LMFDB - Embedded newform 725.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("725.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.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:	$5.78915414654$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.240881.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 9x^{2} + 5x - 7 $ x^5 - 2x^4 - 5x^3 + 9x^2 + 5x - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.33090$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33090 q^{2} -0.318289 q^{3} +3.43308 q^{4} +0.741899 q^{6} -1.09271 q^{7} -3.34037 q^{8} -2.89869 q^{9} +O(q^{10})$	\(q-2.33090 q^{2} -0.318289 q^{3} +3.43308 q^{4} +0.741899 q^{6} -1.09271 q^{7} -3.34037 q^{8} -2.89869 q^{9} +5.26027 q^{11} -1.09271 q^{12} -0.453000 q^{13} +2.54700 q^{14} +0.919897 q^{16} -4.82718 q^{17} +6.75655 q^{18} -1.04329 q^{19} +0.347798 q^{21} -12.2611 q^{22} +2.49327 q^{23} +1.06320 q^{24} +1.05590 q^{26} +1.87749 q^{27} -3.75137 q^{28} +1.00000 q^{29} -6.45517 q^{31} +4.53656 q^{32} -1.67428 q^{33} +11.2517 q^{34} -9.95145 q^{36} +0.535270 q^{37} +2.43180 q^{38} +0.144185 q^{39} -0.228712 q^{41} -0.810682 q^{42} +5.21915 q^{43} +18.0589 q^{44} -5.81156 q^{46} -3.52266 q^{47} -0.292793 q^{48} -5.80598 q^{49} +1.53644 q^{51} -1.55519 q^{52} +4.73447 q^{53} -4.37623 q^{54} +3.65006 q^{56} +0.332067 q^{57} -2.33090 q^{58} -1.78076 q^{59} -14.2394 q^{61} +15.0463 q^{62} +3.16744 q^{63} -12.4140 q^{64} +3.90259 q^{66} -8.62927 q^{67} -16.5721 q^{68} -0.793580 q^{69} -5.08842 q^{71} +9.68271 q^{72} -11.9810 q^{73} -1.24766 q^{74} -3.58169 q^{76} -5.74796 q^{77} -0.336080 q^{78} -12.6314 q^{79} +8.09849 q^{81} +0.533103 q^{82} -9.75840 q^{83} +1.19402 q^{84} -12.1653 q^{86} -0.318289 q^{87} -17.5712 q^{88} -10.0347 q^{89} +0.494998 q^{91} +8.55961 q^{92} +2.05461 q^{93} +8.21096 q^{94} -1.44394 q^{96} -15.4404 q^{97} +13.5331 q^{98} -15.2479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26} - 27 q^{27} - 10 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} + 7 q^{33} + 3 q^{34} - 13 q^{36} - 14 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{41} - 24 q^{42} - 28 q^{43} + 7 q^{44} - 20 q^{46} - 15 q^{47} + 26 q^{48} - 3 q^{49} + 5 q^{51} - 6 q^{52} + 8 q^{53} + 10 q^{54} - 16 q^{56} + 6 q^{57} - 2 q^{58} - 11 q^{59} - 5 q^{61} + 6 q^{62} + 5 q^{63} - 5 q^{64} - 27 q^{66} - 23 q^{67} - q^{68} - 26 q^{69} - 5 q^{71} - 3 q^{72} - 16 q^{73} + 8 q^{74} + 16 q^{76} + 30 q^{77} + 33 q^{78} - 10 q^{79} + 49 q^{81} + 19 q^{82} - 9 q^{83} + 32 q^{84} - 13 q^{86} - 6 q^{87} - 35 q^{88} - 18 q^{89} + q^{91} + 27 q^{92} - 7 q^{93} - 13 q^{94} - 38 q^{96} - 23 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * 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 $

$2$	−2.33090	−1.64819	−0.824097	−	0.566449i	$-0.808317\pi$
$2$	−2.33090	−1.64819	−0.824097	+	0.566449i	$0.808317\pi$
$3$	−0.318289	−0.183764	−0.0918821	−	0.995770i	$-0.529288\pi$
$3$	−0.318289	−0.183764	−0.0918821	+	0.995770i	$0.529288\pi$
$4$	3.43308	1.71654
$5$	0	0
$5$	0	0
$6$	0.741899	0.302879
$7$	−1.09271	−0.413006	−0.206503	−	0.978446i	$-0.566208\pi$
$7$	−1.09271	−0.413006	−0.206503	+	0.978446i	$0.566208\pi$
$8$	−3.34037	−1.18100
$9$	−2.89869	−0.966231
$10$	0	0
$11$	5.26027	1.58603	0.793015	−	0.609202i	$-0.208510\pi$
$11$	5.26027	1.58603	0.793015	+	0.609202i	$0.208510\pi$
$12$	−1.09271	−0.315439
$13$	−0.453000	−0.125640	−0.0628198	−	0.998025i	$-0.520009\pi$
$13$	−0.453000	−0.125640	−0.0628198	+	0.998025i	$0.520009\pi$
$14$	2.54700	0.680714
$15$	0	0
$16$	0.919897	0.229974
$17$	−4.82718	−1.17076	−0.585382	−	0.810758i	$-0.699055\pi$
$17$	−4.82718	−1.17076	−0.585382	+	0.810758i	$0.699055\pi$
$18$	6.75655	1.59254
$19$	−1.04329	−0.239346	−0.119673	−	0.992813i	$-0.538185\pi$
$19$	−1.04329	−0.239346	−0.119673	+	0.992813i	$0.538185\pi$
$20$	0	0
$21$	0.347798	0.0758958
$22$	−12.2611	−2.61409
$23$	2.49327	0.519883	0.259941	−	0.965624i	$-0.416297\pi$
$23$	2.49327	0.519883	0.259941	+	0.965624i	$0.416297\pi$
$24$	1.06320	0.217025
$25$	0	0
$26$	1.05590	0.207078
$27$	1.87749	0.361323
$28$	−3.75137	−0.708943
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−6.45517	−1.15938	−0.579691	−	0.814836i	$-0.696827\pi$
$31$	−6.45517	−1.15938	−0.579691	+	0.814836i	$0.696827\pi$
$32$	4.53656	0.801958
$33$	−1.67428	−0.291456
$34$	11.2517	1.92965
$35$	0	0
$36$	−9.95145	−1.65858
$37$	0.535270	0.0879978	0.0439989	−	0.999032i	$-0.485990\pi$
$37$	0.535270	0.0879978	0.0439989	+	0.999032i	$0.485990\pi$
$38$	2.43180	0.394489
$39$	0.144185	0.0230880
$40$	0	0
$41$	−0.228712	−0.0357187	−0.0178594	−	0.999841i	$-0.505685\pi$
$41$	−0.228712	−0.0357187	−0.0178594	+	0.999841i	$0.505685\pi$
$42$	−0.810682	−0.125091
$43$	5.21915	0.795913	0.397956	−	0.917404i	$-0.369720\pi$
$43$	5.21915	0.795913	0.397956	+	0.917404i	$0.369720\pi$
$44$	18.0589	2.72249
$45$	0	0
$46$	−5.81156	−0.856868
$47$	−3.52266	−0.513833	−0.256916	−	0.966434i	$-0.582707\pi$
$47$	−3.52266	−0.513833	−0.256916	+	0.966434i	$0.582707\pi$
$48$	−0.292793	−0.0422610
$49$	−5.80598	−0.829426
$50$	0	0
$51$	1.53644	0.215144
$52$	−1.55519	−0.215665
$53$	4.73447	0.650330	0.325165	−	0.945657i	$-0.394580\pi$
$53$	4.73447	0.650330	0.325165	+	0.945657i	$0.394580\pi$
$54$	−4.37623	−0.595530
$55$	0	0
$56$	3.65006	0.487760
$57$	0.332067	0.0439833
$58$	−2.33090	−0.306062
$59$	−1.78076	−0.231836	−0.115918	−	0.993259i	$-0.536981\pi$
$59$	−1.78076	−0.231836	−0.115918	+	0.993259i	$0.536981\pi$
$60$	0	0
$61$	−14.2394	−1.82317	−0.911583	−	0.411116i	$-0.865139\pi$
$61$	−14.2394	−1.82317	−0.911583	+	0.411116i	$0.865139\pi$
$62$	15.0463	1.91089
$63$	3.16744	0.399059
$64$	−12.4140	−1.55176
$65$	0	0
$66$	3.90259	0.480375
$67$	−8.62927	−1.05423	−0.527117	−	0.849793i	$-0.676727\pi$
$67$	−8.62927	−1.05423	−0.527117	+	0.849793i	$0.676727\pi$
$68$	−16.5721	−2.00967
$69$	−0.793580	−0.0955359
$70$	0	0
$71$	−5.08842	−0.603884	−0.301942	−	0.953326i	$-0.597635\pi$
$71$	−5.08842	−0.603884	−0.301942	+	0.953326i	$0.597635\pi$
$72$	9.68271	1.14112
$73$	−11.9810	−1.40227	−0.701133	−	0.713031i	$-0.747322\pi$
$73$	−11.9810	−1.40227	−0.701133	+	0.713031i	$0.747322\pi$
$74$	−1.24766	−0.145037
$75$	0	0
$76$	−3.58169	−0.410848
$77$	−5.74796	−0.655041
$78$	−0.336080	−0.0380536
$79$	−12.6314	−1.42115	−0.710574	−	0.703623i	$-0.751565\pi$
$79$	−12.6314	−1.42115	−0.710574	+	0.703623i	$0.751565\pi$
$80$	0	0
$81$	8.09849	0.899833
$82$	0.533103	0.0588714
$83$	−9.75840	−1.07112	−0.535562	−	0.844496i	$-0.679900\pi$
$83$	−9.75840	−1.07112	−0.535562	+	0.844496i	$0.679900\pi$
$84$	1.19402	0.130278
$85$	0	0
$86$	−12.1653	−1.31182
$87$	−0.318289	−0.0341241
$88$	−17.5712	−1.87310
$89$	−10.0347	−1.06368	−0.531838	−	0.846846i	$-0.678498\pi$
$89$	−10.0347	−1.06368	−0.531838	+	0.846846i	$0.678498\pi$
$90$	0	0
$91$	0.494998	0.0518899
$92$	8.55961	0.892401
$93$	2.05461	0.213053
$94$	8.21096	0.846896
$95$	0	0
$96$	−1.44394	−0.147371
$97$	−15.4404	−1.56774	−0.783869	−	0.620927i	$-0.786756\pi$
$97$	−15.4404	−1.56774	−0.783869	+	0.620927i	$0.786756\pi$
$98$	13.5331	1.36705
$99$	−15.2479	−1.53247
$100$	0	0
$101$	14.5211	1.44490	0.722451	−	0.691422i	$-0.243015\pi$
$101$	14.5211	1.44490	0.722451	+	0.691422i	$0.243015\pi$
$102$	−3.58128	−0.354600
$103$	−4.59534	−0.452792	−0.226396	−	0.974035i	$-0.572694\pi$
$103$	−4.59534	−0.452792	−0.226396	+	0.974035i	$0.572694\pi$
$104$	1.51319	0.148380
$105$	0	0
$106$	−11.0356	−1.07187
$107$	20.1825	1.95111	0.975556	−	0.219753i	$-0.0705251\pi$
$107$	20.1825	1.95111	0.975556	+	0.219753i	$0.0705251\pi$
$108$	6.44557	0.620226
$109$	4.36762	0.418343	0.209171	−	0.977879i	$-0.432923\pi$
$109$	4.36762	0.418343	0.209171	+	0.977879i	$0.432923\pi$
$110$	0	0
$111$	−0.170370	−0.0161708
$112$	−1.00518	−0.0949808
$113$	−13.0446	−1.22713	−0.613567	−	0.789643i	$-0.710266\pi$
$113$	−13.0446	−1.22713	−0.613567	+	0.789643i	$0.710266\pi$
$114$	−0.774013	−0.0724930
$115$	0	0
$116$	3.43308	0.318754
$117$	1.31311	0.121397
$118$	4.15077	0.382110
$119$	5.27472	0.483533
$120$	0	0
$121$	16.6704	1.51549
$122$	33.1905	3.00493
$123$	0.0727963	0.00656382
$124$	−22.1611	−1.99013
$125$	0	0
$126$	−7.38297	−0.657727
$127$	−12.0378	−1.06818	−0.534092	−	0.845426i	$-0.679346\pi$
$127$	−12.0378	−1.06818	−0.534092	+	0.845426i	$0.679346\pi$
$128$	19.8628	1.75564
$129$	−1.66120	−0.146260
$130$	0	0
$131$	−18.0578	−1.57772	−0.788860	−	0.614572i	$-0.789329\pi$
$131$	−18.0578	−1.57772	−0.788860	+	0.614572i	$0.789329\pi$
$132$	−5.74796	−0.500296
$133$	1.14001	0.0988516
$134$	20.1139	1.73758
$135$	0	0
$136$	16.1246	1.38267
$137$	11.3447	0.969240	0.484620	−	0.874725i	$-0.338958\pi$
$137$	11.3447	0.969240	0.484620	+	0.874725i	$0.338958\pi$
$138$	1.84975	0.157462
$139$	10.5504	0.894870	0.447435	−	0.894316i	$-0.352338\pi$
$139$	10.5504	0.894870	0.447435	+	0.894316i	$0.352338\pi$
$140$	0	0
$141$	1.12122	0.0944241
$142$	11.8606	0.995318
$143$	−2.38290	−0.199268
$144$	−2.66650	−0.222208
$145$	0	0
$146$	27.9264	2.31121
$147$	1.84798	0.152419
$148$	1.83763	0.151052
$149$	−5.56554	−0.455947	−0.227973	−	0.973667i	$-0.573210\pi$
$149$	−5.56554	−0.455947	−0.227973	+	0.973667i	$0.573210\pi$
$150$	0	0
$151$	13.4696	1.09614	0.548071	−	0.836432i	$-0.315362\pi$
$151$	13.4696	1.09614	0.548071	+	0.836432i	$0.315362\pi$
$152$	3.48497	0.282668
$153$	13.9925	1.13123
$154$	13.3979	1.07963
$155$	0	0
$156$	0.494998	0.0396316
$157$	18.7100	1.49322	0.746612	−	0.665260i	$-0.231679\pi$
$157$	18.7100	1.49322	0.746612	+	0.665260i	$0.231679\pi$
$158$	29.4426	2.34233
$159$	−1.50693	−0.119507
$160$	0	0
$161$	−2.72443	−0.214715
$162$	−18.8768	−1.48310
$163$	−12.3812	−0.969771	−0.484886	−	0.874578i	$-0.661139\pi$
$163$	−12.3812	−0.969771	−0.484886	+	0.874578i	$0.661139\pi$
$164$	−0.785186	−0.0613127
$165$	0	0
$166$	22.7458	1.76542
$167$	−20.6501	−1.59795	−0.798976	−	0.601363i	$-0.794625\pi$
$167$	−20.6501	−1.59795	−0.798976	+	0.601363i	$0.794625\pi$
$168$	−1.16177	−0.0896329
$169$	−12.7948	−0.984215
$170$	0	0
$171$	3.02417	0.231264
$172$	17.9178	1.36622
$173$	−4.75783	−0.361731	−0.180866	−	0.983508i	$-0.557890\pi$
$173$	−4.75783	−0.361731	−0.180866	+	0.983508i	$0.557890\pi$
$174$	0.741899	0.0562432
$175$	0	0
$176$	4.83890	0.364746
$177$	0.566797	0.0426031
$178$	23.3898	1.75314
$179$	11.5557	0.863716	0.431858	−	0.901942i	$-0.357858\pi$
$179$	11.5557	0.863716	0.431858	+	0.901942i	$0.357858\pi$
$180$	0	0
$181$	9.55520	0.710232	0.355116	−	0.934822i	$-0.384441\pi$
$181$	9.55520	0.710232	0.355116	+	0.934822i	$0.384441\pi$
$182$	−1.15379	−0.0855246
$183$	4.53224	0.335033
$184$	−8.32845	−0.613982
$185$	0	0
$186$	−4.78908	−0.351152
$187$	−25.3923	−1.85687
$188$	−12.0936	−0.882016
$189$	−2.05155	−0.149229
$190$	0	0
$191$	−20.9747	−1.51768	−0.758839	−	0.651278i	$-0.774233\pi$
$191$	−20.9747	−1.51768	−0.758839	+	0.651278i	$0.774233\pi$
$192$	3.95125	0.285157
$193$	22.8064	1.64164	0.820821	−	0.571185i	$-0.193516\pi$
$193$	22.8064	1.64164	0.820821	+	0.571185i	$0.193516\pi$
$194$	35.9900	2.58393
$195$	0	0
$196$	−19.9324	−1.42374
$197$	14.1188	1.00592	0.502962	−	0.864309i	$-0.332244\pi$
$197$	14.1188	1.00592	0.502962	+	0.864309i	$0.332244\pi$
$198$	35.5413	2.52581
$199$	−9.06536	−0.642626	−0.321313	−	0.946973i	$-0.604124\pi$
$199$	−9.06536	−0.642626	−0.321313	+	0.946973i	$0.604124\pi$
$200$	0	0
$201$	2.74660	0.193730
$202$	−33.8472	−2.38148
$203$	−1.09271	−0.0766934
$204$	5.27472	0.369305
$205$	0	0
$206$	10.7113	0.746289
$207$	−7.22723	−0.502327
$208$	−0.416713	−0.0288938
$209$	−5.48797	−0.379611
$210$	0	0
$211$	7.15564	0.492614	0.246307	−	0.969192i	$-0.420783\pi$
$211$	7.15564	0.492614	0.246307	+	0.969192i	$0.420783\pi$
$212$	16.2538	1.11632
$213$	1.61959	0.110972
$214$	−47.0432	−3.21581
$215$	0	0
$216$	−6.27151	−0.426722
$217$	7.05364	0.478832
$218$	−10.1805	−0.689509
$219$	3.81341	0.257686
$220$	0	0
$221$	2.18671	0.147094
$222$	0.397116	0.0266527
$223$	−8.90055	−0.596025	−0.298012	−	0.954562i	$-0.596324\pi$
$223$	−8.90055	−0.596025	−0.298012	+	0.954562i	$0.596324\pi$
$224$	−4.95715	−0.331214
$225$	0	0
$226$	30.4056	2.02255
$227$	2.85842	0.189720	0.0948600	−	0.995491i	$-0.469760\pi$
$227$	2.85842	0.189720	0.0948600	+	0.995491i	$0.469760\pi$
$228$	1.14001	0.0754992
$229$	23.3358	1.54207	0.771037	−	0.636791i	$-0.219739\pi$
$229$	23.3358	1.54207	0.771037	+	0.636791i	$0.219739\pi$
$230$	0	0
$231$	1.82951	0.120373
$232$	−3.34037	−0.219306
$233$	−12.3160	−0.806846	−0.403423	−	0.915014i	$-0.632180\pi$
$233$	−12.3160	−0.806846	−0.403423	+	0.915014i	$0.632180\pi$
$234$	−3.06072	−0.200085
$235$	0	0
$236$	−6.11351	−0.397955
$237$	4.02045	0.261156
$238$	−12.2948	−0.796956
$239$	29.7130	1.92198	0.960988	−	0.276591i	$-0.0892047\pi$
$239$	29.7130	1.92198	0.960988	+	0.276591i	$0.0892047\pi$
$240$	0	0
$241$	18.1647	1.17009	0.585045	−	0.811001i	$-0.301077\pi$
$241$	18.1647	1.17009	0.585045	+	0.811001i	$0.301077\pi$
$242$	−38.8570	−2.49783
$243$	−8.21012	−0.526680
$244$	−48.8850	−3.12954
$245$	0	0
$246$	−0.169681	−0.0108185
$247$	0.472609	0.0300714
$248$	21.5627	1.36923
$249$	3.10599	0.196834
$250$	0	0
$251$	15.1232	0.954569	0.477284	−	0.878749i	$-0.341621\pi$
$251$	15.1232	0.954569	0.477284	+	0.878749i	$0.341621\pi$
$252$	10.8741	0.685002
$253$	13.1153	0.824550
$254$	28.0589	1.76057
$255$	0	0
$256$	−21.4700	−1.34187
$257$	21.5436	1.34385	0.671927	−	0.740617i	$-0.265467\pi$
$257$	21.5436	1.34385	0.671927	+	0.740617i	$0.265467\pi$
$258$	3.87208	0.241065
$259$	−0.584896	−0.0363437
$260$	0	0
$261$	−2.89869	−0.179425
$262$	42.0910	2.60039
$263$	−16.4285	−1.01302	−0.506512	−	0.862233i	$-0.669066\pi$
$263$	−16.4285	−1.01302	−0.506512	+	0.862233i	$0.669066\pi$
$264$	5.59273	0.344209
$265$	0	0
$266$	−2.65725	−0.162927
$267$	3.19393	0.195465
$268$	−29.6250	−1.80964
$269$	−9.71327	−0.592228	−0.296114	−	0.955153i	$-0.595691\pi$
$269$	−9.71327	−0.592228	−0.296114	+	0.955153i	$0.595691\pi$
$270$	0	0
$271$	−1.02188	−0.0620749	−0.0310374	−	0.999518i	$-0.509881\pi$
$271$	−1.02188	−0.0620749	−0.0310374	+	0.999518i	$0.509881\pi$
$272$	−4.44051	−0.269245
$273$	−0.157552	−0.00953551
$274$	−26.4432	−1.59750
$275$	0	0
$276$	−2.72443	−0.163991
$277$	4.82608	0.289971	0.144986	−	0.989434i	$-0.453686\pi$
$277$	4.82608	0.289971	0.144986	+	0.989434i	$0.453686\pi$
$278$	−24.5918	−1.47492
$279$	18.7115	1.12023
$280$	0	0
$281$	7.09507	0.423256	0.211628	−	0.977350i	$-0.432123\pi$
$281$	7.09507	0.423256	0.211628	+	0.977350i	$0.432123\pi$
$282$	−2.61346	−0.155629
$283$	−20.7674	−1.23450	−0.617248	−	0.786769i	$-0.711752\pi$
$283$	−20.7674	−1.23450	−0.617248	+	0.786769i	$0.711752\pi$
$284$	−17.4690	−1.03659
$285$	0	0
$286$	5.55430	0.328432
$287$	0.249916	0.0147521
$288$	−13.1501	−0.774876
$289$	6.30171	0.370689
$290$	0	0
$291$	4.91451	0.288094
$292$	−41.1316	−2.40705
$293$	−12.4880	−0.729557	−0.364779	−	0.931094i	$-0.618855\pi$
$293$	−12.4880	−0.729557	−0.364779	+	0.931094i	$0.618855\pi$
$294$	−4.30745	−0.251216
$295$	0	0
$296$	−1.78800	−0.103925
$297$	9.87609	0.573069
$298$	12.9727	0.751488
$299$	−1.12945	−0.0653178
$300$	0	0
$301$	−5.70303	−0.328717
$302$	−31.3963	−1.80665
$303$	−4.62190	−0.265521
$304$	−0.959716	−0.0550435
$305$	0	0
$306$	−32.6151	−1.86448
$307$	−18.1776	−1.03745	−0.518725	−	0.854941i	$-0.673593\pi$
$307$	−18.1776	−1.03745	−0.518725	+	0.854941i	$0.673593\pi$
$308$	−19.7332	−1.12440
$309$	1.46264	0.0832070
$310$	0	0
$311$	−17.6250	−0.999421	−0.499710	−	0.866193i	$-0.666560\pi$
$311$	−17.6250	−0.999421	−0.499710	+	0.866193i	$0.666560\pi$
$312$	−0.481631	−0.0272670
$313$	−5.27338	−0.298069	−0.149034	−	0.988832i	$-0.547617\pi$
$313$	−5.27338	−0.298069	−0.149034	+	0.988832i	$0.547617\pi$
$314$	−43.6112	−2.46112
$315$	0	0
$316$	−43.3648	−2.43946
$317$	19.6121	1.10152	0.550762	−	0.834662i	$-0.314337\pi$
$317$	19.6121	1.10152	0.550762	+	0.834662i	$0.314337\pi$
$318$	3.51250	0.196971
$319$	5.26027	0.294518
$320$	0	0
$321$	−6.42385	−0.358544
$322$	6.35036	0.353892
$323$	5.03614	0.280218
$324$	27.8028	1.54460
$325$	0	0
$326$	28.8593	1.59837
$327$	−1.39017	−0.0768764
$328$	0.763981	0.0421838
$329$	3.84925	0.212216
$330$	0	0
$331$	4.67888	0.257175	0.128587	−	0.991698i	$-0.458956\pi$
$331$	4.67888	0.257175	0.128587	+	0.991698i	$0.458956\pi$
$332$	−33.5014	−1.83863
$333$	−1.55158	−0.0850262
$334$	48.1333	2.63373
$335$	0	0
$336$	0.319938	0.0174541
$337$	−8.06881	−0.439536	−0.219768	−	0.975552i	$-0.570530\pi$
$337$	−8.06881	−0.439536	−0.219768	+	0.975552i	$0.570530\pi$
$338$	29.8233	1.62218
$339$	4.15195	0.225503
$340$	0	0
$341$	−33.9559	−1.83882
$342$	−7.04903	−0.381168
$343$	13.9933	0.755565
$344$	−17.4339	−0.939973
$345$	0	0
$346$	11.0900	0.596203
$347$	7.31950	0.392931	0.196466	−	0.980511i	$-0.437054\pi$
$347$	7.31950	0.392931	0.196466	+	0.980511i	$0.437054\pi$
$348$	−1.09271	−0.0585755
$349$	3.60205	0.192813	0.0964066	−	0.995342i	$-0.469265\pi$
$349$	3.60205	0.192813	0.0964066	+	0.995342i	$0.469265\pi$
$350$	0	0
$351$	−0.850501	−0.0453964
$352$	23.8635	1.27193
$353$	−34.1603	−1.81817	−0.909085	−	0.416610i	$-0.863218\pi$
$353$	−34.1603	−1.81817	−0.909085	+	0.416610i	$0.863218\pi$
$354$	−1.32115	−0.0702181
$355$	0	0
$356$	−34.4499	−1.82584
$357$	−1.67889	−0.0888560
$358$	−26.9352	−1.42357
$359$	−2.30982	−0.121908	−0.0609539	−	0.998141i	$-0.519414\pi$
$359$	−2.30982	−0.121908	−0.0609539	+	0.998141i	$0.519414\pi$
$360$	0	0
$361$	−17.9116	−0.942713
$362$	−22.2722	−1.17060
$363$	−5.30601	−0.278493
$364$	1.69937	0.0890712
$365$	0	0
$366$	−10.5642	−0.552199
$367$	−11.6033	−0.605688	−0.302844	−	0.953040i	$-0.597936\pi$
$367$	−11.6033	−0.605688	−0.302844	+	0.953040i	$0.597936\pi$
$368$	2.29355	0.119560
$369$	0.662964	0.0345125
$370$	0	0
$371$	−5.17342	−0.268590
$372$	7.05364	0.365714
$373$	21.1965	1.09752	0.548758	−	0.835982i	$-0.315101\pi$
$373$	21.1965	1.09752	0.548758	+	0.835982i	$0.315101\pi$
$374$	59.1868	3.06048
$375$	0	0
$376$	11.7670	0.606837
$377$	−0.453000	−0.0233307
$378$	4.78196	0.245958
$379$	−26.3613	−1.35409	−0.677046	−	0.735941i	$-0.736740\pi$
$379$	−26.3613	−1.35409	−0.677046	+	0.735941i	$0.736740\pi$
$380$	0	0
$381$	3.83151	0.196294
$382$	48.8900	2.50143
$383$	12.5563	0.641595	0.320797	−	0.947148i	$-0.396049\pi$
$383$	12.5563	0.641595	0.320797	+	0.947148i	$0.396049\pi$
$384$	−6.32209	−0.322623
$385$	0	0
$386$	−53.1595	−2.70575
$387$	−15.1287	−0.769035
$388$	−53.0083	−2.69109
$389$	−34.1976	−1.73389	−0.866945	−	0.498405i	$-0.833919\pi$
$389$	−34.1976	−1.73389	−0.866945	+	0.498405i	$0.833919\pi$
$390$	0	0
$391$	−12.0355	−0.608660
$392$	19.3941	0.979552
$393$	5.74761	0.289929
$394$	−32.9095	−1.65796
$395$	0	0
$396$	−52.3473	−2.63055
$397$	33.8726	1.70002	0.850008	−	0.526769i	$-0.176597\pi$
$397$	33.8726	1.70002	0.850008	+	0.526769i	$0.176597\pi$
$398$	21.1304	1.05917
$399$	−0.362853	−0.0181654
$400$	0	0
$401$	−0.985155	−0.0491963	−0.0245982	−	0.999697i	$-0.507831\pi$
$401$	−0.985155	−0.0491963	−0.0245982	+	0.999697i	$0.507831\pi$
$402$	−6.40204	−0.319305
$403$	2.92419	0.145664
$404$	49.8521	2.48024
$405$	0	0
$406$	2.54700	0.126406
$407$	2.81566	0.139567
$408$	−5.13228	−0.254086
$409$	22.7925	1.12701	0.563507	−	0.826111i	$-0.309452\pi$
$409$	22.7925	1.12701	0.563507	+	0.826111i	$0.309452\pi$
$410$	0	0
$411$	−3.61088	−0.178112
$412$	−15.7762	−0.777237
$413$	1.94586	0.0957496
$414$	16.8459	0.827932
$415$	0	0
$416$	−2.05506	−0.100758
$417$	−3.35806	−0.164445
$418$	12.7919	0.625672
$419$	12.5213	0.611705	0.305852	−	0.952079i	$-0.401059\pi$
$419$	12.5213	0.611705	0.305852	+	0.952079i	$0.401059\pi$
$420$	0	0
$421$	20.8030	1.01388	0.506939	−	0.861982i	$-0.330777\pi$
$421$	20.8030	1.01388	0.506939	+	0.861982i	$0.330777\pi$
$422$	−16.6791	−0.811924
$423$	10.2111	0.496481
$424$	−15.8149	−0.768039
$425$	0	0
$426$	−3.77509	−0.182904
$427$	15.5595	0.752979
$428$	69.2880	3.34916
$429$	0.758450	0.0366183
$430$	0	0
$431$	7.48833	0.360700	0.180350	−	0.983602i	$-0.442277\pi$
$431$	7.48833	0.360700	0.180350	+	0.983602i	$0.442277\pi$
$432$	1.72709	0.0830949
$433$	15.4670	0.743296	0.371648	−	0.928374i	$-0.378793\pi$
$433$	15.4670	0.743296	0.371648	+	0.928374i	$0.378793\pi$
$434$	−16.4413	−0.789208
$435$	0	0
$436$	14.9944	0.718102
$437$	−2.60120	−0.124432
$438$	−8.88866	−0.424717
$439$	35.3418	1.68677	0.843387	−	0.537306i	$-0.180558\pi$
$439$	35.3418	1.68677	0.843387	+	0.537306i	$0.180558\pi$
$440$	0	0
$441$	16.8297	0.801417
$442$	−5.09700	−0.242440
$443$	−16.1085	−0.765340	−0.382670	−	0.923885i	$-0.624995\pi$
$443$	−16.1085	−0.765340	−0.382670	+	0.923885i	$0.624995\pi$
$444$	−0.584896	−0.0277579
$445$	0	0
$446$	20.7463	0.982364
$447$	1.77145	0.0837866
$448$	13.5650	0.640885
$449$	−7.08842	−0.334523	−0.167262	−	0.985913i	$-0.553492\pi$
$449$	−7.08842	−0.334523	−0.167262	+	0.985913i	$0.553492\pi$
$450$	0	0
$451$	−1.20308	−0.0566510
$452$	−44.7832	−2.10643
$453$	−4.28723	−0.201432
$454$	−6.66269	−0.312695
$455$	0	0
$456$	−1.10923	−0.0519443
$457$	18.5143	0.866065	0.433032	−	0.901378i	$-0.357444\pi$
$457$	18.5143	0.866065	0.433032	+	0.901378i	$0.357444\pi$
$458$	−54.3934	−2.54163
$459$	−9.06298	−0.423024
$460$	0	0
$461$	21.2153	0.988093	0.494047	−	0.869435i	$-0.335517\pi$
$461$	21.2153	0.988093	0.494047	+	0.869435i	$0.335517\pi$
$462$	−4.26440	−0.198398
$463$	−6.41188	−0.297985	−0.148993	−	0.988838i	$-0.547603\pi$
$463$	−6.41188	−0.297985	−0.148993	+	0.988838i	$0.547603\pi$
$464$	0.919897	0.0427051
$465$	0	0
$466$	28.7072	1.32984
$467$	−28.2463	−1.30708	−0.653540	−	0.756892i	$-0.726717\pi$
$467$	−28.2463	−1.30708	−0.653540	+	0.756892i	$0.726717\pi$
$468$	4.50800	0.208383
$469$	9.42931	0.435405
$470$	0	0
$471$	−5.95520	−0.274401
$472$	5.94841	0.273798
$473$	27.4541	1.26234
$474$	−9.37125	−0.430436
$475$	0	0
$476$	18.1086	0.830005
$477$	−13.7238	−0.628369
$478$	−69.2580	−3.16779
$479$	42.0968	1.92345	0.961725	−	0.274015i	$-0.0883517\pi$
$479$	42.0968	1.92345	0.961725	+	0.274015i	$0.0883517\pi$
$480$	0	0
$481$	−0.242477	−0.0110560
$482$	−42.3400	−1.92853
$483$	0.867155	0.0394569
$484$	57.2309	2.60141
$485$	0	0
$486$	19.1370	0.868070
$487$	12.9359	0.586180	0.293090	−	0.956085i	$-0.405316\pi$
$487$	12.9359	0.586180	0.293090	+	0.956085i	$0.405316\pi$
$488$	47.5648	2.15316
$489$	3.94080	0.178209
$490$	0	0
$491$	10.9885	0.495903	0.247951	−	0.968772i	$-0.420243\pi$
$491$	10.9885	0.495903	0.247951	+	0.968772i	$0.420243\pi$
$492$	0.249916	0.0112671
$493$	−4.82718	−0.217405
$494$	−1.10160	−0.0495634
$495$	0	0
$496$	−5.93809	−0.266628
$497$	5.56018	0.249408
$498$	−7.23975	−0.324421
$499$	15.4837	0.693143	0.346572	−	0.938023i	$-0.387346\pi$
$499$	15.4837	0.693143	0.346572	+	0.938023i	$0.387346\pi$
$500$	0	0
$501$	6.57269	0.293646
$502$	−35.2507	−1.57331
$503$	11.6465	0.519293	0.259646	−	0.965704i	$-0.416394\pi$
$503$	11.6465	0.519293	0.259646	+	0.965704i	$0.416394\pi$
$504$	−10.5804	−0.471289
$505$	0	0
$506$	−30.5704	−1.35902
$507$	4.07244	0.180863
$508$	−41.3269	−1.83358
$509$	−14.2587	−0.632004	−0.316002	−	0.948759i	$-0.602341\pi$
$509$	−14.2587	−0.632004	−0.316002	+	0.948759i	$0.602341\pi$
$510$	0	0
$511$	13.0917	0.579145
$512$	10.3188	0.456029
$513$	−1.95876	−0.0864813
$514$	−50.2160	−2.21493
$515$	0	0
$516$	−5.70303	−0.251062
$517$	−18.5301	−0.814955
$518$	1.36333	0.0599014
$519$	1.51436	0.0664732
$520$	0	0
$521$	−21.9107	−0.959923	−0.479962	−	0.877290i	$-0.659349\pi$
$521$	−21.9107	−0.959923	−0.479962	+	0.877290i	$0.659349\pi$
$522$	6.75655	0.295726
$523$	−21.1579	−0.925170	−0.462585	−	0.886575i	$-0.653078\pi$
$523$	−21.1579	−0.925170	−0.462585	+	0.886575i	$0.653078\pi$
$524$	−61.9941	−2.70822
$525$	0	0
$526$	38.2932	1.66966
$527$	31.1603	1.35736
$528$	−1.54017	−0.0670272
$529$	−16.7836	−0.729722
$530$	0	0
$531$	5.16188	0.224007
$532$	3.91376	0.169683
$533$	0.103606	0.00448768
$534$	−7.44472	−0.322165
$535$	0	0
$536$	28.8250	1.24505
$537$	−3.67806	−0.158720
$538$	22.6406	0.976107
$539$	−30.5410	−1.31549
$540$	0	0
$541$	6.75379	0.290368	0.145184	−	0.989405i	$-0.453623\pi$
$541$	6.75379	0.290368	0.145184	+	0.989405i	$0.453623\pi$
$542$	2.38190	0.102311
$543$	−3.04131	−0.130515
$544$	−21.8988	−0.938903
$545$	0	0
$546$	0.367239	0.0157164
$547$	−37.8019	−1.61629	−0.808147	−	0.588981i	$-0.799529\pi$
$547$	−37.8019	−1.61629	−0.808147	+	0.588981i	$0.799529\pi$
$548$	38.9472	1.66374
$549$	41.2756	1.76160
$550$	0	0
$551$	−1.04329	−0.0444455
$552$	2.65085	0.112828
$553$	13.8025	0.586943
$554$	−11.2491	−0.477929
$555$	0	0
$556$	36.2203	1.53608
$557$	−10.1691	−0.430878	−0.215439	−	0.976517i	$-0.569118\pi$
$557$	−10.1691	−0.430878	−0.215439	+	0.976517i	$0.569118\pi$
$558$	−43.6147	−1.84636
$559$	−2.36427	−0.0999981
$560$	0	0
$561$	8.08208	0.341226
$562$	−16.5379	−0.697608
$563$	41.8569	1.76406	0.882029	−	0.471196i	$-0.156178\pi$
$563$	41.8569	1.76406	0.882029	+	0.471196i	$0.156178\pi$
$564$	3.84925	0.162083
$565$	0	0
$566$	48.4068	2.03469
$567$	−8.84932	−0.371637
$568$	16.9972	0.713187
$569$	−25.4072	−1.06512	−0.532562	−	0.846391i	$-0.678771\pi$
$569$	−25.4072	−1.06512	−0.532562	+	0.846391i	$0.678771\pi$
$570$	0	0
$571$	−2.07657	−0.0869018	−0.0434509	−	0.999056i	$-0.513835\pi$
$571$	−2.07657	−0.0869018	−0.0434509	+	0.999056i	$0.513835\pi$
$572$	−8.18069	−0.342052
$573$	6.67602	0.278895
$574$	−0.582528	−0.0243143
$575$	0	0
$576$	35.9845	1.49935
$577$	4.05652	0.168875	0.0844375	−	0.996429i	$-0.473091\pi$
$577$	4.05652	0.168875	0.0844375	+	0.996429i	$0.473091\pi$
$578$	−14.6886	−0.610967
$579$	−7.25903	−0.301675
$580$	0	0
$581$	10.6631	0.442381
$582$	−11.4552	−0.474834
$583$	24.9046	1.03144
$584$	40.0209	1.65608
$585$	0	0
$586$	29.1083	1.20245
$587$	20.3218	0.838770	0.419385	−	0.907809i	$-0.362246\pi$
$587$	20.3218	0.838770	0.419385	+	0.907809i	$0.362246\pi$
$588$	6.34427	0.261633
$589$	6.73459	0.277494
$590$	0	0
$591$	−4.49386	−0.184853
$592$	0.492393	0.0202372
$593$	23.5594	0.967469	0.483734	−	0.875215i	$-0.339280\pi$
$593$	23.5594	0.967469	0.483734	+	0.875215i	$0.339280\pi$
$594$	−23.0202	−0.944528
$595$	0	0
$596$	−19.1070	−0.782652
$597$	2.88540	0.118092
$598$	2.63263	0.107656
$599$	−29.8661	−1.22029	−0.610147	−	0.792288i	$-0.708890\pi$
$599$	−29.8661	−1.22029	−0.610147	+	0.792288i	$0.708890\pi$
$600$	0	0
$601$	−44.3886	−1.81065	−0.905325	−	0.424720i	$-0.860373\pi$
$601$	−44.3886	−1.81065	−0.905325	+	0.424720i	$0.860373\pi$
$602$	13.2932	0.541789
$603$	25.0136	1.01863
$604$	46.2423	1.88157
$605$	0	0
$606$	10.7732	0.437631
$607$	−28.0273	−1.13759	−0.568796	−	0.822479i	$-0.692591\pi$
$607$	−28.0273	−1.13759	−0.568796	+	0.822479i	$0.692591\pi$
$608$	−4.73293	−0.191946
$609$	0.347798	0.0140935
$610$	0	0
$611$	1.59576	0.0645577
$612$	48.0375	1.94180
$613$	−43.2256	−1.74587	−0.872933	−	0.487841i	$-0.837785\pi$
$613$	−43.2256	−1.74587	−0.872933	+	0.487841i	$0.837785\pi$
$614$	42.3701	1.70992
$615$	0	0
$616$	19.2003	0.773603
$617$	−11.6093	−0.467372	−0.233686	−	0.972312i	$-0.575079\pi$
$617$	−11.6093	−0.467372	−0.233686	+	0.972312i	$0.575079\pi$
$618$	−3.40928	−0.137141
$619$	7.25400	0.291563	0.145781	−	0.989317i	$-0.453430\pi$
$619$	7.25400	0.291563	0.145781	+	0.989317i	$0.453430\pi$
$620$	0	0
$621$	4.68109	0.187846
$622$	41.0820	1.64724
$623$	10.9650	0.439305
$624$	0.132635	0.00530965
$625$	0	0
$626$	12.2917	0.491275
$627$	1.74676	0.0697589
$628$	64.2331	2.56318
$629$	−2.58385	−0.103025
$630$	0	0
$631$	−41.0705	−1.63499	−0.817496	−	0.575935i	$-0.804638\pi$
$631$	−41.0705	−1.63499	−0.817496	+	0.575935i	$0.804638\pi$
$632$	42.1937	1.67838
$633$	−2.27756	−0.0905249
$634$	−45.7138	−1.81553
$635$	0	0
$636$	−5.17342	−0.205139
$637$	2.63011	0.104209
$638$	−12.2611	−0.485423
$639$	14.7498	0.583492
$640$	0	0
$641$	35.6090	1.40647	0.703235	−	0.710958i	$-0.251738\pi$
$641$	35.6090	1.40647	0.703235	+	0.710958i	$0.251738\pi$
$642$	14.9733	0.590950
$643$	−14.3315	−0.565179	−0.282590	−	0.959241i	$-0.591193\pi$
$643$	−14.3315	−0.565179	−0.282590	+	0.959241i	$0.591193\pi$
$644$	−9.35319	−0.368567
$645$	0	0
$646$	−11.7387	−0.461854
$647$	36.2899	1.42670	0.713352	−	0.700806i	$-0.247176\pi$
$647$	36.2899	1.42670	0.713352	+	0.700806i	$0.247176\pi$
$648$	−27.0520	−1.06270
$649$	−9.36729	−0.367698
$650$	0	0
$651$	−2.24509	−0.0879922
$652$	−42.5057	−1.66465
$653$	32.6269	1.27679	0.638395	−	0.769709i	$-0.279599\pi$
$653$	32.6269	1.27679	0.638395	+	0.769709i	$0.279599\pi$
$654$	3.24033	0.126707
$655$	0	0
$656$	−0.210391	−0.00821439
$657$	34.7291	1.35491
$658$	−8.97222	−0.349774
$659$	2.94107	0.114568	0.0572839	−	0.998358i	$-0.481756\pi$
$659$	2.94107	0.114568	0.0572839	+	0.998358i	$0.481756\pi$
$660$	0	0
$661$	34.1618	1.32874	0.664370	−	0.747404i	$-0.268700\pi$
$661$	34.1618	1.32874	0.664370	+	0.747404i	$0.268700\pi$
$662$	−10.9060	−0.423874
$663$	−0.696006	−0.0270306
$664$	32.5967	1.26500
$665$	0	0
$666$	3.61658	0.140140
$667$	2.49327	0.0965398
$668$	−70.8935	−2.74295
$669$	2.83295	0.109528
$670$	0	0
$671$	−74.9030	−2.89160
$672$	1.57781	0.0608652
$673$	23.9800	0.924360	0.462180	−	0.886786i	$-0.347067\pi$
$673$	23.9800	0.924360	0.462180	+	0.886786i	$0.347067\pi$
$674$	18.8076	0.724441
$675$	0	0
$676$	−43.9256	−1.68945
$677$	9.44718	0.363085	0.181542	−	0.983383i	$-0.441891\pi$
$677$	9.44718	0.363085	0.181542	+	0.983383i	$0.441891\pi$
$678$	−9.67778	−0.371673
$679$	16.8719	0.647485
$680$	0	0
$681$	−0.909803	−0.0348637
$682$	79.1477	3.03072
$683$	30.0862	1.15122	0.575608	−	0.817726i	$-0.304765\pi$
$683$	30.0862	1.15122	0.575608	+	0.817726i	$0.304765\pi$
$684$	10.3822	0.396974
$685$	0	0
$686$	−32.6168	−1.24532
$687$	−7.42753	−0.283378
$688$	4.80108	0.183039
$689$	−2.14471	−0.0817071
$690$	0	0
$691$	−42.0873	−1.60108	−0.800538	−	0.599282i	$-0.795453\pi$
$691$	−42.0873	−1.60108	−0.800538	+	0.599282i	$0.795453\pi$
$692$	−16.3340	−0.620927
$693$	16.6616	0.632921
$694$	−17.0610	−0.647627
$695$	0	0
$696$	1.06320	0.0403006
$697$	1.10403	0.0418182
$698$	−8.39600	−0.317793
$699$	3.92003	0.148269
$700$	0	0
$701$	−47.4785	−1.79324	−0.896620	−	0.442801i	$-0.853985\pi$
$701$	−47.4785	−1.79324	−0.896620	+	0.442801i	$0.853985\pi$
$702$	1.98243	0.0748221
$703$	−0.558440	−0.0210620
$704$	−65.3012	−2.46113
$705$	0	0
$706$	79.6242	2.99670
$707$	−15.8674	−0.596754
$708$	1.94586	0.0731299
$709$	−25.0996	−0.942634	−0.471317	−	0.881964i	$-0.656221\pi$
$709$	−25.0996	−0.942634	−0.471317	+	0.881964i	$0.656221\pi$
$710$	0	0
$711$	36.6146	1.37316
$712$	33.5196	1.25620
$713$	−16.0945	−0.602743
$714$	3.91331	0.146452
$715$	0	0
$716$	39.6718	1.48260
$717$	−9.45732	−0.353190
$718$	5.38397	0.200928
$719$	−9.06763	−0.338165	−0.169083	−	0.985602i	$-0.554080\pi$
$719$	−9.06763	−0.338165	−0.169083	+	0.985602i	$0.554080\pi$
$720$	0	0
$721$	5.02138	0.187006
$722$	41.7500	1.55377
$723$	−5.78161	−0.215020
$724$	32.8038	1.21914
$725$	0	0
$726$	12.3678	0.459011
$727$	−28.5399	−1.05849	−0.529243	−	0.848470i	$-0.677524\pi$
$727$	−28.5399	−1.05849	−0.529243	+	0.848470i	$0.677524\pi$
$728$	−1.65348	−0.0612820
$729$	−21.6823	−0.803048
$730$	0	0
$731$	−25.1938	−0.931826
$732$	15.5595	0.575097
$733$	29.3871	1.08544	0.542718	−	0.839915i	$-0.317395\pi$
$733$	29.3871	1.08544	0.542718	+	0.839915i	$0.317395\pi$
$734$	27.0461	0.998290
$735$	0	0
$736$	11.3109	0.416924
$737$	−45.3923	−1.67205
$738$	−1.54530	−0.0568833
$739$	11.0473	0.406381	0.203190	−	0.979139i	$-0.434869\pi$
$739$	11.0473	0.406381	0.203190	+	0.979139i	$0.434869\pi$
$740$	0	0
$741$	−0.150426	−0.00552604
$742$	12.0587	0.442689
$743$	16.7348	0.613941	0.306971	−	0.951719i	$-0.400685\pi$
$743$	16.7348	0.613941	0.306971	+	0.951719i	$0.400685\pi$
$744$	−6.86315	−0.251615
$745$	0	0
$746$	−49.4070	−1.80892
$747$	28.2866	1.03495
$748$	−87.1738	−3.18739
$749$	−22.0536	−0.805821
$750$	0	0
$751$	10.5839	0.386212	0.193106	−	0.981178i	$-0.438144\pi$
$751$	10.5839	0.386212	0.193106	+	0.981178i	$0.438144\pi$
$752$	−3.24048	−0.118168
$753$	−4.81355	−0.175415
$754$	1.05590	0.0384535
$755$	0	0
$756$	−7.04316	−0.256157
$757$	−9.19821	−0.334315	−0.167157	−	0.985930i	$-0.553459\pi$
$757$	−9.19821	−0.334315	−0.167157	+	0.985930i	$0.553459\pi$
$758$	61.4456	2.23180
$759$	−4.17445	−0.151523
$760$	0	0
$761$	−18.1554	−0.658134	−0.329067	−	0.944307i	$-0.606734\pi$
$761$	−18.1554	−0.658134	−0.329067	+	0.944307i	$0.606734\pi$
$762$	−8.93085	−0.323530
$763$	−4.77256	−0.172778
$764$	−72.0080	−2.60516
$765$	0	0
$766$	−29.2673	−1.05747
$767$	0.806685	0.0291277
$768$	6.83365	0.246588
$769$	13.9125	0.501697	0.250848	−	0.968026i	$-0.419290\pi$
$769$	13.9125	0.501697	0.250848	+	0.968026i	$0.419290\pi$
$770$	0	0
$771$	−6.85709	−0.246952
$772$	78.2964	2.81795
$773$	−7.95625	−0.286167	−0.143083	−	0.989711i	$-0.545702\pi$
$773$	−7.95625	−0.286167	−0.143083	+	0.989711i	$0.545702\pi$
$774$	35.2635	1.26752
$775$	0	0
$776$	51.5767	1.85150
$777$	0.186166	0.00667866
$778$	79.7112	2.85778
$779$	0.238612	0.00854915
$780$	0	0
$781$	−26.7665	−0.957779
$782$	28.0535	1.00319
$783$	1.87749	0.0670959
$784$	−5.34090	−0.190746
$785$	0	0
$786$	−13.3971	−0.477858
$787$	−10.4325	−0.371877	−0.185939	−	0.982561i	$-0.559533\pi$
$787$	−10.4325	−0.371877	−0.185939	+	0.982561i	$0.559533\pi$
$788$	48.4711	1.72671
$789$	5.22901	0.186158
$790$	0	0
$791$	14.2540	0.506814
$792$	50.9336	1.80985
$793$	6.45044	0.229062
$794$	−78.9536	−2.80196
$795$	0	0
$796$	−31.1221	−1.10309
$797$	43.1743	1.52931	0.764656	−	0.644438i	$-0.222909\pi$
$797$	43.1743	1.52931	0.764656	+	0.644438i	$0.222909\pi$
$798$	0.845774	0.0299401
$799$	17.0045	0.601577
$800$	0	0
$801$	29.0875	1.02776
$802$	2.29630	0.0810850
$803$	−63.0231	−2.22404
$804$	9.42931	0.332546
$805$	0	0
$806$	−6.81598	−0.240083
$807$	3.09162	0.108830
$808$	−48.5058	−1.70643
$809$	−9.00706	−0.316671	−0.158336	−	0.987385i	$-0.550613\pi$
$809$	−9.00706	−0.316671	−0.158336	+	0.987385i	$0.550613\pi$
$810$	0	0
$811$	−22.6431	−0.795108	−0.397554	−	0.917579i	$-0.630141\pi$
$811$	−22.6431	−0.795108	−0.397554	+	0.917579i	$0.630141\pi$
$812$	−3.75137	−0.131647
$813$	0.325254	0.0114071
$814$	−6.56302	−0.230034
$815$	0	0
$816$	1.41336	0.0494777
$817$	−5.44507	−0.190499
$818$	−53.1269	−1.85754
$819$	−1.43485	−0.0501376
$820$	0	0
$821$	22.7306	0.793302	0.396651	−	0.917969i	$-0.370172\pi$
$821$	22.7306	0.793302	0.396651	+	0.917969i	$0.370172\pi$
$822$	8.41659	0.293562
$823$	12.2503	0.427018	0.213509	−	0.976941i	$-0.431511\pi$
$823$	12.2503	0.427018	0.213509	+	0.976941i	$0.431511\pi$
$824$	15.3501	0.534747
$825$	0	0
$826$	−4.53560	−0.157814
$827$	−12.6356	−0.439382	−0.219691	−	0.975569i	$-0.570505\pi$
$827$	−12.6356	−0.439382	−0.219691	+	0.975569i	$0.570505\pi$
$828$	−24.8117	−0.862265
$829$	−6.63044	−0.230285	−0.115142	−	0.993349i	$-0.536732\pi$
$829$	−6.63044	−0.230285	−0.115142	+	0.993349i	$0.536732\pi$
$830$	0	0
$831$	−1.53609	−0.0532863
$832$	5.62356	0.194962
$833$	28.0265	0.971062
$834$	7.82730	0.271037
$835$	0	0
$836$	−18.8407	−0.651618
$837$	−12.1195	−0.418911
$838$	−29.1858	−1.00821
$839$	−19.4935	−0.672989	−0.336495	−	0.941685i	$-0.609241\pi$
$839$	−19.4935	−0.672989	−0.336495	+	0.941685i	$0.609241\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−48.4897	−1.67107
$843$	−2.25828	−0.0777793
$844$	24.5659	0.845593
$845$	0	0
$846$	−23.8011	−0.818297
$847$	−18.2160	−0.625908
$848$	4.35522	0.149559
$849$	6.61004	0.226856
$850$	0	0
$851$	1.33457	0.0457486
$852$	5.56018	0.190489
$853$	−40.5640	−1.38888	−0.694442	−	0.719549i	$-0.744349\pi$
$853$	−40.5640	−1.38888	−0.694442	+	0.719549i	$0.744349\pi$
$854$	−36.2677	−1.24106
$855$	0	0
$856$	−67.4169	−2.30426
$857$	18.3430	0.626584	0.313292	−	0.949657i	$-0.398568\pi$
$857$	18.3430	0.626584	0.313292	+	0.949657i	$0.398568\pi$
$858$	−1.76787	−0.0603541
$859$	7.13688	0.243507	0.121754	−	0.992560i	$-0.461148\pi$
$859$	7.13688	0.243507	0.121754	+	0.992560i	$0.461148\pi$
$860$	0	0
$861$	−0.0795454	−0.00271090
$862$	−17.4545	−0.594504
$863$	−21.8379	−0.743372	−0.371686	−	0.928359i	$-0.621220\pi$
$863$	−21.8379	−0.743372	−0.371686	+	0.928359i	$0.621220\pi$
$864$	8.51733	0.289766
$865$	0	0
$866$	−36.0520	−1.22510
$867$	−2.00576	−0.0681193
$868$	24.2157	0.821936
$869$	−66.4447	−2.25398
$870$	0	0
$871$	3.90906	0.132453
$872$	−14.5895	−0.494062
$873$	44.7570	1.51480
$874$	6.06313	0.205088
$875$	0	0
$876$	13.0917	0.442329
$877$	4.35988	0.147223	0.0736113	−	0.997287i	$-0.476548\pi$
$877$	4.35988	0.147223	0.0736113	+	0.997287i	$0.476548\pi$
$878$	−82.3782	−2.78013
$879$	3.97479	0.134066
$880$	0	0
$881$	−8.41952	−0.283661	−0.141830	−	0.989891i	$-0.545299\pi$
$881$	−8.41952	−0.283661	−0.141830	+	0.989891i	$0.545299\pi$
$882$	−39.2284	−1.32089
$883$	7.23456	0.243462	0.121731	−	0.992563i	$-0.461155\pi$
$883$	7.23456	0.243462	0.121731	+	0.992563i	$0.461155\pi$
$884$	7.50717	0.252493
$885$	0	0
$886$	37.5474	1.26143
$887$	55.0112	1.84710	0.923548	−	0.383484i	$-0.125276\pi$
$887$	55.0112	1.84710	0.923548	+	0.383484i	$0.125276\pi$
$888$	0.569101	0.0190978
$889$	13.1539	0.441167
$890$	0	0
$891$	42.6002	1.42716
$892$	−30.5563	−1.02310
$893$	3.67515	0.122984
$894$	−4.12907	−0.138097
$895$	0	0
$896$	−21.7043	−0.725089
$897$	0.359492	0.0120031
$898$	16.5224	0.551359
$899$	−6.45517	−0.215292
$900$	0	0
$901$	−22.8542	−0.761383
$902$	2.80427	0.0933718
$903$	1.81521	0.0604064
$904$	43.5738	1.44924
$905$	0	0
$906$	9.99309	0.331998
$907$	−53.4584	−1.77506	−0.887528	−	0.460754i	$-0.847579\pi$
$907$	−53.4584	−1.77506	−0.887528	+	0.460754i	$0.847579\pi$
$908$	9.81320	0.325662
$909$	−42.0922	−1.39611
$910$	0	0
$911$	−37.4019	−1.23918	−0.619590	−	0.784926i	$-0.712701\pi$
$911$	−37.4019	−1.23918	−0.619590	+	0.784926i	$0.712701\pi$
$912$	0.305467	0.0101150
$913$	−51.3318	−1.69883
$914$	−43.1550	−1.42744
$915$	0	0
$916$	80.1138	2.64703
$917$	19.7320	0.651609
$918$	21.1249	0.697225
$919$	17.9780	0.593039	0.296520	−	0.955027i	$-0.404174\pi$
$919$	17.9780	0.593039	0.296520	+	0.955027i	$0.404174\pi$
$920$	0	0
$921$	5.78572	0.190646
$922$	−49.4506	−1.62857
$923$	2.30505	0.0758717
$924$	6.28087	0.206625
$925$	0	0
$926$	14.9454	0.491137
$927$	13.3205	0.437502
$928$	4.53656	0.148920
$929$	3.80429	0.124815	0.0624074	−	0.998051i	$-0.480122\pi$
$929$	3.80429	0.124815	0.0624074	+	0.998051i	$0.480122\pi$
$930$	0	0
$931$	6.05730	0.198520
$932$	−42.2817	−1.38498
$933$	5.60983	0.183658
$934$	65.8391	2.15432
$935$	0	0
$936$	−4.38626	−0.143370
$937$	−15.9334	−0.520523	−0.260261	−	0.965538i	$-0.583809\pi$
$937$	−15.9334	−0.520523	−0.260261	+	0.965538i	$0.583809\pi$
$938$	−21.9788	−0.717632
$939$	1.67846	0.0547744
$940$	0	0
$941$	40.9708	1.33561	0.667805	−	0.744337i	$-0.267234\pi$
$941$	40.9708	1.33561	0.667805	+	0.744337i	$0.267234\pi$
$942$	13.8810	0.452266
$943$	−0.570240	−0.0185696
$944$	−1.63812	−0.0533162
$945$	0	0
$946$	−63.9927	−2.08058
$947$	−49.3534	−1.60377	−0.801885	−	0.597478i	$-0.796170\pi$
$947$	−49.3534	−1.60377	−0.801885	+	0.597478i	$0.796170\pi$
$948$	13.8025	0.448285
$949$	5.42737	0.176180
$950$	0	0
$951$	−6.24231	−0.202421
$952$	−17.6195	−0.571052
$953$	25.0523	0.811523	0.405762	−	0.913979i	$-0.367006\pi$
$953$	25.0523	0.811523	0.405762	+	0.913979i	$0.367006\pi$
$954$	31.9887	1.03567
$955$	0	0
$956$	102.007	3.29915
$957$	−1.67428	−0.0541219
$958$	−98.1233	−3.17022
$959$	−12.3965	−0.400302
$960$	0	0
$961$	10.6692	0.344167
$962$	0.565189	0.0182224
$963$	−58.5027	−1.88522
$964$	62.3608	2.00851
$965$	0	0
$966$	−2.02125	−0.0650326
$967$	28.2473	0.908371	0.454185	−	0.890907i	$-0.349930\pi$
$967$	28.2473	0.908371	0.454185	+	0.890907i	$0.349930\pi$
$968$	−55.6854	−1.78980
$969$	−1.60295	−0.0514941
$970$	0	0
$971$	−18.7212	−0.600791	−0.300396	−	0.953815i	$-0.597119\pi$
$971$	−18.7212	−0.600791	−0.300396	+	0.953815i	$0.597119\pi$
$972$	−28.1860	−0.904068
$973$	−11.5285	−0.369587
$974$	−30.1522	−0.966138
$975$	0	0
$976$	−13.0988	−0.419281
$977$	23.5777	0.754317	0.377158	−	0.926149i	$-0.376901\pi$
$977$	23.5777	0.754317	0.377158	+	0.926149i	$0.376901\pi$
$978$	−9.18561	−0.293723
$979$	−52.7852	−1.68702
$980$	0	0
$981$	−12.6604	−0.404215
$982$	−25.6130	−0.817344
$983$	48.0017	1.53102	0.765509	−	0.643426i	$-0.222487\pi$
$983$	48.0017	1.53102	0.765509	+	0.643426i	$0.222487\pi$
$984$	−0.243167	−0.00775187
$985$	0	0
$986$	11.2517	0.358326
$987$	−1.22517	−0.0389977
$988$	1.62251	0.0516188
$989$	13.0128	0.413781
$990$	0	0
$991$	−23.4273	−0.744192	−0.372096	−	0.928194i	$-0.621361\pi$
$991$	−23.4273	−0.744192	−0.372096	+	0.928194i	$0.621361\pi$
$992$	−29.2842	−0.929776
$993$	−1.48924	−0.0472595
$994$	−12.9602	−0.411073
$995$	0	0
$996$	10.6631	0.337874
$997$	−40.8481	−1.29367	−0.646836	−	0.762629i	$-0.723908\pi$
$997$	−40.8481	−1.29367	−0.646836	+	0.762629i	$0.723908\pi$
$998$	−36.0908	−1.14243
$999$	1.00496	0.0317956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.a.h.1.1	✓	5
3.2	odd	2		6525.2.a.bq.1.5		5
5.2	odd	4		725.2.b.f.349.1		10
5.3	odd	4		725.2.b.f.349.10		10
5.4	even	2		725.2.a.k.1.5	yes	5
15.14	odd	2		6525.2.a.bm.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.a.h.1.1	✓	5	1.1	even	1	trivial
725.2.a.k.1.5	yes	5	5.4	even	2
725.2.b.f.349.1		10	5.2	odd	4
725.2.b.f.349.10		10	5.3	odd	4
6525.2.a.bm.1.1		5	15.14	odd	2
6525.2.a.bq.1.5		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33090 q^{2} -0.318289 q^{3} +3.43308 q^{4} +0.741899 q^{6} -1.09271 q^{7} -3.34037 q^{8} -2.89869 q^{9} +O(q^{10})\)	\(q-2.33090 q^{2} -0.318289 q^{3} +3.43308 q^{4} +0.741899 q^{6} -1.09271 q^{7} -3.34037 q^{8} -2.89869 q^{9} +5.26027 q^{11} -1.09271 q^{12} -0.453000 q^{13} +2.54700 q^{14} +0.919897 q^{16} -4.82718 q^{17} +6.75655 q^{18} -1.04329 q^{19} +0.347798 q^{21} -12.2611 q^{22} +2.49327 q^{23} +1.06320 q^{24} +1.05590 q^{26} +1.87749 q^{27} -3.75137 q^{28} +1.00000 q^{29} -6.45517 q^{31} +4.53656 q^{32} -1.67428 q^{33} +11.2517 q^{34} -9.95145 q^{36} +0.535270 q^{37} +2.43180 q^{38} +0.144185 q^{39} -0.228712 q^{41} -0.810682 q^{42} +5.21915 q^{43} +18.0589 q^{44} -5.81156 q^{46} -3.52266 q^{47} -0.292793 q^{48} -5.80598 q^{49} +1.53644 q^{51} -1.55519 q^{52} +4.73447 q^{53} -4.37623 q^{54} +3.65006 q^{56} +0.332067 q^{57} -2.33090 q^{58} -1.78076 q^{59} -14.2394 q^{61} +15.0463 q^{62} +3.16744 q^{63} -12.4140 q^{64} +3.90259 q^{66} -8.62927 q^{67} -16.5721 q^{68} -0.793580 q^{69} -5.08842 q^{71} +9.68271 q^{72} -11.9810 q^{73} -1.24766 q^{74} -3.58169 q^{76} -5.74796 q^{77} -0.336080 q^{78} -12.6314 q^{79} +8.09849 q^{81} +0.533103 q^{82} -9.75840 q^{83} +1.19402 q^{84} -12.1653 q^{86} -0.318289 q^{87} -17.5712 q^{88} -10.0347 q^{89} +0.494998 q^{91} +8.55961 q^{92} +2.05461 q^{93} +8.21096 q^{94} -1.44394 q^{96} -15.4404 q^{97} +13.5331 q^{98} -15.2479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26} - 27 q^{27} - 10 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} + 7 q^{33} + 3 q^{34} - 13 q^{36} - 14 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{41} - 24 q^{42} - 28 q^{43} + 7 q^{44} - 20 q^{46} - 15 q^{47} + 26 q^{48} - 3 q^{49} + 5 q^{51} - 6 q^{52} + 8 q^{53} + 10 q^{54} - 16 q^{56} + 6 q^{57} - 2 q^{58} - 11 q^{59} - 5 q^{61} + 6 q^{62} + 5 q^{63} - 5 q^{64} - 27 q^{66} - 23 q^{67} - q^{68} - 26 q^{69} - 5 q^{71} - 3 q^{72} - 16 q^{73} + 8 q^{74} + 16 q^{76} + 30 q^{77} + 33 q^{78} - 10 q^{79} + 49 q^{81} + 19 q^{82} - 9 q^{83} + 32 q^{84} - 13 q^{86} - 6 q^{87} - 35 q^{88} - 18 q^{89} + q^{91} + 27 q^{92} - 7 q^{93} - 13 q^{94} - 38 q^{96} - 23 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more