LMFDB - Embedded newform 185.2.e.b.26.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(26,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("185.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, degree $2$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 13 x^{12} - 16 x^{11} + 98 x^{10} - 116 x^{9} + 378 x^{8} - 264 x^{7} + 795 x^{6} + \cdots + 9 $ x^14 - 2x^13 + 13x^12 - 16x^11 + 98x^10 - 116x^9 + 378x^8 - 264x^7 + 795x^6 - 520x^5 + 927x^4 - 71x^3 + 94x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.6
Root			$0.945119 - 1.63699i$ of defining polynomial
Character	$\chi$	$=$	185.26
Dual form			185.2.e.b.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.945119 + 1.63699i) q^{2} +(-1.39740 + 2.42036i) q^{3} +(-0.786500 + 1.36226i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.28283 q^{6} +(-1.45316 + 2.51695i) q^{7} +0.807130 q^{8} +(-2.40544 - 4.16634i) q^{9} +O(q^{10})$	\(q+(0.945119 + 1.63699i) q^{2} +(-1.39740 + 2.42036i) q^{3} +(-0.786500 + 1.36226i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.28283 q^{6} +(-1.45316 + 2.51695i) q^{7} +0.807130 q^{8} +(-2.40544 - 4.16634i) q^{9} +1.89024 q^{10} -1.47557 q^{11} +(-2.19811 - 3.80723i) q^{12} +(2.69194 - 4.66258i) q^{13} -5.49364 q^{14} +(1.39740 + 2.42036i) q^{15} +(2.33584 + 4.04578i) q^{16} +(2.56406 + 4.44108i) q^{17} +(4.54685 - 7.87538i) q^{18} +(-0.298898 + 0.517706i) q^{19} +(0.786500 + 1.36226i) q^{20} +(-4.06129 - 7.03436i) q^{21} +(-1.39459 - 2.41551i) q^{22} -0.262996 q^{23} +(-1.12788 + 1.95355i) q^{24} +(-0.500000 - 0.866025i) q^{25} +10.1768 q^{26} +5.06103 q^{27} +(-2.28582 - 3.95916i) q^{28} +4.49216 q^{29} +(-2.64141 + 4.57506i) q^{30} -5.64383 q^{31} +(-3.60815 + 6.24951i) q^{32} +(2.06196 - 3.57143i) q^{33} +(-4.84668 + 8.39470i) q^{34} +(1.45316 + 2.51695i) q^{35} +7.56752 q^{36} +(2.45002 + 5.56753i) q^{37} -1.12998 q^{38} +(7.52342 + 13.0309i) q^{39} +(0.403565 - 0.698995i) q^{40} +(4.97363 - 8.61458i) q^{41} +(7.67680 - 13.2966i) q^{42} +9.62493 q^{43} +(1.16054 - 2.01011i) q^{44} -4.81088 q^{45} +(-0.248563 - 0.430523i) q^{46} +1.89024 q^{47} -13.0564 q^{48} +(-0.723354 - 1.25289i) q^{49} +(0.945119 - 1.63699i) q^{50} -14.3320 q^{51} +(4.23442 + 7.33424i) q^{52} +(-3.68014 - 6.37418i) q^{53} +(4.78328 + 8.28488i) q^{54} +(-0.737787 + 1.27788i) q^{55} +(-1.17289 + 2.03151i) q^{56} +(-0.835357 - 1.44688i) q^{57} +(4.24563 + 7.35365i) q^{58} +(-7.30117 - 12.6460i) q^{59} -4.39621 q^{60} +(-3.78059 + 6.54817i) q^{61} +(-5.33409 - 9.23892i) q^{62} +13.9820 q^{63} -4.29720 q^{64} +(-2.69194 - 4.66258i) q^{65} +7.79521 q^{66} +(0.570450 - 0.988048i) q^{67} -8.06653 q^{68} +(0.367510 - 0.636547i) q^{69} +(-2.74682 + 4.75763i) q^{70} +(6.83729 - 11.8425i) q^{71} +(-1.94150 - 3.36278i) q^{72} -13.7468 q^{73} +(-6.79845 + 9.27265i) q^{74} +2.79479 q^{75} +(-0.470166 - 0.814352i) q^{76} +(2.14425 - 3.71395i) q^{77} +(-14.2211 + 24.6316i) q^{78} +(5.86425 - 10.1572i) q^{79} +4.67167 q^{80} +(0.144041 - 0.249487i) q^{81} +18.8027 q^{82} +(-2.15344 - 3.72987i) q^{83} +12.7768 q^{84} +5.12812 q^{85} +(9.09670 + 15.7559i) q^{86} +(-6.27734 + 10.8727i) q^{87} -1.19098 q^{88} +(-3.73922 - 6.47651i) q^{89} +(-4.54685 - 7.87538i) q^{90} +(7.82364 + 13.5509i) q^{91} +(0.206847 - 0.358269i) q^{92} +(7.88668 - 13.6601i) q^{93} +(1.78650 + 3.09431i) q^{94} +(0.298898 + 0.517706i) q^{95} +(-10.0841 - 17.4661i) q^{96} -16.9163 q^{97} +(1.36731 - 2.36825i) q^{98} +(3.54940 + 6.14775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.945119	+	1.63699i	0.668300	+	1.15753i	0.978379	+	0.206819i	$0.0663111\pi$
$2$	0.945119	+	1.63699i	0.668300	+	1.15753i	−0.310079	+	0.950711i	$0.600356\pi$
$3$	−1.39740	+	2.42036i	−0.806788	+	1.39740i	0.108290	+	0.994119i	$0.465463\pi$
$3$	−1.39740	+	2.42036i	−0.806788	+	1.39740i	−0.915077	+	0.403278i	$0.867871\pi$
$4$	−0.786500	+	1.36226i	−0.393250	+	0.681129i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−5.28283			−2.15671
$7$	−1.45316	+	2.51695i	−0.549243	+	0.951317i	0.449083	+	0.893490i	$0.351751\pi$
$7$	−1.45316	+	2.51695i	−0.549243	+	0.951317i	−0.998327	+	0.0578273i	$0.981583\pi$
$8$	0.807130			0.285364
$9$	−2.40544	−	4.16634i	−0.801813	−	1.38878i
$10$	1.89024			0.597746
$11$	−1.47557			−0.444902			−0.222451	−	0.974944i	$-0.571406\pi$
$11$	−1.47557			−0.444902			−0.222451	+	0.974944i	$0.571406\pi$
$12$	−2.19811	−	3.80723i	−0.634539	−	1.09905i
$13$	2.69194	−	4.66258i	0.746610	−	1.29317i	−0.202829	−	0.979214i	$-0.565014\pi$
$13$	2.69194	−	4.66258i	0.746610	−	1.29317i	0.949439	−	0.313952i	$-0.101653\pi$
$14$	−5.49364			−1.46824
$15$	1.39740	+	2.42036i	0.360806	+	0.624935i
$16$	2.33584	+	4.04578i	0.583959	+	1.01145i
$17$	2.56406	+	4.44108i	0.621875	+	1.07712i	0.989136	+	0.147002i	$0.0469623\pi$
$17$	2.56406	+	4.44108i	0.621875	+	1.07712i	−0.367261	+	0.930118i	$0.619704\pi$
$18$	4.54685	−	7.87538i	1.07170	−	1.85625i
$19$	−0.298898	+	0.517706i	−0.0685718	+	0.118770i	−0.898273	−	0.439438i	$-0.855178\pi$
$19$	−0.298898	+	0.517706i	−0.0685718	+	0.118770i	0.829701	+	0.558208i	$0.188511\pi$
$20$	0.786500	+	1.36226i	0.175867	+	0.304610i
$21$	−4.06129	−	7.03436i	−0.886245	−	1.53502i
$22$	−1.39459	−	2.41551i	−0.297328	−	0.514988i
$23$	−0.262996			−0.0548385			−0.0274193	−	0.999624i	$-0.508729\pi$
$23$	−0.262996			−0.0548385			−0.0274193	+	0.999624i	$0.508729\pi$
$24$	−1.12788	+	1.95355i	−0.230228	+	0.398766i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	10.1768			1.99584
$27$	5.06103			0.973997
$28$	−2.28582	−	3.95916i	−0.431980	−	0.748211i
$29$	4.49216			0.834174			0.417087	−	0.908867i	$-0.363051\pi$
$29$	4.49216			0.834174			0.417087	+	0.908867i	$0.363051\pi$
$30$	−2.64141	+	4.57506i	−0.482254	+	0.835289i
$31$	−5.64383			−1.01366			−0.506831	−	0.862045i	$-0.669183\pi$
$31$	−5.64383			−1.01366			−0.506831	+	0.862045i	$0.669183\pi$
$32$	−3.60815	+	6.24951i	−0.637838	+	1.10477i
$33$	2.06196	−	3.57143i	0.358942	−	0.621706i
$34$	−4.84668	+	8.39470i	−0.831199	+	1.43968i
$35$	1.45316	+	2.51695i	0.245629	+	0.425442i
$36$	7.56752			1.26125
$37$	2.45002	+	5.56753i	0.402781	+	0.915296i
$37$	2.45002	+	5.56753i	0.402781	+	0.915296i
$38$	−1.12998			−0.183306
$39$	7.52342	+	13.0309i	1.20471	+	2.08662i
$40$	0.403565	−	0.698995i	0.0638092	−	0.110521i
$41$	4.97363	−	8.61458i	0.776751	−	1.34537i	−0.157054	−	0.987590i	$-0.550200\pi$
$41$	4.97363	−	8.61458i	0.776751	−	1.34537i	0.933805	−	0.357782i	$-0.116467\pi$
$42$	7.67680	−	13.2966i	1.18456	−	2.05171i
$43$	9.62493			1.46779			0.733894	−	0.679264i	$-0.237701\pi$
$43$	9.62493			1.46779			0.733894	+	0.679264i	$0.237701\pi$
$44$	1.16054	−	2.01011i	0.174958	−	0.303036i
$45$	−4.81088			−0.717163
$46$	−0.248563	−	0.430523i	−0.0366486	−	0.0634772i
$47$	1.89024			0.275720			0.137860	−	0.990452i	$-0.455978\pi$
$47$	1.89024			0.275720			0.137860	+	0.990452i	$0.455978\pi$
$48$	−13.0564			−1.88452
$49$	−0.723354	−	1.25289i	−0.103336	−	0.178984i
$50$	0.945119	−	1.63699i	0.133660	−	0.231506i
$51$	−14.3320			−2.00689
$52$	4.23442	+	7.33424i	0.587209	+	1.01708i
$53$	−3.68014	−	6.37418i	−0.505505	−	0.875561i	−0.999980	−	0.00636886i	$-0.997973\pi$
$53$	−3.68014	−	6.37418i	−0.505505	−	0.875561i	0.494474	−	0.869192i	$-0.335361\pi$
$54$	4.78328	+	8.28488i	0.650922	+	1.12743i
$55$	−0.737787	+	1.27788i	−0.0994832	+	0.172310i
$56$	−1.17289	+	2.03151i	−0.156734	+	0.271471i
$57$	−0.835357	−	1.44688i	−0.110646	−	0.191644i
$58$	4.24563	+	7.35365i	0.557478	+	0.965581i
$59$	−7.30117	−	12.6460i	−0.950531	−	1.64637i	−0.744278	−	0.667869i	$-0.767206\pi$
$59$	−7.30117	−	12.6460i	−0.950531	−	1.64637i	−0.206253	−	0.978499i	$-0.566127\pi$
$60$	−4.39621			−0.567549
$61$	−3.78059	+	6.54817i	−0.484054	+	0.838407i	−0.999832	−	0.0183156i	$-0.994170\pi$
$61$	−3.78059	+	6.54817i	−0.484054	+	0.838407i	0.515778	+	0.856722i	$0.327503\pi$
$62$	−5.33409	−	9.23892i	−0.677430	−	1.17334i
$63$	13.9820			1.76156
$64$	−4.29720			−0.537151
$65$	−2.69194	−	4.66258i	−0.333894	−	0.578321i
$66$	7.79521			0.959524
$67$	0.570450	−	0.988048i	0.0696915	−	0.120709i	−0.829074	−	0.559139i	$-0.811132\pi$
$67$	0.570450	−	0.988048i	0.0696915	−	0.120709i	0.898765	+	0.438430i	$0.144465\pi$
$68$	−8.06653			−0.978211
$69$	0.367510	−	0.636547i	0.0442430	−	0.0766312i
$70$	−2.74682	+	4.75763i	−0.328308	+	0.568646i
$71$	6.83729	−	11.8425i	0.811437	−	1.40545i	−0.100421	−	0.994945i	$-0.532019\pi$
$71$	6.83729	−	11.8425i	0.811437	−	1.40545i	0.911858	−	0.410506i	$-0.134648\pi$
$72$	−1.94150	−	3.36278i	−0.228808	−	0.396308i
$73$	−13.7468			−1.60894			−0.804471	−	0.593992i	$-0.797551\pi$
$73$	−13.7468			−1.60894			−0.804471	+	0.593992i	$0.797551\pi$
$74$	−6.79845	+	9.27265i	−0.790304	+	1.07792i
$75$	2.79479			0.322715
$76$	−0.470166	−	0.814352i	−0.0539318	−	0.0934125i
$77$	2.14425	−	3.71395i	0.244360	−	0.423243i
$78$	−14.2211	+	24.6316i	−1.61022	+	2.78898i
$79$	5.86425	−	10.1572i	0.659780	−	1.14277i	−0.320892	−	0.947116i	$-0.603983\pi$
$79$	5.86425	−	10.1572i	0.659780	−	1.14277i	0.980672	−	0.195657i	$-0.0626839\pi$
$80$	4.67167			0.522309
$81$	0.144041	−	0.249487i	0.0160046	−	0.0277208i
$82$	18.8027			2.07641
$83$	−2.15344	−	3.72987i	−0.236371	−	0.409407i	0.723299	−	0.690535i	$-0.242625\pi$
$83$	−2.15344	−	3.72987i	−0.236371	−	0.409407i	−0.959670	+	0.281128i	$0.909291\pi$
$84$	12.7768			1.39406
$85$	5.12812			0.556222
$86$	9.09670	+	15.7559i	0.980923	+	1.69901i
$87$	−6.27734	+	10.8727i	−0.673001	+	1.16567i
$88$	−1.19098			−0.126959
$89$	−3.73922	−	6.47651i	−0.396356	−	0.686509i	0.596917	−	0.802303i	$-0.296392\pi$
$89$	−3.73922	−	6.47651i	−0.396356	−	0.686509i	−0.993273	+	0.115794i	$0.963059\pi$
$90$	−4.54685	−	7.87538i	−0.479280	−	0.830138i
$91$	7.82364	+	13.5509i	0.820141	+	1.42053i
$92$	0.206847	−	0.358269i	0.0215653	−	0.0373521i
$93$	7.88668	−	13.6601i	0.817810	−	1.41649i
$94$	1.78650	+	3.09431i	0.184263	+	0.319154i
$95$	0.298898	+	0.517706i	0.0306662	+	0.0531155i
$96$	−10.0841	−	17.4661i	−1.02920	−	1.78263i
$97$	−16.9163			−1.71759			−0.858795	−	0.512319i	$-0.828787\pi$
$97$	−16.9163			−1.71759			−0.858795	+	0.512319i	$0.828787\pi$
$98$	1.36731	−	2.36825i	0.138119	−	0.239230i
$99$	3.54940	+	6.14775i	0.356729	+	0.617872i
$100$	1.57300			0.157300
$101$	11.6894			1.16314			0.581569	−	0.813497i	$-0.302439\pi$
$101$	11.6894			1.16314			0.581569	+	0.813497i	$0.302439\pi$
$102$	−13.5455	−	23.4615i	−1.34120	−	2.32303i
$103$	−6.77890			−0.667945			−0.333973	−	0.942583i	$-0.608389\pi$
$103$	−6.77890			−0.667945			−0.333973	+	0.942583i	$0.608389\pi$
$104$	2.17275	−	3.76331i	0.213055	−	0.369023i
$105$	−8.12257			−0.792682
$106$	6.95633	−	12.0487i	0.675659	−	1.17028i
$107$	0.702977	−	1.21759i	0.0679593	−	0.117709i	−0.830044	−	0.557699i	$-0.811685\pi$
$107$	0.702977	−	1.21759i	0.0679593	−	0.117709i	0.898003	+	0.439990i	$0.145018\pi$
$108$	−3.98051	+	6.89444i	−0.383024	+	0.663418i
$109$	9.72835	+	16.8500i	0.931807	+	1.61394i	0.780231	+	0.625492i	$0.215102\pi$
$109$	9.72835	+	16.8500i	0.931807	+	1.61394i	0.151576	+	0.988446i	$0.451565\pi$
$110$	−2.78919			−0.265939
$111$	−16.8991	−	1.85011i	−1.60399	−	0.175605i
$112$	−13.5774			−1.28294
$113$	5.78112	+	10.0132i	0.543842	+	0.941963i	0.998679	+	0.0513877i	$0.0163644\pi$
$113$	5.78112	+	10.0132i	0.543842	+	0.941963i	−0.454836	+	0.890575i	$0.650302\pi$
$114$	1.57902	−	2.73495i	0.147889	−	0.256152i
$115$	−0.131498	+	0.227761i	−0.0122623	+	0.0212389i
$116$	−3.53309	+	6.11949i	−0.328039	+	0.568180i
$117$	−25.9012			−2.39457
$118$	13.8009	−	23.9039i	1.27048	−	2.20054i
$119$	−14.9040			−1.36624
$120$	1.12788	+	1.95355i	0.102961	+	0.178334i
$121$	−8.82268			−0.802062
$122$	−14.2924			−1.29397
$123$	13.9003	+	24.0760i	1.25335	+	2.17086i
$124$	4.43888	−	7.68836i	0.398623	−	0.690435i
$125$	−1.00000			−0.0894427
$126$	13.2146	+	22.8884i	1.17725	+	2.03906i
$127$	2.09366	+	3.62633i	0.185783	+	0.321785i	0.943840	−	0.330403i	$-0.107185\pi$
$127$	2.09366	+	3.62633i	0.185783	+	0.321785i	−0.758057	+	0.652188i	$0.773851\pi$
$128$	3.15494	+	5.46452i	0.278860	+	0.482999i
$129$	−13.4498	+	23.2958i	−1.18419	+	2.05108i
$130$	5.08841	−	8.81338i	0.446283	−	0.772985i
$131$	2.07642	+	3.59647i	0.181418	+	0.314225i	0.942364	−	0.334591i	$-0.108598\pi$
$131$	2.07642	+	3.59647i	0.181418	+	0.314225i	−0.760946	+	0.648815i	$0.775265\pi$
$132$	3.24347	+	5.61786i	0.282308	+	0.488972i
$133$	−0.868693	−	1.50462i	−0.0753252	−	0.130467i
$134$	2.15657			0.186299
$135$	2.53052	−	4.38298i	0.217792	−	0.377227i
$136$	2.06953	+	3.58453i	0.177461	+	0.307371i
$137$	−2.07326			−0.177131			−0.0885654	−	0.996070i	$-0.528228\pi$
$137$	−2.07326			−0.177131			−0.0885654	+	0.996070i	$0.528228\pi$
$138$	1.38936			0.118271
$139$	−2.22254	−	3.84955i	−0.188513	−	0.326515i	0.756241	−	0.654293i	$-0.227034\pi$
$139$	−2.22254	−	3.84955i	−0.188513	−	0.326515i	−0.944755	+	0.327778i	$0.893700\pi$
$140$	−4.57165			−0.386375
$141$	−2.64141	+	4.57506i	−0.222447	+	0.385290i
$142$	25.8482			2.16913
$143$	−3.97216	+	6.87998i	−0.332168	+	0.575333i
$144$	11.2374	−	19.4638i	0.936452	−	1.62198i
$145$	2.24608	−	3.89033i	0.186527	−	0.323074i
$146$	−12.9924	−	22.5034i	−1.07526	−	1.86240i
$147$	4.04325			0.333482
$148$	−9.51136	−	1.04130i	−0.781829	−	0.0855944i
$149$	−5.95376			−0.487751			−0.243876	−	0.969807i	$-0.578419\pi$
$149$	−5.95376			−0.487751			−0.243876	+	0.969807i	$0.578419\pi$
$150$	2.64141	+	4.57506i	0.215671	+	0.373552i
$151$	0.138733	−	0.240293i	0.0112900	−	0.0195548i	−0.860325	−	0.509746i	$-0.829740\pi$
$151$	0.138733	−	0.240293i	0.0112900	−	0.0195548i	0.871615	+	0.490191i	$0.163073\pi$
$152$	−0.241249	+	0.417856i	−0.0195679	+	0.0338926i
$153$	12.3354	−	21.3655i	0.997256	−	1.72730i
$154$	8.10628			0.653222
$155$	−2.82192	+	4.88770i	−0.226662	+	0.392590i
$156$	−23.6687			−1.89501
$157$	3.75982	+	6.51220i	0.300066	+	0.519730i	0.976151	−	0.217094i	$-0.0696579\pi$
$157$	3.75982	+	6.51220i	0.300066	+	0.519730i	−0.676084	+	0.736824i	$0.736325\pi$
$158$	22.1697			1.76372
$159$	20.5704			1.63134
$160$	3.60815	+	6.24951i	0.285250	+	0.494067i
$161$	0.382176	−	0.661948i	0.0301197	−	0.0521688i
$162$	0.544545			0.0427835
$163$	4.10542	+	7.11080i	0.321561	+	0.556961i	0.980810	−	0.194964i	$-0.0624590\pi$
$163$	4.10542	+	7.11080i	0.321561	+	0.556961i	−0.659249	+	0.751925i	$0.729126\pi$
$164$	7.82353	+	13.5507i	0.610915	+	1.05814i
$165$	−2.06196	−	3.57143i	−0.160524	−	0.278035i
$166$	4.07052	−	7.05035i	0.315934	−	0.547213i
$167$	3.30577	−	5.72576i	0.255808	−	0.443073i	−0.709307	−	0.704900i	$-0.750992\pi$
$167$	3.30577	−	5.72576i	0.255808	−	0.443073i	0.965115	+	0.261827i	$0.0843251\pi$
$168$	−3.27799	−	5.67764i	−0.252902	−	0.438039i
$169$	−7.99308	−	13.8444i	−0.614852	−	1.06496i
$170$	4.84668	+	8.39470i	0.371723	+	0.643844i
$171$	2.87592			0.219927
$172$	−7.57001	+	13.1116i	−0.577208	+	0.999753i
$173$	2.33802	+	4.04956i	0.177756	+	0.307882i	0.941112	−	0.338096i	$-0.109783\pi$
$173$	2.33802	+	4.04956i	0.177756	+	0.307882i	−0.763356	+	0.645979i	$0.776450\pi$
$174$	−23.7313			−1.79907
$175$	2.90632			0.219697
$176$	−3.44670	−	5.96986i	−0.259805	−	0.449995i
$177$	40.8105			3.06751
$178$	7.06801	−	12.2422i	0.529770	−	0.917588i
$179$	8.23882			0.615798			0.307899	−	0.951419i	$-0.400374\pi$
$179$	8.23882			0.615798			0.307899	+	0.951419i	$0.400374\pi$
$180$	3.78376	−	6.55366i	0.282025	−	0.488481i
$181$	−9.77831	+	16.9365i	−0.726816	+	1.25888i	0.231406	+	0.972857i	$0.425667\pi$
$181$	−9.77831	+	16.9365i	−0.726816	+	1.25888i	−0.958222	+	0.286025i	$0.907666\pi$
$182$	−14.7886	+	25.6145i	−1.09620	+	1.89867i
$183$	−10.5660	−	18.3008i	−0.781058	−	1.35283i
$184$	−0.212272			−0.0156489
$185$	6.04663	+	0.661984i	0.444557	+	0.0486700i
$186$	29.8154			2.18617
$187$	−3.78346	−	6.55314i	−0.276674	−	0.479213i
$188$	−1.48667	+	2.57499i	−0.108427	+	0.187801i
$189$	−7.35450	+	12.7384i	−0.534961	+	0.926580i
$190$	−0.564988	+	0.978587i	−0.0409885	+	0.0709942i
$191$	−24.8449			−1.79771			−0.898856	−	0.438245i	$-0.855600\pi$
$191$	−24.8449			−1.79771			−0.898856	+	0.438245i	$0.855600\pi$
$192$	6.00490	−	10.4008i	0.433366	−	0.750613i
$193$	−6.68971			−0.481536			−0.240768	−	0.970583i	$-0.577399\pi$
$193$	−6.68971			−0.481536			−0.240768	+	0.970583i	$0.577399\pi$
$194$	−15.9879	−	27.6919i	−1.14787	−	1.98816i
$195$	15.0468			1.07753
$196$	2.27567			0.162548
$197$	−4.90639	−	8.49812i	−0.349566	−	0.605466i	0.636606	−	0.771189i	$-0.280338\pi$
$197$	−4.90639	−	8.49812i	−0.349566	−	0.605466i	−0.986172	+	0.165723i	$0.947004\pi$
$198$	−6.70922	+	11.6207i	−0.476804	+	0.825848i
$199$	6.55698			0.464812			0.232406	−	0.972619i	$-0.425340\pi$
$199$	6.55698			0.464812			0.232406	+	0.972619i	$0.425340\pi$
$200$	−0.403565	−	0.698995i	−0.0285364	−	0.0494264i
$201$	1.59429	+	2.76139i	0.112453	+	0.194773i
$202$	11.0479	+	19.1355i	0.777326	+	1.34637i
$203$	−6.52784	+	11.3065i	−0.458164	+	0.793564i
$204$	11.2721	−	19.5239i	0.789208	−	1.36695i
$205$	−4.97363	−	8.61458i	−0.347374	−	0.601669i
$206$	−6.40687	−	11.0970i	−0.446388	−	0.773166i
$207$	0.632622	+	1.09573i	0.0439702	+	0.0761587i
$208$	25.1517			1.74396
$209$	0.441046	−	0.763913i	0.0305078	−	0.0528410i
$210$	−7.67680	−	13.2966i	−0.529750	−	0.917553i
$211$	−11.0798			−0.762768			−0.381384	−	0.924417i	$-0.624552\pi$
$211$	−11.0798			−0.762768			−0.381384	+	0.924417i	$0.624552\pi$
$212$	11.5777			0.795160
$213$	19.1088	+	33.0975i	1.30932	+	2.26780i
$214$	2.65759			0.181669
$215$	4.81246	−	8.33543i	0.328207	−	0.568472i
$216$	4.08491			0.277943
$217$	8.20140	−	14.2052i	0.556747	−	0.964314i
$218$	−18.3889	+	31.8505i	−1.24545	+	2.15719i
$219$	19.2098	−	33.2723i	1.29807	−	2.24833i
$220$	−1.16054	−	2.01011i	−0.0782436	−	0.135522i
$221$	27.6092			1.85719
$222$	−12.9430	−	29.4123i	−0.868680	−	1.97402i
$223$	−5.49852			−0.368208			−0.184104	−	0.982907i	$-0.558938\pi$
$223$	−5.49852			−0.368208			−0.184104	+	0.982907i	$0.558938\pi$
$224$	−10.4865	−	18.1631i	−0.700656	−	1.21357i
$225$	−2.40544	+	4.16634i	−0.160363	+	0.277756i
$226$	−10.9277	+	18.9273i	−0.726900	+	1.25903i
$227$	1.12689	−	1.95182i	0.0747940	−	0.129547i	−0.826203	−	0.563373i	$-0.809503\pi$
$227$	1.12689	−	1.95182i	0.0747940	−	0.129547i	0.900997	+	0.433826i	$0.142837\pi$
$228$	2.62804			0.174046
$229$	4.80507	−	8.32263i	0.317528	−	0.549975i	−0.662443	−	0.749112i	$-0.730481\pi$
$229$	4.80507	−	8.32263i	0.317528	−	0.549975i	0.979972	+	0.199137i	$0.0638138\pi$
$230$	−0.497126			−0.0327795
$231$	5.99273	+	10.3797i	0.394293	+	0.682935i
$232$	3.62576			0.238043
$233$	−25.7523			−1.68709			−0.843544	−	0.537060i	$-0.819535\pi$
$233$	−25.7523			−1.68709			−0.843544	+	0.537060i	$0.819535\pi$
$234$	−24.4797	−	42.4001i	−1.60029	−	2.77178i
$235$	0.945119	−	1.63699i	0.0616528	−	0.106786i
$236$	22.9695			1.49519
$237$	16.3894	+	28.3872i	1.06460	+	1.84395i
$238$	−14.0860	−	24.3977i	−0.913061	−	1.58147i
$239$	8.19686	+	14.1974i	0.530211	+	0.918352i	0.999379	+	0.0352430i	$0.0112205\pi$
$239$	8.19686	+	14.1974i	0.530211	+	0.918352i	−0.469168	+	0.883109i	$0.655446\pi$
$240$	−6.52818	+	11.3071i	−0.421392	+	0.729873i
$241$	2.25347	−	3.90312i	0.145159	−	0.251422i	−0.784273	−	0.620415i	$-0.786964\pi$
$241$	2.25347	−	3.90312i	0.145159	−	0.251422i	0.929432	+	0.368993i	$0.120297\pi$
$242$	−8.33848	−	14.4427i	−0.536018	−	0.928410i
$243$	7.99412	+	13.8462i	0.512823	+	0.888235i
$244$	−5.94686	−	10.3003i	−0.380709	−	0.659407i
$245$	−1.44671			−0.0924268
$246$	−26.2748	+	45.5094i	−1.67522	+	2.90157i
$247$	1.60923	+	2.78727i	0.102393	+	0.177349i
$248$	−4.55531			−0.289262
$249$	12.0369			0.762805
$250$	−0.945119	−	1.63699i	−0.0597746	−	0.103533i
$251$	7.06896			0.446189			0.223095	−	0.974797i	$-0.428384\pi$
$251$	7.06896			0.446189			0.223095	+	0.974797i	$0.428384\pi$
$252$	−10.9968	+	19.0470i	−0.692734	+	1.19985i
$253$	0.388071			0.0243978
$254$	−3.95752	+	6.85463i	−0.248317	+	0.430098i
$255$	−7.16602	+	12.4119i	−0.448753	+	0.777264i
$256$	−10.2608	+	17.7722i	−0.641299	+	1.11076i
$257$	−0.191704	−	0.332042i	−0.0119582	−	0.0207122i	0.859984	−	0.510320i	$-0.170473\pi$
$257$	−0.191704	−	0.332042i	−0.0119582	−	0.0207122i	−0.871943	+	0.489608i	$0.837140\pi$
$258$	−50.8468			−3.16559
$259$	−17.5735	−	1.92394i	−1.09196	−	0.119548i
$260$	8.46885			0.525216
$261$	−10.8056	−	18.7159i	−0.668851	−	1.15848i
$262$	−3.92493	+	6.79818i	−0.242483	+	0.419993i
$263$	−0.576995	+	0.999384i	−0.0355790	+	0.0616247i	−0.883267	−	0.468871i	$-0.844661\pi$
$263$	−0.576995	+	0.999384i	−0.0355790	+	0.0616247i	0.847688	+	0.530496i	$0.177994\pi$
$264$	1.66427	−	2.88261i	0.102429	−	0.177412i
$265$	−7.36027			−0.452138
$266$	1.64204	−	2.84409i	0.100680	−	0.174382i
$267$	20.9007			1.27910
$268$	0.897318	+	1.55420i	0.0548124	+	0.0949379i
$269$	−16.9334			−1.03245			−0.516224	−	0.856454i	$-0.672663\pi$
$269$	−16.9334			−1.03245			−0.516224	+	0.856454i	$0.672663\pi$
$270$	9.56656			0.582202
$271$	−7.16742	−	12.4143i	−0.435390	−	0.754117i	0.561938	−	0.827180i	$-0.310056\pi$
$271$	−7.16742	−	12.4143i	−0.435390	−	0.754117i	−0.997327	+	0.0730625i	$0.976723\pi$
$272$	−11.9784	+	20.7473i	−0.726299	+	1.25799i
$273$	−43.7310			−2.64672
$274$	−1.95948	−	3.39392i	−0.118377	−	0.205034i
$275$	0.737787	+	1.27788i	0.0444902	+	0.0770594i
$276$	0.578094	+	1.00129i	0.0347972	+	0.0602705i
$277$	−6.91003	+	11.9685i	−0.415184	+	0.719119i	−0.995448	−	0.0953092i	$-0.969616\pi$
$277$	−6.91003	+	11.9685i	−0.415184	+	0.719119i	0.580264	+	0.814428i	$0.302949\pi$
$278$	4.20113	−	7.27657i	0.251967	−	0.436419i
$279$	13.5759	+	23.5141i	0.812767	+	1.40775i
$280$	1.17289	+	2.03151i	0.0700936	+	0.121406i
$281$	−12.1951	−	21.1225i	−0.727499	−	1.26006i	−0.957937	−	0.286978i	$-0.907349\pi$
$281$	−12.1951	−	21.1225i	−0.727499	−	1.26006i	0.230438	−	0.973087i	$-0.425984\pi$
$282$	−9.98580			−0.594646
$283$	10.7279	−	18.5813i	0.637707	−	1.10454i	−0.348228	−	0.937410i	$-0.613216\pi$
$283$	10.7279	−	18.5813i	0.637707	−	1.10454i	0.985935	−	0.167131i	$-0.0534503\pi$
$284$	10.7551	+	18.6283i	0.638196	+	1.10539i
$285$	−1.67071			−0.0989646
$286$	−15.0166			−0.887953
$287$	14.4550	+	25.0368i	0.853250	+	1.47787i
$288$	34.7168			2.04571
$289$	−4.64879	+	8.05194i	−0.273458	+	0.473643i
$290$	8.49126			0.498624
$291$	23.6388	−	40.9436i	1.38573	−	2.40016i
$292$	10.8119	−	18.7267i	0.632717	−	1.09590i
$293$	−3.25034	+	5.62976i	−0.189887	+	0.328894i	−0.945212	−	0.326456i	$-0.894146\pi$
$293$	−3.25034	+	5.62976i	−0.189887	+	0.328894i	0.755325	+	0.655350i	$0.227479\pi$
$294$	3.82135	+	6.61878i	0.222866	+	0.386015i
$295$	−14.6023			−0.850181
$296$	1.97749	+	4.49372i	0.114939	+	0.261192i
$297$	−7.46793			−0.433333
$298$	−5.62701	−	9.74627i	−0.325964	−	0.564586i
$299$	−0.707970	+	1.22624i	−0.0409430	+	0.0709153i
$300$	−2.19811	+	3.80723i	−0.126908	+	0.219811i
$301$	−13.9866	+	24.2254i	−0.806172	+	1.39633i
$302$	0.524478			0.0301803
$303$	−16.3347	+	28.2926i	−0.938406	+	1.62537i
$304$	−2.79270			−0.160172
$305$	3.78059	+	6.54817i	0.216476	+	0.374947i
$306$	46.6336			2.66586
$307$	9.80214			0.559438			0.279719	−	0.960082i	$-0.409759\pi$
$307$	9.80214			0.559438			0.279719	+	0.960082i	$0.409759\pi$
$308$	3.37290	+	5.84204i	0.192189	+	0.332881i
$309$	9.47282	−	16.4074i	0.538890	−	0.933385i
$310$	−10.6682			−0.605912
$311$	−6.45381	−	11.1783i	−0.365962	−	0.633865i	0.622968	−	0.782247i	$-0.285927\pi$
$311$	−6.45381	−	11.1783i	−0.365962	−	0.633865i	−0.988930	+	0.148382i	$0.952593\pi$
$312$	6.07238	+	10.5177i	0.343781	+	0.595446i
$313$	−2.64764	−	4.58585i	−0.149654	−	0.259208i	0.781446	−	0.623973i	$-0.214483\pi$
$313$	−2.64764	−	4.58585i	−0.149654	−	0.259208i	−0.931099	+	0.364765i	$0.881149\pi$
$314$	−7.10695	+	12.3096i	−0.401069	+	0.694671i
$315$	6.99098	−	12.1087i	0.393897	−	0.682250i
$316$	9.22447	+	15.9773i	0.518917	+	0.898791i
$317$	4.17902	+	7.23828i	0.234717	+	0.406542i	0.959190	−	0.282761i	$-0.0912503\pi$
$317$	4.17902	+	7.23828i	0.234717	+	0.406542i	−0.724473	+	0.689303i	$0.757917\pi$
$318$	19.4415	+	33.6737i	1.09023	+	1.88833i
$319$	−6.62852			−0.371126
$320$	−2.14860	+	3.72149i	−0.120111	+	0.208037i
$321$	1.96468	+	3.40292i	0.109657	+	0.189932i
$322$	1.44481			0.0805160
$323$	−3.06556			−0.170572
$324$	0.226577	+	0.392443i	0.0125876	+	0.0218024i
$325$	−5.38388			−0.298644
$326$	−7.76022	+	13.4411i	−0.429799	+	0.744434i
$327$	−54.3775			−3.00708
$328$	4.01437	−	6.95309i	0.221656	−	0.383920i
$329$	−2.74682	+	4.75763i	−0.151437	+	0.262297i
$330$	3.89760	−	6.75085i	0.214556	−	0.371622i
$331$	−11.3452	−	19.6504i	−0.623587	−	1.08008i	−0.988812	−	0.149165i	$-0.952341\pi$
$331$	−11.3452	−	19.6504i	−0.623587	−	1.08008i	0.365225	−	0.930919i	$-0.380992\pi$
$332$	6.77473			0.371812
$333$	17.3029	−	23.6000i	0.948191	−	1.29327i
$334$	12.4974			0.683827
$335$	−0.570450	−	0.988048i	−0.0311670	−	0.0539828i
$336$	18.9730	−	32.8622i	1.03506	−	1.79278i
$337$	13.6686	−	23.6747i	0.744576	−	1.28964i	−0.205816	−	0.978591i	$-0.565985\pi$
$337$	13.6686	−	23.6747i	0.744576	−	1.28964i	0.950392	−	0.311053i	$-0.100682\pi$
$338$	15.1088	−	26.1693i	0.821812	−	1.42342i
$339$	−32.3141			−1.75506
$340$	−4.03327	+	6.98582i	−0.218735	+	0.378859i
$341$	8.32789			0.450981
$342$	2.71809	+	4.70786i	0.146977	+	0.254572i
$343$	−16.1397			−0.871460
$344$	7.76857			0.418853
$345$	−0.367510	−	0.636547i	−0.0197861	−	0.0342705i
$346$	−4.41941	+	7.65464i	−0.237589	+	0.411516i
$347$	23.6531			1.26977			0.634884	−	0.772608i	$-0.281048\pi$
$347$	23.6531			1.26977			0.634884	+	0.772608i	$0.281048\pi$
$348$	−9.87426	−	17.1027i	−0.529316	−	0.916802i
$349$	5.71011	+	9.89020i	0.305655	+	0.529410i	0.977407	−	0.211366i	$-0.0677912\pi$
$349$	5.71011	+	9.89020i	0.305655	+	0.529410i	−0.671752	+	0.740776i	$0.734458\pi$
$350$	2.74682	+	4.75763i	0.146824	+	0.254306i
$351$	13.6240	−	23.5975i	0.727195	−	1.25954i
$352$	5.32410	−	9.22161i	0.283776	−	0.491514i
$353$	−7.99430	−	13.8465i	−0.425493	−	0.736976i	0.570973	−	0.820969i	$-0.306566\pi$
$353$	−7.99430	−	13.8465i	−0.425493	−	0.736976i	−0.996466	+	0.0839926i	$0.973233\pi$
$354$	38.5708	+	66.8066i	2.05002	+	3.55073i
$355$	−6.83729	−	11.8425i	−0.362886	−	0.628537i
$356$	11.7636			0.623469
$357$	20.8268	−	36.0730i	1.10227	−	1.90919i
$358$	7.78667	+	13.4869i	0.411538	+	0.712805i
$359$	13.4209			0.708326			0.354163	−	0.935184i	$-0.384766\pi$
$359$	13.4209			0.708326			0.354163	+	0.935184i	$0.384766\pi$
$360$	−3.88301			−0.204652
$361$	9.32132	+	16.1450i	0.490596	+	0.849737i
$362$	−36.9667			−1.94293
$363$	12.3288	−	21.3541i	0.647094	−	1.12080i
$364$	−24.6132			−1.29008
$365$	−6.87340	+	11.9051i	−0.359770	+	0.623140i
$366$	19.9722	−	34.5928i	1.04396	−	1.80820i
$367$	−11.7012	+	20.2671i	−0.610799	+	1.05793i	0.380307	+	0.924860i	$0.375818\pi$
$367$	−11.7012	+	20.2671i	−0.610799	+	1.05793i	−0.991106	+	0.133075i	$0.957515\pi$
$368$	−0.614316	−	1.06403i	−0.0320234	−	0.0554662i
$369$	−47.8551			−2.49124
$370$	4.63113	+	10.5240i	0.240761	+	0.547115i
$371$	21.3913			1.11058
$372$	12.4057	+	21.4874i	0.643208	+	1.11407i
$373$	2.27109	−	3.93365i	0.117593	−	0.203677i	−0.801220	−	0.598369i	$-0.795816\pi$
$373$	2.27109	−	3.93365i	0.117593	−	0.203677i	0.918813	+	0.394693i	$0.129149\pi$
$374$	7.15164	−	12.3870i	0.369802	−	0.640517i
$375$	1.39740	−	2.42036i	0.0721613	−	0.124987i
$376$	1.52567			0.0786803
$377$	12.0926	−	20.9451i	0.622802	−	1.07873i
$378$	−27.8035			−1.43006
$379$	11.7947	+	20.4291i	0.605855	+	1.04937i	0.991916	+	0.126898i	$0.0405022\pi$
$379$	11.7947	+	20.4291i	0.605855	+	1.04937i	−0.386061	+	0.922473i	$0.626164\pi$
$380$	−0.940332			−0.0482380
$381$	−11.7027			−0.599549
$382$	−23.4814	−	40.6709i	−1.20141	−	2.08090i
$383$	0.605288	−	1.04839i	0.0309288	−	0.0535702i	−0.850147	−	0.526546i	$-0.823487\pi$
$383$	0.605288	−	1.04839i	0.0309288	−	0.0535702i	0.881075	+	0.472976i	$0.156820\pi$
$384$	−17.6348			−0.899923
$385$	−2.14425	−	3.71395i	−0.109281	−	0.189280i
$386$	−6.32257	−	10.9510i	−0.321810	−	0.557392i
$387$	−23.1522	−	40.1007i	−1.17689	−	2.03844i
$388$	13.3047	−	23.0444i	0.675443	−	1.16990i
$389$	16.2193	−	28.0927i	0.822353	−	1.42436i	−0.0815723	−	0.996667i	$-0.525994\pi$
$389$	16.2193	−	28.0927i	0.822353	−	1.42436i	0.903925	−	0.427690i	$-0.140673\pi$
$390$	14.2211	+	24.6316i	0.720111	+	1.24727i
$391$	−0.674338	−	1.16799i	−0.0341027	−	0.0590677i
$392$	−0.583841	−	1.01124i	−0.0294884	−	0.0510754i
$393$	−11.6063			−0.585462
$394$	9.27425	−	16.0635i	0.467230	−	0.809266i
$395$	−5.86425	−	10.1572i	−0.295063	−	0.511063i
$396$	−11.1664			−0.561134
$397$	−13.2408			−0.664534			−0.332267	−	0.943185i	$-0.607814\pi$
$397$	−13.2408			−0.664534			−0.332267	+	0.943185i	$0.607814\pi$
$398$	6.19713	+	10.7337i	0.310634	+	0.538034i
$399$	4.85564			0.243086
$400$	2.33584	−	4.04578i	0.116792	−	0.202289i
$401$	14.0963			0.703938			0.351969	−	0.936012i	$-0.385512\pi$
$401$	14.0963			0.703938			0.351969	+	0.936012i	$0.385512\pi$
$402$	−3.01359	+	5.21969i	−0.150304	+	0.260334i
$403$	−15.1929	+	26.3148i	−0.756810	+	1.31083i
$404$	−9.19371	+	15.9240i	−0.457404	+	0.792248i
$405$	−0.144041	−	0.249487i	−0.00715748	−	0.0123971i
$406$	−24.6783			−1.22477
$407$	−3.61519	−	8.21530i	−0.179198	−	0.407218i
$408$	−11.5678			−0.572692
$409$	13.2419	+	22.9357i	0.654770	+	1.13410i	0.981951	+	0.189134i	$0.0605680\pi$
$409$	13.2419	+	22.9357i	0.654770	+	1.13410i	−0.327181	+	0.944962i	$0.606099\pi$
$410$	9.40135	−	16.2836i	0.464300	−	0.804191i
$411$	2.89717	−	5.01805i	0.142907	−	0.247522i
$412$	5.33161	−	9.23462i	0.262670	−	0.454957i
$413$	42.4391			2.08829
$414$	−1.19581	+	2.07120i	−0.0587706	+	0.101794i
$415$	−4.30689			−0.211417
$416$	19.4259	+	33.6466i	0.952432	+	1.64966i
$417$	12.4231			0.608361
$418$	1.66736			0.0815534
$419$	5.26110	+	9.11249i	0.257021	+	0.445174i	0.965443	−	0.260616i	$-0.0839256\pi$
$419$	5.26110	+	9.11249i	0.257021	+	0.445174i	−0.708421	+	0.705790i	$0.750592\pi$
$420$	6.38841	−	11.0650i	0.311722	−	0.539919i
$421$	15.6587			0.763160			0.381580	−	0.924336i	$-0.375380\pi$
$421$	15.6587			0.763160			0.381580	+	0.924336i	$0.375380\pi$
$422$	−10.4718	−	18.1376i	−0.509758	−	0.882926i
$423$	−4.54685	−	7.87538i	−0.221076	−	0.382914i
$424$	−2.97035	−	5.14479i	−0.144253	−	0.249853i
$425$	2.56406	−	4.44108i	0.124375	−	0.215424i
$426$	−36.1202	+	62.5621i	−1.75003	+	3.03114i
$427$	−10.9876	−	19.0311i	−0.531727	−	0.920978i
$428$	1.10578	+	1.91527i	0.0534500	+	0.0925782i
$429$	−11.1014	−	19.2281i	−0.535979	−	0.928343i
$430$	18.1934			0.877364
$431$	−15.4907	+	26.8306i	−0.746160	+	1.29239i	0.203491	+	0.979077i	$0.434771\pi$
$431$	−15.4907	+	26.8306i	−0.746160	+	1.29239i	−0.949651	+	0.313310i	$0.898562\pi$
$432$	11.8217	+	20.4759i	0.568774	+	0.985145i
$433$	22.9430			1.10257			0.551286	−	0.834316i	$-0.314137\pi$
$433$	22.9430			1.10257			0.551286	+	0.834316i	$0.314137\pi$
$434$	31.0052			1.48830
$435$	6.27734	+	10.8727i	0.300975	+	0.521305i
$436$	−30.6054			−1.46573
$437$	0.0786090	−	0.136155i	0.00376038	−	0.00651316i
$438$	72.6220			3.47001
$439$	−2.66879	+	4.62249i	−0.127375	+	0.220619i	−0.922659	−	0.385618i	$-0.873988\pi$
$439$	−2.66879	+	4.62249i	−0.127375	+	0.220619i	0.795284	+	0.606237i	$0.207322\pi$
$440$	−0.595490	+	1.03142i	−0.0283889	+	0.0491710i
$441$	−3.47997	+	6.02748i	−0.165713	+	0.287023i
$442$	26.0939	+	45.1960i	1.24116	+	2.14976i
$443$	33.4751			1.59045			0.795226	−	0.606313i	$-0.207352\pi$
$443$	33.4751			1.59045			0.795226	+	0.606313i	$0.207352\pi$
$444$	15.8115	−	21.5658i	0.750379	−	1.02347i
$445$	−7.47844			−0.354512
$446$	−5.19675	−	9.00104i	−0.246073	−	0.426212i
$447$	8.31977	−	14.4103i	0.393512	−	0.681582i
$448$	6.24453	−	10.8158i	0.295026	−	0.511001i
$449$	0.166275	−	0.287997i	0.00784700	−	0.0135914i	−0.862075	−	0.506780i	$-0.830836\pi$
$449$	0.166275	−	0.287997i	0.00784700	−	0.0135914i	0.869922	+	0.493189i	$0.164169\pi$
$450$	−9.09371			−0.428681
$451$	−7.33897	+	12.7115i	−0.345578	+	0.598559i
$452$	−18.1874			−0.855465
$453$	0.387731	+	0.671570i	0.0182172	+	0.0315531i
$454$	4.26016			0.199939
$455$	15.6473			0.733556
$456$	−0.674242	−	1.16782i	−0.0315743	−	0.0546883i
$457$	−1.22412	+	2.12023i	−0.0572618	+	0.0991803i	−0.893235	−	0.449589i	$-0.851570\pi$
$457$	−1.22412	+	2.12023i	−0.0572618	+	0.0991803i	0.835974	+	0.548770i	$0.184904\pi$
$458$	18.1655			0.848817
$459$	12.9768	+	22.4765i	0.605704	+	1.04911i
$460$	−0.206847	−	0.358269i	−0.00964428	−	0.0167044i
$461$	6.79669	+	11.7722i	0.316554	+	0.548287i	0.979767	−	0.200144i	$-0.0641410\pi$
$461$	6.79669	+	11.7722i	0.316554	+	0.548287i	−0.663213	+	0.748431i	$0.730808\pi$
$462$	−11.3277	+	19.6201i	−0.527012	+	0.912811i
$463$	−13.7179	+	23.7601i	−0.637526	+	1.10423i	0.348448	+	0.937328i	$0.386709\pi$
$463$	−13.7179	+	23.7601i	−0.637526	+	1.10423i	−0.985974	+	0.166899i	$0.946625\pi$
$464$	10.4930	+	18.1743i	0.487123	+	0.843722i
$465$	−7.88668	−	13.6601i	−0.365736	−	0.633473i
$466$	−24.3390	−	42.1563i	−1.12748	−	1.95285i
$467$	−2.41296			−0.111658			−0.0558292	−	0.998440i	$-0.517780\pi$
$467$	−2.41296			−0.111658			−0.0558292	+	0.998440i	$0.517780\pi$
$468$	20.3713	−	35.2841i	0.941664	−	1.63101i
$469$	1.65791	+	2.87158i	0.0765552	+	0.132597i
$470$	3.57300			0.164810
$471$	−21.0158			−0.968359
$472$	−5.89299	−	10.2070i	−0.271247	−	0.469814i
$473$	−14.2023			−0.653022
$474$	−30.9798	+	53.6587i	−1.42295	+	2.46462i
$475$	0.597795			0.0274287
$476$	11.7220	−	20.3030i	0.537276	−	0.930588i
$477$	−17.7047	+	30.6654i	−0.810642	+	1.40407i
$478$	−15.4940	+	26.8364i	−0.708680	+	1.22747i
$479$	11.4549	+	19.8404i	0.523387	+	0.906532i	0.999630	+	0.0272183i	$0.00866494\pi$
$479$	11.4549	+	19.8404i	0.523387	+	0.906532i	−0.476243	+	0.879314i	$0.658002\pi$
$480$	−20.1681			−0.920544
$481$	32.5543	+	3.56404i	1.48435	+	0.162506i
$482$	8.51919			0.388038
$483$	1.06810	+	1.85001i	0.0486004	+	0.0841783i
$484$	6.93904	−	12.0188i	0.315411	−	0.546308i
$485$	−8.45815	+	14.6500i	−0.384065	+	0.665220i
$486$	−15.1108	+	26.1727i	−0.685439	+	1.18722i
$487$	−29.6639			−1.34420			−0.672100	−	0.740460i	$-0.734608\pi$
$487$	−29.6639			−1.34420			−0.672100	+	0.740460i	$0.734608\pi$
$488$	−3.05142	+	5.28522i	−0.138132	+	0.239251i
$489$	−22.9476			−1.03773
$490$	−1.36731	−	2.36825i	−0.0617688	−	0.106987i
$491$	−19.5820			−0.883724			−0.441862	−	0.897083i	$-0.645682\pi$
$491$	−19.5820			−0.883724			−0.441862	+	0.897083i	$0.645682\pi$
$492$	−43.7303			−1.97151
$493$	11.5182	+	19.9501i	0.518752	+	0.898505i
$494$	−3.04183	+	5.26860i	−0.136858	+	0.237045i
$495$	7.09881			0.319068
$496$	−13.1831	−	22.8337i	−0.591937	−	1.02526i
$497$	19.8714	+	34.4182i	0.891353	+	1.54387i
$498$	11.3763	+	19.7043i	0.509783	+	0.882970i
$499$	10.7528	−	18.6244i	0.481361	−	0.833742i	−0.518410	−	0.855132i	$-0.673476\pi$
$499$	10.7528	−	18.6244i	0.481361	−	0.833742i	0.999771	+	0.0213900i	$0.00680918\pi$
$500$	0.786500	−	1.36226i	0.0351734	−	0.0609221i
$501$	9.23895	+	16.0023i	0.412766	+	0.714931i
$502$	6.68101	+	11.5719i	0.298188	+	0.516477i
$503$	−3.14166	−	5.44151i	−0.140080	−	0.242625i	0.787447	−	0.616383i	$-0.211403\pi$
$503$	−3.14166	−	5.44151i	−0.140080	−	0.242625i	−0.927526	+	0.373758i	$0.878069\pi$
$504$	11.2853			0.502686
$505$	5.84470	−	10.1233i	0.260086	−	0.450482i
$506$	0.366773	+	0.635269i	0.0163050	+	0.0282412i
$507$	44.6780			1.98422
$508$	−6.58667			−0.292236
$509$	0.933480	+	1.61683i	0.0413758	+	0.0716649i	0.885972	−	0.463739i	$-0.153493\pi$
$509$	0.933480	+	1.61683i	0.0413758	+	0.0716649i	−0.844596	+	0.535404i	$0.820159\pi$
$510$	−27.0910			−1.19961
$511$	19.9763	−	34.6000i	0.883700	−	1.53061i
$512$	−26.1709			−1.15660
$513$	−1.51273	+	2.62013i	−0.0667887	+	0.115681i
$514$	0.362367	−	0.627638i	0.0159833	−	0.0276839i
$515$	−3.38945	+	5.87070i	−0.149357	+	0.258694i
$516$	−21.1566	−	36.6443i	−0.931368	−	1.61318i
$517$	−2.78919			−0.122668
$518$	−13.4595	−	30.5860i	−0.591378	−	1.34387i
$519$	−13.0685			−0.573645
$520$	−2.17275	−	3.76331i	−0.0952812	−	0.165032i
$521$	11.8047	−	20.4463i	0.517173	−	0.895770i	−0.482628	−	0.875825i	$-0.660318\pi$
$521$	11.8047	−	20.4463i	0.517173	−	0.895770i	0.999801	−	0.0199443i	$-0.00634887\pi$
$522$	20.4252	−	35.3775i	0.893987	−	1.54843i
$523$	−0.531390	+	0.920395i	−0.0232361	+	0.0402461i	−0.877410	−	0.479742i	$-0.840730\pi$
$523$	−0.531390	+	0.920395i	−0.0232361	+	0.0402461i	0.854174	+	0.519988i	$0.174064\pi$
$524$	−6.53242			−0.285370
$525$	−4.06129	+	7.03436i	−0.177249	+	0.307004i
$526$	−2.18131			−0.0951098
$527$	−14.4711	−	25.0647i	−0.630371	−	1.09184i
$528$	19.2656			0.838429
$529$	−22.9308			−0.996993
$530$	−6.95633	−	12.0487i	−0.302164	−	0.523363i
$531$	−35.1250	+	60.8383i	−1.52430	+	2.64016i
$532$	2.73291			0.118487
$533$	−26.7774	−	46.3799i	−1.15986	−	2.00894i
$534$	19.7536	+	34.2143i	0.854824	+	1.48060i
$535$	−0.702977	−	1.21759i	−0.0303923	−	0.0526411i
$536$	0.460427	−	0.797483i	0.0198874	−	0.0344460i
$537$	−11.5129	+	19.9409i	−0.496819	+	0.860515i
$538$	−16.0041	−	27.7199i	−0.689985	−	1.19509i
$539$	1.06736	+	1.84873i	0.0459745	+	0.0796303i
$540$	3.98051	+	6.89444i	0.171294	+	0.296689i
$541$	−1.48855			−0.0639979			−0.0319990	−	0.999488i	$-0.510187\pi$
$541$	−1.48855			−0.0639979			−0.0319990	+	0.999488i	$0.510187\pi$
$542$	13.5481	−	23.4660i	0.581942	−	1.00795i
$543$	−27.3284	−	47.3341i	−1.17277	−	2.03130i
$544$	−37.0061			−1.58662
$545$	19.4567			0.833434
$546$	−41.3310	−	71.5873i	−1.76880	−	3.06366i
$547$	−4.48327			−0.191691			−0.0958454	−	0.995396i	$-0.530555\pi$
$547$	−4.48327			−0.191691			−0.0958454	+	0.995396i	$0.530555\pi$
$548$	1.63062	−	2.82432i	0.0696567	−	0.120649i
$549$	36.3759			1.55248
$550$	−1.39459	+	2.41551i	−0.0594657	+	0.102998i
$551$	−1.34270	+	2.32562i	−0.0572008	+	0.0990747i
$552$	0.296629	−	0.513776i	0.0126254	−	0.0218678i
$553$	17.0434	+	29.5200i	0.724759	+	1.25532i
$554$	−26.1232			−1.10987
$555$	−10.0518	+	13.7100i	−0.426675	+	0.581957i
$556$	6.99211			0.296532
$557$	−16.1834	−	28.0305i	−0.685712	−	1.18769i	−0.973212	−	0.229908i	$-0.926158\pi$
$557$	−16.1834	−	28.0305i	−0.685712	−	1.18769i	0.287500	−	0.957781i	$-0.407176\pi$
$558$	−25.6617	+	44.4473i	−1.08635	+	1.88161i
$559$	25.9097	−	44.8770i	1.09586	−	1.89809i
$560$	−6.78869	+	11.7584i	−0.286874	+	0.496881i
$561$	21.1480			0.892868
$562$	23.0517	−	39.9266i	0.972375	−	1.68420i
$563$	−38.2476			−1.61194			−0.805971	−	0.591955i	$-0.798356\pi$
$563$	−38.2476			−1.61194			−0.805971	+	0.591955i	$0.798356\pi$
$564$	−4.15495	−	7.19658i	−0.174955	−	0.303031i
$565$	11.5622			0.486428
$566$	40.5566			1.70472
$567$	0.418631	+	0.725090i	0.0175808	+	0.0304509i
$568$	5.51859	−	9.55847i	0.231555	−	0.401065i
$569$	29.1832			1.22342			0.611712	−	0.791081i	$-0.290481\pi$
$569$	29.1832			1.22342			0.611712	+	0.791081i	$0.290481\pi$
$570$	−1.57902	−	2.73495i	−0.0661381	−	0.114554i
$571$	2.15198	+	3.72733i	0.0900574	+	0.155984i	0.907535	−	0.419976i	$-0.137962\pi$
$571$	2.15198	+	3.72733i	0.0900574	+	0.155984i	−0.817478	+	0.575960i	$0.804628\pi$
$572$	−6.24821	−	10.8222i	−0.261251	−	0.452499i
$573$	34.7181	−	60.1336i	1.45037	−	2.51212i
$574$	−27.3234	+	47.3254i	−1.14045	+	1.97533i
$575$	0.131498	+	0.227761i	0.00548385	+	0.00949831i
$576$	10.3367	+	17.9036i	0.430694	+	0.745984i
$577$	−9.14533	−	15.8402i	−0.380725	−	0.659435i	0.610441	−	0.792062i	$-0.290992\pi$
$577$	−9.14533	−	15.8402i	−0.380725	−	0.659435i	−0.991166	+	0.132627i	$0.957659\pi$
$578$	−17.5746			−0.731008
$579$	9.34818	−	16.1915i	0.388497	−	0.672897i
$580$	3.53309	+	6.11949i	0.146704	+	0.254098i
$581$	12.5172			0.519301
$582$	89.3659			3.70434
$583$	5.43031	+	9.40558i	0.224901	+	0.389539i
$584$	−11.0955			−0.459133
$585$	−12.9506	+	22.4311i	−0.535441	+	0.927411i
$586$	−12.2878			−0.507606
$587$	−18.7309	+	32.4428i	−0.773106	+	1.33906i	0.162746	+	0.986668i	$0.447965\pi$
$587$	−18.7309	+	32.4428i	−0.773106	+	1.33906i	−0.935853	+	0.352392i	$0.885369\pi$
$588$	−3.18002	+	5.50795i	−0.131142	+	0.227144i
$589$	1.68693	−	2.92184i	0.0695086	−	0.120392i
$590$	−13.8009	−	23.9039i	−0.568176	−	0.984110i
$591$	27.4247			1.12810
$592$	−16.8022	+	22.9171i	−0.690565	+	0.941887i
$593$	17.3439			0.712227			0.356113	−	0.934443i	$-0.384102\pi$
$593$	17.3439			0.712227			0.356113	+	0.934443i	$0.384102\pi$
$594$	−7.05809	−	12.2250i	−0.289597	−	0.501596i
$595$	−7.45198	+	12.9072i	−0.305501	+	0.529144i
$596$	4.68264	−	8.11056i	0.191808	−	0.332222i
$597$	−9.16271	+	15.8703i	−0.375005	+	0.649527i
$598$	−2.67646			−0.109449
$599$	−16.0096	+	27.7294i	−0.654133	+	1.13299i	0.327978	+	0.944685i	$0.393633\pi$
$599$	−16.0096	+	27.7294i	−0.654133	+	1.13299i	−0.982110	+	0.188306i	$0.939700\pi$
$600$	2.25576			0.0920912
$601$	−0.575610	−	0.996986i	−0.0234796	−	0.0406679i	0.854047	−	0.520196i	$-0.174141\pi$
$601$	−0.575610	−	0.996986i	−0.0234796	−	0.0406679i	−0.877526	+	0.479528i	$0.840808\pi$
$602$	−52.8759			−2.15506
$603$	−5.48873			−0.223518
$604$	0.218228	+	0.377982i	0.00887956	+	0.0153799i
$605$	−4.41134	+	7.64067i	−0.179346	+	0.310637i
$606$	−61.7531			−2.50855
$607$	−13.2458	−	22.9423i	−0.537628	−	0.931200i	−0.999031	−	0.0440089i	$-0.985987\pi$
$607$	−13.2458	−	22.9423i	−0.537628	−	0.931200i	0.461403	−	0.887191i	$-0.347346\pi$
$608$	−2.15694	−	3.73593i	−0.0874754	−	0.151512i
$609$	−18.2440	−	31.5995i	−0.739283	−	1.28048i
$610$	−7.14621	+	12.3776i	−0.289341	+	0.501154i
$611$	5.08841	−	8.81338i	0.205855	−	0.356551i
$612$	19.4036	+	33.6079i	0.784342	+	1.35852i
$613$	−6.36447	−	11.0236i	−0.257059	−	0.445239i	0.708394	−	0.705817i	$-0.249420\pi$
$613$	−6.36447	−	11.0236i	−0.257059	−	0.445239i	−0.965453	+	0.260579i	$0.916087\pi$
$614$	9.26419	+	16.0461i	0.373872	+	0.647566i
$615$	27.8006			1.12103
$616$	1.73069	−	2.99764i	0.0697314	−	0.120778i
$617$	11.7043	+	20.2725i	0.471199	+	0.816140i	0.999457	−	0.0329437i	$-0.0104882\pi$
$617$	11.7043	+	20.2725i	0.471199	+	0.816140i	−0.528259	+	0.849083i	$0.677155\pi$
$618$	35.8118			1.44056
$619$	43.6073			1.75273			0.876363	−	0.481650i	$-0.159962\pi$
$619$	43.6073			1.75273			0.876363	+	0.481650i	$0.159962\pi$
$620$	−4.43888	−	7.68836i	−0.178270	−	0.308772i
$621$	−1.33103			−0.0534125
$622$	12.1992	−	21.1297i	0.489145	−	0.847224i
$623$	21.7347			0.870784
$624$	−35.1469	+	60.8763i	−1.40700	+	2.43700i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.00467	−	8.66835i	0.200027	−	0.346457i
$627$	1.23263	+	2.13498i	0.0492266	+	0.0852629i
$628$	−11.8284			−0.472004
$629$	−18.4438	+	25.1562i	−0.735404	+	1.00304i
$630$	26.4292			1.05297
$631$	18.7321	+	32.4449i	0.745711	+	1.29161i	0.949862	+	0.312671i	$0.101224\pi$
$631$	18.7321	+	32.4449i	0.745711	+	1.29161i	−0.204150	+	0.978940i	$0.565443\pi$
$632$	4.73322	−	8.19817i	0.188277	−	0.326106i
$633$	15.4829	−	26.8172i	0.615392	−	1.06589i
$634$	−7.89934	+	13.6821i	−0.313723	+	0.543384i
$635$	4.18733			0.166169
$636$	−16.1787	+	28.0223i	−0.641526	+	1.11116i
$637$	−7.78890			−0.308607
$638$	−6.26474	−	10.8509i	−0.248024	−	0.429589i
$639$	−65.7868			−2.60248
$640$	6.30988			0.249420
$641$	7.30518	+	12.6529i	0.288537	+	0.499761i	0.973461	−	0.228854i	$-0.0734978\pi$
$641$	7.30518	+	12.6529i	0.288537	+	0.499761i	−0.684924	+	0.728615i	$0.740164\pi$
$642$	−3.71370	+	6.43233i	−0.146568	+	0.253864i
$643$	−24.1525			−0.952480			−0.476240	−	0.879315i	$-0.658001\pi$
$643$	−24.1525			−0.952480			−0.476240	+	0.879315i	$0.658001\pi$
$644$	0.601163	+	1.04124i	0.0236891	+	0.0410308i
$645$	13.4498	+	23.2958i	0.529587	+	0.917272i
$646$	−2.89732	−	5.01831i	−0.113994	−	0.197443i
$647$	−0.812692	+	1.40762i	−0.0319502	+	0.0553394i	−0.881558	−	0.472075i	$-0.843505\pi$
$647$	−0.812692	+	1.40762i	−0.0319502	+	0.0553394i	0.849608	+	0.527414i	$0.176838\pi$
$648$	0.116260	−	0.201369i	0.00456713	−	0.00791050i
$649$	10.7734	+	18.6601i	0.422894	+	0.732473i
$650$	−5.08841	−	8.81338i	−0.199584	−	0.345689i
$651$	22.9212	+	39.7007i	0.898353	+	1.55599i
$652$	−12.9157			−0.505816
$653$	−21.9175	+	37.9622i	−0.857697	+	1.48557i	0.0164236	+	0.999865i	$0.494772\pi$
$653$	−21.9175	+	37.9622i	−0.857697	+	1.48557i	−0.874120	+	0.485709i	$0.838561\pi$
$654$	−51.3932	−	89.0157i	−2.00963	−	3.48079i
$655$	4.15284			0.162265
$656$	46.4703			1.81436
$657$	33.0671	+	57.2739i	1.29007	+	2.23447i
$658$	−10.3843			−0.404822
$659$	−7.15459	+	12.3921i	−0.278703	+	0.482729i	−0.971063	−	0.238824i	$-0.923238\pi$
$659$	−7.15459	+	12.3921i	−0.278703	+	0.482729i	0.692359	+	0.721553i	$0.256571\pi$
$660$	6.48694			0.252504
$661$	21.6525	−	37.5033i	0.842186	−	1.45871i	−0.0458565	−	0.998948i	$-0.514602\pi$
$661$	21.6525	−	37.5033i	0.842186	−	1.45871i	0.888043	−	0.459761i	$-0.152065\pi$
$662$	21.4451	−	37.1440i	0.833486	−	1.44364i
$663$	−38.5810	+	66.8242i	−1.49836	+	2.59524i
$664$	−1.73811	−	3.01049i	−0.0674517	−	0.116830i
$665$	−1.73739			−0.0673729
$666$	54.9863	+	6.01989i	2.13068	+	0.233266i
$667$	−1.18142			−0.0457449
$668$	5.19998	+	9.00663i	0.201193	+	0.348477i
$669$	7.68361	−	13.3084i	0.297066	−	0.514533i
$670$	1.07829	−	1.86765i	0.0416578	−	0.0721535i
$671$	5.57854	−	9.66231i	0.215357	−	0.373009i
$672$	58.6150			2.26112
$673$	14.8747	−	25.7638i	0.573379	−	0.993122i	−0.422836	−	0.906206i	$-0.638965\pi$
$673$	14.8747	−	25.7638i	0.573379	−	0.993122i	0.996216	−	0.0869160i	$-0.0277012\pi$
$674$	51.6738			1.99040
$675$	−2.53052	−	4.38298i	−0.0973997	−	0.168701i
$676$	25.1462			0.967163
$677$	4.17635			0.160510			0.0802552	−	0.996774i	$-0.474426\pi$
$677$	4.17635			0.160510			0.0802552	+	0.996774i	$0.474426\pi$
$678$	−30.5407	−	52.8980i	−1.17291	−	2.03154i
$679$	24.5821	−	42.5775i	0.943375	−	1.63397i
$680$	4.13906			0.158726
$681$	3.14941	+	5.45494i	0.120686	+	0.209034i
$682$	7.87085	+	13.6327i	0.301390	+	0.522024i
$683$	−12.6471	−	21.9054i	−0.483928	−	0.838188i	0.515901	−	0.856648i	$-0.327457\pi$
$683$	−12.6471	−	21.9054i	−0.483928	−	0.838188i	−0.999830	+	0.0184598i	$0.994124\pi$
$684$	−2.26191	+	3.91775i	−0.0864864	+	0.149799i
$685$	−1.03663	+	1.79550i	−0.0396077	+	0.0686025i
$686$	−15.2539	−	26.4205i	−0.582397	−	1.00874i
$687$	13.4292	+	23.2600i	0.512356	+	0.887426i
$688$	22.4822	+	38.9404i	0.857127	+	1.48459i
$689$	−39.6268			−1.50966
$690$	0.694682	−	1.20322i	0.0264461	−	0.0458060i
$691$	−18.5147	−	32.0684i	−0.704333	−	1.21994i	−0.966932	−	0.255035i	$-0.917913\pi$
$691$	−18.5147	−	32.0684i	−0.704333	−	1.21994i	0.262599	−	0.964905i	$-0.415420\pi$
$692$	−7.35540			−0.279610
$693$	−20.6314			−0.783723
$694$	22.3550	+	38.7201i	0.848586	+	1.46979i
$695$	−4.44508			−0.168611
$696$	−5.06663	+	8.77566i	−0.192050	+	0.332640i
$697$	51.0107			1.93217
$698$	−10.7935	+	18.6948i	−0.408539	+	0.707610i
$699$	35.9862	−	62.3299i	1.36112	−	2.35753i
$700$	−2.28582	+	3.95916i	−0.0863960	+	0.149642i
$701$	−2.07990	−	3.60249i	−0.0785567	−	0.136064i	0.824071	−	0.566487i	$-0.191698\pi$
$701$	−2.07990	−	3.60249i	−0.0785567	−	0.136064i	−0.902627	+	0.430423i	$0.858365\pi$
$702$	51.5052			1.94394
$703$	−3.61465	−	0.395731i	−0.136329	−	0.0149253i
$704$	6.34084			0.238980
$705$	2.64141	+	4.57506i	0.0994814	+	0.172307i
$706$	15.1111	−	26.1732i	0.568715	−	0.985043i
$707$	−16.9866	+	29.4216i	−0.638846	+	1.10651i
$708$	−32.0975	+	55.5945i	−1.20630	+	2.08937i
$709$	−17.8069			−0.668751			−0.334376	−	0.942440i	$-0.608525\pi$
$709$	−17.8069			−0.668751			−0.334376	+	0.942440i	$0.608525\pi$
$710$	12.9241	−	22.3852i	0.485033	−	0.840102i
$711$	−56.4244			−2.11608
$712$	−3.01804	−	5.22739i	−0.113106	−	0.195905i
$713$	1.48431			0.0555877
$714$	78.7350			2.94658
$715$	3.97216	+	6.87998i	0.148550	+	0.257297i
$716$	−6.47984	+	11.2234i	−0.242163	+	0.419438i
$717$	−45.8171			−1.71107
$718$	12.6843	+	21.9699i	0.473374	+	0.819909i
$719$	−20.3219	−	35.1985i	−0.757879	−	1.31268i	−0.943930	−	0.330144i	$-0.892903\pi$
$719$	−20.3219	−	35.1985i	−0.757879	−	1.31268i	0.186052	−	0.982540i	$-0.440431\pi$
$720$	−11.2374	−	19.4638i	−0.418794	−	0.725372i
$721$	9.85084	−	17.0621i	0.366864	−	0.635428i
$722$	−17.6195	+	30.5179i	−0.655731	+	1.13576i
$723$	6.29798	+	10.9084i	0.234225	+	0.405689i
$724$	−15.3813	−	26.6412i	−0.571641	−	0.990111i
$725$	−2.24608	−	3.89033i	−0.0834174	−	0.144483i
$726$	46.6087			1.72981
$727$	−9.17577	+	15.8929i	−0.340310	+	0.589435i	−0.984490	−	0.175439i	$-0.943865\pi$
$727$	−9.17577	+	15.8929i	−0.340310	+	0.589435i	0.644180	+	0.764874i	$0.277199\pi$
$728$	6.31470	+	10.9374i	0.234038	+	0.405366i
$729$	−43.8196			−1.62295
$730$	−25.9847			−0.961738
$731$	24.6789	+	42.7451i	0.912781	+	1.58098i
$732$	33.2405			1.22861
$733$	−21.8072	+	37.7712i	−0.805469	+	1.39511i	0.110506	+	0.993875i	$0.464753\pi$
$733$	−21.8072	+	37.7712i	−0.805469	+	1.39511i	−0.915974	+	0.401237i	$0.868580\pi$
$734$	−44.2362			−1.63279
$735$	2.02163	−	3.50156i	0.0745688	−	0.129157i
$736$	0.948931	−	1.64360i	0.0349781	−	0.0605838i
$737$	−0.841741	+	1.45794i	−0.0310059	+	0.0537038i
$738$	−45.2288	−	78.3385i	−1.66489	−	2.88368i
$739$	−9.75963			−0.359014			−0.179507	−	0.983757i	$-0.557450\pi$
$739$	−9.75963			−0.359014			−0.179507	+	0.983757i	$0.557450\pi$
$740$	−5.65747	+	7.71643i	−0.207973	+	0.283662i
$741$	−8.99493			−0.330437
$742$	20.2173	+	35.0175i	0.742202	+	1.28553i
$743$	3.73705	−	6.47275i	0.137099	−	0.237462i	−0.789298	−	0.614010i	$-0.789556\pi$
$743$	3.73705	−	6.47275i	0.137099	−	0.237462i	0.926397	+	0.376548i	$0.122889\pi$
$744$	6.36557	−	11.0255i	0.233373	−	0.404214i
$745$	−2.97688	+	5.15611i	−0.109064	+	0.188905i
$746$	8.58582			0.314349
$747$	−10.3600	+	17.9440i	−0.379051	+	0.656535i
$748$	11.9028			0.435208
$749$	2.04308	+	3.53871i	0.0746524	+	0.129302i
$750$	5.28283			0.192902
$751$	26.8347			0.979213			0.489606	−	0.871944i	$-0.337140\pi$
$751$	26.8347			0.979213			0.489606	+	0.871944i	$0.337140\pi$
$752$	4.41528	+	7.64750i	0.161009	+	0.278876i
$753$	−9.87815	+	17.1095i	−0.359980	+	0.623503i
$754$	45.7159			1.66488
$755$	−0.138733	−	0.240293i	−0.00504902	−	0.00874517i
$756$	−11.5686	−	20.0375i	−0.420747	−	0.728755i
$757$	−18.3855	−	31.8446i	−0.668232	−	1.15741i	−0.978398	−	0.206730i	$-0.933718\pi$
$757$	−18.3855	−	31.8446i	−0.668232	−	1.15741i	0.310166	−	0.950683i	$-0.399615\pi$
$758$	−22.2949	+	38.6158i	−0.809786	+	1.40259i
$759$	−0.542289	+	0.939272i	−0.0196838	+	0.0340934i
$760$	0.241249	+	0.417856i	0.00875103	+	0.0151572i
$761$	10.3483	+	17.9238i	0.375125	+	0.649736i	0.990346	−	0.138619i	$-0.0442664\pi$
$761$	10.3483	+	17.9238i	0.375125	+	0.649736i	−0.615221	+	0.788355i	$0.710933\pi$
$762$	−11.0605	−	19.1573i	−0.400678	−	0.693995i
$763$	−56.5474			−2.04716
$764$	19.5405	−	33.8451i	0.706950	−	1.22447i
$765$	−12.3354	−	21.3655i	−0.445986	−	0.772471i
$766$	2.28828			0.0826788
$767$	−78.6172			−2.83870
$768$	−28.6768	−	49.6697i	−1.03479	−	1.79230i
$769$	−44.1903			−1.59354			−0.796772	−	0.604280i	$-0.793461\pi$
$769$	−44.1903			−1.59354			−0.796772	+	0.604280i	$0.793461\pi$
$770$	4.05314	−	7.02024i	0.146065	−	0.252992i
$771$	1.07155			0.0385909
$772$	5.26146	−	9.11311i	0.189364	−	0.327988i
$773$	7.22373	−	12.5119i	0.259820	−	0.450021i	−0.706374	−	0.707839i	$-0.749670\pi$
$773$	7.22373	−	12.5119i	0.259820	−	0.450021i	0.966193	+	0.257818i	$0.0830036\pi$
$774$	43.7631	−	75.8000i	1.57303	−	2.72457i
$775$	2.82192	+	4.88770i	0.101366	+	0.175571i
$776$	−13.6537			−0.490138
$777$	29.2137	−	39.8457i	1.04804	−	1.42946i
$778$	61.3168			2.19831
$779$	2.97321	+	5.14976i	0.106526	+	0.184509i
$780$	−11.8343	+	20.4977i	−0.423738	+	0.733935i
$781$	−10.0889	+	17.4745i	−0.361010	+	0.625288i
$782$	1.27466	−	2.20777i	0.0455817	−	0.0789498i
$783$	22.7350			0.812482
$784$	3.37927	−	5.85307i	0.120688	−	0.209038i
$785$	7.51964			0.268387
$786$	−10.9694	−	18.9995i	−0.391265	−	0.677690i
$787$	44.9667			1.60289			0.801444	−	0.598069i	$-0.204065\pi$
$787$	44.9667			1.60289			0.801444	+	0.598069i	$0.204065\pi$
$788$	15.4355			0.549868
$789$	−1.61258	−	2.79307i	−0.0574094	−	0.0994361i
$790$	11.0848	−	19.1995i	0.394381	−	0.683088i
$791$	−33.6036			−1.19481
$792$	2.86483	+	4.96203i	0.101797	+	0.176318i
$793$	20.3542	+	35.2545i	0.722799	+	1.25193i
$794$	−12.5141	−	21.6750i	−0.444108	−	0.769218i
$795$	10.2852	−	17.8145i	0.364779	−	0.631816i
$796$	−5.15707	+	8.93231i	−0.182787	+	0.316597i
$797$	−0.168052	−	0.291075i	−0.00595272	−	0.0103104i	0.863034	−	0.505146i	$-0.168561\pi$
$797$	−0.168052	−	0.291075i	−0.00595272	−	0.0103104i	−0.868986	+	0.494836i	$0.835228\pi$
$798$	4.58915	+	7.94865i	0.162454	+	0.281379i
$799$	4.84668	+	8.39470i	0.171463	+	0.296983i
$800$	7.21631			0.255135
$801$	−17.9889	+	31.1577i	−0.635607	+	1.10090i
$802$	13.3227	+	23.0756i	0.470442	+	0.814829i
$803$	20.2844			0.715822
$804$	−5.01564			−0.176888
$805$	−0.382176	−	0.661948i	−0.0134699	−	0.0233306i
$806$	−57.4362			−2.02310
$807$	23.6627	−	40.9850i	0.832966	−	1.44274i
$808$	9.43486			0.331917
$809$	10.6908	−	18.5169i	0.375867	−	0.651021i	−0.614589	−	0.788847i	$-0.710678\pi$
$809$	10.6908	−	18.5169i	0.375867	−	0.651021i	0.990456	+	0.137826i	$0.0440116\pi$
$810$	0.272273	−	0.471590i	0.00956669	−	0.0165700i
$811$	−6.02102	+	10.4287i	−0.211427	+	0.366202i	−0.952161	−	0.305596i	$-0.901144\pi$
$811$	−6.02102	+	10.4287i	−0.211427	+	0.366202i	0.740735	+	0.671798i	$0.234478\pi$
$812$	−10.2683	−	17.7852i	−0.360346	−	0.624138i
$813$	40.0629			1.40507
$814$	10.0316	−	13.6825i	0.351608	−	0.479571i
$815$	8.21084			0.287613
$816$	−33.4773	−	57.9843i	−1.17194	−	2.02986i
$817$	−2.87687	+	4.98288i	−0.100649	+	0.174329i
$818$	−25.0304	+	43.3539i	−0.875166	+	1.51583i
$819$	37.6386	−	65.1920i	1.31520	−	2.27799i
$820$	15.6471			0.546419
$821$	−1.72325	+	2.98475i	−0.0601417	+	0.104169i	−0.894529	−	0.447011i	$-0.852489\pi$
$821$	−1.72325	+	2.98475i	−0.0601417	+	0.104169i	0.834387	+	0.551179i	$0.185822\pi$
$822$	10.9527			0.382019
$823$	−1.21593	−	2.10605i	−0.0423847	−	0.0734124i	0.844055	−	0.536257i	$-0.180162\pi$
$823$	−1.21593	−	2.10605i	−0.0423847	−	0.0734124i	−0.886439	+	0.462844i	$0.846829\pi$
$824$	−5.47146			−0.190607
$825$	−4.12393			−0.143577
$826$	40.1100	+	69.4726i	1.39561	+	2.41726i
$827$	−2.54318	+	4.40492i	−0.0884351	+	0.153174i	−0.906850	−	0.421454i	$-0.861520\pi$
$827$	−2.54318	+	4.40492i	−0.0884351	+	0.153174i	0.818415	+	0.574628i	$0.194853\pi$
$828$	−1.99023			−0.0691652
$829$	22.4450	+	38.8758i	0.779546	+	1.35021i	0.932204	+	0.361934i	$0.117884\pi$
$829$	22.4450	+	38.8758i	0.779546	+	1.35021i	−0.152657	+	0.988279i	$0.548783\pi$
$830$	−4.07052	−	7.05035i	−0.141290	−	0.244721i
$831$	−19.3121	−	33.4496i	−0.669930	−	1.16035i
$832$	−11.5678	+	20.0360i	−0.401042	+	0.694625i
$833$	3.70944	−	6.42494i	0.128525	−	0.222611i
$834$	11.7413	+	20.3365i	0.406568	+	0.704196i
$835$	−3.30577	−	5.72576i	−0.114401	−	0.198148i
$836$	0.693765	+	1.20164i	0.0239944	+	0.0415595i
$837$	−28.5636			−0.987303
$838$	−9.94473	+	17.2248i	−0.343535	+	0.595020i
$839$	6.61095	+	11.4505i	0.228235	+	0.395315i	0.957285	−	0.289145i	$-0.0933711\pi$
$839$	6.61095	+	11.4505i	0.228235	+	0.395315i	−0.729050	+	0.684461i	$0.760038\pi$
$840$	−6.55597			−0.226203
$841$	−8.82047			−0.304154
$842$	14.7994	+	25.6333i	0.510020	+	0.883380i
$843$	68.1656			2.34775
$844$	8.71430	−	15.0936i	0.299958	−	0.519543i
$845$	−15.9862			−0.549941
$846$	8.59464	−	14.8863i	0.295490	−	0.511803i
$847$	12.8208	−	22.2062i	0.440527	−	0.763015i
$848$	17.1924	−	29.7781i	0.590389	−	1.02258i
$849$	29.9823	+	51.9308i	1.02899	+	1.78226i
$850$	9.69336			0.332480
$851$	−0.644347	−	1.46424i	−0.0220879	−	0.0501935i
$852$	−60.1164			−2.05955
$853$	19.1306	+	33.1351i	0.655018	+	1.13452i	0.981889	+	0.189455i	$0.0606722\pi$
$853$	19.1306	+	33.1351i	0.655018	+	1.13452i	−0.326872	+	0.945069i	$0.605994\pi$
$854$	20.7692	−	35.9733i	0.710707	−	1.23098i
$855$	1.43796	−	2.49062i	0.0491772	−	0.0851774i
$856$	0.567394	−	0.982755i	0.0193931	−	0.0335899i
$857$	−5.40854			−0.184752			−0.0923761	−	0.995724i	$-0.529446\pi$
$857$	−5.40854			−0.184752			−0.0923761	+	0.995724i	$0.529446\pi$
$858$	20.9842	−	36.3457i	0.716390	−	1.24082i
$859$	25.4031			0.866744			0.433372	−	0.901215i	$-0.357324\pi$
$859$	25.4031			0.866744			0.433372	+	0.901215i	$0.357324\pi$
$860$	7.57001	+	13.1116i	0.258135	+	0.447103i
$861$	−80.7974			−2.75357
$862$	−58.5621			−1.99463
$863$	−11.7401	−	20.3345i	−0.399638	−	0.692193i	0.594043	−	0.804433i	$-0.297531\pi$
$863$	−11.7401	−	20.3345i	−0.399638	−	0.692193i	−0.993681	+	0.112240i	$0.964198\pi$
$864$	−18.2610	+	31.6290i	−0.621252	+	1.07604i
$865$	4.67603			0.158990
$866$	21.6839	+	37.5576i	0.736849	+	1.27626i
$867$	−12.9924	−	22.5035i	−0.441245	−	0.764259i
$868$	12.9008	+	22.3448i	0.437882	+	0.758433i
$869$	−8.65314	+	14.9877i	−0.293538	+	0.508422i
$870$	−11.8657	+	20.5519i	−0.402284	+	0.696776i
$871$	−3.07123	−	5.31953i	−0.104065	−	0.180245i
$872$	7.85205	+	13.6001i	0.265904	+	0.460559i
$873$	40.6912	+	70.4791i	1.37719	+	2.38536i
$874$	0.297179			0.0100522
$875$	1.45316	−	2.51695i	0.0491258	−	0.0850884i
$876$	30.2170	+	52.3373i	1.02094	+	1.76831i
$877$	−30.6413			−1.03468			−0.517342	−	0.855779i	$-0.673078\pi$
$877$	−30.6413			−1.03468			−0.517342	+	0.855779i	$0.673078\pi$
$878$	−10.0893			−0.340498
$879$	−9.08404	−	15.7340i	−0.306397	−	0.530695i
$880$	−6.89340			−0.232376
$881$	2.21699	−	3.83993i	0.0746921	−	0.129371i	−0.826260	−	0.563289i	$-0.809536\pi$
$881$	2.21699	−	3.83993i	0.0746921	−	0.129371i	0.900952	+	0.433918i	$0.142869\pi$
$882$	−13.1559			−0.442983
$883$	1.52581	−	2.64277i	0.0513475	−	0.0889365i	−0.839209	−	0.543809i	$-0.816982\pi$
$883$	1.52581	−	2.64277i	0.0513475	−	0.0889365i	0.890557	+	0.454872i	$0.150315\pi$
$884$	−21.7146	+	37.6108i	−0.730342	+	1.26499i
$885$	20.4053	−	35.3430i	0.685916	−	1.18804i
$886$	31.6380	+	54.7986i	1.06290	+	1.84100i
$887$	24.5439			0.824105			0.412052	−	0.911160i	$-0.364812\pi$
$887$	24.5439			0.824105			0.412052	+	0.911160i	$0.364812\pi$
$888$	−13.6398	−	1.49328i	−0.457721	−	0.0501111i
$889$	−12.1697			−0.408159
$890$	−7.06801	−	12.2422i	−0.236920	−	0.410358i
$891$	−0.212544	+	0.368137i	−0.00712049	+	0.0123330i
$892$	4.32459	−	7.49040i	0.144798	−	0.250797i
$893$	−0.564988	+	0.978587i	−0.0189066	+	0.0327472i
$894$	31.4527			1.05194
$895$	4.11941	−	7.13503i	0.137697	−	0.238498i
$896$	−18.3385			−0.612648
$897$	−1.97863	−	3.42709i	−0.0660646	−	0.114427i
$898$	0.628599			0.0209766
$899$	−25.3530			−0.845570
$900$	−3.78376	−	6.55366i	−0.126125	−	0.218455i
$901$	18.8722	−	32.6875i	0.628723	−	1.08898i
$902$	−27.7448			−0.923800
$903$	−39.0896	−	67.7051i	−1.30082	−	2.25309i
$904$	4.66612	+	8.08196i	0.155193	+	0.268802i
$905$	9.77831	+	16.9365i	0.325042	+	0.562989i
$906$	−0.732905	+	1.26943i	−0.0243491	+	0.0421739i
$907$	9.67634	−	16.7599i	0.321298	−	0.556504i	−0.659458	−	0.751741i	$-0.729214\pi$
$907$	9.67634	−	16.7599i	0.321298	−	0.556504i	0.980756	+	0.195237i	$0.0625477\pi$
$908$	1.77259	+	3.07022i	0.0588255	+	0.101889i
$909$	−28.1181	−	48.7020i	−0.932620	−	1.61534i
$910$	14.7886	+	25.6145i	0.490236	+	0.849113i
$911$	29.0550			0.962635			0.481318	−	0.876546i	$-0.340158\pi$
$911$	29.0550			0.962635			0.481318	+	0.876546i	$0.340158\pi$
$912$	3.90251	−	6.75935i	0.129225	−	0.223825i
$913$	3.17756	+	5.50370i	0.105162	+	0.182146i
$914$	−4.62775			−0.153072
$915$	−21.1319			−0.698600
$916$	7.55839	+	13.0915i	0.249736	+	0.432556i
$917$	−12.0695			−0.398570
$918$	−24.5292	+	42.4859i	−0.809585	+	1.40224i
$919$	−27.3042			−0.900681			−0.450341	−	0.892857i	$-0.648697\pi$
$919$	−27.3042			−0.900681			−0.450341	+	0.892857i	$0.648697\pi$
$920$	−0.106136	+	0.183833i	−0.00349920	+	0.00606080i
$921$	−13.6975	+	23.7247i	−0.451348	+	0.781757i
$922$	−12.8474	+	22.2523i	−0.423106	+	0.732840i
$923$	−36.8112	−	63.7588i	−1.21165	−	2.09865i
$924$	−18.8531			−0.620223
$925$	3.59661	−	4.90555i	0.118256	−	0.161293i
$926$	−51.8603			−1.70423
$927$	16.3062	+	28.2432i	0.535567	+	0.927629i
$928$	−16.2084	+	28.0738i	−0.532067	+	0.921568i
$929$	−24.9982	+	43.2982i	−0.820164	+	1.42057i	0.0853953	+	0.996347i	$0.472785\pi$
$929$	−24.9982	+	43.2982i	−0.820164	+	1.42057i	−0.905560	+	0.424219i	$0.860549\pi$
$930$	14.9077	−	25.8209i	0.488843	−	0.846700i
$931$	0.864835			0.0283438
$932$	20.2542	−	35.0813i	0.663448	−	1.14913i
$933$	36.0742			1.18102
$934$	−2.28053	−	3.95000i	−0.0746214	−	0.129248i
$935$	−7.56692			−0.247465
$936$	−20.9056			−0.683322
$937$	−3.33222	−	5.77157i	−0.108859	−	0.188549i	0.806449	−	0.591303i	$-0.201386\pi$
$937$	−3.33222	−	5.77157i	−0.108859	−	0.188549i	−0.915308	+	0.402754i	$0.868053\pi$
$938$	−3.13385	+	5.42798i	−0.102324	+	0.177230i
$939$	14.7992			0.482955
$940$	1.48667	+	2.57499i	0.0484899	+	0.0839870i
$941$	−11.9086	−	20.6263i	−0.388210	−	0.672400i	0.603999	−	0.796985i	$-0.293573\pi$
$941$	−11.9086	−	20.6263i	−0.388210	−	0.672400i	−0.992209	+	0.124586i	$0.960240\pi$
$942$	−19.8625	−	34.4028i	−0.647154	−	1.12090i
$943$	−1.30805	+	2.26560i	−0.0425959	+	0.0737782i
$944$	34.1086	−	59.0779i	1.11014	−	1.92282i
$945$	7.35450	+	12.7384i	0.239242	+	0.414379i
$946$	−13.4229	−	23.2491i	−0.436415	−	0.755893i
$947$	9.92493	+	17.1905i	0.322517	+	0.558616i	0.981007	−	0.193974i	$-0.0621378\pi$
$947$	9.92493	+	17.1905i	0.322517	+	0.558616i	−0.658490	+	0.752590i	$0.728804\pi$
$948$	−51.5610			−1.67462
$949$	−37.0056	+	64.0955i	−1.20125	+	2.08063i
$950$	0.564988	+	0.978587i	0.0183306	+	0.0317496i
$951$	−23.3590			−0.757468
$952$	−12.0294			−0.389876
$953$	4.62806	+	8.01603i	0.149917	+	0.259665i	0.931197	−	0.364517i	$-0.118766\pi$
$953$	4.62806	+	8.01603i	0.149917	+	0.259665i	−0.781279	+	0.624182i	$0.785433\pi$
$954$	−66.9321			−2.16701
$955$	−12.4224	+	21.5163i	−0.401980	+	0.696250i
$956$	−25.7873			−0.834022
$957$	9.26268	−	16.0434i	0.299420	−	0.518610i
$958$	−21.6524	+	37.5031i	−0.699559	+	1.21167i
$959$	3.01279	−	5.21830i	0.0972879	−	0.168508i
$960$	−6.00490	−	10.4008i	−0.193807	−	0.335684i
$961$	0.852828			0.0275106
$962$	24.9334	+	56.6597i	0.803886	+	1.82678i
$963$	−6.76387			−0.217963
$964$	3.54471	+	6.13962i	0.114167	+	0.197744i
$965$	−3.34485	+	5.79346i	−0.107675	+	0.186498i
$966$	−2.01897	+	3.49696i	−0.0649593	+	0.112513i
$967$	−12.3399	+	21.3733i	−0.396824	+	0.687319i	−0.993332	−	0.115288i	$-0.963221\pi$
$967$	−12.3399	+	21.3733i	−0.396824	+	0.687319i	0.596508	+	0.802607i	$0.296554\pi$
$968$	−7.12105			−0.228879
$969$	4.28381	−	7.41978i	0.137616	−	0.238358i
$970$	−31.9759			−1.02668
$971$	−5.36988	−	9.30090i	−0.172328	−	0.298480i	0.766906	−	0.641760i	$-0.221795\pi$
$971$	−5.36988	−	9.30090i	−0.172328	−	0.298480i	−0.939233	+	0.343280i	$0.888462\pi$
$972$	−25.1495			−0.806671
$973$	12.9188			0.414159
$974$	−28.0359	−	48.5597i	−0.898329	−	1.55595i
$975$	7.52342	−	13.0309i	0.240942	−	0.417324i
$976$	−35.3233			−1.13067
$977$	−1.65987	−	2.87497i	−0.0531038	−	0.0919785i	0.838252	−	0.545284i	$-0.183578\pi$
$977$	−1.65987	−	2.87497i	−0.0531038	−	0.0919785i	−0.891355	+	0.453305i	$0.850245\pi$
$978$	−21.6882	−	37.5651i	−0.693513	−	1.20120i
$979$	5.51749	+	9.55658i	0.176340	+	0.305430i
$980$	1.13784	−	1.97079i	0.0363468	−	0.0629546i
$981$	46.8019	−	81.0633i	1.49427	−	2.58815i
$982$	−18.5073	−	32.0556i	−0.590593	−	1.02294i
$983$	3.94701	+	6.83642i	0.125890	+	0.218048i	0.922080	−	0.386998i	$-0.126488\pi$
$983$	3.94701	+	6.83642i	0.125890	+	0.218048i	−0.796191	+	0.605046i	$0.793155\pi$
$984$	11.2193	+	19.4325i	0.357659	+	0.619484i
$985$	−9.81279			−0.312661
$986$	−21.7721	+	37.7104i	−0.693364	+	1.20094i
$987$	−7.67680	−	13.2966i	−0.244355	−	0.423236i
$988$	−5.06264			−0.161064
$989$	−2.53132			−0.0804913
$990$	6.70922	+	11.6207i	0.213233	+	0.369330i
$991$	−2.89845			−0.0920722			−0.0460361	−	0.998940i	$-0.514659\pi$
$991$	−2.89845			−0.0920722			−0.0460361	+	0.998940i	$0.514659\pi$
$992$	20.3638	−	35.2712i	0.646552	−	1.11986i
$993$	63.4148			2.01241
$994$	−37.5616	+	65.0587i	−1.19138	+	2.06354i
$995$	3.27849	−	5.67851i	0.103935	−	0.180021i
$996$	−9.46700	+	16.3973i	−0.299973	+	0.519569i
$997$	7.08063	+	12.2640i	0.224246	+	0.388405i	0.956093	−	0.293064i	$-0.0946748\pi$
$997$	7.08063	+	12.2640i	0.224246	+	0.388405i	−0.731847	+	0.681469i	$0.761341\pi$
$998$	40.6507			1.28678
$999$	12.3996	+	28.1775i	0.392307	+	0.891495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.b.26.6	✓	14
5.2	odd	4		925.2.o.c.174.3		28
5.3	odd	4		925.2.o.c.174.12		28
5.4	even	2		925.2.e.b.26.2		14
37.10	even	3	inner	185.2.e.b.121.6	yes	14
37.11	even	6		6845.2.a.m.1.6		7
37.26	even	3		6845.2.a.j.1.2		7
185.47	odd	12		925.2.o.c.824.12		28
185.84	even	6		925.2.e.b.676.2		14
185.158	odd	12		925.2.o.c.824.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.6	✓	14	1.1	even	1	trivial
185.2.e.b.121.6	yes	14	37.10	even	3	inner
925.2.e.b.26.2		14	5.4	even	2
925.2.e.b.676.2		14	185.84	even	6
925.2.o.c.174.3		28	5.2	odd	4
925.2.o.c.174.12		28	5.3	odd	4
925.2.o.c.824.3		28	185.158	odd	12
925.2.o.c.824.12		28	185.47	odd	12
6845.2.a.j.1.2		7	37.26	even	3
6845.2.a.m.1.6		7	37.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.945119 + 1.63699i) q^{2} +(-1.39740 + 2.42036i) q^{3} +(-0.786500 + 1.36226i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.28283 q^{6} +(-1.45316 + 2.51695i) q^{7} +0.807130 q^{8} +(-2.40544 - 4.16634i) q^{9} +O(q^{10})\)	\(q+(0.945119 + 1.63699i) q^{2} +(-1.39740 + 2.42036i) q^{3} +(-0.786500 + 1.36226i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.28283 q^{6} +(-1.45316 + 2.51695i) q^{7} +0.807130 q^{8} +(-2.40544 - 4.16634i) q^{9} +1.89024 q^{10} -1.47557 q^{11} +(-2.19811 - 3.80723i) q^{12} +(2.69194 - 4.66258i) q^{13} -5.49364 q^{14} +(1.39740 + 2.42036i) q^{15} +(2.33584 + 4.04578i) q^{16} +(2.56406 + 4.44108i) q^{17} +(4.54685 - 7.87538i) q^{18} +(-0.298898 + 0.517706i) q^{19} +(0.786500 + 1.36226i) q^{20} +(-4.06129 - 7.03436i) q^{21} +(-1.39459 - 2.41551i) q^{22} -0.262996 q^{23} +(-1.12788 + 1.95355i) q^{24} +(-0.500000 - 0.866025i) q^{25} +10.1768 q^{26} +5.06103 q^{27} +(-2.28582 - 3.95916i) q^{28} +4.49216 q^{29} +(-2.64141 + 4.57506i) q^{30} -5.64383 q^{31} +(-3.60815 + 6.24951i) q^{32} +(2.06196 - 3.57143i) q^{33} +(-4.84668 + 8.39470i) q^{34} +(1.45316 + 2.51695i) q^{35} +7.56752 q^{36} +(2.45002 + 5.56753i) q^{37} -1.12998 q^{38} +(7.52342 + 13.0309i) q^{39} +(0.403565 - 0.698995i) q^{40} +(4.97363 - 8.61458i) q^{41} +(7.67680 - 13.2966i) q^{42} +9.62493 q^{43} +(1.16054 - 2.01011i) q^{44} -4.81088 q^{45} +(-0.248563 - 0.430523i) q^{46} +1.89024 q^{47} -13.0564 q^{48} +(-0.723354 - 1.25289i) q^{49} +(0.945119 - 1.63699i) q^{50} -14.3320 q^{51} +(4.23442 + 7.33424i) q^{52} +(-3.68014 - 6.37418i) q^{53} +(4.78328 + 8.28488i) q^{54} +(-0.737787 + 1.27788i) q^{55} +(-1.17289 + 2.03151i) q^{56} +(-0.835357 - 1.44688i) q^{57} +(4.24563 + 7.35365i) q^{58} +(-7.30117 - 12.6460i) q^{59} -4.39621 q^{60} +(-3.78059 + 6.54817i) q^{61} +(-5.33409 - 9.23892i) q^{62} +13.9820 q^{63} -4.29720 q^{64} +(-2.69194 - 4.66258i) q^{65} +7.79521 q^{66} +(0.570450 - 0.988048i) q^{67} -8.06653 q^{68} +(0.367510 - 0.636547i) q^{69} +(-2.74682 + 4.75763i) q^{70} +(6.83729 - 11.8425i) q^{71} +(-1.94150 - 3.36278i) q^{72} -13.7468 q^{73} +(-6.79845 + 9.27265i) q^{74} +2.79479 q^{75} +(-0.470166 - 0.814352i) q^{76} +(2.14425 - 3.71395i) q^{77} +(-14.2211 + 24.6316i) q^{78} +(5.86425 - 10.1572i) q^{79} +4.67167 q^{80} +(0.144041 - 0.249487i) q^{81} +18.8027 q^{82} +(-2.15344 - 3.72987i) q^{83} +12.7768 q^{84} +5.12812 q^{85} +(9.09670 + 15.7559i) q^{86} +(-6.27734 + 10.8727i) q^{87} -1.19098 q^{88} +(-3.73922 - 6.47651i) q^{89} +(-4.54685 - 7.87538i) q^{90} +(7.82364 + 13.5509i) q^{91} +(0.206847 - 0.358269i) q^{92} +(7.88668 - 13.6601i) q^{93} +(1.78650 + 3.09431i) q^{94} +(0.298898 + 0.517706i) q^{95} +(-10.0841 - 17.4661i) q^{96} -16.9163 q^{97} +(1.36731 - 2.36825i) q^{98} +(3.54940 + 6.14775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more