LMFDB - Embedded newform 1050.2.bc.h.607.1

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			607.1
Root			$0.792206 + 1.03242i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.h.493.1

$q$-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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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	0.967889	−	0.251380i	$-0.0808843\pi$
$11$	0.883028	+	1.52945i	0.266243	+	0.461147i	−0.701645	+	0.712526i	$0.747551\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	2.71395	+	2.71395i	0.752713	+	0.752713i	0.974985	−	0.222272i	$-0.0713472\pi$
$13$	2.71395	+	2.71395i	0.752713	+	0.752713i	−0.222272	+	0.974985i	$0.571347\pi$
$14$	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	0.509410	−	0.860524i	$-0.329864\pi$
$17$	2.14529	+	0.574830i	0.520310	+	0.139417i	0.0109000	+	0.999941i	$0.496530\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	−0.886994	+	1.53632i	−0.203490	+	0.352456i	−0.949651	−	0.313311i	$-0.898562\pi$
$19$	−0.886994	+	1.53632i	−0.203490	+	0.352456i	0.746160	+	0.665766i	$0.231895\pi$
$20$		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	−0.984942	−	0.172887i	$-0.944691\pi$
$23$	−1.04741	−	3.90900i	−0.218401	−	0.815082i	0.766541	−	0.642195i	$-0.221976\pi$
$24$	−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	$-0.883759\pi$
$29$		−	3.84628i		−	0.714236i	0.934059	−	0.357118i	$-0.116241\pi$
$30$		0			0
$31$	−8.94554	+	5.16471i	−1.60667	+	0.927610i	−0.616558	+	0.787310i	$0.711473\pi$
$31$	−8.94554	+	5.16471i	−1.60667	+	0.927610i	−0.990109	+	0.140300i	$0.955193\pi$
$32$	−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	−0.513227	−	0.858253i	$-0.671550\pi$
$37$	−3.21516	+	0.861499i	−0.528569	+	0.141630i	−0.0153416	+	0.999882i	$0.504884\pi$
$38$	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	$0.379487\pi$
$41$			11.8993i			1.85836i	−0.369622	+	0.929182i	$0.620513\pi$
$42$	1.52856	+	2.15951i	0.235862	+	0.333220i
$43$	−3.46335	+	3.46335i	−0.528155	+	0.528155i	−0.920022	−	0.391867i	$-0.871829\pi$
$43$	−3.46335	+	3.46335i	−0.528155	+	0.528155i	0.391867	+	0.920022i	$0.371829\pi$
$44$	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	−0.979436	−	0.201756i	$-0.935335\pi$
$47$	−1.59118	−	5.93837i	−0.232098	−	0.866200i	0.747338	−	0.664444i	$-0.231332\pi$
$48$	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	0.285952	−	0.958244i	$-0.407690\pi$
$53$	0.396561	+	0.106258i	0.0544719	+	0.0145957i	−0.231480	+	0.972840i	$0.574357\pi$
$54$	−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	−0.976506	−	0.215489i	$-0.930865\pi$
$59$	−5.18379	−	8.97859i	−0.674872	−	1.16891i	0.301634	−	0.953424i	$-0.402468\pi$
$60$		0			0
$61$	−5.87936	−	3.39445i	−0.752775	−	0.434615i	0.0739204	−	0.997264i	$-0.476449\pi$
$61$	−5.87936	−	3.39445i	−0.752775	−	0.434615i	−0.826696	+	0.562649i	$0.809782\pi$
$62$	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	0.733563	+	0.679621i	$0.237856\pi$
$67$	−1.97702	+	7.37834i	−0.241532	+	0.901408i	−0.975095	+	0.221787i	$0.928811\pi$
$68$	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	0.595106	+	0.803647i	$0.297110\pi$
$73$	−2.75198	+	10.2705i	−0.322095	+	1.20207i	−0.917200	+	0.398426i	$0.869556\pi$
$74$	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	0.968386	−	0.249455i	$-0.0802515\pi$
$79$	10.9907	+	6.34546i	1.23655	+	0.713920i	0.268159	+	0.963375i	$0.413585\pi$
$80$		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	0.592430	−	0.805622i	$-0.298169\pi$
$83$	−1.94227	−	1.94227i	−0.213191	−	0.213191i	−0.805622	+	0.592430i	$0.798169\pi$
$84$	−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	−0.834928	−	0.550359i	$-0.814491\pi$
$89$	0.558127	−	0.966705i	0.0591614	−	0.102471i	0.894089	+	0.447889i	$0.147824\pi$
$90$		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	−0.972166	−	0.234293i	$-0.924722\pi$
$97$	−7.26720	+	7.26720i	−0.737872	+	0.737872i	0.234293	+	0.972166i	$0.424722\pi$
$98$	−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	0.586265	−	0.810119i	$-0.300598\pi$
$101$	15.8887	−	9.17333i	1.58098	−	0.912780i	0.994716	−	0.102661i	$-0.0327358\pi$
$102$	0.574830	−	2.14529i	0.0569166	−	0.212416i
$103$	−8.80911	+	2.36040i	−0.867988	+	0.232577i	−0.665217	−	0.746650i	$-0.731661\pi$
$103$	−8.80911	+	2.36040i	−0.867988	+	0.232577i	−0.202770	+	0.979226i	$0.564994\pi$
$104$	−3.83810			−0.376356
$105$		0			0
$106$	−0.410550			−0.0398762
$107$	−14.2519	+	3.81880i	−1.37779	+	0.369177i	−0.870317	−	0.492492i	$-0.836086\pi$
$107$	−14.2519	+	3.81880i	−1.37779	+	0.369177i	−0.507471	+	0.861669i	$0.669419\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	−17.4494	+	10.0744i	−1.67135	+	0.964955i	−0.704467	+	0.709736i	$0.748814\pi$
$109$	−17.4494	+	10.0744i	−1.67135	+	0.964955i	−0.966883	+	0.255218i	$0.917853\pi$
$110$		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	−0.328600	−	0.944469i	$-0.606577\pi$
$113$	6.54677	−	6.54677i	0.615869	−	0.615869i	0.944469	+	0.328600i	$0.106577\pi$
$114$	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	−0.992724	−	0.120409i	$-0.961579\pi$
$127$	−12.5444	−	12.5444i	−1.11313	−	1.11313i	−0.120409	−	0.992724i	$-0.538421\pi$
$128$	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	0.535853	−	0.844312i	$-0.319990\pi$
$131$	0.830756	+	0.479637i	0.0725835	+	0.0419061i	−0.463269	+	0.886218i	$0.653324\pi$
$132$	−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	0.726152	+	0.687534i	$0.241307\pi$
$137$	−2.88499	+	10.7669i	−0.246481	+	0.919880i	−0.972633	+	0.232346i	$0.925360\pi$
$138$	−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	0.0969812	−	0.995286i	$-0.469081\pi$
$149$	−8.74565	−	5.04930i	−0.716471	−	0.413655i	−0.813453	+	0.581631i	$0.802415\pi$
$150$		0			0
$151$	7.15497	+	12.3928i	0.582263	+	1.00851i	0.995211	+	0.0977541i	$0.0311659\pi$
$151$	7.15497	+	12.3928i	0.582263	+	1.00851i	−0.412948	+	0.910755i	$0.635501\pi$
$152$	−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	0.608534	−	0.793528i	$-0.291758\pi$
$157$	9.25683	+	2.48036i	0.738776	+	0.197954i	0.130242	+	0.991482i	$0.458425\pi$
$158$	−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	−0.975784	−	0.218736i	$-0.929807\pi$
$163$	−3.06537	−	11.4401i	−0.240098	−	0.896058i	0.735686	−	0.677323i	$-0.236860\pi$
$164$	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	−0.384595	−	0.923085i	$-0.625659\pi$
$167$	6.95883	−	6.95883i	0.538490	−	0.538490i	0.923085	+	0.384595i	$0.125659\pi$
$168$	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	0.0738403	−	0.997270i	$-0.476474\pi$
$173$	8.37084	−	2.24296i	0.636423	−	0.170529i	0.562583	+	0.826741i	$0.309808\pi$
$174$	−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	−0.865476	−	0.500951i	$-0.832984\pi$
$179$	−11.5646	+	6.67682i	−0.864378	+	0.499049i	0.00109809	+	0.999999i	$0.499650\pi$
$180$		0			0
$181$			8.73922i			0.649581i	0.945786	+	0.324791i	$0.105294\pi$
$181$			8.73922i			0.649581i	−0.945786	+	0.324791i	$0.894706\pi$
$182$	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	−0.599428	−	0.800429i	$-0.704605\pi$
$191$	5.43796	−	9.41883i	0.393477	−	0.681523i	0.992906	+	0.118906i	$0.0379386\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	10.8195	+	2.89908i	0.778806	+	0.208680i	0.626258	−	0.779616i	$-0.284586\pi$
$193$	10.8195	+	2.89908i	0.778806	+	0.208680i	0.152548	+	0.988296i	$0.451252\pi$
$194$	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	0.972456	−	0.233088i	$-0.0748831\pi$
$197$	10.3775	+	10.3775i	0.739367	+	0.739367i	−0.233088	+	0.972456i	$0.574883\pi$
$198$	0.457089	+	1.70588i	0.0324839	+	0.121232i
$199$	9.28152	+	16.0761i	0.657949	+	1.13960i	0.981146	+	0.193270i	$0.0619092\pi$
$199$	9.28152	+	16.0761i	0.657949	+	1.13960i	−0.323197	+	0.946332i	$0.604757\pi$
$200$		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	0.846032	−	0.533132i	$-0.178985\pi$
$223$	4.67260	+	4.67260i	0.312901	+	0.312901i	−0.533132	+	0.846032i	$0.678985\pi$
$224$	−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	0.748323	−	0.663335i	$-0.230860\pi$
$227$	16.0416	+	4.29835i	1.06472	+	0.285291i	0.316399	+	0.948626i	$0.397526\pi$
$228$	−1.71354	−	0.459142i	−0.113482	−	0.0304074i
$229$	6.77075	−	11.7273i	0.447423	−	0.774960i	−0.550794	−	0.834641i	$-0.685675\pi$
$229$	6.77075	−	11.7273i	0.447423	−	0.774960i	0.998217	+	0.0596810i	$0.0190084\pi$
$230$		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	−0.991922	−	0.126853i	$-0.959512\pi$
$233$	−2.99668	−	11.1838i	−0.196319	−	0.732672i	0.795603	−	0.605819i	$-0.207154\pi$
$234$	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	$0.185629\pi$
$239$			17.0264i			1.10135i	−0.834721	+	0.550673i	$0.814371\pi$
$240$		0			0
$241$	16.3866	−	9.46081i	1.05555	−	0.609424i	0.131355	−	0.991335i	$-0.458067\pi$
$241$	16.3866	−	9.46081i	1.05555	−	0.609424i	0.924199	+	0.381911i	$0.124734\pi$
$242$	−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	$0.194179\pi$
$251$			18.1527i			1.14579i	−0.819629	+	0.572894i	$0.805821\pi$
$252$	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	0.832403	+	0.554170i	$0.186964\pi$
$257$	6.22983	+	23.2500i	0.388606	+	1.45030i	−0.443797	+	0.896127i	$0.646369\pi$
$258$	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	0.651328	−	0.758797i	$-0.274212\pi$
$263$	13.5576	+	3.63274i	0.835995	+	0.224004i	0.184668	+	0.982801i	$0.440879\pi$
$264$	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	0.913234	+	0.407435i	$0.133577\pi$
$269$	13.2762	+	22.9951i	0.809466	+	1.40204i	−0.103768	+	0.994602i	$0.533090\pi$
$270$		0			0
$271$	10.3582	+	5.98031i	0.629216	+	0.363278i	0.780448	−	0.625220i	$-0.214991\pi$
$271$	10.3582	+	5.98031i	0.629216	+	0.363278i	−0.151232	+	0.988498i	$0.548324\pi$
$272$	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	−0.945129	−	0.326698i	$-0.894064\pi$
$277$	0.611241	−	2.28118i	0.0367259	−	0.137063i	0.981855	+	0.189635i	$0.0607306\pi$
$278$	−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	0.513658	+	0.857995i	$0.328290\pi$
$283$	−6.05917	+	22.6131i	−0.360180	+	1.34421i	−0.873838	+	0.486217i	$0.838377\pi$
$284$	−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	0.0912620	−	0.995827i	$-0.470910\pi$
$293$	−15.4837	−	15.4837i	−0.904565	−	0.904565i	−0.995827	+	0.0912620i	$0.970910\pi$
$294$	−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	−0.643971	−	0.765050i	$-0.722714\pi$
$307$	2.12149	−	2.12149i	0.121080	−	0.121080i	0.765050	+	0.643971i	$0.222714\pi$
$308$	−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	−0.0835796	−	0.996501i	$-0.526635\pi$
$311$	13.0082	−	7.51027i	0.737626	−	0.425868i	0.821205	+	0.570633i	$0.193302\pi$
$312$	0.993373	−	3.70732i	0.0562387	−	0.209886i
$313$	12.8644	−	3.44701i	0.727139	−	0.194836i	0.123784	−	0.992309i	$-0.460497\pi$
$313$	12.8644	−	3.44701i	0.727139	−	0.194836i	0.603355	+	0.797473i	$0.293830\pi$
$314$	−9.58338			−0.540821
$315$		0			0
$316$	12.6909			0.713920
$317$	13.4280	−	3.59802i	0.754192	−	0.202085i	0.138815	−	0.990318i	$-0.455671\pi$
$317$	13.4280	−	3.59802i	0.754192	−	0.202085i	0.615377	+	0.788233i	$0.289004\pi$
$318$	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	−0.487832	−	0.872938i	$-0.662212\pi$
$331$	9.31631	−	16.1363i	0.512071	−	0.886932i	0.999902	−	0.0139944i	$-0.00445470\pi$
$332$	−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	0.394155	−	0.919044i	$-0.371037\pi$
$337$	−9.63568	−	9.63568i	−0.524889	−	0.524889i	−0.919044	+	0.394155i	$0.871037\pi$
$338$	−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	0.0973042	+	0.995255i	$0.468978\pi$
$347$	−9.02693	+	33.6890i	−0.484591	+	1.80852i	−0.581895	+	0.813264i	$0.697689\pi$
$348$	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	−0.912573	−	0.408913i	$-0.865908\pi$
$353$	1.54431	−	5.76343i	0.0821951	−	0.306756i	0.994768	+	0.102157i	$0.0325745\pi$
$354$	−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	0.0489170	−	0.998803i	$-0.484423\pi$
$359$	−14.9989	−	8.65964i	−0.791613	−	0.457038i	−0.840530	+	0.541765i	$0.817756\pi$
$360$		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	0.117876	−	0.993028i	$-0.462391\pi$
$367$	−5.29802	−	1.41960i	−0.276554	−	0.0741025i	−0.394430	+	0.918926i	$0.629058\pi$
$368$	−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	−0.788207	−	0.615410i	$-0.788991\pi$
$373$	−7.98224	−	29.7901i	−0.413305	−	1.54247i	0.374903	−	0.927064i	$-0.377676\pi$
$374$	−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	$0.107668\pi$
$379$			12.9203i			0.663670i	−0.943337	+	0.331835i	$0.892332\pi$
$380$		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	−0.229332	−	0.973348i	$-0.573654\pi$
$383$	1.14948	−	0.308002i	0.0587356	−	0.0157382i	0.288067	+	0.957610i	$0.406987\pi$
$384$	−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	−0.275993	−	0.961160i	$-0.589007\pi$
$389$	8.25213	−	4.76437i	0.418400	−	0.241563i	0.694392	+	0.719597i	$0.255673\pi$
$390$		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	0.859613	+	0.510946i	$0.170705\pi$
$397$	7.38494	+	27.5610i	0.370639	+	1.38324i	−0.488974	+	0.872299i	$0.662629\pi$
$398$	−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	−0.315415	+	0.948954i	$0.602144\pi$
$401$	−19.6150	+	33.9741i	−0.979526	+	1.69659i	−0.664111	+	0.747634i	$0.731190\pi$
$402$	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	0.738920	−	0.673793i	$-0.235336\pi$
$409$	−4.32912	−	7.49826i	−0.214061	−	0.370765i	−0.952982	+	0.303028i	$0.902003\pi$
$410$		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	0.770510	−	0.637428i	$-0.220002\pi$
$431$	−3.46231	−	5.99690i	−0.166774	−	0.288860i	−0.937284	+	0.348567i	$0.886668\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	11.5154	+	11.5154i	0.553393	+	0.553393i	0.927419	−	0.374025i	$-0.122023\pi$
$433$	11.5154	+	11.5154i	0.553393	+	0.553393i	−0.374025	+	0.927419i	$0.622023\pi$
$434$	−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	−0.997287	−	0.0736169i	$-0.976546\pi$
$439$	−9.11194	+	15.7823i	−0.434889	+	0.753250i	0.562397	+	0.826867i	$0.309879\pi$
$440$		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	0.806376	+	0.591403i	$0.201426\pi$
$443$	8.49765	+	31.7136i	0.403735	+	1.50676i	−0.402641	+	0.915358i	$0.631908\pi$
$444$	−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	$0.0615242\pi$
$449$			8.14032i			0.384165i	−0.981379	+	0.192083i	$0.938476\pi$
$450$		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	−0.154184	−	0.988042i	$-0.549275\pi$
$457$	4.41041	−	1.18177i	0.206310	−	0.0552806i	0.360494	+	0.932762i	$0.382608\pi$
$458$	−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	$-0.943751\pi$
$461$		−	7.54894i		−	0.351589i	0.984427	−	0.175795i	$-0.0562495\pi$
$462$	−1.95310	+	4.24477i	−0.0908665	+	0.197485i
$463$	8.87647	−	8.87647i	0.412525	−	0.412525i	−0.470092	−	0.882617i	$-0.655779\pi$
$463$	8.87647	−	8.87647i	0.412525	−	0.412525i	0.882617	+	0.470092i	$0.155779\pi$
$464$	−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	−0.999970	−	0.00772331i	$-0.997542\pi$
$467$	−2.97858	−	11.1162i	−0.137832	−	0.514397i	0.862138	−	0.506674i	$-0.169125\pi$
$468$	−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	0.689811	−	0.723989i	$-0.257694\pi$
$479$	−6.17379	−	10.6933i	−0.282088	−	0.488590i	−0.971899	+	0.235399i	$0.924360\pi$
$480$		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	−0.812286	−	0.583260i	$-0.801777\pi$
$487$	4.03414	−	15.0556i	0.182804	−	0.682235i	0.995090	−	0.0989752i	$-0.0315565\pi$
$488$	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	0.809087	−	0.587688i	$-0.199962\pi$
$499$	15.7413	+	9.08825i	0.704678	+	0.406846i	−0.104410	+	0.994534i	$0.533295\pi$
$500$		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	0.622371	−	0.782722i	$-0.286169\pi$
$503$	−3.59630	−	3.59630i	−0.160351	−	0.160351i	−0.782722	+	0.622371i	$0.786169\pi$
$504$	−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	−0.914414	−	0.404780i	$-0.867348\pi$
$509$	−2.40629	+	4.16782i	−0.106657	+	0.184735i	0.807757	+	0.589516i	$0.200681\pi$
$510$		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	−0.395493	−	0.918469i	$-0.629426\pi$
$521$	4.61481	−	2.66436i	0.202178	−	0.116728i	0.597671	+	0.801741i	$0.296093\pi$
$522$	0.995491	−	3.71522i	0.0435714	−	0.162611i
$523$	−5.91757	+	1.58561i	−0.258757	+	0.0693338i	−0.385866	−	0.922555i	$-0.626097\pi$
$523$	−5.91757	+	1.58561i	−0.258757	+	0.0693338i	0.127108	+	0.991889i	$0.459430\pi$
$524$	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	−0.681604	−	0.731721i	$-0.738717\pi$
$541$	6.81239	−	11.7994i	0.292887	−	0.507296i	0.974491	+	0.224426i	$0.0720506\pi$
$542$	−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	0.949079	−	0.315037i	$-0.102017\pi$
$547$	14.8290	+	14.8290i	0.634042	+	0.634042i	−0.315037	+	0.949079i	$0.602017\pi$
$548$	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	−0.966145	−	0.257998i	$-0.916937\pi$
$557$	−0.0103825	+	0.0387479i	−0.000439920	+	0.00164180i	0.965706	+	0.259640i	$0.0836039\pi$
$558$	−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	0.847674	+	0.530518i	$0.178002\pi$
$563$	−3.59929	+	13.4327i	−0.151692	+	0.566122i	−0.999366	+	0.0356047i	$0.988664\pi$
$564$	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	0.0945677	−	0.995518i	$-0.469853\pi$
$569$	−17.1817	−	9.91984i	−0.720293	−	0.415861i	−0.814860	+	0.579657i	$0.803186\pi$
$570$		0			0
$571$	2.94454	+	5.10010i	0.123225	+	0.213432i	0.921038	−	0.389473i	$-0.127343\pi$
$571$	2.94454	+	5.10010i	0.123225	+	0.213432i	−0.797813	+	0.602906i	$0.794010\pi$
$572$	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	−0.0538132	−	0.998551i	$-0.517138\pi$
$577$	−14.4051	−	3.85984i	−0.599692	−	0.160687i	−0.545879	+	0.837864i	$0.683804\pi$
$578$	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	−0.800264	−	0.599647i	$-0.795308\pi$
$587$	−4.86057	+	4.86057i	−0.200617	+	0.200617i	0.599647	+	0.800264i	$0.295308\pi$
$588$	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	0.187304	−	0.982302i	$-0.440025\pi$
$593$	20.4715	−	5.48532i	0.840664	−	0.225255i	0.653361	+	0.757047i	$0.273359\pi$
$594$	−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	−0.690902	−	0.722949i	$-0.742786\pi$
$599$	−10.0409	+	5.79712i	−0.410260	+	0.236864i	0.280641	+	0.959813i	$0.409453\pi$
$600$		0			0
$601$			15.3561i			0.626387i	0.949689	+	0.313193i	$0.101399\pi$
$601$			15.3561i			0.626387i	−0.949689	+	0.313193i	$0.898601\pi$
$602$	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	−0.977269	−	0.212003i	$-0.932001\pi$
$607$	−5.83734	−	21.7853i	−0.236931	−	0.884237i	0.740339	−	0.672234i	$-0.234665\pi$
$608$	−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	0.164267	−	0.986416i	$-0.447474\pi$
$613$	−4.62200	−	1.23846i	−0.186681	−	0.0500209i	−0.350948	+	0.936395i	$0.614141\pi$
$614$	−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	0.265606	−	0.964082i	$-0.414428\pi$
$617$	−17.3498	−	17.3498i	−0.698475	−	0.698475i	−0.964082	+	0.265606i	$0.914428\pi$
$618$	2.36040	+	8.80911i	0.0949490	+	0.354355i
$619$	−10.4801	−	18.1521i	−0.421232	−	0.729596i	0.574828	−	0.818274i	$-0.305069\pi$
$619$	−10.4801	−	18.1521i	−0.421232	−	0.729596i	−0.996060	+	0.0886786i	$0.971736\pi$
$620$		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	0.721964	−	0.691931i	$-0.243240\pi$
$641$	−6.03196	−	10.4477i	−0.238248	−	0.412658i	−0.960212	+	0.279273i	$0.909906\pi$
$642$	3.81880	+	14.2519i	0.150716	+	0.562480i
$643$	15.5935	+	15.5935i	0.614947	+	0.614947i	0.944231	−	0.329284i	$-0.106807\pi$
$643$	15.5935	+	15.5935i	0.614947	+	0.614947i	−0.329284	+	0.944231i	$0.606807\pi$
$644$	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	0.381135	−	0.924520i	$-0.375533\pi$
$647$	6.33226	+	1.69672i	0.248947	+	0.0667051i	−0.132188	+	0.991225i	$0.542200\pi$
$648$	−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	0.978655	+	0.205508i	$0.0658846\pi$
$653$	5.97625	+	22.3037i	0.233869	+	0.872811i	−0.744787	+	0.667303i	$0.767449\pi$
$654$	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	$0.0554224\pi$
$659$			8.89429i			0.346472i	−0.984880	+	0.173236i	$0.944578\pi$
$660$		0			0
$661$	7.24046	−	4.18028i	0.281621	−	0.162594i	−0.352536	−	0.935798i	$-0.614681\pi$
$661$	7.24046	−	4.18028i	0.281621	−	0.162594i	0.634157	+	0.773204i	$0.281347\pi$
$662$	−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	−0.459256	−	0.888304i	$-0.651884\pi$
$673$	11.1305	−	11.1305i	0.429048	−	0.429048i	0.888304	+	0.459256i	$0.151884\pi$
$674$	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	−0.748526	−	0.663106i	$-0.769238\pi$
$677$	−11.2360	−	41.9335i	−0.431836	−	1.61163i	0.316690	−	0.948529i	$-0.397429\pi$
$678$	−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	−0.0872904	−	0.996183i	$-0.527821\pi$
$683$	−17.2742	−	4.62860i	−0.660977	−	0.177108i	−0.573687	+	0.819075i	$0.694487\pi$
$684$	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	0.951883	−	0.306463i	$-0.0991456\pi$
$691$	30.5564	+	17.6417i	1.16242	+	0.671123i	0.210537	+	0.977586i	$0.432479\pi$
$692$	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	0.358750	−	0.933434i	$-0.383203\pi$
$709$	−7.19605	−	4.15464i	−0.270253	−	0.156031i	−0.629003	+	0.777403i	$0.716537\pi$
$710$		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	−0.967280	−	0.253711i	$-0.918349\pi$
$719$	−7.07678	+	12.2574i	−0.263920	+	0.457122i	0.703360	+	0.710833i	$0.251682\pi$
$720$		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	−0.232290	−	0.972647i	$-0.574622\pi$
$727$	19.9622	−	19.9622i	0.740357	−	0.740357i	0.972647	+	0.232290i	$0.0746217\pi$
$728$	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	0.694570	−	0.719425i	$-0.255595\pi$
$733$	44.8290	−	12.0119i	1.65580	−	0.443670i	0.961228	+	0.275755i	$0.0889279\pi$
$734$	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	−0.751949	−	0.659221i	$-0.770886\pi$
$739$	−15.1424	+	8.74246i	−0.557022	+	0.321597i	0.194927	+	0.980818i	$0.437553\pi$
$740$		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	−0.445927	−	0.895069i	$-0.647126\pi$
$743$	12.2427	−	12.2427i	0.449143	−	0.449143i	0.895069	+	0.445927i	$0.147126\pi$
$744$	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	−0.543543	−	0.839381i	$-0.682917\pi$
$751$	12.4732	−	21.6042i	0.455154	−	0.788350i	0.998697	+	0.0510312i	$0.0162508\pi$
$752$	−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	0.979765	+	0.200149i	$0.0641427\pi$
$757$	32.4637	+	32.4637i	1.17991	+	1.17991i	0.200149	+	0.979765i	$0.435857\pi$
$758$	−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	0.918653	−	0.395065i	$-0.129278\pi$
$761$	28.5750	+	16.4978i	1.03584	+	0.598045i	0.117191	+	0.993109i	$0.462611\pi$
$762$	−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	−0.888779	−	0.458336i	$-0.848446\pi$
$773$	3.06094	−	11.4236i	0.110094	−	0.410878i	0.998873	+	0.0474585i	$0.0151122\pi$
$774$	−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	0.406631	−	0.913593i	$-0.366704\pi$
$787$	8.47179	+	2.27001i	0.301987	+	0.0809171i	−0.104644	+	0.994510i	$0.533370\pi$
$788$	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	−0.998220	−	0.0596400i	$-0.981005\pi$
$797$	−26.4972	+	26.4972i	−0.938580	+	0.938580i	0.0596400	+	0.998220i	$0.481005\pi$
$798$	−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	0.236489	−	0.971634i	$-0.424003\pi$
$809$	34.0232	−	19.6433i	1.19619	−	0.690622i	0.959704	+	0.281012i	$0.0906701\pi$
$810$		0			0
$811$			9.61165i			0.337511i	0.985658	+	0.168755i	$0.0539748\pi$
$811$			9.61165i			0.337511i	−0.985658	+	0.168755i	$0.946025\pi$
$812$	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	−0.0844618	+	0.996427i	$0.526917\pi$
$821$	−25.9357	+	44.9219i	−0.905162	+	1.56779i	−0.820700	+	0.571359i	$0.806416\pi$
$822$	10.7669	+	2.88499i	0.375540	+	0.100626i
$823$	10.0490	+	2.69263i	0.350287	+	0.0938592i	0.429672	−	0.902985i	$-0.358629\pi$
$823$	10.0490	+	2.69263i	0.350287	+	0.0938592i	−0.0793852	+	0.996844i	$0.525296\pi$
$824$	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	0.563349	−	0.826219i	$-0.309513\pi$
$827$	−7.55951	−	7.55951i	−0.262870	−	0.262870i	−0.826219	+	0.563349i	$0.809513\pi$
$828$	1.04741	+	3.90900i	0.0364001	+	0.135847i
$829$	−16.1525	−	27.9770i	−0.561001	−	0.971682i	−0.997409	−	0.0719331i	$-0.977083\pi$
$829$	−16.1525	−	27.9770i	−0.561001	−	0.971682i	0.436409	−	0.899748i	$-0.356250\pi$
$830$		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	0.0390463	−	0.999237i	$-0.487568\pi$
$853$	−28.0435	−	28.0435i	−0.960191	−	0.960191i	−0.999237	+	0.0390463i	$0.987568\pi$
$854$	−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	0.935779	−	0.352587i	$-0.114698\pi$
$857$	45.9579	+	12.3144i	1.56989	+	0.420652i	0.634115	+	0.773239i	$0.281365\pi$
$858$	6.54733	+	1.75435i	0.223522	+	0.0598926i
$859$	−26.8560	+	46.5160i	−0.916315	+	1.58710i	−0.111351	+	0.993781i	$0.535518\pi$
$859$	−26.8560	+	46.5160i	−0.916315	+	1.58710i	−0.804964	+	0.593324i	$0.797815\pi$
$860$		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	−0.883970	−	0.467544i	$-0.845139\pi$
$863$	−10.3466	−	38.6139i	−0.352201	−	1.31443i	0.531768	−	0.846890i	$-0.321528\pi$
$864$	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	−0.380734	−	0.924685i	$-0.624329\pi$
$877$	−7.34780	+	1.96884i	−0.248118	+	0.0664829i	0.132617	+	0.991167i	$0.457662\pi$
$878$	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	$-0.784660\pi$
$881$		−	37.1659i		−	1.25215i	0.779763	−	0.626075i	$-0.215340\pi$
$882$	3.95640	−	5.77468i	0.133219	−	0.194444i
$883$	−25.7803	+	25.7803i	−0.867577	+	0.867577i	−0.992204	−	0.124627i	$-0.960227\pi$
$883$	−25.7803	+	25.7803i	−0.867577	+	0.867577i	0.124627	+	0.992204i	$0.460227\pi$
$884$	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	0.999961	−	0.00881809i	$-0.00280692\pi$
$887$	3.85864	+	14.4006i	0.129560	+	0.483526i	−0.870401	+	0.492344i	$0.836140\pi$
$888$	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	0.809775	+	0.586740i	$0.199589\pi$
$907$	−5.56795	+	20.7799i	−0.184881	+	0.689984i	−0.994656	+	0.103244i	$0.967078\pi$
$908$	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	0.973668	−	0.227971i	$-0.0732090\pi$
$919$	38.2901	+	22.1068i	1.26307	+	0.729236i	0.289406	+	0.957207i	$0.406542\pi$
$920$		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	−0.859587	−	0.510990i	$-0.829279\pi$
$929$	0.388224	−	0.672424i	0.0127372	−	0.0220615i	0.872324	+	0.488929i	$0.162612\pi$
$930$		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	−0.698977	−	0.715144i	$-0.746361\pi$
$937$	0.494892	−	0.494892i	0.0161674	−	0.0161674i	0.715144	+	0.698977i	$0.246361\pi$
$938$	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	−0.216428	−	0.976299i	$-0.569441\pi$
$941$	15.9777	−	9.22471i	0.520857	−	0.300717i	0.737285	+	0.675582i	$0.236107\pi$
$942$	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	−0.417370	−	0.908736i	$-0.637048\pi$
$947$	−9.98459	+	2.67536i	−0.324456	+	0.0869376i	0.0929149	+	0.995674i	$0.470382\pi$
$948$	−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	−0.864645	−	0.502383i	$-0.832457\pi$
$953$	−11.1833	+	11.1833i	−0.362263	+	0.362263i	0.502383	+	0.864645i	$0.332457\pi$
$954$	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	0.760745	−	0.649051i	$-0.224834\pi$
$967$	3.47333	+	3.47333i	0.111695	+	0.111695i	−0.649051	+	0.760745i	$0.724834\pi$
$968$	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	0.911756	−	0.410732i	$-0.134727\pi$
$971$	31.5326	+	18.2054i	1.01193	+	0.584238i	0.100174	+	0.994970i	$0.468060\pi$
$972$	−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	−0.791304	−	0.611422i	$-0.790598\pi$
$977$	6.24191	−	23.2951i	0.199697	−	0.745278i	0.991001	−	0.133855i	$-0.0427357\pi$
$978$	−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	−0.776279	−	0.630390i	$-0.782895\pi$
$983$	6.62151	−	24.7118i	0.211193	−	0.788184i	0.987472	−	0.157794i	$-0.0504382\pi$
$984$	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	0.578915	−	0.815388i	$-0.303476\pi$
$991$	−13.1174	−	22.7201i	−0.416689	−	0.721726i	−0.995604	+	0.0936614i	$0.970143\pi$
$992$	−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	−0.361980	−	0.932186i	$-0.617899\pi$
$997$	−36.0450	−	9.65822i	−1.14156	−	0.305879i	−0.779577	+	0.626307i	$0.784566\pi$
$998$	−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.607.1		16
5.2	odd	4		210.2.u.b.103.2	yes	16
5.3	odd	4		1050.2.bc.g.943.4		16
5.4	even	2		210.2.u.a.187.3	yes	16
7.3	odd	6		1050.2.bc.g.157.4		16
15.2	even	4		630.2.bv.b.523.3		16
15.14	odd	2		630.2.bv.a.397.2		16
35.2	odd	12		1470.2.m.e.1273.2		16
35.3	even	12	inner	1050.2.bc.h.493.1		16
35.9	even	6		1470.2.m.d.97.3		16
35.12	even	12		1470.2.m.d.1273.3		16
35.17	even	12		210.2.u.a.73.3	✓	16
35.19	odd	6		1470.2.m.e.97.2		16
35.24	odd	6		210.2.u.b.157.2	yes	16
105.17	odd	12		630.2.bv.a.73.2		16
105.59	even	6		630.2.bv.b.577.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	35.17	even	12
210.2.u.a.187.3	yes	16	5.4	even	2
210.2.u.b.103.2	yes	16	5.2	odd	4
210.2.u.b.157.2	yes	16	35.24	odd	6
630.2.bv.a.73.2		16	105.17	odd	12
630.2.bv.a.397.2		16	15.14	odd	2
630.2.bv.b.523.3		16	15.2	even	4
630.2.bv.b.577.3		16	105.59	even	6
1050.2.bc.g.157.4		16	7.3	odd	6
1050.2.bc.g.943.4		16	5.3	odd	4
1050.2.bc.h.493.1		16	35.3	even	12	inner
1050.2.bc.h.607.1		16	1.1	even	1	trivial
1470.2.m.d.97.3		16	35.9	even	6
1470.2.m.d.1273.3		16	35.12	even	12
1470.2.m.e.97.2		16	35.19	odd	6
1470.2.m.e.1273.2		16	35.2	odd	12

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

Properties

Related objects

Downloads

Learn more