LMFDB - Embedded newform 1050.2.bc.h.493.1

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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.1
Root			$0.792206 - 1.03242i$ of defining polynomial
Character	$\chi$	$=$	1050.493
Dual form			1050.2.bc.h.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.15951 - 1.52856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.15951 - 1.52856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.883028 - 1.52945i) q^{11} +(0.258819 - 0.965926i) q^{12} +(2.71395 - 2.71395i) q^{13} +(1.69031 + 2.03540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.14529 - 0.574830i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.886994 - 1.53632i) q^{19} +(-0.917556 + 2.48155i) q^{21} +(-1.24879 + 1.24879i) q^{22} +(-1.04741 + 3.90900i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.32389 + 1.91905i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.10591 - 2.40353i) q^{28} +3.84628i q^{29} +(-8.94554 - 5.16471i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.70588 - 0.457089i) q^{33} -2.22097 q^{34} -1.00000 q^{36} +(-3.21516 - 0.861499i) q^{37} +(0.459142 + 1.71354i) q^{38} +(-3.32389 - 1.91905i) q^{39} -11.8993i q^{41} +(1.52856 - 2.15951i) q^{42} +(-3.46335 - 3.46335i) q^{43} +(1.52945 - 0.883028i) q^{44} +(2.02344 - 3.50471i) q^{46} +(-1.59118 + 5.93837i) q^{47} +(0.707107 - 0.707107i) q^{48} +(2.32699 + 6.60190i) q^{49} +(-1.11049 - 1.92342i) q^{51} +(3.70732 - 0.993373i) q^{52} +(0.396561 - 0.106258i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.446149 + 2.60786i) q^{56} +(-1.25440 + 1.25440i) q^{57} +(0.995491 - 3.71522i) q^{58} +(-5.18379 + 8.97859i) q^{59} +(-5.87936 + 3.39445i) q^{61} +(7.30401 + 7.30401i) q^{62} +(2.63447 + 0.244018i) q^{63} +1.00000i q^{64} +(1.52945 + 0.883028i) q^{66} +(-1.97702 - 7.37834i) q^{67} +(2.14529 + 0.574830i) q^{68} +4.04689 q^{69} -10.7193 q^{71} +(0.965926 + 0.258819i) q^{72} +(-2.75198 - 10.2705i) q^{73} +(2.88263 + 1.66429i) q^{74} -1.77399i q^{76} +(-4.24477 + 1.95310i) q^{77} +(2.71395 + 2.71395i) q^{78} +(10.9907 - 6.34546i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-3.07978 + 11.4939i) q^{82} +(-1.94227 + 1.94227i) q^{83} +(-2.03540 + 1.69031i) q^{84} +(2.44896 + 4.24172i) q^{86} +(3.71522 - 0.995491i) q^{87} +(-1.70588 + 0.457089i) q^{88} +(0.558127 + 0.966705i) q^{89} +(-10.0092 + 1.71236i) q^{91} +(-2.86158 + 2.86158i) q^{92} +(-2.67345 + 9.97746i) q^{93} +(3.07393 - 5.32419i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-7.26720 - 7.26720i) q^{97} +(-0.539001 - 6.97922i) q^{98} +1.76606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

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
$7$	−2.15951	−	1.52856i	−0.816219	−	0.577743i
$7$	−2.15951	−	1.52856i	−0.816219	−	0.577743i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	0.883028	−	1.52945i	0.266243	−	0.461147i	−0.701645	−	0.712526i	$-0.747551\pi$
$11$	0.883028	−	1.52945i	0.266243	−	0.461147i	0.967889	+	0.251380i	$0.0808843\pi$
$12$	0.258819	−	0.965926i	0.0747146	−	0.278839i
$13$	2.71395	−	2.71395i	0.752713	−	0.752713i	−0.222272	−	0.974985i	$-0.571347\pi$
$13$	2.71395	−	2.71395i	0.752713	−	0.752713i	0.974985	+	0.222272i	$0.0713472\pi$
$14$	1.69031	+	2.03540i	0.451754	+	0.543984i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.14529	−	0.574830i	0.520310	−	0.139417i	0.0109000	−	0.999941i	$-0.496530\pi$
$17$	2.14529	−	0.574830i	0.520310	−	0.139417i	0.509410	+	0.860524i	$0.329864\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−0.886994	−	1.53632i	−0.203490	−	0.352456i	0.746160	−	0.665766i	$-0.231895\pi$
$19$	−0.886994	−	1.53632i	−0.203490	−	0.352456i	−0.949651	+	0.313311i	$0.898562\pi$
$20$		0			0
$21$	−0.917556	+	2.48155i	−0.200227	+	0.541519i
$22$	−1.24879	+	1.24879i	−0.266243	+	0.266243i
$23$	−1.04741	+	3.90900i	−0.218401	+	0.815082i	0.766541	+	0.642195i	$0.221976\pi$
$23$	−1.04741	+	3.90900i	−0.218401	+	0.815082i	−0.984942	+	0.172887i	$0.944691\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−3.32389	+	1.91905i	−0.651869	+	0.376356i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.10591	−	2.40353i	−0.208998	−	0.454225i
$29$			3.84628i			0.714236i	0.934059	+	0.357118i	$0.116241\pi$
$29$			3.84628i			0.714236i	−0.934059	+	0.357118i	$0.883759\pi$
$30$		0			0
$31$	−8.94554	−	5.16471i	−1.60667	−	0.927610i	−0.990109	−	0.140300i	$-0.955193\pi$
$31$	−8.94554	−	5.16471i	−1.60667	−	0.927610i	−0.616558	−	0.787310i	$-0.711473\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−1.70588	−	0.457089i	−0.296956	−	0.0795690i
$34$	−2.22097			−0.380893
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−3.21516	−	0.861499i	−0.528569	−	0.141630i	−0.0153416	−	0.999882i	$-0.504884\pi$
$37$	−3.21516	−	0.861499i	−0.528569	−	0.141630i	−0.513227	+	0.858253i	$0.671550\pi$
$38$	0.459142	+	1.71354i	0.0744827	+	0.277973i
$39$	−3.32389	−	1.91905i	−0.532248	−	0.307294i
$40$		0			0
$41$		−	11.8993i		−	1.85836i	−0.369622	−	0.929182i	$-0.620513\pi$
$41$		−	11.8993i		−	1.85836i	0.369622	−	0.929182i	$-0.379487\pi$
$42$	1.52856	−	2.15951i	0.235862	−	0.333220i
$43$	−3.46335	−	3.46335i	−0.528155	−	0.528155i	0.391867	−	0.920022i	$-0.371829\pi$
$43$	−3.46335	−	3.46335i	−0.528155	−	0.528155i	−0.920022	+	0.391867i	$0.871829\pi$
$44$	1.52945	−	0.883028i	0.230573	−	0.133122i
$45$		0			0
$46$	2.02344	−	3.50471i	0.298341	−	0.516741i
$47$	−1.59118	+	5.93837i	−0.232098	+	0.866200i	0.747338	+	0.664444i	$0.231332\pi$
$47$	−1.59118	+	5.93837i	−0.232098	+	0.866200i	−0.979436	+	0.201756i	$0.935335\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	2.32699	+	6.60190i	0.332427	+	0.943129i
$50$		0			0
$51$	−1.11049	−	1.92342i	−0.155499	−	0.269332i
$52$	3.70732	−	0.993373i	0.514113	−	0.137756i
$53$	0.396561	−	0.106258i	0.0544719	−	0.0145957i	−0.231480	−	0.972840i	$-0.574357\pi$
$53$	0.396561	−	0.106258i	0.0544719	−	0.0145957i	0.285952	+	0.958244i	$0.407690\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	0.446149	+	2.60786i	0.0596191	+	0.348490i
$57$	−1.25440	+	1.25440i	−0.166149	+	0.166149i
$58$	0.995491	−	3.71522i	0.130714	−	0.487833i
$59$	−5.18379	+	8.97859i	−0.674872	+	1.16891i	0.301634	+	0.953424i	$0.402468\pi$
$59$	−5.18379	+	8.97859i	−0.674872	+	1.16891i	−0.976506	+	0.215489i	$0.930865\pi$
$60$		0			0
$61$	−5.87936	+	3.39445i	−0.752775	+	0.434615i	−0.826696	−	0.562649i	$-0.809782\pi$
$61$	−5.87936	+	3.39445i	−0.752775	+	0.434615i	0.0739204	+	0.997264i	$0.476449\pi$
$62$	7.30401	+	7.30401i	0.927610	+	0.927610i
$63$	2.63447	+	0.244018i	0.331913	+	0.0307434i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	1.52945	+	0.883028i	0.188262	+	0.108693i
$67$	−1.97702	−	7.37834i	−0.241532	−	0.901408i	−0.975095	−	0.221787i	$-0.928811\pi$
$67$	−1.97702	−	7.37834i	−0.241532	−	0.901408i	0.733563	−	0.679621i	$-0.237856\pi$
$68$	2.14529	+	0.574830i	0.260155	+	0.0697083i
$69$	4.04689			0.487188
$70$		0			0
$71$	−10.7193			−1.27214			−0.636072	−	0.771629i	$-0.719442\pi$
$71$	−10.7193			−1.27214			−0.636072	+	0.771629i	$0.719442\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	−2.75198	−	10.2705i	−0.322095	−	1.20207i	−0.917200	−	0.398426i	$-0.869556\pi$
$73$	−2.75198	−	10.2705i	−0.322095	−	1.20207i	0.595106	−	0.803647i	$-0.297110\pi$
$74$	2.88263	+	1.66429i	0.335099	+	0.193470i
$75$		0			0
$76$		−	1.77399i		−	0.203490i
$77$	−4.24477	+	1.95310i	−0.483737	+	0.222577i
$78$	2.71395	+	2.71395i	0.307294	+	0.307294i
$79$	10.9907	−	6.34546i	1.23655	−	0.713920i	0.268159	−	0.963375i	$-0.413585\pi$
$79$	10.9907	−	6.34546i	1.23655	−	0.713920i	0.968386	+	0.249455i	$0.0802515\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−3.07978	+	11.4939i	−0.340104	+	1.26929i
$83$	−1.94227	+	1.94227i	−0.213191	+	0.213191i	−0.805622	−	0.592430i	$-0.798169\pi$
$83$	−1.94227	+	1.94227i	−0.213191	+	0.213191i	0.592430	+	0.805622i	$0.298169\pi$
$84$	−2.03540	+	1.69031i	−0.222081	+	0.184428i
$85$		0			0
$86$	2.44896	+	4.24172i	0.264078	+	0.457396i
$87$	3.71522	−	0.995491i	0.398314	−	0.106728i
$88$	−1.70588	+	0.457089i	−0.181847	+	0.0487259i
$89$	0.558127	+	0.966705i	0.0591614	+	0.102471i	0.894089	−	0.447889i	$-0.147824\pi$
$89$	0.558127	+	0.966705i	0.0591614	+	0.102471i	−0.834928	+	0.550359i	$0.814491\pi$
$90$		0			0
$91$	−10.0092	+	1.71236i	−1.04925	+	0.179504i
$92$	−2.86158	+	2.86158i	−0.298341	+	0.298341i
$93$	−2.67345	+	9.97746i	−0.277224	+	1.03461i
$94$	3.07393	−	5.32419i	0.317051	−	0.549149i
$95$		0			0
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−7.26720	−	7.26720i	−0.737872	−	0.737872i	0.234293	−	0.972166i	$-0.424722\pi$
$97$	−7.26720	−	7.26720i	−0.737872	−	0.737872i	−0.972166	+	0.234293i	$0.924722\pi$
$98$	−0.539001	−	6.97922i	−0.0544473	−	0.705007i
$99$			1.76606i			0.177495i
$100$		0			0
$101$	15.8887	+	9.17333i	1.58098	+	0.912780i	0.994716	+	0.102661i	$0.0327358\pi$
$101$	15.8887	+	9.17333i	1.58098	+	0.912780i	0.586265	+	0.810119i	$0.300598\pi$
$102$	0.574830	+	2.14529i	0.0569166	+	0.212416i
$103$	−8.80911	−	2.36040i	−0.867988	−	0.232577i	−0.202770	−	0.979226i	$-0.564994\pi$
$103$	−8.80911	−	2.36040i	−0.867988	−	0.232577i	−0.665217	+	0.746650i	$0.731661\pi$
$104$	−3.83810			−0.376356
$105$		0			0
$106$	−0.410550			−0.0398762
$107$	−14.2519	−	3.81880i	−1.37779	−	0.369177i	−0.507471	−	0.861669i	$-0.669419\pi$
$107$	−14.2519	−	3.81880i	−1.37779	−	0.369177i	−0.870317	+	0.492492i	$0.836086\pi$
$108$	0.258819	+	0.965926i	0.0249049	+	0.0929463i
$109$	−17.4494	−	10.0744i	−1.67135	−	0.964955i	−0.966883	−	0.255218i	$-0.917853\pi$
$109$	−17.4494	−	10.0744i	−1.67135	−	0.964955i	−0.704467	−	0.709736i	$-0.748814\pi$
$110$		0			0
$111$			3.32858i			0.315935i
$112$	0.244018	−	2.63447i	0.0230576	−	0.248934i
$113$	6.54677	+	6.54677i	0.615869	+	0.615869i	0.944469	−	0.328600i	$-0.106577\pi$
$113$	6.54677	+	6.54677i	0.615869	+	0.615869i	−0.328600	+	0.944469i	$0.606577\pi$
$114$	1.53632	−	0.886994i	0.143889	−	0.0830746i
$115$		0			0
$116$	−1.92314	+	3.33098i	−0.178559	+	0.309273i
$117$	−0.993373	+	3.70732i	−0.0918374	+	0.342742i
$118$	7.33099	−	7.33099i	0.674872	−	0.674872i
$119$	−5.51145	−	2.03786i	−0.505234	−	0.186811i
$120$		0			0
$121$	3.94052	+	6.82518i	0.358229	+	0.620471i
$122$	6.55758	−	1.75710i	0.593695	−	0.159080i
$123$	−11.4939	+	3.07978i	−1.03637	+	0.277694i
$124$	−5.16471	−	8.94554i	−0.463805	−	0.803333i
$125$		0			0
$126$	−2.48155	−	0.917556i	−0.221074	−	0.0817424i
$127$	−12.5444	+	12.5444i	−1.11313	+	1.11313i	−0.120409	+	0.992724i	$0.538421\pi$
$127$	−12.5444	+	12.5444i	−1.11313	+	1.11313i	−0.992724	+	0.120409i	$0.961579\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−2.44896	+	4.24172i	−0.215619	+	0.373462i
$130$		0			0
$131$	0.830756	−	0.479637i	0.0725835	−	0.0419061i	−0.463269	−	0.886218i	$-0.653324\pi$
$131$	0.830756	−	0.479637i	0.0725835	−	0.0419061i	0.535853	+	0.844312i	$0.319990\pi$
$132$	−1.24879	−	1.24879i	−0.108693	−	0.108693i
$133$	−0.432886	+	4.67353i	−0.0375359	+	0.405246i
$134$			7.63862i			0.659877i
$135$		0			0
$136$	−1.92342	−	1.11049i	−0.164932	−	0.0952233i
$137$	−2.88499	−	10.7669i	−0.246481	−	0.919880i	−0.972633	−	0.232346i	$-0.925360\pi$
$137$	−2.88499	−	10.7669i	−0.246481	−	0.919880i	0.726152	−	0.687534i	$-0.241307\pi$
$138$	−3.90900	−	1.04741i	−0.332756	−	0.0891616i
$139$	13.5695			1.15095			0.575477	−	0.817818i	$-0.304816\pi$
$139$	13.5695			1.15095			0.575477	+	0.817818i	$0.304816\pi$
$140$		0			0
$141$	6.14785			0.517742
$142$	10.3540	+	2.77435i	0.868891	+	0.232819i
$143$	−1.75435	−	6.54733i	−0.146706	−	0.547516i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$		0			0
$146$			10.6328i			0.879979i
$147$	5.77468	−	3.95640i	0.476288	−	0.326318i
$148$	−2.35366	−	2.35366i	−0.193470	−	0.193470i
$149$	−8.74565	+	5.04930i	−0.716471	+	0.413655i	−0.813453	−	0.581631i	$-0.802415\pi$
$149$	−8.74565	+	5.04930i	−0.716471	+	0.413655i	0.0969812	+	0.995286i	$0.469081\pi$
$150$		0			0
$151$	7.15497	−	12.3928i	0.582263	−	1.00851i	−0.412948	−	0.910755i	$-0.635501\pi$
$151$	7.15497	−	12.3928i	0.582263	−	1.00851i	0.995211	−	0.0977541i	$-0.0311659\pi$
$152$	−0.459142	+	1.71354i	−0.0372413	+	0.138987i
$153$	−1.57046	+	1.57046i	−0.126964	+	0.126964i
$154$	4.60563	−	0.787924i	0.371133	−	0.0634927i
$155$		0			0
$156$	−1.91905	−	3.32389i	−0.153647	−	0.266124i
$157$	9.25683	−	2.48036i	0.738776	−	0.197954i	0.130242	−	0.991482i	$-0.458425\pi$
$157$	9.25683	−	2.48036i	0.738776	−	0.197954i	0.608534	+	0.793528i	$0.291758\pi$
$158$	−12.2585	+	3.28465i	−0.975233	+	0.261313i
$159$	−0.205275	−	0.355547i	−0.0162794	−	0.0281967i
$160$		0			0
$161$	8.23705	−	6.84049i	0.649170	−	0.539106i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−3.06537	+	11.4401i	−0.240098	+	0.896058i	0.735686	+	0.677323i	$0.236860\pi$
$163$	−3.06537	+	11.4401i	−0.240098	+	0.896058i	−0.975784	+	0.218736i	$0.929807\pi$
$164$	5.94967	−	10.3051i	0.464591	−	0.804695i
$165$		0			0
$166$	2.37878	−	1.37339i	0.184629	−	0.106596i
$167$	6.95883	+	6.95883i	0.538490	+	0.538490i	0.923085	−	0.384595i	$-0.125659\pi$
$167$	6.95883	+	6.95883i	0.538490	+	0.538490i	−0.384595	+	0.923085i	$0.625659\pi$
$168$	2.40353	−	1.10591i	0.185436	−	0.0853229i
$169$		−	1.73100i		−	0.133154i
$170$		0			0
$171$	1.53632	+	0.886994i	0.117485	+	0.0678301i
$172$	−1.26767	−	4.73102i	−0.0966592	−	0.360737i
$173$	8.37084	+	2.24296i	0.636423	+	0.170529i	0.562583	−	0.826741i	$-0.309808\pi$
$173$	8.37084	+	2.24296i	0.636423	+	0.170529i	0.0738403	+	0.997270i	$0.476474\pi$
$174$	−3.84628			−0.291586
$175$		0			0
$176$	1.76606			0.133122
$177$	10.0143	+	2.68333i	0.752722	+	0.201691i
$178$	−0.288908	−	1.07822i	−0.0216546	−	0.0808160i
$179$	−11.5646	−	6.67682i	−0.864378	−	0.499049i	0.00109809	−	0.999999i	$-0.499650\pi$
$179$	−11.5646	−	6.67682i	−0.864378	−	0.499049i	−0.865476	+	0.500951i	$0.832984\pi$
$180$		0			0
$181$		−	8.73922i		−	0.649581i	−0.945786	−	0.324791i	$-0.894706\pi$
$181$		−	8.73922i		−	0.649581i	0.945786	−	0.324791i	$-0.105294\pi$
$182$	10.1114	+	0.936566i	0.749505	+	0.0694229i
$183$	4.80048	+	4.80048i	0.354862	+	0.354862i
$184$	3.50471	−	2.02344i	0.258371	−	0.149170i
$185$		0			0
$186$	5.16471	−	8.94554i	0.378695	−	0.655919i
$187$	1.01518	−	3.78871i	0.0742374	−	0.277058i
$188$	−4.34719	+	4.34719i	−0.317051	+	0.317051i
$189$	−0.446149	−	2.60786i	−0.0324525	−	0.189694i
$190$		0			0
$191$	5.43796	+	9.41883i	0.393477	+	0.681523i	0.992906	−	0.118906i	$-0.0379386\pi$
$191$	5.43796	+	9.41883i	0.393477	+	0.681523i	−0.599428	+	0.800429i	$0.704605\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	10.8195	−	2.89908i	0.778806	−	0.208680i	0.152548	−	0.988296i	$-0.451252\pi$
$193$	10.8195	−	2.89908i	0.778806	−	0.208680i	0.626258	+	0.779616i	$0.284586\pi$
$194$	5.13869	+	8.90047i	0.368936	+	0.639016i
$195$		0			0
$196$	−1.28572	+	6.88091i	−0.0918371	+	0.491494i
$197$	10.3775	−	10.3775i	0.739367	−	0.739367i	−0.233088	−	0.972456i	$-0.574883\pi$
$197$	10.3775	−	10.3775i	0.739367	−	0.739367i	0.972456	+	0.233088i	$0.0748831\pi$
$198$	0.457089	−	1.70588i	0.0324839	−	0.121232i
$199$	9.28152	−	16.0761i	0.657949	−	1.13960i	−0.323197	−	0.946332i	$-0.604757\pi$
$199$	9.28152	−	16.0761i	0.657949	−	1.13960i	0.981146	−	0.193270i	$-0.0619092\pi$
$200$		0			0
$201$	−6.61524	+	3.81931i	−0.466603	+	0.269394i
$202$	−12.9730	−	12.9730i	−0.912780	−	0.912780i
$203$	5.87928	−	8.30609i	0.412645	−	0.582973i
$204$		−	2.22097i		−	0.155499i
$205$		0			0
$206$	7.89804	+	4.55993i	0.550282	+	0.317706i
$207$	−1.04741	−	3.90900i	−0.0728002	−	0.271694i
$208$	3.70732	+	0.993373i	0.257056	+	0.0688780i
$209$	−3.13296			−0.216712
$210$		0			0
$211$	−0.453133			−0.0311950			−0.0155975	−	0.999878i	$-0.504965\pi$
$211$	−0.453133			−0.0311950			−0.0155975	+	0.999878i	$0.504965\pi$
$212$	0.396561	+	0.106258i	0.0272359	+	0.00729784i
$213$	2.77435	+	10.3540i	0.190096	+	0.709446i
$214$	12.7779	+	7.37735i	0.873483	+	0.504305i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	11.4234	+	24.8271i	0.775473	+	1.68537i
$218$	14.2474	+	14.2474i	0.964955	+	0.964955i
$219$	−9.20830	+	5.31641i	−0.622239	+	0.359250i
$220$		0			0
$221$	4.26215	−	7.38226i	0.286703	−	0.496585i
$222$	0.861499	−	3.21516i	0.0578201	−	0.215787i
$223$	4.67260	−	4.67260i	0.312901	−	0.312901i	−0.533132	−	0.846032i	$-0.678985\pi$
$223$	4.67260	−	4.67260i	0.312901	−	0.312901i	0.846032	+	0.533132i	$0.178985\pi$
$224$	−0.917556	+	2.48155i	−0.0613068	+	0.165806i
$225$		0			0
$226$	−4.62927	−	8.01813i	−0.307934	−	0.533358i
$227$	16.0416	−	4.29835i	1.06472	−	0.285291i	0.316399	−	0.948626i	$-0.397526\pi$
$227$	16.0416	−	4.29835i	1.06472	−	0.285291i	0.748323	+	0.663335i	$0.230860\pi$
$228$	−1.71354	+	0.459142i	−0.113482	+	0.0304074i
$229$	6.77075	+	11.7273i	0.447423	+	0.774960i	0.998217	−	0.0596810i	$-0.0190084\pi$
$229$	6.77075	+	11.7273i	0.447423	+	0.774960i	−0.550794	+	0.834641i	$0.685675\pi$
$230$		0			0
$231$	2.98518	+	3.59463i	0.196410	+	0.236510i
$232$	2.71973	−	2.71973i	0.178559	−	0.178559i
$233$	−2.99668	+	11.1838i	−0.196319	+	0.732672i	0.795603	+	0.605819i	$0.207154\pi$
$233$	−2.99668	+	11.1838i	−0.196319	+	0.732672i	−0.991922	+	0.126853i	$0.959512\pi$
$234$	1.91905	−	3.32389i	0.125452	−	0.217290i
$235$		0			0
$236$	−8.97859	+	5.18379i	−0.584456	+	0.337436i
$237$	−8.97383	−	8.97383i	−0.582913	−	0.582913i
$238$	4.79621	+	3.39489i	0.310892	+	0.220058i
$239$		−	17.0264i		−	1.10135i	−0.834721	−	0.550673i	$-0.814371\pi$
$239$		−	17.0264i		−	1.10135i	0.834721	−	0.550673i	$-0.185629\pi$
$240$		0			0
$241$	16.3866	+	9.46081i	1.05555	+	0.609424i	0.924199	−	0.381911i	$-0.124734\pi$
$241$	16.3866	+	9.46081i	1.05555	+	0.609424i	0.131355	+	0.991335i	$0.458067\pi$
$242$	−2.03976	−	7.61250i	−0.131121	−	0.489350i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	−6.78891			−0.434615
$245$		0			0
$246$	11.8993			0.758674
$247$	−6.57674	−	1.76223i	−0.418468	−	0.112128i
$248$	2.67345	+	9.97746i	0.169764	+	0.633569i
$249$	2.37878	+	1.37339i	0.150749	+	0.0870350i
$250$		0			0
$251$		−	18.1527i		−	1.14579i	−0.819629	−	0.572894i	$-0.805821\pi$
$251$		−	18.1527i		−	1.14579i	0.819629	−	0.572894i	$-0.194179\pi$
$252$	2.15951	+	1.52856i	0.136037	+	0.0962904i
$253$	5.05372	+	5.05372i	0.317725	+	0.317725i
$254$	15.3637	−	8.87021i	0.964002	−	0.556567i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.22983	−	23.2500i	0.388606	−	1.45030i	−0.443797	−	0.896127i	$-0.646369\pi$
$257$	6.22983	−	23.2500i	0.388606	−	1.45030i	0.832403	−	0.554170i	$-0.186964\pi$
$258$	3.46335	−	3.46335i	0.215619	−	0.215619i
$259$	5.62632	+	6.77499i	0.349603	+	0.420978i
$260$		0			0
$261$	−1.92314	−	3.33098i	−0.119039	−	0.206182i
$262$	−0.926588	+	0.248279i	−0.0572448	+	0.0153387i
$263$	13.5576	−	3.63274i	0.835995	−	0.224004i	0.184668	−	0.982801i	$-0.440879\pi$
$263$	13.5576	−	3.63274i	0.835995	−	0.224004i	0.651328	+	0.758797i	$0.274212\pi$
$264$	0.883028	+	1.52945i	0.0543466	+	0.0941311i
$265$		0			0
$266$	1.62773	−	4.40224i	0.0998027	−	0.269919i
$267$	0.789311	−	0.789311i	0.0483051	−	0.0483051i
$268$	1.97702	−	7.37834i	0.120766	−	0.450704i
$269$	13.2762	−	22.9951i	0.809466	−	1.40204i	−0.103768	−	0.994602i	$-0.533090\pi$
$269$	13.2762	−	22.9951i	0.809466	−	1.40204i	0.913234	−	0.407435i	$-0.133577\pi$
$270$		0			0
$271$	10.3582	−	5.98031i	0.629216	−	0.363278i	−0.151232	−	0.988498i	$-0.548324\pi$
$271$	10.3582	−	5.98031i	0.629216	−	0.363278i	0.780448	+	0.625220i	$0.214991\pi$
$272$	1.57046	+	1.57046i	0.0952233	+	0.0952233i
$273$	4.24460	+	9.22499i	0.256895	+	0.558322i
$274$			11.1467i			0.673399i
$275$		0			0
$276$	3.50471	+	2.02344i	0.210959	+	0.121797i
$277$	0.611241	+	2.28118i	0.0367259	+	0.137063i	0.981855	−	0.189635i	$-0.0607306\pi$
$277$	0.611241	+	2.28118i	0.0367259	+	0.137063i	−0.945129	+	0.326698i	$0.894064\pi$
$278$	−13.1072	−	3.51206i	−0.786116	−	0.210639i
$279$	10.3294			0.618406
$280$		0			0
$281$	−11.0306			−0.658033			−0.329017	−	0.944324i	$-0.606717\pi$
$281$	−11.0306			−0.658033			−0.329017	+	0.944324i	$0.606717\pi$
$282$	−5.93837	−	1.59118i	−0.353625	−	0.0947534i
$283$	−6.05917	−	22.6131i	−0.360180	−	1.34421i	−0.873838	−	0.486217i	$-0.838377\pi$
$283$	−6.05917	−	22.6131i	−0.360180	−	1.34421i	0.513658	−	0.857995i	$-0.328290\pi$
$284$	−9.28317	−	5.35964i	−0.550855	−	0.318036i
$285$		0			0
$286$			6.77830i			0.400809i
$287$	−18.1889	+	25.6968i	−1.07366	+	1.51683i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−10.4506	+	6.03364i	−0.614740	+	0.354920i
$290$		0			0
$291$	−5.13869	+	8.90047i	−0.301235	+	0.521755i
$292$	2.75198	−	10.2705i	0.161047	−	0.601037i
$293$	−15.4837	+	15.4837i	−0.904565	+	0.904565i	−0.995827	−	0.0912620i	$-0.970910\pi$
$293$	−15.4837	+	15.4837i	−0.904565	+	0.904565i	0.0912620	+	0.995827i	$0.470910\pi$
$294$	−6.60190	+	2.32699i	−0.385031	+	0.135713i
$295$		0			0
$296$	1.66429	+	2.88263i	0.0967348	+	0.167550i
$297$	1.70588	−	0.457089i	0.0989852	−	0.0265230i
$298$	9.75450	−	2.61371i	0.565063	−	0.151408i
$299$	7.76618	+	13.4514i	0.449130	+	0.777916i
$300$		0			0
$301$	2.18520	+	12.7731i	0.125953	+	0.736228i
$302$	−10.1186	+	10.1186i	−0.582263	+	0.582263i
$303$	4.74846	−	17.7215i	0.272792	−	1.01807i
$304$	0.886994	−	1.53632i	0.0508726	−	0.0881139i
$305$		0			0
$306$	1.92342	−	1.11049i	0.109954	−	0.0634822i
$307$	2.12149	+	2.12149i	0.121080	+	0.121080i	0.765050	−	0.643971i	$-0.222714\pi$
$307$	2.12149	+	2.12149i	0.121080	+	0.121080i	−0.643971	+	0.765050i	$0.722714\pi$
$308$	−4.65263	−	0.430950i	−0.265108	−	0.0245557i
$309$			9.11987i			0.518811i
$310$		0			0
$311$	13.0082	+	7.51027i	0.737626	+	0.425868i	0.821205	−	0.570633i	$-0.193302\pi$
$311$	13.0082	+	7.51027i	0.737626	+	0.425868i	−0.0835796	+	0.996501i	$0.526635\pi$
$312$	0.993373	+	3.70732i	0.0562387	+	0.209886i
$313$	12.8644	+	3.44701i	0.727139	+	0.194836i	0.603355	−	0.797473i	$-0.293830\pi$
$313$	12.8644	+	3.44701i	0.727139	+	0.194836i	0.123784	+	0.992309i	$0.460497\pi$
$314$	−9.58338			−0.540821
$315$		0			0
$316$	12.6909			0.713920
$317$	13.4280	+	3.59802i	0.754192	+	0.202085i	0.615377	−	0.788233i	$-0.289004\pi$
$317$	13.4280	+	3.59802i	0.754192	+	0.202085i	0.138815	+	0.990318i	$0.455671\pi$
$318$	0.106258	+	0.396561i	0.00595867	+	0.0222380i
$319$	5.88269	+	3.39638i	0.329368	+	0.190160i
$320$		0			0
$321$			14.7547i			0.823527i
$322$	−9.72682	+	4.47550i	−0.542055	+	0.249410i
$323$	−2.78598	−	2.78598i	−0.155016	−	0.155016i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$		0			0
$326$	5.92183	−	10.2569i	0.327980	−	0.568078i
$327$	−5.21491	+	19.4623i	−0.288385	+	1.07627i
$328$	−8.41410	+	8.41410i	−0.464591	+	0.464591i
$329$	12.5133	−	10.3918i	0.689883	−	0.572916i
$330$		0			0
$331$	9.31631	+	16.1363i	0.512071	+	0.886932i	0.999902	+	0.0139944i	$0.00445470\pi$
$331$	9.31631	+	16.1363i	0.512071	+	0.886932i	−0.487832	+	0.872938i	$0.662212\pi$
$332$	−2.65318	+	0.710918i	−0.145612	+	0.0390167i
$333$	3.21516	−	0.861499i	0.176190	−	0.0472099i
$334$	−4.92063	−	8.52279i	−0.269245	−	0.466346i
$335$		0			0
$336$	−2.60786	+	0.446149i	−0.142271	+	0.0243394i
$337$	−9.63568	+	9.63568i	−0.524889	+	0.524889i	−0.919044	−	0.394155i	$-0.871037\pi$
$337$	−9.63568	+	9.63568i	−0.524889	+	0.524889i	0.394155	+	0.919044i	$0.371037\pi$
$338$	−0.448015	+	1.67202i	−0.0243688	+	0.0909456i
$339$	4.62927	−	8.01813i	0.251427	−	0.435485i
$340$		0			0
$341$	−15.7983	+	9.12117i	−0.855528	+	0.493939i
$342$	−1.25440	−	1.25440i	−0.0678301	−	0.0678301i
$343$	5.06626	−	17.8138i	0.273552	−	0.961857i
$344$			4.89791i			0.264078i
$345$		0			0
$346$	−7.50509	−	4.33306i	−0.403476	−	0.232947i
$347$	−9.02693	−	33.6890i	−0.484591	−	1.80852i	−0.581895	−	0.813264i	$-0.697689\pi$
$347$	−9.02693	−	33.6890i	−0.484591	−	1.80852i	0.0973042	−	0.995255i	$-0.468978\pi$
$348$	3.71522	+	0.995491i	0.199157	+	0.0533639i
$349$	1.49727			0.0801469			0.0400735	−	0.999197i	$-0.487241\pi$
$349$	1.49727			0.0801469			0.0400735	+	0.999197i	$0.487241\pi$
$350$		0			0
$351$	3.83810			0.204863
$352$	−1.70588	−	0.457089i	−0.0909237	−	0.0243629i
$353$	1.54431	+	5.76343i	0.0821951	+	0.306756i	0.994768	−	0.102157i	$-0.0325745\pi$
$353$	1.54431	+	5.76343i	0.0821951	+	0.306756i	−0.912573	+	0.408913i	$0.865908\pi$
$354$	−8.97859	−	5.18379i	−0.477207	−	0.275515i
$355$		0			0
$356$			1.11625i			0.0591614i
$357$	−0.541957	+	5.85109i	−0.0286834	+	0.309673i
$358$	9.44244	+	9.44244i	0.499049	+	0.499049i
$359$	−14.9989	+	8.65964i	−0.791613	+	0.457038i	−0.840530	−	0.541765i	$-0.817756\pi$
$359$	−14.9989	+	8.65964i	−0.791613	+	0.457038i	0.0489170	+	0.998803i	$0.484423\pi$
$360$		0			0
$361$	7.92648	−	13.7291i	0.417183	−	0.722583i
$362$	−2.26188	+	8.44144i	−0.118882	+	0.443672i
$363$	5.57274	−	5.57274i	0.292493	−	0.292493i
$364$	−9.52443	−	3.52167i	−0.499216	−	0.184586i
$365$		0			0
$366$	−3.39445	−	5.87936i	−0.177431	−	0.307319i
$367$	−5.29802	+	1.41960i	−0.276554	+	0.0741025i	−0.394430	−	0.918926i	$-0.629058\pi$
$367$	−5.29802	+	1.41960i	−0.276554	+	0.0741025i	0.117876	+	0.993028i	$0.462391\pi$
$368$	−3.90900	+	1.04741i	−0.203770	+	0.0546001i
$369$	5.94967	+	10.3051i	0.309727	+	0.536464i
$370$		0			0
$371$	−1.01880	−	0.376703i	−0.0528935	−	0.0195574i
$372$	−7.30401	+	7.30401i	−0.378695	+	0.378695i
$373$	−7.98224	+	29.7901i	−0.413305	+	1.54247i	0.374903	+	0.927064i	$0.377676\pi$
$373$	−7.98224	+	29.7901i	−0.413305	+	1.54247i	−0.788207	+	0.615410i	$0.788991\pi$
$374$	−1.96118	+	3.39686i	−0.101410	+	0.175648i
$375$		0			0
$376$	5.32419	−	3.07393i	0.274574	−	0.158526i
$377$	10.4386	+	10.4386i	0.537615	+	0.537615i
$378$	−0.244018	+	2.63447i	−0.0125509	+	0.135503i
$379$		−	12.9203i		−	0.663670i	−0.943337	−	0.331835i	$-0.892332\pi$
$379$		−	12.9203i		−	0.663670i	0.943337	−	0.331835i	$-0.107668\pi$
$380$		0			0
$381$	15.3637	+	8.87021i	0.787104	+	0.454435i
$382$	−2.81490	−	10.5053i	−0.144023	−	0.537500i
$383$	1.14948	+	0.308002i	0.0587356	+	0.0157382i	0.288067	−	0.957610i	$-0.406987\pi$
$383$	1.14948	+	0.308002i	0.0587356	+	0.0157382i	−0.229332	+	0.973348i	$0.573654\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−11.2012			−0.570126
$387$	4.73102	+	1.26767i	0.240491	+	0.0644394i
$388$	−2.65998	−	9.92718i	−0.135040	−	0.503976i
$389$	8.25213	+	4.76437i	0.418400	+	0.241563i	0.694392	−	0.719597i	$-0.255673\pi$
$389$	8.25213	+	4.76437i	0.418400	+	0.241563i	−0.275993	+	0.961160i	$0.589007\pi$
$390$		0			0
$391$			8.98802i			0.454544i
$392$	3.02282	−	6.31368i	0.152675	−	0.318889i
$393$	−0.678310	−	0.678310i	−0.0342162	−	0.0342162i
$394$	−12.7098	+	7.33801i	−0.640311	+	0.369684i
$395$		0			0
$396$	−0.883028	+	1.52945i	−0.0443738	+	0.0768578i
$397$	7.38494	−	27.5610i	0.370639	−	1.38324i	−0.488974	−	0.872299i	$-0.662629\pi$
$397$	7.38494	−	27.5610i	0.370639	−	1.38324i	0.859613	−	0.510946i	$-0.170705\pi$
$398$	−13.1260	+	13.1260i	−0.657949	+	0.657949i
$399$	4.62632	−	0.791463i	0.231606	−	0.0396227i
$400$		0			0
$401$	−19.6150	−	33.9741i	−0.979526	−	1.69659i	−0.664111	−	0.747634i	$-0.731190\pi$
$401$	−19.6150	−	33.9741i	−0.979526	−	1.69659i	−0.315415	−	0.948954i	$-0.602144\pi$
$402$	7.37834	−	1.97702i	0.367998	−	0.0986049i
$403$	−38.2945	+	10.2610i	−1.90758	+	0.511135i
$404$	9.17333	+	15.8887i	0.456390	+	0.790491i
$405$		0			0
$406$	−7.82873	+	6.50140i	−0.388533	+	0.322659i
$407$	−4.15670	+	4.15670i	−0.206040	+	0.206040i
$408$	−0.574830	+	2.14529i	−0.0284583	+	0.106208i
$409$	−4.32912	+	7.49826i	−0.214061	+	0.370765i	−0.952982	−	0.303028i	$-0.902003\pi$
$409$	−4.32912	+	7.49826i	−0.214061	+	0.370765i	0.738920	+	0.673793i	$0.235336\pi$
$410$		0			0
$411$	−9.65336	+	5.57337i	−0.476165	+	0.274914i
$412$	−6.44872	−	6.44872i	−0.317706	−	0.317706i
$413$	24.9188	−	11.4656i	1.22617	−	0.564187i
$414$			4.04689i			0.198894i
$415$		0			0
$416$	−3.32389	−	1.91905i	−0.162967	−	0.0940891i
$417$	−3.51206	−	13.1072i	−0.171986	−	0.641861i
$418$	3.02621	+	0.810871i	0.148017	+	0.0396610i
$419$	−4.29623			−0.209884			−0.104942	−	0.994478i	$-0.533466\pi$
$419$	−4.29623			−0.209884			−0.104942	+	0.994478i	$0.533466\pi$
$420$		0			0
$421$	−18.8346			−0.917945			−0.458972	−	0.888451i	$-0.651782\pi$
$421$	−18.8346			−0.917945			−0.458972	+	0.888451i	$0.651782\pi$
$422$	0.437693	+	0.117279i	0.0213066	+	0.00570907i
$423$	−1.59118	−	5.93837i	−0.0773659	−	0.288733i
$424$	−0.355547	−	0.205275i	−0.0172669	−	0.00996904i
$425$		0			0
$426$		−	10.7193i		−	0.519351i
$427$	17.8852	+	1.65662i	0.865525	+	0.0801693i
$428$	−10.4332	−	10.4332i	−0.504305	−	0.504305i
$429$	−5.87018	+	3.38915i	−0.283415	+	0.163630i
$430$		0			0
$431$	−3.46231	+	5.99690i	−0.166774	+	0.288860i	−0.937284	−	0.348567i	$-0.886668\pi$
$431$	−3.46231	+	5.99690i	−0.166774	+	0.288860i	0.770510	+	0.637428i	$0.220002\pi$
$432$	−0.258819	+	0.965926i	−0.0124524	+	0.0464731i
$433$	11.5154	−	11.5154i	0.553393	−	0.553393i	−0.374025	−	0.927419i	$-0.622023\pi$
$433$	11.5154	−	11.5154i	0.553393	−	0.553393i	0.927419	+	0.374025i	$0.122023\pi$
$434$	−4.60846	−	26.9377i	−0.221213	−	1.29305i
$435$		0			0
$436$	−10.0744	−	17.4494i	−0.482477	−	0.835675i
$437$	6.93451	−	1.85810i	0.331723	−	0.0888848i
$438$	10.2705	−	2.75198i	0.490745	−	0.131495i
$439$	−9.11194	−	15.7823i	−0.434889	−	0.753250i	0.562397	−	0.826867i	$-0.309879\pi$
$439$	−9.11194	−	15.7823i	−0.434889	−	0.753250i	−0.997287	+	0.0736169i	$0.976546\pi$
$440$		0			0
$441$	−5.31618	−	4.55392i	−0.253152	−	0.216853i
$442$	−6.02759	+	6.02759i	−0.286703	+	0.286703i
$443$	8.49765	−	31.7136i	0.403735	−	1.50676i	−0.402641	−	0.915358i	$-0.631908\pi$
$443$	8.49765	−	31.7136i	0.403735	−	1.50676i	0.806376	−	0.591403i	$-0.201426\pi$
$444$	−1.66429	+	2.88263i	−0.0789837	+	0.136804i
$445$		0			0
$446$	−5.72275	+	3.30403i	−0.270980	+	0.156450i
$447$	7.14079	+	7.14079i	0.337748	+	0.337748i
$448$	1.52856	−	2.15951i	0.0722178	−	0.102027i
$449$		−	8.14032i		−	0.384165i	−0.981379	−	0.192083i	$-0.938476\pi$
$449$		−	8.14032i		−	0.384165i	0.981379	−	0.192083i	$-0.0615242\pi$
$450$		0			0
$451$	−18.1994	−	10.5075i	−0.856978	−	0.494777i
$452$	2.39629	+	8.94306i	0.112712	+	0.420646i
$453$	−13.8223	−	3.70368i	−0.649430	−	0.174014i
$454$	−16.6075			−0.779430
$455$		0			0
$456$	1.77399			0.0830746
$457$	4.41041	+	1.18177i	0.206310	+	0.0552806i	0.360494	−	0.932762i	$-0.382608\pi$
$457$	4.41041	+	1.18177i	0.206310	+	0.0552806i	−0.154184	+	0.988042i	$0.549275\pi$
$458$	−3.50480	−	13.0801i	−0.163768	−	0.611192i
$459$	1.92342	+	1.11049i	0.0897774	+	0.0518330i
$460$		0			0
$461$			7.54894i			0.351589i	0.984427	+	0.175795i	$0.0562495\pi$
$461$			7.54894i			0.351589i	−0.984427	+	0.175795i	$0.943751\pi$
$462$	−1.95310	−	4.24477i	−0.0908665	−	0.197485i
$463$	8.87647	+	8.87647i	0.412525	+	0.412525i	0.882617	−	0.470092i	$-0.155779\pi$
$463$	8.87647	+	8.87647i	0.412525	+	0.412525i	−0.470092	+	0.882617i	$0.655779\pi$
$464$	−3.33098	+	1.92314i	−0.154637	+	0.0892796i
$465$		0			0
$466$	5.78914	−	10.0271i	0.268177	−	0.464495i
$467$	−2.97858	+	11.1162i	−0.137832	+	0.514397i	0.862138	+	0.506674i	$0.169125\pi$
$467$	−2.97858	+	11.1162i	−0.137832	+	0.514397i	−0.999970	+	0.00772331i	$0.997542\pi$
$468$	−2.71395	+	2.71395i	−0.125452	+	0.125452i
$469$	−7.00886	+	18.9556i	−0.323639	+	0.875290i
$470$		0			0
$471$	−4.79169	−	8.29945i	−0.220789	−	0.382418i
$472$	10.0143	−	2.68333i	0.460946	−	0.123510i
$473$	−8.35525	+	2.23878i	−0.384175	+	0.102939i
$474$	6.34546	+	10.9907i	0.291457	+	0.504817i
$475$		0			0
$476$	−3.75412	−	4.52057i	−0.172070	−	0.207200i
$477$	−0.290303	+	0.290303i	−0.0132921	+	0.0132921i
$478$	−4.40676	+	16.4462i	−0.201560	+	0.752233i
$479$	−6.17379	+	10.6933i	−0.282088	+	0.488590i	−0.971899	−	0.235399i	$-0.924360\pi$
$479$	−6.17379	+	10.6933i	−0.282088	+	0.488590i	0.689811	+	0.723989i	$0.257694\pi$
$480$		0			0
$481$	−11.0638	+	6.38770i	−0.504467	+	0.291254i
$482$	−13.3796	−	13.3796i	−0.609424	−	0.609424i
$483$	−8.73931	−	6.18593i	−0.397652	−	0.281469i
$484$			7.88104i			0.358229i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	4.03414	+	15.0556i	0.182804	+	0.682235i	0.995090	+	0.0989752i	$0.0315565\pi$
$487$	4.03414	+	15.0556i	0.182804	+	0.682235i	−0.812286	+	0.583260i	$0.801777\pi$
$488$	6.55758	+	1.75710i	0.296848	+	0.0795401i
$489$	11.8437			0.535589
$490$		0			0
$491$	−2.67474			−0.120709			−0.0603547	−	0.998177i	$-0.519223\pi$
$491$	−2.67474			−0.120709			−0.0603547	+	0.998177i	$0.519223\pi$
$492$	−11.4939	−	3.07978i	−0.518184	−	0.138847i
$493$	2.21096	+	8.25140i	0.0995764	+	0.371624i
$494$	5.89654	+	3.40437i	0.265298	+	0.153170i
$495$		0			0
$496$		−	10.3294i		−	0.463805i
$497$	23.1484	+	16.3851i	1.03835	+	0.734972i
$498$	−1.94227	−	1.94227i	−0.0870350	−	0.0870350i
$499$	15.7413	−	9.08825i	0.704678	−	0.406846i	−0.104410	−	0.994534i	$-0.533295\pi$
$499$	15.7413	−	9.08825i	0.704678	−	0.406846i	0.809087	+	0.587688i	$0.199962\pi$
$500$		0			0
$501$	4.92063	−	8.52279i	0.219838	−	0.380770i
$502$	−4.69827	+	17.5342i	−0.209694	+	0.782588i
$503$	−3.59630	+	3.59630i	−0.160351	+	0.160351i	−0.782722	−	0.622371i	$-0.786169\pi$
$503$	−3.59630	+	3.59630i	−0.160351	+	0.160351i	0.622371	+	0.782722i	$0.286169\pi$
$504$	−1.69031	−	2.03540i	−0.0752923	−	0.0906640i
$505$		0			0
$506$	−3.57352	−	6.18952i	−0.158862	−	0.275158i
$507$	−1.67202	+	0.448015i	−0.0742568	+	0.0198971i
$508$	−17.1359	+	4.59156i	−0.760284	+	0.203718i
$509$	−2.40629	−	4.16782i	−0.106657	−	0.184735i	0.807757	−	0.589516i	$-0.200681\pi$
$509$	−2.40629	−	4.16782i	−0.106657	−	0.184735i	−0.914414	+	0.404780i	$0.867348\pi$
$510$		0			0
$511$	−9.75621	+	26.3859i	−0.431589	+	1.16724i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.459142	−	1.71354i	0.0202716	−	0.0756547i
$514$	−12.0351	+	20.8454i	−0.530846	+	0.919452i
$515$		0			0
$516$	−4.24172	+	2.44896i	−0.186731	+	0.107809i
$517$	7.67738	+	7.67738i	0.337651	+	0.337651i
$518$	−3.68111	−	8.00034i	−0.161739	−	0.351515i
$519$		−	8.66613i		−	0.380401i
$520$		0			0
$521$	4.61481	+	2.66436i	0.202178	+	0.116728i	0.597671	−	0.801741i	$-0.296093\pi$
$521$	4.61481	+	2.66436i	0.202178	+	0.116728i	−0.395493	+	0.918469i	$0.629426\pi$
$522$	0.995491	+	3.71522i	0.0435714	+	0.162611i
$523$	−5.91757	−	1.58561i	−0.258757	−	0.0693338i	0.127108	−	0.991889i	$-0.459430\pi$
$523$	−5.91757	−	1.58561i	−0.258757	−	0.0693338i	−0.385866	+	0.922555i	$0.626097\pi$
$524$	0.959275			0.0419061
$525$		0			0
$526$	−14.0358			−0.611991
$527$	−22.1596	−	5.93766i	−0.965289	−	0.258648i
$528$	−0.457089	−	1.70588i	−0.0198923	−	0.0742389i
$529$	5.73541	+	3.31134i	0.249366	+	0.143971i
$530$		0			0
$531$		−	10.3676i		−	0.449915i
$532$	−2.71165	+	3.83095i	−0.117565	+	0.166093i
$533$	−32.2942	−	32.2942i	−1.39881	−	1.39881i
$534$	−0.966705	+	0.558127i	−0.0418334	+	0.0241525i
$535$		0			0
$536$	−3.81931	+	6.61524i	−0.164969	+	0.285735i
$537$	−3.45617	+	12.8986i	−0.149145	+	0.556617i
$538$	−18.7754	+	18.7754i	−0.809466	+	0.809466i
$539$	12.1521	+	2.27065i	0.523427	+	0.0978040i
$540$		0			0
$541$	6.81239	+	11.7994i	0.292887	+	0.507296i	0.974491	−	0.224426i	$-0.0720506\pi$
$541$	6.81239	+	11.7994i	0.292887	+	0.507296i	−0.681604	+	0.731721i	$0.738717\pi$
$542$	−11.5531	+	3.09564i	−0.496247	+	0.132969i
$543$	−8.44144	+	2.26188i	−0.362257	+	0.0970664i
$544$	−1.11049	−	1.92342i	−0.0476117	−	0.0824658i
$545$		0			0
$546$	−1.71236	−	10.0092i	−0.0732823	−	0.428356i
$547$	14.8290	−	14.8290i	0.634042	−	0.634042i	−0.315037	−	0.949079i	$-0.602017\pi$
$547$	14.8290	−	14.8290i	0.634042	−	0.634042i	0.949079	+	0.315037i	$0.102017\pi$
$548$	2.88499	−	10.7669i	0.123241	−	0.459940i
$549$	3.39445	−	5.87936i	0.144872	−	0.250925i
$550$		0			0
$551$	5.90911	−	3.41163i	0.251737	−	0.145340i
$552$	−2.86158	−	2.86158i	−0.121797	−	0.121797i
$553$	−33.4339	−	3.09681i	−1.42175	−	0.131690i
$554$		−	2.36165i		−	0.100337i
$555$		0			0
$556$	11.7516	+	6.78477i	0.498378	+	0.287738i
$557$	−0.0103825	−	0.0387479i	−0.000439920	−	0.00164180i	0.965706	−	0.259640i	$-0.0836039\pi$
$557$	−0.0103825	−	0.0387479i	−0.000439920	−	0.00164180i	−0.966145	+	0.257998i	$0.916937\pi$
$558$	−9.97746	−	2.67345i	−0.422379	−	0.113176i
$559$	−18.7987			−0.795099
$560$		0			0
$561$	−3.92236			−0.165602
$562$	10.6548	+	2.85494i	0.449445	+	0.120428i
$563$	−3.59929	−	13.4327i	−0.151692	−	0.566122i	−0.999366	−	0.0356047i	$-0.988664\pi$
$563$	−3.59929	−	13.4327i	−0.151692	−	0.566122i	0.847674	−	0.530518i	$-0.178002\pi$
$564$	5.32419	+	3.07393i	0.224189	+	0.129436i
$565$		0			0
$566$			23.4108i			0.984031i
$567$	−2.40353	+	1.10591i	−0.100939	+	0.0464439i
$568$	7.57968	+	7.57968i	0.318036	+	0.318036i
$569$	−17.1817	+	9.91984i	−0.720293	+	0.415861i	−0.814860	−	0.579657i	$-0.803186\pi$
$569$	−17.1817	+	9.91984i	−0.720293	+	0.415861i	0.0945677	+	0.995518i	$0.469853\pi$
$570$		0			0
$571$	2.94454	−	5.10010i	0.123225	−	0.213432i	−0.797813	−	0.602906i	$-0.794010\pi$
$571$	2.94454	−	5.10010i	0.123225	−	0.213432i	0.921038	+	0.389473i	$0.127343\pi$
$572$	1.75435	−	6.54733i	0.0733532	−	0.273758i
$573$	7.69044	−	7.69044i	0.321273	−	0.321273i
$574$	24.2199	−	20.1135i	1.01092	−	0.839523i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−14.4051	+	3.85984i	−0.599692	+	0.160687i	−0.545879	−	0.837864i	$-0.683804\pi$
$577$	−14.4051	+	3.85984i	−0.599692	+	0.160687i	−0.0538132	+	0.998551i	$0.517138\pi$
$578$	11.6561	−	3.12324i	0.484830	−	0.129910i
$579$	−5.60060	−	9.70052i	−0.232753	−	0.403140i
$580$		0			0
$581$	7.16322	−	1.22547i	0.297180	−	0.0508411i
$582$	7.26720	−	7.26720i	0.301235	−	0.301235i
$583$	0.187658	−	0.700349i	0.00777200	−	0.0290055i
$584$	−5.31641	+	9.20830i	−0.219995	+	0.381042i
$585$		0			0
$586$	18.9635	−	10.9486i	0.783376	−	0.452282i
$587$	−4.86057	−	4.86057i	−0.200617	−	0.200617i	0.599647	−	0.800264i	$-0.295308\pi$
$587$	−4.86057	−	4.86057i	−0.200617	−	0.200617i	−0.800264	+	0.599647i	$0.795308\pi$
$588$	6.97922	−	0.539001i	0.287818	−	0.0222280i
$589$			18.3243i			0.755039i
$590$		0			0
$591$	−12.7098	−	7.33801i	−0.522812	−	0.301846i
$592$	−0.861499	−	3.21516i	−0.0354074	−	0.132142i
$593$	20.4715	+	5.48532i	0.840664	+	0.225255i	0.653361	−	0.757047i	$-0.273359\pi$
$593$	20.4715	+	5.48532i	0.840664	+	0.225255i	0.187304	+	0.982302i	$0.440025\pi$
$594$	−1.76606			−0.0724622
$595$		0			0
$596$	−10.0986			−0.413655
$597$	−17.9305	−	4.80447i	−0.733847	−	0.196634i
$598$	−4.02007	−	15.0031i	−0.164393	−	0.613523i
$599$	−10.0409	−	5.79712i	−0.410260	−	0.236864i	0.280641	−	0.959813i	$-0.409453\pi$
$599$	−10.0409	−	5.79712i	−0.410260	−	0.236864i	−0.690902	+	0.722949i	$0.742786\pi$
$600$		0			0
$601$		−	15.3561i		−	0.626387i	−0.949689	−	0.313193i	$-0.898601\pi$
$601$		−	15.3561i		−	0.626387i	0.949689	−	0.313193i	$-0.101399\pi$
$602$	1.19518	−	12.9034i	0.0487119	−	0.525904i
$603$	5.40132	+	5.40132i	0.219959	+	0.219959i
$604$	12.3928	−	7.15497i	0.504254	−	0.291131i
$605$		0			0
$606$	−9.17333	+	15.8887i	−0.372641	+	0.645433i
$607$	−5.83734	+	21.7853i	−0.236931	+	0.884237i	0.740339	+	0.672234i	$0.234665\pi$
$607$	−5.83734	+	21.7853i	−0.236931	+	0.884237i	−0.977269	+	0.212003i	$0.932001\pi$
$608$	−1.25440	+	1.25440i	−0.0508726	+	0.0508726i
$609$	−9.54474	−	3.52918i	−0.386772	−	0.143009i
$610$		0			0
$611$	11.7980	+	20.4348i	0.477297	+	0.826703i
$612$	−2.14529	+	0.574830i	−0.0867183	+	0.0232361i
$613$	−4.62200	+	1.23846i	−0.186681	+	0.0500209i	−0.350948	−	0.936395i	$-0.614141\pi$
$613$	−4.62200	+	1.23846i	−0.186681	+	0.0500209i	0.164267	+	0.986416i	$0.447474\pi$
$614$	−1.50012	−	2.59828i	−0.0605399	−	0.104858i
$615$		0			0
$616$	4.38256	+	1.62046i	0.176578	+	0.0652900i
$617$	−17.3498	+	17.3498i	−0.698475	+	0.698475i	−0.964082	−	0.265606i	$-0.914428\pi$
$617$	−17.3498	+	17.3498i	−0.698475	+	0.698475i	0.265606	+	0.964082i	$0.414428\pi$
$618$	2.36040	−	8.80911i	0.0949490	−	0.354355i
$619$	−10.4801	+	18.1521i	−0.421232	+	0.729596i	−0.996060	−	0.0886786i	$-0.971736\pi$
$619$	−10.4801	+	18.1521i	−0.421232	+	0.729596i	0.574828	+	0.818274i	$0.305069\pi$
$620$		0			0
$621$	−3.50471	+	2.02344i	−0.140639	+	0.0811980i
$622$	−10.6211	−	10.6211i	−0.425868	−	0.425868i
$623$	0.272387	−	2.94074i	0.0109129	−	0.117818i
$624$		−	3.83810i		−	0.153647i
$625$		0			0
$626$	−11.5339	−	6.65911i	−0.460988	−	0.266152i
$627$	0.810871	+	3.02621i	0.0323831	+	0.120855i
$628$	9.25683	+	2.48036i	0.369388	+	0.0989772i
$629$	−7.39267			−0.294765
$630$		0			0
$631$	−48.7823			−1.94199			−0.970996	−	0.239095i	$-0.923149\pi$
$631$	−48.7823			−1.94199			−0.970996	+	0.239095i	$0.923149\pi$
$632$	−12.2585	−	3.28465i	−0.487616	−	0.130656i
$633$	0.117279	+	0.437693i	0.00466144	+	0.0173967i
$634$	−12.0392	−	6.95084i	−0.478138	−	0.276053i
$635$		0			0
$636$		−	0.410550i		−	0.0162794i
$637$	24.2325	+	11.6019i	0.960128	+	0.459683i
$638$	−4.80320	−	4.80320i	−0.190160	−	0.190160i
$639$	9.28317	−	5.35964i	0.367237	−	0.212024i
$640$		0			0
$641$	−6.03196	+	10.4477i	−0.238248	+	0.412658i	−0.960212	−	0.279273i	$-0.909906\pi$
$641$	−6.03196	+	10.4477i	−0.238248	+	0.412658i	0.721964	+	0.691931i	$0.243240\pi$
$642$	3.81880	−	14.2519i	0.150716	−	0.562480i
$643$	15.5935	−	15.5935i	0.614947	−	0.614947i	−0.329284	−	0.944231i	$-0.606807\pi$
$643$	15.5935	−	15.5935i	0.614947	−	0.614947i	0.944231	+	0.329284i	$0.106807\pi$
$644$	10.5537	−	1.80551i	0.415875	−	0.0711472i
$645$		0			0
$646$	1.96999	+	3.41212i	0.0775082	+	0.134248i
$647$	6.33226	−	1.69672i	0.248947	−	0.0667051i	−0.132188	−	0.991225i	$-0.542200\pi$
$647$	6.33226	−	1.69672i	0.248947	−	0.0667051i	0.381135	+	0.924520i	$0.375533\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	9.15487	+	15.8567i	0.359360	+	0.622430i
$650$		0			0
$651$	21.0245	−	17.4599i	0.824016	−	0.684308i
$652$	−8.37474	+	8.37474i	−0.327980	+	0.327980i
$653$	5.97625	−	22.3037i	0.233869	−	0.872811i	−0.744787	−	0.667303i	$-0.767449\pi$
$653$	5.97625	−	22.3037i	0.233869	−	0.872811i	0.978655	−	0.205508i	$-0.0658846\pi$
$654$	10.0744	−	17.4494i	0.393941	−	0.682326i
$655$		0			0
$656$	10.3051	−	5.94967i	0.402348	−	0.232296i
$657$	7.51854	+	7.51854i	0.293326	+	0.293326i
$658$	−14.7765	+	6.79898i	−0.576050	+	0.265052i
$659$		−	8.89429i		−	0.346472i	−0.984880	−	0.173236i	$-0.944578\pi$
$659$		−	8.89429i		−	0.346472i	0.984880	−	0.173236i	$-0.0554224\pi$
$660$		0			0
$661$	7.24046	+	4.18028i	0.281621	+	0.162594i	0.634157	−	0.773204i	$-0.281347\pi$
$661$	7.24046	+	4.18028i	0.281621	+	0.162594i	−0.352536	+	0.935798i	$0.614681\pi$
$662$	−4.82248	−	17.9977i	−0.187431	−	0.699501i
$663$	−8.23385	−	2.20625i	−0.319776	−	0.0856837i
$664$	2.74678			0.106596
$665$		0			0
$666$	−3.32858			−0.128980
$667$	−15.0351	−	4.02864i	−0.582161	−	0.155990i
$668$	2.54711	+	9.50594i	0.0985506	+	0.367796i
$669$	−5.72275	−	3.30403i	−0.221254	−	0.127741i
$670$		0			0
$671$			11.9896i			0.462853i
$672$	2.63447	+	0.244018i	0.101627	+	0.00941321i
$673$	11.1305	+	11.1305i	0.429048	+	0.429048i	0.888304	−	0.459256i	$-0.151884\pi$
$673$	11.1305	+	11.1305i	0.429048	+	0.429048i	−0.459256	+	0.888304i	$0.651884\pi$
$674$	11.8013	−	6.81346i	0.454567	−	0.262444i
$675$		0			0
$676$	0.865499	−	1.49909i	0.0332884	−	0.0576572i
$677$	−11.2360	+	41.9335i	−0.431836	+	1.61163i	0.316690	+	0.948529i	$0.397429\pi$
$677$	−11.2360	+	41.9335i	−0.431836	+	1.61163i	−0.748526	+	0.663106i	$0.769238\pi$
$678$	−6.54677	+	6.54677i	−0.251427	+	0.251427i
$679$	4.58524	+	26.8020i	0.175965	+	1.02857i
$680$		0			0
$681$	−8.30377	−	14.3825i	−0.318201	−	0.551140i
$682$	17.6208	−	4.72147i	0.674734	−	0.180794i
$683$	−17.2742	+	4.62860i	−0.660977	+	0.177108i	−0.573687	−	0.819075i	$-0.694487\pi$
$683$	−17.2742	+	4.62860i	−0.660977	+	0.177108i	−0.0872904	+	0.996183i	$0.527821\pi$
$684$	0.886994	+	1.53632i	0.0339151	+	0.0587426i
$685$		0			0
$686$	−9.50420	+	15.8956i	−0.362872	+	0.606897i
$687$	9.57528	−	9.57528i	0.365320	−	0.365320i
$688$	1.26767	−	4.73102i	0.0483296	−	0.180368i
$689$	0.787866	−	1.36462i	0.0300153	−	0.0519880i
$690$		0			0
$691$	30.5564	−	17.6417i	1.16242	−	0.671123i	0.210537	−	0.977586i	$-0.432479\pi$
$691$	30.5564	−	17.6417i	1.16242	−	0.671123i	0.951883	+	0.306463i	$0.0991456\pi$
$692$	6.12788	+	6.12788i	0.232947	+	0.232947i
$693$	2.69953	−	3.81382i	0.102547	−	0.144875i
$694$			34.8774i			1.32393i
$695$		0			0
$696$	−3.33098	−	1.92314i	−0.126260	−	0.0728964i
$697$	−6.84009	−	25.5276i	−0.259087	−	0.966926i
$698$	−1.44625	−	0.387522i	−0.0547414	−	0.0146679i
$699$	11.5783			0.437930
$700$		0			0
$701$	−14.9862			−0.566020			−0.283010	−	0.959117i	$-0.591333\pi$
$701$	−14.9862			−0.566020			−0.283010	+	0.959117i	$0.591333\pi$
$702$	−3.70732	−	0.993373i	−0.139924	−	0.0374924i
$703$	1.52829	+	5.70366i	0.0576405	+	0.215117i
$704$	1.52945	+	0.883028i	0.0576433	+	0.0332804i
$705$		0			0
$706$		−	5.96674i		−	0.224561i
$707$	−20.2898	−	44.0968i	−0.763075	−	1.65843i
$708$	7.33099	+	7.33099i	0.275515	+	0.275515i
$709$	−7.19605	+	4.15464i	−0.270253	+	0.156031i	−0.629003	−	0.777403i	$-0.716537\pi$
$709$	−7.19605	+	4.15464i	−0.270253	+	0.156031i	0.358750	+	0.933434i	$0.383203\pi$
$710$		0			0
$711$	−6.34546	+	10.9907i	−0.237973	+	0.412182i
$712$	0.288908	−	1.07822i	0.0108273	−	0.0404080i
$713$	29.5585	−	29.5585i	1.10697	−	1.10697i
$714$	2.03786	−	5.51145i	0.0762652	−	0.206261i
$715$		0			0
$716$	−6.67682	−	11.5646i	−0.249524	−	0.432189i
$717$	−16.4462	+	4.40676i	−0.614196	+	0.164573i
$718$	16.7291	−	4.48256i	0.624326	−	0.167288i
$719$	−7.07678	−	12.2574i	−0.263920	−	0.457122i	0.703360	−	0.710833i	$-0.251682\pi$
$719$	−7.07678	−	12.2574i	−0.263920	−	0.457122i	−0.967280	+	0.253711i	$0.918349\pi$
$720$		0			0
$721$	15.4154	+	18.5626i	0.574099	+	0.691307i
$722$	−11.2097	+	11.2097i	−0.417183	+	0.417183i
$723$	4.89728	−	18.2769i	0.182132	−	0.679725i
$724$	4.36961	−	7.56839i	0.162395	−	0.281277i
$725$		0			0
$726$	−6.82518	+	3.94052i	−0.253306	+	0.146246i
$727$	19.9622	+	19.9622i	0.740357	+	0.740357i	0.972647	−	0.232290i	$-0.0746217\pi$
$727$	19.9622	+	19.9622i	0.740357	+	0.740357i	−0.232290	+	0.972647i	$0.574622\pi$
$728$	8.28842	+	5.86678i	0.307189	+	0.217437i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−9.42073	−	5.43906i	−0.348438	−	0.201171i
$732$	1.75710	+	6.55758i	0.0649442	+	0.242375i
$733$	44.8290	+	12.0119i	1.65580	+	0.443670i	0.961228	−	0.275755i	$-0.0889279\pi$
$733$	44.8290	+	12.0119i	1.65580	+	0.443670i	0.694570	+	0.719425i	$0.255595\pi$
$734$	5.48491			0.202452
$735$		0			0
$736$	4.04689			0.149170
$737$	−13.0306	−	3.49153i	−0.479987	−	0.128612i
$738$	−3.07978	−	11.4939i	−0.113368	−	0.423095i
$739$	−15.1424	−	8.74246i	−0.557022	−	0.321597i	0.194927	−	0.980818i	$-0.437553\pi$
$739$	−15.1424	−	8.74246i	−0.557022	−	0.321597i	−0.751949	+	0.659221i	$0.770886\pi$
$740$		0			0
$741$			6.80874i			0.250125i
$742$	0.886588	+	0.627552i	0.0325477	+	0.0230382i
$743$	12.2427	+	12.2427i	0.449143	+	0.449143i	0.895069	−	0.445927i	$-0.147126\pi$
$743$	12.2427	+	12.2427i	0.449143	+	0.449143i	−0.445927	+	0.895069i	$0.647126\pi$
$744$	8.94554	−	5.16471i	0.327960	−	0.189348i
$745$		0			0
$746$	15.4205	−	26.7091i	0.564585	−	0.977889i
$747$	0.710918	−	2.65318i	0.0260111	−	0.0970749i
$748$	2.77353	−	2.77353i	0.101410	−	0.101410i
$749$	24.9400	+	30.0317i	0.911287	+	1.09734i
$750$		0			0
$751$	12.4732	+	21.6042i	0.455154	+	0.788350i	0.998697	−	0.0510312i	$-0.0162508\pi$
$751$	12.4732	+	21.6042i	0.455154	+	0.788350i	−0.543543	+	0.839381i	$0.682917\pi$
$752$	−5.93837	+	1.59118i	−0.216550	+	0.0580244i
$753$	−17.5342	+	4.69827i	−0.638981	+	0.171214i
$754$	−7.38120	−	12.7846i	−0.268808	−	0.465588i
$755$		0			0
$756$	0.917556	−	2.48155i	0.0333712	−	0.0902531i
$757$	32.4637	−	32.4637i	1.17991	−	1.17991i	0.200149	−	0.979765i	$-0.435857\pi$
$757$	32.4637	−	32.4637i	1.17991	−	1.17991i	0.979765	−	0.200149i	$-0.0641427\pi$
$758$	−3.34401	+	12.4800i	−0.121460	+	0.453295i
$759$	3.57352	−	6.18952i	0.129711	−	0.224665i
$760$		0			0
$761$	28.5750	−	16.4978i	1.03584	−	0.598045i	0.117191	−	0.993109i	$-0.462611\pi$
$761$	28.5750	−	16.4978i	1.03584	−	0.598045i	0.918653	+	0.395065i	$0.129278\pi$
$762$	−12.5444	−	12.5444i	−0.454435	−	0.454435i
$763$	22.2828	+	48.4284i	0.806693	+	1.75322i
$764$			10.8759i			0.393477i
$765$		0			0
$766$	−1.03059	−	0.595014i	−0.0372369	−	0.0214987i
$767$	10.2989	+	38.4359i	0.371871	+	1.38784i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	−10.0980			−0.364144			−0.182072	−	0.983285i	$-0.558280\pi$
$769$	−10.0980			−0.364144			−0.182072	+	0.983285i	$0.558280\pi$
$770$		0			0
$771$	−24.0702			−0.866867
$772$	10.8195	+	2.89908i	0.389403	+	0.104340i
$773$	3.06094	+	11.4236i	0.110094	+	0.410878i	0.998873	−	0.0474585i	$-0.0151122\pi$
$773$	3.06094	+	11.4236i	0.110094	+	0.410878i	−0.888779	+	0.458336i	$0.848446\pi$
$774$	−4.24172	−	2.44896i	−0.152465	−	0.0880259i
$775$		0			0
$776$			10.2774i			0.368936i
$777$	5.08794	−	7.18811i	0.182529	−	0.257872i
$778$	−6.73784	−	6.73784i	−0.241563	−	0.241563i
$779$	−18.2812	+	10.5546i	−0.654991	+	0.378159i
$780$		0			0
$781$	−9.46543	+	16.3946i	−0.338700	+	0.586645i
$782$	2.32627	−	8.68176i	0.0831873	−	0.310459i
$783$	−2.71973	+	2.71973i	−0.0971953	+	0.0971953i
$784$	−4.55392	+	5.31618i	−0.162640	+	0.189864i
$785$		0			0
$786$	0.479637	+	0.830756i	0.0171081	+	0.0296321i
$787$	8.47179	−	2.27001i	0.301987	−	0.0809171i	−0.104644	−	0.994510i	$-0.533370\pi$
$787$	8.47179	−	2.27001i	0.301987	−	0.0809171i	0.406631	+	0.913593i	$0.366704\pi$
$788$	14.1760	−	3.79843i	0.504997	−	0.135314i
$789$	−7.01791	−	12.1554i	−0.249844	−	0.432743i
$790$		0			0
$791$	−4.13068	−	24.1450i	−0.146870	−	0.858497i
$792$	1.24879	−	1.24879i	0.0443738	−	0.0443738i
$793$	−6.74391	+	25.1686i	−0.239483	+	0.893764i
$794$	−14.2666	+	24.7105i	−0.506303	+	0.876942i
$795$		0			0
$796$	16.0761	−	9.28152i	0.569801	−	0.328975i
$797$	−26.4972	−	26.4972i	−0.938580	−	0.938580i	0.0596400	−	0.998220i	$-0.481005\pi$
$797$	−26.4972	−	26.4972i	−0.938580	−	0.938580i	−0.998220	+	0.0596400i	$0.981005\pi$
$798$	−4.67353	−	0.432886i	−0.165441	−	0.0153240i
$799$			13.6542i			0.483051i
$800$		0			0
$801$	−0.966705	−	0.558127i	−0.0341568	−	0.0197205i
$802$	10.1535	+	37.8932i	0.358531	+	1.33806i
$803$	−18.1383	−	4.86015i	−0.640088	−	0.171511i
$804$	−7.63862			−0.269394
$805$		0			0
$806$	39.6453			1.39645
$807$	−25.6477	−	6.87229i	−0.902842	−	0.241916i
$808$	−4.74846	−	17.7215i	−0.167050	−	0.623441i
$809$	34.0232	+	19.6433i	1.19619	+	0.690622i	0.959704	−	0.281012i	$-0.0906701\pi$
$809$	34.0232	+	19.6433i	1.19619	+	0.690622i	0.236489	+	0.971634i	$0.424003\pi$
$810$		0			0
$811$		−	9.61165i		−	0.337511i	−0.985658	−	0.168755i	$-0.946025\pi$
$811$		−	9.61165i		−	0.337511i	0.985658	−	0.168755i	$-0.0539748\pi$
$812$	9.24465	−	4.25364i	0.324424	−	0.149274i
$813$	−8.45744	−	8.45744i	−0.296615	−	0.296615i
$814$	5.09089	−	2.93923i	0.178436	−	0.103020i
$815$		0			0
$816$	1.11049	−	1.92342i	0.0388748	−	0.0673331i
$817$	−2.24884	+	8.39277i	−0.0786769	+	0.293626i
$818$	6.12230	−	6.12230i	0.214061	−	0.214061i
$819$	7.81207	−	6.48757i	0.272976	−	0.226694i
$820$		0			0
$821$	−25.9357	−	44.9219i	−0.905162	−	1.56779i	−0.820700	−	0.571359i	$-0.806416\pi$
$821$	−25.9357	−	44.9219i	−0.905162	−	1.56779i	−0.0844618	−	0.996427i	$-0.526917\pi$
$822$	10.7669	−	2.88499i	0.375540	−	0.100626i
$823$	10.0490	−	2.69263i	0.350287	−	0.0938592i	−0.0793852	−	0.996844i	$-0.525296\pi$
$823$	10.0490	−	2.69263i	0.350287	−	0.0938592i	0.429672	+	0.902985i	$0.358629\pi$
$824$	4.55993	+	7.89804i	0.158853	+	0.275141i
$825$		0			0
$826$	−27.0372	+	4.62548i	−0.940746	+	0.160941i
$827$	−7.55951	+	7.55951i	−0.262870	+	0.262870i	−0.826219	−	0.563349i	$-0.809513\pi$
$827$	−7.55951	+	7.55951i	−0.262870	+	0.262870i	0.563349	+	0.826219i	$0.309513\pi$
$828$	1.04741	−	3.90900i	0.0364001	−	0.135847i
$829$	−16.1525	+	27.9770i	−0.561001	+	0.971682i	0.436409	+	0.899748i	$0.356250\pi$
$829$	−16.1525	+	27.9770i	−0.561001	+	0.971682i	−0.997409	+	0.0719331i	$0.977083\pi$
$830$		0			0
$831$	2.04525	−	1.18083i	0.0709490	−	0.0409624i
$832$	2.71395	+	2.71395i	0.0940891	+	0.0940891i
$833$	8.78704	+	12.8254i	0.304453	+	0.444374i
$834$			13.5695i			0.469875i
$835$		0			0
$836$	−2.71323	−	1.56648i	−0.0938389	−	0.0541779i
$837$	−2.67345	−	9.97746i	−0.0924080	−	0.344871i
$838$	4.14984	+	1.11195i	0.143354	+	0.0384115i
$839$	24.7218			0.853490			0.426745	−	0.904372i	$-0.359660\pi$
$839$	24.7218			0.853490			0.426745	+	0.904372i	$0.359660\pi$
$840$		0			0
$841$	14.2061			0.489866
$842$	18.1929	+	4.87477i	0.626968	+	0.167996i
$843$	2.85494	+	10.6548i	0.0983294	+	0.366970i
$844$	−0.392425	−	0.226566i	−0.0135078	−	0.00779874i
$845$		0			0
$846$			6.14785i			0.211367i
$847$	1.92312	−	20.7624i	0.0660791	−	0.713405i
$848$	0.290303	+	0.290303i	0.00996904	+	0.00996904i
$849$	−20.2744	+	11.7054i	−0.695815	+	0.401729i
$850$		0			0
$851$	6.73519	−	11.6657i	0.230879	−	0.399895i
$852$	−2.77435	+	10.3540i	−0.0950478	+	0.354723i
$853$	−28.0435	+	28.0435i	−0.960191	+	0.960191i	−0.999237	−	0.0390463i	$-0.987568\pi$
$853$	−28.0435	+	28.0435i	−0.960191	+	0.960191i	0.0390463	+	0.999237i	$0.487568\pi$
$854$	−16.8470	−	6.22920i	−0.576493	−	0.213159i
$855$		0			0
$856$	7.37735	+	12.7779i	0.252153	+	0.436741i
$857$	45.9579	−	12.3144i	1.56989	−	0.420652i	0.634115	−	0.773239i	$-0.281365\pi$
$857$	45.9579	−	12.3144i	1.56989	−	0.420652i	0.935779	+	0.352587i	$0.114698\pi$
$858$	6.54733	−	1.75435i	0.223522	−	0.0598926i
$859$	−26.8560	−	46.5160i	−0.916315	−	1.58710i	−0.804964	−	0.593324i	$-0.797815\pi$
$859$	−26.8560	−	46.5160i	−0.916315	−	1.58710i	−0.111351	−	0.993781i	$-0.535518\pi$
$860$		0			0
$861$	29.5288	+	10.9183i	1.00634	+	0.372095i
$862$	4.89645	−	4.89645i	0.166774	−	0.166774i
$863$	−10.3466	+	38.6139i	−0.352201	+	1.31443i	0.531768	+	0.846890i	$0.321528\pi$
$863$	−10.3466	+	38.6139i	−0.352201	+	1.31443i	−0.883970	+	0.467544i	$0.845139\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−14.1034	+	8.14260i	−0.479253	+	0.276697i
$867$	8.53286	+	8.53286i	0.289791	+	0.289791i
$868$	−2.52057	+	27.2126i	−0.0855536	+	0.923656i
$869$		−	22.4129i		−	0.760305i
$870$		0			0
$871$	−25.3900	−	14.6589i	−0.860306	−	0.496698i
$872$	5.21491	+	19.4623i	0.176599	+	0.659076i
$873$	9.92718	+	2.65998i	0.335984	+	0.0900267i
$874$	−7.17914			−0.242838
$875$		0			0
$876$	−10.6328			−0.359250
$877$	−7.34780	−	1.96884i	−0.248118	−	0.0664829i	0.132617	−	0.991167i	$-0.457662\pi$
$877$	−7.34780	−	1.96884i	−0.248118	−	0.0664829i	−0.380734	+	0.924685i	$0.624329\pi$
$878$	4.71669	+	17.6029i	0.159180	+	0.594070i
$879$	18.9635	+	10.9486i	0.639624	+	0.369287i
$880$		0			0
$881$			37.1659i			1.25215i	0.779763	+	0.626075i	$0.215340\pi$
$881$			37.1659i			1.25215i	−0.779763	+	0.626075i	$0.784660\pi$
$882$	3.95640	+	5.77468i	0.133219	+	0.194444i
$883$	−25.7803	−	25.7803i	−0.867577	−	0.867577i	0.124627	−	0.992204i	$-0.460227\pi$
$883$	−25.7803	−	25.7803i	−0.867577	−	0.867577i	−0.992204	+	0.124627i	$0.960227\pi$
$884$	7.38226	−	4.26215i	0.248292	−	0.143352i
$885$		0			0
$886$	−16.4162	+	28.4337i	−0.551513	+	0.955248i
$887$	3.85864	−	14.4006i	0.129560	−	0.483526i	−0.870401	−	0.492344i	$-0.836140\pi$
$887$	3.85864	−	14.4006i	0.129560	−	0.483526i	0.999961	+	0.00881809i	$0.00280692\pi$
$888$	2.35366	−	2.35366i	0.0789837	−	0.0789837i
$889$	46.2646	−	7.91487i	1.55167	−	0.265456i
$890$		0			0
$891$	−0.883028	−	1.52945i	−0.0295826	−	0.0512385i
$892$	6.38289	−	1.71029i	0.213715	−	0.0572648i
$893$	10.5346	−	2.82274i	0.352527	−	0.0944593i
$894$	−5.04930	−	8.74565i	−0.168874	−	0.292498i
$895$		0			0
$896$	−2.03540	+	1.69031i	−0.0679980	+	0.0564692i
$897$	10.9830	−	10.9830i	0.366713	−	0.366713i
$898$	−2.10687	+	7.86295i	−0.0703072	+	0.262390i
$899$	19.8649	−	34.4071i	0.662533	−	1.14754i
$900$		0			0
$901$	0.789659	−	0.455910i	0.0263074	−	0.0151886i
$902$	14.8598	+	14.8598i	0.494777	+	0.494777i
$903$	11.7723	−	5.41666i	0.391757	−	0.180255i
$904$		−	9.25854i		−	0.307934i
$905$		0			0
$906$	12.3928	+	7.15497i	0.411722	+	0.237708i
$907$	−5.56795	−	20.7799i	−0.184881	−	0.689984i	−0.994656	−	0.103244i	$-0.967078\pi$
$907$	−5.56795	−	20.7799i	−0.184881	−	0.689984i	0.809775	−	0.586740i	$-0.199589\pi$
$908$	16.0416	+	4.29835i	0.532361	+	0.142646i
$909$	−18.3467			−0.608520
$910$		0			0
$911$	23.6120			0.782301			0.391151	−	0.920327i	$-0.372077\pi$
$911$	23.6120			0.782301			0.391151	+	0.920327i	$0.372077\pi$
$912$	−1.71354	−	0.459142i	−0.0567410	−	0.0152037i
$913$	1.25552	+	4.68567i	0.0415517	+	0.155073i
$914$	−3.95426	−	2.28300i	−0.130795	−	0.0755148i
$915$		0			0
$916$			13.5415i			0.447423i
$917$	−2.52719	−	0.234081i	−0.0834550	−	0.00773002i
$918$	−1.57046	−	1.57046i	−0.0518330	−	0.0518330i
$919$	38.2901	−	22.1068i	1.26307	−	0.729236i	0.289406	−	0.957207i	$-0.406542\pi$
$919$	38.2901	−	22.1068i	1.26307	−	0.729236i	0.973668	+	0.227971i	$0.0732090\pi$
$920$		0			0
$921$	1.50012	−	2.59828i	0.0494306	−	0.0856163i
$922$	1.95381	−	7.29172i	0.0643453	−	0.240140i
$923$	−29.0915	+	29.0915i	−0.957560	+	0.957560i
$924$	0.787924	+	4.60563i	0.0259208	+	0.151514i
$925$		0			0
$926$	−6.27661	−	10.8714i	−0.206262	−	0.357257i
$927$	8.80911	−	2.36040i	0.289329	−	0.0775255i
$928$	3.71522	−	0.995491i	0.121958	−	0.0326786i
$929$	0.388224	+	0.672424i	0.0127372	+	0.0220615i	0.872324	−	0.488929i	$-0.162612\pi$
$929$	0.388224	+	0.672424i	0.0127372	+	0.0220615i	−0.859587	+	0.510990i	$0.829279\pi$
$930$		0			0
$931$	8.07860	−	9.43085i	0.264766	−	0.309084i
$932$	−8.18707	+	8.18707i	−0.268177	+	0.268177i
$933$	3.88760	−	14.5087i	0.127274	−	0.474995i
$934$	5.75418	−	9.96652i	0.188282	−	0.326115i
$935$		0			0
$936$	3.32389	−	1.91905i	0.108645	−	0.0627261i
$937$	0.494892	+	0.494892i	0.0161674	+	0.0161674i	0.715144	−	0.698977i	$-0.246361\pi$
$937$	0.494892	+	0.494892i	0.0161674	+	0.0161674i	−0.698977	+	0.715144i	$0.746361\pi$
$938$	11.6761	−	16.4957i	0.381239	−	0.538604i
$939$		−	13.3182i		−	0.434624i
$940$		0			0
$941$	15.9777	+	9.22471i	0.520857	+	0.300717i	0.737285	−	0.675582i	$-0.236107\pi$
$941$	15.9777	+	9.22471i	0.520857	+	0.300717i	−0.216428	+	0.976299i	$0.569441\pi$
$942$	2.48036	+	9.25683i	0.0808145	+	0.301604i
$943$	46.5145	+	12.4635i	1.51472	+	0.405868i
$944$	−10.3676			−0.337436
$945$		0			0
$946$	8.64999			0.281235
$947$	−9.98459	−	2.67536i	−0.324456	−	0.0869376i	0.0929149	−	0.995674i	$-0.470382\pi$
$947$	−9.98459	−	2.67536i	−0.324456	−	0.0869376i	−0.417370	+	0.908736i	$0.637048\pi$
$948$	−3.28465	−	12.2585i	−0.106680	−	0.398137i
$949$	−35.3424	−	20.4049i	−1.14726	−	0.662372i
$950$		0			0
$951$		−	13.9017i		−	0.450793i
$952$	2.45620	+	5.33817i	0.0796058	+	0.173011i
$953$	−11.1833	−	11.1833i	−0.362263	−	0.362263i	0.502383	−	0.864645i	$-0.332457\pi$
$953$	−11.1833	−	11.1833i	−0.362263	−	0.362263i	−0.864645	+	0.502383i	$0.832457\pi$
$954$	0.355547	−	0.205275i	0.0115113	−	0.00664603i
$955$		0			0
$956$	8.51320	−	14.7453i	0.275336	−	0.476897i
$957$	1.75809	−	6.56129i	0.0568311	−	0.212096i
$958$	8.73106	−	8.73106i	0.282088	−	0.282088i
$959$	−10.2278	+	27.6612i	−0.330271	+	0.893227i
$960$		0			0
$961$	37.8485	+	65.5555i	1.22092	+	2.11469i
$962$	12.3401	−	3.30652i	0.397861	−	0.106606i
$963$	14.2519	−	3.81880i	0.459263	−	0.123059i
$964$	9.46081	+	16.3866i	0.304712	+	0.527777i
$965$		0			0
$966$	6.84049	+	8.23705i	0.220089	+	0.265023i
$967$	3.47333	−	3.47333i	0.111695	−	0.111695i	−0.649051	−	0.760745i	$-0.724834\pi$
$967$	3.47333	−	3.47333i	0.111695	−	0.111695i	0.760745	+	0.649051i	$0.224834\pi$
$968$	2.03976	−	7.61250i	0.0655605	−	0.244675i
$969$	−1.96999	+	3.41212i	−0.0632851	+	0.109613i
$970$		0			0
$971$	31.5326	−	18.2054i	1.01193	−	0.584238i	0.100174	−	0.994970i	$-0.468060\pi$
$971$	31.5326	−	18.2054i	1.01193	−	0.584238i	0.911756	+	0.410732i	$0.134727\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−29.3036	−	20.7419i	−0.939430	−	0.664955i
$974$		−	15.5867i		−	0.499431i
$975$		0			0
$976$	−5.87936	−	3.39445i	−0.188194	−	0.108654i
$977$	6.24191	+	23.2951i	0.199697	+	0.745278i	0.991001	+	0.133855i	$0.0427357\pi$
$977$	6.24191	+	23.2951i	0.199697	+	0.745278i	−0.791304	+	0.611422i	$0.790598\pi$
$978$	−11.4401	−	3.06537i	−0.365814	−	0.0980196i
$979$	1.97137			0.0630052
$980$		0			0
$981$	20.1488			0.643303
$982$	2.58360	+	0.692274i	0.0824460	+	0.0220913i
$983$	6.62151	+	24.7118i	0.211193	+	0.788184i	0.987472	+	0.157794i	$0.0504382\pi$
$983$	6.62151	+	24.7118i	0.211193	+	0.788184i	−0.776279	+	0.630390i	$0.782895\pi$
$984$	10.3051	+	5.94967i	0.328516	+	0.189669i
$985$		0			0
$986$		−	8.54248i		−	0.272048i
$987$	−13.2764	−	9.39738i	−0.422591	−	0.299122i
$988$	−4.81451	−	4.81451i	−0.153170	−	0.153170i
$989$	17.1658	−	9.91066i	0.545839	−	0.315141i
$990$		0			0
$991$	−13.1174	+	22.7201i	−0.416689	+	0.721726i	−0.995604	−	0.0936614i	$-0.970143\pi$
$991$	−13.1174	+	22.7201i	−0.416689	+	0.721726i	0.578915	+	0.815388i	$0.303476\pi$
$992$	−2.67345	+	9.97746i	−0.0848822	+	0.316785i
$993$	13.1752	−	13.1752i	0.418104	−	0.418104i
$994$	−18.1189	−	21.8180i	−0.574696	−	0.692026i
$995$		0			0
$996$	1.37339	+	2.37878i	0.0435175	+	0.0753745i
$997$	−36.0450	+	9.65822i	−1.14156	+	0.305879i	−0.779577	−	0.626307i	$-0.784566\pi$
$997$	−36.0450	+	9.65822i	−1.14156	+	0.305879i	−0.361980	+	0.932186i	$0.617899\pi$
$998$	−17.5571	+	4.70442i	−0.555762	+	0.148916i
$999$	−1.66429	−	2.88263i	−0.0526558	−	0.0912025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.h.493.1		16
5.2	odd	4		1050.2.bc.g.157.4		16
5.3	odd	4		210.2.u.b.157.2	yes	16
5.4	even	2		210.2.u.a.73.3	✓	16
7.5	odd	6		1050.2.bc.g.943.4		16
15.8	even	4		630.2.bv.b.577.3		16
15.14	odd	2		630.2.bv.a.73.2		16
35.3	even	12		1470.2.m.d.97.3		16
35.4	even	6		1470.2.m.d.1273.3		16
35.12	even	12	inner	1050.2.bc.h.607.1		16
35.18	odd	12		1470.2.m.e.97.2		16
35.19	odd	6		210.2.u.b.103.2	yes	16
35.24	odd	6		1470.2.m.e.1273.2		16
35.33	even	12		210.2.u.a.187.3	yes	16
105.68	odd	12		630.2.bv.a.397.2		16
105.89	even	6		630.2.bv.b.523.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	5.4	even	2
210.2.u.a.187.3	yes	16	35.33	even	12
210.2.u.b.103.2	yes	16	35.19	odd	6
210.2.u.b.157.2	yes	16	5.3	odd	4
630.2.bv.a.73.2		16	15.14	odd	2
630.2.bv.a.397.2		16	105.68	odd	12
630.2.bv.b.523.3		16	105.89	even	6
630.2.bv.b.577.3		16	15.8	even	4
1050.2.bc.g.157.4		16	5.2	odd	4
1050.2.bc.g.943.4		16	7.5	odd	6
1050.2.bc.h.493.1		16	1.1	even	1	trivial
1050.2.bc.h.607.1		16	35.12	even	12	inner
1470.2.m.d.97.3		16	35.3	even	12
1470.2.m.d.1273.3		16	35.4	even	6
1470.2.m.e.97.2		16	35.18	odd	12
1470.2.m.e.1273.2		16	35.24	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.15951 - 1.52856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.15951 - 1.52856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.883028 - 1.52945i) q^{11} +(0.258819 - 0.965926i) q^{12} +(2.71395 - 2.71395i) q^{13} +(1.69031 + 2.03540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.14529 - 0.574830i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.886994 - 1.53632i) q^{19} +(-0.917556 + 2.48155i) q^{21} +(-1.24879 + 1.24879i) q^{22} +(-1.04741 + 3.90900i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.32389 + 1.91905i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.10591 - 2.40353i) q^{28} +3.84628i q^{29} +(-8.94554 - 5.16471i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.70588 - 0.457089i) q^{33} -2.22097 q^{34} -1.00000 q^{36} +(-3.21516 - 0.861499i) q^{37} +(0.459142 + 1.71354i) q^{38} +(-3.32389 - 1.91905i) q^{39} -11.8993i q^{41} +(1.52856 - 2.15951i) q^{42} +(-3.46335 - 3.46335i) q^{43} +(1.52945 - 0.883028i) q^{44} +(2.02344 - 3.50471i) q^{46} +(-1.59118 + 5.93837i) q^{47} +(0.707107 - 0.707107i) q^{48} +(2.32699 + 6.60190i) q^{49} +(-1.11049 - 1.92342i) q^{51} +(3.70732 - 0.993373i) q^{52} +(0.396561 - 0.106258i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.446149 + 2.60786i) q^{56} +(-1.25440 + 1.25440i) q^{57} +(0.995491 - 3.71522i) q^{58} +(-5.18379 + 8.97859i) q^{59} +(-5.87936 + 3.39445i) q^{61} +(7.30401 + 7.30401i) q^{62} +(2.63447 + 0.244018i) q^{63} +1.00000i q^{64} +(1.52945 + 0.883028i) q^{66} +(-1.97702 - 7.37834i) q^{67} +(2.14529 + 0.574830i) q^{68} +4.04689 q^{69} -10.7193 q^{71} +(0.965926 + 0.258819i) q^{72} +(-2.75198 - 10.2705i) q^{73} +(2.88263 + 1.66429i) q^{74} -1.77399i q^{76} +(-4.24477 + 1.95310i) q^{77} +(2.71395 + 2.71395i) q^{78} +(10.9907 - 6.34546i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-3.07978 + 11.4939i) q^{82} +(-1.94227 + 1.94227i) q^{83} +(-2.03540 + 1.69031i) q^{84} +(2.44896 + 4.24172i) q^{86} +(3.71522 - 0.995491i) q^{87} +(-1.70588 + 0.457089i) q^{88} +(0.558127 + 0.966705i) q^{89} +(-10.0092 + 1.71236i) q^{91} +(-2.86158 + 2.86158i) q^{92} +(-2.67345 + 9.97746i) q^{93} +(3.07393 - 5.32419i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-7.26720 - 7.26720i) q^{97} +(-0.539001 - 6.97922i) q^{98} +1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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