LMFDB - Embedded newform 504.2.bt.a.275.74

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(11,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 4]))

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

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

chi := DirichletCharacter("504.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bt (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.74
Character	$\chi$	$=$	504.275
Dual form			504.2.bt.a.11.74

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13389 + 0.845156i) q^{2} +(-0.862894 - 1.50180i) q^{3} +(0.571423 + 1.91663i) q^{4} +(-1.48267 - 2.56806i) q^{5} +(0.290830 - 2.43216i) q^{6} +(-2.51854 - 0.810517i) q^{7} +(-0.971921 + 2.65619i) q^{8} +(-1.51083 + 2.59179i) q^{9} +O(q^{10})$	\(q+(1.13389 + 0.845156i) q^{2} +(-0.862894 - 1.50180i) q^{3} +(0.571423 + 1.91663i) q^{4} +(-1.48267 - 2.56806i) q^{5} +(0.290830 - 2.43216i) q^{6} +(-2.51854 - 0.810517i) q^{7} +(-0.971921 + 2.65619i) q^{8} +(-1.51083 + 2.59179i) q^{9} +(0.489224 - 4.16500i) q^{10} +(-0.987994 - 0.570419i) q^{11} +(2.38533 - 2.51201i) q^{12} +(-1.20993 - 0.698555i) q^{13} +(-2.17074 - 3.04760i) q^{14} +(-2.57734 + 4.44265i) q^{15} +(-3.34695 + 2.19041i) q^{16} +(-6.02425 + 3.47811i) q^{17} +(-3.90359 + 1.66193i) q^{18} +(1.37831 - 2.38731i) q^{19} +(4.07480 - 4.30919i) q^{20} +(0.955999 + 4.48175i) q^{21} +(-0.638186 - 1.48180i) q^{22} +(-1.47523 - 2.55518i) q^{23} +(4.82775 - 0.832380i) q^{24} +(-1.89664 + 3.28507i) q^{25} +(-0.781545 - 1.81467i) q^{26} +(5.19605 + 0.0325245i) q^{27} +(0.114309 - 5.29027i) q^{28} +(-1.85598 - 3.21465i) q^{29} +(-6.67716 + 2.85923i) q^{30} -9.58567i q^{31} +(-5.64632 - 0.345004i) q^{32} +(-0.00412282 + 1.97598i) q^{33} +(-9.77040 - 1.14764i) q^{34} +(1.65272 + 7.66951i) q^{35} +(-5.83084 - 1.41469i) q^{36} +(5.92474 + 3.42065i) q^{37} +(3.58051 - 1.54206i) q^{38} +(-0.00504895 + 2.41986i) q^{39} +(8.26232 - 1.44231i) q^{40} +(6.20145 + 3.58041i) q^{41} +(-2.70378 + 5.88979i) q^{42} +(0.368441 + 0.638159i) q^{43} +(0.528720 - 2.21957i) q^{44} +(8.89596 + 0.0371224i) q^{45} +(0.486769 - 4.14410i) q^{46} -7.25849 q^{47} +(6.17764 + 3.13637i) q^{48} +(5.68613 + 4.08264i) q^{49} +(-4.92698 + 2.12196i) q^{50} +(10.4217 + 6.04601i) q^{51} +(0.647489 - 2.71816i) q^{52} +(-4.23405 - 7.33359i) q^{53} +(5.86427 + 4.42835i) q^{54} +3.38298i q^{55} +(4.60072 - 5.90198i) q^{56} +(-4.77461 - 0.00996205i) q^{57} +(0.612401 - 5.21366i) q^{58} -13.2645i q^{59} +(-9.98767 - 2.40118i) q^{60} +5.55019i q^{61} +(8.10139 - 10.8691i) q^{62} +(5.90578 - 5.30300i) q^{63} +(-6.11074 - 5.16322i) q^{64} +4.14291i q^{65} +(-1.67469 + 2.23707i) q^{66} +0.0857319 q^{67} +(-10.1086 - 9.55881i) q^{68} +(-2.56441 + 4.42036i) q^{69} +(-4.60793 + 10.0932i) q^{70} +6.13960 q^{71} +(-5.41590 - 6.53207i) q^{72} +(3.22594 + 5.58749i) q^{73} +(3.82703 + 8.88598i) q^{74} +(6.57013 + 0.0137083i) q^{75} +(5.36319 + 1.27756i) q^{76} +(2.02597 + 2.23741i) q^{77} +(-2.05088 + 2.73959i) q^{78} -3.27307i q^{79} +(10.5876 + 5.34752i) q^{80} +(-4.43479 - 7.83151i) q^{81} +(4.00577 + 9.30100i) q^{82} +(1.44667 - 0.835233i) q^{83} +(-8.04358 + 4.39327i) q^{84} +(17.8640 + 10.3138i) q^{85} +(-0.121571 + 1.03499i) q^{86} +(-3.22626 + 5.56122i) q^{87} +(2.47540 - 2.06990i) q^{88} +(-13.7941 - 7.96402i) q^{89} +(10.0557 + 7.56057i) q^{90} +(2.48108 + 2.74001i) q^{91} +(4.05435 - 4.28756i) q^{92} +(-14.3958 + 8.27142i) q^{93} +(-8.23035 - 6.13456i) q^{94} -8.17435 q^{95} +(4.35405 + 8.77737i) q^{96} +(9.27174 + 16.0591i) q^{97} +(2.99698 + 9.43494i) q^{98} +(2.97110 - 1.69887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} - 8 q^{12} + 12 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} - 74 q^{25} - 6 q^{26} - 8 q^{27} + 3 q^{30} - 14 q^{33} - 4 q^{34} + 30 q^{35} - 38 q^{36} + 39 q^{38} + 6 q^{40} - 12 q^{41} - 20 q^{42} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} - 34 q^{51} + 9 q^{52} + 47 q^{54} - 24 q^{56} + 4 q^{57} - 3 q^{58} - 11 q^{60} - 8 q^{64} - 26 q^{66} - 4 q^{67} - 42 q^{68} - 3 q^{70} + 52 q^{72} - 4 q^{73} + 27 q^{74} + 30 q^{75} + 2 q^{76} - 29 q^{78} + 87 q^{80} + 14 q^{81} - 4 q^{82} - 72 q^{83} - 59 q^{84} - 27 q^{86} - 7 q^{88} - 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} - 18 q^{94} + 23 q^{96} - 4 q^{97} + 57 q^{98} + 10 q^{99}+O(q^{100}) $ 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 6 * q^11 - 8 * q^12 + 12 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 - 74 * q^25 - 6 * q^26 - 8 * q^27 + 3 * q^30 - 14 * q^33 - 4 * q^34 + 30 * q^35 - 38 * q^36 + 39 * q^38 + 6 * q^40 - 12 * q^41 - 20 * q^42 - 4 * q^43 + 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 - 34 * q^51 + 9 * q^52 + 47 * q^54 - 24 * q^56 + 4 * q^57 - 3 * q^58 - 11 * q^60 - 8 * q^64 - 26 * q^66 - 4 * q^67 - 42 * q^68 - 3 * q^70 + 52 * q^72 - 4 * q^73 + 27 * q^74 + 30 * q^75 + 2 * q^76 - 29 * q^78 + 87 * q^80 + 14 * q^81 - 4 * q^82 - 72 * q^83 - 59 * q^84 - 27 * q^86 - 7 * q^88 - 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 - 18 * q^94 + 23 * q^96 - 4 * q^97 + 57 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.13389	+	0.845156i	0.801783	+	0.597616i
$2$	1.13389	+	0.845156i	0.801783	+	0.597616i
$3$	−0.862894	−	1.50180i	−0.498192	−	0.867067i
$3$	−0.862894	−	1.50180i	−0.498192	−	0.867067i
$4$	0.571423	+	1.91663i	0.285711	+	0.958316i
$5$	−1.48267	−	2.56806i	−0.663071	−	1.14847i	−0.979804	−	0.199959i	$-0.935919\pi$
$5$	−1.48267	−	2.56806i	−0.663071	−	1.14847i	0.316733	−	0.948515i	$-0.397414\pi$
$6$	0.290830	−	2.43216i	0.118731	−	0.992926i
$7$	−2.51854	−	0.810517i	−0.951920	−	0.306347i
$7$	−2.51854	−	0.810517i	−0.951920	−	0.306347i
$8$	−0.971921	+	2.65619i	−0.343626	+	0.939107i
$9$	−1.51083	+	2.59179i	−0.503609	+	0.863931i
$10$	0.489224	−	4.16500i	0.154706	−	1.31709i
$11$	−0.987994	−	0.570419i	−0.297891	−	0.171988i	0.343604	−	0.939115i	$-0.388352\pi$
$11$	−0.987994	−	0.570419i	−0.297891	−	0.171988i	−0.641495	+	0.767127i	$0.721686\pi$
$12$	2.38533	−	2.51201i	0.688585	−	0.725156i
$13$	−1.20993	−	0.698555i	−0.335575	−	0.193744i	0.322739	−	0.946488i	$-0.395397\pi$
$13$	−1.20993	−	0.698555i	−0.335575	−	0.193744i	−0.658313	+	0.752744i	$0.728730\pi$
$14$	−2.17074	−	3.04760i	−0.580156	−	0.814506i
$15$	−2.57734	+	4.44265i	−0.665466	+	1.14709i
$16$	−3.34695	+	2.19041i	−0.836738	+	0.547603i
$17$	−6.02425	+	3.47811i	−1.46110	+	0.843564i	−0.999062	−	0.0432977i	$-0.986214\pi$
$17$	−6.02425	+	3.47811i	−1.46110	+	0.843564i	−0.462034	+	0.886862i	$0.652880\pi$
$18$	−3.90359	+	1.66193i	−0.920084	+	0.391720i
$19$	1.37831	−	2.38731i	0.316207	−	0.547686i	−0.663486	−	0.748188i	$-0.730924\pi$
$19$	1.37831	−	2.38731i	0.316207	−	0.547686i	0.979693	+	0.200502i	$0.0642573\pi$
$20$	4.07480	−	4.30919i	0.911153	−	0.963564i
$21$	0.955999	+	4.48175i	0.208616	+	0.977998i
$22$	−0.638186	−	1.48180i	−0.136062	−	0.315921i
$23$	−1.47523	−	2.55518i	−0.307607	−	0.532791i	0.670231	−	0.742152i	$-0.266195\pi$
$23$	−1.47523	−	2.55518i	−0.307607	−	0.532791i	−0.977838	+	0.209361i	$0.932862\pi$
$24$	4.82775	−	0.832380i	0.985460	−	0.169909i
$25$	−1.89664	+	3.28507i	−0.379327	+	0.657014i
$26$	−0.781545	−	1.81467i	−0.153274	−	0.355886i
$27$	5.19605	+	0.0325245i	0.999980	+	0.00625935i
$28$	0.114309	−	5.29027i	0.0216023	−	0.999767i
$29$	−1.85598	−	3.21465i	−0.344647	−	0.596946i	0.640643	−	0.767839i	$-0.278668\pi$
$29$	−1.85598	−	3.21465i	−0.344647	−	0.596946i	−0.985290	+	0.170893i	$0.945335\pi$
$30$	−6.67716	+	2.85923i	−1.21908	+	0.522022i
$31$		−	9.58567i		−	1.72164i	−0.508911	−	0.860819i	$-0.669952\pi$
$31$		−	9.58567i		−	1.72164i	0.508911	−	0.860819i	$-0.330048\pi$
$32$	−5.64632	−	0.345004i	−0.998138	−	0.0609887i
$33$	−0.00412282	+	1.97598i	−0.000717691	+	0.343975i
$34$	−9.77040	−	1.14764i	−1.67561	−	0.196818i
$35$	1.65272	+	7.66951i	0.279360	+	1.29638i
$36$	−5.83084	−	1.41469i	−0.971806	−	0.235782i
$37$	5.92474	+	3.42065i	0.974021	+	0.562351i	0.900460	−	0.434939i	$-0.143230\pi$
$37$	5.92474	+	3.42065i	0.974021	+	0.562351i	0.0735613	+	0.997291i	$0.476564\pi$
$38$	3.58051	−	1.54206i	0.580835	−	0.250155i
$39$	−0.00504895	+	2.41986i	−0.000808479	+	0.387488i
$40$	8.26232	−	1.44231i	1.30639	−	0.228050i
$41$	6.20145	+	3.58041i	0.968505	+	0.559166i	0.898780	−	0.438400i	$-0.144455\pi$
$41$	6.20145	+	3.58041i	0.968505	+	0.559166i	0.0697245	+	0.997566i	$0.477788\pi$
$42$	−2.70378	+	5.88979i	−0.417202	+	0.908814i
$43$	0.368441	+	0.638159i	0.0561868	+	0.0973184i	0.892751	−	0.450551i	$-0.148772\pi$
$43$	0.368441	+	0.638159i	0.0561868	+	0.0973184i	−0.836564	+	0.547869i	$0.815439\pi$
$44$	0.528720	−	2.21957i	0.0797076	−	0.334613i
$45$	8.89596	+	0.0371224i	1.32613	+	0.00553388i
$46$	0.486769	−	4.14410i	0.0717702	−	0.611014i
$47$	−7.25849			−1.05876			−0.529380	−	0.848385i	$-0.677575\pi$
$47$	−7.25849			−1.05876			−0.529380	+	0.848385i	$0.677575\pi$
$48$	6.17764	+	3.13637i	0.891665	+	0.452696i
$49$	5.68613	+	4.08264i	0.812304	+	0.583235i
$50$	−4.92698	+	2.12196i	−0.696780	+	0.300091i
$51$	10.4217	+	6.04601i	1.45933	+	0.846611i
$52$	0.647489	−	2.71816i	0.0897906	−	0.376942i
$53$	−4.23405	−	7.33359i	−0.581592	−	1.00735i	−0.995291	−	0.0969327i	$-0.969097\pi$
$53$	−4.23405	−	7.33359i	−0.581592	−	1.00735i	0.413699	−	0.910414i	$-0.364236\pi$
$54$	5.86427	+	4.42835i	0.798026	+	0.602622i
$55$			3.38298i			0.456161i
$56$	4.60072	−	5.90198i	0.614796	−	0.788686i
$57$	−4.77461	−	0.00996205i	−0.632412	−	0.00131951i
$58$	0.612401	−	5.21366i	0.0804121	−	0.684587i
$59$		−	13.2645i		−	1.72689i	−0.504440	−	0.863447i	$-0.668301\pi$
$59$		−	13.2645i		−	1.72689i	0.504440	−	0.863447i	$-0.331699\pi$
$60$	−9.98767	−	2.40118i	−1.28940	−	0.309991i
$61$			5.55019i			0.710629i	0.934747	+	0.355315i	$0.115626\pi$
$61$			5.55019i			0.710629i	−0.934747	+	0.355315i	$0.884374\pi$
$62$	8.10139	−	10.8691i	1.02888	−	1.38038i
$63$	5.90578	−	5.30300i	0.744058	−	0.668115i
$64$	−6.11074	−	5.16322i	−0.763842	−	0.645403i
$65$			4.14291i			0.513865i
$66$	−1.67469	+	2.23707i	−0.206140	+	0.275364i
$67$	0.0857319			0.0104738			0.00523691	−	0.999986i	$-0.498333\pi$
$67$	0.0857319			0.0104738			0.00523691	+	0.999986i	$0.498333\pi$
$68$	−10.1086	−	9.55881i	−1.22585	−	1.15918i
$69$	−2.56441	+	4.42036i	−0.308718	+	0.532148i
$70$	−4.60793	+	10.0932i	−0.550753	+	1.20637i
$71$	6.13960			0.728636			0.364318	−	0.931275i	$-0.381302\pi$
$71$	6.13960			0.728636			0.364318	+	0.931275i	$0.381302\pi$
$72$	−5.41590	−	6.53207i	−0.638270	−	0.769812i
$73$	3.22594	+	5.58749i	0.377568	+	0.653966i	0.990708	−	0.136008i	$-0.0434273\pi$
$73$	3.22594	+	5.58749i	0.377568	+	0.653966i	−0.613140	+	0.789974i	$0.710094\pi$
$74$	3.82703	+	8.88598i	0.444883	+	1.03297i
$75$	6.57013	+	0.0137083i	0.758653	+	0.00158290i
$76$	5.36319	+	1.27756i	0.615200	+	0.146546i
$77$	2.02597	+	2.23741i	0.230881	+	0.254977i
$78$	−2.05088	+	2.73959i	−0.232217	+	0.310198i
$79$		−	3.27307i		−	0.368249i	−0.982903	−	0.184125i	$-0.941055\pi$
$79$		−	3.27307i		−	0.368249i	0.982903	−	0.184125i	$-0.0589450\pi$
$80$	10.5876	+	5.34752i	1.18372	+	0.597871i
$81$	−4.43479	−	7.83151i	−0.492755	−	0.870168i
$82$	4.00577	+	9.30100i	0.442364	+	1.02712i
$83$	1.44667	−	0.835233i	0.158792	−	0.0916787i	−0.418498	−	0.908218i	$-0.637443\pi$
$83$	1.44667	−	0.835233i	0.158792	−	0.0916787i	0.577290	+	0.816539i	$0.304110\pi$
$84$	−8.04358	+	4.39327i	−0.877627	+	0.479345i
$85$	17.8640	+	10.3138i	1.93762	+	1.11869i
$86$	−0.121571	+	1.03499i	−0.0131094	+	0.111606i
$87$	−3.22626	+	5.56122i	−0.345891	+	0.596225i
$88$	2.47540	−	2.06990i	0.263878	−	0.220652i
$89$	−13.7941	−	7.96402i	−1.46217	−	0.844184i	−0.463058	−	0.886328i	$-0.653248\pi$
$89$	−13.7941	−	7.96402i	−1.46217	−	0.844184i	−0.999112	+	0.0421437i	$0.986581\pi$
$90$	10.0557	+	7.56057i	1.05996	+	0.796954i
$91$	2.48108	+	2.74001i	0.260088	+	0.287231i
$92$	4.05435	−	4.28756i	0.422695	−	0.447009i
$93$	−14.3958	+	8.27142i	−1.49278	+	0.857706i
$94$	−8.23035	−	6.13456i	−0.848896	−	0.632731i
$95$	−8.17435			−0.838671
$96$	4.35405	+	8.77737i	0.444383	+	0.895837i
$97$	9.27174	+	16.0591i	0.941402	+	1.63056i	0.762799	+	0.646635i	$0.223824\pi$
$97$	9.27174	+	16.0591i	0.941402	+	1.63056i	0.178603	+	0.983921i	$0.442842\pi$
$98$	2.99698	+	9.43494i	0.302741	+	0.953073i
$99$	2.97110	−	1.69887i	0.298607	−	0.170743i
$100$	−7.38005	−	1.75799i	−0.738005	−	0.175799i
$101$	−0.0161156	+	0.0279130i	−0.00160356	+	0.00277744i	−0.866826	−	0.498611i	$-0.833844\pi$
$101$	−0.0161156	+	0.0279130i	−0.00160356	+	0.00277744i	0.865223	+	0.501388i	$0.167177\pi$
$102$	6.70729	+	15.6635i	0.664120	+	1.55092i
$103$	−12.6817	+	7.32177i	−1.24956	+	0.721435i	−0.971022	−	0.238989i	$-0.923184\pi$
$103$	−12.6817	+	7.32177i	−1.24956	+	0.721435i	−0.278540	+	0.960425i	$0.589851\pi$
$104$	3.03146	−	2.53488i	0.297259	−	0.248565i
$105$	10.0920	−	9.10003i	0.984877	−	0.888072i
$106$	1.39707	−	11.8939i	0.135696	−	1.15524i
$107$	1.41305	+	0.815827i	0.136605	+	0.0788690i	0.566745	−	0.823893i	$-0.308202\pi$
$107$	1.41305	+	0.815827i	0.136605	+	0.0788690i	−0.430140	+	0.902762i	$0.641536\pi$
$108$	2.90680	+	9.97750i	0.279707	+	0.960085i
$109$	−3.53408	+	2.04040i	−0.338504	+	0.195435i	−0.659610	−	0.751608i	$-0.729279\pi$
$109$	−3.53408	+	2.04040i	−0.338504	+	0.195435i	0.321107	+	0.947043i	$0.395945\pi$
$110$	−2.85914	+	3.83593i	−0.272609	+	0.365742i
$111$	0.0247235	−	11.8495i	0.00234665	−	1.12470i
$112$	10.2048	−	2.80389i	0.964264	−	0.264943i
$113$	−0.676838	−	0.390773i	−0.0636716	−	0.0367608i	0.467826	−	0.883820i	$-0.345037\pi$
$113$	−0.676838	−	0.390773i	−0.0636716	−	0.0367608i	−0.531498	+	0.847060i	$0.678371\pi$
$114$	−5.40547	−	4.04658i	−0.506269	−	0.378997i
$115$	−4.37457	+	7.57698i	−0.407931	+	0.706557i
$116$	5.10075	−	5.39415i	0.473593	−	0.500834i
$117$	3.63851	−	2.08050i	0.336380	−	0.192342i
$118$	11.2106	−	15.0405i	1.03202	−	1.38459i
$119$	17.9914	−	3.87700i	1.64927	−	0.355404i
$120$	−9.29557	−	11.1638i	−0.848566	−	1.01911i
$121$	−4.84924	−	8.39914i	−0.440840	−	0.763558i
$122$	−4.69078	+	6.29332i	−0.424683	+	0.569770i
$123$	0.0258782	−	12.4029i	0.00233336	−	1.11833i
$124$	18.3722	−	5.47747i	1.64987	−	0.491892i
$125$	−3.57837			−0.320059
$126$	11.1784	−	1.02172i	0.995849	−	0.0910220i
$127$			0.00882911i			0.000783457i	1.00000		0.000391728i	$0.000124691\pi$
$127$			0.00882911i			0.000783457i	−1.00000		0.000391728i	$0.999875\pi$
$128$	−2.56519	−	11.0191i	−0.226733	−	0.973957i
$129$	0.640464	−	1.10399i	0.0563897	−	0.0972009i
$130$	−3.50141	+	4.69761i	−0.307094	+	0.412008i
$131$	−9.37321	+	5.41163i	−0.818941	+	0.472816i	−0.850051	−	0.526700i	$-0.823429\pi$
$131$	−9.37321	+	5.41163i	−0.818941	+	0.472816i	0.0311101	+	0.999516i	$0.490096\pi$
$132$	−3.78959	+	1.12122i	−0.329841	+	0.0975897i
$133$	−5.40630	+	4.89540i	−0.468785	+	0.424485i
$134$	0.0972108	+	0.0724569i	0.00839773	+	0.00625932i
$135$	−7.62052	−	13.3920i	−0.655870	−	1.15260i
$136$	−3.38343	−	19.3820i	−0.290126	−	1.66200i
$137$	0.692004	+	0.399529i	0.0591219	+	0.0341341i	0.529270	−	0.848454i	$-0.322466\pi$
$137$	0.692004	+	0.399529i	0.0591219	+	0.0341341i	−0.470148	+	0.882588i	$0.655799\pi$
$138$	−6.64365	+	2.84488i	−0.565545	+	0.242173i
$139$	8.58417	−	14.8682i	0.728100	−	1.26111i	−0.229586	−	0.973288i	$-0.573737\pi$
$139$	8.58417	−	14.8682i	0.728100	−	1.26111i	0.957685	−	0.287817i	$-0.0929296\pi$
$140$	−13.7552	+	7.55018i	−1.16253	+	0.638107i
$141$	6.26331	+	10.9008i	0.527466	+	0.918016i
$142$	6.96164	+	5.18892i	0.584208	+	0.435444i
$143$	0.796937	+	1.38034i	0.0666433	+	0.115429i
$144$	−0.620430	−	11.9840i	−0.0517025	−	0.998663i
$145$	−5.50362	+	9.53255i	−0.457051	+	0.791635i
$146$	−1.06443	+	9.06203i	−0.0880932	+	0.749979i
$147$	1.22481	−	12.0623i	0.101020	−	0.994884i
$148$	−3.17059	+	13.3102i	−0.260621	+	1.09409i
$149$	5.37757	+	9.31423i	0.440548	+	0.763051i	0.997730	−	0.0673390i	$-0.0214509\pi$
$149$	5.37757	+	9.31423i	0.440548	+	0.763051i	−0.557182	+	0.830390i	$0.688118\pi$
$150$	7.43823	+	5.56832i	0.607329	+	0.454652i
$151$	11.0928	+	6.40441i	0.902717	+	0.521184i	0.878081	−	0.478513i	$-0.158824\pi$
$151$	11.0928	+	6.40441i	0.902717	+	0.521184i	0.0246360	+	0.999696i	$0.492157\pi$
$152$	5.00155	+	5.98135i	0.405679	+	0.485151i
$153$	0.0870830	−	20.8684i	0.00704024	−	1.68711i
$154$	0.406274	+	4.24925i	0.0327385	+	0.342414i
$155$	−24.6166	+	14.2124i	−1.97726	+	1.14157i
$156$	−4.64086	+	1.37309i	−0.371566	+	0.109935i
$157$			5.09959i			0.406992i	0.979076	+	0.203496i	$0.0652304\pi$
$157$			5.09959i			0.406992i	−0.979076	+	0.203496i	$0.934770\pi$
$158$	2.76625	−	3.71131i	0.220071	−	0.295256i
$159$	−7.36008	+	12.6868i	−0.583692	+	1.00613i
$160$	7.48566	+	15.0117i	0.591793	+	1.18678i
$161$	1.64442	+	7.63103i	0.129599	+	0.601409i
$162$	1.59027	−	12.6282i	0.124944	−	0.992164i
$163$	5.63078	−	9.75279i	0.441036	−	0.763897i	−0.556730	−	0.830693i	$-0.687944\pi$
$163$	5.63078	−	9.75279i	0.441036	−	0.763897i	0.997767	+	0.0667959i	$0.0212776\pi$
$164$	−3.31868	+	13.9318i	−0.259145	+	1.08789i
$165$	5.08057	−	2.91915i	0.395522	−	0.227256i
$166$	2.34627	+	0.275594i	0.182106	+	0.0213903i
$167$	−2.01609	+	3.49197i	−0.156010	+	0.270217i	−0.933426	−	0.358769i	$-0.883196\pi$
$167$	−2.01609	+	3.49197i	−0.156010	+	0.270217i	0.777416	+	0.628986i	$0.216530\pi$
$168$	−12.8336	−	1.81659i	−0.990130	−	0.140153i
$169$	−5.52404	−	9.56792i	−0.424926	−	0.735994i
$170$	11.5391	+	26.7926i	0.885008	+	2.05490i
$171$	4.10502	+	7.17912i	0.313919	+	0.549001i
$172$	−1.01258	+	1.07082i	−0.0772085	+	0.0816496i
$173$	−21.0357			−1.59931			−0.799657	−	0.600457i	$-0.794985\pi$
$173$	−21.0357			−1.59931			−0.799657	+	0.600457i	$0.794985\pi$
$174$	−8.35833	+	3.57913i	−0.633643	+	0.271333i
$175$	7.43936	−	6.73634i	0.562363	−	0.509219i
$176$	4.55622	−	0.254952i	0.343438	−	0.0192177i
$177$	−19.9207	+	11.4459i	−1.49733	+	0.860325i
$178$	−8.91016	−	20.6885i	−0.667845	−	1.55067i
$179$	−18.5382	+	10.7030i	−1.38561	+	0.799983i	−0.992817	−	0.119643i	$-0.961825\pi$
$179$	−18.5382	+	10.7030i	−1.38561	+	0.799983i	−0.392795	+	0.919626i	$0.628492\pi$
$180$	5.01220	+	17.0715i	0.373588	+	1.27243i
$181$		−	25.2709i		−	1.87837i	−0.343410	−	0.939186i	$-0.611582\pi$
$181$		−	25.2709i		−	1.87837i	0.343410	−	0.939186i	$-0.388418\pi$
$182$	0.497537	+	5.20377i	0.0368799	+	0.385729i
$183$	8.33530	−	4.78923i	0.616163	−	0.354030i
$184$	8.22086	−	1.43507i	0.606050	−	0.105795i
$185$		−	20.2868i		−	1.49152i
$186$	−23.3139	−	2.78780i	−1.70946	−	0.204411i
$187$	7.93591			0.580331
$188$	−4.14767	−	13.9119i	−0.302500	−	1.01463i
$189$	−13.0601	−	4.29340i	−0.949984	−	0.312299i
$190$	−9.26883	−	6.90860i	−0.672432	−	0.501203i
$191$	19.9752			1.44535			0.722676	−	0.691187i	$-0.242912\pi$
$191$	19.9752			1.44535			0.722676	+	0.691187i	$0.242912\pi$
$192$	−2.48123	+	13.6324i	−0.179067	+	0.983837i
$193$	−7.63813			−0.549805			−0.274902	−	0.961472i	$-0.588646\pi$
$193$	−7.63813			−0.549805			−0.274902	+	0.961472i	$0.588646\pi$
$194$	−3.05931	+	26.0454i	−0.219646	+	1.86995i
$195$	6.22184	−	3.57489i	0.445555	−	0.256003i
$196$	−4.57574	+	13.2311i	−0.326839	+	0.945080i
$197$	16.9024			1.20425			0.602123	−	0.798403i	$-0.294322\pi$
$197$	16.9024			1.20425			0.602123	+	0.798403i	$0.294322\pi$
$198$	4.80472	+	0.584703i	0.341456	+	0.0415530i
$199$	−8.95516	+	5.17026i	−0.634814	+	0.366510i	−0.782614	−	0.622507i	$-0.786114\pi$
$199$	−8.95516	+	5.17026i	−0.634814	+	0.366510i	0.147800	+	0.989017i	$0.452781\pi$
$200$	−6.88240	−	8.23066i	−0.486660	−	0.581996i
$201$	−0.0739776	−	0.128753i	−0.00521797	−	0.00908150i
$202$	−0.0418641	+	0.0180301i	−0.00294555	+	0.00126860i
$203$	2.06884	+	9.60054i	0.145204	+	0.673826i
$204$	−5.63277	+	23.4294i	−0.394373	+	1.64039i
$205$		−	21.2343i		−	1.48307i
$206$	−20.5677	−	2.41590i	−1.43302	−	0.168324i
$207$	8.85132	+	0.0369361i	0.615209	+	0.00256724i
$208$	5.57971	−	0.312223i	0.386883	−	0.0216487i
$209$	−2.72353	+	1.57243i	−0.188391	+	0.108767i
$210$	19.1342	−	1.78915i	1.32038	−	0.123463i
$211$	5.34466	−	9.25722i	0.367941	−	0.637293i	−0.621302	−	0.783571i	$-0.713396\pi$
$211$	5.34466	−	9.25722i	0.367941	−	0.637293i	0.989244	+	0.146278i	$0.0467294\pi$
$212$	11.6364	−	12.3057i	0.799188	−	0.845159i
$213$	−5.29782	−	9.22047i	−0.363001	−	0.631776i
$214$	0.912749	+	2.11931i	0.0623943	+	0.144873i
$215$	1.09256	−	1.89236i	0.0745117	−	0.129058i
$216$	−5.13654	+	13.7701i	−0.349497	+	0.936937i
$217$	−7.76935	+	24.1419i	−0.527418	+	1.63886i
$218$	−5.73173	−	0.673253i	−0.388201	−	0.0455985i
$219$	5.60767	−	9.66614i	0.378931	−	0.653177i
$220$	−6.48392	+	1.93311i	−0.437146	+	0.130330i
$221$	9.71859			0.653743
$222$	10.0427	−	13.4151i	0.674020	−	0.900363i
$223$	−3.87836	+	2.23917i	−0.259714	+	0.149946i	−0.624204	−	0.781261i	$-0.714577\pi$
$223$	−3.87836	+	2.23917i	−0.259714	+	0.149946i	0.364490	+	0.931207i	$0.381243\pi$
$224$	13.9409	+	5.44535i	0.931464	+	0.363833i
$225$	−5.64873	−	9.87887i	−0.376582	−	0.658591i
$226$	−0.437198	−	1.01513i	−0.0290820	−	0.0675253i
$227$	−8.77885	−	5.06847i	−0.582673	−	0.336406i	0.179522	−	0.983754i	$-0.442545\pi$
$227$	−8.77885	−	5.06847i	−0.582673	−	0.336406i	−0.762195	+	0.647348i	$0.775878\pi$
$228$	−2.70923	−	9.15686i	−0.179423	−	0.606428i
$229$	5.46210	−	3.15354i	0.360946	−	0.208392i	−0.308550	−	0.951208i	$-0.599844\pi$
$229$	5.46210	−	3.15354i	0.360946	−	0.208392i	0.669496	+	0.742816i	$0.266510\pi$
$230$	−11.3640	+	4.89428i	−0.749322	+	0.322720i
$231$	1.61195	−	4.97326i	0.106059	−	0.327217i
$232$	10.3426	−	1.80546i	0.679025	−	0.118534i
$233$	−19.2136	−	11.0930i	−1.25872	−	0.726724i	−0.285897	−	0.958260i	$-0.592291\pi$
$233$	−19.2136	−	11.0930i	−1.25872	−	0.726724i	−0.972826	+	0.231536i	$0.925625\pi$
$234$	5.88402	+	0.716047i	0.384651	+	0.0468095i
$235$	10.7620	+	18.6403i	0.702033	+	1.21596i
$236$	25.4232	−	7.57965i	1.65491	−	0.493393i
$237$	−4.91551	+	2.82431i	−0.319297	+	0.183459i
$238$	23.6770	+	10.8094i	1.53475	+	0.700672i
$239$	−1.04797	+	1.81514i	−0.0677876	+	0.117412i	−0.897927	−	0.440144i	$-0.854927\pi$
$239$	−1.04797	+	1.81514i	−0.0677876	+	0.117412i	0.830140	+	0.557556i	$0.188261\pi$
$240$	−1.10501	−	20.5148i	−0.0713280	−	1.32422i
$241$	−0.650394	+	1.12652i	−0.0418956	+	0.0725652i	−0.886213	−	0.463278i	$-0.846673\pi$
$241$	−0.650394	+	1.12652i	−0.0418956	+	0.0725652i	0.844317	+	0.535844i	$0.180006\pi$
$242$	1.60006	−	13.6221i	0.102856	−	0.875661i
$243$	−7.93464	+	13.4180i	−0.509007	+	0.860762i
$244$	−10.6377	+	3.17151i	−0.681007	+	0.203035i
$245$	2.05383	−	20.6556i	0.131214	−	1.31964i
$246$	10.5117	−	14.0417i	0.670202	−	0.895264i
$247$	−3.33533	+	1.92566i	−0.212222	+	0.122527i
$248$	25.4614	+	9.31652i	1.61680	+	0.591599i
$249$	−2.50268	−	1.45189i	−0.158601	−	0.0920099i
$250$	−4.05748	−	3.02428i	−0.256618	−	0.191272i
$251$		−	29.4615i		−	1.85959i	−0.368075	−	0.929796i	$-0.619983\pi$
$251$		−	29.4615i		−	1.85959i	0.368075	−	0.929796i	$-0.380017\pi$
$252$	13.5386	+	8.28895i	0.852851	+	0.522155i
$253$			3.36600i			0.211619i
$254$	−0.00746198	+	0.0100113i	−0.000468206	+	0.000628162i
$255$	0.0745450	−	35.7279i	0.00466819	−	2.23737i
$256$	6.40418	−	14.6624i	0.400261	−	0.916401i
$257$	11.3672	−	6.56286i	0.709067	−	0.409380i	−0.101648	−	0.994820i	$-0.532412\pi$
$257$	11.3672	−	6.56286i	0.709067	−	0.409380i	0.810715	+	0.585440i	$0.199078\pi$
$258$	1.65926	−	0.710514i	0.103301	−	0.0442347i
$259$	−12.1492	−	13.4172i	−0.754916	−	0.833701i
$260$	−7.94043	+	2.36735i	−0.492445	+	0.146817i
$261$	11.1358	+	0.0464690i	0.689287	+	0.00287636i
$262$	−15.2019	−	1.78563i	−0.939175	−	0.110316i
$263$	−10.3474	+	17.9223i	−0.638049	+	1.10513i	0.347811	+	0.937565i	$0.386925\pi$
$263$	−10.3474	+	17.9223i	−0.638049	+	1.10513i	−0.985860	+	0.167569i	$0.946408\pi$
$264$	−5.24459	−	1.93145i	−0.322782	−	0.118873i
$265$	−12.5554	+	21.7466i	−0.771274	+	1.33588i
$266$	−10.2675	+	0.981687i	−0.629543	+	0.0601911i
$267$	−0.0575616	+	27.5881i	−0.00352271	+	1.68836i
$268$	0.0489892	+	0.164317i	0.00299249	+	0.0100372i
$269$	−1.78790	−	3.09674i	−0.109010	−	0.188812i	0.806359	−	0.591426i	$-0.201435\pi$
$269$	−1.78790	−	3.09674i	−0.109010	−	0.188812i	−0.915370	+	0.402614i	$0.868102\pi$
$270$	2.67750	−	21.6256i	0.162947	−	1.31609i
$271$	−10.2398	−	5.91194i	−0.622022	−	0.359125i	0.155634	−	0.987815i	$-0.450258\pi$
$271$	−10.2398	−	5.91194i	−0.622022	−	0.359125i	−0.777656	+	0.628690i	$0.783591\pi$
$272$	12.5444	−	24.8367i	0.760616	−	1.50594i
$273$	1.97405	−	6.09043i	0.119475	−	0.368610i
$274$	0.446994	+	1.03787i	0.0270039	+	0.0627003i
$275$	3.74773	−	2.16375i	0.225997	−	0.130479i
$276$	−9.93755	−	2.38913i	−0.598170	−	0.143809i
$277$	−9.46656	−	5.46552i	−0.568790	−	0.328391i	0.187876	−	0.982193i	$-0.439840\pi$
$277$	−9.46656	−	5.46552i	−0.568790	−	0.328391i	−0.756666	+	0.653801i	$0.773173\pi$
$278$	22.2995	−	9.60399i	1.33743	−	0.576009i
$279$	24.8441	+	14.4823i	1.48738	+	0.867033i
$280$	−21.9780	−	3.06422i	−1.31344	−	0.183122i
$281$	15.6538	−	9.03770i	0.933825	−	0.539144i	0.0458056	−	0.998950i	$-0.485415\pi$
$281$	15.6538	−	9.03770i	0.933825	−	0.539144i	0.888019	+	0.459806i	$0.152081\pi$
$282$	−2.11099	+	17.6538i	−0.125707	+	1.05127i
$283$	24.4519			1.45352			0.726759	−	0.686893i	$-0.241026\pi$
$283$	24.4519			1.45352			0.726759	+	0.686893i	$0.241026\pi$
$284$	3.50830	+	11.7673i	0.208180	+	0.698263i
$285$	7.05360	+	12.2763i	0.417819	+	0.727184i
$286$	−0.262958	+	2.23869i	−0.0155490	+	0.132376i
$287$	−12.7167	−	14.0438i	−0.750640	−	0.828980i
$288$	9.42481	−	14.1129i	0.555362	−	0.831609i
$289$	15.6944	−	27.1836i	0.923202	−	1.59903i
$290$	−14.2970	+	6.15746i	−0.839549	+	0.361579i
$291$	16.1171	−	27.7816i	0.944802	−	1.62859i
$292$	−8.86578	+	9.37575i	−0.518831	+	0.548675i
$293$	0.645475	−	1.11799i	0.0377090	−	0.0653140i	−0.846555	−	0.532301i	$-0.821327\pi$
$293$	0.645475	−	1.11799i	0.0377090	−	0.0653140i	0.884264	+	0.466987i	$0.154661\pi$
$294$	11.5834	−	12.6422i	0.675555	−	0.737310i
$295$	−34.0641	+	19.6669i	−1.98329	+	1.14505i
$296$	−14.8443	+	12.4127i	−0.862807	+	0.721471i
$297$	−5.11512	−	2.99606i	−0.296809	−	0.173849i
$298$	−1.77439	+	15.1062i	−0.102788	+	0.875079i
$299$			4.12212i			0.238388i
$300$	3.72805	+	12.6003i	0.215239	+	0.727481i
$301$	−0.410697	−	1.90586i	−0.0236722	−	0.109852i
$302$	7.16527	+	16.6370i	0.412315	+	0.957353i
$303$	0.0558258		0.000116479i	0.00320711		6.69152e-6i
$304$	0.616044	+	11.0093i	0.0353326	+	0.631426i
$305$	14.2532	−	8.22912i	0.816139	−	0.471198i
$306$	17.7358	−	23.5890i	1.01389	−	1.34849i
$307$	−24.5811			−1.40292			−0.701458	−	0.712711i	$-0.747467\pi$
$307$	−24.5811			−1.40292			−0.701458	+	0.712711i	$0.747467\pi$
$308$	−3.13060	+	5.16155i	−0.178383	+	0.294107i
$309$	21.9388	+	12.7275i	1.24805	+	0.724041i
$310$	−39.9243	−	4.68954i	−2.26755	−	0.266348i
$311$	−1.77599			−0.100707			−0.0503536	−	0.998731i	$-0.516035\pi$
$311$	−1.77599			−0.100707			−0.0503536	+	0.998731i	$0.516035\pi$
$312$	−6.42271	−	2.36532i	−0.363614	−	0.133910i
$313$	23.3288			1.31862			0.659310	−	0.751871i	$-0.270848\pi$
$313$	23.3288			1.31862			0.659310	+	0.751871i	$0.270848\pi$
$314$	−4.30995	+	5.78239i	−0.243225	+	0.326319i
$315$	−22.3748	−	7.30382i	−1.26068	−	0.411523i
$316$	6.27327	−	1.87031i	0.352899	−	0.105213i
$317$	−10.4508			−0.586973			−0.293487	−	0.955963i	$-0.594816\pi$
$317$	−10.4508			−0.586973			−0.293487	+	0.955963i	$0.594816\pi$
$318$	−19.0679	+	8.16508i	−1.06927	+	0.457875i
$319$			4.23474i			0.237100i
$320$	−4.19926	+	23.3481i	−0.234746	+	1.30520i
$321$	0.00589656	−	2.82610i	0.000329114	−	0.157738i
$322$	−4.58481	+	10.0426i	−0.255501	+	0.559650i
$323$			19.1757i			1.06696i
$324$	12.4760	−	12.9750i	0.693110	−	0.720832i
$325$	4.58960	−	2.64981i	0.254585	−	0.146985i
$326$	14.6273	−	6.29973i	0.810132	−	0.348910i
$327$	6.11382	+	3.54685i	0.338095	+	0.196141i
$328$	−15.5376	+	12.9924i	−0.857920	+	0.717385i
$329$	18.2808	+	5.88313i	1.00785	+	0.324347i
$330$	8.22795	+	0.983871i	0.452934	+	0.0541603i
$331$	−21.9170			−1.20467			−0.602333	−	0.798245i	$-0.705762\pi$
$331$	−21.9170			−1.20467			−0.602333	+	0.798245i	$0.705762\pi$
$332$	2.42749	+	2.29545i	0.133226	+	0.125979i
$333$	−17.8169	+	10.1877i	−0.976359	+	0.558282i
$334$	−5.23729	+	2.25561i	−0.286572	+	0.123421i
$335$	−0.127112	−	0.220165i	−0.00694489	−	0.0120289i
$336$	−13.0166	−	12.9062i	−0.710112	−	0.704089i
$337$	−11.1845	+	19.3722i	−0.609260	+	1.05527i	0.382103	+	0.924120i	$0.375200\pi$
$337$	−11.1845	+	19.3722i	−0.609260	+	1.05527i	−0.991363	+	0.131149i	$0.958133\pi$
$338$	1.82272	−	15.5177i	0.0991428	−	0.844050i
$339$	−0.00282439	+	1.35367i	−0.000153400	+	0.0735215i
$340$	−9.55983	+	40.1322i	−0.518454	+	2.17648i
$341$	−5.46785	+	9.47059i	−0.296101	+	0.512861i
$342$	−1.41283	+	11.6097i	−0.0763970	+	0.627782i
$343$	−11.0117	−	14.8910i	−0.594576	−	0.804039i
$344$	−2.05317	+	0.358412i	−0.110700	+	0.0193243i
$345$	15.1539	+	0.0316181i	0.815860	+	0.00170226i
$346$	−23.8522	−	17.7784i	−1.28230	−	0.955775i
$347$		−	25.9778i		−	1.39456i	−0.716797	−	0.697282i	$-0.754393\pi$
$347$		−	25.9778i		−	1.39456i	0.716797	−	0.697282i	$-0.245607\pi$
$348$	−12.5024	−	3.00575i	−0.670197	−	0.161125i
$349$	0.550681	−	0.317936i	0.0294773	−	0.0170187i	−0.485189	−	0.874409i	$-0.661249\pi$
$349$	0.550681	−	0.317936i	0.0294773	−	0.0170187i	0.514666	+	0.857391i	$0.327916\pi$
$350$	14.1287	−	1.35086i	0.755210	−	0.0722063i
$351$	−6.26415	−	3.66908i	−0.334356	−	0.195841i
$352$	5.38174	+	3.56163i	0.286848	+	0.189836i
$353$	24.8094	+	14.3237i	1.32047	+	0.762374i	0.983804	−	0.179249i	$-0.0573669\pi$
$353$	24.8094	+	14.3237i	1.32047	+	0.762374i	0.336667	+	0.941624i	$0.390700\pi$
$354$	−32.2615	−	3.85772i	−1.71468	−	0.205035i
$355$	−9.10301	−	15.7669i	−0.483138	−	0.836819i
$356$	7.38183	−	30.9890i	0.391236	−	1.64241i
$357$	−21.3472	−	23.6741i	−1.12981	−	1.25297i
$358$	−30.0661	−	3.53159i	−1.58904	−	0.186650i
$359$	−16.5975	+	28.7478i	−0.875984	+	1.51725i	−0.0202742	+	0.999794i	$0.506454\pi$
$359$	−16.5975	+	28.7478i	−0.875984	+	1.51725i	−0.855710	+	0.517455i	$0.826879\pi$
$360$	−8.74477	+	23.5933i	−0.460890	+	1.24348i
$361$	5.70050	+	9.87356i	0.300026	+	0.519661i
$362$	21.3579	−	28.6545i	1.12254	−	1.50605i
$363$	−8.42947	+	14.5302i	−0.442433	+	0.762637i
$364$	−3.83385	+	6.32101i	−0.200948	+	0.331311i
$365$	9.56602	−	16.5688i	0.500708	−	0.867253i
$366$	13.4990	+	1.61416i	0.705603	+	0.0843736i
$367$	15.8743	+	9.16503i	0.828632	+	0.478411i	0.853384	−	0.521283i	$-0.174546\pi$
$367$	15.8743	+	9.16503i	0.828632	+	0.478411i	−0.0247524	+	0.999694i	$0.507880\pi$
$368$	10.5344	+	5.32069i	0.549145	+	0.277360i
$369$	−18.6490	+	10.6635i	−0.970829	+	0.555120i
$370$	17.1455	−	23.0031i	0.891353	−	1.19587i
$371$	4.71964	+	21.9017i	0.245032	+	1.13708i
$372$	−24.0793	−	22.8650i	−1.24846	−	1.18549i
$373$	21.9893	−	12.6955i	1.13856	−	0.657349i	0.192488	−	0.981299i	$-0.438344\pi$
$373$	21.9893	−	12.6955i	1.13856	−	0.657349i	0.946074	+	0.323950i	$0.105011\pi$
$374$	8.99846	+	6.70708i	0.465299	+	0.346815i
$375$	3.08775	+	5.37400i	0.159451	+	0.277512i
$376$	7.05468	−	19.2800i	0.363817	−	0.994289i
$377$			5.18601i			0.267093i
$378$	−11.1802	−	15.9061i	−0.575046	−	0.818121i
$379$	−12.4549			−0.639767			−0.319883	−	0.947457i	$-0.603644\pi$
$379$	−12.4549			−0.639767			−0.319883	+	0.947457i	$0.603644\pi$
$380$	−4.67101	−	15.6672i	−0.239618	−	0.803711i
$381$	0.0132596	−	0.00761858i	0.000679309	−	0.000390312i
$382$	22.6497	+	16.8821i	1.15886	+	0.863765i
$383$	7.04715	+	12.2060i	0.360093	+	0.623699i	0.987976	−	0.154609i	$-0.0494117\pi$
$383$	7.04715	+	12.2060i	0.360093	+	0.623699i	−0.627883	+	0.778308i	$0.716078\pi$
$384$	−14.3350	+	13.3607i	−0.731529	+	0.681810i
$385$	2.74196	−	8.52018i	0.139743	−	0.434228i
$386$	−8.66082	−	6.45541i	−0.440824	−	0.328572i
$387$	−2.21063	−	0.00922484i	−0.112373	−	0.000468925i
$388$	−25.4813	+	26.9470i	−1.29362	+	1.36803i
$389$	0.364741	−	0.631750i	0.0184931	−	0.0320310i	−0.856631	−	0.515930i	$-0.827446\pi$
$389$	0.364741	−	0.631750i	0.0184931	−	0.0320310i	0.875124	+	0.483899i	$0.160780\pi$
$390$	10.0762	+	1.20488i	0.510230	+	0.0610116i
$391$	17.7743	+	10.2620i	0.898887	+	0.518973i
$392$	−16.3708	+	11.1354i	−0.826848	+	0.562425i
$393$	16.2153	+	9.40706i	0.817953	+	0.474524i
$394$	19.1655	+	14.2852i	0.965544	+	0.719676i
$395$	−8.40545	+	4.85289i	−0.422924	+	0.244175i
$396$	4.95387	+	4.72372i	0.248941	+	0.237376i
$397$	−19.8907	−	11.4839i	−0.998284	−	0.576359i	−0.0905437	−	0.995892i	$-0.528860\pi$
$397$	−19.8907	−	11.4839i	−0.998284	−	0.576359i	−0.907740	+	0.419533i	$0.862194\pi$
$398$	−14.5239	−	1.70599i	−0.728016	−	0.0855133i
$399$	12.0170	+	3.89499i	0.601602	+	0.194993i
$400$	−0.847711	−	15.1494i	−0.0423856	−	0.757469i
$401$	15.6393	−	9.02937i	0.780991	−	0.450905i	−0.0557906	−	0.998442i	$-0.517768\pi$
$401$	15.6393	−	9.02937i	0.780991	−	0.450905i	0.836781	+	0.547537i	$0.184435\pi$
$402$	0.0249334	−	0.208514i	0.00124357	−	0.0103997i
$403$	−6.69612	+	11.5980i	−0.333557	+	0.577738i
$404$	−0.0627076	−	0.0149375i	−0.00311982	−	0.000743167i
$405$	−13.5365	+	23.0004i	−0.672633	+	1.14290i
$406$	−5.76811	+	12.6345i	−0.286267	+	0.627038i
$407$	−3.90240	−	6.75916i	−0.193435	−	0.335039i
$408$	−26.1885	+	21.8059i	−1.29652	+	1.07955i
$409$	5.36527			0.265295			0.132648	−	0.991163i	$-0.457652\pi$
$409$	5.36527			0.265295			0.132648	+	0.991163i	$0.457652\pi$
$410$	17.9463	−	24.0774i	0.886305	−	1.18910i
$411$	0.00288768	−	1.38401i	0.000142439	−	0.0682680i
$412$	−21.2797	−	20.1223i	−1.04838	−	0.991353i
$413$	−10.7511	+	33.4073i	−0.529028	+	1.64386i
$414$	10.0052	+	7.52262i	0.491730	+	0.369717i
$415$	−4.28986	−	2.47675i	−0.210581	−	0.121579i
$416$	6.59067	+	4.36170i	0.323134	+	0.213850i
$417$	−29.7364	−	0.0620439i	−1.45620	−	0.00303830i
$418$	−4.41714	−	0.518841i	−0.216049	−	0.0253774i
$419$	−6.06325	−	3.50062i	−0.296209	−	0.171016i	0.344530	−	0.938775i	$-0.388038\pi$
$419$	−6.06325	−	3.50062i	−0.296209	−	0.171016i	−0.640739	+	0.767759i	$0.721372\pi$
$420$	23.2082	+	14.1426i	1.13244	+	0.690091i
$421$	−19.5737	+	11.3009i	−0.953965	+	0.550772i	−0.894310	−	0.447447i	$-0.852333\pi$
$421$	−19.5737	+	11.3009i	−0.953965	+	0.550772i	−0.0596548	+	0.998219i	$0.519000\pi$
$422$	13.8841	−	5.97962i	0.675865	−	0.291083i
$423$	10.9663	−	18.8125i	0.533202	−	0.914696i
$424$	23.5946	−	4.11879i	1.14586	−	0.200026i
$425$		−	26.3868i		−	1.27995i
$426$	1.78558	−	14.9325i	0.0865115	−	0.723482i
$427$	4.49852	−	13.9784i	0.217699	−	0.676462i
$428$	−0.756188	+	3.17448i	−0.0365517	+	0.153445i
$429$	1.38532	−	2.38793i	0.0668839	−	0.115290i
$430$	2.83818	−	1.22235i	0.136869	−	0.0589472i
$431$	0.486209	+	0.842138i	0.0234198	+	0.0405644i	0.877498	−	0.479581i	$-0.159211\pi$
$431$	0.486209	+	0.842138i	0.0234198	+	0.0405644i	−0.854078	+	0.520145i	$0.825878\pi$
$432$	−17.4622	+	11.2726i	−0.840149	+	0.542355i
$433$	12.3302			0.592550			0.296275	−	0.955103i	$-0.404255\pi$
$433$	12.3302			0.592550			0.296275	+	0.955103i	$0.404255\pi$
$434$	−29.2133	+	20.8080i	−1.40228	+	0.998818i
$435$	19.0651	+	0.0397786i	0.914099	+	0.00190724i
$436$	−5.93015	−	5.60760i	−0.284003	−	0.268555i
$437$	−8.13333			−0.389070
$438$	14.5279	−	6.22100i	0.694169	−	0.297251i
$439$			10.7891i			0.514934i	0.966287	+	0.257467i	$0.0828878\pi$
$439$			10.7891i			0.514934i	−0.966287	+	0.257467i	$0.917112\pi$
$440$	−8.98585	−	3.28799i	−0.428383	−	0.156749i
$441$	−19.1721	+	8.56909i	−0.912959	+	0.408052i
$442$	11.0198	+	8.21372i	0.524160	+	0.390687i
$443$			15.8657i			0.753801i	0.926254	+	0.376900i	$0.123010\pi$
$443$			15.8657i			0.753801i	−0.926254	+	0.376900i	$0.876990\pi$
$444$	22.7252	−	6.72366i	1.07849	−	0.319091i
$445$			47.2321i			2.23902i
$446$	−6.29010	−	0.738840i	−0.297845	−	0.0349851i
$447$	9.34787	−	16.1132i	0.442139	−	0.762130i
$448$	11.2053	+	17.9567i	0.529400	+	0.848372i
$449$			1.99481i			0.0941409i	0.998892	+	0.0470705i	$0.0149885\pi$
$449$			1.99481i			0.0941409i	−0.998892	+	0.0470705i	$0.985011\pi$
$450$	1.94413	−	15.9756i	0.0916471	−	0.753098i
$451$	−4.08467	−	7.07485i	−0.192339	−	0.333142i
$452$	0.362207	−	1.52055i	0.0170368	−	0.0715205i
$453$	0.0462892	−	22.1855i	0.00217486	−	1.04236i
$454$	−5.67062	−	13.1666i	−0.266135	−	0.617939i
$455$	3.35790	−	10.4341i	0.157421	−	0.489158i
$456$	4.66700	−	12.6726i	0.218552	−	0.593449i
$457$	14.2346			0.665864			0.332932	−	0.942951i	$-0.391962\pi$
$457$	14.2346			0.665864			0.332932	+	0.942951i	$0.391962\pi$
$458$	8.85867	+	1.04055i	0.413938	+	0.0486215i
$459$	−31.4155	+	17.8765i	−1.46635	+	0.834402i
$460$	−17.0220	−	4.05478i	−0.793655	−	0.189055i
$461$	10.7109	+	18.5519i	0.498858	+	0.864047i	0.999999	−	0.00131840i	$-0.000419659\pi$
$461$	10.7109	+	18.5519i	0.498858	+	0.864047i	−0.501141	+	0.865365i	$0.667086\pi$
$462$	6.03096	−	4.27679i	0.280586	−	0.198974i
$463$	−24.0952	−	13.9114i	−1.11980	−	0.646516i	−0.178449	−	0.983949i	$-0.557108\pi$
$463$	−24.0952	−	13.9114i	−1.11980	−	0.646516i	−0.941350	+	0.337433i	$0.890441\pi$
$464$	13.2533	+	6.69392i	0.615268	+	0.310757i
$465$	42.5858	+	24.7055i	1.97487	+	1.14569i
$466$	−12.4108	−	28.8167i	−0.574921	−	1.33491i
$467$	−2.94612	−	1.70094i	−0.136330	−	0.0787103i	0.430284	−	0.902694i	$-0.358414\pi$
$467$	−2.94612	−	1.70094i	−0.136330	−	0.0787103i	−0.566614	+	0.823983i	$0.691747\pi$
$468$	6.06668	+	5.78484i	0.280432	+	0.267404i
$469$	−0.215920	−	0.0694872i	−0.00997024	−	0.00320862i
$470$	−3.55103	+	30.2316i	−0.163797	+	1.39448i
$471$	7.65859	−	4.40041i	0.352889	−	0.202760i
$472$	35.2331	+	12.8921i	1.62174	+	0.593405i
$473$		−	0.840663i		−	0.0386537i
$474$	−7.96064	−	0.951906i	−0.365644	−	0.0437225i
$475$	5.22832	+	9.05571i	0.239892	+	0.415505i
$476$	17.7115	+	32.2675i	0.811805	+	1.47898i
$477$	25.4041	+	0.106010i	1.16317	+	0.00485386i
$478$	−2.72236	+	1.17247i	−0.124518	+	0.0536277i
$479$	−1.81041	+	3.13571i	−0.0827195	+	0.143274i	−0.904417	−	0.426649i	$-0.859694\pi$
$479$	−1.81041	+	3.13571i	−0.0827195	+	0.143274i	0.821698	+	0.569924i	$0.193027\pi$
$480$	16.0852	−	24.1954i	0.734187	−	1.10437i
$481$	−4.77902	−	8.27751i	−0.217905	−	0.377422i
$482$	−1.68956	+	0.727663i	−0.0769573	+	0.0331441i
$483$	10.0413	−	9.05437i	0.456897	−	0.411988i
$484$	13.3271	−	14.0937i	0.605777	−	0.640622i
$485$	27.4939	−	47.6208i	1.24843	−	2.16235i
$486$	−20.3373	+	8.50851i	−0.922518	+	0.385954i
$487$	14.7575	−	8.52025i	0.668726	−	0.386089i	−0.126868	−	0.991920i	$-0.540492\pi$
$487$	14.7575	−	8.52025i	0.668726	−	0.386089i	0.795594	+	0.605830i	$0.207159\pi$
$488$	−14.7424	−	5.39435i	−0.667357	−	0.244191i
$489$	−19.5055	−	0.0406976i	−0.882071	−	0.00184041i
$490$	19.7860	−	21.6854i	0.893840	−	0.979645i
$491$	8.58757	+	4.95803i	0.387551	+	0.223753i	0.681099	−	0.732192i	$-0.261502\pi$
$491$	8.58757	+	4.95803i	0.387551	+	0.223753i	−0.293547	+	0.955945i	$0.594836\pi$
$492$	23.7865	−	7.03769i	1.07238	−	0.317284i
$493$	22.3618	+	12.9106i	1.00712	+	0.581463i
$494$	−5.40939	−	0.635391i	−0.243380	−	0.0285876i
$495$	−8.76798	−	5.11110i	−0.394091	−	0.229727i
$496$	20.9966	+	32.0828i	0.942775	+	1.44056i
$497$	−15.4628	−	4.97625i	−0.693603	−	0.223215i
$498$	−1.61069	−	3.76144i	−0.0721767	−	0.168554i
$499$	13.1663	+	22.8047i	0.589405	+	1.02088i	0.994311	+	0.106520i	$0.0339710\pi$
$499$	13.1663	+	22.8047i	0.589405	+	1.02088i	−0.404906	+	0.914358i	$0.632696\pi$
$500$	−2.04476	−	6.85841i	−0.0914444	−	0.306717i
$501$	6.98393	+	0.0145717i	0.312019	+	0.000651017i
$502$	24.8995	−	33.4061i	1.11132	−	1.49099i
$503$	41.7727			1.86255			0.931275	−	0.364316i	$-0.118697\pi$
$503$	41.7727			1.86255			0.931275	+	0.364316i	$0.118697\pi$
$504$	8.34584	+	20.8410i	0.371753	+	0.928332i
$505$	0.0955764			0.00425309
$506$	−2.84480	+	3.81668i	−0.126467	+	0.169672i
$507$	−9.60248	+	16.5521i	−0.426461	+	0.735106i
$508$	−0.0169222	+	0.00504515i	−0.000750799	+	0.000223843i
$509$	−2.17065	−	3.75968i	−0.0962125	−	0.166645i	0.813902	−	0.581003i	$-0.197339\pi$
$509$	−2.17065	−	3.75968i	−0.0962125	−	0.166645i	−0.910114	+	0.414358i	$0.864006\pi$
$510$	30.2802	−	40.4486i	1.34083	−	1.79109i
$511$	−3.59591	−	16.6870i	−0.159074	−	0.738190i
$512$	19.6537	−	11.2131i	0.868578	−	0.495552i
$513$	7.23943	−	12.3598i	0.319629	−	0.545696i
$514$	18.4358	+	2.16549i	0.813170	+	0.0955156i
$515$	37.6055	+	21.7116i	1.65710	+	0.956726i
$516$	2.48192	+	0.596688i	0.109260	+	0.0262677i
$517$	7.17135	+	4.14038i	0.315396	+	0.182094i
$518$	−2.43632	−	25.4816i	−0.107046	−	1.11960i
$519$	18.1516	+	31.5915i	0.796765	+	1.38671i
$520$	−11.0044	−	4.02658i	−0.482574	−	0.176577i
$521$	10.7982	−	6.23437i	0.473080	−	0.273133i	−0.244448	−	0.969662i	$-0.578607\pi$
$521$	10.7982	−	6.23437i	0.473080	−	0.273133i	0.717528	+	0.696530i	$0.245273\pi$
$522$	12.5875	+	9.46416i	0.550940	+	0.414235i
$523$	8.96085	−	15.5207i	0.391831	−	0.678671i	−0.600860	−	0.799354i	$-0.705175\pi$
$523$	8.96085	−	15.5207i	0.391831	−	0.678671i	0.992691	+	0.120683i	$0.0385086\pi$
$524$	−15.7282	−	14.8727i	−0.687088	−	0.649715i
$525$	−16.5360	−	5.35972i	−0.721692	−	0.233917i
$526$	−26.8800	+	11.5767i	−1.17202	+	0.504769i
$527$	33.3400	+	57.7465i	1.45231	+	2.51548i
$528$	−4.31442	−	6.62256i	−0.187761	−	0.288210i
$529$	7.14738	−	12.3796i	0.310756	−	0.538245i
$530$	−32.6158	+	14.0470i	−1.41674	+	0.610165i
$531$	34.3789	+	20.0404i	1.49192	+	0.869680i
$532$	−12.4720	−	7.56454i	−0.540728	−	0.327964i
$533$	−5.00223	−	8.66411i	−0.216670	−	0.375284i
$534$	−23.3815	+	31.2333i	−1.01182	+	1.35160i
$535$		−	4.83842i		−	0.209183i
$536$	−0.0833247	+	0.227721i	−0.00359908	+	0.00983604i
$537$	32.0704	+	18.6052i	1.38394	+	0.802872i
$538$	0.589939	−	5.02243i	0.0254341	−	0.216532i
$539$	−3.28904	−	7.27710i	−0.141669	−	0.313447i
$540$	21.3130	−	22.2582i	0.917166	−	0.957841i
$541$	18.7187	+	10.8073i	0.804781	+	0.464641i	0.845140	−	0.534544i	$-0.179517\pi$
$541$	18.7187	+	10.8073i	0.804781	+	0.464641i	−0.0403589	+	0.999185i	$0.512850\pi$
$542$	−6.61429	−	15.3577i	−0.284108	−	0.659670i
$543$	−37.9519	+	21.8061i	−1.62867	+	0.935790i
$544$	35.2149	−	17.5601i	1.50982	−	0.752884i
$545$	10.4798	+	6.05050i	0.448904	+	0.259175i
$546$	7.38573	−	5.23751i	0.316080	−	0.224145i
$547$	−3.38402	−	5.86130i	−0.144690	−	0.250611i	0.784567	−	0.620044i	$-0.212885\pi$
$547$	−3.38402	−	5.86130i	−0.144690	−	0.250611i	−0.929257	+	0.369433i	$0.879552\pi$
$548$	−0.370323	+	1.55462i	−0.0158194	+	0.0664099i
$549$	−14.3850	−	8.38539i	−0.613935	−	0.357880i
$550$	6.07823	+	0.713954i	0.259177	+	0.0304431i
$551$	−10.2325			−0.435919
$552$	−9.24892	−	11.1078i	−0.393660	−	0.472779i
$553$	−2.65288	+	8.24337i	−0.112812	+	0.350544i
$554$	−6.11484	−	14.1980i	−0.259795	−	0.603217i
$555$	−30.4668	+	17.5054i	−1.29324	+	0.743061i
$556$	33.4021	+	7.95665i	1.41656	+	0.337437i
$557$	−16.1137	−	27.9097i	−0.682759	−	1.18257i	−0.974135	−	0.225965i	$-0.927447\pi$
$557$	−16.1137	−	27.9097i	−0.682759	−	1.18257i	0.291377	−	0.956608i	$-0.405887\pi$
$558$	15.9307	+	37.4185i	0.674401	+	1.58405i
$559$		−	1.02951i		−	0.0435435i
$560$	−22.3310	−	22.0494i	−0.943656	−	0.931756i
$561$	−6.84784	−	11.9182i	−0.289116	−	0.503186i
$562$	25.3879	+	2.98209i	1.07093	+	0.125792i
$563$			19.1129i			0.805513i	0.915307	+	0.402757i	$0.131948\pi$
$563$			19.1129i			0.805513i	−0.915307	+	0.402757i	$0.868052\pi$
$564$	−17.3139	+	18.2334i	−0.729046	+	0.767766i
$565$			2.31755i			0.0975002i
$566$	27.7259	+	20.6657i	1.16541	+	0.868644i
$567$	4.82165	+	23.3185i	0.202490	+	0.979284i
$568$	−5.96720	+	16.3080i	−0.250378	+	0.684267i
$569$			27.5472i			1.15484i	0.816447	+	0.577420i	$0.195940\pi$
$569$			27.5472i			1.15484i	−0.816447	+	0.577420i	$0.804060\pi$
$570$	−2.37735	+	19.8814i	−0.0995760	+	0.832738i
$571$	−8.74302			−0.365884			−0.182942	−	0.983124i	$-0.558562\pi$
$571$	−8.74302			−0.365884			−0.182942	+	0.983124i	$0.558562\pi$
$572$	−2.19021	+	2.31619i	−0.0915772	+	0.0968448i
$573$	−17.2364	−	29.9988i	−0.720063	−	1.25322i
$574$	−2.55011	−	26.6717i	−0.106439	−	1.11326i
$575$	11.1919			0.466735
$576$	22.6143	−	8.03704i	0.942262	−	0.334877i
$577$	−22.4732	−	38.9247i	−0.935572	−	1.62046i	−0.773612	−	0.633660i	$-0.781552\pi$
$577$	−22.4732	−	38.9247i	−0.935572	−	1.62046i	−0.161960	−	0.986797i	$-0.551782\pi$
$578$	40.7701	−	17.5590i	1.69581	−	0.730357i
$579$	6.59090	+	11.4710i	0.273908	+	0.476718i
$580$	−21.4153	−	5.10129i	−0.889221	−	0.211820i
$581$	−4.32046	+	0.931024i	−0.179243	+	0.0386254i
$582$	41.7549	−	17.8799i	1.73080	−	0.741146i
$583$			9.66073i			0.400106i
$584$	−17.9768	+	3.13812i	−0.743886	+	0.129856i
$585$	−10.7376	−	6.25923i	−0.443944	−	0.258787i
$586$	1.67678	−	0.722159i	0.0692671	−	0.0298321i
$587$	−8.03849	+	4.64103i	−0.331784	+	0.191556i	−0.656633	−	0.754210i	$-0.728020\pi$
$587$	−8.03849	+	4.64103i	−0.331784	+	0.191556i	0.324849	+	0.945766i	$0.394687\pi$
$588$	23.8189	−	4.54519i	0.982276	−	0.187440i
$589$	−22.8840	−	13.2121i	−0.942918	−	0.544394i
$590$	−55.2467	−	6.48932i	−2.27447	−	0.267161i
$591$	−14.5850	−	25.3841i	−0.599946	−	1.04416i
$592$	−27.3225	+	1.52888i	−1.12295	+	0.0628365i
$593$	−25.0584	−	14.4675i	−1.02902	−	0.594107i	−0.112319	−	0.993672i	$-0.535828\pi$
$593$	−25.0584	−	14.4675i	−1.02902	−	0.594107i	−0.916705	+	0.399565i	$0.869161\pi$
$594$	−3.26785	−	7.72028i	−0.134082	−	0.316767i
$595$	−36.6318	−	40.4548i	−1.50176	−	1.65848i
$596$	−14.7791	+	15.6292i	−0.605374	+	0.640196i
$597$	15.4921	+	8.98750i	0.634048	+	0.367834i
$598$	−3.48384	+	4.67404i	−0.142465	+	0.191136i
$599$	9.37877			0.383206			0.191603	−	0.981473i	$-0.438631\pi$
$599$	9.37877			0.383206			0.191603	+	0.981473i	$0.438631\pi$
$600$	−6.42205	+	17.4382i	−0.262179	+	0.711912i
$601$	−1.59314	−	2.75940i	−0.0649855	−	0.112558i	0.831702	−	0.555222i	$-0.187367\pi$
$601$	−1.59314	−	2.75940i	−0.0649855	−	0.112558i	−0.896688	+	0.442664i	$0.854033\pi$
$602$	1.14506	−	2.50814i	0.0466693	−	0.102224i
$603$	−0.129526	+	0.222200i	−0.00527472	+	0.00904866i
$604$	−5.93624	+	24.9204i	−0.241542	+	1.01400i
$605$	−14.3797	+	24.9063i	−0.584617	+	1.01259i
$606$	0.0632020	+	0.0473136i	0.00256741	+	0.00192198i
$607$	−7.62883	+	4.40451i	−0.309645	+	0.178773i	−0.646767	−	0.762687i	$-0.723880\pi$
$607$	−7.62883	+	4.40451i	−0.309645	+	0.178773i	0.337123	+	0.941461i	$0.390546\pi$
$608$	−8.60604	+	13.0040i	−0.349021	+	0.527382i
$609$	12.6329	−	11.3912i	0.511912	−	0.461596i
$610$	23.1165	+	2.71529i	0.935961	+	0.109939i
$611$	8.78229	+	5.07045i	0.355293	+	0.205129i
$612$	40.0469	−	11.7578i	1.61880	−	0.475281i
$613$	7.60056	−	4.38818i	0.306984	−	0.177237i	−0.338592	−	0.940933i	$-0.609951\pi$
$613$	7.60056	−	4.38818i	0.306984	−	0.177237i	0.645576	+	0.763696i	$0.276617\pi$
$614$	−27.8723	−	20.7748i	−1.12483	−	0.838405i
$615$	−31.8898	+	18.3230i	−1.28592	+	0.738853i
$616$	−7.91208	+	3.20679i	−0.318787	+	0.129205i
$617$	13.5521	+	7.82430i	0.545587	+	0.314995i	0.747340	−	0.664442i	$-0.231331\pi$
$617$	13.5521	+	7.82430i	0.545587	+	0.314995i	−0.201753	+	0.979436i	$0.564664\pi$
$618$	14.1195	+	32.9733i	0.567971	+	1.32638i
$619$	−18.4725	+	31.9953i	−0.742473	+	1.28600i	0.208894	+	0.977938i	$0.433014\pi$
$619$	−18.4725	+	31.9953i	−0.742473	+	1.28600i	−0.951366	+	0.308062i	$0.900320\pi$
$620$	−41.3065	−	39.0597i	−1.65891	−	1.56868i
$621$	−7.58227	−	13.3248i	−0.304266	−	0.534706i
$622$	−2.01378	−	1.50099i	−0.0807453	−	0.0601842i
$623$	28.2860	+	31.2381i	1.13326	+	1.25153i
$624$	−5.28359	−	8.11021i	−0.211513	−	0.324668i
$625$	14.7887	+	25.6148i	0.591549	+	1.02459i
$626$	26.4523	+	19.7165i	1.05725	+	0.788028i
$627$	4.71160	+	2.73337i	0.188163	+	0.109160i
$628$	−9.77404	+	2.91402i	−0.390027	+	0.116282i
$629$	−47.5895			−1.89752
$630$	−19.1977	−	27.1919i	−0.764855	−	1.08335i
$631$			28.0831i			1.11797i	0.829178	+	0.558985i	$0.188809\pi$
$631$			28.0831i			1.11797i	−0.829178	+	0.558985i	$0.811191\pi$
$632$	8.69391	+	3.18117i	0.345825	+	0.126540i
$633$	−18.5144	−	0.0386296i	−0.735881	−	0.00153539i
$634$	−11.8500	−	8.83253i	−0.470625	−	0.350784i
$635$	0.0226737	−	0.0130907i	0.000899779	−	0.000519488i
$636$	−28.5217	−	6.85702i	−1.13096	−	0.271898i
$637$	−4.02788	−	8.91179i	−0.159590	−	0.353098i
$638$	−3.57902	+	4.80174i	−0.141695	+	0.190103i
$639$	−9.27588	+	15.9126i	−0.366948	+	0.629492i
$640$	−24.4943	+	22.9252i	−0.968223	+	0.906200i
$641$	23.1409	+	13.3604i	0.914010	+	0.527704i	0.881719	−	0.471774i	$-0.156386\pi$
$641$	23.1409	+	13.3604i	0.914010	+	0.527704i	0.0322911	+	0.999479i	$0.489720\pi$
$642$	2.39518	−	3.19951i	0.0945303	−	0.126275i
$643$	−0.337904	+	0.585267i	−0.0133256	+	0.0230807i	−0.872611	−	0.488415i	$-0.837575\pi$
$643$	−0.337904	+	0.585267i	−0.0133256	+	0.0230807i	0.859286	+	0.511496i	$0.170908\pi$
$644$	−13.6862	+	7.51229i	−0.539312	+	0.296026i
$645$	−3.78472	−	0.00789668i	−0.149023	−	0.000310931i
$646$	−16.2064	+	21.7432i	−0.637634	+	0.855473i
$647$	−19.5544	−	33.8692i	−0.768761	−	1.33153i	−0.938235	−	0.345999i	$-0.887540\pi$
$647$	−19.5544	−	33.8692i	−0.768761	−	1.33153i	0.169473	−	0.985535i	$-0.445793\pi$
$648$	25.1123	−	4.16807i	0.986504	−	0.163737i
$649$	−7.56633	+	13.1053i	−0.297004	+	0.514427i
$650$	7.44361	+	0.874333i	0.291963	+	0.0342942i
$651$	42.9606	−	9.16389i	1.68376	−	0.359161i
$652$	21.9101	+	5.21916i	0.858064	+	0.204398i
$653$	−11.5857	−	20.0671i	−0.453385	−	0.785286i	0.545209	−	0.838300i	$-0.316450\pi$
$653$	−11.5857	−	20.0671i	−0.453385	−	0.785286i	−0.998594	+	0.0530143i	$0.983117\pi$
$654$	3.93478	+	9.18887i	0.153862	+	0.359313i
$655$	27.7948	+	16.0473i	1.08603	+	0.627021i
$656$	−28.5986	+	1.60028i	−1.11659	+	0.0624806i
$657$	−19.3555	−	0.0807693i	−0.755129	−	0.00315111i
$658$	15.7563	+	22.1210i	0.614246	+	0.862366i
$659$	14.8803	−	8.59117i	0.579656	−	0.334664i	−0.181341	−	0.983420i	$-0.558044\pi$
$659$	14.8803	−	8.59117i	0.579656	−	0.334664i	0.760997	+	0.648756i	$0.224710\pi$
$660$	8.49809	+	8.06951i	0.330788	+	0.314105i
$661$			5.58544i			0.217249i	0.994083	+	0.108624i	$0.0346445\pi$
$661$			5.58544i			0.217249i	−0.994083	+	0.108624i	$0.965355\pi$
$662$	−24.8515	−	18.5233i	−0.965880	−	0.719927i
$663$	−8.38611	−	14.5954i	−0.325689	−	0.566839i
$664$	0.812497	+	4.65441i	0.0315310	+	0.180626i
$665$	20.5875	+	6.62545i	0.798348	+	0.256924i
$666$	−28.8126	−	3.50631i	−1.11647	−	0.135867i
$667$	−5.47600	+	9.48471i	−0.212032	+	0.367249i
$668$	−7.84487	−	1.86871i	−0.303527	−	0.0723026i
$669$	6.70941	+	3.89237i	0.259401	+	0.150488i
$670$	0.0419421	−	0.357073i	0.00162037	−	0.0137949i
$671$	3.16593	−	5.48356i	0.122220	−	0.211690i
$672$	−3.85166	−	25.6352i	−0.148581	−	0.988900i
$673$	−23.7821	−	41.1918i	−0.916732	−	1.58783i	−0.804346	−	0.594162i	$-0.797484\pi$
$673$	−23.7821	−	41.1918i	−0.916732	−	1.58783i	−0.112386	−	0.993665i	$-0.535849\pi$
$674$	−29.0546	+	12.5133i	−1.11914	+	0.481994i
$675$	−9.96186	+	17.0077i	−0.383432	+	0.654627i
$676$	15.1816	−	16.0549i	0.583908	−	0.617495i
$677$	18.9855			0.729674			0.364837	−	0.931071i	$-0.381125\pi$
$677$	18.9855			0.729674			0.364837	+	0.931071i	$0.381125\pi$
$678$	−1.14727	+	1.53253i	−0.0440606	+	0.0588566i
$679$	−10.3351	−	47.9605i	−0.396624	−	1.84055i
$680$	−44.7578	+	37.4261i	−1.71638	+	1.43522i
$681$	−0.0366334	+	17.5577i	−0.00140380	+	0.672811i
$682$	−14.2041	+	6.11744i	−0.543902	+	0.234249i
$683$	11.9017	−	6.87144i	0.455405	−	0.262928i	−0.254705	−	0.967019i	$-0.581978\pi$
$683$	11.9017	−	6.87144i	0.455405	−	0.262928i	0.710110	+	0.704090i	$0.248645\pi$
$684$	−11.4140	+	11.9701i	−0.436426	+	0.457689i
$685$		−	2.36948i		−	0.0905332i
$686$	0.0991450	−	26.1914i	0.00378537	−	0.999993i
$687$	−9.44922	−	5.48183i	−0.360510	−	0.209145i
$688$	−2.63099	−	1.32885i	−0.100305	−	0.0506619i
$689$			11.8309i			0.450720i
$690$	17.1562	+	12.8433i	0.653125	+	0.488936i
$691$	25.5799			0.973104			0.486552	−	0.873652i	$-0.338254\pi$
$691$	25.5799			0.973104			0.486552	+	0.873652i	$0.338254\pi$
$692$	−12.0203	−	40.3177i	−0.456942	−	1.53265i
$693$	−8.85980	+	1.87056i	−0.336556	+	0.0710568i
$694$	21.9553	−	29.4561i	0.833413	−	1.11814i
$695$	−50.9100			−1.93113
$696$	−11.6360	−	13.9746i	−0.441062	−	0.529707i
$697$	−49.8122			−1.88677
$698$	0.893118	+	0.104906i	0.0338050	+	0.00397077i
$699$	−0.0801767	+	38.4271i	−0.00303256	+	1.45344i
$700$	17.1621	+	10.4092i	0.648666	+	0.393432i
$701$	10.6279			0.401412			0.200706	−	0.979652i	$-0.435676\pi$
$701$	10.6279			0.401412			0.200706	+	0.979652i	$0.435676\pi$
$702$	−4.00193	−	9.45452i	−0.151043	−	0.356838i
$703$	16.3323	−	9.42946i	0.615984	−	0.355639i
$704$	3.09218	+	8.58691i	0.116541	+	0.323631i
$705$	18.7076	−	32.2469i	0.704569	−	1.21449i
$706$	16.0254	+	37.2094i	0.603124	+	1.40039i
$707$	0.0632116	−	0.0572381i	0.00237732	−	0.00215266i
$708$	−33.3207	−	31.6402i	−1.25227	−	1.18911i
$709$		−	48.3588i		−	1.81615i	−0.418804	−	0.908077i	$-0.637550\pi$
$709$		−	48.3588i		−	1.81615i	0.418804	−	0.908077i	$-0.362450\pi$
$710$	3.00364	−	25.5714i	0.112725	−	0.959678i
$711$	8.48312	+	4.94505i	0.318142	+	0.185454i
$712$	34.5607	−	28.8994i	1.29522	−	1.08305i
$713$	−24.4931	+	14.1411i	−0.917274	+	0.529588i
$714$	−4.19706	−	44.8856i	−0.157071	−	1.67980i
$715$	2.36319	−	4.09317i	0.0883785	−	0.153076i
$716$	−31.1070	−	29.4150i	−1.16252	−	1.09929i
$717$	3.63027	+	0.00757443i	0.135575	+	0.000282872i
$718$	−43.1162	+	18.5694i	−1.60908	+	0.693003i
$719$	6.31109	−	10.9311i	0.235364	−	0.407663i	−0.724014	−	0.689785i	$-0.757705\pi$
$719$	6.31109	−	10.9311i	0.235364	−	0.407663i	0.959378	+	0.282122i	$0.0910384\pi$
$720$	−29.8557	+	19.3616i	−1.11265	+	0.721563i
$721$	37.8738	−	8.16149i	1.41049	−	0.303950i
$722$	−1.88094	+	16.0134i	−0.0700015	+	0.595956i
$723$	2.25303	+	0.00470086i	0.0837909	+	0.000174827i
$724$	48.4350	−	14.4404i	1.80007	−	0.536672i
$725$	14.0805			0.522935
$726$	−21.8384	+	9.35144i	−0.810498	+	0.347064i
$727$	2.18007	−	1.25867i	0.0808544	−	0.0466813i	−0.459028	−	0.888422i	$-0.651802\pi$
$727$	2.18007	−	1.25867i	0.0808544	−	0.0466813i	0.539882	+	0.841741i	$0.318469\pi$
$728$	−9.68941	+	3.92715i	−0.359114	+	0.145550i
$729$	26.9979	+	0.337998i	0.999922	+	0.0125184i
$730$	24.8501	−	10.7025i	0.919743	−	0.396117i
$731$	−4.43917	−	2.56296i	−0.164189	−	0.0947943i
$732$	13.9422	+	13.2390i	0.515317	+	0.489328i
$733$	−29.4083	+	16.9789i	−1.08622	+	0.627130i	−0.932568	−	0.360995i	$-0.882437\pi$
$733$	−29.4083	+	16.9789i	−1.08622	+	0.627130i	−0.153653	+	0.988125i	$0.549104\pi$
$734$	10.2539	+	23.8084i	0.378477	+	0.878784i
$735$	−32.7928	+	14.7391i	−1.20958	+	0.543660i
$736$	7.44809	+	14.9363i	0.274540	+	0.550560i
$737$	−0.0847027	−	0.0489031i	−0.00312006	−	0.00180137i
$738$	−30.1583	−	3.67007i	−1.11014	−	0.135097i
$739$	−5.29173	−	9.16555i	−0.194660	−	0.337160i	0.752129	−	0.659016i	$-0.229027\pi$
$739$	−5.29173	−	9.16555i	−0.194660	−	0.337160i	−0.946789	+	0.321855i	$0.895694\pi$
$740$	38.8823	−	11.5923i	1.42934	−	0.426143i
$741$	5.76999	+	3.34738i	0.211966	+	0.122969i
$742$	−13.1588	+	28.8230i	−0.483075	+	1.05813i
$743$	20.5354	−	35.5684i	0.753371	−	1.30488i	−0.192809	−	0.981236i	$-0.561760\pi$
$743$	20.5354	−	35.5684i	0.753371	−	1.30488i	0.946180	−	0.323640i	$-0.104907\pi$
$744$	−7.97892	−	46.2772i	−0.292521	−	1.69660i
$745$	15.9464	−	27.6199i	0.584229	−	1.01191i
$746$	35.6632	+	4.18903i	1.30572	+	0.153371i
$747$	−0.0209121	+	5.01135i	−0.000765135	+	0.183356i
$748$	4.53476	+	15.2102i	0.165807	+	0.556140i
$749$	−2.89760	−	3.20000i	−0.105876	−	0.116925i
$750$	−1.04070	+	8.70317i	−0.0380008	+	0.317795i
$751$	0.962367	−	0.555623i	0.0351173	−	0.0202750i	−0.482339	−	0.875985i	$-0.660213\pi$
$751$	0.962367	−	0.555623i	0.0351173	−	0.0202750i	0.517456	+	0.855710i	$0.326879\pi$
$752$	24.2938	−	15.8991i	0.885905	−	0.579781i
$753$	−44.2454	+	25.4221i	−1.61239	+	0.926434i
$754$	−4.38299	+	5.88038i	−0.159619	+	0.214151i
$755$		−	37.9826i		−	1.38233i
$756$	0.766017	−	27.4848i	0.0278598	−	0.999612i
$757$			11.5604i			0.420171i	0.977683	+	0.210086i	$0.0673743\pi$
$757$			11.5604i			0.420171i	−0.977683	+	0.210086i	$0.932626\pi$
$758$	−14.1225	−	10.5264i	−0.512954	−	0.382334i
$759$	5.05507	−	2.90450i	0.183487	−	0.105427i
$760$	7.94482	−	21.7127i	0.288189	−	0.787601i
$761$	7.96657	−	4.59950i	0.288788	−	0.166732i	−0.348607	−	0.937269i	$-0.613345\pi$
$761$	7.96657	−	4.59950i	0.288788	−	0.166732i	0.637395	+	0.770537i	$0.280012\pi$
$762$	0.0214738	+	0.00256777i	0.000777915	+	9.30204e-5i
$763$	10.5545	−	2.27441i	0.382099	−	0.0823392i
$764$	11.4143	+	38.2850i	0.412953	+	1.38510i
$765$	−53.7206	+	30.7174i	−1.94227	+	1.11059i
$766$	−2.32529	+	19.7963i	−0.0840160	+	0.715268i
$767$	−9.26599	+	16.0492i	−0.334576	+	0.579502i
$768$	−27.5462	+	3.03429i	−0.993988	+	0.109491i
$769$	−0.635492	+	1.10070i	−0.0229164	+	0.0396924i	−0.877256	−	0.480022i	$-0.840628\pi$
$769$	−0.635492	+	1.10070i	−0.0229164	+	0.0396924i	0.854340	+	0.519715i	$0.173962\pi$
$770$	10.3100	−	7.34358i	0.371545	−	0.264644i
$771$	−19.6648	−	11.4083i	−0.708211	−	0.410859i
$772$	−4.36460	−	14.6395i	−0.157086	−	0.526887i
$773$	12.9371	+	22.4077i	0.465315	+	0.805949i	0.999216	−	0.0395978i	$-0.0126077\pi$
$773$	12.9371	+	22.4077i	0.465315	+	0.805949i	−0.533901	+	0.845547i	$0.679274\pi$
$774$	−2.49882	−	1.87879i	−0.0898182	−	0.0675316i
$775$	31.4896	+	18.1805i	1.13114	+	0.653064i
$776$	−51.6675	+	9.01934i	−1.85476	+	0.323776i
$777$	−9.66644	+	29.8233i	−0.346782	+	1.06991i
$778$	0.947505	−	0.408074i	0.0339697	−	0.0146301i
$779$	17.0951	−	9.86986i	0.612496	−	0.353624i
$780$	10.4071	+	9.88220i	0.372632	+	0.353839i
$781$	−6.06589	−	3.50214i	−0.217054	−	0.125316i
$782$	11.4812	+	26.6581i	0.410566	+	0.953293i
$783$	−9.53921	−	16.7638i	−0.340903	−	0.599091i
$784$	−27.9739	−	1.20945i	−0.999067	−	0.0431945i
$785$	13.0961	−	7.56103i	0.467419	−	0.269865i
$786$	10.4359	+	24.3710i	0.372238	+	0.869286i
$787$	−26.7481			−0.953466			−0.476733	−	0.879048i	$-0.658179\pi$
$787$	−26.7481			−0.953466			−0.476733	+	0.879048i	$0.658179\pi$
$788$	9.65842	+	32.3957i	0.344067	+	1.15405i
$789$	35.8444	+	0.0747881i	1.27610	+	0.00266253i
$790$	−13.6323	−	1.60126i	−0.485016	−	0.0569704i
$791$	1.38792	+	1.53277i	0.0493487	+	0.0544989i
$792$	1.62487	+	9.54298i	0.0577371	+	0.339095i
$793$	3.87711	−	6.71536i	0.137680	−	0.238469i
$794$	−12.8482	−	29.8322i	−0.455965	−	1.05870i
$795$	43.4932	+	0.0907470i	1.54254	+	0.00321846i
$796$	−15.0267	−	14.2093i	−0.532606	−	0.503636i
$797$	−17.3854	+	30.1124i	−0.615822	+	1.06663i	0.374418	+	0.927260i	$0.377842\pi$
$797$	−17.3854	+	30.1124i	−0.615822	+	1.06663i	−0.990240	+	0.139374i	$0.955491\pi$
$798$	10.3341	+	14.5727i	0.365823	+	0.515869i
$799$	43.7270	−	25.2458i	1.54695	−	0.893132i
$800$	11.8424	−	17.8942i	0.418691	−	0.632656i
$801$	41.4816	−	23.7192i	1.46568	−	0.838075i
$802$	25.3645	+	2.97934i	0.895653	+	0.105204i
$803$		−	7.36054i		−	0.259748i
$804$	0.204499	−	0.215360i	0.00721211	−	0.00759516i
$805$	17.1588	−	15.5373i	0.604769	−	0.547618i
$806$	−17.3948	+	7.49164i	−0.612706	+	0.263882i
$807$	−3.10793	+	5.35724i	−0.109404	+	0.188584i
$808$	−0.0584792	−	0.0699352i	−0.00205729	−	0.00246031i
$809$	23.2688	−	13.4343i	0.818089	−	0.472324i	−0.0316683	−	0.999498i	$-0.510082\pi$
$809$	23.2688	−	13.4343i	0.818089	−	0.472324i	0.849757	+	0.527175i	$0.176749\pi$
$810$	−34.7878	+	14.6395i	−1.22232	+	0.514381i
$811$	8.08609			0.283941			0.141971	−	0.989871i	$-0.454656\pi$
$811$	8.08609			0.283941			0.141971	+	0.989871i	$0.454656\pi$
$812$	−17.2185	+	9.45116i	−0.604251	+	0.331671i
$813$	−0.0427298	+	20.4795i	−0.00149860	+	0.718248i
$814$	1.28764	−	10.9623i	0.0451318	−	0.384229i
$815$	−33.3944			−1.16975
$816$	−48.1243	+	2.59217i	−1.68469	+	0.0907440i
$817$	2.03131			0.0710666
$818$	6.08363	+	4.53449i	0.212709	+	0.158545i
$819$	−10.8500	+	2.29075i	−0.379131	+	0.0800455i
$820$	40.6984	−	12.1338i	1.42125	−	0.423730i
$821$	25.9064			0.904140			0.452070	−	0.891983i	$-0.350686\pi$
$821$	25.9064			0.904140			0.452070	+	0.891983i	$0.350686\pi$
$822$	1.17297	−	1.56687i	0.0409122	−	0.0546509i
$823$		−	44.2510i		−	1.54249i	−0.636537	−	0.771246i	$-0.719634\pi$
$823$		−	44.2510i		−	1.54249i	0.636537	−	0.771246i	$-0.280366\pi$
$824$	−7.12246	−	40.8012i	−0.248123	−	1.42138i
$825$	−6.48343	−	3.76127i	−0.225724	−	0.130950i
$826$	−40.4250	+	28.7939i	−1.40656	+	1.00187i
$827$		−	27.9309i		−	0.971251i	−0.874167	−	0.485626i	$-0.838592\pi$
$827$		−	27.9309i		−	0.971251i	0.874167	−	0.485626i	$-0.161408\pi$
$828$	4.98705	+	16.9858i	0.173312	+	0.590298i
$829$	25.8326	−	14.9145i	0.897205	−	0.518001i	0.0209125	−	0.999781i	$-0.493343\pi$
$829$	25.8326	−	14.9145i	0.897205	−	0.518001i	0.876292	+	0.481780i	$0.160010\pi$
$830$	−2.77100	−	6.43398i	−0.0961828	−	0.223327i
$831$	−0.0395032	+	18.9331i	−0.00137035	+	0.656781i
$832$	3.78679	+	10.5158i	0.131283	+	0.364571i
$833$	−48.4545	−	4.81794i	−1.67885	−	0.166932i
$834$	−33.6654	−	25.2022i	−1.16574	−	0.872682i
$835$	11.9568			0.413783
$836$	−4.57006	−	4.32148i	−0.158059	−	0.149462i
$837$	0.311769	−	49.8076i	0.0107763	−	1.72160i
$838$	−3.91650	−	9.09371i	−0.135293	−	0.314137i
$839$	−9.74941	−	16.8865i	−0.336587	−	0.582986i	0.647201	−	0.762319i	$-0.275939\pi$
$839$	−9.74941	−	16.8865i	−0.336587	−	0.582986i	−0.983788	+	0.179333i	$0.942606\pi$
$840$	14.3628	+	35.6508i	0.495565	+	1.23007i
$841$	7.61068	−	13.1821i	0.262437	−	0.454555i
$842$	−31.7455	−	3.72886i	−1.09402	−	0.128505i
$843$	−27.0804	−	15.7103i	−0.932698	−	0.541091i
$844$	20.7967	+	4.95395i	0.715853	+	0.170522i
$845$	−16.3807	+	28.3722i	−0.563513	+	0.976033i
$846$	28.3342	−	12.0631i	0.974148	−	0.414738i
$847$	5.40539	+	25.0840i	0.185732	+	0.861896i
$848$	30.2348	+	15.2709i	1.03827	+	0.524403i
$849$	−21.0994	−	36.7220i	−0.724131	−	1.26030i
$850$	22.3010	−	29.9198i	0.764917	−	1.02624i
$851$		−	20.1850i		−	0.691933i
$852$	14.6449	−	15.4228i	0.501728	−	0.528375i
$853$	23.8467	−	13.7679i	0.816495	−	0.471404i	−0.0327113	−	0.999465i	$-0.510414\pi$
$853$	23.8467	−	13.7679i	0.816495	−	0.471404i	0.849206	+	0.528061i	$0.177081\pi$
$854$	16.9148	−	12.0480i	0.578811	−	0.412276i
$855$	12.3500	−	21.1862i	0.422363	−	0.724554i
$856$	−3.54037	+	2.96043i	−0.121007	+	0.101185i
$857$	3.19113	+	1.84240i	0.109007	+	0.0629352i	0.553512	−	0.832841i	$-0.313287\pi$
$857$	3.19113	+	1.84240i	0.109007	+	0.0629352i	−0.444505	+	0.895776i	$0.646621\pi$
$858$	3.58898	−	1.53684i	0.122526	−	0.0524668i
$859$	−4.90474	−	8.49527i	−0.167348	−	0.289855i	0.770139	−	0.637876i	$-0.220187\pi$
$859$	−4.90474	−	8.49527i	−0.167348	−	0.289855i	−0.937487	+	0.348022i	$0.886854\pi$
$860$	4.25127	+	1.01269i	0.144967	+	0.0345324i
$861$	−10.1179	+	31.2162i	−0.344818	+	1.06385i
$862$	−0.160430	+	1.36582i	−0.00546426	+	0.0465199i
$863$	10.0742	−	17.4490i	0.342930	−	0.593972i	−0.642046	−	0.766666i	$-0.721914\pi$
$863$	10.0742	−	17.4490i	0.342930	−	0.593972i	0.984975	+	0.172695i	$0.0552474\pi$
$864$	−29.3274	−	1.97630i	−0.997737	−	0.0672352i
$865$	31.1890	+	54.0210i	1.06046	+	1.83677i
$866$	13.9811	+	10.4209i	0.475097	+	0.354117i
$867$	−54.3670	−	0.113435i	−1.84640	−	0.00385245i
$868$	−50.7108	−	1.09573i	−1.72124	−	0.0371913i
$869$	−1.86702	+	3.23377i	−0.0633343	+	0.109698i
$870$	21.5841	+	16.1580i	0.731769	+	0.547809i
$871$	−0.103730	−	0.0598884i	−0.00351475	−	0.00202924i
$872$	−1.98486	−	11.3703i	−0.0672158	−	0.385048i
$873$	−55.6299	−	0.232141i	−1.88279	−	0.00785678i
$874$	−9.22232	−	6.87393i	−0.311950	−	0.232514i
$875$	9.01227	+	2.90032i	0.304670	+	0.0980489i
$876$	21.7308	+	5.22439i	0.734215	+	0.176516i
$877$	18.4198	−	10.6347i	0.621991	−	0.359107i	−0.155653	−	0.987812i	$-0.549748\pi$
$877$	18.4198	−	10.6347i	0.621991	−	0.359107i	0.777644	+	0.628705i	$0.216415\pi$
$878$	−9.11844	+	12.2336i	−0.307732	+	0.412865i
$879$	−2.23598	−	0.00466530i	−0.0754179	−	0.000157357i
$880$	−7.41012	−	11.3227i	−0.249795	−	0.381687i
$881$		−	25.6669i		−	0.864741i	−0.901696	−	0.432370i	$-0.857677\pi$
$881$		−	25.6669i		−	0.864741i	0.901696	−	0.432370i	$-0.142323\pi$
$882$	−28.9813	−	6.48701i	−0.975853	−	0.218429i
$883$	5.00376			0.168390			0.0841949	−	0.996449i	$-0.473168\pi$
$883$	5.00376			0.168390			0.0841949	+	0.996449i	$0.473168\pi$
$884$	5.55342	+	18.6269i	0.186782	+	0.626492i
$885$	58.9296	+	34.1872i	1.98090	+	1.14919i
$886$	−13.4090	+	17.9900i	−0.450483	+	0.604385i
$887$	−26.2627	−	45.4883i	−0.881814	−	1.52735i	−0.849322	−	0.527875i	$-0.822989\pi$
$887$	−26.2627	−	45.4883i	−0.881814	−	1.52735i	−0.0324926	−	0.999472i	$-0.510345\pi$
$888$	31.4504	+	11.5824i	1.05541	+	0.388680i
$889$	0.00715614	−	0.0222365i	0.000240009	−	0.000745788i
$890$	−39.9185	+	53.5561i	−1.33807	+	1.79521i
$891$	−0.0856903	+	10.2672i	−0.00287073	+	0.343963i
$892$	−6.50785	−	6.15388i	−0.217899	−	0.206047i
$893$	−10.0045	+	17.3283i	−0.334787	+	0.579868i
$894$	24.2177	−	10.3703i	0.809960	−	0.346834i
$895$	54.9722	+	31.7382i	1.83752	+	1.06089i
$896$	−2.47059	+	29.8311i	−0.0825365	+	0.996588i
$897$	6.19062	−	3.55695i	0.206699	−	0.118763i
$898$	−1.68593	+	2.26190i	−0.0562601	+	0.0754806i
$899$	−30.8146	+	17.7908i	−1.02772	+	0.593357i
$900$	15.7063	−	16.4715i	0.523544	−	0.549052i
$901$	51.0140	+	29.4530i	1.69952	+	0.981220i
$902$	1.34778	−	11.4743i	0.0448762	−	0.382052i
$903$	−2.50784	+	2.26134i	−0.0834557	+	0.0752527i
$904$	1.69580	−	1.41801i	0.0564015	−	0.0471625i
$905$	−64.8973	+	37.4685i	−2.15726	+	1.24549i
$906$	18.8027	−	25.1168i	0.624677	−	0.834451i
$907$	6.82561	−	11.8223i	0.226641	−	0.392553i	−0.730170	−	0.683266i	$-0.760559\pi$
$907$	6.82561	−	11.8223i	0.226641	−	0.392553i	0.956810	+	0.290713i	$0.0938924\pi$
$908$	4.69796	−	19.7221i	0.155907	−	0.654499i
$909$	−0.0479968	−	0.0839399i	−0.00159195	−	0.00278411i
$910$	12.6259	−	8.99320i	0.418546	−	0.298122i
$911$	−2.80022	−	4.85013i	−0.0927755	−	0.160692i	0.815903	−	0.578189i	$-0.196241\pi$
$911$	−2.80022	−	4.85013i	−0.0927755	−	0.160692i	−0.908678	+	0.417498i	$0.862907\pi$
$912$	16.0022	−	10.4250i	0.529886	−	0.345207i
$913$	−1.90573			−0.0630705
$914$	16.1405	+	12.0304i	0.533879	+	0.397931i
$915$	−24.6576	−	14.3047i	−0.815154	−	0.472900i
$916$	9.16535	+	8.66682i	0.302832	+	0.286360i
$917$	27.9931	−	6.03227i	0.924412	−	0.199203i
$918$	−50.7301	−	6.28097i	−1.67434	−	0.207303i
$919$	−43.7907	−	25.2826i	−1.44452	−	0.833995i	−0.446376	−	0.894846i	$-0.647285\pi$
$919$	−43.7907	−	25.2826i	−1.44452	−	0.833995i	−0.998147	+	0.0608503i	$0.980619\pi$
$920$	−15.8742	−	18.9839i	−0.523357	−	0.625882i
$921$	21.2109	+	36.9160i	0.698922	+	1.21642i
$922$	−3.53419	+	30.0882i	−0.116392	+	0.990903i
$923$	−7.42850	−	4.28884i	−0.244512	−	0.141169i
$924$	10.4530	+	0.247683i	0.343879	+	0.00814817i
$925$	−22.4741	+	12.9755i	−0.738945	+	0.426630i
$926$	−15.5641	−	36.1382i	−0.511467	−	1.18757i
$927$	0.183319	−	43.9302i	0.00602097	−	1.44286i
$928$	9.37039	+	18.7913i	0.307598	+	0.616854i
$929$			10.7894i			0.353989i	0.984212	+	0.176994i	$0.0566374\pi$
$929$			10.7894i			0.353989i	−0.984212	+	0.176994i	$0.943363\pi$
$930$	27.4077	+	64.0051i	0.898733	+	2.09881i
$931$	17.5838	−	7.94738i	0.576286	−	0.260465i
$932$	10.2820	−	43.1641i	0.336800	−	1.41389i
$933$	1.53249	+	2.66719i	0.0501715	+	0.0873198i
$934$	−1.90302	−	4.41862i	−0.0622687	−	0.144582i
$935$	−11.7663	−	20.3799i	−0.384801	−	0.666494i
$936$	1.98987	+	11.6867i	0.0650408	+	0.381991i
$937$	−11.8954			−0.388606			−0.194303	−	0.980942i	$-0.562245\pi$
$937$	−11.8954			−0.388606			−0.194303	+	0.980942i	$0.562245\pi$
$938$	−0.186102	−	0.261277i	−0.00607645	−	0.00853099i
$939$	−20.1303	−	35.0353i	−0.656926	−	1.14333i
$940$	−29.5769	+	31.2782i	−0.964692	+	1.02018i
$941$	−51.3052			−1.67250			−0.836250	−	0.548348i	$-0.815257\pi$
$941$	−51.3052			−1.67250			−0.836250	+	0.548348i	$0.815257\pi$
$942$	12.4030	+	1.48311i	0.404113	+	0.0483225i
$943$		−	21.1278i		−	0.688014i
$944$	29.0548	+	44.3957i	0.945653	+	1.44496i
$945$	8.33815	+	39.9049i	0.271240	+	1.29811i
$946$	0.710492	−	0.953222i	0.0231001	−	0.0309919i
$947$		−	21.4973i		−	0.698568i	−0.937017	−	0.349284i	$-0.886425\pi$
$947$		−	21.4973i		−	0.698568i	0.937017	−	0.349284i	$-0.113575\pi$
$948$	−8.22200	−	7.80734i	−0.267038	−	0.253571i
$949$		−	9.01398i		−	0.292606i
$950$	−1.72514	+	14.6869i	−0.0559710	+	0.476508i
$951$	9.01790	+	15.6950i	0.292425	+	0.508945i
$952$	−7.18816	+	51.5568i	−0.232970	+	1.67097i
$953$			32.9525i			1.06744i	0.845662	+	0.533718i	$0.179206\pi$
$953$			32.9525i			1.06744i	−0.845662	+	0.533718i	$0.820794\pi$
$954$	28.7159	+	21.5906i	0.929712	+	0.699022i
$955$	−29.6166	−	51.2975i	−0.958371	−	1.65995i
$956$	−4.07779	−	0.971363i	−0.131885	−	0.0314161i
$957$	6.35975	−	3.65413i	0.205581	−	0.118121i
$958$	−4.70297	+	2.02549i	−0.151946	+	0.0654405i
$959$	−1.41902	−	1.56711i	−0.0458225	−	0.0506047i
$960$	38.6878	−	13.8405i	1.24864	−	0.446700i
$961$	−60.8852			−1.96404
$962$	1.57689	−	13.4248i	0.0508410	−	0.432834i
$963$	−4.24934	+	2.42977i	−0.136933	+	0.0782982i
$964$	−2.53077	−	0.602849i	−0.0815105	−	0.0194165i
$965$	11.3249	+	19.6152i	0.364560	+	0.631436i
$966$	19.0381	−	1.78018i	0.612542	−	0.0572762i
$967$	−27.1028	−	15.6478i	−0.871567	−	0.503199i	−0.00369833	−	0.999993i	$-0.501177\pi$
$967$	−27.1028	−	15.6478i	−0.871567	−	0.503199i	−0.867869	+	0.496794i	$0.834511\pi$
$968$	27.0228	−	4.71724i	0.868547	−	0.151618i
$969$	28.7981	−	16.5466i	0.925128	−	0.531553i
$970$	71.4221	−	30.7602i	2.29323	−	0.987652i
$971$	4.11794	+	2.37750i	0.132151	+	0.0762975i	0.564618	−	0.825352i	$-0.309023\pi$
$971$	4.11794	+	2.37750i	0.132151	+	0.0762975i	−0.432467	+	0.901650i	$0.642357\pi$
$972$	−30.2513	−	7.54045i	−0.970311	−	0.241860i
$973$	−33.6705	+	30.4886i	−1.07943	+	0.977421i
$974$	23.9343	+	2.81135i	0.766906	+	0.0900814i
$975$	−7.93983	−	4.60618i	−0.254278	−	0.147516i
$976$	−12.1572	−	18.5762i	−0.389143	−	0.594611i
$977$		−	11.4949i		−	0.367756i	−0.982949	−	0.183878i	$-0.941135\pi$
$977$		−	11.4949i		−	0.367756i	0.982949	−	0.183878i	$-0.0588651\pi$
$978$	−22.0828	−	16.5314i	−0.706129	−	0.528615i
$979$	9.08565	+	15.7368i	0.290379	+	0.502950i
$980$	40.7627	−	7.86662i	1.30212	−	0.251290i
$981$	0.0510865	−	12.2423i	0.00163107	−	0.390867i
$982$	5.54706	+	12.8797i	0.177014	+	0.411008i
$983$	4.86963	−	8.43444i	0.155317	−	0.269017i	−0.777857	−	0.628441i	$-0.783693\pi$
$983$	4.86963	−	8.43444i	0.155317	−	0.269017i	0.933174	+	0.359424i	$0.117027\pi$
$984$	32.9193	+	12.1234i	1.04943	+	0.386479i
$985$	−25.0607	−	43.4065i	−0.798501	−	1.38304i
$986$	14.4444	+	33.5384i	0.460003	+	1.06808i
$987$	−6.93911	−	32.5307i	−0.220874	−	1.03546i
$988$	−5.59666	−	5.29224i	−0.178053	−	0.168369i
$989$	1.08707	−	1.88287i	0.0345669	−	0.0598716i
$990$	−5.62227	−	13.2057i	−0.178687	−	0.419706i
$991$	−18.7864	+	10.8463i	−0.596770	+	0.344545i	−0.767770	−	0.640726i	$-0.778634\pi$
$991$	−18.7864	+	10.8463i	−0.596770	+	0.344545i	0.171000	+	0.985271i	$0.445300\pi$
$992$	−3.30710	+	54.1238i	−0.105000	+	1.71843i
$993$	18.9120	+	32.9150i	0.600155	+	1.04453i
$994$	−13.3275	−	18.7110i	−0.422722	−	0.593478i
$995$	26.5551	+	15.3316i	0.841854	+	0.486045i
$996$	1.35265	−	5.62635i	0.0428605	−	0.178278i
$997$	28.2919	+	16.3343i	0.896013	+	0.517313i	0.875905	−	0.482484i	$-0.160265\pi$
$997$	28.2919	+	16.3343i	0.896013	+	0.517313i	0.0201085	+	0.999798i	$0.493599\pi$
$998$	−4.34437	+	36.9857i	−0.137519	+	1.17076i
$999$	30.6740	+	17.9666i	0.970482	+	0.568437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bt.a.275.74	yes	184
7.4	even	3		504.2.cy.a.347.12	yes	184
8.3	odd	2	inner	504.2.bt.a.275.19	yes	184
9.2	odd	6		504.2.cy.a.443.44	yes	184
56.11	odd	6		504.2.cy.a.347.44	yes	184
63.11	odd	6	inner	504.2.bt.a.11.19	✓	184
72.11	even	6		504.2.cy.a.443.12	yes	184
504.11	even	6	inner	504.2.bt.a.11.74	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.19	✓	184	63.11	odd	6	inner
504.2.bt.a.11.74	yes	184	504.11	even	6	inner
504.2.bt.a.275.19	yes	184	8.3	odd	2	inner
504.2.bt.a.275.74	yes	184	1.1	even	1	trivial
504.2.cy.a.347.12	yes	184	7.4	even	3
504.2.cy.a.347.44	yes	184	56.11	odd	6
504.2.cy.a.443.12	yes	184	72.11	even	6
504.2.cy.a.443.44	yes	184	9.2	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13389 + 0.845156i) q^{2} +(-0.862894 - 1.50180i) q^{3} +(0.571423 + 1.91663i) q^{4} +(-1.48267 - 2.56806i) q^{5} +(0.290830 - 2.43216i) q^{6} +(-2.51854 - 0.810517i) q^{7} +(-0.971921 + 2.65619i) q^{8} +(-1.51083 + 2.59179i) q^{9} +O(q^{10})\)	\(q+(1.13389 + 0.845156i) q^{2} +(-0.862894 - 1.50180i) q^{3} +(0.571423 + 1.91663i) q^{4} +(-1.48267 - 2.56806i) q^{5} +(0.290830 - 2.43216i) q^{6} +(-2.51854 - 0.810517i) q^{7} +(-0.971921 + 2.65619i) q^{8} +(-1.51083 + 2.59179i) q^{9} +(0.489224 - 4.16500i) q^{10} +(-0.987994 - 0.570419i) q^{11} +(2.38533 - 2.51201i) q^{12} +(-1.20993 - 0.698555i) q^{13} +(-2.17074 - 3.04760i) q^{14} +(-2.57734 + 4.44265i) q^{15} +(-3.34695 + 2.19041i) q^{16} +(-6.02425 + 3.47811i) q^{17} +(-3.90359 + 1.66193i) q^{18} +(1.37831 - 2.38731i) q^{19} +(4.07480 - 4.30919i) q^{20} +(0.955999 + 4.48175i) q^{21} +(-0.638186 - 1.48180i) q^{22} +(-1.47523 - 2.55518i) q^{23} +(4.82775 - 0.832380i) q^{24} +(-1.89664 + 3.28507i) q^{25} +(-0.781545 - 1.81467i) q^{26} +(5.19605 + 0.0325245i) q^{27} +(0.114309 - 5.29027i) q^{28} +(-1.85598 - 3.21465i) q^{29} +(-6.67716 + 2.85923i) q^{30} -9.58567i q^{31} +(-5.64632 - 0.345004i) q^{32} +(-0.00412282 + 1.97598i) q^{33} +(-9.77040 - 1.14764i) q^{34} +(1.65272 + 7.66951i) q^{35} +(-5.83084 - 1.41469i) q^{36} +(5.92474 + 3.42065i) q^{37} +(3.58051 - 1.54206i) q^{38} +(-0.00504895 + 2.41986i) q^{39} +(8.26232 - 1.44231i) q^{40} +(6.20145 + 3.58041i) q^{41} +(-2.70378 + 5.88979i) q^{42} +(0.368441 + 0.638159i) q^{43} +(0.528720 - 2.21957i) q^{44} +(8.89596 + 0.0371224i) q^{45} +(0.486769 - 4.14410i) q^{46} -7.25849 q^{47} +(6.17764 + 3.13637i) q^{48} +(5.68613 + 4.08264i) q^{49} +(-4.92698 + 2.12196i) q^{50} +(10.4217 + 6.04601i) q^{51} +(0.647489 - 2.71816i) q^{52} +(-4.23405 - 7.33359i) q^{53} +(5.86427 + 4.42835i) q^{54} +3.38298i q^{55} +(4.60072 - 5.90198i) q^{56} +(-4.77461 - 0.00996205i) q^{57} +(0.612401 - 5.21366i) q^{58} -13.2645i q^{59} +(-9.98767 - 2.40118i) q^{60} +5.55019i q^{61} +(8.10139 - 10.8691i) q^{62} +(5.90578 - 5.30300i) q^{63} +(-6.11074 - 5.16322i) q^{64} +4.14291i q^{65} +(-1.67469 + 2.23707i) q^{66} +0.0857319 q^{67} +(-10.1086 - 9.55881i) q^{68} +(-2.56441 + 4.42036i) q^{69} +(-4.60793 + 10.0932i) q^{70} +6.13960 q^{71} +(-5.41590 - 6.53207i) q^{72} +(3.22594 + 5.58749i) q^{73} +(3.82703 + 8.88598i) q^{74} +(6.57013 + 0.0137083i) q^{75} +(5.36319 + 1.27756i) q^{76} +(2.02597 + 2.23741i) q^{77} +(-2.05088 + 2.73959i) q^{78} -3.27307i q^{79} +(10.5876 + 5.34752i) q^{80} +(-4.43479 - 7.83151i) q^{81} +(4.00577 + 9.30100i) q^{82} +(1.44667 - 0.835233i) q^{83} +(-8.04358 + 4.39327i) q^{84} +(17.8640 + 10.3138i) q^{85} +(-0.121571 + 1.03499i) q^{86} +(-3.22626 + 5.56122i) q^{87} +(2.47540 - 2.06990i) q^{88} +(-13.7941 - 7.96402i) q^{89} +(10.0557 + 7.56057i) q^{90} +(2.48108 + 2.74001i) q^{91} +(4.05435 - 4.28756i) q^{92} +(-14.3958 + 8.27142i) q^{93} +(-8.23035 - 6.13456i) q^{94} -8.17435 q^{95} +(4.35405 + 8.77737i) q^{96} +(9.27174 + 16.0591i) q^{97} +(2.99698 + 9.43494i) q^{98} +(2.97110 - 1.69887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} - 8 q^{12} + 12 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} - 74 q^{25} - 6 q^{26} - 8 q^{27} + 3 q^{30} - 14 q^{33} - 4 q^{34} + 30 q^{35} - 38 q^{36} + 39 q^{38} + 6 q^{40} - 12 q^{41} - 20 q^{42} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} - 34 q^{51} + 9 q^{52} + 47 q^{54} - 24 q^{56} + 4 q^{57} - 3 q^{58} - 11 q^{60} - 8 q^{64} - 26 q^{66} - 4 q^{67} - 42 q^{68} - 3 q^{70} + 52 q^{72} - 4 q^{73} + 27 q^{74} + 30 q^{75} + 2 q^{76} - 29 q^{78} + 87 q^{80} + 14 q^{81} - 4 q^{82} - 72 q^{83} - 59 q^{84} - 27 q^{86} - 7 q^{88} - 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} - 18 q^{94} + 23 q^{96} - 4 q^{97} + 57 q^{98} + 10 q^{99}+O(q^{100}) \) 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 6 * q^11 - 8 * q^12 + 12 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 - 74 * q^25 - 6 * q^26 - 8 * q^27 + 3 * q^30 - 14 * q^33 - 4 * q^34 + 30 * q^35 - 38 * q^36 + 39 * q^38 + 6 * q^40 - 12 * q^41 - 20 * q^42 - 4 * q^43 + 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 - 34 * q^51 + 9 * q^52 + 47 * q^54 - 24 * q^56 + 4 * q^57 - 3 * q^58 - 11 * q^60 - 8 * q^64 - 26 * q^66 - 4 * q^67 - 42 * q^68 - 3 * q^70 + 52 * q^72 - 4 * q^73 + 27 * q^74 + 30 * q^75 + 2 * q^76 - 29 * q^78 + 87 * q^80 + 14 * q^81 - 4 * q^82 - 72 * q^83 - 59 * q^84 - 27 * q^86 - 7 * q^88 - 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 - 18 * q^94 + 23 * q^96 - 4 * q^97 + 57 * q^98 + 10 * q^99

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