LMFDB - Embedded newform 35.3.g.a.8.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.g (of order $4$, 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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 70 x^{8} - 248 x^{7} + 464 x^{6} + 432 x^{5} + 1129 x^{4} + \cdots + 100 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 70x^8 - 248x^7 + 464x^6 + 432x^5 + 1129x^4 - 2708x^3 + 3528x^2 + 840*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.5
Root			$-1.36503 + 1.36503i$ of defining polynomial
Character	$\chi$	$=$	35.8
Dual form			35.3.g.a.22.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36503 - 1.36503i) q^{2} +(-3.78207 - 3.78207i) q^{3} +0.273387i q^{4} +(4.98225 + 0.420986i) q^{5} -10.3253 q^{6} +(1.87083 - 1.87083i) q^{7} +(5.83330 + 5.83330i) q^{8} +19.6082i q^{9} +O(q^{10})$	\(q+(1.36503 - 1.36503i) q^{2} +(-3.78207 - 3.78207i) q^{3} +0.273387i q^{4} +(4.98225 + 0.420986i) q^{5} -10.3253 q^{6} +(1.87083 - 1.87083i) q^{7} +(5.83330 + 5.83330i) q^{8} +19.6082i q^{9} +(7.37557 - 6.22626i) q^{10} -4.50279 q^{11} +(1.03397 - 1.03397i) q^{12} +(-4.44076 - 4.44076i) q^{13} -5.10747i q^{14} +(-17.2510 - 20.4354i) q^{15} +14.8317 q^{16} +(-14.0987 + 14.0987i) q^{17} +(26.7657 + 26.7657i) q^{18} +2.86628i q^{19} +(-0.115092 + 1.36208i) q^{20} -14.1512 q^{21} +(-6.14644 + 6.14644i) q^{22} +(-10.2041 - 10.2041i) q^{23} -44.1239i q^{24} +(24.6455 + 4.19491i) q^{25} -12.1235 q^{26} +(40.1209 - 40.1209i) q^{27} +(0.511460 + 0.511460i) q^{28} -0.0602879i q^{29} +(-51.4431 - 4.34681i) q^{30} -3.28496 q^{31} +(-3.08747 + 3.08747i) q^{32} +(17.0299 + 17.0299i) q^{33} +38.4902i q^{34} +(10.1085 - 8.53333i) q^{35} -5.36061 q^{36} +(28.4602 - 28.4602i) q^{37} +(3.91256 + 3.91256i) q^{38} +33.5906i q^{39} +(26.6072 + 31.5187i) q^{40} -11.8206 q^{41} +(-19.3168 + 19.3168i) q^{42} +(-6.81044 - 6.81044i) q^{43} -1.23100i q^{44} +(-8.25477 + 97.6927i) q^{45} -27.8578 q^{46} +(-53.7925 + 53.7925i) q^{47} +(-56.0946 - 56.0946i) q^{48} -7.00000i q^{49} +(39.3681 - 27.9157i) q^{50} +106.644 q^{51} +(1.21404 - 1.21404i) q^{52} +(-52.7265 - 52.7265i) q^{53} -109.532i q^{54} +(-22.4340 - 1.89561i) q^{55} +21.8262 q^{56} +(10.8405 - 10.8405i) q^{57} +(-0.0822948 - 0.0822948i) q^{58} -40.0962i q^{59} +(5.58677 - 4.71620i) q^{60} +64.4732 q^{61} +(-4.48407 + 4.48407i) q^{62} +(36.6835 + 36.6835i) q^{63} +67.7558i q^{64} +(-20.2555 - 23.9945i) q^{65} +46.4926 q^{66} +(30.8766 - 30.8766i) q^{67} +(-3.85438 - 3.85438i) q^{68} +77.1854i q^{69} +(2.15018 - 25.4467i) q^{70} +28.5426 q^{71} +(-114.380 + 114.380i) q^{72} +(-68.5201 - 68.5201i) q^{73} -77.6981i q^{74} +(-77.3458 - 109.077i) q^{75} -0.783604 q^{76} +(-8.42394 + 8.42394i) q^{77} +(45.8521 + 45.8521i) q^{78} -60.6193i q^{79} +(73.8952 + 6.24395i) q^{80} -127.007 q^{81} +(-16.1355 + 16.1355i) q^{82} +(105.994 + 105.994i) q^{83} -3.86876i q^{84} +(-76.1783 + 64.3076i) q^{85} -18.5929 q^{86} +(-0.228013 + 0.228013i) q^{87} +(-26.2661 - 26.2661i) q^{88} +70.6453i q^{89} +(122.085 + 144.621i) q^{90} -16.6158 q^{91} +(2.78967 - 2.78967i) q^{92} +(12.4240 + 12.4240i) q^{93} +146.857i q^{94} +(-1.20667 + 14.2805i) q^{95} +23.3541 q^{96} +(119.045 - 119.045i) q^{97} +(-9.55521 - 9.55521i) q^{98} -88.2914i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.36503	−	1.36503i	0.682515	−	0.682515i	−0.278051	−	0.960566i	$-0.589689\pi$
$2$	1.36503	−	1.36503i	0.682515	−	0.682515i	0.960566	+	0.278051i	$0.0896885\pi$
$3$	−3.78207	−	3.78207i	−1.26069	−	1.26069i	−0.950758	−	0.309933i	$-0.899693\pi$
$3$	−3.78207	−	3.78207i	−1.26069	−	1.26069i	−0.309933	−	0.950758i	$-0.600307\pi$
$4$			0.273387i			0.0683467i
$5$	4.98225	+	0.420986i	0.996449	+	0.0841973i
$5$	4.98225	+	0.420986i	0.996449	+	0.0841973i
$6$	−10.3253			−1.72088
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	5.83330	+	5.83330i	0.729163	+	0.729163i
$9$			19.6082i			2.17868i
$10$	7.37557	−	6.22626i	0.737557	−	0.622626i
$11$	−4.50279			−0.409344			−0.204672	−	0.978831i	$-0.565613\pi$
$11$	−4.50279			−0.409344			−0.204672	+	0.978831i	$0.565613\pi$
$12$	1.03397	−	1.03397i	0.0861640	−	0.0861640i
$13$	−4.44076	−	4.44076i	−0.341597	−	0.341597i	0.515371	−	0.856967i	$-0.327654\pi$
$13$	−4.44076	−	4.44076i	−0.341597	−	0.341597i	−0.856967	+	0.515371i	$0.827654\pi$
$14$		−	5.10747i		−	0.364820i
$15$	−17.2510	−	20.4354i	−1.15007	−	1.36236i
$16$	14.8317			0.926982
$17$	−14.0987	+	14.0987i	−0.829332	+	0.829332i	−0.987424	−	0.158092i	$-0.949466\pi$
$17$	−14.0987	+	14.0987i	−0.829332	+	0.829332i	0.158092	+	0.987424i	$0.449466\pi$
$18$	26.7657	+	26.7657i	1.48698	+	1.48698i
$19$			2.86628i			0.150857i	0.997151	+	0.0754285i	$0.0240325\pi$
$19$			2.86628i			0.150857i	−0.997151	+	0.0754285i	$0.975968\pi$
$20$	−0.115092	+	1.36208i	−0.00575460	+	0.0681040i
$21$	−14.1512			−0.673868
$22$	−6.14644	+	6.14644i	−0.279384	+	0.279384i
$23$	−10.2041	−	10.2041i	−0.443657	−	0.443657i	0.449582	−	0.893239i	$-0.351573\pi$
$23$	−10.2041	−	10.2041i	−0.443657	−	0.443657i	−0.893239	+	0.449582i	$0.851573\pi$
$24$		−	44.1239i		−	1.83850i
$25$	24.6455	+	4.19491i	0.985822	+	0.167797i
$26$	−12.1235			−0.466290
$27$	40.1209	−	40.1209i	1.48596	−	1.48596i
$28$	0.511460	+	0.511460i	0.0182664	+	0.0182664i
$29$		−	0.0602879i		−	0.00207889i	−0.999999	−	0.00103945i	$-0.999669\pi$
$29$		−	0.0602879i		−	0.00207889i	0.999999	−	0.00103945i	$-0.000330866\pi$
$30$	−51.4431	−	4.34681i	−1.71477	−	0.144894i
$31$	−3.28496			−0.105966			−0.0529832	−	0.998595i	$-0.516873\pi$
$31$	−3.28496			−0.105966			−0.0529832	+	0.998595i	$0.516873\pi$
$32$	−3.08747	+	3.08747i	−0.0964835	+	0.0964835i
$33$	17.0299	+	17.0299i	0.516057	+	0.516057i
$34$			38.4902i			1.13206i
$35$	10.1085	−	8.53333i	0.288815	−	0.243810i
$36$	−5.36061			−0.148906
$37$	28.4602	−	28.4602i	0.769195	−	0.769195i	−0.208770	−	0.977965i	$-0.566946\pi$
$37$	28.4602	−	28.4602i	0.769195	−	0.769195i	0.977965	+	0.208770i	$0.0669459\pi$
$38$	3.91256	+	3.91256i	0.102962	+	0.102962i
$39$			33.5906i			0.861296i
$40$	26.6072	+	31.5187i	0.665180	+	0.787967i
$41$	−11.8206			−0.288308			−0.144154	−	0.989555i	$-0.546046\pi$
$41$	−11.8206			−0.288308			−0.144154	+	0.989555i	$0.546046\pi$
$42$	−19.3168	+	19.3168i	−0.459925	+	0.459925i
$43$	−6.81044	−	6.81044i	−0.158382	−	0.158382i	0.623467	−	0.781850i	$-0.285724\pi$
$43$	−6.81044	−	6.81044i	−0.158382	−	0.158382i	−0.781850	+	0.623467i	$0.785724\pi$
$44$		−	1.23100i		−	0.0279773i
$45$	−8.25477	+	97.6927i	−0.183439	+	2.17095i
$46$	−27.8578			−0.605605
$47$	−53.7925	+	53.7925i	−1.14452	+	1.14452i	−0.156908	+	0.987613i	$0.550153\pi$
$47$	−53.7925	+	53.7925i	−1.14452	+	1.14452i	−0.987613	+	0.156908i	$0.949847\pi$
$48$	−56.0946	−	56.0946i	−1.16864	−	1.16864i
$49$		−	7.00000i		−	0.142857i
$50$	39.3681	−	27.9157i	0.787362	−	0.558314i
$51$	106.644			2.09106
$52$	1.21404	−	1.21404i	0.0233470	−	0.0233470i
$53$	−52.7265	−	52.7265i	−0.994840	−	0.994840i	0.00514659	−	0.999987i	$-0.498362\pi$
$53$	−52.7265	−	52.7265i	−0.994840	−	0.994840i	−0.999987	+	0.00514659i	$0.998362\pi$
$54$		−	109.532i		−	2.02838i
$55$	−22.4340	−	1.89561i	−0.407891	−	0.0344657i
$56$	21.8262			0.389754
$57$	10.8405	−	10.8405i	0.190184	−	0.190184i
$58$	−0.0822948	−	0.0822948i	−0.00141888	−	0.00141888i
$59$		−	40.0962i		−	0.679597i	−0.940498	−	0.339799i	$-0.889641\pi$
$59$		−	40.0962i		−	0.679597i	0.940498	−	0.339799i	$-0.110359\pi$
$60$	5.58677	−	4.71620i	0.0931129	−	0.0786033i
$61$	64.4732			1.05694			0.528469	−	0.848953i	$-0.322766\pi$
$61$	64.4732			1.05694			0.528469	+	0.848953i	$0.322766\pi$
$62$	−4.48407	+	4.48407i	−0.0723237	+	0.0723237i
$63$	36.6835	+	36.6835i	0.582278	+	0.582278i
$64$			67.7558i			1.05868i
$65$	−20.2555	−	23.9945i	−0.311622	−	0.369145i
$66$	46.4926			0.704433
$67$	30.8766	−	30.8766i	0.460844	−	0.460844i	−0.438088	−	0.898932i	$-0.644344\pi$
$67$	30.8766	−	30.8766i	0.460844	−	0.460844i	0.898932	+	0.438088i	$0.144344\pi$
$68$	−3.85438	−	3.85438i	−0.0566821	−	0.0566821i
$69$			77.1854i			1.11863i
$70$	2.15018	−	25.4467i	0.0307168	−	0.363524i
$71$	28.5426			0.402009			0.201004	−	0.979590i	$-0.435579\pi$
$71$	28.5426			0.402009			0.201004	+	0.979590i	$0.435579\pi$
$72$	−114.380	+	114.380i	−1.58862	+	1.58862i
$73$	−68.5201	−	68.5201i	−0.938631	−	0.938631i	0.0595916	−	0.998223i	$-0.481020\pi$
$73$	−68.5201	−	68.5201i	−0.938631	−	0.938631i	−0.998223	+	0.0595916i	$0.981020\pi$
$74$		−	77.6981i		−	1.04997i
$75$	−77.3458	−	109.077i	−1.03128	−	1.45436i
$76$	−0.783604			−0.0103106
$77$	−8.42394	+	8.42394i	−0.109402	+	0.109402i
$78$	45.8521	+	45.8521i	0.587848	+	0.587848i
$79$		−	60.6193i		−	0.767333i	−0.923472	−	0.383666i	$-0.874661\pi$
$79$		−	60.6193i		−	0.767333i	0.923472	−	0.383666i	$-0.125339\pi$
$80$	73.8952	+	6.24395i	0.923690	+	0.0780494i
$81$	−127.007			−1.56798
$82$	−16.1355	+	16.1355i	−0.196774	+	0.196774i
$83$	105.994	+	105.994i	1.27704	+	1.27704i	0.942316	+	0.334725i	$0.108643\pi$
$83$	105.994	+	105.994i	1.27704	+	1.27704i	0.334725	+	0.942316i	$0.391357\pi$
$84$		−	3.86876i		−	0.0460566i
$85$	−76.1783	+	64.3076i	−0.896215	+	0.756560i
$86$	−18.5929			−0.216197
$87$	−0.228013	+	0.228013i	−0.00262084	+	0.00262084i
$88$	−26.2661	−	26.2661i	−0.298479	−	0.298479i
$89$			70.6453i			0.793767i	0.917869	+	0.396884i	$0.129908\pi$
$89$			70.6453i			0.793767i	−0.917869	+	0.396884i	$0.870092\pi$
$90$	122.085	+	144.621i	1.35650	+	1.60690i
$91$	−16.6158			−0.182591
$92$	2.78967	−	2.78967i	0.0303225	−	0.0303225i
$93$	12.4240	+	12.4240i	0.133591	+	0.133591i
$94$			146.857i			1.56231i
$95$	−1.20667	+	14.2805i	−0.0127018	+	0.150321i
$96$	23.3541			0.243272
$97$	119.045	−	119.045i	1.22727	−	1.22727i	0.262274	−	0.964993i	$-0.415527\pi$
$97$	119.045	−	119.045i	1.22727	−	1.22727i	0.964993	−	0.262274i	$-0.0844726\pi$
$98$	−9.55521	−	9.55521i	−0.0975021	−	0.0975021i
$99$		−	88.2914i		−	0.891832i
$100$	−1.14683	+	6.73776i	−0.0114683	+	0.0673776i
$101$	83.8955			0.830648			0.415324	−	0.909673i	$-0.363668\pi$
$101$	83.8955			0.830648			0.415324	+	0.909673i	$0.363668\pi$
$102$	145.573	−	145.573i	1.42718	−	1.42718i
$103$	−58.6312	−	58.6312i	−0.569235	−	0.569235i	0.362679	−	0.931914i	$-0.381862\pi$
$103$	−58.6312	−	58.6312i	−0.569235	−	0.569235i	−0.931914	+	0.362679i	$0.881862\pi$
$104$		−	51.8086i		−	0.498159i
$105$	−70.5049	−	5.95747i	−0.671475	−	0.0567378i
$106$	−143.947			−1.35799
$107$	−55.6484	+	55.6484i	−0.520079	+	0.520079i	−0.917595	−	0.397516i	$-0.869872\pi$
$107$	−55.6484	+	55.6484i	−0.520079	+	0.520079i	0.397516	+	0.917595i	$0.369872\pi$
$108$	10.9685	+	10.9685i	0.101560	+	0.101560i
$109$			37.8646i			0.347382i	0.984800	+	0.173691i	$0.0555693\pi$
$109$			37.8646i			0.347382i	−0.984800	+	0.173691i	$0.944431\pi$
$110$	−33.2106	+	28.0355i	−0.301915	+	0.254868i
$111$	−215.277			−1.93943
$112$	27.7476	−	27.7476i	0.247746	−	0.247746i
$113$	92.7728	+	92.7728i	0.820998	+	0.820998i	0.986251	−	0.165253i	$-0.0528440\pi$
$113$	92.7728	+	92.7728i	0.820998	+	0.820998i	−0.165253	+	0.986251i	$0.552844\pi$
$114$		−	29.5952i		−	0.259607i
$115$	−46.5436	−	55.1352i	−0.404727	−	0.479436i
$116$	0.0164819			0.000142086
$117$	87.0751	−	87.0751i	0.744232	−	0.744232i
$118$	−54.7326	−	54.7326i	−0.463835	−	0.463835i
$119$			52.7523i			0.443297i
$120$	18.5756	−	219.836i	0.154796	−	1.83197i
$121$	−100.725			−0.832437
$122$	88.0078	−	88.0078i	0.721376	−	0.721376i
$123$	44.7064	+	44.7064i	0.363467	+	0.363467i
$124$		−	0.898065i		−	0.00724246i
$125$	121.024	+	31.2755i	0.968193	+	0.250204i
$126$	100.148			0.794827
$127$	−142.296	+	142.296i	−1.12044	+	1.12044i	−0.128764	+	0.991675i	$0.541101\pi$
$127$	−142.296	+	142.296i	−1.12044	+	1.12044i	−0.991675	+	0.128764i	$0.958899\pi$
$128$	80.1389	+	80.1389i	0.626085	+	0.626085i
$129$			51.5152i			0.399343i
$130$	−60.4025	−	5.10385i	−0.464634	−	0.0392603i
$131$	−97.3469			−0.743106			−0.371553	−	0.928412i	$-0.621175\pi$
$131$	−97.3469			−0.743106			−0.371553	+	0.928412i	$0.621175\pi$
$132$	−4.65574	+	4.65574i	−0.0352708	+	0.0352708i
$133$	5.36233	+	5.36233i	0.0403182	+	0.0403182i
$134$		−	84.2948i		−	0.629066i
$135$	216.782	−	183.002i	1.60579	−	1.35557i
$136$	−164.483			−1.20944
$137$	−145.197	+	145.197i	−1.05984	+	1.05984i	−0.0617430	+	0.998092i	$0.519666\pi$
$137$	−145.197	+	145.197i	−1.05984	+	1.05984i	−0.998092	+	0.0617430i	$0.980334\pi$
$138$	105.360	+	105.360i	0.763481	+	0.763481i
$139$		−	30.2676i		−	0.217753i	−0.994055	−	0.108876i	$-0.965275\pi$
$139$		−	30.2676i		−	0.217753i	0.994055	−	0.108876i	$-0.0347252\pi$
$140$	2.33290	+	2.76353i	0.0166636	+	0.0197395i
$141$	406.894			2.88578
$142$	38.9615	−	38.9615i	0.274377	−	0.274377i
$143$	19.9958	+	19.9958i	0.139831	+	0.139831i
$144$			290.823i			2.01960i
$145$	0.0253804	−	0.300369i	0.000175037	−	0.00207151i
$146$	−187.064			−1.28126
$147$	−26.4745	+	26.4745i	−0.180099	+	0.180099i
$148$	7.78064	+	7.78064i	0.0525719	+	0.0525719i
$149$		−	268.583i		−	1.80257i	−0.433228	−	0.901285i	$-0.642625\pi$
$149$		−	268.583i		−	1.80257i	0.433228	−	0.901285i	$-0.357375\pi$
$150$	−254.472	−	43.3137i	−1.69648	−	0.288758i
$151$	231.604			1.53380			0.766901	−	0.641765i	$-0.221798\pi$
$151$	231.604			1.53380			0.766901	+	0.641765i	$0.221798\pi$
$152$	−16.7199	+	16.7199i	−0.109999	+	0.109999i
$153$	−276.449	−	276.449i	−1.80685	−	1.80685i
$154$			22.9979i			0.149337i
$155$	−16.3665	−	1.38292i	−0.105590	−	0.00892209i
$156$	−9.18321			−0.0588667
$157$	−27.5058	+	27.5058i	−0.175196	+	0.175196i	−0.789258	−	0.614062i	$-0.789535\pi$
$157$	−27.5058	+	27.5058i	−0.175196	+	0.175196i	0.614062	+	0.789258i	$0.289535\pi$
$158$	−82.7472	−	82.7472i	−0.523716	−	0.523716i
$159$			398.831i			2.50837i
$160$	−16.6823	+	14.0828i	−0.104264	+	0.0880172i
$161$	−38.1803			−0.237145
$162$	−173.368	+	173.368i	−1.07017	+	1.07017i
$163$	192.097	+	192.097i	1.17851	+	1.17851i	0.980124	+	0.198385i	$0.0635695\pi$
$163$	192.097	+	192.097i	1.17851	+	1.17851i	0.198385	+	0.980124i	$0.436431\pi$
$164$		−	3.23160i		−	0.0197049i
$165$	77.6777	+	92.0164i	0.470774	+	0.557675i
$166$	289.371			1.74320
$167$	50.4849	−	50.4849i	0.302305	−	0.302305i	−0.539610	−	0.841915i	$-0.681428\pi$
$167$	50.4849	−	50.4849i	0.302305	−	0.302305i	0.841915	+	0.539610i	$0.181428\pi$
$168$	−82.5483	−	82.5483i	−0.491359	−	0.491359i
$169$		−	129.559i		−	0.766623i
$170$	−16.2038	+	191.767i	−0.0953167	+	1.12804i
$171$	−56.2026			−0.328670
$172$	1.86188	−	1.86188i	0.0108249	−	0.0108249i
$173$	23.8924	+	23.8924i	0.138107	+	0.138107i	0.772780	−	0.634674i	$-0.218865\pi$
$173$	23.8924	+	23.8924i	0.138107	+	0.138107i	−0.634674	+	0.772780i	$0.718865\pi$
$174$			0.622490i			0.00357753i
$175$	53.9556	−	38.2596i	0.308317	−	0.218626i
$176$	−66.7841			−0.379455
$177$	−151.647	+	151.647i	−0.856762	+	0.856762i
$178$	96.4329	+	96.4329i	0.541758	+	0.541758i
$179$		−	98.0752i		−	0.547906i	−0.961743	−	0.273953i	$-0.911669\pi$
$179$		−	98.0752i		−	0.547906i	0.961743	−	0.273953i	$-0.0883313\pi$
$180$	−26.7079	−	2.25674i	−0.148377	−	0.0125375i
$181$	107.659			0.594799			0.297400	−	0.954753i	$-0.403881\pi$
$181$	107.659			0.594799			0.297400	+	0.954753i	$0.403881\pi$
$182$	−22.6811	+	22.6811i	−0.124621	+	0.124621i
$183$	−243.842	−	243.842i	−1.33247	−	1.33247i
$184$		−	119.047i		−	0.646996i
$185$	153.777	−	129.814i	0.831228	−	0.701700i
$186$	33.9182			0.182356
$187$	63.4832	−	63.4832i	0.339483	−	0.339483i
$188$	−14.7061	−	14.7061i	−0.0782242	−	0.0782242i
$189$		−	150.118i		−	0.794278i
$190$	17.8462	+	21.1405i	0.0939275	+	0.111266i
$191$	−136.553			−0.714935			−0.357467	−	0.933926i	$-0.616360\pi$
$191$	−136.553			−0.714935			−0.357467	+	0.933926i	$0.616360\pi$
$192$	256.258	−	256.258i	1.33467	−	1.33467i
$193$	38.3841	+	38.3841i	0.198881	+	0.198881i	0.799520	−	0.600639i	$-0.205087\pi$
$193$	38.3841	+	38.3841i	0.198881	+	0.198881i	−0.600639	+	0.799520i	$0.705087\pi$
$194$		−	325.000i		−	1.67526i
$195$	−14.1412	+	167.356i	−0.0725188	+	0.858238i
$196$	1.91371			0.00976381
$197$	142.649	−	142.649i	0.724106	−	0.724106i	−0.245333	−	0.969439i	$-0.578897\pi$
$197$	142.649	−	142.649i	0.724106	−	0.724106i	0.969439	+	0.245333i	$0.0788973\pi$
$198$	−120.520	−	120.520i	−0.608689	−	0.608689i
$199$			95.7978i			0.481396i	0.970600	+	0.240698i	$0.0773763\pi$
$199$			95.7978i			0.481396i	−0.970600	+	0.240698i	$0.922624\pi$
$200$	119.295	+	168.235i	0.596473	+	0.841175i
$201$	−233.555			−1.16196
$202$	114.520	−	114.520i	0.566930	−	0.566930i
$203$	−0.112788	−	0.112788i	−0.000555608	−	0.000555608i
$204$			29.1551i			0.142917i
$205$	−58.8932	−	4.97632i	−0.287284	−	0.0242747i
$206$	−160.067			−0.777022
$207$	200.084	−	200.084i	0.966588	−	0.966588i
$208$	−65.8641	−	65.8641i	−0.316654	−	0.316654i
$209$		−	12.9063i		−	0.0617525i
$210$	−104.373	+	88.1091i	−0.497016	+	0.419567i
$211$	−162.439			−0.769855			−0.384927	−	0.922947i	$-0.625773\pi$
$211$	−162.439			−0.769855			−0.384927	+	0.922947i	$0.625773\pi$
$212$	14.4147	−	14.4147i	0.0679940	−	0.0679940i
$213$	−107.950	−	107.950i	−0.506809	−	0.506809i
$214$			151.923i			0.709923i
$215$	−31.0642	−	36.7984i	−0.144485	−	0.171155i
$216$	468.074			2.16701
$217$	−6.14560	+	6.14560i	−0.0283207	+	0.0283207i
$218$	51.6863	+	51.6863i	0.237093	+	0.237093i
$219$			518.296i			2.36665i
$220$	0.518235	−	6.13315i	0.00235561	−	0.0278780i
$221$	125.217			0.566595
$222$	−293.860	+	293.860i	−1.32369	+	1.32369i
$223$	206.322	+	206.322i	0.925210	+	0.925210i	0.997392	−	0.0721816i	$-0.0229961\pi$
$223$	206.322	+	206.322i	0.925210	+	0.925210i	−0.0721816	+	0.997392i	$0.522996\pi$
$224$			11.5523i			0.0515726i
$225$	−82.2546	+	483.254i	−0.365576	+	2.14779i
$226$	253.275			1.12069
$227$	−144.195	+	144.195i	−0.635221	+	0.635221i	−0.949373	−	0.314152i	$-0.898280\pi$
$227$	−144.195	+	144.195i	−0.635221	+	0.635221i	0.314152	+	0.949373i	$0.398280\pi$
$228$	2.96365	+	2.96365i	0.0129985	+	0.0129985i
$229$		−	336.334i		−	1.46871i	−0.678767	−	0.734353i	$-0.737486\pi$
$229$		−	336.334i		−	1.46871i	0.678767	−	0.734353i	$-0.262514\pi$
$230$	−138.795	−	11.7278i	−0.603454	−	0.0509903i
$231$	63.7200			0.275844
$232$	0.351678	−	0.351678i	0.00151585	−	0.00151585i
$233$	−40.0522	−	40.0522i	−0.171898	−	0.171898i	0.615915	−	0.787813i	$-0.288787\pi$
$233$	−40.0522	−	40.0522i	−0.171898	−	0.171898i	−0.787813	+	0.615915i	$0.788787\pi$
$234$		−	237.720i		−	1.01590i
$235$	−290.653	+	245.361i	−1.23682	+	1.04409i
$236$	10.9618			0.0464482
$237$	−229.267	+	229.267i	−0.967370	+	0.967370i
$238$	72.0085	+	72.0085i	0.302557	+	0.302557i
$239$		−	132.495i		−	0.554374i	−0.960816	−	0.277187i	$-0.910598\pi$
$239$		−	132.495i		−	0.554374i	0.960816	−	0.277187i	$-0.0894021\pi$
$240$	−255.862	−	303.092i	−1.06609	−	1.26288i
$241$	−19.6055			−0.0813505			−0.0406752	−	0.999172i	$-0.512951\pi$
$241$	−19.6055			−0.0813505			−0.0406752	+	0.999172i	$0.512951\pi$
$242$	−137.493	+	137.493i	−0.568151	+	0.568151i
$243$	119.261	+	119.261i	0.490784	+	0.490784i
$244$			17.6261i			0.0722382i
$245$	2.94690	−	34.8757i	0.0120282	−	0.142350i
$246$	122.051			0.496143
$247$	12.7285	−	12.7285i	0.0515323	−	0.0515323i
$248$	−19.1622	−	19.1622i	−0.0772668	−	0.0772668i
$249$		−	801.757i		−	3.21991i
$250$	207.894	−	122.510i	0.831574	−	0.490038i
$251$	−212.595			−0.846991			−0.423495	−	0.905898i	$-0.639197\pi$
$251$	−212.595			−0.846991			−0.423495	+	0.905898i	$0.639197\pi$
$252$	−10.0288	+	10.0288i	−0.0397968	+	0.0397968i
$253$	45.9469	+	45.9469i	0.181608	+	0.181608i
$254$			388.476i			1.52943i
$255$	531.328	+	44.8958i	2.08364	+	0.176062i
$256$	−52.2395			−0.204060
$257$	84.1625	−	84.1625i	0.327480	−	0.327480i	−0.524147	−	0.851628i	$-0.675616\pi$
$257$	84.1625	−	84.1625i	0.327480	−	0.327480i	0.851628	+	0.524147i	$0.175616\pi$
$258$	70.3198	+	70.3198i	0.272557	+	0.272557i
$259$		−	106.488i		−	0.411152i
$260$	6.55976	−	5.53757i	0.0252299	−	0.0212984i
$261$	1.18214			0.00452926
$262$	−132.881	+	132.881i	−0.507181	+	0.507181i
$263$	−1.16948	−	1.16948i	−0.00444668	−	0.00444668i	0.704880	−	0.709327i	$-0.251001\pi$
$263$	−1.16948	−	1.16948i	−0.00444668	−	0.00444668i	−0.709327	+	0.704880i	$0.751001\pi$
$264$			198.681i			0.752579i
$265$	−240.499	−	284.894i	−0.907545	−	1.07507i
$266$	14.6395			0.0550356
$267$	267.186	−	267.186i	1.00070	−	1.00070i
$268$	8.44124	+	8.44124i	0.0314972	+	0.0314972i
$269$			309.920i			1.15212i	0.817407	+	0.576060i	$0.195411\pi$
$269$			309.920i			1.15212i	−0.817407	+	0.576060i	$0.804589\pi$
$270$	46.1116	−	545.717i	0.170784	−	2.02117i
$271$	255.336			0.942199			0.471100	−	0.882080i	$-0.343857\pi$
$271$	255.336			0.942199			0.471100	+	0.882080i	$0.343857\pi$
$272$	−209.107	+	209.107i	−0.768776	+	0.768776i
$273$	62.8422	+	62.8422i	0.230191	+	0.230191i
$274$			396.398i			1.44671i
$275$	−110.974	−	18.8888i	−0.403540	−	0.0686866i
$276$	−21.1015			−0.0764545
$277$	−178.950	+	178.950i	−0.646028	+	0.646028i	−0.952031	−	0.306003i	$-0.901008\pi$
$277$	−178.950	+	178.950i	−0.646028	+	0.646028i	0.306003	+	0.952031i	$0.401008\pi$
$278$	−41.3162	−	41.3162i	−0.148619	−	0.148619i
$279$		−	64.4121i		−	0.230868i
$280$	108.744	+	9.18854i	0.388370	+	0.0328162i
$281$	56.1473			0.199812			0.0999062	−	0.994997i	$-0.468146\pi$
$281$	56.1473			0.199812			0.0999062	+	0.994997i	$0.468146\pi$
$282$	555.423	−	555.423i	1.96958	−	1.96958i
$283$	78.0403	+	78.0403i	0.275761	+	0.275761i	0.831414	−	0.555653i	$-0.187532\pi$
$283$	78.0403	+	78.0403i	0.275761	+	0.275761i	−0.555653	+	0.831414i	$0.687532\pi$
$284$			7.80317i			0.0274760i
$285$	58.5737	−	49.4463i	0.205522	−	0.173496i
$286$	54.5897			0.190873
$287$	−22.1143	+	22.1143i	−0.0770534	+	0.0770534i
$288$	−60.5396	−	60.5396i	−0.210207	−	0.210207i
$289$		−	108.544i		−	0.375585i
$290$	−0.375368	−	0.444658i	−0.00129437	−	0.00153330i
$291$	−900.474			−3.09441
$292$	18.7325	−	18.7325i	0.0641523	−	0.0641523i
$293$	22.9818	+	22.9818i	0.0784360	+	0.0784360i	0.745236	−	0.666800i	$-0.232337\pi$
$293$	22.9818	+	22.9818i	0.0784360	+	0.0784360i	−0.666800	+	0.745236i	$0.732337\pi$
$294$			72.2770i			0.245840i
$295$	16.8800	−	199.769i	0.0572202	−	0.677184i
$296$	332.034			1.12174
$297$	−180.656	+	180.656i	−0.608268	+	0.608268i
$298$	−366.624	−	366.624i	−1.23028	−	1.23028i
$299$			90.6280i			0.303104i
$300$	29.8201	−	21.1453i	0.0994004	−	0.0704843i
$301$	−25.4823			−0.0846589
$302$	316.147	−	316.147i	1.04684	−	1.04684i
$303$	−317.299	−	317.299i	−1.04719	−	1.04719i
$304$			42.5119i			0.139842i
$305$	321.221	+	27.1423i	1.05318	+	0.0889913i
$306$	−754.721			−2.46641
$307$	161.013	−	161.013i	0.524473	−	0.524473i	−0.394446	−	0.918919i	$-0.629063\pi$
$307$	161.013	−	161.013i	0.524473	−	0.524473i	0.918919	+	0.394446i	$0.129063\pi$
$308$	−2.30299	−	2.30299i	−0.00747725	−	0.00747725i
$309$			443.495i			1.43526i
$310$	−24.2285	+	20.4530i	−0.0781564	+	0.0659774i
$311$	−253.310			−0.814501			−0.407251	−	0.913316i	$-0.633512\pi$
$311$	−253.310			−0.814501			−0.407251	+	0.913316i	$0.633512\pi$
$312$	−195.944	+	195.944i	−0.628025	+	0.628025i
$313$	−139.199	−	139.199i	−0.444724	−	0.444724i	0.448872	−	0.893596i	$-0.351826\pi$
$313$	−139.199	−	139.199i	−0.444724	−	0.444724i	−0.893596	+	0.448872i	$0.851826\pi$
$314$			75.0924i			0.239148i
$315$	167.323	+	198.210i	0.531184	+	0.629237i
$316$	16.5725			0.0524447
$317$	103.014	−	103.014i	0.324966	−	0.324966i	−0.525703	−	0.850668i	$-0.676198\pi$
$317$	103.014	−	103.014i	0.324966	−	0.324966i	0.850668	+	0.525703i	$0.176198\pi$
$318$	544.417	+	544.417i	1.71200	+	1.71200i
$319$			0.271464i			0.000850984i
$320$	−28.5243	+	337.576i	−0.0891384	+	1.05493i
$321$	420.933			1.31132
$322$	−52.1172	+	52.1172i	−0.161855	+	0.161855i
$323$	−40.4107	−	40.4107i	−0.125111	−	0.125111i
$324$		−	34.7219i		−	0.107166i
$325$	−90.8163	−	128.074i	−0.279435	−	0.394072i
$326$	524.436			1.60870
$327$	143.207	−	143.207i	0.437941	−	0.437941i
$328$	−68.9532	−	68.9532i	−0.210223	−	0.210223i
$329$			201.273i			0.611772i
$330$	231.637	+	19.5727i	0.701932	+	0.0593113i
$331$	−277.839			−0.839393			−0.419696	−	0.907665i	$-0.637863\pi$
$331$	−277.839			−0.839393			−0.419696	+	0.907665i	$0.637863\pi$
$332$	−28.9774	+	28.9774i	−0.0872815	+	0.0872815i
$333$	558.053	+	558.053i	1.67583	+	1.67583i
$334$		−	137.827i		−	0.412655i
$335$	166.833	−	140.836i	0.498009	−	0.420406i
$336$	−209.887			−0.624663
$337$	−445.329	+	445.329i	−1.32145	+	1.32145i	−0.408849	+	0.912602i	$0.634070\pi$
$337$	−445.329	+	445.329i	−1.32145	+	1.32145i	−0.912602	+	0.408849i	$0.865930\pi$
$338$	−176.852	−	176.852i	−0.523232	−	0.523232i
$339$		−	701.747i		−	2.07005i
$340$	−17.5808	−	20.8261i	−0.0517084	−	0.0612533i
$341$	14.7915			0.0433768
$342$	−76.7182	+	76.7182i	−0.224322	+	0.224322i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$		−	79.4547i		−	0.230973i
$345$	−32.4940	+	384.556i	−0.0941855	+	1.11466i
$346$	65.2278			0.188520
$347$	254.071	−	254.071i	0.732193	−	0.732193i	−0.238861	−	0.971054i	$-0.576774\pi$
$347$	254.071	−	254.071i	0.732193	−	0.732193i	0.971054	+	0.238861i	$0.0767741\pi$
$348$	−0.0623358	−	0.0623358i	−0.000179126	−	0.000179126i
$349$			673.963i			1.93113i	0.260168	+	0.965563i	$0.416222\pi$
$349$			673.963i			1.93113i	−0.260168	+	0.965563i	$0.583778\pi$
$350$	21.4254	−	125.876i	0.0612155	−	0.359647i
$351$	−356.334			−1.01520
$352$	13.9022	−	13.9022i	0.0394950	−	0.0394950i
$353$	−22.6334	−	22.6334i	−0.0641172	−	0.0641172i	0.674321	−	0.738438i	$-0.264436\pi$
$353$	−22.6334	−	22.6334i	−0.0641172	−	0.0641172i	−0.738438	+	0.674321i	$0.764436\pi$
$354$			414.005i			1.16951i
$355$	142.206	+	12.0161i	0.400581	+	0.0338480i
$356$	−19.3135			−0.0542513
$357$	199.513	−	199.513i	0.558860	−	0.558860i
$358$	−133.876	−	133.876i	−0.373954	−	0.373954i
$359$			358.226i			0.997843i	0.866647	+	0.498921i	$0.166270\pi$
$359$			358.226i			0.997843i	−0.866647	+	0.498921i	$0.833730\pi$
$360$	−618.023	+	521.718i	−1.71673	+	1.44922i
$361$	352.784			0.977242
$362$	146.957	−	146.957i	0.405959	−	0.405959i
$363$	380.949	+	380.949i	1.04945	+	1.04945i
$364$		−	4.54254i		−	0.0124795i
$365$	−312.538	−	370.230i	−0.856268	−	1.01433i
$366$	−665.704			−1.81886
$367$	142.063	−	142.063i	0.387092	−	0.387092i	−0.486557	−	0.873649i	$-0.661747\pi$
$367$	142.063	−	142.063i	0.387092	−	0.387092i	0.873649	+	0.486557i	$0.161747\pi$
$368$	−151.344	−	151.344i	−0.411262	−	0.411262i
$369$		−	231.780i		−	0.628131i
$370$	32.7098	−	387.111i	0.0884050	−	1.04625i
$371$	−197.285			−0.531764
$372$	−3.39655	+	3.39655i	−0.00913050	+	0.00913050i
$373$	−71.2174	−	71.2174i	−0.190931	−	0.190931i	0.605167	−	0.796099i	$-0.293106\pi$
$373$	−71.2174	−	71.2174i	−0.190931	−	0.190931i	−0.796099	+	0.605167i	$0.793106\pi$
$374$		−	173.313i		−	0.463404i
$375$	−339.436	−	576.009i	−0.905162	−	1.53602i
$376$	−627.575			−1.66908
$377$	−0.267724	+	0.267724i	−0.000710144	+	0.000710144i
$378$	−204.916	−	204.916i	−0.542106	−	0.542106i
$379$		−	284.997i		−	0.751970i	−0.926626	−	0.375985i	$-0.877304\pi$
$379$		−	284.997i		−	0.751970i	0.926626	−	0.375985i	$-0.122696\pi$
$380$	−3.90411	−	0.329887i	−0.0102740	−	0.000868123i
$381$	1076.35			2.82506
$382$	−186.398	+	186.398i	−0.487954	+	0.487954i
$383$	142.454	+	142.454i	0.371943	+	0.371943i	0.868184	−	0.496242i	$-0.165287\pi$
$383$	142.454	+	142.454i	0.371943	+	0.371943i	−0.496242	+	0.868184i	$0.665287\pi$
$384$		−	606.182i		−	1.57860i
$385$	−45.5165	+	38.4238i	−0.118225	+	0.0998021i
$386$	104.791			0.271479
$387$	133.540	−	133.540i	0.345065	−	0.345065i
$388$	32.5453	+	32.5453i	0.0838797	+	0.0838797i
$389$			143.853i			0.369801i	0.982757	+	0.184900i	$0.0591963\pi$
$389$			143.853i			0.369801i	−0.982757	+	0.184900i	$0.940804\pi$
$390$	209.143	+	247.750i	0.536265	+	0.635256i
$391$	287.728			0.735878
$392$	40.8331	−	40.8331i	0.104166	−	0.104166i
$393$	368.173	+	368.173i	0.936827	+	0.936827i
$394$		−	389.440i		−	0.988426i
$395$	25.5199	−	302.020i	0.0646073	−	0.764608i
$396$	24.1377			0.0609538
$397$	−284.927	+	284.927i	−0.717701	+	0.717701i	−0.968134	−	0.250433i	$-0.919427\pi$
$397$	−284.927	+	284.927i	−0.717701	+	0.717701i	0.250433	+	0.968134i	$0.419427\pi$
$398$	130.767	+	130.767i	0.328560	+	0.328560i
$399$		−	40.5614i		−	0.101658i
$400$	365.536	+	62.2178i	0.913839	+	0.155544i
$401$	231.528			0.577377			0.288688	−	0.957423i	$-0.406781\pi$
$401$	231.528			0.577377			0.288688	+	0.957423i	$0.406781\pi$
$402$	−318.809	+	318.809i	−0.793058	+	0.793058i
$403$	14.5877	+	14.5877i	0.0361978	+	0.0361978i
$404$			22.9359i			0.0567721i
$405$	−632.778	−	53.4680i	−1.56241	−	0.132020i
$406$	−0.307919			−0.000758421
$407$	−128.150	+	128.150i	−0.314866	+	0.314866i
$408$	622.088	+	622.088i	1.52473	+	1.52473i
$409$		−	10.4783i		−	0.0256193i	−0.999918	−	0.0128096i	$-0.995922\pi$
$409$		−	10.4783i		−	0.0256193i	0.999918	−	0.0128096i	$-0.00407755\pi$
$410$	−87.1838	+	73.5981i	−0.212643	+	0.179508i
$411$	1098.29			2.67225
$412$	16.0290	−	16.0290i	0.0389053	−	0.0389053i
$413$	−75.0132	−	75.0132i	−0.181630	−	0.181630i
$414$		−	546.241i		−	1.31942i
$415$	483.468	+	572.712i	1.16498	+	1.38003i
$416$	27.4214			0.0659169
$417$	−114.474	+	114.474i	−0.274519	+	0.274519i
$418$	−17.6174	−	17.6174i	−0.0421470	−	0.0421470i
$419$		−	538.051i		−	1.28413i	−0.766650	−	0.642065i	$-0.778078\pi$
$419$		−	538.051i		−	1.28413i	0.766650	−	0.642065i	$-0.221922\pi$
$420$	1.62869	−	19.2751i	0.00387784	−	0.0458931i
$421$	−568.844			−1.35117			−0.675587	−	0.737280i	$-0.736110\pi$
$421$	−568.844			−1.35117			−0.675587	+	0.737280i	$0.736110\pi$
$422$	−221.735	+	221.735i	−0.525437	+	0.525437i
$423$	−1054.77	−	1054.77i	−2.49355	−	2.49355i
$424$		−	615.139i		−	1.45080i
$425$	−406.612	+	288.326i	−0.956733	+	0.678415i
$426$	−294.711			−0.691809
$427$	120.618	−	120.618i	0.282478	−	0.282478i
$428$	−15.2135	−	15.2135i	−0.0355456	−	0.0355456i
$429$		−	151.251i		−	0.352567i
$430$	−92.6345	−	7.82736i	−0.215429	−	0.0182032i
$431$	337.569			0.783223			0.391612	−	0.920131i	$-0.371918\pi$
$431$	337.569			0.783223			0.391612	+	0.920131i	$0.371918\pi$
$432$	595.061	−	595.061i	1.37746	−	1.37746i
$433$	−319.625	−	319.625i	−0.738164	−	0.738164i	0.234059	−	0.972222i	$-0.424799\pi$
$433$	−319.625	−	319.625i	−0.738164	−	0.738164i	−0.972222	+	0.234059i	$0.924799\pi$
$434$			16.7779i			0.0386587i
$435$	−1.23201	+	1.04003i	−0.00283221	+	0.00239087i
$436$	−10.3517			−0.0237424
$437$	29.2479	−	29.2479i	0.0669288	−	0.0669288i
$438$	707.490	+	707.490i	1.61527	+	1.61527i
$439$			615.599i			1.40228i	0.713026	+	0.701138i	$0.247324\pi$
$439$			615.599i			1.40228i	−0.713026	+	0.701138i	$0.752676\pi$
$440$	−119.807	−	141.922i	−0.272288	−	0.322550i
$441$	137.257			0.311241
$442$	170.926	−	170.926i	0.386709	−	0.386709i
$443$	−429.539	−	429.539i	−0.969615	−	0.969615i	0.0299367	−	0.999552i	$-0.490469\pi$
$443$	−429.539	−	429.539i	−0.969615	−	0.969615i	−0.999552	+	0.0299367i	$0.990469\pi$
$444$		−	58.8539i		−	0.132554i
$445$	−29.7407	+	351.972i	−0.0668330	+	0.790949i
$446$	563.271			1.26294
$447$	−1015.80	+	1015.80i	−2.27248	+	2.27248i
$448$	126.760	+	126.760i	0.282945	+	0.282945i
$449$			685.059i			1.52574i	0.646550	+	0.762872i	$0.276211\pi$
$449$			685.059i			1.52574i	−0.646550	+	0.762872i	$0.723789\pi$
$450$	547.376	+	771.936i	1.21639	+	1.71541i
$451$	53.2257			0.118017
$452$	−25.3629	+	25.3629i	−0.0561125	+	0.0561125i
$453$	−875.944	−	875.944i	−1.93365	−	1.93365i
$454$			393.661i			0.867095i
$455$	−82.7840	−	6.99503i	−0.181943	−	0.0153737i
$456$	126.472			0.277350
$457$	−553.707	+	553.707i	−1.21161	+	1.21161i	−0.241116	+	0.970496i	$0.577514\pi$
$457$	−553.707	+	553.707i	−1.21161	+	1.21161i	−0.970496	+	0.241116i	$0.922486\pi$
$458$	−459.106	−	459.106i	−1.00241	−	1.00241i
$459$			1131.30i			2.46471i
$460$	15.0732	−	12.7244i	0.0327679	−	0.0276617i
$461$	−435.674			−0.945062			−0.472531	−	0.881314i	$-0.656660\pi$
$461$	−435.674			−0.945062			−0.472531	+	0.881314i	$0.656660\pi$
$462$	86.9796	−	86.9796i	0.188268	−	0.188268i
$463$	313.651	+	313.651i	0.677432	+	0.677432i	0.959418	−	0.281987i	$-0.0909934\pi$
$463$	313.651	+	313.651i	0.677432	+	0.677432i	−0.281987	+	0.959418i	$0.590993\pi$
$464$		−	0.894173i		−	0.00192710i
$465$	56.6689	+	67.1296i	0.121869	+	0.144365i
$466$	−109.345			−0.234646
$467$	178.187	−	178.187i	0.381557	−	0.381557i	−0.490106	−	0.871663i	$-0.663042\pi$
$467$	178.187	−	178.187i	0.381557	−	0.381557i	0.871663	+	0.490106i	$0.163042\pi$
$468$	23.8052	+	23.8052i	0.0508658	+	0.0508658i
$469$		−	115.529i		−	0.246332i
$470$	−61.8247	+	731.676i	−0.131542	+	1.55676i
$471$	208.058			0.441736
$472$	233.893	−	233.893i	0.495537	−	0.495537i
$473$	30.6660	+	30.6660i	0.0648329	+	0.0648329i
$474$			625.912i			1.32049i
$475$	−12.0238	+	70.6411i	−0.0253133	+	0.148718i
$476$	−14.4218			−0.0302979
$477$	1033.87	−	1033.87i	2.16744	−	2.16744i
$478$	−180.860	−	180.860i	−0.378368	−	0.378368i
$479$			541.433i			1.13034i	0.824974	+	0.565171i	$0.191190\pi$
$479$			541.433i			1.13034i	−0.824974	+	0.565171i	$0.808810\pi$
$480$	116.356	+	9.83175i	0.242408	+	0.0204828i
$481$	−252.770			−0.525509
$482$	−26.7620	+	26.7620i	−0.0555229	+	0.0555229i
$483$	144.401	+	144.401i	0.298966	+	0.298966i
$484$		−	27.5368i		−	0.0568943i
$485$	643.228	−	542.995i	1.32624	−	1.11958i
$486$	325.589			0.669935
$487$	344.724	−	344.724i	0.707852	−	0.707852i	−0.258231	−	0.966083i	$-0.583140\pi$
$487$	344.724	−	344.724i	0.707852	−	0.707852i	0.966083	+	0.258231i	$0.0831396\pi$
$488$	376.092	+	376.092i	0.770679	+	0.770679i
$489$		−	1453.05i		−	2.97147i
$490$	−43.5838	−	51.6290i	−0.0889465	−	0.105365i
$491$	−636.355			−1.29604			−0.648019	−	0.761624i	$-0.724402\pi$
$491$	−636.355			−1.29604			−0.648019	+	0.761624i	$0.724402\pi$
$492$	−12.2221	+	12.2221i	−0.0248417	+	0.0248417i
$493$	0.849979	+	0.849979i	0.00172409	+	0.00172409i
$494$		−	34.7495i		−	0.0703431i
$495$	37.1695	−	439.889i	0.0750898	−	0.888665i
$496$	−48.7216			−0.0982290
$497$	53.3983	−	53.3983i	0.107441	−	0.107441i
$498$	−1094.42	−	1094.42i	−2.19764	−	2.19764i
$499$		−	554.687i		−	1.11160i	−0.831317	−	0.555799i	$-0.812413\pi$
$499$		−	554.687i		−	1.11160i	0.831317	−	0.555799i	$-0.187587\pi$
$500$	−8.55031	+	33.0864i	−0.0171006	+	0.0661728i
$501$	−381.875			−0.762226
$502$	−290.198	+	290.198i	−0.578084	+	0.578084i
$503$	289.173	+	289.173i	0.574897	+	0.574897i	0.933493	−	0.358596i	$-0.116744\pi$
$503$	289.173	+	289.173i	0.574897	+	0.574897i	−0.358596	+	0.933493i	$0.616744\pi$
$504$			427.972i			0.849151i
$505$	417.988	+	35.3189i	0.827699	+	0.0699383i
$506$	125.438			0.247901
$507$	−490.003	+	490.003i	−0.966475	+	0.966475i
$508$	−38.9018	−	38.9018i	−0.0765783	−	0.0765783i
$509$		−	106.885i		−	0.209990i	−0.994473	−	0.104995i	$-0.966517\pi$
$509$		−	106.885i		−	0.209990i	0.994473	−	0.104995i	$-0.0334827\pi$
$510$	786.563	−	663.995i	1.54228	−	1.30195i
$511$	−256.379			−0.501719
$512$	−391.864	+	391.864i	−0.765359	+	0.765359i
$513$	114.998	+	114.998i	0.224167	+	0.224167i
$514$		−	229.769i		−	0.447021i
$515$	−267.432	−	316.798i	−0.519285	−	0.615141i
$516$	−14.0836			−0.0272937
$517$	242.216	−	242.216i	0.468503	−	0.468503i
$518$	−145.360	−	145.360i	−0.280617	−	0.280617i
$519$		−	180.726i		−	0.348219i
$520$	21.8107	−	258.123i	0.0419437	−	0.496390i
$521$	367.274			0.704941			0.352470	−	0.935823i	$-0.385342\pi$
$521$	367.274			0.704941			0.352470	+	0.935823i	$0.385342\pi$
$522$	1.61365	−	1.61365i	0.00309128	−	0.00309128i
$523$	401.336	+	401.336i	0.767373	+	0.767373i	0.977643	−	0.210270i	$-0.0674345\pi$
$523$	401.336	+	401.336i	0.767373	+	0.767373i	−0.210270	+	0.977643i	$0.567434\pi$
$524$		−	26.6133i		−	0.0507888i
$525$	−348.765	−	59.3632i	−0.664313	−	0.113073i
$526$	−3.19274			−0.00606985
$527$	46.3135	−	46.3135i	0.0878815	−	0.0878815i
$528$	252.582	+	252.582i	0.478375	+	0.478375i
$529$		−	320.752i		−	0.606337i
$530$	−717.177	−	60.5995i	−1.35316	−	0.114339i
$531$	786.214			1.48063
$532$	−1.46599	+	1.46599i	−0.00275562	+	0.00275562i
$533$	52.4925	+	52.4925i	0.0984850	+	0.0984850i
$534$		−	729.433i		−	1.36598i
$535$	−300.681	+	253.827i	−0.562021	+	0.474443i
$536$	360.224			0.672061
$537$	−370.928	+	370.928i	−0.690741	+	0.690741i
$538$	423.050	+	423.050i	0.786339	+	0.786339i
$539$			31.5195i			0.0584778i
$540$	50.0302	+	59.2654i	0.0926485	+	0.109751i
$541$	−297.740			−0.550351			−0.275176	−	0.961394i	$-0.588736\pi$
$541$	−297.740			−0.550351			−0.275176	+	0.961394i	$0.588736\pi$
$542$	348.541	−	348.541i	0.643065	−	0.643065i
$543$	−407.173	−	407.173i	−0.749858	−	0.749858i
$544$		−	87.0583i		−	0.160034i
$545$	−15.9405	+	188.651i	−0.0292486	+	0.346148i
$546$	171.563			0.314218
$547$	700.711	−	700.711i	1.28101	−	1.28101i	0.340912	−	0.940095i	$-0.389264\pi$
$547$	700.711	−	700.711i	1.28101	−	1.28101i	0.940095	−	0.340912i	$-0.110736\pi$
$548$	−39.6950	−	39.6950i	−0.0724362	−	0.0724362i
$549$			1264.20i			2.30273i
$550$	−177.266	+	125.699i	−0.322302	+	0.228543i
$551$	0.172802			0.000313616
$552$	−450.245	+	450.245i	−0.815662	+	0.815662i
$553$	−113.408	−	113.408i	−0.205078	−	0.205078i
$554$			488.543i			0.881847i
$555$	−1072.56	−	90.6288i	−1.93255	−	0.163295i
$556$	8.27476			0.0148827
$557$	−352.766	+	352.766i	−0.633332	+	0.633332i	−0.948902	−	0.315570i	$-0.897804\pi$
$557$	−352.766	+	352.766i	−0.633332	+	0.633332i	0.315570	+	0.948902i	$0.397804\pi$
$558$	−87.9244	−	87.9244i	−0.157571	−	0.157571i
$559$			60.4871i			0.108206i
$560$	149.927	−	126.564i	0.267726	−	0.226007i
$561$	−480.197			−0.855965
$562$	76.6427	−	76.6427i	0.136375	−	0.136375i
$563$	721.623	+	721.623i	1.28175	+	1.28175i	0.939673	+	0.342073i	$0.111129\pi$
$563$	721.623	+	721.623i	1.28175	+	1.28175i	0.342073	+	0.939673i	$0.388871\pi$
$564$			111.239i			0.197233i
$565$	423.161	+	501.273i	0.748957	+	0.887209i
$566$	213.055			0.376422
$567$	−237.608	+	237.608i	−0.419061	+	0.419061i
$568$	166.498	+	166.498i	0.293130	+	0.293130i
$569$			119.132i			0.209371i	0.994505	+	0.104685i	$0.0333835\pi$
$569$			119.132i			0.209371i	−0.994505	+	0.104685i	$0.966616\pi$
$570$	12.4592	−	147.451i	0.0218582	−	0.258685i
$571$	563.920			0.987601			0.493801	−	0.869575i	$-0.335607\pi$
$571$	563.920			0.987601			0.493801	+	0.869575i	$0.335607\pi$
$572$	−5.46658	+	5.46658i	−0.00955697	+	0.00955697i
$573$	516.452	+	516.452i	0.901312	+	0.901312i
$574$			60.3735i			0.105180i
$575$	−208.680	−	294.291i	−0.362922	−	0.511811i
$576$	−1328.57			−2.30654
$577$	536.862	−	536.862i	0.930436	−	0.930436i	−0.0672967	−	0.997733i	$-0.521437\pi$
$577$	536.862	−	536.862i	0.930436	−	0.930436i	0.997733	+	0.0672967i	$0.0214374\pi$
$578$	−148.166	−	148.166i	−0.256342	−	0.256342i
$579$		−	290.343i		−	0.501456i
$580$	0.0821170	+	0.00693866i	0.000141581	+	1.19632e-5i
$581$	396.595			0.682607
$582$	−1229.17	+	1229.17i	−2.11198	+	2.11198i
$583$	237.416	+	237.416i	0.407232	+	0.407232i
$584$		−	799.396i		−	1.36883i
$585$	470.487	−	397.172i	0.804252	−	0.678927i
$586$	62.7416			0.107068
$587$	298.742	−	298.742i	0.508930	−	0.508930i	−0.405268	−	0.914198i	$-0.632822\pi$
$587$	298.742	−	298.742i	0.508930	−	0.508930i	0.914198	+	0.405268i	$0.132822\pi$
$588$	−7.23778	−	7.23778i	−0.0123091	−	0.0123091i
$589$		−	9.41563i		−	0.0159858i
$590$	−249.649	−	295.733i	−0.423135	−	0.501242i
$591$	−1079.02			−1.82575
$592$	422.114	−	422.114i	0.713030	−	0.713030i
$593$	−74.9832	−	74.9832i	−0.126447	−	0.126447i	0.641051	−	0.767498i	$-0.278499\pi$
$593$	−74.9832	−	74.9832i	−0.126447	−	0.126447i	−0.767498	+	0.641051i	$0.778499\pi$
$594$			493.201i			0.830304i
$595$	−22.2080	+	262.825i	−0.0373244	+	0.441723i
$596$	73.4270			0.123200
$597$	362.314	−	362.314i	0.606892	−	0.606892i
$598$	123.710	+	123.710i	0.206873	+	0.206873i
$599$			110.245i			0.184048i	0.995757	+	0.0920238i	$0.0293336\pi$
$599$			110.245i			0.184048i	−0.995757	+	0.0920238i	$0.970666\pi$
$600$	185.096	−	1087.46i	0.308494	−	1.81243i
$601$	−279.992			−0.465877			−0.232938	−	0.972491i	$-0.574834\pi$
$601$	−279.992			−0.465877			−0.232938	+	0.972491i	$0.574834\pi$
$602$	−34.7842	+	34.7842i	−0.0577810	+	0.0577810i
$603$	605.433	+	605.433i	1.00403	+	1.00403i
$604$			63.3175i			0.104830i
$605$	−501.836	−	42.4038i	−0.829481	−	0.0700889i
$606$	−866.245			−1.42945
$607$	1.08684	−	1.08684i	0.00179051	−	0.00179051i	−0.706211	−	0.708001i	$-0.749597\pi$
$607$	1.08684	−	1.08684i	0.00179051	−	0.00179051i	0.708001	+	0.706211i	$0.249597\pi$
$608$	−8.84957	−	8.84957i	−0.0145552	−	0.0145552i
$609$			0.853148i			0.00140090i
$610$	475.527	−	401.427i	0.779552	−	0.658076i
$611$	477.759			0.781930
$612$	75.5774	−	75.5774i	0.123492	−	0.123492i
$613$	152.929	+	152.929i	0.249477	+	0.249477i	0.820756	−	0.571279i	$-0.193553\pi$
$613$	152.929	+	152.929i	0.249477	+	0.249477i	−0.571279	+	0.820756i	$0.693553\pi$
$614$		−	439.576i		−	0.715921i
$615$	203.918	+	241.559i	0.331573	+	0.392779i
$616$	−98.2788			−0.159544
$617$	371.652	−	371.652i	0.602354	−	0.602354i	−0.338583	−	0.940937i	$-0.609948\pi$
$617$	371.652	−	371.652i	0.602354	−	0.602354i	0.940937	+	0.338583i	$0.109948\pi$
$618$	605.384	+	605.384i	0.979585	+	0.979585i
$619$		−	56.7016i		−	0.0916019i	−0.998951	−	0.0458010i	$-0.985416\pi$
$619$		−	56.7016i		−	0.0916019i	0.998951	−	0.0458010i	$-0.0145840\pi$
$620$	0.378073	−	4.47438i	0.000609795	−	0.00721674i
$621$	−818.795			−1.31851
$622$	−345.776	+	345.776i	−0.555909	+	0.555909i
$623$	132.165	+	132.165i	0.212143	+	0.212143i
$624$			498.206i			0.798406i
$625$	589.805	+	206.772i	0.943689	+	0.330835i
$626$	−380.021			−0.607062
$627$	−48.8125	+	48.8125i	−0.0778508	+	0.0778508i
$628$	−7.51972	−	7.51972i	−0.0119741	−	0.0119741i
$629$			802.501i			1.27584i
$630$	498.963	+	42.1610i	0.792005	+	0.0669223i
$631$	794.990			1.25989			0.629945	−	0.776640i	$-0.283078\pi$
$631$	794.990			1.25989			0.629945	+	0.776640i	$0.283078\pi$
$632$	353.611	−	353.611i	0.559510	−	0.559510i
$633$	614.358	+	614.358i	0.970549	+	0.970549i
$634$		−	281.235i		−	0.443588i
$635$	−768.857	+	649.048i	−1.21080	+	1.02212i
$636$	−109.035			−0.171439
$637$	−31.0853	+	31.0853i	−0.0487996	+	0.0487996i
$638$	0.370556	+	0.370556i	0.000580809	+	0.000580809i
$639$			559.668i			0.875850i
$640$	365.534	+	433.009i	0.571147	+	0.676576i
$641$	−946.319			−1.47632			−0.738158	−	0.674627i	$-0.764304\pi$
$641$	−946.319			−1.47632			−0.738158	+	0.674627i	$0.764304\pi$
$642$	574.586	−	574.586i	0.894993	−	0.894993i
$643$	−901.858	−	901.858i	−1.40258	−	1.40258i	−0.791805	−	0.610774i	$-0.790858\pi$
$643$	−901.858	−	901.858i	−1.40258	−	1.40258i	−0.610774	−	0.791805i	$-0.709142\pi$
$644$		−	10.4380i		−	0.0162080i
$645$	−21.6872	+	256.661i	−0.0336236	+	0.397925i
$646$	−110.324			−0.170780
$647$	−66.7843	+	66.7843i	−0.103221	+	0.103221i	−0.756832	−	0.653610i	$-0.773254\pi$
$647$	−66.7843	+	66.7843i	−0.103221	+	0.103221i	0.653610	+	0.756832i	$0.273254\pi$
$648$	−740.868	−	740.868i	−1.14331	−	1.14331i
$649$			180.545i			0.278189i
$650$	−298.791	−	50.8572i	−0.459679	−	0.0782419i
$651$	46.4862			0.0714074
$652$	−52.5167	+	52.5167i	−0.0805472	+	0.0805472i
$653$	−463.320	−	463.320i	−0.709526	−	0.709526i	0.256909	−	0.966435i	$-0.417296\pi$
$653$	−463.320	−	463.320i	−0.709526	−	0.709526i	−0.966435	+	0.256909i	$0.917296\pi$
$654$		−	390.963i		−	0.597803i
$655$	−485.006	−	40.9817i	−0.740467	−	0.0625675i
$656$	−175.320			−0.267256
$657$	1343.55	−	1343.55i	2.04498	−	2.04498i
$658$	274.744	+	274.744i	0.417544	+	0.417544i
$659$		−	722.439i		−	1.09627i	−0.836391	−	0.548133i	$-0.815339\pi$
$659$		−	722.439i		−	1.09627i	0.836391	−	0.548133i	$-0.184661\pi$
$660$	−25.1560	+	21.2360i	−0.0381152	+	0.0321758i
$661$	−472.481			−0.714797			−0.357399	−	0.933952i	$-0.616336\pi$
$661$	−472.481			−0.714797			−0.357399	+	0.933952i	$0.616336\pi$
$662$	−379.258	+	379.258i	−0.572898	+	0.572898i
$663$	−473.582	−	473.582i	−0.714301	−	0.714301i
$664$			1236.59i			1.86234i
$665$	24.4590	+	28.9739i	0.0367804	+	0.0435698i
$666$	1523.52			2.28756
$667$	−0.615185	+	0.615185i	−0.000922316	+	0.000922316i
$668$	13.8019	+	13.8019i	0.0206615	+	0.0206615i
$669$		−	1560.65i		−	2.33281i
$670$	35.4870	−	419.978i	0.0529656	−	0.626832i
$671$	−290.309			−0.432651
$672$	43.6915	−	43.6915i	0.0650171	−	0.0650171i
$673$	−308.438	−	308.438i	−0.458303	−	0.458303i	0.439795	−	0.898098i	$-0.355051\pi$
$673$	−308.438	−	308.438i	−0.458303	−	0.458303i	−0.898098	+	0.439795i	$0.855051\pi$
$674$			1215.77i			1.80382i
$675$	1157.10	−	820.497i	1.71423	−	1.21555i
$676$	35.4198			0.0523961
$677$	730.773	−	730.773i	1.07943	−	1.07943i	0.0828685	−	0.996560i	$-0.473592\pi$
$677$	730.773	−	730.773i	1.07943	−	1.07943i	0.996560	−	0.0828685i	$-0.0264082\pi$
$678$	−957.906	−	957.906i	−1.41284	−	1.41284i
$679$		−	445.425i		−	0.656002i
$680$	−819.496	−	69.2452i	−1.20514	−	0.101831i
$681$	1090.71			1.60163
$682$	20.1908	−	20.1908i	0.0296053	−	0.0296053i
$683$	−798.406	−	798.406i	−1.16897	−	1.16897i	−0.982451	−	0.186518i	$-0.940280\pi$
$683$	−798.406	−	798.406i	−1.16897	−	1.16897i	−0.186518	−	0.982451i	$-0.559720\pi$
$684$		−	15.3650i		−	0.0224635i
$685$	−784.535	+	662.283i	−1.14531	+	0.966836i
$686$	−35.7523			−0.0521171
$687$	−1272.04	+	1272.04i	−1.85159	+	1.85159i
$688$	−101.011	−	101.011i	−0.146818	−	0.146818i
$689$			468.292i			0.679669i
$690$	480.576	+	569.286i	0.696487	+	0.825053i
$691$	−566.181			−0.819365			−0.409683	−	0.912228i	$-0.634361\pi$
$691$	−566.181			−0.819365			−0.409683	+	0.912228i	$0.634361\pi$
$692$	−6.53187	+	6.53187i	−0.00943912	+	0.00943912i
$693$	−165.178	−	165.178i	−0.238352	−	0.238352i
$694$		−	693.629i		−	0.999465i
$695$	12.7422	−	150.801i	0.0183342	−	0.216979i
$696$	−2.66014			−0.00382204
$697$	166.655	−	166.655i	0.239103	−	0.239103i
$698$	919.980	+	919.980i	1.31802	+	1.31802i
$699$			302.961i			0.433420i
$700$	10.4597	+	14.7507i	0.0149424	+	0.0210725i
$701$	564.427			0.805174			0.402587	−	0.915382i	$-0.368111\pi$
$701$	564.427			0.805174			0.402587	+	0.915382i	$0.368111\pi$
$702$	−486.407	+	486.407i	−0.692887	+	0.692887i
$703$	81.5751	+	81.5751i	0.116039	+	0.116039i
$704$		−	305.090i		−	0.433367i
$705$	2027.25	+	171.297i	2.87553	+	0.242974i
$706$	−61.7905			−0.0875219
$707$	156.954	−	156.954i	0.222000	−	0.222000i
$708$	−41.4583	−	41.4583i	−0.0585569	−	0.0585569i
$709$			514.258i			0.725328i	0.931920	+	0.362664i	$0.118133\pi$
$709$			514.258i			0.725328i	−0.931920	+	0.362664i	$0.881867\pi$
$710$	210.518	−	177.714i	0.296504	−	0.250301i
$711$	1188.63			1.67178
$712$	−412.095	+	412.095i	−0.578785	+	0.578785i
$713$	33.5201	+	33.5201i	0.0470128	+	0.0470128i
$714$		−	544.683i		−	0.762861i
$715$	91.2060	+	108.042i	0.127561	+	0.151108i
$716$	26.8125			0.0374476
$717$	−501.107	+	501.107i	−0.698894	+	0.698894i
$718$	488.989	+	488.989i	0.681043	+	0.681043i
$719$		−	743.521i		−	1.03410i	−0.855954	−	0.517052i	$-0.827029\pi$
$719$		−	743.521i		−	1.03410i	0.855954	−	0.517052i	$-0.172971\pi$
$720$	−122.432	+	1448.95i	−0.170045	+	2.01243i
$721$	−219.378			−0.304269
$722$	481.561	−	481.561i	0.666982	−	0.666982i
$723$	74.1493	+	74.1493i	0.102558	+	0.102558i
$724$			29.4324i			0.0406525i
$725$	0.252903	−	1.48583i	0.000348831	−	0.00204942i
$726$	1040.01			1.43253
$727$	−322.461	+	322.461i	−0.443550	+	0.443550i	−0.893203	−	0.449653i	$-0.851548\pi$
$727$	−322.461	+	322.461i	−0.443550	+	0.443550i	0.449653	+	0.893203i	$0.351548\pi$
$728$	−96.9250	−	96.9250i	−0.133139	−	0.133139i
$729$			240.955i			0.330528i
$730$	−931.998	−	78.7514i	−1.27671	−	0.107879i
$731$	192.036			0.262703
$732$	66.6633	−	66.6633i	0.0910700	−	0.0910700i
$733$	−471.080	−	471.080i	−0.642674	−	0.642674i	0.308538	−	0.951212i	$-0.400160\pi$
$733$	−471.080	−	471.080i	−0.642674	−	0.642674i	−0.951212	+	0.308538i	$0.900160\pi$
$734$		−	387.840i		−	0.528393i
$735$	−143.048	+	120.757i	−0.194623	+	0.164295i
$736$	63.0098			0.0856111
$737$	−139.031	+	139.031i	−0.188644	+	0.188644i
$738$	−316.387	−	316.387i	−0.428709	−	0.428709i
$739$			1172.77i			1.58697i	0.608592	+	0.793483i	$0.291735\pi$
$739$			1172.77i			1.58697i	−0.608592	+	0.793483i	$0.708265\pi$
$740$	35.4895	+	42.0406i	0.0479588	+	0.0568117i
$741$	−96.2801			−0.129933
$742$	−269.299	+	269.299i	−0.362937	+	0.362937i
$743$	833.225	+	833.225i	1.12143	+	1.12143i	0.991526	+	0.129907i	$0.0414680\pi$
$743$	833.225	+	833.225i	1.12143	+	1.12143i	0.129907	+	0.991526i	$0.458532\pi$
$744$			144.945i			0.194819i
$745$	113.070	−	1338.15i	0.151771	−	1.79617i
$746$	−194.428			−0.260627
$747$	−2078.35	+	2078.35i	−2.78227	+	2.78227i
$748$	17.3555	+	17.3555i	0.0232025	+	0.0232025i
$749$			208.217i			0.277994i
$750$	−1249.61	−	322.929i	−1.66615	−	0.430572i
$751$	395.746			0.526958			0.263479	−	0.964665i	$-0.415130\pi$
$751$	395.746			0.526958			0.263479	+	0.964665i	$0.415130\pi$
$752$	−797.835	+	797.835i	−1.06095	+	1.06095i
$753$	804.049	+	804.049i	1.06779	+	1.06779i
$754$			0.730903i			0.000969368i
$755$	1153.91	+	97.5022i	1.52836	+	0.129142i
$756$	41.0404			0.0542862
$757$	−642.840	+	642.840i	−0.849195	+	0.849195i	−0.990033	−	0.140838i	$-0.955020\pi$
$757$	−642.840	+	642.840i	−0.849195	+	0.849195i	0.140838	+	0.990033i	$0.455020\pi$
$758$	−389.029	−	389.029i	−0.513231	−	0.513231i
$759$		−	347.549i		−	0.457904i
$760$	−90.3415	+	76.2638i	−0.118870	+	0.100347i
$761$	−877.122			−1.15259			−0.576296	−	0.817241i	$-0.695502\pi$
$761$	−877.122			−1.15259			−0.576296	+	0.817241i	$0.695502\pi$
$762$	1469.24	−	1469.24i	1.92814	−	1.92814i
$763$	70.8382	+	70.8382i	0.0928417	+	0.0928417i
$764$		−	37.3316i		−	0.0488634i
$765$	−1260.95	−	1493.72i	−1.64831	−	1.95257i
$766$	388.908			0.507713
$767$	−178.058	+	178.058i	−0.232148	+	0.232148i
$768$	197.573	+	197.573i	0.257257	+	0.257257i
$769$		−	482.602i		−	0.627571i	−0.949494	−	0.313785i	$-0.898403\pi$
$769$		−	482.602i		−	0.627571i	0.949494	−	0.313785i	$-0.101597\pi$
$770$	−9.68179	+	114.581i	−0.0125738	+	0.148807i
$771$	−636.617			−0.825703
$772$	−10.4937	+	10.4937i	−0.0135929	+	0.0135929i
$773$	−816.968	−	816.968i	−1.05688	−	1.05688i	−0.998282	−	0.0585982i	$-0.981337\pi$
$773$	−816.968	−	816.968i	−1.05688	−	1.05688i	−0.0585982	−	0.998282i	$-0.518663\pi$
$774$		−	364.573i		−	0.471024i
$775$	−80.9597	−	13.7801i	−0.104464	−	0.0177808i
$776$	1388.85			1.78976
$777$	−402.747	+	402.747i	−0.518336	+	0.518336i
$778$	196.363	+	196.363i	0.252395	+	0.252395i
$779$		−	33.8812i		−	0.0434932i
$780$	−45.7530	−	3.86601i	−0.0586577	−	0.00495642i
$781$	−128.521			−0.164560
$782$	392.758	−	392.758i	0.502248	−	0.502248i
$783$	−2.41880	−	2.41880i	−0.00308915	−	0.00308915i
$784$		−	103.822i		−	0.132426i
$785$	−148.620	+	125.461i	−0.189325	+	0.159823i
$786$	1005.13			1.27880
$787$	−312.439	+	312.439i	−0.397000	+	0.397000i	−0.877174	−	0.480174i	$-0.840574\pi$
$787$	−312.439	+	312.439i	−0.397000	+	0.397000i	0.480174	+	0.877174i	$0.340574\pi$
$788$	38.9983	+	38.9983i	0.0494902	+	0.0494902i
$789$			8.84609i			0.0112118i
$790$	−377.431	−	447.102i	−0.477761	−	0.565952i
$791$	347.124			0.438842
$792$	515.030	−	515.030i	0.650291	−	0.650291i
$793$	−286.310	−	286.310i	−0.361047	−	0.361047i
$794$			777.868i			0.979683i
$795$	−167.903	+	1987.08i	−0.211198	+	2.49947i
$796$	−26.1898			−0.0329018
$797$	236.192	−	236.192i	0.296351	−	0.296351i	−0.543232	−	0.839583i	$-0.682800\pi$
$797$	236.192	−	236.192i	0.296351	−	0.296351i	0.839583	+	0.543232i	$0.182800\pi$
$798$	−55.3676	−	55.3676i	−0.0693829	−	0.0693829i
$799$		−	1516.80i		−	1.89838i
$800$	−89.0441	+	63.1407i	−0.111305	+	0.0789259i
$801$	−1385.22			−1.72937
$802$	316.043	−	316.043i	0.394068	−	0.394068i
$803$	308.531	+	308.531i	0.384223	+	0.384223i
$804$		−	63.8508i		−	0.0794164i
$805$	−190.223	−	16.0734i	−0.236302	−	0.0199669i
$806$	39.8254			0.0494111
$807$	1172.14	−	1172.14i	1.45247	−	1.45247i
$808$	489.388	+	489.388i	0.605678	+	0.605678i
$809$			472.847i			0.584484i	0.956344	+	0.292242i	$0.0944012\pi$
$809$			472.847i			0.584484i	−0.956344	+	0.292242i	$0.905599\pi$
$810$	−936.746	+	790.775i	−1.15648	+	0.976266i
$811$	−114.979			−0.141774			−0.0708869	−	0.997484i	$-0.522583\pi$
$811$	−114.979			−0.141774			−0.0708869	+	0.997484i	$0.522583\pi$
$812$	0.0308348	−	0.0308348i	3.79740e−5	−	3.79740e-5i
$813$	−965.700	−	965.700i	−1.18782	−	1.18782i
$814$			349.858i			0.429801i
$815$	876.204	+	1037.94i	1.07510	+	1.27355i
$816$	1581.72			1.93838
$817$	19.5207	−	19.5207i	0.0238931	−	0.0238931i
$818$	−14.3032	−	14.3032i	−0.0174856	−	0.0174856i
$819$		−	325.805i		−	0.397809i
$820$	1.36046	−	16.1006i	0.00165910	−	0.0196349i
$821$	45.9017			0.0559095			0.0279547	−	0.999609i	$-0.491101\pi$
$821$	45.9017			0.0559095			0.0279547	+	0.999609i	$0.491101\pi$
$822$	1499.20	−	1499.20i	1.82385	−	1.82385i
$823$	419.947	+	419.947i	0.510263	+	0.510263i	0.914607	−	0.404344i	$-0.132500\pi$
$823$	419.947	+	419.947i	0.510263	+	0.510263i	−0.404344	+	0.914607i	$0.632500\pi$
$824$		−	684.027i		−	0.830129i
$825$	348.272	+	491.149i	0.422147	+	0.595333i
$826$	−204.791			−0.247930
$827$	−247.682	+	247.682i	−0.299494	+	0.299494i	−0.840816	−	0.541321i	$-0.817924\pi$
$827$	−247.682	+	247.682i	−0.299494	+	0.299494i	0.541321	+	0.840816i	$0.317924\pi$
$828$	54.7002	+	54.7002i	0.0660631	+	0.0660631i
$829$		−	979.565i		−	1.18162i	−0.806810	−	0.590811i	$-0.798808\pi$
$829$		−	979.565i		−	1.18162i	0.806810	−	0.590811i	$-0.201192\pi$
$830$	1441.72	+	121.821i	1.73701	+	0.146773i
$831$	1353.60			1.62888
$832$	300.887	−	300.887i	0.361643	−	0.361643i
$833$	98.6906	+	98.6906i	0.118476	+	0.118476i
$834$			312.522i			0.374726i
$835$	272.782	−	230.275i	0.326685	−	0.275778i
$836$	3.52840			0.00422058
$837$	−131.795	+	131.795i	−0.157462	+	0.157462i
$838$	−734.456	−	734.456i	−0.876439	−	0.876439i
$839$		−	1013.98i		−	1.20856i	−0.796772	−	0.604281i	$-0.793461\pi$
$839$		−	1013.98i		−	1.20856i	0.796772	−	0.604281i	$-0.206539\pi$
$840$	−376.524	−	446.028i	−0.448243	−	0.530986i
$841$	840.996			0.999996
$842$	−776.489	+	776.489i	−0.922196	+	0.922196i
$843$	−212.353	−	212.353i	−0.251902	−	0.251902i
$844$		−	44.4087i		−	0.0526170i
$845$	54.5427	−	645.496i	0.0645476	−	0.763901i
$846$	−2879.59			−3.40377
$847$	−188.439	+	188.439i	−0.222478	+	0.222478i
$848$	−782.025	−	782.025i	−0.922199	−	0.922199i
$849$		−	590.308i		−	0.695298i
$850$	−161.463	+	948.611i	−0.189956	+	1.11601i
$851$	−580.822			−0.682517
$852$	29.5122	−	29.5122i	0.0346387	−	0.0346387i
$853$	−535.924	−	535.924i	−0.628281	−	0.628281i	0.319354	−	0.947635i	$-0.396534\pi$
$853$	−535.924	−	535.924i	−0.628281	−	0.628281i	−0.947635	+	0.319354i	$0.896534\pi$
$854$		−	329.295i		−	0.385592i
$855$	−280.015	−	23.6605i	−0.327503	−	0.0276731i
$856$	−649.228			−0.758444
$857$	171.853	−	171.853i	0.200529	−	0.200529i	−0.599698	−	0.800227i	$-0.704712\pi$
$857$	171.853	−	171.853i	0.200529	−	0.200529i	0.800227	+	0.599698i	$0.204712\pi$
$858$	−206.462	−	206.462i	−0.240632	−	0.240632i
$859$		−	190.132i		−	0.221341i	−0.993857	−	0.110671i	$-0.964700\pi$
$859$		−	190.132i		−	0.221341i	0.993857	−	0.110671i	$-0.0352998\pi$
$860$	10.0602	−	8.49254i	0.0116979	−	0.00987504i
$861$	167.276			0.194281
$862$	460.792	−	460.792i	0.534561	−	0.534561i
$863$	557.309	+	557.309i	0.645781	+	0.645781i	0.951970	−	0.306190i	$-0.0990542\pi$
$863$	557.309	+	557.309i	0.645781	+	0.645781i	−0.306190	+	0.951970i	$0.599054\pi$
$864$			247.744i			0.286741i
$865$	108.980	+	129.096i	0.125988	+	0.149244i
$866$	−872.595			−1.00762
$867$	−410.521	+	410.521i	−0.473496	+	0.473496i
$868$	−1.68013	−	1.68013i	−0.00193563	−	0.00193563i
$869$			272.956i			0.314103i
$870$	−0.262060	+	3.10140i	−0.000301218	+	0.00356483i
$871$	−274.231			−0.314846
$872$	−220.876	+	220.876i	−0.253298	+	0.253298i
$873$	2334.25	+	2334.25i	2.67383	+	2.67383i
$874$		−	79.8484i		−	0.0913598i
$875$	284.927	−	167.904i	0.325630	−	0.191891i
$876$	−141.695			−0.161753
$877$	−367.168	+	367.168i	−0.418664	+	0.418664i	−0.884743	−	0.466079i	$-0.845666\pi$
$877$	−367.168	+	367.168i	−0.418664	+	0.418664i	0.466079	+	0.884743i	$0.345666\pi$
$878$	840.311	+	840.311i	0.957074	+	0.957074i
$879$		−	173.837i		−	0.197767i
$880$	−332.735	−	28.1152i	−0.378107	−	0.0319491i
$881$	114.349			0.129795			0.0648973	−	0.997892i	$-0.479328\pi$
$881$	114.349			0.129795			0.0648973	+	0.997892i	$0.479328\pi$
$882$	187.360	−	187.360i	0.212426	−	0.212426i
$883$	−1023.71	−	1023.71i	−1.15936	−	1.15936i	−0.984614	−	0.174742i	$-0.944091\pi$
$883$	−1023.71	−	1023.71i	−1.15936	−	1.15936i	−0.174742	−	0.984614i	$-0.555909\pi$
$884$			34.2328i			0.0387249i
$885$	−819.384	+	691.701i	−0.925857	+	0.781583i
$886$	−1172.67			−1.32355
$887$	455.939	−	455.939i	0.514024	−	0.514024i	−0.401733	−	0.915757i	$-0.631592\pi$
$887$	455.939	−	455.939i	0.514024	−	0.514024i	0.915757	+	0.401733i	$0.131592\pi$
$888$	−1255.78	−	1255.78i	−1.41416	−	1.41416i
$889$			532.422i			0.598900i
$890$	439.856	+	521.049i	0.494220	+	0.585449i
$891$	571.884			0.641845
$892$	−56.4056	+	56.4056i	−0.0632350	+	0.0632350i
$893$	−154.185	−	154.185i	−0.172659	−	0.172659i
$894$			2773.19i			3.10201i
$895$	41.2883	−	488.635i	0.0461322	−	0.545961i
$896$	299.852			0.334656
$897$	342.762	−	342.762i	0.382120	−	0.382120i
$898$	935.126	+	935.126i	1.04134	+	1.04134i
$899$			0.198044i			0.000220293i
$900$	−132.115	−	22.4873i	−0.146795	−	0.0249859i
$901$	1486.75			1.65011
$902$	72.6547	−	72.6547i	0.0805484	−	0.0805484i
$903$	96.3761	+	96.3761i	0.106729	+	0.106729i
$904$			1082.34i			1.19728i
$905$	536.382	+	45.3228i	0.592687	+	0.0500805i
$906$	−2391.38			−2.63949
$907$	537.745	−	537.745i	0.592884	−	0.592884i	−0.345526	−	0.938409i	$-0.612299\pi$
$907$	537.745	−	537.745i	0.592884	−	0.592884i	0.938409	+	0.345526i	$0.112299\pi$
$908$	−39.4210	−	39.4210i	−0.0434152	−	0.0434152i
$909$			1645.04i			1.80972i
$910$	−122.551	+	103.454i	−0.134672	+	0.113686i
$911$	−420.630			−0.461723			−0.230862	−	0.972987i	$-0.574154\pi$
$911$	−420.630			−0.461723			−0.230862	+	0.972987i	$0.574154\pi$
$912$	160.783	−	160.783i	0.176297	−	0.176297i
$913$	−477.270	−	477.270i	−0.522749	−	0.522749i
$914$			1511.65i			1.65389i
$915$	−1112.23	−	1317.54i	−1.21555	−	1.43993i
$916$	91.9492			0.100381
$917$	−182.119	+	182.119i	−0.198603	+	0.198603i
$918$	1544.26	+	1544.26i	1.68220	+	1.68220i
$919$		−	331.199i		−	0.360391i	−0.983631	−	0.180196i	$-0.942327\pi$
$919$		−	331.199i		−	0.360391i	0.983631	−	0.180196i	$-0.0576730\pi$
$920$	50.1173	−	593.123i	0.0544753	−	0.644699i
$921$	−1217.93			−1.32240
$922$	−594.707	+	594.707i	−0.645019	+	0.645019i
$923$	−126.751	−	126.751i	−0.137325	−	0.137325i
$924$			17.4202i			0.0188530i
$925$	820.806	−	582.029i	0.887357	−	0.629221i
$926$	856.286			0.924715
$927$	1149.65	−	1149.65i	1.24018	−	1.24018i
$928$	0.186137	+	0.186137i	0.000200579	+	0.000200579i
$929$		−	517.091i		−	0.556611i	−0.960493	−	0.278305i	$-0.910227\pi$
$929$		−	517.091i		−	0.556611i	0.960493	−	0.278305i	$-0.0897727\pi$
$930$	168.989	+	14.2791i	0.181708	+	0.0153539i
$931$	20.0640			0.0215510
$932$	10.9497	−	10.9497i	0.0117486	−	0.0117486i
$933$	958.037	+	958.037i	1.02683	+	1.02683i
$934$		−	486.462i		−	0.520837i
$935$	343.015	−	289.563i	0.366861	−	0.309694i
$936$	1015.87			1.08533
$937$	−665.806	+	665.806i	−0.710572	+	0.710572i	−0.966655	−	0.256083i	$-0.917568\pi$
$937$	−665.806	+	665.806i	−0.710572	+	0.710572i	0.256083	+	0.966655i	$0.417568\pi$
$938$	−157.701	−	157.701i	−0.168125	−	0.168125i
$939$			1052.92i			1.12132i
$940$	−67.0786	−	79.4607i	−0.0713602	−	0.0845327i
$941$	325.422			0.345825			0.172913	−	0.984937i	$-0.444682\pi$
$941$	325.422			0.345825			0.172913	+	0.984937i	$0.444682\pi$
$942$	284.005	−	284.005i	0.301492	−	0.301492i
$943$	120.619	+	120.619i	0.127910	+	0.127910i
$944$		−	594.696i		−	0.629975i
$945$	63.1978	−	747.927i	0.0668760	−	0.791457i
$946$	83.7199			0.0884989
$947$	−550.870	+	550.870i	−0.581700	+	0.581700i	−0.935370	−	0.353670i	$-0.884934\pi$
$947$	−550.870	+	550.870i	−0.581700	+	0.581700i	0.353670	+	0.935370i	$0.384934\pi$
$948$	−62.6785	−	62.6785i	−0.0661165	−	0.0661165i
$949$			608.562i			0.641267i
$950$	80.0144	+	112.840i	0.0842257	+	0.118779i
$951$	−779.214			−0.819362
$952$	−307.720	+	307.720i	−0.323235	+	0.323235i
$953$	1005.61	+	1005.61i	1.05521	+	1.05521i	0.998384	+	0.0568238i	$0.0180973\pi$
$953$	1005.61	+	1005.61i	1.05521	+	1.05521i	0.0568238	+	0.998384i	$0.481903\pi$
$954$		−	2822.53i		−	2.95862i
$955$	−680.338	−	57.4868i	−0.712396	−	0.0601956i
$956$	36.2225			0.0378896
$957$	1.02670	−	1.02670i	0.00107283	−	0.00107283i
$958$	739.073	+	739.073i	0.771475	+	0.771475i
$959$			543.279i			0.566506i
$960$	1384.62	−	1168.86i	1.44231	−	1.21756i
$961$	−950.209			−0.988771
$962$	−345.039	+	345.039i	−0.358668	+	0.358668i
$963$	−1091.16	−	1091.16i	−1.13309	−	1.13309i
$964$		−	5.35987i		−	0.00556003i
$965$	175.080	+	207.398i	0.181430	+	0.214920i
$966$	394.222			0.408098
$967$	−412.798	+	412.798i	−0.426885	+	0.426885i	−0.887566	−	0.460681i	$-0.847605\pi$
$967$	−412.798	+	412.798i	−0.426885	+	0.426885i	0.460681	+	0.887566i	$0.347605\pi$
$968$	−587.559	−	587.559i	−0.606982	−	0.606982i
$969$			305.673i			0.315452i
$970$	136.821	−	1619.23i	0.141052	−	1.66931i
$971$	−832.793			−0.857665			−0.428833	−	0.903384i	$-0.641075\pi$
$971$	−832.793			−0.857665			−0.428833	+	0.903384i	$0.641075\pi$
$972$	−32.6043	+	32.6043i	−0.0335435	+	0.0335435i
$973$	−56.6255	−	56.6255i	−0.0581968	−	0.0581968i
$974$		−	941.117i		−	0.966239i
$975$	−140.910	+	827.858i	−0.144523	+	0.849085i
$976$	956.248			0.979762
$977$	16.2686	−	16.2686i	0.0166515	−	0.0166515i	−0.698732	−	0.715384i	$-0.746252\pi$
$977$	16.2686	−	16.2686i	0.0166515	−	0.0166515i	0.715384	+	0.698732i	$0.246252\pi$
$978$	−1983.46	−	1983.46i	−2.02807	−	2.02807i
$979$		−	318.101i		−	0.324924i
$980$	9.53456	+	0.805644i	0.00972914	+	0.000822086i
$981$	−742.455			−0.756835
$982$	−868.643	+	868.643i	−0.884565	+	0.884565i
$983$	−793.635	−	793.635i	−0.807360	−	0.807360i	0.176874	−	0.984234i	$-0.443402\pi$
$983$	−793.635	−	793.635i	−0.807360	−	0.807360i	−0.984234	+	0.176874i	$0.943402\pi$
$984$			521.572i			0.530053i
$985$	770.765	−	650.658i	0.782502	−	0.660567i
$986$	2.32049			0.00235344
$987$	761.230	−	761.230i	0.771256	−	0.771256i
$988$	3.47980	+	3.47980i	0.00352206	+	0.00352206i
$989$			138.989i			0.140535i
$990$	−549.725	−	651.200i	−0.555278	−	0.657777i
$991$	930.776			0.939229			0.469615	−	0.882872i	$-0.344393\pi$
$991$	930.776			0.939229			0.469615	+	0.882872i	$0.344393\pi$
$992$	10.1422	−	10.1422i	0.0102240	−	0.0102240i
$993$	1050.81	+	1050.81i	1.05821	+	1.05821i
$994$		−	145.781i		−	0.146661i
$995$	−40.3296	+	477.288i	−0.0405322	+	0.479686i
$996$	219.190			0.220070
$997$	487.790	−	487.790i	0.489257	−	0.489257i	−0.418814	−	0.908072i	$-0.637554\pi$
$997$	487.790	−	487.790i	0.489257	−	0.489257i	0.908072	+	0.418814i	$0.137554\pi$
$998$	−757.165	−	757.165i	−0.758682	−	0.758682i
$999$		−	2283.70i		−	2.28598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.g.a.8.5	✓	12
3.2	odd	2		315.3.o.a.253.2		12
4.3	odd	2		560.3.bh.e.113.6		12
5.2	odd	4	inner	35.3.g.a.22.5	yes	12
5.3	odd	4		175.3.g.b.57.2		12
5.4	even	2		175.3.g.b.43.2		12
7.2	even	3		245.3.m.d.18.2		24
7.3	odd	6		245.3.m.c.128.5		24
7.4	even	3		245.3.m.d.128.5		24
7.5	odd	6		245.3.m.c.18.2		24
7.6	odd	2		245.3.g.a.148.5		12
15.2	even	4		315.3.o.a.127.2		12
20.7	even	4		560.3.bh.e.337.6		12
35.2	odd	12		245.3.m.d.67.5		24
35.12	even	12		245.3.m.c.67.5		24
35.17	even	12		245.3.m.c.177.2		24
35.27	even	4		245.3.g.a.197.5		12
35.32	odd	12		245.3.m.d.177.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.g.a.8.5	✓	12	1.1	even	1	trivial
35.3.g.a.22.5	yes	12	5.2	odd	4	inner
175.3.g.b.43.2		12	5.4	even	2
175.3.g.b.57.2		12	5.3	odd	4
245.3.g.a.148.5		12	7.6	odd	2
245.3.g.a.197.5		12	35.27	even	4
245.3.m.c.18.2		24	7.5	odd	6
245.3.m.c.67.5		24	35.12	even	12
245.3.m.c.128.5		24	7.3	odd	6
245.3.m.c.177.2		24	35.17	even	12
245.3.m.d.18.2		24	7.2	even	3
245.3.m.d.67.5		24	35.2	odd	12
245.3.m.d.128.5		24	7.4	even	3
245.3.m.d.177.2		24	35.32	odd	12
315.3.o.a.127.2		12	15.2	even	4
315.3.o.a.253.2		12	3.2	odd	2
560.3.bh.e.113.6		12	4.3	odd	2
560.3.bh.e.337.6		12	20.7	even	4

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36503 - 1.36503i) q^{2} +(-3.78207 - 3.78207i) q^{3} +0.273387i q^{4} +(4.98225 + 0.420986i) q^{5} -10.3253 q^{6} +(1.87083 - 1.87083i) q^{7} +(5.83330 + 5.83330i) q^{8} +19.6082i q^{9} +O(q^{10})\)	\(q+(1.36503 - 1.36503i) q^{2} +(-3.78207 - 3.78207i) q^{3} +0.273387i q^{4} +(4.98225 + 0.420986i) q^{5} -10.3253 q^{6} +(1.87083 - 1.87083i) q^{7} +(5.83330 + 5.83330i) q^{8} +19.6082i q^{9} +(7.37557 - 6.22626i) q^{10} -4.50279 q^{11} +(1.03397 - 1.03397i) q^{12} +(-4.44076 - 4.44076i) q^{13} -5.10747i q^{14} +(-17.2510 - 20.4354i) q^{15} +14.8317 q^{16} +(-14.0987 + 14.0987i) q^{17} +(26.7657 + 26.7657i) q^{18} +2.86628i q^{19} +(-0.115092 + 1.36208i) q^{20} -14.1512 q^{21} +(-6.14644 + 6.14644i) q^{22} +(-10.2041 - 10.2041i) q^{23} -44.1239i q^{24} +(24.6455 + 4.19491i) q^{25} -12.1235 q^{26} +(40.1209 - 40.1209i) q^{27} +(0.511460 + 0.511460i) q^{28} -0.0602879i q^{29} +(-51.4431 - 4.34681i) q^{30} -3.28496 q^{31} +(-3.08747 + 3.08747i) q^{32} +(17.0299 + 17.0299i) q^{33} +38.4902i q^{34} +(10.1085 - 8.53333i) q^{35} -5.36061 q^{36} +(28.4602 - 28.4602i) q^{37} +(3.91256 + 3.91256i) q^{38} +33.5906i q^{39} +(26.6072 + 31.5187i) q^{40} -11.8206 q^{41} +(-19.3168 + 19.3168i) q^{42} +(-6.81044 - 6.81044i) q^{43} -1.23100i q^{44} +(-8.25477 + 97.6927i) q^{45} -27.8578 q^{46} +(-53.7925 + 53.7925i) q^{47} +(-56.0946 - 56.0946i) q^{48} -7.00000i q^{49} +(39.3681 - 27.9157i) q^{50} +106.644 q^{51} +(1.21404 - 1.21404i) q^{52} +(-52.7265 - 52.7265i) q^{53} -109.532i q^{54} +(-22.4340 - 1.89561i) q^{55} +21.8262 q^{56} +(10.8405 - 10.8405i) q^{57} +(-0.0822948 - 0.0822948i) q^{58} -40.0962i q^{59} +(5.58677 - 4.71620i) q^{60} +64.4732 q^{61} +(-4.48407 + 4.48407i) q^{62} +(36.6835 + 36.6835i) q^{63} +67.7558i q^{64} +(-20.2555 - 23.9945i) q^{65} +46.4926 q^{66} +(30.8766 - 30.8766i) q^{67} +(-3.85438 - 3.85438i) q^{68} +77.1854i q^{69} +(2.15018 - 25.4467i) q^{70} +28.5426 q^{71} +(-114.380 + 114.380i) q^{72} +(-68.5201 - 68.5201i) q^{73} -77.6981i q^{74} +(-77.3458 - 109.077i) q^{75} -0.783604 q^{76} +(-8.42394 + 8.42394i) q^{77} +(45.8521 + 45.8521i) q^{78} -60.6193i q^{79} +(73.8952 + 6.24395i) q^{80} -127.007 q^{81} +(-16.1355 + 16.1355i) q^{82} +(105.994 + 105.994i) q^{83} -3.86876i q^{84} +(-76.1783 + 64.3076i) q^{85} -18.5929 q^{86} +(-0.228013 + 0.228013i) q^{87} +(-26.2661 - 26.2661i) q^{88} +70.6453i q^{89} +(122.085 + 144.621i) q^{90} -16.6158 q^{91} +(2.78967 - 2.78967i) q^{92} +(12.4240 + 12.4240i) q^{93} +146.857i q^{94} +(-1.20667 + 14.2805i) q^{95} +23.3541 q^{96} +(119.045 - 119.045i) q^{97} +(-9.55521 - 9.55521i) q^{98} -88.2914i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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