LMFDB - Embedded newform 1150.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.618034 q^{6} -1.61803 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.618034 q^{6} -1.61803 q^{7} -1.00000 q^{8} -2.61803 q^{9} +3.85410 q^{11} +0.618034 q^{12} -4.09017 q^{13} +1.61803 q^{14} +1.00000 q^{16} +5.09017 q^{17} +2.61803 q^{18} -4.85410 q^{19} -1.00000 q^{21} -3.85410 q^{22} -1.00000 q^{23} -0.618034 q^{24} +4.09017 q^{26} -3.47214 q^{27} -1.61803 q^{28} -4.76393 q^{29} -2.09017 q^{31} -1.00000 q^{32} +2.38197 q^{33} -5.09017 q^{34} -2.61803 q^{36} +2.47214 q^{37} +4.85410 q^{38} -2.52786 q^{39} -12.3262 q^{41} +1.00000 q^{42} +3.85410 q^{44} +1.00000 q^{46} -9.70820 q^{47} +0.618034 q^{48} -4.38197 q^{49} +3.14590 q^{51} -4.09017 q^{52} +8.47214 q^{53} +3.47214 q^{54} +1.61803 q^{56} -3.00000 q^{57} +4.76393 q^{58} -11.7082 q^{59} +6.32624 q^{61} +2.09017 q^{62} +4.23607 q^{63} +1.00000 q^{64} -2.38197 q^{66} -5.52786 q^{67} +5.09017 q^{68} -0.618034 q^{69} +7.09017 q^{71} +2.61803 q^{72} +1.23607 q^{73} -2.47214 q^{74} -4.85410 q^{76} -6.23607 q^{77} +2.52786 q^{78} +10.4721 q^{79} +5.70820 q^{81} +12.3262 q^{82} -10.9443 q^{83} -1.00000 q^{84} -2.94427 q^{87} -3.85410 q^{88} -1.52786 q^{89} +6.61803 q^{91} -1.00000 q^{92} -1.29180 q^{93} +9.70820 q^{94} -0.618034 q^{96} -14.6180 q^{97} +4.38197 q^{98} -10.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} - 3 q^{9} + q^{11} - q^{12} + 3 q^{13} + q^{14} + 2 q^{16} - q^{17} + 3 q^{18} - 3 q^{19} - 2 q^{21} - q^{22} - 2 q^{23} + q^{24} - 3 q^{26} + 2 q^{27} - q^{28} - 14 q^{29} + 7 q^{31} - 2 q^{32} + 7 q^{33} + q^{34} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 9 q^{41} + 2 q^{42} + q^{44} + 2 q^{46} - 6 q^{47} - q^{48} - 11 q^{49} + 13 q^{51} + 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{56} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 3 q^{61} - 7 q^{62} + 4 q^{63} + 2 q^{64} - 7 q^{66} - 20 q^{67} - q^{68} + q^{69} + 3 q^{71} + 3 q^{72} - 2 q^{73} + 4 q^{74} - 3 q^{76} - 8 q^{77} + 14 q^{78} + 12 q^{79} - 2 q^{81} + 9 q^{82} - 4 q^{83} - 2 q^{84} + 12 q^{87} - q^{88} - 12 q^{89} + 11 q^{91} - 2 q^{92} - 16 q^{93} + 6 q^{94} + q^{96} - 27 q^{97} + 11 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 - 3 * q^9 + q^11 - q^12 + 3 * q^13 + q^14 + 2 * q^16 - q^17 + 3 * q^18 - 3 * q^19 - 2 * q^21 - q^22 - 2 * q^23 + q^24 - 3 * q^26 + 2 * q^27 - q^28 - 14 * q^29 + 7 * q^31 - 2 * q^32 + 7 * q^33 + q^34 - 3 * q^36 - 4 * q^37 + 3 * q^38 - 14 * q^39 - 9 * q^41 + 2 * q^42 + q^44 + 2 * q^46 - 6 * q^47 - q^48 - 11 * q^49 + 13 * q^51 + 3 * q^52 + 8 * q^53 - 2 * q^54 + q^56 - 6 * q^57 + 14 * q^58 - 10 * q^59 - 3 * q^61 - 7 * q^62 + 4 * q^63 + 2 * q^64 - 7 * q^66 - 20 * q^67 - q^68 + q^69 + 3 * q^71 + 3 * q^72 - 2 * q^73 + 4 * q^74 - 3 * q^76 - 8 * q^77 + 14 * q^78 + 12 * q^79 - 2 * q^81 + 9 * q^82 - 4 * q^83 - 2 * q^84 + 12 * q^87 - q^88 - 12 * q^89 + 11 * q^91 - 2 * q^92 - 16 * q^93 + 6 * q^94 + q^96 - 27 * q^97 + 11 * q^98 - 9 * 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
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−0.618034	−0.252311
$7$	−1.61803	−0.611559	−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803	−0.611559	−0.305780	+	0.952102i	$0.598917\pi$
$8$	−1.00000	−0.353553
$9$	−2.61803	−0.872678
$10$	0	0
$11$	3.85410	1.16206	0.581028	−	0.813884i	$-0.302651\pi$
$11$	3.85410	1.16206	0.581028	+	0.813884i	$0.302651\pi$
$12$	0.618034	0.178411
$13$	−4.09017	−1.13441	−0.567205	−	0.823577i	$-0.691975\pi$
$13$	−4.09017	−1.13441	−0.567205	+	0.823577i	$0.691975\pi$
$14$	1.61803	0.432438
$15$	0	0
$16$	1.00000	0.250000
$17$	5.09017	1.23455	0.617274	−	0.786748i	$-0.288237\pi$
$17$	5.09017	1.23455	0.617274	+	0.786748i	$0.288237\pi$
$18$	2.61803	0.617077
$19$	−4.85410	−1.11361	−0.556804	−	0.830644i	$-0.687972\pi$
$19$	−4.85410	−1.11361	−0.556804	+	0.830644i	$0.687972\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−3.85410	−0.821697
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.618034	−0.126156
$25$	0	0
$26$	4.09017	0.802148
$27$	−3.47214	−0.668213
$28$	−1.61803	−0.305780
$29$	−4.76393	−0.884640	−0.442320	−	0.896857i	$-0.645844\pi$
$29$	−4.76393	−0.884640	−0.442320	+	0.896857i	$0.645844\pi$
$30$	0	0
$31$	−2.09017	−0.375406	−0.187703	−	0.982226i	$-0.560104\pi$
$31$	−2.09017	−0.375406	−0.187703	+	0.982226i	$0.560104\pi$
$32$	−1.00000	−0.176777
$33$	2.38197	0.414647
$34$	−5.09017	−0.872957
$35$	0	0
$36$	−2.61803	−0.436339
$37$	2.47214	0.406417	0.203208	−	0.979136i	$-0.434863\pi$
$37$	2.47214	0.406417	0.203208	+	0.979136i	$0.434863\pi$
$38$	4.85410	0.787439
$39$	−2.52786	−0.404782
$40$	0	0
$41$	−12.3262	−1.92503	−0.962517	−	0.271220i	$-0.912573\pi$
$41$	−12.3262	−1.92503	−0.962517	+	0.271220i	$0.912573\pi$
$42$	1.00000	0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	3.85410	0.581028
$45$	0	0
$46$	1.00000	0.147442
$47$	−9.70820	−1.41609	−0.708044	−	0.706169i	$-0.750422\pi$
$47$	−9.70820	−1.41609	−0.708044	+	0.706169i	$0.750422\pi$
$48$	0.618034	0.0892055
$49$	−4.38197	−0.625995
$50$	0	0
$51$	3.14590	0.440514
$52$	−4.09017	−0.567205
$53$	8.47214	1.16374	0.581869	−	0.813283i	$-0.302322\pi$
$53$	8.47214	1.16374	0.581869	+	0.813283i	$0.302322\pi$
$54$	3.47214	0.472498
$55$	0	0
$56$	1.61803	0.216219
$57$	−3.00000	−0.397360
$58$	4.76393	0.625535
$59$	−11.7082	−1.52428	−0.762139	−	0.647413i	$-0.775851\pi$
$59$	−11.7082	−1.52428	−0.762139	+	0.647413i	$0.775851\pi$
$60$	0	0
$61$	6.32624	0.809992	0.404996	−	0.914319i	$-0.367273\pi$
$61$	6.32624	0.809992	0.404996	+	0.914319i	$0.367273\pi$
$62$	2.09017	0.265452
$63$	4.23607	0.533694
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.38197	−0.293200
$67$	−5.52786	−0.675336	−0.337668	−	0.941265i	$-0.609638\pi$
$67$	−5.52786	−0.675336	−0.337668	+	0.941265i	$0.609638\pi$
$68$	5.09017	0.617274
$69$	−0.618034	−0.0744025
$70$	0	0
$71$	7.09017	0.841448	0.420724	−	0.907189i	$-0.361776\pi$
$71$	7.09017	0.841448	0.420724	+	0.907189i	$0.361776\pi$
$72$	2.61803	0.308538
$73$	1.23607	0.144671	0.0723354	−	0.997380i	$-0.476955\pi$
$73$	1.23607	0.144671	0.0723354	+	0.997380i	$0.476955\pi$
$74$	−2.47214	−0.287380
$75$	0	0
$76$	−4.85410	−0.556804
$77$	−6.23607	−0.710666
$78$	2.52786	0.286224
$79$	10.4721	1.17821	0.589104	−	0.808057i	$-0.299481\pi$
$79$	10.4721	1.17821	0.589104	+	0.808057i	$0.299481\pi$
$80$	0	0
$81$	5.70820	0.634245
$82$	12.3262	1.36121
$83$	−10.9443	−1.20129	−0.600645	−	0.799516i	$-0.705089\pi$
$83$	−10.9443	−1.20129	−0.600645	+	0.799516i	$0.705089\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	0	0
$87$	−2.94427	−0.315659
$88$	−3.85410	−0.410849
$89$	−1.52786	−0.161953	−0.0809766	−	0.996716i	$-0.525804\pi$
$89$	−1.52786	−0.161953	−0.0809766	+	0.996716i	$0.525804\pi$
$90$	0	0
$91$	6.61803	0.693758
$92$	−1.00000	−0.104257
$93$	−1.29180	−0.133953
$94$	9.70820	1.00132
$95$	0	0
$96$	−0.618034	−0.0630778
$97$	−14.6180	−1.48424	−0.742118	−	0.670269i	$-0.766179\pi$
$97$	−14.6180	−1.48424	−0.742118	+	0.670269i	$0.766179\pi$
$98$	4.38197	0.442645
$99$	−10.0902	−1.01410
$100$	0	0
$101$	−13.7082	−1.36402	−0.682009	−	0.731344i	$-0.738893\pi$
$101$	−13.7082	−1.36402	−0.682009	+	0.731344i	$0.738893\pi$
$102$	−3.14590	−0.311490
$103$	3.56231	0.351004	0.175502	−	0.984479i	$-0.443845\pi$
$103$	3.56231	0.351004	0.175502	+	0.984479i	$0.443845\pi$
$104$	4.09017	0.401074
$105$	0	0
$106$	−8.47214	−0.822887
$107$	4.18034	0.404129	0.202064	−	0.979372i	$-0.435235\pi$
$107$	4.18034	0.404129	0.202064	+	0.979372i	$0.435235\pi$
$108$	−3.47214	−0.334106
$109$	8.56231	0.820120	0.410060	−	0.912059i	$-0.365508\pi$
$109$	8.56231	0.820120	0.410060	+	0.912059i	$0.365508\pi$
$110$	0	0
$111$	1.52786	0.145018
$112$	−1.61803	−0.152890
$113$	−18.9443	−1.78213	−0.891064	−	0.453878i	$-0.850040\pi$
$113$	−18.9443	−1.78213	−0.891064	+	0.453878i	$0.850040\pi$
$114$	3.00000	0.280976
$115$	0	0
$116$	−4.76393	−0.442320
$117$	10.7082	0.989974
$118$	11.7082	1.07783
$119$	−8.23607	−0.754999
$120$	0	0
$121$	3.85410	0.350373
$122$	−6.32624	−0.572751
$123$	−7.61803	−0.686895
$124$	−2.09017	−0.187703
$125$	0	0
$126$	−4.23607	−0.377379
$127$	6.18034	0.548416	0.274208	−	0.961670i	$-0.411584\pi$
$127$	6.18034	0.548416	0.274208	+	0.961670i	$0.411584\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−14.9443	−1.30569	−0.652844	−	0.757493i	$-0.726424\pi$
$131$	−14.9443	−1.30569	−0.652844	+	0.757493i	$0.726424\pi$
$132$	2.38197	0.207324
$133$	7.85410	0.681037
$134$	5.52786	0.477535
$135$	0	0
$136$	−5.09017	−0.436478
$137$	−5.32624	−0.455051	−0.227526	−	0.973772i	$-0.573064\pi$
$137$	−5.32624	−0.455051	−0.227526	+	0.973772i	$0.573064\pi$
$138$	0.618034	0.0526105
$139$	17.2361	1.46194	0.730972	−	0.682407i	$-0.239067\pi$
$139$	17.2361	1.46194	0.730972	+	0.682407i	$0.239067\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	−7.09017	−0.594994
$143$	−15.7639	−1.31825
$144$	−2.61803	−0.218169
$145$	0	0
$146$	−1.23607	−0.102298
$147$	−2.70820	−0.223369
$148$	2.47214	0.203208
$149$	−1.14590	−0.0938756	−0.0469378	−	0.998898i	$-0.514946\pi$
$149$	−1.14590	−0.0938756	−0.0469378	+	0.998898i	$0.514946\pi$
$150$	0	0
$151$	17.5623	1.42920	0.714600	−	0.699533i	$-0.246609\pi$
$151$	17.5623	1.42920	0.714600	+	0.699533i	$0.246609\pi$
$152$	4.85410	0.393720
$153$	−13.3262	−1.07736
$154$	6.23607	0.502517
$155$	0	0
$156$	−2.52786	−0.202391
$157$	−9.70820	−0.774799	−0.387400	−	0.921912i	$-0.626627\pi$
$157$	−9.70820	−0.774799	−0.387400	+	0.921912i	$0.626627\pi$
$158$	−10.4721	−0.833118
$159$	5.23607	0.415247
$160$	0	0
$161$	1.61803	0.127519
$162$	−5.70820	−0.448479
$163$	−3.61803	−0.283386	−0.141693	−	0.989911i	$-0.545255\pi$
$163$	−3.61803	−0.283386	−0.141693	+	0.989911i	$0.545255\pi$
$164$	−12.3262	−0.962517
$165$	0	0
$166$	10.9443	0.849440
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	1.00000	0.0771517
$169$	3.72949	0.286884
$170$	0	0
$171$	12.7082	0.971821
$172$	0	0
$173$	21.5623	1.63935	0.819676	−	0.572828i	$-0.194154\pi$
$173$	21.5623	1.63935	0.819676	+	0.572828i	$0.194154\pi$
$174$	2.94427	0.223205
$175$	0	0
$176$	3.85410	0.290514
$177$	−7.23607	−0.543896
$178$	1.52786	0.114518
$179$	−20.1803	−1.50835	−0.754175	−	0.656674i	$-0.771963\pi$
$179$	−20.1803	−1.50835	−0.754175	+	0.656674i	$0.771963\pi$
$180$	0	0
$181$	−18.8541	−1.40141	−0.700707	−	0.713449i	$-0.747132\pi$
$181$	−18.8541	−1.40141	−0.700707	+	0.713449i	$0.747132\pi$
$182$	−6.61803	−0.490561
$183$	3.90983	0.289023
$184$	1.00000	0.0737210
$185$	0	0
$186$	1.29180	0.0947191
$187$	19.6180	1.43461
$188$	−9.70820	−0.708044
$189$	5.61803	0.408652
$190$	0	0
$191$	−0.291796	−0.0211136	−0.0105568	−	0.999944i	$-0.503360\pi$
$191$	−0.291796	−0.0211136	−0.0105568	+	0.999944i	$0.503360\pi$
$192$	0.618034	0.0446028
$193$	−5.23607	−0.376900	−0.188450	−	0.982083i	$-0.560346\pi$
$193$	−5.23607	−0.376900	−0.188450	+	0.982083i	$0.560346\pi$
$194$	14.6180	1.04951
$195$	0	0
$196$	−4.38197	−0.312998
$197$	2.43769	0.173679	0.0868393	−	0.996222i	$-0.472323\pi$
$197$	2.43769	0.173679	0.0868393	+	0.996222i	$0.472323\pi$
$198$	10.0902	0.717077
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	0	0
$201$	−3.41641	−0.240975
$202$	13.7082	0.964506
$203$	7.70820	0.541010
$204$	3.14590	0.220257
$205$	0	0
$206$	−3.56231	−0.248198
$207$	2.61803	0.181966
$208$	−4.09017	−0.283602
$209$	−18.7082	−1.29407
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	8.47214	0.581869
$213$	4.38197	0.300247
$214$	−4.18034	−0.285762
$215$	0	0
$216$	3.47214	0.236249
$217$	3.38197	0.229583
$218$	−8.56231	−0.579913
$219$	0.763932	0.0516217
$220$	0	0
$221$	−20.8197	−1.40048
$222$	−1.52786	−0.102544
$223$	3.05573	0.204627	0.102313	−	0.994752i	$-0.467376\pi$
$223$	3.05573	0.204627	0.102313	+	0.994752i	$0.467376\pi$
$224$	1.61803	0.108109
$225$	0	0
$226$	18.9443	1.26015
$227$	23.2361	1.54223	0.771116	−	0.636695i	$-0.219699\pi$
$227$	23.2361	1.54223	0.771116	+	0.636695i	$0.219699\pi$
$228$	−3.00000	−0.198680
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	−3.85410	−0.253581
$232$	4.76393	0.312767
$233$	−19.7082	−1.29113	−0.645564	−	0.763706i	$-0.723378\pi$
$233$	−19.7082	−1.29113	−0.645564	+	0.763706i	$0.723378\pi$
$234$	−10.7082	−0.700017
$235$	0	0
$236$	−11.7082	−0.762139
$237$	6.47214	0.420410
$238$	8.23607	0.533865
$239$	24.3607	1.57576	0.787881	−	0.615828i	$-0.211178\pi$
$239$	24.3607	1.57576	0.787881	+	0.615828i	$0.211178\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	−3.85410	−0.247751
$243$	13.9443	0.894525
$244$	6.32624	0.404996
$245$	0	0
$246$	7.61803	0.485708
$247$	19.8541	1.26329
$248$	2.09017	0.132726
$249$	−6.76393	−0.428647
$250$	0	0
$251$	12.8541	0.811344	0.405672	−	0.914019i	$-0.367038\pi$
$251$	12.8541	0.811344	0.405672	+	0.914019i	$0.367038\pi$
$252$	4.23607	0.266847
$253$	−3.85410	−0.242305
$254$	−6.18034	−0.387789
$255$	0	0
$256$	1.00000	0.0625000
$257$	30.1803	1.88260	0.941299	−	0.337574i	$-0.109606\pi$
$257$	30.1803	1.88260	0.941299	+	0.337574i	$0.109606\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	0	0
$261$	12.4721	0.772006
$262$	14.9443	0.923260
$263$	21.7426	1.34071	0.670354	−	0.742041i	$-0.266142\pi$
$263$	21.7426	1.34071	0.670354	+	0.742041i	$0.266142\pi$
$264$	−2.38197	−0.146600
$265$	0	0
$266$	−7.85410	−0.481566
$267$	−0.944272	−0.0577885
$268$	−5.52786	−0.337668
$269$	8.18034	0.498764	0.249382	−	0.968405i	$-0.419773\pi$
$269$	8.18034	0.498764	0.249382	+	0.968405i	$0.419773\pi$
$270$	0	0
$271$	−14.6738	−0.891368	−0.445684	−	0.895190i	$-0.647039\pi$
$271$	−14.6738	−0.891368	−0.445684	+	0.895190i	$0.647039\pi$
$272$	5.09017	0.308637
$273$	4.09017	0.247548
$274$	5.32624	0.321770
$275$	0	0
$276$	−0.618034	−0.0372013
$277$	−2.58359	−0.155233	−0.0776165	−	0.996983i	$-0.524731\pi$
$277$	−2.58359	−0.155233	−0.0776165	+	0.996983i	$0.524731\pi$
$278$	−17.2361	−1.03375
$279$	5.47214	0.327608
$280$	0	0
$281$	27.2361	1.62477	0.812384	−	0.583123i	$-0.198169\pi$
$281$	27.2361	1.62477	0.812384	+	0.583123i	$0.198169\pi$
$282$	6.00000	0.357295
$283$	9.05573	0.538307	0.269154	−	0.963097i	$-0.413256\pi$
$283$	9.05573	0.538307	0.269154	+	0.963097i	$0.413256\pi$
$284$	7.09017	0.420724
$285$	0	0
$286$	15.7639	0.932141
$287$	19.9443	1.17727
$288$	2.61803	0.154269
$289$	8.90983	0.524108
$290$	0	0
$291$	−9.03444	−0.529608
$292$	1.23607	0.0723354
$293$	−15.8885	−0.928219	−0.464109	−	0.885778i	$-0.653626\pi$
$293$	−15.8885	−0.928219	−0.464109	+	0.885778i	$0.653626\pi$
$294$	2.70820	0.157946
$295$	0	0
$296$	−2.47214	−0.143690
$297$	−13.3820	−0.776500
$298$	1.14590	0.0663801
$299$	4.09017	0.236541
$300$	0	0
$301$	0	0
$302$	−17.5623	−1.01060
$303$	−8.47214	−0.486711
$304$	−4.85410	−0.278402
$305$	0	0
$306$	13.3262	0.761810
$307$	−27.4508	−1.56670	−0.783351	−	0.621579i	$-0.786491\pi$
$307$	−27.4508	−1.56670	−0.783351	+	0.621579i	$0.786491\pi$
$308$	−6.23607	−0.355333
$309$	2.20163	0.125246
$310$	0	0
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	2.52786	0.143112
$313$	11.7984	0.666884	0.333442	−	0.942771i	$-0.391790\pi$
$313$	11.7984	0.666884	0.333442	+	0.942771i	$0.391790\pi$
$314$	9.70820	0.547866
$315$	0	0
$316$	10.4721	0.589104
$317$	−0.0901699	−0.00506445	−0.00253222	−	0.999997i	$-0.500806\pi$
$317$	−0.0901699	−0.00506445	−0.00253222	+	0.999997i	$0.500806\pi$
$318$	−5.23607	−0.293624
$319$	−18.3607	−1.02800
$320$	0	0
$321$	2.58359	0.144202
$322$	−1.61803	−0.0901695
$323$	−24.7082	−1.37480
$324$	5.70820	0.317122
$325$	0	0
$326$	3.61803	0.200384
$327$	5.29180	0.292637
$328$	12.3262	0.680603
$329$	15.7082	0.866021
$330$	0	0
$331$	14.7639	0.811499	0.405750	−	0.913984i	$-0.367011\pi$
$331$	14.7639	0.811499	0.405750	+	0.913984i	$0.367011\pi$
$332$	−10.9443	−0.600645
$333$	−6.47214	−0.354671
$334$	−8.00000	−0.437741
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	−29.3262	−1.59750	−0.798751	−	0.601662i	$-0.794506\pi$
$337$	−29.3262	−1.59750	−0.798751	+	0.601662i	$0.794506\pi$
$338$	−3.72949	−0.202858
$339$	−11.7082	−0.635902
$340$	0	0
$341$	−8.05573	−0.436242
$342$	−12.7082	−0.687181
$343$	18.4164	0.994393
$344$	0	0
$345$	0	0
$346$	−21.5623	−1.15920
$347$	8.61803	0.462640	0.231320	−	0.972878i	$-0.425696\pi$
$347$	8.61803	0.462640	0.231320	+	0.972878i	$0.425696\pi$
$348$	−2.94427	−0.157830
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	14.2016	0.758027
$352$	−3.85410	−0.205424
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	7.23607	0.384593
$355$	0	0
$356$	−1.52786	−0.0809766
$357$	−5.09017	−0.269400
$358$	20.1803	1.06656
$359$	−18.3607	−0.969040	−0.484520	−	0.874780i	$-0.661006\pi$
$359$	−18.3607	−0.969040	−0.484520	+	0.874780i	$0.661006\pi$
$360$	0	0
$361$	4.56231	0.240121
$362$	18.8541	0.990950
$363$	2.38197	0.125021
$364$	6.61803	0.346879
$365$	0	0
$366$	−3.90983	−0.204370
$367$	2.47214	0.129044	0.0645222	−	0.997916i	$-0.479448\pi$
$367$	2.47214	0.129044	0.0645222	+	0.997916i	$0.479448\pi$
$368$	−1.00000	−0.0521286
$369$	32.2705	1.67994
$370$	0	0
$371$	−13.7082	−0.711694
$372$	−1.29180	−0.0669765
$373$	2.18034	0.112894	0.0564469	−	0.998406i	$-0.482023\pi$
$373$	2.18034	0.112894	0.0564469	+	0.998406i	$0.482023\pi$
$374$	−19.6180	−1.01442
$375$	0	0
$376$	9.70820	0.500662
$377$	19.4853	1.00354
$378$	−5.61803	−0.288960
$379$	33.4508	1.71825	0.859127	−	0.511762i	$-0.171007\pi$
$379$	33.4508	1.71825	0.859127	+	0.511762i	$0.171007\pi$
$380$	0	0
$381$	3.81966	0.195687
$382$	0.291796	0.0149296
$383$	−17.8885	−0.914062	−0.457031	−	0.889451i	$-0.651087\pi$
$383$	−17.8885	−0.914062	−0.457031	+	0.889451i	$0.651087\pi$
$384$	−0.618034	−0.0315389
$385$	0	0
$386$	5.23607	0.266509
$387$	0	0
$388$	−14.6180	−0.742118
$389$	5.67376	0.287671	0.143836	−	0.989602i	$-0.454056\pi$
$389$	5.67376	0.287671	0.143836	+	0.989602i	$0.454056\pi$
$390$	0	0
$391$	−5.09017	−0.257421
$392$	4.38197	0.221323
$393$	−9.23607	−0.465898
$394$	−2.43769	−0.122809
$395$	0	0
$396$	−10.0902	−0.507050
$397$	8.32624	0.417882	0.208941	−	0.977928i	$-0.432998\pi$
$397$	8.32624	0.417882	0.208941	+	0.977928i	$0.432998\pi$
$398$	−2.00000	−0.100251
$399$	4.85410	0.243009
$400$	0	0
$401$	11.7082	0.584680	0.292340	−	0.956314i	$-0.405566\pi$
$401$	11.7082	0.584680	0.292340	+	0.956314i	$0.405566\pi$
$402$	3.41641	0.170395
$403$	8.54915	0.425864
$404$	−13.7082	−0.682009
$405$	0	0
$406$	−7.70820	−0.382552
$407$	9.52786	0.472279
$408$	−3.14590	−0.155745
$409$	21.2148	1.04900	0.524502	−	0.851409i	$-0.324252\pi$
$409$	21.2148	1.04900	0.524502	+	0.851409i	$0.324252\pi$
$410$	0	0
$411$	−3.29180	−0.162372
$412$	3.56231	0.175502
$413$	18.9443	0.932187
$414$	−2.61803	−0.128669
$415$	0	0
$416$	4.09017	0.200537
$417$	10.6525	0.521654
$418$	18.7082	0.915048
$419$	5.52786	0.270054	0.135027	−	0.990842i	$-0.456888\pi$
$419$	5.52786	0.270054	0.135027	+	0.990842i	$0.456888\pi$
$420$	0	0
$421$	−28.7426	−1.40083	−0.700415	−	0.713735i	$-0.747002\pi$
$421$	−28.7426	−1.40083	−0.700415	+	0.713735i	$0.747002\pi$
$422$	−14.0000	−0.681509
$423$	25.4164	1.23579
$424$	−8.47214	−0.411443
$425$	0	0
$426$	−4.38197	−0.212307
$427$	−10.2361	−0.495358
$428$	4.18034	0.202064
$429$	−9.74265	−0.470379
$430$	0	0
$431$	34.6525	1.66915	0.834576	−	0.550894i	$-0.185713\pi$
$431$	34.6525	1.66915	0.834576	+	0.550894i	$0.185713\pi$
$432$	−3.47214	−0.167053
$433$	29.5066	1.41800	0.708998	−	0.705211i	$-0.249148\pi$
$433$	29.5066	1.41800	0.708998	+	0.705211i	$0.249148\pi$
$434$	−3.38197	−0.162340
$435$	0	0
$436$	8.56231	0.410060
$437$	4.85410	0.232203
$438$	−0.763932	−0.0365021
$439$	−15.6180	−0.745408	−0.372704	−	0.927950i	$-0.621569\pi$
$439$	−15.6180	−0.745408	−0.372704	+	0.927950i	$0.621569\pi$
$440$	0	0
$441$	11.4721	0.546292
$442$	20.8197	0.990290
$443$	−13.9098	−0.660876	−0.330438	−	0.943828i	$-0.607196\pi$
$443$	−13.9098	−0.660876	−0.330438	+	0.943828i	$0.607196\pi$
$444$	1.52786	0.0725092
$445$	0	0
$446$	−3.05573	−0.144693
$447$	−0.708204	−0.0334969
$448$	−1.61803	−0.0764449
$449$	18.5623	0.876009	0.438005	−	0.898973i	$-0.355685\pi$
$449$	18.5623	0.876009	0.438005	+	0.898973i	$0.355685\pi$
$450$	0	0
$451$	−47.5066	−2.23700
$452$	−18.9443	−0.891064
$453$	10.8541	0.509970
$454$	−23.2361	−1.09052
$455$	0	0
$456$	3.00000	0.140488
$457$	−33.7771	−1.58003	−0.790013	−	0.613090i	$-0.789926\pi$
$457$	−33.7771	−1.58003	−0.790013	+	0.613090i	$0.789926\pi$
$458$	−10.0000	−0.467269
$459$	−17.6738	−0.824941
$460$	0	0
$461$	−34.7639	−1.61912	−0.809559	−	0.587039i	$-0.800294\pi$
$461$	−34.7639	−1.61912	−0.809559	+	0.587039i	$0.800294\pi$
$462$	3.85410	0.179309
$463$	−2.00000	−0.0929479	−0.0464739	−	0.998920i	$-0.514798\pi$
$463$	−2.00000	−0.0929479	−0.0464739	+	0.998920i	$0.514798\pi$
$464$	−4.76393	−0.221160
$465$	0	0
$466$	19.7082	0.912965
$467$	−23.1246	−1.07008	−0.535040	−	0.844827i	$-0.679703\pi$
$467$	−23.1246	−1.07008	−0.535040	+	0.844827i	$0.679703\pi$
$468$	10.7082	0.494987
$469$	8.94427	0.413008
$470$	0	0
$471$	−6.00000	−0.276465
$472$	11.7082	0.538914
$473$	0	0
$474$	−6.47214	−0.297275
$475$	0	0
$476$	−8.23607	−0.377500
$477$	−22.1803	−1.01557
$478$	−24.3607	−1.11423
$479$	3.88854	0.177672	0.0888361	−	0.996046i	$-0.471685\pi$
$479$	3.88854	0.177672	0.0888361	+	0.996046i	$0.471685\pi$
$480$	0	0
$481$	−10.1115	−0.461043
$482$	0	0
$483$	1.00000	0.0455016
$484$	3.85410	0.175186
$485$	0	0
$486$	−13.9443	−0.632525
$487$	42.1803	1.91137	0.955687	−	0.294385i	$-0.0951149\pi$
$487$	42.1803	1.91137	0.955687	+	0.294385i	$0.0951149\pi$
$488$	−6.32624	−0.286375
$489$	−2.23607	−0.101118
$490$	0	0
$491$	−16.1803	−0.730209	−0.365104	−	0.930967i	$-0.618967\pi$
$491$	−16.1803	−0.730209	−0.365104	+	0.930967i	$0.618967\pi$
$492$	−7.61803	−0.343447
$493$	−24.2492	−1.09213
$494$	−19.8541	−0.893278
$495$	0	0
$496$	−2.09017	−0.0938514
$497$	−11.4721	−0.514596
$498$	6.76393	0.303099
$499$	−32.3607	−1.44866	−0.724331	−	0.689452i	$-0.757851\pi$
$499$	−32.3607	−1.44866	−0.724331	+	0.689452i	$0.757851\pi$
$500$	0	0
$501$	4.94427	0.220894
$502$	−12.8541	−0.573707
$503$	−20.6738	−0.921797	−0.460899	−	0.887453i	$-0.652473\pi$
$503$	−20.6738	−0.921797	−0.460899	+	0.887453i	$0.652473\pi$
$504$	−4.23607	−0.188689
$505$	0	0
$506$	3.85410	0.171336
$507$	2.30495	0.102366
$508$	6.18034	0.274208
$509$	5.34752	0.237025	0.118512	−	0.992953i	$-0.462187\pi$
$509$	5.34752	0.237025	0.118512	+	0.992953i	$0.462187\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	−1.00000	−0.0441942
$513$	16.8541	0.744127
$514$	−30.1803	−1.33120
$515$	0	0
$516$	0	0
$517$	−37.4164	−1.64557
$518$	4.00000	0.175750
$519$	13.3262	0.584957
$520$	0	0
$521$	−24.4721	−1.07214	−0.536072	−	0.844172i	$-0.680092\pi$
$521$	−24.4721	−1.07214	−0.536072	+	0.844172i	$0.680092\pi$
$522$	−12.4721	−0.545891
$523$	26.0000	1.13690	0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000	1.13690	0.568450	+	0.822718i	$0.307543\pi$
$524$	−14.9443	−0.652844
$525$	0	0
$526$	−21.7426	−0.948024
$527$	−10.6393	−0.463456
$528$	2.38197	0.103662
$529$	1.00000	0.0434783
$530$	0	0
$531$	30.6525	1.33020
$532$	7.85410	0.340519
$533$	50.4164	2.18378
$534$	0.944272	0.0408626
$535$	0	0
$536$	5.52786	0.238767
$537$	−12.4721	−0.538212
$538$	−8.18034	−0.352679
$539$	−16.8885	−0.727441
$540$	0	0
$541$	−30.8328	−1.32561	−0.662803	−	0.748794i	$-0.730633\pi$
$541$	−30.8328	−1.32561	−0.662803	+	0.748794i	$0.730633\pi$
$542$	14.6738	0.630292
$543$	−11.6525	−0.500056
$544$	−5.09017	−0.218239
$545$	0	0
$546$	−4.09017	−0.175043
$547$	36.9230	1.57871	0.789356	−	0.613935i	$-0.210414\pi$
$547$	36.9230	1.57871	0.789356	+	0.613935i	$0.210414\pi$
$548$	−5.32624	−0.227526
$549$	−16.5623	−0.706862
$550$	0	0
$551$	23.1246	0.985142
$552$	0.618034	0.0263053
$553$	−16.9443	−0.720544
$554$	2.58359	0.109766
$555$	0	0
$556$	17.2361	0.730972
$557$	−30.8328	−1.30643	−0.653214	−	0.757173i	$-0.726580\pi$
$557$	−30.8328	−1.30643	−0.653214	+	0.757173i	$0.726580\pi$
$558$	−5.47214	−0.231654
$559$	0	0
$560$	0	0
$561$	12.1246	0.511902
$562$	−27.2361	−1.14888
$563$	−21.8885	−0.922492	−0.461246	−	0.887272i	$-0.652597\pi$
$563$	−21.8885	−0.922492	−0.461246	+	0.887272i	$0.652597\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	−9.05573	−0.380641
$567$	−9.23607	−0.387878
$568$	−7.09017	−0.297497
$569$	−2.00000	−0.0838444	−0.0419222	−	0.999121i	$-0.513348\pi$
$569$	−2.00000	−0.0838444	−0.0419222	+	0.999121i	$0.513348\pi$
$570$	0	0
$571$	−30.9787	−1.29642	−0.648209	−	0.761462i	$-0.724482\pi$
$571$	−30.9787	−1.29642	−0.648209	+	0.761462i	$0.724482\pi$
$572$	−15.7639	−0.659123
$573$	−0.180340	−0.00753381
$574$	−19.9443	−0.832458
$575$	0	0
$576$	−2.61803	−0.109085
$577$	12.4721	0.519222	0.259611	−	0.965713i	$-0.416406\pi$
$577$	12.4721	0.519222	0.259611	+	0.965713i	$0.416406\pi$
$578$	−8.90983	−0.370600
$579$	−3.23607	−0.134486
$580$	0	0
$581$	17.7082	0.734660
$582$	9.03444	0.374490
$583$	32.6525	1.35233
$584$	−1.23607	−0.0511489
$585$	0	0
$586$	15.8885	0.656350
$587$	−11.3820	−0.469784	−0.234892	−	0.972021i	$-0.575474\pi$
$587$	−11.3820	−0.469784	−0.234892	+	0.972021i	$0.575474\pi$
$588$	−2.70820	−0.111684
$589$	10.1459	0.418054
$590$	0	0
$591$	1.50658	0.0619723
$592$	2.47214	0.101604
$593$	−34.7639	−1.42758	−0.713792	−	0.700358i	$-0.753024\pi$
$593$	−34.7639	−1.42758	−0.713792	+	0.700358i	$0.753024\pi$
$594$	13.3820	0.549069
$595$	0	0
$596$	−1.14590	−0.0469378
$597$	1.23607	0.0505889
$598$	−4.09017	−0.167259
$599$	−20.6180	−0.842430	−0.421215	−	0.906961i	$-0.638396\pi$
$599$	−20.6180	−0.842430	−0.421215	+	0.906961i	$0.638396\pi$
$600$	0	0
$601$	0.270510	0.0110343	0.00551716	−	0.999985i	$-0.498244\pi$
$601$	0.270510	0.0110343	0.00551716	+	0.999985i	$0.498244\pi$
$602$	0	0
$603$	14.4721	0.589351
$604$	17.5623	0.714600
$605$	0	0
$606$	8.47214	0.344157
$607$	−17.5279	−0.711434	−0.355717	−	0.934594i	$-0.615763\pi$
$607$	−17.5279	−0.711434	−0.355717	+	0.934594i	$0.615763\pi$
$608$	4.85410	0.196860
$609$	4.76393	0.193044
$610$	0	0
$611$	39.7082	1.60642
$612$	−13.3262	−0.538681
$613$	43.3050	1.74907	0.874535	−	0.484962i	$-0.161167\pi$
$613$	43.3050	1.74907	0.874535	+	0.484962i	$0.161167\pi$
$614$	27.4508	1.10783
$615$	0	0
$616$	6.23607	0.251258
$617$	−22.9098	−0.922315	−0.461158	−	0.887318i	$-0.652566\pi$
$617$	−22.9098	−0.922315	−0.461158	+	0.887318i	$0.652566\pi$
$618$	−2.20163	−0.0885624
$619$	21.7984	0.876151	0.438075	−	0.898938i	$-0.355660\pi$
$619$	21.7984	0.876151	0.438075	+	0.898938i	$0.355660\pi$
$620$	0	0
$621$	3.47214	0.139332
$622$	−4.00000	−0.160385
$623$	2.47214	0.0990440
$624$	−2.52786	−0.101196
$625$	0	0
$626$	−11.7984	−0.471558
$627$	−11.5623	−0.461754
$628$	−9.70820	−0.387400
$629$	12.5836	0.501741
$630$	0	0
$631$	−16.0689	−0.639692	−0.319846	−	0.947470i	$-0.603631\pi$
$631$	−16.0689	−0.639692	−0.319846	+	0.947470i	$0.603631\pi$
$632$	−10.4721	−0.416559
$633$	8.65248	0.343905
$634$	0.0901699	0.00358111
$635$	0	0
$636$	5.23607	0.207624
$637$	17.9230	0.710135
$638$	18.3607	0.726906
$639$	−18.5623	−0.734313
$640$	0	0
$641$	−44.3607	−1.75214	−0.876071	−	0.482183i	$-0.839844\pi$
$641$	−44.3607	−1.75214	−0.876071	+	0.482183i	$0.839844\pi$
$642$	−2.58359	−0.101966
$643$	21.7082	0.856088	0.428044	−	0.903758i	$-0.359203\pi$
$643$	21.7082	0.856088	0.428044	+	0.903758i	$0.359203\pi$
$644$	1.61803	0.0637595
$645$	0	0
$646$	24.7082	0.972131
$647$	−44.2492	−1.73962	−0.869808	−	0.493390i	$-0.835758\pi$
$647$	−44.2492	−1.73962	−0.869808	+	0.493390i	$0.835758\pi$
$648$	−5.70820	−0.224239
$649$	−45.1246	−1.77130
$650$	0	0
$651$	2.09017	0.0819202
$652$	−3.61803	−0.141693
$653$	−21.0344	−0.823141	−0.411571	−	0.911378i	$-0.635020\pi$
$653$	−21.0344	−0.823141	−0.411571	+	0.911378i	$0.635020\pi$
$654$	−5.29180	−0.206926
$655$	0	0
$656$	−12.3262	−0.481259
$657$	−3.23607	−0.126251
$658$	−15.7082	−0.612370
$659$	34.2492	1.33416	0.667080	−	0.744986i	$-0.267544\pi$
$659$	34.2492	1.33416	0.667080	+	0.744986i	$0.267544\pi$
$660$	0	0
$661$	34.3262	1.33514	0.667568	−	0.744549i	$-0.267335\pi$
$661$	34.3262	1.33514	0.667568	+	0.744549i	$0.267335\pi$
$662$	−14.7639	−0.573817
$663$	−12.8673	−0.499723
$664$	10.9443	0.424720
$665$	0	0
$666$	6.47214	0.250790
$667$	4.76393	0.184460
$668$	8.00000	0.309529
$669$	1.88854	0.0730153
$670$	0	0
$671$	24.3820	0.941255
$672$	1.00000	0.0385758
$673$	−6.94427	−0.267682	−0.133841	−	0.991003i	$-0.542731\pi$
$673$	−6.94427	−0.267682	−0.133841	+	0.991003i	$0.542731\pi$
$674$	29.3262	1.12960
$675$	0	0
$676$	3.72949	0.143442
$677$	33.0557	1.27043	0.635217	−	0.772333i	$-0.280910\pi$
$677$	33.0557	1.27043	0.635217	+	0.772333i	$0.280910\pi$
$678$	11.7082	0.449651
$679$	23.6525	0.907699
$680$	0	0
$681$	14.3607	0.550302
$682$	8.05573	0.308470
$683$	11.4377	0.437651	0.218826	−	0.975764i	$-0.429777\pi$
$683$	11.4377	0.437651	0.218826	+	0.975764i	$0.429777\pi$
$684$	12.7082	0.485910
$685$	0	0
$686$	−18.4164	−0.703142
$687$	6.18034	0.235795
$688$	0	0
$689$	−34.6525	−1.32015
$690$	0	0
$691$	−24.7639	−0.942064	−0.471032	−	0.882116i	$-0.656118\pi$
$691$	−24.7639	−0.942064	−0.471032	+	0.882116i	$0.656118\pi$
$692$	21.5623	0.819676
$693$	16.3262	0.620182
$694$	−8.61803	−0.327136
$695$	0	0
$696$	2.94427	0.111602
$697$	−62.7426	−2.37655
$698$	2.00000	0.0757011
$699$	−12.1803	−0.460703
$700$	0	0
$701$	−48.3394	−1.82575	−0.912877	−	0.408235i	$-0.866144\pi$
$701$	−48.3394	−1.82575	−0.912877	+	0.408235i	$0.866144\pi$
$702$	−14.2016	−0.536006
$703$	−12.0000	−0.452589
$704$	3.85410	0.145257
$705$	0	0
$706$	24.0000	0.903252
$707$	22.1803	0.834178
$708$	−7.23607	−0.271948
$709$	−14.9098	−0.559950	−0.279975	−	0.960007i	$-0.590326\pi$
$709$	−14.9098	−0.559950	−0.279975	+	0.960007i	$0.590326\pi$
$710$	0	0
$711$	−27.4164	−1.02820
$712$	1.52786	0.0572591
$713$	2.09017	0.0782775
$714$	5.09017	0.190495
$715$	0	0
$716$	−20.1803	−0.754175
$717$	15.0557	0.562266
$718$	18.3607	0.685214
$719$	1.72949	0.0644991	0.0322495	−	0.999480i	$-0.489733\pi$
$719$	1.72949	0.0644991	0.0322495	+	0.999480i	$0.489733\pi$
$720$	0	0
$721$	−5.76393	−0.214660
$722$	−4.56231	−0.169791
$723$	0	0
$724$	−18.8541	−0.700707
$725$	0	0
$726$	−2.38197	−0.0884031
$727$	−52.7984	−1.95818	−0.979092	−	0.203420i	$-0.934794\pi$
$727$	−52.7984	−1.95818	−0.979092	+	0.203420i	$0.934794\pi$
$728$	−6.61803	−0.245281
$729$	−8.50658	−0.315058
$730$	0	0
$731$	0	0
$732$	3.90983	0.144511
$733$	2.58359	0.0954272	0.0477136	−	0.998861i	$-0.484807\pi$
$733$	2.58359	0.0954272	0.0477136	+	0.998861i	$0.484807\pi$
$734$	−2.47214	−0.0912482
$735$	0	0
$736$	1.00000	0.0368605
$737$	−21.3050	−0.784778
$738$	−32.2705	−1.18789
$739$	21.8885	0.805183	0.402592	−	0.915380i	$-0.368110\pi$
$739$	21.8885	0.805183	0.402592	+	0.915380i	$0.368110\pi$
$740$	0	0
$741$	12.2705	0.450768
$742$	13.7082	0.503244
$743$	44.6312	1.63736	0.818680	−	0.574250i	$-0.194706\pi$
$743$	44.6312	1.63736	0.818680	+	0.574250i	$0.194706\pi$
$744$	1.29180	0.0473595
$745$	0	0
$746$	−2.18034	−0.0798279
$747$	28.6525	1.04834
$748$	19.6180	0.717306
$749$	−6.76393	−0.247149
$750$	0	0
$751$	29.0132	1.05871	0.529353	−	0.848402i	$-0.322435\pi$
$751$	29.0132	1.05871	0.529353	+	0.848402i	$0.322435\pi$
$752$	−9.70820	−0.354022
$753$	7.94427	0.289505
$754$	−19.4853	−0.709612
$755$	0	0
$756$	5.61803	0.204326
$757$	−17.8885	−0.650170	−0.325085	−	0.945685i	$-0.605393\pi$
$757$	−17.8885	−0.650170	−0.325085	+	0.945685i	$0.605393\pi$
$758$	−33.4508	−1.21499
$759$	−2.38197	−0.0864599
$760$	0	0
$761$	−35.8673	−1.30019	−0.650094	−	0.759854i	$-0.725270\pi$
$761$	−35.8673	−1.30019	−0.650094	+	0.759854i	$0.725270\pi$
$762$	−3.81966	−0.138372
$763$	−13.8541	−0.501552
$764$	−0.291796	−0.0105568
$765$	0	0
$766$	17.8885	0.646339
$767$	47.8885	1.72916
$768$	0.618034	0.0223014
$769$	−33.4164	−1.20503	−0.602513	−	0.798109i	$-0.705834\pi$
$769$	−33.4164	−1.20503	−0.602513	+	0.798109i	$0.705834\pi$
$770$	0	0
$771$	18.6525	0.671753
$772$	−5.23607	−0.188450
$773$	−11.0557	−0.397647	−0.198823	−	0.980035i	$-0.563712\pi$
$773$	−11.0557	−0.397647	−0.198823	+	0.980035i	$0.563712\pi$
$774$	0	0
$775$	0	0
$776$	14.6180	0.524757
$777$	−2.47214	−0.0886874
$778$	−5.67376	−0.203414
$779$	59.8328	2.14373
$780$	0	0
$781$	27.3262	0.977810
$782$	5.09017	0.182024
$783$	16.5410	0.591128
$784$	−4.38197	−0.156499
$785$	0	0
$786$	9.23607	0.329440
$787$	43.1246	1.53723	0.768613	−	0.639714i	$-0.220947\pi$
$787$	43.1246	1.53723	0.768613	+	0.639714i	$0.220947\pi$
$788$	2.43769	0.0868393
$789$	13.4377	0.478395
$790$	0	0
$791$	30.6525	1.08988
$792$	10.0902	0.358539
$793$	−25.8754	−0.918862
$794$	−8.32624	−0.295487
$795$	0	0
$796$	2.00000	0.0708881
$797$	−0.291796	−0.0103359	−0.00516797	−	0.999987i	$-0.501645\pi$
$797$	−0.291796	−0.0103359	−0.00516797	+	0.999987i	$0.501645\pi$
$798$	−4.85410	−0.171833
$799$	−49.4164	−1.74823
$800$	0	0
$801$	4.00000	0.141333
$802$	−11.7082	−0.413431
$803$	4.76393	0.168116
$804$	−3.41641	−0.120487
$805$	0	0
$806$	−8.54915	−0.301131
$807$	5.05573	0.177970
$808$	13.7082	0.482253
$809$	−4.25735	−0.149681	−0.0748403	−	0.997196i	$-0.523845\pi$
$809$	−4.25735	−0.149681	−0.0748403	+	0.997196i	$0.523845\pi$
$810$	0	0
$811$	44.1803	1.55138	0.775691	−	0.631113i	$-0.217402\pi$
$811$	44.1803	1.55138	0.775691	+	0.631113i	$0.217402\pi$
$812$	7.70820	0.270505
$813$	−9.06888	−0.318060
$814$	−9.52786	−0.333951
$815$	0	0
$816$	3.14590	0.110128
$817$	0	0
$818$	−21.2148	−0.741757
$819$	−17.3262	−0.605428
$820$	0	0
$821$	−50.9443	−1.77797	−0.888984	−	0.457939i	$-0.848588\pi$
$821$	−50.9443	−1.77797	−0.888984	+	0.457939i	$0.848588\pi$
$822$	3.29180	0.114815
$823$	1.41641	0.0493729	0.0246864	−	0.999695i	$-0.492141\pi$
$823$	1.41641	0.0493729	0.0246864	+	0.999695i	$0.492141\pi$
$824$	−3.56231	−0.124099
$825$	0	0
$826$	−18.9443	−0.659156
$827$	−8.29180	−0.288334	−0.144167	−	0.989553i	$-0.546050\pi$
$827$	−8.29180	−0.288334	−0.144167	+	0.989553i	$0.546050\pi$
$828$	2.61803	0.0909830
$829$	1.05573	0.0366670	0.0183335	−	0.999832i	$-0.494164\pi$
$829$	1.05573	0.0366670	0.0183335	+	0.999832i	$0.494164\pi$
$830$	0	0
$831$	−1.59675	−0.0553906
$832$	−4.09017	−0.141801
$833$	−22.3050	−0.772821
$834$	−10.6525	−0.368865
$835$	0	0
$836$	−18.7082	−0.647037
$837$	7.25735	0.250851
$838$	−5.52786	−0.190957
$839$	−43.0132	−1.48498	−0.742490	−	0.669858i	$-0.766355\pi$
$839$	−43.0132	−1.48498	−0.742490	+	0.669858i	$0.766355\pi$
$840$	0	0
$841$	−6.30495	−0.217412
$842$	28.7426	0.990537
$843$	16.8328	0.579753
$844$	14.0000	0.481900
$845$	0	0
$846$	−25.4164	−0.873834
$847$	−6.23607	−0.214274
$848$	8.47214	0.290934
$849$	5.59675	0.192080
$850$	0	0
$851$	−2.47214	−0.0847437
$852$	4.38197	0.150124
$853$	−13.7984	−0.472447	−0.236224	−	0.971699i	$-0.575910\pi$
$853$	−13.7984	−0.472447	−0.236224	+	0.971699i	$0.575910\pi$
$854$	10.2361	0.350271
$855$	0	0
$856$	−4.18034	−0.142881
$857$	33.4164	1.14148	0.570741	−	0.821130i	$-0.306656\pi$
$857$	33.4164	1.14148	0.570741	+	0.821130i	$0.306656\pi$
$858$	9.74265	0.332608
$859$	34.0689	1.16242	0.581208	−	0.813755i	$-0.302580\pi$
$859$	34.0689	1.16242	0.581208	+	0.813755i	$0.302580\pi$
$860$	0	0
$861$	12.3262	0.420077
$862$	−34.6525	−1.18027
$863$	−37.2361	−1.26753	−0.633765	−	0.773525i	$-0.718491\pi$
$863$	−37.2361	−1.26753	−0.633765	+	0.773525i	$0.718491\pi$
$864$	3.47214	0.118124
$865$	0	0
$866$	−29.5066	−1.00267
$867$	5.50658	0.187013
$868$	3.38197	0.114791
$869$	40.3607	1.36914
$870$	0	0
$871$	22.6099	0.766107
$872$	−8.56231	−0.289956
$873$	38.2705	1.29526
$874$	−4.85410	−0.164192
$875$	0	0
$876$	0.763932	0.0258109
$877$	23.7426	0.801732	0.400866	−	0.916137i	$-0.368709\pi$
$877$	23.7426	0.801732	0.400866	+	0.916137i	$0.368709\pi$
$878$	15.6180	0.527083
$879$	−9.81966	−0.331209
$880$	0	0
$881$	35.4164	1.19321	0.596605	−	0.802535i	$-0.296516\pi$
$881$	35.4164	1.19321	0.596605	+	0.802535i	$0.296516\pi$
$882$	−11.4721	−0.386287
$883$	4.56231	0.153534	0.0767669	−	0.997049i	$-0.475540\pi$
$883$	4.56231	0.153534	0.0767669	+	0.997049i	$0.475540\pi$
$884$	−20.8197	−0.700241
$885$	0	0
$886$	13.9098	0.467310
$887$	58.8328	1.97541	0.987706	−	0.156321i	$-0.0499634\pi$
$887$	58.8328	1.97541	0.987706	+	0.156321i	$0.0499634\pi$
$888$	−1.52786	−0.0512718
$889$	−10.0000	−0.335389
$890$	0	0
$891$	22.0000	0.737028
$892$	3.05573	0.102313
$893$	47.1246	1.57697
$894$	0.708204	0.0236859
$895$	0	0
$896$	1.61803	0.0540547
$897$	2.52786	0.0844029
$898$	−18.5623	−0.619432
$899$	9.95743	0.332099
$900$	0	0
$901$	43.1246	1.43669
$902$	47.5066	1.58180
$903$	0	0
$904$	18.9443	0.630077
$905$	0	0
$906$	−10.8541	−0.360603
$907$	33.1246	1.09988	0.549942	−	0.835203i	$-0.314650\pi$
$907$	33.1246	1.09988	0.549942	+	0.835203i	$0.314650\pi$
$908$	23.2361	0.771116
$909$	35.8885	1.19035
$910$	0	0
$911$	−22.0689	−0.731175	−0.365587	−	0.930777i	$-0.619132\pi$
$911$	−22.0689	−0.731175	−0.365587	+	0.930777i	$0.619132\pi$
$912$	−3.00000	−0.0993399
$913$	−42.1803	−1.39597
$914$	33.7771	1.11725
$915$	0	0
$916$	10.0000	0.330409
$917$	24.1803	0.798505
$918$	17.6738	0.583321
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	0	0
$921$	−16.9656	−0.559034
$922$	34.7639	1.14489
$923$	−29.0000	−0.954547
$924$	−3.85410	−0.126791
$925$	0	0
$926$	2.00000	0.0657241
$927$	−9.32624	−0.306314
$928$	4.76393	0.156384
$929$	−12.4721	−0.409198	−0.204599	−	0.978846i	$-0.565589\pi$
$929$	−12.4721	−0.409198	−0.204599	+	0.978846i	$0.565589\pi$
$930$	0	0
$931$	21.2705	0.697113
$932$	−19.7082	−0.645564
$933$	2.47214	0.0809341
$934$	23.1246	0.756660
$935$	0	0
$936$	−10.7082	−0.350009
$937$	12.2016	0.398610	0.199305	−	0.979938i	$-0.436132\pi$
$937$	12.2016	0.398610	0.199305	+	0.979938i	$0.436132\pi$
$938$	−8.94427	−0.292041
$939$	7.29180	0.237959
$940$	0	0
$941$	−60.5066	−1.97246	−0.986229	−	0.165385i	$-0.947113\pi$
$941$	−60.5066	−1.97246	−0.986229	+	0.165385i	$0.947113\pi$
$942$	6.00000	0.195491
$943$	12.3262	0.401398
$944$	−11.7082	−0.381070
$945$	0	0
$946$	0	0
$947$	−5.68692	−0.184800	−0.0924000	−	0.995722i	$-0.529454\pi$
$947$	−5.68692	−0.184800	−0.0924000	+	0.995722i	$0.529454\pi$
$948$	6.47214	0.210205
$949$	−5.05573	−0.164116
$950$	0	0
$951$	−0.0557281	−0.00180711
$952$	8.23607	0.266932
$953$	20.7984	0.673725	0.336863	−	0.941554i	$-0.390634\pi$
$953$	20.7984	0.673725	0.336863	+	0.941554i	$0.390634\pi$
$954$	22.1803	0.718115
$955$	0	0
$956$	24.3607	0.787881
$957$	−11.3475	−0.366813
$958$	−3.88854	−0.125633
$959$	8.61803	0.278291
$960$	0	0
$961$	−26.6312	−0.859071
$962$	10.1115	0.326006
$963$	−10.9443	−0.352674
$964$	0	0
$965$	0	0
$966$	−1.00000	−0.0321745
$967$	−50.5410	−1.62529	−0.812645	−	0.582759i	$-0.801973\pi$
$967$	−50.5410	−1.62529	−0.812645	+	0.582759i	$0.801973\pi$
$968$	−3.85410	−0.123876
$969$	−15.2705	−0.490559
$970$	0	0
$971$	0.729490	0.0234105	0.0117052	−	0.999931i	$-0.496274\pi$
$971$	0.729490	0.0234105	0.0117052	+	0.999931i	$0.496274\pi$
$972$	13.9443	0.447263
$973$	−27.8885	−0.894066
$974$	−42.1803	−1.35155
$975$	0	0
$976$	6.32624	0.202498
$977$	3.43769	0.109982	0.0549908	−	0.998487i	$-0.482487\pi$
$977$	3.43769	0.109982	0.0549908	+	0.998487i	$0.482487\pi$
$978$	2.23607	0.0715016
$979$	−5.88854	−0.188199
$980$	0	0
$981$	−22.4164	−0.715701
$982$	16.1803	0.516335
$983$	−19.2705	−0.614634	−0.307317	−	0.951607i	$-0.599431\pi$
$983$	−19.2705	−0.614634	−0.307317	+	0.951607i	$0.599431\pi$
$984$	7.61803	0.242854
$985$	0	0
$986$	24.2492	0.772253
$987$	9.70820	0.309016
$988$	19.8541	0.631643
$989$	0	0
$990$	0	0
$991$	−10.5066	−0.333752	−0.166876	−	0.985978i	$-0.553368\pi$
$991$	−10.5066	−0.333752	−0.166876	+	0.985978i	$0.553368\pi$
$992$	2.09017	0.0663630
$993$	9.12461	0.289561
$994$	11.4721	0.363874
$995$	0	0
$996$	−6.76393	−0.214323
$997$	41.1935	1.30461	0.652306	−	0.757956i	$-0.273802\pi$
$997$	41.1935	1.30461	0.652306	+	0.757956i	$0.273802\pi$
$998$	32.3607	1.02436
$999$	−8.58359	−0.271573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.j.1.2		2
4.3	odd	2		9200.2.a.bu.1.1		2
5.2	odd	4		1150.2.b.i.599.1		4
5.3	odd	4		1150.2.b.i.599.4		4
5.4	even	2		230.2.a.c.1.1	✓	2
15.14	odd	2		2070.2.a.u.1.2		2
20.19	odd	2		1840.2.a.l.1.2		2
40.19	odd	2		7360.2.a.bn.1.1		2
40.29	even	2		7360.2.a.bh.1.2		2
115.114	odd	2		5290.2.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.c.1.1	✓	2	5.4	even	2
1150.2.a.j.1.2		2	1.1	even	1	trivial
1150.2.b.i.599.1		4	5.2	odd	4
1150.2.b.i.599.4		4	5.3	odd	4
1840.2.a.l.1.2		2	20.19	odd	2
2070.2.a.u.1.2		2	15.14	odd	2
5290.2.a.o.1.1		2	115.114	odd	2
7360.2.a.bh.1.2		2	40.29	even	2
7360.2.a.bn.1.1		2	40.19	odd	2
9200.2.a.bu.1.1		2	4.3	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.618034 q^{6} -1.61803 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.618034 q^{6} -1.61803 q^{7} -1.00000 q^{8} -2.61803 q^{9} +3.85410 q^{11} +0.618034 q^{12} -4.09017 q^{13} +1.61803 q^{14} +1.00000 q^{16} +5.09017 q^{17} +2.61803 q^{18} -4.85410 q^{19} -1.00000 q^{21} -3.85410 q^{22} -1.00000 q^{23} -0.618034 q^{24} +4.09017 q^{26} -3.47214 q^{27} -1.61803 q^{28} -4.76393 q^{29} -2.09017 q^{31} -1.00000 q^{32} +2.38197 q^{33} -5.09017 q^{34} -2.61803 q^{36} +2.47214 q^{37} +4.85410 q^{38} -2.52786 q^{39} -12.3262 q^{41} +1.00000 q^{42} +3.85410 q^{44} +1.00000 q^{46} -9.70820 q^{47} +0.618034 q^{48} -4.38197 q^{49} +3.14590 q^{51} -4.09017 q^{52} +8.47214 q^{53} +3.47214 q^{54} +1.61803 q^{56} -3.00000 q^{57} +4.76393 q^{58} -11.7082 q^{59} +6.32624 q^{61} +2.09017 q^{62} +4.23607 q^{63} +1.00000 q^{64} -2.38197 q^{66} -5.52786 q^{67} +5.09017 q^{68} -0.618034 q^{69} +7.09017 q^{71} +2.61803 q^{72} +1.23607 q^{73} -2.47214 q^{74} -4.85410 q^{76} -6.23607 q^{77} +2.52786 q^{78} +10.4721 q^{79} +5.70820 q^{81} +12.3262 q^{82} -10.9443 q^{83} -1.00000 q^{84} -2.94427 q^{87} -3.85410 q^{88} -1.52786 q^{89} +6.61803 q^{91} -1.00000 q^{92} -1.29180 q^{93} +9.70820 q^{94} -0.618034 q^{96} -14.6180 q^{97} +4.38197 q^{98} -10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} - 3 q^{9} + q^{11} - q^{12} + 3 q^{13} + q^{14} + 2 q^{16} - q^{17} + 3 q^{18} - 3 q^{19} - 2 q^{21} - q^{22} - 2 q^{23} + q^{24} - 3 q^{26} + 2 q^{27} - q^{28} - 14 q^{29} + 7 q^{31} - 2 q^{32} + 7 q^{33} + q^{34} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 9 q^{41} + 2 q^{42} + q^{44} + 2 q^{46} - 6 q^{47} - q^{48} - 11 q^{49} + 13 q^{51} + 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{56} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 3 q^{61} - 7 q^{62} + 4 q^{63} + 2 q^{64} - 7 q^{66} - 20 q^{67} - q^{68} + q^{69} + 3 q^{71} + 3 q^{72} - 2 q^{73} + 4 q^{74} - 3 q^{76} - 8 q^{77} + 14 q^{78} + 12 q^{79} - 2 q^{81} + 9 q^{82} - 4 q^{83} - 2 q^{84} + 12 q^{87} - q^{88} - 12 q^{89} + 11 q^{91} - 2 q^{92} - 16 q^{93} + 6 q^{94} + q^{96} - 27 q^{97} + 11 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 - 3 * q^9 + q^11 - q^12 + 3 * q^13 + q^14 + 2 * q^16 - q^17 + 3 * q^18 - 3 * q^19 - 2 * q^21 - q^22 - 2 * q^23 + q^24 - 3 * q^26 + 2 * q^27 - q^28 - 14 * q^29 + 7 * q^31 - 2 * q^32 + 7 * q^33 + q^34 - 3 * q^36 - 4 * q^37 + 3 * q^38 - 14 * q^39 - 9 * q^41 + 2 * q^42 + q^44 + 2 * q^46 - 6 * q^47 - q^48 - 11 * q^49 + 13 * q^51 + 3 * q^52 + 8 * q^53 - 2 * q^54 + q^56 - 6 * q^57 + 14 * q^58 - 10 * q^59 - 3 * q^61 - 7 * q^62 + 4 * q^63 + 2 * q^64 - 7 * q^66 - 20 * q^67 - q^68 + q^69 + 3 * q^71 + 3 * q^72 - 2 * q^73 + 4 * q^74 - 3 * q^76 - 8 * q^77 + 14 * q^78 + 12 * q^79 - 2 * q^81 + 9 * q^82 - 4 * q^83 - 2 * q^84 + 12 * q^87 - q^88 - 12 * q^89 + 11 * q^91 - 2 * q^92 - 16 * q^93 + 6 * q^94 + q^96 - 27 * q^97 + 11 * q^98 - 9 * q^99

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