LMFDB - Embedded newform 1050.2.bc.e.493.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 $ x^16 - 28x^14 + 519x^12 - 5404x^10 + 40705x^8 - 194544x^6 + 672624x^4 - 1306368*x^2 + 1679616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.4
Root			$-1.90899 - 1.10215i$ of defining polynomial
Character	$\chi$	$=$	1050.493
Dual form			1050.2.bc.e.607.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-0.965926 + 2.46313i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-0.965926 + 2.46313i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.55868 + 2.69971i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-2.30403 + 2.30403i) q^{13} +(-1.57052 + 2.12920i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.10215 + 0.295321i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-2.99522 - 5.18788i) q^{19} +(-2.62920 - 0.295509i) q^{21} +(-2.20431 + 2.20431i) q^{22} +(-0.295321 + 1.10215i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.82185 + 1.62920i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.06808 + 1.65017i) q^{28} -5.39943i q^{29} +(3.68788 + 2.12920i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.01114 - 0.806832i) q^{33} -1.14103 q^{34} -1.00000 q^{36} +(5.55960 + 1.48969i) q^{37} +(-1.55044 - 5.78632i) q^{38} +(-2.82185 - 1.62920i) q^{39} +10.2584i q^{41} +(-2.46313 - 0.965926i) q^{42} +(6.44695 + 6.44695i) q^{43} +(-2.69971 + 1.55868i) q^{44} +(-0.570516 + 0.988164i) q^{46} +(-1.10215 + 4.11329i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-5.13397 - 4.75839i) q^{49} +(-0.570516 - 0.988164i) q^{51} +(-3.14737 + 0.843334i) q^{52} +(-2.78442 + 0.746082i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.42471 + 1.05868i) q^{56} +(4.23588 - 4.23588i) q^{57} +(1.39747 - 5.21545i) q^{58} +(0.117360 - 0.203274i) q^{59} +(7.38403 - 4.26317i) q^{61} +(3.01114 + 3.01114i) q^{62} +(-0.395046 - 2.61609i) q^{63} +1.00000i q^{64} +(-2.69971 - 1.55868i) q^{66} +(3.60425 + 13.4513i) q^{67} +(-1.10215 - 0.295321i) q^{68} -1.14103 q^{69} +1.74161 q^{71} +(-0.965926 - 0.258819i) q^{72} +(-0.293478 - 1.09527i) q^{73} +(4.98460 + 2.87786i) q^{74} -5.99044i q^{76} +(-5.14416 - 6.44695i) q^{77} +(-2.30403 - 2.30403i) q^{78} +(-8.76189 + 5.05868i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.65507 + 9.90885i) q^{82} +(8.06061 - 8.06061i) q^{83} +(-2.12920 - 1.57052i) q^{84} +(4.55868 + 7.89587i) q^{86} +(5.21545 - 1.39747i) q^{87} +(-3.01114 + 0.806832i) q^{88} +(-9.18432 - 15.9077i) q^{89} +(-3.44960 - 7.90064i) q^{91} +(-0.806832 + 0.806832i) q^{92} +(-1.10215 + 4.11329i) q^{93} +(-2.12920 + 3.68788i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-0.740585 - 0.740585i) q^{97} +(-3.72748 - 5.92503i) q^{98} -3.11736i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{11} - 8 q^{14} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 8 q^{24} + 16 q^{34} - 16 q^{36} + 12 q^{44} + 8 q^{46} - 96 q^{49} + 8 q^{51} - 8 q^{54} - 4 q^{56} - 40 q^{59} - 24 q^{61} + 12 q^{66} + 16 q^{69} + 104 q^{71} + 48 q^{74} + 12 q^{79} + 8 q^{81} + 4 q^{84} + 52 q^{86} - 60 q^{89} - 52 q^{91} + 4 q^{94}+O(q^{100}) $ 16 * q - 4 * q^11 - 8 * q^14 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 8 * q^24 + 16 * q^34 - 16 * q^36 + 12 * q^44 + 8 * q^46 - 96 * q^49 + 8 * q^51 - 8 * q^54 - 4 * q^56 - 40 * q^59 - 24 * q^61 + 12 * q^66 + 16 * q^69 + 104 * q^71 + 48 * q^74 + 12 * q^79 + 8 * q^81 + 4 * q^84 + 52 * q^86 - 60 * q^89 - 52 * q^91 + 4 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−0.965926	+	2.46313i	−0.365086	+	0.930974i
$7$	−0.965926	+	2.46313i	−0.365086	+	0.930974i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	−1.55868	+	2.69971i	−0.469960	+	0.813994i	−0.999410	−	0.0343469i	$-0.989065\pi$
$11$	−1.55868	+	2.69971i	−0.469960	+	0.813994i	0.529450	+	0.848341i	$0.322398\pi$
$12$	−0.258819	+	0.965926i	−0.0747146	+	0.278839i
$13$	−2.30403	+	2.30403i	−0.639023	+	0.639023i	−0.950315	−	0.311291i	$-0.899239\pi$
$13$	−2.30403	+	2.30403i	−0.639023	+	0.639023i	0.311291	+	0.950315i	$0.399239\pi$
$14$	−1.57052	+	2.12920i	−0.419738	+	0.569052i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.10215	+	0.295321i	−0.267311	+	0.0716259i	−0.389985	−	0.920821i	$-0.627520\pi$
$17$	−1.10215	+	0.295321i	−0.267311	+	0.0716259i	0.122674	+	0.992447i	$0.460853\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−2.99522	−	5.18788i	−0.687151	−	1.19018i	−0.972756	−	0.231833i	$-0.925528\pi$
$19$	−2.99522	−	5.18788i	−0.687151	−	1.19018i	0.285605	−	0.958348i	$-0.407806\pi$
$20$		0			0
$21$	−2.62920	−	0.295509i	−0.573738	−	0.0644853i
$22$	−2.20431	+	2.20431i	−0.469960	+	0.469960i
$23$	−0.295321	+	1.10215i	−0.0615787	+	0.229815i	−0.989856	−	0.142074i	$-0.954623\pi$
$23$	−0.295321	+	1.10215i	−0.0615787	+	0.229815i	0.928277	+	0.371889i	$0.121290\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−2.82185	+	1.62920i	−0.553411	+	0.319512i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.06808	+	1.65017i	−0.390830	+	0.311852i
$29$		−	5.39943i		−	1.00265i	−0.865260	−	0.501324i	$-0.832846\pi$
$29$		−	5.39943i		−	1.00265i	0.865260	−	0.501324i	$-0.167154\pi$
$30$		0			0
$31$	3.68788	+	2.12920i	0.662362	+	0.382415i	0.793176	−	0.608992i	$-0.208426\pi$
$31$	3.68788	+	2.12920i	0.662362	+	0.382415i	−0.130814	+	0.991407i	$0.541759\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−3.01114	−	0.806832i	−0.524172	−	0.140451i
$34$	−1.14103			−0.195686
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.55960	+	1.48969i	0.913993	+	0.244904i	0.685016	−	0.728528i	$-0.259795\pi$
$37$	5.55960	+	1.48969i	0.913993	+	0.244904i	0.228977	+	0.973432i	$0.426462\pi$
$38$	−1.55044	−	5.78632i	−0.251515	−	0.938666i
$39$	−2.82185	−	1.62920i	−0.451858	−	0.260880i
$40$		0			0
$41$			10.2584i			1.60209i	0.598603	+	0.801046i	$0.295723\pi$
$41$			10.2584i			1.60209i	−0.598603	+	0.801046i	$0.704277\pi$
$42$	−2.46313	−	0.965926i	−0.380069	−	0.149046i
$43$	6.44695	+	6.44695i	0.983150	+	0.983150i	0.999860	−	0.0167102i	$-0.00531925\pi$
$43$	6.44695	+	6.44695i	0.983150	+	0.983150i	−0.0167102	+	0.999860i	$0.505319\pi$
$44$	−2.69971	+	1.55868i	−0.406997	+	0.234980i
$45$		0			0
$46$	−0.570516	+	0.988164i	−0.0841181	+	0.145697i
$47$	−1.10215	+	4.11329i	−0.160766	+	0.599985i	0.837777	+	0.546013i	$0.183855\pi$
$47$	−1.10215	+	4.11329i	−0.160766	+	0.599985i	−0.998542	+	0.0539725i	$0.982812\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−5.13397	−	4.75839i	−0.733425	−	0.679770i
$50$		0			0
$51$	−0.570516	−	0.988164i	−0.0798883	−	0.138371i
$52$	−3.14737	+	0.843334i	−0.436461	+	0.116949i
$53$	−2.78442	+	0.746082i	−0.382469	+	0.102482i	−0.444930	−	0.895565i	$-0.646772\pi$
$53$	−2.78442	+	0.746082i	−0.382469	+	0.102482i	0.0624615	+	0.998047i	$0.480105\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−2.42471	+	1.05868i	−0.324015	+	0.141472i
$57$	4.23588	−	4.23588i	0.561056	−	0.561056i
$58$	1.39747	−	5.21545i	0.183497	−	0.684821i
$59$	0.117360	−	0.203274i	0.0152790	−	0.0264640i	−0.858285	−	0.513174i	$-0.828470\pi$
$59$	0.117360	−	0.203274i	0.0152790	−	0.0264640i	0.873564	+	0.486710i	$0.161803\pi$
$60$		0			0
$61$	7.38403	−	4.26317i	0.945428	−	0.545843i	0.0537703	−	0.998553i	$-0.482876\pi$
$61$	7.38403	−	4.26317i	0.945428	−	0.545843i	0.891658	+	0.452710i	$0.149543\pi$
$62$	3.01114	+	3.01114i	0.382415	+	0.382415i
$63$	−0.395046	−	2.61609i	−0.0497712	−	0.329597i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.69971	−	1.55868i	−0.332312	−	0.191860i
$67$	3.60425	+	13.4513i	0.440330	+	1.64333i	0.727981	+	0.685598i	$0.240459\pi$
$67$	3.60425	+	13.4513i	0.440330	+	1.64333i	−0.287651	+	0.957735i	$0.592874\pi$
$68$	−1.10215	−	0.295321i	−0.133656	−	0.0358129i
$69$	−1.14103			−0.137364
$70$		0			0
$71$	1.74161			0.206691			0.103345	−	0.994646i	$-0.467045\pi$
$71$	1.74161			0.206691			0.103345	+	0.994646i	$0.467045\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	−0.293478	−	1.09527i	−0.0343490	−	0.128192i	0.946622	−	0.322345i	$-0.104471\pi$
$73$	−0.293478	−	1.09527i	−0.0343490	−	0.128192i	−0.980971	+	0.194152i	$0.937804\pi$
$74$	4.98460	+	2.87786i	0.579448	+	0.334545i
$75$		0			0
$76$		−	5.99044i		−	0.687151i
$77$	−5.14416	−	6.44695i	−0.586232	−	0.734698i
$78$	−2.30403	−	2.30403i	−0.260880	−	0.260880i
$79$	−8.76189	+	5.05868i	−0.985790	+	0.569146i	−0.904013	−	0.427505i	$-0.859393\pi$
$79$	−8.76189	+	5.05868i	−0.985790	+	0.569146i	−0.0817766	+	0.996651i	$0.526059\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.65507	+	9.90885i	−0.293203	+	1.09425i
$83$	8.06061	−	8.06061i	0.884767	−	0.884767i	−0.109248	−	0.994015i	$-0.534844\pi$
$83$	8.06061	−	8.06061i	0.884767	−	0.884767i	0.994015	+	0.109248i	$0.0348441\pi$
$84$	−2.12920	−	1.57052i	−0.232314	−	0.171357i
$85$		0			0
$86$	4.55868	+	7.89587i	0.491575	+	0.851433i
$87$	5.21545	−	1.39747i	0.559154	−	0.149825i
$88$	−3.01114	+	0.806832i	−0.320988	+	0.0860086i
$89$	−9.18432	−	15.9077i	−0.973536	−	1.68621i	−0.684685	−	0.728839i	$-0.740060\pi$
$89$	−9.18432	−	15.9077i	−0.973536	−	1.68621i	−0.288850	−	0.957374i	$-0.593273\pi$
$90$		0			0
$91$	−3.44960	−	7.90064i	−0.361616	−	0.828212i
$92$	−0.806832	+	0.806832i	−0.0841181	+	0.0841181i
$93$	−1.10215	+	4.11329i	−0.114288	+	0.426528i
$94$	−2.12920	+	3.68788i	−0.219610	+	0.380375i
$95$		0			0
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−0.740585	−	0.740585i	−0.0751950	−	0.0751950i	0.668509	−	0.743704i	$-0.266933\pi$
$97$	−0.740585	−	0.740585i	−0.0751950	−	0.0751950i	−0.743704	+	0.668509i	$0.766933\pi$
$98$	−3.72748	−	5.92503i	−0.376532	−	0.598518i
$99$		−	3.11736i		−	0.313306i
$100$		0			0
$101$	−10.0755	−	5.81707i	−1.00255	−	0.578820i	−0.0935457	−	0.995615i	$-0.529820\pi$
$101$	−10.0755	−	5.81707i	−1.00255	−	0.578820i	−0.909001	+	0.416795i	$0.863153\pi$
$102$	−0.295321	−	1.10215i	−0.0292411	−	0.109129i
$103$	10.2718	+	2.75232i	1.01211	+	0.271194i	0.726511	−	0.687155i	$-0.241141\pi$
$103$	10.2718	+	2.75232i	1.01211	+	0.271194i	0.285599	+	0.958349i	$0.407807\pi$
$104$	−3.25839			−0.319512
$105$		0			0
$106$	−2.88264			−0.279987
$107$	16.0605	+	4.30339i	1.55262	+	0.416024i	0.930319	−	0.366750i	$-0.119530\pi$
$107$	16.0605	+	4.30339i	1.55262	+	0.416024i	0.622305	+	0.782775i	$0.286196\pi$
$108$	−0.258819	−	0.965926i	−0.0249049	−	0.0929463i
$109$	12.3420	+	7.12564i	1.18215	+	0.682512i	0.956510	−	0.291700i	$-0.0942208\pi$
$109$	12.3420	+	7.12564i	1.18215	+	0.682512i	0.225636	+	0.974212i	$0.427554\pi$
$110$		0			0
$111$			5.75572i			0.546309i
$112$	−2.61609	+	0.395046i	−0.247197	+	0.0373284i
$113$	7.08781	+	7.08781i	0.666765	+	0.666765i	0.956966	−	0.290201i	$-0.0937221\pi$
$113$	7.08781	+	7.08781i	0.666765	+	0.666765i	−0.290201	+	0.956966i	$0.593722\pi$
$114$	5.18788	−	2.99522i	0.485889	−	0.280528i
$115$		0			0
$116$	2.69971	−	4.67604i	0.250662	−	0.434159i
$117$	0.843334	−	3.14737i	0.0779663	−	0.290974i
$118$	0.165972	−	0.165972i	0.0152790	−	0.0152790i
$119$	0.337185	−	3.00000i	0.0309097	−	0.275010i
$120$		0			0
$121$	0.641033	+	1.11030i	0.0582757	+	0.100937i
$122$	8.23581	−	2.20678i	0.745636	−	0.199792i
$123$	−9.90885	+	2.65507i	−0.893451	+	0.239399i
$124$	2.12920	+	3.68788i	0.191207	+	0.331181i
$125$		0			0
$126$	0.295509	−	2.62920i	0.0263260	−	0.234227i
$127$	−0.705385	+	0.705385i	−0.0625928	+	0.0625928i	−0.737710	−	0.675117i	$-0.764093\pi$
$127$	−0.705385	+	0.705385i	−0.0625928	+	0.0625928i	0.675117	+	0.737710i	$0.264093\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−4.55868	+	7.89587i	−0.401369	+	0.695192i
$130$		0			0
$131$	−11.6997	+	6.75483i	−1.02221	+	0.590172i	−0.914743	−	0.404036i	$-0.867607\pi$
$131$	−11.6997	+	6.75483i	−1.02221	+	0.590172i	−0.107466	+	0.994209i	$0.534274\pi$
$132$	−2.20431	−	2.20431i	−0.191860	−	0.191860i
$133$	15.6716	−	2.36650i	1.35890	−	0.205202i
$134$			13.9258i			1.20300i
$135$		0			0
$136$	−0.988164	−	0.570516i	−0.0847343	−	0.0489214i
$137$	−4.44327	−	16.5825i	−0.379614	−	1.41674i	−0.846484	−	0.532414i	$-0.821285\pi$
$137$	−4.44327	−	16.5825i	−0.379614	−	1.41674i	0.466870	−	0.884326i	$-0.345382\pi$
$138$	−1.10215	−	0.295321i	−0.0938215	−	0.0251394i
$139$	11.1551			0.946167			0.473084	−	0.881017i	$-0.343141\pi$
$139$	11.1551			0.946167			0.473084	+	0.881017i	$0.343141\pi$
$140$		0			0
$141$	−4.25839			−0.358621
$142$	1.68226	+	0.450761i	0.141172	+	0.0378270i
$143$	−2.62898	−	9.81147i	−0.219846	−	0.820477i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$		0			0
$146$		−	1.13391i		−	0.0938432i
$147$	3.26748	−	6.19060i	0.269498	−	0.510592i
$148$	4.06991	+	4.06991i	0.334545	+	0.334545i
$149$	16.5790	−	9.57191i	1.35821	−	0.784161i	0.368825	−	0.929499i	$-0.379760\pi$
$149$	16.5790	−	9.57191i	1.35821	−	0.784161i	0.989382	+	0.145338i	$0.0464269\pi$
$150$		0			0
$151$	8.74656	−	15.1495i	0.711785	−	1.23285i	−0.252402	−	0.967622i	$-0.581221\pi$
$151$	8.74656	−	15.1495i	0.711785	−	1.23285i	0.964187	−	0.265225i	$-0.0854462\pi$
$152$	1.55044	−	5.78632i	0.125757	−	0.469333i
$153$	0.806832	−	0.806832i	0.0652285	−	0.0652285i
$154$	−3.30029	−	7.55868i	−0.265945	−	0.609096i
$155$		0			0
$156$	−1.62920	−	2.82185i	−0.130440	−	0.225929i
$157$	−12.1063	+	3.24387i	−0.966186	+	0.258889i	−0.707217	−	0.706997i	$-0.750049\pi$
$157$	−12.1063	+	3.24387i	−0.966186	+	0.258889i	−0.258969	+	0.965886i	$0.583383\pi$
$158$	−9.77262	+	2.61857i	−0.777468	+	0.208322i
$159$	−1.44132	−	2.49644i	−0.114304	−	0.197981i
$160$		0			0
$161$	−2.42948	−	1.79201i	−0.191470	−	0.141230i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−3.91019	+	14.5930i	−0.306270	+	1.14301i	0.625578	+	0.780162i	$0.284863\pi$
$163$	−3.91019	+	14.5930i	−0.306270	+	1.14301i	−0.931847	+	0.362851i	$0.881803\pi$
$164$	−5.12920	+	8.88403i	−0.400523	+	0.693726i
$165$		0			0
$166$	9.87219	−	5.69971i	0.766231	−	0.442384i
$167$	1.44769	+	1.44769i	0.112026	+	0.112026i	0.760898	−	0.648872i	$-0.224759\pi$
$167$	1.44769	+	1.44769i	0.112026	+	0.112026i	−0.648872	+	0.760898i	$0.724759\pi$
$168$	−1.65017	−	2.06808i	−0.127313	−	0.159556i
$169$			2.38287i			0.183298i
$170$		0			0
$171$	5.18788	+	2.99522i	0.396727	+	0.229050i
$172$	2.35975	+	8.80669i	0.179929	+	0.671504i
$173$	−11.8178	−	3.16658i	−0.898493	−	0.240751i	−0.220124	−	0.975472i	$-0.570646\pi$
$173$	−11.8178	−	3.16658i	−0.898493	−	0.240751i	−0.678369	+	0.734721i	$0.737313\pi$
$174$	5.39943			0.409329
$175$		0			0
$176$	−3.11736			−0.234980
$177$	0.226722	+	0.0607501i	0.0170415	+	0.00456625i
$178$	−4.75415	−	17.7427i	−0.356339	−	1.32987i
$179$	16.5790	+	9.57191i	1.23917	+	0.715438i	0.968926	−	0.247353i	$-0.0795606\pi$
$179$	16.5790	+	9.57191i	1.23917	+	0.715438i	0.270249	+	0.962790i	$0.412894\pi$
$180$		0			0
$181$			5.22760i			0.388564i	0.980946	+	0.194282i	$0.0622377\pi$
$181$			5.22760i			0.388564i	−0.980946	+	0.194282i	$0.937762\pi$
$182$	−1.28722	−	8.52426i	−0.0954148	−	0.631860i
$183$	6.02903	+	6.02903i	0.445679	+	0.445679i
$184$	−0.988164	+	0.570516i	−0.0728484	+	0.0420590i
$185$		0			0
$186$	−2.12920	+	3.68788i	−0.156120	+	0.270408i
$187$	0.920622	−	3.43581i	0.0673226	−	0.251251i
$188$	−3.01114	+	3.01114i	−0.219610	+	0.219610i
$189$	2.42471	−	1.05868i	0.176371	−	0.0770076i
$190$		0			0
$191$	−5.12920	−	8.88403i	−0.371136	−	0.642826i	0.618605	−	0.785702i	$-0.287698\pi$
$191$	−5.12920	−	8.88403i	−0.371136	−	0.642826i	−0.989741	+	0.142876i	$0.954365\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−4.69340	+	1.25759i	−0.337838	+	0.0905235i	−0.423750	−	0.905779i	$-0.639286\pi$
$193$	−4.69340	+	1.25759i	−0.337838	+	0.0905235i	0.0859114	+	0.996303i	$0.472620\pi$
$194$	−0.523673	−	0.907028i	−0.0375975	−	0.0651208i
$195$		0			0
$196$	−2.06696	−	6.68788i	−0.147640	−	0.477705i
$197$	4.53011	−	4.53011i	0.322757	−	0.322757i	−0.527067	−	0.849824i	$-0.676708\pi$
$197$	4.53011	−	4.53011i	0.322757	−	0.322757i	0.849824	+	0.527067i	$0.176708\pi$
$198$	0.806832	−	3.01114i	0.0573391	−	0.213992i
$199$	−1.28367	+	2.22339i	−0.0909971	+	0.157612i	−0.907931	−	0.419120i	$-0.862339\pi$
$199$	−1.28367	+	2.22339i	−0.0909971	+	0.157612i	0.816934	+	0.576731i	$0.195672\pi$
$200$		0			0
$201$	−12.0601	+	6.96288i	−0.850652	+	0.491124i
$202$	−8.22658	−	8.22658i	−0.578820	−	0.578820i
$203$	13.2995	+	5.21545i	0.933439	+	0.366052i
$204$		−	1.14103i		−	0.0798883i
$205$		0			0
$206$	9.20944	+	5.31707i	0.641652	+	0.370458i
$207$	−0.295321	−	1.10215i	−0.0205262	−	0.0766049i
$208$	−3.14737	−	0.843334i	−0.218231	−	0.0584747i
$209$	18.6744			1.29173
$210$		0			0
$211$	25.1746			1.73309			0.866546	−	0.499098i	$-0.166335\pi$
$211$	25.1746			1.73309			0.866546	+	0.499098i	$0.166335\pi$
$212$	−2.78442	−	0.746082i	−0.191234	−	0.0512411i
$213$	0.450761	+	1.68226i	0.0308856	+	0.115267i
$214$	14.3994	+	8.31351i	0.984325	+	0.568300i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−8.80669	+	7.02706i	−0.597837	+	0.477028i
$218$	10.0772	+	10.0772i	0.682512	+	0.682512i
$219$	0.981996	−	0.566956i	0.0663572	−	0.0383113i
$220$		0			0
$221$	1.85897	−	3.21983i	0.125048	−	0.216589i
$222$	−1.48969	+	5.55960i	−0.0999815	+	0.373136i
$223$	7.35350	−	7.35350i	0.492427	−	0.492427i	−0.416643	−	0.909070i	$-0.636794\pi$
$223$	7.35350	−	7.35350i	0.492427	−	0.492427i	0.909070	+	0.416643i	$0.136794\pi$
$224$	−2.62920	−	0.295509i	−0.175671	−	0.0197445i
$225$		0			0
$226$	5.01184	+	8.68076i	0.333382	+	0.577435i
$227$	−19.6517	+	5.26566i	−1.30433	+	0.349494i	−0.843086	−	0.537779i	$-0.819264\pi$
$227$	−19.6517	+	5.26566i	−1.30433	+	0.349494i	−0.461245	+	0.887273i	$0.652597\pi$
$228$	5.78632	−	1.55044i	0.383209	−	0.102680i
$229$	3.91643	+	6.78346i	0.258805	+	0.448263i	0.965922	−	0.258833i	$-0.0833380\pi$
$229$	3.91643	+	6.78346i	0.258805	+	0.448263i	−0.707117	+	0.707096i	$0.750005\pi$
$230$		0			0
$231$	4.89587	−	6.63747i	0.322124	−	0.436714i
$232$	3.81797	−	3.81797i	0.250662	−	0.250662i
$233$	−1.44769	+	5.40286i	−0.0948415	+	0.353953i	−0.996995	−	0.0774612i	$-0.975319\pi$
$233$	−1.44769	+	5.40286i	−0.0948415	+	0.353953i	0.902154	+	0.431414i	$0.141985\pi$
$234$	1.62920	−	2.82185i	0.106504	−	0.184470i
$235$		0			0
$236$	0.203274	−	0.117360i	0.0132320	−	0.00763949i
$237$	−7.15405	−	7.15405i	−0.464706	−	0.464706i
$238$	1.10215	−	2.81051i	0.0714420	−	0.182178i
$239$		−	12.3686i		−	0.800060i	−0.916502	−	0.400030i	$-0.869000\pi$
$239$		−	12.3686i		−	0.800060i	0.916502	−	0.400030i	$-0.131000\pi$
$240$		0			0
$241$	12.1145	+	6.99433i	0.780366	+	0.450544i	0.836560	−	0.547875i	$-0.184563\pi$
$241$	12.1145	+	6.99433i	0.780366	+	0.450544i	−0.0561941	+	0.998420i	$0.517897\pi$
$242$	0.331823	+	1.23838i	0.0213304	+	0.0796061i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	8.52634			0.545843
$245$		0			0
$246$	−10.2584			−0.654051
$247$	18.8541	+	5.05195i	1.19966	+	0.321448i
$248$	1.10215	+	4.11329i	0.0699868	+	0.261194i
$249$	9.87219	+	5.69971i	0.625625	+	0.361205i
$250$		0			0
$251$		−	17.0336i		−	1.07515i	−0.843216	−	0.537575i	$-0.819341\pi$
$251$		−	17.0336i		−	1.07515i	0.843216	−	0.537575i	$-0.180659\pi$
$252$	0.965926	−	2.46313i	0.0608476	−	0.155162i
$253$	−2.51519	−	2.51519i	−0.158128	−	0.158128i
$254$	−0.863917	+	0.498783i	−0.0542070	+	0.0312964i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.43164	−	20.2711i	0.338816	−	1.26448i	−0.560856	−	0.827913i	$-0.689528\pi$
$257$	5.43164	−	20.2711i	0.338816	−	1.26448i	0.899672	−	0.436566i	$-0.143805\pi$
$258$	−6.44695	+	6.44695i	−0.401369	+	0.401369i
$259$	−9.03946	+	12.2551i	−0.561685	+	0.761493i
$260$		0			0
$261$	2.69971	+	4.67604i	0.167108	+	0.289440i
$262$	−13.0493	+	3.49656i	−0.806191	+	0.216018i
$263$	−18.4888	+	4.95406i	−1.14007	+	0.305481i	−0.778979	−	0.627050i	$-0.784262\pi$
$263$	−18.4888	+	4.95406i	−1.14007	+	0.305481i	−0.361090	+	0.932531i	$0.617595\pi$
$264$	−1.55868	−	2.69971i	−0.0959301	−	0.166156i
$265$		0			0
$266$	15.7501	+	1.77023i	0.965698	+	0.108540i
$267$	12.9886	−	12.9886i	0.794888	−	0.794888i
$268$	−3.60425	+	13.4513i	−0.220165	+	0.821666i
$269$	−14.6138	+	25.3118i	−0.891019	+	1.54329i	−0.0523636	+	0.998628i	$0.516675\pi$
$269$	−14.6138	+	25.3118i	−0.891019	+	1.54329i	−0.838656	+	0.544662i	$0.816658\pi$
$270$		0			0
$271$	19.4796	−	11.2466i	1.18330	−	0.683180i	0.226526	−	0.974005i	$-0.427263\pi$
$271$	19.4796	−	11.2466i	1.18330	−	0.683180i	0.956776	+	0.290826i	$0.0939299\pi$
$272$	−0.806832	−	0.806832i	−0.0489214	−	0.0489214i
$273$	6.73861	−	5.37689i	0.407840	−	0.325424i
$274$		−	17.1675i		−	1.03713i
$275$		0			0
$276$	−0.988164	−	0.570516i	−0.0594805	−	0.0343411i
$277$	−5.60865	−	20.9318i	−0.336991	−	1.25767i	−0.901694	−	0.432374i	$-0.857676\pi$
$277$	−5.60865	−	20.9318i	−0.336991	−	1.25767i	0.564703	−	0.825294i	$-0.308991\pi$
$278$	10.7750	+	2.88717i	0.646244	+	0.173161i
$279$	−4.25839			−0.254943
$280$		0			0
$281$	19.3758			1.15586			0.577930	−	0.816086i	$-0.303861\pi$
$281$	19.3758			1.15586			0.577930	+	0.816086i	$0.303861\pi$
$282$	−4.11329	−	1.10215i	−0.244943	−	0.0656323i
$283$	−4.82531	−	18.0083i	−0.286835	−	1.07048i	−0.947488	−	0.319792i	$-0.896387\pi$
$283$	−4.82531	−	18.0083i	−0.286835	−	1.07048i	0.660653	−	0.750692i	$-0.270280\pi$
$284$	1.50828	+	0.870803i	0.0894997	+	0.0516727i
$285$		0			0
$286$		−	10.1576i		−	0.600631i
$287$	−25.2677	−	9.90885i	−1.49151	−	0.584901i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	−13.5949	+	7.84902i	−0.799700	+	0.461707i
$290$		0			0
$291$	0.523673	−	0.907028i	0.0306982	−	0.0531709i
$292$	0.293478	−	1.09527i	0.0171745	−	0.0640961i
$293$	−11.4539	+	11.4539i	−0.669145	+	0.669145i	−0.957518	−	0.288373i	$-0.906886\pi$
$293$	−11.4539	+	11.4539i	−0.669145	+	0.669145i	0.288373	+	0.957518i	$0.406886\pi$
$294$	4.75839	−	5.13397i	0.277515	−	0.299419i
$295$		0			0
$296$	2.87786	+	4.98460i	0.167272	+	0.289724i
$297$	3.01114	−	0.806832i	0.174724	−	0.0468172i
$298$	18.4915	−	4.95478i	1.07118	−	0.287023i
$299$	−1.85897	−	3.21983i	−0.107507	−	0.186207i
$300$		0			0
$301$	−22.1069	+	9.65237i	−1.27422	+	0.556353i
$302$	12.3695	−	12.3695i	0.711785	−	0.711785i
$303$	3.01114	−	11.2377i	0.172985	−	0.645590i
$304$	2.99522	−	5.18788i	0.171788	−	0.297545i
$305$		0			0
$306$	0.988164	−	0.570516i	0.0564896	−	0.0326143i
$307$	0.398902	+	0.398902i	0.0227665	+	0.0227665i	0.718398	−	0.695632i	$-0.244876\pi$
$307$	0.398902	+	0.398902i	0.0227665	+	0.0227665i	−0.695632	+	0.718398i	$0.744876\pi$
$308$	−1.23150	−	8.15530i	−0.0701713	−	0.464691i
$309$			10.6341i			0.604955i
$310$		0			0
$311$	−11.2317	−	6.48460i	−0.636889	−	0.367708i	0.146526	−	0.989207i	$-0.453191\pi$
$311$	−11.2317	−	6.48460i	−0.636889	−	0.367708i	−0.783415	+	0.621499i	$0.786524\pi$
$312$	−0.843334	−	3.14737i	−0.0477444	−	0.178185i
$313$	1.78875	+	0.479293i	0.101106	+	0.0270912i	0.309017	−	0.951056i	$-0.400000\pi$
$313$	1.78875	+	0.479293i	0.101106	+	0.0270912i	−0.207911	+	0.978148i	$0.566667\pi$
$314$	−12.5333			−0.707297
$315$		0			0
$316$	−10.1174			−0.569146
$317$	−31.2821	−	8.38202i	−1.75698	−	0.470781i	−0.770886	−	0.636973i	$-0.780186\pi$
$317$	−31.2821	−	8.38202i	−1.75698	−	0.470781i	−0.986094	+	0.166191i	$0.946853\pi$
$318$	−0.746082	−	2.78442i	−0.0418382	−	0.156142i
$319$	14.5769	+	8.41598i	0.816150	+	0.471204i
$320$		0			0
$321$			16.6270i			0.928030i
$322$	−1.88289	−	2.35975i	−0.104930	−	0.131504i
$323$	4.83328	+	4.83328i	0.268931	+	0.268931i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$		0			0
$326$	−7.55390	+	13.0837i	−0.418372	+	0.724641i
$327$	−3.68850	+	13.7657i	−0.203975	+	0.761243i
$328$	−7.25378	+	7.25378i	−0.400523	+	0.400523i
$329$	−9.06696	−	6.68788i	−0.499877	−	0.368715i
$330$		0			0
$331$	5.80168	+	10.0488i	0.318889	+	0.552332i	0.980257	−	0.197730i	$-0.0633570\pi$
$331$	5.80168	+	10.0488i	0.318889	+	0.552332i	−0.661368	+	0.750062i	$0.730024\pi$
$332$	11.0110	−	2.95039i	0.604307	−	0.161924i
$333$	−5.55960	+	1.48969i	−0.304664	+	0.0816346i
$334$	1.02367	+	1.77305i	0.0560129	+	0.0970172i
$335$		0			0
$336$	−1.05868	−	2.42471i	−0.0577557	−	0.132279i
$337$	9.45809	−	9.45809i	0.515215	−	0.515215i	−0.400905	−	0.916120i	$-0.631304\pi$
$337$	9.45809	−	9.45809i	0.515215	−	0.515215i	0.916120	+	0.400905i	$0.131304\pi$
$338$	−0.616733	+	2.30168i	−0.0335459	+	0.125195i
$339$	−5.01184	+	8.68076i	−0.272206	+	0.471474i
$340$		0			0
$341$	−11.4964	+	6.63747i	−0.622567	+	0.359439i
$342$	4.23588	+	4.23588i	0.229050	+	0.229050i
$343$	16.6796	−	8.04937i	0.900611	−	0.434625i
$344$			9.11736i			0.491575i
$345$		0			0
$346$	−10.5956	−	6.11736i	−0.569622	−	0.328871i
$347$	5.58708	+	20.8512i	0.299930	+	1.11935i	0.937223	+	0.348732i	$0.113388\pi$
$347$	5.58708	+	20.8512i	0.299930	+	1.11935i	−0.637293	+	0.770622i	$0.719946\pi$
$348$	5.21545	+	1.39747i	0.279577	+	0.0749125i
$349$	14.9455			0.800016			0.400008	−	0.916512i	$-0.369007\pi$
$349$	14.9455			0.800016			0.400008	+	0.916512i	$0.369007\pi$
$350$		0			0
$351$	3.25839			0.173920
$352$	−3.01114	−	0.806832i	−0.160494	−	0.0430043i
$353$	−9.43970	−	35.2295i	−0.502425	−	1.87507i	−0.483669	−	0.875251i	$-0.660696\pi$
$353$	−9.43970	−	35.2295i	−0.502425	−	1.87507i	−0.0187553	−	0.999824i	$-0.505970\pi$
$354$	0.203274	+	0.117360i	0.0108039	+	0.00623762i
$355$		0			0
$356$		−	18.3686i		−	0.973536i
$357$	2.98505	−	0.450761i	0.157985	−	0.0238568i
$358$	13.5367	+	13.5367i	0.715438	+	0.715438i
$359$	−3.77518	+	2.17960i	−0.199246	+	0.115035i	−0.596304	−	0.802759i	$-0.703365\pi$
$359$	−3.77518	+	2.17960i	−0.199246	+	0.115035i	0.397058	+	0.917794i	$0.370031\pi$
$360$		0			0
$361$	−8.44271	+	14.6232i	−0.444353	+	0.769642i
$362$	−1.35300	+	5.04947i	−0.0711122	+	0.265394i
$363$	−0.906558	+	0.906558i	−0.0475819	+	0.0475819i
$364$	0.962884	−	8.56696i	0.0504688	−	0.449030i
$365$		0			0
$366$	4.26317	+	7.38403i	0.222840	+	0.385969i
$367$	−17.9178	+	4.80106i	−0.935302	+	0.250614i	−0.694114	−	0.719865i	$-0.744204\pi$
$367$	−17.9178	+	4.80106i	−0.935302	+	0.250614i	−0.241188	+	0.970478i	$0.577537\pi$
$368$	−1.10215	+	0.295321i	−0.0574537	+	0.0153947i
$369$	−5.12920	−	8.88403i	−0.267015	−	0.462484i
$370$		0			0
$371$	0.851846	−	7.57903i	0.0442256	−	0.393483i
$372$	−3.01114	+	3.01114i	−0.156120	+	0.156120i
$373$	−5.05195	+	18.8541i	−0.261580	+	0.976229i	0.702731	+	0.711456i	$0.251964\pi$
$373$	−5.05195	+	18.8541i	−0.261580	+	0.976229i	−0.964311	+	0.264773i	$0.914703\pi$
$374$	1.77851	−	3.08046i	0.0919643	−	0.159287i
$375$		0			0
$376$	−3.68788	+	2.12920i	−0.190188	+	0.109805i
$377$	12.4404	+	12.4404i	0.640716	+	0.640716i
$378$	2.61609	−	0.395046i	0.134557	−	0.0203190i
$379$		−	37.4424i		−	1.92329i	−0.274300	−	0.961644i	$-0.588446\pi$
$379$		−	37.4424i		−	1.92329i	0.274300	−	0.961644i	$-0.411554\pi$
$380$		0			0
$381$	−0.863917	−	0.498783i	−0.0442598	−	0.0255534i
$382$	−2.65507	−	9.90885i	−0.135845	−	0.506981i
$383$	0.582793	+	0.156159i	0.0297794	+	0.00797935i	0.273678	−	0.961821i	$-0.411760\pi$
$383$	0.582793	+	0.156159i	0.0297794	+	0.00797935i	−0.243899	+	0.969801i	$0.578426\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−4.85897			−0.247315
$387$	−8.80669	−	2.35975i	−0.447669	−	0.119953i
$388$	−0.271073	−	1.01166i	−0.0137616	−	0.0513592i
$389$	−17.6000	−	10.1614i	−0.892357	−	0.515202i	−0.0176441	−	0.999844i	$-0.505617\pi$
$389$	−17.6000	−	10.1614i	−0.892357	−	0.515202i	−0.874713	+	0.484642i	$0.838950\pi$
$390$		0			0
$391$		−	1.30196i		−	0.0658428i
$392$	−0.265576	−	6.99496i	−0.0134136	−	0.353299i
$393$	−9.55278	−	9.55278i	−0.481874	−	0.481874i
$394$	5.54823	−	3.20327i	0.279516	−	0.161379i
$395$		0			0
$396$	1.55868	−	2.69971i	0.0783266	−	0.135666i
$397$	3.10214	−	11.5774i	0.155692	−	0.581051i	−0.843353	−	0.537360i	$-0.819422\pi$
$397$	3.10214	−	11.5774i	0.155692	−	0.581051i	0.999045	−	0.0436908i	$-0.0139116\pi$
$398$	−1.81539	+	1.81539i	−0.0909971	+	0.0909971i
$399$	6.34196	+	14.5251i	0.317495	+	0.727163i
$400$		0			0
$401$	−10.2584	−	17.7681i	−0.512280	−	0.887294i	−0.999899	−	0.0142379i	$-0.995468\pi$
$401$	−10.2584	−	17.7681i	−0.512280	−	0.887294i	0.487619	−	0.873057i	$-0.337866\pi$
$402$	−13.4513	+	3.60425i	−0.670888	+	0.179764i
$403$	−13.4027	+	3.59125i	−0.667637	+	0.178893i
$404$	−5.81707	−	10.0755i	−0.289410	−	0.501273i
$405$		0			0
$406$	11.4964	+	8.47989i	0.570559	+	0.420850i
$407$	−12.6874	+	12.6874i	−0.628890	+	0.628890i
$408$	0.295321	−	1.10215i	0.0146206	−	0.0545647i
$409$	−6.61219	+	11.4527i	−0.326952	+	0.566297i	−0.981905	−	0.189372i	$-0.939355\pi$
$409$	−6.61219	+	11.4527i	−0.326952	+	0.566297i	0.654954	+	0.755669i	$0.272688\pi$
$410$		0			0
$411$	14.8675	−	8.58374i	0.733359	−	0.423405i
$412$	7.51948	+	7.51948i	0.370458	+	0.370458i
$413$	0.387327	+	0.485420i	0.0190591	+	0.0238860i
$414$		−	1.14103i		−	0.0560787i
$415$		0			0
$416$	−2.82185	−	1.62920i	−0.138353	−	0.0798779i
$417$	2.88717	+	10.7750i	0.141385	+	0.527656i
$418$	18.0381	+	4.83328i	0.882270	+	0.236404i
$419$	19.9791			0.976043			0.488022	−	0.872832i	$-0.337719\pi$
$419$	19.9791			0.976043			0.488022	+	0.872832i	$0.337719\pi$
$420$		0			0
$421$	−20.2920			−0.988970			−0.494485	−	0.869186i	$-0.664643\pi$
$421$	−20.2920			−0.988970			−0.494485	+	0.869186i	$0.664643\pi$
$422$	24.3168	+	6.51567i	1.18372	+	0.317178i
$423$	−1.10215	−	4.11329i	−0.0535885	−	0.199995i
$424$	−2.49644	−	1.44132i	−0.121238	−	0.0699967i
$425$		0			0
$426$			1.74161i			0.0843811i
$427$	3.36830	+	22.3057i	0.163004	+	1.07945i
$428$	11.7571	+	11.7571i	0.568300	+	0.568300i
$429$	8.79673	−	5.07879i	0.424710	−	0.245206i
$430$		0			0
$431$	0.167764	−	0.290576i	0.00808092	−	0.0139966i	−0.861957	−	0.506982i	$-0.830761\pi$
$431$	0.167764	−	0.290576i	0.00808092	−	0.0139966i	0.870038	+	0.492985i	$0.164094\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−4.53678	+	4.53678i	−0.218024	+	0.218024i	−0.807665	−	0.589641i	$-0.799269\pi$
$433$	−4.53678	+	4.53678i	−0.218024	+	0.218024i	0.589641	+	0.807665i	$0.299269\pi$
$434$	−10.3253	+	4.50828i	−0.495633	+	0.216404i
$435$		0			0
$436$	7.12564	+	12.3420i	0.341256	+	0.591073i
$437$	6.60239	−	1.76910i	0.315835	−	0.0846277i
$438$	1.09527	−	0.293478i	0.0523342	−	0.0140229i
$439$	13.6209	+	23.5920i	0.650088	+	1.12599i	0.983101	+	0.183063i	$0.0586013\pi$
$439$	13.6209	+	23.5920i	0.650088	+	1.12599i	−0.333013	+	0.942922i	$0.608065\pi$
$440$		0			0
$441$	6.82535	+	1.55390i	0.325017	+	0.0739953i
$442$	2.62898	−	2.62898i	0.125048	−	0.125048i
$443$	−1.33672	+	4.98872i	−0.0635097	+	0.237021i	−0.990383	−	0.138353i	$-0.955819\pi$
$443$	−1.33672	+	4.98872i	−0.0635097	+	0.237021i	0.926873	+	0.375374i	$0.122486\pi$
$444$	−2.87786	+	4.98460i	−0.136577	+	0.236559i
$445$		0			0
$446$	9.00617	−	5.19971i	0.426454	−	0.246214i
$447$	13.5367	+	13.5367i	0.640265	+	0.640265i
$448$	−2.46313	−	0.965926i	−0.116372	−	0.0456357i
$449$		−	26.0501i		−	1.22938i	−0.788768	−	0.614691i	$-0.789281\pi$
$449$		−	26.0501i		−	1.22938i	0.788768	−	0.614691i	$-0.210719\pi$
$450$		0			0
$451$	−27.6947	−	15.9896i	−1.30409	−	0.752919i
$452$	2.59432	+	9.68212i	0.122026	+	0.455409i
$453$	16.8970	+	4.52755i	0.793893	+	0.212723i
$454$	−20.3450			−0.954836
$455$		0			0
$456$	5.99044			0.280528
$457$	29.2530	+	7.83833i	1.36840	+	0.366661i	0.866894	−	0.498493i	$-0.166113\pi$
$457$	29.2530	+	7.83833i	1.36840	+	0.366661i	0.501506	+	0.865154i	$0.332780\pi$
$458$	2.02729	+	7.56596i	0.0947292	+	0.353534i
$459$	0.988164	+	0.570516i	0.0461235	+	0.0266294i
$460$		0			0
$461$		−	3.71793i		−	0.173161i	−0.996245	−	0.0865807i	$-0.972406\pi$
$461$		−	3.71793i		−	0.173161i	0.996245	−	0.0865807i	$-0.0275940\pi$
$462$	6.44695	−	5.14416i	0.299939	−	0.239328i
$463$	−16.3674	−	16.3674i	−0.760658	−	0.760658i	0.215783	−	0.976441i	$-0.430770\pi$
$463$	−16.3674	−	16.3674i	−0.760658	−	0.760658i	−0.976441	+	0.215783i	$0.930770\pi$
$464$	4.67604	−	2.69971i	0.217080	−	0.125331i
$465$		0			0
$466$	−2.79673	+	4.84407i	−0.129556	+	0.224397i
$467$	−7.00365	+	26.1380i	−0.324090	+	1.20952i	0.591133	+	0.806574i	$0.298681\pi$
$467$	−7.00365	+	26.1380i	−0.324090	+	1.20952i	−0.915223	+	0.402947i	$0.867986\pi$
$468$	2.30403	−	2.30403i	0.106504	−	0.106504i
$469$	−36.6136	−	4.11519i	−1.69066	−	0.190022i
$470$		0			0
$471$	−6.26667	−	10.8542i	−0.288753	−	0.500135i
$472$	0.226722	−	0.0607501i	0.0104357	−	0.00279625i
$473$	−27.4536	+	7.35618i	−1.26232	+	0.338237i
$474$	−5.05868	−	8.76189i	−0.232353	−	0.402447i
$475$		0			0
$476$	1.79201	−	2.42948i	0.0821367	−	0.111355i
$477$	2.03833	−	2.03833i	0.0933289	−	0.0933289i
$478$	3.20124	−	11.9472i	0.146421	−	0.546451i
$479$	−21.0873	+	36.5243i	−0.963503	+	1.66884i	−0.249920	+	0.968266i	$0.580404\pi$
$479$	−21.0873	+	36.5243i	−0.963503	+	1.66884i	−0.713583	+	0.700571i	$0.752929\pi$
$480$		0			0
$481$	−16.2418	+	9.37721i	−0.740562	+	0.427564i
$482$	9.89148	+	9.89148i	0.450544	+	0.450544i
$483$	1.10215	−	2.81051i	0.0501497	−	0.127883i
$484$			1.28207i			0.0582757i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	8.09527	+	30.2120i	0.366832	+	1.36903i	0.864921	+	0.501909i	$0.167369\pi$
$487$	8.09527	+	30.2120i	0.366832	+	1.36903i	−0.498089	+	0.867126i	$0.665965\pi$
$488$	8.23581	+	2.20678i	0.372818	+	0.0998962i
$489$	−15.1078			−0.683199
$490$		0			0
$491$	26.7108			1.20544			0.602721	−	0.797952i	$-0.294083\pi$
$491$	26.7108			1.20544			0.602721	+	0.797952i	$0.294083\pi$
$492$	−9.90885	−	2.65507i	−0.446725	−	0.119700i
$493$	1.59456	+	5.95099i	0.0718156	+	0.268019i
$494$	16.9041	+	9.75961i	0.760553	+	0.439106i
$495$		0			0
$496$			4.25839i			0.191207i
$497$	−1.68226	+	4.28980i	−0.0754598	+	0.192424i
$498$	8.06061	+	8.06061i	0.361205	+	0.361205i
$499$	−6.79373	+	3.92236i	−0.304129	+	0.175589i	−0.644296	−	0.764776i	$-0.722850\pi$
$499$	−6.79373	+	3.92236i	−0.304129	+	0.175589i	0.340167	+	0.940365i	$0.389516\pi$
$500$		0			0
$501$	−1.02367	+	1.77305i	−0.0457343	+	0.0792142i
$502$	4.40861	−	16.4532i	0.196766	−	0.734341i
$503$	23.4463	−	23.4463i	1.04542	−	1.04542i	0.0464999	−	0.998918i	$-0.485193\pi$
$503$	23.4463	−	23.4463i	1.04542	−	1.04542i	0.998918	−	0.0464999i	$-0.0148067\pi$
$504$	1.57052	−	2.12920i	0.0699564	−	0.0948420i
$505$		0			0
$506$	−1.77851	−	3.08046i	−0.0790642	−	0.136943i
$507$	−2.30168	+	0.616733i	−0.102221	+	0.0273901i
$508$	−0.963574	+	0.258189i	−0.0427517	+	0.0114553i
$509$	−6.72339	−	11.6452i	−0.298009	−	0.516166i	0.677671	−	0.735365i	$-0.262989\pi$
$509$	−6.72339	−	11.6452i	−0.298009	−	0.516166i	−0.975680	+	0.219198i	$0.929656\pi$
$510$		0			0
$511$	2.98128	+	0.335081i	0.131884	+	0.0148231i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.55044	+	5.78632i	−0.0684536	+	0.255472i
$514$	10.4931	−	18.1746i	0.462831	−	0.801647i
$515$		0			0
$516$	−7.89587	+	4.55868i	−0.347596	+	0.200685i
$517$	−9.38680	−	9.38680i	−0.412831	−	0.412831i
$518$	−11.9033	+	9.49790i	−0.523001	+	0.417314i
$519$		−	12.2347i		−	0.537045i
$520$		0			0
$521$	5.28346	+	3.05040i	0.231472	+	0.133641i	0.611251	−	0.791437i	$-0.290667\pi$
$521$	5.28346	+	3.05040i	0.231472	+	0.133641i	−0.379779	+	0.925077i	$0.624000\pi$
$522$	1.39747	+	5.21545i	0.0611658	+	0.228274i
$523$	−11.3122	−	3.03110i	−0.494649	−	0.132541i	0.00286635	−	0.999996i	$-0.499088\pi$
$523$	−11.3122	−	3.03110i	−0.494649	−	0.132541i	−0.497516	+	0.867455i	$0.665754\pi$
$524$	−13.5097			−0.590172
$525$		0			0
$526$	−19.1410			−0.834589
$527$	−4.69340	−	1.25759i	−0.204448	−	0.0547816i
$528$	−0.806832	−	3.01114i	−0.0351129	−	0.131043i
$529$	18.7911	+	10.8490i	0.817002	+	0.471697i
$530$		0			0
$531$			0.234720i			0.0101860i
$532$	14.7552	+	5.78632i	0.639720	+	0.250869i
$533$	−23.6357	−	23.6357i	−1.02377	−	1.02377i
$534$	15.9077	−	9.18432i	0.688394	−	0.397444i
$535$		0			0
$536$	−6.96288	+	12.0601i	−0.300751	+	0.520916i
$537$	−4.95478	+	18.4915i	−0.213815	+	0.797967i
$538$	−20.6670	+	20.6670i	−0.891019	+	0.891019i
$539$	20.8485	−	6.44345i	0.898009	−	0.277539i
$540$		0			0
$541$	−0.354252	−	0.613582i	−0.0152305	−	0.0263800i	0.858310	−	0.513132i	$-0.171515\pi$
$541$	−0.354252	−	0.613582i	−0.0152305	−	0.0263800i	−0.873540	+	0.486752i	$0.838182\pi$
$542$	21.7267	−	5.82165i	0.933241	−	0.250061i
$543$	−5.04947	+	1.35300i	−0.216694	+	0.0580629i
$544$	−0.570516	−	0.988164i	−0.0244607	−	0.0423672i
$545$		0			0
$546$	7.90064	−	3.44960i	0.338116	−	0.147629i
$547$	24.3712	−	24.3712i	1.04204	−	1.04204i	0.0429611	−	0.999077i	$-0.486321\pi$
$547$	24.3712	−	24.3712i	1.04204	−	1.04204i	0.999077	−	0.0429611i	$-0.0136792\pi$
$548$	4.44327	−	16.5825i	0.189807	−	0.708370i
$549$	−4.26317	+	7.38403i	−0.181948	+	0.315143i
$550$		0			0
$551$	−28.0116	+	16.1725i	−1.19333	+	0.688971i
$552$	−0.806832	−	0.806832i	−0.0343411	−	0.0343411i
$553$	−3.99683	−	26.4679i	−0.169962	−	1.12553i
$554$		−	21.6702i		−	0.920677i
$555$		0			0
$556$	9.66064	+	5.57757i	0.409703	+	0.236542i
$557$	5.47611	+	20.4371i	0.232030	+	0.865948i	0.979465	+	0.201613i	$0.0646184\pi$
$557$	5.47611	+	20.4371i	0.232030	+	0.865948i	−0.747435	+	0.664335i	$0.768715\pi$
$558$	−4.11329	−	1.10215i	−0.174130	−	0.0466579i
$559$	−29.7079			−1.25651
$560$		0			0
$561$	3.55701			0.150177
$562$	18.7155	+	5.01481i	0.789467	+	0.211537i
$563$	8.98894	+	33.5472i	0.378839	+	1.41385i	0.847654	+	0.530549i	$0.178014\pi$
$563$	8.98894	+	33.5472i	0.378839	+	1.41385i	−0.468815	+	0.883296i	$0.655319\pi$
$564$	−3.68788	−	2.12920i	−0.155288	−	0.0896553i
$565$		0			0
$566$		−	18.6436i		−	0.783648i
$567$	1.65017	+	2.06808i	0.0693005	+	0.0868512i
$568$	1.23150	+	1.23150i	0.0516727	+	0.0516727i
$569$	4.58874	−	2.64931i	0.192370	−	0.111065i	−0.400722	−	0.916200i	$-0.631241\pi$
$569$	4.58874	−	2.64931i	0.192370	−	0.111065i	0.593092	+	0.805135i	$0.297907\pi$
$570$		0			0
$571$	−12.9427	+	22.4174i	−0.541636	+	0.938140i	0.457175	+	0.889377i	$0.348861\pi$
$571$	−12.9427	+	22.4174i	−0.541636	+	0.938140i	−0.998810	+	0.0487634i	$0.984472\pi$
$572$	2.62898	−	9.81147i	0.109923	−	0.410238i
$573$	7.25378	−	7.25378i	0.303031	−	0.303031i
$574$	−21.8421	−	16.1110i	−0.911673	−	0.672459i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−20.2574	+	5.42795i	−0.843326	+	0.225968i	−0.654519	−	0.756046i	$-0.727129\pi$
$577$	−20.2574	+	5.42795i	−0.843326	+	0.225968i	−0.188807	+	0.982014i	$0.560462\pi$
$578$	−15.1631	+	4.06295i	−0.630704	+	0.168997i
$579$	−2.42948	−	4.20799i	−0.100966	−	0.174878i
$580$		0			0
$581$	12.0683	+	27.6403i	0.500679	+	1.14671i
$582$	0.740585	−	0.740585i	0.0306982	−	0.0306982i
$583$	2.32581	−	8.68003i	0.0963251	−	0.359490i
$584$	0.566956	−	0.981996i	0.0234608	−	0.0406353i
$585$		0			0
$586$	−14.0281	+	8.09914i	−0.579496	+	0.334572i
$587$	21.0917	+	21.0917i	0.870548	+	0.870548i	0.992532	−	0.121984i	$-0.0389257\pi$
$587$	21.0917	+	21.0917i	0.870548	+	0.870548i	−0.121984	+	0.992532i	$0.538926\pi$
$588$	5.92503	−	3.72748i	0.244344	−	0.153719i
$589$		−	25.5097i		−	1.05111i
$590$		0			0
$591$	5.54823	+	3.20327i	0.228224	+	0.131765i
$592$	1.48969	+	5.55960i	0.0612259	+	0.228498i
$593$	−23.1242	−	6.19610i	−0.949595	−	0.254443i	−0.249405	−	0.968399i	$-0.580235\pi$
$593$	−23.1242	−	6.19610i	−0.949595	−	0.254443i	−0.700190	+	0.713956i	$0.746902\pi$
$594$	3.11736			0.127907
$595$		0			0
$596$	19.1438			0.784161
$597$	−2.47986	−	0.664478i	−0.101494	−	0.0271953i
$598$	−0.962272	−	3.59125i	−0.0393502	−	0.146857i
$599$	−22.3474	−	12.9022i	−0.913088	−	0.527172i	−0.0316646	−	0.999499i	$-0.510081\pi$
$599$	−22.3474	−	12.9022i	−0.913088	−	0.527172i	−0.881423	+	0.472327i	$0.843414\pi$
$600$		0			0
$601$			26.1745i			1.06768i	0.845586	+	0.533840i	$0.179251\pi$
$601$			26.1745i			1.06768i	−0.845586	+	0.533840i	$0.820749\pi$
$602$	−23.8519	+	3.60178i	−0.972129	+	0.146798i
$603$	−9.84701	−	9.84701i	−0.401001	−	0.401001i
$604$	15.1495	−	8.74656i	0.616424	−	0.355892i
$605$		0			0
$606$	5.81707	−	10.0755i	0.236302	−	0.409288i
$607$	8.50340	−	31.7351i	0.345142	−	1.28809i	−0.547303	−	0.836934i	$-0.684346\pi$
$607$	8.50340	−	31.7351i	0.345142	−	1.28809i	0.892446	−	0.451155i	$-0.148988\pi$
$608$	4.23588	−	4.23588i	0.171788	−	0.171788i
$609$	−1.59558	+	14.1962i	−0.0646561	+	0.575257i
$610$		0			0
$611$	−6.93776	−	12.0166i	−0.280672	−	0.486138i
$612$	1.10215	−	0.295321i	0.0445519	−	0.0119376i
$613$	−37.5024	+	10.0487i	−1.51471	+	0.405864i	−0.917995	−	0.396592i	$-0.870193\pi$
$613$	−37.5024	+	10.0487i	−1.51471	+	0.405864i	−0.596711	+	0.802456i	$0.703526\pi$
$614$	0.282066	+	0.488553i	0.0113833	+	0.0197164i
$615$		0			0
$616$	0.921208	−	8.19615i	0.0371165	−	0.330232i
$617$	−16.2604	+	16.2604i	−0.654618	+	0.654618i	−0.954102	−	0.299483i	$-0.903186\pi$
$617$	−16.2604	+	16.2604i	−0.654618	+	0.654618i	0.299483	+	0.954102i	$0.403186\pi$
$618$	−2.75232	+	10.2718i	−0.110715	+	0.413192i
$619$	13.8100	−	23.9195i	0.555069	−	0.961407i	−0.442829	−	0.896606i	$-0.646025\pi$
$619$	13.8100	−	23.9195i	0.555069	−	0.961407i	0.997898	−	0.0648015i	$-0.0206414\pi$
$620$		0			0
$621$	0.988164	−	0.570516i	0.0396536	−	0.0228940i
$622$	−9.17061	−	9.17061i	−0.367708	−	0.367708i
$623$	48.0540	−	7.25646i	1.92524	−	0.290724i
$624$		−	3.25839i		−	0.130440i
$625$		0			0
$626$	1.60375	+	0.925923i	0.0640986	+	0.0370073i
$627$	4.83328	+	18.0381i	0.193023	+	0.720371i
$628$	−12.1063	−	3.24387i	−0.483093	−	0.129444i
$629$	−6.56747			−0.261862
$630$		0			0
$631$	−19.7151			−0.784844			−0.392422	−	0.919785i	$-0.628363\pi$
$631$	−19.7151			−0.784844			−0.392422	+	0.919785i	$0.628363\pi$
$632$	−9.77262	−	2.61857i	−0.388734	−	0.104161i
$633$	6.51567	+	24.3168i	0.258975	+	0.966506i
$634$	−28.0468	−	16.1928i	−1.11388	−	0.643099i
$635$		0			0
$636$		−	2.88264i		−	0.114304i
$637$	22.7923	−	0.865352i	0.903065	−	0.0342865i
$638$	11.9020	+	11.9020i	0.471204	+	0.471204i
$639$	−1.50828	+	0.870803i	−0.0596665	+	0.0344485i
$640$		0			0
$641$	0.453156	−	0.784890i	0.0178986	−	0.0310013i	−0.856937	−	0.515421i	$-0.827636\pi$
$641$	0.453156	−	0.784890i	0.0178986	−	0.0310013i	0.874836	+	0.484419i	$0.160969\pi$
$642$	−4.30339	+	16.0605i	−0.169841	+	0.633856i
$643$	−4.52704	+	4.52704i	−0.178529	+	0.178529i	−0.790714	−	0.612185i	$-0.790291\pi$
$643$	−4.52704	+	4.52704i	−0.178529	+	0.178529i	0.612185	+	0.790714i	$0.290291\pi$
$644$	−1.20799	−	2.76667i	−0.0476014	−	0.109022i
$645$		0			0
$646$	3.41765	+	5.91954i	0.134466	+	0.232901i
$647$	−10.1722	+	2.72563i	−0.399910	+	0.107156i	−0.453168	−	0.891425i	$-0.649706\pi$
$647$	−10.1722	+	2.72563i	−0.399910	+	0.107156i	0.0532577	+	0.998581i	$0.483040\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	0.365854	+	0.633677i	0.0143610	+	0.0248740i
$650$		0			0
$651$	−9.06696	−	6.68788i	−0.355362	−	0.262119i
$652$	−10.6828	+	10.6828i	−0.418372	+	0.418372i
$653$	−5.97781	+	22.3095i	−0.233930	+	0.873037i	0.744699	+	0.667401i	$0.232593\pi$
$653$	−5.97781	+	22.3095i	−0.233930	+	0.873037i	−0.978628	+	0.205636i	$0.934074\pi$
$654$	−7.12564	+	12.3420i	−0.278634	+	0.482609i
$655$		0			0
$656$	−8.88403	+	5.12920i	−0.346863	+	0.200261i
$657$	0.801797	+	0.801797i	0.0312811	+	0.0312811i
$658$	−7.02706	−	8.80669i	−0.273943	−	0.343321i
$659$			43.2474i			1.68468i	0.538947	+	0.842340i	$0.318822\pi$
$659$			43.2474i			1.68468i	−0.538947	+	0.842340i	$0.681178\pi$
$660$		0			0
$661$	−17.0787	−	9.86042i	−0.664286	−	0.383526i	0.129622	−	0.991563i	$-0.458624\pi$
$661$	−17.0787	−	9.86042i	−0.664286	−	0.383526i	−0.793908	+	0.608038i	$0.791957\pi$
$662$	3.00317	+	11.2080i	0.116721	+	0.435610i
$663$	3.59125	+	0.962272i	0.139473	+	0.0373716i
$664$	11.3994			0.442384
$665$		0			0
$666$	−5.75572			−0.223030
$667$	5.95099	+	1.59456i	0.230423	+	0.0617418i
$668$	0.529892	+	1.97758i	0.0205021	+	0.0765150i
$669$	9.00617	+	5.19971i	0.348199	+	0.201033i
$670$		0			0
$671$			26.5797i			1.02610i
$672$	−0.395046	−	2.61609i	−0.0152392	−	0.100918i
$673$	−15.0859	−	15.0859i	−0.581517	−	0.581517i	0.353803	−	0.935320i	$-0.384888\pi$
$673$	−15.0859	−	15.0859i	−0.581517	−	0.581517i	−0.935320	+	0.353803i	$0.884888\pi$
$674$	11.5837	−	6.68788i	0.446189	−	0.257607i
$675$		0			0
$676$	−1.19144	+	2.06363i	−0.0458245	+	0.0793704i
$677$	−3.45209	+	12.8834i	−0.132674	+	0.495148i	−0.999997	−	0.00259937i	$-0.999173\pi$
$677$	−3.45209	+	12.8834i	−0.132674	+	0.495148i	0.867322	+	0.497747i	$0.165839\pi$
$678$	−7.08781	+	7.08781i	−0.272206	+	0.272206i
$679$	2.53951	−	1.10880i	0.0974573	−	0.0425520i
$680$		0			0
$681$	−10.1725	−	17.6193i	−0.389810	−	0.675171i
$682$	−12.8226	+	3.43581i	−0.491003	+	0.131564i
$683$	31.8622	−	8.53746i	1.21918	−	0.326677i	0.408819	−	0.912615i	$-0.365941\pi$
$683$	31.8622	−	8.53746i	1.21918	−	0.326677i	0.810356	+	0.585938i	$0.199274\pi$
$684$	2.99522	+	5.18788i	0.114525	+	0.198363i
$685$		0			0
$686$	18.1945	−	3.45811i	0.694671	−	0.132031i
$687$	−5.53867	+	5.53867i	−0.211313	+	0.211313i
$688$	−2.35975	+	8.80669i	−0.0899645	+	0.335752i
$689$	4.69639	−	8.13438i	0.178918	−	0.309895i
$690$		0			0
$691$	32.0104	−	18.4812i	1.21773	−	0.703059i	0.253301	−	0.967388i	$-0.418484\pi$
$691$	32.0104	−	18.4812i	1.21773	−	0.703059i	0.964433	+	0.264329i	$0.0851505\pi$
$692$	−8.65125	−	8.65125i	−0.328871	−	0.328871i
$693$	7.67845	+	3.01114i	0.291680	+	0.114384i
$694$			21.5868i			0.819424i
$695$		0			0
$696$	4.67604	+	2.69971i	0.177245	+	0.102332i
$697$	−3.02952	−	11.3063i	−0.114751	−	0.428257i
$698$	14.4363	+	3.86819i	0.546421	+	0.146413i
$699$	−5.59345			−0.211564
$700$		0			0
$701$	18.4397			0.696456			0.348228	−	0.937410i	$-0.386784\pi$
$701$	18.4397			0.696456			0.348228	+	0.937410i	$0.386784\pi$
$702$	3.14737	+	0.843334i	0.118790	+	0.0318296i
$703$	−8.92391	−	33.3045i	−0.336572	−	1.25610i
$704$	−2.69971	−	1.55868i	−0.101749	−	0.0587450i
$705$		0			0
$706$		−	36.4722i		−	1.37265i
$707$	24.0603	−	19.1983i	0.904882	−	0.722026i
$708$	0.165972	+	0.165972i	0.00623762	+	0.00623762i
$709$	−33.7593	+	19.4909i	−1.26786	+	0.731998i	−0.974582	−	0.224030i	$-0.928078\pi$
$709$	−33.7593	+	19.4909i	−1.26786	+	0.731998i	−0.293275	+	0.956028i	$0.594745\pi$
$710$		0			0
$711$	5.05868	−	8.76189i	0.189715	−	0.328597i
$712$	4.75415	−	17.7427i	0.178169	−	0.664937i
$713$	−3.43581	+	3.43581i	−0.128672	+	0.128672i
$714$	3.00000	+	0.337185i	0.112272	+	0.0126188i
$715$		0			0
$716$	9.57191	+	16.5790i	0.357719	+	0.619587i
$717$	11.9472	−	3.20124i	0.446176	−	0.119552i
$718$	−4.21067	+	1.12824i	−0.157141	+	0.0421057i
$719$	9.01794	+	15.6195i	0.336312	+	0.582510i	0.983736	−	0.179620i	$-0.0574869\pi$
$719$	9.01794	+	15.6195i	0.336312	+	0.582510i	−0.647424	+	0.762130i	$0.724154\pi$
$720$		0			0
$721$	−16.7011	+	22.6422i	−0.621982	+	0.843239i
$722$	−11.9398	+	11.9398i	−0.444353	+	0.444353i
$723$	−3.62053	+	13.5120i	−0.134649	+	0.502517i
$724$	−2.61380	+	4.52723i	−0.0971411	+	0.168253i
$725$		0			0
$726$	−1.11030	+	0.641033i	−0.0412072	+	0.0237910i
$727$	−34.0615	−	34.0615i	−1.26327	−	1.26327i	−0.949498	−	0.313774i	$-0.898407\pi$
$727$	−34.0615	−	34.0615i	−1.26327	−	1.26327i	−0.313774	−	0.949498i	$-0.601593\pi$
$728$	3.14737	−	8.02583i	0.116649	−	0.297457i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−9.00944	−	5.20160i	−0.333226	−	0.192388i
$732$	2.20678	+	8.23581i	0.0815649	+	0.304404i
$733$	32.6701	+	8.75391i	1.20670	+	0.323333i	0.805465	−	0.592644i	$-0.201916\pi$
$733$	32.6701	+	8.75391i	1.20670	+	0.323333i	0.401231	+	0.915977i	$0.368582\pi$
$734$	−18.5499			−0.684689
$735$		0			0
$736$	−1.14103			−0.0420590
$737$	−41.9324	−	11.2358i	−1.54460	−	0.413874i
$738$	−2.65507	−	9.90885i	−0.0977344	−	0.364750i
$739$	−15.9959	−	9.23522i	−0.588418	−	0.339723i	0.176054	−	0.984381i	$-0.443667\pi$
$739$	−15.9959	−	9.23522i	−0.588418	−	0.339723i	−0.764472	+	0.644657i	$0.777000\pi$
$740$		0			0
$741$			19.5192i			0.717057i
$742$	2.78442	−	7.10030i	0.102219	−	0.260660i
$743$	32.1999	+	32.1999i	1.18130	+	1.18130i	0.979407	+	0.201894i	$0.0647096\pi$
$743$	32.1999	+	32.1999i	1.18130	+	1.18130i	0.201894	+	0.979407i	$0.435290\pi$
$744$	−3.68788	+	2.12920i	−0.135204	+	0.0780601i
$745$		0			0
$746$	−9.75961	+	16.9041i	−0.357325	+	0.618905i
$747$	−2.95039	+	11.0110i	−0.107949	+	0.402871i
$748$	2.51519	−	2.51519i	0.0919643	−	0.0919643i
$749$	−26.1130	+	35.4022i	−0.954149	+	1.29357i
$750$		0			0
$751$	4.62208	+	8.00567i	0.168662	+	0.292131i	0.937950	−	0.346771i	$-0.112722\pi$
$751$	4.62208	+	8.00567i	0.168662	+	0.292131i	−0.769288	+	0.638902i	$0.779389\pi$
$752$	−4.11329	+	1.10215i	−0.149996	+	0.0401914i
$753$	16.4532	−	4.40861i	0.599587	−	0.160659i
$754$	8.79673	+	15.2364i	0.320358	+	0.554876i
$755$		0			0
$756$	2.62920	+	0.295509i	0.0956230	+	0.0107476i
$757$	−15.1284	+	15.1284i	−0.549850	+	0.549850i	−0.926397	−	0.376548i	$-0.877111\pi$
$757$	−15.1284	+	15.1284i	−0.549850	+	0.549850i	0.376548	+	0.926397i	$0.377111\pi$
$758$	9.69081	−	36.1666i	0.351986	−	1.31363i
$759$	1.77851	−	3.08046i	0.0645557	−	0.111814i
$760$		0			0
$761$	32.4867	−	18.7562i	1.17764	−	0.679913i	0.222175	−	0.975007i	$-0.428684\pi$
$761$	32.4867	−	18.7562i	1.17764	−	0.679913i	0.955468	+	0.295094i	$0.0953511\pi$
$762$	−0.705385	−	0.705385i	−0.0255534	−	0.0255534i
$763$	−29.4728	+	23.5170i	−1.06699	+	0.851371i
$764$		−	10.2584i		−	0.371136i
$765$		0			0
$766$	0.522518	+	0.301676i	0.0188794	+	0.0109000i
$767$	0.197948	+	0.738750i	0.00714747	+	0.0266747i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	−0.469440			−0.0169285			−0.00846423	−	0.999964i	$-0.502694\pi$
$769$	−0.469440			−0.0169285			−0.00846423	+	0.999964i	$0.502694\pi$
$770$		0			0
$771$	20.9862			0.755800
$772$	−4.69340	−	1.25759i	−0.168919	−	0.0452618i
$773$	−6.66314	−	24.8672i	−0.239656	−	0.894410i	−0.975994	−	0.217796i	$-0.930113\pi$
$773$	−6.66314	−	24.8672i	−0.239656	−	0.894410i	0.736338	−	0.676614i	$-0.236553\pi$
$774$	−7.89587	−	4.55868i	−0.283811	−	0.163858i
$775$		0			0
$776$		−	1.04735i		−	0.0375975i
$777$	−14.1771	−	5.55960i	−0.508600	−	0.199450i
$778$	−14.3704	−	14.3704i	−0.515202	−	0.515202i
$779$	53.2193	−	30.7262i	1.90678	−	1.10088i
$780$		0			0
$781$	−2.71461	+	4.70184i	−0.0971363	+	0.168245i
$782$	0.336971	−	1.25759i	0.0120501	−	0.0449714i
$783$	−3.81797	+	3.81797i	−0.136443	+	0.136443i
$784$	1.55390	−	6.82535i	0.0554965	−	0.243762i
$785$		0			0
$786$	−6.75483	−	11.6997i	−0.240937	−	0.417315i
$787$	−24.9641	+	6.68911i	−0.889874	+	0.238441i	−0.674662	−	0.738127i	$-0.735711\pi$
$787$	−24.9641	+	6.68911i	−0.889874	+	0.238441i	−0.215211	+	0.976567i	$0.569044\pi$
$788$	6.18825	−	1.65814i	0.220447	−	0.0590687i
$789$	−9.57052	−	16.5766i	−0.340719	−	0.590143i
$790$		0			0
$791$	−24.3045	+	10.6119i	−0.864167	+	0.377314i
$792$	2.20431	−	2.20431i	0.0783266	−	0.0783266i
$793$	−7.19056	+	26.8355i	−0.255344	+	0.952957i
$794$	5.99288	−	10.3800i	0.212679	−	0.368371i
$795$		0			0
$796$	−2.22339	+	1.28367i	−0.0788058	+	0.0454986i
$797$	30.2041	+	30.2041i	1.06988	+	1.06988i	0.997367	+	0.0725174i	$0.0231033\pi$
$797$	30.2041	+	30.2041i	1.06988	+	1.06988i	0.0725174	+	0.997367i	$0.476897\pi$
$798$	2.36650	+	15.6716i	0.0837733	+	0.554767i
$799$		−	4.85897i		−	0.171898i
$800$		0			0
$801$	15.9077	+	9.18432i	0.562071	+	0.324512i
$802$	−5.31014	−	19.8177i	−0.187507	−	0.699787i
$803$	3.41437	+	0.914876i	0.120490	+	0.0322853i
$804$	−13.9258			−0.491124
$805$		0			0
$806$	−13.8755			−0.488744
$807$	−28.2317	−	7.56466i	−0.993803	−	0.266289i
$808$	−3.01114	−	11.2377i	−0.105931	−	0.395342i
$809$	11.3829	+	6.57191i	0.400201	+	0.231056i	0.686571	−	0.727063i	$-0.259115\pi$
$809$	11.3829	+	6.57191i	0.400201	+	0.231056i	−0.286370	+	0.958119i	$0.592449\pi$
$810$		0			0
$811$			1.45633i			0.0511386i	0.999673	+	0.0255693i	$0.00813985\pi$
$811$			1.45633i			0.0511386i	−0.999673	+	0.0255693i	$0.991860\pi$
$812$	8.90995	+	11.1664i	0.312678	+	0.391865i
$813$	15.9050	+	15.9050i	0.557814	+	0.557814i
$814$	−15.5388	+	8.97133i	−0.544635	+	0.314445i
$815$		0			0
$816$	0.570516	−	0.988164i	0.0199721	−	0.0345926i
$817$	14.1359	−	52.7560i	0.494554	−	1.84570i
$818$	−9.35105	+	9.35105i	−0.326952	+	0.326952i
$819$	6.93776	+	5.11736i	0.242425	+	0.178815i
$820$		0			0
$821$	−3.43420	−	5.94821i	−0.119854	−	0.207594i	0.799855	−	0.600193i	$-0.204909\pi$
$821$	−3.43420	−	5.94821i	−0.119854	−	0.207594i	−0.919710	+	0.392599i	$0.871576\pi$
$822$	16.5825	−	4.44327i	0.578382	−	0.154977i
$823$	−5.25665	+	1.40852i	−0.183235	+	0.0490978i	−0.349270	−	0.937022i	$-0.613570\pi$
$823$	−5.25665	+	1.40852i	−0.183235	+	0.0490978i	0.166035	+	0.986120i	$0.446904\pi$
$824$	5.31707	+	9.20944i	0.185229	+	0.320826i
$825$		0			0
$826$	0.248494	+	0.569127i	0.00864620	+	0.0198025i
$827$	4.02842	−	4.02842i	0.140082	−	0.140082i	−0.633589	−	0.773670i	$-0.718419\pi$
$827$	4.02842	−	4.02842i	0.140082	−	0.140082i	0.773670	+	0.633589i	$0.218419\pi$
$828$	0.295321	−	1.10215i	0.0102631	−	0.0383025i
$829$	9.72816	−	16.8497i	0.337873	−	0.585213i	−0.646159	−	0.763203i	$-0.723626\pi$
$829$	9.72816	−	16.8497i	0.337873	−	0.585213i	0.984032	+	0.177989i	$0.0569592\pi$
$830$		0			0
$831$	18.7669	−	10.8351i	0.651017	−	0.375865i
$832$	−2.30403	−	2.30403i	−0.0798779	−	0.0798779i
$833$	7.06368	+	3.72831i	0.244742	+	0.129178i
$834$			11.1551i			0.386271i
$835$		0			0
$836$	16.1725	+	9.33719i	0.559337	+	0.322933i
$837$	−1.10215	−	4.11329i	−0.0380960	−	0.142176i
$838$	19.2983	+	5.17097i	0.666650	+	0.178628i
$839$	−10.1273			−0.349632			−0.174816	−	0.984601i	$-0.555933\pi$
$839$	−10.1273			−0.349632			−0.174816	+	0.984601i	$0.555933\pi$
$840$		0			0
$841$	−0.153802			−0.00530352
$842$	−19.6005	−	5.25195i	−0.675479	−	0.180994i
$843$	5.01481	+	18.7155i	0.172719	+	0.644597i
$844$	21.8018	+	12.5873i	0.750451	+	0.433273i
$845$		0			0
$846$		−	4.25839i		−	0.146407i
$847$	−3.35400	+	0.506476i	−0.115245	+	0.0174027i
$848$	−2.03833	−	2.03833i	−0.0699967	−	0.0699967i
$849$	16.1458	−	9.32179i	0.554123	−	0.319923i
$850$		0			0
$851$	−3.28374	+	5.68760i	−0.112565	+	0.194968i
$852$	−0.450761	+	1.68226i	−0.0154428	+	0.0576334i
$853$	27.6531	−	27.6531i	0.946824	−	0.946824i	−0.0518322	−	0.998656i	$-0.516506\pi$
$853$	27.6531	−	27.6531i	0.946824	−	0.946824i	0.998656	+	0.0518322i	$0.0165061\pi$
$854$	−2.51961	+	22.4174i	−0.0862193	+	0.767109i
$855$		0			0
$856$	8.31351	+	14.3994i	0.284150	+	0.492162i
$857$	29.4312	−	7.88607i	1.00535	−	0.269383i	0.281665	−	0.959513i	$-0.409113\pi$
$857$	29.4312	−	7.88607i	1.00535	−	0.269383i	0.723686	+	0.690130i	$0.242446\pi$
$858$	9.81147	−	2.62898i	0.334958	−	0.0897518i
$859$	17.6997	+	30.6568i	0.603906	+	1.04600i	0.992223	+	0.124471i	$0.0397233\pi$
$859$	17.6997	+	30.6568i	0.603906	+	1.04600i	−0.388317	+	0.921526i	$0.626943\pi$
$860$		0			0
$861$	3.03145	−	26.9713i	0.103311	−	0.919181i
$862$	0.237255	−	0.237255i	0.00808092	−	0.00808092i
$863$	−1.05194	+	3.92588i	−0.0358083	+	0.133638i	−0.981516	−	0.191380i	$-0.938704\pi$
$863$	−1.05194	+	3.92588i	−0.0358083	+	0.133638i	0.945708	+	0.325018i	$0.105370\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−5.55640	+	3.20799i	−0.188814	+	0.109012i
$867$	−11.1002	−	11.1002i	−0.376982	−	0.376982i
$868$	−11.1403	+	1.68226i	−0.378128	+	0.0570997i
$869$		−	31.5395i		−	1.06990i
$870$		0			0
$871$	−39.2964	−	22.6878i	−1.33151	−	0.768747i
$872$	3.68850	+	13.7657i	0.124908	+	0.466164i
$873$	1.01166	+	0.271073i	0.0342394	+	0.00917443i
$874$	6.83529			0.231207
$875$		0			0
$876$	1.13391			0.0383113
$877$	−24.7603	−	6.63449i	−0.836095	−	0.224031i	−0.184724	−	0.982790i	$-0.559139\pi$
$877$	−24.7603	−	6.63449i	−0.836095	−	0.224031i	−0.651371	+	0.758760i	$0.725806\pi$
$878$	7.05067	+	26.3135i	0.237949	+	0.888037i
$879$	−14.0281	−	8.09914i	−0.473157	−	0.273177i
$880$		0			0
$881$		−	1.74161i		−	0.0586762i	−0.999570	−	0.0293381i	$-0.990660\pi$
$881$		−	1.74161i		−	0.0586762i	0.999570	−	0.0293381i	$-0.00933995\pi$
$882$	6.19060	+	3.26748i	0.208448	+	0.110022i
$883$	3.58173	+	3.58173i	0.120535	+	0.120535i	0.764801	−	0.644266i	$-0.222837\pi$
$883$	3.58173	+	3.58173i	0.120535	+	0.120535i	−0.644266	+	0.764801i	$0.722837\pi$
$884$	3.21983	−	1.85897i	0.108294	−	0.0625238i
$885$		0			0
$886$	−2.58235	+	4.47277i	−0.0867558	+	0.150266i
$887$	5.68177	−	21.2046i	0.190775	−	0.711982i	−0.802545	−	0.596591i	$-0.796521\pi$
$887$	5.68177	−	21.2046i	0.190775	−	0.711982i	0.993320	−	0.115391i	$-0.0368120\pi$
$888$	−4.06991	+	4.06991i	−0.136577	+	0.136577i
$889$	−1.05610	−	2.41880i	−0.0354205	−	0.0811240i
$890$		0			0
$891$	1.55868	+	2.69971i	0.0522177	+	0.0904438i
$892$	10.0451	−	2.69157i	0.336334	−	0.0901204i
$893$	24.6404	−	6.60239i	0.824561	−	0.220940i
$894$	9.57191	+	16.5790i	0.320132	+	0.554486i
$895$		0			0
$896$	−2.12920	−	1.57052i	−0.0711315	−	0.0524673i
$897$	2.62898	−	2.62898i	0.0877790	−	0.0877790i
$898$	6.74227	−	25.1625i	0.224992	−	0.839683i
$899$	11.4964	−	19.9124i	0.383428	−	0.664116i
$900$		0			0
$901$	2.84852	−	1.64459i	0.0948979	−	0.0547894i
$902$	−22.6126	−	22.6126i	−0.752919	−	0.752919i
$903$	−15.0452	−	18.8554i	−0.500672	−	0.627469i
$904$			10.0237i			0.333382i
$905$		0			0
$906$	15.1495	+	8.74656i	0.503308	+	0.290585i
$907$	−0.178339	−	0.665569i	−0.00592164	−	0.0220999i	0.962902	−	0.269852i	$-0.0869748\pi$
$907$	−0.178339	−	0.665569i	−0.00592164	−	0.0220999i	−0.968823	+	0.247752i	$0.920308\pi$
$908$	−19.6517	−	5.26566i	−0.652165	−	0.174747i
$909$	11.6341			0.385880
$910$		0			0
$911$	20.8225			0.689881			0.344941	−	0.938625i	$-0.387899\pi$
$911$	20.8225			0.689881			0.344941	+	0.938625i	$0.387899\pi$
$912$	5.78632	+	1.55044i	0.191604	+	0.0513402i
$913$	9.19742	+	34.3253i	0.304390	+	1.13600i
$914$	26.2276	+	15.1425i	0.867530	+	0.500869i
$915$		0			0
$916$			7.83286i			0.258805i
$917$	−5.33695	−	35.3425i	−0.176241	−	1.16711i
$918$	0.806832	+	0.806832i	0.0266294	+	0.0266294i
$919$	−38.5703	+	22.2686i	−1.27232	+	0.734572i	−0.975423	−	0.220339i	$-0.929284\pi$
$919$	−38.5703	+	22.2686i	−1.27232	+	0.734572i	−0.296893	+	0.954911i	$0.595950\pi$
$920$		0			0
$921$	−0.282066	+	0.488553i	−0.00929439	+	0.0160984i
$922$	0.962272	−	3.59125i	0.0316907	−	0.118271i
$923$	−4.01272	+	4.01272i	−0.132080	+	0.132080i
$924$	7.55868	−	3.30029i	0.248662	−	0.108571i
$925$		0			0
$926$	−11.5735	−	20.0459i	−0.380329	−	0.658750i
$927$	−10.2718	+	2.75232i	−0.337370	+	0.0903980i
$928$	5.21545	−	1.39747i	0.171205	−	0.0458743i
$929$	7.68149	+	13.3047i	0.252022	+	0.436514i	0.964082	−	0.265604i	$-0.0855713\pi$
$929$	7.68149	+	13.3047i	0.252022	+	0.436514i	−0.712061	+	0.702118i	$0.752238\pi$
$930$		0			0
$931$	−9.30856	+	40.8869i	−0.305076	+	1.34001i
$932$	−3.95517	+	3.95517i	−0.129556	+	0.129556i
$933$	3.35668	−	12.5273i	0.109893	−	0.410125i
$934$	−13.5300	+	23.4347i	−0.442716	+	0.766806i
$935$		0			0
$936$	2.82185	−	1.62920i	0.0922351	−	0.0532520i
$937$	−14.8294	−	14.8294i	−0.484456	−	0.484456i	0.422095	−	0.906552i	$-0.361295\pi$
$937$	−14.8294	−	14.8294i	−0.484456	−	0.484456i	−0.906552	+	0.422095i	$0.861295\pi$
$938$	−34.3009	−	13.4513i	−1.11996	−	0.439199i
$939$			1.85185i			0.0604327i
$940$		0			0
$941$	27.0066	+	15.5923i	0.880389	+	0.508293i	0.870787	−	0.491661i	$-0.163610\pi$
$941$	27.0066	+	15.5923i	0.880389	+	0.508293i	0.00960244	+	0.999954i	$0.496943\pi$
$942$	−3.24387	−	12.1063i	−0.105691	−	0.394444i
$943$	−11.3063	−	3.02952i	−0.368184	−	0.0986547i
$944$	0.234720			0.00763949
$945$		0			0
$946$	−28.4221			−0.924082
$947$	18.7182	+	5.01553i	0.608261	+	0.162983i	0.549785	−	0.835306i	$-0.314709\pi$
$947$	18.7182	+	5.01553i	0.608261	+	0.162983i	0.0584752	+	0.998289i	$0.481376\pi$
$948$	−2.61857	−	9.77262i	−0.0850471	−	0.317400i
$949$	3.19973	+	1.84737i	0.103868	+	0.0599680i
$950$		0			0
$951$		−	32.3857i		−	1.05018i
$952$	2.35975	−	1.88289i	0.0764798	−	0.0610250i
$953$	−22.0009	−	22.0009i	−0.712680	−	0.712680i	0.254415	−	0.967095i	$-0.418117\pi$
$953$	−22.0009	−	22.0009i	−0.712680	−	0.712680i	−0.967095	+	0.254415i	$0.918117\pi$
$954$	2.49644	−	1.44132i	0.0808252	−	0.0466645i
$955$		0			0
$956$	6.18432	−	10.7115i	0.200015	−	0.346436i
$957$	−4.35643	+	16.2584i	−0.140823	+	0.525560i
$958$	−29.8219	+	29.8219i	−0.963503	+	0.963503i
$959$	45.1367	+	5.07314i	1.45754	+	0.163820i
$960$		0			0
$961$	−6.43304	−	11.1424i	−0.207518	−	0.359431i
$962$	−18.1154	+	4.85400i	−0.584063	+	0.156499i
$963$	−16.0605	+	4.30339i	−0.517542	+	0.138675i
$964$	6.99433	+	12.1145i	0.225272	+	0.390183i
$965$		0			0
$966$	1.79201	−	2.42948i	0.0576570	−	0.0781674i
$967$	14.6687	−	14.6687i	0.471715	−	0.471715i	−0.430754	−	0.902469i	$-0.641752\pi$
$967$	14.6687	−	14.6687i	0.471715	−	0.471715i	0.902469	+	0.430754i	$0.141752\pi$
$968$	−0.331823	+	1.23838i	−0.0106652	+	0.0398031i
$969$	−3.41765	+	5.91954i	−0.109791	+	0.190163i
$970$		0			0
$971$	9.11356	−	5.26172i	0.292468	−	0.168857i	−0.346586	−	0.938018i	$-0.612659\pi$
$971$	9.11356	−	5.26172i	0.292468	−	0.168857i	0.639054	+	0.769162i	$0.279326\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−10.7750	+	27.4765i	−0.345432	+	0.880857i
$974$			31.2777i			1.00220i
$975$		0			0
$976$	7.38403	+	4.26317i	0.236357	+	0.136461i
$977$	−12.7095	−	47.4327i	−0.406614	−	1.51751i	−0.801059	−	0.598585i	$-0.795730\pi$
$977$	−12.7095	−	47.4327i	−0.406614	−	1.51751i	0.394445	−	0.918920i	$-0.370937\pi$
$978$	−14.5930	−	3.91019i	−0.466633	−	0.125034i
$979$	57.2616			1.83009
$980$		0			0
$981$	−14.2513			−0.455008
$982$	25.8007	+	6.91327i	0.823332	+	0.220611i
$983$	−14.9681	−	55.8618i	−0.477409	−	1.78172i	−0.612048	−	0.790821i	$-0.709654\pi$
$983$	−14.9681	−	55.8618i	−0.477409	−	1.78172i	0.134638	−	0.990895i	$-0.457013\pi$
$984$	−8.88403	−	5.12920i	−0.283213	−	0.163513i
$985$		0			0
$986$			6.16092i			0.196204i
$987$	4.11329	−	10.4890i	0.130928	−	0.333867i
$988$	13.8022	+	13.8022i	0.439106	+	0.439106i
$989$	−9.00944	+	5.20160i	−0.286484	+	0.165401i
$990$		0			0
$991$	29.8317	−	51.6700i	0.947635	−	1.64135i	0.197247	−	0.980354i	$-0.436800\pi$
$991$	29.8317	−	51.6700i	0.947635	−	1.64135i	0.750388	−	0.660998i	$-0.229867\pi$
$992$	−1.10215	+	4.11329i	−0.0349934	+	0.130597i
$993$	−8.20481	+	8.20481i	−0.260372	+	0.260372i
$994$	−2.73522	+	3.70822i	−0.0867560	+	0.117618i
$995$		0			0
$996$	5.69971	+	9.87219i	0.180602	+	0.312812i
$997$	51.2361	−	13.7287i	1.62266	−	0.434791i	0.670880	−	0.741566i	$-0.265916\pi$
$997$	51.2361	−	13.7287i	1.62266	−	0.434791i	0.951782	+	0.306775i	$0.0992498\pi$
$998$	−7.57742	+	2.03036i	−0.239859	+	0.0642701i
$999$	−2.87786	−	4.98460i	−0.0910515	−	0.157706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.e.493.4	yes	16
5.2	odd	4		1050.2.bc.f.157.1	yes	16
5.3	odd	4		1050.2.bc.f.157.4	yes	16
5.4	even	2	inner	1050.2.bc.e.493.1	✓	16
7.5	odd	6		1050.2.bc.f.943.1	yes	16
35.12	even	12	inner	1050.2.bc.e.607.3	yes	16
35.19	odd	6		1050.2.bc.f.943.4	yes	16
35.33	even	12	inner	1050.2.bc.e.607.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.e.493.1	✓	16	5.4	even	2	inner
1050.2.bc.e.493.4	yes	16	1.1	even	1	trivial
1050.2.bc.e.607.2	yes	16	35.33	even	12	inner
1050.2.bc.e.607.3	yes	16	35.12	even	12	inner
1050.2.bc.f.157.1	yes	16	5.2	odd	4
1050.2.bc.f.157.4	yes	16	5.3	odd	4
1050.2.bc.f.943.1	yes	16	7.5	odd	6
1050.2.bc.f.943.4	yes	16	35.19	odd	6

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-0.965926 + 2.46313i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-0.965926 + 2.46313i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.55868 + 2.69971i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-2.30403 + 2.30403i) q^{13} +(-1.57052 + 2.12920i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.10215 + 0.295321i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-2.99522 - 5.18788i) q^{19} +(-2.62920 - 0.295509i) q^{21} +(-2.20431 + 2.20431i) q^{22} +(-0.295321 + 1.10215i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.82185 + 1.62920i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.06808 + 1.65017i) q^{28} -5.39943i q^{29} +(3.68788 + 2.12920i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.01114 - 0.806832i) q^{33} -1.14103 q^{34} -1.00000 q^{36} +(5.55960 + 1.48969i) q^{37} +(-1.55044 - 5.78632i) q^{38} +(-2.82185 - 1.62920i) q^{39} +10.2584i q^{41} +(-2.46313 - 0.965926i) q^{42} +(6.44695 + 6.44695i) q^{43} +(-2.69971 + 1.55868i) q^{44} +(-0.570516 + 0.988164i) q^{46} +(-1.10215 + 4.11329i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-5.13397 - 4.75839i) q^{49} +(-0.570516 - 0.988164i) q^{51} +(-3.14737 + 0.843334i) q^{52} +(-2.78442 + 0.746082i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.42471 + 1.05868i) q^{56} +(4.23588 - 4.23588i) q^{57} +(1.39747 - 5.21545i) q^{58} +(0.117360 - 0.203274i) q^{59} +(7.38403 - 4.26317i) q^{61} +(3.01114 + 3.01114i) q^{62} +(-0.395046 - 2.61609i) q^{63} +1.00000i q^{64} +(-2.69971 - 1.55868i) q^{66} +(3.60425 + 13.4513i) q^{67} +(-1.10215 - 0.295321i) q^{68} -1.14103 q^{69} +1.74161 q^{71} +(-0.965926 - 0.258819i) q^{72} +(-0.293478 - 1.09527i) q^{73} +(4.98460 + 2.87786i) q^{74} -5.99044i q^{76} +(-5.14416 - 6.44695i) q^{77} +(-2.30403 - 2.30403i) q^{78} +(-8.76189 + 5.05868i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.65507 + 9.90885i) q^{82} +(8.06061 - 8.06061i) q^{83} +(-2.12920 - 1.57052i) q^{84} +(4.55868 + 7.89587i) q^{86} +(5.21545 - 1.39747i) q^{87} +(-3.01114 + 0.806832i) q^{88} +(-9.18432 - 15.9077i) q^{89} +(-3.44960 - 7.90064i) q^{91} +(-0.806832 + 0.806832i) q^{92} +(-1.10215 + 4.11329i) q^{93} +(-2.12920 + 3.68788i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-0.740585 - 0.740585i) q^{97} +(-3.72748 - 5.92503i) q^{98} -3.11736i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{11} - 8 q^{14} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 8 q^{24} + 16 q^{34} - 16 q^{36} + 12 q^{44} + 8 q^{46} - 96 q^{49} + 8 q^{51} - 8 q^{54} - 4 q^{56} - 40 q^{59} - 24 q^{61} + 12 q^{66} + 16 q^{69} + 104 q^{71} + 48 q^{74} + 12 q^{79} + 8 q^{81} + 4 q^{84} + 52 q^{86} - 60 q^{89} - 52 q^{91} + 4 q^{94}+O(q^{100}) \) 16 * q - 4 * q^11 - 8 * q^14 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 8 * q^24 + 16 * q^34 - 16 * q^36 + 12 * q^44 + 8 * q^46 - 96 * q^49 + 8 * q^51 - 8 * q^54 - 4 * q^56 - 40 * q^59 - 24 * q^61 + 12 * q^66 + 16 * q^69 + 104 * q^71 + 48 * q^74 + 12 * q^79 + 8 * q^81 + 4 * q^84 + 52 * q^86 - 60 * q^89 - 52 * q^91 + 4 * q^94

Introduction

L-functions

Modular forms

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Database

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