LMFDB - Embedded newform 99.2.e.d.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	99.67
Dual form			99.2.e.d.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.300767i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +(0.205737 - 0.565258i) q^{6} +(-0.266044 - 0.460802i) q^{7} -1.34730 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.300767i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +(0.205737 - 0.565258i) q^{6} +(-0.266044 - 0.460802i) q^{7} -1.34730 q^{8} +(-0.520945 + 2.95442i) q^{9} +0.226682 q^{10} +(0.500000 + 0.866025i) q^{11} +(3.20574 - 0.565258i) q^{12} +(1.15270 - 1.99654i) q^{13} +(-0.0923963 + 0.160035i) q^{14} +(-1.11334 + 0.196312i) q^{15} +(-1.64543 - 2.84997i) q^{16} -4.41147 q^{17} +(0.979055 - 0.356347i) q^{18} -4.18479 q^{19} +(0.613341 + 1.06234i) q^{20} +(0.315207 - 0.866025i) q^{21} +(0.173648 - 0.300767i) q^{22} +(-0.705737 + 1.22237i) q^{23} +(-1.50000 - 1.78763i) q^{24} +(2.28699 + 3.96118i) q^{25} -0.800660 q^{26} +(-4.50000 + 2.59808i) q^{27} -1.00000 q^{28} +(-3.17752 - 5.50362i) q^{29} +(0.252374 + 0.300767i) q^{30} +(1.08125 - 1.87278i) q^{31} +(-1.91875 + 3.32337i) q^{32} +(-0.592396 + 1.62760i) q^{33} +(0.766044 + 1.32683i) q^{34} +0.347296 q^{35} +(4.31908 + 3.62414i) q^{36} -3.16250 q^{37} +(0.726682 + 1.25865i) q^{38} +(3.93242 - 0.693392i) q^{39} +(0.439693 - 0.761570i) q^{40} +(4.65657 - 8.06542i) q^{41} +(-0.315207 + 0.0555796i) q^{42} +(6.14930 + 10.6509i) q^{43} +1.87939 q^{44} +(-1.50000 - 1.25865i) q^{45} +0.490200 q^{46} +(1.93242 + 3.34705i) q^{47} +(1.94949 - 5.35619i) q^{48} +(3.35844 - 5.81699i) q^{49} +(0.794263 - 1.37570i) q^{50} +(-4.91147 - 5.85327i) q^{51} +(-2.16637 - 3.75227i) q^{52} +12.6236 q^{53} +(1.56283 + 0.902302i) q^{54} -0.652704 q^{55} +(0.358441 + 0.620838i) q^{56} +(-4.65910 - 5.55250i) q^{57} +(-1.10354 + 1.91139i) q^{58} +(1.61721 - 2.80109i) q^{59} +(-0.726682 + 1.99654i) q^{60} +(4.26604 + 7.38901i) q^{61} -0.751030 q^{62} +(1.50000 - 0.545955i) q^{63} -5.24897 q^{64} +(0.752374 + 1.30315i) q^{65} +(0.592396 - 0.104455i) q^{66} +(-2.48158 + 4.29823i) q^{67} +(-4.14543 + 7.18009i) q^{68} +(-2.40760 + 0.424525i) q^{69} +(-0.0603074 - 0.104455i) q^{70} +9.98545 q^{71} +(0.701867 - 3.98048i) q^{72} -7.49525 q^{73} +(0.549163 + 0.951178i) q^{74} +(-2.70961 + 7.44459i) q^{75} +(-3.93242 + 6.81115i) q^{76} +(0.266044 - 0.460802i) q^{77} +(-0.891407 - 1.06234i) q^{78} +(2.43969 + 4.22567i) q^{79} +2.14796 q^{80} +(-8.45723 - 3.07818i) q^{81} -3.23442 q^{82} +(2.29813 + 3.98048i) q^{83} +(-1.11334 - 1.32683i) q^{84} +(1.43969 - 2.49362i) q^{85} +(2.13563 - 3.69902i) q^{86} +(3.76470 - 10.3434i) q^{87} +(-0.673648 - 1.16679i) q^{88} -16.9513 q^{89} +(-0.118089 + 0.669713i) q^{90} -1.22668 q^{91} +(1.32635 + 2.29731i) q^{92} +(3.68866 - 0.650411i) q^{93} +(0.671122 - 1.16242i) q^{94} +(1.36571 - 2.36549i) q^{95} +(-6.54576 + 1.15419i) q^{96} +(-6.32295 - 10.9517i) q^{97} -2.33275 q^{98} +(-2.81908 + 1.02606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8} - 12 q^{10} + 3 q^{11} + 9 q^{12} + 9 q^{13} + 3 q^{14} + 6 q^{16} - 6 q^{17} + 9 q^{18} - 18 q^{19} - 3 q^{20} + 9 q^{21} + 6 q^{23} - 9 q^{24} + 6 q^{25} + 24 q^{26} - 27 q^{27} - 6 q^{28} + 6 q^{29} + 18 q^{30} + 9 q^{31} - 9 q^{32} + 9 q^{36} - 24 q^{37} - 9 q^{38} - 3 q^{40} + 6 q^{41} - 9 q^{42} - 3 q^{43} - 9 q^{45} - 12 q^{47} + 9 q^{48} + 12 q^{49} + 15 q^{50} - 9 q^{51} + 6 q^{52} + 6 q^{53} - 6 q^{55} - 6 q^{56} + 9 q^{57} + 3 q^{58} - 21 q^{59} + 9 q^{60} + 21 q^{61} - 30 q^{62} + 9 q^{63} - 6 q^{64} + 21 q^{65} - 3 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 24 q^{71} + 18 q^{72} - 12 q^{73} + 15 q^{74} + 18 q^{75} - 3 q^{77} - 45 q^{78} + 9 q^{79} - 18 q^{80} + 42 q^{82} + 3 q^{85} - 6 q^{86} + 27 q^{87} - 3 q^{88} - 24 q^{89} - 27 q^{90} + 6 q^{91} + 9 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{95} - 9 q^{96} + 3 q^{97} + 24 q^{98}+O(q^{100}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8 - 12 * q^10 + 3 * q^11 + 9 * q^12 + 9 * q^13 + 3 * q^14 + 6 * q^16 - 6 * q^17 + 9 * q^18 - 18 * q^19 - 3 * q^20 + 9 * q^21 + 6 * q^23 - 9 * q^24 + 6 * q^25 + 24 * q^26 - 27 * q^27 - 6 * q^28 + 6 * q^29 + 18 * q^30 + 9 * q^31 - 9 * q^32 + 9 * q^36 - 24 * q^37 - 9 * q^38 - 3 * q^40 + 6 * q^41 - 9 * q^42 - 3 * q^43 - 9 * q^45 - 12 * q^47 + 9 * q^48 + 12 * q^49 + 15 * q^50 - 9 * q^51 + 6 * q^52 + 6 * q^53 - 6 * q^55 - 6 * q^56 + 9 * q^57 + 3 * q^58 - 21 * q^59 + 9 * q^60 + 21 * q^61 - 30 * q^62 + 9 * q^63 - 6 * q^64 + 21 * q^65 - 3 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 24 * q^71 + 18 * q^72 - 12 * q^73 + 15 * q^74 + 18 * q^75 - 3 * q^77 - 45 * q^78 + 9 * q^79 - 18 * q^80 + 42 * q^82 + 3 * q^85 - 6 * q^86 + 27 * q^87 - 3 * q^88 - 24 * q^89 - 27 * q^90 + 6 * q^91 + 9 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^95 - 9 * q^96 + 3 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.173648	−	0.300767i	−0.122788	−	0.212675i	0.798078	−	0.602554i	$-0.205850\pi$
$2$	−0.173648	−	0.300767i	−0.122788	−	0.212675i	−0.920866	+	0.389879i	$0.872517\pi$
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$4$	0.939693	−	1.62760i	0.469846	−	0.813798i
$5$	−0.326352	+	0.565258i	−0.145949	+	0.252791i	−0.929727	−	0.368251i	$-0.879957\pi$
$5$	−0.326352	+	0.565258i	−0.145949	+	0.252791i	0.783778	+	0.621042i	$0.213290\pi$
$6$	0.205737	−	0.565258i	0.0839918	−	0.230766i
$7$	−0.266044	−	0.460802i	−0.100555	−	0.174167i	0.811358	−	0.584549i	$-0.198729\pi$
$7$	−0.266044	−	0.460802i	−0.100555	−	0.174167i	−0.911914	+	0.410382i	$0.865395\pi$
$8$	−1.34730			−0.476341
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$	0.226682			0.0716830
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	3.20574	−	0.565258i	0.925417	−	0.163176i
$13$	1.15270	−	1.99654i	0.319702	−	0.553741i	−0.660723	−	0.750629i	$-0.729750\pi$
$13$	1.15270	−	1.99654i	0.319702	−	0.553741i	0.980426	+	0.196889i	$0.0630837\pi$
$14$	−0.0923963	+	0.160035i	−0.0246939	+	0.0427712i
$15$	−1.11334	+	0.196312i	−0.287463	+	0.0506875i
$16$	−1.64543	−	2.84997i	−0.411357	−	0.712492i
$17$	−4.41147			−1.06994			−0.534970	−	0.844871i	$-0.679677\pi$
$17$	−4.41147			−1.06994			−0.534970	+	0.844871i	$0.679677\pi$
$18$	0.979055	−	0.356347i	0.230766	−	0.0839918i
$19$	−4.18479			−0.960057			−0.480029	−	0.877253i	$-0.659374\pi$
$19$	−4.18479			−0.960057			−0.480029	+	0.877253i	$0.659374\pi$
$20$	0.613341	+	1.06234i	0.137147	+	0.237546i
$21$	0.315207	−	0.866025i	0.0687839	−	0.188982i
$22$	0.173648	−	0.300767i	0.0370219	−	0.0641238i
$23$	−0.705737	+	1.22237i	−0.147156	+	0.254882i	−0.930175	−	0.367115i	$-0.880345\pi$
$23$	−0.705737	+	1.22237i	−0.147156	+	0.254882i	0.783019	+	0.621998i	$0.213679\pi$
$24$	−1.50000	−	1.78763i	−0.306186	−	0.364899i
$25$	2.28699	+	3.96118i	0.457398	+	0.792236i
$26$	−0.800660			−0.157022
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$	−1.00000			−0.188982
$29$	−3.17752	−	5.50362i	−0.590050	−	1.02200i	−0.994225	−	0.107315i	$-0.965775\pi$
$29$	−3.17752	−	5.50362i	−0.590050	−	1.02200i	0.404175	−	0.914682i	$-0.367559\pi$
$30$	0.252374	+	0.300767i	0.0460770	+	0.0549124i
$31$	1.08125	−	1.87278i	0.194199	−	0.336362i	−0.752439	−	0.658662i	$-0.771123\pi$
$31$	1.08125	−	1.87278i	0.194199	−	0.336362i	0.946638	+	0.322300i	$0.104456\pi$
$32$	−1.91875	+	3.32337i	−0.339190	+	0.587494i
$33$	−0.592396	+	1.62760i	−0.103123	+	0.283328i
$34$	0.766044	+	1.32683i	0.131376	+	0.227549i
$35$	0.347296			0.0587038
$36$	4.31908	+	3.62414i	0.719846	+	0.604023i
$37$	−3.16250			−0.519912			−0.259956	−	0.965620i	$-0.583708\pi$
$37$	−3.16250			−0.519912			−0.259956	+	0.965620i	$0.583708\pi$
$38$	0.726682	+	1.25865i	0.117883	+	0.204180i
$39$	3.93242	−	0.693392i	0.629691	−	0.111032i
$40$	0.439693	−	0.761570i	0.0695215	−	0.120415i
$41$	4.65657	−	8.06542i	0.727235	−	1.25961i	−0.230813	−	0.972998i	$-0.574139\pi$
$41$	4.65657	−	8.06542i	0.727235	−	1.25961i	0.958048	−	0.286609i	$-0.0925281\pi$
$42$	−0.315207	+	0.0555796i	−0.0486376	+	0.00857612i
$43$	6.14930	+	10.6509i	0.937759	+	1.62425i	0.769638	+	0.638481i	$0.220437\pi$
$43$	6.14930	+	10.6509i	0.937759	+	1.62425i	0.168122	+	0.985766i	$0.446230\pi$
$44$	1.87939			0.283328
$45$	−1.50000	−	1.25865i	−0.223607	−	0.187628i
$46$	0.490200			0.0722760
$47$	1.93242	+	3.34705i	0.281872	+	0.488217i	0.971846	−	0.235617i	$-0.0757112\pi$
$47$	1.93242	+	3.34705i	0.281872	+	0.488217i	−0.689974	+	0.723834i	$0.742378\pi$
$48$	1.94949	−	5.35619i	0.281385	−	0.773099i
$49$	3.35844	−	5.81699i	0.479777	−	0.830999i
$50$	0.794263	−	1.37570i	0.112326	−	0.194554i
$51$	−4.91147	−	5.85327i	−0.687744	−	0.819621i
$52$	−2.16637	−	3.75227i	−0.300422	−	0.520346i
$53$	12.6236			1.73399			0.866993	−	0.498320i	$-0.166050\pi$
$53$	12.6236			1.73399			0.866993	+	0.498320i	$0.166050\pi$
$54$	1.56283	+	0.902302i	0.212675	+	0.122788i
$55$	−0.652704			−0.0880105
$56$	0.358441	+	0.620838i	0.0478987	+	0.0829629i
$57$	−4.65910	−	5.55250i	−0.617113	−	0.735447i
$58$	−1.10354	+	1.91139i	−0.144902	+	0.250978i
$59$	1.61721	−	2.80109i	0.210543	−	0.364671i	−0.741342	−	0.671128i	$-0.765810\pi$
$59$	1.61721	−	2.80109i	0.210543	−	0.364671i	0.951885	+	0.306457i	$0.0991435\pi$
$60$	−0.726682	+	1.99654i	−0.0938142	+	0.257752i
$61$	4.26604	+	7.38901i	0.546211	+	0.946065i	0.998530	+	0.0542088i	$0.0172637\pi$
$61$	4.26604	+	7.38901i	0.546211	+	0.946065i	−0.452319	+	0.891856i	$0.649403\pi$
$62$	−0.751030			−0.0953809
$63$	1.50000	−	0.545955i	0.188982	−	0.0687839i
$64$	−5.24897			−0.656121
$65$	0.752374	+	1.30315i	0.0933205	+	0.161636i
$66$	0.592396	−	0.104455i	0.0729189	−	0.0128576i
$67$	−2.48158	+	4.29823i	−0.303173	+	0.525112i	−0.976853	−	0.213912i	$-0.931379\pi$
$67$	−2.48158	+	4.29823i	−0.303173	+	0.525112i	0.673680	+	0.739024i	$0.264713\pi$
$68$	−4.14543	+	7.18009i	−0.502707	+	0.870714i
$69$	−2.40760	+	0.424525i	−0.289841	+	0.0511069i
$70$	−0.0603074	−	0.104455i	−0.00720811	−	0.0124848i
$71$	9.98545			1.18506			0.592528	−	0.805550i	$-0.298130\pi$
$71$	9.98545			1.18506			0.592528	+	0.805550i	$0.298130\pi$
$72$	0.701867	−	3.98048i	0.0827158	−	0.469105i
$73$	−7.49525			−0.877253			−0.438626	−	0.898669i	$-0.644535\pi$
$73$	−7.49525			−0.877253			−0.438626	+	0.898669i	$0.644535\pi$
$74$	0.549163	+	0.951178i	0.0638389	+	0.110572i
$75$	−2.70961	+	7.44459i	−0.312879	+	0.859627i
$76$	−3.93242	+	6.81115i	−0.451079	+	0.781292i
$77$	0.266044	−	0.460802i	0.0303186	−	0.0525133i
$78$	−0.891407	−	1.06234i	−0.100932	−	0.120286i
$79$	2.43969	+	4.22567i	0.274487	+	0.475425i	0.970006	−	0.243083i	$-0.0781587\pi$
$79$	2.43969	+	4.22567i	0.274487	+	0.475425i	−0.695519	+	0.718508i	$0.744825\pi$
$80$	2.14796			0.240149
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	−3.23442			−0.357182
$83$	2.29813	+	3.98048i	0.252253	+	0.436915i	0.964146	−	0.265373i	$-0.0854952\pi$
$83$	2.29813	+	3.98048i	0.252253	+	0.436915i	−0.711893	+	0.702288i	$0.752162\pi$
$84$	−1.11334	−	1.32683i	−0.121475	−	0.144769i
$85$	1.43969	−	2.49362i	0.156157	−	0.270471i
$86$	2.13563	−	3.69902i	0.230291	−	0.398875i
$87$	3.76470	−	10.3434i	0.403618	−	1.10893i
$88$	−0.673648	−	1.16679i	−0.0718111	−	0.124381i
$89$	−16.9513			−1.79683			−0.898417	−	0.439143i	$-0.855282\pi$
$89$	−16.9513			−1.79683			−0.898417	+	0.439143i	$0.855282\pi$
$90$	−0.118089	+	0.669713i	−0.0124476	+	0.0705940i
$91$	−1.22668			−0.128591
$92$	1.32635	+	2.29731i	0.138282	+	0.239511i
$93$	3.68866	−	0.650411i	0.382497	−	0.0674445i
$94$	0.671122	−	1.16242i	0.0692209	−	0.119894i
$95$	1.36571	−	2.36549i	0.140119	−	0.242694i
$96$	−6.54576	+	1.15419i	−0.668074	+	0.117799i
$97$	−6.32295	−	10.9517i	−0.641998	−	1.11197i	−0.984986	−	0.172634i	$-0.944772\pi$
$97$	−6.32295	−	10.9517i	−0.641998	−	1.11197i	0.342988	−	0.939340i	$-0.388561\pi$
$98$	−2.33275			−0.235643
$99$	−2.81908	+	1.02606i	−0.283328	+	0.103123i
$100$	8.59627			0.859627
$101$	−8.54576	−	14.8017i	−0.850335	−	1.47282i	−0.880906	−	0.473291i	$-0.843066\pi$
$101$	−8.54576	−	14.8017i	−0.850335	−	1.47282i	0.0305715	−	0.999533i	$-0.490267\pi$
$102$	−0.907604	+	2.49362i	−0.0898662	+	0.246905i
$103$	−1.42989	+	2.47665i	−0.140891	+	0.244031i	−0.927833	−	0.372997i	$-0.878330\pi$
$103$	−1.42989	+	2.47665i	−0.140891	+	0.244031i	0.786941	+	0.617028i	$0.211664\pi$
$104$	−1.55303	+	2.68993i	−0.152287	+	0.263770i
$105$	0.386659	+	0.460802i	0.0377341	+	0.0449697i
$106$	−2.19207	−	3.79677i	−0.212912	−	0.368775i
$107$	9.92902			0.959874			0.479937	−	0.877303i	$-0.340659\pi$
$107$	9.92902			0.959874			0.479937	+	0.877303i	$0.340659\pi$
$108$			9.76557i			0.939693i
$109$	13.8161			1.32335			0.661673	−	0.749792i	$-0.269847\pi$
$109$	13.8161			1.32335			0.661673	+	0.749792i	$0.269847\pi$
$110$	0.113341	+	0.196312i	0.0108066	+	0.0187176i
$111$	−3.52094	−	4.19610i	−0.334193	−	0.398276i
$112$	−0.875515	+	1.51644i	−0.0827284	+	0.143290i
$113$	−0.879385	+	1.52314i	−0.0827256	+	0.143285i	−0.904420	−	0.426644i	$-0.859696\pi$
$113$	−0.879385	+	1.52314i	−0.0827256	+	0.143285i	0.821694	+	0.569929i	$0.193029\pi$
$114$	−0.860967	+	2.36549i	−0.0806369	+	0.221548i
$115$	−0.460637	−	0.797847i	−0.0429546	−	0.0743996i
$116$	−11.9436			−1.10893
$117$	5.29813	+	4.44566i	0.489813	+	0.411002i
$118$	−1.12330			−0.103408
$119$	1.17365	+	2.03282i	0.107588	+	0.186348i
$120$	1.50000	−	0.264490i	0.136931	−	0.0241446i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.48158	−	2.56617i	0.134136	−	0.232331i
$123$	15.8858	−	2.80109i	1.43237	−	0.252566i
$124$	−2.03209	−	3.51968i	−0.182487	−	0.316077i
$125$	−6.24897			−0.558925
$126$	−0.424678	−	0.356347i	−0.0378333	−	0.0317459i
$127$	6.90167			0.612425			0.306212	−	0.951963i	$-0.400938\pi$
$127$	6.90167			0.612425			0.306212	+	0.951963i	$0.400938\pi$
$128$	4.74897	+	8.22546i	0.419754	+	0.727035i
$129$	−7.28564	+	20.0171i	−0.641465	+	1.76241i
$130$	0.261297	−	0.452579i	0.0229172	−	0.0396938i
$131$	−5.17024	+	8.95513i	−0.451726	+	0.782413i	−0.998493	−	0.0548718i	$-0.982525\pi$
$131$	−5.17024	+	8.95513i	−0.451726	+	0.782413i	0.546767	+	0.837285i	$0.315858\pi$
$132$	2.09240	+	2.49362i	0.182120	+	0.217042i
$133$	1.11334	+	1.92836i	0.0965389	+	0.167210i
$134$	1.72369			0.148904
$135$		−	3.39155i		−	0.291898i
$136$	5.94356			0.509656
$137$	−7.09240	−	12.2844i	−0.605944	−	1.04953i	−0.991901	−	0.127010i	$-0.959462\pi$
$137$	−7.09240	−	12.2844i	−0.605944	−	1.04953i	0.385957	−	0.922517i	$-0.373871\pi$
$138$	0.545759	+	0.650411i	0.0464581	+	0.0553666i
$139$	−0.0505072	+	0.0874810i	−0.00428396	+	0.00742004i	−0.868159	−	0.496285i	$-0.834697\pi$
$139$	−0.0505072	+	0.0874810i	−0.00428396	+	0.00742004i	0.863875	+	0.503705i	$0.168030\pi$
$140$	0.326352	−	0.565258i	0.0275818	−	0.0477730i
$141$	−2.28952	+	6.29039i	−0.192812	+	0.529747i
$142$	−1.73396	−	3.00330i	−0.145510	−	0.252031i
$143$	2.30541			0.192788
$144$	9.27719	−	3.37662i	0.773099	−	0.281385i
$145$	4.14796			0.344469
$146$	1.30154	+	2.25433i	0.107716	+	0.186570i
$147$	11.4572	−	2.02022i	0.944977	−	0.166625i
$148$	−2.97178	+	5.14728i	−0.244279	+	0.423104i
$149$	1.53074	−	2.65133i	0.125403	−	0.217205i	−0.796487	−	0.604656i	$-0.793311\pi$
$149$	1.53074	−	2.65133i	0.125403	−	0.217205i	0.921891	+	0.387450i	$0.126644\pi$
$150$	2.70961	−	0.477777i	0.221239	−	0.0390103i
$151$	−9.70099	−	16.8026i	−0.789455	−	1.36738i	−0.926301	−	0.376784i	$-0.877030\pi$
$151$	−9.70099	−	16.8026i	−0.789455	−	1.36738i	0.136846	−	0.990592i	$-0.456304\pi$
$152$	5.63816			0.457315
$153$	2.29813	−	13.0334i	0.185793	−	1.05368i
$154$	−0.184793			−0.0148910
$155$	0.705737	+	1.22237i	0.0566862	+	0.0981833i
$156$	2.56670	−	7.05196i	0.205501	−	0.564609i
$157$	6.36231	−	11.0198i	0.507768	−	0.879479i	−0.492192	−	0.870487i	$-0.663804\pi$
$157$	6.36231	−	11.0198i	0.507768	−	0.879479i	0.999960	−	0.00899272i	$-0.00286251\pi$
$158$	0.847296	−	1.46756i	0.0674073	−	0.116753i
$159$	14.0544	+	16.7494i	1.11458	+	1.32831i
$160$	−1.25237	−	2.16918i	−0.0990088	−	0.171488i
$161$	0.751030			0.0591894
$162$	0.542766	+	3.07818i	0.0426438	+	0.241845i
$163$	−12.7888			−1.00170			−0.500848	−	0.865535i	$-0.666978\pi$
$163$	−12.7888			−1.00170			−0.500848	+	0.865535i	$0.666978\pi$
$164$	−8.75150	−	15.1580i	−0.683377	−	1.18364i
$165$	−0.726682	−	0.866025i	−0.0565721	−	0.0674200i
$166$	0.798133	−	1.38241i	0.0619472	−	0.107296i
$167$	−10.3623	+	17.9480i	−0.801860	+	1.38886i	0.116531	+	0.993187i	$0.462823\pi$
$167$	−10.3623	+	17.9480i	−0.801860	+	1.38886i	−0.918391	+	0.395675i	$0.870511\pi$
$168$	−0.424678	+	1.16679i	−0.0327646	+	0.0900200i
$169$	3.84255	+	6.65549i	0.295581	+	0.511961i
$170$	−1.00000			−0.0766965
$171$	2.18004	−	12.3636i	0.166712	−	0.945472i
$172$	23.1138			1.76241
$173$	11.2515	+	19.4882i	0.855435	+	1.48166i	0.876240	+	0.481874i	$0.160044\pi$
$173$	11.2515	+	19.4882i	0.855435	+	1.48166i	−0.0208050	+	0.999784i	$0.506623\pi$
$174$	−3.76470	+	0.663818i	−0.285401	+	0.0503239i
$175$	1.21688	−	2.10770i	0.0919876	−	0.159327i
$176$	1.64543	−	2.84997i	0.124029	−	0.214824i
$177$	5.51707	−	0.972809i	0.414689	−	0.0731208i
$178$	2.94356	+	5.09840i	0.220629	+	0.382141i
$179$	−10.7219			−0.801395			−0.400697	−	0.916210i	$-0.631232\pi$
$179$	−10.7219			−0.801395			−0.400697	+	0.916210i	$0.631232\pi$
$180$	−3.45811	+	1.25865i	−0.257752	+	0.0938142i
$181$	−4.15745			−0.309021			−0.154510	−	0.987991i	$-0.549380\pi$
$181$	−4.15745			−0.309021			−0.154510	+	0.987991i	$0.549380\pi$
$182$	0.213011	+	0.368946i	0.0157894	+	0.0273481i
$183$	−5.05438	+	13.8868i	−0.373630	+	1.02654i
$184$	0.950837	−	1.64690i	0.0700966	−	0.121411i
$185$	1.03209	−	1.78763i	0.0758807	−	0.131429i
$186$	−0.836152	−	0.996487i	−0.0613096	−	0.0730660i
$187$	−2.20574	−	3.82045i	−0.161299	−	0.279379i
$188$	7.26352			0.529747
$189$	2.39440	+	1.38241i	0.174167	+	0.100555i
$190$	−0.948615			−0.0688198
$191$	−1.20187	−	2.08169i	−0.0869640	−	0.150626i	0.819262	−	0.573419i	$-0.194383\pi$
$191$	−1.20187	−	2.08169i	−0.0869640	−	0.150626i	−0.906226	+	0.422793i	$0.861050\pi$
$192$	−5.84389	−	6.96448i	−0.421747	−	0.502618i
$193$	0.226682	−	0.392624i	0.0163169	−	0.0282617i	−0.857752	−	0.514064i	$-0.828139\pi$
$193$	0.226682	−	0.392624i	0.0163169	−	0.0282617i	0.874069	+	0.485803i	$0.161473\pi$
$194$	−2.19594	+	3.80347i	−0.157659	+	0.273074i
$195$	−0.891407	+	2.44912i	−0.0638350	+	0.175385i
$196$	−6.31180	−	10.9324i	−0.450843	−	0.780883i
$197$	−19.6236			−1.39812			−0.699062	−	0.715061i	$-0.746399\pi$
$197$	−19.6236			−1.39812			−0.699062	+	0.715061i	$0.746399\pi$
$198$	0.798133	+	0.669713i	0.0567209	+	0.0475945i
$199$	3.63041			0.257353			0.128677	−	0.991687i	$-0.458927\pi$
$199$	3.63041			0.257353			0.128677	+	0.991687i	$0.458927\pi$
$200$	−3.08125	−	5.33688i	−0.217877	−	0.377375i
$201$	−8.46585	+	1.49276i	−0.597135	+	0.105291i
$202$	−2.96791	+	5.14057i	−0.208821	+	0.361689i
$203$	−1.69072	+	2.92842i	−0.118665	+	0.205535i
$204$	−14.1420	+	2.49362i	−0.990140	+	0.174588i
$205$	3.03936	+	5.26433i	0.212278	+	0.367677i
$206$	0.993193			0.0691990
$207$	−3.24376	−	2.72183i	−0.225457	−	0.189181i
$208$	−7.58677			−0.526048
$209$	−2.09240	−	3.62414i	−0.144734	−	0.250687i
$210$	0.0714517	−	0.196312i	0.00493064	−	0.0135468i
$211$	−10.8366	+	18.7696i	−0.746024	+	1.29215i	0.203691	+	0.979035i	$0.434706\pi$
$211$	−10.8366	+	18.7696i	−0.746024	+	1.29215i	−0.949715	+	0.313116i	$0.898627\pi$
$212$	11.8623	−	20.5461i	0.814707	−	1.41111i
$213$	11.1172	+	13.2490i	0.761739	+	0.907805i
$214$	−1.72416	−	2.98632i	−0.117861	−	0.204141i
$215$	−8.02734			−0.547460
$216$	6.06283	−	3.50038i	0.412524	−	0.238171i
$217$	−1.15064			−0.0781108
$218$	−2.39915	−	4.15545i	−0.162491	−	0.281442i
$219$	−8.34477	−	9.94491i	−0.563887	−	0.672015i
$220$	−0.613341	+	1.06234i	−0.0413514	+	0.0716228i
$221$	−5.08512	+	8.80769i	−0.342062	+	0.592469i
$222$	−0.650644	+	1.78763i	−0.0436684	+	0.119978i
$223$	−9.56805	−	16.5723i	−0.640724	−	1.10977i	−0.985271	−	0.170997i	$-0.945301\pi$
$223$	−9.56805	−	16.5723i	−0.640724	−	1.10977i	0.344548	−	0.938769i	$-0.388032\pi$
$224$	2.04189			0.136429
$225$	−12.8944	+	4.69318i	−0.859627	+	0.312879i
$226$	0.610815			0.0406308
$227$	7.79679	+	13.5044i	0.517491	+	0.896321i	0.999794	+	0.0203161i	$0.00646726\pi$
$227$	7.79679	+	13.5044i	0.517491	+	0.896321i	−0.482303	+	0.876005i	$0.660199\pi$
$228$	−13.4153	+	2.36549i	−0.888453	+	0.156658i
$229$	7.70574	−	13.3467i	0.509209	−	0.881977i	−0.490734	−	0.871310i	$-0.663271\pi$
$229$	7.70574	−	13.3467i	0.509209	−	0.881977i	0.999943	−	0.0106670i	$-0.00339547\pi$
$230$	−0.159978	+	0.277089i	−0.0105486	+	0.0182707i
$231$	0.907604	−	0.160035i	0.0597159	−	0.0105295i
$232$	4.28106	+	7.41501i	0.281065	+	0.486819i
$233$	4.29086			0.281104			0.140552	−	0.990073i	$-0.455112\pi$
$233$	4.29086			0.281104			0.140552	+	0.990073i	$0.455112\pi$
$234$	0.417099	−	2.36549i	0.0272666	−	0.154637i
$235$	−2.52259			−0.164556
$236$	−3.03936	−	5.26433i	−0.197846	−	0.342679i
$237$	−2.89053	+	7.94166i	−0.187760	+	0.515867i
$238$	0.407604	−	0.705990i	0.0264210	−	0.0457626i
$239$	10.0667	−	17.4360i	0.651161	−	1.12784i	−0.331681	−	0.943392i	$-0.607616\pi$
$239$	10.0667	−	17.4360i	0.651161	−	1.12784i	0.982842	−	0.184452i	$-0.0590511\pi$
$240$	2.39141	+	2.84997i	0.154365	+	0.183965i
$241$	3.72281	+	6.44810i	0.239807	+	0.415359i	0.960659	−	0.277731i	$-0.0895824\pi$
$241$	3.72281	+	6.44810i	0.239807	+	0.415359i	−0.720852	+	0.693090i	$0.756249\pi$
$242$	0.347296			0.0223251
$243$	−5.33157	−	14.6484i	−0.342020	−	0.939693i
$244$	16.0351			1.02654
$245$	2.19207	+	3.79677i	0.140046	+	0.242567i
$246$	−3.60101	−	4.29152i	−0.229592	−	0.273617i
$247$	−4.82383	+	8.35511i	−0.306933	+	0.531623i
$248$	−1.45677	+	2.52319i	−0.0925048	+	0.160223i
$249$	−2.72281	+	7.48086i	−0.172551	+	0.474080i
$250$	1.08512	+	1.87949i	0.0686292	+	0.118869i
$251$	12.5202			0.790270			0.395135	−	0.918623i	$-0.370698\pi$
$251$	12.5202			0.790270			0.395135	+	0.918623i	$0.370698\pi$
$252$	0.520945	−	2.95442i	0.0328164	−	0.186111i
$253$	−1.41147			−0.0887386
$254$	−1.19846	−	2.07580i	−0.0751983	−	0.130247i
$255$	4.91147	−	0.866025i	0.307568	−	0.0542326i
$256$	−3.59967	+	6.23481i	−0.224979	+	0.389676i
$257$	−3.24170	+	5.61478i	−0.202211	+	0.350241i	−0.949241	−	0.314551i	$-0.898146\pi$
$257$	−3.24170	+	5.61478i	−0.202211	+	0.350241i	0.747029	+	0.664791i	$0.231479\pi$
$258$	7.28564	−	1.28466i	0.453584	−	0.0799792i
$259$	0.841367	+	1.45729i	0.0522800	+	0.0905516i
$260$	2.82800			0.175385
$261$	17.9153	−	6.52065i	1.10893	−	0.403618i
$262$	3.59121			0.221866
$263$	−1.04916	−	1.81720i	−0.0646942	−	0.112054i	0.831864	−	0.554979i	$-0.187274\pi$
$263$	−1.04916	−	1.81720i	−0.0646942	−	0.112054i	−0.896558	+	0.442926i	$0.853941\pi$
$264$	0.798133	−	2.19285i	0.0491217	−	0.134961i
$265$	−4.11974	+	7.13559i	−0.253073	+	0.438336i
$266$	0.386659	−	0.669713i	0.0237076	−	0.0410628i
$267$	−18.8726	−	22.4915i	−1.15498	−	1.37646i
$268$	4.66385	+	8.07802i	0.284890	+	0.493444i
$269$	29.2490			1.78334			0.891671	−	0.452685i	$-0.149534\pi$
$269$	29.2490			1.78334			0.891671	+	0.452685i	$0.149534\pi$
$270$	−1.02007	+	0.588936i	−0.0620793	+	0.0358415i
$271$	−21.7246			−1.31968			−0.659838	−	0.751408i	$-0.729375\pi$
$271$	−21.7246			−1.31968			−0.659838	+	0.751408i	$0.729375\pi$
$272$	7.25877	+	12.5726i	0.440128	+	0.762323i
$273$	−1.36571	−	1.62760i	−0.0826568	−	0.0985066i
$274$	−2.46316	+	4.26632i	−0.148805	+	0.257738i
$275$	−2.28699	+	3.96118i	−0.137911	+	0.238868i
$276$	−1.57145	+	4.31753i	−0.0945903	+	0.259885i
$277$	2.22803	+	3.85905i	0.133869	+	0.231868i	0.925165	−	0.379565i	$-0.123926\pi$
$277$	2.22803	+	3.85905i	0.133869	+	0.231868i	−0.791296	+	0.611434i	$0.790593\pi$
$278$	0.0350819			0.00210407
$279$	4.96972	+	4.17009i	0.297529	+	0.249657i
$280$	−0.467911			−0.0279630
$281$	10.2476	+	17.7494i	0.611322	+	1.05884i	0.991018	+	0.133730i	$0.0426953\pi$
$281$	10.2476	+	17.7494i	0.611322	+	1.05884i	−0.379696	+	0.925111i	$0.623971\pi$
$282$	2.28952	−	0.403703i	0.136339	−	0.0240402i
$283$	−3.44356	+	5.96443i	−0.204699	+	0.354548i	−0.950037	−	0.312138i	$-0.898955\pi$
$283$	−3.44356	+	5.96443i	−0.204699	+	0.354548i	0.745338	+	0.666687i	$0.232288\pi$
$284$	9.38326	−	16.2523i	0.556794	−	0.964395i
$285$	4.65910	−	0.821525i	0.275981	−	0.0486629i
$286$	−0.400330	−	0.693392i	−0.0236720	−	0.0410011i
$287$	−4.95542			−0.292509
$288$	−8.81908	−	7.40008i	−0.519669	−	0.436054i
$289$	2.46110			0.144771
$290$	−0.720285	−	1.24757i	−0.0422966	−	0.0732598i
$291$	7.49138	−	20.5824i	0.439153	−	1.20656i
$292$	−7.04323	+	12.1992i	−0.412174	+	0.713906i
$293$	6.90420	−	11.9584i	0.403348	−	0.698619i	−0.590780	−	0.806833i	$-0.701180\pi$
$293$	6.90420	−	11.9584i	0.403348	−	0.698619i	0.994128	+	0.108214i	$0.0345132\pi$
$294$	−2.59714	−	3.09516i	−0.151469	−	0.180513i
$295$	1.05556	+	1.82828i	0.0614571	+	0.106447i
$296$	4.26083			0.247656
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$	−1.06324			−0.0615921
$299$	1.62701	+	2.81807i	0.0940925	+	0.162973i
$300$	9.57057	+	11.4058i	0.552557	+	0.658512i
$301$	3.27197	−	5.66723i	0.188593	−	0.326653i
$302$	−3.36912	+	5.83548i	−0.193871	+	0.335794i
$303$	10.1250	−	27.8181i	0.581663	−	1.59811i
$304$	6.88578	+	11.9265i	0.394927	+	0.684033i
$305$	−5.56893			−0.318876
$306$	−4.31908	+	1.57202i	−0.246905	+	0.0898662i
$307$	−0.601319			−0.0343191			−0.0171595	−	0.999853i	$-0.505462\pi$
$307$	−0.601319			−0.0343191			−0.0171595	+	0.999853i	$0.505462\pi$
$308$	−0.500000	−	0.866025i	−0.0284901	−	0.0493464i
$309$	−4.87804	+	0.860130i	−0.277502	+	0.0489311i
$310$	0.245100	−	0.424525i	0.0139207	−	0.0241114i
$311$	−0.970437	+	1.68085i	−0.0550285	+	0.0953121i	−0.892227	−	0.451586i	$-0.850858\pi$
$311$	−0.970437	+	1.68085i	−0.0550285	+	0.0953121i	0.837199	+	0.546898i	$0.184192\pi$
$312$	−5.29813	+	0.934204i	−0.299948	+	0.0528889i
$313$	−1.00980	−	1.74903i	−0.0570773	−	0.0988608i	0.836075	−	0.548615i	$-0.184845\pi$
$313$	−1.00980	−	1.74903i	−0.0570773	−	0.0988608i	−0.893152	+	0.449755i	$0.851511\pi$
$314$	−4.41921			−0.249391
$315$	−0.180922	+	1.02606i	−0.0101938	+	0.0578120i
$316$	9.17024			0.515867
$317$	−2.92468	−	5.06569i	−0.164266	−	0.284518i	0.772128	−	0.635467i	$-0.219192\pi$
$317$	−2.92468	−	5.06569i	−0.164266	−	0.284518i	−0.936394	+	0.350949i	$0.885859\pi$
$318$	2.59714	−	7.13559i	0.145641	−	0.400144i
$319$	3.17752	−	5.50362i	0.177907	−	0.308144i
$320$	1.71301	−	2.96702i	0.0957602	−	0.165862i
$321$	11.0544	+	13.1741i	0.616995	+	0.735306i
$322$	−0.130415	−	0.225885i	−0.00726774	−	0.0125881i
$323$	18.4611			1.02720
$324$	−12.9572	+	10.8724i	−0.719846	+	0.604023i
$325$	10.5449			0.584925
$326$	2.22075	+	3.84645i	0.122996	+	0.213035i
$327$	15.3821	+	18.3316i	0.850631	+	1.01374i
$328$	−6.27379	+	10.8665i	−0.346412	+	0.600003i
$329$	1.02822	−	1.78093i	0.0566875	−	0.0981857i
$330$	−0.134285	+	0.368946i	−0.00739216	+	0.0203098i
$331$	−5.86097	−	10.1515i	−0.322148	−	0.557976i	0.658783	−	0.752333i	$-0.271071\pi$
$331$	−5.86097	−	10.1515i	−0.322148	−	0.557976i	−0.980931	+	0.194356i	$0.937738\pi$
$332$	8.63816			0.474080
$333$	1.64749	−	9.34337i	0.0902818	−	0.512014i
$334$	7.19759			0.393834
$335$	−1.61974	−	2.80547i	−0.0884957	−	0.153279i
$336$	−2.98680	+	0.526653i	−0.162943	+	0.0287313i
$337$	−6.29813	+	10.9087i	−0.343081	+	0.594234i	−0.985003	−	0.172536i	$-0.944804\pi$
$337$	−6.29813	+	10.9087i	−0.343081	+	0.594234i	0.641922	+	0.766770i	$0.278137\pi$
$338$	1.33450	−	2.31143i	0.0725874	−	0.125725i
$339$	−3.00000	+	0.528981i	−0.162938	+	0.0287303i
$340$	−2.70574	−	4.68647i	−0.146739	−	0.254160i
$341$	2.16250			0.117106
$342$	−4.09714	+	1.49124i	−0.221548	+	0.0806369i
$343$	−7.29860			−0.394087
$344$	−8.28493	−	14.3499i	−0.446693	−	0.773696i
$345$	0.545759	−	1.49946i	0.0293827	−	0.0807283i
$346$	3.90760	−	6.76817i	0.210074	−	0.363859i
$347$	11.9226	−	20.6506i	0.640040	−	1.10858i	−0.345384	−	0.938462i	$-0.612251\pi$
$347$	11.9226	−	20.6506i	0.640040	−	1.10858i	0.985423	−	0.170120i	$-0.0544154\pi$
$348$	−13.2973	−	15.8471i	−0.712808	−	0.849491i
$349$	4.24123	+	7.34603i	0.227028	+	0.393224i	0.956926	−	0.290332i	$-0.0937658\pi$
$349$	4.24123	+	7.34603i	0.227028	+	0.393224i	−0.729898	+	0.683556i	$0.760433\pi$
$350$	−0.845237			−0.0451798
$351$			11.9792i			0.639405i
$352$	−3.83750			−0.204539
$353$	−3.72328	−	6.44891i	−0.198170	−	0.343241i	0.749765	−	0.661704i	$-0.230167\pi$
$353$	−3.72328	−	6.44891i	−0.198170	−	0.343241i	−0.947935	+	0.318463i	$0.896833\pi$
$354$	−1.25062	−	1.49043i	−0.0664697	−	0.0792155i
$355$	−3.25877	+	5.64436i	−0.172958	+	0.299571i
$356$	−15.9290	+	27.5899i	−0.844236	+	1.46226i
$357$	−1.39053	+	3.82045i	−0.0735946	+	0.202200i
$358$	1.86184	+	3.22481i	0.0984015	+	0.170436i
$359$	−22.9290			−1.21015			−0.605074	−	0.796170i	$-0.706856\pi$
$359$	−22.9290			−1.21015			−0.605074	+	0.796170i	$0.706856\pi$
$360$	2.02094	+	1.69577i	0.106513	+	0.0893751i
$361$	−1.48751			−0.0782901
$362$	0.721934	+	1.25043i	0.0379440	+	0.0657209i
$363$	−1.70574	+	0.300767i	−0.0895280	+	0.0157862i
$364$	−1.15270	+	1.99654i	−0.0604181	+	0.104647i
$365$	2.44609	−	4.23675i	0.128034	−	0.221762i
$366$	5.05438	−	0.891223i	0.264197	−	0.0465850i
$367$	−7.65317	−	13.2557i	−0.399492	−	0.691941i	0.594171	−	0.804339i	$-0.297480\pi$
$367$	−7.65317	−	13.2557i	−0.399492	−	0.691941i	−0.993663	+	0.112398i	$0.964147\pi$
$368$	4.64496			0.242135
$369$	21.4029	+	17.9591i	1.11419	+	0.934915i
$370$	−0.716881			−0.0372689
$371$	−3.35844	−	5.81699i	−0.174362	−	0.302003i
$372$	2.40760	−	6.61484i	0.124828	−	0.342963i
$373$	13.6951	−	23.7205i	0.709103	−	1.22820i	−0.256087	−	0.966654i	$-0.582433\pi$
$373$	13.6951	−	23.7205i	0.709103	−	1.22820i	0.965190	−	0.261549i	$-0.0842334\pi$
$374$	−0.766044	+	1.32683i	−0.0396112	+	0.0686086i
$375$	−6.95723	−	8.29131i	−0.359270	−	0.428161i
$376$	−2.60354	−	4.50946i	−0.134267	−	0.232558i
$377$	−14.6509			−0.754562
$378$		−	0.960210i		−	0.0493879i
$379$	11.2713			0.578966			0.289483	−	0.957183i	$-0.406517\pi$
$379$	11.2713			0.578966			0.289483	+	0.957183i	$0.406517\pi$
$380$	−2.56670	−	4.44566i	−0.131669	−	0.228058i
$381$	7.68392	+	9.15733i	0.393659	+	0.469144i
$382$	−0.417404	+	0.722965i	−0.0213562	+	0.0369901i
$383$	−16.6814	+	28.8930i	−0.852379	+	1.47636i	0.0266761	+	0.999644i	$0.491508\pi$
$383$	−16.6814	+	28.8930i	−0.852379	+	1.47636i	−0.879055	+	0.476720i	$0.841826\pi$
$384$	−5.62654	+	15.4588i	−0.287128	+	0.788879i
$385$	0.173648	+	0.300767i	0.00884993	+	0.0153285i
$386$	−0.157451			−0.00801406
$387$	−34.6707	+	12.6191i	−1.76241	+	0.641465i
$388$	−23.7665			−1.20656
$389$	−6.12449	−	10.6079i	−0.310524	−	0.537843i	0.667952	−	0.744204i	$-0.267171\pi$
$389$	−6.12449	−	10.6079i	−0.310524	−	0.537843i	−0.978476	+	0.206361i	$0.933838\pi$
$390$	0.891407	−	0.157179i	0.0451381	−	0.00795907i
$391$	3.11334	−	5.39246i	0.157448	−	0.272709i
$392$	−4.52481	+	7.83721i	−0.228538	+	0.395839i
$393$	−17.6382	+	3.11008i	−0.889727	+	0.156883i
$394$	3.40760	+	5.90214i	0.171673	+	0.297346i
$395$	−3.18479			−0.160244
$396$	−0.979055	+	5.55250i	−0.0491994	+	0.279024i
$397$	−11.4287			−0.573591			−0.286795	−	0.957992i	$-0.592590\pi$
$397$	−11.4287			−0.573591			−0.286795	+	0.957992i	$0.592590\pi$
$398$	−0.630415	−	1.09191i	−0.0315998	−	0.0547325i
$399$	−1.31908	+	3.62414i	−0.0660365	+	0.181434i
$400$	7.52616	−	13.0357i	0.376308	−	0.651784i
$401$	−10.8473	+	18.7881i	−0.541688	+	0.938231i	0.457119	+	0.889405i	$0.348881\pi$
$401$	−10.8473	+	18.7881i	−0.541688	+	0.938231i	−0.998807	+	0.0488259i	$0.984452\pi$
$402$	1.91905	+	2.28704i	0.0957137	+	0.114067i
$403$	−2.49273	−	4.31753i	−0.124172	−	0.215071i
$404$	−32.1215			−1.59811
$405$	4.50000	−	3.77595i	0.223607	−	0.187628i
$406$	1.17436			0.0582827
$407$	−1.58125	−	2.73881i	−0.0783797	−	0.135758i
$408$	6.61721	+	7.88609i	0.327601	+	0.390419i
$409$	14.2947	−	24.7592i	0.706829	−	1.22426i	−0.259199	−	0.965824i	$-0.583458\pi$
$409$	14.2947	−	24.7592i	0.706829	−	1.22426i	0.966027	−	0.258440i	$-0.0832083\pi$
$410$	1.05556	−	1.82828i	0.0521304	−	0.0902925i
$411$	8.40302	−	23.0871i	0.414490	−	1.13880i
$412$	2.68732	+	4.65457i	0.132395	+	0.229314i
$413$	−1.72100			−0.0846849
$414$	−0.255367	+	1.44826i	−0.0125506	+	0.0711780i
$415$	−3.00000			−0.147264
$416$	4.42350	+	7.66172i	0.216880	+	0.375647i
$417$	−0.172304	+	0.0303818i	−0.00843776	+	0.00148781i
$418$	−0.726682	+	1.25865i	−0.0355432	+	0.0615626i
$419$	4.30541	−	7.45718i	0.210333	−	0.364307i	−0.741486	−	0.670969i	$-0.765879\pi$
$419$	4.30541	−	7.45718i	0.210333	−	0.364307i	0.951819	+	0.306661i	$0.0992119\pi$
$420$	1.11334	−	0.196312i	0.0543255	−	0.00957905i
$421$	17.2160	+	29.8190i	0.839057	+	1.45329i	0.890684	+	0.454622i	$0.150226\pi$
$421$	17.2160	+	29.8190i	0.839057	+	1.45329i	−0.0516276	+	0.998666i	$0.516441\pi$
$422$	7.52704			0.366410
$423$	−10.8953	+	3.96556i	−0.529747	+	0.192812i
$424$	−17.0077			−0.825969
$425$	−10.0890	−	17.4746i	−0.489388	−	0.847645i
$426$	2.05438	−	5.64436i	0.0995349	−	0.273470i
$427$	2.26991	−	3.93161i	0.109849	−	0.190264i
$428$	9.33022	−	16.1604i	0.450993	−	0.781143i
$429$	2.56670	+	3.05888i	0.123922	+	0.147684i
$430$	1.39393	+	2.41436i	0.0672214	+	0.116431i
$431$	14.2463			0.686219			0.343110	−	0.939295i	$-0.388520\pi$
$431$	14.2463			0.686219			0.343110	+	0.939295i	$0.388520\pi$
$432$	14.8089	+	8.54990i	0.712492	+	0.411357i
$433$	−24.6023			−1.18231			−0.591154	−	0.806558i	$-0.701328\pi$
$433$	−24.6023			−1.18231			−0.591154	+	0.806558i	$0.701328\pi$
$434$	0.199807	+	0.346076i	0.00959106	+	0.0166122i
$435$	4.61809	+	5.50362i	0.221420	+	0.263879i
$436$	12.9829	−	22.4871i	0.621769	−	1.07694i
$437$	2.95336	−	5.11538i	0.141279	−	0.244702i
$438$	−1.54205	+	4.23675i	−0.0736821	+	0.202440i
$439$	−2.08647	−	3.61387i	−0.0995816	−	0.172480i	0.811930	−	0.583755i	$-0.198417\pi$
$439$	−2.08647	−	3.61387i	−0.0995816	−	0.172480i	−0.911512	+	0.411274i	$0.865084\pi$
$440$	0.879385			0.0419230
$441$	15.4363	+	12.9526i	0.735061	+	0.616790i
$442$	3.53209			0.168004
$443$	14.6322	+	25.3438i	0.695198	+	1.20412i	0.970114	+	0.242650i	$0.0780167\pi$
$443$	14.6322	+	25.3438i	0.695198	+	1.20412i	−0.274916	+	0.961468i	$0.588650\pi$
$444$	−10.1382	+	1.78763i	−0.481136	+	0.0848372i
$445$	5.53209	−	9.58186i	0.262246	−	0.454224i
$446$	−3.32295	+	5.75552i	−0.157346	+	0.272532i
$447$	5.22210	−	0.920796i	0.246997	−	0.0435522i
$448$	1.39646	+	2.41874i	0.0659765	+	0.114275i
$449$	−15.7956			−0.745441			−0.372720	−	0.927944i	$-0.621575\pi$
$449$	−15.7956			−0.745441			−0.372720	+	0.927944i	$0.621575\pi$
$450$	3.65064	+	3.06325i	0.172093	+	0.144403i
$451$	9.31315			0.438539
$452$	1.65270	+	2.86257i	0.0777366	+	0.134644i
$453$	11.4937	−	31.5786i	0.540019	−	1.48369i
$454$	2.70780	−	4.69004i	0.127083	−	0.220115i
$455$	0.400330	−	0.693392i	0.0187677	−	0.0325067i
$456$	6.27719	+	7.48086i	0.293956	+	0.350323i
$457$	−4.74257	−	8.21438i	−0.221848	−	0.384252i	0.733521	−	0.679667i	$-0.237876\pi$
$457$	−4.74257	−	8.21438i	−0.221848	−	0.384252i	−0.955369	+	0.295414i	$0.904542\pi$
$458$	−5.35235			−0.250099
$459$	19.8516	−	11.4613i	0.926595	−	0.534970i
$460$	−1.73143			−0.0807283
$461$	14.4722	+	25.0667i	0.674040	+	1.16747i	0.976749	+	0.214388i	$0.0687757\pi$
$461$	14.4722	+	25.0667i	0.674040	+	1.16747i	−0.302709	+	0.953083i	$0.597891\pi$
$462$	−0.205737	−	0.245188i	−0.00957175	−	0.0114072i
$463$	11.4402	−	19.8149i	0.531669	−	0.920878i	−0.467647	−	0.883915i	$-0.654898\pi$
$463$	11.4402	−	19.8149i	0.531669	−	0.920878i	0.999317	−	0.0369631i	$-0.0117684\pi$
$464$	−10.4568	+	18.1117i	−0.485443	+	0.840812i
$465$	−0.836152	+	2.29731i	−0.0387756	+	0.106535i
$466$	−0.745100	−	1.29055i	−0.0345161	−	0.0597836i
$467$	10.2412			0.473908			0.236954	−	0.971521i	$-0.423851\pi$
$467$	10.2412			0.473908			0.236954	+	0.971521i	$0.423851\pi$
$468$	12.2144	−	4.44566i	0.564609	−	0.205501i
$469$	2.64084			0.121943
$470$	0.438044	+	0.758714i	0.0202055	+	0.0349969i
$471$	21.7049	−	3.82715i	1.00011	−	0.176346i
$472$	−2.17886	+	3.77390i	−0.100290	+	0.173708i
$473$	−6.14930	+	10.6509i	−0.282745	+	0.489729i
$474$	2.89053	−	0.509678i	0.132766	−	0.0234103i
$475$	−9.57057	−	16.5767i	−0.439128	−	0.760592i
$476$	4.41147			0.202200
$477$	−6.57620	+	37.2955i	−0.301103	+	1.70764i
$478$	−6.99226			−0.319818
$479$	−9.66550	−	16.7411i	−0.441628	−	0.764922i	0.556183	−	0.831060i	$-0.312265\pi$
$479$	−9.66550	−	16.7411i	−0.441628	−	0.764922i	−0.997810	+	0.0661383i	$0.978932\pi$
$480$	1.48380	−	4.07672i	0.0677260	−	0.186076i
$481$	−3.64543	+	6.31407i	−0.166217	+	0.287897i
$482$	1.29292	−	2.23940i	0.0588908	−	0.102002i
$483$	0.836152	+	0.996487i	0.0380462	+	0.0453417i
$484$	0.939693	+	1.62760i	0.0427133	+	0.0739816i
$485$	8.25402			0.374796
$486$	−3.47993	+	4.14722i	−0.157853	+	0.188122i
$487$	27.2104			1.23302			0.616510	−	0.787347i	$-0.288546\pi$
$487$	27.2104			1.23302			0.616510	+	0.787347i	$0.288546\pi$
$488$	−5.74763	−	9.95518i	−0.260183	−	0.450650i
$489$	−14.2383	−	16.9685i	−0.643878	−	0.767344i
$490$	0.761297	−	1.31860i	0.0343919	−	0.0595685i
$491$	18.0189	−	31.2096i	0.813181	−	1.40847i	−0.0974459	−	0.995241i	$-0.531067\pi$
$491$	18.0189	−	31.2096i	0.813181	−	1.40847i	0.910627	−	0.413230i	$-0.135599\pi$
$492$	10.3687	−	28.4878i	0.467457	−	1.28433i
$493$	14.0175	+	24.2791i	0.631318	+	1.09348i
$494$	3.35059			0.150750
$495$	0.340022	−	1.92836i	0.0152829	−	0.0866735i
$496$	−7.11650			−0.319540
$497$	−2.65657	−	4.60132i	−0.119164	−	0.206397i
$498$	2.72281	−	0.480105i	0.122012	−	0.0215140i
$499$	3.94609	−	6.83483i	0.176651	−	0.305969i	−0.764080	−	0.645121i	$-0.776807\pi$
$499$	3.94609	−	6.83483i	0.176651	−	0.305969i	0.940731	+	0.339152i	$0.110140\pi$
$500$	−5.87211	+	10.1708i	−0.262609	+	0.454852i
$501$	−35.3508	+	6.23329i	−1.57936	+	0.278483i
$502$	−2.17412	−	3.76568i	−0.0970355	−	0.168070i
$503$	−37.2550			−1.66112			−0.830558	−	0.556932i	$-0.811978\pi$
$503$	−37.2550			−1.66112			−0.830558	+	0.556932i	$0.811978\pi$
$504$	−2.02094	+	0.735564i	−0.0900200	+	0.0327646i
$505$	11.1557			0.496422
$506$	0.245100	+	0.424525i	0.0108960	+	0.0188725i
$507$	−4.55262	+	12.5082i	−0.202189	+	0.555510i
$508$	6.48545	−	11.2331i	0.287745	−	0.498390i
$509$	−2.04458	+	3.54131i	−0.0906243	+	0.156966i	−0.907774	−	0.419460i	$-0.862220\pi$
$509$	−2.04458	+	3.54131i	−0.0906243	+	0.156966i	0.817150	+	0.576426i	$0.195553\pi$
$510$	−1.11334	−	1.32683i	−0.0492996	−	0.0587529i
$511$	1.99407	+	3.45383i	0.0882125	+	0.152788i
$512$	21.4962			0.950006
$513$	18.8316	−	10.8724i	0.831434	−	0.480029i
$514$	2.25166			0.0993164
$515$	−0.933296	−	1.61652i	−0.0411259	−	0.0712322i
$516$	25.7335	+	30.6680i	1.13286	+	1.35009i
$517$	−1.93242	+	3.34705i	−0.0849877	+	0.147203i
$518$	0.292204	−	0.506111i	0.0128387	−	0.0222373i
$519$	−13.3307	+	36.6258i	−0.585152	+	1.60769i
$520$	−1.01367	−	1.75573i	−0.0444524	−	0.0769938i
$521$	7.29322			0.319522			0.159761	−	0.987156i	$-0.448928\pi$
$521$	7.29322			0.319522			0.159761	+	0.987156i	$0.448928\pi$
$522$	−5.07217	−	4.25605i	−0.222003	−	0.186282i
$523$	−14.3105			−0.625753			−0.312876	−	0.949794i	$-0.601293\pi$
$523$	−14.3105			−0.625753			−0.312876	+	0.949794i	$0.601293\pi$
$524$	9.71688	+	16.8301i	0.424484	+	0.735228i
$525$	4.15136	−	0.731997i	0.181180	−	0.0319470i
$526$	−0.364370	+	0.631108i	−0.0158873	+	0.0275176i
$527$	−4.76991	+	8.26173i	−0.207781	+	0.359887i
$528$	5.61334	−	0.989783i	0.244289	−	0.0430748i
$529$	10.5039	+	18.1932i	0.456690	+	0.791010i
$530$	2.86154			0.124297
$531$	7.43313	+	6.23714i	0.322571	+	0.270669i
$532$	4.18479			0.181434
$533$	−10.7353	−	18.5941i	−0.464997	−	0.805399i
$534$	−3.48751	+	9.58186i	−0.150919	+	0.414648i
$535$	−3.24035	+	5.61245i	−0.140093	+	0.242648i
$536$	3.34343	−	5.79098i	0.144414	−	0.250132i
$537$	−11.9372	−	14.2262i	−0.515127	−	0.613904i
$538$	−5.07903	−	8.79714i	−0.218973	−	0.379272i
$539$	6.71688			0.289317
$540$	−5.52007	−	3.18701i	−0.237546	−	0.137147i
$541$	−36.1411			−1.55383			−0.776915	−	0.629606i	$-0.783216\pi$
$541$	−36.1411			−1.55383			−0.776915	+	0.629606i	$0.783216\pi$
$542$	3.77244	+	6.53406i	0.162040	+	0.280662i
$543$	−4.62866	−	5.51622i	−0.198635	−	0.236724i
$544$	8.46451	−	14.6610i	0.362913	−	0.628583i
$545$	−4.50892	+	7.80968i	−0.193141	+	0.334530i
$546$	−0.252374	+	0.693392i	−0.0108006	+	0.0296744i
$547$	9.39352	+	16.2701i	0.401638	+	0.695657i	0.993924	−	0.110071i	$-0.0351077\pi$
$547$	9.39352	+	16.2701i	0.401638	+	0.695657i	−0.592286	+	0.805728i	$0.701774\pi$
$548$	−26.6587			−1.13880
$549$	−24.0526	+	8.75444i	−1.02654	+	0.373630i
$550$	1.58853			0.0677350
$551$	13.2973	+	23.0315i	0.566482	+	0.981176i
$552$	3.24376	−	0.571962i	0.138063	−	0.0243443i
$553$	1.29813	−	2.24843i	0.0552022	−	0.0956131i
$554$	0.773785	−	1.34024i	0.0328750	−	0.0569411i
$555$	3.52094	−	0.620838i	0.149456	−	0.0263531i
$556$	0.0949225	+	0.164411i	0.00402561	+	0.00697256i
$557$	−3.99319			−0.169197			−0.0845985	−	0.996415i	$-0.526961\pi$
$557$	−3.99319			−0.169197			−0.0845985	+	0.996415i	$0.526961\pi$
$558$	0.391245	−	2.21886i	0.0165627	−	0.0939318i
$559$	28.3533			1.19922
$560$	−0.571452	−	0.989783i	−0.0241482	−	0.0418260i
$561$	2.61334	−	7.18009i	0.110335	−	0.303144i
$562$	3.55896	−	6.16431i	0.150126	−	0.260026i
$563$	11.3452	−	19.6505i	0.478145	−	0.828171i	−0.521541	−	0.853226i	$-0.674643\pi$
$563$	11.3452	−	19.6505i	0.478145	−	0.828171i	0.999686	+	0.0250550i	$0.00797610\pi$
$564$	8.08677	+	9.63744i	0.340514	+	0.405809i
$565$	−0.573978	−	0.994159i	−0.0241474	−	0.0418246i
$566$	2.39187			0.100538
$567$	0.831566	+	4.71605i	0.0349225	+	0.198055i
$568$	−13.4534			−0.564491
$569$	−12.6604	−	21.9285i	−0.530753	−	0.919292i	−0.999356	−	0.0358828i	$-0.988576\pi$
$569$	−12.6604	−	21.9285i	−0.530753	−	0.919292i	0.468603	−	0.883409i	$-0.344758\pi$
$570$	−1.05613	−	1.25865i	−0.0442365	−	0.0527190i
$571$	−16.6570	+	28.8508i	−0.697075	+	1.20737i	0.272401	+	0.962184i	$0.412182\pi$
$571$	−16.6570	+	28.8508i	−0.697075	+	1.20737i	−0.969476	+	0.245186i	$0.921151\pi$
$572$	2.16637	−	3.75227i	0.0905807	−	0.156890i
$573$	1.42396	−	3.91231i	0.0594869	−	0.163439i
$574$	0.860500	+	1.49043i	0.0359166	+	0.0622093i
$575$	−6.45605			−0.269236
$576$	2.73442	−	15.5077i	0.113934	−	0.646153i
$577$	−1.18479			−0.0493236			−0.0246618	−	0.999696i	$-0.507851\pi$
$577$	−1.18479			−0.0493236			−0.0246618	+	0.999696i	$0.507851\pi$
$578$	−0.427366	−	0.740220i	−0.0177761	−	0.0307891i
$579$	0.773318	−	0.136357i	0.0321380	−	0.00566680i
$580$	3.89780	−	6.75119i	0.161847	−	0.280328i
$581$	1.22281	−	2.11797i	0.0507308	−	0.0878682i
$582$	−7.49138	+	1.32093i	−0.310528	+	0.0547544i
$583$	6.31180	+	10.9324i	0.261408	+	0.452772i
$584$	10.0983			0.417872
$585$	−4.24200	+	1.54396i	−0.175385	+	0.0638350i
$586$	−4.79561			−0.198105
$587$	−15.9021	−	27.5433i	−0.656352	−	1.13683i	−0.981553	−	0.191190i	$-0.938765\pi$
$587$	−15.9021	−	27.5433i	−0.656352	−	1.13683i	0.325202	−	0.945645i	$-0.394568\pi$
$588$	7.47818	−	20.5461i	0.308395	−	0.847308i
$589$	−4.52481	+	7.83721i	−0.186442	+	0.322927i
$590$	0.366592	−	0.634956i	0.0150924	−	0.0261407i
$591$	−21.8478	−	26.0372i	−0.898697	−	1.07103i
$592$	5.20368	+	9.01303i	0.213870	+	0.370433i
$593$	26.3381			1.08158			0.540789	−	0.841159i	$-0.318126\pi$
$593$	26.3381			1.08158			0.540789	+	0.841159i	$0.318126\pi$
$594$			1.80460i			0.0740438i
$595$	−1.53209			−0.0628095
$596$	−2.87686	−	4.98287i	−0.117841	−	0.204106i
$597$	4.04189	+	4.81694i	0.165424	+	0.197144i
$598$	0.565055	−	0.978704i	0.0231068	−	0.0400222i
$599$	−7.63223	+	13.2194i	−0.311844	+	0.540130i	−0.978762	−	0.205002i	$-0.934280\pi$
$599$	−7.63223	+	13.2194i	−0.311844	+	0.540130i	0.666917	+	0.745132i	$0.267613\pi$
$600$	3.65064	−	10.0301i	0.149037	−	0.409476i
$601$	−4.25356	−	7.36737i	−0.173506	−	0.300521i	0.766137	−	0.642677i	$-0.222176\pi$
$601$	−4.25356	−	7.36737i	−0.173506	−	0.300521i	−0.939643	+	0.342156i	$0.888843\pi$
$602$	−2.27269			−0.0926279
$603$	−11.4060	−	9.57078i	−0.464489	−	0.389752i
$604$	−36.4638			−1.48369
$605$	−0.326352	−	0.565258i	−0.0132681	−	0.0229810i
$606$	−10.1250	+	1.78530i	−0.411298	+	0.0725229i
$607$	−6.26011	+	10.8428i	−0.254090	+	0.440097i	−0.964648	−	0.263542i	$-0.915109\pi$
$607$	−6.26011	+	10.8428i	−0.254090	+	0.440097i	0.710558	+	0.703639i	$0.248443\pi$
$608$	8.02956	−	13.9076i	0.325642	−	0.564028i
$609$	−5.76786	+	1.01703i	−0.233725	+	0.0412121i
$610$	0.967034	+	1.67495i	0.0391541	+	0.0678168i
$611$	8.91002			0.360461
$612$	−19.0535	−	15.9878i	−0.770192	−	0.646268i
$613$	−8.52259			−0.344224			−0.172112	−	0.985077i	$-0.555059\pi$
$613$	−8.52259			−0.344224			−0.172112	+	0.985077i	$0.555059\pi$
$614$	0.104418	+	0.180857i	0.00421397	+	0.00729880i
$615$	−3.60101	+	9.89371i	−0.145207	+	0.398953i
$616$	−0.358441	+	0.620838i	−0.0144420	+	0.0250143i
$617$	10.2442	−	17.7435i	0.412417	−	0.714327i	−0.582737	−	0.812661i	$-0.698018\pi$
$617$	10.2442	−	17.7435i	0.412417	−	0.714327i	0.995153	+	0.0983341i	$0.0313514\pi$
$618$	1.10576	+	1.31780i	0.0444803	+	0.0530095i
$619$	13.4008	+	23.2109i	0.538623	+	0.932923i	0.998978	+	0.0451883i	$0.0143888\pi$
$619$	13.4008	+	23.2109i	0.538623	+	0.932923i	−0.460355	+	0.887735i	$0.652278\pi$
$620$	2.65270			0.106535
$621$		−	7.33423i		−	0.294313i
$622$	0.674059			0.0270273
$623$	4.50980	+	7.81120i	0.180681	+	0.312949i
$624$	−8.44666	−	10.0663i	−0.338137	−	0.402976i
$625$	−9.39558	+	16.2736i	−0.375823	+	0.650945i
$626$	−0.350700	+	0.607430i	−0.0140168	+	0.0242778i
$627$	2.47906	−	6.81115i	0.0990039	−	0.272011i
$628$	−11.9572	−	20.7105i	−0.477146	−	0.826440i
$629$	13.9513			0.556275
$630$	0.340022	−	0.123758i	0.0135468	−	0.00493064i
$631$	18.9736			0.755327			0.377663	−	0.925943i	$-0.376728\pi$
$631$	18.9736			0.755327			0.377663	+	0.925943i	$0.376728\pi$
$632$	−3.28699	−	5.69323i	−0.130749	−	0.226465i
$633$	−36.9688	+	6.51860i	−1.46938	+	0.259091i
$634$	−1.01573	+	1.75930i	−0.0403398	+	0.0698706i
$635$	−2.25237	+	3.90123i	−0.0893827	+	0.154815i
$636$	40.4680	−	7.13559i	1.60466	−	0.282945i
$637$	−7.74257	−	13.4105i	−0.306772	−	0.531345i
$638$	−2.20708			−0.0873792
$639$	−5.20187	+	29.5013i	−0.205783	+	1.16705i
$640$	−6.19934			−0.245050
$641$	14.8157	+	25.6615i	0.585184	+	1.01357i	0.994852	+	0.101334i	$0.0323110\pi$
$641$	14.8157	+	25.6615i	0.585184	+	1.01357i	−0.409669	+	0.912234i	$0.634356\pi$
$642$	2.04277	−	5.61245i	0.0806216	−	0.221506i
$643$	−21.7886	+	37.7390i	−0.859260	+	1.48828i	0.0133759	+	0.999911i	$0.495742\pi$
$643$	−21.7886	+	37.7390i	−0.859260	+	1.48828i	−0.872636	+	0.488371i	$0.837591\pi$
$644$	0.705737	−	1.22237i	0.0278099	−	0.0481682i
$645$	−8.93717	−	10.6509i	−0.351901	−	0.419379i
$646$	−3.20574	−	5.55250i	−0.126128	−	0.218460i
$647$	−21.0583			−0.827887			−0.413944	−	0.910302i	$-0.635849\pi$
$647$	−21.0583			−0.827887			−0.413944	+	0.910302i	$0.635849\pi$
$648$	11.3944	+	4.14722i	0.447614	+	0.162918i
$649$	3.23442			0.126962
$650$	−1.83110	−	3.17156i	−0.0718216	−	0.124399i
$651$	−1.28106	−	1.52671i	−0.0502087	−	0.0598364i
$652$	−12.0175	+	20.8150i	−0.470643	+	0.815178i
$653$	−0.669778	+	1.16009i	−0.0262104	+	0.0453978i	−0.878833	−	0.477129i	$-0.841677\pi$
$653$	−0.669778	+	1.16009i	−0.0262104	+	0.0453978i	0.852623	+	0.522527i	$0.175011\pi$
$654$	2.84249	−	7.80968i	0.111150	−	0.305383i
$655$	−3.37464	−	5.84504i	−0.131858	−	0.228385i
$656$	−30.6483			−1.19661
$657$	3.90461	−	22.1441i	0.152333	−	0.863925i
$658$	−0.714193			−0.0278421
$659$	9.47296	+	16.4077i	0.369014	+	0.639151i	0.989412	−	0.145136i	$-0.0463620\pi$
$659$	9.47296	+	16.4077i	0.369014	+	0.639151i	−0.620397	+	0.784288i	$0.713029\pi$
$660$	−2.09240	+	0.368946i	−0.0814464	+	0.0143612i
$661$	−13.8059	+	23.9125i	−0.536986	+	0.930087i	0.462078	+	0.886839i	$0.347104\pi$
$661$	−13.8059	+	23.9125i	−0.536986	+	0.930087i	−0.999064	+	0.0432483i	$0.986229\pi$
$662$	−2.03549	+	3.52558i	−0.0791117	+	0.137025i
$663$	−17.3478	+	3.05888i	−0.673731	+	0.118797i
$664$	−3.09627	−	5.36289i	−0.120158	−	0.208121i
$665$	−1.45336			−0.0563590
$666$	−3.09627	+	1.12695i	−0.119978	+	0.0436684i
$667$	8.96997			0.347319
$668$	19.4748	+	33.7313i	0.753502	+	1.30510i
$669$	11.3362	−	31.1458i	0.438281	−	1.20417i
$670$	−0.562529	+	0.974329i	−0.0217324	+	0.0376416i
$671$	−4.26604	+	7.38901i	−0.164689	+	0.285249i
$672$	2.27332	+	2.70924i	0.0876952	+	0.104511i
$673$	−10.3712	−	17.9635i	−0.399782	−	0.692442i	0.593917	−	0.804526i	$-0.297581\pi$
$673$	−10.3712	−	17.9635i	−0.399782	−	0.692442i	−0.993699	+	0.112084i	$0.964247\pi$
$674$	4.37464			0.168505
$675$	−20.5829	−	11.8835i	−0.792236	−	0.457398i
$676$	14.4433			0.555510
$677$	13.8032	+	23.9078i	0.530500	+	0.918852i	0.999367	+	0.0355834i	$0.0113290\pi$
$677$	13.8032	+	23.9078i	0.530500	+	0.918852i	−0.468867	+	0.883269i	$0.655338\pi$
$678$	0.680045	+	0.810446i	0.0261170	+	0.0311250i
$679$	−3.36437	+	5.82726i	−0.129113	+	0.223630i
$680$	−1.93969	+	3.35965i	−0.0743838	+	0.128837i
$681$	−9.23758	+	25.3800i	−0.353985	+	0.972565i
$682$	−0.375515	−	0.650411i	−0.0143792	−	0.0249055i
$683$	31.4843			1.20471			0.602357	−	0.798227i	$-0.294228\pi$
$683$	31.4843			1.20471			0.602357	+	0.798227i	$0.294228\pi$
$684$	−18.0744	−	15.1663i	−0.691094	−	0.579896i
$685$	9.25847			0.353748
$686$	1.26739	+	2.19518i	0.0483891	+	0.0838124i
$687$	26.2879	−	4.63527i	1.00295	−	0.176847i
$688$	20.2365	−	35.0506i	0.771509	−	1.33629i
$689$	14.5513	−	25.2036i	0.554360	−	0.960179i
$690$	−0.545759	+	0.0962321i	−0.0207767	+	0.00366349i
$691$	11.9440	+	20.6877i	0.454372	+	0.786996i	0.998652	−	0.0519080i	$-0.0165303\pi$
$691$	11.9440	+	20.6877i	0.454372	+	0.786996i	−0.544280	+	0.838904i	$0.683197\pi$
$692$	42.2918			1.60769
$693$	1.22281	+	1.02606i	0.0464508	+	0.0389768i
$694$	−8.28136			−0.314356
$695$	−0.0329662	−	0.0570992i	−0.00125048	−	0.00216590i
$696$	−5.07217	+	13.9357i	−0.192260	+	0.528230i
$697$	−20.5424	+	35.5804i	−0.778097	+	1.34770i
$698$	1.47296	−	2.55125i	0.0557525	−	0.0965662i
$699$	4.77719	+	5.69323i	0.180690	+	0.215338i
$700$	−2.28699	−	3.96118i	−0.0864401	−	0.149719i
$701$	7.03684			0.265778			0.132889	−	0.991131i	$-0.457575\pi$
$701$	7.03684			0.265778			0.132889	+	0.991131i	$0.457575\pi$
$702$	3.60297	−	2.08017i	0.135985	−	0.0785111i
$703$	13.2344			0.499146
$704$	−2.62449	−	4.54574i	−0.0989140	−	0.171324i
$705$	−2.80851	−	3.34705i	−0.105774	−	0.126057i
$706$	−1.29308	+	2.23968i	−0.0486657	+	0.0842915i
$707$	−4.54710	+	7.87581i	−0.171011	+	0.296200i
$708$	3.60101	−	9.89371i	0.135334	−	0.371828i
$709$	6.45037	+	11.1724i	0.242249	+	0.419587i	0.961354	−	0.275314i	$-0.0887817\pi$
$709$	6.45037	+	11.1724i	0.242249	+	0.419587i	−0.719106	+	0.694901i	$0.755448\pi$
$710$	2.26352			0.0849483
$711$	−13.7554	+	5.00654i	−0.515867	+	0.187760i
$712$	22.8384			0.855906
$713$	1.52616	+	2.64339i	0.0571551	+	0.0989956i
$714$	1.39053	−	0.245188i	0.0520393	−	0.00917593i
$715$	−0.752374	+	1.30315i	−0.0281372	+	0.0487350i
$716$	−10.0753	+	17.4510i	−0.376532	+	0.652173i
$717$	34.3423	−	6.05547i	1.28254	−	0.226146i
$718$	3.98158	+	6.89630i	0.148591	+	0.257368i
$719$	17.2671			0.643956			0.321978	−	0.946747i	$-0.395652\pi$
$719$	17.2671			0.643956			0.321978	+	0.946747i	$0.395652\pi$
$720$	−1.11897	+	6.34597i	−0.0417014	+	0.236500i
$721$	1.52166			0.0566696
$722$	0.258304	+	0.447395i	0.00961307	+	0.0166503i
$723$	−4.41076	+	12.1185i	−0.164038	+	0.450690i
$724$	−3.90673	+	6.76665i	−0.145192	+	0.251481i
$725$	14.5339	−	25.1735i	0.539775	−	0.934919i
$726$	0.386659	+	0.460802i	0.0143503	+	0.0171020i
$727$	−20.3033	−	35.1664i	−0.753009	−	1.30425i	−0.946358	−	0.323121i	$-0.895268\pi$
$727$	−20.3033	−	35.1664i	−0.753009	−	1.30425i	0.193348	−	0.981130i	$-0.438065\pi$
$728$	1.65270			0.0612533
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−1.69904			−0.0628841
$731$	−27.1275	−	46.9862i	−1.00335	−	1.73785i
$732$	17.8525	+	21.2758i	0.659848	+	0.786376i
$733$	7.87464	−	13.6393i	0.290856	−	0.503778i	−0.683156	−	0.730272i	$-0.739393\pi$
$733$	7.87464	−	13.6393i	0.290856	−	0.503778i	0.974012	+	0.226494i	$0.0727265\pi$
$734$	−2.65792	+	4.60365i	−0.0981056	+	0.169924i
$735$	−2.59714	+	7.13559i	−0.0957971	+	0.263200i
$736$	−2.70826	−	4.69085i	−0.0998279	−	0.172907i
$737$	−4.96316			−0.182820
$738$	1.68495	−	9.55585i	0.0620240	−	0.351756i
$739$	2.27538			0.0837011			0.0418506	−	0.999124i	$-0.486675\pi$
$739$	2.27538			0.0837011			0.0418506	+	0.999124i	$0.486675\pi$
$740$	−1.93969	−	3.35965i	−0.0713045	−	0.123503i
$741$	−16.4564	+	2.90170i	−0.604539	+	0.106597i
$742$	−1.16637	+	2.02022i	−0.0428189	+	0.0741646i
$743$	17.5868	−	30.4612i	0.645196	−	1.11751i	−0.339060	−	0.940765i	$-0.610109\pi$
$743$	17.5868	−	30.4612i	0.645196	−	1.11751i	0.984256	−	0.176748i	$-0.0565576\pi$
$744$	−4.96972	+	0.876296i	−0.182199	+	0.0321266i
$745$	0.999123	+	1.73053i	0.0366050	+	0.0634018i
$746$	−9.51249			−0.348277
$747$	−12.9572	+	4.71605i	−0.474080	+	0.172551i
$748$	−8.29086			−0.303144
$749$	−2.64156	−	4.57531i	−0.0965205	−	0.167178i
$750$	−1.28564	+	3.53228i	−0.0469451	+	0.128981i
$751$	16.7533	−	29.0176i	0.611337	−	1.05887i	−0.379678	−	0.925118i	$-0.623965\pi$
$751$	16.7533	−	29.0176i	0.611337	−	1.05887i	0.991015	−	0.133748i	$-0.0427013\pi$
$752$	6.35932	−	11.0147i	0.231900	−	0.401663i
$753$	13.9393	+	16.6122i	0.507976	+	0.605382i
$754$	2.54411	+	4.40653i	0.0926510	+	0.160476i
$755$	12.6637			0.460881
$756$	4.50000	−	2.59808i	0.163663	−	0.0944911i
$757$	45.4570			1.65216			0.826081	−	0.563551i	$-0.190565\pi$
$757$	45.4570			1.65216			0.826081	+	0.563551i	$0.190565\pi$
$758$	−1.95723	−	3.39003i	−0.0710899	−	0.123131i
$759$	−1.57145	−	1.87278i	−0.0570401	−	0.0679777i
$760$	−1.84002	+	3.18701i	−0.0667446	+	0.115605i
$761$	14.6370	−	25.3520i	0.530590	−	0.919009i	−0.468773	−	0.883319i	$-0.655304\pi$
$761$	14.6370	−	25.3520i	0.530590	−	0.919009i	0.999363	−	0.0356900i	$-0.0113629\pi$
$762$	1.41993	−	3.90123i	0.0514386	−	0.141327i
$763$	−3.67571	−	6.36651i	−0.133070	−	0.230483i
$764$	−4.51754			−0.163439
$765$	6.61721	+	5.55250i	0.239246	+	0.200751i
$766$	11.5868			0.418647
$767$	−3.72833	−	6.45766i	−0.134622	−	0.233173i
$768$	−12.2802	+	2.16533i	−0.443123	+	0.0781345i
$769$	22.1830	−	38.4221i	0.799941	−	1.38554i	−0.119713	−	0.992809i	$-0.538198\pi$
$769$	22.1830	−	38.4221i	0.799941	−	1.38554i	0.919654	−	0.392730i	$-0.128469\pi$
$770$	0.0603074	−	0.104455i	0.00217333	−	0.00376431i
$771$	−11.0590	+	1.94999i	−0.398279	+	0.0702273i
$772$	−0.426022	−	0.737892i	−0.0153329	−	0.0265573i
$773$	−21.6372			−0.778237			−0.389118	−	0.921188i	$-0.627220\pi$
$773$	−21.6372			−0.778237			−0.389118	+	0.921188i	$0.627220\pi$
$774$	9.81592	+	8.23654i	0.352826	+	0.296056i
$775$	9.89124			0.355304
$776$	8.51889	+	14.7551i	0.305810	+	0.529679i
$777$	−0.996845	+	2.73881i	−0.0357616	+	0.0982542i
$778$	−2.12701	+	3.68409i	−0.0762571	+	0.132081i
$779$	−19.4868	+	33.7521i	−0.698187	+	1.20930i
$780$	3.14853	+	3.75227i	0.112735	+	0.134353i
$781$	4.99273	+	8.64766i	0.178654	+	0.309437i
$782$	−2.16250			−0.0773310
$783$	28.5977	+	16.5109i	1.02200	+	0.590050i
$784$	−22.1043			−0.789440
$785$	4.15270	+	7.19269i	0.148216	+	0.256718i
$786$	3.99825	+	4.76492i	0.142613	+	0.169959i
$787$	−9.39171	+	16.2669i	−0.334778	+	0.579853i	−0.983442	−	0.181222i	$-0.941995\pi$
$787$	−9.39171	+	16.2669i	−0.334778	+	0.579853i	0.648664	+	0.761075i	$0.275328\pi$
$788$	−18.4402	+	31.9393i	−0.656903	+	1.13779i
$789$	1.24304	−	3.41523i	0.0442534	−	0.121585i
$790$	0.553033	+	0.957882i	0.0196760	+	0.0340799i
$791$	0.935822			0.0332740
$792$	3.79813	−	1.38241i	0.134961	−	0.0491217i
$793$	19.6699			0.698500
$794$	1.98457	+	3.43738i	0.0704299	+	0.121988i
$795$	−14.0544	+	2.47817i	−0.498457	+	0.0878915i
$796$	3.41147	−	5.90885i	0.120916	−	0.209434i
$797$	−13.8601	+	24.0064i	−0.490950	+	0.850350i	−0.999946	−	0.0104192i	$-0.996683\pi$
$797$	−13.8601	+	24.0064i	−0.490950	+	0.850350i	0.508996	+	0.860769i	$0.330017\pi$
$798$	1.31908	−	0.232589i	0.0466949	−	0.00823356i
$799$	−8.52481	−	14.7654i	−0.301586	−	0.522363i
$800$	−17.5526			−0.620579
$801$	8.83069	−	50.0813i	0.312017	−	1.76954i
$802$	7.53445			0.266051
$803$	−3.74763	−	6.49108i	−0.132251	−	0.229065i
$804$	−5.52569	+	15.1817i	−0.194876	+	0.535418i
$805$	−0.245100	+	0.424525i	−0.00863864	+	0.0149626i
$806$	−0.865715	+	1.49946i	−0.0304935	+	0.0528163i
$807$	32.5641	+	38.8083i	1.14631	+	1.36612i
$808$	11.5137	+	19.9423i	0.405050	+	0.701566i
$809$	−5.05737			−0.177808			−0.0889038	−	0.996040i	$-0.528336\pi$
$809$	−5.05737			−0.177808			−0.0889038	+	0.996040i	$0.528336\pi$
$810$	−1.91710	−	0.697767i	−0.0673600	−	0.0245170i
$811$	25.6709			0.901426			0.450713	−	0.892669i	$-0.351170\pi$
$811$	25.6709			0.901426			0.450713	+	0.892669i	$0.351170\pi$
$812$	3.17752	+	5.50362i	0.111509	+	0.193139i
$813$	−24.1869	−	28.8248i	−0.848272	−	1.01093i
$814$	−0.549163	+	0.951178i	−0.0192482	+	0.0333388i
$815$	4.17365	−	7.22897i	0.146197	−	0.253220i
$816$	−8.60014	+	23.6287i	−0.301065	+	0.827169i
$817$	−25.7335	−	44.5718i	−0.900303	−	1.55937i
$818$	−9.92902			−0.347160
$819$	0.639033	−	3.62414i	0.0223296	−	0.126638i
$820$	11.4243			0.398953
$821$	−1.93242	−	3.34705i	−0.0674419	−	0.116813i	0.830333	−	0.557268i	$-0.188150\pi$
$821$	−1.93242	−	3.34705i	−0.0674419	−	0.116813i	−0.897775	+	0.440455i	$0.854817\pi$
$822$	−8.40302	+	1.48168i	−0.293089	+	0.0516795i
$823$	−13.9179	+	24.1065i	−0.485146	+	0.840298i	−0.999854	−	0.0170673i	$-0.994567\pi$
$823$	−13.9179	+	24.1065i	−0.485146	+	0.840298i	0.514708	+	0.857366i	$0.327900\pi$
$824$	1.92649	−	3.33678i	0.0671124	−	0.116242i
$825$	−7.80200	+	1.37570i	−0.271631	+	0.0478959i
$826$	0.298849	+	0.517621i	0.0103983	+	0.0180103i
$827$	−1.24392			−0.0432553			−0.0216276	−	0.999766i	$-0.506885\pi$
$827$	−1.24392			−0.0432553			−0.0216276	+	0.999766i	$0.506885\pi$
$828$	−7.47818	+	2.72183i	−0.259885	+	0.0945903i
$829$	−31.5794			−1.09680			−0.548398	−	0.836217i	$-0.684762\pi$
$829$	−31.5794			−1.09680			−0.548398	+	0.836217i	$0.684762\pi$
$830$	0.520945	+	0.902302i	0.0180822	+	0.0313194i
$831$	−2.63975	+	7.25265i	−0.0915719	+	0.251592i
$832$	−6.05051	+	10.4798i	−0.209764	+	0.363321i
$833$	−14.8157	+	25.6615i	−0.513333	+	0.889118i
$834$	0.0390581	+	0.0465477i	0.00135247	+	0.00161181i
$835$	−6.76352	−	11.7148i	−0.234061	−	0.405406i
$836$	−7.86484			−0.272011
$837$			11.2367i			0.388397i
$838$	−2.99050			−0.103305
$839$	−4.93360	−	8.54525i	−0.170327	−	0.295015i	0.768207	−	0.640201i	$-0.221149\pi$
$839$	−4.93360	−	8.54525i	−0.170327	−	0.295015i	−0.938534	+	0.345186i	$0.887816\pi$
$840$	−0.520945	−	0.620838i	−0.0179743	−	0.0214209i
$841$	−5.69325	+	9.86100i	−0.196319	+	0.340034i
$842$	5.97906	−	10.3560i	0.206052	−	0.356892i
$843$	−12.1413	+	33.3580i	−0.418169	+	1.14891i
$844$	20.3662	+	35.2753i	0.701033	+	1.21422i
$845$	−5.01609			−0.172559
$846$	3.08466	+	2.58833i	0.106053	+	0.0889887i
$847$	0.532089			0.0182828
$848$	−20.7713	−	35.9769i	−0.713288	−	1.23545i
$849$	−11.7476	+	2.07142i	−0.403177	+	0.0710911i
$850$	−3.50387	+	6.06888i	−0.120182	+	0.208161i
$851$	2.23190	−	3.86576i	0.0765084	−	0.132516i
$852$	32.0107	−	5.64436i	1.09667	−	0.193372i
$853$	−28.7683	−	49.8282i	−0.985009	−	1.70608i	−0.641898	−	0.766790i	$-0.721853\pi$
$853$	−28.7683	−	49.8282i	−0.985009	−	1.70608i	−0.343110	−	0.939295i	$-0.611480\pi$
$854$	−1.57667			−0.0539524
$855$	6.27719	+	5.26719i	0.214675	+	0.180134i
$856$	−13.3773			−0.457228
$857$	7.70187	+	13.3400i	0.263091	+	0.455687i	0.967062	−	0.254542i	$-0.0819248\pi$
$857$	7.70187	+	13.3400i	0.263091	+	0.455687i	−0.703971	+	0.710229i	$0.748591\pi$
$858$	0.474308	−	1.30315i	0.0161926	−	0.0444888i
$859$	21.2866	−	36.8694i	0.726289	−	1.25797i	−0.232153	−	0.972679i	$-0.574577\pi$
$859$	21.2866	−	36.8694i	0.726289	−	1.25797i	0.958441	−	0.285290i	$-0.0920898\pi$
$860$	−7.54323	+	13.0653i	−0.257222	+	0.445522i
$861$	−5.51707	−	6.57499i	−0.188021	−	0.224075i
$862$	−2.47384	−	4.28482i	−0.0842594	−	0.145941i
$863$	−38.3536			−1.30557			−0.652786	−	0.757542i	$-0.726400\pi$
$863$	−38.3536			−1.30557			−0.652786	+	0.757542i	$0.726400\pi$
$864$		−	19.9402i		−	0.678380i
$865$	−14.6878			−0.499400
$866$	4.27214	+	7.39956i	0.145173	+	0.251447i
$867$	2.74005	+	3.26546i	0.0930569	+	0.110901i
$868$	−1.08125	+	1.87278i	−0.0367001	+	0.0635664i
$869$	−2.43969	+	4.22567i	−0.0827609	+	0.143346i
$870$	0.853388	−	2.34466i	0.0289326	−	0.0794916i
$871$	5.72106	+	9.90916i	0.193851	+	0.335759i
$872$	−18.6144			−0.630364
$873$	35.6498	−	12.9755i	1.20656	−	0.439153i
$874$	−2.05138			−0.0693891
$875$	1.66250	+	2.87954i	0.0562029	+	0.0973463i
$876$	−24.0278	+	4.23675i	−0.811824	+	0.143147i
$877$	6.23514	−	10.7996i	0.210546	−	0.364676i	−0.741340	−	0.671130i	$-0.765809\pi$
$877$	6.23514	−	10.7996i	0.210546	−	0.364676i	0.951885	+	0.306454i	$0.0991426\pi$
$878$	−0.724622	+	1.25508i	−0.0244548	+	0.0423570i
$879$	23.5535	−	4.15312i	0.794440	−	0.140081i
$880$	1.07398	+	1.86018i	0.0362038	+	0.0627068i
$881$	−22.9172			−0.772099			−0.386049	−	0.922478i	$-0.626161\pi$
$881$	−22.9172			−0.772099			−0.386049	+	0.922478i	$0.626161\pi$
$882$	1.21523	−	6.89193i	0.0409190	−	0.232063i
$883$	44.2300			1.48846			0.744229	−	0.667925i	$-0.232817\pi$
$883$	44.2300			1.48846			0.744229	+	0.667925i	$0.232817\pi$
$884$	9.55690	+	16.5530i	0.321433	+	0.556739i
$885$	−1.25062	+	3.43605i	−0.0420391	+	0.115501i
$886$	5.08172	−	8.80180i	0.170724	−	0.295702i
$887$	−12.3871	+	21.4551i	−0.415919	+	0.720393i	−0.995524	−	0.0945044i	$-0.969873\pi$
$887$	−12.3871	+	21.4551i	−0.415919	+	0.720393i	0.579605	+	0.814897i	$0.303207\pi$
$888$	4.74376	+	5.65339i	0.159190	+	0.189715i
$889$	−1.83615	−	3.18031i	−0.0615826	−	0.106664i
$890$	−3.84255			−0.128803
$891$	−1.56283	−	8.86327i	−0.0523569	−	0.296931i
$892$	−35.9641			−1.20417
$893$	−8.08677	−	14.0067i	−0.270613	−	0.468716i
$894$	−1.18375	−	1.41074i	−0.0395906	−	0.0471823i
$895$	3.49912	−	6.06066i	0.116963	−	0.202585i
$896$	2.52687	−	4.37667i	0.0844169	−	0.146214i
$897$	−1.92767	+	5.29623i	−0.0643631	+	0.176836i
$898$	2.74288	+	4.75080i	0.0915310	+	0.158536i
$899$	−13.7428			−0.458348
$900$	−4.47818	+	25.3970i	−0.149273	+	0.846567i
$901$	−55.6887			−1.85526
$902$	−1.61721	−	2.80109i	−0.0538472	−	0.0932662i
$903$	11.1623	−	1.96821i	0.371457	−	0.0654978i
$904$	1.18479	−	2.05212i	0.0394056	−	0.0682525i
$905$	1.35679	−	2.35003i	0.0451013	−	0.0781177i
$906$	−11.4937	+	2.02664i	−0.381851	+	0.0673307i
$907$	−15.2490	−	26.4120i	−0.506334	−	0.876996i	−0.999973	−	0.00732909i	$-0.997667\pi$
$907$	−15.2490	−	26.4120i	−0.506334	−	0.876996i	0.493639	−	0.869667i	$-0.335666\pi$
$908$	29.3063			0.972565
$909$	48.1823	−	17.5369i	1.59811	−	0.581663i
$910$	−0.278066			−0.00921780
$911$	−26.9413	−	46.6638i	−0.892606	−	1.54604i	−0.836739	−	0.547602i	$-0.815541\pi$
$911$	−26.9413	−	46.6638i	−0.892606	−	1.54604i	−0.0558672	−	0.998438i	$-0.517792\pi$
$912$	−8.15822	+	22.4145i	−0.270146	+	0.742219i
$913$	−2.29813	+	3.98048i	−0.0760571	+	0.131735i
$914$	−1.64708	+	2.85282i	−0.0544805	+	0.0943630i
$915$	−6.20011	−	7.38901i	−0.204969	−	0.244273i
$916$	−14.4820	−	25.0836i	−0.478500	−	0.828787i
$917$	5.50206			0.181694
$918$	−6.89440	−	3.98048i	−0.227549	−	0.131376i
$919$	5.19841			0.171480			0.0857398	−	0.996318i	$-0.472675\pi$
$919$	5.19841			0.171480			0.0857398	+	0.996318i	$0.472675\pi$
$920$	0.620615	+	1.07494i	0.0204611	+	0.0354396i
$921$	−0.669473	−	0.797847i	−0.0220599	−	0.0262900i
$922$	5.02616	−	8.70556i	0.165528	−	0.286702i
$923$	11.5103	−	19.9364i	0.378865	−	0.656214i
$924$	0.592396	−	1.62760i	0.0194884	−	0.0535440i
$925$	−7.23261	−	12.5273i	−0.237807	−	0.411893i
$926$	−7.94625			−0.261130
$927$	−6.57217	−	5.51470i	−0.215858	−	0.181127i
$928$	24.3874			0.800557
$929$	11.9368	+	20.6751i	0.391632	+	0.678327i	0.992665	−	0.120897i	$-0.0385772\pi$
$929$	11.9368	+	20.6751i	0.391632	+	0.678327i	−0.601033	+	0.799224i	$0.705244\pi$
$930$	0.836152	−	0.147436i	0.0274185	−	0.00483462i
$931$	−14.0544	+	24.3429i	−0.460614	+	0.797806i
$932$	4.03209	−	6.98378i	0.132075	−	0.228761i
$933$	−3.31062	+	0.583752i	−0.108385	+	0.0191112i
$934$	−1.77837	−	3.08023i	−0.0581901	−	0.100788i
$935$	2.87939			0.0941660
$936$	−7.13816	−	5.98962i	−0.233318	−	0.195777i
$937$	18.7219			0.611619			0.305809	−	0.952093i	$-0.401073\pi$
$937$	18.7219			0.611619			0.305809	+	0.952093i	$0.401073\pi$
$938$	−0.458578	−	0.794280i	−0.0149731	−	0.0259342i
$939$	1.19640	−	3.28709i	0.0390432	−	0.107270i
$940$	−2.37046	+	4.10576i	−0.0773160	+	0.133915i
$941$	−16.7814	+	29.0662i	−0.547057	+	0.947530i	0.451418	+	0.892313i	$0.350919\pi$
$941$	−16.7814	+	29.0662i	−0.547057	+	0.947530i	−0.998474	+	0.0552174i	$0.982415\pi$
$942$	−4.92009	−	5.86354i	−0.160305	−	0.191044i
$943$	6.57263	+	11.3841i	0.214034	+	0.370718i
$944$	−10.6440			−0.346434
$945$	−1.56283	+	0.902302i	−0.0508390	+	0.0293519i
$946$	4.27126			0.138871
$947$	21.8380	+	37.8245i	0.709638	+	1.22913i	0.964991	+	0.262282i	$0.0844750\pi$
$947$	21.8380	+	37.8245i	0.709638	+	1.22913i	−0.255353	+	0.966848i	$0.582192\pi$
$948$	10.2096	+	12.1673i	0.331593	+	0.395177i
$949$	−8.63980	+	14.9646i	−0.280460	+	0.485771i
$950$	−3.32383	+	5.75703i	−0.107839	+	0.186783i
$951$	3.46514	−	9.52038i	0.112365	−	0.308720i
$952$	−1.58125	−	2.73881i	−0.0512487	−	0.0887653i
$953$	39.4397			1.27758			0.638789	−	0.769382i	$-0.279436\pi$
$953$	39.4397			1.27758			0.638789	+	0.769382i	$0.279436\pi$
$954$	12.3592	−	4.49839i	0.400144	−	0.145641i
$955$	1.56893			0.0507692
$956$	−18.9192	−	32.7690i	−0.611891	−	1.05983i
$957$	10.8400	−	1.91139i	0.350408	−	0.0617864i
$958$	−3.35679	+	5.81413i	−0.108453	+	0.187846i
$959$	−3.77379	+	6.53639i	−0.121862	+	0.211071i
$960$	5.84389	−	1.03044i	0.188611	−	0.0332572i
$961$	13.1618	+	22.7969i	0.424574	+	0.735383i
$962$	2.53209			0.0816378
$963$	−5.17247	+	29.3345i	−0.166680	+	0.945291i
$964$	13.9932			0.450690
$965$	0.147956	+	0.256267i	0.00476287	+	0.00824953i
$966$	0.154515	−	0.424525i	0.00497143	−	0.0136589i
$967$	−3.29426	+	5.70583i	−0.105936	+	0.183487i	−0.914120	−	0.405443i	$-0.867117\pi$
$967$	−3.29426	+	5.70583i	−0.105936	+	0.183487i	0.808184	+	0.588930i	$0.200451\pi$
$968$	0.673648	−	1.16679i	0.0216519	−	0.0375021i
$969$	20.5535	+	24.4947i	0.660274	+	0.786883i
$970$	−1.43330	−	2.48254i	−0.0460204	−	0.0797096i
$971$	17.0327			0.546606			0.273303	−	0.961928i	$-0.411884\pi$
$971$	17.0327			0.546606			0.273303	+	0.961928i	$0.411884\pi$
$972$	−28.8516	−	5.08732i	−0.925417	−	0.163176i
$973$	0.0537486			0.00172310
$974$	−4.72503	−	8.18400i	−0.151400	−	0.262232i
$975$	11.7400	+	13.9912i	0.375982	+	0.448078i
$976$	14.0390	−	24.3162i	0.449376	−	0.778342i
$977$	−3.77450	+	6.53763i	−0.120757	+	0.209157i	−0.920066	−	0.391762i	$-0.871866\pi$
$977$	−3.77450	+	6.53763i	−0.120757	+	0.209157i	0.799309	+	0.600920i	$0.205199\pi$
$978$	−2.63113	+	7.22897i	−0.0841343	+	0.231157i
$979$	−8.47565	−	14.6803i	−0.270883	−	0.469183i
$980$	8.23947			0.263200
$981$	−7.19744	+	40.8187i	−0.229797	+	1.30324i
$982$	−12.5158			−0.399395
$983$	1.92350	+	3.33159i	0.0613500	+	0.106261i	0.895069	−	0.445928i	$-0.147126\pi$
$983$	1.92350	+	3.33159i	0.0613500	+	0.106261i	−0.833719	+	0.552189i	$0.813793\pi$
$984$	−21.4029	+	3.77390i	−0.682298	+	0.120308i
$985$	6.40420	−	11.0924i	0.204055	−	0.353433i
$986$	4.86824	−	8.43204i	0.155036	−	0.268531i
$987$	3.50774	−	0.618509i	0.111653	−	0.0196874i
$988$	9.06583	+	15.7025i	0.288422	+	0.499562i
$989$	−17.3592			−0.551989
$990$	−0.639033	+	0.232589i	−0.0203098	+	0.00739216i
$991$	40.1121			1.27420			0.637101	−	0.770781i	$-0.280134\pi$
$991$	40.1121			1.27420			0.637101	+	0.770781i	$0.280134\pi$
$992$	4.14930	+	7.18680i	0.131740	+	0.228181i
$993$	6.94403	−	19.0786i	0.220362	−	0.605440i
$994$	−0.922618	+	1.59802i	−0.0292637	+	0.0506862i
$995$	−1.18479	+	2.05212i	−0.0375604	+	0.0650566i
$996$	9.61721	+	11.4613i	0.304733	+	0.363167i
$997$	8.28240	+	14.3455i	0.262306	+	0.454328i	0.966854	−	0.255328i	$-0.0821836\pi$
$997$	8.28240	+	14.3455i	0.262306	+	0.454328i	−0.704548	+	0.709656i	$0.748850\pi$
$998$	−2.74092			−0.0867625
$999$	14.2313	−	8.21643i	0.450257	−	0.259956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.d.67.2	yes	6
3.2	odd	2		297.2.e.d.199.2		6
9.2	odd	6		297.2.e.d.100.2		6
9.4	even	3		891.2.a.l.1.2		3
9.5	odd	6		891.2.a.k.1.2		3
9.7	even	3	inner	99.2.e.d.34.2	✓	6
11.10	odd	2		1089.2.e.h.364.2		6
99.32	even	6		9801.2.a.bd.1.2		3
99.43	odd	6		1089.2.e.h.727.2		6
99.76	odd	6		9801.2.a.be.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.d.34.2	✓	6	9.7	even	3	inner
99.2.e.d.67.2	yes	6	1.1	even	1	trivial
297.2.e.d.100.2		6	9.2	odd	6
297.2.e.d.199.2		6	3.2	odd	2
891.2.a.k.1.2		3	9.5	odd	6
891.2.a.l.1.2		3	9.4	even	3
1089.2.e.h.364.2		6	11.10	odd	2
1089.2.e.h.727.2		6	99.43	odd	6
9801.2.a.bd.1.2		3	99.32	even	6
9801.2.a.be.1.2		3	99.76	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.300767i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +(0.205737 - 0.565258i) q^{6} +(-0.266044 - 0.460802i) q^{7} -1.34730 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.300767i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.326352 + 0.565258i) q^{5} +(0.205737 - 0.565258i) q^{6} +(-0.266044 - 0.460802i) q^{7} -1.34730 q^{8} +(-0.520945 + 2.95442i) q^{9} +0.226682 q^{10} +(0.500000 + 0.866025i) q^{11} +(3.20574 - 0.565258i) q^{12} +(1.15270 - 1.99654i) q^{13} +(-0.0923963 + 0.160035i) q^{14} +(-1.11334 + 0.196312i) q^{15} +(-1.64543 - 2.84997i) q^{16} -4.41147 q^{17} +(0.979055 - 0.356347i) q^{18} -4.18479 q^{19} +(0.613341 + 1.06234i) q^{20} +(0.315207 - 0.866025i) q^{21} +(0.173648 - 0.300767i) q^{22} +(-0.705737 + 1.22237i) q^{23} +(-1.50000 - 1.78763i) q^{24} +(2.28699 + 3.96118i) q^{25} -0.800660 q^{26} +(-4.50000 + 2.59808i) q^{27} -1.00000 q^{28} +(-3.17752 - 5.50362i) q^{29} +(0.252374 + 0.300767i) q^{30} +(1.08125 - 1.87278i) q^{31} +(-1.91875 + 3.32337i) q^{32} +(-0.592396 + 1.62760i) q^{33} +(0.766044 + 1.32683i) q^{34} +0.347296 q^{35} +(4.31908 + 3.62414i) q^{36} -3.16250 q^{37} +(0.726682 + 1.25865i) q^{38} +(3.93242 - 0.693392i) q^{39} +(0.439693 - 0.761570i) q^{40} +(4.65657 - 8.06542i) q^{41} +(-0.315207 + 0.0555796i) q^{42} +(6.14930 + 10.6509i) q^{43} +1.87939 q^{44} +(-1.50000 - 1.25865i) q^{45} +0.490200 q^{46} +(1.93242 + 3.34705i) q^{47} +(1.94949 - 5.35619i) q^{48} +(3.35844 - 5.81699i) q^{49} +(0.794263 - 1.37570i) q^{50} +(-4.91147 - 5.85327i) q^{51} +(-2.16637 - 3.75227i) q^{52} +12.6236 q^{53} +(1.56283 + 0.902302i) q^{54} -0.652704 q^{55} +(0.358441 + 0.620838i) q^{56} +(-4.65910 - 5.55250i) q^{57} +(-1.10354 + 1.91139i) q^{58} +(1.61721 - 2.80109i) q^{59} +(-0.726682 + 1.99654i) q^{60} +(4.26604 + 7.38901i) q^{61} -0.751030 q^{62} +(1.50000 - 0.545955i) q^{63} -5.24897 q^{64} +(0.752374 + 1.30315i) q^{65} +(0.592396 - 0.104455i) q^{66} +(-2.48158 + 4.29823i) q^{67} +(-4.14543 + 7.18009i) q^{68} +(-2.40760 + 0.424525i) q^{69} +(-0.0603074 - 0.104455i) q^{70} +9.98545 q^{71} +(0.701867 - 3.98048i) q^{72} -7.49525 q^{73} +(0.549163 + 0.951178i) q^{74} +(-2.70961 + 7.44459i) q^{75} +(-3.93242 + 6.81115i) q^{76} +(0.266044 - 0.460802i) q^{77} +(-0.891407 - 1.06234i) q^{78} +(2.43969 + 4.22567i) q^{79} +2.14796 q^{80} +(-8.45723 - 3.07818i) q^{81} -3.23442 q^{82} +(2.29813 + 3.98048i) q^{83} +(-1.11334 - 1.32683i) q^{84} +(1.43969 - 2.49362i) q^{85} +(2.13563 - 3.69902i) q^{86} +(3.76470 - 10.3434i) q^{87} +(-0.673648 - 1.16679i) q^{88} -16.9513 q^{89} +(-0.118089 + 0.669713i) q^{90} -1.22668 q^{91} +(1.32635 + 2.29731i) q^{92} +(3.68866 - 0.650411i) q^{93} +(0.671122 - 1.16242i) q^{94} +(1.36571 - 2.36549i) q^{95} +(-6.54576 + 1.15419i) q^{96} +(-6.32295 - 10.9517i) q^{97} -2.33275 q^{98} +(-2.81908 + 1.02606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8} - 12 q^{10} + 3 q^{11} + 9 q^{12} + 9 q^{13} + 3 q^{14} + 6 q^{16} - 6 q^{17} + 9 q^{18} - 18 q^{19} - 3 q^{20} + 9 q^{21} + 6 q^{23} - 9 q^{24} + 6 q^{25} + 24 q^{26} - 27 q^{27} - 6 q^{28} + 6 q^{29} + 18 q^{30} + 9 q^{31} - 9 q^{32} + 9 q^{36} - 24 q^{37} - 9 q^{38} - 3 q^{40} + 6 q^{41} - 9 q^{42} - 3 q^{43} - 9 q^{45} - 12 q^{47} + 9 q^{48} + 12 q^{49} + 15 q^{50} - 9 q^{51} + 6 q^{52} + 6 q^{53} - 6 q^{55} - 6 q^{56} + 9 q^{57} + 3 q^{58} - 21 q^{59} + 9 q^{60} + 21 q^{61} - 30 q^{62} + 9 q^{63} - 6 q^{64} + 21 q^{65} - 3 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 24 q^{71} + 18 q^{72} - 12 q^{73} + 15 q^{74} + 18 q^{75} - 3 q^{77} - 45 q^{78} + 9 q^{79} - 18 q^{80} + 42 q^{82} + 3 q^{85} - 6 q^{86} + 27 q^{87} - 3 q^{88} - 24 q^{89} - 27 q^{90} + 6 q^{91} + 9 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{95} - 9 q^{96} + 3 q^{97} + 24 q^{98}+O(q^{100}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8 - 12 * q^10 + 3 * q^11 + 9 * q^12 + 9 * q^13 + 3 * q^14 + 6 * q^16 - 6 * q^17 + 9 * q^18 - 18 * q^19 - 3 * q^20 + 9 * q^21 + 6 * q^23 - 9 * q^24 + 6 * q^25 + 24 * q^26 - 27 * q^27 - 6 * q^28 + 6 * q^29 + 18 * q^30 + 9 * q^31 - 9 * q^32 + 9 * q^36 - 24 * q^37 - 9 * q^38 - 3 * q^40 + 6 * q^41 - 9 * q^42 - 3 * q^43 - 9 * q^45 - 12 * q^47 + 9 * q^48 + 12 * q^49 + 15 * q^50 - 9 * q^51 + 6 * q^52 + 6 * q^53 - 6 * q^55 - 6 * q^56 + 9 * q^57 + 3 * q^58 - 21 * q^59 + 9 * q^60 + 21 * q^61 - 30 * q^62 + 9 * q^63 - 6 * q^64 + 21 * q^65 - 3 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 24 * q^71 + 18 * q^72 - 12 * q^73 + 15 * q^74 + 18 * q^75 - 3 * q^77 - 45 * q^78 + 9 * q^79 - 18 * q^80 + 42 * q^82 + 3 * q^85 - 6 * q^86 + 27 * q^87 - 3 * q^88 - 24 * q^89 - 27 * q^90 + 6 * q^91 + 9 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^95 - 9 * q^96 + 3 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more