LMFDB - Embedded newform 45.4.l.a.23.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, 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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.12
Character	$\chi$	$=$	45.23
Dual form			45.4.l.a.2.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.576664 - 2.15214i) q^{2} +(-2.09209 + 4.75638i) q^{3} +(2.62904 + 1.51788i) q^{4} +(1.05576 + 11.1304i) q^{5} +(9.02996 + 7.24530i) q^{6} +(13.8105 + 3.70051i) q^{7} +(17.3866 - 17.3866i) q^{8} +(-18.2463 - 19.9016i) q^{9} +O(q^{10})$	\(q+(0.576664 - 2.15214i) q^{2} +(-2.09209 + 4.75638i) q^{3} +(2.62904 + 1.51788i) q^{4} +(1.05576 + 11.1304i) q^{5} +(9.02996 + 7.24530i) q^{6} +(13.8105 + 3.70051i) q^{7} +(17.3866 - 17.3866i) q^{8} +(-18.2463 - 19.9016i) q^{9} +(24.5629 + 4.14635i) q^{10} +(-35.0788 + 20.2528i) q^{11} +(-12.7198 + 9.32918i) q^{12} +(53.7760 - 14.4092i) q^{13} +(15.9280 - 27.5881i) q^{14} +(-55.1491 - 18.2642i) q^{15} +(-15.2491 - 26.4122i) q^{16} +(-18.3703 - 18.3703i) q^{17} +(-53.3529 + 27.7921i) q^{18} +29.3394i q^{19} +(-14.1189 + 30.8648i) q^{20} +(-46.4938 + 57.9461i) q^{21} +(23.3581 + 87.1736i) q^{22} +(-47.3257 - 176.622i) q^{23} +(46.3228 + 119.071i) q^{24} +(-122.771 + 23.5020i) q^{25} -124.043i q^{26} +(132.832 - 45.1505i) q^{27} +(30.6914 + 30.6914i) q^{28} +(-39.7429 - 68.8368i) q^{29} +(-71.1095 + 108.156i) q^{30} +(62.6702 - 108.548i) q^{31} +(124.368 - 33.3242i) q^{32} +(-22.9418 - 209.219i) q^{33} +(-50.1290 + 28.9420i) q^{34} +(-26.6075 + 157.623i) q^{35} +(-17.7622 - 80.0177i) q^{36} +(248.921 - 248.921i) q^{37} +(63.1425 + 16.9190i) q^{38} +(-43.9685 + 285.924i) q^{39} +(211.875 + 175.163i) q^{40} +(155.350 + 89.6914i) q^{41} +(97.8968 + 133.477i) q^{42} +(-96.7744 + 361.167i) q^{43} -122.965 q^{44} +(202.248 - 224.100i) q^{45} -407.406 q^{46} +(-67.7961 + 253.018i) q^{47} +(157.529 - 17.2737i) q^{48} +(-120.011 - 69.2884i) q^{49} +(-20.2179 + 277.772i) q^{50} +(125.809 - 48.9438i) q^{51} +(163.251 + 43.7429i) q^{52} +(56.9787 - 56.9787i) q^{53} +(-20.5705 - 311.910i) q^{54} +(-262.456 - 369.059i) q^{55} +(304.456 - 175.778i) q^{56} +(-139.549 - 61.3807i) q^{57} +(-171.065 + 45.8366i) q^{58} +(-213.746 + 370.219i) q^{59} +(-117.266 - 131.727i) q^{60} +(-400.668 - 693.978i) q^{61} +(-197.471 - 197.471i) q^{62} +(-178.344 - 342.371i) q^{63} -530.858i q^{64} +(217.155 + 583.335i) q^{65} +(-463.498 - 71.2751i) q^{66} +(154.507 + 576.627i) q^{67} +(-20.4124 - 76.1803i) q^{68} +(939.091 + 144.410i) q^{69} +(323.883 + 148.158i) q^{70} +655.546i q^{71} +(-663.260 - 28.7792i) q^{72} +(-91.3719 - 91.3719i) q^{73} +(-392.170 - 679.258i) q^{74} +(145.063 - 633.113i) q^{75} +(-44.5337 + 77.1346i) q^{76} +(-559.401 + 149.891i) q^{77} +(589.994 + 259.509i) q^{78} +(-529.437 + 305.671i) q^{79} +(277.878 - 197.613i) q^{80} +(-63.1444 + 726.260i) q^{81} +(282.613 - 282.613i) q^{82} +(-206.409 - 55.3072i) q^{83} +(-210.189 + 81.7708i) q^{84} +(185.074 - 223.863i) q^{85} +(721.475 + 416.544i) q^{86} +(410.560 - 45.0197i) q^{87} +(-257.774 + 962.027i) q^{88} +451.962 q^{89} +(-365.664 - 564.497i) q^{90} +795.994 q^{91} +(143.669 - 536.181i) q^{92} +(385.183 + 525.175i) q^{93} +(505.435 + 291.813i) q^{94} +(-326.559 + 30.9754i) q^{95} +(-101.686 + 661.257i) q^{96} +(-1159.43 - 310.669i) q^{97} +(-218.324 + 218.324i) q^{98} +(1043.12 + 328.585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.576664	−	2.15214i	0.203881	−	0.760896i	−0.785906	−	0.618346i	$-0.787803\pi$
$2$	0.576664	−	2.15214i	0.203881	−	0.760896i	0.989788	−	0.142550i	$-0.0455302\pi$
$3$	−2.09209	+	4.75638i	−0.402623	+	0.915366i
$3$	−2.09209	+	4.75638i	−0.402623	+	0.915366i
$4$	2.62904	+	1.51788i	0.328630	+	0.189735i
$5$	1.05576	+	11.1304i	0.0944300	+	0.995532i
$5$	1.05576	+	11.1304i	0.0944300	+	0.995532i
$6$	9.02996	+	7.24530i	0.614411	+	0.492980i
$7$	13.8105	+	3.70051i	0.745696	+	0.199809i	0.611608	−	0.791161i	$-0.290523\pi$
$7$	13.8105	+	3.70051i	0.745696	+	0.199809i	0.134088	+	0.990969i	$0.457190\pi$
$8$	17.3866	−	17.3866i	0.768385	−	0.768385i
$9$	−18.2463	−	19.9016i	−0.675789	−	0.737095i
$10$	24.5629	+	4.14635i	0.776749	+	0.131119i
$11$	−35.0788	+	20.2528i	−0.961516	+	0.555131i	−0.896639	−	0.442762i	$-0.853999\pi$
$11$	−35.0788	+	20.2528i	−0.961516	+	0.555131i	−0.0648764	+	0.997893i	$0.520665\pi$
$12$	−12.7198	+	9.32918i	−0.305991	+	0.224425i
$13$	53.7760	−	14.4092i	1.14729	−	0.307416i	0.365412	−	0.930846i	$-0.380928\pi$
$13$	53.7760	−	14.4092i	1.14729	−	0.307416i	0.781879	+	0.623431i	$0.214262\pi$
$14$	15.9280	−	27.5881i	0.304067	−	0.526660i
$15$	−55.1491	−	18.2642i	−0.949295	−	0.314386i
$16$	−15.2491	−	26.4122i	−0.238267	−	0.412690i
$17$	−18.3703	−	18.3703i	−0.262086	−	0.262086i	0.563815	−	0.825901i	$-0.309333\pi$
$17$	−18.3703	−	18.3703i	−0.262086	−	0.262086i	−0.825901	+	0.563815i	$0.809333\pi$
$18$	−53.3529	+	27.7921i	−0.698634	+	0.363925i
$19$			29.3394i			0.354259i	0.984188	+	0.177130i	$0.0566812\pi$
$19$			29.3394i			0.354259i	−0.984188	+	0.177130i	$0.943319\pi$
$20$	−14.1189	+	30.8648i	−0.157854	+	0.345078i
$21$	−46.4938	+	57.9461i	−0.483132	+	0.602137i
$22$	23.3581	+	87.1736i	0.226362	+	0.844794i
$23$	−47.3257	−	176.622i	−0.429047	−	1.60123i	−0.754923	−	0.655814i	$-0.772326\pi$
$23$	−47.3257	−	176.622i	−0.429047	−	1.60123i	0.325875	−	0.945413i	$-0.394341\pi$
$24$	46.3228	+	119.071i	0.393984	+	1.01272i
$25$	−122.771	+	23.5020i	−0.982166	+	0.188016i
$26$		−	124.043i		−	0.935645i
$27$	132.832	−	45.1505i	0.946800	−	0.321823i
$28$	30.6914	+	30.6914i	0.207148	+	0.207148i
$29$	−39.7429	−	68.8368i	−0.254486	−	0.440782i	0.710270	−	0.703929i	$-0.248573\pi$
$29$	−39.7429	−	68.8368i	−0.254486	−	0.440782i	−0.964756	+	0.263147i	$0.915239\pi$
$30$	−71.1095	+	108.156i	−0.432759	+	0.658217i
$31$	62.6702	−	108.548i	0.363093	−	0.628896i	−0.625375	−	0.780324i	$-0.715054\pi$
$31$	62.6702	−	108.548i	0.363093	−	0.628896i	0.988468	+	0.151428i	$0.0483873\pi$
$32$	124.368	−	33.3242i	0.687041	−	0.184092i
$33$	−22.9418	−	209.219i	−0.121020	−	1.10365i
$34$	−50.1290	+	28.9420i	−0.252854	+	0.145986i
$35$	−26.6075	+	157.623i	−0.128500	+	0.761232i
$36$	−17.7622	−	80.0177i	−0.0822323	−	0.370452i
$37$	248.921	−	248.921i	1.10601	−	1.10601i	0.112342	−	0.993670i	$-0.464165\pi$
$37$	248.921	−	248.921i	1.10601	−	1.10601i	0.993670	−	0.112342i	$-0.0358353\pi$
$38$	63.1425	+	16.9190i	0.269554	+	0.0722269i
$39$	−43.9685	+	285.924i	−0.180528	+	1.17396i
$40$	211.875	+	175.163i	0.837510	+	0.692393i
$41$	155.350	+	89.6914i	0.591746	+	0.341645i	0.765788	−	0.643093i	$-0.222349\pi$
$41$	155.350	+	89.6914i	0.591746	+	0.341645i	−0.174041	+	0.984738i	$0.555683\pi$
$42$	97.8968	+	133.477i	0.359662	+	0.490378i
$43$	−96.7744	+	361.167i	−0.343208	+	1.28087i	0.551483	+	0.834186i	$0.314062\pi$
$43$	−96.7744	+	361.167i	−0.343208	+	1.28087i	−0.894691	+	0.446685i	$0.852605\pi$
$44$	−122.965			−0.421311
$45$	202.248	−	224.100i	0.669986	−	0.742373i
$46$	−407.406			−1.30584
$47$	−67.7961	+	253.018i	−0.210406	+	0.785245i	0.777328	+	0.629096i	$0.216575\pi$
$47$	−67.7961	+	253.018i	−0.210406	+	0.785245i	−0.987733	+	0.156149i	$0.950092\pi$
$48$	157.529	−	17.2737i	0.473694	−	0.0519426i
$49$	−120.011	−	69.2884i	−0.349886	−	0.202007i
$50$	−20.2179	+	277.772i	−0.0571848	+	0.785659i
$51$	125.809	−	48.9438i	0.345426	−	0.134383i
$52$	163.251	+	43.7429i	0.435362	+	0.116655i
$53$	56.9787	−	56.9787i	0.147672	−	0.147672i	−0.629405	−	0.777077i	$-0.716701\pi$
$53$	56.9787	−	56.9787i	0.147672	−	0.147672i	0.777077	+	0.629405i	$0.216701\pi$
$54$	−20.5705	−	311.910i	−0.0518388	−	0.786030i
$55$	−262.456	−	369.059i	−0.643447	−	0.904798i
$56$	304.456	−	175.778i	0.726511	−	0.419451i
$57$	−139.549	−	61.3807i	−0.324277	−	0.142633i
$58$	−171.065	+	45.8366i	−0.387274	+	0.103770i
$59$	−213.746	+	370.219i	−0.471651	+	0.816923i	−0.999474	−	0.0324311i	$-0.989675\pi$
$59$	−213.746	+	370.219i	−0.471651	+	0.816923i	0.527823	+	0.849354i	$0.323008\pi$
$60$	−117.266	−	131.727i	−0.252317	−	0.283431i
$61$	−400.668	−	693.978i	−0.840989	−	1.45664i	−0.889059	−	0.457792i	$-0.848641\pi$
$61$	−400.668	−	693.978i	−0.840989	−	1.45664i	0.0480704	−	0.998844i	$-0.484693\pi$
$62$	−197.471	−	197.471i	−0.404496	−	0.404496i
$63$	−178.344	−	342.371i	−0.356655	−	0.684677i
$64$		−	530.858i		−	1.03683i
$65$	217.155	+	583.335i	0.414380	+	1.11313i
$66$	−463.498	−	71.2751i	−0.864434	−	0.132930i
$67$	154.507	+	576.627i	0.281732	+	1.05144i	0.951195	+	0.308591i	$0.0998576\pi$
$67$	154.507	+	576.627i	0.281732	+	1.05144i	−0.669463	+	0.742845i	$0.733476\pi$
$68$	−20.4124	−	76.1803i	−0.0364025	−	0.135856i
$69$	939.091	+	144.410i	1.63845	+	0.251956i
$70$	323.883	+	148.158i	0.553019	+	0.252976i
$71$			655.546i			1.09576i	0.836557	+	0.547880i	$0.184565\pi$
$71$			655.546i			1.09576i	−0.836557	+	0.547880i	$0.815435\pi$
$72$	−663.260	−	28.7792i	−1.08564	−	0.0471064i
$73$	−91.3719	−	91.3719i	−0.146497	−	0.146497i	0.630054	−	0.776551i	$-0.283033\pi$
$73$	−91.3719	−	91.3719i	−0.146497	−	0.146497i	−0.776551	+	0.630054i	$0.783033\pi$
$74$	−392.170	−	679.258i	−0.616065	−	1.06706i
$75$	145.063	−	633.113i	0.223339	−	0.974741i
$76$	−44.5337	+	77.1346i	−0.0672153	+	0.116420i
$77$	−559.401	+	149.891i	−0.827918	+	0.221840i
$78$	589.994	+	259.509i	0.856458	+	0.376712i
$79$	−529.437	+	305.671i	−0.754004	+	0.435325i	−0.827139	−	0.561998i	$-0.810033\pi$
$79$	−529.437	+	305.671i	−0.754004	+	0.435325i	0.0731347	+	0.997322i	$0.476700\pi$
$80$	277.878	−	197.613i	0.388346	−	0.276172i
$81$	−63.1444	+	726.260i	−0.0866179	+	0.996242i
$82$	282.613	−	282.613i	0.380602	−	0.380602i
$83$	−206.409	−	55.3072i	−0.272968	−	0.0731417i	0.119738	−	0.992806i	$-0.461795\pi$
$83$	−206.409	−	55.3072i	−0.272968	−	0.0731417i	−0.392707	+	0.919664i	$0.628461\pi$
$84$	−210.189	+	81.7708i	−0.273018	+	0.106213i
$85$	185.074	−	223.863i	0.236166	−	0.285663i
$86$	721.475	+	416.544i	0.904636	+	0.522292i
$87$	410.560	−	45.0197i	0.505938	−	0.0554784i
$88$	−257.774	+	962.027i	−0.312259	+	1.16537i
$89$	451.962			0.538291			0.269146	−	0.963100i	$-0.413259\pi$
$89$	451.962			0.538291			0.269146	+	0.963100i	$0.413259\pi$
$90$	−365.664	−	564.497i	−0.428271	−	0.661146i
$91$	795.994			0.916954
$92$	143.669	−	536.181i	0.162810	−	0.607617i
$93$	385.183	+	525.175i	0.429480	+	0.585571i
$94$	505.435	+	291.813i	0.554592	+	0.320194i
$95$	−326.559	+	30.9754i	−0.352676	+	0.0334527i
$96$	−101.686	+	661.257i	−0.108107	+	0.703013i
$97$	−1159.43	−	310.669i	−1.21364	−	0.325193i	−0.405448	−	0.914118i	$-0.632884\pi$
$97$	−1159.43	−	310.669i	−1.21364	−	0.325193i	−0.808187	+	0.588926i	$0.799551\pi$
$98$	−218.324	+	218.324i	−0.225042	+	0.225042i
$99$	1043.12	+	328.585i	1.05897	+	0.333577i
$100$	−358.443	−	124.563i	−0.358443	−	0.124563i
$101$	919.775	−	531.032i	0.906149	−	0.523165i	0.0269588	−	0.999637i	$-0.491418\pi$
$101$	919.775	−	531.032i	0.906149	−	0.523165i	0.879190	+	0.476471i	$0.158084\pi$
$102$	−32.7847	−	298.982i	−0.0318252	−	0.290231i
$103$	85.1453	−	22.8146i	0.0814526	−	0.0218251i	−0.217863	−	0.975979i	$-0.569908\pi$
$103$	85.1453	−	22.8146i	0.0814526	−	0.0218251i	0.299315	+	0.954154i	$0.403242\pi$
$104$	684.452	−	1185.51i	0.645347	−	1.11777i
$105$	−694.048	−	456.317i	−0.645069	−	0.424114i
$106$	−89.7685	−	155.484i	−0.0822555	−	0.142471i
$107$	422.554	+	422.554i	0.381774	+	0.381774i	0.871741	−	0.489967i	$-0.162991\pi$
$107$	422.554	+	422.554i	0.381774	+	0.381774i	−0.489967	+	0.871741i	$0.662991\pi$
$108$	417.755	+	82.9208i	0.372208	+	0.0738801i
$109$			1529.73i			1.34424i	0.740444	+	0.672118i	$0.234615\pi$
$109$			1529.73i			1.34424i	−0.740444	+	0.672118i	$0.765385\pi$
$110$	−945.615	+	352.019i	−0.819644	+	0.305124i
$111$	663.199	+	1704.73i	0.567100	+	1.45771i
$112$	−112.859	−	421.194i	−0.0952155	−	0.355349i
$113$	−547.128	−	2041.91i	−0.455482	−	1.69988i	−0.686668	−	0.726971i	$-0.740927\pi$
$113$	−547.128	−	2041.91i	−0.455482	−	1.69988i	0.231186	−	0.972910i	$-0.425739\pi$
$114$	−212.573	+	264.934i	−0.174643	+	0.217661i
$115$	1915.90	−	713.223i	1.55356	−	0.578334i
$116$		−	241.300i		−	0.193139i
$117$	−1267.98	−	807.311i	−1.00192	−	0.637914i
$118$	673.504	+	673.504i	0.525433	+	0.525433i
$119$	−185.723	−	321.683i	−0.143069	−	0.247803i
$120$	−1276.40	+	641.301i	−0.970993	+	0.487854i
$121$	154.850	−	268.209i	0.116341	−	0.201509i
$122$	−1724.59	+	462.102i	−1.27981	+	0.342924i
$123$	−751.613	+	551.261i	−0.550981	+	0.404110i
$124$	329.525	−	190.251i	0.238647	−	0.137783i
$125$	−391.203	−	1341.67i	−0.279922	−	0.960023i
$126$	−839.674	+	186.389i	−0.593684	+	0.131785i
$127$	−212.243	+	212.243i	−0.148296	+	0.148296i	−0.777356	−	0.629061i	$-0.783440\pi$
$127$	−212.243	+	212.243i	−0.148296	+	0.148296i	0.629061	+	0.777356i	$0.283440\pi$
$128$	−147.540	−	39.5332i	−0.101881	−	0.0272990i
$129$	−1515.39	−	1215.89i	−1.03428	−	0.829869i
$130$	1380.64	−	130.959i	0.931464	−	0.0883529i
$131$	285.089	+	164.596i	0.190140	+	0.109777i	0.592048	−	0.805903i	$-0.298320\pi$
$131$	285.089	+	164.596i	0.190140	+	0.109777i	−0.401908	+	0.915680i	$0.631653\pi$
$132$	257.254	−	584.868i	0.169629	−	0.385654i
$133$	−108.571	+	405.192i	−0.0707840	+	0.264170i
$134$	1330.08			0.857474
$135$	642.781	+	1430.81i	0.409791	+	0.912179i
$136$	−638.793			−0.402765
$137$	−340.030	+	1269.01i	−0.212049	+	0.791378i	0.775136	+	0.631795i	$0.217682\pi$
$137$	−340.030	+	1269.01i	−0.212049	+	0.791378i	−0.987185	+	0.159583i	$0.948985\pi$
$138$	852.330	−	1937.78i	0.525762	−	1.19532i
$139$	−1886.00	−	1088.88i	−1.15085	−	0.664446i	−0.201759	−	0.979435i	$-0.564666\pi$
$139$	−1886.00	−	1088.88i	−1.15085	−	0.664446i	−0.949095	+	0.314989i	$0.897999\pi$
$140$	−309.204	+	374.010i	−0.186661	+	0.225783i
$141$	−1061.62	−	851.801i	−0.634072	−	0.508756i
$142$	1410.83	+	378.029i	0.833759	+	0.223405i
$143$	−1594.57	+	1594.57i	−0.932482	+	0.932482i
$144$	−247.404	+	785.405i	−0.143174	+	0.454517i
$145$	724.221	−	515.029i	0.414781	−	0.294971i
$146$	−249.336	+	143.954i	−0.141337	+	0.0816009i
$147$	580.636	−	425.861i	0.325783	−	0.238941i
$148$	1032.26	−	276.593i	0.573318	−	0.153620i
$149$	238.236	−	412.637i	0.130987	−	0.226876i	−0.793070	−	0.609130i	$-0.791519\pi$
$149$	238.236	−	412.637i	0.130987	−	0.226876i	0.924057	+	0.382254i	$0.124852\pi$
$150$	−1278.89	−	677.289i	−0.696142	−	0.368670i
$151$	−999.275	−	1730.80i	−0.538542	−	0.932783i	−0.998983	−	0.0450920i	$-0.985642\pi$
$151$	−999.275	−	1730.80i	−0.538542	−	0.932783i	0.460441	−	0.887691i	$-0.347691\pi$
$152$	510.112	+	510.112i	0.272207	+	0.272207i
$153$	−30.4076	+	700.789i	−0.0160674	+	0.370297i
$154$			1290.35i			0.675189i
$155$	1274.34	+	582.942i	0.660373	+	0.302084i
$156$	−549.594	+	684.969i	−0.282069	+	0.351547i
$157$	375.998	+	1403.25i	0.191133	+	0.713320i	0.993234	+	0.116131i	$0.0370491\pi$
$157$	375.998	+	1403.25i	0.191133	+	0.713320i	−0.802101	+	0.597189i	$0.796284\pi$
$158$	352.538	+	1315.69i	0.177509	+	0.662473i
$159$	151.808	+	390.217i	0.0757178	+	0.194630i
$160$	502.213	+	1349.08i	0.248147	+	0.666587i
$161$		−	2614.36i		−	1.27976i
$162$	1526.60	+	554.704i	0.740377	+	0.269022i
$163$	−1588.23	−	1588.23i	−0.763188	−	0.763188i	0.213710	−	0.976897i	$-0.431445\pi$
$163$	−1588.23	−	1588.23i	−0.763188	−	0.763188i	−0.976897	+	0.213710i	$0.931445\pi$
$164$	272.281	+	471.605i	0.129644	+	0.224550i
$165$	2304.47	−	476.236i	1.08729	−	0.224696i
$166$	−238.058	+	412.328i	−0.111306	+	0.192788i
$167$	1869.08	−	500.820i	0.866072	−	0.232063i	0.201684	−	0.979451i	$-0.435359\pi$
$167$	1869.08	−	500.820i	0.866072	−	0.232063i	0.664389	+	0.747387i	$0.268692\pi$
$168$	199.116	+	1815.85i	0.0914413	+	0.833904i
$169$	781.573	−	451.241i	0.355746	−	0.205390i
$170$	−375.059	−	527.399i	−0.169210	−	0.237939i
$171$	583.900	−	535.336i	0.261123	−	0.239405i
$172$	−802.631	+	802.631i	−0.355814	+	0.355814i
$173$	−349.180	−	93.5626i	−0.153455	−	0.0411181i	0.181274	−	0.983433i	$-0.441978\pi$
$173$	−349.180	−	93.5626i	−0.153455	−	0.0411181i	−0.334729	+	0.942315i	$0.608645\pi$
$174$	139.866	−	909.543i	0.0609382	−	0.396278i
$175$	−1782.49	−	129.740i	−0.769964	−	0.0560425i
$176$	1069.84	+	617.672i	0.458194	+	0.264539i
$177$	−1313.73	−	1791.19i	−0.557886	−	0.760645i
$178$	260.630	−	972.686i	0.109748	−	0.409583i
$179$	−1522.98			−0.635937			−0.317969	−	0.948101i	$-0.603001\pi$
$179$	−1522.98			−0.635937			−0.317969	+	0.948101i	$0.603001\pi$
$180$	871.875	−	282.179i	0.361032	−	0.116847i
$181$	2025.51			0.831797			0.415898	−	0.909411i	$-0.363467\pi$
$181$	2025.51			0.831797			0.415898	+	0.909411i	$0.363467\pi$
$182$	459.021	−	1713.09i	0.186950	−	0.697707i
$183$	4139.06	−	453.866i	1.67196	−	0.183337i
$184$	−3893.68	−	2248.02i	−1.56003	−	0.900685i
$185$	3033.39	+	2507.79i	1.20551	+	0.996629i
$186$	1352.37	−	526.119i	0.533122	−	0.207403i
$187$	1016.46	+	272.360i	0.397491	+	0.106508i
$188$	−562.290	+	562.290i	−0.218134	+	0.218134i
$189$	2001.56	−	132.003i	0.770328	−	0.0508032i
$190$	−121.651	+	720.663i	−0.0464501	+	0.275170i
$191$	−1086.41	+	627.242i	−0.411572	+	0.237621i	−0.691465	−	0.722410i	$-0.743034\pi$
$191$	−1086.41	+	627.242i	−0.411572	+	0.237621i	0.279893	+	0.960031i	$0.409701\pi$
$192$	2524.96	+	1110.60i	0.949081	+	0.417453i
$193$	−2803.12	+	751.094i	−1.04546	+	0.280129i	−0.740373	−	0.672196i	$-0.765351\pi$
$193$	−2803.12	+	751.094i	−1.04546	+	0.280129i	−0.305084	+	0.952326i	$0.598684\pi$
$194$	−1337.21	+	2316.11i	−0.494876	+	0.857150i
$195$	−3228.87	−	187.519i	−1.18576	−	0.0688640i
$196$	−210.343	−	364.324i	−0.0766555	−	0.132771i
$197$	1576.77	+	1576.77i	0.570255	+	0.570255i	0.932200	−	0.361945i	$-0.117887\pi$
$197$	1576.77	+	1576.77i	0.570255	+	0.570255i	−0.361945	+	0.932200i	$0.617887\pi$
$198$	1308.69	−	2055.46i	0.469721	−	0.737753i
$199$			3635.06i			1.29489i	0.762113	+	0.647444i	$0.224162\pi$
$199$			3635.06i			1.29489i	−0.762113	+	0.647444i	$0.775838\pi$
$200$	−1725.94	+	2543.18i	−0.610213	+	0.899150i
$201$	−3065.90	−	471.464i	−1.07588	−	0.165445i
$202$	−612.454	−	2285.71i	−0.213327	−	0.796149i
$203$	−294.138	−	1097.74i	−0.101697	−	0.379538i
$204$	405.047	+	62.2867i	0.139015	+	0.0213772i
$205$	−834.287	+	1823.80i	−0.284240	+	0.621364i
$206$		−	196.401i		−	0.0664267i
$207$	−2651.53	+	4164.55i	−0.890310	+	1.39834i
$208$	−1200.61	−	1200.61i	−0.400228	−	0.400228i
$209$	−594.205	−	1029.19i	−0.196660	−	0.340626i
$210$	−1382.29	+	1230.55i	−0.454224	+	0.404361i
$211$	−870.723	+	1508.14i	−0.284090	+	0.492059i	−0.972388	−	0.233369i	$-0.925025\pi$
$211$	−870.723	+	1508.14i	−0.284090	+	0.492059i	0.688298	+	0.725428i	$0.258358\pi$
$212$	236.286	−	63.3126i	0.0765481	−	0.0205110i
$213$	−3118.02	−	1371.46i	−1.00302	−	0.441178i
$214$	1153.07	−	665.724i	0.368327	−	0.212654i
$215$	−4122.10	−	695.830i	−1.30756	−	0.220722i
$216$	1524.49	−	3094.51i	0.480223	−	0.974790i
$217$	1267.19	−	1267.19i	0.396416	−	0.396416i
$218$	3292.20	+	882.142i	1.02282	+	0.274065i
$219$	625.758	−	243.441i	0.193081	−	0.0751152i
$220$	−129.821	−	1368.65i	−0.0397844	−	0.419428i
$221$	−1252.58	−	723.180i	−0.381258	−	0.220119i
$222$	4051.26	−	444.239i	1.22479	−	0.134303i
$223$	1347.06	−	5027.28i	0.404509	−	1.50965i	−0.400451	−	0.916318i	$-0.631146\pi$
$223$	1347.06	−	5027.28i	0.404509	−	1.50965i	0.804960	−	0.593329i	$-0.202187\pi$
$224$	1840.89			0.549107
$225$	2707.84	+	2014.51i	0.802323	+	0.596890i
$226$	−4709.98			−1.38630
$227$	604.406	−	2255.67i	0.176722	−	0.659534i	−0.819530	−	0.573036i	$-0.805766\pi$
$227$	604.406	−	2255.67i	0.176722	−	0.659534i	0.996252	−	0.0864984i	$-0.0275677\pi$
$228$	−273.713	−	373.192i	−0.0795047	−	0.108400i
$229$	2860.05	+	1651.25i	0.825316	+	0.476496i	0.852246	−	0.523141i	$-0.175240\pi$
$229$	2860.05	+	1651.25i	0.825316	+	0.476496i	−0.0269303	+	0.999637i	$0.508573\pi$
$230$	−430.122	−	4534.58i	−0.123311	−	1.30001i
$231$	457.379	−	2974.31i	0.130274	−	0.847166i
$232$	−1887.83	−	505.842i	−0.534233	−	0.143147i
$233$	1380.71	−	1380.71i	0.388213	−	0.388213i	−0.485837	−	0.874049i	$-0.661485\pi$
$233$	1380.71	−	1380.71i	0.388213	−	0.388213i	0.874049	+	0.485837i	$0.161485\pi$
$234$	−2468.64	+	2263.32i	−0.689659	+	0.632299i
$235$	−2887.77	−	487.469i	−0.801605	−	0.135315i
$236$	−1123.90	+	648.882i	−0.309997	+	0.178977i
$237$	−346.255	−	3157.70i	−0.0949017	−	0.865461i
$238$	−799.406	+	214.200i	−0.217722	+	0.0583384i
$239$	−2043.12	+	3538.78i	−0.552963	+	0.957761i	0.445095	+	0.895483i	$0.353170\pi$
$239$	−2043.12	+	3538.78i	−0.552963	+	0.957761i	−0.998059	+	0.0622776i	$0.980164\pi$
$240$	358.575	+	1735.12i	0.0964414	+	0.466672i
$241$	2368.28	+	4101.99i	0.633007	+	1.09640i	0.986934	+	0.161127i	$0.0515128\pi$
$241$	2368.28	+	4101.99i	0.633007	+	1.09640i	−0.353927	+	0.935273i	$0.615154\pi$
$242$	−487.926	−	487.926i	−0.129608	−	0.129608i
$243$	−3322.27	−	1819.74i	−0.877051	−	0.480397i
$244$		−	2432.66i		−	0.638259i
$245$	644.504	−	1408.92i	0.168065	−	0.367398i
$246$	752.963	+	1935.47i	0.195151	+	0.501630i
$247$	422.759	+	1577.76i	0.108905	+	0.406438i
$248$	−797.656	−	2976.89i	−0.204239	−	0.762229i
$249$	694.890	−	866.054i	0.176855	−	0.220417i
$250$	−3113.06	+	68.2280i	−0.787548	+	0.0172605i
$251$			3435.06i			0.863822i	0.901916	+	0.431911i	$0.142161\pi$
$251$			3435.06i			0.863822i	−0.901916	+	0.431911i	$0.857839\pi$
$252$	50.8021	−	1170.81i	0.0126993	−	0.292676i
$253$	5237.22	+	5237.22i	1.30143	+	1.30143i
$254$	334.384	+	579.170i	0.0826028	+	0.143072i
$255$	677.587	+	1348.62i	0.166401	+	0.331193i
$256$	1953.27	−	3383.17i	0.476873	−	0.825968i
$257$	−2294.74	+	614.874i	−0.556973	+	0.149240i	−0.526315	−	0.850289i	$-0.676427\pi$
$257$	−2294.74	+	614.874i	−0.556973	+	0.149240i	−0.0306577	+	0.999530i	$0.509760\pi$
$258$	−3490.63	+	2560.16i	−0.842315	+	0.617786i
$259$	4358.86	−	2516.59i	1.04574	−	0.603758i
$260$	−314.522	+	1863.23i	−0.0750224	+	0.444432i
$261$	−644.798	+	2046.96i	−0.152919	+	0.485456i
$262$	518.634	−	518.634i	0.122295	−	0.122295i
$263$	6469.78	+	1733.57i	1.51690	+	0.406451i	0.918718	−	0.394913i	$-0.129225\pi$
$263$	6469.78	+	1733.57i	1.51690	+	0.406451i	0.598177	+	0.801364i	$0.295892\pi$
$264$	−4036.48	−	3238.72i	−0.941015	−	0.755036i
$265$	694.350	+	574.038i	0.160957	+	0.133068i
$266$	809.420	+	467.319i	0.186574	+	0.107719i
$267$	−945.546	+	2149.70i	−0.216728	+	0.492733i
$268$	−469.045	+	1750.50i	−0.106909	+	0.398988i
$269$	3363.52			0.762370			0.381185	−	0.924499i	$-0.375516\pi$
$269$	3363.52			0.762370			0.381185	+	0.924499i	$0.375516\pi$
$270$	3449.96	−	558.260i	0.777623	−	0.125832i
$271$	6582.75			1.47555			0.737775	−	0.675047i	$-0.235877\pi$
$271$	6582.75			1.47555			0.737775	+	0.675047i	$0.235877\pi$
$272$	−205.070	+	765.330i	−0.0457139	+	0.170606i
$273$	−1665.29	+	3786.05i	−0.369187	+	0.839348i
$274$	2535.00	+	1463.58i	0.558923	+	0.322695i
$275$	3830.68	−	3310.87i	0.839994	−	0.726011i
$276$	2249.71	+	1805.09i	0.490640	+	0.393672i
$277$	−1109.87	−	297.389i	−0.240742	−	0.0645067i	0.136430	−	0.990650i	$-0.456437\pi$
$277$	−1109.87	−	297.389i	−0.240742	−	0.0645067i	−0.377173	+	0.926143i	$0.623104\pi$
$278$	−3431.02	+	3431.02i	−0.740212	+	0.740212i
$279$	−3303.77	+	733.364i	−0.708931	+	0.157367i
$280$	2277.90	+	3203.13i	0.486182	+	0.683656i
$281$	−5577.86	+	3220.38i	−1.18415	+	0.683672i	−0.956972	−	0.290180i	$-0.906285\pi$
$281$	−5577.86	+	3220.38i	−1.18415	+	0.683672i	−0.227183	+	0.973852i	$0.572951\pi$
$282$	−2445.39	+	1793.54i	−0.516386	+	0.378737i
$283$	5499.24	−	1473.52i	1.15511	−	0.309511i	0.370099	−	0.928992i	$-0.379324\pi$
$283$	5499.24	−	1473.52i	1.15511	−	0.309511i	0.785011	+	0.619482i	$0.212657\pi$
$284$	−995.038	+	1723.46i	−0.207904	+	0.360100i
$285$	535.860	−	1618.04i	0.111374	−	0.336297i
$286$	2512.21	+	4351.27i	0.519406	+	0.899637i
$287$	1813.56	+	1813.56i	0.372999	+	0.372999i
$288$	−2932.45	−	1867.07i	−0.599988	−	0.382007i
$289$		−	4238.06i		−	0.862622i
$290$	−690.782	−	1855.62i	−0.139876	−	0.375745i
$291$	3903.30	−	4864.76i	0.786308	−	0.979990i
$292$	−101.529	−	378.912i	−0.0203477	−	0.0759388i
$293$	−264.747	−	988.051i	−0.0527874	−	0.197005i	0.934496	−	0.355972i	$-0.115850\pi$
$293$	−264.747	−	988.051i	−0.0527874	−	0.197005i	−0.987284	+	0.158967i	$0.949184\pi$
$294$	−581.679	−	1495.19i	−0.115388	−	0.296603i
$295$	−4346.35	−	1988.22i	−0.857811	−	0.392401i
$296$		−	8655.78i		−	1.69969i
$297$	−3745.18	+	4274.05i	−0.731709	+	0.835036i
$298$	−750.669	−	750.669i	−0.145923	−	0.145923i
$299$	−5089.97	−	8816.09i	−0.984484	−	1.70518i
$300$	1342.37	−	1444.29i	0.258338	−	0.277954i
$301$	−2673.00	+	4629.77i	−0.511858	+	0.886564i
$302$	−4301.16	+	1152.49i	−0.819549	+	0.219598i
$303$	601.539	+	5485.77i	0.114051	+	1.04010i
$304$	774.917	−	447.399i	0.146199	−	0.0844082i
$305$	7301.23	−	5192.27i	1.37071	−	0.974781i
$306$	1490.66	+	469.561i	0.278482	+	0.0877222i
$307$	337.059	−	337.059i	0.0626611	−	0.0626611i	−0.675082	−	0.737743i	$-0.735892\pi$
$307$	337.059	−	337.059i	0.0626611	−	0.0626611i	0.737743	+	0.675082i	$0.235892\pi$
$308$	−1698.21	−	455.033i	−0.314170	−	0.0841815i
$309$	−69.6167	+	452.714i	−0.0128167	+	0.0833462i
$310$	1989.44	−	2406.40i	0.364492	−	0.440886i
$311$	−4362.60	−	2518.75i	−0.795434	−	0.459244i	0.0464378	−	0.998921i	$-0.485213\pi$
$311$	−4362.60	−	2518.75i	−0.795434	−	0.459244i	−0.841872	+	0.539677i	$0.818546\pi$
$312$	4206.78	+	5735.70i	0.763340	+	1.04077i
$313$	−1222.40	+	4562.05i	−0.220748	+	0.823842i	0.763316	+	0.646025i	$0.223570\pi$
$313$	−1222.40	+	4562.05i	−0.220748	+	0.823842i	−0.984064	+	0.177816i	$0.943097\pi$
$314$	3236.80			0.581731
$315$	3622.43	−	2346.50i	0.647939	−	0.419716i
$316$	−1855.88			−0.330385
$317$	2563.99	−	9568.96i	0.454285	−	1.69541i	−0.235897	−	0.971778i	$-0.575803\pi$
$317$	2563.99	−	9568.96i	0.454285	−	1.69541i	0.690182	−	0.723636i	$-0.257530\pi$
$318$	927.343	−	101.687i	0.163531	−	0.0179319i
$319$	2788.27	+	1609.81i	0.489384	+	0.282546i
$320$	5908.66	−	560.459i	1.03220	−	0.0979081i
$321$	−2893.85	+	1125.81i	−0.503175	+	0.195752i
$322$	−5626.47	−	1507.61i	−0.973761	−	0.260918i
$323$	538.975	−	538.975i	0.0928463	−	0.0928463i
$324$	−1268.38	+	1813.52i	−0.217487	+	0.310961i
$325$	−6263.47	+	3032.88i	−1.06903	+	0.517642i
$326$	−4333.96	+	2502.21i	−0.736306	+	0.425107i
$327$	−7275.99	−	3200.34i	−1.23047	−	0.541221i
$328$	4260.43	−	1141.58i	0.717204	−	0.192174i
$329$	−1872.59	+	3243.43i	−0.313797	+	0.543513i
$330$	303.977	−	5234.16i	0.0507072	−	0.873124i
$331$	−2314.33	−	4008.54i	−0.384312	−	0.665648i	0.607362	−	0.794426i	$-0.292228\pi$
$331$	−2314.33	−	4008.54i	−0.384312	−	0.665648i	−0.991673	+	0.128778i	$0.958895\pi$
$332$	−458.710	−	458.710i	−0.0758282	−	0.0758282i
$333$	−9495.82	−	412.028i	−1.56267	−	0.0678048i
$334$		−	4311.33i		−	0.706304i
$335$	−6254.96	+	2328.50i	−1.02013	+	0.379760i
$336$	2239.47	+	344.378i	0.363610	+	0.0559147i
$337$	−243.531	−	908.869i	−0.0393649	−	0.146912i	0.943446	−	0.331525i	$-0.107563\pi$
$337$	−243.531	−	908.869i	−0.0393649	−	0.146912i	−0.982811	+	0.184614i	$0.940897\pi$
$338$	−520.429	−	1942.27i	−0.0837503	−	0.312561i
$339$	10856.7	+	1669.51i	1.73940	+	0.267479i
$340$	826.365	−	307.626i	0.131812	−	0.0490687i
$341$			5076.98i			0.806258i
$342$	−815.403	−	1565.34i	−0.128924	−	0.247497i
$343$	−4868.73	−	4868.73i	−0.766433	−	0.766433i
$344$	4596.88	+	7962.02i	0.720485	+	1.24792i
$345$	−615.886	+	10604.9i	−0.0961107	+	1.65492i
$346$	−402.719	+	697.531i	−0.0625732	+	0.108380i
$347$	580.155	−	155.452i	0.0897532	−	0.0240493i	−0.213663	−	0.976907i	$-0.568539\pi$
$347$	580.155	−	155.452i	0.0897532	−	0.0240493i	0.303416	+	0.952858i	$0.401873\pi$
$348$	1147.71	+	504.821i	0.176793	+	0.0777622i
$349$	−8983.64	+	5186.71i	−1.37789	+	0.795525i	−0.991905	−	0.126980i	$-0.959471\pi$
$349$	−8983.64	+	5186.71i	−1.37789	+	0.795525i	−0.385984	+	0.922505i	$0.626138\pi$
$350$	−1307.12	+	3761.36i	−0.199624	+	0.574437i
$351$	6492.61	−	4342.02i	0.987321	−	0.660285i
$352$	−3687.77	+	3687.77i	−0.558405	+	0.558405i
$353$	9144.89	+	2450.37i	1.37885	+	0.369461i	0.870702	−	0.491810i	$-0.163665\pi$
$353$	9144.89	+	2450.37i	1.37885	+	0.369461i	0.508145	+	0.861271i	$0.330331\pi$
$354$	−4612.47	+	1794.41i	−0.692515	+	0.269412i
$355$	−7296.47	+	692.098i	−1.09086	+	0.103473i
$356$	1188.23	+	686.024i	0.176899	+	0.102133i
$357$	1918.59	−	210.382i	0.284434	−	0.0311894i
$358$	−878.247	+	3277.66i	−0.129656	+	0.483882i
$359$	−6712.05			−0.986765			−0.493382	−	0.869813i	$-0.664240\pi$
$359$	−6712.05			−0.986765			−0.493382	+	0.869813i	$0.664240\pi$
$360$	−379.920	−	7412.72i	−0.0556209	−	1.08524i
$361$	5998.20			0.874500
$362$	1168.04	−	4359.19i	0.169588	−	0.632911i
$363$	951.742	+	1297.64i	0.137613	+	0.187627i
$364$	2092.70	+	1208.22i	0.301339	+	0.173978i
$365$	920.537	−	1113.47i	0.132009	−	0.159676i
$366$	1410.06	−	9169.56i	0.201380	−	1.30956i
$367$	3097.58	+	829.995i	0.440579	+	0.118053i	0.472288	−	0.881444i	$-0.343428\pi$
$367$	3097.58	+	829.995i	0.440579	+	0.118053i	−0.0317089	+	0.999497i	$0.510095\pi$
$368$	−3943.29	+	3943.29i	−0.558582	+	0.558582i
$369$	−1049.57	−	4728.25i	−0.148071	−	0.667053i
$370$	7146.36	−	5082.13i	1.00411	−	0.714074i
$371$	997.753	−	576.053i	0.139625	−	0.0806123i
$372$	215.511	+	1965.37i	0.0300369	+	0.273924i
$373$	−2960.89	+	793.369i	−0.411017	+	0.110132i	−0.458402	−	0.888745i	$-0.651578\pi$
$373$	−2960.89	+	793.369i	−0.411017	+	0.110132i	0.0473850	+	0.998877i	$0.484911\pi$
$374$	1172.31	−	2030.50i	0.162082	−	0.280735i
$375$	7199.94	+	946.194i	0.991475	+	0.130297i
$376$	3220.38	+	5577.86i	0.441698	+	0.765043i
$377$	−3129.10	−	3129.10i	−0.427472	−	0.427472i
$378$	870.138	−	4383.75i	0.118400	−	0.596497i
$379$		−	8477.84i		−	1.14902i	−0.818499	−	0.574509i	$-0.805193\pi$
$379$		−	8477.84i		−	1.14902i	0.818499	−	0.574509i	$-0.194807\pi$
$380$	−905.554	−	414.241i	−0.122247	−	0.0559214i
$381$	−565.477	−	1453.54i	−0.0760374	−	0.195452i
$382$	723.415	+	2699.82i	0.0968930	+	0.361610i
$383$	1741.00	+	6497.52i	0.232275	+	0.866860i	0.979359	+	0.202131i	$0.0647866\pi$
$383$	1741.00	+	6497.52i	0.232275	+	0.866860i	−0.747084	+	0.664730i	$0.768547\pi$
$384$	496.702	−	619.049i	0.0660084	−	0.0822675i
$385$	−2258.94	−	6068.10i	−0.299029	−	0.803270i
$386$			6465.84i			0.852597i
$387$	8953.56	−	4664.00i	1.17606	−	0.612621i
$388$	−2576.64	−	2576.64i	−0.337137	−	0.337137i
$389$	2078.63	+	3600.30i	0.270928	+	0.469260i	0.969100	−	0.246670i	$-0.0793363\pi$
$389$	2078.63	+	3600.30i	0.270928	+	0.469260i	−0.698172	+	0.715930i	$0.746003\pi$
$390$	−2265.54	+	6840.84i	−0.294154	+	0.888203i
$391$	−2375.21	+	4113.99i	−0.307211	+	0.532106i
$392$	−3291.27	+	881.892i	−0.424066	+	0.113628i
$393$	−1379.31	+	1011.64i	−0.177041	+	0.129849i
$394$	4302.70	−	2484.16i	0.550169	−	0.317640i
$395$	−3961.19	−	5570.12i	−0.504580	−	0.709527i
$396$	2243.66	+	2447.20i	0.284717	+	0.310546i
$397$	2587.31	−	2587.31i	0.327087	−	0.327087i	−0.524391	−	0.851478i	$-0.675707\pi$
$397$	2587.31	−	2587.31i	0.327087	−	0.327087i	0.851478	+	0.524391i	$0.175707\pi$
$398$	7823.16	+	2096.21i	0.985276	+	0.264004i
$399$	−1700.11	−	1364.10i	−0.213313	−	0.171154i
$400$	2492.88	+	2884.26i	0.311610	+	0.360532i
$401$	8012.98	+	4626.29i	0.997878	+	0.576125i	0.907620	−	0.419794i	$-0.137898\pi$
$401$	8012.98	+	4626.29i	0.997878	+	0.576125i	0.0902579	+	0.995918i	$0.471231\pi$
$402$	−2782.65	+	6326.37i	−0.345239	+	0.784902i
$403$	1806.06	−	6740.30i	0.223241	−	0.833147i
$404$	3224.17			0.397051
$405$	−8150.22	+	63.9342i	−0.999969	+	0.00784423i
$406$	−2532.10			−0.309523
$407$	−3690.53	+	13773.2i	−0.449466	+	1.67743i
$408$	1336.41	−	3038.34i	0.162163	−	0.368678i
$409$	6326.24	+	3652.45i	0.764822	+	0.441570i	0.831024	−	0.556236i	$-0.187755\pi$
$409$	6326.24	+	3652.45i	0.764822	+	0.441570i	−0.0662023	+	0.997806i	$0.521088\pi$
$410$	3443.96	+	2847.22i	0.414842	+	0.342961i
$411$	−5324.52	−	4272.19i	−0.639024	−	0.512729i
$412$	258.480	+	69.2596i	0.0309088	+	0.00828198i
$413$	−4321.94	+	4321.94i	−0.514936	+	0.514936i
$414$	7433.65	+	8108.01i	0.882474	+	0.962529i
$415$	397.672	−	2355.81i	0.0470384	−	0.278655i
$416$	6207.82	−	3584.08i	0.731642	−	0.422414i
$417$	9124.84	−	6692.50i	1.07157	−	0.785931i
$418$	−2557.62	+	685.313i	−0.299276	+	0.0801908i
$419$	−2581.15	+	4470.68i	−0.300948	+	0.521257i	−0.976351	−	0.216192i	$-0.930636\pi$
$419$	−2581.15	+	4470.68i	−0.300948	+	0.521257i	0.675403	+	0.737449i	$0.263970\pi$
$420$	−1132.05	−	2253.16i	−0.131520	−	0.261769i
$421$	946.112	+	1638.71i	0.109527	+	0.189705i	0.915579	−	0.402139i	$-0.131733\pi$
$421$	946.112	+	1638.71i	0.109527	+	0.189705i	−0.806052	+	0.591845i	$0.798400\pi$
$422$	2743.61	+	2743.61i	0.316485	+	0.316485i
$423$	6272.49	−	3267.40i	0.720990	−	0.375571i
$424$		−	1981.33i		−	0.226938i
$425$	2687.08	+	1823.60i	0.306688	+	0.208135i
$426$	−4749.63	+	5919.55i	−0.540188	+	0.673247i
$427$	−2965.35	−	11066.8i	−0.336074	−	1.25424i
$428$	469.527	+	1752.30i	0.0530268	+	0.197899i
$429$	−4248.40	−	10920.4i	−0.478123	−	1.22900i
$430$	−3874.59	+	8470.06i	−0.434533	+	0.949913i
$431$		−	12717.6i		−	1.42132i	−0.703538	−	0.710658i	$-0.748397\pi$
$431$		−	12717.6i		−	1.42132i	0.703538	−	0.710658i	$-0.251603\pi$
$432$	−3218.09	−	2819.89i	−0.358404	−	0.314055i
$433$	−4103.64	−	4103.64i	−0.455447	−	0.455447i	0.441711	−	0.897158i	$-0.354372\pi$
$433$	−4103.64	−	4103.64i	−0.455447	−	0.455447i	−0.897158	+	0.441711i	$0.854372\pi$
$434$	−1996.42	−	3457.90i	−0.220810	−	0.382453i
$435$	934.539	+	4522.16i	0.103006	+	0.498439i
$436$	−2321.95	+	4021.73i	−0.255048	+	0.441757i
$437$	5181.98	−	1388.51i	0.567249	−	0.151994i
$438$	−163.067	−	1487.10i	−0.0177892	−	0.162229i
$439$	−7178.99	+	4144.79i	−0.780488	+	0.450615i	−0.836603	−	0.547809i	$-0.815462\pi$
$439$	−7178.99	+	4144.79i	−0.780488	+	0.450615i	0.0561151	+	0.998424i	$0.482129\pi$
$440$	−10979.9	−	1853.46i	−1.18965	−	0.200818i
$441$	810.811	+	3652.67i	0.0875511	+	0.394414i
$442$	−2278.70	+	2278.70i	−0.245219	+	0.245219i
$443$	−5730.24	−	1535.41i	−0.614565	−	0.164672i	−0.0619089	−	0.998082i	$-0.519719\pi$
$443$	−5730.24	−	1535.41i	−0.614565	−	0.164672i	−0.552656	+	0.833410i	$0.686386\pi$
$444$	−843.997	+	5488.47i	−0.0902125	+	0.586647i
$445$	477.163	+	5030.51i	0.0508308	+	0.535886i
$446$	−10042.6	−	5798.10i	−1.06621	−	0.615578i
$447$	1464.25	+	1996.41i	0.154936	+	0.211246i
$448$	1964.45	−	7331.41i	0.207168	−	0.773162i
$449$	3855.25			0.405213			0.202606	−	0.979260i	$-0.435059\pi$
$449$	3855.25			0.405213			0.202606	+	0.979260i	$0.435059\pi$
$450$	5897.01	−	4665.95i	0.617750	−	0.488789i
$451$	−7266.00			−0.758631
$452$	1660.95	−	6198.73i	0.172841	−	0.645053i
$453$	10322.9	−	1131.95i	1.07067	−	0.117403i
$454$	−4505.98	−	2601.53i	−0.465807	−	0.268934i
$455$	840.378	+	8859.71i	0.0865879	+	0.912857i
$456$	−3493.48	+	1359.08i	−0.358766	+	0.139572i
$457$	1728.92	+	463.264i	0.176971	+	0.0474192i	0.346216	−	0.938155i	$-0.387466\pi$
$457$	1728.92	+	463.264i	0.176971	+	0.0474192i	−0.169245	+	0.985574i	$0.554133\pi$
$458$	5203.01	−	5203.01i	0.530831	−	0.530831i
$459$	−3269.60	−	1610.74i	−0.332488	−	0.163798i
$460$	6119.58	+	1033.02i	0.620276	+	0.104706i
$461$	−10218.4	+	5899.62i	−1.03237	+	0.596036i	−0.917661	−	0.397363i	$-0.869925\pi$
$461$	−10218.4	+	5899.62i	−1.03237	+	0.596036i	−0.114704	+	0.993400i	$0.536592\pi$
$462$	−6137.38	−	2699.52i	−0.618045	−	0.271847i
$463$	2392.06	−	640.951i	0.240105	−	0.0643359i	−0.136760	−	0.990604i	$-0.543669\pi$
$463$	2392.06	−	640.951i	0.240105	−	0.0643359i	0.376865	+	0.926268i	$0.377002\pi$
$464$	−1212.09	+	2099.39i	−0.121271	+	0.210047i
$465$	−5438.74	+	4841.70i	−0.542399	+	0.482857i
$466$	−2175.28	−	3767.69i	−0.216240	−	0.374539i
$467$	11085.9	+	11085.9i	1.09849	+	1.09849i	0.994588	+	0.103901i	$0.0331324\pi$
$467$	11085.9	+	11085.9i	1.09849	+	1.09849i	0.103901	+	0.994588i	$0.466868\pi$
$468$	−2108.17	−	4047.09i	−0.208227	−	0.399737i
$469$			8535.26i			0.840344i
$470$	−2714.37	+	5933.77i	−0.266393	+	0.582350i
$471$	−7460.99	−	1147.33i	−0.729903	−	0.112242i
$472$	2720.53	+	10153.2i	0.265302	+	0.990120i
$473$	−3919.90	−	14629.3i	−0.381051	−	1.42210i
$474$	−6995.47	−	1075.74i	−0.677875	−	0.104241i
$475$	−689.535	−	3602.02i	−0.0666064	−	0.347941i
$476$		−	1127.62i		−	0.108581i
$477$	−2173.61	−	94.3142i	−0.208644	−	0.00905314i
$478$	6437.76	+	6437.76i	0.616017	+	0.616017i
$479$	−4528.18	−	7843.03i	−0.431937	−	0.748136i	0.565103	−	0.825020i	$-0.308836\pi$
$479$	−4528.18	−	7843.03i	−0.431937	−	0.748136i	−0.997040	+	0.0768839i	$0.975503\pi$
$480$	−7467.40	−	433.674i	−0.710080	−	0.0412384i
$481$	9799.23	−	16972.8i	0.928912	−	1.60892i
$482$	10193.8	−	2731.41i	0.963305	−	0.258117i
$483$	12434.9	+	5469.49i	1.17144	+	0.515259i
$484$	814.217	−	470.088i	0.0764666	−	0.0441480i
$485$	2233.78	−	13232.9i	0.209136	−	1.23892i
$486$	−5832.17	+	6100.60i	−0.544347	+	0.569401i
$487$	−2327.30	+	2327.30i	−0.216551	+	0.216551i	−0.807043	−	0.590492i	$-0.798934\pi$
$487$	−2327.30	+	2327.30i	−0.216551	+	0.216551i	0.590492	+	0.807043i	$0.298934\pi$
$488$	−19032.1	−	5099.65i	−1.76546	−	0.473053i
$489$	10876.9	−	4231.50i	1.00587	−	0.391319i
$490$	−2660.53	−	2199.54i	−0.245287	−	0.202785i
$491$	−2623.22	−	1514.51i	−0.241108	−	0.139204i	0.374578	−	0.927195i	$-0.377788\pi$
$491$	−2623.22	−	1514.51i	−0.241108	−	0.139204i	−0.615686	+	0.787992i	$0.711121\pi$
$492$	−2812.77	+	308.433i	−0.257743	+	0.0282626i
$493$	−534.463	+	1994.64i	−0.0488256	+	0.182220i
$494$	3639.34			0.331461
$495$	−2556.00	+	11957.2i	−0.232088	+	1.08573i
$496$	−3822.65			−0.346052
$497$	−2425.85	+	9053.40i	−0.218942	+	0.817104i
$498$	−1463.15	−	1994.92i	−0.131657	−	0.179507i
$499$	171.019	+	98.7379i	0.0153424	+	0.00885795i	0.507652	−	0.861562i	$-0.330514\pi$
$499$	171.019	+	98.7379i	0.0153424	+	0.00885795i	−0.492309	+	0.870420i	$0.663847\pi$
$500$	1008.01	−	4121.11i	0.0901590	−	0.368603i
$501$	−1528.21	+	9937.84i	−0.136278	+	0.886207i
$502$	7392.73	+	1980.88i	0.657279	+	0.176117i
$503$	−4650.74	+	4650.74i	−0.412259	+	0.412259i	−0.882525	−	0.470266i	$-0.844158\pi$
$503$	−4650.74	+	4650.74i	−0.412259	+	0.412259i	0.470266	+	0.882525i	$0.344158\pi$
$504$	−9053.45	−	2851.85i	−0.800144	−	0.252047i
$505$	6881.65	+	9676.80i	0.606395	+	0.852697i
$506$	14291.3	−	8251.10i	1.25559	−	0.724914i
$507$	511.154	+	4661.50i	0.0447754	+	0.408332i
$508$	−880.155	+	235.837i	−0.0768712	+	0.0205976i
$509$	7091.29	−	12282.5i	0.617517	−	1.06957i	−0.372420	−	0.928064i	$-0.621472\pi$
$509$	7091.29	−	12282.5i	0.617517	−	1.06957i	0.989937	−	0.141506i	$-0.0451946\pi$
$510$	3293.17	−	680.559i	0.285929	−	0.0590895i
$511$	−923.767	−	1600.01i	−0.0799708	−	0.138513i
$512$	−7018.72	−	7018.72i	−0.605833	−	0.605833i
$513$	1324.69	+	3897.22i	0.114009	+	0.335413i
$514$			5293.18i			0.454226i
$515$	343.828	+	923.613i	0.0294192	+	0.0790276i
$516$	−2138.44	−	5496.80i	−0.182441	−	0.468959i
$517$	−2746.12	−	10248.6i	−0.233606	−	0.871828i
$518$	−2902.45	−	10832.1i	−0.246190	−	0.918794i
$519$	1175.54	−	1465.09i	0.0994226	−	0.123912i
$520$	13917.8	+	6366.61i	1.17372	+	0.536912i
$521$			5590.04i			0.470065i	0.971987	+	0.235033i	$0.0755197\pi$
$521$			5590.04i			0.470065i	−0.971987	+	0.235033i	$0.924480\pi$
$522$	4033.52	+	2568.11i	0.338204	+	0.215331i
$523$	7113.75	+	7113.75i	0.594766	+	0.594766i	0.938915	−	0.344149i	$-0.111833\pi$
$523$	7113.75	+	7113.75i	0.594766	+	0.594766i	−0.344149	+	0.938915i	$0.611833\pi$
$524$	499.673	+	865.459i	0.0416571	+	0.0721522i
$525$	4346.23	−	8206.78i	0.361305	−	0.682235i
$526$	7461.77	−	12924.2i	0.618534	−	1.07133i
$527$	−3145.33	+	842.789i	−0.259986	+	0.0696631i
$528$	−5176.08	+	3796.34i	−0.426629	+	0.312906i
$529$	−18418.6	+	10634.0i	−1.51382	+	0.874004i
$530$	1635.82	−	1163.31i	0.134067	−	0.0953415i
$531$	11268.0	−	2501.25i	0.920886	−	0.204416i
$532$	−900.468	+	900.468i	−0.0733839	+	0.0733839i
$533$	9646.49	+	2584.77i	0.783932	+	0.210054i
$534$	4081.20	+	3274.60i	0.330732	+	0.265367i
$535$	−4257.07	+	5149.31i	−0.344018	+	0.416119i
$536$	12711.9	+	7339.23i	1.02439	+	0.591430i
$537$	3186.21	−	7243.86i	0.256043	−	0.582115i
$538$	1939.62	−	7238.77i	0.155433	−	0.580084i
$539$	5613.13			0.448562
$540$	−481.891	+	4737.31i	−0.0384024	+	0.377521i
$541$	−1631.46			−0.129652			−0.0648261	−	0.997897i	$-0.520649\pi$
$541$	−1631.46			−0.129652			−0.0648261	+	0.997897i	$0.520649\pi$
$542$	3796.04	−	14167.0i	0.300837	−	1.12274i
$543$	−4237.56	+	9634.11i	−0.334901	+	0.761398i
$544$	−2896.85	−	1672.50i	−0.228311	−	0.131816i
$545$	−17026.5	+	1615.03i	−1.33823	+	0.126936i
$546$	7187.79	+	5767.22i	0.563387	+	0.452040i
$547$	15008.2	+	4021.44i	1.17314	+	0.314341i	0.792201	−	0.610260i	$-0.208935\pi$
$547$	15008.2	+	4021.44i	1.17314	+	0.314341i	0.380936	+	0.924601i	$0.375602\pi$
$548$	−2820.15	+	2820.15i	−0.219838	+	0.219838i
$549$	−6500.53	+	20636.5i	−0.505348	+	1.60427i
$550$	−4916.45	−	10153.4i	−0.381160	−	0.787169i
$551$	2019.63	−	1166.03i	0.156151	−	0.0901538i
$552$	18838.4	−	13816.8i	1.45256	−	1.06536i
$553$	−8442.92	+	2262.27i	−0.649239	+	0.173963i
$554$	−1280.04	+	2217.10i	−0.0981658	+	0.170028i
$555$	−18274.1	+	9181.44i	−1.39765	+	0.702217i
$556$	−3305.59	−	5725.45i	−0.252137	−	0.436714i
$557$	1370.40	+	1370.40i	0.104247	+	0.104247i	0.757307	−	0.653059i	$-0.226515\pi$
$557$	1370.40	+	1370.40i	0.104247	+	0.104247i	−0.653059	+	0.757307i	$0.726515\pi$
$558$	−326.864	+	7533.08i	−0.0247979	+	0.571507i
$559$			20816.6i			1.57504i
$560$	4568.90	−	1700.84i	0.344770	−	0.128346i
$561$	−3421.97	+	4264.87i	−0.257533	+	0.320968i
$562$	3714.16	+	13861.4i	0.278776	+	1.04041i
$563$	192.003	+	716.566i	0.0143730	+	0.0536406i	0.972740	−	0.231899i	$-0.0744939\pi$
$563$	192.003	+	716.566i	0.0143730	+	0.0536406i	−0.958367	+	0.285540i	$0.907827\pi$
$564$	−1498.10	−	3850.82i	−0.111847	−	0.287498i
$565$	22149.6	−	8245.50i	1.64927	−	0.613966i
$566$		−	12684.9i		−	0.942022i
$567$	−3559.59	+	9796.34i	−0.263648	+	0.725586i
$568$	11397.7	+	11397.7i	0.841965	+	0.841965i
$569$	−1596.11	−	2764.54i	−0.117596	−	0.203683i	0.801218	−	0.598372i	$-0.204186\pi$
$569$	−1596.11	−	2764.54i	−0.117596	−	0.203683i	−0.918815	+	0.394689i	$0.870852\pi$
$570$	−3173.24	−	2086.31i	−0.233180	−	0.153309i
$571$	5375.08	−	9309.91i	0.393941	−	0.682325i	−0.599025	−	0.800730i	$-0.704445\pi$
$571$	5375.08	−	9309.91i	0.393941	−	0.682325i	0.992965	+	0.118405i	$0.0377783\pi$
$572$	−6612.57	+	1771.83i	−0.483366	+	0.129517i
$573$	−710.522	−	6479.65i	−0.0518019	−	0.472410i
$574$	4948.84	−	2857.21i	0.359861	−	0.207766i
$575$	9961.18	+	20571.8i	0.722452	+	1.49200i
$576$	−10564.9	+	9686.21i	−0.764244	+	0.700680i
$577$	6620.53	−	6620.53i	0.477671	−	0.477671i	−0.426715	−	0.904386i	$-0.640329\pi$
$577$	6620.53	−	6620.53i	0.477671	−	0.477671i	0.904386	+	0.426715i	$0.140329\pi$
$578$	−9120.90	−	2443.94i	−0.656366	−	0.175873i
$579$	2291.90	−	14904.1i	0.164504	−	1.06976i
$580$	2685.76	−	254.754i	0.192276	−	0.0182381i
$581$	−2645.95	−	1527.64i	−0.188937	−	0.109083i
$582$	−8218.74	−	11205.8i	−0.585357	−	0.798100i
$583$	−844.769	+	3152.72i	−0.0600116	+	0.223966i
$584$	−3177.28			−0.225132
$585$	7647.00	−	14965.4i	0.540452	−	1.05768i
$586$	−2279.09			−0.160663
$587$	−2666.44	+	9951.28i	−0.187488	+	0.699716i	0.806596	+	0.591103i	$0.201307\pi$
$587$	−2666.44	+	9951.28i	−0.187488	+	0.699716i	−0.994084	+	0.108613i	$0.965359\pi$
$588$	2172.92	−	238.270i	0.152398	−	0.0167111i
$589$	3184.73	+	1838.71i	0.222792	+	0.128629i
$590$	−6785.30	+	8207.41i	−0.473468	+	0.572701i
$591$	−10798.5	+	4200.97i	−0.751590	+	0.292394i
$592$	−10370.4	−	2778.73i	−0.719966	−	0.192914i
$593$	670.349	−	670.349i	0.0464215	−	0.0464215i	−0.683515	−	0.729936i	$-0.739550\pi$
$593$	670.349	−	670.349i	0.0464215	−	0.0464215i	0.729936	+	0.683515i	$0.239550\pi$
$594$	7038.64	+	10524.8i	0.486194	+	0.727003i
$595$	3384.37	−	2406.79i	0.233186	−	0.165830i
$596$	1252.66	−	723.226i	0.0860925	−	0.0497055i
$597$	−17289.7	−	7604.89i	−1.18530	−	0.521352i
$598$	−21908.7	+	5870.41i	−1.49818	+	0.401436i
$599$	−273.430	+	473.594i	−0.0186511	+	0.0323047i	−0.875200	−	0.483761i	$-0.839271\pi$
$599$	−273.430	+	473.594i	−0.0186511	+	0.0323047i	0.856549	+	0.516065i	$0.172604\pi$
$600$	−8485.50	−	13529.8i	−0.577365	−	0.920586i
$601$	−536.667	−	929.535i	−0.0364245	−	0.0630890i	0.847238	−	0.531213i	$-0.178264\pi$
$601$	−536.667	−	929.535i	−0.0364245	−	0.0630890i	−0.883663	+	0.468124i	$0.844930\pi$
$602$	8422.50	+	8422.50i	0.570225	+	0.570225i
$603$	8656.61	−	13596.3i	0.584617	−	0.918213i
$604$		−	6067.11i		−	0.408721i
$605$	3148.75	+	1440.38i	0.211595	+	0.0967930i
$606$	12153.0	+	1868.85i	0.814658	+	0.125275i
$607$	−2633.05	−	9826.68i	−0.176066	−	0.657089i	−0.996368	−	0.0851568i	$-0.972861\pi$
$607$	−2633.05	−	9826.68i	−0.176066	−	0.657089i	0.820301	−	0.571932i	$-0.193806\pi$
$608$	977.713	+	3648.87i	0.0652163	+	0.243390i
$609$	5836.63	+	897.536i	0.388361	+	0.0597209i
$610$	−6964.12	−	18707.5i	−0.462244	−	1.24171i
$611$			14583.2i			0.965586i
$612$	−1143.65	+	1796.25i	−0.0755384	+	0.118642i
$613$	−10740.6	−	10740.6i	−0.707681	−	0.707681i	0.258366	−	0.966047i	$-0.416816\pi$
$613$	−10740.6	−	10740.6i	−0.707681	−	0.707681i	−0.966047	+	0.258366i	$0.916816\pi$
$614$	−531.028	−	919.767i	−0.0349031	−	0.0604540i
$615$	−6929.27	−	7783.74i	−0.454334	−	0.510359i
$616$	−7119.97	+	12332.2i	−0.465701	+	0.806618i
$617$	−19374.9	+	5191.49i	−1.26419	+	0.338738i	−0.827802	−	0.561021i	$-0.810409\pi$
$617$	−19374.9	+	5191.49i	−1.26419	+	0.338738i	−0.436387	+	0.899759i	$0.643742\pi$
$618$	934.157	+	410.888i	0.0608047	+	0.0267449i
$619$	21899.4	−	12643.6i	1.42199	−	0.820987i	0.425522	−	0.904948i	$-0.360091\pi$
$619$	21899.4	−	12643.6i	1.42199	−	0.820987i	0.996469	+	0.0839615i	$0.0267573\pi$
$620$	2465.47	+	3466.88i	0.159703	+	0.224570i
$621$	−14261.0	−	21324.3i	−0.921533	−	1.37796i
$622$	−7936.44	+	7936.44i	−0.511611	+	0.511611i
$623$	6241.82	+	1672.49i	0.401401	+	0.107555i
$624$	8222.36	−	3198.78i	0.527497	−	0.205214i
$625$	14520.3	−	5770.72i	0.929300	−	0.369326i
$626$	9113.26	+	5261.54i	0.581852	+	0.335932i
$627$	6138.36	−	673.099i	0.390977	−	0.0428724i
$628$	−1141.44	+	4259.91i	−0.0725293	+	0.270683i
$629$	−9145.54			−0.579740
$630$	−2961.08	−	9149.11i	−0.187257	−	0.578586i
$631$	−12431.8			−0.784313			−0.392156	−	0.919899i	$-0.628271\pi$
$631$	−12431.8			−0.784313			−0.392156	+	0.919899i	$0.628271\pi$
$632$	−3890.53	+	14519.7i	−0.244869	+	0.913862i
$633$	−5351.64	−	7296.65i	−0.336033	−	0.458161i
$634$	−19115.2	−	11036.1i	−1.19741	−	0.691327i
$635$	−2586.42	−	2138.27i	−0.161636	−	0.133629i
$636$	−193.193	+	1256.32i	−0.0120450	+	0.0783277i
$637$	−7452.11	−	1996.79i	−0.463521	−	0.124200i
$638$	5072.43	−	5072.43i	0.314764	−	0.314764i
$639$	13046.4	−	11961.3i	0.807679	−	0.740503i
$640$	284.253	−	1683.91i	0.0175564	−	0.104004i
$641$	19099.7	−	11027.2i	1.17690	−	0.679484i	0.221605	−	0.975136i	$-0.428870\pi$
$641$	19099.7	−	11027.2i	1.17690	−	0.679484i	0.955296	+	0.295652i	$0.0955370\pi$
$642$	754.113	+	6877.18i	0.0463590	+	0.422774i
$643$	−5577.39	+	1494.46i	−0.342069	+	0.0916572i	−0.425764	−	0.904834i	$-0.639995\pi$
$643$	−5577.39	+	1494.46i	−0.342069	+	0.0916572i	0.0836947	+	0.996491i	$0.473328\pi$
$644$	3968.28	−	6873.27i	0.242814	−	0.420566i
$645$	11933.4	−	18150.5i	0.728494	−	1.10802i
$646$	−849.141	−	1470.76i	−0.0517167	−	0.0895760i
$647$	−19898.4	−	19898.4i	−1.20910	−	1.20910i	−0.971319	−	0.237779i	$-0.923581\pi$
$647$	−19898.4	−	19898.4i	−1.20910	−	1.20910i	−0.237779	−	0.971319i	$-0.576419\pi$
$648$	11529.3	+	13725.0i	0.698941	+	0.832053i
$649$		−	17315.8i		−	1.04731i
$650$	2915.25	+	15228.8i	0.175916	+	0.918959i
$651$	3376.15	+	8678.30i	0.203259	+	0.522472i
$652$	−1764.78	−	6586.25i	−0.106003	−	0.395610i
$653$	1506.67	+	5622.98i	0.0902920	+	0.336974i	0.996264	−	0.0863641i	$-0.0275248\pi$
$653$	1506.67	+	5622.98i	0.0902920	+	0.336974i	−0.905972	+	0.423338i	$0.860858\pi$
$654$	−11083.4	+	13813.4i	−0.662682	+	0.825914i
$655$	−1531.03	+	3346.92i	−0.0913318	+	0.199656i
$656$		−	5470.84i		−	0.325610i
$657$	−151.244	+	3485.64i	−0.00898109	+	0.206983i
$658$	5900.45	+	5900.45i	0.349579	+	0.349579i
$659$	−10262.3	−	17774.8i	−0.606618	−	1.05069i	−0.991794	−	0.127849i	$-0.959193\pi$
$659$	−10262.3	−	17774.8i	−0.606618	−	1.05069i	0.385176	−	0.922843i	$-0.374141\pi$
$660$	6781.41	+	2245.86i	0.399948	+	0.132454i
$661$	−13997.3	+	24244.1i	−0.823652	+	1.42661i	0.0792938	+	0.996851i	$0.474733\pi$
$661$	−13997.3	+	24244.1i	−0.823652	+	1.42661i	−0.902945	+	0.429755i	$0.858600\pi$
$662$	−9961.53	+	2669.18i	−0.584843	+	0.156708i
$663$	6060.24	−	4444.81i	0.354993	−	0.260365i
$664$	−4550.35	+	2627.15i	−0.265946	+	0.153544i
$665$	−4624.56	−	780.649i	−0.269673	−	0.0455222i
$666$	−6362.64	+	20198.7i	−0.370191	+	1.17520i
$667$	−10277.2	+	10277.2i	−0.596605	+	0.596605i
$668$	5674.08	+	1520.37i	0.328648	+	0.0880610i
$669$	21093.5	+	16924.6i	1.21902	+	0.978093i
$670$	1404.25	+	14804.3i	0.0809712	+	0.853642i
$671$	28110.0	+	16229.3i	1.61725	+	0.933719i
$672$	−3851.32	+	8755.99i	−0.221083	+	0.502633i
$673$	−5498.22	+	20519.6i	−0.314919	+	1.17530i	0.609145	+	0.793059i	$0.291513\pi$
$673$	−5498.22	+	20519.6i	−0.314919	+	1.17530i	−0.924065	+	0.382236i	$0.875154\pi$
$674$	−2096.45			−0.119810
$675$	−15246.8	+	8664.99i	−0.869407	+	0.494097i
$676$	2739.72			0.155878
$677$	1300.65	−	4854.11i	0.0738379	−	0.275567i	−0.919129	−	0.393956i	$-0.871106\pi$
$677$	1300.65	−	4854.11i	0.0738379	−	0.275567i	0.992967	+	0.118389i	$0.0377730\pi$
$678$	9853.70	−	22402.4i	0.558155	−	1.26897i
$679$	−14862.7	−	8580.98i	−0.840027	−	0.484990i
$680$	−674.412	−	7110.01i	−0.0380331	−	0.400966i
$681$	9464.37	+	7593.86i	0.532563	+	0.427309i
$682$	10926.4	+	2927.71i	0.613478	+	0.164381i
$683$	−1391.88	+	1391.88i	−0.0779778	+	0.0779778i	−0.745020	−	0.667042i	$-0.767560\pi$
$683$	−1391.88	+	1391.88i	−0.0779778	+	0.0779778i	0.667042	+	0.745020i	$0.267560\pi$
$684$	2347.67	−	521.132i	0.131236	−	0.0291315i
$685$	−14483.5	−	2444.89i	−0.807865	−	0.136372i
$686$	−13285.8	+	7670.56i	−0.739438	+	0.426915i
$687$	−13837.5	+	10148.9i	−0.768460	+	0.563617i
$688$	11014.9	−	2951.44i	0.610378	−	0.163550i
$689$	2243.06	−	3885.10i	0.124026	−	0.214819i
$690$	22468.1	+	7440.94i	1.23963	+	0.410538i
$691$	1846.79	+	3198.73i	0.101672	+	0.176100i	0.912373	−	0.409359i	$-0.134248\pi$
$691$	1846.79	+	3198.73i	0.101672	+	0.176100i	−0.810702	+	0.585459i	$0.800914\pi$
$692$	−775.993	−	775.993i	−0.0426284	−	0.0426284i
$693$	13190.1	+	8398.00i	0.723015	+	0.460337i
$694$		−	1338.22i		−	0.0731961i
$695$	10128.5	−	22141.5i	0.552802	−	1.20846i
$696$	6355.49	−	7920.96i	0.346127	−	0.431384i
$697$	−1206.17	−	4501.49i	−0.0655480	−	0.244629i
$698$	5981.98	+	22325.0i	0.324386	+	1.21062i
$699$	3678.62	+	9455.78i	0.199053	+	0.511660i
$700$	−4489.32	−	3046.70i	−0.242400	−	0.164506i
$701$			25198.2i			1.35766i	0.734294	+	0.678831i	$0.237513\pi$
$701$			25198.2i			1.35766i	−0.734294	+	0.678831i	$0.762487\pi$
$702$	−5600.59	−	16476.9i	−0.301112	−	0.885869i
$703$	7303.21	+	7303.21i	0.391815	+	0.391815i
$704$	10751.4	+	18621.9i	0.575578	+	0.996931i
$705$	8360.06	−	12715.5i	0.446607	−	0.679281i
$706$	10547.1	−	18268.0i	0.562243	−	0.973834i
$707$	14667.6	−	3930.18i	0.780244	−	0.209066i
$708$	−735.035	−	6703.20i	−0.0390174	−	0.355821i
$709$	215.222	−	124.258i	0.0114003	−	0.00658198i	−0.494289	−	0.869298i	$-0.664572\pi$
$709$	215.222	−	124.258i	0.0114003	−	0.00658198i	0.505689	+	0.862716i	$0.331238\pi$
$710$	−2718.12	+	16102.1i	−0.143675	+	0.851130i
$711$	15743.6	+	4959.26i	0.830423	+	0.261585i
$712$	7858.07	−	7858.07i	0.413615	−	0.413615i
$713$	−22137.8	−	5931.82i	−1.16279	−	0.311568i
$714$	653.612	−	4250.40i	0.0342589	−	0.222783i
$715$	−19431.7	−	16064.7i	−1.01637	−	0.840261i
$716$	−4003.97	−	2311.70i	−0.208988	−	0.120659i
$717$	−12557.4	−	17121.3i	−0.654066	−	0.891780i
$718$	−3870.60	+	14445.3i	−0.201183	+	0.750825i
$719$	5173.80			0.268359			0.134180	−	0.990957i	$-0.457160\pi$
$719$	5173.80			0.268359			0.134180	+	0.990957i	$0.457160\pi$
$720$	−9003.05	−	1924.50i	−0.466005	−	0.0996139i
$721$	1260.32			0.0650997
$722$	3458.94	−	12909.0i	0.178294	−	0.665404i
$723$	−24465.3	+	2682.73i	−1.25847	+	0.137997i
$724$	5325.16	+	3074.48i	0.273354	+	0.157821i
$725$	6497.07	+	7517.11i	0.332821	+	0.385074i
$726$	3341.55	−	1299.98i	0.170822	−	0.0664554i
$727$	19946.1	+	5344.55i	1.01755	+	0.272653i	0.728782	−	0.684745i	$-0.240087\pi$
$727$	19946.1	+	5344.55i	1.01755	+	0.272653i	0.288771	+	0.957398i	$0.406753\pi$
$728$	13839.6	−	13839.6i	0.704573	−	0.704573i
$729$	15605.9	−	11994.9i	0.792860	−	0.609404i
$730$	−1865.50	−	2623.22i	−0.0945827	−	0.133000i
$731$	8412.53	−	4856.98i	0.425648	−	0.245748i
$732$	11570.7	+	5089.35i	0.584241	+	0.256978i
$733$	20372.1	−	5458.69i	1.02655	−	0.275063i	0.294021	−	0.955799i	$-0.405007\pi$
$733$	20372.1	−	5458.69i	1.02655	−	0.275063i	0.732529	+	0.680736i	$0.238340\pi$
$734$	3572.53	−	6187.80i	0.179652	−	0.311166i
$735$	5353.00	+	6013.09i	0.268637	+	0.301764i
$736$	−11771.6	−	20389.0i	−0.589546	−	1.02112i
$737$	−17098.2	−	17098.2i	−0.854575	−	0.854575i
$738$	−10781.1	−	467.797i	−0.537747	−	0.0233331i
$739$			3372.43i			0.167871i	0.996471	+	0.0839356i	$0.0267490\pi$
$739$			3372.43i			0.167871i	−0.996471	+	0.0839356i	$0.973251\pi$
$740$	4168.40	+	11197.4i	0.207072	+	0.556250i
$741$	−8388.86	−	1290.01i	−0.415887	−	0.0639537i
$742$	−664.378	−	2479.49i	−0.0328707	−	0.122675i
$743$	−5227.39	−	19508.9i	−0.258108	−	0.963273i	−0.966335	−	0.257288i	$-0.917171\pi$
$743$	−5227.39	−	19508.9i	−0.258108	−	0.963273i	0.708227	−	0.705985i	$-0.249496\pi$
$744$	15828.0	+	2433.98i	0.779950	+	0.119938i
$745$	4844.32	+	2216.01i	0.238231	+	0.108978i
$746$			6829.76i			0.335195i
$747$	2665.51	+	5117.02i	0.130557	+	0.250632i
$748$	2258.91	+	2258.91i	0.110420	+	0.110420i
$749$	4272.01	+	7399.34i	0.208406	+	0.360970i
$750$	6188.28	−	14949.6i	0.301286	−	0.727844i
$751$	−3536.97	+	6126.21i	−0.171859	+	0.297668i	−0.939070	−	0.343727i	$-0.888311\pi$
$751$	−3536.97	+	6126.21i	−0.171859	+	0.297668i	0.767211	+	0.641395i	$0.221644\pi$
$752$	7716.59	−	2067.65i	0.374195	−	0.100265i
$753$	−16338.5	−	7186.47i	−0.790713	−	0.347795i
$754$	−8538.70	+	4929.82i	−0.412415	+	0.238108i
$755$	18209.4	−	12949.6i	0.877760	−	0.624218i
$756$	5462.55	+	2691.08i	0.262792	+	0.129462i
$757$	6425.25	−	6425.25i	0.308494	−	0.308494i	−0.535831	−	0.844325i	$-0.680002\pi$
$757$	6425.25	−	6425.25i	0.308494	−	0.308494i	0.844325	+	0.535831i	$0.180002\pi$
$758$	−18245.5	−	4888.87i	−0.874283	−	0.234263i
$759$	−35866.9	+	13953.5i	−1.71527	+	0.667297i
$760$	−5139.18	+	6216.29i	−0.245286	+	0.296695i
$761$	−11481.3	−	6628.75i	−0.546909	−	0.315758i	0.200965	−	0.979598i	$-0.435592\pi$
$761$	−11481.3	−	6628.75i	−0.546909	−	0.315758i	−0.747875	+	0.663840i	$0.768926\pi$
$762$	−3454.31	+	378.781i	−0.164221	+	0.0180076i
$763$	−5660.79	+	21126.3i	−0.268590	+	1.00239i
$764$	−3808.30			−0.180340
$765$	−7832.15	+	401.416i	−0.370159	+	0.0189716i
$766$	14987.5			0.706947
$767$	−6159.84	+	22988.8i	−0.289986	+	1.08224i
$768$	12005.2	+	16368.4i	0.564063	+	0.769067i
$769$	19228.5	+	11101.6i	0.901686	+	0.520589i	0.877747	−	0.479125i	$-0.159046\pi$
$769$	19228.5	+	11101.6i	0.901686	+	0.520589i	0.0239392	+	0.999713i	$0.492379\pi$
$770$	−14362.0	+	1362.29i	−0.672172	+	0.0637580i
$771$	1876.23	−	12201.0i	0.0876406	−	0.569922i
$772$	−8509.60	−	2280.14i	−0.396719	−	0.106301i
$773$	13738.9	−	13738.9i	0.639265	−	0.639265i	−0.311109	−	0.950374i	$-0.600700\pi$
$773$	13738.9	−	13738.9i	0.639265	−	0.639265i	0.950374	+	0.311109i	$0.100700\pi$
$774$	−4874.38	−	21958.9i	−0.226364	−	1.01976i
$775$	−5142.97	+	14799.4i	−0.238375	+	0.685948i
$776$	−25560.0	+	14757.1i	−1.18241	+	0.682666i
$777$	2850.72	+	25997.3i	0.131620	+	1.20032i
$778$	8947.01	−	2397.34i	0.412296	−	0.110474i
$779$	−2631.49	+	4557.88i	−0.121031	+	0.209632i
$780$	−8204.20	−	5394.02i	−0.376612	−	0.247612i
$781$	−13276.6	−	22995.8i	−0.608290	−	1.05359i
$782$	7484.18	+	7484.18i	0.342243	+	0.342243i
$783$	−8387.16	−	7349.34i	−0.382801	−	0.335433i
$784$			4226.33i			0.192526i
$785$	−15221.7	+	5666.50i	−0.692083	+	0.257638i
$786$	1381.79	+	3551.85i	0.0627059	+	0.161183i
$787$	9610.38	+	35866.4i	0.435290	+	1.62452i	0.740372	+	0.672197i	$0.234649\pi$
$787$	9610.38	+	35866.4i	0.435290	+	1.62452i	−0.305082	+	0.952326i	$0.598684\pi$
$788$	1752.05	+	6538.74i	0.0792059	+	0.295600i
$789$	−21780.9	+	27145.9i	−0.982788	+	1.22487i
$790$	−14272.0	+	5312.94i	−0.642751	+	0.239273i
$791$		−	30224.4i		−	1.35860i
$792$	23849.3	−	12423.3i	1.07001	−	0.557378i
$793$	−31546.0	−	31546.0i	−1.41265	−	1.41265i
$794$	−4076.25	−	7060.27i	−0.182192	−	0.315566i
$795$	−4182.99	+	2101.65i	−0.186610	+	0.0937584i
$796$	−5517.58	+	9556.74i	−0.245685	+	0.425540i
$797$	17057.3	−	4570.50i	0.758096	−	0.203131i	0.140990	−	0.990011i	$-0.454972\pi$
$797$	17057.3	−	4570.50i	0.758096	−	0.203131i	0.617106	+	0.786880i	$0.288305\pi$
$798$	−3916.13	+	2872.23i	−0.173721	+	0.127414i
$799$	5893.46	−	3402.59i	0.260946	−	0.150657i
$800$	−14485.5	+	7014.13i	−0.640176	+	0.309983i
$801$	−8246.64	−	8994.75i	−0.363771	−	0.396772i
$802$	14577.2	−	14577.2i	0.641820	−	0.641820i
$803$	5055.75	+	1354.69i	0.222184	+	0.0595340i
$804$	−7344.76	−	5893.16i	−0.322176	−	0.258502i
$805$	29098.9	−	2760.14i	1.27404	−	0.120847i
$806$	−13464.6	−	7773.77i	−0.588423	−	0.339726i
$807$	−7036.80	+	15998.2i	−0.306948	+	0.697848i
$808$	6758.90	−	25224.5i	0.294279	−	1.09826i
$809$	−32490.3			−1.41199			−0.705993	−	0.708219i	$-0.749499\pi$
$809$	−32490.3			−1.41199			−0.705993	+	0.708219i	$0.749499\pi$
$810$	−4562.34	+	17577.3i	−0.197907	+	0.762472i
$811$	13686.9			0.592616			0.296308	−	0.955092i	$-0.404244\pi$
$811$	13686.9			0.592616			0.296308	+	0.955092i	$0.404244\pi$
$812$	892.932	−	3332.47i	0.0385908	−	0.144023i
$813$	−13771.7	+	31310.1i	−0.594090	+	1.35067i
$814$	27513.7	+	15885.1i	1.18471	+	0.683994i
$815$	16000.8	−	19354.4i	0.687709	−	0.831845i
$816$	−3211.18	−	2576.53i	−0.137762	−	0.110535i
$817$	−10596.4	−	2839.30i	−0.453760	−	0.121585i
$818$	11508.7	−	11508.7i	0.491922	−	0.491922i
$819$	−14523.9	−	15841.5i	−0.619668	−	0.675882i
$820$	−4961.68	+	3528.50i	−0.211304	+	0.150269i
$821$	28854.2	−	16659.0i	1.22658	−	0.708164i	0.260264	−	0.965537i	$-0.416190\pi$
$821$	28854.2	−	16659.0i	1.22658	−	0.708164i	0.966312	+	0.257373i	$0.0828570\pi$
$822$	−12264.8	+	8995.48i	−0.520419	+	0.381695i
$823$	8616.20	−	2308.70i	0.364936	−	0.0977842i	−0.0716914	−	0.997427i	$-0.522840\pi$
$823$	8616.20	−	2308.70i	0.364936	−	0.0977842i	0.436627	+	0.899643i	$0.356173\pi$
$824$	1083.72	−	1877.05i	0.0458168	−	0.0793570i
$825$	7733.65	+	25146.8i	0.326365	+	1.06121i
$826$	6809.11	+	11793.7i	0.286827	+	0.496799i
$827$	−1754.96	−	1754.96i	−0.0737919	−	0.0737919i	0.669248	−	0.743039i	$-0.266617\pi$
$827$	−1754.96	−	1754.96i	−0.0737919	−	0.0737919i	−0.743039	+	0.669248i	$0.766617\pi$
$828$	−13292.3	+	6924.08i	−0.557897	+	0.290614i
$829$		−	5248.56i		−	0.219891i	−0.993938	−	0.109946i	$-0.964932\pi$
$829$		−	5248.56i		−	0.219891i	0.993938	−	0.109946i	$-0.0350677\pi$
$830$	−4840.70	−	2214.35i	−0.202438	−	0.0926041i
$831$	3736.44	−	4656.80i	0.155976	−	0.194395i
$832$	−7649.26	−	28547.4i	−0.318738	−	1.18955i
$833$	931.791	+	3477.49i	0.0387571	+	0.144643i
$834$	−9141.23	−	23497.3i	−0.379538	−	0.975592i
$835$	7547.61	+	20274.9i	0.312810	+	0.840288i
$836$		−	3607.72i		−	0.149253i
$837$	3423.63	−	17248.3i	0.141384	−	0.712290i
$838$	8133.06	+	8133.06i	0.335265	+	0.335265i
$839$	23083.9	+	39982.5i	0.949876	+	1.64523i	0.745682	+	0.666302i	$0.232124\pi$
$839$	23083.9	+	39982.5i	0.949876	+	1.64523i	0.204194	+	0.978930i	$0.434543\pi$
$840$	−20000.9	+	4133.34i	−0.821543	+	0.169778i
$841$	9035.50	−	15649.9i	0.370474	−	0.641680i
$842$	4072.33	−	1091.18i	0.166677	−	0.0446609i
$843$	−3647.96	−	33267.8i	−0.149042	−	1.35920i
$844$	−4578.34	+	2643.30i	−0.186721	+	0.107804i
$845$	5847.64	+	8222.80i	0.238065	+	0.334761i
$846$	−3414.79	−	15383.5i	−0.138774	−	0.625170i
$847$	3131.07	−	3131.07i	0.127019	−	0.127019i
$848$	−2373.80	−	636.058i	−0.0961281	−	0.0257575i
$849$	−4496.31	+	29239.2i	−0.181758	+	1.18196i
$850$	5474.18	−	4731.36i	0.220897	−	0.190923i
$851$	−55745.4	−	32184.6i	−2.24551	−	1.29644i
$852$	−6115.71	−	8338.41i	−0.245916	−	0.335292i
$853$	2250.10	−	8397.50i	0.0903189	−	0.337075i	−0.905949	−	0.423386i	$-0.860841\pi$
$853$	2250.10	−	8397.50i	0.0903189	−	0.337075i	0.996268	+	0.0863114i	$0.0275080\pi$
$854$	−25527.4			−1.02287
$855$	6574.95	+	5933.85i	0.262993	+	0.237349i
$856$	14693.5			0.586699
$857$	2624.87	−	9796.17i	0.104625	−	0.390467i	−0.893677	−	0.448711i	$-0.851883\pi$
$857$	2624.87	−	9796.17i	0.104625	−	0.390467i	0.998302	+	0.0582434i	$0.0185500\pi$
$858$	−25952.1	+	2845.76i	−1.03262	+	0.113232i
$859$	9807.59	+	5662.41i	0.389558	+	0.224912i	0.681969	−	0.731381i	$-0.261124\pi$
$859$	9807.59	+	5662.41i	0.389558	+	0.224912i	−0.292410	+	0.956293i	$0.594457\pi$
$860$	−9780.98	−	8086.21i	−0.387824	−	0.320625i
$861$	−12420.1	+	4831.84i	−0.491609	+	0.191253i
$862$	−27370.1	−	7333.80i	−1.08147	−	0.289780i
$863$	9646.02	−	9646.02i	0.380480	−	0.380480i	−0.490795	−	0.871275i	$-0.663294\pi$
$863$	9646.02	−	9646.02i	0.380480	−	0.380480i	0.871275	+	0.490795i	$0.163294\pi$
$864$	15015.4	−	10041.8i	0.591245	−	0.395404i
$865$	672.737	−	3985.29i	0.0264436	−	0.156652i
$866$	−11198.0	+	6465.19i	−0.439405	+	0.253691i
$867$	20157.8	+	8866.41i	0.789615	+	0.347312i
$868$	5254.92	−	1408.05i	0.205488	−	0.0550604i
$869$	12381.4	−	21445.2i	0.483324	−	0.837143i
$870$	10271.2	+	596.508i	0.400261	+	0.0232454i
$871$	16617.5	+	28782.4i	0.646456	+	1.11969i
$872$	26596.8	+	26596.8i	1.03289	+	1.03289i
$873$	14972.6	+	28743.1i	0.580464	+	1.11433i
$874$		−	11953.1i		−	0.462606i
$875$	−437.826	−	19976.8i	−0.0169157	−	0.771816i
$876$	2014.66	+	309.807i	0.0777043	+	0.0119491i
$877$	12587.0	+	46975.5i	0.484646	+	1.80872i	0.581651	+	0.813439i	$0.302407\pi$
$877$	12587.0	+	46975.5i	0.484646	+	1.80872i	−0.0970048	+	0.995284i	$0.530926\pi$
$878$	4780.30	+	17840.3i	0.183744	+	0.685742i
$879$	5253.42	+	807.853i	0.201585	+	0.0309991i
$880$	−5745.43	+	12559.8i	−0.220089	+	0.481127i
$881$			26406.8i			1.00984i	0.863166	+	0.504920i	$0.168478\pi$
$881$			26406.8i			1.00984i	−0.863166	+	0.504920i	$0.831522\pi$
$882$	8328.61	+	361.382i	0.317958	+	0.0137963i
$883$	1035.61	+	1035.61i	0.0394689	+	0.0394689i	0.726566	−	0.687097i	$-0.241115\pi$
$883$	1035.61	+	1035.61i	0.0394689	+	0.0394689i	−0.687097	+	0.726566i	$0.741115\pi$
$884$	−2195.40	−	3802.54i	−0.0835285	−	0.144676i
$885$	18549.7	−	16513.4i	0.704565	−	0.627221i
$886$	−6608.85	+	11446.9i	−0.250597	+	0.434046i
$887$	23856.0	−	6392.19i	0.903050	−	0.241972i	0.222724	−	0.974881i	$-0.428505\pi$
$887$	23856.0	−	6392.19i	0.903050	−	0.241972i	0.680326	+	0.732910i	$0.261838\pi$
$888$	41170.2	+	18108.7i	1.55583	+	0.684333i
$889$	−3716.59	+	2145.77i	−0.140214	+	0.0809526i
$890$	11101.5	+	1873.99i	0.418117	+	0.0705802i
$891$	−12493.8	−	26755.2i	−0.469760	−	1.00599i
$892$	11172.3	−	11172.3i	0.419367	−	0.419367i
$893$	−7423.41	−	1989.10i	−0.278180	−	0.0745382i
$894$	5140.94	−	2000.00i	0.192325	−	0.0748211i
$895$	−1607.90	−	16951.3i	−0.0600515	−	0.633095i
$896$	−1891.30	−	1091.95i	−0.0705179	−	0.0407135i
$897$	52581.4	−	5765.78i	1.95724	−	0.214620i
$898$	2223.18	−	8297.03i	0.0826154	−	0.308325i
$899$	−9962.79			−0.369608
$900$	4061.25	+	9406.39i	0.150417	+	0.348385i
$901$	−2093.43			−0.0774055
$902$	−4190.04	+	15637.4i	−0.154671	+	0.577239i
$903$	−16428.8	−	22399.7i	−0.605445	−	0.825489i
$904$	−45014.4	−	25989.1i	−1.65615	−	0.956177i
$905$	2138.45	+	22544.7i	0.0785465	+	0.828080i
$906$	3516.73	−	22869.1i	0.128957	−	0.838603i
$907$	−25088.0	−	6722.31i	−0.918450	−	0.246098i	−0.231527	−	0.972828i	$-0.574372\pi$
$907$	−25088.0	−	6722.31i	−0.918450	−	0.246098i	−0.686923	+	0.726731i	$0.741039\pi$
$908$	5012.84	−	5012.84i	0.183213	−	0.183213i
$909$	−27350.9	−	8615.58i	−0.997988	−	0.314368i
$910$	19552.0	+	3300.47i	0.712243	+	0.120230i
$911$	−3490.35	+	2015.15i	−0.126938	+	0.0732877i	−0.562124	−	0.827053i	$-0.690016\pi$
$911$	−3490.35	+	2015.15i	−0.126938	+	0.0732877i	0.435186	+	0.900340i	$0.356682\pi$
$912$	506.801	+	4621.80i	0.0184012	+	0.167810i
$913$	8360.73	−	2240.25i	0.303067	−	0.0812065i
$914$	1994.02	−	3453.74i	0.0721622	−	0.124989i
$915$	9421.55	+	45590.1i	0.340401	+	1.64717i
$916$	5012.79	+	8682.41i	0.180816	+	0.313182i
$917$	3328.12	+	3328.12i	0.119852	+	0.119852i
$918$	−5352.01	+	6107.78i	−0.192421	+	0.219593i
$919$			33304.4i			1.19544i	0.801704	+	0.597722i	$0.203927\pi$
$919$			33304.4i			1.19544i	−0.801704	+	0.597722i	$0.796073\pi$
$920$	20910.5	−	45711.5i	0.749346	−	1.63811i
$921$	898.022	+	2308.34i	0.0321290	+	0.0825866i
$922$	6804.20	+	25393.6i	0.243042	+	0.907044i
$923$	9445.91	+	35252.6i	0.336854	+	1.25715i
$924$	5717.11	−	7125.34i	0.203549	−	0.253687i
$925$	−24710.1	+	36410.4i	−0.878339	+	1.29424i
$926$		−	5517.66i		−	0.195812i
$927$	−2007.63	−	1278.24i	−0.0711320	−	0.0452891i
$928$	−7236.67	−	7236.67i	−0.255986	−	0.255986i
$929$	6.85930	+	11.8807i	0.000242246	+	0.000419582i	0.866147	−	0.499790i	$-0.166590\pi$
$929$	6.85930	+	11.8807i	0.000242246	+	0.000419582i	−0.865904	+	0.500210i	$0.833256\pi$
$930$	7283.68	+	14497.0i	0.256819	+	0.511155i
$931$	2032.88	−	3521.05i	0.0715628	−	0.123950i
$932$	5725.71	−	1534.20i	0.201236	−	0.0539210i
$933$	21107.1	−	15480.7i	0.740637	−	0.543211i
$934$	30251.2	−	17465.6i	1.05980	−	0.611874i
$935$	−1958.33	+	11601.1i	−0.0684965	+	0.405773i
$936$	−36082.2	+	8009.44i	−1.26002	+	0.279697i
$937$	5283.80	−	5283.80i	0.184220	−	0.184220i	−0.608972	−	0.793192i	$-0.708418\pi$
$937$	5283.80	−	5283.80i	0.184220	−	0.184220i	0.793192	+	0.608972i	$0.208418\pi$
$938$	18369.1	+	4921.97i	0.639415	+	0.171331i
$939$	−19141.5	−	15358.4i	−0.665239	−	0.533763i
$940$	−6852.14	−	5664.86i	−0.237758	−	0.196561i
$941$	23901.0	+	13799.2i	0.828002	+	0.478047i	0.853168	−	0.521636i	$-0.174678\pi$
$941$	23901.0	+	13799.2i	0.828002	+	0.478047i	−0.0251660	+	0.999683i	$0.508011\pi$
$942$	−6771.69	+	15395.5i	−0.234218	+	0.532496i
$943$	8489.42	−	31682.9i	0.293164	−	1.09410i
$944$	13037.7			0.449515
$945$	3582.41	+	22138.7i	0.123318	+	0.762088i
$946$	−33744.7			−1.15976
$947$	2279.84	−	8508.47i	0.0782310	−	0.291962i	−0.915716	−	0.401827i	$-0.868375\pi$
$947$	2279.84	−	8508.47i	0.0782310	−	0.291962i	0.993946	+	0.109865i	$0.0350419\pi$
$948$	3882.68	−	8827.29i	0.133021	−	0.302423i
$949$	−6230.21	−	3597.01i	−0.213110	−	0.123039i
$950$	−8149.68	−	593.181i	−0.278327	−	0.0202582i
$951$	40149.5	+	32214.5i	1.36902	+	1.09845i
$952$	−8822.04	−	2363.86i	−0.300340	−	0.0804760i
$953$	−28229.0	+	28229.0i	−0.959524	+	0.959524i	−0.999212	−	0.0396877i	$-0.987364\pi$
$953$	−28229.0	+	28229.0i	−0.959524	+	0.959524i	0.0396877	+	0.999212i	$0.487364\pi$
$954$	−1456.42	+	4623.53i	−0.0494271	+	0.156910i
$955$	−8128.43	−	11430.0i	−0.275424	−	0.387294i
$956$	−10742.9	+	6202.41i	−0.363441	+	0.209833i
$957$	−13490.2	+	9894.22i	−0.455670	+	0.334206i
$958$	−19490.5	+	5222.47i	−0.657318	+	0.176128i
$959$	−9391.95	+	16267.3i	−0.316248	+	0.547758i
$960$	−9695.69	+	29276.3i	−0.325966	+	0.984260i
$961$	7040.40	+	12194.3i	0.236327	+	0.409330i
$962$	−30876.9	−	30876.9i	−1.03483	−	1.03483i
$963$	699.435	−	16119.5i	0.0234050	−	0.539403i
$964$			14379.1i			0.480414i
$965$	−11319.4	−	30406.8i	−0.377600	−	1.01433i
$966$	18941.9	−	23607.6i	0.630895	−	0.786296i
$967$	−12318.4	−	45973.1i	−0.409653	−	1.52885i	−0.795310	−	0.606203i	$-0.792692\pi$
$967$	−12318.4	−	45973.1i	−0.409653	−	1.52885i	0.385657	−	0.922642i	$-0.373975\pi$
$968$	−1970.91	−	7355.54i	−0.0654417	−	0.244232i
$969$	1435.98	+	3691.15i	0.0476062	+	0.122370i
$970$	−27191.0	−	12438.4i	−0.900050	−	0.411724i
$971$		−	12138.7i		−	0.401183i	−0.979675	−	0.200591i	$-0.935714\pi$
$971$		−	12138.7i		−	0.401183i	0.979675	−	0.200591i	$-0.0642863\pi$
$972$	−5972.23	−	9826.97i	−0.197078	−	0.324280i
$973$	−22017.2	−	22017.2i	−0.725425	−	0.725425i
$974$	3666.61	+	6350.75i	0.120622	+	0.208923i
$975$	−1321.75	−	36136.5i	−0.0434154	−	1.18697i
$976$	−12219.6	+	21165.0i	−0.400759	+	0.694135i
$977$	−5006.88	+	1341.59i	−0.163955	+	0.0439317i	−0.339863	−	0.940475i	$-0.610381\pi$
$977$	−5006.88	+	1341.59i	−0.163955	+	0.0439317i	0.175908	+	0.984407i	$0.443714\pi$
$978$	−2834.44	−	25848.8i	−0.0926741	−	0.845147i
$979$	−15854.3	+	9153.49i	−0.517575	+	0.298822i
$980$	3833.00	−	2725.83i	0.124939	−	0.0888506i
$981$	30444.1	−	27912.0i	0.990830	−	0.908421i
$982$	−4772.16	+	4772.16i	−0.155077	+	0.155077i
$983$	−13267.4	−	3555.00i	−0.430484	−	0.115348i	0.0370695	−	0.999313i	$-0.488198\pi$
$983$	−13267.4	−	3555.00i	−0.430484	−	0.115348i	−0.467553	+	0.883965i	$0.654864\pi$
$984$	−3483.42	+	22652.5i	−0.112853	+	0.733877i
$985$	−15885.4	+	19214.7i	−0.513858	+	0.621556i
$986$	3984.55	+	2300.48i	0.128696	+	0.0743024i
$987$	−11509.3	−	15692.3i	−0.371171	−	0.506070i
$988$	−1283.39	+	4789.68i	−0.0413260	+	0.154231i
$989$	68369.9			2.19822
$990$	24259.7	+	12396.2i	0.778812	+	0.397956i
$991$	10353.2			0.331868			0.165934	−	0.986137i	$-0.446936\pi$
$991$	10353.2			0.331868			0.165934	+	0.986137i	$0.446936\pi$
$992$	4176.87	−	15588.3i	0.133685	−	0.498920i
$993$	23907.9	−	2621.61i	0.764044	−	0.0837808i
$994$	18085.3	+	10441.5i	0.577093	+	0.333185i
$995$	−40459.7	+	3837.75i	−1.28910	+	0.122276i
$996$	3141.46	−	1222.13i	0.0999407	−	0.0388803i
$997$	−12492.8	−	3347.43i	−0.396841	−	0.106333i	0.0548790	−	0.998493i	$-0.482523\pi$
$997$	−12492.8	−	3347.43i	−0.396841	−	0.106333i	−0.451720	+	0.892160i	$0.649189\pi$
$998$	311.118	−	311.118i	0.00986802	−	0.00986802i
$999$	21825.9	−	44303.8i	0.691232	−	1.40311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.23.12	yes	64
3.2	odd	2		135.4.m.a.98.5		64
5.2	odd	4	inner	45.4.l.a.32.12	yes	64
5.3	odd	4		225.4.p.b.32.5		64
5.4	even	2		225.4.p.b.68.5		64
9.2	odd	6	inner	45.4.l.a.38.12	yes	64
9.7	even	3		135.4.m.a.8.5		64
15.2	even	4		135.4.m.a.17.5		64
45.2	even	12	inner	45.4.l.a.2.12	✓	64
45.7	odd	12		135.4.m.a.62.5		64
45.29	odd	6		225.4.p.b.218.5		64
45.38	even	12		225.4.p.b.182.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.12	✓	64	45.2	even	12	inner
45.4.l.a.23.12	yes	64	1.1	even	1	trivial
45.4.l.a.32.12	yes	64	5.2	odd	4	inner
45.4.l.a.38.12	yes	64	9.2	odd	6	inner
135.4.m.a.8.5		64	9.7	even	3
135.4.m.a.17.5		64	15.2	even	4
135.4.m.a.62.5		64	45.7	odd	12
135.4.m.a.98.5		64	3.2	odd	2
225.4.p.b.32.5		64	5.3	odd	4
225.4.p.b.68.5		64	5.4	even	2
225.4.p.b.182.5		64	45.38	even	12
225.4.p.b.218.5		64	45.29	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.576664 - 2.15214i) q^{2} +(-2.09209 + 4.75638i) q^{3} +(2.62904 + 1.51788i) q^{4} +(1.05576 + 11.1304i) q^{5} +(9.02996 + 7.24530i) q^{6} +(13.8105 + 3.70051i) q^{7} +(17.3866 - 17.3866i) q^{8} +(-18.2463 - 19.9016i) q^{9} +O(q^{10})\)	\(q+(0.576664 - 2.15214i) q^{2} +(-2.09209 + 4.75638i) q^{3} +(2.62904 + 1.51788i) q^{4} +(1.05576 + 11.1304i) q^{5} +(9.02996 + 7.24530i) q^{6} +(13.8105 + 3.70051i) q^{7} +(17.3866 - 17.3866i) q^{8} +(-18.2463 - 19.9016i) q^{9} +(24.5629 + 4.14635i) q^{10} +(-35.0788 + 20.2528i) q^{11} +(-12.7198 + 9.32918i) q^{12} +(53.7760 - 14.4092i) q^{13} +(15.9280 - 27.5881i) q^{14} +(-55.1491 - 18.2642i) q^{15} +(-15.2491 - 26.4122i) q^{16} +(-18.3703 - 18.3703i) q^{17} +(-53.3529 + 27.7921i) q^{18} +29.3394i q^{19} +(-14.1189 + 30.8648i) q^{20} +(-46.4938 + 57.9461i) q^{21} +(23.3581 + 87.1736i) q^{22} +(-47.3257 - 176.622i) q^{23} +(46.3228 + 119.071i) q^{24} +(-122.771 + 23.5020i) q^{25} -124.043i q^{26} +(132.832 - 45.1505i) q^{27} +(30.6914 + 30.6914i) q^{28} +(-39.7429 - 68.8368i) q^{29} +(-71.1095 + 108.156i) q^{30} +(62.6702 - 108.548i) q^{31} +(124.368 - 33.3242i) q^{32} +(-22.9418 - 209.219i) q^{33} +(-50.1290 + 28.9420i) q^{34} +(-26.6075 + 157.623i) q^{35} +(-17.7622 - 80.0177i) q^{36} +(248.921 - 248.921i) q^{37} +(63.1425 + 16.9190i) q^{38} +(-43.9685 + 285.924i) q^{39} +(211.875 + 175.163i) q^{40} +(155.350 + 89.6914i) q^{41} +(97.8968 + 133.477i) q^{42} +(-96.7744 + 361.167i) q^{43} -122.965 q^{44} +(202.248 - 224.100i) q^{45} -407.406 q^{46} +(-67.7961 + 253.018i) q^{47} +(157.529 - 17.2737i) q^{48} +(-120.011 - 69.2884i) q^{49} +(-20.2179 + 277.772i) q^{50} +(125.809 - 48.9438i) q^{51} +(163.251 + 43.7429i) q^{52} +(56.9787 - 56.9787i) q^{53} +(-20.5705 - 311.910i) q^{54} +(-262.456 - 369.059i) q^{55} +(304.456 - 175.778i) q^{56} +(-139.549 - 61.3807i) q^{57} +(-171.065 + 45.8366i) q^{58} +(-213.746 + 370.219i) q^{59} +(-117.266 - 131.727i) q^{60} +(-400.668 - 693.978i) q^{61} +(-197.471 - 197.471i) q^{62} +(-178.344 - 342.371i) q^{63} -530.858i q^{64} +(217.155 + 583.335i) q^{65} +(-463.498 - 71.2751i) q^{66} +(154.507 + 576.627i) q^{67} +(-20.4124 - 76.1803i) q^{68} +(939.091 + 144.410i) q^{69} +(323.883 + 148.158i) q^{70} +655.546i q^{71} +(-663.260 - 28.7792i) q^{72} +(-91.3719 - 91.3719i) q^{73} +(-392.170 - 679.258i) q^{74} +(145.063 - 633.113i) q^{75} +(-44.5337 + 77.1346i) q^{76} +(-559.401 + 149.891i) q^{77} +(589.994 + 259.509i) q^{78} +(-529.437 + 305.671i) q^{79} +(277.878 - 197.613i) q^{80} +(-63.1444 + 726.260i) q^{81} +(282.613 - 282.613i) q^{82} +(-206.409 - 55.3072i) q^{83} +(-210.189 + 81.7708i) q^{84} +(185.074 - 223.863i) q^{85} +(721.475 + 416.544i) q^{86} +(410.560 - 45.0197i) q^{87} +(-257.774 + 962.027i) q^{88} +451.962 q^{89} +(-365.664 - 564.497i) q^{90} +795.994 q^{91} +(143.669 - 536.181i) q^{92} +(385.183 + 525.175i) q^{93} +(505.435 + 291.813i) q^{94} +(-326.559 + 30.9754i) q^{95} +(-101.686 + 661.257i) q^{96} +(-1159.43 - 310.669i) q^{97} +(-218.324 + 218.324i) q^{98} +(1043.12 + 328.585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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