LMFDB - Embedded newform 1050.2.bc.f.157.1

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			157.1
Root			$-1.90899 + 1.10215i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.f.943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-2.46313 - 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-2.46313 - 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.55868 + 2.69971i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(2.30403 + 2.30403i) q^{13} +(1.57052 - 2.12920i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.295321 - 1.10215i) q^{17} +(0.258819 + 0.965926i) q^{18} +(2.99522 + 5.18788i) q^{19} +(-2.62920 - 0.295509i) q^{21} +(-2.20431 - 2.20431i) q^{22} +(1.10215 + 0.295321i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.82185 + 1.62920i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.65017 + 2.06808i) q^{28} +5.39943i q^{29} +(3.68788 + 2.12920i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.806832 + 3.01114i) q^{33} +1.14103 q^{34} -1.00000 q^{36} +(-1.48969 + 5.55960i) q^{37} +(-5.78632 + 1.55044i) q^{38} +(2.82185 + 1.62920i) q^{39} +10.2584i q^{41} +(0.965926 - 2.46313i) q^{42} +(6.44695 - 6.44695i) q^{43} +(2.69971 - 1.55868i) q^{44} +(-0.570516 + 0.988164i) q^{46} +(-4.11329 - 1.10215i) q^{47} +(0.707107 + 0.707107i) q^{48} +(5.13397 + 4.75839i) q^{49} +(-0.570516 - 0.988164i) q^{51} +(-0.843334 - 3.14737i) q^{52} +(0.746082 + 2.78442i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.42471 + 1.05868i) q^{56} +(4.23588 + 4.23588i) q^{57} +(-5.21545 - 1.39747i) q^{58} +(-0.117360 + 0.203274i) q^{59} +(7.38403 - 4.26317i) q^{61} +(-3.01114 + 3.01114i) q^{62} +(-2.61609 + 0.395046i) q^{63} -1.00000i q^{64} +(-2.69971 - 1.55868i) q^{66} +(-13.4513 + 3.60425i) q^{67} +(-0.295321 + 1.10215i) q^{68} +1.14103 q^{69} +1.74161 q^{71} +(0.258819 - 0.965926i) q^{72} +(-1.09527 + 0.293478i) q^{73} +(-4.98460 - 2.87786i) q^{74} -5.99044i q^{76} +(6.44695 - 5.14416i) q^{77} +(-2.30403 + 2.30403i) q^{78} +(8.76189 - 5.05868i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-9.90885 - 2.65507i) q^{82} +(-8.06061 - 8.06061i) q^{83} +(2.12920 + 1.57052i) q^{84} +(4.55868 + 7.89587i) q^{86} +(1.39747 + 5.21545i) q^{87} +(0.806832 + 3.01114i) q^{88} +(9.18432 + 15.9077i) q^{89} +(-3.44960 - 7.90064i) q^{91} +(-0.806832 - 0.806832i) q^{92} +(4.11329 + 1.10215i) q^{93} +(2.12920 - 3.68788i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(0.740585 - 0.740585i) q^{97} +(-5.92503 + 3.72748i) 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−2.46313	−	0.965926i	−0.930974	−	0.365086i
$7$	−2.46313	−	0.965926i	−0.930974	−	0.365086i
$8$	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	$0.322398\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	2.30403	+	2.30403i	0.639023	+	0.639023i	0.950315	−	0.311291i	$-0.100761\pi$
$13$	2.30403	+	2.30403i	0.639023	+	0.639023i	−0.311291	+	0.950315i	$0.600761\pi$
$14$	1.57052	−	2.12920i	0.419738	−	0.569052i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.295321	−	1.10215i	−0.0716259	−	0.267311i	0.920821	−	0.389985i	$-0.127520\pi$
$17$	−0.295321	−	1.10215i	−0.0716259	−	0.267311i	−0.992447	+	0.122674i	$0.960853\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	2.99522	+	5.18788i	0.687151	+	1.19018i	0.972756	+	0.231833i	$0.0744723\pi$
$19$	2.99522	+	5.18788i	0.687151	+	1.19018i	−0.285605	+	0.958348i	$0.592194\pi$
$20$		0			0
$21$	−2.62920	−	0.295509i	−0.573738	−	0.0644853i
$22$	−2.20431	−	2.20431i	−0.469960	−	0.469960i
$23$	1.10215	+	0.295321i	0.229815	+	0.0615787i	0.371889	−	0.928277i	$-0.378710\pi$
$23$	1.10215	+	0.295321i	0.229815	+	0.0615787i	−0.142074	+	0.989856i	$0.545377\pi$
$24$	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
$28$	1.65017	+	2.06808i	0.311852	+	0.390830i
$29$			5.39943i			1.00265i	0.865260	+	0.501324i	$0.167154\pi$
$29$			5.39943i			1.00265i	−0.865260	+	0.501324i	$0.832846\pi$
$30$		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	$0.541759\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.806832	+	3.01114i	−0.140451	+	0.524172i
$34$	1.14103			0.195686
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−1.48969	+	5.55960i	−0.244904	+	0.913993i	0.728528	+	0.685016i	$0.240205\pi$
$37$	−1.48969	+	5.55960i	−0.244904	+	0.913993i	−0.973432	+	0.228977i	$0.926462\pi$
$38$	−5.78632	+	1.55044i	−0.938666	+	0.251515i
$39$	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	$0.704277\pi$
$42$	0.965926	−	2.46313i	0.149046	−	0.380069i
$43$	6.44695	−	6.44695i	0.983150	−	0.983150i	−0.0167102	−	0.999860i	$-0.505319\pi$
$43$	6.44695	−	6.44695i	0.983150	−	0.983150i	0.999860	+	0.0167102i	$0.00531925\pi$
$44$	2.69971	−	1.55868i	0.406997	−	0.234980i
$45$		0			0
$46$	−0.570516	+	0.988164i	−0.0841181	+	0.145697i
$47$	−4.11329	−	1.10215i	−0.599985	−	0.160766i	−0.0539725	−	0.998542i	$-0.517188\pi$
$47$	−4.11329	−	1.10215i	−0.599985	−	0.160766i	−0.546013	+	0.837777i	$0.683855\pi$
$48$	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
$52$	−0.843334	−	3.14737i	−0.116949	−	0.436461i
$53$	0.746082	+	2.78442i	0.102482	+	0.382469i	0.998047	−	0.0624615i	$-0.0198951\pi$
$53$	0.746082	+	2.78442i	0.102482	+	0.382469i	−0.895565	+	0.444930i	$0.853228\pi$
$54$	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
$58$	−5.21545	−	1.39747i	−0.684821	−	0.183497i
$59$	−0.117360	+	0.203274i	−0.0152790	+	0.0264640i	−0.873564	−	0.486710i	$-0.838197\pi$
$59$	−0.117360	+	0.203274i	−0.0152790	+	0.0264640i	0.858285	+	0.513174i	$0.171530\pi$
$60$		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
$63$	−2.61609	+	0.395046i	−0.329597	+	0.0497712i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.69971	−	1.55868i	−0.332312	−	0.191860i
$67$	−13.4513	+	3.60425i	−1.64333	+	0.440330i	−0.957735	−	0.287651i	$-0.907126\pi$
$67$	−13.4513	+	3.60425i	−1.64333	+	0.440330i	−0.685598	+	0.727981i	$0.740459\pi$
$68$	−0.295321	+	1.10215i	−0.0358129	+	0.133656i
$69$	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	$0.467045\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−1.09527	+	0.293478i	−0.128192	+	0.0343490i	−0.322345	−	0.946622i	$-0.604471\pi$
$73$	−1.09527	+	0.293478i	−0.128192	+	0.0343490i	0.194152	+	0.980971i	$0.437804\pi$
$74$	−4.98460	−	2.87786i	−0.579448	−	0.334545i
$75$		0			0
$76$		−	5.99044i		−	0.687151i
$77$	6.44695	−	5.14416i	0.734698	−	0.586232i
$78$	−2.30403	+	2.30403i	−0.260880	+	0.260880i
$79$	8.76189	−	5.05868i	0.985790	−	0.569146i	0.0817766	−	0.996651i	$-0.473941\pi$
$79$	8.76189	−	5.05868i	0.985790	−	0.569146i	0.904013	+	0.427505i	$0.140607\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−9.90885	−	2.65507i	−1.09425	−	0.293203i
$83$	−8.06061	−	8.06061i	−0.884767	−	0.884767i	0.109248	−	0.994015i	$-0.465156\pi$
$83$	−8.06061	−	8.06061i	−0.884767	−	0.884767i	−0.994015	+	0.109248i	$0.965156\pi$
$84$	2.12920	+	1.57052i	0.232314	+	0.171357i
$85$		0			0
$86$	4.55868	+	7.89587i	0.491575	+	0.851433i
$87$	1.39747	+	5.21545i	0.149825	+	0.559154i
$88$	0.806832	+	3.01114i	0.0860086	+	0.320988i
$89$	9.18432	+	15.9077i	0.973536	+	1.68621i	0.684685	+	0.728839i	$0.259940\pi$
$89$	9.18432	+	15.9077i	0.973536	+	1.68621i	0.288850	+	0.957374i	$0.406727\pi$
$90$		0			0
$91$	−3.44960	−	7.90064i	−0.361616	−	0.828212i
$92$	−0.806832	−	0.806832i	−0.0841181	−	0.0841181i
$93$	4.11329	+	1.10215i	0.426528	+	0.114288i
$94$	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	$-0.733067\pi$
$97$	0.740585	−	0.740585i	0.0751950	−	0.0751950i	0.743704	+	0.668509i	$0.233067\pi$
$98$	−5.92503	+	3.72748i	−0.598518	+	0.376532i
$99$			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	$0.863153\pi$
$102$	1.10215	−	0.295321i	0.109129	−	0.0292411i
$103$	2.75232	−	10.2718i	0.271194	−	1.01211i	−0.687155	−	0.726511i	$-0.741141\pi$
$103$	2.75232	−	10.2718i	0.271194	−	1.01211i	0.958349	−	0.285599i	$-0.0921927\pi$
$104$	3.25839			0.319512
$105$		0			0
$106$	−2.88264			−0.279987
$107$	−4.30339	+	16.0605i	−0.416024	+	1.55262i	0.366750	+	0.930319i	$0.380470\pi$
$107$	−4.30339	+	16.0605i	−0.416024	+	1.55262i	−0.782775	+	0.622305i	$0.786196\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	−12.3420	−	7.12564i	−1.18215	−	0.682512i	−0.225636	−	0.974212i	$-0.572446\pi$
$109$	−12.3420	−	7.12564i	−1.18215	−	0.682512i	−0.956510	+	0.291700i	$0.905779\pi$
$110$		0			0
$111$			5.75572i			0.546309i
$112$	−0.395046	−	2.61609i	−0.0373284	−	0.247197i
$113$	7.08781	−	7.08781i	0.666765	−	0.666765i	−0.290201	−	0.956966i	$-0.593722\pi$
$113$	7.08781	−	7.08781i	0.666765	−	0.666765i	0.956966	+	0.290201i	$0.0937221\pi$
$114$	−5.18788	+	2.99522i	−0.485889	+	0.280528i
$115$		0			0
$116$	2.69971	−	4.67604i	0.250662	−	0.434159i
$117$	3.14737	+	0.843334i	0.290974	+	0.0779663i
$118$	−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
$122$	2.20678	+	8.23581i	0.199792	+	0.745636i
$123$	2.65507	+	9.90885i	0.239399	+	0.893451i
$124$	−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	0.675117	−	0.737710i	$-0.264093\pi$
$127$	−0.705385	−	0.705385i	−0.0625928	−	0.0625928i	−0.737710	+	0.675117i	$0.764093\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	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
$133$	−2.36650	−	15.6716i	−0.205202	−	1.35890i
$134$		−	13.9258i		−	1.20300i
$135$		0			0
$136$	−0.988164	−	0.570516i	−0.0847343	−	0.0489214i
$137$	16.5825	−	4.44327i	1.41674	−	0.379614i	0.532414	−	0.846484i	$-0.321285\pi$
$137$	16.5825	−	4.44327i	1.41674	−	0.379614i	0.884326	+	0.466870i	$0.154618\pi$
$138$	−0.295321	+	1.10215i	−0.0251394	+	0.0938215i
$139$	−11.1551			−0.946167			−0.473084	−	0.881017i	$-0.656859\pi$
$139$	−11.1551			−0.946167			−0.473084	+	0.881017i	$0.656859\pi$
$140$		0			0
$141$	−4.25839			−0.358621
$142$	−0.450761	+	1.68226i	−0.0378270	+	0.141172i
$143$	−9.81147	+	2.62898i	−0.820477	+	0.219846i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$		0			0
$146$		−	1.13391i		−	0.0938432i
$147$	6.19060	+	3.26748i	0.510592	+	0.269498i
$148$	4.06991	−	4.06991i	0.334545	−	0.334545i
$149$	−16.5790	+	9.57191i	−1.35821	+	0.784161i	−0.989382	−	0.145338i	$-0.953573\pi$
$149$	−16.5790	+	9.57191i	−1.35821	+	0.784161i	−0.368825	+	0.929499i	$0.620240\pi$
$150$		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	$-0.0854462\pi$
$152$	5.78632	+	1.55044i	0.469333	+	0.125757i
$153$	−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
$157$	−3.24387	−	12.1063i	−0.258889	−	0.966186i	−0.965886	−	0.258969i	$-0.916617\pi$
$157$	−3.24387	−	12.1063i	−0.258889	−	0.966186i	0.706997	−	0.707217i	$-0.250049\pi$
$158$	2.61857	+	9.77262i	0.208322	+	0.777468i
$159$	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
$163$	14.5930	+	3.91019i	1.14301	+	0.306270i	0.780162	−	0.625578i	$-0.215137\pi$
$163$	14.5930	+	3.91019i	1.14301	+	0.306270i	0.362851	+	0.931847i	$0.381803\pi$
$164$	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	$-0.775241\pi$
$167$	−1.44769	+	1.44769i	−0.112026	+	0.112026i	0.648872	+	0.760898i	$0.275241\pi$
$168$	−2.06808	+	1.65017i	−0.159556	+	0.127313i
$169$		−	2.38287i		−	0.183298i
$170$		0			0
$171$	5.18788	+	2.99522i	0.396727	+	0.229050i
$172$	−8.80669	+	2.35975i	−0.671504	+	0.179929i
$173$	−3.16658	+	11.8178i	−0.240751	+	0.898493i	0.734721	+	0.678369i	$0.237313\pi$
$173$	−3.16658	+	11.8178i	−0.240751	+	0.898493i	−0.975472	+	0.220124i	$0.929354\pi$
$174$	−5.39943			−0.409329
$175$		0			0
$176$	−3.11736			−0.234980
$177$	−0.0607501	+	0.226722i	−0.00456625	+	0.0170415i
$178$	−17.7427	+	4.75415i	−1.32987	+	0.356339i
$179$	−16.5790	−	9.57191i	−1.23917	−	0.715438i	−0.270249	−	0.962790i	$-0.587106\pi$
$179$	−16.5790	−	9.57191i	−1.23917	−	0.715438i	−0.968926	+	0.247353i	$0.920439\pi$
$180$		0			0
$181$			5.22760i			0.388564i	0.980946	+	0.194282i	$0.0622377\pi$
$181$			5.22760i			0.388564i	−0.980946	+	0.194282i	$0.937762\pi$
$182$	8.52426	−	1.28722i	0.631860	−	0.0954148i
$183$	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
$187$	3.43581	+	0.920622i	0.251251	+	0.0673226i
$188$	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	$0.954365\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	1.25759	+	4.69340i	0.0905235	+	0.337838i	0.996303	−	0.0859114i	$-0.0273802\pi$
$193$	1.25759	+	4.69340i	0.0905235	+	0.337838i	−0.905779	+	0.423750i	$0.860714\pi$
$194$	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	0.849824	−	0.527067i	$-0.176708\pi$
$197$	4.53011	+	4.53011i	0.322757	+	0.322757i	−0.527067	+	0.849824i	$0.676708\pi$
$198$	−3.01114	−	0.806832i	−0.213992	−	0.0573391i
$199$	1.28367	−	2.22339i	0.0909971	−	0.157612i	−0.816934	−	0.576731i	$-0.804328\pi$
$199$	1.28367	−	2.22339i	0.0909971	−	0.157612i	0.907931	+	0.419120i	$0.137661\pi$
$200$		0			0
$201$	−12.0601	+	6.96288i	−0.850652	+	0.491124i
$202$	8.22658	−	8.22658i	0.578820	−	0.578820i
$203$	5.21545	−	13.2995i	0.366052	−	0.933439i
$204$			1.14103i			0.0798883i
$205$		0			0
$206$	9.20944	+	5.31707i	0.641652	+	0.370458i
$207$	1.10215	−	0.295321i	0.0766049	−	0.0205262i
$208$	−0.843334	+	3.14737i	−0.0584747	+	0.218231i
$209$	−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	$0.166335\pi$
$212$	0.746082	−	2.78442i	0.0512411	−	0.191234i
$213$	1.68226	−	0.450761i	0.115267	−	0.0308856i
$214$	−14.3994	−	8.31351i	−0.984325	−	0.568300i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−7.02706	−	8.80669i	−0.477028	−	0.597837i
$218$	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
$222$	−5.55960	−	1.48969i	−0.373136	−	0.0999815i
$223$	−7.35350	−	7.35350i	−0.492427	−	0.492427i	0.416643	−	0.909070i	$-0.363206\pi$
$223$	−7.35350	−	7.35350i	−0.492427	−	0.492427i	−0.909070	+	0.416643i	$0.863206\pi$
$224$	2.62920	+	0.295509i	0.175671	+	0.0197445i
$225$		0			0
$226$	5.01184	+	8.68076i	0.333382	+	0.577435i
$227$	−5.26566	−	19.6517i	−0.349494	−	1.30433i	−0.887273	−	0.461245i	$-0.847403\pi$
$227$	−5.26566	−	19.6517i	−0.349494	−	1.30433i	0.537779	−	0.843086i	$-0.319264\pi$
$228$	−1.55044	−	5.78632i	−0.102680	−	0.383209i
$229$	−3.91643	−	6.78346i	−0.258805	−	0.448263i	0.707117	−	0.707096i	$-0.249995\pi$
$229$	−3.91643	−	6.78346i	−0.258805	−	0.448263i	−0.965922	+	0.258833i	$0.916662\pi$
$230$		0			0
$231$	4.89587	−	6.63747i	0.322124	−	0.436714i
$232$	3.81797	+	3.81797i	0.250662	+	0.250662i
$233$	5.40286	+	1.44769i	0.353953	+	0.0948415i	0.431414	−	0.902154i	$-0.358015\pi$
$233$	5.40286	+	1.44769i	0.353953	+	0.0948415i	−0.0774612	+	0.996995i	$0.524681\pi$
$234$	−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
$238$	−2.81051	−	1.10215i	−0.182178	−	0.0714420i
$239$			12.3686i			0.800060i	0.916502	+	0.400030i	$0.131000\pi$
$239$			12.3686i			0.800060i	−0.916502	+	0.400030i	$0.869000\pi$
$240$		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	$0.517897\pi$
$242$	−1.23838	+	0.331823i	−0.0796061	+	0.0213304i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−8.52634			−0.545843
$245$		0			0
$246$	−10.2584			−0.654051
$247$	−5.05195	+	18.8541i	−0.321448	+	1.19966i
$248$	4.11329	−	1.10215i	0.261194	−	0.0699868i
$249$	−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	$-0.180659\pi$
$252$	2.46313	+	0.965926i	0.155162	+	0.0608476i
$253$	−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
$257$	20.2711	+	5.43164i	1.26448	+	0.338816i	0.827913	−	0.560856i	$-0.189528\pi$
$257$	20.2711	+	5.43164i	1.26448	+	0.338816i	0.436566	+	0.899672i	$0.356195\pi$
$258$	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
$262$	−3.49656	−	13.0493i	−0.216018	−	0.806191i
$263$	4.95406	+	18.4888i	0.305481	+	1.14007i	0.932531	+	0.361090i	$0.117595\pi$
$263$	4.95406	+	18.4888i	0.305481	+	1.14007i	−0.627050	+	0.778979i	$0.715738\pi$
$264$	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
$268$	13.4513	+	3.60425i	0.821666	+	0.220165i
$269$	14.6138	−	25.3118i	0.891019	−	1.54329i	0.0523636	−	0.998628i	$-0.483325\pi$
$269$	14.6138	−	25.3118i	0.891019	−	1.54329i	0.838656	−	0.544662i	$-0.183342\pi$
$270$		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
$273$	−5.37689	−	6.73861i	−0.325424	−	0.407840i
$274$			17.1675i			1.03713i
$275$		0			0
$276$	−0.988164	−	0.570516i	−0.0594805	−	0.0343411i
$277$	20.9318	−	5.60865i	1.25767	−	0.336991i	0.432374	−	0.901694i	$-0.357676\pi$
$277$	20.9318	−	5.60865i	1.25767	−	0.336991i	0.825294	+	0.564703i	$0.191009\pi$
$278$	2.88717	−	10.7750i	0.173161	−	0.646244i
$279$	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	$0.303861\pi$
$282$	1.10215	−	4.11329i	0.0656323	−	0.244943i
$283$	−18.0083	+	4.82531i	−1.07048	+	0.286835i	−0.750692	−	0.660653i	$-0.770280\pi$
$283$	−18.0083	+	4.82531i	−1.07048	+	0.286835i	−0.319792	+	0.947488i	$0.603613\pi$
$284$	−1.50828	−	0.870803i	−0.0894997	−	0.0516727i
$285$		0			0
$286$		−	10.1576i		−	0.600631i
$287$	9.90885	−	25.2677i	0.584901	−	1.49151i
$288$	−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
$292$	1.09527	+	0.293478i	0.0640961	+	0.0171745i
$293$	11.4539	+	11.4539i	0.669145	+	0.669145i	0.957518	−	0.288373i	$-0.0931144\pi$
$293$	11.4539	+	11.4539i	0.669145	+	0.669145i	−0.288373	+	0.957518i	$0.593114\pi$
$294$	−4.75839	+	5.13397i	−0.277515	+	0.299419i
$295$		0			0
$296$	2.87786	+	4.98460i	0.167272	+	0.289724i
$297$	0.806832	+	3.01114i	0.0468172	+	0.174724i
$298$	−4.95478	−	18.4915i	−0.287023	−	1.07118i
$299$	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
$303$	−11.2377	−	3.01114i	−0.645590	−	0.172985i
$304$	−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	$-0.755124\pi$
$307$	−0.398902	+	0.398902i	−0.0227665	+	0.0227665i	0.695632	+	0.718398i	$0.255124\pi$
$308$	−8.15530	+	1.23150i	−0.464691	+	0.0701713i
$309$		−	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	$0.786524\pi$
$312$	3.14737	−	0.843334i	0.178185	−	0.0477444i
$313$	0.479293	−	1.78875i	0.0270912	−	0.101106i	−0.951056	−	0.309017i	$-0.900000\pi$
$313$	0.479293	−	1.78875i	0.0270912	−	0.101106i	0.978148	+	0.207911i	$0.0666666\pi$
$314$	12.5333			0.707297
$315$		0			0
$316$	−10.1174			−0.569146
$317$	8.38202	−	31.2821i	0.470781	−	1.75698i	−0.166191	−	0.986094i	$-0.553147\pi$
$317$	8.38202	−	31.2821i	0.470781	−	1.75698i	0.636973	−	0.770886i	$-0.280186\pi$
$318$	−2.78442	+	0.746082i	−0.156142	+	0.0418382i
$319$	−14.5769	−	8.41598i	−0.816150	−	0.471204i
$320$		0			0
$321$			16.6270i			0.928030i
$322$	2.35975	−	1.88289i	0.131504	−	0.104930i
$323$	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
$327$	−13.7657	−	3.68850i	−0.761243	−	0.203975i
$328$	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	$0.730024\pi$
$332$	2.95039	+	11.0110i	0.161924	+	0.604307i
$333$	1.48969	+	5.55960i	0.0816346	+	0.304664i
$334$	−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	0.916120	−	0.400905i	$-0.131304\pi$
$337$	9.45809	+	9.45809i	0.515215	+	0.515215i	−0.400905	+	0.916120i	$0.631304\pi$
$338$	2.30168	+	0.616733i	0.125195	+	0.0335459i
$339$	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
$343$	−8.04937	−	16.6796i	−0.434625	−	0.900611i
$344$		−	9.11736i		−	0.491575i
$345$		0			0
$346$	−10.5956	−	6.11736i	−0.569622	−	0.328871i
$347$	−20.8512	+	5.58708i	−1.11935	+	0.299930i	−0.770622	−	0.637293i	$-0.780054\pi$
$347$	−20.8512	+	5.58708i	−1.11935	+	0.299930i	−0.348732	+	0.937223i	$0.613388\pi$
$348$	1.39747	−	5.21545i	0.0749125	−	0.279577i
$349$	−14.9455			−0.800016			−0.400008	−	0.916512i	$-0.630993\pi$
$349$	−14.9455			−0.800016			−0.400008	+	0.916512i	$0.630993\pi$
$350$		0			0
$351$	3.25839			0.173920
$352$	0.806832	−	3.01114i	0.0430043	−	0.160494i
$353$	−35.2295	+	9.43970i	−1.87507	+	0.502425i	−0.875251	+	0.483669i	$0.839304\pi$
$353$	−35.2295	+	9.43970i	−1.87507	+	0.502425i	−0.999824	+	0.0187553i	$0.994030\pi$
$354$	−0.203274	−	0.117360i	−0.0108039	−	0.00623762i
$355$		0			0
$356$		−	18.3686i		−	0.973536i
$357$	0.450761	+	2.98505i	0.0238568	+	0.157985i
$358$	13.5367	−	13.5367i	0.715438	−	0.715438i
$359$	3.77518	−	2.17960i	0.199246	−	0.115035i	−0.397058	−	0.917794i	$-0.629969\pi$
$359$	3.77518	−	2.17960i	0.199246	−	0.115035i	0.596304	+	0.802759i	$0.296635\pi$
$360$		0			0
$361$	−8.44271	+	14.6232i	−0.444353	+	0.769642i
$362$	−5.04947	−	1.35300i	−0.265394	−	0.0711122i
$363$	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
$367$	−4.80106	−	17.9178i	−0.250614	−	0.935302i	−0.970478	−	0.241188i	$-0.922463\pi$
$367$	−4.80106	−	17.9178i	−0.250614	−	0.935302i	0.719865	−	0.694114i	$-0.244204\pi$
$368$	0.295321	+	1.10215i	0.0153947	+	0.0574537i
$369$	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
$373$	18.8541	+	5.05195i	0.976229	+	0.261580i	0.711456	−	0.702731i	$-0.248036\pi$
$373$	18.8541	+	5.05195i	0.976229	+	0.261580i	0.264773	+	0.964311i	$0.414703\pi$
$374$	−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
$378$	−0.395046	−	2.61609i	−0.0203190	−	0.134557i
$379$			37.4424i			1.92329i	0.274300	+	0.961644i	$0.411554\pi$
$379$			37.4424i			1.92329i	−0.274300	+	0.961644i	$0.588446\pi$
$380$		0			0
$381$	−0.863917	−	0.498783i	−0.0442598	−	0.0255534i
$382$	9.90885	−	2.65507i	0.506981	−	0.135845i
$383$	0.156159	−	0.582793i	0.00797935	−	0.0297794i	−0.961821	−	0.273678i	$-0.911760\pi$
$383$	0.156159	−	0.582793i	0.00797935	−	0.0297794i	0.969801	+	0.243899i	$0.0784264\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−4.85897			−0.247315
$387$	2.35975	−	8.80669i	0.119953	−	0.447669i
$388$	−1.01166	+	0.271073i	−0.0513592	+	0.0137616i
$389$	17.6000	+	10.1614i	0.892357	+	0.515202i	0.874713	−	0.484642i	$-0.161050\pi$
$389$	17.6000	+	10.1614i	0.892357	+	0.515202i	0.0176441	+	0.999844i	$0.494383\pi$
$390$		0			0
$391$		−	1.30196i		−	0.0658428i
$392$	6.99496	−	0.265576i	0.353299	−	0.0134136i
$393$	−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
$397$	11.5774	+	3.10214i	0.581051	+	0.155692i	0.537360	−	0.843353i	$-0.319422\pi$
$397$	11.5774	+	3.10214i	0.581051	+	0.155692i	0.0436908	+	0.999045i	$0.486088\pi$
$398$	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	$-0.337866\pi$
$402$	−3.60425	−	13.4513i	−0.179764	−	0.670888i
$403$	3.59125	+	13.4027i	0.178893	+	0.667637i
$404$	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
$408$	−1.10215	−	0.295321i	−0.0545647	−	0.0146206i
$409$	6.61219	−	11.4527i	0.326952	−	0.566297i	−0.654954	−	0.755669i	$-0.727312\pi$
$409$	6.61219	−	11.4527i	0.326952	−	0.566297i	0.981905	+	0.189372i	$0.0606452\pi$
$410$		0			0
$411$	14.8675	−	8.58374i	0.733359	−	0.423405i
$412$	−7.51948	+	7.51948i	−0.370458	+	0.370458i
$413$	0.485420	−	0.387327i	0.0238860	−	0.0190591i
$414$			1.14103i			0.0560787i
$415$		0			0
$416$	−2.82185	−	1.62920i	−0.138353	−	0.0798779i
$417$	−10.7750	+	2.88717i	−0.527656	+	0.141385i
$418$	4.83328	−	18.0381i	0.236404	−	0.882270i
$419$	−19.9791			−0.976043			−0.488022	−	0.872832i	$-0.662281\pi$
$419$	−19.9791			−0.976043			−0.488022	+	0.872832i	$0.662281\pi$
$420$		0			0
$421$	−20.2920			−0.988970			−0.494485	−	0.869186i	$-0.664643\pi$
$421$	−20.2920			−0.988970			−0.494485	+	0.869186i	$0.664643\pi$
$422$	−6.51567	+	24.3168i	−0.317178	+	1.18372i
$423$	−4.11329	+	1.10215i	−0.199995	+	0.0535885i
$424$	2.49644	+	1.44132i	0.121238	+	0.0699967i
$425$		0			0
$426$			1.74161i			0.0843811i
$427$	−22.3057	+	3.36830i	−1.07945	+	0.163004i
$428$	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	$0.164094\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	4.53678	+	4.53678i	0.218024	+	0.218024i	0.807665	−	0.589641i	$-0.200731\pi$
$433$	4.53678	+	4.53678i	0.218024	+	0.218024i	−0.589641	+	0.807665i	$0.700731\pi$
$434$	10.3253	−	4.50828i	0.495633	−	0.216404i
$435$		0			0
$436$	7.12564	+	12.3420i	0.341256	+	0.591073i
$437$	1.76910	+	6.60239i	0.0846277	+	0.315835i
$438$	−0.293478	−	1.09527i	−0.0140229	−	0.0523342i
$439$	−13.6209	−	23.5920i	−0.650088	−	1.12599i	−0.983101	−	0.183063i	$-0.941399\pi$
$439$	−13.6209	−	23.5920i	−0.650088	−	1.12599i	0.333013	−	0.942922i	$-0.391935\pi$
$440$		0			0
$441$	6.82535	+	1.55390i	0.325017	+	0.0739953i
$442$	2.62898	+	2.62898i	0.125048	+	0.125048i
$443$	4.98872	+	1.33672i	0.237021	+	0.0635097i	0.375374	−	0.926873i	$-0.377514\pi$
$443$	4.98872	+	1.33672i	0.237021	+	0.0635097i	−0.138353	+	0.990383i	$0.544181\pi$
$444$	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
$448$	−0.965926	+	2.46313i	−0.0456357	+	0.116372i
$449$			26.0501i			1.22938i	0.788768	+	0.614691i	$0.210719\pi$
$449$			26.0501i			1.22938i	−0.788768	+	0.614691i	$0.789281\pi$
$450$		0			0
$451$	−27.6947	−	15.9896i	−1.30409	−	0.752919i
$452$	−9.68212	+	2.59432i	−0.455409	+	0.122026i
$453$	4.52755	−	16.8970i	0.212723	−	0.793893i
$454$	20.3450			0.954836
$455$		0			0
$456$	5.99044			0.280528
$457$	−7.83833	+	29.2530i	−0.366661	+	1.36840i	0.498493	+	0.866894i	$0.333887\pi$
$457$	−7.83833	+	29.2530i	−0.366661	+	1.36840i	−0.865154	+	0.501506i	$0.832780\pi$
$458$	7.56596	−	2.02729i	0.353534	−	0.0947292i
$459$	−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	$-0.0275940\pi$
$462$	5.14416	+	6.44695i	0.239328	+	0.299939i
$463$	−16.3674	+	16.3674i	−0.760658	+	0.760658i	−0.976441	−	0.215783i	$-0.930770\pi$
$463$	−16.3674	+	16.3674i	−0.760658	+	0.760658i	0.215783	+	0.976441i	$0.430770\pi$
$464$	−4.67604	+	2.69971i	−0.217080	+	0.125331i
$465$		0			0
$466$	−2.79673	+	4.84407i	−0.129556	+	0.224397i
$467$	−26.1380	−	7.00365i	−1.20952	−	0.324090i	−0.402947	−	0.915223i	$-0.632014\pi$
$467$	−26.1380	−	7.00365i	−1.20952	−	0.324090i	−0.806574	+	0.591133i	$0.798681\pi$
$468$	−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
$472$	0.0607501	+	0.226722i	0.00279625	+	0.0104357i
$473$	7.35618	+	27.4536i	0.338237	+	1.26232i
$474$	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
$478$	−11.9472	−	3.20124i	−0.546451	−	0.146421i
$479$	21.0873	−	36.5243i	0.963503	−	1.66884i	0.249920	−	0.968266i	$-0.419596\pi$
$479$	21.0873	−	36.5243i	0.963503	−	1.66884i	0.713583	−	0.700571i	$-0.247071\pi$
$480$		0			0
$481$	−16.2418	+	9.37721i	−0.740562	+	0.427564i
$482$	−9.89148	+	9.89148i	−0.450544	+	0.450544i
$483$	−2.81051	−	1.10215i	−0.127883	−	0.0501497i
$484$		−	1.28207i		−	0.0582757i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−30.2120	+	8.09527i	−1.36903	+	0.366832i	−0.867126	−	0.498089i	$-0.834035\pi$
$487$	−30.2120	+	8.09527i	−1.36903	+	0.366832i	−0.501909	+	0.864921i	$0.667369\pi$
$488$	2.20678	−	8.23581i	0.0998962	−	0.372818i
$489$	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	$0.294083\pi$
$492$	2.65507	−	9.90885i	0.119700	−	0.446725i
$493$	5.95099	−	1.59456i	0.268019	−	0.0718156i
$494$	−16.9041	−	9.75961i	−0.760553	−	0.439106i
$495$		0			0
$496$			4.25839i			0.191207i
$497$	−4.28980	−	1.68226i	−0.192424	−	0.0754598i
$498$	8.06061	−	8.06061i	0.361205	−	0.361205i
$499$	6.79373	−	3.92236i	0.304129	−	0.175589i	−0.340167	−	0.940365i	$-0.610484\pi$
$499$	6.79373	−	3.92236i	0.304129	−	0.175589i	0.644296	+	0.764776i	$0.277150\pi$
$500$		0			0
$501$	−1.02367	+	1.77305i	−0.0457343	+	0.0792142i
$502$	16.4532	+	4.40861i	0.734341	+	0.196766i
$503$	−23.4463	−	23.4463i	−1.04542	−	1.04542i	−0.998918	−	0.0464999i	$-0.985193\pi$
$503$	−23.4463	−	23.4463i	−1.04542	−	1.04542i	−0.0464999	−	0.998918i	$-0.514807\pi$
$504$	−1.57052	+	2.12920i	−0.0699564	+	0.0948420i
$505$		0			0
$506$	−1.77851	−	3.08046i	−0.0790642	−	0.136943i
$507$	−0.616733	−	2.30168i	−0.0273901	−	0.102221i
$508$	0.258189	+	0.963574i	0.0114553	+	0.0427517i
$509$	6.72339	+	11.6452i	0.298009	+	0.516166i	0.975680	−	0.219198i	$-0.0703442\pi$
$509$	6.72339	+	11.6452i	0.298009	+	0.516166i	−0.677671	+	0.735365i	$0.737011\pi$
$510$		0			0
$511$	2.98128	+	0.335081i	0.131884	+	0.0148231i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	5.78632	+	1.55044i	0.255472	+	0.0684536i
$514$	−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
$518$	9.49790	+	11.9033i	0.417314	+	0.523001i
$519$			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	$0.624000\pi$
$522$	−5.21545	+	1.39747i	−0.228274	+	0.0611658i
$523$	−3.03110	+	11.3122i	−0.132541	+	0.494649i	−0.999996	−	0.00286635i	$-0.999088\pi$
$523$	−3.03110	+	11.3122i	−0.132541	+	0.494649i	0.867455	+	0.497516i	$0.165754\pi$
$524$	13.5097			0.590172
$525$		0			0
$526$	−19.1410			−0.834589
$527$	1.25759	−	4.69340i	0.0547816	−	0.204448i
$528$	−3.01114	+	0.806832i	−0.131043	+	0.0351129i
$529$	−18.7911	−	10.8490i	−0.817002	−	0.471697i
$530$		0			0
$531$			0.234720i			0.0101860i
$532$	−5.78632	+	14.7552i	−0.250869	+	0.639720i
$533$	−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
$537$	−18.4915	−	4.95478i	−0.797967	−	0.213815i
$538$	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	$0.838182\pi$
$542$	5.82165	+	21.7267i	0.250061	+	0.933241i
$543$	1.35300	+	5.04947i	0.0580629	+	0.216694i
$544$	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	0.999077	+	0.0429611i	$0.0136792\pi$
$547$	24.3712	+	24.3712i	1.04204	+	1.04204i	0.0429611	+	0.999077i	$0.486321\pi$
$548$	−16.5825	−	4.44327i	−0.708370	−	0.189807i
$549$	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
$553$	−26.4679	+	3.99683i	−1.12553	+	0.169962i
$554$			21.6702i			0.920677i
$555$		0			0
$556$	9.66064	+	5.57757i	0.409703	+	0.236542i
$557$	−20.4371	+	5.47611i	−0.865948	+	0.232030i	−0.664335	−	0.747435i	$-0.731285\pi$
$557$	−20.4371	+	5.47611i	−0.865948	+	0.232030i	−0.201613	+	0.979465i	$0.564618\pi$
$558$	−1.10215	+	4.11329i	−0.0466579	+	0.174130i
$559$	29.7079			1.25651
$560$		0			0
$561$	3.55701			0.150177
$562$	−5.01481	+	18.7155i	−0.211537	+	0.789467i
$563$	33.5472	−	8.98894i	1.41385	−	0.378839i	0.530549	−	0.847654i	$-0.321986\pi$
$563$	33.5472	−	8.98894i	1.41385	−	0.378839i	0.883296	+	0.468815i	$0.155319\pi$
$564$	3.68788	+	2.12920i	0.155288	+	0.0896553i
$565$		0			0
$566$		−	18.6436i		−	0.783648i
$567$	−2.06808	+	1.65017i	−0.0868512	+	0.0693005i
$568$	1.23150	−	1.23150i	0.0516727	−	0.0516727i
$569$	−4.58874	+	2.64931i	−0.192370	+	0.111065i	−0.593092	−	0.805135i	$-0.702093\pi$
$569$	−4.58874	+	2.64931i	−0.192370	+	0.111065i	0.400722	+	0.916200i	$0.368759\pi$
$570$		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	$0.984472\pi$
$572$	9.81147	+	2.62898i	0.410238	+	0.109923i
$573$	−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
$577$	−5.42795	−	20.2574i	−0.225968	−	0.843326i	−0.982014	−	0.188807i	$-0.939538\pi$
$577$	−5.42795	−	20.2574i	−0.225968	−	0.843326i	0.756046	−	0.654519i	$-0.227129\pi$
$578$	4.06295	+	15.1631i	0.168997	+	0.630704i
$579$	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
$583$	−8.68003	−	2.32581i	−0.359490	−	0.0963251i
$584$	−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	$-0.961074\pi$
$587$	−21.0917	+	21.0917i	−0.870548	+	0.870548i	0.121984	+	0.992532i	$0.461074\pi$
$588$	−3.72748	−	5.92503i	−0.153719	−	0.244344i
$589$			25.5097i			1.05111i
$590$		0			0
$591$	5.54823	+	3.20327i	0.228224	+	0.131765i
$592$	−5.55960	+	1.48969i	−0.228498	+	0.0612259i
$593$	−6.19610	+	23.1242i	−0.254443	+	0.949595i	0.713956	+	0.700190i	$0.246902\pi$
$593$	−6.19610	+	23.1242i	−0.254443	+	0.949595i	−0.968399	+	0.249405i	$0.919765\pi$
$594$	−3.11736			−0.127907
$595$		0			0
$596$	19.1438			0.784161
$597$	0.664478	−	2.47986i	0.0271953	−	0.101494i
$598$	−3.59125	+	0.962272i	−0.146857	+	0.0393502i
$599$	22.3474	+	12.9022i	0.913088	+	0.527172i	0.881423	−	0.472327i	$-0.156586\pi$
$599$	22.3474	+	12.9022i	0.913088	+	0.527172i	0.0316646	+	0.999499i	$0.489919\pi$
$600$		0			0
$601$			26.1745i			1.06768i	0.845586	+	0.533840i	$0.179251\pi$
$601$			26.1745i			1.06768i	−0.845586	+	0.533840i	$0.820749\pi$
$602$	−3.60178	−	23.8519i	−0.146798	−	0.972129i
$603$	−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
$607$	31.7351	+	8.50340i	1.28809	+	0.345142i	0.836934	−	0.547303i	$-0.184346\pi$
$607$	31.7351	+	8.50340i	1.28809	+	0.345142i	0.451155	+	0.892446i	$0.351012\pi$
$608$	−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
$612$	0.295321	+	1.10215i	0.0119376	+	0.0445519i
$613$	10.0487	+	37.5024i	0.405864	+	1.51471i	0.802456	+	0.596711i	$0.203526\pi$
$613$	10.0487	+	37.5024i	0.405864	+	1.51471i	−0.396592	+	0.917995i	$0.629807\pi$
$614$	−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	0.299483	−	0.954102i	$-0.403186\pi$
$617$	−16.2604	−	16.2604i	−0.654618	−	0.654618i	−0.954102	+	0.299483i	$0.903186\pi$
$618$	10.2718	+	2.75232i	0.413192	+	0.110715i
$619$	−13.8100	+	23.9195i	−0.555069	+	0.961407i	0.442829	+	0.896606i	$0.353975\pi$
$619$	−13.8100	+	23.9195i	−0.555069	+	0.961407i	−0.997898	+	0.0648015i	$0.979359\pi$
$620$		0			0
$621$	0.988164	−	0.570516i	0.0396536	−	0.0228940i
$622$	9.17061	−	9.17061i	0.367708	−	0.367708i
$623$	−7.25646	−	48.0540i	−0.290724	−	1.92524i
$624$			3.25839i			0.130440i
$625$		0			0
$626$	1.60375	+	0.925923i	0.0640986	+	0.0370073i
$627$	−18.0381	+	4.83328i	−0.720371	+	0.193023i
$628$	−3.24387	+	12.1063i	−0.129444	+	0.483093i
$629$	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	$0.628363\pi$
$632$	2.61857	−	9.77262i	0.104161	−	0.388734i
$633$	24.3168	−	6.51567i	0.966506	−	0.258975i
$634$	28.0468	+	16.1928i	1.11388	+	0.643099i
$635$		0			0
$636$		−	2.88264i		−	0.114304i
$637$	0.865352	+	22.7923i	0.0342865	+	0.903065i
$638$	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	$0.160969\pi$
$642$	−16.0605	−	4.30339i	−0.633856	−	0.169841i
$643$	4.52704	+	4.52704i	0.178529	+	0.178529i	0.790714	−	0.612185i	$-0.209709\pi$
$643$	4.52704	+	4.52704i	0.178529	+	0.178529i	−0.612185	+	0.790714i	$0.709709\pi$
$644$	1.20799	+	2.76667i	0.0476014	+	0.109022i
$645$		0			0
$646$	3.41765	+	5.91954i	0.134466	+	0.232901i
$647$	−2.72563	−	10.1722i	−0.107156	−	0.399910i	0.891425	−	0.453168i	$-0.149706\pi$
$647$	−2.72563	−	10.1722i	−0.107156	−	0.399910i	−0.998581	+	0.0532577i	$0.983040\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−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
$653$	22.3095	+	5.97781i	0.873037	+	0.233930i	0.667401	−	0.744699i	$-0.267407\pi$
$653$	22.3095	+	5.97781i	0.873037	+	0.233930i	0.205636	+	0.978628i	$0.434074\pi$
$654$	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
$658$	−8.80669	+	7.02706i	−0.343321	+	0.273943i
$659$		−	43.2474i		−	1.68468i	−0.538947	−	0.842340i	$-0.681178\pi$
$659$		−	43.2474i		−	1.68468i	0.538947	−	0.842340i	$-0.318822\pi$
$660$		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	$0.791957\pi$
$662$	−11.2080	+	3.00317i	−0.435610	+	0.116721i
$663$	0.962272	−	3.59125i	0.0373716	−	0.139473i
$664$	−11.3994			−0.442384
$665$		0			0
$666$	−5.75572			−0.223030
$667$	−1.59456	+	5.95099i	−0.0617418	+	0.230423i
$668$	1.97758	−	0.529892i	0.0765150	−	0.0205021i
$669$	−9.00617	−	5.19971i	−0.348199	−	0.201033i
$670$		0			0
$671$			26.5797i			1.02610i
$672$	2.61609	−	0.395046i	0.100918	−	0.0152392i
$673$	−15.0859	+	15.0859i	−0.581517	+	0.581517i	−0.935320	−	0.353803i	$-0.884888\pi$
$673$	−15.0859	+	15.0859i	−0.581517	+	0.581517i	0.353803	+	0.935320i	$0.384888\pi$
$674$	−11.5837	+	6.68788i	−0.446189	+	0.257607i
$675$		0			0
$676$	−1.19144	+	2.06363i	−0.0458245	+	0.0793704i
$677$	−12.8834	−	3.45209i	−0.495148	−	0.132674i	0.00259937	−	0.999997i	$-0.499173\pi$
$677$	−12.8834	−	3.45209i	−0.495148	−	0.132674i	−0.497747	+	0.867322i	$0.665839\pi$
$678$	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
$682$	−3.43581	−	12.8226i	−0.131564	−	0.491003i
$683$	−8.53746	−	31.8622i	−0.326677	−	1.21918i	−0.912615	−	0.408819i	$-0.865941\pi$
$683$	−8.53746	−	31.8622i	−0.326677	−	1.21918i	0.585938	−	0.810356i	$-0.300726\pi$
$684$	−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
$688$	8.80669	+	2.35975i	0.335752	+	0.0899645i
$689$	−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
$693$	3.01114	−	7.67845i	0.114384	−	0.291680i
$694$		−	21.5868i		−	0.819424i
$695$		0			0
$696$	4.67604	+	2.69971i	0.177245	+	0.102332i
$697$	11.3063	−	3.02952i	0.428257	−	0.114751i
$698$	3.86819	−	14.4363i	0.146413	−	0.546421i
$699$	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	$0.386784\pi$
$702$	−0.843334	+	3.14737i	−0.0318296	+	0.118790i
$703$	−33.3045	+	8.92391i	−1.25610	+	0.336572i
$704$	2.69971	+	1.55868i	0.101749	+	0.0587450i
$705$		0			0
$706$		−	36.4722i		−	1.37265i
$707$	19.1983	+	24.0603i	0.722026	+	0.904882i
$708$	0.165972	−	0.165972i	0.00623762	−	0.00623762i
$709$	33.7593	−	19.4909i	1.26786	−	0.731998i	0.293275	−	0.956028i	$-0.405255\pi$
$709$	33.7593	−	19.4909i	1.26786	−	0.731998i	0.974582	+	0.224030i	$0.0719215\pi$
$710$		0			0
$711$	5.05868	−	8.76189i	0.189715	−	0.328597i
$712$	17.7427	+	4.75415i	0.664937	+	0.178169i
$713$	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
$717$	3.20124	+	11.9472i	0.119552	+	0.446176i
$718$	1.12824	+	4.21067i	0.0421057	+	0.157141i
$719$	−9.01794	−	15.6195i	−0.336312	−	0.582510i	0.647424	−	0.762130i	$-0.275846\pi$
$719$	−9.01794	−	15.6195i	−0.336312	−	0.582510i	−0.983736	+	0.179620i	$0.942513\pi$
$720$		0			0
$721$	−16.7011	+	22.6422i	−0.621982	+	0.843239i
$722$	−11.9398	−	11.9398i	−0.444353	−	0.444353i
$723$	13.5120	+	3.62053i	0.502517	+	0.134649i
$724$	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	0.313774	−	0.949498i	$-0.398407\pi$
$727$	34.0615	−	34.0615i	1.26327	−	1.26327i	0.949498	−	0.313774i	$-0.101593\pi$
$728$	−8.02583	−	3.14737i	−0.297457	−	0.116649i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−9.00944	−	5.20160i	−0.333226	−	0.192388i
$732$	−8.23581	+	2.20678i	−0.304404	+	0.0815649i
$733$	8.75391	−	32.6701i	0.323333	−	1.20670i	−0.592644	−	0.805465i	$-0.701916\pi$
$733$	8.75391	−	32.6701i	0.323333	−	1.20670i	0.915977	−	0.401231i	$-0.131418\pi$
$734$	18.5499			0.684689
$735$		0			0
$736$	−1.14103			−0.0420590
$737$	11.2358	−	41.9324i	0.413874	−	1.54460i
$738$	−9.90885	+	2.65507i	−0.364750	+	0.0977344i
$739$	15.9959	+	9.23522i	0.588418	+	0.339723i	0.764472	−	0.644657i	$-0.223000\pi$
$739$	15.9959	+	9.23522i	0.588418	+	0.339723i	−0.176054	+	0.984381i	$0.556333\pi$
$740$		0			0
$741$			19.5192i			0.717057i
$742$	7.10030	+	2.78442i	0.260660	+	0.102219i
$743$	32.1999	−	32.1999i	1.18130	−	1.18130i	0.201894	−	0.979407i	$-0.435290\pi$
$743$	32.1999	−	32.1999i	1.18130	−	1.18130i	0.979407	−	0.201894i	$-0.0647096\pi$
$744$	3.68788	−	2.12920i	0.135204	−	0.0780601i
$745$		0			0
$746$	−9.75961	+	16.9041i	−0.357325	+	0.618905i
$747$	−11.0110	−	2.95039i	−0.402871	−	0.107949i
$748$	−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	$0.779389\pi$
$752$	−1.10215	−	4.11329i	−0.0401914	−	0.149996i
$753$	−4.40861	−	16.4532i	−0.160659	−	0.599587i
$754$	−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	0.376548	−	0.926397i	$-0.377111\pi$
$757$	−15.1284	−	15.1284i	−0.549850	−	0.549850i	−0.926397	+	0.376548i	$0.877111\pi$
$758$	−36.1666	−	9.69081i	−1.31363	−	0.351986i
$759$	−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
$763$	23.5170	+	29.4728i	0.851371	+	1.06699i
$764$			10.2584i			0.371136i
$765$		0			0
$766$	0.522518	+	0.301676i	0.0188794	+	0.0109000i
$767$	−0.738750	+	0.197948i	−0.0266747	+	0.00714747i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	0.469440			0.0169285			0.00846423	−	0.999964i	$-0.497306\pi$
$769$	0.469440			0.0169285			0.00846423	+	0.999964i	$0.497306\pi$
$770$		0			0
$771$	20.9862			0.755800
$772$	1.25759	−	4.69340i	0.0452618	−	0.168919i
$773$	−24.8672	+	6.66314i	−0.894410	+	0.239656i	−0.676614	−	0.736338i	$-0.736553\pi$
$773$	−24.8672	+	6.66314i	−0.894410	+	0.239656i	−0.217796	+	0.975994i	$0.569887\pi$
$774$	7.89587	+	4.55868i	0.283811	+	0.163858i
$775$		0			0
$776$		−	1.04735i		−	0.0375975i
$777$	5.55960	−	14.1771i	0.199450	−	0.508600i
$778$	−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
$782$	1.25759	+	0.336971i	0.0449714	+	0.0120501i
$783$	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
$787$	−6.68911	−	24.9641i	−0.238441	−	0.889874i	−0.976567	−	0.215211i	$-0.930956\pi$
$787$	−6.68911	−	24.9641i	−0.238441	−	0.889874i	0.738127	−	0.674662i	$-0.235711\pi$
$788$	−1.65814	−	6.18825i	−0.0590687	−	0.220447i
$789$	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
$793$	26.8355	+	7.19056i	0.952957	+	0.255344i
$794$	−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	−0.0725174	+	0.997367i	$0.523103\pi$
$797$	−30.2041	+	30.2041i	−1.06988	+	1.06988i	−0.997367	+	0.0725174i	$0.976897\pi$
$798$	15.6716	−	2.36650i	0.554767	−	0.0837733i
$799$			4.85897i			0.171898i
$800$		0			0
$801$	15.9077	+	9.18432i	0.562071	+	0.324512i
$802$	19.8177	−	5.31014i	0.699787	−	0.187507i
$803$	0.914876	−	3.41437i	0.0322853	−	0.120490i
$804$	13.9258			0.491124
$805$		0			0
$806$	−13.8755			−0.488744
$807$	7.56466	−	28.2317i	0.266289	−	0.993803i
$808$	−11.2377	+	3.01114i	−0.395342	+	0.105931i
$809$	−11.3829	−	6.57191i	−0.400201	−	0.231056i	0.286370	−	0.958119i	$-0.407551\pi$
$809$	−11.3829	−	6.57191i	−0.400201	−	0.231056i	−0.686571	+	0.727063i	$0.740885\pi$
$810$		0			0
$811$			1.45633i			0.0511386i	0.999673	+	0.0255693i	$0.00813985\pi$
$811$			1.45633i			0.0511386i	−0.999673	+	0.0255693i	$0.991860\pi$
$812$	−11.1664	+	8.90995i	−0.391865	+	0.312678i
$813$	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
$817$	52.7560	+	14.1359i	1.84570	+	0.494554i
$818$	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	$0.871576\pi$
$822$	4.44327	+	16.5825i	0.154977	+	0.578382i
$823$	1.40852	+	5.25665i	0.0490978	+	0.183235i	0.986120	−	0.166035i	$-0.0530963\pi$
$823$	1.40852	+	5.25665i	0.0490978	+	0.183235i	−0.937022	+	0.349270i	$0.886430\pi$
$824$	−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	0.773670	−	0.633589i	$-0.218419\pi$
$827$	4.02842	+	4.02842i	0.140082	+	0.140082i	−0.633589	+	0.773670i	$0.718419\pi$
$828$	−1.10215	−	0.295321i	−0.0383025	−	0.0102631i
$829$	−9.72816	+	16.8497i	−0.337873	+	0.585213i	−0.984032	−	0.177989i	$-0.943041\pi$
$829$	−9.72816	+	16.8497i	−0.337873	+	0.585213i	0.646159	+	0.763203i	$0.276374\pi$
$830$		0			0
$831$	18.7669	−	10.8351i	0.651017	−	0.375865i
$832$	2.30403	−	2.30403i	0.0798779	−	0.0798779i
$833$	3.72831	−	7.06368i	0.129178	−	0.244742i
$834$		−	11.1551i		−	0.386271i
$835$		0			0
$836$	16.1725	+	9.33719i	0.559337	+	0.322933i
$837$	4.11329	−	1.10215i	0.142176	−	0.0380960i
$838$	5.17097	−	19.2983i	0.178628	−	0.666650i
$839$	10.1273			0.349632			0.174816	−	0.984601i	$-0.444067\pi$
$839$	10.1273			0.349632			0.174816	+	0.984601i	$0.444067\pi$
$840$		0			0
$841$	−0.153802			−0.00530352
$842$	5.25195	−	19.6005i	0.180994	−	0.675479i
$843$	18.7155	−	5.01481i	0.644597	−	0.172719i
$844$	−21.8018	−	12.5873i	−0.750451	−	0.433273i
$845$		0			0
$846$		−	4.25839i		−	0.146407i
$847$	−0.506476	−	3.35400i	−0.0174027	−	0.115245i
$848$	−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
$852$	−1.68226	−	0.450761i	−0.0576334	−	0.0154428i
$853$	−27.6531	−	27.6531i	−0.946824	−	0.946824i	0.0518322	−	0.998656i	$-0.483494\pi$
$853$	−27.6531	−	27.6531i	−0.946824	−	0.946824i	−0.998656	+	0.0518322i	$0.983494\pi$
$854$	2.51961	−	22.4174i	0.0862193	−	0.767109i
$855$		0			0
$856$	8.31351	+	14.3994i	0.284150	+	0.492162i
$857$	7.88607	+	29.4312i	0.269383	+	1.00535i	0.959513	+	0.281665i	$0.0908868\pi$
$857$	7.88607	+	29.4312i	0.269383	+	1.00535i	−0.690130	+	0.723686i	$0.742446\pi$
$858$	−2.62898	−	9.81147i	−0.0897518	−	0.334958i
$859$	−17.6997	−	30.6568i	−0.603906	−	1.04600i	−0.992223	−	0.124471i	$-0.960277\pi$
$859$	−17.6997	−	30.6568i	−0.603906	−	1.04600i	0.388317	−	0.921526i	$-0.373057\pi$
$860$		0			0
$861$	3.03145	−	26.9713i	0.103311	−	0.919181i
$862$	0.237255	+	0.237255i	0.00808092	+	0.00808092i
$863$	3.92588	+	1.05194i	0.133638	+	0.0358083i	0.325018	−	0.945708i	$-0.394630\pi$
$863$	3.92588	+	1.05194i	0.133638	+	0.0358083i	−0.191380	+	0.981516i	$0.561296\pi$
$864$	−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
$868$	1.68226	+	11.1403i	0.0570997	+	0.378128i
$869$			31.5395i			1.06990i
$870$		0			0
$871$	−39.2964	−	22.6878i	−1.33151	−	0.768747i
$872$	−13.7657	+	3.68850i	−0.466164	+	0.124908i
$873$	0.271073	−	1.01166i	0.00917443	−	0.0342394i
$874$	−6.83529			−0.231207
$875$		0			0
$876$	1.13391			0.0383113
$877$	6.63449	−	24.7603i	0.224031	−	0.836095i	−0.758760	−	0.651371i	$-0.774194\pi$
$877$	6.63449	−	24.7603i	0.224031	−	0.836095i	0.982790	−	0.184724i	$-0.0591391\pi$
$878$	26.3135	−	7.05067i	0.888037	−	0.237949i
$879$	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	$-0.00933995\pi$
$882$	−3.26748	+	6.19060i	−0.110022	+	0.208448i
$883$	3.58173	−	3.58173i	0.120535	−	0.120535i	−0.644266	−	0.764801i	$-0.722837\pi$
$883$	3.58173	−	3.58173i	0.120535	−	0.120535i	0.764801	+	0.644266i	$0.222837\pi$
$884$	−3.21983	+	1.85897i	−0.108294	+	0.0625238i
$885$		0			0
$886$	−2.58235	+	4.47277i	−0.0867558	+	0.150266i
$887$	21.2046	+	5.68177i	0.711982	+	0.190775i	0.596591	−	0.802545i	$-0.296521\pi$
$887$	21.2046	+	5.68177i	0.711982	+	0.190775i	0.115391	+	0.993320i	$0.463188\pi$
$888$	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
$892$	2.69157	+	10.0451i	0.0901204	+	0.336334i
$893$	−6.60239	−	24.6404i	−0.220940	−	0.824561i
$894$	−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
$898$	−25.1625	−	6.74227i	−0.839683	−	0.224992i
$899$	−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
$903$	−18.8554	+	15.0452i	−0.627469	+	0.500672i
$904$		−	10.0237i		−	0.333382i
$905$		0			0
$906$	15.1495	+	8.74656i	0.503308	+	0.290585i
$907$	0.665569	−	0.178339i	0.0220999	−	0.00592164i	−0.247752	−	0.968823i	$-0.579692\pi$
$907$	0.665569	−	0.178339i	0.0220999	−	0.00592164i	0.269852	+	0.962902i	$0.413025\pi$
$908$	−5.26566	+	19.6517i	−0.174747	+	0.652165i
$909$	−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	$0.387899\pi$
$912$	−1.55044	+	5.78632i	−0.0513402	+	0.191604i
$913$	34.3253	−	9.19742i	1.13600	−	0.304390i
$914$	−26.2276	−	15.1425i	−0.867530	−	0.500869i
$915$		0			0
$916$			7.83286i			0.258805i
$917$	35.3425	−	5.33695i	1.16711	−	0.176241i
$918$	0.806832	−	0.806832i	0.0266294	−	0.0266294i
$919$	38.5703	−	22.2686i	1.27232	−	0.734572i	0.296893	−	0.954911i	$-0.404050\pi$
$919$	38.5703	−	22.2686i	1.27232	−	0.734572i	0.975423	+	0.220339i	$0.0707163\pi$
$920$		0			0
$921$	−0.282066	+	0.488553i	−0.00929439	+	0.0160984i
$922$	3.59125	+	0.962272i	0.118271	+	0.0316907i
$923$	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
$927$	−2.75232	−	10.2718i	−0.0903980	−	0.337370i
$928$	−1.39747	−	5.21545i	−0.0458743	−	0.171205i
$929$	−7.68149	−	13.3047i	−0.252022	−	0.436514i	0.712061	−	0.702118i	$-0.247762\pi$
$929$	−7.68149	−	13.3047i	−0.252022	−	0.436514i	−0.964082	+	0.265604i	$0.914429\pi$
$930$		0			0
$931$	−9.30856	+	40.8869i	−0.305076	+	1.34001i
$932$	−3.95517	−	3.95517i	−0.129556	−	0.129556i
$933$	−12.5273	−	3.35668i	−0.410125	−	0.109893i
$934$	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	$-0.638705\pi$
$937$	14.8294	−	14.8294i	0.484456	−	0.484456i	0.906552	+	0.422095i	$0.138705\pi$
$938$	−13.4513	+	34.3009i	−0.439199	+	1.11996i
$939$		−	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	$0.496943\pi$
$942$	12.1063	−	3.24387i	0.394444	−	0.105691i
$943$	−3.02952	+	11.3063i	−0.0986547	+	0.368184i
$944$	−0.234720			−0.00763949
$945$		0			0
$946$	−28.4221			−0.924082
$947$	−5.01553	+	18.7182i	−0.162983	+	0.608261i	0.835306	+	0.549785i	$0.185291\pi$
$947$	−5.01553	+	18.7182i	−0.162983	+	0.608261i	−0.998289	+	0.0584752i	$0.981376\pi$
$948$	−9.77262	+	2.61857i	−0.317400	+	0.0850471i
$949$	−3.19973	−	1.84737i	−0.103868	−	0.0599680i
$950$		0			0
$951$		−	32.3857i		−	1.05018i
$952$	1.88289	+	2.35975i	0.0610250	+	0.0764798i
$953$	−22.0009	+	22.0009i	−0.712680	+	0.712680i	−0.967095	−	0.254415i	$-0.918117\pi$
$953$	−22.0009	+	22.0009i	−0.712680	+	0.712680i	0.254415	+	0.967095i	$0.418117\pi$
$954$	−2.49644	+	1.44132i	−0.0808252	+	0.0466645i
$955$		0			0
$956$	6.18432	−	10.7115i	0.200015	−	0.346436i
$957$	−16.2584	−	4.35643i	−0.525560	−	0.140823i
$958$	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
$962$	−4.85400	−	18.1154i	−0.156499	−	0.584063i
$963$	4.30339	+	16.0605i	0.138675	+	0.517542i
$964$	−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	0.902469	−	0.430754i	$-0.141752\pi$
$967$	14.6687	+	14.6687i	0.471715	+	0.471715i	−0.430754	+	0.902469i	$0.641752\pi$
$968$	1.23838	+	0.331823i	0.0398031	+	0.0106652i
$969$	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
$973$	27.4765	+	10.7750i	0.880857	+	0.345432i
$974$		−	31.2777i		−	1.00220i
$975$		0			0
$976$	7.38403	+	4.26317i	0.236357	+	0.136461i
$977$	47.4327	−	12.7095i	1.51751	−	0.406614i	0.598585	−	0.801059i	$-0.295730\pi$
$977$	47.4327	−	12.7095i	1.51751	−	0.406614i	0.918920	+	0.394445i	$0.129063\pi$
$978$	−3.91019	+	14.5930i	−0.125034	+	0.466633i
$979$	−57.2616			−1.83009
$980$		0			0
$981$	−14.2513			−0.455008
$982$	−6.91327	+	25.8007i	−0.220611	+	0.823332i
$983$	−55.8618	+	14.9681i	−1.78172	+	0.477409i	−0.990895	−	0.134638i	$-0.957013\pi$
$983$	−55.8618	+	14.9681i	−1.78172	+	0.477409i	−0.790821	+	0.612048i	$0.790346\pi$
$984$	8.88403	+	5.12920i	0.283213	+	0.163513i
$985$		0			0
$986$			6.16092i			0.196204i
$987$	10.4890	+	4.11329i	0.333867	+	0.130928i
$988$	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	$-0.229867\pi$
$992$	−4.11329	−	1.10215i	−0.130597	−	0.0349934i
$993$	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
$997$	13.7287	+	51.2361i	0.434791	+	1.62266i	0.741566	+	0.670880i	$0.234084\pi$
$997$	13.7287	+	51.2361i	0.434791	+	1.62266i	−0.306775	+	0.951782i	$0.599250\pi$
$998$	2.03036	+	7.57742i	0.0642701	+	0.239859i
$999$	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.f.157.1	yes	16
5.2	odd	4		1050.2.bc.e.493.1	✓	16
5.3	odd	4		1050.2.bc.e.493.4	yes	16
5.4	even	2	inner	1050.2.bc.f.157.4	yes	16
7.5	odd	6		1050.2.bc.e.607.3	yes	16
35.12	even	12	inner	1050.2.bc.f.943.4	yes	16
35.19	odd	6		1050.2.bc.e.607.2	yes	16
35.33	even	12	inner	1050.2.bc.f.943.1	yes	16

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

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)

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

Varieties

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Database

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