LMFDB - Embedded newform 250.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(1,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("250.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.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:	$1.99626005053$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} +2.61803 q^{6} +2.85410 q^{7} -1.00000 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} +2.61803 q^{6} +2.85410 q^{7} -1.00000 q^{8} +3.85410 q^{9} -5.23607 q^{11} -2.61803 q^{12} -1.23607 q^{13} -2.85410 q^{14} +1.00000 q^{16} -0.763932 q^{17} -3.85410 q^{18} -7.23607 q^{19} -7.47214 q^{21} +5.23607 q^{22} -7.61803 q^{23} +2.61803 q^{24} +1.23607 q^{26} -2.23607 q^{27} +2.85410 q^{28} -1.38197 q^{29} +3.70820 q^{31} -1.00000 q^{32} +13.7082 q^{33} +0.763932 q^{34} +3.85410 q^{36} -6.94427 q^{37} +7.23607 q^{38} +3.23607 q^{39} +3.38197 q^{41} +7.47214 q^{42} +0.145898 q^{43} -5.23607 q^{44} +7.61803 q^{46} -8.32624 q^{47} -2.61803 q^{48} +1.14590 q^{49} +2.00000 q^{51} -1.23607 q^{52} +4.94427 q^{53} +2.23607 q^{54} -2.85410 q^{56} +18.9443 q^{57} +1.38197 q^{58} -2.76393 q^{59} +1.14590 q^{61} -3.70820 q^{62} +11.0000 q^{63} +1.00000 q^{64} -13.7082 q^{66} +6.47214 q^{67} -0.763932 q^{68} +19.9443 q^{69} -0.763932 q^{71} -3.85410 q^{72} -1.23607 q^{73} +6.94427 q^{74} -7.23607 q^{76} -14.9443 q^{77} -3.23607 q^{78} -13.4164 q^{79} -5.70820 q^{81} -3.38197 q^{82} +4.09017 q^{83} -7.47214 q^{84} -0.145898 q^{86} +3.61803 q^{87} +5.23607 q^{88} +8.09017 q^{89} -3.52786 q^{91} -7.61803 q^{92} -9.70820 q^{93} +8.32624 q^{94} +2.61803 q^{96} +18.1803 q^{97} -1.14590 q^{98} -20.1803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^6 - q^7 - 2 * q^8 + q^9	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{6} - q^{7} - 2 q^{8} + q^{9} - 6 q^{11} - 3 q^{12} + 2 q^{13} + q^{14} + 2 q^{16} - 6 q^{17} - q^{18} - 10 q^{19} - 6 q^{21} + 6 q^{22} - 13 q^{23} + 3 q^{24} - 2 q^{26} - q^{28} - 5 q^{29} - 6 q^{31} - 2 q^{32} + 14 q^{33} + 6 q^{34} + q^{36} + 4 q^{37} + 10 q^{38} + 2 q^{39} + 9 q^{41} + 6 q^{42} + 7 q^{43} - 6 q^{44} + 13 q^{46} - q^{47} - 3 q^{48} + 9 q^{49} + 4 q^{51} + 2 q^{52} - 8 q^{53} + q^{56} + 20 q^{57} + 5 q^{58} - 10 q^{59} + 9 q^{61} + 6 q^{62} + 22 q^{63} + 2 q^{64} - 14 q^{66} + 4 q^{67} - 6 q^{68} + 22 q^{69} - 6 q^{71} - q^{72} + 2 q^{73} - 4 q^{74} - 10 q^{76} - 12 q^{77} - 2 q^{78} + 2 q^{81} - 9 q^{82} - 3 q^{83} - 6 q^{84} - 7 q^{86} + 5 q^{87} + 6 q^{88} + 5 q^{89} - 16 q^{91} - 13 q^{92} - 6 q^{93} + q^{94} + 3 q^{96} + 14 q^{97} - 9 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^6 - q^7 - 2 * q^8 + q^9 - 6 * q^11 - 3 * q^12 + 2 * q^13 + q^14 + 2 * q^16 - 6 * q^17 - q^18 - 10 * q^19 - 6 * q^21 + 6 * q^22 - 13 * q^23 + 3 * q^24 - 2 * q^26 - q^28 - 5 * q^29 - 6 * q^31 - 2 * q^32 + 14 * q^33 + 6 * q^34 + q^36 + 4 * q^37 + 10 * q^38 + 2 * q^39 + 9 * q^41 + 6 * q^42 + 7 * q^43 - 6 * q^44 + 13 * q^46 - q^47 - 3 * q^48 + 9 * q^49 + 4 * q^51 + 2 * q^52 - 8 * q^53 + q^56 + 20 * q^57 + 5 * q^58 - 10 * q^59 + 9 * q^61 + 6 * q^62 + 22 * q^63 + 2 * q^64 - 14 * q^66 + 4 * q^67 - 6 * q^68 + 22 * q^69 - 6 * q^71 - q^72 + 2 * q^73 - 4 * q^74 - 10 * q^76 - 12 * q^77 - 2 * q^78 + 2 * q^81 - 9 * q^82 - 3 * q^83 - 6 * q^84 - 7 * q^86 + 5 * q^87 + 6 * q^88 + 5 * q^89 - 16 * q^91 - 13 * q^92 - 6 * q^93 + q^94 + 3 * q^96 + 14 * q^97 - 9 * q^98 - 18 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.61803	1.06881
$7$	2.85410	1.07875	0.539375	−	0.842066i	$-0.318661\pi$
$7$	2.85410	1.07875	0.539375	+	0.842066i	$0.318661\pi$
$8$	−1.00000	−0.353553
$9$	3.85410	1.28470
$10$	0	0
$11$	−5.23607	−1.57873	−0.789367	−	0.613922i	$-0.789591\pi$
$11$	−5.23607	−1.57873	−0.789367	+	0.613922i	$0.789591\pi$
$12$	−2.61803	−0.755761
$13$	−1.23607	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$14$	−2.85410	−0.762791
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.763932	−0.185281	−0.0926404	−	0.995700i	$-0.529531\pi$
$17$	−0.763932	−0.185281	−0.0926404	+	0.995700i	$0.529531\pi$
$18$	−3.85410	−0.908421
$19$	−7.23607	−1.66007	−0.830034	−	0.557713i	$-0.811679\pi$
$19$	−7.23607	−1.66007	−0.830034	+	0.557713i	$0.811679\pi$
$20$	0	0
$21$	−7.47214	−1.63055
$22$	5.23607	1.11633
$23$	−7.61803	−1.58847	−0.794235	−	0.607611i	$-0.792128\pi$
$23$	−7.61803	−1.58847	−0.794235	+	0.607611i	$0.792128\pi$
$24$	2.61803	0.534404
$25$	0	0
$26$	1.23607	0.242413
$27$	−2.23607	−0.430331
$28$	2.85410	0.539375
$29$	−1.38197	−0.256625	−0.128312	−	0.991734i	$-0.540956\pi$
$29$	−1.38197	−0.256625	−0.128312	+	0.991734i	$0.540956\pi$
$30$	0	0
$31$	3.70820	0.666013	0.333007	−	0.942925i	$-0.391937\pi$
$31$	3.70820	0.666013	0.333007	+	0.942925i	$0.391937\pi$
$32$	−1.00000	−0.176777
$33$	13.7082	2.38629
$34$	0.763932	0.131013
$35$	0	0
$36$	3.85410	0.642350
$37$	−6.94427	−1.14163	−0.570816	−	0.821078i	$-0.693373\pi$
$37$	−6.94427	−1.14163	−0.570816	+	0.821078i	$0.693373\pi$
$38$	7.23607	1.17385
$39$	3.23607	0.518186
$40$	0	0
$41$	3.38197	0.528174	0.264087	−	0.964499i	$-0.414929\pi$
$41$	3.38197	0.528174	0.264087	+	0.964499i	$0.414929\pi$
$42$	7.47214	1.15298
$43$	0.145898	0.0222492	0.0111246	−	0.999938i	$-0.496459\pi$
$43$	0.145898	0.0222492	0.0111246	+	0.999938i	$0.496459\pi$
$44$	−5.23607	−0.789367
$45$	0	0
$46$	7.61803	1.12322
$47$	−8.32624	−1.21451	−0.607253	−	0.794508i	$-0.707729\pi$
$47$	−8.32624	−1.21451	−0.607253	+	0.794508i	$0.707729\pi$
$48$	−2.61803	−0.377881
$49$	1.14590	0.163700
$50$	0	0
$51$	2.00000	0.280056
$52$	−1.23607	−0.171412
$53$	4.94427	0.679148	0.339574	−	0.940579i	$-0.389717\pi$
$53$	4.94427	0.679148	0.339574	+	0.940579i	$0.389717\pi$
$54$	2.23607	0.304290
$55$	0	0
$56$	−2.85410	−0.381395
$57$	18.9443	2.50923
$58$	1.38197	0.181461
$59$	−2.76393	−0.359833	−0.179917	−	0.983682i	$-0.557583\pi$
$59$	−2.76393	−0.359833	−0.179917	+	0.983682i	$0.557583\pi$
$60$	0	0
$61$	1.14590	0.146717	0.0733586	−	0.997306i	$-0.476628\pi$
$61$	1.14590	0.146717	0.0733586	+	0.997306i	$0.476628\pi$
$62$	−3.70820	−0.470942
$63$	11.0000	1.38587
$64$	1.00000	0.125000
$65$	0	0
$66$	−13.7082	−1.68736
$67$	6.47214	0.790697	0.395349	−	0.918531i	$-0.370624\pi$
$67$	6.47214	0.790697	0.395349	+	0.918531i	$0.370624\pi$
$68$	−0.763932	−0.0926404
$69$	19.9443	2.40101
$70$	0	0
$71$	−0.763932	−0.0906621	−0.0453310	−	0.998972i	$-0.514434\pi$
$71$	−0.763932	−0.0906621	−0.0453310	+	0.998972i	$0.514434\pi$
$72$	−3.85410	−0.454210
$73$	−1.23607	−0.144671	−0.0723354	−	0.997380i	$-0.523045\pi$
$73$	−1.23607	−0.144671	−0.0723354	+	0.997380i	$0.523045\pi$
$74$	6.94427	0.807255
$75$	0	0
$76$	−7.23607	−0.830034
$77$	−14.9443	−1.70306
$78$	−3.23607	−0.366413
$79$	−13.4164	−1.50946	−0.754732	−	0.656033i	$-0.772233\pi$
$79$	−13.4164	−1.50946	−0.754732	+	0.656033i	$0.772233\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	−3.38197	−0.373476
$83$	4.09017	0.448954	0.224477	−	0.974479i	$-0.427933\pi$
$83$	4.09017	0.448954	0.224477	+	0.974479i	$0.427933\pi$
$84$	−7.47214	−0.815277
$85$	0	0
$86$	−0.145898	−0.0157326
$87$	3.61803	0.387894
$88$	5.23607	0.558167
$89$	8.09017	0.857556	0.428778	−	0.903410i	$-0.358944\pi$
$89$	8.09017	0.857556	0.428778	+	0.903410i	$0.358944\pi$
$90$	0	0
$91$	−3.52786	−0.369821
$92$	−7.61803	−0.794235
$93$	−9.70820	−1.00669
$94$	8.32624	0.858786
$95$	0	0
$96$	2.61803	0.267202
$97$	18.1803	1.84593	0.922967	−	0.384879i	$-0.125757\pi$
$97$	18.1803	1.84593	0.922967	+	0.384879i	$0.125757\pi$
$98$	−1.14590	−0.115753
$99$	−20.1803	−2.02820
$100$	0	0
$101$	8.38197	0.834037	0.417018	−	0.908898i	$-0.363075\pi$
$101$	8.38197	0.834037	0.417018	+	0.908898i	$0.363075\pi$
$102$	−2.00000	−0.198030
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	1.23607	0.121206
$105$	0	0
$106$	−4.94427	−0.480230
$107$	−6.61803	−0.639789	−0.319895	−	0.947453i	$-0.603648\pi$
$107$	−6.61803	−0.639789	−0.319895	+	0.947453i	$0.603648\pi$
$108$	−2.23607	−0.215166
$109$	1.38197	0.132368	0.0661842	−	0.997807i	$-0.478918\pi$
$109$	1.38197	0.132368	0.0661842	+	0.997807i	$0.478918\pi$
$110$	0	0
$111$	18.1803	1.72560
$112$	2.85410	0.269687
$113$	−15.7082	−1.47770	−0.738852	−	0.673868i	$-0.764632\pi$
$113$	−15.7082	−1.47770	−0.738852	+	0.673868i	$0.764632\pi$
$114$	−18.9443	−1.77429
$115$	0	0
$116$	−1.38197	−0.128312
$117$	−4.76393	−0.440426
$118$	2.76393	0.254441
$119$	−2.18034	−0.199871
$120$	0	0
$121$	16.4164	1.49240
$122$	−1.14590	−0.103745
$123$	−8.85410	−0.798347
$124$	3.70820	0.333007
$125$	0	0
$126$	−11.0000	−0.979958
$127$	9.56231	0.848517	0.424259	−	0.905541i	$-0.360535\pi$
$127$	9.56231	0.848517	0.424259	+	0.905541i	$0.360535\pi$
$128$	−1.00000	−0.0883883
$129$	−0.381966	−0.0336302
$130$	0	0
$131$	−3.52786	−0.308231	−0.154115	−	0.988053i	$-0.549253\pi$
$131$	−3.52786	−0.308231	−0.154115	+	0.988053i	$0.549253\pi$
$132$	13.7082	1.19315
$133$	−20.6525	−1.79080
$134$	−6.47214	−0.559107
$135$	0	0
$136$	0.763932	0.0655066
$137$	−15.2361	−1.30171	−0.650853	−	0.759204i	$-0.725588\pi$
$137$	−15.2361	−1.30171	−0.650853	+	0.759204i	$0.725588\pi$
$138$	−19.9443	−1.69777
$139$	13.4164	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$140$	0	0
$141$	21.7984	1.83575
$142$	0.763932	0.0641078
$143$	6.47214	0.541227
$144$	3.85410	0.321175
$145$	0	0
$146$	1.23607	0.102298
$147$	−3.00000	−0.247436
$148$	−6.94427	−0.570816
$149$	1.90983	0.156459	0.0782297	−	0.996935i	$-0.475073\pi$
$149$	1.90983	0.156459	0.0782297	+	0.996935i	$0.475073\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	7.23607	0.586923
$153$	−2.94427	−0.238030
$154$	14.9443	1.20424
$155$	0	0
$156$	3.23607	0.259093
$157$	−15.2361	−1.21597	−0.607985	−	0.793948i	$-0.708022\pi$
$157$	−15.2361	−1.21597	−0.607985	+	0.793948i	$0.708022\pi$
$158$	13.4164	1.06735
$159$	−12.9443	−1.02655
$160$	0	0
$161$	−21.7426	−1.71356
$162$	5.70820	0.448479
$163$	20.2705	1.58771	0.793854	−	0.608108i	$-0.208071\pi$
$163$	20.2705	1.58771	0.793854	+	0.608108i	$0.208071\pi$
$164$	3.38197	0.264087
$165$	0	0
$166$	−4.09017	−0.317459
$167$	3.38197	0.261704	0.130852	−	0.991402i	$-0.458229\pi$
$167$	3.38197	0.261704	0.130852	+	0.991402i	$0.458229\pi$
$168$	7.47214	0.576488
$169$	−11.4721	−0.882472
$170$	0	0
$171$	−27.8885	−2.13269
$172$	0.145898	0.0111246
$173$	12.1803	0.926054	0.463027	−	0.886344i	$-0.346763\pi$
$173$	12.1803	0.926054	0.463027	+	0.886344i	$0.346763\pi$
$174$	−3.61803	−0.274282
$175$	0	0
$176$	−5.23607	−0.394683
$177$	7.23607	0.543896
$178$	−8.09017	−0.606384
$179$	20.6525	1.54364	0.771819	−	0.635842i	$-0.219347\pi$
$179$	20.6525	1.54364	0.771819	+	0.635842i	$0.219347\pi$
$180$	0	0
$181$	−15.5623	−1.15674	−0.578369	−	0.815776i	$-0.696310\pi$
$181$	−15.5623	−1.15674	−0.578369	+	0.815776i	$0.696310\pi$
$182$	3.52786	0.261503
$183$	−3.00000	−0.221766
$184$	7.61803	0.561609
$185$	0	0
$186$	9.70820	0.711840
$187$	4.00000	0.292509
$188$	−8.32624	−0.607253
$189$	−6.38197	−0.464220
$190$	0	0
$191$	19.2361	1.39187	0.695937	−	0.718103i	$-0.254989\pi$
$191$	19.2361	1.39187	0.695937	+	0.718103i	$0.254989\pi$
$192$	−2.61803	−0.188940
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−18.1803	−1.30527
$195$	0	0
$196$	1.14590	0.0818499
$197$	−9.70820	−0.691681	−0.345840	−	0.938293i	$-0.612406\pi$
$197$	−9.70820	−0.691681	−0.345840	+	0.938293i	$0.612406\pi$
$198$	20.1803	1.43415
$199$	1.70820	0.121091	0.0605457	−	0.998165i	$-0.480716\pi$
$199$	1.70820	0.121091	0.0605457	+	0.998165i	$0.480716\pi$
$200$	0	0
$201$	−16.9443	−1.19516
$202$	−8.38197	−0.589753
$203$	−3.94427	−0.276834
$204$	2.00000	0.140028
$205$	0	0
$206$	4.00000	0.278693
$207$	−29.3607	−2.04071
$208$	−1.23607	−0.0857059
$209$	37.8885	2.62081
$210$	0	0
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	4.94427	0.339574
$213$	2.00000	0.137038
$214$	6.61803	0.452399
$215$	0	0
$216$	2.23607	0.152145
$217$	10.5836	0.718461
$218$	−1.38197	−0.0935985
$219$	3.23607	0.218673
$220$	0	0
$221$	0.944272	0.0635186
$222$	−18.1803	−1.22018
$223$	24.6180	1.64855	0.824273	−	0.566193i	$-0.191584\pi$
$223$	24.6180	1.64855	0.824273	+	0.566193i	$0.191584\pi$
$224$	−2.85410	−0.190698
$225$	0	0
$226$	15.7082	1.04489
$227$	27.3262	1.81371	0.906853	−	0.421447i	$-0.138478\pi$
$227$	27.3262	1.81371	0.906853	+	0.421447i	$0.138478\pi$
$228$	18.9443	1.25462
$229$	−10.8541	−0.717259	−0.358630	−	0.933480i	$-0.616756\pi$
$229$	−10.8541	−0.717259	−0.358630	+	0.933480i	$0.616756\pi$
$230$	0	0
$231$	39.1246	2.57421
$232$	1.38197	0.0907305
$233$	3.23607	0.212002	0.106001	−	0.994366i	$-0.466195\pi$
$233$	3.23607	0.212002	0.106001	+	0.994366i	$0.466195\pi$
$234$	4.76393	0.311428
$235$	0	0
$236$	−2.76393	−0.179917
$237$	35.1246	2.28159
$238$	2.18034	0.141330
$239$	−13.4164	−0.867835	−0.433918	−	0.900953i	$-0.642869\pi$
$239$	−13.4164	−0.867835	−0.433918	+	0.900953i	$0.642869\pi$
$240$	0	0
$241$	0.0901699	0.00580836	0.00290418	−	0.999996i	$-0.499076\pi$
$241$	0.0901699	0.00580836	0.00290418	+	0.999996i	$0.499076\pi$
$242$	−16.4164	−1.05529
$243$	21.6525	1.38901
$244$	1.14590	0.0733586
$245$	0	0
$246$	8.85410	0.564517
$247$	8.94427	0.569110
$248$	−3.70820	−0.235471
$249$	−10.7082	−0.678605
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	11.0000	0.692935
$253$	39.8885	2.50777
$254$	−9.56231	−0.599992
$255$	0	0
$256$	1.00000	0.0625000
$257$	3.05573	0.190611	0.0953055	−	0.995448i	$-0.469617\pi$
$257$	3.05573	0.190611	0.0953055	+	0.995448i	$0.469617\pi$
$258$	0.381966	0.0237802
$259$	−19.8197	−1.23153
$260$	0	0
$261$	−5.32624	−0.329686
$262$	3.52786	0.217952
$263$	−15.3820	−0.948493	−0.474246	−	0.880392i	$-0.657279\pi$
$263$	−15.3820	−0.948493	−0.474246	+	0.880392i	$0.657279\pi$
$264$	−13.7082	−0.843682
$265$	0	0
$266$	20.6525	1.26628
$267$	−21.1803	−1.29622
$268$	6.47214	0.395349
$269$	−15.5279	−0.946751	−0.473375	−	0.880861i	$-0.656965\pi$
$269$	−15.5279	−0.946751	−0.473375	+	0.880861i	$0.656965\pi$
$270$	0	0
$271$	−25.8885	−1.57262	−0.786309	−	0.617834i	$-0.788010\pi$
$271$	−25.8885	−1.57262	−0.786309	+	0.617834i	$0.788010\pi$
$272$	−0.763932	−0.0463202
$273$	9.23607	0.558992
$274$	15.2361	0.920445
$275$	0	0
$276$	19.9443	1.20050
$277$	−15.2361	−0.915447	−0.457723	−	0.889095i	$-0.651335\pi$
$277$	−15.2361	−0.915447	−0.457723	+	0.889095i	$0.651335\pi$
$278$	−13.4164	−0.804663
$279$	14.2918	0.855627
$280$	0	0
$281$	0.0901699	0.00537909	0.00268954	−	0.999996i	$-0.499144\pi$
$281$	0.0901699	0.00537909	0.00268954	+	0.999996i	$0.499144\pi$
$282$	−21.7984	−1.29807
$283$	−30.8328	−1.83282	−0.916410	−	0.400240i	$-0.868927\pi$
$283$	−30.8328	−1.83282	−0.916410	+	0.400240i	$0.868927\pi$
$284$	−0.763932	−0.0453310
$285$	0	0
$286$	−6.47214	−0.382705
$287$	9.65248	0.569768
$288$	−3.85410	−0.227105
$289$	−16.4164	−0.965671
$290$	0	0
$291$	−47.5967	−2.79017
$292$	−1.23607	−0.0723354
$293$	22.1803	1.29579	0.647895	−	0.761730i	$-0.275650\pi$
$293$	22.1803	1.29579	0.647895	+	0.761730i	$0.275650\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	6.94427	0.403628
$297$	11.7082	0.679379
$298$	−1.90983	−0.110633
$299$	9.41641	0.544565
$300$	0	0
$301$	0.416408	0.0240014
$302$	−2.00000	−0.115087
$303$	−21.9443	−1.26067
$304$	−7.23607	−0.415017
$305$	0	0
$306$	2.94427	0.168313
$307$	−12.2705	−0.700315	−0.350157	−	0.936691i	$-0.613872\pi$
$307$	−12.2705	−0.700315	−0.350157	+	0.936691i	$0.613872\pi$
$308$	−14.9443	−0.851529
$309$	10.4721	0.595739
$310$	0	0
$311$	3.70820	0.210273	0.105136	−	0.994458i	$-0.466472\pi$
$311$	3.70820	0.210273	0.105136	+	0.994458i	$0.466472\pi$
$312$	−3.23607	−0.183206
$313$	−0.583592	−0.0329866	−0.0164933	−	0.999864i	$-0.505250\pi$
$313$	−0.583592	−0.0329866	−0.0164933	+	0.999864i	$0.505250\pi$
$314$	15.2361	0.859821
$315$	0	0
$316$	−13.4164	−0.754732
$317$	−3.52786	−0.198145	−0.0990723	−	0.995080i	$-0.531588\pi$
$317$	−3.52786	−0.198145	−0.0990723	+	0.995080i	$0.531588\pi$
$318$	12.9443	0.725879
$319$	7.23607	0.405142
$320$	0	0
$321$	17.3262	0.967056
$322$	21.7426	1.21167
$323$	5.52786	0.307579
$324$	−5.70820	−0.317122
$325$	0	0
$326$	−20.2705	−1.12268
$327$	−3.61803	−0.200078
$328$	−3.38197	−0.186738
$329$	−23.7639	−1.31015
$330$	0	0
$331$	−21.4164	−1.17715	−0.588576	−	0.808442i	$-0.700311\pi$
$331$	−21.4164	−1.17715	−0.588576	+	0.808442i	$0.700311\pi$
$332$	4.09017	0.224477
$333$	−26.7639	−1.46665
$334$	−3.38197	−0.185053
$335$	0	0
$336$	−7.47214	−0.407638
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	11.4721	0.624002
$339$	41.1246	2.23358
$340$	0	0
$341$	−19.4164	−1.05146
$342$	27.8885	1.50804
$343$	−16.7082	−0.902158
$344$	−0.145898	−0.00786629
$345$	0	0
$346$	−12.1803	−0.654819
$347$	−14.3820	−0.772064	−0.386032	−	0.922485i	$-0.626155\pi$
$347$	−14.3820	−0.772064	−0.386032	+	0.922485i	$0.626155\pi$
$348$	3.61803	0.193947
$349$	9.14590	0.489569	0.244784	−	0.969578i	$-0.421283\pi$
$349$	9.14590	0.489569	0.244784	+	0.969578i	$0.421283\pi$
$350$	0	0
$351$	2.76393	0.147528
$352$	5.23607	0.279083
$353$	−13.5967	−0.723682	−0.361841	−	0.932240i	$-0.617852\pi$
$353$	−13.5967	−0.723682	−0.361841	+	0.932240i	$0.617852\pi$
$354$	−7.23607	−0.384593
$355$	0	0
$356$	8.09017	0.428778
$357$	5.70820	0.302110
$358$	−20.6525	−1.09152
$359$	−0.652476	−0.0344364	−0.0172182	−	0.999852i	$-0.505481\pi$
$359$	−0.652476	−0.0344364	−0.0172182	+	0.999852i	$0.505481\pi$
$360$	0	0
$361$	33.3607	1.75583
$362$	15.5623	0.817937
$363$	−42.9787	−2.25580
$364$	−3.52786	−0.184910
$365$	0	0
$366$	3.00000	0.156813
$367$	1.14590	0.0598154	0.0299077	−	0.999553i	$-0.490479\pi$
$367$	1.14590	0.0598154	0.0299077	+	0.999553i	$0.490479\pi$
$368$	−7.61803	−0.397117
$369$	13.0344	0.678546
$370$	0	0
$371$	14.1115	0.732630
$372$	−9.70820	−0.503347
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	8.32624	0.429393
$377$	1.70820	0.0879770
$378$	6.38197	0.328253
$379$	−14.4721	−0.743384	−0.371692	−	0.928356i	$-0.621222\pi$
$379$	−14.4721	−0.743384	−0.371692	+	0.928356i	$0.621222\pi$
$380$	0	0
$381$	−25.0344	−1.28255
$382$	−19.2361	−0.984203
$383$	16.3262	0.834232	0.417116	−	0.908853i	$-0.363041\pi$
$383$	16.3262	0.834232	0.417116	+	0.908853i	$0.363041\pi$
$384$	2.61803	0.133601
$385$	0	0
$386$	14.0000	0.712581
$387$	0.562306	0.0285836
$388$	18.1803	0.922967
$389$	−22.0344	−1.11719	−0.558595	−	0.829440i	$-0.688659\pi$
$389$	−22.0344	−1.11719	−0.558595	+	0.829440i	$0.688659\pi$
$390$	0	0
$391$	5.81966	0.294313
$392$	−1.14590	−0.0578766
$393$	9.23607	0.465898
$394$	9.70820	0.489092
$395$	0	0
$396$	−20.1803	−1.01410
$397$	−28.6525	−1.43803	−0.719013	−	0.694996i	$-0.755406\pi$
$397$	−28.6525	−1.43803	−0.719013	+	0.694996i	$0.755406\pi$
$398$	−1.70820	−0.0856245
$399$	54.0689	2.70683
$400$	0	0
$401$	1.79837	0.0898065	0.0449033	−	0.998991i	$-0.485702\pi$
$401$	1.79837	0.0898065	0.0449033	+	0.998991i	$0.485702\pi$
$402$	16.9443	0.845103
$403$	−4.58359	−0.228325
$404$	8.38197	0.417018
$405$	0	0
$406$	3.94427	0.195751
$407$	36.3607	1.80233
$408$	−2.00000	−0.0990148
$409$	−34.9230	−1.72683	−0.863415	−	0.504494i	$-0.831679\pi$
$409$	−34.9230	−1.72683	−0.863415	+	0.504494i	$0.831679\pi$
$410$	0	0
$411$	39.8885	1.96756
$412$	−4.00000	−0.197066
$413$	−7.88854	−0.388170
$414$	29.3607	1.44300
$415$	0	0
$416$	1.23607	0.0606032
$417$	−35.1246	−1.72006
$418$	−37.8885	−1.85319
$419$	−8.94427	−0.436956	−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−8.94427	−0.436956	−0.218478	+	0.975842i	$0.570109\pi$
$420$	0	0
$421$	37.4508	1.82524	0.912621	−	0.408806i	$-0.134055\pi$
$421$	37.4508	1.82524	0.912621	+	0.408806i	$0.134055\pi$
$422$	18.0000	0.876226
$423$	−32.0902	−1.56028
$424$	−4.94427	−0.240115
$425$	0	0
$426$	−2.00000	−0.0969003
$427$	3.27051	0.158271
$428$	−6.61803	−0.319895
$429$	−16.9443	−0.818077
$430$	0	0
$431$	34.3607	1.65510	0.827548	−	0.561395i	$-0.189735\pi$
$431$	34.3607	1.65510	0.827548	+	0.561395i	$0.189735\pi$
$432$	−2.23607	−0.107583
$433$	29.4164	1.41366	0.706831	−	0.707382i	$-0.250124\pi$
$433$	29.4164	1.41366	0.706831	+	0.707382i	$0.250124\pi$
$434$	−10.5836	−0.508029
$435$	0	0
$436$	1.38197	0.0661842
$437$	55.1246	2.63697
$438$	−3.23607	−0.154625
$439$	21.7082	1.03608	0.518038	−	0.855358i	$-0.326663\pi$
$439$	21.7082	1.03608	0.518038	+	0.855358i	$0.326663\pi$
$440$	0	0
$441$	4.41641	0.210305
$442$	−0.944272	−0.0449144
$443$	−19.3262	−0.918217	−0.459109	−	0.888380i	$-0.651831\pi$
$443$	−19.3262	−0.918217	−0.459109	+	0.888380i	$0.651831\pi$
$444$	18.1803	0.862801
$445$	0	0
$446$	−24.6180	−1.16570
$447$	−5.00000	−0.236492
$448$	2.85410	0.134844
$449$	−13.4164	−0.633159	−0.316580	−	0.948566i	$-0.602534\pi$
$449$	−13.4164	−0.633159	−0.316580	+	0.948566i	$0.602534\pi$
$450$	0	0
$451$	−17.7082	−0.833847
$452$	−15.7082	−0.738852
$453$	−5.23607	−0.246012
$454$	−27.3262	−1.28248
$455$	0	0
$456$	−18.9443	−0.887147
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	10.8541	0.507179
$459$	1.70820	0.0797321
$460$	0	0
$461$	−26.0902	−1.21514	−0.607570	−	0.794266i	$-0.707856\pi$
$461$	−26.0902	−1.21514	−0.607570	+	0.794266i	$0.707856\pi$
$462$	−39.1246	−1.82024
$463$	6.85410	0.318537	0.159269	−	0.987235i	$-0.449086\pi$
$463$	6.85410	0.318537	0.159269	+	0.987235i	$0.449086\pi$
$464$	−1.38197	−0.0641562
$465$	0	0
$466$	−3.23607	−0.149908
$467$	14.5623	0.673863	0.336932	−	0.941529i	$-0.390611\pi$
$467$	14.5623	0.673863	0.336932	+	0.941529i	$0.390611\pi$
$468$	−4.76393	−0.220213
$469$	18.4721	0.852964
$470$	0	0
$471$	39.8885	1.83797
$472$	2.76393	0.127220
$473$	−0.763932	−0.0351256
$474$	−35.1246	−1.61333
$475$	0	0
$476$	−2.18034	−0.0999357
$477$	19.0557	0.872502
$478$	13.4164	0.613652
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	8.58359	0.391378
$482$	−0.0901699	−0.00410713
$483$	56.9230	2.59009
$484$	16.4164	0.746200
$485$	0	0
$486$	−21.6525	−0.982176
$487$	−32.3951	−1.46796	−0.733982	−	0.679169i	$-0.762340\pi$
$487$	−32.3951	−1.46796	−0.733982	+	0.679169i	$0.762340\pi$
$488$	−1.14590	−0.0518724
$489$	−53.0689	−2.39986
$490$	0	0
$491$	−38.6525	−1.74436	−0.872181	−	0.489183i	$-0.837295\pi$
$491$	−38.6525	−1.74436	−0.872181	+	0.489183i	$0.837295\pi$
$492$	−8.85410	−0.399174
$493$	1.05573	0.0475476
$494$	−8.94427	−0.402422
$495$	0	0
$496$	3.70820	0.166503
$497$	−2.18034	−0.0978016
$498$	10.7082	0.479846
$499$	−18.2918	−0.818853	−0.409427	−	0.912343i	$-0.634271\pi$
$499$	−18.2918	−0.818853	−0.409427	+	0.912343i	$0.634271\pi$
$500$	0	0
$501$	−8.85410	−0.395572
$502$	−12.0000	−0.535586
$503$	25.1459	1.12120	0.560600	−	0.828087i	$-0.310571\pi$
$503$	25.1459	1.12120	0.560600	+	0.828087i	$0.310571\pi$
$504$	−11.0000	−0.489979
$505$	0	0
$506$	−39.8885	−1.77326
$507$	30.0344	1.33388
$508$	9.56231	0.424259
$509$	−13.4164	−0.594672	−0.297336	−	0.954773i	$-0.596098\pi$
$509$	−13.4164	−0.594672	−0.297336	+	0.954773i	$0.596098\pi$
$510$	0	0
$511$	−3.52786	−0.156064
$512$	−1.00000	−0.0441942
$513$	16.1803	0.714379
$514$	−3.05573	−0.134782
$515$	0	0
$516$	−0.381966	−0.0168151
$517$	43.5967	1.91738
$518$	19.8197	0.870826
$519$	−31.8885	−1.39975
$520$	0	0
$521$	−24.9098	−1.09132	−0.545660	−	0.838007i	$-0.683721\pi$
$521$	−24.9098	−1.09132	−0.545660	+	0.838007i	$0.683721\pi$
$522$	5.32624	0.233123
$523$	12.5066	0.546874	0.273437	−	0.961890i	$-0.411839\pi$
$523$	12.5066	0.546874	0.273437	+	0.961890i	$0.411839\pi$
$524$	−3.52786	−0.154115
$525$	0	0
$526$	15.3820	0.670686
$527$	−2.83282	−0.123399
$528$	13.7082	0.596573
$529$	35.0344	1.52324
$530$	0	0
$531$	−10.6525	−0.462278
$532$	−20.6525	−0.895398
$533$	−4.18034	−0.181071
$534$	21.1803	0.916563
$535$	0	0
$536$	−6.47214	−0.279554
$537$	−54.0689	−2.33324
$538$	15.5279	0.669454
$539$	−6.00000	−0.258438
$540$	0	0
$541$	34.6869	1.49131	0.745654	−	0.666334i	$-0.232137\pi$
$541$	34.6869	1.49131	0.745654	+	0.666334i	$0.232137\pi$
$542$	25.8885	1.11201
$543$	40.7426	1.74843
$544$	0.763932	0.0327533
$545$	0	0
$546$	−9.23607	−0.395267
$547$	31.1459	1.33170	0.665851	−	0.746085i	$-0.268069\pi$
$547$	31.1459	1.33170	0.665851	+	0.746085i	$0.268069\pi$
$548$	−15.2361	−0.650853
$549$	4.41641	0.188488
$550$	0	0
$551$	10.0000	0.426014
$552$	−19.9443	−0.848885
$553$	−38.2918	−1.62833
$554$	15.2361	0.647319
$555$	0	0
$556$	13.4164	0.568982
$557$	33.7082	1.42826	0.714131	−	0.700012i	$-0.246822\pi$
$557$	33.7082	1.42826	0.714131	+	0.700012i	$0.246822\pi$
$558$	−14.2918	−0.605020
$559$	−0.180340	−0.00762756
$560$	0	0
$561$	−10.4721	−0.442134
$562$	−0.0901699	−0.00380359
$563$	27.0557	1.14026	0.570131	−	0.821553i	$-0.306892\pi$
$563$	27.0557	1.14026	0.570131	+	0.821553i	$0.306892\pi$
$564$	21.7984	0.917877
$565$	0	0
$566$	30.8328	1.29600
$567$	−16.2918	−0.684191
$568$	0.763932	0.0320539
$569$	46.5066	1.94966	0.974829	−	0.222956i	$-0.0715705\pi$
$569$	46.5066	1.94966	0.974829	+	0.222956i	$0.0715705\pi$
$570$	0	0
$571$	−20.3607	−0.852068	−0.426034	−	0.904707i	$-0.640090\pi$
$571$	−20.3607	−0.852068	−0.426034	+	0.904707i	$0.640090\pi$
$572$	6.47214	0.270614
$573$	−50.3607	−2.10385
$574$	−9.65248	−0.402887
$575$	0	0
$576$	3.85410	0.160588
$577$	15.4164	0.641793	0.320897	−	0.947114i	$-0.396016\pi$
$577$	15.4164	0.641793	0.320897	+	0.947114i	$0.396016\pi$
$578$	16.4164	0.682833
$579$	36.6525	1.52322
$580$	0	0
$581$	11.6738	0.484309
$582$	47.5967	1.97295
$583$	−25.8885	−1.07219
$584$	1.23607	0.0511489
$585$	0	0
$586$	−22.1803	−0.916261
$587$	−5.88854	−0.243046	−0.121523	−	0.992589i	$-0.538778\pi$
$587$	−5.88854	−0.243046	−0.121523	+	0.992589i	$0.538778\pi$
$588$	−3.00000	−0.123718
$589$	−26.8328	−1.10563
$590$	0	0
$591$	25.4164	1.04549
$592$	−6.94427	−0.285408
$593$	14.9443	0.613688	0.306844	−	0.951760i	$-0.400727\pi$
$593$	14.9443	0.613688	0.306844	+	0.951760i	$0.400727\pi$
$594$	−11.7082	−0.480393
$595$	0	0
$596$	1.90983	0.0782297
$597$	−4.47214	−0.183032
$598$	−9.41641	−0.385066
$599$	−15.5279	−0.634451	−0.317226	−	0.948350i	$-0.602751\pi$
$599$	−15.5279	−0.634451	−0.317226	+	0.948350i	$0.602751\pi$
$600$	0	0
$601$	−2.14590	−0.0875330	−0.0437665	−	0.999042i	$-0.513936\pi$
$601$	−2.14590	−0.0875330	−0.0437665	+	0.999042i	$0.513936\pi$
$602$	−0.416408	−0.0169715
$603$	24.9443	1.01581
$604$	2.00000	0.0813788
$605$	0	0
$606$	21.9443	0.891425
$607$	−4.58359	−0.186042	−0.0930211	−	0.995664i	$-0.529652\pi$
$607$	−4.58359	−0.186042	−0.0930211	+	0.995664i	$0.529652\pi$
$608$	7.23607	0.293461
$609$	10.3262	0.418440
$610$	0	0
$611$	10.2918	0.416362
$612$	−2.94427	−0.119015
$613$	42.8328	1.73000	0.865001	−	0.501771i	$-0.167318\pi$
$613$	42.8328	1.73000	0.865001	+	0.501771i	$0.167318\pi$
$614$	12.2705	0.495197
$615$	0	0
$616$	14.9443	0.602122
$617$	−11.8197	−0.475842	−0.237921	−	0.971285i	$-0.576466\pi$
$617$	−11.8197	−0.475842	−0.237921	+	0.971285i	$0.576466\pi$
$618$	−10.4721	−0.421251
$619$	−16.1803	−0.650343	−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803	−0.650343	−0.325171	+	0.945655i	$0.605422\pi$
$620$	0	0
$621$	17.0344	0.683569
$622$	−3.70820	−0.148685
$623$	23.0902	0.925088
$624$	3.23607	0.129546
$625$	0	0
$626$	0.583592	0.0233250
$627$	−99.1935	−3.96141
$628$	−15.2361	−0.607985
$629$	5.30495	0.211522
$630$	0	0
$631$	23.7082	0.943809	0.471904	−	0.881650i	$-0.343567\pi$
$631$	23.7082	0.943809	0.471904	+	0.881650i	$0.343567\pi$
$632$	13.4164	0.533676
$633$	47.1246	1.87304
$634$	3.52786	0.140109
$635$	0	0
$636$	−12.9443	−0.513274
$637$	−1.41641	−0.0561201
$638$	−7.23607	−0.286479
$639$	−2.94427	−0.116474
$640$	0	0
$641$	28.9098	1.14187	0.570935	−	0.820995i	$-0.306581\pi$
$641$	28.9098	1.14187	0.570935	+	0.820995i	$0.306581\pi$
$642$	−17.3262	−0.683812
$643$	−37.2148	−1.46761	−0.733804	−	0.679361i	$-0.762257\pi$
$643$	−37.2148	−1.46761	−0.733804	+	0.679361i	$0.762257\pi$
$644$	−21.7426	−0.856780
$645$	0	0
$646$	−5.52786	−0.217491
$647$	0.944272	0.0371232	0.0185616	−	0.999828i	$-0.494091\pi$
$647$	0.944272	0.0371232	0.0185616	+	0.999828i	$0.494091\pi$
$648$	5.70820	0.224239
$649$	14.4721	0.568081
$650$	0	0
$651$	−27.7082	−1.08597
$652$	20.2705	0.793854
$653$	−25.0557	−0.980506	−0.490253	−	0.871580i	$-0.663096\pi$
$653$	−25.0557	−0.980506	−0.490253	+	0.871580i	$0.663096\pi$
$654$	3.61803	0.141476
$655$	0	0
$656$	3.38197	0.132044
$657$	−4.76393	−0.185859
$658$	23.7639	0.926415
$659$	30.6525	1.19405	0.597025	−	0.802222i	$-0.296349\pi$
$659$	30.6525	1.19405	0.597025	+	0.802222i	$0.296349\pi$
$660$	0	0
$661$	30.6180	1.19090	0.595452	−	0.803391i	$-0.296973\pi$
$661$	30.6180	1.19090	0.595452	+	0.803391i	$0.296973\pi$
$662$	21.4164	0.832372
$663$	−2.47214	−0.0960098
$664$	−4.09017	−0.158729
$665$	0	0
$666$	26.7639	1.03708
$667$	10.5279	0.407641
$668$	3.38197	0.130852
$669$	−64.4508	−2.49181
$670$	0	0
$671$	−6.00000	−0.231627
$672$	7.47214	0.288244
$673$	−30.1803	−1.16337	−0.581683	−	0.813415i	$-0.697606\pi$
$673$	−30.1803	−1.16337	−0.581683	+	0.813415i	$0.697606\pi$
$674$	18.0000	0.693334
$675$	0	0
$676$	−11.4721	−0.441236
$677$	−13.5279	−0.519918	−0.259959	−	0.965620i	$-0.583709\pi$
$677$	−13.5279	−0.519918	−0.259959	+	0.965620i	$0.583709\pi$
$678$	−41.1246	−1.57938
$679$	51.8885	1.99130
$680$	0	0
$681$	−71.5410	−2.74146
$682$	19.4164	0.743493
$683$	−19.2016	−0.734730	−0.367365	−	0.930077i	$-0.619740\pi$
$683$	−19.2016	−0.734730	−0.367365	+	0.930077i	$0.619740\pi$
$684$	−27.8885	−1.06635
$685$	0	0
$686$	16.7082	0.637922
$687$	28.4164	1.08415
$688$	0.145898	0.00556231
$689$	−6.11146	−0.232828
$690$	0	0
$691$	−18.0000	−0.684752	−0.342376	−	0.939563i	$-0.611232\pi$
$691$	−18.0000	−0.684752	−0.342376	+	0.939563i	$0.611232\pi$
$692$	12.1803	0.463027
$693$	−57.5967	−2.18792
$694$	14.3820	0.545932
$695$	0	0
$696$	−3.61803	−0.137141
$697$	−2.58359	−0.0978605
$698$	−9.14590	−0.346177
$699$	−8.47214	−0.320446
$700$	0	0
$701$	−29.0557	−1.09742	−0.548710	−	0.836013i	$-0.684881\pi$
$701$	−29.0557	−1.09742	−0.548710	+	0.836013i	$0.684881\pi$
$702$	−2.76393	−0.104318
$703$	50.2492	1.89519
$704$	−5.23607	−0.197342
$705$	0	0
$706$	13.5967	0.511720
$707$	23.9230	0.899716
$708$	7.23607	0.271948
$709$	47.0344	1.76642	0.883208	−	0.468982i	$-0.155379\pi$
$709$	47.0344	1.76642	0.883208	+	0.468982i	$0.155379\pi$
$710$	0	0
$711$	−51.7082	−1.93921
$712$	−8.09017	−0.303192
$713$	−28.2492	−1.05794
$714$	−5.70820	−0.213624
$715$	0	0
$716$	20.6525	0.771819
$717$	35.1246	1.31175
$718$	0.652476	0.0243502
$719$	22.3607	0.833913	0.416956	−	0.908927i	$-0.363097\pi$
$719$	22.3607	0.833913	0.416956	+	0.908927i	$0.363097\pi$
$720$	0	0
$721$	−11.4164	−0.425169
$722$	−33.3607	−1.24156
$723$	−0.236068	−0.00877946
$724$	−15.5623	−0.578369
$725$	0	0
$726$	42.9787	1.59509
$727$	−22.1459	−0.821346	−0.410673	−	0.911783i	$-0.634706\pi$
$727$	−22.1459	−0.821346	−0.410673	+	0.911783i	$0.634706\pi$
$728$	3.52786	0.130751
$729$	−39.5623	−1.46527
$730$	0	0
$731$	−0.111456	−0.00412236
$732$	−3.00000	−0.110883
$733$	−28.0689	−1.03675	−0.518374	−	0.855154i	$-0.673462\pi$
$733$	−28.0689	−1.03675	−0.518374	+	0.855154i	$0.673462\pi$
$734$	−1.14590	−0.0422959
$735$	0	0
$736$	7.61803	0.280804
$737$	−33.8885	−1.24830
$738$	−13.0344	−0.479804
$739$	16.8328	0.619205	0.309603	−	0.950866i	$-0.399804\pi$
$739$	16.8328	0.619205	0.309603	+	0.950866i	$0.399804\pi$
$740$	0	0
$741$	−23.4164	−0.860223
$742$	−14.1115	−0.518048
$743$	−48.7214	−1.78741	−0.893707	−	0.448652i	$-0.851904\pi$
$743$	−48.7214	−1.78741	−0.893707	+	0.448652i	$0.851904\pi$
$744$	9.70820	0.355920
$745$	0	0
$746$	−6.00000	−0.219676
$747$	15.7639	0.576772
$748$	4.00000	0.146254
$749$	−18.8885	−0.690172
$750$	0	0
$751$	−28.2492	−1.03083	−0.515414	−	0.856941i	$-0.672362\pi$
$751$	−28.2492	−1.03083	−0.515414	+	0.856941i	$0.672362\pi$
$752$	−8.32624	−0.303627
$753$	−31.4164	−1.14488
$754$	−1.70820	−0.0622091
$755$	0	0
$756$	−6.38197	−0.232110
$757$	−23.1246	−0.840478	−0.420239	−	0.907413i	$-0.638054\pi$
$757$	−23.1246	−0.840478	−0.420239	+	0.907413i	$0.638054\pi$
$758$	14.4721	0.525652
$759$	−104.430	−3.79055
$760$	0	0
$761$	−7.14590	−0.259039	−0.129519	−	0.991577i	$-0.541343\pi$
$761$	−7.14590	−0.259039	−0.129519	+	0.991577i	$0.541343\pi$
$762$	25.0344	0.906902
$763$	3.94427	0.142792
$764$	19.2361	0.695937
$765$	0	0
$766$	−16.3262	−0.589891
$767$	3.41641	0.123359
$768$	−2.61803	−0.0944702
$769$	−14.1459	−0.510114	−0.255057	−	0.966926i	$-0.582094\pi$
$769$	−14.1459	−0.510114	−0.255057	+	0.966926i	$0.582094\pi$
$770$	0	0
$771$	−8.00000	−0.288113
$772$	−14.0000	−0.503871
$773$	−36.3607	−1.30780	−0.653901	−	0.756580i	$-0.726869\pi$
$773$	−36.3607	−1.30780	−0.653901	+	0.756580i	$0.726869\pi$
$774$	−0.562306	−0.0202117
$775$	0	0
$776$	−18.1803	−0.652636
$777$	51.8885	1.86149
$778$	22.0344	0.789973
$779$	−24.4721	−0.876805
$780$	0	0
$781$	4.00000	0.143131
$782$	−5.81966	−0.208111
$783$	3.09017	0.110434
$784$	1.14590	0.0409249
$785$	0	0
$786$	−9.23607	−0.329440
$787$	−38.3262	−1.36618	−0.683091	−	0.730333i	$-0.739365\pi$
$787$	−38.3262	−1.36618	−0.683091	+	0.730333i	$0.739365\pi$
$788$	−9.70820	−0.345840
$789$	40.2705	1.43367
$790$	0	0
$791$	−44.8328	−1.59407
$792$	20.1803	0.717077
$793$	−1.41641	−0.0502981
$794$	28.6525	1.01684
$795$	0	0
$796$	1.70820	0.0605457
$797$	21.5967	0.764996	0.382498	−	0.923956i	$-0.375064\pi$
$797$	21.5967	0.764996	0.382498	+	0.923956i	$0.375064\pi$
$798$	−54.0689	−1.91402
$799$	6.36068	0.225025
$800$	0	0
$801$	31.1803	1.10170
$802$	−1.79837	−0.0635028
$803$	6.47214	0.228397
$804$	−16.9443	−0.597578
$805$	0	0
$806$	4.58359	0.161450
$807$	40.6525	1.43103
$808$	−8.38197	−0.294877
$809$	−15.3262	−0.538842	−0.269421	−	0.963023i	$-0.586832\pi$
$809$	−15.3262	−0.538842	−0.269421	+	0.963023i	$0.586832\pi$
$810$	0	0
$811$	27.1246	0.952474	0.476237	−	0.879317i	$-0.342000\pi$
$811$	27.1246	0.952474	0.476237	+	0.879317i	$0.342000\pi$
$812$	−3.94427	−0.138417
$813$	67.7771	2.37705
$814$	−36.3607	−1.27444
$815$	0	0
$816$	2.00000	0.0700140
$817$	−1.05573	−0.0369353
$818$	34.9230	1.22105
$819$	−13.5967	−0.475109
$820$	0	0
$821$	35.6180	1.24308	0.621539	−	0.783383i	$-0.286508\pi$
$821$	35.6180	1.24308	0.621539	+	0.783383i	$0.286508\pi$
$822$	−39.8885	−1.39127
$823$	−38.4721	−1.34105	−0.670527	−	0.741885i	$-0.733932\pi$
$823$	−38.4721	−1.34105	−0.670527	+	0.741885i	$0.733932\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	7.88854	0.274478
$827$	29.8885	1.03933	0.519663	−	0.854371i	$-0.326057\pi$
$827$	29.8885	1.03933	0.519663	+	0.854371i	$0.326057\pi$
$828$	−29.3607	−1.02035
$829$	−2.03444	−0.0706591	−0.0353295	−	0.999376i	$-0.511248\pi$
$829$	−2.03444	−0.0706591	−0.0353295	+	0.999376i	$0.511248\pi$
$830$	0	0
$831$	39.8885	1.38372
$832$	−1.23607	−0.0428529
$833$	−0.875388	−0.0303304
$834$	35.1246	1.21627
$835$	0	0
$836$	37.8885	1.31040
$837$	−8.29180	−0.286606
$838$	8.94427	0.308975
$839$	−45.7771	−1.58040	−0.790200	−	0.612849i	$-0.790024\pi$
$839$	−45.7771	−1.58040	−0.790200	+	0.612849i	$0.790024\pi$
$840$	0	0
$841$	−27.0902	−0.934144
$842$	−37.4508	−1.29064
$843$	−0.236068	−0.00813061
$844$	−18.0000	−0.619586
$845$	0	0
$846$	32.0902	1.10328
$847$	46.8541	1.60993
$848$	4.94427	0.169787
$849$	80.7214	2.77035
$850$	0	0
$851$	52.9017	1.81345
$852$	2.00000	0.0685189
$853$	30.4721	1.04335	0.521673	−	0.853146i	$-0.325308\pi$
$853$	30.4721	1.04335	0.521673	+	0.853146i	$0.325308\pi$
$854$	−3.27051	−0.111915
$855$	0	0
$856$	6.61803	0.226200
$857$	−32.0689	−1.09545	−0.547726	−	0.836658i	$-0.684506\pi$
$857$	−32.0689	−1.09545	−0.547726	+	0.836658i	$0.684506\pi$
$858$	16.9443	0.578468
$859$	30.2492	1.03209	0.516045	−	0.856561i	$-0.327404\pi$
$859$	30.2492	1.03209	0.516045	+	0.856561i	$0.327404\pi$
$860$	0	0
$861$	−25.2705	−0.861217
$862$	−34.3607	−1.17033
$863$	−18.6738	−0.635662	−0.317831	−	0.948147i	$-0.602955\pi$
$863$	−18.6738	−0.635662	−0.317831	+	0.948147i	$0.602955\pi$
$864$	2.23607	0.0760726
$865$	0	0
$866$	−29.4164	−0.999610
$867$	42.9787	1.45963
$868$	10.5836	0.359231
$869$	70.2492	2.38304
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−1.38197	−0.0467993
$873$	70.0689	2.37147
$874$	−55.1246	−1.86462
$875$	0	0
$876$	3.23607	0.109337
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	−21.7082	−0.732616
$879$	−58.0689	−1.95861
$880$	0	0
$881$	−12.2705	−0.413404	−0.206702	−	0.978404i	$-0.566273\pi$
$881$	−12.2705	−0.413404	−0.206702	+	0.978404i	$0.566273\pi$
$882$	−4.41641	−0.148708
$883$	11.7295	0.394729	0.197364	−	0.980330i	$-0.436762\pi$
$883$	11.7295	0.394729	0.197364	+	0.980330i	$0.436762\pi$
$884$	0.944272	0.0317593
$885$	0	0
$886$	19.3262	0.649278
$887$	−42.2705	−1.41930	−0.709652	−	0.704552i	$-0.751148\pi$
$887$	−42.2705	−1.41930	−0.709652	+	0.704552i	$0.751148\pi$
$888$	−18.1803	−0.610092
$889$	27.2918	0.915337
$890$	0	0
$891$	29.8885	1.00130
$892$	24.6180	0.824273
$893$	60.2492	2.01616
$894$	5.00000	0.167225
$895$	0	0
$896$	−2.85410	−0.0953489
$897$	−24.6525	−0.823122
$898$	13.4164	0.447711
$899$	−5.12461	−0.170915
$900$	0	0
$901$	−3.77709	−0.125833
$902$	17.7082	0.589619
$903$	−1.09017	−0.0362786
$904$	15.7082	0.522447
$905$	0	0
$906$	5.23607	0.173957
$907$	−21.6180	−0.717815	−0.358908	−	0.933373i	$-0.616851\pi$
$907$	−21.6180	−0.717815	−0.358908	+	0.933373i	$0.616851\pi$
$908$	27.3262	0.906853
$909$	32.3050	1.07149
$910$	0	0
$911$	30.5410	1.01187	0.505935	−	0.862572i	$-0.331148\pi$
$911$	30.5410	1.01187	0.505935	+	0.862572i	$0.331148\pi$
$912$	18.9443	0.627308
$913$	−21.4164	−0.708780
$914$	28.0000	0.926158
$915$	0	0
$916$	−10.8541	−0.358630
$917$	−10.0689	−0.332504
$918$	−1.70820	−0.0563791
$919$	46.4296	1.53157	0.765785	−	0.643097i	$-0.222351\pi$
$919$	46.4296	1.53157	0.765785	+	0.643097i	$0.222351\pi$
$920$	0	0
$921$	32.1246	1.05854
$922$	26.0902	0.859234
$923$	0.944272	0.0310811
$924$	39.1246	1.28711
$925$	0	0
$926$	−6.85410	−0.225240
$927$	−15.4164	−0.506341
$928$	1.38197	0.0453653
$929$	−20.4508	−0.670971	−0.335485	−	0.942045i	$-0.608900\pi$
$929$	−20.4508	−0.670971	−0.335485	+	0.942045i	$0.608900\pi$
$930$	0	0
$931$	−8.29180	−0.271753
$932$	3.23607	0.106001
$933$	−9.70820	−0.317832
$934$	−14.5623	−0.476493
$935$	0	0
$936$	4.76393	0.155714
$937$	52.0000	1.69877	0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000	1.69877	0.849383	+	0.527777i	$0.176974\pi$
$938$	−18.4721	−0.603137
$939$	1.52786	0.0498600
$940$	0	0
$941$	−44.8328	−1.46151	−0.730754	−	0.682641i	$-0.760831\pi$
$941$	−44.8328	−1.46151	−0.730754	+	0.682641i	$0.760831\pi$
$942$	−39.8885	−1.29964
$943$	−25.7639	−0.838989
$944$	−2.76393	−0.0899583
$945$	0	0
$946$	0.763932	0.0248376
$947$	−27.2705	−0.886172	−0.443086	−	0.896479i	$-0.646116\pi$
$947$	−27.2705	−0.886172	−0.443086	+	0.896479i	$0.646116\pi$
$948$	35.1246	1.14079
$949$	1.52786	0.0495966
$950$	0	0
$951$	9.23607	0.299500
$952$	2.18034	0.0706652
$953$	−12.9443	−0.419306	−0.209653	−	0.977776i	$-0.567233\pi$
$953$	−12.9443	−0.419306	−0.209653	+	0.977776i	$0.567233\pi$
$954$	−19.0557	−0.616952
$955$	0	0
$956$	−13.4164	−0.433918
$957$	−18.9443	−0.612381
$958$	−30.0000	−0.969256
$959$	−43.4853	−1.40421
$960$	0	0
$961$	−17.2492	−0.556427
$962$	−8.58359	−0.276746
$963$	−25.5066	−0.821938
$964$	0.0901699	0.00290418
$965$	0	0
$966$	−56.9230	−1.83147
$967$	−3.45085	−0.110972	−0.0554859	−	0.998459i	$-0.517671\pi$
$967$	−3.45085	−0.110972	−0.0554859	+	0.998459i	$0.517671\pi$
$968$	−16.4164	−0.527643
$969$	−14.4721	−0.464912
$970$	0	0
$971$	−42.7214	−1.37099	−0.685497	−	0.728076i	$-0.740415\pi$
$971$	−42.7214	−1.37099	−0.685497	+	0.728076i	$0.740415\pi$
$972$	21.6525	0.694503
$973$	38.2918	1.22758
$974$	32.3951	1.03801
$975$	0	0
$976$	1.14590	0.0366793
$977$	24.7639	0.792268	0.396134	−	0.918193i	$-0.370352\pi$
$977$	24.7639	0.792268	0.396134	+	0.918193i	$0.370352\pi$
$978$	53.0689	1.69696
$979$	−42.3607	−1.35385
$980$	0	0
$981$	5.32624	0.170054
$982$	38.6525	1.23345
$983$	19.4164	0.619287	0.309644	−	0.950853i	$-0.399790\pi$
$983$	19.4164	0.619287	0.309644	+	0.950853i	$0.399790\pi$
$984$	8.85410	0.282258
$985$	0	0
$986$	−1.05573	−0.0336212
$987$	62.2148	1.98032
$988$	8.94427	0.284555
$989$	−1.11146	−0.0353423
$990$	0	0
$991$	−20.3607	−0.646778	−0.323389	−	0.946266i	$-0.604822\pi$
$991$	−20.3607	−0.646778	−0.323389	+	0.946266i	$0.604822\pi$
$992$	−3.70820	−0.117736
$993$	56.0689	1.77929
$994$	2.18034	0.0691562
$995$	0	0
$996$	−10.7082	−0.339302
$997$	13.7082	0.434143	0.217072	−	0.976156i	$-0.430349\pi$
$997$	13.7082	0.434143	0.217072	+	0.976156i	$0.430349\pi$
$998$	18.2918	0.579017
$999$	15.5279	0.491280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.a.a.1.1	✓	2
3.2	odd	2		2250.2.a.m.1.2		2
4.3	odd	2		2000.2.a.k.1.2		2
5.2	odd	4		250.2.b.b.249.2		4
5.3	odd	4		250.2.b.b.249.3		4
5.4	even	2		250.2.a.d.1.2	yes	2
8.3	odd	2		8000.2.a.a.1.1		2
8.5	even	2		8000.2.a.x.1.2		2
15.2	even	4		2250.2.c.h.1999.4		4
15.8	even	4		2250.2.c.h.1999.1		4
15.14	odd	2		2250.2.a.f.1.1		2
20.3	even	4		2000.2.c.d.1249.4		4
20.7	even	4		2000.2.c.d.1249.1		4
20.19	odd	2		2000.2.a.b.1.1		2
40.19	odd	2		8000.2.a.w.1.2		2
40.29	even	2		8000.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.a.a.1.1	✓	2	1.1	even	1	trivial
250.2.a.d.1.2	yes	2	5.4	even	2
250.2.b.b.249.2		4	5.2	odd	4
250.2.b.b.249.3		4	5.3	odd	4
2000.2.a.b.1.1		2	20.19	odd	2
2000.2.a.k.1.2		2	4.3	odd	2
2000.2.c.d.1249.1		4	20.7	even	4
2000.2.c.d.1249.4		4	20.3	even	4
2250.2.a.f.1.1		2	15.14	odd	2
2250.2.a.m.1.2		2	3.2	odd	2
2250.2.c.h.1999.1		4	15.8	even	4
2250.2.c.h.1999.4		4	15.2	even	4
8000.2.a.a.1.1		2	8.3	odd	2
8000.2.a.b.1.1		2	40.29	even	2
8000.2.a.w.1.2		2	40.19	odd	2
8000.2.a.x.1.2		2	8.5	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} +2.61803 q^{6} +2.85410 q^{7} -1.00000 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} +2.61803 q^{6} +2.85410 q^{7} -1.00000 q^{8} +3.85410 q^{9} -5.23607 q^{11} -2.61803 q^{12} -1.23607 q^{13} -2.85410 q^{14} +1.00000 q^{16} -0.763932 q^{17} -3.85410 q^{18} -7.23607 q^{19} -7.47214 q^{21} +5.23607 q^{22} -7.61803 q^{23} +2.61803 q^{24} +1.23607 q^{26} -2.23607 q^{27} +2.85410 q^{28} -1.38197 q^{29} +3.70820 q^{31} -1.00000 q^{32} +13.7082 q^{33} +0.763932 q^{34} +3.85410 q^{36} -6.94427 q^{37} +7.23607 q^{38} +3.23607 q^{39} +3.38197 q^{41} +7.47214 q^{42} +0.145898 q^{43} -5.23607 q^{44} +7.61803 q^{46} -8.32624 q^{47} -2.61803 q^{48} +1.14590 q^{49} +2.00000 q^{51} -1.23607 q^{52} +4.94427 q^{53} +2.23607 q^{54} -2.85410 q^{56} +18.9443 q^{57} +1.38197 q^{58} -2.76393 q^{59} +1.14590 q^{61} -3.70820 q^{62} +11.0000 q^{63} +1.00000 q^{64} -13.7082 q^{66} +6.47214 q^{67} -0.763932 q^{68} +19.9443 q^{69} -0.763932 q^{71} -3.85410 q^{72} -1.23607 q^{73} +6.94427 q^{74} -7.23607 q^{76} -14.9443 q^{77} -3.23607 q^{78} -13.4164 q^{79} -5.70820 q^{81} -3.38197 q^{82} +4.09017 q^{83} -7.47214 q^{84} -0.145898 q^{86} +3.61803 q^{87} +5.23607 q^{88} +8.09017 q^{89} -3.52786 q^{91} -7.61803 q^{92} -9.70820 q^{93} +8.32624 q^{94} +2.61803 q^{96} +18.1803 q^{97} -1.14590 q^{98} -20.1803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^6 - q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{6} - q^{7} - 2 q^{8} + q^{9} - 6 q^{11} - 3 q^{12} + 2 q^{13} + q^{14} + 2 q^{16} - 6 q^{17} - q^{18} - 10 q^{19} - 6 q^{21} + 6 q^{22} - 13 q^{23} + 3 q^{24} - 2 q^{26} - q^{28} - 5 q^{29} - 6 q^{31} - 2 q^{32} + 14 q^{33} + 6 q^{34} + q^{36} + 4 q^{37} + 10 q^{38} + 2 q^{39} + 9 q^{41} + 6 q^{42} + 7 q^{43} - 6 q^{44} + 13 q^{46} - q^{47} - 3 q^{48} + 9 q^{49} + 4 q^{51} + 2 q^{52} - 8 q^{53} + q^{56} + 20 q^{57} + 5 q^{58} - 10 q^{59} + 9 q^{61} + 6 q^{62} + 22 q^{63} + 2 q^{64} - 14 q^{66} + 4 q^{67} - 6 q^{68} + 22 q^{69} - 6 q^{71} - q^{72} + 2 q^{73} - 4 q^{74} - 10 q^{76} - 12 q^{77} - 2 q^{78} + 2 q^{81} - 9 q^{82} - 3 q^{83} - 6 q^{84} - 7 q^{86} + 5 q^{87} + 6 q^{88} + 5 q^{89} - 16 q^{91} - 13 q^{92} - 6 q^{93} + q^{94} + 3 q^{96} + 14 q^{97} - 9 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^6 - q^7 - 2 * q^8 + q^9 - 6 * q^11 - 3 * q^12 + 2 * q^13 + q^14 + 2 * q^16 - 6 * q^17 - q^18 - 10 * q^19 - 6 * q^21 + 6 * q^22 - 13 * q^23 + 3 * q^24 - 2 * q^26 - q^28 - 5 * q^29 - 6 * q^31 - 2 * q^32 + 14 * q^33 + 6 * q^34 + q^36 + 4 * q^37 + 10 * q^38 + 2 * q^39 + 9 * q^41 + 6 * q^42 + 7 * q^43 - 6 * q^44 + 13 * q^46 - q^47 - 3 * q^48 + 9 * q^49 + 4 * q^51 + 2 * q^52 - 8 * q^53 + q^56 + 20 * q^57 + 5 * q^58 - 10 * q^59 + 9 * q^61 + 6 * q^62 + 22 * q^63 + 2 * q^64 - 14 * q^66 + 4 * q^67 - 6 * q^68 + 22 * q^69 - 6 * q^71 - q^72 + 2 * q^73 - 4 * q^74 - 10 * q^76 - 12 * q^77 - 2 * q^78 + 2 * q^81 - 9 * q^82 - 3 * q^83 - 6 * q^84 - 7 * q^86 + 5 * q^87 + 6 * q^88 + 5 * q^89 - 16 * q^91 - 13 * q^92 - 6 * q^93 + q^94 + 3 * q^96 + 14 * q^97 - 9 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more