LMFDB - Embedded newform 625.2.d.q.501.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			501.2
Root			$-0.0288455i$ of defining polynomial
Character	$\chi$	$=$	625.501
Dual form			625.2.d.q.126.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326747 + 1.00562i) q^{2} +(-0.556121 - 0.404046i) q^{3} +(0.713519 + 0.518402i) q^{4} +(0.588029 - 0.427228i) q^{6} -1.01199 q^{7} +(-2.46533 + 1.79116i) q^{8} +(-0.781033 - 2.40377i) q^{9} +O(q^{10})$	\(q+(-0.326747 + 1.00562i) q^{2} +(-0.556121 - 0.404046i) q^{3} +(0.713519 + 0.518402i) q^{4} +(0.588029 - 0.427228i) q^{6} -1.01199 q^{7} +(-2.46533 + 1.79116i) q^{8} +(-0.781033 - 2.40377i) q^{9} +(1.58239 - 4.87011i) q^{11} +(-0.187345 - 0.576589i) q^{12} +(-1.88045 - 5.78744i) q^{13} +(0.330666 - 1.01769i) q^{14} +(-0.450619 - 1.38686i) q^{16} +(2.58335 - 1.87691i) q^{17} +2.67249 q^{18} +(-2.77389 + 2.01535i) q^{19} +(0.562792 + 0.408892i) q^{21} +(4.38045 + 3.18259i) q^{22} +(-0.902070 + 2.77629i) q^{23} +2.09473 q^{24} +6.43442 q^{26} +(-1.17414 + 3.61364i) q^{27} +(-0.722078 - 0.524620i) q^{28} +(1.25597 + 0.912514i) q^{29} +(6.46970 - 4.70051i) q^{31} -4.55272 q^{32} +(-2.84775 + 2.06901i) q^{33} +(1.04337 + 3.21115i) q^{34} +(0.688839 - 2.12003i) q^{36} +(-2.59799 - 7.99578i) q^{37} +(-1.12032 - 3.44799i) q^{38} +(-1.29263 + 3.97831i) q^{39} +(-0.575868 - 1.77234i) q^{41} +(-0.595082 + 0.432352i) q^{42} +5.22402 q^{43} +(3.65374 - 2.65460i) q^{44} +(-2.49715 - 1.81429i) q^{46} +(-3.88393 - 2.82184i) q^{47} +(-0.309757 + 0.953334i) q^{48} -5.97587 q^{49} -2.19501 q^{51} +(1.65848 - 5.10428i) q^{52} +(8.13057 + 5.90720i) q^{53} +(-3.25031 - 2.36149i) q^{54} +(2.49490 - 1.81265i) q^{56} +2.35691 q^{57} +(-1.32803 + 0.964869i) q^{58} +(0.894451 + 2.75284i) q^{59} +(-0.713724 + 2.19662i) q^{61} +(2.61299 + 8.04196i) q^{62} +(0.790401 + 2.43261i) q^{63} +(2.38882 - 7.35205i) q^{64} +(-1.15015 - 3.53981i) q^{66} +(3.76108 - 2.73258i) q^{67} +2.81626 q^{68} +(1.62341 - 1.17947i) q^{69} +(6.25945 + 4.54776i) q^{71} +(6.23105 + 4.52712i) q^{72} +(0.184032 - 0.566392i) q^{73} +8.88962 q^{74} -3.02398 q^{76} +(-1.60138 + 4.92853i) q^{77} +(-3.57832 - 2.59980i) q^{78} +(-8.94716 - 6.50050i) q^{79} +(-4.02127 + 2.92163i) q^{81} +1.97047 q^{82} +(11.5667 - 8.40373i) q^{83} +(0.189592 + 0.583505i) q^{84} +(-1.70693 + 5.25339i) q^{86} +(-0.329773 - 1.01494i) q^{87} +(4.82205 + 14.8407i) q^{88} +(-1.97562 + 6.08032i) q^{89} +(1.90301 + 5.85686i) q^{91} +(-2.08288 + 1.51330i) q^{92} -5.49716 q^{93} +(4.10677 - 2.98375i) q^{94} +(2.53186 + 1.83951i) q^{96} +(-11.3936 - 8.27794i) q^{97} +(1.95260 - 6.00947i) q^{98} -12.9425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.326747	+	1.00562i	−0.231045	+	0.711083i	0.766577	+	0.642153i	$0.221959\pi$
$2$	−0.326747	+	1.00562i	−0.231045	+	0.711083i	−0.997621	+	0.0689302i	$0.978041\pi$
$3$	−0.556121	−	0.404046i	−0.321077	−	0.233276i	0.415558	−	0.909567i	$-0.363586\pi$
$3$	−0.556121	−	0.404046i	−0.321077	−	0.233276i	−0.736635	+	0.676291i	$0.763586\pi$
$4$	0.713519	+	0.518402i	0.356760	+	0.259201i
$5$		0			0
$5$		0			0
$6$	0.588029	−	0.427228i	0.240062	−	0.174415i
$7$	−1.01199			−0.382498			−0.191249	−	0.981542i	$-0.561254\pi$
$7$	−1.01199			−0.382498			−0.191249	+	0.981542i	$0.561254\pi$
$8$	−2.46533	+	1.79116i	−0.871624	+	0.633272i
$9$	−0.781033	−	2.40377i	−0.260344	−	0.801258i
$10$		0			0
$11$	1.58239	−	4.87011i	0.477110	−	1.46839i	−0.365981	−	0.930622i	$-0.619266\pi$
$11$	1.58239	−	4.87011i	0.477110	−	1.46839i	0.843091	−	0.537771i	$-0.180734\pi$
$12$	−0.187345	−	0.576589i	−0.0540819	−	0.166447i
$13$	−1.88045	−	5.78744i	−0.521544	−	1.60515i	−0.771050	−	0.636775i	$-0.780268\pi$
$13$	−1.88045	−	5.78744i	−0.521544	−	1.60515i	0.249506	−	0.968373i	$-0.419732\pi$
$14$	0.330666	−	1.01769i	0.0883742	−	0.271988i
$15$		0			0
$16$	−0.450619	−	1.38686i	−0.112655	−	0.346716i
$17$	2.58335	−	1.87691i	0.626554	−	0.455218i	−0.228651	−	0.973509i	$-0.573431\pi$
$17$	2.58335	−	1.87691i	0.626554	−	0.455218i	0.855205	+	0.518290i	$0.173431\pi$
$18$	2.67249			0.629912
$19$	−2.77389	+	2.01535i	−0.636374	+	0.462352i	−0.858602	−	0.512642i	$-0.828667\pi$
$19$	−2.77389	+	2.01535i	−0.636374	+	0.462352i	0.222229	+	0.974995i	$0.428667\pi$
$20$		0			0
$21$	0.562792	+	0.408892i	0.122811	+	0.0892276i
$22$	4.38045	+	3.18259i	0.933916	+	0.678530i
$23$	−0.902070	+	2.77629i	−0.188095	+	0.578896i	−0.999988	−	0.00491011i	$-0.998437\pi$
$23$	−0.902070	+	2.77629i	−0.188095	+	0.578896i	0.811893	+	0.583806i	$0.198437\pi$
$24$	2.09473			0.427585
$25$		0			0
$26$	6.43442			1.26189
$27$	−1.17414	+	3.61364i	−0.225964	+	0.695445i
$28$	−0.722078	−	0.524620i	−0.136460	−	0.0991439i
$29$	1.25597	+	0.912514i	0.233227	+	0.169450i	0.698261	−	0.715844i	$-0.253958\pi$
$29$	1.25597	+	0.912514i	0.233227	+	0.169450i	−0.465033	+	0.885293i	$0.653958\pi$
$30$		0			0
$31$	6.46970	−	4.70051i	1.16199	−	0.844237i	0.171964	−	0.985103i	$-0.444989\pi$
$31$	6.46970	−	4.70051i	1.16199	−	0.844237i	0.990029	+	0.140866i	$0.0449888\pi$
$32$	−4.55272			−0.804815
$33$	−2.84775	+	2.06901i	−0.495730	+	0.360169i
$34$	1.04337	+	3.21115i	0.178936	+	0.550708i
$35$		0			0
$36$	0.688839	−	2.12003i	0.114806	−	0.353338i
$37$	−2.59799	−	7.99578i	−0.427106	−	1.31450i	−0.900963	−	0.433896i	$-0.857139\pi$
$37$	−2.59799	−	7.99578i	−0.427106	−	1.31450i	0.473857	−	0.880602i	$-0.342861\pi$
$38$	−1.12032	−	3.44799i	−0.181740	−	0.559339i
$39$	−1.29263	+	3.97831i	−0.206987	+	0.637039i
$40$		0			0
$41$	−0.575868	−	1.77234i	−0.0899354	−	0.276793i	0.895965	−	0.444124i	$-0.146485\pi$
$41$	−0.575868	−	1.77234i	−0.0899354	−	0.276793i	−0.985901	+	0.167331i	$0.946485\pi$
$42$	−0.595082	+	0.432352i	−0.0918231	+	0.0667134i
$43$	5.22402			0.796655			0.398328	−	0.917243i	$-0.369591\pi$
$43$	5.22402			0.796655			0.398328	+	0.917243i	$0.369591\pi$
$44$	3.65374	−	2.65460i	0.550823	−	0.400196i
$45$		0			0
$46$	−2.49715	−	1.81429i	−0.368185	−	0.267502i
$47$	−3.88393	−	2.82184i	−0.566530	−	0.411608i	0.267313	−	0.963610i	$-0.413864\pi$
$47$	−3.88393	−	2.82184i	−0.566530	−	0.411608i	−0.833843	+	0.552002i	$0.813864\pi$
$48$	−0.309757	+	0.953334i	−0.0447096	+	0.137602i
$49$	−5.97587			−0.853695
$50$		0			0
$51$	−2.19501			−0.307363
$52$	1.65848	−	5.10428i	0.229990	−	0.707837i
$53$	8.13057	+	5.90720i	1.11682	+	0.811417i	0.983724	−	0.179686i	$-0.0575083\pi$
$53$	8.13057	+	5.90720i	1.11682	+	0.811417i	0.133095	+	0.991103i	$0.457508\pi$
$54$	−3.25031	−	2.36149i	−0.442312	−	0.321358i
$55$		0			0
$56$	2.49490	−	1.81265i	0.333395	−	0.242225i
$57$	2.35691			0.312180
$58$	−1.32803	+	0.964869i	−0.174379	+	0.126694i
$59$	0.894451	+	2.75284i	0.116448	+	0.358389i	0.992246	−	0.124288i	$-0.0396646\pi$
$59$	0.894451	+	2.75284i	0.116448	+	0.358389i	−0.875799	+	0.482677i	$0.839665\pi$
$60$		0			0
$61$	−0.713724	+	2.19662i	−0.0913830	+	0.281248i	−0.986294	−	0.164996i	$-0.947239\pi$
$61$	−0.713724	+	2.19662i	−0.0913830	+	0.281248i	0.894911	+	0.446244i	$0.147239\pi$
$62$	2.61299	+	8.04196i	0.331850	+	1.02133i
$63$	0.790401	+	2.43261i	0.0995812	+	0.306479i
$64$	2.38882	−	7.35205i	0.298603	−	0.919006i
$65$		0			0
$66$	−1.15015	−	3.53981i	−0.141574	−	0.435720i
$67$	3.76108	−	2.73258i	0.459489	−	0.333838i	−0.333842	−	0.942629i	$-0.608345\pi$
$67$	3.76108	−	2.73258i	0.459489	−	0.333838i	0.793331	+	0.608791i	$0.208345\pi$
$68$	2.81626			0.341522
$69$	1.62341	−	1.17947i	0.195435	−	0.141992i
$70$		0			0
$71$	6.25945	+	4.54776i	0.742860	+	0.539720i	0.893606	−	0.448853i	$-0.148167\pi$
$71$	6.25945	+	4.54776i	0.742860	+	0.539720i	−0.150745	+	0.988573i	$0.548167\pi$
$72$	6.23105	+	4.52712i	0.734337	+	0.533527i
$73$	0.184032	−	0.566392i	0.0215393	−	0.0662912i	−0.939709	−	0.341975i	$-0.888904\pi$
$73$	0.184032	−	0.566392i	0.0215393	−	0.0662912i	0.961248	+	0.275684i	$0.0889042\pi$
$74$	8.88962			1.03340
$75$		0			0
$76$	−3.02398			−0.346875
$77$	−1.60138	+	4.92853i	−0.182494	+	0.561658i
$78$	−3.57832	−	2.59980i	−0.405165	−	0.294369i
$79$	−8.94716	−	6.50050i	−1.00663	−	0.731363i	−0.0431341	−	0.999069i	$-0.513734\pi$
$79$	−8.94716	−	6.50050i	−1.00663	−	0.731363i	−0.963501	+	0.267706i	$0.913734\pi$
$80$		0			0
$81$	−4.02127	+	2.92163i	−0.446808	+	0.324625i
$82$	1.97047			0.217602
$83$	11.5667	−	8.40373i	1.26961	−	0.922429i	0.270427	−	0.962740i	$-0.412835\pi$
$83$	11.5667	−	8.40373i	1.26961	−	0.922429i	0.999187	+	0.0403114i	$0.0128350\pi$
$84$	0.189592	+	0.583505i	0.0206862	+	0.0636656i
$85$		0			0
$86$	−1.70693	+	5.25339i	−0.184063	+	0.566488i
$87$	−0.329773	−	1.01494i	−0.0353554	−	0.108813i
$88$	4.82205	+	14.8407i	0.514032	+	1.58203i
$89$	−1.97562	+	6.08032i	−0.209415	+	0.644513i	0.790088	+	0.612993i	$0.210035\pi$
$89$	−1.97562	+	6.08032i	−0.209415	+	0.644513i	−0.999503	+	0.0315198i	$0.989965\pi$
$90$		0			0
$91$	1.90301	+	5.85686i	0.199490	+	0.613966i
$92$	−2.08288	+	1.51330i	−0.217155	+	0.157772i
$93$	−5.49716			−0.570029
$94$	4.10677	−	2.98375i	0.423581	−	0.307750i
$95$		0			0
$96$	2.53186	+	1.83951i	0.258407	+	0.187744i
$97$	−11.3936	−	8.27794i	−1.15685	−	0.840498i	−0.167470	−	0.985877i	$-0.553560\pi$
$97$	−11.3936	−	8.27794i	−1.15685	−	0.840498i	−0.989376	+	0.145379i	$0.953560\pi$
$98$	1.95260	−	6.00947i	0.197242	−	0.607048i
$99$	−12.9425			−1.30077
$100$		0			0
$101$	−10.5130			−1.04608			−0.523040	−	0.852308i	$-0.675202\pi$
$101$	−10.5130			−1.04608			−0.523040	+	0.852308i	$0.675202\pi$
$102$	0.717214	−	2.20736i	0.0710147	−	0.218561i
$103$	−2.48991	−	1.80902i	−0.245338	−	0.178248i	0.458320	−	0.888787i	$-0.348451\pi$
$103$	−2.48991	−	1.80902i	−0.245338	−	0.178248i	−0.703658	+	0.710539i	$0.748451\pi$
$104$	15.0022	+	10.8997i	1.47109	+	1.06881i
$105$		0			0
$106$	−8.59706	+	6.24613i	−0.835020	+	0.606678i
$107$	5.24731			0.507277			0.253638	−	0.967299i	$-0.418373\pi$
$107$	5.24731			0.507277			0.253638	+	0.967299i	$0.418373\pi$
$108$	−2.71109	+	1.96972i	−0.260875	+	0.189537i
$109$	−2.01450	−	6.19999i	−0.192954	−	0.593852i	−0.999994	−	0.00335529i	$-0.998932\pi$
$109$	−2.01450	−	6.19999i	−0.192954	−	0.593852i	0.807040	−	0.590496i	$-0.201068\pi$
$110$		0			0
$111$	−1.78586	+	5.49632i	−0.169507	+	0.521688i
$112$	0.456024	+	1.40350i	0.0430902	+	0.132618i
$113$	−0.119143	−	0.366684i	−0.0112080	−	0.0344947i	0.945296	−	0.326214i	$-0.105773\pi$
$113$	−0.119143	−	0.366684i	−0.0112080	−	0.0344947i	−0.956504	+	0.291719i	$0.905773\pi$
$114$	−0.770113	+	2.37016i	−0.0721277	+	0.221986i
$115$		0			0
$116$	0.423108	+	1.30219i	0.0392846	+	0.120906i
$117$	−12.4430	+	9.04037i	−1.15036	+	0.835782i
$118$	−3.06058			−0.281749
$119$	−2.61434	+	1.89943i	−0.239656	+	0.174120i
$120$		0			0
$121$	−12.3148	−	8.94724i	−1.11953	−	0.813385i
$122$	−1.97576	−	1.43548i	−0.178877	−	0.129962i
$123$	−0.395853	+	1.21831i	−0.0356929	+	0.109851i
$124$	7.05301			0.633379
$125$		0			0
$126$	−2.70455			−0.240940
$127$	1.43484	−	4.41598i	0.127321	−	0.391855i	−0.866995	−	0.498316i	$-0.833952\pi$
$127$	1.43484	−	4.41598i	0.127321	−	0.391855i	0.994317	+	0.106461i	$0.0339519\pi$
$128$	−0.753609	−	0.547529i	−0.0666103	−	0.0483952i
$129$	−2.90519	−	2.11074i	−0.255787	−	0.185840i
$130$		0			0
$131$	−13.1233	+	9.53462i	−1.14659	+	0.833044i	−0.988023	−	0.154305i	$-0.950686\pi$
$131$	−13.1233	+	9.53462i	−1.14659	+	0.833044i	−0.158563	+	0.987349i	$0.550686\pi$
$132$	−3.10450			−0.270212
$133$	2.80716	−	2.03952i	0.243412	−	0.176849i
$134$	1.51903	+	4.67509i	0.131224	+	0.403867i
$135$		0			0
$136$	−3.00694	+	9.25440i	−0.257843	+	0.793559i
$137$	5.92699	+	18.2414i	0.506377	+	1.55847i	0.798443	+	0.602070i	$0.205657\pi$
$137$	5.92699	+	18.2414i	0.506377	+	1.55847i	−0.292066	+	0.956398i	$0.594343\pi$
$138$	0.655664	+	2.01792i	0.0558138	+	0.171777i
$139$	1.10864	−	3.41206i	0.0940340	−	0.289407i	−0.892967	−	0.450123i	$-0.851380\pi$
$139$	1.10864	−	3.41206i	0.0940340	−	0.289407i	0.987001	+	0.160716i	$0.0513803\pi$
$140$		0			0
$141$	1.01978	+	3.13857i	0.0858813	+	0.264316i
$142$	−6.61859	+	4.80869i	−0.555420	+	0.403536i
$143$	−31.1611			−2.60582
$144$	−2.98175	+	2.16637i	−0.248479	+	0.180531i
$145$		0			0
$146$	0.509445	+	0.370134i	0.0421620	+	0.0306325i
$147$	3.32331	+	2.41452i	0.274102	+	0.199147i
$148$	2.29131	−	7.05194i	0.188345	−	0.579666i
$149$	1.60192			0.131234			0.0656170	−	0.997845i	$-0.479098\pi$
$149$	1.60192			0.131234			0.0656170	+	0.997845i	$0.479098\pi$
$150$		0			0
$151$	6.74218			0.548671			0.274336	−	0.961634i	$-0.411542\pi$
$151$	6.74218			0.548671			0.274336	+	0.961634i	$0.411542\pi$
$152$	3.22872	−	9.93698i	0.261884	−	0.805995i
$153$	−6.52935	−	4.74385i	−0.527867	−	0.383518i
$154$	−4.43300	−	3.22076i	−0.357221	−	0.259536i
$155$		0			0
$156$	−2.98468	+	2.16850i	−0.238966	+	0.173619i
$157$	14.2612			1.13817			0.569083	−	0.822280i	$-0.307298\pi$
$157$	14.2612			1.13817			0.569083	+	0.822280i	$0.307298\pi$
$158$	9.46051	−	6.87346i	0.752638	−	0.546823i
$159$	−2.13480	−	6.57024i	−0.169301	−	0.521054i
$160$		0			0
$161$	0.912890	−	2.80959i	0.0719458	−	0.221426i
$162$	−1.62412	−	4.99852i	−0.127603	−	0.392721i
$163$	3.12542	+	9.61904i	0.244801	+	0.753421i	0.995669	+	0.0929686i	$0.0296356\pi$
$163$	3.12542	+	9.61904i	0.244801	+	0.753421i	−0.750868	+	0.660453i	$0.770364\pi$
$164$	0.507891	−	1.56313i	0.0396596	−	0.122060i
$165$		0			0
$166$	4.67159	+	14.3777i	0.362586	+	1.11592i
$167$	13.5236	−	9.82548i	1.04649	−	0.760318i	0.0749467	−	0.997188i	$-0.476121\pi$
$167$	13.5236	−	9.82548i	1.04649	−	0.760318i	0.971542	+	0.236869i	$0.0761213\pi$
$168$	−2.11986			−0.163551
$169$	−19.4412	+	14.1248i	−1.49547	+	1.08653i
$170$		0			0
$171$	7.01094	+	5.09374i	0.536140	+	0.389528i
$172$	3.72744	+	2.70814i	0.284214	+	0.206494i
$173$	−1.99090	+	6.12735i	−0.151365	+	0.465853i	−0.997774	−	0.0666791i	$-0.978760\pi$
$173$	−1.99090	+	6.12735i	−0.151365	+	0.465853i	0.846410	+	0.532533i	$0.178760\pi$
$174$	1.12840			0.0855435
$175$		0			0
$176$	−7.46723			−0.562864
$177$	0.614849	−	1.89231i	0.0462149	−	0.142235i
$178$	−5.46899	−	3.97345i	−0.409918	−	0.297823i
$179$	12.4866	+	9.07201i	0.933289	+	0.678074i	0.946796	−	0.321835i	$-0.104300\pi$
$179$	12.4866	+	9.07201i	0.933289	+	0.678074i	−0.0135069	+	0.999909i	$0.504300\pi$
$180$		0			0
$181$	−1.03388	+	0.751154i	−0.0768473	+	0.0558329i	−0.625546	−	0.780188i	$-0.715124\pi$
$181$	−1.03388	+	0.751154i	−0.0768473	+	0.0558329i	0.548698	+	0.836020i	$0.315124\pi$
$182$	−6.51160			−0.482672
$183$	1.28445	−	0.933208i	0.0949493	−	0.0689847i
$184$	−2.74889	−	8.46021i	−0.202651	−	0.623695i
$185$		0			0
$186$	1.79618	−	5.52807i	0.131702	−	0.405338i
$187$	−5.05290	−	15.5512i	−0.369504	−	1.13722i
$188$	−1.30841	−	4.02688i	−0.0954258	−	0.293690i
$189$	1.18823	−	3.65699i	0.0864308	−	0.266007i
$190$		0			0
$191$	1.80346	+	5.55049i	0.130494	+	0.401619i	0.994862	−	0.101241i	$-0.0322812\pi$
$191$	1.80346	+	5.55049i	0.130494	+	0.401619i	−0.864368	+	0.502860i	$0.832281\pi$
$192$	−4.29904	+	3.12343i	−0.310256	+	0.225414i
$193$	4.17773			0.300719			0.150360	−	0.988631i	$-0.451957\pi$
$193$	4.17773			0.300719			0.150360	+	0.988631i	$0.451957\pi$
$194$	12.0473	−	8.75289i	0.864947	−	0.628421i
$195$		0			0
$196$	−4.26390	−	3.09790i	−0.304564	−	0.221279i
$197$	−14.1460	−	10.2777i	−1.00786	−	0.732255i	−0.0441025	−	0.999027i	$-0.514043\pi$
$197$	−14.1460	−	10.2777i	−1.00786	−	0.732255i	−0.963760	+	0.266772i	$0.914043\pi$
$198$	4.22893	−	13.0153i	0.300537	−	0.924959i
$199$	5.89046			0.417564			0.208782	−	0.977962i	$-0.433050\pi$
$199$	5.89046			0.417564			0.208782	+	0.977962i	$0.433050\pi$
$200$		0			0
$201$	−3.19571			−0.225408
$202$	3.43508	−	10.5721i	0.241692	−	0.743850i
$203$	−1.27103	−	0.923459i	−0.0892090	−	0.0648141i
$204$	−1.56618	−	1.13790i	−0.109655	−	0.0796689i
$205$		0			0
$206$	2.63277	−	1.91282i	0.183434	−	0.133272i
$207$	7.37811			0.512814
$208$	−7.17902	+	5.21586i	−0.497775	+	0.361655i
$209$	5.42558	+	16.6982i	0.375295	+	1.15504i
$210$		0			0
$211$	−3.70118	+	11.3911i	−0.254800	+	0.784193i	0.739069	+	0.673629i	$0.235266\pi$
$211$	−3.70118	+	11.3911i	−0.254800	+	0.784193i	−0.993869	+	0.110564i	$0.964734\pi$
$212$	2.73901	+	8.42981i	0.188116	+	0.578962i
$213$	−1.64351	−	5.05821i	−0.112612	−	0.346583i
$214$	−1.71454	+	5.27682i	−0.117204	+	0.360716i
$215$		0			0
$216$	−3.57798	−	11.0119i	−0.243451	−	0.749264i
$217$	−6.54730	+	4.75689i	−0.444460	+	0.322919i
$218$	6.89309			0.466859
$219$	−0.331192	+	0.240625i	−0.0223799	+	0.0162600i
$220$		0			0
$221$	−15.7204	−	11.4215i	−1.05747	−	0.768296i
$222$	−4.94371	−	3.59181i	−0.331800	−	0.241067i
$223$	0.394663	−	1.21465i	0.0264286	−	0.0813389i	−0.936972	−	0.349404i	$-0.886384\pi$
$223$	0.394663	−	1.21465i	0.0264286	−	0.0813389i	0.963401	+	0.268065i	$0.0863842\pi$
$224$	4.60733			0.307840
$225$		0			0
$226$	0.407676			0.0271182
$227$	−8.69517	+	26.7610i	−0.577119	+	1.77619i	0.0517304	+	0.998661i	$0.483526\pi$
$227$	−8.69517	+	26.7610i	−0.577119	+	1.77619i	−0.628849	+	0.777527i	$0.716474\pi$
$228$	1.68170	+	1.22183i	0.111373	+	0.0809175i
$229$	−9.12744	−	6.63147i	−0.603158	−	0.438220i	0.243840	−	0.969815i	$-0.421593\pi$
$229$	−9.12744	−	6.63147i	−0.603158	−	0.438220i	−0.846998	+	0.531595i	$0.821593\pi$
$230$		0			0
$231$	2.88191	−	2.09383i	0.189616	−	0.137764i
$232$	−4.73083			−0.310594
$233$	−10.8990	+	7.91861i	−0.714019	+	0.518765i	−0.884468	−	0.466601i	$-0.845478\pi$
$233$	−10.8990	+	7.91861i	−0.714019	+	0.518765i	0.170448	+	0.985367i	$0.445478\pi$
$234$	−5.02550	−	15.4669i	−0.328527	−	1.01110i
$235$		0			0
$236$	−0.788868	+	2.42789i	−0.0513510	+	0.158042i
$237$	2.34921	+	7.23013i	0.152598	+	0.469647i
$238$	−1.05588	−	3.24967i	−0.0684426	−	0.210645i
$239$	0.587907	−	1.80939i	0.0380285	−	0.117040i	−0.930240	−	0.366951i	$-0.880402\pi$
$239$	0.587907	−	1.80939i	0.0380285	−	0.117040i	0.968269	+	0.249912i	$0.0804015\pi$
$240$		0			0
$241$	−6.04699	−	18.6107i	−0.389521	−	1.19882i	−0.933147	−	0.359495i	$-0.882949\pi$
$241$	−6.04699	−	18.6107i	−0.389521	−	1.19882i	0.543626	−	0.839327i	$-0.317051\pi$
$242$	13.0214	−	9.46058i	0.837046	−	0.608149i
$243$	14.8156			0.950422
$244$	−1.64799	+	1.19733i	−0.105502	+	0.0766514i
$245$		0			0
$246$	−1.09582	−	0.796159i	−0.0698668	−	0.0507612i
$247$	16.8799	+	12.2639i	1.07404	+	0.780336i
$248$	−7.53053	+	23.1766i	−0.478189	+	1.47171i
$249$	−9.82800			−0.622824
$250$		0			0
$251$	20.7096			1.30718			0.653590	−	0.756849i	$-0.273262\pi$
$251$	20.7096			1.30718			0.653590	+	0.756849i	$0.273262\pi$
$252$	−0.697101	+	2.14546i	−0.0439132	+	0.135151i
$253$	12.0934	+	8.78636i	0.760305	+	0.552394i
$254$	3.97199	+	2.88582i	0.249225	+	0.181072i
$255$		0			0
$256$	13.3049	−	9.66657i	0.831556	−	0.604161i
$257$	−15.0730			−0.940225			−0.470113	−	0.882606i	$-0.655787\pi$
$257$	−15.0730			−0.940225			−0.470113	+	0.882606i	$0.655787\pi$
$258$	3.07187	−	2.23184i	0.191246	−	0.138949i
$259$	2.62915	+	8.09168i	0.163367	+	0.502793i
$260$		0			0
$261$	1.21252	−	3.73177i	0.0750534	−	0.230990i
$262$	−5.30025	−	16.3125i	−0.327450	−	1.00779i
$263$	−1.54609	−	4.75839i	−0.0953363	−	0.293415i	0.892005	−	0.452026i	$-0.149298\pi$
$263$	−1.54609	−	4.75839i	−0.0953363	−	0.293415i	−0.987341	+	0.158611i	$0.949298\pi$
$264$	3.31469	−	10.2016i	0.204005	−	0.627864i
$265$		0			0
$266$	1.13376	+	3.48935i	0.0695152	+	0.213946i
$267$	3.55541	−	2.58316i	0.217588	−	0.158087i
$268$	4.10018			0.250458
$269$	22.3939	−	16.2701i	1.36538	−	0.992007i	0.367299	−	0.930103i	$-0.380283\pi$
$269$	22.3939	−	16.2701i	1.36538	−	0.992007i	0.998082	−	0.0619045i	$-0.0197174\pi$
$270$		0			0
$271$	21.3522	+	15.5133i	1.29705	+	0.942365i	0.999922	−	0.0124713i	$-0.00396983\pi$
$271$	21.3522	+	15.5133i	1.29705	+	0.942365i	0.297132	+	0.954836i	$0.403970\pi$
$272$	−3.76713	−	2.73698i	−0.228416	−	0.165954i
$273$	1.30814	−	4.02603i	0.0791720	−	0.243666i
$274$	−20.2806			−1.22520
$275$		0			0
$276$	1.76977			0.106528
$277$	2.20106	−	6.77415i	0.132249	−	0.407019i	−0.862903	−	0.505369i	$-0.831356\pi$
$277$	2.20106	−	6.77415i	0.132249	−	0.407019i	0.995152	+	0.0983496i	$0.0313563\pi$
$278$	3.06900	+	2.22976i	0.184066	+	0.133732i
$279$	−16.3520	−	11.8804i	−0.978970	−	0.711263i
$280$		0			0
$281$	8.35445	−	6.06986i	0.498385	−	0.362098i	−0.310015	−	0.950732i	$-0.600334\pi$
$281$	8.35445	−	6.06986i	0.498385	−	0.362098i	0.808400	+	0.588634i	$0.200334\pi$
$282$	−3.48943			−0.207793
$283$	3.68901	−	2.68023i	0.219289	−	0.159323i	−0.472717	−	0.881214i	$-0.656727\pi$
$283$	3.68901	−	2.68023i	0.219289	−	0.159323i	0.692007	+	0.721891i	$0.256727\pi$
$284$	2.10867	+	6.48983i	0.125127	+	0.385100i
$285$		0			0
$286$	10.1818	−	31.3363i	0.602062	−	1.85296i
$287$	0.582775	+	1.79360i	0.0344001	+	0.105873i
$288$	3.55583	+	10.9437i	0.209529	+	0.644864i
$289$	−2.10240	+	6.47052i	−0.123670	+	0.380619i
$290$		0			0
$291$	2.99156	+	9.20708i	0.175368	+	0.539729i
$292$	0.424929	−	0.308729i	0.0248671	−	0.0180670i
$293$	20.8237			1.21653			0.608267	−	0.793733i	$-0.291865\pi$
$293$	20.8237			1.21653			0.608267	+	0.793733i	$0.291865\pi$
$294$	−3.51398	+	2.55306i	−0.204939	+	0.148897i
$295$		0			0
$296$	20.7266	+	15.0588i	1.20471	+	0.875274i
$297$	15.7409	+	11.4364i	0.913378	+	0.663608i
$298$	−0.523421	+	1.61092i	−0.0303210	+	0.0933183i
$299$	17.7639			1.02731
$300$		0			0
$301$	−5.28668			−0.304719
$302$	−2.20299	+	6.78010i	−0.126768	+	0.390151i
$303$	5.84649	+	4.24772i	0.335872	+	0.244025i
$304$	4.04497	+	2.93885i	0.231995	+	0.168554i
$305$		0			0
$306$	6.90398	−	5.01603i	0.394674	−	0.286747i
$307$	−9.44200			−0.538884			−0.269442	−	0.963017i	$-0.586839\pi$
$307$	−9.44200			−0.538884			−0.269442	+	0.963017i	$0.586839\pi$
$308$	−3.69757	+	2.68644i	−0.210689	+	0.153074i
$309$	0.653762	+	2.01207i	0.0371912	+	0.114463i
$310$		0			0
$311$	4.13477	−	12.7255i	0.234461	−	0.721597i	−0.762731	−	0.646715i	$-0.776142\pi$
$311$	4.13477	−	12.7255i	0.234461	−	0.721597i	0.997192	−	0.0748814i	$-0.0238578\pi$
$312$	−3.93905	−	12.1231i	−0.223005	−	0.686338i
$313$	−7.41478	−	22.8203i	−0.419108	−	1.28988i	−0.908524	−	0.417832i	$-0.862790\pi$
$313$	−7.41478	−	22.8203i	−0.419108	−	1.28988i	0.489416	−	0.872050i	$-0.337210\pi$
$314$	−4.65979	+	14.3414i	−0.262967	+	0.809330i
$315$		0			0
$316$	−3.01410	−	9.27646i	−0.169557	−	0.521841i
$317$	11.7806	−	8.55911i	0.661664	−	0.480727i	−0.205560	−	0.978644i	$-0.565902\pi$
$317$	11.7806	−	8.55911i	0.661664	−	0.480727i	0.867225	+	0.497917i	$0.165902\pi$
$318$	7.30473			0.409629
$319$	6.43148	−	4.67274i	0.360094	−	0.261623i
$320$		0			0
$321$	−2.91814	−	2.12015i	−0.162875	−	0.118335i
$322$	2.52710	+	1.83605i	0.140830	+	0.102319i
$323$	−3.38329	+	10.4127i	−0.188251	+	0.579378i
$324$	−4.38383			−0.243546
$325$		0			0
$326$	−10.6944			−0.592305
$327$	−1.38477	+	4.26190i	−0.0765782	+	0.235683i
$328$	4.59425	+	3.33792i	0.253675	+	0.184306i
$329$	3.93052	+	2.85569i	0.216697	+	0.157439i
$330$		0			0
$331$	19.7601	−	14.3566i	1.08611	−	0.789108i	0.107375	−	0.994219i	$-0.465755\pi$
$331$	19.7601	−	14.3566i	1.08611	−	0.789108i	0.978739	+	0.205111i	$0.0657555\pi$
$332$	12.6096			0.692042
$333$	−17.1909	+	12.4899i	−0.942056	+	0.684444i
$334$	5.46193	+	16.8101i	0.298864	+	0.919808i
$335$		0			0
$336$	0.313472	−	0.964769i	0.0171013	−	0.0526325i
$337$	2.64896	+	8.15266i	0.144298	+	0.444104i	0.996920	−	0.0784246i	$-0.0249890\pi$
$337$	2.64896	+	8.15266i	0.144298	+	0.444104i	−0.852622	+	0.522528i	$0.824989\pi$
$338$	−7.85192	−	24.1657i	−0.427088	−	1.31444i
$339$	−0.0818993	+	0.252060i	−0.00444816	+	0.0136900i
$340$		0			0
$341$	−12.6544	−	38.9462i	−0.685274	−	2.10906i
$342$	−7.41319	+	5.38600i	−0.400859	+	0.291241i
$343$	13.1315			0.709035
$344$	−12.8789	+	9.35707i	−0.694384	+	0.504499i
$345$		0			0
$346$	−5.51128	−	4.00418i	−0.296288	−	0.215266i
$347$	8.74352	+	6.35254i	0.469377	+	0.341022i	0.797198	−	0.603717i	$-0.206314\pi$
$347$	8.74352	+	6.35254i	0.469377	+	0.341022i	−0.327822	+	0.944740i	$0.606314\pi$
$348$	0.290846	−	0.895132i	0.0155910	−	0.0479841i
$349$	−8.13956			−0.435701			−0.217850	−	0.975982i	$-0.569904\pi$
$349$	−8.13956			−0.435701			−0.217850	+	0.975982i	$0.569904\pi$
$350$		0			0
$351$	23.1217			1.23414
$352$	−7.20420	+	22.1723i	−0.383985	+	1.18179i
$353$	17.1237	+	12.4411i	0.911404	+	0.662174i	0.941370	−	0.337377i	$-0.109540\pi$
$353$	17.1237	+	12.4411i	0.911404	+	0.662174i	−0.0299652	+	0.999551i	$0.509540\pi$
$354$	1.70205	+	1.23661i	0.0904630	+	0.0657252i
$355$		0			0
$356$	−4.56169	+	3.31426i	−0.241769	+	0.175656i
$357$	2.22134			0.117566
$358$	−13.2030	+	9.59252i	−0.697799	+	0.506980i
$359$	−1.64578	−	5.06518i	−0.0868608	−	0.267330i	0.898186	−	0.439615i	$-0.144885\pi$
$359$	−1.64578	−	5.06518i	−0.0868608	−	0.267330i	−0.985047	+	0.172285i	$0.944885\pi$
$360$		0			0
$361$	−2.23849	+	6.88938i	−0.117816	+	0.362599i
$362$	−0.417563	−	1.28513i	−0.0219466	−	0.0675447i
$363$	3.23344	+	9.95150i	0.169711	+	0.522318i
$364$	−1.67838	+	5.16551i	−0.0879708	+	0.270746i
$365$		0			0
$366$	0.518766	+	1.59660i	0.0271163	+	0.0834554i
$367$	−13.7753	+	10.0083i	−0.719064	+	0.522431i	−0.886085	−	0.463523i	$-0.846585\pi$
$367$	−13.7753	+	10.0083i	−0.719064	+	0.522431i	0.167021	+	0.985953i	$0.446585\pi$
$368$	4.25682			0.221902
$369$	−3.81053	+	2.76851i	−0.198368	+	0.144123i
$370$		0			0
$371$	−8.22809	−	5.97806i	−0.427181	−	0.310365i
$372$	−3.92233	−	2.84974i	−0.203363	−	0.147752i
$373$	2.11717	−	6.51599i	0.109623	−	0.337385i	−0.881165	−	0.472810i	$-0.843240\pi$
$373$	2.11717	−	6.51599i	0.109623	−	0.337385i	0.990788	+	0.135425i	$0.0432399\pi$
$374$	17.2897			0.894028
$375$		0			0
$376$	14.6295			0.754461
$377$	2.91933	−	8.98478i	0.150353	−	0.462740i
$378$	3.28930	+	2.38982i	0.169183	+	0.122919i
$379$	5.97714	+	4.34265i	0.307025	+	0.223067i	0.730619	−	0.682785i	$-0.239232\pi$
$379$	5.97714	+	4.34265i	0.307025	+	0.223067i	−0.423594	+	0.905852i	$0.639232\pi$
$380$		0			0
$381$	−2.58220	+	1.87608i	−0.132290	+	0.0961145i
$382$	−6.17097			−0.315734
$383$	16.3447	−	11.8751i	0.835175	−	0.606790i	−0.0858436	−	0.996309i	$-0.527359\pi$
$383$	16.3447	−	11.8751i	0.835175	−	0.606790i	0.921019	+	0.389518i	$0.127359\pi$
$384$	0.197871	+	0.608985i	0.0100976	+	0.0310771i
$385$		0			0
$386$	−1.36506	+	4.20122i	−0.0694797	+	0.213836i
$387$	−4.08013	−	12.5573i	−0.207405	−	0.638326i
$388$	−3.83826	−	11.8129i	−0.194858	−	0.599711i
$389$	2.71944	−	8.36957i	0.137881	−	0.424354i	−0.858146	−	0.513406i	$-0.828384\pi$
$389$	2.71944	−	8.36957i	0.137881	−	0.424354i	0.996027	+	0.0890516i	$0.0283836\pi$
$390$		0			0
$391$	2.88049	+	8.86522i	0.145672	+	0.448334i
$392$	14.7325	−	10.7038i	0.744102	−	0.540621i
$393$	11.1506			0.562471
$394$	14.9576	−	10.8674i	0.753555	−	0.547490i
$395$		0			0
$396$	−9.23475	−	6.70944i	−0.464064	−	0.337162i
$397$	4.92939	+	3.58141i	0.247399	+	0.179746i	0.704573	−	0.709631i	$-0.251138\pi$
$397$	4.92939	+	3.58141i	0.247399	+	0.179746i	−0.457174	+	0.889377i	$0.651138\pi$
$398$	−1.92469	+	5.92358i	−0.0964759	+	0.296922i
$399$	−2.38518			−0.119408
$400$		0			0
$401$	−1.71924			−0.0858547			−0.0429274	−	0.999078i	$-0.513668\pi$
$401$	−1.71924			−0.0858547			−0.0429274	+	0.999078i	$0.513668\pi$
$402$	1.04419	−	3.21368i	0.0520793	−	0.160284i
$403$	−39.3699	−	28.6039i	−1.96116	−	1.42486i
$404$	−7.50121	−	5.44995i	−0.373199	−	0.271145i
$405$		0			0
$406$	1.34396	−	0.976443i	0.0666995	−	0.0484600i
$407$	−43.0514			−2.13398
$408$	5.41142	−	3.93163i	0.267905	−	0.194645i
$409$	−8.57257	−	26.3837i	−0.423886	−	1.30459i	−0.904056	−	0.427413i	$-0.859425\pi$
$409$	−8.57257	−	26.3837i	−0.423886	−	1.30459i	0.480170	−	0.877175i	$-0.340575\pi$
$410$		0			0
$411$	4.07423	−	12.5392i	0.200967	−	0.618513i
$412$	−0.838796	−	2.58155i	−0.0413245	−	0.127184i
$413$	−0.905180	−	2.78586i	−0.0445410	−	0.137083i
$414$	−2.41077	+	7.41960i	−0.118483	+	0.364653i
$415$		0			0
$416$	8.56118	+	26.3486i	0.419747	+	1.29185i
$417$	−1.99517	+	1.44957i	−0.0977037	+	0.0709859i
$418$	−18.5649			−0.908039
$419$	−13.2306	+	9.61263i	−0.646359	+	0.469608i	−0.862029	−	0.506859i	$-0.830807\pi$
$419$	−13.2306	+	9.61263i	−0.646359	+	0.469608i	0.215670	+	0.976466i	$0.430807\pi$
$420$		0			0
$421$	8.04616	+	5.84588i	0.392146	+	0.284911i	0.766334	−	0.642442i	$-0.222079\pi$
$421$	8.04616	+	5.84588i	0.392146	+	0.284911i	−0.374188	+	0.927353i	$0.622079\pi$
$422$	−10.2458	−	7.44398i	−0.498756	−	0.362367i
$423$	−3.74959	+	11.5400i	−0.182311	+	0.561096i
$424$	−30.6253			−1.48729
$425$		0			0
$426$	5.62367			0.272467
$427$	0.722285	−	2.22296i	0.0349538	−	0.107577i
$428$	3.74406	+	2.72022i	0.180976	+	0.131487i
$429$	17.3294	+	12.5905i	0.836669	+	0.607876i
$430$		0			0
$431$	16.6093	−	12.0673i	0.800040	−	0.581263i	−0.110886	−	0.993833i	$-0.535369\pi$
$431$	16.6093	−	12.0673i	0.800040	−	0.581263i	0.910926	+	0.412570i	$0.135369\pi$
$432$	5.54071			0.266578
$433$	−20.9914	+	15.2512i	−1.00878	+	0.732925i	−0.963954	−	0.266070i	$-0.914275\pi$
$433$	−20.9914	+	15.2512i	−1.00878	+	0.732925i	−0.0448309	+	0.998995i	$0.514275\pi$
$434$	−2.64433	−	8.13842i	−0.126932	−	0.390657i
$435$		0			0
$436$	1.77671	−	5.46814i	0.0850887	−	0.261876i
$437$	−3.09294	−	9.51909i	−0.147955	−	0.455360i
$438$	−0.133762	−	0.411678i	−0.00639141	−	0.0196708i
$439$	7.76509	−	23.8985i	0.370608	−	1.14061i	−0.575787	−	0.817600i	$-0.695304\pi$
$439$	7.76509	−	23.8985i	0.370608	−	1.14061i	0.946395	−	0.323013i	$-0.104696\pi$
$440$		0			0
$441$	4.66735	+	14.3646i	0.222255	+	0.684030i
$442$	16.6224	−	12.0768i	0.790645	−	0.574437i
$443$	−27.0262			−1.28405			−0.642027	−	0.766682i	$-0.721906\pi$
$443$	−27.0262			−1.28405			−0.642027	+	0.766682i	$0.721906\pi$
$444$	−4.12355	+	2.99594i	−0.195695	+	0.142181i
$445$		0			0
$446$	1.09252	+	0.793765i	0.0517325	+	0.0375859i
$447$	−0.890859	−	0.647247i	−0.0421362	−	0.0306137i
$448$	−2.41748	+	7.44023i	−0.114215	+	0.351518i
$449$	37.9871			1.79272			0.896361	−	0.443325i	$-0.146201\pi$
$449$	37.9871			1.79272			0.896361	+	0.443325i	$0.146201\pi$
$450$		0			0
$451$	−9.54273			−0.449350
$452$	0.105079	−	0.323400i	0.00494250	−	0.0152115i
$453$	−3.74947	−	2.72415i	−0.176166	−	0.127992i
$454$	−24.0703	−	17.4881i	−1.12968	−	0.820759i
$455$		0			0
$456$	−5.81055	+	4.22161i	−0.272104	+	0.197695i
$457$	29.9832			1.40256			0.701278	−	0.712888i	$-0.252613\pi$
$457$	29.9832			1.40256			0.701278	+	0.712888i	$0.252613\pi$
$458$	9.65113	−	7.01195i	0.450967	−	0.327647i
$459$	3.74927	+	11.5391i	0.175001	+	0.538597i
$460$		0			0
$461$	−0.659330	+	2.02921i	−0.0307081	+	0.0945097i	−0.965236	−	0.261380i	$-0.915822\pi$
$461$	−0.659330	+	2.02921i	−0.0307081	+	0.0945097i	0.934528	+	0.355890i	$0.115822\pi$
$462$	1.16395	+	3.58227i	0.0541518	+	0.166662i
$463$	6.79231	+	20.9046i	0.315665	+	0.971518i	0.975480	+	0.220089i	$0.0706348\pi$
$463$	6.79231	+	20.9046i	0.315665	+	0.971518i	−0.659815	+	0.751428i	$0.729365\pi$
$464$	0.699568	−	2.15305i	0.0324766	−	0.0999528i
$465$		0			0
$466$	−4.40192	−	13.5477i	−0.203915	−	0.627585i
$467$	4.29663	−	3.12169i	0.198824	−	0.144454i	−0.483918	−	0.875113i	$-0.660787\pi$
$467$	4.29663	−	3.12169i	0.198824	−	0.144454i	0.682743	+	0.730659i	$0.260787\pi$
$468$	−13.5649			−0.627036
$469$	−3.80619	+	2.76536i	−0.175754	+	0.127693i
$470$		0			0
$471$	−7.93094	−	5.76216i	−0.365438	−	0.265507i
$472$	−7.13590	−	5.18453i	−0.328456	−	0.238637i
$473$	8.26646	−	25.4415i	0.380092	−	1.16980i
$474$	−8.03838			−0.369215
$475$		0			0
$476$	−2.85005			−0.130632
$477$	7.84933	−	24.1578i	0.359396	−	1.10611i
$478$	1.62747	+	1.18243i	0.0744387	+	0.0540829i
$479$	17.0603	+	12.3950i	0.779506	+	0.566344i	0.904831	−	0.425772i	$-0.139997\pi$
$479$	17.0603	+	12.3950i	0.779506	+	0.566344i	−0.125325	+	0.992116i	$0.539997\pi$
$480$		0			0
$481$	−41.3897	+	30.0714i	−1.88721	+	1.37114i
$482$	20.6912			0.942459
$483$	−1.64288	+	1.19362i	−0.0747536	+	0.0543116i
$484$	−4.14859	−	12.7681i	−0.188572	−	0.580366i
$485$		0			0
$486$	−4.84095	+	14.8989i	−0.219590	+	0.675829i
$487$	8.22358	+	25.3096i	0.372646	+	1.14689i	0.945053	+	0.326917i	$0.106010\pi$
$487$	8.22358	+	25.3096i	0.372646	+	1.14689i	−0.572407	+	0.819969i	$0.693990\pi$
$488$	−2.17494	−	6.69377i	−0.0984549	−	0.303013i
$489$	2.14842	−	6.61216i	0.0971550	−	0.299012i
$490$		0			0
$491$	0.556442	+	1.71255i	0.0251119	+	0.0772865i	0.962827	−	0.270119i	$-0.0870629\pi$
$491$	0.556442	+	1.71255i	0.0251119	+	0.0772865i	−0.937715	+	0.347405i	$0.887063\pi$
$492$	−0.914024	+	0.664077i	−0.0412074	+	0.0299389i
$493$	4.95731			0.223266
$494$	−17.8484	+	12.9676i	−0.803036	+	0.583440i
$495$		0			0
$496$	−9.43433	−	6.85444i	−0.423614	−	0.307774i
$497$	−6.33453	−	4.60231i	−0.284143	−	0.206442i
$498$	3.21127	−	9.88326i	0.143900	−	0.442880i
$499$	28.6962			1.28462			0.642309	−	0.766446i	$-0.277977\pi$
$499$	28.6962			1.28462			0.642309	+	0.766446i	$0.277977\pi$
$500$		0			0
$501$	−11.4907			−0.513367
$502$	−6.76681	+	20.8261i	−0.302017	+	0.929514i
$503$	−19.1597	−	13.9204i	−0.854290	−	0.620678i	0.0720355	−	0.997402i	$-0.477051\pi$
$503$	−19.1597	−	13.9204i	−0.854290	−	0.620678i	−0.926326	+	0.376724i	$0.877051\pi$
$504$	−6.30579	−	4.58143i	−0.280882	−	0.204073i
$505$		0			0
$506$	−12.7872	+	9.29048i	−0.568462	+	0.413012i
$507$	16.5187			0.733622
$508$	3.31304	−	2.40706i	0.146992	−	0.106796i
$509$	5.46826	+	16.8296i	0.242376	+	0.745958i	0.996057	+	0.0887168i	$0.0282766\pi$
$509$	5.46826	+	16.8296i	0.242376	+	0.745958i	−0.753681	+	0.657241i	$0.771723\pi$
$510$		0			0
$511$	−0.186239	+	0.573186i	−0.00823874	+	0.0253562i
$512$	4.79789	+	14.7664i	0.212039	+	0.652589i
$513$	−4.02580	−	12.3901i	−0.177743	−	0.547038i
$514$	4.92504	−	15.1577i	0.217234	−	0.668578i
$515$		0			0
$516$	−0.978694	−	3.01211i	−0.0430846	−	0.132601i
$517$	−19.8886	+	14.4499i	−0.874700	+	0.635507i
$518$	−8.99625			−0.395273
$519$	3.58291	−	2.60313i	0.157272	−	0.114265i
$520$		0			0
$521$	−18.5876	−	13.5047i	−0.814338	−	0.591651i	0.100747	−	0.994912i	$-0.467877\pi$
$521$	−18.5876	−	13.5047i	−0.814338	−	0.591651i	−0.915085	+	0.403261i	$0.867877\pi$
$522$	3.35656	+	2.43868i	0.146913	+	0.106738i
$523$	8.95447	−	27.5590i	0.391552	−	1.20507i	−0.540063	−	0.841625i	$-0.681600\pi$
$523$	8.95447	−	27.5590i	0.391552	−	1.20507i	0.931615	−	0.363447i	$-0.118400\pi$
$524$	−14.3065			−0.624982
$525$		0			0
$526$	5.29033			0.230669
$527$	7.89104	−	24.2861i	0.343739	−	1.05792i
$528$	4.15268	+	3.01710i	0.180722	+	0.131302i
$529$	11.7134	+	8.51025i	0.509276	+	0.370011i
$530$		0			0
$531$	5.91860	−	4.30011i	0.256845	−	0.186609i
$532$	3.06025			0.132679
$533$	−9.17441	+	6.66560i	−0.397388	+	0.288719i
$534$	1.43596	+	4.41944i	0.0621402	+	0.191248i
$535$		0			0
$536$	−4.37778	+	13.4734i	−0.189091	+	0.581963i
$537$	−3.27853	−	10.0903i	−0.141479	−	0.435428i
$538$	9.04448	+	27.8361i	0.389935	+	1.20010i
$539$	−9.45618	+	29.1031i	−0.407307	+	1.25356i
$540$		0			0
$541$	7.55563	+	23.2538i	0.324842	+	0.999760i	0.971512	+	0.236990i	$0.0761610\pi$
$541$	7.55563	+	23.2538i	0.324842	+	0.999760i	−0.646670	+	0.762770i	$0.723839\pi$
$542$	−22.5773	+	16.4034i	−0.969778	+	0.704585i
$543$	0.878460			0.0376983
$544$	−11.7613	+	8.54506i	−0.504260	+	0.366367i
$545$		0			0
$546$	3.62124	+	2.63098i	0.154975	+	0.112596i
$547$	−5.26131	−	3.82257i	−0.224957	−	0.163441i	0.469598	−	0.882880i	$-0.344399\pi$
$547$	−5.26131	−	3.82257i	−0.224957	−	0.163441i	−0.694555	+	0.719439i	$0.744399\pi$
$548$	−5.22736	+	16.0882i	−0.223302	+	0.687252i
$549$	5.83761			0.249143
$550$		0			0
$551$	−5.32295			−0.226765
$552$	−1.88959	+	5.81558i	−0.0804265	+	0.247527i
$553$	9.05448	+	6.57847i	0.385036	+	0.279745i
$554$	6.09306	+	4.42687i	0.258869	+	0.188080i
$555$		0			0
$556$	2.55986	−	1.85984i	0.108562	−	0.0788749i
$557$	−3.12305			−0.132328			−0.0661640	−	0.997809i	$-0.521076\pi$
$557$	−3.12305			−0.132328			−0.0661640	+	0.997809i	$0.521076\pi$
$558$	17.2902	−	12.5621i	0.731953	−	0.531795i
$559$	−9.82352	−	30.2337i	−0.415491	−	1.27875i
$560$		0			0
$561$	−3.47338	+	10.6900i	−0.146646	+	0.451330i
$562$	3.37421	+	10.3847i	0.142332	+	0.438054i
$563$	11.2869	+	34.7376i	0.475687	+	1.46401i	0.845029	+	0.534720i	$0.179583\pi$
$563$	11.2869	+	34.7376i	0.475687	+	1.46401i	−0.369342	+	0.929293i	$0.620417\pi$
$564$	−0.899407	+	2.76809i	−0.0378719	+	0.116558i
$565$		0			0
$566$	1.48992	+	4.58551i	0.0626262	+	0.192744i
$567$	4.06951	−	2.95667i	0.170903	−	0.124168i
$568$	−23.5774			−0.989285
$569$	30.5546	−	22.1992i	1.28092	−	0.930640i	0.281336	−	0.959609i	$-0.409222\pi$
$569$	30.5546	−	22.1992i	1.28092	−	0.930640i	0.999580	+	0.0289691i	$0.00922244\pi$
$570$		0			0
$571$	33.3614	+	24.2385i	1.39613	+	1.01435i	0.995161	+	0.0982590i	$0.0313274\pi$
$571$	33.3614	+	24.2385i	1.39613	+	1.01435i	0.400971	+	0.916091i	$0.368673\pi$
$572$	−22.2340	−	16.1540i	−0.929652	−	0.675432i
$573$	1.23971	−	3.81542i	0.0517895	−	0.159392i
$574$	−1.99410			−0.0832322
$575$		0			0
$576$	−19.5384			−0.814100
$577$	1.31928	−	4.06033i	0.0549224	−	0.169034i	−0.919833	−	0.392311i	$-0.871676\pi$
$577$	1.31928	−	4.06033i	0.0549224	−	0.169034i	0.974755	+	0.223277i	$0.0716756\pi$
$578$	−5.81995	−	4.22844i	−0.242078	−	0.175880i
$579$	−2.32332	−	1.68799i	−0.0965540	−	0.0701506i
$580$		0			0
$581$	−11.7055	+	8.50453i	−0.485625	+	0.352827i
$582$	−10.2363			−0.424310
$583$	41.6345	−	30.2492i	1.72432	−	1.25280i
$584$	0.560803	+	1.72597i	0.0232062	+	0.0714213i
$585$		0			0
$586$	−6.80408	+	20.9408i	−0.281074	+	0.865056i
$587$	−3.53301	−	10.8735i	−0.145823	−	0.448797i	0.851293	−	0.524691i	$-0.175819\pi$
$587$	−3.53301	−	10.8735i	−0.145823	−	0.448797i	−0.997116	+	0.0758937i	$0.975819\pi$
$588$	1.11955	+	3.44562i	0.0461694	+	0.142095i
$589$	−8.47306	+	26.0774i	−0.349126	+	1.07450i
$590$		0			0
$591$	3.71425	+	11.4313i	0.152784	+	0.470220i
$592$	−9.91834	+	7.20609i	−0.407641	+	0.296169i
$593$	−30.9375			−1.27045			−0.635225	−	0.772327i	$-0.719092\pi$
$593$	−30.9375			−1.27045			−0.635225	+	0.772327i	$0.719092\pi$
$594$	−16.6440	+	12.0926i	−0.682912	+	0.496164i
$595$		0			0
$596$	1.14300	+	0.830436i	0.0468190	+	0.0340160i
$597$	−3.27581	−	2.38001i	−0.134070	−	0.0974075i
$598$	−5.80430	+	17.8638i	−0.237355	+	0.730505i
$599$	−46.1912			−1.88732			−0.943660	−	0.330916i	$-0.892642\pi$
$599$	−46.1912			−1.88732			−0.943660	+	0.330916i	$0.892642\pi$
$600$		0			0
$601$	−38.0963			−1.55398			−0.776990	−	0.629513i	$-0.783254\pi$
$601$	−38.0963			−1.55398			−0.776990	+	0.629513i	$0.783254\pi$
$602$	1.72740	−	5.31641i	0.0704038	−	0.216681i
$603$	−9.50604	−	6.90654i	−0.387116	−	0.281256i
$604$	4.81068	+	3.49516i	0.195744	+	0.142216i
$605$		0			0
$606$	−6.18193	+	4.49144i	−0.251124	+	0.182452i
$607$	−38.6361			−1.56819			−0.784095	−	0.620641i	$-0.786873\pi$
$607$	−38.6361			−1.56819			−0.784095	+	0.620641i	$0.786873\pi$
$608$	12.6287	−	9.17532i	0.512163	−	0.372108i
$609$	0.333728	+	1.02711i	0.0135234	+	0.0416206i
$610$		0			0
$611$	−9.02770	+	27.7844i	−0.365221	+	1.12404i
$612$	−2.19960	−	6.76966i	−0.0889134	−	0.273647i
$613$	3.32381	+	10.2296i	0.134247	+	0.413171i	0.995472	−	0.0950531i	$-0.0303021\pi$
$613$	3.32381	+	10.2296i	0.134247	+	0.413171i	−0.861225	+	0.508224i	$0.830302\pi$
$614$	3.08515	−	9.49510i	0.124506	−	0.383191i
$615$		0			0
$616$	−4.87989	−	15.0187i	−0.196616	−	0.605123i
$617$	−8.74322	+	6.35232i	−0.351989	+	0.255735i	−0.749703	−	0.661775i	$-0.769804\pi$
$617$	−8.74322	+	6.35232i	−0.351989	+	0.255735i	0.397714	+	0.917509i	$0.369804\pi$
$618$	−2.23700			−0.0899855
$619$	29.8477	−	21.6856i	1.19968	−	0.871619i	0.205427	−	0.978672i	$-0.434142\pi$
$619$	29.8477	−	21.6856i	1.19968	−	0.871619i	0.994253	+	0.107054i	$0.0341417\pi$
$620$		0			0
$621$	−8.97334	−	6.51951i	−0.360088	−	0.261619i
$622$	11.4460	+	8.31603i	0.458944	+	0.333443i
$623$	1.99931	−	6.15325i	0.0801008	−	0.246525i
$624$	6.09985			0.244189
$625$		0			0
$626$	25.3714			1.01405
$627$	3.72956	−	11.4784i	0.148944	−	0.458404i
$628$	10.1756	+	7.39302i	0.406051	+	0.295014i
$629$	−21.7189	−	15.7797i	−0.865988	−	0.629177i
$630$		0			0
$631$	−31.7615	+	23.0761i	−1.26440	+	0.918643i	−0.998965	−	0.0454842i	$-0.985517\pi$
$631$	−31.7615	+	23.0761i	−1.26440	+	0.918643i	−0.265439	+	0.964128i	$0.585517\pi$
$632$	33.7011			1.34056
$633$	6.66081	−	4.83936i	0.264744	−	0.192347i
$634$	4.75796	+	14.6435i	0.188963	+	0.581568i
$635$		0			0
$636$	1.88281	−	5.79468i	0.0746581	−	0.229774i
$637$	11.2373	+	34.5850i	0.445240	+	1.37031i
$638$	2.59755	+	7.99445i	0.102838	+	0.316503i
$639$	6.04294	−	18.5983i	0.239055	−	0.735735i
$640$		0			0
$641$	2.57978	+	7.93973i	0.101895	+	0.313601i	0.988989	−	0.147988i	$-0.0472797\pi$
$641$	2.57978	+	7.93973i	0.101895	+	0.313601i	−0.887094	+	0.461589i	$0.847280\pi$
$642$	3.08557	−	2.24180i	0.121778	−	0.0884767i
$643$	13.1408			0.518223			0.259112	−	0.965847i	$-0.416570\pi$
$643$	13.1408			0.518223			0.259112	+	0.965847i	$0.416570\pi$
$644$	2.10786	−	1.53145i	0.0830613	−	0.0603476i
$645$		0			0
$646$	−9.36577	−	6.80463i	−0.368491	−	0.267725i
$647$	21.0992	+	15.3295i	0.829496	+	0.602664i	0.919417	−	0.393285i	$-0.128661\pi$
$647$	21.0992	+	15.3295i	0.829496	+	0.602664i	−0.0899210	+	0.995949i	$0.528661\pi$
$648$	4.68064	−	14.4055i	0.183873	−	0.565902i
$649$	14.8220			0.581814
$650$		0			0
$651$	5.56310			0.218035
$652$	−2.75649	+	8.48359i	−0.107952	+	0.332243i
$653$	18.6312	+	13.5364i	0.729097	+	0.529720i	0.889278	−	0.457368i	$-0.151208\pi$
$653$	18.6312	+	13.5364i	0.729097	+	0.529720i	−0.160181	+	0.987088i	$0.551208\pi$
$654$	−3.83339	−	2.78512i	−0.149898	−	0.108907i
$655$		0			0
$656$	−2.19849	+	1.59730i	−0.0858367	+	0.0623640i
$657$	−1.50521			−0.0587240
$658$	−4.15603	+	3.01953i	−0.162019	+	0.117714i
$659$	10.7408	+	33.0569i	0.418403	+	1.28771i	0.909171	+	0.416422i	$0.136716\pi$
$659$	10.7408	+	33.0569i	0.418403	+	1.28771i	−0.490768	+	0.871290i	$0.663284\pi$
$660$		0			0
$661$	5.56334	−	17.1222i	0.216389	−	0.665976i	−0.782663	−	0.622445i	$-0.786139\pi$
$661$	5.56334	−	17.1222i	0.216389	−	0.665976i	0.999052	−	0.0435308i	$-0.0138607\pi$
$662$	7.98074	+	24.5622i	0.310180	+	0.954636i
$663$	4.12762	+	12.7035i	0.160304	+	0.493364i
$664$	−13.4633	+	41.4359i	−0.522478	+	1.60802i
$665$		0			0
$666$	−6.94309	−	21.3686i	−0.269039	−	0.828018i
$667$	−3.66637	+	2.66377i	−0.141962	+	0.103142i
$668$	14.7429			0.570420
$669$	−0.710254	+	0.516030i	−0.0274600	+	0.0199509i
$670$		0			0
$671$	9.56838	+	6.95183i	0.369383	+	0.268372i
$672$	−2.56223	−	1.86157i	−0.0988403	−	0.0718117i
$673$	−4.59267	+	14.1348i	−0.177034	+	0.544856i	−0.999721	−	0.0236399i	$-0.992474\pi$
$673$	−4.59267	+	14.1348i	−0.177034	+	0.544856i	0.822686	+	0.568496i	$0.192474\pi$
$674$	−9.06404			−0.349134
$675$		0			0
$676$	−21.1940			−0.815153
$677$	7.14565	−	21.9920i	0.274629	−	0.845223i	−0.714688	−	0.699444i	$-0.753431\pi$
$677$	7.14565	−	21.9920i	0.274629	−	0.845223i	0.989317	−	0.145779i	$-0.0465688\pi$
$678$	−0.226717	−	0.164720i	−0.00870702	−	0.00632602i
$679$	11.5303	+	8.37723i	0.442491	+	0.321489i
$680$		0			0
$681$	15.6482	−	11.3691i	0.599641	−	0.435665i
$682$	43.3000			1.65804
$683$	−15.8848	+	11.5410i	−0.607816	+	0.441604i	−0.848645	−	0.528963i	$-0.822581\pi$
$683$	−15.8848	+	11.5410i	−0.607816	+	0.441604i	0.240828	+	0.970568i	$0.422581\pi$
$684$	2.36183	+	7.26897i	0.0903069	+	0.277936i
$685$		0			0
$686$	−4.29068	+	13.2054i	−0.163819	+	0.504183i
$687$	2.39654	+	7.37580i	0.0914339	+	0.281404i
$688$	−2.35404	−	7.24499i	−0.0897469	−	0.276213i
$689$	18.8984	−	58.1634i	0.719973	−	2.21585i
$690$		0			0
$691$	−1.81635	−	5.59014i	−0.0690970	−	0.212659i	0.910545	−	0.413409i	$-0.135662\pi$
$691$	−1.81635	−	5.59014i	−0.0690970	−	0.212659i	−0.979642	+	0.200750i	$0.935662\pi$
$692$	−4.59697	+	3.33989i	−0.174751	+	0.126964i
$693$	13.0978			0.497544
$694$	−9.24518	+	6.71702i	−0.350942	+	0.254974i
$695$		0			0
$696$	2.63092	+	1.91147i	0.0997246	+	0.0724542i
$697$	−4.81419	−	3.49771i	−0.182351	−	0.132485i
$698$	2.65958	−	8.18533i	0.100666	−	0.309819i
$699$	9.26066			0.350270
$700$		0			0
$701$	−50.0581			−1.89067			−0.945334	−	0.326103i	$-0.894264\pi$
$701$	−50.0581			−1.89067			−0.945334	+	0.326103i	$0.894264\pi$
$702$	−7.55493	+	23.2517i	−0.285142	+	0.877578i
$703$	23.3208	+	16.9435i	0.879560	+	0.639038i
$704$	−32.0252	−	23.2677i	−1.20700	−	0.876934i
$705$		0			0
$706$	−18.1062	+	13.1549i	−0.681436	+	0.495092i
$707$	10.6391			0.400124
$708$	1.41968	−	1.03146i	0.0533550	−	0.0387647i
$709$	4.24917	+	13.0776i	0.159581	+	0.491139i	0.998596	−	0.0529685i	$-0.0168683\pi$
$709$	4.24917	+	13.0776i	0.159581	+	0.491139i	−0.839015	+	0.544108i	$0.816868\pi$
$710$		0			0
$711$	−8.63768	+	26.5841i	−0.323938	+	0.996980i
$712$	−6.02032	−	18.5286i	−0.225621	−	0.694390i
$713$	7.21384	+	22.2019i	0.270161	+	0.831469i
$714$	−0.725816	+	2.23383i	−0.0271630	+	0.0835991i
$715$		0			0
$716$	4.20645	+	12.9461i	0.157202	+	0.483819i
$717$	−1.05802	+	0.768700i	−0.0395126	+	0.0287076i
$718$	5.63142			0.210163
$719$	8.49464	−	6.17172i	0.316797	−	0.230166i	−0.418011	−	0.908442i	$-0.637273\pi$
$719$	8.49464	−	6.17172i	0.316797	−	0.230166i	0.734807	+	0.678276i	$0.237273\pi$
$720$		0			0
$721$	2.51977	+	1.83072i	0.0938413	+	0.0681797i
$722$	−6.19670	−	4.50216i	−0.230617	−	0.167553i
$723$	−4.15672	+	12.7931i	−0.154590	+	0.475780i
$724$	−1.12709			−0.0418880
$725$		0			0
$726$	−11.0640			−0.410623
$727$	1.87377	−	5.76688i	0.0694944	−	0.213882i	−0.910278	−	0.413998i	$-0.864132\pi$
$727$	1.87377	−	5.76688i	0.0694944	−	0.213882i	0.979772	+	0.200116i	$0.0641320\pi$
$728$	−15.1821	−	11.0305i	−0.562687	−	0.408816i
$729$	3.82455	+	2.77870i	0.141650	+	0.102915i
$730$		0			0
$731$	13.4955	−	9.80503i	0.499148	−	0.362652i
$732$	1.40026			0.0517550
$733$	1.89367	−	1.37583i	0.0699442	−	0.0508174i	−0.552264	−	0.833669i	$-0.686236\pi$
$733$	1.89367	−	1.37583i	0.0699442	−	0.0508174i	0.622208	+	0.782852i	$0.286236\pi$
$734$	−5.56358	−	17.1229i	−0.205355	−	0.632019i
$735$		0			0
$736$	4.10687	−	12.6397i	0.151381	−	0.465904i
$737$	−7.35648	−	22.6409i	−0.270979	−	0.833988i
$738$	−1.53900	−	4.73656i	−0.0566514	−	0.174355i
$739$	−12.8351	+	39.5024i	−0.472147	+	1.45312i	0.377621	+	0.925960i	$0.376742\pi$
$739$	−12.8351	+	39.5024i	−0.472147	+	1.45312i	−0.849768	+	0.527158i	$0.823258\pi$
$740$		0			0
$741$	−4.43206	−	13.6405i	−0.162816	−	0.501096i
$742$	8.70018	−	6.32105i	0.319394	−	0.232053i
$743$	0.813821			0.0298562			0.0149281	−	0.999889i	$-0.495248\pi$
$743$	0.813821			0.0298562			0.0149281	+	0.999889i	$0.495248\pi$
$744$	13.5523	−	9.84631i	0.496851	−	0.360983i
$745$		0			0
$746$	5.86085	+	4.25815i	0.214581	+	0.155902i
$747$	−29.2347	−	21.2402i	−1.06964	−	0.777139i
$748$	4.45644	−	13.7155i	0.162944	−	0.501489i
$749$	−5.31025			−0.194032
$750$		0			0
$751$	31.8919			1.16375			0.581877	−	0.813277i	$-0.302319\pi$
$751$	31.8919			1.16375			0.581877	+	0.813277i	$0.302319\pi$
$752$	−2.16333	+	6.65806i	−0.0788886	+	0.242794i
$753$	−11.5171	−	8.36764i	−0.419705	−	0.304934i
$754$	8.08142	+	5.87150i	0.294308	+	0.213827i
$755$		0			0
$756$	2.74361	−	1.99335i	0.0997842	−	0.0724974i
$757$	−26.7040			−0.970572			−0.485286	−	0.874355i	$-0.661285\pi$
$757$	−26.7040			−0.970572			−0.485286	+	0.874355i	$0.661285\pi$
$758$	−6.32008	+	4.59181i	−0.229556	+	0.166782i
$759$	−3.17530	−	9.77256i	−0.115256	−	0.354722i
$760$		0			0
$761$	13.3076	−	40.9567i	0.482402	−	1.48468i	−0.353307	−	0.935507i	$-0.614943\pi$
$761$	13.3076	−	40.9567i	0.482402	−	1.48468i	0.835709	−	0.549172i	$-0.185057\pi$
$762$	−1.04290	−	3.20973i	−0.0377804	−	0.116276i
$763$	2.03866	+	6.27436i	0.0738046	+	0.227147i
$764$	−1.59058	+	4.89530i	−0.0575451	+	0.177106i
$765$		0			0
$766$	6.60132	+	20.3168i	0.238515	+	0.734075i
$767$	14.2499	−	10.3532i	0.514535	−	0.373831i
$768$	−11.3049			−0.407929
$769$	0.852363	−	0.619278i	0.0307370	−	0.0223317i	−0.572311	−	0.820037i	$-0.693953\pi$
$769$	0.852363	−	0.619278i	0.0307370	−	0.0223317i	0.603048	+	0.797705i	$0.293953\pi$
$770$		0			0
$771$	8.38239	+	6.09016i	0.301884	+	0.219332i
$772$	2.98089	+	2.16574i	0.107285	+	0.0779468i
$773$	4.08825	−	12.5823i	0.147044	−	0.452556i	−0.850224	−	0.526421i	$-0.823534\pi$
$773$	4.08825	−	12.5823i	0.147044	−	0.452556i	0.997268	+	0.0738656i	$0.0235336\pi$
$774$	13.9611			0.501823
$775$		0			0
$776$	42.9161			1.54060
$777$	1.80728	−	5.56225i	0.0648360	−	0.199545i
$778$	7.52807	+	5.46946i	0.269894	+	0.196090i
$779$	5.16927	+	3.75569i	0.185208	+	0.134562i
$780$		0			0
$781$	32.0530	−	23.2879i	1.14695	−	0.833306i
$782$	−9.85627			−0.352459
$783$	−4.77218	+	3.46719i	−0.170544	+	0.123907i
$784$	2.69284	+	8.28770i	0.0961728	+	0.295989i
$785$		0			0
$786$	−3.64341	+	11.2133i	−0.129956	+	0.399964i
$787$	−10.3946	−	31.9914i	−0.370529	−	1.14037i	−0.946446	−	0.322862i	$-0.895355\pi$
$787$	−10.3946	−	31.9914i	−0.370529	−	1.14037i	0.575917	−	0.817508i	$-0.304645\pi$
$788$	−4.76548	−	14.6667i	−0.169763	−	0.522478i
$789$	−1.06279	+	3.27093i	−0.0378364	+	0.116448i
$790$		0			0
$791$	0.120572	+	0.371082i	0.00428705	+	0.0131942i
$792$	31.9076	−	23.1822i	1.13379	−	0.823744i
$793$	14.0549			0.499105
$794$	−5.21221	+	3.78689i	−0.184974	+	0.134392i
$795$		0			0
$796$	4.20296	+	3.05363i	0.148970	+	0.108233i
$797$	5.58012	+	4.05419i	0.197658	+	0.143607i	0.682212	−	0.731154i	$-0.261018\pi$
$797$	5.58012	+	4.05419i	0.197658	+	0.143607i	−0.484554	+	0.874761i	$0.661018\pi$
$798$	0.779350	−	2.39859i	0.0275887	−	0.0849093i
$799$	−15.3299			−0.542333
$800$		0			0
$801$	16.1587			0.570941
$802$	0.561756	−	1.72891i	0.0198363	−	0.0610498i
$803$	−2.46718	−	1.79251i	−0.0870649	−	0.0632564i
$804$	−2.28020	−	1.65666i	−0.0804164	−	0.0584259i
$805$		0			0
$806$	41.6288	−	30.2451i	1.46631	−	1.06534i
$807$	−19.0276			−0.669803
$808$	25.9179	−	18.8305i	0.911789	−	0.662454i
$809$	−10.9185	−	33.6037i	−0.383874	−	1.18144i	−0.937294	−	0.348540i	$-0.886678\pi$
$809$	−10.9185	−	33.6037i	−0.383874	−	1.18144i	0.553420	−	0.832902i	$-0.313322\pi$
$810$		0			0
$811$	−1.22742	+	3.77760i	−0.0431005	+	0.132650i	−0.970291	−	0.241940i	$-0.922216\pi$
$811$	−1.22742	+	3.77760i	−0.0431005	+	0.132650i	0.927191	+	0.374589i	$0.122216\pi$
$812$	−0.428183	−	1.31781i	−0.0150263	−	0.0462461i
$813$	−5.60634	−	17.2545i	−0.196623	−	0.605143i
$814$	14.0669	−	43.2934i	0.493044	−	1.51743i
$815$		0			0
$816$	0.989114	+	3.04418i	0.0346259	+	0.106568i
$817$	−14.4908	+	10.5282i	−0.506970	+	0.368335i
$818$	29.3331			1.02561
$819$	12.5923	−	9.14881i	0.440009	−	0.319685i
$820$		0			0
$821$	−19.7204	−	14.3277i	−0.688247	−	0.500041i	0.187836	−	0.982200i	$-0.439853\pi$
$821$	−19.7204	−	14.3277i	−0.688247	−	0.500041i	−0.876083	+	0.482160i	$0.839853\pi$
$822$	11.2785	+	8.19429i	0.393382	+	0.285809i
$823$	−6.87883	+	21.1709i	−0.239781	+	0.737970i	0.756670	+	0.653797i	$0.226825\pi$
$823$	−6.87883	+	21.1709i	−0.239781	+	0.737970i	−0.996451	+	0.0841731i	$0.973175\pi$
$824$	9.37870			0.326722
$825$		0			0
$826$	3.09729			0.107768
$827$	−8.22592	+	25.3168i	−0.286043	+	0.880351i	0.700041	+	0.714103i	$0.253165\pi$
$827$	−8.22592	+	25.3168i	−0.286043	+	0.880351i	−0.986084	+	0.166248i	$0.946835\pi$
$828$	5.26442	+	3.82483i	0.182951	+	0.132922i
$829$	6.33731	+	4.60432i	0.220104	+	0.159915i	0.692373	−	0.721539i	$-0.256565\pi$
$829$	6.33731	+	4.60432i	0.220104	+	0.159915i	−0.472270	+	0.881454i	$0.656565\pi$
$830$		0			0
$831$	−3.96112	+	2.87792i	−0.137410	+	0.0998340i
$832$	−47.0416			−1.63088
$833$	−15.4378	+	11.2162i	−0.534886	+	0.388618i
$834$	−0.805810	−	2.48003i	−0.0279029	−	0.0858764i
$835$		0			0
$836$	−4.78513	+	14.7271i	−0.165497	+	0.509348i
$837$	9.38961	+	28.8982i	0.324552	+	0.998870i
$838$	−5.34361	−	16.4459i	−0.184592	−	0.568116i
$839$	1.81517	−	5.58652i	0.0626666	−	0.192868i	−0.914822	−	0.403858i	$-0.867669\pi$
$839$	1.81517	−	5.58652i	0.0626666	−	0.192868i	0.977488	+	0.210990i	$0.0676689\pi$
$840$		0			0
$841$	−8.21672	−	25.2885i	−0.283335	−	0.872016i
$842$	−8.50781	+	6.18129i	−0.293199	+	0.213021i
$843$	−7.09859			−0.244488
$844$	−8.54601	+	6.20904i	−0.294166	+	0.213724i
$845$		0			0
$846$	−10.3798	−	7.54135i	−0.356864	−	0.259277i
$847$	12.4625	+	9.05456i	0.428218	+	0.311118i
$848$	4.52869	−	13.9379i	0.155516	−	0.478629i
$849$	−3.13447			−0.107575
$850$		0			0
$851$	24.5421			0.841293
$852$	1.44951	−	4.46113i	0.0496594	−	0.152836i
$853$	−22.7695	−	16.5430i	−0.779613	−	0.566422i	0.125250	−	0.992125i	$-0.460027\pi$
$853$	−22.7695	−	16.5430i	−0.779613	−	0.566422i	−0.904863	+	0.425703i	$0.860027\pi$
$854$	1.99946	+	1.45269i	0.0684201	+	0.0497101i
$855$		0			0
$856$	−12.9363	+	9.39880i	−0.442155	+	0.321244i
$857$	36.2976			1.23990			0.619951	−	0.784640i	$-0.287152\pi$
$857$	36.2976			1.23990			0.619951	+	0.784640i	$0.287152\pi$
$858$	−18.3236	+	13.3129i	−0.625558	+	0.454495i
$859$	1.18168	+	3.63684i	0.0403185	+	0.124087i	0.969190	−	0.246315i	$-0.0792198\pi$
$859$	1.18168	+	3.63684i	0.0403185	+	0.124087i	−0.928871	+	0.370402i	$0.879220\pi$
$860$		0			0
$861$	0.400602	−	1.23292i	0.0136525	−	0.0420180i
$862$	6.70817	+	20.6456i	0.228481	+	0.703192i
$863$	−7.90944	−	24.3428i	−0.269240	−	0.828637i	−0.990686	−	0.136166i	$-0.956522\pi$
$863$	−7.90944	−	24.3428i	−0.269240	−	0.828637i	0.721446	−	0.692471i	$-0.243478\pi$
$864$	5.34555	−	16.4519i	0.181859	−	0.559705i
$865$		0			0
$866$	−8.47805	−	26.0928i	−0.288096	−	0.886668i
$867$	3.78357	−	2.74893i	0.128497	−	0.0933584i
$868$	−7.13761			−0.242266
$869$	−45.8161	+	33.2873i	−1.55420	+	1.12920i
$870$		0			0
$871$	−22.8872	−	16.6285i	−0.775504	−	0.563437i
$872$	16.0716	+	11.6767i	0.544253	+	0.395423i
$873$	−10.9995	+	33.8530i	−0.372277	+	1.14575i
$874$	10.5832			0.357983
$875$		0			0
$876$	−0.361053			−0.0121988
$877$	−4.59134	+	14.1307i	−0.155038	+	0.477159i	−0.998165	−	0.0605562i	$-0.980713\pi$
$877$	−4.59134	+	14.1307i	−0.155038	+	0.477159i	0.843126	+	0.537716i	$0.180713\pi$
$878$	21.4957	+	15.6175i	0.725443	+	0.527066i
$879$	−11.5805	−	8.41373i	−0.390601	−	0.283788i
$880$		0			0
$881$	−1.70995	+	1.24235i	−0.0576098	+	0.0418560i	−0.616217	−	0.787576i	$-0.711336\pi$
$881$	−1.70995	+	1.24235i	−0.0576098	+	0.0418560i	0.558608	+	0.829432i	$0.311336\pi$
$882$	−15.9704			−0.537753
$883$	−41.3269	+	30.0257i	−1.39076	+	1.01045i	−0.394978	+	0.918690i	$0.629248\pi$
$883$	−41.3269	+	30.0257i	−1.39076	+	1.01045i	−0.995782	+	0.0917559i	$0.970752\pi$
$884$	−5.29586	−	16.2990i	−0.178119	−	0.548194i
$885$		0			0
$886$	8.83073	−	27.1782i	0.296674	−	0.913069i
$887$	−14.0850	−	43.3491i	−0.472927	−	1.45552i	−0.848733	−	0.528821i	$-0.822634\pi$
$887$	−14.0850	−	43.3491i	−0.472927	−	1.45552i	0.375807	−	0.926698i	$-0.377366\pi$
$888$	−5.44208	−	16.7490i	−0.182624	−	0.562060i
$889$	−1.45205	+	4.46895i	−0.0487002	+	0.149884i
$890$		0			0
$891$	7.86540	+	24.2072i	0.263501	+	0.810972i
$892$	0.911277	−	0.662081i	0.0305118	−	0.0221681i
$893$	16.4606			0.550833
$894$	0.941972	−	0.684383i	0.0315043	−	0.0228892i
$895$		0			0
$896$	0.762649	+	0.554097i	0.0254783	+	0.0185111i
$897$	−9.87888	−	7.17743i	−0.329846	−	0.239647i
$898$	−12.4122	+	38.2007i	−0.414199	+	1.27477i
$899$	12.4150			0.414064
$900$		0			0
$901$	32.0914			1.06912
$902$	3.11806	−	9.59639i	0.103820	−	0.319525i
$903$	2.94003	+	2.13606i	0.0978382	+	0.0710836i
$904$	0.950518	+	0.690592i	0.0316137	+	0.0229687i
$905$		0			0
$906$	3.96460	−	2.88045i	0.131715	−	0.0956965i
$907$	27.5215			0.913837			0.456919	−	0.889508i	$-0.348953\pi$
$907$	27.5215			0.913837			0.456919	+	0.889508i	$0.348953\pi$
$908$	−20.0771	+	14.5869i	−0.666283	+	0.484083i
$909$	8.21099	+	25.2708i	0.272341	+	0.838180i
$910$		0			0
$911$	15.5779	−	47.9437i	0.516118	−	1.58845i	−0.265121	−	0.964215i	$-0.585412\pi$
$911$	15.5779	−	47.9437i	0.516118	−	1.58845i	0.781239	−	0.624232i	$-0.214588\pi$
$912$	−1.06207	−	3.26871i	−0.0351686	−	0.108238i
$913$	−22.6239	−	69.6293i	−0.748743	−	2.30439i
$914$	−9.79692	+	30.1518i	−0.324053	+	0.997334i
$915$		0			0
$916$	−3.07483	−	9.46337i	−0.101595	−	0.312678i
$917$	13.2807	−	9.64899i	0.438567	−	0.318638i
$918$	−12.8290			−0.423420
$919$	−10.2376	+	7.43802i	−0.337706	+	0.245358i	−0.743693	−	0.668521i	$-0.766928\pi$
$919$	−10.2376	+	7.43802i	−0.337706	+	0.245358i	0.405988	+	0.913879i	$0.366928\pi$
$920$		0			0
$921$	5.25090	+	3.81500i	0.173023	+	0.125709i
$922$	−1.82519	−	1.32608i	−0.0601093	−	0.0436720i
$923$	14.5493	−	44.7781i	0.478895	−	1.47389i
$924$	3.14174			0.103356
$925$		0			0
$926$	−23.2415			−0.763763
$927$	−2.40378	+	7.39808i	−0.0789506	+	0.242985i
$928$	−5.71807	−	4.15442i	−0.187705	−	0.136376i
$929$	2.45910	+	1.78664i	0.0806805	+	0.0586178i	0.627394	−	0.778702i	$-0.284121\pi$
$929$	2.45910	+	1.78664i	0.0806805	+	0.0586178i	−0.546714	+	0.837320i	$0.684121\pi$
$930$		0			0
$931$	16.5764	−	12.0434i	0.543269	−	0.394708i
$932$	−11.8817			−0.389198
$933$	−7.44111	+	5.40628i	−0.243611	+	0.176994i
$934$	1.73533	+	5.34080i	0.0567817	+	0.174756i
$935$		0			0
$936$	14.4833	−	44.5749i	0.473400	−	1.45698i
$937$	−0.0148559	−	0.0457219i	−0.000485323	−	0.00149367i	0.950814	−	0.309764i	$-0.100250\pi$
$937$	−0.0148559	−	0.0457219i	−0.000485323	−	0.00149367i	−0.951299	+	0.308270i	$0.900250\pi$
$938$	−1.53725	−	4.73117i	−0.0501930	−	0.154478i
$939$	−5.09694	+	15.6868i	−0.166332	+	0.511919i
$940$		0			0
$941$	−0.387485	−	1.19256i	−0.0126316	−	0.0388762i	0.944542	−	0.328391i	$-0.106506\pi$
$941$	−0.387485	−	1.19256i	−0.0126316	−	0.0388762i	−0.957174	+	0.289514i	$0.906506\pi$
$942$	8.38598	−	6.09277i	0.273230	−	0.198513i
$943$	5.43999			0.177150
$944$	3.41475	−	2.48096i	0.111141	−	0.0807484i
$945$		0			0
$946$	22.8836	+	16.6259i	0.744009	+	0.540554i
$947$	36.0810	+	26.2143i	1.17247	+	0.851852i	0.991303	−	0.131600i	$-0.0420114\pi$
$947$	36.0810	+	26.2143i	1.17247	+	0.851852i	0.181171	+	0.983452i	$0.442011\pi$
$948$	−2.07191	+	6.37667i	−0.0672924	+	0.207105i
$949$	−3.62403			−0.117641
$950$		0			0
$951$	−10.0097			−0.324587
$952$	3.04301	−	9.36541i	0.0986244	−	0.303535i
$953$	−33.8353	−	24.5828i	−1.09603	−	0.796314i	−0.115624	−	0.993293i	$-0.536887\pi$
$953$	−33.8353	−	24.5828i	−1.09603	−	0.796314i	−0.980408	+	0.196980i	$0.936887\pi$
$954$	21.7289	+	15.7869i	0.703498	+	0.511121i
$955$		0			0
$956$	1.35748	−	0.986264i	0.0439039	−	0.0318980i
$957$	−5.46469			−0.176648
$958$	−18.0392	+	13.1062i	−0.582819	+	0.423443i
$959$	−5.99808	−	18.4602i	−0.193688	−	0.596111i
$960$		0			0
$961$	10.1827	−	31.3391i	0.328474	−	1.01094i
$962$	−16.7165	−	51.4482i	−0.538962	−	1.65876i
$963$	−4.09833	−	12.6134i	−0.132067	−	0.406460i
$964$	5.33319	−	16.4139i	0.171771	−	0.528656i
$965$		0			0
$966$	−0.663528	−	2.04213i	−0.0213487	−	0.0657044i
$967$	36.0001	−	26.1556i	1.15769	−	0.841109i	0.168203	−	0.985752i	$-0.446204\pi$
$967$	36.0001	−	26.1556i	1.15769	−	0.841109i	0.989484	+	0.144644i	$0.0462037\pi$
$968$	46.3860			1.49090
$969$	6.08872	−	4.42372i	0.195598	−	0.142110i
$970$		0			0
$971$	−2.96504	−	2.15423i	−0.0951526	−	0.0691324i	0.539192	−	0.842183i	$-0.318730\pi$
$971$	−2.96504	−	2.15423i	−0.0951526	−	0.0691324i	−0.634344	+	0.773051i	$0.718730\pi$
$972$	10.5712	+	7.68044i	0.339072	+	0.246350i
$973$	−1.12194	+	3.45298i	−0.0359678	+	0.110698i
$974$	−28.1389			−0.901629
$975$		0			0
$976$	3.36802			0.107808
$977$	−4.86869	+	14.9843i	−0.155763	+	0.479389i	−0.998237	−	0.0593470i	$-0.981098\pi$
$977$	−4.86869	+	14.9843i	−0.155763	+	0.479389i	0.842474	+	0.538736i	$0.181098\pi$
$978$	5.94735	+	4.32101i	0.190175	+	0.138171i
$979$	26.4856	+	19.2429i	0.846485	+	0.615007i
$980$		0			0
$981$	−13.3300	+	9.68480i	−0.425594	+	0.309212i
$982$	−1.90400			−0.0607591
$983$	21.7641	−	15.8125i	0.694166	−	0.504341i	−0.183861	−	0.982952i	$-0.558860\pi$
$983$	21.7641	−	15.8125i	0.694166	−	0.504341i	0.878027	+	0.478611i	$0.158860\pi$
$984$	−1.20629	−	3.71257i	−0.0384551	−	0.118353i
$985$		0			0
$986$	−1.61979	+	4.98519i	−0.0515845	+	0.158761i
$987$	−1.03202	−	3.17622i	−0.0328494	−	0.101100i
$988$	5.68646	+	17.5011i	0.180910	+	0.556785i
$989$	−4.71243	+	14.5034i	−0.149847	+	0.461180i
$990$		0			0
$991$	4.34725	+	13.3795i	0.138095	+	0.425013i	0.996059	−	0.0886979i	$-0.0282706\pi$
$991$	4.34725	+	13.3795i	0.138095	+	0.425013i	−0.857964	+	0.513710i	$0.828271\pi$
$992$	−29.4547	+	21.4001i	−0.935189	+	0.679455i
$993$	−16.7897			−0.532806
$994$	6.69798	−	4.86636i	0.212447	−	0.154352i
$995$		0			0
$996$	−7.01247	−	5.09485i	−0.222198	−	0.161437i
$997$	0.500493	+	0.363630i	0.0158508	+	0.0115163i	0.595682	−	0.803220i	$-0.296882\pi$
$997$	0.500493	+	0.363630i	0.0158508	+	0.0115163i	−0.579832	+	0.814736i	$0.696882\pi$
$998$	−9.37639	+	28.8575i	−0.296804	+	0.913470i
$999$	31.9443			1.01067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.q.501.2		16
5.2	odd	4		625.2.e.j.124.3		32
5.3	odd	4		625.2.e.j.124.6		32
5.4	even	2		625.2.d.m.501.3		16
25.2	odd	20		625.2.e.k.249.3		32
25.3	odd	20		625.2.e.k.374.3		32
25.4	even	10		625.2.d.n.251.2		16
25.6	even	5	inner	625.2.d.q.126.2		16
25.8	odd	20		625.2.e.j.499.3		32
25.9	even	10		625.2.a.g.1.5	yes	8
25.11	even	5		625.2.d.p.376.3		16
25.12	odd	20		625.2.b.d.624.6		16
25.13	odd	20		625.2.b.d.624.11		16
25.14	even	10		625.2.d.n.376.2		16
25.16	even	5		625.2.a.e.1.4	✓	8
25.17	odd	20		625.2.e.j.499.6		32
25.19	even	10		625.2.d.m.126.3		16
25.21	even	5		625.2.d.p.251.3		16
25.22	odd	20		625.2.e.k.374.6		32
25.23	odd	20		625.2.e.k.249.6		32
75.41	odd	10		5625.2.a.be.1.5		8
75.59	odd	10		5625.2.a.s.1.4		8
100.59	odd	10		10000.2.a.be.1.6		8
100.91	odd	10		10000.2.a.bn.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.4	✓	8	25.16	even	5
625.2.a.g.1.5	yes	8	25.9	even	10
625.2.b.d.624.6		16	25.12	odd	20
625.2.b.d.624.11		16	25.13	odd	20
625.2.d.m.126.3		16	25.19	even	10
625.2.d.m.501.3		16	5.4	even	2
625.2.d.n.251.2		16	25.4	even	10
625.2.d.n.376.2		16	25.14	even	10
625.2.d.p.251.3		16	25.21	even	5
625.2.d.p.376.3		16	25.11	even	5
625.2.d.q.126.2		16	25.6	even	5	inner
625.2.d.q.501.2		16	1.1	even	1	trivial
625.2.e.j.124.3		32	5.2	odd	4
625.2.e.j.124.6		32	5.3	odd	4
625.2.e.j.499.3		32	25.8	odd	20
625.2.e.j.499.6		32	25.17	odd	20
625.2.e.k.249.3		32	25.2	odd	20
625.2.e.k.249.6		32	25.23	odd	20
625.2.e.k.374.3		32	25.3	odd	20
625.2.e.k.374.6		32	25.22	odd	20
5625.2.a.s.1.4		8	75.59	odd	10
5625.2.a.be.1.5		8	75.41	odd	10
10000.2.a.be.1.6		8	100.59	odd	10
10000.2.a.bn.1.3		8	100.91	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.326747 + 1.00562i) q^{2} +(-0.556121 - 0.404046i) q^{3} +(0.713519 + 0.518402i) q^{4} +(0.588029 - 0.427228i) q^{6} -1.01199 q^{7} +(-2.46533 + 1.79116i) q^{8} +(-0.781033 - 2.40377i) q^{9} +O(q^{10})\)	\(q+(-0.326747 + 1.00562i) q^{2} +(-0.556121 - 0.404046i) q^{3} +(0.713519 + 0.518402i) q^{4} +(0.588029 - 0.427228i) q^{6} -1.01199 q^{7} +(-2.46533 + 1.79116i) q^{8} +(-0.781033 - 2.40377i) q^{9} +(1.58239 - 4.87011i) q^{11} +(-0.187345 - 0.576589i) q^{12} +(-1.88045 - 5.78744i) q^{13} +(0.330666 - 1.01769i) q^{14} +(-0.450619 - 1.38686i) q^{16} +(2.58335 - 1.87691i) q^{17} +2.67249 q^{18} +(-2.77389 + 2.01535i) q^{19} +(0.562792 + 0.408892i) q^{21} +(4.38045 + 3.18259i) q^{22} +(-0.902070 + 2.77629i) q^{23} +2.09473 q^{24} +6.43442 q^{26} +(-1.17414 + 3.61364i) q^{27} +(-0.722078 - 0.524620i) q^{28} +(1.25597 + 0.912514i) q^{29} +(6.46970 - 4.70051i) q^{31} -4.55272 q^{32} +(-2.84775 + 2.06901i) q^{33} +(1.04337 + 3.21115i) q^{34} +(0.688839 - 2.12003i) q^{36} +(-2.59799 - 7.99578i) q^{37} +(-1.12032 - 3.44799i) q^{38} +(-1.29263 + 3.97831i) q^{39} +(-0.575868 - 1.77234i) q^{41} +(-0.595082 + 0.432352i) q^{42} +5.22402 q^{43} +(3.65374 - 2.65460i) q^{44} +(-2.49715 - 1.81429i) q^{46} +(-3.88393 - 2.82184i) q^{47} +(-0.309757 + 0.953334i) q^{48} -5.97587 q^{49} -2.19501 q^{51} +(1.65848 - 5.10428i) q^{52} +(8.13057 + 5.90720i) q^{53} +(-3.25031 - 2.36149i) q^{54} +(2.49490 - 1.81265i) q^{56} +2.35691 q^{57} +(-1.32803 + 0.964869i) q^{58} +(0.894451 + 2.75284i) q^{59} +(-0.713724 + 2.19662i) q^{61} +(2.61299 + 8.04196i) q^{62} +(0.790401 + 2.43261i) q^{63} +(2.38882 - 7.35205i) q^{64} +(-1.15015 - 3.53981i) q^{66} +(3.76108 - 2.73258i) q^{67} +2.81626 q^{68} +(1.62341 - 1.17947i) q^{69} +(6.25945 + 4.54776i) q^{71} +(6.23105 + 4.52712i) q^{72} +(0.184032 - 0.566392i) q^{73} +8.88962 q^{74} -3.02398 q^{76} +(-1.60138 + 4.92853i) q^{77} +(-3.57832 - 2.59980i) q^{78} +(-8.94716 - 6.50050i) q^{79} +(-4.02127 + 2.92163i) q^{81} +1.97047 q^{82} +(11.5667 - 8.40373i) q^{83} +(0.189592 + 0.583505i) q^{84} +(-1.70693 + 5.25339i) q^{86} +(-0.329773 - 1.01494i) q^{87} +(4.82205 + 14.8407i) q^{88} +(-1.97562 + 6.08032i) q^{89} +(1.90301 + 5.85686i) q^{91} +(-2.08288 + 1.51330i) q^{92} -5.49716 q^{93} +(4.10677 - 2.98375i) q^{94} +(2.53186 + 1.83951i) q^{96} +(-11.3936 - 8.27794i) q^{97} +(1.95260 - 6.00947i) q^{98} -12.9425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

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