LMFDB - Embedded newform 663.2.z.d.205.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(205,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("663.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.z (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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 602x^{10} + 1212x^{8} + 1259x^{6} + 665x^{4} + 168x^{2} + 16 $ x^16 + 20x^14 + 156x^12 + 602x^10 + 1212x^8 + 1259x^6 + 665x^4 + 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.2
Root			$1.96679i$ of defining polynomial
Character	$\chi$	$=$	663.205
Dual form			663.2.z.d.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70329 + 0.983395i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.934132 - 1.61796i) q^{4} -0.562071i q^{5} +(1.70329 + 0.983395i) q^{6} +(2.67180 + 1.54256i) q^{7} -0.259096i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.70329 + 0.983395i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.934132 - 1.61796i) q^{4} -0.562071i q^{5} +(1.70329 + 0.983395i) q^{6} +(2.67180 + 1.54256i) q^{7} -0.259096i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.552738 + 0.957371i) q^{10} +(5.23117 - 3.02022i) q^{11} -1.86826 q^{12} +(-3.35066 + 1.33157i) q^{13} -6.06779 q^{14} +(-0.486768 + 0.281036i) q^{15} +(2.12306 + 3.67724i) q^{16} +(-0.500000 + 0.866025i) q^{17} -1.96679i q^{18} +(-3.42710 - 1.97863i) q^{19} +(-0.909411 - 0.525049i) q^{20} -3.08512i q^{21} +(-5.94014 + 10.2886i) q^{22} +(-4.08263 - 7.07133i) q^{23} +(-0.224384 + 0.129548i) q^{24} +4.68408 q^{25} +(4.39768 - 5.56308i) q^{26} +1.00000 q^{27} +(4.99162 - 2.88191i) q^{28} +(2.11307 + 3.65994i) q^{29} +(0.552738 - 0.957371i) q^{30} +6.39872i q^{31} +(-6.78360 - 3.91651i) q^{32} +(-5.23117 - 3.02022i) q^{33} -1.96679i q^{34} +(0.867030 - 1.50174i) q^{35} +(0.934132 + 1.61796i) q^{36} +(0.642030 - 0.370676i) q^{37} +7.78312 q^{38} +(2.82850 + 2.23597i) q^{39} -0.145630 q^{40} +(7.77507 - 4.48894i) q^{41} +(3.03390 + 5.25486i) q^{42} +(4.27223 - 7.39973i) q^{43} -11.2851i q^{44} +(0.486768 + 0.281036i) q^{45} +(13.9078 + 8.02968i) q^{46} -5.29432i q^{47} +(2.12306 - 3.67724i) q^{48} +(1.25899 + 2.18064i) q^{49} +(-7.97834 + 4.60630i) q^{50} +1.00000 q^{51} +(-0.975523 + 6.66511i) q^{52} +7.35907 q^{53} +(-1.70329 + 0.983395i) q^{54} +(-1.69758 - 2.94029i) q^{55} +(0.399671 - 0.692251i) q^{56} +3.95727i q^{57} +(-7.19833 - 4.15596i) q^{58} +(-5.18146 - 2.99152i) q^{59} +1.05010i q^{60} +(2.47489 - 4.28664i) q^{61} +(-6.29247 - 10.8989i) q^{62} +(-2.67180 + 1.54256i) q^{63} +6.91370 q^{64} +(0.748438 + 1.88331i) q^{65} +11.8803 q^{66} +(6.73711 - 3.88967i) q^{67} +(0.934132 + 1.61796i) q^{68} +(-4.08263 + 7.07133i) q^{69} +3.41053i q^{70} +(8.50173 + 4.90848i) q^{71} +(0.224384 + 0.129548i) q^{72} +8.70107i q^{73} +(-0.729042 + 1.26274i) q^{74} +(-2.34204 - 4.05653i) q^{75} +(-6.40272 + 3.69661i) q^{76} +18.6355 q^{77} +(-7.01661 - 1.02697i) q^{78} +16.8289 q^{79} +(2.06687 - 1.19331i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.82880 + 15.2919i) q^{82} +4.52040i q^{83} +(-4.99162 - 2.88191i) q^{84} +(0.486768 + 0.281036i) q^{85} +16.8052i q^{86} +(2.11307 - 3.65994i) q^{87} +(-0.782526 - 1.35537i) q^{88} +(-4.60853 + 2.66073i) q^{89} -1.10548 q^{90} +(-11.0063 - 1.61091i) q^{91} -15.2549 q^{92} +(5.54145 - 3.19936i) q^{93} +(5.20641 + 9.01777i) q^{94} +(-1.11213 + 1.92627i) q^{95} +7.83303i q^{96} +(-6.67338 - 3.85288i) q^{97} +(-4.28887 - 2.47618i) q^{98} +6.04044i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.70329	+	0.983395i	−1.20441	+	0.695365i	−0.961532	−	0.274692i	$-0.911424\pi$
$2$	−1.70329	+	0.983395i	−1.20441	+	0.695365i	−0.242876	+	0.970057i	$0.578091\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.934132	−	1.61796i	0.467066	−	0.808982i
$5$		−	0.562071i		−	0.251366i	−0.992070	−	0.125683i	$-0.959888\pi$
$5$		−	0.562071i		−	0.251366i	0.992070	−	0.125683i	$-0.0401122\pi$
$6$	1.70329	+	0.983395i	0.695365	+	0.401469i
$7$	2.67180	+	1.54256i	1.00984	+	0.583034i	0.911146	−	0.412084i	$-0.135199\pi$
$7$	2.67180	+	1.54256i	1.00984	+	0.583034i	0.0986979	+	0.995117i	$0.468532\pi$
$8$		−	0.259096i		−	0.0916042i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.552738	+	0.957371i	0.174791	+	0.302747i
$11$	5.23117	−	3.02022i	1.57726	−	0.910630i	0.582018	−	0.813176i	$-0.302263\pi$
$11$	5.23117	−	3.02022i	1.57726	−	0.910630i	0.995240	−	0.0974543i	$-0.0310700\pi$
$12$	−1.86826			−0.539322
$13$	−3.35066	+	1.33157i	−0.929306	+	0.369311i
$13$	−3.35066	+	1.33157i	−0.929306	+	0.369311i
$14$	−6.06779			−1.62169
$15$	−0.486768	+	0.281036i	−0.125683	+	0.0725631i
$16$	2.12306	+	3.67724i	0.530765	+	0.919311i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$		−	1.96679i		−	0.463577i
$19$	−3.42710	−	1.97863i	−0.786230	−	0.453930i	0.0524039	−	0.998626i	$-0.483312\pi$
$19$	−3.42710	−	1.97863i	−0.786230	−	0.453930i	−0.838633	+	0.544696i	$0.816645\pi$
$20$	−0.909411	−	0.525049i	−0.203351	−	0.117404i
$21$		−	3.08512i		−	0.673229i
$22$	−5.94014	+	10.2886i	−1.26644	+	2.19354i
$23$	−4.08263	−	7.07133i	−0.851288	−	1.47447i	−0.880046	−	0.474888i	$-0.842489\pi$
$23$	−4.08263	−	7.07133i	−0.851288	−	1.47447i	0.0287585	−	0.999586i	$-0.490845\pi$
$24$	−0.224384	+	0.129548i	−0.0458021	+	0.0264439i
$25$	4.68408			0.936815
$26$	4.39768	−	5.56308i	0.862457	−	1.09101i
$27$	1.00000			0.192450
$28$	4.99162	−	2.88191i	0.943328	−	0.544631i
$29$	2.11307	+	3.65994i	0.392387	+	0.679634i	0.992764	−	0.120083i	$-0.0383162\pi$
$29$	2.11307	+	3.65994i	0.392387	+	0.679634i	−0.600377	+	0.799717i	$0.704983\pi$
$30$	0.552738	−	0.957371i	0.100916	−	0.174791i
$31$			6.39872i			1.14924i	0.818419	+	0.574622i	$0.194851\pi$
$31$			6.39872i			1.14924i	−0.818419	+	0.574622i	$0.805149\pi$
$32$	−6.78360	−	3.91651i	−1.19918	−	0.692349i
$33$	−5.23117	−	3.02022i	−0.910630	−	0.525753i
$34$		−	1.96679i		−	0.337302i
$35$	0.867030	−	1.50174i	0.146555	−	0.253840i
$36$	0.934132	+	1.61796i	0.155689	+	0.269661i
$37$	0.642030	−	0.370676i	0.105549	−	0.0609388i	−0.446296	−	0.894885i	$-0.647257\pi$
$37$	0.642030	−	0.370676i	0.105549	−	0.0609388i	0.551845	+	0.833947i	$0.313924\pi$
$38$	7.78312			1.26259
$39$	2.82850	+	2.23597i	0.452923	+	0.358042i
$40$	−0.145630			−0.0230262
$41$	7.77507	−	4.48894i	1.21426	−	0.701054i	0.250577	−	0.968097i	$-0.419380\pi$
$41$	7.77507	−	4.48894i	1.21426	−	0.701054i	0.963685	+	0.267043i	$0.0860465\pi$
$42$	3.03390	+	5.25486i	0.468140	+	0.810843i
$43$	4.27223	−	7.39973i	0.651510	−	1.12845i	−0.331247	−	0.943544i	$-0.607469\pi$
$43$	4.27223	−	7.39973i	0.651510	−	1.12845i	0.982757	−	0.184904i	$-0.0591973\pi$
$44$		−	11.2851i		−	1.70130i
$45$	0.486768	+	0.281036i	0.0725631	+	0.0418943i
$46$	13.9078	+	8.02968i	2.05060	+	1.18391i
$47$		−	5.29432i		−	0.772257i	−0.922445	−	0.386128i	$-0.873812\pi$
$47$		−	5.29432i		−	0.772257i	0.922445	−	0.386128i	$-0.126188\pi$
$48$	2.12306	−	3.67724i	0.306437	−	0.530765i
$49$	1.25899	+	2.18064i	0.179856	+	0.311520i
$50$	−7.97834	+	4.60630i	−1.12831	+	0.651429i
$51$	1.00000			0.140028
$52$	−0.975523	+	6.66511i	−0.135281	+	0.924285i
$53$	7.35907			1.01085			0.505423	−	0.862872i	$-0.331336\pi$
$53$	7.35907			1.01085			0.505423	+	0.862872i	$0.331336\pi$
$54$	−1.70329	+	0.983395i	−0.231788	+	0.133823i
$55$	−1.69758	−	2.94029i	−0.228901	−	0.396469i
$56$	0.399671	−	0.692251i	0.0534083	−	0.0925059i
$57$			3.95727i			0.524153i
$58$	−7.19833	−	4.15596i	−0.945188	−	0.545704i
$59$	−5.18146	−	2.99152i	−0.674569	−	0.389463i	0.123237	−	0.992377i	$-0.460673\pi$
$59$	−5.18146	−	2.99152i	−0.674569	−	0.389463i	−0.797806	+	0.602915i	$0.794006\pi$
$60$			1.05010i			0.135567i
$61$	2.47489	−	4.28664i	0.316877	−	0.548848i	−0.662957	−	0.748657i	$-0.730699\pi$
$61$	2.47489	−	4.28664i	0.316877	−	0.548848i	0.979835	+	0.199809i	$0.0640323\pi$
$62$	−6.29247	−	10.8989i	−0.799144	−	1.38416i
$63$	−2.67180	+	1.54256i	−0.336615	+	0.194345i
$64$	6.91370			0.864212
$65$	0.748438	+	1.88331i	0.0928323	+	0.233596i
$66$	11.8803			1.46236
$67$	6.73711	−	3.88967i	0.823069	−	0.475199i	−0.0284046	−	0.999597i	$-0.509043\pi$
$67$	6.73711	−	3.88967i	0.823069	−	0.475199i	0.851474	+	0.524397i	$0.175709\pi$
$68$	0.934132	+	1.61796i	0.113280	+	0.196207i
$69$	−4.08263	+	7.07133i	−0.491491	+	0.851288i
$70$			3.41053i			0.407636i
$71$	8.50173	+	4.90848i	1.00897	+	0.582529i	0.910890	−	0.412649i	$-0.135396\pi$
$71$	8.50173	+	4.90848i	1.00897	+	0.582529i	0.0980802	+	0.995179i	$0.468730\pi$
$72$	0.224384	+	0.129548i	0.0264439	+	0.0152674i
$73$			8.70107i			1.01838i	0.860653	+	0.509191i	$0.170055\pi$
$73$			8.70107i			1.01838i	−0.860653	+	0.509191i	$0.829945\pi$
$74$	−0.729042	+	1.26274i	−0.0847494	+	0.146790i
$75$	−2.34204	−	4.05653i	−0.270435	−	0.468408i
$76$	−6.40272	+	3.69661i	−0.734442	+	0.424031i
$77$	18.6355			2.12371
$78$	−7.01661	−	1.02697i	−0.794474	−	0.116281i
$79$	16.8289			1.89340			0.946702	−	0.322111i	$-0.104392\pi$
$79$	16.8289			1.89340			0.946702	+	0.322111i	$0.104392\pi$
$80$	2.06687	−	1.19331i	0.231083	−	0.133416i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.82880	+	15.2919i	−0.974978	+	1.68871i
$83$			4.52040i			0.496179i	0.968737	+	0.248089i	$0.0798026\pi$
$83$			4.52040i			0.496179i	−0.968737	+	0.248089i	$0.920197\pi$
$84$	−4.99162	−	2.88191i	−0.544631	−	0.314443i
$85$	0.486768	+	0.281036i	0.0527974	+	0.0304826i
$86$			16.8052i			1.81215i
$87$	2.11307	−	3.65994i	0.226545	−	0.392387i
$88$	−0.782526	−	1.35537i	−0.0834176	−	0.144483i
$89$	−4.60853	+	2.66073i	−0.488503	+	0.282037i	−0.723953	−	0.689849i	$-0.757677\pi$
$89$	−4.60853	+	2.66073i	−0.488503	+	0.282037i	0.235450	+	0.971886i	$0.424344\pi$
$90$	−1.10548			−0.116527
$91$	−11.0063	−	1.61091i	−1.15377	−	0.168869i
$92$	−15.2549			−1.59043
$93$	5.54145	−	3.19936i	0.574622	−	0.331758i
$94$	5.20641	+	9.01777i	0.537001	+	0.930112i
$95$	−1.11213	+	1.92627i	−0.114102	+	0.197631i
$96$			7.83303i			0.799455i
$97$	−6.67338	−	3.85288i	−0.677579	−	0.391201i	0.121363	−	0.992608i	$-0.461273\pi$
$97$	−6.67338	−	3.85288i	−0.677579	−	0.391201i	−0.798942	+	0.601408i	$0.794607\pi$
$98$	−4.28887	−	2.47618i	−0.433241	−	0.250132i
$99$			6.04044i			0.607087i
$100$	4.37555	−	7.57867i	0.437555	−	0.757867i
$101$	−5.38906	−	9.33413i	−0.536232	−	0.928781i	−0.999103	−	0.0423551i	$-0.986514\pi$
$101$	−5.38906	−	9.33413i	−0.536232	−	0.928781i	0.462871	−	0.886426i	$-0.346819\pi$
$102$	−1.70329	+	0.983395i	−0.168651	+	0.0973706i
$103$	15.9795			1.57451			0.787254	−	0.616629i	$-0.211502\pi$
$103$	15.9795			1.57451			0.787254	+	0.616629i	$0.211502\pi$
$104$	0.345005	+	0.868142i	0.0338305	+	0.0851283i
$105$	−1.73406			−0.169227
$106$	−12.5346	+	7.23688i	−1.21747	+	0.702908i
$107$	−1.15183	−	1.99502i	−0.111351	−	0.192866i	0.804964	−	0.593324i	$-0.202185\pi$
$107$	−1.15183	−	1.99502i	−0.111351	−	0.192866i	−0.916315	+	0.400457i	$0.868851\pi$
$108$	0.934132	−	1.61796i	0.0898869	−	0.155689i
$109$			4.13594i			0.396151i	0.980187	+	0.198075i	$0.0634691\pi$
$109$			4.13594i			0.396151i	−0.980187	+	0.198075i	$0.936531\pi$
$110$	5.78294	+	3.33878i	0.551381	+	0.318340i
$111$	−0.642030	−	0.370676i	−0.0609388	−	0.0351830i
$112$			13.0998i			1.23781i
$113$	−5.38880	+	9.33368i	−0.506936	+	0.878038i	0.493032	+	0.870011i	$0.335889\pi$
$113$	−5.38880	+	9.33368i	−0.506936	+	0.878038i	−0.999968	+	0.00802729i	$0.997445\pi$
$114$	−3.89156	−	6.74038i	−0.364478	−	0.631294i
$115$	−3.97459	+	2.29473i	−0.370632	+	0.213985i
$116$	7.89554			0.733082
$117$	0.522155	−	3.56754i	0.0482732	−	0.329819i
$118$	11.7674			1.08328
$119$	−2.67180	+	1.54256i	−0.244923	+	0.141406i
$120$	0.0728151	+	0.126120i	0.00664708	+	0.0115131i
$121$	12.7434	−	22.0723i	1.15849	−	2.00657i
$122$			9.73519i			0.881383i
$123$	−7.77507	−	4.48894i	−0.701054	−	0.404754i
$124$	10.3529	+	5.97725i	0.929718	+	0.536773i
$125$		−	5.44314i		−	0.486849i
$126$	3.03390	−	5.25486i	0.270281	−	0.468140i
$127$	−7.56982	−	13.1113i	−0.671713	−	1.16344i	−0.977418	−	0.211315i	$-0.932226\pi$
$127$	−7.56982	−	13.1113i	−0.671713	−	1.16344i	0.305705	−	0.952126i	$-0.401108\pi$
$128$	1.79117	−	1.03414i	0.158319	−	0.0914055i
$129$	−8.54447			−0.752298
$130$	−3.12684	−	2.47181i	−0.274242	−	0.216792i
$131$	−13.5864			−1.18705			−0.593524	−	0.804816i	$-0.702264\pi$
$131$	−13.5864			−1.18705			−0.593524	+	0.804816i	$0.702264\pi$
$132$	−9.77321	+	5.64257i	−0.850649	+	0.491123i
$133$	−6.10433	−	10.5730i	−0.529313	−	0.916797i
$134$	−7.65017	+	13.2505i	−0.660874	+	1.14467i
$135$		−	0.562071i		−	0.0483754i
$136$	0.224384	+	0.129548i	0.0192407	+	0.0111086i
$137$	−16.6491	−	9.61238i	−1.42243	−	0.821241i	−0.425925	−	0.904759i	$-0.640051\pi$
$137$	−16.6491	−	9.61238i	−1.42243	−	0.821241i	−0.996506	+	0.0835179i	$0.973384\pi$
$138$		−	16.0594i		−	1.36706i
$139$	7.92721	−	13.7303i	0.672377	−	1.16459i	−0.304851	−	0.952400i	$-0.598607\pi$
$139$	7.92721	−	13.7303i	0.672377	−	1.16459i	0.977228	−	0.212192i	$-0.0680601\pi$
$140$	−1.61984	−	2.80565i	−0.136902	−	0.237120i
$141$	−4.58502	+	2.64716i	−0.386128	+	0.222931i
$142$	−19.3079			−1.62028
$143$	−13.5062	+	17.0854i	−1.12945	+	1.42875i
$144$	−4.24612			−0.353843
$145$	2.05715	−	1.18769i	0.170837	−	0.0986326i
$146$	−8.55659	−	14.8204i	−0.708148	−	1.22655i
$147$	1.25899	−	2.18064i	0.103840	−	0.179856i
$148$		−	1.38504i		−	0.113850i
$149$	6.99052	+	4.03598i	0.572686	+	0.330640i	0.758221	−	0.651997i	$-0.226069\pi$
$149$	6.99052	+	4.03598i	0.572686	+	0.330640i	−0.185536	+	0.982638i	$0.559402\pi$
$150$	7.97834	+	4.60630i	0.651429	+	0.376103i
$151$			15.9640i			1.29914i	0.760304	+	0.649568i	$0.225050\pi$
$151$			15.9640i			1.29914i	−0.760304	+	0.649568i	$0.774950\pi$
$152$	−0.512656	+	0.887946i	−0.0415819	+	0.0720219i
$153$	−0.500000	−	0.866025i	−0.0404226	−	0.0700140i
$154$	−31.7417	+	18.3261i	−2.55782	+	1.47676i
$155$	3.59653			0.288881
$156$	6.25992	−	2.48773i	0.501195	−	0.199178i
$157$	−16.2504			−1.29692			−0.648461	−	0.761247i	$-0.724587\pi$
$157$	−16.2504			−1.29692			−0.648461	+	0.761247i	$0.724587\pi$
$158$	−28.6646	+	16.5495i	−2.28043	+	1.31661i
$159$	−3.67954	−	6.37314i	−0.291806	−	0.505423i
$160$	−2.20136	+	3.81287i	−0.174033	+	0.301434i
$161$		−	25.1909i		−	1.98532i
$162$	1.70329	+	0.983395i	0.133823	+	0.0772628i
$163$	1.08834	+	0.628351i	0.0852450	+	0.0492162i	0.542017	−	0.840368i	$-0.317661\pi$
$163$	1.08834	+	0.628351i	0.0852450	+	0.0492162i	−0.456772	+	0.889584i	$0.650994\pi$
$164$		−	16.7730i		−	1.30975i
$165$	−1.69758	+	2.94029i	−0.132156	+	0.228901i
$166$	−4.44534	−	7.69956i	−0.345025	−	0.597602i
$167$	0.796711	−	0.459981i	0.0616514	−	0.0355944i	−0.468857	−	0.883274i	$-0.655334\pi$
$167$	0.796711	−	0.459981i	0.0616514	−	0.0355944i	0.530509	+	0.847679i	$0.322001\pi$
$168$	−0.799343			−0.0616706
$169$	9.45383	−	8.92328i	0.727218	−	0.686407i
$170$	−1.10548			−0.0847862
$171$	3.42710	−	1.97863i	0.262077	−	0.151310i
$172$	−7.98166	−	13.8246i	−0.608596	−	1.05412i
$173$	7.05634	−	12.2219i	0.536483	−	0.929217i	−0.462607	−	0.886564i	$-0.653086\pi$
$173$	7.05634	−	12.2219i	0.536483	−	0.929217i	0.999090	−	0.0426528i	$-0.0135809\pi$
$174$			8.31192i			0.630125i
$175$	12.5149	+	7.22548i	0.946037	+	0.546195i
$176$	22.2122	+	12.8242i	1.67431	+	0.966661i
$177$			5.98304i			0.449713i
$178$	5.23311	−	9.06401i	0.392238	−	0.679376i
$179$	2.85477	+	4.94461i	0.213376	+	0.369578i	0.952769	−	0.303696i	$-0.0982208\pi$
$179$	2.85477	+	4.94461i	0.213376	+	0.369578i	−0.739393	+	0.673274i	$0.764887\pi$
$180$	0.909411	−	0.525049i	0.0677835	−	0.0391348i
$181$	19.4796			1.44791			0.723955	−	0.689847i	$-0.242322\pi$
$181$	19.4796			1.44791			0.723955	+	0.689847i	$0.242322\pi$
$182$	20.3311	−	8.07970i	1.50704	−	0.598907i
$183$	−4.94978			−0.365899
$184$	−1.83215	+	1.05779i	−0.135068	+	0.0779816i
$185$	−0.208346	−	0.360866i	−0.0153179	−	0.0265314i
$186$	−6.29247	+	10.8989i	−0.461386	+	0.799144i
$187$			6.04044i			0.441721i
$188$	−8.56603	−	4.94560i	−0.624742	−	0.360695i
$189$	2.67180	+	1.54256i	0.194345	+	0.112205i
$190$		−	4.37467i		−	0.317372i
$191$	1.27963	−	2.21638i	0.0925907	−	0.160372i	−0.816010	−	0.578038i	$-0.803819\pi$
$191$	1.27963	−	2.21638i	0.0925907	−	0.160372i	0.908601	+	0.417666i	$0.137152\pi$
$192$	−3.45685	−	5.98744i	−0.249476	−	0.432106i
$193$	−10.7148	+	6.18622i	−0.771271	+	0.445294i	−0.833328	−	0.552779i	$-0.813567\pi$
$193$	−10.7148	+	6.18622i	−0.771271	+	0.445294i	0.0620567	+	0.998073i	$0.480234\pi$
$194$	15.1556			1.08811
$195$	1.25677	−	1.58982i	0.0899995	−	0.113849i
$196$	4.70427			0.336019
$197$	−8.74592	+	5.04946i	−0.623121	+	0.359759i	−0.778083	−	0.628161i	$-0.783808\pi$
$197$	−8.74592	+	5.04946i	−0.623121	+	0.359759i	0.154962	+	0.987920i	$0.450474\pi$
$198$	−5.94014	−	10.2886i	−0.422147	−	0.731180i
$199$	−3.99148	+	6.91345i	−0.282949	+	0.490082i	−0.972110	−	0.234527i	$-0.924646\pi$
$199$	−3.99148	+	6.91345i	−0.282949	+	0.490082i	0.689161	+	0.724608i	$0.257979\pi$
$200$		−	1.21362i		−	0.0858162i
$201$	−6.73711	−	3.88967i	−0.475199	−	0.274356i
$202$	18.3583	+	10.5992i	1.29168	+	0.745754i
$203$			13.0381i			0.915099i
$204$	0.934132	−	1.61796i	0.0654023	−	0.113280i
$205$	−2.52310	−	4.37014i	−0.176221	−	0.305224i
$206$	−27.2177	+	15.7142i	−1.89635	+	1.09486i
$207$	8.16527			0.567525
$208$	−12.0102	−	9.49419i	−0.832755	−	0.658304i
$209$	−23.9036			−1.65345
$210$	2.95361	−	1.70527i	0.203818	−	0.117675i
$211$	6.66657	+	11.5468i	0.458946	+	0.794917i	0.998906	−	0.0467736i	$-0.0148939\pi$
$211$	6.66657	+	11.5468i	0.458946	+	0.794917i	−0.539960	+	0.841691i	$0.681561\pi$
$212$	6.87435	−	11.9067i	0.472132	−	0.817757i
$213$		−	9.81696i		−	0.672647i
$214$	3.92379	+	2.26540i	0.268225	+	0.154860i
$215$	−4.15917	−	2.40130i	−0.283653	−	0.163767i
$216$		−	0.259096i		−	0.0176292i
$217$	−9.87042	+	17.0961i	−0.670048	+	1.16056i
$218$	−4.06726	−	7.04470i	−0.275470	−	0.477127i
$219$	7.53535	−	4.35053i	0.509191	−	0.293982i
$220$	−6.34305			−0.427648
$221$	0.522155	−	3.56754i	0.0351239	−	0.239979i
$222$	1.45808			0.0978602
$223$	−23.7080	+	13.6878i	−1.58761	+	0.916604i	−0.593905	+	0.804535i	$0.702414\pi$
$223$	−23.7080	+	13.6878i	−1.58761	+	0.916604i	−0.993700	+	0.112069i	$0.964252\pi$
$224$	−12.0829	−	20.9283i	−0.807325	−	1.39833i
$225$	−2.34204	+	4.05653i	−0.156136	+	0.270435i
$226$		−	21.1973i		−	1.41002i
$227$	16.5212	+	9.53850i	1.09655	+	0.633092i	0.935312	−	0.353824i	$-0.115119\pi$
$227$	16.5212	+	9.53850i	1.09655	+	0.633092i	0.161236	+	0.986916i	$0.448452\pi$
$228$	6.40272	+	3.69661i	0.424031	+	0.244814i
$229$		−	17.1978i		−	1.13646i	−0.822870	−	0.568230i	$-0.807628\pi$
$229$		−	17.1978i		−	1.13646i	0.822870	−	0.568230i	$-0.192372\pi$
$230$	4.51325	−	7.81719i	0.297595	−	0.515450i
$231$	−9.31775	−	16.1388i	−0.613063	−	1.06186i
$232$	0.948275	−	0.547487i	0.0622573	−	0.0359443i
$233$	−9.94963			−0.651822			−0.325911	−	0.945400i	$-0.605671\pi$
$233$	−9.94963			−0.651822			−0.325911	+	0.945400i	$0.605671\pi$
$234$	2.61892	+	6.59004i	0.171204	+	0.430805i
$235$	−2.97579			−0.194119
$236$	−9.68034	+	5.58895i	−0.630137	+	0.363810i
$237$	−8.41447	−	14.5743i	−0.546579	−	0.946702i
$238$	3.03390	−	5.25486i	0.196658	−	0.340622i
$239$			27.2630i			1.76350i	0.471719	+	0.881749i	$0.343634\pi$
$239$			27.2630i			1.76350i	−0.471719	+	0.881749i	$0.656366\pi$
$240$	−2.06687	−	1.19331i	−0.133416	−	0.0770278i
$241$	−2.64793	−	1.52878i	−0.170568	−	0.0984774i	0.412286	−	0.911055i	$-0.364731\pi$
$241$	−2.64793	−	1.52878i	−0.170568	−	0.0984774i	−0.582854	+	0.812577i	$0.698064\pi$
$242$			50.1274i			3.22231i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.62375	−	8.00858i	−0.296006	−	0.512697i
$245$	1.22568	−	0.707645i	0.0783056	−	0.0452098i
$246$	17.6576			1.12581
$247$	14.1177	+	2.06631i	0.898289	+	0.131476i
$248$	1.65788			0.105276
$249$	3.91478	−	2.26020i	0.248089	−	0.143234i
$250$	5.35276	+	9.27125i	0.338538	+	0.586365i
$251$	5.56276	−	9.63499i	0.351119	−	0.608155i	−0.635327	−	0.772243i	$-0.719135\pi$
$251$	5.56276	−	9.63499i	0.351119	−	0.608155i	0.986446	+	0.164088i	$0.0524681\pi$
$252$			5.76383i			0.363087i
$253$	−42.7139	−	24.6609i	−2.68540	−	1.55042i
$254$	25.7872	+	14.8882i	1.61803	+	0.934172i
$255$		−	0.562071i		−	0.0351983i
$256$	−8.94762	+	15.4977i	−0.559226	+	0.968608i
$257$	1.62373	+	2.81239i	0.101286	+	0.175432i	0.912215	−	0.409713i	$-0.134371\pi$
$257$	1.62373	+	2.81239i	0.101286	+	0.175432i	−0.810929	+	0.585145i	$0.801038\pi$
$258$	14.5537	−	8.40259i	0.906075	−	0.523122i
$259$	2.28716			0.142117
$260$	3.74627	+	0.548314i	0.232334	+	0.0340050i
$261$	−4.22613			−0.261591
$262$	23.1416	−	13.3608i	1.42969	−	0.825432i
$263$	15.3194	+	26.5340i	0.944634	+	1.63615i	0.756482	+	0.654015i	$0.226917\pi$
$263$	15.3194	+	26.5340i	0.944634	+	1.63615i	0.188152	+	0.982140i	$0.439750\pi$
$264$	−0.782526	+	1.35537i	−0.0481612	+	0.0834176i
$265$		−	4.13632i		−	0.254092i
$266$	20.7949	+	12.0059i	1.27502	+	0.736132i
$267$	4.60853	+	2.66073i	0.282037	+	0.162834i
$268$		−	14.5339i		−	0.887798i
$269$	−3.72224	+	6.44710i	−0.226949	+	0.393087i	−0.956902	−	0.290410i	$-0.906208\pi$
$269$	−3.72224	+	6.44710i	−0.226949	+	0.393087i	0.729954	+	0.683497i	$0.239542\pi$
$270$	0.552738	+	0.957371i	0.0336386	+	0.0582637i
$271$	−8.84350	+	5.10580i	−0.537205	+	0.310155i	−0.743945	−	0.668241i	$-0.767048\pi$
$271$	−8.84350	+	5.10580i	−0.537205	+	0.310155i	0.206741	+	0.978396i	$0.433714\pi$
$272$	−4.24612			−0.257459
$273$	4.10806	+	10.3372i	0.248631	+	0.625636i
$274$	37.8111			2.28425
$275$	24.5032	−	14.1469i	1.47760	−	0.853092i
$276$	7.62744	+	13.2111i	0.459118	+	0.795216i
$277$	−12.3884	+	21.4574i	−0.744350	+	1.28925i	0.206148	+	0.978521i	$0.433907\pi$
$277$	−12.3884	+	21.4574i	−0.744350	+	1.28925i	−0.950498	+	0.310731i	$0.899426\pi$
$278$			31.1823i			1.87019i
$279$	−5.54145	−	3.19936i	−0.331758	−	0.191541i
$280$	−0.389094	−	0.224644i	−0.0232528	−	0.0134250i
$281$			18.8029i			1.12169i	0.827922	+	0.560843i	$0.189523\pi$
$281$			18.8029i			1.12169i	−0.827922	+	0.560843i	$0.810477\pi$
$282$	5.20641	−	9.01777i	0.310037	−	0.537001i
$283$	−1.80239	−	3.12183i	−0.107141	−	0.185574i	0.807470	−	0.589909i	$-0.200836\pi$
$283$	−1.80239	−	3.12183i	−0.107141	−	0.185574i	−0.914611	+	0.404335i	$0.867503\pi$
$284$	15.8835	−	9.17034i	0.942512	−	0.544159i
$285$	2.22427			0.131754
$286$	6.20334	−	42.3834i	0.366811	−	2.50618i
$287$	27.6979			1.63495
$288$	6.78360	−	3.91651i	0.399728	−	0.230783i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−2.33595	+	4.04598i	−0.137171	+	0.237588i
$291$			7.70576i			0.451719i
$292$	14.0780	+	8.12795i	0.823854	+	0.475652i
$293$	−7.79604	−	4.50104i	−0.455449	−	0.262954i	0.254680	−	0.967025i	$-0.418030\pi$
$293$	−7.79604	−	4.50104i	−0.455449	−	0.262954i	−0.710129	+	0.704072i	$0.751363\pi$
$294$			4.95236i			0.288827i
$295$	−1.68145	+	2.91235i	−0.0978976	+	0.169564i
$296$	−0.0960406	−	0.166347i	−0.00558225	−	0.00966873i
$297$	5.23117	−	3.02022i	0.303543	−	0.175251i
$298$	−15.8758			−0.919663
$299$	23.0955	+	18.2573i	1.33565	+	1.05585i
$300$	−8.75109			−0.505245
$301$	22.8291	−	13.1804i	1.31585	−	0.759704i
$302$	−15.6990	−	27.1914i	−0.903374	−	1.56469i
$303$	−5.38906	+	9.33413i	−0.309594	+	0.536232i
$304$		−	16.8030i		−	0.963720i
$305$	−2.40940	−	1.39107i	−0.137962	−	0.0796522i
$306$	1.70329	+	0.983395i	0.0973706	+	0.0562170i
$307$			4.04928i			0.231105i	0.993301	+	0.115552i	$0.0368638\pi$
$307$			4.04928i			0.231105i	−0.993301	+	0.115552i	$0.963136\pi$
$308$	17.4080	−	30.1516i	0.991914	−	1.71805i
$309$	−7.98975	−	13.8387i	−0.454521	−	0.787254i
$310$	−6.12594	+	3.53681i	−0.347930	+	0.200878i
$311$	1.39386			0.0790388			0.0395194	−	0.999219i	$-0.487417\pi$
$311$	1.39386			0.0790388			0.0395194	+	0.999219i	$0.487417\pi$
$312$	0.579331	−	0.732854i	0.0327981	−	0.0414897i
$313$	−1.24637			−0.0704491			−0.0352246	−	0.999379i	$-0.511215\pi$
$313$	−1.24637			−0.0704491			−0.0352246	+	0.999379i	$0.511215\pi$
$314$	27.6791	−	15.9806i	1.56202	−	0.901835i
$315$	0.867030	+	1.50174i	0.0488516	+	0.0846134i
$316$	15.7205	−	27.2286i	0.884345	−	1.53173i
$317$		−	22.7068i		−	1.27534i	−0.770310	−	0.637670i	$-0.779898\pi$
$317$		−	22.7068i		−	1.27534i	0.770310	−	0.637670i	$-0.220102\pi$
$318$	12.5346	+	7.23688i	0.702908	+	0.405824i
$319$	22.1076	+	12.7639i	1.23779	+	0.714638i
$320$		−	3.88599i		−	0.217233i
$321$	−1.15183	+	1.99502i	−0.0642887	+	0.111351i
$322$	24.7726	+	42.9074i	1.38052	+	2.39113i
$323$	3.42710	−	1.97863i	0.190689	−	0.110094i
$324$	−1.86826			−0.103792
$325$	−15.6947	+	6.23718i	−0.870588	+	0.345977i
$326$	−2.47167			−0.136893
$327$	3.58183	−	2.06797i	0.198075	−	0.114359i
$328$	−1.16306	−	2.01449i	−0.0642195	−	0.111231i
$329$	8.16682	−	14.1454i	0.450252	−	0.779859i
$330$		−	6.67756i		−	0.367588i
$331$	1.23714	+	0.714261i	0.0679992	+	0.0392593i	0.533614	−	0.845728i	$-0.320833\pi$
$331$	1.23714	+	0.714261i	0.0679992	+	0.0392593i	−0.465615	+	0.884987i	$0.654167\pi$
$332$	7.31385	+	4.22265i	0.401400	+	0.231748i
$333$			0.741352i			0.0406258i
$334$	−0.904687	+	1.56696i	−0.0495023	+	0.0857405i
$335$	−2.18627	−	3.78674i	−0.119449	−	0.206891i
$336$	11.3448	−	6.54990i	0.618907	−	0.357326i
$337$	19.7837			1.07769			0.538843	−	0.842406i	$-0.318862\pi$
$337$	19.7837			1.07769			0.538843	+	0.842406i	$0.318862\pi$
$338$	−7.32751	+	24.4958i	−0.398564	+	1.33240i
$339$	10.7776			0.585359
$340$	0.909411	−	0.525049i	0.0493198	−	0.0284748i
$341$	19.3255	+	33.4728i	1.04654	+	1.81265i
$342$	−3.89156	+	6.74038i	−0.210431	+	0.364478i
$343$		−	13.8276i		−	0.746618i
$344$	−1.91724	−	1.10692i	−0.103371	−	0.0596810i
$345$	3.97459	+	2.29473i	0.213985	+	0.123544i
$346$			27.7567i			1.49221i
$347$	3.58413	−	6.20789i	0.192406	−	0.333257i	−0.753641	−	0.657286i	$-0.771704\pi$
$347$	3.58413	−	6.20789i	0.192406	−	0.333257i	0.946047	+	0.324029i	$0.105038\pi$
$348$	−3.94777	−	6.83774i	−0.211623	−	0.366541i
$349$	−2.35600	+	1.36024i	−0.126114	+	0.0728120i	−0.561730	−	0.827321i	$-0.689864\pi$
$349$	−2.35600	+	1.36024i	−0.126114	+	0.0728120i	0.435616	+	0.900133i	$0.356531\pi$
$350$	−28.4220			−1.51922
$351$	−3.35066	+	1.33157i	−0.178845	+	0.0710740i
$352$	−47.3149			−2.52189
$353$	0.606391	−	0.350100i	0.0322749	−	0.0186339i	−0.483776	−	0.875192i	$-0.660735\pi$
$353$	0.606391	−	0.350100i	0.0322749	−	0.0186339i	0.516051	+	0.856558i	$0.327402\pi$
$354$	−5.88369	−	10.1909i	−0.312715	−	0.541638i
$355$	2.75891	−	4.77858i	0.146428	−	0.253621i
$356$			9.94191i			0.526920i
$357$	2.67180	+	1.54256i	0.141406	+	0.0816410i
$358$	−9.72501	−	5.61474i	−0.513983	−	0.296748i
$359$			2.63317i			0.138973i	0.997583	+	0.0694866i	$0.0221361\pi$
$359$			2.63317i			0.138973i	−0.997583	+	0.0694866i	$0.977864\pi$
$360$	0.0728151	−	0.126120i	0.00383770	−	0.00664708i
$361$	−1.67001	−	2.89255i	−0.0878954	−	0.152239i
$362$	−33.1795	+	19.1562i	−1.74387	+	1.00683i
$363$	−25.4869			−1.33771
$364$	−12.8877	+	16.3030i	−0.675502	+	0.854510i
$365$	4.89062			0.255987
$366$	8.43092	−	4.86759i	0.440691	−	0.254433i
$367$	2.20827	+	3.82483i	0.115271	+	0.199654i	0.917888	−	0.396840i	$-0.129893\pi$
$367$	2.20827	+	3.82483i	0.115271	+	0.199654i	−0.802617	+	0.596494i	$0.796560\pi$
$368$	17.3353	−	30.0257i	0.903667	−	1.56520i
$369$			8.97787i			0.467369i
$370$	0.709748	+	0.409773i	0.0368981	+	0.0213031i
$371$	19.6619	+	11.3518i	1.02080	+	0.589357i
$372$		−	11.9545i		−	0.619812i
$373$	−6.55017	+	11.3452i	−0.339155	+	0.587433i	−0.984274	−	0.176649i	$-0.943474\pi$
$373$	−6.55017	+	11.3452i	−0.339155	+	0.587433i	0.645119	+	0.764082i	$0.276808\pi$
$374$	−5.94014	−	10.2886i	−0.307157	−	0.532012i
$375$	−4.71390	+	2.72157i	−0.243425	+	0.140541i
$376$	−1.37174			−0.0707420
$377$	−11.9536	−	9.44951i	−0.615644	−	0.486675i
$378$	−6.06779			−0.312094
$379$	−9.63582	+	5.56325i	−0.494959	+	0.285765i	−0.726629	−	0.687030i	$-0.758914\pi$
$379$	−9.63582	+	5.56325i	−0.494959	+	0.285765i	0.231670	+	0.972794i	$0.425581\pi$
$380$	2.07776	+	3.59878i	0.106587	+	0.184614i
$381$	−7.56982	+	13.1113i	−0.387814	+	0.671713i
$382$			5.03352i			0.257537i
$383$	−5.44975	−	3.14642i	−0.278469	−	0.160774i	0.354261	−	0.935147i	$-0.384732\pi$
$383$	−5.44975	−	3.14642i	−0.278469	−	0.160774i	−0.632730	+	0.774372i	$0.718066\pi$
$384$	−1.79117	−	1.03414i	−0.0914055	−	0.0527730i
$385$		−	10.4745i		−	0.533829i
$386$	12.1670	−	21.0738i	0.619284	−	1.07263i
$387$	4.27223	+	7.39973i	0.217170	+	0.376149i
$388$	−12.4676	+	7.19820i	−0.632949	+	0.365433i
$389$	22.4981			1.14070			0.570349	−	0.821403i	$-0.306808\pi$
$389$	22.4981			1.14070			0.570349	+	0.821403i	$0.306808\pi$
$390$	−0.577230	+	3.94383i	−0.0292292	+	0.199704i
$391$	8.16527			0.412935
$392$	0.564995	−	0.326200i	0.0285366	−	0.0164756i
$393$	6.79319	+	11.7662i	0.342671	+	0.593524i
$394$	9.93123	−	17.2014i	0.500328	−	0.866594i
$395$		−	9.45906i		−	0.475937i
$396$	9.77321	+	5.64257i	0.491123	+	0.283550i
$397$	−5.27472	−	3.04536i	−0.264730	−	0.152842i	0.361760	−	0.932271i	$-0.382176\pi$
$397$	−5.27472	−	3.04536i	−0.264730	−	0.152842i	−0.626490	+	0.779429i	$0.715509\pi$
$398$		−	15.7008i		−	0.787011i
$399$	−6.10433	+	10.5730i	−0.305599	+	0.529313i
$400$	9.94457	+	17.2245i	0.497228	+	0.861225i
$401$	−31.1908	+	18.0080i	−1.55759	+	0.899277i	−0.560107	+	0.828421i	$0.689240\pi$
$401$	−31.1908	+	18.0080i	−1.55759	+	0.899277i	−0.997487	+	0.0708562i	$0.977427\pi$
$402$	15.3003			0.763112
$403$	−8.52035	−	21.4399i	−0.424429	−	1.06800i
$404$	−20.1364			−1.00182
$405$	−0.486768	+	0.281036i	−0.0241877	+	0.0139648i
$406$	−12.8217	−	22.2078i	−0.636328	−	1.10215i
$407$	2.23905	−	3.87814i	0.110985	−	0.192232i
$408$		−	0.259096i		−	0.0128272i
$409$	5.40533	+	3.12077i	0.267276	+	0.154312i	0.627649	−	0.778496i	$-0.284017\pi$
$409$	5.40533	+	3.12077i	0.267276	+	0.154312i	−0.360373	+	0.932808i	$0.617351\pi$
$410$	8.59515	+	4.96241i	0.424484	+	0.245076i
$411$			19.2248i			0.948287i
$412$	14.9270	−	25.8543i	0.735399	−	1.27375i
$413$	−9.22921	−	15.9855i	−0.454140	−	0.786593i
$414$	−13.9078	+	8.02968i	−0.683532	+	0.394637i
$415$	2.54079			0.124722
$416$	27.9447	+	4.09005i	1.37010	+	0.200531i
$417$	−15.8544			−0.776395
$418$	40.7148	−	23.5067i	1.99143	−	1.14975i
$419$	−12.8409	−	22.2411i	−0.627319	−	1.08655i	−0.988087	−	0.153893i	$-0.950819\pi$
$419$	−12.8409	−	22.2411i	−0.627319	−	1.08655i	0.360768	−	0.932656i	$-0.382515\pi$
$420$	−1.61984	+	2.80565i	−0.0790401	+	0.136902i
$421$			3.69748i			0.180204i	0.995933	+	0.0901020i	$0.0287193\pi$
$421$			3.69748i			0.180204i	−0.995933	+	0.0901020i	$0.971281\pi$
$422$	−22.7102	−	13.1117i	−1.10552	−	0.638270i
$423$	4.58502	+	2.64716i	0.222931	+	0.128709i
$424$		−	1.90670i		−	0.0925978i
$425$	−2.34204	+	4.05653i	−0.113606	+	0.196771i
$426$	9.65395	+	16.7211i	0.467735	+	0.810141i
$427$	13.2248	−	7.63535i	0.639994	−	0.369500i
$428$	−4.30384			−0.208034
$429$	21.5495	+	3.15404i	1.04042	+	0.152279i
$430$	9.44571			0.455512
$431$	−16.7407	+	9.66524i	−0.806371	+	0.465558i	−0.845694	−	0.533668i	$-0.820813\pi$
$431$	−16.7407	+	9.66524i	−0.806371	+	0.465558i	0.0393233	+	0.999227i	$0.487480\pi$
$432$	2.12306	+	3.67724i	0.102146	+	0.176922i
$433$	−16.7319	+	28.9805i	−0.804084	+	1.39272i	0.112823	+	0.993615i	$0.464011\pi$
$433$	−16.7319	+	28.9805i	−0.804084	+	1.39272i	−0.916907	+	0.399100i	$0.869323\pi$
$434$		−	38.8261i		−	1.86371i
$435$	−2.05715	−	1.18769i	−0.0986326	−	0.0569456i
$436$	6.69180	+	3.86351i	0.320479	+	0.185029i
$437$			32.3122i			1.54570i
$438$	−8.55659	+	14.8204i	−0.408850	+	0.708148i
$439$	16.8348	+	29.1588i	0.803483	+	1.39167i	0.917310	+	0.398173i	$0.130356\pi$
$439$	16.8348	+	29.1588i	0.803483	+	1.39167i	−0.113827	+	0.993501i	$0.536311\pi$
$440$	−0.761817	+	0.439835i	−0.0363182	+	0.0209683i
$441$	−2.51799			−0.119904
$442$	2.61892	+	6.59004i	0.124569	+	0.313456i
$443$	−37.0256			−1.75914			−0.879569	−	0.475771i	$-0.842169\pi$
$443$	−37.0256			−1.75914			−0.879569	+	0.475771i	$0.842169\pi$
$444$	−1.19948	+	0.692521i	−0.0569249	+	0.0328656i
$445$	1.49552	+	2.59032i	0.0708946	+	0.122793i
$446$	26.9211	−	46.6287i	1.27475	−	2.20793i
$447$		−	8.07196i		−	0.381790i
$448$	18.4720	+	10.6648i	0.872719	+	0.503865i
$449$	−23.1734	−	13.3792i	−1.09362	−	0.631402i	−0.159082	−	0.987265i	$-0.550853\pi$
$449$	−23.1734	−	13.3792i	−1.09362	−	0.631402i	−0.934538	+	0.355863i	$0.884187\pi$
$450$		−	9.21260i		−	0.434286i
$451$	27.1151	−	46.9648i	1.27680	−	2.21149i
$452$	10.0677	+	17.4378i	0.473545	+	0.820204i
$453$	13.8253	−	7.98202i	0.649568	−	0.375028i
$454$	−37.5204			−1.76092
$455$	−0.905447	+	6.18633i	−0.0424480	+	0.290020i
$456$	1.02531			0.0480146
$457$	15.5243	−	8.96294i	0.726195	−	0.419269i	−0.0908337	−	0.995866i	$-0.528953\pi$
$457$	15.5243	−	8.96294i	0.726195	−	0.419269i	0.817028	+	0.576597i	$0.195620\pi$
$458$	16.9122	+	29.2928i	0.790255	+	1.36876i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$			8.57433i			0.399780i
$461$	18.4010	+	10.6238i	0.857018	+	0.494800i	0.863013	−	0.505182i	$-0.168575\pi$
$461$	18.4010	+	10.6238i	0.857018	+	0.494800i	−0.00599449	+	0.999982i	$0.501908\pi$
$462$	31.7417	+	18.3261i	1.47676	+	0.852606i
$463$			7.65201i			0.355619i	0.984065	+	0.177809i	$0.0569011\pi$
$463$			7.65201i			0.355619i	−0.984065	+	0.177809i	$0.943099\pi$
$464$	−8.97233	+	15.5405i	−0.416530	+	0.721451i
$465$	−1.79827	−	3.11469i	−0.0833926	−	0.144440i
$466$	16.9471	−	9.78442i	0.785060	−	0.453255i
$467$	−26.0658			−1.20618			−0.603091	−	0.797672i	$-0.706065\pi$
$467$	−26.0658			−1.20618			−0.603091	+	0.797672i	$0.706065\pi$
$468$	−5.28439	−	4.17738i	−0.244271	−	0.193100i
$469$	24.0002			1.10823
$470$	5.06863	−	2.92638i	0.233798	−	0.134984i
$471$	8.12520	+	14.0733i	0.374389	+	0.648461i
$472$	−0.775090	+	1.34250i	−0.0356764	+	0.0617934i
$473$		−	51.6123i		−	2.37314i
$474$	28.6646	+	16.5495i	1.31661	+	0.760144i
$475$	−16.0528	−	9.26807i	−0.736552	−	0.425248i
$476$			5.76383i			0.264185i
$477$	−3.67954	+	6.37314i	−0.168474	+	0.291806i
$478$	−26.8103	−	46.4368i	−1.22628	−	2.12397i
$479$	−22.7452	+	13.1320i	−1.03926	+	0.600014i	−0.919622	−	0.392804i	$-0.871505\pi$
$479$	−22.7452	+	13.1320i	−1.03926	+	0.600014i	−0.119633	+	0.992818i	$0.538172\pi$
$480$	4.40272			0.200956
$481$	−1.65764	+	2.09692i	−0.0755819	+	0.0956112i
$482$	6.01358			0.273911
$483$	−21.8159	+	12.5954i	−0.992659	+	0.573112i
$484$	−23.8081	−	41.2369i	−1.08219	−	1.87440i
$485$	−2.16559	+	3.75092i	−0.0983345	+	0.170320i
$486$		−	1.96679i		−	0.0892154i
$487$	−20.7002	−	11.9513i	−0.938017	−	0.541564i	−0.0486790	−	0.998814i	$-0.515501\pi$
$487$	−20.7002	−	11.9513i	−0.938017	−	0.541564i	−0.889338	+	0.457250i	$0.848834\pi$
$488$	−1.11065	−	0.641234i	−0.0502768	−	0.0290273i
$489$		−	1.25670i		−	0.0568300i
$490$	−1.39179	+	2.41065i	−0.0628746	+	0.108902i
$491$	8.07466	+	13.9857i	0.364404	+	0.631167i	0.988680	−	0.150037i	$-0.0479392\pi$
$491$	8.07466	+	13.9857i	0.364404	+	0.631167i	−0.624276	+	0.781204i	$0.714606\pi$
$492$	−14.5259	+	8.38652i	−0.654877	+	0.378094i
$493$	−4.22613			−0.190336
$494$	−26.0786	+	10.3638i	−1.17333	+	0.466288i
$495$	3.39516			0.152601
$496$	−23.5296	+	13.5848i	−1.05651	+	0.609978i
$497$	15.1433	+	26.2289i	0.679268	+	1.17653i
$498$	−4.44534	+	7.69956i	−0.199201	+	0.345025i
$499$		−	14.7230i		−	0.659091i	−0.944140	−	0.329546i	$-0.893104\pi$
$499$		−	14.7230i		−	0.659091i	0.944140	−	0.329546i	$-0.106896\pi$
$500$	−8.80681	−	5.08461i	−0.393852	−	0.227391i
$501$	−0.796711	−	0.459981i	−0.0355944	−	0.0205505i
$502$			21.8816i			0.976623i
$503$	15.8169	−	27.3957i	0.705240	−	1.22151i	−0.261364	−	0.965240i	$-0.584172\pi$
$503$	15.8169	−	27.3957i	0.705240	−	1.22151i	0.966605	−	0.256272i	$-0.0824943\pi$
$504$	0.399671	+	0.692251i	0.0178028	+	0.0308353i
$505$	−5.24645	+	3.02904i	−0.233464	+	0.134790i
$506$	97.0056			4.31243
$507$	−12.4547	−	3.72562i	−0.553133	−	0.165461i
$508$	−28.2849			−1.25494
$509$	−6.45996	+	3.72966i	−0.286333	+	0.165314i	−0.636287	−	0.771453i	$-0.719531\pi$
$509$	−6.45996	+	3.72966i	−0.286333	+	0.165314i	0.349954	+	0.936767i	$0.386197\pi$
$510$	0.552738	+	0.957371i	0.0244757	+	0.0423931i
$511$	−13.4219	+	23.2475i	−0.593751	+	1.02841i
$512$		−	31.0597i		−	1.37266i
$513$	−3.42710	−	1.97863i	−0.151310	−	0.0873588i
$514$	−5.53138	−	3.19354i	−0.243979	−	0.140861i
$515$		−	8.98162i		−	0.395778i
$516$	−7.98166	+	13.8246i	−0.351373	+	0.608596i
$517$	−15.9900	−	27.6955i	−0.703240	−	1.21805i
$518$	−3.89570	+	2.24918i	−0.171167	+	0.0988235i
$519$	−14.1127			−0.619478
$520$	0.487957	−	0.193917i	0.0213984	−	0.00850383i
$521$	−13.0678			−0.572511			−0.286256	−	0.958153i	$-0.592411\pi$
$521$	−13.0678			−0.572511			−0.286256	+	0.958153i	$0.592411\pi$
$522$	7.19833	−	4.15596i	0.315063	−	0.181901i
$523$	−12.0462	−	20.8646i	−0.526744	−	0.912347i	−0.999514	−	0.0311614i	$-0.990079\pi$
$523$	−12.0462	−	20.8646i	−0.526744	−	0.912347i	0.472771	−	0.881186i	$-0.343254\pi$
$524$	−12.6915	+	21.9823i	−0.554430	+	0.960301i
$525$		−	14.4510i		−	0.630691i
$526$	−52.1868	−	30.1300i	−2.27545	−	1.31373i
$527$	−5.54145	−	3.19936i	−0.241389	−	0.139366i
$528$		−	25.6484i		−	1.11620i
$529$	−21.8358	+	37.8207i	−0.949382	+	1.64438i
$530$	4.06764	+	7.04536i	0.176687	+	0.306031i
$531$	5.18146	−	2.99152i	0.224856	−	0.129821i
$532$	−22.8090			−0.988896
$533$	−20.0743	+	25.3940i	−0.869513	+	1.09993i
$534$	−10.4662			−0.452917
$535$	−1.12135	+	0.647409i	−0.0484800	+	0.0279899i
$536$	−1.00780	−	1.74556i	−0.0435302	−	0.0753966i
$537$	2.85477	−	4.94461i	0.123193	−	0.213376i
$538$		−	14.6417i		−	0.631249i
$539$	13.1720	+	7.60488i	0.567360	+	0.327565i
$540$	−0.909411	−	0.525049i	−0.0391348	−	0.0225945i
$541$		−	6.66483i		−	0.286543i	−0.989683	−	0.143272i	$-0.954238\pi$
$541$		−	6.66483i		−	0.286543i	0.989683	−	0.143272i	$-0.0457623\pi$
$542$	10.0420	−	17.3933i	0.431342	−	0.747107i
$543$	−9.73982	−	16.8699i	−0.417975	−	0.723955i
$544$	6.78360	−	3.91651i	0.290845	−	0.167919i
$545$	2.32469			0.0995788
$546$	−17.1628	−	13.5674i	−0.734499	−	0.580631i
$547$	28.6141			1.22345			0.611725	−	0.791070i	$-0.290476\pi$
$547$	28.6141			1.22345			0.611725	+	0.791070i	$0.290476\pi$
$548$	−31.1050	+	17.9585i	−1.32874	+	0.767148i
$549$	2.47489	+	4.28664i	0.105626	+	0.182949i
$550$	−27.8241	+	48.1927i	−1.18642	+	2.05494i
$551$		−	16.7239i		−	0.712464i
$552$	1.83215	+	1.05779i	0.0779816	+	0.0450227i
$553$	44.9635	+	25.9597i	1.91204	+	1.10392i
$554$		−	48.7310i		−	2.07038i
$555$	−0.208346	+	0.360866i	−0.00884381	+	0.0153179i
$556$	−14.8101	−	25.6519i	−0.628090	−	1.08788i
$557$	14.9472	−	8.62978i	0.633334	−	0.365656i	−0.148708	−	0.988881i	$-0.547512\pi$
$557$	14.9472	−	8.62978i	0.633334	−	0.365656i	0.782042	+	0.623226i	$0.214178\pi$
$558$	12.5849			0.532763
$559$	−4.46154	+	30.4827i	−0.188703	+	1.28928i
$560$	7.36302			0.311144
$561$	5.23117	−	3.02022i	0.220860	−	0.127514i
$562$	−18.4907	−	32.0267i	−0.779981	−	1.35097i
$563$	−13.1649	+	22.8022i	−0.554833	+	0.960999i	0.443083	+	0.896480i	$0.353885\pi$
$563$	−13.1649	+	22.8022i	−0.554833	+	0.960999i	−0.997916	+	0.0645187i	$0.979449\pi$
$564$			9.89120i			0.416495i
$565$	5.24619	+	3.02889i	0.220709	+	0.127426i
$566$	6.13999	+	3.54493i	0.258083	+	0.149004i
$567$		−	3.08512i		−	0.129563i
$568$	1.27177	−	2.20276i	0.0533621	−	0.0924259i
$569$	−19.5814	−	33.9160i	−0.820895	−	1.42183i	−0.905017	−	0.425376i	$-0.860142\pi$
$569$	−19.5814	−	33.9160i	−0.820895	−	1.42183i	0.0841224	−	0.996455i	$-0.473191\pi$
$570$	−3.78857	+	2.18733i	−0.158686	+	0.0916173i
$571$	29.3757			1.22934			0.614668	−	0.788786i	$-0.289290\pi$
$571$	29.3757			1.22934			0.614668	+	0.788786i	$0.289290\pi$
$572$	15.0270	+	37.8126i	0.628309	+	1.58103i
$573$	−2.55926			−0.106915
$574$	−47.1775	+	27.2379i	−1.96915	+	1.13689i
$575$	−19.1234	−	33.1226i	−0.797499	−	1.38131i
$576$	−3.45685	+	5.98744i	−0.144035	+	0.249476i
$577$			14.9551i			0.622588i	0.950314	+	0.311294i	$0.100762\pi$
$577$			14.9551i			0.622588i	−0.950314	+	0.311294i	$0.899238\pi$
$578$	1.70329	+	0.983395i	0.0708475	+	0.0409038i
$579$	10.7148	+	6.18622i	0.445294	+	0.257090i
$580$		−	4.43785i		−	0.184272i
$581$	−6.97300	+	12.0776i	−0.289289	+	0.501063i
$582$	−7.57780	−	13.1251i	−0.314110	−	0.544055i
$583$	38.4966	−	22.2260i	1.59437	−	0.920507i
$584$	2.25441			0.0932882
$585$	−2.00521	−	0.293488i	−0.0829053	−	0.0121342i
$586$	17.7052			0.731396
$587$	−25.4814	+	14.7117i	−1.05173	+	0.607217i	−0.923133	−	0.384480i	$-0.874381\pi$
$587$	−25.4814	+	14.7117i	−1.05173	+	0.607217i	−0.128597	+	0.991697i	$0.541047\pi$
$588$	−2.35214	−	4.07402i	−0.0970004	−	0.168010i
$589$	12.6607	−	21.9290i	0.521676	−	0.903569i
$590$		−	6.61411i		−	0.272298i
$591$	8.74592	+	5.04946i	0.359759	+	0.207707i
$592$	2.72613	+	1.57393i	0.112043	+	0.0646883i
$593$			5.44237i			0.223491i	0.993737	+	0.111746i	$0.0356442\pi$
$593$			5.44237i			0.223491i	−0.993737	+	0.111746i	$0.964356\pi$
$594$	−5.94014	+	10.2886i	−0.243727	+	0.422147i
$595$	0.867030	+	1.50174i	0.0355447	+	0.0615653i
$596$	13.0601	−	7.54028i	0.534964	−	0.308862i
$597$	7.98297			0.326721
$598$	−57.2925	−	8.38548i	−2.34286	−	0.342908i
$599$	22.9249			0.936684			0.468342	−	0.883547i	$-0.344851\pi$
$599$	22.9249			0.936684			0.468342	+	0.883547i	$0.344851\pi$
$600$	−1.05103	+	0.606812i	−0.0429081	+	0.0247730i
$601$	−5.08894	−	8.81430i	−0.207582	−	0.359543i	0.743370	−	0.668880i	$-0.233226\pi$
$601$	−5.08894	−	8.81430i	−0.207582	−	0.359543i	−0.950952	+	0.309337i	$0.899893\pi$
$602$	−25.9230	+	44.9000i	−1.05654	+	1.82999i
$603$			7.77935i			0.316799i
$604$	25.8293	+	14.9125i	1.05098	+	0.606782i
$605$	−12.4062	−	7.16272i	−0.504384	−	0.291206i
$606$		−	21.1983i		−	0.861123i
$607$	−9.94045	+	17.2174i	−0.403470	+	0.698831i	−0.994142	−	0.108081i	$-0.965530\pi$
$607$	−9.94045	+	17.2174i	−0.403470	+	0.698831i	0.590672	+	0.806912i	$0.298863\pi$
$608$	15.4987	+	26.8445i	0.628555	+	1.08869i
$609$	11.2914	−	6.51907i	0.457549	−	0.264166i
$610$	5.47187			0.221550
$611$	7.04977	+	17.7395i	0.285203	+	0.717662i
$612$	−1.86826			−0.0755201
$613$	8.17757	−	4.72132i	0.330289	−	0.190692i	−0.325680	−	0.945480i	$-0.605593\pi$
$613$	8.17757	−	4.72132i	0.330289	−	0.190692i	0.655969	+	0.754787i	$0.272260\pi$
$614$	−3.98204	−	6.89710i	−0.160702	−	0.278344i
$615$	−2.52310	+	4.37014i	−0.101741	+	0.176221i
$616$		−	4.82838i		−	0.194541i
$617$	−35.9807	−	20.7734i	−1.44853	−	0.836307i	−0.450133	−	0.892961i	$-0.648623\pi$
$617$	−35.9807	−	20.7734i	−1.44853	−	0.836307i	−0.998394	+	0.0566540i	$0.981957\pi$
$618$	27.2177	+	15.7142i	1.09486	+	0.632117i
$619$			14.8723i			0.597767i	0.954290	+	0.298883i	$0.0966142\pi$
$619$			14.8723i			0.597767i	−0.954290	+	0.298883i	$0.903386\pi$
$620$	3.35964	−	5.81907i	0.134926	−	0.233699i
$621$	−4.08263	−	7.07133i	−0.163830	−	0.283763i
$622$	−2.37416	+	1.37072i	−0.0951950	+	0.0549609i
$623$	−16.4174			−0.657749
$624$	−2.21713	+	15.1482i	−0.0887562	+	0.606413i
$625$	20.3609			0.814438
$626$	2.12293	−	1.22568i	0.0848495	−	0.0489879i
$627$	11.9518	+	20.7012i	0.477310	+	0.826725i
$628$	−15.1800	+	26.2926i	−0.605749	+	1.04919i
$629$			0.741352i			0.0295596i
$630$	−2.95361	−	1.70527i	−0.117675	−	0.0679394i
$631$	13.7708	+	7.95060i	0.548209	+	0.316508i	0.748399	−	0.663249i	$-0.230823\pi$
$631$	13.7708	+	7.95060i	0.548209	+	0.316508i	−0.200190	+	0.979757i	$0.564156\pi$
$632$		−	4.36031i		−	0.173444i
$633$	6.66657	−	11.5468i	0.264972	−	0.458946i
$634$	22.3297	+	38.6762i	0.886827	+	1.53603i
$635$	−7.36949	+	4.25478i	−0.292449	+	0.168846i
$636$	−13.7487			−0.545171
$637$	−7.12214	−	5.63015i	−0.282190	−	0.223075i
$638$	−50.2076			−1.98774
$639$	−8.50173	+	4.90848i	−0.336323	+	0.194176i
$640$	−0.581258	−	1.00677i	−0.0229762	−	0.0397960i
$641$	4.90257	−	8.49149i	0.193640	−	0.335394i	−0.752814	−	0.658233i	$-0.771304\pi$
$641$	4.90257	−	8.49149i	0.193640	−	0.335394i	0.946454	+	0.322839i	$0.104637\pi$
$642$		−	4.53081i		−	0.178817i
$643$	20.3680	+	11.7595i	0.803235	+	0.463748i	0.844601	−	0.535396i	$-0.179838\pi$
$643$	20.3680	+	11.7595i	0.803235	+	0.463748i	−0.0413662	+	0.999144i	$0.513171\pi$
$644$	−40.7579	−	23.5316i	−1.60609	−	0.927275i
$645$			4.80260i			0.189102i
$646$	−3.89156	+	6.74038i	−0.153111	+	0.265197i
$647$	12.9919	+	22.5027i	0.510766	+	0.884673i	0.999922	+	0.0124766i	$0.00397154\pi$
$647$	12.9919	+	22.5027i	0.510766	+	0.884673i	−0.489156	+	0.872196i	$0.662695\pi$
$648$	−0.224384	+	0.129548i	−0.00881462	+	0.00508912i
$649$	−36.1402			−1.41863
$650$	20.5991	−	26.0579i	0.807963	−	1.02207i
$651$	19.7408			0.773704
$652$	2.03330	−	1.17393i	0.0796301	−	0.0459745i
$653$	7.11881	+	12.3301i	0.278581	+	0.482516i	0.971032	−	0.238948i	$-0.0768027\pi$
$653$	7.11881	+	12.3301i	0.278581	+	0.482516i	−0.692452	+	0.721464i	$0.743469\pi$
$654$	−4.06726	+	7.04470i	−0.159042	+	0.275470i
$655$			7.63652i			0.298383i
$656$	33.0138	+	19.0605i	1.28897	+	0.744189i
$657$	−7.53535	−	4.35053i	−0.293982	−	0.169730i
$658$			32.1249i			1.25236i
$659$	7.77559	−	13.4677i	0.302894	−	0.524628i	−0.673896	−	0.738826i	$-0.735381\pi$
$659$	7.77559	−	13.4677i	0.302894	−	0.524628i	0.976790	+	0.214198i	$0.0687138\pi$
$660$	3.17153	+	5.49324i	0.123451	+	0.213824i
$661$	−8.46802	+	4.88902i	−0.329368	+	0.190161i	−0.655560	−	0.755143i	$-0.727568\pi$
$661$	−8.46802	+	4.88902i	−0.329368	+	0.190161i	0.326193	+	0.945303i	$0.394234\pi$
$662$	−2.80960			−0.109198
$663$	−3.35066	+	1.33157i	−0.130129	+	0.0517140i
$664$	1.17122			0.0454520
$665$	−5.94279	+	3.43107i	−0.230451	+	0.133051i
$666$	−0.729042	−	1.26274i	−0.0282498	−	0.0489301i
$667$	17.2538	−	29.8844i	0.668068	−	1.15713i
$668$		−	1.71873i		−	0.0664998i
$669$	23.7080	+	13.6878i	0.916604	+	0.529202i
$670$	7.44772	+	4.29994i	0.287730	+	0.166121i
$671$		−	29.8989i		−	1.15423i
$672$	−12.0829	+	20.9283i	−0.466109	+	0.807325i
$673$	2.64019	+	4.57294i	0.101772	+	0.176274i	0.912415	−	0.409267i	$-0.134215\pi$
$673$	2.64019	+	4.57294i	0.101772	+	0.176274i	−0.810643	+	0.585541i	$0.800882\pi$
$674$	−33.6973	+	19.4552i	−1.29797	+	0.749385i
$675$	4.68408			0.180290
$676$	−5.60643	−	23.6315i	−0.215632	−	0.908904i
$677$	−29.5267			−1.13480			−0.567401	−	0.823441i	$-0.692051\pi$
$677$	−29.5267			−1.13480			−0.567401	+	0.823441i	$0.692051\pi$
$678$	−18.3574	+	10.5986i	−0.705011	+	0.407038i
$679$	−11.8866	−	20.5882i	−0.456166	−	0.790103i
$680$	0.0728151	−	0.126120i	0.00279233	−	0.00483646i
$681$		−	19.0770i		−	0.731032i
$682$	−65.8340	−	38.0093i	−2.52091	−	1.45545i
$683$	23.0773	+	13.3237i	0.883030	+	0.509817i	0.871656	−	0.490118i	$-0.163046\pi$
$683$	23.0773	+	13.3237i	0.883030	+	0.509817i	0.0113734	+	0.999935i	$0.496380\pi$
$684$		−	7.39323i		−	0.282687i
$685$	−5.40284	+	9.35799i	−0.206432	+	0.357551i
$686$	13.5980	+	23.5523i	0.519172	+	0.899233i
$687$	−14.8937	+	8.59888i	−0.568230	+	0.328068i
$688$	36.2808			1.38319
$689$	−24.6577	+	9.79913i	−0.939385	+	0.373317i
$690$	−9.02651			−0.343633
$691$	2.84535	−	1.64276i	0.108242	−	0.0624937i	−0.444902	−	0.895579i	$-0.646761\pi$
$691$	2.84535	−	1.64276i	0.108242	−	0.0624937i	0.553144	+	0.833086i	$0.313428\pi$
$692$	−13.1831	−	22.8338i	−0.501147	−	0.868011i
$693$	−9.31775	+	16.1388i	−0.353952	+	0.613063i
$694$			14.0985i			0.535170i
$695$	−7.71743	−	4.45566i	−0.292739	−	0.169013i
$696$	−0.948275	−	0.547487i	−0.0359443	−	0.0207524i
$697$			8.97787i			0.340061i
$698$	2.67531	−	4.63377i	0.101262	−	0.175391i
$699$	4.97482	+	8.61664i	0.188165	+	0.325911i
$700$	23.3811	−	13.4991i	0.883724	−	0.510218i
$701$	−26.0823			−0.985116			−0.492558	−	0.870280i	$-0.663938\pi$
$701$	−26.0823			−0.985116			−0.492558	+	0.870280i	$0.663938\pi$
$702$	4.39768	−	5.56308i	0.165980	−	0.209965i
$703$	−2.93373			−0.110648
$704$	36.1667	−	20.8809i	1.36309	−	0.786977i
$705$	1.48789	+	2.57711i	0.0560373	+	0.0970595i
$706$	−0.688573	+	1.19264i	−0.0259148	+	0.0448857i
$707$		−	33.2519i		−	1.25056i
$708$	9.68034	+	5.58895i	0.363810	+	0.210046i
$709$	−27.9194	−	16.1193i	−1.04853	−	0.605372i	−0.126296	−	0.991993i	$-0.540309\pi$
$709$	−27.9194	−	16.1193i	−1.04853	−	0.605372i	−0.922239	+	0.386621i	$0.873642\pi$
$710$			10.8524i			0.407284i
$711$	−8.41447	+	14.5743i	−0.315567	+	0.546579i
$712$	0.689385	+	1.19405i	0.0258358	+	0.0447489i
$713$	45.2474	−	26.1236i	1.69453	−	0.978337i
$714$	−6.06779			−0.227081
$715$	9.60321	+	7.59147i	0.359140	+	0.283905i
$716$	10.6669			0.398642
$717$	23.6105	−	13.6315i	0.881749	−	0.509078i
$718$	−2.58944	−	4.48505i	−0.0966371	−	0.167380i
$719$	7.55564	−	13.0868i	0.281778	−	0.488053i	−0.690045	−	0.723767i	$-0.742409\pi$
$719$	7.55564	−	13.0868i	0.281778	−	0.488053i	0.971823	+	0.235713i	$0.0757426\pi$
$720$			2.38662i			0.0889441i
$721$	42.6940	+	24.6494i	1.59001	+	0.917991i
$722$	5.68903	+	3.28456i	0.211724	+	0.122239i
$723$			3.05756i			0.113712i
$724$	18.1966	−	31.5174i	0.676270	−	1.17133i
$725$	9.89777	+	17.1434i	0.367594	+	0.636691i
$726$	43.4116	−	25.0637i	1.61115	−	0.930201i
$727$	−12.1366			−0.450120			−0.225060	−	0.974345i	$-0.572258\pi$
$727$	−12.1366			−0.450120			−0.225060	+	0.974345i	$0.572258\pi$
$728$	−0.417381	+	2.85169i	−0.0154692	+	0.105691i
$729$	1.00000			0.0370370
$730$	−8.33015	+	4.80941i	−0.308313	+	0.178004i
$731$	4.27223	+	7.39973i	0.158014	+	0.273689i
$732$	−4.62375	+	8.00858i	−0.170899	+	0.296006i
$733$			33.8030i			1.24854i	0.781207	+	0.624271i	$0.214604\pi$
$733$			33.8030i			1.24854i	−0.781207	+	0.624271i	$0.785396\pi$
$734$	−7.52263	−	4.34320i	−0.277666	−	0.160310i
$735$	−1.22568	−	0.707645i	−0.0452098	−	0.0261019i
$736$			63.9588i			2.35755i
$737$	23.4953	−	40.6951i	0.865461	−	1.49902i
$738$	−8.82880	−	15.2919i	−0.324993	−	0.562904i
$739$	30.5298	−	17.6264i	1.12306	−	0.648396i	0.180876	−	0.983506i	$-0.442107\pi$
$739$	30.5298	−	17.6264i	1.12306	−	0.648396i	0.942179	+	0.335110i	$0.108773\pi$
$740$	−0.778492			−0.0286179
$741$	−5.26939	−	13.2595i	−0.193576	−	0.487098i
$742$	−44.6533			−1.63928
$743$	−20.5586	+	11.8695i	−0.754223	+	0.435451i	−0.827218	−	0.561882i	$-0.810078\pi$
$743$	−20.5586	+	11.8695i	−0.754223	+	0.435451i	0.0729949	+	0.997332i	$0.476744\pi$
$744$	−0.828940	−	1.43577i	−0.0303904	−	0.0526378i
$745$	2.26851	−	3.92917i	0.0831117	−	0.143954i
$746$		−	25.7656i		−	0.943346i
$747$	−3.91478	−	2.26020i	−0.143234	−	0.0826964i
$748$	9.77321	+	5.64257i	0.357344	+	0.206313i
$749$		−	7.10706i		−	0.259686i
$750$	5.35276	−	9.27125i	0.195455	−	0.338538i
$751$	−22.3312	−	38.6788i	−0.814877	−	1.41141i	−0.909416	−	0.415888i	$-0.863471\pi$
$751$	−22.3312	−	38.6788i	−0.814877	−	1.41141i	0.0945387	−	0.995521i	$-0.469862\pi$
$752$	19.4685	−	11.2402i	0.709944	−	0.409886i
$753$	−11.1255			−0.405437
$754$	29.6531	+	4.34011i	1.07990	+	0.158057i
$755$	8.97293			0.326558
$756$	4.99162	−	2.88191i	0.181544	−	0.104814i
$757$	−4.53583	−	7.85629i	−0.164858	−	0.285542i	0.771747	−	0.635929i	$-0.219383\pi$
$757$	−4.53583	−	7.85629i	−0.164858	−	0.285542i	−0.936605	+	0.350388i	$0.886050\pi$
$758$	10.9417	−	18.9516i	0.397422	−	0.688355i
$759$			49.3218i			1.79027i
$760$	0.499089	+	0.288149i	0.0181039	+	0.0104523i
$761$	21.4038	+	12.3575i	0.775887	+	0.447959i	0.834971	−	0.550294i	$-0.185485\pi$
$761$	21.4038	+	12.3575i	0.775887	+	0.447959i	−0.0590836	+	0.998253i	$0.518818\pi$
$762$		−	29.7765i		−	1.07869i
$763$	−6.37994	+	11.0504i	−0.230969	+	0.400051i
$764$	−2.39069	−	4.14079i	−0.0864920	−	0.149808i
$765$	−0.486768	+	0.281036i	−0.0175991	+	0.0101609i
$766$	12.3767			0.447188
$767$	21.3447	+	3.12407i	0.770714	+	0.112804i
$768$	17.8952			0.645739
$769$	−40.1729	+	23.1939i	−1.44867	+	0.836392i	−0.998403	−	0.0565001i	$-0.982006\pi$
$769$	−40.1729	+	23.1939i	−1.44867	+	0.836392i	−0.450271	+	0.892892i	$0.648673\pi$
$770$	10.3006	+	17.8411i	0.371206	+	0.642948i
$771$	1.62373	−	2.81239i	0.0584773	−	0.101286i
$772$			23.1150i			0.831926i
$773$	41.7194	+	24.0867i	1.50054	+	0.866338i	1.00000		0.000624889i	$0.000198909\pi$
$773$	41.7194	+	24.0867i	1.50054	+	0.866338i	0.500541	+	0.865713i	$0.333134\pi$
$774$	−14.5537	−	8.40259i	−0.523122	−	0.302025i
$775$			29.9721i			1.07663i
$776$	−0.998265	+	1.72905i	−0.0358356	+	0.0620691i
$777$	−1.14358	−	1.98074i	−0.0410258	−	0.0710587i
$778$	−38.3208	+	22.1245i	−1.37387	+	0.793202i
$779$	−35.5279			−1.27292
$780$	−1.39828	−	3.51852i	−0.0500665	−	0.125983i
$781$	59.2987			2.12188
$782$	−13.9078	+	8.02968i	−0.497343	+	0.287141i
$783$	2.11307	+	3.65994i	0.0755149	+	0.130796i
$784$	−5.34584	+	9.25926i	−0.190923	+	0.330688i
$785$			9.13388i			0.326002i
$786$	−23.1416	−	13.3608i	−0.825432	−	0.476564i
$787$	−24.0439	−	13.8817i	−0.857071	−	0.494830i	0.00595920	−	0.999982i	$-0.498103\pi$
$787$	−24.0439	−	13.8817i	−0.857071	−	0.494830i	−0.863030	+	0.505152i	$0.831436\pi$
$788$			18.8675i			0.672125i
$789$	15.3194	−	26.5340i	0.545385	−	0.944634i
$790$	9.30200	+	16.1115i	0.330950	+	0.573223i
$791$	−28.7955	+	16.6251i	−1.02385	+	0.591121i
$792$	1.56505			0.0556117
$793$	−2.58455	+	17.6586i	−0.0917802	+	0.627074i
$794$	11.9792			0.425125
$795$	−3.58216	+	2.06816i	−0.127046	+	0.0733501i
$796$	7.45715	+	12.9162i	0.264312	+	0.457801i
$797$	6.87484	−	11.9076i	0.243519	−	0.421788i	−0.718195	−	0.695842i	$-0.755031\pi$
$797$	6.87484	−	11.9076i	0.243519	−	0.421788i	0.961714	+	0.274054i	$0.0883647\pi$
$798$		−	24.0119i		−	0.850011i
$799$	4.58502	+	2.64716i	0.162206	+	0.0936499i
$800$	−31.7749	−	18.3453i	−1.12341	−	0.648603i
$801$		−	5.32147i		−	0.188025i
$802$	35.4180	−	61.3457i	1.25065	−	2.16619i
$803$	26.2791	+	45.5168i	0.927370	+	1.60625i
$804$	−12.5867	+	7.26694i	−0.443899	+	0.256285i
$805$	−14.1591			−0.499041
$806$	35.5965	+	28.1395i	1.25383	+	0.991173i
$807$	7.44447			0.262058
$808$	−2.41843	+	1.39628i	−0.0850802	+	0.0491211i
$809$	−13.9620	−	24.1829i	−0.490879	−	0.850227i	0.509066	−	0.860727i	$-0.329991\pi$
$809$	−13.9620	−	24.1829i	−0.490879	−	0.850227i	−0.999945	+	0.0105004i	$0.996658\pi$
$810$	0.552738	−	0.957371i	0.0194212	−	0.0336386i
$811$			0.352736i			0.0123862i	0.999981	+	0.00619312i	$0.00197134\pi$
$811$			0.352736i			0.0123862i	−0.999981	+	0.00619312i	$0.998029\pi$
$812$	21.0953	+	12.1794i	0.740299	+	0.427412i
$813$	8.84350	+	5.10580i	0.310155	+	0.179068i
$814$			8.80747i			0.308701i
$815$	0.353178	−	0.611722i	0.0123713	−	0.0214277i
$816$	2.12306	+	3.67724i	0.0743219	+	0.128729i
$817$	−29.2827	+	16.9064i	−1.02447	+	0.591479i
$818$	−12.2758			−0.429213
$819$	6.89825	−	8.72629i	0.241044	−	0.304921i
$820$	−9.42764			−0.329228
$821$	5.46131	−	3.15309i	0.190601	−	0.110044i	−0.401663	−	0.915788i	$-0.631568\pi$
$821$	5.46131	−	3.15309i	0.190601	−	0.110044i	0.592264	+	0.805744i	$0.298234\pi$
$822$	−18.9055	−	32.7453i	−0.659406	−	1.14212i
$823$	−5.64543	+	9.77817i	−0.196787	+	0.340846i	−0.947485	−	0.319800i	$-0.896384\pi$
$823$	−5.64543	+	9.77817i	−0.196787	+	0.340846i	0.750698	+	0.660646i	$0.229718\pi$
$824$		−	4.14022i		−	0.144232i
$825$	−24.5032	−	14.1469i	−0.853092	−	0.492533i
$826$	31.4400	+	18.1519i	1.09394	+	0.631586i
$827$			33.2092i			1.15480i	0.816462	+	0.577399i	$0.195932\pi$
$827$			33.2092i			1.15480i	−0.816462	+	0.577399i	$0.804068\pi$
$828$	7.62744	−	13.2111i	0.265072	−	0.459118i
$829$	5.95301	+	10.3109i	0.206757	+	0.358113i	0.950691	−	0.310140i	$-0.100376\pi$
$829$	5.95301	+	10.3109i	0.206757	+	0.358113i	−0.743934	+	0.668253i	$0.767042\pi$
$830$	−4.32770	+	2.49860i	−0.150217	+	0.0867276i
$831$	24.7769			0.859501
$832$	−23.1654	+	9.20608i	−0.803117	+	0.319163i
$833$	−2.51799			−0.0872432
$834$	27.0047	−	15.5912i	0.935096	−	0.539878i
$835$	−0.258542	−	0.447808i	−0.00894723	−	0.0154970i
$836$	−22.3292	+	38.6752i	−0.772270	+	1.33761i
$837$			6.39872i			0.221172i
$838$	43.7436	+	25.2554i	1.51110	+	0.872432i
$839$	−6.77810	−	3.91334i	−0.234006	−	0.135103i	0.378413	−	0.925637i	$-0.376470\pi$
$839$	−6.77810	−	3.91334i	−0.234006	−	0.135103i	−0.612419	+	0.790534i	$0.709803\pi$
$840$			0.449287i			0.0155019i
$841$	5.56990	−	9.64734i	0.192065	−	0.332667i
$842$	−3.63608	−	6.29788i	−0.125308	−	0.217039i
$843$	16.2838	−	9.40143i	0.560843	−	0.323803i
$844$	24.9098			0.857432
$845$	−5.01552	−	5.31373i	−0.172539	−	0.182798i
$846$	−10.4128			−0.358000
$847$	68.0958	−	39.3151i	2.33980	−	1.35088i
$848$	15.6237	+	27.0611i	0.536521	+	0.929282i
$849$	−1.80239	+	3.12183i	−0.0618579	+	0.107141i
$850$		−	9.21260i		−	0.315989i
$851$	−5.24234	−	3.02667i	−0.179705	−	0.103753i
$852$	−15.8835	−	9.17034i	−0.544159	−	0.314171i
$853$		−	7.47045i		−	0.255784i	−0.991788	−	0.127892i	$-0.959179\pi$
$853$		−	7.47045i		−	0.255784i	0.991788	−	0.127892i	$-0.0408210\pi$
$854$	−15.0171	+	26.0104i	−0.513876	+	0.890059i
$855$	−1.11213	−	1.92627i	−0.0380342	−	0.0658771i
$856$	−0.516902	+	0.298434i	−0.0176674	+	0.0102003i
$857$	38.9743			1.33134			0.665668	−	0.746248i	$-0.268147\pi$
$857$	38.9743			1.33134			0.665668	+	0.746248i	$0.268147\pi$
$858$	−39.8068	+	15.8194i	−1.35898	+	0.540067i
$859$	11.0228			0.376092			0.188046	−	0.982160i	$-0.439785\pi$
$859$	11.0228			0.376092			0.188046	+	0.982160i	$0.439785\pi$
$860$	−7.77044	+	4.48626i	−0.264970	+	0.152980i
$861$	−13.8489	−	23.9870i	−0.471970	−	0.817476i
$862$	19.0095	−	32.9254i	0.647466	−	1.12144i
$863$			29.4909i			1.00388i	0.864902	+	0.501941i	$0.167381\pi$
$863$			29.4909i			1.00388i	−0.864902	+	0.501941i	$0.832619\pi$
$864$	−6.78360	−	3.91651i	−0.230783	−	0.133243i
$865$	−6.86960	−	3.96616i	−0.233573	−	0.134854i
$866$		−	65.8163i		−	2.23653i
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$	18.4406	+	31.9400i	0.625913	+	1.08411i
$869$	88.0351	−	50.8271i	2.98639	−	1.72419i
$870$	4.67189			0.158392
$871$	−17.3944	+	22.0039i	−0.589386	+	0.745574i
$872$	1.07160			0.0362891
$873$	6.67338	−	3.85288i	0.225860	−	0.130400i
$874$	−31.7756	−	55.0370i	−1.07483	−	1.86165i
$875$	8.39638	−	14.5430i	0.283849	−	0.491642i
$876$		−	16.2559i		−	0.549236i
$877$	10.3947	+	6.00139i	0.351005	+	0.202653i	0.665128	−	0.746730i	$-0.268377\pi$
$877$	10.3947	+	6.00139i	0.351005	+	0.202653i	−0.314123	+	0.949382i	$0.601710\pi$
$878$	−57.3492	−	33.1106i	−1.93544	−	1.11743i
$879$			9.00209i			0.303633i
$880$	7.20811	−	12.4848i	0.242985	−	0.420863i
$881$	−0.216240	−	0.374538i	−0.00728530	−	0.0126185i	0.862360	−	0.506296i	$-0.168986\pi$
$881$	−0.216240	−	0.374538i	−0.00728530	−	0.0126185i	−0.869645	+	0.493677i	$0.835652\pi$
$882$	4.28887	−	2.47618i	0.144414	−	0.0833773i
$883$	−40.1105			−1.34983			−0.674913	−	0.737898i	$-0.735819\pi$
$883$	−40.1105			−1.34983			−0.674913	+	0.737898i	$0.735819\pi$
$884$	−5.28439	−	4.17738i	−0.177733	−	0.140501i
$885$	3.36289			0.113042
$886$	63.0653	−	36.4108i	2.11872	−	1.22324i
$887$	27.1227	+	46.9778i	0.910690	+	1.57736i	0.813092	+	0.582135i	$0.197783\pi$
$887$	27.1227	+	46.9778i	0.910690	+	1.57736i	0.0975981	+	0.995226i	$0.468884\pi$
$888$	−0.0960406	+	0.166347i	−0.00322291	+	0.00558225i
$889$		−	46.7077i		−	1.56652i
$890$	−5.09462	−	2.94138i	−0.170772	−	0.0985952i
$891$	−5.23117	−	3.02022i	−0.175251	−	0.101181i
$892$			51.1449i			1.71246i
$893$	−10.4755	+	18.1442i	−0.350550	+	0.607171i
$894$	7.93792	+	13.7489i	0.265484	+	0.459832i
$895$	2.77922	−	1.60459i	0.0928992	−	0.0536354i
$896$	6.38087			0.213170
$897$	4.26353	−	29.1299i	0.142355	−	0.972620i
$898$	52.6280			1.75622
$899$	−23.4189	+	13.5209i	−0.781065	+	0.450948i
$900$	4.37555	+	7.57867i	0.145852	+	0.252622i
$901$	−3.67954	+	6.37314i	−0.122583	+	0.212320i
$902$			106.660i			3.55138i
$903$	−22.8291	−	13.1804i	−0.759704	−	0.438615i
$904$	2.41832	+	1.39622i	0.0804320	+	0.0464374i
$905$		−	10.9489i		−	0.363955i
$906$	−15.6990	+	27.1914i	−0.521563	+	0.903374i
$907$	11.3121	+	19.5932i	0.375613	+	0.650581i	0.990419	−	0.138098i	$-0.0440988\pi$
$907$	11.3121	+	19.5932i	0.375613	+	0.650581i	−0.614805	+	0.788679i	$0.710765\pi$
$908$	30.8659	−	17.8204i	1.02432	−	0.591392i
$909$	10.7781			0.357488
$910$	−4.54137	−	11.4275i	−0.150545	−	0.378819i
$911$	−13.7628			−0.455981			−0.227990	−	0.973663i	$-0.573215\pi$
$911$	−13.7628			−0.455981			−0.227990	+	0.973663i	$0.573215\pi$
$912$	−14.5518	+	8.40151i	−0.481860	+	0.278202i
$913$	13.6526	+	23.6470i	0.451835	+	0.782602i
$914$	−17.6282	+	30.5330i	−0.583090	+	1.00994i
$915$			2.78213i			0.0919744i
$916$	−27.8254	−	16.0650i	−0.919376	−	0.530802i
$917$	−36.3001	−	20.9578i	−1.19873	−	0.692089i
$918$		−	1.96679i		−	0.0649138i
$919$	8.33020	−	14.4283i	0.274788	−	0.475947i	−0.695294	−	0.718726i	$-0.744726\pi$
$919$	8.33020	−	14.4283i	0.274788	−	0.475947i	0.970082	+	0.242779i	$0.0780590\pi$
$920$	0.594555	+	1.02980i	0.0196019	+	0.0339515i
$921$	3.50678	−	2.02464i	0.115552	−	0.0667142i
$922$	−41.7896			−1.37627
$923$	−35.0224	−	5.12597i	−1.15278	−	0.168723i
$924$	−34.8160			−1.14536
$925$	3.00732	−	1.73627i	0.0988799	−	0.0570884i
$926$	−7.52495	−	13.0336i	−0.247285	−	0.428310i
$927$	−7.98975	+	13.8387i	−0.262418	+	0.454521i
$928$		−	33.1034i		−	1.08667i
$929$	−16.8682	−	9.73887i	−0.553428	−	0.319522i	0.197075	−	0.980388i	$-0.436856\pi$
$929$	−16.8682	−	9.73887i	−0.553428	−	0.319522i	−0.750503	+	0.660866i	$0.770189\pi$
$930$	6.12594	+	3.53681i	0.200878	+	0.115977i
$931$		−	9.96436i		−	0.326569i
$932$	−9.29427	+	16.0982i	−0.304444	+	0.527313i
$933$	−0.696932	−	1.20712i	−0.0228165	−	0.0395194i
$934$	44.3977	−	25.6330i	1.45274	−	0.838738i
$935$	3.39516			0.111033
$936$	−0.924335	−	0.135288i	−0.0302128	−	0.00442203i
$937$	23.4402			0.765757			0.382879	−	0.923799i	$-0.374933\pi$
$937$	23.4402			0.765757			0.382879	+	0.923799i	$0.374933\pi$
$938$	−40.8794	+	23.6017i	−1.33476	+	0.770624i
$939$	0.623186	+	1.07939i	0.0203369	+	0.0352246i
$940$	−2.77978	+	4.81472i	−0.0906664	+	0.157039i
$941$			6.19102i			0.201822i	0.994895	+	0.100911i	$0.0321757\pi$
$941$			6.19102i			0.201822i	−0.994895	+	0.100911i	$0.967824\pi$
$942$	−27.6791	−	15.9806i	−0.901835	−	0.520675i
$943$	−63.4855	−	36.6534i	−2.06737	−	1.19360i
$944$		−	25.4047i		−	0.826852i
$945$	0.867030	−	1.50174i	0.0282045	−	0.0488516i
$946$	50.7553	+	87.9108i	1.65020	+	2.85823i
$947$	34.5137	−	19.9265i	1.12155	−	0.647525i	0.179750	−	0.983712i	$-0.442471\pi$
$947$	34.5137	−	19.9265i	1.12155	−	0.647525i	0.941795	+	0.336188i	$0.109138\pi$
$948$	−31.4409			−1.02115
$949$	−11.5861	−	29.1543i	−0.376101	−	0.946389i
$950$	36.4567			1.18281
$951$	−19.6646	+	11.3534i	−0.637670	+	0.368159i
$952$	0.399671	+	0.692251i	0.0129534	+	0.0224360i
$953$	8.25152	−	14.2920i	0.267293	−	0.462965i	−0.700869	−	0.713290i	$-0.747204\pi$
$953$	8.25152	−	14.2920i	0.267293	−	0.462965i	0.968162	+	0.250325i	$0.0805376\pi$
$954$		−	14.4738i		−	0.468605i
$955$	−1.24576	−	0.719243i	−0.0403120	−	0.0232741i
$956$	44.1106	+	25.4673i	1.42664	+	0.823670i
$957$		−	25.5277i		−	0.825193i
$958$	25.8278	−	44.7351i	0.834459	−	1.44532i
$959$	−29.6554	−	51.3646i	−0.957622	−	1.65865i
$960$	−3.36536	+	1.94299i	−0.108617	+	0.0627099i
$961$	−9.94358			−0.320761
$962$	0.761346	−	5.20178i	0.0245468	−	0.167712i
$963$	2.30365			0.0742342
$964$	−4.94703	+	2.85617i	−0.159333	+	0.0919910i
$965$	3.47709	+	6.02250i	0.111932	+	0.193871i
$966$	24.7726	−	42.9074i	0.797044	−	1.38052i
$967$		−	18.6447i		−	0.599573i	−0.954006	−	0.299786i	$-0.903085\pi$
$967$		−	18.6447i		−	0.599573i	0.954006	−	0.299786i	$-0.0969154\pi$
$968$	−5.71884	−	3.30177i	−0.183810	−	0.106123i
$969$	−3.42710	−	1.97863i	−0.110094	−	0.0635629i
$970$		−	8.51853i		−	0.273514i
$971$	−18.0869	+	31.3274i	−0.580435	+	1.00534i	0.414992	+	0.909825i	$0.363784\pi$
$971$	−18.0869	+	31.3274i	−0.580435	+	1.00534i	−0.995428	+	0.0955187i	$0.969549\pi$
$972$	0.934132	+	1.61796i	0.0299623	+	0.0518962i
$973$	42.3598	−	24.4564i	1.35799	−	0.784037i
$974$	47.0114			1.50634
$975$	13.2489	+	10.4735i	0.424305	+	0.335419i
$976$	21.0174			0.672749
$977$	−7.95530	+	4.59300i	−0.254513	+	0.146943i	−0.621829	−	0.783153i	$-0.713610\pi$
$977$	−7.95530	+	4.59300i	−0.254513	+	0.146943i	0.367316	+	0.930096i	$0.380277\pi$
$978$	1.23583	+	2.14053i	0.0395176	+	0.0684465i
$979$	−16.0720	+	27.8375i	−0.513663	+	0.889691i
$980$		−	2.64414i		−	0.0844638i
$981$	−3.58183	−	2.06797i	−0.114359	−	0.0660251i
$982$	−27.5070	−	15.8812i	−0.877784	−	0.506789i
$983$		−	9.47337i		−	0.302154i	−0.988522	−	0.151077i	$-0.951726\pi$
$983$		−	9.47337i		−	0.302154i	0.988522	−	0.151077i	$-0.0482741\pi$
$984$	−1.16306	+	2.01449i	−0.0370771	+	0.0642195i
$985$	2.83816	+	4.91583i	0.0904312	+	0.156631i
$986$	7.19833	−	4.15596i	0.229242	−	0.132353i
$987$	−16.3336			−0.519906
$988$	16.5310	−	20.9118i	0.525922	−	0.665292i
$989$	−69.7679			−2.21849
$990$	−5.78294	+	3.33878i	−0.183794	+	0.106113i
$991$	11.6656	+	20.2055i	0.370572	+	0.641849i	0.989654	−	0.143478i	$-0.0458285\pi$
$991$	11.6656	+	20.2055i	0.370572	+	0.641849i	−0.619082	+	0.785326i	$0.712495\pi$
$992$	25.0607	−	43.4064i	0.795677	−	1.37815i
$993$		−	1.42852i		−	0.0453328i
$994$	−51.5868	−	29.7836i	−1.63623	−	0.944679i
$995$	3.88585	+	2.24350i	0.123190	+	0.0711237i
$996$		−	8.44531i		−	0.267600i
$997$	6.62035	−	11.4668i	0.209669	−	0.363157i	−0.741941	−	0.670465i	$-0.766095\pi$
$997$	6.62035	−	11.4668i	0.209669	−	0.363157i	0.951610	+	0.307308i	$0.0994281\pi$
$998$	14.4785	+	25.0775i	0.458309	+	0.793815i
$999$	0.642030	−	0.370676i	0.0203129	−	0.0117277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.z.d.205.2	✓	16
13.2	odd	12		8619.2.a.bn.1.3		16
13.4	even	6	inner	663.2.z.d.511.2	yes	16
13.11	odd	12		8619.2.a.bn.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.2	✓	16	1.1	even	1	trivial
663.2.z.d.511.2	yes	16	13.4	even	6	inner
8619.2.a.bn.1.3		16	13.2	odd	12
8619.2.a.bn.1.14		16	13.11	odd	12

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70329 + 0.983395i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.934132 - 1.61796i) q^{4} -0.562071i q^{5} +(1.70329 + 0.983395i) q^{6} +(2.67180 + 1.54256i) q^{7} -0.259096i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.70329 + 0.983395i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.934132 - 1.61796i) q^{4} -0.562071i q^{5} +(1.70329 + 0.983395i) q^{6} +(2.67180 + 1.54256i) q^{7} -0.259096i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.552738 + 0.957371i) q^{10} +(5.23117 - 3.02022i) q^{11} -1.86826 q^{12} +(-3.35066 + 1.33157i) q^{13} -6.06779 q^{14} +(-0.486768 + 0.281036i) q^{15} +(2.12306 + 3.67724i) q^{16} +(-0.500000 + 0.866025i) q^{17} -1.96679i q^{18} +(-3.42710 - 1.97863i) q^{19} +(-0.909411 - 0.525049i) q^{20} -3.08512i q^{21} +(-5.94014 + 10.2886i) q^{22} +(-4.08263 - 7.07133i) q^{23} +(-0.224384 + 0.129548i) q^{24} +4.68408 q^{25} +(4.39768 - 5.56308i) q^{26} +1.00000 q^{27} +(4.99162 - 2.88191i) q^{28} +(2.11307 + 3.65994i) q^{29} +(0.552738 - 0.957371i) q^{30} +6.39872i q^{31} +(-6.78360 - 3.91651i) q^{32} +(-5.23117 - 3.02022i) q^{33} -1.96679i q^{34} +(0.867030 - 1.50174i) q^{35} +(0.934132 + 1.61796i) q^{36} +(0.642030 - 0.370676i) q^{37} +7.78312 q^{38} +(2.82850 + 2.23597i) q^{39} -0.145630 q^{40} +(7.77507 - 4.48894i) q^{41} +(3.03390 + 5.25486i) q^{42} +(4.27223 - 7.39973i) q^{43} -11.2851i q^{44} +(0.486768 + 0.281036i) q^{45} +(13.9078 + 8.02968i) q^{46} -5.29432i q^{47} +(2.12306 - 3.67724i) q^{48} +(1.25899 + 2.18064i) q^{49} +(-7.97834 + 4.60630i) q^{50} +1.00000 q^{51} +(-0.975523 + 6.66511i) q^{52} +7.35907 q^{53} +(-1.70329 + 0.983395i) q^{54} +(-1.69758 - 2.94029i) q^{55} +(0.399671 - 0.692251i) q^{56} +3.95727i q^{57} +(-7.19833 - 4.15596i) q^{58} +(-5.18146 - 2.99152i) q^{59} +1.05010i q^{60} +(2.47489 - 4.28664i) q^{61} +(-6.29247 - 10.8989i) q^{62} +(-2.67180 + 1.54256i) q^{63} +6.91370 q^{64} +(0.748438 + 1.88331i) q^{65} +11.8803 q^{66} +(6.73711 - 3.88967i) q^{67} +(0.934132 + 1.61796i) q^{68} +(-4.08263 + 7.07133i) q^{69} +3.41053i q^{70} +(8.50173 + 4.90848i) q^{71} +(0.224384 + 0.129548i) q^{72} +8.70107i q^{73} +(-0.729042 + 1.26274i) q^{74} +(-2.34204 - 4.05653i) q^{75} +(-6.40272 + 3.69661i) q^{76} +18.6355 q^{77} +(-7.01661 - 1.02697i) q^{78} +16.8289 q^{79} +(2.06687 - 1.19331i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.82880 + 15.2919i) q^{82} +4.52040i q^{83} +(-4.99162 - 2.88191i) q^{84} +(0.486768 + 0.281036i) q^{85} +16.8052i q^{86} +(2.11307 - 3.65994i) q^{87} +(-0.782526 - 1.35537i) q^{88} +(-4.60853 + 2.66073i) q^{89} -1.10548 q^{90} +(-11.0063 - 1.61091i) q^{91} -15.2549 q^{92} +(5.54145 - 3.19936i) q^{93} +(5.20641 + 9.01777i) q^{94} +(-1.11213 + 1.92627i) q^{95} +7.83303i q^{96} +(-6.67338 - 3.85288i) q^{97} +(-4.28887 - 2.47618i) q^{98} +6.04044i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more