LMFDB - Embedded newform 390.2.t.b.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(307,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("390.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.t (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 396x^{12} + 2412x^{10} + 7716x^{8} + 12984x^{6} + 10756x^{4} + 3648x^{2} + 256 $ x^16 + 32x^14 + 396x^12 + 2412x^10 + 7716x^8 + 12984x^6 + 10756x^4 + 3648*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.1
Root			$1.09662i$ of defining polynomial
Character	$\chi$	$=$	390.343
Dual form			390.2.t.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.09731 + 0.775429i) q^{5} +(-0.707107 + 0.707107i) q^{6} -0.946681 q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.09731 + 0.775429i) q^{5} +(-0.707107 + 0.707107i) q^{6} -0.946681 q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.775429 + 2.09731i) q^{10} +(3.13105 + 3.13105i) q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.59681 + 0.250975i) q^{13} +0.946681i q^{14} +(2.03133 + 0.934711i) q^{15} +1.00000 q^{16} +(3.42154 + 3.42154i) q^{17} +1.00000 q^{18} +(1.00303 + 1.00303i) q^{19} +(2.09731 - 0.775429i) q^{20} +(0.669405 + 0.669405i) q^{21} +(3.13105 - 3.13105i) q^{22} +(-4.25224 + 4.25224i) q^{23} +(0.707107 - 0.707107i) q^{24} +(3.79742 - 3.25263i) q^{25} +(0.250975 + 3.59681i) q^{26} +(0.707107 - 0.707107i) q^{27} +0.946681 q^{28} +5.39250i q^{29} +(0.934711 - 2.03133i) q^{30} +(-2.43972 + 2.43972i) q^{31} -1.00000i q^{32} -4.42797i q^{33} +(3.42154 - 3.42154i) q^{34} +(1.98548 - 0.734084i) q^{35} -1.00000i q^{36} -11.9002 q^{37} +(1.00303 - 1.00303i) q^{38} +(2.72079 + 2.36586i) q^{39} +(-0.775429 - 2.09731i) q^{40} +(6.03479 - 6.03479i) q^{41} +(0.669405 - 0.669405i) q^{42} +(-0.242187 + 0.242187i) q^{43} +(-3.13105 - 3.13105i) q^{44} +(-0.775429 - 2.09731i) q^{45} +(4.25224 + 4.25224i) q^{46} +0.854435 q^{47} +(-0.707107 - 0.707107i) q^{48} -6.10380 q^{49} +(-3.25263 - 3.79742i) q^{50} -4.83878i q^{51} +(3.59681 - 0.250975i) q^{52} +(3.90244 + 3.90244i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-8.99469 - 4.13888i) q^{55} -0.946681i q^{56} -1.41850i q^{57} +5.39250 q^{58} +(-9.38267 + 9.38267i) q^{59} +(-2.03133 - 0.934711i) q^{60} +9.79944 q^{61} +(2.43972 + 2.43972i) q^{62} -0.946681i q^{63} -1.00000 q^{64} +(7.34900 - 3.31544i) q^{65} -4.42797 q^{66} +3.51092i q^{67} +(-3.42154 - 3.42154i) q^{68} +6.01358 q^{69} +(-0.734084 - 1.98548i) q^{70} +(-6.99770 + 6.99770i) q^{71} -1.00000 q^{72} -16.4476i q^{73} +11.9002i q^{74} +(-4.98514 - 0.385225i) q^{75} +(-1.00303 - 1.00303i) q^{76} +(-2.96410 - 2.96410i) q^{77} +(2.36586 - 2.72079i) q^{78} +8.09997i q^{79} +(-2.09731 + 0.775429i) q^{80} -1.00000 q^{81} +(-6.03479 - 6.03479i) q^{82} -15.2370 q^{83} +(-0.669405 - 0.669405i) q^{84} +(-9.82918 - 4.52287i) q^{85} +(0.242187 + 0.242187i) q^{86} +(3.81307 - 3.81307i) q^{87} +(-3.13105 + 3.13105i) q^{88} +(0.244613 - 0.244613i) q^{89} +(-2.09731 + 0.775429i) q^{90} +(3.40503 - 0.237593i) q^{91} +(4.25224 - 4.25224i) q^{92} +3.45028 q^{93} -0.854435i q^{94} +(-2.88145 - 1.32589i) q^{95} +(-0.707107 + 0.707107i) q^{96} +2.67283i q^{97} +6.10380i q^{98} +(-3.13105 + 3.13105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 4 q^{11} - 8 q^{13} - 4 q^{15} + 16 q^{16} - 4 q^{17} + 16 q^{18} - 4 q^{19} - 8 q^{21} + 4 q^{22} - 16 q^{23} + 16 q^{25} + 4 q^{26} - 4 q^{30} + 12 q^{31} - 4 q^{34} - 12 q^{35} - 32 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{41} - 8 q^{42} + 16 q^{43} - 4 q^{44} + 16 q^{46} + 16 q^{47} + 80 q^{49} + 8 q^{50} + 8 q^{52} - 44 q^{53} - 20 q^{55} - 12 q^{59} + 4 q^{60} - 32 q^{61} - 12 q^{62} - 16 q^{64} - 28 q^{65} + 4 q^{68} + 16 q^{69} - 36 q^{70} + 16 q^{71} - 16 q^{72} + 4 q^{76} + 32 q^{77} + 16 q^{78} - 16 q^{81} - 4 q^{82} + 16 q^{83} + 8 q^{84} - 40 q^{85} - 16 q^{86} + 28 q^{87} - 4 q^{88} - 4 q^{89} + 76 q^{91} + 16 q^{92} - 40 q^{95} - 4 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 4 * q^11 - 8 * q^13 - 4 * q^15 + 16 * q^16 - 4 * q^17 + 16 * q^18 - 4 * q^19 - 8 * q^21 + 4 * q^22 - 16 * q^23 + 16 * q^25 + 4 * q^26 - 4 * q^30 + 12 * q^31 - 4 * q^34 - 12 * q^35 - 32 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^41 - 8 * q^42 + 16 * q^43 - 4 * q^44 + 16 * q^46 + 16 * q^47 + 80 * q^49 + 8 * q^50 + 8 * q^52 - 44 * q^53 - 20 * q^55 - 12 * q^59 + 4 * q^60 - 32 * q^61 - 12 * q^62 - 16 * q^64 - 28 * q^65 + 4 * q^68 + 16 * q^69 - 36 * q^70 + 16 * q^71 - 16 * q^72 + 4 * q^76 + 32 * q^77 + 16 * q^78 - 16 * q^81 - 4 * q^82 + 16 * q^83 + 8 * q^84 - 40 * q^85 - 16 * q^86 + 28 * q^87 - 4 * q^88 - 4 * q^89 + 76 * q^91 + 16 * q^92 - 40 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.09731	+	0.775429i	−0.937946	+	0.346782i
$5$	−2.09731	+	0.775429i	−0.937946	+	0.346782i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−0.946681			−0.357812			−0.178906	−	0.983866i	$-0.557256\pi$
$7$	−0.946681			−0.357812			−0.178906	+	0.983866i	$0.557256\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	0.775429	+	2.09731i	0.245212	+	0.663228i
$11$	3.13105	+	3.13105i	0.944047	+	0.944047i	0.998515	−	0.0544686i	$-0.0173465\pi$
$11$	3.13105	+	3.13105i	0.944047	+	0.944047i	−0.0544686	+	0.998515i	$0.517346\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−3.59681	+	0.250975i	−0.997574	+	0.0696079i
$13$	−3.59681	+	0.250975i	−0.997574	+	0.0696079i
$14$			0.946681i			0.253011i
$15$	2.03133	+	0.934711i	0.524488	+	0.241341i
$16$	1.00000			0.250000
$17$	3.42154	+	3.42154i	0.829845	+	0.829845i	0.987495	−	0.157650i	$-0.0503919\pi$
$17$	3.42154	+	3.42154i	0.829845	+	0.829845i	−0.157650	+	0.987495i	$0.550392\pi$
$18$	1.00000			0.235702
$19$	1.00303	+	1.00303i	0.230112	+	0.230112i	0.812739	−	0.582628i	$-0.197975\pi$
$19$	1.00303	+	1.00303i	0.230112	+	0.230112i	−0.582628	+	0.812739i	$0.697975\pi$
$20$	2.09731	−	0.775429i	0.468973	−	0.173391i
$21$	0.669405	+	0.669405i	0.146076	+	0.146076i
$22$	3.13105	−	3.13105i	0.667542	−	0.667542i
$23$	−4.25224	+	4.25224i	−0.886654	+	0.886654i	−0.994200	−	0.107546i	$-0.965701\pi$
$23$	−4.25224	+	4.25224i	−0.886654	+	0.886654i	0.107546	+	0.994200i	$0.465701\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	3.79742	−	3.25263i	0.759484	−	0.650526i
$26$	0.250975	+	3.59681i	0.0492202	+	0.705392i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.946681			0.178906
$29$			5.39250i			1.00136i	0.865632	+	0.500681i	$0.166917\pi$
$29$			5.39250i			1.00136i	−0.865632	+	0.500681i	$0.833083\pi$
$30$	0.934711	−	2.03133i	0.170654	−	0.370869i
$31$	−2.43972	+	2.43972i	−0.438187	+	0.438187i	−0.891401	−	0.453215i	$-0.850277\pi$
$31$	−2.43972	+	2.43972i	−0.438187	+	0.438187i	0.453215	+	0.891401i	$0.350277\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	4.42797i		−	0.770811i
$34$	3.42154	−	3.42154i	0.586789	−	0.586789i
$35$	1.98548	−	0.734084i	0.335608	−	0.124083i
$36$		−	1.00000i		−	0.166667i
$37$	−11.9002			−1.95637			−0.978187	−	0.207725i	$-0.933394\pi$
$37$	−11.9002			−1.95637			−0.978187	+	0.207725i	$0.933394\pi$
$38$	1.00303	−	1.00303i	0.162713	−	0.162713i
$39$	2.72079	+	2.36586i	0.435675	+	0.378841i
$40$	−0.775429	−	2.09731i	−0.122606	−	0.331614i
$41$	6.03479	−	6.03479i	0.942477	−	0.942477i	−0.0559566	−	0.998433i	$-0.517821\pi$
$41$	6.03479	−	6.03479i	0.942477	−	0.942477i	0.998433	+	0.0559566i	$0.0178208\pi$
$42$	0.669405	−	0.669405i	0.103291	−	0.103291i
$43$	−0.242187	+	0.242187i	−0.0369332	+	0.0369332i	−0.725332	−	0.688399i	$-0.758314\pi$
$43$	−0.242187	+	0.242187i	−0.0369332	+	0.0369332i	0.688399	+	0.725332i	$0.258314\pi$
$44$	−3.13105	−	3.13105i	−0.472023	−	0.472023i
$45$	−0.775429	−	2.09731i	−0.115594	−	0.312649i
$46$	4.25224	+	4.25224i	0.626959	+	0.626959i
$47$	0.854435			0.124632			0.0623161	−	0.998056i	$-0.480151\pi$
$47$	0.854435			0.124632			0.0623161	+	0.998056i	$0.480151\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−6.10380			−0.871971
$50$	−3.25263	−	3.79742i	−0.459991	−	0.537036i
$51$		−	4.83878i		−	0.677565i
$52$	3.59681	−	0.250975i	0.498787	−	0.0348039i
$53$	3.90244	+	3.90244i	0.536041	+	0.536041i	0.922364	−	0.386322i	$-0.126255\pi$
$53$	3.90244	+	3.90244i	0.536041	+	0.536041i	−0.386322	+	0.922364i	$0.626255\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−8.99469	−	4.13888i	−1.21284	−	0.558086i
$56$		−	0.946681i		−	0.126506i
$57$		−	1.41850i		−	0.187885i
$58$	5.39250			0.708069
$59$	−9.38267	+	9.38267i	−1.22152	+	1.22152i	−0.254428	+	0.967092i	$0.581887\pi$
$59$	−9.38267	+	9.38267i	−1.22152	+	1.22152i	−0.967092	+	0.254428i	$0.918113\pi$
$60$	−2.03133	−	0.934711i	−0.262244	−	0.120671i
$61$	9.79944			1.25469			0.627345	−	0.778741i	$-0.284142\pi$
$61$	9.79944			1.25469			0.627345	+	0.778741i	$0.284142\pi$
$62$	2.43972	+	2.43972i	0.309845	+	0.309845i
$63$		−	0.946681i		−	0.119271i
$64$	−1.00000			−0.125000
$65$	7.34900	−	3.31544i	0.911532	−	0.411230i
$66$	−4.42797			−0.545046
$67$			3.51092i			0.428927i	0.976732	+	0.214464i	$0.0688003\pi$
$67$			3.51092i			0.428927i	−0.976732	+	0.214464i	$0.931200\pi$
$68$	−3.42154	−	3.42154i	−0.414922	−	0.414922i
$69$	6.01358			0.723950
$70$	−0.734084	−	1.98548i	−0.0877398	−	0.237311i
$71$	−6.99770	+	6.99770i	−0.830475	+	0.830475i	−0.987582	−	0.157107i	$-0.949783\pi$
$71$	−6.99770	+	6.99770i	−0.830475	+	0.830475i	0.157107	+	0.987582i	$0.449783\pi$
$72$	−1.00000			−0.117851
$73$		−	16.4476i		−	1.92505i	−0.271199	−	0.962523i	$-0.587420\pi$
$73$		−	16.4476i		−	1.92505i	0.271199	−	0.962523i	$-0.412580\pi$
$74$			11.9002i			1.38337i
$75$	−4.98514	−	0.385225i	−0.575634	−	0.0444820i
$76$	−1.00303	−	1.00303i	−0.115056	−	0.115056i
$77$	−2.96410	−	2.96410i	−0.337791	−	0.337791i
$78$	2.36586	−	2.72079i	0.267881	−	0.308069i
$79$			8.09997i			0.911317i	0.890155	+	0.455659i	$0.150596\pi$
$79$			8.09997i			0.911317i	−0.890155	+	0.455659i	$0.849404\pi$
$80$	−2.09731	+	0.775429i	−0.234486	+	0.0866956i
$81$	−1.00000			−0.111111
$82$	−6.03479	−	6.03479i	−0.666432	−	0.666432i
$83$	−15.2370			−1.67248			−0.836239	−	0.548365i	$-0.815251\pi$
$83$	−15.2370			−1.67248			−0.836239	+	0.548365i	$0.815251\pi$
$84$	−0.669405	−	0.669405i	−0.0730380	−	0.0730380i
$85$	−9.82918	−	4.52287i	−1.06612	−	0.490574i
$86$	0.242187	+	0.242187i	0.0261157	+	0.0261157i
$87$	3.81307	−	3.81307i	0.408804	−	0.408804i
$88$	−3.13105	+	3.13105i	−0.333771	+	0.333771i
$89$	0.244613	−	0.244613i	0.0259289	−	0.0259289i	−0.694023	−	0.719952i	$-0.744164\pi$
$89$	0.244613	−	0.244613i	0.0259289	−	0.0259289i	0.719952	+	0.694023i	$0.244164\pi$
$90$	−2.09731	+	0.775429i	−0.221076	+	0.0817374i
$91$	3.40503	−	0.237593i	0.356944	−	0.0249065i
$92$	4.25224	−	4.25224i	0.443327	−	0.443327i
$93$	3.45028			0.357778
$94$		−	0.854435i		−	0.0881282i
$95$	−2.88145	−	1.32589i	−0.295631	−	0.136034i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			2.67283i			0.271384i	0.990751	+	0.135692i	$0.0433258\pi$
$97$			2.67283i			0.271384i	−0.990751	+	0.135692i	$0.956674\pi$
$98$			6.10380i			0.616576i
$99$	−3.13105	+	3.13105i	−0.314682	+	0.314682i
$100$	−3.79742	+	3.25263i	−0.379742	+	0.325263i
$101$		−	7.16455i		−	0.712899i	−0.934315	−	0.356450i	$-0.883987\pi$
$101$		−	7.16455i		−	0.712899i	0.934315	−	0.356450i	$-0.116013\pi$
$102$	−4.83878			−0.479111
$103$	8.00473	−	8.00473i	0.788729	−	0.788729i	−0.192557	−	0.981286i	$-0.561678\pi$
$103$	8.00473	−	8.00473i	0.788729	−	0.788729i	0.981286	+	0.192557i	$0.0616779\pi$
$104$	−0.250975	−	3.59681i	−0.0246101	−	0.352696i
$105$	−1.92302	−	0.884873i	−0.187668	−	0.0863548i
$106$	3.90244	−	3.90244i	0.379039	−	0.379039i
$107$	5.33595	−	5.33595i	0.515845	−	0.515845i	−0.400466	−	0.916312i	$-0.631152\pi$
$107$	5.33595	−	5.33595i	0.515845	−	0.515845i	0.916312	+	0.400466i	$0.131152\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	3.93054	+	3.93054i	0.376478	+	0.376478i	0.869830	−	0.493352i	$-0.164229\pi$
$109$	3.93054	+	3.93054i	0.376478	+	0.376478i	−0.493352	+	0.869830i	$0.664229\pi$
$110$	−4.13888	+	8.99469i	−0.394626	+	0.857610i
$111$	8.41469	+	8.41469i	0.798687	+	0.798687i
$112$	−0.946681			−0.0894529
$113$	3.32488	+	3.32488i	0.312778	+	0.312778i	0.845985	−	0.533207i	$-0.179013\pi$
$113$	3.32488	+	3.32488i	0.312778	+	0.312778i	−0.533207	+	0.845985i	$0.679013\pi$
$114$	−1.41850			−0.132855
$115$	5.62096	−	12.2156i	0.524157	−	1.13911i
$116$		−	5.39250i		−	0.500681i
$117$	−0.250975	−	3.59681i	−0.0232026	−	0.332525i
$118$	9.38267	+	9.38267i	0.863745	+	0.863745i
$119$	−3.23910	−	3.23910i	−0.296928	−	0.296928i
$120$	−0.934711	+	2.03133i	−0.0853271	+	0.185435i
$121$			8.60694i			0.782449i
$122$		−	9.79944i		−	0.887200i
$123$	−8.53449			−0.769529
$124$	2.43972	−	2.43972i	0.219093	−	0.219093i
$125$	−5.44219	+	9.76640i	−0.486764	+	0.873534i
$126$	−0.946681			−0.0843370
$127$	−3.09330	−	3.09330i	−0.274486	−	0.274486i	0.556417	−	0.830903i	$-0.312176\pi$
$127$	−3.09330	−	3.09330i	−0.274486	−	0.274486i	−0.830903	+	0.556417i	$0.812176\pi$
$128$			1.00000i			0.0883883i
$129$	0.342504			0.0301558
$130$	−3.31544	−	7.34900i	−0.290783	−	0.644550i
$131$	−2.99792			−0.261930			−0.130965	−	0.991387i	$-0.541808\pi$
$131$	−2.99792			−0.261930			−0.130965	+	0.991387i	$0.541808\pi$
$132$			4.42797i			0.385406i
$133$	−0.949553	−	0.949553i	−0.0823367	−	0.0823367i
$134$	3.51092			0.303297
$135$	−0.934711	+	2.03133i	−0.0804471	+	0.174829i
$136$	−3.42154	+	3.42154i	−0.293394	+	0.293394i
$137$	17.3517			1.48245			0.741227	−	0.671255i	$-0.234244\pi$
$137$	17.3517			1.48245			0.741227	+	0.671255i	$0.234244\pi$
$138$		−	6.01358i		−	0.511910i
$139$		−	2.49588i		−	0.211698i	−0.994382	−	0.105849i	$-0.966244\pi$
$139$		−	2.49588i		−	0.211698i	0.994382	−	0.105849i	$-0.0337560\pi$
$140$	−1.98548	+	0.734084i	−0.167804	+	0.0620414i
$141$	−0.604177	−	0.604177i	−0.0508808	−	0.0508808i
$142$	6.99770	+	6.99770i	0.587234	+	0.587234i
$143$	−12.0476	−	10.4760i	−1.00747	−	0.876044i
$144$			1.00000i			0.0833333i
$145$	−4.18150	−	11.3097i	−0.347254	−	0.939223i
$146$	−16.4476			−1.36121
$147$	4.31603	+	4.31603i	0.355981	+	0.355981i
$148$	11.9002			0.978187
$149$	−1.72580	−	1.72580i	−0.141383	−	0.141383i	0.632873	−	0.774256i	$-0.281876\pi$
$149$	−1.72580	−	1.72580i	−0.141383	−	0.141383i	−0.774256	+	0.632873i	$0.781876\pi$
$150$	−0.385225	+	4.98514i	−0.0314535	+	0.407035i
$151$	1.86471	+	1.86471i	0.151748	+	0.151748i	0.778898	−	0.627150i	$-0.215779\pi$
$151$	1.86471	+	1.86471i	0.151748	+	0.151748i	−0.627150	+	0.778898i	$0.715779\pi$
$152$	−1.00303	+	1.00303i	−0.0813567	+	0.0813567i
$153$	−3.42154	+	3.42154i	−0.276615	+	0.276615i
$154$	−2.96410	+	2.96410i	−0.238854	+	0.238854i
$155$	3.22502	−	7.00868i	0.259040	−	0.562951i
$156$	−2.72079	−	2.36586i	−0.217838	−	0.189420i
$157$	2.33729	−	2.33729i	0.186536	−	0.186536i	−0.607661	−	0.794197i	$-0.707892\pi$
$157$	2.33729	−	2.33729i	0.186536	−	0.186536i	0.794197	+	0.607661i	$0.207892\pi$
$158$	8.09997			0.644399
$159$		−	5.51888i		−	0.437676i
$160$	0.775429	+	2.09731i	0.0613030	+	0.165807i
$161$	4.02552	−	4.02552i	0.317255	−	0.317255i
$162$			1.00000i			0.0785674i
$163$			23.5470i			1.84434i	0.386779	+	0.922172i	$0.373588\pi$
$163$			23.5470i			1.84434i	−0.386779	+	0.922172i	$0.626412\pi$
$164$	−6.03479	+	6.03479i	−0.471238	+	0.471238i
$165$	3.43358	+	9.28683i	0.267304	+	0.722979i
$166$			15.2370i			1.18262i
$167$	9.77190			0.756172			0.378086	−	0.925770i	$-0.376582\pi$
$167$	9.77190			0.756172			0.378086	+	0.925770i	$0.376582\pi$
$168$	−0.669405	+	0.669405i	−0.0516457	+	0.0516457i
$169$	12.8740	−	1.80542i	0.990309	−	0.138878i
$170$	−4.52287	+	9.82918i	−0.346888	+	0.753864i
$171$	−1.00303	+	1.00303i	−0.0767039	+	0.0767039i
$172$	0.242187	−	0.242187i	0.0184666	−	0.0184666i
$173$	5.96615	−	5.96615i	0.453598	−	0.453598i	−0.442949	−	0.896547i	$-0.646068\pi$
$173$	5.96615	−	5.96615i	0.453598	−	0.453598i	0.896547	+	0.442949i	$0.146068\pi$
$174$	−3.81307	−	3.81307i	−0.289068	−	0.289068i
$175$	−3.59495	+	3.07920i	−0.271752	+	0.232766i
$176$	3.13105	+	3.13105i	0.236012	+	0.236012i
$177$	13.2691			0.997367
$178$	−0.244613	−	0.244613i	−0.0183345	−	0.0183345i
$179$	7.96800			0.595557			0.297778	−	0.954635i	$-0.403754\pi$
$179$	7.96800			0.595557			0.297778	+	0.954635i	$0.403754\pi$
$180$	0.775429	+	2.09731i	0.0577970	+	0.156324i
$181$		−	17.3575i		−	1.29017i	−0.764109	−	0.645087i	$-0.776821\pi$
$181$		−	17.3575i		−	1.29017i	0.764109	−	0.645087i	$-0.223179\pi$
$182$	−0.237593	−	3.40503i	−0.0176116	−	0.252397i
$183$	−6.92925	−	6.92925i	−0.512225	−	0.512225i
$184$	−4.25224	−	4.25224i	−0.313479	−	0.313479i
$185$	24.9583	−	9.22773i	1.83497	−	0.678436i
$186$		−	3.45028i		−	0.252987i
$187$			21.4260i			1.56682i
$188$	−0.854435			−0.0623161
$189$	−0.669405	+	0.669405i	−0.0486920	+	0.0486920i
$190$	−1.32589	+	2.88145i	−0.0961903	+	0.209043i
$191$	6.75356			0.488671			0.244335	−	0.969691i	$-0.421430\pi$
$191$	6.75356			0.488671			0.244335	+	0.969691i	$0.421430\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$			7.55869i			0.544086i	0.962285	+	0.272043i	$0.0876994\pi$
$193$			7.55869i			0.544086i	−0.962285	+	0.272043i	$0.912301\pi$
$194$	2.67283			0.191898
$195$	−7.54090	−	2.85216i	−0.540015	−	0.204248i
$196$	6.10380			0.435985
$197$			17.8690i			1.27312i	0.771229	+	0.636558i	$0.219642\pi$
$197$			17.8690i			1.27312i	−0.771229	+	0.636558i	$0.780358\pi$
$198$	3.13105	+	3.13105i	0.222514	+	0.222514i
$199$	6.41529			0.454768			0.227384	−	0.973805i	$-0.426983\pi$
$199$	6.41529			0.454768			0.227384	+	0.973805i	$0.426983\pi$
$200$	3.25263	+	3.79742i	0.229996	+	0.268518i
$201$	2.48260	−	2.48260i	0.175109	−	0.175109i
$202$	−7.16455			−0.504096
$203$		−	5.10497i		−	0.358299i
$204$			4.83878i			0.338783i
$205$	−7.97728	+	17.3364i	−0.557158	+	1.21083i
$206$	−8.00473	−	8.00473i	−0.557716	−	0.557716i
$207$	−4.25224	−	4.25224i	−0.295551	−	0.295551i
$208$	−3.59681	+	0.250975i	−0.249394	+	0.0174020i
$209$			6.28109i			0.434472i
$210$	−0.884873	+	1.92302i	−0.0610621	+	0.132701i
$211$	8.36808			0.576082			0.288041	−	0.957618i	$-0.406996\pi$
$211$	8.36808			0.576082			0.288041	+	0.957618i	$0.406996\pi$
$212$	−3.90244	−	3.90244i	−0.268021	−	0.268021i
$213$	9.89625			0.678080
$214$	−5.33595	−	5.33595i	−0.364758	−	0.364758i
$215$	0.320143	−	0.695741i	0.0218336	−	0.0474491i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	2.30964	−	2.30964i	0.156788	−	0.156788i
$218$	3.93054	−	3.93054i	0.266210	−	0.266210i
$219$	−11.6302	+	11.6302i	−0.785897	+	0.785897i
$220$	8.99469	+	4.13888i	0.606422	+	0.279043i
$221$	−13.1653	−	11.4479i	−0.885595	−	0.770068i
$222$	8.41469	−	8.41469i	0.564757	−	0.564757i
$223$	−6.31913			−0.423160			−0.211580	−	0.977361i	$-0.567861\pi$
$223$	−6.31913			−0.423160			−0.211580	+	0.977361i	$0.567861\pi$
$224$			0.946681i			0.0632528i
$225$	3.25263	+	3.79742i	0.216842	+	0.253161i
$226$	3.32488	−	3.32488i	0.221168	−	0.221168i
$227$		−	2.06238i		−	0.136885i	−0.997655	−	0.0684423i	$-0.978197\pi$
$227$		−	2.06238i		−	0.136885i	0.997655	−	0.0684423i	$-0.0218029\pi$
$228$			1.41850i			0.0939427i
$229$	1.31652	−	1.31652i	0.0869979	−	0.0869979i	−0.662269	−	0.749266i	$-0.730406\pi$
$229$	1.31652	−	1.31652i	0.0869979	−	0.0869979i	0.749266	+	0.662269i	$0.230406\pi$
$230$	−12.2156	−	5.62096i	−0.805472	−	0.370635i
$231$			4.19188i			0.275805i
$232$	−5.39250			−0.354035
$233$	10.4414	−	10.4414i	0.684040	−	0.684040i	−0.276868	−	0.960908i	$-0.589297\pi$
$233$	10.4414	−	10.4414i	0.684040	−	0.684040i	0.960908	+	0.276868i	$0.0892966\pi$
$234$	−3.59681	+	0.250975i	−0.235131	+	0.0164067i
$235$	−1.79201	+	0.662553i	−0.116898	+	0.0432202i
$236$	9.38267	−	9.38267i	0.610760	−	0.610760i
$237$	5.72754	−	5.72754i	0.372044	−	0.372044i
$238$	−3.23910	+	3.23910i	−0.209960	+	0.209960i
$239$	−16.6032	−	16.6032i	−1.07397	−	1.07397i	−0.997036	−	0.0769369i	$-0.975486\pi$
$239$	−16.6032	−	16.6032i	−1.07397	−	1.07397i	−0.0769369	−	0.997036i	$-0.524514\pi$
$240$	2.03133	+	0.934711i	0.131122	+	0.0603354i
$241$	12.3249	+	12.3249i	0.793917	+	0.793917i	0.982128	−	0.188212i	$-0.0602691\pi$
$241$	12.3249	+	12.3249i	0.793917	+	0.793917i	−0.188212	+	0.982128i	$0.560269\pi$
$242$	8.60694			0.553275
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−9.79944			−0.627345
$245$	12.8016	−	4.73306i	0.817861	−	0.302384i
$246$			8.53449i			0.544139i
$247$	−3.85945	−	3.35598i	−0.245571	−	0.213536i
$248$	−2.43972	−	2.43972i	−0.154922	−	0.154922i
$249$	10.7742	+	10.7742i	0.682786	+	0.682786i
$250$	9.76640	+	5.44219i	0.617682	+	0.344194i
$251$			20.9264i			1.32086i	0.750886	+	0.660431i	$0.229627\pi$
$251$			20.9264i			1.32086i	−0.750886	+	0.660431i	$0.770373\pi$
$252$			0.946681i			0.0596353i
$253$	−26.6280			−1.67409
$254$	−3.09330	+	3.09330i	−0.194091	+	0.194091i
$255$	3.75213	+	10.1484i	0.234968	+	0.635519i
$256$	1.00000			0.0625000
$257$	5.26288	+	5.26288i	0.328290	+	0.328290i	0.851936	−	0.523646i	$-0.175429\pi$
$257$	5.26288	+	5.26288i	0.328290	+	0.328290i	−0.523646	+	0.851936i	$0.675429\pi$
$258$		−	0.342504i		−	0.0213234i
$259$	11.2657			0.700014
$260$	−7.34900	+	3.31544i	−0.455766	+	0.205615i
$261$	−5.39250			−0.333787
$262$			2.99792i			0.185212i
$263$	12.1431	+	12.1431i	0.748773	+	0.748773i	0.974249	−	0.225476i	$-0.0723938\pi$
$263$	12.1431	+	12.1431i	0.748773	+	0.748773i	−0.225476	+	0.974249i	$0.572394\pi$
$264$	4.42797			0.272523
$265$	−11.2107	−	5.15856i	−0.688667	−	0.316888i
$266$	−0.949553	+	0.949553i	−0.0582208	+	0.0582208i
$267$	−0.345935			−0.0211709
$268$		−	3.51092i		−	0.214464i
$269$			11.3324i			0.690950i	0.938428	+	0.345475i	$0.112282\pi$
$269$			11.3324i			0.690950i	−0.938428	+	0.345475i	$0.887718\pi$
$270$	2.03133	+	0.934711i	0.123623	+	0.0568847i
$271$	8.07401	+	8.07401i	0.490461	+	0.490461i	0.908452	−	0.417990i	$-0.137265\pi$
$271$	8.07401	+	8.07401i	0.490461	+	0.490461i	−0.417990	+	0.908452i	$0.637265\pi$
$272$	3.42154	+	3.42154i	0.207461	+	0.207461i
$273$	−2.57572	−	2.23971i	−0.155890	−	0.135554i
$274$		−	17.3517i		−	1.04825i
$275$	22.0741	+	1.70577i	1.33112	+	0.102862i
$276$	−6.01358			−0.361975
$277$	−3.26424	−	3.26424i	−0.196129	−	0.196129i	0.602209	−	0.798338i	$-0.294287\pi$
$277$	−3.26424	−	3.26424i	−0.196129	−	0.196129i	−0.798338	+	0.602209i	$0.794287\pi$
$278$	−2.49588			−0.149693
$279$	−2.43972	−	2.43972i	−0.146062	−	0.146062i
$280$	0.734084	+	1.98548i	0.0438699	+	0.118655i
$281$	−22.2236	−	22.2236i	−1.32575	−	1.32575i	−0.909040	−	0.416709i	$-0.863184\pi$
$281$	−22.2236	−	22.2236i	−1.32575	−	1.32575i	−0.416709	−	0.909040i	$-0.636816\pi$
$282$	−0.604177	+	0.604177i	−0.0359782	+	0.0359782i
$283$	−10.4468	+	10.4468i	−0.620997	+	0.620997i	−0.945786	−	0.324789i	$-0.894707\pi$
$283$	−10.4468	+	10.4468i	−0.620997	+	0.620997i	0.324789	+	0.945786i	$0.394707\pi$
$284$	6.99770	−	6.99770i	0.415237	−	0.415237i
$285$	1.09995	+	2.97504i	0.0651553	+	0.176226i
$286$	−10.4760	+	12.0476i	−0.619457	+	0.712389i
$287$	−5.71303	+	5.71303i	−0.337229	+	0.337229i
$288$	1.00000			0.0589256
$289$			6.41383i			0.377284i
$290$	−11.3097	+	4.18150i	−0.664131	+	0.245546i
$291$	1.88997	−	1.88997i	0.110792	−	0.110792i
$292$			16.4476i			0.962523i
$293$		−	24.5333i		−	1.43325i	−0.697458	−	0.716625i	$-0.745686\pi$
$293$		−	24.5333i		−	1.43325i	0.697458	−	0.716625i	$-0.254314\pi$
$294$	4.31603	−	4.31603i	0.251716	−	0.251716i
$295$	12.4028	−	26.9540i	0.722118	−	1.56932i
$296$		−	11.9002i		−	0.691683i
$297$	4.42797			0.256937
$298$	−1.72580	+	1.72580i	−0.0999727	+	0.0999727i
$299$	14.2273	−	16.3617i	0.822785	−	0.946221i
$300$	4.98514	+	0.385225i	0.287817	+	0.0222410i
$301$	0.229274	−	0.229274i	0.0132151	−	0.0132151i
$302$	1.86471	−	1.86471i	0.107302	−	0.107302i
$303$	−5.06610	+	5.06610i	−0.291040	+	0.291040i
$304$	1.00303	+	1.00303i	0.0575279	+	0.0575279i
$305$	−20.5525	+	7.59877i	−1.17683	+	0.435104i
$306$	3.42154	+	3.42154i	0.195596	+	0.195596i
$307$	−26.9486			−1.53804			−0.769019	−	0.639226i	$-0.779255\pi$
$307$	−26.9486			−1.53804			−0.769019	+	0.639226i	$0.779255\pi$
$308$	2.96410	+	2.96410i	0.168896	+	0.168896i
$309$	−11.3204			−0.643995
$310$	−7.00868	−	3.22502i	−0.398066	−	0.183169i
$311$		−	16.4762i		−	0.934281i	−0.884183	−	0.467140i	$-0.845284\pi$
$311$		−	16.4762i		−	0.934281i	0.884183	−	0.467140i	$-0.154716\pi$
$312$	−2.36586	+	2.72079i	−0.133940	+	0.154035i
$313$	2.89698	+	2.89698i	0.163747	+	0.163747i	0.784224	−	0.620477i	$-0.213061\pi$
$313$	2.89698	+	2.89698i	0.163747	+	0.163747i	−0.620477	+	0.784224i	$0.713061\pi$
$314$	−2.33729	−	2.33729i	−0.131901	−	0.131901i
$315$	0.734084	+	1.98548i	0.0413609	+	0.111869i
$316$		−	8.09997i		−	0.455659i
$317$			13.4323i			0.754434i	0.926125	+	0.377217i	$0.123119\pi$
$317$			13.4323i			0.754434i	−0.926125	+	0.377217i	$0.876881\pi$
$318$	−5.51888			−0.309484
$319$	−16.8842	+	16.8842i	−0.945332	+	0.945332i
$320$	2.09731	−	0.775429i	0.117243	−	0.0433478i
$321$	−7.54617			−0.421186
$322$	−4.02552	−	4.02552i	−0.224333	−	0.224333i
$323$			6.86383i			0.381914i
$324$	1.00000			0.0555556
$325$	−12.8423	+	12.6521i	−0.712360	+	0.701814i
$326$	23.5470			1.30415
$327$		−	5.55863i		−	0.307393i
$328$	6.03479	+	6.03479i	0.333216	+	0.333216i
$329$	−0.808877			−0.0445948
$330$	9.28683	−	3.43358i	0.511223	−	0.189012i
$331$	4.34332	−	4.34332i	0.238730	−	0.238730i	−0.577594	−	0.816324i	$-0.696008\pi$
$331$	4.34332	−	4.34332i	0.238730	−	0.238730i	0.816324	+	0.577594i	$0.196008\pi$
$332$	15.2370			0.836239
$333$		−	11.9002i		−	0.652125i
$334$		−	9.77190i		−	0.534695i
$335$	−2.72247	−	7.36349i	−0.148744	−	0.402310i
$336$	0.669405	+	0.669405i	0.0365190	+	0.0365190i
$337$	−2.98172	−	2.98172i	−0.162425	−	0.162425i	0.621215	−	0.783640i	$-0.286639\pi$
$337$	−2.98172	−	2.98172i	−0.162425	−	0.162425i	−0.783640	+	0.621215i	$0.786639\pi$
$338$	−1.80542	−	12.8740i	−0.0982017	−	0.700255i
$339$		−	4.70209i		−	0.255382i
$340$	9.82918	+	4.52287i	0.533062	+	0.245287i
$341$	−15.2778			−0.827337
$342$	1.00303	+	1.00303i	0.0542378	+	0.0542378i
$343$	12.4051			0.669813
$344$	−0.242187	−	0.242187i	−0.0130579	−	0.0130579i
$345$	−12.6123	+	4.66310i	−0.679026	+	0.251053i
$346$	−5.96615	−	5.96615i	−0.320742	−	0.320742i
$347$	−25.3043	+	25.3043i	−1.35841	+	1.35841i	−0.482521	+	0.875884i	$0.660279\pi$
$347$	−25.3043	+	25.3043i	−1.35841	+	1.35841i	−0.875884	+	0.482521i	$0.839721\pi$
$348$	−3.81307	+	3.81307i	−0.204402	+	0.204402i
$349$	10.5348	−	10.5348i	0.563915	−	0.563915i	−0.366502	−	0.930417i	$-0.619445\pi$
$349$	10.5348	−	10.5348i	0.563915	−	0.563915i	0.930417	+	0.366502i	$0.119445\pi$
$350$	3.07920	+	3.59495i	0.164590	+	0.192158i
$351$	−2.36586	+	2.72079i	−0.126280	+	0.145225i
$352$	3.13105	−	3.13105i	0.166885	−	0.166885i
$353$	−24.7214			−1.31579			−0.657893	−	0.753111i	$-0.728552\pi$
$353$	−24.7214			−1.31579			−0.657893	+	0.753111i	$0.728552\pi$
$354$		−	13.2691i		−	0.705245i
$355$	9.25014	−	20.1026i	0.490946	−	1.06693i
$356$	−0.244613	+	0.244613i	−0.0129645	+	0.0129645i
$357$			4.58078i			0.242441i
$358$		−	7.96800i		−	0.421122i
$359$	1.44201	−	1.44201i	0.0761066	−	0.0761066i	−0.668029	−	0.744135i	$-0.732862\pi$
$359$	1.44201	−	1.44201i	0.0761066	−	0.0761066i	0.744135	+	0.668029i	$0.232862\pi$
$360$	2.09731	−	0.775429i	0.110538	−	0.0408687i
$361$		−	16.9878i		−	0.894097i
$362$	−17.3575			−0.912291
$363$	6.08602	−	6.08602i	0.319433	−	0.319433i
$364$	−3.40503	+	0.237593i	−0.178472	+	0.0124533i
$365$	12.7539	+	34.4957i	0.667572	+	1.80559i
$366$	−6.92925	+	6.92925i	−0.362198	+	0.362198i
$367$	0.992346	−	0.992346i	0.0518000	−	0.0518000i	−0.680732	−	0.732532i	$-0.738338\pi$
$367$	0.992346	−	0.992346i	0.0518000	−	0.0518000i	0.732532	+	0.680732i	$0.238338\pi$
$368$	−4.25224	+	4.25224i	−0.221663	+	0.221663i
$369$	6.03479	+	6.03479i	0.314159	+	0.314159i
$370$	−9.22773	−	24.9583i	−0.479727	−	1.29752i
$371$	−3.69437	−	3.69437i	−0.191802	−	0.191802i
$372$	−3.45028			−0.178889
$373$	20.8743	+	20.8743i	1.08083	+	1.08083i	0.996432	+	0.0843970i	$0.0268964\pi$
$373$	20.8743	+	20.8743i	1.08083	+	1.08083i	0.0843970	+	0.996432i	$0.473104\pi$
$374$	21.4260			1.10791
$375$	10.7541	−	3.05768i	0.555339	−	0.157898i
$376$			0.854435i			0.0440641i
$377$	−1.35338	−	19.3958i	−0.0697027	−	0.998932i
$378$	0.669405	+	0.669405i	0.0344305	+	0.0344305i
$379$	−17.6422	−	17.6422i	−0.906221	−	0.906221i	0.0897438	−	0.995965i	$-0.471395\pi$
$379$	−17.6422	−	17.6422i	−0.906221	−	0.906221i	−0.995965	+	0.0897438i	$0.971395\pi$
$380$	2.88145	+	1.32589i	0.147815	+	0.0680168i
$381$			4.37458i			0.224117i
$382$		−	6.75356i		−	0.345542i
$383$	29.6580			1.51545			0.757725	−	0.652574i	$-0.226311\pi$
$383$	29.6580			1.51545			0.757725	+	0.652574i	$0.226311\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	8.51510	+	3.91820i	0.433970	+	0.199690i
$386$	7.55869			0.384727
$387$	−0.242187	−	0.242187i	−0.0123111	−	0.0123111i
$388$		−	2.67283i		−	0.135692i
$389$	−16.8263			−0.853127			−0.426564	−	0.904458i	$-0.640276\pi$
$389$	−16.8263			−0.853127			−0.426564	+	0.904458i	$0.640276\pi$
$390$	−2.85216	+	7.54090i	−0.144425	+	0.381848i
$391$	−29.0984			−1.47157
$392$		−	6.10380i		−	0.308288i
$393$	2.11985	+	2.11985i	0.106932	+	0.106932i
$394$	17.8690			0.900229
$395$	−6.28095	−	16.9881i	−0.316029	−	0.854766i
$396$	3.13105	−	3.13105i	0.157341	−	0.157341i
$397$	−28.3338			−1.42203			−0.711016	−	0.703176i	$-0.751765\pi$
$397$	−28.3338			−1.42203			−0.711016	+	0.703176i	$0.751765\pi$
$398$		−	6.41529i		−	0.321569i
$399$			1.34287i			0.0672276i
$400$	3.79742	−	3.25263i	0.189871	−	0.162631i
$401$	−8.47925	−	8.47925i	−0.423433	−	0.423433i	0.462951	−	0.886384i	$-0.346791\pi$
$401$	−8.47925	−	8.47925i	−0.423433	−	0.423433i	−0.886384	+	0.462951i	$0.846791\pi$
$402$	−2.48260	−	2.48260i	−0.123821	−	0.123821i
$403$	8.16289	−	9.38751i	0.406622	−	0.467625i
$404$			7.16455i			0.356450i
$405$	2.09731	−	0.775429i	0.104216	−	0.0385314i
$406$	−5.10497			−0.253356
$407$	−37.2600	−	37.2600i	−1.84691	−	1.84691i
$408$	4.83878			0.239555
$409$	−24.9472	−	24.9472i	−1.23356	−	1.23356i	−0.962588	−	0.270971i	$-0.912655\pi$
$409$	−24.9472	−	24.9472i	−1.23356	−	1.23356i	−0.270971	−	0.962588i	$-0.587345\pi$
$410$	17.3364	+	7.97728i	0.856183	+	0.393970i
$411$	−12.2695	−	12.2695i	−0.605209	−	0.605209i
$412$	−8.00473	+	8.00473i	−0.394365	+	0.394365i
$413$	8.88240	−	8.88240i	0.437074	−	0.437074i
$414$	−4.25224	+	4.25224i	−0.208986	+	0.208986i
$415$	31.9567	−	11.8152i	1.56869	−	0.579986i
$416$	0.250975	+	3.59681i	0.0123051	+	0.176348i
$417$	−1.76485	+	1.76485i	−0.0864252	+	0.0864252i
$418$	6.28109			0.307218
$419$			12.4367i			0.607574i	0.952740	+	0.303787i	$0.0982511\pi$
$419$			12.4367i			0.607574i	−0.952740	+	0.303787i	$0.901749\pi$
$420$	1.92302	+	0.884873i	0.0938340	+	0.0431774i
$421$	−14.7295	+	14.7295i	−0.717871	+	0.717871i	−0.968169	−	0.250298i	$-0.919471\pi$
$421$	−14.7295	+	14.7295i	−0.717871	+	0.717871i	0.250298	+	0.968169i	$0.419471\pi$
$422$		−	8.36808i		−	0.407352i
$423$			0.854435i			0.0415440i
$424$	−3.90244	+	3.90244i	−0.189519	+	0.189519i
$425$	24.1220	+	1.86402i	1.17009	+	0.0904184i
$426$		−	9.89625i		−	0.479475i
$427$	−9.27695			−0.448943
$428$	−5.33595	+	5.33595i	−0.257923	+	0.257923i
$429$	1.11131	+	15.9266i	0.0536545	+	0.768941i
$430$	−0.695741	−	0.320143i	−0.0335516	−	0.0154387i
$431$	−8.50842	+	8.50842i	−0.409836	+	0.409836i	−0.881681	−	0.471845i	$-0.843588\pi$
$431$	−8.50842	+	8.50842i	−0.409836	+	0.409836i	0.471845	+	0.881681i	$0.343588\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−6.47843	+	6.47843i	−0.311333	+	0.311333i	−0.845426	−	0.534093i	$-0.820653\pi$
$433$	−6.47843	+	6.47843i	−0.311333	+	0.311333i	0.534093	+	0.845426i	$0.320653\pi$
$434$	−2.30964	−	2.30964i	−0.110866	−	0.110866i
$435$	−5.04043	+	10.9540i	−0.241670	+	0.525202i
$436$	−3.93054	−	3.93054i	−0.188239	−	0.188239i
$437$	−8.53028			−0.408059
$438$	11.6302	+	11.6302i	0.555713	+	0.555713i
$439$	40.8316			1.94879			0.974393	−	0.224854i	$-0.0721904\pi$
$439$	40.8316			1.94879			0.974393	+	0.224854i	$0.0721904\pi$
$440$	4.13888	−	8.99469i	0.197313	−	0.428805i
$441$		−	6.10380i		−	0.290657i
$442$	−11.4479	+	13.1653i	−0.544520	+	0.626211i
$443$	−8.09147	−	8.09147i	−0.384437	−	0.384437i	0.488261	−	0.872698i	$-0.337632\pi$
$443$	−8.09147	−	8.09147i	−0.384437	−	0.384437i	−0.872698	+	0.488261i	$0.837632\pi$
$444$	−8.41469	−	8.41469i	−0.399343	−	0.399343i
$445$	−0.323349	+	0.702709i	−0.0153282	+	0.0333116i
$446$			6.31913i			0.299219i
$447$			2.44065i			0.115439i
$448$	0.946681			0.0447265
$449$	22.0410	−	22.0410i	1.04018	−	1.04018i	0.0410213	−	0.999158i	$-0.486939\pi$
$449$	22.0410	−	22.0410i	1.04018	−	1.04018i	0.999158	−	0.0410213i	$-0.0130611\pi$
$450$	3.79742	−	3.25263i	0.179012	−	0.153330i
$451$	37.7905			1.77948
$452$	−3.32488	−	3.32488i	−0.156389	−	0.156389i
$453$		−	2.63710i		−	0.123902i
$454$	−2.06238			−0.0967921
$455$	−6.95716	+	3.13866i	−0.326157	+	0.147143i
$456$	1.41850			0.0664275
$457$			17.5342i			0.820213i	0.912038	+	0.410107i	$0.134509\pi$
$457$			17.5342i			0.820213i	−0.912038	+	0.410107i	$0.865491\pi$
$458$	−1.31652	−	1.31652i	−0.0615168	−	0.0615168i
$459$	4.83878			0.225855
$460$	−5.62096	+	12.2156i	−0.262079	+	0.569554i
$461$	−17.5242	+	17.5242i	−0.816184	+	0.816184i	−0.985553	−	0.169368i	$-0.945827\pi$
$461$	−17.5242	+	17.5242i	−0.816184	+	0.816184i	0.169368	+	0.985553i	$0.445827\pi$
$462$	4.19188			0.195024
$463$		−	12.6976i		−	0.590106i	−0.955481	−	0.295053i	$-0.904663\pi$
$463$		−	12.6976i		−	0.590106i	0.955481	−	0.295053i	$-0.0953372\pi$
$464$			5.39250i			0.250340i
$465$	−7.23632	+	2.67545i	−0.335576	+	0.124071i
$466$	−10.4414	−	10.4414i	−0.483689	−	0.483689i
$467$	−1.17459	−	1.17459i	−0.0543535	−	0.0543535i	0.679408	−	0.733761i	$-0.262237\pi$
$467$	−1.17459	−	1.17459i	−0.0543535	−	0.0543535i	−0.733761	+	0.679408i	$0.762237\pi$
$468$	0.250975	+	3.59681i	0.0116013	+	0.166262i
$469$		−	3.32372i		−	0.153475i
$470$	0.662553	+	1.79201i	0.0305613	+	0.0826595i
$471$	−3.30542			−0.152306
$472$	−9.38267	−	9.38267i	−0.431872	−	0.431872i
$473$	−1.51660			−0.0697334
$474$	−5.72754	−	5.72754i	−0.263075	−	0.263075i
$475$	7.07144	+	0.546443i	0.324460	+	0.0250725i
$476$	3.23910	+	3.23910i	0.148464	+	0.148464i
$477$	−3.90244	+	3.90244i	−0.178680	+	0.178680i
$478$	−16.6032	+	16.6032i	−0.759414	+	0.759414i
$479$	22.2742	−	22.2742i	1.01773	−	1.01773i	0.0178921	−	0.999840i	$-0.494304\pi$
$479$	22.2742	−	22.2742i	1.01773	−	1.01773i	0.999840	−	0.0178921i	$-0.00569553\pi$
$480$	0.934711	−	2.03133i	0.0426635	−	0.0927173i
$481$	42.8026	−	2.98664i	1.95163	−	0.136179i
$482$	12.3249	−	12.3249i	0.561384	−	0.561384i
$483$	−5.69294			−0.259038
$484$		−	8.60694i		−	0.391224i
$485$	−2.07259	−	5.60575i	−0.0941113	−	0.254544i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			33.0320i			1.49682i	0.663234	+	0.748412i	$0.269183\pi$
$487$			33.0320i			1.49682i	−0.663234	+	0.748412i	$0.730817\pi$
$488$			9.79944i			0.443600i
$489$	16.6503	−	16.6503i	0.752951	−	0.752951i
$490$	−4.73306	−	12.8016i	−0.213818	−	0.578315i
$491$			36.4206i			1.64364i	0.569747	+	0.821820i	$0.307041\pi$
$491$			36.4206i			1.64364i	−0.569747	+	0.821820i	$0.692959\pi$
$492$	8.53449			0.384764
$493$	−18.4506	+	18.4506i	−0.830974	+	0.830974i
$494$	−3.35598	+	3.85945i	−0.150993	+	0.173645i
$495$	4.13888	−	8.99469i	0.186029	−	0.404281i
$496$	−2.43972	+	2.43972i	−0.109547	+	0.109547i
$497$	6.62459	−	6.62459i	0.297154	−	0.297154i
$498$	10.7742	−	10.7742i	0.482803	−	0.482803i
$499$	26.4644	+	26.4644i	1.18471	+	1.18471i	0.978510	+	0.206199i	$0.0661094\pi$
$499$	26.4644	+	26.4644i	1.18471	+	1.18471i	0.206199	+	0.978510i	$0.433891\pi$
$500$	5.44219	−	9.76640i	0.243382	−	0.436767i
$501$	−6.90978	−	6.90978i	−0.308706	−	0.308706i
$502$	20.9264			0.933991
$503$	18.3270	+	18.3270i	0.817161	+	0.817161i	0.985696	−	0.168535i	$-0.0539035\pi$
$503$	18.3270	+	18.3270i	0.817161	+	0.817161i	−0.168535	+	0.985696i	$0.553903\pi$
$504$	0.946681			0.0421685
$505$	5.55560	+	15.0263i	0.247221	+	0.668661i
$506$			26.6280i			1.18376i
$507$	−10.3799	−	7.82669i	−0.460989	−	0.347595i
$508$	3.09330	+	3.09330i	0.137243	+	0.137243i
$509$	4.50027	+	4.50027i	0.199471	+	0.199471i	0.799773	−	0.600302i	$-0.204953\pi$
$509$	4.50027	+	4.50027i	0.199471	+	0.199471i	−0.600302	+	0.799773i	$0.704953\pi$
$510$	10.1484	−	3.75213i	0.449380	−	0.166147i
$511$			15.5706i			0.688804i
$512$		−	1.00000i		−	0.0441942i
$513$	1.41850			0.0626285
$514$	5.26288	−	5.26288i	0.232136	−	0.232136i
$515$	−10.5813	+	22.9955i	−0.466268	+	1.01330i
$516$	−0.342504			−0.0150779
$517$	2.67528	+	2.67528i	0.117659	+	0.117659i
$518$		−	11.2657i		−	0.494985i
$519$	−8.43741			−0.370361
$520$	3.31544	+	7.34900i	0.145392	+	0.322275i
$521$	−2.48916			−0.109052			−0.0545260	−	0.998512i	$-0.517365\pi$
$521$	−2.48916			−0.109052			−0.0545260	+	0.998512i	$0.517365\pi$
$522$			5.39250i			0.236023i
$523$	8.64710	+	8.64710i	0.378111	+	0.378111i	0.870420	−	0.492309i	$-0.163847\pi$
$523$	8.64710	+	8.64710i	0.378111	+	0.378111i	−0.492309	+	0.870420i	$0.663847\pi$
$524$	2.99792			0.130965
$525$	4.71934	+	0.364686i	0.205969	+	0.0159162i
$526$	12.1431	−	12.1431i	0.529462	−	0.529462i
$527$	−16.6952			−0.727253
$528$		−	4.42797i		−	0.192703i
$529$		−	13.1631i		−	0.572310i
$530$	−5.15856	+	11.2107i	−0.224074	+	0.486961i
$531$	−9.38267	−	9.38267i	−0.407173	−	0.407173i
$532$	0.949553	+	0.949553i	0.0411683	+	0.0411683i
$533$	−20.1914	+	23.2206i	−0.874587	+	1.00579i
$534$			0.345935i			0.0149701i
$535$	−7.05349	+	15.3288i	−0.304949	+	0.662721i
$536$	−3.51092			−0.151649
$537$	−5.63423	−	5.63423i	−0.243135	−	0.243135i
$538$	11.3324			0.488576
$539$	−19.1113	−	19.1113i	−0.823181	−	0.823181i
$540$	0.934711	−	2.03133i	0.0402236	−	0.0874147i
$541$	−14.9033	−	14.9033i	−0.640743	−	0.640743i	0.309995	−	0.950738i	$-0.399673\pi$
$541$	−14.9033	−	14.9033i	−0.640743	−	0.640743i	−0.950738	+	0.309995i	$0.899673\pi$
$542$	8.07401	−	8.07401i	0.346809	−	0.346809i
$543$	−12.2736	+	12.2736i	−0.526712	+	0.526712i
$544$	3.42154	−	3.42154i	0.146697	−	0.146697i
$545$	−11.2914	−	5.19571i	−0.483672	−	0.222560i
$546$	−2.23971	+	2.57572i	−0.0958509	+	0.110231i
$547$	32.1953	−	32.1953i	1.37657	−	1.37657i	0.526232	−	0.850341i	$-0.323604\pi$
$547$	32.1953	−	32.1953i	1.37657	−	1.37657i	0.850341	−	0.526232i	$-0.176396\pi$
$548$	−17.3517			−0.741227
$549$			9.79944i			0.418230i
$550$	1.70577	−	22.0741i	0.0727342	−	0.941241i
$551$	−5.40885	+	5.40885i	−0.230425	+	0.230425i
$552$			6.01358i			0.255955i
$553$		−	7.66808i		−	0.326080i
$554$	−3.26424	+	3.26424i	−0.138684	+	0.138684i
$555$	−24.1732	−	11.1232i	−1.02609	−	0.472154i
$556$			2.49588i			0.105849i
$557$	38.6878			1.63925			0.819627	−	0.572897i	$-0.194180\pi$
$557$	38.6878			1.63925			0.819627	+	0.572897i	$0.194180\pi$
$558$	−2.43972	+	2.43972i	−0.103282	+	0.103282i
$559$	0.810318	−	0.931883i	0.0342728	−	0.0394145i
$560$	1.98548	−	0.734084i	0.0839020	−	0.0310207i
$561$	15.1505	−	15.1505i	0.639653	−	0.639653i
$562$	−22.2236	+	22.2236i	−0.937446	+	0.937446i
$563$	−17.2310	+	17.2310i	−0.726198	+	0.726198i	−0.969860	−	0.243662i	$-0.921651\pi$
$563$	−17.2310	+	17.2310i	−0.726198	+	0.726198i	0.243662	+	0.969860i	$0.421651\pi$
$564$	0.604177	+	0.604177i	0.0254404	+	0.0254404i
$565$	−9.55151	−	4.39510i	−0.401835	−	0.184903i
$566$	10.4468	+	10.4468i	0.439111	+	0.439111i
$567$	0.946681			0.0397569
$568$	−6.99770	−	6.99770i	−0.293617	−	0.293617i
$569$	7.21162			0.302327			0.151163	−	0.988509i	$-0.451698\pi$
$569$	7.21162			0.302327			0.151163	+	0.988509i	$0.451698\pi$
$570$	2.97504	−	1.09995i	0.124611	−	0.0460718i
$571$			20.5745i			0.861017i	0.902587	+	0.430508i	$0.141666\pi$
$571$			20.5745i			0.861017i	−0.902587	+	0.430508i	$0.858334\pi$
$572$	12.0476	+	10.4760i	0.503735	+	0.438022i
$573$	−4.77549	−	4.77549i	−0.199499	−	0.199499i
$574$	5.71303	+	5.71303i	0.238457	+	0.238457i
$575$	−2.31658	+	29.9785i	−0.0966082	+	1.25019i
$576$		−	1.00000i		−	0.0416667i
$577$			4.77462i			0.198770i	0.995049	+	0.0993850i	$0.0316875\pi$
$577$			4.77462i			0.198770i	−0.995049	+	0.0993850i	$0.968312\pi$
$578$	6.41383			0.266780
$579$	5.34480	−	5.34480i	0.222122	−	0.222122i
$580$	4.18150	+	11.3097i	0.173627	+	0.469611i
$581$	14.4246			0.598433
$582$	−1.88997	−	1.88997i	−0.0783419	−	0.0783419i
$583$			24.4375i			1.01210i
$584$	16.4476			0.680607
$585$	3.31544	+	7.34900i	0.137077	+	0.303844i
$586$	−24.5333			−1.01346
$587$			10.7668i			0.444393i	0.975002	+	0.222196i	$0.0713226\pi$
$587$			10.7668i			0.444393i	−0.975002	+	0.222196i	$0.928677\pi$
$588$	−4.31603	−	4.31603i	−0.177990	−	0.177990i
$589$	−4.89424			−0.201664
$590$	−26.9540	−	12.4028i	−1.10968	−	0.510614i
$591$	12.6353	−	12.6353i	0.519747	−	0.519747i
$592$	−11.9002			−0.489094
$593$			41.5640i			1.70683i	0.521233	+	0.853414i	$0.325472\pi$
$593$			41.5640i			1.70683i	−0.521233	+	0.853414i	$0.674528\pi$
$594$		−	4.42797i		−	0.181682i
$595$	9.30510	+	4.28171i	0.381472	+	0.175533i
$596$	1.72580	+	1.72580i	0.0706914	+	0.0706914i
$597$	−4.53630	−	4.53630i	−0.185658	−	0.185658i
$598$	−16.3617	−	14.2273i	−0.669079	−	0.581797i
$599$			34.5955i			1.41353i	0.707446	+	0.706767i	$0.249847\pi$
$599$			34.5955i			1.41353i	−0.707446	+	0.706767i	$0.750153\pi$
$600$	0.385225	−	4.98514i	0.0157268	−	0.203517i
$601$	−10.8465			−0.442436			−0.221218	−	0.975224i	$-0.571003\pi$
$601$	−10.8465			−0.442436			−0.221218	+	0.975224i	$0.571003\pi$
$602$	−0.229274	−	0.229274i	−0.00934451	−	0.00934451i
$603$	−3.51092			−0.142976
$604$	−1.86471	−	1.86471i	−0.0758739	−	0.0758739i
$605$	−6.67407	−	18.0514i	−0.271339	−	0.733894i
$606$	5.06610	+	5.06610i	0.205796	+	0.205796i
$607$	−2.08924	+	2.08924i	−0.0847995	+	0.0847995i	−0.748234	−	0.663435i	$-0.769098\pi$
$607$	−2.08924	+	2.08924i	−0.0847995	+	0.0847995i	0.663435	+	0.748234i	$0.269098\pi$
$608$	1.00303	−	1.00303i	0.0406784	−	0.0406784i
$609$	−3.60976	+	3.60976i	−0.146275	+	0.146275i
$610$	7.59877	+	20.5525i	0.307665	+	0.832145i
$611$	−3.07324	+	0.214442i	−0.124330	+	0.00867538i
$612$	3.42154	−	3.42154i	0.138307	−	0.138307i
$613$	39.8520			1.60961			0.804804	−	0.593541i	$-0.202270\pi$
$613$	39.8520			1.60961			0.804804	+	0.593541i	$0.202270\pi$
$614$			26.9486i			1.08756i
$615$	17.8995	−	6.61789i	0.721776	−	0.266859i
$616$	2.96410	−	2.96410i	0.119427	−	0.119427i
$617$			35.2269i			1.41818i	0.705118	+	0.709090i	$0.250894\pi$
$617$			35.2269i			1.41818i	−0.705118	+	0.709090i	$0.749106\pi$
$618$			11.3204i			0.455373i
$619$	29.3560	−	29.3560i	1.17992	−	1.17992i	0.200150	−	0.979765i	$-0.435857\pi$
$619$	29.3560	−	29.3560i	1.17992	−	1.17992i	0.979765	−	0.200150i	$-0.0641431\pi$
$620$	−3.22502	+	7.00868i	−0.129520	+	0.281475i
$621$			6.01358i			0.241317i
$622$	−16.4762			−0.660636
$623$	−0.231570	+	0.231570i	−0.00927768	+	0.00927768i
$624$	2.72079	+	2.36586i	0.108919	+	0.0947102i
$625$	3.84080	−	24.7032i	0.153632	−	0.988128i
$626$	2.89698	−	2.89698i	0.115787	−	0.115787i
$627$	4.44140	−	4.44140i	0.177373	−	0.177373i
$628$	−2.33729	+	2.33729i	−0.0932679	+	0.0932679i
$629$	−40.7168	−	40.7168i	−1.62349	−	1.62349i
$630$	1.98548	−	0.734084i	0.0791036	−	0.0292466i
$631$	−10.8434	−	10.8434i	−0.431670	−	0.431670i	0.457526	−	0.889196i	$-0.348736\pi$
$631$	−10.8434	−	10.8434i	−0.431670	−	0.431670i	−0.889196	+	0.457526i	$0.848736\pi$
$632$	−8.09997			−0.322199
$633$	−5.91713	−	5.91713i	−0.235185	−	0.235185i
$634$	13.4323			0.533465
$635$	8.88623	+	4.08897i	0.352639	+	0.162266i
$636$			5.51888i			0.218838i
$637$	21.9542	−	1.53190i	0.869856	−	0.0606960i
$638$	16.8842	+	16.8842i	0.668451	+	0.668451i
$639$	−6.99770	−	6.99770i	−0.276825	−	0.276825i
$640$	−0.775429	−	2.09731i	−0.0306515	−	0.0829035i
$641$			45.5504i			1.79913i	0.436784	+	0.899566i	$0.356117\pi$
$641$			45.5504i			1.79913i	−0.436784	+	0.899566i	$0.643883\pi$
$642$			7.54617i			0.297823i
$643$	13.2934			0.524241			0.262120	−	0.965035i	$-0.415578\pi$
$643$	13.2934			0.524241			0.262120	+	0.965035i	$0.415578\pi$
$644$	−4.02552	+	4.02552i	−0.158628	+	0.158628i
$645$	−0.718338	+	0.265588i	−0.0282845	+	0.0104575i
$646$	6.86383			0.270054
$647$	0.168076	+	0.168076i	0.00660775	+	0.00660775i	0.710403	−	0.703795i	$-0.248513\pi$
$647$	0.168076	+	0.168076i	0.00660775	+	0.00660775i	−0.703795	+	0.710403i	$0.748513\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−58.7552			−2.30634
$650$	12.6521	+	12.8423i	0.496258	+	0.503715i
$651$	−3.26632			−0.128017
$652$		−	23.5470i		−	0.922172i
$653$	16.2763	+	16.2763i	0.636941	+	0.636941i	0.949800	−	0.312859i	$-0.101287\pi$
$653$	16.2763	+	16.2763i	0.636941	+	0.636941i	−0.312859	+	0.949800i	$0.601287\pi$
$654$	−5.55863			−0.217360
$655$	6.28758	−	2.32468i	0.245676	−	0.0908326i
$656$	6.03479	−	6.03479i	0.235619	−	0.235619i
$657$	16.4476			0.641682
$658$			0.808877i			0.0315333i
$659$		−	36.6617i		−	1.42814i	−0.700077	−	0.714068i	$-0.746851\pi$
$659$		−	36.6617i		−	1.42814i	0.700077	−	0.714068i	$-0.253149\pi$
$660$	−3.43358	−	9.28683i	−0.133652	−	0.361489i
$661$	1.76972	+	1.76972i	0.0688341	+	0.0688341i	0.740686	−	0.671852i	$-0.234501\pi$
$661$	1.76972	+	1.76972i	0.0688341	+	0.0688341i	−0.671852	+	0.740686i	$0.734501\pi$
$662$	−4.34332	−	4.34332i	−0.168808	−	0.168808i
$663$	1.21441	+	17.4042i	0.0471639	+	0.675922i
$664$		−	15.2370i		−	0.591310i
$665$	2.72782	+	1.25520i	0.105780	+	0.0486744i
$666$	−11.9002			−0.461122
$667$	−22.9302	−	22.9302i	−0.887861	−	0.887861i
$668$	−9.77190			−0.378086
$669$	4.46830	+	4.46830i	0.172754	+	0.172754i
$670$	−7.36349	+	2.72247i	−0.284476	+	0.105178i
$671$	30.6825	+	30.6825i	1.18449	+	1.18449i
$672$	0.669405	−	0.669405i	0.0258228	−	0.0258228i
$673$	16.5684	−	16.5684i	0.638667	−	0.638667i	−0.311560	−	0.950227i	$-0.600851\pi$
$673$	16.5684	−	16.5684i	0.638667	−	0.638667i	0.950227	+	0.311560i	$0.100851\pi$
$674$	−2.98172	+	2.98172i	−0.114852	+	0.114852i
$675$	0.385225	−	4.98514i	0.0148273	−	0.191878i
$676$	−12.8740	+	1.80542i	−0.495155	+	0.0694391i
$677$	−11.4370	+	11.4370i	−0.439558	+	0.439558i	−0.891863	−	0.452305i	$-0.850602\pi$
$677$	−11.4370	+	11.4370i	−0.439558	+	0.439558i	0.452305	+	0.891863i	$0.350602\pi$
$678$	−4.70209			−0.180583
$679$		−	2.53031i		−	0.0971046i
$680$	4.52287	−	9.82918i	0.173444	−	0.376932i
$681$	−1.45832	+	1.45832i	−0.0558829	+	0.0558829i
$682$			15.2778i			0.585016i
$683$		−	9.80987i		−	0.375364i	−0.982230	−	0.187682i	$-0.939902\pi$
$683$		−	9.80987i		−	0.375364i	0.982230	−	0.187682i	$-0.0600975\pi$
$684$	1.00303	−	1.00303i	0.0383519	−	0.0383519i
$685$	−36.3919	+	13.4550i	−1.39046	+	0.514089i
$686$		−	12.4051i		−	0.473629i
$687$	−1.86184			−0.0710334
$688$	−0.242187	+	0.242187i	−0.00923330	+	0.00923330i
$689$	−15.0157	−	13.0569i	−0.572054	−	0.497429i
$690$	4.66310	+	12.6123i	0.177521	+	0.480144i
$691$	27.4993	−	27.4993i	1.04612	−	1.04612i	0.0472402	−	0.998884i	$-0.484957\pi$
$691$	27.4993	−	27.4993i	1.04612	−	1.04612i	0.998884	−	0.0472402i	$-0.0150426\pi$
$692$	−5.96615	+	5.96615i	−0.226799	+	0.226799i
$693$	2.96410	−	2.96410i	0.112597	−	0.112597i
$694$	25.3043	+	25.3043i	0.960538	+	0.960538i
$695$	1.93538	+	5.23463i	0.0734130	+	0.198561i
$696$	3.81307	+	3.81307i	0.144534	+	0.144534i
$697$	41.2965			1.56422
$698$	−10.5348	−	10.5348i	−0.398748	−	0.398748i
$699$	−14.7664			−0.558516
$700$	3.59495	−	3.07920i	0.135876	−	0.116383i
$701$		−	6.79306i		−	0.256570i	−0.991737	−	0.128285i	$-0.959053\pi$
$701$		−	6.79306i		−	0.256570i	0.991737	−	0.128285i	$-0.0409473\pi$
$702$	2.72079	+	2.36586i	0.102690	+	0.0892936i
$703$	−11.9363	−	11.9363i	−0.450185	−	0.450185i
$704$	−3.13105	−	3.13105i	−0.118006	−	0.118006i
$705$	1.73564	+	0.798650i	0.0653680	+	0.0300789i
$706$			24.7214i			0.930401i
$707$			6.78254i			0.255084i
$708$	−13.2691			−0.498683
$709$	1.32520	−	1.32520i	0.0497688	−	0.0497688i	−0.681784	−	0.731553i	$-0.738796\pi$
$709$	1.32520	−	1.32520i	0.0497688	−	0.0497688i	0.731553	+	0.681784i	$0.238796\pi$
$710$	−20.1026	−	9.25014i	−0.754436	−	0.347151i
$711$	−8.09997			−0.303772
$712$	0.244613	+	0.244613i	0.00916726	+	0.00916726i
$713$		−	20.7486i		−	0.777040i
$714$	4.58078			0.171432
$715$	33.3909	+	12.6293i	1.24875	+	0.472309i
$716$	−7.96800			−0.297778
$717$			23.4805i			0.876895i
$718$	−1.44201	−	1.44201i	−0.0538155	−	0.0538155i
$719$	22.5002			0.839117			0.419558	−	0.907728i	$-0.362185\pi$
$719$	22.5002			0.839117			0.419558	+	0.907728i	$0.362185\pi$
$720$	−0.775429	−	2.09731i	−0.0288985	−	0.0781621i
$721$	−7.57792	+	7.57792i	−0.282217	+	0.282217i
$722$	−16.9878			−0.632222
$723$		−	17.4300i		−	0.648230i
$724$			17.3575i			0.645087i
$725$	17.5398	+	20.4776i	0.651411	+	0.760518i
$726$	−6.08602	−	6.08602i	−0.225874	−	0.225874i
$727$	−19.5890	−	19.5890i	−0.726516	−	0.726516i	0.243408	−	0.969924i	$-0.421735\pi$
$727$	−19.5890	−	19.5890i	−0.726516	−	0.726516i	−0.969924	+	0.243408i	$0.921735\pi$
$728$	0.237593	+	3.40503i	0.00880579	+	0.126199i
$729$		−	1.00000i		−	0.0370370i
$730$	34.4957	−	12.7539i	1.27674	−	0.472045i
$731$	−1.65731			−0.0612976
$732$	6.92925	+	6.92925i	0.256113	+	0.256113i
$733$	8.60108			0.317688			0.158844	−	0.987304i	$-0.449223\pi$
$733$	8.60108			0.317688			0.158844	+	0.987304i	$0.449223\pi$
$734$	−0.992346	−	0.992346i	−0.0366281	−	0.0366281i
$735$	−12.3988	−	5.70529i	−0.457338	−	0.210443i
$736$	4.25224	+	4.25224i	0.156740	+	0.156740i
$737$	−10.9929	+	10.9929i	−0.404927	+	0.404927i
$738$	6.03479	−	6.03479i	0.222144	−	0.222144i
$739$	−1.33478	+	1.33478i	−0.0491006	+	0.0491006i	−0.731231	−	0.682130i	$-0.761054\pi$
$739$	−1.33478	+	1.33478i	−0.0491006	+	0.0491006i	0.682130	+	0.731231i	$0.261054\pi$
$740$	−24.9583	+	9.22773i	−0.917487	+	0.339218i
$741$	0.356009	+	5.10208i	0.0130783	+	0.187430i
$742$	−3.69437	+	3.69437i	−0.135624	+	0.135624i
$743$	−36.1540			−1.32636			−0.663181	−	0.748459i	$-0.730794\pi$
$743$	−36.1540			−1.32636			−0.663181	+	0.748459i	$0.730794\pi$
$744$			3.45028i			0.126494i
$745$	4.95776	+	2.28130i	0.181638	+	0.0835803i
$746$	20.8743	−	20.8743i	0.764262	−	0.764262i
$747$		−	15.2370i		−	0.557493i
$748$		−	21.4260i		−	0.783412i
$749$	−5.05144	+	5.05144i	−0.184576	+	0.184576i
$750$	−3.05768	−	10.7541i	−0.111651	−	0.392684i
$751$		−	46.2231i		−	1.68670i	−0.537361	−	0.843352i	$-0.680579\pi$
$751$		−	46.2231i		−	1.68670i	0.537361	−	0.843352i	$-0.319421\pi$
$752$	0.854435			0.0311580
$753$	14.7972	−	14.7972i	0.539240	−	0.539240i
$754$	−19.3958	+	1.35338i	−0.706352	+	0.0492872i
$755$	−5.35682	−	2.46492i	−0.194955	−	0.0897077i
$756$	0.669405	−	0.669405i	0.0243460	−	0.0243460i
$757$	35.7855	−	35.7855i	1.30065	−	1.30065i	0.372689	−	0.927956i	$-0.378436\pi$
$757$	35.7855	−	35.7855i	1.30065	−	1.30065i	0.927956	−	0.372689i	$-0.121564\pi$
$758$	−17.6422	+	17.6422i	−0.640795	+	0.640795i
$759$	18.8288	+	18.8288i	0.683443	+	0.683443i
$760$	1.32589	−	2.88145i	0.0480951	−	0.104521i
$761$	4.25598	+	4.25598i	0.154279	+	0.154279i	0.780026	−	0.625747i	$-0.215206\pi$
$761$	4.25598	+	4.25598i	0.154279	+	0.154279i	−0.625747	+	0.780026i	$0.715206\pi$
$762$	4.37458			0.158474
$763$	−3.72097	−	3.72097i	−0.134708	−	0.134708i
$764$	−6.75356			−0.244335
$765$	4.52287	−	9.82918i	0.163525	−	0.355375i
$766$		−	29.6580i		−	1.07159i
$767$	31.3928	−	36.1025i	1.13353	−	1.30358i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	6.64731	+	6.64731i	0.239708	+	0.239708i	0.816729	−	0.577021i	$-0.195785\pi$
$769$	6.64731	+	6.64731i	0.239708	+	0.239708i	−0.577021	+	0.816729i	$0.695785\pi$
$770$	3.91820	−	8.51510i	0.141202	−	0.306863i
$771$		−	7.44284i		−	0.268047i
$772$		−	7.55869i		−	0.272043i
$773$	47.1882			1.69724			0.848620	−	0.529002i	$-0.177434\pi$
$773$	47.1882			1.69724			0.848620	+	0.529002i	$0.177434\pi$
$774$	−0.242187	+	0.242187i	−0.00870524	+	0.00870524i
$775$	−1.32914	+	17.2001i	−0.0477440	+	0.617847i
$776$	−2.67283			−0.0959489
$777$	−7.96602	−	7.96602i	−0.285779	−	0.285779i
$778$			16.8263i			0.603252i
$779$	12.1062			0.433750
$780$	7.54090	+	2.85216i	0.270008	+	0.102124i
$781$	−43.8203			−1.56801
$782$			29.0984i			1.04056i
$783$	3.81307	+	3.81307i	0.136268	+	0.136268i
$784$	−6.10380			−0.217993
$785$	−3.08962	+	6.71442i	−0.110273	+	0.239648i
$786$	2.11985	−	2.11985i	0.0756126	−	0.0756126i
$787$	34.7208			1.23766			0.618831	−	0.785524i	$-0.287606\pi$
$787$	34.7208			1.23766			0.618831	+	0.785524i	$0.287606\pi$
$788$		−	17.8690i		−	0.636558i
$789$		−	17.1729i		−	0.611370i
$790$	−16.9881	+	6.28095i	−0.604411	+	0.223466i
$791$	−3.14760	−	3.14760i	−0.111916	−	0.111916i
$792$	−3.13105	−	3.13105i	−0.111257	−	0.111257i
$793$	−35.2467	+	2.45941i	−1.25165	+	0.0873363i
$794$			28.3338i			1.00553i
$795$	4.27950	+	11.5748i	0.151778	+	0.410516i
$796$	−6.41529			−0.227384
$797$	−20.0264	−	20.0264i	−0.709371	−	0.709371i	0.257032	−	0.966403i	$-0.417255\pi$
$797$	−20.0264	−	20.0264i	−0.709371	−	0.709371i	−0.966403	+	0.257032i	$0.917255\pi$
$798$	1.34287			0.0475371
$799$	2.92348	+	2.92348i	0.103425	+	0.103425i
$800$	−3.25263	−	3.79742i	−0.114998	−	0.134259i
$801$	0.244613	+	0.244613i	0.00864298	+	0.00864298i
$802$	−8.47925	+	8.47925i	−0.299413	+	0.299413i
$803$	51.4983	−	51.4983i	1.81733	−	1.81733i
$804$	−2.48260	+	2.48260i	−0.0875544	+	0.0875544i
$805$	−5.32126	+	11.5643i	−0.187550	+	0.407587i
$806$	−9.38751	−	8.16289i	−0.330661	−	0.287525i
$807$	8.01324	−	8.01324i	0.282079	−	0.282079i
$808$	7.16455			0.252048
$809$		−	4.82771i		−	0.169733i	−0.996392	−	0.0848666i	$-0.972954\pi$
$809$		−	4.82771i		−	0.169733i	0.996392	−	0.0848666i	$-0.0270464\pi$
$810$	−0.775429	−	2.09731i	−0.0272458	−	0.0736920i
$811$	−10.2683	+	10.2683i	−0.360568	+	0.360568i	−0.864022	−	0.503454i	$-0.832062\pi$
$811$	−10.2683	+	10.2683i	−0.360568	+	0.360568i	0.503454	+	0.864022i	$0.332062\pi$
$812$			5.10497i			0.179149i
$813$		−	11.4184i		−	0.400460i
$814$	−37.2600	+	37.2600i	−1.30596	+	1.30596i
$815$	−18.2590	−	49.3854i	−0.639586	−	1.72990i
$816$		−	4.83878i		−	0.169391i
$817$	−0.485844			−0.0169975
$818$	−24.9472	+	24.9472i	−0.872258	+	0.872258i
$819$	0.237593	+	3.40503i	0.00830218	+	0.118981i
$820$	7.97728	−	17.3364i	0.278579	−	0.605413i
$821$	17.4758	−	17.4758i	0.609911	−	0.609911i	−0.333012	−	0.942923i	$-0.608065\pi$
$821$	17.4758	−	17.4758i	0.609911	−	0.609911i	0.942923	+	0.333012i	$0.108065\pi$
$822$	−12.2695	+	12.2695i	−0.427948	+	0.427948i
$823$	21.1631	−	21.1631i	0.737699	−	0.737699i	−0.234433	−	0.972132i	$-0.575323\pi$
$823$	21.1631	−	21.1631i	0.737699	−	0.737699i	0.972132	+	0.234433i	$0.0753233\pi$
$824$	8.00473	+	8.00473i	0.278858	+	0.278858i
$825$	−14.4026	−	16.8149i	−0.501433	−	0.585419i
$826$	−8.88240	−	8.88240i	−0.309058	−	0.309058i
$827$	10.0895			0.350847			0.175424	−	0.984493i	$-0.443870\pi$
$827$	10.0895			0.350847			0.175424	+	0.984493i	$0.443870\pi$
$828$	4.25224	+	4.25224i	0.147776	+	0.147776i
$829$	−39.8773			−1.38500			−0.692498	−	0.721420i	$-0.743490\pi$
$829$	−39.8773			−1.38500			−0.692498	+	0.721420i	$0.743490\pi$
$830$	−11.8152	−	31.9567i	−0.410112	−	1.10923i
$831$			4.61634i			0.160139i
$832$	3.59681	−	0.250975i	0.124697	−	0.00870099i
$833$	−20.8844	−	20.8844i	−0.723600	−	0.723600i
$834$	1.76485	+	1.76485i	0.0611119	+	0.0611119i
$835$	−20.4947	+	7.57741i	−0.709249	+	0.262227i
$836$		−	6.28109i		−	0.217236i
$837$			3.45028i			0.119259i
$838$	12.4367			0.429620
$839$	2.34914	−	2.34914i	0.0811013	−	0.0811013i	−0.665392	−	0.746494i	$-0.731736\pi$
$839$	2.34914	−	2.34914i	0.0811013	−	0.0811013i	0.746494	+	0.665392i	$0.231736\pi$
$840$	0.884873	−	1.92302i	0.0305310	−	0.0663507i
$841$	−0.0790110			−0.00272452
$842$	14.7295	+	14.7295i	0.507611	+	0.507611i
$843$			31.4289i			1.08247i
$844$	−8.36808			−0.288041
$845$	−25.6008	+	13.7694i	−0.880696	+	0.473682i
$846$	0.854435			0.0293761
$847$		−	8.14802i		−	0.279969i
$848$	3.90244	+	3.90244i	0.134010	+	0.134010i
$849$	14.7740			0.507042
$850$	1.86402	−	24.1220i	0.0639354	−	0.827378i
$851$	50.6024	−	50.6024i	1.73463	−	1.73463i
$852$	−9.89625			−0.339040
$853$		−	9.94900i		−	0.340647i	−0.985388	−	0.170324i	$-0.945519\pi$
$853$		−	9.94900i		−	0.340647i	0.985388	−	0.170324i	$-0.0544813\pi$
$854$			9.27695i			0.317451i
$855$	1.32589	−	2.88145i	0.0453445	−	0.0985436i
$856$	5.33595	+	5.33595i	0.182379	+	0.182379i
$857$	24.1568	+	24.1568i	0.825182	+	0.825182i	0.986846	−	0.161664i	$-0.0516861\pi$
$857$	24.1568	+	24.1568i	0.825182	+	0.825182i	−0.161664	+	0.986846i	$0.551686\pi$
$858$	15.9266	−	1.11131i	0.543724	−	0.0379395i
$859$			20.4244i			0.696871i	0.937333	+	0.348435i	$0.113287\pi$
$859$			20.4244i			0.696871i	−0.937333	+	0.348435i	$0.886713\pi$
$860$	−0.320143	+	0.695741i	−0.0109168	+	0.0237246i
$861$	8.07944			0.275347
$862$	8.50842	+	8.50842i	0.289798	+	0.289798i
$863$	15.6902			0.534102			0.267051	−	0.963682i	$-0.413951\pi$
$863$	15.6902			0.534102			0.267051	+	0.963682i	$0.413951\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−7.88654	+	17.1392i	−0.268150	+	0.582750i
$866$	6.47843	+	6.47843i	0.220146	+	0.220146i
$867$	4.53526	−	4.53526i	0.154026	−	0.154026i
$868$	−2.30964	+	2.30964i	−0.0783942	+	0.0783942i
$869$	−25.3614	+	25.3614i	−0.860326	+	0.860326i
$870$	10.9540	+	5.04043i	0.371374	+	0.170886i
$871$	−0.881153	−	12.6281i	−0.0298567	−	0.427887i
$872$	−3.93054	+	3.93054i	−0.133105	+	0.133105i
$873$	−2.67283			−0.0904615
$874$			8.53028i			0.288541i
$875$	5.15201	−	9.24567i	0.174170	−	0.312561i
$876$	11.6302	−	11.6302i	0.392948	−	0.392948i
$877$		−	34.2568i		−	1.15677i	−0.815764	−	0.578385i	$-0.803683\pi$
$877$		−	34.2568i		−	1.15677i	0.815764	−	0.578385i	$-0.196317\pi$
$878$		−	40.8316i		−	1.37800i
$879$	−17.3477	+	17.3477i	−0.585122	+	0.585122i
$880$	−8.99469	−	4.13888i	−0.303211	−	0.139521i
$881$		−	31.9208i		−	1.07544i	−0.843124	−	0.537720i	$-0.819286\pi$
$881$		−	31.9208i		−	1.07544i	0.843124	−	0.537720i	$-0.180714\pi$
$882$	−6.10380			−0.205525
$883$	1.59287	−	1.59287i	0.0536043	−	0.0536043i	−0.679796	−	0.733401i	$-0.737932\pi$
$883$	1.59287	−	1.59287i	0.0536043	−	0.0536043i	0.733401	+	0.679796i	$0.237932\pi$
$884$	13.1653	+	11.4479i	0.442798	+	0.385034i
$885$	−27.8294	+	10.2892i	−0.935476	+	0.345869i
$886$	−8.09147	+	8.09147i	−0.271838	+	0.271838i
$887$	−8.72722	+	8.72722i	−0.293031	+	0.293031i	−0.838277	−	0.545245i	$-0.816437\pi$
$887$	−8.72722	+	8.72722i	−0.293031	+	0.293031i	0.545245	+	0.838277i	$0.316437\pi$
$888$	−8.41469	+	8.41469i	−0.282378	+	0.282378i
$889$	2.92836	+	2.92836i	0.0982142	+	0.0982142i
$890$	0.702709	+	0.323349i	0.0235549	+	0.0108387i
$891$	−3.13105	−	3.13105i	−0.104894	−	0.104894i
$892$	6.31913			0.211580
$893$	0.857026	+	0.857026i	0.0286793	+	0.0286793i
$894$	2.44065			0.0816274
$895$	−16.7114	+	6.17862i	−0.558600	+	0.206528i
$896$		−	0.946681i		−	0.0316264i
$897$	−21.6297	+	1.50926i	−0.722194	+	0.0503926i
$898$	−22.0410	−	22.0410i	−0.735518	−	0.735518i
$899$	−13.1562	−	13.1562i	−0.438783	−	0.438783i
$900$	−3.25263	−	3.79742i	−0.108421	−	0.126581i
$901$			26.7047i			0.889662i
$902$		−	37.7905i		−	1.25829i
$903$	−0.324242			−0.0107901
$904$	−3.32488	+	3.32488i	−0.110584	+	0.110584i
$905$	13.4595	+	36.4041i	0.447410	+	1.21011i
$906$	−2.63710			−0.0876116
$907$	−0.0415121	−	0.0415121i	−0.00137839	−	0.00137839i	0.706417	−	0.707796i	$-0.250310\pi$
$907$	−0.0415121	−	0.0415121i	−0.00137839	−	0.00137839i	−0.707796	+	0.706417i	$0.750310\pi$
$908$			2.06238i			0.0684423i
$909$	7.16455			0.237633
$910$	3.13866	+	6.95716i	0.104046	+	0.230628i
$911$	11.6868			0.387201			0.193600	−	0.981080i	$-0.437983\pi$
$911$	11.6868			0.387201			0.193600	+	0.981080i	$0.437983\pi$
$912$		−	1.41850i		−	0.0469713i
$913$	−47.7078	−	47.7078i	−1.57890	−	1.57890i
$914$	17.5342			0.579978
$915$	19.9059	+	9.15965i	0.658070	+	0.302809i
$916$	−1.31652	+	1.31652i	−0.0434989	+	0.0434989i
$917$	2.83808			0.0937216
$918$		−	4.83878i		−	0.159704i
$919$			3.34173i			0.110233i	0.998480	+	0.0551167i	$0.0175531\pi$
$919$			3.34173i			0.110233i	−0.998480	+	0.0551167i	$0.982447\pi$
$920$	12.2156	+	5.62096i	0.402736	+	0.185318i
$921$	19.0555	+	19.0555i	0.627902	+	0.627902i
$922$	17.5242	+	17.5242i	0.577130	+	0.577130i
$923$	23.4131	−	26.9256i	0.770653	−	0.886268i
$924$		−	4.19188i		−	0.137903i
$925$	−45.1899	+	38.7068i	−1.48584	+	1.27267i
$926$	−12.6976			−0.417268
$927$	8.00473	+	8.00473i	0.262910	+	0.262910i
$928$	5.39250			0.177017
$929$	15.0342	+	15.0342i	0.493257	+	0.493257i	0.909331	−	0.416074i	$-0.136594\pi$
$929$	15.0342	+	15.0342i	0.493257	+	0.493257i	−0.416074	+	0.909331i	$0.636594\pi$
$930$	2.67545	+	7.23632i	0.0877315	+	0.237288i
$931$	−6.12231	−	6.12231i	−0.200651	−	0.200651i
$932$	−10.4414	+	10.4414i	−0.342020	+	0.342020i
$933$	−11.6504	+	11.6504i	−0.381419	+	0.381419i
$934$	−1.17459	+	1.17459i	−0.0384337	+	0.0384337i
$935$	−16.6143	−	44.9370i	−0.543347	−	1.46960i
$936$	3.59681	−	0.250975i	0.117565	−	0.00820337i
$937$	21.6372	−	21.6372i	0.706855	−	0.706855i	−0.259018	−	0.965873i	$-0.583399\pi$
$937$	21.6372	−	21.6372i	0.706855	−	0.706855i	0.965873	+	0.259018i	$0.0833988\pi$
$938$	−3.32372			−0.108523
$939$		−	4.09695i		−	0.133699i
$940$	1.79201	−	0.662553i	0.0584491	−	0.0216101i
$941$	−12.0649	+	12.0649i	−0.393303	+	0.393303i	−0.875863	−	0.482560i	$-0.839707\pi$
$941$	−12.0649	+	12.0649i	−0.393303	+	0.393303i	0.482560	+	0.875863i	$0.339707\pi$
$942$			3.30542i			0.107696i
$943$			51.3228i			1.67130i
$944$	−9.38267	+	9.38267i	−0.305380	+	0.305380i
$945$	0.884873	−	1.92302i	0.0287849	−	0.0625560i
$946$			1.51660i			0.0493089i
$947$	−50.1326			−1.62909			−0.814545	−	0.580101i	$-0.803013\pi$
$947$	−50.1326			−1.62909			−0.814545	+	0.580101i	$0.803013\pi$
$948$	−5.72754	+	5.72754i	−0.186022	+	0.186022i
$949$	4.12793	+	59.1588i	0.133998	+	1.92038i
$950$	0.546443	−	7.07144i	0.0177290	−	0.229428i
$951$	9.49808	−	9.49808i	0.307996	−	0.307996i
$952$	3.23910	−	3.23910i	0.104980	−	0.104980i
$953$	−25.6186	+	25.6186i	−0.829869	+	0.829869i	−0.987498	−	0.157630i	$-0.949615\pi$
$953$	−25.6186	+	25.6186i	−0.829869	+	0.829869i	0.157630	+	0.987498i	$0.449615\pi$
$954$	3.90244	+	3.90244i	0.126346	+	0.126346i
$955$	−14.1643	+	5.23691i	−0.458347	+	0.169462i
$956$	16.6032	+	16.6032i	0.536986	+	0.536986i
$957$	23.8778			0.771860
$958$	−22.2742	−	22.2742i	−0.719645	−	0.719645i
$959$	−16.4265			−0.530439
$960$	−2.03133	−	0.934711i	−0.0655610	−	0.0301677i
$961$			19.0955i			0.615985i
$962$	−2.98664	−	42.8026i	−0.0962932	−	1.38001i
$963$	5.33595	+	5.33595i	0.171948	+	0.171948i
$964$	−12.3249	−	12.3249i	−0.396958	−	0.396958i
$965$	−5.86123	−	15.8529i	−0.188680	−	0.510324i
$966$			5.69294i			0.183167i
$967$			30.0366i			0.965912i	0.875645	+	0.482956i	$0.160437\pi$
$967$			30.0366i			0.965912i	−0.875645	+	0.482956i	$0.839563\pi$
$968$	−8.60694			−0.276637
$969$	4.85346	−	4.85346i	0.155916	−	0.155916i
$970$	−5.60575	+	2.07259i	−0.179990	+	0.0665468i
$971$	−58.8047			−1.88713			−0.943567	−	0.331181i	$-0.892553\pi$
$971$	−58.8047			−1.88713			−0.943567	+	0.331181i	$0.892553\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$			2.36280i			0.0757479i
$974$	33.0320			1.05841
$975$	18.0273	+	0.134436i	0.577334	+	0.00430541i
$976$	9.79944			0.313673
$977$		−	24.7981i		−	0.793361i	−0.917957	−	0.396680i	$-0.870162\pi$
$977$		−	24.7981i		−	0.793361i	0.917957	−	0.396680i	$-0.129838\pi$
$978$	−16.6503	−	16.6503i	−0.532416	−	0.532416i
$979$	1.53179			0.0489562
$980$	−12.8016	+	4.73306i	−0.408931	+	0.151192i
$981$	−3.93054	+	3.93054i	−0.125493	+	0.125493i
$982$	36.4206			1.16223
$983$			0.527121i			0.0168125i	0.999965	+	0.00840627i	$0.00267583\pi$
$983$			0.527121i			0.0168125i	−0.999965	+	0.00840627i	$0.997324\pi$
$984$		−	8.53449i		−	0.272070i
$985$	−13.8562	−	37.4769i	−0.441494	−	1.19411i
$986$	18.4506	+	18.4506i	0.587588	+	0.587588i
$987$	0.571962	+	0.571962i	0.0182058	+	0.0182058i
$988$	3.85945	+	3.35598i	0.122786	+	0.106768i
$989$		−	2.05968i		−	0.0654939i
$990$	−8.99469	−	4.13888i	−0.285870	−	0.131542i
$991$	−28.4812			−0.904734			−0.452367	−	0.891832i	$-0.649420\pi$
$991$	−28.4812			−0.904734			−0.452367	+	0.891832i	$0.649420\pi$
$992$	2.43972	+	2.43972i	0.0774612	+	0.0774612i
$993$	−6.14238			−0.194922
$994$	−6.62459	−	6.62459i	−0.210119	−	0.210119i
$995$	−13.4549	+	4.97460i	−0.426548	+	0.157705i
$996$	−10.7742	−	10.7742i	−0.341393	−	0.341393i
$997$	−19.5558	+	19.5558i	−0.619339	+	0.619339i	−0.945362	−	0.326023i	$-0.894291\pi$
$997$	−19.5558	+	19.5558i	−0.619339	+	0.619339i	0.326023	+	0.945362i	$0.394291\pi$
$998$	26.4644	−	26.4644i	0.837716	−	0.837716i
$999$	−8.41469	+	8.41469i	−0.266229	+	0.266229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.t.b.343.1	yes	16
3.2	odd	2		1170.2.w.i.343.7		16
5.2	odd	4		390.2.j.b.187.2	yes	16
5.3	odd	4		1950.2.j.e.1357.7		16
5.4	even	2		1950.2.t.e.343.7		16
13.8	odd	4		390.2.j.b.73.2	✓	16
15.2	even	4		1170.2.m.i.577.6		16
39.8	even	4		1170.2.m.i.73.6		16
65.8	even	4		1950.2.t.e.307.7		16
65.34	odd	4		1950.2.j.e.1243.6		16
65.47	even	4	inner	390.2.t.b.307.1	yes	16
195.47	odd	4		1170.2.w.i.307.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.b.73.2	✓	16	13.8	odd	4
390.2.j.b.187.2	yes	16	5.2	odd	4
390.2.t.b.307.1	yes	16	65.47	even	4	inner
390.2.t.b.343.1	yes	16	1.1	even	1	trivial
1170.2.m.i.73.6		16	39.8	even	4
1170.2.m.i.577.6		16	15.2	even	4
1170.2.w.i.307.7		16	195.47	odd	4
1170.2.w.i.343.7		16	3.2	odd	2
1950.2.j.e.1243.6		16	65.34	odd	4
1950.2.j.e.1357.7		16	5.3	odd	4
1950.2.t.e.307.7		16	65.8	even	4
1950.2.t.e.343.7		16	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.09731 + 0.775429i) q^{5} +(-0.707107 + 0.707107i) q^{6} -0.946681 q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.09731 + 0.775429i) q^{5} +(-0.707107 + 0.707107i) q^{6} -0.946681 q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.775429 + 2.09731i) q^{10} +(3.13105 + 3.13105i) q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.59681 + 0.250975i) q^{13} +0.946681i q^{14} +(2.03133 + 0.934711i) q^{15} +1.00000 q^{16} +(3.42154 + 3.42154i) q^{17} +1.00000 q^{18} +(1.00303 + 1.00303i) q^{19} +(2.09731 - 0.775429i) q^{20} +(0.669405 + 0.669405i) q^{21} +(3.13105 - 3.13105i) q^{22} +(-4.25224 + 4.25224i) q^{23} +(0.707107 - 0.707107i) q^{24} +(3.79742 - 3.25263i) q^{25} +(0.250975 + 3.59681i) q^{26} +(0.707107 - 0.707107i) q^{27} +0.946681 q^{28} +5.39250i q^{29} +(0.934711 - 2.03133i) q^{30} +(-2.43972 + 2.43972i) q^{31} -1.00000i q^{32} -4.42797i q^{33} +(3.42154 - 3.42154i) q^{34} +(1.98548 - 0.734084i) q^{35} -1.00000i q^{36} -11.9002 q^{37} +(1.00303 - 1.00303i) q^{38} +(2.72079 + 2.36586i) q^{39} +(-0.775429 - 2.09731i) q^{40} +(6.03479 - 6.03479i) q^{41} +(0.669405 - 0.669405i) q^{42} +(-0.242187 + 0.242187i) q^{43} +(-3.13105 - 3.13105i) q^{44} +(-0.775429 - 2.09731i) q^{45} +(4.25224 + 4.25224i) q^{46} +0.854435 q^{47} +(-0.707107 - 0.707107i) q^{48} -6.10380 q^{49} +(-3.25263 - 3.79742i) q^{50} -4.83878i q^{51} +(3.59681 - 0.250975i) q^{52} +(3.90244 + 3.90244i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-8.99469 - 4.13888i) q^{55} -0.946681i q^{56} -1.41850i q^{57} +5.39250 q^{58} +(-9.38267 + 9.38267i) q^{59} +(-2.03133 - 0.934711i) q^{60} +9.79944 q^{61} +(2.43972 + 2.43972i) q^{62} -0.946681i q^{63} -1.00000 q^{64} +(7.34900 - 3.31544i) q^{65} -4.42797 q^{66} +3.51092i q^{67} +(-3.42154 - 3.42154i) q^{68} +6.01358 q^{69} +(-0.734084 - 1.98548i) q^{70} +(-6.99770 + 6.99770i) q^{71} -1.00000 q^{72} -16.4476i q^{73} +11.9002i q^{74} +(-4.98514 - 0.385225i) q^{75} +(-1.00303 - 1.00303i) q^{76} +(-2.96410 - 2.96410i) q^{77} +(2.36586 - 2.72079i) q^{78} +8.09997i q^{79} +(-2.09731 + 0.775429i) q^{80} -1.00000 q^{81} +(-6.03479 - 6.03479i) q^{82} -15.2370 q^{83} +(-0.669405 - 0.669405i) q^{84} +(-9.82918 - 4.52287i) q^{85} +(0.242187 + 0.242187i) q^{86} +(3.81307 - 3.81307i) q^{87} +(-3.13105 + 3.13105i) q^{88} +(0.244613 - 0.244613i) q^{89} +(-2.09731 + 0.775429i) q^{90} +(3.40503 - 0.237593i) q^{91} +(4.25224 - 4.25224i) q^{92} +3.45028 q^{93} -0.854435i q^{94} +(-2.88145 - 1.32589i) q^{95} +(-0.707107 + 0.707107i) q^{96} +2.67283i q^{97} +6.10380i q^{98} +(-3.13105 + 3.13105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 4 q^{11} - 8 q^{13} - 4 q^{15} + 16 q^{16} - 4 q^{17} + 16 q^{18} - 4 q^{19} - 8 q^{21} + 4 q^{22} - 16 q^{23} + 16 q^{25} + 4 q^{26} - 4 q^{30} + 12 q^{31} - 4 q^{34} - 12 q^{35} - 32 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{41} - 8 q^{42} + 16 q^{43} - 4 q^{44} + 16 q^{46} + 16 q^{47} + 80 q^{49} + 8 q^{50} + 8 q^{52} - 44 q^{53} - 20 q^{55} - 12 q^{59} + 4 q^{60} - 32 q^{61} - 12 q^{62} - 16 q^{64} - 28 q^{65} + 4 q^{68} + 16 q^{69} - 36 q^{70} + 16 q^{71} - 16 q^{72} + 4 q^{76} + 32 q^{77} + 16 q^{78} - 16 q^{81} - 4 q^{82} + 16 q^{83} + 8 q^{84} - 40 q^{85} - 16 q^{86} + 28 q^{87} - 4 q^{88} - 4 q^{89} + 76 q^{91} + 16 q^{92} - 40 q^{95} - 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 4 * q^11 - 8 * q^13 - 4 * q^15 + 16 * q^16 - 4 * q^17 + 16 * q^18 - 4 * q^19 - 8 * q^21 + 4 * q^22 - 16 * q^23 + 16 * q^25 + 4 * q^26 - 4 * q^30 + 12 * q^31 - 4 * q^34 - 12 * q^35 - 32 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^41 - 8 * q^42 + 16 * q^43 - 4 * q^44 + 16 * q^46 + 16 * q^47 + 80 * q^49 + 8 * q^50 + 8 * q^52 - 44 * q^53 - 20 * q^55 - 12 * q^59 + 4 * q^60 - 32 * q^61 - 12 * q^62 - 16 * q^64 - 28 * q^65 + 4 * q^68 + 16 * q^69 - 36 * q^70 + 16 * q^71 - 16 * q^72 + 4 * q^76 + 32 * q^77 + 16 * q^78 - 16 * q^81 - 4 * q^82 + 16 * q^83 + 8 * q^84 - 40 * q^85 - 16 * q^86 + 28 * q^87 - 4 * q^88 - 4 * q^89 + 76 * q^91 + 16 * q^92 - 40 * q^95 - 4 * q^99

Introduction

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