LMFDB - Embedded newform 1450.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.30278 q^{3} +1.00000 q^{4} -2.30278 q^{6} -0.697224 q^{7} +1.00000 q^{8} +2.30278 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.30278 q^{3} +1.00000 q^{4} -2.30278 q^{6} -0.697224 q^{7} +1.00000 q^{8} +2.30278 q^{9} +2.60555 q^{11} -2.30278 q^{12} -6.30278 q^{13} -0.697224 q^{14} +1.00000 q^{16} +3.90833 q^{17} +2.30278 q^{18} -0.605551 q^{19} +1.60555 q^{21} +2.60555 q^{22} -1.69722 q^{23} -2.30278 q^{24} -6.30278 q^{26} +1.60555 q^{27} -0.697224 q^{28} +1.00000 q^{29} -7.90833 q^{31} +1.00000 q^{32} -6.00000 q^{33} +3.90833 q^{34} +2.30278 q^{36} -9.81665 q^{37} -0.605551 q^{38} +14.5139 q^{39} -8.60555 q^{41} +1.60555 q^{42} -3.30278 q^{43} +2.60555 q^{44} -1.69722 q^{46} -2.30278 q^{48} -6.51388 q^{49} -9.00000 q^{51} -6.30278 q^{52} +3.90833 q^{53} +1.60555 q^{54} -0.697224 q^{56} +1.39445 q^{57} +1.00000 q^{58} -0.908327 q^{59} -3.09167 q^{61} -7.90833 q^{62} -1.60555 q^{63} +1.00000 q^{64} -6.00000 q^{66} +9.21110 q^{67} +3.90833 q^{68} +3.90833 q^{69} +2.30278 q^{72} -2.51388 q^{73} -9.81665 q^{74} -0.605551 q^{76} -1.81665 q^{77} +14.5139 q^{78} -4.90833 q^{79} -10.6056 q^{81} -8.60555 q^{82} +8.60555 q^{83} +1.60555 q^{84} -3.30278 q^{86} -2.30278 q^{87} +2.60555 q^{88} -14.6056 q^{89} +4.39445 q^{91} -1.69722 q^{92} +18.2111 q^{93} -2.30278 q^{96} -1.09167 q^{97} -6.51388 q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{6} - 5 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^6 - 5 * q^7 + 2 * q^8 + q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{6} - 5 q^{7} + 2 q^{8} + q^{9} - 2 q^{11} - q^{12} - 9 q^{13} - 5 q^{14} + 2 q^{16} - 3 q^{17} + q^{18} + 6 q^{19} - 4 q^{21} - 2 q^{22} - 7 q^{23} - q^{24} - 9 q^{26} - 4 q^{27} - 5 q^{28} + 2 q^{29} - 5 q^{31} + 2 q^{32} - 12 q^{33} - 3 q^{34} + q^{36} + 2 q^{37} + 6 q^{38} + 11 q^{39} - 10 q^{41} - 4 q^{42} - 3 q^{43} - 2 q^{44} - 7 q^{46} - q^{48} + 5 q^{49} - 18 q^{51} - 9 q^{52} - 3 q^{53} - 4 q^{54} - 5 q^{56} + 10 q^{57} + 2 q^{58} + 9 q^{59} - 17 q^{61} - 5 q^{62} + 4 q^{63} + 2 q^{64} - 12 q^{66} + 4 q^{67} - 3 q^{68} - 3 q^{69} + q^{72} + 13 q^{73} + 2 q^{74} + 6 q^{76} + 18 q^{77} + 11 q^{78} + q^{79} - 14 q^{81} - 10 q^{82} + 10 q^{83} - 4 q^{84} - 3 q^{86} - q^{87} - 2 q^{88} - 22 q^{89} + 16 q^{91} - 7 q^{92} + 22 q^{93} - q^{96} - 13 q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^6 - 5 * q^7 + 2 * q^8 + q^9 - 2 * q^11 - q^12 - 9 * q^13 - 5 * q^14 + 2 * q^16 - 3 * q^17 + q^18 + 6 * q^19 - 4 * q^21 - 2 * q^22 - 7 * q^23 - q^24 - 9 * q^26 - 4 * q^27 - 5 * q^28 + 2 * q^29 - 5 * q^31 + 2 * q^32 - 12 * q^33 - 3 * q^34 + q^36 + 2 * q^37 + 6 * q^38 + 11 * q^39 - 10 * q^41 - 4 * q^42 - 3 * q^43 - 2 * q^44 - 7 * q^46 - q^48 + 5 * q^49 - 18 * q^51 - 9 * q^52 - 3 * q^53 - 4 * q^54 - 5 * q^56 + 10 * q^57 + 2 * q^58 + 9 * q^59 - 17 * q^61 - 5 * q^62 + 4 * q^63 + 2 * q^64 - 12 * q^66 + 4 * q^67 - 3 * q^68 - 3 * q^69 + q^72 + 13 * q^73 + 2 * q^74 + 6 * q^76 + 18 * q^77 + 11 * q^78 + q^79 - 14 * q^81 - 10 * q^82 + 10 * q^83 - 4 * q^84 - 3 * q^86 - q^87 - 2 * q^88 - 22 * q^89 + 16 * q^91 - 7 * q^92 + 22 * q^93 - q^96 - 13 * q^97 + 5 * q^98 + 12 * 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
$3$	−2.30278	−1.32951	−0.664754	−	0.747062i	$-0.731464\pi$
$3$	−2.30278	−1.32951	−0.664754	+	0.747062i	$0.731464\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.30278	−0.940104
$7$	−0.697224	−0.263526	−0.131763	−	0.991281i	$-0.542064\pi$
$7$	−0.697224	−0.263526	−0.131763	+	0.991281i	$0.542064\pi$
$8$	1.00000	0.353553
$9$	2.30278	0.767592
$10$	0	0
$11$	2.60555	0.785603	0.392802	−	0.919623i	$-0.371506\pi$
$11$	2.60555	0.785603	0.392802	+	0.919623i	$0.371506\pi$
$12$	−2.30278	−0.664754
$13$	−6.30278	−1.74808	−0.874038	−	0.485858i	$-0.838507\pi$
$13$	−6.30278	−1.74808	−0.874038	+	0.485858i	$0.838507\pi$
$14$	−0.697224	−0.186341
$15$	0	0
$16$	1.00000	0.250000
$17$	3.90833	0.947909	0.473954	−	0.880549i	$-0.342826\pi$
$17$	3.90833	0.947909	0.473954	+	0.880549i	$0.342826\pi$
$18$	2.30278	0.542769
$19$	−0.605551	−0.138923	−0.0694615	−	0.997585i	$-0.522128\pi$
$19$	−0.605551	−0.138923	−0.0694615	+	0.997585i	$0.522128\pi$
$20$	0	0
$21$	1.60555	0.350360
$22$	2.60555	0.555505
$23$	−1.69722	−0.353896	−0.176948	−	0.984220i	$-0.556622\pi$
$23$	−1.69722	−0.353896	−0.176948	+	0.984220i	$0.556622\pi$
$24$	−2.30278	−0.470052
$25$	0	0
$26$	−6.30278	−1.23608
$27$	1.60555	0.308988
$28$	−0.697224	−0.131763
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−7.90833	−1.42038	−0.710189	−	0.704011i	$-0.751390\pi$
$31$	−7.90833	−1.42038	−0.710189	+	0.704011i	$0.751390\pi$
$32$	1.00000	0.176777
$33$	−6.00000	−1.04447
$34$	3.90833	0.670273
$35$	0	0
$36$	2.30278	0.383796
$37$	−9.81665	−1.61385	−0.806924	−	0.590655i	$-0.798869\pi$
$37$	−9.81665	−1.61385	−0.806924	+	0.590655i	$0.798869\pi$
$38$	−0.605551	−0.0982334
$39$	14.5139	2.32408
$40$	0	0
$41$	−8.60555	−1.34396	−0.671981	−	0.740569i	$-0.734556\pi$
$41$	−8.60555	−1.34396	−0.671981	+	0.740569i	$0.734556\pi$
$42$	1.60555	0.247742
$43$	−3.30278	−0.503669	−0.251834	−	0.967770i	$-0.581034\pi$
$43$	−3.30278	−0.503669	−0.251834	+	0.967770i	$0.581034\pi$
$44$	2.60555	0.392802
$45$	0	0
$46$	−1.69722	−0.250242
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−2.30278	−0.332377
$49$	−6.51388	−0.930554
$50$	0	0
$51$	−9.00000	−1.26025
$52$	−6.30278	−0.874038
$53$	3.90833	0.536850	0.268425	−	0.963301i	$-0.413497\pi$
$53$	3.90833	0.536850	0.268425	+	0.963301i	$0.413497\pi$
$54$	1.60555	0.218488
$55$	0	0
$56$	−0.697224	−0.0931705
$57$	1.39445	0.184699
$58$	1.00000	0.131306
$59$	−0.908327	−0.118254	−0.0591270	−	0.998250i	$-0.518832\pi$
$59$	−0.908327	−0.118254	−0.0591270	+	0.998250i	$0.518832\pi$
$60$	0	0
$61$	−3.09167	−0.395848	−0.197924	−	0.980217i	$-0.563420\pi$
$61$	−3.09167	−0.395848	−0.197924	+	0.980217i	$0.563420\pi$
$62$	−7.90833	−1.00436
$63$	−1.60555	−0.202280
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	9.21110	1.12532	0.562658	−	0.826690i	$-0.309779\pi$
$67$	9.21110	1.12532	0.562658	+	0.826690i	$0.309779\pi$
$68$	3.90833	0.473954
$69$	3.90833	0.470507
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	2.30278	0.271385
$73$	−2.51388	−0.294227	−0.147114	−	0.989120i	$-0.546998\pi$
$73$	−2.51388	−0.294227	−0.147114	+	0.989120i	$0.546998\pi$
$74$	−9.81665	−1.14116
$75$	0	0
$76$	−0.605551	−0.0694615
$77$	−1.81665	−0.207027
$78$	14.5139	1.64337
$79$	−4.90833	−0.552230	−0.276115	−	0.961125i	$-0.589047\pi$
$79$	−4.90833	−0.552230	−0.276115	+	0.961125i	$0.589047\pi$
$80$	0	0
$81$	−10.6056	−1.17839
$82$	−8.60555	−0.950324
$83$	8.60555	0.944582	0.472291	−	0.881443i	$-0.343427\pi$
$83$	8.60555	0.944582	0.472291	+	0.881443i	$0.343427\pi$
$84$	1.60555	0.175180
$85$	0	0
$86$	−3.30278	−0.356147
$87$	−2.30278	−0.246883
$88$	2.60555	0.277753
$89$	−14.6056	−1.54819	−0.774093	−	0.633072i	$-0.781794\pi$
$89$	−14.6056	−1.54819	−0.774093	+	0.633072i	$0.781794\pi$
$90$	0	0
$91$	4.39445	0.460663
$92$	−1.69722	−0.176948
$93$	18.2111	1.88840
$94$	0	0
$95$	0	0
$96$	−2.30278	−0.235026
$97$	−1.09167	−0.110843	−0.0554213	−	0.998463i	$-0.517650\pi$
$97$	−1.09167	−0.110843	−0.0554213	+	0.998463i	$0.517650\pi$
$98$	−6.51388	−0.658001
$99$	6.00000	0.603023
$100$	0	0
$101$	−12.9083	−1.28443	−0.642213	−	0.766526i	$-0.721984\pi$
$101$	−12.9083	−1.28443	−0.642213	+	0.766526i	$0.721984\pi$
$102$	−9.00000	−0.891133
$103$	−18.4222	−1.81519	−0.907597	−	0.419843i	$-0.862085\pi$
$103$	−18.4222	−1.81519	−0.907597	+	0.419843i	$0.862085\pi$
$104$	−6.30278	−0.618038
$105$	0	0
$106$	3.90833	0.379610
$107$	−8.60555	−0.831930	−0.415965	−	0.909381i	$-0.636556\pi$
$107$	−8.60555	−0.831930	−0.415965	+	0.909381i	$0.636556\pi$
$108$	1.60555	0.154494
$109$	−7.39445	−0.708260	−0.354130	−	0.935196i	$-0.615223\pi$
$109$	−7.39445	−0.708260	−0.354130	+	0.935196i	$0.615223\pi$
$110$	0	0
$111$	22.6056	2.14562
$112$	−0.697224	−0.0658815
$113$	−10.3028	−0.969204	−0.484602	−	0.874735i	$-0.661035\pi$
$113$	−10.3028	−0.969204	−0.484602	+	0.874735i	$0.661035\pi$
$114$	1.39445	0.130602
$115$	0	0
$116$	1.00000	0.0928477
$117$	−14.5139	−1.34181
$118$	−0.908327	−0.0836183
$119$	−2.72498	−0.249799
$120$	0	0
$121$	−4.21110	−0.382828
$122$	−3.09167	−0.279907
$123$	19.8167	1.78681
$124$	−7.90833	−0.710189
$125$	0	0
$126$	−1.60555	−0.143034
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	1.00000	0.0883883
$129$	7.60555	0.669631
$130$	0	0
$131$	21.6333	1.89011	0.945055	−	0.326910i	$-0.106007\pi$
$131$	21.6333	1.89011	0.945055	+	0.326910i	$0.106007\pi$
$132$	−6.00000	−0.522233
$133$	0.422205	0.0366098
$134$	9.21110	0.795718
$135$	0	0
$136$	3.90833	0.335136
$137$	18.9083	1.61545	0.807724	−	0.589561i	$-0.200699\pi$
$137$	18.9083	1.61545	0.807724	+	0.589561i	$0.200699\pi$
$138$	3.90833	0.332699
$139$	6.69722	0.568051	0.284026	−	0.958817i	$-0.408330\pi$
$139$	6.69722	0.568051	0.284026	+	0.958817i	$0.408330\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−16.4222	−1.37329
$144$	2.30278	0.191898
$145$	0	0
$146$	−2.51388	−0.208050
$147$	15.0000	1.23718
$148$	−9.81665	−0.806924
$149$	19.8167	1.62344	0.811722	−	0.584044i	$-0.198531\pi$
$149$	19.8167	1.62344	0.811722	+	0.584044i	$0.198531\pi$
$150$	0	0
$151$	4.60555	0.374794	0.187397	−	0.982284i	$-0.439995\pi$
$151$	4.60555	0.374794	0.187397	+	0.982284i	$0.439995\pi$
$152$	−0.605551	−0.0491167
$153$	9.00000	0.727607
$154$	−1.81665	−0.146390
$155$	0	0
$156$	14.5139	1.16204
$157$	8.42221	0.672165	0.336083	−	0.941833i	$-0.390898\pi$
$157$	8.42221	0.672165	0.336083	+	0.941833i	$0.390898\pi$
$158$	−4.90833	−0.390486
$159$	−9.00000	−0.713746
$160$	0	0
$161$	1.18335	0.0932607
$162$	−10.6056	−0.833251
$163$	21.2111	1.66138	0.830691	−	0.556734i	$-0.187946\pi$
$163$	21.2111	1.66138	0.830691	+	0.556734i	$0.187946\pi$
$164$	−8.60555	−0.671981
$165$	0	0
$166$	8.60555	0.667920
$167$	7.30278	0.565106	0.282553	−	0.959252i	$-0.408819\pi$
$167$	7.30278	0.565106	0.282553	+	0.959252i	$0.408819\pi$
$168$	1.60555	0.123871
$169$	26.7250	2.05577
$170$	0	0
$171$	−1.39445	−0.106636
$172$	−3.30278	−0.251834
$173$	−18.9083	−1.43757	−0.718787	−	0.695231i	$-0.755302\pi$
$173$	−18.9083	−1.43757	−0.718787	+	0.695231i	$0.755302\pi$
$174$	−2.30278	−0.174573
$175$	0	0
$176$	2.60555	0.196401
$177$	2.09167	0.157220
$178$	−14.6056	−1.09473
$179$	0.908327	0.0678915	0.0339458	−	0.999424i	$-0.489193\pi$
$179$	0.908327	0.0678915	0.0339458	+	0.999424i	$0.489193\pi$
$180$	0	0
$181$	−12.6056	−0.936963	−0.468482	−	0.883473i	$-0.655199\pi$
$181$	−12.6056	−0.936963	−0.468482	+	0.883473i	$0.655199\pi$
$182$	4.39445	0.325738
$183$	7.11943	0.526283
$184$	−1.69722	−0.125121
$185$	0	0
$186$	18.2111	1.33530
$187$	10.1833	0.744680
$188$	0	0
$189$	−1.11943	−0.0814265
$190$	0	0
$191$	15.9083	1.15109	0.575543	−	0.817771i	$-0.304791\pi$
$191$	15.9083	1.15109	0.575543	+	0.817771i	$0.304791\pi$
$192$	−2.30278	−0.166189
$193$	24.7250	1.77974	0.889872	−	0.456211i	$-0.150794\pi$
$193$	24.7250	1.77974	0.889872	+	0.456211i	$0.150794\pi$
$194$	−1.09167	−0.0783776
$195$	0	0
$196$	−6.51388	−0.465277
$197$	3.90833	0.278457	0.139228	−	0.990260i	$-0.455538\pi$
$197$	3.90833	0.278457	0.139228	+	0.990260i	$0.455538\pi$
$198$	6.00000	0.426401
$199$	3.81665	0.270555	0.135278	−	0.990808i	$-0.456807\pi$
$199$	3.81665	0.270555	0.135278	+	0.990808i	$0.456807\pi$
$200$	0	0
$201$	−21.2111	−1.49612
$202$	−12.9083	−0.908227
$203$	−0.697224	−0.0489356
$204$	−9.00000	−0.630126
$205$	0	0
$206$	−18.4222	−1.28354
$207$	−3.90833	−0.271647
$208$	−6.30278	−0.437019
$209$	−1.57779	−0.109138
$210$	0	0
$211$	27.8167	1.91498	0.957489	−	0.288471i	$-0.0931468\pi$
$211$	27.8167	1.91498	0.957489	+	0.288471i	$0.0931468\pi$
$212$	3.90833	0.268425
$213$	0	0
$214$	−8.60555	−0.588263
$215$	0	0
$216$	1.60555	0.109244
$217$	5.51388	0.374306
$218$	−7.39445	−0.500815
$219$	5.78890	0.391177
$220$	0	0
$221$	−24.6333	−1.65702
$222$	22.6056	1.51719
$223$	7.51388	0.503166	0.251583	−	0.967836i	$-0.419049\pi$
$223$	7.51388	0.503166	0.251583	+	0.967836i	$0.419049\pi$
$224$	−0.697224	−0.0465853
$225$	0	0
$226$	−10.3028	−0.685330
$227$	−0.788897	−0.0523610	−0.0261805	−	0.999657i	$-0.508334\pi$
$227$	−0.788897	−0.0523610	−0.0261805	+	0.999657i	$0.508334\pi$
$228$	1.39445	0.0923496
$229$	5.90833	0.390433	0.195217	−	0.980760i	$-0.437459\pi$
$229$	5.90833	0.390433	0.195217	+	0.980760i	$0.437459\pi$
$230$	0	0
$231$	4.18335	0.275244
$232$	1.00000	0.0656532
$233$	−23.2111	−1.52061	−0.760305	−	0.649566i	$-0.774950\pi$
$233$	−23.2111	−1.52061	−0.760305	+	0.649566i	$0.774950\pi$
$234$	−14.5139	−0.948802
$235$	0	0
$236$	−0.908327	−0.0591270
$237$	11.3028	0.734194
$238$	−2.72498	−0.176634
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	0.302776	0.0195035	0.00975175	−	0.999952i	$-0.496896\pi$
$241$	0.302776	0.0195035	0.00975175	+	0.999952i	$0.496896\pi$
$242$	−4.21110	−0.270700
$243$	19.6056	1.25770
$244$	−3.09167	−0.197924
$245$	0	0
$246$	19.8167	1.26346
$247$	3.81665	0.242848
$248$	−7.90833	−0.502179
$249$	−19.8167	−1.25583
$250$	0	0
$251$	−8.60555	−0.543178	−0.271589	−	0.962413i	$-0.587549\pi$
$251$	−8.60555	−0.543178	−0.271589	+	0.962413i	$0.587549\pi$
$252$	−1.60555	−0.101140
$253$	−4.42221	−0.278022
$254$	−20.0000	−1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.02776	−0.438379	−0.219190	−	0.975682i	$-0.570341\pi$
$257$	−7.02776	−0.438379	−0.219190	+	0.975682i	$0.570341\pi$
$258$	7.60555	0.473501
$259$	6.84441	0.425291
$260$	0	0
$261$	2.30278	0.142538
$262$	21.6333	1.33651
$263$	−5.21110	−0.321330	−0.160665	−	0.987009i	$-0.551364\pi$
$263$	−5.21110	−0.321330	−0.160665	+	0.987009i	$0.551364\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	0.422205	0.0258871
$267$	33.6333	2.05833
$268$	9.21110	0.562658
$269$	−12.5139	−0.762985	−0.381492	−	0.924372i	$-0.624590\pi$
$269$	−12.5139	−0.762985	−0.381492	+	0.924372i	$0.624590\pi$
$270$	0	0
$271$	13.2111	0.802517	0.401259	−	0.915965i	$-0.368573\pi$
$271$	13.2111	0.802517	0.401259	+	0.915965i	$0.368573\pi$
$272$	3.90833	0.236977
$273$	−10.1194	−0.612456
$274$	18.9083	1.14229
$275$	0	0
$276$	3.90833	0.235254
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	6.69722	0.401673
$279$	−18.2111	−1.09027
$280$	0	0
$281$	15.1194	0.901950	0.450975	−	0.892537i	$-0.351076\pi$
$281$	15.1194	0.901950	0.450975	+	0.892537i	$0.351076\pi$
$282$	0	0
$283$	−15.0278	−0.893307	−0.446654	−	0.894707i	$-0.647384\pi$
$283$	−15.0278	−0.893307	−0.446654	+	0.894707i	$0.647384\pi$
$284$	0	0
$285$	0	0
$286$	−16.4222	−0.971065
$287$	6.00000	0.354169
$288$	2.30278	0.135692
$289$	−1.72498	−0.101469
$290$	0	0
$291$	2.51388	0.147366
$292$	−2.51388	−0.147114
$293$	−25.8167	−1.50823	−0.754113	−	0.656745i	$-0.771933\pi$
$293$	−25.8167	−1.50823	−0.754113	+	0.656745i	$0.771933\pi$
$294$	15.0000	0.874818
$295$	0	0
$296$	−9.81665	−0.570581
$297$	4.18335	0.242742
$298$	19.8167	1.14795
$299$	10.6972	0.618636
$300$	0	0
$301$	2.30278	0.132730
$302$	4.60555	0.265020
$303$	29.7250	1.70766
$304$	−0.605551	−0.0347307
$305$	0	0
$306$	9.00000	0.514496
$307$	−1.21110	−0.0691213	−0.0345606	−	0.999403i	$-0.511003\pi$
$307$	−1.21110	−0.0691213	−0.0345606	+	0.999403i	$0.511003\pi$
$308$	−1.81665	−0.103513
$309$	42.4222	2.41331
$310$	0	0
$311$	24.9083	1.41242	0.706211	−	0.708002i	$-0.250403\pi$
$311$	24.9083	1.41242	0.706211	+	0.708002i	$0.250403\pi$
$312$	14.5139	0.821687
$313$	−0.422205	−0.0238644	−0.0119322	−	0.999929i	$-0.503798\pi$
$313$	−0.422205	−0.0238644	−0.0119322	+	0.999929i	$0.503798\pi$
$314$	8.42221	0.475293
$315$	0	0
$316$	−4.90833	−0.276115
$317$	25.0278	1.40570	0.702849	−	0.711339i	$-0.251911\pi$
$317$	25.0278	1.40570	0.702849	+	0.711339i	$0.251911\pi$
$318$	−9.00000	−0.504695
$319$	2.60555	0.145883
$320$	0	0
$321$	19.8167	1.10606
$322$	1.18335	0.0659453
$323$	−2.36669	−0.131686
$324$	−10.6056	−0.589197
$325$	0	0
$326$	21.2111	1.17477
$327$	17.0278	0.941637
$328$	−8.60555	−0.475162
$329$	0	0
$330$	0	0
$331$	22.6056	1.24251	0.621257	−	0.783607i	$-0.286622\pi$
$331$	22.6056	1.24251	0.621257	+	0.783607i	$0.286622\pi$
$332$	8.60555	0.472291
$333$	−22.6056	−1.23878
$334$	7.30278	0.399590
$335$	0	0
$336$	1.60555	0.0875900
$337$	5.30278	0.288861	0.144430	−	0.989515i	$-0.453865\pi$
$337$	5.30278	0.288861	0.144430	+	0.989515i	$0.453865\pi$
$338$	26.7250	1.45365
$339$	23.7250	1.28856
$340$	0	0
$341$	−20.6056	−1.11585
$342$	−1.39445	−0.0754032
$343$	9.42221	0.508751
$344$	−3.30278	−0.178074
$345$	0	0
$346$	−18.9083	−1.01652
$347$	−13.8167	−0.741717	−0.370858	−	0.928689i	$-0.620936\pi$
$347$	−13.8167	−0.741717	−0.370858	+	0.928689i	$0.620936\pi$
$348$	−2.30278	−0.123442
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	0	0
$351$	−10.1194	−0.540135
$352$	2.60555	0.138876
$353$	−17.2111	−0.916055	−0.458027	−	0.888938i	$-0.651444\pi$
$353$	−17.2111	−0.916055	−0.458027	+	0.888938i	$0.651444\pi$
$354$	2.09167	0.111171
$355$	0	0
$356$	−14.6056	−0.774093
$357$	6.27502	0.332109
$358$	0.908327	0.0480066
$359$	−33.5139	−1.76879	−0.884397	−	0.466735i	$-0.845430\pi$
$359$	−33.5139	−1.76879	−0.884397	+	0.466735i	$0.845430\pi$
$360$	0	0
$361$	−18.6333	−0.980700
$362$	−12.6056	−0.662533
$363$	9.69722	0.508972
$364$	4.39445	0.230332
$365$	0	0
$366$	7.11943	0.372139
$367$	24.6056	1.28440	0.642200	−	0.766537i	$-0.278022\pi$
$367$	24.6056	1.28440	0.642200	+	0.766537i	$0.278022\pi$
$368$	−1.69722	−0.0884739
$369$	−19.8167	−1.03161
$370$	0	0
$371$	−2.72498	−0.141474
$372$	18.2111	0.944202
$373$	31.9083	1.65215	0.826075	−	0.563560i	$-0.190569\pi$
$373$	31.9083	1.65215	0.826075	+	0.563560i	$0.190569\pi$
$374$	10.1833	0.526568
$375$	0	0
$376$	0	0
$377$	−6.30278	−0.324609
$378$	−1.11943	−0.0575772
$379$	−30.6056	−1.57210	−0.786051	−	0.618162i	$-0.787878\pi$
$379$	−30.6056	−1.57210	−0.786051	+	0.618162i	$0.787878\pi$
$380$	0	0
$381$	46.0555	2.35950
$382$	15.9083	0.813941
$383$	−4.69722	−0.240017	−0.120008	−	0.992773i	$-0.538292\pi$
$383$	−4.69722	−0.240017	−0.120008	+	0.992773i	$0.538292\pi$
$384$	−2.30278	−0.117513
$385$	0	0
$386$	24.7250	1.25847
$387$	−7.60555	−0.386612
$388$	−1.09167	−0.0554213
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	−6.63331	−0.335461
$392$	−6.51388	−0.329001
$393$	−49.8167	−2.51292
$394$	3.90833	0.196899
$395$	0	0
$396$	6.00000	0.301511
$397$	−11.9083	−0.597662	−0.298831	−	0.954306i	$-0.596597\pi$
$397$	−11.9083	−0.597662	−0.298831	+	0.954306i	$0.596597\pi$
$398$	3.81665	0.191312
$399$	−0.972244	−0.0486731
$400$	0	0
$401$	28.3028	1.41337	0.706687	−	0.707527i	$-0.250189\pi$
$401$	28.3028	1.41337	0.706687	+	0.707527i	$0.250189\pi$
$402$	−21.2111	−1.05791
$403$	49.8444	2.48293
$404$	−12.9083	−0.642213
$405$	0	0
$406$	−0.697224	−0.0346027
$407$	−25.5778	−1.26784
$408$	−9.00000	−0.445566
$409$	−9.21110	−0.455460	−0.227730	−	0.973724i	$-0.573130\pi$
$409$	−9.21110	−0.455460	−0.227730	+	0.973724i	$0.573130\pi$
$410$	0	0
$411$	−43.5416	−2.14775
$412$	−18.4222	−0.907597
$413$	0.633308	0.0311630
$414$	−3.90833	−0.192084
$415$	0	0
$416$	−6.30278	−0.309019
$417$	−15.4222	−0.755229
$418$	−1.57779	−0.0771725
$419$	−9.11943	−0.445513	−0.222757	−	0.974874i	$-0.571506\pi$
$419$	−9.11943	−0.445513	−0.222757	+	0.974874i	$0.571506\pi$
$420$	0	0
$421$	−25.6333	−1.24929	−0.624645	−	0.780908i	$-0.714757\pi$
$421$	−25.6333	−1.24929	−0.624645	+	0.780908i	$0.714757\pi$
$422$	27.8167	1.35409
$423$	0	0
$424$	3.90833	0.189805
$425$	0	0
$426$	0	0
$427$	2.15559	0.104316
$428$	−8.60555	−0.415965
$429$	37.8167	1.82581
$430$	0	0
$431$	12.2389	0.589525	0.294763	−	0.955571i	$-0.404759\pi$
$431$	12.2389	0.589525	0.294763	+	0.955571i	$0.404759\pi$
$432$	1.60555	0.0772471
$433$	15.2111	0.730999	0.365499	−	0.930812i	$-0.380898\pi$
$433$	15.2111	0.730999	0.365499	+	0.930812i	$0.380898\pi$
$434$	5.51388	0.264675
$435$	0	0
$436$	−7.39445	−0.354130
$437$	1.02776	0.0491643
$438$	5.78890	0.276604
$439$	−37.6333	−1.79614	−0.898070	−	0.439853i	$-0.855031\pi$
$439$	−37.6333	−1.79614	−0.898070	+	0.439853i	$0.855031\pi$
$440$	0	0
$441$	−15.0000	−0.714286
$442$	−24.6333	−1.17169
$443$	−27.7527	−1.31857	−0.659286	−	0.751892i	$-0.729141\pi$
$443$	−27.7527	−1.31857	−0.659286	+	0.751892i	$0.729141\pi$
$444$	22.6056	1.07281
$445$	0	0
$446$	7.51388	0.355792
$447$	−45.6333	−2.15838
$448$	−0.697224	−0.0329408
$449$	−15.3944	−0.726509	−0.363254	−	0.931690i	$-0.618334\pi$
$449$	−15.3944	−0.726509	−0.363254	+	0.931690i	$0.618334\pi$
$450$	0	0
$451$	−22.4222	−1.05582
$452$	−10.3028	−0.484602
$453$	−10.6056	−0.498292
$454$	−0.788897	−0.0370248
$455$	0	0
$456$	1.39445	0.0653010
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	5.90833	0.276078
$459$	6.27502	0.292893
$460$	0	0
$461$	25.5416	1.18959	0.594796	−	0.803876i	$-0.297233\pi$
$461$	25.5416	1.18959	0.594796	+	0.803876i	$0.297233\pi$
$462$	4.18335	0.194627
$463$	−40.8444	−1.89820	−0.949100	−	0.314974i	$-0.898004\pi$
$463$	−40.8444	−1.89820	−0.949100	+	0.314974i	$0.898004\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−23.2111	−1.07523
$467$	37.5416	1.73722	0.868610	−	0.495497i	$-0.165014\pi$
$467$	37.5416	1.73722	0.868610	+	0.495497i	$0.165014\pi$
$468$	−14.5139	−0.670904
$469$	−6.42221	−0.296550
$470$	0	0
$471$	−19.3944	−0.893649
$472$	−0.908327	−0.0418091
$473$	−8.60555	−0.395684
$474$	11.3028	0.519154
$475$	0	0
$476$	−2.72498	−0.124899
$477$	9.00000	0.412082
$478$	6.00000	0.274434
$479$	−11.7250	−0.535728	−0.267864	−	0.963457i	$-0.586318\pi$
$479$	−11.7250	−0.535728	−0.267864	+	0.963457i	$0.586318\pi$
$480$	0	0
$481$	61.8722	2.82113
$482$	0.302776	0.0137911
$483$	−2.72498	−0.123991
$484$	−4.21110	−0.191414
$485$	0	0
$486$	19.6056	0.889326
$487$	−33.9361	−1.53779	−0.768895	−	0.639375i	$-0.779193\pi$
$487$	−33.9361	−1.53779	−0.768895	+	0.639375i	$0.779193\pi$
$488$	−3.09167	−0.139953
$489$	−48.8444	−2.20882
$490$	0	0
$491$	−3.63331	−0.163969	−0.0819844	−	0.996634i	$-0.526126\pi$
$491$	−3.63331	−0.163969	−0.0819844	+	0.996634i	$0.526126\pi$
$492$	19.8167	0.893404
$493$	3.90833	0.176022
$494$	3.81665	0.171719
$495$	0	0
$496$	−7.90833	−0.355094
$497$	0	0
$498$	−19.8167	−0.888005
$499$	−18.7250	−0.838245	−0.419123	−	0.907930i	$-0.637662\pi$
$499$	−18.7250	−0.838245	−0.419123	+	0.907930i	$0.637662\pi$
$500$	0	0
$501$	−16.8167	−0.751313
$502$	−8.60555	−0.384085
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	−1.60555	−0.0715169
$505$	0	0
$506$	−4.42221	−0.196591
$507$	−61.5416	−2.73316
$508$	−20.0000	−0.887357
$509$	1.81665	0.0805218	0.0402609	−	0.999189i	$-0.487181\pi$
$509$	1.81665	0.0805218	0.0402609	+	0.999189i	$0.487181\pi$
$510$	0	0
$511$	1.75274	0.0775365
$512$	1.00000	0.0441942
$513$	−0.972244	−0.0429256
$514$	−7.02776	−0.309981
$515$	0	0
$516$	7.60555	0.334816
$517$	0	0
$518$	6.84441	0.300726
$519$	43.5416	1.91127
$520$	0	0
$521$	4.69722	0.205789	0.102895	−	0.994692i	$-0.467190\pi$
$521$	4.69722	0.205789	0.102895	+	0.994692i	$0.467190\pi$
$522$	2.30278	0.100790
$523$	14.1833	0.620194	0.310097	−	0.950705i	$-0.399638\pi$
$523$	14.1833	0.620194	0.310097	+	0.950705i	$0.399638\pi$
$524$	21.6333	0.945055
$525$	0	0
$526$	−5.21110	−0.227215
$527$	−30.9083	−1.34639
$528$	−6.00000	−0.261116
$529$	−20.1194	−0.874758
$530$	0	0
$531$	−2.09167	−0.0907709
$532$	0.422205	0.0183049
$533$	54.2389	2.34935
$534$	33.6333	1.45546
$535$	0	0
$536$	9.21110	0.397859
$537$	−2.09167	−0.0902624
$538$	−12.5139	−0.539512
$539$	−16.9722	−0.731046
$540$	0	0
$541$	−0.880571	−0.0378587	−0.0189293	−	0.999821i	$-0.506026\pi$
$541$	−0.880571	−0.0378587	−0.0189293	+	0.999821i	$0.506026\pi$
$542$	13.2111	0.567465
$543$	29.0278	1.24570
$544$	3.90833	0.167568
$545$	0	0
$546$	−10.1194	−0.433072
$547$	40.2389	1.72049	0.860245	−	0.509881i	$-0.170311\pi$
$547$	40.2389	1.72049	0.860245	+	0.509881i	$0.170311\pi$
$548$	18.9083	0.807724
$549$	−7.11943	−0.303850
$550$	0	0
$551$	−0.605551	−0.0257974
$552$	3.90833	0.166349
$553$	3.42221	0.145527
$554$	−14.0000	−0.594803
$555$	0	0
$556$	6.69722	0.284026
$557$	−22.5416	−0.955120	−0.477560	−	0.878599i	$-0.658479\pi$
$557$	−22.5416	−0.955120	−0.477560	+	0.878599i	$0.658479\pi$
$558$	−18.2111	−0.770937
$559$	20.8167	0.880451
$560$	0	0
$561$	−23.4500	−0.990058
$562$	15.1194	0.637775
$563$	−17.0917	−0.720328	−0.360164	−	0.932889i	$-0.617279\pi$
$563$	−17.0917	−0.720328	−0.360164	+	0.932889i	$0.617279\pi$
$564$	0	0
$565$	0	0
$566$	−15.0278	−0.631664
$567$	7.39445	0.310538
$568$	0	0
$569$	39.6333	1.66151	0.830757	−	0.556635i	$-0.187908\pi$
$569$	39.6333	1.66151	0.830757	+	0.556635i	$0.187908\pi$
$570$	0	0
$571$	26.1194	1.09306	0.546532	−	0.837438i	$-0.315948\pi$
$571$	26.1194	1.09306	0.546532	+	0.837438i	$0.315948\pi$
$572$	−16.4222	−0.686647
$573$	−36.6333	−1.53038
$574$	6.00000	0.250435
$575$	0	0
$576$	2.30278	0.0959490
$577$	−38.5139	−1.60335	−0.801677	−	0.597758i	$-0.796059\pi$
$577$	−38.5139	−1.60335	−0.801677	+	0.597758i	$0.796059\pi$
$578$	−1.72498	−0.0717497
$579$	−56.9361	−2.36618
$580$	0	0
$581$	−6.00000	−0.248922
$582$	2.51388	0.104204
$583$	10.1833	0.421751
$584$	−2.51388	−0.104025
$585$	0	0
$586$	−25.8167	−1.06648
$587$	0.788897	0.0325613	0.0162806	−	0.999867i	$-0.494817\pi$
$587$	0.788897	0.0325613	0.0162806	+	0.999867i	$0.494817\pi$
$588$	15.0000	0.618590
$589$	4.78890	0.197323
$590$	0	0
$591$	−9.00000	−0.370211
$592$	−9.81665	−0.403462
$593$	−19.8167	−0.813772	−0.406886	−	0.913479i	$-0.633385\pi$
$593$	−19.8167	−0.813772	−0.406886	+	0.913479i	$0.633385\pi$
$594$	4.18335	0.171645
$595$	0	0
$596$	19.8167	0.811722
$597$	−8.78890	−0.359706
$598$	10.6972	0.437442
$599$	20.0917	0.820924	0.410462	−	0.911878i	$-0.365368\pi$
$599$	20.0917	0.820924	0.410462	+	0.911878i	$0.365368\pi$
$600$	0	0
$601$	−37.3944	−1.52535	−0.762676	−	0.646781i	$-0.776115\pi$
$601$	−37.3944	−1.52535	−0.762676	+	0.646781i	$0.776115\pi$
$602$	2.30278	0.0938541
$603$	21.2111	0.863783
$604$	4.60555	0.187397
$605$	0	0
$606$	29.7250	1.20749
$607$	19.6333	0.796891	0.398446	−	0.917192i	$-0.369550\pi$
$607$	19.6333	0.796891	0.398446	+	0.917192i	$0.369550\pi$
$608$	−0.605551	−0.0245583
$609$	1.60555	0.0650602
$610$	0	0
$611$	0	0
$612$	9.00000	0.363803
$613$	42.3305	1.70971	0.854857	−	0.518864i	$-0.173645\pi$
$613$	42.3305	1.70971	0.854857	+	0.518864i	$0.173645\pi$
$614$	−1.21110	−0.0488761
$615$	0	0
$616$	−1.81665	−0.0731951
$617$	−3.90833	−0.157343	−0.0786717	−	0.996901i	$-0.525068\pi$
$617$	−3.90833	−0.157343	−0.0786717	+	0.996901i	$0.525068\pi$
$618$	42.4222	1.70647
$619$	−3.21110	−0.129065	−0.0645326	−	0.997916i	$-0.520556\pi$
$619$	−3.21110	−0.129065	−0.0645326	+	0.997916i	$0.520556\pi$
$620$	0	0
$621$	−2.72498	−0.109350
$622$	24.9083	0.998733
$623$	10.1833	0.407987
$624$	14.5139	0.581020
$625$	0	0
$626$	−0.422205	−0.0168747
$627$	3.63331	0.145100
$628$	8.42221	0.336083
$629$	−38.3667	−1.52978
$630$	0	0
$631$	−18.8444	−0.750184	−0.375092	−	0.926988i	$-0.622389\pi$
$631$	−18.8444	−0.750184	−0.375092	+	0.926988i	$0.622389\pi$
$632$	−4.90833	−0.195243
$633$	−64.0555	−2.54598
$634$	25.0278	0.993979
$635$	0	0
$636$	−9.00000	−0.356873
$637$	41.0555	1.62668
$638$	2.60555	0.103155
$639$	0	0
$640$	0	0
$641$	1.81665	0.0717535	0.0358768	−	0.999356i	$-0.488578\pi$
$641$	1.81665	0.0717535	0.0358768	+	0.999356i	$0.488578\pi$
$642$	19.8167	0.782101
$643$	18.6056	0.733731	0.366866	−	0.930274i	$-0.380431\pi$
$643$	18.6056	0.733731	0.366866	+	0.930274i	$0.380431\pi$
$644$	1.18335	0.0466304
$645$	0	0
$646$	−2.36669	−0.0931163
$647$	−27.6333	−1.08638	−0.543189	−	0.839611i	$-0.682783\pi$
$647$	−27.6333	−1.08638	−0.543189	+	0.839611i	$0.682783\pi$
$648$	−10.6056	−0.416625
$649$	−2.36669	−0.0929008
$650$	0	0
$651$	−12.6972	−0.497643
$652$	21.2111	0.830691
$653$	31.8167	1.24508	0.622541	−	0.782587i	$-0.286100\pi$
$653$	31.8167	1.24508	0.622541	+	0.782587i	$0.286100\pi$
$654$	17.0278	0.665838
$655$	0	0
$656$	−8.60555	−0.335990
$657$	−5.78890	−0.225846
$658$	0	0
$659$	−16.1833	−0.630414	−0.315207	−	0.949023i	$-0.602074\pi$
$659$	−16.1833	−0.630414	−0.315207	+	0.949023i	$0.602074\pi$
$660$	0	0
$661$	−11.8167	−0.459615	−0.229807	−	0.973236i	$-0.573810\pi$
$661$	−11.8167	−0.459615	−0.229807	+	0.973236i	$0.573810\pi$
$662$	22.6056	0.878590
$663$	56.7250	2.20302
$664$	8.60555	0.333960
$665$	0	0
$666$	−22.6056	−0.875947
$667$	−1.69722	−0.0657168
$668$	7.30278	0.282553
$669$	−17.3028	−0.668964
$670$	0	0
$671$	−8.05551	−0.310980
$672$	1.60555	0.0619355
$673$	−49.4500	−1.90616	−0.953078	−	0.302725i	$-0.902104\pi$
$673$	−49.4500	−1.90616	−0.953078	+	0.302725i	$0.902104\pi$
$674$	5.30278	0.204255
$675$	0	0
$676$	26.7250	1.02788
$677$	8.84441	0.339918	0.169959	−	0.985451i	$-0.445636\pi$
$677$	8.84441	0.339918	0.169959	+	0.985451i	$0.445636\pi$
$678$	23.7250	0.911152
$679$	0.761141	0.0292099
$680$	0	0
$681$	1.81665	0.0696143
$682$	−20.6056	−0.789027
$683$	−41.4500	−1.58604	−0.793019	−	0.609196i	$-0.791492\pi$
$683$	−41.4500	−1.58604	−0.793019	+	0.609196i	$0.791492\pi$
$684$	−1.39445	−0.0533181
$685$	0	0
$686$	9.42221	0.359741
$687$	−13.6056	−0.519084
$688$	−3.30278	−0.125917
$689$	−24.6333	−0.938454
$690$	0	0
$691$	−24.0917	−0.916490	−0.458245	−	0.888826i	$-0.651522\pi$
$691$	−24.0917	−0.916490	−0.458245	+	0.888826i	$0.651522\pi$
$692$	−18.9083	−0.718787
$693$	−4.18335	−0.158912
$694$	−13.8167	−0.524473
$695$	0	0
$696$	−2.30278	−0.0872865
$697$	−33.6333	−1.27395
$698$	8.00000	0.302804
$699$	53.4500	2.02166
$700$	0	0
$701$	−9.39445	−0.354823	−0.177412	−	0.984137i	$-0.556772\pi$
$701$	−9.39445	−0.354823	−0.177412	+	0.984137i	$0.556772\pi$
$702$	−10.1194	−0.381933
$703$	5.94449	0.224201
$704$	2.60555	0.0982004
$705$	0	0
$706$	−17.2111	−0.647748
$707$	9.00000	0.338480
$708$	2.09167	0.0786099
$709$	21.0278	0.789714	0.394857	−	0.918743i	$-0.370794\pi$
$709$	21.0278	0.789714	0.394857	+	0.918743i	$0.370794\pi$
$710$	0	0
$711$	−11.3028	−0.423887
$712$	−14.6056	−0.547366
$713$	13.4222	0.502666
$714$	6.27502	0.234837
$715$	0	0
$716$	0.908327	0.0339458
$717$	−13.8167	−0.515992
$718$	−33.5139	−1.25073
$719$	36.2389	1.35148	0.675741	−	0.737139i	$-0.263824\pi$
$719$	36.2389	1.35148	0.675741	+	0.737139i	$0.263824\pi$
$720$	0	0
$721$	12.8444	0.478351
$722$	−18.6333	−0.693460
$723$	−0.697224	−0.0259301
$724$	−12.6056	−0.468482
$725$	0	0
$726$	9.69722	0.359898
$727$	−34.6056	−1.28345	−0.641724	−	0.766935i	$-0.721781\pi$
$727$	−34.6056	−1.28345	−0.641724	+	0.766935i	$0.721781\pi$
$728$	4.39445	0.162869
$729$	−13.3305	−0.493723
$730$	0	0
$731$	−12.9083	−0.477432
$732$	7.11943	0.263142
$733$	12.8444	0.474419	0.237210	−	0.971459i	$-0.423767\pi$
$733$	12.8444	0.474419	0.237210	+	0.971459i	$0.423767\pi$
$734$	24.6056	0.908207
$735$	0	0
$736$	−1.69722	−0.0625605
$737$	24.0000	0.884051
$738$	−19.8167	−0.729461
$739$	13.2111	0.485978	0.242989	−	0.970029i	$-0.421872\pi$
$739$	13.2111	0.485978	0.242989	+	0.970029i	$0.421872\pi$
$740$	0	0
$741$	−8.78890	−0.322868
$742$	−2.72498	−0.100037
$743$	−41.2111	−1.51189	−0.755944	−	0.654636i	$-0.772822\pi$
$743$	−41.2111	−1.51189	−0.755944	+	0.654636i	$0.772822\pi$
$744$	18.2111	0.667651
$745$	0	0
$746$	31.9083	1.16825
$747$	19.8167	0.725053
$748$	10.1833	0.372340
$749$	6.00000	0.219235
$750$	0	0
$751$	40.8444	1.49043	0.745217	−	0.666822i	$-0.232346\pi$
$751$	40.8444	1.49043	0.745217	+	0.666822i	$0.232346\pi$
$752$	0	0
$753$	19.8167	0.722159
$754$	−6.30278	−0.229534
$755$	0	0
$756$	−1.11943	−0.0407133
$757$	21.4500	0.779612	0.389806	−	0.920897i	$-0.372542\pi$
$757$	21.4500	0.779612	0.389806	+	0.920897i	$0.372542\pi$
$758$	−30.6056	−1.11164
$759$	10.1833	0.369632
$760$	0	0
$761$	33.3583	1.20924	0.604619	−	0.796515i	$-0.293326\pi$
$761$	33.3583	1.20924	0.604619	+	0.796515i	$0.293326\pi$
$762$	46.0555	1.66842
$763$	5.15559	0.186645
$764$	15.9083	0.575543
$765$	0	0
$766$	−4.69722	−0.169718
$767$	5.72498	0.206717
$768$	−2.30278	−0.0830943
$769$	45.0278	1.62374	0.811871	−	0.583837i	$-0.198449\pi$
$769$	45.0278	1.62374	0.811871	+	0.583837i	$0.198449\pi$
$770$	0	0
$771$	16.1833	0.582829
$772$	24.7250	0.889872
$773$	40.4222	1.45389	0.726943	−	0.686698i	$-0.240941\pi$
$773$	40.4222	1.45389	0.726943	+	0.686698i	$0.240941\pi$
$774$	−7.60555	−0.273376
$775$	0	0
$776$	−1.09167	−0.0391888
$777$	−15.7611	−0.565428
$778$	−18.0000	−0.645331
$779$	5.21110	0.186707
$780$	0	0
$781$	0	0
$782$	−6.63331	−0.237207
$783$	1.60555	0.0573777
$784$	−6.51388	−0.232639
$785$	0	0
$786$	−49.8167	−1.77690
$787$	−27.0278	−0.963435	−0.481718	−	0.876326i	$-0.659987\pi$
$787$	−27.0278	−0.963435	−0.481718	+	0.876326i	$0.659987\pi$
$788$	3.90833	0.139228
$789$	12.0000	0.427211
$790$	0	0
$791$	7.18335	0.255410
$792$	6.00000	0.213201
$793$	19.4861	0.691972
$794$	−11.9083	−0.422611
$795$	0	0
$796$	3.81665	0.135278
$797$	31.2666	1.10752	0.553760	−	0.832676i	$-0.313192\pi$
$797$	31.2666	1.10752	0.553760	+	0.832676i	$0.313192\pi$
$798$	−0.972244	−0.0344171
$799$	0	0
$800$	0	0
$801$	−33.6333	−1.18837
$802$	28.3028	0.999406
$803$	−6.55004	−0.231146
$804$	−21.2111	−0.748058
$805$	0	0
$806$	49.8444	1.75569
$807$	28.8167	1.01439
$808$	−12.9083	−0.454113
$809$	−26.0555	−0.916063	−0.458032	−	0.888936i	$-0.651445\pi$
$809$	−26.0555	−0.916063	−0.458032	+	0.888936i	$0.651445\pi$
$810$	0	0
$811$	24.9361	0.875624	0.437812	−	0.899066i	$-0.355753\pi$
$811$	24.9361	0.875624	0.437812	+	0.899066i	$0.355753\pi$
$812$	−0.697224	−0.0244678
$813$	−30.4222	−1.06695
$814$	−25.5778	−0.896501
$815$	0	0
$816$	−9.00000	−0.315063
$817$	2.00000	0.0699711
$818$	−9.21110	−0.322059
$819$	10.1194	0.353601
$820$	0	0
$821$	−54.2389	−1.89295	−0.946475	−	0.322778i	$-0.895383\pi$
$821$	−54.2389	−1.89295	−0.946475	+	0.322778i	$0.895383\pi$
$822$	−43.5416	−1.51869
$823$	37.6333	1.31181	0.655907	−	0.754841i	$-0.272286\pi$
$823$	37.6333	1.31181	0.655907	+	0.754841i	$0.272286\pi$
$824$	−18.4222	−0.641768
$825$	0	0
$826$	0.633308	0.0220356
$827$	8.88057	0.308808	0.154404	−	0.988008i	$-0.450654\pi$
$827$	8.88057	0.308808	0.154404	+	0.988008i	$0.450654\pi$
$828$	−3.90833	−0.135824
$829$	50.7527	1.76272	0.881358	−	0.472450i	$-0.156630\pi$
$829$	50.7527	1.76272	0.881358	+	0.472450i	$0.156630\pi$
$830$	0	0
$831$	32.2389	1.11835
$832$	−6.30278	−0.218509
$833$	−25.4584	−0.882080
$834$	−15.4222	−0.534027
$835$	0	0
$836$	−1.57779	−0.0545692
$837$	−12.6972	−0.438880
$838$	−9.11943	−0.315025
$839$	−29.2111	−1.00848	−0.504240	−	0.863564i	$-0.668227\pi$
$839$	−29.2111	−1.00848	−0.504240	+	0.863564i	$0.668227\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−25.6333	−0.883382
$843$	−34.8167	−1.19915
$844$	27.8167	0.957489
$845$	0	0
$846$	0	0
$847$	2.93608	0.100885
$848$	3.90833	0.134212
$849$	34.6056	1.18766
$850$	0	0
$851$	16.6611	0.571134
$852$	0	0
$853$	28.2389	0.966880	0.483440	−	0.875377i	$-0.339387\pi$
$853$	28.2389	0.966880	0.483440	+	0.875377i	$0.339387\pi$
$854$	2.15559	0.0737628
$855$	0	0
$856$	−8.60555	−0.294132
$857$	30.2389	1.03294	0.516470	−	0.856305i	$-0.327246\pi$
$857$	30.2389	1.03294	0.516470	+	0.856305i	$0.327246\pi$
$858$	37.8167	1.29104
$859$	28.6056	0.976009	0.488004	−	0.872841i	$-0.337725\pi$
$859$	28.6056	0.976009	0.488004	+	0.872841i	$0.337725\pi$
$860$	0	0
$861$	−13.8167	−0.470870
$862$	12.2389	0.416857
$863$	−5.09167	−0.173323	−0.0866613	−	0.996238i	$-0.527620\pi$
$863$	−5.09167	−0.173323	−0.0866613	+	0.996238i	$0.527620\pi$
$864$	1.60555	0.0546220
$865$	0	0
$866$	15.2111	0.516894
$867$	3.97224	0.134904
$868$	5.51388	0.187153
$869$	−12.7889	−0.433834
$870$	0	0
$871$	−58.0555	−1.96714
$872$	−7.39445	−0.250408
$873$	−2.51388	−0.0850819
$874$	1.02776	0.0347644
$875$	0	0
$876$	5.78890	0.195589
$877$	−33.6972	−1.13787	−0.568937	−	0.822381i	$-0.692645\pi$
$877$	−33.6972	−1.13787	−0.568937	+	0.822381i	$0.692645\pi$
$878$	−37.6333	−1.27006
$879$	59.4500	2.00520
$880$	0	0
$881$	−31.0278	−1.04535	−0.522676	−	0.852532i	$-0.675066\pi$
$881$	−31.0278	−1.04535	−0.522676	+	0.852532i	$0.675066\pi$
$882$	−15.0000	−0.505076
$883$	−11.3944	−0.383454	−0.191727	−	0.981448i	$-0.561409\pi$
$883$	−11.3944	−0.383454	−0.191727	+	0.981448i	$0.561409\pi$
$884$	−24.6333	−0.828508
$885$	0	0
$886$	−27.7527	−0.932371
$887$	−51.6333	−1.73368	−0.866838	−	0.498589i	$-0.833852\pi$
$887$	−51.6333	−1.73368	−0.866838	+	0.498589i	$0.833852\pi$
$888$	22.6056	0.758593
$889$	13.9445	0.467683
$890$	0	0
$891$	−27.6333	−0.925751
$892$	7.51388	0.251583
$893$	0	0
$894$	−45.6333	−1.52621
$895$	0	0
$896$	−0.697224	−0.0232926
$897$	−24.6333	−0.822482
$898$	−15.3944	−0.513719
$899$	−7.90833	−0.263757
$900$	0	0
$901$	15.2750	0.508885
$902$	−22.4222	−0.746578
$903$	−5.30278	−0.176465
$904$	−10.3028	−0.342665
$905$	0	0
$906$	−10.6056	−0.352346
$907$	−36.6972	−1.21851	−0.609256	−	0.792974i	$-0.708532\pi$
$907$	−36.6972	−1.21851	−0.609256	+	0.792974i	$0.708532\pi$
$908$	−0.788897	−0.0261805
$909$	−29.7250	−0.985915
$910$	0	0
$911$	57.7527	1.91343	0.956717	−	0.291021i	$-0.0939948\pi$
$911$	57.7527	1.91343	0.956717	+	0.291021i	$0.0939948\pi$
$912$	1.39445	0.0461748
$913$	22.4222	0.742067
$914$	10.0000	0.330771
$915$	0	0
$916$	5.90833	0.195217
$917$	−15.0833	−0.498093
$918$	6.27502	0.207106
$919$	35.6333	1.17543	0.587717	−	0.809066i	$-0.300027\pi$
$919$	35.6333	1.17543	0.587717	+	0.809066i	$0.300027\pi$
$920$	0	0
$921$	2.78890	0.0918973
$922$	25.5416	0.841169
$923$	0	0
$924$	4.18335	0.137622
$925$	0	0
$926$	−40.8444	−1.34223
$927$	−42.4222	−1.39333
$928$	1.00000	0.0328266
$929$	−16.6972	−0.547818	−0.273909	−	0.961756i	$-0.588317\pi$
$929$	−16.6972	−0.547818	−0.273909	+	0.961756i	$0.588317\pi$
$930$	0	0
$931$	3.94449	0.129275
$932$	−23.2111	−0.760305
$933$	−57.3583	−1.87783
$934$	37.5416	1.22840
$935$	0	0
$936$	−14.5139	−0.474401
$937$	14.1833	0.463350	0.231675	−	0.972793i	$-0.425579\pi$
$937$	14.1833	0.463350	0.231675	+	0.972793i	$0.425579\pi$
$938$	−6.42221	−0.209692
$939$	0.972244	0.0317280
$940$	0	0
$941$	8.36669	0.272746	0.136373	−	0.990658i	$-0.456455\pi$
$941$	8.36669	0.272746	0.136373	+	0.990658i	$0.456455\pi$
$942$	−19.3944	−0.631905
$943$	14.6056	0.475622
$944$	−0.908327	−0.0295635
$945$	0	0
$946$	−8.60555	−0.279791
$947$	−43.1472	−1.40210	−0.701048	−	0.713115i	$-0.747284\pi$
$947$	−43.1472	−1.40210	−0.701048	+	0.713115i	$0.747284\pi$
$948$	11.3028	0.367097
$949$	15.8444	0.514331
$950$	0	0
$951$	−57.6333	−1.86889
$952$	−2.72498	−0.0883171
$953$	28.4222	0.920686	0.460343	−	0.887741i	$-0.347727\pi$
$953$	28.4222	0.920686	0.460343	+	0.887741i	$0.347727\pi$
$954$	9.00000	0.291386
$955$	0	0
$956$	6.00000	0.194054
$957$	−6.00000	−0.193952
$958$	−11.7250	−0.378817
$959$	−13.1833	−0.425712
$960$	0	0
$961$	31.5416	1.01747
$962$	61.8722	1.99484
$963$	−19.8167	−0.638583
$964$	0.302776	0.00975175
$965$	0	0
$966$	−2.72498	−0.0876748
$967$	−48.6611	−1.56483	−0.782417	−	0.622755i	$-0.786013\pi$
$967$	−48.6611	−1.56483	−0.782417	+	0.622755i	$0.786013\pi$
$968$	−4.21110	−0.135350
$969$	5.44996	0.175078
$970$	0	0
$971$	−25.8167	−0.828496	−0.414248	−	0.910164i	$-0.635955\pi$
$971$	−25.8167	−0.828496	−0.414248	+	0.910164i	$0.635955\pi$
$972$	19.6056	0.628848
$973$	−4.66947	−0.149696
$974$	−33.9361	−1.08738
$975$	0	0
$976$	−3.09167	−0.0989620
$977$	31.8167	1.01790	0.508952	−	0.860795i	$-0.330033\pi$
$977$	31.8167	1.01790	0.508952	+	0.860795i	$0.330033\pi$
$978$	−48.8444	−1.56187
$979$	−38.0555	−1.21626
$980$	0	0
$981$	−17.0278	−0.543654
$982$	−3.63331	−0.115944
$983$	56.0555	1.78789	0.893947	−	0.448173i	$-0.147925\pi$
$983$	56.0555	1.78789	0.893947	+	0.448173i	$0.147925\pi$
$984$	19.8167	0.631732
$985$	0	0
$986$	3.90833	0.124466
$987$	0	0
$988$	3.81665	0.121424
$989$	5.60555	0.178246
$990$	0	0
$991$	34.6056	1.09928	0.549641	−	0.835401i	$-0.314765\pi$
$991$	34.6056	1.09928	0.549641	+	0.835401i	$0.314765\pi$
$992$	−7.90833	−0.251090
$993$	−52.0555	−1.65193
$994$	0	0
$995$	0	0
$996$	−19.8167	−0.627915
$997$	−60.6611	−1.92116	−0.960578	−	0.278012i	$-0.910324\pi$
$997$	−60.6611	−1.92116	−0.960578	+	0.278012i	$0.910324\pi$
$998$	−18.7250	−0.592729
$999$	−15.7611	−0.498660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.m.1.1		2
5.2	odd	4		1450.2.b.g.349.4		4
5.3	odd	4		1450.2.b.g.349.1		4
5.4	even	2		290.2.a.b.1.2	✓	2
15.14	odd	2		2610.2.a.v.1.1		2
20.19	odd	2		2320.2.a.i.1.1		2
40.19	odd	2		9280.2.a.bc.1.2		2
40.29	even	2		9280.2.a.z.1.1		2
145.144	even	2		8410.2.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.b.1.2	✓	2	5.4	even	2
1450.2.a.m.1.1		2	1.1	even	1	trivial
1450.2.b.g.349.1		4	5.3	odd	4
1450.2.b.g.349.4		4	5.2	odd	4
2320.2.a.i.1.1		2	20.19	odd	2
2610.2.a.v.1.1		2	15.14	odd	2
8410.2.a.r.1.1		2	145.144	even	2
9280.2.a.z.1.1		2	40.29	even	2
9280.2.a.bc.1.2		2	40.19	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.30278 q^{3} +1.00000 q^{4} -2.30278 q^{6} -0.697224 q^{7} +1.00000 q^{8} +2.30278 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.30278 q^{3} +1.00000 q^{4} -2.30278 q^{6} -0.697224 q^{7} +1.00000 q^{8} +2.30278 q^{9} +2.60555 q^{11} -2.30278 q^{12} -6.30278 q^{13} -0.697224 q^{14} +1.00000 q^{16} +3.90833 q^{17} +2.30278 q^{18} -0.605551 q^{19} +1.60555 q^{21} +2.60555 q^{22} -1.69722 q^{23} -2.30278 q^{24} -6.30278 q^{26} +1.60555 q^{27} -0.697224 q^{28} +1.00000 q^{29} -7.90833 q^{31} +1.00000 q^{32} -6.00000 q^{33} +3.90833 q^{34} +2.30278 q^{36} -9.81665 q^{37} -0.605551 q^{38} +14.5139 q^{39} -8.60555 q^{41} +1.60555 q^{42} -3.30278 q^{43} +2.60555 q^{44} -1.69722 q^{46} -2.30278 q^{48} -6.51388 q^{49} -9.00000 q^{51} -6.30278 q^{52} +3.90833 q^{53} +1.60555 q^{54} -0.697224 q^{56} +1.39445 q^{57} +1.00000 q^{58} -0.908327 q^{59} -3.09167 q^{61} -7.90833 q^{62} -1.60555 q^{63} +1.00000 q^{64} -6.00000 q^{66} +9.21110 q^{67} +3.90833 q^{68} +3.90833 q^{69} +2.30278 q^{72} -2.51388 q^{73} -9.81665 q^{74} -0.605551 q^{76} -1.81665 q^{77} +14.5139 q^{78} -4.90833 q^{79} -10.6056 q^{81} -8.60555 q^{82} +8.60555 q^{83} +1.60555 q^{84} -3.30278 q^{86} -2.30278 q^{87} +2.60555 q^{88} -14.6056 q^{89} +4.39445 q^{91} -1.69722 q^{92} +18.2111 q^{93} -2.30278 q^{96} -1.09167 q^{97} -6.51388 q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{6} - 5 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^6 - 5 * q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{6} - 5 q^{7} + 2 q^{8} + q^{9} - 2 q^{11} - q^{12} - 9 q^{13} - 5 q^{14} + 2 q^{16} - 3 q^{17} + q^{18} + 6 q^{19} - 4 q^{21} - 2 q^{22} - 7 q^{23} - q^{24} - 9 q^{26} - 4 q^{27} - 5 q^{28} + 2 q^{29} - 5 q^{31} + 2 q^{32} - 12 q^{33} - 3 q^{34} + q^{36} + 2 q^{37} + 6 q^{38} + 11 q^{39} - 10 q^{41} - 4 q^{42} - 3 q^{43} - 2 q^{44} - 7 q^{46} - q^{48} + 5 q^{49} - 18 q^{51} - 9 q^{52} - 3 q^{53} - 4 q^{54} - 5 q^{56} + 10 q^{57} + 2 q^{58} + 9 q^{59} - 17 q^{61} - 5 q^{62} + 4 q^{63} + 2 q^{64} - 12 q^{66} + 4 q^{67} - 3 q^{68} - 3 q^{69} + q^{72} + 13 q^{73} + 2 q^{74} + 6 q^{76} + 18 q^{77} + 11 q^{78} + q^{79} - 14 q^{81} - 10 q^{82} + 10 q^{83} - 4 q^{84} - 3 q^{86} - q^{87} - 2 q^{88} - 22 q^{89} + 16 q^{91} - 7 q^{92} + 22 q^{93} - q^{96} - 13 q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^6 - 5 * q^7 + 2 * q^8 + q^9 - 2 * q^11 - q^12 - 9 * q^13 - 5 * q^14 + 2 * q^16 - 3 * q^17 + q^18 + 6 * q^19 - 4 * q^21 - 2 * q^22 - 7 * q^23 - q^24 - 9 * q^26 - 4 * q^27 - 5 * q^28 + 2 * q^29 - 5 * q^31 + 2 * q^32 - 12 * q^33 - 3 * q^34 + q^36 + 2 * q^37 + 6 * q^38 + 11 * q^39 - 10 * q^41 - 4 * q^42 - 3 * q^43 - 2 * q^44 - 7 * q^46 - q^48 + 5 * q^49 - 18 * q^51 - 9 * q^52 - 3 * q^53 - 4 * q^54 - 5 * q^56 + 10 * q^57 + 2 * q^58 + 9 * q^59 - 17 * q^61 - 5 * q^62 + 4 * q^63 + 2 * q^64 - 12 * q^66 + 4 * q^67 - 3 * q^68 - 3 * q^69 + q^72 + 13 * q^73 + 2 * q^74 + 6 * q^76 + 18 * q^77 + 11 * q^78 + q^79 - 14 * q^81 - 10 * q^82 + 10 * q^83 - 4 * q^84 - 3 * q^86 - q^87 - 2 * q^88 - 22 * q^89 + 16 * q^91 - 7 * q^92 + 22 * q^93 - q^96 - 13 * q^97 + 5 * q^98 + 12 * q^99

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