LMFDB - Embedded newform 140.2.w.b.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(23,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("140.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$140 = 2^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	140.w (of order $12$ , degree $4$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.16

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20559 + 0.739299i) q^{2} +(-2.47915 - 0.664287i) q^{3} +(0.906874 + 1.78258i) q^{4} +(1.93364 + 1.12296i) q^{5} +(-2.49773 - 2.63369i) q^{6} +(1.41045 + 2.23844i) q^{7} +(-0.224544 + 2.81950i) q^{8} +(3.10685 + 1.79374i) q^{9} +(1.50097 + 2.78336i) q^{10} +(1.59653 - 0.921758i) q^{11} +(-1.06414 - 5.02171i) q^{12} +(-2.94578 - 2.94578i) q^{13} +(0.0455440 + 3.74138i) q^{14} +(-4.04783 - 4.06848i) q^{15} +(-2.35516 + 3.23314i) q^{16} +(-2.96933 - 0.795631i) q^{17} +(2.41946 + 4.45940i) q^{18} +(2.66374 - 4.61374i) q^{19} +(-0.248189 + 4.46524i) q^{20} +(-2.00976 - 6.48639i) q^{21} +(2.60621 + 0.0690563i) q^{22} +(-0.654945 - 2.44429i) q^{23} +(2.42964 - 6.84081i) q^{24} +(2.47794 + 4.34279i) q^{25} +(-1.37358 - 5.72920i) q^{26} +(-1.06621 - 1.06621i) q^{27} +(-2.71109 + 4.54422i) q^{28} -6.35796i q^{29} +(-1.87218 - 7.89745i) q^{30} +(-3.78330 + 2.18429i) q^{31} +(-5.22961 + 2.15666i) q^{32} +(-4.57036 + 1.22462i) q^{33} +(-2.99158 - 3.15443i) q^{34} +(0.213637 + 5.91222i) q^{35} +(-0.379961 + 7.16490i) q^{36} +(-1.03655 - 3.86848i) q^{37} +(6.62230 - 3.59295i) q^{38} +(5.34619 + 9.25988i) q^{39} +(-3.60036 + 5.19975i) q^{40} +10.6462 q^{41} +(2.37244 - 9.30571i) q^{42} +(-1.02386 + 1.02386i) q^{43} +(3.09096 + 2.01002i) q^{44} +(3.99324 + 6.95731i) q^{45} +(1.01747 - 3.43100i) q^{46} +(-0.785472 + 0.210467i) q^{47} +(7.98654 - 6.45096i) q^{48} +(-3.02124 + 6.31443i) q^{49} +(-0.223257 + 7.06754i) q^{50} +(6.83291 + 3.94498i) q^{51} +(2.57963 - 7.92252i) q^{52} +(0.699675 - 2.61122i) q^{53} +(-0.497157 - 2.07365i) q^{54} +(4.12221 + 0.0104869i) q^{55} +(-6.62800 + 3.47414i) q^{56} +(-9.66867 + 9.66867i) q^{57} +(4.70044 - 7.66507i) q^{58} +(-2.11446 - 3.66235i) q^{59} +(3.58150 - 10.9052i) q^{60} +(-6.00599 + 10.4027i) q^{61} +(-6.17593 - 0.163643i) q^{62} +(0.366883 + 9.48450i) q^{63} +(-7.89916 - 1.26620i) q^{64} +(-2.38810 - 9.00406i) q^{65} +(-6.41532 - 1.90247i) q^{66} +(0.856208 - 3.19541i) q^{67} +(-1.27454 - 6.01460i) q^{68} +6.49484i q^{69} +(-4.11334 + 7.28563i) q^{70} -10.5316i q^{71} +(-5.75508 + 8.35700i) q^{72} +(-0.529747 + 1.97704i) q^{73} +(1.61030 - 5.43010i) q^{74} +(-3.25832 - 12.4125i) q^{75} +(10.6400 + 0.564249i) q^{76} +(4.31513 + 2.27365i) q^{77} +(-0.400526 + 15.1160i) q^{78} +(-3.95797 + 6.85541i) q^{79} +(-8.18472 + 3.60700i) q^{80} +(-3.44620 - 5.96900i) q^{81} +(12.8349 + 7.87075i) q^{82} +(-0.227439 + 0.227439i) q^{83} +(9.73989 - 9.46489i) q^{84} +(-4.84817 - 4.87290i) q^{85} +(-1.99129 + 0.477413i) q^{86} +(-4.22352 + 15.7624i) q^{87} +(2.24040 + 4.70839i) q^{88} +(3.75731 + 2.16929i) q^{89} +(-0.329341 + 11.3398i) q^{90} +(2.43907 - 10.7488i) q^{91} +(3.76318 - 3.38415i) q^{92} +(10.8304 - 2.90199i) q^{93} +(-1.10255 - 0.326963i) q^{94} +(10.3317 - 5.93004i) q^{95} +(14.3977 - 1.87274i) q^{96} +(0.196142 - 0.196142i) q^{97} +(-8.31062 + 5.37899i) q^{98} +6.61358 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100})$ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$ .

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	1.20559	+	0.739299i	0.852478	+	0.522763i
$2$	1.20559	+	0.739299i	0.852478	+	0.522763i
$3$	−2.47915	−	0.664287i	−1.43134	−	0.383527i	−0.541848	−	0.840476i	$-0.682275\pi$
$3$	−2.47915	−	0.664287i	−1.43134	−	0.383527i	−0.889492	+	0.456950i	$0.848942\pi$
$4$	0.906874	+	1.78258i	0.453437	+	0.891288i
$5$	1.93364	+	1.12296i	0.864751	+	0.502202i
$5$	1.93364	+	1.12296i	0.864751	+	0.502202i
$6$	−2.49773	−	2.63369i	−1.01969	−	1.07520i
$7$	1.41045	+	2.23844i	0.533101	+	0.846051i
$7$	1.41045	+	2.23844i	0.533101	+	0.846051i
$8$	−0.224544	+	2.81950i	−0.0793882	+	0.996844i
$9$	3.10685	+	1.79374i	1.03562	+	0.597914i
$10$	1.50097	+	2.78336i	0.474648	+	0.880176i
$11$	1.59653	−	0.921758i	0.481372	−	0.277920i	−0.239616	−	0.970868i	$-0.577022\pi$
$11$	1.59653	−	0.921758i	0.481372	−	0.277920i	0.720988	+	0.692947i	$0.243688\pi$
$12$	−1.06414	−	5.02171i	−0.307190	−	1.44964i
$13$	−2.94578	−	2.94578i	−0.817012	−	0.817012i	0.168662	−	0.985674i	$-0.446055\pi$
$13$	−2.94578	−	2.94578i	−0.817012	−	0.817012i	−0.985674	+	0.168662i	$0.946055\pi$
$14$	0.0455440	+	3.74138i	0.0121721	+	0.999926i
$15$	−4.04783	−	4.06848i	−1.04514	−	1.05048i
$16$	−2.35516	+	3.23314i	−0.588790	+	0.808286i
$17$	−2.96933	−	0.795631i	−0.720169	−	0.192969i	−0.119922	−	0.992783i	$-0.538264\pi$
$17$	−2.96933	−	0.795631i	−0.720169	−	0.192969i	−0.600247	+	0.799815i	$0.704931\pi$
$18$	2.41946	+	4.45940i	0.570273	+	1.05109i
$19$	2.66374	−	4.61374i	0.611104	−	1.05846i	−0.379950	−	0.925007i	$-0.624059\pi$
$19$	2.66374	−	4.61374i	0.611104	−	1.05846i	0.991055	−	0.133457i	$-0.0426077\pi$
$20$	−0.248189	+	4.46524i	−0.0554967	+	0.998459i
$21$	−2.00976	−	6.48639i	−0.438566	−	1.41545i
$22$	2.60621	+	0.0690563i	0.555646	+	0.0147228i
$23$	−0.654945	−	2.44429i	−0.136565	−	0.509669i	−0.999987	−	0.00518527i	$-0.998349\pi$
$23$	−0.654945	−	2.44429i	−0.136565	−	0.509669i	0.863421	−	0.504484i	$-0.168317\pi$
$24$	2.42964	−	6.84081i	0.495948	−	1.39638i
$25$	2.47794	+	4.34279i	0.495587	+	0.868558i
$26$	−1.37358	−	5.72920i	−0.269380	−	1.12359i
$27$	−1.06621	−	1.06621i	−0.205191	−	0.205191i
$28$	−2.71109	+	4.54422i	−0.512348	+	0.858778i
$29$		−	6.35796i		−	1.18064i	−0.807168	−	0.590322i	$-0.799001\pi$
$29$		−	6.35796i		−	1.18064i	0.807168	−	0.590322i	$-0.200999\pi$
$30$	−1.87218	−	7.89745i	−0.341812	−	1.44187i
$31$	−3.78330	+	2.18429i	−0.679500	+	0.392310i	−0.799667	−	0.600444i	$-0.794991\pi$
$31$	−3.78330	+	2.18429i	−0.679500	+	0.392310i	0.120166	+	0.992754i	$0.461657\pi$
$32$	−5.22961	+	2.15666i	−0.924473	+	0.381248i
$33$	−4.57036	+	1.22462i	−0.795597	+	0.213180i
$34$	−2.99158	−	3.15443i	−0.513051	−	0.540980i
$35$	0.213637	+	5.91222i	0.0361112	+	0.999348i
$36$	−0.379961	+	7.16490i	−0.0633268	+	1.19415i
$37$	−1.03655	−	3.86848i	−0.170409	−	0.635973i	−0.997288	−	0.0735946i	$-0.976553\pi$
$37$	−1.03655	−	3.86848i	−0.170409	−	0.635973i	0.826880	−	0.562379i	$-0.190114\pi$
$38$	6.62230	−	3.59295i	1.07428	−	0.582854i
$39$	5.34619	+	9.25988i	0.856076	+	1.48277i
$40$	−3.60036	+	5.19975i	−0.569268	+	0.822152i
$41$	10.6462			1.66266			0.831331	−	0.555777i	$-0.187579\pi$
$41$	10.6462			1.66266			0.831331	+	0.555777i	$0.187579\pi$
$42$	2.37244	−	9.30571i	0.366076	−	1.43590i
$43$	−1.02386	+	1.02386i	−0.156137	+	0.156137i	−0.780853	−	0.624715i	$-0.785215\pi$
$43$	−1.02386	+	1.02386i	−0.156137	+	0.156137i	0.624715	+	0.780853i	$0.285215\pi$
$44$	3.09096	+	2.01002i	0.465979	+	0.303022i
$45$	3.99324	+	6.95731i	0.595278	+	1.03714i
$46$	1.01747	−	3.43100i	0.150017	−	0.505873i
$47$	−0.785472	+	0.210467i	−0.114573	+	0.0306997i	−0.315650	−	0.948876i	$-0.602223\pi$
$47$	−0.785472	+	0.210467i	−0.114573	+	0.0306997i	0.201077	+	0.979575i	$0.435556\pi$
$48$	7.98654	−	6.45096i	1.15276	−	0.931116i
$49$	−3.02124	+	6.31443i	−0.431606	+	0.902062i
$50$	−0.223257	+	7.06754i	−0.0315734	+	0.999501i
$51$	6.83291	+	3.94498i	0.956799	+	0.552408i
$52$	2.57963	−	7.92252i	0.357730	−	1.09866i
$53$	0.699675	−	2.61122i	0.0961077	−	0.358679i	−0.901077	−	0.433658i	$-0.857222\pi$
$53$	0.699675	−	2.61122i	0.0961077	−	0.358679i	0.997185	+	0.0749796i	$0.0238892\pi$
$54$	−0.497157	−	2.07365i	−0.0676546	−	0.282188i
$55$	4.12221	+	0.0104869i	0.555839	+	0.00141406i
$56$	−6.62800	+	3.47414i	−0.885703	+	0.464252i
$57$	−9.66867	+	9.66867i	−1.28065	+	1.28065i
$58$	4.70044	−	7.66507i	0.617198	−	1.00647i
$59$	−2.11446	−	3.66235i	−0.275279	−	0.476797i	0.694927	−	0.719081i	$-0.255437\pi$
$59$	−2.11446	−	3.66235i	−0.275279	−	0.476797i	−0.970205	+	0.242284i	$0.922104\pi$
$60$	3.58150	−	10.9052i	0.462370	−	1.40785i
$61$	−6.00599	+	10.4027i	−0.768988	+	1.33193i	0.169124	+	0.985595i	$0.445906\pi$
$61$	−6.00599	+	10.4027i	−0.768988	+	1.33193i	−0.938112	+	0.346332i	$0.887427\pi$
$62$	−6.17593	−	0.163643i	−0.784344	−	0.0207826i
$63$	0.366883	+	9.48450i	0.0462229	+	1.19493i
$64$	−7.89916	−	1.26620i	−0.987395	−	0.158275i
$65$	−2.38810	−	9.00406i	−0.296207	−	1.11682i
$66$	−6.41532	−	1.90247i	−0.789672	−	0.234178i
$67$	0.856208	−	3.19541i	0.104602	−	0.390382i	−0.893697	−	0.448670i	$-0.851898\pi$
$67$	0.856208	−	3.19541i	0.104602	−	0.390382i	0.998300	+	0.0582888i	$0.0185644\pi$
$68$	−1.27454	−	6.01460i	−0.154560	−	0.729378i
$69$			6.49484i			0.781886i
$70$	−4.11334	+	7.28563i	−0.491638	+	0.870799i
$71$		−	10.5316i		−	1.24988i	−0.780675	−	0.624938i	$-0.785124\pi$
$71$		−	10.5316i		−	1.24988i	0.780675	−	0.624938i	$-0.214876\pi$
$72$	−5.75508	+	8.35700i	−0.678243	+	0.984882i
$73$	−0.529747	+	1.97704i	−0.0620022	+	0.231395i	−0.989973	−	0.141258i	$-0.954885\pi$
$73$	−0.529747	+	1.97704i	−0.0620022	+	0.231395i	0.927971	+	0.372653i	$0.121552\pi$
$74$	1.61030	−	5.43010i	0.187194	−	0.631237i
$75$	−3.25832	−	12.4125i	−0.376239	−	1.43327i
$76$	10.6400	+	0.564249i	1.22049	+	0.0647238i
$77$	4.31513	+	2.27365i	0.491755	+	0.259106i
$78$	−0.400526	+	15.1160i	−0.0453507	+	1.71155i
$79$	−3.95797	+	6.85541i	−0.445307	+	0.771294i	−0.998074	−	0.0620421i	$-0.980239\pi$
$79$	−3.95797	+	6.85541i	−0.445307	+	0.771294i	0.552767	+	0.833336i	$0.313572\pi$
$80$	−8.18472	+	3.60700i	−0.915079	+	0.403274i
$81$	−3.44620	−	5.96900i	−0.382912	−	0.663222i
$82$	12.8349	+	7.87075i	1.41738	+	0.869179i
$83$	−0.227439	+	0.227439i	−0.0249647	+	0.0249647i	−0.719479	−	0.694514i	$-0.755619\pi$
$83$	−0.227439	+	0.227439i	−0.0249647	+	0.0249647i	0.694514	+	0.719479i	$0.255619\pi$
$84$	9.73989	−	9.46489i	1.06271	−	1.03270i
$85$	−4.84817	−	4.87290i	−0.525858	−	0.528540i
$86$	−1.99129	+	0.477413i	−0.214727	+	0.0514807i
$87$	−4.22352	+	15.7624i	−0.452808	+	1.68990i
$88$	2.24040	+	4.70839i	0.238828	+	0.501917i
$89$	3.75731	+	2.16929i	0.398274	+	0.229944i	0.685739	−	0.727847i	$-0.259479\pi$
$89$	3.75731	+	2.16929i	0.398274	+	0.229944i	−0.287465	+	0.957791i	$0.592812\pi$
$90$	−0.329341	+	11.3398i	−0.0347155	+	1.19532i
$91$	2.43907	−	10.7488i	0.255684	−	1.12678i
$92$	3.76318	−	3.38415i	0.392338	−	0.352822i
$93$	10.8304	−	2.90199i	1.12306	−	0.300922i
$94$	−1.10255	−	0.326963i	−0.113720	−	0.0337237i
$95$	10.3317	−	5.93004i	1.06001	−	0.608410i
$96$	14.3977	−	1.87274i	1.46945	−	0.191136i
$97$	0.196142	−	0.196142i	0.0199152	−	0.0199152i	−0.697079	−	0.716994i	$-0.745517\pi$
$97$	0.196142	−	0.196142i	0.0199152	−	0.0199152i	0.716994	+	0.697079i	$0.245517\pi$
$98$	−8.31062	+	5.37899i	−0.839500	+	0.543360i
$99$	6.61358			0.664690
$100$	−5.49418	+	8.35547i	−0.549418	+	0.835547i
$101$	3.67449	+	6.36440i	0.365625	+	0.633281i	0.988876	−	0.148741i	$-0.0475219\pi$
$101$	3.67449	+	6.36440i	0.365625	+	0.633281i	−0.623251	+	0.782022i	$0.714189\pi$
$102$	5.32114	+	9.80758i	0.526871	+	0.971095i
$103$	3.53030	+	13.1752i	0.347850	+	1.29820i	0.889247	+	0.457428i	$0.151229\pi$
$103$	3.53030	+	13.1752i	0.347850	+	1.29820i	−0.541396	+	0.840768i	$0.682104\pi$
$104$	8.96707	−	7.64416i	0.879294	−	0.749572i
$105$	3.39778	−	14.7992i	0.331589	−	1.44426i
$106$	2.77399	−	2.63078i	0.269434	−	0.255524i
$107$	4.51112	−	1.20875i	0.436107	−	0.116854i	−0.0340847	−	0.999419i	$-0.510852\pi$
$107$	4.51112	−	1.20875i	0.436107	−	0.116854i	0.470191	+	0.882565i	$0.344185\pi$
$108$	0.933680	−	2.86751i	0.0898434	−	0.275926i
$109$	−8.77373	+	5.06552i	−0.840371	+	0.485188i	−0.857390	−	0.514667i	$-0.827916\pi$
$109$	−8.77373	+	5.06552i	−0.840371	+	0.485188i	0.0170193	+	0.999855i	$0.494582\pi$
$110$	4.96193	+	3.06019i	0.473101	+	0.291778i
$111$			10.2791i			0.975651i
$112$	−10.5590	−	0.711693i	−0.997736	−	0.0672486i
$113$	−7.70435	−	7.70435i	−0.724764	−	0.724764i	0.244807	−	0.969572i	$-0.421275\pi$
$113$	−7.70435	−	7.70435i	−0.724764	−	0.724764i	−0.969572	+	0.244807i	$0.921275\pi$
$114$	−18.8045	+	4.50837i	−1.76120	+	0.422248i
$115$	1.47840	−	5.46185i	0.137862	−	0.509320i
$116$	11.3336	−	5.76587i	1.05229	−	0.535348i
$117$	−3.86813	−	14.4361i	−0.357609	−	1.33461i
$118$	0.158411	−	5.97849i	0.0145829	−	0.550365i
$119$	−2.40713	−	7.76888i	−0.220662	−	0.712172i
$120$	12.3800	−	10.4993i	1.13013	−	0.958451i
$121$	−3.80073	+	6.58305i	−0.345521	+	0.598459i
$122$	−14.9314	+	8.10110i	−1.35183	+	0.733439i
$123$	−26.3937	−	7.07216i	−2.37984	−	0.637675i
$124$	−7.32463	−	4.76315i	−0.657772	−	0.427743i
$125$	−0.0853274	+	11.1800i	−0.00763192	+	0.999971i
$126$	−6.56957	+	11.7056i	−0.585264	+	1.04282i
$127$	9.01446	+	9.01446i	0.799904	+	0.799904i	0.983080	−	0.183176i	$-0.0586380\pi$
$127$	9.01446	+	9.01446i	0.799904	+	0.799904i	−0.183176	+	0.983080i	$0.558638\pi$
$128$	−8.58701	−	7.36636i	−0.758992	−	0.651100i
$129$	3.21845	−	1.85817i	0.283369	−	0.163603i
$130$	3.77764	−	12.6207i	0.331321	−	1.10691i
$131$	−16.2391	−	9.37562i	−1.41881	−	0.819152i	−0.422618	−	0.906308i	$-0.638889\pi$
$131$	−16.2391	−	9.37562i	−1.41881	−	0.819152i	−0.996195	+	0.0871562i	$0.972222\pi$
$132$	−6.32772	−	7.03644i	−0.550758	−	0.612443i
$133$	14.0847	−	0.544828i	1.22130	−	0.0472426i
$134$	3.39460	−	3.21935i	0.293248	−	0.278109i
$135$	−0.864356	−	3.25896i	−0.0743920	−	0.280487i
$136$	2.91003	−	8.19338i	0.249533	−	0.702577i
$137$	17.4309	+	4.67059i	1.48922	+	0.399035i	0.909474	−	0.415761i	$-0.136485\pi$
$137$	17.4309	+	4.67059i	1.48922	+	0.399035i	0.579747	+	0.814797i	$0.303151\pi$
$138$	−4.80163	+	7.83008i	−0.408742	+	0.666541i
$139$	2.38747			0.202503			0.101251	−	0.994861i	$-0.467715\pi$
$139$	2.38747			0.202503			0.101251	+	0.994861i	$0.467715\pi$
$140$	−10.3452	+	5.74246i	−0.874333	+	0.485327i
$141$	2.08712			0.175767
$142$	7.78603	−	12.6968i	0.653389	−	1.06549i
$143$	−7.41832	−	1.98773i	−0.620351	−	0.166223i
$144$	−13.1166	+	5.82035i	−1.09305	+	0.485029i
$145$	7.13972	−	12.2940i	0.592921	−	1.02096i
$146$	−2.10028	+	1.99185i	−0.173821	+	0.164847i
$147$	11.6847	−	13.6475i	0.963740	−	1.12563i
$148$	5.95583	−	5.35596i	0.489566	−	0.440257i
$149$	−9.54286	−	5.50957i	−0.781781	−	0.451362i	0.0552800	−	0.998471i	$-0.482395\pi$
$149$	−9.54286	−	5.50957i	−0.781781	−	0.451362i	−0.837061	+	0.547109i	$0.815728\pi$
$150$	5.24837	−	17.3732i	0.428528	−	1.41852i
$151$	−14.3323	+	8.27478i	−1.16635	+	0.673392i	−0.952817	−	0.303544i	$-0.901830\pi$
$151$	−14.3323	+	8.27478i	−1.16635	+	0.673392i	−0.213532	+	0.976936i	$0.568497\pi$
$152$	12.4103	+	8.54641i	1.00661	+	0.693205i
$153$	−7.79813	−	7.79813i	−0.630441	−	0.630441i
$154$	3.52136	+	5.93125i	0.283759	+	0.477954i
$155$	−9.76840	−	0.0248508i	−0.784617	−	0.00199607i
$156$	−11.6581	+	17.9275i	−0.933397	+	1.43535i
$157$	5.47844	+	1.46794i	0.437227	+	0.117155i	0.470717	−	0.882284i	$-0.343995\pi$
$157$	5.47844	+	1.46794i	0.437227	+	0.117155i	−0.0334897	+	0.999439i	$0.510662\pi$
$158$	−9.83987	+	5.33866i	−0.782818	+	0.424721i
$159$	−3.46920	+	6.00883i	−0.275126	+	0.476532i
$160$	−12.5340	−	1.70241i	−0.990902	−	0.134587i
$161$	4.54763	−	4.91361i	0.358403	−	0.387247i
$162$	0.258183	−	9.74392i	0.0202848	−	0.765555i
$163$	0.768508	+	2.86811i	0.0601942	+	0.224648i	0.989470	−	0.144739i	$-0.0462343\pi$
$163$	0.768508	+	2.86811i	0.0601942	+	0.224648i	−0.929276	+	0.369387i	$0.879568\pi$
$164$	9.65479	+	18.9777i	0.753912	+	1.48191i
$165$	−10.2126	−	2.76433i	−0.795052	−	0.215203i
$166$	−0.442343	+	0.106052i	−0.0343324	+	0.00823121i
$167$	−11.1720	−	11.1720i	−0.864517	−	0.864517i	0.127342	−	0.991859i	$-0.459355\pi$
$167$	−11.1720	−	11.1720i	−0.864517	−	0.864517i	−0.991859	+	0.127342i	$0.959355\pi$
$168$	18.7397	−	4.21005i	1.44580	−	0.324812i
$169$			4.35520i			0.335016i
$170$	−2.24235	−	9.45894i	−0.171981	−	0.725468i
$171$	16.5517	−	9.55613i	1.26574	−	0.730776i
$172$	−2.75362	−	0.896599i	−0.209962	−	0.0683650i
$173$	6.70516	−	1.79664i	0.509784	−	0.136596i	0.00524677	−	0.999986i	$-0.498330\pi$
$173$	6.70516	−	1.79664i	0.509784	−	0.136596i	0.504537	+	0.863390i	$0.331663\pi$
$174$	−16.7449	+	15.8805i	−1.26943	+	1.20389i
$175$	−6.22607	+	11.6720i	−0.470647	+	0.882322i
$176$	−0.779913	+	7.33270i	−0.0587881	+	0.552723i
$177$	2.80921	+	10.4841i	0.211154	+	0.788036i
$178$	2.92601	+	5.39304i	0.219314	+	0.404225i
$179$	5.08815	+	8.81294i	0.380307	+	0.658710i	0.991106	−	0.133075i	$-0.0424852\pi$
$179$	5.08815	+	8.81294i	0.380307	+	0.658710i	−0.610799	+	0.791785i	$0.709152\pi$
$180$	−8.78058	+	13.4277i	−0.654466	+	1.00084i
$181$	−10.8055			−0.803166			−0.401583	−	0.915823i	$-0.631540\pi$
$181$	−10.8055			−0.803166			−0.401583	+	0.915823i	$0.631540\pi$
$182$	10.8871	−	11.1554i	0.807006	−	0.826896i
$183$	21.8002	−	21.8002i	1.61151	−	1.61151i
$184$	7.03873	−	1.29777i	0.518902	−	0.0956727i
$185$	2.33981	−	8.64425i	0.172026	−	0.635538i
$186$	15.2024	+	4.50829i	1.11469	+	0.330564i
$187$	−5.47401	+	1.46676i	−0.400299	+	0.107260i
$188$	−1.08750	−	1.20930i	−0.0793139	−	0.0881971i
$189$	0.882806	−	3.89047i	0.0642147	−	0.282990i
$190$	16.8399	+	0.489077i	1.22169	+	0.0354814i
$191$	11.9741	+	6.91324i	0.866415	+	0.500225i	0.866155	−	0.499775i	$-0.166584\pi$
$191$	11.9741	+	6.91324i	0.866415	+	0.500225i	0.000259570		1.00000i	$0.499917\pi$
$192$	18.7421	+	8.38642i	1.35260	+	0.605238i
$193$	1.78515	−	6.66228i	0.128498	−	0.479561i	−0.871442	−	0.490498i	$-0.836815\pi$
$193$	1.78515	−	6.66228i	0.128498	−	0.479561i	0.999940	+	0.0109371i	$0.00348146\pi$
$194$	0.381473	−	0.0914581i	0.0273881	−	0.00656631i
$195$	−0.0608241	+	23.9088i	−0.00435571	+	1.71215i
$196$	−13.9959	+	0.340795i	−0.999704	+	0.0243425i
$197$	−7.85372	+	7.85372i	−0.559554	+	0.559554i	−0.929181	−	0.369626i	$-0.879486\pi$
$197$	−7.85372	+	7.85372i	−0.559554	+	0.559554i	0.369626	+	0.929181i	$0.379486\pi$
$198$	7.97324	+	4.88942i	0.566633	+	0.347476i
$199$	−8.63793	−	14.9613i	−0.612327	−	1.06058i	−0.990847	−	0.134988i	$-0.956900\pi$
$199$	−8.63793	−	14.9613i	−0.612327	−	1.06058i	0.378520	−	0.925593i	$-0.376433\pi$
$200$	−12.8009	+	6.01139i	−0.905161	+	0.425070i
$201$	−4.24534	+	7.35315i	−0.299443	+	0.518651i
$202$	−0.275285	+	10.3894i	−0.0193690	+	0.730994i
$203$	14.2319	−	8.96761i	0.998886	−	0.629403i
$204$	−0.835649	+	15.7578i	−0.0585071	+	1.10327i
$205$	20.5860	+	11.9553i	1.43779	+	0.834992i
$206$	−5.48437	+	18.4938i	−0.382114	+	1.28853i
$207$	2.34960	−	8.76884i	0.163309	−	0.609477i
$208$	16.4619	−	2.58634i	1.14143	−	0.179331i
$209$		−	9.82130i		−	0.679353i
$210$	15.0374	−	15.3298i	1.03768	−	1.05785i
$211$			18.6740i			1.28557i	0.766045	+	0.642787i	$0.222222\pi$
$211$			18.6740i			1.28557i	−0.766045	+	0.642787i	$0.777778\pi$
$212$	5.28922	−	1.12082i	0.363265	−	0.0769785i
$213$	−6.99603	+	26.1096i	−0.479360	+	1.78900i
$214$	6.33217	+	1.87781i	0.432858	+	0.128365i
$215$	−3.12953	+	0.830028i	−0.213432	+	0.0566075i
$216$	3.24558	−	2.76676i	0.220834	−	0.188254i
$217$	−10.2256	−	5.38786i	−0.694157	−	0.365751i
$218$	−14.3224	−	0.379499i	−0.970036	−	0.0257029i
$219$	2.62665	−	4.54949i	0.177492	−	0.307426i
$220$	3.71963	+	7.35767i	0.250777	+	0.496054i
$221$	6.40324	+	11.0907i	0.430729	+	0.746044i
$222$	−7.59934	+	12.3924i	−0.510035	+	0.831721i
$223$	11.0752	−	11.0752i	0.741650	−	0.741650i	−0.231245	−	0.972895i	$-0.574280\pi$
$223$	11.0752	−	11.0752i	0.741650	−	0.741650i	0.972895	+	0.231245i	$0.0742800\pi$
$224$	−12.2037	−	8.66430i	−0.815393	−	0.578908i
$225$	−0.0912651	+	17.9372i	−0.00608434	+	1.19581i
$226$	−3.59243	−	14.9841i	−0.238965	−	0.996726i
$227$	−0.679495	+	2.53591i	−0.0450997	+	0.168314i	−0.984803	−	0.173678i	$-0.944435\pi$
$227$	−0.679495	+	2.53591i	−0.0450997	+	0.168314i	0.939703	+	0.341992i	$0.111102\pi$
$228$	−26.0034	−	8.46689i	−1.72212	−	0.560733i
$229$	1.76043	+	1.01639i	0.116333	+	0.0671646i	0.557037	−	0.830488i	$-0.311938\pi$
$229$	1.76043	+	1.01639i	0.116333	+	0.0671646i	−0.440705	+	0.897652i	$0.645271\pi$
$230$	5.82028	−	5.49175i	0.383778	−	0.362115i
$231$	−9.18753	−	8.50321i	−0.604495	−	0.559470i
$232$	17.9263	+	1.42764i	1.17692	+	0.0937293i
$233$	−13.4574	+	3.60589i	−0.881621	+	0.236230i	−0.671106	−	0.741361i	$-0.734181\pi$
$233$	−13.4574	+	3.60589i	−0.881621	+	0.236230i	−0.210514	+	0.977591i	$0.567514\pi$
$234$	6.00920	−	20.2636i	0.392834	−	1.32467i
$235$	−1.75517	−	0.475084i	−0.114494	−	0.0309911i
$236$	4.61087	−	7.09047i	0.300142	−	0.461550i
$237$	14.3664	−	14.3664i	0.933197	−	0.933197i
$238$	2.84152	−	11.1456i	0.184188	−	0.722465i
$239$	−9.72902			−0.629318			−0.314659	−	0.949205i	$-0.601890\pi$
$239$	−9.72902			−0.629318			−0.314659	+	0.949205i	$0.601890\pi$
$240$	22.6873	−	3.50530i	1.46446	−	0.226266i
$241$	−7.97303	−	13.8097i	−0.513588	−	0.889560i	−0.999876	−	0.0157617i	$-0.994983\pi$
$241$	−7.97303	−	13.8097i	−0.513588	−	0.889560i	0.486288	−	0.873799i	$-0.338351\pi$
$242$	−9.44894	+	5.12656i	−0.607401	+	0.329548i
$243$	5.74932	+	21.4567i	0.368819	+	1.37645i
$244$	−23.9903	−	1.27222i	−1.53582	−	0.0814458i
$245$	−12.9328	+	8.81712i	−0.826249	+	0.563305i
$246$	−26.5914	−	28.0389i	−1.69540	−	1.78770i
$247$	−21.4378	+	5.74425i	−1.36406	+	0.365498i
$248$	−5.30908	−	11.1575i	−0.337127	−	0.708500i
$249$	0.714941	−	0.412771i	0.0453075	−	0.0261583i
$250$	−8.36824	+	13.4154i	−0.529254	+	0.848463i
$251$			5.62289i			0.354913i	0.984129	+	0.177457i	$0.0567870\pi$
$251$			5.62289i			0.354913i	−0.984129	+	0.177457i	$0.943213\pi$
$252$	−16.5741	+	9.25524i	−1.04407	+	0.583025i
$253$	−3.29868	−	3.29868i	−0.207386	−	0.207386i
$254$	4.20332	+	17.5321i	0.263740	+	1.10006i
$255$	8.78235	+	15.3012i	0.549972	+	0.958201i
$256$	−4.90644	−	15.2291i	−0.306652	−	0.951822i
$257$	1.32646	+	4.95043i	0.0827426	+	0.308799i	0.994877	−	0.101091i	$-0.0322335\pi$
$257$	1.32646	+	4.95043i	0.0827426	+	0.308799i	−0.912135	+	0.409891i	$0.865567\pi$
$258$	5.25386	+	0.139211i	0.327091	+	0.00866687i
$259$	7.19735	−	7.77657i	0.447221	−	0.483213i
$260$	13.8847	−	12.4225i	0.861094	−	0.770411i
$261$	11.4045	−	19.7533i	0.705924	−	1.22270i
$262$	−12.6462	−	23.3086i	−0.781284	−	1.44001i
$263$	7.62222	+	2.04237i	0.470006	+	0.125938i	0.486045	−	0.873934i	$-0.338439\pi$
$263$	7.62222	+	2.04237i	0.470006	+	0.125938i	−0.0160390	+	0.999871i	$0.505106\pi$
$264$	−2.42658	−	13.1611i	−0.149346	−	0.810010i
$265$	4.28521	−	4.26346i	0.263238	−	0.261902i
$266$	17.3831	+	9.75594i	1.06582	+	0.598175i
$267$	−7.87393	−	7.87393i	−0.481877	−	0.481877i
$268$	6.47254	−	1.37158i	0.395373	−	0.0837824i
$269$	−3.97953	+	2.29758i	−0.242636	+	0.140086i	−0.616388	−	0.787443i	$-0.711405\pi$
$269$	−3.97953	+	2.29758i	−0.242636	+	0.140086i	0.373752	+	0.927529i	$0.378071\pi$
$270$	1.36729	−	4.56798i	0.0832108	−	0.277998i
$271$	24.8226	+	14.3314i	1.50787	+	0.870568i	0.999958	+	0.00915707i	$0.00291483\pi$
$271$	24.8226	+	14.3314i	1.50787	+	0.870568i	0.507909	+	0.861411i	$0.330419\pi$
$272$	9.56565	−	7.72644i	0.580002	−	0.468485i
$273$	−13.1871	+	25.0278i	−0.798122	+	1.51475i
$274$	17.5615	+	18.5174i	1.06093	+	1.11868i
$275$	7.95910	+	4.64934i	0.479952	+	0.280366i
$276$	−11.5775	+	5.89000i	−0.696886	+	0.354536i
$277$	−5.19134	−	1.39102i	−0.311918	−	0.0835781i	0.0994644	−	0.995041i	$-0.468287\pi$
$277$	−5.19134	−	1.39102i	−0.311918	−	0.0835781i	−0.411382	+	0.911463i	$0.634954\pi$
$278$	2.87830	+	1.76506i	0.172629	+	0.105861i
$279$	−15.6722			−0.938270
$280$	−16.7175	−	0.725204i	−0.999060	−	0.0433392i
$281$	24.2851			1.44873			0.724365	−	0.689417i	$-0.242133\pi$
$281$	24.2851			1.44873			0.724365	+	0.689417i	$0.242133\pi$
$282$	2.51620	+	1.54300i	0.149837	+	0.0918846i
$283$	9.83724	+	2.63588i	0.584763	+	0.156687i	0.539059	−	0.842268i	$-0.318780\pi$
$283$	9.83724	+	2.63588i	0.584763	+	0.156687i	0.0457044	+	0.998955i	$0.485447\pi$
$284$	18.7735	−	9.55086i	1.11400	−	0.566739i
$285$	−29.5532	+	7.83824i	−1.75058	+	0.464297i
$286$	−7.47389	−	7.88074i	−0.441940	−	0.465998i
$287$	15.0160	+	23.8310i	0.886367	+	1.40670i
$288$	−20.1161	−	2.68013i	−1.18535	−	0.157928i
$289$	−6.53852	−	3.77501i	−0.384619	−	0.222060i
$290$	17.6965	−	9.54311i	1.03917	−	0.560391i
$291$	−0.616559	+	0.355971i	−0.0361434	+	0.0208674i
$292$	−4.00464	+	0.848613i	−0.234354	+	0.0496613i
$293$	19.5889	+	19.5889i	1.14440	+	1.14440i	0.987636	+	0.156762i	$0.0501056\pi$
$293$	19.5889	+	19.5889i	1.14440	+	1.14440i	0.156762	+	0.987636i	$0.449894\pi$
$294$	24.1765	−	7.81470i	1.41000	−	0.455763i
$295$	0.0240564	−	9.45611i	0.00140062	−	0.550556i
$296$	11.1399	−	2.05392i	0.647495	−	0.119382i
$297$	−2.68501	−	0.719447i	−0.155800	−	0.0417466i
$298$	−7.43151	−	13.6973i	−0.430496	−	0.793462i
$299$	−5.27100	+	9.12965i	−0.304830	+	0.527981i
$300$	19.1714	−	17.0648i	1.10686	−	0.985236i
$301$	−3.73596	−	0.847746i	−0.215337	−	0.0488632i
$302$	−23.3964	−	0.619930i	−1.34631	−	0.0356730i
$303$	−4.88183	−	18.2192i	−0.280454	−	1.04667i
$304$	8.64333	+	19.4783i	0.495729	+	1.11716i
$305$	−23.2952	+	13.3706i	−1.33388	+	0.765598i
$306$	−3.63616	−	15.1665i	−0.207865	−	0.867009i
$307$	−20.7290	−	20.7290i	−1.18307	−	1.18307i	−0.978946	−	0.204121i	$-0.934567\pi$
$307$	−20.7290	−	20.7290i	−1.18307	−	1.18307i	−0.204121	−	0.978946i	$-0.565433\pi$
$308$	−0.139669	+	9.75397i	−0.00795836	+	0.555784i
$309$		−	35.0086i		−	1.99157i
$310$	−11.7583	−	7.25173i	−0.667825	−	0.411871i
$311$	−3.76125	+	2.17156i	−0.213281	+	0.123138i	−0.602835	−	0.797866i	$-0.705962\pi$
$311$	−3.76125	+	2.17156i	−0.213281	+	0.123138i	0.389554	+	0.921003i	$0.372629\pi$
$312$	−27.3087	+	12.9943i	−1.54605	+	0.735660i
$313$	7.58085	−	2.03128i	0.428495	−	0.114815i	−0.0381246	−	0.999273i	$-0.512138\pi$
$313$	7.58085	−	2.03128i	0.428495	−	0.114815i	0.466620	+	0.884458i	$0.345472\pi$
$314$	5.51948	+	5.81993i	0.311482	+	0.328438i
$315$	−9.94126	+	18.7516i	−0.560127	+	1.05653i
$316$	−15.8097	−	0.838401i	−0.889364	−	0.0471637i
$317$	−0.627741	−	2.34276i	−0.0352574	−	0.131583i	0.946054	−	0.324009i	$-0.105031\pi$
$317$	−0.627741	−	2.34276i	−0.0352574	−	0.131583i	−0.981311	+	0.192427i	$0.938364\pi$
$318$	−8.62475	+	4.67939i	−0.483652	+	0.262407i
$319$	−5.86050	−	10.1507i	−0.328125	−	0.568329i
$320$	−13.8522	−	11.3188i	−0.774364	−	0.632740i
$321$	−11.9867			−0.669034
$322$	9.11518	−	2.56172i	0.507969	−	0.142759i
$323$	−11.5804	+	11.5804i	−0.644349	+	0.644349i
$324$	7.51493	−	11.5563i	0.417496	−	0.642014i
$325$	5.49345	−	20.0923i	0.304722	−	1.11452i
$326$	−1.19389	+	4.02591i	−0.0661234	+	0.222975i
$327$	25.1164	−	6.72992i	1.38894	−	0.372165i
$328$	−2.39055	+	30.0171i	−0.131996	+	1.65741i
$329$	−1.57899	−	1.46138i	−0.0870525	−	0.0805685i
$330$	−10.2685	−	10.8828i	−0.565264	−	0.599080i
$331$	−11.1137	−	6.41652i	−0.610866	−	0.352684i	0.162438	−	0.986719i	$-0.448064\pi$
$331$	−11.1137	−	6.41652i	−0.610866	−	0.352684i	−0.773304	+	0.634035i	$0.781398\pi$
$332$	−0.611686	−	0.199169i	−0.0335706	−	0.0109308i
$333$	3.71862	−	13.8781i	0.203779	−	0.760515i
$334$	−5.20936	−	21.7283i	−0.285044	−	1.18892i
$335$	5.24391	−	5.21729i	0.286505	−	0.285051i
$336$	25.7047	+	8.77864i	1.40231	+	0.478914i
$337$	25.1079	−	25.1079i	1.36771	−	1.36771i	0.504022	−	0.863691i	$-0.331853\pi$
$337$	25.1079	−	25.1079i	1.36771	−	1.36771i	0.863691	−	0.504022i	$-0.168147\pi$
$338$	−3.21980	+	5.25057i	−0.175134	+	0.285593i
$339$	13.9824	+	24.2182i	0.759418	+	1.31535i
$340$	4.28964	−	13.0613i	0.232638	−	0.708350i
$341$	−4.02677	+	6.97457i	−0.218062	+	0.377694i
$342$	27.0193	+	0.715927i	1.46104	+	0.0387129i
$343$	−18.3958	+	2.14334i	−0.993281	+	0.115729i
$344$	−2.65688	−	3.11668i	−0.143249	−	0.168040i
$345$	−7.29342	+	12.5587i	−0.392665	+	0.676137i
$346$	9.41190	+	2.79111i	0.505987	+	0.150051i
$347$	−1.10061	+	4.10753i	−0.0590838	+	0.220504i	−0.989155	−	0.146876i	$-0.953078\pi$
$347$	−1.10061	+	4.10753i	−0.0590838	+	0.220504i	0.930071	+	0.367379i	$0.119745\pi$
$348$	−31.9278	+	6.76574i	−1.71151	+	0.362682i
$349$			4.09263i			0.219074i	0.993983	+	0.109537i	$0.0349368\pi$
$349$			4.09263i			0.219074i	−0.993983	+	0.109537i	$0.965063\pi$
$350$	−16.1352	+	9.46869i	−0.862461	+	0.506123i
$351$			6.28161i			0.335288i
$352$	−6.36131	+	8.26361i	−0.339059	+	0.440452i
$353$	5.17152	−	19.3004i	0.275252	−	1.02726i	−0.680420	−	0.732823i	$-0.738202\pi$
$353$	5.17152	−	19.3004i	0.275252	−	1.02726i	0.955672	−	0.294433i	$-0.0951308\pi$
$354$	−4.36416	+	14.7164i	−0.231953	+	0.782166i
$355$	11.8266	−	20.3644i	0.627689	−	1.08083i
$356$	−0.459511	+	8.66497i	−0.0243540	+	0.459242i
$357$	0.806886	+	20.8593i	0.0427049	+	1.10399i
$358$	−0.381195	+	14.3864i	−0.0201468	+	0.760346i
$359$	4.85897	−	8.41598i	0.256446	−	0.444178i	−0.708841	−	0.705368i	$-0.750782\pi$
$359$	4.85897	−	8.41598i	0.256446	−	0.444178i	0.965287	+	0.261190i	$0.0841150\pi$
$360$	−20.5128	+	9.69673i	−1.08112	+	0.511062i
$361$	−4.69104	−	8.12512i	−0.246897	−	0.427638i
$362$	−13.0270	−	7.98850i	−0.684681	−	0.419866i
$363$	13.7956	−	13.7956i	0.724082	−	0.724082i
$364$	21.3725	−	5.40000i	1.12023	−	0.283037i
$365$	−3.24447	+	3.22801i	−0.169824	+	0.168962i
$366$	42.3988	−	10.1651i	2.21622	−	0.531339i
$367$	3.93209	−	14.6748i	0.205254	−	0.766017i	−0.784119	−	0.620611i	$-0.786885\pi$
$367$	3.93209	−	14.6748i	0.205254	−	0.766017i	0.989372	−	0.145406i	$-0.0464488\pi$
$368$	9.44523	+	3.63916i	0.492367	+	0.189704i
$369$	33.0763	+	19.0966i	1.72188	+	0.994129i
$370$	9.21152	−	8.69157i	0.478884	−	0.451853i
$371$	6.83192	−	2.11682i	0.354696	−	0.109900i
$372$	14.9948	+	16.6742i	0.777444	+	0.864519i
$373$	−31.1771	+	8.35388i	−1.61429	+	0.432548i	−0.949317	−	0.314320i	$-0.898223\pi$
$373$	−31.1771	+	8.35388i	−1.61429	+	0.432548i	−0.664972	+	0.746868i	$0.731557\pi$
$374$	−7.68376	−	2.27863i	−0.397318	−	0.117825i
$375$	7.63828	−	27.6603i	0.394439	−	1.42837i
$376$	−0.417038	−	2.26190i	−0.0215071	−	0.116648i
$377$	−18.7291	+	18.7291i	−0.964600	+	0.964600i
$378$	3.94052	−	4.03764i	0.202679	−	0.207674i
$379$	29.2598			1.50297			0.751487	−	0.659747i	$-0.229337\pi$
$379$	29.2598			1.50297			0.751487	+	0.659747i	$0.229337\pi$
$380$	19.9403	+	13.0393i	1.02292	+	0.668904i
$381$	−16.3600	−	28.3364i	−0.838150	−	1.45172i
$382$	9.32484	+	17.1869i	0.477100	+	0.879360i
$383$	2.92209	+	10.9054i	0.149312	+	0.557240i	0.999526	+	0.0308021i	$0.00980617\pi$
$383$	2.92209	+	10.9054i	0.149312	+	0.557240i	−0.850213	+	0.526438i	$0.823527\pi$
$384$	16.3951	+	23.9666i	0.836661	+	1.22304i
$385$	5.79071	+	9.24212i	0.295122	+	0.471022i
$386$	7.07757	−	6.71218i	0.360239	−	0.341641i
$387$	−5.01753	+	1.34444i	−0.255055	+	0.0683419i
$388$	0.527513	+	0.171762i	0.0267804	+	0.00871988i
$389$	33.4554	−	19.3155i	1.69625	−	0.979333i	0.747000	−	0.664824i	$-0.231494\pi$
$389$	33.4554	−	19.3155i	1.69625	−	0.979333i	0.949255	−	0.314508i	$-0.101840\pi$
$390$	−17.7491	+	28.7792i	−0.898761	+	1.45729i
$391$			7.77900i			0.393401i
$392$	−17.1251	−	9.93626i	−0.864951	−	0.501857i
$393$	34.0310	+	34.0310i	1.71664	+	1.71664i
$394$	−15.2746	+	3.66208i	−0.769522	+	0.184493i
$395$	−15.3516	+	8.81127i	−0.772424	+	0.443343i
$396$	5.99768	+	11.7892i	0.301395	+	0.592431i
$397$	−2.22097	−	8.28877i	−0.111467	−	0.416002i	0.887531	−	0.460748i	$-0.152419\pi$
$397$	−2.22097	−	8.28877i	−0.111467	−	0.416002i	−0.998998	+	0.0447462i	$0.985752\pi$
$398$	0.647137	−	24.4232i	0.0324381	−	1.22422i
$399$	−35.2800	−	8.00555i	−1.76621	−	0.400779i
$400$	−19.8768	−	2.21645i	−0.993840	−	0.110822i
$401$	1.16330	−	2.01489i	0.0580922	−	0.100619i	−0.835517	−	0.549465i	$-0.814832\pi$
$401$	1.16330	−	2.01489i	0.0580922	−	0.100619i	0.893609	+	0.448846i	$0.148165\pi$
$402$	−10.5543	+	5.72627i	−0.526401	+	0.285600i
$403$	17.5792	+	4.71033i	0.875681	+	0.234638i
$404$	−8.01273	+	12.3218i	−0.398648	+	0.613030i
$405$	0.0392078	−	15.4118i	0.00194825	−	0.765821i
$406$	23.7876	−	0.289567i	1.18056	−	0.0143710i
$407$	−5.22069	−	5.22069i	−0.258780	−	0.258780i
$408$	−12.6572	+	18.3796i	−0.626623	+	0.909924i
$409$	−0.162801	+	0.0939930i	−0.00804997	+	0.00464765i	−0.504020	−	0.863692i	$-0.668146\pi$
$409$	−0.162801	+	0.0939930i	−0.00804997	+	0.00464765i	0.495970	+	0.868340i	$0.334813\pi$
$410$	15.9797	+	29.6323i	0.789180	+	1.46344i
$411$	−40.1112	−	23.1582i	−1.97854	−	1.14231i
$412$	−20.2844	+	18.2413i	−0.999339	+	0.898685i
$413$	5.21561	−	9.89866i	0.256643	−	0.487081i
$414$	9.31545	−	8.83453i	0.457829	−	0.434193i
$415$	−0.695189	+	0.184381i	−0.0341255	+	0.00905092i
$416$	21.7583	+	9.05221i	1.06679	+	0.443821i
$417$	−5.91892	−	1.58597i	−0.289851	−	0.0776652i
$418$	7.26088	−	11.8404i	0.355141	−	0.579134i
$419$	−13.0861			−0.639297			−0.319648	−	0.947536i	$-0.603565\pi$
$419$	−13.0861			−0.639297			−0.319648	+	0.947536i	$0.603565\pi$
$420$	29.4621	−	7.36423i	1.43760	−	0.359338i
$421$	3.33535			0.162555			0.0812776	−	0.996692i	$-0.474100\pi$
$421$	3.33535			0.162555			0.0812776	+	0.996692i	$0.474100\pi$
$422$	−13.8057	+	22.5131i	−0.672051	+	1.09592i
$423$	−2.81787	−	0.755046i	−0.137009	−	0.0367116i
$424$	7.20523	+	2.55907i	0.349917	+	0.124279i
$425$	−3.90256	−	14.8667i	−0.189302	−	0.721142i
$426$	−27.7371	+	26.3051i	−1.34387	+	1.27449i
$427$	−31.7570	+	1.22843i	−1.53683	+	0.0594481i
$428$	6.24571	+	6.94524i	0.301898	+	0.335711i
$429$	17.0707	+	9.85579i	0.824183	+	0.475842i
$430$	−4.38656	−	1.31299i	−0.211539	−	0.0633180i
$431$	−2.08778	+	1.20538i	−0.100565	+	0.0580612i	−0.549439	−	0.835534i	$-0.685159\pi$
$431$	−2.08778	+	1.20538i	−0.100565	+	0.0580612i	0.448874	+	0.893595i	$0.351825\pi$
$432$	5.95828	−	0.936111i	0.286668	−	0.0450386i
$433$	0.313016	+	0.313016i	0.0150426	+	0.0150426i	0.714588	−	0.699545i	$-0.246614\pi$
$433$	0.313016	+	0.313016i	0.0150426	+	0.0150426i	−0.699545	+	0.714588i	$0.746614\pi$
$434$	−8.34456	−	14.0553i	−0.400552	−	0.674675i
$435$	−25.8672	+	25.7360i	−1.24024	+	1.23394i
$436$	−16.9863	−	11.0461i	−0.813498	−	0.529011i
$437$	−13.0219	−	3.48921i	−0.622922	−	0.166911i
$438$	6.53008	−	3.54292i	0.312019	−	0.169287i
$439$	11.2300	−	19.4509i	0.535978	−	0.928341i	−0.463138	−	0.886286i	$-0.653276\pi$
$439$	11.2300	−	19.4509i	0.535978	−	0.928341i	0.999115	−	0.0420543i	$-0.0133902\pi$
$440$	−0.955185	+	11.6202i	−0.0455367	+	0.553972i
$441$	−20.7130	+	14.1987i	−0.986335	+	0.676128i
$442$	−0.479719	+	18.1048i	−0.0228179	+	0.861155i
$443$	−4.51489	−	16.8498i	−0.214509	−	0.800559i	−0.986339	−	0.164730i	$-0.947325\pi$
$443$	−4.51489	−	16.8498i	−0.214509	−	0.800559i	0.771830	−	0.635829i	$-0.219342\pi$
$444$	−18.3233	+	9.32186i	−0.869586	+	0.442396i
$445$	4.82928	+	8.41392i	0.228930	+	0.398858i
$446$	21.5400	−	5.16422i	1.01995	−	0.244533i
$447$	19.9983	+	19.9983i	0.945886	+	0.945886i
$448$	−8.30707	−	19.4677i	−0.392472	−	0.919764i
$449$			24.3525i			1.14927i	0.818411	+	0.574633i	$0.194855\pi$
$449$			24.3525i			1.14927i	−0.818411	+	0.574633i	$0.805145\pi$
$450$	−13.3710	+	21.5573i	−0.630314	+	1.01622i
$451$	16.9970	−	9.81325i	0.800360	−	0.462088i
$452$	6.74673	−	20.7205i	0.317339	−	0.974609i
$453$	41.0289	−	10.9937i	1.92771	−	0.516528i
$454$	−2.69399	+	2.55491i	−0.126435	+	0.119908i
$455$	16.7868	−	18.0454i	0.786975	−	0.845982i
$456$	−25.0898	−	29.4319i	−1.17494	−	1.37827i
$457$	−3.60868	−	13.4678i	−0.168807	−	0.629996i	−0.997524	−	0.0703280i	$-0.977595\pi$
$457$	−3.60868	−	13.4678i	−0.168807	−	0.629996i	0.828717	−	0.559668i	$-0.189071\pi$
$458$	1.37094	+	2.52682i	0.0640597	+	0.118071i
$459$	2.31762	+	4.01423i	0.108177	+	0.187368i
$460$	11.0769	−	2.31784i	0.516463	−	0.108070i
$461$	−15.8798			−0.739597			−0.369799	−	0.929112i	$-0.620573\pi$
$461$	−15.8798			−0.739597			−0.369799	+	0.929112i	$0.620573\pi$
$462$	−4.78994	−	17.0437i	−0.222848	−	0.792944i
$463$	−21.2388	+	21.2388i	−0.987052	+	0.987052i	−0.999917	−	0.0128649i	$-0.995905\pi$
$463$	−21.2388	+	21.2388i	−0.987052	+	0.987052i	0.0128649	+	0.999917i	$0.495905\pi$
$464$	20.5562	+	14.9740i	0.954298	+	0.695152i
$465$	24.2009	+	6.55064i	1.12229	+	0.303778i
$466$	−18.8898	−	5.60180i	−0.875054	−	0.259499i
$467$	22.8692	−	6.12778i	1.05826	−	0.283560i	0.312599	−	0.949885i	$-0.398800\pi$
$467$	22.8692	−	6.12778i	1.05826	−	0.283560i	0.745661	+	0.666325i	$0.232134\pi$
$468$	22.2255	−	19.9869i	1.02737	−	0.923896i
$469$	8.36038	−	2.59041i	0.386047	−	0.119614i
$470$	−1.76477	−	1.87035i	−0.0814029	−	0.0862727i
$471$	−12.6068	−	7.27851i	−0.580889	−	0.335376i
$472$	10.8008	−	5.13935i	0.497146	−	0.236558i
$473$	−0.690874	+	2.57838i	−0.0317664	+	0.118554i
$474$	27.9410	−	6.69885i	1.28337	−	0.307688i
$475$	26.6371	+	0.135530i	1.22219	+	0.00621856i
$476$	11.6657	−	11.3363i	0.534695	−	0.519598i
$477$	6.85764	−	6.85764i	0.313990	−	0.313990i
$478$	−11.7292	−	7.19266i	−0.536480	−	0.328985i
$479$	−11.7318	−	20.3200i	−0.536038	−	0.928445i	−0.999112	−	0.0421254i	$-0.986587\pi$
$479$	−11.7318	−	20.3200i	−0.536038	−	0.928445i	0.463074	−	0.886319i	$-0.346746\pi$
$480$	29.9429	+	12.5467i	1.36670	+	0.572678i
$481$	−8.34221	+	14.4491i	−0.380372	+	0.658823i
$482$	0.597324	−	22.5432i	0.0272073	−	1.02682i
$483$	−14.5383	+	9.16066i	−0.661516	+	0.416825i
$484$	−15.1816	−	0.805092i	−0.690071	−	0.0365951i
$485$	0.599526	−	0.159009i	0.0272231	−	0.00722022i
$486$	−8.93166	+	30.1184i	−0.405148	+	1.36620i
$487$	−2.12851	+	7.94369i	−0.0964518	+	0.359963i	−0.997236	−	0.0743048i	$-0.976326\pi$
$487$	−2.12851	+	7.94369i	−0.0964518	+	0.359963i	0.900784	+	0.434268i	$0.142993\pi$
$488$	−27.9818	−	19.2698i	−1.26667	−	0.872301i
$489$		−	7.62100i		−	0.344633i
$490$	−22.1101	+	1.06856i	−0.998834	+	0.0482727i
$491$			25.5075i			1.15114i	0.817753	+	0.575569i	$0.195219\pi$
$491$			25.5075i			1.15114i	−0.817753	+	0.575569i	$0.804781\pi$
$492$	−11.3290	−	53.4623i	−0.510753	−	2.41027i
$493$	−5.05859	+	18.8789i	−0.227827	+	0.850264i
$494$	−30.0919	−	8.92378i	−1.35390	−	0.401500i
$495$	12.7883	+	7.42677i	0.574791	+	0.333808i
$496$	1.84816	−	17.3763i	0.0829847	−	0.780219i
$497$	23.5745	−	14.8544i	1.05746	−	0.666310i
$498$	1.16708	+	0.0309240i	0.0522983	+	0.00138574i
$499$	−12.2280	+	21.1796i	−0.547402	+	0.948128i	0.451049	+	0.892499i	$0.351050\pi$
$499$	−12.2280	+	21.1796i	−0.547402	+	0.948128i	−0.998451	+	0.0556294i	$0.982283\pi$
$500$	−20.0066	+	9.98676i	−0.894723	+	0.446621i
$501$	20.2757	+	35.1186i	0.905853	+	1.56898i
$502$	−4.15700	+	6.77887i	−0.185536	+	0.302556i
$503$	18.7502	−	18.7502i	0.836032	−	0.836032i	−0.152302	−	0.988334i	$-0.548669\pi$
$503$	18.7502	−	18.7502i	0.836032	−	0.836032i	0.988334	+	0.152302i	$0.0486687\pi$
$504$	−26.8239	−	1.09526i	−1.19483	−	0.0487868i
$505$	−0.0418050	+	16.4327i	−0.00186030	+	0.731248i
$506$	−1.53813	−	6.41555i	−0.0683782	−	0.285206i
$507$	2.89311	−	10.7972i	0.128487	−	0.479522i
$508$	−7.89399	+	24.2439i	−0.350239	+	1.07565i
$509$	−16.5443	−	9.55184i	−0.733312	−	0.423378i	0.0863205	−	0.996267i	$-0.472489\pi$
$509$	−16.5443	−	9.55184i	−0.733312	−	0.423378i	−0.819633	+	0.572889i	$0.805822\pi$
$510$	−0.724319	+	24.9397i	−0.0320734	+	1.10435i
$511$	−5.17268	+	1.60272i	−0.228826	+	0.0709001i
$512$	5.34377	−	21.9874i	0.236163	−	0.971713i
$513$	−7.75929	+	2.07910i	−0.342581	+	0.0917943i
$514$	−2.06068	+	6.94882i	−0.0908929	+	0.306499i
$515$	−7.96891	+	29.4406i	−0.351152	+	1.29731i
$516$	6.23106	+	4.05200i	0.274307	+	0.178380i
$517$	−1.06003	+	1.06003i	−0.0466201	+	0.0466201i
$518$	14.4262	−	4.05433i	0.633852	−	0.178137i
$519$	−17.8166			−0.782062
$520$	25.9232	−	4.71143i	1.13681	−	0.206610i
$521$	−5.20016	−	9.00694i	−0.227823	−	0.394601i	0.729340	−	0.684152i	$-0.239827\pi$
$521$	−5.20016	−	9.00694i	−0.227823	−	0.394601i	−0.957163	+	0.289551i	$0.906494\pi$
$522$	28.3527	−	15.3829i	1.24097	−	0.673290i
$523$	1.09296	+	4.07897i	0.0477917	+	0.178361i	0.985696	−	0.168533i	$-0.0539030\pi$
$523$	1.09296	+	4.07897i	0.0477917	+	0.178361i	−0.937904	+	0.346894i	$0.887236\pi$
$524$	1.98600	−	37.4499i	0.0867588	−	1.63600i
$525$	23.1890	−	24.8008i	1.01205	−	1.08240i
$526$	7.67932	+	8.09735i	0.334834	+	0.353061i
$527$	12.9718	−	3.47577i	0.565059	−	0.151407i
$528$	6.80455	−	17.6608i	0.296130	−	0.768588i
$529$	14.3730	−	8.29825i	0.624913	−	0.360794i
$530$	8.31816	−	1.97192i	0.361318	−	0.0856545i
$531$		−	15.1712i		−	0.658372i
$532$	13.7442	+	24.6129i	0.595887	+	1.06710i
$533$	−31.3614	−	31.3614i	−1.35841	−	1.35841i
$534$	−3.67151	−	15.3139i	−0.158882	−	0.662697i
$535$	10.0803	+	2.72850i	0.435808	+	0.117963i
$536$	8.81720	+	3.13159i	0.380845	+	0.135264i
$537$	−6.75999	−	25.2286i	−0.291715	−	1.08870i
$538$	−6.49626	−	0.172130i	−0.280074	−	0.00742106i
$539$	0.996869	+	12.8660i	0.0429382	+	0.554180i
$540$	5.02549	−	4.49625i	0.216263	−	0.193488i
$541$	0.191927	−	0.332427i	0.00825157	−	0.0142921i	−0.861870	−	0.507129i	$-0.830707\pi$
$541$	0.191927	−	0.332427i	0.00825157	−	0.0142921i	0.870122	+	0.492837i	$0.164040\pi$
$542$	19.3306	+	35.6290i	0.830323	+	1.53040i
$543$	26.7885	+	7.17796i	1.14960	+	0.308036i
$544$	17.2444	−	2.24302i	0.739346	−	0.0961685i
$545$	−22.6536	−	0.0576308i	−0.970374	−	0.00246863i
$546$	−34.4012	+	20.4239i	−1.47224	+	0.874061i
$547$	0.879876	+	0.879876i	0.0376208	+	0.0376208i	0.725667	−	0.688046i	$-0.241531\pi$
$547$	0.879876	+	0.879876i	0.0376208	+	0.0376208i	−0.688046	+	0.725667i	$0.741531\pi$
$548$	7.48192	+	35.3075i	0.319612	+	1.50826i
$549$	−37.3195	+	21.5464i	−1.59276	+	0.919578i
$550$	6.15812	+	11.4893i	0.262583	+	0.489907i
$551$	−29.3340	−	16.9360i	−1.24967	−	0.721497i
$552$	−18.3122	−	1.45838i	−0.779419	−	0.0620726i
$553$	−20.9280	+	0.809543i	−0.889948	+	0.0344253i
$554$	−5.23023	−	5.51494i	−0.222211	−	0.234308i
$555$	−11.5430	+	19.8761i	−0.489973	+	0.843695i
$556$	2.16514	+	4.25586i	0.0918223	+	0.180488i
$557$	−37.5586	−	10.0638i	−1.59141	−	0.426417i	−0.648975	−	0.760810i	$-0.724802\pi$
$557$	−37.5586	−	10.0638i	−1.59141	−	0.426417i	−0.942434	+	0.334394i	$0.891469\pi$
$558$	−18.8942	−	11.5864i	−0.799854	−	0.490493i
$559$	6.03213			0.255132
$560$	−19.6182	−	13.2335i	−0.829021	−	0.559218i
$561$	14.5453			0.614102
$562$	29.2778	+	17.9540i	1.23501	+	0.757343i
$563$	−9.14007	−	2.44907i	−0.385208	−	0.103216i	0.0610177	−	0.998137i	$-0.480565\pi$
$563$	−9.14007	−	2.44907i	−0.385208	−	0.103216i	−0.446225	+	0.894921i	$0.647232\pi$
$564$	1.89275	+	3.72045i	0.0796992	+	0.156659i
$565$	−6.24580	−	23.5491i	−0.262763	−	0.990718i
$566$	9.91093	+	10.4504i	0.416587	+	0.439265i
$567$	8.50055	−	16.1331i	0.356990	−	0.677528i
$568$	29.6940	+	2.36481i	1.24593	+	0.0992254i
$569$	−31.4026	−	18.1303i	−1.31647	−	0.760062i	−0.333308	−	0.942818i	$-0.608165\pi$
$569$	−31.4026	−	18.1303i	−1.31647	−	0.760062i	−0.983158	+	0.182756i	$0.941498\pi$
$570$	−41.4238	−	12.3990i	−1.73505	−	0.519338i
$571$	41.2518	−	23.8167i	1.72633	−	0.996699i	0.822575	−	0.568657i	$-0.192537\pi$
$571$	41.2518	−	23.8167i	1.72633	−	0.996699i	0.903759	−	0.428042i	$-0.140797\pi$
$572$	−3.18419	−	15.0263i	−0.133138	−	0.628283i
$573$	−25.0932	−	25.0932i	−1.04828	−	1.04828i
$574$	0.484872	+	39.8316i	0.0202382	+	1.66254i
$575$	8.99212	−	8.90108i	0.374997	−	0.371201i
$576$	−22.2703	−	18.1030i	−0.927929	−	0.754290i
$577$	44.0011	+	11.7901i	1.83179	+	0.490827i	0.998112	−	0.0614241i	$-0.0195642\pi$
$577$	44.0011	+	11.7901i	1.83179	+	0.490827i	0.833678	+	0.552251i	$0.186231\pi$
$578$	−5.09188	−	9.38502i	−0.211794	−	0.390366i
$579$	−8.85133	+	15.3310i	−0.367849	+	0.637133i
$580$	28.3899	+	1.57798i	1.17882	+	0.0655219i
$581$	−0.829901	−	0.188317i	−0.0344301	−	0.00781270i
$582$	−1.00648	−	0.0266686i	−0.0417201	−	0.00110545i
$583$	−1.28986	−	4.81383i	−0.0534206	−	0.199368i
$584$	−5.45532	−	1.93755i	−0.225743	−	0.0801766i
$585$	8.73149	−	32.2579i	0.361003	−	1.33370i
$586$	9.13406	+	38.0982i	0.377325	+	1.57382i
$587$	15.9943	+	15.9943i	0.660155	+	0.660155i	0.955417	−	0.295261i	$-0.0954067\pi$
$587$	15.9943	+	15.9943i	0.660155	+	0.660155i	−0.295261	+	0.955417i	$0.595407\pi$
$588$	34.9243	+	8.45239i	1.44025	+	0.348570i
$589$			23.2735i			0.958968i
$590$	7.01990	−	11.3824i	0.289005	−	0.468605i
$591$	24.6877	−	14.2535i	1.01552	−	0.586309i
$592$	14.9486	+	5.75955i	0.614383	+	0.236716i
$593$	6.44723	−	1.72753i	0.264756	−	0.0709412i	−0.123999	−	0.992282i	$-0.539572\pi$
$593$	6.44723	−	1.72753i	0.264756	−	0.0709412i	0.388755	+	0.921341i	$0.372905\pi$
$594$	−2.70513	−	2.85238i	−0.110993	−	0.117035i
$595$	4.06958	−	17.7253i	0.166837	−	0.726668i
$596$	1.16707	−	22.0074i	0.0478050	−	0.901457i
$597$	11.4761	+	42.8295i	0.469687	+	1.75290i
$598$	−13.1042	+	7.10972i	−0.535870	+	0.290738i
$599$	16.9948	+	29.4358i	0.694387	+	1.20271i	0.970387	+	0.241555i	$0.0776576\pi$
$599$	16.9948	+	29.4358i	0.694387	+	1.20271i	−0.276000	+	0.961158i	$0.589009\pi$
$600$	35.7287	−	6.39969i	1.45862	−	0.261266i
$601$	32.7782			1.33705			0.668526	−	0.743689i	$-0.266926\pi$
$601$	32.7782			1.33705			0.668526	+	0.743689i	$0.266926\pi$
$602$	−3.87729	−	3.78402i	−0.158026	−	0.154225i
$603$	8.39185	−	8.39185i	0.341743	−	0.341743i
$604$	−27.7481	−	18.0443i	−1.12905	−	0.734213i
$605$	−14.7417	+	8.46121i	−0.599336	+	0.343997i
$606$	7.58400	−	25.5740i	0.308079	−	1.03887i
$607$	−20.2807	+	5.43419i	−0.823167	+	0.220567i	−0.645731	−	0.763565i	$-0.723447\pi$
$607$	−20.2807	+	5.43419i	−0.823167	+	0.220567i	−0.177436	+	0.984132i	$0.556780\pi$
$608$	−3.98005	+	29.8728i	−0.161412	+	1.21150i
$609$	−41.2402	+	12.7780i	−1.67114	+	0.517791i
$610$	−37.9692	−	1.10273i	−1.53733	−	0.0446483i
$611$	2.93381	+	1.69384i	0.118689	+	0.0685254i
$612$	6.82885	−	20.9727i	0.276040	−	0.847770i
$613$	−7.58040	+	28.2904i	−0.306169	+	1.14264i	0.625765	+	0.780012i	$0.284787\pi$
$613$	−7.58040	+	28.2904i	−0.306169	+	1.14264i	−0.931934	+	0.362628i	$0.881880\pi$
$614$	−9.66565	−	40.3155i	−0.390074	−	1.62700i
$615$	−43.0941	−	43.3140i	−1.73772	−	1.74659i
$616$	−7.37948	+	11.6560i	−0.297328	+	0.469633i
$617$	−27.0214	+	27.0214i	−1.08784	+	1.08784i	−0.0920892	+	0.995751i	$0.529354\pi$
$617$	−27.0214	+	27.0214i	−1.08784	+	1.08784i	−0.995751	+	0.0920892i	$0.970646\pi$
$618$	25.8818	−	42.2059i	1.04112	−	1.69777i
$619$	6.44385	+	11.1611i	0.259000	+	0.448601i	0.965974	−	0.258638i	$-0.0832737\pi$
$619$	6.44385	+	11.1611i	0.259000	+	0.448601i	−0.706974	+	0.707239i	$0.749940\pi$
$620$	−8.81441	−	17.4355i	−0.353995	−	0.700225i
$621$	−1.90781	+	3.30442i	−0.0765577	+	0.132602i
$622$	−6.13994	−	0.162689i	−0.246189	−	0.00652323i
$623$	0.443694	+	11.4702i	0.0177762	+	0.459544i
$624$	−42.5297	−	4.52349i	−1.70255	−	0.181085i
$625$	−12.7197	+	21.5223i	−0.508787	+	0.860893i
$626$	10.6411	+	3.15563i	0.425304	+	0.126124i
$627$	−6.52416	+	24.3485i	−0.260550	+	0.972386i
$628$	2.35153	+	11.0970i	0.0938362	+	0.442817i
$629$			12.3115i			0.490892i
$630$	−25.8481	+	15.2571i	−1.02981	+	0.607858i
$631$			35.1539i			1.39945i	0.714410	+	0.699727i	$0.246695\pi$
$631$			35.1539i			1.39945i	−0.714410	+	0.699727i	$0.753305\pi$
$632$	−18.4401	−	12.6988i	−0.733507	−	0.505133i
$633$	12.4049	−	46.2958i	0.493052	−	1.84009i
$634$	0.975205	−	3.28849i	0.0387304	−	0.130602i
$635$	7.30788	+	27.5536i	0.290004	+	1.09343i
$636$	−13.8573	−	0.734867i	−0.549479	−	0.0291394i
$637$	27.5008	−	9.70101i	1.08962	−	0.384368i
$638$	0.439057	−	16.5702i	0.0173824	−	0.656020i
$639$	18.8910	−	32.7202i	0.747318	−	1.29439i
$640$	−8.33210	−	23.8867i	−0.329355	−	0.944206i
$641$	−4.98684	−	8.63746i	−0.196968	−	0.341159i	0.750576	−	0.660784i	$-0.229776\pi$
$641$	−4.98684	−	8.63746i	−0.196968	−	0.341159i	−0.947544	+	0.319625i	$0.896443\pi$
$642$	−14.4510	−	8.86178i	−0.570336	−	0.349746i
$643$	−25.3846	+	25.3846i	−1.00107	+	1.00107i	−0.00107009	+	0.999999i	$0.500341\pi$
$643$	−25.3846	+	25.3846i	−1.00107	+	1.00107i	−0.999999	+	0.00107009i	$0.999659\pi$
$644$	12.8830	+	3.65047i	0.507662	+	0.143849i
$645$	8.30997	+	0.0211406i	0.327205	+	0.000832410i
$646$	−22.5225	+	5.39977i	−0.886135	+	0.212451i
$647$	0.521998	−	1.94812i	0.0205218	−	0.0765886i	−0.954906	−	0.296910i	$-0.904044\pi$
$647$	0.521998	−	1.94812i	0.0205218	−	0.0765886i	0.975427	+	0.220321i	$0.0707106\pi$
$648$	17.6034	−	8.37627i	0.691528	−	0.329051i
$649$	−6.75159	−	3.89803i	−0.265023	−	0.153011i
$650$	21.4771	−	20.1617i	0.842400	−	0.790808i
$651$	21.7717	+	20.1500i	0.853299	+	0.789742i
$652$	−4.41569	+	3.97094i	−0.172932	+	0.155514i
$653$	12.7709	−	3.42196i	0.499766	−	0.133912i	−0.000125665	−	1.00000i	$-0.500040\pi$
$653$	12.7709	−	3.42196i	0.499766	−	0.133912i	0.499891	+	0.866088i	$0.333373\pi$
$654$	35.2554	+	10.4550i	1.37859	+	0.408824i
$655$	−20.8721	−	36.3648i	−0.815540	−	1.42089i
$656$	−25.0736	+	34.4208i	−0.978959	+	1.34391i
$657$	−5.19215	+	5.19215i	−0.202565	+	0.202565i
$658$	−0.823209	−	2.92916i	−0.0320920	−	0.114191i
$659$	43.1794			1.68203			0.841015	−	0.541011i	$-0.181958\pi$
$659$	43.1794			1.68203			0.841015	+	0.541011i	$0.181958\pi$
$660$	−4.33393	−	20.7117i	−0.168698	−	0.806202i
$661$	8.09021	+	14.0127i	0.314673	+	0.545029i	0.979368	−	0.202085i	$-0.0647719\pi$
$661$	8.09021	+	14.0127i	0.314673	+	0.545029i	−0.664695	+	0.747115i	$0.731439\pi$
$662$	−8.65484	−	15.9520i	−0.336380	−	0.619994i
$663$	−8.50719	−	31.7493i	−0.330392	−	1.23304i
$664$	−0.590194	−	0.692334i	−0.0229040	−	0.0268678i
$665$	27.8465	+	14.7630i	1.07984	+	0.572483i
$666$	14.7432	−	13.9821i	0.571287	−	0.541794i
$667$	−15.5407	+	4.16412i	−0.601738	+	0.161235i
$668$	9.78337	−	30.0466i	0.378530	−	1.16254i
$669$	−34.8142	+	20.1000i	−1.34600	+	0.777111i
$670$	10.1791	−	2.41308i	0.393254	−	0.0932253i
$671$			22.1443i			0.854870i
$672$	24.4992	+	29.5869i	0.945078	+	1.14134i
$673$	−9.53669	−	9.53669i	−0.367612	−	0.367612i	0.498993	−	0.866606i	$-0.333703\pi$
$673$	−9.53669	−	9.53669i	−0.367612	−	0.367612i	−0.866606	+	0.498993i	$0.833703\pi$
$674$	48.8319	−	11.7075i	1.88093	−	0.450955i
$675$	1.98832	−	7.27230i	0.0765304	−	0.279911i
$676$	−7.76349	+	3.94962i	−0.298596	+	0.151908i
$677$	7.92901	+	29.5915i	0.304737	+	1.13729i	0.933172	+	0.359431i	$0.117029\pi$
$677$	7.92901	+	29.5915i	0.304737	+	1.13729i	−0.628435	+	0.777862i	$0.716304\pi$
$678$	−1.04753	+	39.5342i	−0.0402302	+	1.51830i
$679$	0.715700	+	0.162403i	0.0274660	+	0.00623245i
$680$	14.8278	−	12.5752i	0.568619	−	0.482238i
$681$	3.36915	−	5.83554i	0.129106	−	0.223618i
$682$	−10.0109	+	5.43145i	−0.383337	+	0.207981i
$683$	−20.1250	−	5.39248i	−0.770062	−	0.206338i	−0.147663	−	0.989038i	$-0.547175\pi$
$683$	−20.1250	−	5.39248i	−0.770062	−	0.206338i	−0.622399	+	0.782700i	$0.713842\pi$
$684$	32.0448	+	20.8385i	1.22527	+	0.796779i
$685$	28.4602	+	28.6054i	1.08741	+	1.09296i
$686$	−23.7623	−	11.0160i	−0.907249	−	0.420594i
$687$	−3.68921	−	3.68921i	−0.140752	−	0.140752i
$688$	−0.898933	−	5.72165i	−0.0342715	−	0.218136i
$689$	−9.75316	+	5.63099i	−0.371566	+	0.214524i
$690$	−18.0775	+	9.74855i	−0.688197	+	0.371121i
$691$	−5.07142	−	2.92798i	−0.192926	−	0.111386i	0.400426	−	0.916329i	$-0.368862\pi$
$691$	−5.07142	−	2.92798i	−0.192926	−	0.111386i	−0.593352	+	0.804943i	$0.702196\pi$
$692$	9.28338	+	10.3231i	0.352901	+	0.392427i
$693$	9.32815	+	14.8041i	0.354347	+	0.562362i
$694$	−4.36357	+	4.13830i	−0.165639	+	0.157088i
$695$	4.61652	+	2.68103i	0.175115	+	0.101697i
$696$	−43.4937	−	15.4475i	−1.64862	−	0.585538i
$697$	−31.6122	−	8.47047i	−1.19740	−	0.320842i
$698$	−3.02568	+	4.93402i	−0.114524	+	0.186755i
$699$	35.7582			1.35250
$700$	−26.4525	−	0.513407i	−0.999812	−	0.0194050i
$701$	20.0349			0.756706			0.378353	−	0.925661i	$-0.376491\pi$
$701$	20.0349			0.756706			0.378353	+	0.925661i	$0.376491\pi$
$702$	−4.64399	+	7.57302i	−0.175276	+	0.285825i
$703$	−20.6092	−	5.52223i	−0.777292	−	0.208275i
$704$	−13.7784	+	5.25958i	−0.519292	+	0.198228i
$705$	4.03574	+	2.34374i	0.151995	+	0.0882704i
$706$	20.5035	−	19.4450i	0.771658	−	0.731821i
$707$	−9.06364	+	17.2018i	−0.340873	+	0.646941i
$708$	−16.1412	+	14.5154i	−0.606622	+	0.545523i
$709$	42.7844	+	24.7016i	1.60680	+	0.927688i	0.990080	+	0.140508i	$0.0448735\pi$
$709$	42.7844	+	24.7016i	1.60680	+	0.927688i	0.616723	+	0.787180i	$0.288460\pi$
$710$	29.3133	−	15.8077i	1.10011	−	0.593251i
$711$	−24.5937	+	14.1992i	−0.922335	+	0.532510i
$712$	−6.95998	+	10.1066i	−0.260836	+	0.378763i
$713$	7.81688	+	7.81688i	0.292744	+	0.292744i
$714$	−14.4485	+	25.7442i	−0.540721	+	0.963452i
$715$	−12.1122	−	12.1740i	−0.452972	−	0.455282i
$716$	−11.0954	+	17.0623i	−0.414656	+	0.637646i
$717$	24.1198	+	6.46287i	0.900769	+	0.241360i
$718$	12.0798	−	6.55395i	0.450815	−	0.244591i
$719$	−12.1477	+	21.0405i	−0.453033	+	0.784677i	−0.998573	−	0.0534084i	$-0.982991\pi$
$719$	−12.1477	+	21.0405i	−0.453033	+	0.784677i	0.545539	+	0.838085i	$0.316325\pi$
$720$	−31.8987	−	3.47487i	−1.18880	−	0.129501i
$721$	−24.5127	+	26.4854i	−0.912901	+	0.986369i
$722$	0.351443	−	13.2636i	0.0130794	−	0.493620i
$723$	10.5928	+	39.5327i	0.393949	+	1.47024i
$724$	−9.79922	−	19.2616i	−0.364185	−	0.715853i
$725$	27.6113	−	15.7546i	1.02546	−	0.585112i
$726$	26.8309	−	6.43271i	0.995788	−	0.238740i
$727$	15.7313	+	15.7313i	0.583441	+	0.583441i	0.935847	−	0.352406i	$-0.114636\pi$
$727$	15.7313	+	15.7313i	0.583441	+	0.583441i	−0.352406	+	0.935847i	$0.614636\pi$
$728$	29.7587	+	9.29054i	1.10293	+	0.344330i
$729$		−	36.3365i		−	1.34580i
$730$	−6.29795	+	1.49300i	−0.233098	+	0.0552585i
$731$	3.85480	−	2.22557i	0.142575	−	0.0823157i
$732$	58.6304	+	19.0905i	2.16704	+	0.705604i
$733$	−27.6619	+	7.41199i	−1.02172	+	0.273768i	−0.730517	−	0.682895i	$-0.760721\pi$
$733$	−27.6619	+	7.41199i	−1.02172	+	0.273768i	−0.291199	+	0.956663i	$0.594054\pi$
$734$	15.5895	−	14.7847i	0.575420	−	0.545713i
$735$	37.9196	−	13.2679i	1.39869	−	0.489394i
$736$	8.69661	+	11.3702i	0.320561	+	0.419110i
$737$	−1.57843	−	5.89079i	−0.0581423	−	0.216990i
$738$	25.7582	+	47.4759i	0.948172	+	1.74761i
$739$	−4.43514	−	7.68188i	−0.163149	−	0.282583i	0.772847	−	0.634592i	$-0.218832\pi$
$739$	−4.43514	−	7.68188i	−0.163149	−	0.282583i	−0.935996	+	0.352009i	$0.885498\pi$
$740$	17.5309	−	3.66836i	0.644450	−	0.134852i
$741$	56.9635			2.09261
$742$	9.80144	+	2.49882i	0.359822	+	0.0917347i
$743$	−10.5849	+	10.5849i	−0.388323	+	0.388323i	−0.874089	−	0.485766i	$-0.838541\pi$
$743$	−10.5849	+	10.5849i	−0.388323	+	0.388323i	0.485766	+	0.874089i	$0.338541\pi$
$744$	5.75027	+	31.1879i	0.210815	+	1.14340i
$745$	−12.2654	−	21.3697i	−0.449371	−	0.782927i
$746$	−43.7627	−	12.9779i	−1.60227	−	0.475154i
$747$	−1.11459	+	0.298652i	−0.0407806	+	0.0109271i
$748$	−7.57884	−	8.42768i	−0.277110	−	0.308147i
$749$	9.06844	+	8.39300i	0.331354	+	0.306673i
$750$	29.6578	−	27.6999i	1.08295	−	1.01146i
$751$	26.2007	+	15.1270i	0.956078	+	0.551992i	0.894964	−	0.446139i	$-0.147201\pi$
$751$	26.2007	+	15.1270i	0.956078	+	0.551992i	0.0611139	+	0.998131i	$0.480535\pi$
$752$	1.16944	−	3.03523i	0.0426453	−	0.110683i
$753$	3.73521	−	13.9400i	0.136119	−	0.508002i
$754$	−36.4260	+	8.73315i	−1.32656	+	0.318042i
$755$	−37.0058	−	0.0941429i	−1.34678	−	0.00342621i
$756$	7.73566	−	1.95450i	0.281343	−	0.0710844i
$757$	−18.0236	+	18.0236i	−0.655078	+	0.655078i	−0.954211	−	0.299133i	$-0.903302\pi$
$757$	−18.0236	+	18.0236i	−0.655078	+	0.655078i	0.299133	+	0.954211i	$0.403302\pi$
$758$	35.2752	+	21.6317i	1.28125	+	0.785700i
$759$	5.98667	+	10.3692i	0.217302	+	0.376378i
$760$	14.3998	+	30.4619i	0.522337	+	1.10497i
$761$	12.9621	−	22.4510i	0.469875	−	0.813848i	−0.529532	−	0.848290i	$-0.677632\pi$
$761$	12.9621	−	22.4510i	0.469875	−	0.813848i	0.999407	+	0.0344427i	$0.0109656\pi$
$762$	1.22566	−	46.2569i	0.0444010	−	1.67571i
$763$	−23.7138	−	12.4948i	−0.858497	−	0.452343i
$764$	−1.46440	+	27.6142i	−0.0529803	+	0.999046i
$765$	−6.32182	−	23.8357i	−0.228566	−	0.861783i
$766$	−4.53952	+	15.3077i	−0.164020	+	0.553090i
$767$	−4.55974	+	17.0172i	−0.164643	+	0.614455i
$768$	2.04728	+	41.0147i	0.0738749	+	1.47999i
$769$		−	43.7662i		−	1.57825i	−0.614232	−	0.789125i	$-0.710534\pi$
$769$		−	43.7662i		−	1.57825i	0.614232	−	0.789125i	$-0.289466\pi$
$770$	0.148506	+	15.4232i	0.00535180	+	0.555815i
$771$		−	13.1540i		−	0.473731i
$772$	13.4949	−	2.85967i	0.485693	−	0.102922i
$773$	−2.58809	+	9.65890i	−0.0930873	+	0.347406i	−0.996723	−	0.0808964i	$-0.974222\pi$
$773$	−2.58809	+	9.65890i	−0.0930873	+	0.347406i	0.903635	+	0.428303i	$0.140888\pi$
$774$	−7.04301	−	2.08861i	−0.253156	−	0.0750737i
$775$	−18.8607	−	11.0175i	−0.677495	−	0.395762i
$776$	0.508979	+	0.597063i	0.0182713	+	0.0214333i
$777$	−23.0092	+	14.4982i	−0.825451	+	0.520121i
$778$	54.6132	+	1.44708i	1.95798	+	0.0518802i
$779$	28.3588	−	49.1189i	1.01606	−	1.75987i
$780$	−42.6745	+	21.5739i	−1.52799	+	0.772468i
$781$	−9.70762	−	16.8141i	−0.347366	−	0.601655i
$782$	−5.75101	+	9.37825i	−0.205656	+	0.335366i
$783$	−6.77890	+	6.77890i	−0.242258	+	0.242258i
$784$	−13.3000	−	24.6396i	−0.474999	−	0.879987i
$785$	8.94490	+	8.99052i	0.319257	+	0.320886i
$786$	15.8682	+	66.1864i	0.566000	+	2.36079i
$787$	3.75602	−	14.0177i	0.133888	−	0.499675i	−0.866112	−	0.499849i	$-0.833389\pi$
$787$	3.75602	−	14.0177i	0.133888	−	0.499675i	1.00000		0.000173930i	$5.53638e-5\pi$
$788$	−21.1222	−	6.87753i	−0.752447	−	0.245002i
$789$	−17.5399	−	10.1267i	−0.624439	−	0.360520i
$790$	−25.0219	−	0.726705i	−0.890238	−	0.0258550i
$791$	6.37911	−	28.1124i	0.226815	−	0.999561i
$792$	−1.48504	+	18.6470i	−0.0527686	+	0.662592i
$793$	48.3363	−	12.9517i	1.71647	−	0.459927i
$794$	3.45031	−	11.6348i	0.122447	−	0.412903i
$795$	−13.4559	+	7.72317i	−0.477230	+	0.273912i
$796$	18.8362	−	28.9658i	0.667632	−	1.02667i
$797$	−16.4978	+	16.4978i	−0.584382	+	0.584382i	−0.936104	−	0.351723i	$-0.885596\pi$
$797$	−16.4978	+	16.4978i	−0.584382	+	0.584382i	0.351723	+	0.936104i	$0.385596\pi$
$798$	−36.6145	−	35.7338i	−1.29614	−	1.26496i
$799$	2.49978			0.0884360
$800$	−22.3246	−	17.3670i	−0.789293	−	0.614017i
$801$	7.78228	+	13.4793i	0.274973	+	0.476268i
$802$	2.89206	−	1.56910i	0.102122	−	0.0554067i
$803$	0.976597	+	3.64471i	0.0344633	+	0.128619i
$804$	−16.9575	−	0.899273i	−0.598046	−	0.0317149i
$805$	14.3112	−	4.39437i	0.504405	−	0.154881i
$806$	17.7109	+	18.6750i	0.623839	+	0.657798i
$807$	11.3921	−	3.05251i	0.401021	−	0.107453i
$808$	−18.7695	+	8.93113i	−0.660309	+	0.314196i
$809$	9.19342	−	5.30782i	0.323223	−	0.186613i	−0.329605	−	0.944119i	$-0.606916\pi$
$809$	9.19342	−	5.30782i	0.323223	−	0.186613i	0.652828	+	0.757506i	$0.273582\pi$
$810$	11.4412	−	18.5513i	0.402004	−	0.651827i
$811$		−	51.1988i		−	1.79783i	−0.438122	−	0.898916i	$-0.644356\pi$
$811$		−	51.1988i		−	1.79783i	0.438122	−	0.898916i	$-0.355644\pi$
$812$	28.8920	+	17.2370i	1.01391	+	0.604901i
$813$	−52.0190	−	52.0190i	−1.82439	−	1.82439i
$814$	−2.43434	−	10.1536i	−0.0853235	−	0.355885i
$815$	−1.73475	+	6.40890i	−0.0607655	+	0.224494i
$816$	−28.8473	+	12.8007i	−1.00986	+	0.448114i
$817$	1.99652	+	7.45113i	0.0698495	+	0.260682i
$818$	−0.265759	−	0.00704177i	−0.00929205	−	0.000246210i
$819$	26.8585	−	29.0200i	0.938511	−	1.01404i
$820$	−2.64228	+	47.5380i	−0.0922723	+	1.66010i
$821$	2.15663	−	3.73539i	0.0752668	−	0.130366i	−0.825935	−	0.563765i	$-0.809352\pi$
$821$	2.15663	−	3.73539i	0.0752668	−	0.130366i	0.901202	+	0.433399i	$0.142686\pi$
$822$	−31.2367	−	57.5734i	−1.08950	−	2.00810i
$823$	25.5920	+	6.85735i	0.892080	+	0.239032i	0.675612	−	0.737257i	$-0.263879\pi$
$823$	25.5920	+	6.85735i	0.892080	+	0.239032i	0.216468	+	0.976290i	$0.430546\pi$
$824$	−37.9403	+	6.99525i	−1.32171	+	0.243691i
$825$	−16.6433	−	16.8136i	−0.579447	−	0.585374i
$826$	13.6059	−	8.07779i	0.473411	−	0.281062i
$827$	−37.0665	−	37.0665i	−1.28893	−	1.28893i	−0.935438	−	0.353490i	$-0.884995\pi$
$827$	−37.0665	−	37.0665i	−1.28893	−	1.28893i	−0.353490	−	0.935438i	$-0.615005\pi$
$828$	17.7619	−	3.76388i	0.617270	−	0.130804i
$829$	9.10301	−	5.25563i	0.316161	−	0.182535i	−0.333519	−	0.942743i	$-0.608236\pi$
$829$	9.10301	−	5.25563i	0.316161	−	0.182535i	0.649680	+	0.760208i	$0.274903\pi$
$830$	−0.974423	−	0.291666i	−0.0338227	−	0.0101239i
$831$	11.9461	+	6.89709i	0.414406	+	0.239257i
$832$	19.5392	+	26.9991i	0.677400	+	0.936026i
$833$	13.9950	−	16.3459i	0.484899	−	0.566351i
$834$	−5.96326	−	6.28787i	−0.206491	−	0.217731i
$835$	−9.05698	−	34.1484i	−0.313430	−	1.18175i
$836$	17.5072	−	8.90667i	0.605500	−	0.308044i
$837$	6.36268	+	1.70487i	0.219926	+	0.0589291i
$838$	−15.7764	−	9.67453i	−0.544986	−	0.334201i
$839$	−32.0936			−1.10799			−0.553996	−	0.832519i	$-0.686898\pi$
$839$	−32.0936			−1.10799			−0.553996	+	0.832519i	$0.686898\pi$
$840$	40.9635	+	12.9031i	1.41337	+	0.445199i
$841$	−11.4237			−0.393921
$842$	4.02105	+	2.46582i	0.138575	+	0.0849779i
$843$	−60.2066	−	16.1323i	−2.07363	−	0.555626i
$844$	−33.2879	+	16.9350i	−1.14582	+	0.582926i
$845$	−4.89071	+	8.42140i	−0.168245	+	0.289705i
$846$	−2.83898	−	2.99352i	−0.0976061	−	0.102919i
$847$	−20.0965	+	0.777380i	−0.690525	+	0.0267111i
$848$	6.79461	+	8.41199i	0.233328	+	0.288869i
$849$	−22.6371	−	13.0695i	−0.776902	−	0.448544i
$850$	6.28608	−	20.8083i	0.215611	−	0.713717i
$851$	−8.77678	+	5.06728i	−0.300864	+	0.173704i
$852$	−52.8868	+	11.2071i	−1.81187	+	0.383949i
$853$	−14.4800	−	14.4800i	−0.495785	−	0.495785i	0.414338	−	0.910123i	$-0.364013\pi$
$853$	−14.4800	−	14.4800i	−0.495785	−	0.495785i	−0.910123	+	0.414338i	$0.864013\pi$
$854$	−39.1939	−	21.9969i	−1.34119	−	0.752719i
$855$	42.7362	+	0.108721i	1.46155	+	0.00371818i
$856$	2.39513	+	12.9905i	0.0818638	+	0.444007i
$857$	−4.04846	−	1.08478i	−0.138293	−	0.0370554i	0.189009	−	0.981975i	$-0.439473\pi$
$857$	−4.04846	−	1.08478i	−0.138293	−	0.0370554i	−0.327301	+	0.944920i	$0.606139\pi$
$858$	13.2938	+	24.5024i	0.453844	+	0.836497i
$859$	−17.7614	+	30.7636i	−0.606010	+	1.04964i	0.385881	+	0.922549i	$0.373897\pi$
$859$	−17.7614	+	30.7636i	−0.606010	+	1.04964i	−0.991891	+	0.127091i	$0.959436\pi$
$860$	−4.31768	−	4.82590i	−0.147232	−	0.164562i
$861$	−21.3964	−	69.0556i	−0.729187	−	2.35341i
$862$	−3.40814	−	0.0903049i	−0.116082	−	0.00307580i
$863$	0.907912	+	3.38837i	0.0309057	+	0.115342i	0.979656	−	0.200687i	$-0.0643173\pi$
$863$	0.907912	+	3.38837i	0.0309057	+	0.115342i	−0.948750	+	0.316028i	$0.897651\pi$
$864$	7.87529	+	3.27639i	0.267923	+	0.111465i
$865$	14.9829	+	4.05554i	0.509435	+	0.137893i
$866$	0.145955	+	0.608780i	0.00495975	+	0.0206872i
$867$	13.7023	+	13.7023i	0.465354	+	0.465354i
$868$	0.330973	−	23.1140i	0.0112339	−	0.784539i
$869$			14.5932i			0.495039i
$870$	−50.2117	+	11.9033i	−1.70234	+	0.403559i
$871$	−11.9352	+	6.89077i	−0.404408	+	0.233485i
$872$	−12.3121	−	25.8750i	−0.416941	−	0.876237i
$873$	0.961210	−	0.257555i	0.0325320	−	0.00871693i
$874$	−13.1194	−	13.8336i	−0.443772	−	0.467929i
$875$	−25.1462	+	15.5779i	−0.850095	+	0.526629i
$876$	10.4919	+	0.556392i	0.354487	+	0.0187987i
$877$	−5.75864	−	21.4915i	−0.194455	−	0.725718i	−0.992407	−	0.122996i	$-0.960750\pi$
$877$	−5.75864	−	21.4915i	−0.194455	−	0.725718i	0.797952	−	0.602721i	$-0.205917\pi$
$878$	27.9187	−	15.1474i	0.942212	−	0.511200i
$879$	−35.5513	−	61.5767i	−1.19912	−	2.07693i
$880$	−9.74238	+	13.3030i	−0.328416	+	0.448444i
$881$	−35.9299			−1.21051			−0.605254	−	0.796032i	$-0.706929\pi$
$881$	−35.9299			−1.21051			−0.605254	+	0.796032i	$0.706929\pi$
$882$	−35.4684	+	1.80461i	−1.19428	+	0.0607644i
$883$	39.0358	−	39.0358i	1.31366	−	1.31366i	0.394964	−	0.918697i	$-0.370757\pi$
$883$	39.0358	−	39.0358i	1.31366	−	1.31366i	0.918697	−	0.394964i	$-0.129243\pi$
$884$	−13.9632	+	21.4722i	−0.469632	+	0.722188i
$885$	−6.34121	+	23.4272i	−0.213158	+	0.787496i
$886$	7.01396	−	23.6518i	0.235639	−	0.794596i
$887$	28.2871	−	7.57952i	0.949789	−	0.254495i	0.249516	−	0.968371i	$-0.419728\pi$
$887$	28.2871	−	7.57952i	0.949789	−	0.254495i	0.700273	+	0.713875i	$0.253062\pi$
$888$	−28.9820	−	2.30811i	−0.972571	−	0.0774552i
$889$	−7.46387	+	32.8928i	−0.250330	+	1.10319i
$890$	−0.398292	+	13.7140i	−0.0133508	+	0.459694i
$891$	−11.0039	−	6.35313i	−0.368646	−	0.212838i
$892$	29.7862	+	9.69859i	0.997316	+	0.324733i
$893$	−1.12126	+	4.18459i	−0.0375215	+	0.140032i
$894$	9.32493	+	38.8943i	0.311872	+	1.30082i
$895$	−0.0578884	+	22.7548i	−0.00193500	+	0.760611i
$896$	4.37759	−	29.6114i	0.146245	−	0.989248i
$897$	19.1323	−	19.1323i	0.638810	−	0.638810i
$898$	−18.0038	+	29.3591i	−0.600795	+	0.979724i
$899$	13.8876	+	24.0541i	0.463178	+	0.802248i
$900$	−32.0572	+	16.1041i	−1.06857	+	0.536803i
$901$	−4.15513	+	7.19690i	−0.138428	+	0.239764i
$902$	27.7463	+	0.735189i	0.923851	+	0.0244791i
$903$	8.69888	+	4.58344i	0.289481	+	0.152527i
$904$	23.4524	−	19.9925i	0.780015	−	0.664939i
$905$	−20.8940	−	12.1341i	−0.694539	−	0.403351i
$906$	57.5915	+	17.0788i	1.91335	+	0.567406i
$907$	7.81783	−	29.1765i	0.259587	−	0.968791i	−0.705894	−	0.708317i	$-0.749455\pi$
$907$	7.81783	−	29.1765i	0.259587	−	0.968791i	0.965481	−	0.260474i	$-0.0838787\pi$
$908$	−5.13667	+	1.08850i	−0.170467	+	0.0361231i
$909$			26.3643i			0.874449i
$910$	33.5788	−	9.34485i	1.11313	−	0.309779i
$911$		−	31.4256i		−	1.04118i	−0.853808	−	0.520588i	$-0.825713\pi$
$911$		−	31.4256i		−	1.04118i	0.853808	−	0.520588i	$-0.174287\pi$
$912$	−8.48893	−	54.0315i	−0.281097	−	1.78916i
$913$	−0.153470	+	0.572757i	−0.00507911	+	0.0189555i
$914$	5.60614	−	18.9044i	0.185435	−	0.625304i
$915$	66.6343	−	17.6730i	2.20286	−	0.584253i
$916$	−0.215297	+	4.05984i	−0.00711360	+	0.134141i
$917$	−1.91764	−	49.5740i	−0.0633261	−	1.63708i
$918$	−0.173631	+	6.55291i	−0.00573068	+	0.216278i
$919$	−25.4185	+	44.0262i	−0.838480	+	1.45229i	0.0526848	+	0.998611i	$0.483222\pi$
$919$	−25.4185	+	44.0262i	−0.838480	+	1.45229i	−0.891165	+	0.453679i	$0.850111\pi$
$920$	15.0677	+	5.39478i	0.496768	+	0.177860i
$921$	37.6204	+	65.1604i	1.23963	+	2.14711i
$922$	−19.1445	−	11.7399i	−0.630490	−	0.386634i
$923$	−31.0239	+	31.0239i	−1.02116	+	1.02116i
$924$	6.82570	−	24.0888i	0.224549	−	0.792464i
$925$	14.2315	−	14.0874i	0.467928	−	0.463190i
$926$	−41.3071	+	9.90338i	−1.35744	+	0.325445i
$927$	−12.6649	+	47.2660i	−0.415969	+	1.55242i
$928$	13.7120	+	33.2497i	0.450118	+	1.09147i
$929$	35.1105	+	20.2711i	1.15194	+	0.665073i	0.949359	−	0.314193i	$-0.101734\pi$
$929$	35.1105	+	20.2711i	1.15194	+	0.665073i	0.202580	+	0.979266i	$0.435067\pi$
$930$	24.3333	+	25.7890i	0.797922	+	0.845656i
$931$	21.0853	+	30.7592i	0.691043	+	1.00809i
$932$	−18.6319	−	20.7187i	−0.610308	−	0.678663i
$933$	10.7673	−	2.88508i	0.352504	−	0.0944532i
$934$	32.1010	+	9.51961i	1.05038	+	0.311491i
$935$	−12.2319	−	3.31090i	−0.400025	−	0.108278i
$936$	41.5710	−	7.66467i	1.35879	−	0.250527i
$937$	7.47390	−	7.47390i	0.244162	−	0.244162i	−0.574408	−	0.818569i	$-0.694768\pi$
$937$	7.47390	−	7.47390i	0.244162	−	0.244162i	0.818569	+	0.574408i	$0.194768\pi$
$938$	11.9942	+	3.05787i	0.391626	+	0.0998429i
$939$	−20.1435			−0.657357
$940$	−0.744839	−	3.55956i	−0.0242940	−	0.116100i
$941$	2.77299	+	4.80295i	0.0903968	+	0.156572i	0.907678	−	0.419667i	$-0.137853\pi$
$941$	2.77299	+	4.80295i	0.0903968	+	0.156572i	−0.817281	+	0.576239i	$0.804520\pi$
$942$	−9.81753	−	18.0950i	−0.319872	−	0.589568i
$943$	−6.97270	−	26.0225i	−0.227062	−	0.847408i
$944$	16.8208	+	1.78907i	0.547470	+	0.0582294i
$945$	6.07586	−	6.53143i	0.197648	−	0.212467i
$946$	−2.73910	+	2.59769i	−0.0890559	+	0.0844583i
$947$	20.8206	−	5.57887i	0.676579	−	0.181289i	0.0958624	−	0.995395i	$-0.469439\pi$
$947$	20.8206	−	5.57887i	0.676579	−	0.181289i	0.580717	+	0.814106i	$0.302772\pi$
$948$	38.6377	+	12.5807i	1.25489	+	0.408602i
$949$	7.38444	−	4.26341i	0.239709	−	0.138396i
$950$	32.0131	+	19.8562i	1.03864	+	0.644219i
$951$			6.22506i			0.201862i
$952$	22.4449	−	5.04246i	0.727442	−	0.163427i
$953$	32.3871	+	32.3871i	1.04912	+	1.04912i	0.998730	+	0.0503899i	$0.0160464\pi$
$953$	32.3871	+	32.3871i	1.04912	+	1.04912i	0.0503899	+	0.998730i	$0.483954\pi$
$954$	13.3373	−	3.19763i	0.431812	−	0.103527i
$955$	15.3903	+	26.8141i	0.498019	+	0.867684i
$956$	−8.82299	−	17.3427i	−0.285356	−	0.560904i
$957$	7.78612	+	29.0582i	0.251689	+	0.939318i
$958$	0.878920	−	33.1708i	0.0283966	−	1.07170i
$959$	14.1306	+	45.6057i	0.456301	+	1.47268i
$960$	26.8229	+	37.2629i	0.865706	+	1.20266i
$961$	−5.95777	+	10.3192i	−0.192186	+	0.332876i
$962$	−20.7395	+	11.2523i	−0.668667	+	0.362788i
$963$	16.1836	+	4.33638i	0.521508	+	0.139738i
$964$	17.3863	−	26.7362i	0.559975	−	0.861114i
$965$	10.9333	−	10.8778i	0.351955	−	0.350169i
$966$	−24.2997	+	0.295801i	−0.781829	+	0.00951723i
$967$	10.6422	+	10.6422i	0.342230	+	0.342230i	0.857205	−	0.514975i	$-0.172199\pi$
$967$	10.6422	+	10.6422i	0.342230	+	0.342230i	−0.514975	+	0.857205i	$0.672199\pi$
$968$	−17.7075	−	12.1943i	−0.569140	−	0.391941i
$969$	36.4022	−	21.0168i	1.16941	−	0.675158i
$970$	0.840335	+	0.251530i	0.0269815	+	0.00807614i
$971$	10.1110	+	5.83760i	0.324478	+	0.187337i	0.653387	−	0.757024i	$-0.273348\pi$
$971$	10.1110	+	5.83760i	0.324478	+	0.187337i	−0.328909	+	0.944362i	$0.606681\pi$
$972$	−33.0344	+	29.7071i	−1.05958	+	0.952857i
$973$	3.36742	+	5.34422i	0.107955	+	0.171328i
$974$	−8.43886	+	8.00320i	−0.270399	+	0.256439i
$975$	−26.9662	+	46.1628i	−0.863609	+	1.47839i
$976$	−19.4883	−	43.9182i	−0.623805	−	1.40579i
$977$	29.7605	+	7.97429i	0.952121	+	0.255120i	0.701262	−	0.712903i	$-0.252620\pi$
$977$	29.7605	+	7.97429i	0.952121	+	0.255120i	0.250859	+	0.968024i	$0.419287\pi$
$978$	5.63420	−	9.18777i	0.180162	−	0.293792i
$979$	7.99822			0.255624
$980$	−27.4457	−	15.0578i	−0.876719	−	0.481003i
$981$	−36.3449			−1.16040
$982$	−18.8577	+	30.7515i	−0.601773	+	0.981319i
$983$	45.1780	+	12.1054i	1.44095	+	0.386102i	0.892868	−	0.450319i	$-0.148690\pi$
$983$	45.1780	+	12.1054i	1.44095	+	0.386102i	0.548086	+	0.836422i	$0.315357\pi$
$984$	25.8665	−	72.8289i	0.824594	−	2.32170i
$985$	−24.0057	+	6.36689i	−0.764884	+	0.202866i
$986$	−20.0557	+	19.0203i	−0.638705	+	0.605731i
$987$	2.94378	+	4.67189i	0.0937016	+	0.148708i
$988$	−29.6810	−	33.0053i	−0.944277	−	1.05004i
$989$	3.17318	+	1.83204i	0.100901	+	0.0582554i
$990$	9.92678	+	18.4080i	0.315494	+	0.585044i
$991$	−43.4359	+	25.0777i	−1.37979	+	0.796620i	−0.992133	−	0.125186i	$-0.960047\pi$
$991$	−43.4359	+	25.0777i	−1.37979	+	0.796620i	−0.387652	+	0.921806i	$0.626714\pi$
$992$	15.0744	−	19.5823i	0.478612	−	0.621738i
$993$	23.2903	+	23.2903i	0.739094	+	0.739094i
$994$	39.4029	−	0.479653i	1.24978	−	0.0152137i
$995$	0.0982746	−	38.6299i	0.00311551	−	1.22465i
$996$	1.38416	+	0.900106i	0.0438587	+	0.0285209i
$997$	−28.0782	−	7.52352i	−0.889245	−	0.238272i	−0.214853	−	0.976646i	$-0.568927\pi$
$997$	−28.0782	−	7.52352i	−0.889245	−	0.238272i	−0.674391	+	0.738374i	$0.735594\pi$
$998$	−30.4000	+	16.4936i	−0.962295	+	0.522097i
$999$	−3.01941	+	5.22977i	−0.0955299	+	0.165463i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.16	yes	72
4.3	odd	2	inner	140.2.w.b.23.7	✓	72
5.2	odd	4	inner	140.2.w.b.107.5	yes	72
5.3	odd	4		700.2.be.e.107.14		72
5.4	even	2		700.2.be.e.443.3		72
7.2	even	3		980.2.k.k.883.10		36
7.3	odd	6		980.2.x.m.263.2		72
7.4	even	3	inner	140.2.w.b.123.2	yes	72
7.5	odd	6		980.2.k.j.883.10		36
7.6	odd	2		980.2.x.m.863.16		72
20.3	even	4		700.2.be.e.107.17		72
20.7	even	4	inner	140.2.w.b.107.2	yes	72
20.19	odd	2		700.2.be.e.443.12		72
28.3	even	6		980.2.x.m.263.5		72
28.11	odd	6	inner	140.2.w.b.123.5	yes	72
28.19	even	6		980.2.k.j.883.18		36
28.23	odd	6		980.2.k.k.883.18		36
28.27	even	2		980.2.x.m.863.7		72
35.2	odd	12		980.2.k.k.687.18		36
35.4	even	6		700.2.be.e.543.17		72
35.12	even	12		980.2.k.j.687.18		36
35.17	even	12		980.2.x.m.67.7		72
35.18	odd	12		700.2.be.e.207.12		72
35.27	even	4		980.2.x.m.667.5		72
35.32	odd	12	inner	140.2.w.b.67.7	yes	72
140.27	odd	4		980.2.x.m.667.2		72
140.39	odd	6		700.2.be.e.543.14		72
140.47	odd	12		980.2.k.j.687.10		36
140.67	even	12	inner	140.2.w.b.67.16	yes	72
140.87	odd	12		980.2.x.m.67.16		72
140.107	even	12		980.2.k.k.687.10		36
140.123	even	12		700.2.be.e.207.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.7	✓	72	4.3	odd	2	inner
140.2.w.b.23.16	yes	72	1.1	even	1	trivial
140.2.w.b.67.7	yes	72	35.32	odd	12	inner
140.2.w.b.67.16	yes	72	140.67	even	12	inner
140.2.w.b.107.2	yes	72	20.7	even	4	inner
140.2.w.b.107.5	yes	72	5.2	odd	4	inner
140.2.w.b.123.2	yes	72	7.4	even	3	inner
140.2.w.b.123.5	yes	72	28.11	odd	6	inner
700.2.be.e.107.14		72	5.3	odd	4
700.2.be.e.107.17		72	20.3	even	4
700.2.be.e.207.3		72	140.123	even	12
700.2.be.e.207.12		72	35.18	odd	12
700.2.be.e.443.3		72	5.4	even	2
700.2.be.e.443.12		72	20.19	odd	2
700.2.be.e.543.14		72	140.39	odd	6
700.2.be.e.543.17		72	35.4	even	6
980.2.k.j.687.10		36	140.47	odd	12
980.2.k.j.687.18		36	35.12	even	12
980.2.k.j.883.10		36	7.5	odd	6
980.2.k.j.883.18		36	28.19	even	6
980.2.k.k.687.10		36	140.107	even	12
980.2.k.k.687.18		36	35.2	odd	12
980.2.k.k.883.10		36	7.2	even	3
980.2.k.k.883.18		36	28.23	odd	6
980.2.x.m.67.7		72	35.17	even	12
980.2.x.m.67.16		72	140.87	odd	12
980.2.x.m.263.2		72	7.3	odd	6
980.2.x.m.263.5		72	28.3	even	6
980.2.x.m.667.2		72	140.27	odd	4
980.2.x.m.667.5		72	35.27	even	4
980.2.x.m.863.7		72	28.27	even	2
980.2.x.m.863.16		72	7.6	odd	2

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	140.2.w.b.23.16

Level	$140$
Weight	$2$
Character	140.23
Analytic conductor	$1.118$
Analytic rank	$0$
Dimension	$72$
Inner twists	$8$