LMFDB - Embedded newform 230.2.e.a.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.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:	$1.83655924649$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.4
Root			$-1.22833i$ of defining polynomial
Character	$\chi$	$=$	230.137
Dual form			230.2.e.a.183.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.575666 - 0.575666i) q^{3} +1.00000i q^{4} +(-0.185885 - 2.22833i) q^{5} +0.814115 q^{6} +(2.09689 - 2.09689i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.33722i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.575666 - 0.575666i) q^{3} +1.00000i q^{4} +(-0.185885 - 2.22833i) q^{5} +0.814115 q^{6} +(2.09689 - 2.09689i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.33722i q^{9} +(1.44423 - 1.70711i) q^{10} +1.39990i q^{11} +(0.575666 + 0.575666i) q^{12} +(4.24822 - 4.24822i) q^{13} +2.96545 q^{14} +(-1.38978 - 1.17576i) q^{15} -1.00000 q^{16} +(-4.38978 + 4.38978i) q^{17} +(-1.65266 + 1.65266i) q^{18} -2.37966 q^{19} +(2.22833 - 0.185885i) q^{20} -2.41421i q^{21} +(-0.989880 + 0.989880i) q^{22} +(0.664664 + 4.74955i) q^{23} +0.814115i q^{24} +(-4.93089 + 0.828427i) q^{25} +6.00789 q^{26} +(3.07245 + 3.07245i) q^{27} +(2.09689 + 2.09689i) q^{28} -3.87087i q^{29} +(-0.151332 - 1.81411i) q^{30} -5.74501 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.805875 + 0.805875i) q^{33} -6.20809 q^{34} +(-5.06233 - 4.28277i) q^{35} -2.33722 q^{36} +(-2.27719 + 2.27719i) q^{37} +(-1.68267 - 1.68267i) q^{38} -4.89111i q^{39} +(1.70711 + 1.44423i) q^{40} +2.49121 q^{41} +(1.70711 - 1.70711i) q^{42} +(-2.85390 - 2.85390i) q^{43} -1.39990 q^{44} +(5.20809 - 0.434454i) q^{45} +(-2.88845 + 3.82843i) q^{46} +(-1.26288 - 1.26288i) q^{47} +(-0.575666 + 0.575666i) q^{48} -1.79387i q^{49} +(-4.07245 - 2.90088i) q^{50} +5.05409i q^{51} +(4.24822 + 4.24822i) q^{52} +(4.13375 + 4.13375i) q^{53} +4.34511i q^{54} +(3.11944 - 0.260221i) q^{55} +2.96545i q^{56} +(-1.36989 + 1.36989i) q^{57} +(2.73712 - 2.73712i) q^{58} +5.66801i q^{59} +(1.17576 - 1.38978i) q^{60} -13.1168i q^{61} +(-4.06233 - 4.06233i) q^{62} +(4.90088 + 4.90088i) q^{63} -1.00000i q^{64} +(-10.2561 - 8.67675i) q^{65} +1.13968i q^{66} +(-11.1390 + 11.1390i) q^{67} +(-4.38978 - 4.38978i) q^{68} +(3.11678 + 2.35153i) q^{69} +(-0.551233 - 6.60799i) q^{70} -9.16188 q^{71} +(-1.65266 - 1.65266i) q^{72} +(10.7875 - 10.7875i) q^{73} -3.22044 q^{74} +(-2.36165 + 3.31544i) q^{75} -2.37966i q^{76} +(2.93543 + 2.93543i) q^{77} +(3.45854 - 3.45854i) q^{78} -5.70196 q^{79} +(0.185885 + 2.22833i) q^{80} -3.47424 q^{81} +(1.76155 + 1.76155i) q^{82} +(11.6335 + 11.6335i) q^{83} +2.41421 q^{84} +(10.5979 + 8.96588i) q^{85} -4.03602i q^{86} +(-2.22833 - 2.22833i) q^{87} +(-0.989880 - 0.989880i) q^{88} +1.31441 q^{89} +(3.98988 + 3.37547i) q^{90} -17.8161i q^{91} +(-4.74955 + 0.664664i) q^{92} +(-3.30721 + 3.30721i) q^{93} -1.78598i q^{94} +(0.442344 + 5.30266i) q^{95} -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^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6	$ 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{12} + 4 q^{14} - 8 q^{16} - 24 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 12 q^{22} + 16 q^{23} + 12 q^{26} + 8 q^{27} + 16 q^{30} - 4 q^{31} - 20 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 4 q^{37} - 8 q^{38} + 8 q^{40} + 12 q^{41} + 8 q^{42} + 20 q^{43} - 20 q^{44} - 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} - 20 q^{57} + 16 q^{58} - 8 q^{60} + 4 q^{62} - 12 q^{65} + 4 q^{67} - 24 q^{68} - 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} - 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} - 8 q^{79} + 4 q^{80} - 16 q^{81} + 8 q^{82} + 28 q^{83} + 8 q^{84} + 20 q^{85} - 4 q^{87} + 12 q^{88} + 40 q^{89} + 12 q^{90} - 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} + 8 q^{97} + 16 q^{98} + 36 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^12 + 4 * q^14 - 8 * q^16 - 24 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 12 * q^22 + 16 * q^23 + 12 * q^26 + 8 * q^27 + 16 * q^30 - 4 * q^31 - 20 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 4 * q^37 - 8 * q^38 + 8 * q^40 + 12 * q^41 + 8 * q^42 + 20 * q^43 - 20 * q^44 - 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 - 20 * q^57 + 16 * q^58 - 8 * q^60 + 4 * q^62 - 12 * q^65 + 4 * q^67 - 24 * q^68 - 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 - 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 - 8 * q^79 + 4 * q^80 - 16 * q^81 + 8 * q^82 + 28 * q^83 + 8 * q^84 + 20 * q^85 - 4 * q^87 + 12 * q^88 + 40 * q^89 + 12 * q^90 - 16 * q^92 - 12 * q^93 - 4 * q^95 - 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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	−0.521122	−	0.853482i	$-0.674486\pi$
$3$	0.575666	−	0.575666i	0.332361	−	0.332361i	0.853482	+	0.521122i	$0.174486\pi$
$4$			1.00000i			0.500000i
$5$	−0.185885	−	2.22833i	−0.0831305	−	0.996539i
$5$	−0.185885	−	2.22833i	−0.0831305	−	0.996539i
$6$	0.814115			0.332361
$7$	2.09689	−	2.09689i	0.792549	−	0.792549i	−0.189359	−	0.981908i	$-0.560641\pi$
$7$	2.09689	−	2.09689i	0.792549	−	0.792549i	0.981908	+	0.189359i	$0.0606410\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			2.33722i			0.779072i
$10$	1.44423	−	1.70711i	0.456704	−	0.539835i
$11$			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	$-0.436538\pi$
$13$	4.24822	−	4.24822i	1.17824	−	1.17824i	0.980191	−	0.198053i	$-0.0634617\pi$
$14$	2.96545			0.792549
$15$	−1.38978	−	1.17576i	−0.358840	−	0.303581i
$16$	−1.00000			−0.250000
$17$	−4.38978	+	4.38978i	−1.06468	+	1.06468i	−0.0669198	+	0.997758i	$0.521317\pi$
$17$	−4.38978	+	4.38978i	−1.06468	+	1.06468i	−0.997758	+	0.0669198i	$0.978683\pi$
$18$	−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	$0.588005\pi$
$20$	2.22833	−	0.185885i	0.498269	−	0.0415652i
$21$		−	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
$25$	−4.93089	+	0.828427i	−0.986179	+	0.165685i
$26$	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	$-0.117019\pi$
$30$	−0.151332	−	1.81411i	−0.0276293	−	0.331211i
$31$	−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
$35$	−5.06233	−	4.28277i	−0.855691	−	0.723921i
$36$	−2.33722			−0.389536
$37$	−2.27719	+	2.27719i	−0.374368	+	0.374368i	−0.869065	−	0.494697i	$-0.835279\pi$
$37$	−2.27719	+	2.27719i	−0.374368	+	0.374368i	0.494697	+	0.869065i	$0.335279\pi$
$38$	−1.68267	−	1.68267i	−0.272966	−	0.272966i
$39$		−	4.89111i		−	0.783205i
$40$	1.70711	+	1.44423i	0.269917	+	0.228352i
$41$	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	0.455183	−	0.890398i	$-0.349574\pi$
$43$	−2.85390	−	2.85390i	−0.435215	−	0.435215i	−0.890398	+	0.455183i	$0.849574\pi$
$44$	−1.39990			−0.211043
$45$	5.20809	−	0.434454i	0.776376	−	0.0647646i
$46$	−2.88845	+	3.82843i	−0.425879	+	0.564471i
$47$	−1.26288	−	1.26288i	−0.184210	−	0.184210i	0.608977	−	0.793188i	$-0.291580\pi$
$47$	−1.26288	−	1.26288i	−0.184210	−	0.184210i	−0.793188	+	0.608977i	$0.791580\pi$
$48$	−0.575666	+	0.575666i	−0.0830902	+	0.0830902i
$49$		−	1.79387i		−	0.256268i
$50$	−4.07245	−	2.90088i	−0.575932	−	0.410247i
$51$			5.05409i			0.707715i
$52$	4.24822	+	4.24822i	0.589122	+	0.589122i
$53$	4.13375	+	4.13375i	0.567814	+	0.567814i	0.931516	−	0.363701i	$-0.118487\pi$
$53$	4.13375	+	4.13375i	0.567814	+	0.567814i	−0.363701	+	0.931516i	$0.618487\pi$
$54$			4.34511i			0.591294i
$55$	3.11944	−	0.260221i	0.420625	−	0.0350882i
$56$			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	$0.879715\pi$
$60$	1.17576	−	1.38978i	0.151791	−	0.179420i
$61$		−	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
$65$	−10.2561	−	8.67675i	−1.27211	−	1.07622i
$66$			1.13968i			0.140285i
$67$	−11.1390	+	11.1390i	−1.36084	+	1.36084i	−0.487999	+	0.872844i	$0.662273\pi$
$67$	−11.1390	+	11.1390i	−1.36084	+	1.36084i	−0.872844	+	0.487999i	$0.837727\pi$
$68$	−4.38978	−	4.38978i	−0.532339	−	0.532339i
$69$	3.11678	+	2.35153i	0.375216	+	0.283091i
$70$	−0.551233	−	6.60799i	−0.0658850	−	0.789806i
$71$	−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	$-0.398755\pi$
$73$	10.7875	−	10.7875i	1.26258	−	1.26258i	0.949840	−	0.312735i	$-0.101245\pi$
$74$	−3.22044			−0.374368
$75$	−2.36165	+	3.31544i	−0.272700	+	0.382835i
$76$		−	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	$0.603938\pi$
$80$	0.185885	+	2.22833i	0.0207826	+	0.249135i
$81$	−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	$0.108590\pi$
$83$	11.6335	+	11.6335i	1.27694	+	1.27694i	0.334565	+	0.942373i	$0.391410\pi$
$84$	2.41421			0.263412
$85$	10.5979	+	8.96588i	1.14950	+	0.972486i
$86$		−	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	$0.477807\pi$
$90$	3.98988	+	3.37547i	0.420570	+	0.355806i
$91$		−	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
$95$	0.442344	+	5.30266i	0.0453835	+	0.544042i
$96$	−0.814115			−0.0830902
$97$	7.84001	−	7.84001i	0.796033	−	0.796033i	−0.186435	−	0.982467i	$-0.559693\pi$
$97$	7.84001	−	7.84001i	0.796033	−	0.796033i	0.982467	+	0.186435i	$0.0596932\pi$
$98$	1.26846	−	1.26846i	0.128134	−	0.128134i
$99$	−3.27187			−0.328836
$100$	−0.828427	−	4.93089i	−0.0828427	−	0.493089i
$101$	−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	0.916327	−	0.400430i	$-0.131139\pi$
$103$	5.23579	+	5.23579i	0.515898	+	0.515898i	−0.400430	+	0.916327i	$0.631139\pi$
$104$			6.00789i			0.589122i
$105$	−5.37966	+	0.448767i	−0.525001	+	0.0437952i
$106$			5.84601i			0.567814i
$107$	7.78598	−	7.78598i	0.752700	−	0.752700i	−0.222283	−	0.974982i	$-0.571351\pi$
$107$	7.78598	−	7.78598i	0.752700	−	0.752700i	0.974982	+	0.222283i	$0.0713508\pi$
$108$	−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	$0.307166\pi$
$110$	2.38978	+	2.02177i	0.227857	+	0.192768i
$111$			2.62181i			0.248851i
$112$	−2.09689	+	2.09689i	−0.198137	+	0.198137i
$113$	−7.91065	−	7.91065i	−0.744172	−	0.744172i	0.229206	−	0.973378i	$-0.426387\pi$
$113$	−7.91065	−	7.91065i	−0.744172	−	0.744172i	−0.973378	+	0.229206i	$0.926387\pi$
$114$	−1.93732			−0.181446
$115$	10.4600	−	2.36396i	0.975400	−	0.220441i
$116$	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
$120$	1.81411	−	0.151332i	0.165605	−	0.0138147i
$121$	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
$125$	2.76259	+	10.8337i	0.247093	+	0.968992i
$126$			6.93089i			0.617453i
$127$	6.93732	+	6.93732i	0.615587	+	0.615587i	0.944396	−	0.328809i	$-0.106647\pi$
$127$	6.93732	+	6.93732i	0.615587	+	0.615587i	−0.328809	+	0.944396i	$0.606647\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.28578			−0.289297
$130$	−1.11678	−	13.3875i	−0.0979480	−	1.17417i
$131$	−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
$135$	6.27531	−	7.41756i	0.540093	−	0.638402i
$136$		−	6.20809i		−	0.532339i
$137$	3.78830	−	3.78830i	0.323656	−	0.323656i	−0.526512	−	0.850168i	$-0.676500\pi$
$137$	3.78830	−	3.78830i	0.323656	−	0.323656i	0.850168	+	0.526512i	$0.176500\pi$
$138$	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	$0.921577\pi$
$140$	4.28277	−	5.06233i	0.361960	−	0.427845i
$141$	−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
$145$	−8.62557	+	0.719538i	−0.716315	+	0.0597544i
$146$	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	$0.524000\pi$
$150$	−4.01431	+	0.674435i	−0.327767	+	0.0550674i
$151$	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
$155$	1.06791	+	12.8018i	0.0857768	+	1.02826i
$156$	4.89111			0.391602
$157$	2.30909	−	2.30909i	0.184285	−	0.184285i	−0.608935	−	0.793220i	$-0.708403\pi$
$157$	2.30909	−	2.30909i	0.184285	−	0.184285i	0.793220	+	0.608935i	$0.208403\pi$
$158$	−4.03189	−	4.03189i	−0.320760	−	0.320760i
$159$	4.75932			0.377439
$160$	−1.44423	+	1.70711i	−0.114176	+	0.134959i
$161$	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	$-0.454593\pi$
$163$	14.4525	−	14.4525i	1.13201	−	1.13201i	0.989843	−	0.142168i	$-0.0454074\pi$
$164$			2.49121i			0.194531i
$165$	1.64595	−	1.94556i	0.128137	−	0.151461i
$166$			16.4522i			1.27694i
$167$	−11.7423	−	11.7423i	−0.908650	−	0.908650i	0.0875132	−	0.996163i	$-0.472108\pi$
$167$	−11.7423	−	11.7423i	−0.908650	−	0.908650i	−0.996163	+	0.0875132i	$0.972108\pi$
$168$	1.70711	+	1.70711i	0.131706	+	0.131706i
$169$		−	23.0947i		−	1.77652i
$170$	1.15399	+	13.8337i	0.0885072	+	1.06099i
$171$		−	5.56178i		−	0.425320i
$172$	2.85390	−	2.85390i	0.217608	−	0.217608i
$173$	−7.36165	+	7.36165i	−0.559696	+	0.559696i	−0.929221	−	0.369525i	$-0.879520\pi$
$173$	−7.36165	+	7.36165i	−0.559696	+	0.559696i	0.369525	+	0.929221i	$0.379520\pi$
$174$		−	3.15133i		−	0.238902i
$175$	−8.60241	+	12.0766i	−0.650281	+	0.912909i
$176$		−	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	$-0.0665255\pi$
$180$	0.434454	+	5.20809i	0.0323823	+	0.388188i
$181$		−	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
$185$	5.49763	+	4.65104i	0.404194	+	0.341951i
$186$	−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
$190$	−3.43677	+	4.06233i	−0.249329	+	0.294713i
$191$		−	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	−0.868642	−	0.495440i	$-0.835007\pi$
$193$	−5.18469	+	5.18469i	−0.373202	+	0.373202i	0.495440	+	0.868642i	$0.335007\pi$
$194$	11.0875			0.796033
$195$	−10.8990	+	0.909186i	−0.780494	+	0.0651082i
$196$	1.79387			0.128134
$197$	−3.44191	−	3.44191i	−0.245226	−	0.245226i	0.573782	−	0.819008i	$-0.305476\pi$
$197$	−3.44191	−	3.44191i	−0.245226	−	0.245226i	−0.819008	+	0.573782i	$0.805476\pi$
$198$	−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	$0.689533\pi$
$200$	2.90088	−	4.07245i	0.205123	−	0.287966i
$201$			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
$205$	−0.463079	−	5.55123i	−0.0323429	−	0.387715i
$206$			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
$210$	−4.12132	−	3.48667i	−0.284398	−	0.240603i
$211$	−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
$215$	−5.82892	+	6.88992i	−0.397529	+	0.469888i
$216$	−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
$220$	0.260221	+	3.11944i	0.0175441	+	0.210313i
$221$			37.2975i			2.50890i
$222$	−1.85390	+	1.85390i	−0.124425	+	0.124425i
$223$	−1.18915	+	1.18915i	−0.0796316	+	0.0796316i	−0.745801	−	0.666169i	$-0.767933\pi$
$223$	−1.18915	+	1.18915i	−0.0796316	+	0.0796316i	0.666169	+	0.745801i	$0.267933\pi$
$224$	−2.96545			−0.198137
$225$	−1.93621	−	11.5246i	−0.129081	−	0.768305i
$226$		−	11.1874i		−	0.744172i
$227$	14.3791	−	14.3791i	0.954371	−	0.954371i	−0.0446322	−	0.999003i	$-0.514212\pi$
$227$	14.3791	−	14.3791i	0.954371	−	0.954371i	0.999003	+	0.0446322i	$0.0142116\pi$
$228$	−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	$0.454401\pi$
$230$	9.06791	+	5.72477i	0.597920	+	0.377480i
$231$	3.37966			0.222365
$232$	2.73712	+	2.73712i	0.179701	+	0.179701i
$233$	0.921537	−	0.921537i	0.0603719	−	0.0603719i	−0.676276	−	0.736648i	$-0.736407\pi$
$233$	0.921537	−	0.921537i	0.0603719	−	0.0603719i	0.736648	+	0.676276i	$0.236407\pi$
$234$			14.0417i			0.917937i
$235$	−2.57936	+	3.04887i	−0.168259	+	0.198886i
$236$	−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	$-0.0973280\pi$
$240$	1.38978	+	1.17576i	0.0897100	+	0.0758953i
$241$			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
$245$	−3.99734	+	0.333455i	−0.255381	+	0.0213036i
$246$	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
$250$	−5.70711	+	9.61400i	−0.360949	+	0.608043i
$251$			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
$255$	11.2622	−	0.939482i	0.705265	−	0.0588327i
$256$	1.00000			0.0625000
$257$	−18.5108	−	18.5108i	−1.15467	−	1.15467i	−0.985605	−	0.169064i	$-0.945926\pi$
$257$	−18.5108	−	18.5108i	−1.15467	−	1.15467i	−0.169064	−	0.985605i	$-0.554074\pi$
$258$	−2.32340	−	2.32340i	−0.144649	−	0.144649i
$259$			9.55004i			0.593411i
$260$	8.67675	−	10.2561i	0.538109	−	0.636057i
$261$	9.04706			0.559999
$262$	−8.33722	−	8.33722i	−0.515075	−	0.515075i
$263$	−1.46351	−	1.46351i	−0.0902438	−	0.0902438i	0.660544	−	0.750788i	$-0.270326\pi$
$263$	−1.46351	−	1.46351i	−0.0902438	−	0.0902438i	−0.750788	+	0.660544i	$0.770326\pi$
$264$	−1.13968			−0.0701425
$265$	8.44295	−	9.97976i	0.518646	−	0.613052i
$266$	−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	$-0.0420344\pi$
$270$	9.68232	−	0.807692i	0.589247	−	0.0491546i
$271$	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
$275$	−1.15972	−	6.90276i	−0.0699335	−	0.416252i
$276$	−2.35153	+	3.11678i	−0.141545	+	0.187608i
$277$	−5.49170	−	5.49170i	−0.329965	−	0.329965i	0.522608	−	0.852573i	$-0.324959\pi$
$277$	−5.49170	−	5.49170i	−0.329965	−	0.329965i	−0.852573	+	0.522608i	$0.824959\pi$
$278$	−4.06645	+	4.06645i	−0.243889	+	0.243889i
$279$		−	13.4273i		−	0.803873i
$280$	6.60799	−	0.551233i	0.394903	−	0.0329425i
$281$		−	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	$-0.965521\pi$
$283$	−18.5426	−	18.5426i	−1.10225	−	1.10225i	−0.108106	−	0.994139i	$-0.534479\pi$
$284$		−	9.16188i		−	0.543658i
$285$	3.30721	+	2.79792i	0.195902	+	0.165735i
$286$			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
$290$	−6.60799	−	5.59041i	−0.388034	−	0.328280i
$291$		−	9.02646i		−	0.529140i
$292$	10.7875	+	10.7875i	0.631288	+	0.631288i
$293$	−4.84916	−	4.84916i	−0.283291	−	0.283291i	0.551129	−	0.834420i	$-0.314197\pi$
$293$	−4.84916	−	4.84916i	−0.283291	−	0.283291i	−0.834420	+	0.551129i	$0.814197\pi$
$294$		−	1.46042i		−	0.0851734i
$295$	12.6302	−	1.05360i	0.735358	−	0.0613430i
$296$		−	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
$300$	−3.31544	−	2.36165i	−0.191417	−	0.136350i
$301$	−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
$305$	−29.2285	+	2.43822i	−1.67362	+	0.139612i
$306$		−	14.5096i		−	0.829461i
$307$	14.4992	+	14.4992i	0.827511	+	0.827511i	0.987172	−	0.159661i	$-0.0510401\pi$
$307$	14.4992	+	14.4992i	0.827511	+	0.827511i	−0.159661	+	0.987172i	$0.551040\pi$
$308$	−2.93543	+	2.93543i	−0.167262	+	0.167262i
$309$	6.02813			0.342928
$310$	−8.29709	+	9.80734i	−0.471243	+	0.557020i
$311$	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	0.965925	−	0.258823i	$-0.0833346\pi$
$313$	12.5099	+	12.5099i	0.707102	+	0.707102i	−0.258823	+	0.965925i	$0.583335\pi$
$314$	3.26554			0.184285
$315$	10.0098	−	11.8318i	0.563987	−	0.666645i
$316$		−	5.70196i		−	0.320760i
$317$	14.7988	+	14.7988i	0.831186	+	0.831186i	0.987679	−	0.156493i	$-0.0500189\pi$
$317$	14.7988	+	14.7988i	0.831186	+	0.831186i	−0.156493	+	0.987679i	$0.550019\pi$
$318$	3.36535	+	3.36535i	0.188719	+	0.188719i
$319$	5.41884			0.303397
$320$	−2.22833	+	0.185885i	−0.124567	+	0.0103913i
$321$		−	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
$325$	−17.4282	+	24.4669i	−0.966741	+	1.35718i
$326$	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
$330$	2.53958	−	0.211850i	0.139799	−	0.0116619i
$331$	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
$335$	26.8919	+	22.7507i	1.46926	+	1.24301i
$336$			2.41421i			0.131706i
$337$	1.89342	−	1.89342i	0.103141	−	0.103141i	−0.653653	−	0.756794i	$-0.726764\pi$
$337$	1.89342	−	1.89342i	0.103141	−	0.103141i	0.756794	+	0.653653i	$0.226764\pi$
$338$	16.3304	−	16.3304i	0.888259	−	0.888259i
$339$	−9.10779			−0.494667
$340$	−8.96588	+	10.5979i	−0.486243	+	0.574750i
$341$		−	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
$345$	4.66062	−	7.38232i	0.250919	−	0.397451i
$346$	−10.4109			−0.559696
$347$	5.57833	+	5.57833i	0.299460	+	0.299460i	0.840802	−	0.541342i	$-0.182084\pi$
$347$	5.57833	+	5.57833i	0.299460	+	0.299460i	−0.541342	+	0.840802i	$0.682084\pi$
$348$	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	$0.958767\pi$
$350$	−14.6223	+	2.45666i	−0.781595	+	0.131314i
$351$	26.1049			1.39338
$352$	0.989880	−	0.989880i	0.0527608	−	0.0527608i
$353$	−16.3035	+	16.3035i	−0.867749	+	0.867749i	−0.992223	−	0.124474i	$-0.960276\pi$
$353$	−16.3035	+	16.3035i	−0.867749	+	0.867749i	0.124474	+	0.992223i	$0.460276\pi$
$354$			4.61441i			0.245253i
$355$	1.70306	+	20.4157i	0.0903890	+	1.08355i
$356$			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	$0.787490\pi$
$360$	−3.37547	+	3.98988i	−0.177903	+	0.210285i
$361$	−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
$365$	−26.0432	−	22.0328i	−1.36316	−	1.15325i
$366$		−	10.6786i		−	0.558177i
$367$	22.0933	−	22.0933i	1.15326	−	1.15326i	0.167364	−	0.985895i	$-0.446474\pi$
$367$	22.0933	−	22.0933i	1.15326	−	1.15326i	0.985895	−	0.167364i	$-0.0535256\pi$
$368$	−0.664664	−	4.74955i	−0.0346480	−	0.247587i
$369$			5.82250i			0.303107i
$370$	0.598632	+	7.17619i	0.0311214	+	0.373073i
$371$	17.3360			0.900041
$372$	−3.30721	−	3.30721i	−0.171471	−	0.171471i
$373$	5.68302	+	5.68302i	0.294256	+	0.294256i	0.838759	−	0.544503i	$-0.183282\pi$
$373$	5.68302	+	5.68302i	0.294256	+	0.294256i	−0.544503	+	0.838759i	$0.683282\pi$
$374$		−	8.69071i		−	0.449386i
$375$	7.82690	+	4.64624i	0.404179	+	0.239931i
$376$	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	$0.239163\pi$
$380$	−5.30266	+	0.442344i	−0.272021	+	0.0226918i
$381$	7.98715			0.409194
$382$	5.57610	−	5.57610i	0.285298	−	0.285298i
$383$	−4.38293	−	4.38293i	−0.223957	−	0.223957i	0.586205	−	0.810163i	$-0.300621\pi$
$383$	−4.38293	−	4.38293i	−0.223957	−	0.223957i	−0.810163	+	0.586205i	$0.800621\pi$
$384$		−	0.814115i		−	0.0415451i
$385$	5.99546	−	7.08677i	0.305557	−	0.361175i
$386$	−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	$0.451511\pi$
$390$	−8.34965	−	7.06387i	−0.422801	−	0.357693i
$391$	−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
$395$	1.05991	+	12.7058i	0.0533299	+	0.639300i
$396$		−	3.27187i		−	0.164418i
$397$	22.2577	+	22.2577i	1.11708	+	1.11708i	0.992168	+	0.124912i	$0.0398648\pi$
$397$	22.2577	+	22.2577i	1.11708	+	1.11708i	0.124912	+	0.992168i	$0.460135\pi$
$398$	−11.1893	−	11.1893i	−0.560870	−	0.560870i
$399$			5.74501i			0.287610i
$400$	4.93089	−	0.828427i	0.246545	−	0.0414214i
$401$			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
$405$	0.645810	+	7.74174i	0.0320905	+	0.384690i
$406$		−	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	$0.834143\pi$
$410$	3.59787	−	4.25276i	0.177686	−	0.210029i
$411$		−	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
$415$	23.7607	−	28.0857i	1.16637	−	1.37867i
$416$	−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	$0.683353\pi$
$420$	−0.448767	−	5.37966i	−0.0218976	−	0.262501i
$421$			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
$425$	18.0089	−	25.2822i	0.873561	−	1.22636i
$426$	−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
$430$	−8.99358	+	0.750237i	−0.433709	+	0.0361796i
$431$			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	0.589011	−	0.808125i	$-0.299518\pi$
$433$	−4.55947	−	4.55947i	−0.219114	−	0.219114i	−0.808125	+	0.589011i	$0.799518\pi$
$434$	−17.0365			−0.817779
$435$	−4.55123	+	5.37966i	−0.218215	+	0.257935i
$436$			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	$0.886766\pi$
$440$	−2.02177	+	2.38978i	−0.0963842	+	0.113928i
$441$	4.19267			0.199651
$442$	−26.3733	+	26.3733i	−1.25445	+	1.25445i
$443$	15.6502	−	15.6502i	0.743563	−	0.743563i	−0.229699	−	0.973262i	$-0.573774\pi$
$443$	15.6502	−	15.6502i	0.743563	−	0.743563i	0.973262	+	0.229699i	$0.0737741\pi$
$444$	−2.62181			−0.124425
$445$	−0.244329	−	2.92893i	−0.0115823	−	0.138845i
$446$	−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	$-0.308772\pi$
$450$	6.77999	−	9.51821i	0.319612	−	0.448693i
$451$			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
$455$	−39.7001	+	3.31175i	−1.86117	+	0.155257i
$456$		−	1.93732i		−	0.0907231i
$457$	0.286885	−	0.286885i	0.0134199	−	0.0134199i	−0.700365	−	0.713785i	$-0.746979\pi$
$457$	0.286885	−	0.286885i	0.0134199	−	0.0134199i	0.713785	+	0.700365i	$0.246979\pi$
$458$	3.05529	+	3.05529i	0.142764	+	0.142764i
$459$	−26.9748			−1.25908
$460$	2.36396	+	10.4600i	0.110220	+	0.487700i
$461$	−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	−0.312794	−	0.949821i	$-0.601265\pi$
$463$	13.7072	−	13.7072i	0.637027	−	0.637027i	0.949821	+	0.312794i	$0.101265\pi$
$464$			3.87087i			0.179701i
$465$	7.98430	+	6.75478i	0.370263	+	0.313245i
$466$	1.30325			0.0603719
$467$	−6.28132	+	6.28132i	−0.290665	+	0.290665i	−0.837343	−	0.546678i	$-0.815892\pi$
$467$	−6.28132	+	6.28132i	−0.290665	+	0.290665i	0.546678	+	0.837343i	$0.315892\pi$
$468$	−9.92901	+	9.92901i	−0.458969	+	0.458969i
$469$			46.7144i			2.15707i
$470$	−3.97976	+	0.331988i	−0.183573	+	0.0153135i
$471$		−	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
$475$	11.7339	−	1.97138i	0.538386	−	0.0904529i
$476$	−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	$0.529068\pi$
$480$	0.151332	+	1.81411i	0.00690733	+	0.0828026i
$481$			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
$485$	−18.9275	−	16.0128i	−0.859452	−	0.727103i
$486$	−15.8637			−0.719594
$487$	−7.64836	−	7.64836i	−0.346580	−	0.346580i	0.512254	−	0.858834i	$-0.328811\pi$
$487$	−7.64836	−	7.64836i	−0.346580	−	0.346580i	−0.858834	+	0.512254i	$0.828811\pi$
$488$	9.27496	+	9.27496i	0.419858	+	0.419858i
$489$		−	16.6397i		−	0.752472i
$490$	−3.06233	−	2.59076i	−0.138342	−	0.117039i
$491$	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
$495$	0.608193	+	7.29081i	0.0273363	+	0.327697i
$496$	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	$0.800875\pi$
$500$	−10.8337	+	2.76259i	−0.484496	+	0.123547i
$501$	−13.5193			−0.604000
$502$	−4.44646	+	4.44646i	−0.198455	+	0.198455i
$503$	−8.73893	−	8.73893i	−0.389650	−	0.389650i	0.484913	−	0.874563i	$-0.338851\pi$
$503$	−8.73893	−	8.73893i	−0.389650	−	0.389650i	−0.874563	+	0.484913i	$0.838851\pi$
$504$	−6.93089			−0.308727
$505$	0.300590	+	3.60337i	0.0133761	+	0.160348i
$506$	−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	$0.916168\pi$
$510$	8.62788	+	7.29925i	0.382049	+	0.323216i
$511$		−	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
$515$	10.6938	−	12.6403i	0.471225	−	0.556999i
$516$		−	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
$520$	13.3875	−	1.11678i	0.587083	−	0.0489740i
$521$			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	0.773332	−	0.634001i	$-0.218589\pi$
$523$	3.18638	+	3.18638i	0.139331	+	0.139331i	−0.634001	+	0.773332i	$0.718589\pi$
$524$		−	11.7906i		−	0.515075i
$525$	2.00000	+	11.9042i	0.0872872	+	0.519543i
$526$		−	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
$530$	13.0268	−	1.08669i	0.565849	−	0.0472027i
$531$	−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
$535$	−18.7970	−	15.9024i	−0.812666	−	0.687522i
$536$		−	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
$540$	7.41756	+	6.27531i	0.319201	+	0.270046i
$541$	−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
$545$	−2.21016	−	26.4946i	−0.0946729	−	1.13491i
$546$		−	14.5043i		−	0.620728i
$547$	22.5810	+	22.5810i	0.965493	+	0.965493i	0.999424	−	0.0339314i	$-0.0108028\pi$
$547$	22.5810	+	22.5810i	0.965493	+	0.965493i	−0.0339314	+	0.999424i	$0.510803\pi$
$548$	3.78830	+	3.78830i	0.161828	+	0.161828i
$549$	30.6568			1.30840
$550$	4.06095	−	5.70103i	0.173159	−	0.243093i
$551$			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
$555$	5.84225	−	0.487355i	0.247989	−	0.0206871i
$556$	−5.75082			−0.243889
$557$	8.12733	−	8.12733i	0.344366	−	0.344366i	−0.513640	−	0.858006i	$-0.671703\pi$
$557$	8.12733	−	8.12733i	0.344366	−	0.344366i	0.858006	+	0.513640i	$0.171703\pi$
$558$	9.49456	−	9.49456i	0.401937	−	0.401937i
$559$	−24.2480			−1.02558
$560$	5.06233	+	4.28277i	0.213923	+	0.180980i
$561$	−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	$0.162071\pi$
$563$	32.2838	+	32.2838i	1.36060	+	1.36060i	0.487446	+	0.873153i	$0.337929\pi$
$564$		−	1.45400i		−	0.0612243i
$565$	−16.1571	+	19.0980i	−0.679732	+	0.803459i
$566$		−	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	$0.939627\pi$
$570$	0.360119	+	4.31698i	0.0150837	+	0.180818i
$571$			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
$575$	−7.21204	−	22.8689i	−0.300763	−	0.953699i
$576$	2.33722			0.0973841
$577$	3.64168	+	3.64168i	0.151605	+	0.151605i	0.778835	−	0.627229i	$-0.215811\pi$
$577$	3.64168	+	3.64168i	0.151605	+	0.151605i	−0.627229	+	0.778835i	$0.715811\pi$
$578$	15.2313	−	15.2313i	0.633540	−	0.633540i
$579$			5.96930i			0.248076i
$580$	−0.719538	−	8.62557i	−0.0298772	−	0.358157i
$581$	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
$585$	20.2794	−	23.9708i	0.838452	−	0.991069i
$586$		−	6.85775i		−	0.283291i
$587$	20.8064	+	20.8064i	0.858774	+	0.858774i	0.991194	−	0.132420i	$-0.0422747\pi$
$587$	20.8064	+	20.8064i	0.858774	+	0.858774i	−0.132420	+	0.991194i	$0.542275\pi$
$588$	1.03267	−	1.03267i	0.0425867	−	0.0425867i
$589$	13.6712			0.563311
$590$	9.67590	+	8.18589i	0.398351	+	0.337008i
$591$	−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	$-0.426048\pi$
$593$	29.3041	−	29.3041i	1.20338	−	1.20338i	0.973133	−	0.230243i	$-0.0739522\pi$
$594$	−6.08272			−0.249577
$595$	41.0230	−	3.42210i	1.68178	−	0.140293i
$596$		−	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	$0.753398\pi$
$600$	−0.674435	−	4.01431i	−0.0275337	−	0.163884i
$601$	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
$605$	−1.68046	−	20.1447i	−0.0683202	−	0.818999i
$606$	−1.31648			−0.0534784
$607$	−10.3099	−	10.3099i	−0.418468	−	0.418468i	0.466208	−	0.884675i	$-0.345620\pi$
$607$	−10.3099	−	10.3099i	−0.418468	−	0.418468i	−0.884675	+	0.466208i	$0.845620\pi$
$608$	1.68267	+	1.68267i	0.0682414	+	0.0682414i
$609$	−9.34511			−0.378683
$610$	−22.3917	−	18.9436i	−0.906615	−	0.767003i
$611$	−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	$0.00324372\pi$
$613$	25.0099	+	25.0099i	1.01014	+	1.01014i	0.0101903	+	0.999948i	$0.496756\pi$
$614$			20.5049i			0.827511i
$615$	−3.46224	−	2.92908i	−0.139611	−	0.118112i
$616$	−4.15133			−0.167262
$617$	−25.6567	+	25.6567i	−1.03290	+	1.03290i	−0.0334597	+	0.999440i	$0.510653\pi$
$617$	−25.6567	+	25.6567i	−1.03290	+	1.03290i	−0.999440	+	0.0334597i	$0.989347\pi$
$618$	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	$0.858404\pi$
$620$	−12.8018	+	1.06791i	−0.514131	+	0.0428884i
$621$	−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
$625$	23.6274	−	8.16977i	0.945097	−	0.326791i
$626$			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
$630$	15.4443	−	1.28835i	0.615316	−	0.0513292i
$631$			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
$635$	14.1691	−	16.7482i	0.562282	−	0.664631i
$636$			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
$640$	−1.70711	−	1.44423i	−0.0674793	−	0.0570880i
$641$		−	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	0.340135	−	0.940377i	$-0.389527\pi$
$643$	−15.2206	−	15.2206i	−0.600242	−	0.600242i	−0.940377	+	0.340135i	$0.889527\pi$
$644$	−8.56555	+	11.3530i	−0.337530	+	0.447371i
$645$	0.610779	+	7.32180i	0.0240494	+	0.288296i
$646$	14.7731			0.581241
$647$	−10.8512	−	10.8512i	−0.426606	−	0.426606i	0.460864	−	0.887471i	$-0.347539\pi$
$647$	−10.8512	−	10.8512i	−0.426606	−	0.426606i	−0.887471	+	0.460864i	$0.847539\pi$
$648$	2.45666	−	2.45666i	0.0965066	−	0.0965066i
$649$	−7.93466			−0.311462
$650$	−29.6243	+	4.97710i	−1.16196	+	0.195218i
$651$			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	$-0.473959\pi$
$653$	27.5566	−	27.5566i	1.07837	−	1.07837i	0.996656	−	0.0817179i	$-0.0260406\pi$
$654$	9.67976			0.378508
$655$	2.19170	+	26.2733i	0.0856368	+	1.02658i
$656$	−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	$0.582317\pi$
$660$	1.94556	+	1.64595i	0.0757306	+	0.0640687i
$661$		−	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
$665$	12.0466	+	10.1915i	0.467148	+	0.395211i
$666$		−	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
$670$	2.92823	+	35.1026i	0.113128	+	1.35613i
$671$	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	$0.571696\pi$
$673$	−31.0809	+	31.0809i	−1.19808	+	1.19808i	−0.974740	+	0.223341i	$0.928304\pi$
$674$	2.67770			0.103141
$675$	−17.6952	−	12.6046i	−0.681090	−	0.485153i
$676$	23.0947			0.888259
$677$	30.4764	−	30.4764i	1.17130	−	1.17130i	0.189402	−	0.981900i	$-0.439345\pi$
$677$	30.4764	−	30.4764i	1.17130	−	1.17130i	0.981900	−	0.189402i	$-0.0606549\pi$
$678$	−6.44018	−	6.44018i	−0.247334	−	0.247334i
$679$		−	32.8793i		−	1.26179i
$680$	−13.8337	+	1.15399i	−0.530496	+	0.0442536i
$681$		−	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	$0.564885\pi$
$683$	−30.8836	+	30.8836i	−1.18173	+	1.18173i	−0.979296	+	0.202434i	$0.935115\pi$
$684$	5.56178			0.212660
$685$	−9.14575	−	7.73738i	−0.349441	−	0.295630i
$686$			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
$690$	8.51564	−	1.92454i	0.324185	−	0.0732658i
$691$	−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
$695$	12.8147	−	1.06899i	0.486090	−	0.0405492i
$696$	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
$700$	−12.0766	−	8.60241i	−0.456454	−	0.325141i
$701$		−	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
$705$	0.270277	+	3.23998i	0.0101792	+	0.122025i
$706$	−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	$0.495502\pi$
$710$	−13.2318	+	15.6403i	−0.496581	+	0.586970i
$711$		−	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
$715$	12.1466	−	14.3575i	0.454257	−	0.536941i
$716$	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	$0.915708\pi$
$720$	−5.20809	+	0.434454i	−0.194094	+	0.0161912i
$721$	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
$725$	3.20673	+	19.0868i	0.119095	+	0.708868i
$726$	7.35982			0.273149
$727$	−12.3873	+	12.3873i	−0.459419	+	0.459419i	−0.898465	−	0.439046i	$-0.855317\pi$
$727$	−12.3873	+	12.3873i	−0.459419	+	0.459419i	0.439046	+	0.898465i	$0.355317\pi$
$728$	12.5979	+	12.5979i	0.466908	+	0.466908i
$729$			2.49220i			0.0923037i
$730$	−2.83582	−	33.9948i	−0.104958	−	1.25821i
$731$	25.0560			0.926728
$732$	7.55088	−	7.55088i	0.279089	−	0.279089i
$733$	7.76852	+	7.76852i	0.286937	+	0.286937i	0.835868	−	0.548931i	$-0.184965\pi$
$733$	7.76852	+	7.76852i	0.286937	+	0.286937i	−0.548931	+	0.835868i	$0.684965\pi$
$734$	31.2446			1.15326
$735$	−2.10917	+	2.49309i	−0.0777980	+	0.0919590i
$736$	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	$-0.0478977\pi$
$740$	−4.65104	+	5.49763i	−0.170976	+	0.202097i
$741$			11.6392i			0.427576i
$742$	12.2584	+	12.2584i	0.450021	+	0.450021i
$743$	23.1386	+	23.1386i	0.848874	+	0.848874i	0.989993	−	0.141119i	$-0.0450699\pi$
$743$	23.1386	+	23.1386i	0.848874	+	0.848874i	−0.141119	+	0.989993i	$0.545070\pi$
$744$		−	4.67710i		−	0.171471i
$745$	0.341839	+	4.09784i	0.0125240	+	0.150133i
$746$			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
$750$	2.24906	+	8.81984i	0.0821242	+	0.322055i
$751$			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
$755$	−0.333090	−	3.99297i	−0.0121224	−	0.145319i
$756$			12.8852i			0.468630i
$757$	−22.6178	+	22.6178i	−0.822059	+	0.822059i	−0.986403	−	0.164344i	$-0.947449\pi$
$757$	−22.6178	+	22.6178i	−0.822059	+	0.822059i	0.164344	+	0.986403i	$0.447449\pi$
$758$	20.1193	+	20.1193i	0.730765	+	0.730765i
$759$	−3.29191	+	4.36318i	−0.119489	+	0.158373i
$760$	−4.06233	−	3.43677i	−0.147356	−	0.124665i
$761$	−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
$765$	−20.9552	+	24.7695i	−0.757637	+	0.895544i
$766$		−	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	$0.440191\pi$
$770$	9.25053	−	0.771672i	0.333366	−	0.0278091i
$771$	−21.3120			−0.767534
$772$	−5.18469	−	5.18469i	−0.186601	−	0.186601i
$773$	−24.0445	−	24.0445i	−0.864821	−	0.864821i	0.127072	−	0.991893i	$-0.459442\pi$
$773$	−24.0445	−	24.0445i	−0.864821	−	0.864821i	−0.991893	+	0.127072i	$0.959442\pi$
$774$	9.43306			0.339064
$775$	28.3280	−	4.75932i	1.01757	−	0.170960i
$776$			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
$780$	−0.909186	−	10.8990i	−0.0325541	−	0.390247i
$781$		−	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
$785$	−5.57463	−	4.71618i	−0.198967	−	0.168328i
$786$	−9.59890			−0.342382
$787$	−5.07531	+	5.07531i	−0.180915	+	0.180915i	−0.791755	−	0.610839i	$-0.790832\pi$
$787$	−5.07531	+	5.07531i	−0.180915	+	0.180915i	0.610839	+	0.791755i	$0.290832\pi$
$788$	3.44191	−	3.44191i	0.122613	−	0.122613i
$789$	−1.68498			−0.0599870
$790$	−8.23491	+	9.73385i	−0.292985	+	0.346315i
$791$	−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
$795$	−0.884688	−	10.6053i	−0.0313766	−	0.376132i
$796$		−	15.8241i		−	0.560870i
$797$	−4.54720	+	4.54720i	−0.161070	+	0.161070i	−0.783041	−	0.621971i	$-0.786332\pi$
$797$	−4.54720	+	4.54720i	−0.161070	+	0.161070i	0.621971	+	0.783041i	$0.286332\pi$
$798$	−4.06233	+	4.06233i	−0.143805	+	0.143805i
$799$	11.0875			0.392249
$800$	4.07245	+	2.90088i	0.143983	+	0.102562i
$801$			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
$805$	16.9765	−	26.8904i	0.598343	−	0.947762i
$806$	−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	$0.656075\pi$
$810$	−5.01758	+	5.93089i	−0.176300	+	0.208390i
$811$	−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
$815$	−34.8915	−	29.5185i	−1.22220	−	1.03399i
$816$		−	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
$820$	5.55123	−	0.463079i	0.193857	−	0.0161714i
$821$	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	−0.842032	−	0.539427i	$-0.818641\pi$
$823$	−8.68113	+	8.68113i	−0.302605	+	0.302605i	0.539427	+	0.842032i	$0.318641\pi$
$824$	−7.40452			−0.257949
$825$	−4.64129	−	3.30608i	−0.161589	−	0.115103i
$826$			16.8082i			0.584832i
$827$	1.62311	−	1.62311i	0.0564412	−	0.0564412i	−0.678323	−	0.734764i	$-0.737293\pi$
$827$	1.62311	−	1.62311i	0.0564412	−	0.0564412i	0.734764	+	0.678323i	$0.237293\pi$
$828$	−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	$0.956484\pi$
$830$	36.6609	−	3.05822i	1.27252	−	0.106152i
$831$	−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
$835$	−23.9831	+	28.3485i	−0.829968	+	0.981041i
$836$	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	$0.354882\pi$
$840$	3.48667	−	4.12132i	0.120301	−	0.142199i
$841$	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
$845$	−51.4627	+	4.29297i	−1.77037	+	0.147683i
$846$	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
$850$	30.6114	−	5.14295i	1.04996	−	0.176402i
$851$	−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	−0.132701	−	0.991156i	$-0.542365\pi$
$853$	25.0722	−	25.0722i	0.858455	−	0.858455i	0.991156	+	0.132701i	$0.0423650\pi$
$854$		−	38.8971i		−	1.33103i
$855$	−12.3935	+	1.03385i	−0.423848	+	0.0353571i
$856$			11.0110i			0.376350i
$857$	−5.96703	−	5.96703i	−0.203830	−	0.203830i	0.597809	−	0.801639i	$-0.296038\pi$
$857$	−5.96703	−	5.96703i	−0.203830	−	0.203830i	−0.801639	+	0.597809i	$0.796038\pi$
$858$	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	$-0.303585\pi$
$860$	−6.88992	−	5.82892i	−0.234944	−	0.198765i
$861$		−	6.01431i		−	0.204967i
$862$	−18.9781	+	18.9781i	−0.646396	+	0.646396i
$863$	−7.90989	+	7.90989i	−0.269256	+	0.269256i	−0.828800	−	0.559545i	$-0.810976\pi$
$863$	−7.90989	+	7.90989i	−0.269256	+	0.269256i	0.559545	+	0.828800i	$0.310976\pi$
$864$		−	4.34511i		−	0.147824i
$865$	17.7726	+	15.0358i	0.604286	+	0.511231i
$866$		−	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
$870$	−7.02220	+	0.585786i	−0.238075	+	0.0198600i
$871$			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
$875$	28.5098	+	16.9241i	0.963807	+	0.572140i
$876$	12.4199			0.419631
$877$	−21.3111	−	21.3111i	−0.719625	−	0.719625i	0.248904	−	0.968528i	$-0.419930\pi$
$877$	−21.3111	−	21.3111i	−0.719625	−	0.719625i	−0.968528	+	0.248904i	$0.919930\pi$
$878$	−10.3199	+	10.3199i	−0.348280	+	0.348280i
$879$	−5.58300			−0.188310
$880$	−3.11944	+	0.260221i	−0.105156	+	0.00877205i
$881$			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	−0.691581	−	0.722299i	$-0.743085\pi$
$883$	0.912803	−	0.912803i	0.0307183	−	0.0307183i	0.722299	+	0.691581i	$0.243085\pi$
$884$	−37.2975			−1.25445
$885$	6.66425	−	7.87729i	0.224016	−	0.264792i
$886$	22.1327			0.743563
$887$	21.4132	+	21.4132i	0.718984	+	0.718984i	0.968397	−	0.249413i	$-0.0802377\pi$
$887$	21.4132	+	21.4132i	0.718984	+	0.718984i	−0.249413	+	0.968397i	$0.580238\pi$
$888$	−1.85390	−	1.85390i	−0.0622127	−	0.0622127i
$889$	29.0935			0.975766
$890$	1.89830	−	2.24383i	0.0636312	−	0.0752135i
$891$		−	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
$895$	−12.3711	+	1.03198i	−0.413519	+	0.0344954i
$896$		−	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
$900$	11.5246	−	1.93621i	0.384152	−	0.0645405i
$901$	−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
$905$	−51.4524	+	4.29211i	−1.71033	+	0.142675i
$906$	1.45882			0.0484661
$907$	24.6313	−	24.6313i	0.817869	−	0.817869i	−0.167930	−	0.985799i	$-0.553708\pi$
$907$	24.6313	−	24.6313i	0.817869	−	0.817869i	0.985799	+	0.167930i	$0.0537083\pi$
$908$	14.3791	+	14.3791i	0.477186	+	0.477186i
$909$		−	3.77945i		−	0.125356i
$910$	−30.4139	−	25.7304i	−1.00821	−	0.852955i
$911$		−	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
$915$	−15.4222	+	18.2294i	−0.509844	+	0.602647i
$916$			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	$0.527582\pi$
$920$	−5.72477	+	9.06791i	−0.188740	+	0.298960i
$921$	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
$925$	9.34211	−	13.1151i	0.307167	−	0.431222i
$926$	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	$0.800829\pi$
$930$	0.869403	+	10.4221i	0.0285089	+	0.341754i
$931$			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
$935$	−12.5513	+	14.8360i	−0.410473	+	0.485188i
$936$	−14.0417			−0.458969
$937$	27.6575	−	27.6575i	0.903530	−	0.903530i	−0.0922093	−	0.995740i	$-0.529393\pi$
$937$	27.6575	−	27.6575i	0.903530	−	0.903530i	0.995740	+	0.0922093i	$0.0293929\pi$
$938$	−33.0321	+	33.0321i	−1.07853	+	1.07853i
$939$	14.4031			0.470026
$940$	−3.04887	−	2.57936i	−0.0994430	−	0.0841296i
$941$			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
$945$	−2.39517	−	28.7124i	−0.0779148	−	0.934015i
$946$	5.65003			0.183698
$947$	−40.5901	−	40.5901i	−1.31900	−	1.31900i	−0.914568	−	0.404431i	$-0.867469\pi$
$947$	−40.5901	−	40.5901i	−1.31900	−	1.31900i	−0.404431	−	0.914568i	$-0.632531\pi$
$948$	−3.28242	−	3.28242i	−0.106608	−	0.106608i
$949$		−	91.6549i		−	2.97524i
$950$	9.69106	+	6.90311i	0.314419	+	0.223967i
$951$	17.0384			0.552507
$952$	−13.0177	−	13.0177i	−0.421905	−	0.421905i
$953$	−14.1269	−	14.1269i	−0.457615	−	0.457615i	0.440257	−	0.897872i	$-0.354887\pi$
$953$	−14.1269	−	14.1269i	−0.457615	−	0.457615i	−0.897872	+	0.440257i	$0.854887\pi$
$954$	−13.6634			−0.442369
$955$	−17.5721	+	1.46585i	−0.568621	+	0.0474339i
$956$	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
$960$	−1.17576	+	1.38978i	−0.0379476	+	0.0448550i
$961$	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
$965$	12.5170	+	10.5894i	0.402935	+	0.340886i
$966$	9.24264	+	6.97334i	0.297377	+	0.224363i
$967$	−11.5304	−	11.5304i	−0.370792	−	0.370792i	0.496974	−	0.867766i	$-0.334445\pi$
$967$	−11.5304	−	11.5304i	−0.370792	−	0.370792i	−0.867766	+	0.496974i	$0.834445\pi$
$968$	−6.39244	+	6.39244i	−0.205461	+	0.205461i
$969$		−	12.0270i		−	0.386364i
$970$	−2.06100	−	24.7065i	−0.0661746	−	0.793277i
$971$		−	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
$975$	4.05193	+	24.1175i	0.129766	+	0.772380i
$976$			13.1168i			0.419858i
$977$	10.4018	−	10.4018i	0.332785	−	0.332785i	−0.520858	−	0.853643i	$-0.674388\pi$
$977$	10.4018	−	10.4018i	0.332785	−	0.332785i	0.853643	+	0.520858i	$0.174388\pi$
$978$	11.7660	−	11.7660i	0.376236	−	0.376236i
$979$			1.84004i			0.0588080i
$980$	−0.333455	−	3.99734i	−0.0106518	−	0.127690i
$981$			27.7893i			0.887245i
$982$	4.83546	+	4.83546i	0.154306	+	0.154306i
$983$	−16.4444	−	16.4444i	−0.524494	−	0.524494i	0.394431	−	0.918925i	$-0.370942\pi$
$983$	−16.4444	−	16.4444i	−0.524494	−	0.524494i	−0.918925	+	0.394431i	$0.870942\pi$
$984$			2.02813i			0.0646544i
$985$	−7.02991	+	8.30952i	−0.223992	+	0.264763i
$986$			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
$990$	−4.72532	+	5.58544i	−0.150181	+	0.177517i
$991$	−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
$995$	2.94146	+	35.2612i	0.0932507	+	1.11786i
$996$			13.3940i			0.424404i
$997$	38.7536	+	38.7536i	1.22734	+	1.22734i	0.964966	+	0.262374i	$0.0845054\pi$
$997$	38.7536	+	38.7536i	1.22734	+	1.22734i	0.262374	+	0.964966i	$0.415495\pi$
$998$	−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	230.2.e.a.137.4	✓	8
5.2	odd	4		1150.2.e.b.643.1		8
5.3	odd	4		230.2.e.b.183.4	yes	8
5.4	even	2		1150.2.e.c.1057.1		8
23.22	odd	2		230.2.e.b.137.4	yes	8
115.22	even	4		1150.2.e.c.643.1		8
115.68	even	4	inner	230.2.e.a.183.4	yes	8
115.114	odd	2		1150.2.e.b.1057.1		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.575666 - 0.575666i) q^{3} +1.00000i q^{4} +(-0.185885 - 2.22833i) q^{5} +0.814115 q^{6} +(2.09689 - 2.09689i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.33722i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.575666 - 0.575666i) q^{3} +1.00000i q^{4} +(-0.185885 - 2.22833i) q^{5} +0.814115 q^{6} +(2.09689 - 2.09689i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.33722i q^{9} +(1.44423 - 1.70711i) q^{10} +1.39990i q^{11} +(0.575666 + 0.575666i) q^{12} +(4.24822 - 4.24822i) q^{13} +2.96545 q^{14} +(-1.38978 - 1.17576i) q^{15} -1.00000 q^{16} +(-4.38978 + 4.38978i) q^{17} +(-1.65266 + 1.65266i) q^{18} -2.37966 q^{19} +(2.22833 - 0.185885i) q^{20} -2.41421i q^{21} +(-0.989880 + 0.989880i) q^{22} +(0.664664 + 4.74955i) q^{23} +0.814115i q^{24} +(-4.93089 + 0.828427i) q^{25} +6.00789 q^{26} +(3.07245 + 3.07245i) q^{27} +(2.09689 + 2.09689i) q^{28} -3.87087i q^{29} +(-0.151332 - 1.81411i) q^{30} -5.74501 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.805875 + 0.805875i) q^{33} -6.20809 q^{34} +(-5.06233 - 4.28277i) q^{35} -2.33722 q^{36} +(-2.27719 + 2.27719i) q^{37} +(-1.68267 - 1.68267i) q^{38} -4.89111i q^{39} +(1.70711 + 1.44423i) q^{40} +2.49121 q^{41} +(1.70711 - 1.70711i) q^{42} +(-2.85390 - 2.85390i) q^{43} -1.39990 q^{44} +(5.20809 - 0.434454i) q^{45} +(-2.88845 + 3.82843i) q^{46} +(-1.26288 - 1.26288i) q^{47} +(-0.575666 + 0.575666i) q^{48} -1.79387i q^{49} +(-4.07245 - 2.90088i) q^{50} +5.05409i q^{51} +(4.24822 + 4.24822i) q^{52} +(4.13375 + 4.13375i) q^{53} +4.34511i q^{54} +(3.11944 - 0.260221i) q^{55} +2.96545i q^{56} +(-1.36989 + 1.36989i) q^{57} +(2.73712 - 2.73712i) q^{58} +5.66801i q^{59} +(1.17576 - 1.38978i) q^{60} -13.1168i q^{61} +(-4.06233 - 4.06233i) q^{62} +(4.90088 + 4.90088i) q^{63} -1.00000i q^{64} +(-10.2561 - 8.67675i) q^{65} +1.13968i q^{66} +(-11.1390 + 11.1390i) q^{67} +(-4.38978 - 4.38978i) q^{68} +(3.11678 + 2.35153i) q^{69} +(-0.551233 - 6.60799i) q^{70} -9.16188 q^{71} +(-1.65266 - 1.65266i) q^{72} +(10.7875 - 10.7875i) q^{73} -3.22044 q^{74} +(-2.36165 + 3.31544i) q^{75} -2.37966i q^{76} +(2.93543 + 2.93543i) q^{77} +(3.45854 - 3.45854i) q^{78} -5.70196 q^{79} +(0.185885 + 2.22833i) q^{80} -3.47424 q^{81} +(1.76155 + 1.76155i) q^{82} +(11.6335 + 11.6335i) q^{83} +2.41421 q^{84} +(10.5979 + 8.96588i) q^{85} -4.03602i q^{86} +(-2.22833 - 2.22833i) q^{87} +(-0.989880 - 0.989880i) q^{88} +1.31441 q^{89} +(3.98988 + 3.37547i) q^{90} -17.8161i q^{91} +(-4.74955 + 0.664664i) q^{92} +(-3.30721 + 3.30721i) q^{93} -1.78598i q^{94} +(0.442344 + 5.30266i) q^{95} -0.814115 q^{96} +(7.84001 - 7.84001i) q^{97} +(1.26846 - 1.26846i) q^{98} -3.27187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6	\( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{12} + 4 q^{14} - 8 q^{16} - 24 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 12 q^{22} + 16 q^{23} + 12 q^{26} + 8 q^{27} + 16 q^{30} - 4 q^{31} - 20 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 4 q^{37} - 8 q^{38} + 8 q^{40} + 12 q^{41} + 8 q^{42} + 20 q^{43} - 20 q^{44} - 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} - 20 q^{57} + 16 q^{58} - 8 q^{60} + 4 q^{62} - 12 q^{65} + 4 q^{67} - 24 q^{68} - 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} - 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} - 8 q^{79} + 4 q^{80} - 16 q^{81} + 8 q^{82} + 28 q^{83} + 8 q^{84} + 20 q^{85} - 4 q^{87} + 12 q^{88} + 40 q^{89} + 12 q^{90} - 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} + 8 q^{97} + 16 q^{98} + 36 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^12 + 4 * q^14 - 8 * q^16 - 24 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 12 * q^22 + 16 * q^23 + 12 * q^26 + 8 * q^27 + 16 * q^30 - 4 * q^31 - 20 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 4 * q^37 - 8 * q^38 + 8 * q^40 + 12 * q^41 + 8 * q^42 + 20 * q^43 - 20 * q^44 - 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 - 20 * q^57 + 16 * q^58 - 8 * q^60 + 4 * q^62 - 12 * q^65 + 4 * q^67 - 24 * q^68 - 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 - 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 - 8 * q^79 + 4 * q^80 - 16 * q^81 + 8 * q^82 + 28 * q^83 + 8 * q^84 + 20 * q^85 - 4 * q^87 + 12 * q^88 + 40 * q^89 + 12 * q^90 - 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 + 8 * q^97 + 16 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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