LMFDB - Embedded newform 273.2.t.d.205.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.10
Root			$2.50900i$ of defining polynomial
Character	$\chi$	$=$	273.205
Dual form			273.2.t.d.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.50900i q^{2} +(0.500000 - 0.866025i) q^{3} -4.29509 q^{4} +(-2.97008 - 1.71478i) q^{5} +(2.17286 + 1.25450i) q^{6} +(-0.0473512 - 2.64533i) q^{7} -5.75840i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+2.50900i q^{2} +(0.500000 - 0.866025i) q^{3} -4.29509 q^{4} +(-2.97008 - 1.71478i) q^{5} +(2.17286 + 1.25450i) q^{6} +(-0.0473512 - 2.64533i) q^{7} -5.75840i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.30238 - 7.45195i) q^{10} +(-4.35178 - 2.51250i) q^{11} +(-2.14755 + 3.71966i) q^{12} +(0.135561 + 3.60300i) q^{13} +(6.63713 - 0.118804i) q^{14} +(-2.97008 + 1.71478i) q^{15} +5.85764 q^{16} +0.199310 q^{17} +(2.17286 - 1.25450i) q^{18} +(3.99823 - 2.30838i) q^{19} +(12.7568 + 7.36513i) q^{20} +(-2.31460 - 1.28166i) q^{21} +(6.30387 - 10.9186i) q^{22} -7.52372 q^{23} +(-4.98692 - 2.87920i) q^{24} +(3.38093 + 5.85594i) q^{25} +(-9.03994 + 0.340122i) q^{26} -1.00000 q^{27} +(0.203378 + 11.3619i) q^{28} +(1.58334 + 2.74243i) q^{29} +(-4.30238 - 7.45195i) q^{30} +(-3.65876 + 2.11239i) q^{31} +3.18005i q^{32} +(-4.35178 + 2.51250i) q^{33} +0.500070i q^{34} +(-4.39551 + 7.93804i) q^{35} +(2.14755 + 3.71966i) q^{36} -9.11903i q^{37} +(5.79173 + 10.0316i) q^{38} +(3.18807 + 1.68410i) q^{39} +(-9.87437 + 17.1029i) q^{40} +(4.67486 - 2.69903i) q^{41} +(3.21568 - 5.80733i) q^{42} +(1.27860 - 2.21461i) q^{43} +(18.6913 + 10.7914i) q^{44} +3.42956i q^{45} -18.8770i q^{46} +(6.19804 + 3.57844i) q^{47} +(2.92882 - 5.07287i) q^{48} +(-6.99552 + 0.250519i) q^{49} +(-14.6926 + 8.48276i) q^{50} +(0.0996552 - 0.172608i) q^{51} +(-0.582245 - 15.4752i) q^{52} +(-0.215922 - 0.373988i) q^{53} -2.50900i q^{54} +(8.61676 + 14.9247i) q^{55} +(-15.2328 + 0.272667i) q^{56} -4.61676i q^{57} +(-6.88077 + 3.97261i) q^{58} -0.838256i q^{59} +(12.7568 - 7.36513i) q^{60} +(1.33262 + 2.30816i) q^{61} +(-5.29999 - 9.17985i) q^{62} +(-2.26725 + 1.36367i) q^{63} +3.73654 q^{64} +(5.77572 - 10.9337i) q^{65} +(-6.30387 - 10.9186i) q^{66} +(-9.67775 - 5.58745i) q^{67} -0.856057 q^{68} +(-3.76186 + 6.51573i) q^{69} +(-19.9166 - 11.0284i) q^{70} +(-4.95582 - 2.86124i) q^{71} +(-4.98692 + 2.87920i) q^{72} +(2.73161 - 1.57710i) q^{73} +22.8797 q^{74} +6.76186 q^{75} +(-17.1728 + 9.91470i) q^{76} +(-6.44032 + 11.6308i) q^{77} +(-4.22542 + 7.99888i) q^{78} +(2.25566 - 3.90692i) q^{79} +(-17.3977 - 10.0446i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.77187 + 11.7292i) q^{82} -14.7167i q^{83} +(9.94141 + 5.50483i) q^{84} +(-0.591968 - 0.341773i) q^{85} +(5.55645 + 3.20802i) q^{86} +3.16669 q^{87} +(-14.4680 + 25.0593i) q^{88} +2.34608i q^{89} -8.60477 q^{90} +(9.52470 - 0.529209i) q^{91} +32.3151 q^{92} +4.22478i q^{93} +(-8.97832 + 15.5509i) q^{94} -15.8334 q^{95} +(2.75400 + 1.59002i) q^{96} +(-5.02047 - 2.89857i) q^{97} +(-0.628552 - 17.5518i) q^{98} +5.02500i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			2.50900i			1.77413i	0.461642	+	0.887066i	$0.347260\pi$
$2$			2.50900i			1.77413i	−0.461642	+	0.887066i	$0.652740\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−4.29509			−2.14755
$5$	−2.97008	−	1.71478i	−1.32826	−	0.766872i	−0.343231	−	0.939251i	$-0.611521\pi$
$5$	−2.97008	−	1.71478i	−1.32826	−	0.766872i	−0.985031	+	0.172379i	$0.944855\pi$
$6$	2.17286	+	1.25450i	0.887066	+	0.512148i
$7$	−0.0473512	−	2.64533i	−0.0178971	−	0.999840i
$7$	−0.0473512	−	2.64533i	−0.0178971	−	0.999840i
$8$		−	5.75840i		−	2.03590i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	4.30238	−	7.45195i	1.36053	−	2.35651i
$11$	−4.35178	−	2.51250i	−1.31211	−	0.757547i	−0.329665	−	0.944098i	$-0.606936\pi$
$11$	−4.35178	−	2.51250i	−1.31211	−	0.757547i	−0.982445	+	0.186551i	$0.940269\pi$
$12$	−2.14755	+	3.71966i	−0.619943	+	1.07377i
$13$	0.135561	+	3.60300i	0.0375977	+	0.999293i
$13$	0.135561	+	3.60300i	0.0375977	+	0.999293i
$14$	6.63713	−	0.118804i	1.77385	−	0.0317518i
$15$	−2.97008	+	1.71478i	−0.766872	+	0.442754i
$16$	5.85764			1.46441
$17$	0.199310			0.0483399			0.0241699	−	0.999708i	$-0.492306\pi$
$17$	0.199310			0.0483399			0.0241699	+	0.999708i	$0.492306\pi$
$18$	2.17286	−	1.25450i	0.512148	−	0.295689i
$19$	3.99823	−	2.30838i	0.917256	−	0.529578i	0.0344977	−	0.999405i	$-0.489017\pi$
$19$	3.99823	−	2.30838i	0.917256	−	0.529578i	0.882759	+	0.469827i	$0.155684\pi$
$20$	12.7568	+	7.36513i	2.85250	+	1.64689i
$21$	−2.31460	−	1.28166i	−0.505086	−	0.279680i
$22$	6.30387	−	10.9186i	1.34399	−	2.32786i
$23$	−7.52372			−1.56880			−0.784402	−	0.620253i	$-0.787030\pi$
$23$	−7.52372			−1.56880			−0.784402	+	0.620253i	$0.787030\pi$
$24$	−4.98692	−	2.87920i	−1.01795	−	0.587714i
$25$	3.38093	+	5.85594i	0.676186	+	1.17119i
$26$	−9.03994	+	0.340122i	−1.77288	+	0.0667034i
$27$	−1.00000			−0.192450
$28$	0.203378	+	11.3619i	0.0384348	+	2.14720i
$29$	1.58334	+	2.74243i	0.294020	+	0.509257i	0.974756	−	0.223271i	$-0.0716736\pi$
$29$	1.58334	+	2.74243i	0.294020	+	0.509257i	−0.680737	+	0.732528i	$0.738340\pi$
$30$	−4.30238	−	7.45195i	−0.785504	−	1.36053i
$31$	−3.65876	+	2.11239i	−0.657133	+	0.379396i	−0.791184	−	0.611578i	$-0.790535\pi$
$31$	−3.65876	+	2.11239i	−0.657133	+	0.379396i	0.134051	+	0.990974i	$0.457202\pi$
$32$			3.18005i			0.562158i
$33$	−4.35178	+	2.51250i	−0.757547	+	0.437370i
$34$			0.500070i			0.0857613i
$35$	−4.39551	+	7.93804i	−0.742977	+	1.34177i
$36$	2.14755	+	3.71966i	0.357924	+	0.619943i
$37$		−	9.11903i		−	1.49916i	−0.661914	−	0.749580i	$-0.730256\pi$
$37$		−	9.11903i		−	1.49916i	0.661914	−	0.749580i	$-0.269744\pi$
$38$	5.79173	+	10.0316i	0.939542	+	1.62733i
$39$	3.18807	+	1.68410i	0.510500	+	0.269672i
$40$	−9.87437	+	17.1029i	−1.56128	+	2.70421i
$41$	4.67486	−	2.69903i	0.730090	−	0.421517i	−0.0883653	−	0.996088i	$-0.528164\pi$
$41$	4.67486	−	2.69903i	0.730090	−	0.421517i	0.818455	+	0.574571i	$0.194831\pi$
$42$	3.21568	−	5.80733i	0.496190	−	0.896090i
$43$	1.27860	−	2.21461i	0.194985	−	0.337724i	−0.751910	−	0.659265i	$-0.770867\pi$
$43$	1.27860	−	2.21461i	0.194985	−	0.337724i	0.946896	+	0.321541i	$0.104201\pi$
$44$	18.6913	+	10.7914i	2.81782	+	1.62687i
$45$			3.42956i			0.511248i
$46$		−	18.8770i		−	2.78327i
$47$	6.19804	+	3.57844i	0.904077	+	0.521969i	0.878521	−	0.477704i	$-0.158531\pi$
$47$	6.19804	+	3.57844i	0.904077	+	0.521969i	0.0255566	+	0.999673i	$0.491864\pi$
$48$	2.92882	−	5.07287i	0.422739	−	0.732205i
$49$	−6.99552	+	0.250519i	−0.999359	+	0.0357884i
$50$	−14.6926	+	8.48276i	−2.07784	+	1.19964i
$51$	0.0996552	−	0.172608i	0.0139545	−	0.0241699i
$52$	−0.582245	−	15.4752i	−0.0807429	−	2.14603i
$53$	−0.215922	−	0.373988i	−0.0296592	−	0.0513712i	0.850815	−	0.525466i	$-0.176109\pi$
$53$	−0.215922	−	0.373988i	−0.0296592	−	0.0513712i	−0.880474	+	0.474094i	$0.842776\pi$
$54$		−	2.50900i		−	0.341432i
$55$	8.61676	+	14.9247i	1.16188	+	2.01244i
$56$	−15.2328	+	0.272667i	−2.03557	+	0.0364366i
$57$		−	4.61676i		−	0.611504i
$58$	−6.88077	+	3.97261i	−0.903489	+	0.521630i
$59$		−	0.838256i		−	0.109132i	−0.998510	−	0.0545658i	$-0.982623\pi$
$59$		−	0.838256i		−	0.109132i	0.998510	−	0.0545658i	$-0.0173775\pi$
$60$	12.7568	−	7.36513i	1.64689	−	0.950835i
$61$	1.33262	+	2.30816i	0.170624	+	0.295530i	0.938638	−	0.344903i	$-0.112088\pi$
$61$	1.33262	+	2.30816i	0.170624	+	0.295530i	−0.768014	+	0.640433i	$0.778755\pi$
$62$	−5.29999	−	9.17985i	−0.673099	−	1.16584i
$63$	−2.26725	+	1.36367i	−0.285646	+	0.171806i
$64$	3.73654			0.467068
$65$	5.77572	−	10.9337i	0.716390	−	1.35616i
$66$	−6.30387	−	10.9186i	−0.775952	−	1.34399i
$67$	−9.67775	−	5.58745i	−1.18233	−	0.682616i	−0.225774	−	0.974180i	$-0.572491\pi$
$67$	−9.67775	−	5.58745i	−1.18233	−	0.682616i	−0.956551	+	0.291564i	$0.905824\pi$
$68$	−0.856057			−0.103812
$69$	−3.76186	+	6.51573i	−0.452875	+	0.784402i
$70$	−19.9166	−	11.0284i	−2.38048	−	1.31814i
$71$	−4.95582	−	2.86124i	−0.588148	−	0.339567i	0.176217	−	0.984351i	$-0.443614\pi$
$71$	−4.95582	−	2.86124i	−0.588148	−	0.339567i	−0.764365	+	0.644784i	$0.776947\pi$
$72$	−4.98692	+	2.87920i	−0.587714	+	0.339317i
$73$	2.73161	−	1.57710i	0.319711	−	0.184585i	−0.331553	−	0.943437i	$-0.607573\pi$
$73$	2.73161	−	1.57710i	0.319711	−	0.184585i	0.651264	+	0.758851i	$0.274239\pi$
$74$	22.8797			2.65971
$75$	6.76186			0.780792
$76$	−17.1728	+	9.91470i	−1.96985	+	1.13729i
$77$	−6.44032	+	11.6308i	−0.733943	+	1.32546i
$78$	−4.22542	+	7.99888i	−0.478434	+	0.905695i
$79$	2.25566	−	3.90692i	0.253782	−	0.439563i	−0.710782	−	0.703412i	$-0.751659\pi$
$79$	2.25566	−	3.90692i	0.253782	−	0.439563i	0.964564	+	0.263849i	$0.0849921\pi$
$80$	−17.3977	−	10.0446i	−1.94512	−	1.12302i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.77187	+	11.7292i	0.747828	+	1.29528i
$83$		−	14.7167i		−	1.61537i	−0.589613	−	0.807686i	$-0.700720\pi$
$83$		−	14.7167i		−	1.61537i	0.589613	−	0.807686i	$-0.299280\pi$
$84$	9.94141	+	5.50483i	1.08470	+	0.600627i
$85$	−0.591968	−	0.341773i	−0.0642080	−	0.0370705i
$86$	5.55645	+	3.20802i	0.599168	+	0.345930i
$87$	3.16669			0.339505
$88$	−14.4680	+	25.0593i	−1.54229	+	2.67133i
$89$			2.34608i			0.248684i	0.992239	+	0.124342i	$0.0396820\pi$
$89$			2.34608i			0.248684i	−0.992239	+	0.124342i	$0.960318\pi$
$90$	−8.60477			−0.907022
$91$	9.52470	−	0.529209i	0.998460	−	0.0554761i
$92$	32.3151			3.36908
$93$			4.22478i			0.438089i
$94$	−8.97832	+	15.5509i	−0.926043	+	1.60395i
$95$	−15.8334			−1.62448
$96$	2.75400	+	1.59002i	0.281079	+	0.162281i
$97$	−5.02047	−	2.89857i	−0.509751	−	0.294305i	0.222980	−	0.974823i	$-0.428421\pi$
$97$	−5.02047	−	2.89857i	−0.509751	−	0.294305i	−0.732731	+	0.680518i	$0.761755\pi$
$98$	−0.628552	−	17.5518i	−0.0634934	−	1.77300i
$99$			5.02500i			0.505031i
$100$	−14.5214	−	25.1518i	−1.45214	−	2.51518i
$101$	2.10772	−	3.65067i	0.209726	−	0.363256i	−0.741902	−	0.670508i	$-0.766076\pi$
$101$	2.10772	−	3.65067i	0.209726	−	0.363256i	0.951628	+	0.307252i	$0.0994095\pi$
$102$	0.433074	+	0.250035i	0.0428807	+	0.0247572i
$103$	−2.11287	+	3.65960i	−0.208187	+	0.360591i	−0.951144	−	0.308749i	$-0.900090\pi$
$103$	−2.11287	+	3.65960i	−0.208187	+	0.360591i	0.742956	+	0.669340i	$0.233423\pi$
$104$	20.7475	−	0.780612i	2.03446	−	0.0765453i
$105$	4.67679	+	7.77565i	0.456408	+	0.758825i
$106$	0.938336	−	0.541749i	0.0911393	−	0.0526193i
$107$	4.65458			0.449975			0.224988	−	0.974362i	$-0.427766\pi$
$107$	4.65458			0.449975			0.224988	+	0.974362i	$0.427766\pi$
$108$	4.29509			0.413296
$109$	−0.524968	+	0.303090i	−0.0502828	+	0.0290308i	−0.524931	−	0.851145i	$-0.675909\pi$
$109$	−0.524968	+	0.303090i	−0.0502828	+	0.0290308i	0.474648	+	0.880176i	$0.342575\pi$
$110$	−37.4460	+	21.6195i	−3.57034	+	2.06134i
$111$	−7.89731	−	4.55951i	−0.749580	−	0.432770i
$112$	−0.277366	−	15.4954i	−0.0262086	−	1.46418i
$113$	−4.15517	+	7.19697i	−0.390886	+	0.677034i	−0.992567	−	0.121703i	$-0.961165\pi$
$113$	−4.15517	+	7.19697i	−0.390886	+	0.677034i	0.601681	+	0.798737i	$0.294498\pi$
$114$	11.5835			1.08489
$115$	22.3461	+	12.9015i	2.08378	+	1.20307i
$116$	−6.80061	−	11.7790i	−0.631421	−	1.09365i
$117$	3.05251	−	1.91890i	0.282205	−	0.177402i
$118$	2.10319			0.193614
$119$	−0.00943758	−	0.527241i	−0.000865142	−	0.0483321i
$120$	9.87437	+	17.1029i	0.901403	+	1.56128i
$121$	7.12531	+	12.3414i	0.647755	+	1.12195i
$122$	−5.79118	+	3.34354i	−0.524309	+	0.302710i
$123$		−	5.39806i		−	0.486726i
$124$	15.7147	−	9.07290i	1.41122	−	0.814771i
$125$		−	6.04239i		−	0.540448i
$126$	−3.42145	−	5.68852i	−0.304807	−	0.506774i
$127$	5.03862	+	8.72715i	0.447105	+	0.774409i	0.998196	−	0.0600359i	$-0.0191215\pi$
$127$	5.03862	+	8.72715i	0.447105	+	0.774409i	−0.551091	+	0.834445i	$0.685788\pi$
$128$			15.7351i			1.39080i
$129$	−1.27860	−	2.21461i	−0.112575	−	0.194985i
$130$	27.4326	+	14.4913i	2.40600	+	1.27097i
$131$	5.52188	−	9.56417i	0.482449	−	0.835626i	−0.517348	−	0.855775i	$-0.673081\pi$
$131$	5.52188	−	9.56417i	0.482449	−	0.835626i	0.999797	+	0.0201493i	$0.00641417\pi$
$132$	18.6913	−	10.7914i	1.62687	−	0.939273i
$133$	−6.29574	−	10.4673i	−0.545910	−	0.907632i
$134$	14.0189	−	24.2815i	1.21105	−	2.09760i
$135$	2.97008	+	1.71478i	0.255624	+	0.147585i
$136$		−	1.14771i		−	0.0984151i
$137$			11.3738i			0.971730i	0.874034	+	0.485865i	$0.161495\pi$
$137$			11.3738i			0.971730i	−0.874034	+	0.485865i	$0.838505\pi$
$138$	−16.3480	−	9.43851i	−1.39163	−	0.803459i
$139$	8.76143	−	15.1752i	0.743135	−	1.28715i	−0.207926	−	0.978145i	$-0.566671\pi$
$139$	8.76143	−	15.1752i	0.743135	−	1.28715i	0.951061	−	0.309003i	$-0.0999954\pi$
$140$	18.8791	−	34.0946i	1.59558	−	2.88152i
$141$	6.19804	−	3.57844i	0.521969	−	0.301359i
$142$	7.17887	−	12.4342i	0.602437	−	1.04345i
$143$	8.46261	−	16.0201i	0.707679	−	1.33966i
$144$	−2.92882	−	5.07287i	−0.244068	−	0.422739i
$145$		−	10.8603i		−	0.901902i
$146$	3.95694	+	6.85362i	0.327479	+	0.567209i
$147$	−3.28080	+	6.18355i	−0.270596	+	0.510011i
$148$			39.1671i			3.21951i
$149$	10.2864	−	5.93887i	0.842696	−	0.486531i	−0.0154836	−	0.999880i	$-0.504929\pi$
$149$	10.2864	−	5.93887i	0.842696	−	0.486531i	0.858180	+	0.513349i	$0.171595\pi$
$150$			16.9655i			1.38523i
$151$	−11.5380	+	6.66145i	−0.938946	+	0.542101i	−0.889630	−	0.456682i	$-0.849038\pi$
$151$	−11.5380	+	6.66145i	−0.938946	+	0.542101i	−0.0493164	+	0.998783i	$0.515704\pi$
$152$	−13.2926	−	23.0234i	−1.07817	−	1.86744i
$153$	−0.0996552	−	0.172608i	−0.00805664	−	0.0139545i
$154$	−29.1818	−	16.1588i	−2.35154	−	1.30211i
$155$	14.4891			1.16379
$156$	−13.6931	−	7.23338i	−1.09632	−	0.579134i
$157$	5.62062	+	9.73519i	0.448574	+	0.776953i	0.998293	−	0.0583963i	$-0.0185987\pi$
$157$	5.62062	+	9.73519i	0.448574	+	0.776953i	−0.549719	+	0.835349i	$0.685265\pi$
$158$	9.80248	+	5.65947i	0.779844	+	0.450243i
$159$	−0.431844			−0.0342474
$160$	5.45307	−	9.44500i	0.431103	−	0.746693i
$161$	0.356257	+	19.9027i	0.0280770	+	1.56855i
$162$	−2.17286	−	1.25450i	−0.170716	−	0.0985629i
$163$	3.14511	−	1.81583i	0.246344	−	0.142227i	−0.371745	−	0.928335i	$-0.621240\pi$
$163$	3.14511	−	1.81583i	0.246344	−	0.142227i	0.618089	+	0.786108i	$0.287907\pi$
$164$	−20.0789	+	11.5926i	−1.56790	+	0.905228i
$165$	17.2335			1.34163
$166$	36.9243			2.86588
$167$	−8.95880	+	5.17237i	−0.693253	+	0.400250i	−0.804829	−	0.593506i	$-0.797743\pi$
$167$	−8.95880	+	5.17237i	−0.693253	+	0.400250i	0.111577	+	0.993756i	$0.464410\pi$
$168$	−7.38028	+	13.3284i	−0.569401	+	1.02831i
$169$	−12.9632	+	0.976850i	−0.997173	+	0.0751423i
$170$	0.857510	−	1.48525i	0.0657680	−	0.113913i
$171$	−3.99823	−	2.30838i	−0.305752	−	0.176526i
$172$	−5.49172	+	9.51194i	−0.418740	+	0.725279i
$173$	2.29902	+	3.98202i	0.174791	+	0.302747i	0.940089	−	0.340929i	$-0.110742\pi$
$173$	2.29902	+	3.98202i	0.174791	+	0.302747i	−0.765298	+	0.643676i	$0.777408\pi$
$174$			7.94523i			0.602326i
$175$	15.3308	−	9.22095i	1.15890	−	0.697038i
$176$	−25.4911	−	14.7173i	−1.92147	−	1.10936i
$177$	−0.725951	−	0.419128i	−0.0545658	−	0.0315036i
$178$	−5.88633			−0.441199
$179$	−0.453209	+	0.784982i	−0.0338745	+	0.0586723i	−0.882466	−	0.470377i	$-0.844118\pi$
$179$	−0.453209	+	0.784982i	−0.0338745	+	0.0586723i	0.848591	+	0.529049i	$0.177451\pi$
$180$		−	14.7303i		−	1.09793i
$181$	−18.9155			−1.40598			−0.702991	−	0.711199i	$-0.748152\pi$
$181$	−18.9155			−1.40598			−0.702991	+	0.711199i	$0.748152\pi$
$182$	1.32779	+	23.8975i	0.0984220	+	1.77140i
$183$	2.66523			0.197020
$184$			43.3245i			3.19393i
$185$	−15.6371	+	27.0843i	−1.14966	+	1.99128i
$186$	−10.6000			−0.777228
$187$	−0.867354	−	0.500767i	−0.0634272	−	0.0366197i
$188$	−26.6212	−	15.3697i	−1.94155	−	1.12095i
$189$	0.0473512	+	2.64533i	0.00344429	+	0.192419i
$190$		−	39.7261i		−	2.88203i
$191$	−7.70584	−	13.3469i	−0.557575	−	0.965749i	−0.997698	−	0.0678112i	$-0.978398\pi$
$191$	−7.70584	−	13.3469i	−0.557575	−	0.965749i	0.440123	−	0.897938i	$-0.354935\pi$
$192$	1.86827	−	3.23594i	0.134831	−	0.233534i
$193$	6.89839	+	3.98279i	0.496557	+	0.286688i	0.727291	−	0.686330i	$-0.240779\pi$
$193$	6.89839	+	3.98279i	0.496557	+	0.286688i	−0.230733	+	0.973017i	$0.574113\pi$
$194$	7.27252	−	12.5964i	0.522136	−	0.904366i
$195$	−6.58098	−	10.4688i	−0.471273	−	0.749683i
$196$	30.0464	−	1.07600i	2.14617	−	0.0768573i
$197$	−11.3638	+	6.56087i	−0.809634	+	0.467443i	−0.846829	−	0.531865i	$-0.821491\pi$
$197$	−11.3638	+	6.56087i	−0.809634	+	0.467443i	0.0371945	+	0.999308i	$0.488158\pi$
$198$	−12.6077			−0.895993
$199$	19.5203			1.38375			0.691877	−	0.722015i	$-0.256784\pi$
$199$	19.5203			1.38375			0.691877	+	0.722015i	$0.256784\pi$
$200$	33.7208	−	19.4687i	2.38442	−	1.37665i
$201$	−9.67775	+	5.58745i	−0.682616	+	0.394108i
$202$	9.15955	+	5.28827i	0.644464	+	0.372081i
$203$	7.17966	−	4.31832i	0.503913	−	0.303087i
$204$	−0.428028	+	0.741367i	−0.0299680	+	0.0519061i
$205$	−18.5129			−1.29300
$206$	−9.18195	−	5.30120i	−0.639737	−	0.369352i
$207$	3.76186	+	6.51573i	0.261467	+	0.452875i
$208$	0.794065	+	21.1051i	0.0550585	+	1.46337i
$209$	−23.1992			−1.60472
$210$	−19.5091	+	11.7341i	−1.34626	+	0.809728i
$211$	−11.9554	−	20.7074i	−0.823046	−	1.42556i	−0.903404	−	0.428791i	$-0.858940\pi$
$211$	−11.9554	−	20.7074i	−0.823046	−	1.42556i	0.0803582	−	0.996766i	$-0.474394\pi$
$212$	0.927405	+	1.60631i	0.0636944	+	0.110322i
$213$	−4.95582	+	2.86124i	−0.339567	+	0.196049i
$214$			11.6784i			0.798316i
$215$	−7.59512	+	4.38504i	−0.517983	+	0.299057i
$216$			5.75840i			0.391809i
$217$	5.76120	+	9.57860i	0.391096	+	0.650238i
$218$	−0.760454	−	1.31715i	−0.0515045	−	0.0892083i
$219$		−	3.15419i		−	0.213141i
$220$	−37.0098	−	64.1028i	−2.49520	−	4.32181i
$221$	0.0270186	+	0.718116i	0.00181747	+	0.0483057i
$222$	11.4398	−	19.8144i	0.767791	−	1.32985i
$223$	9.03870	−	5.21849i	0.605276	−	0.349456i	−0.165838	−	0.986153i	$-0.553033\pi$
$223$	9.03870	−	5.21849i	0.605276	−	0.349456i	0.771114	+	0.636697i	$0.219700\pi$
$224$	8.41226	−	0.150579i	0.562068	−	0.0100610i
$225$	3.38093	−	5.85594i	0.225395	−	0.390396i
$226$	−18.0572	−	10.4253i	−1.20115	−	0.693483i
$227$		−	9.90050i		−	0.657119i	−0.944483	−	0.328560i	$-0.893437\pi$
$227$		−	9.90050i		−	0.657119i	0.944483	−	0.328560i	$-0.106563\pi$
$228$			19.8294i			1.31323i
$229$	−13.6564	−	7.88453i	−0.902441	−	0.521025i	−0.0244498	−	0.999701i	$-0.507783\pi$
$229$	−13.6564	−	7.88453i	−0.902441	−	0.521025i	−0.877991	+	0.478676i	$0.841117\pi$
$230$	−32.3699	+	56.0663i	−2.13441	+	3.69690i
$231$	6.85245	+	11.3929i	0.450858	+	0.749598i
$232$	15.7920	−	9.11752i	1.03680	−	0.598595i
$233$	−0.952488	+	1.64976i	−0.0623996	+	0.108079i	−0.895538	−	0.444986i	$-0.853209\pi$
$233$	−0.952488	+	1.64976i	−0.0623996	+	0.108079i	0.833138	+	0.553065i	$0.186542\pi$
$234$	4.81452	+	7.65876i	0.314735	+	0.500669i
$235$	−12.2725	−	21.2565i	−0.800567	−	1.38662i
$236$			3.60039i			0.234365i
$237$	−2.25566	−	3.90692i	−0.146521	−	0.253782i
$238$	1.32285	−	0.0236789i	0.0857476	−	0.00153488i
$239$		−	26.3087i		−	1.70177i	−0.525352	−	0.850885i	$-0.676066\pi$
$239$		−	26.3087i		−	1.70177i	0.525352	−	0.850885i	$-0.323934\pi$
$240$	−17.3977	+	10.0446i	−1.12302	+	0.648373i
$241$		−	22.5867i		−	1.45494i	−0.686139	−	0.727470i	$-0.740696\pi$
$241$		−	22.5867i		−	1.45494i	0.686139	−	0.727470i	$-0.259304\pi$
$242$	−30.9646	+	17.8774i	−1.99048	+	1.14920i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.72371	−	9.91376i	−0.366423	−	0.634664i
$245$	21.2068	+	11.2517i	1.35486	+	0.718845i
$246$	13.5437			0.863517
$247$	8.85909	+	14.0927i	0.563691	+	0.896697i
$248$	12.1640	+	21.0686i	0.772412	+	1.33786i
$249$	−12.7451	−	7.35837i	−0.807686	−	0.466318i
$250$	15.1604			0.958827
$251$	14.4466	−	25.0222i	0.911859	−	1.57939i	0.100424	−	0.994945i	$-0.467980\pi$
$251$	14.4466	−	25.0222i	0.911859	−	1.57939i	0.811436	−	0.584442i	$-0.198686\pi$
$252$	9.73803	−	5.85709i	0.613438	−	0.368962i
$253$	32.7415	+	18.9033i	2.05844	+	1.18844i
$254$	−21.8964	+	12.6419i	−1.37390	+	0.793224i
$255$	−0.591968	+	0.341773i	−0.0370705	+	0.0214027i
$256$	−32.0063			−2.00039
$257$	16.0503			1.00119			0.500595	−	0.865682i	$-0.333115\pi$
$257$	16.0503			1.00119			0.500595	+	0.865682i	$0.333115\pi$
$258$	5.55645	−	3.20802i	0.345930	−	0.199723i
$259$	−24.1228	+	0.431797i	−1.49892	+	0.0268305i
$260$	−24.8073	+	46.9611i	−1.53848	+	2.91241i
$261$	1.58334	−	2.74243i	0.0980065	−	0.169752i
$262$	23.9965	+	13.8544i	1.48251	+	0.855928i
$263$	−7.23551	+	12.5323i	−0.446161	+	0.772773i	−0.998132	−	0.0610900i	$-0.980542\pi$
$263$	−7.23551	+	12.5323i	−0.446161	+	0.772773i	0.551972	+	0.833863i	$0.313876\pi$
$264$	14.4680	+	25.0593i	0.890442	+	1.54229i
$265$			1.48103i			0.0909791i
$266$	26.2625	−	15.7960i	1.61026	−	0.968516i
$267$	2.03177	+	1.17304i	0.124342	+	0.0717890i
$268$	41.5668	+	23.9986i	2.53910	+	1.46595i
$269$	16.2953			0.993542			0.496771	−	0.867882i	$-0.334519\pi$
$269$	16.2953			0.993542			0.496771	+	0.867882i	$0.334519\pi$
$270$	−4.30238	+	7.45195i	−0.261835	+	0.453511i
$271$			11.2296i			0.682153i	0.940036	+	0.341076i	$0.110791\pi$
$271$			11.2296i			0.682153i	−0.940036	+	0.341076i	$0.889209\pi$
$272$	1.16749			0.0707894
$273$	4.30404	−	8.51324i	0.260493	−	0.515245i
$274$	−28.5369			−1.72398
$275$		−	33.9783i		−	2.04897i
$276$	16.1575	−	27.9857i	0.972569	−	1.68454i
$277$	−19.2059			−1.15397			−0.576984	−	0.816755i	$-0.695771\pi$
$277$	−19.2059			−1.15397			−0.576984	+	0.816755i	$0.695771\pi$
$278$	38.0747	+	21.9825i	2.28357	+	1.31842i
$279$	3.65876	+	2.11239i	0.219044	+	0.126465i
$280$	45.7104	+	25.3111i	2.73172	+	1.51263i
$281$		−	21.4527i		−	1.27976i	−0.768474	−	0.639881i	$-0.778984\pi$
$281$		−	21.4527i		−	1.27976i	0.768474	−	0.639881i	$-0.221016\pi$
$282$	8.97832	+	15.5509i	0.534651	+	0.926043i
$283$	−4.10738	+	7.11419i	−0.244159	+	0.422895i	−0.961895	−	0.273420i	$-0.911845\pi$
$283$	−4.10738	+	7.11419i	−0.244159	+	0.422895i	0.717736	+	0.696315i	$0.245178\pi$
$284$	21.2857	+	12.2893i	1.26307	+	0.729236i
$285$	−7.91671	+	13.7121i	−0.468946	+	0.812238i
$286$	40.1944	+	21.2327i	2.37674	+	1.25552i
$287$	−7.36118	−	12.2387i	−0.434516	−	0.722429i
$288$	2.75400	−	1.59002i	0.162281	−	0.0936930i
$289$	−16.9603			−0.997663
$290$	27.2486			1.60009
$291$	−5.02047	+	2.89857i	−0.294305	+	0.169917i
$292$	−11.7325	+	6.77378i	−0.686594	+	0.396405i
$293$	8.05762	+	4.65207i	0.470731	+	0.271777i	0.716546	−	0.697540i	$-0.245722\pi$
$293$	8.05762	+	4.65207i	0.470731	+	0.271777i	−0.245815	+	0.969317i	$0.579055\pi$
$294$	−15.5146	−	8.23154i	−0.904827	−	0.480073i
$295$	−1.43742	+	2.48969i	−0.0836901	+	0.144955i
$296$	−52.5110			−3.05214
$297$	4.35178	+	2.51250i	0.252516	+	0.145790i
$298$	14.9006	+	25.8086i	0.863170	+	1.49505i
$299$	−1.01992	−	27.1080i	−0.0589835	−	1.56769i
$300$	−29.0428			−1.67679
$301$	−5.91890	−	3.27746i	−0.341160	−	0.188910i
$302$	−16.7136	−	28.9488i	−0.961759	−	1.66582i
$303$	−2.10772	−	3.65067i	−0.121085	−	0.209726i
$304$	23.4202	−	13.5216i	1.34324	−	0.775520i
$305$		−	9.14057i		−	0.523388i
$306$	0.433074	−	0.250035i	0.0247572	−	0.0142936i
$307$			17.3759i			0.991695i	0.868410	+	0.495848i	$0.165143\pi$
$307$			17.3759i			0.991695i	−0.868410	+	0.495848i	$0.834857\pi$
$308$	27.6618	−	49.9556i	1.57618	−	2.84648i
$309$	2.11287	+	3.65960i	0.120197	+	0.208187i
$310$			36.3532i			2.06472i
$311$	−2.53895	−	4.39760i	−0.143971	−	0.249365i	0.785018	−	0.619473i	$-0.212654\pi$
$311$	−2.53895	−	4.39760i	−0.143971	−	0.249365i	−0.928988	+	0.370109i	$0.879320\pi$
$312$	9.69773	−	18.3582i	0.549026	−	1.03933i
$313$	−3.64621	+	6.31543i	−0.206096	+	0.356969i	−0.950481	−	0.310781i	$-0.899409\pi$
$313$	−3.64621	+	6.31543i	−0.206096	+	0.356969i	0.744385	+	0.667750i	$0.232743\pi$
$314$	−24.4256	+	14.1021i	−1.37842	+	0.795830i
$315$	9.07230	−	0.162394i	0.511166	−	0.00914984i
$316$	−9.68829	+	16.7806i	−0.545009	+	0.943983i
$317$	−20.5617	−	11.8713i	−1.15486	−	0.666757i	−0.204791	−	0.978806i	$-0.565652\pi$
$317$	−20.5617	−	11.8713i	−1.15486	−	0.666757i	−0.950066	+	0.312048i	$0.898985\pi$
$318$		−	1.08350i		−	0.0607595i
$319$		−	15.9126i		−	0.890935i
$320$	−11.0978	−	6.40734i	−0.620388	−	0.358181i
$321$	2.32729	−	4.03099i	0.129897	−	0.224988i
$322$	−49.9359	+	0.893849i	−2.78282	+	0.0498123i
$323$	0.796888	−	0.460084i	0.0443401	−	0.0255997i
$324$	2.14755	−	3.71966i	0.119308	−	0.206648i
$325$	−20.6406	+	12.9753i	−1.14494	+	0.719742i
$326$	4.55593	+	7.89110i	0.252330	+	0.437048i
$327$			0.606180i			0.0335219i
$328$	−15.5421	−	26.9197i	−0.858167	−	1.48639i
$329$	9.17266	−	16.5653i	0.505705	−	0.913274i
$330$			43.2389i			2.38023i
$331$	−0.0199341	+	0.0115089i	−0.00109568	+	0.000632589i	−0.500548	−	0.865709i	$-0.666868\pi$
$331$	−0.0199341	+	0.0115089i	−0.00109568	+	0.000632589i	0.499452	+	0.866342i	$0.333535\pi$
$332$			63.2097i			3.46909i
$333$	−7.89731	+	4.55951i	−0.432770	+	0.249860i
$334$	−12.9775	−	22.4777i	−0.710096	−	1.22992i
$335$	19.1625	+	33.1904i	1.04696	+	1.81338i
$336$	−13.5581	−	7.50748i	−0.739654	−	0.409567i
$337$	12.3103			0.670583			0.335291	−	0.942114i	$-0.391165\pi$
$337$	12.3103			0.670583			0.335291	+	0.942114i	$0.391165\pi$
$338$	−2.45092	−	32.5248i	−0.133312	−	1.76912i
$339$	4.15517	+	7.19697i	0.225678	+	0.390886i
$340$	2.54256	+	1.46795i	0.137890	+	0.0796106i
$341$	21.2295			1.14964
$342$	5.79173	−	10.0316i	0.313181	−	0.542445i
$343$	0.993950	+	18.4936i	0.0536683	+	0.998559i
$344$	−12.7526	−	7.36270i	−0.687573	−	0.396970i
$345$	22.3461	−	12.9015i	1.20307	−	0.694594i
$346$	−9.99089	+	5.76824i	−0.537114	+	0.310103i
$347$	31.5302			1.69263			0.846315	−	0.532683i	$-0.178816\pi$
$347$	31.5302			1.69263			0.846315	+	0.532683i	$0.178816\pi$
$348$	−13.6012			−0.729102
$349$	1.69290	−	0.977398i	0.0906191	−	0.0523189i	−0.454006	−	0.890999i	$-0.650005\pi$
$349$	1.69290	−	0.977398i	0.0906191	−	0.0523189i	0.544625	+	0.838680i	$0.316672\pi$
$350$	23.1354	+	38.4650i	1.23664	+	2.05604i
$351$	−0.135561	−	3.60300i	−0.00723569	−	0.192314i
$352$	7.98986	−	13.8388i	0.425861	−	0.737613i
$353$	−14.1302	−	8.15806i	−0.752073	−	0.434210i	0.0743694	−	0.997231i	$-0.476306\pi$
$353$	−14.1302	−	8.15806i	−0.752073	−	0.434210i	−0.826442	+	0.563021i	$0.809639\pi$
$354$	1.05159	−	1.82141i	0.0558916	−	0.0968070i
$355$	9.81280	+	16.9963i	0.520809	+	0.902068i
$356$		−	10.0766i		−	0.534061i
$357$	−0.461323	−	0.255447i	−0.0244158	−	0.0135197i
$358$	−1.96952	−	1.13710i	−0.104092	−	0.0600978i
$359$	19.2335	+	11.1044i	1.01510	+	0.586070i	0.912682	−	0.408671i	$-0.134008\pi$
$359$	19.2335	+	11.1044i	1.01510	+	0.586070i	0.102421	+	0.994741i	$0.467341\pi$
$360$	19.7487			1.04085
$361$	1.15722	−	2.00436i	0.0609062	−	0.105493i
$362$		−	47.4592i		−	2.49440i
$363$	14.2506			0.747963
$364$	−40.9095	+	2.27300i	−2.14424	+	0.119138i
$365$	−10.8175			−0.566213
$366$			6.68708i			0.349539i
$367$	4.00293	−	6.93327i	0.208951	−	0.361914i	−0.742433	−	0.669920i	$-0.766328\pi$
$367$	4.00293	−	6.93327i	0.208951	−	0.361914i	0.951384	+	0.308006i	$0.0996617\pi$
$368$	−44.0712			−2.29737
$369$	−4.67486	−	2.69903i	−0.243363	−	0.140506i
$370$	−67.9545	−	39.2336i	−3.53279	−	2.03966i
$371$	−0.979096	+	0.588893i	−0.0508321	+	0.0305738i
$372$		−	18.1458i		−	0.940816i
$373$	−14.9023	−	25.8116i	−0.771614	−	1.33647i	−0.936678	−	0.350191i	$-0.886117\pi$
$373$	−14.9023	−	25.8116i	−0.771614	−	1.33647i	0.165065	−	0.986283i	$-0.447217\pi$
$374$	1.25643	−	2.17619i	0.0649683	−	0.112528i
$375$	−5.23287	−	3.02120i	−0.270224	−	0.156014i
$376$	20.6061	−	35.6908i	1.06268	−	1.84061i
$377$	−9.66635	+	6.07656i	−0.497842	+	0.312959i
$378$	−6.63713	+	0.118804i	−0.341377	+	0.00611063i
$379$	9.17101	−	5.29489i	0.471083	−	0.271980i	−0.245610	−	0.969369i	$-0.578988\pi$
$379$	9.17101	−	5.29489i	0.471083	−	0.271980i	0.716693	+	0.697389i	$0.245655\pi$
$380$	68.0060			3.48864
$381$	10.0772			0.516273
$382$	33.4874	−	19.3340i	1.71337	−	0.989213i
$383$	−24.0899	+	13.9083i	−1.23094	+	0.710681i	−0.967225	−	0.253920i	$-0.918280\pi$
$383$	−24.0899	+	13.9083i	−1.23094	+	0.710681i	−0.263711	+	0.964602i	$0.584947\pi$
$384$	13.6270	+	7.86754i	0.695399	+	0.401489i
$385$	39.0726	−	23.5009i	1.99132	−	1.19771i
$386$	−9.99283	+	17.3081i	−0.508622	+	0.880959i
$387$	−2.55721			−0.129990
$388$	21.5634	+	12.4496i	1.09471	+	0.632034i
$389$	−10.2034	−	17.6728i	−0.517331	−	0.896044i	−0.999797	−	0.0201295i	$-0.993592\pi$
$389$	−10.2034	−	17.6728i	−0.517331	−	0.896044i	0.482466	−	0.875915i	$-0.339741\pi$
$390$	26.2661	−	16.5117i	1.33004	−	0.836102i
$391$	−1.49955			−0.0758357
$392$	1.44259	+	40.2829i	0.0728616	+	2.03460i
$393$	−5.52188	−	9.56417i	−0.278542	−	0.482449i
$394$	−16.4612	−	28.5117i	−0.829305	−	1.43640i
$395$	−13.3990	+	7.73593i	−0.674178	+	0.389237i
$396$		−	21.5828i		−	1.08458i
$397$	−12.1438	+	7.01122i	−0.609479	+	0.351883i	−0.772762	−	0.634696i	$-0.781125\pi$
$397$	−12.1438	+	7.01122i	−0.609479	+	0.351883i	0.163282	+	0.986579i	$0.447792\pi$
$398$			48.9764i			2.45496i
$399$	−12.2128	+	0.218609i	−0.611406	+	0.0109441i
$400$	19.8043	+	34.3020i	0.990213	+	1.71510i
$401$			5.30040i			0.264689i	0.991204	+	0.132345i	$0.0422506\pi$
$401$			5.30040i			0.264689i	−0.991204	+	0.132345i	$0.957749\pi$
$402$	−14.0189	−	24.2815i	−0.699201	−	1.21105i
$403$	−8.10692	−	12.8962i	−0.403835	−	0.642404i
$404$	−9.05284	+	15.6800i	−0.450396	+	0.780108i
$405$	2.97008	−	1.71478i	0.147585	−	0.0852080i
$406$	10.8347	+	18.0138i	0.537716	+	0.894009i
$407$	−22.9116	+	39.6840i	−1.13568	+	1.96706i
$408$	−0.993944	−	0.573854i	−0.0492076	−	0.0284100i
$409$			29.0175i			1.43482i	0.696649	+	0.717412i	$0.254673\pi$
$409$			29.0175i			1.43482i	−0.696649	+	0.717412i	$0.745327\pi$
$410$		−	46.4490i		−	2.29395i
$411$	9.85001	+	5.68690i	0.485865	+	0.280514i
$412$	9.07498	−	15.7183i	0.447092	−	0.774387i
$413$	−2.21746	+	0.0396924i	−0.109114	+	0.00195314i
$414$	−16.3480	+	9.43851i	−0.803459	+	0.463878i
$415$	−25.2359	+	43.7099i	−1.23878	+	2.14564i
$416$	−11.4577	+	0.431089i	−0.561760	+	0.0211359i
$417$	−8.76143	−	15.1752i	−0.429049	−	0.743135i
$418$		−	58.2068i		−	2.84699i
$419$	−6.43099	−	11.1388i	−0.314174	−	0.544166i	0.665087	−	0.746766i	$-0.268394\pi$
$419$	−6.43099	−	11.1388i	−0.314174	−	0.544166i	−0.979262	+	0.202600i	$0.935061\pi$
$420$	−20.0872	−	33.3971i	−0.980157	−	1.62961i
$421$			5.25836i			0.256277i	0.991756	+	0.128138i	$0.0409002\pi$
$421$			5.25836i			0.256277i	−0.991756	+	0.128138i	$0.959100\pi$
$422$	51.9549	−	29.9962i	2.52913	−	1.46019i
$423$		−	7.15688i		−	0.347980i
$424$	−2.15357	+	1.24336i	−0.104587	+	0.0603831i
$425$	0.673854	+	1.16715i	0.0326867	+	0.0566151i
$426$	−7.17887	−	12.4342i	−0.347817	−	0.602437i
$427$	6.04274	−	3.63450i	0.292429	−	0.175886i
$428$	−19.9919			−0.966343
$429$	−9.64247	−	15.3389i	−0.465543	−	0.740567i
$430$	−11.0021	−	19.0562i	−0.530568	−	0.918970i
$431$	21.4053	+	12.3584i	1.03106	+	0.595281i	0.917287	−	0.398226i	$-0.130374\pi$
$431$	21.4053	+	12.3584i	1.03106	+	0.595281i	0.113770	+	0.993507i	$0.463707\pi$
$432$	−5.85764			−0.281826
$433$	10.8239	−	18.7476i	0.520166	−	0.900953i	−0.479560	−	0.877509i	$-0.659204\pi$
$433$	10.8239	−	18.7476i	0.520166	−	0.900953i	0.999725	−	0.0234439i	$-0.00746310\pi$
$434$	−24.0327	+	14.4549i	−1.15361	+	0.693856i
$435$	−9.40533	−	5.43017i	−0.450951	−	0.260357i
$436$	2.25479	−	1.30180i	0.107985	−	0.0623450i
$437$	−30.0815	+	17.3676i	−1.43899	+	0.830804i
$438$	7.91388			0.378140
$439$	−7.75058			−0.369915			−0.184957	−	0.982747i	$-0.559215\pi$
$439$	−7.75058			−0.369915			−0.184957	+	0.982747i	$0.559215\pi$
$440$	85.9421	−	49.6187i	4.09713	−	2.36548i
$441$	3.71471	+	5.93303i	0.176891	+	0.282525i
$442$	−1.80175	+	0.0677898i	−0.0857007	+	0.00322443i
$443$	3.55156	−	6.15148i	0.168740	−	0.292265i	−0.769237	−	0.638963i	$-0.779364\pi$
$443$	3.55156	−	6.15148i	0.168740	−	0.292265i	0.937977	+	0.346698i	$0.112697\pi$
$444$	33.9197	+	19.5835i	1.60976	+	0.929394i
$445$	4.02301	−	6.96806i	0.190709	−	0.330318i
$446$	13.0932	+	22.6781i	0.619982	+	1.07384i
$447$		−	11.8777i		−	0.561797i
$448$	−0.176930	−	9.88437i	−0.00835914	−	0.466993i
$449$	25.1353	+	14.5119i	1.18621	+	0.684858i	0.957443	−	0.288623i	$-0.0931974\pi$
$449$	25.1353	+	14.5119i	1.18621	+	0.684858i	0.228767	+	0.973481i	$0.426531\pi$
$450$	14.6926	+	8.48276i	0.692614	+	0.399881i
$451$	−27.1252			−1.27728
$452$	17.8469	−	30.9117i	0.839445	−	1.45396i
$453$			13.3229i			0.625964i
$454$	24.8404			1.16582
$455$	−29.1966	−	14.7610i	−1.36876	−	0.692004i
$456$	−26.5851			−1.24496
$457$			27.0304i			1.26443i	0.774794	+	0.632213i	$0.217853\pi$
$457$			27.0304i			1.26443i	−0.774794	+	0.632213i	$0.782147\pi$
$458$	19.7823	−	34.2640i	0.924367	−	1.60105i
$459$	−0.199310			−0.00930301
$460$	−95.9784	−	55.4132i	−4.47502	−	2.58365i
$461$	2.16474	+	1.24981i	0.100822	+	0.0582096i	0.549563	−	0.835452i	$-0.314794\pi$
$461$	2.16474	+	1.24981i	0.100822	+	0.0582096i	−0.448741	+	0.893662i	$0.648127\pi$
$462$	−28.5848	+	17.1928i	−1.32989	+	0.799882i
$463$			28.9351i			1.34473i	0.740222	+	0.672363i	$0.234721\pi$
$463$			28.9351i			1.34473i	−0.740222	+	0.672363i	$0.765279\pi$
$464$	9.27466	+	16.0642i	0.430565	+	0.745761i
$465$	7.24455	−	12.5479i	0.335958	−	0.581897i
$466$	−4.13925	−	2.38979i	−0.191747	−	0.110705i
$467$	−4.23383	+	7.33321i	−0.195918	+	0.339340i	−0.947201	−	0.320640i	$-0.896102\pi$
$467$	−4.23383	+	7.33321i	−0.195918	+	0.339340i	0.751283	+	0.659980i	$0.229435\pi$
$468$	−13.1108	+	8.24185i	−0.606048	+	0.380980i
$469$	−14.3224	+	25.8654i	−0.661346	+	1.19435i
$470$	53.3327	−	30.7917i	2.46005	−	1.42031i
$471$	11.2412			0.517969
$472$	−4.82701			−0.222181
$473$	−11.1284	+	6.42498i	−0.511684	+	0.295421i
$474$	9.80248	−	5.65947i	0.450243	−	0.259948i
$475$	27.0355	+	15.6089i	1.24047	+	0.716187i
$476$	0.0405353	+	2.26455i	0.00185793	+	0.103795i
$477$	−0.215922	+	0.373988i	−0.00988639	+	0.0171237i
$478$	66.0087			3.01917
$479$	20.7557	+	11.9833i	0.948351	+	0.547531i	0.892568	−	0.450912i	$-0.148901\pi$
$479$	20.7557	+	11.9833i	0.948351	+	0.547531i	0.0557827	+	0.998443i	$0.482235\pi$
$480$	−5.45307	−	9.44500i	−0.248898	−	0.431103i
$481$	32.8559	−	1.23618i	1.49810	−	0.0563650i
$482$	56.6702			2.58126
$483$	17.4144	+	9.64282i	0.792381	+	0.438763i
$484$	−30.6039	−	53.0075i	−1.39108	−	2.40943i
$485$	9.94081	+	17.2180i	0.451389	+	0.781828i
$486$	−2.17286	+	1.25450i	−0.0985629	+	0.0569053i
$487$		−	36.7256i		−	1.66420i	−0.554628	−	0.832099i	$-0.687139\pi$
$487$		−	36.7256i		−	1.66420i	0.554628	−	0.832099i	$-0.312861\pi$
$488$	13.2913	−	7.67373i	0.601669	−	0.347374i
$489$		−	3.63167i		−	0.164230i
$490$	−28.2305	+	53.2080i	−1.27533	+	2.40369i
$491$	4.83577	+	8.37579i	0.218235	+	0.377994i	0.954268	−	0.298951i	$-0.0966367\pi$
$491$	4.83577	+	8.37579i	0.218235	+	0.377994i	−0.736033	+	0.676945i	$0.763303\pi$
$492$			23.1852i			1.04527i
$493$	0.315577	+	0.546595i	0.0142129	+	0.0246174i
$494$	−35.3586	+	22.2275i	−1.59086	+	1.00006i
$495$	8.61676	−	14.9247i	0.387295	−	0.670814i
$496$	−21.4317	+	12.3736i	−0.962313	+	0.555591i
$497$	−7.33426	+	13.2453i	−0.328987	+	0.594131i
$498$	18.4622	−	31.9774i	0.827309	−	1.43294i
$499$	−24.0357	−	13.8770i	−1.07599	−	0.621221i	−0.146176	−	0.989259i	$-0.546697\pi$
$499$	−24.0357	−	13.8770i	−1.07599	−	0.621221i	−0.929811	+	0.368037i	$0.880030\pi$
$500$			25.9526i			1.16064i
$501$			10.3447i			0.462169i
$502$	62.7807	+	36.2465i	2.80204	+	1.61776i
$503$	6.56936	−	11.3785i	0.292913	−	0.507341i	−0.681584	−	0.731740i	$-0.738709\pi$
$503$	6.56936	−	11.3785i	0.292913	−	0.507341i	0.974497	+	0.224399i	$0.0720419\pi$
$504$	7.85256	+	13.0557i	0.349781	+	0.581547i
$505$	−12.5202	+	7.22854i	−0.557141	+	0.321666i
$506$	−47.4285	+	82.1486i	−2.10845	+	3.65195i
$507$	−5.63565	+	11.7149i	−0.250288	+	0.520278i
$508$	−21.6414	−	37.4839i	−0.960180	−	1.66308i
$509$			29.1555i			1.29230i	0.763212	+	0.646148i	$0.223621\pi$
$509$			29.1555i			1.29230i	−0.763212	+	0.646148i	$0.776379\pi$
$510$	−0.857510	−	1.48525i	−0.0379712	−	0.0657680i
$511$	−4.30128	−	7.15133i	−0.190277	−	0.316356i
$512$		−	48.8337i		−	2.15816i
$513$	−3.99823	+	2.30838i	−0.176526	+	0.101917i
$514$			40.2702i			1.77624i
$515$	12.5508	−	7.24621i	0.553055	−	0.319306i
$516$	5.49172	+	9.51194i	0.241760	+	0.418740i
$517$	−17.9817	−	31.1452i	−0.790833	−	1.36976i
$518$	−1.08338	−	60.5242i	−0.0476010	−	2.65928i
$519$	4.59804			0.201831
$520$	−62.9604	−	33.2589i	−2.76100	−	1.45850i
$521$	7.62747	+	13.2112i	0.334166	+	0.578792i	0.983324	−	0.181861i	$-0.0582122\pi$
$521$	7.62747	+	13.2112i	0.334166	+	0.578792i	−0.649159	+	0.760653i	$0.724879\pi$
$522$	6.88077	+	3.97261i	0.301163	+	0.173877i
$523$	−24.9370			−1.09042			−0.545209	−	0.838300i	$-0.683550\pi$
$523$	−24.9370			−1.09042			−0.545209	+	0.838300i	$0.683550\pi$
$524$	−23.7170	+	41.0790i	−1.03608	+	1.79454i
$525$	−0.320182	−	17.8873i	−0.0139739	−	0.780667i
$526$	−31.4435	−	18.1539i	−1.37100	−	0.791548i
$527$	−0.729229	+	0.421021i	−0.0317657	+	0.0183400i
$528$	−25.4911	+	14.7173i	−1.10936	+	0.640489i
$529$	33.6063			1.46114
$530$	−3.71592			−0.161409
$531$	−0.725951	+	0.419128i	−0.0315036	+	0.0181886i
$532$	27.0408	+	44.9581i	1.17237	+	1.94918i
$533$	10.3583	+	16.4776i	0.448669	+	0.713725i
$534$	−2.94316	+	5.09771i	−0.127363	+	0.220600i
$535$	−13.8245	−	7.98158i	−0.597685	−	0.345074i
$536$	−32.1748	+	55.7283i	−1.38974	+	2.40710i
$537$	0.453209	+	0.784982i	0.0195574	+	0.0338745i
$538$			40.8849i			1.76267i
$539$	31.0724	+	16.4860i	1.33838	+	0.710104i
$540$	−12.7568	−	7.36513i	−0.548965	−	0.316945i
$541$	−21.8817	−	12.6334i	−0.940767	−	0.543152i	−0.0505664	−	0.998721i	$-0.516103\pi$
$541$	−21.8817	−	12.6334i	−0.940767	−	0.543152i	−0.890201	+	0.455569i	$0.849436\pi$
$542$	−28.1752			−1.21023
$543$	−9.45777	+	16.3813i	−0.405872	+	0.702991i
$544$			0.633816i			0.0271746i
$545$	2.07893			0.0890516
$546$	21.3597	+	10.7989i	0.914112	+	0.462148i
$547$	31.0477			1.32750			0.663752	−	0.747953i	$-0.268963\pi$
$547$	31.0477			1.32750			0.663752	+	0.747953i	$0.268963\pi$
$548$		−	48.8516i		−	2.08684i
$549$	1.33262	−	2.30816i	0.0568747	−	0.0985099i
$550$	85.2517			3.63515
$551$	12.6611	+	7.30991i	0.539383	+	0.311413i
$552$	37.5201	+	21.6623i	1.59696	+	0.922007i
$553$	−10.4419	−	5.78197i	−0.444035	−	0.245874i
$554$		−	48.1876i		−	2.04729i
$555$	15.6371	+	27.0843i	0.663759	+	1.14966i
$556$	−37.6312	+	65.1791i	−1.59592	+	2.76421i
$557$	22.2174	+	12.8272i	0.941380	+	0.543506i	0.890393	−	0.455193i	$-0.150430\pi$
$557$	22.2174	+	12.8272i	0.941380	+	0.543506i	0.0509872	+	0.998699i	$0.483763\pi$
$558$	−5.29999	+	9.17985i	−0.224366	+	0.388614i
$559$	8.15256	+	4.30660i	0.344816	+	0.182150i
$560$	−25.7473	+	46.4982i	−1.08802	+	1.96491i
$561$	−0.867354	+	0.500767i	−0.0366197	+	0.0211424i
$562$	53.8249			2.27047
$563$	9.04397			0.381158			0.190579	−	0.981672i	$-0.438964\pi$
$563$	9.04397			0.381158			0.190579	+	0.981672i	$0.438964\pi$
$564$	−26.6212	+	15.3697i	−1.12095	+	0.647183i
$565$	24.6824	−	14.2504i	1.03840	−	0.599519i
$566$	−17.8495	−	10.3054i	−0.750272	−	0.433170i
$567$	2.31460	+	1.28166i	0.0972039	+	0.0538245i
$568$	−16.4762	+	28.5376i	−0.691325	+	1.19741i
$569$	43.9957			1.84440			0.922198	−	0.386719i	$-0.126391\pi$
$569$	43.9957			1.84440			0.922198	+	0.386719i	$0.126391\pi$
$570$	−34.4038	−	19.8631i	−1.44102	−	0.831972i
$571$	−8.12709	−	14.0765i	−0.340108	−	0.589085i	0.644344	−	0.764735i	$-0.277130\pi$
$571$	−8.12709	−	14.0765i	−0.340108	−	0.589085i	−0.984453	+	0.175651i	$0.943797\pi$
$572$	−36.3477	+	68.8076i	−1.51977	+	2.87699i
$573$	−15.4117			−0.643833
$574$	30.7070	−	18.4692i	1.28168	−	0.770890i
$575$	−25.4372	−	44.0584i	−1.06080	−	1.83736i
$576$	−1.86827	−	3.23594i	−0.0778446	−	0.134831i
$577$	2.00627	−	1.15832i	0.0835222	−	0.0482216i	−0.457657	−	0.889129i	$-0.651311\pi$
$577$	2.00627	−	1.15832i	0.0835222	−	0.0482216i	0.541179	+	0.840907i	$0.317978\pi$
$578$		−	42.5534i		−	1.76999i
$579$	6.89839	−	3.98279i	0.286688	−	0.165519i
$580$			46.6462i			1.93688i
$581$	−38.9306	+	0.696855i	−1.61511	+	0.0289104i
$582$	−7.27252	−	12.5964i	−0.301455	−	0.522136i
$583$			2.17001i			0.0898728i
$584$	−9.08154	−	15.7297i	−0.375797	−	0.650899i
$585$	−12.3567	+	0.464913i	−0.510887	+	0.0192218i
$586$	−11.6720	+	20.2166i	−0.482168	+	0.835139i
$587$	−29.7041	+	17.1497i	−1.22602	+	0.707843i	−0.966195	−	0.257813i	$-0.916998\pi$
$587$	−29.7041	+	17.1497i	−1.22602	+	0.707843i	−0.259825	+	0.965656i	$0.583665\pi$
$588$	14.0914	−	26.5589i	0.581118	−	1.09527i
$589$	−9.75238	+	16.8916i	−0.401840	+	0.696007i
$590$	−6.24664	−	3.60650i	−0.257170	−	0.148477i
$591$			13.1217i			0.539756i
$592$		−	53.4160i		−	2.19538i
$593$	−21.2551	−	12.2717i	−0.872844	−	0.503937i	−0.00455184	−	0.999990i	$-0.501449\pi$
$593$	−21.2551	−	12.2717i	−0.872844	−	0.503937i	−0.868292	+	0.496053i	$0.834782\pi$
$594$	−6.30387	+	10.9186i	−0.258651	+	0.447996i
$595$	−0.876071	+	1.58213i	−0.0359154	+	0.0648612i
$596$	−44.1811	+	25.5080i	−1.80973	+	1.04485i
$597$	9.76013	−	16.9050i	0.399456	−	0.691877i
$598$	68.0140	−	2.55898i	2.78130	−	0.104644i
$599$	8.47361	+	14.6767i	0.346222	+	0.599675i	0.985575	−	0.169239i	$-0.0541309\pi$
$599$	8.47361	+	14.6767i	0.346222	+	0.599675i	−0.639353	+	0.768914i	$0.720798\pi$
$600$		−	38.9375i		−	1.58961i
$601$	20.0508	+	34.7290i	0.817888	+	1.41662i	0.907235	+	0.420624i	$0.138189\pi$
$601$	20.0508	+	34.7290i	0.817888	+	1.41662i	−0.0893467	+	0.996001i	$0.528478\pi$
$602$	8.22316	−	14.8505i	0.335151	−	0.605263i
$603$			11.1749i			0.455077i
$604$	49.5566	−	28.6115i	2.01643	−	1.16419i
$605$		−	48.8733i		−	1.98698i
$606$	9.15955	−	5.28827i	0.372081	−	0.214821i
$607$	21.9043	+	37.9393i	0.889067	+	1.53991i	0.840980	+	0.541066i	$0.181979\pi$
$607$	21.9043	+	37.9393i	0.889067	+	1.53991i	0.0480874	+	0.998843i	$0.484687\pi$
$608$	7.34075	+	12.7145i	0.297707	+	0.515643i
$609$	−0.149946	−	8.37693i	−0.00607614	−	0.339450i
$610$	22.9337			0.928559
$611$	−12.0529	+	22.8167i	−0.487609	+	0.923063i
$612$	0.428028	+	0.741367i	0.0173020	+	0.0299680i
$613$	−8.91783	−	5.14871i	−0.360188	−	0.207954i	0.308975	−	0.951070i	$-0.400014\pi$
$613$	−8.91783	−	5.14871i	−0.360188	−	0.207954i	−0.669163	+	0.743116i	$0.733347\pi$
$614$	−43.5962			−1.75940
$615$	−9.25647	+	16.0327i	−0.373257	+	0.646500i
$616$	66.9750	+	37.0859i	2.69850	+	1.49423i
$617$	12.1246	+	7.00015i	0.488119	+	0.281815i	0.723794	−	0.690017i	$-0.242397\pi$
$617$	12.1246	+	7.00015i	0.488119	+	0.281815i	−0.235675	+	0.971832i	$0.575730\pi$
$618$	−9.18195	+	5.30120i	−0.369352	+	0.213246i
$619$	25.0425	−	14.4583i	1.00654	−	0.581127i	0.0963641	−	0.995346i	$-0.469279\pi$
$619$	25.0425	−	14.4583i	1.00654	−	0.581127i	0.910177	+	0.414219i	$0.135945\pi$
$620$	−62.2321			−2.49930
$621$	7.52372			0.301916
$622$	11.0336	−	6.37024i	0.442406	−	0.255423i
$623$	6.20616	−	0.111090i	0.248645	−	0.00445072i
$624$	18.6746	+	9.86487i	0.747581	+	0.394911i
$625$	6.54328	−	11.3333i	0.261731	−	0.453332i
$626$	−15.8454	−	9.14836i	−0.633310	−	0.365642i
$627$	−11.5996	+	20.0911i	−0.463243	+	0.802361i
$628$	−24.1411	−	41.8136i	−0.963334	−	1.66854i
$629$		−	1.81752i		−	0.0724692i
$630$	0.407446	+	22.7624i	0.0162330	+	0.906877i
$631$	−36.5812	−	21.1202i	−1.45628	−	0.840782i	−0.457451	−	0.889235i	$-0.651237\pi$
$631$	−36.5812	−	21.1202i	−1.45628	−	0.840782i	−0.998825	+	0.0484534i	$0.984571\pi$
$632$	−22.4976	−	12.9890i	−0.894907	−	0.516675i
$633$	−23.9109			−0.950371
$634$	29.7851	−	51.5892i	1.18292	−	2.04887i
$635$		−	34.5605i		−	1.37149i
$636$	1.85481			0.0735480
$637$	−1.85094	−	25.1709i	−0.0733368	−	0.997307i
$638$	39.9248			1.58064
$639$			5.72249i			0.226378i
$640$	26.9822	−	46.7345i	1.06656	−	1.84734i
$641$	−22.6364			−0.894086			−0.447043	−	0.894512i	$-0.647523\pi$
$641$	−22.6364			−0.894086			−0.447043	+	0.894512i	$0.647523\pi$
$642$	10.1138	+	5.83918i	0.399158	+	0.230454i
$643$	21.1425	+	12.2066i	0.833778	+	0.481382i	0.855145	−	0.518389i	$-0.173468\pi$
$643$	21.1425	+	12.2066i	0.833778	+	0.481382i	−0.0213662	+	0.999772i	$0.506802\pi$
$644$	−1.53016	−	85.4839i	−0.0602966	−	3.36854i
$645$			8.77009i			0.345322i
$646$	1.15435	+	1.99939i	0.0454173	+	0.0786651i
$647$	13.1968	−	22.8574i	0.518818	−	0.898619i	−0.480943	−	0.876752i	$-0.659706\pi$
$647$	13.1968	−	22.8574i	0.518818	−	0.898619i	0.999761	−	0.0218670i	$-0.00696104\pi$
$648$	4.98692	+	2.87920i	0.195905	+	0.113106i
$649$	−2.10612	+	3.64790i	−0.0826724	+	0.143193i
$650$	−32.5551	−	51.7874i	−1.27692	−	2.03127i
$651$	11.1759	−	0.200048i	0.438019	−	0.00784050i
$652$	−13.5086	+	7.79917i	−0.529036	+	0.305439i
$653$	15.9908			0.625766			0.312883	−	0.949792i	$-0.398705\pi$
$653$	15.9908			0.625766			0.312883	+	0.949792i	$0.398705\pi$
$654$	−1.52091			−0.0594722
$655$	−32.8009	+	18.9376i	−1.28164	+	0.739953i
$656$	27.3836	−	15.8099i	1.06915	−	0.617275i
$657$	−2.73161	−	1.57710i	−0.106570	−	0.0615284i
$658$	41.5624	+	23.0142i	1.62027	+	0.897188i
$659$	1.71887	−	2.97717i	0.0669576	−	0.115974i	−0.830603	−	0.556865i	$-0.812004\pi$
$659$	1.71887	−	2.97717i	0.0669576	−	0.115974i	0.897561	+	0.440891i	$0.145337\pi$
$660$	−74.0196			−2.88121
$661$	7.12554	+	4.11393i	0.277151	+	0.160013i	0.632133	−	0.774860i	$-0.282180\pi$
$661$	7.12554	+	4.11393i	0.277151	+	0.160013i	−0.354982	+	0.934873i	$0.615513\pi$
$662$	−0.0288760	−	0.0500147i	−0.00112230	−	0.00194388i
$663$	0.635416	+	0.335659i	0.0246775	+	0.0130359i
$664$	−84.7448			−3.28873
$665$	0.749731	+	41.8846i	0.0290733	+	1.62422i
$666$	−11.4398	−	19.8144i	−0.443285	−	0.767791i
$667$	−11.9126	−	20.6333i	−0.461259	−	0.798924i
$668$	38.4789	−	22.2158i	1.48879	−	0.859555i
$669$		−	10.4370i		−	0.403517i
$670$	−83.2748	+	48.0787i	−3.21719	+	1.85744i
$671$		−	13.3928i		−	0.517023i
$672$	4.07573	−	7.36052i	0.157225	−	0.283938i
$673$	−12.6425	−	21.8974i	−0.487332	−	0.844084i	0.512562	−	0.858650i	$-0.328697\pi$
$673$	−12.6425	−	21.8974i	−0.487332	−	0.844084i	−0.999894	+	0.0145663i	$0.995363\pi$
$674$			30.8865i			1.18970i
$675$	−3.38093	−	5.85594i	−0.130132	−	0.225395i
$676$	55.6784	−	4.19566i	2.14148	−	0.161372i
$677$	3.17568	−	5.50044i	0.122051	−	0.211399i	−0.798525	−	0.601961i	$-0.794386\pi$
$677$	3.17568	−	5.50044i	0.122051	−	0.211399i	0.920576	+	0.390562i	$0.127719\pi$
$678$	−18.0572	+	10.4253i	−0.693483	+	0.400383i
$679$	−7.42994	+	13.4180i	−0.285135	+	0.514937i
$680$	−1.96806	+	3.40879i	−0.0754718	+	0.130721i
$681$	−8.57408	−	4.95025i	−0.328560	−	0.189694i
$682$			53.2649i			2.03962i
$683$			47.9352i			1.83419i	0.398671	+	0.917094i	$0.369471\pi$
$683$			47.9352i			1.83419i	−0.398671	+	0.917094i	$0.630529\pi$
$684$	17.1728	+	9.91470i	0.656617	+	0.379098i
$685$	19.5036	−	33.7812i	0.745193	−	1.29071i
$686$	−46.4004	+	2.49382i	−1.77158	+	0.0952146i
$687$	−13.6564	+	7.88453i	−0.521025	+	0.300814i
$688$	7.48960	−	12.9724i	0.285538	−	0.494567i
$689$	1.31821	−	0.828665i	0.0502197	−	0.0315696i
$690$	32.3699	+	56.0663i	1.23230	+	2.13441i
$691$		−	25.5592i		−	0.972317i	−0.873871	−	0.486159i	$-0.838398\pi$
$691$		−	25.5592i		−	0.972317i	0.873871	−	0.486159i	$-0.161602\pi$
$692$	−9.87450	−	17.1031i	−0.375372	−	0.650164i
$693$	13.2928	−	0.237940i	0.504951	−	0.00903858i
$694$			79.1094i			3.00295i
$695$	−52.0444	+	30.0478i	−1.97416	+	1.13978i
$696$		−	18.2350i		−	0.691198i
$697$	0.931747	−	0.537944i	0.0352924	−	0.0203761i
$698$	2.45230	+	4.24750i	0.0928207	+	0.160770i
$699$	0.952488	+	1.64976i	0.0360264	+	0.0623996i
$700$	−65.8472	+	39.6048i	−2.48879	+	1.49692i
$701$	−14.6478			−0.553238			−0.276619	−	0.960980i	$-0.589214\pi$
$701$	−14.6478			−0.553238			−0.276619	+	0.960980i	$0.589214\pi$
$702$	9.03994	−	0.340122i	0.341191	−	0.0128371i
$703$	−21.0502	−	36.4600i	−0.793922	−	1.37511i
$704$	−16.2606	−	9.38806i	−0.612844	−	0.353826i
$705$	−24.5449			−0.924416
$706$	20.4686	−	35.4526i	0.770345	−	1.33428i
$707$	−9.75703	−	5.40274i	−0.366951	−	0.203191i
$708$	3.11803	+	1.80019i	0.117183	+	0.0676555i
$709$	16.2182	−	9.36357i	0.609087	−	0.351656i	−0.163521	−	0.986540i	$-0.552285\pi$
$709$	16.2182	−	9.36357i	0.609087	−	0.351656i	0.772608	+	0.634883i	$0.218952\pi$
$710$	−42.6437	+	24.6203i	−1.60039	+	0.923985i
$711$	−4.51133			−0.169188
$712$	13.5097			0.506297
$713$	27.5275	−	15.8930i	1.03091	−	0.595198i
$714$	0.640918	−	1.15746i	0.0239858	−	0.0433169i
$715$	−52.6055	+	33.0694i	−1.96733	+	1.23673i
$716$	1.94658	−	3.37157i	0.0727470	−	0.126001i
$717$	−22.7840	−	13.1544i	−0.850885	−	0.491259i
$718$	−27.8611	+	48.2568i	−1.03977	+	1.80093i
$719$	−8.57680	−	14.8555i	−0.319861	−	0.554015i	0.660598	−	0.750740i	$-0.270303\pi$
$719$	−8.57680	−	14.8555i	−0.319861	−	0.554015i	−0.980459	+	0.196725i	$0.936969\pi$
$720$			20.0891i			0.748677i
$721$	9.78089	+	5.41595i	0.364259	+	0.201701i
$722$	5.02895	+	2.90346i	0.187158	+	0.108056i
$723$	−19.5607	−	11.2934i	−0.727470	−	0.420005i
$724$	81.2440			3.01941
$725$	−10.7063	+	18.5439i	−0.397624	+	0.688705i
$726$			35.7548i			1.32699i
$727$	7.13494			0.264620			0.132310	−	0.991208i	$-0.457760\pi$
$727$	7.13494			0.264620			0.132310	+	0.991208i	$0.457760\pi$
$728$	−3.04739	−	54.8470i	−0.112944	−	2.03276i
$729$	1.00000			0.0370370
$730$		−	27.1411i		−	1.00454i
$731$	0.254839	−	0.441394i	0.00942556	−	0.0163255i
$732$	−11.4474			−0.423109
$733$	17.0588	+	9.84891i	0.630082	+	0.363778i	0.780784	−	0.624801i	$-0.214820\pi$
$733$	17.0588	+	9.84891i	0.630082	+	0.363778i	−0.150702	+	0.988579i	$0.548153\pi$
$734$	17.3956	+	10.0434i	0.642083	+	0.370707i
$735$	20.3477	−	12.7398i	0.750535	−	0.469915i
$736$		−	23.9258i		−	0.881915i
$737$	28.0769	+	48.6307i	1.03423	+	1.79133i
$738$	6.77187	−	11.7292i	0.249276	−	0.431759i
$739$	9.67092	+	5.58351i	0.355751	+	0.205393i	0.667215	−	0.744865i	$-0.267486\pi$
$739$	9.67092	+	5.58351i	0.355751	+	0.205393i	−0.311464	+	0.950258i	$0.600819\pi$
$740$	67.1629	−	116.329i	2.46896	−	4.27636i
$741$	16.6342	−	0.625850i	0.611072	−	0.0229912i
$742$	−1.47753	−	2.45655i	−0.0542420	−	0.0901829i
$743$	−19.2388	+	11.1075i	−0.705802	+	0.407495i	−0.809505	−	0.587114i	$-0.800264\pi$
$743$	−19.2388	+	11.1075i	−0.705802	+	0.407495i	0.103703	+	0.994608i	$0.466931\pi$
$744$	24.3279			0.891905
$745$	−40.7354			−1.49243
$746$	64.7614	−	37.3900i	2.37108	−	1.36895i
$747$	−12.7451	+	7.35837i	−0.466318	+	0.269229i
$748$	3.72537	+	2.15084i	0.136213	+	0.0786426i
$749$	−0.220400	−	12.3129i	−0.00805324	−	0.449903i
$750$	7.58019	−	13.1293i	0.276789	−	0.479413i
$751$	−29.2653			−1.06791			−0.533954	−	0.845514i	$-0.679294\pi$
$751$	−29.2653			−1.06791			−0.533954	+	0.845514i	$0.679294\pi$
$752$	36.3059	+	20.9612i	1.32394	+	0.764377i
$753$	−14.4466	−	25.0222i	−0.526462	−	0.911859i
$754$	−15.2461	−	24.2529i	−0.555230	−	0.883238i
$755$	45.6916			1.66289
$756$	−0.203378	−	11.3619i	−0.00739678	−	0.413229i
$757$	26.6911	+	46.2303i	0.970104	+	1.68027i	0.695226	+	0.718791i	$0.255304\pi$
$757$	26.6911	+	46.2303i	0.970104	+	1.68027i	0.274878	+	0.961479i	$0.411363\pi$
$758$	13.2849	+	23.0101i	0.482529	+	0.835764i
$759$	32.7415	−	18.9033i	1.18844	−	0.686148i
$760$			91.1751i			3.30727i
$761$	−8.96431	+	5.17555i	−0.324956	+	0.187613i	−0.653599	−	0.756841i	$-0.726742\pi$
$761$	−8.96431	+	5.17555i	−0.324956	+	0.187613i	0.328644	+	0.944454i	$0.393409\pi$
$762$			25.2838i			0.915937i
$763$	0.826631	+	1.37436i	0.0299260	+	0.0497552i
$764$	33.0973	+	57.3262i	1.19742	+	2.07399i
$765$			0.683546i			0.0247137i
$766$	−34.8960	−	60.4416i	−1.26084	−	2.18384i
$767$	3.02024	−	0.113635i	0.109055	−	0.00410311i
$768$	−16.0031	+	27.7182i	−0.577463	+	1.00020i
$769$	11.0010	−	6.35144i	0.396707	−	0.229039i	−0.288355	−	0.957523i	$-0.593108\pi$
$769$	11.0010	−	6.35144i	0.396707	−	0.229039i	0.685062	+	0.728485i	$0.259775\pi$
$770$	58.9637	+	98.0333i	2.12490	+	3.53287i
$771$	8.02514	−	13.9000i	0.289018	−	0.500595i
$772$	−29.6292	−	17.1065i	−1.06638	−	0.615675i
$773$		−	52.0546i		−	1.87227i	−0.351637	−	0.936137i	$-0.614375\pi$
$773$		−	52.0546i		−	1.87227i	0.351637	−	0.936137i	$-0.385625\pi$
$774$		−	6.41604i		−	0.230620i
$775$	−24.7400	−	14.2837i	−0.888688	−	0.513085i
$776$	−16.6911	+	28.9098i	−0.599176	+	1.03780i
$777$	−11.6875	+	21.1069i	−0.419285	+	0.757205i
$778$	44.3410	−	25.6003i	1.58970	−	0.917814i
$779$	12.4608	−	21.5827i	0.446453	−	0.773279i
$780$	28.2659	+	44.9643i	1.01208	+	1.60998i
$781$	14.3777	+	24.9030i	0.514476	+	0.891099i
$782$		−	3.76239i		−	0.134543i
$783$	−1.58334	−	2.74243i	−0.0565841	−	0.0980065i
$784$	−40.9772	+	1.46745i	−1.46347	+	0.0524089i
$785$		−	38.5524i		−	1.37600i
$786$	23.9965	−	13.8544i	0.855928	−	0.494170i
$787$			28.6226i			1.02028i	0.860090	+	0.510142i	$0.170407\pi$
$787$			28.6226i			1.02028i	−0.860090	+	0.510142i	$0.829593\pi$
$788$	48.8084	−	28.1795i	1.73873	−	1.00385i
$789$	7.23551	+	12.5323i	0.257591	+	0.446161i
$790$	−19.4095	−	33.6182i	−0.690558	−	1.19608i
$791$	19.2351	+	10.6510i	0.683921	+	0.378706i
$792$	28.9359			1.02819
$793$	−8.13566	+	5.11432i	−0.288906	+	0.181615i
$794$	−17.5912	−	30.4688i	−0.624287	−	1.08130i
$795$	1.28261	+	0.740516i	0.0454896	+	0.0262634i
$796$	−83.8414			−2.97168
$797$	−7.72007	+	13.3715i	−0.273459	+	0.473644i	−0.969745	−	0.244120i	$-0.921501\pi$
$797$	−7.72007	+	13.3715i	−0.273459	+	0.473644i	0.696286	+	0.717764i	$0.254834\pi$
$798$	−0.548490	−	30.6420i	−0.0194163	−	1.08472i
$799$	1.23533	+	0.713220i	0.0437030	+	0.0252319i
$800$	−18.6222	+	10.7515i	−0.658393	+	0.380123i
$801$	2.03177	−	1.17304i	0.0717890	−	0.0414474i
$802$	−13.2987			−0.469594
$803$	−15.8498			−0.559328
$804$	41.5668	−	23.9986i	1.46595	−	0.846366i
$805$	33.0706	−	59.7236i	1.16559	−	2.10498i
$806$	32.3565	−	20.3403i	1.13971	−	0.716456i
$807$	8.14765	−	14.1121i	0.286811	−	0.496771i
$808$	−21.0220	−	12.1371i	−0.739552	−	0.426981i
$809$	−1.85814	+	3.21840i	−0.0653289	+	0.113153i	−0.896840	−	0.442355i	$-0.854143\pi$
$809$	−1.85814	+	3.21840i	−0.0653289	+	0.113153i	0.831511	+	0.555508i	$0.187476\pi$
$810$	4.30238	+	7.45195i	0.151170	+	0.261835i
$811$			22.6432i			0.795111i	0.917578	+	0.397555i	$0.130141\pi$
$811$			22.6432i			0.795111i	−0.917578	+	0.397555i	$0.869859\pi$
$812$	−30.8373	+	18.5476i	−1.08218	+	0.650893i
$813$	9.72516	+	5.61482i	0.341076	+	0.196920i
$814$	−99.5672	−	57.4852i	−3.48983	−	2.01485i
$815$	−12.4550			−0.436280
$816$	0.583744	−	1.01107i	0.0204351	−	0.0353947i
$817$		−	11.8060i		−	0.413040i
$818$	−72.8050			−2.54557
$819$	−5.22066	−	7.98403i	−0.182425	−	0.278985i
$820$	79.5148			2.77678
$821$		−	0.279111i		−	0.00974104i	−0.999988	−	0.00487052i	$-0.998450\pi$
$821$		−	0.279111i		−	0.00974104i	0.999988	−	0.00487052i	$-0.00155034\pi$
$822$	−14.2685	+	24.7137i	−0.497669	+	0.861989i
$823$	12.0751			0.420913			0.210456	−	0.977603i	$-0.432505\pi$
$823$	12.0751			0.420913			0.210456	+	0.977603i	$0.432505\pi$
$824$	21.0734	+	12.1668i	0.734128	+	0.423849i
$825$	−29.4261	−	16.9892i	−1.02449	−	0.591487i
$826$	−0.0995884	−	5.56362i	−0.00346512	−	0.193583i
$827$		−	8.62027i		−	0.299756i	−0.988704	−	0.149878i	$-0.952112\pi$
$827$		−	8.62027i		−	0.299756i	0.988704	−	0.149878i	$-0.0478881\pi$
$828$	−16.1575	−	27.9857i	−0.561513	−	0.972569i
$829$	−6.28936	+	10.8935i	−0.218438	+	0.378346i	−0.954331	−	0.298752i	$-0.903430\pi$
$829$	−6.28936	+	10.8935i	−0.218438	+	0.378346i	0.735892	+	0.677099i	$0.236763\pi$
$830$	−109.668	−	63.3170i	−3.80664	−	2.19777i
$831$	−9.60293	+	16.6328i	−0.333122	+	0.576984i
$832$	0.506528	+	13.4628i	0.0175607	+	0.466737i
$833$	−1.39428	+	0.0499310i	−0.0483089	+	0.00173001i
$834$	38.0747	−	21.9825i	1.31842	−	0.761190i
$835$	35.4778			1.22776
$836$	99.6427			3.44622
$837$	3.65876	−	2.11239i	0.126465	−	0.0730148i
$838$	27.9473	−	16.1354i	0.965423	−	0.557387i
$839$	−21.7367	−	12.5497i	−0.750435	−	0.433264i	0.0754160	−	0.997152i	$-0.475972\pi$
$839$	−21.7367	−	12.5497i	−0.750435	−	0.433264i	−0.825851	+	0.563888i	$0.809305\pi$
$840$	44.7752	−	26.9308i	1.54489	−	0.929201i
$841$	9.48604	−	16.4303i	0.327105	−	0.566562i
$842$	−13.1932			−0.454669
$843$	−18.5786	−	10.7264i	−0.639881	−	0.369435i
$844$	51.3497	+	88.9403i	1.76753	+	3.06145i
$845$	40.1770	+	19.3278i	1.38213	+	0.664895i
$846$	17.9566			0.617362
$847$	32.3096	−	19.4332i	1.11017	−	0.667731i
$848$	−1.26479	−	2.19069i	−0.0434332	−	0.0752285i
$849$	4.10738	+	7.11419i	0.140965	+	0.244159i
$850$	−2.92838	+	1.69070i	−0.100443	+	0.0579906i
$851$			68.6090i			2.35189i
$852$	21.2857	−	12.2893i	0.729236	−	0.421025i
$853$		−	41.0459i		−	1.40538i	−0.711494	−	0.702692i	$-0.751981\pi$
$853$		−	41.0459i		−	1.40538i	0.711494	−	0.702692i	$-0.248019\pi$
$854$	9.11898	+	15.1612i	0.312045	+	0.518807i
$855$	7.91671	+	13.7121i	0.270746	+	0.468946i
$856$		−	26.8029i		−	0.916105i
$857$	5.36867	+	9.29880i	0.183390	+	0.317641i	0.943033	−	0.332700i	$-0.107959\pi$
$857$	5.36867	+	9.29880i	0.183390	+	0.317641i	−0.759643	+	0.650341i	$0.774626\pi$
$858$	38.4853	−	24.1930i	1.31386	−	0.825935i
$859$	26.1491	−	45.2917i	0.892197	−	1.54533i	0.0549622	−	0.998488i	$-0.482496\pi$
$859$	26.1491	−	45.2917i	0.892197	−	1.54533i	0.837235	−	0.546843i	$-0.184171\pi$
$860$	32.6217	−	18.8342i	1.11239	−	0.642240i
$861$	−14.2796	+	0.255604i	−0.486649	+	0.00871098i
$862$	−31.0072	+	53.7060i	−1.05611	+	1.82923i
$863$	−37.4567	−	21.6256i	−1.27504	−	0.736145i	−0.299109	−	0.954219i	$-0.596689\pi$
$863$	−37.4567	−	21.6256i	−1.27504	−	0.736145i	−0.975932	+	0.218073i	$0.930023\pi$
$864$		−	3.18005i		−	0.108187i
$865$		−	15.7692i		−	0.536170i
$866$	47.0378	+	27.1573i	1.59841	+	0.922843i
$867$	−8.48014	+	14.6880i	−0.288001	+	0.498832i
$868$	−24.7449	−	41.1410i	−0.839897	−	1.39642i
$869$	−19.6323	+	11.3347i	−0.665980	+	0.384504i
$870$	13.6243	−	23.5980i	0.461907	−	0.800047i
$871$	18.8197	−	35.6264i	0.637680	−	1.20715i
$872$	1.74531	+	3.02297i	0.0591038	+	0.102371i
$873$			5.79714i			0.196203i
$874$	−43.5753	−	75.4746i	−1.47396	−	2.55297i
$875$	−15.9841	+	0.286115i	−0.540362	+	0.00967244i
$876$			13.5476i			0.457729i
$877$	−30.7866	+	17.7747i	−1.03959	+	0.600208i	−0.919717	−	0.392582i	$-0.871582\pi$
$877$	−30.7866	+	17.7747i	−1.03959	+	0.600208i	−0.119873	+	0.992789i	$0.538249\pi$
$878$		−	19.4462i		−	0.656278i
$879$	8.05762	−	4.65207i	0.271777	−	0.156910i
$880$	50.4739	+	87.4233i	1.70147	+	2.94704i
$881$	16.3098	+	28.2494i	0.549491	+	0.951746i	0.998309	+	0.0581231i	$0.0185116\pi$
$881$	16.3098	+	28.2494i	0.549491	+	0.951746i	−0.448819	+	0.893623i	$0.648155\pi$
$882$	−14.8860	+	9.32023i	−0.501238	+	0.313828i
$883$	26.9860			0.908151			0.454075	−	0.890963i	$-0.349970\pi$
$883$	26.9860			0.908151			0.454075	+	0.890963i	$0.349970\pi$
$884$	−0.116048	−	3.08437i	−0.00390310	−	0.103739i
$885$	1.43742	+	2.48969i	0.0483185	+	0.0836901i
$886$	15.4341	+	8.91086i	0.518518	+	0.299366i
$887$	28.8798			0.969687			0.484844	−	0.874601i	$-0.338877\pi$
$887$	28.8798			0.969687			0.484844	+	0.874601i	$0.338877\pi$
$888$	−26.2555	+	45.4758i	−0.881076	+	1.52607i
$889$	22.8476	−	13.7420i	0.766283	−	0.460893i
$890$	17.4829	+	10.0937i	0.586028	+	0.338343i
$891$	4.35178	−	2.51250i	0.145790	−	0.0841719i
$892$	−38.8220	+	22.4139i	−1.29986	+	0.750473i
$893$	33.0416			1.10569
$894$	29.8013			0.996703
$895$	2.69214	−	1.55431i	0.0899883	−	0.0519548i
$896$	41.6244	−	0.745075i	1.39057	−	0.0248912i
$897$	−23.9861	−	12.6707i	−0.800874	−	0.423063i
$898$	−36.4104	+	63.0646i	−1.21503	+	2.10449i
$899$	−11.5862	−	6.68927i	−0.386420	−	0.223100i
$900$	−14.5214	+	25.1518i	−0.484047	+	0.838394i
$901$	−0.0430355	−	0.0745396i	−0.00143372	−	0.00248328i
$902$		−	68.0573i		−	2.26606i
$903$	−5.79782	+	3.48719i	−0.192939	+	0.116046i
$904$	41.4430	+	23.9271i	1.37837	+	0.795804i
$905$	56.1807	+	32.4360i	1.86751	+	1.07821i
$906$	−33.4272			−1.11054
$907$	0.289244	−	0.500985i	0.00960418	−	0.0166349i	−0.861183	−	0.508294i	$-0.830276\pi$
$907$	0.289244	−	0.500985i	0.00960418	−	0.0166349i	0.870788	+	0.491659i	$0.163610\pi$
$908$			42.5236i			1.41119i
$909$	−4.21544			−0.139817
$910$	37.0353	−	73.2544i	1.22771	−	2.42836i
$911$	−46.6019			−1.54399			−0.771994	−	0.635629i	$-0.780741\pi$
$911$	−46.6019			−1.54399			−0.771994	+	0.635629i	$0.780741\pi$
$912$		−	27.0433i		−	0.895493i
$913$	−36.9758	+	64.0439i	−1.22372	+	2.11955i
$914$	−67.8192			−2.24326
$915$	−7.91597	−	4.57029i	−0.261694	−	0.151089i
$916$	58.6556	+	33.8648i	1.93803	+	1.11892i
$917$	−25.5618	−	14.1543i	−0.844126	−	0.467416i
$918$		−	0.500070i		−	0.0165048i
$919$	7.80769	+	13.5233i	0.257552	+	0.446093i	0.965586	−	0.260086i	$-0.0837508\pi$
$919$	7.80769	+	13.5233i	0.257552	+	0.446093i	−0.708034	+	0.706179i	$0.750417\pi$
$920$	74.2920	−	128.677i	2.44933	−	4.24237i
$921$	15.0480	+	8.68795i	0.495848	+	0.286278i
$922$	−3.13579	+	5.43134i	−0.103272	+	0.178872i
$923$	9.63725	−	18.2437i	0.317214	−	0.600499i
$924$	−29.4319	−	48.9336i	−0.968238	−	1.60980i
$925$	53.4005	−	30.8308i	1.75580	−	1.01371i
$926$	−72.5981			−2.38572
$927$	4.22574			0.138792
$928$	−8.72106	+	5.03511i	−0.286283	+	0.165285i
$929$	9.06186	−	5.23187i	0.297310	−	0.171652i	−0.343924	−	0.938998i	$-0.611756\pi$
$929$	9.06186	−	5.23187i	0.297310	−	0.171652i	0.641234	+	0.767346i	$0.278423\pi$
$930$	31.4828	+	18.1766i	1.03236	+	0.596034i
$931$	−27.3914	+	17.1499i	−0.897716	+	0.562066i
$932$	4.09102	−	7.08586i	0.134006	−	0.232105i
$933$	−5.07791			−0.166243
$934$	−18.3990	−	10.6227i	−0.602035	−	0.347585i
$935$	1.71741	+	2.97464i	0.0561653	+	0.0972812i
$936$	−11.0498	−	17.5776i	−0.361173	−	0.574541i
$937$	−37.2603			−1.21724			−0.608621	−	0.793461i	$-0.708277\pi$
$937$	−37.2603			−1.21724			−0.608621	+	0.793461i	$0.708277\pi$
$938$	−64.8963	−	35.9349i	−2.11894	−	1.17332i
$939$	3.64621	+	6.31543i	0.118990	+	0.206096i
$940$	52.7114	+	91.2988i	1.71926	+	2.97784i
$941$	9.05253	−	5.22648i	0.295104	−	0.170378i	−0.345137	−	0.938552i	$-0.612168\pi$
$941$	9.05253	−	5.22648i	0.295104	−	0.170378i	0.640241	+	0.768174i	$0.278834\pi$
$942$			28.2043i			0.918945i
$943$	−35.1723	+	20.3067i	−1.14537	+	0.661278i
$944$		−	4.91020i		−	0.159814i
$945$	4.39551	−	7.93804i	0.142986	−	0.258224i
$946$	−16.1203	−	27.9212i	−0.524116	−	0.907796i
$947$			10.7568i			0.349549i	0.984609	+	0.174774i	$0.0559196\pi$
$947$			10.7568i			0.349549i	−0.984609	+	0.174774i	$0.944080\pi$
$948$	9.68829	+	16.7806i	0.314661	+	0.545009i
$949$	6.05258	+	9.62821i	0.196475	+	0.312545i
$950$	−39.1628	+	67.8320i	−1.27061	+	2.20076i
$951$	−20.5617	+	11.8713i	−0.666757	+	0.384953i
$952$	−3.03606	+	0.0543453i	−0.0983994	+	0.00176134i
$953$	−22.9984	+	39.8344i	−0.744992	+	1.29036i	0.205207	+	0.978719i	$0.434213\pi$
$953$	−22.9984	+	39.8344i	−0.744992	+	1.29036i	−0.950199	+	0.311645i	$0.899120\pi$
$954$	−0.938336	−	0.541749i	−0.0303798	−	0.0175398i
$955$			52.8553i			1.71036i
$956$			112.998i			3.65463i
$957$	−13.7807	−	7.95630i	−0.445467	−	0.257191i
$958$	−30.0661	+	52.0760i	−0.971392	+	1.68250i
$959$	30.0874	−	0.538563i	0.971574	−	0.0173911i
$960$	−11.0978	+	6.40734i	−0.358181	+	0.206796i
$961$	−6.57564	+	11.3893i	−0.212117	+	0.367398i
$962$	3.10158	+	82.4355i	0.0999990	+	2.65783i
$963$	−2.32729	−	4.03099i	−0.0749959	−	0.129897i
$964$			97.0122i			3.12455i
$965$	−13.6592	−	23.6584i	−0.439705	−	0.761592i
$966$	−24.1939	+	43.6927i	−0.778425	+	1.40579i
$967$		−	54.8212i		−	1.76293i	−0.472250	−	0.881465i	$-0.656558\pi$
$967$		−	54.8212i		−	1.76293i	0.472250	−	0.881465i	$-0.343442\pi$
$968$	71.0666	−	41.0303i	2.28417	−	1.31877i
$969$		−	0.920167i		−	0.0295600i
$970$	−43.2000	+	24.9415i	−1.38707	+	0.800823i
$971$	−18.9408	−	32.8064i	−0.607838	−	1.05281i	−0.991596	−	0.129373i	$-0.958704\pi$
$971$	−18.9408	−	32.8064i	−0.607838	−	1.05281i	0.383758	−	0.923434i	$-0.374630\pi$
$972$	−2.14755	−	3.71966i	−0.0688826	−	0.119308i
$973$	−40.5584	−	22.4583i	−1.30024	−	0.719980i
$974$	92.1447			2.95251
$975$	0.916642	+	24.3630i	0.0293560	+	0.780240i
$976$	7.80599	+	13.5204i	0.249864	+	0.432777i
$977$	−45.3003	−	26.1541i	−1.44928	−	0.836745i	−0.450846	−	0.892602i	$-0.648877\pi$
$977$	−45.3003	−	26.1541i	−1.44928	−	0.836745i	−0.998439	+	0.0558573i	$0.982211\pi$
$978$	9.11186			0.291365
$979$	5.89453	−	10.2096i	0.188390	−	0.326301i
$980$	−91.0854	−	48.3271i	−2.90962	−	1.54375i
$981$	0.524968	+	0.303090i	0.0167609	+	0.00967693i
$982$	−21.0149	+	12.1330i	−0.670612	+	0.387178i
$983$	−29.7363	+	17.1683i	−0.948442	+	0.547583i	−0.892597	−	0.450856i	$-0.851119\pi$
$983$	−29.7363	+	17.1683i	−0.948442	+	0.547583i	−0.0558452	+	0.998439i	$0.517785\pi$
$984$	−31.0841			−0.990926
$985$	45.0018			1.43388
$986$	−1.37141	+	0.791783i	−0.0436746	+	0.0252155i
$987$	−9.75963	−	16.2264i	−0.310653	−	0.516492i
$988$	−38.0506	−	60.5295i	−1.21055	−	1.92570i
$989$	−9.61985	+	16.6621i	−0.305893	+	0.529823i
$990$	37.4460	+	21.6195i	1.19011	+	0.687112i
$991$	16.2263	−	28.1048i	0.515446	−	0.892778i	−0.484393	−	0.874850i	$-0.660960\pi$
$991$	16.2263	−	28.1048i	0.515446	−	0.892778i	0.999839	−	0.0179281i	$-0.00570701\pi$
$992$	−6.71749	−	11.6350i	−0.213280	−	0.369413i
$993$			0.0230179i			0.000730451i
$994$	−33.2324	−	18.4017i	−1.05407	−	0.583666i
$995$	−57.9768	−	33.4729i	−1.83799	−	1.06116i
$996$	54.7412	+	31.6049i	1.73454	+	1.00144i
$997$	−2.32191			−0.0735355			−0.0367677	−	0.999324i	$-0.511706\pi$
$997$	−2.32191			−0.0735355			−0.0367677	+	0.999324i	$0.511706\pi$
$998$	34.8175	−	60.3057i	1.10213	−	1.90894i
$999$			9.11903i			0.288513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.d.205.10	yes	20
3.2	odd	2		819.2.bm.g.478.1		20
7.4	even	3		273.2.bl.d.88.1	yes	20
13.4	even	6		273.2.bl.d.121.1	yes	20
21.11	odd	6		819.2.do.g.361.10		20
39.17	odd	6		819.2.do.g.667.10		20
91.4	even	6	inner	273.2.t.d.4.1	✓	20
273.95	odd	6		819.2.bm.g.550.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.1	✓	20	91.4	even	6	inner
273.2.t.d.205.10	yes	20	1.1	even	1	trivial
273.2.bl.d.88.1	yes	20	7.4	even	3
273.2.bl.d.121.1	yes	20	13.4	even	6
819.2.bm.g.478.1		20	3.2	odd	2
819.2.bm.g.550.10		20	273.95	odd	6
819.2.do.g.361.10		20	21.11	odd	6
819.2.do.g.667.10		20	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.50900i q^{2} +(0.500000 - 0.866025i) q^{3} -4.29509 q^{4} +(-2.97008 - 1.71478i) q^{5} +(2.17286 + 1.25450i) q^{6} +(-0.0473512 - 2.64533i) q^{7} -5.75840i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+2.50900i q^{2} +(0.500000 - 0.866025i) q^{3} -4.29509 q^{4} +(-2.97008 - 1.71478i) q^{5} +(2.17286 + 1.25450i) q^{6} +(-0.0473512 - 2.64533i) q^{7} -5.75840i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.30238 - 7.45195i) q^{10} +(-4.35178 - 2.51250i) q^{11} +(-2.14755 + 3.71966i) q^{12} +(0.135561 + 3.60300i) q^{13} +(6.63713 - 0.118804i) q^{14} +(-2.97008 + 1.71478i) q^{15} +5.85764 q^{16} +0.199310 q^{17} +(2.17286 - 1.25450i) q^{18} +(3.99823 - 2.30838i) q^{19} +(12.7568 + 7.36513i) q^{20} +(-2.31460 - 1.28166i) q^{21} +(6.30387 - 10.9186i) q^{22} -7.52372 q^{23} +(-4.98692 - 2.87920i) q^{24} +(3.38093 + 5.85594i) q^{25} +(-9.03994 + 0.340122i) q^{26} -1.00000 q^{27} +(0.203378 + 11.3619i) q^{28} +(1.58334 + 2.74243i) q^{29} +(-4.30238 - 7.45195i) q^{30} +(-3.65876 + 2.11239i) q^{31} +3.18005i q^{32} +(-4.35178 + 2.51250i) q^{33} +0.500070i q^{34} +(-4.39551 + 7.93804i) q^{35} +(2.14755 + 3.71966i) q^{36} -9.11903i q^{37} +(5.79173 + 10.0316i) q^{38} +(3.18807 + 1.68410i) q^{39} +(-9.87437 + 17.1029i) q^{40} +(4.67486 - 2.69903i) q^{41} +(3.21568 - 5.80733i) q^{42} +(1.27860 - 2.21461i) q^{43} +(18.6913 + 10.7914i) q^{44} +3.42956i q^{45} -18.8770i q^{46} +(6.19804 + 3.57844i) q^{47} +(2.92882 - 5.07287i) q^{48} +(-6.99552 + 0.250519i) q^{49} +(-14.6926 + 8.48276i) q^{50} +(0.0996552 - 0.172608i) q^{51} +(-0.582245 - 15.4752i) q^{52} +(-0.215922 - 0.373988i) q^{53} -2.50900i q^{54} +(8.61676 + 14.9247i) q^{55} +(-15.2328 + 0.272667i) q^{56} -4.61676i q^{57} +(-6.88077 + 3.97261i) q^{58} -0.838256i q^{59} +(12.7568 - 7.36513i) q^{60} +(1.33262 + 2.30816i) q^{61} +(-5.29999 - 9.17985i) q^{62} +(-2.26725 + 1.36367i) q^{63} +3.73654 q^{64} +(5.77572 - 10.9337i) q^{65} +(-6.30387 - 10.9186i) q^{66} +(-9.67775 - 5.58745i) q^{67} -0.856057 q^{68} +(-3.76186 + 6.51573i) q^{69} +(-19.9166 - 11.0284i) q^{70} +(-4.95582 - 2.86124i) q^{71} +(-4.98692 + 2.87920i) q^{72} +(2.73161 - 1.57710i) q^{73} +22.8797 q^{74} +6.76186 q^{75} +(-17.1728 + 9.91470i) q^{76} +(-6.44032 + 11.6308i) q^{77} +(-4.22542 + 7.99888i) q^{78} +(2.25566 - 3.90692i) q^{79} +(-17.3977 - 10.0446i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.77187 + 11.7292i) q^{82} -14.7167i q^{83} +(9.94141 + 5.50483i) q^{84} +(-0.591968 - 0.341773i) q^{85} +(5.55645 + 3.20802i) q^{86} +3.16669 q^{87} +(-14.4680 + 25.0593i) q^{88} +2.34608i q^{89} -8.60477 q^{90} +(9.52470 - 0.529209i) q^{91} +32.3151 q^{92} +4.22478i q^{93} +(-8.97832 + 15.5509i) q^{94} -15.8334 q^{95} +(2.75400 + 1.59002i) q^{96} +(-5.02047 - 2.89857i) q^{97} +(-0.628552 - 17.5518i) q^{98} +5.02500i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

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