LMFDB - Embedded newform 170.2.n.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.3
Root			$0.236338 - 0.0978946i$ of defining polynomial
Character	$\chi$	$=$	170.19
Dual form			170.2.n.b.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.0978946 + 0.236338i) q^{3} -1.00000i q^{4} +(-1.19048 - 1.89281i) q^{5} +(0.236338 + 0.0978946i) q^{6} +(3.48449 + 1.44332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07505 - 2.07505i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.0978946 + 0.236338i) q^{3} -1.00000i q^{4} +(-1.19048 - 1.89281i) q^{5} +(0.236338 + 0.0978946i) q^{6} +(3.48449 + 1.44332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07505 - 2.07505i) q^{9} +(-2.18022 - 0.496623i) q^{10} +(-3.09654 - 1.28263i) q^{11} +(0.236338 - 0.0978946i) q^{12} +0.0184233 q^{13} +(3.48449 - 1.44332i) q^{14} +(0.330803 - 0.466653i) q^{15} -1.00000 q^{16} +(-2.88005 + 2.95048i) q^{17} -2.93456i q^{18} +(4.04837 + 4.04837i) q^{19} +(-1.89281 + 1.19048i) q^{20} +0.964811i q^{21} +(-3.09654 + 1.28263i) q^{22} +(-2.00137 + 4.83175i) q^{23} +(0.0978946 - 0.236338i) q^{24} +(-2.16549 + 4.50673i) q^{25} +(0.0130272 - 0.0130272i) q^{26} +(1.40256 + 0.580961i) q^{27} +(1.44332 - 3.48449i) q^{28} +(-0.238317 - 0.575348i) q^{29} +(-0.0960608 - 0.563887i) q^{30} +(-0.958512 + 0.397029i) q^{31} +(-0.707107 + 0.707107i) q^{32} -0.857395i q^{33} +(0.0498002 + 4.12280i) q^{34} +(-1.41629 - 8.31374i) q^{35} +(-2.07505 - 2.07505i) q^{36} +(-1.49475 - 3.60864i) q^{37} +5.72526 q^{38} +(0.00180354 + 0.00435413i) q^{39} +(-0.496623 + 2.18022i) q^{40} +(-2.68162 + 6.47400i) q^{41} +(0.682224 + 0.682224i) q^{42} +(-3.22622 - 3.22622i) q^{43} +(-1.28263 + 3.09654i) q^{44} +(-6.39799 - 1.45737i) q^{45} +(2.00137 + 4.83175i) q^{46} +9.78698 q^{47} +(-0.0978946 - 0.236338i) q^{48} +(5.10871 + 5.10871i) q^{49} +(1.65550 + 4.71798i) q^{50} +(-0.979252 - 0.391831i) q^{51} -0.0184233i q^{52} +(-9.03342 + 9.03342i) q^{53} +(1.40256 - 0.580961i) q^{54} +(1.25860 + 7.38814i) q^{55} +(-1.44332 - 3.48449i) q^{56} +(-0.560472 + 1.35310i) q^{57} +(-0.575348 - 0.238317i) q^{58} +(10.1864 - 10.1864i) q^{59} +(-0.466653 - 0.330803i) q^{60} +(2.19720 - 5.30451i) q^{61} +(-0.397029 + 0.958512i) q^{62} +(10.2254 - 4.23551i) q^{63} +1.00000i q^{64} +(-0.0219326 - 0.0348718i) q^{65} +(-0.606270 - 0.606270i) q^{66} -11.7199i q^{67} +(2.95048 + 2.88005i) q^{68} -1.33785 q^{69} +(-6.88016 - 4.87723i) q^{70} +(-3.61871 + 1.49892i) q^{71} -2.93456 q^{72} +(-9.33558 + 3.86692i) q^{73} +(-3.60864 - 1.49475i) q^{74} +(-1.27710 - 0.0706050i) q^{75} +(4.04837 - 4.04837i) q^{76} +(-8.93861 - 8.93861i) q^{77} +(0.00435413 + 0.00180354i) q^{78} +(4.92071 + 2.03822i) q^{79} +(1.19048 + 1.89281i) q^{80} -8.41533i q^{81} +(2.68162 + 6.47400i) q^{82} +(-0.848148 + 0.848148i) q^{83} +0.964811 q^{84} +(9.01336 + 1.93890i) q^{85} -4.56256 q^{86} +(0.112647 - 0.112647i) q^{87} +(1.28263 + 3.09654i) q^{88} -14.4887i q^{89} +(-5.55458 + 3.49355i) q^{90} +(0.0641956 + 0.0265907i) q^{91} +(4.83175 + 2.00137i) q^{92} +(-0.187666 - 0.187666i) q^{93} +(6.92044 - 6.92044i) q^{94} +(2.84330 - 12.4823i) q^{95} +(-0.236338 - 0.0978946i) q^{96} +(-6.49752 + 2.69136i) q^{97} +7.22481 q^{98} +(-9.08700 + 3.76396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^25 - 12 * q^26 - 24 * q^27 - 12 * q^29 + 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 8 * q^37 + 8 * q^38 - 4 * q^40 + 4 * q^41 - 8 * q^42 - 16 * q^43 - 8 * q^44 - 32 * q^45 + 16 * q^46 - 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 - 44 * q^53 - 24 * q^54 + 72 * q^57 + 16 * q^59 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.0978946	+	0.236338i	0.0565195	+	0.136450i	0.949617	−	0.313414i	$-0.101473\pi$
$3$	0.0978946	+	0.236338i	0.0565195	+	0.136450i	−0.893097	+	0.449864i	$0.851473\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.19048	−	1.89281i	−0.532401	−	0.846492i
$5$	−1.19048	−	1.89281i	−0.532401	−	0.846492i
$6$	0.236338	+	0.0978946i	0.0964847	+	0.0399653i
$7$	3.48449	+	1.44332i	1.31701	+	0.545524i	0.926922	−	0.375253i	$-0.122444\pi$
$7$	3.48449	+	1.44332i	1.31701	+	0.545524i	0.390089	+	0.920777i	$0.372444\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.07505	−	2.07505i	0.691683	−	0.691683i
$10$	−2.18022	−	0.496623i	−0.689447	−	0.157046i
$11$	−3.09654	−	1.28263i	−0.933643	−	0.386728i	−0.136584	−	0.990629i	$-0.543612\pi$
$11$	−3.09654	−	1.28263i	−0.933643	−	0.386728i	−0.797059	+	0.603901i	$0.793612\pi$
$12$	0.236338	−	0.0978946i	0.0682250	−	0.0282597i
$13$	0.0184233			0.00510970			0.00255485	−	0.999997i	$-0.499187\pi$
$13$	0.0184233			0.00510970			0.00255485	+	0.999997i	$0.499187\pi$
$14$	3.48449	−	1.44332i	0.931268	−	0.385744i
$15$	0.330803	−	0.466653i	0.0854129	−	0.120489i
$16$	−1.00000			−0.250000
$17$	−2.88005	+	2.95048i	−0.698515	+	0.715596i
$17$	−2.88005	+	2.95048i	−0.698515	+	0.715596i
$18$		−	2.93456i		−	0.691683i
$19$	4.04837	+	4.04837i	0.928760	+	0.928760i	0.997626	−	0.0688657i	$-0.0219380\pi$
$19$	4.04837	+	4.04837i	0.928760	+	0.928760i	−0.0688657	+	0.997626i	$0.521938\pi$
$20$	−1.89281	+	1.19048i	−0.423246	+	0.266200i
$21$			0.964811i			0.210539i
$22$	−3.09654	+	1.28263i	−0.660185	+	0.273458i
$23$	−2.00137	+	4.83175i	−0.417315	+	1.00749i	0.565807	+	0.824538i	$0.308565\pi$
$23$	−2.00137	+	4.83175i	−0.417315	+	1.00749i	−0.983122	+	0.182951i	$0.941435\pi$
$24$	0.0978946	−	0.236338i	0.0199826	−	0.0482424i
$25$	−2.16549	+	4.50673i	−0.433099	+	0.901346i
$26$	0.0130272	−	0.0130272i	0.00255485	−	0.00255485i
$27$	1.40256	+	0.580961i	0.269924	+	0.111806i
$28$	1.44332	−	3.48449i	0.272762	−	0.658506i
$29$	−0.238317	−	0.575348i	−0.0442543	−	0.106839i	0.900207	−	0.435463i	$-0.143415\pi$
$29$	−0.238317	−	0.575348i	−0.0442543	−	0.106839i	−0.944461	+	0.328624i	$0.893415\pi$
$30$	−0.0960608	−	0.563887i	−0.0175382	−	0.102951i
$31$	−0.958512	+	0.397029i	−0.172154	+	0.0713085i	−0.467096	−	0.884207i	$-0.654700\pi$
$31$	−0.958512	+	0.397029i	−0.172154	+	0.0713085i	0.294942	+	0.955515i	$0.404700\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		−	0.857395i		−	0.149253i
$34$	0.0498002	+	4.12280i	0.00854067	+	0.707055i
$35$	−1.41629	−	8.31374i	−0.239396	−	1.40528i
$36$	−2.07505	−	2.07505i	−0.345841	−	0.345841i
$37$	−1.49475	−	3.60864i	−0.245735	−	0.593257i	0.752098	−	0.659051i	$-0.229042\pi$
$37$	−1.49475	−	3.60864i	−0.245735	−	0.593257i	−0.997833	+	0.0657942i	$0.979042\pi$
$38$	5.72526			0.928760
$39$	0.00180354	+	0.00435413i	0.000288797	+	0.000697218i
$40$	−0.496623	+	2.18022i	−0.0785229	+	0.344723i
$41$	−2.68162	+	6.47400i	−0.418799	+	1.01107i	0.563897	+	0.825845i	$0.309301\pi$
$41$	−2.68162	+	6.47400i	−0.418799	+	1.01107i	−0.982696	+	0.185225i	$0.940699\pi$
$42$	0.682224	+	0.682224i	0.105270	+	0.105270i
$43$	−3.22622	−	3.22622i	−0.491994	−	0.491994i	0.416940	−	0.908934i	$-0.363102\pi$
$43$	−3.22622	−	3.22622i	−0.491994	−	0.491994i	−0.908934	+	0.416940i	$0.863102\pi$
$44$	−1.28263	+	3.09654i	−0.193364	+	0.466822i
$45$	−6.39799	−	1.45737i	−0.953756	−	0.217252i
$46$	2.00137	+	4.83175i	0.295087	+	0.712402i
$47$	9.78698			1.42758			0.713789	−	0.700361i	$-0.246978\pi$
$47$	9.78698			1.42758			0.713789	+	0.700361i	$0.246978\pi$
$48$	−0.0978946	−	0.236338i	−0.0141299	−	0.0341125i
$49$	5.10871	+	5.10871i	0.729816	+	0.729816i
$50$	1.65550	+	4.71798i	0.234124	+	0.667223i
$51$	−0.979252	−	0.391831i	−0.137123	−	0.0548672i
$52$		−	0.0184233i		−	0.00255485i
$53$	−9.03342	+	9.03342i	−1.24084	+	1.24084i	−0.281180	+	0.959655i	$0.590726\pi$
$53$	−9.03342	+	9.03342i	−1.24084	+	1.24084i	−0.959655	+	0.281180i	$0.909274\pi$
$54$	1.40256	−	0.580961i	0.190865	−	0.0790588i
$55$	1.25860	+	7.38814i	0.169710	+	0.996216i
$56$	−1.44332	−	3.48449i	−0.192872	−	0.465634i
$57$	−0.560472	+	1.35310i	−0.0742363	+	0.179222i
$58$	−0.575348	−	0.238317i	−0.0755468	−	0.0312925i
$59$	10.1864	−	10.1864i	1.32616	−	1.32616i	0.417466	−	0.908693i	$-0.362918\pi$
$59$	10.1864	−	10.1864i	1.32616	−	1.32616i	0.908693	−	0.417466i	$-0.137082\pi$
$60$	−0.466653	−	0.330803i	−0.0602447	−	0.0427065i
$61$	2.19720	−	5.30451i	0.281323	−	0.679173i	−0.718545	−	0.695481i	$-0.755191\pi$
$61$	2.19720	−	5.30451i	0.281323	−	0.679173i	0.999867	+	0.0163084i	$0.00519135\pi$
$62$	−0.397029	+	0.958512i	−0.0504227	+	0.121731i
$63$	10.2254	−	4.23551i	1.28828	−	0.533625i
$64$			1.00000i			0.125000i
$65$	−0.0219326	−	0.0348718i	−0.00272041	−	0.00432532i
$66$	−0.606270	−	0.606270i	−0.0746266	−	0.0746266i
$67$		−	11.7199i		−	1.43182i	−0.698194	−	0.715909i	$-0.746013\pi$
$67$		−	11.7199i		−	1.43182i	0.698194	−	0.715909i	$-0.253987\pi$
$68$	2.95048	+	2.88005i	0.357798	+	0.349257i
$69$	−1.33785			−0.161058
$70$	−6.88016	−	4.87723i	−0.822337	−	0.582941i
$71$	−3.61871	+	1.49892i	−0.429462	+	0.177889i	−0.586934	−	0.809634i	$-0.699665\pi$
$71$	−3.61871	+	1.49892i	−0.429462	+	0.177889i	0.157473	+	0.987523i	$0.449665\pi$
$72$	−2.93456			−0.345841
$73$	−9.33558	+	3.86692i	−1.09265	+	0.452589i	−0.854929	−	0.518745i	$-0.826399\pi$
$73$	−9.33558	+	3.86692i	−1.09265	+	0.452589i	−0.237718	+	0.971334i	$0.576399\pi$
$74$	−3.60864	−	1.49475i	−0.419496	−	0.173761i
$75$	−1.27710	−	0.0706050i	−0.147467	−	0.00815277i
$76$	4.04837	−	4.04837i	0.464380	−	0.464380i
$77$	−8.93861	−	8.93861i	−1.01865	−	1.01865i
$78$	0.00435413	+	0.00180354i	0.000493008	+	0.000204210i
$79$	4.92071	+	2.03822i	0.553623	+	0.229318i	0.641914	−	0.766777i	$-0.278141\pi$
$79$	4.92071	+	2.03822i	0.553623	+	0.229318i	−0.0882910	+	0.996095i	$0.528141\pi$
$80$	1.19048	+	1.89281i	0.133100	+	0.211623i
$81$		−	8.41533i		−	0.935037i
$82$	2.68162	+	6.47400i	0.296135	+	0.714934i
$83$	−0.848148	+	0.848148i	−0.0930964	+	0.0930964i	−0.752121	−	0.659025i	$-0.770969\pi$
$83$	−0.848148	+	0.848148i	−0.0930964	+	0.0930964i	0.659025	+	0.752121i	$0.270969\pi$
$84$	0.964811			0.105270
$85$	9.01336	+	1.93890i	0.977636	+	0.210304i
$86$	−4.56256			−0.491994
$87$	0.112647	−	0.112647i	0.0120770	−	0.0120770i
$88$	1.28263	+	3.09654i	0.136729	+	0.330093i
$89$		−	14.4887i		−	1.53580i	−0.640572	−	0.767898i	$-0.721303\pi$
$89$		−	14.4887i		−	1.53580i	0.640572	−	0.767898i	$-0.278697\pi$
$90$	−5.55458	+	3.49355i	−0.585504	+	0.368252i
$91$	0.0641956	+	0.0265907i	0.00672953	+	0.00278746i
$92$	4.83175	+	2.00137i	0.503744	+	0.208658i
$93$	−0.187666	−	0.187666i	−0.0194601	−	0.0194601i
$94$	6.92044	−	6.92044i	0.713789	−	0.713789i
$95$	2.84330	−	12.4823i	0.291716	−	1.28066i
$96$	−0.236338	−	0.0978946i	−0.0241212	−	0.00999132i
$97$	−6.49752	+	2.69136i	−0.659723	+	0.273266i	−0.687322	−	0.726353i	$-0.741214\pi$
$97$	−6.49752	+	2.69136i	−0.659723	+	0.273266i	0.0275987	+	0.999619i	$0.491214\pi$
$98$	7.22481			0.729816
$99$	−9.08700	+	3.76396i	−0.913278	+	0.378292i
$100$	4.50673	+	2.16549i	0.450673	+	0.216549i
$101$	8.10737			0.806713			0.403357	−	0.915043i	$-0.367843\pi$
$101$	8.10737			0.806713			0.403357	+	0.915043i	$0.367843\pi$
$102$	−0.969502	+	0.415370i	−0.0959950	+	0.0411277i
$103$			4.39853i			0.433400i	0.976238	+	0.216700i	$0.0695294\pi$
$103$			4.39853i			0.433400i	−0.976238	+	0.216700i	$0.930471\pi$
$104$	−0.0130272	−	0.0130272i	−0.00127742	−	0.00127742i
$105$	1.82621	−	1.14859i	0.178220	−	0.112091i
$106$			12.7752i			1.24084i
$107$	−9.58715	+	3.97113i	−0.926825	+	0.383903i	−0.794473	−	0.607299i	$-0.792253\pi$
$107$	−9.58715	+	3.97113i	−0.926825	+	0.383903i	−0.132352	+	0.991203i	$0.542253\pi$
$108$	0.580961	−	1.40256i	0.0559030	−	0.134962i
$109$	−2.89425	+	6.98733i	−0.277219	+	0.669265i	−0.999757	−	0.0220664i	$-0.992975\pi$
$109$	−2.89425	+	6.98733i	−0.277219	+	0.669265i	0.722538	+	0.691331i	$0.242975\pi$
$110$	6.11417	+	4.33423i	0.582963	+	0.413253i
$111$	0.706533	−	0.706533i	0.0670611	−	0.0670611i
$112$	−3.48449	−	1.44332i	−0.329253	−	0.136381i
$113$	6.05130	−	14.6091i	0.569258	−	1.37431i	−0.332923	−	0.942954i	$-0.608035\pi$
$113$	6.05130	−	14.6091i	0.569258	−	1.37431i	0.902181	−	0.431357i	$-0.141965\pi$
$114$	0.560472	+	1.35310i	0.0524930	+	0.126729i
$115$	11.5282	−	1.96389i	1.07501	−	0.183133i
$116$	−0.575348	+	0.238317i	−0.0534197	+	0.0221272i
$117$	0.0382292	−	0.0382292i	0.00353429	−	0.00353429i
$118$		−	14.4058i		−	1.32616i
$119$	−14.2940	+	6.12406i	−1.31033	+	0.561392i
$120$	−0.563887	+	0.0960608i	−0.0514756	+	0.00876911i
$121$	0.165270	+	0.165270i	0.0150245	+	0.0150245i
$122$	−2.19720	−	5.30451i	−0.198925	−	0.480248i
$123$	−1.79257			−0.161631
$124$	0.397029	+	0.958512i	0.0356542	+	0.0860770i
$125$	11.1084	−	1.26631i	0.993565	−	0.113262i
$126$	4.23551	−	10.2254i	0.377330	−	0.910954i
$127$	8.11850	+	8.11850i	0.720400	+	0.720400i	0.968687	−	0.248286i	$-0.0798674\pi$
$127$	8.11850	+	8.11850i	0.720400	+	0.720400i	−0.248286	+	0.968687i	$0.579867\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.446650	−	1.07831i	0.0393253	−	0.0949397i
$130$	−0.0401668	−	0.00914941i	−0.00352286	−	0.000802457i
$131$	0.819795	+	1.97916i	0.0716258	+	0.172920i	0.955638	−	0.294544i	$-0.0951678\pi$
$131$	0.819795	+	1.97916i	0.0716258	+	0.172920i	−0.884012	+	0.467464i	$0.845168\pi$
$132$	−0.857395			−0.0746266
$133$	8.26339	+	19.9496i	0.716527	+	1.72985i
$134$	−8.28724	−	8.28724i	−0.715909	−	0.715909i
$135$	−0.570079	−	3.34642i	−0.0490646	−	0.288014i
$136$	4.12280	−	0.0498002i	0.353528	−	0.00427033i
$137$		−	15.3881i		−	1.31469i	−0.753589	−	0.657346i	$-0.771679\pi$
$137$		−	15.3881i		−	1.31469i	0.753589	−	0.657346i	$-0.228321\pi$
$138$	−0.946003	+	0.946003i	−0.0805291	+	0.0805291i
$139$	−3.45430	+	1.43082i	−0.292990	+	0.121360i	−0.524337	−	0.851511i	$-0.675687\pi$
$139$	−3.45430	+	1.43082i	−0.292990	+	0.121360i	0.231347	+	0.972871i	$0.425687\pi$
$140$	−8.31374	+	1.41629i	−0.702639	+	0.119698i
$141$	0.958092	+	2.31304i	0.0806859	+	0.194793i
$142$	−1.49892	+	3.61871i	−0.125786	+	0.303675i
$143$	−0.0570485	−	0.0236303i	−0.00477063	−	0.00197606i
$144$	−2.07505	+	2.07505i	−0.172921	+	0.172921i
$145$	−0.805314	+	1.13603i	−0.0668777	+	0.0943423i
$146$	−3.86692	+	9.33558i	−0.320029	+	0.772618i
$147$	−0.707270	+	1.70750i	−0.0583346	+	0.140832i
$148$	−3.60864	+	1.49475i	−0.296628	+	0.122868i
$149$			12.3746i			1.01377i	0.862014	+	0.506884i	$0.169203\pi$
$149$			12.3746i			1.01377i	−0.862014	+	0.506884i	$0.830797\pi$
$150$	−0.952974	+	0.853124i	−0.0778100	+	0.0696572i
$151$	7.00868	+	7.00868i	0.570358	+	0.570358i	0.932228	−	0.361870i	$-0.117862\pi$
$151$	7.00868	+	7.00868i	0.570358	+	0.570358i	−0.361870	+	0.932228i	$0.617862\pi$
$152$		−	5.72526i		−	0.464380i
$153$	0.146142	+	12.0986i	0.0118149	+	0.978116i
$154$	−12.6411			−1.01865
$155$	1.89260	+	1.34163i	0.152017	+	0.107762i
$156$	0.00435413	−	0.00180354i	0.000348609	−	0.000144399i
$157$	8.23758			0.657431			0.328715	−	0.944429i	$-0.393384\pi$
$157$	8.23758			0.657431			0.328715	+	0.944429i	$0.393384\pi$
$158$	4.92071	−	2.03822i	0.391471	−	0.162152i
$159$	−3.01927	−	1.25062i	−0.239443	−	0.0991807i
$160$	2.18022	+	0.496623i	0.172362	+	0.0392615i
$161$	−13.9475	+	13.9475i	−1.09922	+	1.09922i
$162$	−5.95054	−	5.95054i	−0.467518	−	0.467518i
$163$	−18.0205	−	7.46435i	−1.41148	−	0.584653i	−0.458774	−	0.888553i	$-0.651711\pi$
$163$	−18.0205	−	7.46435i	−1.41148	−	0.584653i	−0.952704	+	0.303900i	$0.901711\pi$
$164$	6.47400	+	2.68162i	0.505535	+	0.209399i
$165$	−1.62289	+	1.02071i	−0.126342	+	0.0794626i
$166$			1.19946i			0.0930964i
$167$	6.91021	+	16.6827i	0.534728	+	1.29095i	0.928361	+	0.371680i	$0.121218\pi$
$167$	6.91021	+	16.6827i	0.534728	+	1.29095i	−0.393633	+	0.919268i	$0.628782\pi$
$168$	0.682224	−	0.682224i	0.0526348	−	0.0526348i
$169$	−12.9997			−0.999974
$170$	7.74442	−	5.00240i	0.593970	−	0.383666i
$171$	16.8011			1.28481
$172$	−3.22622	+	3.22622i	−0.245997	+	0.245997i
$173$	−2.74366	−	6.62378i	−0.208597	−	0.503597i	0.784606	−	0.619995i	$-0.212865\pi$
$173$	−2.74366	−	6.62378i	−0.208597	−	0.503597i	−0.993203	+	0.116398i	$0.962865\pi$
$174$		−	0.159307i		−	0.0120770i
$175$	−14.0503	+	12.5781i	−1.06210	+	0.950818i
$176$	3.09654	+	1.28263i	0.233411	+	0.0966819i
$177$	3.40464	+	1.41025i	0.255908	+	0.106001i
$178$	−10.2450	−	10.2450i	−0.767898	−	0.767898i
$179$	−8.77745	+	8.77745i	−0.656058	+	0.656058i	−0.954445	−	0.298387i	$-0.903551\pi$
$179$	−8.77745	+	8.77745i	−0.656058	+	0.656058i	0.298387	+	0.954445i	$0.403551\pi$
$180$	−1.45737	+	6.39799i	−0.108626	+	0.476878i
$181$	−13.6800	−	5.66646i	−1.01683	−	0.421185i	−0.188888	−	0.981999i	$-0.560488\pi$
$181$	−13.6800	−	5.66646i	−1.01683	−	0.421185i	−0.827942	+	0.560814i	$0.810488\pi$
$182$	0.0641956	−	0.0265907i	0.00475850	−	0.00197103i
$183$	1.46875			0.108573
$184$	4.83175	−	2.00137i	0.356201	−	0.147543i
$185$	−5.05101	+	7.12531i	−0.371358	+	0.523863i
$186$	−0.265400			−0.0194601
$187$	12.7026	−	5.44224i	0.928904	−	0.397976i
$188$		−	9.78698i		−	0.713789i
$189$	4.04870	+	4.04870i	0.294500	+	0.294500i
$190$	−6.81583	−	10.8369i	−0.494473	−	0.786189i
$191$		−	14.1264i		−	1.02215i	−0.859537	−	0.511074i	$-0.829248\pi$
$191$		−	14.1264i		−	1.02215i	0.859537	−	0.511074i	$-0.170752\pi$
$192$	−0.236338	+	0.0978946i	−0.0170563	+	0.00706493i
$193$	−3.23534	+	7.81080i	−0.232885	+	0.562234i	−0.996514	−	0.0834210i	$-0.973415\pi$
$193$	−3.23534	+	7.81080i	−0.232885	+	0.562234i	0.763630	+	0.645655i	$0.223415\pi$
$194$	−2.69136	+	6.49752i	−0.193229	+	0.466495i
$195$	0.00609447	−	0.00859728i	0.000436434	−	0.000615664i
$196$	5.10871	−	5.10871i	0.364908	−	0.364908i
$197$	−3.62856	−	1.50300i	−0.258524	−	0.107084i	0.249657	−	0.968334i	$-0.419682\pi$
$197$	−3.62856	−	1.50300i	−0.258524	−	0.107084i	−0.508181	+	0.861250i	$0.669682\pi$
$198$	−3.76396	+	9.08700i	−0.267493	+	0.645785i
$199$	−4.87200	−	11.7621i	−0.345367	−	0.833790i	−0.997154	−	0.0753879i	$-0.975980\pi$
$199$	−4.87200	−	11.7621i	−0.345367	−	0.833790i	0.651787	−	0.758402i	$-0.274020\pi$
$200$	4.71798	−	1.65550i	0.333611	−	0.117062i
$201$	2.76987	−	1.14732i	0.195372	−	0.0809256i
$202$	5.73278	−	5.73278i	0.403357	−	0.403357i
$203$		−	2.34876i		−	0.164850i
$204$	−0.391831	+	0.979252i	−0.0274336	+	0.0685614i
$205$	15.4465	−	2.63139i	1.07883	−	0.183784i
$206$	3.11023	+	3.11023i	0.216700	+	0.216700i
$207$	5.87316	+	14.1791i	0.408212	+	0.985512i
$208$	−0.0184233			−0.00127742
$209$	−7.34340	−	17.7285i	−0.507953	−	1.22631i
$210$	0.479147	−	2.10350i	0.0330643	−	0.145155i
$211$	1.59347	−	3.84699i	0.109699	−	0.264838i	−0.859491	−	0.511151i	$-0.829219\pi$
$211$	1.59347	−	3.84699i	0.109699	−	0.264838i	0.969190	+	0.246313i	$0.0792193\pi$
$212$	9.03342	+	9.03342i	0.620418	+	0.620418i
$213$	−0.708504	−	0.708504i	−0.0485459	−	0.0485459i
$214$	−3.97113	+	9.58715i	−0.271461	+	0.655364i
$215$	−2.26587	+	9.94739i	−0.154531	+	0.678407i
$216$	−0.580961	−	1.40256i	−0.0395294	−	0.0954324i
$217$	−3.91296			−0.265629
$218$	2.89425	+	6.98733i	0.196023	+	0.473242i
$219$	−1.82780	−	1.82780i	−0.123512	−	0.123512i
$220$	7.38814	−	1.25860i	0.498108	−	0.0848551i
$221$	−0.0530599	+	0.0543574i	−0.00356920	+	0.00365648i
$222$		−	0.999188i		−	0.0670611i
$223$	−4.76470	+	4.76470i	−0.319068	+	0.319068i	−0.848409	−	0.529341i	$-0.822439\pi$
$223$	−4.76470	+	4.76470i	−0.319068	+	0.319068i	0.529341	+	0.848409i	$0.322439\pi$
$224$	−3.48449	+	1.44332i	−0.232817	+	0.0964359i
$225$	4.85818	+	13.8452i	0.323879	+	0.923013i
$226$	−6.05130	−	14.6091i	−0.402526	−	0.971785i
$227$	−2.15299	+	5.19778i	−0.142899	+	0.344989i	−0.979083	−	0.203460i	$-0.934781\pi$
$227$	−2.15299	+	5.19778i	−0.142899	+	0.344989i	0.836184	+	0.548449i	$0.184781\pi$
$228$	1.35310	+	0.560472i	0.0896112	+	0.0371182i
$229$	−9.03385	+	9.03385i	−0.596974	+	0.596974i	−0.939506	−	0.342532i	$-0.888715\pi$
$229$	−9.03385	+	9.03385i	−0.596974	+	0.596974i	0.342532	+	0.939506i	$0.388715\pi$
$230$	6.76299	−	9.54035i	0.445939	−	0.629072i
$231$	1.23750	−	2.98758i	0.0814213	−	0.196568i
$232$	−0.238317	+	0.575348i	−0.0156463	+	0.0377734i
$233$	27.8378	−	11.5308i	1.82372	−	0.755408i	0.850325	−	0.526258i	$-0.176405\pi$
$233$	27.8378	−	11.5308i	1.82372	−	0.755408i	0.973391	−	0.229150i	$-0.0735946\pi$
$234$		−	0.0540642i		−	0.00353429i
$235$	−11.6512	−	18.5249i	−0.760043	−	1.20843i
$236$	−10.1864	−	10.1864i	−0.663079	−	0.663079i
$237$			1.36248i			0.0885028i
$238$	−5.77700	+	14.4377i	−0.374467	+	0.935859i
$239$	5.41113			0.350017			0.175008	−	0.984567i	$-0.444005\pi$
$239$	5.41113			0.350017			0.175008	+	0.984567i	$0.444005\pi$
$240$	−0.330803	+	0.466653i	−0.0213532	+	0.0301223i
$241$	24.4491	−	10.1272i	1.57491	−	0.652348i	0.587312	−	0.809361i	$-0.300186\pi$
$241$	24.4491	−	10.1272i	1.57491	−	0.652348i	0.987597	+	0.157013i	$0.0501863\pi$
$242$	0.233727			0.0150245
$243$	6.19656	−	2.56670i	0.397509	−	0.164654i
$244$	−5.30451	−	2.19720i	−0.339586	−	0.140661i
$245$	3.58801	−	15.7517i	0.229229	−	1.00634i
$246$	−1.26754	+	1.26754i	−0.0808154	+	0.0808154i
$247$	0.0745843	+	0.0745843i	0.00474568	+	0.00474568i
$248$	0.958512	+	0.397029i	0.0608656	+	0.0252114i
$249$	−0.283479	−	0.117421i	−0.0179648	−	0.00744125i
$250$	6.95940	−	8.75024i	0.440151	−	0.553414i
$251$			9.44685i			0.596280i	0.954522	+	0.298140i	$0.0963663\pi$
$251$			9.44685i			0.596280i	−0.954522	+	0.298140i	$0.903634\pi$
$252$	−4.23551	−	10.2254i	−0.266812	−	0.644142i
$253$	12.3947	−	12.3947i	0.779247	−	0.779247i
$254$	11.4813			0.720400
$255$	0.424122	+	2.32001i	0.0265595	+	0.145285i
$256$	1.00000			0.0625000
$257$	0.572107	−	0.572107i	0.0356870	−	0.0356870i	−0.689038	−	0.724725i	$-0.741967\pi$
$257$	0.572107	−	0.572107i	0.0356870	−	0.0356870i	0.724725	+	0.689038i	$0.241967\pi$
$258$	−0.446650	−	1.07831i	−0.0278072	−	0.0671325i
$259$		−	14.7317i		−	0.915381i
$260$	−0.0348718	+	0.0219326i	−0.00216266	+	0.00136020i
$261$	−1.68839	−	0.699355i	−0.104509	−	0.0432890i
$262$	1.97916	+	0.819795i	0.122273	+	0.0506471i
$263$	−12.1880	−	12.1880i	−0.751542	−	0.751542i	0.223225	−	0.974767i	$-0.428342\pi$
$263$	−12.1880	−	12.1880i	−0.751542	−	0.751542i	−0.974767	+	0.223225i	$0.928342\pi$
$264$	−0.606270	+	0.606270i	−0.0373133	+	0.0373133i
$265$	27.8527	+	6.34445i	1.71098	+	0.389736i
$266$	19.9496	+	8.26339i	1.22319	+	0.506661i
$267$	3.42423	−	1.41836i	0.209560	−	0.0868024i
$268$	−11.7199			−0.715909
$269$	13.4595	−	5.57511i	0.820641	−	0.339921i	0.0674501	−	0.997723i	$-0.478514\pi$
$269$	13.4595	−	5.57511i	0.820641	−	0.339921i	0.753191	+	0.657802i	$0.228514\pi$
$270$	−2.76938	−	1.96317i	−0.168539	−	0.119475i
$271$	−4.04446			−0.245683			−0.122842	−	0.992426i	$-0.539201\pi$
$271$	−4.04446			−0.245683			−0.122842	+	0.992426i	$0.539201\pi$
$272$	2.88005	−	2.95048i	0.174629	−	0.178899i
$273$			0.0177750i			0.00107579i
$274$	−10.8810	−	10.8810i	−0.657346	−	0.657346i
$275$	12.4860	−	11.1778i	0.752936	−	0.674045i
$276$			1.33785i			0.0805291i
$277$	−12.5470	+	5.19716i	−0.753879	+	0.312267i	−0.726323	−	0.687353i	$-0.758772\pi$
$277$	−12.5470	+	5.19716i	−0.753879	+	0.312267i	−0.0275559	+	0.999620i	$0.508772\pi$
$278$	−1.43082	+	3.45430i	−0.0858148	+	0.207175i
$279$	−1.16511	+	2.81281i	−0.0697530	+	0.168399i
$280$	−4.87723	+	6.88016i	−0.291470	+	0.411168i
$281$	−11.8071	+	11.8071i	−0.704353	+	0.704353i	−0.965342	−	0.260989i	$-0.915952\pi$
$281$	−11.8071	+	11.8071i	−0.704353	+	0.704353i	0.260989	+	0.965342i	$0.415952\pi$
$282$	2.31304	+	0.958092i	0.137739	+	0.0570536i
$283$	4.22517	−	10.2005i	0.251160	−	0.606354i	−0.747138	−	0.664669i	$-0.768573\pi$
$283$	4.22517	−	10.2005i	0.251160	−	0.606354i	0.998298	+	0.0583146i	$0.0185727\pi$
$284$	1.49892	+	3.61871i	0.0889444	+	0.214731i
$285$	3.22840	−	0.549973i	0.191234	−	0.0325776i
$286$	−0.0570485	+	0.0236303i	−0.00337335	+	0.00139729i
$287$	−18.6881	+	18.6881i	−1.10313	+	1.10313i
$288$			2.93456i			0.172921i
$289$	−0.410633	−	16.9950i	−0.0241549	−	0.999708i
$290$	0.233853	+	1.37274i	0.0137323	+	0.0806100i
$291$	−1.27214	−	1.27214i	−0.0745744	−	0.0745744i
$292$	3.86692	+	9.33558i	0.226295	+	0.546323i
$293$	1.82971			0.106893			0.0534464	−	0.998571i	$-0.482979\pi$
$293$	1.82971			0.106893			0.0534464	+	0.998571i	$0.482979\pi$
$294$	0.707270	+	1.70750i	0.0412488	+	0.0995835i
$295$	−31.4078	−	7.15423i	−1.82863	−	0.416535i
$296$	−1.49475	+	3.60864i	−0.0868805	+	0.209748i
$297$	−3.59794	−	3.59794i	−0.208774	−	0.208774i
$298$	8.75018	+	8.75018i	0.506884	+	0.506884i
$299$	−0.0368719	+	0.0890166i	−0.00213236	+	0.00514796i
$300$	−0.0706050	+	1.27710i	−0.00407638	+	0.0737336i
$301$	−6.58524	−	15.8982i	−0.379567	−	0.916356i
$302$	9.91177			0.570358
$303$	0.793668	+	1.91608i	0.0455950	+	0.110076i
$304$	−4.04837	−	4.04837i	−0.232190	−	0.232190i
$305$	−12.6562	+	2.15604i	−0.724691	+	0.123455i
$306$	8.65836	+	8.45168i	0.494965	+	0.483150i
$307$		−	5.39278i		−	0.307782i	−0.988088	−	0.153891i	$-0.950820\pi$
$307$		−	5.39278i		−	0.307782i	0.988088	−	0.153891i	$-0.0491805\pi$
$308$	−8.93861	+	8.93861i	−0.509325	+	0.509325i
$309$	−1.03954	+	0.430592i	−0.0591375	+	0.0244955i
$310$	2.28694	−	0.389592i	0.129890	−	0.0221273i
$311$	11.7529	+	28.3739i	0.666444	+	1.60894i	0.787517	+	0.616294i	$0.211367\pi$
$311$	11.7529	+	28.3739i	0.666444	+	1.60894i	−0.121073	+	0.992644i	$0.538633\pi$
$312$	0.00180354	−	0.00435413i	0.000102105	−	0.000246504i
$313$	17.7837	+	7.36626i	1.00520	+	0.416366i	0.823700	−	0.567026i	$-0.191906\pi$
$313$	17.7837	+	7.36626i	1.00520	+	0.416366i	0.181496	+	0.983392i	$0.441906\pi$
$314$	5.82485	−	5.82485i	0.328715	−	0.328715i
$315$	−20.1903	−	14.3125i	−1.13759	−	0.806420i
$316$	2.03822	−	4.92071i	0.114659	−	0.276812i
$317$	7.39242	−	17.8469i	0.415200	−	1.00238i	−0.568520	−	0.822670i	$-0.692484\pi$
$317$	7.39242	−	17.8469i	0.415200	−	1.00238i	0.983719	−	0.179711i	$-0.0575163\pi$
$318$	−3.01927	+	1.25062i	−0.169312	+	0.0701313i
$319$			2.08726i			0.116864i
$320$	1.89281	−	1.19048i	0.105812	−	0.0665501i
$321$	−1.87706	−	1.87706i	−0.104767	−	0.104767i
$322$			19.7248i			1.09922i
$323$	−23.6041	+	0.285119i	−1.31337	+	0.0158645i
$324$	−8.41533			−0.467518
$325$	−0.0398955	+	0.0830287i	−0.00221300	+	0.00460561i
$326$	−18.0205	+	7.46435i	−0.998066	+	0.413412i
$327$	−1.93471			−0.106989
$328$	6.47400	−	2.68162i	0.357467	−	0.148068i
$329$	34.1026	+	14.1258i	1.88014	+	0.778778i
$330$	−0.425802	+	1.86931i	−0.0234396	+	0.102902i
$331$	13.6677	−	13.6677i	0.751245	−	0.751245i	−0.223467	−	0.974712i	$-0.571737\pi$
$331$	13.6677	−	13.6677i	0.751245	−	0.751245i	0.974712	+	0.223467i	$0.0717374\pi$
$332$	0.848148	+	0.848148i	0.0465482	+	0.0465482i
$333$	−10.5898	−	4.38643i	−0.580316	−	0.240375i
$334$	16.6827	+	6.91021i	0.912838	+	0.378110i
$335$	−22.1837	+	13.9524i	−1.21202	+	0.762301i
$336$		−	0.964811i		−	0.0526348i
$337$	−13.2424	−	31.9699i	−0.721357	−	1.74151i	−0.669448	−	0.742859i	$-0.733469\pi$
$337$	−13.2424	−	31.9699i	−0.721357	−	1.74151i	−0.0519097	−	0.998652i	$-0.516531\pi$
$338$	−9.19215	+	9.19215i	−0.499987	+	0.499987i
$339$	4.04509			0.219699
$340$	1.93890	−	9.01336i	0.105152	−	0.488818i
$341$	3.47732			0.188307
$342$	11.8802	−	11.8802i	0.642407	−	0.642407i
$343$	0.324477	+	0.783356i	0.0175201	+	0.0422973i
$344$			4.56256i			0.245997i
$345$	1.59269	+	2.53230i	0.0857475	+	0.136335i
$346$	−6.62378	−	2.74366i	−0.356097	−	0.147500i
$347$	−0.0173964	−	0.00720582i	−0.000933887	−	0.000386829i	0.382216	−	0.924073i	$-0.375161\pi$
$347$	−0.0173964	−	0.00720582i	−0.000933887	−	0.000386829i	−0.383150	+	0.923686i	$0.625161\pi$
$348$	−0.112647	−	0.112647i	−0.00603850	−	0.00603850i
$349$	−23.0436	+	23.0436i	−1.23350	+	1.23350i	−0.270887	+	0.962611i	$0.587317\pi$
$349$	−23.0436	+	23.0436i	−1.23350	+	1.23350i	−0.962611	+	0.270887i	$0.912683\pi$
$350$	−1.04097	+	18.8291i	−0.0556424	+	1.00646i
$351$	0.0258398	+	0.0107032i	0.00137923	+	0.000571295i
$352$	3.09654	−	1.28263i	0.165046	−	0.0683644i
$353$	−9.13594			−0.486257			−0.243129	−	0.969994i	$-0.578174\pi$
$353$	−9.13594			−0.486257			−0.243129	+	0.969994i	$0.578174\pi$
$354$	3.40464	−	1.41025i	0.180954	−	0.0749537i
$355$	7.14519	+	5.06511i	0.379227	+	0.268828i
$356$	−14.4887			−0.767898
$357$	−2.84665	−	2.77870i	−0.150661	−	0.147065i
$358$			12.4132i			0.656058i
$359$	4.60790	+	4.60790i	0.243196	+	0.243196i	0.818171	−	0.574975i	$-0.194988\pi$
$359$	4.60790	+	4.60790i	0.243196	+	0.243196i	−0.574975	+	0.818171i	$0.694988\pi$
$360$	3.49355	+	5.55458i	0.184126	+	0.292752i
$361$			13.7786i			0.725191i
$362$	−13.6800	+	5.66646i	−0.719007	+	0.297823i
$363$	−0.0228806	+	0.0552387i	−0.00120092	+	0.00289928i
$364$	0.0265907	−	0.0641956i	0.00139373	−	0.00336476i
$365$	18.4332	+	13.0670i	0.964839	+	0.683959i
$366$	1.03856	−	1.03856i	0.0542867	−	0.0542867i
$367$	16.0161	+	6.63410i	0.836035	+	0.346297i	0.759289	−	0.650753i	$-0.225547\pi$
$367$	16.0161	+	6.63410i	0.836035	+	0.346297i	0.0767463	+	0.997051i	$0.475547\pi$
$368$	2.00137	−	4.83175i	0.104329	−	0.251872i
$369$	7.86938	+	18.9984i	0.409663	+	0.989015i
$370$	1.46675	+	8.60996i	0.0762526	+	0.447611i
$371$	−44.5149	+	18.4387i	−2.31110	+	0.957289i
$372$	−0.187666	+	0.187666i	−0.00973005	+	0.00973005i
$373$		−	12.0591i		−	0.624398i	−0.950017	−	0.312199i	$-0.898934\pi$
$373$		−	12.0591i		−	0.624398i	0.950017	−	0.312199i	$-0.101066\pi$
$374$	5.13383	−	12.8303i	0.265464	−	0.663440i
$375$	1.38673	+	2.50138i	0.0716104	+	0.129170i
$376$	−6.92044	−	6.92044i	−0.356894	−	0.356894i
$377$	−0.00439057	−	0.0105998i	−0.000226126	−	0.000545917i
$378$	5.72573			0.294500
$379$	1.64620	+	3.97427i	0.0845595	+	0.204145i	0.960503	−	0.278268i	$-0.0897604\pi$
$379$	1.64620	+	3.97427i	0.0845595	+	0.204145i	−0.875944	+	0.482413i	$0.839760\pi$
$380$	−12.4823	−	2.84330i	−0.640331	−	0.145858i
$381$	−1.12396	+	2.71347i	−0.0575820	+	0.139015i
$382$	−9.98885	−	9.98885i	−0.511074	−	0.511074i
$383$	12.0347	+	12.0347i	0.614945	+	0.614945i	0.944230	−	0.329286i	$-0.106808\pi$
$383$	12.0347	+	12.0347i	0.614945	+	0.614945i	−0.329286	+	0.944230i	$0.606808\pi$
$384$	−0.0978946	+	0.236338i	−0.00499566	+	0.0120606i
$385$	−6.27786	+	27.5604i	−0.319949	+	1.40461i
$386$	3.23534	+	7.81080i	0.164674	+	0.397559i
$387$	−13.3891			−0.680607
$388$	2.69136	+	6.49752i	0.136633	+	0.329862i
$389$	−9.17678	−	9.17678i	−0.465281	−	0.465281i	0.435101	−	0.900382i	$-0.356713\pi$
$389$	−9.17678	−	9.17678i	−0.465281	−	0.465281i	−0.900382	+	0.435101i	$0.856713\pi$
$390$	−0.00176975	−	0.0103886i	−8.96150e−5	−	0.000526049i
$391$	−8.49190	−	19.8207i	−0.429454	−	1.00237i
$392$		−	7.22481i		−	0.364908i
$393$	−0.387498	+	0.387498i	−0.0195467	+	0.0195467i
$394$	−3.62856	+	1.50300i	−0.182804	+	0.0757199i
$395$	−2.00005	−	11.7405i	−0.100633	−	0.590727i
$396$	3.76396	+	9.08700i	0.189146	+	0.456639i
$397$	3.61663	−	8.73132i	0.181514	−	0.438213i	−0.806765	−	0.590872i	$-0.798784\pi$
$397$	3.61663	−	8.73132i	0.181514	−	0.438213i	0.988279	+	0.152660i	$0.0487838\pi$
$398$	−11.7621	−	4.87200i	−0.589578	−	0.244211i
$399$	−3.90591	+	3.90591i	−0.195540	+	0.195540i
$400$	2.16549	−	4.50673i	0.108275	−	0.225337i
$401$	0.663235	−	1.60119i	0.0331204	−	0.0799596i	−0.906454	−	0.422305i	$-0.861221\pi$
$401$	0.663235	−	1.60119i	0.0331204	−	0.0799596i	0.939574	+	0.342345i	$0.111221\pi$
$402$	1.14732	−	2.76987i	0.0572230	−	0.138149i
$403$	−0.0176589	+	0.00731457i	−0.000879654	+	0.000364365i
$404$		−	8.10737i		−	0.403357i
$405$	−15.9287	+	10.0183i	−0.791501	+	0.497814i
$406$	−1.66082	−	1.66082i	−0.0824252	−	0.0824252i
$407$			13.0915i			0.648923i
$408$	0.415370	+	0.969502i	0.0205639	+	0.0479975i
$409$	6.81555			0.337007			0.168504	−	0.985701i	$-0.446106\pi$
$409$	6.81555			0.337007			0.168504	+	0.985701i	$0.446106\pi$
$410$	9.06166	−	12.7830i	0.447524	−	0.631308i
$411$	3.63679	−	1.50641i	0.179390	−	0.0743057i
$412$	4.39853			0.216700
$413$	50.1967	−	20.7921i	2.47002	−	1.02311i
$414$	14.1791	+	5.87316i	0.696862	+	0.288650i
$415$	2.61509	+	0.595680i	0.128370	+	0.0292408i
$416$	−0.0130272	+	0.0130272i	−0.000638712	+	0.000638712i
$417$	−0.676315	−	0.676315i	−0.0331193	−	0.0331193i
$418$	−17.7285	−	7.34340i	−0.867131	−	0.359177i
$419$	16.6715	+	6.90556i	0.814456	+	0.337359i	0.750730	−	0.660609i	$-0.229702\pi$
$419$	16.6715	+	6.90556i	0.814456	+	0.337359i	0.0637258	+	0.997967i	$0.479702\pi$
$420$	−1.14859	−	1.82621i	−0.0560456	−	0.0891098i
$421$			10.6098i			0.517090i	0.965999	+	0.258545i	$0.0832430\pi$
$421$			10.6098i			0.517090i	−0.965999	+	0.258545i	$0.916757\pi$
$422$	−1.59347	−	3.84699i	−0.0775691	−	0.187268i
$423$	20.3085	−	20.3085i	0.987431	−	0.987431i
$424$	12.7752			0.620418
$425$	−7.06028	−	19.3689i	−0.342474	−	0.939527i
$426$	−1.00198			−0.0485459
$427$	15.3122	−	15.3122i	0.741010	−	0.741010i
$428$	3.97113	+	9.58715i	0.191952	+	0.463412i
$429$		−	0.0157960i		−	0.000762639i
$430$	5.43166	+	8.63608i	0.261938	+	0.416469i
$431$	−20.2493	−	8.38753i	−0.975374	−	0.404013i	−0.162664	−	0.986682i	$-0.552009\pi$
$431$	−20.2493	−	8.38753i	−0.975374	−	0.404013i	−0.812710	+	0.582669i	$0.802009\pi$
$432$	−1.40256	−	0.580961i	−0.0674809	−	0.0279515i
$433$	−23.6546	−	23.6546i	−1.13677	−	1.13677i	−0.989026	−	0.147742i	$-0.952799\pi$
$433$	−23.6546	−	23.6546i	−1.13677	−	1.13677i	−0.147742	−	0.989026i	$-0.547201\pi$
$434$	−2.76688	+	2.76688i	−0.132815	+	0.132815i
$435$	−0.347324	−	0.0791153i	−0.0166529	−	0.00379329i
$436$	6.98733	+	2.89425i	0.334632	+	0.138609i
$437$	−27.6630	+	11.4584i	−1.32330	+	0.548129i
$438$	−2.58491			−0.123512
$439$	33.3486	−	13.8134i	1.59164	−	0.659280i	0.601440	−	0.798918i	$-0.294594\pi$
$439$	33.3486	−	13.8134i	1.59164	−	0.659280i	0.990203	+	0.139638i	$0.0445940\pi$
$440$	4.33423	−	6.11417i	0.206626	−	0.291482i
$441$	21.2017			1.00960
$442$	0.000917483		0.0759556i	4.36402e−5		0.00361284i
$443$			23.2758i			1.10587i	0.833226	+	0.552933i	$0.186492\pi$
$443$			23.2758i			1.10587i	−0.833226	+	0.552933i	$0.813508\pi$
$444$	−0.706533	−	0.706533i	−0.0335306	−	0.0335306i
$445$	−27.4244	+	17.2485i	−1.30004	+	0.817659i
$446$			6.73830i			0.319068i
$447$	−2.92460	+	1.21141i	−0.138329	+	0.0572977i
$448$	−1.44332	+	3.48449i	−0.0681905	+	0.164626i
$449$	−2.51876	+	6.08083i	−0.118868	+	0.286972i	−0.972103	−	0.234554i	$-0.924637\pi$
$449$	−2.51876	+	6.08083i	−0.118868	+	0.286972i	0.853235	+	0.521526i	$0.174637\pi$
$450$	13.2253	+	6.35478i	0.623446	+	0.299567i
$451$	16.6075	−	16.6075i	0.782017	−	0.782017i
$452$	−14.6091	−	6.05130i	−0.687156	−	0.284629i
$453$	−0.970308	+	2.34253i	−0.0455891	+	0.110062i
$454$	2.15299	+	5.19778i	0.101045	+	0.243944i
$455$	−0.0260926	−	0.153166i	−0.00122324	−	0.00718054i
$456$	1.35310	−	0.560472i	0.0633647	−	0.0262465i
$457$	10.3736	−	10.3736i	0.485256	−	0.485256i	−0.421549	−	0.906806i	$-0.638513\pi$
$457$	10.3736	−	10.3736i	0.485256	−	0.485256i	0.906806	+	0.421549i	$0.138513\pi$
$458$			12.7758i			0.596974i
$459$	−5.75357	+	2.46504i	−0.268554	+	0.115058i
$460$	−1.96389	−	11.5282i	−0.0915666	−	0.537505i
$461$	−4.71031	−	4.71031i	−0.219381	−	0.219381i	0.588857	−	0.808238i	$-0.299578\pi$
$461$	−4.71031	−	4.71031i	−0.219381	−	0.219381i	−0.808238	+	0.588857i	$0.799578\pi$
$462$	−1.23750	−	2.98758i	−0.0575735	−	0.138995i
$463$	11.3238			0.526262			0.263131	−	0.964760i	$-0.415245\pi$
$463$	11.3238			0.526262			0.263131	+	0.964760i	$0.415245\pi$
$464$	0.238317	+	0.575348i	0.0110636	+	0.0267098i
$465$	−0.131804	+	0.578631i	−0.00611225	+	0.0268334i
$466$	11.5308	−	27.8378i	0.534154	−	1.28956i
$467$	12.3133	+	12.3133i	0.569793	+	0.569793i	0.932070	−	0.362277i	$-0.118001\pi$
$467$	12.3133	+	12.3133i	0.569793	+	0.569793i	−0.362277	+	0.932070i	$0.618001\pi$
$468$	−0.0382292	−	0.0382292i	−0.00176714	−	0.00176714i
$469$	16.9156	−	40.8379i	0.781091	−	1.88572i
$470$	−21.3378	−	4.86044i	−0.984239	−	0.224195i
$471$	0.806415	+	1.94686i	0.0371576	+	0.0897064i
$472$	−14.4058			−0.663079
$473$	5.85208	+	14.1282i	0.269079	+	0.649614i
$474$	0.963422	+	0.963422i	0.0442514	+	0.0442514i
$475$	−27.0117	+	9.47820i	−1.23938	+	0.434890i
$476$	6.12406	+	14.2940i	0.280696	+	0.655163i
$477$			37.4895i			1.71653i
$478$	3.82624	−	3.82624i	0.175008	−	0.175008i
$479$	13.3890	−	5.54593i	0.611761	−	0.253400i	−0.0552201	−	0.998474i	$-0.517586\pi$
$479$	13.3890	−	5.54593i	0.611761	−	0.253400i	0.666981	+	0.745074i	$0.267586\pi$
$480$	0.0960608	+	0.563887i	0.00438456	+	0.0257378i
$481$	−0.0275381	−	0.0664830i	−0.00125563	−	0.00303136i
$482$	10.1272	−	24.4491i	0.461280	−	1.11363i
$483$	−4.66172	−	1.93095i	−0.212116	−	0.0878612i
$484$	0.165270	−	0.165270i	0.00751227	−	0.00751227i
$485$	12.8294	+	9.09458i	0.582555	+	0.412964i
$486$	2.56670	−	6.19656i	0.116428	−	0.281082i
$487$	−13.2685	+	32.0330i	−0.601253	+	1.45155i	0.271039	+	0.962568i	$0.412633\pi$
$487$	−13.2685	+	32.0330i	−0.601253	+	1.45155i	−0.872292	+	0.488985i	$0.837367\pi$
$488$	−5.30451	+	2.19720i	−0.240124	+	0.0994625i
$489$		−	4.98967i		−	0.225640i
$490$	−8.60102	−	13.6752i	−0.388555	−	0.617784i
$491$	10.7439	+	10.7439i	0.484866	+	0.484866i	0.906682	−	0.421816i	$-0.138607\pi$
$491$	10.7439	+	10.7439i	0.484866	+	0.484866i	−0.421816	+	0.906682i	$0.638607\pi$
$492$			1.79257i			0.0808154i
$493$	2.38391	+	0.953881i	0.107366	+	0.0429606i
$494$	0.105478			0.00474568
$495$	17.9424	+	12.7191i	0.806451	+	0.571680i
$496$	0.958512	−	0.397029i	0.0430385	−	0.0178271i
$497$	−14.7728			−0.662649
$498$	−0.283479	+	0.117421i	−0.0127030	+	0.00526176i
$499$	15.8876	+	6.58086i	0.711226	+	0.294600i	0.708812	−	0.705398i	$-0.249231\pi$
$499$	15.8876	+	6.58086i	0.711226	+	0.294600i	0.00241435	+	0.999997i	$0.499231\pi$
$500$	−1.26631	−	11.1084i	−0.0566312	−	0.496783i
$501$	−3.26630	+	3.26630i	−0.145927	+	0.145927i
$502$	6.67993	+	6.67993i	0.298140	+	0.298140i
$503$	8.66009	+	3.58713i	0.386134	+	0.159942i	0.567301	−	0.823510i	$-0.307987\pi$
$503$	8.66009	+	3.58713i	0.386134	+	0.159942i	−0.181167	+	0.983452i	$0.557987\pi$
$504$	−10.2254	−	4.23551i	−0.455477	−	0.188665i
$505$	−9.65170	−	15.3457i	−0.429495	−	0.682877i
$506$		−	17.5287i		−	0.779247i
$507$	−1.27260	−	3.07232i	−0.0565180	−	0.136446i
$508$	8.11850	−	8.11850i	0.360200	−	0.360200i
$509$	27.2208			1.20654			0.603270	−	0.797537i	$-0.293864\pi$
$509$	27.2208			1.20654			0.603270	+	0.797537i	$0.293864\pi$
$510$	1.94039	+	1.34060i	0.0859221	+	0.0593626i
$511$	−38.1109			−1.68593
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.32616	+	8.03005i	0.146853	+	0.354535i
$514$		−	0.809081i		−	0.0356870i
$515$	8.32560	−	5.23638i	0.366870	−	0.230743i
$516$	−1.07831	−	0.446650i	−0.0474699	−	0.0196627i
$517$	−30.3058	−	12.5531i	−1.33285	−	0.552084i
$518$	−10.4169	−	10.4169i	−0.457690	−	0.457690i
$519$	1.29686	−	1.29686i	0.0569261	−	0.0569261i
$520$	−0.00914941	+	0.0401668i	−0.000401228	+	0.00176143i
$521$	−14.7843	−	6.12385i	−0.647711	−	0.268291i	0.0345461	−	0.999403i	$-0.489001\pi$
$521$	−14.7843	−	6.12385i	−0.647711	−	0.268291i	−0.682257	+	0.731112i	$0.739001\pi$
$522$	−1.68839	+	0.699355i	−0.0738989	+	0.0306099i
$523$	−31.2545			−1.36666			−0.683332	−	0.730108i	$-0.739470\pi$
$523$	−31.2545			−1.36666			−0.683332	+	0.730108i	$0.739470\pi$
$524$	1.97916	−	0.819795i	0.0864600	−	0.0358129i
$525$	−4.34814	−	2.08929i	−0.189769	−	0.0911842i
$526$	−17.2364			−0.751542
$527$	1.58914	−	3.97153i	0.0692239	−	0.173003i
$528$			0.857395i			0.0373133i
$529$	−3.07681	−	3.07681i	−0.133774	−	0.133774i
$530$	24.1811	−	15.2087i	1.05036	−	0.660622i
$531$		−	42.2746i		−	1.83456i
$532$	19.9496	−	8.26339i	0.864925	−	0.358263i
$533$	−0.0494042	+	0.119272i	−0.00213993	+	0.00516626i
$534$	1.41836	−	3.42423i	0.0613786	−	0.148181i
$535$	18.9300	+	13.4191i	0.818413	+	0.580160i
$536$	−8.28724	+	8.28724i	−0.357954	+	0.357954i
$537$	−2.93371	−	1.21518i	−0.126599	−	0.0524391i
$538$	5.57511	−	13.4595i	0.240360	−	0.580281i
$539$	−9.26677	−	22.3720i	−0.399148	−	0.963628i
$540$	−3.34642	+	0.570079i	−0.144007	+	0.0245323i
$541$	22.4347	−	9.29274i	0.964541	−	0.399526i	0.155864	−	0.987779i	$-0.450184\pi$
$541$	22.4347	−	9.29274i	0.964541	−	0.399526i	0.808677	+	0.588253i	$0.200184\pi$
$542$	−2.85986	+	2.85986i	−0.122842	+	0.122842i
$543$		−	3.78784i		−	0.162552i
$544$	−0.0498002	−	4.12280i	−0.00213517	−	0.176764i
$545$	16.6713	−	2.84003i	0.714119	−	0.121654i
$546$	0.0125688	+	0.0125688i	0.000537895	+	0.000537895i
$547$	−9.57044	−	23.1051i	−0.409203	−	0.987903i	−0.985348	−	0.170555i	$-0.945444\pi$
$547$	−9.57044	−	23.1051i	−0.409203	−	0.987903i	0.576145	−	0.817347i	$-0.304556\pi$
$548$	−15.3881			−0.657346
$549$	−6.44781	−	15.5664i	−0.275186	−	0.664358i
$550$	0.925079	−	16.7328i	0.0394455	−	0.713490i
$551$	1.36443	−	3.29402i	0.0581265	−	0.140330i
$552$	0.946003	+	0.946003i	0.0402646	+	0.0402646i
$553$	14.2043	+	14.2043i	0.604030	+	0.604030i
$554$	−5.19716	+	12.5470i	−0.220806	+	0.533073i
$555$	−2.17845	−	0.496219i	−0.0924701	−	0.0210633i
$556$	1.43082	+	3.45430i	0.0606802	+	0.146495i
$557$	44.5132			1.88608			0.943042	−	0.332674i	$-0.107951\pi$
$557$	44.5132			1.88608			0.943042	+	0.332674i	$0.107951\pi$
$558$	1.16511	+	2.81281i	0.0493228	+	0.119076i
$559$	−0.0594375	−	0.0594375i	−0.00251394	−	0.00251394i
$560$	1.41629	+	8.31374i	0.0598490	+	0.351319i
$561$	2.52972	+	2.46934i	0.106805	+	0.104256i
$562$			16.6978i			0.704353i
$563$	−22.0064	+	22.0064i	−0.927460	+	0.927460i	−0.997541	−	0.0700816i	$-0.977674\pi$
$563$	−22.0064	+	22.0064i	−0.927460	+	0.927460i	0.0700816	+	0.997541i	$0.477674\pi$
$564$	2.31304	−	0.958092i	0.0973965	−	0.0403430i
$565$	−34.8563	+	5.93795i	−1.46642	+	0.249811i
$566$	−4.22517	−	10.2005i	−0.177597	−	0.428757i
$567$	12.1460	−	29.3231i	0.510085	−	1.23145i
$568$	3.61871	+	1.49892i	0.151838	+	0.0628932i
$569$	−14.0791	+	14.0791i	−0.590226	+	0.590226i	−0.937693	−	0.347466i	$-0.887042\pi$
$569$	−14.0791	+	14.0791i	−0.590226	+	0.590226i	0.347466	+	0.937693i	$0.387042\pi$
$570$	1.89393	−	2.67171i	0.0793281	−	0.111906i
$571$	−14.4226	+	34.8193i	−0.603568	+	1.45714i	0.266315	+	0.963886i	$0.414194\pi$
$571$	−14.4226	+	34.8193i	−0.603568	+	1.45714i	−0.869884	+	0.493257i	$0.835806\pi$
$572$	−0.0236303	+	0.0570485i	−0.000988030	+	0.00238532i
$573$	3.33860	−	1.38289i	0.139472	−	0.0577712i
$574$			26.4290i			1.10313i
$575$	−17.4414	−	19.4828i	−0.727357	−	0.812488i
$576$	2.07505	+	2.07505i	0.0864603	+	0.0864603i
$577$			33.7924i			1.40680i	0.710796	+	0.703398i	$0.248335\pi$
$577$			33.7924i			1.40680i	−0.710796	+	0.703398i	$0.751665\pi$
$578$	−12.3077	−	11.7269i	−0.511932	−	0.487777i
$579$	−2.16271			−0.0898793
$580$	1.13603	+	0.805314i	0.0471711	+	0.0334388i
$581$	−4.17951	+	1.73121i	−0.173395	+	0.0718227i
$582$	−1.79908			−0.0745744
$583$	39.5589	−	16.3858i	1.63836	−	0.678632i
$584$	9.33558	+	3.86692i	0.386309	+	0.160014i
$585$	−0.117872	−	0.0268495i	−0.00487341	−	0.00111009i
$586$	1.29380	−	1.29380i	0.0534464	−	0.0534464i
$587$	29.7628	+	29.7628i	1.22844	+	1.22844i	0.964553	+	0.263889i	$0.0850053\pi$
$587$	29.7628	+	29.7628i	1.22844	+	1.22844i	0.263889	+	0.964553i	$0.414995\pi$
$588$	1.70750	+	0.707270i	0.0704161	+	0.0291673i
$589$	−5.48773	−	2.27309i	−0.226118	−	0.0936612i
$590$	−27.2674	+	17.1498i	−1.12258	+	0.706048i
$591$		−	1.00470i		−	0.0413279i
$592$	1.49475	+	3.60864i	0.0614338	+	0.148314i
$593$	−24.2183	+	24.2183i	−0.994525	+	0.994525i	−0.999985	−	0.00546017i	$-0.998262\pi$
$593$	−24.2183	+	24.2183i	−0.994525	+	0.994525i	0.00546017	+	0.999985i	$0.498262\pi$
$594$	−5.08826			−0.208774
$595$	28.6085	+	19.7653i	1.17283	+	0.810296i
$596$	12.3746			0.506884
$597$	2.30288	−	2.30288i	0.0942507	−	0.0942507i
$598$	0.0368719	+	0.0890166i	0.00150780	+	0.00364016i
$599$			13.7921i			0.563530i	0.959483	+	0.281765i	$0.0909199\pi$
$599$			13.7921i			0.563530i	−0.959483	+	0.281765i	$0.909080\pi$
$600$	0.853124	+	0.952974i	0.0348286	+	0.0389050i
$601$	14.6285	+	6.05931i	0.596708	+	0.247164i	0.660533	−	0.750797i	$-0.270330\pi$
$601$	14.6285	+	6.05931i	0.596708	+	0.247164i	−0.0638257	+	0.997961i	$0.520330\pi$
$602$	−15.8982	−	6.58524i	−0.647961	−	0.268394i
$603$	−24.3194	−	24.3194i	−0.990364	−	0.990364i
$604$	7.00868	−	7.00868i	0.285179	−	0.285179i
$605$	0.116074	−	0.509577i	0.00471909	−	0.0207172i
$606$	1.91608	+	0.793668i	0.0778355	+	0.0322405i
$607$	10.2036	−	4.22647i	0.414151	−	0.171547i	−0.165872	−	0.986147i	$-0.553044\pi$
$607$	10.2036	−	4.22647i	0.414151	−	0.171547i	0.580023	+	0.814600i	$0.303044\pi$
$608$	−5.72526			−0.232190
$609$	0.555102	−	0.229931i	0.0224939	−	0.00931726i
$610$	−7.42472	+	10.4738i	−0.300618	+	0.424073i
$611$	0.180308			0.00729449
$612$	12.0986	−	0.146142i	0.489058	−	0.00590743i
$613$			44.0174i			1.77785i	0.458057	+	0.888923i	$0.348546\pi$
$613$			44.0174i			1.77785i	−0.458057	+	0.888923i	$0.651454\pi$
$614$	−3.81327	−	3.81327i	−0.153891	−	0.153891i
$615$	2.13403	+	3.39301i	0.0860523	+	0.136819i
$616$			12.6411i			0.509325i
$617$	24.4415	−	10.1240i	0.983977	−	0.407577i	0.168080	−	0.985773i	$-0.446243\pi$
$617$	24.4415	−	10.1240i	0.983977	−	0.407577i	0.815897	+	0.578197i	$0.196243\pi$
$618$	−0.430592	+	1.03954i	−0.0173210	+	0.0418165i
$619$	−9.96376	+	24.0546i	−0.400477	+	0.966838i	0.587073	+	0.809534i	$0.300280\pi$
$619$	−9.96376	+	24.0546i	−0.400477	+	0.966838i	−0.987550	+	0.157304i	$0.949720\pi$
$620$	1.34163	−	1.89260i	0.0538811	−	0.0760085i
$621$	−5.61411	+	5.61411i	−0.225287	+	0.225287i
$622$	28.3739	+	11.7529i	1.13769	+	0.471247i
$623$	20.9118	−	50.4856i	0.837814	−	2.02266i
$624$	−0.00180354	−	0.00435413i	−7.21993e−5	−	0.000174305i
$625$	−15.6213	−	19.5186i	−0.624851	−	0.780744i
$626$	17.7837	−	7.36626i	0.710781	−	0.294415i
$627$	3.47105	−	3.47105i	0.138621	−	0.138621i
$628$		−	8.23758i		−	0.328715i
$629$	14.9522	+	5.98284i	0.596182	+	0.238552i
$630$	−24.3972	+	4.15617i	−0.972006	+	0.165586i
$631$	32.5699	+	32.5699i	1.29659	+	1.29659i	0.930633	+	0.365954i	$0.119257\pi$
$631$	32.5699	+	32.5699i	1.29659	+	1.29659i	0.365954	+	0.930633i	$0.380743\pi$
$632$	−2.03822	−	4.92071i	−0.0810762	−	0.195735i
$633$	1.06518			0.0423372
$634$	−7.39242	−	17.8469i	−0.293591	−	0.708790i
$635$	5.70187	−	25.0318i	0.226272	−	0.993355i
$636$	−1.25062	+	3.01927i	−0.0495903	+	0.119722i
$637$	0.0941192	+	0.0941192i	0.00372914	+	0.00372914i
$638$	1.47592	+	1.47592i	0.0584321	+	0.0584321i
$639$	−4.39867	+	10.6193i	−0.174009	+	0.420094i
$640$	0.496623	−	2.18022i	0.0196307	−	0.0861808i
$641$	−6.81140	−	16.4442i	−0.269034	−	0.649506i	0.730404	−	0.683015i	$-0.239332\pi$
$641$	−6.81140	−	16.4442i	−0.269034	−	0.649506i	−0.999438	+	0.0335091i	$0.989332\pi$
$642$	−2.65456			−0.104767
$643$	3.28336	+	7.92672i	0.129483	+	0.312599i	0.975304	−	0.220868i	$-0.0708888\pi$
$643$	3.28336	+	7.92672i	0.129483	+	0.312599i	−0.845821	+	0.533467i	$0.820889\pi$
$644$	13.9475	+	13.9475i	0.549609	+	0.549609i
$645$	−2.57277	+	0.438283i	−0.101303	+	0.0172574i
$646$	−16.4890	+	16.8923i	−0.648753	+	0.664617i
$647$		−	7.55698i		−	0.297096i	−0.988905	−	0.148548i	$-0.952540\pi$
$647$		−	7.55698i		−	0.297096i	0.988905	−	0.148548i	$-0.0474599\pi$
$648$	−5.95054	+	5.95054i	−0.233759	+	0.233759i
$649$	−44.6081	+	18.4773i	−1.75102	+	0.725297i
$650$	0.0304998	+	0.0869206i	0.00119630	+	0.00340931i
$651$	−0.383058	−	0.924783i	−0.0150132	−	0.0362451i
$652$	−7.46435	+	18.0205i	−0.292327	+	0.705739i
$653$	−38.7782	−	16.0625i	−1.51751	−	0.628573i	−0.540418	−	0.841396i	$-0.681734\pi$
$653$	−38.7782	−	16.0625i	−1.51751	−	0.628573i	−0.977091	+	0.212824i	$0.931734\pi$
$654$	−1.36804	+	1.36804i	−0.0534947	+	0.0534947i
$655$	2.77023	−	3.90788i	0.108242	−	0.152693i
$656$	2.68162	−	6.47400i	0.104700	−	0.252767i
$657$	−11.3477	+	27.3958i	−0.442717	+	1.06881i
$658$	34.1026	−	14.1258i	1.32946	−	0.550679i
$659$		−	16.5021i		−	0.642831i	−0.946938	−	0.321415i	$-0.895841\pi$
$659$		−	16.5021i		−	0.642831i	0.946938	−	0.321415i	$-0.104159\pi$
$660$	1.02071	+	1.62289i	0.0397313	+	0.0631709i
$661$	13.4414	+	13.4414i	0.522810	+	0.522810i	0.918419	−	0.395609i	$-0.129466\pi$
$661$	13.4414	+	13.4414i	0.522810	+	0.522810i	−0.395609	+	0.918419i	$0.629466\pi$
$662$		−	19.3291i		−	0.751245i
$663$	−0.0180410	−	0.00721880i	−0.000700656	−	0.000280355i
$664$	1.19946			0.0465482
$665$	27.9234	−	39.3907i	1.08282	−	1.52751i
$666$	−10.5898	+	4.38643i	−0.410345	+	0.169971i
$667$	3.25689			0.126107
$668$	16.6827	−	6.91021i	0.645474	−	0.267364i
$669$	−1.59252	−	0.659643i	−0.0615703	−	0.0255033i
$670$	−5.82039	+	25.5521i	−0.224861	+	0.987162i
$671$	−13.6074	+	13.6074i	−0.525310	+	0.525310i
$672$	−0.682224	−	0.682224i	−0.0263174	−	0.0263174i
$673$	−4.60137	−	1.90595i	−0.177370	−	0.0734690i	0.292231	−	0.956348i	$-0.405602\pi$
$673$	−4.60137	−	1.90595i	−0.177370	−	0.0734690i	−0.469601	+	0.882879i	$0.655602\pi$
$674$	−31.9699	−	13.2424i	−1.23143	−	0.510077i
$675$	−5.65548	+	5.06291i	−0.217680	+	0.194872i
$676$			12.9997i			0.499987i
$677$	−10.2143	−	24.6595i	−0.392567	−	0.947742i	−0.989379	−	0.145360i	$-0.953566\pi$
$677$	−10.2143	−	24.6595i	−0.392567	−	0.947742i	0.596811	−	0.802382i	$-0.296434\pi$
$678$	2.86031	−	2.86031i	0.109849	−	0.109849i
$679$	−26.5250			−1.01794
$680$	−5.00240	−	7.74442i	−0.191833	−	0.296985i
$681$	−1.43920			−0.0551503
$682$	2.45883	−	2.45883i	0.0941536	−	0.0941536i
$683$	9.80233	+	23.6649i	0.375076	+	0.905513i	0.992873	+	0.119176i	$0.0380252\pi$
$683$	9.80233	+	23.6649i	0.375076	+	0.905513i	−0.617797	+	0.786337i	$0.711975\pi$
$684$		−	16.8011i		−	0.642407i
$685$	−29.1268	+	18.3193i	−1.11288	+	0.699943i
$686$	0.783356	+	0.324477i	0.0299087	+	0.0123886i
$687$	−3.01941	−	1.25068i	−0.115198	−	0.0477165i
$688$	3.22622	+	3.22622i	0.122998	+	0.122998i
$689$	−0.166425	+	0.166425i	−0.00634029	+	0.00634029i
$690$	2.91681	+	0.664407i	0.111041	+	0.0252935i
$691$	−30.5236	−	12.6433i	−1.16117	−	0.480974i	−0.282908	−	0.959147i	$-0.591299\pi$
$691$	−30.5236	−	12.6433i	−1.16117	−	0.480974i	−0.878265	+	0.478174i	$0.841299\pi$
$692$	−6.62378	+	2.74366i	−0.251798	+	0.104298i
$693$	−37.0961			−1.40916
$694$	−0.0173964	+	0.00720582i	−0.000660358	+	0.000273529i
$695$	6.82057	+	4.83499i	0.258719	+	0.183402i
$696$	−0.159307			−0.00603850
$697$	−11.3782	−	26.5575i	−0.430980	−	1.00594i
$698$			32.5886i			1.23350i
$699$	5.45034	+	5.45034i	0.206151	+	0.206151i
$700$	12.5781	+	14.0503i	0.475409	+	0.531051i
$701$			26.5193i			1.00162i	0.865557	+	0.500810i	$0.166965\pi$
$701$			26.5193i			1.00162i	−0.865557	+	0.500810i	$0.833035\pi$
$702$	0.0258398	−	0.0107032i	0.000975261	−	0.000403967i
$703$	8.55782	−	20.6604i	0.322764	−	0.779222i
$704$	1.28263	−	3.09654i	0.0483410	−	0.116705i
$705$	3.23756	−	4.56713i	0.121934	−	0.172008i
$706$	−6.46009	+	6.46009i	−0.243129	+	0.243129i
$707$	28.2500	+	11.7015i	1.06245	+	0.440082i
$708$	1.41025	−	3.40464i	0.0530003	−	0.127954i
$709$	10.6595	+	25.7344i	0.400327	+	0.966474i	0.987587	+	0.157076i	$0.0502066\pi$
$709$	10.6595	+	25.7344i	0.400327	+	0.966474i	−0.587260	+	0.809398i	$0.699793\pi$
$710$	8.63398	−	1.47084i	0.324028	−	0.0551997i
$711$	14.4401	−	5.98130i	0.541547	−	0.224316i
$712$	−10.2450	+	10.2450i	−0.383949	+	0.383949i
$713$		−	5.42589i		−	0.203201i
$714$	−3.97773	+	0.0480478i	−0.148863	+	0.00179814i
$715$	0.0231876	+	0.136114i	0.000867168	+	0.00509036i
$716$	8.77745	+	8.77745i	0.328029	+	0.328029i
$717$	0.529720	+	1.27886i	0.0197827	+	0.0477598i
$718$	6.51656			0.243196
$719$	0.942923	+	2.27642i	0.0351651	+	0.0848960i	0.940486	−	0.339831i	$-0.110370\pi$
$719$	0.942923	+	2.27642i	0.0351651	+	0.0848960i	−0.905321	+	0.424727i	$0.860370\pi$
$720$	6.39799	+	1.45737i	0.238439	+	0.0543130i
$721$	−6.34849	+	15.3266i	−0.236430	+	0.570793i
$722$	9.74296	+	9.74296i	0.362596	+	0.362596i
$723$	4.78688	+	4.78688i	0.178026	+	0.178026i
$724$	−5.66646	+	13.6800i	−0.210592	+	0.508415i
$725$	3.10901	+	0.171883i	0.115466	+	0.00638356i
$726$	0.0228806	+	0.0552387i	0.000849179	+	0.00205010i
$727$	−46.8620			−1.73802			−0.869008	−	0.494798i	$-0.835242\pi$
$727$	−46.8620			−1.73802			−0.869008	+	0.494798i	$0.835242\pi$
$728$	−0.0265907	−	0.0641956i	−0.000985517	−	0.00237925i
$729$	−16.6384	−	16.6384i	−0.616237	−	0.616237i
$730$	22.2740	−	3.79449i	0.824399	−	0.140440i
$731$	18.8105	−	0.227217i	0.695733	−	0.00840391i
$732$		−	1.46875i		−	0.0542867i
$733$	3.58653	−	3.58653i	0.132472	−	0.132472i	−0.637762	−	0.770234i	$-0.720140\pi$
$733$	3.58653	−	3.58653i	0.132472	−	0.132472i	0.770234	+	0.637762i	$0.220140\pi$
$734$	16.0161	−	6.63410i	0.591166	−	0.244869i
$735$	4.07398	−	0.694022i	0.150271	−	0.0255994i
$736$	−2.00137	−	4.83175i	−0.0737716	−	0.178100i
$737$	−15.0323	+	36.2913i	−0.553724	+	1.33681i
$738$	18.9984	+	7.86938i	0.699339	+	0.289676i
$739$	24.1638	−	24.1638i	0.888878	−	0.888878i	−0.105537	−	0.994415i	$-0.533656\pi$
$739$	24.1638	−	24.1638i	0.888878	−	0.888878i	0.994415	+	0.105537i	$0.0336561\pi$
$740$	7.12531	+	5.05101i	0.261932	+	0.185679i
$741$	−0.0103257	+	0.0249285i	−0.000379325	+	0.000915772i
$742$	−18.4387	+	44.5149i	−0.676906	+	1.63419i
$743$	−4.47389	+	1.85315i	−0.164131	+	0.0679853i	−0.463236	−	0.886235i	$-0.653312\pi$
$743$	−4.47389	+	1.85315i	−0.164131	+	0.0679853i	0.299105	+	0.954220i	$0.403312\pi$
$744$			0.265400i			0.00973005i
$745$	23.4229	−	14.7318i	0.858148	−	0.539731i
$746$	−8.52710	−	8.52710i	−0.312199	−	0.312199i
$747$			3.51990i			0.128786i
$748$	−5.44224	−	12.7026i	−0.198988	−	0.464452i
$749$	−39.1379			−1.43007
$750$	2.74931	+	0.788173i	0.100390	+	0.0287800i
$751$	20.6307	−	8.54552i	0.752826	−	0.311831i	0.0269317	−	0.999637i	$-0.491426\pi$
$751$	20.6307	−	8.54552i	0.752826	−	0.311831i	0.725894	+	0.687807i	$0.241426\pi$
$752$	−9.78698			−0.356894
$753$	−2.23265	+	0.924796i	−0.0813624	+	0.0337014i
$754$	−0.0105998	−	0.00439057i	−0.000386021	−	0.000159895i
$755$	4.92241	−	21.6099i	0.179145	−	0.786463i
$756$	4.04870	−	4.04870i	0.147250	−	0.147250i
$757$	−16.0869	−	16.0869i	−0.584689	−	0.584689i	0.351499	−	0.936188i	$-0.385672\pi$
$757$	−16.0869	−	16.0869i	−0.584689	−	0.584689i	−0.936188	+	0.351499i	$0.885672\pi$
$758$	3.97427	+	1.64620i	0.144352	+	0.0597926i
$759$	4.14271	+	1.71597i	0.150371	+	0.0622857i
$760$	−10.8369	+	6.81583i	−0.393094	+	0.247236i
$761$		−	29.0870i		−	1.05440i	−0.849741	−	0.527201i	$-0.823242\pi$
$761$		−	29.0870i		−	1.05440i	0.849741	−	0.527201i	$-0.176758\pi$
$762$	1.12396	+	2.71347i	0.0407166	+	0.0982986i
$763$	−20.1699	+	20.1699i	−0.730200	+	0.730200i
$764$	−14.1264			−0.511074
$765$	22.7265	−	14.6798i	0.821677	−	0.530751i
$766$	17.0196			0.614945
$767$	0.187667	−	0.187667i	0.00677627	−	0.00677627i
$768$	0.0978946	+	0.236338i	0.00353247	+	0.00852813i
$769$			15.8002i			0.569769i	0.958562	+	0.284885i	$0.0919553\pi$
$769$			15.8002i			0.569769i	−0.958562	+	0.284885i	$0.908045\pi$
$770$	15.0490	+	23.9273i	0.542330	+	0.862279i
$771$	0.191217	+	0.0792046i	0.00688651	+	0.00285249i
$772$	7.81080	+	3.23534i	0.281117	+	0.116442i
$773$	−26.0167	−	26.0167i	−0.935756	−	0.935756i	0.0623010	−	0.998057i	$-0.480156\pi$
$773$	−26.0167	−	26.0167i	−0.935756	−	0.935756i	−0.998057	+	0.0623010i	$0.980156\pi$
$774$	−9.46753	+	9.46753i	−0.340303	+	0.340303i
$775$	0.286351	−	5.17952i	0.0102860	−	0.186054i
$776$	6.49752	+	2.69136i	0.233247	+	0.0966143i
$777$	3.48166	−	1.44215i	0.124904	−	0.0517368i
$778$	−12.9779			−0.465281
$779$	−37.0654	+	15.3530i	−1.32800	+	0.550078i
$780$	−0.00859728	−	0.00609447i	−0.000307832	−	0.000218217i
$781$	13.1281			0.469759
$782$	−20.0200	−	8.01065i	−0.715914	−	0.286460i
$783$		−	0.945415i		−	0.0337864i
$784$	−5.10871	−	5.10871i	−0.182454	−	0.182454i
$785$	−9.80671	−	15.5922i	−0.350016	−	0.556510i
$786$			0.548005i			0.0195467i
$787$	25.3491	−	10.5000i	0.903599	−	0.374283i	0.117996	−	0.993014i	$-0.462353\pi$
$787$	25.3491	−	10.5000i	0.903599	−	0.374283i	0.785603	+	0.618731i	$0.212353\pi$
$788$	−1.50300	+	3.62856i	−0.0535421	+	0.129262i
$789$	1.68735	−	4.07362i	0.0600712	−	0.145025i
$790$	−9.71601	−	6.88752i	−0.345680	−	0.245047i
$791$	42.1713	−	42.1713i	1.49944	−	1.49944i
$792$	9.08700	+	3.76396i	0.322892	+	0.133746i
$793$	0.0404796	−	0.0977264i	0.00143747	−	0.00347037i
$794$	−3.61663	−	8.73132i	−0.128349	−	0.309863i
$795$	1.22719	+	7.20376i	0.0435241	+	0.255491i
$796$	−11.7621	+	4.87200i	−0.416895	+	0.172684i
$797$	9.38070	−	9.38070i	0.332281	−	0.332281i	−0.521171	−	0.853452i	$-0.674505\pi$
$797$	9.38070	−	9.38070i	0.332281	−	0.332281i	0.853452	+	0.521171i	$0.174505\pi$
$798$			5.52380i			0.195540i
$799$	−28.1870	+	28.8763i	−0.997184	+	1.02157i
$800$	−1.65550	−	4.71798i	−0.0585309	−	0.166806i
$801$	−30.0647	−	30.0647i	−1.06228	−	1.06228i
$802$	−0.663235	−	1.60119i	−0.0234196	−	0.0565400i
$803$	33.8679			1.19517
$804$	−1.14732	−	2.76987i	−0.0404628	−	0.0976858i
$805$	43.0044	+	9.79577i	1.51570	+	0.345255i
$806$	−0.00731457	+	0.0176589i	−0.000257645	+	0.000622009i
$807$	2.63523	+	2.63523i	0.0927644	+	0.0927644i
$808$	−5.73278	−	5.73278i	−0.201678	−	0.201678i
$809$	5.86093	−	14.1495i	0.206059	−	0.497471i	−0.786737	−	0.617289i	$-0.788231\pi$
$809$	5.86093	−	14.1495i	0.206059	−	0.497471i	0.992796	+	0.119818i	$0.0382310\pi$
$810$	−4.17924	+	18.3473i	−0.146844	+	0.644658i
$811$	5.37486	+	12.9761i	0.188737	+	0.455651i	0.989717	−	0.143040i	$-0.0456877\pi$
$811$	5.37486	+	12.9761i	0.188737	+	0.455651i	−0.800980	+	0.598691i	$0.795688\pi$
$812$	−2.34876			−0.0824252
$813$	−0.395930	−	0.955861i	−0.0138859	−	0.0335235i
$814$	9.25711	+	9.25711i	0.324461	+	0.324461i
$815$	7.32453	+	42.9957i	0.256567	+	1.50608i
$816$	0.979252	+	0.391831i	0.0342807	+	0.0137168i
$817$		−	26.1219i		−	0.913888i
$818$	4.81932	−	4.81932i	0.168504	−	0.168504i
$819$	0.188386	−	0.0780320i	0.00658274	−	0.00272666i
$820$	−2.63139	−	15.4465i	−0.0918921	−	0.539416i
$821$	0.0584100	+	0.141014i	0.00203852	+	0.00492143i	0.924896	−	0.380221i	$-0.124152\pi$
$821$	0.0584100	+	0.141014i	0.00203852	+	0.00492143i	−0.922857	+	0.385143i	$0.874152\pi$
$822$	1.50641	−	3.63679i	0.0525420	−	0.126848i
$823$	3.96960	+	1.64426i	0.138371	+	0.0573153i	0.450795	−	0.892628i	$-0.351141\pi$
$823$	3.96960	+	1.64426i	0.138371	+	0.0573153i	−0.312423	+	0.949943i	$0.601141\pi$
$824$	3.11023	−	3.11023i	0.108350	−	0.108350i
$825$	3.86405	+	1.85668i	0.134529	+	0.0646414i
$826$	20.7921	−	50.1967i	0.723451	−	1.74657i
$827$	6.26098	−	15.1153i	0.217716	−	0.525612i	−0.776854	−	0.629680i	$-0.783186\pi$
$827$	6.26098	−	15.1153i	0.217716	−	0.525612i	0.994570	+	0.104068i	$0.0331860\pi$
$828$	14.1791	−	5.87316i	0.492756	−	0.204106i
$829$		−	28.8036i		−	1.00039i	−0.865912	−	0.500196i	$-0.833261\pi$
$829$		−	28.8036i		−	1.00039i	0.865912	−	0.500196i	$-0.166739\pi$
$830$	2.27036	−	1.42794i	0.0788054	−	0.0495646i
$831$	−2.45658	−	2.45658i	−0.0852177	−	0.0852177i
$832$			0.0184233i			0.000638712i
$833$	−29.7865	+	0.359797i	−1.03204	+	0.0124662i
$834$	−0.956454			−0.0331193
$835$	23.3508	−	32.9403i	0.808088	−	1.13994i
$836$	−17.7285	+	7.34340i	−0.613154	+	0.253977i
$837$	−1.57503			−0.0544411
$838$	16.6715	−	6.90556i	0.575908	−	0.238549i
$839$	−48.9607	−	20.2802i	−1.69031	−	0.700149i	−0.690576	−	0.723259i	$-0.742643\pi$
$839$	−48.9607	−	20.2802i	−1.69031	−	0.700149i	−0.999733	+	0.0231103i	$0.992643\pi$
$840$	−2.10350	−	0.479147i	−0.0725777	−	0.0165321i
$841$	20.2319	−	20.2319i	0.697651	−	0.697651i
$842$	7.50226	+	7.50226i	0.258545	+	0.258545i
$843$	−3.94633	−	1.63462i	−0.135919	−	0.0562994i
$844$	−3.84699	−	1.59347i	−0.132419	−	0.0548497i
$845$	15.4759	+	24.6059i	0.532387	+	0.846470i
$846$		−	28.7205i		−	0.987431i
$847$	0.337343	+	0.814419i	0.0115913	+	0.0279838i
$848$	9.03342	−	9.03342i	0.310209	−	0.310209i
$849$	2.82438			0.0969325
$850$	−18.6882	−	8.70348i	−0.641001	−	0.298527i
$851$	20.4276			0.700248
$852$	−0.708504	+	0.708504i	−0.0242729	+	0.0242729i
$853$	16.2421	+	39.2118i	0.556118	+	1.34259i	0.912817	+	0.408368i	$0.133902\pi$
$853$	16.2421	+	39.2118i	0.556118	+	1.34259i	−0.356699	+	0.934219i	$0.616098\pi$
$854$		−	21.6547i		−	0.741010i
$855$	−20.0015	−	31.8014i	−0.684036	−	1.08759i
$856$	9.58715	+	3.97113i	0.327682	+	0.135730i
$857$	10.4175	+	4.31505i	0.355854	+	0.147399i	0.553446	−	0.832885i	$-0.313312\pi$
$857$	10.4175	+	4.31505i	0.355854	+	0.147399i	−0.197593	+	0.980284i	$0.563312\pi$
$858$	−0.0111695	−	0.0111695i	−0.000381319	−	0.000381319i
$859$	24.4052	−	24.4052i	0.832693	−	0.832693i	−0.155191	−	0.987884i	$-0.549599\pi$
$859$	24.4052	−	24.4052i	0.832693	−	0.832693i	0.987884	+	0.155191i	$0.0495994\pi$
$860$	9.94739	+	2.26587i	0.339203	+	0.0772656i
$861$	−6.24619	−	2.58726i	−0.212870	−	0.0881735i
$862$	−20.2493	+	8.38753i	−0.689693	+	0.285680i
$863$	−3.77491			−0.128499			−0.0642497	−	0.997934i	$-0.520465\pi$
$863$	−3.77491			−0.128499			−0.0642497	+	0.997934i	$0.520465\pi$
$864$	−1.40256	+	0.580961i	−0.0477162	+	0.0197647i
$865$	−9.27131	+	13.0788i	−0.315234	+	0.444691i
$866$	−33.4527			−1.13677
$867$	3.97638	−	1.76077i	0.135045	−	0.0597989i
$868$			3.91296i			0.132815i
$869$	−12.6229	−	12.6229i	−0.428203	−	0.428203i
$870$	−0.301538	+	0.189652i	−0.0102231	+	0.00642981i
$871$		−	0.215920i		−	0.00731615i
$872$	6.98733	−	2.89425i	0.236621	−	0.0980116i
$873$	−7.89797	+	19.0674i	−0.267306	+	0.645333i
$874$	−11.4584	+	27.6630i	−0.387586	+	0.935715i
$875$	40.5347	+	11.6205i	1.37032	+	0.392846i
$876$	−1.82780	+	1.82780i	−0.0617558	+	0.0617558i
$877$	−5.81504	−	2.40867i	−0.196360	−	0.0813349i	0.282337	−	0.959315i	$-0.408891\pi$
$877$	−5.81504	−	2.40867i	−0.196360	−	0.0813349i	−0.478696	+	0.877981i	$0.658891\pi$
$878$	13.8134	−	33.3486i	0.466181	−	1.12546i
$879$	0.179119	+	0.432431i	0.00604152	+	0.0145855i
$880$	−1.25860	−	7.38814i	−0.0424276	−	0.249054i
$881$	−12.3589	+	5.11923i	−0.416382	+	0.172471i	−0.581032	−	0.813881i	$-0.697351\pi$
$881$	−12.3589	+	5.11923i	−0.416382	+	0.172471i	0.164649	+	0.986352i	$0.447351\pi$
$882$	14.9918	−	14.9918i	0.504801	−	0.504801i
$883$			8.57418i			0.288544i	0.989538	+	0.144272i	$0.0460840\pi$
$883$			8.57418i			0.288544i	−0.989538	+	0.144272i	$0.953916\pi$
$884$	0.0543574	+	0.0530599i	0.00182824	+	0.00178460i
$885$	−1.38383	−	8.12322i	−0.0465169	−	0.273059i
$886$	16.4585	+	16.4585i	0.552933	+	0.552933i
$887$	−12.4722	−	30.1106i	−0.418776	−	1.01101i	−0.982703	−	0.185189i	$-0.940710\pi$
$887$	−12.4722	−	30.1106i	−0.418776	−	1.01101i	0.563927	−	0.825825i	$-0.309290\pi$
$888$	−0.999188			−0.0335306
$889$	16.5712	+	40.0064i	0.555780	+	1.34177i
$890$	−7.19541	+	31.5885i	−0.241191	+	1.05885i
$891$	−10.7938	+	26.0584i	−0.361605	+	0.872991i
$892$	4.76470	+	4.76470i	0.159534	+	0.159534i
$893$	39.6213	+	39.6213i	1.32588	+	1.32588i
$894$	−1.21141	+	2.92460i	−0.0405156	+	0.0978132i
$895$	27.0635	+	6.16467i	0.904634	+	0.206062i
$896$	1.44332	+	3.48449i	0.0482180	+	0.116408i
$897$	−0.0246476			−0.000822959
$898$	2.51876	+	6.08083i	0.0840522	+	0.202920i
$899$	0.456859	+	0.456859i	0.0152371	+	0.0152371i
$900$	13.8452	−	4.85818i	0.461506	−	0.161939i
$901$	−0.636207	−	52.6696i	−0.0211951	−	1.75468i
$902$		−	23.4866i		−	0.782017i
$903$	3.11269	−	3.11269i	0.103584	−	0.103584i
$904$	−14.6091	+	6.05130i	−0.485892	+	0.201263i
$905$	5.56032	+	32.6396i	0.184831	+	1.08498i
$906$	0.970308	+	2.34253i	0.0322363	+	0.0778254i
$907$	9.61431	−	23.2110i	0.319238	−	0.770708i	−0.680057	−	0.733159i	$-0.738045\pi$
$907$	9.61431	−	23.2110i	0.319238	−	0.770708i	0.999295	−	0.0375490i	$-0.0119550\pi$
$908$	5.19778	+	2.15299i	0.172494	+	0.0714495i
$909$	16.8232	−	16.8232i	0.557990	−	0.557990i
$910$	−0.126755	−	0.0898546i	−0.00420189	−	0.00297865i
$911$	−7.35603	+	17.7590i	−0.243716	+	0.588383i	−0.997646	−	0.0685720i	$-0.978156\pi$
$911$	−7.35603	+	17.7590i	−0.243716	+	0.588383i	0.753930	+	0.656955i	$0.228156\pi$
$912$	0.560472	−	1.35310i	0.0185591	−	0.0448056i
$913$	3.71419	−	1.53847i	0.122922	−	0.0509159i
$914$		−	14.6705i		−	0.485256i
$915$	−1.74853	−	2.78008i	−0.0578045	−	0.0919065i
$916$	9.03385	+	9.03385i	0.298487	+	0.298487i
$917$			8.07958i			0.266811i
$918$	−2.32534	+	5.81143i	−0.0767477	+	0.191806i
$919$	−8.14764			−0.268766			−0.134383	−	0.990929i	$-0.542905\pi$
$919$	−8.14764			−0.268766			−0.134383	+	0.990929i	$0.542905\pi$
$920$	−9.54035	−	6.76299i	−0.314536	−	0.222969i
$921$	1.27452	−	0.527924i	0.0419969	−	0.0173957i
$922$	−6.66138			−0.219381
$923$	−0.0666685	+	0.0276150i	−0.00219442	+	0.000908958i
$924$	−2.98758	−	1.23750i	−0.0982842	−	0.0407106i
$925$	19.5000	+	1.07807i	0.641157	+	0.0354466i
$926$	8.00714	−	8.00714i	0.263131	−	0.263131i
$927$	9.12716	+	9.12716i	0.299775	+	0.299775i
$928$	0.575348	+	0.238317i	0.0188867	+	0.00782313i
$929$	−5.65710	−	2.34325i	−0.185603	−	0.0768794i	0.287946	−	0.957647i	$-0.407028\pi$
$929$	−5.65710	−	2.34325i	−0.185603	−	0.0768794i	−0.473550	+	0.880767i	$0.657028\pi$
$930$	0.315955	+	0.502353i	0.0103606	+	0.0164728i
$931$			41.3639i			1.35565i
$932$	−11.5308	−	27.8378i	−0.377704	−	0.911858i
$933$	−5.55530	+	5.55530i	−0.181873	+	0.181873i
$934$	17.4137			0.569793
$935$	−25.4234	−	17.5647i	−0.831433	−	0.574427i
$936$	−0.0540642			−0.00176714
$937$	−6.75756	+	6.75756i	−0.220760	+	0.220760i	−0.808818	−	0.588059i	$-0.799892\pi$
$937$	−6.75756	+	6.75756i	−0.220760	+	0.220760i	0.588059	+	0.808818i	$0.299892\pi$
$938$	−16.9156	−	40.8379i	−0.552315	−	1.33341i
$939$			4.92410i			0.160692i
$940$	−18.5249	+	11.6512i	−0.604217	+	0.380022i
$941$	17.8286	+	7.38483i	0.581194	+	0.240738i	0.653857	−	0.756618i	$-0.273150\pi$
$941$	17.8286	+	7.38483i	0.581194	+	0.240738i	−0.0726630	+	0.997357i	$0.523150\pi$
$942$	1.94686	+	0.806415i	0.0634320	+	0.0262744i
$943$	−25.9138	−	25.9138i	−0.843870	−	0.843870i
$944$	−10.1864	+	10.1864i	−0.331540	+	0.331540i
$945$	2.84353	−	12.4834i	0.0924999	−	0.406084i
$946$	14.1282	+	5.85208i	0.459346	+	0.190268i
$947$	−6.59771	+	2.73286i	−0.214397	+	0.0888060i	−0.487297	−	0.873236i	$-0.662017\pi$
$947$	−6.59771	+	2.73286i	−0.214397	+	0.0888060i	0.272900	+	0.962042i	$0.412017\pi$
$948$	1.36248			0.0442514
$949$	−0.171992	+	0.0712414i	−0.00558309	+	0.00231259i
$950$	−12.3980	+	25.8022i	−0.402245	+	0.837135i
$951$	4.94158			0.160242
$952$	14.4377	+	5.77700i	0.467930	+	0.187234i
$953$		−	35.2588i		−	1.14214i	−0.820900	−	0.571072i	$-0.806528\pi$
$953$		−	35.2588i		−	1.14214i	0.820900	−	0.571072i	$-0.193472\pi$
$954$	26.5091	+	26.5091i	0.858264	+	0.858264i
$955$	−26.7386	+	16.8172i	−0.865241	+	0.544192i
$956$		−	5.41113i		−	0.175008i
$957$	−0.493300	+	0.204332i	−0.0159461	+	0.00660510i
$958$	5.54593	−	13.3890i	0.179181	−	0.432580i
$959$	22.2099	−	53.6195i	0.717196	−	1.73146i
$960$	0.466653	+	0.330803i	0.0150612	+	0.0106766i
$961$	−21.1592	+	21.1592i	−0.682555	+	0.682555i
$962$	−0.0664830	−	0.0275381i	−0.00214350	−	0.000887865i
$963$	−11.6535	+	28.1341i	−0.375529	+	0.906608i
$964$	−10.1272	−	24.4491i	−0.326174	−	0.787454i
$965$	18.6360	−	3.17473i	0.599914	−	0.102198i
$966$	−4.66172	+	1.93095i	−0.149988	+	0.0621272i
$967$	6.68740	−	6.68740i	0.215052	−	0.215052i	−0.591357	−	0.806410i	$-0.701408\pi$
$967$	6.68740	−	6.68740i	0.215052	−	0.215052i	0.806410	+	0.591357i	$0.201408\pi$
$968$		−	0.233727i		−	0.00751227i
$969$	−2.37810	−	5.55065i	−0.0763956	−	0.178313i
$970$	15.5026	−	2.64095i	0.497759	−	0.0847957i
$971$	−13.8176	−	13.8176i	−0.443428	−	0.443428i	0.449734	−	0.893162i	$-0.351519\pi$
$971$	−13.8176	−	13.8176i	−0.443428	−	0.443428i	−0.893162	+	0.449734i	$0.851519\pi$
$972$	−2.56670	−	6.19656i	−0.0823269	−	0.198755i
$973$	−14.1016			−0.452076
$974$	13.2685	+	32.0330i	0.425150	+	1.02640i
$975$	−0.0235284	−	0.00130078i	−0.000753513	−	4.16582e-5i
$976$	−2.19720	+	5.30451i	−0.0703306	+	0.169793i
$977$	26.5863	+	26.5863i	0.850570	+	0.850570i	0.990203	−	0.139634i	$-0.0445924\pi$
$977$	26.5863	+	26.5863i	0.850570	+	0.850570i	−0.139634	+	0.990203i	$0.544592\pi$
$978$	−3.52823	−	3.52823i	−0.112820	−	0.112820i
$979$	−18.5836	+	44.8648i	−0.593935	+	1.43389i
$980$	−15.7517	−	3.58801i	−0.503169	−	0.114615i
$981$	8.49335	+	20.5047i	0.271172	+	0.654666i
$982$	15.1942			0.484866
$983$	7.16926	+	17.3081i	0.228664	+	0.552043i	0.996015	−	0.0891836i	$-0.0284258\pi$
$983$	7.16926	+	17.3081i	0.228664	+	0.552043i	−0.767351	+	0.641227i	$0.778426\pi$
$984$	1.26754	+	1.26754i	0.0404077	+	0.0404077i
$985$	1.47484	+	8.65748i	0.0469924	+	0.275850i
$986$	2.36018	−	1.01119i	0.0751634	−	0.0322027i
$987$			9.44259i			0.300561i
$988$	0.0745843	−	0.0745843i	0.00237284	−	0.00237284i
$989$	22.0451	−	9.13139i	0.700994	−	0.290361i
$990$	21.6809	−	3.69345i	0.689065	−	0.117386i
$991$	5.33279	+	12.8745i	0.169402	+	0.408972i	0.985666	−	0.168706i	$-0.0539590\pi$
$991$	5.33279	+	12.8745i	0.169402	+	0.408972i	−0.816265	+	0.577678i	$0.803959\pi$
$992$	0.397029	−	0.958512i	0.0126057	−	0.0304328i
$993$	4.56820	+	1.89221i	0.144967	+	0.0600474i
$994$	−10.4459	+	10.4459i	−0.331324	+	0.331324i
$995$	−16.4633	+	23.2243i	−0.521923	+	0.736261i
$996$	−0.117421	+	0.283479i	−0.00372062	+	0.00898238i
$997$	−7.17227	+	17.3154i	−0.227148	+	0.548384i	−0.995828	−	0.0912496i	$-0.970914\pi$
$997$	−7.17227	+	17.3154i	−0.227148	+	0.548384i	0.768680	+	0.639634i	$0.220914\pi$
$998$	15.8876	−	6.58086i	0.502913	−	0.208313i
$999$		−	5.92974i		−	0.187609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.b.19.3	yes	20
5.2	odd	4		850.2.l.i.801.3		20
5.3	odd	4		850.2.l.h.801.3		20
5.4	even	2		170.2.n.a.19.3	yes	20
17.9	even	8		170.2.n.a.9.3	✓	20
85.9	even	8	inner	170.2.n.b.9.3	yes	20
85.43	odd	8		850.2.l.h.451.3		20
85.77	odd	8		850.2.l.i.451.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.9.3	✓	20	17.9	even	8
170.2.n.a.19.3	yes	20	5.4	even	2
170.2.n.b.9.3	yes	20	85.9	even	8	inner
170.2.n.b.19.3	yes	20	1.1	even	1	trivial
850.2.l.h.451.3		20	85.43	odd	8
850.2.l.h.801.3		20	5.3	odd	4
850.2.l.i.451.3		20	85.77	odd	8
850.2.l.i.801.3		20	5.2	odd	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.0978946 + 0.236338i) q^{3} -1.00000i q^{4} +(-1.19048 - 1.89281i) q^{5} +(0.236338 + 0.0978946i) q^{6} +(3.48449 + 1.44332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07505 - 2.07505i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.0978946 + 0.236338i) q^{3} -1.00000i q^{4} +(-1.19048 - 1.89281i) q^{5} +(0.236338 + 0.0978946i) q^{6} +(3.48449 + 1.44332i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07505 - 2.07505i) q^{9} +(-2.18022 - 0.496623i) q^{10} +(-3.09654 - 1.28263i) q^{11} +(0.236338 - 0.0978946i) q^{12} +0.0184233 q^{13} +(3.48449 - 1.44332i) q^{14} +(0.330803 - 0.466653i) q^{15} -1.00000 q^{16} +(-2.88005 + 2.95048i) q^{17} -2.93456i q^{18} +(4.04837 + 4.04837i) q^{19} +(-1.89281 + 1.19048i) q^{20} +0.964811i q^{21} +(-3.09654 + 1.28263i) q^{22} +(-2.00137 + 4.83175i) q^{23} +(0.0978946 - 0.236338i) q^{24} +(-2.16549 + 4.50673i) q^{25} +(0.0130272 - 0.0130272i) q^{26} +(1.40256 + 0.580961i) q^{27} +(1.44332 - 3.48449i) q^{28} +(-0.238317 - 0.575348i) q^{29} +(-0.0960608 - 0.563887i) q^{30} +(-0.958512 + 0.397029i) q^{31} +(-0.707107 + 0.707107i) q^{32} -0.857395i q^{33} +(0.0498002 + 4.12280i) q^{34} +(-1.41629 - 8.31374i) q^{35} +(-2.07505 - 2.07505i) q^{36} +(-1.49475 - 3.60864i) q^{37} +5.72526 q^{38} +(0.00180354 + 0.00435413i) q^{39} +(-0.496623 + 2.18022i) q^{40} +(-2.68162 + 6.47400i) q^{41} +(0.682224 + 0.682224i) q^{42} +(-3.22622 - 3.22622i) q^{43} +(-1.28263 + 3.09654i) q^{44} +(-6.39799 - 1.45737i) q^{45} +(2.00137 + 4.83175i) q^{46} +9.78698 q^{47} +(-0.0978946 - 0.236338i) q^{48} +(5.10871 + 5.10871i) q^{49} +(1.65550 + 4.71798i) q^{50} +(-0.979252 - 0.391831i) q^{51} -0.0184233i q^{52} +(-9.03342 + 9.03342i) q^{53} +(1.40256 - 0.580961i) q^{54} +(1.25860 + 7.38814i) q^{55} +(-1.44332 - 3.48449i) q^{56} +(-0.560472 + 1.35310i) q^{57} +(-0.575348 - 0.238317i) q^{58} +(10.1864 - 10.1864i) q^{59} +(-0.466653 - 0.330803i) q^{60} +(2.19720 - 5.30451i) q^{61} +(-0.397029 + 0.958512i) q^{62} +(10.2254 - 4.23551i) q^{63} +1.00000i q^{64} +(-0.0219326 - 0.0348718i) q^{65} +(-0.606270 - 0.606270i) q^{66} -11.7199i q^{67} +(2.95048 + 2.88005i) q^{68} -1.33785 q^{69} +(-6.88016 - 4.87723i) q^{70} +(-3.61871 + 1.49892i) q^{71} -2.93456 q^{72} +(-9.33558 + 3.86692i) q^{73} +(-3.60864 - 1.49475i) q^{74} +(-1.27710 - 0.0706050i) q^{75} +(4.04837 - 4.04837i) q^{76} +(-8.93861 - 8.93861i) q^{77} +(0.00435413 + 0.00180354i) q^{78} +(4.92071 + 2.03822i) q^{79} +(1.19048 + 1.89281i) q^{80} -8.41533i q^{81} +(2.68162 + 6.47400i) q^{82} +(-0.848148 + 0.848148i) q^{83} +0.964811 q^{84} +(9.01336 + 1.93890i) q^{85} -4.56256 q^{86} +(0.112647 - 0.112647i) q^{87} +(1.28263 + 3.09654i) q^{88} -14.4887i q^{89} +(-5.55458 + 3.49355i) q^{90} +(0.0641956 + 0.0265907i) q^{91} +(4.83175 + 2.00137i) q^{92} +(-0.187666 - 0.187666i) q^{93} +(6.92044 - 6.92044i) q^{94} +(2.84330 - 12.4823i) q^{95} +(-0.236338 - 0.0978946i) q^{96} +(-6.49752 + 2.69136i) q^{97} +7.22481 q^{98} +(-9.08700 + 3.76396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^25 - 12 * q^26 - 24 * q^27 - 12 * q^29 + 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 8 * q^37 + 8 * q^38 - 4 * q^40 + 4 * q^41 - 8 * q^42 - 16 * q^43 - 8 * q^44 - 32 * q^45 + 16 * q^46 - 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 - 44 * q^53 - 24 * q^54 + 72 * q^57 + 16 * q^59 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

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