LMFDB - Embedded newform 869.2.l.a.710.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [869,2,Mod(315,869)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(869, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("869.315");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 869 = 11 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	869.l (of order $10$, 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:	$6.93899993565$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			710.1
Root			$-1.73855 + 1.26313i$ of defining polynomial
Character	$\chi$	$=$	869.710
Dual form			869.2.l.a.552.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 - 0.587785i) q^{2} +(-1.48490 + 2.04378i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.19098 - 3.66547i) q^{5} +(-1.48490 + 4.57004i) q^{6} +(1.07448 - 0.780656i) q^{7} +(-0.427051 + 0.587785i) q^{8} +(-1.04508 - 3.21644i) q^{9} +O(q^{10})$	\(q+(1.80902 - 0.587785i) q^{2} +(-1.48490 + 2.04378i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.19098 - 3.66547i) q^{5} +(-1.48490 + 4.57004i) q^{6} +(1.07448 - 0.780656i) q^{7} +(-0.427051 + 0.587785i) q^{8} +(-1.04508 - 3.21644i) q^{9} -7.33094i q^{10} +(2.54508 + 2.12663i) q^{11} +4.08757i q^{12} +(-1.38197 + 0.449028i) q^{13} +(1.48490 - 2.04378i) q^{14} +(5.72294 + 7.87695i) q^{15} +(-1.42705 + 4.39201i) q^{16} +(1.99220 - 6.13135i) q^{17} +(-3.78115 - 5.20431i) q^{18} +(4.47214 - 6.15537i) q^{19} +(-1.92705 - 5.93085i) q^{20} +3.35520i q^{21} +(5.85410 + 2.35114i) q^{22} +4.09017 q^{23} +(-0.567180 - 1.74560i) q^{24} +(-7.97214 - 5.79210i) q^{25} +(-2.23607 + 1.62460i) q^{26} +(0.917716 + 0.298184i) q^{27} +(0.664066 - 2.04378i) q^{28} +(3.88751 - 2.82444i) q^{29} +(14.9828 + 10.8857i) q^{30} +(1.11803 + 3.44095i) q^{31} +7.33094i q^{32} +(-8.12555 + 2.04378i) q^{33} -12.2627i q^{34} +(-1.58178 - 4.86822i) q^{35} +(-4.42705 - 3.21644i) q^{36} +(5.37240 + 7.39448i) q^{37} +(4.47214 - 13.7638i) q^{38} +(1.13436 - 3.49120i) q^{39} +(1.64590 + 2.26538i) q^{40} +(-8.84950 - 6.42953i) q^{41} +(1.97214 + 6.06961i) q^{42} +11.5656 q^{43} +(5.35410 + 0.363271i) q^{44} -13.0344 q^{45} +(7.39919 - 2.40414i) q^{46} +(-2.05208 + 2.82444i) q^{47} +(-6.85730 - 9.43826i) q^{48} +(-1.61803 + 4.97980i) q^{49} +(-17.8262 - 5.79210i) q^{50} +(9.57295 + 13.1760i) q^{51} +(-1.38197 + 1.90211i) q^{52} +1.83543 q^{54} +(10.8262 - 6.79615i) q^{55} +0.964944i q^{56} +(5.93958 + 18.2802i) q^{57} +(5.37240 - 7.39448i) q^{58} +(2.40261 + 3.30691i) q^{59} +(14.9828 + 4.86822i) q^{60} +(-2.81303 + 8.65761i) q^{61} +(4.04508 + 5.56758i) q^{62} +(-3.63386 - 2.64015i) q^{63} +(1.45492 + 4.47777i) q^{64} +5.60034i q^{65} +(-13.4980 + 8.47332i) q^{66} -11.9443 q^{67} +(-3.22344 - 9.92073i) q^{68} +(-6.07348 + 8.35942i) q^{69} +(-5.72294 - 7.87695i) q^{70} +(-10.7448 - 3.49120i) q^{71} +(2.33688 + 0.759299i) q^{72} +(-0.427051 - 0.587785i) q^{73} +(14.0651 + 10.2189i) q^{74} +(23.6756 - 7.69266i) q^{75} -12.3107i q^{76} +(4.39481 + 0.298184i) q^{77} -6.98240i q^{78} +(4.22272 - 7.82104i) q^{79} +(14.3992 + 10.4616i) q^{80} +(6.23607 - 4.53077i) q^{81} +(-19.7881 - 6.42953i) q^{82} +(-7.39919 - 2.40414i) q^{83} +(3.19098 + 4.39201i) q^{84} +(-20.1016 - 14.6047i) q^{85} +(20.9224 - 6.79811i) q^{86} +12.1392i q^{87} +(-2.33688 + 0.587785i) q^{88} -2.23607 q^{89} +(-23.5795 + 7.66145i) q^{90} +(-1.13436 + 1.56131i) q^{91} +(5.35410 - 3.88998i) q^{92} +(-8.69273 - 2.82444i) q^{93} +(-2.05208 + 6.31564i) q^{94} +(-17.2361 - 23.7234i) q^{95} +(-14.9828 - 10.8857i) q^{96} +(-0.618034 - 1.90211i) q^{97} +9.95959i q^{98} +(4.18034 - 10.4086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 6 q^{4} + 14 q^{5} + 10 q^{8} + 14 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 6 * q^4 + 14 * q^5 + 10 * q^8 + 14 * q^9	$ 8 q + 10 q^{2} + 6 q^{4} + 14 q^{5} + 10 q^{8} + 14 q^{9} - 2 q^{11} - 20 q^{13} + 2 q^{16} + 10 q^{18} - 2 q^{20} + 20 q^{22} - 12 q^{23} - 28 q^{25} - 22 q^{36} + 40 q^{40} - 20 q^{42} + 16 q^{44} + 12 q^{45} + 10 q^{46} - 4 q^{49} - 80 q^{50} + 90 q^{51} - 20 q^{52} + 24 q^{55} + 10 q^{62} + 34 q^{64} - 24 q^{67} + 50 q^{72} + 10 q^{73} + 40 q^{79} + 66 q^{80} + 32 q^{81} - 10 q^{83} + 30 q^{84} - 50 q^{88} - 50 q^{90} + 16 q^{92} - 120 q^{95} + 4 q^{97} - 56 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 6 * q^4 + 14 * q^5 + 10 * q^8 + 14 * q^9 - 2 * q^11 - 20 * q^13 + 2 * q^16 + 10 * q^18 - 2 * q^20 + 20 * q^22 - 12 * q^23 - 28 * q^25 - 22 * q^36 + 40 * q^40 - 20 * q^42 + 16 * q^44 + 12 * q^45 + 10 * q^46 - 4 * q^49 - 80 * q^50 + 90 * q^51 - 20 * q^52 + 24 * q^55 + 10 * q^62 + 34 * q^64 - 24 * q^67 + 50 * q^72 + 10 * q^73 + 40 * q^79 + 66 * q^80 + 32 * q^81 - 10 * q^83 + 30 * q^84 - 50 * q^88 - 50 * q^90 + 16 * q^92 - 120 * q^95 + 4 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/869\mathbb{Z}\right)^\times$.

$n$	$475$	$793$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	1.80902	−	0.587785i	1.27917	−	0.415627i	0.410881	−	0.911689i	$-0.365221\pi$
$2$	1.80902	−	0.587785i	1.27917	−	0.415627i	0.868287	+	0.496062i	$0.165221\pi$
$3$	−1.48490	+	2.04378i	−0.857305	+	1.17998i	0.124901	+	0.992169i	$0.460139\pi$
$3$	−1.48490	+	2.04378i	−0.857305	+	1.17998i	−0.982205	+	0.187810i	$0.939861\pi$
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$	1.19098	−	3.66547i	0.532624	−	1.63925i	−0.216104	−	0.976370i	$-0.569335\pi$
$5$	1.19098	−	3.66547i	0.532624	−	1.63925i	0.748728	−	0.662877i	$-0.230665\pi$
$6$	−1.48490	+	4.57004i	−0.606206	+	1.86571i
$7$	1.07448	−	0.780656i	0.406115	−	0.295060i	−0.365912	−	0.930650i	$-0.619243\pi$
$7$	1.07448	−	0.780656i	0.406115	−	0.295060i	0.772027	+	0.635589i	$0.219243\pi$
$8$	−0.427051	+	0.587785i	−0.150985	+	0.207813i
$9$	−1.04508	−	3.21644i	−0.348362	−	1.07215i
$10$		−	7.33094i		−	2.31825i
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$12$			4.08757i			1.17998i
$13$	−1.38197	+	0.449028i	−0.383288	+	0.124538i	−0.494322	−	0.869279i	$-0.664584\pi$
$13$	−1.38197	+	0.449028i	−0.383288	+	0.124538i	0.111034	+	0.993817i	$0.464584\pi$
$14$	1.48490	−	2.04378i	0.396855	−	0.546224i
$15$	5.72294	+	7.87695i	1.47766	+	2.03382i
$16$	−1.42705	+	4.39201i	−0.356763	+	1.09800i
$17$	1.99220	−	6.13135i	0.483179	−	1.48707i	−0.351423	−	0.936217i	$-0.614302\pi$
$17$	1.99220	−	6.13135i	0.483179	−	1.48707i	0.834602	−	0.550854i	$-0.185698\pi$
$18$	−3.78115	−	5.20431i	−0.891226	−	1.22667i
$19$	4.47214	−	6.15537i	1.02598	−	1.41214i	0.118052	−	0.993007i	$-0.462335\pi$
$19$	4.47214	−	6.15537i	1.02598	−	1.41214i	0.907926	−	0.419131i	$-0.137665\pi$
$20$	−1.92705	−	5.93085i	−0.430902	−	1.32618i
$21$			3.35520i			0.732164i
$22$	5.85410	+	2.35114i	1.24810	+	0.501265i
$23$	4.09017			0.852859			0.426430	−	0.904521i	$-0.359771\pi$
$23$	4.09017			0.852859			0.426430	+	0.904521i	$0.359771\pi$
$24$	−0.567180	−	1.74560i	−0.115775	−	0.356319i
$25$	−7.97214	−	5.79210i	−1.59443	−	1.15842i
$26$	−2.23607	+	1.62460i	−0.438529	+	0.318610i
$27$	0.917716	+	0.298184i	0.176615	+	0.0573855i
$28$	0.664066	−	2.04378i	0.125497	−	0.386239i
$29$	3.88751	−	2.82444i	0.721892	−	0.524485i	−0.165096	−	0.986277i	$-0.552793\pi$
$29$	3.88751	−	2.82444i	0.721892	−	0.524485i	0.886988	+	0.461792i	$0.152793\pi$
$30$	14.9828	+	10.8857i	2.73548	+	1.98744i
$31$	1.11803	+	3.44095i	0.200805	+	0.618014i	0.999860	+	0.0167555i	$0.00533369\pi$
$31$	1.11803	+	3.44095i	0.200805	+	0.618014i	−0.799055	+	0.601258i	$0.794666\pi$
$32$			7.33094i			1.29594i
$33$	−8.12555	+	2.04378i	−1.41448	+	0.355777i
$34$		−	12.2627i		−	2.10304i
$35$	−1.58178	−	4.86822i	−0.267370	−	0.822880i
$36$	−4.42705	−	3.21644i	−0.737842	−	0.536073i
$37$	5.37240	+	7.39448i	0.883218	+	1.21564i	0.975519	+	0.219914i	$0.0705776\pi$
$37$	5.37240	+	7.39448i	0.883218	+	1.21564i	−0.0923018	+	0.995731i	$0.529422\pi$
$38$	4.47214	−	13.7638i	0.725476	−	2.23279i
$39$	1.13436	−	3.49120i	0.181643	−	0.559039i
$40$	1.64590	+	2.26538i	0.260239	+	0.358189i
$41$	−8.84950	−	6.42953i	−1.38206	−	1.00412i	−0.996684	−	0.0813643i	$-0.974072\pi$
$41$	−8.84950	−	6.42953i	−1.38206	−	1.00412i	−0.385375	−	0.922760i	$-0.625928\pi$
$42$	1.97214	+	6.06961i	0.304307	+	0.936561i
$43$	11.5656			1.76374			0.881871	−	0.471490i	$-0.156284\pi$
$43$	11.5656			1.76374			0.881871	+	0.471490i	$0.156284\pi$
$44$	5.35410	+	0.363271i	0.807161	+	0.0547652i
$45$	−13.0344			−1.94306
$46$	7.39919	−	2.40414i	1.09095	−	0.354471i
$47$	−2.05208	+	2.82444i	−0.299326	+	0.411987i	−0.932015	−	0.362419i	$-0.881951\pi$
$47$	−2.05208	+	2.82444i	−0.299326	+	0.411987i	0.632689	+	0.774406i	$0.281951\pi$
$48$	−6.85730	−	9.43826i	−0.989766	−	1.36230i
$49$	−1.61803	+	4.97980i	−0.231148	+	0.711400i
$50$	−17.8262	−	5.79210i	−2.52101	−	0.819126i
$51$	9.57295	+	13.1760i	1.34048	+	1.84501i
$52$	−1.38197	+	1.90211i	−0.191644	+	0.263776i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$	1.83543			0.249771
$55$	10.8262	−	6.79615i	1.45981	−	0.916393i
$56$			0.964944i			0.128946i
$57$	5.93958	+	18.2802i	0.786717	+	2.42127i
$58$	5.37240	−	7.39448i	0.705431	−	0.970943i
$59$	2.40261	+	3.30691i	0.312793	+	0.430523i	0.936250	−	0.351335i	$-0.114272\pi$
$59$	2.40261	+	3.30691i	0.312793	+	0.430523i	−0.623456	+	0.781858i	$0.714272\pi$
$60$	14.9828	+	4.86822i	1.93428	+	0.628485i
$61$	−2.81303	+	8.65761i	−0.360171	+	1.10849i	0.592779	+	0.805365i	$0.298031\pi$
$61$	−2.81303	+	8.65761i	−0.360171	+	1.10849i	−0.952950	+	0.303128i	$0.901969\pi$
$62$	4.04508	+	5.56758i	0.513726	+	0.707084i
$63$	−3.63386	−	2.64015i	−0.457823	−	0.332628i
$64$	1.45492	+	4.47777i	0.181864	+	0.559721i
$65$			5.60034i			0.694636i
$66$	−13.4980	+	8.47332i	−1.66148	+	1.04299i
$67$	−11.9443			−1.45923			−0.729613	−	0.683861i	$-0.760300\pi$
$67$	−11.9443			−1.45923			−0.729613	+	0.683861i	$0.760300\pi$
$68$	−3.22344	−	9.92073i	−0.390900	−	1.20307i
$69$	−6.07348	+	8.35942i	−0.731161	+	1.00636i
$70$	−5.72294	−	7.87695i	−0.684022	−	0.941476i
$71$	−10.7448	−	3.49120i	−1.27517	−	0.414329i	−0.408296	−	0.912850i	$-0.633877\pi$
$71$	−10.7448	−	3.49120i	−1.27517	−	0.414329i	−0.866878	+	0.498521i	$0.833877\pi$
$72$	2.33688	+	0.759299i	0.275404	+	0.0894842i
$73$	−0.427051	−	0.587785i	−0.0499825	−	0.0687951i	0.783294	−	0.621651i	$-0.213538\pi$
$73$	−0.427051	−	0.587785i	−0.0499825	−	0.0687951i	−0.833277	+	0.552856i	$0.813538\pi$
$74$	14.0651	+	10.2189i	1.63504	+	1.18793i
$75$	23.6756	−	7.69266i	2.73382	−	0.888272i
$76$		−	12.3107i		−	1.41214i
$77$	4.39481	+	0.298184i	0.500835	+	0.0339812i
$78$		−	6.98240i		−	0.790601i
$79$	4.22272	−	7.82104i	0.475093	−	0.879935i
$79$	4.22272	−	7.82104i	0.475093	−	0.879935i
$80$	14.3992	+	10.4616i	1.60988	+	1.16964i
$81$	6.23607	−	4.53077i	0.692896	−	0.503419i
$82$	−19.7881	−	6.42953i	−2.18523	−	0.710023i
$83$	−7.39919	−	2.40414i	−0.812166	−	0.263889i	−0.126651	−	0.991947i	$-0.540423\pi$
$83$	−7.39919	−	2.40414i	−0.812166	−	0.263889i	−0.685515	+	0.728058i	$0.740423\pi$
$84$	3.19098	+	4.39201i	0.348165	+	0.479208i
$85$	−20.1016	−	14.6047i	−2.18032	−	1.58410i
$86$	20.9224	−	6.79811i	2.25612	−	0.733059i
$87$			12.1392i			1.30146i
$88$	−2.33688	+	0.587785i	−0.249112	+	0.0626581i
$89$	−2.23607			−0.237023			−0.118511	−	0.992953i	$-0.537812\pi$
$89$	−2.23607			−0.237023			−0.118511	+	0.992953i	$0.537812\pi$
$90$	−23.5795	+	7.66145i	−2.48550	+	0.807588i
$91$	−1.13436	+	1.56131i	−0.118913	+	0.163670i
$92$	5.35410	−	3.88998i	0.558204	−	0.405559i
$93$	−8.69273	−	2.82444i	−0.901394	−	0.292881i
$94$	−2.05208	+	6.31564i	−0.211655	+	0.651408i
$95$	−17.2361	−	23.7234i	−1.76838	−	2.43397i
$96$	−14.9828	−	10.8857i	−1.52918	−	1.11101i
$97$	−0.618034	−	1.90211i	−0.0627518	−	0.193130i	0.914766	−	0.403985i	$-0.132375\pi$
$97$	−0.618034	−	1.90211i	−0.0627518	−	0.193130i	−0.977517	+	0.210855i	$0.932375\pi$
$98$			9.95959i			1.00607i
$99$	4.18034	−	10.4086i	0.420140	−	1.04611i
$100$	−15.9443			−1.59443
$101$	−0.163119	+	0.0530006i	−0.0162309	+	0.00527375i	−0.317121	−	0.948385i	$-0.602716\pi$
$101$	−0.163119	+	0.0530006i	−0.0162309	+	0.00527375i	0.300890	+	0.953659i	$0.402716\pi$
$102$	25.0623	+	18.2088i	2.48154	+	1.80294i
$103$	3.53697	+	4.86822i	0.348508	+	0.479680i	0.946902	−	0.321522i	$-0.104194\pi$
$103$	3.53697	+	4.86822i	0.348508	+	0.479680i	−0.598394	+	0.801202i	$0.704194\pi$
$104$	0.326238	−	1.00406i	0.0319903	−	0.0984559i
$105$	12.2984	+	3.99598i	1.20020	+	0.389968i
$106$		0			0
$107$	−4.29792	−	3.12262i	−0.415496	−	0.301875i	0.360327	−	0.932826i	$-0.382665\pi$
$107$	−4.29792	−	3.12262i	−0.415496	−	0.301875i	−0.775823	+	0.630951i	$0.782665\pi$
$108$	1.48490	−	0.482472i	0.142884	−	0.0464259i
$109$	−8.78962			−0.841893			−0.420946	−	0.907086i	$-0.638302\pi$
$109$	−8.78962			−0.841893			−0.420946	+	0.907086i	$0.638302\pi$
$110$	15.5902	−	18.6579i	1.48646	−	1.77896i
$111$	−23.0902			−2.19162
$112$	1.89531	+	5.83317i	0.179090	+	0.551182i
$113$	−3.88751	+	5.35069i	−0.365706	+	0.503351i	−0.951727	−	0.306944i	$-0.900693\pi$
$113$	−3.88751	+	5.35069i	−0.365706	+	0.503351i	0.586022	+	0.810296i	$0.300693\pi$
$114$	21.4896	+	29.5779i	2.01269	+	2.77023i
$115$	4.87132	−	14.9924i	0.454253	−	1.39805i
$116$	2.40261	−	7.39448i	0.223077	−	0.686560i
$117$	2.88854	+	3.97574i	0.267046	+	0.367557i
$118$	6.29012	+	4.57004i	0.579052	+	0.420706i
$119$	−2.64590	−	8.14324i	−0.242549	−	0.746489i
$120$	−7.07394			−0.645760
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$			17.3152i			1.56765i
$123$	26.2812	−	8.53926i	2.36969	−	0.769960i
$124$	4.73607	+	3.44095i	0.425311	+	0.309007i
$125$	−15.1353	+	10.9964i	−1.35374	+	0.983548i
$126$	−8.12555	−	2.64015i	−0.723882	−	0.235203i
$127$	−3.73074	+	11.4820i	−0.331050	+	1.01887i	0.637585	+	0.770380i	$0.279933\pi$
$127$	−3.73074	+	11.4820i	−0.331050	+	1.01887i	−0.968635	+	0.248487i	$0.920067\pi$
$128$	−3.35410	−	4.61653i	−0.296464	−	0.408047i
$129$	−17.1738	+	23.6377i	−1.51207	+	2.08118i
$130$	3.29180	+	10.1311i	0.288710	+	0.888557i
$131$			4.42477i			0.386594i	0.981140	+	0.193297i	$0.0619180\pi$
$131$			4.42477i			0.386594i	−0.981140	+	0.193297i	$0.938082\pi$
$132$	−8.69273	+	10.4032i	−0.756605	+	0.905483i
$133$		−	10.1050i		−	0.876216i
$134$	−21.6074	+	7.02067i	−1.86659	+	0.606493i
$135$	2.18597	−	3.00873i	0.188138	−	0.258950i
$136$	2.75315	+	3.78938i	0.236080	+	0.324937i
$137$	14.6323	+	4.75433i	1.25012	+	0.406190i	0.857965	−	0.513708i	$-0.171729\pi$
$137$	14.6323	+	4.75433i	1.25012	+	0.406190i	0.392158	+	0.919898i	$0.371729\pi$
$138$	−6.07348	+	18.6922i	−0.517009	+	1.59119i
$139$	−5.62605	+	4.08757i	−0.477196	+	0.346703i	−0.800239	−	0.599681i	$-0.795294\pi$
$139$	−5.62605	+	4.08757i	−0.477196	+	0.346703i	0.323043	+	0.946384i	$0.395294\pi$
$140$	−6.70053	−	4.86822i	−0.566298	−	0.411440i
$141$	−2.72542	−	8.38800i	−0.229522	−	0.706397i
$142$	−21.4896			−1.80337
$143$	−4.47214	−	1.79611i	−0.373979	−	0.150198i
$144$	15.6180			1.30150
$145$	−5.72294	−	17.6134i	−0.475264	−	1.46271i
$146$	−1.11803	−	0.812299i	−0.0925292	−	0.0672264i
$147$	−7.77501	−	10.7014i	−0.641272	−	0.882636i
$148$	14.0651	+	4.57004i	1.15615	+	0.375655i
$149$	−0.0968859	+	0.298184i	−0.00793720	+	0.0244282i	−0.954947	−	0.296777i	$-0.904088\pi$
$149$	−0.0968859	+	0.298184i	−0.00793720	+	0.0244282i	0.947009	+	0.321206i	$0.104088\pi$
$150$	38.3079	−	27.8323i	3.12783	−	2.27250i
$151$	−11.0172	+	15.1639i	−0.896569	+	1.23402i	0.0749809	+	0.997185i	$0.476110\pi$
$151$	−11.0172	+	15.1639i	−0.896569	+	1.23402i	−0.971550	+	0.236836i	$0.923890\pi$
$152$	1.70820	+	5.25731i	0.138554	+	0.426424i
$153$	−21.8031			−1.76268
$154$	8.12555	−	2.04378i	0.654776	−	0.164693i
$155$	13.9443			1.12003
$156$	−1.83543	−	5.64888i	−0.146952	−	0.452272i
$157$	6.07348	−	8.35942i	0.484716	−	0.667154i	−0.494687	−	0.869071i	$-0.664717\pi$
$157$	6.07348	−	8.35942i	0.484716	−	0.667154i	0.979403	+	0.201917i	$0.0647171\pi$
$158$	3.04189	−	16.6304i	0.242000	−	1.32305i
$159$		0			0
$160$	26.8713	+	8.73102i	2.12436	+	0.690248i
$161$	4.39481	−	3.19302i	0.346359	−	0.251645i
$162$	8.61803	−	11.8617i	0.677097	−	0.931944i
$163$	6.07295	+	18.6906i	0.475670	+	1.46396i	0.845052	+	0.534684i	$0.179569\pi$
$163$	6.07295	+	18.6906i	0.475670	+	1.46396i	−0.369382	+	0.929278i	$0.620431\pi$
$164$	−17.6990			−1.38206
$165$	−2.18597	+	32.2181i	−0.170177	+	2.50817i
$166$	−14.7984			−1.14858
$167$	0.590170	−	0.191758i	0.0456687	−	0.0148387i	−0.286094	−	0.958202i	$-0.592357\pi$
$167$	0.590170	−	0.191758i	0.0456687	−	0.0148387i	0.331762	+	0.943363i	$0.392357\pi$
$168$	−1.97214	−	1.43284i	−0.152154	−	0.110546i
$169$	−8.80902	+	6.40013i	−0.677617	+	0.492317i
$170$	−44.9485	−	14.6047i	−3.44740	−	1.12013i
$171$	−24.4721	−	7.95148i	−1.87143	−	0.608065i
$172$	15.1396	−	10.9996i	1.15438	−	0.838710i
$173$	−7.11095	−	5.16641i	−0.540635	−	0.392795i	0.283686	−	0.958917i	$-0.408443\pi$
$173$	−7.11095	−	5.16641i	−0.540635	−	0.392795i	−0.824321	+	0.566123i	$0.808443\pi$
$174$	7.13525	+	21.9601i	0.540922	+	1.66479i
$175$	−13.0875			−0.989325
$176$	−12.9721	+	8.14324i	−0.977812	+	0.613820i
$177$	−10.3262			−0.776168
$178$	−4.04508	+	1.31433i	−0.303192	+	0.0985130i
$179$	−15.0172	−	10.9106i	−1.12244	−	0.815500i	−0.137863	−	0.990451i	$-0.544023\pi$
$179$	−15.0172	−	10.9106i	−1.12244	−	0.815500i	−0.984577	+	0.174951i	$0.944023\pi$
$180$	−17.0623	+	12.3965i	−1.27175	+	0.923980i
$181$	0.763932	−	2.35114i	0.0567826	−	0.174759i	−0.918643	−	0.395089i	$-0.870714\pi$
$181$	0.763932	−	2.35114i	0.0567826	−	0.174759i	0.975425	+	0.220331i	$0.0707136\pi$
$182$	−1.13436	+	3.49120i	−0.0840843	+	0.258785i
$183$	−13.5172	−	18.6049i	−0.999222	−	1.37531i
$184$	−1.74671	+	2.40414i	−0.128769	+	0.177236i
$185$	33.5027	−	10.8857i	2.46317	−	0.800331i
$186$	−17.3855			−1.27476
$187$	18.1094	−	11.3681i	1.32429	−	0.831321i
$188$			5.64888i			0.411987i
$189$	1.21885	−	0.396027i	0.0886581	−	0.0288068i
$190$	−45.1246	−	32.7849i	−3.27368	−	2.37847i
$191$	15.1995	+	20.9203i	1.09980	+	1.51374i	0.835654	+	0.549257i	$0.185089\pi$
$191$	15.1995	+	20.9203i	1.09980	+	1.51374i	0.264143	+	0.964484i	$0.414911\pi$
$192$	−11.3120	−	3.67549i	−0.816372	−	0.265255i
$193$	4.55157	−	14.0083i	0.327629	−	1.00834i	−0.642610	−	0.766193i	$-0.722149\pi$
$193$	4.55157	−	14.0083i	0.327629	−	1.00834i	0.970240	−	0.242146i	$-0.0778514\pi$
$194$	−2.23607	−	3.07768i	−0.160540	−	0.220965i
$195$	−11.4459	−	8.31592i	−0.819656	−	0.595515i
$196$	2.61803	+	8.05748i	0.187002	+	0.575534i
$197$	−10.2375			−0.729392			−0.364696	−	0.931127i	$-0.618827\pi$
$197$	−10.2375			−0.729392			−0.364696	+	0.931127i	$0.618827\pi$
$198$	1.44427	−	21.2865i	0.102640	−	1.51277i
$199$		−	15.3853i		−	1.09064i	−0.838229	−	0.545318i	$-0.816409\pi$
$199$		−	15.3853i		−	1.09064i	0.838229	−	0.545318i	$-0.183591\pi$
$200$	6.80902	−	2.21238i	0.481470	−	0.156439i
$201$	17.7360	−	24.4115i	1.25100	−	1.72185i
$202$	−0.263932	+	0.191758i	−0.0185702	+	0.0134920i
$203$	1.97214	−	6.06961i	0.138417	−	0.426003i
$204$	25.0623	+	8.14324i	1.75471	+	0.570141i
$205$	−34.1069	+	24.7801i	−2.38213	+	1.73072i
$206$	9.25991	+	6.72772i	0.645169	+	0.468742i
$207$	−4.27458	−	13.1558i	−0.297104	−	0.914391i
$208$		−	6.71040i		−	0.465282i
$209$	24.4721	−	6.15537i	1.69277	−	0.425776i
$210$	24.5967			1.69734
$211$	−1.32813	−	4.08757i	−0.0914323	−	0.281400i	0.894875	−	0.446317i	$-0.147264\pi$
$211$	−1.32813	−	4.08757i	−0.0914323	−	0.281400i	−0.986307	+	0.164917i	$0.947264\pi$
$212$		0			0
$213$	23.0902	−	16.7760i	1.58211	−	1.14947i
$214$	−9.61045	−	3.12262i	−0.656957	−	0.213458i
$215$	13.7745	−	42.3935i	0.939411	−	2.89121i
$216$	−0.567180	+	0.412080i	−0.0385917	+	0.0280385i
$217$	3.88751	+	2.82444i	0.263901	+	0.191735i
$218$	−15.9006	+	5.16641i	−1.07692	+	0.349913i
$219$	1.83543			0.124027
$220$	7.70820	−	19.1926i	0.519687	−	1.29397i
$221$			9.36787i			0.630151i
$222$	−41.7705	+	13.5721i	−2.80345	+	0.910897i
$223$	5.97214	+	4.33901i	0.399924	+	0.290562i	0.769510	−	0.638635i	$-0.220501\pi$
$223$	5.97214	+	4.33901i	0.399924	+	0.290562i	−0.369586	+	0.929196i	$0.620501\pi$
$224$	5.72294	+	7.87695i	0.382380	+	0.526301i
$225$	−10.2984	+	31.6951i	−0.686558	+	2.11301i
$226$	−3.88751	+	11.9645i	−0.258593	+	0.795868i
$227$	18.3631	−	13.3415i	1.21880	−	0.885509i	0.222799	−	0.974864i	$-0.428481\pi$
$227$	18.3631	−	13.3415i	1.21880	−	0.885509i	0.996000	+	0.0893552i	$0.0284806\pi$
$228$	25.1605	+	18.2802i	1.66629	+	1.21063i
$229$	−21.2730	+	6.91201i	−1.40576	+	0.456758i	−0.911048	−	0.412300i	$-0.864725\pi$
$229$	−21.2730	+	6.91201i	−1.40576	+	0.456758i	−0.494709	+	0.869059i	$0.664725\pi$
$230$		−	29.9848i		−	1.97714i
$231$	−7.13525	+	8.53926i	−0.469465	+	0.561842i
$232$			3.49120i			0.229208i
$233$	7.67813	+	23.6308i	0.503011	+	1.54811i	0.804089	+	0.594509i	$0.202654\pi$
$233$	7.67813	+	23.6308i	0.503011	+	1.54811i	−0.301078	+	0.953599i	$0.597346\pi$
$234$	7.56231	+	5.49434i	0.494363	+	0.359176i
$235$	7.90891	+	10.8857i	0.515920	+	0.710103i
$236$	6.29012	+	2.04378i	0.409452	+	0.133039i
$237$	9.71420	+	20.2438i	0.631005	+	1.31497i
$238$	−9.57295	−	13.1760i	−0.620522	−	0.854075i
$239$	5.22542	−	7.19218i	0.338005	−	0.465223i	−0.605853	−	0.795577i	$-0.707168\pi$
$239$	5.22542	−	7.19218i	0.338005	−	0.465223i	0.943857	+	0.330353i	$0.107168\pi$
$240$	−42.7626	+	13.8944i	−2.76031	+	0.896880i
$241$			20.0252i			1.28994i	0.764210	+	0.644968i	$0.223129\pi$
$241$			20.0252i			1.28994i	−0.764210	+	0.644968i	$0.776871\pi$
$242$	9.89919	+	18.4333i	0.636344	+	1.18494i
$243$			22.3677i			1.43489i
$244$	4.55157	+	14.0083i	0.291385	+	0.896790i
$245$	16.3262	+	11.8617i	1.04305	+	0.757817i
$246$	42.5238	−	30.8953i	2.71122	−	1.96982i
$247$	−3.41641	+	10.5146i	−0.217381	+	0.669029i
$248$	−2.50000	−	0.812299i	−0.158750	−	0.0515811i
$249$	15.9006	−	11.5524i	1.00766	−	0.732106i
$250$	−20.9164	+	28.7890i	−1.32287	+	1.82077i
$251$	3.32033	−	1.07884i	0.209577	−	0.0680958i	−0.202347	−	0.979314i	$-0.564857\pi$
$251$	3.32033	−	1.07884i	0.209577	−	0.0680958i	0.411924	+	0.911218i	$0.364857\pi$
$252$	−7.26771			−0.457823
$253$	10.4098	+	8.69827i	0.654460	+	0.546855i
$254$			22.9641i			1.44090i
$255$	59.6976	−	19.3969i	3.73841	−	1.21468i
$256$	−16.3992	−	11.9147i	−1.02495	−	0.744669i
$257$	−6.47214	+	4.70228i	−0.403721	+	0.293320i	−0.771055	−	0.636769i	$-0.780271\pi$
$257$	−6.47214	+	4.70228i	−0.403721	+	0.293320i	0.367334	+	0.930089i	$0.380271\pi$
$258$	−17.1738	+	52.8554i	−1.06919	+	3.29063i
$259$	11.5451	+	3.75123i	0.717377	+	0.233090i
$260$	5.32624	+	7.33094i	0.330319	+	0.454645i
$261$	−13.1474	−	9.55216i	−0.813805	−	0.591264i
$262$	2.60081	+	8.00448i	0.160679	+	0.494518i
$263$			12.0332i			0.742000i	0.928633	+	0.371000i	$0.120985\pi$
$263$			12.0332i			0.742000i	−0.928633	+	0.371000i	$0.879015\pi$
$264$	2.26872	−	5.64888i	0.139630	−	0.347664i
$265$		0			0
$266$	−5.93958	−	18.2802i	−0.364179	−	1.12083i
$267$	3.32033	−	4.57004i	0.203201	−	0.279682i
$268$	−15.6353	+	11.3597i	−0.955075	+	0.693903i
$269$	4.25329	−	13.0903i	0.259328	−	0.798128i	−0.733618	−	0.679562i	$-0.762170\pi$
$269$	4.25329	−	13.0903i	0.259328	−	0.798128i	0.992946	−	0.118567i	$-0.0378300\pi$
$270$	2.18597	−	6.72772i	0.133034	−	0.409436i
$271$	9.61045	−	6.98240i	0.583793	−	0.424150i	−0.256297	−	0.966598i	$-0.582502\pi$
$271$	9.61045	−	6.98240i	0.583793	−	0.424150i	0.840090	+	0.542448i	$0.182502\pi$
$272$	24.0860	+	17.4995i	1.46043	+	1.06106i
$273$	−1.50658	−	4.63677i	−0.0911822	−	0.280630i
$274$	29.2646			1.76794
$275$	−7.97214	−	31.6951i	−0.480738	−	1.91129i
$276$			16.7188i			1.00636i
$277$	7.56231	−	2.45714i	0.454375	−	0.147635i	−0.0728833	−	0.997340i	$-0.523220\pi$
$277$	7.56231	−	2.45714i	0.454375	−	0.147635i	0.527258	+	0.849705i	$0.323220\pi$
$278$	−7.77501	+	10.7014i	−0.466314	+	0.641827i
$279$	9.89919	−	7.19218i	0.592649	−	0.430585i
$280$	3.53697	+	1.14923i	0.211374	+	0.0686797i
$281$	13.3541	+	4.33901i	0.796639	+	0.258844i	0.678929	−	0.734204i	$-0.262445\pi$
$281$	13.3541	+	4.33901i	0.796639	+	0.258844i	0.117710	+	0.993048i	$0.462445\pi$
$282$	−9.86068	−	13.5721i	−0.587195	−	0.808204i
$283$	−3.68034	+	5.06555i	−0.218773	+	0.301116i	−0.904271	−	0.426959i	$-0.859585\pi$
$283$	−3.68034	+	5.06555i	−0.218773	+	0.301116i	0.685497	+	0.728075i	$0.259585\pi$
$284$	−17.3855	+	5.64888i	−1.03164	+	0.335199i
$285$	74.0793			4.38808
$286$	−9.14590	−	0.620541i	−0.540808	−	0.0366934i
$287$	−14.5279			−0.857553
$288$	23.5795	−	7.66145i	1.38944	−	0.451455i
$289$	−19.8713	−	14.4374i	−1.16890	−	0.849257i
$290$	−20.7058	−	28.4991i	−1.21589	−	1.67352i
$291$	4.80522	+	1.56131i	0.281687	+	0.0915257i
$292$	−1.11803	−	0.363271i	−0.0654280	−	0.0212588i
$293$	−6.19323	+	4.49965i	−0.361813	+	0.262872i	−0.753808	−	0.657095i	$-0.771785\pi$
$293$	−6.19323	+	4.49965i	−0.361813	+	0.262872i	0.391995	+	0.919967i	$0.371785\pi$
$294$	−20.3553	−	14.7890i	−1.18714	−	0.862509i
$295$	14.9828	−	4.86822i	0.872335	−	0.283439i
$296$	−6.64066			−0.385980
$297$	1.70154	+	2.71054i	0.0987333	+	0.157282i
$298$			0.596368i			0.0345467i
$299$	−5.65248	+	1.83660i	−0.326891	+	0.106213i
$300$	23.6756	−	32.5866i	1.36691	−	1.88139i
$301$	12.4271	−	9.02878i	0.716283	−	0.520410i
$302$	−11.0172	+	33.9075i	−0.633970	+	1.95116i
$303$	0.133893	−	0.412080i	0.00769195	−	0.0236734i
$304$	20.6525	+	28.4257i	1.18450	+	1.63033i
$305$	28.3839	+	20.6221i	1.62526	+	1.18082i
$306$	−39.4423	+	12.8156i	−2.25476	+	0.732617i
$307$	7.96879			0.454803			0.227401	−	0.973801i	$-0.426977\pi$
$307$	7.96879			0.454803			0.227401	+	0.973801i	$0.426977\pi$
$308$	6.03647	−	3.78938i	0.343960	−	0.215920i
$309$	−15.2016			−0.864790
$310$	25.2254	−	8.19624i	1.43271	−	0.465515i
$311$	7.07394	−	9.73645i	0.401126	−	0.552103i	−0.559900	−	0.828560i	$-0.689160\pi$
$311$	7.07394	−	9.73645i	0.401126	−	0.552103i	0.961026	+	0.276457i	$0.0891604\pi$
$312$	1.56765	+	2.15768i	0.0887505	+	0.122155i
$313$	1.85410	−	5.70634i	0.104800	−	0.322541i	−0.884883	−	0.465813i	$-0.845762\pi$
$313$	1.85410	−	5.70634i	0.104800	−	0.322541i	0.989683	+	0.143271i	$0.0457621\pi$
$314$	6.07348	−	18.6922i	0.342746	−	1.05486i
$315$	−14.0053	+	10.1754i	−0.789107	+	0.573320i
$316$	−1.91063	−	14.2539i	−0.107481	−	0.801846i
$317$	−4.60739	−	14.1801i	−0.258777	−	0.796433i	−0.993062	−	0.117592i	$-0.962482\pi$
$317$	−4.60739	−	14.1801i	−0.258777	−	0.796433i	0.734285	−	0.678841i	$-0.237518\pi$
$318$		0			0
$319$	15.9006	+	1.07884i	0.890261	+	0.0604034i
$320$	18.1459			1.01439
$321$	12.7639	−	4.14725i	0.712413	−	0.231477i
$322$	6.07348	−	8.35942i	0.338462	−	0.465852i
$323$	−28.8313	−	39.6829i	−1.60422	−	2.20802i
$324$	3.85410	−	11.8617i	0.214117	−	0.658984i
$325$	13.6180	+	4.42477i	0.755393	+	0.245442i
$326$	21.9721	+	30.2421i	1.21692	+	1.67495i
$327$	13.0517	−	17.9641i	0.721759	−	0.993415i
$328$	7.55837	−	2.45586i	0.417341	−	0.135602i
$329$			4.63677i			0.255633i
$330$	14.9828	+	59.5679i	0.824779	+	3.27911i
$331$		−	9.36787i		−	0.514905i	−0.966291	−	0.257452i	$-0.917117\pi$
$331$		−	9.36787i		−	0.514905i	0.966291	−	0.257452i	$-0.0828830\pi$
$332$	−11.9721	+	3.88998i	−0.657056	+	0.213491i
$333$	18.1693	−	25.0079i	0.995671	−	1.37042i
$334$	0.954915	−	0.693786i	0.0522506	−	0.0379623i
$335$	−14.2254	+	43.7814i	−0.777218	+	2.39203i
$336$	−14.7361	−	4.78804i	−0.803918	−	0.261209i
$337$	6.70820	+	9.23305i	0.365419	+	0.502956i	0.951649	−	0.307189i	$-0.0993883\pi$
$337$	6.70820	+	9.23305i	0.365419	+	0.502956i	−0.586229	+	0.810145i	$0.699388\pi$
$338$	−12.1738	+	16.7557i	−0.662165	+	0.911392i
$339$	−5.16312	−	15.8904i	−0.280422	−	0.863051i
$340$	−40.2032			−2.18032
$341$	−4.47214	+	11.1352i	−0.242180	+	0.603003i
$342$	−48.9443			−2.64660
$343$	5.02187	+	15.4557i	0.271155	+	0.834530i
$344$	−4.93912	+	6.79811i	−0.266299	+	0.366530i
$345$	23.4078	+	32.2181i	1.26023	+	1.73456i
$346$	−15.9006	−	5.16641i	−0.854820	−	0.277748i
$347$	20.4894	+	6.65740i	1.09993	+	0.357388i	0.802074	−	0.597224i	$-0.203730\pi$
$347$	20.4894	+	6.65740i	1.09993	+	0.357388i	0.297852	+	0.954612i	$0.403730\pi$
$348$	11.5451	+	15.8904i	0.618882	+	0.851817i
$349$	13.8115	+	10.0346i	0.739312	+	0.537141i	0.892495	−	0.451056i	$-0.148953\pi$
$349$	13.8115	+	10.0346i	0.739312	+	0.537141i	−0.153184	+	0.988198i	$0.548953\pi$
$350$	−23.6756	+	7.69266i	−1.26551	+	0.411190i
$351$	−1.40215			−0.0748410
$352$	−15.5902	+	18.6579i	−0.830959	+	0.994467i
$353$		−	2.75405i		−	0.146583i	−0.997311	−	0.0732916i	$-0.976650\pi$
$353$		−	2.75405i		−	0.146583i	0.997311	−	0.0732916i	$-0.0233504\pi$
$354$	−18.6803	+	6.06961i	−0.992849	+	0.322596i
$355$	−25.5938	+	35.2268i	−1.35838	+	1.86964i
$356$	−2.92705	+	2.12663i	−0.155133	+	0.112711i
$357$	20.5719	+	6.68421i	1.08878	+	0.353766i
$358$	−33.5795	−	10.9106i	−1.77473	−	0.576646i
$359$	26.0782	−	18.9469i	1.37635	−	0.999980i	0.379144	−	0.925338i	$-0.376219\pi$
$359$	26.0782	−	18.9469i	1.37635	−	0.999980i	0.997210	−	0.0746422i	$-0.0237815\pi$
$360$	5.56637	−	7.66145i	0.293374	−	0.403794i
$361$	−12.0172	−	36.9852i	−0.632485	−	1.94659i
$362$		−	4.70228i		−	0.247146i
$363$	−25.0266	−	12.0784i	−1.31355	−	0.633952i
$364$			3.12262i			0.163670i
$365$	−2.66312	+	0.865300i	−0.139394	+	0.0452919i
$366$	−35.3885	−	25.7113i	−1.84979	−	1.34395i
$367$	−0.763932	+	0.555029i	−0.0398769	+	0.0289723i	−0.607545	−	0.794285i	$-0.707846\pi$
$367$	−0.763932	+	0.555029i	−0.0398769	+	0.0289723i	0.567668	+	0.823257i	$0.307846\pi$
$368$	−5.83688	+	17.9641i	−0.304268	+	0.936442i
$369$	−11.4317	+	35.1833i	−0.595113	+	1.83157i
$370$	54.2085	−	39.3847i	2.81816	−	2.04752i
$371$		0			0
$372$	−14.0651	+	4.57004i	−0.729243	+	0.236945i
$373$	−12.8938			−0.667614			−0.333807	−	0.942641i	$-0.608333\pi$
$373$	−12.8938			−0.667614			−0.333807	+	0.942641i	$0.608333\pi$
$374$	26.0782	−	31.2096i	1.34847	−	1.61381i
$375$		−	47.2617i		−	2.44058i
$376$	−0.783823	−	2.41236i	−0.0404226	−	0.124408i
$377$	−4.10415	+	5.64888i	−0.211375	+	0.290932i
$378$	1.97214	−	1.43284i	0.101436	−	0.0736974i
$379$	−11.6625	−	3.78938i	−0.599063	−	0.194648i	−0.00624079	−	0.999981i	$-0.501987\pi$
$379$	−11.6625	−	3.78938i	−0.599063	−	0.194648i	−0.592823	+	0.805333i	$0.701987\pi$
$380$	−45.1246	−	14.6619i	−2.31484	−	0.752138i
$381$	−17.9271	−	24.6745i	−0.918431	−	1.26411i
$382$	39.7928	+	28.9112i	2.03598	+	1.47922i
$383$	5.60739	+	17.2578i	0.286524	+	0.881831i	0.985938	+	0.167114i	$0.0534447\pi$
$383$	5.60739	+	17.2578i	0.286524	+	0.881831i	−0.699413	+	0.714717i	$0.746555\pi$
$384$	14.4157			0.735647
$385$	6.32713	−	15.7539i	0.322460	−	0.802893i
$386$		−	28.0166i		−	1.42601i
$387$	−12.0871	−	37.2002i	−0.614420	−	1.89099i
$388$	−2.61803	−	1.90211i	−0.132911	−	0.0965652i
$389$	−3.61803	+	2.62866i	−0.183442	+	0.133278i	−0.675716	−	0.737162i	$-0.736166\pi$
$389$	−3.61803	+	2.62866i	−0.183442	+	0.133278i	0.492275	+	0.870440i	$0.336166\pi$
$390$	−25.5938	−	8.31592i	−1.29599	−	0.421093i
$391$	8.14842	−	25.0783i	0.412083	−	1.26826i
$392$	−2.23607	−	3.07768i	−0.112938	−	0.155446i
$393$	−9.04327	−	6.57032i	−0.456172	−	0.331429i
$394$	−18.5198	+	6.01745i	−0.933015	+	0.303155i
$395$	−23.6386	−	24.7930i	−1.18939	−	1.24747i
$396$	−4.42705	−	17.6008i	−0.222468	−	0.884474i
$397$	18.7082			0.938938			0.469469	−	0.882949i	$-0.344445\pi$
$397$	18.7082			0.938938			0.469469	+	0.882949i	$0.344445\pi$
$398$	−9.04327	−	27.8323i	−0.453298	−	1.39511i
$399$	20.6525	+	15.0049i	1.03392	+	0.751185i
$400$	36.8156	−	26.7481i	1.84078	−	1.33740i
$401$	−6.85730	−	2.22807i	−0.342437	−	0.111265i	0.132749	−	0.991150i	$-0.457619\pi$
$401$	−6.85730	−	2.22807i	−0.342437	−	0.111265i	−0.475187	+	0.879885i	$0.657619\pi$
$402$	17.7360	−	54.5858i	0.884591	−	2.72249i
$403$	−3.09017	−	4.25325i	−0.153932	−	0.211870i
$404$	−0.163119	+	0.224514i	−0.00811547	+	0.0111700i
$405$	−9.18034	−	28.2542i	−0.456175	−	1.40396i
$406$		−	12.1392i		−	0.602459i
$407$	−2.05208	+	30.2447i	−0.101718	+	1.49917i
$408$	−11.8328			−0.585812
$409$	11.4459	+	35.2268i	0.565962	+	1.74185i	0.665075	+	0.746777i	$0.268400\pi$
$409$	11.4459	+	35.2268i	0.565962	+	1.74185i	−0.0991128	+	0.995076i	$0.531600\pi$
$410$	−47.1345	+	64.8751i	−2.32781	+	3.20395i
$411$	−31.4443	+	22.8456i	−1.55103	+	1.12689i
$412$	9.25991	+	3.00873i	0.456203	+	0.148229i
$413$	5.16312	+	1.67760i	0.254060	+	0.0825493i
$414$	−15.4656	−	21.2865i	−0.760091	−	1.04618i
$415$	−17.6246	+	24.2582i	−0.865158	+	1.19079i
$416$	−3.29180	−	10.1311i	−0.161394	−	0.496718i
$417$		−	17.5680i		−	0.860311i
$418$	40.6525	−	25.5195i	1.98838	−	1.24820i
$419$			24.5254i			1.19814i	0.800695	+	0.599072i	$0.204464\pi$
$419$			24.5254i			1.19814i	−0.800695	+	0.599072i	$0.795536\pi$
$420$	19.8992	−	6.46564i	0.970981	−	0.315491i
$421$	−14.9894	−	10.8904i	−0.730537	−	0.530766i	0.159197	−	0.987247i	$-0.449110\pi$
$421$	−14.9894	−	10.8904i	−0.730537	−	0.530766i	−0.889733	+	0.456481i	$0.849110\pi$
$422$	−4.80522	−	6.61382i	−0.233915	−	0.321956i
$423$	11.2292	+	3.64860i	0.545984	+	0.177401i
$424$		0			0
$425$	−51.3954	+	37.3410i	−2.49304	+	1.81130i
$426$	31.9098	−	43.9201i	1.54604	−	2.12794i
$427$	3.73607	+	11.4984i	0.180801	+	0.556448i
$428$	−8.59584			−0.415496
$429$	10.3115	−	6.47304i	0.497845	−	0.312521i
$430$		−	84.7870i		−	4.08879i
$431$	3.61803	−	1.17557i	0.174275	−	0.0566252i	−0.220580	−	0.975369i	$-0.570795\pi$
$431$	3.61803	−	1.17557i	0.174275	−	0.0566252i	0.394855	+	0.918744i	$0.370795\pi$
$432$	−2.61925	+	3.60510i	−0.126019	+	0.173450i
$433$	−14.1631	+	10.2901i	−0.680636	+	0.494511i	−0.873569	−	0.486701i	$-0.838200\pi$
$433$	−14.1631	+	10.2901i	−0.680636	+	0.494511i	0.192933	+	0.981212i	$0.438200\pi$
$434$	8.69273	+	2.82444i	0.417264	+	0.135577i
$435$	44.4959	+	14.4576i	2.13342	+	0.693189i
$436$	−11.5058	+	8.35942i	−0.551026	+	0.400344i
$437$	18.2918	−	25.1765i	0.875015	−	1.20436i
$438$	3.32033	−	1.07884i	0.158651	−	0.0515490i
$439$		−	32.7849i		−	1.56474i	−0.622814	−	0.782370i	$-0.714011\pi$
$439$		−	32.7849i		−	1.56474i	0.622814	−	0.782370i	$-0.285989\pi$
$440$	−0.628677	+	9.26581i	−0.0299710	+	0.441730i
$441$	17.7082			0.843248
$442$	5.50630	+	16.9466i	0.261908	+	0.806069i
$443$	3.53697	−	4.86822i	0.168047	−	0.231296i	−0.716685	−	0.697397i	$-0.754342\pi$
$443$	3.53697	−	4.86822i	0.168047	−	0.231296i	0.884732	+	0.466101i	$0.154342\pi$
$444$	−30.2254	+	21.9601i	−1.43444	+	1.04218i
$445$	−2.66312	+	8.19624i	−0.126244	+	0.388539i
$446$	13.3541	+	4.33901i	0.632335	+	0.205458i
$447$	−0.465558	−	0.640786i	−0.0220201	−	0.0303081i
$448$	5.05887	+	3.67549i	0.239009	+	0.173650i
$449$	−31.4506	+	10.2189i	−1.48425	+	0.482261i	−0.935378	−	0.353649i	$-0.884941\pi$
$449$	−31.4506	+	10.2189i	−1.48425	+	0.482261i	−0.548867	+	0.835910i	$0.684941\pi$
$450$			63.3903i			2.98825i
$451$	−8.84950	−	35.1833i	−0.416706	−	1.65672i
$452$			10.7014i			0.503351i
$453$	−14.6323	−	45.0336i	−0.687486	−	2.11586i
$454$	25.3771	−	34.9286i	1.19101	−	1.63928i
$455$	4.37194	+	6.01745i	0.204960	+	0.282103i
$456$	−13.2813	−	4.31536i	−0.621954	−	0.202085i
$457$	−32.8885	−	10.6861i	−1.53846	−	0.499876i	−0.587510	−	0.809217i	$-0.699892\pi$
$457$	−32.8885	−	10.6861i	−1.53846	−	0.499876i	−0.950951	+	0.309341i	$0.899892\pi$
$458$	−34.4204	+	25.0079i	−1.60836	+	1.16854i
$459$	3.65654	−	5.03280i	0.170673	−	0.234911i
$460$	−7.88197	−	24.2582i	−0.367499	−	1.13104i
$461$	−15.1167			−0.704057			−0.352028	−	0.935989i	$-0.614508\pi$
$461$	−15.1167			−0.704057			−0.352028	+	0.935989i	$0.614508\pi$
$462$	−7.88854	+	19.6417i	−0.367008	+	0.913813i
$463$			26.8239i			1.24661i	0.781979	+	0.623305i	$0.214211\pi$
$463$			26.8239i			1.24661i	−0.781979	+	0.623305i	$0.785789\pi$
$464$	6.85730	+	21.1046i	0.318342	+	0.979756i
$465$	−20.7058	+	28.4991i	−0.960208	+	1.32161i
$466$	27.7797	+	38.2355i	1.28687	+	1.77123i
$467$	6.39261	−	19.6744i	0.295815	−	0.910424i	−0.687132	−	0.726533i	$-0.741131\pi$
$467$	6.39261	−	19.6744i	0.295815	−	0.910424i	0.982947	−	0.183891i	$-0.0588694\pi$
$468$	7.56231	+	2.45714i	0.349568	+	0.113581i
$469$	−12.8339	+	9.32437i	−0.592614	+	0.430559i
$470$	20.7058	+	15.0436i	0.955087	+	0.693911i
$471$	8.06637	+	24.8257i	0.371679	+	1.14391i
$472$	−2.96979			−0.136696
$473$	29.4355	+	24.5958i	1.35345	+	1.13092i
$474$	29.4721	+	30.9114i	1.35370	+	1.41981i
$475$	−71.3050	+	23.1684i	−3.27170	+	1.06304i
$476$	−11.2082	−	8.14324i	−0.513727	−	0.373245i
$477$		0			0
$478$	5.22542	−	16.0822i	0.239005	−	0.735583i
$479$	−22.1353	−	7.19218i	−1.01139	−	0.328619i	−0.243979	−	0.969780i	$-0.578453\pi$
$479$	−22.1353	−	7.19218i	−1.01139	−	0.328619i	−0.767406	+	0.641161i	$0.778453\pi$
$480$	−57.7454	+	41.9545i	−2.63571	+	1.91495i
$481$	−10.7448	−	7.80656i	−0.489921	−	0.355948i
$482$	11.7705	+	36.2259i	0.536132	+	1.65004i
$483$			13.7233i			0.624433i
$484$	12.8541	+	12.3107i	0.584277	+	0.559579i
$485$	−7.70820			−0.350012
$486$	13.1474	+	40.4636i	0.596379	+	1.83547i
$487$	13.3262	+	9.68208i	0.603869	+	0.438737i	0.847250	−	0.531194i	$-0.178256\pi$
$487$	13.3262	+	9.68208i	0.603869	+	0.438737i	−0.243381	+	0.969931i	$0.578256\pi$
$488$	−3.88751	−	5.35069i	−0.175979	−	0.242215i
$489$	−47.2173	−	15.3418i	−2.13524	−	0.693781i
$490$	36.5066	+	11.8617i	1.64920	+	0.535857i
$491$	−5.72294	+	4.15796i	−0.258273	+	0.187646i	−0.709385	−	0.704821i	$-0.751027\pi$
$491$	−5.72294	+	4.15796i	−0.258273	+	0.187646i	0.451113	+	0.892467i	$0.351027\pi$
$492$	26.2812	−	36.1729i	1.18485	−	1.63080i
$493$	−9.57295	−	29.4625i	−0.431144	−	1.32692i
$494$			21.0292i			0.946150i
$495$	−33.1738	−	27.7194i	−1.49105	−	1.24589i
$496$	−16.7082			−0.750221
$497$	−14.2705	+	4.63677i	−0.640120	+	0.207988i
$498$	21.9740	−	30.2447i	0.984680	−	1.35530i
$499$	9.69098	−	7.04091i	0.433828	−	0.315194i	−0.349350	−	0.936992i	$-0.613597\pi$
$499$	9.69098	−	7.04091i	0.433828	−	0.315194i	0.783178	+	0.621798i	$0.213597\pi$
$500$	−9.35410	+	28.7890i	−0.418328	+	1.28748i
$501$	−0.484429	+	1.49092i	−0.0216427	+	0.0666094i
$502$	5.37240	−	3.90328i	0.239782	−	0.174212i
$503$	28.2272	+	20.5082i	1.25859	+	0.914417i	0.998687	−	0.0512192i	$-0.0163107\pi$
$503$	28.2272	+	20.5082i	1.25859	+	0.914417i	0.259899	+	0.965636i	$0.416311\pi$
$504$	3.10368	−	1.00845i	0.138249	−	0.0449199i
$505$			0.661030i			0.0294155i
$506$	23.9443	+	9.61657i	1.06445	+	0.427509i
$507$		−	27.5072i		−	1.22164i
$508$	6.03647	+	18.5783i	0.267825	+	0.824281i
$509$	5.72294	−	7.87695i	0.253665	−	0.349140i	−0.663126	−	0.748508i	$-0.730771\pi$
$509$	5.72294	−	7.87695i	0.253665	−	0.349140i	0.916791	+	0.399368i	$0.130771\pi$
$510$	96.5927	−	70.1787i	4.27720	−	3.10756i
$511$	−0.917716	−	0.298184i	−0.0405974	−	0.0131909i
$512$	−25.8156	−	8.38800i	−1.14090	−	0.370701i
$513$	5.93958	−	4.31536i	0.262239	−	0.190528i
$514$	−8.94427	+	12.3107i	−0.394515	+	0.543003i
$515$	22.0568	−	7.16669i	0.971938	−	0.315802i
$516$			47.2753i			2.08118i
$517$	−11.2292	+	2.82444i	−0.493861	+	0.124219i
$518$	23.0902			1.01452
$519$	21.1180	−	6.86167i	0.926979	−	0.301194i
$520$	−3.29180	−	2.39163i	−0.144355	−	0.104880i
$521$	6.99119	+	9.62255i	0.306290	+	0.421572i	0.934220	−	0.356698i	$-0.116098\pi$
$521$	6.99119	+	9.62255i	0.306290	+	0.421572i	−0.627930	+	0.778270i	$0.716098\pi$
$522$	−29.3985	−	9.55216i	−1.28674	−	0.418087i
$523$	−4.63525	−	1.50609i	−0.202686	−	0.0658565i	0.205915	−	0.978570i	$-0.433983\pi$
$523$	−4.63525	−	1.50609i	−0.202686	−	0.0658565i	−0.408600	+	0.912713i	$0.633983\pi$
$524$	4.20820	+	5.79210i	0.183836	+	0.253029i
$525$	19.4336	−	26.7481i	0.848153	−	1.16738i
$526$	7.07295	+	21.7683i	0.308395	+	0.949143i
$527$	23.3250			1.01605
$528$	2.61925	−	38.6041i	0.113988	−	1.68003i
$529$	−6.27051			−0.272631
$530$		0			0
$531$	8.12555	−	11.1839i	0.352619	−	0.485338i
$532$	−9.61045	−	13.2276i	−0.416666	−	0.573491i
$533$	15.1167	+	4.91173i	0.654779	+	0.212751i
$534$	3.32033	−	10.2189i	0.143685	−	0.442216i
$535$	−16.5646	+	12.0349i	−0.716151	+	0.520314i
$536$	5.10081	−	7.02067i	0.220322	−	0.303247i
$537$	44.5980	−	14.4908i	1.92455	−	0.625323i
$538$		−	26.1806i		−	1.12872i
$539$	−14.7082	+	9.23305i	−0.633527	+	0.397696i
$540$		−	6.01745i		−	0.258950i
$541$	−14.0451	+	4.56352i	−0.603845	+	0.196201i	−0.594955	−	0.803759i	$-0.702830\pi$
$541$	−14.0451	+	4.56352i	−0.603845	+	0.196201i	−0.00889065	+	0.999960i	$0.502830\pi$
$542$	13.2813	−	18.2802i	0.570481	−	0.785200i
$543$	3.67086	+	5.05251i	0.157532	+	0.216824i
$544$	44.9485	+	14.6047i	1.92715	+	0.626170i
$545$	−10.4683	+	32.2181i	−0.448412	+	1.38007i
$546$	−5.45085	−	7.50245i	−0.233275	−	0.321075i
$547$	−7.33688	+	10.0984i	−0.313702	+	0.431774i	−0.936531	−	0.350584i	$-0.885983\pi$
$547$	−7.33688	+	10.0984i	−0.313702	+	0.431774i	0.622829	+	0.782358i	$0.285983\pi$
$548$	23.6756	−	7.69266i	1.01137	−	0.328614i
$549$	30.7865			1.31394
$550$	−33.0517	−	52.6511i	−1.40933	−	2.24505i
$551$		−	36.5603i		−	1.55752i
$552$	−2.31986	−	7.13980i	−0.0987398	−	0.303890i
$553$	−1.56830	−	11.7000i	−0.0666910	−	0.497537i
$554$	12.2361	−	8.89002i	0.519861	−	0.377701i
$555$	−27.5000	+	84.6363i	−1.16731	+	3.59261i
$556$	−3.47709	+	10.7014i	−0.147462	+	0.453840i
$557$	−14.6976	−	20.2295i	−0.622756	−	0.857150i	0.374794	−	0.927108i	$-0.377713\pi$
$557$	−14.6976	−	20.2295i	−0.622756	−	0.857150i	−0.997550	+	0.0699584i	$0.977713\pi$
$558$	13.6803	−	18.8294i	0.579135	−	0.797111i
$559$	−15.9833	+	5.19329i	−0.676022	+	0.219653i
$560$	23.6386			0.998912
$561$	−3.65654	+	53.8922i	−0.154379	+	2.27533i
$562$	26.7082			1.12662
$563$	−21.1803	+	6.88191i	−0.892645	+	0.290038i	−0.719198	−	0.694805i	$-0.755491\pi$
$563$	−21.1803	+	6.88191i	−0.892645	+	0.290038i	−0.173447	+	0.984843i	$0.555491\pi$
$564$	−11.5451	−	8.38800i	−0.486136	−	0.353198i
$565$	14.9828	+	20.6221i	0.630333	+	0.867579i
$566$	−3.68034	+	11.3269i	−0.154696	+	0.476106i
$567$	3.16356	−	9.73645i	0.132857	−	0.408892i
$568$	6.64066	−	4.82472i	0.278636	−	0.202441i
$569$	20.7148	−	28.5115i	0.868409	−	1.19526i	−0.111090	−	0.993810i	$-0.535434\pi$
$569$	20.7148	−	28.5115i	0.868409	−	1.19526i	0.979498	−	0.201452i	$-0.0645659\pi$
$570$	134.011	−	43.5427i	5.61309	−	1.82380i
$571$		−	31.8869i		−	1.33442i	−0.744867	−	0.667212i	$-0.767487\pi$
$571$		−	31.8869i		−	1.33442i	0.744867	−	0.667212i	$-0.232513\pi$
$572$	−7.56231	+	1.90211i	−0.316196	+	0.0795313i
$573$	−65.3262			−2.72904
$574$	−26.2812	+	8.53926i	−1.09695	+	0.356422i
$575$	−32.6074	−	23.6907i	−1.35982	−	0.987969i
$576$	12.8820	−	9.35930i	0.536749	−	0.389971i
$577$	−26.6454	−	8.65761i	−1.10926	−	0.360421i	−0.303601	−	0.952799i	$-0.598189\pi$
$577$	−26.6454	−	8.65761i	−1.10926	−	0.360421i	−0.805660	+	0.592378i	$0.798189\pi$
$578$	−44.4336	−	14.4374i	−1.84820	−	0.600515i
$579$	21.8713	+	30.1033i	0.908941	+	1.25105i
$580$	−24.2428	−	17.6134i	−1.00663	−	0.731356i
$581$	−9.82709	+	3.19302i	−0.407696	+	0.132469i
$582$	9.61045			0.398366
$583$		0			0
$584$	0.527864			0.0218432
$585$	18.0132	−	5.85283i	0.744752	−	0.241985i
$586$	−8.55884	+	11.7802i	−0.353562	+	0.486637i
$587$	14.2818	+	19.6572i	0.589472	+	0.811339i	0.994694	−	0.102880i	$-0.0328057\pi$
$587$	14.2818	+	19.6572i	0.589472	+	0.811339i	−0.405222	+	0.914218i	$0.632806\pi$
$588$	−20.3553	−	6.61382i	−0.839436	−	0.272749i
$589$	26.1803	+	8.50651i	1.07874	+	0.350505i
$590$	24.2428	−	17.6134i	0.998059	−	0.725132i
$591$	15.2016	−	20.9232i	0.625311	−	0.860667i
$592$	−40.1433	+	13.0434i	−1.64988	+	0.536079i
$593$			9.85359i			0.404639i	0.979320	+	0.202319i	$0.0648479\pi$
$593$			9.85359i			0.404639i	−0.979320	+	0.202319i	$0.935152\pi$
$594$	4.67133	+	3.90328i	0.191667	+	0.160153i
$595$	−33.0000			−1.35287
$596$	0.156765	+	0.482472i	0.00642133	+	0.0197628i
$597$	31.4443	+	22.8456i	1.28693	+	0.935008i
$598$	−9.14590	+	6.64488i	−0.374004	+	0.271730i
$599$	−0.364745	+	1.12257i	−0.0149031	+	0.0458670i	−0.958232	−	0.285994i	$-0.907676\pi$
$599$	−0.364745	+	1.12257i	−0.0149031	+	0.0458670i	0.943328	+	0.331861i	$0.107676\pi$
$600$	−5.58905	+	17.2013i	−0.228172	+	0.702241i
$601$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$601$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$602$	17.1738	−	23.6377i	0.699950	−	0.963399i
$603$	12.4828	+	38.4180i	0.508338	+	1.56450i
$604$			30.3278i			1.23402i
$605$	42.0066	+	5.72658i	1.70781	+	0.232819i
$606$		−	0.824160i		−	0.0334792i
$607$	−4.61145	−	14.1926i	−0.187173	−	0.576059i	0.812806	−	0.582534i	$-0.197939\pi$
$607$	−4.61145	−	14.1926i	−0.187173	−	0.576059i	−0.999979	+	0.00647509i	$0.997939\pi$
$608$	45.1246	+	32.7849i	1.83004	+	1.32961i
$609$	9.47655	+	13.0434i	0.384009	+	0.528543i
$610$	63.4684	+	20.6221i	2.56976	+	0.834965i
$611$	1.56765	−	4.82472i	0.0634202	−	0.195187i
$612$	−28.5407	+	20.7360i	−1.15369	+	0.838204i
$613$	−5.27552	−	3.83289i	−0.213076	−	0.154809i	0.476128	−	0.879376i	$-0.342040\pi$
$613$	−5.27552	−	3.83289i	−0.213076	−	0.154809i	−0.689204	+	0.724567i	$0.742040\pi$
$614$	14.4157	−	4.68393i	0.581769	−	0.189028i
$615$		−	106.503i		−	4.29461i
$616$	−2.05208	+	2.45586i	−0.0826805	+	0.0989496i
$617$	48.3050			1.94468			0.972342	−	0.233561i	$-0.0750380\pi$
$617$	48.3050			1.94468			0.972342	+	0.233561i	$0.0750380\pi$
$618$	−27.5000	+	8.93529i	−1.10621	+	0.359430i
$619$	−2.61925	+	3.60510i	−0.105277	+	0.144901i	−0.858405	−	0.512973i	$-0.828544\pi$
$619$	−2.61925	+	3.60510i	−0.105277	+	0.144901i	0.753128	+	0.657874i	$0.228544\pi$
$620$	18.2533	−	13.2618i	0.733070	−	0.532606i
$621$	3.75361	+	1.21962i	0.150627	+	0.0489418i
$622$	7.07394	−	21.7714i	0.283639	−	0.872952i
$623$	−2.40261	+	1.74560i	−0.0962586	+	0.0699360i
$624$	13.7146	+	9.96424i	0.549023	+	0.398889i
$625$	7.05573	+	21.7153i	0.282229	+	0.868612i
$626$		−	11.4127i		−	0.456142i
$627$	−23.7583	+	59.1558i	−0.948816	+	2.36246i
$628$		−	16.7188i		−	0.667154i
$629$	56.0410	−	18.2088i	2.23450	−	0.726034i
$630$	−19.3548	+	26.6396i	−0.771113	+	1.06135i
$631$	−21.2730	−	29.2797i	−0.846863	−	1.16561i	−0.984545	−	0.175131i	$-0.943965\pi$
$631$	−21.2730	−	29.2797i	−0.846863	−	1.16561i	0.137682	−	0.990477i	$-0.456035\pi$
$632$	2.79377	+	5.82204i	0.111130	+	0.231588i
$633$	10.3262	+	3.35520i	0.410431	+	0.133357i
$634$	−16.6697	−	22.9439i	−0.662038	−	0.911217i
$635$	37.6438	+	27.3498i	1.49385	+	1.08535i
$636$		0			0
$637$		−	7.60845i		−	0.301458i
$638$	29.3985	−	7.39448i	1.16390	−	0.292750i
$639$			38.2086i			1.51151i
$640$	−20.9164	+	6.79615i	−0.826794	+	0.268642i
$641$	−19.3992	−	14.0943i	−0.766222	−	0.556693i	0.134591	−	0.990901i	$-0.457028\pi$
$641$	−19.3992	−	14.0943i	−0.766222	−	0.556693i	−0.900812	+	0.434209i	$0.857028\pi$
$642$	20.6525	−	15.0049i	0.815088	−	0.592196i
$643$	3.83688	−	11.8087i	0.151312	−	0.465690i	−0.846457	−	0.532458i	$-0.821269\pi$
$643$	3.83688	−	11.8087i	0.151312	−	0.465690i	0.997769	+	0.0667676i	$0.0212686\pi$
$644$	2.71614	−	8.35942i	0.107031	−	0.329407i
$645$	66.1894	+	91.1019i	2.60621	+	3.58714i
$646$	−75.4814	−	54.8405i	−2.96978	−	2.15767i
$647$	−7.99166	+	2.59665i	−0.314184	+	0.102085i	−0.461865	−	0.886950i	$-0.652819\pi$
$647$	−7.99166	+	2.59665i	−0.314184	+	0.102085i	0.147680	+	0.989035i	$0.452819\pi$
$648$			5.60034i			0.220002i
$649$	−0.917716	+	13.5258i	−0.0360235	+	0.530935i
$650$	27.2361			1.06829
$651$	−11.5451	+	3.75123i	−0.452488	+	0.147022i
$652$	25.7254	+	18.6906i	1.00749	+	0.731981i
$653$	32.3156	−	23.4787i	1.26461	−	0.918791i	0.265633	−	0.964074i	$-0.414419\pi$
$653$	32.3156	−	23.4787i	1.26461	−	0.918791i	0.998974	+	0.0452836i	$0.0144191\pi$
$654$	13.0517	−	40.1689i	0.510360	−	1.57073i
$655$	16.2188	+	5.26982i	0.633723	+	0.205909i
$656$	40.8673	−	29.6918i	1.59560	−	1.15927i
$657$	−1.44427	+	1.98787i	−0.0563464	+	0.0775542i
$658$	2.72542	+	8.38800i	0.106248	+	0.326998i
$659$	5.81983			0.226708			0.113354	−	0.993555i	$-0.463841\pi$
$659$	5.81983			0.226708			0.113354	+	0.993555i	$0.463841\pi$
$660$	27.7797	+	44.2530i	1.08132	+	1.72254i
$661$		−	18.5079i		−	0.719876i	−0.932976	−	0.359938i	$-0.882798\pi$
$661$		−	18.5079i		−	0.719876i	0.932976	−	0.359938i	$-0.117202\pi$
$662$	−5.50630	−	16.9466i	−0.214008	−	0.658650i
$663$	−19.1459	−	13.9103i	−0.743565	−	0.540232i
$664$	4.57295	−	3.32244i	0.177465	−	0.128936i
$665$	−37.0396	−	12.0349i	−1.43634	−	0.466694i
$666$	18.1693	−	55.9193i	0.704045	−	2.16683i
$667$	15.9006	−	11.5524i	0.615672	−	0.447312i
$668$	0.590170	−	0.812299i	0.0228344	−	0.0314288i
$669$	−17.7360	+	5.76277i	−0.685713	+	0.222802i
$670$			87.5627i			3.38284i
$671$	−25.5709	+	16.0521i	−0.987153	+	0.619684i
$672$	−24.5967			−0.948840
$673$	7.87190	+	24.2272i	0.303439	+	0.933891i	0.980255	+	0.197738i	$0.0633595\pi$
$673$	7.87190	+	24.2272i	0.303439	+	0.933891i	−0.676815	+	0.736153i	$0.736641\pi$
$674$	17.5623	+	12.7598i	0.676475	+	0.491488i
$675$	−5.58905	−	7.69266i	−0.215122	−	0.296091i
$676$	−5.44427	+	16.7557i	−0.209395	+	0.644452i
$677$	8.55573	+	2.77992i	0.328823	+	0.106841i	0.468776	−	0.883317i	$-0.344695\pi$
$677$	8.55573	+	2.77992i	0.328823	+	0.106841i	−0.139953	+	0.990158i	$0.544695\pi$
$678$	−18.6803	−	25.7113i	−0.717414	−	0.987436i
$679$	−2.14896	−	1.56131i	−0.0824696	−	0.0599176i
$680$	17.1688	−	5.57849i	0.658394	−	0.213925i
$681$			57.3409i			2.19731i
$682$	−1.54508	+	22.7724i	−0.0591644	+	0.871999i
$683$	1.65248			0.0632302			0.0316151	−	0.999500i	$-0.489935\pi$
$683$	1.65248			0.0632302			0.0316151	+	0.999500i	$0.489935\pi$
$684$	−39.5967	+	12.8658i	−1.51402	+	0.491935i
$685$	34.8537	−	47.9720i	1.33169	−	1.83291i
$686$	18.1693	+	25.0079i	0.693706	+	0.954805i
$687$	17.4615	−	53.7409i	0.666198	−	2.05035i
$688$	−16.5048	+	50.7964i	−0.629238	+	1.93659i
$689$		0			0
$690$	61.2824	+	44.5243i	2.33298	+	1.69501i
$691$	−35.3381	+	11.4820i	−1.34432	+	0.436798i	−0.890780	−	0.454436i	$-0.849841\pi$
$691$	−35.3381	+	11.4820i	−1.34432	+	0.436798i	−0.453545	+	0.891233i	$0.649841\pi$
$692$	−14.2219			−0.540635
$693$	−3.63386	−	14.4473i	−0.138039	−	0.548806i
$694$	40.9787			1.55553
$695$	8.28232	+	25.4903i	0.314166	+	0.966904i
$696$	−7.13525	−	5.18407i	−0.270461	−	0.196502i
$697$	−57.0517	+	41.4505i	−2.16099	+	1.57005i
$698$	30.8834	+	10.0346i	1.16895	+	0.379816i
$699$	−59.6976	−	19.3969i	−2.25797	−	0.733659i
$700$	−17.1318	+	12.4470i	−0.647522	+	0.470452i
$701$	−13.1474	−	9.55216i	−0.496571	−	0.360780i	0.311135	−	0.950366i	$-0.399291\pi$
$701$	−13.1474	−	9.55216i	−0.496571	−	0.360780i	−0.807706	+	0.589586i	$0.799291\pi$
$702$	−2.53650	+	0.824160i	−0.0957342	+	0.0311059i
$703$	69.5418			2.62282
$704$	−5.81966	+	14.4904i	−0.219337	+	0.546126i
$705$	−33.9919			−1.28021
$706$	−1.61879	−	4.98212i	−0.0609239	−	0.187505i
$707$	−0.133893	+	0.184288i	−0.00503556	+	0.00693086i
$708$	−13.5172	+	9.82084i	−0.508008	+	0.369090i
$709$	−16.4677	−	5.35069i	−0.618459	−	0.200950i	−0.0170031	−	0.999855i	$-0.505413\pi$
$709$	−16.4677	−	5.35069i	−0.618459	−	0.200950i	−0.601456	+	0.798906i	$0.705413\pi$
$710$	−25.5938	+	78.7695i	−0.960517	+	2.95617i
$711$	−29.5690	−	5.40849i	−1.10892	−	0.202834i
$712$	0.954915	−	1.31433i	0.0357870	−	0.0492565i
$713$	4.57295	+	14.0741i	0.171258	+	0.527079i
$714$	41.1438			1.53977
$715$	−11.9098	+	14.2533i	−0.445402	+	0.533045i
$716$	−30.0344			−1.12244
$717$	6.94005	+	21.3593i	0.259181	+	0.797677i
$718$	36.0392	−	49.6037i	1.34497	−	1.85119i
$719$	−26.0344	+	18.9151i	−0.970921	+	0.705415i	−0.955661	−	0.294468i	$-0.904857\pi$
$719$	−26.0344	+	18.9151i	−0.970921	+	0.705415i	−0.0152596	+	0.999884i	$0.504857\pi$
$720$	18.6008	−	57.2474i	0.693211	−	2.13349i
$721$	7.60081	+	2.46965i	0.283069	+	0.0919747i
$722$	−43.4787	−	59.8433i	−1.61811	−	2.22714i
$723$	−40.9271	−	29.7353i	−1.52210	−	1.10587i
$724$	−1.23607	−	3.80423i	−0.0459381	−	0.141383i
$725$	−47.3512			−1.75858
$726$	−52.3730	−	7.13980i	−1.94375	−	0.264983i
$727$	26.5967			0.986419			0.493209	−	0.869911i	$-0.335824\pi$
$727$	26.5967			0.986419			0.493209	+	0.869911i	$0.335824\pi$
$728$	−0.433287	−	1.33352i	−0.0160587	−	0.0494235i
$729$	−27.0066	−	19.6214i	−1.00024	−	0.726720i
$730$	−4.30902	+	3.13068i	−0.159484	+	0.115872i
$731$	23.0410	−	70.9130i	0.852203	−	2.62281i
$732$	−35.3885	−	11.4984i	−1.30800	−	0.424994i
$733$	−21.0795	−	29.0135i	−0.778590	−	1.07164i	−0.995436	−	0.0954315i	$-0.969577\pi$
$733$	−21.0795	−	29.0135i	−0.778590	−	1.07164i	0.216846	−	0.976206i	$-0.430423\pi$
$734$	−1.05573	+	1.45309i	−0.0389676	+	0.0536343i
$735$	−48.4855	+	15.7539i	−1.78842	+	0.581091i
$736$			29.9848i			1.10525i
$737$	−30.3992	−	25.4010i	−1.11977	−	0.935658i
$738$			70.3666i			2.59023i
$739$	−9.39380	−	28.9112i	−0.345557	−	1.06351i	−0.961285	−	0.275556i	$-0.911138\pi$
$739$	−9.39380	−	28.9112i	−0.345557	−	1.06351i	0.615729	−	0.787958i	$-0.288862\pi$
$740$	33.5027	−	46.1125i	1.23158	−	1.69513i
$741$	−16.4166	−	22.5955i	−0.603079	−	0.830067i
$742$		0			0
$743$	4.47214	+	1.45309i	0.164067	+	0.0533085i	0.389899	−	0.920858i	$-0.372510\pi$
$743$	4.47214	+	1.45309i	0.164067	+	0.0533085i	−0.225832	+	0.974166i	$0.572510\pi$
$744$	5.37240	−	3.90328i	0.196962	−	0.143101i
$745$	0.977595	+	0.710264i	0.0358163	+	0.0260221i
$746$	−23.3250	+	7.57877i	−0.853991	+	0.277478i
$747$			26.3116i			0.962690i
$748$	12.8938	−	32.1042i	0.471443	−	1.17384i
$749$	−7.05573			−0.257811
$750$	−27.7797	−	85.4972i	−1.01437	−	3.12192i
$751$	25.7533	+	18.7109i	0.939751	+	0.682769i	0.948361	−	0.317194i	$-0.102741\pi$
$751$	25.7533	+	18.7109i	0.939751	+	0.682769i	−0.00860982	+	0.999963i	$0.502741\pi$
$752$	−9.47655	−	13.0434i	−0.345574	−	0.475642i
$753$	−2.72542	+	8.38800i	−0.0993200	+	0.305676i
$754$	−4.10415	+	12.6313i	−0.149464	+	0.460004i
$755$	42.4615	+	58.4432i	1.54533	+	2.12697i
$756$	1.21885	−	1.67760i	0.0443290	−	0.0610137i
$757$	−4.11146	−	12.6538i	−0.149433	−	0.459909i	0.848121	−	0.529803i	$-0.177734\pi$
$757$	−4.11146	−	12.6538i	−0.149433	−	0.459909i	−0.997554	+	0.0698938i	$0.977734\pi$
$758$	−23.3250			−0.847204
$759$	−33.2349	+	8.35942i	−1.20635	+	0.303428i
$760$	21.3050			0.772812
$761$	0.892609	−	0.290026i	0.0323571	−	0.0105134i	−0.292794	−	0.956176i	$-0.594585\pi$
$761$	0.892609	−	0.290026i	0.0323571	−	0.0105134i	0.325151	+	0.945662i	$0.394585\pi$
$762$	−46.9336	−	34.0993i	−1.70023	−	1.23529i
$763$	−9.44427	+	6.86167i	−0.341906	+	0.248409i
$764$	39.7928	+	12.9295i	1.43965	+	0.467771i
$765$	−25.9672	+	79.9187i	−0.938845	+	2.88947i
$766$	20.2877	+	27.9237i	0.733026	+	1.00892i
$767$	−4.80522	−	3.49120i	−0.173507	−	0.126060i
$768$	48.7022	−	15.8243i	1.75739	−	0.571010i
$769$	−12.9678			−0.467630			−0.233815	−	0.972281i	$-0.575121\pi$
$769$	−12.9678			−0.467630			−0.233815	+	0.972281i	$0.575121\pi$
$770$	2.18597	−	32.2181i	0.0787768	−	1.16106i
$771$		−	20.2100i		−	0.727847i
$772$	−7.36460	−	22.6659i	−0.265058	−	0.815764i
$773$	28.9615	+	21.0418i	1.04167	+	0.756819i	0.970611	−	0.240653i	$-0.0773614\pi$
$773$	28.9615	+	21.0418i	1.04167	+	0.756819i	0.0710612	+	0.997472i	$0.477361\pi$
$774$	−43.7314	−	60.1912i	−1.57189	−	2.16353i
$775$	11.0172	−	33.9075i	0.395750	−	1.21799i
$776$	1.38197	+	0.449028i	0.0496097	+	0.0161192i
$777$	−24.8099	+	18.0255i	−0.890052	+	0.646660i
$778$	−5.00000	+	6.88191i	−0.179259	+	0.246728i
$779$	−79.1523	+	25.7181i	−2.83593	+	0.921448i
$780$	−22.8918			−0.819656
$781$	−19.9220	−	31.7356i	−0.712864	−	1.13559i
$782$		−	50.1565i		−	1.79359i
$783$	4.40983	−	1.43284i	0.157594	−	0.0512055i
$784$	−19.5623	−	14.2128i	−0.698654	−	0.507602i
$785$	−23.4078	−	32.2181i	−0.835460	−	1.14991i
$786$	−20.2214	−	6.57032i	−0.721272	−	0.234355i
$787$	10.9164	+	3.54696i	0.389128	+	0.126435i	0.497045	−	0.867725i	$-0.334418\pi$
$787$	10.9164	+	3.54696i	0.389128	+	0.126435i	−0.107917	+	0.994160i	$0.534418\pi$
$788$	−13.4011	+	9.73645i	−0.477393	+	0.346847i
$789$	−24.5933	−	17.8681i	−0.875545	−	0.636120i
$790$	−57.3355	−	30.9565i	−2.03991	−	1.10138i
$791$			8.78402i			0.312324i
$792$	4.33282	+	6.90215i	0.153960	+	0.245257i
$793$		−	13.2276i		−	0.469727i
$794$	33.8435	−	10.9964i	1.20106	−	0.390248i
$795$		0			0
$796$	−14.6323	−	20.1397i	−0.518629	−	0.713831i
$797$	21.4896	+	6.98240i	0.761201	+	0.247329i	0.663794	−	0.747915i	$-0.268945\pi$
$797$	21.4896	+	6.98240i	0.761201	+	0.247329i	0.0974070	+	0.995245i	$0.468945\pi$
$798$	46.1803	+	15.0049i	1.63477	+	0.531168i
$799$	13.2295	+	18.2088i	0.468026	+	0.644182i
$800$	42.4615	−	58.4432i	1.50124	−	2.06628i
$801$	2.33688	+	7.19218i	0.0825696	+	0.254123i
$802$	−13.7146			−0.484279
$803$	0.163119	−	2.40414i	0.00575634	−	0.0848403i
$804$		−	48.8230i		−	1.72185i
$805$	−6.46976	−	19.9119i	−0.228029	−	0.701801i
$806$	−8.09017	−	5.87785i	−0.284964	−	0.207039i
$807$	20.4380	+	28.1305i	0.719452	+	0.990240i
$808$	0.0385072	−	0.118513i	0.00135468	−	0.00416927i
$809$	17.2361	+	5.60034i	0.605988	+	0.196897i	0.595909	−	0.803052i	$-0.296792\pi$
$809$	17.2361	+	5.60034i	0.605988	+	0.196897i	0.0100787	+	0.999949i	$0.496792\pi$
$810$	−33.2148	−	45.7162i	−1.16705	−	1.60630i
$811$	−22.9894	+	31.6421i	−0.807266	+	1.11111i	0.184474	+	0.982837i	$0.440942\pi$
$811$	−22.9894	+	31.6421i	−0.807266	+	1.11111i	−0.991740	+	0.128268i	$0.959058\pi$
$812$	−3.19098	−	9.82084i	−0.111982	−	0.344644i
$813$			30.0098i			1.05249i
$814$	14.0651	+	55.9193i	0.492983	+	1.95997i
$815$	75.7426			2.65315
$816$	−71.5304	+	23.2416i	−2.50406	+	0.813620i
$817$	51.7231	−	71.1907i	1.80956	−	2.49065i
$818$	41.4116	+	56.9981i	1.44792	+	1.99289i
$819$	6.20737	+	2.01690i	0.216903	+	0.0704761i
$820$	−21.0792	+	64.8751i	−0.736117	+	2.26554i
$821$	−27.3369	−	37.6260i	−0.954064	−	1.31316i	−0.949699	−	0.313166i	$-0.898611\pi$
$821$	−27.3369	−	37.6260i	−0.954064	−	1.31316i	−0.00436519	−	0.999990i	$-0.501389\pi$
$822$	−43.4549	+	59.8106i	−1.51566	+	2.08613i
$823$	−10.9614	+	3.56159i	−0.382092	+	0.124149i	−0.493764	−	0.869596i	$-0.664379\pi$
$823$	−10.9614	+	3.56159i	−0.382092	+	0.124149i	0.111672	+	0.993745i	$0.464379\pi$
$824$	−4.37194			−0.152304
$825$	76.6158	+	30.7706i	2.66742	+	1.07130i
$826$	10.3262			0.359296
$827$	5.91671	+	18.2098i	0.205744	+	0.633216i	0.999682	+	0.0252166i	$0.00802753\pi$
$827$	5.91671	+	18.2098i	0.205744	+	0.633216i	−0.793938	+	0.607999i	$0.791972\pi$
$828$	−18.1074	−	13.1558i	−0.629275	−	0.457195i
$829$	−5.58905	−	7.69266i	−0.194116	−	0.267177i	0.700854	−	0.713305i	$-0.252803\pi$
$829$	−5.58905	−	7.69266i	−0.194116	−	0.267177i	−0.894969	+	0.446128i	$0.852803\pi$
$830$	−17.6246	+	54.2430i	−0.611759	+	1.88280i
$831$	−6.20737	+	19.1043i	−0.215331	+	0.662721i
$832$	−4.02129	−	5.53483i	−0.139413	−	0.191886i
$833$	27.3094	+	19.8415i	0.946216	+	0.687466i
$834$	−10.3262	−	31.7809i	−0.357568	−	1.10048i
$835$		−	2.39163i		−	0.0827658i
$836$	26.1803	−	31.3319i	0.905466	−	1.08364i
$837$			3.49120i			0.120673i
$838$	14.4157	+	44.3669i	0.497981	+	1.53263i
$839$	−17.2984	−	12.5680i	−0.597206	−	0.433896i	0.247680	−	0.968842i	$-0.420332\pi$
$839$	−17.2984	−	12.5680i	−0.597206	−	0.433896i	−0.844886	+	0.534946i	$0.820332\pi$
$840$	−7.60081	+	5.52231i	−0.262253	+	0.190538i
$841$	−1.82624	+	5.62058i	−0.0629737	+	0.193813i
$842$	−33.5172	−	10.8904i	−1.15508	−	0.375308i
$843$	−28.6974	+	20.8499i	−0.988393	+	0.718109i
$844$	−5.62605	−	4.08757i	−0.193657	−	0.140700i
$845$	12.9681	+	39.9116i	0.446115	+	1.37300i
$846$	22.4585			0.772138
$847$	10.5510	+	10.1050i	0.362538	+	0.347213i
$848$		0			0
$849$	−4.88797	−	15.0436i	−0.167755	−	0.516296i
$850$	−71.0267	+	97.7599i	−2.43620	+	3.35314i
$851$	21.9740	+	30.2447i	0.753260	+	1.03677i
$852$	14.2705	−	43.9201i	0.488900	−	1.50468i
$853$	2.36560	−	7.28058i	0.0809968	−	0.249282i	−0.902355	−	0.430993i	$-0.858163\pi$
$853$	2.36560	−	7.28058i	0.0809968	−	0.249282i	0.983352	+	0.181711i	$0.0581634\pi$
$854$	13.5172	+	18.6049i	0.462550	+	0.636645i
$855$	−58.2918	+	80.2318i	−1.99354	+	2.74387i
$856$	3.67086	−	1.19274i	0.125468	−	0.0407669i
$857$			48.3449i			1.65143i	0.564088	+	0.825715i	$0.309228\pi$
$857$			48.3449i			1.65143i	−0.564088	+	0.825715i	$0.690772\pi$
$858$	14.8490	−	17.7708i	0.506935	−	0.606685i
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	−22.2876	−	68.5941i	−0.760000	−	2.33904i
$861$	21.5724	−	29.6918i	0.735184	−	1.01189i
$862$	5.85410	−	4.25325i	0.199392	−	0.144866i
$863$	−15.2467	+	46.9246i	−0.519004	+	1.59733i	0.256872	+	0.966445i	$0.417308\pi$
$863$	−15.2467	+	46.9246i	−0.519004	+	1.59733i	−0.775876	+	0.630885i	$0.782692\pi$
$864$	−2.18597	+	6.72772i	−0.0743681	+	0.228882i
$865$	−27.4063	+	19.9119i	−0.931843	+	0.677024i
$866$	−19.5729	+	26.9399i	−0.665116	+	0.915453i
$867$	59.0137	−	19.1747i	2.00421	−	0.651207i
$868$	7.77501			0.263901
$869$	27.3796	−	10.9250i	0.928790	−	0.370607i
$870$	88.9919			3.01711
$871$	16.5066	−	5.36331i	0.559304	−	0.181729i
$872$	3.75361	−	5.16641i	0.127113	−	0.174957i
$873$	−5.47214	+	3.97574i	−0.185204	+	0.134558i
$874$	18.2918	−	56.2964i	0.618729	−	1.90425i
$875$	−7.67813	+	23.6308i	−0.259568	+	0.798869i
$876$	2.40261	−	1.74560i	0.0811767	−	0.0589783i
$877$	−5.65248	+	7.77997i	−0.190871	+	0.262711i	−0.893717	−	0.448630i	$-0.851912\pi$
$877$	−5.65248	+	7.77997i	−0.190871	+	0.262711i	0.702847	+	0.711341i	$0.251912\pi$
$878$	−19.2705	−	59.3085i	−0.650348	−	2.00157i
$879$		−	19.3391i		−	0.652293i
$880$	14.3992	+	57.2474i	0.485396	+	1.92981i
$881$		−	19.6137i		−	0.660801i	−0.943841	−	0.330401i	$-0.892816\pi$
$881$		−	19.6137i		−	0.660801i	0.943841	−	0.330401i	$-0.107184\pi$
$882$	32.0344	−	10.4086i	1.07866	−	0.350477i
$883$	3.75361	−	5.16641i	0.126319	−	0.173863i	−0.741173	−	0.671314i	$-0.765730\pi$
$883$	3.75361	−	5.16641i	0.126319	−	0.173863i	0.867492	+	0.497450i	$0.165730\pi$
$884$	8.90937	+	12.2627i	0.299655	+	0.412439i
$885$	−12.2984	+	37.8505i	−0.413405	+	1.27233i
$886$	3.53697	−	10.8857i	0.118827	−	0.365711i
$887$	−6.80902	−	9.37181i	−0.228624	−	0.314675i	0.679258	−	0.733900i	$-0.262302\pi$
$887$	−6.80902	−	9.37181i	−0.228624	−	0.314675i	−0.907882	+	0.419225i	$0.862302\pi$
$888$	9.86068	−	13.5721i	0.330903	−	0.455449i
$889$	4.95492	+	15.2497i	0.166183	+	0.511457i
$890$			16.3925i			0.549477i
$891$	25.5066	+	1.73060i	0.854503	+	0.0579773i
$892$	11.9443			0.399924
$893$	8.20830	+	25.2626i	0.274680	+	0.845379i
$894$	−1.21885	−	0.885544i	−0.0407643	−	0.0296170i
$895$	−57.8779	+	42.0508i	−1.93464	+	1.40560i
$896$	−7.20783	−	2.34197i	−0.240797	−	0.0782396i
$897$	4.63972	−	14.2796i	0.154916	−	0.476782i
$898$	−50.8881	+	36.9724i	−1.69816	+	1.23378i
$899$	14.0651	+	10.2189i	0.469098	+	0.340820i
$900$	16.6631	+	51.2838i	0.555437	+	1.70946i
$901$		0			0
$902$	−36.6891	−	58.4456i	−1.22161	−	1.94602i
$903$			38.8050i			1.29135i
$904$	−1.48490	−	4.57004i	−0.0493869	−	0.151997i
$905$	−7.70820	−	5.60034i	−0.256229	−	0.186162i
$906$	−52.9402	−	72.8659i	−1.75882	−	2.42081i
$907$	−4.87132	+	14.9924i	−0.161750	+	0.497814i	−0.998782	−	0.0493391i	$-0.984289\pi$
$907$	−4.87132	+	14.9924i	−0.161750	+	0.497814i	0.837032	+	0.547153i	$0.184289\pi$
$908$	11.3490	−	34.9286i	0.376630	−	1.15915i
$909$	0.340946	+	0.469272i	0.0113085	+	0.0155648i
$910$	11.4459	+	8.31592i	0.379427	+	0.275670i
$911$	−4.89919	−	15.0781i	−0.162317	−	0.499561i	0.836511	−	0.547950i	$-0.184591\pi$
$911$	−4.89919	−	15.0781i	−0.162317	−	0.499561i	−0.998829	+	0.0483884i	$0.984591\pi$
$912$	−88.7627			−2.93923
$913$	−13.7188	−	21.8541i	−0.454028	−	0.723264i
$914$	−65.7771			−2.17571
$915$	−84.2943	+	27.3889i	−2.78668	+	0.905448i
$916$	−21.2730	+	29.2797i	−0.702879	+	0.967429i
$917$	3.45422	+	4.75433i	0.114068	+	0.157002i
$918$	3.65654	−	11.2537i	0.120684	−	0.371427i
$919$	24.8369	+	8.06999i	0.819293	+	0.266204i	0.688529	−	0.725209i	$-0.258257\pi$
$919$	24.8369	+	8.06999i	0.819293	+	0.266204i	0.130764	+	0.991413i	$0.458257\pi$
$920$	6.73200	+	9.26581i	0.221948	+	0.305485i
$921$	−11.8328	+	16.2865i	−0.389905	+	0.536658i
$922$	−27.3464	+	8.88540i	−0.900607	+	0.292625i
$923$	16.4166			0.540359
$924$	−1.21885	+	17.9641i	−0.0400971	+	0.590975i
$925$		−	90.0673i		−	2.96139i
$926$	15.7667	+	48.5248i	0.518125	+	1.59462i
$927$	11.9619	−	16.4642i	0.392881	−	0.540754i
$928$	20.7058	+	28.4991i	0.679701	+	0.935528i
$929$	−30.1823	−	9.80684i	−0.990251	−	0.321752i	−0.231287	−	0.972885i	$-0.574294\pi$
$929$	−30.1823	−	9.80684i	−0.990251	−	0.321752i	−0.758963	+	0.651134i	$0.774294\pi$
$930$	−20.7058	+	63.7259i	−0.678970	+	2.08965i
$931$	23.4164	+	32.2299i	0.767442	+	1.05629i
$932$	32.5251	+	23.6308i	1.06539	+	0.774054i
$933$	9.39512	+	28.9152i	0.307582	+	0.946642i
$934$		−	39.3489i		−	1.28753i
$935$	−20.1016	−	79.9187i	−0.657393	−	2.61362i
$936$	−3.57044			−0.116703
$937$	−11.7224	−	36.0778i	−0.382954	−	1.17861i	−0.937954	−	0.346761i	$-0.887282\pi$
$937$	−11.7224	−	36.0778i	−0.382954	−	1.17861i	0.554999	−	0.831851i	$-0.312718\pi$
$938$	−17.7360	+	24.4115i	−0.579101	+	0.797064i
$939$	8.90937	+	12.2627i	0.290746	+	0.400178i
$940$	20.7058	+	6.72772i	0.675348	+	0.219434i
$941$	56.2426	+	18.2743i	1.83346	+	0.595727i	0.999003	+	0.0446508i	$0.0142175\pi$
$941$	56.2426	+	18.2743i	1.83346	+	0.595727i	0.834455	+	0.551076i	$0.185782\pi$
$942$	29.1844	+	40.1689i	0.950879	+	1.30877i
$943$	−36.1959	−	26.2979i	−1.17870	−	0.856377i
$944$	−17.9526	+	5.83317i	−0.584309	+	0.189853i
$945$		−	4.93931i		−	0.160676i
$946$	67.7064	+	27.1924i	2.20133	+	0.884103i
$947$		−	28.1574i		−	0.914992i	−0.889212	−	0.457496i	$-0.848746\pi$
$947$		−	28.1574i		−	0.914992i	0.889212	−	0.457496i	$-0.151254\pi$
$948$	31.9690	+	17.2607i	1.03831	+	0.560600i
$949$	0.854102	+	0.620541i	0.0277253	+	0.0201436i
$950$	−115.374	+	83.8240i	−3.74322	+	2.71961i
$951$	35.8225	+	11.6394i	1.16163	+	0.377435i
$952$	5.91641	+	1.92236i	0.191752	+	0.0623040i
$953$	−4.53444	−	6.24112i	−0.146885	−	0.202170i	0.729234	−	0.684264i	$-0.239876\pi$
$953$	−4.53444	−	6.24112i	−0.146885	−	0.202170i	−0.876119	+	0.482094i	$0.839876\pi$
$954$		0			0
$955$	94.7851	−	30.7975i	3.06717	−	0.996585i
$956$		−	14.3844i		−	0.465223i
$957$	−25.8156	+	30.8953i	−0.834500	+	0.998705i
$958$	−44.2705			−1.43032
$959$	19.4336	−	6.31437i	0.627545	−	0.203902i
$960$	−26.9448	+	37.0863i	−0.869639	+	1.19695i
$961$	14.4894	−	10.5271i	0.467399	−	0.339585i
$962$	−24.0261	−	7.80656i	−0.774633	−	0.251694i
$963$	−5.55204	+	17.0874i	−0.178912	+	0.550634i
$964$	19.0451	+	26.2133i	0.613401	+	0.844274i
$965$	−45.9261	−	33.3673i	−1.47841	−	1.07413i
$966$	8.06637	+	24.8257i	0.259531	+	0.798755i
$967$		−	34.6871i		−	1.11546i	−0.830022	−	0.557730i	$-0.811672\pi$
$967$		−	34.6871i		−	1.11546i	0.830022	−	0.557730i	$-0.188328\pi$
$968$	−7.19756	−	3.47371i	−0.231338	−	0.111649i
$969$	123.915			3.98072
$970$	−13.9443	+	4.53077i	−0.447724	+	0.145474i
$971$	−12.8262	−	9.31881i	−0.411614	−	0.299055i	0.362641	−	0.931929i	$-0.381875\pi$
$971$	−12.8262	−	9.31881i	−0.411614	−	0.299055i	−0.774255	+	0.632874i	$0.781875\pi$
$972$	21.2730	+	29.2797i	0.682331	+	0.939148i
$973$	−2.85410	+	8.78402i	−0.0914983	+	0.281603i
$974$	29.7984	+	9.68208i	0.954801	+	0.310234i
$975$	−29.2646	+	21.2620i	−0.937218	+	0.680929i
$976$	−34.0100	−	24.7097i	−1.08863	−	0.790938i
$977$	−2.96979	+	0.964944i	−0.0950120	+	0.0308713i	−0.356137	−	0.934434i	$-0.615906\pi$
$977$	−2.96979	+	0.964944i	−0.0950120	+	0.0308713i	0.261125	+	0.965305i	$0.415906\pi$
$978$	−94.4345			−3.01968
$979$	−5.69098	−	4.75528i	−0.181885	−	0.151979i
$980$	32.6525			1.04305
$981$	9.18590	+	28.2713i	0.293283	+	0.902633i
$982$	−7.90891	+	10.8857i	−0.252383	+	0.347376i
$983$	−0.834966	−	1.14923i	−0.0266313	−	0.0366548i	0.795494	−	0.605962i	$-0.207212\pi$
$983$	−0.834966	−	1.14923i	−0.0266313	−	0.0366548i	−0.822125	+	0.569307i	$0.807212\pi$
$984$	−6.20414	+	19.0944i	−0.197781	+	0.608706i
$985$	−12.1927	+	37.5253i	−0.388492	+	1.19565i
$986$	−34.6353	−	47.6713i	−1.10301	−	1.51816i
$987$	−9.47655	−	6.88512i	−0.301642	−	0.219156i
$988$	5.52786	+	17.0130i	0.175865	+	0.541256i
$989$	47.3054			1.50422
$990$	−76.3050	−	30.6458i	−2.42513	−	0.973988i
$991$			24.8940i			0.790783i	0.918513	+	0.395392i	$0.129391\pi$
$991$			24.8940i			0.790783i	−0.918513	+	0.395392i	$0.870609\pi$
$992$	−25.2254	+	8.19624i	−0.800908	+	0.260231i
$993$	19.1459	+	13.9103i	0.607577	+	0.441430i
$994$	−23.0902	+	16.7760i	−0.732376	+	0.532102i
$995$	−56.3944	−	18.3237i	−1.78782	−	0.580899i
$996$	9.82709	−	30.2447i	0.311383	−	0.958339i
$997$	−6.34346	−	8.73102i	−0.200899	−	0.276514i	0.696666	−	0.717396i	$-0.254666\pi$
$997$	−6.34346	−	8.73102i	−0.200899	−	0.276514i	−0.897565	+	0.440881i	$0.854666\pi$
$998$	13.3926	−	18.4333i	0.423936	−	0.583497i
$999$	2.72542	+	8.38800i	0.0862286	+	0.265384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	869.2.l.a.710.1	yes	8
11.2	odd	10	inner	869.2.l.a.552.2	yes	8
79.78	odd	2	inner	869.2.l.a.710.2	yes	8
869.552	even	10	inner	869.2.l.a.552.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
869.2.l.a.552.1	✓	8	869.552	even	10	inner
869.2.l.a.552.2	yes	8	11.2	odd	10	inner
869.2.l.a.710.1	yes	8	1.1	even	1	trivial
869.2.l.a.710.2	yes	8	79.78	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 869 = 11 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	869.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 - 0.587785i) q^{2} +(-1.48490 + 2.04378i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.19098 - 3.66547i) q^{5} +(-1.48490 + 4.57004i) q^{6} +(1.07448 - 0.780656i) q^{7} +(-0.427051 + 0.587785i) q^{8} +(-1.04508 - 3.21644i) q^{9} +O(q^{10})\)	\(q+(1.80902 - 0.587785i) q^{2} +(-1.48490 + 2.04378i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.19098 - 3.66547i) q^{5} +(-1.48490 + 4.57004i) q^{6} +(1.07448 - 0.780656i) q^{7} +(-0.427051 + 0.587785i) q^{8} +(-1.04508 - 3.21644i) q^{9} -7.33094i q^{10} +(2.54508 + 2.12663i) q^{11} +4.08757i q^{12} +(-1.38197 + 0.449028i) q^{13} +(1.48490 - 2.04378i) q^{14} +(5.72294 + 7.87695i) q^{15} +(-1.42705 + 4.39201i) q^{16} +(1.99220 - 6.13135i) q^{17} +(-3.78115 - 5.20431i) q^{18} +(4.47214 - 6.15537i) q^{19} +(-1.92705 - 5.93085i) q^{20} +3.35520i q^{21} +(5.85410 + 2.35114i) q^{22} +4.09017 q^{23} +(-0.567180 - 1.74560i) q^{24} +(-7.97214 - 5.79210i) q^{25} +(-2.23607 + 1.62460i) q^{26} +(0.917716 + 0.298184i) q^{27} +(0.664066 - 2.04378i) q^{28} +(3.88751 - 2.82444i) q^{29} +(14.9828 + 10.8857i) q^{30} +(1.11803 + 3.44095i) q^{31} +7.33094i q^{32} +(-8.12555 + 2.04378i) q^{33} -12.2627i q^{34} +(-1.58178 - 4.86822i) q^{35} +(-4.42705 - 3.21644i) q^{36} +(5.37240 + 7.39448i) q^{37} +(4.47214 - 13.7638i) q^{38} +(1.13436 - 3.49120i) q^{39} +(1.64590 + 2.26538i) q^{40} +(-8.84950 - 6.42953i) q^{41} +(1.97214 + 6.06961i) q^{42} +11.5656 q^{43} +(5.35410 + 0.363271i) q^{44} -13.0344 q^{45} +(7.39919 - 2.40414i) q^{46} +(-2.05208 + 2.82444i) q^{47} +(-6.85730 - 9.43826i) q^{48} +(-1.61803 + 4.97980i) q^{49} +(-17.8262 - 5.79210i) q^{50} +(9.57295 + 13.1760i) q^{51} +(-1.38197 + 1.90211i) q^{52} +1.83543 q^{54} +(10.8262 - 6.79615i) q^{55} +0.964944i q^{56} +(5.93958 + 18.2802i) q^{57} +(5.37240 - 7.39448i) q^{58} +(2.40261 + 3.30691i) q^{59} +(14.9828 + 4.86822i) q^{60} +(-2.81303 + 8.65761i) q^{61} +(4.04508 + 5.56758i) q^{62} +(-3.63386 - 2.64015i) q^{63} +(1.45492 + 4.47777i) q^{64} +5.60034i q^{65} +(-13.4980 + 8.47332i) q^{66} -11.9443 q^{67} +(-3.22344 - 9.92073i) q^{68} +(-6.07348 + 8.35942i) q^{69} +(-5.72294 - 7.87695i) q^{70} +(-10.7448 - 3.49120i) q^{71} +(2.33688 + 0.759299i) q^{72} +(-0.427051 - 0.587785i) q^{73} +(14.0651 + 10.2189i) q^{74} +(23.6756 - 7.69266i) q^{75} -12.3107i q^{76} +(4.39481 + 0.298184i) q^{77} -6.98240i q^{78} +(4.22272 - 7.82104i) q^{79} +(14.3992 + 10.4616i) q^{80} +(6.23607 - 4.53077i) q^{81} +(-19.7881 - 6.42953i) q^{82} +(-7.39919 - 2.40414i) q^{83} +(3.19098 + 4.39201i) q^{84} +(-20.1016 - 14.6047i) q^{85} +(20.9224 - 6.79811i) q^{86} +12.1392i q^{87} +(-2.33688 + 0.587785i) q^{88} -2.23607 q^{89} +(-23.5795 + 7.66145i) q^{90} +(-1.13436 + 1.56131i) q^{91} +(5.35410 - 3.88998i) q^{92} +(-8.69273 - 2.82444i) q^{93} +(-2.05208 + 6.31564i) q^{94} +(-17.2361 - 23.7234i) q^{95} +(-14.9828 - 10.8857i) q^{96} +(-0.618034 - 1.90211i) q^{97} +9.95959i q^{98} +(4.18034 - 10.4086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 6 q^{4} + 14 q^{5} + 10 q^{8} + 14 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 6 * q^4 + 14 * q^5 + 10 * q^8 + 14 * q^9	\( 8 q + 10 q^{2} + 6 q^{4} + 14 q^{5} + 10 q^{8} + 14 q^{9} - 2 q^{11} - 20 q^{13} + 2 q^{16} + 10 q^{18} - 2 q^{20} + 20 q^{22} - 12 q^{23} - 28 q^{25} - 22 q^{36} + 40 q^{40} - 20 q^{42} + 16 q^{44} + 12 q^{45} + 10 q^{46} - 4 q^{49} - 80 q^{50} + 90 q^{51} - 20 q^{52} + 24 q^{55} + 10 q^{62} + 34 q^{64} - 24 q^{67} + 50 q^{72} + 10 q^{73} + 40 q^{79} + 66 q^{80} + 32 q^{81} - 10 q^{83} + 30 q^{84} - 50 q^{88} - 50 q^{90} + 16 q^{92} - 120 q^{95} + 4 q^{97} - 56 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 6 * q^4 + 14 * q^5 + 10 * q^8 + 14 * q^9 - 2 * q^11 - 20 * q^13 + 2 * q^16 + 10 * q^18 - 2 * q^20 + 20 * q^22 - 12 * q^23 - 28 * q^25 - 22 * q^36 + 40 * q^40 - 20 * q^42 + 16 * q^44 + 12 * q^45 + 10 * q^46 - 4 * q^49 - 80 * q^50 + 90 * q^51 - 20 * q^52 + 24 * q^55 + 10 * q^62 + 34 * q^64 - 24 * q^67 + 50 * q^72 + 10 * q^73 + 40 * q^79 + 66 * q^80 + 32 * q^81 - 10 * q^83 + 30 * q^84 - 50 * q^88 - 50 * q^90 + 16 * q^92 - 120 * q^95 + 4 * q^97 - 56 * q^99

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