LMFDB - Embedded newform 273.2.bl.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.1
Root			$0.655911 - 1.25291i$ of defining polynomial
Character	$\chi$	$=$	273.121
Dual form			273.2.bl.c.88.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.17010 + 1.25291i) q^{2} +1.00000 q^{3} +(2.13956 - 3.70583i) q^{4} +(-2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-0.393717 + 2.61629i) q^{7} +5.71107i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-2.17010 + 1.25291i) q^{2} +1.00000 q^{3} +(2.13956 - 3.70583i) q^{4} +(-2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-0.393717 + 2.61629i) q^{7} +5.71107i q^{8} +1.00000 q^{9} +7.55962 q^{10} -1.55123i q^{11} +(2.13956 - 3.70583i) q^{12} +(-0.822385 - 3.51051i) q^{13} +(-2.42357 - 6.17091i) q^{14} +(-2.61265 - 1.50841i) q^{15} +(-2.87633 - 4.98195i) q^{16} +(0.757096 - 1.31133i) q^{17} +(-2.17010 + 1.25291i) q^{18} -8.21689i q^{19} +(-11.1799 + 6.45469i) q^{20} +(-0.393717 + 2.61629i) q^{21} +(1.94355 + 3.36632i) q^{22} +(-1.82307 - 3.15765i) q^{23} +5.71107i q^{24} +(2.05063 + 3.55179i) q^{25} +(6.18301 + 6.58779i) q^{26} +1.00000 q^{27} +(8.85315 + 7.05677i) q^{28} +(2.75027 - 4.76361i) q^{29} +7.55962 q^{30} +(4.47820 - 2.58549i) q^{31} +(2.59199 + 1.49648i) q^{32} -1.55123i q^{33} +3.79429i q^{34} +(4.97510 - 6.24157i) q^{35} +(2.13956 - 3.70583i) q^{36} +(-7.96792 + 4.60028i) q^{37} +(10.2950 + 17.8315i) q^{38} +(-0.822385 - 3.51051i) q^{39} +(8.61466 - 14.9210i) q^{40} +(2.85275 + 1.64704i) q^{41} +(-2.42357 - 6.17091i) q^{42} +(-1.97898 - 3.42770i) q^{43} +(-5.74858 - 3.31895i) q^{44} +(-2.61265 - 1.50841i) q^{45} +(7.91251 + 4.56829i) q^{46} +(8.00565 + 4.62206i) q^{47} +(-2.87633 - 4.98195i) q^{48} +(-6.68997 - 2.06016i) q^{49} +(-8.90014 - 5.13850i) q^{50} +(0.757096 - 1.31133i) q^{51} +(-14.7689 - 4.46334i) q^{52} +(3.90722 + 6.76751i) q^{53} +(-2.17010 + 1.25291i) q^{54} +(-2.33989 + 4.05281i) q^{55} +(-14.9418 - 2.24855i) q^{56} -8.21689i q^{57} +13.7834i q^{58} +(-8.67795 - 5.01022i) q^{59} +(-11.1799 + 6.45469i) q^{60} -10.4713 q^{61} +(-6.47877 + 11.2216i) q^{62} +(-0.393717 + 2.61629i) q^{63} +4.00548 q^{64} +(-3.14670 + 10.4122i) q^{65} +(1.94355 + 3.36632i) q^{66} +2.91388i q^{67} +(-3.23971 - 5.61134i) q^{68} +(-1.82307 - 3.15765i) q^{69} +(-2.97635 + 19.7782i) q^{70} +(-1.11232 + 0.642201i) q^{71} +5.71107i q^{72} +(2.27528 - 1.31363i) q^{73} +(11.5275 - 19.9662i) q^{74} +(2.05063 + 3.55179i) q^{75} +(-30.4504 - 17.5805i) q^{76} +(4.05846 + 0.610745i) q^{77} +(6.18301 + 6.58779i) q^{78} +(-3.28050 + 5.68199i) q^{79} +17.3548i q^{80} +1.00000 q^{81} -8.25435 q^{82} -5.49127i q^{83} +(8.85315 + 7.05677i) q^{84} +(-3.95605 + 2.28403i) q^{85} +(8.58919 + 4.95897i) q^{86} +(2.75027 - 4.76361i) q^{87} +8.85917 q^{88} +(8.45584 - 4.88198i) q^{89} +7.55962 q^{90} +(9.50831 - 0.769452i) q^{91} -15.6023 q^{92} +(4.47820 - 2.58549i) q^{93} -23.1641 q^{94} +(-12.3945 + 21.4679i) q^{95} +(2.59199 + 1.49648i) q^{96} +(10.8340 - 6.25500i) q^{97} +(17.0991 - 3.91117i) q^{98} -1.55123i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.17010	+	1.25291i	−1.53449	+	0.885940i	−0.535347	+	0.844632i	$0.679819\pi$
$2$	−2.17010	+	1.25291i	−1.53449	+	0.885940i	−0.999146	+	0.0413086i	$0.986847\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	2.13956	−	3.70583i	1.06978	−	1.85292i
$5$	−2.61265	−	1.50841i	−1.16841	−	0.674583i	−0.215107	−	0.976591i	$-0.569010\pi$
$5$	−2.61265	−	1.50841i	−1.16841	−	0.674583i	−0.953306	+	0.302007i	$0.902343\pi$
$6$	−2.17010	+	1.25291i	−0.885940	+	0.511498i
$7$	−0.393717	+	2.61629i	−0.148811	+	0.988866i
$7$	−0.393717	+	2.61629i	−0.148811	+	0.988866i
$8$			5.71107i			2.01917i
$9$	1.00000			0.333333
$10$	7.55962			2.39056
$11$		−	1.55123i		−	0.467713i	−0.972271	−	0.233856i	$-0.924865\pi$
$11$		−	1.55123i		−	0.467713i	0.972271	−	0.233856i	$-0.0751345\pi$
$12$	2.13956	−	3.70583i	0.617638	−	1.06978i
$13$	−0.822385	−	3.51051i	−0.228089	−	0.973640i
$13$	−0.822385	−	3.51051i	−0.228089	−	0.973640i
$14$	−2.42357	−	6.17091i	−0.647726	−	1.64925i
$15$	−2.61265	−	1.50841i	−0.674583	−	0.389471i
$16$	−2.87633	−	4.98195i	−0.719082	−	1.24549i
$17$	0.757096	−	1.31133i	0.183623	−	0.318044i	−0.759489	−	0.650520i	$-0.774551\pi$
$17$	0.757096	−	1.31133i	0.183623	−	0.318044i	0.943112	+	0.332477i	$0.107884\pi$
$18$	−2.17010	+	1.25291i	−0.511498	+	0.295313i
$19$		−	8.21689i		−	1.88508i	−0.334088	−	0.942542i	$-0.608428\pi$
$19$		−	8.21689i		−	1.88508i	0.334088	−	0.942542i	$-0.391572\pi$
$20$	−11.1799	+	6.45469i	−2.49989	+	1.44331i
$21$	−0.393717	+	2.61629i	−0.0859161	+	0.570922i
$22$	1.94355	+	3.36632i	0.414365	+	0.717702i
$23$	−1.82307	−	3.15765i	−0.380137	−	0.658416i	0.610945	−	0.791673i	$-0.290790\pi$
$23$	−1.82307	−	3.15765i	−0.380137	−	0.658416i	−0.991082	+	0.133257i	$0.957456\pi$
$24$			5.71107i			1.16577i
$25$	2.05063	+	3.55179i	0.410125	+	0.710358i
$26$	6.18301	+	6.58779i	1.21259	+	1.29197i
$27$	1.00000			0.192450
$28$	8.85315	+	7.05677i	1.67309	+	1.33360i
$29$	2.75027	−	4.76361i	0.510712	−	0.884580i	−0.489211	−	0.872166i	$-0.662715\pi$
$29$	2.75027	−	4.76361i	0.510712	−	0.884580i	0.999923	−	0.0124140i	$-0.00395161\pi$
$30$	7.55962			1.38019
$31$	4.47820	−	2.58549i	0.804308	−	0.464368i	−0.0406670	−	0.999173i	$-0.512948\pi$
$31$	4.47820	−	2.58549i	0.804308	−	0.464368i	0.844975	+	0.534805i	$0.179615\pi$
$32$	2.59199	+	1.49648i	0.458203	+	0.264544i
$33$		−	1.55123i		−	0.270034i
$34$			3.79429i			0.650715i
$35$	4.97510	−	6.24157i	0.840945	−	1.05502i
$36$	2.13956	−	3.70583i	0.356594	−	0.617638i
$37$	−7.96792	+	4.60028i	−1.30992	+	0.756281i	−0.982082	−	0.188453i	$-0.939653\pi$
$37$	−7.96792	+	4.60028i	−1.30992	+	0.756281i	−0.327836	+	0.944735i	$0.606319\pi$
$38$	10.2950	+	17.8315i	1.67007	+	2.89265i
$39$	−0.822385	−	3.51051i	−0.131687	−	0.562132i
$40$	8.61466	−	14.9210i	1.36210	−	2.35922i
$41$	2.85275	+	1.64704i	0.445525	+	0.257224i	0.705938	−	0.708273i	$-0.250526\pi$
$41$	2.85275	+	1.64704i	0.445525	+	0.257224i	−0.260413	+	0.965497i	$0.583859\pi$
$42$	−2.42357	−	6.17091i	−0.373965	−	0.952193i
$43$	−1.97898	−	3.42770i	−0.301792	−	0.522719i	0.674750	−	0.738046i	$-0.264252\pi$
$43$	−1.97898	−	3.42770i	−0.301792	−	0.522719i	−0.976542	+	0.215327i	$0.930918\pi$
$44$	−5.74858	−	3.31895i	−0.866632	−	0.500350i
$45$	−2.61265	−	1.50841i	−0.389471	−	0.224861i
$46$	7.91251	+	4.56829i	1.16664	+	0.673557i
$47$	8.00565	+	4.62206i	1.16774	+	0.674197i	0.953148	−	0.302505i	$-0.0978230\pi$
$47$	8.00565	+	4.62206i	1.16774	+	0.674197i	0.214597	+	0.976703i	$0.431156\pi$
$48$	−2.87633	−	4.98195i	−0.415162	−	0.719082i
$49$	−6.68997	−	2.06016i	−0.955710	−	0.294308i
$50$	−8.90014	−	5.13850i	−1.25867	−	0.726693i
$51$	0.757096	−	1.31133i	0.106015	−	0.183623i
$52$	−14.7689	−	4.46334i	−2.04808	−	0.618953i
$53$	3.90722	+	6.76751i	0.536698	+	0.929588i	0.999079	+	0.0429071i	$0.0136619\pi$
$53$	3.90722	+	6.76751i	0.536698	+	0.929588i	−0.462381	+	0.886681i	$0.653005\pi$
$54$	−2.17010	+	1.25291i	−0.295313	+	0.170499i
$55$	−2.33989	+	4.05281i	−0.315511	+	0.546481i
$56$	−14.9418	−	2.24855i	−1.99669	−	0.300475i
$57$		−	8.21689i		−	1.08835i
$58$			13.7834i			1.80984i
$59$	−8.67795	−	5.01022i	−1.12977	−	0.652275i	−0.185895	−	0.982570i	$-0.559519\pi$
$59$	−8.67795	−	5.01022i	−1.12977	−	0.652275i	−0.943878	+	0.330295i	$0.892852\pi$
$60$	−11.1799	+	6.45469i	−1.44331	+	0.833297i
$61$	−10.4713			−1.34071			−0.670356	−	0.742039i	$-0.733859\pi$
$61$	−10.4713			−1.34071			−0.670356	+	0.742039i	$0.733859\pi$
$62$	−6.47877	+	11.2216i	−0.822804	+	1.42514i
$63$	−0.393717	+	2.61629i	−0.0496037	+	0.329622i
$64$	4.00548			0.500685
$65$	−3.14670	+	10.4122i	−0.390300	+	1.29148i
$66$	1.94355	+	3.36632i	0.239234	+	0.414365i
$67$			2.91388i			0.355987i	0.984032	+	0.177994i	$0.0569606\pi$
$67$			2.91388i			0.355987i	−0.984032	+	0.177994i	$0.943039\pi$
$68$	−3.23971	−	5.61134i	−0.392872	−	0.680474i
$69$	−1.82307	−	3.15765i	−0.219472	−	0.380137i
$70$	−2.97635	+	19.7782i	−0.355742	+	2.36395i
$71$	−1.11232	+	0.642201i	−0.132009	+	0.0762152i	−0.564550	−	0.825399i	$-0.690950\pi$
$71$	−1.11232	+	0.642201i	−0.132009	+	0.0762152i	0.432541	+	0.901614i	$0.357617\pi$
$72$			5.71107i			0.673056i
$73$	2.27528	−	1.31363i	0.266301	−	0.153749i	−0.360905	−	0.932603i	$-0.617532\pi$
$73$	2.27528	−	1.31363i	0.266301	−	0.153749i	0.627205	+	0.778854i	$0.284199\pi$
$74$	11.5275	−	19.9662i	1.34004	−	2.32102i
$75$	2.05063	+	3.55179i	0.236786	+	0.410125i
$76$	−30.4504	−	17.5805i	−3.49290	−	2.01663i
$77$	4.05846	+	0.610745i	0.462505	+	0.0696008i
$78$	6.18301	+	6.58779i	0.700088	+	0.745921i
$79$	−3.28050	+	5.68199i	−0.369085	+	0.639274i	−0.989423	−	0.145061i	$-0.953662\pi$
$79$	−3.28050	+	5.68199i	−0.369085	+	0.639274i	0.620338	+	0.784335i	$0.286996\pi$
$80$			17.3548i			1.94032i
$81$	1.00000			0.111111
$82$	−8.25435			−0.911541
$83$		−	5.49127i		−	0.602746i	−0.953506	−	0.301373i	$-0.902555\pi$
$83$		−	5.49127i		−	0.602746i	0.953506	−	0.301373i	$-0.0974449\pi$
$84$	8.85315	+	7.05677i	0.965958	+	0.769957i
$85$	−3.95605	+	2.28403i	−0.429094	+	0.247738i
$86$	8.58919	+	4.95897i	0.926196	+	0.534740i
$87$	2.75027	−	4.76361i	0.294860	−	0.510712i
$88$	8.85917			0.944390
$89$	8.45584	−	4.88198i	0.896317	−	0.517489i	0.0203135	−	0.999794i	$-0.493534\pi$
$89$	8.45584	−	4.88198i	0.896317	−	0.517489i	0.876003	+	0.482305i	$0.160200\pi$
$90$	7.55962			0.796854
$91$	9.50831	−	0.769452i	0.996742	−	0.0806604i
$92$	−15.6023			−1.62665
$93$	4.47820	−	2.58549i	0.464368	−	0.268103i
$94$	−23.1641			−2.38920
$95$	−12.3945	+	21.4679i	−1.27165	+	2.20256i
$96$	2.59199	+	1.49648i	0.264544	+	0.152734i
$97$	10.8340	−	6.25500i	1.10002	−	0.635099i	0.163796	−	0.986494i	$-0.447626\pi$
$97$	10.8340	−	6.25500i	1.10002	−	0.635099i	0.936227	+	0.351395i	$0.114293\pi$
$98$	17.0991	−	3.91117i	1.72727	−	0.395088i
$99$		−	1.55123i		−	0.155904i
$100$	17.5498			1.75498
$101$	−11.5876			−1.15301			−0.576505	−	0.817094i	$-0.695584\pi$
$101$	−11.5876			−1.15301			−0.576505	+	0.817094i	$0.695584\pi$
$102$			3.79429i			0.375691i
$103$	−0.750179	+	1.29935i	−0.0739174	+	0.128029i	−0.900615	−	0.434618i	$-0.856883\pi$
$103$	−0.750179	+	1.29935i	−0.0739174	+	0.128029i	0.826698	+	0.562647i	$0.190217\pi$
$104$	20.0488	−	4.69670i	1.96594	−	0.460549i
$105$	4.97510	−	6.24157i	0.485520	−	0.609115i
$106$	−16.9581	−	9.79079i	−1.64712	−	0.950965i
$107$	−10.1167	−	17.5226i	−0.978018	−	1.69398i	−0.669594	−	0.742727i	$-0.733532\pi$
$107$	−10.1167	−	17.5226i	−0.978018	−	1.69398i	−0.308423	−	0.951249i	$-0.599801\pi$
$108$	2.13956	−	3.70583i	0.205879	−	0.356594i
$109$	−1.55541	+	0.898018i	−0.148982	+	0.0860145i	−0.572638	−	0.819809i	$-0.694080\pi$
$109$	−1.55541	+	0.898018i	−0.148982	+	0.0860145i	0.423656	+	0.905823i	$0.360746\pi$
$110$		−	11.7267i		−	1.11810i
$111$	−7.96792	+	4.60028i	−0.756281	+	0.436639i
$112$	14.1667	−	5.56384i	1.33863	−	0.525733i
$113$	8.44912	+	14.6343i	0.794826	+	1.37668i	0.922950	+	0.384921i	$0.125771\pi$
$113$	8.44912	+	14.6343i	0.794826	+	1.37668i	−0.128124	+	0.991758i	$0.540895\pi$
$114$	10.2950	+	17.8315i	0.964216	+	1.67007i
$115$			10.9998i			1.02574i
$116$	−11.7687	−	20.3841i	−1.09270	−	1.89261i
$117$	−0.822385	−	3.51051i	−0.0760295	−	0.324547i
$118$	25.1094			2.31151
$119$	3.13274	+	2.49708i	0.287177	+	0.228907i
$120$	8.61466	−	14.9210i	0.786407	−	1.36210i
$121$	8.59369			0.781245
$122$	22.7238	−	13.1196i	2.05732	−	1.18779i
$123$	2.85275	+	1.64704i	0.257224	+	0.148508i
$124$		−	22.1273i		−	1.98709i
$125$			2.71137i			0.242512i
$126$	−2.42357	−	6.17091i	−0.215909	−	0.549749i
$127$	−5.34134	+	9.25146i	−0.473967	+	0.820935i	−0.999556	−	0.0298040i	$-0.990512\pi$
$127$	−5.34134	+	9.25146i	−0.473967	+	0.820935i	0.525589	+	0.850739i	$0.323845\pi$
$128$	−13.8763	+	8.01147i	−1.22650	+	0.708120i
$129$	−1.97898	−	3.42770i	−0.174240	−	0.301792i
$130$	−6.21692	−	26.5381i	−0.545260	−	2.32755i
$131$	−0.296957	+	0.514345i	−0.0259453	+	0.0449386i	−0.878707	−	0.477362i	$-0.841593\pi$
$131$	−0.296957	+	0.514345i	−0.0259453	+	0.0449386i	0.852761	+	0.522301i	$0.174926\pi$
$132$	−5.74858	−	3.31895i	−0.500350	−	0.288877i
$133$	21.4978	+	3.23513i	1.86409	+	0.280521i
$134$	−3.65083	−	6.32342i	−0.315383	−	0.546260i
$135$	−2.61265	−	1.50841i	−0.224861	−	0.129824i
$136$	7.48909	+	4.32383i	0.642184	+	0.370765i
$137$	4.33949	+	2.50540i	0.370747	+	0.214051i	0.673785	−	0.738928i	$-0.264667\pi$
$137$	4.33949	+	2.50540i	0.370747	+	0.214051i	−0.303038	+	0.952979i	$0.598001\pi$
$138$	7.91251	+	4.56829i	0.673557	+	0.388878i
$139$	8.33459	+	14.4359i	0.706930	+	1.22444i	0.965990	+	0.258578i	$0.0832539\pi$
$139$	8.33459	+	14.4359i	0.706930	+	1.22444i	−0.259060	+	0.965861i	$0.583413\pi$
$140$	−12.4857	−	31.7911i	−1.05523	−	2.68684i
$141$	8.00565	+	4.62206i	0.674197	+	0.389248i
$142$	1.60924	−	2.78728i	0.135044	−	0.233903i
$143$	−5.44560	+	1.27571i	−0.455384	+	0.106680i
$144$	−2.87633	−	4.98195i	−0.239694	−	0.415162i
$145$	−14.3710	+	8.29709i	−1.19345	+	0.689036i
$146$	−3.29172	+	5.70143i	−0.272425	+	0.471853i
$147$	−6.68997	−	2.06016i	−0.551780	−	0.169919i
$148$			39.3703i			3.23622i
$149$		−	2.02603i		−	0.165978i	−0.996550	−	0.0829892i	$-0.973553\pi$
$149$		−	2.02603i		−	0.165978i	0.996550	−	0.0829892i	$-0.0264467\pi$
$150$	−8.90014	−	5.13850i	−0.726693	−	0.419557i
$151$	8.08579	−	4.66833i	0.658012	−	0.379904i	−0.133507	−	0.991048i	$-0.542624\pi$
$151$	8.08579	−	4.66833i	0.658012	−	0.379904i	0.791519	+	0.611144i	$0.209290\pi$
$152$	46.9272			3.80630
$153$	0.757096	−	1.31133i	0.0612076	−	0.106015i
$154$	−9.57249	+	3.75951i	−0.771373	+	0.302950i
$155$	−15.6000			−1.25302
$156$	−14.7689	−	4.46334i	−1.18246	−	0.357353i
$157$	−5.90209	−	10.2227i	−0.471038	−	0.815862i	0.528413	−	0.848988i	$-0.322787\pi$
$157$	−5.90209	−	10.2227i	−0.471038	−	0.815862i	−0.999451	+	0.0331251i	$0.989454\pi$
$158$		−	16.4407i		−	1.30795i
$159$	3.90722	+	6.76751i	0.309863	+	0.536698i
$160$	−4.51464	−	7.81958i	−0.356913	−	0.618192i
$161$	8.97912	−	3.52647i	0.707654	−	0.277925i
$162$	−2.17010	+	1.25291i	−0.170499	+	0.0984378i
$163$		−	0.592417i		−	0.0464017i	−0.999731	−	0.0232008i	$-0.992614\pi$
$163$		−	0.592417i		−	0.0464017i	0.999731	−	0.0232008i	$-0.00738572\pi$
$164$	12.2073	−	7.04788i	0.953228	−	0.550347i
$165$	−2.33989	+	4.05281i	−0.182160	+	0.315511i
$166$	6.88007	+	11.9166i	0.533997	+	0.924909i
$167$	7.52026	+	4.34182i	0.581935	+	0.335980i	0.761902	−	0.647692i	$-0.224266\pi$
$167$	7.52026	+	4.34182i	0.581935	+	0.335980i	−0.179967	+	0.983673i	$0.557599\pi$
$168$	−14.9418	−	2.24855i	−1.15279	−	0.173479i
$169$	−11.6474	+	5.77398i	−0.895951	+	0.444153i
$170$	5.72336	−	9.91315i	0.438962	−	0.760304i
$171$		−	8.21689i		−	0.628361i
$172$	−16.9366			−1.29141
$173$	13.7590			1.04608			0.523041	−	0.852308i	$-0.324798\pi$
$173$	13.7590			1.04608			0.523041	+	0.852308i	$0.324798\pi$
$174$			13.7834i			1.04491i
$175$	−10.0999	+	3.96664i	−0.763480	+	0.299850i
$176$	−7.72813	+	4.46184i	−0.582530	+	0.336324i
$177$	−8.67795	−	5.01022i	−0.652275	−	0.376591i
$178$	−12.2334	+	21.1888i	−0.916929	+	1.58817i
$179$	1.07062			0.0800223			0.0400111	−	0.999199i	$-0.487261\pi$
$179$	1.07062			0.0800223			0.0400111	+	0.999199i	$0.487261\pi$
$180$	−11.1799	+	6.45469i	−0.833297	+	0.481104i
$181$	9.60905			0.714235			0.357117	−	0.934059i	$-0.383760\pi$
$181$	9.60905			0.714235			0.357117	+	0.934059i	$0.383760\pi$
$182$	−19.6699	+	13.5828i	−1.45803	+	1.00683i
$183$	−10.4713			−0.774061
$184$	18.0336	−	10.4117i	1.32945	−	0.767560i
$185$	27.7565			2.04070
$186$	−6.47877	+	11.2216i	−0.475046	+	0.822804i
$187$	−2.03417	−	1.17443i	−0.148753	−	0.0858826i
$188$	34.2572	−	19.7784i	2.49846	−	1.44249i
$189$	−0.393717	+	2.61629i	−0.0286387	+	0.190307i
$190$		−	62.1166i		−	4.50641i
$191$	−21.0359			−1.52210			−0.761051	−	0.648692i	$-0.775316\pi$
$191$	−21.0359			−1.52210			−0.761051	+	0.648692i	$0.775316\pi$
$192$	4.00548			0.289071
$193$			7.87112i			0.566576i	0.959035	+	0.283288i	$0.0914252\pi$
$193$			7.87112i			0.566576i	−0.959035	+	0.283288i	$0.908575\pi$
$194$	−15.6739	+	27.1480i	−1.12532	+	1.94911i
$195$	−3.14670	+	10.4122i	−0.225340	+	0.745635i
$196$	−21.9482	+	20.3841i	−1.56773	+	1.45600i
$197$	0.193007	+	0.111433i	0.0137512	+	0.00793924i	0.506860	−	0.862028i	$-0.330806\pi$
$197$	0.193007	+	0.111433i	0.0137512	+	0.00793924i	−0.493109	+	0.869968i	$0.664140\pi$
$198$	1.94355	+	3.36632i	0.138122	+	0.239234i
$199$	5.81292	−	10.0683i	0.412067	−	0.713720i	−0.583049	−	0.812437i	$-0.698140\pi$
$199$	5.81292	−	10.0683i	0.412067	−	0.713720i	0.995116	+	0.0987166i	$0.0314737\pi$
$200$	−20.2845	+	11.7113i	−1.43433	+	0.828112i
$201$			2.91388i			0.205529i
$202$	25.1463	−	14.5182i	1.76929	−	1.02150i
$203$	11.3802	+	9.07103i	0.798731	+	0.636661i
$204$	−3.23971	−	5.61134i	−0.226825	−	0.392872i
$205$	−4.96883	−	8.60626i	−0.347038	−	0.601087i
$206$		−	3.75963i		−	0.261946i
$207$	−1.82307	−	3.15765i	−0.126712	−	0.219472i
$208$	−15.1237	+	14.1945i	−1.04864	+	0.984209i
$209$	−12.7463			−0.881677
$210$	−2.97635	+	19.7782i	−0.205388	+	1.36482i
$211$	8.79477	−	15.2330i	0.605457	−	1.04868i	−0.386522	−	0.922280i	$-0.626324\pi$
$211$	8.79477	−	15.2330i	0.605457	−	1.04868i	0.991979	−	0.126402i	$-0.0403430\pi$
$212$	33.4390			2.29660
$213$	−1.11232	+	0.642201i	−0.0762152	+	0.0440029i
$214$	43.9085	+	25.3506i	3.00152	+	1.73293i
$215$			11.9405i			0.814336i
$216$			5.71107i			0.388589i
$217$	5.00125	+	12.7342i	0.339507	+	0.864456i
$218$	2.25027	−	3.89758i	0.152408	−	0.263978i
$219$	2.27528	−	1.31363i	0.153749	−	0.0887670i
$220$	10.0127	+	17.3425i	0.675056	+	1.16923i
$221$	−5.22606	−	1.57938i	−0.351543	−	0.106240i
$222$	11.5275	−	19.9662i	0.773673	−	1.34004i
$223$	−15.7545	−	9.09585i	−1.05500	−	0.609103i	−0.130953	−	0.991389i	$-0.541804\pi$
$223$	−15.7545	−	9.09585i	−1.05500	−	0.609103i	−0.924044	+	0.382285i	$0.875137\pi$
$224$	−4.93575	+	6.19220i	−0.329784	+	0.413734i
$225$	2.05063	+	3.55179i	0.136708	+	0.236786i
$226$	−36.6709	−	21.1719i	−2.43931	−	1.40834i
$227$	−17.8461	−	10.3034i	−1.18449	−	0.683863i	−0.227438	−	0.973793i	$-0.573035\pi$
$227$	−17.8461	−	10.3034i	−1.18449	−	0.683863i	−0.957048	+	0.289929i	$0.906368\pi$
$228$	−30.4504	−	17.5805i	−2.01663	−	1.16430i
$229$	6.95359	+	4.01466i	0.459506	+	0.265296i	0.711837	−	0.702345i	$-0.247864\pi$
$229$	6.95359	+	4.01466i	0.459506	+	0.265296i	−0.252330	+	0.967641i	$0.581197\pi$
$230$	−13.7817	−	23.8707i	−0.908741	−	1.57399i
$231$	4.05846	+	0.610745i	0.267027	+	0.0401841i
$232$	27.2053	+	15.7070i	1.78612	+	1.03121i
$233$	7.15034	−	12.3848i	0.468434	−	0.811352i	−0.530915	−	0.847425i	$-0.678152\pi$
$233$	7.15034	−	12.3848i	0.468434	−	0.811352i	0.999349	+	0.0360731i	$0.0114849\pi$
$234$	6.18301	+	6.58779i	0.404196	+	0.430657i
$235$	−13.9440	−	24.1517i	−0.909605	−	1.57548i
$236$	−37.1340	+	21.4393i	−2.41722	+	1.39558i
$237$	−3.28050	+	5.68199i	−0.213091	+	0.369085i
$238$	−9.92697	−	1.49388i	−0.643470	−	0.0968336i
$239$			4.31863i			0.279349i	0.990197	+	0.139674i	$0.0446056\pi$
$239$			4.31863i			0.279349i	−0.990197	+	0.139674i	$0.955394\pi$
$240$			17.3548i			1.12025i
$241$	1.15146	+	0.664798i	0.0741723	+	0.0428234i	0.536627	−	0.843819i	$-0.319698\pi$
$241$	1.15146	+	0.664798i	0.0741723	+	0.0428234i	−0.462455	+	0.886643i	$0.653031\pi$
$242$	−18.6492	+	10.7671i	−1.19882	+	0.692137i
$243$	1.00000			0.0641500
$244$	−22.4040	+	38.8049i	−1.43427	+	2.48423i
$245$	14.3710	+	15.4737i	0.918129	+	0.988580i
$246$	−8.25435			−0.526278
$247$	−28.8455	+	6.75745i	−1.83539	+	0.429966i
$248$	14.7659	+	25.5753i	0.937637	+	1.62403i
$249$		−	5.49127i		−	0.347995i
$250$	−3.39709	−	5.88394i	−0.214851	−	0.372133i
$251$	1.13399	+	1.96413i	0.0715769	+	0.123975i	0.899593	−	0.436730i	$-0.143864\pi$
$251$	1.13399	+	1.96413i	0.0715769	+	0.123975i	−0.828016	+	0.560705i	$0.810530\pi$
$252$	8.85315	+	7.05677i	0.557696	+	0.444535i
$253$	−4.89824	+	2.82800i	−0.307950	+	0.177795i
$254$		−	26.7688i		−	1.67963i
$255$	−3.95605	+	2.28403i	−0.247738	+	0.143031i
$256$	16.0698	−	27.8337i	1.00436	−	1.73961i
$257$	5.92412	+	10.2609i	0.369537	+	0.640056i	0.989493	−	0.144580i	$-0.0461831\pi$
$257$	5.92412	+	10.2609i	0.369537	+	0.640056i	−0.619956	+	0.784636i	$0.712850\pi$
$258$	8.58919	+	4.95897i	0.534740	+	0.308732i
$259$	−8.89857	−	22.6576i	−0.552930	−	1.40788i
$260$	31.8534	+	33.9388i	1.97546	+	2.10479i
$261$	2.75027	−	4.76361i	0.170237	−	0.294860i
$262$		−	1.48824i		−	0.0919440i
$263$	−20.8767			−1.28731			−0.643655	−	0.765316i	$-0.722583\pi$
$263$	−20.8767			−1.28731			−0.643655	+	0.765316i	$0.722583\pi$
$264$	8.85917			0.545244
$265$		−	23.5748i		−	1.44819i
$266$	−50.7057	+	19.9142i	−3.10897	+	1.22102i
$267$	8.45584	−	4.88198i	0.517489	−	0.298772i
$268$	10.7983	+	6.23443i	0.659614	+	0.380828i
$269$	6.15988	−	10.6692i	0.375574	−	0.650514i	−0.614838	−	0.788653i	$-0.710779\pi$
$269$	6.15988	−	10.6692i	0.375574	−	0.650514i	0.990413	+	0.138139i	$0.0441121\pi$
$270$	7.55962			0.460064
$271$	17.9051	−	10.3375i	1.08766	−	0.627960i	0.154707	−	0.987960i	$-0.450557\pi$
$271$	17.9051	−	10.3375i	1.08766	−	0.627960i	0.932952	+	0.360000i	$0.117223\pi$
$272$	−8.71062			−0.528159
$273$	9.50831	−	0.769452i	0.575469	−	0.0465693i
$274$	−12.5562			−0.758546
$275$	5.50963	−	3.18099i	0.332243	−	0.191821i
$276$	−15.6023			−0.939148
$277$	3.55165	−	6.15163i	0.213398	−	0.369616i	−0.739378	−	0.673291i	$-0.764880\pi$
$277$	3.55165	−	6.15163i	0.213398	−	0.369616i	0.952776	+	0.303675i	$0.0982136\pi$
$278$	−36.1738	−	20.8850i	−2.16956	−	1.25260i
$279$	4.47820	−	2.58549i	0.268103	−	0.154789i
$280$	35.6460	+	28.4131i	2.13026	+	1.69801i
$281$		−	25.8932i		−	1.54466i	−0.635223	−	0.772329i	$-0.719092\pi$
$281$		−	25.8932i		−	1.54466i	0.635223	−	0.772329i	$-0.280908\pi$
$282$	−23.1641			−1.37940
$283$	26.1969			1.55724			0.778621	−	0.627494i	$-0.215919\pi$
$283$	26.1969			1.55724			0.778621	+	0.627494i	$0.215919\pi$
$284$			5.49611i			0.326134i
$285$	−12.3945	+	21.4679i	−0.734185	+	1.27165i
$286$	10.2192	−	9.59125i	0.604272	−	0.567143i
$287$	−5.43231	+	6.81517i	−0.320659	+	0.402287i
$288$	2.59199	+	1.49648i	0.152734	+	0.0881812i
$289$	7.35361	+	12.7368i	0.432565	+	0.749225i
$290$	20.7910	−	36.0111i	1.22089	−	2.11464i
$291$	10.8340	−	6.25500i	0.635099	−	0.366674i
$292$		−	11.2424i		−	0.657911i
$293$	7.57306	−	4.37231i	0.442423	−	0.255433i	−0.262202	−	0.965013i	$-0.584449\pi$
$293$	7.57306	−	4.37231i	0.442423	−	0.255433i	0.704625	+	0.709580i	$0.251115\pi$
$294$	17.0991	−	3.91117i	0.997241	−	0.228104i
$295$	15.1150	+	26.1799i	0.880028	+	1.52425i
$296$	−26.2725	−	45.5054i	−1.52706	−	2.64494i
$297$		−	1.55123i		−	0.0900113i
$298$	2.53843	+	4.39668i	0.147047	+	0.254693i
$299$	−9.58571	+	8.99672i	−0.554356	+	0.520294i
$300$	17.5498			1.01324
$301$	9.74702	−	3.82805i	0.561809	−	0.220645i
$302$	−11.6980	+	20.2615i	−0.673144	+	1.16592i
$303$	−11.5876			−0.665690
$304$	−40.9361	+	23.6345i	−2.34785	+	1.35553i
$305$	27.3578	+	15.7951i	1.56651	+	0.904422i
$306$			3.79429i			0.216905i
$307$		−	1.43567i		−	0.0819379i	−0.999160	−	0.0409689i	$-0.986956\pi$
$307$		−	1.43567i		−	0.0819379i	0.999160	−	0.0409689i	$-0.0130445\pi$
$308$	10.9467	−	13.7333i	0.623743	−	0.782525i
$309$	−0.750179	+	1.29935i	−0.0426762	+	0.0739174i
$310$	33.8535	−	19.5453i	1.92275	−	1.11010i
$311$	11.8624	+	20.5463i	0.672655	+	1.16507i	0.977148	+	0.212558i	$0.0681794\pi$
$311$	11.8624	+	20.5463i	0.672655	+	1.16507i	−0.304494	+	0.952514i	$0.598487\pi$
$312$	20.0488	−	4.69670i	1.13504	−	0.265898i
$313$	10.9459	−	18.9588i	0.618697	−	1.07161i	−0.371027	−	0.928622i	$-0.620994\pi$
$313$	10.9459	−	18.9588i	0.618697	−	1.07161i	0.989724	−	0.142993i	$-0.0456725\pi$
$314$	25.6163	+	14.7896i	1.44561	+	0.834624i
$315$	4.97510	−	6.24157i	0.280315	−	0.351673i
$316$	14.0377	+	24.3139i	0.789680	+	1.36777i
$317$	25.9713	+	14.9946i	1.45869	+	0.842178i	0.998947	−	0.0458717i	$-0.0146065\pi$
$317$	25.9713	+	14.9946i	1.45869	+	0.842178i	0.459748	+	0.888050i	$0.347940\pi$
$318$	−16.9581	−	9.79079i	−0.950965	−	0.549040i
$319$	−7.38944	−	4.26629i	−0.413729	−	0.238867i
$320$	−10.4649	−	6.04192i	−0.585006	−	0.337754i
$321$	−10.1167	−	17.5226i	−0.564659	−	0.978018i
$322$	−15.0673	+	18.9028i	−0.839666	+	1.05341i
$323$	−10.7750	−	6.22097i	−0.599539	−	0.346144i
$324$	2.13956	−	3.70583i	0.118865	−	0.205879i
$325$	10.7822	−	10.1197i	0.598088	−	0.561339i
$326$	0.742245	+	1.28561i	0.0411091	+	0.0712031i
$327$	−1.55541	+	0.898018i	−0.0860145	+	0.0496605i
$328$	−9.40635	+	16.2923i	−0.519379	+	0.899590i
$329$	−15.2446	+	19.1253i	−0.840464	+	1.05441i
$330$		−	11.7267i		−	0.645533i
$331$			16.3588i			0.899163i	0.893239	+	0.449581i	$0.148427\pi$
$331$			16.3588i			0.899163i	−0.893239	+	0.449581i	$0.851573\pi$
$332$	−20.3497	−	11.7489i	−1.11684	−	0.644806i
$333$	−7.96792	+	4.60028i	−0.436639	+	0.252094i
$334$	−21.7596			−1.19063
$335$	4.39534	−	7.61295i	0.240143	−	0.415940i
$336$	14.1667	−	5.56384i	0.772856	−	0.303532i
$337$	30.4117			1.65663			0.828316	−	0.560261i	$-0.189299\pi$
$337$	30.4117			1.65663			0.828316	+	0.560261i	$0.189299\pi$
$338$	18.0417	−	27.1232i	0.981339	−	1.47531i
$339$	8.44912	+	14.6343i	0.458893	+	0.794826i
$340$			19.5473i			1.06010i
$341$	−4.01068	−	6.94671i	−0.217191	−	0.376185i
$342$	10.2950	+	17.8315i	0.556691	+	0.964216i
$343$	8.02394	−	16.6918i	0.433252	−	0.901273i
$344$	19.5758	−	11.3021i	1.05546	−	0.609369i
$345$			10.9998i			0.592209i
$346$	−29.8585	+	17.2388i	−1.60521	+	0.926766i
$347$	−7.65336	+	13.2560i	−0.410854	+	0.711620i	−0.994983	−	0.100041i	$-0.968103\pi$
$347$	−7.65336	+	13.2560i	−0.410854	+	0.711620i	0.584130	+	0.811660i	$0.301436\pi$
$348$	−11.7687	−	20.3841i	−0.630871	−	1.09270i
$349$	8.28543	+	4.78359i	0.443509	+	0.256060i	0.705085	−	0.709123i	$-0.250909\pi$
$349$	8.28543	+	4.78359i	0.443509	+	0.256060i	−0.261576	+	0.965183i	$0.584242\pi$
$350$	16.9479	−	21.2623i	0.905906	−	1.13652i
$351$	−0.822385	−	3.51051i	−0.0438957	−	0.187377i
$352$	2.32139	−	4.02076i	0.123730	−	0.214307i
$353$		−	12.4900i		−	0.664774i	−0.943143	−	0.332387i	$-0.892146\pi$
$353$		−	12.4900i		−	0.664774i	0.943143	−	0.332387i	$-0.107854\pi$
$354$	25.1094			1.33455
$355$	3.87482			0.205654
$356$		−	41.7812i		−	2.21440i
$357$	3.13274	+	2.49708i	0.165802	+	0.132159i
$358$	−2.32337	+	1.34140i	−0.122794	+	0.0708950i
$359$	9.56860	+	5.52443i	0.505012	+	0.291569i	0.730781	−	0.682612i	$-0.239156\pi$
$359$	9.56860	+	5.52443i	0.505012	+	0.291569i	−0.225769	+	0.974181i	$0.572490\pi$
$360$	8.61466	−	14.9210i	0.454032	−	0.786407i
$361$	−48.5173			−2.55354
$362$	−20.8526	+	12.0393i	−1.09599	+	0.632770i
$363$	8.59369			0.451052
$364$	17.4922	−	36.8825i	0.916838	−	1.93317i
$365$	−7.92600			−0.414866
$366$	22.7238	−	13.1196i	1.18779	−	0.685772i
$367$	−12.9217			−0.674505			−0.337253	−	0.941414i	$-0.609498\pi$
$367$	−12.9217			−0.674505			−0.337253	+	0.941414i	$0.609498\pi$
$368$	−10.4875	+	18.1649i	−0.546699	+	0.946911i
$369$	2.85275	+	1.64704i	0.148508	+	0.0857413i
$370$	−60.2345	+	34.7764i	−3.13144	+	1.80794i
$371$	−19.2441	+	7.55795i	−0.999105	+	0.392389i
$372$		−	22.1273i		−	1.14725i
$373$	−9.02766			−0.467434			−0.233717	−	0.972305i	$-0.575089\pi$
$373$	−9.02766			−0.467434			−0.233717	+	0.972305i	$0.575089\pi$
$374$	5.88580			0.304348
$375$			2.71137i			0.140014i
$376$	−26.3969	+	45.7208i	−1.36132	+	2.35787i
$377$	−18.9845	−	5.73733i	−0.977750	−	0.295488i
$378$	−2.42357	−	6.17091i	−0.124655	−	0.317398i
$379$	−14.6856	−	8.47871i	−0.754346	−	0.435522i	0.0729159	−	0.997338i	$-0.476770\pi$
$379$	−14.6856	−	8.47871i	−0.754346	−	0.435522i	−0.827262	+	0.561816i	$0.810103\pi$
$380$	53.0375	+	91.8636i	2.72077	+	4.71250i
$381$	−5.34134	+	9.25146i	−0.273645	+	0.473967i
$382$	45.6500	−	26.3560i	2.33566	−	1.34849i
$383$		−	2.05258i		−	0.104882i	−0.998624	−	0.0524409i	$-0.983300\pi$
$383$		−	2.05258i		−	0.104882i	0.998624	−	0.0524409i	$-0.0167001\pi$
$384$	−13.8763	+	8.01147i	−0.708120	+	0.408834i
$385$	−9.68209	−	7.71751i	−0.493445	−	0.393321i
$386$	−9.86180	−	17.0811i	−0.501953	−	0.869407i
$387$	−1.97898	−	3.42770i	−0.100597	−	0.174240i
$388$		−	53.5318i		−	2.71767i
$389$	15.7463	+	27.2733i	0.798367	+	1.38281i	0.920679	+	0.390321i	$0.127636\pi$
$389$	15.7463	+	27.2733i	0.798367	+	1.38281i	−0.122312	+	0.992492i	$0.539031\pi$
$390$	−6.21692	−	26.5381i	−0.314806	−	1.34381i
$391$	−5.52096			−0.279207
$392$	11.7657	−	38.2069i	0.594258	−	1.92974i
$393$	−0.296957	+	0.514345i	−0.0149795	+	0.0259453i
$394$	−0.558460			−0.0281348
$395$	17.1416	−	9.89670i	0.862487	−	0.497957i
$396$	−5.74858	−	3.31895i	−0.288877	−	0.166783i
$397$			11.5650i			0.580431i	0.956961	+	0.290216i	$0.0937270\pi$
$397$			11.5650i			0.580431i	−0.956961	+	0.290216i	$0.906273\pi$
$398$			29.1322i			1.46027i
$399$	21.4978	+	3.23513i	1.07624	+	0.161959i
$400$	11.7965	−	20.4322i	0.589827	−	1.02161i
$401$	3.68588	−	2.12805i	0.184064	−	0.106270i	−0.405137	−	0.914256i	$-0.632776\pi$
$401$	3.68588	−	2.12805i	0.184064	−	0.106270i	0.589201	+	0.807987i	$0.299443\pi$
$402$	−3.65083	−	6.32342i	−0.182087	−	0.315383i
$403$	−12.7592	−	13.5945i	−0.635581	−	0.677190i
$404$	−24.7924	+	42.9417i	−1.23347	+	2.13643i
$405$	−2.61265	−	1.50841i	−0.129824	−	0.0749537i
$406$	−36.0613	−	5.42674i	−1.78969	−	0.269325i
$407$	7.13608	+	12.3601i	0.353722	+	0.612665i
$408$	7.48909	+	4.32383i	0.370765	+	0.214061i
$409$	−9.59029	−	5.53696i	−0.474209	−	0.273785i	0.243791	−	0.969828i	$-0.421609\pi$
$409$	−9.59029	−	5.53696i	−0.474209	−	0.273785i	−0.718000	+	0.696043i	$0.754942\pi$
$410$	21.5657	+	12.4510i	1.06506	+	0.614910i
$411$	4.33949	+	2.50540i	0.214051	+	0.123582i
$412$	3.21011	+	5.56008i	0.158151	+	0.273925i
$413$	16.5249	−	20.7315i	0.813135	−	1.02013i
$414$	7.91251	+	4.56829i	0.388878	+	0.224519i
$415$	−8.28311	+	14.3468i	−0.406602	+	0.704255i
$416$	3.12181	−	10.3299i	0.153059	−	0.506464i
$417$	8.33459	+	14.4359i	0.408146	+	0.706930i
$418$	27.6607	−	15.9699i	1.35293	−	0.781114i
$419$	−1.10511	+	1.91411i	−0.0539884	+	0.0935106i	−0.891757	−	0.452515i	$-0.850527\pi$
$419$	−1.10511	+	1.91411i	−0.0539884	+	0.0935106i	0.837768	+	0.546026i	$0.183860\pi$
$420$	−12.4857	−	31.7911i	−0.609238	−	1.55125i
$421$			15.9741i			0.778532i	0.921125	+	0.389266i	$0.127271\pi$
$421$			15.9741i			0.778532i	−0.921125	+	0.389266i	$0.872729\pi$
$422$			44.0762i			2.14560i
$423$	8.00565	+	4.62206i	0.389248	+	0.224732i
$424$	−38.6497	+	22.3144i	−1.87700	+	1.08368i
$425$	6.21008			0.301233
$426$	1.60924	−	2.78728i	0.0779678	−	0.135044i
$427$	4.12273	−	27.3960i	0.199513	−	1.32578i
$428$	−86.5812			−4.18506
$429$	−5.44560	+	1.27571i	−0.262916	+	0.0615917i
$430$	−14.9604	−	25.9121i	−0.721453	−	1.24959i
$431$		−	23.6203i		−	1.13775i	−0.822423	−	0.568876i	$-0.807378\pi$
$431$		−	23.6203i		−	1.13775i	0.822423	−	0.568876i	$-0.192622\pi$
$432$	−2.87633	−	4.98195i	−0.138387	−	0.239694i
$433$	0.771302	+	1.33593i	0.0370664	+	0.0642009i	0.883963	−	0.467556i	$-0.154865\pi$
$433$	0.771302	+	1.33593i	0.0370664	+	0.0642009i	−0.846897	+	0.531757i	$0.821532\pi$
$434$	−26.8081	−	21.3685i	−1.28683	−	1.02572i
$435$	−14.3710	+	8.29709i	−0.689036	+	0.397815i
$436$			7.68546i			0.368067i
$437$	−25.9461	+	14.9800i	−1.24117	+	0.716590i
$438$	−3.29172	+	5.70143i	−0.157284	+	0.272425i
$439$	−15.8570	−	27.4651i	−0.756813	−	1.31084i	−0.944468	−	0.328604i	$-0.893422\pi$
$439$	−15.8570	−	27.4651i	−0.756813	−	1.31084i	0.187654	−	0.982235i	$-0.439912\pi$
$440$	−23.1459	−	13.3633i	−1.10344	−	0.637070i
$441$	−6.68997	−	2.06016i	−0.318570	−	0.0981028i
$442$	13.3199	−	3.12037i	0.633562	−	0.148421i
$443$	−3.37631	+	5.84795i	−0.160414	+	0.277844i	−0.935017	−	0.354603i	$-0.884616\pi$
$443$	−3.37631	+	5.84795i	−0.160414	+	0.277844i	0.774604	+	0.632447i	$0.217949\pi$
$444$			39.3703i			1.86843i
$445$	−29.4562			−1.39636
$446$	45.5851			2.15852
$447$		−	2.02603i		−	0.0958277i
$448$	−1.57703	+	10.4795i	−0.0745075	+	0.495110i
$449$	−2.75752	+	1.59206i	−0.130136	+	0.0751338i	−0.563655	−	0.826011i	$-0.690605\pi$
$449$	−2.75752	+	1.59206i	−0.130136	+	0.0751338i	0.433519	+	0.901144i	$0.357272\pi$
$450$	−8.90014	−	5.13850i	−0.419557	−	0.242231i
$451$	2.55493	−	4.42527i	0.120307	−	0.208378i
$452$	72.3096			3.40116
$453$	8.08579	−	4.66833i	0.379904	−	0.219337i
$454$	51.6371			2.42345
$455$	−26.0025	−	12.3322i	−1.21902	−	0.578141i
$456$	46.9272			2.19757
$457$	−23.6118	+	13.6323i	−1.10451	+	0.637690i	−0.937402	−	0.348248i	$-0.886777\pi$
$457$	−23.6118	+	13.6323i	−1.10451	+	0.637690i	−0.167110	+	0.985938i	$0.553443\pi$
$458$	−20.1200			−0.940146
$459$	0.757096	−	1.31133i	0.0353382	−	0.0612076i
$460$	40.7634	+	23.5347i	1.90060	+	1.09731i
$461$	−0.946746	+	0.546604i	−0.0440943	+	0.0254579i	−0.521885	−	0.853016i	$-0.674771\pi$
$461$	−0.946746	+	0.546604i	−0.0440943	+	0.0254579i	0.477791	+	0.878474i	$0.341438\pi$
$462$	−9.57249	+	3.75951i	−0.445352	+	0.174908i
$463$		−	4.50452i		−	0.209343i	−0.994507	−	0.104671i	$-0.966621\pi$
$463$		−	4.50452i		−	0.209343i	0.994507	−	0.104671i	$-0.0333791\pi$
$464$	−31.6427			−1.46898
$465$	−15.6000			−0.723431
$466$			35.8349i			1.66002i
$467$	5.98771	−	10.3710i	0.277078	−	0.479913i	−0.693579	−	0.720380i	$-0.743967\pi$
$467$	5.98771	−	10.3710i	0.277078	−	0.479913i	0.970657	+	0.240467i	$0.0773006\pi$
$468$	−14.7689	−	4.46334i	−0.682693	−	0.206318i
$469$	−7.62356	−	1.14724i	−0.352023	−	0.0529748i
$470$	60.5197	+	34.9411i	2.79157	+	1.61171i
$471$	−5.90209	−	10.2227i	−0.271954	−	0.471038i
$472$	28.6137	−	49.5604i	1.31705	−	2.28120i
$473$	−5.31714	+	3.06985i	−0.244482	+	0.141152i
$474$		−	16.4407i		−	0.755145i
$475$	29.1847	−	16.8498i	1.33908	−	0.773121i
$476$	15.9564	−	6.26674i	0.731362	−	0.287236i
$477$	3.90722	+	6.76751i	0.178899	+	0.309863i
$478$	−5.41084	−	9.37186i	−0.247486	−	0.428659i
$479$		−	1.78939i		−	0.0817594i	−0.999164	−	0.0408797i	$-0.986984\pi$
$479$		−	1.78939i		−	0.0817594i	0.999164	−	0.0408797i	$-0.0130160\pi$
$480$	−4.51464	−	7.81958i	−0.206064	−	0.356913i
$481$	22.7020	+	24.1883i	1.03512	+	1.10289i
$482$	−3.33173			−0.151756
$483$	8.97912	−	3.52647i	0.408564	−	0.160460i
$484$	18.3867	−	31.8468i	0.835761	−	1.44758i
$485$	−37.7405			−1.71371
$486$	−2.17010	+	1.25291i	−0.0984378	+	0.0568331i
$487$	4.60289	+	2.65748i	0.208577	+	0.120422i	0.600650	−	0.799512i	$-0.294909\pi$
$487$	4.60289	+	2.65748i	0.208577	+	0.120422i	−0.392073	+	0.919934i	$0.628242\pi$
$488$		−	59.8023i		−	2.70712i
$489$		−	0.592417i		−	0.0267900i
$490$	−50.5737	−	15.5740i	−2.28469	−	0.703563i
$491$	9.96478	−	17.2595i	0.449704	−	0.778910i	−0.548662	−	0.836044i	$-0.684863\pi$
$491$	9.96478	−	17.2595i	0.449704	−	0.778910i	0.998367	+	0.0571337i	$0.0181961\pi$
$492$	12.2073	−	7.04788i	0.550347	−	0.317743i
$493$	−4.16444	−	7.21301i	−0.187557	−	0.324858i
$494$	54.1312	−	50.8051i	2.43548	−	2.28583i
$495$	−2.33989	+	4.05281i	−0.105170	+	0.182160i
$496$	−25.7615	−	14.8734i	−1.15673	−	0.667837i
$497$	−1.24224	−	3.16301i	−0.0557222	−	0.141880i
$498$	6.88007	+	11.9166i	0.308303	+	0.533997i
$499$	27.9202	+	16.1198i	1.24988	+	0.721620i	0.971086	−	0.238731i	$-0.0767313\pi$
$499$	27.9202	+	16.1198i	1.24988	+	0.721620i	0.278796	+	0.960350i	$0.410065\pi$
$500$	10.0479	+	5.80113i	0.449354	+	0.259435i
$501$	7.52026	+	4.34182i	0.335980	+	0.193978i
$502$	−4.92175	−	2.84158i	−0.219669	−	0.126826i
$503$	−4.27646	−	7.40705i	−0.190678	−	0.330264i	0.754797	−	0.655958i	$-0.227735\pi$
$503$	−4.27646	−	7.40705i	−0.190678	−	0.330264i	−0.945475	+	0.325694i	$0.894402\pi$
$504$	−14.9418	−	2.24855i	−0.665562	−	0.100158i
$505$	30.2744	+	17.4789i	1.34719	+	0.777801i
$506$	7.08645	−	12.2741i	0.315031	−	0.545650i
$507$	−11.6474	+	5.77398i	−0.517278	+	0.256432i
$508$	22.8562	+	39.5882i	1.01408	+	1.75644i
$509$	11.6807	−	6.74384i	0.517736	−	0.298915i	−0.218272	−	0.975888i	$-0.570042\pi$
$509$	11.6807	−	6.74384i	0.517736	−	0.298915i	0.736008	+	0.676973i	$0.236709\pi$
$510$	5.72336	−	9.91315i	0.253435	−	0.438962i
$511$	2.54103	+	6.46999i	0.112408	+	0.286215i
$512$			48.4901i			2.14298i
$513$		−	8.21689i		−	0.362785i
$514$	−25.7119	−	14.8448i	−1.13410	−	0.654775i
$515$	3.91991	−	2.26316i	0.172732	−	0.0997269i
$516$	−16.9366			−0.745594
$517$	7.16987	−	12.4186i	0.315331	−	0.546169i
$518$	47.6987	+	38.0202i	2.09576	+	1.67051i
$519$	13.7590			0.603955
$520$	−59.4650	−	17.9710i	−2.60771	−	0.788081i
$521$	0.258151	+	0.447130i	0.0113098	+	0.0195891i	0.871625	−	0.490173i	$-0.163067\pi$
$521$	0.258151	+	0.447130i	0.0113098	+	0.0195891i	−0.860315	+	0.509763i	$0.829733\pi$
$522$			13.7834i			0.603281i
$523$	19.1857	+	33.2306i	0.838932	+	1.45307i	0.890788	+	0.454419i	$0.150153\pi$
$523$	19.1857	+	33.2306i	0.838932	+	1.45307i	−0.0518558	+	0.998655i	$0.516514\pi$
$524$	1.27072	+	2.20095i	0.0555116	+	0.0961489i
$525$	−10.0999	+	3.96664i	−0.440795	+	0.173118i
$526$	45.3045	−	26.1566i	1.97537	−	1.14048i
$527$		−	7.82985i		−	0.341074i
$528$	−7.72813	+	4.46184i	−0.336324	+	0.194177i
$529$	4.85281	−	8.40532i	0.210992	−	0.365449i
$530$	29.5371	+	51.1598i	1.28301	+	2.22224i
$531$	−8.67795	−	5.01022i	−0.376591	−	0.217425i
$532$	57.9847	−	72.7454i	2.51396	−	3.15391i
$533$	3.43588	−	11.3691i	0.148824	−	0.492451i
$534$	−12.2334	+	21.1888i	−0.529389	+	0.916929i
$535$			61.0407i			2.63902i
$536$	−16.6414			−0.718798
$537$	1.07062			0.0462009
$538$			30.8711i			1.33095i
$539$	−3.19577	+	10.3777i	−0.137652	+	0.446998i
$540$	−11.1799	+	6.45469i	−0.481104	+	0.277766i
$541$	21.9830	+	12.6919i	0.945121	+	0.545666i	0.891562	−	0.452899i	$-0.149610\pi$
$541$	21.9830	+	12.6919i	0.945121	+	0.545666i	0.0535592	+	0.998565i	$0.482943\pi$
$542$	−25.9040	+	44.8670i	−1.11267	+	1.92720i
$543$	9.60905			0.412364
$544$	3.92476	−	2.26596i	0.168273	−	0.0971524i
$545$	5.41833			0.232096
$546$	−19.6699	+	13.5828i	−0.841796	+	0.581292i
$547$	−17.9501			−0.767491			−0.383746	−	0.923439i	$-0.625366\pi$
$547$	−17.9501			−0.767491			−0.383746	+	0.923439i	$0.625366\pi$
$548$	18.5692	−	10.7209i	0.793237	−	0.457975i
$549$	−10.4713			−0.446904
$550$	−7.97098	+	13.8061i	−0.339884	+	0.588696i
$551$	−39.1420	−	22.5987i	−1.66751	−	0.962735i
$552$	18.0336	−	10.4117i	0.767560	−	0.443151i
$553$	−13.5742	−	10.8198i	−0.577232	−	0.460106i
$554$			17.7996i			0.756231i
$555$	27.7565			1.17820
$556$	71.3295			3.02504
$557$			3.11951i			0.132178i	0.997814	+	0.0660890i	$0.0210521\pi$
$557$			3.11951i			0.132178i	−0.997814	+	0.0660890i	$0.978948\pi$
$558$	−6.47877	+	11.2216i	−0.274268	+	0.475046i
$559$	−10.4055	+	9.76613i	−0.440105	+	0.413063i
$560$	−45.4052	−	6.83287i	−1.91872	−	0.288742i
$561$	−2.03417	−	1.17443i	−0.0858826	−	0.0495844i
$562$	32.4418	+	56.1908i	1.36847	+	2.37027i
$563$	−7.95826	+	13.7841i	−0.335401	+	0.580931i	−0.983562	−	0.180572i	$-0.942205\pi$
$563$	−7.95826	+	13.7841i	−0.335401	+	0.580931i	0.648161	+	0.761503i	$0.275538\pi$
$564$	34.2572	−	19.7784i	1.44249	−	0.832820i
$565$		−	50.9791i		−	2.14471i
$566$	−56.8499	+	32.8223i	−2.38958	+	1.37962i
$567$	−0.393717	+	2.61629i	−0.0165346	+	0.109874i
$568$	−3.66765	−	6.35256i	−0.153891	−	0.266548i
$569$	−1.00105	−	1.73388i	−0.0419664	−	0.0726879i	0.844279	−	0.535903i	$-0.180029\pi$
$569$	−1.00105	−	1.73388i	−0.0419664	−	0.0726879i	−0.886246	+	0.463216i	$0.846696\pi$
$570$		−	62.1166i		−	2.60178i
$571$	15.4415	+	26.7455i	0.646208	+	1.11927i	0.984021	+	0.178052i	$0.0569797\pi$
$571$	15.4415	+	26.7455i	0.646208	+	1.11927i	−0.337813	+	0.941213i	$0.609687\pi$
$572$	−6.92365	+	22.9099i	−0.289492	+	0.957912i
$573$	−21.0359			−0.878786
$574$	3.24988	−	21.5958i	0.135647	−	0.901391i
$575$	7.47688	−	12.9503i	0.311807	−	0.540066i
$576$	4.00548			0.166895
$577$	−17.4279	+	10.0620i	−0.725533	+	0.418887i	−0.816786	−	0.576941i	$-0.804246\pi$
$577$	−17.4279	+	10.0620i	−0.725533	+	0.418887i	0.0912526	+	0.995828i	$0.470913\pi$
$578$	−31.9162	−	18.4268i	−1.32754	−	0.766454i
$579$			7.87112i			0.327113i
$580$			71.0086i			2.94847i
$581$	14.3668	+	2.16201i	0.596034	+	0.0896952i
$582$	−15.6739	+	27.1480i	−0.649704	+	1.12532i
$583$	10.4979	−	6.06099i	0.434780	−	0.251020i
$584$	7.50224	+	12.9943i	0.310445	+	0.537706i
$585$	−3.14670	+	10.4122i	−0.130100	+	0.430493i
$586$	−10.9562	+	18.9767i	−0.452597	+	0.783921i
$587$	1.07751	+	0.622102i	0.0444737	+	0.0256769i	0.522072	−	0.852901i	$-0.325159\pi$
$587$	1.07751	+	0.622102i	0.0444737	+	0.0256769i	−0.477598	+	0.878578i	$0.658493\pi$
$588$	−21.9482	+	20.3841i	−0.905129	+	0.840625i
$589$	−21.2447	−	36.7969i	−0.875372	−	1.51619i
$590$	−65.6021	−	37.8754i	−2.70079	−	1.55930i
$591$	0.193007	+	0.111433i	0.00793924	+	0.00458372i
$592$	45.8367	+	26.4638i	1.88388	+	1.08766i
$593$	−24.2540	−	14.0031i	−0.995994	−	0.575037i	−0.0889335	−	0.996038i	$-0.528346\pi$
$593$	−24.2540	−	14.0031i	−0.995994	−	0.575037i	−0.907061	+	0.421000i	$0.861679\pi$
$594$	1.94355	+	3.36632i	0.0797447	+	0.138122i
$595$	−4.41812	−	11.2495i	−0.181125	−	0.461183i
$596$	−7.50811	−	4.33481i	−0.307544	−	0.177561i
$597$	5.81292	−	10.0683i	0.237907	−	0.412067i
$598$	9.52989	−	31.5338i	0.389706	−	1.28951i
$599$	1.33444	+	2.31132i	0.0545238	+	0.0944380i	0.891999	−	0.452037i	$-0.149303\pi$
$599$	1.33444	+	2.31132i	0.0545238	+	0.0944380i	−0.837475	+	0.546475i	$0.815969\pi$
$600$	−20.2845	+	11.7113i	−0.828112	+	0.478111i
$601$	20.5235	−	35.5478i	0.837172	−	1.45003i	−0.0550770	−	0.998482i	$-0.517540\pi$
$601$	20.5235	−	35.5478i	0.837172	−	1.45003i	0.892249	−	0.451543i	$-0.149126\pi$
$602$	−16.3558	+	20.5194i	−0.666614	+	0.836308i
$603$			2.91388i			0.118662i
$604$		−	39.9528i		−	1.62566i
$605$	−22.4523	−	12.9629i	−0.912816	−	0.527015i
$606$	25.1463	−	14.5182i	1.02150	−	0.589762i
$607$	−37.5256			−1.52312			−0.761560	−	0.648095i	$-0.775566\pi$
$607$	−37.5256			−1.52312			−0.761560	+	0.648095i	$0.775566\pi$
$608$	12.2964	−	21.2981i	0.498687	−	0.863751i
$609$	11.3802	+	9.07103i	0.461147	+	0.367577i
$610$	−79.1591			−3.20506
$611$	9.64208	−	31.9050i	0.390077	−	1.29074i
$612$	−3.23971	−	5.61134i	−0.130957	−	0.226825i
$613$			3.26482i			0.131865i	0.997824	+	0.0659324i	$0.0210022\pi$
$613$			3.26482i			0.131865i	−0.997824	+	0.0659324i	$0.978998\pi$
$614$	1.79876	+	3.11555i	0.0725921	+	0.125733i
$615$	−4.96883	−	8.60626i	−0.200362	−	0.347038i
$616$	−3.48801	+	23.1782i	−0.140536	+	0.933875i
$617$	−30.8621	+	17.8182i	−1.24246	+	0.717334i	−0.969594	−	0.244718i	$-0.921305\pi$
$617$	−30.8621	+	17.8182i	−1.24246	+	0.717334i	−0.272865	+	0.962052i	$0.587971\pi$
$618$		−	3.75963i		−	0.151234i
$619$	13.6521	−	7.88206i	0.548725	−	0.316807i	−0.199882	−	0.979820i	$-0.564056\pi$
$619$	13.6521	−	7.88206i	0.548725	−	0.316807i	0.748608	+	0.663013i	$0.230723\pi$
$620$	−33.3771	+	57.8108i	−1.34046	+	2.32174i
$621$	−1.82307	−	3.15765i	−0.0731574	−	0.126712i
$622$	−51.4852	−	29.7250i	−2.06437	−	1.19186i
$623$	9.44348	+	24.0451i	0.378345	+	0.963345i
$624$	−15.1237	+	14.1945i	−0.605434	+	0.568233i
$625$	14.3430	−	24.8428i	0.573720	−	0.993712i
$626$			54.8567i			2.19252i
$627$	−12.7463			−0.509037
$628$	−50.5116			−2.01563
$629$			13.9314i			0.555482i
$630$	−2.97635	+	19.7782i	−0.118581	+	0.787982i
$631$	34.9566	−	20.1822i	1.39160	−	0.803441i	0.398109	−	0.917338i	$-0.369667\pi$
$631$	34.9566	−	20.1822i	1.39160	−	0.803441i	0.993493	+	0.113897i	$0.0363333\pi$
$632$	−32.4502	−	18.7352i	−1.29080	−	0.745245i
$633$	8.79477	−	15.2330i	0.349561	−	0.605457i
$634$	−75.1472			−2.98448
$635$	27.9101	−	16.1139i	1.10758	−	0.639460i
$636$	33.4390			1.32594
$637$	−1.73047	+	25.1795i	−0.0685639	+	0.997647i
$638$	21.3811			0.846486
$639$	−1.11232	+	0.642201i	−0.0440029	+	0.0254051i
$640$	48.3385			1.91075
$641$	15.6257	−	27.0644i	0.617176	−	1.06898i	−0.372822	−	0.927903i	$-0.621610\pi$
$641$	15.6257	−	27.0644i	0.617176	−	1.06898i	0.989999	−	0.141078i	$-0.0450568\pi$
$642$	43.9085	+	25.3506i	1.73293	+	1.00051i
$643$	−27.5603	+	15.9120i	−1.08687	+	0.627507i	−0.932742	−	0.360544i	$-0.882591\pi$
$643$	−27.5603	+	15.9120i	−1.08687	+	0.627507i	−0.154131	+	0.988050i	$0.549258\pi$
$644$	6.14290	−	40.8202i	0.242064	−	1.60854i
$645$			11.9405i			0.470157i
$646$	31.1772			1.22665
$647$	15.0060			0.589946			0.294973	−	0.955506i	$-0.404689\pi$
$647$	15.0060			0.589946			0.294973	+	0.955506i	$0.404689\pi$
$648$			5.71107i			0.224352i
$649$	−7.77199	+	13.4615i	−0.305077	+	0.528409i
$650$	−10.7194	+	35.4699i	−0.420450	+	1.39124i
$651$	5.00125	+	12.7342i	0.196015	+	0.499094i
$652$	−2.19540	−	1.26751i	−0.0859784	−	0.0496396i
$653$	21.4863	+	37.2153i	0.840822	+	1.45635i	0.889200	+	0.457518i	$0.151261\pi$
$653$	21.4863	+	37.2153i	0.840822	+	1.45635i	−0.0483782	+	0.998829i	$0.515405\pi$
$654$	2.25027	−	3.89758i	0.0879925	−	0.152408i
$655$	1.55169	−	0.895870i	0.0606296	−	0.0350045i
$656$		−	18.9497i		−	0.739861i
$657$	2.27528	−	1.31363i	0.0887670	−	0.0512496i
$658$	9.12011	−	60.6041i	0.355539	−	2.36259i
$659$	23.8419	+	41.2953i	0.928747	+	1.60864i	0.785421	+	0.618962i	$0.212446\pi$
$659$	23.8419	+	41.2953i	0.928747	+	1.60864i	0.143326	+	0.989676i	$0.454220\pi$
$660$	10.0127	+	17.3425i	0.389744	+	0.675056i
$661$			18.0026i			0.700221i	0.936708	+	0.350111i	$0.113856\pi$
$661$			18.0026i			0.700221i	−0.936708	+	0.350111i	$0.886144\pi$
$662$	−20.4961	−	35.5003i	−0.796605	−	1.37976i
$663$	−5.22606	−	1.57938i	−0.202963	−	0.0613379i
$664$	31.3611			1.21704
$665$	−51.2863	−	40.8798i	−1.98880	−	1.58525i
$666$	11.5275	−	19.9662i	0.446680	−	0.773673i
$667$	−20.0558			−0.776562
$668$	32.1801	−	18.5792i	1.24509	−	0.718851i
$669$	−15.7545	−	9.09585i	−0.609103	−	0.351666i
$670$			22.0278i			0.851009i
$671$			16.2434i			0.627068i
$672$	−4.93575	+	6.19220i	−0.190401	+	0.238869i
$673$	−5.90181	+	10.2222i	−0.227498	+	0.394038i	−0.957066	−	0.289870i	$-0.906388\pi$
$673$	−5.90181	+	10.2222i	−0.227498	+	0.394038i	0.729568	+	0.683908i	$0.239721\pi$
$674$	−65.9965	+	38.1031i	−2.54209	+	1.46768i
$675$	2.05063	+	3.55179i	0.0789287	+	0.136708i
$676$	−3.52286	+	55.5170i	−0.135495	+	2.13527i
$677$	5.84113	−	10.1171i	0.224493	−	0.388833i	−0.731674	−	0.681654i	$-0.761261\pi$
$677$	5.84113	−	10.1171i	0.224493	−	0.388833i	0.956167	+	0.292821i	$0.0945941\pi$
$678$	−36.6709	−	21.1719i	−1.40834	−	0.813104i
$679$	12.0994	+	30.8075i	0.464332	+	1.18229i
$680$	−13.0442	−	22.5933i	−0.500224	−	0.866413i
$681$	−17.8461	−	10.3034i	−0.683863	−	0.394829i
$682$	17.4072	+	10.0500i	0.666555	+	0.384836i
$683$	−1.73122	−	0.999520i	−0.0662432	−	0.0382456i	0.466513	−	0.884515i	$-0.345510\pi$
$683$	−1.73122	−	0.999520i	−0.0662432	−	0.0382456i	−0.532756	+	0.846269i	$0.678844\pi$
$684$	−30.4504	−	17.5805i	−1.16430	−	0.672209i
$685$	−7.55837	−	13.0915i	−0.288791	−	0.500200i
$686$	3.50056	+	46.2762i	0.133652	+	1.76683i
$687$	6.95359	+	4.01466i	0.265296	+	0.153169i
$688$	−11.3844	+	19.7184i	−0.434027	+	0.751756i
$689$	20.5442	−	19.2818i	0.782670	−	0.734579i
$690$	−13.7817	−	23.8707i	−0.524662	−	0.908741i
$691$	15.7465	−	9.09122i	0.599024	−	0.345846i	−0.169634	−	0.985507i	$-0.554258\pi$
$691$	15.7465	−	9.09122i	0.599024	−	0.345846i	0.768657	+	0.639661i	$0.220925\pi$
$692$	29.4383	−	50.9887i	1.11908	−	1.93830i
$693$	4.05846	+	0.610745i	0.154168	+	0.0232003i
$694$		−	38.3558i		−	1.45597i
$695$		−	50.2880i		−	1.90753i
$696$	27.2053	+	15.7070i	1.03121	+	0.595372i
$697$	4.31961	−	2.49393i	0.163617	−	0.0944643i
$698$	−23.9736			−0.907415
$699$	7.15034	−	12.3848i	0.270451	−	0.468434i
$700$	−6.90965	+	45.9153i	−0.261160	+	1.73544i
$701$	−22.5231			−0.850684			−0.425342	−	0.905033i	$-0.639846\pi$
$701$	−22.5231			−0.850684			−0.425342	+	0.905033i	$0.639846\pi$
$702$	6.18301	+	6.58779i	0.233363	+	0.248640i
$703$	37.8000	+	65.4715i	1.42565	+	2.46930i
$704$		−	6.21341i		−	0.234177i
$705$	−13.9440	−	24.1517i	−0.525161	−	0.909605i
$706$	15.6488	+	27.1045i	0.588950	+	1.02009i
$707$	4.56224	−	30.3166i	0.171581	−	1.14017i
$708$	−37.1340	+	21.4393i	−1.39558	+	0.805740i
$709$			7.15333i			0.268649i	0.990937	+	0.134324i	$0.0428864\pi$
$709$			7.15333i			0.268649i	−0.990937	+	0.134324i	$0.957114\pi$
$710$	−8.40875	+	4.85479i	−0.315575	+	0.182197i
$711$	−3.28050	+	5.68199i	−0.123028	+	0.213091i
$712$	27.8813	+	48.2919i	1.04490	+	1.80981i
$713$	−16.3282	−	9.42707i	−0.611495	−	0.353047i
$714$	−9.92697	−	1.49388i	−0.371507	−	0.0559069i
$715$	16.1517	+	4.88124i	0.604041	+	0.182548i
$716$	2.29067	−	3.96755i	0.0856063	−	0.148274i
$717$			4.31863i			0.161282i
$718$	−27.6865			−1.03325
$719$	7.88015			0.293880			0.146940	−	0.989145i	$-0.453058\pi$
$719$	7.88015			0.293880			0.146940	+	0.989145i	$0.453058\pi$
$720$			17.3548i			0.646774i
$721$	−3.10412	−	2.47426i	−0.115603	−	0.0921464i
$722$	105.287	−	60.7877i	3.91839	−	2.26228i
$723$	1.15146	+	0.664798i	0.0428234	+	0.0247241i
$724$	20.5592	−	35.6095i	0.764075	−	1.32342i
$725$	22.5591			0.837824
$726$	−18.6492	+	10.7671i	−0.692137	+	0.399605i
$727$	−18.8301			−0.698371			−0.349185	−	0.937054i	$-0.613542\pi$
$727$	−18.8301			−0.698371			−0.349185	+	0.937054i	$0.613542\pi$
$728$	4.39439	+	54.3026i	0.162867	+	2.01259i
$729$	1.00000			0.0370370
$730$	17.2002	−	9.93056i	0.636609	−	0.367546i
$731$	−5.99312			−0.221663
$732$	−22.4040	+	38.8049i	−0.828075	+	1.43427i
$733$	24.7277	+	14.2766i	0.913339	+	0.527317i	0.881504	−	0.472177i	$-0.156532\pi$
$733$	24.7277	+	14.2766i	0.913339	+	0.527317i	0.0318352	+	0.999493i	$0.489865\pi$
$734$	28.0413	−	16.1897i	1.03502	−	0.597571i
$735$	14.3710	+	15.4737i	0.530082	+	0.570757i
$736$		−	10.9128i		−	0.402251i
$737$	4.52009			0.166500
$738$	−8.25435			−0.303847
$739$			7.61947i			0.280287i	0.990131	+	0.140143i	$0.0447563\pi$
$739$			7.61947i			0.280287i	−0.990131	+	0.140143i	$0.955244\pi$
$740$	59.3868	−	102.861i	2.18310	−	3.78124i
$741$	−28.8455	+	6.75745i	−1.05966	+	0.248241i
$742$	32.2923	−	40.5127i	1.18549	−	1.48727i
$743$	−42.4488	−	24.5078i	−1.55730	−	0.899105i	−0.997514	−	0.0704641i	$-0.977552\pi$
$743$	−42.4488	−	24.5078i	−1.55730	−	0.899105i	−0.559781	−	0.828641i	$-0.689115\pi$
$744$	14.7659	+	25.5753i	0.541345	+	0.937637i
$745$	−3.05609	+	5.29330i	−0.111966	+	0.193931i
$746$	19.5909	−	11.3108i	0.717275	−	0.414119i
$747$		−	5.49127i		−	0.200915i
$748$	−8.70446	+	5.02552i	−0.318266	+	0.183751i
$749$	49.8274	−	19.5693i	1.82065	−	0.715046i
$750$	−3.39709	−	5.88394i	−0.124044	−	0.214851i
$751$	−11.8405	−	20.5084i	−0.432067	−	0.748362i	0.564984	−	0.825102i	$-0.308882\pi$
$751$	−11.8405	−	20.5084i	−0.432067	−	0.748362i	−0.997051	+	0.0767395i	$0.975549\pi$
$752$		−	53.1783i		−	1.93921i
$753$	1.13399	+	1.96413i	0.0413249	+	0.0715769i
$754$	48.3866	−	11.3352i	1.76214	−	0.412805i
$755$	−28.1671			−1.02511
$756$	8.85315	+	7.05677i	0.321986	+	0.256652i
$757$	16.7491	−	29.0103i	0.608756	−	1.05440i	−0.382689	−	0.923877i	$-0.625002\pi$
$757$	16.7491	−	29.0103i	0.608756	−	1.05440i	0.991446	−	0.130520i	$-0.0416646\pi$
$758$	42.4922			1.54339
$759$	−4.89824	+	2.82800i	−0.177795	+	0.102650i
$760$	−122.604	−	70.7857i	−4.44733	−	2.56767i
$761$			50.4840i			1.83004i	0.403406	+	0.915021i	$0.367826\pi$
$761$			50.4840i			1.83004i	−0.403406	+	0.915021i	$0.632174\pi$
$762$		−	26.7688i		−	0.969732i
$763$	−1.73709	−	4.42298i	−0.0628867	−	0.160123i
$764$	−45.0076	+	77.9554i	−1.62832	+	2.82033i
$765$	−3.95605	+	2.28403i	−0.143031	+	0.0825792i
$766$	2.57169	+	4.45430i	0.0929190	+	0.160940i
$767$	−10.4518	+	34.5844i	−0.377393	+	1.24877i
$768$	16.0698	−	27.8337i	0.579869	−	1.00436i
$769$	32.2438	+	18.6160i	1.16274	+	0.671309i	0.951959	−	0.306224i	$-0.0990657\pi$
$769$	32.2438	+	18.6160i	1.16274	+	0.671309i	0.210782	+	0.977533i	$0.432399\pi$
$770$	30.6805	+	4.61700i	1.10565	+	0.166385i
$771$	5.92412	+	10.2609i	0.213352	+	0.369537i
$772$	29.1691	+	16.8408i	1.04982	+	0.606112i
$773$	−14.6112	−	8.43577i	−0.525528	−	0.303414i	0.213666	−	0.976907i	$-0.431460\pi$
$773$	−14.6112	−	8.43577i	−0.525528	−	0.303414i	−0.739193	+	0.673493i	$0.764793\pi$
$774$	8.58919	+	4.95897i	0.308732	+	0.178247i
$775$	18.3662	+	10.6037i	0.659735	+	0.380898i
$776$	35.7227	+	61.8736i	1.28237	+	2.22113i
$777$	−8.89857	−	22.6576i	−0.319234	−	0.812837i
$778$	−68.3420	−	39.4573i	−2.45018	−	1.41461i
$779$	13.5335	−	23.4407i	0.484889	−	0.839852i
$780$	31.8534	+	33.9388i	1.14053	+	1.21520i
$781$	0.996199	+	1.72547i	0.0356468	+	0.0617421i
$782$	11.9810	−	6.91726i	0.428441	−	0.247361i
$783$	2.75027	−	4.76361i	0.0982866	−	0.170237i
$784$	8.97896	+	39.2548i	0.320677	+	1.40196i
$785$			35.6112i			1.27102i
$786$		−	1.48824i		−	0.0530839i
$787$	−29.7913	−	17.2000i	−1.06194	−	0.613113i	−0.135974	−	0.990712i	$-0.543416\pi$
$787$	−29.7913	−	17.2000i	−1.06194	−	0.613113i	−0.925969	+	0.377599i	$0.876750\pi$
$788$	0.825901	−	0.476834i	0.0294215	−	0.0169865i
$789$	−20.8767			−0.743229
$790$	−24.7993	+	42.9537i	−0.882321	+	1.52822i
$791$	−41.6142	+	16.3436i	−1.47963	+	0.581111i
$792$	8.85917			0.314797
$793$	8.61144	+	36.7596i	0.305801	+	1.30537i
$794$	−14.4899	−	25.0973i	−0.514228	−	0.890668i
$795$		−	23.5748i		−	0.836113i
$796$	−24.8742	−	43.0834i	−0.881642	−	1.52705i
$797$	2.27035	+	3.93236i	0.0804200	+	0.139291i	0.903430	−	0.428735i	$-0.141041\pi$
$797$	2.27035	+	3.93236i	0.0804200	+	0.139291i	−0.823010	+	0.568026i	$0.807707\pi$
$798$	−50.7057	+	19.9142i	−1.79496	+	0.704955i
$799$	12.1221	−	6.99869i	0.428849	−	0.247596i
$800$			12.2749i			0.433984i
$801$	8.45584	−	4.88198i	0.298772	−	0.172496i
$802$	−5.33249	+	9.23615i	−0.188297	+	0.326140i
$803$	−2.03774	−	3.52947i	−0.0719103	−	0.124552i
$804$	10.7983	+	6.23443i	0.380828	+	0.219871i
$805$	−28.7787	−	4.33081i	−1.01431	−	0.152641i
$806$	44.7214	+	13.5153i	1.57525	+	0.476058i
$807$	6.15988	−	10.6692i	0.216838	−	0.375574i
$808$		−	66.1776i		−	2.32812i
$809$	5.83966			0.205311			0.102656	−	0.994717i	$-0.467266\pi$
$809$	5.83966			0.205311			0.102656	+	0.994717i	$0.467266\pi$
$810$	7.55962			0.265618
$811$			4.79606i			0.168412i	0.996448	+	0.0842061i	$0.0268354\pi$
$811$			4.79606i			0.168412i	−0.996448	+	0.0842061i	$0.973165\pi$
$812$	57.9642	−	22.7649i	2.03415	−	0.798892i
$813$	17.9051	−	10.3375i	0.627960	−	0.362553i
$814$	−30.9720	−	17.8817i	−1.08557	−	0.626754i
$815$	−0.893610	+	1.54778i	−0.0313018	+	0.0542163i
$816$	−8.71062			−0.304933
$817$	−28.1650	+	16.2611i	−0.985369	+	0.568903i
$818$	27.7492			0.970229
$819$	9.50831	−	0.769452i	0.332247	−	0.0268868i
$820$	−42.5245			−1.48502
$821$	16.2795	−	9.39897i	0.568158	−	0.328026i	−0.188255	−	0.982120i	$-0.560283\pi$
$821$	16.2795	−	9.39897i	0.568158	−	0.328026i	0.756413	+	0.654094i	$0.226950\pi$
$822$	−12.5562			−0.437947
$823$	8.90870	−	15.4303i	0.310538	−	0.537867i	−0.667941	−	0.744214i	$-0.732824\pi$
$823$	8.90870	−	15.4303i	0.310538	−	0.537867i	0.978479	+	0.206347i	$0.0661575\pi$
$824$	−7.42067	−	4.28433i	−0.258511	−	0.149252i
$825$	5.50963	−	3.18099i	0.191821	−	0.110748i
$826$	−9.88600	+	65.6935i	−0.343978	+	2.28577i
$827$		−	32.3754i		−	1.12580i	−0.826524	−	0.562902i	$-0.809685\pi$
$827$		−	32.3754i		−	1.12580i	0.826524	−	0.562902i	$-0.190315\pi$
$828$	−15.6023			−0.542218
$829$	−31.9763			−1.11058			−0.555291	−	0.831656i	$-0.687393\pi$
$829$	−31.9763			−1.11058			−0.555291	+	0.831656i	$0.687393\pi$
$830$		−	41.5120i		−	1.44090i
$831$	3.55165	−	6.15163i	0.123205	−	0.213398i
$832$	−3.29405	−	14.0613i	−0.114200	−	0.487487i
$833$	−7.76649	+	7.21301i	−0.269093	+	0.249916i
$834$	−36.1738	−	20.8850i	−1.25260	−	0.723187i
$835$	−13.0985	−	22.6873i	−0.453294	−	0.785128i
$836$	−27.2714	+	47.2355i	−0.943202	+	1.63367i
$837$	4.47820	−	2.58549i	0.154789	−	0.0893676i
$838$		−	5.53843i		−	0.191322i
$839$	0.0485960	−	0.0280569i	0.00167772	−	0.000968633i	−0.499161	−	0.866509i	$-0.666358\pi$
$839$	0.0485960	−	0.0280569i	0.00167772	−	0.000968633i	0.500839	+	0.865541i	$0.333025\pi$
$840$	35.6460	+	28.4131i	1.22991	+	0.980346i
$841$	−0.627971	−	1.08768i	−0.0216542	−	0.0375061i
$842$	−20.0141	−	34.6655i	−0.689733	−	1.19465i
$843$		−	25.8932i		−	0.891808i
$844$	−37.6339	−	65.1839i	−1.29541	−	2.24372i
$845$	39.1400	+	2.48366i	1.34646	+	0.0854403i
$846$	−23.1641			−0.796398
$847$	−3.38349	+	22.4836i	−0.116258	+	0.772546i
$848$	22.4769	−	38.9311i	0.771860	−	1.33690i
$849$	26.1969			0.899074
$850$	−13.4765	+	7.78067i	−0.462241	+	0.266875i
$851$	29.0522	+	16.7733i	0.995896	+	0.574981i
$852$			5.49611i			0.188294i
$853$		−	21.8470i		−	0.748028i	−0.927423	−	0.374014i	$-0.877981\pi$
$853$		−	21.8470i		−	0.748028i	0.927423	−	0.374014i	$-0.122019\pi$
$854$	25.3779	+	64.6175i	0.868415	+	2.21116i
$855$	−12.3945	+	21.4679i	−0.423882	+	0.734185i
$856$	100.073	−	57.7772i	3.42042	−	1.97478i
$857$	−4.56160	−	7.90092i	−0.155821	−	0.269890i	0.777536	−	0.628838i	$-0.216469\pi$
$857$	−4.56160	−	7.90092i	−0.155821	−	0.269890i	−0.933358	+	0.358947i	$0.883136\pi$
$858$	10.2192	−	9.59125i	0.348876	−	0.327440i
$859$	−10.4710	+	18.1363i	−0.357266	+	0.618803i	−0.987503	−	0.157600i	$-0.949624\pi$
$859$	−10.4710	+	18.1363i	−0.357266	+	0.618803i	0.630237	+	0.776403i	$0.282958\pi$
$860$	44.2495	+	25.5475i	1.50889	+	0.871161i
$861$	−5.43231	+	6.81517i	−0.185133	+	0.232260i
$862$	29.5941	+	51.2586i	1.00798	+	1.74587i
$863$	5.75442	+	3.32232i	0.195883	+	0.113093i	0.594734	−	0.803923i	$-0.297258\pi$
$863$	5.75442	+	3.32232i	0.195883	+	0.113093i	−0.398851	+	0.917016i	$0.630591\pi$
$864$	2.59199	+	1.49648i	0.0881812	+	0.0509114i
$865$	−35.9476	−	20.7543i	−1.22225	−	0.705669i
$866$	−3.34761	−	1.93274i	−0.113756	−	0.0656772i
$867$	7.35361	+	12.7368i	0.249742	+	0.432565i
$868$	57.8914	+	8.71189i	1.96496	+	0.295701i
$869$	8.81406	+	5.08880i	0.298996	+	0.172626i
$870$	20.7910	−	36.0111i	0.704881	−	1.22089i
$871$	10.2292	−	2.39633i	0.346603	−	0.0811966i
$872$	−5.12865	−	8.88307i	−0.173678	−	0.300819i
$873$	10.8340	−	6.25500i	0.366674	−	0.211700i
$874$	37.5371	−	65.0162i	1.26971	−	2.19921i
$875$	−7.09372	−	1.06751i	−0.239812	−	0.0360885i
$876$		−	11.2424i		−	0.379845i
$877$			32.7212i			1.10492i	0.833541	+	0.552458i	$0.186310\pi$
$877$			32.7212i			1.10492i	−0.833541	+	0.552458i	$0.813690\pi$
$878$	68.8226	+	39.7348i	2.32265	+	1.34098i
$879$	7.57306	−	4.37231i	0.255433	−	0.147474i
$880$	26.9212			0.907513
$881$	15.0565	−	26.0786i	0.507267	−	0.878612i	−0.492698	−	0.870201i	$-0.663989\pi$
$881$	15.0565	−	26.0786i	0.507267	−	0.878612i	0.999965	−	0.00841150i	$-0.00267750\pi$
$882$	17.0991	−	3.91117i	0.575757	−	0.131696i
$883$	−17.3595			−0.584194			−0.292097	−	0.956389i	$-0.594353\pi$
$883$	−17.3595			−0.584194			−0.292097	+	0.956389i	$0.594353\pi$
$884$	−17.0344	+	15.9877i	−0.572928	+	0.537725i
$885$	15.1150	+	26.1799i	0.508084	+	0.880028i
$886$		−	16.9209i		−	0.568467i
$887$	−21.7840	−	37.7310i	−0.731434	−	1.26688i	−0.956270	−	0.292485i	$-0.905518\pi$
$887$	−21.7840	−	37.7310i	−0.731434	−	1.26688i	0.224836	−	0.974397i	$-0.427815\pi$
$888$	−26.2725	−	45.5054i	−0.881648	−	1.52706i
$889$	−22.1016	−	17.6170i	−0.741263	−	0.590854i
$890$	63.9229	−	36.9059i	2.14270	−	1.23709i
$891$		−	1.55123i		−	0.0519681i
$892$	−67.4153	+	38.9223i	−2.25723	+	1.30321i
$893$	37.9790	−	65.7815i	1.27092	−	2.20130i
$894$	2.53843	+	4.39668i	0.0848977	+	0.147047i
$895$	−2.79717	−	1.61495i	−0.0934990	−	0.0539817i
$896$	−15.4970	−	39.4586i	−0.517719	−	1.31822i
$897$	−9.58571	+	8.99672i	−0.320058	+	0.300392i
$898$	3.98941	−	6.90985i	0.133128	−	0.230585i
$899$		−	28.4432i		−	0.948633i
$900$	17.5498			0.584992
$901$	11.8326			0.394200
$902$			12.8044i			0.426339i
$903$	9.74702	−	3.82805i	0.324361	−	0.127390i
$904$	−83.5775	+	48.2535i	−2.77975	+	1.60489i
$905$	−25.1051	−	14.4944i	−0.834521	−	0.481811i
$906$	−11.6980	+	20.2615i	−0.388640	+	0.673144i
$907$	14.3146			0.475309			0.237655	−	0.971350i	$-0.423621\pi$
$907$	14.3146			0.475309			0.237655	+	0.971350i	$0.423621\pi$
$908$	−76.3656	+	44.0897i	−2.53428	+	1.46317i
$909$	−11.5876			−0.384337
$910$	71.8792	−	5.81676i	2.38277	−	0.192824i
$911$	29.9541			0.992422			0.496211	−	0.868202i	$-0.334724\pi$
$911$	29.9541			0.992422			0.496211	+	0.868202i	$0.334724\pi$
$912$	−40.9361	+	23.6345i	−1.35553	+	0.782615i
$913$	−8.51821			−0.281912
$914$	34.1600	−	59.1668i	1.12991	−	1.95706i
$915$	27.3578	+	15.7951i	0.904422	+	0.522168i
$916$	29.7553	−	17.1792i	0.983142	−	0.567617i
$917$	−1.22876	−	0.979434i	−0.0405773	−	0.0323438i
$918$			3.79429i			0.125230i
$919$	15.3478			0.506276			0.253138	−	0.967430i	$-0.418537\pi$
$919$	15.3478			0.506276			0.253138	+	0.967430i	$0.418537\pi$
$920$	−62.8206			−2.07113
$921$		−	1.43567i		−	0.0473069i
$922$	1.36969	−	2.37237i	0.0451083	−	0.0781299i
$923$	3.16921	+	3.37669i	0.104316	+	0.111145i
$924$	10.9467	−	13.7333i	0.360118	−	0.451791i
$925$	−32.6785	−	18.8669i	−1.07446	−	0.620340i
$926$	5.64375	+	9.77526i	0.185465	+	0.321235i
$927$	−0.750179	+	1.29935i	−0.0246391	+	0.0426762i
$928$	14.2573	−	8.23147i	0.468020	−	0.270211i
$929$			6.06377i			0.198946i	0.995040	+	0.0994729i	$0.0317157\pi$
$929$			6.06377i			0.198946i	−0.995040	+	0.0994729i	$0.968284\pi$
$930$	33.8535	−	19.5453i	1.11010	−	0.640917i
$931$	−16.9281	+	54.9708i	−0.554796	+	1.80159i
$932$	−30.5972	−	52.9959i	−1.00224	−	1.73594i
$933$	11.8624	+	20.5463i	0.388357	+	0.672655i
$934$			30.0082i			0.981899i
$935$	3.54305	+	6.13673i	0.115870	+	0.200693i
$936$	20.0488	−	4.69670i	0.655315	−	0.153516i
$937$	17.7949			0.581333			0.290666	−	0.956824i	$-0.406123\pi$
$937$	17.7949			0.581333			0.290666	+	0.956824i	$0.406123\pi$
$938$	17.9813	−	7.06199i	0.587110	−	0.230582i
$939$	10.9459	−	18.9588i	0.357205	−	0.618697i
$940$	−119.336			−3.89231
$941$	−37.1431	+	21.4446i	−1.21083	+	0.699074i	−0.962941	−	0.269714i	$-0.913071\pi$
$941$	−37.1431	+	21.4446i	−1.21083	+	0.699074i	−0.247891	+	0.968788i	$0.579738\pi$
$942$	25.6163	+	14.7896i	0.834624	+	0.481870i
$943$		−	12.0107i		−	0.391121i
$944$			57.6441i			1.87616i
$945$	4.97510	−	6.24157i	0.161840	−	0.203038i
$946$	7.69249	−	13.3238i	0.250104	−	0.433194i
$947$	37.5418	−	21.6748i	1.21995	−	0.704336i	0.255039	−	0.966931i	$-0.417912\pi$
$947$	37.5418	−	21.6748i	1.21995	−	0.704336i	0.964906	+	0.262595i	$0.0845783\pi$
$948$	14.0377	+	24.3139i	0.455922	+	0.789680i
$949$	−6.48267	−	6.90707i	−0.210436	−	0.224213i
$950$	−42.2225	+	73.1314i	−1.36988	+	2.37270i
$951$	25.9713	+	14.9946i	0.842178	+	0.486232i
$952$	−14.2610	+	17.8913i	−0.462201	+	0.579860i
$953$	−11.7522	−	20.3554i	−0.380692	−	0.659378i	0.610469	−	0.792040i	$-0.290981\pi$
$953$	−11.7522	−	20.3554i	−0.380692	−	0.659378i	−0.991161	+	0.132662i	$0.957647\pi$
$954$	−16.9581	−	9.79079i	−0.549040	−	0.316988i
$955$	54.9594	+	31.7308i	1.77844	+	1.02678i
$956$	16.0041	+	9.23997i	0.517609	+	0.298842i
$957$	−7.38944	−	4.26629i	−0.238867	−	0.137910i
$958$	2.24194	+	3.88316i	0.0724339	+	0.125459i
$959$	−8.26340	+	10.3669i	−0.266839	+	0.334766i
$960$	−10.4649	−	6.04192i	−0.337754	−	0.195002i
$961$	−2.13048	+	3.69010i	−0.0687252	+	0.119036i
$962$	−79.5714	−	24.0474i	−2.56549	−	0.775320i
$963$	−10.1167	−	17.5226i	−0.326006	−	0.564659i
$964$	4.92726	−	2.84475i	0.158696	−	0.0916234i
$965$	11.8729	−	20.5645i	0.382203	−	0.661994i
$966$	−15.0673	+	18.9028i	−0.484781	+	0.608188i
$967$		−	25.9127i		−	0.833296i	−0.909068	−	0.416648i	$-0.863205\pi$
$967$		−	25.9127i		−	0.833296i	0.909068	−	0.416648i	$-0.136795\pi$
$968$			49.0792i			1.57747i
$969$	−10.7750	−	6.22097i	−0.346144	−	0.199846i
$970$	81.9008	−	47.2854i	2.62968	−	1.51824i
$971$	28.2352			0.906112			0.453056	−	0.891482i	$-0.350334\pi$
$971$	28.2352			0.906112			0.453056	+	0.891482i	$0.350334\pi$
$972$	2.13956	−	3.70583i	0.0686265	−	0.118865i
$973$	−41.0501	+	16.1220i	−1.31601	+	0.516849i
$974$	−13.3183			−0.426747
$975$	10.7822	−	10.1197i	0.345306	−	0.324089i
$976$	30.1189	+	52.1674i	0.964082	+	1.66984i
$977$			25.9939i			0.831619i	0.909452	+	0.415809i	$0.136502\pi$
$977$			25.9939i			0.831619i	−0.909452	+	0.415809i	$0.863498\pi$
$978$	0.742245	+	1.28561i	0.0237344	+	0.0411091i
$979$	−7.57306	−	13.1169i	−0.242036	−	0.419219i
$980$	88.0906	−	20.1494i	2.81395	−	0.643650i
$981$	−1.55541	+	0.898018i	−0.0496605	+	0.0286715i
$982$			49.9398i			1.59364i
$983$	−14.9096	+	8.60807i	−0.475543	+	0.274555i	−0.718557	−	0.695468i	$-0.755197\pi$
$983$	−14.9096	+	8.60807i	−0.475543	+	0.274555i	0.243014	+	0.970023i	$0.421864\pi$
$984$	−9.40635	+	16.2923i	−0.299863	+	0.519379i
$985$	−0.336173	−	0.582269i	−0.0107114	−	0.0185526i
$986$	18.0745	+	10.4353i	0.575609	+	0.332328i
$987$	−15.2446	+	19.1253i	−0.485242	+	0.608766i
$988$	−36.6747	+	121.354i	−1.16678	+	3.86080i
$989$	−7.21566	+	12.4979i	−0.229445	+	0.397410i
$990$		−	11.7267i		−	0.372699i
$991$	15.6497			0.497129			0.248565	−	0.968615i	$-0.420041\pi$
$991$	15.6497			0.497129			0.248565	+	0.968615i	$0.420041\pi$
$992$	15.4766			0.491382
$993$			16.3588i			0.519132i
$994$	6.65876	+	5.30764i	0.211203	+	0.168348i
$995$	−30.3742	+	17.5366i	−0.962928	+	0.555947i
$996$	−20.3497	−	11.7489i	−0.644806	−	0.372279i
$997$	−22.0137	+	38.1288i	−0.697181	+	1.20755i	0.272259	+	0.962224i	$0.412229\pi$
$997$	−22.0137	+	38.1288i	−0.697181	+	1.20755i	−0.969440	+	0.245328i	$0.921104\pi$
$998$	−80.7864			−2.55725
$999$	−7.96792	+	4.60028i	−0.252094	+	0.145546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.c.121.1	yes	12
3.2	odd	2		819.2.do.f.667.6		12
7.4	even	3		273.2.t.c.4.1	✓	12
13.10	even	6		273.2.t.c.205.6	yes	12
21.11	odd	6		819.2.bm.e.550.6		12
39.23	odd	6		819.2.bm.e.478.1		12
91.88	even	6	inner	273.2.bl.c.88.1	yes	12
273.179	odd	6		819.2.do.f.361.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.1	✓	12	7.4	even	3
273.2.t.c.205.6	yes	12	13.10	even	6
273.2.bl.c.88.1	yes	12	91.88	even	6	inner
273.2.bl.c.121.1	yes	12	1.1	even	1	trivial
819.2.bm.e.478.1		12	39.23	odd	6
819.2.bm.e.550.6		12	21.11	odd	6
819.2.do.f.361.6		12	273.179	odd	6
819.2.do.f.667.6		12	3.2	odd	2

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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.17010 + 1.25291i) q^{2} +1.00000 q^{3} +(2.13956 - 3.70583i) q^{4} +(-2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-0.393717 + 2.61629i) q^{7} +5.71107i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-2.17010 + 1.25291i) q^{2} +1.00000 q^{3} +(2.13956 - 3.70583i) q^{4} +(-2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-0.393717 + 2.61629i) q^{7} +5.71107i q^{8} +1.00000 q^{9} +7.55962 q^{10} -1.55123i q^{11} +(2.13956 - 3.70583i) q^{12} +(-0.822385 - 3.51051i) q^{13} +(-2.42357 - 6.17091i) q^{14} +(-2.61265 - 1.50841i) q^{15} +(-2.87633 - 4.98195i) q^{16} +(0.757096 - 1.31133i) q^{17} +(-2.17010 + 1.25291i) q^{18} -8.21689i q^{19} +(-11.1799 + 6.45469i) q^{20} +(-0.393717 + 2.61629i) q^{21} +(1.94355 + 3.36632i) q^{22} +(-1.82307 - 3.15765i) q^{23} +5.71107i q^{24} +(2.05063 + 3.55179i) q^{25} +(6.18301 + 6.58779i) q^{26} +1.00000 q^{27} +(8.85315 + 7.05677i) q^{28} +(2.75027 - 4.76361i) q^{29} +7.55962 q^{30} +(4.47820 - 2.58549i) q^{31} +(2.59199 + 1.49648i) q^{32} -1.55123i q^{33} +3.79429i q^{34} +(4.97510 - 6.24157i) q^{35} +(2.13956 - 3.70583i) q^{36} +(-7.96792 + 4.60028i) q^{37} +(10.2950 + 17.8315i) q^{38} +(-0.822385 - 3.51051i) q^{39} +(8.61466 - 14.9210i) q^{40} +(2.85275 + 1.64704i) q^{41} +(-2.42357 - 6.17091i) q^{42} +(-1.97898 - 3.42770i) q^{43} +(-5.74858 - 3.31895i) q^{44} +(-2.61265 - 1.50841i) q^{45} +(7.91251 + 4.56829i) q^{46} +(8.00565 + 4.62206i) q^{47} +(-2.87633 - 4.98195i) q^{48} +(-6.68997 - 2.06016i) q^{49} +(-8.90014 - 5.13850i) q^{50} +(0.757096 - 1.31133i) q^{51} +(-14.7689 - 4.46334i) q^{52} +(3.90722 + 6.76751i) q^{53} +(-2.17010 + 1.25291i) q^{54} +(-2.33989 + 4.05281i) q^{55} +(-14.9418 - 2.24855i) q^{56} -8.21689i q^{57} +13.7834i q^{58} +(-8.67795 - 5.01022i) q^{59} +(-11.1799 + 6.45469i) q^{60} -10.4713 q^{61} +(-6.47877 + 11.2216i) q^{62} +(-0.393717 + 2.61629i) q^{63} +4.00548 q^{64} +(-3.14670 + 10.4122i) q^{65} +(1.94355 + 3.36632i) q^{66} +2.91388i q^{67} +(-3.23971 - 5.61134i) q^{68} +(-1.82307 - 3.15765i) q^{69} +(-2.97635 + 19.7782i) q^{70} +(-1.11232 + 0.642201i) q^{71} +5.71107i q^{72} +(2.27528 - 1.31363i) q^{73} +(11.5275 - 19.9662i) q^{74} +(2.05063 + 3.55179i) q^{75} +(-30.4504 - 17.5805i) q^{76} +(4.05846 + 0.610745i) q^{77} +(6.18301 + 6.58779i) q^{78} +(-3.28050 + 5.68199i) q^{79} +17.3548i q^{80} +1.00000 q^{81} -8.25435 q^{82} -5.49127i q^{83} +(8.85315 + 7.05677i) q^{84} +(-3.95605 + 2.28403i) q^{85} +(8.58919 + 4.95897i) q^{86} +(2.75027 - 4.76361i) q^{87} +8.85917 q^{88} +(8.45584 - 4.88198i) q^{89} +7.55962 q^{90} +(9.50831 - 0.769452i) q^{91} -15.6023 q^{92} +(4.47820 - 2.58549i) q^{93} -23.1641 q^{94} +(-12.3945 + 21.4679i) q^{95} +(2.59199 + 1.49648i) q^{96} +(10.8340 - 6.25500i) q^{97} +(17.0991 - 3.91117i) q^{98} -1.55123i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

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