217554i	$0.930192\pi$
$662$	− 52128.7i	− 3.06048i
$663$	1934.83i	0.113337i
$664$	30341.9	1.77333
$665$	0	0
$666$	6860.17	0.399138
$667$	31235.4i	1.81326i
$668$	2065.89i	0.119658i
$669$	−2451.58	−0.141680
$670$	0	0
$671$	−17437.5	−1.00323
$672$	2639.40i	0.151514i
$673$	753.881i	0.0431797i	0.999767	+	0.0215899i	$0.00687280\pi$
$673$	753.881i	0.0431797i	−0.999767	+	0.0215899i	$0.993127\pi$
$674$	−56976.9	−3.25619
$675$	0	0
$676$	−13694.3	−0.779149
$677$	− 15668.8i	− 0.889511i	−0.895652	−	0.444756i	$-0.853291\pi$
$677$	− 15668.8i	− 0.889511i	0.895652	−	0.444756i	$-0.146709\pi$
$678$	− 23388.3i	− 1.32481i
$679$	−3885.24	−0.219590
$680$	0	0
$681$	10967.5	0.617147
$682$	10252.9i	0.575665i
$683$	− 11557.4i	− 0.647485i	−0.946145	−	0.323742i	$-0.895059\pi$
$683$	− 11557.4i	− 0.647485i	0.946145	−	0.323742i	$-0.104941\pi$
$684$	8556.30	0.478302
$685$	0	0
$686$	1612.64	0.0897532
$687$	− 2818.18i	− 0.156507i
$688$	2700.22i	0.149630i
$689$	23694.7	1.31016
$690$	0	0
$691$	−18503.1	−1.01866	−0.509328	−	0.860572i	$-0.670106\pi$
$691$	−18503.1	−1.01866	−0.509328	+	0.860572i	$0.670106\pi$
$692$	20086.8i	1.10344i
$693$	1549.60i	0.0849416i
$694$	29907.7	1.63585
$695$	0	0
$696$	18462.5	1.00549
$697$	− 6221.28i	− 0.338088i
$698$	− 14646.2i	− 0.794223i
$699$	22.9410	0.00124136
$700$	0	0
$701$	22580.4	1.21662	0.608311	−	0.793699i	$-0.291847\pi$
$701$	22580.4	1.21662	0.608311	+	0.793699i	$0.291847\pi$
$702$	4444.96i	0.238980i
$703$	− 10927.7i	− 0.586269i
$704$	18884.4	1.01099
$705$	0	0
$706$	−56077.4	−2.98938
$707$	− 13231.0i	− 0.703823i
$708$	21212.8i	1.12603i
$709$	27426.6	1.45279	0.726394	−	0.687278i	$-0.241195\pi$
$709$	27426.6	1.45279	0.726394	+	0.687278i	$0.241195\pi$
$710$	0	0
$711$	8013.49	0.422685
$712$	− 42298.2i	− 2.22639i
$713$	12915.5i	0.678383i
$714$	1818.53	0.0953178
$715$	0	0
$716$	17556.1	0.916342
$717$	2667.35i	0.138931i
$718$	− 28886.1i	− 1.50142i
$719$	−19383.0	−1.00538	−0.502688	−	0.864468i	$-0.667656\pi$
$719$	−19383.0	−1.00538	−0.502688	+	0.864468i	$0.667656\pi$
$720$	0	0
$721$	4638.90	0.239614
$722$	10888.0i	0.561230i
$723$	6420.69i	0.330274i
$724$	54713.3	2.80857
$725$	0	0
$726$	−10239.9	−0.523469
$727$	12317.3i	0.628368i	0.949362	+	0.314184i	$0.101731\pi$
$727$	12317.3i	0.628368i	−0.949362	+	0.314184i	$0.898269\pi$
$728$	− 7035.02i	− 0.358153i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−2249.96	−0.113841
$732$	29997.8i	1.51468i
$733$	1234.02i	0.0621822i	0.999517	+	0.0310911i	$0.00989821\pi$
$733$	1234.02i	0.0621822i	−0.999517	+	0.0310911i	$0.990102\pi$
$734$	9063.05	0.455754
$735$	0	0
$736$	18309.3	0.916970
$737$	22332.9i	1.11620i
$738$	− 14292.4i	− 0.712885i
$739$	15257.3	0.759473	0.379736	−	0.925095i	$-0.376015\pi$
$739$	15257.3	0.759473	0.379736	+	0.925095i	$0.376015\pi$
$740$	0	0
$741$	7080.49	0.351023
$742$	− 22270.5i	− 1.10186i
$743$	− 35565.1i	− 1.75606i	−0.478602	−	0.878032i	$-0.658856\pi$
$743$	− 35565.1i	− 1.75606i	0.478602	−	0.878032i	$-0.341144\pi$
$744$	7633.99	0.376177
$745$	0	0
$746$	49140.8	2.41176
$747$	9514.35i	0.466013i
$748$	− 6390.04i	− 0.312357i
$749$	−11301.7	−0.551343
$750$	0	0
$751$	14266.7	0.693209	0.346605	−	0.938011i	$-0.387335\pi$
$751$	14266.7	0.693209	0.346605	+	0.938011i	$0.387335\pi$
$752$	− 7829.89i	− 0.379690i
$753$	− 20249.4i	− 0.979986i
$754$	35299.4	1.70494
$755$	0	0
$756$	2665.79	0.128246
$757$	15927.9i	0.764744i	0.924009	+	0.382372i	$0.124893\pi$
$757$	15927.9i	0.764744i	−0.924009	+	0.382372i	$0.875107\pi$
$758$	33223.3i	1.59198i
$759$	10749.4	0.514071
$760$	0	0
$761$	−2566.48	−0.122253	−0.0611266	−	0.998130i	$-0.519469\pi$
$761$	−2566.48	−0.122253	−0.0611266	+	0.998130i	$0.519469\pi$
$762$	15639.4i	0.743514i
$763$	1520.44i	0.0721413i
$764$	−22213.5	−1.05191
$765$	0	0
$766$	33701.0	1.58964
$767$	17554.0i	0.826386i
$768$	− 18304.9i	− 0.860052i
$769$	−14433.1	−0.676816	−0.338408	−	0.940999i	$-0.609888\pi$
$769$	−14433.1	−0.676816	−0.338408	+	0.940999i	$0.609888\pi$
$770$	0	0
$771$	9205.91	0.430017
$772$	67359.4i	3.14031i
$773$	− 29443.2i	− 1.36999i	−0.728550	−	0.684993i	$-0.759805\pi$
$773$	− 29443.2i	− 1.36999i	0.728550	−	0.684993i	$-0.240195\pi$
$774$	−5168.93	−0.240043
$775$	0	0
$776$	15930.4	0.736941
$777$	− 3404.62i	− 0.157195i
$778$	− 34857.7i	− 1.60631i
$779$	−22766.7	−1.04711
$780$	0	0
$781$	10584.9	0.484964
$782$	− 12615.0i	− 0.576869i
$783$	5789.31i	0.264231i
$784$	−1083.13	−0.0493408
$785$	0	0
$786$	2616.24	0.118726
$787$	− 26390.6i	− 1.19533i	−0.801747	−	0.597664i	$-0.796096\pi$
$787$	− 26390.6i	− 1.19533i	0.801747	−	0.597664i	$-0.203904\pi$
$788$	− 39543.6i	− 1.78767i
$789$	14022.4	0.632711
$790$	0	0
$791$	−11607.4	−0.521758
$792$	− 6353.72i	− 0.285063i
$793$	24823.7i	1.11162i
$794$	42013.2	1.87783
$795$	0	0
$796$	57870.3	2.57683
$797$	3738.33i	0.166146i	0.996543	+	0.0830730i	$0.0264735\pi$
$797$	3738.33i	0.166146i	−0.996543	+	0.0830730i	$0.973527\pi$
$798$	− 6654.90i	− 0.295214i
$799$	6524.26	0.288876
$800$	0	0
$801$	13263.5	0.585073
$802$	− 8382.48i	− 0.369072i
$803$	1016.85i	0.0446873i
$804$	38419.3	1.68525
$805$	0	0
$806$	14595.8	0.637861
$807$	− 7252.14i	− 0.316341i
$808$	54250.1i	2.36202i
$809$	−43204.1	−1.87760	−0.938798	−	0.344468i	$-0.888059\pi$
$809$	−43204.1	−1.87760	−0.938798	+	0.344468i	$0.888059\pi$
$810$	0	0
$811$	−30192.4	−1.30727	−0.653637	−	0.756809i	$-0.726758\pi$
$811$	−30192.4	−1.30727	−0.653637	+	0.756809i	$0.726758\pi$
$812$	− 21170.2i	− 0.914935i
$813$	23172.9i	0.999642i
$814$	−18748.7	−0.807301
$815$	0	0
$816$	−1221.42	−0.0523999
$817$	8233.71i	0.352584i
$818$	− 41185.3i	− 1.76041i
$819$	2205.98	0.0941188
$820$	0	0
$821$	−40274.7	−1.71206	−0.856028	−	0.516929i	$-0.827075\pi$
$821$	−40274.7	−1.71206	−0.856028	+	0.516929i	$0.827075\pi$
$822$	535.847i	0.0227370i
$823$	25184.2i	1.06667i	0.845905	+	0.533334i	$0.179061\pi$
$823$	25184.2i	1.06667i	−0.845905	+	0.533334i	$0.820939\pi$
$824$	−19020.5	−0.804140
$825$	0	0
$826$	16498.9	0.694999
$827$	38941.7i	1.63741i	0.574218	+	0.818703i	$0.305306\pi$
$827$	38941.7i	1.63741i	−0.574218	+	0.818703i	$0.694694\pi$
$828$	− 18492.3i	− 0.776150i
$829$	8327.05	0.348867	0.174433	−	0.984669i	$-0.444191\pi$
$829$	8327.05	0.348867	0.174433	+	0.984669i	$0.444191\pi$
$830$	0	0
$831$	−13728.5	−0.573089
$832$	− 26883.5i	− 1.12021i
$833$	− 902.519i	− 0.0375395i
$834$	−2589.75	−0.107525
$835$	0	0
$836$	−23384.2	−0.967418
$837$	2393.80i	0.0988553i
$838$	− 15104.9i	− 0.622660i
$839$	−8784.41	−0.361468	−0.180734	−	0.983532i	$-0.557847\pi$
$839$	−8784.41	−0.361468	−0.180734	+	0.983532i	$0.557847\pi$
$840$	0	0
$841$	21586.4	0.885087
$842$	− 74086.4i	− 3.03229i
$843$	− 4075.67i	− 0.166517i
$844$	11615.4	0.473718
$845$	0	0
$846$	14988.4	0.609117
$847$	5081.96i	0.206161i
$848$	14958.0i	0.605732i
$849$	−11655.1	−0.471145
$850$	0	0
$851$	−23617.6	−0.951350
$852$	− 18209.2i	− 0.732203i
$853$	− 9076.15i	− 0.364316i	−0.983269	−	0.182158i	$-0.941692\pi$
$853$	− 9076.15i	− 0.364316i	0.983269	−	0.182158i	$-0.0583082\pi$
$854$	23331.6	0.934884
$855$	0	0
$856$	46339.6	1.85030
$857$	− 36396.7i	− 1.45074i	−0.688357	−	0.725372i	$-0.741668\pi$
$857$	− 36396.7i	− 1.45074i	0.688357	−	0.725372i	$-0.258332\pi$
$858$	− 12148.0i	− 0.483364i
$859$	−8915.27	−0.354115	−0.177058	−	0.984200i	$-0.556658\pi$
$859$	−8915.27	−0.354115	−0.177058	+	0.984200i	$0.556658\pi$
$860$	0	0
$861$	−7093.14	−0.280759
$862$	1908.44i	0.0754081i
$863$	− 6148.26i	− 0.242514i	−0.992621	−	0.121257i	$-0.961308\pi$
$863$	− 6148.26i	− 0.242514i	0.992621	−	0.121257i	$-0.0386925\pi$
$864$	3393.52	0.133623
$865$	0	0
$866$	−36884.9	−1.44735
$867$	13721.2i	0.537483i
$868$	− 8753.59i	− 0.342300i
$869$	−21900.8	−0.854928
$870$	0	0
$871$	31792.6	1.23680
$872$	− 6234.16i	− 0.242105i
$873$	4995.31i	0.193660i
$874$	−46164.4	−1.78665
$875$	0	0
$876$	1749.29	0.0674692
$877$	14287.0i	0.550101i	0.961430	+	0.275050i	$0.0886945\pi$
$877$	14287.0i	0.550101i	−0.961430	+	0.275050i	$0.911306\pi$
$878$	1988.90i	0.0764488i
$879$	12101.7	0.464370
$880$	0	0
$881$	−13315.9	−0.509221	−0.254610	−	0.967044i	$-0.581947\pi$
$881$	−13315.9	−0.509221	−0.254610	+	0.967044i	$0.581947\pi$
$882$	− 2073.39i	− 0.0791549i
$883$	− 5271.78i	− 0.200917i	−0.994941	−	0.100458i	$-0.967969\pi$
$883$	− 5271.78i	− 0.200917i	0.994941	−	0.100458i	$-0.0320309\pi$
$884$	−9096.73	−0.346104
$885$	0	0
$886$	−75501.1	−2.86288
$887$	− 2606.07i	− 0.0986507i	−0.998783	−	0.0493253i	$-0.984293\pi$
$887$	− 2606.07i	− 0.0986507i	0.998783	−	0.0493253i	$-0.0157071\pi$
$888$	13959.7i	0.527542i
$889$	7761.69	0.292822
$890$	0	0
$891$	1992.35	0.0749115
$892$	− 11526.3i	− 0.432654i
$893$	− 23875.4i	− 0.894694i
$894$	19511.5	0.729937
$895$	0	0
$896$	−18229.2	−0.679682
$897$	− 15302.7i	− 0.569612i
$898$	10281.1i	0.382056i
$899$	19010.2	0.705258
$900$	0	0
$901$	−12463.8	−0.460854
$902$	39060.8i	1.44189i
$903$	2565.28i	0.0945373i
$904$	47592.8	1.75101
$905$	0	0
$906$	10793.7	0.395802
$907$	− 18610.6i	− 0.681317i	−0.940187	−	0.340659i	$-0.889350\pi$
$907$	− 18610.6i	− 0.681317i	0.940187	−	0.340659i	$-0.110650\pi$
$908$	51564.6i	1.88462i
$909$	−17011.3	−0.620714
$910$	0	0
$911$	41091.7	1.49443	0.747216	−	0.664581i	$-0.231390\pi$
$911$	41091.7	1.49443	0.747216	+	0.664581i	$0.231390\pi$
$912$	4469.77i	0.162291i
$913$	− 26002.6i	− 0.942563i
$914$	27265.4	0.986716
$915$	0	0
$916$	13249.8	0.477934
$917$	− 1298.41i	− 0.0467583i
$918$	− 2338.12i	− 0.0840624i
$919$	−38891.3	−1.39598	−0.697990	−	0.716107i	$-0.745922\pi$
$919$	−38891.3	−1.39598	−0.697990	+	0.716107i	$0.745922\pi$
$920$	0	0
$921$	−13861.1	−0.495915
$922$	− 46420.2i	− 1.65810i
$923$	− 15068.4i	− 0.537360i
$924$	−7285.56	−0.259391
$925$	0	0
$926$	−29064.3	−1.03144
$927$	− 5964.30i	− 0.211320i
$928$	− 26949.4i	− 0.953295i
$929$	−18699.4	−0.660396	−0.330198	−	0.943912i	$-0.607115\pi$
$929$	−18699.4	−0.660396	−0.330198	+	0.943912i	$0.607115\pi$
$930$	0	0
$931$	−3302.75	−0.116266
$932$	107.859i	0.00379080i
$933$	20027.7i	0.702761i
$934$	−28893.4	−1.01223
$935$	0	0
$936$	−9045.03	−0.315861
$937$	− 21509.6i	− 0.749933i	−0.927038	−	0.374967i	$-0.877654\pi$
$937$	− 21509.6i	− 0.749933i	0.927038	−	0.374967i	$-0.122346\pi$
$938$	− 29881.7i	− 1.04016i
$939$	−8510.35	−0.295767
$940$	0	0
$941$	−11241.7	−0.389448	−0.194724	−	0.980858i	$-0.562381\pi$
$941$	−11241.7	−0.389448	−0.194724	+	0.980858i	$0.562381\pi$
$942$	33382.4i	1.15463i
$943$	49204.5i	1.69917i
$944$	−11081.5	−0.382068
$945$	0	0
$946$	14126.6	0.485513
$947$	36556.3i	1.25441i	0.778856	+	0.627203i	$0.215800\pi$
$947$	36556.3i	1.25441i	−0.778856	+	0.627203i	$0.784200\pi$
$948$	37675.9i	1.29078i
$949$	1447.57	0.0495153
$950$	0	0
$951$	12031.9	0.410263
$952$	3700.53i	0.125982i
$953$	− 36633.4i	− 1.24520i	−0.782542	−	0.622598i	$-0.786077\pi$
$953$	− 36633.4i	− 1.24520i	0.782542	−	0.622598i	$-0.213923\pi$
$954$	−28633.5	−0.971745
$955$	0	0
$956$	−12540.7	−0.424263
$957$	− 15822.1i	− 0.534436i
$958$	51150.3i	1.72504i
$959$	265.935	0.00895462
$960$	0	0
$961$	−21930.5	−0.736146
$962$	26690.3i	0.894523i
$963$	14530.8i	0.486239i
$964$	−30187.3	−1.00858
$965$	0	0
$966$	−14382.9	−0.479050
$967$	35515.8i	1.18109i	0.807006	+	0.590544i	$0.201087\pi$
$967$	35515.8i	1.18109i	−0.807006	+	0.590544i	$0.798913\pi$
$968$	− 20837.2i	− 0.691871i
$969$	−3724.44	−0.123474
$970$	0	0
$971$	−39661.0	−1.31080	−0.655398	−	0.755283i	$-0.727499\pi$
$971$	−39661.0	−1.31080	−0.655398	+	0.755283i	$0.727499\pi$
$972$	− 3427.44i	− 0.113102i
$973$	1285.26i	0.0423471i
$974$	−38023.9	−1.25089
$975$	0	0
$976$	−15670.7	−0.513942
$977$	− 50325.3i	− 1.64795i	−0.566624	−	0.823977i	$-0.691751\pi$
$977$	− 50325.3i	− 1.64795i	0.566624	−	0.823977i	$-0.308249\pi$
$978$	− 44256.2i	− 1.44699i
$979$	−36249.0	−1.18337
$980$	0	0
$981$	1954.86	0.0636226
$982$	32722.4i	1.06335i
$983$	51189.0i	1.66091i	0.557084	+	0.830456i	$0.311920\pi$
$983$	51189.0i	1.66091i	−0.557084	+	0.830456i	$0.688080\pi$
$984$	29083.5	0.942223
$985$	0	0
$986$	−18568.0	−0.599721
$987$	− 7438.59i	− 0.239892i
$988$	33289.3i	1.07194i
$989$	17795.1	0.572145
$990$	0	0
$991$	−55137.3	−1.76740	−0.883700	−	0.468054i	$-0.844955\pi$
$991$	−55137.3	−1.76740	−0.883700	+	0.468054i	$0.844955\pi$
$992$	− 11143.2i	− 0.356651i
$993$	33262.6i	1.06300i
$994$	−14162.7	−0.451925
$995$	0	0
$996$	−44732.3	−1.42309
$997$	− 41606.5i	− 1.32166i	−0.750537	−	0.660828i	$-0.770205\pi$
$997$	− 41606.5i	− 1.32166i	0.750537	−	0.660828i	$-0.229795\pi$
$998$	87599.6i	2.77848i
$999$	−4377.37	−0.138633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.j.274.1		4
5.2	odd	4		105.4.a.g.1.2	✓	2
5.3	odd	4		525.4.a.i.1.1		2
5.4	even	2	inner	525.4.d.j.274.4		4
15.2	even	4		315.4.a.g.1.1		2
15.8	even	4		1575.4.a.y.1.2		2
20.7	even	4		1680.4.a.y.1.2		2
35.27	even	4		735.4.a.q.1.2		2
105.62	odd	4		2205.4.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.g.1.2	✓	2	5.2	odd	4
315.4.a.g.1.1		2	15.2	even	4
525.4.a.i.1.1		2	5.3	odd	4
525.4.d.j.274.1		4	1.1	even	1	trivial
525.4.d.j.274.4		4	5.4	even	2	inner
735.4.a.q.1.2		2	35.27	even	4
1575.4.a.y.1.2		2	15.8	even	4
1680.4.a.y.1.2		2	20.7	even	4
2205.4.a.v.1.1		2	105.62	odd	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.70156i q^{2} +3.00000i q^{3} -14.1047 q^{4} +14.1047 q^{6} -7.00000i q^{7} +28.7016i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-4.70156i q^{2} +3.00000i q^{3} -14.1047 q^{4} +14.1047 q^{6} -7.00000i q^{7} +28.7016i q^{8} -9.00000 q^{9} +24.5969 q^{11} -42.3141i q^{12} -35.0156i q^{13} -32.9109 q^{14} +22.1047 q^{16} +18.4187i q^{17} +42.3141i q^{18} +67.4031 q^{19} +21.0000 q^{21} -115.644i q^{22} -145.675i q^{23} -86.1047 q^{24} -164.628 q^{26} -27.0000i q^{27} +98.7328i q^{28} -214.419 q^{29} -88.6594 q^{31} +125.686i q^{32} +73.7906i q^{33} +86.5969 q^{34} +126.942 q^{36} -162.125i q^{37} -316.900i q^{38} +105.047 q^{39} -337.769 q^{41} -98.7328i q^{42} +122.156i q^{43} -346.931 q^{44} -684.900 q^{46} -354.219i q^{47} +66.3141i q^{48} -49.0000 q^{49} -55.2562 q^{51} +493.884i q^{52} +676.691i q^{53} -126.942 q^{54} +200.911 q^{56} +202.209i q^{57} +1008.10i q^{58} -501.319 q^{59} -708.931 q^{61} +416.837i q^{62} +63.0000i q^{63} +767.758 q^{64} +346.931 q^{66} +907.956i q^{67} -259.791i q^{68} +437.025 q^{69} +430.334 q^{71} -258.314i q^{72} +41.3406i q^{73} -762.241 q^{74} -950.700 q^{76} -172.178i q^{77} -493.884i q^{78} -890.388 q^{79} +81.0000 q^{81} +1588.04i q^{82} -1057.15i q^{83} -296.198 q^{84} +574.325 q^{86} -643.256i q^{87} +705.969i q^{88} -1473.72 q^{89} -245.109 q^{91} +2054.70i q^{92} -265.978i q^{93} -1665.38 q^{94} -377.058 q^{96} -555.034i q^{97} +230.377i q^{98} -221.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9	\( 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9} + 124 q^{11} - 42 q^{14} + 50 q^{16} + 244 q^{19} + 84 q^{21} - 306 q^{24} - 428 q^{26} - 704 q^{29} + 132 q^{31} + 372 q^{34} + 162 q^{36} + 36 q^{39} + 32 q^{41} - 312 q^{44} - 1920 q^{46} - 196 q^{49} + 240 q^{51} - 162 q^{54} + 714 q^{56} - 1032 q^{59} - 1760 q^{61} + 958 q^{64} + 312 q^{66} - 96 q^{69} + 620 q^{71} - 2716 q^{74} - 1344 q^{76} - 3664 q^{79} + 324 q^{81} - 378 q^{84} + 2912 q^{86} - 1592 q^{89} - 84 q^{91} - 5176 q^{94} - 1854 q^{96} - 1116 q^{99}+O(q^{100}) \) 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9 + 124 * q^11 - 42 * q^14 + 50 * q^16 + 244 * q^19 + 84 * q^21 - 306 * q^24 - 428 * q^26 - 704 * q^29 + 132 * q^31 + 372 * q^34 + 162 * q^36 + 36 * q^39 + 32 * q^41 - 312 * q^44 - 1920 * q^46 - 196 * q^49 + 240 * q^51 - 162 * q^54 + 714 * q^56 - 1032 * q^59 - 1760 * q^61 + 958 * q^64 + 312 * q^66 - 96 * q^69 + 620 * q^71 - 2716 * q^74 - 1344 * q^76 - 3664 * q^79 + 324 * q^81 - 378 * q^84 + 2912 * q^86 - 1592 * q^89 - 84 * q^91 - 5176 * q^94 - 1854 * q^96 - 1116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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