LMFDB - Embedded newform 805.2.i.e.116.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(116,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("805.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.i (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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.11
Character	$\chi$	$=$	805.116
Dual form			805.2.i.e.576.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.270268 + 0.468117i) q^{2} +(1.08279 - 1.87545i) q^{3} +(0.853911 - 1.47902i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.17058 q^{6} +(-1.51572 - 2.16855i) q^{7} +2.00421 q^{8} +(-0.844883 - 1.46338i) q^{9} +O(q^{10})$	\(q+(0.270268 + 0.468117i) q^{2} +(1.08279 - 1.87545i) q^{3} +(0.853911 - 1.47902i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.17058 q^{6} +(-1.51572 - 2.16855i) q^{7} +2.00421 q^{8} +(-0.844883 - 1.46338i) q^{9} +(-0.270268 + 0.468117i) q^{10} +(-0.0442043 + 0.0765640i) q^{11} +(-1.84922 - 3.20294i) q^{12} -2.83822 q^{13} +(0.605486 - 1.29562i) q^{14} +2.16559 q^{15} +(-1.16615 - 2.01983i) q^{16} +(3.34157 - 5.78778i) q^{17} +(0.456689 - 0.791009i) q^{18} +(2.11602 + 3.66505i) q^{19} +1.70782 q^{20} +(-5.70822 + 0.494566i) q^{21} -0.0477879 q^{22} +(-0.500000 - 0.866025i) q^{23} +(2.17014 - 3.75880i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.767079 - 1.32862i) q^{26} +2.83742 q^{27} +(-4.50161 + 0.390024i) q^{28} -4.39559 q^{29} +(0.585288 + 1.01375i) q^{30} +(-0.375761 + 0.650838i) q^{31} +(2.63455 - 4.56318i) q^{32} +(0.0957282 + 0.165806i) q^{33} +3.61248 q^{34} +(1.12016 - 2.39692i) q^{35} -2.88582 q^{36} +(1.43093 + 2.47844i) q^{37} +(-1.14378 + 1.98109i) q^{38} +(-3.07321 + 5.32295i) q^{39} +(1.00210 + 1.73570i) q^{40} -1.21574 q^{41} +(-1.77426 - 2.53845i) q^{42} +2.09390 q^{43} +(0.0754930 + 0.130758i) q^{44} +(0.844883 - 1.46338i) q^{45} +(0.270268 - 0.468117i) q^{46} +(1.06536 + 1.84526i) q^{47} -5.05080 q^{48} +(-2.40521 + 6.57381i) q^{49} -0.540535 q^{50} +(-7.23647 - 12.5339i) q^{51} +(-2.42359 + 4.19778i) q^{52} +(-5.03019 + 8.71255i) q^{53} +(0.766864 + 1.32825i) q^{54} -0.0884085 q^{55} +(-3.03781 - 4.34622i) q^{56} +9.16485 q^{57} +(-1.18799 - 2.05765i) q^{58} +(3.94617 - 6.83497i) q^{59} +(1.84922 - 3.20294i) q^{60} +(2.88925 + 5.00432i) q^{61} -0.406225 q^{62} +(-1.89281 + 4.05024i) q^{63} -1.81646 q^{64} +(-1.41911 - 2.45797i) q^{65} +(-0.0517444 + 0.0896240i) q^{66} +(3.06733 - 5.31277i) q^{67} +(-5.70681 - 9.88449i) q^{68} -2.16559 q^{69} +(1.42478 - 0.123445i) q^{70} -12.7014 q^{71} +(-1.69332 - 2.93292i) q^{72} +(3.93552 - 6.81651i) q^{73} +(-0.773467 + 1.33968i) q^{74} +(1.08279 + 1.87545i) q^{75} +7.22757 q^{76} +(0.233034 - 0.0201903i) q^{77} -3.32235 q^{78} +(8.05814 + 13.9571i) q^{79} +(1.16615 - 2.01983i) q^{80} +(5.60699 - 9.71160i) q^{81} +(-0.328576 - 0.569111i) q^{82} +7.61763 q^{83} +(-4.14284 + 8.86487i) q^{84} +6.68315 q^{85} +(0.565912 + 0.980189i) q^{86} +(-4.75952 + 8.24372i) q^{87} +(-0.0885945 + 0.153450i) q^{88} +(1.60243 + 2.77550i) q^{89} +0.913378 q^{90} +(4.30194 + 6.15482i) q^{91} -1.70782 q^{92} +(0.813744 + 1.40945i) q^{93} +(-0.575866 + 0.997429i) q^{94} +(-2.11602 + 3.66505i) q^{95} +(-5.70535 - 9.88196i) q^{96} -7.75152 q^{97} +(-3.72736 + 0.650770i) q^{98} +0.149390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9}+O(q^{10}) $ 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9	\( 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9} + 5 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} - 43 q^{16} + q^{17} + 13 q^{18} + 17 q^{19} - 38 q^{20} - 3 q^{21} + 50 q^{22} - 15 q^{23} + 4 q^{24} - 15 q^{25} + 14 q^{26} - 6 q^{27} - q^{28} + 62 q^{29} - 8 q^{30} + 23 q^{31} - 30 q^{32} - 28 q^{33} - 20 q^{34} + 6 q^{35} + 30 q^{36} - 20 q^{37} - 12 q^{38} - 4 q^{39} + 15 q^{40} - 16 q^{42} + 8 q^{43} - 33 q^{44} + 27 q^{45} - 5 q^{46} + q^{47} + 52 q^{48} + 33 q^{49} + 10 q^{50} - 27 q^{51} - 11 q^{52} - 36 q^{53} - 12 q^{54} - 22 q^{55} + 18 q^{56} + 56 q^{57} - 14 q^{58} + 10 q^{59} + 10 q^{61} + 28 q^{62} - 51 q^{63} + 18 q^{64} + 3 q^{65} + 17 q^{66} - 13 q^{67} - 3 q^{68} - q^{70} - 14 q^{71} - 35 q^{72} - 9 q^{73} - 62 q^{74} + 10 q^{76} - 26 q^{77} - 34 q^{78} - 4 q^{79} + 43 q^{80} - 43 q^{81} - 32 q^{82} + 58 q^{83} - 78 q^{84} + 2 q^{85} - 100 q^{86} + 22 q^{87} - 24 q^{88} + 6 q^{89} + 26 q^{90} - 6 q^{91} + 38 q^{92} - q^{93} + 62 q^{94} - 17 q^{95} + 63 q^{96} + 72 q^{97} + q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9 + 5 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 - 43 * q^16 + q^17 + 13 * q^18 + 17 * q^19 - 38 * q^20 - 3 * q^21 + 50 * q^22 - 15 * q^23 + 4 * q^24 - 15 * q^25 + 14 * q^26 - 6 * q^27 - q^28 + 62 * q^29 - 8 * q^30 + 23 * q^31 - 30 * q^32 - 28 * q^33 - 20 * q^34 + 6 * q^35 + 30 * q^36 - 20 * q^37 - 12 * q^38 - 4 * q^39 + 15 * q^40 - 16 * q^42 + 8 * q^43 - 33 * q^44 + 27 * q^45 - 5 * q^46 + q^47 + 52 * q^48 + 33 * q^49 + 10 * q^50 - 27 * q^51 - 11 * q^52 - 36 * q^53 - 12 * q^54 - 22 * q^55 + 18 * q^56 + 56 * q^57 - 14 * q^58 + 10 * q^59 + 10 * q^61 + 28 * q^62 - 51 * q^63 + 18 * q^64 + 3 * q^65 + 17 * q^66 - 13 * q^67 - 3 * q^68 - q^70 - 14 * q^71 - 35 * q^72 - 9 * q^73 - 62 * q^74 + 10 * q^76 - 26 * q^77 - 34 * q^78 - 4 * q^79 + 43 * q^80 - 43 * q^81 - 32 * q^82 + 58 * q^83 - 78 * q^84 + 2 * q^85 - 100 * q^86 + 22 * q^87 - 24 * q^88 + 6 * q^89 + 26 * q^90 - 6 * q^91 + 38 * q^92 - q^93 + 62 * q^94 - 17 * q^95 + 63 * q^96 + 72 * q^97 + q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.270268	+	0.468117i	0.191108	+	0.331009i	0.945618	−	0.325280i	$-0.105459\pi$
$2$	0.270268	+	0.468117i	0.191108	+	0.331009i	−0.754510	+	0.656289i	$0.772125\pi$
$3$	1.08279	−	1.87545i	0.625151	−	1.08279i	−0.363361	−	0.931649i	$-0.618371\pi$
$3$	1.08279	−	1.87545i	0.625151	−	1.08279i	0.988512	−	0.151145i	$-0.0482960\pi$
$4$	0.853911	−	1.47902i	0.426955	−	0.739509i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.17058			0.477886
$7$	−1.51572	−	2.16855i	−0.572887	−	0.819634i
$7$	−1.51572	−	2.16855i	−0.572887	−	0.819634i
$8$	2.00421			0.708595
$9$	−0.844883	−	1.46338i	−0.281628	−	0.487794i
$10$	−0.270268	+	0.468117i	−0.0854661	+	0.148032i
$11$	−0.0442043	+	0.0765640i	−0.0133281	+	0.0230849i	−0.872613	−	0.488413i	$-0.837576\pi$
$11$	−0.0442043	+	0.0765640i	−0.0133281	+	0.0230849i	0.859284	+	0.511498i	$0.170909\pi$
$12$	−1.84922	−	3.20294i	−0.533823	−	0.924609i
$13$	−2.83822			−0.787181			−0.393590	−	0.919286i	$-0.628767\pi$
$13$	−2.83822			−0.787181			−0.393590	+	0.919286i	$0.628767\pi$
$14$	0.605486	−	1.29562i	0.161823	−	0.346269i
$15$	2.16559			0.559152
$16$	−1.16615	−	2.01983i	−0.291537	−	0.504957i
$17$	3.34157	−	5.78778i	0.810451	−	1.40374i	−0.102098	−	0.994774i	$-0.532556\pi$
$17$	3.34157	−	5.78778i	0.810451	−	1.40374i	0.912549	−	0.408968i	$-0.134111\pi$
$18$	0.456689	−	0.791009i	0.107643	−	0.186443i
$19$	2.11602	+	3.66505i	0.485448	+	0.840821i	0.999860	−	0.0167222i	$-0.00532308\pi$
$19$	2.11602	+	3.66505i	0.485448	+	0.840821i	−0.514412	+	0.857543i	$0.671990\pi$
$20$	1.70782			0.381881
$21$	−5.70822	+	0.494566i	−1.24564	+	0.107923i
$22$	−0.0477879			−0.0101884
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	2.17014	−	3.75880i	0.442979	−	0.767262i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.767079	−	1.32862i	−0.150437	−	0.260564i
$27$	2.83742			0.546063
$28$	−4.50161	+	0.390024i	−0.850724	+	0.0737076i
$29$	−4.39559			−0.816241			−0.408120	−	0.912928i	$-0.633816\pi$
$29$	−4.39559			−0.816241			−0.408120	+	0.912928i	$0.633816\pi$
$30$	0.585288	+	1.01375i	0.106858	+	0.185084i
$31$	−0.375761	+	0.650838i	−0.0674887	+	0.116894i	−0.897795	−	0.440413i	$-0.854832\pi$
$31$	−0.375761	+	0.650838i	−0.0674887	+	0.116894i	0.830307	+	0.557307i	$0.188165\pi$
$32$	2.63455	−	4.56318i	0.465728	−	0.806664i
$33$	0.0957282	+	0.165806i	0.0166641	+	0.0288631i
$34$	3.61248			0.619535
$35$	1.12016	−	2.39692i	0.189342	−	0.405154i
$36$	−2.88582			−0.480970
$37$	1.43093	+	2.47844i	0.235243	+	0.407453i	0.959343	−	0.282242i	$-0.0910780\pi$
$37$	1.43093	+	2.47844i	0.235243	+	0.407453i	−0.724100	+	0.689695i	$0.757745\pi$
$38$	−1.14378	+	1.98109i	−0.185546	+	0.321375i
$39$	−3.07321	+	5.32295i	−0.492107	+	0.852354i
$40$	1.00210	+	1.73570i	0.158447	+	0.274437i
$41$	−1.21574			−0.189867			−0.0949337	−	0.995484i	$-0.530264\pi$
$41$	−1.21574			−0.189867			−0.0949337	+	0.995484i	$0.530264\pi$
$42$	−1.77426	−	2.53845i	−0.273774	−	0.391691i
$43$	2.09390			0.319316			0.159658	−	0.987172i	$-0.448961\pi$
$43$	2.09390			0.319316			0.159658	+	0.987172i	$0.448961\pi$
$44$	0.0754930	+	0.130758i	0.0113810	+	0.0197125i
$45$	0.844883	−	1.46338i	0.125948	−	0.218148i
$46$	0.270268	−	0.468117i	0.0398488	−	0.0690201i
$47$	1.06536	+	1.84526i	0.155399	+	0.269159i	0.933204	−	0.359346i	$-0.117000\pi$
$47$	1.06536	+	1.84526i	0.155399	+	0.269159i	−0.777805	+	0.628505i	$0.783667\pi$
$48$	−5.05080			−0.729020
$49$	−2.40521	+	6.57381i	−0.343601	+	0.939116i
$50$	−0.540535			−0.0764432
$51$	−7.23647	−	12.5339i	−1.01331	−	1.75510i
$52$	−2.42359	+	4.19778i	−0.336091	+	0.582127i
$53$	−5.03019	+	8.71255i	−0.690950	+	1.19676i	0.280577	+	0.959832i	$0.409474\pi$
$53$	−5.03019	+	8.71255i	−0.690950	+	1.19676i	−0.971527	+	0.236929i	$0.923859\pi$
$54$	0.766864	+	1.32825i	0.104357	+	0.180752i
$55$	−0.0884085			−0.0119210
$56$	−3.03781	−	4.34622i	−0.405945	−	0.580788i
$57$	9.16485			1.21391
$58$	−1.18799	−	2.05765i	−0.155990	−	0.270183i
$59$	3.94617	−	6.83497i	0.513748	−	0.889838i	−0.486125	−	0.873889i	$-0.661590\pi$
$59$	3.94617	−	6.83497i	0.513748	−	0.889838i	0.999873	−	0.0159484i	$-0.00507676\pi$
$60$	1.84922	−	3.20294i	0.238733	−	0.413498i
$61$	2.88925	+	5.00432i	0.369930	+	0.640738i	0.989554	−	0.144161i	$-0.0460483\pi$
$61$	2.88925	+	5.00432i	0.369930	+	0.640738i	−0.619624	+	0.784899i	$0.712715\pi$
$62$	−0.406225			−0.0515906
$63$	−1.89281	+	4.05024i	−0.238471	+	0.510282i
$64$	−1.81646			−0.227058
$65$	−1.41911	−	2.45797i	−0.176019	−	0.304874i
$66$	−0.0517444	+	0.0896240i	−0.00636930	+	0.0110320i
$67$	3.06733	−	5.31277i	0.374734	−	0.649058i	−0.615553	−	0.788095i	$-0.711067\pi$
$67$	3.06733	−	5.31277i	0.374734	−	0.649058i	0.990287	+	0.139037i	$0.0444007\pi$
$68$	−5.70681	−	9.88449i	−0.692053	−	1.19867i
$69$	−2.16559			−0.260706
$70$	1.42478	−	0.123445i	0.170294	−	0.0147545i
$71$	−12.7014			−1.50738			−0.753692	−	0.657228i	$-0.771729\pi$
$71$	−12.7014			−1.50738			−0.753692	+	0.657228i	$0.771729\pi$
$72$	−1.69332	−	2.93292i	−0.199560	−	0.345648i
$73$	3.93552	−	6.81651i	0.460617	−	0.797813i	−0.538374	−	0.842706i	$-0.680961\pi$
$73$	3.93552	−	6.81651i	0.460617	−	0.797813i	0.998992	+	0.0448930i	$0.0142947\pi$
$74$	−0.773467	+	1.33968i	−0.0899137	+	0.155735i
$75$	1.08279	+	1.87545i	0.125030	+	0.216559i
$76$	7.22757			0.829059
$77$	0.233034	−	0.0201903i	0.0265567	−	0.00230090i
$78$	−3.32235			−0.376182
$79$	8.05814	+	13.9571i	0.906612	+	1.57030i	0.818739	+	0.574166i	$0.194674\pi$
$79$	8.05814	+	13.9571i	0.906612	+	1.57030i	0.0878731	+	0.996132i	$0.471993\pi$
$80$	1.16615	−	2.01983i	0.130379	−	0.225824i
$81$	5.60699	−	9.71160i	0.622999	−	1.07907i
$82$	−0.328576	−	0.569111i	−0.0362852	−	0.0628478i
$83$	7.61763			0.836143			0.418072	−	0.908414i	$-0.362706\pi$
$83$	7.61763			0.836143			0.418072	+	0.908414i	$0.362706\pi$
$84$	−4.14284	+	8.86487i	−0.452021	+	0.967237i
$85$	6.68315			0.724889
$86$	0.565912	+	0.980189i	0.0610239	+	0.105697i
$87$	−4.75952	+	8.24372i	−0.510274	+	0.883820i
$88$	−0.0885945	+	0.153450i	−0.00944421	+	0.0163578i
$89$	1.60243	+	2.77550i	0.169858	+	0.294202i	0.938370	−	0.345633i	$-0.112336\pi$
$89$	1.60243	+	2.77550i	0.169858	+	0.294202i	−0.768512	+	0.639835i	$0.779003\pi$
$90$	0.913378			0.0962785
$91$	4.30194	+	6.15482i	0.450966	+	0.645200i
$92$	−1.70782			−0.178053
$93$	0.813744	+	1.40945i	0.0843813	+	0.146153i
$94$	−0.575866	+	0.997429i	−0.0593960	+	0.102877i
$95$	−2.11602	+	3.66505i	−0.217099	+	0.376027i
$96$	−5.70535	−	9.88196i	−0.582300	−	1.00857i
$97$	−7.75152			−0.787048			−0.393524	−	0.919314i	$-0.628744\pi$
$97$	−7.75152			−0.787048			−0.393524	+	0.919314i	$0.628744\pi$
$98$	−3.72736	+	0.650770i	−0.376520	+	0.0657377i
$99$	0.149390			0.0150142
$100$	0.853911	+	1.47902i	0.0853911	+	0.147902i
$101$	5.37080	−	9.30250i	0.534415	−	0.925634i	−0.464777	−	0.885428i	$-0.653865\pi$
$101$	5.37080	−	9.30250i	0.534415	−	0.925634i	0.999191	−	0.0402056i	$-0.0128013\pi$
$102$	3.91157	−	6.77503i	0.387303	−	0.670828i
$103$	4.62660	+	8.01351i	0.455873	+	0.789595i	0.998738	−	0.0502249i	$-0.0159938\pi$
$103$	4.62660	+	8.01351i	0.455873	+	0.789595i	−0.542865	+	0.839820i	$0.682660\pi$
$104$	−5.68838			−0.557792
$105$	−3.28242	−	4.69618i	−0.320331	−	0.458300i
$106$	−5.43799			−0.528184
$107$	9.26456	+	16.0467i	0.895639	+	1.55129i	0.833012	+	0.553255i	$0.186615\pi$
$107$	9.26456	+	16.0467i	0.895639	+	1.55129i	0.0626272	+	0.998037i	$0.480052\pi$
$108$	2.42291	−	4.19660i	0.233144	−	0.403818i
$109$	4.52859	−	7.84374i	0.433760	−	0.751294i	−0.563434	−	0.826161i	$-0.690520\pi$
$109$	4.52859	−	7.84374i	0.433760	−	0.751294i	0.997194	+	0.0748672i	$0.0238533\pi$
$110$	−0.0238940	−	0.0413855i	−0.00227820	−	0.00394596i
$111$	6.19760			0.588250
$112$	−2.61255	+	5.59034i	−0.246862	+	0.528238i
$113$	0.583819			0.0549211			0.0274605	−	0.999623i	$-0.491258\pi$
$113$	0.583819			0.0549211			0.0274605	+	0.999623i	$0.491258\pi$
$114$	2.47696	+	4.29022i	0.231989	+	0.401816i
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	−3.75344	+	6.50115i	−0.348498	+	0.603617i
$117$	2.39796	+	4.15340i	0.221692	+	0.383982i
$118$	4.26609			0.392726
$119$	−17.6160	+	1.52626i	−1.61485	+	0.139912i
$120$	4.34029			0.396212
$121$	5.49609	+	9.51951i	0.499645	+	0.865410i
$122$	−1.56174	+	2.70501i	−0.141393	+	0.244900i
$123$	−1.31640	+	2.28007i	−0.118696	+	0.205587i
$124$	0.641734	+	1.11152i	0.0576294	+	0.0998170i
$125$	−1.00000			−0.0894427
$126$	−2.40755	+	0.208593i	−0.214482	+	0.0185829i
$127$	13.2900			1.17930			0.589650	−	0.807659i	$-0.299266\pi$
$127$	13.2900			1.17930			0.589650	+	0.807659i	$0.299266\pi$
$128$	−5.76004	−	9.97667i	−0.509120	−	0.881822i
$129$	2.26726	−	3.92701i	0.199621	−	0.345754i
$130$	0.767079	−	1.32862i	0.0672773	−	0.116528i
$131$	3.25555	+	5.63878i	0.284439	+	0.492663i	0.972473	−	0.233016i	$-0.0748593\pi$
$131$	3.25555	+	5.63878i	0.284439	+	0.492663i	−0.688034	+	0.725679i	$0.741526\pi$
$132$	0.326973			0.0284594
$133$	4.74056	−	10.1439i	0.411059	−	0.879586i
$134$	3.31600			0.286459
$135$	1.41871	+	2.45728i	0.122103	+	0.211489i
$136$	6.69721	−	11.5999i	0.574281	−	0.994684i
$137$	3.34185	−	5.78825i	0.285513	−	0.494524i	−0.687220	−	0.726449i	$-0.741169\pi$
$137$	3.34185	−	5.78825i	0.285513	−	0.494524i	0.972734	+	0.231925i	$0.0745025\pi$
$138$	−0.585288	−	1.01375i	−0.0498230	−	0.0862960i
$139$	1.38709			0.117652			0.0588258	−	0.998268i	$-0.481264\pi$
$139$	1.38709			0.117652			0.0588258	+	0.998268i	$0.481264\pi$
$140$	−2.58857	−	3.70349i	−0.218774	−	0.313002i
$141$	4.61427			0.388591
$142$	−3.43279	−	5.94576i	−0.288073	−	0.498957i
$143$	0.125461	−	0.217306i	0.0104916	−	0.0181720i
$144$	−1.97052	+	3.41304i	−0.164210	+	0.284420i
$145$	−2.19780	−	3.80669i	−0.182517	−	0.316129i
$146$	4.25457			0.352111
$147$	9.72453	+	11.6289i	0.802066	+	0.959138i
$148$	4.88754			0.401754
$149$	−3.49733	−	6.05756i	−0.286513	−	0.496255i	0.686462	−	0.727166i	$-0.259163\pi$
$149$	−3.49733	−	6.05756i	−0.286513	−	0.496255i	−0.972975	+	0.230911i	$0.925829\pi$
$150$	−0.585288	+	1.01375i	−0.0477886	+	0.0827722i
$151$	−9.03754	+	15.6535i	−0.735464	+	1.27386i	0.219055	+	0.975712i	$0.429703\pi$
$151$	−9.03754	+	15.6535i	−0.735464	+	1.27386i	−0.954519	+	0.298149i	$0.903631\pi$
$152$	4.24094	+	7.34553i	0.343986	+	0.595801i
$153$	−11.2930			−0.912982
$154$	0.0724329	+	0.103630i	0.00583681	+	0.00835078i
$155$	−0.751523			−0.0603638
$156$	5.24849	+	9.09065i	0.420215	+	0.727834i
$157$	11.7856	−	20.4133i	0.940597	−	1.62916i	0.176261	−	0.984344i	$-0.443600\pi$
$157$	11.7856	−	20.4133i	0.940597	−	1.62916i	0.764336	−	0.644818i	$-0.223067\pi$
$158$	−4.35571	+	7.54431i	−0.346522	+	0.600193i
$159$	10.8933	+	18.8678i	0.863896	+	1.49631i
$160$	5.26911			0.416559
$161$	−1.12016	+	2.39692i	−0.0882809	+	0.188904i
$162$	6.06155			0.476241
$163$	−2.43250	−	4.21322i	−0.190528	−	0.330005i	0.754897	−	0.655843i	$-0.227687\pi$
$163$	−2.43250	−	4.21322i	−0.190528	−	0.330005i	−0.945425	+	0.325839i	$0.894353\pi$
$164$	−1.03814	+	1.79811i	−0.0810649	+	0.140409i
$165$	−0.0957282	+	0.165806i	−0.00745243	+	0.0129080i
$166$	2.05880	+	3.56594i	0.159794	+	0.276771i
$167$	−3.20214			−0.247789			−0.123895	−	0.992295i	$-0.539538\pi$
$167$	−3.20214			−0.247789			−0.123895	+	0.992295i	$0.539538\pi$
$168$	−11.4405	+	0.991213i	−0.882651	+	0.0764737i
$169$	−4.94451			−0.380347
$170$	1.80624	+	3.12850i	0.138532	+	0.239945i
$171$	3.57558	−	6.19309i	0.273431	−	0.473597i
$172$	1.78800	−	3.09691i	0.136334	−	0.236137i
$173$	7.84170	+	13.5822i	0.596194	+	1.03264i	0.993377	+	0.114898i	$0.0366543\pi$
$173$	7.84170	+	13.5822i	0.596194	+	1.03264i	−0.397184	+	0.917739i	$0.630012\pi$
$174$	−5.14537			−0.390070
$175$	2.63588	−	0.228375i	0.199254	−	0.0172635i
$176$	0.206195			0.0155425
$177$	−8.54578	−	14.8017i	−0.642340	−	1.11257i
$178$	−0.866172	+	1.50025i	−0.0649223	+	0.112449i
$179$	−12.6042	+	21.8312i	−0.942085	+	1.63174i	−0.180600	+	0.983557i	$0.557804\pi$
$179$	−12.6042	+	21.8312i	−0.942085	+	1.63174i	−0.761485	+	0.648182i	$0.775529\pi$
$180$	−1.44291	−	2.49919i	−0.107548	−	0.186279i
$181$	12.3607			0.918762			0.459381	−	0.888239i	$-0.348071\pi$
$181$	12.3607			0.918762			0.459381	+	0.888239i	$0.348071\pi$
$182$	−1.71850	+	3.67726i	−0.127384	+	0.272577i
$183$	12.5138			0.925049
$184$	−1.00210	−	1.73570i	−0.0738761	−	0.127957i
$185$	−1.43093	+	2.47844i	−0.105204	+	0.182219i
$186$	−0.439857	+	0.761855i	−0.0322519	+	0.0558619i
$187$	0.295424	+	0.511689i	0.0216035	+	0.0374184i
$188$	3.63890			0.265394
$189$	−4.30073	−	6.15309i	−0.312832	−	0.447572i
$190$	−2.28757			−0.165957
$191$	−3.41827	−	5.92062i	−0.247337	−	0.428401i	0.715449	−	0.698665i	$-0.246222\pi$
$191$	−3.41827	−	5.92062i	−0.247337	−	0.428401i	−0.962786	+	0.270264i	$0.912889\pi$
$192$	−1.96685	+	3.40669i	−0.141945	+	0.245856i
$193$	−12.3813	+	21.4450i	−0.891226	+	1.54365i	−0.0528183	+	0.998604i	$0.516820\pi$
$193$	−12.3813	+	21.4450i	−0.891226	+	1.54365i	−0.838407	+	0.545044i	$0.816513\pi$
$194$	−2.09499	−	3.62862i	−0.150411	−	0.260520i
$195$	−6.14641			−0.440154
$196$	7.66895	+	9.17079i	0.547782	+	0.655056i
$197$	−6.74571			−0.480612			−0.240306	−	0.970697i	$-0.577248\pi$
$197$	−6.74571			−0.480612			−0.240306	+	0.970697i	$0.577248\pi$
$198$	0.0403752	+	0.0699319i	0.00286934	+	0.00496984i
$199$	−0.0579257	+	0.100330i	−0.00410624	+	0.00711222i	−0.868071	−	0.496440i	$-0.834640\pi$
$199$	−0.0579257	+	0.100330i	−0.00410624	+	0.00711222i	0.863965	+	0.503552i	$0.167974\pi$
$200$	−1.00210	+	1.73570i	−0.0708595	+	0.122732i
$201$	−6.64257	−	11.5053i	−0.468531	−	0.811519i
$202$	5.80621			0.408524
$203$	6.66247	+	9.53205i	0.467614	+	0.669019i
$204$	−24.7172			−1.73055
$205$	−0.607872	−	1.05287i	−0.0424556	−	0.0735353i
$206$	−2.50084	+	4.33159i	−0.174242	+	0.301796i
$207$	−0.844883	+	1.46338i	−0.0587234	+	0.101712i
$208$	3.30979	+	5.73272i	0.229493	+	0.397493i
$209$	−0.374148			−0.0258804
$210$	1.31123	−	2.80578i	0.0904836	−	0.193617i
$211$	−21.2800			−1.46498			−0.732489	−	0.680779i	$-0.761642\pi$
$211$	−21.2800			−1.46498			−0.732489	+	0.680779i	$0.761642\pi$
$212$	8.59067	+	14.8795i	0.590010	+	1.02193i
$213$	−13.7530	+	23.8210i	−0.942343	+	1.63219i
$214$	−5.00782	+	8.67380i	−0.342328	+	0.592929i
$215$	1.04695	+	1.81337i	0.0714013	+	0.123671i
$216$	5.68679			0.386937
$217$	1.98092	−	0.171629i	0.134474	−	0.0116509i
$218$	4.89572			0.331580
$219$	−8.52270	−	14.7618i	−0.575911	−	0.997507i
$220$	−0.0754930	+	0.130758i	−0.00508974	+	0.00881568i
$221$	−9.48412	+	16.4270i	−0.637971	+	1.10500i
$222$	1.67501	+	2.90120i	0.112419	+	0.194716i
$223$	−20.4322			−1.36824			−0.684122	−	0.729368i	$-0.739814\pi$
$223$	−20.4322			−1.36824			−0.684122	+	0.729368i	$0.739814\pi$
$224$	−13.8887	+	1.20333i	−0.927979	+	0.0804010i
$225$	1.68977			0.112651
$226$	0.157787	+	0.273296i	0.0104959	+	0.0181794i
$227$	10.1104	−	17.5117i	0.671049	−	1.16229i	−0.306557	−	0.951852i	$-0.599177\pi$
$227$	10.1104	−	17.5117i	0.671049	−	1.16229i	0.977607	−	0.210440i	$-0.0674895\pi$
$228$	7.82597	−	13.5550i	0.518287	−	0.897700i
$229$	−2.84159	−	4.92178i	−0.187778	−	0.325241i	0.756731	−	0.653726i	$-0.226795\pi$
$229$	−2.84159	−	4.92178i	−0.187778	−	0.325241i	−0.944509	+	0.328486i	$0.893462\pi$
$230$	0.540535			0.0356418
$231$	0.214462	−	0.458906i	0.0141105	−	0.0301938i
$232$	−8.80968			−0.578384
$233$	−0.130047	−	0.225248i	−0.00851968	−	0.0147565i	0.861734	−	0.507360i	$-0.169379\pi$
$233$	−0.130047	−	0.225248i	−0.00851968	−	0.0147565i	−0.870254	+	0.492604i	$0.836045\pi$
$234$	−1.29618	+	2.24506i	−0.0847342	+	0.146764i
$235$	−1.06536	+	1.84526i	−0.0694966	+	0.120372i
$236$	−6.73936	−	11.6729i	−0.438695	−	0.759842i
$237$	34.9012			2.26708
$238$	−5.47549	−	7.83383i	−0.354923	−	0.507792i
$239$	−7.61827			−0.492785			−0.246392	−	0.969170i	$-0.579245\pi$
$239$	−7.61827			−0.492785			−0.246392	+	0.969170i	$0.579245\pi$
$240$	−2.52540	−	4.37412i	−0.163014	−	0.282348i
$241$	−1.04082	+	1.80275i	−0.0670450	+	0.116125i	−0.897599	−	0.440812i	$-0.854690\pi$
$241$	−1.04082	+	1.80275i	−0.0670450	+	0.116125i	0.830554	+	0.556938i	$0.188024\pi$
$242$	−2.97083	+	5.14563i	−0.190972	+	0.330774i
$243$	−7.88630	−	13.6595i	−0.505906	−	0.876255i
$244$	9.86864			0.631775
$245$	−6.89569	+	1.20394i	−0.440549	+	0.0769167i
$246$	−1.42312			−0.0907349
$247$	−6.00573	−	10.4022i	−0.382135	−	0.661878i
$248$	−0.753104	+	1.30441i	−0.0478222	+	0.0828304i
$249$	8.24832	−	14.2865i	0.522716	−	0.905370i
$250$	−0.270268	−	0.468117i	−0.0170932	−	0.0296063i
$251$	12.0728			0.762026			0.381013	−	0.924570i	$-0.375575\pi$
$251$	12.0728			0.762026			0.381013	+	0.924570i	$0.375575\pi$
$252$	4.37409	+	6.25804i	0.275542	+	0.394220i
$253$	0.0884085			0.00555820
$254$	3.59187	+	6.22129i	0.225374	+	0.390359i
$255$	7.23647	−	12.5339i	0.453165	−	0.784905i
$256$	1.29704	−	2.24654i	0.0810651	−	0.140409i
$257$	−2.88187	−	4.99155i	−0.179766	−	0.311364i	0.762034	−	0.647537i	$-0.224201\pi$
$257$	−2.88187	−	4.99155i	−0.179766	−	0.311364i	−0.941800	+	0.336173i	$0.890867\pi$
$258$	2.45107			0.152597
$259$	3.20574	−	6.85965i	0.199195	−	0.426238i
$260$	−4.84717			−0.300609
$261$	3.71376	+	6.43242i	0.229876	+	0.398157i
$262$	−1.75974	+	3.04796i	−0.108717	+	0.188304i
$263$	−9.90546	+	17.1568i	−0.610797	+	1.05793i	0.380310	+	0.924859i	$0.375817\pi$
$263$	−9.90546	+	17.1568i	−0.610797	+	1.05793i	−0.991106	+	0.133072i	$0.957516\pi$
$264$	0.191859	+	0.332310i	0.0118081	+	0.0204523i
$265$	−10.0604			−0.618004
$266$	6.02974	−	0.522423i	0.369707	−	0.0320318i
$267$	6.94042			0.424747
$268$	−5.23845	−	9.07326i	−0.319989	−	0.554238i
$269$	−1.48830	+	2.57781i	−0.0907434	+	0.157172i	−0.907824	−	0.419351i	$-0.862258\pi$
$269$	−1.48830	+	2.57781i	−0.0907434	+	0.157172i	0.817081	+	0.576523i	$0.195591\pi$
$270$	−0.766864	+	1.32825i	−0.0466698	+	0.0808345i
$271$	6.91186	+	11.9717i	0.419866	+	0.727229i	0.995926	−	0.0901786i	$-0.0287438\pi$
$271$	6.91186	+	11.9717i	0.419866	+	0.727229i	−0.576060	+	0.817408i	$0.695410\pi$
$272$	−15.5871			−0.945107
$273$	16.2012	−	1.40369i	0.980540	−	0.0849550i
$274$	3.61277			0.218256
$275$	−0.0442043	−	0.0765640i	−0.00266562	−	0.00461698i
$276$	−1.84922	+	3.20294i	−0.111310	+	0.192794i
$277$	1.96046	−	3.39561i	0.117792	−	0.204022i	−0.801100	−	0.598530i	$-0.795752\pi$
$277$	1.96046	−	3.39561i	0.117792	−	0.204022i	0.918893	+	0.394508i	$0.129085\pi$
$278$	0.374886	+	0.649321i	0.0224842	+	0.0389437i
$279$	1.26990			0.0760268
$280$	2.24503	−	4.80393i	0.134166	−	0.287090i
$281$	−33.2562			−1.98390			−0.991950	−	0.126628i	$-0.959584\pi$
$281$	−33.2562			−1.98390			−0.991950	+	0.126628i	$0.959584\pi$
$282$	1.24709	+	2.16002i	0.0742630	+	0.128627i
$283$	−14.5891	+	25.2690i	−0.867231	+	1.50209i	−0.00241723	+	0.999997i	$0.500769\pi$
$283$	−14.5891	+	25.2690i	−0.867231	+	1.50209i	−0.864814	+	0.502092i	$0.832564\pi$
$284$	−10.8459	+	18.7856i	−0.643586	+	1.11472i
$285$	4.58242	+	7.93699i	0.271439	+	0.470147i
$286$	0.135633			0.00802013
$287$	1.84272	+	2.63640i	0.108773	+	0.155622i
$288$	−8.90356			−0.524647
$289$	−13.8322	−	23.9581i	−0.813661	−	1.40930i
$290$	1.18799	−	2.05765i	0.0697609	−	0.120829i
$291$	−8.39330	+	14.5376i	−0.492024	+	0.852210i
$292$	−6.72116	−	11.6414i	−0.393326	−	0.681261i
$293$	9.30440			0.543569			0.271784	−	0.962358i	$-0.412386\pi$
$293$	9.30440			0.543569			0.271784	+	0.962358i	$0.412386\pi$
$294$	−2.81547	+	7.69514i	−0.164202	+	0.448790i
$295$	7.89235			0.459510
$296$	2.86788	+	4.96731i	0.166692	+	0.288719i
$297$	−0.125426	+	0.217245i	−0.00727797	+	0.0126058i
$298$	1.89043	−	3.27432i	0.109510	−	0.189677i
$299$	1.41911	+	2.45797i	0.0820693	+	0.142148i
$300$	3.69844			0.213529
$301$	−3.17375	−	4.54072i	−0.182932	−	0.261723i
$302$	−9.77021			−0.562212
$303$	−11.6309	−	20.1454i	−0.668180	−	1.15732i
$304$	4.93519	−	8.54800i	0.283053	−	0.490261i
$305$	−2.88925	+	5.00432i	−0.165438	+	0.286547i
$306$	−3.05212	−	5.28643i	−0.174478	−	0.302205i
$307$	31.3806			1.79099			0.895493	−	0.445076i	$-0.146823\pi$
$307$	31.3806			1.79099			0.895493	+	0.445076i	$0.146823\pi$
$308$	0.169128	−	0.361902i	0.00963699	−	0.0206213i
$309$	20.0386			1.13996
$310$	−0.203112	−	0.351801i	−0.0115360	−	0.0199809i
$311$	−11.0042	+	19.0598i	−0.623991	+	1.08078i	0.364744	+	0.931108i	$0.381157\pi$
$311$	−11.0042	+	19.0598i	−0.623991	+	1.08078i	−0.988735	+	0.149677i	$0.952177\pi$
$312$	−6.15934	+	10.6683i	−0.348704	+	0.603973i
$313$	0.494834	+	0.857078i	0.0279697	+	0.0484449i	0.879671	−	0.475582i	$-0.157762\pi$
$313$	0.494834	+	0.857078i	0.0279697	+	0.0484449i	−0.851702	+	0.524027i	$0.824429\pi$
$314$	12.7411			0.719022
$315$	−4.45402	+	0.385900i	−0.250955	+	0.0217430i
$316$	27.5237			1.54833
$317$	−14.0229	−	24.2884i	−0.787607	−	1.36417i	−0.927429	−	0.373998i	$-0.877987\pi$
$317$	−14.0229	−	24.2884i	−0.787607	−	1.36417i	0.139823	−	0.990177i	$-0.455347\pi$
$318$	−5.88822	+	10.1987i	−0.330195	+	0.571915i
$319$	0.194304	−	0.336544i	0.0108789	−	0.0188429i
$320$	−0.908230	−	1.57310i	−0.0507716	−	0.0879390i
$321$	40.1264			2.23964
$322$	−1.42478	+	0.123445i	−0.0794001	+	0.00687931i
$323$	28.2833			1.57373
$324$	−9.57575	−	16.5857i	−0.531986	−	0.921427i
$325$	1.41911	−	2.45797i	0.0787181	−	0.136344i
$326$	1.31485	−	2.27739i	0.0728229	−	0.126133i
$327$	−9.80705	−	16.9863i	−0.542331	−	0.939345i
$328$	−2.43660			−0.134539
$329$	2.38675	−	5.10718i	0.131586	−	0.281568i
$330$	−0.103489			−0.00569688
$331$	−1.78340	−	3.08894i	−0.0980244	−	0.169783i	0.812842	−	0.582484i	$-0.197919\pi$
$331$	−1.78340	−	3.08894i	−0.0980244	−	0.169783i	−0.910867	+	0.412700i	$0.864586\pi$
$332$	6.50477	−	11.2666i	0.356996	−	0.618335i
$333$	2.41794	−	4.18799i	0.132502	−	0.229500i
$334$	−0.865435	−	1.49898i	−0.0473545	−	0.0820204i
$335$	6.13466			0.335172
$336$	7.65558	+	10.9529i	0.417646	+	0.597529i
$337$	30.5724			1.66538			0.832691	−	0.553738i	$-0.186799\pi$
$337$	30.5724			1.66538			0.832691	+	0.553738i	$0.186799\pi$
$338$	−1.33634	−	2.31461i	−0.0726873	−	0.125898i
$339$	0.632156	−	1.09493i	0.0343340	−	0.0594682i
$340$	5.70681	−	9.88449i	0.309495	−	0.536062i
$341$	−0.0332205	−	0.0575396i	−0.00179899	−	0.00311595i
$342$	3.86545			0.209020
$343$	17.9012	−	4.74823i	0.966576	−	0.256380i
$344$	4.19661			0.226266
$345$	−1.08279	−	1.87545i	−0.0582956	−	0.100971i
$346$	−4.23872	+	7.34167i	−0.227875	+	0.394691i
$347$	11.1712	−	19.3491i	0.599703	−	1.03872i	−0.393162	−	0.919469i	$-0.628619\pi$
$347$	11.1712	−	19.3491i	0.599703	−	1.03872i	0.992865	−	0.119246i	$-0.0380478\pi$
$348$	8.12841	+	14.0788i	0.435728	+	0.754704i
$349$	−33.3032			−1.78268			−0.891341	−	0.453334i	$-0.850235\pi$
$349$	−33.3032			−1.78268			−0.891341	+	0.453334i	$0.850235\pi$
$350$	0.819298	+	1.17218i	0.0437933	+	0.0626555i
$351$	−8.05324			−0.429850
$352$	0.232917	+	0.403424i	0.0124145	+	0.0215026i
$353$	10.9645	−	18.9910i	0.583580	−	1.01079i	−0.411471	−	0.911423i	$-0.634985\pi$
$353$	10.9645	−	18.9910i	0.583580	−	1.01079i	0.995051	−	0.0993670i	$-0.0316818\pi$
$354$	4.61930	−	8.00086i	0.245513	−	0.425241i
$355$	−6.35072	−	10.9998i	−0.337061	−	0.583807i
$356$	5.47334			0.290087
$357$	−16.2120	+	34.6905i	−0.858030	+	1.83602i
$358$	−13.6261			−0.720160
$359$	0.168262	+	0.291438i	0.00888052	+	0.0153815i	0.870432	−	0.492290i	$-0.163840\pi$
$359$	0.168262	+	0.291438i	0.00888052	+	0.0153815i	−0.861551	+	0.507671i	$0.830507\pi$
$360$	1.69332	−	2.93292i	0.0892459	−	0.154578i
$361$	0.544920	−	0.943828i	0.0286800	−	0.0496752i
$362$	3.34069	+	5.78624i	0.175583	+	0.304118i
$363$	23.8045			1.24941
$364$	12.7766	−	1.10697i	0.669673	−	0.0580212i
$365$	7.87103			0.411989
$366$	3.38208	+	5.85794i	0.176784	+	0.306199i
$367$	0.135882	−	0.235354i	0.00709296	−	0.0122854i	−0.862457	−	0.506130i	$-0.831076\pi$
$367$	0.135882	−	0.235354i	0.00709296	−	0.0122854i	0.869550	+	0.493845i	$0.164409\pi$
$368$	−1.16615	+	2.01983i	−0.0607897	+	0.105291i
$369$	1.02716	+	1.77910i	0.0534719	+	0.0926161i
$370$	−1.54693			−0.0804213
$371$	26.5179	−	2.29754i	1.37674	−	0.119282i
$372$	2.77946			0.144108
$373$	−6.67965	−	11.5695i	−0.345859	−	0.599046i	0.639650	−	0.768666i	$-0.279079\pi$
$373$	−6.67965	−	11.5695i	−0.345859	−	0.599046i	−0.985510	+	0.169620i	$0.945746\pi$
$374$	−0.159687	+	0.276586i	−0.00825721	+	0.0143019i
$375$	−1.08279	+	1.87545i	−0.0559152	+	0.0968480i
$376$	2.13521	+	3.69829i	0.110115	+	0.190725i
$377$	12.4757			0.642529
$378$	1.71802	−	3.67623i	0.0883654	−	0.189085i
$379$	2.45917			0.126319			0.0631597	−	0.998003i	$-0.479882\pi$
$379$	2.45917			0.126319			0.0631597	+	0.998003i	$0.479882\pi$
$380$	3.61378	+	6.25926i	0.185383	+	0.321093i
$381$	14.3904	−	24.9248i	0.737241	−	1.27694i
$382$	1.84770	−	3.20030i	0.0945364	−	0.163742i
$383$	−2.08648	−	3.61389i	−0.106614	−	0.184661i	0.807782	−	0.589481i	$-0.200668\pi$
$383$	−2.08648	−	3.61389i	−0.106614	−	0.184661i	−0.914397	+	0.404820i	$0.867334\pi$
$384$	−24.9477			−1.27311
$385$	0.134002	+	0.191718i	0.00682939	+	0.00977086i
$386$	−13.3851			−0.681282
$387$	−1.76910	−	3.06417i	−0.0899283	−	0.155760i
$388$	−6.61911	+	11.4646i	−0.336034	+	0.582029i
$389$	1.83810	−	3.18368i	0.0931953	−	0.161419i	−0.815659	−	0.578533i	$-0.803625\pi$
$389$	1.83810	−	3.18368i	0.0931953	−	0.161419i	0.908854	+	0.417114i	$0.136959\pi$
$390$	−1.66118	−	2.87724i	−0.0841169	−	0.145695i
$391$	−6.68315			−0.337981
$392$	−4.82053	+	13.1753i	−0.243474	+	0.665452i
$393$	14.1004			0.711270
$394$	−1.82315	−	3.15778i	−0.0918488	−	0.159087i
$395$	−8.05814	+	13.9571i	−0.405449	+	0.702259i
$396$	0.127566	−	0.220950i	0.00641041	−	0.0111032i
$397$	−5.09736	−	8.82889i	−0.255829	−	0.443109i	0.709291	−	0.704916i	$-0.249015\pi$
$397$	−5.09736	−	8.82889i	−0.255829	−	0.443109i	−0.965120	+	0.261806i	$0.915682\pi$
$398$	−0.0626218			−0.00313895
$399$	−13.8913	−	19.8744i	−0.695436	−	0.994966i
$400$	2.33230			0.116615
$401$	8.63880	+	14.9628i	0.431401	+	0.747208i	0.996994	−	0.0774759i	$-0.0246861\pi$
$401$	8.63880	+	14.9628i	0.431401	+	0.747208i	−0.565593	+	0.824684i	$0.691353\pi$
$402$	3.59054	−	6.21900i	0.179080	−	0.310176i
$403$	1.06649	−	1.84722i	0.0531258	−	0.0920166i
$404$	−9.17237	−	15.8870i	−0.456343	−	0.790409i
$405$	11.2140			0.557228
$406$	−2.66147	+	5.69502i	−0.132086	+	0.282639i
$407$	−0.253013			−0.0125414
$408$	−14.5034	−	25.1206i	−0.718025	−	1.24366i
$409$	4.75564	−	8.23702i	0.235152	−	0.407294i	−0.724165	−	0.689627i	$-0.757775\pi$
$409$	4.75564	−	8.23702i	0.235152	−	0.407294i	0.959317	+	0.282332i	$0.0911080\pi$
$410$	0.328576	−	0.569111i	0.0162272	−	0.0281064i
$411$	−7.23707	−	12.5350i	−0.356978	−	0.618304i
$412$	15.8028			0.778550
$413$	−20.8033	+	1.80242i	−1.02366	+	0.0886911i
$414$	−0.913378			−0.0448901
$415$	3.80881	+	6.59706i	0.186967	+	0.323837i
$416$	−7.47744	+	12.9513i	−0.366612	+	0.634990i
$417$	1.50193	−	2.60142i	0.0735500	−	0.127392i
$418$	−0.101120	−	0.175145i	−0.00494595	−	0.00856664i
$419$	−31.4619			−1.53701			−0.768506	−	0.639842i	$-0.779000\pi$
$419$	−31.4619			−1.53701			−0.768506	+	0.639842i	$0.779000\pi$
$420$	−9.74862	+	0.844631i	−0.475684	+	0.0412137i
$421$	0.683985			0.0333354			0.0166677	−	0.999861i	$-0.494694\pi$
$421$	0.683985			0.0333354			0.0166677	+	0.999861i	$0.494694\pi$
$422$	−5.75131	−	9.96155i	−0.279969	−	0.484921i
$423$	1.80021	−	3.11806i	0.0875294	−	0.151605i
$424$	−10.0815	+	17.4618i	−0.489603	+	0.848018i
$425$	3.34157	+	5.78778i	0.162090	+	0.280748i
$426$	−14.8680			−0.720357
$427$	6.47284	−	13.8506i	0.313243	−	0.670278i
$428$	31.6444			1.52959
$429$	−0.271698	−	0.470594i	−0.0131177	−	0.0227205i
$430$	−0.565912	+	0.980189i	−0.0272907	+	0.0472689i
$431$	13.5020	−	23.3862i	0.650370	−	1.12647i	−0.332663	−	0.943046i	$-0.607947\pi$
$431$	13.5020	−	23.3862i	0.650370	−	1.12647i	0.983033	−	0.183429i	$-0.0587196\pi$
$432$	−3.30886	−	5.73111i	−0.159198	−	0.275738i
$433$	15.5525			0.747403			0.373702	−	0.927549i	$-0.378088\pi$
$433$	15.5525			0.747403			0.373702	+	0.927549i	$0.378088\pi$
$434$	0.615721	+	0.880918i	0.0295556	+	0.0422854i
$435$	−9.51903			−0.456403
$436$	−7.73402	−	13.3957i	−0.370392	−	0.641538i
$437$	2.11602	−	3.66505i	0.101223	−	0.175323i
$438$	4.60682	−	7.97925i	0.220122	−	0.381263i
$439$	10.0216	+	17.3579i	0.478304	+	0.828447i	0.999691	−	0.0248733i	$-0.00791824\pi$
$439$	10.0216	+	17.3579i	0.478304	+	0.828447i	−0.521386	+	0.853321i	$0.674585\pi$
$440$	−0.177189			−0.00844716
$441$	11.6521	−	2.03437i	0.554862	−	0.0968749i
$442$	−10.2530			−0.487686
$443$	−14.6667	−	25.4035i	−0.696836	−	1.20695i	−0.969558	−	0.244862i	$-0.921257\pi$
$443$	−14.6667	−	25.4035i	−0.696836	−	1.20695i	0.272722	−	0.962093i	$-0.412076\pi$
$444$	5.29220	−	9.16636i	0.251157	−	0.435016i
$445$	−1.60243	+	2.77550i	−0.0759626	+	0.131571i
$446$	−5.52217	−	9.56468i	−0.261482	−	0.452901i
$447$	−15.1476			−0.716455
$448$	2.75324	+	3.93908i	0.130078	+	0.186104i
$449$	−14.0859			−0.664756			−0.332378	−	0.943146i	$-0.607851\pi$
$449$	−14.0859			−0.664756			−0.332378	+	0.943146i	$0.607851\pi$
$450$	0.456689	+	0.791009i	0.0215285	+	0.0372885i
$451$	0.0537411	−	0.0930823i	0.00253057	−	0.00438307i
$452$	0.498529	−	0.863478i	0.0234489	−	0.0406146i
$453$	19.5716	+	33.8990i	0.919553	+	1.59271i
$454$	10.9300			0.512972
$455$	−3.17926	+	6.80300i	−0.149046	+	0.318929i
$456$	18.3683			0.860173
$457$	−11.7259	−	20.3099i	−0.548516	−	0.950057i	−0.998377	−	0.0569582i	$-0.981860\pi$
$457$	−11.7259	−	20.3099i	−0.548516	−	0.950057i	0.449861	−	0.893099i	$-0.351474\pi$
$458$	1.53598	−	2.66040i	0.0717717	−	0.124312i
$459$	9.48146	−	16.4224i	0.442557	−	0.766531i
$460$	−0.853911	−	1.47902i	−0.0398138	−	0.0689595i
$461$	−0.570818			−0.0265857			−0.0132928	−	0.999912i	$-0.504231\pi$
$461$	−0.570818			−0.0265857			−0.0132928	+	0.999912i	$0.504231\pi$
$462$	0.272784	−	0.0236343i	0.0126911	−	0.00109957i
$463$	−9.39444			−0.436597			−0.218298	−	0.975882i	$-0.570051\pi$
$463$	−9.39444			−0.436597			−0.218298	+	0.975882i	$0.570051\pi$
$464$	5.12591	+	8.87835i	0.237965	+	0.412167i
$465$	−0.813744	+	1.40945i	−0.0377365	+	0.0653615i
$466$	0.0702951	−	0.121755i	0.00325636	−	0.00564018i
$467$	−17.6071	−	30.4964i	−0.814759	−	1.41120i	−0.909501	−	0.415702i	$-0.863536\pi$
$467$	−17.6071	−	30.4964i	−0.814759	−	1.41120i	0.0947416	−	0.995502i	$-0.469798\pi$
$468$	8.19059			0.378610
$469$	−16.1702	+	1.40100i	−0.746670	+	0.0646923i
$470$	−1.15173			−0.0531254
$471$	−25.5228	−	44.2069i	−1.17603	−	2.03694i
$472$	7.90895	−	13.6987i	0.364039	−	0.630534i
$473$	−0.0925592	+	0.160317i	−0.00425588	+	0.00737139i
$474$	9.43267	+	16.3379i	0.433257	+	0.750423i
$475$	−4.23204			−0.194179
$476$	−12.7851	+	27.3576i	−0.586003	+	1.25393i
$477$	16.9997			0.778363
$478$	−2.05897	−	3.56624i	−0.0941751	−	0.163116i
$479$	−7.58049	+	13.1298i	−0.346361	+	0.599916i	−0.985600	−	0.169093i	$-0.945916\pi$
$479$	−7.58049	+	13.1298i	−0.346361	+	0.599916i	0.639239	+	0.769008i	$0.279250\pi$
$480$	5.70535	−	9.88196i	0.260413	−	0.451048i
$481$	−4.06129	−	7.03436i	−0.185179	−	0.320739i
$482$	−1.12520			−0.0512513
$483$	3.28242	+	4.69618i	0.149355	+	0.213684i
$484$	18.7727			0.853304
$485$	−3.87576	−	6.71302i	−0.175989	−	0.304822i
$486$	4.26282	−	7.38342i	0.193365	−	0.334919i
$487$	3.20404	−	5.54956i	0.145189	−	0.251475i	−0.784254	−	0.620439i	$-0.786954\pi$
$487$	3.20404	−	5.54956i	0.145189	−	0.251475i	0.929443	+	0.368965i	$0.120288\pi$
$488$	5.79065	+	10.0297i	0.262131	+	0.454023i
$489$	−10.5356			−0.476436
$490$	−2.42726	−	2.90261i	−0.109653	−	0.131126i
$491$	−18.7609			−0.846668			−0.423334	−	0.905974i	$-0.639140\pi$
$491$	−18.7609			−0.846668			−0.423334	+	0.905974i	$0.639140\pi$
$492$	2.24818	+	3.89396i	0.101356	+	0.175553i
$493$	−14.6882	+	25.4407i	−0.661523	+	1.14579i
$494$	3.24631	−	5.62277i	0.146058	−	0.252980i
$495$	0.0746949	+	0.129375i	0.00335729	+	0.00581499i
$496$	1.75278			0.0787020
$497$	19.2518	+	27.5437i	0.863561	+	1.23550i
$498$	8.91701			0.399581
$499$	16.9753	+	29.4020i	0.759918	+	1.31622i	0.942892	+	0.333098i	$0.108094\pi$
$499$	16.9753	+	29.4020i	0.759918	+	1.31622i	−0.182975	+	0.983118i	$0.558573\pi$
$500$	−0.853911	+	1.47902i	−0.0381881	+	0.0661437i
$501$	−3.46726	+	6.00547i	−0.154906	+	0.268305i
$502$	3.26288	+	5.65147i	0.145629	+	0.252237i
$503$	0.487293			0.0217273			0.0108637	−	0.999941i	$-0.496542\pi$
$503$	0.487293			0.0217273			0.0108637	+	0.999941i	$0.496542\pi$
$504$	−3.79358	+	8.11753i	−0.168980	+	0.361583i
$505$	10.7416			0.477995
$506$	0.0238940	+	0.0413855i	0.00106222	+	0.00183981i
$507$	−5.35388	+	9.27319i	−0.237774	+	0.411837i
$508$	11.3485	−	19.6562i	0.503509	−	0.872102i
$509$	−16.0957	−	27.8785i	−0.713427	−	1.23569i	−0.963563	−	0.267481i	$-0.913809\pi$
$509$	−16.0957	−	27.8785i	−0.713427	−	1.23569i	0.250136	−	0.968211i	$-0.419525\pi$
$510$	7.82313			0.346414
$511$	−20.7471	+	1.79755i	−0.917796	+	0.0795188i
$512$	−21.6380			−0.956271
$513$	6.00405	+	10.3993i	0.265085	+	0.459141i
$514$	1.55775	−	2.69811i	0.0687095	−	0.119008i
$515$	−4.62660	+	8.01351i	−0.203873	+	0.353118i
$516$	−3.87207	−	6.70663i	−0.170458	−	0.295243i
$517$	−0.188374			−0.00828469
$518$	4.07753	−	0.353281i	0.179156	−	0.0155223i
$519$	33.9638			1.49084
$520$	−2.84419	−	4.92628i	−0.124726	−	0.216032i
$521$	4.49121	−	7.77901i	0.196764	−	0.340805i	−0.750714	−	0.660628i	$-0.770290\pi$
$521$	4.49121	−	7.77901i	0.196764	−	0.340805i	0.947477	+	0.319823i	$0.103624\pi$
$522$	−2.00742	+	3.47695i	−0.0878623	+	0.152182i
$523$	7.56180	+	13.0974i	0.330655	+	0.572710i	0.982640	−	0.185521i	$-0.0593972\pi$
$523$	7.56180	+	13.0974i	0.330655	+	0.572710i	−0.651986	+	0.758231i	$0.726064\pi$
$524$	11.1198			0.485771
$525$	2.42580	−	5.19075i	0.105871	−	0.226543i
$526$	−10.7085			−0.466913
$527$	2.51127	+	4.34965i	0.109393	+	0.189474i
$528$	0.223267	−	0.386709i	0.00971644	−	0.0168294i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−2.71900	−	4.70944i	−0.118106	−	0.204565i
$531$	−13.3362			−0.578743
$532$	−10.9549	−	15.6733i	−0.474957	−	0.679525i
$533$	3.45055			0.149460
$534$	1.87577	+	3.24893i	0.0811725	+	0.140595i
$535$	−9.26456	+	16.0467i	−0.400542	+	0.693759i
$536$	6.14757	−	10.6479i	0.265534	−	0.459919i
$537$	27.2956	+	47.2773i	1.17789	+	2.04017i
$538$	−1.60896			−0.0693672
$539$	−0.396997	−	0.474743i	−0.0170999	−	0.0204486i
$540$	4.84582			0.208531
$541$	6.35685	+	11.0104i	0.273303	+	0.473374i	0.969705	−	0.244277i	$-0.0785507\pi$
$541$	6.35685	+	11.0104i	0.273303	+	0.473374i	−0.696403	+	0.717651i	$0.745217\pi$
$542$	−3.73611	+	6.47112i	−0.160479	+	0.277959i
$543$	13.3841	−	23.1819i	0.574365	−	0.994829i
$544$	−17.6071	−	30.4964i	−0.754898	−	1.30752i
$545$	9.05717			0.387967
$546$	5.03574	+	7.20468i	0.215510	+	0.308332i
$547$	−31.2396			−1.33571			−0.667855	−	0.744292i	$-0.732787\pi$
$547$	−31.2396			−1.33571			−0.667855	+	0.744292i	$0.732787\pi$
$548$	−5.70728	−	9.88531i	−0.243803	−	0.422279i
$549$	4.88215	−	8.45614i	0.208365	−	0.360899i
$550$	0.0238940	−	0.0413855i	0.00101884	−	0.00176469i
$551$	−9.30116	−	16.1101i	−0.396243	−	0.686312i
$552$	−4.34029			−0.184735
$553$	18.0528	−	38.6295i	0.767684	−	1.64269i
$554$	2.11939			0.0900443
$555$	3.09880	+	5.36728i	0.131537	+	0.227828i
$556$	1.18445	−	2.05153i	0.0502320	−	0.0870043i
$557$	−19.7111	+	34.1407i	−0.835188	+	1.44659i	0.0586893	+	0.998276i	$0.481308\pi$
$557$	−19.7111	+	34.1407i	−0.835188	+	1.44659i	−0.893877	+	0.448312i	$0.852025\pi$
$558$	0.343212	+	0.594461i	0.0145293	+	0.0251655i
$559$	−5.94294			−0.251360
$560$	−6.14765	+	0.532639i	−0.259786	+	0.0225081i
$561$	1.27953			0.0540218
$562$	−8.98808	−	15.5678i	−0.379139	−	0.656689i
$563$	−12.8020	+	22.1738i	−0.539541	+	0.934513i	0.459387	+	0.888236i	$0.348069\pi$
$563$	−12.8020	+	22.1738i	−0.539541	+	0.934513i	−0.998929	+	0.0462770i	$0.985264\pi$
$564$	3.94017	−	6.82458i	0.165911	−	0.287367i
$565$	0.291910	+	0.505602i	0.0122807	+	0.0212708i
$566$	−15.7718			−0.662940
$567$	−29.5587	+	2.56099i	−1.24135	+	0.107552i
$568$	−25.4563			−1.06812
$569$	−1.13105	−	1.95903i	−0.0474159	−	0.0821268i	0.841343	−	0.540501i	$-0.181765\pi$
$569$	−1.13105	−	1.95903i	−0.0474159	−	0.0821268i	−0.888759	+	0.458374i	$0.848432\pi$
$570$	−2.47696	+	4.29022i	−0.103749	+	0.179698i
$571$	−8.68048	+	15.0350i	−0.363267	+	0.629196i	−0.988496	−	0.151244i	$-0.951672\pi$
$571$	−8.68048	+	15.0350i	−0.363267	+	0.629196i	0.625230	+	0.780441i	$0.285005\pi$
$572$	−0.214266	−	0.371119i	−0.00895890	−	0.0155173i
$573$	−14.8051			−0.618493
$574$	−0.736116	+	1.57514i	−0.0307249	+	0.0657452i
$575$	1.00000			0.0417029
$576$	1.53470	+	2.65817i	0.0639457	+	0.110757i
$577$	2.68401	−	4.64885i	0.111737	−	0.193534i	−0.804734	−	0.593636i	$-0.797692\pi$
$577$	2.68401	−	4.64885i	0.111737	−	0.193534i	0.916471	+	0.400102i	$0.131025\pi$
$578$	7.47681	−	12.9502i	0.310994	−	0.538658i
$579$	26.8128	+	46.4411i	1.11430	+	1.93003i
$580$	−7.50689			−0.311706
$581$	−11.5462	−	16.5192i	−0.479016	−	0.685332i
$582$	−9.07375			−0.376119
$583$	−0.444712	−	0.770263i	−0.0184181	−	0.0319011i
$584$	7.88759	−	13.6617i	0.326391	−	0.565326i
$585$	−2.39796	+	4.15340i	−0.0991436	+	0.171722i
$586$	2.51468	+	4.35555i	0.103880	+	0.179926i
$587$	−33.4034			−1.37870			−0.689352	−	0.724427i	$-0.742105\pi$
$587$	−33.4034			−1.37870			−0.689352	+	0.724427i	$0.742105\pi$
$588$	25.5033	−	4.45268i	1.05174	−	0.183626i
$589$	−3.18047			−0.131049
$590$	2.13305	+	3.69454i	0.0878161	+	0.152102i
$591$	−7.30421	+	12.6513i	−0.300455	+	0.520404i
$592$	3.33735	−	5.78047i	0.137164	−	0.237576i
$593$	−7.03898	−	12.1919i	−0.289056	−	0.500660i	0.684529	−	0.728986i	$-0.260008\pi$
$593$	−7.03898	−	12.1919i	−0.289056	−	0.500660i	−0.973585	+	0.228326i	$0.926675\pi$
$594$	−0.135595			−0.00556351
$595$	−10.1298	−	14.4927i	−0.415280	−	0.594144i
$596$	−11.9456			−0.489313
$597$	0.125443	+	0.217274i	0.00513405	+	0.00889243i
$598$	−0.767079	+	1.32862i	−0.0313682	+	0.0543313i
$599$	7.26667	−	12.5862i	0.296908	−	0.514260i	−0.678519	−	0.734583i	$-0.737378\pi$
$599$	7.26667	−	12.5862i	0.296908	−	0.514260i	0.975427	+	0.220323i	$0.0707112\pi$
$600$	2.17014	+	3.75880i	0.0885957	+	0.153452i
$601$	18.9459			0.772820			0.386410	−	0.922327i	$-0.373715\pi$
$601$	18.9459			0.772820			0.386410	+	0.922327i	$0.373715\pi$
$602$	1.26782	−	2.71290i	0.0516727	−	0.110569i
$603$	−10.3661			−0.422142
$604$	15.4345	+	26.7333i	0.628021	+	1.08776i
$605$	−5.49609	+	9.51951i	−0.223448	+	0.387023i
$606$	6.28693	−	10.8893i	0.255389	−	0.442347i
$607$	1.88032	+	3.25681i	0.0763198	+	0.132190i	0.901659	−	0.432447i	$-0.142350\pi$
$607$	1.88032	+	3.25681i	0.0763198	+	0.132190i	−0.825340	+	0.564637i	$0.809016\pi$
$608$	22.2991			0.904346
$609$	25.0910	−	2.17391i	1.01674	−	0.0880913i
$610$	−3.12348			−0.126466
$611$	−3.02373	−	5.23726i	−0.122327	−	0.211877i
$612$	−9.64318	+	16.7025i	−0.389803	+	0.675158i
$613$	−23.5252	+	40.7469i	−0.950174	+	1.64575i	−0.205130	+	0.978735i	$0.565762\pi$
$613$	−23.5252	+	40.7469i	−0.950174	+	1.64575i	−0.745044	+	0.667016i	$0.767571\pi$
$614$	8.48116	+	14.6898i	0.342272	+	0.592832i
$615$	−2.63280			−0.106165
$616$	0.467048	−	0.0404656i	0.0188179	−	0.00163040i
$617$	−6.02290			−0.242473			−0.121236	−	0.992624i	$-0.538686\pi$
$617$	−6.02290			−0.242473			−0.121236	+	0.992624i	$0.538686\pi$
$618$	5.41579	+	9.38043i	0.217855	+	0.377336i
$619$	11.9120	−	20.6321i	0.478782	−	0.829274i	−0.520922	−	0.853604i	$-0.674412\pi$
$619$	11.9120	−	20.6321i	0.478782	−	0.829274i	0.999704	+	0.0243298i	$0.00774520\pi$
$620$	−0.641734	+	1.11152i	−0.0257726	+	0.0446395i
$621$	−1.41871	−	2.45728i	−0.0569310	−	0.0986073i
$622$	−11.8963			−0.476999
$623$	3.58996	−	7.68182i	0.143829	−	0.307766i
$624$	14.3353			0.573870
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.267475	+	0.463281i	−0.0106905	+	0.0185164i
$627$	−0.405125	+	0.701698i	−0.0161792	+	0.0280231i
$628$	−20.1278	−	34.8623i	−0.803186	−	1.39116i
$629$	19.1262			0.762612
$630$	−1.38442	−	1.98070i	−0.0551567	−	0.0789132i
$631$	3.19986			0.127384			0.0636922	−	0.997970i	$-0.479712\pi$
$631$	3.19986			0.127384			0.0636922	+	0.997970i	$0.479712\pi$
$632$	16.1502	+	27.9730i	0.642420	+	1.11270i
$633$	−23.0419	+	39.9097i	−0.915833	+	1.58627i
$634$	7.57989	−	13.1288i	0.301036	−	0.521410i
$635$	6.64502	+	11.5095i	0.263700	+	0.456741i
$636$	37.2077			1.47538
$637$	6.82650	−	18.6579i	0.270476	−	0.739254i
$638$	0.210056			0.00831620
$639$	10.7312	+	18.5870i	0.424521	+	0.735292i
$640$	5.76004	−	9.97667i	0.227685	−	0.394363i
$641$	−15.9725	+	27.6652i	−0.630875	+	1.09271i	0.356498	+	0.934296i	$0.383971\pi$
$641$	−15.9725	+	27.6652i	−0.630875	+	1.09271i	−0.987373	+	0.158412i	$0.949363\pi$
$642$	10.8449	+	18.7839i	0.428013	+	0.741340i
$643$	−23.9356			−0.943928			−0.471964	−	0.881618i	$-0.656455\pi$
$643$	−23.9356			−0.943928			−0.471964	+	0.881618i	$0.656455\pi$
$644$	2.58857	+	3.70349i	0.102004	+	0.145938i
$645$	4.53452			0.178546
$646$	7.64407	+	13.2399i	0.300752	+	0.520918i
$647$	2.87564	−	4.98076i	0.113053	−	0.195814i	−0.803947	−	0.594701i	$-0.797270\pi$
$647$	2.87564	−	4.98076i	0.113053	−	0.195814i	0.917000	+	0.398888i	$0.130604\pi$
$648$	11.2376	−	19.4641i	0.441454	−	0.764621i
$649$	0.348875	+	0.604270i	0.0136946	+	0.0237197i
$650$	1.53416			0.0601746
$651$	1.82305	−	3.90096i	0.0714508	−	0.152891i
$652$	−8.30856			−0.325388
$653$	−12.7485	−	22.0810i	−0.498887	−	0.864098i	0.501112	−	0.865382i	$-0.332924\pi$
$653$	−12.7485	−	22.0810i	−0.498887	−	0.864098i	−0.999999	+	0.00128471i	$0.999591\pi$
$654$	5.30105	−	9.18169i	0.207288	−	0.359033i
$655$	−3.25555	+	5.63878i	−0.127205	+	0.220326i
$656$	1.41774	+	2.45560i	0.0553534	+	0.0958749i
$657$	−13.3002			−0.518891
$658$	3.03582	−	0.263027i	0.118349	−	0.0102538i
$659$	−15.7644			−0.614093			−0.307046	−	0.951695i	$-0.599341\pi$
$659$	−15.7644			−0.614093			−0.307046	+	0.951695i	$0.599341\pi$
$660$	0.163487	+	0.283167i	0.00636371	+	0.0110223i
$661$	−2.79214	+	4.83613i	−0.108602	+	0.188104i	−0.915204	−	0.402991i	$-0.867971\pi$
$661$	−2.79214	+	4.83613i	−0.108602	+	0.188104i	0.806602	+	0.591094i	$0.201304\pi$
$662$	0.963989	−	1.66968i	0.0374665	−	0.0648939i
$663$	20.5387	+	35.5741i	0.797657	+	1.38158i
$664$	15.2673			0.592486
$665$	11.1551	−	0.966492i	0.432578	−	0.0374790i
$666$	2.61396			0.101289
$667$	2.19780	+	3.80669i	0.0850990	+	0.147396i
$668$	−2.73434	+	4.73602i	−0.105795	+	0.183242i
$669$	−22.1239	+	38.3197i	−0.855359	+	1.48152i
$670$	1.65800	+	2.87174i	0.0640541	+	0.110945i
$671$	−0.510868			−0.0197218
$672$	−12.7818	+	27.3506i	−0.493069	+	1.05507i
$673$	−13.8385			−0.533435			−0.266717	−	0.963775i	$-0.585939\pi$
$673$	−13.8385			−0.533435			−0.266717	+	0.963775i	$0.585939\pi$
$674$	8.26272	+	14.3114i	0.318268	+	0.551256i
$675$	−1.41871	+	2.45728i	−0.0546063	+	0.0945808i
$676$	−4.22217	+	7.31301i	−0.162391	+	0.281270i
$677$	−18.2939	−	31.6860i	−0.703093	−	1.21779i	−0.967375	−	0.253348i	$-0.918468\pi$
$677$	−18.2939	−	31.6860i	−0.703093	−	1.21779i	0.264282	−	0.964446i	$-0.414865\pi$
$678$	0.683405			0.0262460
$679$	11.7491	+	16.8096i	0.450890	+	0.645092i
$680$	13.3944			0.513653
$681$	−21.8949	−	37.9231i	−0.839015	−	1.45322i
$682$	0.0179569	−	0.0311022i	0.000687604	−	0.00119096i
$683$	−1.25718	+	2.17750i	−0.0481046	+	0.0833196i	−0.889075	−	0.457761i	$-0.848651\pi$
$683$	−1.25718	+	2.17750i	−0.0481046	+	0.0833196i	0.840971	+	0.541081i	$0.181985\pi$
$684$	−6.10645	−	10.5767i	−0.233486	−	0.404410i
$685$	6.68370			0.255371
$686$	7.06085	+	7.09658i	0.269585	+	0.270949i
$687$	−12.3074			−0.469558
$688$	−2.44180	−	4.22932i	−0.0930926	−	0.161241i
$689$	14.2768	−	24.7281i	0.543902	−	0.942067i
$690$	0.585288	−	1.01375i	0.0222815	−	0.0385927i
$691$	−0.0897790	−	0.155502i	−0.00341535	−	0.00591557i	0.864313	−	0.502955i	$-0.167754\pi$
$691$	−0.0897790	−	0.155502i	−0.00341535	−	0.00591557i	−0.867728	+	0.497039i	$0.834420\pi$
$692$	26.7845			1.01819
$693$	−0.226433	−	0.323959i	−0.00860146	−	0.0123062i
$694$	12.0769			0.458432
$695$	0.693546	+	1.20126i	0.0263077	+	0.0455663i
$696$	−9.53906	+	16.5221i	−0.361577	+	0.626270i
$697$	−4.06250	+	7.03645i	−0.153878	+	0.266525i
$698$	−9.00079	−	15.5898i	−0.340685	−	0.590083i
$699$	−0.563257			−0.0213043
$700$	1.91303	−	4.09352i	0.0723059	−	0.154720i
$701$	25.3729			0.958320			0.479160	−	0.877728i	$-0.340941\pi$
$701$	25.3729			0.958320			0.479160	+	0.877728i	$0.340941\pi$
$702$	−2.17653	−	3.76986i	−0.0821478	−	0.142284i
$703$	−6.05575	+	10.4889i	−0.228397	+	0.395595i
$704$	0.0802953	−	0.139076i	0.00302624	−	0.00524161i
$705$	2.30713	+	3.99607i	0.0868917	+	0.150501i
$706$	11.8534			0.446107
$707$	−28.3135	+	2.45311i	−1.06484	+	0.0922588i
$708$	−29.1894			−1.09700
$709$	5.81482	+	10.0716i	0.218380	+	0.378245i	0.954313	−	0.298809i	$-0.0965894\pi$
$709$	5.81482	+	10.0716i	0.218380	+	0.378245i	−0.735933	+	0.677055i	$0.763256\pi$
$710$	3.43279	−	5.94576i	0.128830	−	0.223140i
$711$	13.6164	−	23.5843i	0.510654	−	0.884479i
$712$	3.21161	+	5.56267i	0.120360	+	0.208470i
$713$	0.751523			0.0281448
$714$	−20.6208	+	1.78661i	−0.771714	+	0.0668621i
$715$	0.250923			0.00938398
$716$	21.5258	+	37.2838i	0.804457	+	1.39336i
$717$	−8.24901	+	14.2877i	−0.308065	+	0.533584i
$718$	−0.0909515	+	0.157533i	−0.00339428	+	0.00587906i
$719$	6.58564	+	11.4067i	0.245603	+	0.425397i	0.962301	−	0.271987i	$-0.0876807\pi$
$719$	6.58564	+	11.4067i	0.245603	+	0.425397i	−0.716698	+	0.697384i	$0.754347\pi$
$720$	−3.94104			−0.146874
$721$	10.3651	−	22.1792i	0.386015	−	0.825998i
$722$	0.589096			0.0219239
$723$	2.25398	+	3.90401i	0.0838265	+	0.145192i
$724$	10.5549	−	18.2816i	0.392270	−	0.679432i
$725$	2.19780	−	3.80669i	0.0816241	−	0.141377i
$726$	6.43359	+	11.1433i	0.238773	+	0.413567i
$727$	−25.4396			−0.943501			−0.471750	−	0.881732i	$-0.656378\pi$
$727$	−25.4396			−0.943501			−0.471750	+	0.881732i	$0.656378\pi$
$728$	8.62198	+	12.3355i	0.319552	+	0.457185i
$729$	−0.514956			−0.0190725
$730$	2.12729	+	3.68457i	0.0787344	+	0.136372i
$731$	6.99691	−	12.1190i	0.258790	−	0.448238i
$732$	10.6857	−	18.5082i	0.394955	−	0.684082i
$733$	4.13260	+	7.15787i	0.152641	+	0.264382i	0.932198	−	0.361950i	$-0.117889\pi$
$733$	4.13260	+	7.15787i	0.152641	+	0.264382i	−0.779557	+	0.626332i	$0.784555\pi$
$734$	0.146898			0.00542209
$735$	−5.20868	+	14.2362i	−0.192125	+	0.525109i
$736$	−5.26911			−0.194222
$737$	0.271178	+	0.469694i	0.00998897	+	0.0173014i
$738$	−0.555217	+	0.961664i	−0.0204378	+	0.0353993i
$739$	13.2928	−	23.0238i	0.488984	−	0.846945i	−0.510936	−	0.859619i	$-0.670701\pi$
$739$	13.2928	−	23.0238i	0.488984	−	0.846945i	0.999920	+	0.0126737i	$0.00403426\pi$
$740$	2.44377	+	4.23274i	0.0898348	+	0.155598i
$741$	−26.0119			−0.955570
$742$	8.24245	+	11.7925i	0.302590	+	0.432918i
$743$	−25.4608			−0.934066			−0.467033	−	0.884240i	$-0.654677\pi$
$743$	−25.4608			−0.934066			−0.467033	+	0.884240i	$0.654677\pi$
$744$	1.63091	+	2.82482i	0.0597921	+	0.103563i
$745$	3.49733	−	6.05756i	0.128132	−	0.221932i
$746$	3.61059	−	6.25372i	0.132193	−	0.228965i
$747$	−6.43601	−	11.1475i	−0.235481	−	0.407865i
$748$	1.00906			0.0368950
$749$	20.7556	−	44.4129i	0.758392	−	1.62281i
$750$	−1.17058			−0.0427434
$751$	9.13755	+	15.8267i	0.333434	+	0.577524i	0.983183	−	0.182625i	$-0.0584593\pi$
$751$	9.13755	+	15.8267i	0.333434	+	0.577524i	−0.649749	+	0.760149i	$0.725126\pi$
$752$	2.48474	−	4.30370i	0.0906092	−	0.156940i
$753$	13.0723	−	22.6419i	0.476382	−	0.825117i
$754$	3.37176	+	5.84007i	0.122792	+	0.212683i
$755$	−18.0751			−0.657819
$756$	−12.7730	+	1.10666i	−0.464548	+	0.0402489i
$757$	−9.85470			−0.358175			−0.179088	−	0.983833i	$-0.557315\pi$
$757$	−9.85470			−0.358175			−0.179088	+	0.983833i	$0.557315\pi$
$758$	0.664635	+	1.15118i	0.0241406	+	0.0418128i
$759$	0.0957282	−	0.165806i	0.00347471	−	0.00601838i
$760$	−4.24094	+	7.34553i	−0.153835	+	0.266450i
$761$	−24.5423	−	42.5085i	−0.889658	−	1.54093i	−0.840280	−	0.542153i	$-0.817609\pi$
$761$	−24.5423	−	42.5085i	−0.889658	−	1.54093i	−0.0493786	−	0.998780i	$-0.515724\pi$
$762$	15.5570			0.563571
$763$	−23.8736	+	2.06843i	−0.864282	+	0.0748823i
$764$	−11.6756			−0.422408
$765$	−5.64648	−	9.77999i	−0.204149	−	0.353596i
$766$	1.12782	−	1.95343i	0.0407496	−	0.0705804i
$767$	−11.2001	+	19.3992i	−0.404413	+	0.700463i
$768$	−2.80885	−	4.86508i	−0.101356	−	0.175553i
$769$	2.98864			0.107773			0.0538865	−	0.998547i	$-0.482839\pi$
$769$	2.98864			0.107773			0.0538865	+	0.998547i	$0.482839\pi$
$770$	−0.0535301	+	0.114544i	−0.00192909	+	0.00412788i
$771$	−12.4819			−0.449524
$772$	21.1451	+	36.6243i	0.761027	+	1.31814i
$773$	−12.0338	+	20.8431i	−0.432825	+	0.749674i	−0.997115	−	0.0759021i	$-0.975816\pi$
$773$	−12.0338	+	20.8431i	−0.432825	+	0.749674i	0.564291	+	0.825576i	$0.309150\pi$
$774$	0.956260	−	1.65629i	0.0343721	−	0.0595341i
$775$	−0.375761	−	0.650838i	−0.0134977	−	0.0233788i
$776$	−15.5357			−0.557698
$777$	−9.39381	−	13.4398i	−0.337001	−	0.482150i
$778$	1.98711			0.0712415
$779$	−2.57254	−	4.45577i	−0.0921708	−	0.159644i
$780$	−5.24849	+	9.09065i	−0.187926	+	0.325497i
$781$	0.561458	−	0.972473i	0.0200905	−	0.0347978i
$782$	−1.80624	−	3.12850i	−0.0645909	−	0.111875i
$783$	−12.4722			−0.445718
$784$	16.0828	−	2.80794i	0.574386	−	0.100284i
$785$	23.5713			0.841295
$786$	3.81087	+	6.60063i	0.135929	+	0.235437i
$787$	−20.0956	+	34.8066i	−0.716330	+	1.24072i	0.246115	+	0.969241i	$0.420846\pi$
$787$	−20.0956	+	34.8066i	−0.716330	+	1.24072i	−0.962444	+	0.271479i	$0.912487\pi$
$788$	−5.76024	+	9.97702i	−0.205200	+	0.355417i
$789$	21.4511	+	37.1545i	0.763681	+	1.32273i
$790$	−8.71142			−0.309938
$791$	−0.884904	−	1.26604i	−0.0314636	−	0.0450152i
$792$	0.299408			0.0106390
$793$	−8.20032	−	14.2034i	−0.291202	−	0.504376i
$794$	2.75530	−	4.77232i	0.0977820	−	0.169363i
$795$	−10.8933	+	18.8678i	−0.386346	+	0.669171i
$796$	0.0989268	+	0.171346i	0.00350637	+	0.00607321i
$797$	−49.4274			−1.75081			−0.875404	−	0.483392i	$-0.839405\pi$
$797$	−49.4274			−1.75081			−0.875404	+	0.483392i	$0.839405\pi$
$798$	5.54919	−	11.8742i	0.196439	−	0.420341i
$799$	14.2399			0.503773
$800$	2.63455	+	4.56318i	0.0931455	+	0.161333i
$801$	2.70774	−	4.68994i	0.0956732	−	0.165711i
$802$	−4.66957	+	8.08794i	−0.164888	+	0.285595i
$803$	0.347933	+	0.602638i	0.0122783	+	0.0212666i
$804$	−22.6886			−0.800167
$805$	−2.63588	+	0.228375i	−0.0929024	+	0.00804916i
$806$	1.15295			0.0406111
$807$	3.22305	+	5.58248i	0.113457	+	0.196513i
$808$	10.7642	−	18.6441i	0.378683	−	0.655899i
$809$	6.19930	−	10.7375i	0.217956	−	0.377510i	−0.736227	−	0.676735i	$-0.763394\pi$
$809$	6.19930	−	10.7375i	0.217956	−	0.377510i	0.954183	+	0.299224i	$0.0967278\pi$
$810$	3.03078	+	5.24946i	0.106491	+	0.184447i
$811$	38.3630			1.34711			0.673553	−	0.739139i	$-0.264767\pi$
$811$	38.3630			1.34711			0.673553	+	0.739139i	$0.264767\pi$
$812$	19.7872	−	1.71439i	0.694395	−	0.0601631i
$813$	29.9365			1.04992
$814$	−0.0683811	−	0.118440i	−0.00239676	−	0.00415130i
$815$	2.43250	−	4.21322i	0.0852068	−	0.147583i
$816$	−16.8776	+	29.2329i	−0.590834	+	1.02336i
$817$	4.43073	+	7.67425i	0.155012	+	0.268488i
$818$	5.14119			0.179757
$819$	5.37221	−	11.4955i	0.187720	−	0.401684i
$820$	−2.07627			−0.0725066
$821$	−8.41611	−	14.5771i	−0.293724	−	0.508745i	0.680963	−	0.732318i	$-0.261561\pi$
$821$	−8.41611	−	14.5771i	−0.293724	−	0.508745i	−0.974687	+	0.223573i	$0.928228\pi$
$822$	3.91189	−	6.77559i	0.136443	−	0.236326i
$823$	25.1650	−	43.5870i	0.877196	−	1.51935i	0.0227916	−	0.999740i	$-0.492745\pi$
$823$	25.1650	−	43.5870i	0.877196	−	1.51935i	0.854405	−	0.519608i	$-0.173922\pi$
$824$	9.27268	+	16.0607i	0.323029	+	0.559503i
$825$	−0.191456			−0.00666565
$826$	−6.46619	−	9.25123i	−0.224987	−	0.321891i
$827$	23.1562			0.805221			0.402610	−	0.915371i	$-0.368103\pi$
$827$	23.1562			0.805221			0.402610	+	0.915371i	$0.368103\pi$
$828$	1.44291	+	2.49919i	0.0501446	+	0.0868530i
$829$	18.6607	−	32.3212i	0.648111	−	1.12256i	−0.335462	−	0.942054i	$-0.608893\pi$
$829$	18.6607	−	32.3212i	0.648111	−	1.12256i	0.983574	−	0.180508i	$-0.0577741\pi$
$830$	−2.05880	+	3.56594i	−0.0714619	+	0.123776i
$831$	−4.24554	−	7.35349i	−0.147276	−	0.255090i
$832$	5.15552			0.178735
$833$	30.0106	+	35.8877i	1.03980	+	1.24343i
$834$	1.62370			0.0562240
$835$	−1.60107	−	2.77314i	−0.0554074	−	0.0959683i
$836$	−0.319489	+	0.553372i	−0.0110498	+	0.0191388i
$837$	−1.06619	+	1.84670i	−0.0368531	+	0.0638314i
$838$	−8.50312	−	14.7278i	−0.293735	−	0.508765i
$839$	2.46470			0.0850908			0.0425454	−	0.999095i	$-0.486453\pi$
$839$	2.46470			0.0850908			0.0425454	+	0.999095i	$0.486453\pi$
$840$	−6.57865	−	9.41212i	−0.226985	−	0.324749i
$841$	−9.67878			−0.333751
$842$	0.184859	+	0.320185i	0.00637067	+	0.0110343i
$843$	−36.0096	+	62.3705i	−1.24024	+	2.14815i
$844$	−18.1713	+	31.4735i	−0.625481	+	1.08336i
$845$	−2.47225	−	4.28207i	−0.0850481	−	0.147308i
$846$	1.94616			0.0669103
$847$	12.3130	−	26.3474i	0.423080	−	0.905308i
$848$	23.4638			0.805751
$849$	31.5939	+	54.7223i	1.08430	+	1.87807i
$850$	−1.80624	+	3.12850i	−0.0619535	+	0.107307i
$851$	1.43093	−	2.47844i	0.0490516	−	0.0849599i
$852$	23.4877	+	40.6820i	0.804677	+	1.39374i
$853$	38.6612			1.32373			0.661867	−	0.749622i	$-0.269765\pi$
$853$	38.6612			1.32373			0.661867	+	0.749622i	$0.269765\pi$
$854$	8.23311	−	0.713325i	0.281731	−	0.0244095i
$855$	7.15116			0.244564
$856$	18.5681	+	32.1609i	0.634645	+	1.09924i
$857$	−28.6283	+	49.5857i	−0.977925	+	1.69382i	−0.308003	+	0.951385i	$0.599661\pi$
$857$	−28.6283	+	49.5857i	−0.977925	+	1.69382i	−0.669923	+	0.742431i	$0.733673\pi$
$858$	0.146862	−	0.254373i	0.00501379	−	0.00868414i
$859$	6.98425	+	12.0971i	0.238299	+	0.412747i	0.960226	−	0.279223i	$-0.0900767\pi$
$859$	6.98425	+	12.0971i	0.238299	+	0.412747i	−0.721927	+	0.691969i	$0.756743\pi$
$860$	3.57600			0.121941
$861$	6.93973	−	0.601266i	0.236506	−	0.0204911i
$862$	14.5967			0.497164
$863$	−15.6977	−	27.1892i	−0.534355	−	0.925530i	−0.999194	−	0.0401348i	$-0.987221\pi$
$863$	−15.6977	−	27.1892i	−0.534355	−	0.925530i	0.464839	−	0.885395i	$-0.346112\pi$
$864$	7.47534	−	12.9477i	0.254316	−	0.440489i
$865$	−7.84170	+	13.5822i	−0.266626	+	0.461810i
$866$	4.20333	+	7.28037i	0.142835	+	0.247397i
$867$	−59.9098			−2.03464
$868$	1.43769	−	3.07637i	0.0487983	−	0.104419i
$869$	−1.42482			−0.0483336
$870$	−2.57269	−	4.45602i	−0.0872222	−	0.151073i
$871$	−8.70576	+	15.0788i	−0.294983	+	0.510926i
$872$	9.07623	−	15.7205i	0.307360	−	0.532363i
$873$	6.54913	+	11.3434i	0.221655	+	0.383917i
$874$	2.28757			0.0773781
$875$	1.51572	+	2.16855i	0.0512406	+	0.0733103i
$876$	−29.1105			−0.983553
$877$	21.1108	+	36.5650i	0.712861	+	1.23471i	0.963779	+	0.266703i	$0.0859343\pi$
$877$	21.1108	+	36.5650i	0.712861	+	1.23471i	−0.250918	+	0.968008i	$0.580732\pi$
$878$	−5.41702	+	9.38256i	−0.182816	+	0.316646i
$879$	10.0747	−	17.4500i	0.339813	−	0.588573i
$880$	0.103098	+	0.178570i	0.00347542	+	0.00601960i
$881$	17.3413			0.584244			0.292122	−	0.956381i	$-0.405639\pi$
$881$	17.3413			0.584244			0.292122	+	0.956381i	$0.405639\pi$
$882$	4.10151	+	4.90473i	0.138105	+	0.165151i
$883$	−17.1705			−0.577834			−0.288917	−	0.957354i	$-0.593295\pi$
$883$	−17.1705			−0.577834			−0.288917	+	0.957354i	$0.593295\pi$
$884$	16.1972	+	28.0544i	0.544771	+	0.943570i
$885$	8.54578	−	14.8017i	0.287263	−	0.497555i
$886$	7.92786	−	13.7315i	0.266342	−	0.461318i
$887$	−0.729892	−	1.26421i	−0.0245074	−	0.0424480i	0.853512	−	0.521074i	$-0.174468\pi$
$887$	−0.729892	−	1.26421i	−0.0245074	−	0.0424480i	−0.878019	+	0.478626i	$0.841135\pi$
$888$	12.4213			0.416831
$889$	−20.1439	−	28.8201i	−0.675606	−	0.966595i
$890$	−1.73234			−0.0580683
$891$	0.495706	+	0.858588i	0.0166068	+	0.0287638i
$892$	−17.4473	+	30.2196i	−0.584179	+	1.01183i
$893$	−4.50865	+	7.80922i	−0.150876	+	0.261326i
$894$	−4.09390	−	7.09083i	−0.136920	−	0.237153i
$895$	−25.2085			−0.842626
$896$	−12.9043	+	27.6127i	−0.431103	+	0.922477i
$897$	6.14641			0.205223
$898$	−3.80697	−	6.59387i	−0.127040	−	0.220040i
$899$	1.65169	−	2.86082i	0.0550871	−	0.0954136i
$900$	1.44291	−	2.49919i	0.0480970	−	0.0833065i
$901$	33.6175	+	58.2272i	1.11996	+	1.93983i
$902$	0.0580979			0.00193445
$903$	−11.9524	+	1.03557i	−0.397752	+	0.0344616i
$904$	1.17009			0.0389168
$905$	6.18034	+	10.7047i	0.205441	+	0.355835i
$906$	−10.5791	+	18.3236i	−0.351468	+	0.608760i
$907$	24.1113	−	41.7620i	0.800602	−	1.38668i	−0.118618	−	0.992940i	$-0.537846\pi$
$907$	24.1113	−	41.7620i	0.800602	−	1.38668i	0.919220	−	0.393744i	$-0.128820\pi$
$908$	−17.2667	−	29.9068i	−0.573016	−	0.992494i
$909$	−18.1508			−0.602024
$910$	−4.04385	+	0.350363i	−0.134052	+	0.0116144i
$911$	20.9858			0.695292			0.347646	−	0.937626i	$-0.386981\pi$
$911$	20.9858			0.695292			0.347646	+	0.937626i	$0.386981\pi$
$912$	−10.6876	−	18.5114i	−0.353901	−	0.612975i
$913$	−0.336732	+	0.583236i	−0.0111442	+	0.0193023i
$914$	6.33827	−	10.9782i	0.209651	−	0.363127i
$915$	6.25692	+	10.8373i	0.206847	+	0.358270i
$916$	−9.70587			−0.320691
$917$	7.29348	−	15.6066i	0.240852	−	0.515376i
$918$	10.2501			0.338305
$919$	24.9633	+	43.2377i	0.823463	+	1.42628i	0.903088	+	0.429455i	$0.141294\pi$
$919$	24.9633	+	43.2377i	0.823463	+	1.42628i	−0.0796252	+	0.996825i	$0.525372\pi$
$920$	1.00210	−	1.73570i	0.0330384	−	0.0572242i
$921$	33.9787	−	58.8529i	1.11964	−	1.93927i
$922$	−0.154274	−	0.267210i	−0.00508073	−	0.00880009i
$923$	36.0495			1.18658
$924$	−0.495599	−	0.709057i	−0.0163040	−	0.0233263i
$925$	−2.86186			−0.0940973
$926$	−2.53901	−	4.39770i	−0.0834371	−	0.144517i
$927$	7.81788	−	13.5410i	0.256773	−	0.444744i
$928$	−11.5804	+	20.0579i	−0.380146	+	0.658432i
$929$	−0.759403	−	1.31532i	−0.0249152	−	0.0431544i	0.853299	−	0.521422i	$-0.174598\pi$
$929$	−0.759403	−	1.31532i	−0.0249152	−	0.0431544i	−0.878214	+	0.478268i	$0.841265\pi$
$930$	−0.879715			−0.0288470
$931$	−29.1828	+	5.09511i	−0.956429	+	0.166985i
$932$	−0.444195			−0.0145501
$933$	23.8306	+	41.2758i	0.780178	+	1.35131i
$934$	9.51725	−	16.4844i	0.311414	−	0.539385i
$935$	−0.295424	+	0.511689i	−0.00966139	+	0.0167340i
$936$	4.80602	+	8.32427i	0.157090	+	0.272087i
$937$	60.6661			1.98188			0.990938	−	0.134322i	$-0.0428857\pi$
$937$	60.6661			1.98188			0.990938	+	0.134322i	$0.0428857\pi$
$938$	−5.02611	−	7.19090i	−0.164108	−	0.234791i
$939$	2.14321			0.0699411
$940$	1.81945	+	3.15138i	0.0593439	+	0.102787i
$941$	0.0587054	−	0.101681i	0.00191374	−	0.00331470i	−0.865067	−	0.501656i	$-0.832724\pi$
$941$	0.0587054	−	0.101681i	0.00191374	−	0.00331470i	0.866981	+	0.498342i	$0.166058\pi$
$942$	13.7960	−	23.8954i	0.449498	−	0.778553i
$943$	0.607872	+	1.05287i	0.0197950	+	0.0342860i
$944$	−18.4073			−0.599107
$945$	3.17837	−	6.80109i	0.103392	−	0.221239i
$946$	−0.100063			−0.00325333
$947$	−19.7670	−	34.2375i	−0.642342	−	1.11257i	−0.984909	−	0.173076i	$-0.944630\pi$
$947$	−19.7670	−	34.2375i	−0.642342	−	1.11257i	0.342566	−	0.939494i	$-0.388704\pi$
$948$	29.8025	−	51.6195i	0.967941	−	1.67652i
$949$	−11.1699	+	19.3468i	−0.362589	+	0.628023i
$950$	−1.14378	−	1.98109i	−0.0371092	−	0.0642751i
$951$	−60.7358			−1.96949
$952$	−35.3060	+	3.05895i	−1.14428	+	0.0991412i
$953$	−6.90967			−0.223826			−0.111913	−	0.993718i	$-0.535698\pi$
$953$	−6.90967			−0.223826			−0.111913	+	0.993718i	$0.535698\pi$
$954$	4.59447	+	7.95785i	0.148751	+	0.257645i
$955$	3.41827	−	5.92062i	0.110613	−	0.191587i
$956$	−6.50532	+	11.2675i	−0.210397	+	0.364418i
$957$	−0.420782	−	0.728816i	−0.0136019	−	0.0235593i
$958$	−8.19504			−0.264770
$959$	−17.6174	+	1.52639i	−0.568896	+	0.0492897i
$960$	−3.93370			−0.126960
$961$	15.2176	+	26.3577i	0.490891	+	0.850247i
$962$	2.19527	−	3.80232i	0.0707784	−	0.122592i
$963$	15.6549	−	27.1152i	0.504474	−	0.873774i
$964$	1.77753	+	3.07877i	0.0572504	+	0.0991607i
$965$	−24.7626			−0.797136
$966$	−1.31123	+	2.80578i	−0.0421882	+	0.0902745i
$967$	−1.73607			−0.0558282			−0.0279141	−	0.999610i	$-0.508886\pi$
$967$	−1.73607			−0.0558282			−0.0279141	+	0.999610i	$0.508886\pi$
$968$	11.0153	+	19.0791i	0.354046	+	0.613225i
$969$	30.6250	−	53.0441i	0.983818	−	1.70402i
$970$	2.09499	−	3.62862i	0.0672659	−	0.116508i
$971$	28.4677	+	49.3074i	0.913570	+	1.58235i	0.808981	+	0.587835i	$0.200019\pi$
$971$	28.4677	+	49.3074i	0.913570	+	1.58235i	0.104589	+	0.994515i	$0.466647\pi$
$972$	−26.9368			−0.863998
$973$	−2.10244	−	3.00797i	−0.0674011	−	0.0964312i
$974$	3.46379			0.110987
$975$	−3.07321	−	5.32295i	−0.0984214	−	0.170471i
$976$	6.73859	−	11.6716i	0.215697	−	0.373598i
$977$	−11.2063	+	19.4099i	−0.358522	+	0.620978i	−0.987714	−	0.156272i	$-0.950052\pi$
$977$	−11.2063	+	19.4099i	−0.358522	+	0.620978i	0.629193	+	0.777249i	$0.283386\pi$
$978$	−2.84743	−	4.93189i	−0.0910507	−	0.157704i
$979$	−0.283338			−0.00905551
$980$	−4.10766	+	11.2269i	−0.131214	+	0.358630i
$981$	−15.3045			−0.488635
$982$	−5.07047	−	8.78231i	−0.161805	−	0.280255i
$983$	16.7557	−	29.0217i	0.534424	−	0.925650i	−0.464767	−	0.885433i	$-0.653862\pi$
$983$	16.7557	−	29.0217i	0.534424	−	0.925650i	0.999191	−	0.0402168i	$-0.0128049\pi$
$984$	−2.63834	+	4.56974i	−0.0841072	+	0.145678i
$985$	−3.37286	−	5.84196i	−0.107468	−	0.186140i
$986$	−15.8790			−0.505689
$987$	−6.99392	−	10.0063i	−0.222619	−	0.318503i
$988$	−20.5134			−0.652619
$989$	−1.04695	−	1.81337i	−0.0332910	−	0.0576617i
$990$	−0.0403752	+	0.0699319i	−0.00128321	+	0.00222258i
$991$	12.2601	−	21.2352i	0.389456	−	0.674558i	−0.602920	−	0.797801i	$-0.705996\pi$
$991$	12.2601	−	21.2352i	0.389456	−	0.674558i	0.992376	+	0.123244i	$0.0393296\pi$
$992$	1.97993	+	3.42933i	0.0628627	+	0.108881i
$993$	−7.72421			−0.245120
$994$	−7.69054	+	16.4563i	−0.243929	+	0.521961i
$995$	−0.115851			−0.00367274
$996$	−14.0867	−	24.3988i	−0.446353	−	0.773106i
$997$	−11.4998	+	19.9182i	−0.364202	+	0.630817i	−0.988648	−	0.150251i	$-0.951992\pi$
$997$	−11.4998	+	19.9182i	−0.364202	+	0.630817i	0.624445	+	0.781068i	$0.285325\pi$
$998$	−9.17573	+	15.8928i	−0.290453	+	0.503079i
$999$	4.06015	+	7.03239i	0.128458	+	0.222495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.i.e.116.11	✓	30
7.2	even	3	inner	805.2.i.e.576.11	yes	30
7.3	odd	6		5635.2.a.bj.1.5		15
7.4	even	3		5635.2.a.bi.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.i.e.116.11	✓	30	1.1	even	1	trivial
805.2.i.e.576.11	yes	30	7.2	even	3	inner
5635.2.a.bi.1.5		15	7.4	even	3
5635.2.a.bj.1.5		15	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.270268 + 0.468117i) q^{2} +(1.08279 - 1.87545i) q^{3} +(0.853911 - 1.47902i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.17058 q^{6} +(-1.51572 - 2.16855i) q^{7} +2.00421 q^{8} +(-0.844883 - 1.46338i) q^{9} +O(q^{10})\)	\(q+(0.270268 + 0.468117i) q^{2} +(1.08279 - 1.87545i) q^{3} +(0.853911 - 1.47902i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.17058 q^{6} +(-1.51572 - 2.16855i) q^{7} +2.00421 q^{8} +(-0.844883 - 1.46338i) q^{9} +(-0.270268 + 0.468117i) q^{10} +(-0.0442043 + 0.0765640i) q^{11} +(-1.84922 - 3.20294i) q^{12} -2.83822 q^{13} +(0.605486 - 1.29562i) q^{14} +2.16559 q^{15} +(-1.16615 - 2.01983i) q^{16} +(3.34157 - 5.78778i) q^{17} +(0.456689 - 0.791009i) q^{18} +(2.11602 + 3.66505i) q^{19} +1.70782 q^{20} +(-5.70822 + 0.494566i) q^{21} -0.0477879 q^{22} +(-0.500000 - 0.866025i) q^{23} +(2.17014 - 3.75880i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.767079 - 1.32862i) q^{26} +2.83742 q^{27} +(-4.50161 + 0.390024i) q^{28} -4.39559 q^{29} +(0.585288 + 1.01375i) q^{30} +(-0.375761 + 0.650838i) q^{31} +(2.63455 - 4.56318i) q^{32} +(0.0957282 + 0.165806i) q^{33} +3.61248 q^{34} +(1.12016 - 2.39692i) q^{35} -2.88582 q^{36} +(1.43093 + 2.47844i) q^{37} +(-1.14378 + 1.98109i) q^{38} +(-3.07321 + 5.32295i) q^{39} +(1.00210 + 1.73570i) q^{40} -1.21574 q^{41} +(-1.77426 - 2.53845i) q^{42} +2.09390 q^{43} +(0.0754930 + 0.130758i) q^{44} +(0.844883 - 1.46338i) q^{45} +(0.270268 - 0.468117i) q^{46} +(1.06536 + 1.84526i) q^{47} -5.05080 q^{48} +(-2.40521 + 6.57381i) q^{49} -0.540535 q^{50} +(-7.23647 - 12.5339i) q^{51} +(-2.42359 + 4.19778i) q^{52} +(-5.03019 + 8.71255i) q^{53} +(0.766864 + 1.32825i) q^{54} -0.0884085 q^{55} +(-3.03781 - 4.34622i) q^{56} +9.16485 q^{57} +(-1.18799 - 2.05765i) q^{58} +(3.94617 - 6.83497i) q^{59} +(1.84922 - 3.20294i) q^{60} +(2.88925 + 5.00432i) q^{61} -0.406225 q^{62} +(-1.89281 + 4.05024i) q^{63} -1.81646 q^{64} +(-1.41911 - 2.45797i) q^{65} +(-0.0517444 + 0.0896240i) q^{66} +(3.06733 - 5.31277i) q^{67} +(-5.70681 - 9.88449i) q^{68} -2.16559 q^{69} +(1.42478 - 0.123445i) q^{70} -12.7014 q^{71} +(-1.69332 - 2.93292i) q^{72} +(3.93552 - 6.81651i) q^{73} +(-0.773467 + 1.33968i) q^{74} +(1.08279 + 1.87545i) q^{75} +7.22757 q^{76} +(0.233034 - 0.0201903i) q^{77} -3.32235 q^{78} +(8.05814 + 13.9571i) q^{79} +(1.16615 - 2.01983i) q^{80} +(5.60699 - 9.71160i) q^{81} +(-0.328576 - 0.569111i) q^{82} +7.61763 q^{83} +(-4.14284 + 8.86487i) q^{84} +6.68315 q^{85} +(0.565912 + 0.980189i) q^{86} +(-4.75952 + 8.24372i) q^{87} +(-0.0885945 + 0.153450i) q^{88} +(1.60243 + 2.77550i) q^{89} +0.913378 q^{90} +(4.30194 + 6.15482i) q^{91} -1.70782 q^{92} +(0.813744 + 1.40945i) q^{93} +(-0.575866 + 0.997429i) q^{94} +(-2.11602 + 3.66505i) q^{95} +(-5.70535 - 9.88196i) q^{96} -7.75152 q^{97} +(-3.72736 + 0.650770i) q^{98} +0.149390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9}+O(q^{10}) \) 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9	\( 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9} + 5 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} - 43 q^{16} + q^{17} + 13 q^{18} + 17 q^{19} - 38 q^{20} - 3 q^{21} + 50 q^{22} - 15 q^{23} + 4 q^{24} - 15 q^{25} + 14 q^{26} - 6 q^{27} - q^{28} + 62 q^{29} - 8 q^{30} + 23 q^{31} - 30 q^{32} - 28 q^{33} - 20 q^{34} + 6 q^{35} + 30 q^{36} - 20 q^{37} - 12 q^{38} - 4 q^{39} + 15 q^{40} - 16 q^{42} + 8 q^{43} - 33 q^{44} + 27 q^{45} - 5 q^{46} + q^{47} + 52 q^{48} + 33 q^{49} + 10 q^{50} - 27 q^{51} - 11 q^{52} - 36 q^{53} - 12 q^{54} - 22 q^{55} + 18 q^{56} + 56 q^{57} - 14 q^{58} + 10 q^{59} + 10 q^{61} + 28 q^{62} - 51 q^{63} + 18 q^{64} + 3 q^{65} + 17 q^{66} - 13 q^{67} - 3 q^{68} - q^{70} - 14 q^{71} - 35 q^{72} - 9 q^{73} - 62 q^{74} + 10 q^{76} - 26 q^{77} - 34 q^{78} - 4 q^{79} + 43 q^{80} - 43 q^{81} - 32 q^{82} + 58 q^{83} - 78 q^{84} + 2 q^{85} - 100 q^{86} + 22 q^{87} - 24 q^{88} + 6 q^{89} + 26 q^{90} - 6 q^{91} + 38 q^{92} - q^{93} + 62 q^{94} - 17 q^{95} + 63 q^{96} + 72 q^{97} + q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9 + 5 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 - 43 * q^16 + q^17 + 13 * q^18 + 17 * q^19 - 38 * q^20 - 3 * q^21 + 50 * q^22 - 15 * q^23 + 4 * q^24 - 15 * q^25 + 14 * q^26 - 6 * q^27 - q^28 + 62 * q^29 - 8 * q^30 + 23 * q^31 - 30 * q^32 - 28 * q^33 - 20 * q^34 + 6 * q^35 + 30 * q^36 - 20 * q^37 - 12 * q^38 - 4 * q^39 + 15 * q^40 - 16 * q^42 + 8 * q^43 - 33 * q^44 + 27 * q^45 - 5 * q^46 + q^47 + 52 * q^48 + 33 * q^49 + 10 * q^50 - 27 * q^51 - 11 * q^52 - 36 * q^53 - 12 * q^54 - 22 * q^55 + 18 * q^56 + 56 * q^57 - 14 * q^58 + 10 * q^59 + 10 * q^61 + 28 * q^62 - 51 * q^63 + 18 * q^64 + 3 * q^65 + 17 * q^66 - 13 * q^67 - 3 * q^68 - q^70 - 14 * q^71 - 35 * q^72 - 9 * q^73 - 62 * q^74 + 10 * q^76 - 26 * q^77 - 34 * q^78 - 4 * q^79 + 43 * q^80 - 43 * q^81 - 32 * q^82 + 58 * q^83 - 78 * q^84 + 2 * q^85 - 100 * q^86 + 22 * q^87 - 24 * q^88 + 6 * q^89 + 26 * q^90 - 6 * q^91 + 38 * q^92 - q^93 + 62 * q^94 - 17 * q^95 + 63 * q^96 + 72 * q^97 + q^98 + 26 * q^99

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