LMFDB - Embedded newform 520.2.ca.a.101.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$520 = 2^{3} \cdot 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$ , 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.15
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.15

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0710713 - 1.41243i) q^{2} +(-2.41987 + 1.39711i) q^{3} +(-1.98990 - 0.200766i) q^{4} -1.00000 q^{5} +(1.80134 + 3.51719i) q^{6} +(-3.43922 - 1.98564i) q^{7} +(-0.424992 + 2.79632i) q^{8} +(2.40385 - 4.16359i) q^{9} +(-0.0710713 + 1.41243i) q^{10} +(-1.07821 - 1.86751i) q^{11} +(5.09579 - 2.29429i) q^{12} +(1.33307 + 3.35007i) q^{13} +(-3.04900 + 4.71653i) q^{14} +(2.41987 - 1.39711i) q^{15} +(3.91939 + 0.799007i) q^{16} +(-0.140752 + 0.243789i) q^{17} +(-5.70993 - 3.69118i) q^{18} +(0.504833 - 0.874396i) q^{19} +(1.98990 + 0.200766i) q^{20} +11.0966 q^{21} +(-2.71436 + 1.39017i) q^{22} +(4.54261 + 7.86803i) q^{23} +(-2.87835 - 7.36049i) q^{24} +1.00000 q^{25} +(4.82646 - 1.64476i) q^{26} +5.05114i q^{27} +(6.44505 + 4.64169i) q^{28} +(8.35275 - 4.82246i) q^{29} +(-1.80134 - 3.51719i) q^{30} -4.26770i q^{31} +(1.40710 - 5.47906i) q^{32} +(5.21826 + 3.01276i) q^{33} +(0.334331 + 0.216128i) q^{34} +(3.43922 + 1.98564i) q^{35} +(-5.61933 + 7.80251i) q^{36} +(3.82691 + 6.62840i) q^{37} +(-1.19914 - 0.775184i) q^{38} +(-7.90627 - 6.24428i) q^{39} +(0.424992 - 2.79632i) q^{40} +(-6.99083 + 4.03616i) q^{41} +(0.788652 - 15.6732i) q^{42} +(-3.60318 - 2.08029i) q^{43} +(1.77059 + 3.93263i) q^{44} +(-2.40385 + 4.16359i) q^{45} +(11.4359 - 5.85691i) q^{46} -5.74879i q^{47} +(-10.6007 + 3.54233i) q^{48} +(4.38550 + 7.59591i) q^{49} +(0.0710713 - 1.41243i) q^{50} -0.786584i q^{51} +(-1.98008 - 6.93392i) q^{52} -4.23944i q^{53} +(7.13436 + 0.358991i) q^{54} +(1.07821 + 1.86751i) q^{55} +(7.01411 - 8.77327i) q^{56} +2.82124i q^{57} +(-6.21773 - 12.1404i) q^{58} +(-3.28770 + 5.69446i) q^{59} +(-5.09579 + 2.29429i) q^{60} +(5.54372 + 3.20067i) q^{61} +(-6.02782 - 0.303311i) q^{62} +(-16.5348 + 9.54635i) q^{63} +(-7.63876 - 2.37682i) q^{64} +(-1.33307 - 3.35007i) q^{65} +(4.62617 - 7.15628i) q^{66} +(4.64814 + 8.05082i) q^{67} +(0.329026 - 0.456857i) q^{68} +(-21.9851 - 12.6931i) q^{69} +(3.04900 - 4.71653i) q^{70} +(6.53123 + 3.77081i) q^{71} +(10.6211 + 8.49142i) q^{72} -7.29316i q^{73} +(9.63412 - 4.93414i) q^{74} +(-2.41987 + 1.39711i) q^{75} +(-1.18012 + 1.63861i) q^{76} +8.56373i q^{77} +(-9.38150 + 10.7232i) q^{78} +13.1317 q^{79} +(-3.91939 - 0.799007i) q^{80} +(0.154547 + 0.267684i) q^{81} +(5.20393 + 10.1609i) q^{82} -11.5605 q^{83} +(-22.0812 - 2.22783i) q^{84} +(0.140752 - 0.243789i) q^{85} +(-3.19435 + 4.94137i) q^{86} +(-13.4750 + 23.3395i) q^{87} +(5.68039 - 2.22134i) q^{88} +(-5.96222 + 3.44229i) q^{89} +(5.70993 + 3.69118i) q^{90} +(2.06730 - 14.1686i) q^{91} +(-7.45970 - 16.5686i) q^{92} +(5.96247 + 10.3273i) q^{93} +(-8.11975 - 0.408574i) q^{94} +(-0.504833 + 0.874396i) q^{95} +(4.24988 + 15.2245i) q^{96} +(0.344878 + 0.199116i) q^{97} +(11.0404 - 5.65435i) q^{98} -10.3674 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100})$ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$ .

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.0710713	−	1.41243i	0.0502550	−	0.998736i
$2$	0.0710713	−	1.41243i	0.0502550	−	0.998736i
$3$	−2.41987	+	1.39711i	−1.39711	+	0.806624i	−0.994089	−	0.108566i	$-0.965374\pi$
$3$	−2.41987	+	1.39711i	−1.39711	+	0.806624i	−0.403024	+	0.915189i	$0.632041\pi$
$4$	−1.98990	−	0.200766i	−0.994949	−	0.100383i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.80134	+	3.51719i	0.735393	+	1.43588i
$7$	−3.43922	−	1.98564i	−1.29990	−	0.750500i	−0.319517	−	0.947581i	$-0.603521\pi$
$7$	−3.43922	−	1.98564i	−1.29990	−	0.750500i	−0.980387	+	0.197081i	$0.936854\pi$
$8$	−0.424992	+	2.79632i	−0.150257	+	0.988647i
$9$	2.40385	−	4.16359i	0.801284	−	1.38786i
$10$	−0.0710713	+	1.41243i	−0.0224747	+	0.446649i
$11$	−1.07821	−	1.86751i	−0.325092	−	0.563076i	0.656439	−	0.754379i	$-0.272062\pi$
$11$	−1.07821	−	1.86751i	−0.325092	−	0.563076i	−0.981531	+	0.191303i	$0.938729\pi$
$12$	5.09579	−	2.29429i	1.47103	−	0.662303i
$13$	1.33307	+	3.35007i	0.369726	+	0.929141i
$13$	1.33307	+	3.35007i	0.369726	+	0.929141i
$14$	−3.04900	+	4.71653i	−0.814878	+	1.26055i
$15$	2.41987	−	1.39711i	0.624808	−	0.360733i
$16$	3.91939	+	0.799007i	0.979847	+	0.199752i
$17$	−0.140752	+	0.243789i	−0.0341373	+	0.0591275i	−0.882589	−	0.470145i	$-0.844202\pi$
$17$	−0.140752	+	0.243789i	−0.0341373	+	0.0591275i	0.848452	+	0.529272i	$0.177535\pi$
$18$	−5.70993	−	3.69118i	−1.34584	−	0.870019i
$19$	0.504833	−	0.874396i	0.115817	−	0.200600i	−0.802289	−	0.596935i	$-0.796385\pi$
$19$	0.504833	−	0.874396i	0.115817	−	0.200600i	0.918106	+	0.396335i	$0.129718\pi$
$20$	1.98990	+	0.200766i	0.444955	+	0.0448926i
$21$	11.0966			2.42148
$22$	−2.71436	+	1.39017i	−0.578703	+	0.296384i
$23$	4.54261	+	7.86803i	0.947200	+	1.64060i	0.751286	+	0.659976i	$0.229434\pi$
$23$	4.54261	+	7.86803i	0.947200	+	1.64060i	0.195913	+	0.980621i	$0.437233\pi$
$24$	−2.87835	−	7.36049i	−0.587540	−	1.50245i
$25$	1.00000			0.200000
$26$	4.82646	−	1.64476i	0.946547	−	0.322565i
$27$			5.05114i			0.972091i
$28$	6.44505	+	4.64169i	1.21800	+	0.877197i
$29$	8.35275	−	4.82246i	1.55107	−	0.895508i	0.553011	−	0.833174i	$-0.313479\pi$
$29$	8.35275	−	4.82246i	1.55107	−	0.895508i	0.998055	−	0.0623343i	$-0.0198545\pi$
$30$	−1.80134	−	3.51719i	−0.328878	−	0.642147i
$31$		−	4.26770i		−	0.766502i	−0.923644	−	0.383251i	$-0.874804\pi$
$31$		−	4.26770i		−	0.766502i	0.923644	−	0.383251i	$-0.125196\pi$
$32$	1.40710	−	5.47906i	0.248742	−	0.968570i
$33$	5.21826	+	3.01276i	0.908382	+	0.524454i
$34$	0.334331	+	0.216128i	0.0573373	+	0.0370656i
$35$	3.43922	+	1.98564i	0.581335	+	0.335634i
$36$	−5.61933	+	7.80251i	−0.936555	+	1.30042i
$37$	3.82691	+	6.62840i	0.629140	+	1.08970i	0.987725	+	0.156205i	$0.0499262\pi$
$37$	3.82691	+	6.62840i	0.629140	+	1.08970i	−0.358584	+	0.933497i	$0.616740\pi$
$38$	−1.19914	−	0.775184i	−0.194526	−	0.125751i
$39$	−7.90627	−	6.24428i	−1.26602	−	0.999886i
$40$	0.424992	−	2.79632i	0.0671971	−	0.442136i
$41$	−6.99083	+	4.03616i	−1.09178	+	0.630342i	−0.934051	−	0.357140i	$-0.883752\pi$
$41$	−6.99083	+	4.03616i	−1.09178	+	0.630342i	−0.157733	+	0.987482i	$0.550419\pi$
$42$	0.788652	−	15.6732i	0.121692	−	2.41842i
$43$	−3.60318	−	2.08029i	−0.549479	−	0.317242i	0.199433	−	0.979912i	$-0.436090\pi$
$43$	−3.60318	−	2.08029i	−0.549479	−	0.317242i	−0.748912	+	0.662670i	$0.769423\pi$
$44$	1.77059	+	3.93263i	0.266927	+	0.592866i
$45$	−2.40385	+	4.16359i	−0.358345	+	0.620672i
$46$	11.4359	−	5.85691i	1.68613	−	0.863554i
$47$		−	5.74879i		−	0.838548i	−0.907860	−	0.419274i	$-0.862285\pi$
$47$		−	5.74879i		−	0.838548i	0.907860	−	0.419274i	$-0.137715\pi$
$48$	−10.6007	+	3.54233i	−1.53008	+	0.511292i
$49$	4.38550	+	7.59591i	0.626500	+	1.08513i
$50$	0.0710713	−	1.41243i	0.0100510	−	0.199747i
$51$		−	0.786584i		−	0.110144i
$52$	−1.98008	−	6.93392i	−0.274588	−	0.961562i
$53$		−	4.23944i		−	0.582331i	−0.956673	−	0.291166i	$-0.905957\pi$
$53$		−	4.23944i		−	0.582331i	0.956673	−	0.291166i	$-0.0940431\pi$
$54$	7.13436	+	0.358991i	0.970863	+	0.0488524i
$55$	1.07821	+	1.86751i	0.145386	+	0.251815i
$56$	7.01411	−	8.77327i	0.937300	−	1.17238i
$57$			2.82124i			0.373682i
$58$	−6.21773	−	12.1404i	−0.816428	−	1.59411i
$59$	−3.28770	+	5.69446i	−0.428022	+	0.741355i	−0.996697	−	0.0812066i	$-0.974123\pi$
$59$	−3.28770	+	5.69446i	−0.428022	+	0.741355i	0.568676	+	0.822562i	$0.307456\pi$
$60$	−5.09579	+	2.29429i	−0.657864	+	0.296191i
$61$	5.54372	+	3.20067i	0.709801	+	0.409804i	0.810987	−	0.585064i	$-0.198931\pi$
$61$	5.54372	+	3.20067i	0.709801	+	0.409804i	−0.101187	+	0.994867i	$0.532264\pi$
$62$	−6.02782	−	0.303311i	−0.765534	−	0.0385206i
$63$	−16.5348	+	9.54635i	−2.08318	+	1.20273i
$64$	−7.63876	−	2.37682i	−0.954846	−	0.297103i
$65$	−1.33307	−	3.35007i	−0.165346	−	0.415524i
$66$	4.62617	−	7.15628i	0.569443	−	0.880878i
$67$	4.64814	+	8.05082i	0.567861	+	0.983565i	0.996777	+	0.0802201i	$0.0255623\pi$
$67$	4.64814	+	8.05082i	0.567861	+	0.983565i	−0.428916	+	0.903344i	$0.641104\pi$
$68$	0.329026	−	0.456857i	0.0399003	−	0.0554021i
$69$	−21.9851	−	12.6931i	−2.64669	−	1.52807i
$70$	3.04900	−	4.71653i	0.364425	−	0.563733i
$71$	6.53123	+	3.77081i	0.775114	+	0.447512i	0.834696	−	0.550711i	$-0.185643\pi$
$71$	6.53123	+	3.77081i	0.775114	+	0.447512i	−0.0595819	+	0.998223i	$0.518977\pi$
$72$	10.6211	+	8.49142i	1.25171	+	1.00072i
$73$		−	7.29316i		−	0.853600i	−0.904346	−	0.426800i	$-0.859641\pi$
$73$		−	7.29316i		−	0.853600i	0.904346	−	0.426800i	$-0.140359\pi$
$74$	9.63412	−	4.93414i	1.11994	−	0.573582i
$75$	−2.41987	+	1.39711i	−0.279423	+	0.161325i
$76$	−1.18012	+	1.63861i	−0.135368	+	0.187961i
$77$			8.56373i			0.975927i
$78$	−9.38150	+	10.7232i	−1.06225	+	1.21417i
$79$	13.1317			1.47744			0.738718	−	0.674014i	$-0.235431\pi$
$79$	13.1317			1.47744			0.738718	+	0.674014i	$0.235431\pi$
$80$	−3.91939	−	0.799007i	−0.438201	−	0.0893317i
$81$	0.154547	+	0.267684i	0.0171719	+	0.0297426i
$82$	5.20393	+	10.1609i	0.574678	+	1.12208i
$83$	−11.5605			−1.26893			−0.634467	−	0.772950i	$-0.718780\pi$
$83$	−11.5605			−1.26893			−0.634467	+	0.772950i	$0.718780\pi$
$84$	−22.0812	−	2.22783i	−2.40925	−	0.243076i
$85$	0.140752	−	0.243789i	0.0152667	−	0.0264426i
$86$	−3.19435	+	4.94137i	−0.344455	+	0.532842i
$87$	−13.4750	+	23.3395i	−1.44468	+	2.50225i
$88$	5.68039	−	2.22134i	0.605531	−	0.236795i
$89$	−5.96222	+	3.44229i	−0.631994	+	0.364882i	−0.781524	−	0.623875i	$-0.785557\pi$
$89$	−5.96222	+	3.44229i	−0.631994	+	0.364882i	0.149530	+	0.988757i	$0.452224\pi$
$90$	5.70993	+	3.69118i	0.601879	+	0.389084i
$91$	2.06730	−	14.1686i	0.216712	−	1.48527i
$92$	−7.45970	−	16.5686i	−0.777727	−	1.72739i
$93$	5.96247	+	10.3273i	0.618279	+	1.07089i
$94$	−8.11975	−	0.408574i	−0.837488	−	0.0421412i
$95$	−0.504833	+	0.874396i	−0.0517948	+	0.0897112i
$96$	4.24988	+	15.2245i	0.433751	+	1.55384i
$97$	0.344878	+	0.199116i	0.0350171	+	0.0202171i	0.517406	−	0.855740i	$-0.326898\pi$
$97$	0.344878	+	0.199116i	0.0350171	+	0.0202171i	−0.482389	+	0.875957i	$0.660231\pi$
$98$	11.0404	−	5.65435i	1.11524	−	0.571176i
$99$	−10.3674			−1.04197
$100$	−1.98990	−	0.200766i	−0.198990	−	0.0200766i
$101$	2.55126	−	1.47297i	0.253860	−	0.146566i	−0.367670	−	0.929956i	$-0.619845\pi$
$101$	2.55126	−	1.47297i	0.253860	−	0.146566i	0.621530	+	0.783390i	$0.286511\pi$
$102$	−1.11099	−	0.0559036i	−0.110005	−	0.00553528i
$103$	0.880821			0.0867899			0.0433949	−	0.999058i	$-0.486183\pi$
$103$	0.880821			0.0867899			0.0433949	+	0.999058i	$0.486183\pi$
$104$	−9.93438	+	2.30392i	−0.974146	+	0.225918i
$105$	−11.0966			−1.08292
$106$	−5.98789	−	0.301302i	−0.581596	−	0.0292651i
$107$	−0.0875776	+	0.0505629i	−0.00846644	+	0.00488810i	−0.504227	−	0.863571i	$-0.668223\pi$
$107$	−0.0875776	+	0.0505629i	−0.00846644	+	0.00488810i	0.495761	+	0.868459i	$0.334889\pi$
$108$	1.01410	−	10.0512i	0.0975814	−	0.967181i
$109$	1.13209			0.108434			0.0542171	−	0.998529i	$-0.482734\pi$
$109$	1.13209			0.108434			0.0542171	+	0.998529i	$0.482734\pi$
$110$	2.71436	−	1.39017i	0.258804	−	0.132547i
$111$	−18.5213	−	10.6933i	−1.75796	−	1.01496i
$112$	−11.8931	−	10.5304i	−1.12379	−	0.995033i
$113$	7.84233	−	13.5833i	0.737744	−	1.27781i	−0.215765	−	0.976445i	$-0.569224\pi$
$113$	7.84233	−	13.5833i	0.737744	−	1.27781i	0.953509	−	0.301365i	$-0.0974423\pi$
$114$	3.98479	+	0.200509i	0.373210	+	0.0187794i
$115$	−4.54261	−	7.86803i	−0.423601	−	0.733698i
$116$	−17.5893	+	7.91926i	−1.63313	+	0.735284i
$117$	17.1528	+	2.50272i	1.58578	+	0.231376i
$118$	7.80934	+	5.04834i	0.718908	+	0.464738i
$119$	0.968153	−	0.558963i	0.0887504	−	0.0512401i
$120$	2.87835	+	7.36049i	0.262756	+	0.671917i
$121$	3.17493	−	5.49914i	0.288630	−	0.499922i
$122$	4.91471	−	7.60262i	0.444957	−	0.688309i
$123$	11.2779	−	19.5340i	1.01690	−	1.76132i
$124$	−0.856810	+	8.49229i	−0.0769438	+	0.762631i
$125$	−1.00000			−0.0894427
$126$	12.3084	+	24.0326i	1.09652	+	2.14100i
$127$	10.8617	+	18.8130i	0.963817	+	1.66938i	0.712760	+	0.701408i	$0.247445\pi$
$127$	10.8617	+	18.8130i	0.963817	+	1.66938i	0.251057	+	0.967972i	$0.419222\pi$
$128$	−3.89998	+	10.6203i	−0.344713	+	0.938708i
$129$	11.6256			1.02358
$130$	−4.82646	+	1.64476i	−0.423309	+	0.144255i
$131$			4.42074i			0.386242i	0.981175	+	0.193121i	$0.0618610\pi$
$131$			4.42074i			0.386242i	−0.981175	+	0.193121i	$0.938139\pi$
$132$	−9.77894	−	7.04274i	−0.851147	−	0.612991i
$133$	−3.47247	+	2.00483i	−0.301101	+	0.173841i
$134$	11.7015	−	5.99298i	1.01086	−	0.517715i
$135$		−	5.05114i		−	0.434732i
$136$	−0.621893	−	0.497195i	−0.0533269	−	0.0426341i
$137$	−1.48576	−	0.857802i	−0.126937	−	0.0732870i	0.435187	−	0.900340i	$-0.356682\pi$
$137$	−1.48576	−	0.857802i	−0.126937	−	0.0732870i	−0.562124	+	0.827053i	$0.690016\pi$
$138$	−19.4906	+	30.1502i	−1.65915	+	2.56655i
$139$	18.8005	+	10.8545i	1.59464	+	0.920667i	0.992496	+	0.122281i	$0.0390209\pi$
$139$	18.8005	+	10.8545i	1.59464	+	0.920667i	0.602146	+	0.798386i	$0.294312\pi$
$140$	−6.44505	−	4.64169i	−0.544706	−	0.392295i
$141$	8.03172	+	13.9113i	0.676393	+	1.17155i
$142$	5.79017	−	8.95688i	0.485900	−	0.751645i
$143$	4.81897	−	6.10159i	0.402982	−	0.510241i
$144$	12.7484	−	14.3980i	1.06236	−	1.19984i
$145$	−8.35275	+	4.82246i	−0.693658	+	0.400484i
$146$	−10.3011	−	0.518334i	−0.852521	−	0.0428976i
$147$	−21.2247	−	12.2541i	−1.75058	−	1.01070i
$148$	−6.28440	−	13.9582i	−0.516575	−	1.14735i
$149$	2.48346	−	4.30147i	0.203453	−	0.352390i	−0.746186	−	0.665738i	$-0.768117\pi$
$149$	2.48346	−	4.30147i	0.203453	−	0.352390i	0.949639	+	0.313347i	$0.101450\pi$
$150$	1.80134	+	3.51719i	0.147079	+	0.287177i
$151$			13.4275i			1.09271i	0.837553	+	0.546356i	$0.183985\pi$
$151$			13.4275i			1.09271i	−0.837553	+	0.546356i	$0.816015\pi$
$152$	2.23054	+	1.78328i	0.180921	+	0.144643i
$153$	0.676693	+	1.17207i	0.0547073	+	0.0947559i
$154$	12.0956	+	0.608635i	0.974694	+	0.0490452i
$155$			4.26770i			0.342790i
$156$	14.4790	+	14.0128i	1.15925	+	1.12192i
$157$			17.1735i			1.37060i	0.728262	+	0.685299i	$0.240328\pi$
$157$			17.1735i			1.37060i	−0.728262	+	0.685299i	$0.759672\pi$
$158$	0.933290	−	18.5476i	0.0742485	−	1.47557i
$159$	5.92297	+	10.2589i	0.469722	+	0.813583i
$160$	−1.40710	+	5.47906i	−0.111241	+	0.433158i
$161$		−	36.0799i		−	2.84349i
$162$	0.389067	−	0.199262i	0.0305680	−	0.0156555i
$163$	−3.04528	+	5.27458i	−0.238525	+	0.413137i	−0.960291	−	0.279000i	$-0.909997\pi$
$163$	−3.04528	+	5.27458i	−0.238525	+	0.413137i	0.721766	+	0.692137i	$0.243330\pi$
$164$	14.7214	−	6.62802i	1.14955	−	0.517561i
$165$	−5.21826	−	3.01276i	−0.406241	−	0.234543i
$166$	−0.821622	+	16.3284i	−0.0637702	+	1.26733i
$167$	9.07640	−	5.24026i	0.702353	−	0.405504i	−0.105870	−	0.994380i	$-0.533763\pi$
$167$	9.07640	−	5.24026i	0.702353	−	0.405504i	0.808223	+	0.588876i	$0.200429\pi$
$168$	−4.71598	+	31.0297i	−0.363846	+	2.39399i
$169$	−9.44587	+	8.93171i	−0.726606	+	0.687055i
$170$	−0.334331	−	0.216128i	−0.0256420	−	0.0165762i
$171$	−2.42709	−	4.20384i	−0.185604	−	0.321476i
$172$	6.75230	+	4.86297i	0.514858	+	0.370798i
$173$	6.92035	+	3.99546i	0.526144	+	0.303769i	0.739445	−	0.673217i	$-0.235088\pi$
$173$	6.92035	+	3.99546i	0.526144	+	0.303769i	−0.213301	+	0.976987i	$0.568421\pi$
$174$	32.0076	+	20.6913i	2.42649	+	1.56860i
$175$	−3.43922	−	1.98564i	−0.259981	−	0.150100i
$176$	−2.73376	−	8.18100i	−0.206065	−	0.616666i
$177$		−	18.3731i		−	1.38101i
$178$	4.43824	+	8.66585i	0.332660	+	0.649533i
$179$	1.48544	−	0.857617i	0.111027	−	0.0641013i	−0.443458	−	0.896295i	$-0.646249\pi$
$179$	1.48544	−	0.857617i	0.111027	−	0.0641013i	0.554485	+	0.832194i	$0.312915\pi$
$180$	5.61933	−	7.80251i	0.418840	−	0.581565i
$181$			2.58029i			0.191791i	0.995391	+	0.0958957i	$0.0305715\pi$
$181$			2.58029i			0.191791i	−0.995391	+	0.0958957i	$0.969428\pi$
$182$	−19.8652	−	3.92689i	−1.47251	−	0.291081i
$183$	−17.8868			−1.32223
$184$	−23.9321	+	9.35872i	−1.76430	+	0.689934i
$185$	−3.82691	−	6.62840i	−0.281360	−	0.487330i
$186$	15.0103	−	7.68757i	1.10061	−	0.563680i
$187$	0.607039			0.0443911
$188$	−1.15416	+	11.4395i	−0.0841759	+	0.834312i
$189$	10.0297	−	17.3720i	0.729555	−	1.26363i
$190$	1.19914	+	0.775184i	0.0869949	+	0.0562378i
$191$	4.15570	−	7.19788i	0.300696	−	0.520820i	−0.675598	−	0.737270i	$-0.736114\pi$
$191$	4.15570	−	7.19788i	0.300696	−	0.520820i	0.976294	+	0.216450i	$0.0694478\pi$
$192$	21.8055	−	4.92062i	1.57368	−	0.355115i
$193$	−4.15101	+	2.39658i	−0.298796	+	0.172510i	−0.641902	−	0.766787i	$-0.721854\pi$
$193$	−4.15101	+	2.39658i	−0.298796	+	0.172510i	0.343106	+	0.939297i	$0.388521\pi$
$194$	0.305747	−	0.472964i	0.0219514	−	0.0339568i
$195$	7.90627	+	6.24428i	0.566180	+	0.447162i
$196$	−7.20170	−	15.9956i	−0.514407	−	1.14254i
$197$	−11.3796	−	19.7100i	−0.810763	−	1.40428i	−0.912331	−	0.409453i	$-0.865719\pi$
$197$	−11.3796	−	19.7100i	−0.810763	−	1.40428i	0.101569	−	0.994829i	$-0.467614\pi$
$198$	−0.736826	+	14.6432i	−0.0523640	+	1.04065i
$199$	5.51853	−	9.55837i	0.391198	−	0.677575i	−0.601410	−	0.798941i	$-0.705394\pi$
$199$	5.51853	−	9.55837i	0.391198	−	0.677575i	0.992608	+	0.121366i	$0.0387274\pi$
$200$	−0.424992	+	2.79632i	−0.0300515	+	0.197729i
$201$	−22.4958	−	12.9880i	−1.58673	−	0.916101i
$202$	−1.89914	−	3.70816i	−0.133623	−	0.260905i
$203$	−38.3026			−2.68832
$204$	−0.157919	+	1.56522i	−0.0110566	+	0.109587i
$205$	6.99083	−	4.03616i	0.488261	−	0.281897i
$206$	0.0626011	−	1.24410i	0.00436162	−	0.0866802i
$207$	43.6790			3.03590
$208$	2.54807	+	14.1953i	0.176677	+	0.984269i
$209$	−2.17726			−0.150604
$210$	−0.788652	+	15.6732i	−0.0544222	+	1.08155i
$211$	15.2491	−	8.80406i	1.04979	−	0.606096i	0.127199	−	0.991877i	$-0.459401\pi$
$211$	15.2491	−	8.80406i	1.04979	−	0.606096i	0.922590	+	0.385781i	$0.126068\pi$
$212$	−0.851135	+	8.43605i	−0.0584562	+	0.579390i
$213$	−21.0730			−1.44390
$214$	0.0651922	+	0.127290i	0.00445645	+	0.00870140i
$215$	3.60318	+	2.08029i	0.245735	+	0.141875i
$216$	−14.1246	−	2.14669i	−0.961055	−	0.146064i
$217$	−8.47411	+	14.6776i	−0.575260	+	0.996379i
$218$	0.0804588	−	1.59899i	0.00544936	−	0.108297i
$219$	10.1894	+	17.6485i	0.688534	+	1.19258i
$220$	−1.77059	−	3.93263i	−0.119373	−	0.265138i
$221$	−1.00434	−	0.146541i	−0.0675593	−	0.00985739i
$222$	−16.4198	+	25.3999i	−1.10202	+	1.70473i
$223$	13.4742	−	7.77933i	0.902298	−	0.520942i	0.0243533	−	0.999703i	$-0.492247\pi$
$223$	13.4742	−	7.77933i	0.902298	−	0.520942i	0.877945	+	0.478761i	$0.158914\pi$
$224$	−15.7187	+	16.0497i	−1.05025	+	1.07237i
$225$	2.40385	−	4.16359i	0.160257	−	0.277573i
$226$	−18.6281	−	12.0421i	−1.23912	−	0.801028i
$227$	10.8927	−	18.8667i	0.722974	−	1.25223i	−0.236829	−	0.971551i	$-0.576108\pi$
$227$	10.8927	−	18.8667i	0.722974	−	1.25223i	0.959803	−	0.280676i	$-0.0905585\pi$
$228$	0.566408	−	5.61397i	0.0375113	−	0.371794i
$229$	3.22752			0.213280			0.106640	−	0.994298i	$-0.465991\pi$
$229$	3.22752			0.213280			0.106640	+	0.994298i	$0.465991\pi$
$230$	−11.4359	+	5.85691i	−0.754059	+	0.386193i
$231$	−11.9645	−	20.7231i	−0.787206	−	1.36348i
$232$	9.93527	+	25.4064i	0.652283	+	1.66801i
$233$	10.4843			0.686848			0.343424	−	0.939180i	$-0.388413\pi$
$233$	10.4843			0.686848			0.343424	+	0.939180i	$0.388413\pi$
$234$	4.75398	−	24.0492i	0.310777	−	1.57215i
$235$			5.74879i			0.375010i
$236$	7.68543	−	10.6713i	0.500279	−	0.694645i
$237$	−31.7771	+	18.3465i	−2.06415	+	1.19174i
$238$	−0.720687	−	1.40717i	−0.0467152	−	0.0912134i
$239$			17.9499i			1.16108i	0.814232	+	0.580540i	$0.197158\pi$
$239$			17.9499i			1.16108i	−0.814232	+	0.580540i	$0.802842\pi$
$240$	10.6007	−	3.54233i	0.684273	−	0.228657i
$241$	13.7612	+	7.94503i	0.886437	+	0.511784i	0.872775	−	0.488122i	$-0.162318\pi$
$241$	13.7612	+	7.94503i	0.886437	+	0.511784i	0.0136613	+	0.999907i	$0.495651\pi$
$242$	−7.54148	−	4.87518i	−0.484785	−	0.313389i
$243$	−13.8712	−	8.00854i	−0.889838	−	0.513748i
$244$	−10.3889	−	7.48199i	−0.665078	−	0.478986i
$245$	−4.38550	−	7.59591i	−0.280180	−	0.485285i
$246$	−26.7888	−	17.3176i	−1.70799	−	1.10413i
$247$	3.60226	+	0.525596i	0.229206	+	0.0334429i
$248$	11.9338	+	1.81374i	0.757800	+	0.115173i
$249$	27.9750	−	16.1514i	1.77284	−	1.02355i
$250$	−0.0710713	+	1.41243i	−0.00449494	+	0.0893297i
$251$	2.08906	+	1.20612i	0.131860	+	0.0761294i	0.564479	−	0.825447i	$-0.309077\pi$
$251$	2.08906	+	1.20612i	0.131860	+	0.0761294i	−0.432619	+	0.901577i	$0.642410\pi$
$252$	34.8191	−	15.6766i	2.19340	−	0.987536i
$253$	9.79577	−	16.9668i	0.615855	−	1.06669i
$254$	27.3439	−	14.0042i	1.71571	−	0.878705i
$255$			0.786584i			0.0492578i
$256$	14.7232	+	6.26324i	0.920198	+	0.391452i
$257$	2.39072	+	4.14086i	0.149129	+	0.258300i	0.930906	−	0.365259i	$-0.119020\pi$
$257$	2.39072	+	4.14086i	0.149129	+	0.258300i	−0.781777	+	0.623559i	$0.785686\pi$
$258$	0.826248	−	16.4203i	0.0514400	−	1.02229i
$259$		−	30.3954i		−	1.88868i
$260$	1.98008	+	6.93392i	0.122800	+	0.430024i
$261$		−	46.3699i		−	2.87023i
$262$	6.24398	+	0.314188i	0.385754	+	0.0194106i
$263$	−8.13497	−	14.0902i	−0.501624	−	0.868838i	−0.999998	−	0.00187619i	$-0.999403\pi$
$263$	−8.13497	−	14.0902i	−0.501624	−	0.868838i	0.498374	−	0.866962i	$-0.333931\pi$
$264$	−10.6423	+	13.3115i	−0.654991	+	0.819266i
$265$			4.23944i			0.260427i
$266$	2.58488	+	5.04709i	0.158489	+	0.309457i
$267$	9.61854	−	16.6598i	0.588645	−	1.01956i
$268$	−7.63300	−	16.9535i	−0.466260	−	1.03560i
$269$	−24.4578	−	14.1207i	−1.49122	−	0.860954i	−0.491266	−	0.871010i	$-0.663466\pi$
$269$	−24.4578	−	14.1207i	−1.49122	−	0.860954i	−0.999949	+	0.0100558i	$0.996799\pi$
$270$	−7.13436	−	0.358991i	−0.434183	−	0.0218475i
$271$	−15.4629	+	8.92750i	−0.939303	+	0.542307i	−0.889742	−	0.456464i	$-0.849116\pi$
$271$	−15.4629	+	8.92750i	−0.939303	+	0.542307i	−0.0495613	+	0.998771i	$0.515782\pi$
$272$	−0.746450	+	0.843042i	−0.0452602	+	0.0511169i
$273$	14.7925	+	37.1745i	0.895285	+	2.24990i
$274$	−1.31718	+	2.03756i	−0.0795736	+	0.123093i
$275$	−1.07821	−	1.86751i	−0.0650185	−	0.112615i
$276$	41.1997	+	29.6718i	2.47993	+	1.78603i
$277$	−23.7433	−	13.7082i	−1.42660	−	0.823647i	−0.429747	−	0.902949i	$-0.641397\pi$
$277$	−23.7433	−	13.7082i	−1.42660	−	0.823647i	−0.996851	+	0.0793027i	$0.974731\pi$
$278$	16.6674	−	25.7830i	0.999642	−	1.54636i
$279$	−17.7690	−	10.2589i	−1.06380	−	0.614186i
$280$	−7.01411	+	8.77327i	−0.419173	+	0.524303i
$281$		−	1.89195i		−	0.112865i	−0.998406	−	0.0564323i	$-0.982028\pi$
$281$		−	1.89195i		−	0.112865i	0.998406	−	0.0564323i	$-0.0179725\pi$
$282$	20.2196	−	10.3555i	1.20406	−	0.616662i
$283$	6.73416	−	3.88797i	0.400304	−	0.231116i	−0.286311	−	0.958137i	$-0.592429\pi$
$283$	6.73416	−	3.88797i	0.400304	−	0.231116i	0.686615	+	0.727021i	$0.259096\pi$
$284$	−12.2394	−	8.81477i	−0.726276	−	0.523060i
$285$		−	2.82124i		−	0.167116i
$286$	−8.27556	−	7.24009i	−0.489344	−	0.428115i
$287$	32.0574			1.89229
$288$	−19.4301	−	19.0294i	−1.14493	−	1.12132i
$289$	8.46038	+	14.6538i	0.497669	+	0.861988i
$290$	6.21773	+	12.1404i	0.365118	+	0.712908i
$291$	−1.11275			−0.0652304
$292$	−1.46422	+	14.5126i	−0.0856869	+	0.849288i
$293$	−15.0218	+	26.0185i	−0.877583	+	1.52002i	−0.0235976	+	0.999722i	$0.507512\pi$
$293$	−15.0218	+	26.0185i	−0.877583	+	1.52002i	−0.853985	+	0.520297i	$0.825821\pi$
$294$	−18.8165	+	29.1074i	−1.09740	+	1.69758i
$295$	3.28770	−	5.69446i	0.191417	−	0.331544i
$296$	−20.1615	+	7.88423i	−1.17186	+	0.458262i
$297$	9.43306	−	5.44618i	0.547362	−	0.316019i
$298$	−5.89901	−	3.81341i	−0.341720	−	0.220905i
$299$	−20.3028	+	25.7066i	−1.17414	+	1.48665i
$300$	5.09579	−	2.29429i	0.294206	−	0.132461i
$301$	8.26142	+	14.3092i	0.476180	+	0.824768i
$302$	18.9653	+	0.954307i	1.09133	+	0.0549142i
$303$	−4.11582	+	7.12881i	−0.236448	+	0.409539i
$304$	2.67728	−	3.02373i	0.153553	−	0.173423i
$305$	−5.54372	−	3.20067i	−0.317433	−	0.183270i
$306$	1.70355	−	0.872478i	0.0973855	−	0.0498763i
$307$	12.3926			0.707281			0.353640	−	0.935381i	$-0.384944\pi$
$307$	12.3926			0.707281			0.353640	+	0.935381i	$0.384944\pi$
$308$	1.71930	−	17.0409i	0.0979665	−	0.970998i
$309$	−2.13147	+	1.23061i	−0.121255	+	0.0700068i
$310$	6.02782	+	0.303311i	0.342357	+	0.0172269i
$311$	−8.13147			−0.461093			−0.230547	−	0.973061i	$-0.574051\pi$
$311$	−8.13147			−0.461093			−0.230547	+	0.973061i	$0.574051\pi$
$312$	20.8211	−	19.4547i	1.17876	−	1.10140i
$313$	18.3666			1.03814			0.519071	−	0.854731i	$-0.326278\pi$
$313$	18.3666			1.03814			0.519071	+	0.854731i	$0.326278\pi$
$314$	24.2564	+	1.22055i	1.36887	+	0.0688794i
$315$	16.5348	−	9.54635i	0.931629	−	0.537876i
$316$	−26.1308	−	2.63641i	−1.46997	−	0.148309i
$317$	26.3754			1.48139			0.740696	−	0.671840i	$-0.234496\pi$
$317$	26.3754			1.48139			0.740696	+	0.671840i	$0.234496\pi$
$318$	14.9109	−	7.63665i	0.836161	−	0.428242i
$319$	−18.0120	−	10.3992i	−1.00848	−	0.582246i
$320$	7.63876	+	2.37682i	0.427020	+	0.132868i
$321$	0.141284	−	0.244712i	0.00788572	−	0.0136585i
$322$	−50.9602	−	2.56424i	−2.83990	−	0.142900i
$323$	0.142112	+	0.246146i	0.00790733	+	0.0136959i
$324$	−0.253791	−	0.563691i	−0.0140995	−	0.0313161i
$325$	1.33307	+	3.35007i	0.0739452	+	0.185828i
$326$	7.23352	+	4.67610i	0.400628	+	0.258986i
$327$	−2.73950	+	1.58165i	−0.151495	+	0.0874656i
$328$	−8.31533	−	21.2639i	−0.459137	−	1.17410i
$329$	−11.4150	+	19.7714i	−0.629330	+	1.09003i
$330$	−4.62617	+	7.15628i	−0.254662	+	0.393940i
$331$	−0.725107	+	1.25592i	−0.0398555	+	0.0690317i	−0.885265	−	0.465087i	$-0.846023\pi$
$331$	−0.725107	+	1.25592i	−0.0398555	+	0.0690317i	0.845410	+	0.534119i	$0.179356\pi$
$332$	23.0043	+	2.32096i	1.26252	+	0.127379i
$333$	36.7973			2.01648
$334$	−6.75641	−	13.1922i	−0.369695	−	0.721844i
$335$	−4.64814	−	8.05082i	−0.253955	−	0.439863i
$336$	43.4920	+	8.86630i	2.37268	+	0.483696i
$337$	−25.3440			−1.38057			−0.690287	−	0.723536i	$-0.742516\pi$
$337$	−25.3440			−1.38057			−0.690287	+	0.723536i	$0.742516\pi$
$338$	11.9441	+	13.9764i	0.649671	+	0.760216i
$339$			43.8265i			2.38033i
$340$	−0.329026	+	0.456857i	−0.0178439	+	0.0247766i
$341$	−7.97000	+	4.60148i	−0.431599	+	0.249184i
$342$	−6.11011	+	3.12931i	−0.330397	+	0.169214i
$343$		−	7.03315i		−	0.379754i
$344$	7.34848	−	9.19151i	0.396203	−	0.495573i
$345$	21.9851	+	12.6931i	1.18364	+	0.683373i
$346$	6.13514	−	9.49052i	0.329827	−	0.510213i
$347$	−2.70437	−	1.56137i	−0.145178	−	0.0838186i	0.425652	−	0.904887i	$-0.360045\pi$
$347$	−2.70437	−	1.56137i	−0.145178	−	0.0838186i	−0.570830	+	0.821069i	$0.693378\pi$
$348$	31.4997	−	43.7378i	1.68856	−	2.34459i
$349$	16.3561	+	28.3296i	0.875521	+	1.51645i	0.856207	+	0.516633i	$0.172815\pi$
$349$	16.3561	+	28.3296i	0.875521	+	1.51645i	0.0193141	+	0.999813i	$0.493852\pi$
$350$	−3.04900	+	4.71653i	−0.162976	+	0.252109i
$351$	−16.9216	+	6.73349i	−0.903210	+	0.359407i
$352$	−11.7494	+	3.27980i	−0.626243	+	0.174814i
$353$	−14.7193	+	8.49817i	−0.783428	+	0.452312i	−0.837644	−	0.546217i	$-0.816067\pi$
$353$	−14.7193	+	8.49817i	−0.783428	+	0.452312i	0.0542160	+	0.998529i	$0.482734\pi$
$354$	−25.9507	−	1.30580i	−1.37926	−	0.0694026i
$355$	−6.53123	−	3.77081i	−0.346642	−	0.200134i
$356$	12.5553	−	5.65279i	0.665430	−	0.299597i
$357$	−1.56187	+	2.70524i	−0.0826630	+	0.143176i
$358$	−1.10575	−	2.15902i	−0.0584407	−	0.114108i
$359$		−	12.9675i		−	0.684397i	−0.939628	−	0.342199i	$-0.888828\pi$
$359$		−	12.9675i		−	0.684397i	0.939628	−	0.342199i	$-0.111172\pi$
$360$	−10.6211	−	8.49142i	−0.559781	−	0.447537i
$361$	8.99029	+	15.5716i	0.473173	+	0.819560i
$362$	3.64447	+	0.183384i	0.191549	+	0.00963847i
$363$			17.7429i			0.931263i
$364$	−6.95829	+	27.7790i	−0.364714	+	1.45602i
$365$			7.29316i			0.381741i
$366$	−1.27124	+	25.2638i	−0.0664486	+	1.32056i
$367$	5.10260	+	8.83797i	0.266354	+	0.461338i	0.967917	−	0.251269i	$-0.0808478\pi$
$367$	5.10260	+	8.83797i	0.266354	+	0.461338i	−0.701564	+	0.712607i	$0.747514\pi$
$368$	11.5176	+	34.4674i	0.600398	+	1.79674i
$369$			38.8093i			2.02033i
$370$	−9.63412	+	4.93414i	−0.500854	+	0.256514i
$371$	−8.41798	+	14.5804i	−0.437040	+	0.756975i
$372$	−9.79133	−	21.7473i	−0.507657	−	1.12755i
$373$	−2.92582	−	1.68922i	−0.151493	−	0.0874646i	0.422337	−	0.906439i	$-0.361210\pi$
$373$	−2.92582	−	1.68922i	−0.151493	−	0.0874646i	−0.573830	+	0.818974i	$0.694543\pi$
$374$	0.0431431	−	0.857398i	0.00223087	−	0.0443350i
$375$	2.41987	−	1.39711i	0.124962	−	0.0721466i
$376$	16.0754	+	2.44319i	0.829028	+	0.125998i
$377$	27.2903	+	21.5536i	1.40552	+	1.11007i
$378$	−23.8238	−	15.4009i	−1.22537	−	0.792136i
$379$	10.0454	+	17.3991i	0.515996	+	0.893731i	0.999828	+	0.0185702i	$0.00591143\pi$
$379$	10.0454	+	17.3991i	0.515996	+	0.893731i	−0.483831	+	0.875161i	$0.660755\pi$
$380$	1.18012	−	1.63861i	0.0605386	−	0.0840587i
$381$	−52.5677	−	30.3500i	−2.69312	−	1.55488i
$382$	−9.87112	−	6.38118i	−0.505051	−	0.326490i
$383$	14.0510	+	8.11232i	0.717970	+	0.414520i	0.814005	−	0.580858i	$-0.197283\pi$
$383$	14.0510	+	8.11232i	0.717970	+	0.414520i	−0.0960348	+	0.995378i	$0.530616\pi$
$384$	−5.40026	−	31.1484i	−0.275581	−	1.58954i
$385$		−	8.56373i		−	0.436448i
$386$	3.08998	+	6.03332i	0.157276	+	0.307088i
$387$	−17.3230	+	10.0014i	−0.880578	+	0.508402i
$388$	−0.646297	−	0.465459i	−0.0328107	−	0.0236301i
$389$			27.3387i			1.38613i	0.720876	+	0.693064i	$0.243740\pi$
$389$			27.3387i			1.38613i	−0.720876	+	0.693064i	$0.756260\pi$
$390$	9.38150	−	10.7232i	0.475051	−	0.542992i
$391$	−2.55752			−0.129339
$392$	−23.1044	+	9.03505i	−1.16695	+	0.456339i
$393$	−6.17628	−	10.6976i	−0.311552	−	0.539624i
$394$	−28.6477	+	14.6720i	−1.44325	+	0.739166i
$395$	−13.1317			−0.660730
$396$	20.6301	+	2.08143i	1.03670	+	0.104596i
$397$	−0.160300	+	0.277648i	−0.00804523	+	0.0139347i	−0.870020	−	0.493016i	$-0.835894\pi$
$397$	−0.160300	+	0.277648i	−0.00804523	+	0.0139347i	0.861975	+	0.506951i	$0.169228\pi$
$398$	−13.1083	−	8.47384i	−0.657059	−	0.424755i
$399$	5.60195	−	9.70286i	0.280448	−	0.485751i
$400$	3.91939	+	0.799007i	0.195969	+	0.0399504i
$401$	8.76355	−	5.05964i	0.437631	−	0.252666i	−0.264961	−	0.964259i	$-0.585359\pi$
$401$	8.76355	−	5.05964i	0.437631	−	0.252666i	0.702592	+	0.711593i	$0.252026\pi$
$402$	−19.9434	+	30.8506i	−0.994685	+	1.53869i
$403$	14.2971	−	5.68913i	0.712189	−	0.283396i
$404$	−5.37247	+	2.41886i	−0.267291	+	0.120343i
$405$	−0.154547	−	0.267684i	−0.00767951	−	0.0133013i
$406$	−2.72222	+	54.0996i	−0.135101	+	2.68492i
$407$	8.25242	−	14.2936i	0.409057	−	0.708508i
$408$	2.19954	+	0.334292i	0.108893	+	0.0165499i
$409$	−3.93945	−	2.27444i	−0.194793	−	0.112464i	0.399431	−	0.916763i	$-0.369208\pi$
$409$	−3.93945	−	2.27444i	−0.194793	−	0.112464i	−0.594224	+	0.804299i	$0.702541\pi$
$410$	−5.20393	−	10.1609i	−0.257004	−	0.501811i
$411$	4.79379			0.236460
$412$	−1.75274	−	0.176839i	−0.0863515	−	0.00871223i
$413$	22.6142	−	13.0563i	1.11277	−	0.642461i
$414$	3.10433	−	61.6934i	0.152569	−	3.03207i
$415$	11.5605			0.567484
$416$	20.2310	−	2.59008i	0.991904	−	0.126989i
$417$	−60.6599			−2.97053
$418$	−0.154741	+	3.07522i	−0.00756862	+	0.150414i
$419$	17.3355	−	10.0087i	0.846895	−	0.488955i	−0.0127070	−	0.999919i	$-0.504045\pi$
$419$	17.3355	−	10.0087i	0.846895	−	0.488955i	0.859602	+	0.510964i	$0.170712\pi$
$420$	22.0812	+	2.22783i	1.07745	+	0.108707i
$421$	16.6161			0.809820			0.404910	−	0.914356i	$-0.367303\pi$
$421$	16.6161			0.809820			0.404910	+	0.914356i	$0.367303\pi$
$422$	−11.3513	−	22.1639i	−0.552573	−	1.07892i
$423$	−23.9356	−	13.8193i	−1.16379	−	0.671915i
$424$	11.8548	+	1.80173i	0.575720	+	0.0874995i
$425$	−0.140752	+	0.243789i	−0.00682746	+	0.0118255i
$426$	−1.49768	+	29.7640i	−0.0725630	+	1.44207i
$427$	−12.7107	−	22.0156i	−0.615115	−	1.06541i
$428$	0.184422	−	0.0830325i	0.00891436	−	0.00401353i
$429$	−3.13667	+	21.4977i	−0.151440	+	1.03792i
$430$	3.19435	−	4.94137i	0.154045	−	0.238294i
$431$	28.7209	−	16.5820i	1.38344	−	0.798729i	0.390874	−	0.920444i	$-0.372173\pi$
$431$	28.7209	−	16.5820i	1.38344	−	0.798729i	0.992565	+	0.121715i	$0.0388395\pi$
$432$	−4.03589	+	19.7973i	−0.194177	+	0.952500i
$433$	8.54708	−	14.8040i	0.410746	−	0.711434i	−0.584225	−	0.811592i	$-0.698602\pi$
$433$	8.54708	−	14.8040i	0.410746	−	0.711434i	0.994972	+	0.100158i	$0.0319348\pi$
$434$	20.1287	+	13.0122i	0.966211	+	0.624606i
$435$	13.4750	−	23.3395i	0.646079	−	1.11904i
$436$	−2.25274	−	0.227284i	−0.107886	−	0.0108849i
$437$	9.17304			0.438806
$438$	25.6514	−	13.1374i	1.22567	−	0.627731i
$439$	−0.0989915	−	0.171458i	−0.00472461	−	0.00818326i	0.863653	−	0.504086i	$-0.168171\pi$
$439$	−0.0989915	−	0.171458i	−0.00472461	−	0.00818326i	−0.868378	+	0.495903i	$0.834837\pi$
$440$	−5.68039	+	2.22134i	−0.270802	+	0.105898i
$441$	42.1684			2.00802
$442$	−0.278358	+	1.40814i	−0.0132401	+	0.0669785i
$443$			5.73378i			0.272420i	0.990680	+	0.136210i	$0.0434922\pi$
$443$			5.73378i			0.272420i	−0.990680	+	0.136210i	$0.956508\pi$
$444$	34.7086	+	24.9969i	1.64720	+	1.18630i
$445$	5.96222	−	3.44229i	0.282636	−	0.163180i
$446$	−10.0301	−	19.5842i	−0.474939	−	0.927338i
$447$			13.8787i			0.656439i
$448$	21.5519	+	23.3422i	1.01823	+	1.10282i
$449$	−5.88060	−	3.39517i	−0.277523	−	0.160228i	0.354779	−	0.934950i	$-0.384556\pi$
$449$	−5.88060	−	3.39517i	−0.277523	−	0.160228i	−0.632301	+	0.774722i	$0.717890\pi$
$450$	−5.70993	−	3.69118i	−0.269168	−	0.174004i
$451$	15.0752	+	8.70365i	0.709861	+	0.409839i
$452$	−18.3325	+	25.4549i	−0.862288	+	1.19730i
$453$	−18.7597	−	32.4927i	−0.881407	−	1.52664i
$454$	−25.8737	−	16.7260i	−1.21431	−	0.784991i
$455$	−2.06730	+	14.1686i	−0.0969167	+	0.664234i
$456$	−7.88907	−	1.19900i	−0.369439	−	0.0561484i
$457$	13.4880	−	7.78731i	0.630943	−	0.364275i	−0.150174	−	0.988660i	$-0.547983\pi$
$457$	13.4880	−	7.78731i	0.630943	−	0.364275i	0.781117	+	0.624384i	$0.214650\pi$
$458$	0.229384	−	4.55863i	0.0107184	−	0.213011i
$459$	−1.23141	−	0.710956i	−0.0574774	−	0.0331846i
$460$	7.45970	+	16.5686i	0.347810	+	0.772514i
$461$	6.09111	−	10.5501i	0.283691	−	0.491368i	−0.688600	−	0.725142i	$-0.741774\pi$
$461$	6.09111	−	10.5501i	0.283691	−	0.491368i	0.972291	+	0.233774i	$0.0751076\pi$
$462$	−30.1202	+	15.4262i	−1.40132	+	0.717690i
$463$			8.85167i			0.411372i	0.978618	+	0.205686i	$0.0659426\pi$
$463$			8.85167i			0.411372i	−0.978618	+	0.205686i	$0.934057\pi$
$464$	36.5908	−	12.2272i	1.69869	−	0.567632i
$465$	−5.96247	−	10.3273i	−0.276503	−	0.478917i
$466$	0.745131	−	14.8083i	0.0345175	−	0.685980i
$467$			4.52677i			0.209474i	0.994500	+	0.104737i	$0.0334001\pi$
$467$			4.52677i			0.209474i	−0.994500	+	0.104737i	$0.966600\pi$
$468$	−33.6299	−	8.42385i	−1.55454	−	0.389393i
$469$		−	36.9181i		−	1.70472i
$470$	8.11975	+	0.408574i	0.374536	+	0.0188461i
$471$	−23.9934	−	41.5578i	−1.10556	−	1.91488i
$472$	−14.5263	−	11.6135i	−0.668625	−	0.534556i
$473$			8.97197i			0.412532i
$474$	23.6547	+	46.1868i	1.08650	+	2.12143i
$475$	0.504833	−	0.874396i	0.0231633	−	0.0401201i
$476$	−2.03875	+	0.917908i	−0.0934458	+	0.0420722i
$477$	−17.6513	−	10.1910i	−0.808197	−	0.466613i
$478$	25.3529	+	1.27572i	1.15961	+	0.0583501i
$479$	−33.8650	+	19.5520i	−1.54733	+	0.893352i	−0.548986	+	0.835831i	$0.684986\pi$
$479$	−33.8650	+	19.5520i	−1.54733	+	0.893352i	−0.998344	+	0.0575202i	$0.981681\pi$
$480$	−4.24988	−	15.2245i	−0.193979	−	0.694900i
$481$	−17.1041	+	21.6565i	−0.779878	+	0.987451i
$482$	12.1998	−	18.8720i	0.555686	−	0.859597i
$483$	50.4077	+	87.3087i	2.29363	+	3.97268i
$484$	−7.42182	+	10.3053i	−0.337356	+	0.468423i
$485$	−0.344878	−	0.199116i	−0.0156601	−	0.00904137i
$486$	−12.2973	+	19.0229i	−0.557818	+	0.862895i
$487$	−13.1467	−	7.59026i	−0.595735	−	0.343948i	0.171627	−	0.985162i	$-0.445098\pi$
$487$	−13.1467	−	7.59026i	−0.595735	−	0.343948i	−0.767362	+	0.641214i	$0.778431\pi$
$488$	−11.3061	+	14.1417i	−0.511804	+	0.640166i
$489$		−	17.0184i		−	0.769599i
$490$	−11.0404	+	5.65435i	−0.498752	+	0.255438i
$491$	−37.4908	+	21.6453i	−1.69193	+	0.976839i	−0.738979	+	0.673728i	$0.764692\pi$
$491$	−37.4908	+	21.6453i	−1.69193	+	0.976839i	−0.952955	+	0.303110i	$0.901975\pi$
$492$	−26.3637	+	36.6064i	−1.18857	+	1.65034i
$493$			2.71508i			0.122281i
$494$	0.998383	−	5.05057i	0.0449194	−	0.227236i
$495$	10.3674			0.465981
$496$	3.40993	−	16.7268i	0.153110	−	0.751055i
$497$	−14.9749	−	25.9373i	−0.671716	−	1.16345i
$498$	−20.8244	−	40.6605i	−0.933164	−	1.82204i
$499$	−19.8752			−0.889737			−0.444868	−	0.895596i	$-0.646750\pi$
$499$	−19.8752			−0.889737			−0.444868	+	0.895596i	$0.646750\pi$
$500$	1.98990	+	0.200766i	0.0889909	+	0.00897853i
$501$	−14.6425	+	25.3615i	−0.654178	+	1.13307i
$502$	1.85202	−	2.86492i	0.0826599	−	0.127868i
$503$	4.39518	−	7.61268i	0.195972	−	0.339433i	−0.751247	−	0.660021i	$-0.770547\pi$
$503$	4.39518	−	7.61268i	0.195972	−	0.339433i	0.947219	+	0.320588i	$0.103881\pi$
$504$	−19.6675	−	50.2935i	−0.876059	−	2.24025i
$505$	−2.55126	+	1.47297i	−0.113530	+	0.0655464i
$506$	−23.2681	−	15.0417i	−1.03439	−	0.668683i
$507$	10.3792	−	34.8106i	0.460956	−	1.54599i
$508$	−17.8366	−	39.6165i	−0.791371	−	1.75770i
$509$	−1.81811	−	3.14906i	−0.0805864	−	0.139580i	0.822916	−	0.568164i	$-0.192346\pi$
$509$	−1.81811	−	3.14906i	−0.0805864	−	0.139580i	−0.903502	+	0.428584i	$0.859013\pi$
$510$	1.11099	+	0.0559036i	0.0491956	+	0.00247545i
$511$	−14.4816	+	25.0828i	−0.640626	+	1.10960i
$512$	9.89276	−	20.3503i	0.437202	−	0.899363i
$513$	4.41669	+	2.54998i	0.195002	+	0.112584i
$514$	6.01857	−	3.08243i	0.265468	−	0.135960i
$515$	−0.880821			−0.0388136
$516$	−23.1338	−	2.33403i	−1.01841	−	0.102750i
$517$	−10.7360	+	6.19840i	−0.472167	+	0.272606i
$518$	−42.9313	−	2.16024i	−1.88629	−	0.0949155i
$519$	−22.3285			−0.980111
$520$	9.93438	−	2.30392i	0.435651	−	0.101034i
$521$	−34.2013			−1.49839			−0.749193	−	0.662352i	$-0.769559\pi$
$521$	−34.2013			−1.49839			−0.749193	+	0.662352i	$0.769559\pi$
$522$	−65.4941	−	3.29557i	−2.86660	−	0.144243i
$523$	7.37882	−	4.26016i	0.322653	−	0.186284i	−0.329921	−	0.944008i	$-0.607022\pi$
$523$	7.37882	−	4.26016i	0.322653	−	0.186284i	0.652575	+	0.757725i	$0.273689\pi$
$524$	0.887535	−	8.79683i	0.0387721	−	0.384291i
$525$	11.0966			0.484297
$526$	−20.4795	+	10.4886i	−0.892949	+	0.457327i
$527$	1.04042	+	0.600687i	0.0453214	+	0.0261663i
$528$	18.0451	+	15.9776i	0.785314	+	0.695336i
$529$	−29.7706	+	51.5642i	−1.29437	+	2.24192i
$530$	5.98789	+	0.301302i	0.260097	+	0.0130877i
$531$	15.8063	+	27.3773i	0.685934	+	1.18807i
$532$	7.31236	−	3.29225i	0.317031	−	0.142737i
$533$	−22.8406	−	18.0393i	−0.989337	−	0.781368i
$534$	−22.8471	−	14.7695i	−0.988692	−	0.639139i
$535$	0.0875776	−	0.0505629i	0.00378631	−	0.00218603i
$536$	−24.4881	+	9.57615i	−1.05772	+	0.413627i
$537$	−2.39638	+	4.15065i	−0.103411	+	0.179114i
$538$	−21.6827	+	33.5412i	−0.934807	+	1.44606i
$539$	9.45698	−	16.3800i	0.407341	−	0.705535i
$540$	−1.01410	+	10.0512i	−0.0436397	+	0.432537i
$541$	19.8849			0.854918			0.427459	−	0.904035i	$-0.359409\pi$
$541$	19.8849			0.854918			0.427459	+	0.904035i	$0.359409\pi$
$542$	11.5105	+	22.4747i	0.494417	+	0.965370i
$543$	−3.60496	−	6.24397i	−0.154703	−	0.267954i
$544$	1.13768	+	1.11422i	0.0487778	+	0.0477718i
$545$	−1.13209			−0.0484932
$546$	53.5575	−	18.2513i	2.29205	−	0.781085i
$547$		−	12.9908i		−	0.555448i	−0.960661	−	0.277724i	$-0.910420\pi$
$547$		−	12.9908i		−	0.555448i	0.960661	−	0.277724i	$-0.0895801\pi$
$548$	2.78429	+	2.00523i	0.118939	+	0.0856591i
$549$	26.6526	−	15.3879i	1.13750	−	0.656738i
$550$	−2.71436	+	1.39017i	−0.115741	+	0.0592768i
$551$		−	9.73815i		−	0.414859i
$552$	44.8373	−	56.0827i	1.90840	−	2.38704i
$553$	−45.1630	−	26.0749i	−1.92053	−	1.10882i
$554$	−21.0493	+	32.5614i	−0.894299	+	1.38340i
$555$	18.5213	+	10.6933i	0.786184	+	0.453903i
$556$	−35.2320	−	25.3739i	−1.49417	−	1.07609i
$557$	3.50427	+	6.06958i	0.148481	+	0.257176i	0.930666	−	0.365870i	$-0.119228\pi$
$557$	3.50427	+	6.06958i	0.148481	+	0.257176i	−0.782185	+	0.623046i	$0.785895\pi$
$558$	−15.7528	+	24.3683i	−0.666871	+	1.03159i
$559$	2.16585	−	14.8440i	0.0916059	−	0.627836i
$560$	11.8931	+	10.5304i	0.502575	+	0.444992i
$561$	−1.46896	+	0.848103i	−0.0620194	+	0.0358069i
$562$	−2.67225	−	0.134464i	−0.112722	−	0.00567201i
$563$	27.0033	+	15.5904i	1.13805	+	0.657056i	0.945948	−	0.324319i	$-0.105135\pi$
$563$	27.0033	+	15.5904i	1.13805	+	0.657056i	0.192106	+	0.981374i	$0.438468\pi$
$564$	−13.1894	−	29.2946i	−0.555373	−	1.23353i
$565$	−7.84233	+	13.5833i	−0.329929	+	0.571454i
$566$	−5.01287	−	9.78783i	−0.210706	−	0.411413i
$567$		−	1.22750i		−	0.0515501i
$568$	−13.3201	+	16.6608i	−0.558898	+	0.699072i
$569$	−16.9231	−	29.3117i	−0.709455	−	1.22881i	−0.965060	−	0.262030i	$-0.915608\pi$
$569$	−16.9231	−	29.3117i	−0.709455	−	1.22881i	0.255605	−	0.966781i	$-0.417725\pi$
$570$	−3.98479	−	0.200509i	−0.166904	−	0.00839839i
$571$			9.30526i			0.389413i	0.980862	+	0.194706i	$0.0623754\pi$
$571$			9.30526i			0.389413i	−0.980862	+	0.194706i	$0.937625\pi$
$572$	−10.8142	+	11.1741i	−0.452166	+	0.467211i
$573$			23.2239i			0.970193i
$574$	2.27836	−	45.2787i	0.0950968	−	1.88990i
$575$	4.54261	+	7.86803i	0.189440	+	0.328120i
$576$	−28.2586	+	26.0912i	−1.17744	+	1.08713i
$577$			30.4537i			1.26780i	0.773414	+	0.633902i	$0.218548\pi$
$577$			30.4537i			1.26780i	−0.773414	+	0.633902i	$0.781452\pi$
$578$	21.2987	−	10.9082i	0.885910	−	0.453721i
$579$	6.69660	−	11.5989i	0.278301	−	0.482032i
$580$	17.5893	−	7.91926i	0.730356	−	0.328829i
$581$	39.7592	+	22.9550i	1.64949	+	0.952334i
$582$	−0.0790844	+	1.57167i	−0.00327815	+	0.0651480i
$583$	−7.91721	+	4.57100i	−0.327897	+	0.189312i
$584$	20.3940	+	3.09953i	0.843909	+	0.128260i
$585$	−17.1528	−	2.50272i	−0.709181	−	0.103475i
$586$	35.6816	+	23.0664i	1.47399	+	0.952863i
$587$	2.37309	+	4.11032i	0.0979480	+	0.169651i	0.910835	−	0.412770i	$-0.135439\pi$
$587$	2.37309	+	4.11032i	0.0979480	+	0.169651i	−0.812887	+	0.582421i	$0.802105\pi$
$588$	39.7748	+	28.6456i	1.64028	+	1.18132i
$589$	−3.73167	−	2.15448i	−0.153761	−	0.0887737i
$590$	−7.80934	−	5.04834i	−0.321506	−	0.207837i
$591$	55.0743	+	31.7972i	2.26545	+	1.30796i
$592$	9.70300	+	29.0370i	0.398791	+	1.19341i
$593$		−	9.67639i		−	0.397362i	−0.980064	−	0.198681i	$-0.936334\pi$
$593$		−	9.67639i		−	0.397362i	0.980064	−	0.198681i	$-0.0636657\pi$
$594$	−7.02191	−	13.7106i	−0.288113	−	0.562552i
$595$	−0.968153	+	0.558963i	−0.0396904	+	0.0229153i
$596$	−5.80541	+	8.06089i	−0.237799	+	0.330187i
$597$			30.8400i			1.26220i
$598$	34.8658	+	30.5032i	1.42577	+	1.24737i
$599$	−32.5501			−1.32996			−0.664981	−	0.746860i	$-0.731561\pi$
$599$	−32.5501			−1.32996			−0.664981	+	0.746860i	$0.731561\pi$
$600$	−2.87835	−	7.36049i	−0.117508	−	0.300491i
$601$	−15.7204	−	27.2285i	−0.641248	−	1.11067i	−0.985154	−	0.171670i	$-0.945084\pi$
$601$	−15.7204	−	27.2285i	−0.641248	−	1.11067i	0.343907	−	0.939004i	$-0.388250\pi$
$602$	20.7978	−	10.6517i	0.847656	−	0.434130i
$603$	44.6938			1.82007
$604$	2.69578	−	26.7193i	0.109690	−	1.08719i
$605$	−3.17493	+	5.49914i	−0.129079	+	0.223572i
$606$	9.77640	+	6.31994i	0.397139	+	0.256730i
$607$	11.5552	−	20.0142i	0.469011	−	0.812350i	−0.530362	−	0.847771i	$-0.677944\pi$
$607$	11.5552	−	20.0142i	0.469011	−	0.812350i	0.999372	+	0.0354210i	$0.0112772\pi$
$608$	−4.08052	−	3.99637i	−0.165487	−	0.162074i
$609$	92.6874	−	53.5131i	3.75588	−	2.16846i
$610$	−4.91471	+	7.60262i	−0.198991	+	0.307821i
$611$	19.2588	−	7.66352i	0.779129	−	0.310033i
$612$	−1.11124	−	2.46815i	−0.0449191	−	0.0997690i
$613$	−6.97983	−	12.0894i	−0.281913	−	0.488287i	0.689943	−	0.723864i	$-0.257636\pi$
$613$	−6.97983	−	12.0894i	−0.281913	−	0.488287i	−0.971856	+	0.235576i	$0.924302\pi$
$614$	0.880755	−	17.5036i	0.0355444	−	0.706387i
$615$	−11.2779	+	19.5340i	−0.454770	+	0.787686i
$616$	−23.9469	−	3.63951i	−0.964848	−	0.146640i
$617$	−19.6330	−	11.3351i	−0.790394	−	0.456334i	0.0497071	−	0.998764i	$-0.484171\pi$
$617$	−19.6330	−	11.3351i	−0.790394	−	0.456334i	−0.840101	+	0.542430i	$0.817505\pi$
$618$	1.58666	+	3.09801i	0.0638246	+	0.124620i
$619$	−13.3222			−0.535463			−0.267732	−	0.963494i	$-0.586274\pi$
$619$	−13.3222			−0.535463			−0.267732	+	0.963494i	$0.586274\pi$
$620$	0.856810	−	8.49229i	0.0344103	−	0.341059i
$621$	−39.7425	+	22.9453i	−1.59481	+	0.920765i
$622$	−0.577914	+	11.4851i	−0.0231722	+	0.460511i
$623$	27.3405			1.09538
$624$	−25.9985	−	30.7909i	−1.04077	−	1.23262i
$625$	1.00000			0.0400000
$626$	1.30534	−	25.9415i	0.0521718	−	1.03683i
$627$	5.26870	−	3.04188i	0.210411	−	0.121481i
$628$	3.44786	−	34.1736i	0.137585	−	1.36367i
$629$	−2.15458			−0.0859086
$630$	−12.3084	−	24.0326i	−0.490377	−	0.957482i
$631$	17.4292	+	10.0627i	0.693844	+	0.400591i	0.805050	−	0.593207i	$-0.202138\pi$
$631$	17.4292	+	10.0627i	0.693844	+	0.400591i	−0.111207	+	0.993797i	$0.535472\pi$
$632$	−5.58088	+	36.7205i	−0.221996	+	1.46066i
$633$	−24.6005	+	42.6094i	−0.977783	+	1.69357i
$634$	1.87454	−	37.2534i	0.0744473	−	1.47952i
$635$	−10.8617	−	18.8130i	−0.431032	−	0.746569i
$636$	−9.72648	−	21.6033i	−0.385680	−	0.856626i
$637$	−19.6006	+	24.8176i	−0.776606	+	0.983308i
$638$	−15.9683	+	24.7016i	−0.632191	+	0.977944i
$639$	31.4002	−	18.1289i	1.24217	−	0.717169i
$640$	3.89998	−	10.6203i	0.154160	−	0.419803i
$641$	−16.3493	+	28.3178i	−0.645757	+	1.11848i	0.338369	+	0.941014i	$0.390125\pi$
$641$	−16.3493	+	28.3178i	−0.645757	+	1.11848i	−0.984126	+	0.177471i	$0.943208\pi$
$642$	−0.335596	−	0.216946i	−0.0132449	−	0.00856216i
$643$	19.2558	−	33.3520i	0.759374	−	1.31527i	−0.183797	−	0.982964i	$-0.558839\pi$
$643$	19.2558	−	33.3520i	0.759374	−	1.31527i	0.943170	−	0.332309i	$-0.107828\pi$
$644$	−7.24361	+	71.7953i	−0.285438	+	2.82913i
$645$	−11.6256			−0.457759
$646$	0.357763	−	0.183229i	0.0140760	−	0.00720906i
$647$	13.2218	+	22.9009i	0.519804	+	0.900326i	0.999735	+	0.0230203i	$0.00732823\pi$
$647$	13.2218	+	22.9009i	0.519804	+	0.900326i	−0.479931	+	0.877306i	$0.659338\pi$
$648$	−0.814209	+	0.318399i	−0.0319851	+	0.0125079i
$649$	14.1793			0.556586
$650$	4.82646	−	1.64476i	0.189309	−	0.0645129i
$651$		−	47.3572i		−	1.85607i
$652$	7.11875	−	9.88448i	0.278792	−	0.387106i
$653$	−4.88665	+	2.82131i	−0.191229	+	0.110406i	−0.592558	−	0.805528i	$-0.701882\pi$
$653$	−4.88665	+	2.82131i	−0.191229	+	0.110406i	0.401329	+	0.915934i	$0.368549\pi$
$654$	2.03927	+	3.98176i	0.0797417	+	0.155699i
$655$		−	4.42074i		−	0.172733i
$656$	−30.6247	+	10.2335i	−1.19569	+	0.399552i
$657$	−30.3657	−	17.5317i	−1.18468	−	0.683976i
$658$	27.1144	+	17.5281i	1.05703	+	0.683315i
$659$	−15.6572	−	9.03969i	−0.609918	−	0.352136i	0.163015	−	0.986624i	$-0.447878\pi$
$659$	−15.6572	−	9.03969i	−0.609918	−	0.352136i	−0.772933	+	0.634487i	$0.781211\pi$
$660$	9.77894	+	7.04274i	0.380645	+	0.274138i
$661$	−15.4975	−	26.8425i	−0.602784	−	1.04405i	−0.992397	−	0.123074i	$-0.960725\pi$
$661$	−15.4975	−	26.8425i	−0.602784	−	1.04405i	0.389613	−	0.920979i	$-0.372609\pi$
$662$	1.72236	+	1.11342i	0.0669416	+	0.0432743i
$663$	2.63511	−	1.04857i	0.102339	−	0.0407230i
$664$	4.91313	−	32.3269i	0.190666	−	1.25453i
$665$	3.47247	−	2.00483i	0.134656	−	0.0777440i
$666$	2.61523	−	51.9735i	0.101338	−	2.01393i
$667$	75.8865	+	43.8131i	2.93834	+	1.69645i
$668$	−19.1132	+	8.60535i	−0.739511	+	0.332951i
$669$	−21.7372	+	37.6499i	−0.840409	+	1.45563i
$670$	−11.7015	+	5.99298i	−0.452070	+	0.231529i
$671$		−	13.8040i		−	0.532896i
$672$	15.6140	−	60.7991i	0.602324	−	2.34538i
$673$	−2.07045	−	3.58612i	−0.0798099	−	0.138235i	0.823358	−	0.567522i	$-0.192098\pi$
$673$	−2.07045	−	3.58612i	−0.0798099	−	0.138235i	−0.903168	+	0.429288i	$0.858765\pi$
$674$	−1.80123	+	35.7965i	−0.0693807	+	1.37883i
$675$			5.05114i			0.194418i
$676$	20.5895	−	15.8768i	0.791904	−	0.610645i
$677$			20.5399i			0.789414i	0.918807	+	0.394707i	$0.129154\pi$
$677$			20.5399i			0.789414i	−0.918807	+	0.394707i	$0.870846\pi$
$678$	61.9017	+	3.11481i	2.37732	+	0.119623i
$679$	−0.790742	−	1.36961i	−0.0303459	−	0.0525606i
$680$	0.621893	+	0.497195i	0.0238485	+	0.0190665i
$681$			60.8733i			2.33267i
$682$	5.93281	+	11.5841i	0.227179	+	0.443577i
$683$	22.5403	−	39.0410i	0.862481	−	1.49386i	−0.00704534	−	0.999975i	$-0.502243\pi$
$683$	22.5403	−	39.0410i	0.862481	−	1.49386i	0.869527	−	0.493886i	$-0.164424\pi$
$684$	3.98567	+	8.85249i	0.152396	+	0.338483i
$685$	1.48576	+	0.857802i	0.0567678	+	0.0327749i
$686$	−9.93381	−	0.499855i	−0.379275	−	0.0190846i
$687$	−7.81017	+	4.50921i	−0.297977	+	0.172037i
$688$	−12.4601	−	11.0324i	−0.475036	−	0.420608i
$689$	14.2024	−	5.65145i	0.541068	−	0.215303i
$690$	19.4906	−	30.1502i	0.741993	−	1.14780i
$691$	−6.18648	−	10.7153i	−0.235345	−	0.407629i	0.724028	−	0.689770i	$-0.242289\pi$
$691$	−6.18648	−	10.7153i	−0.235345	−	0.407629i	−0.959373	+	0.282142i	$0.908955\pi$
$692$	−12.9686	−	9.33993i	−0.492993	−	0.355051i
$693$	35.6559	+	20.5859i	1.35445	+	0.781995i
$694$	−2.39752	+	3.70875i	−0.0910086	+	0.140782i
$695$	−18.8005	−	10.8545i	−0.713145	−	0.411735i
$696$	−59.5377	−	47.5996i	−2.25677	−	1.80426i
$697$		−	2.27238i		−	0.0860727i
$698$	41.1759	−	21.0883i	1.55853	−	0.798206i
$699$	−25.3706	+	14.6477i	−0.959604	+	0.554028i
$700$	6.44505	+	4.64169i	0.243600	+	0.175439i
$701$		−	8.06557i		−	0.304632i	−0.988332	−	0.152316i	$-0.951327\pi$
$701$		−	8.06557i		−	0.304632i	0.988332	−	0.152316i	$-0.0486732\pi$
$702$	8.30792	+	24.3791i	0.313562	+	0.920131i
$703$	7.72780			0.291460
$704$	3.79744	+	16.8282i	0.143121	+	0.634237i
$705$	−8.03172	−	13.9113i	−0.302492	−	0.523932i
$706$	10.9569	+	21.3939i	0.412370	+	0.805169i
$707$	−11.6991			−0.439992
$708$	−3.68870	+	36.5607i	−0.138630	+	1.37403i
$709$	8.73212	−	15.1245i	0.327942	−	0.568012i	−0.654162	−	0.756355i	$-0.726978\pi$
$709$	8.73212	−	15.1245i	0.327942	−	0.568012i	0.982103	+	0.188343i	$0.0603117\pi$
$710$	−5.79017	+	8.95688i	−0.217301	+	0.336146i
$711$	31.5668	−	54.6752i	1.18385	−	2.05048i
$712$	−7.09183	−	18.1352i	−0.265778	−	0.679645i
$713$	33.5784	−	19.3865i	1.25752	−	0.726031i
$714$	3.70995	+	2.39829i	0.138841	+	0.0897538i
$715$	−4.81897	+	6.10159i	−0.180219	+	0.228186i
$716$	−3.12805	+	1.40835i	−0.116901	+	0.0526324i
$717$	−25.0780	−	43.4364i	−0.936555	−	1.62216i
$718$	−18.3156	−	0.921615i	−0.683533	−	0.0343944i
$719$	−22.9363	+	39.7268i	−0.855378	+	1.48156i	0.0209160	+	0.999781i	$0.493342\pi$
$719$	−22.9363	+	39.7268i	−0.855378	+	1.48156i	−0.876294	+	0.481777i	$0.839992\pi$
$720$	−12.7484	+	14.3980i	−0.475104	+	0.536583i
$721$	−3.02934	−	1.74899i	−0.112819	−	0.0651358i
$722$	22.6327	−	11.5914i	0.842303	−	0.431388i
$723$	−44.4004			−1.65127
$724$	0.518034	−	5.13451i	0.0192526	−	0.190823i
$725$	8.35275	−	4.82246i	0.310213	−	0.179102i
$726$	25.0606	+	1.26101i	0.930086	+	0.0468006i
$727$	−26.2247			−0.972622			−0.486311	−	0.873786i	$-0.661658\pi$
$727$	−26.2247			−0.972622			−0.486311	+	0.873786i	$0.661658\pi$
$728$	38.7413	+	11.8024i	1.43585	+	0.437425i
$729$	43.8281			1.62326
$730$	10.3011	+	0.518334i	0.381259	+	0.0191844i
$731$	1.01431	−	0.585610i	0.0375155	−	0.0216596i
$732$	35.5929	+	3.59106i	1.31555	+	0.132729i
$733$	−19.1079			−0.705766			−0.352883	−	0.935667i	$-0.614799\pi$
$733$	−19.1079			−0.705766			−0.352883	+	0.935667i	$0.614799\pi$
$734$	12.8456	−	6.57893i	0.474141	−	0.242833i
$735$	21.2247	+	12.2541i	0.782885	+	0.451999i
$736$	49.5013	−	13.8182i	1.82464	−	0.509344i
$737$	10.0233	−	17.3609i	0.369215	−	0.639499i
$738$	54.8153	+	2.75823i	2.01778	+	0.101532i
$739$	−1.18897	−	2.05936i	−0.0437370	−	0.0757547i	0.843328	−	0.537399i	$-0.180593\pi$
$739$	−1.18897	−	2.05936i	−0.0437370	−	0.0757547i	−0.887065	+	0.461644i	$0.847260\pi$
$740$	6.28440	+	13.9582i	0.231019	+	0.513112i
$741$	−9.45132	+	3.76089i	−0.347203	+	0.138160i
$742$	19.9954	+	12.9260i	0.734055	+	0.474529i
$743$	−1.37371	+	0.793112i	−0.0503965	+	0.0290964i	−0.524987	−	0.851111i	$-0.675930\pi$
$743$	−1.37371	+	0.793112i	−0.0503965	+	0.0290964i	0.474590	+	0.880207i	$0.342596\pi$
$744$	−31.4124	+	12.2839i	−1.15163	+	0.450351i
$745$	−2.48346	+	4.30147i	−0.0909868	+	0.157594i
$746$	−2.59384	+	4.01245i	−0.0949674	+	0.146906i
$747$	−27.7898	+	48.1334i	−1.01678	+	1.76111i
$748$	−1.20795	−	0.121873i	−0.0441669	−	0.00445611i
$749$	0.401598			0.0146741
$750$	−1.80134	−	3.51719i	−0.0657755	−	0.128429i
$751$	9.87313	+	17.1008i	0.360276	+	0.624016i	0.988006	−	0.154415i	$-0.0493493\pi$
$751$	9.87313	+	17.1008i	0.360276	+	0.624016i	−0.627730	+	0.778431i	$0.716016\pi$
$752$	4.59333	−	22.5317i	0.167501	−	0.821648i
$753$	−6.74033			−0.245631
$754$	32.3824	−	37.0137i	1.17930	−	1.34796i
$755$		−	13.4275i		−	0.488675i
$756$	−23.4458	+	32.5548i	−0.852716	+	1.18401i
$757$	−12.9517	+	7.47767i	−0.470738	+	0.271780i	−0.716548	−	0.697537i	$-0.754279\pi$
$757$	−12.9517	+	7.47767i	−0.470738	+	0.271780i	0.245811	+	0.969318i	$0.420946\pi$
$758$	25.2889	−	12.9518i	0.918533	−	0.470430i
$759$			54.7432i			1.98705i
$760$	−2.23054	−	1.78328i	−0.0809101	−	0.0646865i
$761$	2.31345	+	1.33567i	0.0838624	+	0.0484180i	0.541345	−	0.840801i	$-0.317915\pi$
$761$	2.31345	+	1.33567i	0.0838624	+	0.0484180i	−0.457482	+	0.889219i	$0.651249\pi$
$762$	−46.6031	+	72.0910i	−1.68825	+	2.61158i
$763$	−3.89350	−	2.24791i	−0.140954	−	0.0813799i
$764$	−9.71450	+	13.4887i	−0.351458	+	0.488005i
$765$	−0.676693	−	1.17207i	−0.0244659	−	0.0423761i
$766$	12.4567	−	19.2694i	0.450078	−	0.696232i
$767$	−23.4595	−	3.42292i	−0.847074	−	0.123594i
$768$	−44.3786	+	5.41372i	−1.60138	+	0.195351i
$769$	22.8657	−	13.2015i	0.824557	−	0.476058i	−0.0274283	−	0.999624i	$-0.508732\pi$
$769$	22.8657	−	13.2015i	0.824557	−	0.476058i	0.851985	+	0.523566i	$0.175398\pi$
$770$	−12.0956	−	0.608635i	−0.435896	−	0.0219337i
$771$	−11.5705	−	6.68023i	−0.416701	−	0.240583i
$772$	8.74123	−	3.93558i	0.314604	−	0.141645i
$773$	3.67042	−	6.35736i	0.132016	−	0.228658i	−0.792438	−	0.609953i	$-0.791188\pi$
$773$	3.67042	−	6.35736i	0.132016	−	0.228658i	0.924454	+	0.381295i	$0.124522\pi$
$774$	12.8951	+	25.1783i	0.463506	+	0.905015i
$775$		−	4.26770i		−	0.153300i
$776$	−0.703360	+	0.879766i	−0.0252492	+	0.0315818i
$777$	42.4658	+	73.5530i	1.52345	+	2.63870i
$778$	38.6139	+	1.94300i	1.38438	+	0.0696598i
$779$			8.15034i			0.292016i
$780$	−14.4790	−	14.0128i	−0.518432	−	0.501739i
$781$		−	16.2629i		−	0.581931i
$782$	−0.181766	+	3.61231i	−0.00649995	+	0.129176i
$783$	24.3589	+	42.1909i	0.870516	+	1.50778i
$784$	11.1193	+	33.2754i	0.397117	+	1.18841i
$785$		−	17.1735i		−	0.612950i
$786$	−15.5486	+	7.96325i	−0.554599	+	0.284040i
$787$	−3.95977	+	6.85852i	−0.141151	+	0.244480i	−0.927930	−	0.372754i	$-0.878413\pi$
$787$	−3.95977	+	6.85852i	−0.141151	+	0.244480i	0.786780	+	0.617234i	$0.211747\pi$
$788$	18.6871	+	41.5056i	0.665701	+	1.47858i
$789$	39.3712	+	22.7310i	1.40165	+	0.809244i
$790$	−0.933290	+	18.5476i	−0.0332050	+	0.659895i
$791$	−53.9430	+	31.1440i	−1.91799	+	1.10735i
$792$	4.40607	−	28.9906i	0.156563	−	1.03014i
$793$	−3.33231	+	22.8385i	−0.118334	+	0.811020i
$794$	0.380764	+	0.246145i	0.0135128	+	0.00873535i
$795$	−5.92297	−	10.2589i	−0.210066	−	0.363845i
$796$	−12.9003	+	17.9122i	−0.457239	+	0.634883i
$797$	−4.97037	−	2.86964i	−0.176059	−	0.101648i	0.409381	−	0.912364i	$-0.365745\pi$
$797$	−4.97037	−	2.86964i	−0.176059	−	0.101648i	−0.585440	+	0.810716i	$0.699078\pi$
$798$	−13.3064	−	8.60194i	−0.471043	−	0.304505i
$799$	1.40149	+	0.809153i	0.0495813	+	0.0286258i
$800$	1.40710	−	5.47906i	0.0497483	−	0.193714i
$801$			33.0990i			1.16950i
$802$	−6.52353	−	12.7375i	−0.230354	−	0.449775i
$803$	−13.6201	+	7.86355i	−0.480642	+	0.277499i
$804$	42.1569	+	30.3611i	1.48676	+	1.07075i
$805$			36.0799i			1.27165i
$806$	−7.01936	−	20.5979i	−0.247247	−	0.725531i
$807$	78.9128			2.77786
$808$	3.03463	+	7.76014i	0.106758	+	0.273001i
$809$	−12.5752	−	21.7809i	−0.442121	−	0.765776i	0.555726	−	0.831366i	$-0.312441\pi$
$809$	−12.5752	−	21.7809i	−0.442121	−	0.765776i	−0.997847	+	0.0655896i	$0.979107\pi$
$810$	−0.389067	+	0.199262i	−0.0136704	+	0.00700135i
$811$	−5.92991			−0.208227			−0.104114	−	0.994565i	$-0.533201\pi$
$811$	−5.92991			−0.208227			−0.104114	+	0.994565i	$0.533201\pi$
$812$	76.2183	+	7.68986i	2.67474	+	0.269861i
$813$	24.9455	−	43.2068i	0.874875	−	1.51533i
$814$	−19.6022	−	12.6718i	−0.687056	−	0.444147i
$815$	3.04528	−	5.27458i	0.106671	−	0.184760i
$816$	0.628487	−	3.08293i	0.0220014	−	0.107924i
$817$	−3.63800	+	2.10040i	−0.127278	+	0.0734838i
$818$	−3.49246	+	5.40253i	−0.122111	+	0.188895i
$819$	−54.0228	−	42.6666i	−1.88771	−	1.49089i
$820$	−14.7214	+	6.62802i	−0.514092	+	0.231461i
$821$	2.40179	+	4.16002i	0.0838231	+	0.145186i	0.904889	−	0.425647i	$-0.139954\pi$
$821$	2.40179	+	4.16002i	0.0838231	+	0.145186i	−0.821066	+	0.570833i	$0.806620\pi$
$822$	0.340700	−	6.77087i	0.0118833	−	0.236161i
$823$	−5.68311	+	9.84344i	−0.198101	+	0.343121i	−0.947913	−	0.318531i	$-0.896811\pi$
$823$	−5.68311	+	9.84344i	−0.198101	+	0.343121i	0.749812	+	0.661651i	$0.230144\pi$
$824$	−0.374342	+	2.46305i	−0.0130408	+	0.0858046i
$825$	5.21826	+	3.01276i	0.181676	+	0.104891i
$826$	−16.8339	−	32.8689i	−0.585726	−	1.14366i
$827$	43.5713			1.51512			0.757562	−	0.652764i	$-0.226391\pi$
$827$	43.5713			1.51512			0.757562	+	0.652764i	$0.226391\pi$
$828$	−86.9168	−	8.76926i	−3.02057	−	0.304753i
$829$	24.4054	−	14.0905i	0.847635	−	0.489382i	−0.0122175	−	0.999925i	$-0.503889\pi$
$829$	24.4054	−	14.0905i	0.847635	−	0.489382i	0.859852	+	0.510543i	$0.170556\pi$
$830$	0.821622	−	16.3284i	0.0285189	−	0.566767i
$831$	76.6077			2.65749
$832$	−2.22046	−	28.7588i	−0.0769806	−	0.997033i
$833$	−2.46907			−0.0855481
$834$	−4.31118	+	85.6776i	−0.149284	+	2.96677i
$835$	−9.07640	+	5.24026i	−0.314102	+	0.181347i
$836$	4.33253	+	0.437120i	0.149844	+	0.0151181i
$837$	21.5568			0.745110
$838$	−12.9044	−	25.1965i	−0.445776	−	0.870397i
$839$	18.2561	+	10.5402i	0.630272	+	0.363888i	0.780857	−	0.624709i	$-0.214783\pi$
$839$	18.2561	+	10.5402i	0.630272	+	0.363888i	−0.150585	+	0.988597i	$0.548116\pi$
$840$	4.71598	−	31.0297i	0.162717	−	1.07063i
$841$	32.0122	−	55.4468i	1.10387	−	1.91196i
$842$	1.18093	−	23.4691i	0.0406975	−	0.808797i
$843$	2.64328	+	4.57829i	0.0910392	+	0.157685i
$844$	−32.1116	+	14.4577i	−1.10533	+	0.497654i
$845$	9.44587	−	8.93171i	0.324948	−	0.307260i
$846$	−21.2198	+	32.8252i	−0.729552	+	1.12855i
$847$	−21.8386	+	12.6085i	−0.750382	+	0.433233i
$848$	3.38734	−	16.6160i	0.116322	−	0.570595i
$849$	−10.8639	+	18.8168i	−0.372847	+	0.645790i
$850$	0.334331	+	0.216128i	0.0114675	+	0.00741312i
$851$	−34.7683	+	60.2205i	−1.19184	+	2.06433i
$852$	41.9331	+	4.23074i	1.43660	+	0.144943i
$853$	−22.7627			−0.779380			−0.389690	−	0.920946i	$-0.627418\pi$
$853$	−22.7627			−0.779380			−0.389690	+	0.920946i	$0.627418\pi$
$854$	−31.9988	+	16.3883i	−1.09498	+	0.560796i
$855$	2.42709	+	4.20384i	0.0830046	+	0.143768i
$856$	−0.104170	−	0.266383i	−0.00356046	−	0.00910480i
$857$	−12.8688			−0.439591			−0.219795	−	0.975546i	$-0.570539\pi$
$857$	−12.8688			−0.439591			−0.219795	+	0.975546i	$0.570539\pi$
$858$	30.1410	+	5.95819i	1.02900	+	0.203409i
$859$		−	36.6584i		−	1.25077i	−0.780317	−	0.625384i	$-0.784942\pi$
$859$		−	36.6584i		−	1.25077i	0.780317	−	0.625384i	$-0.215058\pi$
$860$	−6.75230	−	4.86297i	−0.230251	−	0.165826i
$861$	−77.5747	+	44.7878i	−2.64374	+	1.52636i
$862$	−21.3797	−	41.7447i	−0.728195	−	1.42183i
$863$		−	10.5489i		−	0.359088i	−0.983750	−	0.179544i	$-0.942538\pi$
$863$		−	10.5489i		−	0.359088i	0.983750	−	0.179544i	$-0.0574622\pi$
$864$	27.6755	+	7.10743i	0.941538	+	0.241800i
$865$	−6.92035	−	3.99546i	−0.235299	−	0.135850i
$866$	−20.3021	−	13.1243i	−0.689893	−	0.445980i
$867$	−40.9461	−	23.6402i	−1.39060	−	0.802864i
$868$	19.8094	−	27.5056i	0.672374	−	0.933600i
$869$	−14.1588	−	24.5237i	−0.480303	−	0.831910i
$870$	−32.0076	−	20.6913i	−1.08516	−	0.701500i
$871$	−20.7745	+	26.3039i	−0.703917	+	0.891272i
$872$	−0.481127	+	3.16567i	−0.0162930	+	0.107203i
$873$	1.65807	−	0.957288i	0.0561172	−	0.0323993i
$874$	0.651939	−	12.9562i	0.0220522	−	0.438251i
$875$	3.43922	+	1.98564i	0.116267	+	0.0671268i
$876$	−16.7326	−	37.1644i	−0.565342	−	1.25567i
$877$	16.1790	−	28.0229i	0.546327	−	0.946265i	−0.452196	−	0.891919i	$-0.649359\pi$
$877$	16.1790	−	28.0229i	0.546327	−	0.946265i	0.998522	−	0.0543466i	$-0.0173076\pi$
$878$	−0.249208	+	0.127632i	−0.00841035	+	0.00430739i
$879$		−	83.9486i		−	2.83152i
$880$	2.73376	+	8.18100i	0.0921551	+	0.275782i
$881$	0.0276902	+	0.0479609i	0.000932908	+	0.00161584i	0.866491	−	0.499192i	$-0.166370\pi$
$881$	0.0276902	+	0.0479609i	0.000932908	+	0.00161584i	−0.865559	+	0.500808i	$0.833036\pi$
$882$	2.99696	−	59.5598i	0.100913	−	2.00548i
$883$		−	8.50963i		−	0.286372i	−0.989696	−	0.143186i	$-0.954265\pi$
$883$		−	8.50963i		−	0.286372i	0.989696	−	0.143186i	$-0.0457347\pi$
$884$	1.96911	+	0.493238i	0.0662285	+	0.0165894i
$885$			18.3731i			0.617606i
$886$	8.09854	+	0.407507i	0.272076	+	0.0136905i
$887$	20.0873	+	34.7923i	0.674467	+	1.16821i	0.976624	+	0.214953i	$0.0689598\pi$
$887$	20.0873	+	34.7923i	0.674467	+	1.16821i	−0.302158	+	0.953258i	$0.597707\pi$
$888$	37.7731	−	47.2468i	1.26758	−	1.58550i
$889$		−	86.2693i		−	2.89338i
$890$	−4.43824	−	8.66585i	−0.148770	−	0.290480i
$891$	0.333268	−	0.577238i	0.0111649	−	0.0193382i
$892$	−28.3741	+	12.7749i	−0.950035	+	0.427736i
$893$	−5.02673	−	2.90218i	−0.168213	−	0.0971178i
$894$	19.6026	+	0.986375i	0.655609	+	0.0329893i
$895$	−1.48544	+	0.857617i	−0.0496527	+	0.0286670i
$896$	34.5009	−	28.7815i	1.15259	−	0.961523i
$897$	13.2151	−	90.5721i	0.441240	−	3.02411i
$898$	−5.21337	+	8.06462i	−0.173972	+	0.269120i
$899$	−20.5808	−	35.6471i	−0.686409	−	1.18890i
$900$	−5.61933	+	7.80251i	−0.187311	+	0.260084i
$901$	1.03353	+	0.596708i	0.0344318	+	0.0198792i
$902$	13.3647	−	20.6740i	0.444995	−	0.688368i
$903$	−39.9831	−	23.0843i	−1.33056	−	0.768196i
$904$	34.6503	+	27.7024i	1.15245	+	0.921369i
$905$		−	2.58029i		−	0.0857717i
$906$	−47.2269	+	24.1874i	−1.56901	+	0.803572i
$907$	−45.9462	+	26.5271i	−1.52562	+	0.880816i	−0.526080	+	0.850435i	$0.676339\pi$
$907$	−45.9462	+	26.5271i	−1.52562	+	0.880816i	−0.999538	+	0.0303816i	$0.990328\pi$
$908$	−25.4631	+	35.3559i	−0.845024	+	1.17333i
$909$		−	14.1632i		−	0.469765i
$910$	19.8652	+	3.92689i	0.658525	+	0.130175i
$911$	33.2608			1.10198			0.550990	−	0.834512i	$-0.314250\pi$
$911$	33.2608			1.10198			0.550990	+	0.834512i	$0.314250\pi$
$912$	−2.25419	+	11.0575i	−0.0746436	+	0.366151i
$913$	12.4647	+	21.5894i	0.412520	+	0.714506i
$914$	−10.0404	−	19.6043i	−0.332107	−	0.648453i
$915$	17.8868			0.591319
$916$	−6.42243	−	0.647975i	−0.212203	−	0.0214097i
$917$	8.77799	−	15.2039i	0.289875	−	0.502078i
$918$	−1.09169	+	1.68875i	−0.0360312	+	0.0557371i
$919$	17.3338	−	30.0230i	0.571789	−	0.990368i	−0.424593	−	0.905384i	$-0.639583\pi$
$919$	17.3338	−	30.0230i	0.571789	−	0.990368i	0.996382	−	0.0849835i	$-0.0270838\pi$
$920$	23.9321	−	9.35872i	0.789017	−	0.308548i
$921$	−29.9884	+	17.3138i	−0.988152	+	0.570510i
$922$	−14.4684	−	9.35305i	−0.476490	−	0.308026i
$923$	−3.92589	+	26.9068i	−0.129222	+	0.885647i
$924$	19.6476	+	43.6390i	0.646360	+	1.43562i
$925$	3.82691	+	6.62840i	0.125828	+	0.217941i
$926$	12.5023	+	0.629100i	0.410852	+	0.0206735i
$927$	2.11736	−	3.66738i	0.0695433	−	0.120453i
$928$	−14.6694	−	52.5508i	−0.481548	−	1.72507i
$929$	35.5058	+	20.4993i	1.16491	+	0.672560i	0.952476	−	0.304615i	$-0.0985279\pi$
$929$	35.5058	+	20.4993i	1.16491	+	0.672560i	0.212433	+	0.977176i	$0.431861\pi$
$930$	−15.0103	+	7.68757i	−0.492207	+	0.252085i
$931$	8.85579			0.290237
$932$	−20.8626	−	2.10489i	−0.683379	−	0.0689478i
$933$	19.6771	−	11.3606i	0.644200	−	0.371929i
$934$	6.39373	+	0.321723i	0.209209	+	0.0105271i
$935$	−0.607039			−0.0198523
$936$	−14.2882	+	46.9010i	−0.467024	+	1.53301i
$937$	30.0726			0.982430			0.491215	−	0.871038i	$-0.336553\pi$
$937$	30.0726			0.982430			0.491215	+	0.871038i	$0.336553\pi$
$938$	−52.1441	−	2.62382i	−1.70257	−	0.0856707i
$939$	−44.4448	+	25.6602i	−1.45040	+	0.837390i
$940$	1.15416	−	11.4395i	0.0376446	−	0.373116i
$941$	49.8784			1.62599			0.812995	−	0.582271i	$-0.197836\pi$
$941$	49.8784			1.62599			0.812995	+	0.582271i	$0.197836\pi$
$942$	−60.4025	+	30.9353i	−1.96802	+	1.00793i
$943$	−63.5132	−	36.6694i	−2.06828	−	1.19412i
$944$	−17.4357	+	19.6919i	−0.567483	+	0.640916i
$945$	−10.0297	+	17.3720i	−0.326267	+	0.565111i
$946$	12.6723	+	0.637650i	0.412010	+	0.0207318i
$947$	6.96763	+	12.0683i	0.226418	+	0.392167i	0.956744	−	0.290932i	$-0.0939652\pi$
$947$	6.96763	+	12.0683i	0.226418	+	0.392167i	−0.730326	+	0.683099i	$0.760632\pi$
$948$	66.9166	−	30.1280i	2.17335	−	0.978511i
$949$	24.4326	−	9.72225i	0.793114	−	0.315598i
$950$	−1.19914	−	0.775184i	−0.0389053	−	0.0251503i
$951$	−63.8252	+	36.8495i	−2.06967	+	1.19493i
$952$	1.15158	+	2.94482i	0.0373230	+	0.0954420i
$953$	1.24890	−	2.16317i	0.0404560	−	0.0700718i	−0.845088	−	0.534627i	$-0.820452\pi$
$953$	1.24890	−	2.16317i	0.0404560	−	0.0700718i	0.885544	+	0.464555i	$0.153786\pi$
$954$	−15.6485	+	24.2069i	−0.506639	+	0.783726i
$955$	−4.15570	+	7.19788i	−0.134475	+	0.232918i
$956$	3.60372	−	35.7184i	0.116553	−	1.15522i
$957$	58.1157			1.87861
$958$	25.2089	+	49.2214i	0.814462	+	1.59027i
$959$	3.40656	+	5.90034i	0.110004	+	0.190532i
$960$	−21.8055	+	4.92062i	−0.703770	+	0.158812i
$961$	12.7867			0.412474
$962$	29.3726	+	25.6974i	0.947011	+	0.828517i
$963$			0.486183i			0.0156670i
$964$	−25.7883	−	18.5726i	−0.830585	−	0.598182i
$965$	4.15101	−	2.39658i	0.133626	−	0.0771488i
$966$	126.900	−	64.9920i	4.08293	−	2.09108i
$967$		−	39.0263i		−	1.25500i	−0.778616	−	0.627501i	$-0.784078\pi$
$967$		−	39.0263i		−	1.25500i	0.778616	−	0.627501i	$-0.215922\pi$
$968$	14.0280	+	11.2152i	0.450877	+	0.360470i
$969$	−0.687787	−	0.397094i	−0.0220949	−	0.0127565i
$970$	−0.305747	+	0.472964i	−0.00981694	+	0.0151859i
$971$	−40.5327	−	23.4016i	−1.30076	−	0.750992i	−0.320223	−	0.947342i	$-0.603758\pi$
$971$	−40.5327	−	23.4016i	−1.30076	−	0.750992i	−0.980534	+	0.196350i	$0.937091\pi$
$972$	25.9944	+	18.7210i	0.833772	+	0.600478i
$973$	−43.1062	−	74.6621i	−1.38192	−	2.39356i
$974$	−11.6550	+	18.0293i	−0.373452	+	0.577697i
$975$	−7.90627	−	6.24428i	−0.253203	−	0.199977i
$976$	19.1706	+	16.9741i	0.613637	+	0.543329i
$977$	−30.5823	+	17.6567i	−0.978414	+	0.564887i	−0.901791	−	0.432173i	$-0.857747\pi$
$977$	−30.5823	+	17.6567i	−0.978414	+	0.564887i	−0.0766228	+	0.997060i	$0.524414\pi$
$978$	−24.0372	−	1.20952i	−0.768626	−	0.0386762i
$979$	12.8570	+	7.42302i	0.410913	+	0.237241i
$980$	7.20170	+	15.9956i	0.230050	+	0.510959i
$981$	2.72137	−	4.71355i	0.0868866	−	0.150492i
$982$	27.9079	+	54.4913i	0.890576	+	1.73889i
$983$		−	8.27406i		−	0.263901i	−0.991256	−	0.131951i	$-0.957876\pi$
$983$		−	8.27406i		−	0.263901i	0.991256	−	0.131951i	$-0.0421241\pi$
$984$	49.8301	+	39.8385i	1.58853	+	1.27000i
$985$	11.3796	+	19.7100i	0.362584	+	0.628014i
$986$	3.83485	+	0.192964i	0.122126	+	0.00614523i
$987$		−	63.7923i		−	2.03053i
$988$	−7.06261	−	1.76909i	−0.224691	−	0.0562824i
$989$		−	37.7999i		−	1.20197i
$990$	0.736826	−	14.6432i	0.0234179	−	0.465392i
$991$	−12.2373	−	21.1957i	−0.388732	−	0.673304i	0.603547	−	0.797327i	$-0.293754\pi$
$991$	−12.2373	−	21.1957i	−0.388732	−	0.673304i	−0.992279	+	0.124023i	$0.960420\pi$
$992$	−23.3830	−	6.00507i	−0.742411	−	0.190661i
$993$		−	4.05223i		−	0.128594i
$994$	−37.6988	+	19.3075i	−1.19573	+	0.612398i
$995$	−5.51853	+	9.55837i	−0.174949	+	0.303021i
$996$	−58.9100	+	26.5232i	−1.86664	+	0.840418i
$997$	21.1904	+	12.2343i	0.671108	+	0.387465i	0.796496	−	0.604643i	$-0.206684\pi$
$997$	21.1904	+	12.2343i	0.671108	+	0.387465i	−0.125388	+	0.992108i	$0.540018\pi$
$998$	−1.41256	+	28.0723i	−0.0447137	+	0.888612i
$999$	−33.4810	+	19.3302i	−1.05929	+	0.611582i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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up to: 50 250 1000 (See only

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.a.101.15	✓	56
8.5	even	2		520.2.ca.b.101.24	yes	56
13.4	even	6		520.2.ca.b.381.24	yes	56
104.69	even	6	inner	520.2.ca.a.381.15	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.15	✓	56	1.1	even	1	trivial
520.2.ca.a.381.15	yes	56	104.69	even	6	inner
520.2.ca.b.101.24	yes	56	8.5	even	2
520.2.ca.b.381.24	yes	56	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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	520.2.ca.a.101.15

Level	$520$
Weight	$2$
Character	520.101
Analytic conductor	$4.152$
Analytic rank	$0$
Dimension	$56$
Inner twists	$2$