LMFDB - Embedded newform 429.2.bb.a.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.5
Character	$\chi$	$=$	429.64
Dual form			429.2.bb.a.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23441 - 0.401083i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.255144 - 0.185373i) q^{4} +(3.32808 - 1.08136i) q^{5} +(1.23441 - 0.401083i) q^{6} +(-1.47987 + 2.03686i) q^{7} +(1.76641 + 2.43126i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.23441 - 0.401083i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.255144 - 0.185373i) q^{4} +(3.32808 - 1.08136i) q^{5} +(1.23441 - 0.401083i) q^{6} +(-1.47987 + 2.03686i) q^{7} +(1.76641 + 2.43126i) q^{8} +(0.309017 - 0.951057i) q^{9} -4.54192 q^{10} +(-2.69535 + 1.93263i) q^{11} +0.315375 q^{12} +(2.77732 - 2.29924i) q^{13} +(2.64371 - 1.92077i) q^{14} +(-2.05687 + 2.83104i) q^{15} +(-1.01042 - 3.10975i) q^{16} +(0.403998 + 1.24338i) q^{17} +(-0.762905 + 1.05005i) q^{18} +(2.88171 + 3.96634i) q^{19} +(-1.04959 - 0.341034i) q^{20} -2.51770i q^{21} +(4.10231 - 1.30459i) q^{22} -6.92738 q^{23} +(-2.85811 - 0.928657i) q^{24} +(5.86171 - 4.25878i) q^{25} +(-4.35052 + 1.72426i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.755159 - 0.245366i) q^{28} +(5.95373 + 4.32564i) q^{29} +(3.67449 - 2.66967i) q^{30} +(9.30903 + 3.02469i) q^{31} -1.76644i q^{32} +(1.04461 - 3.14782i) q^{33} -1.69687i q^{34} +(-2.72254 + 8.37912i) q^{35} +(-0.255144 + 0.185373i) q^{36} +(1.68877 - 2.32440i) q^{37} +(-1.96637 - 6.05187i) q^{38} +(-0.895442 + 3.49259i) q^{39} +(8.50782 + 6.18129i) q^{40} +(4.31177 + 5.93464i) q^{41} +(-1.00981 + 3.10787i) q^{42} +8.59883 q^{43} +(1.04596 + 0.00654606i) q^{44} -3.49935i q^{45} +(8.55120 + 2.77845i) q^{46} +(1.68164 + 2.31458i) q^{47} +(2.64531 + 1.92193i) q^{48} +(0.204315 + 0.628816i) q^{49} +(-8.94385 + 2.90603i) q^{50} +(-1.05768 - 0.768451i) q^{51} +(-1.13483 + 0.0717964i) q^{52} +(-0.637481 + 1.96196i) q^{53} -1.29793i q^{54} +(-6.88049 + 9.34661i) q^{55} -7.56619 q^{56} +(-4.66271 - 1.51501i) q^{57} +(-5.61438 - 7.72753i) q^{58} +(2.97594 - 4.09603i) q^{59} +(1.04959 - 0.341034i) q^{60} +(-1.55519 - 4.78637i) q^{61} +(-10.2780 - 7.46738i) q^{62} +(1.47987 + 2.03686i) q^{63} +(-2.72933 + 8.40000i) q^{64} +(6.75685 - 10.6553i) q^{65} +(-2.55201 + 3.46671i) q^{66} -7.84044i q^{67} +(0.127411 - 0.392131i) q^{68} +(5.60437 - 4.07181i) q^{69} +(6.72144 - 9.25127i) q^{70} +(-9.41617 + 3.05950i) q^{71} +(2.85811 - 0.928657i) q^{72} +(-8.40978 + 11.5751i) q^{73} +(-3.01691 + 2.19191i) q^{74} +(-2.23897 + 6.89085i) q^{75} -1.54618i q^{76} +(0.0522584 - 8.35011i) q^{77} +(2.50616 - 3.95213i) q^{78} +(5.25823 - 16.1832i) q^{79} +(-6.72552 - 9.25689i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.94219 - 9.05513i) q^{82} +(-7.27966 + 2.36530i) q^{83} +(-0.466714 + 0.642376i) q^{84} +(2.68908 + 3.70120i) q^{85} +(-10.6144 - 3.44884i) q^{86} -7.35922 q^{87} +(-9.45983 - 3.13927i) q^{88} -2.42919i q^{89} +(-1.40353 + 4.31962i) q^{90} +(0.573165 + 9.05959i) q^{91} +(1.76748 + 1.28415i) q^{92} +(-9.30903 + 3.02469i) q^{93} +(-1.14749 - 3.53161i) q^{94} +(13.8796 + 10.0841i) q^{95} +(1.03828 + 1.42908i) q^{96} +(-0.384116 - 0.124807i) q^{97} -0.858161i q^{98} +(1.00513 + 3.16065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.23441	−	0.401083i	−0.872857	−	0.283608i	−0.161869	−	0.986812i	$-0.551752\pi$
$2$	−1.23441	−	0.401083i	−0.872857	−	0.283608i	−0.710988	+	0.703204i	$0.751752\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.255144	−	0.185373i	−0.127572	−	0.0926865i
$5$	3.32808	−	1.08136i	1.48836	−	0.483599i	0.551764	−	0.834000i	$-0.313955\pi$
$5$	3.32808	−	1.08136i	1.48836	−	0.483599i	0.936600	+	0.350402i	$0.113955\pi$
$6$	1.23441	−	0.401083i	0.503944	−	0.163741i
$7$	−1.47987	+	2.03686i	−0.559338	+	0.769862i	−0.991242	−	0.132057i	$-0.957842\pi$
$7$	−1.47987	+	2.03686i	−0.559338	+	0.769862i	0.431905	+	0.901919i	$0.357842\pi$
$8$	1.76641	+	2.43126i	0.624520	+	0.859579i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−4.54192			−1.43628
$11$	−2.69535	+	1.93263i	−0.812680	+	0.582711i
$11$	−2.69535	+	1.93263i	−0.812680	+	0.582711i
$12$	0.315375			0.0910410
$13$	2.77732	−	2.29924i	0.770290	−	0.637694i
$13$	2.77732	−	2.29924i	0.770290	−	0.637694i
$14$	2.64371	−	1.92077i	0.706561	−	0.513346i
$15$	−2.05687	+	2.83104i	−0.531081	+	0.730970i
$16$	−1.01042	−	3.10975i	−0.252605	−	0.777438i
$17$	0.403998	+	1.24338i	0.0979840	+	0.301564i	0.988020	−	0.154327i	$-0.0493208\pi$
$17$	0.403998	+	1.24338i	0.0979840	+	0.301564i	−0.890036	+	0.455891i	$0.849321\pi$
$18$	−0.762905	+	1.05005i	−0.179818	+	0.247499i
$19$	2.88171	+	3.96634i	0.661110	+	0.909940i	0.999518	−	0.0310599i	$-0.00988826\pi$
$19$	2.88171	+	3.96634i	0.661110	+	0.909940i	−0.338408	+	0.941000i	$0.609888\pi$
$20$	−1.04959	−	0.341034i	−0.234697	−	0.0762575i
$21$		−	2.51770i		−	0.549408i
$22$	4.10231	−	1.30459i	0.874614	−	0.278140i
$23$	−6.92738			−1.44446			−0.722230	−	0.691653i	$-0.756883\pi$
$23$	−6.92738			−1.44446			−0.722230	+	0.691653i	$0.756883\pi$
$24$	−2.85811	−	0.928657i	−0.583410	−	0.189561i
$25$	5.86171	−	4.25878i	1.17234	−	0.851756i
$26$	−4.35052	+	1.72426i	−0.853208	+	0.338154i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.755159	−	0.245366i	0.142712	−	0.0463698i
$29$	5.95373	+	4.32564i	1.10558	+	0.803251i	0.981962	−	0.189079i	$-0.0605502\pi$
$29$	5.95373	+	4.32564i	1.10558	+	0.803251i	0.123618	+	0.992330i	$0.460550\pi$
$30$	3.67449	−	2.66967i	0.670867	−	0.487413i
$31$	9.30903	+	3.02469i	1.67195	+	0.543250i	0.983323	−	0.181865i	$-0.0582135\pi$
$31$	9.30903	+	3.02469i	1.67195	+	0.543250i	0.688628	+	0.725115i	$0.258213\pi$
$32$		−	1.76644i		−	0.312265i
$33$	1.04461	−	3.14782i	0.181844	−	0.547965i
$34$		−	1.69687i		−	0.291011i
$35$	−2.72254	+	8.37912i	−0.460193	+	1.41633i
$36$	−0.255144	+	0.185373i	−0.0425240	+	0.0308955i
$37$	1.68877	−	2.32440i	0.277633	−	0.382129i	−0.647315	−	0.762222i	$-0.724108\pi$
$37$	1.68877	−	2.32440i	0.277633	−	0.382129i	0.924948	+	0.380094i	$0.124108\pi$
$38$	−1.96637	−	6.05187i	−0.318988	−	0.981743i
$39$	−0.895442	+	3.49259i	−0.143385	+	0.559262i
$40$	8.50782	+	6.18129i	1.34520	+	0.977348i
$41$	4.31177	+	5.93464i	0.673385	+	0.926835i	0.999831	−	0.0183810i	$-0.00585117\pi$
$41$	4.31177	+	5.93464i	0.673385	+	0.926835i	−0.326446	+	0.945216i	$0.605851\pi$
$42$	−1.00981	+	3.10787i	−0.155817	+	0.479554i
$43$	8.59883			1.31131			0.655655	−	0.755061i	$-0.272393\pi$
$43$	8.59883			1.31131			0.655655	+	0.755061i	$0.272393\pi$
$44$	1.04596	+	0.00654606i	0.157685	+	0.000986855i
$45$		−	3.49935i		−	0.521653i
$46$	8.55120	+	2.77845i	1.26081	+	0.409661i
$47$	1.68164	+	2.31458i	0.245293	+	0.337616i	0.913856	−	0.406039i	$-0.133090\pi$
$47$	1.68164	+	2.31458i	0.245293	+	0.337616i	−0.668563	+	0.743655i	$0.733090\pi$
$48$	2.64531	+	1.92193i	0.381818	+	0.277407i
$49$	0.204315	+	0.628816i	0.0291878	+	0.0898309i
$50$	−8.94385	+	2.90603i	−1.26485	+	0.410975i
$51$	−1.05768	−	0.768451i	−0.148105	−	0.107605i
$52$	−1.13483	+	0.0717964i	−0.157373	+	0.00995637i
$53$	−0.637481	+	1.96196i	−0.0875647	+	0.269497i	−0.985245	−	0.171151i	$-0.945251\pi$
$53$	−0.637481	+	1.96196i	−0.0875647	+	0.269497i	0.897680	+	0.440648i	$0.145251\pi$
$54$		−	1.29793i		−	0.176626i
$55$	−6.88049	+	9.34661i	−0.927765	+	1.26030i
$56$	−7.56619			−1.01107
$57$	−4.66271	−	1.51501i	−0.617591	−	0.200667i
$58$	−5.61438	−	7.72753i	−0.737204	−	1.01467i
$59$	2.97594	−	4.09603i	0.387434	−	0.533257i	−0.570101	−	0.821575i	$-0.693096\pi$
$59$	2.97594	−	4.09603i	0.387434	−	0.533257i	0.957535	+	0.288317i	$0.0930958\pi$
$60$	1.04959	−	0.341034i	0.135502	−	0.0440273i
$61$	−1.55519	−	4.78637i	−0.199121	−	0.612832i	−0.999904	−	0.0138767i	$-0.995583\pi$
$61$	−1.55519	−	4.78637i	−0.199121	−	0.612832i	0.800783	−	0.598955i	$-0.204417\pi$
$62$	−10.2780	−	7.46738i	−1.30530	−	0.948358i
$63$	1.47987	+	2.03686i	0.186446	+	0.256621i
$64$	−2.72933	+	8.40000i	−0.341166	+	1.05000i
$65$	6.75685	−	10.6553i	0.838084	−	1.32163i
$66$	−2.55201	+	3.46671i	−0.314131	+	0.426723i
$67$		−	7.84044i		−	0.957862i	−0.877853	−	0.478931i	$-0.841024\pi$
$67$		−	7.84044i		−	0.957862i	0.877853	−	0.478931i	$-0.158976\pi$
$68$	0.127411	−	0.392131i	0.0154509	−	0.0475529i
$69$	5.60437	−	4.07181i	0.674687	−	0.490189i
$70$	6.72144	−	9.25127i	0.803366	−	1.10574i
$71$	−9.41617	+	3.05950i	−1.11749	+	0.363096i	−0.808811	−	0.588069i	$-0.799888\pi$
$71$	−9.41617	+	3.05950i	−1.11749	+	0.363096i	−0.308683	+	0.951165i	$0.599888\pi$
$72$	2.85811	−	0.928657i	0.336832	−	0.109443i
$73$	−8.40978	+	11.5751i	−0.984290	+	1.35476i	−0.0498045	+	0.998759i	$0.515860\pi$
$73$	−8.40978	+	11.5751i	−0.984290	+	1.35476i	−0.934486	+	0.356000i	$0.884140\pi$
$74$	−3.01691	+	2.19191i	−0.350708	+	0.254805i
$75$	−2.23897	+	6.89085i	−0.258534	+	0.795687i
$76$		−	1.54618i		−	0.177359i
$77$	0.0522584	−	8.35011i	0.00595540	−	0.951583i
$78$	2.50616	−	3.95213i	0.283766	−	0.447490i
$79$	5.25823	−	16.1832i	0.591597	−	1.82075i	0.0206147	−	0.999787i	$-0.493438\pi$
$79$	5.25823	−	16.1832i	0.591597	−	1.82075i	0.570983	−	0.820962i	$-0.306562\pi$
$80$	−6.72552	−	9.25689i	−0.751936	−	1.03495i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−2.94219	−	9.05513i	−0.324910	−	0.999972i
$83$	−7.27966	+	2.36530i	−0.799046	+	0.259626i	−0.679952	−	0.733257i	$-0.737999\pi$
$83$	−7.27966	+	2.36530i	−0.799046	+	0.259626i	−0.119095	+	0.992883i	$0.537999\pi$
$84$	−0.466714	+	0.642376i	−0.0509227	+	0.0700890i
$85$	2.68908	+	3.70120i	0.291672	+	0.401452i
$86$	−10.6144	−	3.44884i	−1.14458	−	0.371898i
$87$	−7.35922			−0.788991
$88$	−9.45983	−	3.13927i	−1.00842	−	0.334647i
$89$		−	2.42919i		−	0.257494i	−0.991677	−	0.128747i	$-0.958904\pi$
$89$		−	2.42919i		−	0.257494i	0.991677	−	0.128747i	$-0.0410955\pi$
$90$	−1.40353	+	4.31962i	−0.147945	+	0.455328i
$91$	0.573165	+	9.05959i	0.0600840	+	0.949703i
$92$	1.76748	+	1.28415i	0.184273	+	0.133882i
$93$	−9.30903	+	3.02469i	−0.965301	+	0.313645i
$94$	−1.14749	−	3.53161i	−0.118355	−	0.364258i
$95$	13.8796	+	10.0841i	1.42402	+	1.03461i
$96$	1.03828	+	1.42908i	0.105969	+	0.145854i
$97$	−0.384116	−	0.124807i	−0.0390011	−	0.0126722i	0.289451	−	0.957193i	$-0.406527\pi$
$97$	−0.384116	−	0.124807i	−0.0390011	−	0.0126722i	−0.328453	+	0.944520i	$0.606527\pi$
$98$		−	0.858161i		−	0.0866874i
$99$	1.00513	+	3.16065i	0.101020	+	0.317657i
$100$	−2.28504			−0.228504
$101$	−2.60463	+	8.01622i	−0.259170	+	0.797643i	0.733809	+	0.679356i	$0.237741\pi$
$101$	−2.60463	+	8.01622i	−0.259170	+	0.797643i	−0.992979	+	0.118288i	$0.962259\pi$
$102$	0.997396	+	1.37280i	0.0987569	+	0.135927i
$103$	−9.13586	−	6.63759i	−0.900183	−	0.654021i	0.0383300	−	0.999265i	$-0.487796\pi$
$103$	−9.13586	−	6.63759i	−0.900183	−	0.654021i	−0.938513	+	0.345244i	$0.887796\pi$
$104$	10.4959	+	2.69098i	1.02921	+	0.263872i
$105$	−2.72254	−	8.37912i	−0.265693	−	0.817718i
$106$	1.57382	−	2.16618i	0.152863	−	0.210398i
$107$	11.2190	−	8.15109i	1.08458	−	0.787996i	0.106107	−	0.994355i	$-0.466161\pi$
$107$	11.2190	−	8.15109i	1.08458	−	0.787996i	0.978476	+	0.206359i	$0.0661614\pi$
$108$	0.0974563	−	0.299940i	0.00937774	−	0.0288617i
$109$		−	3.95857i		−	0.379162i	−0.981865	−	0.189581i	$-0.939287\pi$
$109$		−	3.95857i		−	0.379162i	0.981865	−	0.189581i	$-0.0607129\pi$
$110$	12.2421	−	8.77786i	1.16724	−	0.836936i
$111$			2.87311i			0.272704i
$112$	7.82943	+	2.54394i	0.739812	+	0.240379i
$113$	−13.5551	+	9.84839i	−1.27516	+	0.926458i	−0.999395	−	0.0347668i	$-0.988931\pi$
$113$	−13.5551	+	9.84839i	−1.27516	+	0.926458i	−0.275765	+	0.961225i	$0.588931\pi$
$114$	5.14803	+	3.74026i	0.482157	+	0.350308i
$115$	−23.0549	+	7.49099i	−2.14988	+	0.698539i
$116$	−0.717202	−	2.20732i	−0.0665905	−	0.204945i
$117$	−1.32847	−	3.35189i	−0.122817	−	0.309883i
$118$	−5.31636	+	3.86256i	−0.489411	+	0.355578i
$119$	−3.13046	−	1.01715i	−0.286969	−	0.0932418i
$120$	−10.5162			−0.959997
$121$	3.52986	−	10.4183i	0.320897	−	0.947114i
$122$			6.53208i			0.591387i
$123$	−6.97659	−	2.26683i	−0.629058	−	0.204393i
$124$	−1.81445	−	2.49737i	−0.162942	−	0.224271i
$125$	4.61863	−	6.35700i	0.413103	−	0.568587i
$126$	−1.00981	−	3.10787i	−0.0899607	−	0.276871i
$127$	2.95359	+	9.09023i	0.262089	+	0.806627i	0.992350	+	0.123458i	$0.0393986\pi$
$127$	2.95359	+	9.09023i	0.262089	+	0.806627i	−0.730261	+	0.683169i	$0.760601\pi$
$128$	4.66162	−	6.41617i	0.412033	−	0.567115i
$129$	−6.95660	+	5.05426i	−0.612494	+	0.445003i
$130$	−12.6144	+	10.4429i	−1.10635	+	0.915907i
$131$	3.23038			0.282239			0.141120	−	0.989993i	$-0.454930\pi$
$131$	3.23038			0.282239			0.141120	+	0.989993i	$0.454930\pi$
$132$	−0.850048	+	0.609505i	−0.0739872	+	0.0530506i
$133$	−12.3434			−1.07031
$134$	−3.14466	+	9.67828i	−0.271658	+	0.836076i
$135$	2.05687	+	2.83104i	0.177027	+	0.243657i
$136$	−2.30935	+	3.17854i	−0.198025	+	0.272558i
$137$	5.35257	−	1.73916i	0.457301	−	0.148586i	−0.0713028	−	0.997455i	$-0.522716\pi$
$137$	5.35257	−	1.73916i	0.457301	−	0.148586i	0.528604	+	0.848869i	$0.322716\pi$
$138$	−8.55120	+	2.77845i	−0.727927	+	0.236518i
$139$	3.72882	+	2.70915i	0.316275	+	0.229787i	0.734584	−	0.678518i	$-0.237377\pi$
$139$	3.72882	+	2.70915i	0.316275	+	0.229787i	−0.418310	+	0.908305i	$0.637377\pi$
$140$	2.24790	−	1.63320i	0.189982	−	0.138030i
$141$	−2.72095	−	0.884091i	−0.229146	−	0.0744539i
$142$	12.8505			1.07839
$143$	−3.04228	+	11.5648i	−0.254408	+	0.967097i
$144$	−3.26979			−0.272482
$145$	24.4921	+	7.95796i	2.03396	+	0.660872i
$146$	15.0236	−	10.9153i	1.24337	−	0.903358i
$147$	−0.534903	−	0.388630i	−0.0441181	−	0.0320536i
$148$	−0.861761	+	0.280003i	−0.0708363	+	0.0230161i
$149$	−3.84840	+	1.25042i	−0.315273	+	0.102439i	−0.462379	−	0.886682i	$-0.653004\pi$
$149$	−3.84840	+	1.25042i	−0.315273	+	0.102439i	0.147106	+	0.989121i	$0.453004\pi$
$150$	5.52760	−	7.60809i	0.451327	−	0.621198i
$151$	0.998208	+	1.37392i	0.0812330	+	0.111808i	0.847700	−	0.530476i	$-0.177987\pi$
$151$	0.998208	+	1.37392i	0.0812330	+	0.111808i	−0.766467	+	0.642284i	$0.777987\pi$
$152$	−4.55289	+	14.0124i	−0.369288	+	1.13655i
$153$	1.30737			0.105694
$154$	−3.41359	+	10.2865i	−0.275075	+	0.828907i
$155$	34.2520			2.75119
$156$	0.875898	−	0.725123i	0.0701280	−	0.0580563i
$157$	2.16878	−	1.57571i	0.173087	−	0.125755i	−0.497869	−	0.867252i	$-0.665884\pi$
$157$	2.16878	−	1.57571i	0.173087	−	0.125755i	0.670956	+	0.741497i	$0.265884\pi$
$158$	−12.9816	+	17.8676i	−1.03276	+	1.42147i
$159$	−0.637481	−	1.96196i	−0.0505555	−	0.155594i
$160$	−1.91015	−	5.87884i	−0.151011	−	0.464763i
$161$	10.2516	−	14.1101i	0.807940	−	1.11203i
$162$	0.762905	+	1.05005i	0.0599395	+	0.0824996i
$163$	4.64776	+	1.51015i	0.364040	+	0.118284i	0.485325	−	0.874334i	$-0.338701\pi$
$163$	4.64776	+	1.51015i	0.364040	+	0.118284i	−0.121285	+	0.992618i	$0.538701\pi$
$164$		−	2.31347i		−	0.180652i
$165$	0.0726340	−	11.6058i	0.00565455	−	0.903511i
$166$	9.93473			0.771085
$167$	−22.0486	−	7.16402i	−1.70617	−	0.554368i	−0.716482	−	0.697606i	$-0.754249\pi$
$167$	−22.0486	−	7.16402i	−1.70617	−	0.554368i	−0.989688	+	0.143238i	$0.954249\pi$
$168$	6.12118	−	4.44730i	0.472259	−	0.343116i
$169$	2.42702	−	12.7714i	0.186694	−	0.982418i
$170$	−1.83493	−	5.64733i	−0.140733	−	0.433130i
$171$	4.66271	−	1.51501i	0.356566	−	0.115855i
$172$	−2.19394	−	1.59399i	−0.167286	−	0.121541i
$173$	−13.4595	+	9.77887i	−1.02330	+	0.743474i	−0.966958	−	0.254938i	$-0.917945\pi$
$173$	−13.4595	+	9.77887i	−1.02330	+	0.743474i	−0.0563462	+	0.998411i	$0.517945\pi$
$174$	9.08426	+	2.95165i	0.688676	+	0.223764i
$175$			18.2419i			1.37896i
$176$	8.73345	+	6.42911i	0.658309	+	0.484613i
$177$			5.06297i			0.380556i
$178$	−0.974308	+	2.99861i	−0.0730275	+	0.224755i
$179$	18.2255	−	13.2416i	1.36224	−	0.989726i	0.363942	−	0.931421i	$-0.381430\pi$
$179$	18.2255	−	13.2416i	1.36224	−	0.989726i	0.998299	−	0.0583048i	$-0.0185695\pi$
$180$	−0.648685	+	0.892839i	−0.0483501	+	0.0665483i
$181$	2.30827	+	7.10412i	0.171572	+	0.528045i	0.999460	−	0.0328481i	$-0.0104577\pi$
$181$	2.30827	+	7.10412i	0.171572	+	0.528045i	−0.827888	+	0.560893i	$0.810458\pi$
$182$	2.92613	−	11.4131i	0.216899	−	0.845995i
$183$	4.07153	+	2.95814i	0.300976	+	0.218672i
$184$	−12.2366	−	16.8422i	−0.902094	−	1.24163i
$185$	3.10687	−	9.56196i	0.228422	−	0.703009i
$186$	12.7043			0.931522
$187$	−3.49191	−	2.57057i	−0.255354	−	0.187978i
$188$		−	0.902282i		−	0.0658057i
$189$	−2.39448	−	0.778013i	−0.174173	−	0.0565921i
$190$	−13.0885	−	18.0148i	−0.949539	−	1.30693i
$191$	−21.5620	−	15.6657i	−1.56017	−	1.13353i	−0.935868	−	0.352352i	$-0.885382\pi$
$191$	−21.5620	−	15.6657i	−1.56017	−	1.13353i	−0.624306	−	0.781180i	$-0.714618\pi$
$192$	−2.72933	−	8.40000i	−0.196972	−	0.606218i
$193$	−11.0751	+	3.59851i	−0.797201	+	0.259026i	−0.679168	−	0.733983i	$-0.737659\pi$
$193$	−11.0751	+	3.59851i	−0.797201	+	0.259026i	−0.118034	+	0.993010i	$0.537659\pi$
$194$	0.424097	+	0.308125i	0.0304484	+	0.0221221i
$195$	0.796641	+	12.5919i	0.0570487	+	0.901726i
$196$	0.0644358	−	0.198313i	0.00460256	−	0.0141652i
$197$		−	0.252478i		−	0.0179883i	−0.999960	−	0.00899416i	$-0.997137\pi$
$197$		−	0.252478i		−	0.0179883i	0.999960	−	0.00899416i	$-0.00286297\pi$
$198$	0.0269404	−	4.30467i	0.00191457	−	0.305919i
$199$	4.08670			0.289698			0.144849	−	0.989454i	$-0.453730\pi$
$199$	4.08670			0.289698			0.144849	+	0.989454i	$0.453730\pi$
$200$	20.7084	+	6.72855i	1.46430	+	0.475781i
$201$	4.60849	+	6.34305i	0.325058	+	0.447404i
$202$	6.43033	−	8.85059i	0.452437	−	0.622726i
$203$	−17.6215	+	5.72556i	−1.23678	+	0.401856i
$204$	0.127411	+	0.392131i	0.00892056	+	0.0274547i
$205$	20.7674	+	15.0884i	1.45046	+	1.05382i
$206$	8.61513	+	11.8577i	0.600245	+	0.826166i
$207$	−2.14068	+	6.58833i	−0.148787	+	0.457921i
$208$	−9.95632	−	6.31359i	−0.690347	−	0.437768i
$209$	−15.4327	−	5.12139i	−1.06750	−	0.354254i
$210$			11.4352i			0.789103i
$211$	0.385431	−	1.18624i	0.0265342	−	0.0816639i	−0.936912	−	0.349564i	$-0.886330\pi$
$211$	0.385431	−	1.18624i	0.0265342	−	0.0816639i	0.963447	+	0.267900i	$0.0863297\pi$
$212$	0.526344	−	0.382412i	0.0361495	−	0.0262641i
$213$	5.81952	−	8.00988i	0.398747	−	0.548828i
$214$	−17.1181	+	5.56200i	−1.17017	+	0.380211i
$215$	28.6176	−	9.29842i	1.95170	−	0.634147i
$216$	−1.76641	+	2.43126i	−0.120189	+	0.165426i
$217$	−19.9370	+	14.4851i	−1.35341	+	0.983312i
$218$	−1.58771	+	4.88648i	−0.107533	+	0.330954i
$219$		−	14.3076i		−	0.966816i
$220$	3.48812	−	1.10927i	0.235169	−	0.0747872i
$221$	3.98086	+	2.52437i	0.267781	+	0.169808i
$222$	1.15236	−	3.54659i	0.0773411	−	0.238031i
$223$	−5.74229	−	7.90359i	−0.384532	−	0.529263i	0.572246	−	0.820082i	$-0.306072\pi$
$223$	−5.74229	−	7.90359i	−0.384532	−	0.529263i	−0.956778	+	0.290819i	$0.906072\pi$
$224$	3.59799	+	2.61409i	0.240401	+	0.174661i
$225$	−2.23897	−	6.89085i	−0.149265	−	0.459390i
$226$	20.6826	−	6.72017i	1.37578	−	0.447019i
$227$	2.34979	−	3.23421i	0.155961	−	0.214662i	−0.723885	−	0.689921i	$-0.757645\pi$
$227$	2.34979	−	3.23421i	0.155961	−	0.214662i	0.879846	+	0.475258i	$0.157645\pi$
$228$	0.908821	+	1.25088i	0.0601881	+	0.0828418i
$229$	−4.46589	−	1.45105i	−0.295114	−	0.0958884i	0.157718	−	0.987484i	$-0.449586\pi$
$229$	−4.46589	−	1.45105i	−0.295114	−	0.0958884i	−0.452832	+	0.891596i	$0.649586\pi$
$230$	31.4636			2.07465
$231$	4.86579	+	6.78610i	0.320146	+	0.446492i
$232$			22.1159i			1.45198i
$233$	3.57537	−	11.0039i	0.234230	−	0.720887i	−0.762992	−	0.646408i	$-0.776271\pi$
$233$	3.57537	−	11.0039i	0.234230	−	0.720887i	0.997223	−	0.0744791i	$-0.0237294\pi$
$234$	0.295479	+	4.67042i	0.0193161	+	0.305315i
$235$	8.09954	+	5.88466i	0.528355	+	0.383873i
$236$	−1.51859	+	0.493418i	−0.0988515	+	0.0321188i
$237$	5.25823	+	16.1832i	0.341559	+	1.05121i
$238$	3.45630	+	2.51115i	0.224038	+	0.162773i
$239$	5.77965	+	7.95501i	0.373855	+	0.514567i	0.953943	−	0.299986i	$-0.0969821\pi$
$239$	5.77965	+	7.95501i	0.373855	+	0.514567i	−0.580089	+	0.814553i	$0.696982\pi$
$240$	10.8821	+	3.53582i	0.702438	+	0.228236i
$241$			23.8379i			1.53553i	0.640729	+	0.767767i	$0.278632\pi$
$241$			23.8379i			1.53553i	−0.640729	+	0.767767i	$0.721368\pi$
$242$	−8.53586	+	11.4446i	−0.548706	+	0.735686i
$243$	1.00000			0.0641500
$244$	−0.490467	+	1.50950i	−0.0313989	+	0.0966360i
$245$	1.35995	+	1.87181i	0.0868842	+	0.119586i
$246$	7.70275	+	5.59638i	0.491109	+	0.356812i
$247$	17.1230	+	4.39005i	1.08951	+	0.279332i
$248$	9.08978	+	27.9755i	0.577202	+	1.77644i
$249$	4.49908	−	6.19245i	0.285117	−	0.392430i
$250$	−8.25095	+	5.99466i	−0.521836	+	0.379136i
$251$	2.12824	−	6.55005i	0.134333	−	0.413435i	−0.861152	−	0.508347i	$-0.830257\pi$
$251$	2.12824	−	6.55005i	0.134333	−	0.413435i	0.995486	+	0.0949114i	$0.0302568\pi$
$252$		−	0.794021i		−	0.0500186i
$253$	18.6717	−	13.3881i	1.17388	−	0.841702i
$254$		−	12.4057i		−	0.778400i
$255$	−4.35102	−	1.41373i	−0.272472	−	0.0885314i
$256$	5.96319	−	4.33251i	0.372699	−	0.270782i
$257$	−2.32290	−	1.68769i	−0.144898	−	0.105275i	0.512974	−	0.858404i	$-0.328544\pi$
$257$	−2.32290	−	1.68769i	−0.144898	−	0.105275i	−0.657873	+	0.753129i	$0.728544\pi$
$258$	10.6144	−	3.44884i	0.660826	−	0.214715i
$259$	2.23532	+	6.87960i	0.138896	+	0.427478i
$260$	−3.69918	+	1.46611i	−0.229413	+	0.0909241i
$261$	5.95373	−	4.32564i	0.368527	−	0.267750i
$262$	−3.98760	−	1.29565i	−0.246355	−	0.0800455i
$263$	−14.5680			−0.898302			−0.449151	−	0.893456i	$-0.648273\pi$
$263$	−14.5680			−0.898302			−0.449151	+	0.893456i	$0.648273\pi$
$264$	9.49838	−	3.02062i	0.584585	−	0.185906i
$265$			7.21892i			0.443455i
$266$	15.2368	+	4.95074i	0.934229	+	0.303549i
$267$	1.42784	+	1.96526i	0.0873827	+	0.120272i
$268$	−1.45341	+	2.00044i	−0.0887809	+	0.122196i
$269$	−3.34196	−	10.2855i	−0.203763	−	0.627118i	−0.999762	−	0.0218200i	$-0.993054\pi$
$269$	−3.34196	−	10.2855i	−0.203763	−	0.627118i	0.795999	−	0.605298i	$-0.206946\pi$
$270$	−1.40353	−	4.31962i	−0.0854161	−	0.262884i
$271$	−0.773371	+	1.06445i	−0.0469789	+	0.0646609i	−0.831860	−	0.554985i	$-0.812724\pi$
$271$	−0.773371	+	1.06445i	−0.0469789	+	0.0646609i	0.784881	+	0.619646i	$0.212724\pi$
$272$	3.45840	−	2.51267i	0.209696	−	0.152353i
$273$	−5.78879	−	6.99247i	−0.350354	−	0.423203i
$274$	−7.30479			−0.441299
$275$	−7.56872	+	22.8074i	−0.456411	+	1.37534i
$276$	−2.18473			−0.131505
$277$	2.50611	−	7.71301i	0.150578	−	0.463430i	−0.847108	−	0.531420i	$-0.821659\pi$
$277$	2.50611	−	7.71301i	0.150578	−	0.463430i	0.997686	+	0.0679900i	$0.0216586\pi$
$278$	−3.51629	−	4.83975i	−0.210893	−	0.290269i
$279$	5.75330	−	7.91873i	0.344441	−	0.474082i
$280$	−25.1809	+	8.18177i	−1.50485	+	0.488954i
$281$	−0.511259	+	0.166118i	−0.0304992	+	0.00990978i	−0.324227	−	0.945979i	$-0.605104\pi$
$281$	−0.511259	+	0.166118i	−0.0304992	+	0.00990978i	0.293728	+	0.955889i	$0.405104\pi$
$282$	3.00417	+	2.18265i	0.178896	+	0.129975i
$283$	7.97397	−	5.79343i	0.474003	−	0.344383i	−0.324996	−	0.945715i	$-0.605363\pi$
$283$	7.97397	−	5.79343i	0.474003	−	0.344383i	0.798999	+	0.601332i	$0.205363\pi$
$284$	2.96963	+	0.964891i	0.176215	+	0.0572557i
$285$	−17.1561			−1.01624
$286$	8.39385	−	13.0554i	0.496339	−	0.771985i
$287$	−18.4689			−1.09018
$288$	−1.67998	−	0.545859i	−0.0989938	−	0.0321650i
$289$	12.3705	−	8.98770i	0.727677	−	0.528688i
$290$	−27.0414	−	19.6467i	−1.58792	−	1.15369i
$291$	0.384116	−	0.124807i	0.0225173	−	0.00731631i
$292$	4.29141	−	1.39436i	0.251136	−	0.0815989i
$293$	−4.89004	+	6.73057i	−0.285679	+	0.393204i	−0.927605	−	0.373563i	$-0.878136\pi$
$293$	−4.89004	+	6.73057i	−0.285679	+	0.393204i	0.641925	+	0.766767i	$0.278136\pi$
$294$	0.504415	+	0.694267i	0.0294181	+	0.0404905i
$295$	5.47489	−	16.8500i	0.318760	−	0.981043i
$296$	8.63427			0.501857
$297$	−2.67095	−	1.96622i	−0.154984	−	0.114091i
$298$	5.25201			0.304241
$299$	−19.2396	+	15.9277i	−1.11265	+	0.921123i
$300$	1.84864	−	1.34311i	0.106731	−	0.0775447i
$301$	−12.7251	+	17.5146i	−0.733464	+	1.00953i
$302$	−0.681140	−	2.09633i	−0.0391952	−	0.120630i
$303$	−2.60463	−	8.01622i	−0.149632	−	0.460520i
$304$	9.42258	−	12.9691i	0.540422	−	0.743827i
$305$	−10.3516	−	14.2477i	−0.592729	−	0.815822i
$306$	−1.61382	−	0.524362i	−0.0922560	−	0.0299758i
$307$		−	4.75545i		−	0.271408i	−0.990749	−	0.135704i	$-0.956670\pi$
$307$		−	4.75545i		−	0.271408i	0.990749	−	0.135704i	$-0.0433296\pi$
$308$	−1.56122	+	2.12079i	−0.0889586	+	0.120843i
$309$	11.2925			0.642410
$310$	−42.2808	−	13.7379i	−2.40139	−	0.780259i
$311$	15.3495	−	11.1521i	0.870391	−	0.632376i	−0.0603005	−	0.998180i	$-0.519206\pi$
$311$	15.3495	−	11.1521i	0.870391	−	0.632376i	0.930692	+	0.365804i	$0.119206\pi$
$312$	−10.0731	+	3.99230i	−0.570277	+	0.226019i
$313$	−6.47491	−	19.9277i	−0.365984	−	1.12638i	−0.949363	−	0.314182i	$-0.898270\pi$
$313$	−6.47491	−	19.9277i	−0.365984	−	1.12638i	0.583379	−	0.812200i	$-0.301730\pi$
$314$	−3.30914	+	1.07520i	−0.186745	+	0.0606773i
$315$	7.12770	+	5.17858i	0.401601	+	0.291780i
$316$	−4.34153	+	3.15431i	−0.244230	+	0.177444i
$317$	14.5897	+	4.74047i	0.819438	+	0.266251i	0.688590	−	0.725151i	$-0.258230\pi$
$317$	14.5897	+	4.74047i	0.819438	+	0.266251i	0.130848	+	0.991402i	$0.458230\pi$
$318$			2.67754i			0.150149i
$319$	−24.4073	−	0.152751i	−1.36655	−	0.00855241i
$320$			30.9073i			1.72777i
$321$	−4.28528	+	13.1887i	−0.239181	+	0.736124i
$322$	−18.3140	+	13.3059i	−1.02060	+	0.741508i
$323$	−3.76745	+	5.18545i	−0.209627	+	0.288526i
$324$	0.0974563	+	0.299940i	0.00541424	+	0.0166633i
$325$	6.48789	−	25.3054i	0.359884	−	1.40369i
$326$	−5.13152	−	3.72827i	−0.284209	−	0.206490i
$327$	2.32679	+	3.20255i	0.128672	+	0.177101i
$328$	−6.81227	+	20.9660i	−0.376145	+	1.15765i
$329$	−7.20309			−0.397119
$330$	−4.74455	+	14.2971i	−0.261179	+	0.787032i
$331$		−	25.8268i		−	1.41957i	−0.704419	−	0.709784i	$-0.748792\pi$
$331$		−	25.8268i		−	1.41957i	0.704419	−	0.709784i	$-0.251208\pi$
$332$	2.29582	+	0.745958i	0.126000	+	0.0409398i
$333$	−1.68877	−	2.32440i	−0.0925442	−	0.127376i
$334$	24.3435	+	17.6866i	1.33202	+	0.967768i
$335$	−8.47833	−	26.0936i	−0.463221	−	1.42565i
$336$	−7.82943	+	2.54394i	−0.427131	+	0.138783i
$337$	−14.5940	−	10.6031i	−0.794983	−	0.577589i	0.114455	−	0.993428i	$-0.463488\pi$
$337$	−14.5940	−	10.6031i	−0.794983	−	0.577589i	−0.909438	+	0.415839i	$0.863488\pi$
$338$	−8.11833	+	14.7917i	−0.441579	+	0.804562i
$339$	5.17760	−	15.9350i	0.281209	−	0.865472i
$340$		−	1.44282i		−	0.0782480i
$341$	−30.9367	+	9.83833i	−1.67532	+	0.532776i
$342$	−6.36331			−0.344089
$343$	−18.3445	−	5.96049i	−0.990510	−	0.321836i
$344$	15.1891	+	20.9059i	0.818939	+	1.12717i
$345$	14.2487	−	19.6117i	0.767125	−	1.05586i
$346$	20.5366	−	6.67274i	1.10405	−	0.358728i
$347$	−1.26573	−	3.89552i	−0.0679481	−	0.209123i	0.911317	−	0.411705i	$-0.135067\pi$
$347$	−1.26573	−	3.89552i	−0.0679481	−	0.209123i	−0.979265	+	0.202582i	$0.935067\pi$
$348$	1.87766	+	1.36420i	0.100653	+	0.0731288i
$349$	2.48466	+	3.41983i	0.133001	+	0.183060i	0.870323	−	0.492482i	$-0.163910\pi$
$349$	2.48466	+	3.41983i	0.133001	+	0.183060i	−0.737322	+	0.675541i	$0.763910\pi$
$350$	7.31652	−	22.5179i	0.391085	−	1.20363i
$351$	3.04494	+	1.93089i	0.162527	+	0.103063i
$352$	3.41387	+	4.76117i	0.181960	+	0.253771i
$353$		−	32.7763i		−	1.74451i	−0.489054	−	0.872254i	$-0.662658\pi$
$353$		−	32.7763i		−	1.74451i	0.489054	−	0.872254i	$-0.337342\pi$
$354$	2.03067	−	6.24976i	0.107929	−	0.332171i
$355$	−28.0294	+	20.3645i	−1.48764	+	1.08084i
$356$	−0.450307	+	0.619794i	−0.0238662	+	0.0328490i
$357$	3.13046	−	1.01715i	0.165681	−	0.0538332i
$358$	−27.8087	+	9.03560i	−1.46974	+	0.477546i
$359$	−11.8768	+	16.3470i	−0.626835	+	0.862764i	−0.997828	−	0.0658717i	$-0.979017\pi$
$359$	−11.8768	+	16.3470i	−0.626835	+	0.862764i	0.370994	+	0.928635i	$0.379017\pi$
$360$	8.50782	−	6.18129i	0.448402	−	0.325783i
$361$	−1.55623	+	4.78959i	−0.0819070	+	0.252084i
$362$		−	9.69518i		−	0.509567i
$363$	3.26798	+	10.5033i	0.171524	+	0.551283i
$364$	1.53316	−	2.41775i	0.0803596	−	0.126724i
$365$	−15.4716	+	47.6168i	−0.809822	+	2.49238i
$366$	−3.83946	−	5.28456i	−0.200692	−	0.276229i
$367$	23.1747	+	16.8374i	1.20971	+	0.878906i	0.995204	−	0.0978167i	$-0.0311859\pi$
$367$	23.1747	+	16.8374i	1.20971	+	0.878906i	0.214506	+	0.976723i	$0.431186\pi$
$368$	6.99957	+	21.5425i	0.364878	+	1.12298i
$369$	6.97659	−	2.26683i	0.363187	−	0.118006i
$370$	−7.67027	+	10.5572i	−0.398758	+	0.548844i
$371$	−3.05287	−	4.20191i	−0.158497	−	0.218152i
$372$	2.93584	+	0.953912i	0.152216	+	0.0494580i
$373$	−11.5238			−0.596680			−0.298340	−	0.954460i	$-0.596433\pi$
$373$	−11.5238			−0.596680			−0.298340	+	0.954460i	$0.596433\pi$
$374$	3.27943	+	4.57367i	0.169575	+	0.236499i
$375$			7.85768i			0.405769i
$376$	−2.65687	+	8.17700i	−0.137018	+	0.421697i
$377$	26.4811	−	1.67535i	1.36385	−	0.0862851i
$378$	2.64371	+	1.92077i	0.135978	+	0.0987936i
$379$	−24.6741	+	8.01711i	−1.26742	+	0.411811i	−0.864134	−	0.503261i	$-0.832133\pi$
$379$	−24.6741	+	8.01711i	−1.26742	+	0.411811i	−0.403290	+	0.915072i	$0.632133\pi$
$380$	−1.67197	−	5.14581i	−0.0857704	−	0.263974i
$381$	−7.73261	−	5.61807i	−0.396153	−	0.287822i
$382$	20.3330	+	27.9860i	1.04033	+	1.43189i
$383$	5.29713	+	1.72114i	0.270670	+	0.0879462i	0.441208	−	0.897405i	$-0.354550\pi$
$383$	5.29713	+	1.72114i	0.270670	+	0.0879462i	−0.170537	+	0.985351i	$0.554550\pi$
$384$			7.93083i			0.404718i
$385$	−8.85555	−	27.8464i	−0.451321	−	1.41918i
$386$	15.1144			0.769304
$387$	2.65718	−	8.17797i	0.135072	−	0.415710i
$388$	0.0748691	+	0.103049i	0.00380090	+	0.00523150i
$389$	−17.1121	−	12.4327i	−0.867620	−	0.630363i	0.0623270	−	0.998056i	$-0.480148\pi$
$389$	−17.1121	−	12.4327i	−0.867620	−	0.630363i	−0.929947	+	0.367693i	$0.880148\pi$
$390$	4.06702	−	15.8631i	0.205942	−	0.803257i
$391$	−2.79865	−	8.61337i	−0.141534	−	0.435597i
$392$	−1.16791	+	1.60749i	−0.0589883	+	0.0811904i
$393$	−2.61343	+	1.89877i	−0.131830	+	0.0957802i
$394$	−0.101265	+	0.311660i	−0.00510163	+	0.0157012i
$395$		−	59.5450i		−	2.99603i
$396$	0.329445	−	0.992745i	0.0165553	−	0.0498873i
$397$		−	21.0870i		−	1.05833i	−0.848519	−	0.529164i	$-0.822506\pi$
$397$		−	21.0870i		−	1.05833i	0.848519	−	0.529164i	$-0.177494\pi$
$398$	−5.04464	−	1.63910i	−0.252865	−	0.0821608i
$399$	9.98605	−	7.25529i	0.499928	−	0.363219i
$400$	−19.1665	−	13.9253i	−0.958327	−	0.696265i
$401$	12.2543	−	3.98165i	0.611948	−	0.198834i	0.0133862	−	0.999910i	$-0.495739\pi$
$401$	12.2543	−	3.98165i	0.611948	−	0.198834i	0.598562	+	0.801076i	$0.295739\pi$
$402$	−3.14466	−	9.67828i	−0.156842	−	0.482709i
$403$	32.8086	−	13.0031i	1.63431	−	0.647733i
$404$	2.15054	−	1.56246i	0.106994	−	0.0777354i
$405$	−3.32808	−	1.08136i	−0.165374	−	0.0537332i
$406$	24.0485			1.19351
$407$	−0.0596355	+	9.52885i	−0.00295602	+	0.472328i
$408$		−	3.92889i		−	0.194509i
$409$	10.1698	+	3.30438i	0.502867	+	0.163391i	0.549456	−	0.835523i	$-0.314835\pi$
$409$	10.1698	+	3.30438i	0.502867	+	0.163391i	−0.0465891	+	0.998914i	$0.514835\pi$
$410$	−19.5837	−	26.9546i	−0.967170	−	1.33119i
$411$	−3.30807	+	4.55317i	−0.163175	+	0.224591i
$412$	1.10053	+	3.38708i	0.0542192	+	0.166870i
$413$	3.93905	+	12.1232i	0.193828	+	0.596542i
$414$	5.28493	−	7.27409i	0.259740	−	0.357502i
$415$	−21.6696	+	15.7439i	−1.06372	+	0.772835i
$416$	−4.06145	−	4.90596i	−0.199129	−	0.240534i
$417$	−4.60908			−0.225708
$418$	16.9961	+	12.5117i	0.831307	+	0.611965i
$419$	12.5289			0.612079			0.306040	−	0.952019i	$-0.400996\pi$
$419$	12.5289			0.612079			0.306040	+	0.952019i	$0.400996\pi$
$420$	−0.858622	+	2.64257i	−0.0418965	+	0.128944i
$421$	−20.7401	−	28.5463i	−1.01081	−	1.39126i	−0.918451	−	0.395536i	$-0.870559\pi$
$421$	−20.7401	−	28.5463i	−1.01081	−	1.39126i	−0.0923599	−	0.995726i	$-0.529441\pi$
$422$	−0.951558	+	1.30971i	−0.0463211	+	0.0637555i
$423$	2.72095	−	0.884091i	0.132297	−	0.0429860i
$424$	−5.89609	+	1.91576i	−0.286339	+	0.0930373i
$425$	7.66340	+	5.56779i	0.371729	+	0.270077i
$426$	−10.3963	+	7.55333i	−0.503701	+	0.365960i
$427$	12.0507	+	3.91549i	0.583172	+	0.189484i
$428$	−4.37346			−0.211399
$429$	−4.33636	−	11.1443i	−0.209361	−	0.538053i
$430$	−39.0552			−1.88341
$431$	32.1934	+	10.4603i	1.55070	+	0.503854i	0.954305	−	0.298834i	$-0.0965977\pi$
$431$	32.1934	+	10.4603i	1.55070	+	0.503854i	0.596399	+	0.802688i	$0.296598\pi$
$432$	2.64531	−	1.92193i	0.127273	−	0.0924690i
$433$	31.9127	+	23.1860i	1.53363	+	1.11425i	0.954178	+	0.299239i	$0.0967328\pi$
$433$	31.9127	+	23.1860i	1.53363	+	1.11425i	0.579450	+	0.815007i	$0.303267\pi$
$434$	30.4201	−	9.88408i	1.46021	−	0.474451i
$435$	−24.4921	+	7.95796i	−1.17430	+	0.381555i
$436$	−0.733811	+	1.01000i	−0.0351432	+	0.0483704i
$437$	−19.9627	−	27.4763i	−0.954946	−	1.31437i
$438$	−5.73852	+	17.6613i	−0.274197	+	0.843892i
$439$	7.26536			0.346757			0.173378	−	0.984855i	$-0.444532\pi$
$439$	7.26536			0.346757			0.173378	+	0.984855i	$0.444532\pi$
$440$	−34.8778	−	0.218279i	−1.66273	−	0.0104061i
$441$	0.661176			0.0314846
$442$	−3.90151	−	4.71276i	−0.185576	−	0.224163i
$443$	−15.7830	+	11.4670i	−0.749871	+	0.544813i	−0.895787	−	0.444484i	$-0.853387\pi$
$443$	−15.7830	+	11.4670i	−0.749871	+	0.544813i	0.145916	+	0.989297i	$0.453387\pi$
$444$	0.532598	−	0.733058i	0.0252760	−	0.0347894i
$445$	−2.62683	−	8.08456i	−0.124524	−	0.383245i
$446$	3.91833	+	12.0594i	0.185538	+	0.571027i
$447$	2.37844	−	3.27365i	0.112496	−	0.154838i
$448$	−13.0706	−	17.9902i	−0.617529	−	0.849955i
$449$	26.4647	+	8.59890i	1.24895	+	0.405807i	0.857543	−	0.514412i	$-0.171990\pi$
$449$	26.4647	+	8.59890i	1.24895	+	0.405807i	0.391403	+	0.920219i	$0.371990\pi$
$450$			9.40412i			0.443314i
$451$	−23.0912	−	7.66289i	−1.08732	−	0.360831i
$452$	5.28414			0.248545
$453$	−1.61513	−	0.524789i	−0.0758856	−	0.0246567i
$454$	−4.19778	+	3.04987i	−0.197012	+	0.143137i
$455$	11.7042	+	29.5313i	0.548702	+	1.38445i
$456$	−4.55289	−	14.0124i	−0.213209	−	0.656189i
$457$	5.47912	−	1.78027i	0.256302	−	0.0832777i	−0.178048	−	0.984022i	$-0.556978\pi$
$457$	5.47912	−	1.78027i	0.256302	−	0.0832777i	0.434350	+	0.900744i	$0.356978\pi$
$458$	4.93072	+	3.58238i	0.230398	+	0.167394i
$459$	−1.05768	+	0.768451i	−0.0493684	+	0.0358682i
$460$	7.27095	+	2.36247i	0.339010	+	0.110151i
$461$			15.5066i			0.722212i	0.932525	+	0.361106i	$0.117601\pi$
$461$			15.5066i			0.722212i	−0.932525	+	0.361106i	$0.882399\pi$
$462$	−3.28458	−	10.3284i	−0.152812	−	0.480520i
$463$		−	19.9869i		−	0.928871i	−0.885607	−	0.464436i	$-0.846257\pi$
$463$		−	19.9869i		−	0.928871i	0.885607	−	0.464436i	$-0.153743\pi$
$464$	7.43590	−	22.8853i	0.345203	−	1.06243i
$465$	−27.7104	+	20.1328i	−1.28504	+	0.933637i
$466$	−8.82691	+	12.1492i	−0.408899	+	0.562801i
$467$	10.8042	+	33.2520i	0.499961	+	1.53872i	0.809080	+	0.587698i	$0.199966\pi$
$467$	10.8042	+	33.2520i	0.499961	+	1.53872i	−0.309119	+	0.951023i	$0.600034\pi$
$468$	−0.282400	+	1.10148i	−0.0130540	+	0.0509158i
$469$	15.9699	+	11.6028i	0.737422	+	0.535768i
$470$	−7.63788	−	10.5126i	−0.352309	−	0.484912i
$471$	−0.828399	+	2.54955i	−0.0381706	+	0.117477i
$472$	15.2152			0.700337
$473$	−23.1769	+	16.6184i	−1.06567	+	0.764114i
$474$		−	22.0856i		−	1.01442i
$475$	33.7835	+	10.9769i	1.55009	+	0.503656i
$476$	0.610166	+	0.839822i	0.0279669	+	0.0384932i
$477$	1.66895	+	1.21256i	0.0764158	+	0.0555193i
$478$	−3.94382	−	12.1378i	−0.180386	−	0.555171i
$479$	23.8378	−	7.74537i	1.08918	−	0.353895i	0.291249	−	0.956647i	$-0.405929\pi$
$479$	23.8378	−	7.74537i	1.08918	−	0.353895i	0.797928	+	0.602752i	$0.205929\pi$
$480$	5.00084	+	3.63332i	0.228256	+	0.165838i
$481$	−0.654076	−	10.3385i	−0.0298233	−	0.471395i
$482$	9.56097	−	29.4256i	0.435490	−	1.34030i
$483$			17.4411i			0.793597i
$484$	−2.83189	+	2.00381i	−0.128722	+	0.0910825i
$485$	−1.41333			−0.0641761
$486$	−1.23441	−	0.401083i	−0.0559938	−	0.0181935i
$487$	6.30510	+	8.67822i	0.285711	+	0.393248i	0.927615	−	0.373537i	$-0.121855\pi$
$487$	6.30510	+	8.67822i	0.285711	+	0.393248i	−0.641904	+	0.766785i	$0.721855\pi$
$488$	8.88979	−	12.2357i	0.402422	−	0.553886i
$489$	−4.64776	+	1.51015i	−0.210179	+	0.0682912i
$490$	−0.927981	−	2.85603i	−0.0419219	−	0.129022i
$491$	−13.8937	−	10.0944i	−0.627015	−	0.455553i	0.228350	−	0.973579i	$-0.426667\pi$
$491$	−13.8937	−	10.0944i	−0.627015	−	0.455553i	−0.855365	+	0.518026i	$0.826667\pi$
$492$	1.35982	+	1.87164i	0.0613056	+	0.0843800i
$493$	−2.97311	+	9.15030i	−0.133902	+	0.412109i
$494$	−19.3759	−	12.2868i	−0.871764	−	0.552811i
$495$	6.76296	+	9.43199i	0.303973	+	0.423937i
$496$		−	32.0050i		−	1.43707i
$497$	7.70291	−	23.7071i	0.345523	−	1.06341i
$498$	−8.03737	+	5.83949i	−0.360163	+	0.261674i
$499$	−20.0535	+	27.6013i	−0.897719	+	1.23560i	0.0734710	+	0.997297i	$0.476592\pi$
$499$	−20.0535	+	27.6013i	−0.897719	+	1.23560i	−0.971190	+	0.238307i	$0.923408\pi$
$500$	−2.35683	+	0.765781i	−0.105401	+	0.0342468i
$501$	22.0486	−	7.16402i	0.985058	−	0.320065i
$502$	−5.25422	+	7.23182i	−0.234507	+	0.322772i
$503$	1.40184	−	1.01850i	0.0625050	−	0.0454126i	−0.556094	−	0.831119i	$-0.687701\pi$
$503$	1.40184	−	1.01850i	0.0625050	−	0.0454126i	0.618599	+	0.785707i	$0.287701\pi$
$504$	−2.33808	+	7.19588i	−0.104146	+	0.320530i
$505$			29.4952i			1.31252i
$506$	−28.4182	+	9.03742i	−1.26335	+	0.401762i
$507$	5.54336	+	11.7589i	0.246189	+	0.522230i
$508$	0.931490	−	2.86683i	0.0413282	−	0.127195i
$509$	−0.291087	−	0.400647i	−0.0129022	−	0.0177584i	0.802517	−	0.596629i	$-0.203494\pi$
$509$	−0.291087	−	0.400647i	−0.0129022	−	0.0177584i	−0.815419	+	0.578871i	$0.803494\pi$
$510$	4.80390	+	3.49024i	0.212720	+	0.154550i
$511$	−11.1315	−	34.2592i	−0.492427	−	1.51554i
$512$	−24.1840	+	7.85786i	−1.06879	+	0.347272i
$513$	−2.88171	+	3.96634i	−0.127231	+	0.175118i
$514$	2.19050	+	3.01496i	0.0966188	+	0.132984i
$515$	−37.5825	−	12.2113i	−1.65608	−	0.538094i
$516$	2.71186			0.119383
$517$	−9.00585	−	2.98862i	−0.396077	−	0.131439i
$518$		−	9.38877i		−	0.412519i
$519$	5.14106	−	15.8225i	0.225667	−	0.694533i
$520$	37.8412	−	2.39406i	1.65945	−	0.104987i
$521$	14.0922	+	10.2386i	0.617392	+	0.448561i	0.852009	−	0.523526i	$-0.175384\pi$
$521$	14.0922	+	10.2386i	0.617392	+	0.448561i	−0.234618	+	0.972088i	$0.575384\pi$
$522$	−9.08426	+	2.95165i	−0.397607	+	0.129190i
$523$	4.47679	+	13.7782i	0.195757	+	0.602477i	0.999967	+	0.00813197i	$0.00258852\pi$
$523$	4.47679	+	13.7782i	0.195757	+	0.602477i	−0.804210	+	0.594345i	$0.797411\pi$
$524$	−0.824212	−	0.598825i	−0.0360059	−	0.0261598i
$525$	−10.7223	−	14.7580i	−0.467961	−	0.644093i
$526$	17.9828	+	5.84298i	0.784089	+	0.254766i
$527$			12.7966i			0.557430i
$528$	−10.8444	−	0.0678690i	−0.471944	−	0.00295362i
$529$	24.9886			1.08646
$530$	2.89539	−	8.91108i	0.125768	−	0.387073i
$531$	−2.97594	−	4.09603i	−0.129145	−	0.177752i
$532$	3.14935	+	2.28814i	0.136542	+	0.0992034i
$533$	25.6203	+	6.56862i	1.10974	+	0.284518i
$534$	−0.974308	−	2.99861i	−0.0421624	−	0.129763i
$535$	28.5235	−	39.2593i	1.23318	−	1.69733i
$536$	19.0621	−	13.8494i	0.823358	−	0.598204i
$537$	−6.96154	+	21.4254i	−0.300413	+	0.924575i
$538$			14.0369i			0.605173i
$539$	−1.76597	−	1.30002i	−0.0760658	−	0.0559957i
$540$		−	1.10361i		−	0.0474918i
$541$	2.02157	+	0.656847i	0.0869139	+	0.0282400i	0.352151	−	0.935943i	$-0.385450\pi$
$541$	2.02157	+	0.656847i	0.0869139	+	0.0282400i	−0.265237	+	0.964183i	$0.585450\pi$
$542$	1.38159	−	1.00378i	0.0593442	−	0.0431161i
$543$	−6.04313	−	4.39059i	−0.259335	−	0.188418i
$544$	2.19635	−	0.713637i	0.0941677	−	0.0305969i
$545$	−4.28063	−	13.1744i	−0.183362	−	0.564331i
$546$	4.34116	+	10.9533i	0.185785	+	0.468759i
$547$	9.76104	−	7.09181i	0.417352	−	0.303224i	−0.359220	−	0.933253i	$-0.616957\pi$
$547$	9.76104	−	7.09181i	0.417352	−	0.303224i	0.776571	+	0.630029i	$0.216957\pi$
$548$	−1.68807	−	0.548487i	−0.0721107	−	0.0234302i
$549$	−5.03269			−0.214790
$550$	18.4905	−	25.1180i	0.788439	−	1.07103i
$551$			36.0797i			1.53705i
$552$	19.7992	+	6.43316i	0.842712	+	0.273814i
$553$	25.1814	+	34.6593i	1.07082	+	1.47386i
$554$	−6.18711	+	8.51583i	−0.262865	+	0.361803i
$555$	3.10687	+	9.56196i	0.131879	+	0.405883i
$556$	−0.449184	−	1.38245i	−0.0190496	−	0.0586288i
$557$	9.90705	−	13.6359i	0.419775	−	0.577771i	−0.545793	−	0.837920i	$-0.683772\pi$
$557$	9.90705	−	13.6359i	0.419775	−	0.577771i	0.965569	+	0.260149i	$0.0837716\pi$
$558$	−10.2780	+	7.46738i	−0.435101	+	0.316119i
$559$	23.8817	−	19.7707i	1.01009	−	0.836213i
$560$	28.8079			1.21736
$561$	4.33596	+	0.0271362i	0.183064	+	0.00114569i
$562$	0.697729			0.0294319
$563$	0.296128	−	0.911389i	0.0124803	−	0.0384105i	−0.944622	−	0.328159i	$-0.893572\pi$
$563$	0.296128	−	0.911389i	0.0124803	−	0.0384105i	0.957103	+	0.289749i	$0.0935718\pi$
$564$	0.530348	+	0.729962i	0.0223317	+	0.0307369i
$565$	−34.4630	+	47.4342i	−1.44987	+	1.99557i
$566$	−12.1668	+	3.95322i	−0.511407	+	0.166166i
$567$	2.39448	−	0.778013i	0.100559	−	0.0326735i
$568$	−24.0713	−	17.4888i	−1.01001	−	0.733813i
$569$	−3.31028	+	2.40506i	−0.138774	+	0.100825i	−0.655006	−	0.755623i	$-0.727334\pi$
$569$	−3.31028	+	2.40506i	−0.138774	+	0.100825i	0.516232	+	0.856449i	$0.327334\pi$
$570$	21.1776	+	6.88103i	0.887033	+	0.288215i
$571$	−31.9081			−1.33531			−0.667657	−	0.744469i	$-0.732703\pi$
$571$	−31.9081			−1.33531			−0.667657	+	0.744469i	$0.732703\pi$
$572$	2.92002	−	2.38673i	0.122092	−	0.0997943i
$573$	26.6521			1.11341
$574$	22.7981	+	7.40756i	0.951575	+	0.309185i
$575$	−40.6063	+	29.5022i	−1.69340	+	1.23033i
$576$	7.14547	+	5.19149i	0.297728	+	0.216312i
$577$	3.37284	−	1.09590i	0.140413	−	0.0456230i	−0.237967	−	0.971273i	$-0.576481\pi$
$577$	3.37284	−	1.09590i	0.140413	−	0.0456230i	0.378380	+	0.925650i	$0.376481\pi$
$578$	−18.8750	+	6.13287i	−0.785098	+	0.255094i
$579$	6.84477	−	9.42102i	0.284459	−	0.391524i
$580$	−4.77381	−	6.57059i	−0.198222	−	0.272829i
$581$	5.95513	−	18.3280i	0.247060	−	0.760374i
$582$	−0.524213			−0.0217293
$583$	−2.07352	−	6.52020i	−0.0858764	−	0.270039i
$584$	−42.9971			−1.77923
$585$	−8.04584	−	9.71882i	−0.332655	−	0.401824i
$586$	8.73581	−	6.34694i	0.360873	−	0.262190i
$587$	−15.0220	+	20.6760i	−0.620024	+	0.853389i	−0.997355	−	0.0726891i	$-0.976842\pi$
$587$	−15.0220	+	20.6760i	−0.620024	+	0.853389i	0.377331	+	0.926078i	$0.376842\pi$
$588$	0.0644358	+	0.198313i	0.00265729	+	0.00817829i
$589$	14.8290	+	45.6390i	0.611019	+	1.88052i
$590$	−13.5165	+	18.6038i	−0.556464	+	0.765907i
$591$	0.148403	+	0.204259i	0.00610448	+	0.00840209i
$592$	−8.93467	−	2.90305i	−0.367213	−	0.119315i
$593$			3.54530i			0.145588i	0.997347	+	0.0727940i	$0.0231915\pi$
$593$			3.54530i			0.145588i	−0.997347	+	0.0727940i	$0.976808\pi$
$594$	2.50842	+	3.49838i	0.102922	+	0.143540i
$595$	−11.5183			−0.472205
$596$	1.21369	+	0.394352i	0.0497147	+	0.0161533i
$597$	−3.30621	+	2.40210i	−0.135314	+	0.0983114i
$598$	30.1378	−	11.9446i	1.23242	−	0.488450i
$599$	4.48988	+	13.8184i	0.183452	+	0.564606i	0.999918	−	0.0127864i	$-0.00407015\pi$
$599$	4.48988	+	13.8184i	0.183452	+	0.564606i	−0.816467	+	0.577393i	$0.804070\pi$
$600$	−20.7084	+	6.72855i	−0.845415	+	0.274692i
$601$	−12.2538	−	8.90290i	−0.499842	−	0.363157i	0.309114	−	0.951025i	$-0.399967\pi$
$601$	−12.2538	−	8.90290i	−0.499842	−	0.363157i	−0.808957	+	0.587868i	$0.799967\pi$
$602$	22.7328	−	16.5163i	0.926520	−	0.673156i
$603$	−7.45670	−	2.42283i	−0.303660	−	0.0986652i
$604$		−	0.535587i		−	0.0217927i
$605$	0.481790	−	38.4899i	0.0195875	−	1.56484i
$606$			10.9399i			0.444405i
$607$	−0.148208	+	0.456137i	−0.00601557	+	0.0185140i	−0.954019	−	0.299745i	$-0.903098\pi$
$607$	−0.148208	+	0.456137i	−0.00601557	+	0.0185140i	0.948004	+	0.318259i	$0.103098\pi$
$608$	7.00628	−	5.09036i	0.284142	−	0.206441i
$609$	10.8907	−	14.9897i	0.441312	−	0.607414i
$610$	7.06353	+	21.7393i	0.285994	+	0.880198i
$611$	9.99223	+	2.56184i	0.404242	+	0.103641i
$612$	−0.333567	−	0.242350i	−0.0134836	−	0.00979643i
$613$	0.112566	+	0.154933i	0.00454648	+	0.00625770i	0.811284	−	0.584652i	$-0.198769\pi$
$613$	0.112566	+	0.154933i	0.00454648	+	0.00625770i	−0.806738	+	0.590910i	$0.798769\pi$
$614$	−1.90733	+	5.87015i	−0.0769735	+	0.236900i
$615$	−25.6699			−1.03511
$616$	20.3936	−	14.6227i	0.821680	−	0.589164i
$617$		−	27.8854i		−	1.12262i	−0.827604	−	0.561312i	$-0.810297\pi$
$617$		−	27.8854i		−	1.12262i	0.827604	−	0.561312i	$-0.189703\pi$
$618$	−13.9396	−	4.52924i	−0.560732	−	0.182193i
$619$	7.63867	+	10.5137i	0.307024	+	0.422582i	0.934450	−	0.356094i	$-0.115892\pi$
$619$	7.63867	+	10.5137i	0.307024	+	0.422582i	−0.627426	+	0.778676i	$0.715892\pi$
$620$	−8.73919	−	6.34939i	−0.350974	−	0.254998i
$621$	−2.14068	−	6.58833i	−0.0859025	−	0.264381i
$622$	−23.4204	+	7.60976i	−0.939074	+	0.305124i
$623$	4.94794	+	3.59489i	0.198235	+	0.144026i
$624$	11.7659	−	0.744380i	0.471012	−	0.0297990i
$625$	−2.69788	+	8.30323i	−0.107915	+	0.332129i
$626$			27.1959i			1.08697i
$627$	15.4956	−	4.92782i	0.618834	−	0.196798i
$628$	−0.845444			−0.0337369
$629$	3.57237	+	1.16073i	0.142440	+	0.0462815i
$630$	−6.72144	−	9.25127i	−0.267789	−	0.368579i
$631$	−9.04881	+	12.4546i	−0.360227	+	0.495810i	−0.950212	−	0.311604i	$-0.899134\pi$
$631$	−9.04881	+	12.4546i	−0.360227	+	0.495810i	0.589985	+	0.807414i	$0.299134\pi$
$632$	48.6336	−	15.8020i	1.93454	−	0.628571i
$633$	0.385431	+	1.18624i	0.0153195	+	0.0471487i
$634$	−16.1083	−	11.7033i	−0.639741	−	0.464799i
$635$	19.6596	+	27.0591i	0.780167	+	1.07381i
$636$	−0.201046	+	0.618755i	−0.00797198	+	0.0245352i
$637$	2.01324	+	1.27666i	0.0797677	+	0.0505829i
$638$	30.0672	+	9.97789i	1.19037	+	0.395029i
$639$			9.90075i			0.391668i
$640$	8.57607	−	26.3944i	0.338999	−	1.04333i
$641$	12.6647	−	9.20148i	0.500228	−	0.363437i	−0.308876	−	0.951102i	$-0.599953\pi$
$641$	12.6647	−	9.20148i	0.500228	−	0.363437i	0.809104	+	0.587666i	$0.199953\pi$
$642$	10.5796	−	14.5615i	0.417542	−	0.574697i
$643$	−9.48696	+	3.08250i	−0.374129	+	0.121562i	−0.490045	−	0.871697i	$-0.663020\pi$
$643$	−9.48696	+	3.08250i	−0.374129	+	0.121562i	0.115916	+	0.993259i	$0.463020\pi$
$644$	−5.23127	+	1.69974i	−0.206141	+	0.0669793i
$645$	−17.6867	+	24.3436i	−0.696411	+	0.958528i
$646$	6.73036	−	4.88989i	0.264803	−	0.192390i
$647$	15.3728	−	47.3127i	0.604369	−	1.86006i	0.103296	−	0.994651i	$-0.467061\pi$
$647$	15.3728	−	47.3127i	0.604369	−	1.86006i	0.501073	−	0.865405i	$-0.332939\pi$
$648$		−	3.00520i		−	0.118055i
$649$	−0.105089	+	16.7916i	−0.00412511	+	0.659129i
$650$	−18.1583	+	28.6350i	−0.712226	+	1.12316i
$651$	7.61526	−	23.4374i	0.298466	−	0.918583i
$652$	−0.905906	−	1.24687i	−0.0354780	−	0.0488313i
$653$	−34.9844	−	25.4177i	−1.36905	−	0.994670i	−0.997811	−	0.0661314i	$-0.978934\pi$
$653$	−34.9844	−	25.4177i	−1.36905	−	0.994670i	−0.371235	−	0.928539i	$-0.621066\pi$
$654$	−1.58771	−	4.88648i	−0.0620845	−	0.191076i
$655$	10.7510	−	3.49320i	0.420075	−	0.136491i
$656$	14.0986	−	19.4050i	0.550456	−	0.757638i
$657$	8.40978	+	11.5751i	0.328097	+	0.451586i
$658$	8.89154	+	2.88904i	0.346628	+	0.112626i
$659$	26.6856			1.03952			0.519762	−	0.854311i	$-0.326021\pi$
$659$	26.6856			1.03952			0.519762	+	0.854311i	$0.326021\pi$
$660$	−2.16994	+	2.94769i	−0.0844646	+	0.114739i
$661$			24.1473i			0.939221i	0.882874	+	0.469611i	$0.155606\pi$
$661$			24.1473i			0.939221i	−0.882874	+	0.469611i	$0.844394\pi$
$662$	−10.3587	+	31.8807i	−0.402602	+	1.23908i
$663$	−4.70437	+	0.297627i	−0.182703	+	0.0115589i
$664$	−18.6095	−	13.5206i	−0.722190	−	0.524701i
$665$	−41.0800	+	13.3477i	−1.59301	+	0.517601i
$666$	1.15236	+	3.54659i	0.0446529	+	0.137427i
$667$	−41.2438	−	29.9654i	−1.59697	−	1.16026i
$668$	4.29755	+	5.91506i	0.166277	+	0.228861i
$669$	9.29122	+	3.01890i	0.359219	+	0.116717i
$670$			35.6106i			1.37576i
$671$	13.4421	+	9.89535i	0.518925	+	0.382006i
$672$	−4.44736			−0.171561
$673$	8.24378	−	25.3717i	0.317774	−	0.978009i	−0.656823	−	0.754045i	$-0.728100\pi$
$673$	8.24378	−	25.3717i	0.317774	−	0.978009i	0.974597	−	0.223964i	$-0.0718998\pi$
$674$	13.7621	+	18.9419i	0.530097	+	0.729616i
$675$	5.86171	+	4.25878i	0.225617	+	0.163920i
$676$	−2.98672	+	2.80865i	−0.114874	+	0.108025i
$677$	−2.09010	−	6.43266i	−0.0803290	−	0.247227i	0.902824	−	0.430009i	$-0.141490\pi$
$677$	−2.09010	−	6.43266i	−0.0803290	−	0.247227i	−0.983153	+	0.182782i	$0.941490\pi$
$678$	−12.7825	+	17.5936i	−0.490910	+	0.675680i
$679$	0.822656	−	0.597695i	0.0315706	−	0.0229374i
$680$	−4.24855	+	13.0757i	−0.162924	+	0.501430i
$681$			3.99771i			0.153192i
$682$	42.1345	+	0.263695i	1.61341	+	0.0100974i
$683$			24.6347i			0.942619i	0.881968	+	0.471310i	$0.156219\pi$
$683$			24.6347i			0.942619i	−0.881968	+	0.471310i	$0.843781\pi$
$684$	−1.47050	−	0.477795i	−0.0562261	−	0.0182690i
$685$	15.9331	−	11.5761i	0.608774	−	0.442300i
$686$	20.2539	+	14.7153i	0.773298	+	0.561834i
$687$	4.46589	−	1.45105i	0.170384	−	0.0553612i
$688$	−8.68843	−	26.7402i	−0.331243	−	1.01946i
$689$	2.74053	+	6.91472i	0.104406	+	0.263430i
$690$	−25.4546	+	18.4938i	−0.969040	+	0.704049i
$691$	28.3307	+	9.20519i	1.07775	+	0.350182i	0.793501	−	0.608569i	$-0.208256\pi$
$691$	28.3307	+	9.20519i	1.07775	+	0.350182i	0.284248	+	0.958751i	$0.408256\pi$
$692$	5.24684			0.199455
$693$	−7.92528	−	2.63003i	−0.301056	−	0.0999064i
$694$			5.31632i			0.201805i
$695$	15.3394	+	4.98407i	0.581856	+	0.189057i
$696$	−12.9994	−	17.8921i	−0.492741	−	0.678200i
$697$	−5.63706	+	7.75875i	−0.213519	+	0.293884i
$698$	−1.69544	−	5.21802i	−0.0641732	−	0.197505i
$699$	3.57537	+	11.0039i	0.135233	+	0.416204i
$700$	3.38156	−	4.65432i	0.127811	−	0.175917i
$701$	−2.94782	+	2.14171i	−0.111338	+	0.0808914i	−0.642061	−	0.766654i	$-0.721920\pi$
$701$	−2.94782	+	2.14171i	−0.111338	+	0.0808914i	0.530723	+	0.847545i	$0.321920\pi$
$702$	−2.98425	−	3.60477i	−0.112633	−	0.136053i
$703$	14.0859			0.531260
$704$	−8.87762	−	27.9158i	−0.334588	−	1.05212i
$705$	−10.0116			−0.377058
$706$	−13.1460	+	40.4593i	−0.494757	+	1.52270i
$707$	−12.4734	−	17.1682i	−0.469112	−	0.645677i
$708$	0.938537	−	1.29179i	0.0352724	−	0.0485483i
$709$	11.8949	−	3.86488i	0.446722	−	0.145149i	−0.0770129	−	0.997030i	$-0.524538\pi$
$709$	11.8949	−	3.86488i	0.446722	−	0.145149i	0.523735	+	0.851881i	$0.324538\pi$
$710$	42.7675	−	13.8960i	1.60504	−	0.521508i
$711$	−13.7662	−	10.0018i	−0.516274	−	0.375095i
$712$	5.90599	−	4.29095i	0.221336	−	0.160810i
$713$	−64.4872	−	20.9532i	−2.41507	−	0.784702i
$714$	−4.27222			−0.159884
$715$	2.38075	+	41.7784i	0.0890348	+	1.56242i
$716$	−7.10478			−0.265518
$717$	−9.35168	−	3.03854i	−0.349245	−	0.113476i
$718$	21.2173	−	15.4153i	0.791824	−	0.575294i
$719$	−20.6196	−	14.9810i	−0.768980	−	0.558696i	0.132672	−	0.991160i	$-0.457644\pi$
$719$	−20.6196	−	14.9810i	−0.768980	−	0.558696i	−0.901651	+	0.432464i	$0.857644\pi$
$720$	−10.8821	+	3.53582i	−0.405553	+	0.131772i
$721$	27.0397	−	8.78574i	1.00701	−	0.327198i
$722$	3.84205	−	5.28812i	0.142986	−	0.196804i
$723$	−14.0116	−	19.2853i	−0.521096	−	0.717227i
$724$	0.727971	−	2.24046i	0.0270548	−	0.0832662i
$725$	53.3210			1.98029
$726$	0.178699	−	14.2761i	0.00663213	−	0.529837i
$727$	2.06657			0.0766447			0.0383223	−	0.999265i	$-0.487799\pi$
$727$	2.06657			0.0766447			0.0383223	+	0.999265i	$0.487799\pi$
$728$	−21.0137	+	17.3965i	−0.778821	+	0.644756i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	38.1965	−	52.5730i	1.41372	−	1.94581i
$731$	3.47391	+	10.6916i	0.128487	+	0.395443i
$732$	−0.490467	−	1.50950i	−0.0181282	−	0.0557928i
$733$	13.6552	−	18.7947i	0.504365	−	0.694199i	−0.478592	−	0.878038i	$-0.658853\pi$
$733$	13.6552	−	18.7947i	0.504365	−	0.694199i	0.982956	+	0.183839i	$0.0588525\pi$
$734$	−21.8538	−	30.0792i	−0.806639	−	1.11024i
$735$	−2.20045	−	0.714969i	−0.0811648	−	0.0263720i
$736$			12.2368i			0.451054i
$737$	15.1527	+	21.1328i	0.558156	+	0.778435i
$738$	−9.52112			−0.350477
$739$	−44.7564	−	14.5422i	−1.64639	−	0.534945i	−0.668437	−	0.743768i	$-0.733037\pi$
$739$	−44.7564	−	14.5422i	−1.64639	−	0.534945i	−0.977953	+	0.208824i	$0.933037\pi$
$740$	−2.56523	+	1.86375i	−0.0942996	+	0.0685127i
$741$	−16.4332	+	6.51301i	−0.603688	+	0.239262i
$742$	2.08316	+	6.41131i	0.0764753	+	0.235367i
$743$	16.4277	−	5.33769i	0.602674	−	0.195821i	0.00824151	−	0.999966i	$-0.497377\pi$
$743$	16.4277	−	5.33769i	0.602674	−	0.195821i	0.594433	+	0.804145i	$0.297377\pi$
$744$	−23.7974	−	17.2898i	−0.872453	−	0.633875i
$745$	−11.4556	+	8.32301i	−0.419702	+	0.304931i
$746$	14.2251	+	4.62200i	0.520816	+	0.169223i
$747$			7.65428i			0.280056i
$748$	0.414427	+	1.30317i	0.0151530	+	0.0476487i
$749$			34.9142i			1.27574i
$750$	3.15158	−	9.69957i	0.115079	−	0.354178i
$751$	0.901814	−	0.655206i	0.0329077	−	0.0239088i	−0.571210	−	0.820804i	$-0.693526\pi$
$751$	0.901814	−	0.655206i	0.0329077	−	0.0239088i	0.604118	+	0.796895i	$0.293526\pi$
$752$	5.49861	−	7.56819i	0.200514	−	0.275983i
$753$	2.12824	+	6.55005i	0.0775574	+	0.238697i
$754$	−33.3604	−	8.55304i	−1.21491	−	0.311483i
$755$	4.80781	+	3.49308i	0.174974	+	0.127126i
$756$	0.466714	+	0.642376i	0.0169742	+	0.0233630i
$757$	14.9393	−	45.9783i	0.542977	−	1.67111i	−0.182776	−	0.983155i	$-0.558508\pi$
$757$	14.9393	−	45.9783i	0.542977	−	1.67111i	0.725753	−	0.687956i	$-0.241492\pi$
$758$	33.6734			1.22307
$759$	−7.23644	+	21.8062i	−0.262666	+	0.791514i
$760$			51.5576i			1.87019i
$761$	−5.74963	−	1.86817i	−0.208424	−	0.0677211i	0.202944	−	0.979190i	$-0.434949\pi$
$761$	−5.74963	−	1.86817i	−0.208424	−	0.0677211i	−0.411368	+	0.911469i	$0.634949\pi$
$762$	7.29186	+	10.0364i	0.264156	+	0.363580i
$763$	8.06306	+	5.85816i	0.291902	+	0.212079i
$764$	2.59742	+	7.99403i	0.0939713	+	0.289214i
$765$	4.35102	−	1.41373i	0.157312	−	0.0511136i
$766$	−5.84848	−	4.24917i	−0.211314	−	0.153529i
$767$	−1.15260	−	18.2184i	−0.0416181	−	0.657827i
$768$	−2.27774	+	7.01015i	−0.0821907	+	0.252957i
$769$		−	36.6906i		−	1.32310i	−0.749903	−	0.661548i	$-0.769900\pi$
$769$		−	36.6906i		−	1.32310i	0.749903	−	0.661548i	$-0.230100\pi$
$770$	−0.237354	+	37.9255i	−0.00855363	+	1.36674i
$771$	2.87126			0.103406
$772$	3.49280	+	1.13488i	0.125709	+	0.0408453i
$773$	−14.3393	−	19.7364i	−0.515750	−	0.709870i	0.469125	−	0.883132i	$-0.344569\pi$
$773$	−14.3393	−	19.7364i	−0.515750	−	0.709870i	−0.984876	+	0.173262i	$0.944569\pi$
$774$	−6.56009	+	9.02918i	−0.235797	+	0.324547i
$775$	67.4483	−	21.9153i	2.42281	−	0.787220i
$776$	−0.375069	−	1.15435i	−0.0134642	−	0.0414386i
$777$	−5.85214	−	4.25183i	−0.209944	−	0.152534i
$778$	16.1368	+	22.2104i	0.578532	+	0.796281i
$779$	−11.1135	+	34.2038i	−0.398182	+	1.22548i
$780$	2.13094	−	3.36043i	0.0763000	−	0.120323i
$781$	19.4670	−	26.4444i	0.696585	−	0.946256i
$782$			11.7549i			0.420354i
$783$	−2.27412	+	6.99903i	−0.0812705	+	0.250125i
$784$	1.74902	−	1.27074i	0.0624650	−	0.0453835i
$785$	5.51396	−	7.58931i	0.196802	−	0.270874i
$786$	3.98760	−	1.29565i	0.142233	−	0.0462143i
$787$	−38.5104	+	12.5128i	−1.37275	+	0.446032i	−0.900278	−	0.435316i	$-0.856637\pi$
$787$	−38.5104	+	12.5128i	−1.37275	+	0.446032i	−0.472468	+	0.881348i	$0.656637\pi$
$788$	−0.0468026	+	0.0644182i	−0.00166727	+	0.00229480i
$789$	11.7858	−	8.56286i	0.419584	−	0.304846i
$790$	−23.8825	+	73.5027i	−0.849700	+	2.61511i
$791$		−	42.1843i		−	1.49990i
$792$	−5.90887	+	8.02674i	−0.209963	+	0.285218i
$793$	−15.3242	−	9.71754i	−0.544180	−	0.345080i
$794$	−8.45765	+	26.0300i	−0.300151	+	0.923769i
$795$	−4.24318	−	5.84023i	−0.150490	−	0.207132i
$796$	−1.04270	−	0.757563i	−0.0369574	−	0.0268511i
$797$	−7.18067	−	22.0998i	−0.254352	−	0.782816i	−0.993957	−	0.109774i	$-0.964987\pi$
$797$	−7.18067	−	22.0998i	−0.254352	−	0.782816i	0.739604	−	0.673042i	$-0.235013\pi$
$798$	−15.2368	+	4.95074i	−0.539377	+	0.175254i
$799$	−2.19852	+	3.02601i	−0.0777781	+	0.107052i
$800$	−7.52286	−	10.3543i	−0.265973	−	0.366081i
$801$	−2.31030	−	0.750662i	−0.0816305	−	0.0265234i
$802$	−16.7237			−0.590534
$803$	0.296974	−	47.4519i	0.0104800	−	1.67454i
$804$		−	2.47268i		−	0.0872047i
$805$	18.8601	−	58.0454i	0.664731	−	2.04583i
$806$	−45.7145	+	2.89218i	−1.61022	+	0.101873i
$807$	8.74937	+	6.35679i	0.307992	+	0.223770i
$808$	−24.0903	+	7.82742i	−0.847494	+	0.275368i
$809$	−14.4210	−	44.3832i	−0.507015	−	1.56043i	−0.797356	−	0.603509i	$-0.793769\pi$
$809$	−14.4210	−	44.3832i	−0.507015	−	1.56043i	0.290342	−	0.956923i	$-0.406231\pi$
$810$	3.67449	+	2.66967i	0.129108	+	0.0938027i
$811$	14.2225	+	19.5756i	0.499421	+	0.687394i	0.982091	−	0.188409i	$-0.0603329\pi$
$811$	14.2225	+	19.5756i	0.499421	+	0.687394i	−0.482670	+	0.875802i	$0.660333\pi$
$812$	5.55738	+	1.80570i	0.195026	+	0.0633677i
$813$		−	1.31574i		−	0.0461449i
$814$	3.89547	−	11.7386i	0.136536	−	0.411436i
$815$	17.1011			0.599026
$816$	−1.32099	+	4.06559i	−0.0462439	+	0.142324i
$817$	24.7793	+	34.1058i	0.866919	+	1.19321i
$818$	−11.2284	−	8.15790i	−0.392591	−	0.285234i
$819$	8.79330	+	2.25446i	0.307263	+	0.0787771i
$820$	−2.50169	−	7.69943i	−0.0873630	−	0.268876i
$821$	−1.31020	+	1.80333i	−0.0457262	+	0.0629367i	−0.831268	−	0.555872i	$-0.812384\pi$
$821$	−1.31020	+	1.80333i	−0.0457262	+	0.0629367i	0.785542	+	0.618809i	$0.212384\pi$
$822$	5.90970	−	4.29365i	0.206124	−	0.149758i
$823$	−2.37545	+	7.31089i	−0.0828030	+	0.254841i	−0.983884	−	0.178810i	$-0.942775\pi$
$823$	−2.37545	+	7.31089i	−0.0828030	+	0.254841i	0.901081	+	0.433652i	$0.142775\pi$
$824$		−	33.9363i		−	1.18223i
$825$	−7.28266	−	22.9004i	−0.253550	−	0.797289i
$826$		−	16.5448i		−	0.575667i
$827$	12.0756	+	3.92362i	0.419911	+	0.136437i	0.511349	−	0.859373i	$-0.329146\pi$
$827$	12.0756	+	3.92362i	0.419911	+	0.136437i	−0.0914373	+	0.995811i	$0.529146\pi$
$828$	1.76748	−	1.28415i	0.0614242	−	0.0446273i
$829$	23.7044	+	17.2223i	0.823288	+	0.598154i	0.917652	−	0.397384i	$-0.130082\pi$
$829$	23.7044	+	17.2223i	0.823288	+	0.598154i	−0.0943643	+	0.995538i	$0.530082\pi$
$830$	33.0636	−	10.7430i	1.14765	−	0.372896i
$831$	2.50611	+	7.71301i	0.0869360	+	0.267561i
$832$	11.7334	+	29.6049i	0.406782	+	1.02636i
$833$	−0.699314	+	0.508082i	−0.0242298	+	0.0176040i
$834$	5.68947	+	1.84862i	0.197010	+	0.0640125i
$835$	−81.1263			−2.80749
$836$	2.98819	+	4.16750i	0.103349	+	0.144136i
$837$			9.78809i			0.338326i
$838$	−15.4658	−	5.02514i	−0.534257	−	0.173591i
$839$	3.01694	+	4.15246i	0.104156	+	0.143359i	0.857913	−	0.513794i	$-0.171761\pi$
$839$	3.01694	+	4.15246i	0.104156	+	0.143359i	−0.753757	+	0.657153i	$0.771761\pi$
$840$	15.5627	−	21.4202i	0.536963	−	0.739066i
$841$	7.77427	+	23.9267i	0.268078	+	0.825060i
$842$	14.1523	+	43.5562i	0.487719	+	1.50105i
$843$	0.315976	−	0.434903i	0.0108828	−	0.0149789i
$844$	−0.318237	+	0.231212i	−0.0109542	+	0.00795866i
$845$	−5.73320	−	45.1289i	−0.197228	−	1.55248i
$846$	−3.71335			−0.127668
$847$	15.9968	+	22.6075i	0.549658	+	0.776803i
$848$	6.74535			0.231636
$849$	−3.04578	+	9.37396i	−0.104531	+	0.321714i
$850$	−7.22660	−	9.94656i	−0.247870	−	0.341164i
$851$	−11.6988	+	16.1020i	−0.401029	+	0.551969i
$852$	−2.96963	+	0.964891i	−0.101738	+	0.0330566i
$853$	12.1546	−	3.94926i	0.416164	−	0.135220i	−0.0934479	−	0.995624i	$-0.529789\pi$
$853$	12.1546	−	3.94926i	0.416164	−	0.135220i	0.509612	+	0.860404i	$0.329789\pi$
$854$	−13.3050	−	9.66662i	−0.455286	−	0.330785i
$855$	13.8796	−	10.0841i	0.474672	−	0.344870i
$856$	39.6348	+	12.8781i	1.35469	+	0.440165i
$857$	−18.6668			−0.637644			−0.318822	−	0.947815i	$-0.603287\pi$
$857$	−18.6668			−0.637644			−0.318822	+	0.947815i	$0.603287\pi$
$858$	0.883033	+	15.4959i	0.0301462	+	0.529020i
$859$	33.8863			1.15619			0.578093	−	0.815971i	$-0.303797\pi$
$859$	33.8863			1.15619			0.578093	+	0.815971i	$0.303797\pi$
$860$	−9.02529	−	2.93249i	−0.307760	−	0.0999972i
$861$	14.9417	−	10.8557i	0.509210	−	0.369963i
$862$	−35.5443	−	25.8245i	−1.21064	−	0.879585i
$863$	−52.5443	+	17.0727i	−1.78863	+	0.581160i	−0.999455	−	0.0330109i	$-0.989490\pi$
$863$	−52.5443	+	17.0727i	−1.78863	+	0.581160i	−0.789173	+	0.614171i	$0.789490\pi$
$864$	1.67998	−	0.545859i	0.0571541	−	0.0185705i
$865$	−34.2197	+	47.0994i	−1.16351	+	1.60143i
$866$	−30.0938	−	41.4205i	−1.02263	−	1.40753i
$867$	−4.72511	+	14.5424i	−0.160473	+	0.493886i
$868$	7.77195			0.263797
$869$	17.1033	+	53.7816i	0.580191	+	1.82442i
$870$	33.4250			1.13321
$871$	−18.0270	−	21.7754i	−0.610823	−	0.737832i
$872$	9.62429	−	6.99245i	0.325919	−	0.236794i
$873$	−0.237397	+	0.326749i	−0.00803467	+	0.0110588i
$874$	13.6218	+	41.9236i	0.460765	+	1.41809i
$875$	6.11338	+	18.8150i	0.206670	+	0.636065i
$876$	−2.65224	+	3.65049i	−0.0896108	+	0.123339i
$877$	−31.4680	−	43.3120i	−1.06260	−	1.46254i	−0.877350	−	0.479852i	$-0.840691\pi$
$877$	−31.4680	−	43.3120i	−1.06260	−	1.46254i	−0.185250	−	0.982691i	$-0.559309\pi$
$878$	−8.96840	−	2.91401i	−0.302669	−	0.0983431i
$879$		−	8.31944i		−	0.280608i
$880$	36.0178	+	11.9526i	1.21416	+	0.402923i
$881$	24.1081			0.812223			0.406111	−	0.913824i	$-0.366884\pi$
$881$	24.1081			0.812223			0.406111	+	0.913824i	$0.366884\pi$
$882$	−0.816160	−	0.265186i	−0.0274815	−	0.00892929i
$883$	−10.4549	+	7.59592i	−0.351835	+	0.255623i	−0.749638	−	0.661848i	$-0.769773\pi$
$883$	−10.4549	+	7.59592i	−0.351835	+	0.255623i	0.397803	+	0.917471i	$0.369773\pi$
$884$	−0.547741	−	1.38202i	−0.0184225	−	0.0464824i
$885$	5.47489	+	16.8500i	0.184036	+	0.566406i
$886$	24.0818	−	7.82464i	0.809043	−	0.262874i
$887$	23.2379	+	16.8833i	0.780251	+	0.566885i	0.905054	−	0.425296i	$-0.139830\pi$
$887$	23.2379	+	16.8833i	0.780251	+	0.566885i	−0.124803	+	0.992181i	$0.539830\pi$
$888$	−6.98527	+	5.07510i	−0.234410	+	0.170309i
$889$	−22.8865	−	7.43627i	−0.767588	−	0.249404i
$890$			11.0332i			0.369834i
$891$	3.31656	+	0.0207564i	0.111109	+	0.000695366i
$892$			3.08102i			0.103160i
$893$	−4.33440	+	13.3399i	−0.145045	+	0.446403i
$894$	−4.24897	+	3.08705i	−0.142107	+	0.103247i
$895$	46.3371	−	63.7776i	1.54888	−	2.13185i
$896$	6.17028	+	18.9902i	0.206135	+	0.634418i
$897$	6.20307	−	24.1945i	0.207114	−	0.807831i
$898$	−29.2193	−	21.2291i	−0.975061	−	0.708423i
$899$	42.3397	+	58.2757i	1.41211	+	1.94360i
$900$	−0.706117	+	2.17320i	−0.0235372	+	0.0724401i
$901$	−2.69701			−0.0898503
$902$	25.4305	+	18.7206i	0.846742	+	0.623328i
$903$		−	21.6493i		−	0.720443i
$904$	−47.8879	−	15.5597i	−1.59273	−	0.517509i
$905$	15.3642	+	21.1470i	0.510724	+	0.702951i
$906$	1.78325	+	1.29560i	0.0592444	+	0.0430436i
$907$	18.1703	+	55.9223i	0.603334	+	1.85687i	0.507863	+	0.861438i	$0.330436\pi$
$907$	18.1703	+	55.9223i	0.603334	+	1.85687i	0.0954706	+	0.995432i	$0.469564\pi$
$908$	−1.19907	+	0.389602i	−0.0397926	+	0.0129294i
$909$	6.81900	+	4.95430i	0.226172	+	0.164324i
$910$	−2.60327	−	41.1479i	−0.0862975	−	1.36404i
$911$	−3.65710	+	11.2554i	−0.121165	+	0.372908i	−0.993183	−	0.116566i	$-0.962811\pi$
$911$	−3.65710	+	11.2554i	−0.121165	+	0.372908i	0.872018	+	0.489474i	$0.162811\pi$
$912$			16.0307i			0.530828i
$913$	15.0500	−	20.4442i	0.498082	−	0.676605i
$914$	−7.47749			−0.247334
$915$	16.7492	+	5.44214i	0.553711	+	0.179912i
$916$	0.870458	+	1.19808i	0.0287607	+	0.0395858i
$917$	−4.78053	+	6.57984i	−0.157867	+	0.217285i
$918$	1.61382	−	0.524362i	0.0532640	−	0.0173065i
$919$	−1.13291	−	3.48673i	−0.0373712	−	0.115017i	0.930631	−	0.365960i	$-0.119259\pi$
$919$	−1.13291	−	3.48673i	−0.0373712	−	0.115017i	−0.968002	+	0.250943i	$0.919259\pi$
$920$	−58.9369	−	42.8202i	−1.94309	−	1.41174i
$921$	2.79518	+	3.84724i	0.0921044	+	0.126771i
$922$	6.21941	−	19.1414i	0.204825	−	0.630388i
$923$	−19.1172	+	30.1472i	−0.629251	+	0.992308i
$924$	0.0164810	−	2.63342i	0.000542186	−	0.0866331i
$925$		−	20.8171i		−	0.684461i
$926$	−8.01641	+	24.6720i	−0.263436	+	0.810772i
$927$	−9.13586	+	6.63759i	−0.300061	+	0.218007i
$928$	7.64096	−	10.5169i	0.250827	−	0.345234i
$929$	42.7325	−	13.8846i	1.40201	−	0.455540i	0.492168	−	0.870500i	$-0.336205\pi$
$929$	42.7325	−	13.8846i	1.40201	−	0.455540i	0.909839	+	0.414961i	$0.136205\pi$
$930$	42.2808	−	13.7379i	1.38644	−	0.450483i
$931$	−1.90532	+	2.62245i	−0.0624443	+	0.0859472i
$932$	−2.95205	+	2.14479i	−0.0966977	+	0.0702550i
$933$	−5.86300	+	18.0444i	−0.191946	+	0.590749i
$934$		−	45.3799i		−	1.48488i
$935$	−14.4011	−	4.77904i	−0.470966	−	0.156291i
$936$	5.80269	−	9.15066i	0.189667	−	0.299099i
$937$	−14.7717	+	45.4626i	−0.482571	+	1.48520i	0.352898	+	0.935662i	$0.385196\pi$
$937$	−14.7717	+	45.4626i	−0.482571	+	1.48520i	−0.835469	+	0.549538i	$0.814804\pi$
$938$	−15.0597	−	20.7278i	−0.491715	−	0.676788i
$939$	16.9515	+	12.3160i	0.553193	+	0.401918i
$940$	−0.975691	−	3.00287i	−0.0318235	−	0.0979428i
$941$	−25.2631	+	8.20847i	−0.823553	+	0.267589i	−0.690327	−	0.723497i	$-0.742533\pi$
$941$	−25.2631	+	8.20847i	−0.823553	+	0.267589i	−0.133226	+	0.991086i	$0.542533\pi$
$942$	2.04516	−	2.81492i	0.0666349	−	0.0917151i
$943$	−29.8693	−	41.1115i	−0.972677	−	1.33878i
$944$	−15.7446	−	5.11572i	−0.512443	−	0.166503i
$945$	−8.81033			−0.286600
$946$	35.2750	−	11.2180i	1.14689	−	0.364728i
$947$		−	18.1390i		−	0.589437i	−0.955584	−	0.294719i	$-0.904774\pi$
$947$		−	18.1390i		−	0.589437i	0.955584	−	0.294719i	$-0.0952259\pi$
$948$	1.65832	−	5.10377i	0.0538596	−	0.165763i
$949$	3.25717	+	51.4838i	0.105732	+	1.67123i
$950$	−37.2999	−	27.1000i	−1.21017	−	0.879238i
$951$	−14.5897	+	4.74047i	−0.473103	+	0.153720i
$952$	−3.05673	−	9.40765i	−0.0990692	−	0.304904i
$953$	6.68543	+	4.85725i	0.216562	+	0.157342i	0.690778	−	0.723067i	$-0.257268\pi$
$953$	6.68543	+	4.85725i	0.216562	+	0.157342i	−0.474216	+	0.880409i	$0.657268\pi$
$954$	−1.57382	−	2.16618i	−0.0509543	−	0.0701326i
$955$	−88.7005	−	28.8205i	−2.87028	−	0.932610i
$956$		−	3.10106i		−	0.100296i
$957$	19.8357	−	14.2227i	0.641197	−	0.459753i
$958$	−32.5320			−1.05106
$959$	−4.37868	+	13.4762i	−0.141395	+	0.435169i
$960$	−18.1668	−	25.0045i	−0.586332	−	0.807017i
$961$	52.4298	+	38.0925i	1.69128	+	1.22879i
$962$	−3.33919	+	13.0242i	−0.107660	+	0.419918i
$963$	−4.28528	−	13.1887i	−0.138091	−	0.425001i
$964$	4.41890	−	6.08210i	0.142323	−	0.195891i
$965$	−32.9675	+	23.9523i	−1.06126	+	0.771051i
$966$	6.99532	−	21.5294i	0.225071	−	0.692696i
$967$		−	24.7316i		−	0.795315i	−0.917534	−	0.397658i	$-0.869823\pi$
$967$		−	24.7316i		−	0.795315i	0.917534	−	0.397658i	$-0.130177\pi$
$968$	31.5646	−	9.82092i	1.01453	−	0.315656i
$969$		−	6.40957i		−	0.205905i
$970$	1.74462	+	0.566863i	0.0560165	+	0.0182009i
$971$	−41.8073	+	30.3748i	−1.34166	+	0.974774i	−0.342280	+	0.939598i	$0.611199\pi$
$971$	−41.8073	+	30.3748i	−1.34166	+	0.974774i	−0.999381	+	0.0351761i	$0.988801\pi$
$972$	−0.255144	−	0.185373i	−0.00818375	−	0.00594584i
$973$	−11.0363	+	3.58592i	−0.353809	+	0.114959i
$974$	−4.30236	−	13.2413i	−0.137857	−	0.424279i
$975$	9.62535	+	24.2860i	0.308258	+	0.777775i
$976$	−13.3130	+	9.67249i	−0.426140	+	0.309609i
$977$	−10.9395	−	3.55444i	−0.349984	−	0.113717i	0.128749	−	0.991677i	$-0.458904\pi$
$977$	−10.9395	−	3.55444i	−0.349984	−	0.113717i	−0.478733	+	0.877961i	$0.658904\pi$
$978$	6.34291			0.202824
$979$	4.69474	+	6.54754i	0.150045	+	0.209260i
$980$		−	0.729680i		−	0.0233088i
$981$	−3.76482	−	1.22326i	−0.120201	−	0.0390558i
$982$	13.1018	+	18.0331i	0.418095	+	0.575459i
$983$	11.8326	−	16.2862i	0.377403	−	0.519450i	−0.577491	−	0.816397i	$-0.695968\pi$
$983$	11.8326	−	16.2862i	0.377403	−	0.519450i	0.954894	+	0.296946i	$0.0959683\pi$
$984$	−6.81227	−	20.9660i	−0.217167	−	0.668372i
$985$	−0.273019	−	0.840267i	−0.00869912	−	0.0267731i
$986$	7.34005	−	10.1027i	0.233755	−	0.321736i
$987$	5.82743	−	4.23387i	0.185489	−	0.134766i
$988$	−3.55503	−	4.29423i	−0.113101	−	0.136618i
$989$	−59.5674			−1.89413
$990$	−4.56523	−	14.3554i	−0.145093	−	0.456245i
$991$	−2.19259			−0.0696500			−0.0348250	−	0.999393i	$-0.511087\pi$
$991$	−2.19259			−0.0696500			−0.0348250	+	0.999393i	$0.511087\pi$
$992$	5.34291	−	16.4438i	0.169638	−	0.522091i
$993$	15.1806	+	20.8943i	0.481742	+	0.663061i
$994$	−19.0170	+	26.1747i	−0.603184	+	0.830211i
$995$	13.6009	−	4.41919i	0.431176	−	0.140098i
$996$	−2.29582	+	0.745958i	−0.0727460	+	0.0236366i
$997$	−21.7654	−	15.8135i	−0.689317	−	0.500818i	0.187119	−	0.982337i	$-0.440085\pi$
$997$	−21.7654	−	15.8135i	−0.689317	−	0.500818i	−0.876436	+	0.481519i	$0.840085\pi$
$998$	35.8246	−	26.0281i	1.13401	−	0.823905i
$999$	2.73249	+	0.887841i	0.0864523	+	0.0280900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.64.5	✓	56
11.5	even	5	inner	429.2.bb.a.181.10	yes	56
13.12	even	2	inner	429.2.bb.a.64.10	yes	56
143.38	even	10	inner	429.2.bb.a.181.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.64.5	✓	56	1.1	even	1	trivial
429.2.bb.a.64.10	yes	56	13.12	even	2	inner
429.2.bb.a.181.5	yes	56	143.38	even	10	inner
429.2.bb.a.181.10	yes	56	11.5	even	5	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23441 - 0.401083i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.255144 - 0.185373i) q^{4} +(3.32808 - 1.08136i) q^{5} +(1.23441 - 0.401083i) q^{6} +(-1.47987 + 2.03686i) q^{7} +(1.76641 + 2.43126i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.23441 - 0.401083i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.255144 - 0.185373i) q^{4} +(3.32808 - 1.08136i) q^{5} +(1.23441 - 0.401083i) q^{6} +(-1.47987 + 2.03686i) q^{7} +(1.76641 + 2.43126i) q^{8} +(0.309017 - 0.951057i) q^{9} -4.54192 q^{10} +(-2.69535 + 1.93263i) q^{11} +0.315375 q^{12} +(2.77732 - 2.29924i) q^{13} +(2.64371 - 1.92077i) q^{14} +(-2.05687 + 2.83104i) q^{15} +(-1.01042 - 3.10975i) q^{16} +(0.403998 + 1.24338i) q^{17} +(-0.762905 + 1.05005i) q^{18} +(2.88171 + 3.96634i) q^{19} +(-1.04959 - 0.341034i) q^{20} -2.51770i q^{21} +(4.10231 - 1.30459i) q^{22} -6.92738 q^{23} +(-2.85811 - 0.928657i) q^{24} +(5.86171 - 4.25878i) q^{25} +(-4.35052 + 1.72426i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.755159 - 0.245366i) q^{28} +(5.95373 + 4.32564i) q^{29} +(3.67449 - 2.66967i) q^{30} +(9.30903 + 3.02469i) q^{31} -1.76644i q^{32} +(1.04461 - 3.14782i) q^{33} -1.69687i q^{34} +(-2.72254 + 8.37912i) q^{35} +(-0.255144 + 0.185373i) q^{36} +(1.68877 - 2.32440i) q^{37} +(-1.96637 - 6.05187i) q^{38} +(-0.895442 + 3.49259i) q^{39} +(8.50782 + 6.18129i) q^{40} +(4.31177 + 5.93464i) q^{41} +(-1.00981 + 3.10787i) q^{42} +8.59883 q^{43} +(1.04596 + 0.00654606i) q^{44} -3.49935i q^{45} +(8.55120 + 2.77845i) q^{46} +(1.68164 + 2.31458i) q^{47} +(2.64531 + 1.92193i) q^{48} +(0.204315 + 0.628816i) q^{49} +(-8.94385 + 2.90603i) q^{50} +(-1.05768 - 0.768451i) q^{51} +(-1.13483 + 0.0717964i) q^{52} +(-0.637481 + 1.96196i) q^{53} -1.29793i q^{54} +(-6.88049 + 9.34661i) q^{55} -7.56619 q^{56} +(-4.66271 - 1.51501i) q^{57} +(-5.61438 - 7.72753i) q^{58} +(2.97594 - 4.09603i) q^{59} +(1.04959 - 0.341034i) q^{60} +(-1.55519 - 4.78637i) q^{61} +(-10.2780 - 7.46738i) q^{62} +(1.47987 + 2.03686i) q^{63} +(-2.72933 + 8.40000i) q^{64} +(6.75685 - 10.6553i) q^{65} +(-2.55201 + 3.46671i) q^{66} -7.84044i q^{67} +(0.127411 - 0.392131i) q^{68} +(5.60437 - 4.07181i) q^{69} +(6.72144 - 9.25127i) q^{70} +(-9.41617 + 3.05950i) q^{71} +(2.85811 - 0.928657i) q^{72} +(-8.40978 + 11.5751i) q^{73} +(-3.01691 + 2.19191i) q^{74} +(-2.23897 + 6.89085i) q^{75} -1.54618i q^{76} +(0.0522584 - 8.35011i) q^{77} +(2.50616 - 3.95213i) q^{78} +(5.25823 - 16.1832i) q^{79} +(-6.72552 - 9.25689i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.94219 - 9.05513i) q^{82} +(-7.27966 + 2.36530i) q^{83} +(-0.466714 + 0.642376i) q^{84} +(2.68908 + 3.70120i) q^{85} +(-10.6144 - 3.44884i) q^{86} -7.35922 q^{87} +(-9.45983 - 3.13927i) q^{88} -2.42919i q^{89} +(-1.40353 + 4.31962i) q^{90} +(0.573165 + 9.05959i) q^{91} +(1.76748 + 1.28415i) q^{92} +(-9.30903 + 3.02469i) q^{93} +(-1.14749 - 3.53161i) q^{94} +(13.8796 + 10.0841i) q^{95} +(1.03828 + 1.42908i) q^{96} +(-0.384116 - 0.124807i) q^{97} -0.858161i q^{98} +(1.00513 + 3.16065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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