LMFDB - Embedded newform 833.2.o.d.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(30,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("833.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.o (of order $12$, degree $4$, not 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.1
Character	$\chi$	$=$	833.667
Dual form			833.2.o.d.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13058 - 1.23009i) q^{2} +(2.49914 + 0.669644i) q^{3} +(2.02625 + 3.50956i) q^{4} +(-0.777383 - 2.90123i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} +(3.19922 + 1.84707i) q^{9} +O(q^{10})$	\(q+(-2.13058 - 1.23009i) q^{2} +(2.49914 + 0.669644i) q^{3} +(2.02625 + 3.50956i) q^{4} +(-0.777383 - 2.90123i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} +(3.19922 + 1.84707i) q^{9} +(-1.91250 + 7.13756i) q^{10} +(0.0222896 - 0.0831859i) q^{11} +(2.71373 + 10.1278i) q^{12} -4.28579 q^{13} -7.77117i q^{15} +(-2.15886 + 3.73926i) q^{16} +(-1.18696 - 3.94856i) q^{17} +(-4.54413 - 7.87067i) q^{18} +(-5.93600 - 3.42715i) q^{19} +(8.60689 - 8.60689i) q^{20} +(-0.149816 + 0.149816i) q^{22} +(0.681429 - 0.182588i) q^{23} +(3.38137 - 12.6195i) q^{24} +(-3.48271 + 2.01074i) q^{25} +(9.13123 + 5.27192i) q^{26} +(1.26994 + 1.26994i) q^{27} +(1.07782 - 1.07782i) q^{29} +(-9.55925 + 16.5571i) q^{30} +(-0.780485 - 0.209130i) q^{31} +(0.453253 - 0.261686i) q^{32} +(0.111410 - 0.192967i) q^{33} +(-2.32818 + 9.87279i) q^{34} +14.9705i q^{36} +(-0.995688 - 3.71596i) q^{37} +(8.43142 + 14.6036i) q^{38} +(-10.7108 - 2.86996i) q^{39} +(-14.6498 + 3.92541i) q^{40} +(-0.0255918 - 0.0255918i) q^{41} +8.49396i q^{43} +(0.337110 - 0.0903285i) q^{44} +(2.87177 - 10.7176i) q^{45} +(-1.67644 - 0.449200i) q^{46} +(4.88296 - 8.45753i) q^{47} +(-7.89929 + 7.89929i) q^{48} +9.89358 q^{50} +(-0.322250 - 10.6629i) q^{51} +(-8.68408 - 15.0413i) q^{52} +(10.2543 - 5.92031i) q^{53} +(-1.14357 - 4.26785i) q^{54} -0.258669 q^{55} +(-12.5400 - 12.5400i) q^{57} +(-3.62219 + 0.970563i) q^{58} +(-3.68791 + 2.12921i) q^{59} +(27.2734 - 15.7463i) q^{60} +(2.43864 - 0.653430i) q^{61} +(1.40564 + 1.40564i) q^{62} +7.34787 q^{64} +(3.33170 + 12.4341i) q^{65} +(-0.474735 + 0.274088i) q^{66} +(-2.46222 - 4.26468i) q^{67} +(11.4527 - 12.1665i) q^{68} +1.82526 q^{69} +(4.95688 - 4.95688i) q^{71} +(9.32682 - 16.1545i) q^{72} +(-3.68341 - 0.986967i) q^{73} +(-2.44957 + 9.14194i) q^{74} +(-10.0503 + 2.69296i) q^{75} -27.7770i q^{76} +(19.2900 + 19.2900i) q^{78} +(-6.34401 + 1.69987i) q^{79} +(12.5267 + 3.35653i) q^{80} +(-3.21786 - 5.57350i) q^{81} +(0.0230451 + 0.0860056i) q^{82} +3.86659i q^{83} +(-10.5330 + 6.51319i) q^{85} +(10.4483 - 18.0971i) q^{86} +(3.41537 - 1.97187i) q^{87} +(-0.420048 - 0.112552i) q^{88} +(-2.52025 + 4.36520i) q^{89} +(-19.3021 + 19.3021i) q^{90} +(2.02155 + 2.02155i) q^{92} +(-1.81050 - 1.04529i) q^{93} +(-20.8071 + 12.0130i) q^{94} +(-5.32842 + 19.8859i) q^{95} +(1.30798 - 0.350473i) q^{96} +(6.55546 - 6.55546i) q^{97} +(0.224960 - 0.224960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 8 q^{5} + 12 q^{6}+O(q^{10}) $ 32 * q + 16 * q^4 + 8 * q^5 + 12 * q^6	$ 32 q + 16 q^{4} + 8 q^{5} + 12 q^{6} + 6 q^{10} - 18 q^{11} - 26 q^{12} - 8 q^{16} - 10 q^{17} - 40 q^{18} + 24 q^{20} + 52 q^{22} - 12 q^{23} - 14 q^{24} - 60 q^{27} - 32 q^{29} - 44 q^{30} + 6 q^{31} + 8 q^{33} + 40 q^{34} - 2 q^{37} + 32 q^{38} + 14 q^{39} - 72 q^{40} - 4 q^{41} + 24 q^{44} + 4 q^{46} + 36 q^{47} - 72 q^{48} - 80 q^{50} - 20 q^{51} - 12 q^{52} + 18 q^{54} - 72 q^{55} - 48 q^{57} + 8 q^{58} + 52 q^{61} - 36 q^{62} + 24 q^{64} - 2 q^{65} - 28 q^{67} - 24 q^{68} + 8 q^{69} + 80 q^{71} + 36 q^{72} + 16 q^{73} + 60 q^{74} + 2 q^{75} + 64 q^{78} - 6 q^{79} - 30 q^{80} + 40 q^{82} + 68 q^{85} - 4 q^{86} + 30 q^{88} - 8 q^{89} + 20 q^{90} - 40 q^{92} - 12 q^{95} + 30 q^{96} + 76 q^{97} - 92 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 8 * q^5 + 12 * q^6 + 6 * q^10 - 18 * q^11 - 26 * q^12 - 8 * q^16 - 10 * q^17 - 40 * q^18 + 24 * q^20 + 52 * q^22 - 12 * q^23 - 14 * q^24 - 60 * q^27 - 32 * q^29 - 44 * q^30 + 6 * q^31 + 8 * q^33 + 40 * q^34 - 2 * q^37 + 32 * q^38 + 14 * q^39 - 72 * q^40 - 4 * q^41 + 24 * q^44 + 4 * q^46 + 36 * q^47 - 72 * q^48 - 80 * q^50 - 20 * q^51 - 12 * q^52 + 18 * q^54 - 72 * q^55 - 48 * q^57 + 8 * q^58 + 52 * q^61 - 36 * q^62 + 24 * q^64 - 2 * q^65 - 28 * q^67 - 24 * q^68 + 8 * q^69 + 80 * q^71 + 36 * q^72 + 16 * q^73 + 60 * q^74 + 2 * q^75 + 64 * q^78 - 6 * q^79 - 30 * q^80 + 40 * q^82 + 68 * q^85 - 4 * q^86 + 30 * q^88 - 8 * q^89 + 20 * q^90 - 40 * q^92 - 12 * q^95 + 30 * q^96 + 76 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.13058	−	1.23009i	−1.50655	−	0.869806i	−0.999971	−	0.00761071i	$-0.997577\pi$
$2$	−2.13058	−	1.23009i	−1.50655	−	0.869806i	−0.506577	−	0.862195i	$-0.669089\pi$
$3$	2.49914	+	0.669644i	1.44288	+	0.386619i	0.893542	−	0.448980i	$-0.148213\pi$
$3$	2.49914	+	0.669644i	1.44288	+	0.386619i	0.549340	+	0.835599i	$0.314879\pi$
$4$	2.02625	+	3.50956i	1.01312	+	1.75478i
$5$	−0.777383	−	2.90123i	−0.347656	−	1.29747i	−0.889478	−	0.456978i	$-0.848932\pi$
$5$	−0.777383	−	2.90123i	−0.347656	−	1.29747i	0.541822	−	0.840493i	$-0.317735\pi$
$6$	−4.50090	−	4.50090i	−1.83749	−	1.83749i
$7$		0			0
$7$		0			0
$8$		−	5.04951i		−	1.78527i
$9$	3.19922	+	1.84707i	1.06641	+	0.615691i
$10$	−1.91250	+	7.13756i	−0.604787	+	2.25710i
$11$	0.0222896	−	0.0831859i	0.00672056	−	0.0250815i	−0.962484	−	0.271338i	$-0.912534\pi$
$11$	0.0222896	−	0.0831859i	0.00672056	−	0.0250815i	0.969205	+	0.246256i	$0.0792006\pi$
$12$	2.71373	+	10.1278i	0.783386	+	2.92364i
$13$	−4.28579			−1.18867			−0.594333	−	0.804219i	$-0.702584\pi$
$13$	−4.28579			−1.18867			−0.594333	+	0.804219i	$0.702584\pi$
$14$		0			0
$15$		−	7.77117i		−	2.00651i
$16$	−2.15886	+	3.73926i	−0.539716	+	0.934815i
$17$	−1.18696	−	3.94856i	−0.287880	−	0.957667i
$17$	−1.18696	−	3.94856i	−0.287880	−	0.957667i
$18$	−4.54413	−	7.87067i	−1.07106	−	1.85514i
$19$	−5.93600	−	3.42715i	−1.36181	−	0.786243i	−0.371947	−	0.928254i	$-0.621310\pi$
$19$	−5.93600	−	3.42715i	−1.36181	−	0.786243i	−0.989865	+	0.142011i	$0.954643\pi$
$20$	8.60689	−	8.60689i	1.92456	−	1.92456i
$21$		0			0
$22$	−0.149816	+	0.149816i	−0.0319409	+	0.0319409i
$23$	0.681429	−	0.182588i	0.142088	−	0.0380723i	−0.187074	−	0.982346i	$-0.559900\pi$
$23$	0.681429	−	0.182588i	0.142088	−	0.0380723i	0.329162	+	0.944274i	$0.393234\pi$
$24$	3.38137	−	12.6195i	0.690220	−	2.57594i
$25$	−3.48271	+	2.01074i	−0.696541	+	0.402148i
$26$	9.13123	+	5.27192i	1.79078	+	1.03391i
$27$	1.26994	+	1.26994i	0.244400	+	0.244400i
$28$		0			0
$29$	1.07782	−	1.07782i	0.200146	−	0.200146i	−0.599917	−	0.800062i	$-0.704800\pi$
$29$	1.07782	−	1.07782i	0.200146	−	0.200146i	0.800062	+	0.599917i	$0.204800\pi$
$30$	−9.55925	+	16.5571i	−1.74527	+	3.02290i
$31$	−0.780485	−	0.209130i	−0.140179	−	0.0375609i	0.188047	−	0.982160i	$-0.439784\pi$
$31$	−0.780485	−	0.209130i	−0.140179	−	0.0375609i	−0.328226	+	0.944599i	$0.606451\pi$
$32$	0.453253	−	0.261686i	0.0801246	−	0.0462600i
$33$	0.111410	−	0.192967i	0.0193940	−	0.0335913i
$34$	−2.32818	+	9.87279i	−0.399280	+	1.69317i
$35$		0			0
$36$			14.9705i			2.49508i
$37$	−0.995688	−	3.71596i	−0.163690	−	0.610900i	−0.998204	−	0.0599125i	$-0.980918\pi$
$37$	−0.995688	−	3.71596i	−0.163690	−	0.610900i	0.834513	−	0.550988i	$-0.185749\pi$
$38$	8.43142	+	14.6036i	1.36776	+	2.36902i
$39$	−10.7108	−	2.86996i	−1.71510	−	0.459561i
$40$	−14.6498	+	3.92541i	−2.31634	+	0.620661i
$41$	−0.0255918	−	0.0255918i	−0.00399677	−	0.00399677i	0.705106	−	0.709102i	$-0.250900\pi$
$41$	−0.0255918	−	0.0255918i	−0.00399677	−	0.00399677i	−0.709102	+	0.705106i	$0.750900\pi$
$42$		0			0
$43$			8.49396i			1.29532i	0.761931	+	0.647658i	$0.224252\pi$
$43$			8.49396i			1.29532i	−0.761931	+	0.647658i	$0.775748\pi$
$44$	0.337110	−	0.0903285i	0.0508213	−	0.0136175i
$45$	2.87177	−	10.7176i	0.428098	−	1.59768i
$46$	−1.67644	−	0.449200i	−0.247177	−	0.0662310i
$47$	4.88296	−	8.45753i	0.712253	−	1.23366i	−0.251757	−	0.967790i	$-0.581008\pi$
$47$	4.88296	−	8.45753i	0.712253	−	1.23366i	0.964010	−	0.265867i	$-0.0856583\pi$
$48$	−7.89929	+	7.89929i	−1.14016	+	1.14016i
$49$		0			0
$50$	9.89358			1.39916
$51$	−0.322250	−	10.6629i	−0.0451240	−	1.49310i
$52$	−8.68408	−	15.0413i	−1.20427	−	2.08585i
$53$	10.2543	−	5.92031i	1.40853	−	0.813218i	0.413287	−	0.910601i	$-0.364380\pi$
$53$	10.2543	−	5.92031i	1.40853	−	0.813218i	0.995247	+	0.0973830i	$0.0310472\pi$
$54$	−1.14357	−	4.26785i	−0.155620	−	0.580780i
$55$	−0.258669			−0.0348790
$56$		0			0
$57$	−12.5400	−	12.5400i	−1.66096	−	1.66096i
$58$	−3.62219	+	0.970563i	−0.475617	+	0.127441i
$59$	−3.68791	+	2.12921i	−0.480125	+	0.277200i	−0.720468	−	0.693488i	$-0.756073\pi$
$59$	−3.68791	+	2.12921i	−0.480125	+	0.277200i	0.240344	+	0.970688i	$0.422740\pi$
$60$	27.2734	−	15.7463i	3.52098	−	2.03284i
$61$	2.43864	−	0.653430i	0.312235	−	0.0836632i	−0.0992985	−	0.995058i	$-0.531660\pi$
$61$	2.43864	−	0.653430i	0.312235	−	0.0836632i	0.411534	+	0.911394i	$0.364993\pi$
$62$	1.40564	+	1.40564i	0.178516	+	0.178516i
$63$		0			0
$64$	7.34787			0.918483
$65$	3.33170	+	12.4341i	0.413247	+	1.54226i
$66$	−0.474735	+	0.274088i	−0.0584358	+	0.0337380i
$67$	−2.46222	−	4.26468i	−0.300808	−	0.521014i	0.675512	−	0.737349i	$-0.263923\pi$
$67$	−2.46222	−	4.26468i	−0.300808	−	0.521014i	−0.976319	+	0.216335i	$0.930590\pi$
$68$	11.4527	−	12.1665i	1.38884	−	1.47540i
$69$	1.82526			0.219735
$70$		0			0
$71$	4.95688	−	4.95688i	0.588274	−	0.588274i	−0.348890	−	0.937164i	$-0.613441\pi$
$71$	4.95688	−	4.95688i	0.588274	−	0.588274i	0.937164	+	0.348890i	$0.113441\pi$
$72$	9.32682	−	16.1545i	1.09918	−	1.90383i
$73$	−3.68341	−	0.986967i	−0.431111	−	0.115516i	0.0367367	−	0.999325i	$-0.488304\pi$
$73$	−3.68341	−	0.986967i	−0.431111	−	0.115516i	−0.467848	+	0.883809i	$0.654970\pi$
$74$	−2.44957	+	9.14194i	−0.284757	+	1.06273i
$75$	−10.0503	+	2.69296i	−1.16050	+	0.310956i
$76$		−	27.7770i		−	3.18625i
$77$		0			0
$78$	19.2900	+	19.2900i	2.18416	+	2.18416i
$79$	−6.34401	+	1.69987i	−0.713757	+	0.191251i	−0.597384	−	0.801955i	$-0.703793\pi$
$79$	−6.34401	+	1.69987i	−0.713757	+	0.191251i	−0.116373	+	0.993206i	$0.537127\pi$
$80$	12.5267	+	3.35653i	1.40053	+	0.375271i
$81$	−3.21786	−	5.57350i	−0.357540	−	0.619278i
$82$	0.0230451	+	0.0860056i	0.00254491	+	0.00949773i
$83$			3.86659i			0.424413i	0.977225	+	0.212207i	$0.0680650\pi$
$83$			3.86659i			0.424413i	−0.977225	+	0.212207i	$0.931935\pi$
$84$		0			0
$85$	−10.5330	+	6.51319i	−1.14246	+	0.706454i
$86$	10.4483	−	18.0971i	1.12667	−	1.95146i
$87$	3.41537	−	1.97187i	0.366167	−	0.211406i
$88$	−0.420048	−	0.112552i	−0.0447773	−	0.0119980i
$89$	−2.52025	+	4.36520i	−0.267146	+	0.462710i	−0.968124	−	0.250473i	$-0.919414\pi$
$89$	−2.52025	+	4.36520i	−0.267146	+	0.462710i	0.700978	+	0.713183i	$0.252747\pi$
$90$	−19.3021	+	19.3021i	−2.03462	+	2.03462i
$91$		0			0
$92$	2.02155	+	2.02155i	0.210761	+	0.210761i
$93$	−1.81050	−	1.04529i	−0.187740	−	0.108392i
$94$	−20.8071	+	12.0130i	−2.14608	+	1.23904i
$95$	−5.32842	+	19.8859i	−0.546685	+	2.04025i
$96$	1.30798	−	0.350473i	0.133495	−	0.0357700i
$97$	6.55546	−	6.55546i	0.665606	−	0.665606i	−0.291090	−	0.956696i	$-0.594018\pi$
$97$	6.55546	−	6.55546i	0.665606	−	0.665606i	0.956696	+	0.291090i	$0.0940178\pi$
$98$		0			0
$99$	0.224960	−	0.224960i	0.0226093	−	0.0226093i
$100$	−14.1136	−	8.14852i	−1.41136	−	0.814852i
$101$	−1.25949	−	2.18150i	−0.125324	−	0.217068i	0.796535	−	0.604592i	$-0.206664\pi$
$101$	−1.25949	−	2.18150i	−0.125324	−	0.217068i	−0.921860	+	0.387524i	$0.873330\pi$
$102$	−12.4297	+	23.1145i	−1.23072	+	2.28867i
$103$	−2.93151	+	5.07753i	−0.288851	+	0.500304i	−0.973536	−	0.228535i	$-0.926606\pi$
$103$	−2.93151	+	5.07753i	−0.288851	+	0.500304i	0.684685	+	0.728839i	$0.259940\pi$
$104$			21.6412i			2.12209i
$105$		0			0
$106$	−29.1301			−2.82937
$107$	−0.212066	−	0.791440i	−0.0205012	−	0.0765114i	0.954917	−	0.296872i	$-0.0959434\pi$
$107$	−0.212066	−	0.791440i	−0.0205012	−	0.0765114i	−0.975419	+	0.220360i	$0.929277\pi$
$108$	−1.88372	+	7.03014i	−0.181261	+	0.676476i
$109$	−2.01814	+	7.53179i	−0.193303	+	0.721415i	0.799397	+	0.600803i	$0.205152\pi$
$109$	−2.01814	+	7.53179i	−0.193303	+	0.721415i	−0.992700	+	0.120612i	$0.961514\pi$
$110$	0.551116	+	0.318187i	0.0525468	+	0.0303379i
$111$		−	9.95348i		−	0.944742i
$112$		0			0
$113$	−10.7494	−	10.7494i	−1.01122	−	1.01122i	−0.999936	−	0.0112860i	$-0.996407\pi$
$113$	−10.7494	−	10.7494i	−1.01122	−	1.01122i	−0.0112860	−	0.999936i	$-0.503593\pi$
$114$	11.2921	+	42.1427i	1.05760	+	3.94702i
$115$	−1.05946	−	1.83504i	−0.0987954	−	0.171119i
$116$	5.96659	+	1.59874i	0.553984	+	0.148440i
$117$	−13.7112	−	7.91617i	−1.26760	−	0.731851i
$118$	10.4765			0.964441
$119$		0			0
$120$	−39.2406			−3.58216
$121$	9.51986	+	5.49629i	0.865441	+	0.499663i
$122$	−5.99949	−	1.60756i	−0.543168	−	0.145541i
$123$	−0.0468202	−	0.0810950i	−0.00422164	−	0.00731209i
$124$	−0.847500	−	3.16291i	−0.0761078	−	0.284038i
$125$	−2.07823	−	2.07823i	−0.185882	−	0.185882i
$126$		0			0
$127$			11.6441i			1.03324i	0.856214	+	0.516622i	$0.172811\pi$
$127$			11.6441i			1.03324i	−0.856214	+	0.516622i	$0.827189\pi$
$128$	−16.5617	−	9.56191i	−1.46386	−	0.845162i
$129$	−5.68793	+	21.2276i	−0.500794	+	1.86899i
$130$	8.19660	−	30.5901i	0.718889	−	2.68293i
$131$	5.14793	+	19.2123i	0.449777	+	1.67859i	0.703006	+	0.711184i	$0.251841\pi$
$131$	5.14793	+	19.2123i	0.449777	+	1.67859i	−0.253229	+	0.967406i	$0.581493\pi$
$132$	0.902976			0.0785939
$133$		0			0
$134$			12.1150i			1.04658i
$135$	2.69716	−	4.67162i	0.232135	−	0.402069i
$136$	−19.9383	+	5.99356i	−1.70970	+	0.513943i
$137$	3.21313	+	5.56531i	0.274517	+	0.475477i	0.970013	−	0.243053i	$-0.0781489\pi$
$137$	3.21313	+	5.56531i	0.274517	+	0.475477i	−0.695497	+	0.718529i	$0.744816\pi$
$138$	−3.88886	−	2.24523i	−0.331041	−	0.191127i
$139$	1.97504	−	1.97504i	0.167521	−	0.167521i	−0.618368	−	0.785889i	$-0.712206\pi$
$139$	1.97504	−	1.97504i	0.167521	−	0.167521i	0.785889	+	0.618368i	$0.212206\pi$
$140$		0			0
$141$	17.8667	−	17.8667i	1.50465	−	1.50465i
$142$	−16.6585	+	4.46362i	−1.39795	+	0.374579i
$143$	−0.0955286	+	0.356518i	−0.00798850	+	0.0298135i
$144$	−13.8134	+	7.97516i	−1.15111	+	0.664596i
$145$	−3.96488	−	2.28912i	−0.329265	−	0.190101i
$146$	6.63374	+	6.63374i	0.549013	+	0.549013i
$147$		0			0
$148$	11.0239	−	11.0239i	0.906158	−	0.906158i
$149$	6.28634	−	10.8883i	0.514997	−	0.892002i	−0.484851	−	0.874597i	$-0.661126\pi$
$149$	6.28634	−	10.8883i	0.514997	−	0.892002i	0.999849	−	0.0174050i	$-0.00554047\pi$
$150$	24.7255	+	6.62517i	2.01883	+	0.540943i
$151$	11.2201	−	6.47793i	0.913079	−	0.527166i	0.0316585	−	0.999499i	$-0.489921\pi$
$151$	11.2201	−	6.47793i	0.913079	−	0.527166i	0.881421	+	0.472332i	$0.156588\pi$
$152$	−17.3055	+	29.9739i	−1.40366	+	2.43121i
$153$	3.49593	−	14.8247i	0.282630	−	1.19851i
$154$		0			0
$155$			2.42695i			0.194937i
$156$	−11.6305	−	43.4055i	−0.931184	−	3.47522i
$157$	−1.44727	−	2.50675i	−0.115505	−	0.200060i	0.802477	−	0.596684i	$-0.203515\pi$
$157$	−1.44727	−	2.50675i	−0.115505	−	0.200060i	−0.917981	+	0.396623i	$0.870182\pi$
$158$	15.6074	+	4.18200i	1.24166	+	0.332702i
$159$	29.5914	−	7.92900i	2.34675	−	0.628811i
$160$	−1.11156	−	1.11156i	−0.0878768	−	0.0878768i
$161$		0			0
$162$			15.8331i			1.24396i
$163$	5.02270	−	1.34583i	0.393408	−	0.105413i	−0.0566914	−	0.998392i	$-0.518055\pi$
$163$	5.02270	−	1.34583i	0.393408	−	0.105413i	0.450100	+	0.892978i	$0.351388\pi$
$164$	0.0379607	−	0.141671i	0.00296423	−	0.0110627i
$165$	−0.646452	−	0.173216i	−0.0503262	−	0.0134849i
$166$	4.75626	−	8.23808i	0.369157	−	0.639399i
$167$	11.0613	−	11.0613i	0.855946	−	0.855946i	−0.134911	−	0.990858i	$-0.543075\pi$
$167$	11.0613	−	11.0613i	0.855946	−	0.855946i	0.990858	+	0.134911i	$0.0430750\pi$
$168$		0			0
$169$	5.36803			0.412926
$170$	30.4532	−	0.920347i	2.33565	−	0.0705874i
$171$	−12.6604	−	21.9285i	−0.968165	−	1.67691i
$172$	−29.8101	+	17.2109i	−2.27300	+	1.31232i
$173$	−4.21849	−	15.7436i	−0.320726	−	1.19697i	−0.918539	−	0.395330i	$-0.870630\pi$
$173$	−4.21849	−	15.7436i	−0.320726	−	1.19697i	0.597813	−	0.801635i	$-0.296036\pi$
$174$	−9.70230			−0.735530
$175$		0			0
$176$	0.262934	+	0.262934i	0.0198194	+	0.0198194i
$177$	−10.6424	+	2.85163i	−0.799934	+	0.214342i
$178$	10.7392	−	6.20028i	0.804936	−	0.464730i
$179$	−14.7184	+	8.49770i	−1.10011	+	0.635148i	−0.936249	−	0.351336i	$-0.885727\pi$
$179$	−14.7184	+	8.49770i	−1.10011	+	0.635148i	−0.163859	+	0.986484i	$0.552394\pi$
$180$	43.4329	−	11.6378i	3.23730	−	0.867432i
$181$	−7.97604	−	7.97604i	−0.592854	−	0.592854i	0.345547	−	0.938401i	$-0.387693\pi$
$181$	−7.97604	−	7.97604i	−0.592854	−	0.592854i	−0.938401	+	0.345547i	$0.887693\pi$
$182$		0			0
$183$	6.53207			0.482864
$184$	−0.921981	−	3.44088i	−0.0679694	−	0.253665i
$185$	−10.0068	+	5.77745i	−0.735717	+	0.424767i
$186$	2.57161	+	4.45417i	0.188560	+	0.326595i
$187$	−0.354921	+	0.0107263i	−0.0259544	+	0.000784387i
$188$	39.5763			2.88640
$189$		0			0
$190$	35.8142	−	35.8142i	2.59823	−	2.59823i
$191$	−2.64768	+	4.58591i	−0.191579	+	0.331825i	−0.945774	−	0.324826i	$-0.894694\pi$
$191$	−2.64768	+	4.58591i	−0.191579	+	0.331825i	0.754195	+	0.656651i	$0.228028\pi$
$192$	18.3634	+	4.92045i	1.32526	+	0.355103i
$193$	3.02549	−	11.2913i	0.217780	−	0.812765i	−0.767390	−	0.641181i	$-0.778445\pi$
$193$	3.02549	−	11.2913i	0.217780	−	0.812765i	0.985170	−	0.171584i	$-0.0548885\pi$
$194$	−22.0307	+	5.90312i	−1.58172	+	0.423819i
$195$			33.3056i			2.38507i
$196$		0			0
$197$	−8.06724	−	8.06724i	−0.574767	−	0.574767i	0.358690	−	0.933457i	$-0.383224\pi$
$197$	−8.06724	−	8.06724i	−0.574767	−	0.574767i	−0.933457	+	0.358690i	$0.883224\pi$
$198$	−0.756016	+	0.202574i	−0.0537277	+	0.0143963i
$199$	18.8782	+	5.05840i	1.33824	+	0.358580i	0.855781	−	0.517338i	$-0.173077\pi$
$199$	18.8782	+	5.05840i	1.33824	+	0.358580i	0.482459	+	0.875919i	$0.339744\pi$
$200$	10.1533	+	17.5860i	0.717944	+	1.24352i
$201$	−3.29762	−	12.3069i	−0.232596	−	0.868059i
$202$			6.19716i			0.436030i
$203$		0			0
$204$	36.7690	−	22.7366i	2.57435	−	1.59188i
$205$	−0.0543531	+	0.0941424i	−0.00379619	+	0.00657519i
$206$	12.4917	−	7.21206i	0.870335	−	0.502488i
$207$	2.51730	+	0.674507i	0.174964	+	0.0468815i
$208$	9.25245	−	16.0257i	0.641542	−	1.11118i
$209$	−0.417402	+	0.417402i	−0.0288723	+	0.0288723i
$210$		0			0
$211$	9.68185	+	9.68185i	0.666526	+	0.666526i	0.956910	−	0.290384i	$-0.0937831\pi$
$211$	9.68185	+	9.68185i	0.666526	+	0.666526i	−0.290384	+	0.956910i	$0.593783\pi$
$212$	41.5554	+	23.9920i	2.85404	+	1.64778i
$213$	15.7073	−	9.06862i	1.07625	−	0.621372i
$214$	−0.521720	+	1.94709i	−0.0356640	+	0.133100i
$215$	24.6430	−	6.60306i	1.68064	−	0.450325i
$216$	6.41257	−	6.41257i	0.436320	−	0.436320i
$217$		0			0
$218$	13.5646	−	13.5646i	0.918710	−	0.918710i
$219$	−8.54446	−	4.93315i	−0.577381	−	0.333351i
$220$	−0.524128	−	0.907816i	−0.0353367	−	0.0612050i
$221$	5.08706	+	16.9227i	0.342192	+	1.13835i
$222$	−12.2437	+	21.2067i	−0.821742	+	1.42330i
$223$			26.7496i			1.79129i	0.444772	+	0.895644i	$0.353285\pi$
$223$			26.7496i			1.79129i	−0.444772	+	0.895644i	$0.646715\pi$
$224$		0			0
$225$	−14.8559			−0.990396
$226$	9.67975	+	36.1253i	0.643888	+	2.40302i
$227$	−0.420439	+	1.56910i	−0.0279055	+	0.104145i	−0.978474	−	0.206370i	$-0.933835\pi$
$227$	−0.420439	+	1.56910i	−0.0279055	+	0.104145i	0.950568	+	0.310515i	$0.100502\pi$
$228$	18.6007	−	69.4188i	1.23186	−	4.59738i
$229$	21.6881	+	12.5217i	1.43319	+	0.827454i	0.997363	−	0.0725746i	$-0.0231215\pi$
$229$	21.6881	+	12.5217i	1.43319	+	0.827454i	0.435830	+	0.900029i	$0.356455\pi$
$230$			5.21294i			0.343731i
$231$		0			0
$232$	−5.44245	−	5.44245i	−0.357314	−	0.357314i
$233$	−2.15348	−	8.03690i	−0.141079	−	0.526515i	−0.999899	−	0.0142363i	$-0.995468\pi$
$233$	−2.15348	−	8.03690i	−0.141079	−	0.526515i	0.858819	−	0.512278i	$-0.171198\pi$
$234$	19.4752	+	33.7321i	1.27314	+	2.20514i
$235$	−28.3332	−	7.59186i	−1.84825	−	0.495238i
$236$	−14.9452	−	8.62863i	−0.972852	−	0.561676i
$237$	−16.9929			−1.10381
$238$		0			0
$239$	−11.3488			−0.734093			−0.367046	−	0.930203i	$-0.619631\pi$
$239$	−11.3488			−0.734093			−0.367046	+	0.930203i	$0.619631\pi$
$240$	29.0584	+	16.7769i	1.87571	+	1.08294i
$241$	6.38604	+	1.71113i	0.411361	+	0.110224i	0.458564	−	0.888661i	$-0.348364\pi$
$241$	6.38604	+	1.71113i	0.411361	+	0.110224i	−0.0472028	+	0.998885i	$0.515031\pi$
$242$	−13.5219	−	23.4206i	−0.869219	−	1.50553i
$243$	−5.70413	−	21.2881i	−0.365920	−	1.36563i
$244$	7.23454	+	7.23454i	0.463144	+	0.463144i
$245$		0			0
$246$			0.230372i			0.0146880i
$247$	25.4405	+	14.6881i	1.61874	+	0.934580i
$248$	−1.05601	+	3.94107i	−0.0670565	+	0.250258i
$249$	−2.58924	+	9.66317i	−0.164086	+	0.612378i
$250$	1.87142	+	6.98423i	0.118359	+	0.441722i
$251$	−12.3828			−0.781595			−0.390798	−	0.920477i	$-0.627801\pi$
$251$	−12.3828			−0.781595			−0.390798	+	0.920477i	$0.627801\pi$
$252$		0			0
$253$		−	0.0607551i		−	0.00381964i
$254$	14.3233	−	24.8086i	0.898721	−	1.55663i
$255$	−30.6849	+	9.22405i	−1.92157	+	0.577633i
$256$	16.1762	+	28.0180i	1.01101	+	1.75112i
$257$	23.7024	+	13.6846i	1.47852	+	0.853623i	0.999705	−	0.0242943i	$-0.00773389\pi$
$257$	23.7024	+	13.6846i	1.47852	+	0.853623i	0.478813	+	0.877917i	$0.341067\pi$
$258$	38.2305	−	38.2305i	2.38013	−	2.38013i
$259$		0			0
$260$	−36.8874	+	36.8874i	−2.28766	+	2.28766i
$261$	5.43898	−	1.45737i	0.336665	−	0.0902090i
$262$	12.6649	−	47.2659i	0.782437	−	2.92010i
$263$	16.1711	−	9.33639i	0.997153	−	0.575706i	0.0897480	−	0.995965i	$-0.471394\pi$
$263$	16.1711	−	9.33639i	0.997153	−	0.575706i	0.907405	+	0.420258i	$0.138061\pi$
$264$	−0.974392	−	0.562565i	−0.0599697	−	0.0346235i
$265$	−25.1477	−	25.1477i	−1.54481	−	1.54481i
$266$		0			0
$267$	−9.22160	+	9.22160i	−0.564353	+	0.564353i
$268$	9.97812	−	17.2826i	0.609511	−	1.05570i
$269$	−0.179498	−	0.0480962i	−0.0109442	−	0.00293248i	0.253343	−	0.967377i	$-0.418470\pi$
$269$	−0.179498	−	0.0480962i	−0.0109442	−	0.00293248i	−0.264287	+	0.964444i	$0.585137\pi$
$270$	−11.4930	+	6.63551i	−0.699444	+	0.403824i
$271$	2.63316	−	4.56076i	0.159953	−	0.277047i	−0.774899	−	0.632086i	$-0.782199\pi$
$271$	2.63316	−	4.56076i	0.159953	−	0.277047i	0.934852	+	0.355039i	$0.115532\pi$
$272$	17.3272	+	4.08606i	1.05061	+	0.247754i
$273$		0			0
$274$		−	15.8098i		−	0.955104i
$275$	0.0896372	+	0.334531i	0.00540533	+	0.0201730i
$276$	3.69842	+	6.40586i	0.222619	+	0.385587i
$277$	12.2787	+	3.29007i	0.737755	+	0.197681i	0.608080	−	0.793876i	$-0.291940\pi$
$277$	12.2787	+	3.29007i	0.737755	+	0.197681i	0.129675	+	0.991557i	$0.458607\pi$
$278$	−6.63746	+	1.77850i	−0.398088	+	0.106667i
$279$	−2.11067	−	2.11067i	−0.126362	−	0.126362i
$280$		0			0
$281$		−	5.52979i		−	0.329879i	−0.986304	−	0.164940i	$-0.947257\pi$
$281$		−	5.52979i		−	0.329879i	0.986304	−	0.164940i	$-0.0527429\pi$
$282$	−60.0443	+	16.0888i	−3.57558	+	0.958075i
$283$	2.45155	−	9.14931i	0.145730	−	0.543870i	−0.853992	−	0.520286i	$-0.825825\pi$
$283$	2.45155	−	9.14931i	0.145730	−	0.543870i	0.999722	−	0.0235844i	$-0.00750785\pi$
$284$	27.4404	+	7.35263i	1.62829	+	0.436298i
$285$	−26.6330	+	46.1297i	−1.57760	+	2.73249i
$286$	0.642080	−	0.642080i	0.0379670	−	0.0379670i
$287$		0			0
$288$	1.93341			0.113927
$289$	−14.1823	+	9.37355i	−0.834251	+	0.551385i
$290$	5.63166	+	9.75432i	0.330702	+	0.572793i
$291$	20.7729	−	11.9932i	1.21773	−	0.703055i
$292$	−3.99968	−	14.9270i	−0.234064	−	0.873537i
$293$	4.68516			0.273710			0.136855	−	0.990591i	$-0.456301\pi$
$293$	4.68516			0.273710			0.136855	+	0.990591i	$0.456301\pi$
$294$		0			0
$295$	9.04427	+	9.04427i	0.526578	+	0.526578i
$296$	−18.7638	+	5.02774i	−1.09062	+	0.292231i
$297$	0.133947	−	0.0773346i	0.00777242	−	0.00448741i
$298$	−26.7871	+	15.4656i	−1.55174	+	0.895895i
$299$	−2.92046	+	0.782536i	−0.168895	+	0.0452552i
$300$	−29.8154	−	29.8154i	−1.72140	−	1.72140i
$301$		0			0
$302$	−31.8738			−1.83413
$303$	−1.68682	−	6.29530i	−0.0969054	−	0.361656i
$304$	25.6300	−	14.7975i	1.46998	−	0.848696i
$305$	−3.79151	−	6.56709i	−0.217101	−	0.376030i
$306$	−25.6841	+	27.2849i	−1.46826	+	1.55978i
$307$	1.84567			0.105338			0.0526689	−	0.998612i	$-0.483227\pi$
$307$	1.84567			0.105338			0.0526689	+	0.998612i	$0.483227\pi$
$308$		0			0
$309$	−10.7264	+	10.7264i	−0.610204	+	0.610204i
$310$	2.98536	−	5.17080i	0.169557	−	0.293682i
$311$	27.4132	+	7.34536i	1.55446	+	0.416517i	0.930905	−	0.365261i	$-0.119020\pi$
$311$	27.4132	+	7.34536i	1.55446	+	0.416517i	0.623557	+	0.781778i	$0.285687\pi$
$312$	−14.4919	+	54.0844i	−0.820441	+	3.06193i
$313$	21.0973	−	5.65300i	1.19249	−	0.319526i	0.392619	−	0.919701i	$-0.371569\pi$
$313$	21.0973	−	5.65300i	1.19249	−	0.319526i	0.799869	+	0.600175i	$0.204902\pi$
$314$			7.12110i			0.401867i
$315$		0			0
$316$	−18.8203	−	18.8203i	−1.05873	−	1.05873i
$317$	29.0857	−	7.79348i	1.63361	−	0.437725i	0.678653	−	0.734459i	$-0.262564\pi$
$317$	29.0857	−	7.79348i	1.63361	−	0.437725i	0.954960	+	0.296733i	$0.0958972\pi$
$318$	−72.8003	−	19.5068i	−4.08244	−	1.09389i
$319$	−0.0656351	−	0.113683i	−0.00367486	−	0.00636504i
$320$	−5.71211	−	21.3179i	−0.319317	−	1.19171i
$321$		−	2.11993i		−	0.118323i
$322$		0			0
$323$	−6.48654	+	27.5066i	−0.360921	+	1.53051i
$324$	13.0404	−	22.5866i	0.724465	−	1.25481i
$325$	14.9262	−	8.61762i	0.827954	−	0.478020i
$326$	−12.3568	−	3.31098i	−0.684378	−	0.183378i
$327$	−10.0872	+	17.4716i	−0.557825	+	0.966182i
$328$	−0.129226	+	0.129226i	−0.00713532	+	0.00713532i
$329$		0			0
$330$	1.16425	+	1.16425i	0.0640896	+	0.0640896i
$331$	−21.9629	−	12.6803i	−1.20719	−	0.696971i	−0.245045	−	0.969512i	$-0.578803\pi$
$331$	−21.9629	−	12.6803i	−1.20719	−	0.696971i	−0.962144	+	0.272541i	$0.912136\pi$
$332$	−13.5700	+	7.83467i	−0.744753	+	0.429983i
$333$	3.67822	−	13.7273i	0.201565	−	0.752251i
$334$	−37.1733	+	9.96055i	−2.03403	+	0.545017i
$335$	−10.4588	+	10.4588i	−0.571423	+	0.571423i
$336$		0			0
$337$	−4.86208	+	4.86208i	−0.264854	+	0.264854i	−0.827023	−	0.562168i	$-0.809967\pi$
$337$	−4.86208	+	4.86208i	−0.264854	+	0.264854i	0.562168	+	0.827023i	$0.309967\pi$
$338$	−11.4370	−	6.60317i	−0.622092	−	0.359165i
$339$	−19.6661	−	34.0627i	−1.06812	−	1.85003i
$340$	−44.2009	−	23.7688i	−2.39713	−	1.28905i
$341$	−0.0347934	+	0.0602639i	−0.00188417	+	0.00326348i
$342$			62.2938i			3.36846i
$343$		0			0
$344$	42.8903			2.31249
$345$	−1.41892	−	5.29550i	−0.0763923	−	0.285100i
$346$	−10.3783	+	38.7322i	−0.557938	+	2.08225i
$347$	1.39391	−	5.20216i	0.0748292	−	0.279266i	−0.918365	−	0.395734i	$-0.870490\pi$
$347$	1.39391	−	5.20216i	0.0748292	−	0.279266i	0.993195	+	0.116467i	$0.0371570\pi$
$348$	13.8408	+	7.99098i	0.741944	+	0.428362i
$349$			9.88628i			0.529201i	0.964358	+	0.264600i	$0.0852400\pi$
$349$			9.88628i			0.529201i	−0.964358	+	0.264600i	$0.914760\pi$
$350$		0			0
$351$	−5.44270	−	5.44270i	−0.290510	−	0.290510i
$352$	−0.0116657	−	0.0435371i	−0.000621786	−	0.00232054i
$353$	−10.7543	−	18.6269i	−0.572392	−	0.991412i	−0.996320	−	0.0857157i	$-0.972682\pi$
$353$	−10.7543	−	18.6269i	−0.572392	−	0.991412i	0.423928	−	0.905696i	$-0.360651\pi$
$354$	26.1823	+	7.01553i	1.39157	+	0.372871i
$355$	−18.2345	−	10.5277i	−0.967785	−	0.558751i
$356$	−20.4266			−1.08261
$357$		0			0
$358$	41.8118			2.20982
$359$	16.1219	+	9.30800i	0.850883	+	0.491257i	0.860949	−	0.508692i	$-0.169871\pi$
$359$	16.1219	+	9.30800i	0.850883	+	0.491257i	−0.0100658	+	0.999949i	$0.503204\pi$
$360$	−54.1185	−	14.5010i	−2.85230	−	0.764271i
$361$	13.9908	+	24.2327i	0.736356	+	1.27541i
$362$	7.18234	+	26.8048i	0.377495	+	1.40883i
$363$	20.1109	+	20.1109i	1.05555	+	1.05555i
$364$		0			0
$365$			11.4537i			0.599514i
$366$	−13.9171	−	8.03504i	−0.727458	−	0.419998i
$367$	−2.14584	+	8.00839i	−0.112012	+	0.418034i	−0.999046	−	0.0436697i	$-0.986095\pi$
$367$	−2.14584	+	8.00839i	−0.112012	+	0.418034i	0.887034	+	0.461704i	$0.152762\pi$
$368$	−0.788366	+	2.94222i	−0.0410964	+	0.153374i
$369$	−0.0346040	−	0.129144i	−0.00180141	−	0.00672296i
$370$	28.4272			1.47786
$371$		0			0
$372$		−	8.47210i		−	0.439258i
$373$	11.4747	−	19.8748i	0.594140	−	1.02908i	−0.399528	−	0.916721i	$-0.630826\pi$
$373$	11.4747	−	19.8748i	0.594140	−	1.02908i	0.993668	−	0.112359i	$-0.0358406\pi$
$374$	0.769383	+	0.413732i	0.0397838	+	0.0213936i
$375$	−3.80211	−	6.58546i	−0.196340	−	0.340071i
$376$	−42.7064	−	24.6566i	−2.20241	−	1.27156i
$377$	−4.61930	+	4.61930i	−0.237906	+	0.237906i
$378$		0			0
$379$	18.4121	−	18.4121i	0.945764	−	0.945764i	−0.0528386	−	0.998603i	$-0.516827\pi$
$379$	18.4121	−	18.4121i	0.945764	−	0.945764i	0.998603	+	0.0528386i	$0.0168269\pi$
$380$	−80.5877	+	21.5934i	−4.13406	+	1.10772i
$381$	−7.79737	+	29.1002i	−0.399472	+	1.49085i
$382$	11.2822	−	6.51377i	0.577246	−	0.333273i
$383$	4.21533	+	2.43372i	0.215393	+	0.124357i	0.603815	−	0.797124i	$-0.293646\pi$
$383$	4.21533	+	2.43372i	0.215393	+	0.124357i	−0.388422	+	0.921482i	$0.626980\pi$
$384$	−34.9871	−	34.9871i	−1.78543	−	1.78543i
$385$		0			0
$386$	−20.3354	+	20.3354i	−1.03504	+	1.03504i
$387$	−15.6890	+	27.1741i	−0.797514	+	1.38134i
$388$	36.2898	+	9.72382i	1.84233	+	0.493652i
$389$	−2.56003	+	1.47803i	−0.129799	+	0.0749392i	−0.563493	−	0.826121i	$-0.690543\pi$
$389$	−2.56003	+	1.47803i	−0.129799	+	0.0749392i	0.433695	+	0.901060i	$0.357210\pi$
$390$	40.9690	−	70.9603i	2.07454	−	3.59322i
$391$	−1.52979	−	2.47394i	−0.0773647	−	0.125112i
$392$		0			0
$393$			51.4617i			2.59590i
$394$	7.26446	+	27.1113i	0.365978	+	1.36585i
$395$	9.86346	+	17.0840i	0.496284	+	0.859590i
$396$	1.24533	+	0.333686i	0.0625804	+	0.0167684i
$397$	−12.8496	+	3.44304i	−0.644903	+	0.172801i	−0.566423	−	0.824114i	$-0.691673\pi$
$397$	−12.8496	+	3.44304i	−0.644903	+	0.172801i	−0.0784798	+	0.996916i	$0.525007\pi$
$398$	−33.9992	−	33.9992i	−1.70423	−	1.70423i
$399$		0			0
$400$		−	17.3637i		−	0.868183i
$401$	23.6059	−	6.32519i	1.17882	−	0.315865i	0.384364	−	0.923182i	$-0.374421\pi$
$401$	23.6059	−	6.32519i	1.17882	−	0.315865i	0.794460	+	0.607317i	$0.207754\pi$
$402$	−8.11273	+	30.2771i	−0.404626	+	1.51009i
$403$	3.34500	+	0.896290i	0.166626	+	0.0446474i
$404$	5.10408	−	8.84053i	0.253938	−	0.439833i
$405$	−13.6685	+	13.6685i	−0.679194	+	0.679194i
$406$		0			0
$407$	−0.331309			−0.0164224
$408$	−53.8422	+	1.62720i	−2.66559	+	0.0805586i
$409$	17.0770	+	29.5782i	0.844402	+	1.46255i	0.886139	+	0.463419i	$0.153377\pi$
$409$	17.0770	+	29.5782i	0.844402	+	1.46255i	−0.0417373	+	0.999129i	$0.513289\pi$
$410$	0.231607	−	0.133719i	0.0114383	−	0.00660389i
$411$	4.30331	+	16.0602i	0.212267	+	0.792190i
$412$	−23.7599			−1.17057
$413$		0			0
$414$	−4.53360	−	4.53360i	−0.222814	−	0.222814i
$415$	11.2179	−	3.00582i	0.550664	−	0.147550i
$416$	−1.94255	+	1.12153i	−0.0952414	+	0.0549876i
$417$	6.25848	−	3.61334i	0.306479	−	0.176946i
$418$	1.40275	−	0.375866i	0.0686108	−	0.0183842i
$419$	14.4175	+	14.4175i	0.704341	+	0.704341i	0.965339	−	0.260999i	$-0.0840518\pi$
$419$	14.4175	+	14.4175i	0.704341	+	0.704341i	−0.260999	+	0.965339i	$0.584052\pi$
$420$		0			0
$421$	−13.3004			−0.648223			−0.324111	−	0.946019i	$-0.605065\pi$
$421$	−13.3004			−0.648223			−0.324111	+	0.946019i	$0.605065\pi$
$422$	−8.71840	−	32.5375i	−0.424405	−	1.58390i
$423$	31.2433	−	18.0384i	1.51910	−	0.877055i
$424$	−29.8947	−	51.7791i	−1.45181	−	2.51462i
$425$	12.0734	+	11.3650i	0.585644	+	0.551284i
$426$	−44.6209			−2.16189
$427$		0			0
$428$	2.34791	−	2.34791i	0.113491	−	0.113491i
$429$	−0.477480	+	0.827019i	−0.0230529	+	0.0399288i
$430$	−60.6262	−	16.2447i	−2.92365	−	0.783390i
$431$	−2.22956	+	8.32083i	−0.107394	+	0.400800i	−0.998606	−	0.0527874i	$-0.983189\pi$
$431$	−2.22956	+	8.32083i	−0.107394	+	0.400800i	0.891212	+	0.453588i	$0.149856\pi$
$432$	−7.49026	+	2.00701i	−0.360375	+	0.0965623i
$433$			0.475114i			0.0228325i	0.999935	+	0.0114163i	$0.00363399\pi$
$433$			0.475114i			0.0228325i	−0.999935	+	0.0114163i	$0.996366\pi$
$434$		0			0
$435$	−8.37590	−	8.37590i	−0.401594	−	0.401594i
$436$	−30.5226	+	8.17850i	−1.46177	+	0.391679i
$437$	−4.67072	−	1.25152i	−0.223431	−	0.0598681i
$438$	12.1364	+	21.0209i	0.579902	+	1.00442i
$439$	−5.05162	−	18.8529i	−0.241100	−	0.899799i	−0.975303	−	0.220869i	$-0.929111\pi$
$439$	−5.05162	−	18.8529i	−0.241100	−	0.899799i	0.734203	−	0.678930i	$-0.237556\pi$
$440$			1.30615i			0.0622684i
$441$		0			0
$442$	9.97810	−	42.3128i	0.474610	−	2.01261i
$443$	−8.89023	+	15.3983i	−0.422388	+	0.731597i	−0.996172	−	0.0874092i	$-0.972141\pi$
$443$	−8.89023	+	15.3983i	−0.422388	+	0.731597i	0.573785	+	0.819006i	$0.305475\pi$
$444$	34.9324	−	20.1682i	1.65782	−	0.957141i
$445$	14.6237	+	3.91840i	0.693229	+	0.185750i
$446$	32.9045	−	56.9922i	1.55807	−	2.69866i
$447$	23.0017	−	23.0017i	1.08795	−	1.08795i
$448$		0			0
$449$	−22.2726	−	22.2726i	−1.05111	−	1.05111i	−0.998622	−	0.0524889i	$-0.983285\pi$
$449$	−22.2726	−	22.2726i	−1.05111	−	1.05111i	−0.0524889	−	0.998622i	$-0.516715\pi$
$450$	31.6518	+	18.2742i	1.49208	+	0.861452i
$451$	−0.00269931	+	0.00155845i	−0.000127105	+	7.33843e-5i
$452$	15.9448	−	59.5069i	0.749981	−	2.79897i
$453$	32.3786	−	8.67581i	1.52128	−	0.407625i
$454$	2.82591	−	2.82591i	0.132627	−	0.132627i
$455$		0			0
$456$	−63.3207	+	63.3207i	−2.96526	+	2.96526i
$457$	−30.7772	−	17.7692i	−1.43970	−	0.831209i	−0.441868	−	0.897080i	$-0.645684\pi$
$457$	−30.7772	−	17.7692i	−1.43970	−	0.831209i	−0.997828	+	0.0658713i	$0.979017\pi$
$458$	−30.8056	−	53.3568i	−1.43945	−	2.49320i
$459$	3.50707	−	6.52180i	0.163696	−	0.304411i
$460$	4.29347	−	7.43650i	0.200184	−	0.346729i
$461$		−	0.834154i		−	0.0388504i	−0.999811	−	0.0194252i	$-0.993816\pi$
$461$		−	0.834154i		−	0.0388504i	0.999811	−	0.0194252i	$-0.00618362\pi$
$462$		0			0
$463$	24.3516			1.13172			0.565858	−	0.824503i	$-0.308545\pi$
$463$	24.3516			1.13172			0.565858	+	0.824503i	$0.308545\pi$
$464$	1.70338	+	6.35710i	0.0790774	+	0.295121i
$465$	−1.62519	+	6.06529i	−0.0753663	+	0.281271i
$466$	−5.29795	+	19.7722i	−0.245423	+	0.915931i
$467$	−20.5981	−	11.8923i	−0.953168	−	0.550312i	−0.0591044	−	0.998252i	$-0.518824\pi$
$467$	−20.5981	−	11.8923i	−0.953168	−	0.550312i	−0.894064	+	0.447940i	$0.852158\pi$
$468$		−	64.1605i		−	2.96582i
$469$		0			0
$470$	51.0275	+	51.0275i	2.35372	+	2.35372i
$471$	−1.93831	−	7.23388i	−0.0893127	−	0.333319i
$472$	10.7515	+	18.6221i	0.494878	+	0.857153i
$473$	0.706577	+	0.189327i	0.0324885	+	0.00870526i
$474$	36.2048	+	20.9028i	1.66294	+	0.960098i
$475$	27.5645			1.26474
$476$		0			0
$477$	43.7410			2.00276
$478$	24.1795	+	13.9601i	1.10595	+	0.638518i
$479$	−28.1500	−	7.54277i	−1.28621	−	0.344638i	−0.449988	−	0.893035i	$-0.648572\pi$
$479$	−28.1500	−	7.54277i	−1.28621	−	0.344638i	−0.836218	+	0.548397i	$0.815238\pi$
$480$	−2.03361	−	3.52231i	−0.0928210	−	0.160771i
$481$	4.26732	+	15.9258i	0.194573	+	0.726156i
$482$	−11.5011	−	11.5011i	−0.523862	−	0.523862i
$483$		0			0
$484$			44.5474i			2.02488i
$485$	−24.1150	−	13.9228i	−1.09501	−	0.632203i
$486$	−14.0332	+	52.3726i	−0.636559	+	2.37567i
$487$	6.43003	−	23.9972i	0.291373	−	1.08742i	−0.652683	−	0.757631i	$-0.726357\pi$
$487$	6.43003	−	23.9972i	0.291373	−	1.08742i	0.944056	−	0.329786i	$-0.106977\pi$
$488$	−3.29950	−	12.3139i	−0.149362	−	0.557425i
$489$	13.4537			0.608396
$490$		0			0
$491$			16.3483i			0.737790i	0.929471	+	0.368895i	$0.120264\pi$
$491$			16.3483i			0.737790i	−0.929471	+	0.368895i	$0.879736\pi$
$492$	0.189739	−	0.328637i	0.00855408	−	0.0148161i
$493$	−5.53515	−	2.97650i	−0.249291	−	0.134055i
$494$	−36.1353	−	62.5882i	−1.62581	−	2.81598i
$495$	−0.827541	−	0.477781i	−0.0371952	−	0.0214747i
$496$	2.46696	−	2.46696i	0.110770	−	0.110770i
$497$		0			0
$498$	17.4032	−	17.4032i	0.779854	−	0.779854i
$499$	−22.9004	+	6.13613i	−1.02516	+	0.274691i	−0.731951	−	0.681357i	$-0.761390\pi$
$499$	−22.9004	+	6.13613i	−1.02516	+	0.274691i	−0.293210	+	0.956048i	$0.594723\pi$
$500$	3.08267	−	11.5047i	0.137861	−	0.514504i
$501$	35.0508	−	20.2366i	1.56595	−	0.904104i
$502$	26.3825	+	15.2320i	1.17751	+	0.679836i
$503$	9.37050	+	9.37050i	0.417810	+	0.417810i	0.884448	−	0.466638i	$-0.154535\pi$
$503$	9.37050	+	9.37050i	0.417810	+	0.417810i	−0.466638	+	0.884448i	$0.654535\pi$
$504$		0			0
$505$	−5.34994	+	5.34994i	−0.238069	+	0.238069i
$506$	−0.0747342	+	0.129444i	−0.00332234	+	0.00575447i
$507$	13.4155	+	3.59467i	0.595803	+	0.159645i
$508$	−40.8656	+	23.5938i	−1.81312	+	1.04680i
$509$	−11.6255	+	20.1359i	−0.515290	+	0.892509i	0.484552	+	0.874762i	$0.338983\pi$
$509$	−11.6255	+	20.1359i	−0.515290	+	0.892509i	−0.999843	+	0.0177468i	$0.994351\pi$
$510$	76.7232	+	18.0927i	3.39736	+	0.801158i
$511$		0			0
$512$		−	41.3451i		−	1.82721i
$513$	−3.18609	−	11.8906i	−0.140669	−	0.524984i
$514$	−33.6666	−	58.3123i	−1.48497	−	2.57205i
$515$	17.0100	+	4.55782i	0.749551	+	0.200842i
$516$	−86.0249	+	23.0503i	−3.78703	+	1.01473i
$517$	−0.594708	−	0.594708i	−0.0261552	−	0.0261552i
$518$		0			0
$519$		−	42.1705i		−	1.85108i
$520$	62.7861	−	16.8235i	2.75335	−	0.737759i
$521$	2.94432	−	10.9884i	0.128993	−	0.481409i	−0.870957	−	0.491358i	$-0.836501\pi$
$521$	2.94432	−	10.9884i	0.128993	−	0.481409i	0.999950	+	0.00994984i	$0.00316718\pi$
$522$	−13.3809	−	3.58540i	−0.585666	−	0.156929i
$523$	22.0552	−	38.2008i	0.964407	−	1.67040i	0.253208	−	0.967412i	$-0.418514\pi$
$523$	22.0552	−	38.2008i	0.964407	−	1.67040i	0.711199	−	0.702991i	$-0.248152\pi$
$524$	−56.9960	+	56.9960i	−2.48988	+	2.48988i
$525$		0			0
$526$	−45.9384			−2.00301
$527$	0.100639	+	3.33002i	0.00438390	+	0.145058i
$528$	0.481037	+	0.833181i	0.0209345	+	0.0362595i
$529$	−19.4876	+	11.2512i	−0.847286	+	0.489181i
$530$	22.6453	+	84.5132i	0.983647	+	3.67102i
$531$	−15.7313			−0.682678
$532$		0			0
$533$	0.109681	+	0.109681i	0.00475082	+	0.00475082i
$534$	30.9908	−	8.30395i	1.34110	−	0.359347i
$535$	−2.13130	+	1.23050i	−0.0921439	+	0.0531993i
$536$	−21.5346	+	12.4330i	−0.930152	+	0.537023i
$537$	−42.4739	+	11.3809i	−1.83289	+	0.491120i
$538$	0.323271	+	0.323271i	0.0139372	+	0.0139372i
$539$		0			0
$540$	21.8605			0.940725
$541$	6.59565	+	24.6153i	0.283569	+	1.05829i	0.949879	+	0.312619i	$0.101206\pi$
$541$	6.59565	+	24.6153i	0.283569	+	1.05829i	−0.666310	+	0.745675i	$0.732127\pi$
$542$	−11.2203	+	6.47805i	−0.481954	+	0.278256i
$543$	−14.5922	−	25.2744i	−0.626210	−	1.08463i
$544$	−1.57127	−	1.47909i	−0.0673679	−	0.0634154i
$545$	23.4204			1.00322
$546$		0			0
$547$	1.86454	−	1.86454i	0.0797218	−	0.0797218i	−0.666121	−	0.745843i	$-0.732047\pi$
$547$	1.86454	−	1.86454i	0.0797218	−	0.0797218i	0.745843	+	0.666121i	$0.232047\pi$
$548$	−13.0212	+	22.5534i	−0.556238	+	0.963433i
$549$	9.00867	+	2.41387i	0.384481	+	0.103021i
$550$	0.220524	−	0.823006i	0.00940317	−	0.0350931i
$551$	−10.0918	+	2.70408i	−0.429924	+	0.115198i
$552$		−	9.21666i		−	0.392287i
$553$		0			0
$554$	−22.1137	−	22.1137i	−0.939520	−	0.939520i
$555$	−28.8774	+	7.73767i	−1.22578	+	0.328446i
$556$	10.9334	+	2.92961i	0.463682	+	0.124243i
$557$	−9.95779	−	17.2474i	−0.421925	−	0.730796i	0.574203	−	0.818713i	$-0.305312\pi$
$557$	−9.95779	−	17.2474i	−0.421925	−	0.730796i	−0.996128	+	0.0879173i	$0.971979\pi$
$558$	1.90063	+	7.09326i	0.0804602	+	0.300282i
$559$		−	36.4034i		−	1.53970i
$560$		0			0
$561$	−0.894182	−	0.210864i	−0.0377524	−	0.00890269i
$562$	−6.80214	+	11.7817i	−0.286931	+	0.496979i
$563$	11.9951	−	6.92536i	0.505532	−	0.291869i	−0.225463	−	0.974252i	$-0.572390\pi$
$563$	11.9951	−	6.92536i	0.505532	−	0.291869i	0.730995	+	0.682383i	$0.239056\pi$
$564$	98.9070	+	26.5020i	4.16473	+	1.11594i
$565$	−22.8302	+	39.5431i	−0.960474	+	1.66359i
$566$	−16.4777	+	16.4777i	−0.692610	+	0.692610i
$567$		0			0
$568$	−25.0298	−	25.0298i	−1.05023	−	1.05023i
$569$	−27.8980	−	16.1069i	−1.16954	−	0.675236i	−0.215971	−	0.976400i	$-0.569292\pi$
$569$	−27.8980	−	16.1069i	−1.16954	−	0.675236i	−0.953572	+	0.301164i	$0.902625\pi$
$570$	113.487	−	65.5220i	4.75347	−	2.74442i
$571$	−12.2710	+	45.7961i	−0.513527	+	1.91651i	−0.135263	+	0.990810i	$0.543188\pi$
$571$	−12.2710	+	45.7961i	−0.513527	+	1.91651i	−0.378264	+	0.925698i	$0.623479\pi$
$572$	−1.44479	+	0.387129i	−0.0604095	+	0.0161867i
$573$	−9.68785	+	9.68785i	−0.404716	+	0.404716i
$574$		0			0
$575$	−2.00608	+	2.00608i	−0.0836592	+	0.0836592i
$576$	23.5075	+	13.5720i	0.979478	+	0.565502i
$577$	21.4895	+	37.2209i	0.894619	+	1.54953i	0.834275	+	0.551348i	$0.185886\pi$
$577$	21.4895	+	37.2209i	0.894619	+	1.54953i	0.0603441	+	0.998178i	$0.480780\pi$
$578$	41.7468	−	2.52562i	1.73644	−	0.105052i
$579$	15.1223	−	26.1926i	0.628460	−	1.08853i
$580$		−	18.5533i		−	0.770385i
$581$		0			0
$582$	−59.0110			−2.44608
$583$	−0.263923	−	0.984973i	−0.0109306	−	0.0407934i
$584$	−4.98370	+	18.5994i	−0.206227	+	0.769650i
$585$	−12.3078	+	45.9333i	−0.508865	+	1.89911i
$586$	−9.98212	−	5.76318i	−0.412357	−	0.238075i
$587$		−	22.7031i		−	0.937056i	−0.883449	−	0.468528i	$-0.844785\pi$
$587$		−	22.7031i		−	0.937056i	0.883449	−	0.468528i	$-0.155215\pi$
$588$		0			0
$589$	3.91624	+	3.91624i	0.161366	+	0.161366i
$590$	−8.14426	−	30.3948i	−0.335294	−	1.25133i
$591$	−14.7590	−	25.5634i	−0.607105	−	1.05154i
$592$	16.0445	+	4.29911i	0.659425	+	0.176692i
$593$	−15.1456	−	8.74433i	−0.621956	−	0.359087i	0.155674	−	0.987808i	$-0.450245\pi$
$593$	−15.1456	−	8.74433i	−0.621956	−	0.359087i	−0.777630	+	0.628722i	$0.783578\pi$
$594$	−0.380514			−0.0156127
$595$		0			0
$596$	50.9508			2.08702
$597$	43.7920	+	25.2833i	1.79229	+	1.03478i
$598$	7.18487	+	1.92518i	0.293811	+	0.0787265i
$599$	−4.21111	−	7.29385i	−0.172061	−	0.298019i	0.767079	−	0.641553i	$-0.221709\pi$
$599$	−4.21111	−	7.29385i	−0.172061	−	0.298019i	−0.939140	+	0.343534i	$0.888376\pi$
$600$	13.5981	+	50.7489i	0.555142	+	2.07182i
$601$	−12.1106	−	12.1106i	−0.494002	−	0.494002i	0.415563	−	0.909565i	$-0.363585\pi$
$601$	−12.1106	−	12.1106i	−0.494002	−	0.494002i	−0.909565	+	0.415563i	$0.863585\pi$
$602$		0			0
$603$		−	18.1916i		−	0.740818i
$604$	45.4694	+	26.2518i	1.85012	+	1.06817i
$605$	8.54545	−	31.8921i	0.347422	−	1.29660i
$606$	−4.14989	+	15.4876i	−0.168578	+	0.629140i
$607$	2.13724	+	7.97627i	0.0867477	+	0.323747i	0.995639	−	0.0932853i	$-0.0297369\pi$
$607$	2.13724	+	7.97627i	0.0867477	+	0.323747i	−0.908892	+	0.417032i	$0.863070\pi$
$608$	−3.58735			−0.145486
$609$		0			0
$610$			18.6556i			0.755343i
$611$	−20.9274	+	36.2472i	−0.846630	+	1.46641i
$612$	59.1120	−	17.7694i	2.38946	−	0.718284i
$613$	−1.50773	−	2.61146i	−0.0608965	−	0.105476i	0.833970	−	0.551810i	$-0.186063\pi$
$613$	−1.50773	−	2.61146i	−0.0608965	−	0.105476i	−0.894866	+	0.446334i	$0.852729\pi$
$614$	−3.93234	−	2.27034i	−0.158696	−	0.0916234i
$615$	−0.198878	+	0.198878i	−0.00801954	+	0.00801954i
$616$		0			0
$617$	17.1700	−	17.1700i	0.691237	−	0.691237i	−0.271267	−	0.962504i	$-0.587443\pi$
$617$	17.1700	−	17.1700i	0.691237	−	0.691237i	0.962504	+	0.271267i	$0.0874426\pi$
$618$	36.0480	−	9.65902i	1.45006	−	0.388543i
$619$	−7.09043	+	26.4618i	−0.284988	+	1.06359i	0.663860	+	0.747857i	$0.268917\pi$
$619$	−7.09043	+	26.4618i	−0.284988	+	1.06359i	−0.948848	+	0.315733i	$0.897749\pi$
$620$	−8.51752	+	4.91759i	−0.342072	+	0.197495i
$621$	1.09725	+	0.633497i	0.0440311	+	0.0254214i
$622$	−49.3707	−	49.3707i	−1.97958	−	1.97958i
$623$		0			0
$624$	33.8547	−	33.8547i	1.35527	−	1.35527i
$625$	−14.4675	+	25.0585i	−0.578702	+	1.00234i
$626$	−51.9031	−	13.9074i	−2.07447	−	0.555851i
$627$	−1.32266	+	0.763637i	−0.0528219	+	0.0304967i
$628$	5.86506	−	10.1586i	0.234041	−	0.405371i
$629$	−13.4909	+	8.34222i	−0.537915	+	0.332626i
$630$		0			0
$631$		−	47.9472i		−	1.90875i	−0.298615	−	0.954374i	$-0.596525\pi$
$631$		−	47.9472i		−	1.90875i	0.298615	−	0.954374i	$-0.403475\pi$
$632$	8.58353	+	32.0342i	0.341434	+	1.27425i
$633$	17.7129	+	30.6797i	0.704026	+	1.21941i
$634$	−71.5560	−	19.1734i	−2.84185	−	0.761472i
$635$	33.7822	−	9.05190i	1.34060	−	0.359214i
$636$	87.7869	+	87.7869i	3.48098	+	3.48098i
$637$		0			0
$638$			0.322948i			0.0127857i
$639$	25.0139	−	6.70245i	0.989535	−	0.265145i
$640$	−14.8665	+	55.4827i	−0.587652	+	2.19315i
$641$	−15.3277	−	4.10705i	−0.605408	−	0.162219i	−0.0569223	−	0.998379i	$-0.518129\pi$
$641$	−15.3277	−	4.10705i	−0.605408	−	0.162219i	−0.548486	+	0.836160i	$0.684795\pi$
$642$	−2.60771	+	4.51668i	−0.102918	+	0.178259i
$643$	−24.0648	+	24.0648i	−0.949024	+	0.949024i	−0.998762	−	0.0497384i	$-0.984161\pi$
$643$	−24.0648	+	24.0648i	−0.949024	+	0.949024i	0.0497384	+	0.998762i	$0.484161\pi$
$644$		0			0
$645$	66.0080			2.59906
$646$	47.6557	−	50.6259i	1.87499	−	1.99185i
$647$	1.16058	+	2.01018i	0.0456270	+	0.0790282i	0.887937	−	0.459965i	$-0.152138\pi$
$647$	1.16058	+	2.01018i	0.0456270	+	0.0790282i	−0.842310	+	0.538993i	$0.818805\pi$
$648$	−28.1435	+	16.2486i	−1.10558	+	0.638307i
$649$	0.0949186	+	0.354241i	0.00372588	+	0.0139052i
$650$	−42.4018			−1.66314
$651$		0			0
$652$	14.9005	+	14.9005i	0.583549	+	0.583549i
$653$	44.9855	−	12.0538i	1.76042	−	0.471703i	0.773619	−	0.633650i	$-0.218444\pi$
$653$	44.9855	−	12.0538i	1.76042	−	0.471703i	0.986799	+	0.161948i	$0.0517776\pi$
$654$	42.9833	−	24.8164i	1.68078	−	0.970400i
$655$	51.7376	−	29.8707i	2.02156	−	1.16715i
$656$	0.150944	−	0.0404452i	0.00589336	−	0.00157912i
$657$	−9.96106	−	9.96106i	−0.388618	−	0.388618i
$658$		0			0
$659$	−24.5226			−0.955264			−0.477632	−	0.878560i	$-0.658505\pi$
$659$	−24.5226			−0.955264			−0.477632	+	0.878560i	$0.658505\pi$
$660$	−0.701958	−	2.61974i	−0.0273237	−	0.101973i
$661$	−6.38555	+	3.68670i	−0.248369	+	0.143396i	−0.619017	−	0.785377i	$-0.712469\pi$
$661$	−6.38555	+	3.68670i	−0.248369	+	0.143396i	0.370648	+	0.928773i	$0.379136\pi$
$662$	31.1958	+	54.0327i	1.21246	+	2.10004i
$663$	1.38110	+	45.6988i	0.0536374	+	1.77480i
$664$	19.5244			0.757693
$665$		0			0
$666$	−24.7226	+	24.7226i	−0.957980	+	0.957980i
$667$	0.537659	−	0.931252i	0.0208182	−	0.0360582i
$668$	61.2331	+	16.4074i	2.36918	+	0.634820i
$669$	−17.9127	+	66.8512i	−0.692546	+	2.58462i
$670$	35.1484	−	9.41800i	1.35790	−	0.363849i
$671$		−	0.217425i		−	0.00839359i
$672$		0			0
$673$	−25.5728	−	25.5728i	−0.985757	−	0.985757i	0.0141427	−	0.999900i	$-0.495498\pi$
$673$	−25.5728	−	25.5728i	−0.985757	−	0.985757i	−0.999900	+	0.0141427i	$0.995498\pi$
$674$	16.3398	−	4.37825i	0.629387	−	0.168644i
$675$	−6.97634	−	1.86931i	−0.268520	−	0.0719496i
$676$	10.8770	+	18.8395i	0.418345	+	0.724595i
$677$	1.81184	+	6.76188i	0.0696347	+	0.259880i	0.991963	−	0.126526i	$-0.0403828\pi$
$677$	1.81184	+	6.76188i	0.0696347	+	0.259880i	−0.922329	+	0.386407i	$0.873716\pi$
$678$			96.7644i			3.71621i
$679$		0			0
$680$	32.8884	+	53.1864i	1.26121	+	2.03961i
$681$	−2.10147	+	3.63986i	−0.0805286	+	0.139480i
$682$	0.148260	−	0.0855981i	0.00567718	−	0.00327772i
$683$	−8.51309	−	2.28108i	−0.325744	−	0.0872829i	0.0922410	−	0.995737i	$-0.470597\pi$
$683$	−8.51309	−	2.28108i	−0.325744	−	0.0872829i	−0.417985	+	0.908454i	$0.637264\pi$
$684$	51.3062	−	88.8650i	1.96174	−	3.39784i
$685$	13.6484	−	13.6484i	0.521480	−	0.521480i
$686$		0			0
$687$	45.8168	+	45.8168i	1.74802	+	1.74802i
$688$	−31.7611	−	18.3373i	−1.21088	−	0.699103i
$689$	−43.9478	+	25.3733i	−1.67428	+	0.966644i
$690$	−3.49081	+	13.0279i	−0.132893	+	0.495963i
$691$	−47.3608	+	12.6903i	−1.80169	+	0.482761i	−0.994240	−	0.107174i	$-0.965820\pi$
$691$	−47.3608	+	12.6903i	−1.80169	+	0.482761i	−0.807450	+	0.589936i	$0.799153\pi$
$692$	46.7055	−	46.7055i	1.77548	−	1.77548i
$693$		0			0
$694$	−9.36897	+	9.36897i	−0.355641	+	0.355641i
$695$	−7.26542	−	4.19469i	−0.275593	−	0.159114i
$696$	−9.95697	−	17.2460i	−0.377418	−	0.653707i
$697$	−0.0706744	+	0.131427i	−0.00267698	+	0.00497816i
$698$	12.1610	−	21.0635i	0.460302	−	0.797266i
$699$		−	21.5274i		−	0.814242i
$700$		0			0
$701$	−44.4219			−1.67779			−0.838897	−	0.544290i	$-0.816799\pi$
$701$	−44.4219			−1.67779			−0.838897	+	0.544290i	$0.816799\pi$
$702$	4.90109	+	18.2911i	0.184980	+	0.690354i
$703$	−6.82475	+	25.4703i	−0.257400	+	0.960631i
$704$	0.163781	−	0.611239i	0.00617273	−	0.0230369i
$705$	−65.7249	−	37.9463i	−2.47534	−	1.42914i
$706$			52.9149i			1.99148i
$707$		0			0
$708$	−31.5722	−	31.5722i	−1.18655	−	1.18655i
$709$	2.31432	+	8.63716i	0.0869161	+	0.324375i	0.995670	−	0.0929568i	$-0.0296318\pi$
$709$	2.31432	+	8.63716i	0.0869161	+	0.324375i	−0.908754	+	0.417332i	$0.862965\pi$
$710$	25.9000	+	44.8601i	0.972010	+	1.68357i
$711$	−23.4357	−	6.27958i	−0.878907	−	0.235503i
$712$	22.0421	+	12.7260i	0.826064	+	0.476928i
$713$	−0.570030			−0.0213478
$714$		0			0
$715$	1.10860			0.0414594
$716$	−59.6464	−	34.4369i	−2.22909	−	1.28697i
$717$	−28.3623	−	7.59965i	−1.05921	−	0.283814i
$718$	−22.8994	−	39.6629i	−0.854597	−	1.48021i
$719$	−8.82488	−	32.9349i	−0.329113	−	1.22826i	−0.910113	−	0.414361i	$-0.864005\pi$
$719$	−8.82488	−	32.9349i	−0.329113	−	1.22826i	0.581000	−	0.813904i	$-0.302662\pi$
$720$	33.8761	+	33.8761i	1.26249	+	1.26249i
$721$		0			0
$722$		−	68.8396i		−	2.56195i
$723$	14.8138	+	8.55274i	0.550931	+	0.318080i
$724$	11.8310	−	44.1538i	0.439695	−	1.64096i
$725$	−1.58651	+	5.92093i	−0.0589215	+	0.219898i
$726$	−18.1097	−	67.5862i	−0.672113	−	2.50836i
$727$	10.9742			0.407009			0.203504	−	0.979074i	$-0.434767\pi$
$727$	10.9742			0.407009			0.203504	+	0.979074i	$0.434767\pi$
$728$		0			0
$729$		−	37.7146i		−	1.39684i
$730$	14.0891	−	24.4030i	0.521460	−	0.903196i
$731$	33.5389	−	10.0820i	1.24048	−	0.372895i
$732$	13.2356	+	22.9247i	0.489201	+	0.847322i
$733$	−16.0011	−	9.23822i	−0.591013	−	0.341221i	0.174485	−	0.984660i	$-0.444174\pi$
$733$	−16.0011	−	9.23822i	−0.591013	−	0.341221i	−0.765498	+	0.643438i	$0.777507\pi$
$734$	14.4229	−	14.4229i	0.532360	−	0.532360i
$735$		0			0
$736$	0.261079	−	0.261079i	0.00962350	−	0.00962350i
$737$	−0.409643	+	0.109764i	−0.0150894	+	0.00404319i
$738$	−0.0851321	+	0.317717i	−0.00313375	+	0.0116953i
$739$	27.9555	−	16.1401i	1.02836	−	0.593725i	0.111847	−	0.993725i	$-0.464323\pi$
$739$	27.9555	−	16.1401i	1.02836	−	0.593725i	0.916515	+	0.400001i	$0.130990\pi$
$740$	−40.5527	−	23.4131i	−1.49075	−	0.860682i
$741$	53.7437	+	53.7437i	1.97432	+	1.97432i
$742$		0			0
$743$	11.9889	−	11.9889i	0.439832	−	0.439832i	−0.452124	−	0.891955i	$-0.649333\pi$
$743$	11.9889	−	11.9889i	0.439832	−	0.439832i	0.891955	+	0.452124i	$0.149333\pi$
$744$	−5.27823	+	9.14216i	−0.193509	+	0.335168i
$745$	−36.4763	−	9.77380i	−1.33639	−	0.358084i
$746$	−48.8957	+	28.2299i	−1.79020	+	1.03357i
$747$	−7.14187	+	12.3701i	−0.261307	+	0.452598i
$748$	−0.756803	−	1.22388i	−0.0276715	−	0.0447497i
$749$		0			0
$750$			18.7078i			0.683112i
$751$	−11.5324	−	43.0396i	−0.420824	−	1.57054i	−0.772876	−	0.634556i	$-0.781183\pi$
$751$	−11.5324	−	43.0396i	−0.420824	−	1.57054i	0.352052	−	0.935980i	$-0.385484\pi$
$752$	21.0833	+	36.5173i	0.768828	+	1.33165i
$753$	−30.9464	−	8.29206i	−1.12775	−	0.302179i
$754$	15.5240	−	4.15963i	0.565349	−	0.151485i
$755$	−27.5163	−	27.5163i	−1.00142	−	1.00142i
$756$		0			0
$757$			19.1445i			0.695817i	0.937528	+	0.347909i	$0.113108\pi$
$757$			19.1445i			0.695817i	−0.937528	+	0.347909i	$0.886892\pi$
$758$	−61.8769	+	16.5799i	−2.24747	+	0.602208i
$759$	0.0406842	−	0.151836i	0.00147674	−	0.00551129i
$760$	100.414	+	26.9059i	3.64241	+	0.975981i
$761$	−10.6091	+	18.3755i	−0.384580	+	0.666112i	−0.991711	−	0.128490i	$-0.958987\pi$
$761$	−10.6091	+	18.3755i	−0.384580	+	0.666112i	0.607131	+	0.794602i	$0.292320\pi$
$762$	52.4088	−	52.4088i	1.89857	−	1.89857i
$763$		0			0
$764$	−21.4594			−0.776374
$765$	−45.7277	+	1.38197i	−1.65329	+	0.0499652i
$766$	−5.98740	−	10.3705i	−0.216334	−	0.374701i
$767$	15.8056	−	9.12538i	0.570708	−	0.329498i
$768$	21.6646	+	80.8532i	0.781753	+	2.91754i
$769$	30.7011			1.10711			0.553556	−	0.832812i	$-0.313271\pi$
$769$	30.7011			1.10711			0.553556	+	0.832812i	$0.313271\pi$
$770$		0			0
$771$	50.0720	+	50.0720i	1.80330	+	1.80330i
$772$	45.7579	−	12.2608i	1.64686	−	0.441275i
$773$	34.8214	−	20.1041i	1.25244	−	0.723096i	0.280845	−	0.959753i	$-0.409385\pi$
$773$	34.8214	−	20.1041i	1.25244	−	0.723096i	0.971593	+	0.236657i	$0.0760519\pi$
$774$	66.8532	−	38.5977i	2.40299	−	1.38737i
$775$	3.13871	−	0.841014i	0.112746	−	0.0302101i
$776$	−33.1019	−	33.1019i	−1.18829	−	1.18829i
$777$		0			0
$778$	7.27246			0.260730
$779$	0.0642060	+	0.239620i	0.00230042	+	0.00858528i
$780$	−116.888	+	67.4855i	−4.18527	+	2.41637i
$781$	−0.301856	−	0.522830i	−0.0108013	−	0.0187083i
$782$	0.216167	+	7.15270i	0.00773011	+	0.255780i
$783$	2.73752			0.0978311
$784$		0			0
$785$	−6.14757	+	6.14757i	−0.219416	+	0.219416i
$786$	63.3026	−	109.643i	2.25793	−	3.91085i
$787$	−15.8822	−	4.25561i	−0.566138	−	0.151696i	−0.0356132	−	0.999366i	$-0.511338\pi$
$787$	−15.8822	−	4.25561i	−0.566138	−	0.151696i	−0.530525	+	0.847669i	$0.678005\pi$
$788$	11.9663	−	44.6587i	0.426280	−	1.59090i
$789$	46.6660	−	12.5041i	1.66135	−	0.445158i
$790$		−	48.5318i		−	1.72668i
$791$		0			0
$792$	−1.13594	−	1.13594i	−0.0403638	−	0.0403638i
$793$	−10.4515	+	2.80047i	−0.371143	+	0.0994475i
$794$	31.6124	+	8.47051i	1.12188	+	0.300607i
$795$	−46.0078	−	79.6878i	−1.63173	−	2.82624i
$796$	20.4991	+	76.5038i	0.726573	+	2.71161i
$797$		−	5.05018i		−	0.178887i	−0.995992	−	0.0894433i	$-0.971491\pi$
$797$		−	5.05018i		−	0.178887i	0.995992	−	0.0894433i	$-0.0285088\pi$
$798$		0			0
$799$	−39.1909	−	9.24192i	−1.38648	−	0.326956i
$800$	−1.05237	+	1.82275i	−0.0372067	+	0.0644439i
$801$	−16.1257	+	9.31017i	−0.569773	+	0.328959i
$802$	−58.0749	−	15.5611i	−2.05069	−	0.549482i
$803$	−0.164204	+	0.284409i	−0.00579462	+	0.0100366i
$804$	36.5100	−	36.5100i	1.28761	−	1.28761i
$805$		0			0
$806$	−6.02427	−	6.02427i	−0.212196	−	0.212196i
$807$	−0.416383	−	0.240399i	−0.0146574	−	0.00846244i
$808$	−11.0155	+	6.35982i	−0.387525	+	0.223738i
$809$	1.41363	−	5.27574i	0.0497006	−	0.185485i	−0.936613	−	0.350366i	$-0.886057\pi$
$809$	1.41363	−	5.27574i	0.0497006	−	0.185485i	0.986314	+	0.164881i	$0.0527239\pi$
$810$	45.9354	−	12.3084i	1.61401	−	0.432472i
$811$	15.7978	−	15.7978i	0.554737	−	0.554737i	−0.373067	−	0.927804i	$-0.621694\pi$
$811$	15.7978	−	15.7978i	0.554737	−	0.554737i	0.927804	+	0.373067i	$0.121694\pi$
$812$		0			0
$813$	9.63473	−	9.63473i	0.337905	−	0.337905i
$814$	0.705880	+	0.407540i	0.0247411	+	0.0142843i
$815$	−7.80913	−	13.5258i	−0.273542	−	0.473788i
$816$	40.5669	+	21.8147i	1.42013	+	0.763667i
$817$	29.1101	−	50.4202i	1.01843	−	1.76398i
$818$		−	84.0249i		−	2.93786i
$819$		0			0
$820$	−0.440532			−0.0153840
$821$	12.5342	+	46.7784i	0.437448	+	1.63258i	0.735140	+	0.677915i	$0.237116\pi$
$821$	12.5342	+	46.7784i	0.437448	+	1.63258i	−0.297693	+	0.954662i	$0.596217\pi$
$822$	10.5869	−	39.5109i	0.369261	−	1.37810i
$823$	3.90440	−	14.5714i	0.136099	−	0.507928i	−0.863892	−	0.503677i	$-0.831980\pi$
$823$	3.90440	−	14.5714i	0.136099	−	0.507928i	0.999991	−	0.00425100i	$-0.00135314\pi$
$824$	25.6391	+	14.8027i	0.893179	+	0.515677i
$825$			0.896065i			0.0311970i
$826$		0			0
$827$	−10.6145	−	10.6145i	−0.369104	−	0.369104i	0.498047	−	0.867150i	$-0.334051\pi$
$827$	−10.6145	−	10.6145i	−0.369104	−	0.369104i	−0.867150	+	0.498047i	$0.834051\pi$
$828$	2.73344	+	10.2013i	0.0949935	+	0.354521i
$829$	−6.54304	−	11.3329i	−0.227249	−	0.393607i	0.729743	−	0.683722i	$-0.239640\pi$
$829$	−6.54304	−	11.3329i	−0.227249	−	0.393607i	−0.956992	+	0.290115i	$0.906307\pi$
$830$	−27.5980	−	7.39487i	−0.957942	−	0.256680i
$831$	28.4831	+	16.4447i	0.988066	+	0.570460i
$832$	−31.4914			−1.09177
$833$		0			0
$834$	−17.7789			−0.615634
$835$	−40.6902	−	23.4925i	−1.40814	−	0.812991i
$836$	−2.31066	−	0.619139i	−0.0799158	−	0.0214134i
$837$	−0.725586	−	1.25675i	−0.0250799	−	0.0434397i
$838$	−12.9828	−	48.4524i	−0.448483	−	1.67376i
$839$	−18.6567	−	18.6567i	−0.644099	−	0.644099i	0.307461	−	0.951561i	$-0.400521\pi$
$839$	−18.6567	−	18.6567i	−0.644099	−	0.644099i	−0.951561	+	0.307461i	$0.900521\pi$
$840$		0			0
$841$			26.6766i			0.919883i
$842$	28.3376	+	16.3607i	0.976578	+	0.563828i
$843$	3.70299	−	13.8197i	0.127538	−	0.475977i
$844$	−14.3612	+	53.5969i	−0.494334	+	1.84488i
$845$	−4.17302	−	15.5739i	−0.143556	−	0.535759i
$846$	−88.7553			−3.05147
$847$		0			0
$848$			51.1246i			1.75563i
$849$	12.2536	−	21.2238i	0.420541	−	0.728398i
$850$	−11.7433	−	39.0654i	−0.402790	−	1.33993i
$851$	−1.35698	−	2.35036i	−0.0465167	−	0.0805693i
$852$	63.6538	+	36.7505i	2.18074	+	1.25905i
$853$	−33.7388	+	33.7388i	−1.15519	+	1.15519i	−0.169697	+	0.985496i	$0.554279\pi$
$853$	−33.7388	+	33.7388i	−1.15519	+	1.15519i	−0.985496	+	0.169697i	$0.945721\pi$
$854$		0			0
$855$	−53.7776	+	53.7776i	−1.83916	+	1.83916i
$856$	−3.99638	+	1.07083i	−0.136594	+	0.0366001i
$857$	−3.26866	+	12.1988i	−0.111655	+	0.416704i	−0.999015	−	0.0443744i	$-0.985871\pi$
$857$	−3.26866	+	12.1988i	−0.111655	+	0.416704i	0.887360	+	0.461078i	$0.152537\pi$
$858$	2.03462	−	1.17469i	0.0694607	−	0.0401031i
$859$	27.0386	+	15.6107i	0.922545	+	0.532632i	0.884446	−	0.466642i	$-0.154536\pi$
$859$	27.0386	+	15.6107i	0.922545	+	0.532632i	0.0380990	+	0.999274i	$0.487870\pi$
$860$	73.1066	+	73.1066i	2.49291	+	2.49291i
$861$		0			0
$862$	14.9856	−	14.9856i	0.510413	−	0.510413i
$863$	10.1742	−	17.6223i	0.346334	−	0.599868i	−0.639261	−	0.768990i	$-0.720760\pi$
$863$	10.1742	−	17.6223i	0.346334	−	0.599868i	0.985595	+	0.169121i	$0.0540930\pi$
$864$	0.907929	+	0.243279i	0.0308884	+	0.00827651i
$865$	−42.3965	+	24.4777i	−1.44153	+	0.832265i
$866$	0.584434	−	1.01227i	0.0198599	−	0.0343983i
$867$	−41.7205	+	13.9288i	−1.41690	+	0.473047i
$868$		0			0
$869$			0.565622i			0.0191874i
$870$	7.54241	+	28.1487i	0.255712	+	0.954329i
$871$	10.5526	+	18.2776i	0.357560	+	0.619311i
$872$	38.0319	+	10.1906i	1.28792	+	0.345098i
$873$	33.0808	−	8.86397i	1.11962	−	0.300000i
$874$	8.41186	+	8.41186i	0.284536	+	0.284536i
$875$		0			0
$876$		−	39.9831i		−	1.35090i
$877$	−41.3342	+	11.0755i	−1.39576	+	0.373992i	−0.876819	−	0.480820i	$-0.840339\pi$
$877$	−41.3342	+	11.0755i	−1.39576	+	0.373992i	−0.518938	+	0.854812i	$0.673672\pi$
$878$	−12.4279	+	46.3815i	−0.419421	+	1.56530i
$879$	11.7089	+	3.13739i	0.394931	+	0.105822i
$880$	0.558432	−	0.967232i	0.0188247	−	0.0326054i
$881$	−33.0350	+	33.0350i	−1.11298	+	1.11298i	−0.120231	+	0.992746i	$0.538363\pi$
$881$	−33.0350	+	33.0350i	−1.11298	+	1.11298i	−0.992746	+	0.120231i	$0.961637\pi$
$882$		0			0
$883$	20.4430			0.687962			0.343981	−	0.938977i	$-0.388224\pi$
$883$	20.4430			0.687962			0.343981	+	0.938977i	$0.388224\pi$
$884$	−49.0837	+	52.1430i	−1.65086	+	1.75376i
$885$	16.5465	+	28.6594i	0.556204	+	0.963374i
$886$	37.8827	−	21.8716i	1.27269	−	0.734790i
$887$	−4.62997	−	17.2793i	−0.155459	−	0.580182i	−0.999066	−	0.0432197i	$-0.986238\pi$
$887$	−4.62997	−	17.2793i	−0.155459	−	0.580182i	0.843606	−	0.536962i	$-0.180428\pi$
$888$	−50.2602			−1.68662
$889$		0			0
$890$	−26.3369	−	26.3369i	−0.882815	−	0.882815i
$891$	−0.535362	+	0.143450i	−0.0179353	+	0.00480575i
$892$	−93.8796	+	54.2014i	−3.14332	+	1.81480i
$893$	−57.9705	+	33.4693i	−1.93991	+	1.12001i
$894$	−77.3013	+	20.7128i	−2.58534	+	0.692740i
$895$	36.0957	+	36.0957i	1.20655	+	1.20655i
$896$		0			0
$897$	−7.82268			−0.261192
$898$	20.0563	+	74.8510i	0.669286	+	2.49781i
$899$	−1.06662	+	0.615816i	−0.0355739	+	0.0205386i
$900$	−30.1018	−	52.1379i	−1.00339	−	1.73793i
$901$	−35.5481	−	33.4625i	−1.18428	−	1.11480i
$902$	0.00766812			0.000255320
$903$		0			0
$904$	−54.2794	+	54.2794i	−1.80531	+	1.80531i
$905$	−16.9399	+	29.3408i	−0.563102	+	0.975321i
$906$	−79.6572	−	21.3441i	−2.64643	−	0.709109i
$907$	6.08897	−	22.7243i	0.202181	−	0.754549i	−0.788110	−	0.615535i	$-0.788940\pi$
$907$	6.08897	−	22.7243i	0.202181	−	0.754549i	0.990290	−	0.139014i	$-0.0443934\pi$
$908$	−6.35876	+	1.70383i	−0.211023	+	0.0565434i
$909$		−	9.30549i		−	0.308644i
$910$		0			0
$911$	22.2004	+	22.2004i	0.735532	+	0.735532i	0.971710	−	0.236178i	$-0.0758948\pi$
$911$	22.2004	+	22.2004i	0.735532	+	0.735532i	−0.236178	+	0.971710i	$0.575895\pi$
$912$	73.9622	−	19.8181i	2.44913	−	0.656244i
$913$	0.321646	+	0.0861847i	0.0106449	+	0.00285230i
$914$	43.7155	+	75.7175i	1.44598	+	2.50451i
$915$	−5.07792	−	18.9511i	−0.167871	−	0.626503i
$916$			101.488i			3.35326i
$917$		0			0
$918$	−15.4945	+	9.58120i	−0.511394	+	0.316227i
$919$	22.0094	−	38.1214i	0.726024	−	1.25751i	−0.232528	−	0.972590i	$-0.574700\pi$
$919$	22.0094	−	38.1214i	0.726024	−	1.25751i	0.958551	−	0.284920i	$-0.0919671\pi$
$920$	−9.26607	+	5.34977i	−0.305493	+	0.176377i
$921$	4.61259	+	1.23594i	0.151990	+	0.0407256i
$922$	−1.02608	+	1.77723i	−0.0337923	+	0.0585300i
$923$	−21.2442	+	21.2442i	−0.699261	+	0.699261i
$924$		0			0
$925$	10.9395	+	10.9395i	0.359689	+	0.359689i
$926$	−51.8831	−	29.9547i	−1.70498	−	0.984373i
$927$	−18.7571	+	10.8294i	−0.616065	+	0.355685i
$928$	0.206475	−	0.770574i	0.00677786	−	0.0252953i
$929$	−42.4556	+	11.3759i	−1.39292	+	0.373233i	−0.875798	−	0.482677i	$-0.839665\pi$
$929$	−42.4556	+	11.3759i	−1.39292	+	0.373233i	−0.517125	+	0.855910i	$0.672998\pi$
$930$	10.9234	−	10.9234i	0.358194	−	0.358194i
$931$		0			0
$932$	23.8425	−	23.8425i	0.780988	−	0.780988i
$933$	63.5909	+	36.7142i	2.08187	+	1.20197i
$934$	29.2573	+	50.6752i	0.957329	+	1.65814i
$935$	0.307029	+	1.02137i	0.0100409	+	0.0334024i
$936$	−39.9728	+	69.2349i	−1.30655	+	2.26301i
$937$			0.0537818i			0.00175697i	1.00000		0.000878487i	$0.000279631\pi$
$937$			0.0537818i			0.00175697i	−1.00000		0.000878487i	$0.999720\pi$
$938$		0			0
$939$	56.5106			1.84415
$940$	−30.7660	−	114.820i	−1.00348	−	3.74502i
$941$	8.28872	−	30.9339i	0.270205	−	1.00842i	−0.688783	−	0.724968i	$-0.741855\pi$
$941$	8.28872	−	30.9339i	0.270205	−	1.00842i	0.958987	−	0.283449i	$-0.0914788\pi$
$942$	−4.76860	+	17.7967i	−0.155369	+	0.579846i
$943$	−0.0221117	−	0.0127662i	−0.000720057	−	0.000415725i
$944$		−	18.3867i		−	0.598437i
$945$		0			0
$946$	−1.27253	−	1.27253i	−0.0413735	−	0.0413735i
$947$	6.55379	+	24.4591i	0.212970	+	0.794813i	0.986871	+	0.161508i	$0.0516357\pi$
$947$	6.55379	+	24.4591i	0.212970	+	0.794813i	−0.773902	+	0.633306i	$0.781698\pi$
$948$	−34.4318	−	59.6377i	−1.11829	−	1.93694i
$949$	15.7863	+	4.22994i	0.512447	+	0.137310i
$950$	−58.7283	−	33.9068i	−1.90540	−	1.10008i
$951$	77.9081			2.52634
$952$		0			0
$953$	18.3016			0.592847			0.296424	−	0.955057i	$-0.404206\pi$
$953$	18.3016			0.592847			0.296424	+	0.955057i	$0.404206\pi$
$954$	−93.1937	−	53.8054i	−3.01726	−	1.74201i
$955$	15.3631	+	4.11652i	0.497137	+	0.133207i
$956$	−22.9955	−	39.8293i	−0.743727	−	1.28817i
$957$	−0.0879042	−	0.328063i	−0.00284154	−	0.0106048i
$958$	50.6975	+	50.6975i	1.63796	+	1.63796i
$959$		0			0
$960$		−	57.1015i		−	1.84294i
$961$	−26.2814	−	15.1736i	−0.847786	−	0.489469i
$962$	10.4984	−	39.1805i	0.338481	−	1.26323i
$963$	0.783401	−	2.92369i	0.0252448	−	0.0942147i
$964$	6.93436	+	25.8794i	0.223341	+	0.833519i
$965$	−35.1106			−1.13025
$966$		0			0
$967$		−	12.0520i		−	0.387567i	−0.981044	−	0.193784i	$-0.937924\pi$
$967$		−	12.0520i		−	0.387567i	0.981044	−	0.193784i	$-0.0620760\pi$
$968$	27.7536	−	48.0706i	0.892034	−	1.54505i
$969$	−34.6304	+	64.3992i	−1.11249	+	2.06880i
$970$	34.2527	+	59.3274i	1.09979	+	1.90489i
$971$	−2.34626	−	1.35461i	−0.0752950	−	0.0434716i	0.461880	−	0.886943i	$-0.347175\pi$
$971$	−2.34626	−	1.35461i	−0.0752950	−	0.0434716i	−0.537175	+	0.843471i	$0.680508\pi$
$972$	63.1540	−	63.1540i	2.02567	−	2.02567i
$973$		0			0
$974$	−43.2185	+	43.2185i	−1.38481	+	1.38481i
$975$	43.0734	−	11.5415i	1.37945	−	0.369623i
$976$	−2.82133	+	10.5294i	−0.0903087	+	0.337037i
$977$	−5.59973	+	3.23301i	−0.179151	+	0.103433i	−0.586894	−	0.809664i	$-0.699649\pi$
$977$	−5.59973	+	3.23301i	−0.179151	+	0.103433i	0.407743	+	0.913097i	$0.366316\pi$
$978$	−28.6641	−	16.5493i	−0.916578	−	0.529187i
$979$	0.306948	+	0.306948i	0.00981010	+	0.00981010i
$980$		0			0
$981$	−20.3682	+	20.3682i	−0.650308	+	0.650308i
$982$	20.1099	−	34.8314i	0.641734	−	1.11152i
$983$	38.1265	+	10.2160i	1.21605	+	0.325838i	0.809131	−	0.587628i	$-0.199938\pi$
$983$	38.1265	+	10.2160i	1.21605	+	0.325838i	0.406914	+	0.913466i	$0.366605\pi$
$984$	−0.409490	+	0.236419i	−0.0130541	+	0.00753677i
$985$	−17.1336	+	29.6763i	−0.545922	+	0.945565i
$986$	8.13171	+	13.1504i	0.258966	+	0.418795i
$987$		0			0
$988$			119.047i			3.78738i
$989$	1.55090	+	5.78803i	0.0493156	+	0.184048i
$990$	1.17543	+	2.03590i	0.0373576	+	0.0647052i
$991$	−3.65933	−	0.980514i	−0.116242	−	0.0311471i	0.200229	−	0.979749i	$-0.435831\pi$
$991$	−3.65933	−	0.980514i	−0.116242	−	0.0311471i	−0.316471	+	0.948602i	$0.602498\pi$
$992$	−0.408484	+	0.109453i	−0.0129694	+	0.00347514i
$993$	−46.3971	−	46.3971i	−1.47237	−	1.47237i
$994$		0			0
$995$		−	58.7024i		−	1.86099i
$996$	−39.1599	+	10.4929i	−1.24083	+	0.332479i
$997$	8.99232	−	33.5598i	0.284790	−	1.06285i	−0.664203	−	0.747552i	$-0.731229\pi$
$997$	8.99232	−	33.5598i	0.284790	−	1.06285i	0.948993	−	0.315298i	$-0.102104\pi$
$998$	56.3390	+	15.0960i	1.78338	+	0.477856i
$999$	3.45458	−	5.98351i	0.109298	−	0.189310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.o.d.667.1		32
7.2	even	3		833.2.g.f.344.8		16
7.3	odd	6		119.2.n.b.4.8	✓	32
7.4	even	3	inner	833.2.o.d.361.8		32
7.5	odd	6		833.2.g.g.344.8		16
7.6	odd	2		119.2.n.b.72.1	yes	32
17.13	even	4	inner	833.2.o.d.30.8		32
119.13	odd	4		119.2.n.b.30.8	yes	32
119.30	even	12		833.2.g.f.540.1		16
119.47	odd	12		833.2.g.g.540.1		16
119.81	even	12	inner	833.2.o.d.557.1		32
119.115	odd	12		119.2.n.b.81.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.n.b.4.8	✓	32	7.3	odd	6
119.2.n.b.30.8	yes	32	119.13	odd	4
119.2.n.b.72.1	yes	32	7.6	odd	2
119.2.n.b.81.1	yes	32	119.115	odd	12
833.2.g.f.344.8		16	7.2	even	3
833.2.g.f.540.1		16	119.30	even	12
833.2.g.g.344.8		16	7.5	odd	6
833.2.g.g.540.1		16	119.47	odd	12
833.2.o.d.30.8		32	17.13	even	4	inner
833.2.o.d.361.8		32	7.4	even	3	inner
833.2.o.d.557.1		32	119.81	even	12	inner
833.2.o.d.667.1		32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.13058 - 1.23009i) q^{2} +(2.49914 + 0.669644i) q^{3} +(2.02625 + 3.50956i) q^{4} +(-0.777383 - 2.90123i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} +(3.19922 + 1.84707i) q^{9} +O(q^{10})\)	\(q+(-2.13058 - 1.23009i) q^{2} +(2.49914 + 0.669644i) q^{3} +(2.02625 + 3.50956i) q^{4} +(-0.777383 - 2.90123i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} +(3.19922 + 1.84707i) q^{9} +(-1.91250 + 7.13756i) q^{10} +(0.0222896 - 0.0831859i) q^{11} +(2.71373 + 10.1278i) q^{12} -4.28579 q^{13} -7.77117i q^{15} +(-2.15886 + 3.73926i) q^{16} +(-1.18696 - 3.94856i) q^{17} +(-4.54413 - 7.87067i) q^{18} +(-5.93600 - 3.42715i) q^{19} +(8.60689 - 8.60689i) q^{20} +(-0.149816 + 0.149816i) q^{22} +(0.681429 - 0.182588i) q^{23} +(3.38137 - 12.6195i) q^{24} +(-3.48271 + 2.01074i) q^{25} +(9.13123 + 5.27192i) q^{26} +(1.26994 + 1.26994i) q^{27} +(1.07782 - 1.07782i) q^{29} +(-9.55925 + 16.5571i) q^{30} +(-0.780485 - 0.209130i) q^{31} +(0.453253 - 0.261686i) q^{32} +(0.111410 - 0.192967i) q^{33} +(-2.32818 + 9.87279i) q^{34} +14.9705i q^{36} +(-0.995688 - 3.71596i) q^{37} +(8.43142 + 14.6036i) q^{38} +(-10.7108 - 2.86996i) q^{39} +(-14.6498 + 3.92541i) q^{40} +(-0.0255918 - 0.0255918i) q^{41} +8.49396i q^{43} +(0.337110 - 0.0903285i) q^{44} +(2.87177 - 10.7176i) q^{45} +(-1.67644 - 0.449200i) q^{46} +(4.88296 - 8.45753i) q^{47} +(-7.89929 + 7.89929i) q^{48} +9.89358 q^{50} +(-0.322250 - 10.6629i) q^{51} +(-8.68408 - 15.0413i) q^{52} +(10.2543 - 5.92031i) q^{53} +(-1.14357 - 4.26785i) q^{54} -0.258669 q^{55} +(-12.5400 - 12.5400i) q^{57} +(-3.62219 + 0.970563i) q^{58} +(-3.68791 + 2.12921i) q^{59} +(27.2734 - 15.7463i) q^{60} +(2.43864 - 0.653430i) q^{61} +(1.40564 + 1.40564i) q^{62} +7.34787 q^{64} +(3.33170 + 12.4341i) q^{65} +(-0.474735 + 0.274088i) q^{66} +(-2.46222 - 4.26468i) q^{67} +(11.4527 - 12.1665i) q^{68} +1.82526 q^{69} +(4.95688 - 4.95688i) q^{71} +(9.32682 - 16.1545i) q^{72} +(-3.68341 - 0.986967i) q^{73} +(-2.44957 + 9.14194i) q^{74} +(-10.0503 + 2.69296i) q^{75} -27.7770i q^{76} +(19.2900 + 19.2900i) q^{78} +(-6.34401 + 1.69987i) q^{79} +(12.5267 + 3.35653i) q^{80} +(-3.21786 - 5.57350i) q^{81} +(0.0230451 + 0.0860056i) q^{82} +3.86659i q^{83} +(-10.5330 + 6.51319i) q^{85} +(10.4483 - 18.0971i) q^{86} +(3.41537 - 1.97187i) q^{87} +(-0.420048 - 0.112552i) q^{88} +(-2.52025 + 4.36520i) q^{89} +(-19.3021 + 19.3021i) q^{90} +(2.02155 + 2.02155i) q^{92} +(-1.81050 - 1.04529i) q^{93} +(-20.8071 + 12.0130i) q^{94} +(-5.32842 + 19.8859i) q^{95} +(1.30798 - 0.350473i) q^{96} +(6.55546 - 6.55546i) q^{97} +(0.224960 - 0.224960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 8 q^{5} + 12 q^{6}+O(q^{10}) \) 32 * q + 16 * q^4 + 8 * q^5 + 12 * q^6	\( 32 q + 16 q^{4} + 8 q^{5} + 12 q^{6} + 6 q^{10} - 18 q^{11} - 26 q^{12} - 8 q^{16} - 10 q^{17} - 40 q^{18} + 24 q^{20} + 52 q^{22} - 12 q^{23} - 14 q^{24} - 60 q^{27} - 32 q^{29} - 44 q^{30} + 6 q^{31} + 8 q^{33} + 40 q^{34} - 2 q^{37} + 32 q^{38} + 14 q^{39} - 72 q^{40} - 4 q^{41} + 24 q^{44} + 4 q^{46} + 36 q^{47} - 72 q^{48} - 80 q^{50} - 20 q^{51} - 12 q^{52} + 18 q^{54} - 72 q^{55} - 48 q^{57} + 8 q^{58} + 52 q^{61} - 36 q^{62} + 24 q^{64} - 2 q^{65} - 28 q^{67} - 24 q^{68} + 8 q^{69} + 80 q^{71} + 36 q^{72} + 16 q^{73} + 60 q^{74} + 2 q^{75} + 64 q^{78} - 6 q^{79} - 30 q^{80} + 40 q^{82} + 68 q^{85} - 4 q^{86} + 30 q^{88} - 8 q^{89} + 20 q^{90} - 40 q^{92} - 12 q^{95} + 30 q^{96} + 76 q^{97} - 92 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 8 * q^5 + 12 * q^6 + 6 * q^10 - 18 * q^11 - 26 * q^12 - 8 * q^16 - 10 * q^17 - 40 * q^18 + 24 * q^20 + 52 * q^22 - 12 * q^23 - 14 * q^24 - 60 * q^27 - 32 * q^29 - 44 * q^30 + 6 * q^31 + 8 * q^33 + 40 * q^34 - 2 * q^37 + 32 * q^38 + 14 * q^39 - 72 * q^40 - 4 * q^41 + 24 * q^44 + 4 * q^46 + 36 * q^47 - 72 * q^48 - 80 * q^50 - 20 * q^51 - 12 * q^52 + 18 * q^54 - 72 * q^55 - 48 * q^57 + 8 * q^58 + 52 * q^61 - 36 * q^62 + 24 * q^64 - 2 * q^65 - 28 * q^67 - 24 * q^68 + 8 * q^69 + 80 * q^71 + 36 * q^72 + 16 * q^73 + 60 * q^74 + 2 * q^75 + 64 * q^78 - 6 * q^79 - 30 * q^80 + 40 * q^82 + 68 * q^85 - 4 * q^86 + 30 * q^88 - 8 * q^89 + 20 * q^90 - 40 * q^92 - 12 * q^95 + 30 * q^96 + 76 * q^97 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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