LMFDB - Embedded newform 273.2.j.b.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.1
Root			$-1.27528 + 2.20885i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27528 + 2.20885i) q^{2} -1.00000 q^{3} +(-2.25269 - 3.90177i) q^{4} +(-1.39351 - 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(2.06947 + 1.64842i) q^{7} +6.39011 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.27528 + 2.20885i) q^{2} -1.00000 q^{3} +(-2.25269 - 3.90177i) q^{4} +(-1.39351 - 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(2.06947 + 1.64842i) q^{7} +6.39011 q^{8} +1.00000 q^{9} +7.10846 q^{10} -2.76747 q^{11} +(2.25269 + 3.90177i) q^{12} +(2.99297 + 2.01050i) q^{13} +(-6.28028 + 2.46895i) q^{14} +(1.39351 + 2.41363i) q^{15} +(-3.64382 + 6.31127i) q^{16} +(2.94340 + 5.09812i) q^{17} +(-1.27528 + 2.20885i) q^{18} +3.40075 q^{19} +(-6.27828 + 10.8743i) q^{20} +(-2.06947 - 1.64842i) q^{21} +(3.52930 - 6.11292i) q^{22} +(3.67246 - 6.36089i) q^{23} -6.39011 q^{24} +(-1.38373 + 2.39670i) q^{25} +(-8.25778 + 4.04708i) q^{26} -1.00000 q^{27} +(1.76989 - 11.7880i) q^{28} +(1.56328 + 2.70768i) q^{29} -7.10846 q^{30} +(1.93352 - 3.34896i) q^{31} +(-2.90367 - 5.02931i) q^{32} +2.76747 q^{33} -15.0147 q^{34} +(1.09485 - 7.29202i) q^{35} +(-2.25269 - 3.90177i) q^{36} +(-2.92173 + 5.06059i) q^{37} +(-4.33691 + 7.51175i) q^{38} +(-2.99297 - 2.01050i) q^{39} +(-8.90467 - 15.4233i) q^{40} +(3.24124 + 5.61400i) q^{41} +(6.28028 - 2.46895i) q^{42} +(2.99197 - 5.18224i) q^{43} +(6.23423 + 10.7980i) q^{44} +(-1.39351 - 2.41363i) q^{45} +(9.36684 + 16.2238i) q^{46} +(3.95673 + 6.85325i) q^{47} +(3.64382 - 6.31127i) q^{48} +(1.56542 + 6.82272i) q^{49} +(-3.52930 - 6.11292i) q^{50} +(-2.94340 - 5.09812i) q^{51} +(1.10228 - 16.2069i) q^{52} +(6.34471 - 10.9894i) q^{53} +(1.27528 - 2.20885i) q^{54} +(3.85649 + 6.67963i) q^{55} +(13.2241 + 10.5336i) q^{56} -3.40075 q^{57} -7.97449 q^{58} +(-1.36824 - 2.36987i) q^{59} +(6.27828 - 10.8743i) q^{60} +9.55263 q^{61} +(4.93157 + 8.54173i) q^{62} +(2.06947 + 1.64842i) q^{63} +0.236742 q^{64} +(0.681870 - 10.0256i) q^{65} +(-3.52930 + 6.11292i) q^{66} -8.68066 q^{67} +(13.2611 - 22.9689i) q^{68} +(-3.67246 + 6.36089i) q^{69} +(14.7108 + 11.7177i) q^{70} +(-1.57062 + 2.72039i) q^{71} +6.39011 q^{72} +(-4.80291 + 8.31889i) q^{73} +(-7.45207 - 12.9074i) q^{74} +(1.38373 - 2.39670i) q^{75} +(-7.66082 - 13.2689i) q^{76} +(-5.72719 - 4.56195i) q^{77} +(8.25778 - 4.04708i) q^{78} +(-1.88112 - 3.25819i) q^{79} +20.3108 q^{80} +1.00000 q^{81} -16.5340 q^{82} +4.82088 q^{83} +(-1.76989 + 11.7880i) q^{84} +(8.20331 - 14.2086i) q^{85} +(7.63120 + 13.2176i) q^{86} +(-1.56328 - 2.70768i) q^{87} -17.6844 q^{88} +(-0.877787 + 1.52037i) q^{89} +7.10846 q^{90} +(2.87972 + 9.09435i) q^{91} -33.0916 q^{92} +(-1.93352 + 3.34896i) q^{93} -20.1838 q^{94} +(-4.73897 - 8.20814i) q^{95} +(2.90367 + 5.02931i) q^{96} +(8.48637 - 14.6988i) q^{97} +(-17.0667 - 5.24311i) q^{98} -2.76747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.27528	+	2.20885i	−0.901760	+	1.56189i	−0.0765522	+	0.997066i	$0.524391\pi$
$2$	−1.27528	+	2.20885i	−0.901760	+	1.56189i	−0.825208	+	0.564829i	$0.808942\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−2.25269	−	3.90177i	−1.12634	−	1.95088i
$5$	−1.39351	−	2.41363i	−0.623196	−	1.07941i	−0.988887	−	0.148671i	$-0.952501\pi$
$5$	−1.39351	−	2.41363i	−0.623196	−	1.07941i	0.365691	−	0.930736i	$-0.380833\pi$
$6$	1.27528	−	2.20885i	0.520632	−	0.901760i
$7$	2.06947	+	1.64842i	0.782186	+	0.623044i
$7$	2.06947	+	1.64842i	0.782186	+	0.623044i
$8$	6.39011			2.25924
$9$	1.00000			0.333333
$10$	7.10846			2.24789
$11$	−2.76747			−0.834422			−0.417211	−	0.908810i	$-0.636992\pi$
$11$	−2.76747			−0.834422			−0.417211	+	0.908810i	$0.636992\pi$
$12$	2.25269	+	3.90177i	0.650294	+	1.12634i
$13$	2.99297	+	2.01050i	0.830101	+	0.557613i
$13$	2.99297	+	2.01050i	0.830101	+	0.557613i
$14$	−6.28028	+	2.46895i	−1.67847	+	0.659856i
$15$	1.39351	+	2.41363i	0.359802	+	0.623196i
$16$	−3.64382	+	6.31127i	−0.910954	+	1.57782i
$17$	2.94340	+	5.09812i	0.713880	+	1.23648i	0.963390	+	0.268104i	$0.0863971\pi$
$17$	2.94340	+	5.09812i	0.713880	+	1.23648i	−0.249510	+	0.968372i	$0.580270\pi$
$18$	−1.27528	+	2.20885i	−0.300587	+	0.520632i
$19$	3.40075			0.780185			0.390093	−	0.920776i	$-0.372443\pi$
$19$	3.40075			0.780185			0.390093	+	0.920776i	$0.372443\pi$
$20$	−6.27828	+	10.8743i	−1.40386	+	2.43157i
$21$	−2.06947	−	1.64842i	−0.451596	−	0.359715i
$22$	3.52930	−	6.11292i	0.752449	−	1.30328i
$23$	3.67246	−	6.36089i	0.765761	−	1.32634i	−0.174083	−	0.984731i	$-0.555696\pi$
$23$	3.67246	−	6.36089i	0.765761	−	1.32634i	0.939843	−	0.341605i	$-0.110971\pi$
$24$	−6.39011			−1.30438
$25$	−1.38373	+	2.39670i	−0.276747	+	0.479339i
$26$	−8.25778	+	4.04708i	−1.61948	+	0.793697i
$27$	−1.00000			−0.192450
$28$	1.76989	−	11.7880i	0.334477	−	2.22772i
$29$	1.56328	+	2.70768i	0.290294	+	0.502803i	0.973879	−	0.227067i	$-0.0729137\pi$
$29$	1.56328	+	2.70768i	0.290294	+	0.502803i	−0.683585	+	0.729871i	$0.739580\pi$
$30$	−7.10846			−1.29782
$31$	1.93352	−	3.34896i	0.347271	−	0.601491i	−0.638493	−	0.769628i	$-0.720442\pi$
$31$	1.93352	−	3.34896i	0.347271	−	0.601491i	0.985764	+	0.168137i	$0.0537751\pi$
$32$	−2.90367	−	5.02931i	−0.513302	−	0.889065i
$33$	2.76747			0.481754
$34$	−15.0147			−2.57499
$35$	1.09485	−	7.29202i	0.185063	−	1.23258i
$36$	−2.25269	−	3.90177i	−0.375448	−	0.650294i
$37$	−2.92173	+	5.06059i	−0.480330	+	0.831956i	−0.999745	−	0.0225659i	$-0.992816\pi$
$37$	−2.92173	+	5.06059i	−0.480330	+	0.831956i	0.519415	+	0.854522i	$0.326150\pi$
$38$	−4.33691	+	7.51175i	−0.703540	+	1.21857i
$39$	−2.99297	−	2.01050i	−0.479259	−	0.321938i
$40$	−8.90467	−	15.4233i	−1.40795	−	2.43865i
$41$	3.24124	+	5.61400i	0.506197	+	0.876759i	0.999974	+	0.00717054i	$0.00228247\pi$
$41$	3.24124	+	5.61400i	0.506197	+	0.876759i	−0.493777	+	0.869588i	$0.664384\pi$
$42$	6.28028	−	2.46895i	0.969068	−	0.380968i
$43$	2.99197	−	5.18224i	0.456271	−	0.790284i	−0.542489	−	0.840063i	$-0.682518\pi$
$43$	2.99197	−	5.18224i	0.456271	−	0.790284i	0.998760	+	0.0497783i	$0.0158515\pi$
$44$	6.23423	+	10.7980i	0.939846	+	1.62786i
$45$	−1.39351	−	2.41363i	−0.207732	−	0.359802i
$46$	9.36684	+	16.2238i	1.38106	+	2.39207i
$47$	3.95673	+	6.85325i	0.577148	+	0.999650i	0.995805	+	0.0915053i	$0.0291678\pi$
$47$	3.95673	+	6.85325i	0.577148	+	0.999650i	−0.418656	+	0.908145i	$0.637499\pi$
$48$	3.64382	−	6.31127i	0.525940	−	0.910954i
$49$	1.56542	+	6.82272i	0.223631	+	0.974674i
$50$	−3.52930	−	6.11292i	−0.499118	−	0.864498i
$51$	−2.94340	−	5.09812i	−0.412159	−	0.713880i
$52$	1.10228	−	16.2069i	0.152859	−	2.24749i
$53$	6.34471	−	10.9894i	0.871513	−	1.50951i	0.0110819	−	0.999939i	$-0.496472\pi$
$53$	6.34471	−	10.9894i	0.871513	−	1.50951i	0.860431	−	0.509567i	$-0.170194\pi$
$54$	1.27528	−	2.20885i	0.173544	−	0.300587i
$55$	3.85649	+	6.67963i	0.520009	+	0.900682i
$56$	13.2241	+	10.5336i	1.76715	+	1.40761i
$57$	−3.40075			−0.450440
$58$	−7.97449			−1.04710
$59$	−1.36824	−	2.36987i	−0.178130	−	0.308530i	0.763110	−	0.646269i	$-0.223671\pi$
$59$	−1.36824	−	2.36987i	−0.178130	−	0.308530i	−0.941240	+	0.337738i	$0.890338\pi$
$60$	6.27828	−	10.8743i	0.810522	−	1.40386i
$61$	9.55263			1.22309			0.611544	−	0.791210i	$-0.290549\pi$
$61$	9.55263			1.22309			0.611544	+	0.791210i	$0.290549\pi$
$62$	4.93157	+	8.54173i	0.626310	+	1.08480i
$63$	2.06947	+	1.64842i	0.260729	+	0.207681i
$64$	0.236742			0.0295928
$65$	0.681870	−	10.0256i	0.0845756	−	1.24352i
$66$	−3.52930	+	6.11292i	−0.434427	+	0.752449i
$67$	−8.68066			−1.06051			−0.530255	−	0.847838i	$-0.677904\pi$
$67$	−8.68066			−1.06051			−0.530255	+	0.847838i	$0.677904\pi$
$68$	13.2611	−	22.9689i	1.60815	−	2.78539i
$69$	−3.67246	+	6.36089i	−0.442112	+	0.765761i
$70$	14.7108	+	11.7177i	1.75827	+	1.40054i
$71$	−1.57062	+	2.72039i	−0.186398	+	0.322851i	−0.944047	−	0.329812i	$-0.893015\pi$
$71$	−1.57062	+	2.72039i	−0.186398	+	0.322851i	0.757649	+	0.652663i	$0.226348\pi$
$72$	6.39011			0.753082
$73$	−4.80291	+	8.31889i	−0.562138	+	0.973652i	0.435171	+	0.900348i	$0.356688\pi$
$73$	−4.80291	+	8.31889i	−0.562138	+	0.973652i	−0.997310	+	0.0733045i	$0.976646\pi$
$74$	−7.45207	−	12.9074i	−0.866285	−	1.50045i
$75$	1.38373	−	2.39670i	0.159780	−	0.276747i
$76$	−7.66082	−	13.2689i	−0.878756	−	1.52205i
$77$	−5.72719	−	4.56195i	−0.652674	−	0.519882i
$78$	8.25778	−	4.04708i	0.935010	−	0.458241i
$79$	−1.88112	−	3.25819i	−0.211642	−	0.366575i	0.740586	−	0.671961i	$-0.234548\pi$
$79$	−1.88112	−	3.25819i	−0.211642	−	0.366575i	−0.952229	+	0.305386i	$0.901215\pi$
$80$	20.3108			2.27081
$81$	1.00000			0.111111
$82$	−16.5340			−1.82587
$83$	4.82088			0.529161			0.264580	−	0.964364i	$-0.414767\pi$
$83$	4.82088			0.529161			0.264580	+	0.964364i	$0.414767\pi$
$84$	−1.76989	+	11.7880i	−0.193110	+	1.28617i
$85$	8.20331	−	14.2086i	0.889774	−	1.54113i
$86$	7.63120	+	13.2176i	0.822894	+	1.42529i
$87$	−1.56328	−	2.70768i	−0.167601	−	0.290294i
$88$	−17.6844			−1.88516
$89$	−0.877787	+	1.52037i	−0.0930453	+	0.161159i	−0.908791	−	0.417251i	$-0.862993\pi$
$89$	−0.877787	+	1.52037i	−0.0930453	+	0.161159i	0.815746	+	0.578411i	$0.196327\pi$
$90$	7.10846			0.749298
$91$	2.87972	+	9.09435i	0.301876	+	0.953347i
$92$	−33.0916			−3.45004
$93$	−1.93352	+	3.34896i	−0.200497	+	0.347271i
$94$	−20.1838			−2.08180
$95$	−4.73897	−	8.20814i	−0.486208	−	0.842137i
$96$	2.90367	+	5.02931i	0.296355	+	0.513302i
$97$	8.48637	−	14.6988i	0.861660	−	1.49244i	−0.00866511	−	0.999962i	$-0.502758\pi$
$97$	8.48637	−	14.6988i	0.861660	−	1.49244i	0.870325	−	0.492477i	$-0.163908\pi$
$98$	−17.0667	−	5.24311i	−1.72400	−	0.529634i
$99$	−2.76747			−0.278141
$100$	12.4685			1.24685
$101$	−1.84273			−0.183358			−0.0916791	−	0.995789i	$-0.529223\pi$
$101$	−1.84273			−0.183358			−0.0916791	+	0.995789i	$0.529223\pi$
$102$	15.0147			1.48667
$103$	−2.38506	−	4.13105i	−0.235007	−	0.407045i	0.724267	−	0.689519i	$-0.242178\pi$
$103$	−2.38506	−	4.13105i	−0.235007	−	0.407045i	−0.959275	+	0.282474i	$0.908845\pi$
$104$	19.1254	+	12.8473i	1.87540	+	1.25978i
$105$	−1.09485	+	7.29202i	−0.106846	+	0.711628i
$106$	16.1826	+	28.0291i	1.57179	+	2.72242i
$107$	6.03771	−	10.4576i	0.583688	−	1.01098i	−0.411350	−	0.911478i	$-0.634942\pi$
$107$	6.03771	−	10.4576i	0.583688	−	1.01098i	0.995038	−	0.0994995i	$-0.0317242\pi$
$108$	2.25269	+	3.90177i	0.216765	+	0.375448i
$109$	3.40885	−	5.90430i	0.326508	−	0.565529i	−0.655308	−	0.755362i	$-0.727461\pi$
$109$	3.40885	−	5.90430i	0.326508	−	0.565529i	0.981816	+	0.189832i	$0.0607945\pi$
$110$	−19.6724			−1.87569
$111$	2.92173	−	5.06059i	0.277319	−	0.480330i
$112$	−17.9444	+	7.05446i	−1.69559	+	0.666583i
$113$	−2.72463	+	4.71920i	−0.256312	+	0.443945i	−0.965251	−	0.261325i	$-0.915841\pi$
$113$	−2.72463	+	4.71920i	−0.256312	+	0.443945i	0.708939	+	0.705270i	$0.249174\pi$
$114$	4.33691	−	7.51175i	0.406189	−	0.703540i
$115$	−20.4704			−1.90888
$116$	7.04316	−	12.1991i	0.653941	−	1.13266i
$117$	2.99297	+	2.01050i	0.276700	+	0.185871i
$118$	6.97958			0.642522
$119$	−2.31257	+	15.4024i	−0.211993	+	1.41193i
$120$	8.90467	+	15.4233i	0.812882	+	1.40795i
$121$	−3.34113			−0.303739
$122$	−12.1823	+	21.1003i	−1.10293	+	1.91034i
$123$	−3.24124	−	5.61400i	−0.292253	−	0.506197i
$124$	−17.4225			−1.56458
$125$	−6.22211			−0.556523
$126$	−6.28028	+	2.46895i	−0.559491	+	0.219952i
$127$	−0.886520	−	1.53550i	−0.0786660	−	0.136253i	0.824009	−	0.566577i	$-0.191733\pi$
$127$	−0.886520	−	1.53550i	−0.0786660	−	0.136253i	−0.902675	+	0.430324i	$0.858399\pi$
$128$	5.50543	−	9.53569i	0.486616	−	0.842844i
$129$	−2.99197	+	5.18224i	−0.263428	+	0.456271i
$130$	21.2754	+	14.2916i	1.86598	+	1.25345i
$131$	−3.50734	−	6.07490i	−0.306438	−	0.530766i	0.671143	−	0.741328i	$-0.265804\pi$
$131$	−3.50734	−	6.07490i	−0.306438	−	0.530766i	−0.977580	+	0.210562i	$0.932471\pi$
$132$	−6.23423	−	10.7980i	−0.542620	−	0.939846i
$133$	7.03775	+	5.60586i	0.610250	+	0.486090i
$134$	11.0703	−	19.1743i	0.956326	−	1.65641i
$135$	1.39351	+	2.41363i	0.119934	+	0.207732i
$136$	18.8087	+	32.5776i	1.61283	+	2.79350i
$137$	9.82872	+	17.0239i	0.839725	+	1.45445i	0.890125	+	0.455717i	$0.150617\pi$
$137$	9.82872	+	17.0239i	0.839725	+	1.45445i	−0.0504003	+	0.998729i	$0.516050\pi$
$138$	−9.36684	−	16.2238i	−0.797358	−	1.38106i
$139$	−9.17342	+	15.8888i	−0.778079	+	1.34767i	0.154968	+	0.987919i	$0.450472\pi$
$139$	−9.17342	+	15.8888i	−0.778079	+	1.34767i	−0.933048	+	0.359753i	$0.882861\pi$
$140$	−30.9181	+	12.1548i	−2.61306	+	1.02727i
$141$	−3.95673	−	6.85325i	−0.333217	−	0.577148i
$142$	−4.00596	−	6.93852i	−0.336173	−	0.582268i
$143$	−8.28295	−	5.56400i	−0.692655	−	0.465285i
$144$	−3.64382	+	6.31127i	−0.303651	+	0.525940i
$145$	4.35689	−	7.54635i	0.361820	−	0.626690i
$146$	−12.2501	−	21.2178i	−1.01383	−	1.75600i
$147$	−1.56542	−	6.82272i	−0.129114	−	0.562728i
$148$	26.3270			2.16407
$149$	−8.80290			−0.721162			−0.360581	−	0.932728i	$-0.617422\pi$
$149$	−8.80290			−0.721162			−0.360581	+	0.932728i	$0.617422\pi$
$150$	3.52930	+	6.11292i	0.288166	+	0.499118i
$151$	−4.83567	+	8.37562i	−0.393521	+	0.681598i	−0.992911	−	0.118859i	$-0.962076\pi$
$151$	−4.83567	+	8.37562i	−0.393521	+	0.681598i	0.599390	+	0.800457i	$0.295410\pi$
$152$	21.7311			1.76263
$153$	2.94340	+	5.09812i	0.237960	+	0.412159i
$154$	17.3805	−	6.83275i	1.40056	−	0.550599i
$155$	−10.7775			−0.865672
$156$	−1.10228	+	16.2069i	−0.0882532	+	1.29759i
$157$	−5.76601	+	9.98702i	−0.460177	+	0.797051i	−0.998969	−	0.0453882i	$-0.985548\pi$
$157$	−5.76601	+	9.98702i	−0.460177	+	0.797051i	0.538792	+	0.842439i	$0.318881\pi$
$158$	9.59583			0.763403
$159$	−6.34471	+	10.9894i	−0.503168	+	0.871513i
$160$	−8.09259	+	14.0168i	−0.639775	+	1.10812i
$161$	18.0855	−	7.10991i	1.42533	−	0.560339i
$162$	−1.27528	+	2.20885i	−0.100196	+	0.173544i
$163$	−12.1704			−0.953261			−0.476631	−	0.879104i	$-0.658142\pi$
$163$	−12.1704			−0.953261			−0.476631	+	0.879104i	$0.658142\pi$
$164$	14.6030	−	25.2931i	1.14030	−	1.97506i
$165$	−3.85649	−	6.67963i	−0.300227	−	0.520009i
$166$	−6.14798	+	10.6486i	−0.477176	+	0.826493i
$167$	4.54697	+	7.87559i	0.351855	+	0.609431i	0.986575	−	0.163311i	$-0.0522175\pi$
$167$	4.54697	+	7.87559i	0.351855	+	0.609431i	−0.634719	+	0.772743i	$0.718884\pi$
$168$	−13.2241	−	10.5336i	−1.02026	−	0.812684i
$169$	4.91577	+	12.0348i	0.378136	+	0.925750i
$170$	20.9231	+	36.2398i	1.60473	+	2.77947i
$171$	3.40075			0.260062
$172$	−26.9599			−2.05567
$173$	−1.34730			−0.102433			−0.0512165	−	0.998688i	$-0.516310\pi$
$173$	−1.34730			−0.102433			−0.0512165	+	0.998688i	$0.516310\pi$
$174$	7.97449			0.604544
$175$	−6.81436	+	2.67892i	−0.515117	+	0.202507i
$176$	10.0841	−	17.4662i	0.760121	−	1.31657i
$177$	1.36824	+	2.36987i	0.102843	+	0.178130i
$178$	−2.23885	−	3.87781i	−0.167809	−	0.290654i
$179$	−5.95993			−0.445466			−0.222733	−	0.974880i	$-0.571498\pi$
$179$	−5.95993			−0.445466			−0.222733	+	0.974880i	$0.571498\pi$
$180$	−6.27828	+	10.8743i	−0.467955	+	0.810522i
$181$	10.4495			0.776707			0.388354	−	0.921510i	$-0.373044\pi$
$181$	10.4495			0.776707			0.388354	+	0.921510i	$0.373044\pi$
$182$	−23.7605	−	5.23699i	−1.76125	−	0.388192i
$183$	−9.55263			−0.706151
$184$	23.4674	−	40.6468i	1.73004	−	2.99652i
$185$	16.2858			1.19736
$186$	−4.93157	−	8.54173i	−0.361600	−	0.626310i
$187$	−8.14577	−	14.1089i	−0.595677	−	1.03174i
$188$	17.8265	−	30.8765i	1.30013	−	2.25190i
$189$	−2.06947	−	1.64842i	−0.150532	−	0.119905i
$190$	24.1741			1.75377
$191$	−0.658114			−0.0476194			−0.0238097	−	0.999717i	$-0.507580\pi$
$191$	−0.658114			−0.0476194			−0.0238097	+	0.999717i	$0.507580\pi$
$192$	−0.236742			−0.0170854
$193$	8.78557			0.632399			0.316200	−	0.948693i	$-0.397593\pi$
$193$	8.78557			0.632399			0.316200	+	0.948693i	$0.397593\pi$
$194$	21.6450	+	37.4903i	1.55402	+	2.69165i
$195$	−0.681870	+	10.0256i	−0.0488297	+	0.717946i
$196$	23.0943	−	21.4773i	1.64959	−	1.53410i
$197$	−9.29781	−	16.1043i	−0.662442	−	1.14738i	−0.979972	−	0.199135i	$-0.936187\pi$
$197$	−9.29781	−	16.1043i	−0.662442	−	1.14738i	0.317530	−	0.948248i	$-0.397146\pi$
$198$	3.52930	−	6.11292i	0.250816	−	0.434427i
$199$	−7.61283	−	13.1858i	−0.539659	−	0.934717i	−0.998922	−	0.0464164i	$-0.985220\pi$
$199$	−7.61283	−	13.1858i	−0.539659	−	0.934717i	0.459263	−	0.888300i	$-0.348113\pi$
$200$	−8.84221	+	15.3151i	−0.625238	+	1.08294i
$201$	8.68066			0.612286
$202$	2.35000	−	4.07031i	0.165345	−	0.286386i
$203$	−1.22823	+	8.18041i	−0.0862051	+	0.574152i
$204$	−13.2611	+	22.9689i	−0.928464	+	1.60815i
$205$	9.03340	−	15.6463i	0.630920	−	1.09279i
$206$	12.1665			0.847681
$207$	3.67246	−	6.36089i	0.255254	−	0.442112i
$208$	−23.5947	+	11.5636i	−1.63600	+	0.801789i
$209$	−9.41145			−0.651004
$210$	−14.7108	−	11.7177i	−1.01514	−	0.808601i
$211$	−10.5945	−	18.3503i	−0.729357	−	1.26328i	−0.957155	−	0.289575i	$-0.906486\pi$
$211$	−10.5945	−	18.3503i	−0.729357	−	1.26328i	0.227798	−	0.973708i	$-0.426847\pi$
$212$	−57.1706			−3.92649
$213$	1.57062	−	2.72039i	0.107617	−	0.186398i
$214$	15.3996	+	26.6728i	1.05269	+	1.82332i
$215$	−16.6773			−1.13738
$216$	−6.39011			−0.434792
$217$	9.52186	−	3.74332i	0.646386	−	0.254113i
$218$	8.69448	+	15.0593i	0.588865	+	1.01994i
$219$	4.80291	−	8.31889i	0.324551	−	0.562138i
$220$	17.3749	−	30.0942i	1.17142	−	2.02895i
$221$	−1.44026	+	21.1763i	−0.0968825	+	1.42447i
$222$	7.45207	+	12.9074i	0.500150	+	0.866285i
$223$	−0.453274	−	0.785093i	−0.0303534	−	0.0525737i	0.850450	−	0.526056i	$-0.176330\pi$
$223$	−0.453274	−	0.785093i	−0.0303534	−	0.0525737i	−0.880803	+	0.473483i	$0.842997\pi$
$224$	2.28135	−	15.1945i	0.152429	−	1.01522i
$225$	−1.38373	+	2.39670i	−0.0922489	+	0.159780i
$226$	−6.94935	−	12.0366i	−0.462264	−	0.800664i
$227$	−0.964045	−	1.66977i	−0.0639859	−	0.110827i	0.832258	−	0.554389i	$-0.187048\pi$
$227$	−0.964045	−	1.66977i	−0.0639859	−	0.110827i	−0.896244	+	0.443562i	$0.853715\pi$
$228$	7.66082	+	13.2689i	0.507350	+	0.878756i
$229$	5.05578	+	8.75686i	0.334095	+	0.578670i	0.983311	−	0.181935i	$-0.0582360\pi$
$229$	5.05578	+	8.75686i	0.334095	+	0.578670i	−0.649216	+	0.760604i	$0.724903\pi$
$230$	26.1055	−	45.2161i	1.72135	−	2.98146i
$231$	5.72719	+	4.56195i	0.376821	+	0.300154i
$232$	9.98953	+	17.3024i	0.655845	+	1.13596i
$233$	13.1134	+	22.7130i	0.859085	+	1.48798i	0.872803	+	0.488073i	$0.162300\pi$
$233$	13.1134	+	22.7130i	0.859085	+	1.48798i	−0.0137178	+	0.999906i	$0.504367\pi$
$234$	−8.25778	+	4.04708i	−0.539828	+	0.264566i
$235$	11.0275	−	19.1001i	0.719353	−	1.24596i
$236$	−6.16444	+	10.6771i	−0.401271	+	0.695022i
$237$	1.88112	+	3.25819i	0.122192	+	0.211642i
$238$	−31.0724	−	24.7505i	−2.01413	−	1.60434i
$239$	28.0556			1.81476			0.907382	−	0.420306i	$-0.138077\pi$
$239$	28.0556			1.81476			0.907382	+	0.420306i	$0.138077\pi$
$240$	−20.3108			−1.31105
$241$	2.22625	+	3.85597i	0.143405	+	0.248385i	0.928777	−	0.370640i	$-0.120861\pi$
$241$	2.22625	+	3.85597i	0.143405	+	0.248385i	−0.785372	+	0.619025i	$0.787528\pi$
$242$	4.26088	−	7.38007i	0.273900	−	0.474409i
$243$	−1.00000			−0.0641500
$244$	−21.5191	−	37.2721i	−1.37762	−	2.38610i
$245$	14.2861	−	13.2859i	0.912704	−	0.848802i
$246$	16.5340			1.05417
$247$	10.1783	+	6.83721i	0.647632	+	0.435041i
$248$	12.3554	−	21.4002i	0.784570	−	1.35892i
$249$	−4.82088			−0.305511
$250$	7.93494	−	13.7437i	0.501850	−	0.869229i
$251$	1.55413	−	2.69183i	0.0980956	−	0.169907i	−0.812801	−	0.582542i	$-0.802058\pi$
$251$	1.55413	−	2.69183i	0.0980956	−	0.169907i	0.910896	+	0.412635i	$0.135392\pi$
$252$	1.76989	−	11.7880i	0.111492	−	0.742572i
$253$	−10.1634	+	17.6035i	−0.638968	+	1.10672i
$254$	4.52225			0.283751
$255$	−8.20331	+	14.2086i	−0.513711	+	0.889774i
$256$	14.2787	+	24.7314i	0.892419	+	1.54571i
$257$	12.9927	−	22.5040i	0.810461	−	1.40376i	−0.102081	−	0.994776i	$-0.532550\pi$
$257$	12.9927	−	22.5040i	0.810461	−	1.40376i	0.912542	−	0.408984i	$-0.134117\pi$
$258$	−7.63120	−	13.2176i	−0.475098	−	0.822894i
$259$	−14.3884	+	5.65650i	−0.894053	+	0.351478i
$260$	−40.6535	+	19.9240i	−2.52122	+	1.23563i
$261$	1.56328	+	2.70768i	0.0967646	+	0.167601i
$262$	17.8914			1.10533
$263$	12.7806			0.788083			0.394042	−	0.919093i	$-0.371077\pi$
$263$	12.7806			0.788083			0.394042	+	0.919093i	$0.371077\pi$
$264$	17.6844			1.08840
$265$	−35.3656			−2.17249
$266$	−21.3576	+	8.39629i	−1.30952	+	0.514810i
$267$	0.877787	−	1.52037i	0.0537197	−	0.0930453i
$268$	19.5548	+	33.8699i	1.19450	+	2.06893i
$269$	−0.978744	−	1.69523i	−0.0596751	−	0.103360i	0.834644	−	0.550789i	$-0.185673\pi$
$269$	−0.978744	−	1.69523i	−0.0596751	−	0.103360i	−0.894320	+	0.447429i	$0.852340\pi$
$270$	−7.10846			−0.432607
$271$	−13.4609	+	23.3150i	−0.817692	+	1.41628i	0.0896863	+	0.995970i	$0.471414\pi$
$271$	−13.4609	+	23.3150i	−0.817692	+	1.41628i	−0.907379	+	0.420314i	$0.861920\pi$
$272$	−42.9009			−2.60125
$273$	−2.87972	−	9.09435i	−0.174288	−	0.550415i
$274$	−50.1376			−3.02892
$275$	3.82943	−	6.63277i	0.230924	−	0.399971i
$276$	33.0916			1.99188
$277$	11.5778	+	20.0533i	0.695643	+	1.20489i	0.969964	+	0.243250i	$0.0782136\pi$
$277$	11.5778	+	20.0533i	0.695643	+	1.20489i	−0.274321	+	0.961638i	$0.588453\pi$
$278$	−23.3974	−	40.5254i	−1.40328	−	2.43055i
$279$	1.93352	−	3.34896i	0.115757	−	0.200497i
$280$	6.99620	−	46.5968i	0.418103	−	2.78469i
$281$	−26.9347			−1.60679			−0.803396	−	0.595446i	$-0.796976\pi$
$281$	−26.9347			−1.60679			−0.803396	+	0.595446i	$0.796976\pi$
$282$	20.1838			1.20193
$283$	15.2443			0.906181			0.453091	−	0.891464i	$-0.350321\pi$
$283$	15.2443			0.906181			0.453091	+	0.891464i	$0.350321\pi$
$284$	14.1524			0.839792
$285$	4.73897	+	8.20814i	0.280712	+	0.486208i
$286$	22.8531	−	11.2002i	1.35133	−	0.662279i
$287$	−2.54657	+	16.9609i	−0.150319	+	1.00117i
$288$	−2.90367	−	5.02931i	−0.171101	−	0.296355i
$289$	−8.82723	+	15.2892i	−0.519249	+	0.899365i
$290$	11.1125	+	19.2474i	0.652549	+	1.13025i
$291$	−8.48637	+	14.6988i	−0.497480	+	0.861660i
$292$	43.2778			2.53264
$293$	−2.04388	+	3.54010i	−0.119405	+	0.206815i	−0.919532	−	0.393015i	$-0.871432\pi$
$293$	−2.04388	+	3.54010i	−0.119405	+	0.206815i	0.800127	+	0.599830i	$0.204765\pi$
$294$	17.0667	+	5.24311i	0.995352	+	0.305784i
$295$	−3.81332	+	6.60486i	−0.222020	+	0.384550i
$296$	−18.6702	+	32.3377i	−1.08518	+	1.87959i
$297$	2.76747			0.160585
$298$	11.2262	−	19.4443i	0.650315	−	1.12638i
$299$	23.7801	−	11.6545i	1.37524	−	0.673995i
$300$	−12.4685			−0.719867
$301$	14.7343	−	5.79247i	0.849271	−	0.333873i
$302$	−12.3337	−	21.3625i	−0.709723	−	1.22928i
$303$	1.84273			0.105862
$304$	−12.3917	+	21.4631i	−0.710713	+	1.23099i
$305$	−13.3117	−	23.0565i	−0.762224	−	1.32021i
$306$	−15.0147			−0.858331
$307$	1.04296			0.0595250			0.0297625	−	0.999557i	$-0.490525\pi$
$307$	1.04296			0.0595250			0.0297625	+	0.999557i	$0.490525\pi$
$308$	−4.89810	+	32.6228i	−0.279095	+	1.85886i
$309$	2.38506	+	4.13105i	0.135682	+	0.235007i
$310$	13.7444	−	23.8060i	0.780628	−	1.35209i
$311$	−3.88724	+	6.73290i	−0.220425	+	0.381788i	−0.954937	−	0.296808i	$-0.904078\pi$
$311$	−3.88724	+	6.73290i	−0.220425	+	0.381788i	0.734512	+	0.678596i	$0.237411\pi$
$312$	−19.1254	−	12.8473i	−1.08276	−	0.727337i
$313$	−12.1950	−	21.1224i	−0.689304	−	1.19391i	−0.972063	−	0.234719i	$-0.924583\pi$
$313$	−12.1950	−	21.1224i	−0.689304	−	1.19391i	0.282759	−	0.959191i	$-0.408750\pi$
$314$	−14.7066	−	25.4725i	−0.829939	−	1.43750i
$315$	1.09485	−	7.29202i	0.0616877	−	0.410859i
$316$	−8.47514	+	14.6794i	−0.476764	+	0.825779i
$317$	−5.38045	−	9.31922i	−0.302196	−	0.523419i	0.674437	−	0.738333i	$-0.264386\pi$
$317$	−5.38045	−	9.31922i	−0.302196	−	0.523419i	−0.976633	+	0.214913i	$0.931053\pi$
$318$	−16.1826	−	28.0291i	−0.907474	−	1.57179i
$319$	−4.32632	−	7.49341i	−0.242228	−	0.419550i
$320$	−0.329903	−	0.571408i	−0.0184421	−	0.0319427i
$321$	−6.03771	+	10.4576i	−0.336992	+	0.583688i
$322$	−7.35932	+	49.0153i	−0.410119	+	2.73151i
$323$	10.0098	+	17.3374i	0.556958	+	0.964680i
$324$	−2.25269	−	3.90177i	−0.125149	−	0.216765i
$325$	−8.96004	+	4.39125i	−0.497013	+	0.243583i
$326$	15.5207	−	26.8827i	0.859613	−	1.48889i
$327$	−3.40885	+	5.90430i	−0.188510	+	0.326508i
$328$	20.7119	+	35.8741i	1.14362	+	1.98081i
$329$	−3.10871	+	20.7050i	−0.171389	+	1.14150i
$330$	19.6724			1.08293
$331$	−22.9691			−1.26250			−0.631248	−	0.775581i	$-0.717457\pi$
$331$	−22.9691			−1.26250			−0.631248	+	0.775581i	$0.717457\pi$
$332$	−10.8599	−	18.8100i	−0.596017	−	1.03233i
$333$	−2.92173	+	5.06059i	−0.160110	+	0.277319i
$334$	−23.1947			−1.26916
$335$	12.0966	+	20.9519i	0.660906	+	1.14472i
$336$	17.9444	−	7.05446i	0.978948	−	0.384852i
$337$	6.99034			0.380788			0.190394	−	0.981708i	$-0.439023\pi$
$337$	6.99034			0.380788			0.190394	+	0.981708i	$0.439023\pi$
$338$	−32.8520	−	4.48950i	−1.78691	−	0.244196i
$339$	2.72463	−	4.71920i	0.147982	−	0.256312i
$340$	−73.9179			−4.00876
$341$	−5.35096	+	9.26813i	−0.289771	+	0.501898i
$342$	−4.33691	+	7.51175i	−0.234513	+	0.406189i
$343$	−8.00712	+	16.6999i	−0.432344	+	0.901709i
$344$	19.1190	−	33.1151i	1.03083	−	1.78545i
$345$	20.4704			1.10209
$346$	1.71818	−	2.97598i	0.0923701	−	0.159990i
$347$	1.07692	+	1.86528i	0.0578120	+	0.100133i	0.893483	−	0.449097i	$-0.148254\pi$
$347$	1.07692	+	1.86528i	0.0578120	+	0.100133i	−0.835671	+	0.549230i	$0.814921\pi$
$348$	−7.04316	+	12.1991i	−0.377553	+	0.653941i
$349$	−0.756384	−	1.31010i	−0.0404883	−	0.0701278i	0.845071	−	0.534654i	$-0.179558\pi$
$349$	−0.756384	−	1.31010i	−0.0404883	−	0.0701278i	−0.885559	+	0.464526i	$0.846225\pi$
$350$	2.77289	−	18.4683i	0.148217	−	0.987171i
$351$	−2.99297	−	2.01050i	−0.159753	−	0.107313i
$352$	8.03582	+	13.9184i	0.428311	+	0.741856i
$353$	−32.3938			−1.72415			−0.862073	−	0.506784i	$-0.830834\pi$
$353$	−32.3938			−1.72415			−0.862073	+	0.506784i	$0.830834\pi$
$354$	−6.97958			−0.370960
$355$	8.75467			0.464650
$356$	7.90952			0.419204
$357$	2.31257	−	15.4024i	0.122394	−	0.815180i
$358$	7.60058	−	13.1646i	0.401703	−	0.695771i
$359$	−7.93156	−	13.7379i	−0.418612	−	0.725057i	0.577188	−	0.816611i	$-0.304150\pi$
$359$	−7.93156	−	13.7379i	−0.418612	−	0.725057i	−0.995800	+	0.0915543i	$0.970816\pi$
$360$	−8.90467	−	15.4233i	−0.469317	−	0.812882i
$361$	−7.43492			−0.391311
$362$	−13.3261	+	23.0815i	−0.700404	+	1.21314i
$363$	3.34113			0.175364
$364$	28.9969	−	31.7227i	1.51985	−	1.66272i
$365$	26.7716			1.40129
$366$	12.1823	−	21.1003i	0.636779	−	1.10293i
$367$	12.5937			0.657388			0.328694	−	0.944436i	$-0.393391\pi$
$367$	12.5937			0.657388			0.328694	+	0.944436i	$0.393391\pi$
$368$	26.7635	+	46.3558i	1.39515	+	2.41646i
$369$	3.24124	+	5.61400i	0.168732	+	0.292253i
$370$	−20.7690	+	35.9730i	−1.07973	+	1.87015i
$371$	31.2453	−	12.2834i	1.62217	−	0.637723i
$372$	17.4225			0.903313
$373$	−11.7036			−0.605987			−0.302994	−	0.952993i	$-0.597986\pi$
$373$	−11.7036			−0.605987			−0.302994	+	0.952993i	$0.597986\pi$
$374$	41.5526			2.14863
$375$	6.22211			0.321308
$376$	25.2839	+	43.7930i	1.30392	+	2.25845i
$377$	−0.764942	+	11.2470i	−0.0393965	+	0.579249i
$378$	6.28028	−	2.46895i	0.323023	−	0.126989i
$379$	−16.4778	−	28.5403i	−0.846406	−	1.46602i	−0.884395	−	0.466740i	$-0.845428\pi$
$379$	−16.4778	−	28.5403i	−0.846406	−	1.46602i	0.0379888	−	0.999278i	$-0.487905\pi$
$380$	−21.3508	+	36.9807i	−1.09527	+	1.89707i
$381$	0.886520	+	1.53550i	0.0454178	+	0.0786660i
$382$	0.839280	−	1.45368i	0.0429413	−	0.0743765i
$383$	12.6361			0.645672			0.322836	−	0.946455i	$-0.395364\pi$
$383$	12.6361			0.645672			0.322836	+	0.946455i	$0.395364\pi$
$384$	−5.50543	+	9.53569i	−0.280948	+	0.486616i
$385$	−3.02996	+	20.1804i	−0.154421	+	1.02849i
$386$	−11.2041	+	19.4060i	−0.570272	+	0.987741i
$387$	2.99197	−	5.18224i	0.152090	−	0.263428i
$388$	−76.4685			−3.88210
$389$	−0.0593906	+	0.102868i	−0.00301122	+	0.00521559i	−0.867527	−	0.497390i	$-0.834292\pi$
$389$	−0.0593906	+	0.102868i	−0.00301122	+	0.00521559i	0.864516	+	0.502606i	$0.167625\pi$
$390$	−21.2754	−	14.2916i	−1.07732	−	0.723682i
$391$	43.2381			2.18664
$392$	10.0032	+	43.5979i	0.505238	+	2.20203i
$393$	3.50734	+	6.07490i	0.176922	+	0.306438i
$394$	47.4293			2.38945
$395$	−5.24271	+	9.08064i	−0.263789	+	0.456897i
$396$	6.23423	+	10.7980i	0.313282	+	0.542620i
$397$	6.98302			0.350468			0.175234	−	0.984527i	$-0.443932\pi$
$397$	6.98302			0.350468			0.175234	+	0.984527i	$0.443932\pi$
$398$	38.8340			1.94657
$399$	−7.03775	−	5.60586i	−0.352328	−	0.280644i
$400$	−10.0841	−	17.4662i	−0.504207	−	0.873312i
$401$	9.57584	−	16.5858i	0.478194	−	0.828257i	−0.521493	−	0.853256i	$-0.674625\pi$
$401$	9.57584	−	16.5858i	0.478194	−	0.828257i	0.999687	+	0.0249985i	$0.00795810\pi$
$402$	−11.0703	+	19.1743i	−0.552135	+	0.956326i
$403$	12.5201	−	6.13599i	0.623669	−	0.305656i
$404$	4.15109	+	7.18989i	0.206524	+	0.357711i
$405$	−1.39351	−	2.41363i	−0.0692440	−	0.119934i
$406$	−16.5030	−	13.1453i	−0.819028	−	0.652391i
$407$	8.08580	−	14.0050i	0.400798	−	0.694203i
$408$	−18.8087	−	32.5776i	−0.931167	−	1.61283i
$409$	−5.84506	−	10.1239i	−0.289019	−	0.500596i	0.684557	−	0.728960i	$-0.259996\pi$
$409$	−5.84506	−	10.1239i	−0.289019	−	0.500596i	−0.973576	+	0.228363i	$0.926663\pi$
$410$	23.0403	+	39.9069i	1.13788	+	1.97086i
$411$	−9.82872	−	17.0239i	−0.484815	−	0.839725i
$412$	−10.7456	+	18.6119i	−0.529398	+	0.916944i
$413$	1.07500	−	7.15981i	0.0528972	−	0.352311i
$414$	9.36684	+	16.2238i	0.460355	+	0.797358i
$415$	−6.71794	−	11.6358i	−0.329771	−	0.571180i
$416$	1.42082	−	20.8904i	0.0696616	−	1.02424i
$417$	9.17342	−	15.8888i	0.449224	−	0.778079i
$418$	12.0023	−	20.7885i	0.587049	−	1.01680i
$419$	7.89905	+	13.6816i	0.385894	+	0.668388i	0.991893	−	0.127078i	$-0.0405598\pi$
$419$	7.89905	+	13.6816i	0.385894	+	0.668388i	−0.605999	+	0.795465i	$0.707226\pi$
$420$	30.9181	−	12.1548i	1.50865	−	0.593093i
$421$	8.58170			0.418247			0.209123	−	0.977889i	$-0.432939\pi$
$421$	8.58170			0.418247			0.209123	+	0.977889i	$0.432939\pi$
$422$	54.0440			2.63082
$423$	3.95673	+	6.85325i	0.192383	+	0.333217i
$424$	40.5434	−	70.2232i	1.96896	−	3.41034i
$425$	−16.2915			−0.790255
$426$	4.00596	+	6.93852i	0.194089	+	0.336173i
$427$	19.7689	+	15.7468i	0.956684	+	0.762039i
$428$	−54.4043			−2.62973
$429$	8.28295	+	5.56400i	0.399905	+	0.268632i
$430$	21.2683	−	36.8378i	1.02565	−	1.77648i
$431$	−19.4446			−0.936615			−0.468308	−	0.883565i	$-0.655136\pi$
$431$	−19.4446			−0.936615			−0.468308	+	0.883565i	$0.655136\pi$
$432$	3.64382	−	6.31127i	0.175313	−	0.303651i
$433$	2.35409	−	4.07740i	0.113130	−	0.195948i	−0.803900	−	0.594764i	$-0.797246\pi$
$433$	2.35409	−	4.07740i	0.113130	−	0.195948i	0.917031	+	0.398816i	$0.130579\pi$
$434$	−3.87463	+	25.8062i	−0.185988	+	1.23874i
$435$	−4.35689	+	7.54635i	−0.208897	+	0.361820i
$436$	−30.7163			−1.47104
$437$	12.4891	−	21.6318i	0.597435	−	1.03479i
$438$	12.2501	+	21.2178i	0.585334	+	1.01383i
$439$	10.3311	−	17.8941i	0.493078	−	0.854037i	−0.506890	−	0.862011i	$-0.669205\pi$
$439$	10.3311	−	17.8941i	0.493078	−	0.854037i	0.999968	+	0.00797405i	$0.00253825\pi$
$440$	24.6434	+	42.6836i	1.17483	+	2.03486i
$441$	1.56542	+	6.82272i	0.0745437	+	0.324891i
$442$	−44.9385	−	30.1870i	−2.13751	−	1.43585i
$443$	6.14100	+	10.6365i	0.291768	+	0.505357i	0.974228	−	0.225566i	$-0.0724232\pi$
$443$	6.14100	+	10.6365i	0.291768	+	0.505357i	−0.682460	+	0.730923i	$0.739090\pi$
$444$	−26.3270			−1.24942
$445$	4.89282			0.231942
$446$	2.31221			0.109486
$447$	8.80290			0.416363
$448$	0.489931	+	0.390251i	0.0231471	+	0.0184376i
$449$	13.7884	−	23.8822i	0.650714	−	1.12707i	−0.332235	−	0.943196i	$-0.607803\pi$
$449$	13.7884	−	23.8822i	0.650714	−	1.12707i	0.982950	−	0.183874i	$-0.0588638\pi$
$450$	−3.52930	−	6.11292i	−0.166373	−	0.288166i
$451$	−8.97003	−	15.5365i	−0.422382	−	0.731587i
$452$	24.5510			1.15478
$453$	4.83567	−	8.37562i	0.227199	−	0.393521i
$454$	4.91771			0.230800
$455$	17.9375	−	19.6236i	0.840922	−	0.919970i
$456$	−21.7311			−1.01765
$457$	−6.93931	+	12.0192i	−0.324607	+	0.562236i	−0.981433	−	0.191806i	$-0.938565\pi$
$457$	−6.93931	+	12.0192i	−0.324607	+	0.562236i	0.656826	+	0.754042i	$0.271899\pi$
$458$	−25.7901			−1.20509
$459$	−2.94340	−	5.09812i	−0.137386	−	0.237960i
$460$	46.1134	+	79.8708i	2.15005	+	3.72399i
$461$	−12.2050	+	21.1396i	−0.568441	+	0.984569i	0.428279	+	0.903647i	$0.359120\pi$
$461$	−12.2050	+	21.1396i	−0.568441	+	0.984569i	−0.996720	+	0.0809228i	$0.974213\pi$
$462$	−17.3805	+	6.83275i	−0.808612	+	0.317888i
$463$	−11.6449			−0.541185			−0.270593	−	0.962694i	$-0.587220\pi$
$463$	−11.6449			−0.541185			−0.270593	+	0.962694i	$0.587220\pi$
$464$	−22.7852			−1.05778
$465$	10.7775			0.499796
$466$	−66.8929			−3.09875
$467$	2.09483	+	3.62835i	0.0969370	+	0.167900i	0.910415	−	0.413695i	$-0.135762\pi$
$467$	2.09483	+	3.62835i	0.0969370	+	0.167900i	−0.813478	+	0.581595i	$0.802429\pi$
$468$	1.10228	−	16.2069i	0.0509530	−	0.749165i
$469$	−17.9644	−	14.3094i	−0.829517	−	0.660745i
$470$	28.1263	+	48.7161i	1.29737	+	2.24711i
$471$	5.76601	−	9.98702i	0.265684	−	0.460177i
$472$	−8.74322	−	15.1437i	−0.402439	−	0.697045i
$473$	−8.28017	+	14.3417i	−0.380723	+	0.659431i
$474$	−9.59583			−0.440751
$475$	−4.70573	+	8.15056i	−0.215914	+	0.373973i
$476$	65.3060	−	25.6736i	2.99329	−	1.17675i
$477$	6.34471	−	10.9894i	0.290504	−	0.503168i
$478$	−35.7788	+	61.9706i	−1.63648	+	2.83447i
$479$	−15.0085			−0.685754			−0.342877	−	0.939380i	$-0.611401\pi$
$479$	−15.0085			−0.685754			−0.342877	+	0.939380i	$0.611401\pi$
$480$	8.09259	−	14.0168i	0.369375	−	0.639775i
$481$	−18.9190	+	9.27206i	−0.862632	+	0.422769i
$482$	−11.3564			−0.517268
$483$	−18.0855	+	7.10991i	−0.822917	+	0.323512i
$484$	7.52652	+	13.0363i	0.342115	+	0.592560i
$485$	−47.3033			−2.14793
$486$	1.27528	−	2.20885i	0.0578479	−	0.100196i
$487$	−3.30409	−	5.72285i	−0.149722	−	0.259327i	0.781402	−	0.624027i	$-0.214505\pi$
$487$	−3.30409	−	5.72285i	−0.149722	−	0.259327i	−0.931125	+	0.364701i	$0.881171\pi$
$488$	61.0423			2.76326
$489$	12.1704			0.550366
$490$	11.1277	+	48.4990i	0.502699	+	2.19096i
$491$	−16.4555	−	28.5018i	−0.742628	−	1.28627i	−0.951295	−	0.308283i	$-0.900246\pi$
$491$	−16.4555	−	28.5018i	−0.742628	−	1.28627i	0.208666	−	0.977987i	$-0.433088\pi$
$492$	−14.6030	+	25.2931i	−0.658354	+	1.14030i
$493$	−9.20272	+	15.9396i	−0.414470	+	0.717883i
$494$	−28.0826	+	13.7631i	−1.26350	+	0.619231i
$495$	3.85649	+	6.67963i	0.173336	+	0.300227i
$496$	14.0908	+	24.4060i	0.632696	+	1.09586i
$497$	−7.73469	+	3.04073i	−0.346948	+	0.136395i
$498$	6.14798	−	10.6486i	0.275498	−	0.477176i
$499$	−17.9199	−	31.0381i	−0.802204	−	1.38946i	−0.918163	−	0.396203i	$-0.870328\pi$
$499$	−17.9199	−	31.0381i	−0.802204	−	1.38946i	0.115959	−	0.993254i	$-0.463006\pi$
$500$	14.0165	+	24.2772i	0.626835	+	1.08571i
$501$	−4.54697	−	7.87559i	−0.203144	−	0.351855i
$502$	3.96390	+	6.86567i	0.176917	+	0.306430i
$503$	−9.67700	+	16.7610i	−0.431476	+	0.747338i	−0.997001	−	0.0773931i	$-0.975340\pi$
$503$	−9.67700	+	16.7610i	−0.431476	+	0.747338i	0.565525	+	0.824731i	$0.308674\pi$
$504$	13.2241	+	10.5336i	0.589050	+	0.469203i
$505$	2.56786	+	4.44766i	0.114268	+	0.197918i
$506$	−25.9224	−	44.8989i	−1.15239	−	1.99600i
$507$	−4.91577	−	12.0348i	−0.218317	−	0.534482i
$508$	−3.99410	+	6.91799i	−0.177210	+	0.306936i
$509$	−5.24874	+	9.09108i	−0.232646	+	0.402955i	−0.958586	−	0.284803i	$-0.908072\pi$
$509$	−5.24874	+	9.09108i	−0.232646	+	0.402955i	0.725940	+	0.687758i	$0.241405\pi$
$510$	−20.9231	−	36.2398i	−0.926489	−	1.60473i
$511$	−23.6525	+	9.29847i	−1.04633	+	0.411340i
$512$	−50.8157			−2.24576
$513$	−3.40075			−0.150147
$514$	33.1386	+	57.3978i	1.46168	+	2.53171i
$515$	−6.64721	+	11.5133i	−0.292911	+	0.507337i
$516$	26.9599			1.18684
$517$	−10.9501	−	18.9662i	−0.481585	−	0.834130i
$518$	5.85492	−	38.9955i	0.257250	−	1.71337i
$519$	1.34730			0.0591398
$520$	4.35722	−	64.0645i	0.191077	−	2.80941i
$521$	10.7923	−	18.6928i	0.472818	−	0.818945i	−0.526698	−	0.850053i	$-0.676570\pi$
$521$	10.7923	−	18.6928i	0.472818	−	0.818945i	0.999516	+	0.0311074i	$0.00990340\pi$
$522$	−7.97449			−0.349034
$523$	−1.73189	+	2.99973i	−0.0757304	+	0.131169i	−0.901404	−	0.432980i	$-0.857462\pi$
$523$	−1.73189	+	2.99973i	−0.0757304	+	0.131169i	0.825673	+	0.564149i	$0.190796\pi$
$524$	−15.8019	+	27.3697i	−0.690308	+	1.19565i
$525$	6.81436	−	2.67892i	0.297403	−	0.116918i
$526$	−16.2988	+	28.2304i	−0.710662	+	1.23090i
$527$	22.7645			0.991639
$528$	−10.0841	+	17.4662i	−0.438856	+	0.760121i
$529$	−15.4739	−	26.8016i	−0.672779	−	1.16529i
$530$	45.1012	−	78.1175i	1.95907	−	3.39321i
$531$	−1.36824	−	2.36987i	−0.0593767	−	0.102843i
$532$	6.01893	−	40.0879i	0.260954	−	1.73803i
$533$	−1.58600	+	23.3191i	−0.0686973	+	1.01006i
$534$	2.23885	+	3.87781i	0.0968846	+	0.167809i
$535$	−33.6544			−1.45501
$536$	−55.4703			−2.39595
$537$	5.95993			0.257190
$538$	4.99270			0.215250
$539$	−4.33224	−	18.8816i	−0.186603	−	0.813290i
$540$	6.27828	−	10.8743i	0.270174	−	0.467955i
$541$	4.46427	+	7.73234i	0.191934	+	0.332439i	0.945891	−	0.324484i	$-0.105191\pi$
$541$	4.46427	+	7.73234i	0.191934	+	0.332439i	−0.753957	+	0.656924i	$0.771857\pi$
$542$	−34.3329	−	59.4663i	−1.47472	−	2.55430i
$543$	−10.4495			−0.448432
$544$	17.0934	−	29.6066i	0.732872	−	1.26937i
$545$	−19.0010			−0.813915
$546$	23.7605	+	5.23699i	1.01686	+	0.224123i
$547$	−3.62704			−0.155081			−0.0775405	−	0.996989i	$-0.524707\pi$
$547$	−3.62704			−0.155081			−0.0775405	+	0.996989i	$0.524707\pi$
$548$	44.2821	−	76.6988i	1.89164	−	3.27641i
$549$	9.55263			0.407696
$550$	9.76721	+	16.9173i	0.416475	+	0.721357i
$551$	5.31632	+	9.20813i	0.226483	+	0.392280i
$552$	−23.4674	+	40.6468i	−0.998839	+	1.73004i
$553$	1.47795	−	9.84361i	0.0628490	−	0.418593i
$554$	−59.0598			−2.50921
$555$	−16.2858			−0.691296
$556$	82.6593			3.50554
$557$	−20.0447			−0.849320			−0.424660	−	0.905353i	$-0.639606\pi$
$557$	−20.0447			−0.849320			−0.424660	+	0.905353i	$0.639606\pi$
$558$	4.93157	+	8.54173i	0.208770	+	0.361600i
$559$	19.3738	−	9.49495i	0.819424	−	0.401593i
$560$	42.0325	+	33.4807i	1.77620	+	1.41482i
$561$	8.14577	+	14.1089i	0.343914	+	0.595677i
$562$	34.3494	−	59.4948i	1.44894	−	2.50964i
$563$	3.77715	+	6.54221i	0.159188	+	0.275721i	0.934576	−	0.355763i	$-0.115779\pi$
$563$	3.77715	+	6.54221i	0.159188	+	0.275721i	−0.775388	+	0.631485i	$0.782446\pi$
$564$	−17.8265	+	30.8765i	−0.750632	+	1.30013i
$565$	15.1872			0.638930
$566$	−19.4408	+	33.6725i	−0.817158	+	1.41536i
$567$	2.06947	+	1.64842i	0.0869096	+	0.0692272i
$568$	−10.0364	+	17.3836i	−0.421119	+	0.729399i
$569$	−14.0828	+	24.3921i	−0.590381	+	1.02257i	0.403800	+	0.914847i	$0.367689\pi$
$569$	−14.0828	+	24.3921i	−0.590381	+	1.02257i	−0.994181	+	0.107723i	$0.965644\pi$
$570$	−24.1741			−1.01254
$571$	9.03604	−	15.6509i	0.378146	−	0.654969i	−0.612646	−	0.790357i	$-0.709895\pi$
$571$	9.03604	−	15.6509i	0.378146	−	0.654969i	0.990793	+	0.135389i	$0.0432283\pi$
$572$	−3.05053	+	44.8521i	−0.127549	+	1.87536i
$573$	0.658114			0.0274931
$574$	−34.2166	−	27.2550i	−1.42817	−	1.13760i
$575$	10.1634	+	17.6035i	0.423843	+	0.734118i
$576$	0.236742			0.00986427
$577$	21.5383	−	37.3054i	0.896651	−	1.55305i	0.0649040	−	0.997892i	$-0.479326\pi$
$577$	21.5383	−	37.3054i	0.896651	−	1.55305i	0.831747	−	0.555154i	$-0.187341\pi$
$578$	−22.5144	−	38.9961i	−0.936476	−	1.62202i
$579$	−8.78557			−0.365116
$580$	−39.2588			−1.63013
$581$	9.97668	+	7.94684i	0.413902	+	0.329691i
$582$	−21.6450	−	37.4903i	−0.897215	−	1.55402i
$583$	−17.5588	+	30.4127i	−0.727210	+	1.25956i
$584$	−30.6911	+	53.1586i	−1.27001	+	2.19972i
$585$	0.681870	−	10.0256i	0.0281919	−	0.414506i
$586$	−5.21304	−	9.02925i	−0.215349	−	0.372995i
$587$	2.26101	+	3.91619i	0.0933220	+	0.161638i	0.908907	−	0.416999i	$-0.136918\pi$
$587$	2.26101	+	3.91619i	0.0933220	+	0.161638i	−0.815585	+	0.578637i	$0.803585\pi$
$588$	−23.0943	+	21.4773i	−0.952391	+	0.885710i
$589$	6.57542	−	11.3890i	0.270936	−	0.469274i
$590$	−9.72610	−	16.8461i	−0.400417	−	0.693543i
$591$	9.29781	+	16.1043i	0.382461	+	0.662442i
$592$	−21.2925	−	36.8797i	−0.875117	−	1.51575i
$593$	1.43449	+	2.48460i	0.0589073	+	0.102030i	0.893975	−	0.448117i	$-0.147905\pi$
$593$	1.43449	+	2.48460i	0.0589073	+	0.102030i	−0.835068	+	0.550147i	$0.814572\pi$
$594$	−3.52930	+	6.11292i	−0.144809	+	0.250816i
$595$	40.3982	−	15.8817i	1.65616	−	0.651085i
$596$	19.8302	+	34.3469i	0.812276	+	1.40690i
$597$	7.61283	+	13.1858i	0.311572	+	0.539659i
$598$	−4.58337	+	67.3895i	−0.187428	+	2.75576i
$599$	−2.94653	+	5.10354i	−0.120392	+	0.208525i	−0.919922	−	0.392101i	$-0.871748\pi$
$599$	−2.94653	+	5.10354i	−0.120392	+	0.208525i	0.799530	+	0.600626i	$0.205082\pi$
$600$	8.84221	−	15.3151i	0.360982	−	0.625238i
$601$	−9.46284	−	16.3901i	−0.385997	−	0.668567i	0.605910	−	0.795533i	$-0.292809\pi$
$601$	−9.46284	−	16.3901i	−0.385997	−	0.668567i	−0.991907	+	0.126967i	$0.959476\pi$
$602$	−5.99567	+	39.9329i	−0.244365	+	1.62754i
$603$	−8.68066			−0.353504
$604$	43.5730			1.77296
$605$	4.65590	+	8.06425i	0.189289	+	0.327858i
$606$	−2.35000	+	4.07031i	−0.0954621	+	0.165345i
$607$	43.8783			1.78096			0.890482	−	0.455019i	$-0.150367\pi$
$607$	43.8783			1.78096			0.890482	+	0.455019i	$0.150367\pi$
$608$	−9.87466	−	17.1034i	−0.400470	−	0.693635i
$609$	1.22823	−	8.18041i	0.0497705	−	0.331487i
$610$	67.9045			2.74937
$611$	−1.93610	+	28.4666i	−0.0783263	+	1.15164i
$612$	13.2611	−	22.9689i	0.536049	−	0.928464i
$613$	30.5826			1.23522			0.617610	−	0.786484i	$-0.288101\pi$
$613$	30.5826			1.23522			0.617610	+	0.786484i	$0.288101\pi$
$614$	−1.33007	+	2.30375i	−0.0536773	+	0.0929718i
$615$	−9.03340	+	15.6463i	−0.364262	+	0.630920i
$616$	−36.5974	−	29.1513i	−1.47455	−	1.17454i
$617$	22.1042	−	38.2856i	0.889881	−	1.54132i	0.0498659	−	0.998756i	$-0.484121\pi$
$617$	22.1042	−	38.2856i	0.889881	−	1.54132i	0.840015	−	0.542563i	$-0.182546\pi$
$618$	−12.1665			−0.489409
$619$	0.184678	−	0.319871i	0.00742283	−	0.0128567i	−0.862290	−	0.506415i	$-0.830971\pi$
$619$	0.184678	−	0.319871i	0.00742283	−	0.0128567i	0.869713	+	0.493558i	$0.164304\pi$
$620$	24.2784	+	42.0514i	0.975043	+	1.68882i
$621$	−3.67246	+	6.36089i	−0.147371	+	0.255254i
$622$	−9.91466	−	17.1727i	−0.397542	−	0.688562i
$623$	−4.32277	+	1.69940i	−0.173188	+	0.0680851i
$624$	23.5947	−	11.5636i	0.944543	−	0.462913i
$625$	15.5892	+	27.0013i	0.623569	+	1.08005i
$626$	62.2084			2.48635
$627$	9.41145			0.375857
$628$	51.9560			2.07327
$629$	−34.3993			−1.37159
$630$	14.7108	+	11.7177i	0.586091	+	0.466846i
$631$	6.70906	−	11.6204i	0.267083	−	0.462602i	−0.701024	−	0.713138i	$-0.747273\pi$
$631$	6.70906	−	11.6204i	0.267083	−	0.462602i	0.968107	+	0.250536i	$0.0806067\pi$
$632$	−12.0206	−	20.8202i	−0.478152	−	0.828184i
$633$	10.5945	+	18.3503i	0.421095	+	0.729357i
$634$	27.4464			1.09003
$635$	−2.47075	+	4.27946i	−0.0980486	+	0.169825i
$636$	57.1706			2.26696
$637$	−9.03183	+	23.5675i	−0.357854	+	0.933777i
$638$	22.0691			0.873725
$639$	−1.57062	+	2.72039i	−0.0621327	+	0.107617i
$640$	−30.6875			−1.21303
$641$	−21.5169	−	37.2683i	−0.849865	−	1.47201i	−0.881328	−	0.472505i	$-0.843350\pi$
$641$	−21.5169	−	37.2683i	−0.849865	−	1.47201i	0.0314626	−	0.999505i	$-0.489984\pi$
$642$	−15.3996	−	26.6728i	−0.607773	−	1.05269i
$643$	14.6688	−	25.4071i	0.578482	−	1.00196i	−0.417172	−	0.908828i	$-0.636979\pi$
$643$	14.6688	−	25.4071i	0.578482	−	1.00196i	0.995654	−	0.0931324i	$-0.0296880\pi$
$644$	−68.4821	−	54.5489i	−2.69857	−	2.14953i
$645$	16.6773			0.656669
$646$	−51.0611			−2.00897
$647$	−18.0070			−0.707930			−0.353965	−	0.935259i	$-0.615167\pi$
$647$	−18.0070			−0.707930			−0.353965	+	0.935259i	$0.615167\pi$
$648$	6.39011			0.251027
$649$	3.78656	+	6.55852i	0.148636	+	0.257445i
$650$	1.72695	−	25.3915i	0.0677366	−	0.995936i
$651$	−9.52186	+	3.74332i	−0.373191	+	0.146712i
$652$	27.4161	+	47.4862i	1.07370	+	1.85970i
$653$	−17.3270	+	30.0113i	−0.678059	+	1.17443i	0.297505	+	0.954720i	$0.403845\pi$
$653$	−17.3270	+	30.0113i	−0.678059	+	1.17443i	−0.975565	+	0.219713i	$0.929488\pi$
$654$	−8.69448	−	15.0593i	−0.339981	−	0.588865i
$655$	−9.77502	+	16.9308i	−0.381942	+	0.661543i
$656$	−47.2420			−1.84449
$657$	−4.80291	+	8.31889i	−0.187379	+	0.324551i
$658$	−41.7697	−	33.2713i	−1.62835	−	1.29705i
$659$	−2.68796	+	4.65569i	−0.104708	+	0.181360i	−0.913619	−	0.406572i	$-0.866724\pi$
$659$	−2.68796	+	4.65569i	−0.104708	+	0.181360i	0.808911	+	0.587931i	$0.200058\pi$
$660$	−17.3749	+	30.0942i	−0.676318	+	1.17142i
$661$	40.4711			1.57414			0.787072	−	0.616861i	$-0.211596\pi$
$661$	40.4711			1.57414			0.787072	+	0.616861i	$0.211596\pi$
$662$	29.2921	−	50.7353i	1.13847	−	1.97188i
$663$	1.44026	−	21.1763i	0.0559351	−	0.822417i
$664$	30.8060			1.19550
$665$	3.72330	−	24.7983i	0.144384	−	0.961638i
$666$	−7.45207	−	12.9074i	−0.288762	−	0.500150i
$667$	22.9643			0.889182
$668$	20.4858	−	35.4825i	0.792620	−	1.37286i
$669$	0.453274	+	0.785093i	0.0175246	+	0.0303534i
$670$	−61.7061			−2.38392
$671$	−26.4366			−1.02057
$672$	−2.28135	+	15.1945i	−0.0880051	+	0.586140i
$673$	13.1634	+	22.7996i	0.507411	+	0.878861i	0.999963	+	0.00857837i	$0.00273061\pi$
$673$	13.1634	+	22.7996i	0.507411	+	0.878861i	−0.492553	+	0.870283i	$0.663936\pi$
$674$	−8.91465	+	15.4406i	−0.343380	+	0.594751i
$675$	1.38373	−	2.39670i	0.0532599	−	0.0922489i
$676$	35.8831	−	46.2907i	1.38012	−	1.78041i
$677$	−1.90262	−	3.29544i	−0.0731236	−	0.126654i	0.827145	−	0.561988i	$-0.189963\pi$
$677$	−1.90262	−	3.29544i	−0.0731236	−	0.126654i	−0.900269	+	0.435335i	$0.856630\pi$
$678$	6.94935	+	12.0366i	0.266888	+	0.462264i
$679$	41.7921	−	16.4297i	1.60384	−	0.630513i
$680$	52.4201	−	90.7942i	2.01022	−	3.48180i
$681$	0.964045	+	1.66977i	0.0369423	+	0.0639859i
$682$	−13.6480	−	23.6390i	−0.522607	−	0.905182i
$683$	−5.19765	−	9.00259i	−0.198882	−	0.344474i	0.749284	−	0.662249i	$-0.230398\pi$
$683$	−5.19765	−	9.00259i	−0.198882	−	0.344474i	−0.948166	+	0.317774i	$0.897065\pi$
$684$	−7.66082	−	13.2689i	−0.292919	−	0.507350i
$685$	27.3928	−	47.4458i	1.04663	−	1.81281i
$686$	−26.6762	−	38.9836i	−1.01850	−	1.48840i
$687$	−5.05578	−	8.75686i	−0.192890	−	0.334095i
$688$	21.8044	+	37.7663i	0.831284	+	1.43983i
$689$	41.0837	−	20.1348i	1.56516	−	0.767075i
$690$	−26.1055	+	45.2161i	−0.993821	+	1.72135i
$691$	4.09958	−	7.10067i	0.155955	−	0.270122i	−0.777451	−	0.628943i	$-0.783488\pi$
$691$	4.09958	−	7.10067i	0.155955	−	0.270122i	0.933406	+	0.358821i	$0.116821\pi$
$692$	3.03504	+	5.25684i	0.115375	+	0.199835i
$693$	−5.72719	−	4.56195i	−0.217558	−	0.173294i
$694$	−5.49350			−0.208530
$695$	51.1329			1.93958
$696$	−9.98953	−	17.3024i	−0.378652	−	0.655845i
$697$	−19.0806	+	33.0485i	−0.722728	+	1.25180i
$698$	3.85841			0.146043
$699$	−13.1134	−	22.7130i	−0.495993	−	0.859085i
$700$	25.8031	+	20.5533i	0.975266	+	0.776841i
$701$	4.64503			0.175440			0.0877201	−	0.996145i	$-0.472042\pi$
$701$	4.64503			0.175440			0.0877201	+	0.996145i	$0.472042\pi$
$702$	8.25778	−	4.04708i	0.311670	−	0.152747i
$703$	−9.93608	+	17.2098i	−0.374746	+	0.649080i
$704$	−0.655177			−0.0246929
$705$	−11.0275	+	19.1001i	−0.415319	+	0.719353i
$706$	41.3112	−	71.5531i	1.55477	−	2.69293i
$707$	−3.81347	−	3.03759i	−0.143420	−	0.114240i
$708$	6.16444	−	10.6771i	0.231674	−	0.401271i
$709$	−44.3975			−1.66738			−0.833691	−	0.552231i	$-0.813777\pi$
$709$	−44.3975			−1.66738			−0.833691	+	0.552231i	$0.813777\pi$
$710$	−11.1647	+	19.3378i	−0.419003	+	0.725734i
$711$	−1.88112	−	3.25819i	−0.0705475	−	0.122192i
$712$	−5.60916	+	9.71534i	−0.210212	+	0.364098i
$713$	−14.2016	−	24.5978i	−0.531853	−	0.921196i
$714$	31.0724	+	24.7505i	1.16286	+	0.926264i
$715$	−1.88705	+	27.7454i	−0.0705718	+	1.03762i
$716$	13.4258	+	23.2542i	0.501747	+	0.869052i
$717$	−28.0556			−1.04775
$718$	40.4599			1.50995
$719$	−44.9378			−1.67590			−0.837949	−	0.545748i	$-0.816246\pi$
$719$	−44.9378			−1.67590			−0.837949	+	0.545748i	$0.816246\pi$
$720$	20.3108			0.756937
$721$	1.87389	−	12.4807i	0.0697874	−	0.464805i
$722$	9.48161	−	16.4226i	0.352869	−	0.611187i
$723$	−2.22625	−	3.85597i	−0.0827950	−	0.143405i
$724$	−23.5395	−	40.7716i	−0.874839	−	1.51527i
$725$	−8.65265			−0.321351
$726$	−4.26088	+	7.38007i	−0.158136	+	0.273900i
$727$	−49.7876			−1.84652			−0.923260	−	0.384177i	$-0.874485\pi$
$727$	−49.7876			−1.84652			−0.923260	+	0.384177i	$0.874485\pi$
$728$	18.4017	+	58.1139i	0.682012	+	2.15384i
$729$	1.00000			0.0370370
$730$	−34.1413	+	59.1345i	−1.26363	+	2.18867i
$731$	35.2263			1.30289
$732$	21.5191	+	37.2721i	0.795368	+	1.37762i
$733$	9.96819	+	17.2654i	0.368184	+	0.637713i	0.989282	−	0.146020i	$-0.0466465\pi$
$733$	9.96819	+	17.2654i	0.368184	+	0.637713i	−0.621098	+	0.783733i	$0.713313\pi$
$734$	−16.0606	+	27.8177i	−0.592807	+	1.02677i
$735$	−14.2861	+	13.2859i	−0.526950	+	0.490056i
$736$	−42.6545			−1.57227
$737$	24.0234			0.884914
$738$	−16.5340			−0.608624
$739$	48.0471			1.76744			0.883721	−	0.468014i	$-0.155030\pi$
$739$	48.0471			1.76744			0.883721	+	0.468014i	$0.155030\pi$
$740$	−36.6869	−	63.5436i	−1.34864	−	2.33591i
$741$	−10.1783	−	6.83721i	−0.373911	−	0.251171i
$742$	−12.7143	+	84.6810i	−0.466757	+	3.10874i
$743$	−0.250266	−	0.433473i	−0.00918137	−	0.0159026i	0.861398	−	0.507930i	$-0.169589\pi$
$743$	−0.250266	−	0.433473i	−0.00918137	−	0.0159026i	−0.870580	+	0.492028i	$0.836256\pi$
$744$	−12.3554	+	21.4002i	−0.452972	+	0.784570i
$745$	12.2669	+	21.2469i	0.449425	+	0.778427i
$746$	14.9253	−	25.8514i	0.546455	−	0.946488i
$747$	4.82088			0.176387
$748$	−36.6997	+	63.5657i	−1.34187	+	2.32419i
$749$	29.7334	−	11.6891i	1.08644	−	0.427109i
$750$	−7.93494	+	13.7437i	−0.289743	+	0.501850i
$751$	−21.9025	+	37.9363i	−0.799235	+	1.38432i	0.120880	+	0.992667i	$0.461428\pi$
$751$	−21.9025	+	37.9363i	−0.799235	+	1.38432i	−0.920115	+	0.391648i	$0.871905\pi$
$752$	−57.6704			−2.10302
$753$	−1.55413	+	2.69183i	−0.0566355	+	0.0980956i
$754$	−23.8674	−	16.0327i	−0.869200	−	0.583877i
$755$	26.9542			0.980963
$756$	−1.76989	+	11.7880i	−0.0643701	+	0.428724i
$757$	1.91271	+	3.31291i	0.0695186	+	0.120410i	0.898689	−	0.438585i	$-0.144520\pi$
$757$	1.91271	+	3.31291i	0.0695186	+	0.120410i	−0.829171	+	0.558995i	$0.811187\pi$
$758$	84.0552			3.05302
$759$	10.1634	−	17.6035i	0.368908	−	0.638968i
$760$	−30.2825	−	52.4509i	−1.09846	−	1.90259i
$761$	−5.73144			−0.207765			−0.103882	−	0.994590i	$-0.533127\pi$
$761$	−5.73144			−0.207765			−0.103882	+	0.994590i	$0.533127\pi$
$762$	−4.52225			−0.163824
$763$	16.7873	−	6.59956i	0.607740	−	0.238920i
$764$	1.48252	+	2.56781i	0.0536358	+	0.0928999i
$765$	8.20331	−	14.2086i	0.296591	−	0.513711i
$766$	−16.1145	+	27.9112i	−0.582242	+	1.00847i
$767$	0.669507	−	9.84380i	0.0241745	−	0.355439i
$768$	−14.2787	−	24.7314i	−0.515238	−	0.892419i
$769$	8.50053	+	14.7234i	0.306537	+	0.530938i	0.977602	−	0.210461i	$-0.0674964\pi$
$769$	8.50053	+	14.7234i	0.306537	+	0.530938i	−0.671065	+	0.741398i	$0.734163\pi$
$770$	−40.7115	−	32.4284i	−1.46714	−	1.16864i
$771$	−12.9927	+	22.5040i	−0.467920	+	0.810461i
$772$	−19.7911	−	34.2792i	−0.712298	−	1.23374i
$773$	6.09320	+	10.5537i	0.219157	+	0.379591i	0.954550	−	0.298049i	$-0.0963360\pi$
$773$	6.09320	+	10.5537i	0.219157	+	0.379591i	−0.735393	+	0.677640i	$0.763003\pi$
$774$	7.63120	+	13.2176i	0.274298	+	0.475098i
$775$	5.35096	+	9.26813i	0.192212	+	0.332921i
$776$	54.2288	−	93.9271i	1.94670	−	3.37179i
$777$	14.3884	−	5.65650i	0.516182	−	0.202926i
$778$	−0.151480	−	0.262370i	−0.00543080	−	0.00940643i
$779$	11.0226	+	19.0918i	0.394927	+	0.684034i
$780$	40.6535	−	19.9240i	1.45563	−	0.713393i
$781$	4.34663	−	7.52858i	0.155535	−	0.269394i
$782$	−55.1407	+	95.5066i	−1.97183	+	3.41531i
$783$	−1.56328	−	2.70768i	−0.0558671	−	0.0967646i
$784$	−48.7641	−	14.9809i	−1.74158	−	0.535034i
$785$	32.1399			1.14712
$786$	−17.8914			−0.638165
$787$	2.31021	+	4.00140i	0.0823501	+	0.142635i	0.904259	−	0.426984i	$-0.140424\pi$
$787$	2.31021	+	4.00140i	0.0823501	+	0.142635i	−0.821909	+	0.569619i	$0.807091\pi$
$788$	−41.8901	+	72.5558i	−1.49227	+	2.58469i
$789$	−12.7806			−0.455000
$790$	−13.3719	−	23.1608i	−0.475750	−	0.824023i
$791$	−13.4178	+	5.27491i	−0.477081	+	0.187554i
$792$	−17.6844			−0.628388
$793$	28.5908	+	19.2056i	1.01529	+	0.682010i
$794$	−8.90531	+	15.4245i	−0.316038	+	0.547393i
$795$	35.3656			1.25429
$796$	−34.2986	+	59.4069i	−1.21568	+	2.10562i
$797$	−9.12087	+	15.7978i	−0.323078	+	0.559587i	−0.981121	−	0.193393i	$-0.938051\pi$
$797$	−9.12087	+	15.7978i	−0.323078	+	0.559587i	0.658044	+	0.752980i	$0.271384\pi$
$798$	21.3576	−	8.39629i	0.756052	−	0.297226i
$799$	−23.2925	+	40.3438i	−0.824029	+	1.42726i
$800$	16.0716			0.568218
$801$	−0.877787	+	1.52037i	−0.0310151	+	0.0537197i
$802$	24.4238	+	42.3032i	0.862433	+	1.49378i
$803$	13.2919	−	23.0222i	0.469061	−	0.812437i
$804$	−19.5548	−	33.8699i	−0.689644	−	1.19450i
$805$	−42.3629	−	33.7439i	−1.49310	−	1.18931i
$806$	−2.41311	+	35.4801i	−0.0849982	+	1.24973i
$807$	0.978744	+	1.69523i	0.0344534	+	0.0596751i
$808$	−11.7752			−0.414251
$809$	−34.5921			−1.21619			−0.608096	−	0.793863i	$-0.708067\pi$
$809$	−34.5921			−1.21619			−0.608096	+	0.793863i	$0.708067\pi$
$810$	7.10846			0.249766
$811$	−11.9774			−0.420582			−0.210291	−	0.977639i	$-0.567441\pi$
$811$	−11.9774			−0.420582			−0.210291	+	0.977639i	$0.567441\pi$
$812$	34.6849	−	13.6356i	1.21720	−	0.478516i
$813$	13.4609	−	23.3150i	0.472095	−	0.817692i
$814$	20.6233	+	35.7207i	0.722848	+	1.25201i
$815$	16.9596	+	29.3749i	0.594069	+	1.02896i
$816$	42.9009			1.50183
$817$	10.1749	−	17.6235i	0.355976	−	0.616568i
$818$	29.8164			1.04250
$819$	2.87972	+	9.09435i	0.100625	+	0.317782i
$820$	−81.3976			−2.84253
$821$	−10.5936	+	18.3486i	−0.369719	+	0.640372i	−0.989521	−	0.144386i	$-0.953879\pi$
$821$	−10.5936	+	18.3486i	−0.369719	+	0.640372i	0.619803	+	0.784758i	$0.287213\pi$
$822$	50.1376			1.74875
$823$	−9.96806	−	17.2652i	−0.347465	−	0.601827i	0.638334	−	0.769760i	$-0.279624\pi$
$823$	−9.96806	−	17.2652i	−0.347465	−	0.601827i	−0.985798	+	0.167933i	$0.946291\pi$
$824$	−15.2408	−	26.3979i	−0.530939	−	0.919614i
$825$	−3.82943	+	6.63277i	−0.133324	+	0.230924i
$826$	14.4440	+	11.5053i	0.502572	+	0.400320i
$827$	−15.0299			−0.522639			−0.261320	−	0.965252i	$-0.584158\pi$
$827$	−15.0299			−0.522639			−0.261320	+	0.965252i	$0.584158\pi$
$828$	−33.0916			−1.15001
$829$	16.0717			0.558195			0.279097	−	0.960263i	$-0.409965\pi$
$829$	16.0717			0.558195			0.279097	+	0.960263i	$0.409965\pi$
$830$	34.2691			1.18950
$831$	−11.5778	−	20.0533i	−0.401629	−	0.695643i
$832$	0.708563	+	0.475971i	0.0245650	+	0.0165013i
$833$	−30.1754	+	28.0627i	−1.04552	+	0.972315i
$834$	23.3974	+	40.5254i	0.810185	+	1.40328i
$835$	12.6725	−	21.9494i	0.438550	−	0.759591i
$836$	21.2011	+	36.7213i	0.733254	+	1.27003i
$837$	−1.93352	+	3.34896i	−0.0668323	+	0.115757i
$838$	−40.2940			−1.39193
$839$	2.50930	−	4.34624i	0.0866307	−	0.150049i	−0.819454	−	0.573145i	$-0.805723\pi$
$839$	2.50930	−	4.34624i	0.0866307	−	0.150049i	0.906085	+	0.423096i	$0.139057\pi$
$840$	−6.99620	+	46.5968i	−0.241392	+	1.60774i
$841$	9.61231	−	16.6490i	0.331459	−	0.574104i
$842$	−10.9441	+	18.9557i	−0.377158	+	0.653257i
$843$	26.9347			0.927681
$844$	−47.7323	+	82.6747i	−1.64301	+	2.84578i
$845$	22.1972	−	28.6354i	0.763609	−	0.985086i
$846$	−20.1838			−0.693932
$847$	−6.91437	−	5.50759i	−0.237581	−	0.189243i
$848$	46.2379	+	80.0864i	1.58782	+	2.75018i
$849$	−15.2443			−0.523184
$850$	20.7763	−	35.9856i	0.712621	−	1.23430i
$851$	21.4599	+	37.1696i	0.735636	+	1.27416i
$852$	−14.1524			−0.484854
$853$	−4.22423			−0.144635			−0.0723175	−	0.997382i	$-0.523039\pi$
$853$	−4.22423			−0.144635			−0.0723175	+	0.997382i	$0.523039\pi$
$854$	−59.9931	+	23.5850i	−2.05292	+	0.807063i
$855$	−4.73897	−	8.20814i	−0.162069	−	0.280712i
$856$	38.5817	−	66.8254i	1.31869	−	2.28404i
$857$	4.48428	−	7.76700i	0.153180	−	0.265316i	−0.779215	−	0.626757i	$-0.784382\pi$
$857$	4.48428	−	7.76700i	0.153180	−	0.265316i	0.932395	+	0.361441i	$0.117715\pi$
$858$	−22.8531	+	11.2002i	−0.780193	+	0.382367i
$859$	18.3400	+	31.7658i	0.625753	+	1.08384i	0.988395	+	0.151907i	$0.0485414\pi$
$859$	18.3400	+	31.7658i	0.625753	+	1.08384i	−0.362642	+	0.931928i	$0.618125\pi$
$860$	37.5688	+	65.0711i	1.28109	+	2.21890i
$861$	2.54657	−	16.9609i	0.0867869	−	0.578027i
$862$	24.7974	−	42.9503i	0.844602	−	1.46289i
$863$	−10.4237	−	18.0544i	−0.354828	−	0.614580i	0.632261	−	0.774756i	$-0.282127\pi$
$863$	−10.4237	−	18.0544i	−0.354828	−	0.614580i	−0.987088	+	0.160176i	$0.948794\pi$
$864$	2.90367	+	5.02931i	0.0987850	+	0.171101i
$865$	1.87747	+	3.25187i	0.0638359	+	0.110567i
$866$	6.00426	+	10.3997i	0.204033	+	0.353395i
$867$	8.82723	−	15.2892i	0.299788	−	0.519249i
$868$	−36.0553	−	28.7196i	−1.22380	−	0.974806i
$869$	5.20593	+	9.01694i	0.176599	+	0.305879i
$870$	−11.1125	−	19.2474i	−0.376750	−	0.652549i
$871$	−25.9810	−	17.4525i	−0.880331	−	0.591354i
$872$	21.7829	−	37.7291i	0.737663	−	1.27767i
$873$	8.48637	−	14.6988i	0.287220	−	0.497480i
$874$	31.8543	+	55.1732i	1.07749	+	1.86626i
$875$	−12.8765	−	10.2567i	−0.435304	−	0.346738i
$876$	−43.2778			−1.46222
$877$	−27.6200			−0.932662			−0.466331	−	0.884610i	$-0.654425\pi$
$877$	−27.6200			−0.932662			−0.466331	+	0.884610i	$0.654425\pi$
$878$	26.3502	+	45.6399i	0.889277	+	1.54027i
$879$	2.04388	−	3.54010i	0.0689383	−	0.119405i
$880$	−56.2093			−1.89482
$881$	−12.7092	−	22.0130i	−0.428183	−	0.741635i	0.568528	−	0.822664i	$-0.307513\pi$
$881$	−12.7092	−	22.0130i	−0.428183	−	0.741635i	−0.996712	+	0.0810283i	$0.974180\pi$
$882$	−17.0667	−	5.24311i	−0.574666	−	0.176545i
$883$	32.7921			1.10354			0.551771	−	0.833995i	$-0.313952\pi$
$883$	32.7921			1.10354			0.551771	+	0.833995i	$0.313952\pi$
$884$	85.8692	−	42.0839i	2.88810	−	1.41543i
$885$	3.81332	−	6.60486i	0.128183	−	0.222020i
$886$	−31.3260			−1.05242
$887$	3.96660	−	6.87036i	0.133185	−	0.230684i	−0.791717	−	0.610888i	$-0.790813\pi$
$887$	3.96660	−	6.87036i	0.133185	−	0.230684i	0.924903	+	0.380204i	$0.124146\pi$
$888$	18.6702	−	32.3377i	0.626531	−	1.08518i
$889$	0.696519	−	4.63903i	0.0233605	−	0.155588i
$890$	−6.23972	+	10.8075i	−0.209156	+	0.362269i
$891$	−2.76747			−0.0927136
$892$	−2.04217	+	3.53713i	−0.0683768	+	0.118432i
$893$	13.4558	+	23.3062i	0.450282	+	0.779912i
$894$	−11.2262	+	19.4443i	−0.375460	+	0.650315i
$895$	8.30521	+	14.3850i	0.277613	+	0.480839i
$896$	27.1122	−	10.6586i	0.905754	−	0.356078i
$897$	−23.7801	+	11.6545i	−0.793996	+	0.389131i
$898$	35.1682	+	60.9130i	1.17358	+	2.03269i
$899$	12.0905			0.403242
$900$	12.4685			0.415615
$901$	74.7001			2.48862
$902$	45.7572			1.52355
$903$	−14.7343	+	5.79247i	−0.490327	+	0.192761i
$904$	−17.4107	+	30.1562i	−0.579071	+	1.00298i
$905$	−14.5615	−	25.2213i	−0.484041	−	0.838384i
$906$	12.3337	+	21.3625i	0.409759	+	0.709723i
$907$	−46.2372			−1.53528			−0.767640	−	0.640881i	$-0.778569\pi$
$907$	−46.2372			−1.53528			−0.767640	+	0.640881i	$0.778569\pi$
$908$	−4.34338	+	7.52295i	−0.144140	+	0.249658i
$909$	−1.84273			−0.0611194
$910$	20.4704	+	64.6469i	0.678586	+	2.14302i
$911$	−21.5838			−0.715102			−0.357551	−	0.933894i	$-0.616388\pi$
$911$	−21.5838			−0.715102			−0.357551	+	0.933894i	$0.616388\pi$
$912$	12.3917	−	21.4631i	0.410330	−	0.710713i
$913$	−13.3416			−0.441544
$914$	−17.6991	−	30.6558i	−0.585436	−	1.01400i
$915$	13.3117	+	23.0565i	0.440070	+	0.762224i
$916$	22.7781	−	39.4529i	0.752611	−	1.30356i
$917$	2.75564	−	18.3534i	0.0909993	−	0.606082i
$918$	15.0147			0.495558
$919$	−8.80978			−0.290608			−0.145304	−	0.989387i	$-0.546416\pi$
$919$	−8.80978			−0.290608			−0.145304	+	0.989387i	$0.546416\pi$
$920$	−130.808			−4.31262
$921$	−1.04296			−0.0343668
$922$	−31.1295	−	53.9179i	−1.02520	−	1.77569i
$923$	−10.1702	+	4.98432i	−0.334755	+	0.164061i
$924$	4.89810	−	32.6228i	0.161136	−	1.07321i
$925$	−8.08580	−	14.0050i	−0.265859	−	0.460482i
$926$	14.8505	−	25.7219i	0.488019	−	0.845274i
$927$	−2.38506	−	4.13105i	−0.0783358	−	0.135682i
$928$	9.07851	−	15.7244i	0.298017	−	0.516180i
$929$	−52.4694			−1.72147			−0.860733	−	0.509057i	$-0.829994\pi$
$929$	−52.4694			−1.72147			−0.860733	+	0.509057i	$0.829994\pi$
$930$	−13.7444	+	23.8060i	−0.450696	+	0.780628i
$931$	5.32359	+	23.2023i	0.174474	+	0.760426i
$932$	59.0806	−	102.331i	1.93525	−	3.35195i
$933$	3.88724	−	6.73290i	0.127263	−	0.220425i
$934$	−10.6860			−0.349656
$935$	−22.7024	+	39.3217i	−0.742448	+	1.28596i
$936$	19.1254	+	12.8473i	0.625134	+	0.419928i
$937$	−19.3131			−0.630932			−0.315466	−	0.948937i	$-0.602161\pi$
$937$	−19.3131			−0.630932			−0.315466	+	0.948937i	$0.602161\pi$
$938$	54.5169	−	21.4321i	1.78004	−	0.699784i
$939$	12.1950	+	21.1224i	0.397970	+	0.689304i
$940$	−99.3657			−3.24095
$941$	−8.45918	+	14.6517i	−0.275761	+	0.477633i	−0.970327	−	0.241797i	$-0.922263\pi$
$941$	−8.45918	+	14.6517i	−0.275761	+	0.477633i	0.694566	+	0.719429i	$0.255597\pi$
$942$	14.7066	+	25.4725i	0.479166	+	0.829939i
$943$	47.6133			1.55050
$944$	19.9425			0.649073
$945$	−1.09485	+	7.29202i	−0.0356154	+	0.237209i
$946$	−21.1191	−	36.5793i	−0.686641	−	1.18930i
$947$	22.3511	−	38.7132i	0.726313	−	1.25801i	−0.232119	−	0.972687i	$-0.574566\pi$
$947$	22.3511	−	38.7132i	0.726313	−	1.25801i	0.958431	−	0.285323i	$-0.0921008\pi$
$948$	8.47514	−	14.6794i	0.275260	−	0.476764i
$949$	−31.1001	+	15.2419i	−1.00955	+	0.494774i
$950$	−12.0023	−	20.7885i	−0.389405	−	0.674468i
$951$	5.38045	+	9.31922i	0.174473	+	0.302196i
$952$	−14.7775	+	98.4229i	−0.478943	+	3.18990i
$953$	−24.8774	+	43.0888i	−0.805857	+	1.39578i	0.109855	+	0.993948i	$0.464962\pi$
$953$	−24.8774	+	43.0888i	−0.805857	+	1.39578i	−0.915711	+	0.401837i	$0.868372\pi$
$954$	16.1826	+	28.0291i	0.523931	+	0.907474i
$955$	0.917087	+	1.58844i	0.0296762	+	0.0514008i
$956$	−63.2004	−	109.466i	−2.04405	−	3.54039i
$957$	4.32632	+	7.49341i	0.139850	+	0.242228i
$958$	19.1400	−	33.1515i	0.618386	−	1.07108i
$959$	−7.72221	+	51.4322i	−0.249363	+	1.66083i
$960$	0.329903	+	0.571408i	0.0106476	+	0.0184421i
$961$	8.02298	+	13.8962i	0.258806	+	0.448265i
$962$	3.64644	−	53.6137i	0.117566	−	1.72858i
$963$	6.03771	−	10.4576i	0.194563	−	0.336992i
$964$	10.0301	−	17.3726i	0.323047	−	0.559533i
$965$	−12.2428	−	21.2051i	−0.394109	−	0.682616i
$966$	7.35932	−	49.0153i	0.236782	−	1.57704i
$967$	1.92897			0.0620315			0.0310158	−	0.999519i	$-0.490126\pi$
$967$	1.92897			0.0620315			0.0310158	+	0.999519i	$0.490126\pi$
$968$	−21.3502			−0.686221
$969$	−10.0098	−	17.3374i	−0.321560	−	0.556958i
$970$	60.3251	−	104.486i	1.93692	−	3.35485i
$971$	−36.1232			−1.15925			−0.579624	−	0.814884i	$-0.696801\pi$
$971$	−36.1232			−1.15925			−0.579624	+	0.814884i	$0.696801\pi$
$972$	2.25269	+	3.90177i	0.0722549	+	0.125149i
$973$	−45.1756	+	17.7598i	−1.44826	+	0.569353i
$974$	16.8546			0.540055
$975$	8.96004	−	4.39125i	0.286951	−	0.140632i
$976$	−34.8080	+	60.2893i	−1.11418	+	1.92981i
$977$	32.9682			1.05475			0.527373	−	0.849634i	$-0.323177\pi$
$977$	32.9682			1.05475			0.527373	+	0.849634i	$0.323177\pi$
$978$	−15.5207	+	26.8827i	−0.496298	+	0.859613i
$979$	2.42925	−	4.20758i	0.0776391	−	0.134475i
$980$	−84.0203	−	25.8121i	−2.68393	−	0.824537i
$981$	3.40885	−	5.90430i	0.108836	−	0.188510i
$982$	83.9418			2.67869
$983$	7.52903	−	13.0407i	0.240139	−	0.415933i	−0.720615	−	0.693336i	$-0.756140\pi$
$983$	7.52903	−	13.0407i	0.240139	−	0.415933i	0.960754	+	0.277403i	$0.0894737\pi$
$984$	−20.7119	−	35.8741i	−0.660271	−	1.14362i
$985$	−25.9132	+	44.8829i	−0.825662	+	1.43009i
$986$	−23.4721	−	40.6549i	−0.747504	−	1.29472i
$987$	3.10871	−	20.7050i	0.0989514	−	0.659046i
$988$	3.74858	−	55.1156i	0.119258	−	1.75346i
$989$	−21.9758	−	38.0631i	−0.698789	−	1.21034i
$990$	−19.6724			−0.625231
$991$	36.1351			1.14787			0.573935	−	0.818901i	$-0.305416\pi$
$991$	36.1351			1.14787			0.573935	+	0.818901i	$0.305416\pi$
$992$	−22.4573			−0.713019
$993$	22.9691			0.728902
$994$	3.14739	−	20.9626i	0.0998292	−	0.664892i
$995$	−21.2171	+	36.7491i	−0.672627	+	1.16502i
$996$	10.8599	+	18.8100i	0.344110	+	0.596017i
$997$	−1.90762	−	3.30409i	−0.0604149	−	0.104642i	0.834236	−	0.551408i	$-0.185909\pi$
$997$	−1.90762	−	3.30409i	−0.0604149	−	0.104642i	−0.894651	+	0.446766i	$0.852576\pi$
$998$	91.4115			2.89358
$999$	2.92173	−	5.06059i	0.0924396	−	0.160110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.b.172.1	yes	16
3.2	odd	2		819.2.n.e.172.8		16
7.2	even	3		273.2.l.b.16.8	yes	16
13.9	even	3		273.2.l.b.256.8	yes	16
21.2	odd	6		819.2.s.e.289.1		16
39.35	odd	6		819.2.s.e.802.1		16
91.9	even	3	inner	273.2.j.b.100.1	✓	16
273.191	odd	6		819.2.n.e.100.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.1	✓	16	91.9	even	3	inner
273.2.j.b.172.1	yes	16	1.1	even	1	trivial
273.2.l.b.16.8	yes	16	7.2	even	3
273.2.l.b.256.8	yes	16	13.9	even	3
819.2.n.e.100.8		16	273.191	odd	6
819.2.n.e.172.8		16	3.2	odd	2
819.2.s.e.289.1		16	21.2	odd	6
819.2.s.e.802.1		16	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27528 + 2.20885i) q^{2} -1.00000 q^{3} +(-2.25269 - 3.90177i) q^{4} +(-1.39351 - 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(2.06947 + 1.64842i) q^{7} +6.39011 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.27528 + 2.20885i) q^{2} -1.00000 q^{3} +(-2.25269 - 3.90177i) q^{4} +(-1.39351 - 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(2.06947 + 1.64842i) q^{7} +6.39011 q^{8} +1.00000 q^{9} +7.10846 q^{10} -2.76747 q^{11} +(2.25269 + 3.90177i) q^{12} +(2.99297 + 2.01050i) q^{13} +(-6.28028 + 2.46895i) q^{14} +(1.39351 + 2.41363i) q^{15} +(-3.64382 + 6.31127i) q^{16} +(2.94340 + 5.09812i) q^{17} +(-1.27528 + 2.20885i) q^{18} +3.40075 q^{19} +(-6.27828 + 10.8743i) q^{20} +(-2.06947 - 1.64842i) q^{21} +(3.52930 - 6.11292i) q^{22} +(3.67246 - 6.36089i) q^{23} -6.39011 q^{24} +(-1.38373 + 2.39670i) q^{25} +(-8.25778 + 4.04708i) q^{26} -1.00000 q^{27} +(1.76989 - 11.7880i) q^{28} +(1.56328 + 2.70768i) q^{29} -7.10846 q^{30} +(1.93352 - 3.34896i) q^{31} +(-2.90367 - 5.02931i) q^{32} +2.76747 q^{33} -15.0147 q^{34} +(1.09485 - 7.29202i) q^{35} +(-2.25269 - 3.90177i) q^{36} +(-2.92173 + 5.06059i) q^{37} +(-4.33691 + 7.51175i) q^{38} +(-2.99297 - 2.01050i) q^{39} +(-8.90467 - 15.4233i) q^{40} +(3.24124 + 5.61400i) q^{41} +(6.28028 - 2.46895i) q^{42} +(2.99197 - 5.18224i) q^{43} +(6.23423 + 10.7980i) q^{44} +(-1.39351 - 2.41363i) q^{45} +(9.36684 + 16.2238i) q^{46} +(3.95673 + 6.85325i) q^{47} +(3.64382 - 6.31127i) q^{48} +(1.56542 + 6.82272i) q^{49} +(-3.52930 - 6.11292i) q^{50} +(-2.94340 - 5.09812i) q^{51} +(1.10228 - 16.2069i) q^{52} +(6.34471 - 10.9894i) q^{53} +(1.27528 - 2.20885i) q^{54} +(3.85649 + 6.67963i) q^{55} +(13.2241 + 10.5336i) q^{56} -3.40075 q^{57} -7.97449 q^{58} +(-1.36824 - 2.36987i) q^{59} +(6.27828 - 10.8743i) q^{60} +9.55263 q^{61} +(4.93157 + 8.54173i) q^{62} +(2.06947 + 1.64842i) q^{63} +0.236742 q^{64} +(0.681870 - 10.0256i) q^{65} +(-3.52930 + 6.11292i) q^{66} -8.68066 q^{67} +(13.2611 - 22.9689i) q^{68} +(-3.67246 + 6.36089i) q^{69} +(14.7108 + 11.7177i) q^{70} +(-1.57062 + 2.72039i) q^{71} +6.39011 q^{72} +(-4.80291 + 8.31889i) q^{73} +(-7.45207 - 12.9074i) q^{74} +(1.38373 - 2.39670i) q^{75} +(-7.66082 - 13.2689i) q^{76} +(-5.72719 - 4.56195i) q^{77} +(8.25778 - 4.04708i) q^{78} +(-1.88112 - 3.25819i) q^{79} +20.3108 q^{80} +1.00000 q^{81} -16.5340 q^{82} +4.82088 q^{83} +(-1.76989 + 11.7880i) q^{84} +(8.20331 - 14.2086i) q^{85} +(7.63120 + 13.2176i) q^{86} +(-1.56328 - 2.70768i) q^{87} -17.6844 q^{88} +(-0.877787 + 1.52037i) q^{89} +7.10846 q^{90} +(2.87972 + 9.09435i) q^{91} -33.0916 q^{92} +(-1.93352 + 3.34896i) q^{93} -20.1838 q^{94} +(-4.73897 - 8.20814i) q^{95} +(2.90367 + 5.02931i) q^{96} +(8.48637 - 14.6988i) q^{97} +(-17.0667 - 5.24311i) q^{98} -2.76747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Introduction

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