LMFDB - Embedded newform 700.2.bj.a.687.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(127,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1, 0]))

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

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

chi := DirichletCharacter("700.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			687.2
Character	$\chi$	$=$	700.687
Dual form			700.2.bj.a.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41279 + 0.0633751i) q^{2} +(0.834190 - 1.63719i) q^{3} +(1.99197 - 0.179072i) q^{4} +(-1.91219 + 1.15911i) q^{5} +(-1.07478 + 2.36588i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.80289 + 0.379233i) q^{8} +(-0.221165 - 0.304407i) q^{9} +(2.62807 - 1.75877i) q^{10} +(0.917897 - 1.26338i) q^{11} +(1.36851 - 3.41061i) q^{12} +(-0.136798 + 0.863706i) q^{13} +(-0.954182 + 1.04381i) q^{14} +(0.302556 + 4.09754i) q^{15} +(3.93587 - 0.713411i) q^{16} +(-1.39517 + 0.710875i) q^{17} +(0.331752 + 0.416048i) q^{18} +(2.27371 - 6.99775i) q^{19} +(-3.60145 + 2.65133i) q^{20} +(-0.567807 - 1.74753i) q^{21} +(-1.21673 + 1.84306i) q^{22} +(-1.02865 - 6.49463i) q^{23} +(-1.71727 + 4.90522i) q^{24} +(2.31293 - 4.43287i) q^{25} +(0.138529 - 1.22891i) q^{26} +(4.76165 - 0.754172i) q^{27} +(1.28191 - 1.53516i) q^{28} +(-0.567208 + 0.184297i) q^{29} +(-0.687131 - 5.76979i) q^{30} +(6.39327 + 2.07730i) q^{31} +(-5.51535 + 1.25734i) q^{32} +(-1.30269 - 2.55667i) q^{33} +(1.92603 - 1.09274i) q^{34} +(-0.532506 + 2.17174i) q^{35} +(-0.495063 - 0.566764i) q^{36} +(-5.42145 - 0.858673i) q^{37} +(-2.76879 + 10.0305i) q^{38} +(1.29994 + 0.944460i) q^{39} +(4.92008 - 3.97402i) q^{40} +(7.10317 - 5.16075i) q^{41} +(0.912944 + 2.43291i) q^{42} +(-4.06563 - 4.06563i) q^{43} +(1.60219 - 2.68097i) q^{44} +(0.775750 + 0.325729i) q^{45} +(1.86487 + 9.11038i) q^{46} +(-5.50151 - 2.80316i) q^{47} +(2.11527 - 7.03889i) q^{48} -1.00000i q^{49} +(-2.98675 + 6.40932i) q^{50} +2.87716i q^{51} +(-0.117831 + 1.74497i) q^{52} +(2.25678 + 1.14989i) q^{53} +(-6.67944 + 1.36726i) q^{54} +(-0.290798 + 3.47976i) q^{55} +(-1.71378 + 2.25010i) q^{56} +(-9.55995 - 9.55995i) q^{57} +(0.789668 - 0.296320i) q^{58} +(-10.8163 + 7.85848i) q^{59} +(1.33644 + 8.10798i) q^{60} +(-0.470316 - 0.341705i) q^{61} +(-9.16402 - 2.52962i) q^{62} +(-0.371635 - 0.0588612i) q^{63} +(7.71237 - 2.12589i) q^{64} +(-0.739548 - 1.81013i) q^{65} +(2.00246 + 3.52949i) q^{66} +(-3.37846 - 6.63059i) q^{67} +(-2.65184 + 1.66587i) q^{68} +(-11.4910 - 3.73367i) q^{69} +(0.614687 - 3.10196i) q^{70} +(-6.49492 + 2.11033i) q^{71} +(0.735341 + 0.769346i) q^{72} +(13.5462 - 2.14550i) q^{73} +(7.71380 + 0.869542i) q^{74} +(-5.32804 - 7.48456i) q^{75} +(3.27605 - 14.3464i) q^{76} +(-0.244291 - 1.54239i) q^{77} +(-1.89640 - 1.25194i) q^{78} +(0.112435 + 0.346038i) q^{79} +(-6.69919 + 5.92628i) q^{80} +(3.08622 - 9.49842i) q^{81} +(-9.70824 + 7.74124i) q^{82} +(8.12296 - 4.13885i) q^{83} +(-1.44399 - 3.37935i) q^{84} +(1.84385 - 2.97648i) q^{85} +(6.00155 + 5.48623i) q^{86} +(-0.171430 + 1.08237i) q^{87} +(-2.09365 + 3.88920i) q^{88} +(6.83491 - 9.40744i) q^{89} +(-1.11662 - 0.411024i) q^{90} +(0.514002 + 0.707463i) q^{91} +(-3.21204 - 12.7529i) q^{92} +(8.73414 - 8.73414i) q^{93} +(7.95014 + 3.61162i) q^{94} +(3.76341 + 16.0165i) q^{95} +(-2.54235 + 10.0785i) q^{96} +(-6.10824 + 11.9881i) q^{97} +(0.0633751 + 1.41279i) q^{98} -0.587587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−1.41279	+	0.0633751i	−0.998995	+	0.0448130i
$2$	−1.41279	+	0.0633751i	−0.998995	+	0.0448130i
$3$	0.834190	−	1.63719i	0.481620	−	0.945233i	−0.514522	−	0.857477i	$-0.672031\pi$
$3$	0.834190	−	1.63719i	0.481620	−	0.945233i	0.996142	−	0.0877554i	$-0.0279694\pi$
$4$	1.99197	−	0.179072i	0.995984	−	0.0895359i
$5$	−1.91219	+	1.15911i	−0.855156	+	0.518370i
$5$	−1.91219	+	1.15911i	−0.855156	+	0.518370i
$6$	−1.07478	+	2.36588i	−0.438778	+	0.965866i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.80289	+	0.379233i	−0.990971	+	0.134079i
$9$	−0.221165	−	0.304407i	−0.0737215	−	0.101469i
$10$	2.62807	−	1.75877i	0.831068	−	0.556171i
$11$	0.917897	−	1.26338i	0.276756	−	0.380922i	−0.647900	−	0.761726i	$-0.724352\pi$
$11$	0.917897	−	1.26338i	0.276756	−	0.380922i	0.924656	+	0.380803i	$0.124352\pi$
$12$	1.36851	−	3.41061i	0.395053	−	0.984558i
$13$	−0.136798	+	0.863706i	−0.0379408	+	0.239549i	−0.999369	−	0.0355054i	$-0.988696\pi$
$13$	−0.136798	+	0.863706i	−0.0379408	+	0.239549i	0.961429	+	0.275054i	$0.0886959\pi$
$14$	−0.954182	+	1.04381i	−0.255016	+	0.278970i
$15$	0.302556	+	4.09754i	0.0781197	+	1.05798i
$16$	3.93587	−	0.713411i	0.983967	−	0.178353i
$17$	−1.39517	+	0.710875i	−0.338378	+	0.172412i	−0.614920	−	0.788590i	$-0.710812\pi$
$17$	−1.39517	+	0.710875i	−0.338378	+	0.172412i	0.276541	+	0.961002i	$0.410812\pi$
$18$	0.331752	+	0.416048i	0.0781946	+	0.0980634i
$19$	2.27371	−	6.99775i	0.521624	−	1.60539i	−0.249272	−	0.968433i	$-0.580191\pi$
$19$	2.27371	−	6.99775i	0.521624	−	1.60539i	0.770896	−	0.636961i	$-0.219809\pi$
$20$	−3.60145	+	2.65133i	−0.805309	+	0.592855i
$21$	−0.567807	−	1.74753i	−0.123906	−	0.381342i
$22$	−1.21673	+	1.84306i	−0.259408	+	0.392942i
$23$	−1.02865	−	6.49463i	−0.214488	−	1.35422i	−0.826304	−	0.563224i	$-0.809561\pi$
$23$	−1.02865	−	6.49463i	−0.214488	−	1.35422i	0.611816	−	0.791000i	$-0.290439\pi$
$24$	−1.71727	+	4.90522i	−0.350536	+	1.00127i
$25$	2.31293	−	4.43287i	0.462585	−	0.886575i
$26$	0.138529	−	1.22891i	0.0271678	−	0.241009i
$27$	4.76165	−	0.754172i	0.916381	−	0.145140i
$28$	1.28191	−	1.53516i	0.242258	−	0.290117i
$29$	−0.567208	+	0.184297i	−0.105328	+	0.0342231i	−0.361207	−	0.932486i	$-0.617635\pi$
$29$	−0.567208	+	0.184297i	−0.105328	+	0.0342231i	0.255879	+	0.966709i	$0.417635\pi$
$30$	−0.687131	−	5.76979i	−0.125452	−	1.05342i
$31$	6.39327	+	2.07730i	1.14827	+	0.373094i	0.820490	−	0.571662i	$-0.193701\pi$
$31$	6.39327	+	2.07730i	1.14827	+	0.373094i	0.327776	+	0.944756i	$0.393701\pi$
$32$	−5.51535	+	1.25734i	−0.974986	+	0.222268i
$33$	−1.30269	−	2.55667i	−0.226769	−	0.445059i
$34$	1.92603	−	1.09274i	0.330312	−	0.187403i
$35$	−0.532506	+	2.17174i	−0.0900100	+	0.367090i
$36$	−0.495063	−	0.566764i	−0.0825106	−	0.0944607i
$37$	−5.42145	−	0.858673i	−0.891281	−	0.141165i	−0.306034	−	0.952020i	$-0.599002\pi$
$37$	−5.42145	−	0.858673i	−0.891281	−	0.141165i	−0.585246	+	0.810856i	$0.699002\pi$
$38$	−2.76879	+	10.0305i	−0.449158	+	1.62716i
$39$	1.29994	+	0.944460i	0.208157	+	0.151235i
$40$	4.92008	−	3.97402i	0.777932	−	0.628348i
$41$	7.10317	−	5.16075i	1.10933	−	0.805974i	0.126771	−	0.991932i	$-0.459539\pi$
$41$	7.10317	−	5.16075i	1.10933	−	0.805974i	0.982558	+	0.185958i	$0.0595387\pi$
$42$	0.912944	+	2.43291i	0.140870	+	0.375407i
$43$	−4.06563	−	4.06563i	−0.620002	−	0.620002i	0.325529	−	0.945532i	$-0.394457\pi$
$43$	−4.06563	−	4.06563i	−0.620002	−	0.620002i	−0.945532	+	0.325529i	$0.894457\pi$
$44$	1.60219	−	2.68097i	0.241538	−	0.404172i
$45$	0.775750	+	0.325729i	0.115642	+	0.0485568i
$46$	1.86487	+	9.11038i	0.274959	+	1.34325i
$47$	−5.50151	−	2.80316i	−0.802477	−	0.408883i	0.00411439	−	0.999992i	$-0.498690\pi$
$47$	−5.50151	−	2.80316i	−0.802477	−	0.408883i	−0.806592	+	0.591109i	$0.798690\pi$
$48$	2.11527	−	7.03889i	0.305313	−	1.01598i
$49$		−	1.00000i		−	0.142857i
$50$	−2.98675	+	6.40932i	−0.422390	+	0.906414i
$51$			2.87716i			0.402884i
$52$	−0.117831	+	1.74497i	−0.0163402	+	0.241984i
$53$	2.25678	+	1.14989i	0.309992	+	0.157949i	0.602065	−	0.798447i	$-0.294345\pi$
$53$	2.25678	+	1.14989i	0.309992	+	0.157949i	−0.292073	+	0.956396i	$0.594345\pi$
$54$	−6.67944	+	1.36726i	−0.908956	+	0.186060i
$55$	−0.290798	+	3.47976i	−0.0392112	+	0.469210i
$56$	−1.71378	+	2.25010i	−0.229014	+	0.300682i
$57$	−9.55995	−	9.55995i	−1.26625	−	1.26625i
$58$	0.789668	−	0.296320i	0.103688	−	0.0389088i
$59$	−10.8163	+	7.85848i	−1.40816	+	1.02309i	−0.414572	+	0.910017i	$0.636069\pi$
$59$	−10.8163	+	7.85848i	−1.40816	+	1.02309i	−0.993587	+	0.113070i	$0.963931\pi$
$60$	1.33644	+	8.10798i	0.172533	+	1.04674i
$61$	−0.470316	−	0.341705i	−0.0602179	−	0.0437508i	0.557269	−	0.830332i	$-0.311849\pi$
$61$	−0.470316	−	0.341705i	−0.0602179	−	0.0437508i	−0.617487	+	0.786581i	$0.711849\pi$
$62$	−9.16402	−	2.52962i	−1.16383	−	0.321262i
$63$	−0.371635	−	0.0588612i	−0.0468216	−	0.00741582i
$64$	7.71237	−	2.12589i	0.964046	−	0.265737i
$65$	−0.739548	−	1.81013i	−0.0917297	−	0.224519i
$66$	2.00246	+	3.52949i	0.246485	+	0.434450i
$67$	−3.37846	−	6.63059i	−0.412744	−	0.810056i	−1.00000		0.000654498i	$-0.999792\pi$
$67$	−3.37846	−	6.63059i	−0.412744	−	0.810056i	0.587256	−	0.809402i	$-0.300208\pi$
$68$	−2.65184	+	1.66587i	−0.321582	+	0.202017i
$69$	−11.4910	−	3.73367i	−1.38336	−	0.449481i
$70$	0.614687	−	3.10196i	0.0734691	−	0.370755i
$71$	−6.49492	+	2.11033i	−0.770805	+	0.250450i	−0.667910	−	0.744242i	$-0.732811\pi$
$71$	−6.49492	+	2.11033i	−0.770805	+	0.250450i	−0.102896	+	0.994692i	$0.532811\pi$
$72$	0.735341	+	0.769346i	0.0866607	+	0.0906683i
$73$	13.5462	−	2.14550i	1.58546	−	0.251112i	0.699417	−	0.714714i	$-0.253443\pi$
$73$	13.5462	−	2.14550i	1.58546	−	0.251112i	0.886044	+	0.463601i	$0.153443\pi$
$74$	7.71380	+	0.869542i	0.896711	+	0.101082i
$75$	−5.32804	−	7.48456i	−0.615229	−	0.864243i
$76$	3.27605	−	14.3464i	0.375789	−	1.64565i
$77$	−0.244291	−	1.54239i	−0.0278396	−	0.175772i
$78$	−1.89640	−	1.25194i	−0.214725	−	0.141755i
$79$	0.112435	+	0.346038i	0.0126499	+	0.0389323i	0.957182	−	0.289486i	$-0.0934844\pi$
$79$	0.112435	+	0.346038i	0.0126499	+	0.0389323i	−0.944532	+	0.328418i	$0.893484\pi$
$80$	−6.69919	+	5.92628i	−0.748993	+	0.662578i
$81$	3.08622	−	9.49842i	0.342914	−	1.05538i
$82$	−9.70824	+	7.74124i	−1.07210	+	0.854877i
$83$	8.12296	−	4.13885i	0.891610	−	0.454298i	0.0527268	−	0.998609i	$-0.483209\pi$
$83$	8.12296	−	4.13885i	0.891610	−	0.454298i	0.838884	+	0.544311i	$0.183209\pi$
$84$	−1.44399	−	3.37935i	−0.157552	−	0.368717i
$85$	1.84385	−	2.97648i	0.199993	−	0.322845i
$86$	6.00155	+	5.48623i	0.647164	+	0.591595i
$87$	−0.171430	+	1.08237i	−0.0183792	+	0.116042i
$88$	−2.09365	+	3.88920i	−0.223184	+	0.414590i
$89$	6.83491	−	9.40744i	0.724499	−	0.997187i	−0.274864	−	0.961483i	$-0.588633\pi$
$89$	6.83491	−	9.40744i	0.724499	−	0.997187i	0.999362	−	0.0357038i	$-0.0113673\pi$
$90$	−1.11662	−	0.411024i	−0.117702	−	0.0433258i
$91$	0.514002	+	0.707463i	0.0538821	+	0.0741623i
$92$	−3.21204	−	12.7529i	−0.334878	−	1.32958i
$93$	8.73414	−	8.73414i	0.905688	−	0.905688i
$94$	7.95014	+	3.61162i	0.819994	+	0.372510i
$95$	3.76341	+	16.0165i	0.386118	+	1.64326i
$96$	−2.54235	+	10.0785i	−0.259478	+	1.02864i
$97$	−6.10824	+	11.9881i	−0.620198	+	1.21721i	0.340666	+	0.940184i	$0.389348\pi$
$97$	−6.10824	+	11.9881i	−0.620198	+	1.21721i	−0.960864	+	0.277022i	$0.910652\pi$
$98$	0.0633751	+	1.41279i	0.00640186	+	0.142714i
$99$	−0.587587			−0.0590547
$100$	3.81347	−	9.24432i	0.381347	−	0.924432i
$101$	13.3617			1.32954			0.664771	−	0.747047i	$-0.268529\pi$
$101$	13.3617			1.32954			0.664771	+	0.747047i	$0.268529\pi$
$102$	−0.182341	−	4.06484i	−0.0180544	−	0.402479i
$103$	3.79068	−	7.43963i	0.373507	−	0.733049i	−0.625375	−	0.780324i	$-0.715054\pi$
$103$	3.79068	−	7.43963i	0.373507	−	0.733049i	0.998882	+	0.0472758i	$0.0150540\pi$
$104$	0.0558829	−	2.47275i	0.00547977	−	0.242473i
$105$	3.11133	+	2.68346i	0.303635	+	0.261878i
$106$	−3.26123	−	1.48153i	−0.316759	−	0.143899i
$107$	2.17485	−	2.17485i	0.210251	−	0.210251i	−0.594123	−	0.804374i	$-0.702501\pi$
$107$	2.17485	−	2.17485i	0.210251	−	0.210251i	0.804374	+	0.594123i	$0.202501\pi$
$108$	9.35001	−	2.35496i	0.899705	−	0.226607i
$109$	−8.14004	−	11.2038i	−0.779675	−	1.07313i	−0.995318	−	0.0966579i	$-0.969185\pi$
$109$	−8.14004	−	11.2038i	−0.779675	−	1.07313i	0.215643	−	0.976472i	$-0.430815\pi$
$110$	0.190307	−	4.93461i	0.0181451	−	0.470496i
$111$	−5.92833	+	8.15965i	−0.562692	+	0.774480i
$112$	2.27862	−	3.28754i	0.215309	−	0.310643i
$113$	0.139808	−	0.882714i	0.0131521	−	0.0830388i	−0.980239	−	0.197816i	$-0.936615\pi$
$113$	0.139808	−	0.882714i	0.0131521	−	0.0830388i	0.993391	+	0.114777i	$0.0366153\pi$
$114$	14.1121	+	12.9004i	1.32172	+	1.20823i
$115$	9.49497	+	11.2266i	0.885410	+	1.04689i
$116$	−1.09686	+	0.468685i	−0.101841	+	0.0435163i
$117$	0.293173	−	0.149379i	0.0271039	−	0.0138101i
$118$	14.7831	−	11.7879i	1.36090	−	1.08516i
$119$	−0.483870	+	1.48920i	−0.0443563	+	0.136515i
$120$	−2.40195	−	11.3702i	−0.219267	−	1.03795i
$121$	2.64560	+	8.14232i	0.240509	+	0.740211i
$122$	0.686115	+	0.452952i	0.0621180	+	0.0410083i
$123$	−2.52374	−	15.9343i	−0.227558	−	1.43675i
$124$	13.1072	+	2.99306i	1.17706	+	0.268784i
$125$	0.715444	+	11.1574i	0.0639912	+	0.997950i
$126$	0.528774	+	0.0596063i	0.0471069	+	0.00531015i
$127$	−2.19028	+	0.346906i	−0.194356	+	0.0307830i	−0.252853	−	0.967505i	$-0.581369\pi$
$127$	−2.19028	+	0.346906i	−0.194356	+	0.0307830i	0.0584975	+	0.998288i	$0.481369\pi$
$128$	−10.7612	+	3.49222i	−0.951169	+	0.308671i
$129$	−10.0477	+	3.26470i	−0.884652	+	0.287441i
$130$	1.15955	+	2.51047i	0.101699	+	0.220183i
$131$	−16.0196	−	5.20510i	−1.39964	−	0.454772i	−0.490567	−	0.871403i	$-0.663210\pi$
$131$	−16.0196	−	5.20510i	−1.39964	−	0.454772i	−0.909075	+	0.416632i	$0.863210\pi$
$132$	−3.05274	−	4.85953i	−0.265707	−	0.422967i
$133$	−3.34040	−	6.55591i	−0.289650	−	0.568469i
$134$	5.19327	+	9.15355i	0.448631	+	0.790746i
$135$	−8.23101	+	6.96140i	−0.708413	+	0.599142i
$136$	3.64092	−	2.52160i	0.312206	−	0.216225i
$137$	−7.96951	−	1.26225i	−0.680881	−	0.107841i	−0.193592	−	0.981082i	$-0.562014\pi$
$137$	−7.96951	−	1.26225i	−0.680881	−	0.107841i	−0.487288	+	0.873241i	$0.662014\pi$
$138$	16.4711	+	4.54665i	1.40211	+	0.387037i
$139$	10.8438	+	7.87845i	0.919755	+	0.668241i	0.943463	−	0.331478i	$-0.107547\pi$
$139$	10.8438	+	7.87845i	0.919755	+	0.668241i	−0.0237077	+	0.999719i	$0.507547\pi$
$140$	−0.671838	+	4.42138i	−0.0567807	+	0.373675i
$141$	−9.17861	+	6.66865i	−0.772978	+	0.561602i
$142$	9.04224	−	3.39307i	0.758808	−	0.284740i
$143$	0.965620	+	0.965620i	0.0807492	+	0.0807492i
$144$	−1.08764	−	1.04032i	−0.0906368	−	0.0866937i
$145$	0.870988	−	1.00987i	0.0723316	−	0.0838649i
$146$	−19.0020	+	3.88965i	−1.57262	+	0.321909i
$147$	−1.63719	−	0.834190i	−0.135033	−	0.0688029i
$148$	−10.9531	−	0.739620i	−0.900340	−	0.0607964i
$149$			22.8135i			1.86895i	0.356024	+	0.934477i	$0.384132\pi$
$149$			22.8135i			1.86895i	−0.356024	+	0.934477i	$0.615868\pi$
$150$	8.00175	+	10.2365i	0.653340	+	0.835804i
$151$			18.1954i			1.48072i	0.672211	+	0.740360i	$0.265345\pi$
$151$			18.1954i			1.48072i	−0.672211	+	0.740360i	$0.734655\pi$
$152$	−3.71917	+	20.4762i	−0.301665	+	1.66084i
$153$	0.524957	+	0.267479i	0.0424403	+	0.0216244i
$154$	0.442882	+	2.16360i	0.0356885	+	0.174348i
$155$	−14.6330	+	3.43832i	−1.17535	+	0.276173i
$156$	2.75856	+	1.64855i	0.220861	+	0.131990i
$157$	0.401008	+	0.401008i	0.0320040	+	0.0320040i	0.722928	−	0.690924i	$-0.242796\pi$
$157$	0.401008	+	0.401008i	0.0320040	+	0.0320040i	−0.690924	+	0.722928i	$0.742796\pi$
$158$	−0.180777	−	0.481755i	−0.0143819	−	0.0383264i
$159$	3.76516	−	2.73555i	0.298597	−	0.216943i
$160$	9.08900	−	8.79717i	0.718548	−	0.695477i
$161$	−5.31976	−	3.86503i	−0.419256	−	0.304607i
$162$	−3.75823	+	13.6149i	−0.295274	+	1.06969i
$163$	−4.33524	−	0.686635i	−0.339562	−	0.0537814i	−0.0156752	−	0.999877i	$-0.504990\pi$
$163$	−4.33524	−	0.686635i	−0.339562	−	0.0537814i	−0.323887	+	0.946096i	$0.604990\pi$
$164$	13.2251	−	11.5520i	1.03271	−	0.902062i
$165$	5.45445	+	3.37887i	0.424628	+	0.263045i
$166$	−11.2138	+	6.36214i	−0.870356	+	0.493798i
$167$	7.10011	+	13.9348i	0.549423	+	1.07830i	0.984083	+	0.177709i	$0.0568686\pi$
$167$	7.10011	+	13.9348i	0.549423	+	1.07830i	−0.434660	+	0.900595i	$0.643131\pi$
$168$	2.25422	+	4.68280i	0.173917	+	0.361286i
$169$	11.6365	+	3.78091i	0.895112	+	0.290840i
$170$	−2.41634	+	4.32201i	−0.185325	+	0.331483i
$171$	−2.63303	+	0.855522i	−0.201353	+	0.0654234i
$172$	−8.82664	−	7.37056i	−0.673025	−	0.562000i
$173$	10.9679	−	1.73715i	0.833875	−	0.132073i	0.275125	−	0.961409i	$-0.411281\pi$
$173$	10.9679	−	1.73715i	0.833875	−	0.132073i	0.558751	+	0.829336i	$0.311281\pi$
$174$	0.173600	−	1.54002i	0.0131606	−	0.116749i
$175$	−1.49903	−	4.77000i	−0.113316	−	0.360578i
$176$	2.71141	−	5.62732i	0.204380	−	0.424175i
$177$	3.84300	+	24.2638i	0.288858	+	1.82378i
$178$	−9.06011	+	13.7239i	−0.679084	+	1.02865i
$179$	0.956101	+	2.94258i	0.0714624	+	0.219939i	0.980409	−	0.196975i	$-0.0631118\pi$
$179$	0.956101	+	2.94258i	0.0714624	+	0.219939i	−0.908946	+	0.416914i	$0.863112\pi$
$180$	1.60360	+	0.509927i	0.119525	+	0.0380077i
$181$	3.75172	−	11.5466i	0.278863	−	0.858253i	−0.709308	−	0.704899i	$-0.750993\pi$
$181$	3.75172	−	11.5466i	0.278863	−	0.858253i	0.988171	−	0.153354i	$-0.0490075\pi$
$182$	−0.771014	−	0.966924i	−0.0571514	−	0.0716732i
$183$	−0.951770	+	0.484951i	−0.0703568	+	0.0358486i
$184$	5.34616	+	17.8136i	0.394124	+	1.31324i
$185$	11.3621	−	4.64211i	0.835360	−	0.341295i
$186$	−11.7860	+	12.8931i	−0.864192	+	0.945365i
$187$	−0.382520	+	2.41513i	−0.0279726	+	0.176612i
$188$	−11.4608	−	4.59863i	−0.835864	−	0.335390i
$189$	2.83372	−	3.90028i	0.206123	−	0.283704i
$190$	−6.33197	−	22.3895i	−0.459369	−	1.62430i
$191$	7.29942	+	10.0468i	0.528167	+	0.726960i	0.986850	−	0.161640i	$-0.0516784\pi$
$191$	7.29942	+	10.0468i	0.528167	+	0.726960i	−0.458682	+	0.888600i	$0.651678\pi$
$192$	2.95309	−	14.4000i	0.213121	−	1.03923i
$193$	−6.87839	+	6.87839i	−0.495117	+	0.495117i	−0.909914	−	0.414797i	$-0.863853\pi$
$193$	−6.87839	+	6.87839i	−0.495117	+	0.495117i	0.414797	+	0.909914i	$0.363853\pi$
$194$	7.86993	−	17.3238i	0.565028	−	1.24378i
$195$	−3.58046	−	0.299213i	−0.256402	−	0.0214271i
$196$	−0.179072	−	1.99197i	−0.0127908	−	0.142283i
$197$	−1.77359	+	3.48086i	−0.126363	+	0.248001i	−0.945517	−	0.325572i	$-0.894443\pi$
$197$	−1.77359	+	3.48086i	−0.126363	+	0.248001i	0.819154	+	0.573573i	$0.194443\pi$
$198$	0.830138	−	0.0372384i	0.0589954	−	0.00264642i
$199$	10.3009			0.730210			0.365105	−	0.930966i	$-0.381033\pi$
$199$	10.3009			0.730210			0.365105	+	0.930966i	$0.381033\pi$
$200$	−4.80178	+	13.3020i	−0.339537	+	0.940593i
$201$	−13.6738			−0.964477
$202$	−18.8773	+	0.846801i	−1.32821	+	0.0595807i
$203$	−0.270759	+	0.531394i	−0.0190036	+	0.0372966i
$204$	0.515219	+	5.73122i	0.0360726	+	0.401266i
$205$	−7.60071	+	18.1017i	−0.530857	+	1.26428i
$206$	−4.88396	+	10.7509i	−0.340282	+	0.749050i
$207$	−1.74951	+	1.74951i	−0.121599	+	0.121599i
$208$	0.0777600	+	3.49703i	0.00539168	+	0.242475i
$209$	−6.75376	−	9.29576i	−0.467168	−	0.643001i
$210$	−4.56574	−	3.59399i	−0.315066	−	0.248009i
$211$	6.89265	−	9.48692i	0.474510	−	0.653106i	−0.502929	−	0.864328i	$-0.667744\pi$
$211$	6.89265	−	9.48692i	0.474510	−	0.653106i	0.977438	+	0.211222i	$0.0677441\pi$
$212$	4.70134	+	1.88641i	0.322889	+	0.129559i
$213$	−1.96299	+	12.3938i	−0.134502	+	0.849212i
$214$	−2.93479	+	3.21045i	−0.200618	+	0.219462i
$215$	12.4868	+	3.06173i	0.851590	+	0.208808i
$216$	−13.0604	+	3.91963i	−0.888646	+	0.266697i
$217$	5.98960	−	3.05185i	0.406600	−	0.207173i
$218$	12.2102	+	15.3128i	0.826982	+	1.03711i
$219$	7.78750	−	23.9675i	0.526230	−	1.61957i
$220$	0.0438664	+	6.98364i	0.00295747	+	0.470837i
$221$	−0.423131	−	1.30226i	−0.0284629	−	0.0875997i
$222$	7.85839	−	11.9036i	0.527420	−	0.798918i
$223$	2.53275	+	15.9912i	0.169606	+	1.07085i	0.914773	+	0.403969i	$0.132370\pi$
$223$	2.53275	+	15.9912i	0.169606	+	1.07085i	−0.745167	+	0.666878i	$0.767630\pi$
$224$	−3.01087	+	4.78901i	−0.201172	+	0.319979i
$225$	−1.86093	+	0.276324i	−0.124062	+	0.0184216i
$226$	−0.141578	+	1.25595i	−0.00941762	+	0.0835447i
$227$	8.80383	−	1.39439i	0.584331	−	0.0925489i	0.142732	−	0.989761i	$-0.454411\pi$
$227$	8.80383	−	1.39439i	0.584331	−	0.0925489i	0.441599	+	0.897213i	$0.354411\pi$
$228$	−20.7550	−	17.3312i	−1.37453	−	1.14779i
$229$	−28.6774	+	9.31785i	−1.89505	+	0.615741i	−0.920930	+	0.389727i	$0.872569\pi$
$229$	−28.6774	+	9.31785i	−1.89505	+	0.615741i	−0.974124	+	0.226013i	$0.927431\pi$
$230$	−14.1259	−	15.2592i	−0.931435	−	1.00616i
$231$	−2.72898	−	0.886698i	−0.179554	−	0.0583405i
$232$	1.51993	−	0.731668i	0.0997882	−	0.0480363i
$233$	1.67099	+	3.27951i	0.109470	+	0.214848i	0.939242	−	0.343255i	$-0.111530\pi$
$233$	1.67099	+	3.27951i	0.109470	+	0.214848i	−0.829772	+	0.558103i	$0.811530\pi$
$234$	−0.404726	+	0.229622i	−0.0264578	+	0.0150108i
$235$	13.7691	−	1.01669i	0.898196	−	0.0663216i
$236$	−20.1384	+	17.5907i	−1.31090	+	1.14506i
$237$	0.660323	+	0.104585i	0.0428926	+	0.00679351i
$238$	0.589230	−	2.13459i	0.0381941	−	0.138365i
$239$	4.18917	+	3.04361i	0.270975	+	0.196875i	0.714971	−	0.699154i	$-0.246440\pi$
$239$	4.18917	+	3.04361i	0.270975	+	0.196875i	−0.443996	+	0.896029i	$0.646440\pi$
$240$	4.11405	+	15.9115i	0.265561	+	1.02708i
$241$	−1.52063	+	1.10481i	−0.0979527	+	0.0711668i	−0.635684	−	0.771950i	$-0.719282\pi$
$241$	−1.52063	+	1.10481i	−0.0979527	+	0.0711668i	0.537731	+	0.843117i	$0.319282\pi$
$242$	−4.25371	−	11.3358i	−0.273439	−	0.728690i
$243$	−2.74932	−	2.74932i	−0.176369	−	0.176369i
$244$	−0.998045	−	0.596445i	−0.0638933	−	0.0381834i
$245$	1.15911	+	1.91219i	0.0740529	+	0.122165i
$246$	4.57537	+	22.3519i	0.291715	+	1.42511i
$247$	5.73296	+	2.92109i	0.364780	+	0.185865i
$248$	−18.7074	−	3.39790i	−1.18792	−	0.215767i
$249$		−	16.7514i		−	1.06158i
$250$	−1.71788	−	15.7178i	−0.108648	−	0.994080i
$251$		−	9.71920i		−	0.613471i	−0.951795	−	0.306735i	$-0.900763\pi$
$251$		−	9.71920i		−	0.613471i	0.951795	−	0.306735i	$-0.0992366\pi$
$252$	−0.750825	−	0.0507002i	−0.0472976	−	0.00319381i
$253$	−9.14936	−	4.66183i	−0.575215	−	0.293087i
$254$	3.07243	−	0.628916i	0.192781	−	0.0394617i
$255$	−3.33495	−	5.50168i	−0.208843	−	0.344529i
$256$	14.9821	−	5.61578i	0.936381	−	0.350986i
$257$	8.90329	+	8.90329i	0.555372	+	0.555372i	0.927986	−	0.372615i	$-0.121539\pi$
$257$	8.90329	+	8.90329i	0.555372	+	0.555372i	−0.372615	+	0.927986i	$0.621539\pi$
$258$	13.9884	−	5.24912i	0.870882	−	0.326796i
$259$	−4.44072	+	3.22637i	−0.275933	+	0.200477i
$260$	−1.79730	−	3.47329i	−0.111464	−	0.215404i
$261$	0.181548	+	0.131902i	0.0112375	+	0.00816453i
$262$	22.9623	+	6.33848i	1.41862	+	0.391592i
$263$	1.09646	+	0.173661i	0.0676103	+	0.0107084i	0.190148	−	0.981755i	$-0.439103\pi$
$263$	1.09646	+	0.173661i	0.0676103	+	0.0107084i	−0.122538	+	0.992464i	$0.539103\pi$
$264$	4.62086	+	6.67204i	0.284394	+	0.410635i
$265$	−5.64823	+	0.417057i	−0.346968	+	0.0256196i
$266$	5.13478	+	9.05044i	0.314834	+	0.554918i
$267$	−9.70017	−	19.0376i	−0.593641	−	1.16509i
$268$	−7.91713	−	12.6029i	−0.483616	−	0.769847i
$269$	7.46362	+	2.42508i	0.455065	+	0.147860i	0.527576	−	0.849508i	$-0.323101\pi$
$269$	7.46362	+	2.42508i	0.455065	+	0.147860i	−0.0725105	+	0.997368i	$0.523101\pi$
$270$	11.1875	−	10.3567i	0.680852	−	0.630286i
$271$	−3.48100	+	1.13104i	−0.211455	+	0.0687060i	−0.412829	−	0.910808i	$-0.635459\pi$
$271$	−3.48100	+	1.13104i	−0.211455	+	0.0687060i	0.201374	+	0.979514i	$0.435459\pi$
$272$	−4.98406	+	3.79324i	−0.302203	+	0.229999i
$273$	1.58703	−	0.251361i	0.0960513	−	0.0152130i
$274$	11.3393	+	1.27822i	0.685030	+	0.0772203i
$275$	−3.47736	−	6.99102i	−0.209693	−	0.421574i
$276$	−23.5584	−	5.37962i	−1.41805	−	0.323815i
$277$	3.11661	+	19.6775i	0.187259	+	1.18231i	0.884872	+	0.465833i	$0.154245\pi$
$277$	3.11661	+	19.6775i	0.187259	+	1.18231i	−0.697613	+	0.716475i	$0.745755\pi$
$278$	−15.8193	−	10.4434i	−0.948777	−	0.626353i
$279$	−0.781621	−	2.40558i	−0.0467944	−	0.144018i
$280$	0.668962	−	6.28908i	0.0399781	−	0.375844i
$281$	2.63483	−	8.10918i	0.157181	−	0.483753i	−0.841194	−	0.540733i	$-0.818147\pi$
$281$	2.63483	−	8.10918i	0.157181	−	0.483753i	0.998375	+	0.0569797i	$0.0181470\pi$
$282$	12.5448	−	10.0031i	0.747035	−	0.595677i
$283$	−4.69504	+	2.39224i	−0.279091	+	0.142204i	−0.587934	−	0.808909i	$-0.700058\pi$
$283$	−4.69504	+	2.39224i	−0.279091	+	0.142204i	0.308842	+	0.951113i	$0.400058\pi$
$284$	−12.5598	+	5.36676i	−0.745285	+	0.318459i
$285$	29.3615	+	7.19938i	1.73922	+	0.426455i
$286$	−1.42542	−	1.30303i	−0.0842867	−	0.0770495i
$287$	1.37349	−	8.67190i	0.0810748	−	0.511886i
$288$	1.60254	+	1.40083i	0.0944307	+	0.0825449i
$289$	−8.55119	+	11.7697i	−0.503011	+	0.692336i
$290$	−1.16652	+	1.48193i	−0.0685007	+	0.0870221i
$291$	14.5314	+	20.0007i	0.851844	+	1.17246i
$292$	26.5994	−	6.69952i	1.55661	−	0.392060i
$293$	17.0319	−	17.0319i	0.995013	−	0.995013i	−0.00497457	−	0.999988i	$-0.501583\pi$
$293$	17.0319	−	17.0319i	0.995013	−	0.995013i	0.999988	+	0.00497457i	$0.00158346\pi$
$294$	2.36588	+	1.07478i	0.137981	+	0.0626825i
$295$	11.5739	−	27.5641i	0.673858	−	1.60485i
$296$	15.5214	+	0.350775i	0.902160	+	0.0203884i
$297$	3.41790	−	6.70801i	0.198327	−	0.389238i
$298$	−1.44581	−	32.2307i	−0.0837534	−	1.86708i
$299$	5.75017			0.332541
$300$	−11.9536	−	13.9549i	−0.690139	−	0.805686i
$301$	−5.74967			−0.331405
$302$	−1.15314	−	25.7063i	−0.0663555	−	1.47923i
$303$	11.1462	−	21.8757i	0.640334	−	1.25673i
$304$	3.95674	−	29.1643i	0.226934	−	1.67269i
$305$	1.29541	+	0.108255i	0.0741748	+	0.00619868i
$306$	−0.758608	−	0.344623i	−0.0433667	−	0.0197008i
$307$	−5.32707	+	5.32707i	−0.304032	+	0.304032i	−0.842589	−	0.538557i	$-0.818970\pi$
$307$	−5.32707	+	5.32707i	−0.304032	+	0.304032i	0.538557	+	0.842589i	$0.318970\pi$
$308$	−0.762819	−	3.02865i	−0.0434656	−	0.172573i
$309$	−9.01795	−	12.4121i	−0.513013	−	0.706102i
$310$	20.4554	−	5.78500i	1.16179	−	0.328566i
$311$	13.8425	−	19.0526i	0.784937	−	1.08037i	−0.209783	−	0.977748i	$-0.567276\pi$
$311$	13.8425	−	19.0526i	0.784937	−	1.08037i	0.994720	−	0.102625i	$-0.0327242\pi$
$312$	−4.00175	−	2.15424i	−0.226554	−	0.121960i
$313$	1.63340	−	10.3129i	0.0923255	−	0.582920i	−0.897542	−	0.440928i	$-0.854649\pi$
$313$	1.63340	−	10.3129i	0.0923255	−	0.582920i	0.989868	−	0.141992i	$-0.0453507\pi$
$314$	−0.591956	−	0.541128i	−0.0334060	−	0.0305376i
$315$	0.778863	−	0.318213i	0.0438840	−	0.0179292i
$316$	0.285932	+	0.669163i	0.0160849	+	0.0376434i
$317$	−25.1901	+	12.8350i	−1.41482	+	0.720886i	−0.983431	−	0.181281i	$-0.941976\pi$
$317$	−25.1901	+	12.8350i	−1.41482	+	0.720886i	−0.431387	+	0.902167i	$0.641976\pi$
$318$	−5.14603	+	4.10338i	−0.288575	+	0.230106i
$319$	−0.287802	+	0.885763i	−0.0161138	+	0.0495932i
$320$	−12.2833	+	13.0046i	−0.686660	+	0.726979i
$321$	−1.74641	−	5.37489i	−0.0974750	−	0.299997i
$322$	7.76067	+	5.12335i	0.432485	+	0.285513i
$323$	1.80232	+	11.3794i	0.100284	+	0.633165i
$324$	4.44675	−	19.4732i	0.247042	−	1.08184i
$325$	3.51230	+	2.60410i	0.194827	+	0.144449i
$326$	6.16831	+	0.695326i	0.341631	+	0.0385106i
$327$	−25.1331	+	3.98069i	−1.38986	+	0.220133i
$328$	−17.9523	+	17.1588i	−0.991248	+	0.947435i
$329$	−5.87229	+	1.90802i	−0.323750	+	0.105193i
$330$	−7.92014	−	4.42797i	−0.435989	−	0.243752i
$331$	−31.5213	−	10.2419i	−1.73257	−	0.562946i	−0.738752	−	0.673977i	$-0.764585\pi$
$331$	−31.5213	−	10.2419i	−1.73257	−	0.562946i	−0.993817	+	0.111031i	$0.964585\pi$
$332$	15.4395	−	9.69905i	0.847353	−	0.532305i
$333$	0.937646	+	1.84023i	0.0513827	+	0.100844i
$334$	−10.9141	−	19.2370i	−0.597193	−	1.05260i
$335$	14.1458	+	8.76294i	0.772870	+	0.478770i
$336$	−3.48152	−	6.47297i	−0.189932	−	0.353129i
$337$	29.1114	+	4.61079i	1.58580	+	0.251166i	0.886177	−	0.463347i	$-0.153352\pi$
$337$	29.1114	+	4.61079i	1.58580	+	0.251166i	0.699622	+	0.714513i	$0.253352\pi$
$338$	−16.6795	−	4.60419i	−0.907246	−	0.250435i
$339$	−1.32855	−	0.965245i	−0.0721567	−	0.0524249i
$340$	3.13987	−	6.25924i	0.170284	−	0.339455i
$341$	8.49277	−	6.17036i	0.459909	−	0.334144i
$342$	3.66570	−	1.37554i	0.198219	−	0.0743809i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	12.9373	+	9.85368i	0.697534	+	0.531275i
$345$	26.3008	−	6.17992i	1.41599	−	0.332716i
$346$	−15.3853	+	3.14932i	−0.827119	+	0.169309i
$347$	−7.32897	−	3.73430i	−0.393440	−	0.200468i	0.246067	−	0.969253i	$-0.420862\pi$
$347$	−7.32897	−	3.73430i	−0.393440	−	0.200468i	−0.639507	+	0.768785i	$0.720862\pi$
$348$	−0.147662	+	2.18674i	−0.00791549	+	0.117221i
$349$			3.49531i			0.187100i	0.995615	+	0.0935499i	$0.0298215\pi$
$349$			3.49531i			0.187100i	−0.995615	+	0.0935499i	$0.970179\pi$
$350$	2.42012	+	6.64402i	0.129361	+	0.355138i
$351$			4.21584i			0.225025i
$352$	−3.47403	+	8.12207i	−0.185167	+	0.432908i
$353$	10.1869	+	5.19050i	0.542196	+	0.276263i	0.703564	−	0.710632i	$-0.251591\pi$
$353$	10.1869	+	5.19050i	0.542196	+	0.276263i	−0.161368	+	0.986894i	$0.551591\pi$
$354$	−6.96709	−	34.0361i	−0.370297	−	1.80900i
$355$	9.97341	−	11.5637i	0.529334	−	0.613736i
$356$	11.9303	−	19.9633i	0.632305	−	1.05805i
$357$	2.03446	+	2.03446i	0.107675	+	0.107675i
$358$	−1.53726	−	4.09666i	−0.0812467	−	0.216515i
$359$	−8.23859	+	5.98568i	−0.434816	+	0.315912i	−0.783572	−	0.621301i	$-0.786604\pi$
$359$	−8.23859	+	5.98568i	−0.434816	+	0.315912i	0.348756	+	0.937214i	$0.386604\pi$
$360$	−2.29787	−	0.618793i	−0.121108	−	0.0326132i
$361$	−28.4274	−	20.6537i	−1.49618	−	1.08704i
$362$	−4.56864	+	16.5507i	−0.240122	+	0.869887i
$363$	15.5375	+	2.46089i	0.815506	+	0.129163i
$364$	1.15056	+	1.31720i	0.0603058	+	0.0690401i
$365$	−23.4160	+	19.8041i	−1.22565	+	1.03660i
$366$	1.31392	−	0.745454i	0.0686797	−	0.0389655i
$367$	−9.93211	−	19.4929i	−0.518452	−	1.01752i	−0.990701	−	0.136054i	$-0.956558\pi$
$367$	−9.93211	−	19.4929i	−0.518452	−	1.01752i	0.472250	−	0.881465i	$-0.343442\pi$
$368$	−8.68196	−	24.8282i	−0.452579	−	1.29426i
$369$	−3.14194	−	1.02088i	−0.163563	−	0.0531448i
$370$	−15.7581	+	7.27842i	−0.819226	+	0.378387i
$371$	2.40887	−	0.782691i	0.125063	−	0.0406353i
$372$	15.8341	−	18.9622i	0.820959	−	0.983142i
$373$	0.254939	−	0.0403784i	0.0132002	−	0.00209071i	−0.149831	−	0.988712i	$-0.547873\pi$
$373$	0.254939	−	0.0403784i	0.0132002	−	0.00209071i	0.163031	+	0.986621i	$0.447873\pi$
$374$	0.387362	−	3.43633i	0.0200300	−	0.177688i
$375$	18.8637	+	8.13610i	0.974115	+	0.420146i
$376$	16.4832	+	5.77059i	0.850054	+	0.297595i
$377$	−0.0815858	−	0.515113i	−0.00420188	−	0.0265296i
$378$	−3.75628	+	5.68987i	−0.193202	+	0.292655i
$379$	−9.20077	−	28.3171i	−0.472612	−	1.45455i	−0.849151	−	0.528150i	$-0.822886\pi$
$379$	−9.20077	−	28.3171i	−0.472612	−	1.45455i	0.376539	−	0.926401i	$-0.377114\pi$
$380$	10.3647	+	31.2304i	0.531698	+	1.60209i
$381$	−1.25916	+	3.87529i	−0.0645087	+	0.198537i
$382$	−10.9493	−	13.7314i	−0.560214	−	0.702561i
$383$	−12.3531	+	6.29423i	−0.631215	+	0.321620i	−0.740163	−	0.672427i	$-0.765252\pi$
$383$	−12.3531	+	6.29423i	−0.631215	+	0.321620i	0.108948	+	0.994047i	$0.465252\pi$
$384$	−3.25950	+	20.5314i	−0.166336	+	1.04774i
$385$	2.25493	+	2.66619i	0.114922	+	0.135881i
$386$	9.28181	−	10.1537i	0.472432	−	0.516807i
$387$	−0.338432	+	2.13678i	−0.0172035	+	0.108619i
$388$	−10.0207	+	24.9737i	−0.508723	+	1.26785i
$389$	15.0045	−	20.6519i	0.760758	−	1.04709i	−0.236393	−	0.971657i	$-0.575965\pi$
$389$	15.0045	−	20.6519i	0.760758	−	1.04709i	0.997151	−	0.0754355i	$-0.0240347\pi$
$390$	5.07741	+	0.195815i	0.257104	+	0.00991546i
$391$	6.05201	+	8.32988i	0.306063	+	0.421260i
$392$	0.379233	+	2.80289i	0.0191541	+	0.141567i
$393$	−21.8852	+	21.8852i	−1.10396	+	1.10396i
$394$	2.28511	−	5.03013i	0.115122	−	0.253415i
$395$	−0.616093	−	0.531366i	−0.0309990	−	0.0267359i
$396$	−1.17045	+	0.105220i	−0.0588175	+	0.00528752i
$397$	−17.5987	+	34.5394i	−0.883254	+	1.73348i	−0.235103	+	0.971970i	$0.575543\pi$
$397$	−17.5987	+	34.5394i	−0.883254	+	1.73348i	−0.648151	+	0.761512i	$0.724457\pi$
$398$	−14.5530	+	0.652819i	−0.729476	+	0.0327229i
$399$	−13.5198			−0.676837
$400$	5.94091	−	19.0973i	0.297045	−	0.954863i
$401$	19.1670			0.957152			0.478576	−	0.878046i	$-0.341153\pi$
$401$	19.1670			0.957152			0.478576	+	0.878046i	$0.341153\pi$
$402$	19.3183	−	0.866580i	0.963508	−	0.0432211i
$403$	−2.66876	+	5.23774i	−0.132940	+	0.260910i
$404$	26.6161	−	2.39271i	1.32420	−	0.119042i
$405$	5.10828	+	21.7400i	0.253832	+	1.08027i
$406$	0.348849	−	0.767909i	0.0173131	−	0.0381107i
$407$	−6.06116	+	6.06116i	−0.300440	+	0.300440i
$408$	−1.09111	−	8.06437i	−0.0540182	−	0.399246i
$409$	14.1475	+	19.4724i	0.699551	+	0.962849i	0.999959	+	0.00903813i	$0.00287697\pi$
$409$	14.1475	+	19.4724i	0.699551	+	0.962849i	−0.300409	+	0.953811i	$0.597123\pi$
$410$	9.59103	−	26.0556i	0.473667	−	1.28680i
$411$	−8.71462	+	11.9947i	−0.429861	+	0.591652i
$412$	6.21868	−	15.4983i	0.306373	−	0.763547i
$413$	−2.09147	+	13.2050i	−0.102915	+	0.649778i
$414$	2.36082	−	2.58257i	0.116028	−	0.126926i
$415$	−10.7352	+	17.3297i	−0.526972	+	0.850680i
$416$	−0.331483	−	4.93565i	−0.0162523	−	0.241990i
$417$	21.9443	−	11.1812i	1.07462	−	0.547544i
$418$	10.1308	+	12.7050i	0.495513	+	0.621420i
$419$	−6.37100	+	19.6079i	−0.311244	+	0.957909i	0.666030	+	0.745925i	$0.267992\pi$
$419$	−6.37100	+	19.6079i	−0.311244	+	0.957909i	−0.977273	+	0.211984i	$0.932008\pi$
$420$	6.67821	+	4.78820i	0.325863	+	0.233640i
$421$	−4.04116	−	12.4374i	−0.196954	−	0.606162i	−0.999948	−	0.0101752i	$-0.996761\pi$
$421$	−4.04116	−	12.4374i	−0.196954	−	0.606162i	0.802994	−	0.595987i	$-0.203239\pi$
$422$	−9.13665	+	13.8399i	−0.444765	+	0.673715i
$423$	0.363438	+	2.29466i	0.0176710	+	0.111570i
$424$	−6.76157	−	2.36716i	−0.328371	−	0.114959i
$425$	−0.0757062	+	7.82881i	−0.00367229	+	0.379753i
$426$	1.98784	−	17.6343i	0.0963111	−	0.854386i
$427$	−0.574186	+	0.0909421i	−0.0277868	+	0.00440100i
$428$	3.94278	−	4.72169i	0.190582	−	0.228232i
$429$	2.38642	−	0.775394i	0.115217	−	0.0374364i
$430$	−17.8352	−	3.53424i	−0.860092	−	0.170436i
$431$	−23.1350	−	7.51701i	−1.11437	−	0.362081i	−0.306755	−	0.951789i	$-0.599243\pi$
$431$	−23.1350	−	7.51701i	−1.11437	−	0.362081i	−0.807617	+	0.589707i	$0.799243\pi$
$432$	18.2032	−	6.36534i	0.875802	−	0.306252i
$433$	1.37600	+	2.70056i	0.0661266	+	0.129781i	0.921704	−	0.387895i	$-0.126798\pi$
$433$	1.37600	+	2.70056i	0.0661266	+	0.129781i	−0.855577	+	0.517675i	$0.826798\pi$
$434$	−8.26865	+	4.69123i	−0.396908	+	0.225186i
$435$	−0.926776	−	2.26839i	−0.0444355	−	0.108761i
$436$	−18.2210	−	20.8600i	−0.872627	−	0.999011i
$437$	−47.7867	−	7.56866i	−2.28595	−	0.362058i
$438$	−9.48318	+	34.3546i	−0.453124	+	1.64153i
$439$	22.4113	+	16.2827i	1.06963	+	0.777132i	0.975846	−	0.218460i	$-0.0701034\pi$
$439$	22.4113	+	16.2827i	1.06963	+	0.777132i	0.0937850	+	0.995592i	$0.470103\pi$
$440$	−0.504563	−	9.86365i	−0.0240541	−	0.470231i
$441$	−0.304407	+	0.221165i	−0.0144956	+	0.0105316i
$442$	0.680328	+	1.81301i	0.0323599	+	0.0862362i
$443$	−14.7788	−	14.7788i	−0.702162	−	0.702162i	0.262713	−	0.964874i	$-0.415383\pi$
$443$	−14.7788	−	14.7788i	−0.702162	−	0.702162i	−0.964874	+	0.262713i	$0.915383\pi$
$444$	−10.3479	+	17.3154i	−0.491089	+	0.821750i
$445$	−2.16536	+	25.9112i	−0.102648	+	1.22831i
$446$	−4.59169	−	22.4317i	−0.217423	−	1.06217i
$447$	37.3500	+	19.0308i	1.76660	+	0.900126i
$448$	3.95023	−	6.95670i	0.186631	−	0.328673i
$449$		−	9.63653i		−	0.454776i	−0.973804	−	0.227388i	$-0.926981\pi$
$449$		−	9.63653i		−	0.454776i	0.973804	−	0.227388i	$-0.0730186\pi$
$450$	2.61160	−	0.508326i	0.123112	−	0.0239627i
$451$		−	13.7110i		−	0.645627i
$452$	0.120424	−	1.78337i	0.00566427	−	0.0838828i
$453$	29.7893	+	15.1784i	1.39962	+	0.713144i
$454$	−12.3496	+	2.52793i	−0.579596	+	0.118641i
$455$	−1.80290	−	0.757017i	−0.0845211	−	0.0354895i
$456$	30.4209	+	23.1700i	1.42459	+	1.08504i
$457$	−9.95549	−	9.95549i	−0.465698	−	0.465698i	0.434820	−	0.900518i	$-0.356812\pi$
$457$	−9.95549	−	9.95549i	−0.465698	−	0.465698i	−0.900518	+	0.434820i	$0.856812\pi$
$458$	39.9247	−	14.9816i	1.86556	−	0.700045i
$459$	−6.10720	+	4.43714i	−0.285060	+	0.207108i
$460$	20.9240	+	20.6628i	0.975588	+	0.963409i
$461$	−21.7208	−	15.7811i	−1.01164	−	0.734998i	−0.0470854	−	0.998891i	$-0.514993\pi$
$461$	−21.7208	−	15.7811i	−1.01164	−	0.734998i	−0.964552	+	0.263893i	$0.914993\pi$
$462$	3.91167	+	1.07977i	0.181988	+	0.0502355i
$463$	15.8375	+	2.50842i	0.736032	+	0.116576i	0.513186	−	0.858278i	$-0.328465\pi$
$463$	15.8375	+	2.50842i	0.736032	+	0.116576i	0.222846	+	0.974854i	$0.428465\pi$
$464$	−2.10098	+	1.13002i	−0.0975353	+	0.0524599i
$465$	−6.57748	+	26.8252i	−0.305024	+	1.24399i
$466$	−2.56860	−	4.52736i	−0.118988	−	0.209726i
$467$	−0.843425	−	1.65531i	−0.0390291	−	0.0765988i	0.870668	−	0.491870i	$-0.163687\pi$
$467$	−0.843425	−	1.65531i	−0.0390291	−	0.0765988i	−0.909698	+	0.415271i	$0.863687\pi$
$468$	0.557241	−	0.350057i	0.0257585	−	0.0161814i
$469$	−7.07747	−	2.29961i	−0.326807	−	0.106186i
$470$	−19.3884	+	2.30899i	−0.894322	+	0.106506i
$471$	0.991045	−	0.322010i	0.0456649	−	0.0148374i
$472$	27.3366	−	26.1283i	1.25827	−	1.20265i
$473$	−8.86825	+	1.40459i	−0.407762	+	0.0645832i
$474$	−0.939527	−	0.105909i	−0.0431539	−	0.00486455i
$475$	−25.7612	−	26.2643i	−1.18201	−	1.20509i
$476$	−0.697180	+	3.05308i	−0.0319552	+	0.139938i
$477$	−0.149086	−	0.941292i	−0.00682618	−	0.0430988i
$478$	−6.11132	−	4.03450i	−0.279525	−	0.184534i
$479$	3.20628	+	9.86791i	0.146499	+	0.450876i	0.997201	−	0.0747718i	$-0.0238228\pi$
$479$	3.20628	+	9.86791i	0.146499	+	0.450876i	−0.850702	+	0.525648i	$0.823823\pi$
$480$	−6.82069	−	22.2189i	−0.311320	−	1.01415i
$481$	1.48328	−	4.56508i	0.0676319	−	0.208150i
$482$	2.07832	−	1.65723i	0.0946651	−	0.0754848i
$483$	−10.7655	+	5.48529i	−0.489847	+	0.249589i
$484$	6.72801	+	15.7455i	0.305819	+	0.715704i
$485$	−2.21543	−	30.0036i	−0.100597	−	1.36239i
$486$	4.05846	+	3.70998i	0.184095	+	0.168288i
$487$	−0.969090	+	6.11859i	−0.0439137	+	0.277260i	−0.999868	−	0.0162559i	$-0.994825\pi$
$487$	−0.969090	+	6.11859i	−0.0439137	+	0.277260i	0.955954	+	0.293516i	$0.0948254\pi$
$488$	1.44783	+	0.779401i	0.0655402	+	0.0352818i
$489$	−4.74057	+	6.52483i	−0.214376	+	0.295063i
$490$	−1.75877	−	2.62807i	−0.0794531	−	0.118724i
$491$	−14.4929	−	19.9478i	−0.654055	−	0.900229i	0.345211	−	0.938525i	$-0.387807\pi$
$491$	−14.4929	−	19.9478i	−0.654055	−	0.900229i	−0.999266	+	0.0382955i	$0.987807\pi$
$492$	−7.88060	−	31.2887i	−0.355285	−	1.41060i
$493$	0.660340	−	0.660340i	0.0297402	−	0.0297402i
$494$	−8.28462	−	3.76357i	−0.372742	−	0.169331i
$495$	1.12358	−	0.681078i	0.0505010	−	0.0306122i
$496$	26.6450	+	3.61495i	1.19640	+	0.162316i
$497$	−3.10038	+	6.08483i	−0.139071	+	0.272942i
$498$	1.06162	+	23.6663i	0.0475725	+	1.06051i
$499$	−12.1323			−0.543116			−0.271558	−	0.962422i	$-0.587539\pi$
$499$	−12.1323			−0.543116			−0.271558	+	0.962422i	$0.587539\pi$
$500$	3.42312	+	22.0971i	0.153087	+	0.988213i
$501$	28.7367			1.28386
$502$	0.615956	+	13.7312i	0.0274914	+	0.612854i
$503$	−5.33333	+	10.4673i	−0.237801	+	0.466712i	−0.978806	−	0.204788i	$-0.934350\pi$
$503$	−5.33333	+	10.4673i	−0.237801	+	0.466712i	0.741005	+	0.671500i	$0.234350\pi$
$504$	1.06397	+	0.0240453i	0.0473932	+	0.00107106i
$505$	−25.5501	+	15.4877i	−1.13697	+	0.689194i
$506$	13.2216	+	6.00636i	0.587771	+	0.267015i
$507$	15.8971	−	15.8971i	0.706015	−	0.706015i
$508$	−4.30085	+	1.08324i	−0.190819	+	0.0480612i
$509$	−15.6045	−	21.4777i	−0.691656	−	0.951983i	−1.00000		0.000708128i	$-0.999775\pi$
$509$	−15.6045	−	21.4777i	−0.691656	−	0.951983i	0.308343	−	0.951275i	$-0.400225\pi$
$510$	5.06027	+	7.56138i	0.224072	+	0.334824i
$511$	8.06150	−	11.0957i	0.356620	−	0.490845i
$512$	−20.8107	+	8.88342i	−0.919711	+	0.392596i
$513$	5.54910	−	35.0356i	0.244999	−	1.54686i
$514$	−13.1427	−	12.0143i	−0.579702	−	0.529926i
$515$	1.37486	+	18.6198i	0.0605836	+	0.820486i
$516$	−19.4301	+	8.30244i	−0.855363	+	0.365495i
$517$	−8.59126	+	4.37747i	−0.377843	+	0.192521i
$518$	6.06934	−	4.83962i	0.266672	−	0.212641i
$519$	6.30529	−	19.4057i	0.276772	−	0.851815i
$520$	2.75933	+	4.79314i	0.121005	+	0.210193i
$521$	8.26017	+	25.4222i	0.361885	+	1.11377i	0.951909	+	0.306381i	$0.0991182\pi$
$521$	8.26017	+	25.4222i	0.361885	+	1.11377i	−0.590024	+	0.807386i	$0.700882\pi$
$522$	−0.264848	−	0.174845i	−0.0115921	−	0.00765274i
$523$	5.89983	+	37.2500i	0.257981	+	1.62883i	0.687790	+	0.725910i	$0.258581\pi$
$523$	5.89983	+	37.2500i	0.257981	+	1.62883i	−0.429808	+	0.902920i	$0.641419\pi$
$524$	−32.8427	−	7.49972i	−1.43474	−	0.327627i
$525$	−9.05988	−	1.52489i	−0.395406	−	0.0665517i
$526$	−1.56007	−	0.175860i	−0.0680223	−	0.00766785i
$527$	−10.3964	+	1.64663i	−0.452874	+	0.0717282i
$528$	−6.95116	−	9.13336i	−0.302510	−	0.397478i
$529$	−19.2478	+	6.25400i	−0.836862	+	0.271913i
$530$	7.95334	−	0.947172i	0.345471	−	0.0411425i
$531$	4.78435	+	1.55453i	0.207623	+	0.0674609i
$532$	−7.82795	−	12.4610i	−0.339385	−	0.540252i
$533$	3.48568	+	6.84103i	0.150982	+	0.296318i
$534$	14.9108	+	26.2815i	0.645255	+	1.13731i
$535$	−1.63783	+	6.67963i	−0.0708097	+	0.288785i
$536$	11.9840	+	17.3036i	0.517629	+	0.747401i
$537$	5.61513	+	0.889349i	0.242311	+	0.0383783i
$538$	−10.6982	−	2.95313i	−0.461234	−	0.127318i
$539$	−1.26338	−	0.917897i	−0.0544175	−	0.0395366i
$540$	−15.1493	+	15.3408i	−0.651922	+	0.660164i
$541$	16.7206	−	12.1483i	0.718877	−	0.522295i	−0.167148	−	0.985932i	$-0.553456\pi$
$541$	16.7206	−	12.1483i	0.718877	−	0.522295i	0.886025	+	0.463637i	$0.153456\pi$
$542$	4.84625	−	1.81854i	0.208164	−	0.0781130i
$543$	−15.7744	−	15.7744i	−0.676942	−	0.676942i
$544$	6.80104	−	5.67492i	0.291592	−	0.243310i
$545$	28.5517	+	11.9886i	1.22302	+	0.513534i
$546$	−2.22621	+	0.455698i	−0.0952731	+	0.0195021i
$547$	26.3928	+	13.4478i	1.12847	+	0.574986i	0.915599	−	0.402094i	$-0.131717\pi$
$547$	26.3928	+	13.4478i	1.12847	+	0.574986i	0.212875	+	0.977079i	$0.431717\pi$
$548$	−16.1010	−	1.08724i	−0.687802	−	0.0464445i
$549$			0.218741i			0.00933562i
$550$	5.35585	+	9.65648i	0.228374	+	0.411754i
$551$			4.38822i			0.186944i
$552$	33.6240	+	6.10727i	1.43113	+	0.259943i
$553$	0.324189	+	0.165183i	0.0137859	+	0.00702428i
$554$	−5.65020	−	27.6028i	−0.240054	−	1.17273i
$555$	1.87815	−	22.4744i	0.0797230	−	0.953984i
$556$	23.0112	+	13.7518i	0.975893	+	0.583206i
$557$	−9.98336	−	9.98336i	−0.423009	−	0.423009i	0.463230	−	0.886238i	$-0.346690\pi$
$557$	−9.98336	−	9.98336i	−0.423009	−	0.423009i	−0.886238	+	0.463230i	$0.846690\pi$
$558$	1.25672	+	3.34905i	0.0532013	+	0.141777i
$559$	4.06768	−	2.95534i	0.172044	−	0.124998i
$560$	−0.546534	+	8.92756i	−0.0230953	+	0.377258i
$561$	3.63494	+	2.64094i	0.153467	+	0.111501i
$562$	−3.20855	+	11.6236i	−0.135345	+	0.490311i
$563$	10.9636	+	1.73646i	0.462060	+	0.0731830i	0.383124	−	0.923697i	$-0.374848\pi$
$563$	10.9636	+	1.73646i	0.462060	+	0.0731830i	0.0789350	+	0.996880i	$0.474848\pi$
$564$	−17.0893	+	14.9274i	−0.719590	+	0.628555i
$565$	0.755824	+	1.84997i	0.0317978	+	0.0778288i
$566$	6.48151	−	3.67729i	0.272438	−	0.154568i
$567$	−4.53411	−	8.89868i	−0.190415	−	0.373710i
$568$	17.4042	−	8.37810i	0.730265	−	0.351537i
$569$	−31.0555	−	10.0906i	−1.30192	−	0.423018i	−0.425669	−	0.904879i	$-0.639961\pi$
$569$	−31.0555	−	10.0906i	−1.30192	−	0.423018i	−0.876248	+	0.481861i	$0.839961\pi$
$570$	−41.9379	−	8.31045i	−1.75659	−	0.348086i
$571$	38.5498	−	12.5256i	1.61326	−	0.524180i	0.642922	−	0.765932i	$-0.277722\pi$
$571$	38.5498	−	12.5256i	1.61326	−	0.524180i	0.970338	+	0.241752i	$0.0777220\pi$
$572$	2.09640	+	1.75057i	0.0876549	+	0.0731949i
$573$	22.5376	−	3.56961i	0.941522	−	0.149123i
$574$	−1.39088	+	12.3386i	−0.0580542	+	0.515005i
$575$	−31.1691	−	10.4617i	−1.29984	−	0.436284i
$576$	−2.35284	−	1.87753i	−0.0980349	−	0.0782302i
$577$	1.03461	+	6.53230i	0.0430716	+	0.271943i	0.999820	−	0.0189734i	$-0.00603979\pi$
$577$	1.03461	+	6.53230i	0.0430716	+	0.271943i	−0.956748	+	0.290917i	$0.906040\pi$
$578$	11.3352	−	17.1701i	0.471480	−	0.714182i
$579$	5.52335	+	16.9991i	0.229542	+	0.706459i
$580$	1.55414	−	2.16759i	0.0645321	−	0.0900044i
$581$	2.81719	−	8.67041i	0.116877	−	0.359709i
$582$	−21.7974	−	27.3359i	−0.903529	−	1.13311i
$583$	3.52423	−	1.79568i	0.145959	−	0.0743696i
$584$	−37.1548	+	11.1508i	−1.53748	+	0.461422i
$585$	−0.387455	+	0.625461i	−0.0160193	+	0.0258596i
$586$	−22.9831	+	25.1419i	−0.949424	+	1.03860i
$587$	−0.306516	+	1.93527i	−0.0126513	+	0.0798770i	−0.993206	−	0.116368i	$-0.962875\pi$
$587$	−0.306516	+	1.93527i	−0.0126513	+	0.0798770i	0.980555	+	0.196245i	$0.0628748\pi$
$588$	−3.41061	−	1.36851i	−0.140651	−	0.0564362i
$589$	29.0728	−	40.0153i	1.19793	−	1.64880i
$590$	−14.6046	+	39.6759i	−0.601263	+	1.63343i
$591$	4.21932	+	5.80740i	0.173560	+	0.238884i
$592$	−21.9507	+	0.488096i	−0.902168	+	0.0200606i
$593$	−3.10695	+	3.10695i	−0.127587	+	0.127587i	−0.768017	−	0.640430i	$-0.778756\pi$
$593$	−3.10695	+	3.10695i	−0.127587	+	0.127587i	0.640430	+	0.768017i	$0.278756\pi$
$594$	−4.40367	+	9.69365i	−0.180685	+	0.397735i
$595$	−0.800896	−	3.40849i	−0.0328335	−	0.139734i
$596$	4.08525	+	45.4437i	0.167339	+	1.86145i
$597$	8.59289	−	16.8645i	0.351684	−	0.690218i
$598$	−8.12380	+	0.364418i	−0.332207	+	0.0149022i
$599$	31.4841			1.28640			0.643202	−	0.765696i	$-0.277606\pi$
$599$	31.4841			1.28640			0.643202	+	0.765696i	$0.277606\pi$
$600$	17.7723	+	18.9578i	0.725551	+	0.773950i
$601$	−37.1216			−1.51422			−0.757111	−	0.653286i	$-0.773390\pi$
$601$	−37.1216			−1.51422			−0.757111	+	0.653286i	$0.773390\pi$
$602$	8.12309	−	0.364386i	0.331072	−	0.0148513i
$603$	−1.27120	+	2.49488i	−0.0517674	+	0.101599i
$604$	3.25828	+	36.2446i	0.132578	+	1.47477i
$605$	−14.4967	−	12.5031i	−0.589376	−	0.508324i
$606$	−14.3609	+	31.6122i	−0.583373	+	1.28416i
$607$	−8.34507	+	8.34507i	−0.338716	+	0.338716i	−0.855884	−	0.517168i	$-0.826986\pi$
$607$	−8.34507	+	8.34507i	−0.338716	+	0.338716i	0.517168	+	0.855884i	$0.326986\pi$
$608$	−3.74176	+	41.4539i	−0.151748	+	1.68118i
$609$	0.644129	+	0.886568i	0.0261014	+	0.0359256i
$610$	−1.83700	−	0.0708456i	−0.0743781	−	0.00286845i
$611$	3.17370	−	4.36822i	0.128394	−	0.176719i
$612$	1.09360	+	0.438805i	0.0442060	+	0.0177376i
$613$	−3.12942	+	19.7584i	−0.126396	+	0.798033i	0.840303	+	0.542117i	$0.182377\pi$
$613$	−3.12942	+	19.7584i	−0.126396	+	0.798033i	−0.966699	+	0.255916i	$0.917623\pi$
$614$	7.18844	−	7.86365i	0.290102	−	0.317351i
$615$	23.2955	+	27.5441i	0.939365	+	1.11068i
$616$	1.26965	+	4.23051i	0.0511555	+	0.170452i
$617$	38.1855	−	19.4565i	1.53729	−	0.783288i	0.539031	−	0.842286i	$-0.318790\pi$
$617$	38.1855	−	19.4565i	1.53729	−	0.783288i	0.998258	+	0.0589976i	$0.0187904\pi$
$618$	13.5271	+	16.9643i	0.544140	+	0.682403i
$619$	−10.1656	+	31.2865i	−0.408590	+	1.25751i	0.509271	+	0.860607i	$0.329915\pi$
$619$	−10.1656	+	31.2865i	−0.408590	+	1.25751i	−0.917860	+	0.396904i	$0.870085\pi$
$620$	−28.5327	+	9.46937i	−1.14590	+	0.380299i
$621$	−9.79614	−	30.1494i	−0.393106	−	1.20985i
$622$	−18.3491	+	27.7946i	−0.735734	+	1.11446i
$623$	−1.81906	−	11.4851i	−0.0728790	−	0.460140i
$624$	5.79017	+	2.78988i	0.231792	+	0.111684i
$625$	−14.3008	−	20.5058i	−0.572030	−	0.820233i
$626$	−1.65408	+	14.6735i	−0.0661103	+	0.586472i
$627$	−20.8529	+	3.30277i	−0.832783	+	0.131900i
$628$	0.870605	+	0.726986i	0.0347409	+	0.0290099i
$629$	8.17425	−	2.65598i	0.325929	−	0.105901i
$630$	−1.08021	+	0.498929i	−0.0430364	+	0.0198778i
$631$	−31.0577	−	10.0913i	−1.23639	−	0.401727i	−0.383364	−	0.923597i	$-0.625235\pi$
$631$	−31.0577	−	10.0913i	−1.23639	−	0.401727i	−0.853025	+	0.521870i	$0.825235\pi$
$632$	−0.446371	−	0.927268i	−0.0177557	−	0.0368847i
$633$	−9.78211	−	19.1985i	−0.388804	−	0.763071i
$634$	34.7750	−	19.7296i	1.38109	−	0.783564i
$635$	3.78613	−	3.20213i	0.150248	−	0.127073i
$636$	7.01022	−	6.12336i	0.277973	−	0.242807i
$637$	0.863706	+	0.136798i	0.0342213	+	0.00542012i
$638$	0.350469	−	1.26964i	0.0138752	−	0.0502655i
$639$	2.07885	+	1.51037i	0.0822378	+	0.0597493i
$640$	16.5297	−	19.1513i	0.653392	−	0.757020i
$641$	−16.3183	+	11.8560i	−0.644536	+	0.468283i	−0.861406	−	0.507918i	$-0.830415\pi$
$641$	−16.3183	+	11.8560i	−0.644536	+	0.468283i	0.216870	+	0.976201i	$0.430415\pi$
$642$	2.80795	+	7.48293i	0.110821	+	0.295328i
$643$	28.4620	+	28.4620i	1.12243	+	1.12243i	0.991375	+	0.131056i	$0.0418369\pi$
$643$	28.4620	+	28.4620i	1.12243	+	1.12243i	0.131056	+	0.991375i	$0.458163\pi$
$644$	−11.2889	−	6.74640i	−0.444845	−	0.265845i
$645$	15.4290	−	17.8891i	0.607515	−	0.704384i
$646$	−3.26747	−	15.9625i	−0.128557	−	0.628035i
$647$	−8.64588	−	4.40529i	−0.339904	−	0.173190i	0.275703	−	0.961243i	$-0.411089\pi$
$647$	−8.64588	−	4.40529i	−0.339904	−	0.173190i	−0.615608	+	0.788053i	$0.711089\pi$
$648$	−5.04823	+	27.7934i	−0.198313	+	1.09183i
$649$			20.8783i			0.819545i
$650$	−5.12719	−	3.45645i	−0.201105	−	0.135573i
$651$		−	12.3519i		−	0.484111i
$652$	−8.75861	−	0.591434i	−0.343014	−	0.0231623i
$653$	42.0942	+	21.4481i	1.64727	+	0.839327i	0.996812	+	0.0797868i	$0.0254240\pi$
$653$	42.0942	+	21.4481i	1.64727	+	0.839327i	0.650460	+	0.759540i	$0.274576\pi$
$654$	35.2556	−	7.21671i	1.37860	−	0.282196i
$655$	36.6659	−	8.61541i	1.43265	−	0.336632i
$656$	24.2754	−	25.3795i	0.947795	−	0.990904i
$657$	−3.64904	−	3.64904i	−0.142363	−	0.142363i
$658$	8.17540	−	3.06780i	0.318710	−	0.119595i
$659$	−29.5299	+	21.4547i	−1.15032	+	0.835758i	−0.988524	−	0.151066i	$-0.951730\pi$
$659$	−29.5299	+	21.4547i	−1.15032	+	0.835758i	−0.161799	+	0.986824i	$0.551730\pi$
$660$	11.4701	+	5.75386i	0.446475	+	0.223969i
$661$	16.9829	+	12.3388i	0.660560	+	0.479925i	0.866852	−	0.498566i	$-0.166140\pi$
$661$	16.9829	+	12.3388i	0.660560	+	0.479925i	−0.206292	+	0.978490i	$0.566140\pi$
$662$	45.1822	+	12.4720i	1.75606	+	0.484739i
$663$	−2.48503	−	0.393589i	−0.0965104	−	0.0152857i
$664$	−21.1982	+	14.6812i	−0.822648	+	0.569742i
$665$	13.9865	+	8.66424i	0.542373	+	0.335985i
$666$	−1.44133	−	2.54045i	−0.0558502	−	0.0984403i
$667$	1.78040	+	3.49423i	0.0689373	+	0.135297i
$668$	16.6385	+	26.4861i	0.643763	+	1.02478i
$669$	28.2934	+	9.19307i	1.09389	+	0.355425i
$670$	−20.5405	−	11.4837i	−0.793548	−	0.443655i
$671$	−0.863404	+	0.280537i	−0.0333313	+	0.0108300i
$672$	5.32889	+	8.92432i	0.205566	+	0.344263i
$673$	−24.1940	+	3.83195i	−0.932610	+	0.147711i	−0.604208	−	0.796827i	$-0.706510\pi$
$673$	−24.1940	+	3.83195i	−0.932610	+	0.147711i	−0.328403	+	0.944538i	$0.606510\pi$
$674$	−41.4206	−	4.66916i	−1.59546	−	0.179849i
$675$	7.67020	−	22.8522i	0.295226	−	0.879580i
$676$	23.8565	+	5.44770i	0.917558	+	0.209527i
$677$	−1.46793	−	9.26814i	−0.0564171	−	0.356204i	−0.999706	−	0.0242316i	$-0.992286\pi$
$677$	−1.46793	−	9.26814i	−0.0564171	−	0.356204i	0.943289	−	0.331972i	$-0.107714\pi$
$678$	1.93813	+	1.27949i	0.0744335	+	0.0491387i
$679$	4.15769	+	12.7960i	0.159557	+	0.491067i
$680$	−4.03931	+	9.04199i	−0.154901	+	0.346745i
$681$	5.06119	−	15.5767i	0.193945	−	0.596902i
$682$	−11.6075	+	9.25567i	−0.444473	+	0.354418i
$683$	−19.3503	+	9.85945i	−0.740417	+	0.377261i	−0.783156	−	0.621825i	$-0.786391\pi$
$683$	−19.3503	+	9.85945i	−0.740417	+	0.377261i	0.0427394	+	0.999086i	$0.486391\pi$
$684$	−5.09170	+	2.17567i	−0.194686	+	0.0831890i
$685$	16.7023	−	6.82389i	0.638161	−	0.260727i
$686$	1.04381	+	0.954182i	0.0398528	+	0.0364309i
$687$	−8.66730	+	54.7232i	−0.330678	+	2.08782i
$688$	−18.9022	−	13.1013i	−0.720641	−	0.499483i
$689$	−1.30189	+	1.79189i	−0.0495979	+	0.0682656i
$690$	−36.7659	+	10.3978i	−1.39965	+	0.395836i
$691$	−27.6318	−	38.0319i	−1.05116	−	1.44680i	−0.887798	−	0.460234i	$-0.847765\pi$
$691$	−27.6318	−	38.0319i	−1.05116	−	1.44680i	−0.163364	−	0.986566i	$-0.552235\pi$
$692$	21.5367	−	5.42439i	0.818701	−	0.206204i
$693$	−0.415487	+	0.415487i	−0.0157830	+	0.0157830i
$694$	10.5910	+	4.81131i	0.402028	+	0.182635i
$695$	−29.8673	−	2.49596i	−1.13293	−	0.0946773i
$696$	0.0700305	−	3.09876i	0.00265450	−	0.117458i
$697$	−6.24148	+	12.2496i	−0.236413	+	0.463986i
$698$	−0.221516	−	4.93815i	−0.00838450	−	0.186912i
$699$	6.76310			0.255804
$700$	−3.84019	−	9.23325i	−0.145146	−	0.348984i
$701$	36.0942			1.36326			0.681630	−	0.731697i	$-0.261271\pi$
$701$	36.0942			1.36326			0.681630	+	0.731697i	$0.261271\pi$
$702$	−0.267179	−	5.95611i	−0.0100840	−	0.224799i
$703$	−18.3356	+	35.9856i	−0.691539	+	1.35722i
$704$	4.39335	−	11.6950i	0.165581	−	0.440771i
$705$	9.82152	−	23.3907i	0.369900	−	0.880946i
$706$	−14.7210	−	6.68751i	−0.554031	−	0.251688i
$707$	9.44817	−	9.44817i	0.355335	−	0.355335i
$708$	12.0001	+	47.6445i	0.450991	+	1.79059i
$709$	−24.7116	−	34.0126i	−0.928063	−	1.27737i	−0.960610	−	0.277899i	$-0.910362\pi$
$709$	−24.7116	−	34.0126i	−0.928063	−	1.27737i	0.0325470	−	0.999470i	$-0.489638\pi$
$710$	−13.3575	+	16.9691i	−0.501298	+	0.636841i
$711$	0.0804699	−	0.110757i	0.00301786	−	0.00415372i
$712$	−15.5899	+	28.9600i	−0.584255	+	1.08532i
$713$	6.91487	−	43.6587i	0.258964	−	1.63503i
$714$	−3.00321	−	2.74534i	−0.112392	−	0.102742i
$715$	−2.96571	−	0.727187i	−0.110911	−	0.0271952i
$716$	2.43146	+	5.69031i	0.0908677	+	0.212657i
$717$	8.47753	−	4.31952i	0.316599	−	0.161315i
$718$	11.2601	−	8.97865i	0.420222	−	0.335080i
$719$	4.91791	−	15.1358i	0.183407	−	0.564469i	−0.816510	−	0.577331i	$-0.804094\pi$
$719$	4.91791	−	15.1358i	0.183407	−	0.564469i	0.999917	+	0.0128620i	$0.00409421\pi$
$720$	3.28563	+	0.728598i	0.122448	+	0.0271533i
$721$	−2.58020	−	7.94103i	−0.0960916	−	0.295739i
$722$	41.4710	+	27.3779i	1.54339	+	1.01890i
$723$	0.540279	+	3.41119i	0.0200932	+	0.126863i
$724$	5.40563	−	23.6723i	0.200899	−	0.879774i
$725$	−0.494944	+	2.94063i	−0.0183818	+	0.109212i
$726$	−22.1072	−	2.49204i	−0.820475	−	0.0924884i
$727$	19.4902	−	3.08694i	0.722851	−	0.114488i	0.215841	−	0.976429i	$-0.430751\pi$
$727$	19.4902	−	3.08694i	0.722851	−	0.114488i	0.507010	+	0.861940i	$0.330751\pi$
$728$	−1.70898	−	1.78801i	−0.0633391	−	0.0662682i
$729$	21.7006	−	7.05096i	0.803727	−	0.261147i
$730$	31.8268	−	29.4631i	1.17796	−	1.09048i
$731$	8.56240	+	2.78209i	0.316692	+	0.102899i
$732$	−1.80905	+	1.13644i	−0.0668645	+	0.0420041i
$733$	−7.98088	−	15.6634i	−0.294781	−	0.578540i	0.695353	−	0.718669i	$-0.255248\pi$
$733$	−7.98088	−	15.6634i	−0.294781	−	0.578540i	−0.990133	+	0.140129i	$0.955248\pi$
$734$	15.2674	+	26.9099i	0.563529	+	0.993263i
$735$	4.09754	−	0.302556i	0.151140	−	0.0111600i
$736$	13.8393	+	34.5268i	0.510123	+	1.27268i
$737$	−11.4780	−	1.81794i	−0.422798	−	0.0669646i
$738$	4.50361	+	1.24317i	0.165780	+	0.0457616i
$739$	8.30266	+	6.03224i	0.305418	+	0.221899i	0.729928	−	0.683524i	$-0.239554\pi$
$739$	8.30266	+	6.03224i	0.305418	+	0.221899i	−0.424510	+	0.905423i	$0.639554\pi$
$740$	21.8017	−	11.2816i	0.801447	−	0.414719i
$741$	9.56477	−	6.94921i	0.351371	−	0.255286i
$742$	−3.35364	+	1.25844i	−0.123116	+	0.0461989i
$743$	27.6990	+	27.6990i	1.01618	+	1.01618i	0.999867	+	0.0163104i	$0.00519200\pi$
$743$	27.6990	+	27.6990i	1.01618	+	1.01618i	0.0163104	+	0.999867i	$0.494808\pi$
$744$	−21.1685	+	27.7931i	−0.776077	+	1.01894i
$745$	−26.4434	−	43.6237i	−0.968810	−	1.59825i
$746$	−0.357617	+	0.0732031i	−0.0130933	+	0.00268016i
$747$	−3.05641	−	1.55732i	−0.111828	−	0.0569792i
$748$	−0.329484	+	4.87937i	−0.0120471	+	0.178407i
$749$		−	3.07571i		−	0.112384i
$750$	−27.1661	−	10.2991i	−0.991964	−	0.376071i
$751$			38.0313i			1.38778i	0.720081	+	0.693890i	$0.244105\pi$
$751$			38.0313i			1.38778i	−0.720081	+	0.693890i	$0.755895\pi$
$752$	−23.6530	−	7.10802i	−0.862536	−	0.259203i
$753$	−15.9122	−	8.10766i	−0.579872	−	0.295460i
$754$	0.147909	+	0.722577i	0.00538654	+	0.0263147i
$755$	−21.0905	−	34.7930i	−0.767561	−	1.26625i
$756$	4.94624	−	8.27667i	0.179893	−	0.301019i
$757$	−31.0881	−	31.0881i	−1.12992	−	1.12992i	−0.990190	−	0.139727i	$-0.955377\pi$
$757$	−31.0881	−	31.0881i	−1.12992	−	1.12992i	−0.139727	−	0.990190i	$-0.544623\pi$
$758$	14.7934	+	39.4231i	0.537320	+	1.43191i
$759$	−15.2646	+	11.0904i	−0.554070	+	0.402556i
$760$	−16.6224	−	43.4652i	−0.602958	−	1.57665i
$761$	27.1056	+	19.6934i	0.982578	+	0.713885i	0.958283	−	0.285820i	$-0.0922659\pi$
$761$	27.1056	+	19.6934i	0.982578	+	0.713885i	0.0242951	+	0.999705i	$0.492266\pi$
$762$	1.53333	−	5.55479i	0.0555468	−	0.201229i
$763$	−13.6782	−	2.16641i	−0.495183	−	0.0784293i
$764$	16.3393	+	18.7058i	0.591135	+	0.676750i
$765$	−1.31386	+	0.0970133i	−0.0475025	+	0.00350752i
$766$	17.0535	−	9.67533i	0.616168	−	0.349584i
$767$	−5.30778	−	10.4171i	−0.191653	−	0.376140i
$768$	3.30382	−	29.2132i	0.119216	−	1.05414i
$769$	23.9360	+	7.77727i	0.863153	+	0.280456i	0.706945	−	0.707269i	$-0.250073\pi$
$769$	23.9360	+	7.77727i	0.863153	+	0.280456i	0.156208	+	0.987724i	$0.450073\pi$
$770$	−3.35473	−	3.62386i	−0.120896	−	0.130595i
$771$	22.0034	−	7.14934i	0.792434	−	0.257477i
$772$	−12.4698	+	14.9332i	−0.448798	+	0.537459i
$773$	50.3383	−	7.97280i	1.81054	−	0.286762i	0.842712	−	0.538365i	$-0.180958\pi$
$773$	50.3383	−	7.97280i	1.81054	−	0.286762i	0.967830	+	0.251604i	$0.0809579\pi$
$774$	0.342716	−	3.04027i	0.0123187	−	0.109280i
$775$	23.9956	−	23.5359i	0.861946	−	0.845435i
$776$	12.5744	−	35.9177i	0.451396	−	1.28937i
$777$	1.57778	+	9.96171i	0.0566025	+	0.357374i
$778$	−19.8894	+	30.1278i	−0.713070	+	1.08013i
$779$	−19.9631	−	61.4402i	−0.715254	−	2.20133i
$780$	−7.18573	+	0.0451359i	−0.257291	+	0.00161612i
$781$	−3.29553	+	10.1426i	−0.117923	+	0.362931i
$782$	−9.07814	−	11.3848i	−0.324634	−	0.407121i
$783$	−2.56186	+	1.30533i	−0.0915533	+	0.0466487i
$784$	−0.713411	−	3.93587i	−0.0254789	−	0.140567i
$785$	−1.23162	−	0.301990i	−0.0439583	−	0.0107785i
$786$	29.5322	−	32.3062i	1.05338	−	1.15232i
$787$	−5.28651	+	33.3777i	−0.188444	+	1.18979i	0.694213	+	0.719770i	$0.255753\pi$
$787$	−5.28651	+	33.3777i	−0.188444	+	1.18979i	−0.882657	+	0.470018i	$0.844247\pi$
$788$	−2.90960	+	7.25136i	−0.103650	+	0.258319i
$789$	1.19897	−	1.65024i	0.0426844	−	0.0587501i
$790$	0.904087	+	0.711665i	0.0321660	+	0.0253199i
$791$	−0.525314	−	0.723033i	−0.0186780	−	0.0257081i
$792$	1.64694	−	0.222832i	0.0585215	−	0.00791799i
$793$	0.359471	−	0.359471i	0.0127652	−	0.0127652i
$794$	22.6744	−	49.9123i	0.804684	−	1.77132i
$795$	−4.02889	+	9.59513i	−0.142890	+	0.340304i
$796$	20.5190	−	1.84460i	0.727277	−	0.0653800i
$797$	10.4194	−	20.4492i	0.369074	−	0.724349i	−0.629540	−	0.776968i	$-0.716757\pi$
$797$	10.4194	−	20.4492i	0.369074	−	0.724349i	0.998615	+	0.0526184i	$0.0167567\pi$
$798$	19.1007	−	0.856820i	0.676157	−	0.0303311i
$799$	9.66823			0.342038
$800$	−7.18298	+	27.3570i	−0.253957	+	0.967216i
$801$	−4.37533			−0.154595
$802$	−27.0789	+	1.21471i	−0.956191	+	0.0428929i
$803$	9.72342	−	19.0833i	0.343132	−	0.673434i
$804$	−27.2378	+	2.44860i	−0.960603	+	0.0863554i
$805$	14.6524	+	1.22448i	0.516429	+	0.0431572i
$806$	3.43846	−	7.56897i	0.121115	−	0.266606i
$807$	10.1964	−	10.1964i	0.358930	−	0.358930i
$808$	−37.4514	+	5.06720i	−1.31754	+	0.178264i
$809$	9.18336	+	12.6398i	0.322870	+	0.444392i	0.939341	−	0.342986i	$-0.111438\pi$
$809$	9.18336	+	12.6398i	0.322870	+	0.444392i	−0.616471	+	0.787378i	$0.711438\pi$
$810$	−8.59471	−	30.3904i	−0.301987	−	1.06781i
$811$	17.2749	−	23.7768i	0.606602	−	0.834916i	−0.389691	−	0.920946i	$-0.627418\pi$
$811$	17.2749	−	23.7768i	0.606602	−	0.834916i	0.996293	+	0.0860298i	$0.0274180\pi$
$812$	−0.444185	+	1.10701i	−0.0155878	+	0.0388483i
$813$	−1.05208	+	6.64256i	−0.0368980	+	0.232965i
$814$	8.17903	−	8.94729i	0.286675	−	0.313602i
$815$	9.08568	−	3.71205i	0.318258	−	0.130027i
$816$	2.05260	+	11.3241i	0.0718554	+	0.396424i
$817$	−37.6943	+	19.2062i	−1.31876	+	0.671940i
$818$	−21.2216	−	26.6139i	−0.741996	−	0.930533i
$819$	0.101678	−	0.312932i	0.00355290	−	0.0109347i
$820$	−11.8989	+	37.4190i	−0.415526	+	1.30673i
$821$	−9.47631	−	29.1651i	−0.330725	−	1.01787i	−0.968790	−	0.247885i	$-0.920265\pi$
$821$	−9.47631	−	29.1651i	−0.330725	−	1.01787i	0.638064	−	0.769983i	$-0.279735\pi$
$822$	11.5518	−	17.4982i	0.402915	−	0.610321i
$823$	3.71458	+	23.4529i	0.129482	+	0.817517i	0.963877	+	0.266349i	$0.0858175\pi$
$823$	3.71458	+	23.4529i	0.129482	+	0.817517i	−0.834395	+	0.551168i	$0.814182\pi$
$824$	−7.80351	+	22.2900i	−0.271848	+	0.776509i
$825$	−14.3464	−	0.138733i	−0.499478	−	0.00483005i
$826$	2.11795	−	18.7885i	0.0736928	−	0.653737i
$827$	−7.58352	+	1.20111i	−0.263705	+	0.0417667i	−0.286887	−	0.957965i	$-0.592620\pi$
$827$	−7.58352	+	1.20111i	−0.263705	+	0.0417667i	0.0231819	+	0.999731i	$0.492620\pi$
$828$	−3.17168	+	3.79826i	−0.110223	+	0.131998i
$829$	−37.4332	+	12.1628i	−1.30011	+	0.422431i	−0.875619	−	0.483002i	$-0.839546\pi$
$829$	−37.4332	+	12.1628i	−1.30011	+	0.422431i	−0.424489	+	0.905433i	$0.639546\pi$
$830$	14.0684	−	25.1636i	0.488321	−	0.873441i
$831$	34.8157	+	11.3123i	1.20774	+	0.392420i
$832$	0.781114	+	6.95204i	0.0270803	+	0.241019i
$833$	0.710875	+	1.39517i	0.0246303	+	0.0483398i
$834$	−30.2941	+	17.1874i	−1.04900	+	0.595151i
$835$	−29.7287	−	18.4161i	−1.02880	−	0.637314i
$836$	−15.1179	−	17.3074i	−0.522863	−	0.598590i
$837$	32.0092	+	5.06976i	1.10640	+	0.175236i
$838$	7.75824	−	28.1057i	0.268004	−	0.970894i
$839$	−9.54592	−	6.93552i	−0.329562	−	0.239441i	0.410683	−	0.911778i	$-0.365290\pi$
$839$	−9.54592	−	6.93552i	−0.329562	−	0.239441i	−0.740245	+	0.672338i	$0.765290\pi$
$840$	−9.73838	−	6.34151i	−0.336006	−	0.218803i
$841$	−23.1737	+	16.8367i	−0.799094	+	0.580576i
$842$	6.49754	+	17.3154i	0.223920	+	0.596727i
$843$	−11.0783	−	11.0783i	−0.381558	−	0.381558i
$844$	12.0311	−	20.1319i	0.414127	−	0.692969i
$845$	−26.6336	+	6.25812i	−0.916224	+	0.215286i
$846$	−0.658887	−	3.21884i	−0.0226530	−	0.110666i
$847$	7.62821	+	3.88677i	0.262109	+	0.133551i
$848$	9.70271	+	2.91579i	0.333193	+	0.100129i
$849$			9.68226i			0.332294i
$850$	−0.389195	−	11.0653i	−0.0133493	−	0.379536i
$851$			36.0936i			1.23727i
$852$	−1.69083	+	25.0396i	−0.0579268	+	0.857844i
$853$	1.35185	+	0.688802i	0.0462864	+	0.0235841i	0.476981	−	0.878914i	$-0.341731\pi$
$853$	1.35185	+	0.688802i	0.0462864	+	0.0235841i	−0.430694	+	0.902498i	$0.641731\pi$
$854$	0.805442	−	0.164871i	0.0275617	−	0.00564178i
$855$	4.04320	−	4.68789i	0.138274	−	0.160322i
$856$	−5.27110	+	6.92065i	−0.180162	+	0.236543i
$857$	−17.9334	−	17.9334i	−0.612594	−	0.612594i	0.331028	−	0.943621i	$-0.392605\pi$
$857$	−17.9334	−	17.9334i	−0.612594	−	0.612594i	−0.943621	+	0.331028i	$0.892605\pi$
$858$	−3.32237	+	1.24671i	−0.113424	+	0.0425620i
$859$	−22.8014	+	16.5662i	−0.777973	+	0.565231i	−0.904370	−	0.426749i	$-0.859659\pi$
$859$	−22.8014	+	16.5662i	−0.777973	+	0.565231i	0.126397	+	0.991980i	$0.459659\pi$
$860$	25.4215	+	3.86284i	0.866865	+	0.131722i
$861$	−13.0518	−	9.48269i	−0.444804	−	0.323169i
$862$	33.1613	+	9.15379i	1.12948	+	0.311779i
$863$	21.1540	+	3.35047i	0.720092	+	0.114051i	0.505716	−	0.862700i	$-0.331228\pi$
$863$	21.1540	+	3.35047i	0.720092	+	0.114051i	0.214376	+	0.976751i	$0.431228\pi$
$864$	−25.3140	+	10.1465i	−0.861198	+	0.345192i
$865$	−18.9592	+	16.0348i	−0.644631	+	0.545199i
$866$	−2.11516	−	3.72813i	−0.0718760	−	0.126687i
$867$	12.1359	+	23.8181i	0.412158	+	0.808905i
$868$	11.3846	−	7.15176i	0.386418	−	0.242746i
$869$	0.540380	+	0.175580i	0.0183311	+	0.00595615i
$870$	1.45310	+	3.14604i	0.0492648	+	0.106661i
$871$	6.18905	−	2.01094i	0.209708	−	0.0681383i
$872$	27.0645	+	28.3161i	0.916519	+	0.958902i
$873$	5.00019	−	0.791952i	0.169231	−	0.0268035i
$874$	67.9923	+	7.66447i	2.29987	+	0.259254i
$875$	8.39539	+	7.38360i	0.283816	+	0.249611i
$876$	11.2205	−	49.1369i	0.379107	−	1.66018i
$877$	2.33178	+	14.7223i	0.0787387	+	0.497137i	0.995268	+	0.0971689i	$0.0309787\pi$
$877$	2.33178	+	14.7223i	0.0787387	+	0.497137i	−0.916529	+	0.399968i	$0.869021\pi$
$878$	−32.6944	−	21.5838i	−1.10338	−	0.728418i
$879$	−13.6766	−	42.0923i	−0.461301	−	1.41974i
$880$	1.33795	+	13.9033i	0.0451024	+	0.468681i
$881$	−1.79231	+	5.51616i	−0.0603844	+	0.185844i	−0.976698	−	0.214617i	$-0.931150\pi$
$881$	−1.79231	+	5.51616i	−0.0603844	+	0.185844i	0.916314	+	0.400461i	$0.131150\pi$
$882$	0.416048	−	0.331752i	0.0140091	−	0.0111707i
$883$	−0.637496	+	0.324820i	−0.0214534	+	0.0109311i	−0.464684	−	0.885476i	$-0.653832\pi$
$883$	−0.637496	+	0.324820i	−0.0214534	+	0.0109311i	0.443231	+	0.896407i	$0.353832\pi$
$884$	−1.07606	−	2.51830i	−0.0361919	−	0.0846994i
$885$	−35.4729	−	41.9424i	−1.19241	−	1.40988i
$886$	21.8160	+	19.9428i	0.732922	+	0.669990i
$887$	1.87024	−	11.8082i	0.0627965	−	0.396481i	−0.936191	−	0.351492i	$-0.885675\pi$
$887$	1.87024	−	11.8082i	0.0627965	−	0.396481i	0.998987	−	0.0449896i	$-0.0143255\pi$
$888$	13.5220	−	25.1188i	0.453770	−	0.842932i
$889$	−1.30346	+	1.79406i	−0.0437167	+	0.0601709i
$890$	1.41708	−	36.7444i	0.0475006	−	1.23168i
$891$	−9.16724	−	12.6176i	−0.307114	−	0.422706i
$892$	7.90872	+	31.4003i	0.264804	+	1.05136i
$893$	−32.1246	+	32.1246i	−1.07501	+	1.07501i
$894$	−53.9739	−	24.5195i	−1.80516	−	0.820055i
$895$	−5.23902	−	4.51853i	−0.175121	−	0.151038i
$896$	−5.13998	+	10.0787i	−0.171715	+	0.336706i
$897$	4.79674	−	9.41413i	0.160158	−	0.314329i
$898$	0.610716	+	13.6144i	0.0203799	+	0.454319i
$899$	−4.00915			−0.133713
$900$	−3.65744	+	0.883670i	−0.121915	+	0.0294557i
$901$	−3.96601			−0.132127
$902$	0.868937	+	19.3708i	0.0289325	+	0.644978i
$903$	−4.79632	+	9.41330i	−0.159611	+	0.313255i
$904$	−0.0571127	+	2.52717i	−0.00189954	+	0.0840524i
$905$	6.20980	+	26.4279i	0.206421	+	0.878495i
$906$	−43.0481	−	19.5561i	−1.43018	−	0.649707i
$907$	3.00470	−	3.00470i	0.0997696	−	0.0997696i	−0.655460	−	0.755230i	$-0.727525\pi$
$907$	3.00470	−	3.00470i	0.0997696	−	0.0997696i	0.755230	+	0.655460i	$0.227525\pi$
$908$	17.2872	−	4.35410i	0.573697	−	0.144496i
$909$	−2.95514	−	4.06740i	−0.0980158	−	0.134907i
$910$	2.59510	+	0.955250i	0.0860266	+	0.0316662i
$911$	−13.5325	+	18.6259i	−0.448352	+	0.617104i	−0.972043	−	0.234805i	$-0.924555\pi$
$911$	−13.5325	+	18.6259i	−0.448352	+	0.617104i	0.523690	+	0.851909i	$0.324555\pi$
$912$	−44.4468	−	30.8065i	−1.47178	−	1.02011i
$913$	2.22711	−	14.0614i	0.0737065	−	0.465364i
$914$	14.6960	+	13.4341i	0.486099	+	0.444361i
$915$	1.25785	−	2.03052i	0.0415833	−	0.0671270i
$916$	−55.4558	+	23.6962i	−1.83231	+	0.782943i
$917$	−15.0082	+	7.64704i	−0.495613	+	0.252527i
$918$	8.34700	−	6.65580i	0.275492	−	0.219674i
$919$	2.56973	−	7.90880i	0.0847674	−	0.260887i	−0.899685	−	0.436540i	$-0.856204\pi$
$919$	2.56973	−	7.90880i	0.0847674	−	0.260887i	0.984452	+	0.175653i	$0.0562037\pi$
$920$	−30.8708	−	27.8662i	−1.01778	−	0.918722i
$921$	4.27764	+	13.1652i	0.140953	+	0.433809i
$922$	31.6871	+	20.9188i	1.04356	+	0.688925i
$923$	−0.934214	−	5.89839i	−0.0307500	−	0.194148i
$924$	−5.59482	−	1.27759i	−0.184056	−	0.0420297i
$925$	−16.3458	+	22.0466i	−0.537446	+	0.724886i
$926$	−22.5341	−	2.54017i	−0.740516	−	0.0834751i
$927$	−3.10304	+	0.491473i	−0.101917	+	0.0161421i
$928$	2.89663	−	1.72963i	0.0950865	−	0.0567780i
$929$	−47.0350	+	15.2826i	−1.54317	+	0.501406i	−0.952248	−	0.305325i	$-0.901235\pi$
$929$	−47.0350	+	15.2826i	−1.54317	+	0.501406i	−0.590920	+	0.806730i	$0.701235\pi$
$930$	7.59257	−	38.3152i	0.248970	−	1.25641i
$931$	−6.99775	−	2.27371i	−0.229342	−	0.0745177i
$932$	3.91583	+	6.23344i	0.128267	+	0.204183i
$933$	−19.6454	−	38.5563i	−0.643162	−	1.26228i
$934$	1.29649	+	2.28516i	0.0424225	+	0.0747729i
$935$	−2.06796	−	5.06157i	−0.0676295	−	0.165531i
$936$	−0.765082	+	0.529874i	−0.0250075	+	0.0173195i
$937$	50.1737	+	7.94674i	1.63910	+	0.259609i	0.906860	−	0.421433i	$-0.138473\pi$
$937$	50.1737	+	7.94674i	1.63910	+	0.259609i	0.732245	+	0.681041i	$0.238473\pi$
$938$	10.1447	+	2.80034i	0.331237	+	0.0914342i
$939$	−15.5216	−	11.2771i	−0.506529	−	0.368015i
$940$	27.2455	−	4.49087i	0.888651	−	0.146476i
$941$	9.70702	−	7.05256i	0.316440	−	0.229907i	−0.418215	−	0.908348i	$-0.637344\pi$
$941$	9.70702	−	7.05256i	0.316440	−	0.229907i	0.734655	+	0.678441i	$0.237344\pi$
$942$	−1.37973	+	0.517741i	−0.0449541	+	0.0168689i
$943$	−40.8239	−	40.8239i	−1.32941	−	1.32941i
$944$	−36.9651	+	38.6464i	−1.20311	+	1.25783i
$945$	−0.897748	+	10.7427i	−0.0292037	+	0.349459i
$946$	12.4400	−	2.54642i	0.404459	−	0.0827914i
$947$	41.2480	+	21.0169i	1.34038	+	0.682957i	0.969355	−	0.245666i	$-0.0790066\pi$
$947$	41.2480	+	21.0169i	1.34038	+	0.682957i	0.371024	+	0.928623i	$0.379007\pi$
$948$	1.33407	+	0.0900843i	0.0433285	+	0.00292580i
$949$			11.9934i			0.389323i
$950$	38.0598	+	35.4734i	1.23482	+	1.15091i
$951$			51.9479i			1.68453i
$952$	0.791481	−	4.35756i	0.0256520	−	0.141229i
$953$	48.9071	+	24.9194i	1.58426	+	0.807219i	0.999991	−	0.00434412i	$-0.00138278\pi$
$953$	48.9071	+	24.9194i	1.58426	+	0.807219i	0.584265	+	0.811563i	$0.301383\pi$
$954$	0.270282	+	1.32040i	0.00875071	+	0.0427496i
$955$	−25.6032	−	10.7505i	−0.828500	−	0.347878i
$956$	8.88971	+	5.31261i	0.287514	+	0.171822i
$957$	1.21008	+	1.21008i	0.0391164	+	0.0391164i
$958$	−5.15519	−	13.7381i	−0.166557	−	0.443858i
$959$	−6.52783	+	4.74275i	−0.210795	+	0.153151i
$960$	11.0443	+	30.9585i	0.356455	+	0.999181i
$961$	11.4792	+	8.34013i	0.370297	+	0.269037i
$962$	−1.80626	+	6.54351i	−0.0582361	+	0.210971i
$963$	−1.14304	−	0.181040i	−0.0368340	−	0.00583393i
$964$	−2.83121	+	2.47304i	−0.0911873	+	0.0796512i
$965$	5.17996	−	21.1256i	0.166749	−	0.680056i
$966$	14.8618	−	8.43185i	0.478170	−	0.271290i
$967$	−7.39923	−	14.5218i	−0.237943	−	0.466990i	0.740896	−	0.671619i	$-0.234401\pi$
$967$	−7.39923	−	14.5218i	−0.237943	−	0.466990i	−0.978839	+	0.204630i	$0.934401\pi$
$968$	−10.5032	−	21.8187i	−0.337584	−	0.701280i
$969$	20.1337	+	6.54183i	0.646787	+	0.210154i
$970$	5.03142	+	42.2485i	0.161549	+	1.35652i
$971$	45.9447	−	14.9283i	1.47443	−	0.479073i	0.541990	−	0.840385i	$-0.317671\pi$
$971$	45.9447	−	14.9283i	1.47443	−	0.479073i	0.932445	+	0.361312i	$0.117671\pi$
$972$	−5.96888	−	4.98423i	−0.191452	−	0.159869i
$973$	13.2386	−	2.09679i	0.424410	−	0.0672199i
$974$	0.981357	−	8.70572i	0.0314447	−	0.278949i
$975$	7.19333	−	3.57799i	0.230371	−	0.114587i
$976$	−2.09488	−	1.00938i	−0.0670554	−	0.0323093i
$977$	−4.58436	−	28.9445i	−0.146667	−	0.926017i	−0.945773	−	0.324828i	$-0.894694\pi$
$977$	−4.58436	−	28.9445i	−0.146667	−	0.926017i	0.799106	−	0.601189i	$-0.205306\pi$
$978$	6.28393	−	9.51867i	0.200938	−	0.304374i
$979$	−5.61140	−	17.2701i	−0.179341	−	0.551956i
$980$	2.65133	+	3.60145i	0.0846936	+	0.115044i
$981$	−1.61023	+	4.95577i	−0.0514106	+	0.158226i
$982$	21.7396	+	27.2636i	0.693740	+	0.870015i
$983$	−25.0619	+	12.7697i	−0.799351	+	0.407290i	−0.805429	−	0.592692i	$-0.798065\pi$
$983$	−25.0619	+	12.7697i	−0.799351	+	0.407290i	0.00607835	+	0.999982i	$0.498065\pi$
$984$	13.1166	+	43.7050i	0.418141	+	1.39326i
$985$	−0.643270	−	8.71184i	−0.0204963	−	0.277582i
$986$	−0.891074	+	0.974772i	−0.0283776	+	0.0310431i
$987$	−1.77481	+	11.2057i	−0.0564928	+	0.356682i
$988$	11.9430	+	4.79211i	0.379956	+	0.152457i
$989$	−22.2227	+	30.5869i	−0.706639	+	0.972606i
$990$	−1.54422	+	1.03343i	−0.0490784	+	0.0328445i
$991$	−27.1023	−	37.3031i	−0.860932	−	1.18497i	−0.981346	−	0.192248i	$-0.938422\pi$
$991$	−27.1023	−	37.3031i	−0.860932	−	1.18497i	0.120414	−	0.992724i	$-0.461578\pi$
$992$	−37.8730	−	3.41854i	−1.20247	−	0.108539i
$993$	−43.0628	+	43.0628i	−1.36656	+	1.36656i
$994$	3.99456	−	8.79309i	0.126700	−	0.278900i
$995$	−19.6972	+	11.9399i	−0.624443	+	0.378519i
$996$	−2.99971	−	33.3683i	−0.0950494	−	1.05731i
$997$	6.69011	−	13.1301i	0.211878	−	0.415834i	−0.760469	−	0.649374i	$-0.775031\pi$
$997$	6.69011	−	13.1301i	0.211878	−	0.415834i	0.972347	+	0.233540i	$0.0750310\pi$
$998$	17.1404	−	0.768886i	0.542571	−	0.0243387i
$999$	−26.4627			−0.837241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.687.2	yes	720
4.3	odd	2	inner	700.2.bj.a.687.83	yes	720
25.23	odd	20	inner	700.2.bj.a.323.83	yes	720
100.23	even	20	inner	700.2.bj.a.323.2	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.2	✓	720	100.23	even	20	inner
700.2.bj.a.323.83	yes	720	25.23	odd	20	inner
700.2.bj.a.687.2	yes	720	1.1	even	1	trivial
700.2.bj.a.687.83	yes	720	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41279 + 0.0633751i) q^{2} +(0.834190 - 1.63719i) q^{3} +(1.99197 - 0.179072i) q^{4} +(-1.91219 + 1.15911i) q^{5} +(-1.07478 + 2.36588i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.80289 + 0.379233i) q^{8} +(-0.221165 - 0.304407i) q^{9} +(2.62807 - 1.75877i) q^{10} +(0.917897 - 1.26338i) q^{11} +(1.36851 - 3.41061i) q^{12} +(-0.136798 + 0.863706i) q^{13} +(-0.954182 + 1.04381i) q^{14} +(0.302556 + 4.09754i) q^{15} +(3.93587 - 0.713411i) q^{16} +(-1.39517 + 0.710875i) q^{17} +(0.331752 + 0.416048i) q^{18} +(2.27371 - 6.99775i) q^{19} +(-3.60145 + 2.65133i) q^{20} +(-0.567807 - 1.74753i) q^{21} +(-1.21673 + 1.84306i) q^{22} +(-1.02865 - 6.49463i) q^{23} +(-1.71727 + 4.90522i) q^{24} +(2.31293 - 4.43287i) q^{25} +(0.138529 - 1.22891i) q^{26} +(4.76165 - 0.754172i) q^{27} +(1.28191 - 1.53516i) q^{28} +(-0.567208 + 0.184297i) q^{29} +(-0.687131 - 5.76979i) q^{30} +(6.39327 + 2.07730i) q^{31} +(-5.51535 + 1.25734i) q^{32} +(-1.30269 - 2.55667i) q^{33} +(1.92603 - 1.09274i) q^{34} +(-0.532506 + 2.17174i) q^{35} +(-0.495063 - 0.566764i) q^{36} +(-5.42145 - 0.858673i) q^{37} +(-2.76879 + 10.0305i) q^{38} +(1.29994 + 0.944460i) q^{39} +(4.92008 - 3.97402i) q^{40} +(7.10317 - 5.16075i) q^{41} +(0.912944 + 2.43291i) q^{42} +(-4.06563 - 4.06563i) q^{43} +(1.60219 - 2.68097i) q^{44} +(0.775750 + 0.325729i) q^{45} +(1.86487 + 9.11038i) q^{46} +(-5.50151 - 2.80316i) q^{47} +(2.11527 - 7.03889i) q^{48} -1.00000i q^{49} +(-2.98675 + 6.40932i) q^{50} +2.87716i q^{51} +(-0.117831 + 1.74497i) q^{52} +(2.25678 + 1.14989i) q^{53} +(-6.67944 + 1.36726i) q^{54} +(-0.290798 + 3.47976i) q^{55} +(-1.71378 + 2.25010i) q^{56} +(-9.55995 - 9.55995i) q^{57} +(0.789668 - 0.296320i) q^{58} +(-10.8163 + 7.85848i) q^{59} +(1.33644 + 8.10798i) q^{60} +(-0.470316 - 0.341705i) q^{61} +(-9.16402 - 2.52962i) q^{62} +(-0.371635 - 0.0588612i) q^{63} +(7.71237 - 2.12589i) q^{64} +(-0.739548 - 1.81013i) q^{65} +(2.00246 + 3.52949i) q^{66} +(-3.37846 - 6.63059i) q^{67} +(-2.65184 + 1.66587i) q^{68} +(-11.4910 - 3.73367i) q^{69} +(0.614687 - 3.10196i) q^{70} +(-6.49492 + 2.11033i) q^{71} +(0.735341 + 0.769346i) q^{72} +(13.5462 - 2.14550i) q^{73} +(7.71380 + 0.869542i) q^{74} +(-5.32804 - 7.48456i) q^{75} +(3.27605 - 14.3464i) q^{76} +(-0.244291 - 1.54239i) q^{77} +(-1.89640 - 1.25194i) q^{78} +(0.112435 + 0.346038i) q^{79} +(-6.69919 + 5.92628i) q^{80} +(3.08622 - 9.49842i) q^{81} +(-9.70824 + 7.74124i) q^{82} +(8.12296 - 4.13885i) q^{83} +(-1.44399 - 3.37935i) q^{84} +(1.84385 - 2.97648i) q^{85} +(6.00155 + 5.48623i) q^{86} +(-0.171430 + 1.08237i) q^{87} +(-2.09365 + 3.88920i) q^{88} +(6.83491 - 9.40744i) q^{89} +(-1.11662 - 0.411024i) q^{90} +(0.514002 + 0.707463i) q^{91} +(-3.21204 - 12.7529i) q^{92} +(8.73414 - 8.73414i) q^{93} +(7.95014 + 3.61162i) q^{94} +(3.76341 + 16.0165i) q^{95} +(-2.54235 + 10.0785i) q^{96} +(-6.10824 + 11.9881i) q^{97} +(0.0633751 + 1.41279i) q^{98} -0.587587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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