LMFDB - Embedded newform 403.2.k.d.66.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.11
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.700746 + 2.15667i) q^{2} +(-0.672668 + 2.07026i) q^{3} +(-2.54216 + 1.84699i) q^{4} -3.69852 q^{5} -4.93624 q^{6} +(0.888338 - 0.645416i) q^{7} +(-2.09561 - 1.52255i) q^{8} +(-1.40643 - 1.02183i) q^{9} +O(q^{10})$	\(q+(0.700746 + 2.15667i) q^{2} +(-0.672668 + 2.07026i) q^{3} +(-2.54216 + 1.84699i) q^{4} -3.69852 q^{5} -4.93624 q^{6} +(0.888338 - 0.645416i) q^{7} +(-2.09561 - 1.52255i) q^{8} +(-1.40643 - 1.02183i) q^{9} +(-2.59172 - 7.97650i) q^{10} +(0.853209 - 0.619892i) q^{11} +(-2.11371 - 6.50534i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(2.01445 + 1.46358i) q^{14} +(2.48787 - 7.65689i) q^{15} +(-0.126889 + 0.390525i) q^{16} +(0.552744 + 0.401592i) q^{17} +(1.21821 - 3.74927i) q^{18} +(1.56729 + 4.82362i) q^{19} +(9.40223 - 6.83112i) q^{20} +(0.738620 + 2.27324i) q^{21} +(1.93479 + 1.40571i) q^{22} +(-6.03452 - 4.38434i) q^{23} +(4.56171 - 3.31428i) q^{24} +8.67906 q^{25} -2.26766 q^{26} +(-2.22168 + 1.61414i) q^{27} +(-1.06622 + 3.28150i) q^{28} +(-0.805733 - 2.47979i) q^{29} +18.2568 q^{30} +(-5.56723 + 0.0773616i) q^{31} -6.11177 q^{32} +(0.709411 + 2.18334i) q^{33} +(-0.478770 + 1.47350i) q^{34} +(-3.28554 + 2.38708i) q^{35} +5.46270 q^{36} +1.72951 q^{37} +(-9.30471 + 6.76027i) q^{38} +(-1.76107 - 1.27949i) q^{39} +(7.75064 + 5.63117i) q^{40} +(-1.60556 - 4.94139i) q^{41} +(-4.38505 + 3.18593i) q^{42} +(2.41693 + 7.43854i) q^{43} +(-1.02406 + 3.15173i) q^{44} +(5.20173 + 3.77928i) q^{45} +(5.22692 - 16.0868i) q^{46} +(-0.0982375 + 0.302344i) q^{47} +(-0.723133 - 0.525387i) q^{48} +(-1.79054 + 5.51070i) q^{49} +(6.08181 + 18.7179i) q^{50} +(-1.20321 + 0.874185i) q^{51} +(-0.971019 - 2.98849i) q^{52} +(7.09673 + 5.15608i) q^{53} +(-5.03800 - 3.66032i) q^{54} +(-3.15561 + 2.29268i) q^{55} -2.84428 q^{56} -11.0404 q^{57} +(4.78349 - 3.47541i) q^{58} +(0.691656 - 2.12870i) q^{59} +(7.81761 + 24.0601i) q^{60} +9.70342 q^{61} +(-4.06805 - 11.9525i) q^{62} -1.90890 q^{63} +(-4.02902 - 12.4000i) q^{64} +(1.14291 - 3.51750i) q^{65} +(-4.21164 + 3.05994i) q^{66} +1.01091 q^{67} -2.14690 q^{68} +(13.1359 - 9.54382i) q^{69} +(-7.45049 - 5.41309i) q^{70} +(0.475616 + 0.345555i) q^{71} +(1.39154 + 4.28272i) q^{72} +(-13.5076 + 9.81386i) q^{73} +(1.21195 + 3.72999i) q^{74} +(-5.83812 + 17.9679i) q^{75} +(-12.8935 - 9.36766i) q^{76} +(0.357850 - 1.10135i) q^{77} +(1.52538 - 4.69464i) q^{78} +(2.50362 + 1.81899i) q^{79} +(0.469303 - 1.44436i) q^{80} +(-3.45887 - 10.6453i) q^{81} +(9.53189 - 6.92532i) q^{82} +(1.03392 + 3.18208i) q^{83} +(-6.07634 - 4.41472i) q^{84} +(-2.04434 - 1.48530i) q^{85} +(-14.3488 + 10.4250i) q^{86} +5.67580 q^{87} -2.73180 q^{88} +(-6.91905 + 5.02699i) q^{89} +(-4.50558 + 13.8667i) q^{90} +(0.339315 + 1.04430i) q^{91} +23.4385 q^{92} +(3.58473 - 11.5776i) q^{93} -0.720897 q^{94} +(-5.79666 - 17.8403i) q^{95} +(4.11119 - 12.6529i) q^{96} +(0.391352 - 0.284334i) q^{97} -13.1395 q^{98} -1.83341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.700746	+	2.15667i	0.495502	+	1.52500i	0.816173	+	0.577808i	$0.196092\pi$
$2$	0.700746	+	2.15667i	0.495502	+	1.52500i	−0.320671	+	0.947191i	$0.603908\pi$
$3$	−0.672668	+	2.07026i	−0.388365	+	1.19526i	0.545645	+	0.838016i	$0.316285\pi$
$3$	−0.672668	+	2.07026i	−0.388365	+	1.19526i	−0.934010	+	0.357247i	$0.883715\pi$
$4$	−2.54216	+	1.84699i	−1.27108	+	0.923494i
$5$	−3.69852			−1.65403			−0.827014	−	0.562181i	$-0.809963\pi$
$5$	−3.69852			−1.65403			−0.827014	+	0.562181i	$0.809963\pi$
$6$	−4.93624			−2.01521
$7$	0.888338	−	0.645416i	0.335760	−	0.243944i	−0.407111	−	0.913379i	$-0.633464\pi$
$7$	0.888338	−	0.645416i	0.335760	−	0.243944i	0.742871	+	0.669435i	$0.233464\pi$
$8$	−2.09561	−	1.52255i	−0.740908	−	0.538301i
$9$	−1.40643	−	1.02183i	−0.468812	−	0.340612i
$10$	−2.59172	−	7.97650i	−0.819575	−	2.52239i
$11$	0.853209	−	0.619892i	0.257252	−	0.186905i	−0.451683	−	0.892179i	$-0.649176\pi$
$11$	0.853209	−	0.619892i	0.257252	−	0.186905i	0.708935	+	0.705274i	$0.249176\pi$
$12$	−2.11371	−	6.50534i	−0.610176	−	1.87793i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	2.01445	+	1.46358i	0.538384	+	0.391159i
$15$	2.48787	−	7.65689i	0.642367	−	1.97700i
$16$	−0.126889	+	0.390525i	−0.0317223	+	0.0976313i
$17$	0.552744	+	0.401592i	0.134060	+	0.0974004i	0.652794	−	0.757535i	$-0.273597\pi$
$17$	0.552744	+	0.401592i	0.134060	+	0.0974004i	−0.518734	+	0.854936i	$0.673597\pi$
$18$	1.21821	−	3.74927i	0.287135	−	0.883711i
$19$	1.56729	+	4.82362i	0.359561	+	1.10662i	0.953317	+	0.301970i	$0.0976443\pi$
$19$	1.56729	+	4.82362i	0.359561	+	1.10662i	−0.593756	+	0.804645i	$0.702356\pi$
$20$	9.40223	−	6.83112i	2.10240	−	1.52749i
$21$	0.738620	+	2.27324i	0.161180	+	0.496062i
$22$	1.93479	+	1.40571i	0.412498	+	0.299697i
$23$	−6.03452	−	4.38434i	−1.25828	−	0.914198i	−0.259613	−	0.965713i	$-0.583595\pi$
$23$	−6.03452	−	4.38434i	−1.25828	−	0.914198i	−0.998672	+	0.0515153i	$0.983595\pi$
$24$	4.56171	−	3.31428i	0.931155	−	0.676524i
$25$	8.67906			1.73581
$26$	−2.26766			−0.444725
$27$	−2.22168	+	1.61414i	−0.427562	+	0.310642i
$28$	−1.06622	+	3.28150i	−0.201497	+	0.620145i
$29$	−0.805733	−	2.47979i	−0.149621	−	0.460486i	0.847955	−	0.530068i	$-0.177833\pi$
$29$	−0.805733	−	2.47979i	−0.149621	−	0.460486i	−0.997576	+	0.0695819i	$0.977833\pi$
$30$	18.2568			3.33322
$31$	−5.56723	+	0.0773616i	−0.999903	+	0.0138946i
$31$	−5.56723	+	0.0773616i	−0.999903	+	0.0138946i
$32$	−6.11177			−1.08042
$33$	0.709411	+	2.18334i	0.123493	+	0.380071i
$34$	−0.478770	+	1.47350i	−0.0821083	+	0.252704i
$35$	−3.28554	+	2.38708i	−0.555357	+	0.403491i
$36$	5.46270			0.910450
$37$	1.72951			0.284330			0.142165	−	0.989843i	$-0.454594\pi$
$37$	1.72951			0.284330			0.142165	+	0.989843i	$0.454594\pi$
$38$	−9.30471	+	6.76027i	−1.50942	+	1.09666i
$39$	−1.76107	−	1.27949i	−0.281996	−	0.204882i
$40$	7.75064	+	5.63117i	1.22548	+	0.890366i
$41$	−1.60556	−	4.94139i	−0.250746	−	0.771716i	−0.994638	−	0.103417i	$-0.967022\pi$
$41$	−1.60556	−	4.94139i	−0.250746	−	0.771716i	0.743892	−	0.668299i	$-0.232978\pi$
$42$	−4.38505	+	3.18593i	−0.676628	+	0.491599i
$43$	2.41693	+	7.43854i	0.368578	+	1.13437i	0.947710	+	0.319133i	$0.103392\pi$
$43$	2.41693	+	7.43854i	0.368578	+	1.13437i	−0.579132	+	0.815234i	$0.696608\pi$
$44$	−1.02406	+	3.15173i	−0.154383	+	0.475141i
$45$	5.20173	+	3.77928i	0.775428	+	0.563381i
$46$	5.22692	−	16.0868i	0.770667	−	2.37187i
$47$	−0.0982375	+	0.302344i	−0.0143294	+	0.0441014i	−0.957966	−	0.286883i	$-0.907381\pi$
$47$	−0.0982375	+	0.302344i	−0.0143294	+	0.0441014i	0.943636	+	0.330985i	$0.107381\pi$
$48$	−0.723133	−	0.525387i	−0.104375	−	0.0758331i
$49$	−1.79054	+	5.51070i	−0.255791	+	0.787243i
$50$	6.08181	+	18.7179i	0.860098	+	2.64711i
$51$	−1.20321	+	0.874185i	−0.168483	+	0.122410i
$52$	−0.971019	−	2.98849i	−0.134656	−	0.414429i
$53$	7.09673	+	5.15608i	0.974811	+	0.708242i	0.956543	−	0.291591i	$-0.0941847\pi$
$53$	7.09673	+	5.15608i	0.974811	+	0.708242i	0.0182682	+	0.999833i	$0.494185\pi$
$54$	−5.03800	−	3.66032i	−0.685586	−	0.498107i
$55$	−3.15561	+	2.29268i	−0.425502	+	0.309146i
$56$	−2.84428			−0.380083
$57$	−11.0404			−1.46234
$58$	4.78349	−	3.47541i	0.628103	−	0.456343i
$59$	0.691656	−	2.12870i	0.0900459	−	0.277133i	−0.895885	−	0.444286i	$-0.853457\pi$
$59$	0.691656	−	2.12870i	0.0900459	−	0.277133i	0.985931	+	0.167153i	$0.0534574\pi$
$60$	7.81761	+	24.0601i	1.00925	+	3.10615i
$61$	9.70342			1.24240			0.621198	−	0.783654i	$-0.286646\pi$
$61$	9.70342			1.24240			0.621198	+	0.783654i	$0.286646\pi$
$62$	−4.06805	−	11.9525i	−0.516643	−	1.51797i
$63$	−1.90890			−0.240499
$64$	−4.02902	−	12.4000i	−0.503627	−	1.55001i
$65$	1.14291	−	3.51750i	0.141760	−	0.436292i
$66$	−4.21164	+	3.05994i	−0.518417	+	0.376652i
$67$	1.01091			0.123502			0.0617510	−	0.998092i	$-0.480332\pi$
$67$	1.01091			0.123502			0.0617510	+	0.998092i	$0.480332\pi$
$68$	−2.14690			−0.260350
$69$	13.1359	−	9.54382i	1.58138	−	1.14894i
$70$	−7.45049	−	5.41309i	−0.890503	−	0.646989i
$71$	0.475616	+	0.345555i	0.0564453	+	0.0410099i	0.615650	−	0.788020i	$-0.288893\pi$
$71$	0.475616	+	0.345555i	0.0564453	+	0.0410099i	−0.559205	+	0.829030i	$0.688893\pi$
$72$	1.39154	+	4.28272i	0.163995	+	0.504724i
$73$	−13.5076	+	9.81386i	−1.58095	+	1.14863i	−0.665350	+	0.746532i	$0.731717\pi$
$73$	−13.5076	+	9.81386i	−1.58095	+	1.14863i	−0.915598	+	0.402094i	$0.868283\pi$
$74$	1.21195	+	3.72999i	0.140886	+	0.433602i
$75$	−5.83812	+	17.9679i	−0.674128	+	2.07475i
$76$	−12.8935	−	9.36766i	−1.47898	−	1.07454i
$77$	0.357850	−	1.10135i	0.0407808	−	0.125510i
$78$	1.52538	−	4.69464i	0.172715	−	0.531563i
$79$	2.50362	+	1.81899i	0.281679	+	0.204652i	0.719650	−	0.694337i	$-0.244302\pi$
$79$	2.50362	+	1.81899i	0.281679	+	0.204652i	−0.437970	+	0.898989i	$0.644302\pi$
$80$	0.469303	−	1.44436i	0.0524696	−	0.161485i
$81$	−3.45887	−	10.6453i	−0.384319	−	1.18281i
$82$	9.53189	−	6.92532i	1.05262	−	0.764774i
$83$	1.03392	+	3.18208i	0.113488	+	0.349279i	0.991629	−	0.129123i	$-0.0412162\pi$
$83$	1.03392	+	3.18208i	0.113488	+	0.349279i	−0.878141	+	0.478402i	$0.841216\pi$
$84$	−6.07634	−	4.41472i	−0.662983	−	0.481685i
$85$	−2.04434	−	1.48530i	−0.221739	−	0.161103i
$86$	−14.3488	+	10.4250i	−1.54728	+	1.12416i
$87$	5.67580			0.608510
$88$	−2.73180			−0.291211
$89$	−6.91905	+	5.02699i	−0.733418	+	0.532860i	−0.890643	−	0.454703i	$-0.849745\pi$
$89$	−6.91905	+	5.02699i	−0.733418	+	0.532860i	0.157225	+	0.987563i	$0.449745\pi$
$90$	−4.50558	+	13.8667i	−0.474929	+	1.46168i
$91$	0.339315	+	1.04430i	0.0355699	+	0.109473i
$92$	23.4385			2.44364
$93$	3.58473	−	11.5776i	0.371720	−	1.20054i
$94$	−0.720897			−0.0743548
$95$	−5.79666	−	17.8403i	−0.594724	−	1.83037i
$96$	4.11119	−	12.6529i	0.419597	−	1.29139i
$97$	0.391352	−	0.284334i	0.0397358	−	0.0288697i	−0.567740	−	0.823208i	$-0.692182\pi$
$97$	0.391352	−	0.284334i	0.0397358	−	0.0288697i	0.607476	+	0.794338i	$0.292182\pi$
$98$	−13.1395			−1.32729
$99$	−1.83341			−0.184265
$100$	−22.0636	+	16.0301i	−2.20636	+	1.60301i
$101$	8.78862	+	6.38531i	0.874500	+	0.635362i	0.931791	−	0.362996i	$-0.118246\pi$
$101$	8.78862	+	6.38531i	0.874500	+	0.635362i	−0.0572904	+	0.998358i	$0.518246\pi$
$102$	−2.72848	−	1.98235i	−0.270159	−	0.196282i
$103$	6.16150	+	18.9631i	0.607110	+	1.86849i	0.481575	+	0.876405i	$0.340065\pi$
$103$	6.16150	+	18.9631i	0.607110	+	1.86849i	0.125535	+	0.992089i	$0.459935\pi$
$104$	2.09561	−	1.52255i	0.205491	−	0.149298i
$105$	−2.73180	−	8.40763i	−0.266597	−	0.820500i
$106$	−6.14697	+	18.9184i	−0.597047	+	1.83752i
$107$	12.3540	+	8.97574i	1.19431	+	0.867717i	0.993713	−	0.111957i	$-0.0357118\pi$
$107$	12.3540	+	8.97574i	1.19431	+	0.867717i	0.200597	+	0.979674i	$0.435712\pi$
$108$	2.66656	−	8.20681i	0.256589	−	0.789701i
$109$	3.12623	−	9.62154i	0.299438	−	0.921577i	−0.682256	−	0.731113i	$-0.739001\pi$
$109$	3.12623	−	9.62154i	0.299438	−	0.921577i	0.981694	−	0.190463i	$-0.0609990\pi$
$110$	−7.15585	−	5.19903i	−0.682284	−	0.495708i
$111$	−1.16338	+	3.58053i	−0.110424	+	0.339849i
$112$	0.139330	+	0.428815i	0.0131655	+	0.0405192i
$113$	−1.98583	+	1.44279i	−0.186811	+	0.135726i	−0.677260	−	0.735744i	$-0.736833\pi$
$113$	−1.98583	+	1.44279i	−0.186811	+	0.135726i	0.490449	+	0.871470i	$0.336833\pi$
$114$	−7.73652	−	23.8106i	−0.724591	−	2.23006i
$115$	22.3188	+	16.2156i	2.08124	+	1.51211i
$116$	6.62845	+	4.81585i	0.615436	+	0.447140i
$117$	1.40643	−	1.02183i	0.130025	−	0.0944686i
$118$	5.07558			0.467245
$119$	0.750218			0.0687723
$120$	−16.8716	+	12.2579i	−1.54016	+	1.11899i
$121$	−3.05549	+	9.40383i	−0.277772	+	0.854893i
$122$	6.79963	+	20.9271i	0.615610	+	1.89465i
$123$	11.3100			1.01979
$124$	14.0099	−	10.4793i	1.25813	−	0.941066i
$125$	−13.6071			−1.21705
$126$	−1.33765	−	4.11687i	−0.119168	−	0.366760i
$127$	−2.23163	+	6.86826i	−0.198025	+	0.609460i	0.801903	+	0.597455i	$0.203821\pi$
$127$	−2.23163	+	6.86826i	−0.198025	+	0.609460i	−0.999928	+	0.0120047i	$0.996179\pi$
$128$	14.0305	−	10.1937i	1.24013	−	0.901007i
$129$	−17.0255			−1.49901
$130$	8.38699			0.735588
$131$	−16.4721	+	11.9677i	−1.43918	+	1.04562i	−0.450963	+	0.892543i	$0.648919\pi$
$131$	−16.4721	+	11.9677i	−1.43918	+	1.04562i	−0.988214	+	0.153080i	$0.951081\pi$
$132$	−5.83605	−	4.24013i	−0.507963	−	0.369056i
$133$	4.50553	+	3.27346i	0.390679	+	0.283845i
$134$	0.708389	+	2.18020i	0.0611955	+	0.188340i
$135$	8.21691	−	5.96994i	0.707199	−	0.513810i
$136$	−0.546891	−	1.68316i	−0.0468955	−	0.144329i
$137$	4.87120	−	14.9920i	0.416175	−	1.28085i	−0.495021	−	0.868881i	$-0.664840\pi$
$137$	4.87120	−	14.9920i	0.416175	−	1.28085i	0.911196	−	0.411973i	$-0.135160\pi$
$138$	29.7878	+	21.6421i	2.53571	+	1.84230i
$139$	1.88222	−	5.79289i	0.159648	−	0.491347i	−0.838954	−	0.544202i	$-0.816832\pi$
$139$	1.88222	−	5.79289i	0.159648	−	0.491347i	0.998602	+	0.0528558i	$0.0168324\pi$
$140$	3.94345	−	12.1367i	0.333283	−	1.02574i
$141$	−0.559849	−	0.406754i	−0.0471478	−	0.0342549i
$142$	−0.411964	+	1.26790i	−0.0345713	+	0.106399i
$143$	0.325897	+	1.00301i	0.0272528	+	0.0838756i
$144$	0.577513	−	0.419588i	0.0481261	−	0.0349657i
$145$	2.98002	+	9.17156i	0.247477	+	0.761657i
$146$	−30.6307	−	22.2545i	−2.53502	−	1.84180i
$147$	−10.2041	−	7.41374i	−0.841623	−	0.611475i
$148$	−4.39669	+	3.19438i	−0.361406	+	0.262577i
$149$	−18.1339			−1.48559			−0.742793	−	0.669521i	$-0.766500\pi$
$149$	−18.1339			−1.48559			−0.742793	+	0.669521i	$0.766500\pi$
$150$	−42.8419			−3.49803
$151$	6.66243	−	4.84054i	0.542180	−	0.393917i	−0.282714	−	0.959204i	$-0.591235\pi$
$151$	6.66243	−	4.84054i	0.542180	−	0.393917i	0.824894	+	0.565287i	$0.191235\pi$
$152$	4.05977	−	12.4947i	0.329291	−	1.01345i
$153$	−0.367038	−	1.12963i	−0.0296732	−	0.0913249i
$154$	2.62601			0.211610
$155$	20.5905	−	0.286124i	1.65387	−	0.0229820i
$156$	6.84012			0.547648
$157$	−3.10011	−	9.54115i	−0.247416	−	0.761467i	−0.995230	−	0.0975588i	$-0.968897\pi$
$157$	−3.10011	−	9.54115i	−0.247416	−	0.761467i	0.747814	−	0.663908i	$-0.231103\pi$
$158$	−2.16856	+	6.67414i	−0.172521	+	0.530966i
$159$	−15.4482	+	11.2237i	−1.22512	+	0.890100i
$160$	22.6045			1.78704
$161$	−8.19042			−0.645495
$162$	20.5347	−	14.9193i	1.61336	−	1.17217i
$163$	17.9589	+	13.0479i	1.40665	+	1.02199i	0.993798	+	0.111196i	$0.0354681\pi$
$163$	17.9589	+	13.0479i	1.40665	+	1.02199i	0.412854	+	0.910797i	$0.364532\pi$
$164$	13.2083	+	9.59637i	1.03139	+	0.749351i
$165$	−2.62377	−	8.07514i	−0.204260	−	0.628649i
$166$	−6.13820	+	4.45966i	−0.476416	+	0.346137i
$167$	−2.39248	−	7.36328i	−0.185135	−	0.569788i	0.814815	−	0.579721i	$-0.196838\pi$
$167$	−2.39248	−	7.36328i	−0.185135	−	0.569788i	−0.999951	+	0.00993270i	$0.996838\pi$
$168$	1.91326	−	5.88840i	0.147611	−	0.454300i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	1.77074	−	5.44978i	0.135810	−	0.417979i
$171$	2.72465	−	8.38562i	0.208360	−	0.641265i
$172$	−19.8831	−	14.4459i	−1.51607	−	1.10149i
$173$	−5.55863	+	17.1077i	−0.422615	+	1.30067i	0.482646	+	0.875816i	$0.339676\pi$
$173$	−5.55863	+	17.1077i	−0.422615	+	1.30067i	−0.905260	+	0.424858i	$0.860324\pi$
$174$	3.97729	+	12.2408i	0.301518	+	0.927976i
$175$	7.70994	−	5.60160i	0.582817	−	0.423441i
$176$	0.133820	+	0.411857i	0.0100871	+	0.0310449i
$177$	3.94170	+	2.86381i	0.296276	+	0.215257i
$178$	−15.6901	−	11.3995i	−1.17602	−	0.854429i
$179$	13.6655	−	9.92858i	1.02141	−	0.742097i	0.0548374	−	0.998495i	$-0.482536\pi$
$179$	13.6655	−	9.92858i	1.02141	−	0.742097i	0.966571	+	0.256399i	$0.0825360\pi$
$180$	−20.2039			−1.50591
$181$	−6.69513			−0.497645			−0.248822	−	0.968549i	$-0.580044\pi$
$181$	−6.69513			−0.497645			−0.248822	+	0.968549i	$0.580044\pi$
$182$	−2.01445	+	1.46358i	−0.149321	+	0.108488i
$183$	−6.52718	+	20.0886i	−0.482503	+	1.48499i
$184$	5.97062	+	18.3757i	0.440160	+	1.35467i
$185$	−6.39663			−0.470289
$186$	27.4812	−	0.381875i	2.01502	−	0.0280005i
$187$	0.720550			0.0526918
$188$	−0.308690	−	0.950050i	−0.0225135	−	0.0692895i
$189$	−0.931807	+	2.86781i	−0.0677790	+	0.208602i
$190$	34.4137	−	25.0030i	2.49663	−	1.81391i
$191$	−4.00168			−0.289552			−0.144776	−	0.989464i	$-0.546246\pi$
$191$	−4.00168			−0.289552			−0.144776	+	0.989464i	$0.546246\pi$
$192$	28.3815			2.04826
$193$	12.8062	−	9.30426i	0.921812	−	0.669735i	−0.0221627	−	0.999754i	$-0.507055\pi$
$193$	12.8062	−	9.30426i	0.921812	−	0.669735i	0.943974	+	0.330019i	$0.107055\pi$
$194$	0.887454	+	0.644773i	0.0637155	+	0.0462920i
$195$	6.51334	+	4.73222i	0.466430	+	0.338881i
$196$	−5.62637	−	17.3162i	−0.401883	−	1.23687i
$197$	16.8186	−	12.2194i	1.19827	−	0.870596i	0.204159	−	0.978938i	$-0.434554\pi$
$197$	16.8186	−	12.2194i	1.19827	−	0.870596i	0.994114	+	0.108341i	$0.0345539\pi$
$198$	−1.28475	−	3.95407i	−0.0913035	−	0.281003i
$199$	5.29016	−	16.2814i	0.375010	−	1.15416i	−0.568462	−	0.822709i	$-0.692462\pi$
$199$	5.29016	−	16.2814i	0.375010	−	1.15416i	0.943472	−	0.331452i	$-0.107538\pi$
$200$	−18.1879	−	13.2143i	−1.28608	−	0.934390i
$201$	−0.680005	+	2.09284i	−0.0479638	+	0.147618i
$202$	−7.61243	+	23.4287i	−0.535609	+	1.64843i
$203$	−2.31626	−	1.68286i	−0.162570	−	0.118114i
$204$	1.44415	−	4.44464i	0.101111	−	0.311187i
$205$	5.93818	+	18.2758i	0.414741	+	1.27644i
$206$	−36.5797	+	26.5767i	−2.54863	+	1.85168i
$207$	4.00709	+	12.3326i	0.278512	+	0.857173i
$208$	−0.332200	−	0.241358i	−0.0230340	−	0.0167351i
$209$	4.32735	+	3.14401i	0.299329	+	0.217475i
$210$	16.2182	−	11.7832i	1.11916	−	0.813119i
$211$	9.58318			0.659733			0.329867	−	0.944028i	$-0.392996\pi$
$211$	9.58318			0.659733			0.329867	+	0.944028i	$0.392996\pi$
$212$	−27.5642			−1.89312
$213$	−1.03532	+	0.752204i	−0.0709390	+	0.0515402i
$214$	−10.7007	+	32.9333i	−0.731484	+	2.25128i
$215$	−8.93906	−	27.5116i	−0.609639	−	1.87628i
$216$	7.11336			0.484003
$217$	−4.89565	+	3.66190i	−0.332338	+	0.248586i
$218$	22.9412			1.55378
$219$	−11.2311	−	34.5657i	−0.758927	−	2.33574i
$220$	3.78751	−	11.6567i	0.255354	−	0.785898i
$221$	−0.552744	+	0.401592i	−0.0371816	+	0.0270140i
$222$	−8.53727			−0.572984
$223$	25.2488			1.69078			0.845392	−	0.534147i	$-0.179367\pi$
$223$	25.2488			1.69078			0.845392	+	0.534147i	$0.179367\pi$
$224$	−5.42932	+	3.94463i	−0.362762	+	0.263562i
$225$	−12.2065	−	8.86856i	−0.813769	−	0.591237i
$226$	−4.50319	−	3.27176i	−0.299548	−	0.217634i
$227$	−2.01928	−	6.21471i	−0.134024	−	0.412484i	0.861413	−	0.507906i	$-0.169580\pi$
$227$	−2.01928	−	6.21471i	−0.134024	−	0.412484i	−0.995437	+	0.0954213i	$0.969580\pi$
$228$	28.0665	−	20.3915i	1.85875	−	1.35046i
$229$	−7.18819	−	22.1230i	−0.475009	−	1.46193i	−0.845945	−	0.533269i	$-0.820963\pi$
$229$	−7.18819	−	22.1230i	−0.475009	−	1.46193i	0.370936	−	0.928658i	$-0.379037\pi$
$230$	−19.3319	+	59.4974i	−1.27471	+	3.92314i
$231$	2.03936	+	1.48168i	0.134180	+	0.0974876i
$232$	−2.08710	+	6.42343i	−0.137025	+	0.421719i
$233$	1.05681	−	3.25251i	0.0692336	−	0.213079i	−0.910453	−	0.413612i	$-0.864267\pi$
$233$	1.05681	−	3.25251i	0.0692336	−	0.213079i	0.979687	+	0.200532i	$0.0642672\pi$
$234$	3.18932	+	2.31717i	0.208492	+	0.151478i
$235$	0.363333	−	1.11823i	0.0237013	−	0.0729450i
$236$	2.17338	+	6.68897i	0.141475	+	0.435415i
$237$	−5.44988	+	3.95957i	−0.354008	+	0.257202i
$238$	0.525712	+	1.61797i	0.0340768	+	0.104878i
$239$	12.9978	+	9.44349i	0.840761	+	0.610849i	0.922583	−	0.385798i	$-0.126074\pi$
$239$	12.9978	+	9.44349i	0.840761	+	0.610849i	−0.0818222	+	0.996647i	$0.526074\pi$
$240$	2.67452	+	1.94315i	0.172640	+	0.125430i
$241$	21.3324	−	15.4989i	1.37414	−	0.998373i	0.376741	−	0.926318i	$-0.377045\pi$
$241$	21.3324	−	15.4989i	1.37414	−	0.998373i	0.997401	−	0.0720541i	$-0.0229554\pi$
$242$	−22.4221			−1.44135
$243$	16.1268			1.03453
$244$	−24.6677	+	17.9221i	−1.57919	+	1.14735i
$245$	6.62233	−	20.3814i	0.423085	−	1.30212i
$246$	7.92541	+	24.3919i	0.505306	+	1.55517i
$247$	−5.07186			−0.322715
$248$	11.7845	+	8.31424i	0.748316	+	0.527955i
$249$	−7.28322			−0.461555
$250$	−9.53509	−	29.3460i	−0.603052	−	1.85600i
$251$	−1.55486	+	4.78537i	−0.0981420	+	0.302050i	−0.988060	−	0.154071i	$-0.950762\pi$
$251$	−1.55486	+	4.78537i	−0.0981420	+	0.302050i	0.889918	+	0.456121i	$0.150762\pi$
$252$	4.85273	−	3.52571i	0.305693	−	0.222099i
$253$	−7.86652			−0.494564
$254$	−16.3764			−1.02755
$255$	4.45010	−	3.23319i	0.278676	−	0.202470i
$256$	10.7201	+	7.78863i	0.670008	+	0.486789i
$257$	21.3494	+	15.5113i	1.33174	+	0.967567i	0.999705	+	0.0242999i	$0.00773566\pi$
$257$	21.3494	+	15.5113i	1.33174	+	0.967567i	0.332036	+	0.943267i	$0.392264\pi$
$258$	−11.9305	−	36.7184i	−0.742762	−	2.28599i
$259$	1.53639	−	1.11625i	0.0954666	−	0.0693606i
$260$	3.59133	+	11.0530i	0.222725	+	0.685477i
$261$	−1.40073	+	4.31099i	−0.0867028	+	0.266844i
$262$	−37.3532	−	27.1387i	−2.30769	−	1.67663i
$263$	−0.740550	+	2.27918i	−0.0456643	+	0.140540i	−0.971289	−	0.237902i	$-0.923540\pi$
$263$	−0.740550	+	2.27918i	−0.0456643	+	0.140540i	0.925625	+	0.378442i	$0.123540\pi$
$264$	1.83760	−	5.65554i	0.113096	−	0.348074i
$265$	−26.2474	−	19.0699i	−1.61237	−	1.17145i
$266$	−3.90255	+	12.0108i	−0.239281	+	0.736430i
$267$	−5.75294	−	17.7057i	−0.352074	−	1.08357i
$268$	−2.56989	+	1.86713i	−0.156981	+	0.114053i
$269$	1.99372	+	6.13605i	0.121559	+	0.374121i	0.993259	−	0.115920i	$-0.0369817\pi$
$269$	1.99372	+	6.13605i	0.121559	+	0.374121i	−0.871699	+	0.490041i	$0.836982\pi$
$270$	18.6332	+	13.5378i	1.13398	+	0.823884i
$271$	−21.4135	−	15.5578i	−1.30078	−	0.945071i	−0.300816	−	0.953682i	$-0.597259\pi$
$271$	−21.4135	−	15.5578i	−1.30078	−	0.945071i	−0.999963	+	0.00861077i	$0.997259\pi$
$272$	−0.226969	+	0.164903i	−0.0137620	+	0.00999869i
$273$	−2.39023			−0.144663
$274$	35.7464			2.15952
$275$	7.40505	−	5.38008i	0.446541	−	0.324431i
$276$	−15.7663	+	48.5238i	−0.949023	+	2.92079i
$277$	−6.80522	−	20.9443i	−0.408886	−	1.25842i	−0.917607	−	0.397490i	$-0.869881\pi$
$277$	−6.80522	−	20.9443i	−0.408886	−	1.25842i	0.508721	−	0.860932i	$-0.330119\pi$
$278$	13.8123			0.828409
$279$	7.90899	+	5.57998i	0.473499	+	0.334065i
$280$	10.5196			0.628669
$281$	−4.82137	−	14.8386i	−0.287619	−	0.885199i	−0.985602	−	0.169085i	$-0.945919\pi$
$281$	−4.82137	−	14.8386i	−0.287619	−	0.885199i	0.697983	−	0.716114i	$-0.254081\pi$
$282$	0.484924	−	1.49244i	0.0288768	−	0.0888736i
$283$	−12.6550	+	9.19441i	−0.752262	+	0.546551i	−0.896527	−	0.442988i	$-0.853918\pi$
$283$	−12.6550	+	9.19441i	−0.752262	+	0.546551i	0.144265	+	0.989539i	$0.453918\pi$
$284$	−1.84733			−0.109619
$285$	40.8332			2.41875
$286$	−1.93479	+	1.40571i	−0.114406	+	0.0831211i
$287$	−4.61553	−	3.35338i	−0.272446	−	0.197944i
$288$	8.59581	+	6.24522i	0.506513	+	0.368003i
$289$	−5.10904	−	15.7240i	−0.300532	−	0.924942i
$290$	−17.6918	+	12.8539i	−1.03890	+	0.754805i
$291$	0.325395	+	1.00146i	0.0190750	+	0.0587067i
$292$	16.2125	−	49.8968i	0.948763	−	2.91999i
$293$	8.75368	+	6.35992i	0.511396	+	0.371551i	0.813353	−	0.581771i	$-0.197640\pi$
$293$	8.75368	+	6.35992i	0.511396	+	0.371551i	−0.301957	+	0.953321i	$0.597640\pi$
$294$	8.83851	−	27.2021i	0.515472	−	1.58646i
$295$	−2.55810	+	7.87303i	−0.148939	+	0.458386i
$296$	−3.62437	−	2.63326i	−0.210662	−	0.153055i
$297$	−0.894958	+	2.75440i	−0.0519308	+	0.159826i
$298$	−12.7073	−	39.1089i	−0.736111	−	2.26552i
$299$	6.03452	−	4.38434i	0.348985	−	0.253553i
$300$	−18.3450	−	56.4602i	−1.05915	−	3.25973i
$301$	6.94800	+	5.04802i	0.400476	+	0.290963i
$302$	15.1081	+	10.9767i	0.869374	+	0.631638i
$303$	−19.1310	+	13.8995i	−1.09905	+	0.798507i
$304$	−2.08262			−0.119446
$305$	−35.8883			−2.05496
$306$	2.17903	−	1.58316i	0.124567	−	0.0905033i
$307$	−3.30461	+	10.1706i	−0.188604	+	0.580464i	−0.999992	−	0.00404430i	$-0.998713\pi$
$307$	−3.30461	+	10.1706i	−0.188604	+	0.580464i	0.811388	+	0.584509i	$0.198713\pi$
$308$	1.12447	+	3.46075i	0.0640724	+	0.197194i
$309$	−43.4032			−2.46912
$310$	15.0458	+	44.2065i	0.854543	+	2.51076i
$311$	19.5226			1.10702			0.553511	−	0.832842i	$-0.313288\pi$
$311$	19.5226			1.10702			0.553511	+	0.832842i	$0.313288\pi$
$312$	1.74242	+	5.36261i	0.0986450	+	0.303598i
$313$	−8.95356	+	27.5562i	−0.506085	+	1.55757i	0.292854	+	0.956157i	$0.405395\pi$
$313$	−8.95356	+	27.5562i	−0.506085	+	1.55757i	−0.798939	+	0.601412i	$0.794605\pi$
$314$	18.4048	−	13.3718i	1.03864	−	0.754617i
$315$	7.06010			0.397792
$316$	−9.72425			−0.547032
$317$	−28.4092	+	20.6405i	−1.59562	+	1.15928i	−0.700307	+	0.713842i	$0.746954\pi$
$317$	−28.4092	+	20.6405i	−1.59562	+	1.15928i	−0.895311	+	0.445442i	$0.853046\pi$
$318$	−35.0312	−	25.4516i	−1.96445	−	1.42726i
$319$	−2.22466	−	1.61631i	−0.124557	−	0.0904961i
$320$	14.9014	+	45.8618i	0.833014	+	2.56375i
$321$	−26.8922	+	19.5384i	−1.50098	+	1.09053i
$322$	−5.73940	−	17.6641i	−0.319844	−	0.984379i
$323$	−1.07082	+	3.29564i	−0.0595819	+	0.183374i
$324$	28.4548	+	20.6736i	1.58082	+	1.14853i
$325$	−2.68198	+	8.25427i	−0.148769	+	0.457865i
$326$	−15.5555	+	47.8748i	−0.861538	+	2.65154i
$327$	17.8162	+	12.9442i	0.985236	+	0.715816i
$328$	−4.15889	+	12.7997i	−0.229636	+	0.706748i
$329$	0.107869	+	0.331988i	0.00594703	+	0.0183031i
$330$	15.5768	−	11.3172i	0.857477	−	0.622993i
$331$	5.46652	+	16.8242i	0.300467	+	0.924742i	0.981330	+	0.192331i	$0.0616049\pi$
$331$	5.46652	+	16.8242i	0.300467	+	0.924742i	−0.680863	+	0.732411i	$0.738395\pi$
$332$	−8.50566	−	6.17972i	−0.466809	−	0.339156i
$333$	−2.43244	−	1.76727i	−0.133297	−	0.0968460i
$334$	14.2037	−	10.3196i	0.777191	−	0.564662i
$335$	−3.73886			−0.204276
$336$	−0.981480			−0.0535441
$337$	12.3850	−	8.99820i	0.674652	−	0.490163i	−0.196927	−	0.980418i	$-0.563096\pi$
$337$	12.3850	−	8.99820i	0.674652	−	0.490163i	0.871579	+	0.490255i	$0.163096\pi$
$338$	0.700746	−	2.15667i	0.0381155	−	0.117308i
$339$	−1.65115	−	5.08170i	−0.0896779	−	0.276000i
$340$	7.94035			0.430626
$341$	−4.70205	+	3.51709i	−0.254630	+	0.190461i
$342$	19.9943			1.08117
$343$	4.34130	+	13.3611i	0.234408	+	0.721434i
$344$	6.26059	−	19.2681i	0.337549	−	1.03887i
$345$	−48.5835	+	35.2980i	−2.61565	+	1.90038i
$346$	−40.7909			−2.19293
$347$	15.3508			0.824075			0.412037	−	0.911167i	$-0.364817\pi$
$347$	15.3508			0.824075			0.412037	+	0.911167i	$0.364817\pi$
$348$	−14.4288	+	10.4831i	−0.773464	+	0.561955i
$349$	−3.03058	−	2.20184i	−0.162223	−	0.117862i	0.503712	−	0.863872i	$-0.331967\pi$
$349$	−3.03058	−	2.20184i	−0.162223	−	0.117862i	−0.665935	+	0.746010i	$0.731967\pi$
$350$	17.4835	+	12.7025i	0.934534	+	0.678979i
$351$	−0.848604	−	2.61174i	−0.0452952	−	0.139404i
$352$	−5.21462	+	3.78864i	−0.277940	+	0.201935i
$353$	0.143211	+	0.440760i	0.00762238	+	0.0234593i	0.954795	−	0.297264i	$-0.0960741\pi$
$353$	0.143211	+	0.440760i	0.00762238	+	0.0234593i	−0.947173	+	0.320723i	$0.896074\pi$
$354$	−3.41418	+	10.5078i	−0.181461	+	0.558481i
$355$	−1.75908	−	1.27804i	−0.0933621	−	0.0678315i
$356$	8.30456	−	25.5588i	0.440141	−	1.35461i
$357$	−0.504647	+	1.55314i	−0.0267088	+	0.0822011i
$358$	30.9887	+	22.5146i	1.63781	+	1.18994i
$359$	4.93101	−	15.1761i	0.260249	−	0.800963i	−0.732501	−	0.680766i	$-0.761647\pi$
$359$	4.93101	−	15.1761i	0.260249	−	0.800963i	0.992750	−	0.120197i	$-0.0383528\pi$
$360$	−5.14665	−	15.8397i	−0.271252	−	0.834828i
$361$	−5.43962	+	3.95211i	−0.286296	+	0.208006i
$362$	−4.69158	−	14.4392i	−0.246584	−	0.758907i
$363$	−17.4130	−	12.6513i	−0.913946	−	0.664021i
$364$	−2.79141	−	2.02808i	−0.146310	−	0.106300i
$365$	49.9582	−	36.2968i	2.61493	−	1.89986i
$366$	−47.8984			−2.50369
$367$	0.0769864			0.00401866			0.00200933	−	0.999998i	$-0.499360\pi$
$367$	0.0769864			0.00401866			0.00200933	+	0.999998i	$0.499360\pi$
$368$	2.47791	−	1.80031i	0.129170	−	0.0938475i
$369$	−2.79118	+	8.59036i	−0.145303	+	0.447196i
$370$	−4.48241	−	13.7954i	−0.233029	−	0.717190i
$371$	9.63211			0.500074
$372$	12.2708	+	36.0532i	0.636210	+	1.86927i
$373$	8.86553			0.459040			0.229520	−	0.973304i	$-0.426284\pi$
$373$	8.86553			0.459040			0.229520	+	0.973304i	$0.426284\pi$
$374$	0.504922	+	1.55399i	0.0261089	+	0.0803549i
$375$	9.15303	−	28.1701i	0.472661	−	1.45470i
$376$	0.666200	−	0.484022i	0.0343566	−	0.0249616i
$377$	2.60741			0.134288
$378$	−6.83788			−0.351703
$379$	−5.70274	+	4.14329i	−0.292930	+	0.212826i	−0.724538	−	0.689235i	$-0.757947\pi$
$379$	−5.70274	+	4.14329i	−0.292930	+	0.212826i	0.431607	+	0.902062i	$0.357947\pi$
$380$	47.6868	+	34.6465i	2.44628	+	1.77733i
$381$	−12.7179	−	9.24011i	−0.651559	−	0.473385i
$382$	−2.80416	−	8.63032i	−0.143473	−	0.441566i
$383$	−11.8892	+	8.63803i	−0.607511	+	0.441383i	−0.848537	−	0.529136i	$-0.822516\pi$
$383$	−11.8892	+	8.63803i	−0.607511	+	0.441383i	0.241026	+	0.970519i	$0.422516\pi$
$384$	11.6658	+	35.9037i	0.595319	+	1.83220i
$385$	−1.32351	+	4.07336i	−0.0674526	+	0.207598i
$386$	29.0401	+	21.0989i	1.47810	+	1.07391i
$387$	4.20171	−	12.9315i	0.213585	−	0.657346i
$388$	−0.469719	+	1.44564i	−0.0238463	+	0.0733915i
$389$	−20.3887	−	14.8132i	−1.03375	−	0.751061i	−0.0646915	−	0.997905i	$-0.520606\pi$
$389$	−20.3887	−	14.8132i	−1.03375	−	0.751061i	−0.969055	+	0.246844i	$0.920606\pi$
$390$	−5.64166	+	17.3632i	−0.285676	+	0.879221i
$391$	−1.57483	−	4.84683i	−0.0796426	−	0.245115i
$392$	12.1426	−	8.82208i	0.613291	−	0.445582i
$393$	−13.6960	−	42.1518i	−0.690870	−	2.12628i
$394$	38.1388	+	27.7095i	1.92140	+	1.39598i
$395$	−9.25969	−	6.72756i	−0.465906	−	0.338500i
$396$	4.66082	−	3.38629i	0.234215	−	0.170167i
$397$	12.5962			0.632183			0.316091	−	0.948729i	$-0.397629\pi$
$397$	12.5962			0.632183			0.316091	+	0.948729i	$0.397629\pi$
$398$	38.8208			1.94591
$399$	−9.80762	+	7.12565i	−0.490995	+	0.356729i
$400$	−1.10128	+	3.38939i	−0.0550640	+	0.169469i
$401$	3.33231	+	10.2558i	0.166408	+	0.512150i	0.999137	−	0.0415300i	$-0.0132232\pi$
$401$	3.33231	+	10.2558i	0.166408	+	0.512150i	−0.832730	+	0.553680i	$0.813223\pi$
$402$	−4.99008			−0.248883
$403$	1.64679	−	5.31865i	0.0820326	−	0.264941i
$404$	−34.1357			−1.69831
$405$	12.7927	+	39.3719i	0.635675	+	1.95641i
$406$	2.00627	−	6.17467i	0.0995697	−	0.306444i
$407$	1.47563	−	1.07211i	0.0731444	−	0.0531425i
$408$	3.85244			0.190724
$409$	−13.7378			−0.679292			−0.339646	−	0.940553i	$-0.610307\pi$
$409$	−13.7378			−0.679292			−0.339646	+	0.940553i	$0.610307\pi$
$410$	−35.2539	+	25.6134i	−1.74106	+	1.26496i
$411$	27.7606	+	20.1693i	1.36933	+	0.994878i
$412$	−50.6882	−	36.8271i	−2.49723	−	1.81434i
$413$	−0.759470	−	2.33741i	−0.0373711	−	0.115016i
$414$	−23.7894	+	17.2840i	−1.16918	+	0.849462i
$415$	−3.82398	−	11.7690i	−0.187712	−	0.577717i
$416$	1.88864	−	5.81264i	0.0925983	−	0.284988i
$417$	10.7267	+	7.79338i	0.525287	+	0.381643i
$418$	−3.74822	+	11.5358i	−0.183331	+	0.564236i
$419$	−9.78776	+	30.1236i	−0.478163	+	1.47164i	0.363480	+	0.931602i	$0.381588\pi$
$419$	−9.78776	+	30.1236i	−0.478163	+	1.47164i	−0.841644	+	0.540033i	$0.818412\pi$
$420$	22.4735	+	16.3279i	1.09659	+	0.796721i
$421$	−1.41328	+	4.34963i	−0.0688791	+	0.211988i	−0.979571	−	0.201098i	$-0.935549\pi$
$421$	−1.41328	+	4.34963i	−0.0688791	+	0.211988i	0.910692	+	0.413086i	$0.135549\pi$
$422$	6.71537	+	20.6678i	0.326899	+	1.00609i
$423$	0.447110	−	0.324845i	0.0217392	−	0.0157945i
$424$	−7.02158	−	21.6102i	−0.340998	−	1.04948i
$425$	4.79730	+	3.48544i	0.232703	+	0.169069i
$426$	−2.34776	−	1.70574i	−0.113749	−	0.0826436i
$427$	8.61993	−	6.26274i	0.417147	−	0.303075i
$428$	−47.9840			−2.31940
$429$	−2.29570			−0.110838
$430$	53.0695	−	38.5573i	2.55924	−	1.85940i
$431$	−10.8902	+	33.5166i	−0.524563	+	1.61444i	0.240617	+	0.970620i	$0.422650\pi$
$431$	−10.8902	+	33.5166i	−0.524563	+	1.61444i	−0.765179	+	0.643817i	$0.777350\pi$
$432$	−0.348456	−	1.07244i	−0.0167651	−	0.0515976i
$433$	1.51320			0.0727196			0.0363598	−	0.999339i	$-0.488424\pi$
$433$	1.51320			0.0727196			0.0363598	+	0.999339i	$0.488424\pi$
$434$	−11.3281	−	7.99226i	−0.543767	−	0.383641i
$435$	−20.9921			−1.00649
$436$	9.82350	+	30.2336i	0.470460	+	1.44793i
$437$	11.6905	−	35.9798i	0.559235	−	1.72115i
$438$	66.6769	−	48.4436i	3.18594	−	2.31472i
$439$	23.2386			1.10912			0.554559	−	0.832144i	$-0.312887\pi$
$439$	23.2386			1.10912			0.554559	+	0.832144i	$0.312887\pi$
$440$	10.1036			0.481672
$441$	8.14930	−	5.92081i	0.388062	−	0.281943i
$442$	−1.25344	−	0.910674i	−0.0596199	−	0.0433164i
$443$	−3.57554	−	2.59778i	−0.169879	−	0.123424i	0.499597	−	0.866258i	$-0.333481\pi$
$443$	−3.57554	−	2.59778i	−0.169879	−	0.123424i	−0.669476	+	0.742833i	$0.733481\pi$
$444$	−3.65569	−	11.2510i	−0.173491	−	0.533951i
$445$	25.5903	−	18.5924i	1.21310	−	0.881365i
$446$	17.6930	+	54.4534i	0.837787	+	2.57844i
$447$	12.1981	−	37.5418i	0.576950	−	1.77567i
$448$	−11.5823	−	8.41505i	−0.547213	−	0.397574i
$449$	−2.88479	+	8.87847i	−0.136142	+	0.419001i	−0.995766	−	0.0919259i	$-0.970698\pi$
$449$	−2.88479	+	8.87847i	−0.136142	+	0.419001i	0.859624	+	0.510927i	$0.170698\pi$
$450$	10.5729	−	32.5401i	0.498412	−	1.53395i
$451$	−4.43301	−	3.22077i	−0.208742	−	0.151660i
$452$	2.38349	−	7.33561i	0.112110	−	0.345038i
$453$	5.53956	+	17.0490i	0.260271	+	0.801032i
$454$	11.9881	−	8.70985i	0.562629	−	0.408774i
$455$	−1.25496	−	3.86238i	−0.0588336	−	0.181071i
$456$	23.1363	+	16.8095i	1.08346	+	0.787179i
$457$	−28.0041	−	20.3462i	−1.30998	−	0.951754i	−0.999999	−	0.00101040i	$-0.999678\pi$
$457$	−28.0041	−	20.3462i	−1.30998	−	0.951754i	−0.309978	−	0.950744i	$-0.600322\pi$
$458$	42.6749	−	31.0052i	1.99407	−	1.44878i
$459$	−1.87624			−0.0875756
$460$	−86.6879			−4.04185
$461$	15.3330	−	11.1401i	0.714129	−	0.518845i	−0.170374	−	0.985380i	$-0.554498\pi$
$461$	15.3330	−	11.1401i	0.714129	−	0.518845i	0.884503	+	0.466534i	$0.154498\pi$
$462$	−1.76643	+	5.43652i	−0.0821818	+	0.252930i
$463$	−0.335081	−	1.03127i	−0.0155725	−	0.0479273i	0.942968	−	0.332883i	$-0.108021\pi$
$463$	−0.335081	−	1.03127i	−0.0155725	−	0.0479273i	−0.958541	+	0.284955i	$0.908021\pi$
$464$	1.07066			0.0497041
$465$	−13.2582	+	42.8201i	−0.614835	+	1.98574i
$466$	7.75516			0.359251
$467$	7.72525	+	23.7759i	0.357482	+	1.10022i	0.954556	+	0.298031i	$0.0963298\pi$
$467$	7.72525	+	23.7759i	0.357482	+	1.10022i	−0.597074	+	0.802186i	$0.703670\pi$
$468$	−1.68807	+	5.19534i	−0.0780309	+	0.240154i
$469$	0.898028	−	0.652456i	0.0414671	−	0.0301276i
$470$	2.66625			0.122985
$471$	21.8380			1.00624
$472$	−4.69048	+	3.40783i	−0.215897	+	0.156858i
$473$	6.67324	+	4.84839i	0.306836	+	0.222929i
$474$	−12.3585	−	8.97895i	−0.567643	−	0.412417i
$475$	13.6026	+	41.8645i	0.624130	+	1.92088i
$476$	−1.90717	+	1.38564i	−0.0874152	+	0.0635108i
$477$	−4.71243	−	14.5034i	−0.215767	−	0.664064i
$478$	−11.2583	+	34.6496i	−0.514944	+	1.58484i
$479$	−7.38613	−	5.36634i	−0.337481	−	0.245194i	0.406117	−	0.913821i	$-0.366882\pi$
$479$	−7.38613	−	5.36634i	−0.337481	−	0.245194i	−0.743598	+	0.668627i	$0.766882\pi$
$480$	−15.2053	+	46.7972i	−0.694025	+	2.13599i
$481$	−0.534448	+	1.64486i	−0.0243687	+	0.0749992i
$482$	48.3747	+	35.1463i	2.20341	+	1.60087i
$483$	5.50943	−	16.9563i	0.250688	−	0.771537i
$484$	−9.60121	−	29.5495i	−0.436419	−	1.34316i
$485$	−1.44742	+	1.05161i	−0.0657241	+	0.0477514i
$486$	11.3008	+	34.7802i	0.512613	+	1.57766i
$487$	8.02866	+	5.83316i	0.363813	+	0.264326i	0.754641	−	0.656138i	$-0.227811\pi$
$487$	8.02866	+	5.83316i	0.363813	+	0.264326i	−0.390828	+	0.920464i	$0.627811\pi$
$488$	−20.3345	−	14.7739i	−0.920502	−	0.668784i
$489$	−39.0930	+	28.4027i	−1.76785	+	1.28442i
$490$	48.5967			2.19537
$491$	−5.37711			−0.242666			−0.121333	−	0.992612i	$-0.538717\pi$
$491$	−5.37711			−0.242666			−0.121333	+	0.992612i	$0.538717\pi$
$492$	−28.7517	+	20.8894i	−1.29623	+	0.941765i
$493$	0.550500	−	1.69427i	0.0247933	−	0.0763059i
$494$	−3.55408	−	10.9383i	−0.159906	−	0.492139i
$495$	6.78090			0.304779
$496$	0.676210	−	2.18396i	0.0303627	−	0.0980626i
$497$	0.645535			0.0289562
$498$	−5.10368	−	15.7075i	−0.228701	−	0.703871i
$499$	−10.0822	+	31.0299i	−0.451343	+	1.38909i	0.424032	+	0.905647i	$0.360614\pi$
$499$	−10.0822	+	31.0299i	−0.451343	+	1.38909i	−0.875375	+	0.483444i	$0.839386\pi$
$500$	34.5914	−	25.1321i	1.54697	−	1.12394i
$501$	16.8532			0.752947
$502$	−11.4100			−0.509255
$503$	−31.7822	+	23.0912i	−1.41710	+	1.02958i	−0.424858	+	0.905260i	$0.639676\pi$
$503$	−31.7822	+	23.0912i	−1.41710	+	1.02958i	−0.992242	+	0.124324i	$0.960324\pi$
$504$	4.00030	+	2.90639i	0.178187	+	0.129461i
$505$	−32.5049	−	23.6162i	−1.44645	−	1.05091i
$506$	−5.51243	−	16.9655i	−0.245057	−	0.754209i
$507$	1.76107	−	1.27949i	0.0782117	−	0.0568241i
$508$	−7.01242	−	21.5820i	−0.311126	−	0.957547i
$509$	−2.43873	+	7.50565i	−0.108095	+	0.332682i	−0.990444	−	0.137913i	$-0.955961\pi$
$509$	−2.43873	+	7.50565i	−0.108095	+	0.332682i	0.882349	+	0.470595i	$0.155961\pi$
$510$	10.0913	+	7.33178i	0.446851	+	0.324657i
$511$	−5.66532	+	17.4361i	−0.250619	+	0.771326i
$512$	1.43288	−	4.40996i	0.0633251	−	0.194895i
$513$	−11.2680	−	8.18670i	−0.497495	−	0.361451i
$514$	−18.4922	+	56.9132i	−0.815657	+	2.51033i
$515$	−22.7884	−	70.1356i	−1.00418	−	3.09054i
$516$	43.2815	−	31.4459i	1.90536	−	1.38433i
$517$	0.103604	+	0.318859i	0.00455648	+	0.0140234i
$518$	3.48401	+	2.53128i	0.153079	+	0.111218i
$519$	−31.6782	−	23.0156i	−1.39052	−	1.01027i
$520$	−7.75064	+	5.63117i	−0.339888	+	0.246943i
$521$	2.27390			0.0996212			0.0498106	−	0.998759i	$-0.484138\pi$
$521$	2.27390			0.0996212			0.0498106	+	0.998759i	$0.484138\pi$
$522$	−10.2790			−0.449898
$523$	30.0785	−	21.8533i	1.31524	−	0.955577i	0.315261	−	0.949005i	$-0.397908\pi$
$523$	30.0785	−	21.8533i	1.31524	−	0.955577i	0.999978	−	0.00657196i	$-0.00209194\pi$
$524$	19.7706	−	60.8476i	0.863682	−	2.65814i
$525$	6.41053	+	19.7296i	0.279778	+	0.861069i
$526$	−5.43438			−0.236950
$527$	−3.10832	−	2.19299i	−0.135401	−	0.0955283i
$528$	−0.942667			−0.0410243
$529$	10.0857	+	31.0405i	0.438507	+	1.34959i
$530$	22.7347	−	69.9702i	0.987532	−	3.03931i
$531$	−3.14795	+	2.28712i	−0.136609	+	0.0992524i
$532$	−17.4998			−0.758713
$533$	5.19569			0.225050
$534$	34.1541	−	24.8144i	1.47799	−	1.07382i
$535$	−45.6917	−	33.1969i	−1.97542	−	1.43523i
$536$	−2.11846	−	1.53915i	−0.0915037	−	0.0664813i
$537$	11.3624	+	34.9698i	0.490322	+	1.50906i
$538$	−11.8364	+	8.59961i	−0.510301	+	0.370756i
$539$	1.88834	+	5.81172i	0.0813366	+	0.250328i
$540$	−9.86231	+	30.3531i	−0.424406	+	1.30619i
$541$	−6.00772	−	4.36486i	−0.258292	−	0.187660i	0.451102	−	0.892473i	$-0.351031\pi$
$541$	−6.00772	−	4.36486i	−0.258292	−	0.187660i	−0.709394	+	0.704812i	$0.751031\pi$
$542$	18.5477	−	57.0841i	0.796694	−	2.45197i
$543$	4.50359	−	13.8606i	0.193268	−	0.594817i
$544$	−3.37825	−	2.45444i	−0.144841	−	0.105233i
$545$	−11.5624	+	35.5855i	−0.495280	+	1.52431i
$546$	−1.67494	−	5.15494i	−0.0716808	−	0.220611i
$547$	−28.5502	+	20.7429i	−1.22072	+	0.886904i	−0.996160	−	0.0875565i	$-0.972094\pi$
$547$	−28.5502	+	20.7429i	−1.22072	+	0.886904i	−0.224559	+	0.974460i	$0.572094\pi$
$548$	15.3067	+	47.1092i	0.653870	+	2.01240i
$549$	−13.6472	−	9.91530i	−0.582450	−	0.423175i
$550$	16.7921	+	12.2002i	0.716019	+	0.520218i
$551$	10.6988	−	7.77311i	0.455783	−	0.331145i
$552$	−42.0586			−1.79013
$553$	3.39807			0.144500
$554$	40.4013	−	29.3533i	1.71649	−	1.24710i
$555$	4.30280	−	13.2427i	0.182644	−	0.562120i
$556$	5.91448	+	18.2029i	0.250830	+	0.771975i
$557$	−17.4702			−0.740238			−0.370119	−	0.928984i	$-0.620683\pi$
$557$	−17.4702			−0.740238			−0.370119	+	0.928984i	$0.620683\pi$
$558$	−6.49200	+	20.9673i	−0.274828	+	0.887615i
$559$	−7.82134			−0.330808
$560$	−0.515316	−	1.58598i	−0.0217761	−	0.0670199i
$561$	−0.484690	+	1.49172i	−0.0204636	+	0.0629806i
$562$	28.6235	−	20.7962i	1.20741	−	0.877236i
$563$	−36.8126			−1.55147			−0.775733	−	0.631061i	$-0.782620\pi$
$563$	−36.8126			−1.55147			−0.775733	+	0.631061i	$0.782620\pi$
$564$	2.17450			0.0915628
$565$	7.34464	−	5.33619i	0.308991	−	0.224495i
$566$	−28.6973	−	20.8498i	−1.20624	−	0.876382i
$567$	−9.94330	−	7.22423i	−0.417579	−	0.303389i
$568$	−0.470580	−	1.44830i	−0.0197451	−	0.0607691i
$569$	14.0786	−	10.2287i	0.590204	−	0.428809i	−0.252184	−	0.967679i	$-0.581149\pi$
$569$	14.0786	−	10.2287i	0.590204	−	0.428809i	0.842389	+	0.538871i	$0.181149\pi$
$570$	28.6137	+	88.0638i	1.19849	+	3.68859i
$571$	4.64386	−	14.2923i	0.194339	−	0.598115i	−0.805644	−	0.592400i	$-0.798181\pi$
$571$	4.64386	−	14.2923i	0.194339	−	0.598115i	0.999984	−	0.00571556i	$-0.00181933\pi$
$572$	−2.68102	−	1.94788i	−0.112099	−	0.0814448i
$573$	2.69180	−	8.28451i	0.112452	−	0.346091i
$574$	3.99783	−	12.3041i	0.166866	−	0.513561i
$575$	−52.3740	−	38.0519i	−2.18415	−	1.58687i
$576$	−7.00424	+	21.5568i	−0.291844	+	0.898202i
$577$	−0.185937	−	0.572254i	−0.00774064	−	0.0238232i	0.947112	−	0.320904i	$-0.103987\pi$
$577$	−0.185937	−	0.572254i	−0.00774064	−	0.0238232i	−0.954852	+	0.297081i	$0.903987\pi$
$578$	30.3314	−	22.0371i	1.26162	−	0.916621i
$579$	10.6479	+	32.7708i	0.442511	+	1.36191i
$580$	−24.5155	−	17.8115i	−1.01795	−	0.739583i
$581$	2.97224	+	2.15946i	0.123309	+	0.0895894i
$582$	−1.93181	+	1.40354i	−0.0800760	+	0.0581786i
$583$	9.25121			0.383146
$584$	43.2487			1.78964
$585$	−5.20173	+	3.77928i	−0.215065	+	0.156254i
$586$	−7.58217	+	23.3355i	−0.313217	+	0.963981i
$587$	−8.84218	−	27.2134i	−0.364956	−	1.12322i	−0.950009	−	0.312223i	$-0.898926\pi$
$587$	−8.84218	−	27.2134i	−0.364956	−	1.12322i	0.585053	−	0.810995i	$-0.301074\pi$
$588$	39.6336			1.63446
$589$	−9.09862	−	26.7330i	−0.374902	−	1.10151i
$590$	−18.7721			−0.772837
$591$	13.9840	+	43.0384i	0.575225	+	1.77036i
$592$	−0.219456	+	0.675417i	−0.00901959	+	0.0277595i
$593$	30.7045	−	22.3081i	1.26088	−	0.916085i	0.262082	−	0.965046i	$-0.415591\pi$
$593$	30.7045	−	22.3081i	1.26088	−	0.916085i	0.998801	+	0.0489604i	$0.0155908\pi$
$594$	−6.56748			−0.269467
$595$	−2.77470			−0.113751
$596$	46.0993	−	33.4931i	1.88830	−	1.37193i
$597$	30.1483	+	21.9040i	1.23389	+	0.896471i
$598$	13.6842	+	9.94219i	0.559590	+	0.406566i
$599$	−0.151597	−	0.466568i	−0.00619409	−	0.0190635i	0.947912	−	0.318533i	$-0.103190\pi$
$599$	−0.151597	−	0.466568i	−0.00619409	−	0.0190635i	−0.954106	+	0.299470i	$0.903190\pi$
$600$	39.5913	−	28.7648i	1.61631	−	1.17432i
$601$	−12.0614	−	37.1212i	−0.491995	−	1.51421i	−0.821587	−	0.570083i	$-0.806911\pi$
$601$	−12.0614	−	37.1212i	−0.491995	−	1.51421i	0.329592	−	0.944123i	$-0.393089\pi$
$602$	−6.01814	+	18.5219i	−0.245281	+	0.754898i
$603$	−1.42178	−	1.03298i	−0.0578992	−	0.0420662i
$604$	−7.99655	+	24.6108i	−0.325375	+	1.00140i
$605$	11.3008	−	34.7803i	0.459442	−	1.41402i
$606$	−43.3827	−	31.5194i	−1.76230	−	1.28039i
$607$	12.2882	−	37.8193i	0.498764	−	1.53504i	−0.312244	−	0.950002i	$-0.601081\pi$
$607$	12.2882	−	37.8193i	0.498764	−	1.53504i	0.811008	−	0.585035i	$-0.198919\pi$
$608$	−9.57892	−	29.4809i	−0.388477	−	1.19561i
$609$	5.04203	−	3.66325i	0.204313	−	0.148442i
$610$	−25.1486	−	77.3994i	−1.01824	−	3.13381i
$611$	−0.257189	−	0.186859i	−0.0104048	−	0.00755950i
$612$	3.01947	+	2.19378i	0.122055	+	0.0886782i
$613$	−30.4987	+	22.1586i	−1.23183	+	0.894977i	−0.997026	−	0.0770655i	$-0.975445\pi$
$613$	−30.4987	+	22.1586i	−1.23183	+	0.894977i	−0.234804	+	0.972043i	$0.575445\pi$
$614$	−24.2503			−0.978661
$615$	−41.8301			−1.68675
$616$	−2.42677	+	1.76315i	−0.0977772	+	0.0710393i
$617$	−5.98813	+	18.4296i	−0.241073	+	0.741946i	0.755185	+	0.655512i	$0.227547\pi$
$617$	−5.98813	+	18.4296i	−0.241073	+	0.741946i	−0.996258	+	0.0864341i	$0.972453\pi$
$618$	−30.4146	−	93.6066i	−1.22346	−	3.76541i
$619$	22.9421			0.922121			0.461061	−	0.887369i	$-0.347469\pi$
$619$	22.9421			0.922121			0.461061	+	0.887369i	$0.347469\pi$
$620$	−51.8159	+	38.7578i	−2.08098	+	1.55655i
$621$	20.4837			0.821982
$622$	13.6803	+	42.1038i	0.548532	+	1.68821i
$623$	−2.90197	+	8.93133i	−0.116265	+	0.357826i
$624$	0.723133	−	0.525387i	0.0289485	−	0.0210323i
$625$	6.93075			0.277230
$626$	−65.7039			−2.62606
$627$	−9.41977	+	6.84386i	−0.376189	+	0.273318i
$628$	25.5034	+	18.5293i	1.01770	+	0.739399i
$629$	0.955976	+	0.694557i	0.0381173	+	0.0276938i
$630$	4.94733	+	15.2263i	0.197107	+	0.606631i
$631$	−2.83552	+	2.06013i	−0.112880	+	0.0820124i	−0.642793	−	0.766040i	$-0.722225\pi$
$631$	−2.83552	+	2.06013i	−0.112880	+	0.0820124i	0.529913	+	0.848052i	$0.322225\pi$
$632$	−2.47711	−	7.62376i	−0.0985341	−	0.303257i
$633$	−6.44629	+	19.8397i	−0.256217	+	0.788555i
$634$	−64.4223	−	46.8056i	−2.55854	−	1.85889i
$635$	8.25374	−	25.4024i	0.327540	−	1.00806i
$636$	18.5416	−	57.0651i	0.735221	−	2.26278i
$637$	−4.68768	−	3.40580i	−0.185733	−	0.134943i
$638$	1.92693	−	5.93049i	0.0762880	−	0.234790i
$639$	−0.315823	−	0.972002i	−0.0124938	−	0.0384518i
$640$	−51.8920	+	37.7017i	−2.05121	+	1.49029i
$641$	1.37875	+	4.24336i	0.0544574	+	0.167603i	0.974586	−	0.224014i	$-0.0719160\pi$
$641$	1.37875	+	4.24336i	0.0544574	+	0.167603i	−0.920129	+	0.391616i	$0.871916\pi$
$642$	−60.9825	−	44.3064i	−2.40679	−	1.74863i
$643$	9.63913	+	7.00324i	0.380130	+	0.276181i	0.761399	−	0.648283i	$-0.224513\pi$
$643$	9.63913	+	7.00324i	0.380130	+	0.276181i	−0.381269	+	0.924464i	$0.624513\pi$
$644$	20.8214	−	15.1276i	0.820477	−	0.596111i
$645$	62.9691			2.47941
$646$	−7.85799			−0.309168
$647$	20.4908	−	14.8875i	0.805578	−	0.585287i	−0.106967	−	0.994263i	$-0.534114\pi$
$647$	20.4908	−	14.8875i	0.805578	−	0.585287i	0.912545	+	0.408976i	$0.134114\pi$
$648$	−8.95955	+	27.5747i	−0.351964	+	1.08323i
$649$	−0.729437	−	2.24497i	−0.0286329	−	0.0881230i
$650$	−19.6812			−0.771958
$651$	−4.28793	−	12.5985i	−0.168057	−	0.493774i
$652$	−69.7539			−2.73177
$653$	3.46462	+	10.6630i	0.135581	+	0.417275i	0.995680	−	0.0928519i	$-0.0295983\pi$
$653$	3.46462	+	10.6630i	0.135581	+	0.417275i	−0.860099	+	0.510127i	$0.829598\pi$
$654$	−15.4318	+	47.4942i	−0.603432	+	1.85717i
$655$	60.9225	−	44.2628i	2.38044	−	1.72949i
$656$	2.13347			0.0832978
$657$	29.0257			1.13240
$658$	−0.640400	+	0.465278i	−0.0249654	+	0.0181384i
$659$	18.0860	+	13.1402i	0.704530	+	0.511871i	0.881405	−	0.472362i	$-0.156599\pi$
$659$	18.0860	+	13.1402i	0.704530	+	0.511871i	−0.176874	+	0.984233i	$0.556599\pi$
$660$	21.5847	+	15.6822i	0.840185	+	0.610430i
$661$	−3.02596	−	9.31293i	−0.117696	−	0.362231i	0.874804	−	0.484477i	$-0.160990\pi$
$661$	−3.02596	−	9.31293i	−0.117696	−	0.362231i	−0.992500	+	0.122246i	$0.960990\pi$
$662$	−32.4537	+	23.5790i	−1.26135	+	0.916423i
$663$	−0.459586	−	1.41446i	−0.0178488	−	0.0549331i
$664$	2.67818	−	8.24258i	0.103933	−	0.319874i
$665$	−16.6638	−	12.1069i	−0.646194	−	0.469487i
$666$	2.10691	−	6.48439i	0.0816410	−	0.251265i
$667$	−6.01003	+	18.4970i	−0.232709	+	0.716205i
$668$	19.6819	+	14.2998i	0.761517	+	0.553275i
$669$	−16.9840	+	52.2715i	−0.656641	+	2.02093i
$670$	−2.61999	−	8.06351i	−0.101219	−	0.311520i
$671$	8.27904	−	6.01508i	0.319609	−	0.232210i
$672$	−4.51428	−	13.8935i	−0.174142	−	0.535954i
$673$	−10.5762	−	7.68403i	−0.407681	−	0.296198i	0.364981	−	0.931015i	$-0.381075\pi$
$673$	−10.5762	−	7.68403i	−0.407681	−	0.296198i	−0.772662	+	0.634817i	$0.781075\pi$
$674$	28.0849	+	20.4049i	1.08179	+	0.785966i
$675$	−19.2820	+	14.0092i	−0.742166	+	0.539215i
$676$	3.14228			0.120857
$677$	16.4352			0.631655			0.315828	−	0.948817i	$-0.397718\pi$
$677$	16.4352			0.631655			0.315828	+	0.948817i	$0.397718\pi$
$678$	9.80254	−	7.12196i	0.376464	−	0.273517i
$679$	0.164140	−	0.505170i	0.00629910	−	0.0193866i
$680$	2.02269	+	6.22519i	0.0775665	+	0.238725i
$681$	14.2243			0.545078
$682$	−10.8801	−	7.67620i	−0.416622	−	0.293937i
$683$	−24.9210			−0.953575			−0.476788	−	0.879019i	$-0.658199\pi$
$683$	−24.9210			−0.953575			−0.476788	+	0.879019i	$0.658199\pi$
$684$	8.56163	+	26.3500i	0.327362	+	1.00752i
$685$	−18.0162	+	55.4483i	−0.688365	+	2.11857i
$686$	−25.7735	+	18.7255i	−0.984035	+	0.714944i
$687$	50.6355			1.93187
$688$	−3.21162			−0.122442
$689$	−7.09673	+	5.15608i	−0.270364	+	0.196431i
$690$	−110.171	−	80.0439i	−4.19414	−	3.04722i
$691$	−10.2424	−	7.44153i	−0.389639	−	0.283089i	0.375669	−	0.926754i	$-0.377413\pi$
$691$	−10.2424	−	7.44153i	−0.389639	−	0.283089i	−0.765308	+	0.643665i	$0.777413\pi$
$692$	−17.4668	−	53.7572i	−0.663987	−	2.04354i
$693$	−1.62869	+	1.18331i	−0.0618688	+	0.0449503i
$694$	10.7570	+	33.1067i	0.408331	+	1.25671i
$695$	−6.96145	+	21.4251i	−0.264063	+	0.812702i
$696$	−11.8942	−	8.64167i	−0.450850	−	0.327562i
$697$	1.09696	−	3.37610i	0.0415504	−	0.127879i
$698$	2.62499	−	8.07889i	0.0993574	−	0.305791i
$699$	6.02266	+	4.37572i	0.227798	+	0.165505i
$700$	−9.25382	+	28.4803i	−0.349762	+	1.07646i
$701$	7.28824	+	22.4309i	0.275273	+	0.847203i	0.989147	+	0.146929i	$0.0469390\pi$
$701$	7.28824	+	22.4309i	0.275273	+	0.847203i	−0.713874	+	0.700274i	$0.753061\pi$
$702$	5.03800	−	3.66032i	0.190147	−	0.138150i
$703$	2.71064	+	8.34250i	0.102234	+	0.314643i
$704$	−11.1243	−	8.08227i	−0.419262	−	0.304612i
$705$	2.07061	+	1.50439i	0.0779838	+	0.0566585i
$706$	−0.850220	+	0.617721i	−0.0319984	+	0.0232482i
$707$	11.9284			0.448615
$708$	−15.3099			−0.575380
$709$	−5.56941	+	4.04641i	−0.209164	+	0.151966i	−0.687435	−	0.726246i	$-0.741263\pi$
$709$	−5.56941	+	4.04641i	−0.209164	+	0.151966i	0.478272	+	0.878212i	$0.341263\pi$
$710$	1.52366	−	4.68934i	0.0571819	−	0.175988i
$711$	−1.66248	−	5.11657i	−0.0623477	−	0.191886i
$712$	22.1534			0.830235
$713$	33.9347	+	23.9418i	1.27087	+	0.896626i
$714$	−3.70325			−0.138591
$715$	−1.20534	−	3.70964i	−0.0450770	−	0.138733i
$716$	−16.4020	+	50.4801i	−0.612970	+	1.88653i
$717$	−28.2937	+	20.5566i	−1.05665	+	0.767699i
$718$	36.1852			1.35042
$719$	10.3107			0.384523			0.192261	−	0.981344i	$-0.438418\pi$
$719$	10.3107			0.384523			0.192261	+	0.981344i	$0.438418\pi$
$720$	−2.13595	+	1.55186i	−0.0796020	+	0.0578342i
$721$	17.7126	+	12.8690i	0.659652	+	0.479265i
$722$	−12.3352	−	8.96205i	−0.459069	−	0.333533i
$723$	17.7371	+	54.5892i	0.659650	+	2.03020i
$724$	17.0201	−	12.3658i	0.632547	−	0.459572i
$725$	−6.99300	−	21.5223i	−0.259714	−	0.799317i
$726$	15.0826	−	46.4195i	0.559769	−	1.72279i
$727$	−7.63515	−	5.54726i	−0.283172	−	0.205737i	0.437128	−	0.899399i	$-0.355996\pi$
$727$	−7.63515	−	5.54726i	−0.283172	−	0.205737i	−0.720300	+	0.693663i	$0.755996\pi$
$728$	0.878931	−	2.70507i	0.0325754	−	0.100257i
$729$	−0.471350	+	1.45067i	−0.0174574	+	0.0537284i
$730$	113.288	+	82.3088i	4.19299	+	3.04638i
$731$	−1.65132	+	5.08223i	−0.0610761	+	0.187973i
$732$	−20.5102	−	63.1240i	−0.758080	−	2.33313i
$733$	24.1209	−	17.5249i	0.890927	−	0.647297i	−0.0451922	−	0.998978i	$-0.514390\pi$
$733$	24.1209	−	17.5249i	0.890927	−	0.647297i	0.936120	+	0.351682i	$0.114390\pi$
$734$	0.0539479	+	0.166034i	0.00199125	+	0.00612844i
$735$	37.7402	+	27.4199i	1.39207	+	1.01140i
$736$	36.8816	+	26.7961i	1.35947	+	0.987716i
$737$	0.862515	−	0.626654i	0.0317712	−	0.0230831i
$738$	−20.4825			−0.753972
$739$	15.8685			0.583733			0.291866	−	0.956459i	$-0.405724\pi$
$739$	15.8685			0.583733			0.291866	+	0.956459i	$0.405724\pi$
$740$	16.2613	−	11.8145i	0.597776	−	0.434309i
$741$	3.41167	−	10.5001i	0.125331	−	0.385729i
$742$	6.74966	+	20.7733i	0.247788	+	0.762613i
$743$	20.7281			0.760439			0.380219	−	0.924896i	$-0.375848\pi$
$743$	20.7281			0.760439			0.380219	+	0.924896i	$0.375848\pi$
$744$	−25.1397	+	18.8042i	−0.921665	+	0.689396i
$745$	67.0686			2.45720
$746$	6.21248	+	19.1201i	0.227455	+	0.700035i
$747$	1.79742	−	5.53189i	0.0657641	−	0.202401i
$748$	−1.83175	+	1.33085i	−0.0669755	+	0.0486606i
$749$	16.7676			0.612677
$750$	67.1677			2.45262
$751$	12.7756	−	9.28201i	0.466188	−	0.338705i	−0.329766	−	0.944063i	$-0.606970\pi$
$751$	12.7756	−	9.28201i	0.466188	−	0.338705i	0.795954	+	0.605357i	$0.206970\pi$
$752$	−0.105608	−	0.0767284i	−0.00385111	−	0.00279800i
$753$	−8.86105	−	6.43793i	−0.322915	−	0.234611i
$754$	1.82713	+	5.62333i	0.0665401	+	0.204789i
$755$	−24.6411	+	17.9028i	−0.896782	+	0.651550i
$756$	−2.92800	−	9.01147i	−0.106490	−	0.327744i
$757$	5.55647	−	17.1011i	0.201953	−	0.621548i	−0.797871	−	0.602828i	$-0.794041\pi$
$757$	5.55647	−	17.1011i	0.201953	−	0.621548i	0.999825	−	0.0187207i	$-0.00595935\pi$
$758$	−12.9319	−	9.39556i	−0.469707	−	0.341262i
$759$	5.29155	−	16.2857i	0.192071	−	0.591135i
$760$	−15.0151	+	46.2118i	−0.544656	+	1.67628i
$761$	−33.3137	−	24.2038i	−1.20762	−	0.877387i	−0.212607	−	0.977138i	$-0.568195\pi$
$761$	−33.3137	−	24.2038i	−1.20762	−	0.877387i	−0.995012	+	0.0997509i	$0.968195\pi$
$762$	11.0159	−	33.9034i	0.399063	−	1.22819i
$763$	−3.43275	−	10.5649i	−0.124274	−	0.382475i
$764$	10.1729	−	7.39106i	0.368043	−	0.267399i
$765$	1.35750	+	4.17795i	0.0490804	+	0.151054i
$766$	−26.9607	−	19.5881i	−0.974131	−	0.707747i
$767$	1.81078	+	1.31561i	0.0653834	+	0.0475038i
$768$	−23.3356	+	16.9543i	−0.842049	+	0.611785i
$769$	−13.2753			−0.478718			−0.239359	−	0.970931i	$-0.576937\pi$
$769$	−13.2753			−0.478718			−0.239359	+	0.970931i	$0.576937\pi$
$770$	−9.71235			−0.350009
$771$	−46.4734	+	33.7649i	−1.67370	+	1.21601i
$772$	−15.3706	+	47.3058i	−0.553200	+	1.70257i
$773$	1.10640	+	3.40515i	0.0397945	+	0.122475i	0.968980	−	0.247138i	$-0.0794902\pi$
$773$	1.10640	+	3.40515i	0.0397945	+	0.122475i	−0.929186	+	0.369613i	$0.879490\pi$
$774$	30.8334			1.10828
$775$	−48.3183	+	0.671426i	−1.73564	+	0.0241183i
$776$	−1.25303			−0.0449812
$777$	1.27745	+	3.93159i	0.0458283	+	0.141045i
$778$	17.6600	−	54.3520i	0.633143	−	1.94861i
$779$	21.3191	−	15.4892i	0.763834	−	0.554958i
$780$	−25.2983			−0.905825
$781$	0.620007			0.0221856
$782$	9.34948	−	6.79279i	0.334337	−	0.242910i
$783$	5.79281	+	4.20872i	0.207018	+	0.150408i
$784$	−1.92487	−	1.39850i	−0.0687452	−	0.0499463i
$785$	11.4658	+	35.2882i	0.409233	+	1.25949i
$786$	81.3103	−	59.0754i	2.90024	−	2.10715i
$787$	−2.92350	−	8.99760i	−0.104211	−	0.320730i	0.885333	−	0.464957i	$-0.153930\pi$
$787$	−2.92350	−	8.99760i	−0.104211	−	0.320730i	−0.989545	+	0.144227i	$0.953930\pi$
$788$	−20.1864	+	62.1274i	−0.719111	+	2.21320i
$789$	−4.22034	−	3.06626i	−0.150248	−	0.109162i
$790$	8.02046	−	24.6844i	0.285355	−	0.878233i
$791$	−0.832891	+	2.56337i	−0.0296142	+	0.0911431i
$792$	3.84210	+	2.79145i	0.136523	+	0.0991899i
$793$	−2.99852	+	9.22851i	−0.106481	+	0.327714i
$794$	8.82670	+	27.1658i	0.313248	+	0.964078i
$795$	57.1353	−	41.5112i	2.02638	−	1.47225i
$796$	16.6232	+	51.1609i	0.589193	+	1.81335i
$797$	22.1627	+	16.1021i	0.785043	+	0.570367i	0.906488	−	0.422231i	$-0.138753\pi$
$797$	22.1627	+	16.1021i	0.785043	+	0.570367i	−0.121445	+	0.992598i	$0.538753\pi$
$798$	−22.2404	−	16.1586i	−0.787300	−	0.572007i
$799$	−0.175719	+	0.127667i	−0.00621650	+	0.00451655i
$800$	−53.0444			−1.87540
$801$	14.8679			0.525333
$802$	−19.7833	+	14.3734i	−0.698572	+	0.507542i
$803$	−5.44128	+	16.7465i	−0.192019	+	0.590973i
$804$	−2.13677	−	6.57630i	−0.0753580	−	0.231928i
$805$	30.2924			1.06767
$806$	12.6246	−	0.175430i	0.444682	−	0.00617925i
$807$	−14.0443			−0.494383
$808$	−8.69555	−	26.7622i	−0.305909	−	0.941490i
$809$	5.37068	−	16.5293i	0.188823	−	0.581138i	−0.811170	−	0.584810i	$-0.801169\pi$
$809$	5.37068	−	16.5293i	0.188823	−	0.581138i	0.999993	+	0.00367258i	$0.00116902\pi$
$810$	−75.9479	+	55.1794i	−2.66854	+	1.93881i
$811$	38.9323			1.36710			0.683549	−	0.729904i	$-0.260435\pi$
$811$	38.9323			1.36710			0.683549	+	0.729904i	$0.260435\pi$
$812$	8.99653			0.315716
$813$	46.6129	−	33.8663i	1.63479	−	1.18774i
$814$	3.34623	+	2.43118i	0.117285	+	0.0852128i
$815$	−66.4215	−	48.2581i	−2.32664	−	1.69041i
$816$	−0.188716	−	0.580809i	−0.00660639	−	0.0203324i
$817$	−32.0927	+	23.3167i	−1.12278	+	0.815748i
$818$	−9.62672	−	29.6280i	−0.336591	−	1.03592i
$819$	0.589882	−	1.81547i	0.0206121	−	0.0634377i
$820$	−48.8511	−	35.4924i	−1.70595	−	1.23945i
$821$	−1.50353	+	4.62738i	−0.0524735	+	0.161497i	−0.973859	−	0.227153i	$-0.927058\pi$
$821$	−1.50353	+	4.62738i	−0.0524735	+	0.161497i	0.921386	+	0.388650i	$0.127058\pi$
$822$	−24.0454	+	74.0042i	−0.838680	+	2.58119i
$823$	35.8178	+	26.0231i	1.24853	+	0.907109i	0.998136	−	0.0610347i	$-0.0194400\pi$
$823$	35.8178	+	26.0231i	1.24853	+	0.907109i	0.250393	+	0.968144i	$0.419440\pi$
$824$	15.9602	−	49.1204i	0.556000	−	1.71119i
$825$	6.15702	+	18.9494i	0.214360	+	0.659732i
$826$	4.50883	−	3.27586i	0.156882	−	0.113982i
$827$	−0.489263	−	1.50580i	−0.0170133	−	0.0523617i	0.942189	−	0.335081i	$-0.108764\pi$
$827$	−0.489263	−	1.50580i	−0.0170133	−	0.0523617i	−0.959203	+	0.282719i	$0.908764\pi$
$828$	−32.9648	−	23.9503i	−1.14561	−	0.832331i
$829$	16.5307	+	12.0103i	0.574136	+	0.417134i	0.836605	−	0.547806i	$-0.184537\pi$
$829$	16.5307	+	12.0103i	0.574136	+	0.417134i	−0.262470	+	0.964940i	$0.584537\pi$
$830$	22.7022	−	16.4941i	0.788006	−	0.572520i
$831$	47.9378			1.66294
$832$	13.0382			0.452018
$833$	−3.20276	+	2.32694i	−0.110969	+	0.0806238i
$834$	−9.29111	+	28.5951i	−0.321725	+	0.990167i
$835$	8.84862	+	27.2333i	0.306219	+	0.942446i
$836$	−16.8078			−0.581309
$837$	12.2437	−	9.15816i	0.423204	−	0.316552i
$838$	−71.8255			−2.48117
$839$	−10.5052	−	32.3318i	−0.362681	−	1.11622i	−0.951421	−	0.307894i	$-0.900376\pi$
$839$	−10.5052	−	32.3318i	−0.362681	−	1.11622i	0.588740	−	0.808323i	$-0.299624\pi$
$840$	−7.07622	+	21.7784i	−0.244153	+	0.751425i
$841$	17.9613	−	13.0497i	0.619356	−	0.449989i
$842$	−10.3711			−0.357411
$843$	33.9630			1.16975
$844$	−24.3620	+	17.7000i	−0.838574	+	0.609260i
$845$	2.99217	+	2.17394i	0.102934	+	0.0747857i
$846$	1.01389	+	0.736637i	0.0348584	+	0.0253261i
$847$	3.35507	+	10.3258i	0.115282	+	0.354800i
$848$	−2.91408	+	2.11720i	−0.100070	+	0.0727050i
$849$	−10.5222	−	32.3839i	−0.361120	−	1.11141i
$850$	−4.15527	+	12.7886i	−0.142525	+	0.438646i
$851$	−10.4368	−	7.58275i	−0.357768	−	0.259933i
$852$	1.24264	−	3.82445i	0.0425721	−	0.131023i
$853$	−1.80173	+	5.54515i	−0.0616901	+	0.189862i	−0.977152	−	0.212542i	$-0.931826\pi$
$853$	−1.80173	+	5.54515i	−0.0616901	+	0.189862i	0.915462	+	0.402405i	$0.131826\pi$
$854$	19.5471	+	14.2018i	0.668887	+	0.485975i
$855$	−10.0772	+	31.0144i	−0.344633	+	1.06067i
$856$	−12.2232	−	37.6192i	−0.417781	−	1.28580i
$857$	−9.19000	+	6.67693i	−0.313924	+	0.228079i	−0.733579	−	0.679605i	$-0.762151\pi$
$857$	−9.19000	+	6.67693i	−0.313924	+	0.228079i	0.419654	+	0.907684i	$0.362151\pi$
$858$	−1.60870	−	4.95108i	−0.0549202	−	0.169027i
$859$	26.8901	+	19.5368i	0.917480	+	0.666588i	0.942895	−	0.333089i	$-0.108091\pi$
$859$	26.8901	+	19.5368i	0.917480	+	0.666588i	−0.0254154	+	0.999677i	$0.508091\pi$
$860$	73.5381	+	53.4286i	2.50763	+	1.82190i
$861$	10.0471	−	7.29963i	0.342403	−	0.248771i
$862$	−79.9156			−2.72194
$863$	45.5692			1.55119			0.775597	−	0.631228i	$-0.217449\pi$
$863$	45.5692			1.55119			0.775597	+	0.631228i	$0.217449\pi$
$864$	13.5784	−	9.86527i	0.461946	−	0.335623i
$865$	20.5587	−	63.2732i	0.699017	−	2.15135i
$866$	1.06037	+	3.26347i	0.0360327	+	0.110897i
$867$	35.9894			1.22227
$868$	5.68205	−	18.3513i	0.192861	−	0.622885i
$869$	3.26369			0.110713
$870$	−14.7101	−	45.2730i	−0.498719	−	1.53490i
$871$	−0.312388	+	0.961430i	−0.0105849	+	0.0325768i
$872$	−21.2006	+	15.4031i	−0.717942	+	0.521616i
$873$	−0.840953			−0.0284620
$874$	85.7887			2.90185
$875$	−12.0877	+	8.78222i	−0.408638	+	0.296893i
$876$	92.3937	+	67.1280i	3.12169	+	2.26804i
$877$	−12.3274	−	8.95640i	−0.416268	−	0.302436i	0.359867	−	0.933004i	$-0.382822\pi$
$877$	−12.3274	−	8.95640i	−0.416268	−	0.302436i	−0.776134	+	0.630568i	$0.782822\pi$
$878$	16.2844	+	50.1181i	0.549570	+	1.69140i
$879$	−19.0550	+	13.8443i	−0.642709	+	0.466955i
$880$	−0.494938	−	1.52326i	−0.0166843	−	0.0513491i
$881$	11.9898	−	36.9007i	0.403945	−	1.24322i	−0.517827	−	0.855485i	$-0.673259\pi$
$881$	11.9898	−	36.9007i	0.403945	−	1.24322i	0.921773	−	0.387731i	$-0.126741\pi$
$882$	18.4798	+	13.4264i	0.622248	+	0.452090i
$883$	−18.2073	+	56.0363i	−0.612725	+	1.88577i	−0.181969	+	0.983304i	$0.558247\pi$
$883$	−18.2073	+	56.0363i	−0.612725	+	1.88577i	−0.430756	+	0.902469i	$0.641753\pi$
$884$	0.663428	−	2.04182i	0.0223135	−	0.0686739i
$885$	−14.5785	−	10.5919i	−0.490049	−	0.356042i
$886$	3.09703	−	9.53166i	0.104047	−	0.320223i
$887$	4.18146	+	12.8692i	0.140400	+	0.432105i	0.996391	−	0.0848849i	$-0.0270523\pi$
$887$	4.18146	+	12.8692i	0.140400	+	0.432105i	−0.855991	+	0.516990i	$0.827052\pi$
$888$	7.88952	−	5.73207i	0.264755	−	0.192356i
$889$	2.45044	+	7.54167i	0.0821850	+	0.252940i
$890$	58.0300	+	42.1613i	1.94517	+	1.41325i
$891$	−9.55008	−	6.93854i	−0.319940	−	0.232450i
$892$	−64.1865	+	46.6342i	−2.14912	+	1.56143i
$893$	−1.61236			−0.0539556
$894$	89.5133			2.99377
$895$	−50.5422	+	36.7211i	−1.68944	+	1.22745i
$896$	5.88461	−	18.1110i	0.196591	−	0.605045i
$897$	5.01748	+	15.4422i	0.167529	+	0.515601i
$898$	−21.1695			−0.706434
$899$	4.67754	+	13.7432i	0.156005	+	0.458362i
$900$	47.4111			1.58037
$901$	1.85204	+	5.69998i	0.0617003	+	0.189894i
$902$	3.83973	−	11.8175i	0.127849	−	0.393479i
$903$	−15.1244	+	10.9885i	−0.503308	+	0.365675i
$904$	6.35824			0.211472
$905$	24.7621			0.823119
$906$	−32.8873	+	23.8940i	−1.09261	+	0.793826i
$907$	40.9161	+	29.7273i	1.35860	+	0.987079i	0.998533	+	0.0541518i	$0.0172455\pi$
$907$	40.9161	+	29.7273i	1.35860	+	0.987079i	0.360065	+	0.932927i	$0.382754\pi$
$908$	16.6118	+	12.0692i	0.551283	+	0.400530i
$909$	−5.83589	−	17.9610i	−0.193564	−	0.595730i
$910$	7.45049	−	5.41309i	0.246981	−	0.179442i
$911$	−4.09301	−	12.5970i	−0.135608	−	0.417357i	0.860076	−	0.510165i	$-0.170416\pi$
$911$	−4.09301	−	12.5970i	−0.135608	−	0.417357i	−0.995684	+	0.0928079i	$0.970416\pi$
$912$	1.40091	−	4.31156i	0.0463887	−	0.142770i
$913$	2.85470	+	2.07406i	0.0944767	+	0.0686414i
$914$	24.2563	−	74.6532i	0.802327	−	2.46931i
$915$	24.1409	−	74.2981i	0.798074	−	2.45622i
$916$	59.1344	+	42.9637i	1.95386	+	1.41956i
$917$	−6.90868	+	21.2627i	−0.228145	+	0.702157i
$918$	−1.31477	−	4.04645i	−0.0433939	−	0.133553i
$919$	−1.66509	+	1.20976i	−0.0549262	+	0.0399063i	−0.614910	−	0.788598i	$-0.710808\pi$
$919$	−1.66509	+	1.20976i	−0.0549262	+	0.0399063i	0.559983	+	0.828504i	$0.310808\pi$
$920$	−22.0825	−	67.9628i	−0.728037	−	2.24067i
$921$	−18.8328	−	13.6828i	−0.620561	−	0.450864i
$922$	34.7701	+	25.2619i	1.14509	+	0.831957i
$923$	−0.475616	+	0.345555i	−0.0156551	+	0.0113741i
$924$	−7.92103			−0.260583
$925$	15.0105			0.493543
$926$	1.98931	−	1.44532i	0.0653728	−	0.0474961i
$927$	10.7115	−	32.9665i	0.351810	−	1.08276i
$928$	4.92446	+	15.1559i	0.161653	+	0.497518i
$929$	−22.0060			−0.721992			−0.360996	−	0.932567i	$-0.617563\pi$
$929$	−22.0060			−0.721992			−0.360996	+	0.932567i	$0.617563\pi$
$930$	−101.640	+	1.41237i	−3.33290	+	0.0463136i
$931$	−29.3878			−0.963147
$932$	3.32078	+	10.2203i	0.108776	+	0.334778i
$933$	−13.1322	+	40.4167i	−0.429929	+	1.32318i
$934$	−45.8634	+	33.3217i	−1.50070	+	1.09032i
$935$	−2.66497			−0.0871538
$936$	−4.50312			−0.147189
$937$	45.0201	−	32.7090i	1.47074	−	1.06856i	0.490343	−	0.871530i	$-0.336871\pi$
$937$	45.0201	−	32.7090i	1.47074	−	1.06856i	0.980398	−	0.197027i	$-0.0631285\pi$
$938$	2.03642	+	1.47955i	0.0664916	+	0.0483090i
$939$	−51.0257	−	37.0723i	−1.66516	−	1.20981i
$940$	1.14170	+	3.51378i	0.0372380	+	0.114607i
$941$	−4.58262	+	3.32947i	−0.149389	+	0.108537i	−0.659969	−	0.751293i	$-0.729431\pi$
$941$	−4.58262	+	3.32947i	−0.149389	+	0.108537i	0.510580	+	0.859830i	$0.329431\pi$
$942$	15.3029	+	47.0974i	0.498595	+	1.53452i
$943$	−11.9760	+	36.8583i	−0.389991	+	1.20027i
$944$	0.743546	+	0.540218i	0.0242004	+	0.0175826i
$945$	3.44631	−	10.6066i	0.112108	−	0.345034i
$946$	−5.78015	+	17.7895i	−0.187929	+	0.578386i
$947$	36.0817	+	26.2149i	1.17250	+	0.851870i	0.991306	−	0.131577i	$-0.0420041\pi$
$947$	36.0817	+	26.2149i	1.17250	+	0.851870i	0.181193	+	0.983448i	$0.442004\pi$
$948$	6.54119	−	20.1317i	0.212448	−	0.653848i
$949$	−5.15945	−	15.8792i	−0.167483	−	0.515460i
$950$	−80.7561	+	58.6727i	−2.62007	+	1.90359i
$951$	−23.6212	−	72.6985i	−0.765969	−	2.35741i
$952$	−1.57216	−	1.14224i	−0.0509540	−	0.0370202i
$953$	−21.4560	−	15.5887i	−0.695030	−	0.504969i	0.183280	−	0.983061i	$-0.441328\pi$
$953$	−21.4560	−	15.5887i	−0.695030	−	0.504969i	−0.878310	+	0.478092i	$0.841328\pi$
$954$	27.9768	−	20.3264i	0.905783	−	0.658090i
$955$	14.8003			0.478927
$956$	−50.4846			−1.63279
$957$	4.84264	−	3.51838i	0.156540	−	0.113733i
$958$	6.39764	−	19.6899i	0.206698	−	0.636152i
$959$	−5.34881	−	16.4619i	−0.172722	−	0.531584i
$960$	−104.970			−3.38788
$961$	30.9880	−	0.861379i	0.999614	−	0.0277864i
$962$	−3.92194			−0.126448
$963$	−8.20343	−	25.2476i	−0.264352	−	0.813592i
$964$	−25.6041	+	78.8014i	−0.824654	+	2.53802i
$965$	−47.3641	+	34.4120i	−1.52470	+	1.10776i
$966$	40.4299			1.30081
$967$	−4.99659			−0.160679			−0.0803397	−	0.996768i	$-0.525601\pi$
$967$	−4.99659			−0.160679			−0.0803397	+	0.996768i	$0.525601\pi$
$968$	20.7209	−	15.0546i	0.665994	−	0.483873i
$969$	−6.10252	−	4.43374i	−0.196041	−	0.142432i
$970$	−3.28227	−	2.38471i	−0.105387	−	0.0765683i
$971$	−12.5553	−	38.6413i	−0.402919	−	1.24006i	−0.922620	−	0.385710i	$-0.873957\pi$
$971$	−12.5553	−	38.6413i	−0.402919	−	1.24006i	0.519701	−	0.854348i	$-0.326043\pi$
$972$	−40.9969	+	29.7860i	−1.31498	+	0.955385i
$973$	−2.06677	−	6.36087i	−0.0662576	−	0.203920i
$974$	−6.95418	+	21.4028i	−0.222826	+	0.685789i
$975$	−15.2844	−	11.1048i	−0.489492	−	0.355637i
$976$	−1.23126	+	3.78943i	−0.0394117	+	0.121297i
$977$	2.99036	−	9.20337i	0.0956699	−	0.294442i	−0.891758	−	0.452513i	$-0.850528\pi$
$977$	2.99036	−	9.20337i	0.0956699	−	0.294442i	0.987428	+	0.158071i	$0.0505276\pi$
$978$	−88.6496	−	64.4077i	−2.83470	−	2.05953i
$979$	−2.78721	+	8.57814i	−0.0890795	+	0.274158i
$980$	20.8092	+	64.0443i	0.664727	+	2.04582i
$981$	−14.2285	+	10.3376i	−0.454280	+	0.330054i
$982$	−3.76799	−	11.5967i	−0.120241	−	0.370065i
$983$	−39.7519	−	28.8815i	−1.26789	−	0.921176i	−0.268773	−	0.963203i	$-0.586618\pi$
$983$	−39.7519	−	28.8815i	−1.26789	−	0.921176i	−0.999116	+	0.0420275i	$0.986618\pi$
$984$	−23.7012	−	17.2199i	−0.755567	−	0.548952i
$985$	−62.2038	+	45.1937i	−1.98198	+	1.43999i
$986$	4.03974			0.128652
$987$	−0.759861			−0.0241866
$988$	12.8935	−	9.36766i	0.410196	−	0.298025i
$989$	18.0281	−	55.4847i	0.573259	−	1.76431i
$990$	4.75169	+	14.6242i	0.151019	+	0.464787i
$991$	−32.3502			−1.02764			−0.513818	−	0.857899i	$-0.671769\pi$
$991$	−32.3502			−1.02764			−0.513818	+	0.857899i	$0.671769\pi$
$992$	34.0256	−	0.472817i	1.08031	−	0.0150119i
$993$	−38.5076			−1.22200
$994$	0.452356	+	1.39221i	0.0143479	+	0.0441582i
$995$	−19.5658	+	60.2173i	−0.620277	+	1.90902i
$996$	18.5151	−	13.4520i	0.586674	−	0.426243i
$997$	−47.5686			−1.50651			−0.753256	−	0.657727i	$-0.771518\pi$
$997$	−47.5686			−1.50651			−0.753256	+	0.657727i	$0.771518\pi$
$998$	−73.9865			−2.34200
$999$	−3.84241	+	2.79167i	−0.121568	+	0.0883246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.11	✓	48
31.8	even	5	inner	403.2.k.d.287.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.11	✓	48	1.1	even	1	trivial
403.2.k.d.287.11	yes	48	31.8	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.700746 + 2.15667i) q^{2} +(-0.672668 + 2.07026i) q^{3} +(-2.54216 + 1.84699i) q^{4} -3.69852 q^{5} -4.93624 q^{6} +(0.888338 - 0.645416i) q^{7} +(-2.09561 - 1.52255i) q^{8} +(-1.40643 - 1.02183i) q^{9} +O(q^{10})\)	\(q+(0.700746 + 2.15667i) q^{2} +(-0.672668 + 2.07026i) q^{3} +(-2.54216 + 1.84699i) q^{4} -3.69852 q^{5} -4.93624 q^{6} +(0.888338 - 0.645416i) q^{7} +(-2.09561 - 1.52255i) q^{8} +(-1.40643 - 1.02183i) q^{9} +(-2.59172 - 7.97650i) q^{10} +(0.853209 - 0.619892i) q^{11} +(-2.11371 - 6.50534i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(2.01445 + 1.46358i) q^{14} +(2.48787 - 7.65689i) q^{15} +(-0.126889 + 0.390525i) q^{16} +(0.552744 + 0.401592i) q^{17} +(1.21821 - 3.74927i) q^{18} +(1.56729 + 4.82362i) q^{19} +(9.40223 - 6.83112i) q^{20} +(0.738620 + 2.27324i) q^{21} +(1.93479 + 1.40571i) q^{22} +(-6.03452 - 4.38434i) q^{23} +(4.56171 - 3.31428i) q^{24} +8.67906 q^{25} -2.26766 q^{26} +(-2.22168 + 1.61414i) q^{27} +(-1.06622 + 3.28150i) q^{28} +(-0.805733 - 2.47979i) q^{29} +18.2568 q^{30} +(-5.56723 + 0.0773616i) q^{31} -6.11177 q^{32} +(0.709411 + 2.18334i) q^{33} +(-0.478770 + 1.47350i) q^{34} +(-3.28554 + 2.38708i) q^{35} +5.46270 q^{36} +1.72951 q^{37} +(-9.30471 + 6.76027i) q^{38} +(-1.76107 - 1.27949i) q^{39} +(7.75064 + 5.63117i) q^{40} +(-1.60556 - 4.94139i) q^{41} +(-4.38505 + 3.18593i) q^{42} +(2.41693 + 7.43854i) q^{43} +(-1.02406 + 3.15173i) q^{44} +(5.20173 + 3.77928i) q^{45} +(5.22692 - 16.0868i) q^{46} +(-0.0982375 + 0.302344i) q^{47} +(-0.723133 - 0.525387i) q^{48} +(-1.79054 + 5.51070i) q^{49} +(6.08181 + 18.7179i) q^{50} +(-1.20321 + 0.874185i) q^{51} +(-0.971019 - 2.98849i) q^{52} +(7.09673 + 5.15608i) q^{53} +(-5.03800 - 3.66032i) q^{54} +(-3.15561 + 2.29268i) q^{55} -2.84428 q^{56} -11.0404 q^{57} +(4.78349 - 3.47541i) q^{58} +(0.691656 - 2.12870i) q^{59} +(7.81761 + 24.0601i) q^{60} +9.70342 q^{61} +(-4.06805 - 11.9525i) q^{62} -1.90890 q^{63} +(-4.02902 - 12.4000i) q^{64} +(1.14291 - 3.51750i) q^{65} +(-4.21164 + 3.05994i) q^{66} +1.01091 q^{67} -2.14690 q^{68} +(13.1359 - 9.54382i) q^{69} +(-7.45049 - 5.41309i) q^{70} +(0.475616 + 0.345555i) q^{71} +(1.39154 + 4.28272i) q^{72} +(-13.5076 + 9.81386i) q^{73} +(1.21195 + 3.72999i) q^{74} +(-5.83812 + 17.9679i) q^{75} +(-12.8935 - 9.36766i) q^{76} +(0.357850 - 1.10135i) q^{77} +(1.52538 - 4.69464i) q^{78} +(2.50362 + 1.81899i) q^{79} +(0.469303 - 1.44436i) q^{80} +(-3.45887 - 10.6453i) q^{81} +(9.53189 - 6.92532i) q^{82} +(1.03392 + 3.18208i) q^{83} +(-6.07634 - 4.41472i) q^{84} +(-2.04434 - 1.48530i) q^{85} +(-14.3488 + 10.4250i) q^{86} +5.67580 q^{87} -2.73180 q^{88} +(-6.91905 + 5.02699i) q^{89} +(-4.50558 + 13.8667i) q^{90} +(0.339315 + 1.04430i) q^{91} +23.4385 q^{92} +(3.58473 - 11.5776i) q^{93} -0.720897 q^{94} +(-5.79666 - 17.8403i) q^{95} +(4.11119 - 12.6529i) q^{96} +(0.391352 - 0.284334i) q^{97} -13.1395 q^{98} -1.83341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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