LMFDB - Embedded newform 429.2.i.c.100.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.7965937851507.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 $ x^10 - 2x^9 + 8x^8 - 6x^7 + 28x^6 - 23x^5 + 51x^4 - 10x^3 + 25x^2 - 6*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.4
Root			$-0.362459 - 0.627798i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.c.133.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.362459 - 0.627798i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.737247 + 1.27695i) q^{4} +4.26830 q^{5} +(0.362459 + 0.627798i) q^{6} +(-0.335344 - 0.580832i) q^{7} +2.51872 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.362459 - 0.627798i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.737247 + 1.27695i) q^{4} +4.26830 q^{5} +(0.362459 + 0.627798i) q^{6} +(-0.335344 - 0.580832i) q^{7} +2.51872 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.54708 - 2.67963i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.47449 q^{12} +(-3.10150 + 1.83867i) q^{13} -0.486193 q^{14} +(-2.13415 + 3.69646i) q^{15} +(-0.561559 + 0.972649i) q^{16} +(-2.17230 - 3.76253i) q^{17} -0.724918 q^{18} +(-1.19695 - 2.07318i) q^{19} +(3.14679 + 5.45040i) q^{20} +0.670687 q^{21} +(-0.362459 - 0.627798i) q^{22} +(-3.47628 + 6.02110i) q^{23} +(-1.25936 + 2.18128i) q^{24} +13.2184 q^{25} +(0.0301500 + 2.61356i) q^{26} +1.00000 q^{27} +(0.494462 - 0.856433i) q^{28} +(3.22153 - 5.57985i) q^{29} +(1.54708 + 2.67963i) q^{30} -3.82338 q^{31} +(2.92581 + 5.06765i) q^{32} +(0.500000 + 0.866025i) q^{33} -3.14947 q^{34} +(-1.43135 - 2.47916i) q^{35} +(0.737247 - 1.27695i) q^{36} +(2.73904 - 4.74415i) q^{37} -1.73539 q^{38} +(-0.0415910 - 3.60531i) q^{39} +10.7507 q^{40} +(-6.32123 + 10.9487i) q^{41} +(0.243097 - 0.421056i) q^{42} +(-3.45292 - 5.98064i) q^{43} +1.47449 q^{44} +(-2.13415 - 3.69646i) q^{45} +(2.52002 + 4.36480i) q^{46} +2.08059 q^{47} +(-0.561559 - 0.972649i) q^{48} +(3.27509 - 5.67262i) q^{49} +(4.79112 - 8.29847i) q^{50} +4.34459 q^{51} +(-4.63446 - 2.60489i) q^{52} -5.80739 q^{53} +(0.362459 - 0.627798i) q^{54} +(2.13415 - 3.69646i) q^{55} +(-0.844638 - 1.46296i) q^{56} +2.39391 q^{57} +(-2.33534 - 4.04493i) q^{58} +(4.64734 + 8.04942i) q^{59} -6.29358 q^{60} +(0.685293 + 1.18696i) q^{61} +(-1.38582 + 2.40031i) q^{62} +(-0.335344 + 0.580832i) q^{63} +1.99571 q^{64} +(-13.2381 + 7.84801i) q^{65} +0.724918 q^{66} +(-4.32266 + 7.48706i) q^{67} +(3.20304 - 5.54782i) q^{68} +(-3.47628 - 6.02110i) q^{69} -2.07522 q^{70} +(-4.77415 - 8.26907i) q^{71} +(-1.25936 - 2.18128i) q^{72} +6.15269 q^{73} +(-1.98558 - 3.43912i) q^{74} +(-6.60919 + 11.4475i) q^{75} +(1.76490 - 3.05690i) q^{76} -0.670687 q^{77} +(-2.27848 - 1.28067i) q^{78} +3.19583 q^{79} +(-2.39690 + 4.15156i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.58238 + 7.93691i) q^{82} -14.4977 q^{83} +(0.494462 + 0.856433i) q^{84} +(-9.27201 - 16.0596i) q^{85} -5.00617 q^{86} +(3.22153 + 5.57985i) q^{87} +(1.25936 - 2.18128i) q^{88} +(3.17574 - 5.50054i) q^{89} -3.09417 q^{90} +(2.10803 + 1.18486i) q^{91} -10.2515 q^{92} +(1.91169 - 3.31114i) q^{93} +(0.754128 - 1.30619i) q^{94} +(-5.10895 - 8.84897i) q^{95} -5.85162 q^{96} +(-6.76467 - 11.7168i) q^{97} +(-2.37417 - 4.11219i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.362459	−	0.627798i	0.256297	−	0.443920i	−0.708950	−	0.705259i	$-0.750831\pi$
$2$	0.362459	−	0.627798i	0.256297	−	0.443920i	0.965247	+	0.261339i	$0.0841641\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.737247	+	1.27695i	0.368623	+	0.638474i
$5$	4.26830			1.90884			0.954421	−	0.298465i	$-0.0964745\pi$
$5$	4.26830			1.90884			0.954421	+	0.298465i	$0.0964745\pi$
$6$	0.362459	+	0.627798i	0.147973	+	0.256297i
$7$	−0.335344	−	0.580832i	−0.126748	−	0.219534i	0.795667	−	0.605734i	$-0.207121\pi$
$7$	−0.335344	−	0.580832i	−0.126748	−	0.219534i	−0.922415	+	0.386201i	$0.873787\pi$
$8$	2.51872			0.890503
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.54708	−	2.67963i	0.489231	−	0.847373i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.47449			−0.425650
$13$	−3.10150	+	1.83867i	−0.860200	+	0.509957i
$13$	−3.10150	+	1.83867i	−0.860200	+	0.509957i
$14$	−0.486193			−0.129941
$15$	−2.13415	+	3.69646i	−0.551035	+	0.954421i
$16$	−0.561559	+	0.972649i	−0.140390	+	0.243162i
$17$	−2.17230	−	3.76253i	−0.526859	−	0.912547i	−0.999510	−	0.0312972i	$-0.990036\pi$
$17$	−2.17230	−	3.76253i	−0.526859	−	0.912547i	0.472651	−	0.881250i	$-0.343297\pi$
$18$	−0.724918			−0.170865
$19$	−1.19695	−	2.07318i	−0.274600	−	0.475621i	0.695434	−	0.718590i	$-0.255212\pi$
$19$	−1.19695	−	2.07318i	−0.274600	−	0.475621i	−0.970034	+	0.242969i	$0.921879\pi$
$20$	3.14679	+	5.45040i	0.703644	+	1.21875i
$21$	0.670687			0.146356
$22$	−0.362459	−	0.627798i	−0.0772765	−	0.133847i
$23$	−3.47628	+	6.02110i	−0.724855	+	1.25549i	0.234178	+	0.972194i	$0.424760\pi$
$23$	−3.47628	+	6.02110i	−0.724855	+	1.25549i	−0.959034	+	0.283292i	$0.908573\pi$
$24$	−1.25936	+	2.18128i	−0.257066	+	0.445252i
$25$	13.2184			2.64368
$26$	0.0301500	+	2.61356i	0.00591291	+	0.512560i
$27$	1.00000			0.192450
$28$	0.494462	−	0.856433i	0.0934445	−	0.161851i
$29$	3.22153	−	5.57985i	0.598223	−	1.03615i	−0.394861	−	0.918741i	$-0.629207\pi$
$29$	3.22153	−	5.57985i	0.598223	−	1.03615i	0.993083	−	0.117411i	$-0.0374594\pi$
$30$	1.54708	+	2.67963i	0.282458	+	0.489231i
$31$	−3.82338			−0.686699			−0.343350	−	0.939208i	$-0.611562\pi$
$31$	−3.82338			−0.686699			−0.343350	+	0.939208i	$0.611562\pi$
$32$	2.92581	+	5.06765i	0.517215	+	0.895842i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−3.14947			−0.540130
$35$	−1.43135	−	2.47916i	−0.241942	−	0.419055i
$36$	0.737247	−	1.27695i	0.122874	−	0.212825i
$37$	2.73904	−	4.74415i	0.450295	−	0.779934i	−0.548109	−	0.836407i	$-0.684652\pi$
$37$	2.73904	−	4.74415i	0.450295	−	0.779934i	0.998404	+	0.0564732i	$0.0179855\pi$
$38$	−1.73539			−0.281517
$39$	−0.0415910	−	3.60531i	−0.00665988	−	0.577312i
$40$	10.7507			1.69983
$41$	−6.32123	+	10.9487i	−0.987211	+	1.70990i	−0.355543	+	0.934660i	$0.615704\pi$
$41$	−6.32123	+	10.9487i	−0.987211	+	1.70990i	−0.631668	+	0.775239i	$0.717629\pi$
$42$	0.243097	−	0.421056i	0.0375106	−	0.0649703i
$43$	−3.45292	−	5.98064i	−0.526566	−	0.912039i	−0.999521	−	0.0309523i	$-0.990146\pi$
$43$	−3.45292	−	5.98064i	−0.526566	−	0.912039i	0.472955	−	0.881087i	$-0.343187\pi$
$44$	1.47449			0.222288
$45$	−2.13415	−	3.69646i	−0.318140	−	0.551035i
$46$	2.52002	+	4.36480i	0.371557	+	0.643555i
$47$	2.08059			0.303485			0.151742	−	0.988420i	$-0.451512\pi$
$47$	2.08059			0.303485			0.151742	+	0.988420i	$0.451512\pi$
$48$	−0.561559	−	0.972649i	−0.0810541	−	0.140390i
$49$	3.27509	−	5.67262i	0.467870	−	0.810374i
$50$	4.79112	−	8.29847i	0.677567	−	1.17358i
$51$	4.34459			0.608365
$52$	−4.63446	−	2.60489i	−0.642684	−	0.361234i
$53$	−5.80739			−0.797706			−0.398853	−	0.917015i	$-0.630592\pi$
$53$	−5.80739			−0.797706			−0.398853	+	0.917015i	$0.630592\pi$
$54$	0.362459	−	0.627798i	0.0493244	−	0.0854324i
$55$	2.13415	−	3.69646i	0.287769	−	0.498430i
$56$	−0.844638	−	1.46296i	−0.112869	−	0.195496i
$57$	2.39391			0.317081
$58$	−2.33534	−	4.04493i	−0.306646	−	0.531126i
$59$	4.64734	+	8.04942i	0.605031	+	1.04795i	0.992047	+	0.125872i	$0.0401728\pi$
$59$	4.64734	+	8.04942i	0.605031	+	1.04795i	−0.387015	+	0.922073i	$0.626494\pi$
$60$	−6.29358			−0.812498
$61$	0.685293	+	1.18696i	0.0877428	+	0.151975i	0.906557	−	0.422084i	$-0.138701\pi$
$61$	0.685293	+	1.18696i	0.0877428	+	0.151975i	−0.818814	+	0.574059i	$0.805368\pi$
$62$	−1.38582	+	2.40031i	−0.175999	+	0.304839i
$63$	−0.335344	+	0.580832i	−0.0422493	+	0.0731780i
$64$	1.99571			0.249463
$65$	−13.2381	+	7.84801i	−1.64199	+	0.973426i
$66$	0.724918			0.0892313
$67$	−4.32266	+	7.48706i	−0.528097	+	0.914690i	0.471367	+	0.881937i	$0.343761\pi$
$67$	−4.32266	+	7.48706i	−0.528097	+	0.914690i	−0.999463	+	0.0327531i	$0.989573\pi$
$68$	3.20304	−	5.54782i	0.388425	−	0.672772i
$69$	−3.47628	−	6.02110i	−0.418495	−	0.724855i
$70$	−2.07522			−0.248036
$71$	−4.77415	−	8.26907i	−0.566587	−	0.981358i	−0.996900	−	0.0786781i	$-0.974930\pi$
$71$	−4.77415	−	8.26907i	−0.566587	−	0.981358i	0.430313	−	0.902680i	$-0.358403\pi$
$72$	−1.25936	−	2.18128i	−0.148417	−	0.257066i
$73$	6.15269			0.720118			0.360059	−	0.932929i	$-0.382757\pi$
$73$	6.15269			0.720118			0.360059	+	0.932929i	$0.382757\pi$
$74$	−1.98558	−	3.43912i	−0.230819	−	0.399790i
$75$	−6.60919	+	11.4475i	−0.763163	+	1.32184i
$76$	1.76490	−	3.05690i	0.202448	−	0.350650i
$77$	−0.670687			−0.0764319
$78$	−2.27848	−	1.28067i	−0.257987	−	0.145007i
$79$	3.19583			0.359559			0.179780	−	0.983707i	$-0.442462\pi$
$79$	3.19583			0.359559			0.179780	+	0.983707i	$0.442462\pi$
$80$	−2.39690	+	4.15156i	−0.267982	+	0.464158i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.58238	+	7.93691i	0.506039	+	0.876485i
$83$	−14.4977			−1.59133			−0.795663	−	0.605740i	$-0.792877\pi$
$83$	−14.4977			−1.59133			−0.795663	+	0.605740i	$0.792877\pi$
$84$	0.494462	+	0.856433i	0.0539502	+	0.0934445i
$85$	−9.27201	−	16.0596i	−1.00569	−	1.74191i
$86$	−5.00617			−0.539830
$87$	3.22153	+	5.57985i	0.345384	+	0.598223i
$88$	1.25936	−	2.18128i	0.134248	−	0.232525i
$89$	3.17574	−	5.50054i	0.336628	−	0.583056i	−0.647168	−	0.762347i	$-0.724047\pi$
$89$	3.17574	−	5.50054i	0.336628	−	0.583056i	0.983796	+	0.179291i	$0.0573802\pi$
$90$	−3.09417			−0.326154
$91$	2.10803	+	1.18486i	0.220981	+	0.124207i
$92$	−10.2515			−1.06879
$93$	1.91169	−	3.31114i	0.198233	−	0.343350i
$94$	0.754128	−	1.30619i	0.0777823	−	0.134723i
$95$	−5.10895	−	8.84897i	−0.524168	−	0.907885i
$96$	−5.85162			−0.597228
$97$	−6.76467	−	11.7168i	−0.686849	−	1.18966i	−0.972852	−	0.231428i	$-0.925660\pi$
$97$	−6.76467	−	11.7168i	−0.686849	−	1.18966i	0.286003	−	0.958229i	$-0.407673\pi$
$98$	−2.37417	−	4.11219i	−0.239828	−	0.415394i
$99$	−1.00000			−0.100504
$100$	9.74521	+	16.8792i	0.974521	+	1.68792i
$101$	5.91563	−	10.2462i	0.588628	−	1.01953i	−0.405785	−	0.913969i	$-0.633002\pi$
$101$	5.91563	−	10.2462i	0.588628	−	1.01953i	0.994412	−	0.105564i	$-0.0336649\pi$
$102$	1.57474	−	2.72752i	0.155922	−	0.270065i
$103$	−11.5505			−1.13811			−0.569054	−	0.822300i	$-0.692691\pi$
$103$	−11.5505			−1.13811			−0.569054	+	0.822300i	$0.692691\pi$
$104$	−7.81181	+	4.63111i	−0.766011	+	0.454118i
$105$	2.86269			0.279370
$106$	−2.10494	+	3.64586i	−0.204450	+	0.354118i
$107$	−0.360546	+	0.624484i	−0.0348553	+	0.0603711i	−0.882927	−	0.469511i	$-0.844430\pi$
$107$	−0.360546	+	0.624484i	−0.0348553	+	0.0603711i	0.848072	+	0.529882i	$0.177764\pi$
$108$	0.737247	+	1.27695i	0.0709416	+	0.122874i
$109$	−0.668198			−0.0640017			−0.0320009	−	0.999488i	$-0.510188\pi$
$109$	−0.668198			−0.0640017			−0.0320009	+	0.999488i	$0.510188\pi$
$110$	−1.54708	−	2.67963i	−0.147509	−	0.255492i
$111$	2.73904	+	4.74415i	0.259978	+	0.450295i
$112$	0.753261			0.0711765
$113$	9.83916	+	17.0419i	0.925590	+	1.60317i	0.790609	+	0.612321i	$0.209764\pi$
$113$	9.83916	+	17.0419i	0.925590	+	1.60317i	0.134981	+	0.990848i	$0.456903\pi$
$114$	0.867693	−	1.50289i	0.0812669	−	0.140758i
$115$	−14.8378	+	25.6999i	−1.38363	+	2.39652i
$116$	9.50024			0.882075
$117$	3.14309	+	1.76664i	0.290578	+	0.163326i
$118$	6.73788			0.620272
$119$	−1.45693	+	2.52348i	−0.133557	+	0.231327i
$120$	−5.37533	+	9.31035i	−0.490699	+	0.849915i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.993563			0.0899530
$123$	−6.32123	−	10.9487i	−0.569966	−	0.987211i
$124$	−2.81877	−	4.88226i	−0.253133	−	0.438440i
$125$	35.0785			3.13752
$126$	0.243097	+	0.421056i	0.0216568	+	0.0375106i
$127$	−2.25172	+	3.90010i	−0.199808	+	0.346078i	−0.948466	−	0.316879i	$-0.897365\pi$
$127$	−2.25172	+	3.90010i	−0.199808	+	0.346078i	0.748658	+	0.662956i	$0.230699\pi$
$128$	−5.12825	+	8.88240i	−0.453278	+	0.785100i
$129$	6.90585			0.608026
$130$	0.128689	+	11.1554i	0.0112868	+	0.978397i
$131$	6.01268			0.525331			0.262665	−	0.964887i	$-0.415398\pi$
$131$	6.01268			0.525331			0.262665	+	0.964887i	$0.415398\pi$
$132$	−0.737247	+	1.27695i	−0.0641691	+	0.111144i
$133$	−0.802781	+	1.39046i	−0.0696099	+	0.120568i
$134$	3.13357	+	5.42751i	0.270700	+	0.468865i
$135$	4.26830			0.367357
$136$	−5.47141	−	9.47677i	−0.469170	−	0.812626i
$137$	−0.775477	−	1.34317i	−0.0662535	−	0.114754i	0.830996	−	0.556279i	$-0.187771\pi$
$137$	−0.775477	−	1.34317i	−0.0662535	−	0.114754i	−0.897249	+	0.441524i	$0.854438\pi$
$138$	−5.04004			−0.429037
$139$	−7.87909	−	13.6470i	−0.668296	−	1.15752i	−0.978380	−	0.206813i	$-0.933691\pi$
$139$	−7.87909	−	13.6470i	−0.668296	−	1.15752i	0.310085	−	0.950709i	$-0.399643\pi$
$140$	2.11051	−	3.65551i	0.178371	−	0.308947i
$141$	−1.04029	+	1.80184i	−0.0876085	+	0.151742i
$142$	−6.92173			−0.580859
$143$	0.0415910	+	3.60531i	0.00347801	+	0.301491i
$144$	1.12312			0.0935932
$145$	13.7504	−	23.8165i	1.14191	−	1.97785i
$146$	2.23010	−	3.86265i	0.184564	−	0.319675i
$147$	3.27509	+	5.67262i	0.270125	+	0.467870i
$148$	8.07738			0.663957
$149$	−2.73028	−	4.72898i	−0.223673	−	0.387413i	0.732247	−	0.681039i	$-0.238472\pi$
$149$	−2.73028	−	4.72898i	−0.223673	−	0.387413i	−0.955921	+	0.293625i	$0.905138\pi$
$150$	4.79112	+	8.29847i	0.391193	+	0.677567i
$151$	6.24498			0.508209			0.254105	−	0.967177i	$-0.418219\pi$
$151$	6.24498			0.508209			0.254105	+	0.967177i	$0.418219\pi$
$152$	−3.01479	−	5.22178i	−0.244532	−	0.423542i
$153$	−2.17230	+	3.76253i	−0.175620	+	0.304182i
$154$	−0.243097	+	0.421056i	−0.0195893	+	0.0339296i
$155$	−16.3193			−1.31080
$156$	4.57314	−	2.71111i	0.366144	−	0.217063i
$157$	10.9923			0.877282			0.438641	−	0.898662i	$-0.355460\pi$
$157$	10.9923			0.877282			0.438641	+	0.898662i	$0.355460\pi$
$158$	1.15836	−	2.00634i	0.0921540	−	0.159615i
$159$	2.90369	−	5.02934i	0.230278	−	0.398853i
$160$	12.4882	+	21.6302i	0.987281	+	1.71002i
$161$	4.66300			0.367496
$162$	0.362459	+	0.627798i	0.0284775	+	0.0493244i
$163$	−0.345935	−	0.599177i	−0.0270957	−	0.0469312i	0.852160	−	0.523282i	$-0.175293\pi$
$163$	−0.345935	−	0.599177i	−0.0270957	−	0.0469312i	−0.879255	+	0.476351i	$0.841959\pi$
$164$	−18.6412			−1.45564
$165$	2.13415	+	3.69646i	0.166143	+	0.287769i
$166$	−5.25481	+	9.10160i	−0.407852	+	0.706421i
$167$	1.74212	−	3.01745i	0.134810	−	0.233497i	−0.790715	−	0.612184i	$-0.790291\pi$
$167$	1.74212	−	3.01745i	0.134810	−	0.233497i	0.925525	+	0.378687i	$0.123624\pi$
$168$	1.68928			0.130330
$169$	6.23855	−	11.4053i	0.479889	−	0.877329i
$170$	−13.4429			−1.03102
$171$	−1.19695	+	2.07318i	−0.0915333	+	0.158540i
$172$	5.09131	−	8.81841i	0.388209	−	0.672398i
$173$	1.52497	+	2.64132i	0.115941	+	0.200816i	0.918156	−	0.396220i	$-0.129678\pi$
$173$	1.52497	+	2.64132i	0.115941	+	0.200816i	−0.802214	+	0.597036i	$0.796345\pi$
$174$	4.67069			0.354084
$175$	−4.43270	−	7.67766i	−0.335080	−	0.580376i
$176$	0.561559	+	0.972649i	0.0423291	+	0.0733162i
$177$	−9.29467			−0.698630
$178$	−2.30215	−	3.98744i	−0.172554	−	0.298872i
$179$	3.91218	−	6.77610i	0.292410	−	0.506469i	−0.681969	−	0.731381i	$-0.738876\pi$
$179$	3.91218	−	6.77610i	0.292410	−	0.506469i	0.974379	+	0.224912i	$0.0722094\pi$
$180$	3.14679	−	5.45040i	0.234548	−	0.406249i
$181$	−10.0205			−0.744816			−0.372408	−	0.928069i	$-0.621468\pi$
$181$	−10.0205			−0.744816			−0.372408	+	0.928069i	$0.621468\pi$
$182$	1.50793	−	0.893951i	0.111775	−	0.0662641i
$183$	−1.37059			−0.101317
$184$	−8.75580	+	15.1655i	−0.645486	+	1.11801i
$185$	11.6910	−	20.2495i	0.859541	−	1.48877i
$186$	−1.38582	−	2.40031i	−0.101613	−	0.175999i
$187$	−4.34459			−0.317708
$188$	1.53391	+	2.65680i	0.111872	+	0.193767i
$189$	−0.335344	−	0.580832i	−0.0243927	−	0.0422493i
$190$	−7.40715			−0.537371
$191$	2.73997	+	4.74577i	0.198257	+	0.343392i	0.947963	−	0.318379i	$-0.103139\pi$
$191$	2.73997	+	4.74577i	0.198257	+	0.343392i	−0.749706	+	0.661771i	$0.769805\pi$
$192$	−0.997853	+	1.72833i	−0.0720139	+	0.124732i
$193$	3.58122	−	6.20285i	0.257782	−	0.446491i	−0.707866	−	0.706347i	$-0.750342\pi$
$193$	3.58122	−	6.20285i	0.257782	−	0.446491i	0.965647	+	0.259856i	$0.0836752\pi$
$194$	−9.80767			−0.704150
$195$	−0.177523	−	15.3885i	−0.0127127	−	1.10200i
$196$	9.65820			0.689871
$197$	−3.20161	+	5.54535i	−0.228105	+	0.395090i	−0.957247	−	0.289273i	$-0.906586\pi$
$197$	−3.20161	+	5.54535i	−0.228105	+	0.395090i	0.729141	+	0.684363i	$0.239920\pi$
$198$	−0.362459	+	0.627798i	−0.0257588	+	0.0446156i
$199$	0.199228	+	0.345073i	0.0141229	+	0.0244616i	0.873000	−	0.487719i	$-0.162171\pi$
$199$	0.199228	+	0.345073i	0.0141229	+	0.0244616i	−0.858878	+	0.512181i	$0.828838\pi$
$200$	33.2934			2.35420
$201$	−4.32266	−	7.48706i	−0.304897	−	0.528097i
$202$	−4.28835	−	7.42764i	−0.301727	−	0.522607i
$203$	−4.32127			−0.303294
$204$	3.20304	+	5.54782i	0.224257	+	0.388425i
$205$	−26.9809	+	46.7323i	−1.88443	+	3.26393i
$206$	−4.18660	+	7.25140i	−0.291694	+	0.505229i
$207$	6.95257			0.483237
$208$	−0.0467116	−	4.04919i	−0.00323887	−	0.280761i
$209$	−2.39391			−0.165590
$210$	1.03761	−	1.79719i	0.0716018	−	0.124018i
$211$	1.87345	−	3.24491i	0.128974	−	0.223389i	−0.794306	−	0.607518i	$-0.792165\pi$
$211$	1.87345	−	3.24491i	0.128974	−	0.223389i	0.923279	+	0.384130i	$0.125498\pi$
$212$	−4.28148	−	7.41574i	−0.294053	−	0.509315i
$213$	9.54830			0.654239
$214$	0.261366	+	0.452700i	0.0178666	+	0.0309459i
$215$	−14.7381	−	25.5272i	−1.00513	−	1.74094i
$216$	2.51872			0.171377
$217$	1.28215	+	2.22074i	0.0870377	+	0.150754i
$218$	−0.242194	+	0.419493i	−0.0164035	+	0.0284117i
$219$	−3.07635	+	5.32839i	−0.207880	+	0.360059i
$220$	6.29358			0.424313
$221$	13.6554	+	7.67532i	0.918564	+	0.516298i
$222$	3.97116			0.266526
$223$	10.8460	−	18.7857i	0.726299	−	1.25799i	−0.232139	−	0.972683i	$-0.574572\pi$
$223$	10.8460	−	18.7857i	0.726299	−	1.25799i	0.958437	−	0.285303i	$-0.0920943\pi$
$224$	1.96230	−	3.39881i	0.131112	−	0.227092i
$225$	−6.60919	−	11.4475i	−0.440613	−	0.763163i
$226$	14.2652			0.948905
$227$	6.86386	+	11.8886i	0.455570	+	0.789071i	0.998721	−	0.0505643i	$-0.0161020\pi$
$227$	6.86386	+	11.8886i	0.455570	+	0.789071i	−0.543150	+	0.839635i	$0.682769\pi$
$228$	1.76490	+	3.05690i	0.116883	+	0.202448i
$229$	−11.2094			−0.740735			−0.370367	−	0.928885i	$-0.620768\pi$
$229$	−11.2094			−0.740735			−0.370367	+	0.928885i	$0.620768\pi$
$230$	10.7562	+	18.6303i	0.709243	+	1.22845i
$231$	0.335344	−	0.580832i	0.0220640	−	0.0382159i
$232$	8.11414	−	14.0541i	0.532719	−	0.922697i
$233$	−13.8831			−0.909509			−0.454755	−	0.890617i	$-0.650273\pi$
$233$	−13.8831			−0.909509			−0.454755	+	0.890617i	$0.650273\pi$
$234$	2.24833	−	1.33289i	0.146978	−	0.0871337i
$235$	8.88057			0.579304
$236$	−6.85247	+	11.8688i	−0.446058	+	0.772594i
$237$	−1.59792	+	2.76767i	−0.103796	+	0.179780i
$238$	1.05616	+	1.82932i	0.0684604	+	0.118577i
$239$	23.2323			1.50277			0.751387	−	0.659862i	$-0.229385\pi$
$239$	23.2323			1.50277			0.751387	+	0.659862i	$0.229385\pi$
$240$	−2.39690	−	4.15156i	−0.154719	−	0.267982i
$241$	7.42015	+	12.8521i	0.477974	+	0.827875i	0.999681	−	0.0252497i	$-0.00803810\pi$
$241$	7.42015	+	12.8521i	0.477974	+	0.827875i	−0.521708	+	0.853124i	$0.674705\pi$
$242$	−0.724918			−0.0465995
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.01046	+	1.75017i	−0.0646881	+	0.112043i
$245$	13.9791	−	24.2124i	0.893089	−	1.54688i
$246$	−9.16475			−0.584323
$247$	7.52426	+	4.22916i	0.478757	+	0.269095i
$248$	−9.63004			−0.611508
$249$	7.24883	−	12.5553i	0.459376	−	0.795663i
$250$	12.7145	−	22.0222i	0.804137	−	1.39281i
$251$	12.7295	+	22.0482i	0.803481	+	1.39167i	0.917312	+	0.398170i	$0.130355\pi$
$251$	12.7295	+	22.0482i	0.803481	+	1.39167i	−0.113830	+	0.993500i	$0.536312\pi$
$252$	−0.988924			−0.0622963
$253$	3.47628	+	6.02110i	0.218552	+	0.378543i
$254$	1.63231	+	2.82725i	0.102421	+	0.177398i
$255$	18.5440			1.16127
$256$	5.71327	+	9.89568i	0.357079	+	0.618480i
$257$	−14.6688	+	25.4071i	−0.915014	+	1.58485i	−0.108132	+	0.994137i	$0.534487\pi$
$257$	−14.6688	+	25.4071i	−0.915014	+	1.58485i	−0.806881	+	0.590714i	$0.798846\pi$
$258$	2.50309	−	4.33547i	0.155835	−	0.269915i
$259$	−3.67407			−0.228296
$260$	−19.7813	−	11.1185i	−1.22678	−	0.689538i
$261$	−6.44305			−0.398815
$262$	2.17935	−	3.77475i	0.134641	−	0.233205i
$263$	−5.94171	+	10.2913i	−0.366381	+	0.634591i	−0.988997	−	0.147937i	$-0.952737\pi$
$263$	−5.94171	+	10.2913i	−0.366381	+	0.634591i	0.622615	+	0.782528i	$0.286070\pi$
$264$	1.25936	+	2.18128i	0.0775084	+	0.134248i
$265$	−24.7877			−1.52269
$266$	0.581951	+	1.00797i	0.0356817	+	0.0618025i
$267$	3.17574	+	5.50054i	0.194352	+	0.336628i
$268$	−12.7475			−0.778675
$269$	10.5231	+	18.2265i	0.641602	+	1.11129i	0.985075	+	0.172125i	$0.0550632\pi$
$269$	10.5231	+	18.2265i	0.641602	+	1.11129i	−0.343473	+	0.939163i	$0.611603\pi$
$270$	1.54708	−	2.67963i	0.0941525	−	0.163077i
$271$	−13.4096	+	23.2261i	−0.814575	+	1.41089i	0.0950570	+	0.995472i	$0.469697\pi$
$271$	−13.4096	+	23.2261i	−0.814575	+	1.41089i	−0.909632	+	0.415414i	$0.863637\pi$
$272$	4.87949			0.295863
$273$	−2.08013	+	1.23318i	−0.125895	+	0.0746352i
$274$	−1.12431			−0.0679223
$275$	6.60919	−	11.4475i	0.398549	−	0.690307i
$276$	5.12576	−	8.87807i	0.308534	−	0.534397i
$277$	6.36322	+	11.0214i	0.382329	+	0.662213i	0.991395	−	0.130907i	$-0.0417888\pi$
$277$	6.36322	+	11.0214i	0.382329	+	0.662213i	−0.609066	+	0.793120i	$0.708456\pi$
$278$	−11.4234			−0.685129
$279$	1.91169	+	3.31114i	0.114450	+	0.198233i
$280$	−3.60517	−	6.24433i	−0.215450	−	0.373170i
$281$	31.2130			1.86201			0.931007	−	0.365002i	$-0.118932\pi$
$281$	31.2130			1.86201			0.931007	+	0.365002i	$0.118932\pi$
$282$	0.754128	+	1.30619i	0.0449076	+	0.0777823i
$283$	1.48058	−	2.56443i	0.0880112	−	0.152440i	−0.818659	−	0.574280i	$-0.805282\pi$
$283$	1.48058	−	2.56443i	0.0880112	−	0.152440i	0.906670	+	0.421840i	$0.138616\pi$
$284$	7.03945	−	12.1927i	0.417715	−	0.723503i
$285$	10.2179			0.605257
$286$	2.27848	+	1.28067i	0.134729	+	0.0757274i
$287$	8.47914			0.500508
$288$	2.92581	−	5.06765i	0.172405	−	0.298614i
$289$	−0.937741	+	1.62422i	−0.0551613	+	0.0955421i
$290$	−9.96794	−	17.2650i	−0.585338	−	1.01383i
$291$	13.5293			0.793104
$292$	4.53605	+	7.85667i	0.265452	+	0.459777i
$293$	2.06057	+	3.56902i	0.120380	+	0.208504i	0.919918	−	0.392112i	$-0.128255\pi$
$293$	2.06057	+	3.56902i	0.120380	+	0.208504i	−0.799538	+	0.600616i	$0.794922\pi$
$294$	4.74834			0.276929
$295$	19.8362	+	34.3573i	1.15491	+	2.00036i
$296$	6.89888	−	11.9492i	0.400989	−	0.694533i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−3.95846			−0.229307
$299$	−0.289164	−	25.0662i	−0.0167228	−	1.44961i
$300$	−19.4904			−1.12528
$301$	−2.31583	+	4.01114i	−0.133482	+	0.231198i
$302$	2.26355	−	3.92058i	0.130253	−	0.225604i
$303$	5.91563	+	10.2462i	0.339844	+	0.588628i
$304$	2.68864			0.154204
$305$	2.92504	+	5.06631i	0.167487	+	0.290096i
$306$	1.57474	+	2.72752i	0.0900217	+	0.155922i
$307$	−27.6347			−1.57720			−0.788598	−	0.614909i	$-0.789193\pi$
$307$	−27.6347			−1.57720			−0.788598	+	0.614909i	$0.789193\pi$
$308$	−0.494462	−	0.856433i	−0.0281746	−	0.0487998i
$309$	5.77527	−	10.0031i	0.328544	−	0.569054i
$310$	−5.91509	+	10.2452i	−0.335954	+	0.581890i
$311$	15.9244			0.902992			0.451496	−	0.892273i	$-0.350891\pi$
$311$	15.9244			0.902992			0.451496	+	0.892273i	$0.350891\pi$
$312$	−0.104756	−	9.08078i	−0.00593065	−	0.514098i
$313$	−12.6968			−0.717666			−0.358833	−	0.933402i	$-0.616825\pi$
$313$	−12.6968			−0.717666			−0.358833	+	0.933402i	$0.616825\pi$
$314$	3.98426	−	6.90095i	0.224845	−	0.389443i
$315$	−1.43135	+	2.47916i	−0.0806472	+	0.139685i
$316$	2.35612	+	4.08091i	0.132542	+	0.229569i
$317$	−10.4373			−0.586215			−0.293107	−	0.956080i	$-0.594689\pi$
$317$	−10.4373			−0.586215			−0.293107	+	0.956080i	$0.594689\pi$
$318$	−2.10494	−	3.64586i	−0.118039	−	0.204450i
$319$	−3.22153	−	5.57985i	−0.180371	−	0.312412i
$320$	8.51827			0.476186
$321$	−0.360546	−	0.624484i	−0.0201237	−	0.0348553i
$322$	1.69015	−	2.92742i	0.0941881	−	0.163139i
$323$	−5.20027	+	9.00714i	−0.289351	+	0.501171i
$324$	−1.47449			−0.0819163
$325$	−40.9967	+	24.3043i	−2.27409	+	1.34816i
$326$	−0.501549			−0.0277783
$327$	0.334099	−	0.578676i	0.0184757	−	0.0320009i
$328$	−15.9214	+	27.5767i	−0.879114	+	1.52267i
$329$	−0.697711	−	1.20847i	−0.0384661	−	0.0666252i
$330$	3.09417			0.170328
$331$	3.04472	+	5.27361i	0.167353	+	0.289864i	0.937488	−	0.348016i	$-0.113145\pi$
$331$	3.04472	+	5.27361i	0.167353	+	0.289864i	−0.770135	+	0.637881i	$0.779811\pi$
$332$	−10.6884	−	18.5128i	−0.586600	−	1.01602i
$333$	−5.47807			−0.300197
$334$	−1.26290	−	2.18740i	−0.0691027	−	0.119689i
$335$	−18.4504	+	31.9570i	−1.00805	+	1.74600i
$336$	−0.376630	+	0.652343i	−0.0205469	+	0.0355882i
$337$	1.87647			0.102218			0.0511089	−	0.998693i	$-0.483724\pi$
$337$	1.87647			0.102218			0.0511089	+	0.998693i	$0.483724\pi$
$338$	−4.89899	−	8.05050i	−0.266470	−	0.437889i
$339$	−19.6783			−1.06878
$340$	13.6715	−	23.6798i	0.741442	−	1.28422i
$341$	−1.91169	+	3.31114i	−0.103524	+	0.179308i
$342$	0.867693	+	1.50289i	0.0469195	+	0.0812669i
$343$	−9.08793			−0.490702
$344$	−8.69696	−	15.0636i	−0.468909	−	0.812174i
$345$	−14.8378	−	25.6999i	−0.798841	−	1.38363i
$346$	2.21096			0.118862
$347$	−4.22162	−	7.31207i	−0.226629	−	0.392532i	0.730178	−	0.683257i	$-0.239437\pi$
$347$	−4.22162	−	7.31207i	−0.226629	−	0.392532i	−0.956807	+	0.290724i	$0.906104\pi$
$348$	−4.75012	+	8.22745i	−0.254633	+	0.441038i
$349$	−8.96080	+	15.5206i	−0.479660	+	0.830796i	−0.999728	−	0.0233289i	$-0.992573\pi$
$349$	−8.96080	+	15.5206i	−0.479660	+	0.830796i	0.520067	+	0.854125i	$0.325907\pi$
$350$	−6.42669			−0.343521
$351$	−3.10150	+	1.83867i	−0.165546	+	0.0981412i
$352$	5.85162			0.311892
$353$	−9.65399	+	16.7212i	−0.513830	+	0.889980i	0.486041	+	0.873936i	$0.338440\pi$
$353$	−9.65399	+	16.7212i	−0.513830	+	0.889980i	−0.999871	+	0.0160438i	$0.994893\pi$
$354$	−3.36894	+	5.83517i	−0.179057	+	0.310136i
$355$	−20.3775	−	35.2949i	−1.08153	−	1.87326i
$356$	9.36522			0.496356
$357$	−1.45693	−	2.52348i	−0.0771090	−	0.133557i
$358$	−2.83601	−	4.91212i	−0.149888	−	0.259613i
$359$	19.0522			1.00554			0.502768	−	0.864421i	$-0.332315\pi$
$359$	19.0522			1.00554			0.502768	+	0.864421i	$0.332315\pi$
$360$	−5.37533	−	9.31035i	−0.283305	−	0.490699i
$361$	6.63461	−	11.4915i	0.349190	−	0.604814i
$362$	−3.63201	+	6.29083i	−0.190894	+	0.330639i
$363$	1.00000			0.0524864
$364$	0.0411303	+	3.56538i	0.00215581	+	0.186877i
$365$	26.2615			1.37459
$366$	−0.496782	+	0.860451i	−0.0259672	+	0.0449765i
$367$	5.19793	−	9.00307i	0.271330	−	0.469957i	−0.697873	−	0.716222i	$-0.745870\pi$
$367$	5.19793	−	9.00307i	0.271330	−	0.469957i	0.969203	+	0.246265i	$0.0792034\pi$
$368$	−3.90428	−	6.76241i	−0.203525	−	0.352515i
$369$	12.6425			0.658140
$370$	−8.47504	−	14.6792i	−0.440596	−	0.763135i
$371$	1.94747	+	3.37312i	0.101108	+	0.175123i
$372$	5.63755			0.292293
$373$	3.93273	+	6.81168i	0.203629	+	0.352696i	0.949695	−	0.313176i	$-0.101393\pi$
$373$	3.93273	+	6.81168i	0.203629	+	0.352696i	−0.746066	+	0.665872i	$0.768060\pi$
$374$	−1.57474	+	2.72752i	−0.0814277	+	0.141037i
$375$	−17.5392	+	30.3789i	−0.905723	+	1.56876i
$376$	5.24042			0.270254
$377$	0.267973	+	23.2292i	0.0138013	+	1.19637i
$378$	−0.486193			−0.0250071
$379$	−3.13948	+	5.43774i	−0.161264	+	0.279318i	−0.935322	−	0.353797i	$-0.884890\pi$
$379$	−3.13948	+	5.43774i	−0.161264	+	0.279318i	0.774058	+	0.633115i	$0.218224\pi$
$380$	7.53312	−	13.0477i	0.386441	−	0.669335i
$381$	−2.25172	−	3.90010i	−0.115359	−	0.199808i
$382$	3.97251			0.203251
$383$	−12.0950	−	20.9491i	−0.618025	−	1.07045i	−0.989846	−	0.142146i	$-0.954600\pi$
$383$	−12.0950	−	20.9491i	−0.618025	−	1.07045i	0.371821	−	0.928304i	$-0.378733\pi$
$384$	−5.12825	−	8.88240i	−0.261700	−	0.453278i
$385$	−2.86269			−0.145896
$386$	−2.59609	−	4.49656i	−0.132137	−	0.228869i
$387$	−3.45292	+	5.98064i	−0.175522	+	0.304013i
$388$	9.97447	−	17.2763i	0.506377	−	0.877071i
$389$	−15.3139			−0.776447			−0.388223	−	0.921565i	$-0.626911\pi$
$389$	−15.3139			−0.776447			−0.388223	+	0.921565i	$0.626911\pi$
$390$	−9.72524	−	5.46627i	−0.492457	−	0.276795i
$391$	30.2061			1.52759
$392$	8.24905	−	14.2878i	0.416640	−	0.721641i
$393$	−3.00634	+	5.20714i	−0.151650	+	0.262665i
$394$	2.32091	+	4.01993i	0.116926	+	0.202521i
$395$	13.6408			0.686341
$396$	−0.737247	−	1.27695i	−0.0370480	−	0.0641691i
$397$	1.19169	+	2.06406i	0.0598091	+	0.103592i	0.894380	−	0.447309i	$-0.147617\pi$
$397$	1.19169	+	2.06406i	0.0598091	+	0.103592i	−0.834571	+	0.550901i	$0.814284\pi$
$398$	0.288848			0.0144786
$399$	−0.802781	−	1.39046i	−0.0401893	−	0.0696099i
$400$	−7.42290	+	12.8568i	−0.371145	+	0.642842i
$401$	2.90058	−	5.02394i	0.144848	−	0.250884i	−0.784468	−	0.620169i	$-0.787064\pi$
$401$	2.90058	−	5.02394i	0.144848	−	0.250884i	0.929316	+	0.369285i	$0.120397\pi$
$402$	−6.26715			−0.312577
$403$	11.8582	−	7.02995i	0.590699	−	0.350187i
$404$	17.4451			0.867928
$405$	−2.13415	+	3.69646i	−0.106047	+	0.183678i
$406$	−1.56628	+	2.71288i	−0.0777334	+	0.134638i
$407$	−2.73904	−	4.74415i	−0.135769	−	0.235159i
$408$	10.9428			0.541751
$409$	3.62674	+	6.28169i	0.179331	+	0.310610i	0.941651	−	0.336590i	$-0.109273\pi$
$409$	3.62674	+	6.28169i	0.179331	+	0.310610i	−0.762321	+	0.647199i	$0.775940\pi$
$410$	19.5590	+	33.8771i	0.965948	+	1.67307i
$411$	1.55095			0.0765029
$412$	−8.51560	−	14.7494i	−0.419533	−	0.726653i
$413$	3.11691	−	5.39864i	0.153373	−	0.265650i
$414$	2.52002	−	4.36480i	0.123852	−	0.214518i
$415$	−61.8804			−3.03759
$416$	−18.3921	−	10.3377i	−0.901749	−	0.506847i
$417$	15.7582			0.771681
$418$	−0.867693	+	1.50289i	−0.0424403	+	0.0735087i
$419$	−6.17895	+	10.7023i	−0.301862	+	0.522839i	−0.976558	−	0.215256i	$-0.930941\pi$
$419$	−6.17895	+	10.7023i	−0.301862	+	0.522839i	0.674696	+	0.738096i	$0.264275\pi$
$420$	2.11051	+	3.65551i	0.102982	+	0.178371i
$421$	26.9942			1.31562			0.657808	−	0.753186i	$-0.271484\pi$
$421$	26.9942			1.31562			0.657808	+	0.753186i	$0.271484\pi$
$422$	−1.35810	−	2.35230i	−0.0661112	−	0.114508i
$423$	−1.04029	−	1.80184i	−0.0505808	−	0.0876085i
$424$	−14.6272			−0.710360
$425$	−28.7142	−	49.7345i	−1.39284	−	2.41248i
$426$	3.46087	−	5.99440i	0.167680	−	0.290430i
$427$	0.459617	−	0.796081i	0.0222424	−	0.0385250i
$428$	−1.06325			−0.0513939
$429$	−3.14309	−	1.76664i	−0.151750	−	0.0852940i
$430$	−21.3679			−1.03045
$431$	−17.7613	+	30.7635i	−0.855533	+	1.48183i	0.0206176	+	0.999787i	$0.493437\pi$
$431$	−17.7613	+	30.7635i	−0.855533	+	1.48183i	−0.876150	+	0.482038i	$0.839897\pi$
$432$	−0.561559	+	0.972649i	−0.0270180	+	0.0467966i
$433$	6.29090	+	10.8962i	0.302321	+	0.523636i	0.976661	−	0.214785i	$-0.0689051\pi$
$433$	6.29090	+	10.8962i	0.302321	+	0.523636i	−0.674340	+	0.738421i	$0.735572\pi$
$434$	1.85890			0.0892301
$435$	13.7504	+	23.8165i	0.659283	+	1.14191i
$436$	−0.492627	−	0.853255i	−0.0235925	−	0.0408635i
$437$	16.6438			0.796181
$438$	2.23010	+	3.86265i	0.106558	+	0.184564i
$439$	−13.0381	+	22.5826i	−0.622273	+	1.07781i	0.366788	+	0.930304i	$0.380457\pi$
$439$	−13.0381	+	22.5826i	−0.622273	+	1.07781i	−0.989061	+	0.147504i	$0.952876\pi$
$440$	5.37533	−	9.31035i	0.256259	−	0.443854i
$441$	−6.55018			−0.311913
$442$	9.76808	−	5.79086i	0.464620	−	0.275443i
$443$	−4.04854			−0.192352			−0.0961759	−	0.995364i	$-0.530661\pi$
$443$	−4.04854			−0.192352			−0.0961759	+	0.995364i	$0.530661\pi$
$444$	−4.03869	+	6.99522i	−0.191668	+	0.331978i
$445$	13.5550	−	23.4780i	0.642569	−	1.11296i
$446$	−7.86243	−	13.6181i	−0.372297	−	0.644837i
$447$	5.46056			0.258276
$448$	−0.669247	−	1.15917i	−0.0316190	−	0.0547656i
$449$	−1.85889	−	3.21969i	−0.0877265	−	0.151947i	0.818823	−	0.574046i	$-0.194627\pi$
$449$	−1.85889	−	3.21969i	−0.0877265	−	0.151947i	−0.906550	+	0.422099i	$0.861293\pi$
$450$	−9.58224			−0.451711
$451$	6.32123	+	10.9487i	0.297655	+	0.515554i
$452$	−14.5078	+	25.1282i	−0.682388	+	1.18193i
$453$	−3.12249	+	5.40831i	−0.146707	+	0.254105i
$454$	9.95148			0.467046
$455$	8.99769	+	5.05734i	0.421818	+	0.237092i
$456$	6.02959			0.282361
$457$	1.33495	−	2.31220i	0.0624462	−	0.108160i	−0.833112	−	0.553104i	$-0.813443\pi$
$457$	1.33495	−	2.31220i	0.0624462	−	0.108160i	0.895558	+	0.444944i	$0.146776\pi$
$458$	−4.06293	+	7.03720i	−0.189848	+	0.328827i
$459$	−2.17230	−	3.76253i	−0.101394	−	0.175620i
$460$	−43.7565			−2.04016
$461$	−10.2521	−	17.7572i	−0.477489	−	0.827035i	0.522178	−	0.852836i	$-0.325120\pi$
$461$	−10.2521	−	17.7572i	−0.477489	−	0.827035i	−0.999667	+	0.0258016i	$0.991786\pi$
$462$	−0.243097	−	0.421056i	−0.0113099	−	0.0195893i
$463$	9.74000			0.452656			0.226328	−	0.974051i	$-0.427328\pi$
$463$	9.74000			0.452656			0.226328	+	0.974051i	$0.427328\pi$
$464$	3.61816	+	6.26683i	0.167969	+	0.290930i
$465$	8.15966	−	14.1330i	0.378395	−	0.655400i
$466$	−5.03204	+	8.71575i	−0.233105	+	0.403749i
$467$	36.3717			1.68308			0.841541	−	0.540193i	$-0.181649\pi$
$467$	36.3717			1.68308			0.841541	+	0.540193i	$0.181649\pi$
$468$	0.0613256	+	5.31601i	0.00283478	+	0.245733i
$469$	5.79830			0.267741
$470$	3.21884	−	5.57520i	0.148474	−	0.257165i
$471$	−5.49615	+	9.51962i	−0.253249	+	0.438641i
$472$	11.7054	+	20.2743i	0.538783	+	0.933199i
$473$	−6.90585			−0.317531
$474$	1.15836	+	2.00634i	0.0532052	+	0.0921540i
$475$	−15.8218	−	27.4041i	−0.725953	−	1.25739i
$476$	−4.29647			−0.196928
$477$	2.90369	+	5.02934i	0.132951	+	0.230278i
$478$	8.42077	−	14.5852i	0.385157	−	0.667111i
$479$	4.06283	−	7.03702i	0.185635	−	0.321530i	−0.758155	−	0.652074i	$-0.773899\pi$
$479$	4.06283	−	7.03702i	0.185635	−	0.321530i	0.943790	+	0.330545i	$0.107232\pi$
$480$	−24.9764			−1.14001
$481$	0.227838	+	19.7502i	0.0103885	+	0.900530i
$482$	10.7580			0.490013
$483$	−2.33150	+	4.03827i	−0.106087	+	0.183748i
$484$	0.737247	−	1.27695i	0.0335112	−	0.0580431i
$485$	−28.8737	−	50.0106i	−1.31108	−	2.27087i
$486$	−0.724918			−0.0328830
$487$	−17.0478	−	29.5276i	−0.772509	−	1.33802i	−0.936184	−	0.351510i	$-0.885668\pi$
$487$	−17.0478	−	29.5276i	−0.772509	−	1.33802i	0.163675	−	0.986514i	$-0.447665\pi$
$488$	1.72606	+	2.98963i	0.0781353	+	0.135334i
$489$	0.691870			0.0312875
$490$	−10.1337	−	17.5520i	−0.457793	−	0.792920i
$491$	15.9698	−	27.6605i	0.720708	−	1.24830i	−0.240009	−	0.970771i	$-0.577150\pi$
$491$	15.9698	−	27.6605i	0.720708	−	1.24830i	0.960716	−	0.277532i	$-0.0895164\pi$
$492$	9.32062	−	16.1438i	0.420206	−	0.727818i
$493$	−27.9924			−1.26072
$494$	5.38229	−	3.19081i	0.242161	−	0.143561i
$495$	−4.26830			−0.191846
$496$	2.14705	−	3.71881i	0.0964056	−	0.166979i
$497$	−3.20196	+	5.54596i	−0.143628	+	0.248770i
$498$	−5.25481	−	9.10160i	−0.235474	−	0.407852i
$499$	−17.9024			−0.801423			−0.400711	−	0.916204i	$-0.631237\pi$
$499$	−17.9024			−0.801423			−0.400711	+	0.916204i	$0.631237\pi$
$500$	25.8615	+	44.7934i	1.15656	+	2.00322i
$501$	1.74212	+	3.01745i	0.0778324	+	0.134810i
$502$	18.4557			0.823720
$503$	−4.78889	−	8.29460i	−0.213526	−	0.369838i	0.739290	−	0.673388i	$-0.235162\pi$
$503$	−4.78889	−	8.29460i	−0.213526	−	0.369838i	−0.952816	+	0.303550i	$0.901828\pi$
$504$	−0.844638	+	1.46296i	−0.0376232	+	0.0651652i
$505$	25.2497	−	43.7338i	1.12360	−	1.94613i
$506$	5.04004			0.224057
$507$	6.75799	+	11.1054i	0.300133	+	0.493207i
$508$	−6.64030			−0.294616
$509$	−14.1692	+	24.5418i	−0.628040	+	1.08780i	0.359904	+	0.932989i	$0.382809\pi$
$509$	−14.1692	+	24.5418i	−0.628040	+	1.08780i	−0.987944	+	0.154809i	$0.950524\pi$
$510$	6.72145	−	11.6419i	0.297631	−	0.515512i
$511$	−2.06327	−	3.57368i	−0.0912735	−	0.158090i
$512$	−12.2297			−0.540482
$513$	−1.19695	−	2.07318i	−0.0528468	−	0.0915333i
$514$	10.6337	+	18.4181i	0.469031	+	0.812386i
$515$	−49.3012			−2.17247
$516$	5.09131	+	8.81841i	0.224133	+	0.388209i
$517$	1.04029	−	1.80184i	0.0457521	−	0.0792449i
$518$	−1.33170	+	2.30657i	−0.0585116	+	0.101345i
$519$	−3.04994			−0.133877
$520$	−33.3431	+	19.7670i	−1.46219	+	0.866839i
$521$	−23.1345			−1.01354			−0.506770	−	0.862081i	$-0.669161\pi$
$521$	−23.1345			−1.01354			−0.506770	+	0.862081i	$0.669161\pi$
$522$	−2.33534	+	4.04493i	−0.102215	+	0.177042i
$523$	14.7850	−	25.6083i	0.646501	−	1.11977i	−0.337452	−	0.941343i	$-0.609565\pi$
$523$	14.7850	−	25.6083i	0.646501	−	1.11977i	0.983953	−	0.178430i	$-0.0571017\pi$
$524$	4.43283	+	7.67789i	0.193649	+	0.335410i
$525$	8.86539			0.386917
$526$	4.30725	+	7.46038i	0.187805	+	0.325288i
$527$	8.30551	+	14.3856i	0.361794	+	0.626645i
$528$	−1.12312			−0.0488775
$529$	−12.6691	−	21.9435i	−0.550830	−	0.954066i
$530$	−8.98451	+	15.5616i	−0.390262	+	0.675954i
$531$	4.64734	−	8.04942i	0.201677	−	0.349315i
$532$	−2.36739			−0.102639
$533$	−0.525812	−	45.5800i	−0.0227755	−	1.97429i
$534$	4.60430			0.199248
$535$	−1.53892	+	2.66548i	−0.0665332	+	0.115239i
$536$	−10.8876	+	18.8578i	−0.470272	+	0.814535i
$537$	3.91218	+	6.77610i	0.168823	+	0.292410i
$538$	15.2567			0.657763
$539$	−3.27509	−	5.67262i	−0.141068	−	0.244337i
$540$	3.14679	+	5.45040i	0.135416	+	0.234548i
$541$	23.5558			1.01274			0.506371	−	0.862316i	$-0.330987\pi$
$541$	23.5558			1.01274			0.506371	+	0.862316i	$0.330987\pi$
$542$	9.72087	+	16.8370i	0.417547	+	0.723213i
$543$	5.01023	−	8.67798i	0.215010	−	0.372408i
$544$	12.7114	−	22.0169i	0.544999	−	0.943965i
$545$	−2.85207			−0.122169
$546$	0.0202212	+	1.75288i	0.000865389	+	0.0750163i
$547$	35.6164			1.52285			0.761423	−	0.648255i	$-0.224501\pi$
$547$	35.6164			1.52285			0.761423	+	0.648255i	$0.224501\pi$
$548$	1.14344	−	1.98049i	0.0488452	−	0.0846023i
$549$	0.685293	−	1.18696i	0.0292476	−	0.0506583i
$550$	−4.79112	−	8.29847i	−0.204294	−	0.353848i
$551$	−15.4241			−0.657087
$552$	−8.75580	−	15.1655i	−0.372671	−	0.645486i
$553$	−1.07170	−	1.85624i	−0.0455734	−	0.0789354i
$554$	9.22563			0.391959
$555$	11.6910	+	20.2495i	0.496256	+	0.859541i
$556$	11.6177	−	20.1224i	0.492699	−	0.853379i
$557$	−6.67292	+	11.5578i	−0.282741	+	0.489721i	−0.972059	−	0.234738i	$-0.924577\pi$
$557$	−6.67292	+	11.5578i	−0.282741	+	0.489721i	0.689318	+	0.724459i	$0.257910\pi$
$558$	2.77164			0.117333
$559$	21.7057	+	12.2001i	0.918052	+	0.516010i
$560$	3.21514			0.135865
$561$	2.17230	−	3.76253i	0.0917144	−	0.158854i
$562$	11.3134	−	19.5955i	0.477229	−	0.826585i
$563$	16.8716	+	29.2225i	0.711055	+	1.23158i	0.964462	+	0.264223i	$0.0851155\pi$
$563$	16.8716	+	29.2225i	0.711055	+	1.23158i	−0.253407	+	0.967360i	$0.581551\pi$
$564$	−3.06781			−0.129178
$565$	41.9965	+	72.7400i	1.76681	+	3.06020i
$566$	−1.07330	−	1.85901i	−0.0451140	−	0.0781398i
$567$	0.670687			0.0281662
$568$	−12.0248	−	20.8275i	−0.504548	−	0.873902i
$569$	−5.61668	+	9.72838i	−0.235464	+	0.407835i	−0.959407	−	0.282024i	$-0.908994\pi$
$569$	−5.61668	+	9.72838i	−0.235464	+	0.407835i	0.723944	+	0.689859i	$0.242328\pi$
$570$	3.70357	−	6.41478i	0.155126	−	0.268686i
$571$	37.5746			1.57245			0.786224	−	0.617941i	$-0.212033\pi$
$571$	37.5746			1.57245			0.786224	+	0.617941i	$0.212033\pi$
$572$	−4.57314	+	2.71111i	−0.191212	+	0.113357i
$573$	−5.47994			−0.228928
$574$	3.07334	−	5.32318i	0.128279	−	0.222185i
$575$	−45.9508	+	79.5892i	−1.91628	+	3.31910i
$576$	−0.997853	−	1.72833i	−0.0415772	−	0.0720139i
$577$	−15.2880			−0.636449			−0.318224	−	0.948015i	$-0.603087\pi$
$577$	−15.2880			−0.636449			−0.318224	+	0.948015i	$0.603087\pi$
$578$	0.679786	+	1.17742i	0.0282754	+	0.0489744i
$579$	3.58122	+	6.20285i	0.148830	+	0.257782i
$580$	40.5499			1.68374
$581$	4.86170	+	8.42071i	0.201697	+	0.349350i
$582$	4.90384	−	8.49369i	0.203271	−	0.352075i
$583$	−2.90369	+	5.02934i	−0.120259	+	0.208294i
$584$	15.4969			0.641268
$585$	13.4156	+	7.54053i	0.554668	+	0.311763i
$586$	2.98749			0.123412
$587$	−0.415795	+	0.720178i	−0.0171617	+	0.0297249i	−0.874479	−	0.485064i	$-0.838796\pi$
$587$	−0.415795	+	0.720178i	−0.0171617	+	0.0297249i	0.857317	+	0.514789i	$0.172130\pi$
$588$	−4.82910	+	8.36424i	−0.199149	+	0.344936i
$589$	4.57641	+	7.92657i	0.188568	+	0.326609i
$590$	28.7593			1.18400
$591$	−3.20161	−	5.54535i	−0.131697	−	0.228105i
$592$	3.07626	+	5.32824i	0.126434	+	0.218989i
$593$	−17.9822			−0.738442			−0.369221	−	0.929342i	$-0.620375\pi$
$593$	−17.9822			−0.738442			−0.369221	+	0.929342i	$0.620375\pi$
$594$	−0.362459	−	0.627798i	−0.0148719	−	0.0257588i
$595$	−6.21862	+	10.7710i	−0.254938	+	0.441566i
$596$	4.02578	−	6.97286i	0.164902	−	0.285619i
$597$	−0.398456			−0.0163077
$598$	−15.8413	−	8.90392i	−0.647799	−	0.364109i
$599$	38.0114			1.55311			0.776553	−	0.630052i	$-0.216967\pi$
$599$	38.0114			1.55311			0.776553	+	0.630052i	$0.216967\pi$
$600$	−16.6467	+	28.8330i	−0.679599	+	1.17710i
$601$	7.19862	−	12.4684i	0.293638	−	0.508596i	−0.681029	−	0.732256i	$-0.738467\pi$
$601$	7.19862	−	12.4684i	0.293638	−	0.508596i	0.974667	+	0.223661i	$0.0718007\pi$
$602$	1.67879	+	2.90775i	0.0684223	+	0.118511i
$603$	8.64532			0.352064
$604$	4.60409	+	7.97452i	0.187338	+	0.324479i
$605$	−2.13415	−	3.69646i	−0.0867655	−	0.150282i
$606$	8.57670			0.348405
$607$	−18.1068	−	31.3619i	−0.734931	−	1.27294i	−0.954753	−	0.297399i	$-0.903881\pi$
$607$	−18.1068	−	31.3619i	−0.734931	−	1.27294i	0.219822	−	0.975540i	$-0.429452\pi$
$608$	7.00411	−	12.1315i	0.284054	−	0.491996i
$609$	2.16064	−	3.74233i	0.0875534	−	0.151647i
$610$	4.24083			0.171706
$611$	−6.45293	+	3.82552i	−0.261058	+	0.154764i
$612$	−6.40607			−0.258950
$613$	6.32781	−	10.9601i	0.255578	−	0.442674i	−0.709475	−	0.704731i	$-0.751068\pi$
$613$	6.32781	−	10.9601i	0.255578	−	0.442674i	0.965052	+	0.262057i	$0.0844010\pi$
$614$	−10.0165	+	17.3490i	−0.404231	+	0.700149i
$615$	−26.9809	−	46.7323i	−1.08798	−	1.88443i
$616$	−1.68928			−0.0680628
$617$	−9.34500	−	16.1860i	−0.376216	−	0.651624i	0.614293	−	0.789078i	$-0.289441\pi$
$617$	−9.34500	−	16.1860i	−0.376216	−	0.651624i	−0.990508	+	0.137454i	$0.956108\pi$
$618$	−4.18660	−	7.25140i	−0.168410	−	0.291694i
$619$	−10.7867			−0.433555			−0.216777	−	0.976221i	$-0.569555\pi$
$619$	−10.7867			−0.433555			−0.216777	+	0.976221i	$0.569555\pi$
$620$	−12.0314	−	20.8389i	−0.483192	−	0.836912i
$621$	−3.47628	+	6.02110i	−0.139498	+	0.241618i
$622$	5.77196	−	9.99732i	0.231434	−	0.400856i
$623$	−4.25986			−0.170668
$624$	3.53006	+	1.98414i	0.141315	+	0.0794293i
$625$	83.6336			3.34534
$626$	−4.60207	+	7.97103i	−0.183936	+	0.318586i
$627$	1.19695	−	2.07318i	0.0478017	−	0.0827950i
$628$	8.10404	+	14.0366i	0.323387	+	0.560122i
$629$	−23.8000			−0.948968
$630$	1.03761	+	1.79719i	0.0413393	+	0.0716018i
$631$	−8.86599	−	15.3563i	−0.352949	−	0.611326i	0.633815	−	0.773484i	$-0.281488\pi$
$631$	−8.86599	−	15.3563i	−0.352949	−	0.611326i	−0.986765	+	0.162158i	$0.948155\pi$
$632$	8.04942			0.320189
$633$	1.87345	+	3.24491i	0.0744630	+	0.128974i
$634$	−3.78308	+	6.55248i	−0.150245	+	0.260232i
$635$	−9.61102	+	16.6468i	−0.381402	+	0.660607i
$636$	8.56295			0.339543
$637$	0.272428	+	23.6154i	0.0107940	+	0.935678i
$638$	−4.67069			−0.184914
$639$	−4.77415	+	8.26907i	−0.188862	+	0.327119i
$640$	−21.8889	+	37.9127i	−0.865236	+	1.49863i
$641$	17.0977	+	29.6140i	0.675317	+	1.16968i	0.976376	+	0.216078i	$0.0693267\pi$
$641$	17.0977	+	29.6140i	0.675317	+	1.16968i	−0.301059	+	0.953606i	$0.597340\pi$
$642$	−0.522733			−0.0206306
$643$	2.64160	+	4.57539i	0.104175	+	0.180436i	0.913401	−	0.407062i	$-0.133447\pi$
$643$	2.64160	+	4.57539i	0.104175	+	0.180436i	−0.809226	+	0.587497i	$0.800113\pi$
$644$	3.43778	+	5.95441i	0.135467	+	0.234637i
$645$	29.4762			1.16063
$646$	3.76977	+	6.52944i	0.148320	+	0.256897i
$647$	11.6416	−	20.1638i	0.457678	−	0.792722i	−0.541160	−	0.840920i	$-0.682014\pi$
$647$	11.6416	−	20.1638i	0.457678	−	0.792722i	0.998838	+	0.0481979i	$0.0153478\pi$
$648$	−1.25936	+	2.18128i	−0.0494724	+	0.0856887i
$649$	9.29467			0.364848
$650$	0.398535	+	34.5470i	0.0156318	+	1.35504i
$651$	−2.56429			−0.100502
$652$	0.510079	−	0.883483i	0.0199762	−	0.0345999i
$653$	5.11113	−	8.85274i	0.200014	−	0.346435i	−0.748519	−	0.663114i	$-0.769235\pi$
$653$	5.11113	−	8.85274i	0.200014	−	0.346435i	0.948533	+	0.316679i	$0.102568\pi$
$654$	−0.242194	−	0.419493i	−0.00947055	−	0.0164035i
$655$	25.6639			1.00277
$656$	−7.09949	−	12.2967i	−0.277189	−	0.480105i
$657$	−3.07635	−	5.32839i	−0.120020	−	0.207880i
$658$	−1.01157			−0.0394350
$659$	10.2381	+	17.7330i	0.398822	+	0.690779i	0.993581	−	0.113125i	$-0.0360859\pi$
$659$	10.2381	+	17.7330i	0.398822	+	0.690779i	−0.594759	+	0.803904i	$0.702753\pi$
$660$	−3.14679	+	5.45040i	−0.122489	+	0.212157i
$661$	22.6929	−	39.3053i	0.882653	−	1.52880i	0.0342721	−	0.999413i	$-0.489089\pi$
$661$	22.6929	−	39.3053i	0.882653	−	1.52880i	0.848381	−	0.529387i	$-0.177578\pi$
$662$	4.41435			0.171569
$663$	−13.4747	+	7.98829i	−0.523315	+	0.310240i
$664$	−36.5156			−1.41708
$665$	−3.42651	+	5.93489i	−0.132874	+	0.230145i
$666$	−1.98558	+	3.43912i	−0.0769396	+	0.133263i
$667$	22.3979	+	38.7943i	0.867249	+	1.50212i
$668$	5.13750			0.198776
$669$	10.8460	+	18.7857i	0.419329	+	0.726299i
$670$	13.3750	+	23.1662i	0.516722	+	0.894990i
$671$	1.37059			0.0529109
$672$	1.96230	+	3.39881i	0.0756974	+	0.131112i
$673$	−20.8387	+	36.0937i	−0.803273	+	1.39131i	0.114177	+	0.993460i	$0.463577\pi$
$673$	−20.8387	+	36.0937i	−0.803273	+	1.39131i	−0.917451	+	0.397850i	$0.869757\pi$
$674$	0.680143	−	1.17804i	0.0261981	−	0.0453765i
$675$	13.2184			0.508776
$676$	19.1633	−	0.442196i	0.737051	−	0.0170075i
$677$	22.7075			0.872721			0.436361	−	0.899772i	$-0.356267\pi$
$677$	22.7075			0.872721			0.436361	+	0.899772i	$0.356267\pi$
$678$	−7.13259	+	12.3540i	−0.273925	+	0.474453i
$679$	−4.53698	+	7.85828i	−0.174113	+	0.301573i
$680$	−23.3536	−	40.4497i	−0.895571	−	1.55117i
$681$	−13.7277			−0.526047
$682$	1.38582	+	2.40031i	0.0530657	+	0.0919126i
$683$	3.58713	+	6.21308i	0.137258	+	0.237737i	0.926458	−	0.376399i	$-0.122838\pi$
$683$	3.58713	+	6.21308i	0.137258	+	0.237737i	−0.789200	+	0.614136i	$0.789505\pi$
$684$	−3.52980			−0.134965
$685$	−3.30997	−	5.73303i	−0.126467	−	0.219048i
$686$	−3.29400	+	5.70538i	−0.125766	+	0.217832i
$687$	5.60468	−	9.70758i	0.213832	−	0.370367i
$688$	7.75608			0.295698
$689$	18.0116	−	10.6779i	0.686187	−	0.406795i
$690$	−21.5124			−0.818963
$691$	12.3711	−	21.4274i	0.470619	−	0.815136i	−0.528816	−	0.848736i	$-0.677364\pi$
$691$	12.3711	−	21.4274i	0.470619	−	0.815136i	0.999435	+	0.0336003i	$0.0106973\pi$
$692$	−2.24856	+	3.89461i	−0.0854773	+	0.148051i
$693$	0.335344	+	0.580832i	0.0127386	+	0.0220640i
$694$	−6.12066			−0.232337
$695$	−33.6303	−	58.2494i	−1.27567	−	2.20953i
$696$	8.11414	+	14.0541i	0.307566	+	0.532719i
$697$	54.9264			2.08048
$698$	6.49585	+	11.2511i	0.245871	+	0.425862i
$699$	6.94153	−	12.0231i	0.262553	−	0.454755i
$700$	6.53598	−	11.3207i	0.247037	−	0.427881i
$701$	−28.3474			−1.07067			−0.535333	−	0.844641i	$-0.679814\pi$
$701$	−28.3474			−1.07067			−0.535333	+	0.844641i	$0.679814\pi$
$702$	0.0301500	+	2.61356i	0.00113794	+	0.0986423i
$703$	−13.1140			−0.494604
$704$	0.997853	−	1.72833i	0.0376080	−	0.0651390i
$705$	−4.44028	+	7.69080i	−0.167231	+	0.289652i
$706$	6.99835	+	12.1215i	0.263386	+	0.456199i
$707$	−7.93508			−0.298429
$708$	−6.85247	−	11.8688i	−0.257531	−	0.446058i
$709$	−16.2206	−	28.0950i	−0.609179	−	1.05513i	−0.991376	−	0.131048i	$-0.958166\pi$
$709$	−16.2206	−	28.0950i	−0.609179	−	1.05513i	0.382197	−	0.924081i	$-0.375168\pi$
$710$	−29.5440			−1.10877
$711$	−1.59792	−	2.76767i	−0.0599265	−	0.103796i
$712$	7.99881	−	13.8544i	0.299768	−	0.519214i
$713$	13.2912	−	23.0209i	0.497758	−	0.862141i
$714$	−2.11231			−0.0790513
$715$	0.177523	+	15.3885i	0.00663897	+	0.575499i
$716$	11.5370			0.431157
$717$	−11.6162	+	20.1198i	−0.433813	+	0.751387i
$718$	6.90564	−	11.9609i	0.257716	−	0.446377i
$719$	2.33090	+	4.03723i	0.0869278	+	0.150563i	0.906211	−	0.422826i	$-0.138962\pi$
$719$	2.33090	+	4.03723i	0.0869278	+	0.150563i	−0.819283	+	0.573389i	$0.805628\pi$
$720$	4.79381			0.178655
$721$	3.87340	+	6.70892i	0.144253	+	0.249853i
$722$	−4.80955	−	8.33038i	−0.178993	−	0.310025i
$723$	−14.8403			−0.551916
$724$	−7.38756	−	12.7956i	−0.274556	−	0.475546i
$725$	42.5834	−	73.7565i	1.58151	−	2.73925i
$726$	0.362459	−	0.627798i	0.0134521	−	0.0232998i
$727$	12.0923			0.448478			0.224239	−	0.974534i	$-0.428010\pi$
$727$	12.0923			0.448478			0.224239	+	0.974534i	$0.428010\pi$
$728$	5.30954	+	2.98434i	0.196785	+	0.110607i
$729$	1.00000			0.0370370
$730$	9.51873	−	16.4869i	0.352304	−	0.610209i
$731$	−15.0015	+	25.9834i	−0.554852	+	0.961032i
$732$	−1.01046	−	1.75017i	−0.0373477	−	0.0646881i
$733$	−41.6349			−1.53782			−0.768910	−	0.639357i	$-0.779200\pi$
$733$	−41.6349			−1.53782			−0.768910	+	0.639357i	$0.779200\pi$
$734$	−3.76807	−	6.52649i	−0.139082	−	0.240897i
$735$	13.9791	+	24.2124i	0.515625	+	0.893089i
$736$	−40.6838			−1.49962
$737$	4.32266	+	7.48706i	0.159227	+	0.275790i
$738$	4.58238	−	7.93691i	0.168680	−	0.292162i
$739$	−5.64352	+	9.77486i	−0.207600	+	0.359574i	−0.950958	−	0.309320i	$-0.899899\pi$
$739$	−5.64352	+	9.77486i	−0.207600	+	0.359574i	0.743358	+	0.668894i	$0.233232\pi$
$740$	34.4767			1.26739
$741$	−7.42469	+	4.40162i	−0.272753	+	0.161697i
$742$	2.82351			0.103654
$743$	−21.4277	+	37.1139i	−0.786107	+	1.36158i	0.142228	+	0.989834i	$0.454573\pi$
$743$	−21.4277	+	37.1139i	−0.786107	+	1.36158i	−0.928335	+	0.371744i	$0.878760\pi$
$744$	4.81502	−	8.33986i	0.176527	−	0.305754i
$745$	−11.6537	−	20.1847i	−0.426957	−	0.739511i
$746$	5.70181			0.208758
$747$	7.24883	+	12.5553i	0.265221	+	0.459376i
$748$	−3.20304	−	5.54782i	−0.117115	−	0.202848i
$749$	0.483627			0.0176713
$750$	12.7145	+	22.0222i	0.464269	+	0.804137i
$751$	12.6800	−	21.9624i	0.462699	−	0.801418i	−0.536395	−	0.843967i	$-0.680214\pi$
$751$	12.6800	−	21.9624i	0.462699	−	0.801418i	0.999094	+	0.0425485i	$0.0135477\pi$
$752$	−1.16837	+	2.02368i	−0.0426062	+	0.0737961i
$753$	−25.4591			−0.927780
$754$	14.6804	+	8.25141i	0.534628	+	0.300499i
$755$	26.6554			0.970091
$756$	0.494462	−	0.856433i	0.0179834	−	0.0311482i
$757$	15.3079	−	26.5141i	0.556376	−	0.963671i	−0.441419	−	0.897301i	$-0.645525\pi$
$757$	15.3079	−	26.5141i	0.556376	−	0.963671i	0.997795	−	0.0663703i	$-0.0211419\pi$
$758$	2.27587	+	3.94192i	0.0826632	+	0.143177i
$759$	−6.95257			−0.252362
$760$	−12.8680	−	22.2881i	−0.466773	−	0.808475i
$761$	−12.4253	−	21.5213i	−0.450418	−	0.780147i	0.547994	−	0.836482i	$-0.315392\pi$
$761$	−12.4253	−	21.5213i	−0.450418	−	0.780147i	−0.998412	+	0.0563355i	$0.982058\pi$
$762$	−3.26463			−0.118265
$763$	0.224076	+	0.388111i	0.00811209	+	0.0140506i
$764$	−4.04007	+	6.99760i	−0.146165	+	0.253164i
$765$	−9.27201	+	16.0596i	−0.335230	+	0.580636i
$766$	−17.5357			−0.633592
$767$	−29.2140	−	16.4203i	−1.05485	−	0.592903i
$768$	−11.4265			−0.412320
$769$	−18.8353	+	32.6237i	−0.679219	+	1.17644i	0.295998	+	0.955189i	$0.404348\pi$
$769$	−18.8353	+	32.6237i	−0.679219	+	1.17644i	−0.975217	+	0.221253i	$0.928985\pi$
$770$	−1.03761	+	1.79719i	−0.0373928	+	0.0647663i
$771$	−14.6688	−	25.4071i	−0.528283	−	0.915014i
$772$	10.5610			0.380097
$773$	9.09714	+	15.7567i	0.327201	+	0.566729i	0.981955	−	0.189113i	$-0.0605612\pi$
$773$	9.09714	+	15.7567i	0.327201	+	0.566729i	−0.654754	+	0.755842i	$0.727228\pi$
$774$	2.50309	+	4.33547i	0.0899716	+	0.155835i
$775$	−50.5389			−1.81541
$776$	−17.0383	−	29.5113i	−0.611641	−	1.05939i
$777$	1.83704	−	3.18184i	0.0659033	−	0.114148i
$778$	−5.55067	+	9.61405i	−0.199001	+	0.344680i
$779$	30.2649			1.08435
$780$	19.5195	−	11.5718i	0.698911	−	0.414338i
$781$	−9.54830			−0.341665
$782$	10.9485	−	18.9633i	0.391516	−	0.678126i
$783$	3.22153	−	5.57985i	0.115128	−	0.199408i
$784$	3.67831	+	6.37103i	0.131368	+	0.227537i
$785$	46.9185			1.67459
$786$	2.17935	+	3.77475i	0.0777349	+	0.134641i
$787$	20.1011	+	34.8162i	0.716527	+	1.24106i	0.962367	+	0.271751i	$0.0876029\pi$
$787$	20.1011	+	34.8162i	0.716527	+	1.24106i	−0.245840	+	0.969310i	$0.579064\pi$
$788$	−9.44151			−0.336340
$789$	−5.94171	−	10.2913i	−0.211530	−	0.366381i
$790$	4.94422	−	8.56364i	0.175907	−	0.304681i
$791$	6.59900	−	11.4298i	0.234633	−	0.406397i
$792$	−2.51872			−0.0894989
$793$	−4.30787	−	2.42133i	−0.152977	−	0.0859839i
$794$	1.72775			0.0613157
$795$	12.3938	−	21.4667i	0.439564	−	0.761347i
$796$	−0.293760	+	0.508808i	−0.0104121	+	0.0180342i
$797$	10.2343	+	17.7263i	0.362518	+	0.627899i	0.988374	−	0.152039i	$-0.0485839\pi$
$797$	10.2343	+	17.7263i	0.362518	+	0.627899i	−0.625857	+	0.779938i	$0.715251\pi$
$798$	−1.16390			−0.0412017
$799$	−4.51965	−	7.82827i	−0.159894	−	0.276944i
$800$	38.6744	+	66.9861i	1.36735	+	2.36832i
$801$	−6.35148			−0.224419
$802$	−2.10268	−	3.64195i	−0.0742482	−	0.128602i
$803$	3.07635	−	5.32839i	0.108562	−	0.188035i
$804$	6.37373	−	11.0396i	0.224784	−	0.389338i
$805$	19.9031			0.701491
$806$	−0.115275	−	9.99262i	−0.00406039	−	0.351975i
$807$	−21.0461			−0.740858
$808$	14.8998	−	25.8073i	0.524175	−	0.907897i
$809$	17.8452	−	30.9088i	0.627403	−	1.08669i	−0.360668	−	0.932694i	$-0.617451\pi$
$809$	17.8452	−	30.9088i	0.627403	−	1.08669i	0.988071	−	0.154000i	$-0.0492156\pi$
$810$	1.54708	+	2.67963i	0.0543590	+	0.0941525i
$811$	−7.79291			−0.273646			−0.136823	−	0.990596i	$-0.543689\pi$
$811$	−7.79291			−0.273646			−0.136823	+	0.990596i	$0.543689\pi$
$812$	−3.18584	−	5.51804i	−0.111801	−	0.193645i
$813$	−13.4096	−	23.2261i	−0.470295	−	0.814575i
$814$	−3.97116			−0.139189
$815$	−1.47655	−	2.55747i	−0.0517215	−	0.0895842i
$816$	−2.43975	+	4.22576i	−0.0854082	+	0.147931i
$817$	−8.26598	+	14.3171i	−0.289190	+	0.500892i
$818$	5.25818			0.183848
$819$	−0.0278945	−	2.41804i	−0.000974713	−	0.0844930i
$820$	−79.5664			−2.77858
$821$	0.692239	−	1.19899i	0.0241593	−	0.0418452i	−0.853693	−	0.520777i	$-0.825642\pi$
$821$	0.692239	−	1.19899i	0.0241593	−	0.0418452i	0.877852	+	0.478931i	$0.158976\pi$
$822$	0.562157	−	0.973685i	0.0196075	−	0.0339612i
$823$	−6.58620	−	11.4076i	−0.229581	−	0.397645i	0.728103	−	0.685467i	$-0.240402\pi$
$823$	−6.58620	−	11.4076i	−0.229581	−	0.397645i	−0.957684	+	0.287822i	$0.907069\pi$
$824$	−29.0926			−1.01349
$825$	6.60919	+	11.4475i	0.230102	+	0.398549i
$826$	−2.25950	−	3.91357i	−0.0786182	−	0.136171i
$827$	−20.2035			−0.702546			−0.351273	−	0.936273i	$-0.614251\pi$
$827$	−20.2035			−0.702546			−0.351273	+	0.936273i	$0.614251\pi$
$828$	5.12576	+	8.87807i	0.178132	+	0.308534i
$829$	−1.05602	+	1.82908i	−0.0366771	+	0.0635266i	−0.883781	−	0.467900i	$-0.845011\pi$
$829$	−1.05602	+	1.82908i	−0.0366771	+	0.0635266i	0.847104	+	0.531427i	$0.178344\pi$
$830$	−22.4291	+	38.8483i	−0.778525	+	1.34845i
$831$	−12.7264			−0.441475
$832$	−6.18968	+	3.66945i	−0.214588	+	0.127215i
$833$	−28.4579			−0.986006
$834$	5.71170	−	9.89295i	0.197780	−	0.342565i
$835$	7.43591	−	12.8794i	0.257330	−	0.445709i
$836$	−1.76490	−	3.05690i	−0.0610403	−	0.105725i
$837$	−3.82338			−0.132155
$838$	4.47923	+	7.75826i	0.154733	+	0.268005i
$839$	−5.77943	−	10.0103i	−0.199528	−	0.345593i	0.748847	−	0.662742i	$-0.230608\pi$
$839$	−5.77943	−	10.0103i	−0.199528	−	0.345593i	−0.948376	+	0.317150i	$0.897274\pi$
$840$	7.21033			0.248780
$841$	−6.25647	−	10.8365i	−0.215740	−	0.373673i
$842$	9.78428	−	16.9469i	0.337189	−	0.584028i
$843$	−15.6065	+	27.0313i	−0.537517	+	0.931007i
$844$	5.52478			0.190171
$845$	26.6280	−	48.6812i	0.916031	−	1.67468i
$846$	−1.50826			−0.0518549
$847$	−0.335344	+	0.580832i	−0.0115225	+	0.0199576i
$848$	3.26119	−	5.64855i	0.111990	−	0.193972i
$849$	1.48058	+	2.56443i	0.0508133	+	0.0880112i
$850$	−41.6309			−1.42793
$851$	19.0433	+	32.9840i	0.652797	+	1.13068i
$852$	7.03945	+	12.1927i	0.241168	+	0.417715i
$853$	−35.9712			−1.23163			−0.615816	−	0.787890i	$-0.711173\pi$
$853$	−35.9712			−1.23163			−0.615816	+	0.787890i	$0.711173\pi$
$854$	−0.333185	−	0.577093i	−0.0114014	−	0.0197477i
$855$	−5.10895	+	8.84897i	−0.174723	+	0.302628i
$856$	−0.908116	+	1.57290i	−0.0310388	+	0.0537607i
$857$	−43.5188			−1.48657			−0.743287	−	0.668973i	$-0.766734\pi$
$857$	−43.5188			−1.48657			−0.743287	+	0.668973i	$0.766734\pi$
$858$	−2.24833	+	1.33289i	−0.0767567	+	0.0455041i
$859$	−7.91840			−0.270172			−0.135086	−	0.990834i	$-0.543131\pi$
$859$	−7.91840			−0.270172			−0.135086	+	0.990834i	$0.543131\pi$
$860$	21.7313	−	37.6396i	0.741029	−	1.28350i
$861$	−4.23957	+	7.34315i	−0.144484	+	0.250254i
$862$	12.8755	+	22.3010i	0.438541	+	0.759576i
$863$	19.0290			0.647754			0.323877	−	0.946099i	$-0.395014\pi$
$863$	19.0290			0.647754			0.323877	+	0.946099i	$0.395014\pi$
$864$	2.92581	+	5.06765i	0.0995380	+	0.172405i
$865$	6.50902	+	11.2740i	0.221313	+	0.383326i
$866$	9.12078			0.309937
$867$	−0.937741	−	1.62422i	−0.0318474	−	0.0551613i
$868$	−1.89052	+	3.27447i	−0.0641683	+	0.111143i
$869$	1.59792	−	2.76767i	0.0542056	−	0.0938868i
$870$	19.9359			0.675890
$871$	−0.359567	−	31.1691i	−0.0121835	−	1.05612i
$872$	−1.68301			−0.0569938
$873$	−6.76467	+	11.7168i	−0.228950	+	0.396552i
$874$	6.03270	−	10.4489i	0.204059	−	0.353441i
$875$	−11.7633	−	20.3747i	−0.397674	−	0.688791i
$876$	−9.07211			−0.306518
$877$	10.8522	+	18.7966i	0.366454	+	0.634716i	0.989008	−	0.147860i	$-0.0472385\pi$
$877$	10.8522	+	18.7966i	0.366454	+	0.634716i	−0.622555	+	0.782576i	$0.713905\pi$
$878$	9.45153	+	16.3705i	0.318974	+	0.552479i
$879$	−4.12115			−0.139003
$880$	2.39690	+	4.15156i	0.0807996	+	0.139949i
$881$	12.3748	−	21.4338i	0.416918	−	0.722123i	−0.578710	−	0.815533i	$-0.696444\pi$
$881$	12.3748	−	21.4338i	0.416918	−	0.722123i	0.995628	+	0.0934108i	$0.0297770\pi$
$882$	−2.37417	+	4.11219i	−0.0799425	+	0.138465i
$883$	49.0266			1.64988			0.824938	−	0.565223i	$-0.191210\pi$
$883$	49.0266			1.64988			0.824938	+	0.565223i	$0.191210\pi$
$884$	0.266435	+	23.0959i	0.00896117	+	0.776799i
$885$	−39.6724			−1.33357
$886$	−1.46743	+	2.54166i	−0.0492993	+	0.0853888i
$887$	−19.9108	+	34.4866i	−0.668541	+	1.15795i	0.309772	+	0.950811i	$0.399747\pi$
$887$	−19.9108	+	34.4866i	−0.668541	+	1.15795i	−0.978312	+	0.207135i	$0.933586\pi$
$888$	6.89888	+	11.9492i	0.231511	+	0.400989i
$889$	3.02040			0.101301
$890$	−9.82627	−	17.0196i	−0.329377	−	0.570498i
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	31.9846			1.07092
$893$	−2.49037	−	4.31344i	−0.0833369	−	0.144344i
$894$	1.97923	−	3.42813i	0.0661953	−	0.114654i
$895$	16.6984	−	28.9224i	0.558165	−	0.966770i
$896$	6.87891			0.229808
$897$	21.8525	+	12.2827i	0.729634	+	0.410106i
$898$	−2.69509			−0.0899363
$899$	−12.3171	+	21.3339i	−0.410799	+	0.711525i
$900$	9.74521	−	16.8792i	0.324840	−	0.562640i
$901$	12.6154	+	21.8504i	0.420279	+	0.727944i
$902$	9.16475			0.305153
$903$	−2.31583	−	4.01114i	−0.0770660	−	0.133482i
$904$	24.7821	+	42.9239i	0.824241	+	1.42763i
$905$	−42.7704			−1.42173
$906$	2.26355	+	3.92058i	0.0752014	+	0.130253i
$907$	11.3263	−	19.6178i	0.376084	−	0.651397i	−0.614404	−	0.788991i	$-0.710604\pi$
$907$	11.3263	−	19.6178i	0.376084	−	0.651397i	0.990489	+	0.137594i	$0.0439370\pi$
$908$	−10.1207	+	17.5296i	−0.335868	+	0.581740i
$909$	−11.8313			−0.392418
$910$	6.43628	−	3.81565i	0.213361	−	0.126488i
$911$	−7.48253			−0.247907			−0.123954	−	0.992288i	$-0.539557\pi$
$911$	−7.48253			−0.247907			−0.123954	+	0.992288i	$0.539557\pi$
$912$	−1.34432	+	2.32843i	−0.0445149	+	0.0771021i
$913$	−7.24883	+	12.5553i	−0.239901	+	0.415521i
$914$	−0.967728	−	1.67615i	−0.0320096	−	0.0554423i
$915$	−5.85007			−0.193397
$916$	−8.26406	−	14.3138i	−0.273052	−	0.472940i
$917$	−2.01631	−	3.49236i	−0.0665846	−	0.115328i
$918$	−3.14947			−0.103948
$919$	16.9022	+	29.2755i	0.557552	+	0.965709i	0.997700	+	0.0677836i	$0.0215927\pi$
$919$	16.9022	+	29.2755i	0.557552	+	0.965709i	−0.440148	+	0.897925i	$0.645074\pi$
$920$	−37.3724	+	64.7308i	−1.23213	+	2.13411i
$921$	13.8174	−	23.9324i	0.455297	−	0.788598i
$922$	−14.8639			−0.489516
$923$	30.0111	+	16.8684i	0.987828	+	0.555229i
$924$	0.988924			0.0325332
$925$	36.2056	−	62.7100i	1.19043	−	2.06189i
$926$	3.53035	−	6.11475i	0.116015	−	0.200943i
$927$	5.77527	+	10.0031i	0.189685	+	0.328544i
$928$	37.7023			1.23764
$929$	−4.84218	−	8.38691i	−0.158867	−	0.275166i	0.775593	−	0.631233i	$-0.217451\pi$
$929$	−4.84218	−	8.38691i	−0.158867	−	0.275166i	−0.934460	+	0.356067i	$0.884117\pi$
$930$	−5.91509	−	10.2452i	−0.193963	−	0.335954i
$931$	−15.6805			−0.513908
$932$	−10.2352	−	17.7280i	−0.335266	−	0.580698i
$933$	−7.96222	+	13.7910i	−0.260671	+	0.451496i
$934$	13.1833	−	22.8341i	0.431369	−	0.747154i
$935$	−18.5440			−0.606454
$936$	7.91657	+	4.44967i	0.258761	+	0.145442i
$937$	−40.0325			−1.30781			−0.653903	−	0.756578i	$-0.726870\pi$
$937$	−40.0325			−1.30781			−0.653903	+	0.756578i	$0.726870\pi$
$938$	2.10165	−	3.64016i	0.0686212	−	0.118855i
$939$	6.34841	−	10.9958i	0.207172	−	0.358833i
$940$	6.54717	+	11.3400i	0.213545	+	0.369871i
$941$	−10.8173			−0.352635			−0.176318	−	0.984333i	$-0.556419\pi$
$941$	−10.8173			−0.352635			−0.176318	+	0.984333i	$0.556419\pi$
$942$	3.98426	+	6.90095i	0.129814	+	0.224845i
$943$	−43.9488	−	76.1215i	−1.43117	−	2.47886i
$944$	−10.4390			−0.339761
$945$	−1.43135	−	2.47916i	−0.0465617	−	0.0806472i
$946$	−2.50309	+	4.33547i	−0.0813824	+	0.140958i
$947$	−7.21849	+	12.5028i	−0.234569	+	0.406286i	−0.959147	−	0.282907i	$-0.908701\pi$
$947$	−7.21849	+	12.5028i	−0.234569	+	0.406286i	0.724578	+	0.689193i	$0.242035\pi$
$948$	−4.71223			−0.153046
$949$	−19.0825	+	11.3128i	−0.619446	+	0.367229i
$950$	−22.9390			−0.744239
$951$	5.21863	−	9.03893i	0.169226	−	0.293107i
$952$	−3.66961	+	6.35594i	−0.118933	+	0.205997i
$953$	−4.31481	−	7.47346i	−0.139770	−	0.242089i	0.787639	−	0.616137i	$-0.211303\pi$
$953$	−4.31481	−	7.47346i	−0.139770	−	0.242089i	−0.927410	+	0.374047i	$0.877970\pi$
$954$	4.20988			0.136300
$955$	11.6950	+	20.2564i	0.378442	+	0.655480i
$956$	17.1280	+	29.6665i	0.553958	+	0.959483i
$957$	6.44305			0.208274
$958$	−2.94522	−	5.10126i	−0.0951556	−	0.164814i
$959$	−0.520102	+	0.900844i	−0.0167950	+	0.0290898i
$960$	−4.25914	+	7.37704i	−0.137463	+	0.238093i
$961$	−16.3818			−0.528444
$962$	12.4817	+	7.01559i	0.402426	+	0.226192i
$963$	0.721092			0.0232369
$964$	−10.9410	+	18.9503i	−0.352385	+	0.610348i
$965$	15.2857	−	26.4756i	0.492064	−	0.852280i
$966$	1.69015	+	2.92742i	0.0543795	+	0.0941881i
$967$	−26.5338			−0.853270			−0.426635	−	0.904424i	$-0.640301\pi$
$967$	−26.5338			−0.853270			−0.426635	+	0.904424i	$0.640301\pi$
$968$	−1.25936	−	2.18128i	−0.0404774	−	0.0701090i
$969$	−5.20027	−	9.00714i	−0.167057	−	0.289351i
$970$	−41.8621			−1.34411
$971$	6.87248	+	11.9035i	0.220548	+	0.382001i	0.954975	−	0.296688i	$-0.0958820\pi$
$971$	6.87248	+	11.9035i	0.220548	+	0.382001i	−0.734426	+	0.678689i	$0.762549\pi$
$972$	0.737247	−	1.27695i	0.0236472	−	0.0409582i
$973$	−5.28440	+	9.15285i	−0.169410	+	0.293427i
$974$	−24.7165			−0.791968
$975$	−0.549765	−	47.6564i	−0.0176066	−	1.52623i
$976$	−1.53933			−0.0492728
$977$	10.4153	−	18.0399i	0.333216	−	0.577148i	−0.649924	−	0.759999i	$-0.725199\pi$
$977$	10.4153	−	18.0399i	0.333216	−	0.577148i	0.983141	+	0.182851i	$0.0585327\pi$
$978$	0.250775	−	0.434354i	0.00801889	−	0.0138891i
$979$	−3.17574	−	5.50054i	−0.101497	−	0.175798i
$980$	41.2241			1.31685
$981$	0.334099	+	0.578676i	0.0106670	+	0.0184757i
$982$	−11.5768	−	20.0516i	−0.369431	−	0.639873i
$983$	−32.0759			−1.02306			−0.511531	−	0.859265i	$-0.670921\pi$
$983$	−32.0759			−1.02306			−0.511531	+	0.859265i	$0.670921\pi$
$984$	−15.9214	−	27.5767i	−0.507557	−	0.879114i
$985$	−13.6654	+	23.6692i	−0.435417	+	0.754164i
$986$	−10.1461	+	17.5736i	−0.323118	+	0.559657i
$987$	1.39542			0.0444168
$988$	0.146808	+	12.7260i	0.00467058	+	0.404869i
$989$	48.0134			1.52674
$990$	−1.54708	+	2.67963i	−0.0491696	+	0.0851642i
$991$	−5.46687	+	9.46889i	−0.173661	+	0.300789i	−0.939697	−	0.342008i	$-0.888893\pi$
$991$	−5.46687	+	9.46889i	−0.173661	+	0.300789i	0.766036	+	0.642797i	$0.222226\pi$
$992$	−11.1865	−	19.3755i	−0.355171	−	0.615174i
$993$	−6.08944			−0.193243
$994$	2.32116	+	4.02037i	0.0736227	+	0.127518i
$995$	0.850364	+	1.47287i	0.0269584	+	0.0466932i
$996$	21.3767			0.677347
$997$	11.9813	+	20.7521i	0.379450	+	0.657227i	0.990982	−	0.133993i	$-0.0427799\pi$
$997$	11.9813	+	20.7521i	0.379450	+	0.657227i	−0.611532	+	0.791219i	$0.709447\pi$
$998$	−6.48890	+	11.2391i	−0.205402	+	0.355767i
$999$	2.73904	−	4.74415i	0.0866593	−	0.150098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.c.100.4	✓	10
13.3	even	3	inner	429.2.i.c.133.4	yes	10
13.4	even	6		5577.2.a.p.1.4		5
13.9	even	3		5577.2.a.v.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.c.100.4	✓	10	1.1	even	1	trivial
429.2.i.c.133.4	yes	10	13.3	even	3	inner
5577.2.a.p.1.4		5	13.4	even	6
5577.2.a.v.1.2		5	13.9	even	3

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.362459 - 0.627798i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.737247 + 1.27695i) q^{4} +4.26830 q^{5} +(0.362459 + 0.627798i) q^{6} +(-0.335344 - 0.580832i) q^{7} +2.51872 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.362459 - 0.627798i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.737247 + 1.27695i) q^{4} +4.26830 q^{5} +(0.362459 + 0.627798i) q^{6} +(-0.335344 - 0.580832i) q^{7} +2.51872 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.54708 - 2.67963i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.47449 q^{12} +(-3.10150 + 1.83867i) q^{13} -0.486193 q^{14} +(-2.13415 + 3.69646i) q^{15} +(-0.561559 + 0.972649i) q^{16} +(-2.17230 - 3.76253i) q^{17} -0.724918 q^{18} +(-1.19695 - 2.07318i) q^{19} +(3.14679 + 5.45040i) q^{20} +0.670687 q^{21} +(-0.362459 - 0.627798i) q^{22} +(-3.47628 + 6.02110i) q^{23} +(-1.25936 + 2.18128i) q^{24} +13.2184 q^{25} +(0.0301500 + 2.61356i) q^{26} +1.00000 q^{27} +(0.494462 - 0.856433i) q^{28} +(3.22153 - 5.57985i) q^{29} +(1.54708 + 2.67963i) q^{30} -3.82338 q^{31} +(2.92581 + 5.06765i) q^{32} +(0.500000 + 0.866025i) q^{33} -3.14947 q^{34} +(-1.43135 - 2.47916i) q^{35} +(0.737247 - 1.27695i) q^{36} +(2.73904 - 4.74415i) q^{37} -1.73539 q^{38} +(-0.0415910 - 3.60531i) q^{39} +10.7507 q^{40} +(-6.32123 + 10.9487i) q^{41} +(0.243097 - 0.421056i) q^{42} +(-3.45292 - 5.98064i) q^{43} +1.47449 q^{44} +(-2.13415 - 3.69646i) q^{45} +(2.52002 + 4.36480i) q^{46} +2.08059 q^{47} +(-0.561559 - 0.972649i) q^{48} +(3.27509 - 5.67262i) q^{49} +(4.79112 - 8.29847i) q^{50} +4.34459 q^{51} +(-4.63446 - 2.60489i) q^{52} -5.80739 q^{53} +(0.362459 - 0.627798i) q^{54} +(2.13415 - 3.69646i) q^{55} +(-0.844638 - 1.46296i) q^{56} +2.39391 q^{57} +(-2.33534 - 4.04493i) q^{58} +(4.64734 + 8.04942i) q^{59} -6.29358 q^{60} +(0.685293 + 1.18696i) q^{61} +(-1.38582 + 2.40031i) q^{62} +(-0.335344 + 0.580832i) q^{63} +1.99571 q^{64} +(-13.2381 + 7.84801i) q^{65} +0.724918 q^{66} +(-4.32266 + 7.48706i) q^{67} +(3.20304 - 5.54782i) q^{68} +(-3.47628 - 6.02110i) q^{69} -2.07522 q^{70} +(-4.77415 - 8.26907i) q^{71} +(-1.25936 - 2.18128i) q^{72} +6.15269 q^{73} +(-1.98558 - 3.43912i) q^{74} +(-6.60919 + 11.4475i) q^{75} +(1.76490 - 3.05690i) q^{76} -0.670687 q^{77} +(-2.27848 - 1.28067i) q^{78} +3.19583 q^{79} +(-2.39690 + 4.15156i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.58238 + 7.93691i) q^{82} -14.4977 q^{83} +(0.494462 + 0.856433i) q^{84} +(-9.27201 - 16.0596i) q^{85} -5.00617 q^{86} +(3.22153 + 5.57985i) q^{87} +(1.25936 - 2.18128i) q^{88} +(3.17574 - 5.50054i) q^{89} -3.09417 q^{90} +(2.10803 + 1.18486i) q^{91} -10.2515 q^{92} +(1.91169 - 3.31114i) q^{93} +(0.754128 - 1.30619i) q^{94} +(-5.10895 - 8.84897i) q^{95} -5.85162 q^{96} +(-6.76467 - 11.7168i) q^{97} +(-2.37417 - 4.11219i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

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