LMFDB - Embedded newform 1150.2.e.c.1057.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.1
Root			$-0.814115i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.c.643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.575666 + 0.575666i) q^{3} +1.00000i q^{4} +0.814115 q^{6} +(-2.09689 + 2.09689i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.33722i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.575666 + 0.575666i) q^{3} +1.00000i q^{4} +0.814115 q^{6} +(-2.09689 + 2.09689i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.33722i q^{9} +1.39990i q^{11} +(-0.575666 - 0.575666i) q^{12} +(-4.24822 + 4.24822i) q^{13} +2.96545 q^{14} -1.00000 q^{16} +(4.38978 - 4.38978i) q^{17} +(1.65266 - 1.65266i) q^{18} -2.37966 q^{19} -2.41421i q^{21} +(0.989880 - 0.989880i) q^{22} +(-0.664664 - 4.74955i) q^{23} +0.814115i q^{24} +6.00789 q^{26} +(-3.07245 - 3.07245i) q^{27} +(-2.09689 - 2.09689i) q^{28} -3.87087i q^{29} -5.74501 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.805875 - 0.805875i) q^{33} -6.20809 q^{34} -2.33722 q^{36} +(2.27719 - 2.27719i) q^{37} +(1.68267 + 1.68267i) q^{38} -4.89111i q^{39} +2.49121 q^{41} +(-1.70711 + 1.70711i) q^{42} +(2.85390 + 2.85390i) q^{43} -1.39990 q^{44} +(-2.88845 + 3.82843i) q^{46} +(1.26288 + 1.26288i) q^{47} +(0.575666 - 0.575666i) q^{48} -1.79387i q^{49} +5.05409i q^{51} +(-4.24822 - 4.24822i) q^{52} +(-4.13375 - 4.13375i) q^{53} +4.34511i q^{54} +2.96545i q^{56} +(1.36989 - 1.36989i) q^{57} +(-2.73712 + 2.73712i) q^{58} +5.66801i q^{59} -13.1168i q^{61} +(4.06233 + 4.06233i) q^{62} +(-4.90088 - 4.90088i) q^{63} -1.00000i q^{64} +1.13968i q^{66} +(11.1390 - 11.1390i) q^{67} +(4.38978 + 4.38978i) q^{68} +(3.11678 + 2.35153i) q^{69} -9.16188 q^{71} +(1.65266 + 1.65266i) q^{72} +(-10.7875 + 10.7875i) q^{73} -3.22044 q^{74} -2.37966i q^{76} +(-2.93543 - 2.93543i) q^{77} +(-3.45854 + 3.45854i) q^{78} -5.70196 q^{79} -3.47424 q^{81} +(-1.76155 - 1.76155i) q^{82} +(-11.6335 - 11.6335i) q^{83} +2.41421 q^{84} -4.03602i q^{86} +(2.22833 + 2.22833i) q^{87} +(0.989880 + 0.989880i) q^{88} +1.31441 q^{89} -17.8161i q^{91} +(4.74955 - 0.664664i) q^{92} +(3.30721 - 3.30721i) q^{93} -1.78598i q^{94} -0.814115 q^{96} +(-7.84001 + 7.84001i) q^{97} +(-1.26846 + 1.26846i) q^{98} -3.27187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{6}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^6	$ 8 q + 4 q^{3} + 4 q^{6} + 4 q^{12} + 4 q^{14} - 8 q^{16} + 24 q^{17} + 8 q^{18} + 12 q^{19} - 12 q^{22} - 16 q^{23} + 12 q^{26} - 8 q^{27} - 4 q^{31} + 20 q^{33} + 4 q^{34} - 4 q^{36} + 4 q^{37} + 8 q^{38} + 12 q^{41} - 8 q^{42} - 20 q^{43} - 20 q^{44} + 16 q^{47} - 4 q^{48} + 20 q^{57} - 16 q^{58} - 4 q^{62} - 4 q^{67} + 24 q^{68} - 12 q^{69} - 44 q^{71} + 8 q^{72} - 28 q^{73} - 48 q^{74} - 4 q^{77} + 4 q^{78} - 8 q^{79} - 16 q^{81} - 8 q^{82} - 28 q^{83} + 8 q^{84} + 4 q^{87} - 12 q^{88} + 40 q^{89} + 16 q^{92} + 12 q^{93} - 4 q^{96} - 8 q^{97} - 16 q^{98} + 36 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^6 + 4 * q^12 + 4 * q^14 - 8 * q^16 + 24 * q^17 + 8 * q^18 + 12 * q^19 - 12 * q^22 - 16 * q^23 + 12 * q^26 - 8 * q^27 - 4 * q^31 + 20 * q^33 + 4 * q^34 - 4 * q^36 + 4 * q^37 + 8 * q^38 + 12 * q^41 - 8 * q^42 - 20 * q^43 - 20 * q^44 + 16 * q^47 - 4 * q^48 + 20 * q^57 - 16 * q^58 - 4 * q^62 - 4 * q^67 + 24 * q^68 - 12 * q^69 - 44 * q^71 + 8 * q^72 - 28 * q^73 - 48 * q^74 - 4 * q^77 + 4 * q^78 - 8 * q^79 - 16 * q^81 - 8 * q^82 - 28 * q^83 + 8 * q^84 + 4 * q^87 - 12 * q^88 + 40 * q^89 + 16 * q^92 + 12 * q^93 - 4 * q^96 - 8 * q^97 - 16 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.575666	+	0.575666i	−0.332361	+	0.332361i	−0.853482	−	0.521122i	$-0.825514\pi$
$3$	−0.575666	+	0.575666i	−0.332361	+	0.332361i	0.521122	+	0.853482i	$0.325514\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	0.814115			0.332361
$7$	−2.09689	+	2.09689i	−0.792549	+	0.792549i	−0.981908	−	0.189359i	$-0.939359\pi$
$7$	−2.09689	+	2.09689i	−0.792549	+	0.792549i	0.189359	+	0.981908i	$0.439359\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			2.33722i			0.779072i
$10$		0			0
$11$			1.39990i			0.422086i	0.977477	+	0.211043i	$0.0676860\pi$
$11$			1.39990i			0.422086i	−0.977477	+	0.211043i	$0.932314\pi$
$12$	−0.575666	−	0.575666i	−0.166180	−	0.166180i
$13$	−4.24822	+	4.24822i	−1.17824	+	1.17824i	−0.198053	+	0.980191i	$0.563462\pi$
$13$	−4.24822	+	4.24822i	−1.17824	+	1.17824i	−0.980191	+	0.198053i	$0.936538\pi$
$14$	2.96545			0.792549
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.38978	−	4.38978i	1.06468	−	1.06468i	0.0669198	−	0.997758i	$-0.478683\pi$
$17$	4.38978	−	4.38978i	1.06468	−	1.06468i	0.997758	−	0.0669198i	$-0.0213172\pi$
$18$	1.65266	−	1.65266i	0.389536	−	0.389536i
$19$	−2.37966			−0.545931			−0.272966	−	0.962024i	$-0.588005\pi$
$19$	−2.37966			−0.545931			−0.272966	+	0.962024i	$0.588005\pi$
$20$		0			0
$21$		−	2.41421i		−	0.526825i
$22$	0.989880	−	0.989880i	0.211043	−	0.211043i
$23$	−0.664664	−	4.74955i	−0.138592	−	0.990350i
$23$	−0.664664	−	4.74955i	−0.138592	−	0.990350i
$24$			0.814115i			0.166180i
$25$		0			0
$26$	6.00789			1.17824
$27$	−3.07245	−	3.07245i	−0.591294	−	0.591294i
$28$	−2.09689	−	2.09689i	−0.396274	−	0.396274i
$29$		−	3.87087i		−	0.718803i	−0.933183	−	0.359401i	$-0.882981\pi$
$29$		−	3.87087i		−	0.718803i	0.933183	−	0.359401i	$-0.117019\pi$
$30$		0			0
$31$	−5.74501			−1.03183			−0.515917	−	0.856639i	$-0.672549\pi$
$31$	−5.74501			−1.03183			−0.515917	+	0.856639i	$0.672549\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.805875	−	0.805875i	−0.140285	−	0.140285i
$34$	−6.20809			−1.06468
$35$		0			0
$36$	−2.33722			−0.389536
$37$	2.27719	−	2.27719i	0.374368	−	0.374368i	−0.494697	−	0.869065i	$-0.664721\pi$
$37$	2.27719	−	2.27719i	0.374368	−	0.374368i	0.869065	+	0.494697i	$0.164721\pi$
$38$	1.68267	+	1.68267i	0.272966	+	0.272966i
$39$		−	4.89111i		−	0.783205i
$40$		0			0
$41$	2.49121			0.389062			0.194531	−	0.980896i	$-0.437682\pi$
$41$	2.49121			0.389062			0.194531	+	0.980896i	$0.437682\pi$
$42$	−1.70711	+	1.70711i	−0.263412	+	0.263412i
$43$	2.85390	+	2.85390i	0.435215	+	0.435215i	0.890398	−	0.455183i	$-0.150426\pi$
$43$	2.85390	+	2.85390i	0.435215	+	0.435215i	−0.455183	+	0.890398i	$0.650426\pi$
$44$	−1.39990			−0.211043
$45$		0			0
$46$	−2.88845	+	3.82843i	−0.425879	+	0.564471i
$47$	1.26288	+	1.26288i	0.184210	+	0.184210i	0.793188	−	0.608977i	$-0.208420\pi$
$47$	1.26288	+	1.26288i	0.184210	+	0.184210i	−0.608977	+	0.793188i	$0.708420\pi$
$48$	0.575666	−	0.575666i	0.0830902	−	0.0830902i
$49$		−	1.79387i		−	0.256268i
$50$		0			0
$51$			5.05409i			0.707715i
$52$	−4.24822	−	4.24822i	−0.589122	−	0.589122i
$53$	−4.13375	−	4.13375i	−0.567814	−	0.567814i	0.363701	−	0.931516i	$-0.381513\pi$
$53$	−4.13375	−	4.13375i	−0.567814	−	0.567814i	−0.931516	+	0.363701i	$0.881513\pi$
$54$			4.34511i			0.591294i
$55$		0			0
$56$			2.96545i			0.396274i
$57$	1.36989	−	1.36989i	0.181446	−	0.181446i
$58$	−2.73712	+	2.73712i	−0.359401	+	0.359401i
$59$			5.66801i			0.737912i	0.929447	+	0.368956i	$0.120285\pi$
$59$			5.66801i			0.737912i	−0.929447	+	0.368956i	$0.879715\pi$
$60$		0			0
$61$		−	13.1168i		−	1.67943i	−0.543026	−	0.839716i	$-0.682722\pi$
$61$		−	13.1168i		−	1.67943i	0.543026	−	0.839716i	$-0.317278\pi$
$62$	4.06233	+	4.06233i	0.515917	+	0.515917i
$63$	−4.90088	−	4.90088i	−0.617453	−	0.617453i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			1.13968i			0.140285i
$67$	11.1390	−	11.1390i	1.36084	−	1.36084i	0.487999	−	0.872844i	$-0.337727\pi$
$67$	11.1390	−	11.1390i	1.36084	−	1.36084i	0.872844	−	0.487999i	$-0.162273\pi$
$68$	4.38978	+	4.38978i	0.532339	+	0.532339i
$69$	3.11678	+	2.35153i	0.375216	+	0.283091i
$70$		0			0
$71$	−9.16188			−1.08732			−0.543658	−	0.839307i	$-0.682961\pi$
$71$	−9.16188			−1.08732			−0.543658	+	0.839307i	$0.682961\pi$
$72$	1.65266	+	1.65266i	0.194768	+	0.194768i
$73$	−10.7875	+	10.7875i	−1.26258	+	1.26258i	−0.312735	+	0.949840i	$0.601245\pi$
$73$	−10.7875	+	10.7875i	−1.26258	+	1.26258i	−0.949840	+	0.312735i	$0.898755\pi$
$74$	−3.22044			−0.374368
$75$		0			0
$76$		−	2.37966i		−	0.272966i
$77$	−2.93543	−	2.93543i	−0.334524	−	0.334524i
$78$	−3.45854	+	3.45854i	−0.391602	+	0.391602i
$79$	−5.70196			−0.641520			−0.320760	−	0.947160i	$-0.603938\pi$
$79$	−5.70196			−0.641520			−0.320760	+	0.947160i	$0.603938\pi$
$80$		0			0
$81$	−3.47424			−0.386026
$82$	−1.76155	−	1.76155i	−0.194531	−	0.194531i
$83$	−11.6335	−	11.6335i	−1.27694	−	1.27694i	−0.942373	−	0.334565i	$-0.891410\pi$
$83$	−11.6335	−	11.6335i	−1.27694	−	1.27694i	−0.334565	−	0.942373i	$-0.608590\pi$
$84$	2.41421			0.263412
$85$		0			0
$86$		−	4.03602i		−	0.435215i
$87$	2.22833	+	2.22833i	0.238902	+	0.238902i
$88$	0.989880	+	0.989880i	0.105522	+	0.105522i
$89$	1.31441			0.139327			0.0696635	−	0.997571i	$-0.477807\pi$
$89$	1.31441			0.139327			0.0696635	+	0.997571i	$0.477807\pi$
$90$		0			0
$91$		−	17.8161i		−	1.86763i
$92$	4.74955	−	0.664664i	0.495175	−	0.0692960i
$93$	3.30721	−	3.30721i	0.342941	−	0.342941i
$94$		−	1.78598i		−	0.184210i
$95$		0			0
$96$	−0.814115			−0.0830902
$97$	−7.84001	+	7.84001i	−0.796033	+	0.796033i	−0.982467	−	0.186435i	$-0.940307\pi$
$97$	−7.84001	+	7.84001i	−0.796033	+	0.796033i	0.186435	+	0.982467i	$0.440307\pi$
$98$	−1.26846	+	1.26846i	−0.128134	+	0.128134i
$99$	−3.27187			−0.328836
$100$		0			0
$101$	−1.61707			−0.160905			−0.0804523	−	0.996758i	$-0.525636\pi$
$101$	−1.61707			−0.160905			−0.0804523	+	0.996758i	$0.525636\pi$
$102$	3.57378	−	3.57378i	0.353857	−	0.353857i
$103$	−5.23579	−	5.23579i	−0.515898	−	0.515898i	0.400430	−	0.916327i	$-0.368861\pi$
$103$	−5.23579	−	5.23579i	−0.515898	−	0.515898i	−0.916327	+	0.400430i	$0.868861\pi$
$104$			6.00789i			0.589122i
$105$		0			0
$106$			5.84601i			0.567814i
$107$	−7.78598	+	7.78598i	−0.752700	+	0.752700i	−0.974982	−	0.222283i	$-0.928649\pi$
$107$	−7.78598	+	7.78598i	−0.752700	+	0.752700i	0.222283	+	0.974982i	$0.428649\pi$
$108$	3.07245	−	3.07245i	0.295647	−	0.295647i
$109$	11.8899			1.13885			0.569424	−	0.822044i	$-0.307166\pi$
$109$	11.8899			1.13885			0.569424	+	0.822044i	$0.307166\pi$
$110$		0			0
$111$			2.62181i			0.248851i
$112$	2.09689	−	2.09689i	0.198137	−	0.198137i
$113$	7.91065	+	7.91065i	0.744172	+	0.744172i	0.973378	−	0.229206i	$-0.0736130\pi$
$113$	7.91065	+	7.91065i	0.744172	+	0.744172i	−0.229206	+	0.973378i	$0.573613\pi$
$114$	−1.93732			−0.181446
$115$		0			0
$116$	3.87087			0.359401
$117$	−9.92901	−	9.92901i	−0.917937	−	0.917937i
$118$	4.00789	−	4.00789i	0.368956	−	0.368956i
$119$			18.4098i			1.68762i
$120$		0			0
$121$	9.04028			0.821843
$122$	−9.27496	+	9.27496i	−0.839716	+	0.839716i
$123$	−1.43410	+	1.43410i	−0.129309	+	0.129309i
$124$		−	5.74501i		−	0.515917i
$125$		0			0
$126$			6.93089i			0.617453i
$127$	−6.93732	−	6.93732i	−0.615587	−	0.615587i	0.328809	−	0.944396i	$-0.393353\pi$
$127$	−6.93732	−	6.93732i	−0.615587	−	0.615587i	−0.944396	+	0.328809i	$0.893353\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−3.28578			−0.289297
$130$		0			0
$131$	−11.7906			−1.03015			−0.515075	−	0.857145i	$-0.672236\pi$
$131$	−11.7906			−1.03015			−0.515075	+	0.857145i	$0.672236\pi$
$132$	0.805875	−	0.805875i	0.0701425	−	0.0701425i
$133$	4.98988	−	4.98988i	0.432677	−	0.432677i
$134$	−15.7529			−1.36084
$135$		0			0
$136$		−	6.20809i		−	0.532339i
$137$	−3.78830	+	3.78830i	−0.323656	+	0.323656i	−0.850168	−	0.526512i	$-0.823500\pi$
$137$	−3.78830	+	3.78830i	−0.323656	+	0.323656i	0.526512	+	0.850168i	$0.323500\pi$
$138$	−0.541113	−	3.86668i	−0.0460626	−	0.329153i
$139$			5.75082i			0.487778i	0.969803	+	0.243889i	$0.0784233\pi$
$139$			5.75082i			0.487778i	−0.969803	+	0.243889i	$0.921577\pi$
$140$		0			0
$141$	−1.45400			−0.122449
$142$	6.47843	+	6.47843i	0.543658	+	0.543658i
$143$	−5.94709	−	5.94709i	−0.497320	−	0.497320i
$144$		−	2.33722i		−	0.194768i
$145$		0			0
$146$	15.2558			1.26258
$147$	1.03267	+	1.03267i	0.0851734	+	0.0851734i
$148$	2.27719	+	2.27719i	0.187184	+	0.187184i
$149$	−1.83898			−0.150655			−0.0753274	−	0.997159i	$-0.524000\pi$
$149$	−1.83898			−0.150655			−0.0753274	+	0.997159i	$0.524000\pi$
$150$		0			0
$151$	1.79191			0.145824			0.0729119	−	0.997338i	$-0.476771\pi$
$151$	1.79191			0.145824			0.0729119	+	0.997338i	$0.476771\pi$
$152$	−1.68267	+	1.68267i	−0.136483	+	0.136483i
$153$	10.2599	+	10.2599i	0.829461	+	0.829461i
$154$			4.15133i			0.334524i
$155$		0			0
$156$	4.89111			0.391602
$157$	−2.30909	+	2.30909i	−0.184285	+	0.184285i	−0.793220	−	0.608935i	$-0.791597\pi$
$157$	−2.30909	+	2.30909i	−0.184285	+	0.184285i	0.608935	+	0.793220i	$0.291597\pi$
$158$	4.03189	+	4.03189i	0.320760	+	0.320760i
$159$	4.75932			0.377439
$160$		0			0
$161$	11.3530	+	8.56555i	0.894741	+	0.675060i
$162$	2.45666	+	2.45666i	0.193013	+	0.193013i
$163$	−14.4525	+	14.4525i	−1.13201	+	1.13201i	−0.142168	+	0.989843i	$0.545407\pi$
$163$	−14.4525	+	14.4525i	−1.13201	+	1.13201i	−0.989843	+	0.142168i	$0.954593\pi$
$164$			2.49121i			0.194531i
$165$		0			0
$166$			16.4522i			1.27694i
$167$	11.7423	+	11.7423i	0.908650	+	0.908650i	0.996163	−	0.0875132i	$-0.0278920\pi$
$167$	11.7423	+	11.7423i	0.908650	+	0.908650i	−0.0875132	+	0.996163i	$0.527892\pi$
$168$	−1.70711	−	1.70711i	−0.131706	−	0.131706i
$169$		−	23.0947i		−	1.77652i
$170$		0			0
$171$		−	5.56178i		−	0.425320i
$172$	−2.85390	+	2.85390i	−0.217608	+	0.217608i
$173$	7.36165	−	7.36165i	0.559696	−	0.559696i	−0.369525	−	0.929221i	$-0.620480\pi$
$173$	7.36165	−	7.36165i	0.559696	−	0.559696i	0.929221	+	0.369525i	$0.120480\pi$
$174$		−	3.15133i		−	0.238902i
$175$		0			0
$176$		−	1.39990i		−	0.105522i
$177$	−3.26288	−	3.26288i	−0.245253	−	0.245253i
$178$	−0.929427	−	0.929427i	−0.0696635	−	0.0696635i
$179$		−	5.55173i		−	0.414956i	−0.978240	−	0.207478i	$-0.933475\pi$
$179$		−	5.55173i		−	0.414956i	0.978240	−	0.207478i	$-0.0665255\pi$
$180$		0			0
$181$		−	23.0901i		−	1.71627i	−0.513420	−	0.858137i	$-0.671622\pi$
$181$		−	23.0901i		−	1.71627i	0.513420	−	0.858137i	$-0.328378\pi$
$182$	−12.5979	+	12.5979i	−0.933816	+	0.933816i
$183$	7.55088	+	7.55088i	0.558177	+	0.558177i
$184$	−3.82843	−	2.88845i	−0.282235	−	0.212939i
$185$		0			0
$186$	−4.67710			−0.342941
$187$	6.14526	+	6.14526i	0.449386	+	0.449386i
$188$	−1.26288	+	1.26288i	−0.0921051	+	0.0921051i
$189$	12.8852			0.937259
$190$		0			0
$191$		−	7.88579i		−	0.570596i	−0.958439	−	0.285298i	$-0.907907\pi$
$191$		−	7.88579i		−	0.570596i	0.958439	−	0.285298i	$-0.0920925\pi$
$192$	0.575666	+	0.575666i	0.0415451	+	0.0415451i
$193$	5.18469	−	5.18469i	0.373202	−	0.373202i	−0.495440	−	0.868642i	$-0.664993\pi$
$193$	5.18469	−	5.18469i	0.373202	−	0.373202i	0.868642	+	0.495440i	$0.164993\pi$
$194$	11.0875			0.796033
$195$		0			0
$196$	1.79387			0.128134
$197$	3.44191	+	3.44191i	0.245226	+	0.245226i	0.819008	−	0.573782i	$-0.194524\pi$
$197$	3.44191	+	3.44191i	0.245226	+	0.245226i	−0.573782	+	0.819008i	$0.694524\pi$
$198$	2.31356	+	2.31356i	0.164418	+	0.164418i
$199$	−15.8241			−1.12174			−0.560870	−	0.827904i	$-0.689533\pi$
$199$	−15.8241			−1.12174			−0.560870	+	0.827904i	$0.689533\pi$
$200$		0			0
$201$			12.8247i			0.904582i
$202$	1.14344	+	1.14344i	0.0804523	+	0.0804523i
$203$	8.11678	+	8.11678i	0.569686	+	0.569686i
$204$	−5.05409			−0.353857
$205$		0			0
$206$			7.40452i			0.515898i
$207$	11.1007	−	1.55346i	0.771554	−	0.107973i
$208$	4.24822	−	4.24822i	0.294561	−	0.294561i
$209$		−	3.33129i		−	0.230430i
$210$		0			0
$211$	−17.0575			−1.17429			−0.587144	−	0.809482i	$-0.699748\pi$
$211$	−17.0575			−1.17429			−0.587144	+	0.809482i	$0.699748\pi$
$212$	4.13375	−	4.13375i	0.283907	−	0.283907i
$213$	5.27418	−	5.27418i	0.361381	−	0.361381i
$214$	11.0110			0.752700
$215$		0			0
$216$	−4.34511			−0.295647
$217$	12.0466	−	12.0466i	0.817779	−	0.817779i
$218$	−8.40744	−	8.40744i	−0.569424	−	0.569424i
$219$		−	12.4199i		−	0.839262i
$220$		0			0
$221$			37.2975i			2.50890i
$222$	1.85390	−	1.85390i	0.124425	−	0.124425i
$223$	1.18915	−	1.18915i	0.0796316	−	0.0796316i	−0.666169	−	0.745801i	$-0.732067\pi$
$223$	1.18915	−	1.18915i	0.0796316	−	0.0796316i	0.745801	+	0.666169i	$0.232067\pi$
$224$	−2.96545			−0.198137
$225$		0			0
$226$		−	11.1874i		−	0.744172i
$227$	−14.3791	+	14.3791i	−0.954371	+	0.954371i	−0.999003	−	0.0446322i	$-0.985788\pi$
$227$	−14.3791	+	14.3791i	−0.954371	+	0.954371i	0.0446322	+	0.999003i	$0.485788\pi$
$228$	1.36989	+	1.36989i	0.0907231	+	0.0907231i
$229$	4.32083			0.285529			0.142764	−	0.989757i	$-0.454401\pi$
$229$	4.32083			0.285529			0.142764	+	0.989757i	$0.454401\pi$
$230$		0			0
$231$	3.37966			0.222365
$232$	−2.73712	−	2.73712i	−0.179701	−	0.179701i
$233$	−0.921537	+	0.921537i	−0.0603719	+	0.0603719i	−0.736648	−	0.676276i	$-0.763593\pi$
$233$	−0.921537	+	0.921537i	−0.0603719	+	0.0603719i	0.676276	+	0.736648i	$0.263593\pi$
$234$			14.0417i			0.917937i
$235$		0			0
$236$	−5.66801			−0.368956
$237$	3.28242	−	3.28242i	0.213216	−	0.213216i
$238$	13.0177	−	13.0177i	0.843810	−	0.843810i
$239$		−	9.30740i		−	0.602046i	−0.953617	−	0.301023i	$-0.902672\pi$
$239$		−	9.30740i		−	0.602046i	0.953617	−	0.301023i	$-0.0973280\pi$
$240$		0			0
$241$			21.4247i			1.38008i	0.723769	+	0.690042i	$0.242408\pi$
$241$			21.4247i			1.38008i	−0.723769	+	0.690042i	$0.757592\pi$
$242$	−6.39244	−	6.39244i	−0.410922	−	0.410922i
$243$	11.2174	−	11.2174i	0.719594	−	0.719594i
$244$	13.1168			0.839716
$245$		0			0
$246$	2.02813			0.129309
$247$	10.1093	−	10.1093i	0.643241	−	0.643241i
$248$	−4.06233	+	4.06233i	−0.257958	+	0.257958i
$249$	13.3940			0.848809
$250$		0			0
$251$			6.28824i			0.396910i	0.980110	+	0.198455i	$0.0635924\pi$
$251$			6.28824i			0.396910i	−0.980110	+	0.198455i	$0.936408\pi$
$252$	4.90088	−	4.90088i	0.308727	−	0.308727i
$253$	6.64890	−	0.930464i	0.418013	−	0.0584978i
$254$			9.81085i			0.615587i
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.5108	+	18.5108i	1.15467	+	1.15467i	0.985605	+	0.169064i	$0.0540744\pi$
$257$	18.5108	+	18.5108i	1.15467	+	1.15467i	0.169064	+	0.985605i	$0.445926\pi$
$258$	2.32340	+	2.32340i	0.144649	+	0.144649i
$259$			9.55004i			0.593411i
$260$		0			0
$261$	9.04706			0.559999
$262$	8.33722	+	8.33722i	0.515075	+	0.515075i
$263$	1.46351	+	1.46351i	0.0902438	+	0.0902438i	0.750788	−	0.660544i	$-0.229674\pi$
$263$	1.46351	+	1.46351i	0.0902438	+	0.0902438i	−0.660544	+	0.750788i	$0.729674\pi$
$264$	−1.13968			−0.0701425
$265$		0			0
$266$	−7.05676			−0.432677
$267$	−0.756660	+	0.756660i	−0.0463068	+	0.0463068i
$268$	11.1390	+	11.1390i	0.680422	+	0.680422i
$269$		−	4.31914i		−	0.263343i	−0.991293	−	0.131671i	$-0.957966\pi$
$269$		−	4.31914i		−	0.263343i	0.991293	−	0.131671i	$-0.0420344\pi$
$270$		0			0
$271$	1.68875			0.102584			0.0512920	−	0.998684i	$-0.483666\pi$
$271$	1.68875			0.102584			0.0512920	+	0.998684i	$0.483666\pi$
$272$	−4.38978	+	4.38978i	−0.266170	+	0.266170i
$273$	10.2561	+	10.2561i	0.620728	+	0.620728i
$274$	5.35746			0.323656
$275$		0			0
$276$	−2.35153	+	3.11678i	−0.141545	+	0.187608i
$277$	5.49170	+	5.49170i	0.329965	+	0.329965i	0.852573	−	0.522608i	$-0.175041\pi$
$277$	5.49170	+	5.49170i	0.329965	+	0.329965i	−0.522608	+	0.852573i	$0.675041\pi$
$278$	4.06645	−	4.06645i	0.243889	−	0.243889i
$279$		−	13.4273i		−	0.803873i
$280$		0			0
$281$		−	4.64597i		−	0.277155i	−0.990352	−	0.138578i	$-0.955747\pi$
$281$		−	4.64597i		−	0.277155i	0.990352	−	0.138578i	$-0.0442531\pi$
$282$	1.02813	+	1.02813i	0.0612243	+	0.0612243i
$283$	18.5426	+	18.5426i	1.10225	+	1.10225i	0.994139	+	0.108106i	$0.0344787\pi$
$283$	18.5426	+	18.5426i	1.10225	+	1.10225i	0.108106	+	0.994139i	$0.465521\pi$
$284$		−	9.16188i		−	0.543658i
$285$		0			0
$286$			8.41045i			0.497320i
$287$	−5.22379	+	5.22379i	−0.308350	+	0.308350i
$288$	−1.65266	+	1.65266i	−0.0973841	+	0.0973841i
$289$		−	21.5403i		−	1.26708i
$290$		0			0
$291$		−	9.02646i		−	0.529140i
$292$	−10.7875	−	10.7875i	−0.631288	−	0.631288i
$293$	4.84916	+	4.84916i	0.283291	+	0.283291i	0.834420	−	0.551129i	$-0.185803\pi$
$293$	4.84916	+	4.84916i	0.283291	+	0.283291i	−0.551129	+	0.834420i	$0.685803\pi$
$294$		−	1.46042i		−	0.0851734i
$295$		0			0
$296$		−	3.22044i		−	0.187184i
$297$	4.30113	−	4.30113i	0.249577	−	0.249577i
$298$	1.30035	+	1.30035i	0.0753274	+	0.0753274i
$299$	23.0008	+	17.3535i	1.33017	+	1.00358i
$300$		0			0
$301$	−11.9686			−0.689859
$302$	−1.26707	−	1.26707i	−0.0729119	−	0.0729119i
$303$	0.930893	−	0.930893i	0.0534784	−	0.0534784i
$304$	2.37966			0.136483
$305$		0			0
$306$		−	14.5096i		−	0.829461i
$307$	−14.4992	−	14.4992i	−0.827511	−	0.827511i	0.159661	−	0.987172i	$-0.448960\pi$
$307$	−14.4992	−	14.4992i	−0.827511	−	0.827511i	−0.987172	+	0.159661i	$0.948960\pi$
$308$	2.93543	−	2.93543i	0.167262	−	0.167262i
$309$	6.02813			0.342928
$310$		0			0
$311$	22.7346			1.28916			0.644581	−	0.764536i	$-0.277032\pi$
$311$	22.7346			1.28916			0.644581	+	0.764536i	$0.277032\pi$
$312$	−3.45854	−	3.45854i	−0.195801	−	0.195801i
$313$	−12.5099	−	12.5099i	−0.707102	−	0.707102i	0.258823	−	0.965925i	$-0.416665\pi$
$313$	−12.5099	−	12.5099i	−0.707102	−	0.707102i	−0.965925	+	0.258823i	$0.916665\pi$
$314$	3.26554			0.184285
$315$		0			0
$316$		−	5.70196i		−	0.320760i
$317$	−14.7988	−	14.7988i	−0.831186	−	0.831186i	0.156493	−	0.987679i	$-0.449981\pi$
$317$	−14.7988	−	14.7988i	−0.831186	−	0.831186i	−0.987679	+	0.156493i	$0.949981\pi$
$318$	−3.36535	−	3.36535i	−0.188719	−	0.188719i
$319$	5.41884			0.303397
$320$		0			0
$321$		−	8.96425i		−	0.500336i
$322$	−1.97103	−	14.0845i	−0.109841	−	0.784901i
$323$	−10.4462	+	10.4462i	−0.581241	+	0.581241i
$324$		−	3.47424i		−	0.193013i
$325$		0			0
$326$	20.4390			1.13201
$327$	−6.84462	+	6.84462i	−0.378508	+	0.378508i
$328$	1.76155	−	1.76155i	0.0972654	−	0.0972654i
$329$	−5.29624			−0.291991
$330$		0			0
$331$	14.3184			0.787013			0.393506	−	0.919322i	$-0.371262\pi$
$331$	14.3184			0.787013			0.393506	+	0.919322i	$0.371262\pi$
$332$	11.6335	−	11.6335i	0.638469	−	0.638469i
$333$	5.32230	+	5.32230i	0.291660	+	0.291660i
$334$		−	16.6062i		−	0.908650i
$335$		0			0
$336$			2.41421i			0.131706i
$337$	−1.89342	+	1.89342i	−0.103141	+	0.103141i	−0.756794	−	0.653653i	$-0.773236\pi$
$337$	−1.89342	+	1.89342i	−0.103141	+	0.103141i	0.653653	+	0.756794i	$0.273236\pi$
$338$	−16.3304	+	16.3304i	−0.888259	+	0.888259i
$339$	−9.10779			−0.494667
$340$		0			0
$341$		−	8.04244i		−	0.435523i
$342$	−3.93277	+	3.93277i	−0.212660	+	0.212660i
$343$	−10.9167	−	10.9167i	−0.589444	−	0.589444i
$344$	4.03602			0.217608
$345$		0			0
$346$	−10.4109			−0.559696
$347$	−5.57833	−	5.57833i	−0.299460	−	0.299460i	0.541342	−	0.840802i	$-0.317916\pi$
$347$	−5.57833	−	5.57833i	−0.299460	−	0.299460i	−0.840802	+	0.541342i	$0.817916\pi$
$348$	−2.22833	+	2.22833i	−0.119451	+	0.119451i
$349$			4.82635i			0.258349i	0.991622	+	0.129174i	$0.0412327\pi$
$349$			4.82635i			0.258349i	−0.991622	+	0.129174i	$0.958767\pi$
$350$		0			0
$351$	26.1049			1.39338
$352$	−0.989880	+	0.989880i	−0.0527608	+	0.0527608i
$353$	16.3035	−	16.3035i	0.867749	−	0.867749i	−0.124474	−	0.992223i	$-0.539724\pi$
$353$	16.3035	−	16.3035i	0.867749	−	0.867749i	0.992223	+	0.124474i	$0.0397243\pi$
$354$			4.61441i			0.245253i
$355$		0			0
$356$			1.31441i			0.0696635i
$357$	−10.5979	−	10.5979i	−0.560899	−	0.560899i
$358$	−3.92566	+	3.92566i	−0.207478	+	0.207478i
$359$	−29.7585			−1.57059			−0.785297	−	0.619119i	$-0.787490\pi$
$359$	−29.7585			−1.57059			−0.785297	+	0.619119i	$0.787490\pi$
$360$		0			0
$361$	−13.3372			−0.701959
$362$	−16.3272	+	16.3272i	−0.858137	+	0.858137i
$363$	−5.20418	+	5.20418i	−0.273149	+	0.273149i
$364$	17.8161			0.933816
$365$		0			0
$366$		−	10.6786i		−	0.558177i
$367$	−22.0933	+	22.0933i	−1.15326	+	1.15326i	−0.167364	+	0.985895i	$0.553526\pi$
$367$	−22.0933	+	22.0933i	−1.15326	+	1.15326i	−0.985895	+	0.167364i	$0.946474\pi$
$368$	0.664664	+	4.74955i	0.0346480	+	0.247587i
$369$			5.82250i			0.303107i
$370$		0			0
$371$	17.3360			0.900041
$372$	3.30721	+	3.30721i	0.171471	+	0.171471i
$373$	−5.68302	−	5.68302i	−0.294256	−	0.294256i	0.544503	−	0.838759i	$-0.316718\pi$
$373$	−5.68302	−	5.68302i	−0.294256	−	0.294256i	−0.838759	+	0.544503i	$0.816718\pi$
$374$		−	8.69071i		−	0.449386i
$375$		0			0
$376$	1.78598			0.0921051
$377$	16.4443	+	16.4443i	0.846925	+	0.846925i
$378$	−9.11120	−	9.11120i	−0.468630	−	0.468630i
$379$	28.4530			1.46153			0.730765	−	0.682629i	$-0.239163\pi$
$379$	28.4530			1.46153			0.730765	+	0.682629i	$0.239163\pi$
$380$		0			0
$381$	7.98715			0.409194
$382$	−5.57610	+	5.57610i	−0.285298	+	0.285298i
$383$	4.38293	+	4.38293i	0.223957	+	0.223957i	0.810163	−	0.586205i	$-0.199379\pi$
$383$	4.38293	+	4.38293i	0.223957	+	0.223957i	−0.586205	+	0.810163i	$0.699379\pi$
$384$		−	0.814115i		−	0.0415451i
$385$		0			0
$386$	−7.33226			−0.373202
$387$	−6.67018	+	6.67018i	−0.339064	+	0.339064i
$388$	−7.84001	−	7.84001i	−0.398016	−	0.398016i
$389$	5.98569			0.303486			0.151743	−	0.988420i	$-0.451511\pi$
$389$	5.98569			0.303486			0.151743	+	0.988420i	$0.451511\pi$
$390$		0			0
$391$	−23.7672	−	17.9318i	−1.20196	−	0.906848i
$392$	−1.26846	−	1.26846i	−0.0640669	−	0.0640669i
$393$	6.78745	−	6.78745i	0.342382	−	0.342382i
$394$		−	4.86760i		−	0.245226i
$395$		0			0
$396$		−	3.27187i		−	0.164418i
$397$	−22.2577	−	22.2577i	−1.11708	−	1.11708i	−0.992168	−	0.124912i	$-0.960135\pi$
$397$	−22.2577	−	22.2577i	−1.11708	−	1.11708i	−0.124912	−	0.992168i	$-0.539865\pi$
$398$	11.1893	+	11.1893i	0.560870	+	0.560870i
$399$			5.74501i			0.287610i
$400$		0			0
$401$			23.0951i			1.15331i	0.816987	+	0.576656i	$0.195643\pi$
$401$			23.0951i			1.15331i	−0.816987	+	0.576656i	$0.804357\pi$
$402$	9.06841	−	9.06841i	0.452291	−	0.452291i
$403$	24.4061	−	24.4061i	1.21575	−	1.21575i
$404$		−	1.61707i		−	0.0804523i
$405$		0			0
$406$		−	11.4789i		−	0.569686i
$407$	3.18785	+	3.18785i	0.158016	+	0.158016i
$408$	3.57378	+	3.57378i	0.176929	+	0.176929i
$409$			20.1346i			0.995593i	0.867294	+	0.497797i	$0.165857\pi$
$409$			20.1346i			0.995593i	−0.867294	+	0.497797i	$0.834143\pi$
$410$		0			0
$411$		−	4.36159i		−	0.215141i
$412$	5.23579	−	5.23579i	0.257949	−	0.257949i
$413$	−11.8852	−	11.8852i	−0.584832	−	0.584832i
$414$	−8.94787	−	6.75094i	−0.439764	−	0.331790i
$415$		0			0
$416$	−6.00789			−0.294561
$417$	−3.31055	−	3.31055i	−0.162119	−	0.162119i
$418$	−2.35558	+	2.35558i	−0.115215	+	0.115215i
$419$	−22.2991			−1.08938			−0.544690	−	0.838637i	$-0.683353\pi$
$419$	−22.2991			−1.08938			−0.544690	+	0.838637i	$0.683353\pi$
$420$		0			0
$421$			11.3853i			0.554883i	0.960742	+	0.277442i	$0.0894865\pi$
$421$			11.3853i			0.554883i	−0.960742	+	0.277442i	$0.910513\pi$
$422$	12.0615	+	12.0615i	0.587144	+	0.587144i
$423$	−2.95163	+	2.95163i	−0.143513	+	0.143513i
$424$	−5.84601			−0.283907
$425$		0			0
$426$	−7.45882			−0.361381
$427$	27.5044	+	27.5044i	1.33103	+	1.33103i
$428$	−7.78598	−	7.78598i	−0.376350	−	0.376350i
$429$	6.84707			0.330580
$430$		0			0
$431$			26.8390i			1.29279i	0.763002	+	0.646396i	$0.223724\pi$
$431$			26.8390i			1.29279i	−0.763002	+	0.646396i	$0.776276\pi$
$432$	3.07245	+	3.07245i	0.147824	+	0.147824i
$433$	4.55947	+	4.55947i	0.219114	+	0.219114i	0.808125	−	0.589011i	$-0.200482\pi$
$433$	4.55947	+	4.55947i	0.219114	+	0.219114i	−0.589011	+	0.808125i	$0.700482\pi$
$434$	−17.0365			−0.817779
$435$		0			0
$436$			11.8899i			0.569424i
$437$	1.58167	+	11.3023i	0.0756617	+	0.540663i
$438$	−8.78222	+	8.78222i	−0.419631	+	0.419631i
$439$			14.5945i			0.696559i	0.937391	+	0.348280i	$0.113234\pi$
$439$			14.5945i			0.696559i	−0.937391	+	0.348280i	$0.886766\pi$
$440$		0			0
$441$	4.19267			0.199651
$442$	26.3733	−	26.3733i	1.25445	−	1.25445i
$443$	−15.6502	+	15.6502i	−0.743563	+	0.743563i	−0.973262	−	0.229699i	$-0.926226\pi$
$443$	−15.6502	+	15.6502i	−0.743563	+	0.743563i	0.229699	+	0.973262i	$0.426226\pi$
$444$	−2.62181			−0.124425
$445$		0			0
$446$	−1.68172			−0.0796316
$447$	1.05864	−	1.05864i	0.0500718	−	0.0500718i
$448$	2.09689	+	2.09689i	0.0990686	+	0.0990686i
$449$		−	34.9589i		−	1.64981i	−0.565269	−	0.824907i	$-0.691228\pi$
$449$		−	34.9589i		−	1.64981i	0.565269	−	0.824907i	$-0.308772\pi$
$450$		0			0
$451$			3.48745i			0.164217i
$452$	−7.91065	+	7.91065i	−0.372086	+	0.372086i
$453$	−1.03154	+	1.03154i	−0.0484661	+	0.0484661i
$454$	20.3351			0.954371
$455$		0			0
$456$		−	1.93732i		−	0.0907231i
$457$	−0.286885	+	0.286885i	−0.0134199	+	0.0134199i	−0.713785	−	0.700365i	$-0.753021\pi$
$457$	−0.286885	+	0.286885i	−0.0134199	+	0.0134199i	0.700365	+	0.713785i	$0.253021\pi$
$458$	−3.05529	−	3.05529i	−0.142764	−	0.142764i
$459$	−26.9748			−1.25908
$460$		0			0
$461$	−16.9780			−0.790742			−0.395371	−	0.918521i	$-0.629384\pi$
$461$	−16.9780			−0.790742			−0.395371	+	0.918521i	$0.629384\pi$
$462$	−2.38978	−	2.38978i	−0.111183	−	0.111183i
$463$	−13.7072	+	13.7072i	−0.637027	+	0.637027i	−0.949821	−	0.312794i	$-0.898735\pi$
$463$	−13.7072	+	13.7072i	−0.637027	+	0.637027i	0.312794	+	0.949821i	$0.398735\pi$
$464$			3.87087i			0.179701i
$465$		0			0
$466$	1.30325			0.0603719
$467$	6.28132	−	6.28132i	0.290665	−	0.290665i	−0.546678	−	0.837343i	$-0.684108\pi$
$467$	6.28132	−	6.28132i	0.290665	−	0.290665i	0.837343	+	0.546678i	$0.184108\pi$
$468$	9.92901	−	9.92901i	0.458969	−	0.458969i
$469$			46.7144i			2.15707i
$470$		0			0
$471$		−	2.65853i		−	0.122498i
$472$	4.00789	+	4.00789i	0.184478	+	0.184478i
$473$	−3.99517	+	3.99517i	−0.183698	+	0.183698i
$474$	−4.64205			−0.213216
$475$		0			0
$476$	−18.4098			−0.843810
$477$	9.66148	−	9.66148i	0.442369	−	0.442369i
$478$	−6.58132	+	6.58132i	−0.301023	+	0.301023i
$479$	−3.99175			−0.182388			−0.0911938	−	0.995833i	$-0.529068\pi$
$479$	−3.99175			−0.182388			−0.0911938	+	0.995833i	$0.529068\pi$
$480$		0			0
$481$			19.3480i			0.882195i
$482$	15.1495	−	15.1495i	0.690042	−	0.690042i
$483$	−11.4664	+	1.60464i	−0.521741	+	0.0730137i
$484$			9.04028i			0.410922i
$485$		0			0
$486$	−15.8637			−0.719594
$487$	7.64836	+	7.64836i	0.346580	+	0.346580i	0.858834	−	0.512254i	$-0.171189\pi$
$487$	7.64836	+	7.64836i	0.346580	+	0.346580i	−0.512254	+	0.858834i	$0.671189\pi$
$488$	−9.27496	−	9.27496i	−0.419858	−	0.419858i
$489$		−	16.6397i		−	0.752472i
$490$		0			0
$491$	6.83837			0.308611			0.154306	−	0.988023i	$-0.450686\pi$
$491$	6.83837			0.308611			0.154306	+	0.988023i	$0.450686\pi$
$492$	−1.43410	−	1.43410i	−0.0646544	−	0.0646544i
$493$	−16.9923	−	16.9923i	−0.765293	−	0.765293i
$494$	−14.2967			−0.643241
$495$		0			0
$496$	5.74501			0.257958
$497$	19.2114	−	19.2114i	0.861751	−	0.861751i
$498$	−9.47097	−	9.47097i	−0.424404	−	0.424404i
$499$			26.1608i			1.17112i	0.810629	+	0.585560i	$0.199125\pi$
$499$			26.1608i			1.17112i	−0.810629	+	0.585560i	$0.800875\pi$
$500$		0			0
$501$	−13.5193			−0.604000
$502$	4.44646	−	4.44646i	0.198455	−	0.198455i
$503$	8.73893	+	8.73893i	0.389650	+	0.389650i	0.874563	−	0.484913i	$-0.161149\pi$
$503$	8.73893	+	8.73893i	0.389650	+	0.389650i	−0.484913	+	0.874563i	$0.661149\pi$
$504$	−6.93089			−0.308727
$505$		0			0
$506$	−5.35942	−	4.04354i	−0.238255	−	0.179757i
$507$	13.2949	+	13.2949i	0.590445	+	0.590445i
$508$	6.93732	−	6.93732i	0.307794	−	0.307794i
$509$			11.7467i			0.520664i	0.965519	+	0.260332i	$0.0838320\pi$
$509$			11.7467i			0.520664i	−0.965519	+	0.260332i	$0.916168\pi$
$510$		0			0
$511$		−	45.2401i		−	2.00131i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	7.31140	+	7.31140i	0.322806	+	0.322806i
$514$		−	26.1782i		−	1.15467i
$515$		0			0
$516$		−	3.28578i		−	0.144649i
$517$	−1.76791	+	1.76791i	−0.0777526	+	0.0777526i
$518$	6.75290	−	6.75290i	0.296705	−	0.296705i
$519$			8.47570i			0.372042i
$520$		0			0
$521$			14.9999i			0.657157i	0.944477	+	0.328578i	$0.106570\pi$
$521$			14.9999i			0.657157i	−0.944477	+	0.328578i	$0.893430\pi$
$522$	−6.39724	−	6.39724i	−0.280000	−	0.280000i
$523$	−3.18638	−	3.18638i	−0.139331	−	0.139331i	0.634001	−	0.773332i	$-0.281411\pi$
$523$	−3.18638	−	3.18638i	−0.139331	−	0.139331i	−0.773332	+	0.634001i	$0.781411\pi$
$524$		−	11.7906i		−	0.515075i
$525$		0			0
$526$		−	2.06971i		−	0.0902438i
$527$	−25.2193	+	25.2193i	−1.09857	+	1.09857i
$528$	0.805875	+	0.805875i	0.0350712	+	0.0350712i
$529$	−22.1164	+	6.31371i	−0.961585	+	0.274509i
$530$		0			0
$531$	−13.2474			−0.574887
$532$	4.98988	+	4.98988i	0.216339	+	0.216339i
$533$	−10.5832	+	10.5832i	−0.458410	+	0.458410i
$534$	1.07008			0.0463068
$535$		0			0
$536$		−	15.7529i		−	0.680422i
$537$	3.19594	+	3.19594i	0.137915	+	0.137915i
$538$	−3.05409	+	3.05409i	−0.131671	+	0.131671i
$539$	2.51125			0.108167
$540$		0			0
$541$	−19.8436			−0.853144			−0.426572	−	0.904454i	$-0.640279\pi$
$541$	−19.8436			−0.853144			−0.426572	+	0.904454i	$0.640279\pi$
$542$	−1.19412	−	1.19412i	−0.0512920	−	0.0512920i
$543$	13.2922	+	13.2922i	0.570423	+	0.570423i
$544$	6.20809			0.266170
$545$		0			0
$546$		−	14.5043i		−	0.620728i
$547$	−22.5810	−	22.5810i	−0.965493	−	0.965493i	0.0339314	−	0.999424i	$-0.489197\pi$
$547$	−22.5810	−	22.5810i	−0.965493	−	0.965493i	−0.999424	+	0.0339314i	$0.989197\pi$
$548$	−3.78830	−	3.78830i	−0.161828	−	0.161828i
$549$	30.6568			1.30840
$550$		0			0
$551$			9.21136i			0.392417i
$552$	3.86668	−	0.541113i	0.164577	−	0.0230313i
$553$	11.9564	−	11.9564i	0.508436	−	0.508436i
$554$		−	7.76644i		−	0.329965i
$555$		0			0
$556$	−5.75082			−0.243889
$557$	−8.12733	+	8.12733i	−0.344366	+	0.344366i	−0.858006	−	0.513640i	$-0.828297\pi$
$557$	−8.12733	+	8.12733i	−0.344366	+	0.344366i	0.513640	+	0.858006i	$0.328297\pi$
$558$	−9.49456	+	9.49456i	−0.401937	+	0.401937i
$559$	−24.2480			−1.02558
$560$		0			0
$561$	−7.07523			−0.298717
$562$	−3.28520	+	3.28520i	−0.138578	+	0.138578i
$563$	−32.2838	−	32.2838i	−1.36060	−	1.36060i	−0.873153	−	0.487446i	$-0.837929\pi$
$563$	−32.2838	−	32.2838i	−1.36060	−	1.36060i	−0.487446	−	0.873153i	$-0.662071\pi$
$564$		−	1.45400i		−	0.0612243i
$565$		0			0
$566$		−	26.2233i		−	1.10225i
$567$	7.28508	−	7.28508i	0.305945	−	0.305945i
$568$	−6.47843	+	6.47843i	−0.271829	+	0.271829i
$569$	−46.8519			−1.96413			−0.982067	−	0.188534i	$-0.939627\pi$
$569$	−46.8519			−1.96413			−0.982067	+	0.188534i	$0.939627\pi$
$570$		0			0
$571$			10.3665i			0.433826i	0.976191	+	0.216913i	$0.0695988\pi$
$571$			10.3665i			0.433826i	−0.976191	+	0.216913i	$0.930401\pi$
$572$	5.94709	−	5.94709i	0.248660	−	0.248660i
$573$	4.53958	+	4.53958i	0.189644	+	0.189644i
$574$	7.38755			0.308350
$575$		0			0
$576$	2.33722			0.0973841
$577$	−3.64168	−	3.64168i	−0.151605	−	0.151605i	0.627229	−	0.778835i	$-0.284189\pi$
$577$	−3.64168	−	3.64168i	−0.151605	−	0.151605i	−0.778835	+	0.627229i	$0.784189\pi$
$578$	−15.2313	+	15.2313i	−0.633540	+	0.633540i
$579$			5.96930i			0.248076i
$580$		0			0
$581$	48.7881			2.02407
$582$	−6.38267	+	6.38267i	−0.264570	+	0.264570i
$583$	5.78684	−	5.78684i	0.239667	−	0.239667i
$584$			15.2558i			0.631288i
$585$		0			0
$586$		−	6.85775i		−	0.283291i
$587$	−20.8064	−	20.8064i	−0.858774	−	0.858774i	0.132420	−	0.991194i	$-0.457725\pi$
$587$	−20.8064	−	20.8064i	−0.858774	−	0.858774i	−0.991194	+	0.132420i	$0.957725\pi$
$588$	−1.03267	+	1.03267i	−0.0425867	+	0.0425867i
$589$	13.6712			0.563311
$590$		0			0
$591$	−3.96279			−0.163007
$592$	−2.27719	+	2.27719i	−0.0935921	+	0.0935921i
$593$	−29.3041	+	29.3041i	−1.20338	+	1.20338i	−0.230243	+	0.973133i	$0.573952\pi$
$593$	−29.3041	+	29.3041i	−1.20338	+	1.20338i	−0.973133	+	0.230243i	$0.926048\pi$
$594$	−6.08272			−0.249577
$595$		0			0
$596$		−	1.83898i		−	0.0753274i
$597$	9.10938	−	9.10938i	0.372822	−	0.372822i
$598$	−3.99323	−	28.5348i	−0.163295	−	1.16687i
$599$			34.2406i			1.39903i	0.714616	+	0.699517i	$0.246602\pi$
$599$			34.2406i			1.39903i	−0.714616	+	0.699517i	$0.753398\pi$
$600$		0			0
$601$	30.0146			1.22432			0.612160	−	0.790734i	$-0.290301\pi$
$601$	30.0146			1.22432			0.612160	+	0.790734i	$0.290301\pi$
$602$	8.46308	+	8.46308i	0.344929	+	0.344929i
$603$	26.0342	+	26.0342i	1.06020	+	1.06020i
$604$			1.79191i			0.0729119i
$605$		0			0
$606$	−1.31648			−0.0534784
$607$	10.3099	+	10.3099i	0.418468	+	0.418468i	0.884675	−	0.466208i	$-0.154380\pi$
$607$	10.3099	+	10.3099i	0.418468	+	0.418468i	−0.466208	+	0.884675i	$0.654380\pi$
$608$	−1.68267	−	1.68267i	−0.0682414	−	0.0682414i
$609$	−9.34511			−0.378683
$610$		0			0
$611$	−10.7300			−0.434089
$612$	−10.2599	+	10.2599i	−0.414731	+	0.414731i
$613$	−25.0099	−	25.0099i	−1.01014	−	1.01014i	−0.999948	−	0.0101903i	$-0.996756\pi$
$613$	−25.0099	−	25.0099i	−1.01014	−	1.01014i	−0.0101903	−	0.999948i	$-0.503244\pi$
$614$			20.5049i			0.827511i
$615$		0			0
$616$	−4.15133			−0.167262
$617$	25.6567	−	25.6567i	1.03290	−	1.03290i	0.0334597	−	0.999440i	$-0.489347\pi$
$617$	25.6567	−	25.6567i	1.03290	−	1.03290i	0.999440	−	0.0334597i	$-0.0106525\pi$
$618$	−4.26253	−	4.26253i	−0.171464	−	0.171464i
$619$	−44.9169			−1.80536			−0.902681	−	0.430311i	$-0.858404\pi$
$619$	−44.9169			−1.80536			−0.902681	+	0.430311i	$0.858404\pi$
$620$		0			0
$621$	−12.5506	+	16.6349i	−0.503639	+	0.667537i
$622$	−16.0758	−	16.0758i	−0.644581	−	0.644581i
$623$	−2.75617	+	2.75617i	−0.110423	+	0.110423i
$624$			4.89111i			0.195801i
$625$		0			0
$626$			17.6917i			0.707102i
$627$	1.91771	+	1.91771i	0.0765859	+	0.0765859i
$628$	−2.30909	−	2.30909i	−0.0921426	−	0.0921426i
$629$		−	19.9928i		−	0.797164i
$630$		0			0
$631$			1.07470i			0.0427831i	0.999771	+	0.0213916i	$0.00680967\pi$
$631$			1.07470i			0.0427831i	−0.999771	+	0.0213916i	$0.993190\pi$
$632$	−4.03189	+	4.03189i	−0.160380	+	0.160380i
$633$	9.81944	−	9.81944i	0.390288	−	0.390288i
$634$			20.9287i			0.831186i
$635$		0			0
$636$			4.75932i			0.188719i
$637$	7.62077	+	7.62077i	0.301946	+	0.301946i
$638$	−3.83170	−	3.83170i	−0.151698	−	0.151698i
$639$		−	21.4133i		−	0.847097i
$640$		0			0
$641$		−	27.4605i		−	1.08462i	−0.840177	−	0.542312i	$-0.817549\pi$
$641$		−	27.4605i		−	1.08462i	0.840177	−	0.542312i	$-0.182451\pi$
$642$	−6.33868	+	6.33868i	−0.250168	+	0.250168i
$643$	15.2206	+	15.2206i	0.600242	+	0.600242i	0.940377	−	0.340135i	$-0.110473\pi$
$643$	15.2206	+	15.2206i	0.600242	+	0.600242i	−0.340135	+	0.940377i	$0.610473\pi$
$644$	−8.56555	+	11.3530i	−0.337530	+	0.447371i
$645$		0			0
$646$	14.7731			0.581241
$647$	10.8512	+	10.8512i	0.426606	+	0.426606i	0.887471	−	0.460864i	$-0.152461\pi$
$647$	10.8512	+	10.8512i	0.426606	+	0.426606i	−0.460864	+	0.887471i	$0.652461\pi$
$648$	−2.45666	+	2.45666i	−0.0965066	+	0.0965066i
$649$	−7.93466			−0.311462
$650$		0			0
$651$			13.8697i			0.543595i
$652$	−14.4525	−	14.4525i	−0.566005	−	0.566005i
$653$	−27.5566	+	27.5566i	−1.07837	+	1.07837i	−0.0817179	+	0.996656i	$0.526041\pi$
$653$	−27.5566	+	27.5566i	−1.07837	+	1.07837i	−0.996656	+	0.0817179i	$0.973959\pi$
$654$	9.67976			0.378508
$655$		0			0
$656$	−2.49121			−0.0972654
$657$	−25.2126	−	25.2126i	−0.983638	−	0.983638i
$658$	3.74501	+	3.74501i	0.145996	+	0.145996i
$659$	−13.1299			−0.511467			−0.255734	−	0.966747i	$-0.582317\pi$
$659$	−13.1299			−0.511467			−0.255734	+	0.966747i	$0.582317\pi$
$660$		0			0
$661$		−	20.2923i		−	0.789278i	−0.918836	−	0.394639i	$-0.870870\pi$
$661$		−	20.2923i		−	0.789278i	0.918836	−	0.394639i	$-0.129130\pi$
$662$	−10.1247	−	10.1247i	−0.393506	−	0.393506i
$663$	−21.4709	−	21.4709i	−0.833861	−	0.833861i
$664$	−16.4522			−0.638469
$665$		0			0
$666$		−	7.52687i		−	0.291660i
$667$	−18.3849	+	2.57283i	−0.711866	+	0.0996203i
$668$	−11.7423	+	11.7423i	−0.454325	+	0.454325i
$669$			1.36911i			0.0529329i
$670$		0			0
$671$	18.3622			0.708865
$672$	1.70711	−	1.70711i	0.0658531	−	0.0658531i
$673$	31.0809	−	31.0809i	1.19808	−	1.19808i	0.223341	−	0.974740i	$-0.428304\pi$
$673$	31.0809	−	31.0809i	1.19808	−	1.19808i	0.974740	−	0.223341i	$-0.0716963\pi$
$674$	2.67770			0.103141
$675$		0			0
$676$	23.0947			0.888259
$677$	−30.4764	+	30.4764i	−1.17130	+	1.17130i	−0.189402	+	0.981900i	$0.560655\pi$
$677$	−30.4764	+	30.4764i	−1.17130	+	1.17130i	−0.981900	+	0.189402i	$0.939345\pi$
$678$	6.44018	+	6.44018i	0.247334	+	0.247334i
$679$		−	32.8793i		−	1.26179i
$680$		0			0
$681$		−	16.5551i		−	0.634391i
$682$	−5.68687	+	5.68687i	−0.217761	+	0.217761i
$683$	30.8836	−	30.8836i	1.18173	−	1.18173i	0.202434	−	0.979296i	$-0.435115\pi$
$683$	30.8836	−	30.8836i	1.18173	−	1.18173i	0.979296	−	0.202434i	$-0.0648850\pi$
$684$	5.56178			0.212660
$685$		0			0
$686$			15.4385i			0.589444i
$687$	−2.48736	+	2.48736i	−0.0948985	+	0.0948985i
$688$	−2.85390	−	2.85390i	−0.108804	−	0.108804i
$689$	35.1222			1.33805
$690$		0			0
$691$	−37.6570			−1.43254			−0.716270	−	0.697823i	$-0.754152\pi$
$691$	−37.6570			−1.43254			−0.716270	+	0.697823i	$0.754152\pi$
$692$	7.36165	+	7.36165i	0.279848	+	0.279848i
$693$	6.86075	−	6.86075i	0.260618	−	0.260618i
$694$			7.88894i			0.299460i
$695$		0			0
$696$	3.15133			0.119451
$697$	10.9359	−	10.9359i	0.414225	−	0.414225i
$698$	3.41275	−	3.41275i	0.129174	−	0.129174i
$699$		−	1.06100i		−	0.0401305i
$700$		0			0
$701$		−	36.4494i		−	1.37668i	−0.725390	−	0.688338i	$-0.758341\pi$
$701$		−	36.4494i		−	1.37668i	0.725390	−	0.688338i	$-0.241659\pi$
$702$	−18.4590	−	18.4590i	−0.696689	−	0.696689i
$703$	−5.41895	+	5.41895i	−0.204379	+	0.204379i
$704$	1.39990			0.0527608
$705$		0			0
$706$	−23.0567			−0.867749
$707$	3.39082	−	3.39082i	0.127525	−	0.127525i
$708$	3.26288	−	3.26288i	0.122627	−	0.122627i
$709$	0.752533			0.0282620			0.0141310	−	0.999900i	$-0.495502\pi$
$709$	0.752533			0.0282620			0.0141310	+	0.999900i	$0.495502\pi$
$710$		0			0
$711$		−	13.3267i		−	0.499791i
$712$	0.929427	−	0.929427i	0.0348317	−	0.0348317i
$713$	3.81850	+	27.2862i	0.143004	+	1.02188i
$714$			14.9876i			0.560899i
$715$		0			0
$716$	5.55173			0.207478
$717$	5.35795	+	5.35795i	0.200096	+	0.200096i
$718$	21.0424	+	21.0424i	0.785297	+	0.785297i
$719$			14.0360i			0.523456i	0.965142	+	0.261728i	$0.0842923\pi$
$719$			14.0360i			0.523456i	−0.965142	+	0.261728i	$0.915708\pi$
$720$		0			0
$721$	21.9577			0.817748
$722$	9.43084	+	9.43084i	0.350979	+	0.350979i
$723$	−12.3335	−	12.3335i	−0.458686	−	0.458686i
$724$	23.0901			0.858137
$725$		0			0
$726$	7.35982			0.273149
$727$	12.3873	−	12.3873i	0.459419	−	0.459419i	−0.439046	−	0.898465i	$-0.644683\pi$
$727$	12.3873	−	12.3873i	0.459419	−	0.459419i	0.898465	+	0.439046i	$0.144683\pi$
$728$	−12.5979	−	12.5979i	−0.466908	−	0.466908i
$729$			2.49220i			0.0923037i
$730$		0			0
$731$	25.0560			0.926728
$732$	−7.55088	+	7.55088i	−0.279089	+	0.279089i
$733$	−7.76852	−	7.76852i	−0.286937	−	0.286937i	0.548931	−	0.835868i	$-0.315035\pi$
$733$	−7.76852	−	7.76852i	−0.286937	−	0.286937i	−0.835868	+	0.548931i	$0.815035\pi$
$734$	31.2446			1.15326
$735$		0			0
$736$	2.88845	−	3.82843i	0.106470	−	0.141118i
$737$	15.5935	+	15.5935i	0.574393	+	0.574393i
$738$	4.11713	−	4.11713i	0.151554	−	0.151554i
$739$		−	8.15036i		−	0.299816i	−0.988700	−	0.149908i	$-0.952102\pi$
$739$		−	8.15036i		−	0.299816i	0.988700	−	0.149908i	$-0.0478977\pi$
$740$		0			0
$741$			11.6392i			0.427576i
$742$	−12.2584	−	12.2584i	−0.450021	−	0.450021i
$743$	−23.1386	−	23.1386i	−0.848874	−	0.848874i	0.141119	−	0.989993i	$-0.454930\pi$
$743$	−23.1386	−	23.1386i	−0.848874	−	0.848874i	−0.989993	+	0.141119i	$0.954930\pi$
$744$		−	4.67710i		−	0.171471i
$745$		0			0
$746$			8.03701i			0.294256i
$747$	27.1899	−	27.1899i	0.994827	−	0.994827i
$748$	−6.14526	+	6.14526i	−0.224693	+	0.224693i
$749$		−	32.6527i		−	1.19310i
$750$		0			0
$751$			12.9246i			0.471625i	0.971799	+	0.235813i	$0.0757752\pi$
$751$			12.9246i			0.471625i	−0.971799	+	0.235813i	$0.924225\pi$
$752$	−1.26288	−	1.26288i	−0.0460526	−	0.0460526i
$753$	−3.61993	−	3.61993i	−0.131917	−	0.131917i
$754$		−	23.2558i		−	0.846925i
$755$		0			0
$756$			12.8852i			0.468630i
$757$	22.6178	−	22.6178i	0.822059	−	0.822059i	−0.164344	−	0.986403i	$-0.552551\pi$
$757$	22.6178	−	22.6178i	0.822059	−	0.822059i	0.986403	+	0.164344i	$0.0525506\pi$
$758$	−20.1193	−	20.1193i	−0.730765	−	0.730765i
$759$	−3.29191	+	4.36318i	−0.119489	+	0.158373i
$760$		0			0
$761$	−14.9443			−0.541732			−0.270866	−	0.962617i	$-0.587310\pi$
$761$	−14.9443			−0.541732			−0.270866	+	0.962617i	$0.587310\pi$
$762$	−5.64777	−	5.64777i	−0.204597	−	0.204597i
$763$	−24.9318	+	24.9318i	−0.902592	+	0.902592i
$764$	7.88579			0.285298
$765$		0			0
$766$		−	6.19840i		−	0.223957i
$767$	−24.0790	−	24.0790i	−0.869441	−	0.869441i
$768$	−0.575666	+	0.575666i	−0.0207726	+	0.0207726i
$769$	10.3598			0.373583			0.186792	−	0.982400i	$-0.440191\pi$
$769$	10.3598			0.373583			0.186792	+	0.982400i	$0.440191\pi$
$770$		0			0
$771$	−21.3120			−0.767534
$772$	5.18469	+	5.18469i	0.186601	+	0.186601i
$773$	24.0445	+	24.0445i	0.864821	+	0.864821i	0.991893	−	0.127072i	$-0.0405580\pi$
$773$	24.0445	+	24.0445i	0.864821	+	0.864821i	−0.127072	+	0.991893i	$0.540558\pi$
$774$	9.43306			0.339064
$775$		0			0
$776$			11.0875i			0.398016i
$777$	−5.49763	−	5.49763i	−0.197226	−	0.197226i
$778$	−4.23252	−	4.23252i	−0.151743	−	0.151743i
$779$	−5.92823			−0.212401
$780$		0			0
$781$		−	12.8257i		−	0.458941i
$782$	4.12629	+	29.4856i	0.147556	+	1.05440i
$783$	−11.8931	+	11.8931i	−0.425024	+	0.425024i
$784$			1.79387i			0.0640669i
$785$		0			0
$786$	−9.59890			−0.342382
$787$	5.07531	−	5.07531i	0.180915	−	0.180915i	−0.610839	−	0.791755i	$-0.709168\pi$
$787$	5.07531	−	5.07531i	0.180915	−	0.180915i	0.791755	+	0.610839i	$0.209168\pi$
$788$	−3.44191	+	3.44191i	−0.122613	+	0.122613i
$789$	−1.68498			−0.0599870
$790$		0			0
$791$	−33.1755			−1.17958
$792$	−2.31356	+	2.31356i	−0.0822089	+	0.0822089i
$793$	55.7230	+	55.7230i	1.97878	+	1.97878i
$794$			31.4771i			1.11708i
$795$		0			0
$796$		−	15.8241i		−	0.560870i
$797$	4.54720	−	4.54720i	0.161070	−	0.161070i	−0.621971	−	0.783041i	$-0.713668\pi$
$797$	4.54720	−	4.54720i	0.161070	−	0.161070i	0.783041	+	0.621971i	$0.213668\pi$
$798$	4.06233	−	4.06233i	0.143805	−	0.143805i
$799$	11.0875			0.392249
$800$		0			0
$801$			3.07206i			0.108546i
$802$	16.3307	−	16.3307i	0.576656	−	0.576656i
$803$	−15.1014	−	15.1014i	−0.532916	−	0.532916i
$804$	−12.8247			−0.452291
$805$		0			0
$806$	−34.5154			−1.21575
$807$	2.48638	+	2.48638i	0.0875248	+	0.0875248i
$808$	−1.14344	+	1.14344i	−0.0402262	+	0.0402262i
$809$			50.1835i			1.76436i	0.470913	+	0.882180i	$0.343925\pi$
$809$			50.1835i			1.76436i	−0.470913	+	0.882180i	$0.656075\pi$
$810$		0			0
$811$	−6.03654			−0.211971			−0.105986	−	0.994368i	$-0.533800\pi$
$811$	−6.03654			−0.211971			−0.105986	+	0.994368i	$0.533800\pi$
$812$	−8.11678	+	8.11678i	−0.284843	+	0.284843i
$813$	−0.972154	+	0.972154i	−0.0340949	+	0.0340949i
$814$		−	4.50830i		−	0.158016i
$815$		0			0
$816$		−	5.05409i		−	0.176929i
$817$	−6.79131	−	6.79131i	−0.237598	−	0.237598i
$818$	14.2373	−	14.2373i	0.497797	−	0.497797i
$819$	41.6400			1.45502
$820$		0			0
$821$	42.8651			1.49600			0.748002	−	0.663697i	$-0.231014\pi$
$821$	42.8651			1.49600			0.748002	+	0.663697i	$0.231014\pi$
$822$	−3.08411	+	3.08411i	−0.107571	+	0.107571i
$823$	8.68113	−	8.68113i	0.302605	−	0.302605i	−0.539427	−	0.842032i	$-0.681359\pi$
$823$	8.68113	−	8.68113i	0.302605	−	0.302605i	0.842032	+	0.539427i	$0.181359\pi$
$824$	−7.40452			−0.257949
$825$		0			0
$826$			16.8082i			0.584832i
$827$	−1.62311	+	1.62311i	−0.0564412	+	0.0564412i	−0.734764	−	0.678323i	$-0.762707\pi$
$827$	−1.62311	+	1.62311i	−0.0564412	+	0.0564412i	0.678323	+	0.734764i	$0.262707\pi$
$828$	1.55346	+	11.1007i	0.0539866	+	0.385777i
$829$			7.84786i			0.272567i	0.990670	+	0.136284i	$0.0435159\pi$
$829$			7.84786i			0.272567i	−0.990670	+	0.136284i	$0.956484\pi$
$830$		0			0
$831$	−6.32277			−0.219335
$832$	4.24822	+	4.24822i	0.147281	+	0.147281i
$833$	−7.87471	−	7.87471i	−0.272843	−	0.272843i
$834$			4.68183i			0.162119i
$835$		0			0
$836$	3.33129			0.115215
$837$	17.6513	+	17.6513i	0.610117	+	0.610117i
$838$	15.7678	+	15.7678i	0.544690	+	0.544690i
$839$	25.5054			0.880545			0.440272	−	0.897864i	$-0.354882\pi$
$839$	25.5054			0.880545			0.440272	+	0.897864i	$0.354882\pi$
$840$		0			0
$841$	14.0164			0.483323
$842$	8.05059	−	8.05059i	0.277442	−	0.277442i
$843$	2.67453	+	2.67453i	0.0921156	+	0.0921156i
$844$		−	17.0575i		−	0.587144i
$845$		0			0
$846$	4.17423			0.143513
$847$	−18.9564	+	18.9564i	−0.651351	+	0.651351i
$848$	4.13375	+	4.13375i	0.141954	+	0.141954i
$849$	−21.3487			−0.732687
$850$		0			0
$851$	−12.3292	−	9.30208i	−0.422640	−	0.318871i
$852$	5.27418	+	5.27418i	0.180691	+	0.180691i
$853$	−25.0722	+	25.0722i	−0.858455	+	0.858455i	−0.991156	−	0.132701i	$-0.957635\pi$
$853$	−25.0722	+	25.0722i	−0.858455	+	0.858455i	0.132701	+	0.991156i	$0.457635\pi$
$854$		−	38.8971i		−	1.33103i
$855$		0			0
$856$			11.0110i			0.376350i
$857$	5.96703	+	5.96703i	0.203830	+	0.203830i	0.801639	−	0.597809i	$-0.203962\pi$
$857$	5.96703	+	5.96703i	0.203830	+	0.203830i	−0.597809	+	0.801639i	$0.703962\pi$
$858$	−4.84161	−	4.84161i	−0.165290	−	0.165290i
$859$		−	47.8075i		−	1.63117i	−0.578636	−	0.815586i	$-0.696415\pi$
$859$		−	47.8075i		−	1.63117i	0.578636	−	0.815586i	$-0.303585\pi$
$860$		0			0
$861$		−	6.01431i		−	0.204967i
$862$	18.9781	−	18.9781i	0.646396	−	0.646396i
$863$	7.90989	−	7.90989i	0.269256	−	0.269256i	−0.559545	−	0.828800i	$-0.689024\pi$
$863$	7.90989	−	7.90989i	0.269256	−	0.269256i	0.828800	+	0.559545i	$0.189024\pi$
$864$		−	4.34511i		−	0.147824i
$865$		0			0
$866$		−	6.44807i		−	0.219114i
$867$	12.4000	+	12.4000i	0.421128	+	0.421128i
$868$	12.0466	+	12.0466i	0.408889	+	0.408889i
$869$		−	7.98218i		−	0.270777i
$870$		0			0
$871$			94.6417i			3.20681i
$872$	8.40744	−	8.40744i	0.284712	−	0.284712i
$873$	−18.3238	−	18.3238i	−0.620167	−	0.620167i
$874$	6.87353	−	9.11036i	0.232501	−	0.308162i
$875$		0			0
$876$	12.4199			0.419631
$877$	21.3111	+	21.3111i	0.719625	+	0.719625i	0.968528	−	0.248904i	$-0.0800703\pi$
$877$	21.3111	+	21.3111i	0.719625	+	0.719625i	−0.248904	+	0.968528i	$0.580070\pi$
$878$	10.3199	−	10.3199i	0.348280	−	0.348280i
$879$	−5.58300			−0.188310
$880$		0			0
$881$			21.1772i			0.713477i	0.934204	+	0.356739i	$0.116111\pi$
$881$			21.1772i			0.713477i	−0.934204	+	0.356739i	$0.883889\pi$
$882$	−2.96467	−	2.96467i	−0.0998255	−	0.0998255i
$883$	−0.912803	+	0.912803i	−0.0307183	+	0.0307183i	−0.722299	−	0.691581i	$-0.756915\pi$
$883$	−0.912803	+	0.912803i	−0.0307183	+	0.0307183i	0.691581	+	0.722299i	$0.256915\pi$
$884$	−37.2975			−1.25445
$885$		0			0
$886$	22.1327			0.743563
$887$	−21.4132	−	21.4132i	−0.718984	−	0.718984i	0.249413	−	0.968397i	$-0.419762\pi$
$887$	−21.4132	−	21.4132i	−0.718984	−	0.718984i	−0.968397	+	0.249413i	$0.919762\pi$
$888$	1.85390	+	1.85390i	0.0622127	+	0.0622127i
$889$	29.0935			0.975766
$890$		0			0
$891$		−	4.86359i		−	0.162936i
$892$	1.18915	+	1.18915i	0.0398158	+	0.0398158i
$893$	−3.00523	−	3.00523i	−0.100566	−	0.100566i
$894$	−1.49714			−0.0500718
$895$		0			0
$896$		−	2.96545i		−	0.0990686i
$897$	−23.2306	+	3.25094i	−0.775646	+	0.108546i
$898$	−24.7197	+	24.7197i	−0.824907	+	0.824907i
$899$			22.2382i			0.741685i
$900$		0			0
$901$	−36.2925			−1.20908
$902$	2.46600	−	2.46600i	0.0821087	−	0.0821087i
$903$	6.88992	−	6.88992i	0.229282	−	0.229282i
$904$	11.1874			0.372086
$905$		0			0
$906$	1.45882			0.0484661
$907$	−24.6313	+	24.6313i	−0.817869	+	0.817869i	−0.985799	−	0.167930i	$-0.946292\pi$
$907$	−24.6313	+	24.6313i	−0.817869	+	0.817869i	0.167930	+	0.985799i	$0.446292\pi$
$908$	−14.3791	−	14.3791i	−0.477186	−	0.477186i
$909$		−	3.77945i		−	0.125356i
$910$		0			0
$911$		−	31.5922i		−	1.04670i	−0.852119	−	0.523348i	$-0.824683\pi$
$911$		−	31.5922i		−	1.04670i	0.852119	−	0.523348i	$-0.175317\pi$
$912$	−1.36989	+	1.36989i	−0.0453616	+	0.0453616i
$913$	16.2857	−	16.2857i	0.538978	−	0.538978i
$914$	0.405717			0.0134199
$915$		0			0
$916$			4.32083i			0.142764i
$917$	24.7236	−	24.7236i	0.816444	−	0.816444i
$918$	19.0741	+	19.0741i	0.629538	+	0.629538i
$919$	−5.24715			−0.173087			−0.0865437	−	0.996248i	$-0.527582\pi$
$919$	−5.24715			−0.173087			−0.0865437	+	0.996248i	$0.527582\pi$
$920$		0			0
$921$	16.6934			0.550065
$922$	12.0052	+	12.0052i	0.395371	+	0.395371i
$923$	38.9217	−	38.9217i	1.28112	−	1.28112i
$924$			3.37966i			0.111183i
$925$		0			0
$926$	19.3849			0.637027
$927$	12.2372	−	12.2372i	0.401922	−	0.401922i
$928$	2.73712	−	2.73712i	0.0898503	−	0.0898503i
$929$			35.7022i			1.17135i	0.810545	+	0.585676i	$0.199171\pi$
$929$			35.7022i			1.17135i	−0.810545	+	0.585676i	$0.800829\pi$
$930$		0			0
$931$			4.26881i			0.139905i
$932$	−0.921537	−	0.921537i	−0.0301860	−	0.0301860i
$933$	−13.0875	+	13.0875i	−0.428467	+	0.428467i
$934$	−8.88313			−0.290665
$935$		0			0
$936$	−14.0417			−0.458969
$937$	−27.6575	+	27.6575i	−0.903530	+	0.903530i	−0.995740	−	0.0922093i	$-0.970607\pi$
$937$	−27.6575	+	27.6575i	−0.903530	+	0.903530i	0.0922093	+	0.995740i	$0.470607\pi$
$938$	33.0321	−	33.0321i	1.07853	−	1.07853i
$939$	14.4031			0.470026
$940$		0			0
$941$			15.6518i			0.510234i	0.966910	+	0.255117i	$0.0821139\pi$
$941$			15.6518i			0.510234i	−0.966910	+	0.255117i	$0.917886\pi$
$942$	−1.87986	+	1.87986i	−0.0612492	+	0.0612492i
$943$	−1.65582	−	11.8321i	−0.0539208	−	0.385307i
$944$		−	5.66801i		−	0.184478i
$945$		0			0
$946$	5.65003			0.183698
$947$	40.5901	+	40.5901i	1.31900	+	1.31900i	0.914568	+	0.404431i	$0.132531\pi$
$947$	40.5901	+	40.5901i	1.31900	+	1.31900i	0.404431	+	0.914568i	$0.367469\pi$
$948$	3.28242	+	3.28242i	0.106608	+	0.106608i
$949$		−	91.6549i		−	2.97524i
$950$		0			0
$951$	17.0384			0.552507
$952$	13.0177	+	13.0177i	0.421905	+	0.421905i
$953$	14.1269	+	14.1269i	0.457615	+	0.457615i	0.897872	−	0.440257i	$-0.145113\pi$
$953$	14.1269	+	14.1269i	0.457615	+	0.457615i	−0.440257	+	0.897872i	$0.645113\pi$
$954$	−13.6634			−0.442369
$955$		0			0
$956$	9.30740			0.301023
$957$	−3.11944	+	3.11944i	−0.100837	+	0.100837i
$958$	2.82259	+	2.82259i	0.0911938	+	0.0911938i
$959$		−	15.8873i		−	0.513026i
$960$		0			0
$961$	2.00512			0.0646812
$962$	13.6811	−	13.6811i	0.441097	−	0.441097i
$963$	−18.1975	−	18.1975i	−0.586407	−	0.586407i
$964$	−21.4247			−0.690042
$965$		0			0
$966$	9.24264	+	6.97334i	0.297377	+	0.224363i
$967$	11.5304	+	11.5304i	0.370792	+	0.370792i	0.867766	−	0.496974i	$-0.165555\pi$
$967$	11.5304	+	11.5304i	0.370792	+	0.370792i	−0.496974	+	0.867766i	$0.665555\pi$
$968$	6.39244	−	6.39244i	0.205461	−	0.205461i
$969$		−	12.0270i		−	0.386364i
$970$		0			0
$971$		−	36.5063i		−	1.17154i	−0.810476	−	0.585771i	$-0.800792\pi$
$971$		−	36.5063i		−	1.17154i	0.810476	−	0.585771i	$-0.199208\pi$
$972$	11.2174	+	11.2174i	0.359797	+	0.359797i
$973$	−12.0588	−	12.0588i	−0.386588	−	0.386588i
$974$		−	10.8164i		−	0.346580i
$975$		0			0
$976$			13.1168i			0.419858i
$977$	−10.4018	+	10.4018i	−0.332785	+	0.332785i	−0.853643	−	0.520858i	$-0.825612\pi$
$977$	−10.4018	+	10.4018i	−0.332785	+	0.332785i	0.520858	+	0.853643i	$0.325612\pi$
$978$	−11.7660	+	11.7660i	−0.376236	+	0.376236i
$979$			1.84004i			0.0588080i
$980$		0			0
$981$			27.7893i			0.887245i
$982$	−4.83546	−	4.83546i	−0.154306	−	0.154306i
$983$	16.4444	+	16.4444i	0.524494	+	0.524494i	0.918925	−	0.394431i	$-0.129058\pi$
$983$	16.4444	+	16.4444i	0.524494	+	0.524494i	−0.394431	+	0.918925i	$0.629058\pi$
$984$			2.02813i			0.0646544i
$985$		0			0
$986$			24.0307i			0.765293i
$987$	3.04887	−	3.04887i	0.0970465	−	0.0970465i
$988$	10.1093	+	10.1093i	0.321620	+	0.321620i
$989$	11.6578	−	15.4516i	0.370698	−	0.491333i
$990$		0			0
$991$	−23.2243			−0.737743			−0.368872	−	0.929480i	$-0.620256\pi$
$991$	−23.2243			−0.737743			−0.368872	+	0.929480i	$0.620256\pi$
$992$	−4.06233	−	4.06233i	−0.128979	−	0.128979i
$993$	−8.24264	+	8.24264i	−0.261572	+	0.261572i
$994$	−27.1691			−0.861751
$995$		0			0
$996$			13.3940i			0.424404i
$997$	−38.7536	−	38.7536i	−1.22734	−	1.22734i	−0.964966	−	0.262374i	$-0.915495\pi$
$997$	−38.7536	−	38.7536i	−1.22734	−	1.22734i	−0.262374	−	0.964966i	$-0.584505\pi$
$998$	18.4985	−	18.4985i	0.585560	−	0.585560i
$999$	−13.9932			−0.442724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.c.1057.1		8
5.2	odd	4		230.2.e.b.183.4	yes	8
5.3	odd	4		1150.2.e.b.643.1		8
5.4	even	2		230.2.e.a.137.4	✓	8
23.22	odd	2		1150.2.e.b.1057.1		8
115.22	even	4		230.2.e.a.183.4	yes	8
115.68	even	4	inner	1150.2.e.c.643.1		8
115.114	odd	2		230.2.e.b.137.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.e.a.137.4	✓	8	5.4	even	2
230.2.e.a.183.4	yes	8	115.22	even	4
230.2.e.b.137.4	yes	8	115.114	odd	2
230.2.e.b.183.4	yes	8	5.2	odd	4
1150.2.e.b.643.1		8	5.3	odd	4
1150.2.e.b.1057.1		8	23.22	odd	2
1150.2.e.c.643.1		8	115.68	even	4	inner
1150.2.e.c.1057.1		8	1.1	even	1	trivial

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.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.575666 + 0.575666i) q^{3} +1.00000i q^{4} +0.814115 q^{6} +(-2.09689 + 2.09689i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.33722i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.575666 + 0.575666i) q^{3} +1.00000i q^{4} +0.814115 q^{6} +(-2.09689 + 2.09689i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.33722i q^{9} +1.39990i q^{11} +(-0.575666 - 0.575666i) q^{12} +(-4.24822 + 4.24822i) q^{13} +2.96545 q^{14} -1.00000 q^{16} +(4.38978 - 4.38978i) q^{17} +(1.65266 - 1.65266i) q^{18} -2.37966 q^{19} -2.41421i q^{21} +(0.989880 - 0.989880i) q^{22} +(-0.664664 - 4.74955i) q^{23} +0.814115i q^{24} +6.00789 q^{26} +(-3.07245 - 3.07245i) q^{27} +(-2.09689 - 2.09689i) q^{28} -3.87087i q^{29} -5.74501 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.805875 - 0.805875i) q^{33} -6.20809 q^{34} -2.33722 q^{36} +(2.27719 - 2.27719i) q^{37} +(1.68267 + 1.68267i) q^{38} -4.89111i q^{39} +2.49121 q^{41} +(-1.70711 + 1.70711i) q^{42} +(2.85390 + 2.85390i) q^{43} -1.39990 q^{44} +(-2.88845 + 3.82843i) q^{46} +(1.26288 + 1.26288i) q^{47} +(0.575666 - 0.575666i) q^{48} -1.79387i q^{49} +5.05409i q^{51} +(-4.24822 - 4.24822i) q^{52} +(-4.13375 - 4.13375i) q^{53} +4.34511i q^{54} +2.96545i q^{56} +(1.36989 - 1.36989i) q^{57} +(-2.73712 + 2.73712i) q^{58} +5.66801i q^{59} -13.1168i q^{61} +(4.06233 + 4.06233i) q^{62} +(-4.90088 - 4.90088i) q^{63} -1.00000i q^{64} +1.13968i q^{66} +(11.1390 - 11.1390i) q^{67} +(4.38978 + 4.38978i) q^{68} +(3.11678 + 2.35153i) q^{69} -9.16188 q^{71} +(1.65266 + 1.65266i) q^{72} +(-10.7875 + 10.7875i) q^{73} -3.22044 q^{74} -2.37966i q^{76} +(-2.93543 - 2.93543i) q^{77} +(-3.45854 + 3.45854i) q^{78} -5.70196 q^{79} -3.47424 q^{81} +(-1.76155 - 1.76155i) q^{82} +(-11.6335 - 11.6335i) q^{83} +2.41421 q^{84} -4.03602i q^{86} +(2.22833 + 2.22833i) q^{87} +(0.989880 + 0.989880i) q^{88} +1.31441 q^{89} -17.8161i q^{91} +(4.74955 - 0.664664i) q^{92} +(3.30721 - 3.30721i) q^{93} -1.78598i q^{94} -0.814115 q^{96} +(-7.84001 + 7.84001i) q^{97} +(-1.26846 + 1.26846i) q^{98} -3.27187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{6}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^6	\( 8 q + 4 q^{3} + 4 q^{6} + 4 q^{12} + 4 q^{14} - 8 q^{16} + 24 q^{17} + 8 q^{18} + 12 q^{19} - 12 q^{22} - 16 q^{23} + 12 q^{26} - 8 q^{27} - 4 q^{31} + 20 q^{33} + 4 q^{34} - 4 q^{36} + 4 q^{37} + 8 q^{38} + 12 q^{41} - 8 q^{42} - 20 q^{43} - 20 q^{44} + 16 q^{47} - 4 q^{48} + 20 q^{57} - 16 q^{58} - 4 q^{62} - 4 q^{67} + 24 q^{68} - 12 q^{69} - 44 q^{71} + 8 q^{72} - 28 q^{73} - 48 q^{74} - 4 q^{77} + 4 q^{78} - 8 q^{79} - 16 q^{81} - 8 q^{82} - 28 q^{83} + 8 q^{84} + 4 q^{87} - 12 q^{88} + 40 q^{89} + 16 q^{92} + 12 q^{93} - 4 q^{96} - 8 q^{97} - 16 q^{98} + 36 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^6 + 4 * q^12 + 4 * q^14 - 8 * q^16 + 24 * q^17 + 8 * q^18 + 12 * q^19 - 12 * q^22 - 16 * q^23 + 12 * q^26 - 8 * q^27 - 4 * q^31 + 20 * q^33 + 4 * q^34 - 4 * q^36 + 4 * q^37 + 8 * q^38 + 12 * q^41 - 8 * q^42 - 20 * q^43 - 20 * q^44 + 16 * q^47 - 4 * q^48 + 20 * q^57 - 16 * q^58 - 4 * q^62 - 4 * q^67 + 24 * q^68 - 12 * q^69 - 44 * q^71 + 8 * q^72 - 28 * q^73 - 48 * q^74 - 4 * q^77 + 4 * q^78 - 8 * q^79 - 16 * q^81 - 8 * q^82 - 28 * q^83 + 8 * q^84 + 4 * q^87 - 12 * q^88 + 40 * q^89 + 16 * q^92 + 12 * q^93 - 4 * q^96 - 8 * q^97 - 16 * q^98 + 36 * q^99

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