LMFDB - Embedded newform 390.2.j.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(73,390)]

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, 3, 1]))

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

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

chi := DirichletCharacter("390.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.j (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			73.2
Root			$1.09662i$ of defining polynomial
Character	$\chi$	$=$	390.73
Dual form			390.2.j.b.187.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.775429 - 2.09731i) q^{5} +(-0.707107 - 0.707107i) q^{6} +0.946681i q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.775429 - 2.09731i) q^{5} +(-0.707107 - 0.707107i) q^{6} +0.946681i q^{7} +1.00000 q^{8} +1.00000i q^{9} +(-0.775429 - 2.09731i) q^{10} +(3.13105 - 3.13105i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(0.250975 - 3.59681i) q^{13} +0.946681i q^{14} +(-0.934711 + 2.03133i) q^{15} +1.00000 q^{16} +(-3.42154 - 3.42154i) q^{17} +1.00000i q^{18} +(-1.00303 + 1.00303i) q^{19} +(-0.775429 - 2.09731i) 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} +0.946681i q^{28} +5.39250i q^{29} +(-0.934711 + 2.03133i) q^{30} +(-2.43972 - 2.43972i) q^{31} +1.00000 q^{32} -4.42797 q^{33} +(-3.42154 - 3.42154i) q^{34} +(1.98548 - 0.734084i) q^{35} +1.00000i q^{36} +11.9002i 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} +(2.09731 - 0.775429i) q^{45} +(4.25224 - 4.25224i) q^{46} -0.854435i q^{47} +(-0.707107 - 0.707107i) q^{48} +6.10380 q^{49} +(-3.79742 + 3.25263i) q^{50} +4.83878i q^{51} +(0.250975 - 3.59681i) q^{52} +(3.90244 + 3.90244i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-8.99469 - 4.13888i) q^{55} +0.946681i q^{56} +1.41850 q^{57} +5.39250i q^{58} +(9.38267 + 9.38267i) q^{59} +(-0.934711 + 2.03133i) q^{60} +9.79944 q^{61} +(-2.43972 - 2.43972i) q^{62} -0.946681 q^{63} +1.00000 q^{64} +(-7.73823 + 2.26269i) q^{65} -4.42797 q^{66} -3.51092 q^{67} +(-3.42154 - 3.42154i) q^{68} -6.01358 q^{69} +(1.98548 - 0.734084i) q^{70} +(-6.99770 - 6.99770i) q^{71} +1.00000i q^{72} -16.4476 q^{73} +11.9002i q^{74} +(4.98514 + 0.385225i) q^{75} +(-1.00303 + 1.00303i) q^{76} +(2.96410 + 2.96410i) q^{77} +(-2.72079 + 2.36586i) q^{78} +8.09997i q^{79} +(-0.775429 - 2.09731i) q^{80} -1.00000 q^{81} +(6.03479 + 6.03479i) q^{82} -15.2370i q^{83} +(0.669405 - 0.669405i) q^{84} +(-4.52287 + 9.82918i) 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} +3.45028i q^{93} -0.854435i q^{94} +(2.88145 + 1.32589i) q^{95} +(-0.707107 - 0.707107i) q^{96} -2.67283 q^{97} +6.10380 q^{98} +(3.13105 + 3.13105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 4 q^{11} + 4 q^{13} + 4 q^{15} + 16 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{21} + 4 q^{22} + 16 q^{23} - 16 q^{25} + 4 q^{26} + 4 q^{30} + 12 q^{31} + 16 q^{32} + 4 q^{34} - 12 q^{35} + 4 q^{38} - 4 q^{39} + 4 q^{41} - 8 q^{42} - 16 q^{43} + 4 q^{44} + 16 q^{46} - 80 q^{49} - 16 q^{50} + 4 q^{52} - 44 q^{53} - 20 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{60} - 32 q^{61} + 12 q^{62} + 16 q^{64} - 44 q^{65} - 32 q^{67} + 4 q^{68} - 16 q^{69} - 12 q^{70} + 16 q^{71} + 4 q^{76} - 32 q^{77} - 4 q^{78} - 16 q^{81} + 4 q^{82} - 8 q^{84} - 64 q^{85} - 16 q^{86} + 28 q^{87} + 4 q^{88} + 4 q^{89} + 76 q^{91} + 16 q^{92} + 40 q^{95} - 8 q^{97} - 80 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 4 * q^11 + 4 * q^13 + 4 * q^15 + 16 * q^16 + 4 * q^17 + 4 * q^19 - 8 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 + 4 * q^26 + 4 * q^30 + 12 * q^31 + 16 * q^32 + 4 * q^34 - 12 * q^35 + 4 * q^38 - 4 * q^39 + 4 * q^41 - 8 * q^42 - 16 * q^43 + 4 * q^44 + 16 * q^46 - 80 * q^49 - 16 * q^50 + 4 * q^52 - 44 * q^53 - 20 * q^55 - 16 * q^57 + 12 * q^59 + 4 * q^60 - 32 * q^61 + 12 * q^62 + 16 * q^64 - 44 * q^65 - 32 * q^67 + 4 * q^68 - 16 * q^69 - 12 * q^70 + 16 * q^71 + 4 * q^76 - 32 * q^77 - 4 * q^78 - 16 * q^81 + 4 * q^82 - 8 * q^84 - 64 * q^85 - 16 * q^86 + 28 * q^87 + 4 * q^88 + 4 * q^89 + 76 * q^91 + 16 * q^92 + 40 * q^95 - 8 * q^97 - 80 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−0.775429	−	2.09731i	−0.346782	−	0.937946i
$5$	−0.775429	−	2.09731i	−0.346782	−	0.937946i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$			0.946681i			0.357812i	0.983866	+	0.178906i	$0.0572558\pi$
$7$			0.946681i			0.357812i	−0.983866	+	0.178906i	$0.942744\pi$
$8$	1.00000			0.353553
$9$			1.00000i			0.333333i
$10$	−0.775429	−	2.09731i	−0.245212	−	0.663228i
$11$	3.13105	−	3.13105i	0.944047	−	0.944047i	−0.0544686	−	0.998515i	$-0.517346\pi$
$11$	3.13105	−	3.13105i	0.944047	−	0.944047i	0.998515	+	0.0544686i	$0.0173465\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	0.250975	−	3.59681i	0.0696079	−	0.997574i
$13$	0.250975	−	3.59681i	0.0696079	−	0.997574i
$14$			0.946681i			0.253011i
$15$	−0.934711	+	2.03133i	−0.241341	+	0.524488i
$16$	1.00000			0.250000
$17$	−3.42154	−	3.42154i	−0.829845	−	0.829845i	0.157650	−	0.987495i	$-0.449608\pi$
$17$	−3.42154	−	3.42154i	−0.829845	−	0.829845i	−0.987495	+	0.157650i	$0.949608\pi$
$18$			1.00000i			0.235702i
$19$	−1.00303	+	1.00303i	−0.230112	+	0.230112i	−0.812739	−	0.582628i	$-0.802025\pi$
$19$	−1.00303	+	1.00303i	−0.230112	+	0.230112i	0.582628	+	0.812739i	$0.302025\pi$
$20$	−0.775429	−	2.09731i	−0.173391	−	0.468973i
$21$	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	−0.107546	−	0.994200i	$-0.534299\pi$
$23$	4.25224	−	4.25224i	0.886654	−	0.886654i	0.994200	+	0.107546i	$0.0342994\pi$
$24$	−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
$28$			0.946681i			0.178906i
$29$			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	0.453215	−	0.891401i	$-0.350277\pi$
$31$	−2.43972	−	2.43972i	−0.438187	−	0.438187i	−0.891401	+	0.453215i	$0.850277\pi$
$32$	1.00000			0.176777
$33$	−4.42797			−0.770811
$34$	−3.42154	−	3.42154i	−0.586789	−	0.586789i
$35$	1.98548	−	0.734084i	0.335608	−	0.124083i
$36$			1.00000i			0.166667i
$37$			11.9002i			1.95637i	0.207725	+	0.978187i	$0.433394\pi$
$37$			11.9002i			1.95637i	−0.207725	+	0.978187i	$0.566606\pi$
$38$	−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	0.998433	−	0.0559566i	$-0.0178208\pi$
$41$	6.03479	+	6.03479i	0.942477	+	0.942477i	−0.0559566	+	0.998433i	$0.517821\pi$
$42$	0.669405	−	0.669405i	0.103291	−	0.103291i
$43$	0.242187	−	0.242187i	0.0369332	−	0.0369332i	−0.688399	−	0.725332i	$-0.741686\pi$
$43$	0.242187	−	0.242187i	0.0369332	−	0.0369332i	0.725332	+	0.688399i	$0.241686\pi$
$44$	3.13105	−	3.13105i	0.472023	−	0.472023i
$45$	2.09731	−	0.775429i	0.312649	−	0.115594i
$46$	4.25224	−	4.25224i	0.626959	−	0.626959i
$47$		−	0.854435i		−	0.124632i	−0.998056	−	0.0623161i	$-0.980151\pi$
$47$		−	0.854435i		−	0.124632i	0.998056	−	0.0623161i	$-0.0198487\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	6.10380			0.871971
$50$	−3.79742	+	3.25263i	−0.537036	+	0.459991i
$51$			4.83878i			0.677565i
$52$	0.250975	−	3.59681i	0.0348039	−	0.498787i
$53$	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
$57$	1.41850			0.187885
$58$			5.39250i			0.708069i
$59$	9.38267	+	9.38267i	1.22152	+	1.22152i	0.967092	+	0.254428i	$0.0818871\pi$
$59$	9.38267	+	9.38267i	1.22152	+	1.22152i	0.254428	+	0.967092i	$0.418113\pi$
$60$	−0.934711	+	2.03133i	−0.120671	+	0.262244i
$61$	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
$63$	−0.946681			−0.119271
$64$	1.00000			0.125000
$65$	−7.73823	+	2.26269i	−0.959809	+	0.280653i
$66$	−4.42797			−0.545046
$67$	−3.51092			−0.428927			−0.214464	−	0.976732i	$-0.568800\pi$
$67$	−3.51092			−0.428927			−0.214464	+	0.976732i	$0.568800\pi$
$68$	−3.42154	−	3.42154i	−0.414922	−	0.414922i
$69$	−6.01358			−0.723950
$70$	1.98548	−	0.734084i	0.237311	−	0.0877398i
$71$	−6.99770	−	6.99770i	−0.830475	−	0.830475i	0.157107	−	0.987582i	$-0.449783\pi$
$71$	−6.99770	−	6.99770i	−0.830475	−	0.830475i	−0.987582	+	0.157107i	$0.949783\pi$
$72$			1.00000i			0.117851i
$73$	−16.4476			−1.92505			−0.962523	−	0.271199i	$-0.912580\pi$
$73$	−16.4476			−1.92505			−0.962523	+	0.271199i	$0.912580\pi$
$74$			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
$78$	−2.72079	+	2.36586i	−0.308069	+	0.267881i
$79$			8.09997i			0.911317i	0.890155	+	0.455659i	$0.150596\pi$
$79$			8.09997i			0.911317i	−0.890155	+	0.455659i	$0.849404\pi$
$80$	−0.775429	−	2.09731i	−0.0866956	−	0.234486i
$81$	−1.00000			−0.111111
$82$	6.03479	+	6.03479i	0.666432	+	0.666432i
$83$		−	15.2370i		−	1.67248i	−0.548365	−	0.836239i	$-0.684749\pi$
$83$		−	15.2370i		−	1.67248i	0.548365	−	0.836239i	$-0.315251\pi$
$84$	0.669405	−	0.669405i	0.0730380	−	0.0730380i
$85$	−4.52287	+	9.82918i	−0.490574	+	1.06612i
$86$	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	$-0.255836\pi$
$89$	−0.244613	−	0.244613i	−0.0259289	−	0.0259289i	−0.719952	+	0.694023i	$0.755836\pi$
$90$	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
$93$			3.45028i			0.357778i
$94$		−	0.854435i		−	0.0881282i
$95$	2.88145	+	1.32589i	0.295631	+	0.136034i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−2.67283			−0.271384			−0.135692	−	0.990751i	$-0.543326\pi$
$97$	−2.67283			−0.271384			−0.135692	+	0.990751i	$0.543326\pi$
$98$	6.10380			0.616576
$99$	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	$0.116013\pi$
$101$			7.16455i			0.712899i	−0.934315	+	0.356450i	$0.883987\pi$
$102$			4.83878i			0.479111i
$103$	−8.00473	+	8.00473i	−0.788729	+	0.788729i	−0.981286	−	0.192557i	$-0.938322\pi$
$103$	−8.00473	+	8.00473i	−0.788729	+	0.788729i	0.192557	+	0.981286i	$0.438322\pi$
$104$	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	$-0.835771\pi$
$109$	−3.93054	+	3.93054i	−0.376478	+	0.376478i	0.493352	+	0.869830i	$0.335771\pi$
$110$	−8.99469	−	4.13888i	−0.857610	−	0.394626i
$111$	8.41469	−	8.41469i	0.798687	−	0.798687i
$112$			0.946681i			0.0894529i
$113$	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
$115$	−12.2156	−	5.62096i	−1.13911	−	0.524157i
$116$			5.39250i			0.500681i
$117$	3.59681	+	0.250975i	0.332525	+	0.0232026i
$118$	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
$122$	9.79944			0.887200
$123$		−	8.53449i		−	0.769529i
$124$	−2.43972	−	2.43972i	−0.219093	−	0.219093i
$125$	9.76640	+	5.44219i	0.873534	+	0.486764i
$126$	−0.946681			−0.0843370
$127$	3.09330	+	3.09330i	0.274486	+	0.274486i	0.830903	−	0.556417i	$-0.187824\pi$
$127$	3.09330	+	3.09330i	0.274486	+	0.274486i	−0.556417	+	0.830903i	$0.687824\pi$
$128$	1.00000			0.0883883
$129$	−0.342504			−0.0301558
$130$	−7.73823	+	2.26269i	−0.678688	+	0.198451i
$131$	−2.99792			−0.261930			−0.130965	−	0.991387i	$-0.541808\pi$
$131$	−2.99792			−0.261930			−0.130965	+	0.991387i	$0.541808\pi$
$132$	−4.42797			−0.385406
$133$	−0.949553	−	0.949553i	−0.0823367	−	0.0823367i
$134$	−3.51092			−0.303297
$135$	−2.03133	−	0.934711i	−0.174829	−	0.0804471i
$136$	−3.42154	−	3.42154i	−0.293394	−	0.293394i
$137$		−	17.3517i		−	1.48245i	−0.671255	−	0.741227i	$-0.734244\pi$
$137$		−	17.3517i		−	1.48245i	0.671255	−	0.741227i	$-0.265756\pi$
$138$	−6.01358			−0.511910
$139$		−	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
$143$	−10.4760	−	12.0476i	−0.876044	−	1.00747i
$144$			1.00000i			0.0833333i
$145$	11.3097	−	4.18150i	0.939223	−	0.347254i
$146$	−16.4476			−1.36121
$147$	−4.31603	−	4.31603i	−0.355981	−	0.355981i
$148$			11.9002i			0.978187i
$149$	1.72580	−	1.72580i	0.141383	−	0.141383i	−0.632873	−	0.774256i	$-0.718124\pi$
$149$	1.72580	−	1.72580i	0.141383	−	0.141383i	0.774256	+	0.632873i	$0.218124\pi$
$150$	4.98514	+	0.385225i	0.407035	+	0.0314535i
$151$	1.86471	−	1.86471i	0.151748	−	0.151748i	−0.627150	−	0.778898i	$-0.715779\pi$
$151$	1.86471	−	1.86471i	0.151748	−	0.151748i	0.778898	+	0.627150i	$0.215779\pi$
$152$	−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	$0.207892\pi$
$158$			8.09997i			0.644399i
$159$		−	5.51888i		−	0.437676i
$160$	−0.775429	−	2.09731i	−0.0613030	−	0.165807i
$161$	4.02552	+	4.02552i	0.317255	+	0.317255i
$162$	−1.00000			−0.0785674
$163$	23.5470			1.84434			0.922172	−	0.386779i	$-0.126412\pi$
$163$	23.5470			1.84434			0.922172	+	0.386779i	$0.126412\pi$
$164$	6.03479	+	6.03479i	0.471238	+	0.471238i
$165$	3.43358	+	9.28683i	0.267304	+	0.722979i
$166$		−	15.2370i		−	1.18262i
$167$		−	9.77190i		−	0.756172i	−0.925770	−	0.378086i	$-0.876582\pi$
$167$		−	9.77190i		−	0.756172i	0.925770	−	0.378086i	$-0.123418\pi$
$168$	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	−0.896547	−	0.442949i	$-0.853932\pi$
$173$	−5.96615	+	5.96615i	−0.453598	+	0.453598i	0.442949	+	0.896547i	$0.353932\pi$
$174$	3.81307	−	3.81307i	0.289068	−	0.289068i
$175$	−3.07920	−	3.59495i	−0.232766	−	0.271752i
$176$	3.13105	−	3.13105i	0.236012	−	0.236012i
$177$		−	13.2691i		−	0.997367i
$178$	−0.244613	−	0.244613i	−0.0183345	−	0.0183345i
$179$	−7.96800			−0.595557			−0.297778	−	0.954635i	$-0.596246\pi$
$179$	−7.96800			−0.595557			−0.297778	+	0.954635i	$0.596246\pi$
$180$	2.09731	−	0.775429i	0.156324	−	0.0577970i
$181$			17.3575i			1.29017i	0.764109	+	0.645087i	$0.223179\pi$
$181$			17.3575i			1.29017i	−0.764109	+	0.645087i	$0.776821\pi$
$182$	3.40503	+	0.237593i	0.252397	+	0.0176116i
$183$	−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
$187$	−21.4260			−1.56682
$188$		−	0.854435i		−	0.0623161i
$189$	0.669405	+	0.669405i	0.0486920	+	0.0486920i
$190$	2.88145	+	1.32589i	0.209043	+	0.0961903i
$191$	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
$193$	7.55869			0.544086			0.272043	−	0.962285i	$-0.412301\pi$
$193$	7.55869			0.544086			0.272043	+	0.962285i	$0.412301\pi$
$194$	−2.67283			−0.191898
$195$	7.07172	+	3.87179i	0.506417	+	0.277265i
$196$	6.10380			0.435985
$197$	−17.8690			−1.27312			−0.636558	−	0.771229i	$-0.719642\pi$
$197$	−17.8690			−1.27312			−0.636558	+	0.771229i	$0.719642\pi$
$198$	3.13105	+	3.13105i	0.222514	+	0.222514i
$199$	−6.41529			−0.454768			−0.227384	−	0.973805i	$-0.573017\pi$
$199$	−6.41529			−0.454768			−0.227384	+	0.973805i	$0.573017\pi$
$200$	−3.79742	+	3.25263i	−0.268518	+	0.229996i
$201$	2.48260	+	2.48260i	0.175109	+	0.175109i
$202$			7.16455i			0.504096i
$203$	−5.10497			−0.358299
$204$			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
$208$	0.250975	−	3.59681i	0.0174020	−	0.249394i
$209$			6.28109i			0.434472i
$210$	−1.92302	−	0.884873i	−0.132701	−	0.0610621i
$211$	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
$213$			9.89625i			0.678080i
$214$	5.33595	−	5.33595i	0.364758	−	0.364758i
$215$	−0.695741	−	0.320143i	−0.0474491	−	0.0218336i
$216$	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
$223$		−	6.31913i		−	0.423160i	−0.977361	−	0.211580i	$-0.932139\pi$
$223$		−	6.31913i		−	0.423160i	0.977361	−	0.211580i	$-0.0678609\pi$
$224$			0.946681i			0.0632528i
$225$	−3.25263	−	3.79742i	−0.216842	−	0.253161i
$226$	3.32488	+	3.32488i	0.221168	+	0.221168i
$227$	2.06238			0.136885			0.0684423	−	0.997655i	$-0.478197\pi$
$227$	2.06238			0.136885			0.0684423	+	0.997655i	$0.478197\pi$
$228$	1.41850			0.0939427
$229$	−1.31652	−	1.31652i	−0.0869979	−	0.0869979i	0.662269	−	0.749266i	$-0.269594\pi$
$229$	−1.31652	−	1.31652i	−0.0869979	−	0.0869979i	−0.749266	+	0.662269i	$0.769594\pi$
$230$	−12.2156	−	5.62096i	−0.805472	−	0.370635i
$231$		−	4.19188i		−	0.275805i
$232$			5.39250i			0.354035i
$233$	−10.4414	+	10.4414i	−0.684040	+	0.684040i	−0.960908	−	0.276868i	$-0.910703\pi$
$233$	−10.4414	+	10.4414i	−0.684040	+	0.684040i	0.276868	+	0.960908i	$0.410703\pi$
$234$	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	0.0769369	−	0.997036i	$-0.475486\pi$
$239$	16.6032	−	16.6032i	1.07397	−	1.07397i	0.997036	−	0.0769369i	$-0.0245140\pi$
$240$	−0.934711	+	2.03133i	−0.0603354	+	0.131122i
$241$	12.3249	−	12.3249i	0.793917	−	0.793917i	−0.188212	−	0.982128i	$-0.560269\pi$
$241$	12.3249	−	12.3249i	0.793917	−	0.793917i	0.982128	+	0.188212i	$0.0602691\pi$
$242$		−	8.60694i		−	0.553275i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	9.79944			0.627345
$245$	−4.73306	−	12.8016i	−0.302384	−	0.817861i
$246$		−	8.53449i		−	0.544139i
$247$	3.35598	+	3.85945i	0.213536	+	0.245571i
$248$	−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	$-0.770373\pi$
$251$		−	20.9264i		−	1.32086i	0.750886	−	0.660431i	$-0.229627\pi$
$252$	−0.946681			−0.0596353
$253$		−	26.6280i		−	1.67409i
$254$	3.09330	+	3.09330i	0.194091	+	0.194091i
$255$	10.1484	−	3.75213i	0.635519	−	0.234968i
$256$	1.00000			0.0625000
$257$	−5.26288	−	5.26288i	−0.328290	−	0.328290i	0.523646	−	0.851936i	$-0.324571\pi$
$257$	−5.26288	−	5.26288i	−0.328290	−	0.328290i	−0.851936	+	0.523646i	$0.824571\pi$
$258$	−0.342504			−0.0213234
$259$	−11.2657			−0.700014
$260$	−7.73823	+	2.26269i	−0.479905	+	0.140326i
$261$	−5.39250			−0.333787
$262$	−2.99792			−0.185212
$263$	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
$265$	5.15856	−	11.2107i	0.316888	−	0.688667i
$266$	−0.949553	−	0.949553i	−0.0582208	−	0.0582208i
$267$			0.345935i			0.0211709i
$268$	−3.51092			−0.214464
$269$			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	−0.417990	−	0.908452i	$-0.637265\pi$
$271$	8.07401	−	8.07401i	0.490461	−	0.490461i	0.908452	+	0.417990i	$0.137265\pi$
$272$	−3.42154	−	3.42154i	−0.207461	−	0.207461i
$273$	−2.23971	−	2.57572i	−0.135554	−	0.155890i
$274$		−	17.3517i		−	1.04825i
$275$	−1.70577	+	22.0741i	−0.102862	+	1.33112i
$276$	−6.01358			−0.361975
$277$	3.26424	+	3.26424i	0.196129	+	0.196129i	0.798338	−	0.602209i	$-0.205713\pi$
$277$	3.26424	+	3.26424i	0.196129	+	0.196129i	−0.602209	+	0.798338i	$0.705713\pi$
$278$		−	2.49588i		−	0.149693i
$279$	2.43972	−	2.43972i	0.146062	−	0.146062i
$280$	1.98548	−	0.734084i	0.118655	−	0.0438699i
$281$	−22.2236	+	22.2236i	−1.32575	+	1.32575i	−0.416709	+	0.909040i	$0.636816\pi$
$281$	−22.2236	+	22.2236i	−1.32575	+	1.32575i	−0.909040	+	0.416709i	$0.863184\pi$
$282$	−0.604177	+	0.604177i	−0.0359782	+	0.0359782i
$283$	10.4468	−	10.4468i	0.620997	−	0.620997i	−0.324789	−	0.945786i	$-0.605293\pi$
$283$	10.4468	−	10.4468i	0.620997	−	0.620997i	0.945786	+	0.324789i	$0.105293\pi$
$284$	−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
$288$			1.00000i			0.0589256i
$289$			6.41383i			0.377284i
$290$	11.3097	−	4.18150i	0.664131	−	0.245546i
$291$	1.88997	+	1.88997i	0.110792	+	0.110792i
$292$	−16.4476			−0.962523
$293$	−24.5333			−1.43325			−0.716625	−	0.697458i	$-0.754314\pi$
$293$	−24.5333			−1.43325			−0.716625	+	0.697458i	$0.754314\pi$
$294$	−4.31603	−	4.31603i	−0.251716	−	0.251716i
$295$	12.4028	−	26.9540i	0.722118	−	1.56932i
$296$			11.9002i			0.691683i
$297$		−	4.42797i		−	0.256937i
$298$	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
$305$	−7.59877	−	20.5525i	−0.435104	−	1.17683i
$306$	3.42154	−	3.42154i	0.195596	−	0.195596i
$307$			26.9486i			1.53804i	0.639226	+	0.769019i	$0.279255\pi$
$307$			26.9486i			1.53804i	−0.639226	+	0.769019i	$0.720745\pi$
$308$	2.96410	+	2.96410i	0.168896	+	0.168896i
$309$	11.3204			0.643995
$310$	−3.22502	+	7.00868i	−0.183169	+	0.398066i
$311$			16.4762i			0.934281i	0.884183	+	0.467140i	$0.154716\pi$
$311$			16.4762i			0.934281i	−0.884183	+	0.467140i	$0.845284\pi$
$312$	−2.72079	+	2.36586i	−0.154035	+	0.133940i
$313$	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
$317$	−13.4323			−0.754434			−0.377217	−	0.926125i	$-0.623119\pi$
$317$	−13.4323			−0.754434			−0.377217	+	0.926125i	$0.623119\pi$
$318$		−	5.51888i		−	0.309484i
$319$	16.8842	+	16.8842i	0.945332	+	0.945332i
$320$	−0.775429	−	2.09731i	−0.0433478	−	0.117243i
$321$	−7.54617			−0.421186
$322$	4.02552	+	4.02552i	0.224333	+	0.224333i
$323$	6.86383			0.381914
$324$	−1.00000			−0.0555556
$325$	10.7460	+	14.4749i	0.596082	+	0.802924i
$326$	23.5470			1.30415
$327$	5.55863			0.307393
$328$	6.03479	+	6.03479i	0.333216	+	0.333216i
$329$	0.808877			0.0445948
$330$	3.43358	+	9.28683i	0.189012	+	0.511223i
$331$	4.34332	+	4.34332i	0.238730	+	0.238730i	0.816324	−	0.577594i	$-0.196008\pi$
$331$	4.34332	+	4.34332i	0.238730	+	0.238730i	−0.577594	+	0.816324i	$0.696008\pi$
$332$		−	15.2370i		−	0.836239i
$333$	−11.9002			−0.652125
$334$		−	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	0.783640	−	0.621215i	$-0.213361\pi$
$337$	2.98172	+	2.98172i	0.162425	+	0.162425i	−0.621215	+	0.783640i	$0.713361\pi$
$338$	−12.8740	−	1.80542i	−0.700255	−	0.0982017i
$339$		−	4.70209i		−	0.255382i
$340$	−4.52287	+	9.82918i	−0.245287	+	0.533062i
$341$	−15.2778			−0.827337
$342$	−1.00303	−	1.00303i	−0.0542378	−	0.0542378i
$343$			12.4051i			0.669813i
$344$	0.242187	−	0.242187i	0.0130579	−	0.0130579i
$345$	4.66310	+	12.6123i	0.251053	+	0.679026i
$346$	−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	$-0.380555\pi$
$349$	−10.5348	−	10.5348i	−0.563915	−	0.563915i	−0.930417	+	0.366502i	$0.880555\pi$
$350$	−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
$353$		−	24.7214i		−	1.31579i	−0.753111	−	0.657893i	$-0.771448\pi$
$353$		−	24.7214i		−	1.31579i	0.753111	−	0.657893i	$-0.228552\pi$
$354$		−	13.2691i		−	0.705245i
$355$	−9.25014	+	20.1026i	−0.490946	+	1.06693i
$356$	−0.244613	−	0.244613i	−0.0129645	−	0.0129645i
$357$	−4.58078			−0.242441
$358$	−7.96800			−0.421122
$359$	−1.44201	−	1.44201i	−0.0761066	−	0.0761066i	0.668029	−	0.744135i	$-0.267138\pi$
$359$	−1.44201	−	1.44201i	−0.0761066	−	0.0761066i	−0.744135	+	0.668029i	$0.767138\pi$
$360$	2.09731	−	0.775429i	0.110538	−	0.0408687i
$361$			16.9878i			0.894097i
$362$			17.3575i			0.912291i
$363$	−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
$370$	24.9583	−	9.22773i	1.29752	−	0.479727i
$371$	−3.69437	+	3.69437i	−0.191802	+	0.191802i
$372$			3.45028i			0.178889i
$373$	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
$375$	−3.05768	−	10.7541i	−0.157898	−	0.555339i
$376$		−	0.854435i		−	0.0440641i
$377$	19.3958	+	1.35338i	0.998932	+	0.0697027i
$378$	0.669405	+	0.669405i	0.0344305	+	0.0344305i
$379$	17.6422	−	17.6422i	0.906221	−	0.906221i	−0.0897438	−	0.995965i	$-0.528605\pi$
$379$	17.6422	−	17.6422i	0.906221	−	0.906221i	0.995965	+	0.0897438i	$0.0286048\pi$
$380$	2.88145	+	1.32589i	0.147815	+	0.0680168i
$381$		−	4.37458i		−	0.224117i
$382$	6.75356			0.345542
$383$			29.6580i			1.51545i	0.652574	+	0.757725i	$0.273689\pi$
$383$			29.6580i			1.51545i	−0.652574	+	0.757725i	$0.726311\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	3.91820	−	8.51510i	0.199690	−	0.433970i
$386$	7.55869			0.384727
$387$	0.242187	+	0.242187i	0.0123111	+	0.0123111i
$388$	−2.67283			−0.135692
$389$	16.8263			0.853127			0.426564	−	0.904458i	$-0.359724\pi$
$389$	16.8263			0.853127			0.426564	+	0.904458i	$0.359724\pi$
$390$	7.07172	+	3.87179i	0.358091	+	0.196056i
$391$	−29.0984			−1.47157
$392$	6.10380			0.308288
$393$	2.11985	+	2.11985i	0.106932	+	0.106932i
$394$	−17.8690			−0.900229
$395$	16.9881	−	6.28095i	0.854766	−	0.316029i
$396$	3.13105	+	3.13105i	0.157341	+	0.157341i
$397$			28.3338i			1.42203i	0.703176	+	0.711016i	$0.251765\pi$
$397$			28.3338i			1.42203i	−0.703176	+	0.711016i	$0.748235\pi$
$398$	−6.41529			−0.321569
$399$			1.34287i			0.0672276i
$400$	−3.79742	+	3.25263i	−0.189871	+	0.162631i
$401$	−8.47925	+	8.47925i	−0.423433	+	0.423433i	−0.886384	−	0.462951i	$-0.846791\pi$
$401$	−8.47925	+	8.47925i	−0.423433	+	0.423433i	0.462951	+	0.886384i	$0.346791\pi$
$402$	2.48260	+	2.48260i	0.123821	+	0.123821i
$403$	−9.38751	+	8.16289i	−0.467625	+	0.406622i
$404$			7.16455i			0.356450i
$405$	0.775429	+	2.09731i	0.0385314	+	0.104216i
$406$	−5.10497			−0.253356
$407$	37.2600	+	37.2600i	1.84691	+	1.84691i
$408$			4.83878i			0.239555i
$409$	24.9472	−	24.9472i	1.23356	−	1.23356i	0.270971	−	0.962588i	$-0.412655\pi$
$409$	24.9472	−	24.9472i	1.23356	−	1.23356i	0.962588	−	0.270971i	$-0.0873448\pi$
$410$	7.97728	−	17.3364i	0.393970	−	0.856183i
$411$	−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
$418$			6.28109i			0.307218i
$419$			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	0.250298	−	0.968169i	$-0.419471\pi$
$421$	−14.7295	−	14.7295i	−0.717871	−	0.717871i	−0.968169	+	0.250298i	$0.919471\pi$
$422$	8.36808			0.407352
$423$	0.854435			0.0415440
$424$	3.90244	+	3.90244i	0.189519	+	0.189519i
$425$	24.1220	+	1.86402i	1.17009	+	0.0904184i
$426$			9.89625i			0.479475i
$427$			9.27695i			0.448943i
$428$	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	0.471845	−	0.881681i	$-0.343588\pi$
$431$	−8.50842	−	8.50842i	−0.409836	−	0.409836i	−0.881681	+	0.471845i	$0.843588\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	6.47843	−	6.47843i	0.311333	−	0.311333i	−0.534093	−	0.845426i	$-0.679347\pi$
$433$	6.47843	−	6.47843i	0.311333	−	0.311333i	0.845426	+	0.534093i	$0.179347\pi$
$434$	2.30964	−	2.30964i	0.110866	−	0.110866i
$435$	−10.9540	−	5.04043i	−0.525202	−	0.241670i
$436$	−3.93054	+	3.93054i	−0.188239	+	0.188239i
$437$			8.53028i			0.408059i
$438$	11.6302	+	11.6302i	0.555713	+	0.555713i
$439$	−40.8316			−1.94879			−0.974393	−	0.224854i	$-0.927810\pi$
$439$	−40.8316			−1.94879			−0.974393	+	0.224854i	$0.927810\pi$
$440$	−8.99469	−	4.13888i	−0.428805	−	0.197313i
$441$			6.10380i			0.290657i
$442$	−13.1653	+	11.4479i	−0.626211	+	0.544520i
$443$	−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
$447$	−2.44065			−0.115439
$448$			0.946681i			0.0447265i
$449$	−22.0410	−	22.0410i	−1.04018	−	1.04018i	−0.999158	−	0.0410213i	$-0.986939\pi$
$449$	−22.0410	−	22.0410i	−1.04018	−	1.04018i	−0.0410213	−	0.999158i	$-0.513061\pi$
$450$	−3.25263	−	3.79742i	−0.153330	−	0.179012i
$451$	37.7905			1.77948
$452$	3.32488	+	3.32488i	0.156389	+	0.156389i
$453$	−2.63710			−0.123902
$454$	2.06238			0.0967921
$455$	−2.14205	−	7.32564i	−0.100421	−	0.343431i
$456$	1.41850			0.0664275
$457$	−17.5342			−0.820213			−0.410107	−	0.912038i	$-0.634509\pi$
$457$	−17.5342			−0.820213			−0.410107	+	0.912038i	$0.634509\pi$
$458$	−1.31652	−	1.31652i	−0.0615168	−	0.0615168i
$459$	−4.83878			−0.225855
$460$	−12.2156	−	5.62096i	−0.569554	−	0.262079i
$461$	−17.5242	−	17.5242i	−0.816184	−	0.816184i	0.169368	−	0.985553i	$-0.445827\pi$
$461$	−17.5242	−	17.5242i	−0.816184	−	0.816184i	−0.985553	+	0.169368i	$0.945827\pi$
$462$		−	4.19188i		−	0.195024i
$463$	−12.6976			−0.590106			−0.295053	−	0.955481i	$-0.595337\pi$
$463$	−12.6976			−0.590106			−0.295053	+	0.955481i	$0.595337\pi$
$464$			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	0.733761	−	0.679408i	$-0.237763\pi$
$467$	1.17459	+	1.17459i	0.0543535	+	0.0543535i	−0.679408	+	0.733761i	$0.737763\pi$
$468$	3.59681	+	0.250975i	0.166262	+	0.0116013i
$469$		−	3.32372i		−	0.153475i
$470$	−1.79201	+	0.662553i	−0.0826595	+	0.0305613i
$471$	−3.30542			−0.152306
$472$	9.38267	+	9.38267i	0.431872	+	0.431872i
$473$		−	1.51660i		−	0.0697334i
$474$	5.72754	−	5.72754i	0.263075	−	0.263075i
$475$	0.546443	−	7.07144i	0.0250725	−	0.324460i
$476$	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	−0.999840	−	0.0178921i	$-0.994304\pi$
$479$	−22.2742	−	22.2742i	−1.01773	−	1.01773i	−0.0178921	−	0.999840i	$-0.505696\pi$
$480$	−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
$483$		−	5.69294i		−	0.259038i
$484$		−	8.60694i		−	0.391224i
$485$	2.07259	+	5.60575i	0.0941113	+	0.254544i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−33.0320			−1.49682			−0.748412	−	0.663234i	$-0.769183\pi$
$487$	−33.0320			−1.49682			−0.748412	+	0.663234i	$0.769183\pi$
$488$	9.79944			0.443600
$489$	−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	$-0.692959\pi$
$491$		−	36.4206i		−	1.64364i	0.569747	−	0.821820i	$-0.307041\pi$
$492$		−	8.53449i		−	0.384764i
$493$	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	−0.206199	+	0.978510i	$0.566109\pi$
$499$	−26.4644	+	26.4644i	−1.18471	+	1.18471i	−0.978510	+	0.206199i	$0.933891\pi$
$500$	9.76640	+	5.44219i	0.436767	+	0.243382i
$501$	−6.90978	+	6.90978i	−0.308706	+	0.308706i
$502$		−	20.9264i		−	0.933991i
$503$	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
$505$	15.0263	−	5.55560i	0.668661	−	0.247221i
$506$		−	26.6280i		−	1.18376i
$507$	7.82669	+	10.3799i	0.347595	+	0.460989i
$508$	3.09330	+	3.09330i	0.137243	+	0.137243i
$509$	−4.50027	+	4.50027i	−0.199471	+	0.199471i	−0.799773	−	0.600302i	$-0.795047\pi$
$509$	−4.50027	+	4.50027i	−0.199471	+	0.199471i	0.600302	+	0.799773i	$0.295047\pi$
$510$	10.1484	−	3.75213i	0.449380	−	0.166147i
$511$		−	15.5706i		−	0.688804i
$512$	1.00000			0.0441942
$513$			1.41850i			0.0626285i
$514$	−5.26288	−	5.26288i	−0.232136	−	0.232136i
$515$	22.9955	+	10.5813i	1.01330	+	0.466268i
$516$	−0.342504			−0.0150779
$517$	−2.67528	−	2.67528i	−0.117659	−	0.117659i
$518$	−11.2657			−0.494985
$519$	8.43741			0.370361
$520$	−7.73823	+	2.26269i	−0.339344	+	0.0992257i
$521$	−2.48916			−0.109052			−0.0545260	−	0.998512i	$-0.517365\pi$
$521$	−2.48916			−0.109052			−0.0545260	+	0.998512i	$0.517365\pi$
$522$	−5.39250			−0.236023
$523$	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
$525$	−0.364686	+	4.71934i	−0.0159162	+	0.205969i
$526$	12.1431	+	12.1431i	0.529462	+	0.529462i
$527$			16.6952i			0.727253i
$528$	−4.42797			−0.192703
$529$		−	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
$533$	23.2206	−	20.1914i	1.00579	−	0.874587i
$534$			0.345935i			0.0149701i
$535$	−15.3288	−	7.05349i	−0.662721	−	0.304949i
$536$	−3.51092			−0.151649
$537$	5.63423	+	5.63423i	0.243135	+	0.243135i
$538$			11.3324i			0.488576i
$539$	19.1113	−	19.1113i	0.823181	−	0.823181i
$540$	−2.03133	−	0.934711i	−0.0874147	−	0.0402236i
$541$	−14.9033	+	14.9033i	−0.640743	+	0.640743i	−0.950738	−	0.309995i	$-0.899673\pi$
$541$	−14.9033	+	14.9033i	−0.640743	+	0.640743i	0.309995	+	0.950738i	$0.399673\pi$
$542$	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	$-0.176396\pi$
$548$		−	17.3517i		−	0.741227i
$549$			9.79944i			0.418230i
$550$	−1.70577	+	22.0741i	−0.0727342	+	0.941241i
$551$	−5.40885	−	5.40885i	−0.230425	−	0.230425i
$552$	−6.01358			−0.255955
$553$	−7.66808			−0.326080
$554$	3.26424	+	3.26424i	0.138684	+	0.138684i
$555$	−24.1732	−	11.1232i	−1.02609	−	0.472154i
$556$		−	2.49588i		−	0.105849i
$557$		−	38.6878i		−	1.63925i	−0.572897	−	0.819627i	$-0.694180\pi$
$557$		−	38.6878i		−	1.63925i	0.572897	−	0.819627i	$-0.305820\pi$
$558$	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	−0.243662	−	0.969860i	$-0.578349\pi$
$563$	17.2310	−	17.2310i	0.726198	−	0.726198i	0.969860	+	0.243662i	$0.0783487\pi$
$564$	−0.604177	+	0.604177i	−0.0254404	+	0.0254404i
$565$	4.39510	−	9.55151i	0.184903	−	0.401835i
$566$	10.4468	−	10.4468i	0.439111	−	0.439111i
$567$		−	0.946681i		−	0.0397569i
$568$	−6.99770	−	6.99770i	−0.293617	−	0.293617i
$569$	−7.21162			−0.302327			−0.151163	−	0.988509i	$-0.548302\pi$
$569$	−7.21162			−0.302327			−0.151163	+	0.988509i	$0.548302\pi$
$570$	−1.09995	−	2.97504i	−0.0460718	−	0.124611i
$571$		−	20.5745i		−	0.861017i	−0.902587	−	0.430508i	$-0.858334\pi$
$571$		−	20.5745i		−	0.861017i	0.902587	−	0.430508i	$-0.141666\pi$
$572$	−10.4760	−	12.0476i	−0.438022	−	0.503735i
$573$	−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
$577$	−4.77462			−0.198770			−0.0993850	−	0.995049i	$-0.531688\pi$
$577$	−4.77462			−0.198770			−0.0993850	+	0.995049i	$0.531688\pi$
$578$			6.41383i			0.266780i
$579$	−5.34480	−	5.34480i	−0.222122	−	0.222122i
$580$	11.3097	−	4.18150i	0.469611	−	0.173627i
$581$	14.4246			0.598433
$582$	1.88997	+	1.88997i	0.0783419	+	0.0783419i
$583$	24.4375			1.01210
$584$	−16.4476			−0.680607
$585$	−2.26269	−	7.73823i	−0.0935509	−	0.319936i
$586$	−24.5333			−1.01346
$587$	−10.7668			−0.444393			−0.222196	−	0.975002i	$-0.571323\pi$
$587$	−10.7668			−0.444393			−0.222196	+	0.975002i	$0.571323\pi$
$588$	−4.31603	−	4.31603i	−0.177990	−	0.177990i
$589$	4.89424			0.201664
$590$	12.4028	−	26.9540i	0.510614	−	1.10968i
$591$	12.6353	+	12.6353i	0.519747	+	0.519747i
$592$			11.9002i			0.489094i
$593$	41.5640			1.70683			0.853414	−	0.521233i	$-0.174528\pi$
$593$	41.5640			1.70683			0.853414	+	0.521233i	$0.174528\pi$
$594$		−	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
$598$	−14.2273	−	16.3617i	−0.581797	−	0.669079i
$599$			34.5955i			1.41353i	0.707446	+	0.706767i	$0.249847\pi$
$599$			34.5955i			1.41353i	−0.707446	+	0.706767i	$0.750153\pi$
$600$	4.98514	+	0.385225i	0.203517	+	0.0157268i
$601$	−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
$603$		−	3.51092i		−	0.142976i
$604$	1.86471	−	1.86471i	0.0758739	−	0.0758739i
$605$	−18.0514	+	6.67407i	−0.733894	+	0.271339i
$606$	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
$613$			39.8520i			1.60961i	0.593541	+	0.804804i	$0.297730\pi$
$613$			39.8520i			1.60961i	−0.593541	+	0.804804i	$0.702270\pi$
$614$			26.9486i			1.08756i
$615$	−17.8995	+	6.61789i	−0.721776	+	0.266859i
$616$	2.96410	+	2.96410i	0.119427	+	0.119427i
$617$	−35.2269			−1.41818			−0.709090	−	0.705118i	$-0.750894\pi$
$617$	−35.2269			−1.41818			−0.709090	+	0.705118i	$0.750894\pi$
$618$	11.3204			0.455373
$619$	−29.3560	−	29.3560i	−1.17992	−	1.17992i	−0.979765	−	0.200150i	$-0.935857\pi$
$619$	−29.3560	−	29.3560i	−1.17992	−	1.17992i	−0.200150	−	0.979765i	$-0.564143\pi$
$620$	−3.22502	+	7.00868i	−0.129520	+	0.281475i
$621$		−	6.01358i		−	0.241317i
$622$			16.4762i			0.660636i
$623$	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
$630$	0.734084	+	1.98548i	0.0292466	+	0.0791036i
$631$	−10.8434	+	10.8434i	−0.431670	+	0.431670i	−0.889196	−	0.457526i	$-0.848736\pi$
$631$	−10.8434	+	10.8434i	−0.431670	+	0.431670i	0.457526	+	0.889196i	$0.348736\pi$
$632$			8.09997i			0.322199i
$633$	−5.91713	−	5.91713i	−0.235185	−	0.235185i
$634$	−13.4323			−0.533465
$635$	4.08897	−	8.88623i	0.162266	−	0.352639i
$636$		−	5.51888i		−	0.218838i
$637$	1.53190	−	21.9542i	0.0606960	−	0.869856i
$638$	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	$-0.643883\pi$
$641$		−	45.5504i		−	1.79913i	0.436784	−	0.899566i	$-0.356117\pi$
$642$	−7.54617			−0.297823
$643$			13.2934i			0.524241i	0.965035	+	0.262120i	$0.0844218\pi$
$643$			13.2934i			0.524241i	−0.965035	+	0.262120i	$0.915578\pi$
$644$	4.02552	+	4.02552i	0.158628	+	0.158628i
$645$	0.265588	+	0.718338i	0.0104575	+	0.0282845i
$646$	6.86383			0.270054
$647$	−0.168076	−	0.168076i	−0.00660775	−	0.00660775i	0.703795	−	0.710403i	$-0.251487\pi$
$647$	−0.168076	−	0.168076i	−0.00660775	−	0.00660775i	−0.710403	+	0.703795i	$0.751487\pi$
$648$	−1.00000			−0.0392837
$649$	58.7552			2.30634
$650$	10.7460	+	14.4749i	0.421494	+	0.567753i
$651$	−3.26632			−0.128017
$652$	23.5470			0.922172
$653$	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
$655$	2.32468	+	6.28758i	0.0908326	+	0.245676i
$656$	6.03479	+	6.03479i	0.235619	+	0.235619i
$657$		−	16.4476i		−	0.641682i
$658$	0.808877			0.0315333
$659$		−	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	−0.671852	−	0.740686i	$-0.734501\pi$
$661$	1.76972	−	1.76972i	0.0688341	−	0.0688341i	0.740686	+	0.671852i	$0.234501\pi$
$662$	4.34332	+	4.34332i	0.168808	+	0.168808i
$663$	17.4042	+	1.21441i	0.675922	+	0.0471639i
$664$		−	15.2370i		−	0.591310i
$665$	−1.25520	+	2.72782i	−0.0486744	+	0.105780i
$666$	−11.9002			−0.461122
$667$	22.9302	+	22.9302i	0.887861	+	0.887861i
$668$		−	9.77190i		−	0.378086i
$669$	−4.46830	+	4.46830i	−0.172754	+	0.172754i
$670$	2.72247	+	7.36349i	0.105178	+	0.284476i
$671$	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	−0.950227	−	0.311560i	$-0.899149\pi$
$673$	−16.5684	+	16.5684i	−0.638667	+	0.638667i	0.311560	+	0.950227i	$0.399149\pi$
$674$	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	$0.350602\pi$
$678$		−	4.70209i		−	0.180583i
$679$		−	2.53031i		−	0.0971046i
$680$	−4.52287	+	9.82918i	−0.173444	+	0.376932i
$681$	−1.45832	−	1.45832i	−0.0558829	−	0.0558829i
$682$	−15.2778			−0.585016
$683$	−9.80987			−0.375364			−0.187682	−	0.982230i	$-0.560098\pi$
$683$	−9.80987			−0.375364			−0.187682	+	0.982230i	$0.560098\pi$
$684$	−1.00303	−	1.00303i	−0.0383519	−	0.0383519i
$685$	−36.3919	+	13.4550i	−1.39046	+	0.514089i
$686$			12.4051i			0.473629i
$687$			1.86184i			0.0710334i
$688$	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	0.998884	+	0.0472402i	$0.0150426\pi$
$691$	27.4993	+	27.4993i	1.04612	+	1.04612i	0.0472402	+	0.998884i	$0.484957\pi$
$692$	−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
$695$	−5.23463	+	1.93538i	−0.198561	+	0.0734130i
$696$	3.81307	−	3.81307i	0.144534	−	0.144534i
$697$		−	41.2965i		−	1.56422i
$698$	−10.5348	−	10.5348i	−0.398748	−	0.398748i
$699$	14.7664			0.558516
$700$	−3.07920	−	3.59495i	−0.116383	−	0.135876i
$701$			6.79306i			0.256570i	0.991737	+	0.128285i	$0.0409473\pi$
$701$			6.79306i			0.256570i	−0.991737	+	0.128285i	$0.959053\pi$
$702$	−2.36586	−	2.72079i	−0.0892936	−	0.102690i
$703$	−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
$707$	−6.78254			−0.255084
$708$		−	13.2691i		−	0.498683i
$709$	−1.32520	−	1.32520i	−0.0497688	−	0.0497688i	0.681784	−	0.731553i	$-0.261204\pi$
$709$	−1.32520	−	1.32520i	−0.0497688	−	0.0497688i	−0.731553	+	0.681784i	$0.761204\pi$
$710$	−9.25014	+	20.1026i	−0.347151	+	0.754436i
$711$	−8.09997			−0.303772
$712$	−0.244613	−	0.244613i	−0.00916726	−	0.00916726i
$713$	−20.7486			−0.777040
$714$	−4.58078			−0.171432
$715$	−17.1442	+	31.3134i	−0.641156	+	1.17105i
$716$	−7.96800			−0.297778
$717$	−23.4805			−0.876895
$718$	−1.44201	−	1.44201i	−0.0538155	−	0.0538155i
$719$	−22.5002			−0.839117			−0.419558	−	0.907728i	$-0.637815\pi$
$719$	−22.5002			−0.839117			−0.419558	+	0.907728i	$0.637815\pi$
$720$	2.09731	−	0.775429i	0.0781621	−	0.0288985i
$721$	−7.57792	−	7.57792i	−0.282217	−	0.282217i
$722$			16.9878i			0.632222i
$723$	−17.4300			−0.648230
$724$			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	0.969924	−	0.243408i	$-0.0782653\pi$
$727$	19.5890	+	19.5890i	0.726516	+	0.726516i	−0.243408	+	0.969924i	$0.578265\pi$
$728$	3.40503	+	0.237593i	0.126199	+	0.00880579i
$729$		−	1.00000i		−	0.0370370i
$730$	12.7539	+	34.4957i	0.472045	+	1.27674i
$731$	−1.65731			−0.0612976
$732$	−6.92925	−	6.92925i	−0.256113	−	0.256113i
$733$			8.60108i			0.317688i	0.987304	+	0.158844i	$0.0507767\pi$
$733$			8.60108i			0.317688i	−0.987304	+	0.158844i	$0.949223\pi$
$734$	0.992346	−	0.992346i	0.0366281	−	0.0366281i
$735$	−5.70529	+	12.3988i	−0.210443	+	0.457338i
$736$	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	$-0.238946\pi$
$739$	1.33478	+	1.33478i	0.0491006	+	0.0491006i	−0.682130	+	0.731231i	$0.738946\pi$
$740$	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
$743$		−	36.1540i		−	1.32636i	−0.748459	−	0.663181i	$-0.769206\pi$
$743$		−	36.1540i		−	1.32636i	0.748459	−	0.663181i	$-0.230794\pi$
$744$			3.45028i			0.126494i
$745$	−4.95776	−	2.28130i	−0.181638	−	0.0835803i
$746$	20.8743	+	20.8743i	0.764262	+	0.764262i
$747$	15.2370			0.557493
$748$	−21.4260			−0.783412
$749$	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	$0.319421\pi$
$751$			46.2231i			1.68670i	−0.537361	+	0.843352i	$0.680579\pi$
$752$		−	0.854435i		−	0.0311580i
$753$	−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
$760$	2.88145	+	1.32589i	0.104521	+	0.0480951i
$761$	4.25598	−	4.25598i	0.154279	−	0.154279i	−0.625747	−	0.780026i	$-0.715206\pi$
$761$	4.25598	−	4.25598i	0.154279	−	0.154279i	0.780026	+	0.625747i	$0.215206\pi$
$762$		−	4.37458i		−	0.158474i
$763$	−3.72097	−	3.72097i	−0.134708	−	0.134708i
$764$	6.75356			0.244335
$765$	−9.82918	−	4.52287i	−0.355375	−	0.163525i
$766$			29.6580i			1.07159i
$767$	36.1025	−	31.3928i	1.30358	−	1.13353i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−6.64731	+	6.64731i	−0.239708	+	0.239708i	−0.816729	−	0.577021i	$-0.804215\pi$
$769$	−6.64731	+	6.64731i	−0.239708	+	0.239708i	0.577021	+	0.816729i	$0.304215\pi$
$770$	3.91820	−	8.51510i	0.141202	−	0.306863i
$771$			7.44284i			0.268047i
$772$	7.55869			0.272043
$773$			47.1882i			1.69724i	0.529002	+	0.848620i	$0.322566\pi$
$773$			47.1882i			1.69724i	−0.529002	+	0.848620i	$0.677434\pi$
$774$	0.242187	+	0.242187i	0.00870524	+	0.00870524i
$775$	17.2001	+	1.32914i	0.617847	+	0.0477440i
$776$	−2.67283			−0.0959489
$777$	7.96602	+	7.96602i	0.285779	+	0.285779i
$778$	16.8263			0.603252
$779$	−12.1062			−0.433750
$780$	7.07172	+	3.87179i	0.253208	+	0.138632i
$781$	−43.8203			−1.56801
$782$	−29.0984			−1.04056
$783$	3.81307	+	3.81307i	0.136268	+	0.136268i
$784$	6.10380			0.217993
$785$	−6.71442	−	3.08962i	−0.239648	−	0.110273i
$786$	2.11985	+	2.11985i	0.0756126	+	0.0756126i
$787$		−	34.7208i		−	1.23766i	−0.785524	−	0.618831i	$-0.787606\pi$
$787$		−	34.7208i		−	1.23766i	0.785524	−	0.618831i	$-0.212394\pi$
$788$	−17.8690			−0.636558
$789$		−	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
$793$	2.45941	−	35.2467i	0.0873363	−	1.25165i
$794$			28.3338i			1.00553i
$795$	−11.5748	+	4.27950i	−0.410516	+	0.151778i
$796$	−6.41529			−0.227384
$797$	20.0264	+	20.0264i	0.709371	+	0.709371i	0.966403	−	0.257032i	$-0.0827446\pi$
$797$	20.0264	+	20.0264i	0.709371	+	0.709371i	−0.257032	+	0.966403i	$0.582745\pi$
$798$			1.34287i			0.0475371i
$799$	−2.92348	+	2.92348i	−0.103425	+	0.103425i
$800$	−3.79742	+	3.25263i	−0.134259	+	0.114998i
$801$	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
$808$			7.16455i			0.252048i
$809$		−	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	0.503454	−	0.864022i	$-0.332062\pi$
$811$	−10.2683	−	10.2683i	−0.360568	−	0.360568i	−0.864022	+	0.503454i	$0.832062\pi$
$812$	−5.10497			−0.179149
$813$	−11.4184			−0.400460
$814$	37.2600	+	37.2600i	1.30596	+	1.30596i
$815$	−18.2590	−	49.3854i	−0.639586	−	1.72990i
$816$			4.83878i			0.169391i
$817$			0.485844i			0.0169975i
$818$	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	0.942923	−	0.333012i	$-0.108065\pi$
$821$	17.4758	+	17.4758i	0.609911	+	0.609911i	−0.333012	+	0.942923i	$0.608065\pi$
$822$	−12.2695	+	12.2695i	−0.427948	+	0.427948i
$823$	−21.1631	+	21.1631i	−0.737699	+	0.737699i	−0.972132	−	0.234433i	$-0.924677\pi$
$823$	−21.1631	+	21.1631i	−0.737699	+	0.737699i	0.234433	+	0.972132i	$0.424677\pi$
$824$	−8.00473	+	8.00473i	−0.278858	+	0.278858i
$825$	16.8149	−	14.4026i	0.585419	−	0.501433i
$826$	−8.88240	+	8.88240i	−0.309058	+	0.309058i
$827$		−	10.0895i		−	0.350847i	−0.984493	−	0.175424i	$-0.943870\pi$
$827$		−	10.0895i		−	0.350847i	0.984493	−	0.175424i	$-0.0561295\pi$
$828$	4.25224	+	4.25224i	0.147776	+	0.147776i
$829$	39.8773			1.38500			0.692498	−	0.721420i	$-0.256510\pi$
$829$	39.8773			1.38500			0.692498	+	0.721420i	$0.256510\pi$
$830$	−31.9567	+	11.8152i	−1.10923	+	0.410112i
$831$		−	4.61634i		−	0.160139i
$832$	0.250975	−	3.59681i	0.00870099	−	0.124697i
$833$	−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
$837$	−3.45028			−0.119259
$838$			12.4367i			0.429620i
$839$	−2.34914	−	2.34914i	−0.0811013	−	0.0811013i	0.665392	−	0.746494i	$-0.268264\pi$
$839$	−2.34914	−	2.34914i	−0.0811013	−	0.0811013i	−0.746494	+	0.665392i	$0.768264\pi$
$840$	−1.92302	−	0.884873i	−0.0663507	−	0.0305310i
$841$	−0.0790110			−0.00272452
$842$	−14.7295	−	14.7295i	−0.507611	−	0.507611i
$843$	31.4289			1.08247
$844$	8.36808			0.288041
$845$	6.19637	+	28.4008i	0.213162	+	0.977017i
$846$	0.854435			0.0293761
$847$	8.14802			0.279969
$848$	3.90244	+	3.90244i	0.134010	+	0.134010i
$849$	−14.7740			−0.507042
$850$	24.1220	+	1.86402i	0.827378	+	0.0639354i
$851$	50.6024	+	50.6024i	1.73463	+	1.73463i
$852$			9.89625i			0.339040i
$853$	−9.94900			−0.340647			−0.170324	−	0.985388i	$-0.554481\pi$
$853$	−9.94900			−0.340647			−0.170324	+	0.985388i	$0.554481\pi$
$854$			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	0.161664	−	0.986846i	$-0.448314\pi$
$857$	−24.1568	−	24.1568i	−0.825182	−	0.825182i	−0.986846	+	0.161664i	$0.948314\pi$
$858$	−1.11131	+	15.9266i	−0.0379395	+	0.543724i
$859$			20.4244i			0.696871i	0.937333	+	0.348435i	$0.113287\pi$
$859$			20.4244i			0.696871i	−0.937333	+	0.348435i	$0.886713\pi$
$860$	−0.695741	−	0.320143i	−0.0237246	−	0.0109168i
$861$	8.07944			0.275347
$862$	−8.50842	−	8.50842i	−0.289798	−	0.289798i
$863$			15.6902i			0.534102i	0.963682	+	0.267051i	$0.0860492\pi$
$863$			15.6902i			0.534102i	−0.963682	+	0.267051i	$0.913951\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	17.1392	+	7.88654i	0.582750	+	0.268150i
$866$	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
$873$		−	2.67283i		−	0.0904615i
$874$			8.53028i			0.288541i
$875$	−5.15201	+	9.24567i	−0.174170	+	0.312561i
$876$	11.6302	+	11.6302i	0.392948	+	0.392948i
$877$	34.2568			1.15677			0.578385	−	0.815764i	$-0.303683\pi$
$877$	34.2568			1.15677			0.578385	+	0.815764i	$0.303683\pi$
$878$	−40.8316			−1.37800
$879$	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	$0.180714\pi$
$881$			31.9208i			1.07544i	−0.843124	+	0.537720i	$0.819286\pi$
$882$			6.10380i			0.205525i
$883$	−1.59287	+	1.59287i	−0.0536043	+	0.0536043i	−0.733401	−	0.679796i	$-0.762068\pi$
$883$	−1.59287	+	1.59287i	−0.0536043	+	0.0536043i	0.679796	+	0.733401i	$0.262068\pi$
$884$	−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
$890$	−0.323349	+	0.702709i	−0.0108387	+	0.0235549i
$891$	−3.13105	+	3.13105i	−0.104894	+	0.104894i
$892$		−	6.31913i		−	0.211580i
$893$	0.857026	+	0.857026i	0.0286793	+	0.0286793i
$894$	−2.44065			−0.0816274
$895$	6.17862	+	16.7114i	0.206528	+	0.558600i
$896$			0.946681i			0.0316264i
$897$	−1.50926	+	21.6297i	−0.0503926	+	0.722194i
$898$	−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
$902$	37.7905			1.25829
$903$		−	0.324242i		−	0.0107901i
$904$	3.32488	+	3.32488i	0.110584	+	0.110584i
$905$	36.4041	−	13.4595i	1.21011	−	0.447410i
$906$	−2.63710			−0.0876116
$907$	0.0415121	+	0.0415121i	0.00137839	+	0.00137839i	0.707796	−	0.706417i	$-0.249690\pi$
$907$	0.0415121	+	0.0415121i	0.00137839	+	0.00137839i	−0.706417	+	0.707796i	$0.749690\pi$
$908$	2.06238			0.0684423
$909$	−7.16455			−0.237633
$910$	−2.14205	−	7.32564i	−0.0710083	−	0.242842i
$911$	11.6868			0.387201			0.193600	−	0.981080i	$-0.437983\pi$
$911$	11.6868			0.387201			0.193600	+	0.981080i	$0.437983\pi$
$912$	1.41850			0.0469713
$913$	−47.7078	−	47.7078i	−1.57890	−	1.57890i
$914$	−17.5342			−0.579978
$915$	−9.15965	+	19.9059i	−0.302809	+	0.658070i
$916$	−1.31652	−	1.31652i	−0.0434989	−	0.0434989i
$917$		−	2.83808i		−	0.0937216i
$918$	−4.83878			−0.159704
$919$			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
$923$	−26.9256	+	23.4131i	−0.886268	+	0.770653i
$924$		−	4.19188i		−	0.137903i
$925$	−38.7068	−	45.1899i	−1.27267	−	1.48584i
$926$	−12.6976			−0.417268
$927$	−8.00473	−	8.00473i	−0.262910	−	0.262910i
$928$			5.39250i			0.177017i
$929$	−15.0342	+	15.0342i	−0.493257	+	0.493257i	−0.909331	−	0.416074i	$-0.863406\pi$
$929$	−15.0342	+	15.0342i	−0.493257	+	0.493257i	0.416074	+	0.909331i	$0.363406\pi$
$930$	7.23632	−	2.67545i	0.237288	−	0.0877315i
$931$	−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	$0.0833988\pi$
$938$		−	3.32372i		−	0.108523i
$939$		−	4.09695i		−	0.133699i
$940$	−1.79201	+	0.662553i	−0.0584491	+	0.0216101i
$941$	−12.0649	−	12.0649i	−0.393303	−	0.393303i	0.482560	−	0.875863i	$-0.339707\pi$
$941$	−12.0649	−	12.0649i	−0.393303	−	0.393303i	−0.875863	+	0.482560i	$0.839707\pi$
$942$	−3.30542			−0.107696
$943$	51.3228			1.67130
$944$	9.38267	+	9.38267i	0.305380	+	0.305380i
$945$	0.884873	−	1.92302i	0.0287849	−	0.0625560i
$946$		−	1.51660i		−	0.0493089i
$947$			50.1326i			1.62909i	0.580101	+	0.814545i	$0.303013\pi$
$947$			50.1326i			1.62909i	−0.580101	+	0.814545i	$0.696987\pi$
$948$	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	−0.157630	−	0.987498i	$-0.550385\pi$
$953$	25.6186	−	25.6186i	0.829869	−	0.829869i	0.987498	+	0.157630i	$0.0503853\pi$
$954$	−3.90244	+	3.90244i	−0.126346	+	0.126346i
$955$	−5.23691	−	14.1643i	−0.169462	−	0.458347i
$956$	16.6032	−	16.6032i	0.536986	−	0.536986i
$957$		−	23.8778i		−	0.771860i
$958$	−22.2742	−	22.2742i	−0.719645	−	0.719645i
$959$	16.4265			0.530439
$960$	−0.934711	+	2.03133i	−0.0301677	+	0.0655610i
$961$		−	19.0955i		−	0.615985i
$962$	42.8026	+	2.98664i	1.38001	+	0.0962932i
$963$	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
$967$	−30.0366			−0.965912			−0.482956	−	0.875645i	$-0.660437\pi$
$967$	−30.0366			−0.965912			−0.482956	+	0.875645i	$0.660437\pi$
$968$		−	8.60694i		−	0.276637i
$969$	−4.85346	−	4.85346i	−0.155916	−	0.155916i
$970$	2.07259	+	5.60575i	0.0665468	+	0.179990i
$971$	−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
$973$	2.36280			0.0757479
$974$	−33.0320			−1.05841
$975$	2.63673	−	17.8339i	0.0844428	−	0.571142i
$976$	9.79944			0.313673
$977$	24.7981			0.793361			0.396680	−	0.917957i	$-0.370162\pi$
$977$	24.7981			0.793361			0.396680	+	0.917957i	$0.370162\pi$
$978$	−16.6503	−	16.6503i	−0.532416	−	0.532416i
$979$	−1.53179			−0.0489562
$980$	−4.73306	−	12.8016i	−0.151192	−	0.408931i
$981$	−3.93054	−	3.93054i	−0.125493	−	0.125493i
$982$		−	36.4206i		−	1.16223i
$983$	0.527121			0.0168125			0.00840627	−	0.999965i	$-0.497324\pi$
$983$	0.527121			0.0168125			0.00840627	+	0.999965i	$0.497324\pi$
$984$		−	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
$988$	3.35598	+	3.85945i	0.106768	+	0.122786i
$989$		−	2.05968i		−	0.0654939i
$990$	4.13888	−	8.99469i	0.131542	−	0.285870i
$991$	−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
$993$		−	6.14238i		−	0.194922i
$994$	6.62459	−	6.62459i	0.210119	−	0.210119i
$995$	4.97460	+	13.4549i	0.157705	+	0.426548i
$996$	−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.j.b.73.2	✓	16
3.2	odd	2		1170.2.m.i.73.6		16
5.2	odd	4		390.2.t.b.307.1	yes	16
5.3	odd	4		1950.2.t.e.307.7		16
5.4	even	2		1950.2.j.e.1243.6		16
13.5	odd	4		390.2.t.b.343.1	yes	16
15.2	even	4		1170.2.w.i.307.7		16
39.5	even	4		1170.2.w.i.343.7		16
65.18	even	4		1950.2.j.e.1357.7		16
65.44	odd	4		1950.2.t.e.343.7		16
65.57	even	4	inner	390.2.j.b.187.2	yes	16
195.122	odd	4		1170.2.m.i.577.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.b.73.2	✓	16	1.1	even	1	trivial
390.2.j.b.187.2	yes	16	65.57	even	4	inner
390.2.t.b.307.1	yes	16	5.2	odd	4
390.2.t.b.343.1	yes	16	13.5	odd	4
1170.2.m.i.73.6		16	3.2	odd	2
1170.2.m.i.577.6		16	195.122	odd	4
1170.2.w.i.307.7		16	15.2	even	4
1170.2.w.i.343.7		16	39.5	even	4
1950.2.j.e.1243.6		16	5.4	even	2
1950.2.j.e.1357.7		16	65.18	even	4
1950.2.t.e.307.7		16	5.3	odd	4
1950.2.t.e.343.7		16	65.44	odd	4

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.775429 - 2.09731i) q^{5} +(-0.707107 - 0.707107i) q^{6} +0.946681i q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.775429 - 2.09731i) q^{5} +(-0.707107 - 0.707107i) q^{6} +0.946681i q^{7} +1.00000 q^{8} +1.00000i q^{9} +(-0.775429 - 2.09731i) q^{10} +(3.13105 - 3.13105i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(0.250975 - 3.59681i) q^{13} +0.946681i q^{14} +(-0.934711 + 2.03133i) q^{15} +1.00000 q^{16} +(-3.42154 - 3.42154i) q^{17} +1.00000i q^{18} +(-1.00303 + 1.00303i) q^{19} +(-0.775429 - 2.09731i) 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} +0.946681i q^{28} +5.39250i q^{29} +(-0.934711 + 2.03133i) q^{30} +(-2.43972 - 2.43972i) q^{31} +1.00000 q^{32} -4.42797 q^{33} +(-3.42154 - 3.42154i) q^{34} +(1.98548 - 0.734084i) q^{35} +1.00000i q^{36} +11.9002i 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} +(2.09731 - 0.775429i) q^{45} +(4.25224 - 4.25224i) q^{46} -0.854435i q^{47} +(-0.707107 - 0.707107i) q^{48} +6.10380 q^{49} +(-3.79742 + 3.25263i) q^{50} +4.83878i q^{51} +(0.250975 - 3.59681i) q^{52} +(3.90244 + 3.90244i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-8.99469 - 4.13888i) q^{55} +0.946681i q^{56} +1.41850 q^{57} +5.39250i q^{58} +(9.38267 + 9.38267i) q^{59} +(-0.934711 + 2.03133i) q^{60} +9.79944 q^{61} +(-2.43972 - 2.43972i) q^{62} -0.946681 q^{63} +1.00000 q^{64} +(-7.73823 + 2.26269i) q^{65} -4.42797 q^{66} -3.51092 q^{67} +(-3.42154 - 3.42154i) q^{68} -6.01358 q^{69} +(1.98548 - 0.734084i) q^{70} +(-6.99770 - 6.99770i) q^{71} +1.00000i q^{72} -16.4476 q^{73} +11.9002i q^{74} +(4.98514 + 0.385225i) q^{75} +(-1.00303 + 1.00303i) q^{76} +(2.96410 + 2.96410i) q^{77} +(-2.72079 + 2.36586i) q^{78} +8.09997i q^{79} +(-0.775429 - 2.09731i) q^{80} -1.00000 q^{81} +(6.03479 + 6.03479i) q^{82} -15.2370i q^{83} +(0.669405 - 0.669405i) q^{84} +(-4.52287 + 9.82918i) 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} +3.45028i q^{93} -0.854435i q^{94} +(2.88145 + 1.32589i) q^{95} +(-0.707107 - 0.707107i) q^{96} -2.67283 q^{97} +6.10380 q^{98} +(3.13105 + 3.13105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 4 q^{11} + 4 q^{13} + 4 q^{15} + 16 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{21} + 4 q^{22} + 16 q^{23} - 16 q^{25} + 4 q^{26} + 4 q^{30} + 12 q^{31} + 16 q^{32} + 4 q^{34} - 12 q^{35} + 4 q^{38} - 4 q^{39} + 4 q^{41} - 8 q^{42} - 16 q^{43} + 4 q^{44} + 16 q^{46} - 80 q^{49} - 16 q^{50} + 4 q^{52} - 44 q^{53} - 20 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{60} - 32 q^{61} + 12 q^{62} + 16 q^{64} - 44 q^{65} - 32 q^{67} + 4 q^{68} - 16 q^{69} - 12 q^{70} + 16 q^{71} + 4 q^{76} - 32 q^{77} - 4 q^{78} - 16 q^{81} + 4 q^{82} - 8 q^{84} - 64 q^{85} - 16 q^{86} + 28 q^{87} + 4 q^{88} + 4 q^{89} + 76 q^{91} + 16 q^{92} + 40 q^{95} - 8 q^{97} - 80 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 4 * q^11 + 4 * q^13 + 4 * q^15 + 16 * q^16 + 4 * q^17 + 4 * q^19 - 8 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 + 4 * q^26 + 4 * q^30 + 12 * q^31 + 16 * q^32 + 4 * q^34 - 12 * q^35 + 4 * q^38 - 4 * q^39 + 4 * q^41 - 8 * q^42 - 16 * q^43 + 4 * q^44 + 16 * q^46 - 80 * q^49 - 16 * q^50 + 4 * q^52 - 44 * q^53 - 20 * q^55 - 16 * q^57 + 12 * q^59 + 4 * q^60 - 32 * q^61 + 12 * q^62 + 16 * q^64 - 44 * q^65 - 32 * q^67 + 4 * q^68 - 16 * q^69 - 12 * q^70 + 16 * q^71 + 4 * q^76 - 32 * q^77 - 4 * q^78 - 16 * q^81 + 4 * q^82 - 8 * q^84 - 64 * q^85 - 16 * q^86 + 28 * q^87 + 4 * q^88 + 4 * q^89 + 76 * q^91 + 16 * q^92 + 40 * q^95 - 8 * q^97 - 80 * q^98 + 4 * q^99

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