LMFDB - Embedded newform 240.3.be.a.133.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(133,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("240.133");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.be (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			133.32
Character	$\chi$	$=$	240.133
Dual form			240.3.be.a.157.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.976638 + 1.74533i) q^{2} +1.73205 q^{3} +(-2.09236 + 3.40911i) q^{4} +(3.81012 + 3.23774i) q^{5} +(1.69159 + 3.02300i) q^{6} +(2.47993 + 2.47993i) q^{7} +(-7.99350 - 0.322385i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(0.976638 + 1.74533i) q^{2} +1.73205 q^{3} +(-2.09236 + 3.40911i) q^{4} +(3.81012 + 3.23774i) q^{5} +(1.69159 + 3.02300i) q^{6} +(2.47993 + 2.47993i) q^{7} +(-7.99350 - 0.322385i) q^{8} +3.00000 q^{9} +(-1.92981 + 9.81202i) q^{10} +(0.348209 + 0.348209i) q^{11} +(-3.62407 + 5.90476i) q^{12} -6.32796 q^{13} +(-1.90631 + 6.75030i) q^{14} +(6.59933 + 5.60793i) q^{15} +(-7.24409 - 14.2662i) q^{16} +(11.8771 - 11.8771i) q^{17} +(2.92991 + 5.23599i) q^{18} +(6.07794 + 6.07794i) q^{19} +(-19.0100 + 6.21463i) q^{20} +(4.29537 + 4.29537i) q^{21} +(-0.267666 + 0.947815i) q^{22} +(-17.0846 + 17.0846i) q^{23} +(-13.8452 - 0.558387i) q^{24} +(4.03408 + 24.6724i) q^{25} +(-6.18013 - 11.0444i) q^{26} +5.19615 q^{27} +(-13.6433 + 3.26547i) q^{28} +(-21.6151 - 21.6151i) q^{29} +(-3.34254 + 16.9949i) q^{30} +2.86002 q^{31} +(17.8243 - 26.5762i) q^{32} +(0.603116 + 0.603116i) q^{33} +(32.3291 + 9.12985i) q^{34} +(1.41947 + 17.4782i) q^{35} +(-6.27707 + 10.2273i) q^{36} +53.4598 q^{37} +(-4.67206 + 16.5440i) q^{38} -10.9604 q^{39} +(-29.4124 - 27.1092i) q^{40} -10.1296i q^{41} +(-3.30182 + 11.6919i) q^{42} -31.6559i q^{43} +(-1.91566 + 0.458507i) q^{44} +(11.4304 + 9.71322i) q^{45} +(-46.5036 - 13.1328i) q^{46} +(9.33506 - 9.33506i) q^{47} +(-12.5471 - 24.7097i) q^{48} -36.6998i q^{49} +(-39.1216 + 31.1368i) q^{50} +(20.5718 - 20.5718i) q^{51} +(13.2404 - 21.5727i) q^{52} +21.2609i q^{53} +(5.07476 + 9.06900i) q^{54} +(0.199309 + 2.45413i) q^{55} +(-19.0239 - 20.6229i) q^{56} +(10.5273 + 10.5273i) q^{57} +(16.6154 - 58.8357i) q^{58} +(-24.4012 + 24.4012i) q^{59} +(-32.9262 + 10.7641i) q^{60} +(47.9384 - 47.9384i) q^{61} +(2.79321 + 4.99169i) q^{62} +(7.43980 + 7.43980i) q^{63} +(63.7921 + 5.15397i) q^{64} +(-24.1103 - 20.4883i) q^{65} +(-0.463611 + 1.64166i) q^{66} -98.7782i q^{67} +(15.6393 + 65.3416i) q^{68} +(-29.5913 + 29.5913i) q^{69} +(-29.1190 + 19.5474i) q^{70} +7.58516i q^{71} +(-23.9805 - 0.967155i) q^{72} +(71.1095 - 71.1095i) q^{73} +(52.2109 + 93.3050i) q^{74} +(6.98723 + 42.7338i) q^{75} +(-33.4376 + 8.00316i) q^{76} +1.72707i q^{77} +(-10.7043 - 19.1294i) q^{78} +146.874i q^{79} +(18.5892 - 77.8103i) q^{80} +9.00000 q^{81} +(17.6795 - 9.89296i) q^{82} -78.3344 q^{83} +(-23.6309 + 5.65596i) q^{84} +(83.7083 - 6.79826i) q^{85} +(55.2499 - 30.9163i) q^{86} +(-37.4385 - 37.4385i) q^{87} +(-2.67115 - 2.89567i) q^{88} +129.469 q^{89} +(-5.78944 + 29.4361i) q^{90} +(-15.6929 - 15.6929i) q^{91} +(-22.4962 - 93.9902i) q^{92} +4.95371 q^{93} +(25.4097 + 7.17579i) q^{94} +(3.47891 + 42.8365i) q^{95} +(30.8726 - 46.0313i) q^{96} +(44.2193 - 44.2193i) q^{97} +(64.0534 - 35.8425i) q^{98} +(1.04463 + 1.04463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4} + 12 q^{8} + 288 q^{9}+O(q^{10}) $ 96 * q + 4 * q^4 + 12 * q^8 + 288 * q^9	$ 96 q + 4 q^{4} + 12 q^{8} + 288 q^{9} + 24 q^{12} - 28 q^{16} + 32 q^{19} + 84 q^{20} + 4 q^{22} + 124 q^{28} + 120 q^{30} + 140 q^{32} - 148 q^{34} - 96 q^{35} + 12 q^{36} - 104 q^{38} - 284 q^{40} - 60 q^{42} - 48 q^{44} - 28 q^{46} - 144 q^{48} - 416 q^{50} + 96 q^{51} - 352 q^{52} + 336 q^{56} - 452 q^{58} + 128 q^{59} + 32 q^{61} - 8 q^{62} - 44 q^{64} - 72 q^{66} - 352 q^{68} - 96 q^{69} - 676 q^{70} + 36 q^{72} + 96 q^{73} + 32 q^{74} + 192 q^{75} - 148 q^{76} - 216 q^{78} + 404 q^{80} + 864 q^{81} + 328 q^{82} - 320 q^{83} + 216 q^{84} - 48 q^{86} + 140 q^{88} - 384 q^{91} + 408 q^{92} - 340 q^{94} - 768 q^{95} + 768 q^{98}+O(q^{100}) $ 96 * q + 4 * q^4 + 12 * q^8 + 288 * q^9 + 24 * q^12 - 28 * q^16 + 32 * q^19 + 84 * q^20 + 4 * q^22 + 124 * q^28 + 120 * q^30 + 140 * q^32 - 148 * q^34 - 96 * q^35 + 12 * q^36 - 104 * q^38 - 284 * q^40 - 60 * q^42 - 48 * q^44 - 28 * q^46 - 144 * q^48 - 416 * q^50 + 96 * q^51 - 352 * q^52 + 336 * q^56 - 452 * q^58 + 128 * q^59 + 32 * q^61 - 8 * q^62 - 44 * q^64 - 72 * q^66 - 352 * q^68 - 96 * q^69 - 676 * q^70 + 36 * q^72 + 96 * q^73 + 32 * q^74 + 192 * q^75 - 148 * q^76 - 216 * q^78 + 404 * q^80 + 864 * q^81 + 328 * q^82 - 320 * q^83 + 216 * q^84 - 48 * q^86 + 140 * q^88 - 384 * q^91 + 408 * q^92 - 340 * q^94 - 768 * q^95 + 768 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.976638	+	1.74533i	0.488319	+	0.872665i
$2$	0.976638	+	1.74533i	0.488319	+	0.872665i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−2.09236	+	3.40911i	−0.523089	+	0.852278i
$5$	3.81012	+	3.23774i	0.762025	+	0.647548i
$5$	3.81012	+	3.23774i	0.762025	+	0.647548i
$6$	1.69159	+	3.02300i	0.281931	+	0.503833i
$7$	2.47993	+	2.47993i	0.354276	+	0.354276i	0.861698	−	0.507422i	$-0.169401\pi$
$7$	2.47993	+	2.47993i	0.354276	+	0.354276i	−0.507422	+	0.861698i	$0.669401\pi$
$8$	−7.99350	−	0.322385i	−0.999188	−	0.0402981i
$9$	3.00000			0.333333
$10$	−1.92981	+	9.81202i	−0.192981	+	0.981202i
$11$	0.348209	+	0.348209i	0.0316554	+	0.0316554i	0.722757	−	0.691102i	$-0.242874\pi$
$11$	0.348209	+	0.348209i	0.0316554	+	0.0316554i	−0.691102	+	0.722757i	$0.742874\pi$
$12$	−3.62407	+	5.90476i	−0.302006	+	0.492063i
$13$	−6.32796			−0.486766			−0.243383	−	0.969930i	$-0.578257\pi$
$13$	−6.32796			−0.486766			−0.243383	+	0.969930i	$0.578257\pi$
$14$	−1.90631	+	6.75030i	−0.136165	+	0.482165i
$15$	6.59933	+	5.60793i	0.439955	+	0.373862i
$16$	−7.24409	−	14.2662i	−0.452756	−	0.891635i
$17$	11.8771	−	11.8771i	0.698654	−	0.698654i	−0.265466	−	0.964120i	$-0.585526\pi$
$17$	11.8771	−	11.8771i	0.698654	−	0.698654i	0.964120	+	0.265466i	$0.0855259\pi$
$18$	2.92991	+	5.23599i	0.162773	+	0.290888i
$19$	6.07794	+	6.07794i	0.319891	+	0.319891i	0.848725	−	0.528834i	$-0.177371\pi$
$19$	6.07794	+	6.07794i	0.319891	+	0.319891i	−0.528834	+	0.848725i	$0.677371\pi$
$20$	−19.0100	+	6.21463i	−0.950498	+	0.310732i
$21$	4.29537	+	4.29537i	0.204542	+	0.204542i
$22$	−0.267666	+	0.947815i	−0.0121666	+	0.0430825i
$23$	−17.0846	+	17.0846i	−0.742807	+	0.742807i	−0.973117	−	0.230310i	$-0.926026\pi$
$23$	−17.0846	+	17.0846i	−0.742807	+	0.742807i	0.230310	+	0.973117i	$0.426026\pi$
$24$	−13.8452	−	0.558387i	−0.576881	−	0.0232661i
$25$	4.03408	+	24.6724i	0.161363	+	0.986895i
$26$	−6.18013	−	11.0444i	−0.237697	−	0.424784i
$27$	5.19615			0.192450
$28$	−13.6433	+	3.26547i	−0.487260	+	0.116624i
$29$	−21.6151	−	21.6151i	−0.745350	−	0.745350i	0.228252	−	0.973602i	$-0.426699\pi$
$29$	−21.6151	−	21.6151i	−0.745350	−	0.745350i	−0.973602	+	0.228252i	$0.926699\pi$
$30$	−3.34254	+	16.9949i	−0.111418	+	0.566497i
$31$	2.86002			0.0922588			0.0461294	−	0.998935i	$-0.485311\pi$
$31$	2.86002			0.0922588			0.0461294	+	0.998935i	$0.485311\pi$
$32$	17.8243	−	26.5762i	0.557009	−	0.830506i
$33$	0.603116	+	0.603116i	0.0182763	+	0.0182763i
$34$	32.3291	+	9.12985i	0.950857	+	0.268525i
$35$	1.41947	+	17.4782i	0.0405564	+	0.499378i
$36$	−6.27707	+	10.2273i	−0.174363	+	0.284093i
$37$	53.4598			1.44486			0.722430	−	0.691444i	$-0.243025\pi$
$37$	53.4598			1.44486			0.722430	+	0.691444i	$0.243025\pi$
$38$	−4.67206	+	16.5440i	−0.122949	+	0.435367i
$39$	−10.9604			−0.281035
$40$	−29.4124	−	27.1092i	−0.735311	−	0.677730i
$41$		−	10.1296i		−	0.247063i	−0.992341	−	0.123532i	$-0.960578\pi$
$41$		−	10.1296i		−	0.247063i	0.992341	−	0.123532i	$-0.0394221\pi$
$42$	−3.30182	+	11.6919i	−0.0786148	+	0.278378i
$43$		−	31.6559i		−	0.736183i	−0.929790	−	0.368091i	$-0.880011\pi$
$43$		−	31.6559i		−	0.736183i	0.929790	−	0.368091i	$-0.119989\pi$
$44$	−1.91566	+	0.458507i	−0.0435378	+	0.0104206i
$45$	11.4304	+	9.71322i	0.254008	+	0.215849i
$46$	−46.5036	−	13.1328i	−1.01095	−	0.285495i
$47$	9.33506	−	9.33506i	0.198618	−	0.198618i	−0.600789	−	0.799407i	$-0.705147\pi$
$47$	9.33506	−	9.33506i	0.198618	−	0.198618i	0.799407	+	0.600789i	$0.205147\pi$
$48$	−12.5471	−	24.7097i	−0.261399	−	0.514786i
$49$		−	36.6998i		−	0.748976i
$50$	−39.1216	+	31.1368i	−0.782432	+	0.622736i
$51$	20.5718	−	20.5718i	0.403368	−	0.403368i
$52$	13.2404	−	21.5727i	0.254622	−	0.414860i
$53$			21.2609i			0.401150i	0.979678	+	0.200575i	$0.0642810\pi$
$53$			21.2609i			0.401150i	−0.979678	+	0.200575i	$0.935719\pi$
$54$	5.07476	+	9.06900i	0.0939770	+	0.167944i
$55$	0.199309	+	2.45413i	0.00362380	+	0.0446206i
$56$	−19.0239	−	20.6229i	−0.339712	−	0.368265i
$57$	10.5273	+	10.5273i	0.184689	+	0.184689i
$58$	16.6154	−	58.8357i	0.286472	−	1.01441i
$59$	−24.4012	+	24.4012i	−0.413580	+	0.413580i	−0.882984	−	0.469404i	$-0.844469\pi$
$59$	−24.4012	+	24.4012i	−0.413580	+	0.413580i	0.469404	+	0.882984i	$0.344469\pi$
$60$	−32.9262	+	10.7641i	−0.548770	+	0.179401i
$61$	47.9384	−	47.9384i	0.785876	−	0.785876i	−0.194939	−	0.980815i	$-0.562451\pi$
$61$	47.9384	−	47.9384i	0.785876	−	0.785876i	0.980815	+	0.194939i	$0.0624510\pi$
$62$	2.79321	+	4.99169i	0.0450517	+	0.0805111i
$63$	7.43980	+	7.43980i	0.118092	+	0.118092i
$64$	63.7921	+	5.15397i	0.996752	+	0.0805308i
$65$	−24.1103	−	20.4883i	−0.370928	−	0.315205i
$66$	−0.463611	+	1.64166i	−0.00702441	+	0.0248737i
$67$		−	98.7782i		−	1.47430i	−0.675729	−	0.737151i	$-0.736171\pi$
$67$		−	98.7782i		−	1.47430i	0.675729	−	0.737151i	$-0.263829\pi$
$68$	15.6393	+	65.3416i	0.229989	+	0.960906i
$69$	−29.5913	+	29.5913i	−0.428860	+	0.428860i
$70$	−29.1190	+	19.5474i	−0.415986	+	0.279248i
$71$			7.58516i			0.106833i	0.998572	+	0.0534166i	$0.0170111\pi$
$71$			7.58516i			0.106833i	−0.998572	+	0.0534166i	$0.982989\pi$
$72$	−23.9805	−	0.967155i	−0.333063	−	0.0134327i
$73$	71.1095	−	71.1095i	0.974103	−	0.974103i	−0.0255703	−	0.999673i	$-0.508140\pi$
$73$	71.1095	−	71.1095i	0.974103	−	0.974103i	0.999673	+	0.0255703i	$0.00814015\pi$
$74$	52.2109	+	93.3050i	0.705552	+	1.26088i
$75$	6.98723	+	42.7338i	0.0931631	+	0.569784i
$76$	−33.4376	+	8.00316i	−0.439968	+	0.105305i
$77$			1.72707i			0.0224295i
$78$	−10.7043	−	19.1294i	−0.137235	−	0.245249i
$79$			146.874i			1.85917i	0.368608	+	0.929585i	$0.379835\pi$
$79$			146.874i			1.85917i	−0.368608	+	0.929585i	$0.620165\pi$
$80$	18.5892	−	77.8103i	0.232365	−	0.972629i
$81$	9.00000			0.111111
$82$	17.6795	−	9.89296i	0.215604	−	0.120646i
$83$	−78.3344			−0.943788			−0.471894	−	0.881655i	$-0.656430\pi$
$83$	−78.3344			−0.943788			−0.471894	+	0.881655i	$0.656430\pi$
$84$	−23.6309	+	5.65596i	−0.281320	+	0.0673328i
$85$	83.7083	−	6.79826i	0.984803	−	0.0799796i
$86$	55.2499	−	30.9163i	0.642441	−	0.359492i
$87$	−37.4385	−	37.4385i	−0.430328	−	0.430328i
$88$	−2.67115	−	2.89567i	−0.0303540	−	0.0329053i
$89$	129.469			1.45471			0.727353	−	0.686264i	$-0.240750\pi$
$89$	129.469			1.45471			0.727353	+	0.686264i	$0.240750\pi$
$90$	−5.78944	+	29.4361i	−0.0643272	+	0.327067i
$91$	−15.6929	−	15.6929i	−0.172450	−	0.172450i
$92$	−22.4962	−	93.9902i	−0.244524	−	1.02163i
$93$	4.95371			0.0532657
$94$	25.4097	+	7.17579i	0.270316	+	0.0763382i
$95$	3.47891	+	42.8365i	0.0366201	+	0.450910i
$96$	30.8726	−	46.0313i	0.321590	−	0.479493i
$97$	44.2193	−	44.2193i	0.455869	−	0.455869i	−0.441428	−	0.897297i	$-0.645528\pi$
$97$	44.2193	−	44.2193i	0.455869	−	0.455869i	0.897297	+	0.441428i	$0.145528\pi$
$98$	64.0534	−	35.8425i	0.653606	−	0.365739i
$99$	1.04463	+	1.04463i	0.0105518	+	0.0105518i
$100$	−92.5516	−	37.8708i	−0.925516	−	0.378708i
$101$	20.9448	+	20.9448i	0.207374	+	0.207374i	0.803150	−	0.595776i	$-0.203156\pi$
$101$	20.9448	+	20.9448i	0.207374	+	0.207374i	−0.595776	+	0.803150i	$0.703156\pi$
$102$	55.9957	+	15.8134i	0.548978	+	0.155033i
$103$	98.9454	−	98.9454i	0.960635	−	0.960635i	−0.0386192	−	0.999254i	$-0.512296\pi$
$103$	98.9454	−	98.9454i	0.960635	−	0.960635i	0.999254	+	0.0386192i	$0.0122959\pi$
$104$	50.5826	+	2.04004i	0.486371	+	0.0196158i
$105$	2.45860	+	30.2732i	0.0234152	+	0.288316i
$106$	−37.1074	+	20.7642i	−0.350069	+	0.195889i
$107$	−136.473			−1.27545			−0.637723	−	0.770266i	$-0.720124\pi$
$107$	−136.473			−1.27545			−0.637723	+	0.770266i	$0.720124\pi$
$108$	−10.8722	+	17.7143i	−0.100669	+	0.164021i
$109$	26.0921	+	26.0921i	0.239377	+	0.239377i	0.816592	−	0.577215i	$-0.195861\pi$
$109$	26.0921	+	26.0921i	0.239377	+	0.239377i	−0.577215	+	0.816592i	$0.695861\pi$
$110$	−4.08862	+	2.74466i	−0.0371693	+	0.0249514i
$111$	92.5951			0.834190
$112$	17.4143	−	53.3440i	0.155485	−	0.476286i
$113$	−145.030	−	145.030i	−1.28345	−	1.28345i	−0.938693	−	0.344755i	$-0.887962\pi$
$113$	−145.030	−	145.030i	−1.28345	−	1.28345i	−0.344755	−	0.938693i	$-0.612038\pi$
$114$	−8.09225	+	28.6550i	−0.0709847	+	0.251359i
$115$	−120.410	+	9.77892i	−1.04704	+	0.0850341i
$116$	118.915	−	28.4619i	1.02513	−	0.245361i
$117$	−18.9839			−0.162255
$118$	−66.4193	−	18.7570i	−0.562875	−	0.158958i
$119$	58.9089			0.495033
$120$	−50.9438	−	46.9545i	−0.424532	−	0.391288i
$121$		−	120.758i		−	0.997996i
$122$	130.487	+	36.8499i	1.06956	+	0.302049i
$123$		−	17.5450i		−	0.142642i
$124$	−5.98419	+	9.75014i	−0.0482596	+	0.0786302i
$125$	−64.5124	+	107.066i	−0.516099	+	0.856529i
$126$	−5.71892	+	20.2509i	−0.0453883	+	0.160722i
$127$	−150.676	+	150.676i	−1.18643	+	1.18643i	−0.208381	+	0.978048i	$0.566820\pi$
$127$	−150.676	+	150.676i	−1.18643	+	1.18643i	−0.978048	+	0.208381i	$0.933180\pi$
$128$	53.3064	+	116.372i	0.416457	+	0.909156i
$129$		−	54.8295i		−	0.425035i
$130$	12.2118	−	62.0901i	0.0939369	−	0.477616i
$131$	−123.018	+	123.018i	−0.939070	+	0.939070i	−0.998247	−	0.0591777i	$-0.981152\pi$
$131$	−123.018	+	123.018i	−0.939070	+	0.939070i	0.0591777	+	0.998247i	$0.481152\pi$
$132$	−3.31803	+	0.794157i	−0.0251366	+	0.00601634i
$133$			30.1458i			0.226660i
$134$	172.401	−	96.4705i	1.28657	−	0.719929i
$135$	19.7980	+	16.8238i	0.146652	+	0.124621i
$136$	−98.7688	+	91.1107i	−0.726241	+	0.669932i
$137$	45.2883	+	45.2883i	0.330571	+	0.330571i	0.852803	−	0.522232i	$-0.174901\pi$
$137$	45.2883	+	45.2883i	0.330571	+	0.330571i	−0.522232	+	0.852803i	$0.674901\pi$
$138$	−80.5467	−	22.7466i	−0.583672	−	0.164831i
$139$	−111.230	+	111.230i	−0.800218	+	0.800218i	−0.983129	−	0.182911i	$-0.941448\pi$
$139$	−111.230	+	111.230i	−0.800218	+	0.800218i	0.182911	+	0.983129i	$0.441448\pi$
$140$	−62.5553	−	31.7316i	−0.446824	−	0.226654i
$141$	16.1688	−	16.1688i	0.114672	−	0.114672i
$142$	−13.2386	+	7.40796i	−0.0932297	+	0.0521687i
$143$	−2.20346	−	2.20346i	−0.0154088	−	0.0154088i
$144$	−21.7323	−	42.7985i	−0.150919	−	0.297212i
$145$	−12.3721	−	152.341i	−0.0853251	−	1.05062i
$146$	193.558	+	54.6613i	1.32574	+	0.374393i
$147$		−	63.5660i		−	0.432422i
$148$	−111.857	+	182.250i	−0.755790	+	1.23142i
$149$	−147.057	+	147.057i	−0.986962	+	0.986962i	−0.999916	−	0.0129541i	$-0.995876\pi$
$149$	−147.057	+	147.057i	−0.986962	+	0.986962i	0.0129541	+	0.999916i	$0.495876\pi$
$150$	−67.7606	+	53.9305i	−0.451738	+	0.359537i
$151$			86.9772i			0.576008i	0.957629	+	0.288004i	$0.0929917\pi$
$151$			86.9772i			0.576008i	−0.957629	+	0.288004i	$0.907008\pi$
$152$	−46.6246	−	50.5434i	−0.306741	−	0.332523i
$153$	35.6313	−	35.6313i	0.232885	−	0.232885i
$154$	−3.01431	+	1.68673i	−0.0195735	+	0.0109528i
$155$	10.8970	+	9.26001i	0.0703035	+	0.0597420i
$156$	22.9330	−	37.3651i	0.147006	−	0.239520i
$157$		−	90.6356i		−	0.577297i	−0.957435	−	0.288648i	$-0.906794\pi$
$157$		−	90.6356i		−	0.577297i	0.957435	−	0.288648i	$-0.0932058\pi$
$158$	−256.344	+	143.443i	−1.62243	+	0.907868i
$159$			36.8250i			0.231604i
$160$	153.960	−	43.5481i	0.962248	−	0.272176i
$161$	−84.7372			−0.526318
$162$	8.78974	+	15.7080i	0.0542577	+	0.0969628i
$163$	−136.683			−0.838549			−0.419274	−	0.907860i	$-0.637715\pi$
$163$	−136.683			−0.838549			−0.419274	+	0.907860i	$0.637715\pi$
$164$	34.5330	+	21.1947i	0.210567	+	0.129236i
$165$	0.345214	+	4.25068i	0.00209220	+	0.0257617i
$166$	−76.5044	−	136.719i	−0.460870	−	0.823611i
$167$	−93.7702	−	93.7702i	−0.561498	−	0.561498i	0.368235	−	0.929733i	$-0.379962\pi$
$167$	−93.7702	−	93.7702i	−0.561498	−	0.561498i	−0.929733	+	0.368235i	$0.879962\pi$
$168$	−32.9503	−	35.7198i	−0.196133	−	0.212618i
$169$	−128.957			−0.763059
$170$	93.6179	+	139.459i	0.550694	+	0.820348i
$171$	18.2338	+	18.2338i	0.106630	+	0.106630i
$172$	107.918	+	66.2353i	0.627432	+	0.385089i
$173$	−147.827			−0.854490			−0.427245	−	0.904136i	$-0.640516\pi$
$173$	−147.827			−0.854490			−0.427245	+	0.904136i	$0.640516\pi$
$174$	28.7787	−	101.906i	0.165395	−	0.585669i
$175$	−51.1816	+	71.1901i	−0.292466	+	0.406801i
$176$	2.44515	−	7.49007i	0.0138929	−	0.0425572i
$177$	−42.2641	+	42.2641i	−0.238780	+	0.238780i
$178$	126.444	+	225.966i	0.710360	+	1.26947i
$179$	−9.91598	−	9.91598i	−0.0553965	−	0.0553965i	0.678866	−	0.734262i	$-0.262472\pi$
$179$	−9.91598	−	9.91598i	−0.0553965	−	0.0553965i	−0.734262	+	0.678866i	$0.762472\pi$
$180$	−57.0299	+	18.6439i	−0.316833	+	0.103577i
$181$	106.279	+	106.279i	0.587175	+	0.587175i	0.936865	−	0.349690i	$-0.113713\pi$
$181$	106.279	+	106.279i	0.587175	+	0.587175i	−0.349690	+	0.936865i	$0.613713\pi$
$182$	12.0630	−	42.7157i	0.0662804	−	0.234701i
$183$	83.0318	−	83.0318i	0.453726	−	0.453726i
$184$	142.073	−	131.058i	0.772137	−	0.712270i
$185$	203.688	+	173.089i	1.10102	+	0.935616i
$186$	4.83798	+	8.64585i	0.0260106	+	0.0464831i
$187$	8.27145			0.0442323
$188$	12.2920	+	51.3565i	0.0653829	+	0.273173i
$189$	12.8861	+	12.8861i	0.0681805	+	0.0681805i
$190$	−71.3662	+	47.9076i	−0.375611	+	0.252145i
$191$	129.132			0.676086			0.338043	−	0.941131i	$-0.390235\pi$
$191$	129.132			0.676086			0.338043	+	0.941131i	$0.390235\pi$
$192$	110.491	+	8.92694i	0.575475	+	0.0464945i
$193$	145.081	+	145.081i	0.751717	+	0.751717i	0.974800	−	0.223082i	$-0.0716119\pi$
$193$	145.081	+	145.081i	0.751717	+	0.751717i	−0.223082	+	0.974800i	$0.571612\pi$
$194$	120.364	+	33.9910i	0.620431	+	0.175212i
$195$	−41.7603	−	35.4868i	−0.214155	−	0.181983i
$196$	125.114	+	76.7892i	0.638336	+	0.391781i
$197$	−391.730			−1.98848			−0.994239	−	0.107189i	$-0.965815\pi$
$197$	−391.730			−1.98848			−0.994239	+	0.107189i	$0.965815\pi$
$198$	−0.802998	+	2.84344i	−0.00405554	+	0.0143608i
$199$	110.455			0.555050			0.277525	−	0.960718i	$-0.410486\pi$
$199$	110.455			0.555050			0.277525	+	0.960718i	$0.410486\pi$
$200$	−24.2924	−	198.519i	−0.121462	−	0.992596i
$201$		−	171.089i		−	0.851188i
$202$	−16.1001	+	57.0110i	−0.0797034	+	0.282233i
$203$		−	107.208i		−	0.528120i
$204$	27.0880	+	113.175i	0.132784	+	0.554779i
$205$	32.7970	−	38.5950i	0.159985	−	0.188268i
$206$	269.326	+	76.0586i	1.30741	+	0.369216i
$207$	−51.2537	+	51.2537i	−0.247602	+	0.247602i
$208$	45.8403	+	90.2757i	0.220386	+	0.434018i
$209$			4.23279i			0.0202526i
$210$	−50.4356	+	33.8570i	−0.240169	+	0.161224i
$211$	−195.650	+	195.650i	−0.927250	+	0.927250i	−0.997527	−	0.0702773i	$-0.977612\pi$
$211$	−195.650	+	195.650i	−0.927250	+	0.927250i	0.0702773	+	0.997527i	$0.477612\pi$
$212$	−72.4809	−	44.4854i	−0.341891	−	0.209837i
$213$			13.1379i			0.0616802i
$214$	−133.284	−	238.190i	−0.622825	−	1.11304i
$215$	102.493	−	120.613i	0.476714	−	0.560989i
$216$	−41.5355	−	1.67516i	−0.192294	−	0.00775538i
$217$	7.09267	+	7.09267i	0.0326851	+	0.0326851i
$218$	−20.0568	+	71.0218i	−0.0920035	+	0.325788i
$219$	123.165	−	123.165i	0.562398	−	0.562398i
$220$	−8.78344	−	4.45545i	−0.0399247	−	0.0202521i
$221$	−75.1579	+	75.1579i	−0.340081	+	0.340081i
$222$	90.4319	+	161.609i	0.407351	+	0.727969i
$223$	151.191	+	151.191i	0.677987	+	0.677987i	0.959544	−	0.281557i	$-0.0908509\pi$
$223$	151.191	+	151.191i	0.677987	+	0.677987i	−0.281557	+	0.959544i	$0.590851\pi$
$224$	110.110	−	21.7041i	0.491564	−	0.0968934i
$225$	12.1022	+	74.0171i	0.0537877	+	0.328965i
$226$	111.483	−	394.766i	0.493288	−	1.74675i
$227$		−	300.586i		−	1.32417i	−0.749431	−	0.662083i	$-0.769673\pi$
$227$		−	300.586i		−	1.32417i	0.749431	−	0.662083i	$-0.230327\pi$
$228$	−57.9156	+	13.8619i	−0.254016	+	0.0607977i
$229$	−321.239	+	321.239i	−1.40279	+	1.40279i	−0.611710	+	0.791082i	$0.709518\pi$
$229$	−321.239	+	321.239i	−1.40279	+	1.40279i	−0.791082	+	0.611710i	$0.790482\pi$
$230$	−134.664	−	200.604i	−0.585496	−	0.872192i
$231$			2.99138i			0.0129497i
$232$	165.812	+	179.749i	0.714708	+	0.774780i
$233$	96.0956	−	96.0956i	0.412427	−	0.412427i	−0.470156	−	0.882583i	$-0.655802\pi$
$233$	96.0956	−	96.0956i	0.412427	−	0.412427i	0.882583	+	0.470156i	$0.155802\pi$
$234$	−18.5404	−	33.1332i	−0.0792324	−	0.141595i
$235$	65.7922	−	5.34323i	0.279967	−	0.0227372i
$236$	−32.1304	−	134.242i	−0.136146	−	0.568824i
$237$			254.394i			1.07339i
$238$	57.5327	+	102.816i	0.241734	+	0.431998i
$239$		−	397.633i		−	1.66374i	−0.554974	−	0.831868i	$-0.687272\pi$
$239$		−	397.633i		−	1.66374i	0.554974	−	0.831868i	$-0.312728\pi$
$240$	32.1975	−	134.771i	0.134156	−	0.561547i
$241$	176.586			0.732722			0.366361	−	0.930473i	$-0.380603\pi$
$241$	176.586			0.732722			0.366361	+	0.930473i	$0.380603\pi$
$242$	210.762	−	117.936i	0.870916	−	0.487340i
$243$	15.5885			0.0641500
$244$	63.1232	+	263.732i	0.258702	+	1.08087i
$245$	118.825	−	139.831i	0.484998	−	0.570739i
$246$	30.6218	−	17.1351i	0.124479	−	0.0696549i
$247$	−38.4609	−	38.4609i	−0.155712	−	0.155712i
$248$	−22.8616	−	0.922029i	−0.0921839	−	0.00371786i
$249$	−135.679			−0.544896
$250$	−249.871	−	8.03064i	−0.999484	−	0.0321226i
$251$	155.376	+	155.376i	0.619029	+	0.619029i	0.945282	−	0.326254i	$-0.105786\pi$
$251$	155.376	+	155.376i	0.619029	+	0.619029i	−0.326254	+	0.945282i	$0.605786\pi$
$252$	−40.9298	+	9.79640i	−0.162420	+	0.0388746i
$253$	−11.8980			−0.0470277
$254$	−410.137	−	115.824i	−1.61471	−	0.456000i
$255$	144.987	−	11.7749i	0.568577	−	0.0461762i
$256$	−151.046	+	206.691i	−0.590025	+	0.807385i
$257$	−321.383	+	321.383i	−1.25052	+	1.25052i	−0.295029	+	0.955488i	$0.595329\pi$
$257$	−321.383	+	321.383i	−1.25052	+	1.25052i	−0.955488	+	0.295029i	$0.904671\pi$
$258$	95.6957	−	53.5486i	0.370913	−	0.207553i
$259$	132.577	+	132.577i	0.511880	+	0.511880i
$260$	120.294	−	39.3259i	0.462670	−	0.151254i
$261$	−64.8454	−	64.8454i	−0.248450	−	0.248450i
$262$	−334.852	−	94.5631i	−1.27806	−	0.360928i
$263$	242.346	−	242.346i	0.921467	−	0.921467i	−0.0756659	−	0.997133i	$-0.524108\pi$
$263$	242.346	−	242.346i	0.921467	−	0.921467i	0.997133	+	0.0756659i	$0.0241082\pi$
$264$	−4.62658	−	5.01545i	−0.0175249	−	0.0189979i
$265$	−68.8374	+	81.0068i	−0.259764	+	0.305686i
$266$	−52.6143	+	29.4415i	−0.197798	+	0.110682i
$267$	224.246			0.839874
$268$	336.746	+	206.679i	1.25651	+	0.771191i
$269$	−164.004	−	164.004i	−0.609681	−	0.609681i	0.333182	−	0.942863i	$-0.391878\pi$
$269$	−164.004	−	164.004i	−0.609681	−	0.609681i	−0.942863	+	0.333182i	$0.891878\pi$
$270$	−10.0276	+	50.9848i	−0.0371393	+	0.188832i
$271$	−31.2546			−0.115331			−0.0576654	−	0.998336i	$-0.518366\pi$
$271$	−31.2546			−0.115331			−0.0576654	+	0.998336i	$0.518366\pi$
$272$	−255.480	−	83.4019i	−0.939263	−	0.306625i
$273$	−27.1810	−	27.1810i	−0.0995639	−	0.0995639i
$274$	−34.8128	+	123.273i	−0.127054	+	0.449902i
$275$	−7.18645	+	9.99586i	−0.0261325	+	0.0363486i
$276$	−38.9645	−	162.796i	−0.141176	−	0.589840i
$277$	257.269			0.928769			0.464384	−	0.885634i	$-0.346276\pi$
$277$	257.269			0.928769			0.464384	+	0.885634i	$0.346276\pi$
$278$	−302.765	−	85.5019i	−1.08908	−	0.307561i
$279$	8.58007			0.0307529
$280$	−5.71184	−	140.170i	−0.0203994	−	0.500607i
$281$		−	139.247i		−	0.495543i	−0.968819	−	0.247771i	$-0.920302\pi$
$281$		−	139.247i		−	0.495543i	0.968819	−	0.247771i	$-0.0796981\pi$
$282$	44.0110	+	12.4288i	0.156067	+	0.0440739i
$283$		−	516.051i		−	1.82350i	−0.410745	−	0.911750i	$-0.634731\pi$
$283$		−	516.051i		−	1.82350i	0.410745	−	0.911750i	$-0.365269\pi$
$284$	−25.8587	−	15.8709i	−0.0910516	−	0.0558833i
$285$	6.02565	+	74.1949i	0.0211426	+	0.260333i
$286$	1.69378	−	5.99774i	0.00592231	−	0.0209711i
$287$	25.1208	−	25.1208i	0.0875288	−	0.0875288i
$288$	53.4729	−	79.7286i	0.185670	−	0.276835i
$289$			6.86821i			0.0237654i
$290$	253.801	−	170.375i	0.875178	−	0.587500i
$291$	76.5901	−	76.5901i	0.263196	−	0.263196i
$292$	93.6338	+	391.207i	0.320664	+	1.33975i
$293$			178.541i			0.609356i	0.952455	+	0.304678i	$0.0985488\pi$
$293$			178.541i			0.609356i	−0.952455	+	0.304678i	$0.901451\pi$
$294$	110.944	−	62.0810i	0.377359	−	0.211160i
$295$	−171.976	+	13.9668i	−0.582971	+	0.0473452i
$296$	−427.331	−	17.2346i	−1.44369	−	0.0582251i
$297$	1.80935	+	1.80935i	0.00609208	+	0.00609208i
$298$	−400.285	−	113.042i	−1.34324	−	0.379335i
$299$	108.110	−	108.110i	0.361573	−	0.361573i
$300$	−160.304	−	65.5941i	−0.534347	−	0.218647i
$301$	78.5044	−	78.5044i	0.260812	−	0.260812i
$302$	−151.804	+	84.9453i	−0.502662	+	0.281276i
$303$	36.2774	+	36.2774i	0.119727	+	0.119727i
$304$	42.6797	−	130.738i	0.140394	−	0.430059i
$305$	337.864	−	27.4392i	1.10775	−	0.0899645i
$306$	96.9874	+	27.3895i	0.316952	+	0.0895083i
$307$		−	103.189i		−	0.336120i	−0.985777	−	0.168060i	$-0.946250\pi$
$307$		−	103.189i		−	0.336120i	0.985777	−	0.168060i	$-0.0537503\pi$
$308$	−5.88779	−	3.61365i	−0.0191162	−	0.0117326i
$309$	171.378	−	171.378i	0.554623	−	0.554623i
$310$	−5.51932	+	28.0626i	−0.0178042	+	0.0905246i
$311$			577.264i			1.85615i	0.372388	+	0.928077i	$0.378539\pi$
$311$			577.264i			1.85615i	−0.372388	+	0.928077i	$0.621461\pi$
$312$	87.6116	+	3.53345i	0.280806	+	0.0113252i
$313$	72.0336	−	72.0336i	0.230139	−	0.230139i	−0.582612	−	0.812751i	$-0.697969\pi$
$313$	72.0336	−	72.0336i	0.230139	−	0.230139i	0.812751	+	0.582612i	$0.197969\pi$
$314$	158.189	−	88.5181i	0.503787	−	0.281905i
$315$	4.25842	+	52.4347i	0.0135188	+	0.166459i
$316$	−500.711	−	307.314i	−1.58453	−	0.972512i
$317$		−	470.061i		−	1.48284i	−0.671040	−	0.741421i	$-0.734152\pi$
$317$		−	470.061i		−	1.48284i	0.671040	−	0.741421i	$-0.265848\pi$
$318$	−64.2718	+	35.9647i	−0.202113	+	0.113097i
$319$		−	15.0532i		−	0.0471887i
$320$	226.369	+	226.180i	0.707402	+	0.706811i
$321$	−236.378			−0.736379
$322$	−82.7576	−	147.894i	−0.257011	−	0.459299i
$323$	144.377			0.446987
$324$	−18.8312	+	30.6820i	−0.0581210	+	0.0946976i
$325$	−25.5275	−	156.126i	−0.0785462	−	0.480387i
$326$	−133.490	−	238.558i	−0.409479	−	0.731772i
$327$	45.1928	+	45.1928i	0.138204	+	0.138204i
$328$	−3.26563	+	80.9710i	−0.00995620	+	0.246863i
$329$	46.3007			0.140732
$330$	−7.08170	+	4.75389i	−0.0214597	+	0.0144057i
$331$	192.710	+	192.710i	0.582206	+	0.582206i	0.935509	−	0.353303i	$-0.114942\pi$
$331$	192.710	+	192.710i	0.582206	+	0.582206i	−0.353303	+	0.935509i	$0.614942\pi$
$332$	163.904	−	267.051i	0.493685	−	0.804370i
$333$	160.379			0.481620
$334$	72.0804	−	255.239i	0.215810	−	0.764190i
$335$	319.818	−	376.357i	0.954681	−	1.12345i
$336$	30.1624	−	92.3945i	0.0897690	−	0.274984i
$337$	256.418	−	256.418i	0.760883	−	0.760883i	−0.215599	−	0.976482i	$-0.569170\pi$
$337$	256.418	−	256.418i	0.760883	−	0.760883i	0.976482	+	0.215599i	$0.0691704\pi$
$338$	−125.944	−	225.072i	−0.372616	−	0.665895i
$339$	−251.199	−	251.199i	−0.740999	−	0.740999i
$340$	−151.972	+	299.595i	−0.446975	+	0.881163i
$341$	0.995887	+	0.995887i	0.00292049	+	0.00292049i
$342$	−14.0162	+	49.6319i	−0.0409830	+	0.145122i
$343$	212.530	−	212.530i	0.619621	−	0.619621i
$344$	−10.2054	+	253.041i	−0.0296668	+	0.735585i
$345$	−208.556	+	16.9376i	−0.604509	+	0.0490944i
$346$	−144.373	−	258.006i	−0.417264	−	0.745683i
$347$	165.582			0.477182			0.238591	−	0.971120i	$-0.423315\pi$
$347$	165.582			0.477182			0.238591	+	0.971120i	$0.423315\pi$
$348$	205.967	−	49.2974i	0.591859	−	0.141659i
$349$	−33.8885	−	33.8885i	−0.0971016	−	0.0971016i	0.656887	−	0.753989i	$-0.271873\pi$
$349$	−33.8885	−	33.8885i	−0.0971016	−	0.0971016i	−0.753989	+	0.656887i	$0.771873\pi$
$350$	−174.236	−	19.8019i	−0.497818	−	0.0565768i
$351$	−32.8811			−0.0936782
$352$	15.4607	−	3.04749i	0.0439224	−	0.00865765i
$353$	121.788	+	121.788i	0.345009	+	0.345009i	0.858247	−	0.513238i	$-0.171554\pi$
$353$	121.788	+	121.788i	0.345009	+	0.345009i	−0.513238	+	0.858247i	$0.671554\pi$
$354$	−115.042	−	32.4881i	−0.324976	−	0.0917743i
$355$	−24.5588	+	28.9004i	−0.0691797	+	0.0814096i
$356$	−270.895	+	441.374i	−0.760940	+	1.23981i
$357$	102.033			0.285808
$358$	7.62234	−	26.9910i	0.0212914	−	0.0753938i
$359$	149.331			0.415963			0.207982	−	0.978133i	$-0.433311\pi$
$359$	149.331			0.415963			0.207982	+	0.978133i	$0.433311\pi$
$360$	−88.2373	−	81.3276i	−0.245104	−	0.225910i
$361$		−	287.117i		−	0.795339i
$362$	−81.6957	+	289.287i	−0.225679	+	0.799136i
$363$		−	209.158i		−	0.576193i
$364$	86.3342	−	20.6638i	0.237182	−	0.0567686i
$365$	501.170	−	40.7019i	1.37307	−	0.111512i
$366$	226.010	+	63.8259i	0.617514	+	0.174388i
$367$	−119.158	+	119.158i	−0.324682	+	0.324682i	−0.850560	−	0.525878i	$-0.823737\pi$
$367$	−119.158	+	119.158i	−0.324682	+	0.324682i	0.525878	+	0.850560i	$0.323737\pi$
$368$	367.493	+	119.969i	0.998623	+	0.326003i
$369$		−	30.3888i		−	0.0823545i
$370$	−103.168	+	524.549i	−0.278831	+	1.41770i
$371$	−52.7257	+	52.7257i	−0.142118	+	0.142118i
$372$	−10.3649	+	16.8877i	−0.0278627	+	0.0453971i
$373$			172.603i			0.462744i	0.972865	+	0.231372i	$0.0743214\pi$
$373$			172.603i			0.462744i	−0.972865	+	0.231372i	$0.925679\pi$
$374$	8.07821	+	14.4364i	0.0215995	+	0.0386000i
$375$	−111.739	+	185.444i	−0.297970	+	0.494517i
$376$	−77.6293	+	71.6103i	−0.206461	+	0.190453i
$377$	136.780	+	136.780i	0.362811	+	0.362811i
$378$	−9.90546	+	35.0756i	−0.0262049	+	0.0927926i
$379$	0.854693	−	0.854693i	0.00225513	−	0.00225513i	−0.705978	−	0.708233i	$-0.749492\pi$
$379$	0.854693	−	0.854693i	0.00225513	−	0.00225513i	0.708233	+	0.705978i	$0.249492\pi$
$380$	−153.313	−	77.7692i	−0.403456	−	0.204656i
$381$	−260.979	+	260.979i	−0.684985	+	0.684985i
$382$	126.116	+	225.379i	0.330146	+	0.589997i
$383$	217.613	+	217.613i	0.568181	+	0.568181i	0.931619	−	0.363438i	$-0.118397\pi$
$383$	217.613	+	217.613i	0.568181	+	0.568181i	−0.363438	+	0.931619i	$0.618397\pi$
$384$	92.3295	+	201.562i	0.240441	+	0.524901i
$385$	−5.59181	+	6.58036i	−0.0145242	+	0.0170918i
$386$	−111.523	+	394.907i	−0.288920	+	1.02308i
$387$		−	94.9676i		−	0.245394i
$388$	58.2260	+	243.271i	0.150067	+	0.626987i
$389$	−377.146	+	377.146i	−0.969527	+	0.969527i	−0.999549	−	0.0300219i	$-0.990442\pi$
$389$	−377.146	+	377.146i	−0.969527	+	0.969527i	0.0300219	+	0.999549i	$0.490442\pi$
$390$	21.1514	−	107.543i	0.0542345	−	0.275752i
$391$			405.831i			1.03793i
$392$	−11.8315	+	293.360i	−0.0301824	+	0.748368i
$393$	−213.074	+	213.074i	−0.542172	+	0.542172i
$394$	−382.578	−	683.698i	−0.971011	−	1.73528i
$395$	−475.541	+	559.610i	−1.20390	+	1.41673i
$396$	−5.74699	+	1.37552i	−0.0145126	+	0.00347354i
$397$			78.3445i			0.197341i	0.995120	+	0.0986706i	$0.0314590\pi$
$397$			78.3445i			0.197341i	−0.995120	+	0.0986706i	$0.968541\pi$
$398$	107.874	+	192.780i	0.271041	+	0.484372i
$399$			52.2140i			0.130862i
$400$	322.757	−	236.280i	0.806892	−	0.590699i
$401$	−107.929			−0.269149			−0.134574	−	0.990903i	$-0.542967\pi$
$401$	−107.929			−0.269149			−0.134574	+	0.990903i	$0.542967\pi$
$402$	298.607	−	167.092i	0.742802	−	0.415651i
$403$	−18.0981			−0.0449085
$404$	−115.227	+	27.5791i	−0.285215	+	0.0682652i
$405$	34.2911	+	29.1397i	0.0846694	+	0.0719498i
$406$	187.114	−	104.704i	0.460872	−	0.257891i
$407$	18.6152	+	18.6152i	0.0457376	+	0.0457376i
$408$	−171.073	+	157.808i	−0.419295	+	0.386785i
$409$	−590.912			−1.44477			−0.722386	−	0.691490i	$-0.756955\pi$
$409$	−590.912			−1.44477			−0.722386	+	0.691490i	$0.756955\pi$
$410$	99.3919	+	19.5483i	0.242419	+	0.0476787i
$411$	78.4416	+	78.4416i	0.190855	+	0.190855i
$412$	130.287	+	544.345i	0.316230	+	1.32123i
$413$	−121.027			−0.293043
$414$	−139.511	−	39.3983i	−0.336983	−	0.0951650i
$415$	−298.464	−	253.626i	−0.719190	−	0.611148i
$416$	−112.791	+	168.173i	−0.271133	+	0.404262i
$417$	−192.657	+	192.657i	−0.462006	+	0.462006i
$418$	−7.38762	+	4.13390i	−0.0176737	+	0.00988972i
$419$	355.925	+	355.925i	0.849463	+	0.849463i	0.990066	−	0.140603i	$-0.0449041\pi$
$419$	355.925	+	355.925i	0.849463	+	0.849463i	−0.140603	+	0.990066i	$0.544904\pi$
$420$	−108.349	−	54.9607i	−0.257974	−	0.130859i
$421$	6.82808	+	6.82808i	0.0162187	+	0.0162187i	0.715170	−	0.698951i	$-0.246349\pi$
$421$	6.82808	+	6.82808i	0.0162187	+	0.0162187i	−0.698951	+	0.715170i	$0.746349\pi$
$422$	−532.553	−	150.395i	−1.26197	−	0.356385i
$423$	28.0052	−	28.0052i	0.0662061	−	0.0662061i
$424$	6.85421	−	169.949i	0.0161656	−	0.400824i
$425$	340.950	+	245.123i	0.802235	+	0.576761i
$426$	−22.9300	+	12.8310i	−0.0538262	+	0.0301196i
$427$	237.768			0.556835
$428$	285.550	−	465.251i	0.667172	−	1.08703i
$429$	−3.81650	−	3.81650i	−0.00889626	−	0.00889626i
$430$	310.608	+	61.0899i	0.722344	+	0.142070i
$431$	195.688			0.454033			0.227016	−	0.973891i	$-0.427103\pi$
$431$	195.688			0.454033			0.227016	+	0.973891i	$0.427103\pi$
$432$	−37.6414	−	74.1291i	−0.0871328	−	0.171595i
$433$	−241.662	−	241.662i	−0.558112	−	0.558112i	0.370658	−	0.928770i	$-0.379132\pi$
$433$	−241.662	−	241.662i	−0.558112	−	0.558112i	−0.928770	+	0.370658i	$0.879132\pi$
$434$	−5.45208	+	19.3060i	−0.0125624	+	0.0444839i
$435$	−21.4292	−	263.862i	−0.0492625	−	0.606578i
$436$	−143.545	+	34.3569i	−0.329231	+	0.0788002i
$437$	−207.678			−0.475235
$438$	335.252	+	94.6762i	0.765415	+	0.216156i
$439$	−377.052			−0.858889			−0.429444	−	0.903093i	$-0.641291\pi$
$439$	−377.052			−0.858889			−0.429444	+	0.903093i	$0.641291\pi$
$440$	−0.802003	−	19.6814i	−0.00182273	−	0.0447304i
$441$		−	110.100i		−	0.249659i
$442$	−204.578	−	57.7733i	−0.462845	−	0.130709i
$443$			208.703i			0.471112i	0.971861	+	0.235556i	$0.0756911\pi$
$443$			208.703i			0.471112i	−0.971861	+	0.235556i	$0.924309\pi$
$444$	−193.742	+	315.667i	−0.436356	+	0.710962i
$445$	493.292	+	419.186i	1.10852	+	0.941991i
$446$	−116.219	+	411.538i	−0.260582	+	0.922730i
$447$	−254.711	+	254.711i	−0.569823	+	0.569823i
$448$	145.419	+	170.982i	0.324596	+	0.381656i
$449$			147.313i			0.328091i	0.986453	+	0.164046i	$0.0524544\pi$
$449$			147.313i			0.328091i	−0.986453	+	0.164046i	$0.947546\pi$
$450$	−117.365	+	93.4103i	−0.260811	+	0.207579i
$451$	3.52722	−	3.52722i	0.00782089	−	0.00782089i
$452$	797.876	−	190.969i	1.76521	−	0.422497i
$453$			150.649i			0.332559i
$454$	524.621	−	293.563i	1.15555	−	0.646615i
$455$	−8.98237	−	110.602i	−0.0197415	−	0.243081i
$456$	−80.7561	−	87.5438i	−0.177097	−	0.191982i
$457$	321.992	+	321.992i	0.704578	+	0.704578i	0.965390	−	0.260812i	$-0.0839901\pi$
$457$	321.992	+	321.992i	0.704578	+	0.704578i	−0.260812	+	0.965390i	$0.583990\pi$
$458$	−874.404	−	246.934i	−1.90918	−	0.539158i
$459$	61.7153	−	61.7153i	0.134456	−	0.134456i
$460$	218.603	−	430.951i	0.475223	−	0.936850i
$461$	−14.3839	+	14.3839i	−0.0312014	+	0.0312014i	−0.722535	−	0.691334i	$-0.757023\pi$
$461$	−14.3839	+	14.3839i	−0.0312014	+	0.0312014i	0.691334	+	0.722535i	$0.257023\pi$
$462$	−5.22094	+	2.92149i	−0.0113007	+	0.00632358i
$463$	−470.642	−	470.642i	−1.01651	−	1.01651i	−0.999861	−	0.0166443i	$-0.994702\pi$
$463$	−470.642	−	470.642i	−1.01651	−	1.01651i	−0.0166443	−	0.999861i	$-0.505298\pi$
$464$	−151.783	+	464.947i	−0.327118	+	1.00204i
$465$	18.8742	+	16.0388i	0.0405897	+	0.0344921i
$466$	261.569	+	73.8679i	0.561307	+	0.158515i
$467$			112.993i			0.241954i	0.992655	+	0.120977i	$0.0386028\pi$
$467$			112.993i			0.241954i	−0.992655	+	0.120977i	$0.961397\pi$
$468$	39.7211	−	64.7182i	0.0848740	−	0.138287i
$469$	244.963	−	244.963i	0.522310	−	0.522310i
$470$	73.5809	+	109.611i	0.156555	+	0.233214i
$471$		−	156.985i		−	0.333302i
$472$	202.918	−	187.184i	0.429910	−	0.396577i
$473$	11.0229	−	11.0229i	0.0233042	−	0.0233042i
$474$	−444.002	+	248.451i	−0.936712	+	0.524158i
$475$	−125.438	+	174.476i	−0.264081	+	0.367318i
$476$	−123.259	+	200.827i	−0.258946	+	0.421906i
$477$			63.7828i			0.133717i
$478$	694.001	−	388.343i	1.45188	−	0.812434i
$479$		−	731.858i		−	1.52789i	−0.645283	−	0.763943i	$-0.723261\pi$
$479$		−	731.858i		−	1.52789i	0.645283	−	0.763943i	$-0.276739\pi$
$480$	266.666	−	75.4276i	0.555554	−	0.157141i
$481$	−338.292			−0.703309
$482$	172.461	+	308.201i	0.357802	+	0.639421i
$483$	−146.769			−0.303870
$484$	411.676	+	252.668i	0.850570	+	0.522041i
$485$	311.652	−	25.3104i	0.642581	−	0.0521864i
$486$	15.2243	+	27.2070i	0.0313257	+	0.0559815i
$487$	259.467	+	259.467i	0.532787	+	0.532787i	0.921401	−	0.388613i	$-0.127046\pi$
$487$	259.467	+	259.467i	0.532787	+	0.532787i	−0.388613	+	0.921401i	$0.627046\pi$
$488$	−398.651	+	367.741i	−0.816907	+	0.753568i
$489$	−236.743			−0.484136
$490$	360.100	+	70.8239i	0.734898	+	0.144539i
$491$	−316.449	−	316.449i	−0.644500	−	0.644500i	0.307159	−	0.951658i	$-0.400622\pi$
$491$	−316.449	−	316.449i	−0.644500	−	0.644500i	−0.951658	+	0.307159i	$0.900622\pi$
$492$	59.8128	+	36.7104i	0.121571	+	0.0746146i
$493$	−513.451			−1.04148
$494$	29.5646	−	104.689i	0.0598474	−	0.211922i
$495$	0.597928	+	7.36240i	0.00120793	+	0.0148735i
$496$	−20.7183	−	40.8015i	−0.0417707	−	0.0822612i
$497$	−18.8107	+	18.8107i	−0.0378485	+	0.0378485i
$498$	−132.509	−	236.805i	−0.266083	−	0.475512i
$499$	54.3250	+	54.3250i	0.108868	+	0.108868i	0.759442	−	0.650575i	$-0.225472\pi$
$499$	54.3250	+	54.3250i	0.108868	+	0.108868i	−0.650575	+	0.759442i	$0.725472\pi$
$500$	−230.017	−	443.950i	−0.460035	−	0.887901i
$501$	−162.415	−	162.415i	−0.324181	−	0.324181i
$502$	−119.436	+	422.929i	−0.237921	+	0.842488i
$503$	−293.378	+	293.378i	−0.583255	+	0.583255i	−0.935796	−	0.352541i	$-0.885318\pi$
$503$	−293.378	+	293.378i	−0.583255	+	0.583255i	0.352541	+	0.935796i	$0.385318\pi$
$504$	−57.0716	−	61.8686i	−0.113237	−	0.122755i
$505$	11.9884	+	147.616i	0.0237395	+	0.292309i
$506$	−11.6200	−	20.7660i	−0.0229645	−	0.0410394i
$507$	−223.360			−0.440552
$508$	−198.404	−	828.942i	−0.390559	−	1.63178i
$509$	123.743	+	123.743i	0.243111	+	0.243111i	0.818136	−	0.575025i	$-0.195008\pi$
$509$	123.743	+	123.743i	0.243111	+	0.243111i	−0.575025	+	0.818136i	$0.695008\pi$
$510$	162.151	+	241.550i	0.317943	+	0.473628i
$511$	352.694			0.690203
$512$	−508.261	−	61.7639i	−0.992697	−	0.120633i
$513$	31.5819	+	31.5819i	0.0615631	+	0.0615631i
$514$	−874.794	−	247.045i	−1.70193	−	0.480631i
$515$	697.354	−	56.6347i	1.35408	−	0.109970i
$516$	186.920	+	114.723i	0.362248	+	0.222331i
$517$	6.50111			0.0125747
$518$	−101.911	+	360.870i	−0.196739	+	0.696660i
$519$	−256.043			−0.493340
$520$	186.121	+	171.546i	0.357924	+	0.329896i
$521$		−	507.415i		−	0.973925i	−0.873423	−	0.486963i	$-0.838105\pi$
$521$		−	507.415i		−	0.973925i	0.873423	−	0.486963i	$-0.161895\pi$
$522$	49.8462	−	176.507i	0.0954908	−	0.338136i
$523$		−	608.027i		−	1.16258i	−0.813698	−	0.581288i	$-0.802549\pi$
$523$		−	608.027i		−	1.16258i	0.813698	−	0.581288i	$-0.197451\pi$
$524$	−161.985	−	676.780i	−0.309131	−	1.29157i
$525$	−88.6492	+	123.305i	−0.168856	+	0.234867i
$526$	659.658	+	186.289i	1.25410	+	0.354162i
$527$	33.9688	−	33.9688i	0.0644570	−	0.0644570i
$528$	4.23512	−	12.9732i	0.00802107	−	0.0245704i
$529$		−	54.7646i		−	0.103525i
$530$	−208.613	−	41.0297i	−0.393609	−	0.0774145i
$531$	−73.2036	+	73.2036i	−0.137860	+	0.137860i
$532$	−102.770	−	63.0757i	−0.193177	−	0.118563i
$533$			64.0997i			0.120262i
$534$	219.008	+	391.384i	0.410127	+	0.732929i
$535$	−519.978	−	441.863i	−0.971921	−	0.825913i
$536$	−31.8446	+	789.584i	−0.0594116	+	1.47310i
$537$	−17.1750	−	17.1750i	−0.0319832	−	0.0319832i
$538$	126.069	−	446.414i	0.234329	−	0.829766i
$539$	12.7792	−	12.7792i	0.0237092	−	0.0237092i
$540$	−98.7786	+	32.2922i	−0.182923	+	0.0598003i
$541$	184.245	−	184.245i	0.340563	−	0.340563i	−0.516016	−	0.856579i	$-0.672585\pi$
$541$	184.245	−	184.245i	0.340563	−	0.340563i	0.856579	+	0.516016i	$0.172585\pi$
$542$	−30.5245	−	54.5497i	−0.0563182	−	0.100645i
$543$	184.080	+	184.080i	0.339006	+	0.339006i
$544$	−103.947	−	527.350i	−0.191080	−	0.969393i
$545$	14.9347	+	183.893i	0.0274030	+	0.337419i
$546$	20.8938	−	73.9857i	0.0382670	−	0.135505i
$547$			235.706i			0.430907i	0.976514	+	0.215454i	$0.0691230\pi$
$547$			235.706i			0.430907i	−0.976514	+	0.215454i	$0.930877\pi$
$548$	−249.152	+	59.6336i	−0.454657	+	0.108820i
$549$	143.815	−	143.815i	0.261959	−	0.261959i
$550$	−24.4646	−	2.78039i	−0.0444812	−	0.00505526i
$551$		−	262.751i		−	0.476862i
$552$	246.078	−	226.999i	0.445794	−	0.411229i
$553$	−364.239	+	364.239i	−0.658660	+	0.658660i
$554$	251.259	+	449.019i	0.453535	+	0.810504i
$555$	352.799	+	299.799i	0.635673	+	0.540178i
$556$	−146.463	−	611.930i	−0.263423	−	1.10059i
$557$		−	625.647i		−	1.12324i	−0.827394	−	0.561622i	$-0.810178\pi$
$557$		−	625.647i		−	1.12324i	0.827394	−	0.561622i	$-0.189822\pi$
$558$	8.37962	+	14.9751i	0.0150172	+	0.0268370i
$559$			200.317i			0.358349i
$560$	239.065	−	146.864i	0.426901	−	0.262258i
$561$	14.3266			0.0255376
$562$	243.033	−	135.994i	0.432443	−	0.241983i
$563$	488.327			0.867366			0.433683	−	0.901065i	$-0.357214\pi$
$563$	488.327			0.867366			0.433683	+	0.901065i	$0.357214\pi$
$564$	21.2904	+	88.9521i	0.0377488	+	0.157717i
$565$	−83.0125	−	1022.15i	−0.146925	−	1.80911i
$566$	900.679	−	503.995i	1.59131	−	0.890450i
$567$	22.3194	+	22.3194i	0.0393640	+	0.0393640i
$568$	2.44534	−	60.6320i	0.00430518	−	0.106746i
$569$	−568.948			−0.999908			−0.499954	−	0.866052i	$-0.666650\pi$
$569$	−568.948			−0.999908			−0.499954	+	0.866052i	$0.666650\pi$
$570$	−123.610	+	82.9783i	−0.216859	+	0.145576i
$571$	−278.362	−	278.362i	−0.487500	−	0.487500i	0.420017	−	0.907516i	$-0.362024\pi$
$571$	−278.362	−	278.362i	−0.487500	−	0.487500i	−0.907516	+	0.420017i	$0.862024\pi$
$572$	12.1222	−	2.90141i	0.0211927	−	0.00507240i
$573$	223.664			0.390339
$574$	68.3779	+	19.3101i	0.119125	+	0.0336413i
$575$	−490.437	−	352.596i	−0.852934	−	0.613211i
$576$	191.376	+	15.4619i	0.332251	+	0.0268436i
$577$	99.8357	−	99.8357i	0.173025	−	0.173025i	−0.615282	−	0.788307i	$-0.710958\pi$
$577$	99.8357	−	99.8357i	0.173025	−	0.173025i	0.788307	+	0.615282i	$0.210958\pi$
$578$	−11.9873	+	6.70775i	−0.0207393	+	0.0116051i
$579$	251.288	+	251.288i	0.434004	+	0.434004i
$580$	545.233	+	276.573i	0.940057	+	0.476849i
$581$	−194.264	−	194.264i	−0.334362	−	0.334362i
$582$	208.476	+	58.8742i	0.358206	+	0.101158i
$583$	−7.40326	+	7.40326i	−0.0126986	+	0.0126986i
$584$	−591.339	+	545.489i	−1.01257	+	0.934057i
$585$	−72.3309	−	61.4649i	−0.123643	−	0.105068i
$586$	−311.613	+	174.370i	−0.531763	+	0.297560i
$587$	−557.705			−0.950094			−0.475047	−	0.879960i	$-0.657569\pi$
$587$	−557.705			−0.950094			−0.475047	+	0.879960i	$0.657569\pi$
$588$	216.704	+	133.003i	0.368544	+	0.226195i
$589$	17.3830	+	17.3830i	0.0295128	+	0.0295128i
$590$	−192.335	−	286.515i	−0.325992	−	0.485619i
$591$	−678.496			−1.14805
$592$	−387.268	−	762.666i	−0.654168	−	1.28829i
$593$	271.601	+	271.601i	0.458012	+	0.458012i	0.898002	−	0.439991i	$-0.145018\pi$
$593$	271.601	+	271.601i	0.458012	+	0.458012i	−0.439991	+	0.898002i	$0.645018\pi$
$594$	−1.39083	+	4.92499i	−0.00234147	+	0.00829123i
$595$	224.450	+	190.732i	0.377227	+	0.320558i
$596$	−193.639	−	809.031i	−0.324897	−	1.35744i
$597$	191.313			0.320458
$598$	294.273	+	83.1037i	0.492096	+	0.138969i
$599$	173.826			0.290194			0.145097	−	0.989417i	$-0.453651\pi$
$599$	173.826			0.290194			0.145097	+	0.989417i	$0.453651\pi$
$600$	−42.0757	−	343.845i	−0.0701262	−	0.573076i
$601$		−	502.850i		−	0.836689i	−0.908288	−	0.418345i	$-0.862610\pi$
$601$		−	502.850i		−	0.836689i	0.908288	−	0.418345i	$-0.137390\pi$
$602$	213.687	+	60.3458i	0.354961	+	0.100242i
$603$		−	296.335i		−	0.491434i
$604$	−296.515	−	181.987i	−0.490919	−	0.301304i
$605$	390.981	−	460.101i	0.646250	−	0.760497i
$606$	−27.8862	+	98.7460i	−0.0460168	+	0.162947i
$607$	−664.932	+	664.932i	−1.09544	+	1.09544i	−0.100502	+	0.994937i	$0.532045\pi$
$607$	−664.932	+	664.932i	−1.09544	+	1.09544i	−0.994937	+	0.100502i	$0.967955\pi$
$608$	269.863	−	53.1935i	0.443854	−	0.0874893i
$609$		−	185.690i		−	0.304910i
$610$	377.861	+	562.885i	0.619444	+	0.922763i
$611$	−59.0719	+	59.0719i	−0.0966807	+	0.0966807i
$612$	46.9178	+	196.025i	0.0766630	+	0.320302i
$613$		−	474.479i		−	0.774027i	−0.922074	−	0.387014i	$-0.873507\pi$
$613$		−	474.479i		−	0.774027i	0.922074	−	0.387014i	$-0.126493\pi$
$614$	180.099	−	100.778i	0.293321	−	0.164134i
$615$	56.8061	−	66.8486i	0.0923677	−	0.108697i
$616$	0.556783	−	13.8054i	0.000903868	−	0.0224113i
$617$	807.635	+	807.635i	1.30897	+	1.30897i	0.922159	+	0.386812i	$0.126424\pi$
$617$	807.635	+	807.635i	1.30897	+	1.30897i	0.386812	+	0.922159i	$0.373576\pi$
$618$	466.487	+	131.737i	0.754833	+	0.213167i
$619$	−461.288	+	461.288i	−0.745215	+	0.745215i	−0.973576	−	0.228361i	$-0.926663\pi$
$619$	−461.288	+	461.288i	−0.745215	+	0.745215i	0.228361	+	0.973576i	$0.426663\pi$
$620$	−54.3689	+	17.7740i	−0.0876918	+	0.0286677i
$621$	−88.7740	+	88.7740i	−0.142953	+	0.142953i
$622$	−1007.52	+	563.778i	−1.61980	+	0.906395i
$623$	321.074	+	321.074i	0.515368	+	0.515368i
$624$	79.3978	+	156.362i	0.127240	+	0.250580i
$625$	−592.452	+	199.061i	−0.947924	+	0.318497i
$626$	196.073	+	55.3717i	0.313216	+	0.0884531i
$627$			7.33141i			0.0116928i
$628$	308.987	+	189.642i	0.492017	+	0.301978i
$629$	634.948	−	634.948i	1.00946	−	1.00946i
$630$	−87.3570	+	58.6421i	−0.138662	+	0.0930827i
$631$			278.307i			0.441057i	0.975381	+	0.220529i	$0.0707782\pi$
$631$			278.307i			0.441057i	−0.975381	+	0.220529i	$0.929222\pi$
$632$	47.3501	−	1174.04i	0.0749211	−	1.85766i
$633$	−338.875	+	338.875i	−0.535348	+	0.535348i
$634$	820.412	−	459.079i	1.29402	−	0.724100i
$635$	−1061.95	+	86.2447i	−1.67236	+	0.135818i
$636$	−125.541	−	77.0511i	−0.197391	−	0.121149i
$637$			232.235i			0.364576i
$638$	26.2728	−	14.7015i	0.0411799	−	0.0230431i
$639$			22.7555i			0.0356111i
$640$	−173.678	+	615.984i	−0.271372	+	0.962475i
$641$	565.878			0.882804			0.441402	−	0.897309i	$-0.354481\pi$
$641$	565.878			0.882804			0.441402	+	0.897309i	$0.354481\pi$
$642$	−230.855	−	412.557i	−0.359588	−	0.642612i
$643$	226.198			0.351785			0.175893	−	0.984409i	$-0.443719\pi$
$643$	226.198			0.351785			0.175893	+	0.984409i	$0.443719\pi$
$644$	177.300	−	288.879i	0.275311	−	0.448569i
$645$	177.524	−	208.907i	0.275231	−	0.323887i
$646$	141.004	+	251.985i	0.218272	+	0.390070i
$647$	−537.803	−	537.803i	−0.831225	−	0.831225i	0.156459	−	0.987684i	$-0.449992\pi$
$647$	−537.803	−	537.803i	−0.831225	−	0.831225i	−0.987684	+	0.156459i	$0.949992\pi$
$648$	−71.9415	−	2.90147i	−0.111021	−	0.00447757i
$649$	−16.9935			−0.0261841
$650$	247.560	−	197.032i	0.380862	−	0.303127i
$651$	12.2849	+	12.2849i	0.0188708	+	0.0188708i
$652$	285.990	−	465.969i	0.438636	−	0.714677i
$653$	−747.369			−1.14452			−0.572258	−	0.820074i	$-0.693932\pi$
$653$	−747.369			−1.14452			−0.572258	+	0.820074i	$0.693932\pi$
$654$	−34.7393	+	123.013i	−0.0531183	+	0.188094i
$655$	−867.015	+	70.4135i	−1.32369	+	0.107502i
$656$	−144.510	+	73.3797i	−0.220290	+	0.111859i
$657$	213.329	−	213.329i	0.324701	−	0.324701i
$658$	45.2190	+	80.8100i	0.0687219	+	0.122812i
$659$	714.948	+	714.948i	1.08490	+	1.08490i	0.996045	+	0.0888541i	$0.0283205\pi$
$659$	714.948	+	714.948i	1.08490	+	1.08490i	0.0888541	+	0.996045i	$0.471680\pi$
$660$	−15.2134	−	7.71707i	−0.0230505	−	0.0116925i
$661$	1.34879	+	1.34879i	0.00204053	+	0.00204053i	0.708126	−	0.706086i	$-0.249541\pi$
$661$	1.34879	+	1.34879i	0.00204053	+	0.00204053i	−0.706086	+	0.708126i	$0.749541\pi$
$662$	−148.135	+	524.551i	−0.223769	+	0.792373i
$663$	−130.177	+	130.177i	−0.196346	+	0.196346i
$664$	626.166	+	25.2538i	0.943021	+	0.0380329i
$665$	−97.6042	+	114.859i	−0.146773	+	0.172720i
$666$	156.633	+	279.915i	0.235184	+	0.420293i
$667$	738.570			1.10730
$668$	515.874	−	123.472i	0.772266	−	0.184839i
$669$	261.871	+	261.871i	0.391436	+	0.391436i
$670$	969.214	+	190.624i	1.44659	+	0.284513i
$671$	33.3852			0.0497544
$672$	190.717	−	37.5927i	0.283805	−	0.0559415i
$673$	618.150	+	618.150i	0.918499	+	0.918499i	0.996920	−	0.0784214i	$-0.0249880\pi$
$673$	618.150	+	618.150i	0.918499	+	0.918499i	−0.0784214	+	0.996920i	$0.524988\pi$
$674$	697.961	+	197.106i	1.03555	+	0.292443i
$675$	20.9617	+	128.201i	0.0310544	+	0.189928i
$676$	269.824	−	439.629i	0.399148	−	0.650338i
$677$	−523.647			−0.773481			−0.386741	−	0.922189i	$-0.626399\pi$
$677$	−523.647			−0.773481			−0.386741	+	0.922189i	$0.626399\pi$
$678$	193.094	−	683.755i	0.284800	−	1.00849i
$679$	219.322			0.323007
$680$	−671.314	+	27.3556i	−0.987227	+	0.0402289i
$681$		−	520.629i		−	0.764507i
$682$	−0.765531	+	2.71077i	−0.00112248	+	0.00397474i
$683$			1171.63i			1.71542i	0.514130	+	0.857712i	$0.328115\pi$
$683$			1171.63i			1.71542i	−0.514130	+	0.857712i	$0.671885\pi$
$684$	−100.313	+	24.0095i	−0.146656	+	0.0351016i
$685$	25.9223	+	319.186i	0.0378427	+	0.465964i
$686$	578.500	+	163.370i	0.843294	+	0.238149i
$687$	−556.403	+	556.403i	−0.809902	+	0.809902i
$688$	−451.607	+	229.318i	−0.656406	+	0.333311i
$689$		−	134.538i		−	0.195266i
$690$	−233.245	−	347.457i	−0.338036	−	0.503560i
$691$	462.015	−	462.015i	0.668618	−	0.668618i	−0.288778	−	0.957396i	$-0.593249\pi$
$691$	462.015	−	462.015i	0.668618	−	0.668618i	0.957396	+	0.288778i	$0.0932489\pi$
$692$	309.306	−	503.958i	0.446974	−	0.728263i
$693$			5.18122i			0.00747651i
$694$	161.714	+	288.995i	0.233017	+	0.416420i
$695$	−783.936	+	63.6664i	−1.12797	+	0.0916063i
$696$	287.195	+	311.334i	0.412637	+	0.447320i
$697$	−120.310	−	120.310i	−0.172612	−	0.172612i
$698$	26.0498	−	92.2434i	0.0373206	−	0.132154i
$699$	166.442	−	166.442i	0.238115	−	0.238115i
$700$	−135.605	−	323.439i	−0.193721	−	0.462056i
$701$	−389.869	+	389.869i	−0.556161	+	0.556161i	−0.928212	−	0.372051i	$-0.878655\pi$
$701$	−389.869	+	389.869i	−0.556161	+	0.556161i	0.372051	+	0.928212i	$0.378655\pi$
$702$	−32.1129	−	57.3883i	−0.0457449	−	0.0817497i
$703$	324.925	+	324.925i	0.462198	+	0.462198i
$704$	20.4184	+	24.0077i	0.0290034	+	0.0341018i
$705$	113.955	−	9.25475i	0.161639	−	0.0131273i
$706$	−93.6177	+	331.504i	−0.132603	+	0.469552i
$707$			103.883i			0.146935i
$708$	−55.6515	−	232.515i	−0.0786038	−	0.328411i
$709$	783.751	−	783.751i	1.10543	−	1.10543i	0.111689	−	0.993743i	$-0.464374\pi$
$709$	783.751	−	783.751i	1.10543	−	1.10543i	0.993743	−	0.111689i	$-0.0356260\pi$
$710$	−74.4258	−	14.6380i	−0.104825	−	0.0206168i
$711$			440.623i			0.619723i
$712$	−1034.91	−	41.7388i	−1.45352	−	0.0586219i
$713$	−48.8623	+	48.8623i	−0.0685305	+	0.0685305i
$714$	99.6496	+	178.082i	0.139565	+	0.249414i
$715$	−1.26122	−	15.5297i	−0.00176395	−	0.0217198i
$716$	54.5524	−	13.0569i	0.0761905	−	0.0182359i
$717$		−	688.720i		−	0.960558i
$718$	145.842	+	260.632i	0.203123	+	0.362997i
$719$		−	1035.43i		−	1.44009i	−0.693925	−	0.720047i	$-0.744120\pi$
$719$		−	1035.43i		−	1.44009i	0.693925	−	0.720047i	$-0.255880\pi$
$720$	55.7677	−	233.431i	0.0774551	−	0.324210i
$721$	490.756			0.680660
$722$	501.115	−	280.410i	0.694065	−	0.388379i
$723$	305.856			0.423037
$724$	−584.689	+	139.943i	−0.807582	+	0.193292i
$725$	446.100	−	620.494i	0.615310	−	0.855854i
$726$	365.050	−	204.272i	0.502824	−	0.281366i
$727$	−564.170	−	564.170i	−0.776024	−	0.776024i	0.203128	−	0.979152i	$-0.434889\pi$
$727$	−564.170	−	564.170i	−0.776024	−	0.776024i	−0.979152	+	0.203128i	$0.934889\pi$
$728$	120.382	+	130.501i	0.165360	+	0.179259i
$729$	27.0000			0.0370370
$730$	560.500	+	834.956i	0.767808	+	1.14378i
$731$	−375.980	−	375.980i	−0.514337	−	0.514337i
$732$	109.333	+	456.797i	0.149361	+	0.624040i
$733$	−663.374			−0.905012			−0.452506	−	0.891761i	$-0.649470\pi$
$733$	−663.374			−0.905012			−0.452506	+	0.891761i	$0.649470\pi$
$734$	−324.345	−	91.5962i	−0.441888	−	0.124790i
$735$	205.810	−	242.194i	0.280014	−	0.329516i
$736$	149.522	+	758.563i	0.203155	+	1.03066i
$737$	34.3955	−	34.3955i	0.0466696	−	0.0466696i
$738$	53.0385	−	29.6789i	0.0718679	−	0.0402153i
$739$	132.239	+	132.239i	0.178944	+	0.178944i	0.790895	−	0.611952i	$-0.209615\pi$
$739$	132.239	+	132.239i	0.178944	+	0.178944i	−0.611952	+	0.790895i	$0.709615\pi$
$740$	−1016.27	+	332.233i	−1.37334	+	0.448963i
$741$	−66.6163	−	66.6163i	−0.0899006	−	0.0899006i
$742$	−143.518	−	40.5299i	−0.193420	−	0.0546225i
$743$	−654.544	+	654.544i	−0.880947	+	0.880947i	−0.993631	−	0.112684i	$-0.964055\pi$
$743$	−654.544	+	654.544i	−0.880947	+	0.880947i	0.112684	+	0.993631i	$0.464055\pi$
$744$	−39.5975	−	1.59700i	−0.0532224	−	0.00214651i
$745$	−1036.44	+	84.1732i	−1.39119	+	0.112984i
$746$	−301.250	+	168.571i	−0.403821	+	0.225967i
$747$	−235.003			−0.314596
$748$	−17.3068	+	28.1983i	−0.0231375	+	0.0376982i
$749$	−338.443	−	338.443i	−0.451860	−	0.451860i
$750$	−432.789	−	13.9095i	−0.577052	−	0.0185460i
$751$	1444.23			1.92308			0.961539	−	0.274668i	$-0.0885678\pi$
$751$	1444.23			1.92308			0.961539	+	0.274668i	$0.0885678\pi$
$752$	−200.799	−	65.5514i	−0.267020	−	0.0871694i
$753$	269.119	+	269.119i	0.357396	+	0.357396i
$754$	−105.142	+	372.310i	−0.139445	+	0.493780i
$755$	−281.610	+	331.394i	−0.372993	+	0.438932i
$756$	−70.8926	+	16.9679i	−0.0937732	+	0.0224443i
$757$	1058.07			1.39771			0.698855	−	0.715264i	$-0.253693\pi$
$757$	1058.07			1.39771			0.698855	+	0.715264i	$0.253693\pi$
$758$	2.32645	+	0.656996i	0.00306919	+	0.000866749i
$759$	−20.6080			−0.0271515
$760$	−13.9988	−	343.535i	−0.0184195	−	0.452020i
$761$			282.437i			0.371139i	0.982631	+	0.185569i	$0.0594129\pi$
$761$			282.437i			0.371139i	−0.982631	+	0.185569i	$0.940587\pi$
$762$	−710.378	−	200.613i	−0.932254	−	0.263271i
$763$			129.413i			0.169611i
$764$	−270.191	+	440.227i	−0.353653	+	0.576213i
$765$	251.125	−	20.3948i	0.328268	−	0.0266599i
$766$	−167.278	+	592.336i	−0.218378	+	0.773285i
$767$	154.410	−	154.410i	0.201317	−	0.201317i
$768$	−261.620	+	357.999i	−0.340651	+	0.466144i
$769$			1321.92i			1.71901i	0.511127	+	0.859505i	$0.329228\pi$
$769$			1321.92i			1.71901i	−0.511127	+	0.859505i	$0.670772\pi$
$770$	−16.9461	−	3.33293i	−0.0220079	−	0.00432848i
$771$	−556.651	+	556.651i	−0.721986	+	0.721986i
$772$	−798.161	+	191.037i	−1.03389	+	0.247457i
$773$		−	88.8442i		−	0.114934i	−0.998347	−	0.0574671i	$-0.981698\pi$
$773$		−	88.8442i		−	0.114934i	0.998347	−	0.0574671i	$-0.0183024\pi$
$774$	165.750	−	92.7489i	0.214147	−	0.119831i
$775$	11.5376	+	70.5636i	0.0148872	+	0.0910498i
$776$	−367.723	+	339.211i	−0.473870	+	0.437128i
$777$	229.630	+	229.630i	0.295534	+	0.295534i
$778$	−1026.58	−	289.909i	−1.31951	−	0.372634i
$779$	61.5671	−	61.5671i	0.0790335	−	0.0790335i
$780$	208.356	−	68.1145i	0.267123	−	0.0873263i
$781$	−2.64122	+	2.64122i	−0.00338185	+	0.00338185i
$782$	−708.309	+	396.350i	−0.905766	+	0.506841i
$783$	−112.316	−	112.316i	−0.143443	−	0.143443i
$784$	−523.566	+	265.857i	−0.667813	+	0.339103i
$785$	293.454	−	345.333i	0.373827	−	0.439914i
$786$	−579.980	−	163.788i	−0.737888	−	0.208382i
$787$		−	1408.42i		−	1.78961i	−0.446459	−	0.894804i	$-0.647315\pi$
$787$		−	1408.42i		−	1.78961i	0.446459	−	0.894804i	$-0.352685\pi$
$788$	819.639	−	1335.45i	1.04015	−	1.69474i
$789$	419.755	−	419.755i	0.532009	−	0.532009i
$790$	−1441.14	−	283.440i	−1.82422	−	0.358785i
$791$		−	719.328i		−	0.909390i
$792$	−8.01346	−	8.68701i	−0.0101180	−	0.0109684i
$793$	−303.353	+	303.353i	−0.382538	+	0.382538i
$794$	−136.737	+	76.5142i	−0.172213	+	0.0963655i
$795$	−119.230	+	140.308i	−0.149975	+	0.176488i
$796$	−231.111	+	376.553i	−0.290340	+	0.473057i
$797$			214.836i			0.269556i	0.990876	+	0.134778i	$0.0430321\pi$
$797$			214.836i			0.269556i	−0.990876	+	0.134778i	$0.956968\pi$
$798$	−91.1307	+	50.9942i	−0.114199	+	0.0639025i
$799$		−	221.747i		−	0.277531i
$800$	727.603	+	332.557i	0.909503	+	0.415697i
$801$	388.406			0.484902
$802$	−105.407	−	188.371i	−0.131430	−	0.234877i
$803$	49.5220			0.0616712
$804$	583.261	+	357.979i	0.725449	+	0.445247i
$805$	−322.859	−	274.357i	−0.401067	−	0.340816i
$806$	−17.6753	−	31.5872i	−0.0219297	−	0.0391901i
$807$	−284.064	−	284.064i	−0.352000	−	0.352000i
$808$	−160.670	−	174.174i	−0.198849	−	0.215562i
$809$	1149.79			1.42124			0.710622	−	0.703574i	$-0.248413\pi$
$809$	1149.79			1.42124			0.710622	+	0.703574i	$0.248413\pi$
$810$	−17.3683	+	88.3082i	−0.0214424	+	0.109022i
$811$	612.466	+	612.466i	0.755198	+	0.755198i	0.975444	−	0.220246i	$-0.0706861\pi$
$811$	612.466	+	612.466i	0.755198	+	0.755198i	−0.220246	+	0.975444i	$0.570686\pi$
$812$	365.485	+	224.318i	0.450105	+	0.276254i
$813$	−54.1346			−0.0665862
$814$	−14.3094	+	50.6700i	−0.0175791	+	0.0622482i
$815$	−520.781	−	442.545i	−0.638995	−	0.543000i
$816$	−442.504	−	144.456i	−0.542284	−	0.177030i
$817$	192.402	−	192.402i	0.235498	−	0.235498i
$818$	−577.107	−	1031.34i	−0.705509	−	1.26080i
$819$	−47.0788	−	47.0788i	−0.0574833	−	0.0574833i
$820$	62.9517	+	192.563i	0.0767704	+	0.234833i
$821$	117.719	+	117.719i	0.143385	+	0.143385i	0.775155	−	0.631771i	$-0.217672\pi$
$821$	117.719	+	117.719i	0.143385	+	0.143385i	−0.631771	+	0.775155i	$0.717672\pi$
$822$	−60.2975	+	213.516i	−0.0733546	+	0.259751i
$823$	−503.108	+	503.108i	−0.611310	+	0.611310i	−0.943287	−	0.331978i	$-0.892284\pi$
$823$	−503.108	+	503.108i	−0.611310	+	0.611310i	0.331978	+	0.943287i	$0.392284\pi$
$824$	−822.819	+	759.022i	−0.998566	+	0.921143i
$825$	−12.4473	+	17.3133i	−0.0150876	+	0.0209859i
$826$	−118.199	−	211.232i	−0.143098	−	0.255728i
$827$	1133.23			1.37029			0.685145	−	0.728406i	$-0.259739\pi$
$827$	1133.23			1.37029			0.685145	+	0.728406i	$0.259739\pi$
$828$	−67.4886	−	281.971i	−0.0815079	−	0.340544i
$829$	1059.24	+	1059.24i	1.27773	+	1.27773i	0.941935	+	0.335794i	$0.109005\pi$
$829$	1059.24	+	1059.24i	1.27773	+	1.27773i	0.335794	+	0.941935i	$0.390995\pi$
$830$	151.171	−	768.619i	0.182134	−	0.926047i
$831$	445.603			0.536225
$832$	−403.674	−	32.6141i	−0.485185	−	0.0391997i
$833$	−435.888	−	435.888i	−0.523275	−	0.523275i
$834$	−524.405	−	148.094i	−0.628783	−	0.177570i
$835$	−53.6725	−	660.879i	−0.0642784	−	0.791472i
$836$	−14.4301	−	8.85650i	−0.0172608	−	0.0105939i
$837$	14.8611			0.0177552
$838$	−273.597	+	968.817i	−0.326488	+	1.15611i
$839$	634.998			0.756851			0.378426	−	0.925632i	$-0.376466\pi$
$839$	634.998			0.756851			0.378426	+	0.925632i	$0.376466\pi$
$840$	−9.89319	−	242.781i	−0.0117776	−	0.289026i
$841$			93.4285i			0.111092i
$842$	−5.24869	+	18.5858i	−0.00623360	+	0.0220734i
$843$		−	241.184i		−	0.286102i
$844$	−257.623	−	1076.36i	−0.305240	−	1.27531i
$845$	−491.342	−	417.529i	−0.581469	−	0.494117i
$846$	76.2292	+	21.5274i	0.0901054	+	0.0254461i
$847$	299.471	−	299.471i	0.353566	−	0.353566i
$848$	303.312	−	154.016i	0.357679	−	0.181623i
$849$		−	893.826i		−	1.05280i
$850$	−94.8368	+	834.467i	−0.111573	+	0.981726i
$851$	−913.337	+	913.337i	−1.07325	+	1.07325i
$852$	−44.7885	−	27.4891i	−0.0525687	−	0.0322643i
$853$			736.362i			0.863261i	0.902051	+	0.431630i	$0.142062\pi$
$853$			736.362i			0.863261i	−0.902051	+	0.431630i	$0.857938\pi$
$854$	232.214	+	414.984i	0.271913	+	0.485930i
$855$	10.4367	+	128.509i	0.0122067	+	0.150303i
$856$	1090.89	+	43.9968i	1.27441	+	0.0513981i
$857$	285.114	+	285.114i	0.332688	+	0.332688i	0.853607	−	0.520918i	$-0.174410\pi$
$857$	285.114	+	285.114i	0.332688	+	0.332688i	−0.520918	+	0.853607i	$0.674410\pi$
$858$	2.93371	−	10.3884i	0.00341925	−	0.0121077i
$859$	−535.646	+	535.646i	−0.623570	+	0.623570i	−0.946442	−	0.322873i	$-0.895351\pi$
$859$	−535.646	+	535.646i	−0.623570	+	0.623570i	0.322873	+	0.946442i	$0.395351\pi$
$860$	196.729	+	601.776i	0.228755	+	0.699740i
$861$	43.5104	−	43.5104i	0.0505348	−	0.0505348i
$862$	191.116	+	341.541i	0.221713	+	0.396219i
$863$	−152.045	−	152.045i	−0.176182	−	0.176182i	0.613507	−	0.789689i	$-0.289758\pi$
$863$	−152.045	−	152.045i	−0.176182	−	0.176182i	−0.789689	+	0.613507i	$0.789758\pi$
$864$	92.6178	−	138.094i	0.107197	−	0.159831i
$865$	−563.238	−	478.624i	−0.651142	−	0.553323i
$866$	185.764	−	657.798i	0.214508	−	0.759582i
$867$			11.8961i			0.0137210i
$868$	−39.0201	+	9.33931i	−0.0449540	+	0.0107596i
$869$	−51.1431	+	51.1431i	−0.0588528	+	0.0588528i
$870$	439.597	−	295.098i	0.505284	−	0.339193i
$871$			625.065i			0.717640i
$872$	−200.155	−	216.979i	−0.229536	−	0.248829i
$873$	132.658	−	132.658i	0.151956	−	0.151956i
$874$	−202.826	−	362.466i	−0.232066	−	0.414721i
$875$	−425.503	+	105.530i	−0.486290	+	0.120606i
$876$	162.179	+	677.590i	0.185135	+	0.773504i
$877$		−	777.146i		−	0.886142i	−0.896487	−	0.443071i	$-0.853889\pi$
$877$		−	777.146i		−	0.886142i	0.896487	−	0.443071i	$-0.146111\pi$
$878$	−368.244	−	658.081i	−0.419412	−	0.749522i
$879$			309.242i			0.351812i
$880$	33.5672	−	20.6213i	0.0381446	−	0.0234333i
$881$	359.196			0.407715			0.203857	−	0.979001i	$-0.434652\pi$
$881$	359.196			0.407715			0.203857	+	0.979001i	$0.434652\pi$
$882$	192.160	−	107.527i	0.217869	−	0.121913i
$883$	−634.549			−0.718629			−0.359314	−	0.933217i	$-0.616989\pi$
$883$	−634.549			−0.718629			−0.359314	+	0.933217i	$0.616989\pi$
$884$	−98.9646	−	413.479i	−0.111951	−	0.467736i
$885$	−297.872	+	24.1913i	−0.336578	+	0.0273348i
$886$	−364.255	+	203.827i	−0.411123	+	0.230053i
$887$	1206.72	+	1206.72i	1.36045	+	1.36045i	0.873340	+	0.487112i	$0.161950\pi$
$887$	1206.72	+	1206.72i	1.36045	+	1.36045i	0.487112	+	0.873340i	$0.338050\pi$
$888$	−740.159	−	29.8513i	−0.833512	−	0.0336163i
$889$	−747.336			−0.840648
$890$	−249.851	+	1270.35i	−0.280731	+	1.42736i
$891$	3.13388	+	3.13388i	0.00351727	+	0.00351727i
$892$	−831.773	+	199.082i	−0.932481	+	0.223186i
$893$	113.476			0.127073
$894$	−693.315	−	195.794i	−0.775520	−	0.219009i
$895$	−5.67574	−	69.8864i	−0.00634161	−	0.0780854i
$896$	−156.398	+	420.791i	−0.174552	+	0.469633i
$897$	187.253	−	187.253i	0.208755	−	0.208755i
$898$	−257.110	+	143.871i	−0.286314	+	0.160213i
$899$	−61.8198	−	61.8198i	−0.0687651	−	0.0687651i
$900$	−277.655	−	113.612i	−0.308505	−	0.126236i
$901$	252.519	+	252.519i	0.280265	+	0.280265i
$902$	9.60099	+	2.71135i	0.0106441	+	0.00300593i
$903$	135.974	−	135.974i	0.150580	−	0.150580i
$904$	1112.54	+	1206.05i	1.23068	+	1.33413i
$905$	60.8322	+	749.038i	0.0672179	+	0.827666i
$906$	−262.932	+	147.130i	−0.290212	+	0.162395i
$907$	1583.66			1.74604			0.873020	−	0.487685i	$-0.162159\pi$
$907$	1583.66			1.74604			0.873020	+	0.487685i	$0.162159\pi$
$908$	1024.73	+	628.932i	1.12856	+	0.692656i
$909$	62.8343	+	62.8343i	0.0691247	+	0.0691247i
$910$	184.264	−	123.695i	0.202488	−	0.135929i
$911$	−518.048			−0.568658			−0.284329	−	0.958727i	$-0.591771\pi$
$911$	−518.048			−0.568658			−0.284329	+	0.958727i	$0.591771\pi$
$912$	73.9234	−	226.445i	0.0810563	−	0.248295i
$913$	−27.2768	−	27.2768i	−0.0298760	−	0.0298760i
$914$	−247.513	+	876.453i	−0.270802	+	0.958920i
$915$	585.197	−	47.5260i	0.639559	−	0.0519410i
$916$	−422.994	−	1767.29i	−0.461784	−	1.92935i
$917$	−610.154			−0.665381
$918$	167.987	+	47.4401i	0.182993	+	0.0516777i
$919$	840.571			0.914658			0.457329	−	0.889298i	$-0.348806\pi$
$919$	840.571			0.914658			0.457329	+	0.889298i	$0.348806\pi$
$920$	965.647	−	39.3495i	1.04962	−	0.0427712i
$921$		−	178.729i		−	0.194059i
$922$	−39.1524	−	11.0568i	−0.0424646	−	0.0119921i
$923$		−	47.9986i		−	0.0520028i
$924$	−10.1979	−	6.25903i	−0.0110367	−	0.00677384i
$925$	215.661	+	1318.98i	0.233147	+	1.42592i
$926$	361.779	−	1281.07i	0.390690	−	1.38345i
$927$	296.836	−	296.836i	0.320212	−	0.320212i
$928$	−959.723	+	189.173i	−1.03418	+	0.203851i
$929$			211.525i			0.227691i	0.993498	+	0.113846i	$0.0363169\pi$
$929$			211.525i			0.227691i	−0.993498	+	0.113846i	$0.963683\pi$
$930$	−9.55974	+	48.6059i	−0.0102793	+	0.0522644i
$931$	223.059	−	223.059i	0.239591	−	0.239591i
$932$	126.534	+	528.667i	0.135766	+	0.567239i
$933$			999.850i			1.07165i
$934$	−197.210	+	110.353i	−0.211145	+	0.118151i
$935$	31.5152	+	26.7808i	0.0337061	+	0.0286426i
$936$	151.748	+	6.12012i	0.162124	+	0.00653859i
$937$	1120.07	+	1120.07i	1.19538	+	1.19538i	0.975535	+	0.219846i	$0.0705554\pi$
$937$	1120.07	+	1120.07i	1.19538	+	1.19538i	0.219846	+	0.975535i	$0.429445\pi$
$938$	666.783	+	188.302i	0.710856	+	0.200748i
$939$	124.766	−	124.766i	0.132871	−	0.132871i
$940$	−119.445	+	235.473i	−0.127069	+	0.250503i
$941$	694.013	−	694.013i	0.737527	−	0.737527i	−0.234572	−	0.972099i	$-0.575369\pi$
$941$	694.013	−	694.013i	0.737527	−	0.737527i	0.972099	+	0.234572i	$0.0753688\pi$
$942$	273.991	−	153.318i	0.290861	−	0.162758i
$943$	173.060	+	173.060i	0.183521	+	0.183521i
$944$	524.876	+	171.347i	0.556013	+	0.181512i
$945$	7.37580	+	90.8196i	0.00780508	+	0.0961054i
$946$	30.0039	+	8.47319i	0.0317166	+	0.00895686i
$947$			296.948i			0.313567i	0.987633	+	0.156784i	$0.0501126\pi$
$947$			296.948i			0.313567i	−0.987633	+	0.156784i	$0.949887\pi$
$948$	−867.258	−	532.283i	−0.914829	−	0.561480i
$949$	−449.978	+	449.978i	−0.474160	+	0.474160i
$950$	−427.026	−	48.5313i	−0.449501	−	0.0510856i
$951$		−	814.169i		−	0.856119i
$952$	−470.889	−	18.9914i	−0.494631	−	0.0199489i
$953$	936.638	−	936.638i	0.982831	−	0.982831i	−0.0170241	−	0.999855i	$-0.505419\pi$
$953$	936.638	−	936.638i	0.982831	−	0.982831i	0.999855	+	0.0170241i	$0.00541920\pi$
$954$	−111.322	+	62.2927i	−0.116690	+	0.0652963i
$955$	492.011	+	418.097i	0.515194	+	0.437798i
$956$	1355.57	+	831.989i	1.41797	+	0.870282i
$957$		−	26.0729i		−	0.0272444i
$958$	1277.33	−	714.760i	1.33333	−	0.746096i
$959$			224.624i			0.234227i
$960$	392.082	+	391.755i	0.408419	+	0.408078i
$961$	−952.820			−0.991488
$962$	−330.388	−	590.430i	−0.343439	−	0.613753i
$963$	−409.418			−0.425149
$964$	−369.481	+	602.002i	−0.383279	+	0.624483i
$965$	83.0422	+	1022.51i	0.0860541	+	1.05960i
$966$	−143.340	−	256.161i	−0.148385	−	0.265177i
$967$	−547.943	−	547.943i	−0.566643	−	0.566643i	0.364544	−	0.931186i	$-0.381225\pi$
$967$	−547.943	−	547.943i	−0.566643	−	0.566643i	−0.931186	+	0.364544i	$0.881225\pi$
$968$	−38.9304	+	965.275i	−0.0402174	+	0.997185i
$969$	250.068			0.258068
$970$	348.546	+	519.216i	0.359326	+	0.535274i
$971$	−473.250	−	473.250i	−0.487384	−	0.487384i	0.420096	−	0.907480i	$-0.361996\pi$
$971$	−473.250	−	473.250i	−0.487384	−	0.487384i	−0.907480	+	0.420096i	$0.861996\pi$
$972$	−32.6166	+	53.1428i	−0.0335562	+	0.0546737i
$973$	−551.688			−0.566997
$974$	−199.451	+	706.262i	−0.204775	+	0.725115i
$975$	−44.2149	−	270.418i	−0.0453486	−	0.277352i
$976$	−1031.17	−	336.627i	−1.05652	−	0.344905i
$977$	24.5422	−	24.5422i	0.0251200	−	0.0251200i	−0.694435	−	0.719555i	$-0.744346\pi$
$977$	24.5422	−	24.5422i	0.0251200	−	0.0251200i	0.719555	+	0.694435i	$0.244346\pi$
$978$	−231.212	−	413.194i	−0.236413	−	0.422489i
$979$	45.0822	+	45.0822i	0.0460493	+	0.0460493i
$980$	228.076	+	697.662i	0.232731	+	0.711900i
$981$	78.2762	+	78.2762i	0.0797922	+	0.0797922i
$982$	243.252	−	861.365i	0.247711	−	0.877154i
$983$	67.9656	−	67.9656i	0.0691410	−	0.0691410i	−0.671691	−	0.740832i	$-0.734432\pi$
$983$	67.9656	−	67.9656i	0.0691410	−	0.0691410i	0.740832	+	0.671691i	$0.234432\pi$
$984$	−5.65624	+	140.246i	−0.00574821	+	0.142526i
$985$	−1492.54	−	1268.32i	−1.51527	−	1.28763i
$986$	−501.456	−	896.142i	−0.508576	−	0.908866i
$987$	80.1951			0.0812514
$988$	211.592	−	50.6437i	0.214162	−	0.0512588i
$989$	540.826	+	540.826i	0.546842	+	0.546842i
$990$	−12.2659	+	8.23398i	−0.0123898	+	0.00831715i
$991$	1243.98			1.25528			0.627641	−	0.778503i	$-0.284021\pi$
$991$	1243.98			1.25528			0.627641	+	0.778503i	$0.284021\pi$
$992$	50.9779	−	76.0085i	0.0513890	−	0.0766215i
$993$	333.784	+	333.784i	0.336137	+	0.336137i
$994$	−51.2021	−	14.4596i	−0.0515112	−	0.0145469i
$995$	420.847	+	357.624i	0.422961	+	0.359421i
$996$	283.889	−	462.545i	0.285029	−	0.464403i
$997$	−1682.45			−1.68752			−0.843758	−	0.536723i	$-0.819662\pi$
$997$	−1682.45			−1.68752			−0.843758	+	0.536723i	$0.819662\pi$
$998$	−41.7592	+	147.871i	−0.0418429	+	0.148167i
$999$	277.785			0.278063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.be.a.133.32	yes	96
4.3	odd	2		960.3.be.a.433.16		96
5.2	odd	4		240.3.ba.a.37.8	yes	96
16.3	odd	4		960.3.ba.a.913.16		96
16.13	even	4		240.3.ba.a.13.8	✓	96
20.7	even	4		960.3.ba.a.817.33		96
80.67	even	4		960.3.be.a.337.16		96
80.77	odd	4	inner	240.3.be.a.157.32	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.3.ba.a.13.8	✓	96	16.13	even	4
240.3.ba.a.37.8	yes	96	5.2	odd	4
240.3.be.a.133.32	yes	96	1.1	even	1	trivial
240.3.be.a.157.32	yes	96	80.77	odd	4	inner
960.3.ba.a.817.33		96	20.7	even	4
960.3.ba.a.913.16		96	16.3	odd	4
960.3.be.a.337.16		96	80.67	even	4
960.3.be.a.433.16		96	4.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.be (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.976638 + 1.74533i) q^{2} +1.73205 q^{3} +(-2.09236 + 3.40911i) q^{4} +(3.81012 + 3.23774i) q^{5} +(1.69159 + 3.02300i) q^{6} +(2.47993 + 2.47993i) q^{7} +(-7.99350 - 0.322385i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(0.976638 + 1.74533i) q^{2} +1.73205 q^{3} +(-2.09236 + 3.40911i) q^{4} +(3.81012 + 3.23774i) q^{5} +(1.69159 + 3.02300i) q^{6} +(2.47993 + 2.47993i) q^{7} +(-7.99350 - 0.322385i) q^{8} +3.00000 q^{9} +(-1.92981 + 9.81202i) q^{10} +(0.348209 + 0.348209i) q^{11} +(-3.62407 + 5.90476i) q^{12} -6.32796 q^{13} +(-1.90631 + 6.75030i) q^{14} +(6.59933 + 5.60793i) q^{15} +(-7.24409 - 14.2662i) q^{16} +(11.8771 - 11.8771i) q^{17} +(2.92991 + 5.23599i) q^{18} +(6.07794 + 6.07794i) q^{19} +(-19.0100 + 6.21463i) q^{20} +(4.29537 + 4.29537i) q^{21} +(-0.267666 + 0.947815i) q^{22} +(-17.0846 + 17.0846i) q^{23} +(-13.8452 - 0.558387i) q^{24} +(4.03408 + 24.6724i) q^{25} +(-6.18013 - 11.0444i) q^{26} +5.19615 q^{27} +(-13.6433 + 3.26547i) q^{28} +(-21.6151 - 21.6151i) q^{29} +(-3.34254 + 16.9949i) q^{30} +2.86002 q^{31} +(17.8243 - 26.5762i) q^{32} +(0.603116 + 0.603116i) q^{33} +(32.3291 + 9.12985i) q^{34} +(1.41947 + 17.4782i) q^{35} +(-6.27707 + 10.2273i) q^{36} +53.4598 q^{37} +(-4.67206 + 16.5440i) q^{38} -10.9604 q^{39} +(-29.4124 - 27.1092i) q^{40} -10.1296i q^{41} +(-3.30182 + 11.6919i) q^{42} -31.6559i q^{43} +(-1.91566 + 0.458507i) q^{44} +(11.4304 + 9.71322i) q^{45} +(-46.5036 - 13.1328i) q^{46} +(9.33506 - 9.33506i) q^{47} +(-12.5471 - 24.7097i) q^{48} -36.6998i q^{49} +(-39.1216 + 31.1368i) q^{50} +(20.5718 - 20.5718i) q^{51} +(13.2404 - 21.5727i) q^{52} +21.2609i q^{53} +(5.07476 + 9.06900i) q^{54} +(0.199309 + 2.45413i) q^{55} +(-19.0239 - 20.6229i) q^{56} +(10.5273 + 10.5273i) q^{57} +(16.6154 - 58.8357i) q^{58} +(-24.4012 + 24.4012i) q^{59} +(-32.9262 + 10.7641i) q^{60} +(47.9384 - 47.9384i) q^{61} +(2.79321 + 4.99169i) q^{62} +(7.43980 + 7.43980i) q^{63} +(63.7921 + 5.15397i) q^{64} +(-24.1103 - 20.4883i) q^{65} +(-0.463611 + 1.64166i) q^{66} -98.7782i q^{67} +(15.6393 + 65.3416i) q^{68} +(-29.5913 + 29.5913i) q^{69} +(-29.1190 + 19.5474i) q^{70} +7.58516i q^{71} +(-23.9805 - 0.967155i) q^{72} +(71.1095 - 71.1095i) q^{73} +(52.2109 + 93.3050i) q^{74} +(6.98723 + 42.7338i) q^{75} +(-33.4376 + 8.00316i) q^{76} +1.72707i q^{77} +(-10.7043 - 19.1294i) q^{78} +146.874i q^{79} +(18.5892 - 77.8103i) q^{80} +9.00000 q^{81} +(17.6795 - 9.89296i) q^{82} -78.3344 q^{83} +(-23.6309 + 5.65596i) q^{84} +(83.7083 - 6.79826i) q^{85} +(55.2499 - 30.9163i) q^{86} +(-37.4385 - 37.4385i) q^{87} +(-2.67115 - 2.89567i) q^{88} +129.469 q^{89} +(-5.78944 + 29.4361i) q^{90} +(-15.6929 - 15.6929i) q^{91} +(-22.4962 - 93.9902i) q^{92} +4.95371 q^{93} +(25.4097 + 7.17579i) q^{94} +(3.47891 + 42.8365i) q^{95} +(30.8726 - 46.0313i) q^{96} +(44.2193 - 44.2193i) q^{97} +(64.0534 - 35.8425i) q^{98} +(1.04463 + 1.04463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4} + 12 q^{8} + 288 q^{9}+O(q^{10}) \) 96 * q + 4 * q^4 + 12 * q^8 + 288 * q^9	\( 96 q + 4 q^{4} + 12 q^{8} + 288 q^{9} + 24 q^{12} - 28 q^{16} + 32 q^{19} + 84 q^{20} + 4 q^{22} + 124 q^{28} + 120 q^{30} + 140 q^{32} - 148 q^{34} - 96 q^{35} + 12 q^{36} - 104 q^{38} - 284 q^{40} - 60 q^{42} - 48 q^{44} - 28 q^{46} - 144 q^{48} - 416 q^{50} + 96 q^{51} - 352 q^{52} + 336 q^{56} - 452 q^{58} + 128 q^{59} + 32 q^{61} - 8 q^{62} - 44 q^{64} - 72 q^{66} - 352 q^{68} - 96 q^{69} - 676 q^{70} + 36 q^{72} + 96 q^{73} + 32 q^{74} + 192 q^{75} - 148 q^{76} - 216 q^{78} + 404 q^{80} + 864 q^{81} + 328 q^{82} - 320 q^{83} + 216 q^{84} - 48 q^{86} + 140 q^{88} - 384 q^{91} + 408 q^{92} - 340 q^{94} - 768 q^{95} + 768 q^{98}+O(q^{100}) \) 96 * q + 4 * q^4 + 12 * q^8 + 288 * q^9 + 24 * q^12 - 28 * q^16 + 32 * q^19 + 84 * q^20 + 4 * q^22 + 124 * q^28 + 120 * q^30 + 140 * q^32 - 148 * q^34 - 96 * q^35 + 12 * q^36 - 104 * q^38 - 284 * q^40 - 60 * q^42 - 48 * q^44 - 28 * q^46 - 144 * q^48 - 416 * q^50 + 96 * q^51 - 352 * q^52 + 336 * q^56 - 452 * q^58 + 128 * q^59 + 32 * q^61 - 8 * q^62 - 44 * q^64 - 72 * q^66 - 352 * q^68 - 96 * q^69 - 676 * q^70 + 36 * q^72 + 96 * q^73 + 32 * q^74 + 192 * q^75 - 148 * q^76 - 216 * q^78 + 404 * q^80 + 864 * q^81 + 328 * q^82 - 320 * q^83 + 216 * q^84 - 48 * q^86 + 140 * q^88 - 384 * q^91 + 408 * q^92 - 340 * q^94 - 768 * q^95 + 768 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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