LMFDB - Embedded newform 403.2.f.c.94.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.15
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809863 + 1.40272i) q^{2} +(-0.263517 - 0.456425i) q^{3} +(-0.311757 + 0.539980i) q^{4} -1.44443 q^{5} +(0.426825 - 0.739283i) q^{6} +(1.00072 - 1.73330i) q^{7} +2.22953 q^{8} +(1.36112 - 2.35752i) q^{9} +O(q^{10})$	\(q+(0.809863 + 1.40272i) q^{2} +(-0.263517 - 0.456425i) q^{3} +(-0.311757 + 0.539980i) q^{4} -1.44443 q^{5} +(0.426825 - 0.739283i) q^{6} +(1.00072 - 1.73330i) q^{7} +2.22953 q^{8} +(1.36112 - 2.35752i) q^{9} +(-1.16979 - 2.02614i) q^{10} +(0.723118 + 1.25248i) q^{11} +0.328613 q^{12} +(2.39783 + 2.69266i) q^{13} +3.24179 q^{14} +(0.380633 + 0.659275i) q^{15} +(2.42913 + 4.20738i) q^{16} +(3.39235 - 5.87572i) q^{17} +4.40928 q^{18} +(-1.87759 + 3.25209i) q^{19} +(0.450313 - 0.779965i) q^{20} -1.05483 q^{21} +(-1.17125 + 2.02867i) q^{22} +(0.430341 + 0.745372i) q^{23} +(-0.587519 - 1.01761i) q^{24} -2.91361 q^{25} +(-1.83514 + 5.54418i) q^{26} -3.01581 q^{27} +(0.623964 + 1.08074i) q^{28} +(0.627142 + 1.08624i) q^{29} +(-0.616521 + 1.06785i) q^{30} +1.00000 q^{31} +(-1.70500 + 2.95314i) q^{32} +(0.381108 - 0.660098i) q^{33} +10.9894 q^{34} +(-1.44547 + 2.50364i) q^{35} +(0.848677 + 1.46995i) q^{36} +(2.56440 + 4.44168i) q^{37} -6.08238 q^{38} +(0.597127 - 1.80399i) q^{39} -3.22041 q^{40} +(-4.36621 - 7.56250i) q^{41} +(-0.854266 - 1.47963i) q^{42} +(4.84385 - 8.38979i) q^{43} -0.901749 q^{44} +(-1.96604 + 3.40529i) q^{45} +(-0.697034 + 1.20730i) q^{46} -7.35190 q^{47} +(1.28023 - 2.21743i) q^{48} +(1.49712 + 2.59308i) q^{49} +(-2.35963 - 4.08699i) q^{50} -3.57576 q^{51} +(-2.20152 + 0.455323i) q^{52} -10.9189 q^{53} +(-2.44240 - 4.23035i) q^{54} +(-1.04450 - 1.80912i) q^{55} +(2.23114 - 3.86444i) q^{56} +1.97911 q^{57} +(-1.01580 + 1.75941i) q^{58} +(-0.770537 + 1.33461i) q^{59} -0.474660 q^{60} +(-2.62173 + 4.54097i) q^{61} +(0.809863 + 1.40272i) q^{62} +(-2.72420 - 4.71845i) q^{63} +4.19326 q^{64} +(-3.46351 - 3.88937i) q^{65} +1.23458 q^{66} +(7.04802 + 12.2075i) q^{67} +(2.11518 + 3.66360i) q^{68} +(0.226804 - 0.392836i) q^{69} -4.68255 q^{70} +(-3.77365 + 6.53615i) q^{71} +(3.03465 - 5.25617i) q^{72} -10.1044 q^{73} +(-4.15363 + 7.19430i) q^{74} +(0.767786 + 1.32984i) q^{75} +(-1.17071 - 2.02773i) q^{76} +2.89456 q^{77} +(3.01409 - 0.623381i) q^{78} +5.48108 q^{79} +(-3.50872 - 6.07727i) q^{80} +(-3.28864 - 5.69608i) q^{81} +(7.07207 - 12.2492i) q^{82} +2.29085 q^{83} +(0.328850 - 0.569586i) q^{84} +(-4.90002 + 8.48709i) q^{85} +15.6914 q^{86} +(0.330525 - 0.572486i) q^{87} +(1.61221 + 2.79243i) q^{88} +(0.376062 + 0.651358i) q^{89} -6.36891 q^{90} +(7.06674 - 1.46156i) q^{91} -0.536648 q^{92} +(-0.263517 - 0.456425i) q^{93} +(-5.95403 - 10.3127i) q^{94} +(2.71206 - 4.69743i) q^{95} +1.79718 q^{96} +(-2.03204 + 3.51960i) q^{97} +(-2.42492 + 4.20008i) q^{98} +3.93699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.809863	+	1.40272i	0.572660	+	0.991876i	0.996292	+	0.0860415i	$0.0274218\pi$
$2$	0.809863	+	1.40272i	0.572660	+	0.991876i	−0.423632	+	0.905835i	$0.639245\pi$
$3$	−0.263517	−	0.456425i	−0.152142	−	0.263517i	0.779873	−	0.625938i	$-0.215284\pi$
$3$	−0.263517	−	0.456425i	−0.152142	−	0.263517i	−0.932015	+	0.362421i	$0.881950\pi$
$4$	−0.311757	+	0.539980i	−0.155879	+	0.269990i
$5$	−1.44443			−0.645970			−0.322985	−	0.946404i	$-0.604686\pi$
$5$	−1.44443			−0.645970			−0.322985	+	0.946404i	$0.604686\pi$
$6$	0.426825	−	0.739283i	0.174251	−	0.301811i
$7$	1.00072	−	1.73330i	0.378237	−	0.655126i	−0.612569	−	0.790417i	$-0.709864\pi$
$7$	1.00072	−	1.73330i	0.378237	−	0.655126i	0.990806	+	0.135292i	$0.0431971\pi$
$8$	2.22953			0.788258
$9$	1.36112	−	2.35752i	0.453706	−	0.785842i
$10$	−1.16979	−	2.02614i	−0.369921	−	0.640722i
$11$	0.723118	+	1.25248i	0.218028	+	0.377636i	0.954205	−	0.299153i	$-0.0967042\pi$
$11$	0.723118	+	1.25248i	0.218028	+	0.377636i	−0.736177	+	0.676789i	$0.763371\pi$
$12$	0.328613			0.0948625
$13$	2.39783	+	2.69266i	0.665038	+	0.746809i
$13$	2.39783	+	2.69266i	0.665038	+	0.746809i
$14$	3.24179			0.866405
$15$	0.380633	+	0.659275i	0.0982789	+	0.170224i
$16$	2.42913	+	4.20738i	0.607282	+	1.05184i
$17$	3.39235	−	5.87572i	0.822765	−	1.42507i	−0.0808500	−	0.996726i	$-0.525763\pi$
$17$	3.39235	−	5.87572i	0.822765	−	1.42507i	0.903615	−	0.428345i	$-0.140903\pi$
$18$	4.40928			1.03928
$19$	−1.87759	+	3.25209i	−0.430750	+	0.746081i	−0.996938	−	0.0781954i	$-0.975084\pi$
$19$	−1.87759	+	3.25209i	−0.430750	+	0.746081i	0.566188	+	0.824276i	$0.308418\pi$
$20$	0.450313	−	0.779965i	0.100693	−	0.174405i
$21$	−1.05483			−0.230182
$22$	−1.17125	+	2.02867i	−0.249712	+	0.432514i
$23$	0.430341	+	0.745372i	0.0897323	+	0.155421i	0.907398	−	0.420273i	$-0.138066\pi$
$23$	0.430341	+	0.745372i	0.0897323	+	0.155421i	−0.817666	+	0.575693i	$0.804732\pi$
$24$	−0.587519	−	1.01761i	−0.119927	−	0.207719i
$25$	−2.91361			−0.582722
$26$	−1.83514	+	5.54418i	−0.359901	+	1.08730i
$27$	−3.01581			−0.580393
$28$	0.623964	+	1.08074i	0.117918	+	0.204240i
$29$	0.627142	+	1.08624i	0.116457	+	0.201710i	0.918361	−	0.395743i	$-0.129513\pi$
$29$	0.627142	+	1.08624i	0.116457	+	0.201710i	−0.801904	+	0.597453i	$0.796180\pi$
$30$	−0.616521	+	1.06785i	−0.112561	+	0.194961i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−1.70500	+	2.95314i	−0.301404	+	0.522046i
$33$	0.381108	−	0.660098i	0.0663423	−	0.114908i
$34$	10.9894			1.88466
$35$	−1.44547	+	2.50364i	−0.244330	+	0.423192i
$36$	0.848677	+	1.46995i	0.141446	+	0.244992i
$37$	2.56440	+	4.44168i	0.421585	+	0.730207i	0.996095	−	0.0882909i	$-0.0281405\pi$
$37$	2.56440	+	4.44168i	0.421585	+	0.730207i	−0.574510	+	0.818498i	$0.694807\pi$
$38$	−6.08238			−0.986693
$39$	0.597127	−	1.80399i	0.0956169	−	0.288870i
$40$	−3.22041			−0.509191
$41$	−4.36621	−	7.56250i	−0.681888	−	1.18106i	−0.974404	−	0.224804i	$-0.927826\pi$
$41$	−4.36621	−	7.56250i	−0.681888	−	1.18106i	0.292516	−	0.956261i	$-0.405507\pi$
$42$	−0.854266	−	1.47963i	−0.131816	−	0.228312i
$43$	4.84385	−	8.38979i	0.738680	−	1.27943i	−0.214410	−	0.976744i	$-0.568783\pi$
$43$	4.84385	−	8.38979i	0.738680	−	1.27943i	0.953090	−	0.302687i	$-0.0978838\pi$
$44$	−0.901749			−0.135944
$45$	−1.96604	+	3.40529i	−0.293081	+	0.507630i
$46$	−0.697034	+	1.20730i	−0.102772	+	0.178007i
$47$	−7.35190			−1.07238			−0.536192	−	0.844096i	$-0.680138\pi$
$47$	−7.35190			−1.07238			−0.536192	+	0.844096i	$0.680138\pi$
$48$	1.28023	−	2.21743i	0.184786	−	0.320058i
$49$	1.49712	+	2.59308i	0.213874	+	0.370440i
$50$	−2.35963	−	4.08699i	−0.333702	−	0.577988i
$51$	−3.57576			−0.500707
$52$	−2.20152	+	0.455323i	−0.305296	+	0.0631420i
$53$	−10.9189			−1.49982			−0.749910	−	0.661540i	$-0.769903\pi$
$53$	−10.9189			−1.49982			−0.749910	+	0.661540i	$0.769903\pi$
$54$	−2.44240	−	4.23035i	−0.332368	−	0.575678i
$55$	−1.04450	−	1.80912i	−0.140840	−	0.243942i
$56$	2.23114	−	3.86444i	0.298148	−	0.516408i
$57$	1.97911			0.262140
$58$	−1.01580	+	1.75941i	−0.133381	+	0.231022i
$59$	−0.770537	+	1.33461i	−0.100315	+	0.173751i	−0.911815	−	0.410602i	$-0.865318\pi$
$59$	−0.770537	+	1.33461i	−0.100315	+	0.173751i	0.811499	+	0.584353i	$0.198652\pi$
$60$	−0.474660			−0.0612784
$61$	−2.62173	+	4.54097i	−0.335678	+	0.581412i	−0.983615	−	0.180282i	$-0.942299\pi$
$61$	−2.62173	+	4.54097i	−0.335678	+	0.581412i	0.647937	+	0.761694i	$0.275632\pi$
$62$	0.809863	+	1.40272i	0.102853	+	0.178146i
$63$	−2.72420	−	4.71845i	−0.343217	−	0.594469i
$64$	4.19326			0.524158
$65$	−3.46351	−	3.88937i	−0.429595	−	0.482417i
$66$	1.23458			0.151966
$67$	7.04802	+	12.2075i	0.861053	+	1.49139i	0.870914	+	0.491435i	$0.163528\pi$
$67$	7.04802	+	12.2075i	0.861053	+	1.49139i	−0.00986153	+	0.999951i	$0.503139\pi$
$68$	2.11518	+	3.66360i	0.256503	+	0.444277i
$69$	0.226804	−	0.392836i	0.0273040	−	0.0472919i
$70$	−4.68255			−0.559672
$71$	−3.77365	+	6.53615i	−0.447849	+	0.775698i	−0.998246	−	0.0592056i	$-0.981143\pi$
$71$	−3.77365	+	6.53615i	−0.447849	+	0.775698i	0.550396	+	0.834903i	$0.314477\pi$
$72$	3.03465	−	5.25617i	0.357637	−	0.619446i
$73$	−10.1044			−1.18263			−0.591317	−	0.806439i	$-0.701392\pi$
$73$	−10.1044			−1.18263			−0.591317	+	0.806439i	$0.701392\pi$
$74$	−4.15363	+	7.19430i	−0.482850	+	0.836320i
$75$	0.767786	+	1.32984i	0.0886563	+	0.153557i
$76$	−1.17071	−	2.02773i	−0.134289	−	0.232596i
$77$	2.89456			0.329865
$78$	3.01409	−	0.623381i	0.341279	−	0.0705840i
$79$	5.48108			0.616670			0.308335	−	0.951278i	$-0.400228\pi$
$79$	5.48108			0.616670			0.308335	+	0.951278i	$0.400228\pi$
$80$	−3.50872	−	6.07727i	−0.392286	−	0.679460i
$81$	−3.28864	−	5.69608i	−0.365404	−	0.632898i
$82$	7.07207	−	12.2492i	0.780980	−	1.35270i
$83$	2.29085			0.251453			0.125727	−	0.992065i	$-0.459874\pi$
$83$	2.29085			0.251453			0.125727	+	0.992065i	$0.459874\pi$
$84$	0.328850	−	0.569586i	0.0358805	−	0.0621469i
$85$	−4.90002	+	8.48709i	−0.531482	+	0.920554i
$86$	15.6914			1.69205
$87$	0.330525	−	0.572486i	0.0354360	−	0.0613770i
$88$	1.61221	+	2.79243i	0.171862	+	0.297674i
$89$	0.376062	+	0.651358i	0.0398625	+	0.0690438i	0.885268	−	0.465081i	$-0.153975\pi$
$89$	0.376062	+	0.651358i	0.0398625	+	0.0690438i	−0.845406	+	0.534124i	$0.820641\pi$
$90$	−6.36891			−0.671342
$91$	7.06674	−	1.46156i	0.740796	−	0.153213i
$92$	−0.536648			−0.0559494
$93$	−0.263517	−	0.456425i	−0.0273254	−	0.0473290i
$94$	−5.95403	−	10.3127i	−0.614112	−	1.06367i
$95$	2.71206	−	4.69743i	0.278252	−	0.481946i
$96$	1.79718			0.183424
$97$	−2.03204	+	3.51960i	−0.206322	+	0.357361i	−0.950553	−	0.310562i	$-0.899483\pi$
$97$	−2.03204	+	3.51960i	−0.206322	+	0.357361i	0.744231	+	0.667922i	$0.232816\pi$
$98$	−2.42492	+	4.20008i	−0.244954	+	0.424272i
$99$	3.93699			0.395683
$100$	0.908340	−	1.57329i	0.0908340	−	0.157329i
$101$	−3.14561	−	5.44836i	−0.313000	−	0.542132i	0.666010	−	0.745943i	$-0.268001\pi$
$101$	−3.14561	−	5.44836i	−0.313000	−	0.542132i	−0.979010	+	0.203810i	$0.934667\pi$
$102$	−2.89588	−	5.01581i	−0.286735	−	0.496640i
$103$	−12.8380			−1.26496			−0.632482	−	0.774575i	$-0.717964\pi$
$103$	−12.8380			−1.26496			−0.632482	+	0.774575i	$0.717964\pi$
$104$	5.34603	+	6.00336i	0.524222	+	0.588678i
$105$	1.52363			0.148691
$106$	−8.84278	−	15.3162i	−0.858887	−	1.48764i
$107$	2.77412	+	4.80492i	0.268184	+	0.464509i	0.968393	−	0.249429i	$-0.0802431\pi$
$107$	2.77412	+	4.80492i	0.268184	+	0.464509i	−0.700209	+	0.713938i	$0.746910\pi$
$108$	0.940202	−	1.62848i	0.0904710	−	0.156700i
$109$	−15.2763			−1.46320			−0.731602	−	0.681732i	$-0.761227\pi$
$109$	−15.2763			−1.46320			−0.731602	+	0.681732i	$0.761227\pi$
$110$	1.69180	−	2.93028i	0.161307	−	0.279391i
$111$	1.35153	−	2.34091i	0.128281	−	0.222190i
$112$	9.72352			0.918787
$113$	−2.74500	+	4.75449i	−0.258228	+	0.447264i	−0.965767	−	0.259410i	$-0.916472\pi$
$113$	−2.74500	+	4.75449i	−0.258228	+	0.447264i	0.707539	+	0.706674i	$0.249805\pi$
$114$	1.60281	+	2.77615i	0.150117	+	0.260010i
$115$	−0.621599	−	1.07664i	−0.0579644	−	0.100397i
$116$	−0.782065			−0.0726129
$117$	9.61174	−	1.98792i	0.888606	−	0.183783i
$118$	−2.49612			−0.229786
$119$	−6.78959	−	11.7599i	−0.622400	−	1.07803i
$120$	0.848632	+	1.46987i	0.0774692	+	0.134181i
$121$	4.45420	−	7.71490i	0.404927	−	0.701355i
$122$	−8.49298			−0.768918
$123$	−2.30114	+	3.98569i	−0.207487	+	0.359378i
$124$	−0.311757	+	0.539980i	−0.0279966	+	0.0484916i
$125$	11.4307			1.02239
$126$	4.41246	−	7.64260i	0.393093	−	0.680857i
$127$	3.04281	+	5.27030i	0.270006	+	0.467663i	0.968863	−	0.247598i	$-0.0796411\pi$
$127$	3.04281	+	5.27030i	0.270006	+	0.467663i	−0.698857	+	0.715261i	$0.746308\pi$
$128$	6.80596	+	11.7883i	0.601568	+	1.04195i
$129$	−5.10574			−0.449536
$130$	2.65074	−	8.00820i	0.232486	−	0.702366i
$131$	−15.7664			−1.37752			−0.688759	−	0.724990i	$-0.741844\pi$
$131$	−15.7664			−1.37752			−0.688759	+	0.724990i	$0.741844\pi$
$132$	0.237626	+	0.411581i	0.0206827	+	0.0358235i
$133$	3.75790	+	6.50887i	0.325851	+	0.564390i
$134$	−11.4159	+	19.7729i	−0.986181	+	1.70811i
$135$	4.35614			0.374917
$136$	7.56334	−	13.1001i	0.648551	−	1.12332i
$137$	3.32650	−	5.76167i	0.284202	−	0.492253i	−0.688213	−	0.725509i	$-0.741605\pi$
$137$	3.32650	−	5.76167i	0.284202	−	0.492253i	0.972415	+	0.233256i	$0.0749379\pi$
$138$	0.734722			0.0625437
$139$	−2.56386	+	4.44073i	−0.217464	+	0.376658i	−0.954032	−	0.299705i	$-0.903112\pi$
$139$	−2.56386	+	4.44073i	−0.217464	+	0.376658i	0.736568	+	0.676363i	$0.236445\pi$
$140$	−0.901275	−	1.56105i	−0.0761717	−	0.131933i
$141$	1.93735	+	3.35559i	0.163154	+	0.282592i
$142$	−12.2246			−1.02586
$143$	−1.63858	+	4.95034i	−0.137025	+	0.413968i
$144$	13.2253			1.10211
$145$	−0.905865	−	1.56900i	−0.0752280	−	0.130299i
$146$	−8.18321	−	14.1737i	−0.677247	−	1.17303i
$147$	0.789030	−	1.36664i	0.0650781	−	0.112719i
$148$	−3.19789			−0.262865
$149$	7.65157	−	13.2529i	0.626841	−	1.08572i	−0.361341	−	0.932434i	$-0.617681\pi$
$149$	7.65157	−	13.2529i	0.626841	−	1.08572i	0.988182	−	0.153287i	$-0.0489858\pi$
$150$	−1.24360	+	2.15398i	−0.101540	+	0.175872i
$151$	20.4286			1.66246			0.831228	−	0.555932i	$-0.187639\pi$
$151$	20.4286			1.66246			0.831228	+	0.555932i	$0.187639\pi$
$152$	−4.18615	+	7.25063i	−0.339542	+	0.588104i
$153$	−9.23477	−	15.9951i	−0.746587	−	1.29313i
$154$	2.34420	+	4.06027i	0.188901	+	0.327185i
$155$	−1.44443			−0.116020
$156$	0.787959	+	0.884844i	0.0630872	+	0.0708442i
$157$	21.7068			1.73239			0.866197	−	0.499703i	$-0.166558\pi$
$157$	21.7068			1.73239			0.866197	+	0.499703i	$0.166558\pi$
$158$	4.43893	+	7.68845i	0.353142	+	0.611660i
$159$	2.87730	+	4.98364i	0.228185	+	0.395228i
$160$	2.46275	−	4.26561i	0.194698	−	0.337226i
$161$	1.72260			0.135760
$162$	5.32669	−	9.22610i	0.418504	−	0.724871i
$163$	−11.5192	+	19.9519i	−0.902256	+	1.56275i	−0.0776978	+	0.996977i	$0.524757\pi$
$163$	−11.5192	+	19.9519i	−0.902256	+	1.56275i	−0.824558	+	0.565777i	$0.808576\pi$
$164$	5.44480			0.425167
$165$	−0.550485	+	0.953467i	−0.0428552	+	0.0742273i
$166$	1.85527	+	3.21343i	0.143997	+	0.249411i
$167$	4.68783	+	8.11956i	0.362755	+	0.628311i	0.988413	−	0.151787i	$-0.0485028\pi$
$167$	4.68783	+	8.11956i	0.362755	+	0.628311i	−0.625658	+	0.780097i	$0.715169\pi$
$168$	−2.35177			−0.181443
$169$	−1.50082	+	12.9131i	−0.115448	+	0.993314i
$170$	−15.8734			−1.21743
$171$	5.11125	+	8.85295i	0.390867	+	0.677002i
$172$	3.02021	+	5.23116i	0.230289	+	0.398872i
$173$	−0.544596	+	0.943269i	−0.0414049	+	0.0717154i	−0.885985	−	0.463714i	$-0.846517\pi$
$173$	−0.544596	+	0.943269i	−0.0414049	+	0.0717154i	0.844580	+	0.535429i	$0.179850\pi$
$174$	1.07072			0.0811711
$175$	−2.91571	+	5.05016i	−0.220407	+	0.381756i
$176$	−3.51309	+	6.08486i	−0.264809	+	0.458663i
$177$	0.812198			0.0610485
$178$	−0.609117	+	1.05502i	−0.0456553	+	0.0790773i
$179$	−7.58910	−	13.1447i	−0.567236	−	0.982481i	−0.996838	−	0.0794628i	$-0.974680\pi$
$179$	−7.58910	−	13.1447i	−0.567236	−	0.982481i	0.429602	−	0.903018i	$-0.358654\pi$
$180$	−1.22586	−	2.12325i	−0.0913700	−	0.158258i
$181$	−17.1476			−1.27457			−0.637285	−	0.770628i	$-0.719943\pi$
$181$	−17.1476			−1.27457			−0.637285	+	0.770628i	$0.719943\pi$
$182$	7.77326	+	8.72903i	0.576192	+	0.647039i
$183$	2.76348			0.204283
$184$	0.959458	+	1.66183i	0.0707322	+	0.122512i
$185$	−3.70411	−	6.41571i	−0.272332	−	0.471692i
$186$	0.426825	−	0.739283i	0.0312964	−	0.0542069i
$187$	9.81227			0.717544
$188$	2.29201	−	3.96988i	0.167162	−	0.289533i
$189$	−3.01799	+	5.22731i	−0.219526	+	0.380231i
$190$	8.78560			0.637374
$191$	−7.93480	+	13.7435i	−0.574142	+	0.994443i	0.421992	+	0.906599i	$0.361331\pi$
$191$	−7.93480	+	13.7435i	−0.574142	+	0.994443i	−0.996134	+	0.0878437i	$0.972002\pi$
$192$	−1.10500	−	1.91391i	−0.0797462	−	0.138124i
$193$	1.60834	+	2.78573i	0.115771	+	0.200521i	0.918088	−	0.396377i	$-0.129733\pi$
$193$	1.60834	+	2.78573i	0.115771	+	0.200521i	−0.802317	+	0.596899i	$0.796399\pi$
$194$	−6.58270			−0.472610
$195$	−0.862511	+	2.60574i	−0.0617657	+	0.186601i
$196$	−1.86695			−0.133353
$197$	1.28934	+	2.23320i	0.0918614	+	0.159109i	0.908294	−	0.418332i	$-0.137385\pi$
$197$	1.28934	+	2.23320i	0.0918614	+	0.159109i	−0.816433	+	0.577440i	$0.804052\pi$
$198$	3.18843	+	5.52252i	0.226592	+	0.392468i
$199$	−4.46956	+	7.74151i	−0.316839	+	0.548781i	−0.979827	−	0.199849i	$-0.935955\pi$
$199$	−4.46956	+	7.74151i	−0.316839	+	0.548781i	0.662988	+	0.748630i	$0.269288\pi$
$200$	−6.49598			−0.459335
$201$	3.71454	−	6.43378i	0.262004	−	0.453804i
$202$	5.09503	−	8.82486i	0.358485	−	0.620915i
$203$	2.51038			0.176194
$204$	1.11477	−	1.93084i	0.0780496	−	0.135186i
$205$	6.30670	+	10.9235i	0.440479	+	0.762932i
$206$	−10.3970	−	18.0082i	−0.724395	−	1.25469i
$207$	2.34298			0.162848
$208$	−5.50439	+	16.6294i	−0.381661	+	1.15304i
$209$	−5.43089			−0.375662
$210$	1.23393	+	2.13723i	0.0851493	+	0.147483i
$211$	4.13134	+	7.15569i	0.284413	+	0.492618i	0.972467	−	0.233042i	$-0.0748679\pi$
$211$	4.13134	+	7.15569i	0.284413	+	0.492618i	−0.688054	+	0.725660i	$0.741535\pi$
$212$	3.40404	−	5.89596i	0.233790	−	0.404936i
$213$	3.97768			0.272546
$214$	−4.49332	+	7.78265i	−0.307157	+	0.532011i
$215$	−6.99662	+	12.1185i	−0.477165	+	0.826475i
$216$	−6.72384			−0.457500
$217$	1.00072	−	1.73330i	0.0679334	−	0.117664i
$218$	−12.3717	−	21.4284i	−0.837918	−	1.45132i
$219$	2.66269	+	4.61191i	0.179928	+	0.311644i
$220$	1.30252			0.0878157
$221$	23.9556	−	4.95454i	1.61143	−	0.333278i
$222$	4.37821			0.293846
$223$	1.70110	+	2.94638i	0.113914	+	0.197305i	0.917345	−	0.398093i	$-0.130328\pi$
$223$	1.70110	+	2.94638i	0.113914	+	0.197305i	−0.803431	+	0.595398i	$0.796995\pi$
$224$	3.41245	+	5.91054i	0.228004	+	0.394914i
$225$	−3.96577	+	6.86891i	−0.264385	+	0.457927i
$226$	−8.89231			−0.591508
$227$	−10.1650	+	17.6062i	−0.674672	+	1.16857i	0.301892	+	0.953342i	$0.402382\pi$
$227$	−10.1650	+	17.6062i	−0.674672	+	1.16857i	−0.976565	+	0.215224i	$0.930952\pi$
$228$	−0.617003	+	1.06868i	−0.0408620	+	0.0707751i
$229$	3.17305			0.209681			0.104840	−	0.994489i	$-0.466567\pi$
$229$	3.17305			0.209681			0.104840	+	0.994489i	$0.466567\pi$
$230$	1.00682	−	1.74386i	0.0663877	−	0.114987i
$231$	−0.762765	−	1.32115i	−0.0501862	−	0.0869251i
$232$	1.39823	+	2.42181i	0.0917984	+	0.159000i
$233$	−18.3027			−1.19905			−0.599526	−	0.800355i	$-0.704644\pi$
$233$	−18.3027			−1.19905			−0.599526	+	0.800355i	$0.704644\pi$
$234$	10.5727	+	11.8727i	0.691159	+	0.776141i
$235$	10.6193			0.692729
$236$	−0.480441	−	0.832148i	−0.0312740	−	0.0541682i
$237$	−1.44436	−	2.50170i	−0.0938211	−	0.162503i
$238$	10.9973	−	19.0478i	0.712848	−	1.23469i
$239$	28.2750			1.82896			0.914480	−	0.404631i	$-0.132600\pi$
$239$	28.2750			1.82896			0.914480	+	0.404631i	$0.132600\pi$
$240$	−1.84921	+	3.20293i	−0.119366	+	0.206748i
$241$	14.0066	−	24.2601i	0.902243	−	1.56273i	0.0776661	−	0.996979i	$-0.475253\pi$
$241$	14.0066	−	24.2601i	0.902243	−	1.56273i	0.824576	−	0.565751i	$-0.191413\pi$
$242$	14.4292			0.927543
$243$	−6.25694	+	10.8373i	−0.401383	+	0.695216i
$244$	−1.63469	−	2.83136i	−0.104650	−	0.181260i
$245$	−2.16248	−	3.74553i	−0.138156	−	0.239293i
$246$	−7.45444			−0.475278
$247$	−13.2589	+	2.74224i	−0.843645	+	0.174484i
$248$	2.22953			0.141575
$249$	−0.603678	−	1.04560i	−0.0382565	−	0.0662622i
$250$	9.25729	+	16.0341i	0.585483	+	1.01409i
$251$	5.57195	−	9.65089i	0.351698	−	0.609159i	−0.634849	−	0.772636i	$-0.718938\pi$
$251$	5.57195	−	9.65089i	0.351698	−	0.609159i	0.986547	+	0.163477i	$0.0522710\pi$
$252$	3.39716			0.214001
$253$	−0.622374	+	1.07798i	−0.0391283	+	0.0677722i
$254$	−4.92852	+	8.53644i	−0.309243	+	0.535624i
$255$	5.16495			0.323442
$256$	−6.83054	+	11.8308i	−0.426909	+	0.739427i
$257$	0.0638978	+	0.110674i	0.00398584	+	0.00690367i	0.868011	−	0.496544i	$-0.165398\pi$
$257$	0.0638978	+	0.110674i	0.00398584	+	0.00690367i	−0.864026	+	0.503448i	$0.832065\pi$
$258$	−4.13496	−	7.16195i	−0.257431	−	0.445884i
$259$	10.2650			0.637836
$260$	3.17995	−	0.657684i	0.197212	−	0.0407878i
$261$	3.41446			0.211350
$262$	−12.7686	−	22.1159i	−0.788849	−	1.36633i
$263$	−5.48775	−	9.50507i	−0.338389	−	0.586107i	0.645741	−	0.763557i	$-0.276549\pi$
$263$	−5.48775	−	9.50507i	−0.338389	−	0.586107i	−0.984130	+	0.177449i	$0.943215\pi$
$264$	0.849691	−	1.47171i	0.0522948	−	0.0905773i
$265$	15.7716			0.968840
$266$	−6.08677	+	10.5426i	−0.373204	+	0.646408i
$267$	0.198197	−	0.343288i	0.0121295	−	0.0210089i
$268$	−8.78909			−0.536879
$269$	8.06580	−	13.9704i	0.491780	−	0.851789i	−0.508175	−	0.861254i	$-0.669680\pi$
$269$	8.06580	−	13.9704i	0.491780	−	0.851789i	0.999955	+	0.00946536i	$0.00301296\pi$
$270$	3.52788	+	6.11046i	0.214700	+	0.371871i
$271$	3.88683	+	6.73219i	0.236108	+	0.408951i	0.959594	−	0.281388i	$-0.0907947\pi$
$271$	3.88683	+	6.73219i	0.236108	+	0.408951i	−0.723486	+	0.690339i	$0.757461\pi$
$272$	32.9618			1.99860
$273$	−2.52930	−	2.84029i	−0.153080	−	0.171902i
$274$	10.7761			0.651005
$275$	−2.10688	−	3.64923i	−0.127050	−	0.220057i
$276$	0.141416	+	0.244939i	0.00851223	+	0.0147436i
$277$	15.7210	−	27.2296i	0.944584	−	1.63607i	0.188002	−	0.982169i	$-0.439799\pi$
$277$	15.7210	−	27.2296i	0.944584	−	1.63607i	0.756582	−	0.653899i	$-0.226868\pi$
$278$	−8.30550			−0.498131
$279$	1.36112	−	2.35752i	0.0814880	−	0.141141i
$280$	−3.22273	+	5.58193i	−0.192595	+	0.333584i
$281$	−13.5217			−0.806636			−0.403318	−	0.915060i	$-0.632143\pi$
$281$	−13.5217			−0.806636			−0.403318	+	0.915060i	$0.632143\pi$
$282$	−3.13798	+	5.43514i	−0.186864	+	0.323658i
$283$	−14.7929	−	25.6220i	−0.879344	−	1.52307i	−0.852062	−	0.523441i	$-0.824648\pi$
$283$	−14.7929	−	25.6220i	−0.879344	−	1.52307i	−0.0272820	−	0.999628i	$-0.508685\pi$
$284$	−2.35292	−	4.07538i	−0.139620	−	0.241830i
$285$	−2.85870			−0.169335
$286$	−8.27098	+	1.71062i	−0.489073	+	0.101151i
$287$	−17.4774			−1.03166
$288$	4.64140	+	8.03914i	0.273497	+	0.473711i
$289$	−14.5161	−	25.1425i	−0.853885	−	1.47897i
$290$	1.46725	−	2.54136i	0.0861601	−	0.149234i
$291$	2.14191			0.125561
$292$	3.15013	−	5.45619i	0.184348	−	0.319299i
$293$	−6.51626	+	11.2865i	−0.380684	+	0.659364i	−0.991160	−	0.132670i	$-0.957645\pi$
$293$	−6.51626	+	11.2865i	−0.380684	+	0.659364i	0.610476	+	0.792035i	$0.290978\pi$
$294$	2.55603			0.149071
$295$	1.11299	−	1.92775i	0.0648007	−	0.112238i
$296$	5.71741	+	9.90285i	0.332318	+	0.575591i
$297$	−2.18079	−	3.77723i	−0.126542	−	0.219177i
$298$	24.7869			1.43587
$299$	−0.975149	+	2.94604i	−0.0563943	+	0.170374i
$300$	−0.957452			−0.0552785
$301$	−9.69468	−	16.7917i	−0.558792	−	0.967856i
$302$	16.5444	+	28.6557i	0.952022	+	1.64895i
$303$	−1.65784	+	2.87147i	−0.0952407	+	0.164962i
$304$	−18.2437			−1.04635
$305$	3.78692	−	6.55913i	0.216838	−	0.375575i
$306$	14.9578	−	25.9077i	0.855081	−	1.48104i
$307$	3.26904			0.186574			0.0932869	−	0.995639i	$-0.470263\pi$
$307$	3.26904			0.186574			0.0932869	+	0.995639i	$0.470263\pi$
$308$	−0.902399	+	1.56300i	−0.0514190	+	0.0890603i
$309$	3.38303	+	5.85958i	0.192454	+	0.333340i
$310$	−1.16979	−	2.02614i	−0.0664398	−	0.115077i
$311$	−8.02060			−0.454806			−0.227403	−	0.973801i	$-0.573024\pi$
$311$	−8.02060			−0.454806			−0.227403	+	0.973801i	$0.573024\pi$
$312$	1.33131	−	4.02205i	0.0753707	−	0.227704i
$313$	20.9636			1.18493			0.592467	−	0.805594i	$-0.298154\pi$
$313$	20.9636			1.18493			0.592467	+	0.805594i	$0.298154\pi$
$314$	17.5796	+	30.4487i	0.992072	+	1.71832i
$315$	3.93492	+	6.81549i	0.221708	+	0.384009i
$316$	−1.70877	+	2.95967i	−0.0961257	+	0.166495i
$317$	21.6600			1.21655			0.608275	−	0.793727i	$-0.291862\pi$
$317$	21.6600			1.21655			0.608275	+	0.793727i	$0.291862\pi$
$318$	−4.66045	+	8.07213i	−0.261345	+	0.452663i
$319$	−0.906995	+	1.57096i	−0.0507820	+	0.0879570i
$320$	−6.05689			−0.338590
$321$	1.46206	−	2.53235i	0.0816040	−	0.141342i
$322$	1.39507	+	2.41634i	0.0777444	+	0.134657i
$323$	12.7389	+	22.0644i	0.708812	+	1.22770i
$324$	4.10103			0.227835
$325$	−6.98635	−	7.84536i	−0.387533	−	0.435182i
$326$	−37.3160			−2.06674
$327$	4.02556	+	6.97248i	0.222614	+	0.385579i
$328$	−9.73460	−	16.8608i	−0.537503	−	0.930983i
$329$	−7.35720	+	12.7430i	−0.405616	+	0.702547i
$330$	−1.78327			−0.0981657
$331$	10.2181	−	17.6983i	0.561639	−	0.972788i	−0.435714	−	0.900085i	$-0.643504\pi$
$331$	10.2181	−	17.6983i	0.561639	−	0.972788i	0.997354	−	0.0727029i	$-0.0231625\pi$
$332$	−0.714189	+	1.23701i	−0.0391962	+	0.0678899i
$333$	13.9618			0.765103
$334$	−7.59301	+	13.1515i	−0.415471	+	0.719616i
$335$	−10.1804	−	17.6330i	−0.556214	−	0.963392i
$336$	−2.56231	−	4.43806i	−0.139786	−	0.242116i
$337$	−12.0421			−0.655976			−0.327988	−	0.944682i	$-0.606370\pi$
$337$	−12.0421			−0.655976			−0.327988	+	0.944682i	$0.606370\pi$
$338$	−19.3289	+	8.35259i	−1.05136	+	0.454321i
$339$	2.89342			0.157149
$340$	−3.05524	−	5.29182i	−0.165693	−	0.286989i
$341$	0.723118	+	1.25248i	0.0391590	+	0.0678254i
$342$	−8.27884	+	14.3394i	−0.447668	+	0.775384i
$343$	20.0029			1.08005
$344$	10.7995	−	18.7053i	0.582270	−	1.00852i
$345$	−0.327604	+	0.567426i	−0.0176376	+	0.0305492i
$346$	−1.76419			−0.0948437
$347$	7.42605	−	12.8623i	0.398651	−	0.690484i	−0.594909	−	0.803793i	$-0.702812\pi$
$347$	7.42605	−	12.8623i	0.398651	−	0.690484i	0.993560	+	0.113309i	$0.0361451\pi$
$348$	0.206087	+	0.356954i	0.0110474	+	0.0191347i
$349$	−14.6793	−	25.4252i	−0.785763	−	1.36098i	−0.928542	−	0.371227i	$-0.878937\pi$
$349$	−14.6793	−	25.4252i	−0.785763	−	1.36098i	0.142779	−	0.989755i	$-0.454396\pi$
$350$	−9.44531			−0.504873
$351$	−7.23140	−	8.12055i	−0.385984	−	0.433443i
$352$	−4.93165			−0.262858
$353$	−12.1543	−	21.0519i	−0.646908	−	1.12048i	−0.983857	−	0.178955i	$-0.942728\pi$
$353$	−12.1543	−	21.0519i	−0.646908	−	1.12048i	0.336949	−	0.941523i	$-0.390605\pi$
$354$	0.657769	+	1.13929i	0.0349600	+	0.0605526i
$355$	5.45078	−	9.44103i	0.289297	−	0.501078i
$356$	−0.468960			−0.0248548
$357$	−3.57834	+	6.19787i	−0.189386	+	0.328026i
$358$	12.2923	−	21.2908i	0.649666	−	1.12526i
$359$	18.0503			0.952661			0.476330	−	0.879266i	$-0.341967\pi$
$359$	18.0503			0.952661			0.476330	+	0.879266i	$0.341967\pi$
$360$	−4.38335	+	7.59219i	−0.231023	+	0.400144i
$361$	2.44928	+	4.24227i	0.128909	+	0.223277i
$362$	−13.8872	−	24.0533i	−0.729895	−	1.26422i
$363$	−4.69503			−0.246425
$364$	−1.41390	+	4.27155i	−0.0741084	+	0.223890i
$365$	14.5952			0.763947
$366$	2.23804	+	3.87641i	0.116984	+	0.202623i
$367$	13.5854	+	23.5306i	0.709152	+	1.22829i	0.965172	+	0.261616i	$0.0842554\pi$
$367$	13.5854	+	23.5306i	0.709152	+	1.22829i	−0.256020	+	0.966671i	$0.582411\pi$
$368$	−2.09071	+	3.62121i	−0.108986	+	0.188769i
$369$	−23.7717			−1.23751
$370$	5.99964	−	10.3917i	0.311907	−	0.540238i
$371$	−10.9267	+	18.9257i	−0.567288	+	0.982571i
$372$	0.328613			0.0170378
$373$	−1.31713	+	2.28134i	−0.0681985	+	0.118123i	−0.898108	−	0.439774i	$-0.855058\pi$
$373$	−1.31713	+	2.28134i	−0.0681985	+	0.118123i	0.829910	+	0.557898i	$0.188392\pi$
$374$	7.94660	+	13.7639i	0.410909	+	0.711715i
$375$	−3.01218	−	5.21725i	−0.155548	−	0.269418i
$376$	−16.3913			−0.845316
$377$	−1.42110	+	4.29330i	−0.0731903	+	0.221116i
$378$	−9.77663			−0.502855
$379$	−0.334480	−	0.579337i	−0.0171811	−	0.0297585i	0.857307	−	0.514805i	$-0.172136\pi$
$379$	−0.334480	−	0.579337i	−0.0171811	−	0.0297585i	−0.874488	+	0.485047i	$0.838803\pi$
$380$	1.69101	+	2.92892i	0.0867470	+	0.150250i
$381$	1.60366	−	2.77763i	0.0821581	−	0.142302i
$382$	−25.7044			−1.31515
$383$	−4.81607	+	8.34168i	−0.246090	+	0.426240i	−0.962437	−	0.271504i	$-0.912479\pi$
$383$	−4.81607	+	8.34168i	−0.246090	+	0.426240i	0.716348	+	0.697743i	$0.245812\pi$
$384$	3.58697	−	6.21282i	0.183047	−	0.317047i
$385$	−4.18099			−0.213083
$386$	−2.60507	+	4.51212i	−0.132595	+	0.229661i
$387$	−13.1861	−	22.8390i	−0.670287	−	1.16097i
$388$	−1.26701	−	2.19452i	−0.0643225	−	0.111410i
$389$	0.166494			0.00844160			0.00422080	−	0.999991i	$-0.498656\pi$
$389$	0.166494			0.00844160			0.00422080	+	0.999991i	$0.498656\pi$
$390$	−4.35366	+	0.900432i	−0.220456	+	0.0455951i
$391$	5.83946			0.295314
$392$	3.33786	+	5.78135i	0.168588	+	0.292002i
$393$	4.15472	+	7.19618i	0.209578	+	0.362999i
$394$	−2.08837	+	3.61717i	−0.105211	+	0.182230i
$395$	−7.91706			−0.398350
$396$	−1.22739	+	2.12590i	−0.0616785	+	0.106830i
$397$	4.09453	−	7.09193i	0.205498	−	0.355934i	−0.744793	−	0.667296i	$-0.767452\pi$
$397$	4.09453	−	7.09193i	0.205498	−	0.355934i	0.950291	+	0.311362i	$0.100785\pi$
$398$	−14.4789			−0.725764
$399$	1.98054	−	3.43039i	0.0991510	−	0.171735i
$400$	−7.07754	−	12.2587i	−0.353877	−	0.612933i
$401$	−9.23240	−	15.9910i	−0.461044	−	0.798552i	0.537969	−	0.842964i	$-0.319192\pi$
$401$	−9.23240	−	15.9910i	−0.461044	−	0.798552i	−0.999013	+	0.0444129i	$0.985858\pi$
$402$	12.0331			0.600156
$403$	2.39783	+	2.69266i	0.119444	+	0.134131i
$404$	3.92267			0.195160
$405$	4.75022	+	8.22761i	0.236040	+	0.408833i
$406$	2.03306	+	3.52137i	0.100899	+	0.174763i
$407$	−3.70873	+	6.42371i	−0.183835	+	0.318411i
$408$	−7.97227			−0.394686
$409$	−0.461538	+	0.799407i	−0.0228216	+	0.0395282i	−0.877211	−	0.480106i	$-0.840598\pi$
$409$	−0.461538	+	0.799407i	−0.0228216	+	0.0395282i	0.854389	+	0.519634i	$0.173932\pi$
$410$	−10.2151	+	17.6931i	−0.504490	+	0.873802i
$411$	−3.50636			−0.172956
$412$	4.00234	−	6.93225i	0.197181	−	0.341528i
$413$	1.54218	+	2.67114i	0.0758859	+	0.131438i
$414$	1.89749	+	3.28655i	0.0932566	+	0.161525i
$415$	−3.30898			−0.162431
$416$	−12.0401	+	2.49016i	−0.590314	+	0.122090i
$417$	2.70248			0.132341
$418$	−4.39828	−	7.61804i	−0.215127	−	0.372611i
$419$	−16.4894	−	28.5604i	−0.805558	−	1.39527i	−0.915914	−	0.401375i	$-0.868532\pi$
$419$	−16.4894	−	28.5604i	−0.805558	−	1.39527i	0.110356	−	0.993892i	$-0.464801\pi$
$420$	−0.475003	+	0.822729i	−0.0231778	+	0.0401450i
$421$	4.19542			0.204472			0.102236	−	0.994760i	$-0.467400\pi$
$421$	4.19542			0.204472			0.102236	+	0.994760i	$0.467400\pi$
$422$	−6.69164	+	11.5903i	−0.325744	+	0.564205i
$423$	−10.0068	+	17.3323i	−0.486547	+	0.842725i
$424$	−24.3439			−1.18225
$425$	−9.88399	+	17.1196i	−0.479444	+	0.830421i
$426$	3.22138	+	5.57959i	0.156076	+	0.270332i
$427$	5.24724	+	9.08849i	0.253932	+	0.439823i
$428$	−3.45941			−0.167217
$429$	2.69125	−	0.556609i	0.129935	−	0.0268734i
$430$	−22.6652			−1.09301
$431$	13.7061	+	23.7397i	0.660199	+	1.14350i	0.980563	+	0.196204i	$0.0628615\pi$
$431$	13.7061	+	23.7397i	0.660199	+	1.14350i	−0.320364	+	0.947295i	$0.603805\pi$
$432$	−7.32580	−	12.6887i	−0.352463	−	0.610483i
$433$	−14.9385	+	25.8742i	−0.717898	+	1.24344i	0.243932	+	0.969792i	$0.421562\pi$
$433$	−14.9385	+	25.8742i	−0.717898	+	1.24344i	−0.961831	+	0.273644i	$0.911771\pi$
$434$	3.24179			0.155611
$435$	−0.477422	+	0.826918i	−0.0228906	+	0.0396477i
$436$	4.76250	−	8.24889i	0.228082	−	0.395050i
$437$	−3.23202			−0.154609
$438$	−4.31283	+	7.47004i	−0.206075	+	0.356932i
$439$	−9.02970	−	15.6399i	−0.430964	−	0.746451i	0.565993	−	0.824410i	$-0.308493\pi$
$439$	−9.02970	−	15.6399i	−0.430964	−	0.746451i	−0.996957	+	0.0779589i	$0.975160\pi$
$440$	−2.32873	−	4.03349i	−0.111018	−	0.192289i
$441$	8.15100			0.388143
$442$	26.3506	+	29.5906i	1.25337	+	1.40748i
$443$	6.44026			0.305986			0.152993	−	0.988227i	$-0.451109\pi$
$443$	6.44026			0.305986			0.152993	+	0.988227i	$0.451109\pi$
$444$	0.842697	+	1.45959i	0.0399926	+	0.0692693i
$445$	−0.543196	−	0.940844i	−0.0257500	−	0.0446003i
$446$	−2.75531	+	4.77234i	−0.130468	+	0.225977i
$447$	−8.06527			−0.381474
$448$	4.19628	−	7.26818i	0.198256	−	0.343389i
$449$	13.0108	−	22.5354i	0.614019	−	1.06351i	−0.376537	−	0.926402i	$-0.622885\pi$
$449$	13.0108	−	22.5354i	0.614019	−	1.06351i	0.990556	−	0.137111i	$-0.0437816\pi$
$450$	−12.8469			−0.605610
$451$	6.31457	−	10.9372i	0.297342	−	0.515011i
$452$	−1.71155	−	2.96449i	−0.0805046	−	0.139438i
$453$	−5.38328	−	9.32412i	−0.252929	−	0.438085i
$454$	−32.9289			−1.54543
$455$	−10.2074	+	2.11112i	−0.478532	+	0.0989710i
$456$	4.41249			0.206634
$457$	−3.40853	−	5.90374i	−0.159444	−	0.276165i	0.775224	−	0.631686i	$-0.217637\pi$
$457$	−3.40853	−	5.90374i	−0.159444	−	0.276165i	−0.934668	+	0.355521i	$0.884304\pi$
$458$	2.56973	+	4.45091i	0.120076	+	0.207977i
$459$	−10.2307	+	17.7201i	−0.477527	+	0.827102i
$460$	0.775152			0.0361416
$461$	6.72482	−	11.6477i	0.313206	−	0.542489i	−0.665848	−	0.746087i	$-0.731930\pi$
$461$	6.72482	−	11.6477i	0.313206	−	0.542489i	0.979055	+	0.203598i	$0.0652636\pi$
$462$	1.23547	−	2.13990i	0.0574793	−	0.0995570i
$463$	−27.2467			−1.26626			−0.633132	−	0.774044i	$-0.718231\pi$
$463$	−27.2467			−1.26626			−0.633132	+	0.774044i	$0.718231\pi$
$464$	−3.04682	+	5.27724i	−0.141445	+	0.244990i
$465$	0.380633	+	0.659275i	0.0176514	+	0.0305732i
$466$	−14.8227	−	25.6737i	−0.686649	−	1.18931i
$467$	19.7642			0.914577			0.457288	−	0.889319i	$-0.348821\pi$
$467$	19.7642			0.914577			0.457288	+	0.889319i	$0.348821\pi$
$468$	−1.92310	+	5.80989i	−0.0888951	+	0.268562i
$469$	28.2124			1.30273
$470$	8.60021	+	14.8960i	0.396698	+	0.687101i
$471$	−5.72012	−	9.90753i	−0.263569	−	0.456515i
$472$	−1.71793	+	2.97555i	−0.0790743	+	0.136961i
$473$	14.0107			0.644212
$474$	2.33946	−	4.05207i	0.107455	−	0.186118i
$475$	5.47058	−	9.47533i	0.251008	−	0.434758i
$476$	8.46682			0.388076
$477$	−14.8619	+	25.7415i	−0.680477	+	1.17862i
$478$	22.8989	+	39.6621i	1.04737	+	1.81410i
$479$	−19.8758	−	34.4260i	−0.908151	−	1.57296i	−0.816631	−	0.577160i	$-0.804161\pi$
$479$	−19.8758	−	34.4260i	−0.908151	−	1.57296i	−0.0915194	−	0.995803i	$-0.529172\pi$
$480$	−2.59591			−0.118487
$481$	−5.81091	+	17.5554i	−0.264955	+	0.800459i
$482$	45.3736			2.06671
$483$	−0.453935	−	0.786239i	−0.0206548	−	0.0357751i
$484$	2.77726	+	4.81036i	0.126239	+	0.218653i
$485$	2.93515	−	5.08382i	0.133278	−	0.230844i
$486$	−20.2691			−0.919424
$487$	9.38501	−	16.2553i	0.425275	−	0.736599i	−0.571171	−	0.820831i	$-0.693511\pi$
$487$	9.38501	−	16.2553i	0.425275	−	0.736599i	0.996446	+	0.0842327i	$0.0268439\pi$
$488$	−5.84523	+	10.1242i	−0.264601	+	0.458303i
$489$	12.1421			0.549083
$490$	3.50263	−	6.06674i	0.158233	−	0.274067i
$491$	−5.23904	−	9.07429i	−0.236435	−	0.409517i	0.723254	−	0.690582i	$-0.242646\pi$
$491$	−5.23904	−	9.07429i	−0.236435	−	0.409517i	−0.959689	+	0.281065i	$0.909312\pi$
$492$	−1.43480	−	2.48514i	−0.0646856	−	0.112039i
$493$	8.50994			0.383268
$494$	−14.5845	−	16.3778i	−0.656188	−	0.736871i
$495$	−5.68673			−0.255599
$496$	2.42913	+	4.20738i	0.109071	+	0.188917i
$497$	7.55273	+	13.0817i	0.338786	+	0.586795i
$498$	0.977793	−	1.69359i	0.0438159	−	0.0758914i
$499$	27.2992			1.22208			0.611039	−	0.791600i	$-0.290752\pi$
$499$	27.2992			1.22208			0.611039	+	0.791600i	$0.290752\pi$
$500$	−3.56360	+	6.17234i	−0.159369	+	0.276035i
$501$	2.47065	−	4.27928i	0.110380	−	0.191184i
$502$	18.0501			0.805614
$503$	−0.572859	+	0.992222i	−0.0255425	+	0.0442410i	−0.878514	−	0.477716i	$-0.841465\pi$
$503$	−0.572859	+	0.992222i	−0.0255425	+	0.0442410i	0.852972	+	0.521957i	$0.174798\pi$
$504$	−6.07368	−	10.5199i	−0.270543	−	0.468595i
$505$	4.54363	+	7.86980i	0.202189	+	0.350201i
$506$	−2.01615			−0.0896289
$507$	6.28934	−	2.71780i	0.279319	−	0.120702i
$508$	−3.79447			−0.168352
$509$	−9.93045	−	17.2001i	−0.440160	−	0.762379i	0.557541	−	0.830149i	$-0.311745\pi$
$509$	−9.93045	−	17.2001i	−0.440160	−	0.762379i	−0.997701	+	0.0677703i	$0.978411\pi$
$510$	4.18291	+	7.24501i	0.185222	+	0.320814i
$511$	−10.1117	+	17.5140i	−0.447316	+	0.774774i
$512$	5.09664			0.225242
$513$	5.66247	−	9.80769i	0.250004	−	0.433020i
$514$	−0.103497	+	0.179262i	−0.00456506	+	0.00790691i
$515$	18.5436			0.817130
$516$	1.59175	−	2.75700i	0.0700731	−	0.121370i
$517$	−5.31629	−	9.20808i	−0.233810	−	0.404971i
$518$	8.31325	+	14.3990i	0.365263	+	0.632655i
$519$	0.574041			0.0251976
$520$	−7.72199	−	8.67146i	−0.338632	−	0.380269i
$521$	−21.3480			−0.935272			−0.467636	−	0.883921i	$-0.654894\pi$
$521$	−21.3480			−0.935272			−0.467636	+	0.883921i	$0.654894\pi$
$522$	2.76524	+	4.78954i	0.121031	+	0.209633i
$523$	18.4355	+	31.9312i	0.806128	+	1.39625i	0.915527	+	0.402257i	$0.131774\pi$
$523$	18.4355	+	31.9312i	0.806128	+	1.39625i	−0.109399	+	0.993998i	$0.534893\pi$
$524$	4.91530	−	8.51354i	0.214726	−	0.371916i
$525$	3.07336			0.134132
$526$	8.88866	−	15.3956i	0.387564	−	0.671280i
$527$	3.39235	−	5.87572i	0.147773	−	0.255950i
$528$	3.70304			0.161154
$529$	11.1296	−	19.2771i	0.483896	−	0.838133i
$530$	12.7728	+	22.1232i	0.554816	+	0.960969i
$531$	2.09758	+	3.63312i	0.0910273	+	0.157664i
$532$	−4.68621			−0.203173
$533$	9.89380	−	29.8903i	0.428548	−	1.29469i
$534$	0.642051			0.0277843
$535$	−4.00703	−	6.94038i	−0.173239	−	0.300059i
$536$	15.7138	+	27.2170i	0.678731	+	1.17560i
$537$	−3.99971	+	6.92770i	−0.172600	+	0.298952i
$538$	26.1288			1.12649
$539$	−2.16518	+	3.75020i	−0.0932609	+	0.161533i
$540$	−1.35806	+	2.35223i	−0.0584416	+	0.101224i
$541$	−33.2618			−1.43004			−0.715019	−	0.699105i	$-0.753582\pi$
$541$	−33.2618			−1.43004			−0.715019	+	0.699105i	$0.753582\pi$
$542$	−6.29560	+	10.9043i	−0.270419	+	0.468380i
$543$	4.51868	+	7.82658i	0.193915	+	0.335871i
$544$	11.5679	+	20.0362i	0.495969	+	0.859043i
$545$	22.0656			0.945186
$546$	1.93576	−	5.84816i	0.0828429	−	0.250278i
$547$	−18.3043			−0.782635			−0.391318	−	0.920256i	$-0.627981\pi$
$547$	−18.3043			−0.782635			−0.391318	+	0.920256i	$0.627981\pi$
$548$	2.07412	+	3.59249i	0.0886022	+	0.153464i
$549$	7.13697	+	12.3616i	0.304599	+	0.527580i
$550$	3.41258	−	5.91076i	0.145513	−	0.252036i
$551$	−4.71007			−0.200656
$552$	0.505667	−	0.875840i	0.0215226	−	0.0372782i
$553$	5.48503	−	9.50036i	0.233247	−	0.403996i
$554$	50.9275			2.16370
$555$	−1.95219	+	3.38129i	−0.0828659	+	0.143528i
$556$	−1.59860	−	2.76886i	−0.0677959	−	0.117426i
$557$	6.53615	+	11.3209i	0.276946	+	0.479684i	0.970624	−	0.240601i	$-0.0773445\pi$
$557$	6.53615	+	11.3209i	0.276946	+	0.479684i	−0.693679	+	0.720285i	$0.744011\pi$
$558$	4.40928			0.186660
$559$	34.2056	−	7.07446i	1.44674	−	0.299218i
$560$	−14.0450			−0.593509
$561$	−2.58570	−	4.47856i	−0.109168	−	0.189085i
$562$	−10.9507	−	18.9672i	−0.461928	−	0.800083i
$563$	−12.5936	+	21.8128i	−0.530758	+	0.919300i	0.468598	+	0.883412i	$0.344759\pi$
$563$	−12.5936	+	21.8128i	−0.530758	+	0.919300i	−0.999356	+	0.0358883i	$0.988574\pi$
$564$	−2.41593			−0.101729
$565$	3.96498	−	6.86754i	0.166808	−	0.288920i
$566$	23.9604	−	41.5006i	1.00713	−	1.74440i
$567$	−13.1640			−0.552837
$568$	−8.41346	+	14.5725i	−0.353021	+	0.611450i
$569$	6.39672	+	11.0794i	0.268164	+	0.464474i	0.968388	−	0.249449i	$-0.0802496\pi$
$569$	6.39672	+	11.0794i	0.268164	+	0.464474i	−0.700223	+	0.713924i	$0.746916\pi$
$570$	−2.31515	−	4.00996i	−0.0969711	−	0.167959i
$571$	−10.6470			−0.445562			−0.222781	−	0.974869i	$-0.571513\pi$
$571$	−10.6470			−0.445562			−0.222781	+	0.974869i	$0.571513\pi$
$572$	−2.16224	−	2.42810i	−0.0904079	−	0.101524i
$573$	8.36382			0.349403
$574$	−14.1543	−	24.5160i	−0.590791	−	1.02328i
$575$	−1.25385	−	2.17172i	−0.0522890	−	0.0905672i
$576$	5.70752	−	9.88572i	0.237813	−	0.411905i
$577$	2.37186			0.0987419			0.0493710	−	0.998781i	$-0.484278\pi$
$577$	2.37186			0.0987419			0.0493710	+	0.998781i	$0.484278\pi$
$578$	23.5120	−	40.7240i	0.977972	−	1.69390i
$579$	0.847650	−	1.46817i	0.0352271	−	0.0610152i
$580$	1.12964			0.0469058
$581$	2.29250	−	3.97073i	0.0951090	−	0.164734i
$582$	1.73465	+	3.00451i	0.0719037	+	0.124541i
$583$	−7.89562	−	13.6756i	−0.327003	−	0.566386i
$584$	−22.5281			−0.932221
$585$	−13.8835	+	2.87142i	−0.574013	+	0.118718i
$586$	−21.1091			−0.872010
$587$	−3.44208	−	5.96186i	−0.142070	−	0.246072i	0.786206	−	0.617964i	$-0.212042\pi$
$587$	−3.44208	−	5.96186i	−0.142070	−	0.246072i	−0.928276	+	0.371892i	$0.878709\pi$
$588$	0.491972	+	0.852121i	0.0202886	+	0.0351409i
$589$	−1.87759	+	3.25209i	−0.0773649	+	0.134000i
$590$	3.60548			0.148435
$591$	0.679524	−	1.17697i	0.0279519	−	0.0484141i
$592$	−12.4585	+	21.5788i	−0.512042	+	0.886884i
$593$	−1.06867			−0.0438849			−0.0219424	−	0.999759i	$-0.506985\pi$
$593$	−1.06867			−0.0438849			−0.0219424	+	0.999759i	$0.506985\pi$
$594$	3.53228	−	6.11809i	0.144931	−	0.251028i
$595$	9.80711	+	16.9864i	0.402052	+	0.696375i
$596$	4.77087	+	8.26339i	0.195422	+	0.338481i
$597$	4.71122			0.192818
$598$	−4.92221	+	1.01802i	−0.201284	+	0.0416300i
$599$	30.2653			1.23661			0.618304	−	0.785939i	$-0.287820\pi$
$599$	30.2653			1.23661			0.618304	+	0.785939i	$0.287820\pi$
$600$	1.71180	+	2.96493i	0.0698840	+	0.121043i
$601$	0.671115	+	1.16241i	0.0273754	+	0.0474155i	0.879389	−	0.476105i	$-0.157952\pi$
$601$	0.671115	+	1.16241i	0.0273754	+	0.0474155i	−0.852013	+	0.523520i	$0.824618\pi$
$602$	15.7027	−	27.1979i	0.639996	−	1.10851i
$603$	38.3727			1.56266
$604$	−6.36877	+	11.0310i	−0.259141	+	0.448846i
$605$	−6.43380	+	11.1437i	−0.261571	+	0.453054i
$606$	−5.37051			−0.218162
$607$	−0.817964	+	1.41675i	−0.0332001	+	0.0575043i	−0.882148	−	0.470972i	$-0.843903\pi$
$607$	−0.817964	+	1.41675i	−0.0332001	+	0.0575043i	0.848948	+	0.528477i	$0.177237\pi$
$608$	−6.40258	−	11.0896i	−0.259659	−	0.449743i
$609$	−0.661527	−	1.14580i	−0.0268064	−	0.0464301i
$610$	12.2675			0.496698
$611$	−17.6286	−	19.7962i	−0.713177	−	0.800867i
$612$	11.5160			0.465508
$613$	15.7934	+	27.3550i	0.637891	+	1.10486i	0.985895	+	0.167366i	$0.0535262\pi$
$613$	15.7934	+	27.3550i	0.637891	+	1.10486i	−0.348004	+	0.937493i	$0.613140\pi$
$614$	2.64747	+	4.58556i	0.106843	+	0.185058i
$615$	3.32385	−	5.75707i	0.134030	−	0.232148i
$616$	6.45350			0.260019
$617$	−8.63555	+	14.9572i	−0.347654	+	0.602155i	−0.985832	−	0.167734i	$-0.946355\pi$
$617$	−8.63555	+	14.9572i	−0.347654	+	0.602155i	0.638178	+	0.769889i	$0.279688\pi$
$618$	−5.47958	+	9.49091i	−0.220421	+	0.381780i
$619$	0.561810			0.0225811			0.0112905	−	0.999936i	$-0.496406\pi$
$619$	0.561810			0.0225811			0.0112905	+	0.999936i	$0.496406\pi$
$620$	0.450313	−	0.779965i	0.0180850	−	0.0313241i
$621$	−1.29783	−	2.24790i	−0.0520800	−	0.0902052i
$622$	−6.49559	−	11.2507i	−0.260449	−	0.451112i
$623$	1.50533			0.0603098
$624$	9.04056	−	1.86979i	0.361912	−	0.0748514i
$625$	−1.94281			−0.0777124
$626$	16.9777	+	29.4062i	0.678565	+	1.17531i
$627$	1.43113	+	2.47879i	0.0571539	+	0.0989934i
$628$	−6.76726	+	11.7212i	−0.270043	+	0.467729i
$629$	34.7974			1.38746
$630$	−6.37350	+	11.0392i	−0.253926	+	0.439813i
$631$	−18.2223	+	31.5620i	−0.725420	+	1.25646i	0.233381	+	0.972385i	$0.425021\pi$
$631$	−18.2223	+	31.5620i	−0.725420	+	1.25646i	−0.958801	+	0.284079i	$0.908312\pi$
$632$	12.2202			0.486095
$633$	2.17736	−	3.77129i	0.0865421	−	0.149895i
$634$	17.5417	+	30.3831i	0.696669	+	1.20667i
$635$	−4.39513	−	7.61260i	−0.174416	−	0.302097i
$636$	−3.58808			−0.142277
$637$	−3.39245	+	10.2490i	−0.134414	+	0.406080i
$638$	−2.93817			−0.116323
$639$	10.2728	+	17.7929i	0.406384	+	0.703877i
$640$	−9.83076	−	17.0274i	−0.388595	−	0.673066i
$641$	−3.91285	+	6.77725i	−0.154548	+	0.267685i	−0.932894	−	0.360150i	$-0.882726\pi$
$641$	−3.91285	+	6.77725i	−0.154548	+	0.267685i	0.778346	+	0.627835i	$0.216059\pi$
$642$	4.73626			0.186925
$643$	−1.13063	+	1.95831i	−0.0445877	+	0.0772282i	−0.887458	−	0.460889i	$-0.847531\pi$
$643$	−1.13063	+	1.95831i	−0.0445877	+	0.0772282i	0.842870	+	0.538117i	$0.180864\pi$
$644$	−0.537035	+	0.930171i	−0.0211621	+	0.0366539i
$645$	7.37491			0.290387
$646$	−20.6336	+	35.7384i	−0.811816	+	1.40611i
$647$	6.81110	+	11.7972i	0.267772	+	0.463795i	0.968286	−	0.249844i	$-0.0803792\pi$
$647$	6.81110	+	11.7972i	0.267772	+	0.463795i	−0.700514	+	0.713639i	$0.747046\pi$
$648$	−7.33211	−	12.6996i	−0.288033	−	0.498887i
$649$	−2.22875			−0.0874863
$650$	5.34690	−	16.1536i	0.209723	−	0.633596i
$651$	−1.05483			−0.0413420
$652$	−7.18242	−	12.4403i	−0.281285	−	0.487200i
$653$	2.82250	+	4.88871i	0.110453	+	0.191310i	0.915953	−	0.401286i	$-0.131437\pi$
$653$	2.82250	+	4.88871i	0.110453	+	0.191310i	−0.805500	+	0.592596i	$0.798103\pi$
$654$	−6.52031	+	11.2935i	−0.254964	+	0.441611i
$655$	22.7735			0.889836
$656$	21.2122	−	36.7406i	0.828197	−	1.43448i
$657$	−13.7533	+	23.8214i	−0.536568	+	0.929363i
$658$	−23.8333			−0.929119
$659$	−1.34635	+	2.33195i	−0.0524465	+	0.0908399i	−0.891057	−	0.453892i	$-0.850035\pi$
$659$	−1.34635	+	2.33195i	−0.0524465	+	0.0908399i	0.838610	+	0.544732i	$0.183369\pi$
$660$	−0.343235	−	0.594501i	−0.0133604	−	0.0231409i
$661$	−0.0287582	−	0.0498106i	−0.00111856	−	0.00193741i	0.865466	−	0.500968i	$-0.167023\pi$
$661$	−0.0287582	−	0.0498106i	−0.00111856	−	0.00193741i	−0.866584	+	0.499031i	$0.833689\pi$
$662$	33.1012			1.28651
$663$	−8.57408	−	9.62831i	−0.332990	−	0.373933i
$664$	5.10752			0.198210
$665$	−5.42803	−	9.40163i	−0.210490	−	0.364580i
$666$	11.3072	+	19.5846i	0.438144	+	0.758887i
$667$	−0.539770	+	0.934908i	−0.0209000	+	0.0361998i
$668$	−5.84586			−0.226183
$669$	0.896535	−	1.55284i	0.0346621	−	0.0600364i
$670$	16.4895	−	28.5606i	0.637043	−	1.10339i
$671$	−7.58328			−0.292749
$672$	1.79848	−	3.11505i	0.0693778	−	0.120166i
$673$	−17.7331	−	30.7146i	−0.683560	−	1.18396i	−0.973887	−	0.227033i	$-0.927098\pi$
$673$	−17.7331	−	30.7146i	−0.683560	−	1.18396i	0.290328	−	0.956927i	$-0.406236\pi$
$674$	−9.75247	−	16.8918i	−0.375651	−	0.650646i
$675$	8.78690			0.338208
$676$	−6.50491	−	4.83616i	−0.250189	−	0.186006i
$677$	26.7437			1.02784			0.513922	−	0.857837i	$-0.328192\pi$
$677$	26.7437			1.02784			0.513922	+	0.857837i	$0.328192\pi$
$678$	2.34327	+	4.05867i	0.0899929	+	0.155872i
$679$	4.06701	+	7.04427i	0.156077	+	0.270334i
$680$	−10.9247	+	18.9222i	−0.418945	+	0.725634i
$681$	10.7146			0.410583
$682$	−1.17125	+	2.02867i	−0.0448496	+	0.0776818i
$683$	2.52931	−	4.38089i	0.0967813	−	0.167630i	−0.813569	−	0.581468i	$-0.802479\pi$
$683$	2.52931	−	4.38089i	0.0967813	−	0.167630i	0.910351	+	0.413838i	$0.135812\pi$
$684$	−6.37389			−0.243712
$685$	−4.80491	+	8.32236i	−0.183586	+	0.317981i
$686$	16.1996	+	28.0585i	0.618503	+	1.07128i
$687$	−0.836151	−	1.44826i	−0.0319012	−	0.0552544i
$688$	47.0653			1.79435
$689$	−26.1816	−	29.4008i	−0.997438	−	1.12008i
$690$	−1.06126			−0.0404013
$691$	−4.15114	−	7.18998i	−0.157917	−	0.273520i	0.776201	−	0.630486i	$-0.217144\pi$
$691$	−4.15114	−	7.18998i	−0.157917	−	0.273520i	−0.934117	+	0.356966i	$0.883811\pi$
$692$	−0.339564	−	0.588142i	−0.0129083	−	0.0223578i
$693$	3.93983	−	6.82399i	0.149662	−	0.259222i
$694$	24.0563			0.913166
$695$	3.70332	−	6.41434i	0.140475	−	0.243310i
$696$	0.736916	−	1.27638i	0.0279327	−	0.0483809i
$697$	−59.2468			−2.24413
$698$	23.7764	−	41.1819i	0.899950	−	1.55876i
$699$	4.82308	+	8.35382i	0.182426	+	0.315971i
$700$	−1.81799	−	3.14885i	−0.0687136	−	0.119015i
$701$	31.5385			1.19119			0.595597	−	0.803283i	$-0.296915\pi$
$701$	31.5385			1.19119			0.595597	+	0.803283i	$0.296915\pi$
$702$	5.53445	−	16.7202i	0.208884	−	0.631064i
$703$	−19.2596			−0.726391
$704$	3.03222	+	5.25196i	0.114281	+	0.197941i
$705$	−2.79837	−	4.84692i	−0.105393	−	0.182546i
$706$	19.6867	−	34.0983i	0.740917	−	1.28331i
$707$	−12.5915			−0.473553
$708$	−0.253209	+	0.438570i	−0.00951617	+	0.0164825i
$709$	−17.1381	+	29.6841i	−0.643636	+	1.11481i	0.340978	+	0.940071i	$0.389242\pi$
$709$	−17.1381	+	29.6841i	−0.643636	+	1.11481i	−0.984615	+	0.174740i	$0.944092\pi$
$710$	17.6576			0.662676
$711$	7.46040	−	12.9218i	0.279787	−	0.484605i
$712$	0.838441	+	1.45222i	0.0314219	+	0.0544243i
$713$	0.430341	+	0.745372i	0.0161164	+	0.0279144i
$714$	−11.5919			−0.433815
$715$	2.36682	−	7.15043i	0.0885140	−	0.267411i
$716$	9.46383			0.353680
$717$	−7.45095	−	12.9054i	−0.278261	−	0.481962i
$718$	14.6183	+	25.3197i	0.545551	+	0.944921i
$719$	−10.9042	+	18.8867i	−0.406660	+	0.704355i	−0.994513	−	0.104612i	$-0.966640\pi$
$719$	−10.9042	+	18.8867i	−0.406660	+	0.704355i	0.587853	+	0.808968i	$0.299973\pi$
$720$	−19.1031			−0.711931
$721$	−12.8472	+	22.2521i	−0.478456	+	0.828711i
$722$	−3.96716	+	6.87132i	−0.147642	+	0.255724i
$723$	−14.7639			−0.549074
$724$	5.34589	−	9.25935i	0.198678	−	0.344121i
$725$	−1.82725	−	3.16489i	−0.0678623	−	0.117541i
$726$	−3.80233	−	6.58583i	−0.141118	−	0.244423i
$727$	11.6908			0.433586			0.216793	−	0.976218i	$-0.430440\pi$
$727$	11.6908			0.433586			0.216793	+	0.976218i	$0.430440\pi$
$728$	15.7555	−	3.25859i	0.583938	−	0.120771i
$729$	−13.1366			−0.486540
$730$	11.8201	+	20.4730i	0.437482	+	0.757740i
$731$	−32.8640	−	56.9222i	−1.21552	−	2.10534i
$732$	−0.861537	+	1.49223i	−0.0318433	+	0.0551542i
$733$	−10.3804			−0.383408			−0.191704	−	0.981453i	$-0.561401\pi$
$733$	−10.3804			−0.383408			−0.191704	+	0.981453i	$0.561401\pi$
$734$	−22.0046	+	38.1131i	−0.812206	+	1.40678i
$735$	−1.13970	+	1.97402i	−0.0420385	+	0.0728129i
$736$	−2.93492			−0.108182
$737$	−10.1931	+	17.6550i	−0.375467	+	0.650329i
$738$	−19.2518	−	33.3452i	−0.708670	−	1.22745i
$739$	16.9505	+	29.3592i	0.623536	+	1.08000i	0.988822	+	0.149100i	$0.0476377\pi$
$739$	16.9505	+	29.3592i	0.623536	+	1.08000i	−0.365287	+	0.930895i	$0.619029\pi$
$740$	4.61913			0.169803
$741$	4.74557	+	5.32907i	0.174333	+	0.195768i
$742$	−35.3966			−1.29945
$743$	9.93091	+	17.2008i	0.364330	+	0.631038i	0.988668	−	0.150116i	$-0.0479648\pi$
$743$	9.93091	+	17.2008i	0.364330	+	0.631038i	−0.624339	+	0.781154i	$0.714631\pi$
$744$	−0.587519	−	1.01761i	−0.0215395	−	0.0373075i
$745$	−11.0522	+	19.1429i	−0.404921	+	0.701343i
$746$	−4.26679			−0.156218
$747$	3.11812	−	5.40073i	0.114086	−	0.197603i
$748$	−3.05905	+	5.29843i	−0.111850	+	0.193730i
$749$	11.1045			0.405749
$750$	4.87891	−	8.45052i	0.178153	−	0.308569i
$751$	3.34553	+	5.79463i	0.122080	+	0.211449i	0.920588	−	0.390536i	$-0.127710\pi$
$751$	3.34553	+	5.79463i	0.122080	+	0.211449i	−0.798508	+	0.601985i	$0.794377\pi$
$752$	−17.8587	−	30.9322i	−0.651240	−	1.12798i
$753$	−5.87321			−0.214032
$754$	−7.17322	+	1.48358i	−0.261233	+	0.0540288i
$755$	−29.5077			−1.07390
$756$	−1.88176	−	3.25930i	−0.0684389	−	0.118540i
$757$	11.0867	+	19.2027i	0.402952	+	0.697933i	0.994081	−	0.108644i	$-0.0346509\pi$
$757$	11.0867	+	19.2027i	0.402952	+	0.697933i	−0.591129	+	0.806577i	$0.701318\pi$
$758$	0.541767	−	0.938367i	0.0196778	−	0.0340830i
$759$	0.656024			0.0238122
$760$	6.04662	−	10.4731i	0.219334	−	0.379898i
$761$	−22.8099	+	39.5079i	−0.826859	+	1.43216i	0.0736312	+	0.997286i	$0.476541\pi$
$761$	−22.8099	+	39.5079i	−0.826859	+	1.43216i	−0.900490	+	0.434876i	$0.856792\pi$
$762$	5.19499			0.188195
$763$	−15.2873	+	26.4784i	−0.553438	+	0.958582i
$764$	−4.94747	−	8.56926i	−0.178993	−	0.310025i
$765$	13.3390	+	23.1038i	0.482273	+	0.835321i
$766$	−15.6014			−0.563703
$767$	−5.44126	+	1.12537i	−0.196473	+	0.0406348i
$768$	7.19985			0.259802
$769$	−2.84933	−	4.93519i	−0.102750	−	0.177968i	0.810067	−	0.586337i	$-0.199431\pi$
$769$	−2.84933	−	4.93519i	−0.102750	−	0.177968i	−0.912817	+	0.408370i	$0.866097\pi$
$770$	−3.38603	−	5.86478i	−0.122024	−	0.211352i
$771$	0.0336763	−	0.0583291i	0.00121282	−	0.00210067i
$772$	−2.00565			−0.0721849
$773$	−24.6486	+	42.6926i	−0.886547	+	1.53555i	−0.0426175	+	0.999091i	$0.513570\pi$
$773$	−24.6486	+	42.6926i	−0.886547	+	1.53555i	−0.843930	+	0.536454i	$0.819764\pi$
$774$	21.3579	−	36.9929i	0.767693	−	1.32968i
$775$	−2.91361			−0.104660
$776$	−4.53049	+	7.84704i	−0.162635	+	0.281692i
$777$	−2.70500	−	4.68520i	−0.0970414	−	0.168081i
$778$	0.134838	+	0.233546i	0.00483417	+	0.00837302i
$779$	32.7919			1.17489
$780$	−1.13815	−	1.27810i	−0.0407525	−	0.0457633i
$781$	−10.9152			−0.390575
$782$	4.72917	+	8.19116i	0.169115	+	0.292915i
$783$	−1.89134	−	3.27590i	−0.0675911	−	0.117071i
$784$	−7.27337	+	12.5979i	−0.259763	+	0.449923i
$785$	−31.3541			−1.11907
$786$	−6.72951	+	11.6558i	−0.240034	+	0.415750i
$787$	−3.39071	+	5.87289i	−0.120866	+	0.209346i	−0.920109	−	0.391661i	$-0.871900\pi$
$787$	−3.39071	+	5.87289i	−0.120866	+	0.209346i	0.799243	+	0.601007i	$0.205234\pi$
$788$	−1.60784			−0.0572770
$789$	−2.89223	+	5.00949i	−0.102966	+	0.178343i
$790$	−6.41174	−	11.1055i	−0.228119	−	0.395114i
$791$	5.49396	+	9.51583i	0.195343	+	0.338344i
$792$	8.77764			0.311900
$793$	−18.5138	+	3.82905i	−0.657443	+	0.135974i
$794$	13.2640			0.470723
$795$	−4.15607	−	7.19853i	−0.147401	−	0.255306i
$796$	−2.78684	−	4.82695i	−0.0987769	−	0.171087i
$797$	−11.0093	+	19.0687i	−0.389970	+	0.675449i	−0.992445	−	0.122689i	$-0.960848\pi$
$797$	−11.0093	+	19.0687i	−0.389970	+	0.675449i	0.602475	+	0.798138i	$0.294181\pi$
$798$	6.41586			0.227119
$799$	−24.9402	+	43.1977i	−0.882321	+	1.52822i
$800$	4.96770	−	8.60430i	0.175635	−	0.304208i
$801$	2.04746			0.0723433
$802$	14.9540	−	25.9010i	0.528043	−	0.914597i
$803$	−7.30669	−	12.6556i	−0.257848	−	0.446605i
$804$	2.31607	+	4.01156i	0.0816816	+	0.141477i
$805$	−2.48819			−0.0876971
$806$	−1.83514	+	5.54418i	−0.0646402	+	0.195285i
$807$	−8.50190			−0.299281
$808$	−7.01324	−	12.1473i	−0.246725	−	0.427340i
$809$	−25.5630	−	44.2764i	−0.898748	−	1.55668i	−0.829096	−	0.559106i	$-0.811145\pi$
$809$	−25.5630	−	44.2764i	−0.898748	−	1.55668i	−0.0696514	−	0.997571i	$-0.522189\pi$
$810$	−7.69405	+	13.3265i	−0.270341	+	0.468245i
$811$	15.2773			0.536458			0.268229	−	0.963355i	$-0.413562\pi$
$811$	15.2773			0.536458			0.268229	+	0.963355i	$0.413562\pi$
$812$	−0.782629	+	1.35555i	−0.0274649	+	0.0475706i
$813$	2.04849	−	3.54809i	0.0718437	−	0.124437i
$814$	−12.0143			−0.421100
$815$	16.6388	−	28.8192i	0.582831	−	1.00949i
$816$	−8.68600	−	15.0446i	−0.304071	−	0.526666i
$817$	18.1896	+	31.5053i	0.636372	+	1.10223i
$818$	−1.49513			−0.0522760
$819$	6.17301	−	18.6494i	0.215702	−	0.651662i
$820$	−7.86465			−0.274645
$821$	−7.74207	−	13.4097i	−0.270200	−	0.468000i	0.698713	−	0.715402i	$-0.253757\pi$
$821$	−7.74207	−	13.4097i	−0.270200	−	0.468000i	−0.968913	+	0.247402i	$0.920423\pi$
$822$	−2.83967	−	4.91846i	−0.0990450	−	0.171551i
$823$	25.6947	−	44.5046i	0.895663	−	1.55133i	0.0626801	−	0.998034i	$-0.480035\pi$
$823$	25.6947	−	44.5046i	0.895663	−	1.55133i	0.832982	−	0.553299i	$-0.186631\pi$
$824$	−28.6227			−0.997118
$825$	−1.11040	+	1.92327i	−0.0386591	+	0.0669596i
$826$	−2.49792	+	4.32652i	−0.0869137	+	0.150539i
$827$	−1.59147			−0.0553408			−0.0276704	−	0.999617i	$-0.508809\pi$
$827$	−1.59147			−0.0553408			−0.0276704	+	0.999617i	$0.508809\pi$
$828$	−0.730441	+	1.26516i	−0.0253846	+	0.0439674i
$829$	9.71091	+	16.8198i	0.337274	+	0.584176i	0.983919	−	0.178615i	$-0.0571618\pi$
$829$	9.71091	+	16.8198i	0.337274	+	0.584176i	−0.646645	+	0.762791i	$0.723828\pi$
$830$	−2.67982	−	4.64159i	−0.0930180	−	0.161112i
$831$	−16.5710			−0.574842
$832$	10.0547	+	11.2910i	0.348585	+	0.391446i
$833$	20.3149			0.703871
$834$	2.18864	+	3.79083i	0.0757864	+	0.131266i
$835$	−6.77126	−	11.7282i	−0.234329	−	0.405870i
$836$	1.69312	−	2.93257i	0.0585578	−	0.101425i
$837$	−3.01581			−0.104242
$838$	26.7083	−	46.2600i	0.922621	−	1.59803i
$839$	17.4592	−	30.2403i	0.602760	−	1.04401i	−0.389642	−	0.920967i	$-0.627401\pi$
$839$	17.4592	−	30.2403i	0.602760	−	1.04401i	0.992401	−	0.123044i	$-0.0392655\pi$
$840$	3.39698			0.117207
$841$	13.7134	−	23.7523i	0.472875	−	0.819044i
$842$	3.39771	+	5.88501i	0.117093	+	0.202811i
$843$	3.56319	+	6.17163i	0.122723	+	0.212562i
$844$	−5.15190			−0.177336
$845$	2.16784	−	18.6521i	0.0745759	−	0.641651i
$846$	−32.4166			−1.11450
$847$	−8.91483	−	15.4409i	−0.306317	−	0.530557i
$848$	−26.5233	−	45.9397i	−0.910815	−	1.57758i
$849$	−7.79634	+	13.5037i	−0.267570	+	0.463444i
$850$	−32.0187			−1.09823
$851$	−2.20713	+	3.82287i	−0.0756596	+	0.131046i
$852$	−1.24007	+	2.14787i	−0.0424841	+	0.0735847i
$853$	−11.9938			−0.410660			−0.205330	−	0.978693i	$-0.565827\pi$
$853$	−11.9938			−0.410660			−0.205330	+	0.978693i	$0.565827\pi$
$854$	−8.49910	+	14.7209i	−0.290833	+	0.503738i
$855$	−7.38287	−	12.7875i	−0.252489	−	0.437323i
$856$	6.18498	+	10.7127i	0.211398	+	0.366153i
$857$	31.4263			1.07350			0.536752	−	0.843740i	$-0.319651\pi$
$857$	31.4263			1.07350			0.536752	+	0.843740i	$0.319651\pi$
$858$	2.96031	+	3.32430i	0.101063	+	0.113490i
$859$	16.4418			0.560989			0.280494	−	0.959856i	$-0.409502\pi$
$859$	16.4418			0.560989			0.280494	+	0.959856i	$0.409502\pi$
$860$	−4.36249	−	7.55606i	−0.148760	−	0.257660i
$861$	4.60560	+	7.97714i	0.156958	+	0.271860i
$862$	−22.2001	+	38.4518i	−0.756139	+	1.30967i
$863$	−16.4864			−0.561203			−0.280601	−	0.959824i	$-0.590534\pi$
$863$	−16.4864			−0.561203			−0.280601	+	0.959824i	$0.590534\pi$
$864$	5.14195	−	8.90612i	0.174933	−	0.302992i
$865$	0.786633	−	1.36249i	0.0267463	−	0.0463260i
$866$	−48.3926			−1.64445
$867$	−7.65045	+	13.2510i	−0.259823	+	0.450027i
$868$	0.623964	+	1.08074i	0.0211787	+	0.0366826i
$869$	3.96347	+	6.86493i	0.134451	+	0.232877i
$870$	−1.54658			−0.0524341
$871$	−15.9708	+	48.2495i	−0.541148	+	1.63487i
$872$	−34.0590			−1.15338
$873$	5.53169	+	9.58117i	0.187219	+	0.324273i
$874$	−2.61750	−	4.53364i	−0.0885381	−	0.153353i
$875$	11.4389	−	19.8128i	0.386706	−	0.669795i
$876$	−3.32045			−0.112188
$877$	−1.12556	+	1.94953i	−0.0380074	+	0.0658308i	−0.884403	−	0.466723i	$-0.845434\pi$
$877$	−1.12556	+	1.94953i	−0.0380074	+	0.0658308i	0.846396	+	0.532554i	$0.178768\pi$
$878$	14.6256	−	25.3324i	0.493591	−	0.854925i
$879$	6.86858			0.231672
$880$	5.07443	−	8.78917i	0.171059	−	0.296283i
$881$	−18.8880	−	32.7150i	−0.636353	−	1.10219i	−0.986227	−	0.165398i	$-0.947109\pi$
$881$	−18.8880	−	32.7150i	−0.636353	−	1.10219i	0.349874	−	0.936797i	$-0.386224\pi$
$882$	6.60120	+	11.4336i	0.222274	+	0.384990i
$883$	−23.6408			−0.795577			−0.397788	−	0.917477i	$-0.630222\pi$
$883$	−23.6408			−0.795577			−0.397788	+	0.917477i	$0.630222\pi$
$884$	−4.79298	+	14.4801i	−0.161205	+	0.487020i
$885$	−1.17317			−0.0394355
$886$	5.21573	+	9.03391i	0.175226	+	0.303500i
$887$	17.8164	+	30.8590i	0.598217	+	1.03614i	0.993084	+	0.117404i	$0.0374573\pi$
$887$	17.8164	+	30.8590i	0.598217	+	1.03614i	−0.394867	+	0.918738i	$0.629209\pi$
$888$	3.01327	−	5.21914i	0.101119	−	0.175143i
$889$	12.1800			0.408504
$890$	0.879830	−	1.52391i	0.0294920	−	0.0510816i
$891$	4.75614	−	8.23788i	0.159337	−	0.275979i
$892$	−2.12132			−0.0710270
$893$	13.8039	−	23.9090i	0.461929	−	0.800085i
$894$	−6.53177	−	11.3134i	−0.218455	−	0.378375i
$895$	10.9619	+	18.9866i	0.366417	+	0.634654i
$896$	27.2435			0.910141
$897$	1.60161	−	0.331249i	0.0534763	−	0.0110601i
$898$	42.1480			1.40650
$899$	0.627142	+	1.08624i	0.0209164	+	0.0362282i
$900$	−2.47272	−	4.28287i	−0.0824238	−	0.142762i
$901$	−37.0406	+	64.1561i	−1.23400	+	2.13735i
$902$	20.4558			0.681102
$903$	−5.10943	+	8.84978i	−0.170031	+	0.294502i
$904$	−6.12007	+	10.6003i	−0.203550	+	0.352560i
$905$	24.7685			0.823334
$906$	8.71944	−	15.1025i	0.289684	−	0.501748i
$907$	−13.2394	−	22.9313i	−0.439607	−	0.761422i	0.558052	−	0.829806i	$-0.311549\pi$
$907$	−13.2394	−	22.9313i	−0.439607	−	0.761422i	−0.997659	+	0.0683843i	$0.978216\pi$
$908$	−6.33800	−	10.9777i	−0.210334	−	0.364309i
$909$	−17.1262			−0.568040
$910$	−11.2280	−	12.6085i	−0.372203	−	0.417968i
$911$	−28.5298			−0.945234			−0.472617	−	0.881268i	$-0.656691\pi$
$911$	−28.5298			−0.945234			−0.472617	+	0.881268i	$0.656691\pi$
$912$	4.80752	+	8.32687i	0.159193	+	0.275730i
$913$	1.65655	+	2.86924i	0.0548239	+	0.0949578i
$914$	5.52088	−	9.56245i	0.182615	−	0.316298i
$915$	−3.99167			−0.131960
$916$	−0.989221	+	1.71338i	−0.0326848	+	0.0566117i
$917$	−15.7778	+	27.3279i	−0.521028	+	0.902447i
$918$	−33.1418			−1.09384
$919$	−14.2813	+	24.7359i	−0.471096	+	0.815962i	−0.999453	−	0.0330599i	$-0.989475\pi$
$919$	−14.2813	+	24.7359i	−0.471096	+	0.815962i	0.528357	+	0.849022i	$0.322808\pi$
$920$	−1.38587	−	2.40040i	−0.0456909	−	0.0791389i
$921$	−0.861447	−	1.49207i	−0.0283856	−	0.0491654i
$922$	21.7848			0.717443
$923$	−26.6482	+	5.51143i	−0.877135	+	0.181411i
$924$	0.951190			0.0312919
$925$	−7.47167	−	12.9413i	−0.245667	−	0.425508i
$926$	−22.0661	−	38.2197i	−0.725138	−	1.25598i
$927$	−17.4740	+	30.2659i	−0.573922	+	0.994062i
$928$	−4.27710			−0.140403
$929$	10.0775	−	17.4547i	0.330632	−	0.572672i	−0.652004	−	0.758216i	$-0.726071\pi$
$929$	10.0775	−	17.4547i	0.330632	−	0.572672i	0.982636	+	0.185544i	$0.0594047\pi$
$930$	−0.616521	+	1.06785i	−0.0202165	+	0.0350160i
$931$	−11.2439			−0.368504
$932$	5.70602	−	9.88311i	0.186907	−	0.323732i
$933$	2.11356	+	3.66080i	0.0691950	+	0.119849i
$934$	16.0063	+	27.7237i	0.523741	+	0.907147i
$935$	−14.1732			−0.463512
$936$	21.4297	−	4.43212i	0.700450	−	0.144869i
$937$	39.0742			1.27650			0.638249	−	0.769830i	$-0.279659\pi$
$937$	39.0742			1.27650			0.638249	+	0.769830i	$0.279659\pi$
$938$	22.8482	+	39.5742i	0.746020	+	1.29214i
$939$	−5.52427	−	9.56832i	−0.180278	−	0.312250i
$940$	−3.31065	+	5.73422i	−0.107982	+	0.187030i
$941$	44.8670			1.46262			0.731311	−	0.682044i	$-0.238909\pi$
$941$	44.8670			1.46262			0.731311	+	0.682044i	$0.238909\pi$
$942$	9.26503	−	16.0475i	0.301871	−	0.522856i
$943$	3.75792	−	6.50891i	0.122375	−	0.211959i
$944$	−7.48693			−0.243679
$945$	4.35928	−	7.55050i	0.141807	−	0.245618i
$946$	11.3467	+	19.6531i	0.368915	+	0.638979i
$947$	10.0675	+	17.4374i	0.327149	+	0.566640i	0.981945	−	0.189167i	$-0.0605786\pi$
$947$	10.0675	+	17.4374i	0.327149	+	0.566640i	−0.654796	+	0.755806i	$0.727245\pi$
$948$	1.80116			0.0584989
$949$	−24.2287	−	27.2078i	−0.786497	−	0.883202i
$950$	17.7217			0.574968
$951$	−5.70779	−	9.88618i	−0.185088	−	0.320581i
$952$	−15.1376	−	26.2191i	−0.490612	−	0.849765i
$953$	27.3232	−	47.3251i	0.885084	−	1.53301i	0.0394662	−	0.999221i	$-0.487434\pi$
$953$	27.3232	−	47.3251i	0.885084	−	1.53301i	0.845618	−	0.533789i	$-0.179232\pi$
$954$	−48.1443			−1.55873
$955$	11.4613	−	19.8515i	0.370879	−	0.642381i
$956$	−8.81495	+	15.2679i	−0.285096	+	0.493801i
$957$	0.956034			0.0309042
$958$	32.1934	−	55.7607i	1.04012	−	1.80155i
$959$	−6.65780	−	11.5317i	−0.214992	−	0.372377i
$960$	1.59609	+	2.76451i	0.0515137	+	0.0892243i
$961$	1.00000			0.0322581
$962$	−29.3315	+	6.06640i	−0.945685	+	0.195589i
$963$	15.1036			0.486707
$964$	8.73331	+	15.1265i	0.281281	+	0.487193i
$965$	−2.32314	−	4.02380i	−0.0747846	−	0.129531i
$966$	0.735251	−	1.27349i	0.0236563	−	0.0409740i
$967$	−42.6900			−1.37282			−0.686408	−	0.727216i	$-0.740814\pi$
$967$	−42.6900			−1.37282			−0.686408	+	0.727216i	$0.740814\pi$
$968$	9.93078	−	17.2006i	0.319187	−	0.552848i
$969$	6.71384	−	11.6287i	0.215680	−	0.373568i
$970$	9.50827			0.305292
$971$	17.1811	−	29.7586i	0.551369	−	0.954999i	−0.446807	−	0.894630i	$-0.647439\pi$
$971$	17.1811	−	29.7586i	0.551369	−	0.954999i	0.998176	−	0.0603687i	$-0.0192276\pi$
$972$	−3.90130	−	6.75724i	−0.125134	−	0.216739i
$973$	5.13141	+	8.88786i	0.164505	+	0.284932i
$974$	30.4023			0.974153
$975$	−1.73980	+	5.25613i	−0.0557181	+	0.168331i
$976$	−25.4741			−0.815406
$977$	7.36601	+	12.7583i	0.235660	+	0.408175i	0.959464	−	0.281831i	$-0.0909416\pi$
$977$	7.36601	+	12.7583i	0.235660	+	0.408175i	−0.723805	+	0.690005i	$0.757608\pi$
$978$	9.83341	+	17.0320i	0.314438	+	0.544622i
$979$	−0.543874	+	0.942017i	−0.0173823	+	0.0301070i
$980$	2.69668			0.0861423
$981$	−20.7928	+	36.0142i	−0.663864	+	1.14985i
$982$	8.48582	−	14.6979i	0.270793	−	0.469028i
$983$	45.1634			1.44049			0.720245	−	0.693720i	$-0.244029\pi$
$983$	45.1634			1.44049			0.720245	+	0.693720i	$0.244029\pi$
$984$	−5.13046	+	8.88622i	−0.163553	+	0.283282i
$985$	−1.86236	−	3.22570i	−0.0593398	−	0.102779i
$986$	6.89189	+	11.9371i	0.219482	+	0.380155i
$987$	7.75499			0.246844
$988$	2.65282	−	8.01446i	0.0843973	−	0.254974i
$989$	8.33802			0.265134
$990$	−4.60547	−	7.97691i	−0.146371	−	0.253523i
$991$	5.54412	+	9.60271i	0.176115	+	0.305040i	0.940547	−	0.339665i	$-0.110314\pi$
$991$	5.54412	+	9.60271i	0.176115	+	0.305040i	−0.764432	+	0.644705i	$0.776980\pi$
$992$	−1.70500	+	2.95314i	−0.0541337	+	0.0937623i
$993$	−10.7706			−0.341795
$994$	−12.2334	+	21.1888i	−0.388019	+	0.672068i
$995$	6.45599	−	11.1821i	0.204669	−	0.354496i
$996$	0.752804			0.0238535
$997$	19.8244	−	34.3369i	0.627845	−	1.08746i	−0.360138	−	0.932899i	$-0.617271\pi$
$997$	19.8244	−	34.3369i	0.627845	−	1.08746i	0.987983	−	0.154560i	$-0.0493961\pi$
$998$	22.1086	+	38.2932i	0.699836	+	1.21215i
$999$	−7.73376	−	13.3953i	−0.244685	−	0.423807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.15	✓	36
13.3	even	3		5239.2.a.p.1.4		18
13.9	even	3	inner	403.2.f.c.373.15	yes	36
13.10	even	6		5239.2.a.o.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.15	✓	36	1.1	even	1	trivial
403.2.f.c.373.15	yes	36	13.9	even	3	inner
5239.2.a.o.1.15		18	13.10	even	6
5239.2.a.p.1.4		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809863 + 1.40272i) q^{2} +(-0.263517 - 0.456425i) q^{3} +(-0.311757 + 0.539980i) q^{4} -1.44443 q^{5} +(0.426825 - 0.739283i) q^{6} +(1.00072 - 1.73330i) q^{7} +2.22953 q^{8} +(1.36112 - 2.35752i) q^{9} +O(q^{10})\)	\(q+(0.809863 + 1.40272i) q^{2} +(-0.263517 - 0.456425i) q^{3} +(-0.311757 + 0.539980i) q^{4} -1.44443 q^{5} +(0.426825 - 0.739283i) q^{6} +(1.00072 - 1.73330i) q^{7} +2.22953 q^{8} +(1.36112 - 2.35752i) q^{9} +(-1.16979 - 2.02614i) q^{10} +(0.723118 + 1.25248i) q^{11} +0.328613 q^{12} +(2.39783 + 2.69266i) q^{13} +3.24179 q^{14} +(0.380633 + 0.659275i) q^{15} +(2.42913 + 4.20738i) q^{16} +(3.39235 - 5.87572i) q^{17} +4.40928 q^{18} +(-1.87759 + 3.25209i) q^{19} +(0.450313 - 0.779965i) q^{20} -1.05483 q^{21} +(-1.17125 + 2.02867i) q^{22} +(0.430341 + 0.745372i) q^{23} +(-0.587519 - 1.01761i) q^{24} -2.91361 q^{25} +(-1.83514 + 5.54418i) q^{26} -3.01581 q^{27} +(0.623964 + 1.08074i) q^{28} +(0.627142 + 1.08624i) q^{29} +(-0.616521 + 1.06785i) q^{30} +1.00000 q^{31} +(-1.70500 + 2.95314i) q^{32} +(0.381108 - 0.660098i) q^{33} +10.9894 q^{34} +(-1.44547 + 2.50364i) q^{35} +(0.848677 + 1.46995i) q^{36} +(2.56440 + 4.44168i) q^{37} -6.08238 q^{38} +(0.597127 - 1.80399i) q^{39} -3.22041 q^{40} +(-4.36621 - 7.56250i) q^{41} +(-0.854266 - 1.47963i) q^{42} +(4.84385 - 8.38979i) q^{43} -0.901749 q^{44} +(-1.96604 + 3.40529i) q^{45} +(-0.697034 + 1.20730i) q^{46} -7.35190 q^{47} +(1.28023 - 2.21743i) q^{48} +(1.49712 + 2.59308i) q^{49} +(-2.35963 - 4.08699i) q^{50} -3.57576 q^{51} +(-2.20152 + 0.455323i) q^{52} -10.9189 q^{53} +(-2.44240 - 4.23035i) q^{54} +(-1.04450 - 1.80912i) q^{55} +(2.23114 - 3.86444i) q^{56} +1.97911 q^{57} +(-1.01580 + 1.75941i) q^{58} +(-0.770537 + 1.33461i) q^{59} -0.474660 q^{60} +(-2.62173 + 4.54097i) q^{61} +(0.809863 + 1.40272i) q^{62} +(-2.72420 - 4.71845i) q^{63} +4.19326 q^{64} +(-3.46351 - 3.88937i) q^{65} +1.23458 q^{66} +(7.04802 + 12.2075i) q^{67} +(2.11518 + 3.66360i) q^{68} +(0.226804 - 0.392836i) q^{69} -4.68255 q^{70} +(-3.77365 + 6.53615i) q^{71} +(3.03465 - 5.25617i) q^{72} -10.1044 q^{73} +(-4.15363 + 7.19430i) q^{74} +(0.767786 + 1.32984i) q^{75} +(-1.17071 - 2.02773i) q^{76} +2.89456 q^{77} +(3.01409 - 0.623381i) q^{78} +5.48108 q^{79} +(-3.50872 - 6.07727i) q^{80} +(-3.28864 - 5.69608i) q^{81} +(7.07207 - 12.2492i) q^{82} +2.29085 q^{83} +(0.328850 - 0.569586i) q^{84} +(-4.90002 + 8.48709i) q^{85} +15.6914 q^{86} +(0.330525 - 0.572486i) q^{87} +(1.61221 + 2.79243i) q^{88} +(0.376062 + 0.651358i) q^{89} -6.36891 q^{90} +(7.06674 - 1.46156i) q^{91} -0.536648 q^{92} +(-0.263517 - 0.456425i) q^{93} +(-5.95403 - 10.3127i) q^{94} +(2.71206 - 4.69743i) q^{95} +1.79718 q^{96} +(-2.03204 + 3.51960i) q^{97} +(-2.42492 + 4.20008i) q^{98} +3.93699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

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