LMFDB - Embedded newform 72.3.p.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	72.67
Dual form			72.3.p.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99054 - 0.194264i) q^{2} +(-0.136174 - 2.99691i) q^{3} +(3.92452 + 0.773382i) q^{4} +(-3.84571 - 2.22032i) q^{5} +(-0.311131 + 5.99193i) q^{6} +(-0.704321 + 0.406640i) q^{7} +(-7.66169 - 2.30184i) q^{8} +(-8.96291 + 0.816203i) q^{9} +O(q^{10})$	\(q+(-1.99054 - 0.194264i) q^{2} +(-0.136174 - 2.99691i) q^{3} +(3.92452 + 0.773382i) q^{4} +(-3.84571 - 2.22032i) q^{5} +(-0.311131 + 5.99193i) q^{6} +(-0.704321 + 0.406640i) q^{7} +(-7.66169 - 2.30184i) q^{8} +(-8.96291 + 0.816203i) q^{9} +(7.22371 + 5.16672i) q^{10} +(-3.72022 - 6.44360i) q^{11} +(1.78333 - 11.8667i) q^{12} +(-18.0943 - 10.4468i) q^{13} +(1.48098 - 0.672610i) q^{14} +(-6.13041 + 11.8276i) q^{15} +(14.8038 + 6.07031i) q^{16} +1.74716 q^{17} +(17.9996 + 0.116483i) q^{18} +31.7920 q^{19} +(-13.3754 - 11.6879i) q^{20} +(1.31457 + 2.05541i) q^{21} +(6.15349 + 13.5490i) q^{22} +(6.44927 + 3.72348i) q^{23} +(-5.85509 + 23.2748i) q^{24} +(-2.64036 - 4.57325i) q^{25} +(33.9881 + 24.3098i) q^{26} +(3.66660 + 26.7499i) q^{27} +(-3.07861 + 1.05116i) q^{28} +(26.9672 - 15.5695i) q^{29} +(14.5005 - 22.3524i) q^{30} +(4.91458 + 2.83744i) q^{31} +(-28.2883 - 14.9590i) q^{32} +(-18.8043 + 12.0266i) q^{33} +(-3.47779 - 0.339410i) q^{34} +3.61148 q^{35} +(-35.8064 - 3.72854i) q^{36} -62.0787i q^{37} +(-63.2833 - 6.17604i) q^{38} +(-28.8440 + 55.6496i) q^{39} +(24.3538 + 25.8636i) q^{40} +(2.74032 - 4.74637i) q^{41} +(-2.21742 - 4.34676i) q^{42} +(-22.3782 - 38.7602i) q^{43} +(-9.61671 - 28.1652i) q^{44} +(36.2810 + 16.7617i) q^{45} +(-12.1142 - 8.66462i) q^{46} +(71.1253 - 41.0642i) q^{47} +(16.1763 - 45.1921i) q^{48} +(-24.1693 + 41.8624i) q^{49} +(4.36734 + 9.61617i) q^{50} +(-0.237918 - 5.23607i) q^{51} +(-62.9323 - 54.9924i) q^{52} +85.0348i q^{53} +(-2.10200 - 53.9591i) q^{54} +33.0403i q^{55} +(6.33232 - 1.49431i) q^{56} +(-4.32925 - 95.2776i) q^{57} +(-56.7040 + 25.7530i) q^{58} +(-21.8641 + 37.8697i) q^{59} +(-33.2061 + 41.6765i) q^{60} +(-61.1107 + 35.2823i) q^{61} +(-9.23148 - 6.60276i) q^{62} +(5.98087 - 4.21955i) q^{63} +(53.4030 + 35.2720i) q^{64} +(46.3903 + 80.3504i) q^{65} +(39.7671 - 20.2865i) q^{66} +(9.91758 - 17.1778i) q^{67} +(6.85675 + 1.35122i) q^{68} +(10.2807 - 19.8349i) q^{69} +(-7.18881 - 0.701581i) q^{70} -69.3125i q^{71} +(70.5498 + 14.3777i) q^{72} -21.7177 q^{73} +(-12.0597 + 123.570i) q^{74} +(-13.3460 + 8.53569i) q^{75} +(124.768 + 24.5873i) q^{76} +(5.24046 + 3.02558i) q^{77} +(68.2260 - 105.170i) q^{78} +(37.1475 - 21.4471i) q^{79} +(-43.4529 - 56.2137i) q^{80} +(79.6676 - 14.6311i) q^{81} +(-6.37677 + 8.91551i) q^{82} +(-3.53270 - 6.11881i) q^{83} +(3.56946 + 9.08318i) q^{84} +(-6.71905 - 3.87924i) q^{85} +(37.0151 + 81.5012i) q^{86} +(-50.3327 - 78.6981i) q^{87} +(13.6710 + 57.9323i) q^{88} +37.1192 q^{89} +(-68.9626 - 40.4129i) q^{90} +16.9923 q^{91} +(22.4306 + 19.6006i) q^{92} +(7.83429 - 15.1149i) q^{93} +(-149.555 + 67.9230i) q^{94} +(-122.263 - 70.5883i) q^{95} +(-40.9788 + 86.8144i) q^{96} +(9.38806 + 16.2606i) q^{97} +(56.2424 - 78.6338i) q^{98} +(38.6033 + 54.7170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9	$ 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) $ 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9 - 12 * q^10 - 16 * q^11 - 12 * q^12 + 6 * q^14 + 31 * q^16 - 4 * q^17 - 114 * q^18 - 76 * q^19 - 12 * q^20 + 35 * q^22 + 39 * q^24 + 118 * q^25 - 72 * q^26 - 144 * q^27 - 36 * q^28 - 90 * q^30 - 5 * q^32 + 156 * q^33 + 5 * q^34 - 108 * q^35 + 51 * q^36 - 169 * q^38 - 6 * q^40 + 20 * q^41 - 42 * q^42 - 16 * q^43 + 362 * q^44 - 96 * q^46 + 183 * q^48 + 166 * q^49 + 73 * q^50 + 330 * q^51 - 24 * q^52 + 57 * q^54 + 186 * q^56 - 258 * q^57 + 36 * q^58 - 64 * q^59 + 150 * q^60 + 384 * q^62 - 518 * q^64 - 102 * q^65 + 486 * q^66 - 64 * q^67 - 295 * q^68 - 6 * q^70 - 225 * q^72 - 292 * q^73 + 318 * q^74 + 138 * q^75 + 197 * q^76 + 174 * q^78 - 720 * q^80 - 42 * q^81 + 386 * q^82 + 554 * q^83 - 720 * q^84 - 295 * q^86 + 59 * q^88 - 688 * q^89 - 696 * q^90 - 204 * q^91 - 378 * q^92 - 66 * q^94 - 222 * q^96 + 92 * q^97 - 614 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.99054	−	0.194264i	−0.995272	−	0.0971320i
$2$	−1.99054	−	0.194264i	−0.995272	−	0.0971320i
$3$	−0.136174	−	2.99691i	−0.0453914	−	0.998969i
$3$	−0.136174	−	2.99691i	−0.0453914	−	0.998969i
$4$	3.92452	+	0.773382i	0.981131	+	0.193345i
$5$	−3.84571	−	2.22032i	−0.769141	−	0.444064i	0.0634270	−	0.997986i	$-0.479797\pi$
$5$	−3.84571	−	2.22032i	−0.769141	−	0.444064i	−0.832568	+	0.553923i	$0.813130\pi$
$6$	−0.311131	+	5.99193i	−0.0518551	+	0.998655i
$7$	−0.704321	+	0.406640i	−0.100617	+	0.0580915i	−0.549464	−	0.835517i	$-0.685168\pi$
$7$	−0.704321	+	0.406640i	−0.100617	+	0.0580915i	0.448847	+	0.893609i	$0.351835\pi$
$8$	−7.66169	−	2.30184i	−0.957711	−	0.287730i
$9$	−8.96291	+	0.816203i	−0.995879	+	0.0906893i
$10$	7.22371	+	5.16672i	0.722371	+	0.516672i
$11$	−3.72022	−	6.44360i	−0.338201	−	0.585782i	0.645893	−	0.763428i	$-0.276485\pi$
$11$	−3.72022	−	6.44360i	−0.338201	−	0.585782i	−0.984094	+	0.177646i	$0.943152\pi$
$12$	1.78333	−	11.8667i	0.148611	−	0.988896i
$13$	−18.0943	−	10.4468i	−1.39187	−	0.803598i	−0.398349	−	0.917234i	$-0.630417\pi$
$13$	−18.0943	−	10.4468i	−1.39187	−	0.803598i	−0.993522	+	0.113636i	$0.963750\pi$
$14$	1.48098	−	0.672610i	0.105784	−	0.0480436i
$15$	−6.13041	+	11.8276i	−0.408694	+	0.788505i
$16$	14.8038	+	6.07031i	0.925235	+	0.379394i
$17$	1.74716			0.102774			0.0513869	−	0.998679i	$-0.483636\pi$
$17$	1.74716			0.102774			0.0513869	+	0.998679i	$0.483636\pi$
$18$	17.9996	+	0.116483i	0.999979	+	0.00647129i
$19$	31.7920			1.67326			0.836631	−	0.547767i	$-0.184522\pi$
$19$	31.7920			1.67326			0.836631	+	0.547767i	$0.184522\pi$
$20$	−13.3754	−	11.6879i	−0.668770	−	0.584395i
$21$	1.31457	+	2.05541i	0.0625987	+	0.0978768i
$22$	6.15349	+	13.5490i	0.279704	+	0.615862i
$23$	6.44927	+	3.72348i	0.280403	+	0.161891i	0.633606	−	0.773656i	$-0.281574\pi$
$23$	6.44927	+	3.72348i	0.280403	+	0.161891i	−0.353203	+	0.935547i	$0.614907\pi$
$24$	−5.85509	+	23.2748i	−0.243962	+	0.969785i
$25$	−2.64036	−	4.57325i	−0.105615	−	0.182930i
$26$	33.9881	+	24.3098i	1.30724	+	0.934993i
$27$	3.66660	+	26.7499i	0.135800	+	0.990736i
$28$	−3.07861	+	1.05116i	−0.109950	+	0.0375414i
$29$	26.9672	−	15.5695i	0.929904	−	0.536880i	0.0431225	−	0.999070i	$-0.486269\pi$
$29$	26.9672	−	15.5695i	0.929904	−	0.536880i	0.886781	+	0.462190i	$0.152936\pi$
$30$	14.5005	−	22.3524i	0.483350	−	0.745079i
$31$	4.91458	+	2.83744i	0.158535	+	0.0915302i	0.577169	−	0.816625i	$-0.304158\pi$
$31$	4.91458	+	2.83744i	0.158535	+	0.0915302i	−0.418634	+	0.908155i	$0.637491\pi$
$32$	−28.2883	−	14.9590i	−0.884009	−	0.467470i
$33$	−18.8043	+	12.0266i	−0.569827	+	0.364442i
$34$	−3.47779	−	0.339410i	−0.102288	−	0.00998263i
$35$	3.61148			0.103185
$36$	−35.8064	−	3.72854i	−0.994622	−	0.103571i
$37$		−	62.0787i		−	1.67780i	−0.544283	−	0.838902i	$-0.683198\pi$
$37$		−	62.0787i		−	1.67780i	0.544283	−	0.838902i	$-0.316802\pi$
$38$	−63.2833	−	6.17604i	−1.66535	−	0.162527i
$39$	−28.8440	+	55.6496i	−0.739590	+	1.42691i
$40$	24.3538	+	25.8636i	0.608845	+	0.646590i
$41$	2.74032	−	4.74637i	0.0668370	−	0.115765i	−0.830670	−	0.556765i	$-0.812043\pi$
$41$	2.74032	−	4.74637i	0.0668370	−	0.115765i	0.897507	+	0.440999i	$0.145376\pi$
$42$	−2.21742	−	4.34676i	−0.0527958	−	0.103494i
$43$	−22.3782	−	38.7602i	−0.520424	−	0.901401i	−0.999718	−	0.0237465i	$-0.992441\pi$
$43$	−22.3782	−	38.7602i	−0.520424	−	0.901401i	0.479294	−	0.877654i	$-0.340893\pi$
$44$	−9.61671	−	28.1652i	−0.218562	−	0.640119i
$45$	36.2810	+	16.7617i	0.806244	+	0.372481i
$46$	−12.1142	−	8.66462i	−0.263352	−	0.188361i
$47$	71.1253	−	41.0642i	1.51330	−	0.873707i	0.513425	−	0.858134i	$-0.328376\pi$
$47$	71.1253	−	41.0642i	1.51330	−	0.873707i	0.999879	−	0.0155723i	$-0.00495702\pi$
$48$	16.1763	−	45.1921i	0.337005	−	0.941503i
$49$	−24.1693	+	41.8624i	−0.493251	+	0.854335i
$50$	4.36734	+	9.61617i	0.0873469	+	0.192323i
$51$	−0.237918	−	5.23607i	−0.00466505	−	0.102668i
$52$	−62.9323	−	54.9924i	−1.21024	−	1.05755i
$53$			85.0348i			1.60443i	0.597035	+	0.802215i	$0.296345\pi$
$53$			85.0348i			1.60443i	−0.597035	+	0.802215i	$0.703655\pi$
$54$	−2.10200	−	53.9591i	−0.0389258	−	0.999242i
$55$			33.0403i			0.600732i
$56$	6.33232	−	1.49431i	0.113077	−	0.0266842i
$57$	−4.32925	−	95.2776i	−0.0759517	−	1.67154i
$58$	−56.7040	+	25.7530i	−0.977655	+	0.444018i
$59$	−21.8641	+	37.8697i	−0.370578	+	0.641860i	−0.989655	−	0.143471i	$-0.954174\pi$
$59$	−21.8641	+	37.8697i	−0.370578	+	0.641860i	0.619077	+	0.785331i	$0.287507\pi$
$60$	−33.2061	+	41.6765i	−0.553436	+	0.694608i
$61$	−61.1107	+	35.2823i	−1.00182	+	0.578398i	−0.908785	−	0.417265i	$-0.862989\pi$
$61$	−61.1107	+	35.2823i	−1.00182	+	0.578398i	−0.0930305	+	0.995663i	$0.529655\pi$
$62$	−9.23148	−	6.60276i	−0.148895	−	0.106496i
$63$	5.98087	−	4.21955i	0.0949345	−	0.0669770i
$64$	53.4030	+	35.2720i	0.834422	+	0.551125i
$65$	46.3903	+	80.3504i	0.713697	+	1.23616i
$66$	39.7671	−	20.2865i	0.602531	−	0.307371i
$67$	9.91758	−	17.1778i	0.148024	−	0.256384i	−0.782473	−	0.622684i	$-0.786042\pi$
$67$	9.91758	−	17.1778i	0.148024	−	0.256384i	0.930497	+	0.366300i	$0.119376\pi$
$68$	6.85675	+	1.35122i	0.100835	+	0.0198709i
$69$	10.2807	−	19.8349i	0.148996	−	0.287462i
$70$	−7.18881	−	0.701581i	−0.102697	−	0.0100226i
$71$		−	69.3125i		−	0.976232i	−0.872779	−	0.488116i	$-0.837684\pi$
$71$		−	69.3125i		−	0.976232i	0.872779	−	0.488116i	$-0.162316\pi$
$72$	70.5498	+	14.3777i	0.979859	+	0.199691i
$73$	−21.7177			−0.297502			−0.148751	−	0.988875i	$-0.547525\pi$
$73$	−21.7177			−0.297502			−0.148751	+	0.988875i	$0.547525\pi$
$74$	−12.0597	+	123.570i	−0.162968	+	1.66987i
$75$	−13.3460	+	8.53569i	−0.177947	+	0.113809i
$76$	124.768	+	24.5873i	1.64169	+	0.323518i
$77$	5.24046	+	3.02558i	0.0680579	+	0.0392932i
$78$	68.2260	−	105.170i	0.874692	−	1.34833i
$79$	37.1475	−	21.4471i	0.470221	−	0.271482i	−0.246111	−	0.969242i	$-0.579153\pi$
$79$	37.1475	−	21.4471i	0.470221	−	0.271482i	0.716332	+	0.697759i	$0.245820\pi$
$80$	−43.4529	−	56.2137i	−0.543161	−	0.702671i
$81$	79.6676	−	14.6311i	0.983551	−	0.180631i
$82$	−6.37677	+	8.91551i	−0.0777655	+	0.108726i
$83$	−3.53270	−	6.11881i	−0.0425626	−	0.0737206i	0.843959	−	0.536407i	$-0.180219\pi$
$83$	−3.53270	−	6.11881i	−0.0425626	−	0.0737206i	−0.886522	+	0.462687i	$0.846886\pi$
$84$	3.56946	+	9.08318i	0.0424935	+	0.108133i
$85$	−6.71905	−	3.87924i	−0.0790476	−	0.0456382i
$86$	37.0151	+	81.5012i	0.430408	+	0.947689i
$87$	−50.3327	−	78.6981i	−0.578536	−	0.904575i
$88$	13.6710	+	57.9323i	0.155352	+	0.658321i
$89$	37.1192			0.417070			0.208535	−	0.978015i	$-0.433130\pi$
$89$	37.1192			0.417070			0.208535	+	0.978015i	$0.433130\pi$
$90$	−68.9626	−	40.4129i	−0.766251	−	0.449032i
$91$	16.9923			0.186729
$92$	22.4306	+	19.6006i	0.243811	+	0.213050i
$93$	7.83429	−	15.1149i	0.0842397	−	0.162526i
$94$	−149.555	+	67.9230i	−1.59101	+	0.722585i
$95$	−122.263	−	70.5883i	−1.28697	−	0.743035i
$96$	−40.9788	+	86.8144i	−0.426862	+	0.904317i
$97$	9.38806	+	16.2606i	0.0967841	+	0.167635i	0.910352	−	0.413835i	$-0.135811\pi$
$97$	9.38806	+	16.2606i	0.0967841	+	0.167635i	−0.813568	+	0.581470i	$0.802478\pi$
$98$	56.2424	−	78.6338i	0.573902	−	0.802385i
$99$	38.6033	+	54.7170i	0.389932	+	0.552697i
$100$	−6.82531	−	19.9898i	−0.0682531	−	0.199898i
$101$	−70.1044	+	40.4748i	−0.694103	+	0.400740i	−0.805147	−	0.593075i	$-0.797914\pi$
$101$	−70.1044	+	40.4748i	−0.694103	+	0.400740i	0.111044	+	0.993815i	$0.464580\pi$
$102$	−0.543594	+	10.4688i	−0.00532935	+	0.102636i
$103$	28.0494	+	16.1943i	0.272324	+	0.157226i	0.629943	−	0.776641i	$-0.283078\pi$
$103$	28.0494	+	16.1943i	0.272324	+	0.157226i	−0.357619	+	0.933867i	$0.616411\pi$
$104$	114.586	+	121.690i	1.10179	+	1.17010i
$105$	−0.491791	−	10.8233i	−0.00468373	−	0.103079i
$106$	16.5192	−	169.265i	0.155842	−	1.59684i
$107$	−182.822			−1.70862			−0.854309	−	0.519765i	$-0.826019\pi$
$107$	−182.822			−1.70862			−0.854309	+	0.519765i	$0.826019\pi$
$108$	−6.29819	+	107.816i	−0.0583166	+	0.998298i
$109$		−	7.30063i		−	0.0669782i	−0.999439	−	0.0334891i	$-0.989338\pi$
$109$		−	7.30063i		−	0.0669782i	0.999439	−	0.0334891i	$-0.0106619\pi$
$110$	6.41853	−	65.7681i	0.0583503	−	0.597892i
$111$	−186.044	+	8.45352i	−1.67607	+	0.0761579i
$112$	−12.8950	+	1.74436i	−0.115134	+	0.0155746i
$113$	70.9810	−	122.943i	0.628151	−	1.08799i	−0.359772	−	0.933040i	$-0.617145\pi$
$113$	70.9810	−	122.943i	0.628151	−	1.08799i	0.987923	−	0.154949i	$-0.0495212\pi$
$114$	−9.89146	+	190.495i	−0.0867672	+	1.67101i
$115$	−16.5347	−	28.6389i	−0.143780	−	0.249034i
$116$	117.875	−	40.2470i	1.01616	−	0.346957i
$117$	170.705	+	78.8648i	1.45901	+	0.674058i
$118$	50.8781	−	71.1339i	0.431171	−	0.602830i
$119$	−1.23056	+	0.710464i	−0.0103408	+	0.00597028i
$120$	74.1945	−	76.5080i	0.618288	−	0.637567i
$121$	32.8200	−	56.8459i	0.271240	−	0.469801i
$122$	128.498	−	58.3593i	1.05326	−	0.478355i
$123$	−14.5976	−	7.56615i	−0.118680	−	0.0615134i
$124$	17.0930	+	14.9364i	0.137847	+	0.120455i
$125$			134.466i			1.07573i
$126$	−12.7249	+	7.23733i	−0.100991	+	0.0574391i
$127$			113.378i			0.892740i	0.894849	+	0.446370i	$0.147283\pi$
$127$			113.378i			0.892740i	−0.894849	+	0.446370i	$0.852717\pi$
$128$	−99.4490	−	80.5848i	−0.776945	−	0.629568i
$129$	−113.114	+	72.3437i	−0.876849	+	0.560804i
$130$	−76.7327	−	168.953i	−0.590252	−	1.29964i
$131$	77.7152	−	134.607i	0.593245	−	1.02753i	−0.400546	−	0.916276i	$-0.631180\pi$
$131$	77.7152	−	134.607i	0.593245	−	1.02753i	0.993792	−	0.111255i	$-0.0354870\pi$
$132$	−83.0990	+	32.6558i	−0.629538	+	0.247392i
$133$	−22.3918	+	12.9279i	−0.168359	+	0.0972022i
$134$	−23.0784	+	32.2664i	−0.172227	+	0.240794i
$135$	45.2926	−	111.013i	0.335501	−	0.822320i
$136$	−13.3862	−	4.02168i	−0.0984277	−	0.0295712i
$137$	−30.9899	−	53.6760i	−0.226203	−	0.391796i	0.730476	−	0.682938i	$-0.239298\pi$
$137$	−30.9899	−	53.6760i	−0.226203	−	0.391796i	−0.956680	+	0.291142i	$0.905965\pi$
$138$	−24.3174	+	37.4850i	−0.176213	+	0.271631i
$139$	−67.1343	+	116.280i	−0.482981	+	0.836547i	−0.999809	−	0.0195419i	$-0.993779\pi$
$139$	−67.1343	+	116.280i	−0.482981	+	0.836547i	0.516828	+	0.856089i	$0.327113\pi$
$140$	14.1734	+	2.79306i	0.101238	+	0.0199504i
$141$	−132.751	−	207.564i	−0.941497	−	1.47209i
$142$	−13.4649	+	137.970i	−0.0948234	+	0.971616i
$143$			155.457i			1.08711i
$144$	−137.639	−	42.3248i	−0.955829	−	0.293922i
$145$	−138.277			−0.953636
$146$	43.2299	+	4.21896i	0.296095	+	0.0288970i
$147$	128.749	+	66.7325i	0.875844	+	0.453963i
$148$	48.0105	−	243.629i	0.324396	−	1.64614i
$149$	−137.914	−	79.6250i	−0.925600	−	0.534396i	−0.0401830	−	0.999192i	$-0.512794\pi$
$149$	−137.914	−	79.6250i	−0.925600	−	0.534396i	−0.885417	+	0.464797i	$0.846127\pi$
$150$	28.2241	−	14.3980i	0.188160	−	0.0959867i
$151$	170.069	−	98.1895i	1.12629	−	0.650261i	0.183288	−	0.983059i	$-0.441326\pi$
$151$	170.069	−	98.1895i	1.12629	−	0.650261i	0.942998	+	0.332798i	$0.107993\pi$
$152$	−243.580	−	73.1801i	−1.60250	−	0.481448i
$153$	−15.6596	+	1.42603i	−0.102350	+	0.00932049i
$154$	−9.84359	−	7.04058i	−0.0639194	−	0.0457180i
$155$	−12.6000	−	21.8239i	−0.0812905	−	0.140799i
$156$	−156.237	+	196.091i	−1.00152	+	1.25699i
$157$	179.848	+	103.835i	1.14553	+	0.661371i	0.947794	−	0.318884i	$-0.103308\pi$
$157$	179.848	+	103.835i	1.14553	+	0.661371i	0.197735	+	0.980256i	$0.436642\pi$
$158$	−78.1100	+	35.4750i	−0.494367	+	0.224525i
$159$	254.841	−	11.5796i	1.60278	−	0.0728274i
$160$	75.5745	+	120.337i	0.472341	+	0.752107i
$161$	−6.05647			−0.0376179
$162$	−161.424	+	13.6473i	−0.996445	+	0.0842427i
$163$	194.579			1.19373			0.596867	−	0.802340i	$-0.296412\pi$
$163$	194.579			1.19373			0.596867	+	0.802340i	$0.296412\pi$
$164$	14.4252	−	16.5079i	0.0879585	−	0.100658i
$165$	99.0186	−	4.49923i	0.600113	−	0.0272681i
$166$	5.84332	+	12.8660i	0.0352007	+	0.0775063i
$167$	−40.2285	−	23.2259i	−0.240889	−	0.139077i	0.374696	−	0.927148i	$-0.377747\pi$
$167$	−40.2285	−	23.2259i	−0.240889	−	0.139077i	−0.615585	+	0.788070i	$0.711080\pi$
$168$	−5.34062	−	18.7739i	−0.0317894	−	0.111749i
$169$	133.770	+	231.696i	0.791538	+	1.37098i
$170$	12.6210	+	9.02707i	0.0742409	+	0.0531004i
$171$	−284.949	+	25.9487i	−1.66637	+	0.151747i
$172$	−57.8474	−	169.422i	−0.336322	−	0.985014i
$173$	52.2672	−	30.1765i	0.302123	−	0.174431i	−0.341273	−	0.939964i	$-0.610858\pi$
$173$	52.2672	−	30.1765i	0.302123	−	0.174431i	0.643396	+	0.765533i	$0.277525\pi$
$174$	84.9011	+	166.430i	0.487938	+	0.956492i
$175$	3.71933	+	2.14736i	0.0212533	+	0.0122706i
$176$	−15.9585	−	117.972i	−0.0906735	−	0.670298i
$177$	116.469	+	60.3678i	0.658019	+	0.341061i
$178$	−73.8874	−	7.21093i	−0.415098	−	0.0405108i
$179$	123.945			0.692427			0.346214	−	0.938156i	$-0.387467\pi$
$179$	123.945			0.692427			0.346214	+	0.938156i	$0.387467\pi$
$180$	129.422	+	93.8405i	0.719013	+	0.521336i
$181$		−	114.095i		−	0.630359i	−0.949032	−	0.315179i	$-0.897935\pi$
$181$		−	114.095i		−	0.630359i	0.949032	−	0.315179i	$-0.102065\pi$
$182$	−33.8239	−	3.30099i	−0.185846	−	0.0181373i
$183$	114.060	+	178.339i	0.623276	+	0.974528i
$184$	−40.8414	−	43.3734i	−0.221964	−	0.235725i
$185$	−137.835	+	238.736i	−0.745052	+	1.29047i
$186$	−18.5308	+	28.5650i	−0.0996279	+	0.153575i
$187$	−6.49980	−	11.2580i	−0.0347583	−	0.0602031i
$188$	310.891	−	106.150i	1.65368	−	0.564630i
$189$	−13.4600	−	17.3495i	−0.0712172	−	0.0917964i
$190$	229.656	+	164.260i	1.20872	+	0.864528i
$191$	12.0842	−	6.97684i	0.0632683	−	0.0365280i	−0.468032	−	0.883711i	$-0.655037\pi$
$191$	12.0842	−	6.97684i	0.0632683	−	0.0365280i	0.531300	+	0.847183i	$0.321704\pi$
$192$	98.4349	−	164.847i	0.512682	−	0.858579i
$193$	30.2654	−	52.4212i	0.156816	−	0.271613i	−0.776903	−	0.629620i	$-0.783210\pi$
$193$	30.2654	−	52.4212i	0.156816	−	0.271613i	0.933719	+	0.358008i	$0.116544\pi$
$194$	−15.5285	−	34.1912i	−0.0800437	−	0.176243i
$195$	234.486	−	149.969i	1.20249	−	0.769073i
$196$	−127.229	+	145.598i	−0.649125	+	0.742847i
$197$		−	154.506i		−	0.784296i	−0.919902	−	0.392148i	$-0.871732\pi$
$197$		−	154.506i		−	0.784296i	0.919902	−	0.392148i	$-0.128268\pi$
$198$	−66.2119	−	116.416i	−0.334404	−	0.587958i
$199$			268.439i			1.34894i	0.738301	+	0.674471i	$0.235628\pi$
$199$			268.439i			1.34894i	−0.738301	+	0.674471i	$0.764372\pi$
$200$	9.70277	+	41.1165i	0.0485138	+	0.205583i
$201$	−52.8307	−	27.3829i	−0.262839	−	0.136233i
$202$	147.409	−	66.9480i	0.729745	−	0.331426i
$203$	−12.6624	+	21.9319i	−0.0623763	+	0.108039i
$204$	3.11576	−	20.7331i	0.0152734	−	0.101633i
$205$	−21.0769	+	12.1688i	−0.102814	+	0.0593598i
$206$	−52.6875	−	37.6845i	−0.255765	−	0.182934i
$207$	−60.8433	−	28.1094i	−0.293929	−	0.135794i
$208$	−204.449	−	264.490i	−0.982928	−	1.27158i
$209$	−118.273	−	204.855i	−0.565900	−	0.980167i
$210$	−1.12364	+	21.6398i	−0.00535068	+	0.103046i
$211$	59.5357	−	103.119i	0.282159	−	0.488715i	−0.689757	−	0.724041i	$-0.742283\pi$
$211$	59.5357	−	103.119i	0.282159	−	0.488715i	0.971916	+	0.235326i	$0.0756159\pi$
$212$	−65.7644	+	333.721i	−0.310209	+	1.57416i
$213$	−207.723	+	9.43858i	−0.975226	+	0.0443126i
$214$	363.915	+	35.5158i	1.70054	+	0.165962i
$215$			198.747i			0.924406i
$216$	33.4816	−	213.389i	0.155008	−	0.987913i
$217$	−4.61526			−0.0212685
$218$	−1.41825	+	14.5322i	−0.00650573	+	0.0666615i
$219$	2.95739	+	65.0858i	0.0135040	+	0.297196i
$220$	−25.5527	+	129.667i	−0.116149	+	0.589397i
$221$	−31.6136	−	18.2521i	−0.143048	−	0.0825888i
$222$	371.971	+	19.3146i	1.67555	+	0.0870026i
$223$	−93.8558	+	54.1876i	−0.420878	+	0.242994i	−0.695453	−	0.718572i	$-0.744796\pi$
$223$	−93.8558	+	54.1876i	−0.420878	+	0.242994i	0.274575	+	0.961566i	$0.411463\pi$
$224$	26.0070	−	0.967174i	0.116103	−	0.00431774i
$225$	27.3981	+	38.8345i	0.121769	+	0.172598i
$226$	−165.174	+	230.934i	−0.730859	+	1.02183i
$227$	135.060	+	233.930i	0.594977	+	1.03053i	0.993550	+	0.113394i	$0.0361721\pi$
$227$	135.060	+	233.930i	0.594977	+	1.03053i	−0.398573	+	0.917136i	$0.630495\pi$
$228$	56.6957	−	377.267i	0.248666	−	1.65468i
$229$	92.7803	+	53.5667i	0.405154	+	0.233916i	0.688705	−	0.725041i	$-0.258179\pi$
$229$	92.7803	+	53.5667i	0.405154	+	0.233916i	−0.283551	+	0.958957i	$0.591513\pi$
$230$	27.3494	+	60.2190i	0.118911	+	0.261822i
$231$	8.35376	−	16.1172i	0.0361635	−	0.0697713i
$232$	−242.453	+	57.2146i	−1.04506	+	0.246615i
$233$	−224.925			−0.965344			−0.482672	−	0.875801i	$-0.660334\pi$
$233$	−224.925			−0.965344			−0.482672	+	0.875801i	$0.660334\pi$
$234$	−324.474	−	190.146i	−1.38664	−	0.812588i
$235$	−364.703			−1.55193
$236$	−115.094	+	131.711i	−0.487686	+	0.558099i
$237$	−69.3335	−	108.407i	−0.292546	−	0.457413i
$238$	2.58750	−	1.17516i	0.0108718	−	0.00493763i
$239$	77.4022	+	44.6882i	0.323859	+	0.186980i	0.653111	−	0.757262i	$-0.273463\pi$
$239$	77.4022	+	44.6882i	0.323859	+	0.186980i	−0.329253	+	0.944242i	$0.606797\pi$
$240$	−162.550	+	137.879i	−0.677292	+	0.574497i
$241$	−135.051	−	233.915i	−0.560377	−	0.970602i	−0.997463	−	0.0711821i	$-0.977323\pi$
$241$	−135.051	−	233.915i	−0.560377	−	0.970602i	0.437086	−	0.899420i	$-0.356010\pi$
$242$	−76.3727	+	106.778i	−0.315590	+	0.441233i
$243$	−54.6968	−	236.764i	−0.225090	−	0.974338i
$244$	−267.117	+	91.2043i	−1.09474	+	0.373788i
$245$	185.896	−	107.327i	0.758759	−	0.438070i
$246$	27.5873	+	17.8965i	0.112144	+	0.0727501i
$247$	−575.255	−	332.123i	−2.32897	−	1.34463i
$248$	−31.1227	−	33.0522i	−0.125495	−	0.133275i
$249$	−17.8565	+	11.4204i	−0.0717127	+	0.0458650i
$250$	26.1219	−	267.660i	0.104487	−	1.07064i
$251$	247.901			0.987654			0.493827	−	0.869560i	$-0.335598\pi$
$251$	247.901			0.987654			0.493827	+	0.869560i	$0.335598\pi$
$252$	26.7354	−	11.9342i	0.106093	−	0.0473580i
$253$		−	55.4087i		−	0.219007i
$254$	22.0253	−	225.684i	0.0867136	−	0.888518i
$255$	−10.7108	+	20.6646i	−0.0420030	+	0.0810377i
$256$	182.303	+	179.727i	0.712120	+	0.702058i
$257$	43.2996	−	74.9972i	0.168481	−	0.291818i	−0.769405	−	0.638761i	$-0.779447\pi$
$257$	43.2996	−	74.9972i	0.168481	−	0.291818i	0.937886	+	0.346944i	$0.112780\pi$
$258$	239.211	−	122.029i	0.927175	−	0.472982i
$259$	25.2437	+	43.7234i	0.0974660	+	0.168816i
$260$	119.918	+	351.214i	0.461224	+	1.35082i
$261$	−228.997	+	161.559i	−0.877382	+	0.619000i
$262$	−180.845	+	252.843i	−0.690247	+	0.965050i
$263$	−36.7606	+	21.2237i	−0.139774	+	0.0806986i	−0.568256	−	0.822852i	$-0.692382\pi$
$263$	−36.7606	+	21.2237i	−0.139774	+	0.0806986i	0.428482	+	0.903550i	$0.359048\pi$
$264$	171.756	−	48.8596i	0.650591	−	0.185074i
$265$	188.804	−	327.019i	0.712470	−	1.23403i
$266$	47.0832	−	21.3836i	0.177005	−	0.0803895i
$267$	−5.05468	−	111.243i	−0.0189314	−	0.416640i
$268$	52.2067	−	59.7444i	0.194801	−	0.222927i
$269$		−	329.459i		−	1.22475i	−0.790566	−	0.612377i	$-0.790214\pi$
$269$		−	329.459i		−	1.22475i	0.790566	−	0.612377i	$-0.209786\pi$
$270$	−111.723	+	212.178i	−0.413788	+	0.785844i
$271$		−	369.325i		−	1.36282i	−0.731901	−	0.681411i	$-0.761367\pi$
$271$		−	369.325i		−	1.36282i	0.731901	−	0.681411i	$-0.238633\pi$
$272$	25.8645	+	10.6058i	0.0950900	+	0.0389918i
$273$	−2.31391	−	50.9244i	−0.00847588	−	0.186536i
$274$	51.2594	+	112.865i	0.187078	+	0.411915i
$275$	−19.6455	+	34.0269i	−0.0714380	+	0.123734i
$276$	55.6869	−	69.8916i	0.201764	−	0.253230i
$277$	−159.324	+	91.9857i	−0.575177	+	0.332078i	−0.759214	−	0.650841i	$-0.774417\pi$
$277$	−159.324	+	91.9857i	−0.575177	+	0.332078i	0.184038	+	0.982919i	$0.441083\pi$
$278$	156.223	−	218.419i	0.561952	−	0.785679i
$279$	−46.3649	−	21.4204i	−0.166182	−	0.0767756i
$280$	−27.6701	−	8.31307i	−0.0988217	−	0.0296895i
$281$	197.079	+	341.350i	0.701348	+	1.21477i	0.967993	+	0.250976i	$0.0807514\pi$
$281$	197.079	+	341.350i	0.701348	+	1.21477i	−0.266646	+	0.963795i	$0.585915\pi$
$282$	223.925	+	438.954i	0.794059	+	1.55657i
$283$	−147.257	+	255.057i	−0.520344	+	0.901262i	0.479377	+	0.877609i	$0.340863\pi$
$283$	−147.257	+	255.057i	−0.520344	+	0.901262i	−0.999720	+	0.0236524i	$0.992471\pi$
$284$	53.6050	−	272.019i	0.188750	−	0.957812i
$285$	−194.898	+	376.022i	−0.683852	+	1.31938i
$286$	30.1997	−	309.444i	0.105593	−	1.08197i
$287$			4.45729i			0.0155306i
$288$	265.755	+	110.988i	0.922761	+	0.385374i
$289$	−285.947			−0.989438
$290$	275.247	+	26.8623i	0.949127	+	0.0926286i
$291$	47.4531	−	30.3494i	0.163069	−	0.104294i
$292$	−85.2314	−	16.7960i	−0.291889	−	0.0575207i
$293$	230.417	+	133.031i	0.786406	+	0.454032i	0.838696	−	0.544600i	$-0.183319\pi$
$293$	230.417	+	133.031i	0.786406	+	0.454032i	−0.0522899	+	0.998632i	$0.516652\pi$
$294$	−243.317	−	157.845i	−0.827608	−	0.536889i
$295$	168.166	−	97.0905i	0.570053	−	0.329120i
$296$	−142.895	+	475.628i	−0.482755	+	1.60685i
$297$	158.725	−	123.141i	0.534428	−	0.414618i
$298$	259.056	+	185.289i	0.869317	+	0.621774i
$299$	−77.7968	−	134.748i	−0.260190	−	0.450662i
$300$	−58.9782	+	23.1769i	−0.196594	+	0.0772564i
$301$	31.5229	+	18.1998i	0.104727	+	0.0604644i
$302$	−357.605	+	162.412i	−1.18412	+	0.537788i
$303$	130.846	+	204.585i	0.431834	+	0.675197i
$304$	470.641	+	192.987i	1.54816	+	0.634826i
$305$	313.352			1.02738
$306$	31.4482	+	0.203514i	0.102772	+	0.000665080i
$307$	104.646			0.340865			0.170433	−	0.985369i	$-0.445483\pi$
$307$	104.646			0.340865			0.170433	+	0.985369i	$0.445483\pi$
$308$	18.2264	+	15.9268i	0.0591765	+	0.0517105i
$309$	44.7133	−	86.2667i	0.144703	−	0.279180i
$310$	20.8413	+	45.8891i	0.0672300	+	0.148029i
$311$	268.616	+	155.085i	0.863716	+	0.498667i	0.865255	−	0.501332i	$-0.167157\pi$
$311$	268.616	+	155.085i	0.863716	+	0.498667i	−0.00153895	+	0.999999i	$0.500490\pi$
$312$	349.091	−	359.976i	1.11888	−	1.15377i
$313$	201.331	+	348.715i	0.643229	+	1.11411i	0.984708	+	0.174216i	$0.0557390\pi$
$313$	201.331	+	348.715i	0.643229	+	1.11411i	−0.341479	+	0.939890i	$0.610928\pi$
$314$	−337.824	−	241.627i	−1.07587	−	0.769511i
$315$	−32.3694	+	2.94771i	−0.102760	+	0.00935780i
$316$	162.373	−	55.4405i	0.513838	−	0.175444i
$317$	162.167	−	93.6269i	0.511566	−	0.295353i	−0.221911	−	0.975067i	$-0.571229\pi$
$317$	162.167	−	93.6269i	0.511566	−	0.295353i	0.733477	+	0.679714i	$0.237896\pi$
$318$	−509.522	−	26.4569i	−1.60227	−	0.0831979i
$319$	−200.648	−	115.844i	−0.628989	−	0.363147i
$320$	−127.057	−	254.218i	−0.397054	−	0.794430i
$321$	24.8957	+	547.901i	0.0775566	+	1.70686i
$322$	12.0557	+	1.17655i	0.0374400	+	0.00365390i
$323$	55.5456			0.171968
$324$	323.973	+	4.19331i	0.999916	+	0.0129423i
$325$			110.333i			0.339487i
$326$	−387.317	−	37.7996i	−1.18809	−	0.115950i
$327$	−21.8793	+	0.994158i	−0.0669092	+	0.00304024i
$328$	−31.9209	+	30.0574i	−0.0973197	+	0.0916386i
$329$	−33.3967	+	57.8448i	−0.101510	+	0.175820i
$330$	−197.975	−	10.2798i	−0.599924	−	0.0311510i
$331$	−77.0344	−	133.427i	−0.232732	−	0.403104i	0.725879	−	0.687822i	$-0.241433\pi$
$331$	−77.0344	−	133.427i	−0.232732	−	0.403104i	−0.958611	+	0.284718i	$0.908100\pi$
$332$	−9.13198	−	26.7455i	−0.0275060	−	0.0805589i
$333$	50.6689	+	556.406i	0.152159	+	1.67089i
$334$	75.5646	+	54.0472i	0.226241	+	0.161818i
$335$	−76.2802	+	44.0404i	−0.227702	+	0.131464i
$336$	6.98365	+	38.4077i	0.0207847	+	0.114309i
$337$	199.096	−	344.845i	0.590790	−	1.02328i	−0.403336	−	0.915052i	$-0.632150\pi$
$337$	199.096	−	344.845i	0.590790	−	1.02328i	0.994126	−	0.108226i	$-0.0345171\pi$
$338$	−221.265	−	487.188i	−0.654629	−	1.44139i
$339$	−378.114	−	195.982i	−1.11538	−	0.578118i
$340$	−23.3689	−	20.4206i	−0.0687321	−	0.0600605i
$341$		−	42.2235i		−	0.123823i
$342$	572.244	+	3.70323i	1.67323	+	0.0108282i
$343$		−	79.1635i		−	0.230798i
$344$	82.2352	+	348.480i	0.239056	+	1.01302i
$345$	−83.5764	+	53.4527i	−0.242250	+	0.154935i
$346$	−109.902	+	49.9140i	−0.317637	+	0.144260i
$347$	−211.923	+	367.061i	−0.610729	+	1.05781i	0.380389	+	0.924827i	$0.375790\pi$
$347$	−211.923	+	367.061i	−0.610729	+	1.05781i	−0.991118	+	0.132987i	$0.957543\pi$
$348$	−136.668	−	347.779i	−0.392724	−	0.999364i
$349$	−140.567	+	81.1564i	−0.402771	+	0.232540i	−0.687679	−	0.726015i	$-0.741370\pi$
$349$	−140.567	+	81.1564i	−0.402771	+	0.232540i	0.284908	+	0.958555i	$0.408037\pi$
$350$	−6.98633	−	4.99694i	−0.0199610	−	0.0142770i
$351$	213.105	−	522.325i	0.607137	−	1.48811i
$352$	8.84836	+	237.929i	0.0251374	+	0.675936i
$353$	−162.240	−	281.009i	−0.459605	−	0.796059i	0.539335	−	0.842091i	$-0.318676\pi$
$353$	−162.240	−	281.009i	−0.459605	−	0.796059i	−0.998940	+	0.0460324i	$0.985342\pi$
$354$	−220.110	−	142.791i	−0.621780	−	0.403363i
$355$	−153.896	+	266.555i	−0.433510	+	0.750861i
$356$	145.675	+	28.7073i	0.409200	+	0.0806386i
$357$	2.29677	+	3.59113i	0.00643352	+	0.0100592i
$358$	−246.717	−	24.0780i	−0.689153	−	0.0672569i
$359$		−	344.963i		−	0.960899i	−0.877022	−	0.480449i	$-0.840474\pi$
$359$		−	344.963i		−	0.960899i	0.877022	−	0.480449i	$-0.159526\pi$
$360$	−239.391	−	211.936i	−0.664975	−	0.588710i
$361$	649.730			1.79981
$362$	−22.1645	+	227.111i	−0.0612280	+	0.627378i
$363$	−174.831	−	90.6175i	−0.481628	−	0.249635i
$364$	66.6867	+	13.1415i	0.183205	+	0.0361031i
$365$	83.5197	+	48.2201i	0.228821	+	0.132110i
$366$	−192.396	−	377.149i	−0.525671	−	1.03046i
$367$	16.3628	−	9.44709i	0.0445854	−	0.0257414i	−0.477542	−	0.878609i	$-0.658472\pi$
$367$	16.3628	−	9.44709i	0.0445854	−	0.0257414i	0.522127	+	0.852868i	$0.325139\pi$
$368$	72.8707	+	94.2706i	0.198018	+	0.256170i
$369$	−20.6872	+	44.7780i	−0.0560630	+	0.121350i
$370$	320.744	−	448.439i	0.866874	−	1.21200i
$371$	−34.5786	−	59.8918i	−0.0932037	−	0.161434i
$372$	42.4355	−	53.2600i	0.114074	−	0.143172i
$373$	465.036	+	268.489i	1.24675	+	0.719809i	0.970459	−	0.241267i	$-0.0775628\pi$
$373$	465.036	+	268.489i	1.24675	+	0.719809i	0.276286	+	0.961075i	$0.410896\pi$
$374$	10.7511	+	23.6722i	0.0287463	+	0.0632946i
$375$	402.982	−	18.3108i	1.07462	−	0.0488287i
$376$	−639.463	+	150.902i	−1.70070	+	0.401335i
$377$	−650.605			−1.72574
$378$	23.4224	+	37.1498i	0.0619640	+	0.0982798i
$379$	439.491			1.15961			0.579804	−	0.814756i	$-0.303129\pi$
$379$	439.491			1.15961			0.579804	+	0.814756i	$0.303129\pi$
$380$	−425.231	−	371.581i	−1.11903	−	0.977845i
$381$	339.783	−	15.4392i	0.891820	−	0.0405227i
$382$	−25.4096	+	11.5402i	−0.0665172	+	0.0302099i
$383$	225.692	+	130.303i	0.589275	+	0.340218i	0.764811	−	0.644255i	$-0.222833\pi$
$383$	225.692	+	130.303i	0.589275	+	0.340218i	−0.175536	+	0.984473i	$0.556166\pi$
$384$	−227.963	+	309.013i	−0.593653	+	0.804721i
$385$	−13.4355	−	23.2710i	−0.0348974	−	0.0604441i
$386$	−70.4282	+	98.4672i	−0.182456	+	0.255096i
$387$	232.210	+	329.139i	0.600027	+	0.850490i
$388$	24.2680	+	71.0756i	0.0625464	+	0.183185i
$389$	−166.109	+	95.9029i	−0.427015	+	0.246537i	−0.698074	−	0.716026i	$-0.745959\pi$
$389$	−166.109	+	95.9029i	−0.427015	+	0.246537i	0.271059	+	0.962563i	$0.412626\pi$
$390$	−495.887	+	252.968i	−1.27151	+	0.648636i
$391$	11.2679	+	6.50551i	0.0288181	+	0.0166381i
$392$	281.538	−	265.103i	0.718210	−	0.676284i
$393$	−413.986	−	214.575i	−1.05340	−	0.545993i
$394$	−30.0150	+	307.551i	−0.0761802	+	0.780587i
$395$	−190.478			−0.482222
$396$	109.182	+	244.593i	0.275713	+	0.617660i
$397$		−	154.843i		−	0.390032i	−0.980800	−	0.195016i	$-0.937524\pi$
$397$		−	154.843i		−	0.390032i	0.980800	−	0.195016i	$-0.0624760\pi$
$398$	52.1481	−	534.340i	0.131025	−	1.34256i
$399$	41.7929	+	65.3456i	0.104744	+	0.163774i
$400$	−11.3263	−	83.7291i	−0.0283158	−	0.209323i
$401$	185.704	−	321.649i	0.463103	−	0.802118i	−0.536010	−	0.844211i	$-0.680069\pi$
$401$	185.704	−	321.649i	0.463103	−	0.802118i	0.999114	+	0.0420930i	$0.0134026\pi$
$402$	99.8422	+	64.7699i	0.248364	+	0.161119i
$403$	−59.2841	−	102.683i	−0.147107	−	0.254797i
$404$	−306.429	+	104.627i	−0.758487	+	0.258977i
$405$	−338.864	−	120.621i	−0.836701	−	0.297829i
$406$	29.4656	−	41.1965i	0.0725754	−	0.101469i
$407$	−400.011	+	230.946i	−0.982827	+	0.567435i
$408$	−10.2297	+	40.6648i	−0.0250729	+	0.0996686i
$409$	−95.0595	+	164.648i	−0.232419	+	0.402562i	−0.958520	−	0.285027i	$-0.907997\pi$
$409$	−95.0595	+	164.648i	−0.232419	+	0.402562i	0.726100	+	0.687589i	$0.241331\pi$
$410$	44.3185	−	20.1280i	0.108094	−	0.0490926i
$411$	−156.642	+	100.183i	−0.381124	+	0.243754i
$412$	97.5561	+	85.2479i	0.236787	+	0.206912i
$413$		−	35.5633i		−	0.0861096i
$414$	115.651	+	67.7726i	0.279349	+	0.163702i
$415$			31.3749i			0.0756021i
$416$	355.584	+	566.195i	0.854769	+	1.36105i
$417$	357.623	+	185.361i	0.857608	+	0.444511i
$418$	195.632	+	430.749i	0.468018	+	1.03050i
$419$	311.307	−	539.200i	0.742976	−	1.28687i	−0.208158	−	0.978095i	$-0.566747\pi$
$419$	311.307	−	539.200i	0.742976	−	1.28687i	0.951134	−	0.308778i	$-0.0999199\pi$
$420$	6.44048	−	42.8566i	0.0153345	−	0.102039i
$421$	202.420	−	116.867i	0.480808	−	0.277595i	−0.239945	−	0.970786i	$-0.577129\pi$
$421$	202.420	−	116.867i	0.480808	−	0.277595i	0.720753	+	0.693192i	$0.243796\pi$
$422$	−138.541	+	193.697i	−0.328295	+	0.458997i
$423$	−603.973	+	426.108i	−1.42783	+	1.00735i
$424$	195.737	−	651.510i	0.461643	−	1.53658i
$425$	−4.61313	−	7.99018i	−0.0108544	−	0.0188004i
$426$	415.315	+	21.5652i	0.974919	+	0.0506226i
$427$	28.6944	−	49.7002i	0.0672000	−	0.116394i
$428$	−717.490	−	141.391i	−1.67638	−	0.330354i
$429$	465.890	−	21.1692i	1.08599	−	0.0493455i
$430$	38.6094	−	395.615i	0.0897894	−	0.920035i
$431$		−	458.401i		−	1.06358i	−0.846878	−	0.531788i	$-0.821520\pi$
$431$		−	458.401i		−	1.06358i	0.846878	−	0.531788i	$-0.178480\pi$
$432$	−108.100	+	418.256i	−0.250233	+	0.968186i
$433$	−281.824			−0.650864			−0.325432	−	0.945565i	$-0.605510\pi$
$433$	−281.824			−0.650864			−0.325432	+	0.945565i	$0.605510\pi$
$434$	9.18688	+	0.896579i	0.0211679	+	0.00206585i
$435$	18.8298	+	414.404i	0.0432869	+	0.952653i
$436$	5.64617	−	28.6515i	0.0129499	−	0.0657144i
$437$	205.035	+	118.377i	0.469187	+	0.270885i
$438$	6.75703	−	130.131i	0.0154270	−	0.297102i
$439$	−148.016	+	85.4568i	−0.337165	+	0.194662i	−0.659018	−	0.752127i	$-0.729028\pi$
$439$	−148.016	+	85.4568i	−0.337165	+	0.194662i	0.321853	+	0.946790i	$0.395694\pi$
$440$	76.0535	−	253.144i	0.172849	−	0.575328i
$441$	182.459	−	394.936i	0.413739	−	0.895547i
$442$	59.3825	+	42.4730i	0.134350	+	0.0960929i
$443$	−14.6968	−	25.4556i	−0.0331756	−	0.0574618i	0.848961	−	0.528456i	$-0.177229\pi$
$443$	−14.6968	−	25.4556i	−0.0331756	−	0.0574618i	−0.882136	+	0.470994i	$0.843895\pi$
$444$	−736.673	−	110.707i	−1.65917	−	0.249340i
$445$	−142.750	−	82.4165i	−0.320786	−	0.185206i
$446$	197.351	−	89.6300i	0.442490	−	0.200964i
$447$	−219.848	+	424.160i	−0.491831	+	0.948903i
$448$	−51.9559	−	3.12702i	−0.115973	−	0.00697996i
$449$	426.134			0.949074			0.474537	−	0.880236i	$-0.342616\pi$
$449$	426.134			0.949074			0.474537	+	0.880236i	$0.342616\pi$
$450$	−46.9929	−	82.6243i	−0.104429	−	0.183609i
$451$	−40.7783			−0.0904175
$452$	373.648	−	427.596i	0.826656	−	0.946009i
$453$	−317.424	−	496.311i	−0.700715	−	1.09561i
$454$	−223.398	−	491.886i	−0.492066	−	1.08345i
$455$	−65.3474	−	37.7283i	−0.143621	−	0.0829194i
$456$	−186.145	+	739.953i	−0.408212	+	1.62270i
$457$	−178.504	−	309.178i	−0.390600	−	0.676539i	0.601929	−	0.798550i	$-0.294399\pi$
$457$	−178.504	−	309.178i	−0.390600	−	0.676539i	−0.992529	+	0.122011i	$0.961066\pi$
$458$	−174.277	−	124.651i	−0.380517	−	0.272163i
$459$	6.40613	+	46.7362i	0.0139567	+	0.101822i
$460$	−42.7419	−	125.181i	−0.0929171	−	0.272134i
$461$	−724.146	+	418.086i	−1.57082	+	0.906911i	−0.574746	+	0.818332i	$0.694899\pi$
$461$	−724.146	+	418.086i	−1.57082	+	0.906911i	−0.996069	+	0.0885790i	$0.971767\pi$
$462$	−19.7595	+	30.4591i	−0.0427695	+	0.0659287i
$463$	401.085	+	231.566i	0.866274	+	0.500143i	0.866108	−	0.499857i	$-0.166614\pi$
$463$	401.085	+	231.566i	0.866274	+	0.500143i	0.000165490		1.00000i	$0.499947\pi$
$464$	493.728	−	66.7883i	1.06407	−	0.143940i
$465$	−63.6884	+	40.7330i	−0.136964	+	0.0875978i
$466$	447.723	+	43.6949i	0.960779	+	0.0937658i
$467$	221.217			0.473698			0.236849	−	0.971546i	$-0.423885\pi$
$467$	221.217			0.473698			0.236849	+	0.971546i	$0.423885\pi$
$468$	608.942	+	441.527i	1.30116	+	0.943433i
$469$			16.1315i			0.0343956i
$470$	725.956	+	70.8486i	1.54459	+	0.150742i
$471$	286.694	−	553.127i	0.608692	−	1.17437i
$472$	254.686	−	239.818i	0.539589	−	0.508090i
$473$	−166.504	+	288.393i	−0.352016	+	0.609710i
$474$	116.952	+	229.258i	0.246734	+	0.483666i
$475$	−83.9424	−	145.393i	−0.176721	−	0.306090i
$476$	−5.37882	+	1.83654i	−0.0113000	+	0.00385828i
$477$	−69.4057	−	762.160i	−0.145505	−	1.59782i
$478$	−145.391	−	103.990i	−0.304166	−	0.217553i
$479$	−496.351	+	286.569i	−1.03622	+	0.598264i	−0.918761	−	0.394813i	$-0.870809\pi$
$479$	−496.351	+	286.569i	−1.03622	+	0.598264i	−0.117463	+	0.993077i	$0.537476\pi$
$480$	350.348	−	242.877i	0.729892	−	0.505993i
$481$	−648.522	+	1123.27i	−1.34828	+	2.33529i
$482$	223.383	+	491.853i	0.463451	+	1.02044i
$483$	0.824736	+	18.1507i	0.00170753	+	0.0375791i
$484$	172.766	−	197.711i	0.356955	−	0.408493i
$485$		−	83.3779i		−	0.171913i
$486$	62.8816	+	481.915i	0.129386	+	0.991594i
$487$			391.908i			0.804739i	0.915477	+	0.402369i	$0.131813\pi$
$487$			391.908i			0.804739i	−0.915477	+	0.402369i	$0.868187\pi$
$488$	549.426	−	129.655i	1.12587	−	0.265686i
$489$	−26.4966	−	583.134i	−0.0541853	−	1.19250i
$490$	−390.884	+	177.526i	−0.797722	+	0.362298i
$491$	−58.8904	+	102.001i	−0.119940	+	0.207742i	−0.919744	−	0.392520i	$-0.871603\pi$
$491$	−58.8904	+	102.001i	−0.119940	+	0.207742i	0.799804	+	0.600261i	$0.204937\pi$
$492$	−51.4371	−	40.9830i	−0.104547	−	0.0832989i
$493$	47.1159	−	27.2024i	0.0955698	−	0.0551773i
$494$	1080.55	+	772.857i	2.18735	+	1.56449i
$495$	−26.9676	−	296.137i	−0.0544800	−	0.598257i
$496$	55.5302	+	71.8378i	0.111956	+	0.144834i
$497$	28.1852	+	48.8183i	0.0567108	+	0.0982259i
$498$	37.7626	−	19.2639i	0.0758286	−	0.0386826i
$499$	30.7207	−	53.2099i	0.0615646	−	0.106633i	−0.833600	−	0.552368i	$-0.813724\pi$
$499$	30.7207	−	53.2099i	0.0615646	−	0.106633i	0.895165	+	0.445735i	$0.147058\pi$
$500$	−103.993	+	527.714i	−0.207987	+	1.05543i
$501$	−64.1279	+	123.724i	−0.128000	+	0.246954i
$502$	−493.458	−	48.1583i	−0.982984	−	0.0959328i
$503$			284.541i			0.565688i	0.959166	+	0.282844i	$0.0912779\pi$
$503$			284.541i			0.565688i	−0.959166	+	0.282844i	$0.908722\pi$
$504$	−55.5363	+	18.5619i	−0.110191	+	0.0368291i
$505$	359.468			0.711817
$506$	−10.7639	+	110.293i	−0.0212725	+	0.217971i
$507$	676.157	−	432.447i	1.33364	−	0.852953i
$508$	−87.6844	+	444.954i	−0.172607	+	0.875894i
$509$	−445.430	−	257.169i	−0.875109	−	0.505244i	−0.00606608	−	0.999982i	$-0.501931\pi$
$509$	−445.430	−	257.169i	−0.875109	−	0.505244i	−0.869043	+	0.494737i	$0.835264\pi$
$510$	25.3347	−	39.0531i	0.0496758	−	0.0765747i
$511$	15.2962	−	8.83127i	0.0299339	−	0.0172823i
$512$	−327.967	−	393.169i	−0.640560	−	0.767908i
$513$	116.569	+	850.432i	0.227229	+	1.65776i
$514$	−100.759	+	140.874i	−0.196029	+	0.274073i
$515$	−71.9131	−	124.557i	−0.139637	−	0.241859i
$516$	−499.866	+	196.434i	−0.968732	+	0.380687i
$517$	−529.203	−	305.535i	−1.02360	−	0.590978i
$518$	−41.7548	−	91.9372i	−0.0806077	−	0.177485i
$519$	−97.5536	−	152.531i	−0.187965	−	0.293894i
$520$	−170.474	−	722.403i	−0.327835	−	1.38924i
$521$	208.517			0.400224			0.200112	−	0.979773i	$-0.435869\pi$
$521$	208.517			0.400224			0.200112	+	0.979773i	$0.435869\pi$
$522$	487.213	−	277.104i	0.933358	−	0.530851i
$523$	−17.5861			−0.0336254			−0.0168127	−	0.999859i	$-0.505352\pi$
$523$	−17.5861			−0.0336254			−0.0168127	+	0.999859i	$0.505352\pi$
$524$	409.097	−	468.163i	0.780720	−	0.893441i
$525$	5.92895	−	11.4389i	0.0112932	−	0.0217884i
$526$	77.2965	−	35.1055i	0.146952	−	0.0667405i
$527$	8.58654	+	4.95744i	0.0162933	+	0.00940691i
$528$	−351.379	+	63.8911i	−0.665491	+	0.121006i
$529$	−236.771	−	410.100i	−0.447583	−	0.775236i
$530$	−439.351	+	614.267i	−0.828965	+	1.15899i
$531$	165.057	−	357.269i	0.310841	−	0.672822i
$532$	−97.8752	+	33.4184i	−0.183976	+	0.0628166i
$533$	−99.1685	+	57.2549i	−0.186057	+	0.107420i
$534$	−11.5489	+	222.416i	−0.0216272	+	0.416509i
$535$	703.080	+	405.924i	1.31417	+	0.758736i
$536$	−115.526	+	108.782i	−0.215533	+	0.202951i
$537$	−16.8781	−	371.450i	−0.0314303	−	0.691714i
$538$	−64.0020	+	655.802i	−0.118963	+	1.21896i
$539$	359.660			0.667273
$540$	263.607	−	400.645i	0.488162	−	0.741936i
$541$		−	476.226i		−	0.880271i	−0.897931	−	0.440135i	$-0.854930\pi$
$541$		−	476.226i		−	0.880271i	0.897931	−	0.440135i	$-0.145070\pi$
$542$	−71.7465	+	735.156i	−0.132374	+	1.35638i
$543$	−341.932	+	15.5368i	−0.629709	+	0.0286129i
$544$	−49.4240	−	26.1358i	−0.0908530	−	0.0480437i
$545$	−16.2097	+	28.0761i	−0.0297426	+	0.0515157i
$546$	−5.28682	+	101.817i	−0.00968283	+	0.186477i
$547$	−64.5016	−	111.720i	−0.117919	−	0.204241i	0.801024	−	0.598632i	$-0.204289\pi$
$547$	−64.5016	−	111.720i	−0.117919	−	0.204241i	−0.918943	+	0.394391i	$0.870956\pi$
$548$	−80.1084	−	234.620i	−0.146183	−	0.428138i
$549$	518.933	−	366.111i	0.945233	−	0.666869i
$550$	45.7153	−	63.9157i	0.0831188	−	0.116210i
$551$	857.341	−	494.986i	1.55597	−	0.898341i
$552$	−124.425	+	128.304i	−0.225407	+	0.232435i
$553$	−17.4425	+	30.2113i	−0.0315416	+	0.0546316i
$554$	335.011	−	152.151i	0.604712	−	0.274640i
$555$	734.241	+	380.568i	1.32296	+	0.685708i
$556$	−353.399	+	404.423i	−0.635610	+	0.727380i
$557$			325.840i			0.584991i	0.956267	+	0.292495i	$0.0944856\pi$
$557$			325.840i			0.584991i	−0.956267	+	0.292495i	$0.905514\pi$
$558$	88.1301	+	51.6452i	0.157939	+	0.0925542i
$559$			935.121i			1.67285i
$560$	53.4635	+	21.9228i	0.0954706	+	0.0391479i
$561$	−32.8540	+	21.0123i	−0.0585633	+	0.0374552i
$562$	−325.982	−	717.758i	−0.580039	−	1.27715i
$563$	−372.114	+	644.521i	−0.660949	+	1.14480i	0.319418	+	0.947614i	$0.396513\pi$
$563$	−372.114	+	644.521i	−0.660949	+	1.14480i	−0.980367	+	0.197183i	$0.936821\pi$
$564$	−360.458	−	917.257i	−0.639111	−	1.62634i
$565$	−545.944	+	315.201i	−0.966273	+	0.557878i
$566$	342.670	−	479.095i	0.605425	−	0.846458i
$567$	−50.1620	+	42.7011i	−0.0884692	+	0.0753105i
$568$	−159.546	+	531.051i	−0.280892	+	0.934949i
$569$	−128.890	−	223.244i	−0.226520	−	0.392344i	0.730255	−	0.683175i	$-0.239401\pi$
$569$	−128.890	−	223.244i	−0.226520	−	0.392344i	−0.956774	+	0.290831i	$0.906068\pi$
$570$	461.000	−	710.626i	0.808772	−	1.24671i
$571$	300.850	−	521.087i	0.526883	−	0.912587i	−0.472627	−	0.881263i	$-0.656694\pi$
$571$	300.850	−	521.087i	0.526883	−	0.912587i	0.999509	−	0.0313247i	$-0.00997259\pi$
$572$	−120.228	+	610.094i	−0.210188	+	1.06660i
$573$	−22.5545	−	35.2653i	−0.0393621	−	0.0615450i
$574$	0.865892	−	8.87244i	0.00150852	−	0.0154572i
$575$		−	39.3254i		−	0.0683921i
$576$	−507.436	−	272.552i	−0.880965	−	0.473181i
$577$	−1095.59			−1.89878			−0.949388	−	0.314105i	$-0.898296\pi$
$577$	−1095.59			−1.89878			−0.949388	+	0.314105i	$0.898296\pi$
$578$	569.191	+	55.5493i	0.984759	+	0.0961060i
$579$	−161.223	−	83.5642i	−0.278451	−	0.144325i
$580$	−542.672	−	106.941i	−0.935642	−	0.184381i
$581$	4.97631	+	2.87307i	0.00856508	+	0.00494505i
$582$	−100.353	+	51.1934i	−0.172428	+	0.0879611i
$583$	547.931	−	316.348i	0.939847	−	0.542621i
$584$	166.394	+	49.9906i	0.284921	+	0.0856004i
$585$	−481.375	−	682.310i	−0.822863	−	1.16634i
$586$	−432.812	−	309.566i	−0.738586	−	0.528270i
$587$	−229.342	−	397.231i	−0.390701	−	0.676714i	0.601841	−	0.798616i	$-0.294434\pi$
$587$	−229.342	−	397.231i	−0.390701	−	0.676714i	−0.992542	+	0.121902i	$0.961101\pi$
$588$	453.669	+	361.466i	0.771546	+	0.614737i
$589$	156.244	+	90.2077i	0.265270	+	0.153154i
$590$	−353.602	+	160.594i	−0.599326	+	0.272194i
$591$	−463.041	+	21.0398i	−0.783487	+	0.0356003i
$592$	376.837	−	918.999i	0.636549	−	1.55236i
$593$	660.704			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$593$	660.704			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$594$	−339.871	+	214.284i	−0.572173	+	0.360747i
$595$	6.30983			0.0106048
$596$	−479.668	−	419.150i	−0.804812	−	0.703273i
$597$	804.488	−	36.5545i	1.34755	−	0.0612304i
$598$	128.681	+	283.335i	0.215186	+	0.473804i
$599$	−787.521	−	454.676i	−1.31473	−	0.759058i	−0.331852	−	0.943332i	$-0.607673\pi$
$599$	−787.521	−	454.676i	−1.31473	−	0.759058i	−0.982875	+	0.184274i	$0.941007\pi$
$600$	121.901	−	34.6773i	0.203169	−	0.0577955i
$601$	177.135	+	306.806i	0.294733	+	0.510493i	0.974923	−	0.222543i	$-0.0714358\pi$
$601$	177.135	+	306.806i	0.294733	+	0.510493i	−0.680189	+	0.733036i	$0.738103\pi$
$602$	−59.2122	−	42.3512i	−0.0983592	−	0.0703509i
$603$	−74.8699	+	162.057i	−0.124162	+	0.268752i
$604$	743.378	−	253.819i	1.23076	−	0.420229i
$605$	−252.432	+	145.742i	−0.417243	+	0.240895i
$606$	−220.710	−	432.653i	−0.364208	−	0.713949i
$607$	452.946	+	261.509i	0.746205	+	0.430822i	0.824321	−	0.566123i	$-0.191557\pi$
$607$	452.946	+	261.509i	0.746205	+	0.430822i	−0.0781160	+	0.996944i	$0.524890\pi$
$608$	−899.341	−	475.578i	−1.47918	−	0.782200i
$609$	67.4522	+	34.9614i	0.110759	+	0.0574080i
$610$	−623.740	−	60.8730i	−1.02253	−	0.0997918i
$611$	−1715.95			−2.80843
$612$	−62.5594	−	6.51435i	−0.102221	−	0.0106444i
$613$			642.493i			1.04811i	0.851684	+	0.524056i	$0.175582\pi$
$613$			642.493i			1.04811i	−0.851684	+	0.524056i	$0.824418\pi$
$614$	−208.302	−	20.3289i	−0.339254	−	0.0331089i
$615$	39.3388	+	61.5085i	0.0639655	+	0.100014i
$616$	−33.1863	−	35.2438i	−0.0538739	−	0.0572139i
$617$	−489.218	+	847.351i	−0.792899	+	1.37334i	0.131266	+	0.991347i	$0.458096\pi$
$617$	−489.218	+	847.351i	−0.792899	+	1.37334i	−0.924165	+	0.381994i	$0.875238\pi$
$618$	−105.762	+	163.031i	−0.171136	+	0.263805i
$619$	297.240	+	514.836i	0.480195	+	0.831721i	0.999742	−	0.0227203i	$-0.00723273\pi$
$619$	297.240	+	514.836i	0.480195	+	0.831721i	−0.519547	+	0.854442i	$0.673899\pi$
$620$	−32.5709	−	95.3930i	−0.0525337	−	0.153860i
$621$	−75.9559	+	186.170i	−0.122312	+	0.299790i
$622$	−504.564	−	360.886i	−0.811195	−	0.580203i
$623$	−26.1439	+	15.0942i	−0.0419645	+	0.0242282i
$624$	−764.810	+	648.732i	−1.22566	+	1.03963i
$625$	232.548	−	402.785i	0.372077	−	0.644455i
$626$	−333.015	−	733.243i	−0.531972	−	1.17132i
$627$	−597.826	+	382.349i	−0.953470	+	0.609808i
$628$	625.513	+	546.595i	0.996040	+	0.870374i
$629$		−	108.461i		−	0.172434i
$630$	65.0054	+	0.420677i	0.103183	+	0.000667742i
$631$		−	259.788i		−	0.411709i	−0.978583	−	0.205854i	$-0.934003\pi$
$631$		−	259.788i		−	0.411709i	0.978583	−	0.205854i	$-0.0659973\pi$
$632$	−333.980	+	78.8134i	−0.528450	+	0.124705i
$633$	−317.145	−	164.381i	−0.501018	−	0.259685i
$634$	−340.988	+	154.865i	−0.537836	+	0.244267i
$635$	251.735	−	436.018i	0.396433	−	0.686643i
$636$	1009.09	+	151.646i	1.58661	+	0.238436i
$637$	874.654	−	504.982i	1.37308	−	0.792750i
$638$	376.893	+	269.571i	0.590742	+	0.422525i
$639$	56.5731	+	621.242i	0.0885338	+	0.972210i
$640$	203.528	+	530.714i	0.318012	+	0.829240i
$641$	308.536	+	534.401i	0.481336	+	0.833698i	0.999771	−	0.0214189i	$-0.00681837\pi$
$641$	308.536	+	534.401i	0.481336	+	0.833698i	−0.518435	+	0.855117i	$0.673485\pi$
$642$	56.8816	−	1095.46i	0.0886006	−	1.70632i
$643$	−79.5086	+	137.713i	−0.123653	+	0.214172i	−0.921205	−	0.389077i	$-0.872794\pi$
$643$	−79.5086	+	137.713i	−0.123653	+	0.214172i	0.797553	+	0.603249i	$0.206127\pi$
$644$	−23.7688	−	4.68397i	−0.0369080	−	0.00727324i
$645$	595.627	−	27.0643i	0.923453	−	0.0419601i
$646$	−110.566	−	10.7905i	−0.171155	−	0.0167036i
$647$			53.2623i			0.0823219i	0.999153	+	0.0411610i	$0.0131056\pi$
$647$			53.2623i			0.0823219i	−0.999153	+	0.0411610i	$0.986894\pi$
$648$	−644.067	−	71.2832i	−0.993931	−	0.110005i
$649$	325.357			0.501320
$650$	21.4338	−	219.623i	0.0329750	−	0.337881i
$651$	0.628480	+	13.8315i	0.000965407	+	0.0212466i
$652$	763.628	+	150.484i	1.17121	+	0.230803i
$653$	971.623	+	560.967i	1.48794	+	0.859061i	0.999905	−	0.0137652i	$-0.00438174\pi$
$653$	971.623	+	560.967i	1.48794	+	0.859061i	0.488032	+	0.872826i	$0.337715\pi$
$654$	43.7448	+	2.27145i	0.0668881	+	0.00347316i
$655$	−597.739	+	345.105i	−0.912579	+	0.526878i
$656$	69.3790	−	53.6296i	0.105761	−	0.0817524i
$657$	194.653	−	17.7260i	0.296276	−	0.0269803i
$658$	77.7148	−	108.655i	0.118108	−	0.165129i
$659$	225.540	+	390.647i	0.342246	+	0.592788i	0.984850	−	0.173411i	$-0.0554789\pi$
$659$	225.540	+	390.647i	0.342246	+	0.592788i	−0.642603	+	0.766199i	$0.722146\pi$
$660$	392.081	+	58.9219i	0.594061	+	0.0892755i
$661$	−593.593	−	342.711i	−0.898023	−	0.518474i	−0.0214650	−	0.999770i	$-0.506833\pi$
$661$	−593.593	−	342.711i	−0.898023	−	0.518474i	−0.876558	+	0.481296i	$0.840166\pi$
$662$	127.420	+	280.558i	0.192477	+	0.423804i
$663$	−50.3950	+	97.2286i	−0.0760106	+	0.146649i
$664$	12.9819	+	55.0122i	0.0195511	+	0.0828497i
$665$	114.816			0.172656
$666$	7.23113	−	1117.39i	0.0108576	−	1.67777i
$667$	231.892			0.347663
$668$	−139.915	−	122.263i	−0.209454	−	0.183028i
$669$	175.176	+	273.898i	0.261848	+	0.409414i
$670$	160.394	−	72.8458i	0.239395	−	0.108725i
$671$	454.690	+	262.516i	0.677631	+	0.391230i
$672$	−6.44002	−	77.8089i	−0.00958336	−	0.115787i
$673$	218.694	+	378.790i	0.324954	+	0.562838i	0.981503	−	0.191446i	$-0.0613177\pi$
$673$	218.694	+	378.790i	0.324954	+	0.562838i	−0.656549	+	0.754284i	$0.727984\pi$
$674$	−463.300	+	647.751i	−0.687389	+	0.961055i
$675$	112.653	−	87.3977i	0.166893	−	0.129478i
$676$	345.794	+	1012.75i	0.511529	+	1.49816i
$677$	326.939	−	188.758i	0.482923	−	0.278815i	−0.238711	−	0.971091i	$-0.576725\pi$
$677$	326.939	−	188.758i	0.482923	−	0.278815i	0.721634	+	0.692275i	$0.243392\pi$
$678$	714.580	+	463.564i	1.05395	+	0.683723i
$679$	−13.2244	−	7.63512i	−0.0194763	−	0.0112447i
$680$	42.5499	+	45.1878i	0.0625733	+	0.0664526i
$681$	682.676	−	436.617i	1.00246	−	0.641141i
$682$	−8.20250	+	84.0477i	−0.0120271	+	0.123237i
$683$	1023.64			1.49874			0.749371	−	0.662151i	$-0.230356\pi$
$683$	1023.64			1.49874			0.749371	+	0.662151i	$0.230356\pi$
$684$	−1138.36	−	118.538i	−1.66426	−	0.173301i
$685$			275.230i			0.401795i
$686$	−15.3786	+	157.578i	−0.0224178	+	0.229706i
$687$	147.900	−	285.348i	0.215284	−	0.415354i
$688$	−95.9955	−	709.640i	−0.139528	−	1.03145i
$689$	888.339	−	1538.65i	1.28932	−	2.23316i
$690$	176.746	−	90.1640i	0.256154	−	0.130672i
$691$	134.426	+	232.833i	0.194539	+	0.336951i	0.946749	−	0.321972i	$-0.104346\pi$
$691$	134.426	+	232.833i	0.194539	+	0.336951i	−0.752210	+	0.658923i	$0.771012\pi$
$692$	228.462	−	78.0058i	0.330147	−	0.112725i
$693$	−49.4392	−	22.8407i	−0.0713409	−	0.0329592i
$694$	493.149	−	689.483i	0.710589	−	0.993491i
$695$	516.358	−	298.119i	0.742961	−	0.428949i
$696$	204.483	+	718.818i	0.293797	+	1.03278i
$697$	4.78776	−	8.29265i	0.00686910	−	0.0118976i
$698$	295.570	−	134.238i	0.423453	−	0.192318i
$699$	30.6290	+	674.080i	0.0438183	+	0.964349i
$700$	12.9359	+	11.3038i	0.0184798	+	0.0161483i
$701$			888.158i			1.26699i	0.773748	+	0.633494i	$0.218380\pi$
$701$			888.158i			1.26699i	−0.773748	+	0.633494i	$0.781620\pi$
$702$	−525.664	+	998.313i	−0.748809	+	1.42210i
$703$		−	1973.61i		−	2.80740i
$704$	28.6081	−	475.328i	0.0406365	−	0.675181i
$705$	49.6631	+	1092.98i	0.0704441	+	1.55033i
$706$	268.357	+	590.878i	0.380109	+	0.836937i
$707$	32.9173	−	57.0145i	0.0465592	−	0.0806429i
$708$	410.399	+	326.990i	0.579660	+	0.461850i
$709$	158.288	−	91.3877i	0.223256	−	0.128897i	−0.384201	−	0.923249i	$-0.625523\pi$
$709$	158.288	−	91.3877i	0.223256	−	0.128897i	0.607457	+	0.794353i	$0.292190\pi$
$710$	358.119	−	500.694i	0.504392	−	0.705202i
$711$	−315.444	+	222.548i	−0.443663	+	0.313008i
$712$	−284.396	−	85.4426i	−0.399433	−	0.120004i
$713$	21.1303	+	36.5987i	0.0296358	+	0.0513306i
$714$	−3.87418	−	7.59447i	−0.00542603	−	0.0106365i
$715$	345.164	−	597.842i	0.482747	−	0.836142i
$716$	486.423	+	95.8564i	0.679362	+	0.133878i
$717$	123.386	−	238.053i	0.172087	−	0.332012i
$718$	−67.0138	+	686.663i	−0.0933340	+	0.956355i
$719$		−	1086.03i		−	1.51047i	−0.655454	−	0.755235i	$-0.727523\pi$
$719$		−	1086.03i		−	1.51047i	0.655454	−	0.755235i	$-0.272477\pi$
$720$	435.346	+	468.372i	0.604648	+	0.650517i
$721$	−26.3410			−0.0365340
$722$	−1293.32	−	126.219i	−1.79130	−	0.174819i
$723$	−682.631	+	436.588i	−0.944165	+	0.603857i
$724$	88.2389	−	447.768i	0.121877	−	0.618464i
$725$	−142.407	−	82.2184i	−0.196423	−	0.113405i
$726$	330.405	+	214.341i	0.455103	+	0.295236i
$727$	−672.535	+	388.288i	−0.925082	+	0.534096i	−0.885253	−	0.465110i	$-0.846015\pi$
$727$	−672.535	+	388.288i	−0.925082	+	0.534096i	−0.0398294	+	0.999206i	$0.512681\pi$
$728$	−130.190	−	39.1136i	−0.178832	−	0.0537275i
$729$	−702.112	+	196.162i	−0.963117	+	0.269084i
$730$	−156.882	−	112.209i	−0.214907	−	0.153711i
$731$	−39.0983	−	67.7202i	−0.0534860	−	0.0926405i
$732$	309.705	+	788.106i	0.423095	+	1.07665i
$733$	−1046.17	−	604.007i	−1.42724	−	0.824020i	−0.430342	−	0.902666i	$-0.641607\pi$
$733$	−1046.17	−	604.007i	−1.42724	−	0.824020i	−0.996903	+	0.0786463i	$0.974940\pi$
$734$	−34.4062	+	15.6261i	−0.0468749	+	0.0212890i
$735$	−346.964	−	542.498i	−0.472059	−	0.738092i
$736$	−126.739	−	201.806i	−0.172200	−	0.274193i
$737$	−147.582			−0.200247
$738$	49.8776	−	85.1137i	0.0675848	−	0.115330i
$739$	−1269.30			−1.71759			−0.858794	−	0.512322i	$-0.828786\pi$
$739$	−1269.30			−1.71759			−0.858794	+	0.512322i	$0.828786\pi$
$740$	−725.569	+	830.328i	−0.980499	+	1.12207i
$741$	−917.009	+	1769.21i	−1.23753	+	2.38760i
$742$	57.1953	+	125.935i	0.0770826	+	0.169723i
$743$	−49.1224	−	28.3609i	−0.0661136	−	0.0381707i	0.466579	−	0.884480i	$-0.345486\pi$
$743$	−49.1224	−	28.3609i	−0.0661136	−	0.0381707i	−0.532692	+	0.846309i	$0.678820\pi$
$744$	−94.8162	+	97.7727i	−0.127441	+	0.131415i
$745$	353.586	+	612.428i	0.474612	+	0.822051i
$746$	−873.516	−	624.778i	−1.17093	−	0.837504i
$747$	36.6575	+	51.9590i	0.0490729	+	0.0695569i
$748$	−16.8019	−	49.2090i	−0.0224624	−	0.0657875i
$749$	128.766	−	74.3428i	0.171917	−	0.0992561i
$750$	−805.709	−	41.8364i	−1.07428	−	0.0557819i
$751$	79.1677	+	45.7075i	0.105416	+	0.0608622i	0.551781	−	0.833989i	$-0.313948\pi$
$751$	79.1677	+	45.7075i	0.105416	+	0.0608622i	−0.446365	+	0.894851i	$0.647282\pi$
$752$	1302.19	−	176.152i	1.73164	−	0.234245i
$753$	−33.7578	−	742.937i	−0.0448310	−	0.986636i
$754$	1295.06	+	126.389i	1.71758	+	0.167625i
$755$	−872.048			−1.15503
$756$	−39.4064	−	78.4984i	−0.0521249	−	0.103834i
$757$		−	883.777i		−	1.16747i	−0.811943	−	0.583736i	$-0.801590\pi$
$757$		−	883.777i		−	1.16747i	0.811943	−	0.583736i	$-0.198410\pi$
$758$	−874.826	−	85.3773i	−1.15412	−	0.112635i
$759$	−166.055	+	7.54524i	−0.218781	+	0.00994102i
$760$	774.255	+	822.255i	1.01876	+	1.08192i
$761$	−210.778	+	365.078i	−0.276975	+	0.479734i	−0.970631	−	0.240571i	$-0.922665\pi$
$761$	−210.778	+	365.078i	−0.276975	+	0.479734i	0.693657	+	0.720306i	$0.255999\pi$
$762$	−679.352	−	35.2753i	−0.891539	−	0.0462931i
$763$	2.96873	+	5.14199i	0.00389086	+	0.00673917i
$764$	52.8206	−	18.0350i	0.0691370	−	0.0236061i
$765$	63.3885	+	29.2852i	0.0828608	+	0.0382813i
$766$	−423.937	−	303.218i	−0.553442	−	0.395847i
$767$	791.232	−	456.818i	1.03159	−	0.595591i
$768$	513.800	−	570.819i	0.669010	−	0.743253i
$769$	−37.4028	+	64.7836i	−0.0486383	+	0.0842440i	−0.889320	−	0.457286i	$-0.848821\pi$
$769$	−37.4028	+	64.7836i	−0.0486383	+	0.0842440i	0.840681	+	0.541530i	$0.182155\pi$
$770$	22.2232	+	48.9319i	0.0288613	+	0.0635479i
$771$	−230.656	−	119.552i	−0.299165	−	0.155061i
$772$	159.319	−	182.322i	0.206372	−	0.236168i
$773$			723.612i			0.936108i	0.883700	+	0.468054i	$0.155045\pi$
$773$			723.612i			0.936108i	−0.883700	+	0.468054i	$0.844955\pi$
$774$	−398.285	−	700.276i	−0.514580	−	0.904750i
$775$		−	29.9675i		−	0.0386677i
$776$	−34.4991	−	146.193i	−0.0444576	−	0.188394i
$777$	127.597	−	81.6070i	0.164218	−	0.105028i
$778$	349.277	−	158.630i	0.448942	−	0.203894i
$779$	87.1202	−	150.897i	0.111836	−	0.193705i
$780$	1036.23	−	407.211i	1.32850	−	0.522065i
$781$	−446.622	+	257.857i	−0.571859	+	0.330163i
$782$	−21.1654	−	15.1384i	−0.0270657	−	0.0193586i
$783$	515.361	+	664.282i	0.658188	+	0.848381i
$784$	−611.914	+	473.006i	−0.780503	+	0.603325i
$785$	−461.095	−	798.640i	−0.587382	−	1.01738i
$786$	782.373	+	507.544i	0.995386	+	0.645730i
$787$	608.548	−	1054.04i	0.773251	−	1.33931i	−0.162522	−	0.986705i	$-0.551963\pi$
$787$	608.548	−	1054.04i	0.773251	−	1.33931i	0.935773	−	0.352604i	$-0.114704\pi$
$788$	119.492	−	606.363i	0.151640	−	0.769496i
$789$	68.6114	+	107.278i	0.0869600	+	0.135967i
$790$	379.154	+	37.0029i	0.479942	+	0.0468392i
$791$			115.455i			0.145961i
$792$	−169.816	−	508.083i	−0.214415	−	0.641520i
$793$	1474.34			1.85920
$794$	−30.0804	+	308.221i	−0.0378846	+	0.388188i
$795$	−1005.76	−	521.298i	−1.26510	−	0.655721i
$796$	−207.606	+	1053.50i	−0.260812	+	1.32349i
$797$	−571.321	−	329.853i	−0.716840	−	0.413868i	0.0967485	−	0.995309i	$-0.469156\pi$
$797$	−571.321	−	329.853i	−0.716840	−	0.413868i	−0.813588	+	0.581441i	$0.802489\pi$
$798$	−70.4963	−	138.192i	−0.0883412	−	0.173173i
$799$	124.267	−	71.7456i	0.155528	−	0.0897942i
$800$	6.27998	+	168.867i	0.00784998	+	0.211083i
$801$	−332.696	+	30.2968i	−0.415351	+	0.0378238i
$802$	−432.137	+	604.181i	−0.538825	+	0.753343i
$803$	80.7944	+	139.940i	0.100616	+	0.174271i
$804$	−186.158	−	148.323i	−0.231539	−	0.184481i
$805$	23.2914	+	13.4473i	0.0289334	+	0.0167047i
$806$	98.0599	+	215.912i	0.121662	+	0.267881i
$807$	−987.358	+	44.8638i	−1.22349	+	0.0555933i
$808$	630.285	−	148.736i	0.780055	−	0.184079i
$809$	−409.864			−0.506631			−0.253315	−	0.967384i	$-0.581521\pi$
$809$	−409.864			−0.506631			−0.253315	+	0.967384i	$0.581521\pi$
$810$	651.091	+	305.930i	0.803816	+	0.377691i
$811$	283.012			0.348967			0.174483	−	0.984660i	$-0.444174\pi$
$811$	283.012			0.348967			0.174483	+	0.984660i	$0.444174\pi$
$812$	−66.6556	+	76.2794i	−0.0820881	+	0.0939401i
$813$	−1106.83	+	50.2925i	−1.36142	+	0.0618604i
$814$	841.103	−	382.001i	1.03330	−	0.469288i
$815$	−748.292	−	432.027i	−0.918150	−	0.530094i
$816$	28.2625	−	78.9577i	0.0346354	−	0.0967619i
$817$	−711.448	−	1232.26i	−0.870806	−	1.50828i
$818$	221.205	−	309.272i	0.270422	−	0.378083i
$819$	−152.301	+	13.8692i	−0.185959	+	0.0169343i
$820$	−92.1279	+	31.4561i	−0.112351	+	0.0383611i
$821$	−14.8260	+	8.55980i	−0.0180585	+	0.0104261i	−0.509002	−	0.860765i	$-0.669985\pi$
$821$	−14.8260	+	8.55980i	−0.0180585	+	0.0104261i	0.490944	+	0.871191i	$0.336652\pi$
$822$	331.265	−	168.989i	0.402999	−	0.205583i
$823$	−1015.98	−	586.577i	−1.23449	−	0.712731i	−0.266524	−	0.963828i	$-0.585875\pi$
$823$	−1015.98	−	586.577i	−1.23449	−	0.712731i	−0.967962	+	0.251098i	$0.919208\pi$
$824$	−177.629	−	188.641i	−0.215569	−	0.228933i
$825$	104.651	+	54.2420i	0.126849	+	0.0657479i
$826$	−6.90866	+	70.7902i	−0.00836400	+	0.0857025i
$827$	219.406			0.265304			0.132652	−	0.991163i	$-0.457651\pi$
$827$	219.406			0.265304			0.132652	+	0.991163i	$0.457651\pi$
$828$	−217.042	−	157.371i	−0.262128	−	0.190062i
$829$			1596.80i			1.92618i	0.269180	+	0.963090i	$0.413247\pi$
$829$			1596.80i			1.92618i	−0.269180	+	0.963090i	$0.586753\pi$
$830$	6.09501	−	62.4530i	0.00734338	−	0.0752446i
$831$	297.369	+	464.953i	0.357844	+	0.559510i
$832$	−597.814	−	1196.11i	−0.718526	−	1.43764i
$833$	−42.2275	+	73.1402i	−0.0506933	+	0.0878034i
$834$	−675.854	−	438.442i	−0.810377	−	0.525710i
$835$	103.138	+	178.640i	0.123519	+	0.213940i
$836$	−305.734	−	895.428i	−0.365711	−	1.07109i
$837$	−57.8812	+	141.868i	−0.0691532	+	0.169496i
$838$	−724.417	+	1012.82i	−0.864460	+	1.20862i
$839$	−774.395	+	447.097i	−0.922997	+	0.532893i	−0.884590	−	0.466370i	$-0.845562\pi$
$839$	−774.395	+	447.097i	−0.922997	+	0.532893i	−0.0384071	+	0.999262i	$0.512228\pi$
$840$	−21.1455	+	84.0567i	−0.0251733	+	0.100067i
$841$	64.3200	−	111.406i	0.0764804	−	0.132468i
$842$	−425.629	+	193.307i	−0.505498	+	0.229580i
$843$	996.159	−	637.110i	1.18168	−	0.755765i
$844$	313.399	−	358.648i	0.371326	−	0.424939i
$845$		−	1188.05i		−	1.40597i
$846$	1285.01	−	730.855i	1.51893	−	0.863895i
$847$			53.3837i			0.0630268i
$848$	−516.187	+	1258.84i	−0.608712	+	1.48448i
$849$	784.435	+	406.584i	0.923952	+	0.478898i
$850$	7.63043	+	16.8010i	0.00897698	+	0.0197658i
$851$	231.149	−	400.362i	0.271621	−	0.470461i
$852$	−822.514	−	123.607i	−0.965392	−	0.145079i
$853$	997.466	−	575.887i	1.16936	−	0.675132i	0.215833	−	0.976430i	$-0.430753\pi$
$853$	997.466	−	575.887i	1.16936	−	0.675132i	0.953530	+	0.301298i	$0.0974201\pi$
$854$	−66.7724	+	93.3560i	−0.0781878	+	0.109316i
$855$	1153.44	+	532.886i	1.34906	+	0.623259i
$856$	1400.73	+	420.828i	1.63636	+	0.491621i
$857$	548.214	+	949.534i	0.639689	+	1.10797i	0.985501	+	0.169670i	$0.0542702\pi$
$857$	548.214	+	949.534i	0.639689	+	1.10797i	−0.345812	+	0.938304i	$0.612396\pi$
$858$	−931.487	−	48.3674i	−1.08565	−	0.0563723i
$859$	−3.03512	+	5.25698i	−0.00353332	+	0.00611989i	−0.867787	−	0.496937i	$-0.834458\pi$
$859$	−3.03512	+	5.25698i	−0.00353332	+	0.00611989i	0.864253	+	0.503057i	$0.167791\pi$
$860$	−153.708	+	779.988i	−0.178730	+	0.906963i
$861$	13.3581	−	0.606969i	0.0155146	−	0.000704958i
$862$	−89.0508	+	912.467i	−0.103307	+	1.05855i
$863$			1246.70i			1.44461i	0.691573	+	0.722306i	$0.256918\pi$
$863$			1246.70i			1.44461i	−0.691573	+	0.722306i	$0.743082\pi$
$864$	296.431	−	811.557i	0.343091	−	0.939302i
$865$	−268.006			−0.309833
$866$	560.983	+	54.7483i	0.647786	+	0.0632197i
$867$	38.9387	+	856.958i	0.0449120	+	0.988418i
$868$	−18.1127	−	3.56936i	−0.0208672	−	0.00411216i
$869$	−276.393	−	159.576i	−0.318059	−	0.183631i
$870$	43.0223	−	828.547i	0.0494509	−	0.952353i
$871$	−358.904	+	207.213i	−0.412060	+	0.237903i
$872$	−16.8049	+	55.9352i	−0.0192717	+	0.0641458i
$873$	−97.4163	−	138.080i	−0.111588	−	0.158167i
$874$	−385.134	−	275.465i	−0.440657	−	0.315178i
$875$	−54.6792	−	94.7071i	−0.0624905	−	0.108237i
$876$	−38.7298	+	257.718i	−0.0442122	+	0.294199i
$877$	−73.4991	−	42.4347i	−0.0838074	−	0.0483862i	0.457511	−	0.889204i	$-0.348741\pi$
$877$	−73.4991	−	42.4347i	−0.0838074	−	0.0483862i	−0.541318	+	0.840818i	$0.682074\pi$
$878$	311.232	−	141.351i	0.354479	−	0.160992i
$879$	367.306	−	708.654i	0.417868	−	0.806204i
$880$	−200.565	+	489.120i	−0.227914	+	0.555818i
$881$	−377.451			−0.428434			−0.214217	−	0.976786i	$-0.568720\pi$
$881$	−377.451			−0.428434			−0.214217	+	0.976786i	$0.568720\pi$
$882$	−439.914	+	750.693i	−0.498769	+	0.851126i
$883$	−586.966			−0.664741			−0.332370	−	0.943149i	$-0.607848\pi$
$883$	−586.966			−0.664741			−0.332370	+	0.943149i	$0.607848\pi$
$884$	−109.953	−	96.0803i	−0.124381	−	0.108688i
$885$	−313.871	−	490.756i	−0.354657	−	0.554527i
$886$	24.3095	+	53.5255i	0.0274374	+	0.0604126i
$887$	955.774	+	551.816i	1.07754	+	0.622115i	0.930230	−	0.366976i	$-0.119607\pi$
$887$	955.774	+	551.816i	1.07754	+	0.622115i	0.147305	+	0.989091i	$0.452940\pi$
$888$	1444.87	+	363.476i	1.62711	+	0.409320i
$889$	−46.1040	−	79.8545i	−0.0518605	−	0.0898251i
$890$	268.139	+	191.785i	0.301279	+	0.215488i
$891$	−390.658	−	458.916i	−0.438449	−	0.515057i
$892$	−410.247	+	140.074i	−0.459918	+	0.157034i
$893$	2261.21	−	1305.51i	2.53215	−	1.46194i
$894$	520.016	−	801.600i	0.581674	−	0.896644i
$895$	−476.654	−	275.196i	−0.532574	−	0.307482i
$896$	102.813	+	16.3176i	0.114747	+	0.0182116i
$897$	−393.233	+	251.499i	−0.438387	+	0.280378i
$898$	−848.238	−	82.7825i	−0.944586	−	0.0921854i
$899$	176.710			0.196563
$900$	77.4904	+	173.596i	0.0861004	+	0.192885i
$901$			148.569i			0.164894i
$902$	81.1710	+	7.92176i	0.0899900	+	0.00878244i
$903$	50.2504	−	96.9497i	0.0556483	−	0.107364i
$904$	−826.830	+	778.562i	−0.914635	+	0.861241i
$905$	−253.327	+	438.776i	−0.279920	+	0.484835i
$906$	535.431	+	1049.59i	0.590983	+	1.15849i
$907$	616.897	+	1068.50i	0.680151	+	1.17806i	0.974934	+	0.222493i	$0.0714193\pi$
$907$	616.897	+	1068.50i	0.680151	+	1.17806i	−0.294783	+	0.955564i	$0.595247\pi$
$908$	349.128	+	1022.52i	0.384502	+	1.12612i
$909$	595.304	−	419.991i	0.654900	−	0.462037i
$910$	122.748	+	87.7945i	0.134887	+	0.0964775i
$911$	430.671	−	248.648i	0.472746	−	0.272940i	−0.244643	−	0.969613i	$-0.578671\pi$
$911$	430.671	−	248.648i	0.472746	−	0.272940i	0.717388	+	0.696673i	$0.245337\pi$
$912$	514.275	−	1436.75i	0.563898	−	1.57538i
$913$	−26.2848	+	45.5266i	−0.0287895	+	0.0498649i
$914$	295.258	+	650.110i	0.323040	+	0.711280i
$915$	−42.6705	−	939.087i	−0.0466344	−	1.02632i
$916$	322.691	+	281.978i	0.352282	+	0.307837i
$917$			126.408i			0.137850i
$918$	−3.67251	−	94.2749i	−0.00400056	−	0.102696i
$919$		−	222.255i		−	0.241845i	−0.992662	−	0.120922i	$-0.961415\pi$
$919$		−	222.255i		−	0.241845i	0.992662	−	0.120922i	$-0.0385852\pi$
$920$	60.7612	+	257.482i	0.0660448	+	0.279872i
$921$	−14.2500	−	313.613i	−0.0154724	−	0.340514i
$922$	1522.66	−	691.542i	1.65148	−	0.750046i
$923$	−724.092	+	1254.16i	−0.784498	+	1.35879i
$924$	45.2493	−	56.7916i	0.0489711	−	0.0614627i
$925$	−283.901	+	163.910i	−0.306920	+	0.177201i
$926$	−753.391	−	538.859i	−0.813598	−	0.581921i
$927$	−264.622	−	122.254i	−0.285461	−	0.131882i
$928$	−995.761	+	37.0314i	−1.07302	+	0.0399045i
$929$	481.758	+	834.429i	0.518577	+	0.898201i	0.999767	+	0.0215848i	$0.00687120\pi$
$929$	481.758	+	834.429i	0.518577	+	0.898201i	−0.481190	+	0.876616i	$0.659795\pi$
$930$	134.687	−	68.7084i	0.144825	−	0.0738800i
$931$	−768.390	+	1330.89i	−0.825338	+	1.42953i
$932$	−882.724	−	173.953i	−0.947129	−	0.186645i
$933$	428.198	−	826.135i	0.458947	−	0.885461i
$934$	−440.342	−	42.9745i	−0.471459	−	0.0460113i
$935$			57.7265i			0.0617396i
$936$	−1126.35	−	997.173i	−1.20337	−	1.06536i
$937$	7.75413			0.00827549			0.00413774	−	0.999991i	$-0.498683\pi$
$937$	7.75413			0.00827549			0.00413774	+	0.999991i	$0.498683\pi$
$938$	3.13378	−	32.1105i	0.00334091	−	0.0342330i
$939$	1017.65	−	650.855i	1.08376	−	0.693137i
$940$	−1431.28	−	282.054i	−1.52264	−	0.300058i
$941$	−407.216	−	235.106i	−0.432748	−	0.249847i	0.267768	−	0.963483i	$-0.413714\pi$
$941$	−407.216	−	235.106i	−0.432748	−	0.249847i	−0.700517	+	0.713636i	$0.747047\pi$
$942$	−678.130	+	1045.33i	−0.719883	+	1.10969i
$943$	35.3461	−	20.4071i	0.0374826	−	0.0216406i
$944$	−553.552	+	427.893i	−0.586390	+	0.453276i
$945$	13.2419	+	96.6068i	0.0140126	+	0.102229i
$946$	387.457	−	541.713i	0.409574	−	0.572635i
$947$	881.063	+	1526.05i	0.930372	+	1.61145i	0.782685	+	0.622418i	$0.213850\pi$
$947$	881.063	+	1526.05i	0.930372	+	1.61145i	0.147687	+	0.989034i	$0.452817\pi$
$948$	−188.261	−	479.067i	−0.198587	−	0.505345i
$949$	392.967	+	226.879i	0.414085	+	0.239072i
$950$	138.846	+	305.717i	0.146154	+	0.321807i
$951$	−302.674	−	473.249i	−0.318269	−	0.497633i
$952$	11.0635	−	2.61080i	0.0116214	−	0.00274244i
$953$	−1271.02			−1.33371			−0.666854	−	0.745188i	$-0.732360\pi$
$953$	−1271.02			−1.33371			−0.666854	+	0.745188i	$0.732360\pi$
$954$	−9.90513	+	1530.59i	−0.0103827	+	1.60440i
$955$	−61.9632			−0.0648830
$956$	269.206	+	235.241i	0.281596	+	0.246068i
$957$	−319.851	+	617.097i	−0.334222	+	0.644825i
$958$	1043.68	−	474.004i	1.08943	−	0.494785i
$959$	43.6537	+	25.2035i	0.0455200	+	0.0262810i
$960$	−744.565	+	415.397i	−0.775588	+	0.432705i
$961$	−464.398	−	804.361i	−0.483244	−	0.837004i
$962$	1509.12	−	2109.94i	1.56873	−	2.19328i
$963$	1638.62	−	149.220i	1.70158	−	0.154953i
$964$	−349.105	−	1022.45i	−0.362142	−	1.06063i
$965$	−232.784	+	134.398i	−0.241227	+	0.139272i
$966$	1.88435	−	36.2900i	0.00195068	−	0.0375672i
$967$	1466.93	+	846.934i	1.51699	+	0.875836i	0.999801	+	0.0199668i	$0.00635606\pi$
$967$	1466.93	+	846.934i	1.51699	+	0.875836i	0.517192	+	0.855869i	$0.326977\pi$
$968$	−382.307	+	359.989i	−0.394945	+	0.371890i
$969$	−7.56387	−	166.465i	−0.00780586	−	0.171790i
$970$	−16.1973	+	165.967i	−0.0166983	+	0.171100i
$971$	1414.92			1.45717			0.728587	−	0.684953i	$-0.240177\pi$
$971$	1414.92			1.45717			0.728587	+	0.684953i	$0.240177\pi$
$972$	−31.5498	−	971.488i	−0.0324586	−	0.999473i
$973$		−	109.198i		−	0.112228i
$974$	76.1335	−	780.109i	0.0781659	−	0.800933i
$975$	330.658	−	15.0245i	0.339137	−	0.0154098i
$976$	−1118.84	+	151.350i	−1.14636	+	0.155071i
$977$	717.018	−	1241.91i	0.733897	−	1.27115i	−0.221308	−	0.975204i	$-0.571033\pi$
$977$	717.018	−	1241.91i	0.733897	−	1.27115i	0.955205	−	0.295944i	$-0.0956341\pi$
$978$	−60.5393	+	1165.90i	−0.0619012	+	1.19213i
$979$	−138.092	−	239.182i	−0.141054	−	0.244312i
$980$	812.558	−	277.439i	0.829140	−	0.283101i
$981$	5.95880	+	65.4349i	0.00607421	+	0.0667022i
$982$	137.039	−	191.597i	0.139551	−	0.195109i
$983$	−702.617	+	405.656i	−0.714768	+	0.412672i	−0.812824	−	0.582509i	$-0.802071\pi$
$983$	−702.617	+	405.656i	−0.714768	+	0.412672i	0.0980558	+	0.995181i	$0.468738\pi$
$984$	94.4262	+	91.5709i	0.0959616	+	0.0930598i
$985$	−343.053	+	594.185i	−0.348277	+	0.603234i
$986$	−99.0707	+	44.9946i	−0.100477	+	0.0456335i
$987$	177.903	+	92.2099i	0.180247	+	0.0934244i
$988$	−2000.74	−	1748.32i	−2.02504	−	1.76955i
$989$		−	333.300i		−	0.337007i
$990$	−3.84864	+	594.712i	−0.00388751	+	0.600720i
$991$			1111.56i			1.12166i	0.827931	+	0.560829i	$0.189518\pi$
$991$			1111.56i			1.12166i	−0.827931	+	0.560829i	$0.810482\pi$
$992$	−96.5798	−	153.784i	−0.0973586	−	0.155024i
$993$	−389.380	+	249.034i	−0.392125	+	0.250790i
$994$	−46.6203	−	102.650i	−0.0469017	−	0.103270i
$995$	596.021	−	1032.34i	0.599016	−	1.03753i
$996$	−78.9104	+	31.0098i	−0.0792273	+	0.0311343i
$997$	1017.90	−	587.682i	1.02096	−	0.589451i	0.106577	−	0.994304i	$-0.466011\pi$
$997$	1017.90	−	587.682i	1.02096	−	0.589451i	0.914381	+	0.404854i	$0.132678\pi$
$998$	−71.4877	+	99.9486i	−0.0716310	+	0.100149i
$999$	1660.60	−	227.618i	1.66226	−	0.227846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.p.b.67.1	yes	40
3.2	odd	2		216.3.p.b.91.20		40
4.3	odd	2		288.3.t.b.175.11		40
8.3	odd	2	inner	72.3.p.b.67.14	yes	40
8.5	even	2		288.3.t.b.175.12		40
9.2	odd	6		216.3.p.b.19.7		40
9.4	even	3		648.3.b.f.163.13		20
9.5	odd	6		648.3.b.e.163.8		20
9.7	even	3	inner	72.3.p.b.43.14	yes	40
12.11	even	2		864.3.t.b.847.14		40
24.5	odd	2		864.3.t.b.847.7		40
24.11	even	2		216.3.p.b.91.7		40
36.7	odd	6		288.3.t.b.79.12		40
36.11	even	6		864.3.t.b.559.7		40
36.23	even	6		2592.3.b.f.1135.7		20
36.31	odd	6		2592.3.b.e.1135.14		20
72.5	odd	6		2592.3.b.f.1135.14		20
72.11	even	6		216.3.p.b.19.20		40
72.13	even	6		2592.3.b.e.1135.7		20
72.29	odd	6		864.3.t.b.559.14		40
72.43	odd	6	inner	72.3.p.b.43.1	✓	40
72.59	even	6		648.3.b.e.163.7		20
72.61	even	6		288.3.t.b.79.11		40
72.67	odd	6		648.3.b.f.163.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.1	✓	40	72.43	odd	6	inner
72.3.p.b.43.14	yes	40	9.7	even	3	inner
72.3.p.b.67.1	yes	40	1.1	even	1	trivial
72.3.p.b.67.14	yes	40	8.3	odd	2	inner
216.3.p.b.19.7		40	9.2	odd	6
216.3.p.b.19.20		40	72.11	even	6
216.3.p.b.91.7		40	24.11	even	2
216.3.p.b.91.20		40	3.2	odd	2
288.3.t.b.79.11		40	72.61	even	6
288.3.t.b.79.12		40	36.7	odd	6
288.3.t.b.175.11		40	4.3	odd	2
288.3.t.b.175.12		40	8.5	even	2
648.3.b.e.163.7		20	72.59	even	6
648.3.b.e.163.8		20	9.5	odd	6
648.3.b.f.163.13		20	9.4	even	3
648.3.b.f.163.14		20	72.67	odd	6
864.3.t.b.559.7		40	36.11	even	6
864.3.t.b.559.14		40	72.29	odd	6
864.3.t.b.847.7		40	24.5	odd	2
864.3.t.b.847.14		40	12.11	even	2
2592.3.b.e.1135.7		20	72.13	even	6
2592.3.b.e.1135.14		20	36.31	odd	6
2592.3.b.f.1135.7		20	36.23	even	6
2592.3.b.f.1135.14		20	72.5	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99054 - 0.194264i) q^{2} +(-0.136174 - 2.99691i) q^{3} +(3.92452 + 0.773382i) q^{4} +(-3.84571 - 2.22032i) q^{5} +(-0.311131 + 5.99193i) q^{6} +(-0.704321 + 0.406640i) q^{7} +(-7.66169 - 2.30184i) q^{8} +(-8.96291 + 0.816203i) q^{9} +O(q^{10})\)	\(q+(-1.99054 - 0.194264i) q^{2} +(-0.136174 - 2.99691i) q^{3} +(3.92452 + 0.773382i) q^{4} +(-3.84571 - 2.22032i) q^{5} +(-0.311131 + 5.99193i) q^{6} +(-0.704321 + 0.406640i) q^{7} +(-7.66169 - 2.30184i) q^{8} +(-8.96291 + 0.816203i) q^{9} +(7.22371 + 5.16672i) q^{10} +(-3.72022 - 6.44360i) q^{11} +(1.78333 - 11.8667i) q^{12} +(-18.0943 - 10.4468i) q^{13} +(1.48098 - 0.672610i) q^{14} +(-6.13041 + 11.8276i) q^{15} +(14.8038 + 6.07031i) q^{16} +1.74716 q^{17} +(17.9996 + 0.116483i) q^{18} +31.7920 q^{19} +(-13.3754 - 11.6879i) q^{20} +(1.31457 + 2.05541i) q^{21} +(6.15349 + 13.5490i) q^{22} +(6.44927 + 3.72348i) q^{23} +(-5.85509 + 23.2748i) q^{24} +(-2.64036 - 4.57325i) q^{25} +(33.9881 + 24.3098i) q^{26} +(3.66660 + 26.7499i) q^{27} +(-3.07861 + 1.05116i) q^{28} +(26.9672 - 15.5695i) q^{29} +(14.5005 - 22.3524i) q^{30} +(4.91458 + 2.83744i) q^{31} +(-28.2883 - 14.9590i) q^{32} +(-18.8043 + 12.0266i) q^{33} +(-3.47779 - 0.339410i) q^{34} +3.61148 q^{35} +(-35.8064 - 3.72854i) q^{36} -62.0787i q^{37} +(-63.2833 - 6.17604i) q^{38} +(-28.8440 + 55.6496i) q^{39} +(24.3538 + 25.8636i) q^{40} +(2.74032 - 4.74637i) q^{41} +(-2.21742 - 4.34676i) q^{42} +(-22.3782 - 38.7602i) q^{43} +(-9.61671 - 28.1652i) q^{44} +(36.2810 + 16.7617i) q^{45} +(-12.1142 - 8.66462i) q^{46} +(71.1253 - 41.0642i) q^{47} +(16.1763 - 45.1921i) q^{48} +(-24.1693 + 41.8624i) q^{49} +(4.36734 + 9.61617i) q^{50} +(-0.237918 - 5.23607i) q^{51} +(-62.9323 - 54.9924i) q^{52} +85.0348i q^{53} +(-2.10200 - 53.9591i) q^{54} +33.0403i q^{55} +(6.33232 - 1.49431i) q^{56} +(-4.32925 - 95.2776i) q^{57} +(-56.7040 + 25.7530i) q^{58} +(-21.8641 + 37.8697i) q^{59} +(-33.2061 + 41.6765i) q^{60} +(-61.1107 + 35.2823i) q^{61} +(-9.23148 - 6.60276i) q^{62} +(5.98087 - 4.21955i) q^{63} +(53.4030 + 35.2720i) q^{64} +(46.3903 + 80.3504i) q^{65} +(39.7671 - 20.2865i) q^{66} +(9.91758 - 17.1778i) q^{67} +(6.85675 + 1.35122i) q^{68} +(10.2807 - 19.8349i) q^{69} +(-7.18881 - 0.701581i) q^{70} -69.3125i q^{71} +(70.5498 + 14.3777i) q^{72} -21.7177 q^{73} +(-12.0597 + 123.570i) q^{74} +(-13.3460 + 8.53569i) q^{75} +(124.768 + 24.5873i) q^{76} +(5.24046 + 3.02558i) q^{77} +(68.2260 - 105.170i) q^{78} +(37.1475 - 21.4471i) q^{79} +(-43.4529 - 56.2137i) q^{80} +(79.6676 - 14.6311i) q^{81} +(-6.37677 + 8.91551i) q^{82} +(-3.53270 - 6.11881i) q^{83} +(3.56946 + 9.08318i) q^{84} +(-6.71905 - 3.87924i) q^{85} +(37.0151 + 81.5012i) q^{86} +(-50.3327 - 78.6981i) q^{87} +(13.6710 + 57.9323i) q^{88} +37.1192 q^{89} +(-68.9626 - 40.4129i) q^{90} +16.9923 q^{91} +(22.4306 + 19.6006i) q^{92} +(7.83429 - 15.1149i) q^{93} +(-149.555 + 67.9230i) q^{94} +(-122.263 - 70.5883i) q^{95} +(-40.9788 + 86.8144i) q^{96} +(9.38806 + 16.2606i) q^{97} +(56.2424 - 78.6338i) q^{98} +(38.6033 + 54.7170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9	\( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9 - 12 * q^10 - 16 * q^11 - 12 * q^12 + 6 * q^14 + 31 * q^16 - 4 * q^17 - 114 * q^18 - 76 * q^19 - 12 * q^20 + 35 * q^22 + 39 * q^24 + 118 * q^25 - 72 * q^26 - 144 * q^27 - 36 * q^28 - 90 * q^30 - 5 * q^32 + 156 * q^33 + 5 * q^34 - 108 * q^35 + 51 * q^36 - 169 * q^38 - 6 * q^40 + 20 * q^41 - 42 * q^42 - 16 * q^43 + 362 * q^44 - 96 * q^46 + 183 * q^48 + 166 * q^49 + 73 * q^50 + 330 * q^51 - 24 * q^52 + 57 * q^54 + 186 * q^56 - 258 * q^57 + 36 * q^58 - 64 * q^59 + 150 * q^60 + 384 * q^62 - 518 * q^64 - 102 * q^65 + 486 * q^66 - 64 * q^67 - 295 * q^68 - 6 * q^70 - 225 * q^72 - 292 * q^73 + 318 * q^74 + 138 * q^75 + 197 * q^76 + 174 * q^78 - 720 * q^80 - 42 * q^81 + 386 * q^82 + 554 * q^83 - 720 * q^84 - 295 * q^86 + 59 * q^88 - 688 * q^89 - 696 * q^90 - 204 * q^91 - 378 * q^92 - 66 * q^94 - 222 * q^96 + 92 * q^97 - 614 * q^98 + 90 * q^99

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