LMFDB - Embedded newform 273.2.bl.d.121.4

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:	$20$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.4
Root			$0.915396i$ of defining polynomial
Character	$\chi$	$=$	273.121
Dual form			273.2.bl.d.88.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.792756 + 0.457698i) q^{2} -1.00000 q^{3} +(-0.581025 + 1.00636i) q^{4} +(2.26729 + 1.30902i) q^{5} +(0.792756 - 0.457698i) q^{6} +(1.81456 - 1.92545i) q^{7} -2.89453i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.792756 + 0.457698i) q^{2} -1.00000 q^{3} +(-0.581025 + 1.00636i) q^{4} +(2.26729 + 1.30902i) q^{5} +(0.792756 - 0.457698i) q^{6} +(1.81456 - 1.92545i) q^{7} -2.89453i q^{8} +1.00000 q^{9} -2.39655 q^{10} +2.54641i q^{11} +(0.581025 - 1.00636i) q^{12} +(0.523154 + 3.56740i) q^{13} +(-0.557231 + 2.35694i) q^{14} +(-2.26729 - 1.30902i) q^{15} +(0.162771 + 0.281927i) q^{16} +(-3.09980 + 5.36901i) q^{17} +(-0.792756 + 0.457698i) q^{18} -2.73290i q^{19} +(-2.63470 + 1.52115i) q^{20} +(-1.81456 + 1.92545i) q^{21} +(-1.16549 - 2.01868i) q^{22} +(3.94513 + 6.83316i) q^{23} +2.89453i q^{24} +(0.927071 + 1.60573i) q^{25} +(-2.04752 - 2.58863i) q^{26} -1.00000 q^{27} +(0.883400 + 2.94485i) q^{28} +(-1.77706 + 3.07796i) q^{29} +2.39655 q^{30} +(7.91220 - 4.56811i) q^{31} +(4.75540 + 2.74553i) q^{32} -2.54641i q^{33} -5.67509i q^{34} +(6.63460 - 1.99026i) q^{35} +(-0.581025 + 1.00636i) q^{36} +(-7.52303 + 4.34342i) q^{37} +(1.25084 + 2.16652i) q^{38} +(-0.523154 - 3.56740i) q^{39} +(3.78900 - 6.56274i) q^{40} +(-3.98821 - 2.30259i) q^{41} +(0.557231 - 2.35694i) q^{42} +(-2.11228 - 3.65857i) q^{43} +(-2.56262 - 1.47953i) q^{44} +(2.26729 + 1.30902i) q^{45} +(-6.25505 - 3.61135i) q^{46} +(1.53652 + 0.887113i) q^{47} +(-0.162771 - 0.281927i) q^{48} +(-0.414724 - 6.98770i) q^{49} +(-1.46988 - 0.848638i) q^{50} +(3.09980 - 5.36901i) q^{51} +(-3.89407 - 1.54626i) q^{52} +(-3.42283 - 5.92852i) q^{53} +(0.792756 - 0.457698i) q^{54} +(-3.33331 + 5.77345i) q^{55} +(-5.57327 - 5.25230i) q^{56} +2.73290i q^{57} -3.25343i q^{58} +(1.95579 + 1.12918i) q^{59} +(2.63470 - 1.52115i) q^{60} +12.3720 q^{61} +(-4.18163 + 7.24280i) q^{62} +(1.81456 - 1.92545i) q^{63} -5.67758 q^{64} +(-3.48365 + 8.77314i) q^{65} +(1.16549 + 2.01868i) q^{66} +0.619532i q^{67} +(-3.60212 - 6.23906i) q^{68} +(-3.94513 - 6.83316i) q^{69} +(-4.34868 + 4.61443i) q^{70} +(6.48057 - 3.74156i) q^{71} -2.89453i q^{72} +(10.8250 - 6.24982i) q^{73} +(3.97595 - 6.88655i) q^{74} +(-0.927071 - 1.60573i) q^{75} +(2.75029 + 1.58788i) q^{76} +(4.90299 + 4.62062i) q^{77} +(2.04752 + 2.58863i) q^{78} +(0.621752 - 1.07691i) q^{79} +0.852282i q^{80} +1.00000 q^{81} +4.21557 q^{82} +2.10018i q^{83} +(-0.883400 - 2.94485i) q^{84} +(-14.0563 + 8.11541i) q^{85} +(3.34904 + 1.93357i) q^{86} +(1.77706 - 3.07796i) q^{87} +7.37066 q^{88} +(9.87880 - 5.70353i) q^{89} -2.39655 q^{90} +(7.81814 + 5.46595i) q^{91} -9.16886 q^{92} +(-7.91220 + 4.56811i) q^{93} -1.62412 q^{94} +(3.57742 - 6.19627i) q^{95} +(-4.75540 - 2.74553i) q^{96} +(-1.32935 + 0.767503i) q^{97} +(3.52703 + 5.34973i) q^{98} +2.54641i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * 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 $

$2$	−0.792756	+	0.457698i	−0.560563	+	0.323641i	−0.753372	−	0.657595i	$-0.771574\pi$
$2$	−0.792756	+	0.457698i	−0.560563	+	0.323641i	0.192808	+	0.981236i	$0.438240\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.581025	+	1.00636i	−0.290512	+	0.503182i
$5$	2.26729	+	1.30902i	1.01396	+	0.585412i	0.912350	−	0.409412i	$-0.134266\pi$
$5$	2.26729	+	1.30902i	1.01396	+	0.585412i	0.101614	+	0.994824i	$0.467599\pi$
$6$	0.792756	−	0.457698i	0.323641	−	0.186854i
$7$	1.81456	−	1.92545i	0.685840	−	0.727752i
$7$	1.81456	−	1.92545i	0.685840	−	0.727752i
$8$		−	2.89453i		−	1.02337i
$9$	1.00000			0.333333
$10$	−2.39655			−0.757854
$11$			2.54641i			0.767772i	0.923381	+	0.383886i	$0.125414\pi$
$11$			2.54641i			0.767772i	−0.923381	+	0.383886i	$0.874586\pi$
$12$	0.581025	−	1.00636i	0.167727	−	0.290512i
$13$	0.523154	+	3.56740i	0.145097	+	0.989417i
$13$	0.523154	+	3.56740i	0.145097	+	0.989417i
$14$	−0.557231	+	2.35694i	−0.148926	+	0.629918i
$15$	−2.26729	−	1.30902i	−0.585412	−	0.337988i
$16$	0.162771	+	0.281927i	0.0406927	+	0.0704819i
$17$	−3.09980	+	5.36901i	−0.751812	+	1.30218i	0.195131	+	0.980777i	$0.437487\pi$
$17$	−3.09980	+	5.36901i	−0.751812	+	1.30218i	−0.946944	+	0.321400i	$0.895847\pi$
$18$	−0.792756	+	0.457698i	−0.186854	+	0.107880i
$19$		−	2.73290i		−	0.626969i	−0.949593	−	0.313485i	$-0.898504\pi$
$19$		−	2.73290i		−	0.626969i	0.949593	−	0.313485i	$-0.101496\pi$
$20$	−2.63470	+	1.52115i	−0.589138	+	0.340139i
$21$	−1.81456	+	1.92545i	−0.395970	+	0.420168i
$22$	−1.16549	−	2.01868i	−0.248483	−	0.430385i
$23$	3.94513	+	6.83316i	0.822616	+	1.42481i	0.903728	+	0.428107i	$0.140819\pi$
$23$	3.94513	+	6.83316i	0.822616	+	1.42481i	−0.0811124	+	0.996705i	$0.525847\pi$
$24$			2.89453i			0.590843i
$25$	0.927071	+	1.60573i	0.185414	+	0.321147i
$26$	−2.04752	−	2.58863i	−0.401553	−	0.507672i
$27$	−1.00000			−0.192450
$28$	0.883400	+	2.94485i	0.166947	+	0.556524i
$29$	−1.77706	+	3.07796i	−0.329992	+	0.571562i	−0.982510	−	0.186211i	$-0.940379\pi$
$29$	−1.77706	+	3.07796i	−0.329992	+	0.571562i	0.652518	+	0.757773i	$0.273713\pi$
$30$	2.39655			0.437547
$31$	7.91220	−	4.56811i	1.42107	−	0.820457i	0.424683	−	0.905342i	$-0.360386\pi$
$31$	7.91220	−	4.56811i	1.42107	−	0.820457i	0.996391	+	0.0848850i	$0.0270523\pi$
$32$	4.75540	+	2.74553i	0.840643	+	0.485345i
$33$		−	2.54641i		−	0.443273i
$34$		−	5.67509i		−	0.973270i
$35$	6.63460	−	1.99026i	1.12145	−	0.336415i
$36$	−0.581025	+	1.00636i	−0.0968375	+	0.167727i
$37$	−7.52303	+	4.34342i	−1.23678	+	0.714054i	−0.968434	−	0.249269i	$-0.919810\pi$
$37$	−7.52303	+	4.34342i	−1.23678	+	0.714054i	−0.268344	+	0.963323i	$0.586476\pi$
$38$	1.25084	+	2.16652i	0.202913	+	0.351456i
$39$	−0.523154	−	3.56740i	−0.0837718	−	0.571240i
$40$	3.78900	−	6.56274i	0.599093	−	1.03766i
$41$	−3.98821	−	2.30259i	−0.622854	−	0.359605i	0.155125	−	0.987895i	$-0.450422\pi$
$41$	−3.98821	−	2.30259i	−0.622854	−	0.359605i	−0.777979	+	0.628290i	$0.783755\pi$
$42$	0.557231	−	2.35694i	0.0859826	−	0.363683i
$43$	−2.11228	−	3.65857i	−0.322119	−	0.557926i	0.658806	−	0.752313i	$-0.271062\pi$
$43$	−2.11228	−	3.65857i	−0.322119	−	0.557926i	−0.980925	+	0.194386i	$0.937728\pi$
$44$	−2.56262	−	1.47953i	−0.386329	−	0.223047i
$45$	2.26729	+	1.30902i	0.337988	+	0.195137i
$46$	−6.25505	−	3.61135i	−0.922257	−	0.532465i
$47$	1.53652	+	0.887113i	0.224125	+	0.129399i	0.607859	−	0.794045i	$-0.292029\pi$
$47$	1.53652	+	0.887113i	0.224125	+	0.129399i	−0.383734	+	0.923444i	$0.625362\pi$
$48$	−0.162771	−	0.281927i	−0.0234940	−	0.0406927i
$49$	−0.414724	−	6.98770i	−0.0592462	−	0.998243i
$50$	−1.46988	−	0.848638i	−0.207873	−	0.120015i
$51$	3.09980	−	5.36901i	0.434059	−	0.751812i
$52$	−3.89407	−	1.54626i	−0.540010	−	0.214428i
$53$	−3.42283	−	5.92852i	−0.470162	−	0.814345i	0.529255	−	0.848463i	$-0.322471\pi$
$53$	−3.42283	−	5.92852i	−0.470162	−	0.814345i	−0.999418	+	0.0341173i	$0.989138\pi$
$54$	0.792756	−	0.457698i	0.107880	−	0.0622848i
$55$	−3.33331	+	5.77345i	−0.449463	+	0.778492i
$56$	−5.57327	−	5.25230i	−0.744760	−	0.701869i
$57$			2.73290i			0.361981i
$58$		−	3.25343i		−	0.427196i
$59$	1.95579	+	1.12918i	0.254622	+	0.147006i	0.621879	−	0.783113i	$-0.286370\pi$
$59$	1.95579	+	1.12918i	0.254622	+	0.147006i	−0.367257	+	0.930120i	$0.619703\pi$
$60$	2.63470	−	1.52115i	0.340139	−	0.196379i
$61$	12.3720			1.58408			0.792038	−	0.610472i	$-0.209020\pi$
$61$	12.3720			1.58408			0.792038	+	0.610472i	$0.209020\pi$
$62$	−4.18163	+	7.24280i	−0.531068	+	0.919837i
$63$	1.81456	−	1.92545i	0.228613	−	0.242584i
$64$	−5.67758			−0.709697
$65$	−3.48365	+	8.77314i	−0.432094	+	1.08817i
$66$	1.16549	+	2.01868i	0.143462	+	0.248483i
$67$			0.619532i			0.0756878i	0.999284	+	0.0378439i	$0.0120490\pi$
$67$			0.619532i			0.0756878i	−0.999284	+	0.0378439i	$0.987951\pi$
$68$	−3.60212	−	6.23906i	−0.436821	−	0.756597i
$69$	−3.94513	−	6.83316i	−0.474937	−	0.822616i
$70$	−4.34868	+	4.61443i	−0.519767	+	0.551530i
$71$	6.48057	−	3.74156i	0.769102	−	0.444041i	−0.0634524	−	0.997985i	$-0.520211\pi$
$71$	6.48057	−	3.74156i	0.769102	−	0.444041i	0.832554	+	0.553944i	$0.186878\pi$
$72$		−	2.89453i		−	0.341123i
$73$	10.8250	−	6.24982i	1.26697	−	0.731486i	0.292557	−	0.956248i	$-0.405494\pi$
$73$	10.8250	−	6.24982i	1.26697	−	0.731486i	0.974414	+	0.224762i	$0.0721605\pi$
$74$	3.97595	−	6.88655i	0.462195	−	0.800545i
$75$	−0.927071	−	1.60573i	−0.107049	−	0.185414i
$76$	2.75029	+	1.58788i	0.315480	+	0.182142i
$77$	4.90299	+	4.62062i	0.558748	+	0.526569i
$78$	2.04752	+	2.58863i	0.231836	+	0.293105i
$79$	0.621752	−	1.07691i	0.0699526	−	0.121161i	−0.828928	−	0.559356i	$-0.811049\pi$
$79$	0.621752	−	1.07691i	0.0699526	−	0.121161i	0.898880	+	0.438194i	$0.144382\pi$
$80$			0.852282i			0.0952880i
$81$	1.00000			0.111111
$82$	4.21557			0.465532
$83$			2.10018i			0.230524i	0.993335	+	0.115262i	$0.0367708\pi$
$83$			2.10018i			0.230524i	−0.993335	+	0.115262i	$0.963229\pi$
$84$	−0.883400	−	2.94485i	−0.0963868	−	0.321309i
$85$	−14.0563	+	8.11541i	−1.52462	+	0.880240i
$86$	3.34904	+	1.93357i	0.361136	+	0.208502i
$87$	1.77706	−	3.07796i	0.190521	−	0.329992i
$88$	7.37066			0.785715
$89$	9.87880	−	5.70353i	1.04715	−	0.604573i	0.125301	−	0.992119i	$-0.460010\pi$
$89$	9.87880	−	5.70353i	1.04715	−	0.604573i	0.921850	+	0.387546i	$0.126677\pi$
$90$	−2.39655			−0.252618
$91$	7.81814	+	5.46595i	0.819564	+	0.572988i
$92$	−9.16886			−0.955920
$93$	−7.91220	+	4.56811i	−0.820457	+	0.473691i
$94$	−1.62412			−0.167515
$95$	3.57742	−	6.19627i	0.367035	−	0.635724i
$96$	−4.75540	−	2.74553i	−0.485345	−	0.280214i
$97$	−1.32935	+	0.767503i	−0.134975	+	0.0779281i	−0.565967	−	0.824428i	$-0.691497\pi$
$97$	−1.32935	+	0.767503i	−0.134975	+	0.0779281i	0.430992	+	0.902356i	$0.358164\pi$
$98$	3.52703	+	5.34973i	0.356284	+	0.540404i
$99$			2.54641i			0.255924i
$100$	−2.15461			−0.215461
$101$	0.504753			0.0502248			0.0251124	−	0.999685i	$-0.492006\pi$
$101$	0.504753			0.0502248			0.0251124	+	0.999685i	$0.492006\pi$
$102$			5.67509i			0.561918i
$103$	−2.66915	+	4.62310i	−0.262999	+	0.455528i	−0.967038	−	0.254634i	$-0.918045\pi$
$103$	−2.66915	+	4.62310i	−0.262999	+	0.455528i	0.704038	+	0.710162i	$0.251378\pi$
$104$	10.3259	−	1.51429i	1.01254	−	0.148488i
$105$	−6.63460	+	1.99026i	−0.647470	+	0.194229i
$106$	5.42695	+	3.13325i	0.527112	+	0.304328i
$107$	−8.90567	−	15.4251i	−0.860944	−	1.49120i	−0.871019	−	0.491249i	$-0.836540\pi$
$107$	−8.90567	−	15.4251i	−0.860944	−	1.49120i	0.0100752	−	0.999949i	$-0.496793\pi$
$108$	0.581025	−	1.00636i	0.0559091	−	0.0968375i
$109$	−16.0930	+	9.29129i	−1.54143	+	0.889944i	−0.542679	+	0.839940i	$0.682590\pi$
$109$	−16.0930	+	9.29129i	−1.54143	+	0.889944i	−0.998749	+	0.0500036i	$0.984077\pi$
$110$		−	6.10259i		−	0.581859i
$111$	7.52303	−	4.34342i	0.714054	−	0.412259i
$112$	0.838195	+	0.198168i	0.0792020	+	0.0187251i
$113$	−3.61615	−	6.26336i	−0.340179	−	0.589207i	0.644287	−	0.764784i	$-0.277154\pi$
$113$	−3.61615	−	6.26336i	−0.340179	−	0.589207i	−0.984466	+	0.175577i	$0.943821\pi$
$114$	−1.25084	−	2.16652i	−0.117152	−	0.202913i
$115$			20.6570i			1.92628i
$116$	−2.06503	−	3.57674i	−0.191733	−	0.332092i
$117$	0.523154	+	3.56740i	0.0483656	+	0.329806i
$118$	−2.06729			−0.190309
$119$	4.71299	+	15.7109i	0.432039	+	1.44022i
$120$	−3.78900	+	6.56274i	−0.345887	+	0.599093i
$121$	4.51579			0.410526
$122$	−9.80800	+	5.66265i	−0.887975	+	0.512672i
$123$	3.98821	+	2.30259i	0.359605	+	0.207618i
$124$			10.6167i			0.953412i
$125$		−	8.23599i		−	0.736649i
$126$	−0.557231	+	2.35694i	−0.0496421	+	0.209973i
$127$	4.21069	−	7.29312i	0.373638	−	0.647160i	−0.616484	−	0.787367i	$-0.711444\pi$
$127$	4.21069	−	7.29312i	0.373638	−	0.647160i	0.990122	+	0.140207i	$0.0447769\pi$
$128$	−5.00985	+	2.89244i	−0.442813	+	0.255658i
$129$	2.11228	+	3.65857i	0.185975	+	0.322119i
$130$	−1.25376	−	8.54943i	−0.109962	−	0.749834i
$131$	8.26809	−	14.3207i	0.722386	−	1.25121i	−0.237655	−	0.971350i	$-0.576379\pi$
$131$	8.26809	−	14.3207i	0.722386	−	1.25121i	0.960041	−	0.279860i	$-0.0902879\pi$
$132$	2.56262	+	1.47953i	0.223047	+	0.128776i
$133$	−5.26206	−	4.95901i	−0.456278	−	0.430001i
$134$	−0.283559	−	0.491138i	−0.0244957	−	0.0424278i
$135$	−2.26729	−	1.30902i	−0.195137	−	0.112663i
$136$	15.5408	+	8.97246i	1.33261	+	0.769382i
$137$	1.66150	+	0.959268i	0.141952	+	0.0819558i	0.569294	−	0.822134i	$-0.307217\pi$
$137$	1.66150	+	0.959268i	0.141952	+	0.0819558i	−0.427342	+	0.904090i	$0.640550\pi$
$138$	6.25505	+	3.61135i	0.532465	+	0.307419i
$139$	−11.0300	−	19.1046i	−0.935556	−	1.62043i	−0.773640	−	0.633626i	$-0.781566\pi$
$139$	−11.0300	−	19.1046i	−0.935556	−	1.62043i	−0.161916	−	0.986805i	$-0.551767\pi$
$140$	−1.85194	+	7.83321i	−0.156518	+	0.662027i
$141$	−1.53652	−	0.887113i	−0.129399	−	0.0747084i
$142$	−3.42501	+	5.93229i	−0.287420	+	0.497826i
$143$	−9.08405	+	1.33217i	−0.759647	+	0.111401i
$144$	0.162771	+	0.281927i	0.0135642	+	0.0234940i
$145$	−8.05822	+	4.65241i	−0.669198	+	0.386362i
$146$	−5.72106	+	9.90917i	−0.473478	+	0.820089i
$147$	0.414724	+	6.98770i	0.0342058	+	0.576336i
$148$		−	10.0945i		−	0.829766i
$149$			14.9944i			1.22839i	0.789155	+	0.614195i	$0.210519\pi$
$149$			14.9944i			1.22839i	−0.789155	+	0.614195i	$0.789481\pi$
$150$	1.46988	+	0.848638i	0.120015	+	0.0692910i
$151$	−7.81993	+	4.51484i	−0.636377	+	0.367413i	−0.783218	−	0.621748i	$-0.786423\pi$
$151$	−7.81993	+	4.51484i	−0.636377	+	0.367413i	0.146840	+	0.989160i	$0.453090\pi$
$152$	−7.91045			−0.641622
$153$	−3.09980	+	5.36901i	−0.250604	+	0.434059i
$154$	−6.00173	−	1.41894i	−0.483633	−	0.114341i
$155$	23.9190			1.92122
$156$	3.89407	+	1.54626i	0.311775	+	0.123800i
$157$	0.0998014	+	0.172861i	0.00796501	+	0.0137958i	0.869980	−	0.493086i	$-0.164131\pi$
$157$	0.0998014	+	0.172861i	0.00796501	+	0.0137958i	−0.862015	+	0.506882i	$0.830798\pi$
$158$			1.13830i			0.0905583i
$159$	3.42283	+	5.92852i	0.271448	+	0.470162i
$160$	7.18791	+	12.4498i	0.568254	+	0.984245i
$161$	20.3156	+	4.80305i	1.60109	+	0.378533i
$162$	−0.792756	+	0.457698i	−0.0622848	+	0.0359602i
$163$			7.05212i			0.552364i	0.961105	+	0.276182i	$0.0890693\pi$
$163$			7.05212i			0.552364i	−0.961105	+	0.276182i	$0.910931\pi$
$164$	4.63450	−	2.67573i	0.361894	−	0.208939i
$165$	3.33331	−	5.77345i	0.259497	−	0.449463i
$166$	−0.961247	−	1.66493i	−0.0746072	−	0.129223i
$167$	−1.55981	−	0.900559i	−0.120702	−	0.0696874i	0.438433	−	0.898764i	$-0.355534\pi$
$167$	−1.55981	−	0.900559i	−0.120702	−	0.0696874i	−0.559135	+	0.829076i	$0.688867\pi$
$168$	5.57327	+	5.25230i	0.429987	+	0.405224i
$169$	−12.4526	+	3.73260i	−0.957894	+	0.287123i
$170$	7.42881	−	12.8671i	0.569764	−	0.986860i
$171$		−	2.73290i		−	0.208990i
$172$	4.90914			0.374318
$173$	−11.9257			−0.906693			−0.453346	−	0.891334i	$-0.649770\pi$
$173$	−11.9257			−0.906693			−0.453346	+	0.891334i	$0.649770\pi$
$174$			3.25343i			0.246642i
$175$	4.77399	+	1.12868i	0.360880	+	0.0853199i
$176$	−0.717903	+	0.414482i	−0.0541140	+	0.0312427i
$177$	−1.95579	−	1.12918i	−0.147006	−	0.0848741i
$178$	−5.22099	+	9.04302i	−0.391330	+	0.677803i
$179$	−16.3400			−1.22131			−0.610655	−	0.791897i	$-0.709094\pi$
$179$	−16.3400			−1.22131			−0.610655	+	0.791897i	$0.709094\pi$
$180$	−2.63470	+	1.52115i	−0.196379	+	0.113380i
$181$	16.7748			1.24686			0.623429	−	0.781880i	$-0.285739\pi$
$181$	16.7748			1.24686			0.623429	+	0.781880i	$0.285739\pi$
$182$	−8.69964	−	0.754822i	−0.644860	−	0.0559511i
$183$	−12.3720			−0.914566
$184$	19.7788	−	11.4193i	1.45811	−	0.841840i
$185$	−22.7425			−1.67206
$186$	4.18163	−	7.24280i	0.306612	−	0.531068i
$187$	−13.6717	−	7.89337i	−0.999775	−	0.577220i
$188$	−1.78552	+	1.03087i	−0.130222	+	0.0751839i
$189$	−1.81456	+	1.92545i	−0.131990	+	0.140056i
$190$			6.54951i			0.475151i
$191$	7.48391			0.541516			0.270758	−	0.962647i	$-0.412726\pi$
$191$	7.48391			0.541516			0.270758	+	0.962647i	$0.412726\pi$
$192$	5.67758			0.409744
$193$		−	11.6862i		−	0.841193i	−0.907248	−	0.420596i	$-0.861821\pi$
$193$		−	11.6862i		−	0.841193i	0.907248	−	0.420596i	$-0.138179\pi$
$194$	0.702569	−	1.21689i	0.0504416	−	0.0873673i
$195$	3.48365	−	8.77314i	0.249469	−	0.628258i
$196$	7.27314	+	3.64267i	0.519510	+	0.260190i
$197$	0.388915	+	0.224540i	0.0277091	+	0.0159978i	0.513791	−	0.857916i	$-0.328241\pi$
$197$	0.388915	+	0.224540i	0.0277091	+	0.0159978i	−0.486081	+	0.873913i	$0.661574\pi$
$198$	−1.16549	−	2.01868i	−0.0828276	−	0.143462i
$199$	4.91166	−	8.50724i	0.348178	−	0.603062i	−0.637748	−	0.770245i	$-0.720134\pi$
$199$	4.91166	−	8.50724i	0.348178	−	0.603062i	0.985926	+	0.167183i	$0.0534671\pi$
$200$	4.64784	−	2.68343i	0.328652	−	0.189747i
$201$		−	0.619532i		−	0.0436984i
$202$	−0.400146	+	0.231024i	−0.0281542	+	0.0162548i
$203$	2.70187	+	9.00678i	0.189634	+	0.632152i
$204$	3.60212	+	6.23906i	0.252199	+	0.436821i
$205$	−6.02829	−	10.4413i	−0.421034	−	0.729252i
$206$		−	4.88666i		−	0.340470i
$207$	3.94513	+	6.83316i	0.274205	+	0.474937i
$208$	−0.920592	+	0.728160i	−0.0638316	+	0.0504888i
$209$	6.95908			0.481369
$210$	4.34868	−	4.61443i	0.300088	−	0.318426i
$211$	1.80752	−	3.13072i	0.124435	−	0.215528i	−0.797077	−	0.603878i	$-0.793621\pi$
$211$	1.80752	−	3.13072i	0.124435	−	0.215528i	0.921512	+	0.388350i	$0.126955\pi$
$212$	7.95501			0.546352
$213$	−6.48057	+	3.74156i	−0.444041	+	0.256367i
$214$	14.1201	+	8.15222i	0.965227	+	0.557274i
$215$		−	11.0600i		−	0.754289i
$216$			2.89453i			0.196948i
$217$	5.56151	−	23.5237i	0.377540	−	1.59689i
$218$	8.50521	−	14.7315i	0.576045	−	0.997740i
$219$	−10.8250	+	6.24982i	−0.731486	+	0.422324i
$220$	−3.87347	−	6.70904i	−0.261149	−	0.452323i
$221$	−20.7751	−	8.24939i	−1.39748	−	0.554914i
$222$	−3.97595	+	6.88655i	−0.266848	+	0.462195i
$223$	3.07998	+	1.77823i	0.206251	+	0.119079i	0.599568	−	0.800324i	$-0.295339\pi$
$223$	3.07998	+	1.77823i	0.206251	+	0.119079i	−0.393317	+	0.919403i	$0.628672\pi$
$224$	13.9153	−	4.17435i	0.929758	−	0.278910i
$225$	0.927071	+	1.60573i	0.0618047	+	0.107049i
$226$	5.73345	+	3.31021i	0.381384	+	0.220192i
$227$	−6.75066	−	3.89750i	−0.448057	−	0.258686i	0.258952	−	0.965890i	$-0.416623\pi$
$227$	−6.75066	−	3.89750i	−0.448057	−	0.258686i	−0.707009	+	0.707204i	$0.749956\pi$
$228$	−2.75029	−	1.58788i	−0.182142	−	0.105160i
$229$	14.2182	+	8.20887i	0.939563	+	0.542457i	0.889823	−	0.456305i	$-0.150827\pi$
$229$	14.2182	+	8.20887i	0.939563	+	0.542457i	0.0497400	+	0.998762i	$0.484161\pi$
$230$	−9.45467	−	16.3760i	−0.623423	−	1.07980i
$231$	−4.90299	−	4.62062i	−0.322593	−	0.304015i
$232$	8.90923	+	5.14375i	0.584920	+	0.337704i
$233$	−3.78863	+	6.56210i	−0.248201	+	0.429898i	−0.963027	−	0.269405i	$-0.913173\pi$
$233$	−3.78863	+	6.56210i	−0.248201	+	0.429898i	0.714825	+	0.699303i	$0.246506\pi$
$234$	−2.04752	−	2.58863i	−0.133851	−	0.169224i
$235$	2.32250	+	4.02269i	0.151503	+	0.262411i
$236$	−2.27273	+	1.31216i	−0.147942	+	0.0854143i
$237$	−0.621752	+	1.07691i	−0.0403872	+	0.0699526i
$238$	−10.9271	−	10.2978i	−0.708300	−	0.667508i
$239$		−	4.68654i		−	0.303147i	−0.988446	−	0.151574i	$-0.951566\pi$
$239$		−	4.68654i		−	0.303147i	0.988446	−	0.151574i	$-0.0484341\pi$
$240$		−	0.852282i		−	0.0550146i
$241$	−9.28664	−	5.36164i	−0.598205	−	0.345374i	0.170130	−	0.985422i	$-0.445581\pi$
$241$	−9.28664	−	5.36164i	−0.598205	−	0.345374i	−0.768335	+	0.640048i	$0.778915\pi$
$242$	−3.57992	+	2.06687i	−0.230126	+	0.132863i
$243$	−1.00000			−0.0641500
$244$	−7.18845	+	12.4508i	−0.460193	+	0.797078i
$245$	8.20675	−	16.3860i	0.524310	−	1.04687i
$246$	−4.21557			−0.268775
$247$	9.74932	−	1.42973i	0.620334	−	0.0909713i
$248$	−13.2225	−	22.9021i	−0.839632	−	1.45428i
$249$		−	2.10018i		−	0.133093i
$250$	3.76960	+	6.52913i	0.238410	+	0.412939i
$251$	5.93135	+	10.2734i	0.374384	+	0.648452i	0.990235	−	0.139411i	$-0.0445209\pi$
$251$	5.93135	+	10.2734i	0.374384	+	0.648452i	−0.615851	+	0.787863i	$0.711188\pi$
$252$	0.883400	+	2.94485i	0.0556489	+	0.185508i
$253$	−17.4000	+	10.0459i	−1.09393	+	0.631581i
$254$			7.70889i			0.483699i
$255$	14.0563	−	8.11541i	0.880240	−	0.508207i
$256$	8.32531	−	14.4199i	0.520332	−	0.901241i
$257$	−4.67378	−	8.09523i	−0.291542	−	0.504966i	0.682632	−	0.730762i	$-0.260835\pi$
$257$	−4.67378	−	8.09523i	−0.291542	−	0.504966i	−0.974175	+	0.225796i	$0.927502\pi$
$258$	−3.34904	−	1.93357i	−0.208502	−	0.120379i
$259$	−5.28796	+	22.3666i	−0.328578	+	1.38979i
$260$	−6.80489	−	8.60324i	−0.422021	−	0.533550i
$261$	−1.77706	+	3.07796i	−0.109997	+	0.190521i
$262$			15.1372i			0.935176i
$263$	0.943420			0.0581738			0.0290869	−	0.999577i	$-0.490740\pi$
$263$	0.943420			0.0581738			0.0290869	+	0.999577i	$0.490740\pi$
$264$	−7.37066			−0.453633
$265$		−	17.9222i		−	1.10095i
$266$	6.44126	+	1.52285i	0.394939	+	0.0933722i
$267$	−9.87880	+	5.70353i	−0.604573	+	0.349050i
$268$	−0.623475	−	0.359963i	−0.0380848	−	0.0219883i
$269$	3.79153	−	6.56712i	0.231174	−	0.400404i	−0.726980	−	0.686658i	$-0.759077\pi$
$269$	3.79153	−	6.56712i	0.231174	−	0.400404i	0.958154	+	0.286254i	$0.0924101\pi$
$270$	2.39655			0.145849
$271$	17.8317	−	10.2951i	1.08320	−	0.625384i	0.151440	−	0.988466i	$-0.451609\pi$
$271$	17.8317	−	10.2951i	1.08320	−	0.625384i	0.931757	+	0.363083i	$0.118276\pi$
$272$	−2.01823			−0.122373
$273$	−7.81814	−	5.46595i	−0.473175	−	0.330815i
$274$	−1.75622			−0.106097
$275$	−4.08886	+	2.36070i	−0.246568	+	0.142356i
$276$	9.16886			0.551901
$277$	−10.2128	+	17.6891i	−0.613628	+	1.06283i	0.376996	+	0.926215i	$0.376957\pi$
$277$	−10.2128	+	17.6891i	−0.613628	+	1.06283i	−0.990624	+	0.136620i	$0.956376\pi$
$278$	17.4883	+	10.0969i	1.04888	+	0.605569i
$279$	7.91220	−	4.56811i	0.473691	−	0.273486i
$280$	−5.76085	−	19.2040i	−0.344277	−	1.14766i
$281$		−	10.8703i		−	0.648466i	−0.945977	−	0.324233i	$-0.894894\pi$
$281$		−	10.8703i		−	0.648466i	0.945977	−	0.324233i	$-0.105106\pi$
$282$	1.62412			0.0967149
$283$	3.82154			0.227167			0.113583	−	0.993528i	$-0.463767\pi$
$283$	3.82154			0.227167			0.113583	+	0.993528i	$0.463767\pi$
$284$			8.69575i			0.515998i
$285$	−3.57742	+	6.19627i	−0.211908	+	0.367035i
$286$	6.59171	−	5.21384i	0.389776	−	0.308301i
$287$	−11.6704	+	3.50090i	−0.688882	+	0.206652i
$288$	4.75540	+	2.74553i	0.280214	+	0.161782i
$289$	−10.7175	−	18.5633i	−0.630443	−	1.09196i
$290$	4.25880	−	7.37646i	0.250085	−	0.433161i
$291$	1.32935	−	0.767503i	0.0779281	−	0.0449918i
$292$			14.5252i			0.850023i
$293$	15.6392	−	9.02929i	0.913651	−	0.527497i	0.0320472	−	0.999486i	$-0.489797\pi$
$293$	15.6392	−	9.02929i	0.913651	−	0.527497i	0.881604	+	0.471989i	$0.156464\pi$
$294$	−3.52703	−	5.34973i	−0.205701	−	0.312003i
$295$	2.95623	+	5.12034i	0.172118	+	0.298118i
$296$	12.5722	+	21.7756i	0.730742	+	1.26568i
$297$		−	2.54641i		−	0.147758i
$298$	−6.86291	−	11.8869i	−0.397558	−	0.688590i
$299$	−22.3127	+	17.6486i	−1.29037	+	1.02065i
$300$	2.15461			0.124396
$301$	−10.8772	−	2.57162i	−0.626954	−	0.148226i
$302$	4.13287	−	7.15834i	0.237820	−	0.411916i
$303$	−0.504753			−0.0289973
$304$	0.770478	−	0.444836i	0.0441900	−	0.0255131i
$305$	28.0510	+	16.1952i	1.60619	+	0.927336i
$306$		−	5.67509i		−	0.324423i
$307$		−	8.88791i		−	0.507260i	−0.967301	−	0.253630i	$-0.918375\pi$
$307$		−	8.88791i		−	0.507260i	0.967301	−	0.253630i	$-0.0816246\pi$
$308$	−7.49879	+	2.24950i	−0.427283	+	0.128177i
$309$	2.66915	−	4.62310i	0.151843	−	0.262999i
$310$	−18.9620	+	10.9477i	−1.07697	+	0.621787i
$311$	−8.24533	−	14.2813i	−0.467550	−	0.809820i	0.531763	−	0.846893i	$-0.321530\pi$
$311$	−8.24533	−	14.2813i	−0.467550	−	0.809820i	−0.999313	+	0.0370736i	$0.988196\pi$
$312$	−10.3259	+	1.51429i	−0.584591	+	0.0857295i
$313$	−11.0236	+	19.0935i	−0.623092	+	1.07923i	0.365815	+	0.930688i	$0.380790\pi$
$313$	−11.0236	+	19.0935i	−0.623092	+	1.07923i	−0.988907	+	0.148539i	$0.952543\pi$
$314$	−0.158236	−	0.0913578i	−0.00892979	−	0.00515562i
$315$	6.63460	−	1.99026i	0.373817	−	0.112138i
$316$	0.722507	+	1.25142i	0.0406442	+	0.0703978i
$317$	19.7541	+	11.4050i	1.10950	+	0.640569i	0.938699	−	0.344737i	$-0.112032\pi$
$317$	19.7541	+	11.4050i	1.10950	+	0.640569i	0.170799	+	0.985306i	$0.445365\pi$
$318$	−5.42695	−	3.13325i	−0.304328	−	0.175704i
$319$	−7.83774	−	4.52512i	−0.438829	−	0.253358i
$320$	−12.8727	−	7.43207i	−0.719607	−	0.415465i
$321$	8.90567	+	15.4251i	0.497066	+	0.860944i
$322$	−18.3037	+	5.49076i	−1.02002	+	0.305988i
$323$	14.6730	+	8.47143i	0.816425	+	0.471363i
$324$	−0.581025	+	1.00636i	−0.0322792	+	0.0559091i
$325$	−5.24329	+	4.14728i	−0.290845	+	0.230049i
$326$	−3.22774	−	5.59061i	−0.178768	−	0.309635i
$327$	16.0930	−	9.29129i	0.889944	−	0.513809i
$328$	−6.66493	+	11.5440i	−0.368009	+	0.637410i
$329$	4.49621	−	1.34878i	0.247884	−	0.0743607i
$330$			6.10259i			0.335937i
$331$		−	32.0157i		−	1.75974i	−0.475212	−	0.879871i	$-0.657629\pi$
$331$		−	32.0157i		−	1.75974i	0.475212	−	0.879871i	$-0.342371\pi$
$332$	−2.11354	−	1.22025i	−0.115996	−	0.0669702i
$333$	−7.52303	+	4.34342i	−0.412259	+	0.238018i
$334$	1.64874			0.0902149
$335$	−0.810980	+	1.40466i	−0.0443086	+	0.0767447i
$336$	−0.838195	−	0.198168i	−0.0457273	−	0.0108109i
$337$	4.99719			0.272214			0.136107	−	0.990694i	$-0.456541\pi$
$337$	4.99719			0.272214			0.136107	+	0.990694i	$0.456541\pi$
$338$	8.16349	−	8.65858i	0.444035	−	0.470965i
$339$	3.61615	+	6.26336i	0.196402	+	0.340179i
$340$		−	18.8610i		−	1.02288i
$341$	11.6323	+	20.1477i	0.629924	+	1.09106i
$342$	1.25084	+	2.16652i	0.0676378	+	0.117152i
$343$	−14.2070	−	11.8811i	−0.767107	−	0.641519i
$344$	−10.5898	+	6.11404i	−0.570965	+	0.329647i
$345$		−	20.6570i		−	1.11214i
$346$	9.45416	−	5.45836i	0.508259	−	0.293443i
$347$	−17.1710	+	29.7411i	−0.921789	+	1.59659i	−0.125143	+	0.992139i	$0.539939\pi$
$347$	−17.1710	+	29.7411i	−0.921789	+	1.59659i	−0.796646	+	0.604446i	$0.793394\pi$
$348$	2.06503	+	3.57674i	0.110697	+	0.191733i
$349$	8.51580	+	4.91660i	0.455841	+	0.263180i	0.710294	−	0.703905i	$-0.248562\pi$
$349$	8.51580	+	4.91660i	0.455841	+	0.263180i	−0.254453	+	0.967085i	$0.581895\pi$
$350$	−4.30121	+	1.29028i	−0.229909	+	0.0689685i
$351$	−0.523154	−	3.56740i	−0.0279239	−	0.190413i
$352$	−6.99124	+	12.1092i	−0.372635	+	0.645422i
$353$			15.3426i			0.816603i	0.912847	+	0.408302i	$0.133879\pi$
$353$			15.3426i			0.816603i	−0.912847	+	0.408302i	$0.866121\pi$
$354$	2.06729			0.109875
$355$	19.5911			1.03979
$356$			13.2556i			0.702544i
$357$	−4.71299	−	15.7109i	−0.249438	−	0.831510i
$358$	12.9536	−	7.47879i	0.684621	−	0.395266i
$359$	−25.1701	−	14.5319i	−1.32842	−	0.766966i	−0.343369	−	0.939201i	$-0.611568\pi$
$359$	−25.1701	−	14.5319i	−1.32842	−	0.766966i	−0.985056	+	0.172235i	$0.944901\pi$
$360$	3.78900	−	6.56274i	0.199698	−	0.345887i
$361$	11.5313			0.606909
$362$	−13.2983	+	7.67777i	−0.698943	+	0.403535i
$363$	−4.51579			−0.237018
$364$	−10.0433	+	4.69204i	−0.526411	+	0.245930i
$365$	32.7246			1.71288
$366$	9.80800	−	5.66265i	0.512672	−	0.295992i
$367$	18.3021			0.955362			0.477681	−	0.878533i	$-0.341478\pi$
$367$	18.3021			0.955362			0.477681	+	0.878533i	$0.341478\pi$
$368$	−1.28430	+	2.22448i	−0.0669489	+	0.115959i
$369$	−3.98821	−	2.30259i	−0.207618	−	0.119868i
$370$	18.0293	−	10.4092i	0.937297	−	0.541149i
$371$	−17.6260	−	4.16718i	−0.915098	−	0.216349i
$372$		−	10.6167i		−	0.550453i
$373$	12.8655			0.666149			0.333074	−	0.942901i	$-0.391914\pi$
$373$	12.8655			0.666149			0.333074	+	0.942901i	$0.391914\pi$
$374$	14.4511			0.747250
$375$			8.23599i			0.425305i
$376$	2.56777	−	4.44752i	0.132423	−	0.229363i
$377$	−11.9100	−	4.72922i	−0.613394	−	0.243567i
$378$	0.557231	−	2.35694i	0.0286609	−	0.121228i
$379$	22.8080	+	13.1682i	1.17157	+	0.676405i	0.954049	−	0.299651i	$-0.0968703\pi$
$379$	22.8080	+	13.1682i	1.17157	+	0.676405i	0.217519	+	0.976056i	$0.430204\pi$
$380$	4.15714	+	7.20037i	0.213257	+	0.369371i
$381$	−4.21069	+	7.29312i	−0.215720	+	0.373638i
$382$	−5.93291	+	3.42537i	−0.303554	+	0.175257i
$383$			14.4045i			0.736035i	0.929819	+	0.368017i	$0.119963\pi$
$383$			14.4045i			0.736035i	−0.929819	+	0.368017i	$0.880037\pi$
$384$	5.00985	−	2.89244i	0.255658	−	0.147604i
$385$	5.06801	+	16.8944i	0.258290	+	0.861019i
$386$	5.34876	+	9.26433i	0.272245	+	0.471542i
$387$	−2.11228	−	3.65857i	−0.107373	−	0.185975i
$388$		−	1.78375i		−	0.0905563i
$389$	3.30891	+	5.73120i	0.167768	+	0.290584i	0.937635	−	0.347621i	$-0.113011\pi$
$389$	3.30891	+	5.73120i	0.167768	+	0.290584i	−0.769866	+	0.638205i	$0.779677\pi$
$390$	1.25376	+	8.54943i	0.0634868	+	0.432917i
$391$	−48.9164			−2.47381
$392$	−20.2261	+	1.20043i	−1.02157	+	0.0606308i
$393$	−8.26809	+	14.3207i	−0.417070	+	0.722386i
$394$	−0.411087			−0.0207103
$395$	2.81939	−	1.62777i	0.141859	−	0.0819022i
$396$	−2.56262	−	1.47953i	−0.128776	−	0.0743491i
$397$			22.6357i			1.13605i	0.823010	+	0.568027i	$0.192293\pi$
$397$			22.6357i			1.13605i	−0.823010	+	0.568027i	$0.807707\pi$
$398$			8.99222i			0.450739i
$399$	5.26206	+	4.95901i	0.263432	+	0.248261i
$400$	−0.301800	+	0.522734i	−0.0150900	+	0.0261367i
$401$	0.390199	−	0.225281i	0.0194856	−	0.0112500i	−0.490226	−	0.871596i	$-0.663086\pi$
$401$	0.390199	−	0.225281i	0.0194856	−	0.0112500i	0.509711	+	0.860346i	$0.329752\pi$
$402$	0.283559	+	0.491138i	0.0141426	+	0.0244957i
$403$	20.4356	+	25.8361i	1.01797	+	1.28699i
$404$	−0.293274	+	0.507965i	−0.0145909	+	0.0252722i
$405$	2.26729	+	1.30902i	0.112663	+	0.0650458i
$406$	−6.26431	−	5.90355i	−0.310893	−	0.292988i
$407$	−11.0601	−	19.1567i	−0.548231	−	0.949563i
$408$	−15.5408	−	8.97246i	−0.769382	−	0.444203i
$409$	−29.8446	−	17.2308i	−1.47572	−	0.852008i	−0.476096	−	0.879393i	$-0.657949\pi$
$409$	−29.8446	−	17.2308i	−1.47572	−	0.852008i	−0.999625	+	0.0273852i	$0.991282\pi$
$410$	9.55793	+	5.51827i	0.472033	+	0.272528i
$411$	−1.66150	−	0.959268i	−0.0819558	−	0.0473172i
$412$	−3.10169	−	5.37228i	−0.152809	−	0.264673i
$413$	5.72308	−	1.71682i	0.281614	−	0.0844791i
$414$	−6.25505	−	3.61135i	−0.307419	−	0.177488i
$415$	−2.74917	+	4.76171i	−0.134952	+	0.233743i
$416$	−7.30658	+	18.4007i	−0.358235	+	0.902169i
$417$	11.0300	+	19.1046i	0.540143	+	0.935556i
$418$	−5.51685	+	3.18516i	−0.269838	+	0.155791i
$419$	0.195021	−	0.337787i	0.00952742	−	0.0165020i	−0.861222	−	0.508228i	$-0.830301\pi$
$419$	0.195021	−	0.337787i	0.00952742	−	0.0165020i	0.870750	+	0.491726i	$0.163634\pi$
$420$	1.85194	−	7.83321i	0.0903655	−	0.382222i
$421$			24.5494i			1.19646i	0.801323	+	0.598232i	$0.204130\pi$
$421$			24.5494i			1.19646i	−0.801323	+	0.598232i	$0.795870\pi$
$422$			3.30920i			0.161089i
$423$	1.53652	+	0.887113i	0.0747084	+	0.0431329i
$424$	−17.1603	+	9.90749i	−0.833377	+	0.481150i
$425$	−11.4949			−0.557587
$426$	3.42501	−	5.93229i	0.165942	−	0.287420i
$427$	22.4498	−	23.8217i	1.08642	−	1.15281i
$428$	20.6977			1.00046
$429$	9.08405	−	1.33217i	0.438582	−	0.0643176i
$430$	5.06216	+	8.76793i	0.244119	+	0.422827i
$431$		−	1.13549i		−	0.0546945i	−0.999626	−	0.0273473i	$-0.991294\pi$
$431$		−	1.13549i		−	0.0546945i	0.999626	−	0.0273473i	$-0.00870599\pi$
$432$	−0.162771	−	0.281927i	−0.00783132	−	0.0135642i
$433$	10.1233	+	17.5341i	0.486495	+	0.842634i	0.999879	−	0.0155250i	$-0.00494195\pi$
$433$	10.1233	+	17.5341i	0.486495	+	0.842634i	−0.513385	+	0.858159i	$0.671609\pi$
$434$	6.35782	+	21.1940i	0.305185	+	1.01735i
$435$	8.05822	−	4.65241i	0.386362	−	0.223066i
$436$		−	21.5939i		−	1.03416i
$437$	18.6743	−	10.7816i	0.893313	−	0.515755i
$438$	5.72106	−	9.90917i	0.273363	−	0.473478i
$439$	−13.9882	−	24.2283i	−0.667621	−	1.15635i	−0.978567	−	0.205926i	$-0.933979\pi$
$439$	−13.9882	−	24.2283i	−0.667621	−	1.15635i	0.310946	−	0.950428i	$-0.399354\pi$
$440$	16.7114	+	9.64835i	0.796686	+	0.459967i
$441$	−0.414724	−	6.98770i	−0.0197487	−	0.332748i
$442$	20.2453	−	2.96895i	0.962971	−	0.141219i
$443$	10.7712	−	18.6562i	0.511755	−	0.886385i	−0.488153	−	0.872758i	$-0.662329\pi$
$443$	10.7712	−	18.6562i	0.511755	−	0.886385i	0.999907	−	0.0136266i	$-0.00433761\pi$
$444$			10.0945i			0.479066i
$445$	29.8642			1.41570
$446$	−3.25557			−0.154156
$447$		−	14.9944i		−	0.709211i
$448$	−10.3023	+	10.9319i	−0.486739	+	0.516484i
$449$	−2.50177	+	1.44440i	−0.118066	+	0.0681652i	−0.557870	−	0.829928i	$-0.688381\pi$
$449$	−2.50177	+	1.44440i	−0.118066	+	0.0681652i	0.439804	+	0.898094i	$0.355048\pi$
$450$	−1.46988	−	0.848638i	−0.0692910	−	0.0400052i
$451$	5.86335	−	10.1556i	0.276095	−	0.478210i
$452$	8.40429			0.395305
$453$	7.81993	−	4.51484i	0.367413	−	0.212126i
$454$	7.13551			0.334886
$455$	10.5710	+	22.6270i	0.495574	+	1.06077i
$456$	7.91045			0.370441
$457$	−28.2917	+	16.3342i	−1.32343	+	0.764083i	−0.984274	−	0.176647i	$-0.943475\pi$
$457$	−28.2917	+	16.3342i	−1.32343	+	0.764083i	−0.339156	+	0.940730i	$0.610142\pi$
$458$	−15.0287			−0.702247
$459$	3.09980	−	5.36901i	0.144686	−	0.250604i
$460$	−20.7885	−	12.0022i	−0.969268	−	0.559607i
$461$	−32.7978	+	18.9358i	−1.52755	+	0.881930i	−0.528084	+	0.849192i	$0.677089\pi$
$461$	−32.7978	+	18.9358i	−1.52755	+	0.881930i	−0.999464	+	0.0327376i	$0.989577\pi$
$462$	6.00173	+	1.41894i	0.279226	+	0.0660150i
$463$			20.8936i			0.971006i	0.874235	+	0.485503i	$0.161364\pi$
$463$			20.8936i			0.971006i	−0.874235	+	0.485503i	$0.838636\pi$
$464$	−1.15701			−0.0537130
$465$	−23.9190			−1.10922
$466$		−	6.93620i		−	0.321313i
$467$	−10.8858	+	18.8548i	−0.503735	+	0.872494i	0.496256	+	0.868176i	$0.334708\pi$
$467$	−10.8858	+	18.8548i	−0.503735	+	0.872494i	−0.999991	+	0.00431766i	$0.998626\pi$
$468$	−3.89407	−	1.54626i	−0.180003	−	0.0714759i
$469$	1.19288	+	1.12418i	0.0550820	+	0.0519098i
$470$	−3.68235	−	2.12601i	−0.169854	−	0.0980654i
$471$	−0.0998014	−	0.172861i	−0.00459860	−	0.00796501i
$472$	3.26843	−	5.66109i	0.150442	−	0.260573i
$473$	9.31622	−	5.37872i	0.428360	−	0.247314i
$474$		−	1.13830i		−	0.0522838i
$475$	4.38830	−	2.53359i	0.201349	−	0.116249i
$476$	−18.5493	−	4.38545i	−0.850205	−	0.201007i
$477$	−3.42283	−	5.92852i	−0.156721	−	0.271448i
$478$	2.14502	+	3.71529i	0.0981110	+	0.169933i
$479$		−	10.8998i		−	0.498025i	−0.968500	−	0.249013i	$-0.919894\pi$
$479$		−	10.8998i		−	0.498025i	0.968500	−	0.249013i	$-0.0801061\pi$
$480$	−7.18791	−	12.4498i	−0.328082	−	0.568254i
$481$	−19.4304	−	24.5653i	−0.885950	−	1.12008i
$482$	9.81606			0.447109
$483$	−20.3156	−	4.80305i	−0.924391	−	0.218546i
$484$	−2.62379	+	4.54453i	−0.119263	+	0.206570i
$485$	−4.01871			−0.182480
$486$	0.792756	−	0.457698i	0.0359602	−	0.0207616i
$487$	5.32787	+	3.07605i	0.241429	+	0.139389i	0.615833	−	0.787877i	$-0.288820\pi$
$487$	5.32787	+	3.07605i	0.241429	+	0.139389i	−0.374404	+	0.927265i	$0.622153\pi$
$488$		−	35.8112i		−	1.62110i
$489$		−	7.05212i		−	0.318908i
$490$	0.993904	+	16.7464i	0.0449000	+	0.756523i
$491$	5.40015	−	9.35334i	0.243705	−	0.422110i	−0.718061	−	0.695980i	$-0.754970\pi$
$491$	5.40015	−	9.35334i	0.243705	−	0.422110i	0.961767	+	0.273869i	$0.0883036\pi$
$492$	−4.63450	+	2.67573i	−0.208939	+	0.120631i
$493$	−11.0171	−	19.0821i	−0.496183	−	0.859415i
$494$	−7.07445	+	5.59567i	−0.318295	+	0.251761i
$495$	−3.33331	+	5.77345i	−0.149821	+	0.259497i
$496$	2.57575	+	1.48711i	0.115655	+	0.0667733i
$497$	4.55521	−	19.2673i	0.204329	−	0.864257i
$498$	0.961247	+	1.66493i	0.0430745	+	0.0746072i
$499$	1.85936	+	1.07350i	0.0832362	+	0.0480565i	0.541040	−	0.840997i	$-0.318031\pi$
$499$	1.85936	+	1.07350i	0.0832362	+	0.0480565i	−0.457804	+	0.889053i	$0.651364\pi$
$500$	8.28840	+	4.78531i	0.370669	+	0.214006i
$501$	1.55981	+	0.900559i	0.0696874	+	0.0402340i
$502$	−9.40424	−	5.42954i	−0.419732	−	0.242332i
$503$	−3.07639	−	5.32846i	−0.137169	−	0.237584i	0.789255	−	0.614066i	$-0.210467\pi$
$503$	−3.07639	−	5.32846i	−0.137169	−	0.237584i	−0.926424	+	0.376482i	$0.877134\pi$
$504$	−5.57327	−	5.25230i	−0.248253	−	0.233956i
$505$	1.14442	+	0.660732i	0.0509261	+	0.0294022i
$506$	9.19599	−	15.9279i	0.408812	−	0.708083i
$507$	12.4526	−	3.73260i	0.553040	−	0.165770i
$508$	4.89302	+	8.47497i	0.217093	+	0.376016i
$509$	−3.97233	+	2.29343i	−0.176070	+	0.101654i	−0.585445	−	0.810712i	$-0.699080\pi$
$509$	−3.97233	+	2.29343i	−0.176070	+	0.101654i	0.409375	+	0.912366i	$0.365747\pi$
$510$	−7.42881	+	12.8671i	−0.328953	+	0.569764i
$511$	7.60893	−	32.1837i	0.336599	−	1.42372i
$512$			3.67215i			0.162288i
$513$			2.73290i			0.120660i
$514$	7.41034	+	4.27836i	0.326856	+	0.188710i
$515$	−12.1035	+	6.98795i	−0.533343	+	0.307926i
$516$	−4.90914			−0.216113
$517$	−2.25895	+	3.91262i	−0.0993487	+	0.172077i
$518$	−6.04510	−	20.1516i	−0.265607	−	0.885410i
$519$	11.9257			0.523479
$520$	25.3941	+	10.0835i	1.11361	+	0.442192i
$521$	10.7536	+	18.6258i	0.471123	+	0.816009i	0.999454	−	0.0330292i	$-0.0105154\pi$
$521$	10.7536	+	18.6258i	0.471123	+	0.816009i	−0.528331	+	0.849038i	$0.677182\pi$
$522$		−	3.25343i		−	0.142399i
$523$	6.01902	+	10.4252i	0.263193	+	0.455864i	0.967089	−	0.254439i	$-0.0818910\pi$
$523$	6.01902	+	10.4252i	0.263193	+	0.455864i	−0.703895	+	0.710304i	$0.748558\pi$
$524$	9.60793	+	16.6414i	0.419724	+	0.726984i
$525$	−4.77399	−	1.12868i	−0.208354	−	0.0492594i
$526$	−0.747902	+	0.431802i	−0.0326101	+	0.0188274i
$527$			56.6410i			2.46732i
$528$	0.717903	−	0.414482i	0.0312427	−	0.0180380i
$529$	−19.6280	+	33.9968i	−0.853393	+	1.47812i
$530$	8.20298	+	14.2080i	0.356315	+	0.617155i
$531$	1.95579	+	1.12918i	0.0848741	+	0.0490021i
$532$	8.04796	−	2.41424i	0.348923	−	0.104671i
$533$	6.12782	−	15.4321i	0.265425	−	0.668440i
$534$	5.22099	−	9.04302i	0.225934	−	0.391330i
$535$		−	46.6308i		−	2.01603i
$536$	1.79325			0.0774567
$537$	16.3400			0.705123
$538$			6.94150i			0.299269i
$539$	17.7936	−	1.05606i	0.766423	−	0.0454876i
$540$	2.63470	−	1.52115i	0.113380	−	0.0654597i
$541$	1.68945	+	0.975405i	0.0726352	+	0.0419360i	0.535878	−	0.844296i	$-0.319981\pi$
$541$	1.68945	+	0.975405i	0.0726352	+	0.0419360i	−0.463243	+	0.886232i	$0.653314\pi$
$542$	−9.42411	+	16.3230i	−0.404800	+	0.701135i
$543$	−16.7748			−0.719874
$544$	−29.4816	+	17.0212i	−1.26401	+	0.729777i
$545$	−48.6500			−2.08393
$546$	8.69964	+	0.754822i	0.372310	+	0.0323034i
$547$	4.27037			0.182588			0.0912940	−	0.995824i	$-0.470900\pi$
$547$	4.27037			0.182588			0.0912940	+	0.995824i	$0.470900\pi$
$548$	−1.93075	+	1.11472i	−0.0824774	+	0.0476183i
$549$	12.3720			0.528025
$550$	2.16098	−	3.74293i	0.0921445	−	0.159599i
$551$	8.41173	+	4.85652i	0.358352	+	0.206895i
$552$	−19.7788	+	11.4193i	−0.841840	+	0.486037i
$553$	−0.945323	−	3.15127i	−0.0401992	−	0.134006i
$554$		−	18.6975i		−	0.794382i
$555$	22.7425			0.965366
$556$	25.6349			1.08716
$557$		−	39.9834i		−	1.69415i	−0.531473	−	0.847075i	$-0.678361\pi$
$557$		−	39.9834i		−	1.69415i	0.531473	−	0.847075i	$-0.321639\pi$
$558$	−4.18163	+	7.24280i	−0.177023	+	0.306612i
$559$	11.9465	−	9.44932i	0.505284	−	0.399663i
$560$	1.64103	+	1.54652i	0.0693460	+	0.0653524i
$561$	13.6717	+	7.89337i	0.577220	+	0.333258i
$562$	4.97530	+	8.61748i	0.209871	+	0.363506i
$563$	−16.7574	+	29.0246i	−0.706239	+	1.22324i	0.260004	+	0.965608i	$0.416276\pi$
$563$	−16.7574	+	29.0246i	−0.706239	+	1.22324i	−0.966243	+	0.257634i	$0.917057\pi$
$564$	1.78552	−	1.03087i	0.0751839	−	0.0434074i
$565$		−	18.9345i		−	0.796579i
$566$	−3.02955	+	1.74911i	−0.127342	+	0.0735207i
$567$	1.81456	−	1.92545i	0.0762045	−	0.0808613i
$568$	−10.8300	−	18.7582i	−0.454418	−	0.787076i
$569$	19.4418	+	33.6742i	0.815043	+	1.41170i	0.909297	+	0.416147i	$0.136620\pi$
$569$	19.4418	+	33.6742i	0.815043	+	1.41170i	−0.0942547	+	0.995548i	$0.530047\pi$
$570$		−	6.54951i		−	0.274329i
$571$	11.3324	+	19.6282i	0.474245	+	0.821417i	0.999565	−	0.0294882i	$-0.00938774\pi$
$571$	11.3324	+	19.6282i	0.474245	+	0.821417i	−0.525320	+	0.850905i	$0.676054\pi$
$572$	3.93742	−	9.91589i	0.164632	−	0.414604i
$573$	−7.48391			−0.312645
$574$	7.64942	−	8.11688i	0.319281	−	0.338792i
$575$	−7.31482	+	12.6696i	−0.305049	+	0.528361i
$576$	−5.67758			−0.236566
$577$	−20.1472	+	11.6320i	−0.838740	+	0.484247i	−0.856836	−	0.515589i	$-0.827573\pi$
$577$	−20.1472	+	11.6320i	−0.838740	+	0.484247i	0.0180956	+	0.999836i	$0.494240\pi$
$578$	16.9928	+	9.81079i	0.706807	+	0.408075i
$579$			11.6862i			0.485663i
$580$		−	10.8127i		−	0.448972i
$581$	4.04379	+	3.81090i	0.167765	+	0.158103i
$582$	−0.702569	+	1.21689i	−0.0291224	+	0.0504416i
$583$	15.0965	−	8.71594i	0.625231	−	0.360977i
$584$	−18.0903	−	31.3333i	−0.748581	−	1.29658i
$585$	−3.48365	+	8.77314i	−0.144031	+	0.362725i
$586$	−8.26538	+	14.3161i	−0.341440	+	0.591391i
$587$	−11.6230	−	6.71057i	−0.479734	−	0.276975i	0.240571	−	0.970631i	$-0.422665\pi$
$587$	−11.6230	−	6.71057i	−0.479734	−	0.276975i	−0.720306	+	0.693657i	$0.755998\pi$
$588$	−7.27314	−	3.64267i	−0.299939	−	0.150221i
$589$	−12.4842	−	21.6232i	−0.514402	−	0.890970i
$590$	−4.68714	−	2.70612i	−0.192967	−	0.111409i
$591$	−0.388915	−	0.224540i	−0.0159978	−	0.00923636i
$592$	−2.44906	−	1.41396i	−0.100656	−	0.0581136i
$593$	7.76746	+	4.48455i	0.318972	+	0.184158i	0.650934	−	0.759134i	$-0.274377\pi$
$593$	7.76746	+	4.48455i	0.318972	+	0.184158i	−0.331963	+	0.943293i	$0.607711\pi$
$594$	1.16549	+	2.01868i	0.0478205	+	0.0828276i
$595$	−9.88022	+	41.7906i	−0.405049	+	1.71325i
$596$	−15.0898	−	8.71212i	−0.618104	−	0.356862i
$597$	−4.91166	+	8.50724i	−0.201021	+	0.348178i
$598$	9.61077	−	24.2035i	0.393014	−	0.989756i
$599$	−17.2505	−	29.8787i	−0.704836	−	1.22081i	−0.966751	−	0.255721i	$-0.917687\pi$
$599$	−17.2505	−	29.8787i	−0.704836	−	1.22081i	0.261914	−	0.965091i	$-0.415646\pi$
$600$	−4.64784	+	2.68343i	−0.189747	+	0.109551i
$601$	10.6843	−	18.5058i	0.435824	−	0.754869i	−0.561539	−	0.827450i	$-0.689791\pi$
$601$	10.6843	−	18.5058i	0.435824	−	0.754869i	0.997362	+	0.0725818i	$0.0231238\pi$
$602$	9.80003	−	2.93983i	0.399420	−	0.119819i
$603$			0.619532i			0.0252293i
$604$		−	10.4929i		−	0.426952i
$605$	10.2386	+	5.91126i	0.416259	+	0.240327i
$606$	0.400146	−	0.231024i	0.0162548	−	0.00938472i
$607$	−1.12616			−0.0457096			−0.0228548	−	0.999739i	$-0.507276\pi$
$607$	−1.12616			−0.0457096			−0.0228548	+	0.999739i	$0.507276\pi$
$608$	7.50324	−	12.9960i	0.304297	−	0.527057i
$609$	−2.70187	−	9.00678i	−0.109485	−	0.364973i
$610$	−29.6501			−1.20050
$611$	−2.36084	+	5.94549i	−0.0955095	+	0.240529i
$612$	−3.60212	−	6.23906i	−0.145607	−	0.252199i
$613$		−	28.9424i		−	1.16897i	−0.811404	−	0.584486i	$-0.801296\pi$
$613$		−	28.9424i		−	1.16897i	0.811404	−	0.584486i	$-0.198704\pi$
$614$	4.06798	+	7.04595i	0.164170	+	0.284351i
$615$	6.02829	+	10.4413i	0.243084	+	0.421034i
$616$	13.3745	−	14.1918i	0.538875	−	0.571806i
$617$	−3.55424	+	2.05204i	−0.143088	+	0.0826120i	−0.569835	−	0.821759i	$-0.692993\pi$
$617$	−3.55424	+	2.05204i	−0.143088	+	0.0826120i	0.426747	+	0.904371i	$0.359660\pi$
$618$			4.88666i			0.196570i
$619$	−9.06150	+	5.23166i	−0.364212	+	0.210278i	−0.670927	−	0.741523i	$-0.734104\pi$
$619$	−9.06150	+	5.23166i	−0.364212	+	0.210278i	0.306715	+	0.951802i	$0.400770\pi$
$620$	−13.8975	+	24.0712i	−0.558139	+	0.966725i
$621$	−3.94513	−	6.83316i	−0.158312	−	0.274205i
$622$	13.0731	+	7.54774i	0.524182	+	0.302637i
$623$	6.94384	−	29.3706i	0.278199	−	1.17671i
$624$	0.920592	−	0.728160i	0.0368532	−	0.0291497i
$625$	15.4164	−	26.7020i	0.616657	−	1.06808i
$626$		−	20.1820i		−	0.806633i
$627$	−6.95908			−0.277919
$628$	−0.231948			−0.00925574
$629$		−	53.8550i		−	2.14734i
$630$	−4.34868	+	4.61443i	−0.173256	+	0.183843i
$631$	24.3336	−	14.0490i	0.968704	−	0.559281i	0.0698630	−	0.997557i	$-0.477744\pi$
$631$	24.3336	−	14.0490i	0.968704	−	0.559281i	0.898841	+	0.438275i	$0.144410\pi$
$632$	−3.11714	−	1.79968i	−0.123993	−	0.0715874i
$633$	−1.80752	+	3.13072i	−0.0718426	+	0.124435i
$634$	−20.8802			−0.829259
$635$	19.0937	−	11.0237i	0.757710	−	0.437464i
$636$	−7.95501			−0.315437
$637$	24.7109	−	5.13513i	0.979083	−	0.203461i
$638$	8.28456			0.327989
$639$	6.48057	−	3.74156i	0.256367	−	0.148014i
$640$	−15.1451			−0.598661
$641$	14.3138	−	24.7923i	0.565362	−	0.979235i	−0.431654	−	0.902039i	$-0.642070\pi$
$641$	14.3138	−	24.7923i	0.565362	−	0.979235i	0.997016	−	0.0771962i	$-0.0245968\pi$
$642$	−14.1201	−	8.15222i	−0.557274	−	0.321742i
$643$	−7.81711	+	4.51321i	−0.308277	+	0.177984i	−0.646155	−	0.763206i	$-0.723624\pi$
$643$	−7.81711	+	4.51321i	−0.308277	+	0.177984i	0.337878	+	0.941190i	$0.390291\pi$
$644$	−16.6375	+	17.6542i	−0.655609	+	0.695673i
$645$			11.0600i			0.435489i
$646$	−15.5094			−0.610211
$647$	−26.2048			−1.03022			−0.515109	−	0.857125i	$-0.672249\pi$
$647$	−26.2048			−1.03022			−0.515109	+	0.857125i	$0.672249\pi$
$648$		−	2.89453i		−	0.113708i
$649$	−2.87535	+	4.98025i	−0.112867	+	0.195492i
$650$	2.25845	−	5.68762i	0.0885837	−	0.223087i
$651$	−5.56151	+	23.5237i	−0.217973	+	0.921966i
$652$	−7.09700	−	4.09745i	−0.277940	−	0.160469i
$653$	−22.7395	−	39.3859i	−0.889864	−	1.54129i	−0.840035	−	0.542532i	$-0.817466\pi$
$653$	−22.7395	−	39.3859i	−0.889864	−	1.54129i	−0.0498291	−	0.998758i	$-0.515868\pi$
$654$	−8.50521	+	14.7315i	−0.332580	+	0.576045i
$655$	37.4923	−	21.6462i	1.46495	−	0.845787i
$656$		−	1.49918i		−	0.0585332i
$657$	10.8250	−	6.24982i	0.422324	−	0.243829i
$658$	−2.94707	+	3.12716i	−0.114889	+	0.121910i
$659$	10.1806	+	17.6334i	0.396581	+	0.686899i	0.993302	−	0.115550i	$-0.0368632\pi$
$659$	10.1806	+	17.6334i	0.396581	+	0.686899i	−0.596720	+	0.802449i	$0.703530\pi$
$660$	3.87347	+	6.70904i	0.150774	+	0.261149i
$661$			40.1037i			1.55985i	0.625871	+	0.779926i	$0.284744\pi$
$661$			40.1037i			1.55985i	−0.625871	+	0.779926i	$0.715256\pi$
$662$	14.6535	+	25.3807i	0.569526	+	0.986447i
$663$	20.7751	+	8.24939i	0.806837	+	0.320380i
$664$	6.07902			0.235912
$665$	−5.43916	−	18.1317i	−0.210922	−	0.703116i
$666$	3.97595	−	6.88655i	0.154065	−	0.266848i
$667$	−28.0429			−1.08582
$668$	1.81258	−	1.04649i	0.0701309	−	0.0404901i
$669$	−3.07998	−	1.77823i	−0.119079	−	0.0687503i
$670$		−	1.48474i		−	0.0573604i
$671$			31.5043i			1.21621i
$672$	−13.9153	+	4.17435i	−0.536796	+	0.161029i
$673$	10.2385	−	17.7336i	0.394666	−	0.683581i	−0.598393	−	0.801203i	$-0.704194\pi$
$673$	10.2385	−	17.7336i	0.394666	−	0.683581i	0.993058	+	0.117622i	$0.0375270\pi$
$674$	−3.96155	+	2.28720i	−0.152593	+	0.0880998i
$675$	−0.927071	−	1.60573i	−0.0356830	−	0.0618047i
$676$	3.47893	−	14.7006i	0.133805	−	0.565408i
$677$	18.6224	−	32.2549i	0.715717	−	1.23966i	−0.246966	−	0.969024i	$-0.579433\pi$
$677$	18.6224	−	32.2549i	0.715717	−	1.23966i	0.962682	−	0.270634i	$-0.0872332\pi$
$678$	−5.73345	−	3.31021i	−0.220192	−	0.127128i
$679$	−0.934407	+	3.95229i	−0.0358593	+	0.151675i
$680$	23.4903	+	40.6864i	0.900811	+	1.56025i
$681$	6.75066	+	3.89750i	0.258686	+	0.149352i
$682$	−18.4431	−	10.6482i	−0.706225	−	0.407739i
$683$	5.13090	+	2.96232i	0.196328	+	0.113350i	0.594942	−	0.803769i	$-0.297175\pi$
$683$	5.13090	+	2.96232i	0.196328	+	0.113350i	−0.398613	+	0.917119i	$0.630508\pi$
$684$	2.75029	+	1.58788i	0.105160	+	0.0607141i
$685$	2.51140	+	4.34988i	0.0959558	+	0.166200i
$686$	16.7007	+	2.91629i	0.637634	+	0.111344i
$687$	−14.2182	−	8.20887i	−0.542457	−	0.313188i
$688$	0.687634	−	1.19102i	0.0262158	−	0.0454071i
$689$	19.3587	−	15.3121i	0.737508	−	0.583346i
$690$	9.45467	+	16.3760i	0.359933	+	0.623423i
$691$	−2.64755	+	1.52856i	−0.100718	+	0.0581493i	−0.549513	−	0.835485i	$-0.685187\pi$
$691$	−2.64755	+	1.52856i	−0.100718	+	0.0581493i	0.448795	+	0.893635i	$0.351853\pi$
$692$	6.92912	−	12.0016i	0.263405	−	0.456232i
$693$	4.90299	+	4.62062i	0.186249	+	0.175523i
$694$		−	31.4366i		−	1.19332i
$695$		−	57.7542i		−	2.19074i
$696$	−8.90923	−	5.14375i	−0.337704	−	0.194973i
$697$	24.7253	−	14.2752i	0.936538	−	0.540711i
$698$	−9.00128			−0.340703
$699$	3.78863	−	6.56210i	0.143299	−	0.248201i
$700$	−3.90967	+	4.14859i	−0.147772	+	0.156802i
$701$	−2.81064			−0.106156			−0.0530782	−	0.998590i	$-0.516903\pi$
$701$	−2.81064			−0.106156			−0.0530782	+	0.998590i	$0.516903\pi$
$702$	2.04752	+	2.58863i	0.0772788	+	0.0977015i
$703$	11.8701	+	20.5596i	0.447690	+	0.775422i
$704$		−	14.4574i		−	0.544885i
$705$	−2.32250	−	4.02269i	−0.0874704	−	0.151503i
$706$	−7.02227	−	12.1629i	−0.264287	−	0.457758i
$707$	0.915906	−	0.971877i	0.0344462	−	0.0365512i
$708$	2.27273	−	1.31216i	0.0854143	−	0.0493139i
$709$			38.4283i			1.44320i	0.692308	+	0.721602i	$0.256594\pi$
$709$			38.4283i			1.44320i	−0.692308	+	0.721602i	$0.743406\pi$
$710$	−15.5310	+	8.96681i	−0.582867	+	0.336518i
$711$	0.621752	−	1.07691i	0.0233175	−	0.0403872i
$712$	−16.5090	−	28.5945i	−0.618702	−	1.07162i
$713$	62.4293	+	36.0436i	2.33799	+	1.34984i
$714$	10.9271	+	10.2978i	0.408937	+	0.385386i
$715$	−22.3400	−	8.87081i	−0.835470	−	0.331749i
$716$	9.49395	−	16.4440i	0.354805	−	0.614541i
$717$			4.68654i			0.175022i
$718$	26.6050			0.992888
$719$	−26.5885			−0.991584			−0.495792	−	0.868441i	$-0.665122\pi$
$719$	−26.5885			−0.991584			−0.495792	+	0.868441i	$0.665122\pi$
$720$			0.852282i			0.0317627i
$721$	4.05822	+	13.5282i	0.151136	+	0.503818i
$722$	−9.14150	+	5.27785i	−0.340211	+	0.196421i
$723$	9.28664	+	5.36164i	0.345374	+	0.199402i
$724$	−9.74655	+	16.8815i	−0.362228	+	0.627397i
$725$	−6.58984			−0.244740
$726$	3.57992	−	2.06687i	0.132863	−	0.0767087i
$727$	−26.5203			−0.983583			−0.491792	−	0.870713i	$-0.663658\pi$
$727$	−26.5203			−0.983583			−0.491792	+	0.870713i	$0.663658\pi$
$728$	15.8214	−	22.6298i	0.586379	−	0.838717i
$729$	1.00000			0.0370370
$730$	−25.9426	+	14.9780i	−0.960179	+	0.554360i
$731$	26.1905			0.968692
$732$	7.18845	−	12.4508i	0.265693	−	0.460193i
$733$	22.0215	+	12.7141i	0.813384	+	0.469607i	0.848130	−	0.529789i	$-0.177729\pi$
$733$	22.0215	+	12.7141i	0.813384	+	0.469607i	−0.0347458	+	0.999396i	$0.511062\pi$
$734$	−14.5091	+	8.37684i	−0.535541	+	0.309195i
$735$	−8.20675	+	16.3860i	−0.302711	+	0.604408i
$736$			43.3258i			1.59701i
$737$	−1.57758			−0.0581110
$738$	4.21557			0.155177
$739$		−	29.2795i		−	1.07706i	−0.842606	−	0.538531i	$-0.818979\pi$
$739$		−	29.2795i		−	1.07706i	0.842606	−	0.538531i	$-0.181021\pi$
$740$	13.2140	−	22.8873i	0.485755	−	0.841352i
$741$	−9.74932	+	1.42973i	−0.358150	+	0.0525223i
$742$	15.8805	−	4.76384i	0.582990	−	0.174886i
$743$	11.9142	+	6.87868i	0.437090	+	0.252354i	0.702363	−	0.711819i	$-0.252129\pi$
$743$	11.9142	+	6.87868i	0.437090	+	0.252354i	−0.265272	+	0.964174i	$0.585462\pi$
$744$	13.2225	+	22.9021i	0.484762	+	0.839632i
$745$	−19.6280	+	33.9967i	−0.719114	+	1.24554i
$746$	−10.1992	+	5.88850i	−0.373419	+	0.215593i
$747$			2.10018i			0.0768414i
$748$	15.8872	−	9.17248i	0.580894	−	0.335379i
$749$	−45.8601	−	10.8423i	−1.67569	−	0.396170i
$750$	−3.76960	−	6.52913i	−0.137646	−	0.238410i
$751$	−15.7344	−	27.2528i	−0.574156	−	0.994468i	−0.996133	−	0.0878612i	$-0.971997\pi$
$751$	−15.7344	−	27.2528i	−0.574156	−	0.994468i	0.421976	−	0.906607i	$-0.361337\pi$
$752$			0.577585i			0.0210623i
$753$	−5.93135	−	10.2734i	−0.216151	−	0.374384i
$754$	11.6063	−	1.70204i	0.422675	−	0.0619848i
$755$	−23.6401			−0.860351
$756$	−0.883400	−	2.94485i	−0.0321289	−	0.107103i
$757$	−20.2956	+	35.1531i	−0.737657	+	1.27766i	0.215890	+	0.976418i	$0.430735\pi$
$757$	−20.2956	+	35.1531i	−0.737657	+	1.27766i	−0.953548	+	0.301243i	$0.902599\pi$
$758$	−24.1082			−0.875651
$759$	17.4000	−	10.0459i	0.631581	−	0.364644i
$760$	−17.9353	−	10.3549i	−0.650581	−	0.375613i
$761$			40.5022i			1.46821i	0.679039	+	0.734103i	$0.262397\pi$
$761$			40.5022i			1.46821i	−0.679039	+	0.734103i	$0.737603\pi$
$762$		−	7.70889i		−	0.279264i
$763$	−11.3118	+	47.8459i	−0.409515	+	1.73214i
$764$	−4.34833	+	7.53154i	−0.157317	+	0.272481i
$765$	−14.0563	+	8.11541i	−0.508207	+	0.293413i
$766$	−6.59291	−	11.4193i	−0.238211	−	0.412594i
$767$	−3.00504	+	7.56781i	−0.108506	+	0.273258i
$768$	−8.32531	+	14.4199i	−0.300414	+	0.520332i
$769$	25.2026	+	14.5507i	0.908828	+	0.524712i	0.880054	−	0.474874i	$-0.157506\pi$
$769$	25.2026	+	14.5507i	0.908828	+	0.524712i	0.0287743	+	0.999586i	$0.490840\pi$
$770$	−11.7502	−	11.0735i	−0.423449	−	0.399062i
$771$	4.67378	+	8.09523i	0.168322	+	0.291542i
$772$	11.7606	+	6.78998i	0.423273	+	0.244377i
$773$	8.96149	+	5.17392i	0.322322	+	0.186093i	0.652427	−	0.757851i	$-0.273751\pi$
$773$	8.96149	+	5.17392i	0.322322	+	0.186093i	−0.330105	+	0.943944i	$0.607084\pi$
$774$	3.34904	+	1.93357i	0.120379	+	0.0695007i
$775$	14.6704	+	8.46993i	0.526975	+	0.304249i
$776$	2.22156	+	3.84785i	0.0797493	+	0.138130i
$777$	5.28796	−	22.3666i	0.189704	−	0.802398i
$778$	−5.24632	−	3.02897i	−0.188090	−	0.108594i
$779$	−6.29275	+	10.8994i	−0.225461	+	0.390510i
$780$	6.80489	+	8.60324i	0.243654	+	0.308045i
$781$	9.52754	+	16.5022i	0.340922	+	0.590495i
$782$	38.7788	−	22.3890i	1.38673	−	0.800627i
$783$	1.77706	−	3.07796i	0.0635069	−	0.109997i
$784$	1.90252	−	1.25432i	0.0679472	−	0.0447970i
$785$			0.522568i			0.0186513i
$786$		−	15.1372i		−	0.539924i
$787$	25.2027	+	14.5508i	0.898381	+	0.518680i	0.876674	−	0.481084i	$-0.159757\pi$
$787$	25.2027	+	14.5508i	0.898381	+	0.518680i	0.0217062	+	0.999764i	$0.493090\pi$
$788$	−0.451939	+	0.260927i	−0.0160997	+	0.00929514i
$789$	−0.943420			−0.0335866
$790$	−1.49006	+	2.58086i	−0.0530139	+	0.0918228i
$791$	−18.6215	−	4.40253i	−0.662105	−	0.156536i
$792$	7.37066			0.261905
$793$	6.47248	+	44.1359i	0.229844	+	1.56731i
$794$	−10.3603	−	17.9446i	−0.367674	−	0.636830i
$795$			17.9222i			0.635637i
$796$	5.70759	+	9.88583i	0.202300	+	0.350394i
$797$	−14.9812	−	25.9482i	−0.530661	−	0.919131i	−0.999360	−	0.0357733i	$-0.988611\pi$
$797$	−14.9812	−	25.9482i	−0.530661	−	0.919131i	0.468699	−	0.883358i	$-0.344723\pi$
$798$	−6.44126	−	1.52285i	−0.228018	−	0.0539085i
$799$	−9.52584	+	5.49975i	−0.337000	+	0.194567i
$800$			10.1812i			0.359960i
$801$	9.87880	−	5.70353i	0.349050	−	0.201524i
$802$	−0.206222	+	0.357186i	−0.00728194	+	0.0126127i
$803$	15.9146	+	27.5649i	0.561614	+	0.972745i
$804$	0.623475	+	0.359963i	0.0219883	+	0.0126949i
$805$	39.7741	+	37.4834i	1.40185	+	1.32112i
$806$	−28.0256	−	11.1284i	−0.987159	−	0.391982i
$807$	−3.79153	+	6.56712i	−0.133468	+	0.231174i
$808$		−	1.46102i		−	0.0513985i
$809$	−16.0767			−0.565227			−0.282614	−	0.959234i	$-0.591201\pi$
$809$	−16.0767			−0.565227			−0.282614	+	0.959234i	$0.591201\pi$
$810$	−2.39655			−0.0842060
$811$			41.5793i			1.46005i	0.683423	+	0.730023i	$0.260491\pi$
$811$			41.5793i			1.46005i	−0.683423	+	0.730023i	$0.739509\pi$
$812$	−10.6340	−	2.51410i	−0.373179	−	0.0882276i
$813$	−17.8317	+	10.2951i	−0.625384	+	0.361066i
$814$	17.5360	+	10.1244i	0.614636	+	0.354860i
$815$	−9.23137	+	15.9892i	−0.323361	+	0.560077i
$816$	2.01823			0.0706521
$817$	−9.99849	+	5.77263i	−0.349803	+	0.201959i
$818$	31.5460			1.10298
$819$	7.81814	+	5.46595i	0.273188	+	0.190996i
$820$	14.0103			0.489262
$821$	−3.52804	+	2.03691i	−0.123129	+	0.0710888i	−0.560300	−	0.828290i	$-0.689314\pi$
$821$	−3.52804	+	2.03691i	−0.123129	+	0.0710888i	0.437170	+	0.899379i	$0.355981\pi$
$822$	1.75622			0.0612552
$823$	−21.3186	+	36.9248i	−0.743118	+	1.28712i	0.207951	+	0.978139i	$0.433321\pi$
$823$	−21.3186	+	36.9248i	−0.743118	+	1.28712i	−0.951069	+	0.308979i	$0.900013\pi$
$824$	13.3817	+	7.72593i	0.466174	+	0.269146i
$825$	4.08886	−	2.36070i	0.142356	−	0.0821892i
$826$	−3.75122	+	3.98046i	−0.130522	+	0.138498i
$827$			21.7244i			0.755431i	0.925922	+	0.377716i	$0.123290\pi$
$827$			21.7244i			0.755431i	−0.925922	+	0.377716i	$0.876710\pi$
$828$	−9.16886			−0.318640
$829$	0.922945			0.0320552			0.0160276	−	0.999872i	$-0.494898\pi$
$829$	0.922945			0.0320552			0.0160276	+	0.999872i	$0.494898\pi$
$830$		−	5.03317i		−	0.174704i
$831$	10.2128	−	17.6891i	0.354278	−	0.613628i
$832$	−2.97025	−	20.2542i	−0.102975	−	0.702187i
$833$	38.8026	+	19.4338i	1.34443	+	0.673342i
$834$	−17.4883	−	10.0969i	−0.605569	−	0.349626i
$835$	−2.35770	−	4.08366i	−0.0815916	−	0.141321i
$836$	−4.04340	+	7.00337i	−0.139844	+	0.242217i
$837$	−7.91220	+	4.56811i	−0.273486	+	0.157897i
$838$			0.357044i			0.0123339i
$839$	10.4845	−	6.05325i	0.361966	−	0.208981i	−0.307977	−	0.951394i	$-0.599652\pi$
$839$	10.4845	−	6.05325i	0.361966	−	0.208981i	0.669943	+	0.742413i	$0.266319\pi$
$840$	5.76085	+	19.2040i	0.198768	+	0.662602i
$841$	8.18413	+	14.1753i	0.282211	+	0.488804i
$842$	−11.2362	−	19.4617i	−0.387225	−	0.670694i
$843$			10.8703i			0.374392i
$844$	2.10043	+	3.63805i	0.0722998	+	0.125227i
$845$	−33.1198	−	7.83786i	−1.13935	−	0.269630i
$846$	−1.62412			−0.0558384
$847$	8.19419	−	8.69493i	0.281556	−	0.298761i
$848$	1.11428	−	1.92998i	0.0382644	−	0.0662758i
$849$	−3.82154			−0.131155
$850$	9.11269	−	5.26121i	0.312563	−	0.180458i
$851$	−59.3586	−	34.2707i	−2.03479	−	1.17478i
$852$		−	8.69575i		−	0.297911i
$853$		−	25.9127i		−	0.887233i	−0.896217	−	0.443616i	$-0.853695\pi$
$853$		−	25.9127i		−	0.887233i	0.896217	−	0.443616i	$-0.146305\pi$
$854$	−6.89407	+	29.1601i	−0.235910	+	0.997837i
$855$	3.57742	−	6.19627i	0.122345	−	0.211908i
$856$	−44.6483	+	25.7777i	−1.52605	+	0.881064i
$857$	−7.12117	−	12.3342i	−0.243255	−	0.421329i	0.718385	−	0.695646i	$-0.244882\pi$
$857$	−7.12117	−	12.3342i	−0.243255	−	0.421329i	−0.961639	+	0.274317i	$0.911548\pi$
$858$	−6.59171	+	5.21384i	−0.225037	+	0.177998i
$859$	−7.79426	+	13.5001i	−0.265937	+	0.460616i	−0.967809	−	0.251687i	$-0.919015\pi$
$859$	−7.79426	+	13.5001i	−0.265937	+	0.460616i	0.701872	+	0.712303i	$0.252348\pi$
$860$	11.1304	+	6.42616i	0.379545	+	0.219130i
$861$	11.6704	−	3.50090i	0.397726	−	0.119310i
$862$	0.519711	+	0.900165i	0.0177014	+	0.0306597i
$863$	−18.3943	−	10.6200i	−0.626150	−	0.361508i	0.153109	−	0.988209i	$-0.451071\pi$
$863$	−18.3943	−	10.6200i	−0.626150	−	0.361508i	−0.779260	+	0.626701i	$0.784405\pi$
$864$	−4.75540	−	2.74553i	−0.161782	−	0.0934048i
$865$	−27.0390	−	15.6110i	−0.919353	−	0.530789i
$866$	−16.0506	−	9.26683i	−0.545422	−	0.314900i
$867$	10.7175	+	18.5633i	0.363986	+	0.630443i
$868$	20.4420	+	19.2648i	0.693848	+	0.653888i
$869$	2.74225	+	1.58324i	0.0930244	+	0.0537077i
$870$	−4.25880	+	7.37646i	−0.144387	+	0.250085i
$871$	−2.21011	+	0.324111i	−0.0748869	+	0.0109821i
$872$	26.8939	+	46.5816i	0.910742	+	1.57745i
$873$	−1.32935	+	0.767503i	−0.0449918	+	0.0259760i
$874$	−9.86945	+	17.0944i	−0.333839	+	0.578227i
$875$	−15.8580	−	14.9447i	−0.536098	−	0.505224i
$876$		−	14.5252i		−	0.490761i
$877$		−	30.0882i		−	1.01601i	−0.861355	−	0.508004i	$-0.830384\pi$
$877$		−	30.0882i		−	1.01601i	0.861355	−	0.508004i	$-0.169616\pi$
$878$	22.1785	+	12.8048i	0.748488	+	0.432140i
$879$	−15.6392	+	9.02929i	−0.527497	+	0.304550i
$880$	−2.17026			−0.0731594
$881$	22.2785	−	38.5876i	0.750583	−	1.30005i	−0.196957	−	0.980412i	$-0.563106\pi$
$881$	22.2785	−	38.5876i	0.750583	−	1.30005i	0.947540	−	0.319636i	$-0.103561\pi$
$882$	3.52703	+	5.34973i	0.118761	+	0.180135i
$883$	−1.96438			−0.0661066			−0.0330533	−	0.999454i	$-0.510523\pi$
$883$	−1.96438			−0.0661066			−0.0330533	+	0.999454i	$0.510523\pi$
$884$	20.3727	−	16.1142i	0.685209	−	0.541979i
$885$	−2.95623	−	5.12034i	−0.0993726	−	0.172118i
$886$			19.7198i			0.662500i
$887$	−2.30867	−	3.99873i	−0.0775175	−	0.134264i	0.824661	−	0.565628i	$-0.191366\pi$
$887$	−2.30867	−	3.99873i	−0.0775175	−	0.134264i	−0.902178	+	0.431363i	$0.858033\pi$
$888$	−12.5722	−	21.7756i	−0.421894	−	0.730742i
$889$	−6.40199	−	21.3413i	−0.214716	−	0.715764i
$890$	−23.6750	+	13.6688i	−0.793588	+	0.458178i
$891$			2.54641i			0.0853080i
$892$	−3.57909	+	2.06639i	−0.119837	+	0.0691879i
$893$	2.42439	−	4.19916i	0.0811290	−	0.140520i
$894$	6.86291	+	11.8869i	0.229530	+	0.397558i
$895$	−37.0475	−	21.3894i	−1.23836	−	0.714969i
$896$	−3.52144	+	14.8947i	−0.117643	+	0.497598i
$897$	22.3127	−	17.6486i	0.744998	−	0.589270i
$898$	1.32219	−	2.29011i	0.0441222	−	0.0764219i
$899$			32.4712i			1.08298i
$900$	−2.15461			−0.0718202
$901$	42.4404			1.41390
$902$			10.7346i			0.357423i
$903$	10.8772	+	2.57162i	0.361972	+	0.0855781i
$904$	−18.1295	+	10.4671i	−0.602977	+	0.348129i
$905$	38.0332	+	21.9585i	1.26427	+	0.729925i
$906$	−4.13287	+	7.15834i	−0.137305	+	0.237820i
$907$	−20.7647			−0.689480			−0.344740	−	0.938698i	$-0.612033\pi$
$907$	−20.7647			−0.689480			−0.344740	+	0.938698i	$0.612033\pi$
$908$	7.84461	−	4.52909i	0.260332	−	0.150303i
$909$	0.504753			0.0167416
$910$	−18.7365	−	13.0994i	−0.621110	−	0.434241i
$911$	−49.6547			−1.64513			−0.822567	−	0.568669i	$-0.807459\pi$
$911$	−49.6547			−1.64513			−0.822567	+	0.568669i	$0.807459\pi$
$912$	−0.770478	+	0.444836i	−0.0255131	+	0.0147300i
$913$	−5.34791			−0.176990
$914$	14.9523	−	25.8981i	0.494578	−	0.856634i
$915$	−28.0510	−	16.1952i	−0.927336	−	0.535398i
$916$	−16.5222	+	9.53911i	−0.545910	+	0.315181i
$917$	−12.5709	−	41.9057i	−0.415129	−	1.38385i
$918$			5.67509i			0.187306i
$919$	55.1462			1.81911			0.909553	−	0.415588i	$-0.136424\pi$
$919$	55.1462			1.81911			0.909553	+	0.415588i	$0.136424\pi$
$920$	59.7923			1.97129
$921$			8.88791i			0.292867i
$922$	17.3338	−	30.0230i	0.570858	−	0.988756i
$923$	16.7379	+	21.1613i	0.550936	+	0.696534i
$924$	7.49879	−	2.24950i	0.246692	−	0.0740031i
$925$	−13.9488	−	8.05332i	−0.458632	−	0.264792i
$926$	−9.56295	−	16.5635i	−0.314258	−	0.544311i
$927$	−2.66915	+	4.62310i	−0.0876664	+	0.151843i
$928$	−16.9012	+	9.75793i	−0.554810	+	0.320320i
$929$			4.35353i			0.142835i	0.997447	+	0.0714174i	$0.0227522\pi$
$929$			4.35353i			0.142835i	−0.997447	+	0.0714174i	$0.977248\pi$
$930$	18.9620	−	10.9477i	0.621787	−	0.358989i
$931$	−19.0967	+	1.13340i	−0.625868	+	0.0371456i
$932$	−4.40258	−	7.62549i	−0.144211	−	0.249781i
$933$	8.24533	+	14.2813i	0.269940	+	0.467550i
$934$		−	19.9296i		−	0.652118i
$935$	−20.6652	−	35.7931i	−0.675823	−	1.17056i
$936$	10.3259	−	1.51429i	0.337514	−	0.0494960i
$937$	0.712633			0.0232807			0.0116404	−	0.999932i	$-0.496295\pi$
$937$	0.712633			0.0232807			0.0116404	+	0.999932i	$0.496295\pi$
$938$	−1.46020	−	0.345222i	−0.0476771	−	0.0112719i
$939$	11.0236	−	19.0935i	0.359742	−	0.623092i
$940$	−5.39772			−0.176054
$941$	10.1930	−	5.88493i	0.332282	−	0.191843i	−0.324572	−	0.945861i	$-0.605220\pi$
$941$	10.1930	−	5.88493i	0.332282	−	0.191843i	0.656854	+	0.754018i	$0.271887\pi$
$942$	0.158236	+	0.0913578i	0.00515562	+	0.00297660i
$943$		−	36.3361i		−	1.18327i
$944$			0.735188i			0.0239283i
$945$	−6.63460	+	1.99026i	−0.215823	+	0.0647431i
$946$	−4.92366	+	8.52803i	−0.160082	+	0.277270i
$947$	−26.6022	+	15.3588i	−0.864455	+	0.499093i	−0.865502	−	0.500906i	$-0.833000\pi$
$947$	−26.6022	+	15.3588i	−0.864455	+	0.499093i	0.00104667	+	0.999999i	$0.499667\pi$
$948$	−0.722507	−	1.25142i	−0.0234659	−	0.0406442i
$949$	27.9587	+	35.3474i	0.907579	+	1.14743i
$950$	−2.31924	+	4.01704i	−0.0752460	+	0.130330i
$951$	−19.7541	−	11.4050i	−0.640569	−	0.369833i
$952$	45.4757	−	13.6419i	1.47388	−	0.442136i
$953$	−13.0794	−	22.6542i	−0.423684	−	0.733843i	0.572612	−	0.819826i	$-0.305930\pi$
$953$	−13.0794	−	22.6542i	−0.423684	−	0.733843i	−0.996297	+	0.0859835i	$0.972597\pi$
$954$	5.42695	+	3.13325i	0.175704	+	0.101443i
$955$	16.9682	+	9.79659i	0.549078	+	0.317010i
$956$	4.71637	+	2.72300i	0.152538	+	0.0880680i
$957$	7.83774	+	4.52512i	0.253358	+	0.146276i
$958$	4.98883	+	8.64090i	0.161182	+	0.279175i
$959$	4.86192	−	1.45849i	0.157000	−	0.0470970i
$960$	12.8727	+	7.43207i	0.415465	+	0.239869i
$961$	26.2353	−	45.4409i	0.846300	−	1.46583i
$962$	26.6471	+	10.5811i	0.859136	+	0.341147i
$963$	−8.90567	−	15.4251i	−0.286981	−	0.497066i
$964$	10.7915	−	6.23050i	0.347572	−	0.200671i
$965$	15.2975	−	26.4961i	0.492444	−	0.852938i
$966$	18.3037	−	5.49076i	0.588911	−	0.176662i
$967$		−	2.99020i		−	0.0961582i	−0.998844	−	0.0480791i	$-0.984690\pi$
$967$		−	2.99020i		−	0.0961582i	0.998844	−	0.0480791i	$-0.0153100\pi$
$968$		−	13.0711i		−	0.420121i
$969$	−14.6730	−	8.47143i	−0.471363	−	0.272142i
$970$	3.18586	−	1.83936i	0.102292	−	0.0590582i
$971$	−18.5506			−0.595318			−0.297659	−	0.954672i	$-0.596206\pi$
$971$	−18.5506			−0.595318			−0.297659	+	0.954672i	$0.596206\pi$
$972$	0.581025	−	1.00636i	0.0186364	−	0.0322792i
$973$	−56.7997	−	13.4287i	−1.82091	−	0.430504i
$974$	−5.63160			−0.180448
$975$	5.24329	−	4.14728i	0.167920	−	0.132819i
$976$	2.01380	+	3.48801i	0.0644603	+	0.111649i
$977$			3.82828i			0.122477i	0.998123	+	0.0612387i	$0.0195051\pi$
$977$			3.82828i			0.122477i	−0.998123	+	0.0612387i	$0.980495\pi$
$978$	3.22774	+	5.59061i	0.103212	+	0.178768i
$979$	14.5235	+	25.1555i	0.464174	+	0.803973i
$980$	11.7220	+	17.7797i	0.374446	+	0.567951i
$981$	−16.0930	+	9.29129i	−0.513809	+	0.296648i
$982$			9.88656i			0.315493i
$983$	27.0572	−	15.6215i	0.862992	−	0.498248i	−0.00202132	−	0.999998i	$-0.500643\pi$
$983$	27.0572	−	15.6215i	0.862992	−	0.498248i	0.865013	+	0.501749i	$0.167310\pi$
$984$	6.66493	−	11.5440i	0.212470	−	0.368009i
$985$	0.587856	+	1.01820i	0.0187307	+	0.0324425i
$986$	17.4677	+	10.0850i	0.556284	+	0.321171i
$987$	−4.49621	+	1.34878i	−0.143116	+	0.0429322i
$988$	−4.22577	+	10.6421i	−0.134440	+	0.338570i
$989$	16.6664	−	28.8670i	0.529960	−	0.917918i
$990$		−	6.10259i		−	0.193953i
$991$	5.93593			0.188561			0.0942805	−	0.995546i	$-0.469945\pi$
$991$	5.93593			0.188561			0.0942805	+	0.995546i	$0.469945\pi$
$992$	50.1675			1.59282
$993$			32.0157i			1.01599i
$994$	5.20744	+	17.3592i	0.165170	+	0.550600i
$995$	22.2723	−	12.8589i	0.706079	−	0.407655i
$996$	2.11354	+	1.22025i	0.0669702	+	0.0386652i
$997$	3.92320	−	6.79518i	0.124249	−	0.215206i	−0.797190	−	0.603728i	$-0.793681\pi$
$997$	3.92320	−	6.79518i	0.124249	−	0.215206i	0.921439	+	0.388523i	$0.127014\pi$
$998$	−1.96536			−0.0622123
$999$	7.52303	−	4.34342i	0.238018	−	0.137420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.d.121.4	yes	20
3.2	odd	2		819.2.do.g.667.7		20
7.4	even	3		273.2.t.d.4.4	✓	20
13.10	even	6		273.2.t.d.205.7	yes	20
21.11	odd	6		819.2.bm.g.550.7		20
39.23	odd	6		819.2.bm.g.478.4		20
91.88	even	6	inner	273.2.bl.d.88.4	yes	20
273.179	odd	6		819.2.do.g.361.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.4	✓	20	7.4	even	3
273.2.t.d.205.7	yes	20	13.10	even	6
273.2.bl.d.88.4	yes	20	91.88	even	6	inner
273.2.bl.d.121.4	yes	20	1.1	even	1	trivial
819.2.bm.g.478.4		20	39.23	odd	6
819.2.bm.g.550.7		20	21.11	odd	6
819.2.do.g.361.7		20	273.179	odd	6
819.2.do.g.667.7		20	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)

\(f(q)\)	\(=\)	\(q+(-0.792756 + 0.457698i) q^{2} -1.00000 q^{3} +(-0.581025 + 1.00636i) q^{4} +(2.26729 + 1.30902i) q^{5} +(0.792756 - 0.457698i) q^{6} +(1.81456 - 1.92545i) q^{7} -2.89453i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.792756 + 0.457698i) q^{2} -1.00000 q^{3} +(-0.581025 + 1.00636i) q^{4} +(2.26729 + 1.30902i) q^{5} +(0.792756 - 0.457698i) q^{6} +(1.81456 - 1.92545i) q^{7} -2.89453i q^{8} +1.00000 q^{9} -2.39655 q^{10} +2.54641i q^{11} +(0.581025 - 1.00636i) q^{12} +(0.523154 + 3.56740i) q^{13} +(-0.557231 + 2.35694i) q^{14} +(-2.26729 - 1.30902i) q^{15} +(0.162771 + 0.281927i) q^{16} +(-3.09980 + 5.36901i) q^{17} +(-0.792756 + 0.457698i) q^{18} -2.73290i q^{19} +(-2.63470 + 1.52115i) q^{20} +(-1.81456 + 1.92545i) q^{21} +(-1.16549 - 2.01868i) q^{22} +(3.94513 + 6.83316i) q^{23} +2.89453i q^{24} +(0.927071 + 1.60573i) q^{25} +(-2.04752 - 2.58863i) q^{26} -1.00000 q^{27} +(0.883400 + 2.94485i) q^{28} +(-1.77706 + 3.07796i) q^{29} +2.39655 q^{30} +(7.91220 - 4.56811i) q^{31} +(4.75540 + 2.74553i) q^{32} -2.54641i q^{33} -5.67509i q^{34} +(6.63460 - 1.99026i) q^{35} +(-0.581025 + 1.00636i) q^{36} +(-7.52303 + 4.34342i) q^{37} +(1.25084 + 2.16652i) q^{38} +(-0.523154 - 3.56740i) q^{39} +(3.78900 - 6.56274i) q^{40} +(-3.98821 - 2.30259i) q^{41} +(0.557231 - 2.35694i) q^{42} +(-2.11228 - 3.65857i) q^{43} +(-2.56262 - 1.47953i) q^{44} +(2.26729 + 1.30902i) q^{45} +(-6.25505 - 3.61135i) q^{46} +(1.53652 + 0.887113i) q^{47} +(-0.162771 - 0.281927i) q^{48} +(-0.414724 - 6.98770i) q^{49} +(-1.46988 - 0.848638i) q^{50} +(3.09980 - 5.36901i) q^{51} +(-3.89407 - 1.54626i) q^{52} +(-3.42283 - 5.92852i) q^{53} +(0.792756 - 0.457698i) q^{54} +(-3.33331 + 5.77345i) q^{55} +(-5.57327 - 5.25230i) q^{56} +2.73290i q^{57} -3.25343i q^{58} +(1.95579 + 1.12918i) q^{59} +(2.63470 - 1.52115i) q^{60} +12.3720 q^{61} +(-4.18163 + 7.24280i) q^{62} +(1.81456 - 1.92545i) q^{63} -5.67758 q^{64} +(-3.48365 + 8.77314i) q^{65} +(1.16549 + 2.01868i) q^{66} +0.619532i q^{67} +(-3.60212 - 6.23906i) q^{68} +(-3.94513 - 6.83316i) q^{69} +(-4.34868 + 4.61443i) q^{70} +(6.48057 - 3.74156i) q^{71} -2.89453i q^{72} +(10.8250 - 6.24982i) q^{73} +(3.97595 - 6.88655i) q^{74} +(-0.927071 - 1.60573i) q^{75} +(2.75029 + 1.58788i) q^{76} +(4.90299 + 4.62062i) q^{77} +(2.04752 + 2.58863i) q^{78} +(0.621752 - 1.07691i) q^{79} +0.852282i q^{80} +1.00000 q^{81} +4.21557 q^{82} +2.10018i q^{83} +(-0.883400 - 2.94485i) q^{84} +(-14.0563 + 8.11541i) q^{85} +(3.34904 + 1.93357i) q^{86} +(1.77706 - 3.07796i) q^{87} +7.37066 q^{88} +(9.87880 - 5.70353i) q^{89} -2.39655 q^{90} +(7.81814 + 5.46595i) q^{91} -9.16886 q^{92} +(-7.91220 + 4.56811i) q^{93} -1.62412 q^{94} +(3.57742 - 6.19627i) q^{95} +(-4.75540 - 2.74553i) q^{96} +(-1.32935 + 0.767503i) q^{97} +(3.52703 + 5.34973i) q^{98} +2.54641i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

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