LMFDB - Embedded newform 273.2.bj.d.142.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 310x^{10} + 807x^{8} - 1196x^{6} + 1273x^{4} - 688x^{2} + 256 $ x^16 - 11x^14 + 85x^12 - 310x^10 + 807x^8 - 1196x^6 + 1273x^4 - 688*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.3
Root			$0.725066 - 0.418617i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.d.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.558156 - 0.322252i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.792308 - 1.37232i) q^{4} +(3.70788 + 2.14075i) q^{5} -0.644503i q^{6} +(-2.12926 + 1.57043i) q^{7} +2.31030i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.558156 - 0.322252i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.792308 - 1.37232i) q^{4} +(3.70788 + 2.14075i) q^{5} -0.644503i q^{6} +(-2.12926 + 1.57043i) q^{7} +2.31030i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.37972 - 2.38974i) q^{10} +(0.166910 - 0.0963656i) q^{11} +(0.792308 - 1.37232i) q^{12} +(3.06884 + 1.89268i) q^{13} +(1.69453 - 0.190385i) q^{14} +4.28149i q^{15} +(-0.840118 + 1.45513i) q^{16} +(-2.82155 - 4.88706i) q^{17} +(0.558156 - 0.322252i) q^{18} +(2.43796 + 1.40756i) q^{19} -6.78452i q^{20} +(-2.42466 - 1.05878i) q^{21} -0.124216 q^{22} +(-0.551746 + 0.955651i) q^{23} +(-2.00078 + 1.15515i) q^{24} +(6.66560 + 11.5452i) q^{25} +(-1.10297 - 2.04535i) q^{26} -1.00000 q^{27} +(3.84215 + 1.67776i) q^{28} +8.94213 q^{29} +(1.37972 - 2.38974i) q^{30} +(1.79544 - 1.03660i) q^{31} +(4.93939 - 2.85176i) q^{32} +(0.166910 + 0.0963656i) q^{33} +3.63699i q^{34} +(-11.2569 + 1.26474i) q^{35} +1.58462 q^{36} +(-6.55470 - 3.78436i) q^{37} +(-0.907174 - 1.57127i) q^{38} +(-0.104688 + 3.60403i) q^{39} +(-4.94576 + 8.56631i) q^{40} -5.28245i q^{41} +(1.01215 + 1.37232i) q^{42} -6.04501 q^{43} +(-0.264488 - 0.152702i) q^{44} +(-3.70788 + 2.14075i) q^{45} +(0.615920 - 0.355602i) q^{46} +(-0.924615 - 0.533827i) q^{47} -1.68024 q^{48} +(2.06752 - 6.68770i) q^{49} -8.59200i q^{50} +(2.82155 - 4.88706i) q^{51} +(0.165890 - 5.71100i) q^{52} +(-4.27915 - 7.41170i) q^{53} +(0.558156 + 0.322252i) q^{54} +0.825178 q^{55} +(-3.62815 - 4.91923i) q^{56} +2.81511i q^{57} +(-4.99111 - 2.88162i) q^{58} +(-4.23340 + 2.44416i) q^{59} +(5.87557 - 3.39226i) q^{60} +(4.32696 - 7.49451i) q^{61} -1.33618 q^{62} +(-0.295398 - 2.62921i) q^{63} -0.315459 q^{64} +(7.32715 + 13.5874i) q^{65} +(-0.0621080 - 0.107574i) q^{66} +(-13.1704 + 7.60391i) q^{67} +(-4.47106 + 7.74411i) q^{68} -1.10349 q^{69} +(6.69070 + 2.92165i) q^{70} -8.59200i q^{71} +(-2.00078 - 1.15515i) q^{72} +(-1.01295 + 0.584827i) q^{73} +(2.43903 + 4.22453i) q^{74} +(-6.66560 + 11.5452i) q^{75} -4.46087i q^{76} +(-0.204060 + 0.467308i) q^{77} +(1.21984 - 1.97788i) q^{78} +(1.92110 - 3.32745i) q^{79} +(-6.23012 + 3.59696i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.70228 + 2.94843i) q^{82} -9.35386i q^{83} +(0.468092 + 4.16629i) q^{84} -24.1609i q^{85} +(3.37406 + 1.94802i) q^{86} +(4.47106 + 7.74411i) q^{87} +(0.222633 + 0.385612i) q^{88} +(-0.0247871 - 0.0143109i) q^{89} +2.75944 q^{90} +(-9.50668 + 0.789375i) q^{91} +1.74861 q^{92} +(1.79544 + 1.03660i) q^{93} +(0.344053 + 0.595918i) q^{94} +(6.02644 + 10.4381i) q^{95} +(4.93939 + 2.85176i) q^{96} +6.43675i q^{97} +(-3.30912 + 3.06652i) q^{98} +0.192731i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.558156	−	0.322252i	−0.394676	−	0.227866i	0.289508	−	0.957176i	$-0.406508\pi$
$2$	−0.558156	−	0.322252i	−0.394676	−	0.227866i	−0.684184	+	0.729309i	$0.739842\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.792308	−	1.37232i	−0.396154	−	0.686159i
$5$	3.70788	+	2.14075i	1.65822	+	0.957371i	0.973538	+	0.228526i	$0.0733905\pi$
$5$	3.70788	+	2.14075i	1.65822	+	0.957371i	0.684678	+	0.728846i	$0.259943\pi$
$6$		−	0.644503i		−	0.263117i
$7$	−2.12926	+	1.57043i	−0.804786	+	0.593565i
$7$	−2.12926	+	1.57043i	−0.804786	+	0.593565i
$8$			2.31030i			0.816813i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.37972	−	2.38974i	−0.436305	−	0.755703i
$11$	0.166910	−	0.0963656i	0.0503253	−	0.0290553i	−0.474626	−	0.880187i	$-0.657417\pi$
$11$	0.166910	−	0.0963656i	0.0503253	−	0.0290553i	0.524952	+	0.851132i	$0.324083\pi$
$12$	0.792308	−	1.37232i	0.228720	−	0.396154i
$13$	3.06884	+	1.89268i	0.851143	+	0.524934i
$13$	3.06884	+	1.89268i	0.851143	+	0.524934i
$14$	1.69453	−	0.190385i	0.452883	−	0.0508825i
$15$			4.28149i			1.10548i
$16$	−0.840118	+	1.45513i	−0.210030	+	0.363782i
$17$	−2.82155	−	4.88706i	−0.684325	−	1.18529i	−0.973648	−	0.228055i	$-0.926763\pi$
$17$	−2.82155	−	4.88706i	−0.684325	−	1.18529i	0.289323	−	0.957232i	$-0.406570\pi$
$18$	0.558156	−	0.322252i	0.131559	−	0.0759554i
$19$	2.43796	+	1.40756i	0.559306	+	0.322915i	0.752867	−	0.658173i	$-0.228670\pi$
$19$	2.43796	+	1.40756i	0.559306	+	0.322915i	−0.193561	+	0.981088i	$0.562004\pi$
$20$		−	6.78452i		−	1.51707i
$21$	−2.42466	−	1.05878i	−0.529104	−	0.231045i
$22$	−0.124216			−0.0264829
$23$	−0.551746	+	0.955651i	−0.115047	+	0.199267i	−0.917798	−	0.397046i	$-0.870035\pi$
$23$	−0.551746	+	0.955651i	−0.115047	+	0.199267i	0.802752	+	0.596314i	$0.203368\pi$
$24$	−2.00078	+	1.15515i	−0.408407	+	0.235794i
$25$	6.66560	+	11.5452i	1.33312	+	2.30903i
$26$	−1.10297	−	2.04535i	−0.216311	−	0.401126i
$27$	−1.00000			−0.192450
$28$	3.84215	+	1.67776i	0.726099	+	0.317067i
$29$	8.94213			1.66051			0.830256	−	0.557382i	$-0.188194\pi$
$29$	8.94213			1.66051			0.830256	+	0.557382i	$0.188194\pi$
$30$	1.37972	−	2.38974i	0.251901	−	0.436305i
$31$	1.79544	−	1.03660i	0.322471	−	0.186179i	−0.330022	−	0.943973i	$-0.607056\pi$
$31$	1.79544	−	1.03660i	0.322471	−	0.186179i	0.652493	+	0.757794i	$0.273723\pi$
$32$	4.93939	−	2.85176i	0.873168	−	0.504124i
$33$	0.166910	+	0.0963656i	0.0290553	+	0.0167751i
$34$			3.63699i			0.623739i
$35$	−11.2569	+	1.26474i	−1.90277	+	0.213781i
$36$	1.58462			0.264103
$37$	−6.55470	−	3.78436i	−1.07759	−	0.622145i	−0.147342	−	0.989086i	$-0.547072\pi$
$37$	−6.55470	−	3.78436i	−1.07759	−	0.622145i	−0.930244	+	0.366941i	$0.880405\pi$
$38$	−0.907174	−	1.57127i	−0.147163	−	0.254894i
$39$	−0.104688	+	3.60403i	−0.0167635	+	0.577107i
$40$	−4.94576	+	8.56631i	−0.781994	+	1.35445i
$41$		−	5.28245i		−	0.824980i	−0.910962	−	0.412490i	$-0.864659\pi$
$41$		−	5.28245i		−	0.824980i	0.910962	−	0.412490i	$-0.135341\pi$
$42$	1.01215	+	1.37232i	0.156177	+	0.211753i
$43$	−6.04501			−0.921856			−0.460928	−	0.887438i	$-0.652483\pi$
$43$	−6.04501			−0.921856			−0.460928	+	0.887438i	$0.652483\pi$
$44$	−0.264488	−	0.152702i	−0.0398731	−	0.0230208i
$45$	−3.70788	+	2.14075i	−0.552739	+	0.319124i
$46$	0.615920	−	0.355602i	0.0908125	−	0.0524306i
$47$	−0.924615	−	0.533827i	−0.134869	−	0.0778667i	0.431047	−	0.902329i	$-0.358144\pi$
$47$	−0.924615	−	0.533827i	−0.134869	−	0.0778667i	−0.565916	+	0.824463i	$0.691478\pi$
$48$	−1.68024			−0.242521
$49$	2.06752	−	6.68770i	0.295360	−	0.955386i
$50$		−	8.59200i		−	1.21509i
$51$	2.82155	−	4.88706i	0.395095	−	0.684325i
$52$	0.165890	−	5.71100i	0.0230048	−	0.791974i
$53$	−4.27915	−	7.41170i	−0.587786	−	1.01808i	−0.994522	−	0.104530i	$-0.966666\pi$
$53$	−4.27915	−	7.41170i	−0.587786	−	1.01808i	0.406735	−	0.913546i	$-0.366667\pi$
$54$	0.558156	+	0.322252i	0.0759554	+	0.0438529i
$55$	0.825178			0.111267
$56$	−3.62815	−	4.91923i	−0.484832	−	0.657360i
$57$			2.81511i			0.372871i
$58$	−4.99111	−	2.88162i	−0.655364	−	0.378375i
$59$	−4.23340	+	2.44416i	−0.551142	+	0.318202i	−0.749582	−	0.661911i	$-0.769746\pi$
$59$	−4.23340	+	2.44416i	−0.551142	+	0.318202i	0.198441	+	0.980113i	$0.436412\pi$
$60$	5.87557	−	3.39226i	0.758533	−	0.437939i
$61$	4.32696	−	7.49451i	0.554010	−	0.959574i	−0.443969	−	0.896042i	$-0.646430\pi$
$61$	4.32696	−	7.49451i	0.554010	−	0.959574i	0.997980	−	0.0635323i	$-0.0202366\pi$
$62$	−1.33618			−0.169695
$63$	−0.295398	−	2.62921i	−0.0372166	−	0.331249i
$64$	−0.315459			−0.0394323
$65$	7.32715	+	13.5874i	0.908821	+	1.68531i
$66$	−0.0621080	−	0.107574i	−0.00764496	−	0.0132415i
$67$	−13.1704	+	7.60391i	−1.60902	+	0.928966i	−0.619425	+	0.785056i	$0.712634\pi$
$67$	−13.1704	+	7.60391i	−1.60902	+	0.928966i	−0.989591	+	0.143910i	$0.954032\pi$
$68$	−4.47106	+	7.74411i	−0.542196	+	0.939111i
$69$	−1.10349			−0.132845
$70$	6.69070	+	2.92165i	0.799692	+	0.349203i
$71$		−	8.59200i		−	1.01968i	−0.860268	−	0.509842i	$-0.829704\pi$
$71$		−	8.59200i		−	1.01968i	0.860268	−	0.509842i	$-0.170296\pi$
$72$	−2.00078	−	1.15515i	−0.235794	−	0.136136i
$73$	−1.01295	+	0.584827i	−0.118557	+	0.0684489i	−0.558106	−	0.829770i	$-0.688472\pi$
$73$	−1.01295	+	0.584827i	−0.118557	+	0.0684489i	0.439549	+	0.898219i	$0.355138\pi$
$74$	2.43903	+	4.22453i	0.283532	+	0.491091i
$75$	−6.66560	+	11.5452i	−0.769677	+	1.33312i
$76$		−	4.46087i		−	0.511697i
$77$	−0.204060	+	0.467308i	−0.0232548	+	0.0532547i
$78$	1.21984	−	1.97788i	0.138119	−	0.223950i
$79$	1.92110	−	3.32745i	0.216141	−	0.374367i	−0.737484	−	0.675365i	$-0.763986\pi$
$79$	1.92110	−	3.32745i	0.216141	−	0.374367i	0.953625	+	0.300998i	$0.0973196\pi$
$80$	−6.23012	+	3.59696i	−0.696549	+	0.402153i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.70228	+	2.94843i	−0.187985	+	0.325600i
$83$		−	9.35386i		−	1.02672i	−0.858173	−	0.513360i	$-0.828401\pi$
$83$		−	9.35386i		−	1.02672i	0.858173	−	0.513360i	$-0.171599\pi$
$84$	0.468092	+	4.16629i	0.0510730	+	0.454579i
$85$		−	24.1609i		−	2.62061i
$86$	3.37406	+	1.94802i	0.363835	+	0.210060i
$87$	4.47106	+	7.74411i	0.479348	+	0.830256i
$88$	0.222633	+	0.385612i	0.0237328	+	0.0411064i
$89$	−0.0247871	−	0.0143109i	−0.00262743	−	0.00151695i	0.498686	−	0.866783i	$-0.333816\pi$
$89$	−0.0247871	−	0.0143109i	−0.00262743	−	0.00151695i	−0.501313	+	0.865266i	$0.667150\pi$
$90$	2.75944			0.290870
$91$	−9.50668	+	0.789375i	−0.996570	+	0.0827490i
$92$	1.74861			0.182305
$93$	1.79544	+	1.03660i	0.186179	+	0.107490i
$94$	0.344053	+	0.595918i	0.0354864	+	0.0614642i
$95$	6.02644	+	10.4381i	0.618300	+	1.07093i
$96$	4.93939	+	2.85176i	0.504124	+	0.291056i
$97$			6.43675i			0.653553i	0.945102	+	0.326776i	$0.105962\pi$
$97$			6.43675i			0.653553i	−0.945102	+	0.326776i	$0.894038\pi$
$98$	−3.30912	+	3.06652i	−0.334272	+	0.309765i
$99$			0.192731i			0.0193702i
$100$	10.5624	−	18.2946i	1.05624	−	1.82946i
$101$	2.40764	+	4.17016i	0.239569	+	0.414946i	0.960591	−	0.277967i	$-0.0896605\pi$
$101$	2.40764	+	4.17016i	0.239569	+	0.414946i	−0.721022	+	0.692913i	$0.756327\pi$
$102$	−3.14973	+	1.81850i	−0.311869	+	0.180058i
$103$	−5.60349	+	9.70553i	−0.552128	+	0.956314i	0.445992	+	0.895037i	$0.352851\pi$
$103$	−5.60349	+	9.70553i	−0.552128	+	0.956314i	−0.998121	+	0.0612776i	$0.980482\pi$
$104$	−4.37265	+	7.08993i	−0.428773	+	0.695225i
$105$	−6.72377	−	9.11643i	−0.656173	−	0.889672i
$106$			5.51585i			0.535747i
$107$	5.59676	−	9.69387i	0.541059	−	0.937142i	−0.457784	−	0.889063i	$-0.651357\pi$
$107$	5.59676	−	9.69387i	0.541059	−	0.937142i	0.998844	−	0.0480788i	$-0.0153099\pi$
$108$	0.792308	+	1.37232i	0.0762398	+	0.132051i
$109$	−2.26353	+	1.30685i	−0.216807	+	0.125174i	−0.604471	−	0.796627i	$-0.706615\pi$
$109$	−2.26353	+	1.30685i	−0.216807	+	0.125174i	0.387664	+	0.921801i	$0.373282\pi$
$110$	−0.460578	−	0.265915i	−0.0439144	−	0.0253540i
$111$		−	7.56871i		−	0.718391i
$112$	−0.496338	−	4.41769i	−0.0468995	−	0.417433i
$113$	13.1304			1.23521			0.617603	−	0.786490i	$-0.288104\pi$
$113$	13.1304			1.23521			0.617603	+	0.786490i	$0.288104\pi$
$114$	0.907174	−	1.57127i	0.0849647	−	0.147163i
$115$	−4.09162	+	2.36230i	−0.381545	+	0.220285i
$116$	−7.08492	−	12.2714i	−0.657818	−	1.13937i
$117$	−3.17353	+	1.71135i	−0.293393	+	0.158215i
$118$	3.15053			0.290030
$119$	13.6826	+	5.97481i	1.25428	+	0.547710i
$120$	−9.89152			−0.902968
$121$	−5.48143	+	9.49411i	−0.498312	+	0.863101i
$122$	−4.83024	+	2.78874i	−0.437309	+	0.252481i
$123$	4.57473	−	2.64122i	0.412490	−	0.238151i
$124$	−2.84509	−	1.64261i	−0.255496	−	0.147511i
$125$			35.6700i			3.19042i
$126$	−0.682389	+	1.56270i	−0.0607920	+	0.139217i
$127$	9.61678			0.853351			0.426675	−	0.904405i	$-0.359685\pi$
$127$	9.61678			0.853351			0.426675	+	0.904405i	$0.359685\pi$
$128$	−9.70270	−	5.60185i	−0.857605	−	0.495139i
$129$	−3.02251	−	5.23514i	−0.266117	−	0.460928i
$130$	0.288880	−	9.94510i	0.0253364	−	0.872243i
$131$	6.16560	−	10.6791i	0.538691	−	0.933040i	−0.460284	−	0.887772i	$-0.652252\pi$
$131$	6.16560	−	10.6791i	0.538691	−	0.933040i	0.998975	−	0.0452682i	$-0.0144143\pi$
$132$		−	0.305405i		−	0.0265821i
$133$	−7.40152	+	0.831577i	−0.641793	+	0.0721069i
$134$	9.80149			0.846720
$135$	−3.70788	−	2.14075i	−0.319124	−	0.184246i
$136$	11.2906	−	6.51861i	0.968158	−	0.558966i
$137$	−0.959501	+	0.553968i	−0.0819757	+	0.0473287i	−0.540428	−	0.841391i	$-0.681737\pi$
$137$	−0.959501	+	0.553968i	−0.0819757	+	0.0473287i	0.458452	+	0.888719i	$0.348404\pi$
$138$	0.615920	+	0.355602i	0.0524306	+	0.0302708i
$139$	−7.79362			−0.661047			−0.330523	−	0.943798i	$-0.607225\pi$
$139$	−7.79362			−0.661047			−0.330523	+	0.943798i	$0.607225\pi$
$140$	10.6546	+	14.4460i	0.900477	+	1.22091i
$141$		−	1.06765i		−	0.0899127i
$142$	−2.76879	+	4.79568i	−0.232351	+	0.402445i
$143$	0.694609	+	0.0201766i	0.0580861	+	0.00168725i
$144$	−0.840118	−	1.45513i	−0.0700099	−	0.121261i
$145$	33.1564	+	19.1428i	2.75349	+	1.58973i
$146$	0.753846			0.0623888
$147$	6.82548	−	1.55332i	0.562956	−	0.128116i
$148$			11.9935i			0.985860i
$149$	1.84923	+	1.06765i	0.151495	+	0.0874656i	0.573831	−	0.818974i	$-0.305457\pi$
$149$	1.84923	+	1.06765i	0.151495	+	0.0874656i	−0.422336	+	0.906439i	$0.638790\pi$
$150$	7.44089	−	4.29600i	0.607546	−	0.350767i
$151$	13.1244	−	7.57739i	1.06805	−	0.616639i	0.140402	−	0.990095i	$-0.455160\pi$
$151$	13.1244	−	7.57739i	1.06805	−	0.616639i	0.927648	+	0.373455i	$0.121827\pi$
$152$	−3.25187	+	5.63241i	−0.263762	+	0.456848i
$153$	5.64309			0.456217
$154$	0.264488	−	0.195072i	0.0213131	−	0.0157193i
$155$	8.87639			0.712969
$156$	5.02882	−	2.71184i	0.402628	−	0.217121i
$157$	0.317611	+	0.550118i	0.0253481	+	0.0439042i	0.878421	−	0.477887i	$-0.158597\pi$
$157$	0.317611	+	0.550118i	0.0253481	+	0.0439042i	−0.853073	+	0.521791i	$0.825264\pi$
$158$	−2.14455	+	1.23816i	−0.170611	+	0.0985025i
$159$	4.27915	−	7.41170i	0.339359	−	0.587786i
$160$	24.4196			1.93054
$161$	−0.325969	−	2.90131i	−0.0256899	−	0.228655i
$162$			0.644503i			0.0506370i
$163$	6.87669	+	3.97026i	0.538624	+	0.310975i	0.744521	−	0.667599i	$-0.232678\pi$
$163$	6.87669	+	3.97026i	0.538624	+	0.310975i	−0.205897	+	0.978574i	$0.566011\pi$
$164$	−7.24919	+	4.18532i	−0.566067	+	0.326819i
$165$	0.412589	+	0.714625i	0.0321200	+	0.0556335i
$166$	−3.01430	+	5.22092i	−0.233955	+	0.405222i
$167$		−	15.0574i		−	1.16517i	−0.812768	−	0.582587i	$-0.802040\pi$
$167$		−	15.0574i		−	1.16517i	0.812768	−	0.582587i	$-0.197960\pi$
$168$	2.44610	−	5.60169i	0.188721	−	0.432179i
$169$	5.83554	+	11.6166i	0.448888	+	0.893588i
$170$	−7.78588	+	13.4855i	−0.597150	+	1.03429i
$171$	−2.43796	+	1.40756i	−0.186435	+	0.107638i
$172$	4.78951	+	8.29568i	0.365197	+	0.632540i
$173$	−1.11927	+	1.93863i	−0.0850964	+	0.147391i	−0.905432	−	0.424491i	$-0.860453\pi$
$173$	−1.11927	+	1.93863i	−0.0850964	+	0.147391i	0.820336	+	0.571882i	$0.193786\pi$
$174$		−	5.76323i		−	0.436910i
$175$	−32.3236	−	14.1148i	−2.44344	−	1.06698i
$176$			0.323834i			0.0244099i
$177$	−4.23340	−	2.44416i	−0.318202	−	0.183714i
$178$	0.00922340	+	0.0159754i	0.000691323	+	0.00119741i
$179$	1.11487	+	1.93101i	0.0833290	+	0.144330i	0.904678	−	0.426096i	$-0.140111\pi$
$179$	1.11487	+	1.93101i	0.0833290	+	0.144330i	−0.821349	+	0.570426i	$0.806778\pi$
$180$	5.87557	+	3.39226i	0.437939	+	0.252844i
$181$	−14.9871			−1.11399			−0.556993	−	0.830517i	$-0.688045\pi$
$181$	−14.9871			−1.11399			−0.556993	+	0.830517i	$0.688045\pi$
$182$	5.56059	+	2.62295i	0.412178	+	0.194426i
$183$	8.65392			0.639716
$184$	−2.20784	−	1.27470i	−0.162764	−	0.0939718i
$185$	−16.2027	−	28.0639i	−1.19125	−	2.06330i
$186$	−0.668092	−	1.15717i	−0.0489869	−	0.0848477i
$187$	−0.941889	−	0.543800i	−0.0688777	−	0.0397666i
$188$			1.69182i			0.123389i
$189$	2.12926	−	1.57043i	0.154881	−	0.114232i
$190$		−	7.76812i		−	0.563559i
$191$	−3.74087	+	6.47937i	−0.270680	+	0.468831i	−0.969036	−	0.246919i	$-0.920582\pi$
$191$	−3.74087	+	6.47937i	−0.270680	+	0.468831i	0.698357	+	0.715750i	$0.253915\pi$
$192$	−0.157729	−	0.273195i	−0.0113831	−	0.0197162i
$193$	15.6952	−	9.06162i	1.12976	−	0.652270i	0.185889	−	0.982571i	$-0.440484\pi$
$193$	15.6952	−	9.06162i	1.12976	−	0.652270i	0.943876	+	0.330301i	$0.107150\pi$
$194$	2.07425	−	3.59271i	0.148923	−	0.257942i
$195$	−8.10349	+	13.1392i	−0.580303	+	0.940919i
$196$	−10.8158	+	2.46142i	−0.772554	+	0.175816i
$197$			6.02266i			0.429097i	0.976713	+	0.214549i	$0.0688280\pi$
$197$			6.02266i			0.429097i	−0.976713	+	0.214549i	$0.931172\pi$
$198$	0.0621080	−	0.107574i	0.00441382	−	0.00764496i
$199$	2.67876	+	4.63974i	0.189892	+	0.328903i	0.945214	−	0.326451i	$-0.105853\pi$
$199$	2.67876	+	4.63974i	0.189892	+	0.328903i	−0.755322	+	0.655354i	$0.772520\pi$
$200$	−26.6727	+	15.3995i	−1.88605	+	1.08891i
$201$	−13.1704	−	7.60391i	−0.928966	−	0.536339i
$202$		−	3.10347i		−	0.218359i
$203$	−19.0401	+	14.0430i	−1.33636	+	0.985622i
$204$	−8.94213			−0.626074
$205$	11.3084	−	19.5867i	0.789812	−	1.36799i
$206$	6.25525	−	3.61147i	0.435824	−	0.251623i
$207$	−0.551746	−	0.955651i	−0.0383490	−	0.0664224i
$208$	−5.33228	+	2.87548i	−0.369727	+	0.199379i
$209$	0.542560			0.0375296
$210$	0.815131	+	7.25514i	0.0562494	+	0.500652i
$211$	−16.4455			−1.13216			−0.566078	−	0.824352i	$-0.691540\pi$
$211$	−16.4455			−1.13216			−0.566078	+	0.824352i	$0.691540\pi$
$212$	−6.78081	+	11.7447i	−0.465708	+	0.806629i
$213$	7.44089	−	4.29600i	0.509842	−	0.294357i
$214$	−6.24773	+	3.60713i	−0.427086	+	0.246578i
$215$	−22.4142	−	12.9409i	−1.52864	−	0.882559i
$216$		−	2.31030i		−	0.157196i
$217$	−2.19507	+	5.02680i	−0.149011	+	0.341242i
$218$	1.68454			0.114092
$219$	−1.01295	−	0.584827i	−0.0684489	−	0.0395190i
$220$	−0.653795	−	1.13241i	−0.0440788	−	0.0763468i
$221$	0.590764	−	20.3379i	0.0397391	−	1.36807i
$222$	−2.43903	+	4.22453i	−0.163697	+	0.283532i
$223$		−	8.28660i		−	0.554912i	−0.960738	−	0.277456i	$-0.910509\pi$
$223$		−	8.28660i		−	0.554912i	0.960738	−	0.277456i	$-0.0894912\pi$
$224$	−6.03878	+	13.8291i	−0.403483	+	0.923994i
$225$	−13.3312			−0.888747
$226$	−7.32882	−	4.23130i	−0.487506	−	0.281462i
$227$	0.256975	−	0.148365i	0.0170560	−	0.00984730i	−0.491448	−	0.870907i	$-0.663532\pi$
$227$	0.256975	−	0.148365i	0.0170560	−	0.00984730i	0.508504	+	0.861060i	$0.330199\pi$
$228$	3.86323	−	2.23043i	0.255848	−	0.147714i
$229$	−5.66048	−	3.26808i	−0.374055	−	0.215961i	0.301174	−	0.953569i	$-0.402622\pi$
$229$	−5.66048	−	3.26808i	−0.374055	−	0.215961i	−0.675228	+	0.737609i	$0.735955\pi$
$230$	3.04501			0.200782
$231$	−0.506731	+	0.0569323i	−0.0333404	+	0.00374587i
$232$			20.6590i			1.35633i
$233$	−3.85573	+	6.67832i	−0.252597	+	0.437512i	−0.964240	−	0.265030i	$-0.914618\pi$
$233$	−3.85573	+	6.67832i	−0.252597	+	0.437512i	0.711643	+	0.702541i	$0.247951\pi$
$234$	2.32281	+	0.0674717i	0.151847	+	0.00441077i
$235$	−2.28558	−	3.95874i	−0.149095	−	0.258239i
$236$	6.70831	+	3.87305i	0.436674	+	0.252114i
$237$	3.84220			0.249578
$238$	−5.71163	−	7.74411i	−0.370230	−	0.501976i
$239$			3.63660i			0.235232i	0.993059	+	0.117616i	$0.0375252\pi$
$239$			3.63660i			0.235232i	−0.993059	+	0.117616i	$0.962475\pi$
$240$	−6.23012	−	3.59696i	−0.402153	−	0.232183i
$241$	4.68275	−	2.70359i	0.301642	−	0.174153i	−0.341538	−	0.939868i	$-0.610948\pi$
$241$	4.68275	−	2.70359i	0.301642	−	0.174153i	0.643180	+	0.765715i	$0.277614\pi$
$242$	6.11899	−	3.53280i	0.393343	−	0.227097i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−13.7131			−0.877894
$245$	21.9828	−	20.3712i	1.40443	−	1.30147i
$246$	−3.40456			−0.217067
$247$	4.81765	+	8.93383i	0.306540	+	0.568446i
$248$	2.39485	+	4.14801i	0.152073	+	0.263399i
$249$	8.10068	−	4.67693i	0.513360	−	0.296388i
$250$	11.4947	−	19.9094i	0.726989	−	1.25918i
$251$	5.93593			0.374673			0.187336	−	0.982296i	$-0.440015\pi$
$251$	5.93593			0.374673			0.187336	+	0.982296i	$0.440015\pi$
$252$	−3.37406	+	2.48852i	−0.212546	+	0.156762i
$253$			0.212677i			0.0133709i
$254$	−5.36766	−	3.09902i	−0.336797	−	0.194450i
$255$	20.9239	−	12.0804i	1.31031	−	0.756506i
$256$	3.92587	+	6.79981i	0.245367	+	0.424988i
$257$	1.58873	−	2.75176i	0.0991021	−	0.171650i	−0.812211	−	0.583364i	$-0.801736\pi$
$257$	1.58873	−	2.75176i	0.0991021	−	0.171650i	0.911313	+	0.411714i	$0.135070\pi$
$258$			3.89603i			0.242556i
$259$	19.8997	−	2.23578i	1.23651	−	0.138925i
$260$	12.8409	−	20.8206i	0.796360	−	1.29124i
$261$	−4.47106	+	7.74411i	−0.276752	+	0.479348i
$262$	−6.88274	+	3.97375i	−0.425217	+	0.245499i
$263$	13.4383	+	23.2759i	0.828642	+	1.43525i	0.899103	+	0.437736i	$0.144220\pi$
$263$	13.4383	+	23.2759i	0.828642	+	1.43525i	−0.0704611	+	0.997515i	$0.522447\pi$
$264$	−0.222633	+	0.385612i	−0.0137021	+	0.0237328i
$265$		−	36.6423i		−	2.25092i
$266$	4.39918	+	1.92100i	0.269731	+	0.117784i
$267$		−	0.0286217i		−	0.00175162i
$268$	20.8700	+	12.0493i	1.27484	+	0.736027i
$269$	1.51184	+	2.61859i	0.0921786	+	0.159658i	0.908428	−	0.418042i	$-0.137284\pi$
$269$	1.51184	+	2.61859i	0.0921786	+	0.159658i	−0.816249	+	0.577700i	$0.803950\pi$
$270$	1.37972	+	2.38974i	0.0839670	+	0.145435i
$271$	−20.6996	−	11.9509i	−1.25741	−	0.725966i	−0.284840	−	0.958575i	$-0.591940\pi$
$271$	−20.6996	−	11.9509i	−1.25741	−	0.725966i	−0.972570	+	0.232609i	$0.925274\pi$
$272$	9.48173			0.574914
$273$	−5.43696	−	7.83834i	−0.329060	−	0.474398i
$274$	0.714069			0.0431385
$275$	2.22511	+	1.28467i	0.134179	+	0.0774684i
$276$	0.874304	+	1.51434i	0.0526269	+	0.0911525i
$277$	−7.32155	−	12.6813i	−0.439909	−	0.761945i	0.557773	−	0.829994i	$-0.311656\pi$
$277$	−7.32155	−	12.6813i	−0.439909	−	0.761945i	−0.997682	+	0.0680488i	$0.978323\pi$
$278$	4.35006	+	2.51151i	0.260899	+	0.150630i
$279$			2.07320i			0.124119i
$280$	−2.92193	−	26.0069i	−0.174619	−	1.55421i
$281$			9.21009i			0.549428i	0.961526	+	0.274714i	$0.0885831\pi$
$281$			9.21009i			0.549428i	−0.961526	+	0.274714i	$0.911417\pi$
$282$	−0.344053	+	0.595918i	−0.0204881	+	0.0354864i
$283$	2.67334	+	4.63037i	0.158914	+	0.275247i	0.934477	−	0.356023i	$-0.115867\pi$
$283$	2.67334	+	4.63037i	0.158914	+	0.275247i	−0.775563	+	0.631270i	$0.782534\pi$
$284$	−11.7910	+	6.80751i	−0.699664	+	0.403951i
$285$	−6.02644	+	10.4381i	−0.356976	+	0.618300i
$286$	−0.381199	−	0.235101i	−0.0225407	−	0.0139018i
$287$	8.29570	+	11.2477i	0.489679	+	0.663932i
$288$			5.70351i			0.336083i
$289$	−7.42224	+	12.8557i	−0.436602	+	0.756218i
$290$	−12.3376	−	21.3694i	−0.724490	−	1.25485i
$291$	−5.57439	+	3.21837i	−0.326776	+	0.188664i
$292$	1.60514	+	0.926726i	0.0939335	+	0.0542326i
$293$			17.9918i			1.05109i	0.850764	+	0.525547i	$0.176139\pi$
$293$			17.9918i			1.05109i	−0.850764	+	0.525547i	$0.823861\pi$
$294$	−4.31025	−	1.33253i	−0.251379	−	0.0777144i
$295$	−20.9293			−1.21855
$296$	8.74299	−	15.1433i	0.508176	−	0.880186i
$297$	−0.166910	+	0.0963656i	−0.00968511	+	0.00559170i
$298$	−0.688106	−	1.19184i	−0.0398609	−	0.0690412i
$299$	−3.50196	+	1.88846i	−0.202523	+	0.109213i
$300$	21.1248			1.21964
$301$	12.8714	−	9.49325i	0.741897	−	0.547182i
$302$	−9.76731			−0.562045
$303$	−2.40764	+	4.17016i	−0.138315	+	0.239569i
$304$	−4.09635	+	2.36503i	−0.234942	+	0.135644i
$305$	32.0877	−	18.5259i	1.83734	−	1.06079i
$306$	−3.14973	−	1.81850i	−0.180058	−	0.103956i
$307$			14.3286i			0.817777i	0.912584	+	0.408888i	$0.134084\pi$
$307$			14.3286i			0.817777i	−0.912584	+	0.408888i	$0.865916\pi$
$308$	0.802973	−	0.0902158i	0.0457536	−	0.00514052i
$309$	−11.2070			−0.637543
$310$	−4.95441	−	2.86043i	−0.281392	−	0.162462i
$311$	−7.20490	−	12.4792i	−0.408552	−	0.707633i	0.586176	−	0.810184i	$-0.300633\pi$
$311$	−7.20490	−	12.4792i	−0.408552	−	0.707633i	−0.994728	+	0.102551i	$0.967300\pi$
$312$	−8.32638	−	0.241860i	−0.471389	−	0.0136926i
$313$	2.23152	−	3.86510i	0.126133	−	0.218468i	−0.796042	−	0.605241i	$-0.793077\pi$
$313$	2.23152	−	3.86510i	0.126133	−	0.218468i	0.922175	+	0.386773i	$0.126410\pi$
$314$		−	0.409403i		−	0.0231039i
$315$	4.53317	−	10.3812i	0.255415	−	0.584913i
$316$	−6.08842			−0.342500
$317$	−4.39280	−	2.53618i	−0.246724	−	0.142446i	0.371539	−	0.928417i	$-0.378830\pi$
$317$	−4.39280	−	2.53618i	−0.246724	−	0.142446i	−0.618263	+	0.785971i	$0.712163\pi$
$318$	−4.77687	+	2.75793i	−0.267873	+	0.154657i
$319$	1.49253	−	0.861714i	0.0835657	−	0.0482467i
$320$	−1.16968	−	0.675318i	−0.0653873	−	0.0377514i
$321$	11.1935			0.624761
$322$	−0.753010	+	1.72443i	−0.0419636	+	0.0960986i
$323$		−	15.8859i		−	0.883917i
$324$	−0.792308	+	1.37232i	−0.0440171	+	0.0762398i
$325$	−1.39562	+	48.0461i	−0.0774148	+	2.66512i
$326$	−2.55885	−	4.43205i	−0.141721	−	0.245469i
$327$	−2.26353	−	1.30685i	−0.125174	−	0.0722691i
$328$	12.2040			0.673854
$329$	2.80709	−	0.315382i	0.154760	−	0.0173876i
$330$		−	0.531830i		−	0.0292763i
$331$	20.5209	+	11.8477i	1.12793	+	0.651210i	0.943413	−	0.331620i	$-0.107595\pi$
$331$	20.5209	+	11.8477i	1.12793	+	0.651210i	0.184515	+	0.982830i	$0.440929\pi$
$332$	−12.8365	+	7.41114i	−0.704492	+	0.406739i
$333$	6.55470	−	3.78436i	0.359195	−	0.207382i
$334$	−4.85226	+	8.40437i	−0.265504	+	0.459866i
$335$	−65.1122			−3.55746
$336$	3.57767	−	2.63869i	0.195178	−	0.143952i
$337$	−11.6609			−0.635207			−0.317604	−	0.948224i	$-0.602878\pi$
$337$	−11.6609			−0.635207			−0.317604	+	0.948224i	$0.602878\pi$
$338$	0.486340	−	8.36442i	0.0264534	−	0.454964i
$339$	6.56521	+	11.3713i	0.356573	+	0.617603i
$340$	−33.1564	+	19.1428i	−1.79816	+	1.03817i
$341$	0.199785	−	0.346038i	0.0108190	−	0.0187390i
$342$	1.81435			0.0981087
$343$	6.10024	+	17.4868i	0.329382	+	0.944197i
$344$		−	13.9658i		−	0.752984i
$345$	−4.09162	−	2.36230i	−0.220285	−	0.127182i
$346$	1.24945	−	0.721372i	0.0671710	−	0.0387812i
$347$	−4.40896	−	7.63654i	−0.236685	−	0.409951i	0.723076	−	0.690769i	$-0.242728\pi$
$347$	−4.40896	−	7.63654i	−0.236685	−	0.409951i	−0.959761	+	0.280818i	$0.909394\pi$
$348$	7.08492	−	12.2714i	0.379791	−	0.657818i
$349$		−	3.78037i		−	0.202359i	−0.994868	−	0.101179i	$-0.967738\pi$
$349$		−	3.78037i		−	0.202359i	0.994868	−	0.101179i	$-0.0322616\pi$
$350$	13.4931	+	18.2946i	0.721237	+	0.977889i
$351$	−3.06884	−	1.89268i	−0.163802	−	0.101024i
$352$	0.549622	−	0.951974i	0.0292950	−	0.0507404i
$353$	−13.0415	+	7.52953i	−0.694131	+	0.400757i	−0.805158	−	0.593061i	$-0.797919\pi$
$353$	−13.0415	+	7.52953i	−0.694131	+	0.400757i	0.111027	+	0.993817i	$0.464586\pi$
$354$	1.57527	+	2.72844i	0.0837245	+	0.145015i
$355$	18.3933	−	31.8581i	0.976215	−	1.69085i
$356$			0.0453544i			0.00240378i
$357$	1.66696	+	14.8369i	0.0882246	+	0.785250i
$358$		−	1.43707i		−	0.0759515i
$359$	−0.772732	−	0.446137i	−0.0407832	−	0.0235462i	0.479470	−	0.877558i	$-0.340829\pi$
$359$	−0.772732	−	0.446137i	−0.0407832	−	0.0235462i	−0.520253	+	0.854012i	$0.674162\pi$
$360$	−4.94576	−	8.56631i	−0.260665	−	0.451484i
$361$	−5.53757	−	9.59136i	−0.291451	−	0.504808i
$362$	8.36517	+	4.82963i	0.439664	+	0.253840i
$363$	−10.9629			−0.575401
$364$	8.61549	+	12.4207i	0.451574	+	0.651024i
$365$	−5.00787			−0.262124
$366$	−4.83024	−	2.78874i	−0.252481	−	0.145770i
$367$	17.0581	+	29.5456i	0.890427	+	1.54227i	0.839364	+	0.543570i	$0.182928\pi$
$367$	17.0581	+	29.5456i	0.890427	+	1.54227i	0.0510637	+	0.998695i	$0.483739\pi$
$368$	−0.927063	−	1.60572i	−0.0483265	−	0.0837040i
$369$	4.57473	+	2.64122i	0.238151	+	0.137497i
$370$			20.8854i			1.08578i
$371$	20.7510	+	9.06138i	1.07734	+	0.470443i
$372$		−	3.28522i		−	0.170331i
$373$	−5.54765	+	9.60881i	−0.287246	+	0.497525i	−0.973151	−	0.230166i	$-0.926073\pi$
$373$	−5.54765	+	9.60881i	−0.287246	+	0.497525i	0.685905	+	0.727691i	$0.259406\pi$
$374$	0.350481	+	0.607051i	0.0181229	+	0.0313898i
$375$	−30.8911	+	17.8350i	−1.59521	+	0.920995i
$376$	1.23330	−	2.13614i	0.0636025	−	0.110163i
$377$	27.4420	+	16.9246i	1.41333	+	0.871660i
$378$	−1.69453	+	0.190385i	−0.0871574	+	0.00979233i
$379$		−	13.6416i		−	0.700724i	−0.936614	−	0.350362i	$-0.886059\pi$
$379$		−	13.6416i		−	0.700724i	0.936614	−	0.350362i	$-0.113941\pi$
$380$	9.54959	−	16.5404i	0.489884	−	0.848504i
$381$	4.80839	+	8.32837i	0.246341	+	0.426675i
$382$	4.17597	−	2.41100i	0.213661	−	0.123358i
$383$	−25.2362	−	14.5701i	−1.28951	−	0.744498i	−0.310941	−	0.950429i	$-0.600644\pi$
$383$	−25.2362	−	14.5701i	−1.28951	−	0.744498i	−0.978566	+	0.205932i	$0.933978\pi$
$384$		−	11.2037i		−	0.571737i
$385$	−1.75702	+	1.29588i	−0.0895460	+	0.0660442i
$386$	−11.6805			−0.594521
$387$	3.02251	−	5.23514i	0.153643	−	0.266117i
$388$	8.83326	−	5.09989i	0.448441	−	0.258907i
$389$	12.5966	+	21.8179i	0.638673	+	1.10621i	0.985724	+	0.168368i	$0.0538496\pi$
$389$	12.5966	+	21.8179i	0.638673	+	1.10621i	−0.347051	+	0.937846i	$0.612817\pi$
$390$	8.75715	−	4.72237i	0.443435	−	0.239127i
$391$	6.22710			0.314918
$392$	15.4506	+	4.77659i	0.780372	+	0.241254i
$393$	12.3312			0.622027
$394$	1.94081	−	3.36159i	0.0977768	−	0.169354i
$395$	14.2464	−	8.22519i	0.716816	−	0.413854i
$396$	0.264488	−	0.152702i	0.0132910	−	0.00767358i
$397$	−12.1535	−	7.01685i	−0.609968	−	0.352165i	0.162985	−	0.986629i	$-0.447888\pi$
$397$	−12.1535	−	7.01685i	−0.609968	−	0.352165i	−0.772953	+	0.634463i	$0.781221\pi$
$398$		−	3.45294i		−	0.173080i
$399$	−4.42092	−	5.99411i	−0.221323	−	0.300081i
$400$	−22.3996			−1.11998
$401$	24.5111	+	14.1515i	1.22403	+	0.706692i	0.965774	−	0.259386i	$-0.0835202\pi$
$401$	24.5111	+	14.1515i	1.22403	+	0.706692i	0.258252	+	0.966078i	$0.416854\pi$
$402$	4.90075	+	8.48834i	0.244427	+	0.423360i
$403$	7.47187	+	0.217039i	0.372201	+	0.0108115i
$404$	3.81518	−	6.60809i	0.189813	−	0.328765i
$405$		−	4.28149i		−	0.212749i
$406$	15.1527	−	1.70244i	0.752018	−	0.0844909i
$407$	−1.45873			−0.0723064
$408$	11.2906	+	6.51861i	0.558966	+	0.322719i
$409$	−5.10051	+	2.94478i	−0.252204	+	0.145610i	−0.620773	−	0.783990i	$-0.713181\pi$
$409$	−5.10051	+	2.94478i	−0.252204	+	0.145610i	0.368569	+	0.929600i	$0.379848\pi$
$410$	−12.6237	+	7.28829i	−0.623440	+	0.359943i
$411$	−0.959501	−	0.553968i	−0.0473287	−	0.0273252i
$412$	17.7588			0.874911
$413$	5.17566	−	11.8525i	0.254678	−	0.583223i
$414$			0.711204i			0.0349538i
$415$	20.0243	−	34.6830i	0.982952	−	1.70252i
$416$	20.5556	+	0.597089i	1.00782	+	0.0292747i
$417$	−3.89681	−	6.74948i	−0.190828	−	0.330523i
$418$	−0.302833	−	0.174841i	−0.0148121	−	0.00855174i
$419$	−15.8527			−0.774455			−0.387228	−	0.921984i	$-0.626567\pi$
$419$	−15.8527			−0.774455			−0.387228	+	0.921984i	$0.626567\pi$
$420$	−7.18334	+	16.4502i	−0.350511	+	0.802686i
$421$			18.9929i			0.925656i	0.886448	+	0.462828i	$0.153165\pi$
$421$			18.9929i			0.925656i	−0.886448	+	0.462828i	$0.846835\pi$
$422$	9.17917	+	5.29960i	0.446835	+	0.257980i
$423$	0.924615	−	0.533827i	0.0449563	−	0.0259556i
$424$	17.1232	−	9.88610i	0.831578	−	0.480112i
$425$	37.6146	−	65.1504i	1.82458	−	3.16026i
$426$	−5.53757			−0.268296
$427$	2.55635	+	22.7530i	0.123710	+	1.10109i
$428$	−17.7374			−0.857371
$429$	0.329831	+	0.611638i	0.0159244	+	0.0295301i
$430$	8.34042	+	14.4460i	0.402211	+	0.696650i
$431$	17.4543	−	10.0772i	0.840743	−	0.485403i	−0.0167739	−	0.999859i	$-0.505340\pi$
$431$	17.4543	−	10.0772i	0.840743	−	0.485403i	0.857517	+	0.514456i	$0.172006\pi$
$432$	0.840118	−	1.45513i	0.0404202	−	0.0700099i
$433$	−1.45933			−0.0701311			−0.0350655	−	0.999385i	$-0.511164\pi$
$433$	−1.45933			−0.0701311			−0.0350655	+	0.999385i	$0.511164\pi$
$434$	2.84509	−	2.09838i	0.136569	−	0.100725i
$435$			38.2857i			1.83566i
$436$	3.58683	+	2.07086i	0.171778	+	0.0991761i
$437$	−2.69026	+	1.55323i	−0.128693	+	0.0743008i
$438$	0.376923	+	0.652850i	0.0180101	+	0.0311944i
$439$	−6.68602	+	11.5805i	−0.319106	+	0.552708i	−0.980302	−	0.197505i	$-0.936716\pi$
$439$	−6.68602	+	11.5805i	−0.319106	+	0.552708i	0.661195	+	0.750214i	$0.270049\pi$
$440$			1.90641i			0.0908843i
$441$	4.75796	+	5.13438i	0.226569	+	0.244494i
$442$	−6.88365	+	11.1613i	−0.327422	+	0.530891i
$443$	−15.2499	+	26.4136i	−0.724545	+	1.25495i	0.234616	+	0.972088i	$0.424617\pi$
$443$	−15.2499	+	26.4136i	−0.724545	+	1.25495i	−0.959161	+	0.282861i	$0.908717\pi$
$444$	−10.3867	+	5.99675i	−0.492930	+	0.284593i
$445$	−0.0612719	−	0.106126i	−0.00290457	−	0.00503086i
$446$	−2.67037	+	4.62522i	−0.126446	+	0.219010i
$447$			2.13531i			0.100997i
$448$	0.671695	−	0.495405i	0.0317346	−	0.0234057i
$449$			4.38848i			0.207105i	0.994624	+	0.103553i	$0.0330210\pi$
$449$			4.38848i			0.207105i	−0.994624	+	0.103553i	$0.966979\pi$
$450$	7.44089	+	4.29600i	0.350767	+	0.202515i
$451$	−0.509046	−	0.881694i	−0.0239701	−	0.0415173i
$452$	−10.4033	−	18.0191i	−0.489331	−	0.847547i
$453$	13.1244	+	7.57739i	0.616639	+	0.356017i
$454$	−0.191243			−0.00897547
$455$	−36.9395	−	17.4245i	−1.73175	−	0.816872i
$456$	−6.50374			−0.304566
$457$	−15.8981	−	9.17878i	−0.743682	−	0.429365i	0.0797243	−	0.996817i	$-0.474596\pi$
$457$	−15.8981	−	9.17878i	−0.743682	−	0.429365i	−0.823407	+	0.567452i	$0.807929\pi$
$458$	2.10629	+	3.64820i	0.0984203	+	0.170469i
$459$	2.82155	+	4.88706i	0.131698	+	0.228108i
$460$	6.48364	+	3.74333i	0.302301	+	0.174534i
$461$		−	31.9152i		−	1.48644i	−0.669046	−	0.743221i	$-0.733297\pi$
$461$		−	31.9152i		−	1.48644i	0.669046	−	0.743221i	$-0.266703\pi$
$462$	0.301181	+	0.131518i	0.0140122	+	0.00611875i
$463$			8.50297i			0.395166i	0.980286	+	0.197583i	$0.0633093\pi$
$463$			8.50297i			0.395166i	−0.980286	+	0.197583i	$0.936691\pi$
$464$	−7.51245	+	13.0119i	−0.348757	+	0.604064i
$465$	4.43820	+	7.68718i	0.205816	+	0.356484i
$466$	4.30420	−	2.48503i	0.199388	−	0.115117i
$467$	6.36323	−	11.0214i	0.294455	−	0.510011i	−0.680403	−	0.732838i	$-0.738195\pi$
$467$	6.36323	−	11.0214i	0.294455	−	0.510011i	0.974858	+	0.222827i	$0.0715285\pi$
$468$	4.86293	+	2.99917i	0.224789	+	0.138637i
$469$	16.1018	−	36.8738i	0.743511	−	1.70267i
$470$			2.94612i			0.135895i
$471$	−0.317611	+	0.550118i	−0.0146347	+	0.0253481i
$472$	−5.64672	−	9.78041i	−0.259912	−	0.450180i
$473$	−1.00897	+	0.582531i	−0.0463927	+	0.0267848i
$474$	−2.14455	−	1.23816i	−0.0985025	−	0.0568704i
$475$			37.5288i			1.72194i
$476$	−2.64148	−	23.5107i	−0.121072	−	1.07761i
$477$	8.55830			0.391858
$478$	1.17190	−	2.02979i	0.0536015	−	0.0928405i
$479$	−2.97272	+	1.71630i	−0.135827	+	0.0784197i	−0.566374	−	0.824149i	$-0.691654\pi$
$479$	−2.97272	+	1.71630i	−0.135827	+	0.0784197i	0.430547	+	0.902568i	$0.358321\pi$
$480$	12.2098	+	21.1480i	0.557298	+	0.965268i
$481$	−12.9527	−	24.0195i	−0.590594	−	1.09520i
$482$	−3.48494			−0.158735
$483$	2.34962	−	1.73295i	0.106912	−	0.0788520i
$484$	17.3719			0.789632
$485$	−13.7795	+	23.8667i	−0.625693	+	1.08373i
$486$	−0.558156	+	0.322252i	−0.0253185	+	0.0146176i
$487$	−34.6029	+	19.9780i	−1.56801	+	0.905288i	−0.571604	+	0.820530i	$0.693679\pi$
$487$	−34.6029	+	19.9780i	−1.56801	+	0.905288i	−0.996401	+	0.0847590i	$0.972988\pi$
$488$	17.3146	+	9.99656i	0.783793	+	0.452523i
$489$			7.94052i			0.359083i
$490$	−18.8345	+	4.28630i	−0.850855	+	0.193635i
$491$	33.0722			1.49253			0.746263	−	0.665651i	$-0.231846\pi$
$491$	33.0722			1.49253			0.746263	+	0.665651i	$0.231846\pi$
$492$	−7.24919	−	4.18532i	−0.326819	−	0.188689i
$493$	−25.2306	−	43.7007i	−1.13633	−	1.96818i
$494$	0.189940	−	6.53897i	0.00854582	−	0.294202i
$495$	−0.412589	+	0.714625i	−0.0185445	+	0.0321200i
$496$			3.48347i			0.156412i
$497$	13.4931	+	18.2946i	0.605249	+	0.820626i
$498$	−6.02859			−0.270148
$499$	−16.2068	−	9.35700i	−0.725516	−	0.418877i	0.0912633	−	0.995827i	$-0.470910\pi$
$499$	−16.2068	−	9.35700i	−0.725516	−	0.418877i	−0.816780	+	0.576950i	$0.804243\pi$
$500$	48.9505	−	28.2616i	2.18913	−	1.26390i
$501$	13.0401	−	7.52869i	0.582587	−	0.336357i
$502$	−3.31318	−	1.91286i	−0.147874	−	0.0853753i
$503$	−3.22913			−0.143980			−0.0719898	−	0.997405i	$-0.522935\pi$
$503$	−3.22913			−0.143980			−0.0719898	+	0.997405i	$0.522935\pi$
$504$	6.07425	−	0.682456i	0.270569	−	0.0303990i
$505$			20.6166i			0.917427i
$506$	0.0685356	−	0.118707i	0.00304678	−	0.00527717i
$507$	−7.14254	+	10.8620i	−0.317211	+	0.482401i
$508$	−7.61945	−	13.1973i	−0.338058	−	0.585534i
$509$	−22.5436	−	13.0155i	−0.999225	−	0.576903i	−0.0912064	−	0.995832i	$-0.529072\pi$
$509$	−22.5436	−	13.0155i	−0.999225	−	0.576903i	−0.908019	+	0.418929i	$0.862406\pi$
$510$	−15.5718			−0.689529
$511$	1.23841	−	2.83602i	0.0547840	−	0.125458i
$512$			17.3469i			0.766634i
$513$	−2.43796	−	1.40756i	−0.107638	−	0.0621451i
$514$	−1.77352	+	1.02394i	−0.0782265	+	0.0451641i
$515$	−41.5542	+	23.9913i	−1.83110	+	1.05718i
$516$	−4.78951	+	8.29568i	−0.210847	+	0.365197i
$517$	−0.205770			−0.00904976
$518$	−11.8276	−	5.16481i	−0.519677	−	0.226929i
$519$	−2.23854			−0.0982608
$520$	−31.3910	+	16.9279i	−1.37659	+	0.742337i
$521$	1.54121	+	2.66945i	0.0675215	+	0.116951i	0.897810	−	0.440384i	$-0.145158\pi$
$521$	1.54121	+	2.66945i	0.0675215	+	0.116951i	−0.830288	+	0.557334i	$0.811824\pi$
$522$	4.99111	−	2.88162i	0.218455	−	0.126125i
$523$	−15.6199	+	27.0544i	−0.683009	+	1.18301i	0.291049	+	0.956708i	$0.405996\pi$
$523$	−15.6199	+	27.0544i	−0.683009	+	1.18301i	−0.974058	+	0.226299i	$0.927337\pi$
$524$	−19.5402			−0.853618
$525$	−3.93800	−	35.0505i	−0.171869	−	1.52973i
$526$		−	17.3221i		−	0.755279i
$527$	−10.1318	−	5.84963i	−0.441350	−	0.254814i
$528$	−0.280449	+	0.161917i	−0.0122050	+	0.00704653i
$529$	10.8912	+	18.8640i	0.473528	+	0.820175i
$530$	−11.8080	+	20.4521i	−0.512909	+	0.888384i
$531$		−	4.88831i		−	0.212135i
$532$	7.00547	+	9.49836i	0.303725	+	0.411806i
$533$	9.99797	−	16.2110i	0.433060	−	0.702176i
$534$	−0.00922340	+	0.0159754i	−0.000399136	+	0.000691323i
$535$	41.5043	−	23.9625i	1.79439	−	1.03599i
$536$	−17.5673	−	30.4274i	−0.758791	−	1.31427i
$537$	−1.11487	+	1.93101i	−0.0481100	+	0.0833290i
$538$		−	1.94877i		−	0.0840176i
$539$	−0.299374	−	1.31548i	−0.0128949	−	0.0566619i
$540$			6.78452i			0.291959i
$541$	−23.6076	−	13.6299i	−1.01497	−	0.585994i	−0.102328	−	0.994751i	$-0.532629\pi$
$541$	−23.6076	−	13.6299i	−1.01497	−	0.585994i	−0.912643	+	0.408757i	$0.865962\pi$
$542$	7.70240	+	13.3410i	0.330847	+	0.573043i
$543$	−7.49357	−	12.9792i	−0.321580	−	0.556993i
$544$	−27.8734	−	16.0927i	−1.19506	−	0.689970i
$545$	−11.1906			−0.479351
$546$	0.508755	+	6.12708i	0.0217727	+	0.262215i
$547$	27.0394			1.15612			0.578061	−	0.815993i	$-0.303810\pi$
$547$	27.0394			1.15612			0.578061	+	0.815993i	$0.303810\pi$
$548$	1.52044	+	0.877826i	0.0649500	+	0.0374989i
$549$	4.32696	+	7.49451i	0.184670	+	0.319858i
$550$	−0.827973	−	1.43409i	−0.0353049	−	0.0611499i
$551$	21.8005	+	12.5865i	0.928734	+	0.536205i
$552$		−	2.54939i		−	0.108509i
$553$	1.13498	+	10.1020i	0.0482642	+	0.429579i
$554$			9.43752i			0.400962i
$555$	16.2027	−	28.0639i	0.687767	−	1.19125i
$556$	6.17495	+	10.6953i	0.261876	+	0.453583i
$557$	2.73906	−	1.58140i	0.116058	−	0.0670060i	−0.440847	−	0.897582i	$-0.645322\pi$
$557$	2.73906	−	1.58140i	0.116058	−	0.0670060i	0.556905	+	0.830576i	$0.311989\pi$
$558$	0.668092	−	1.15717i	0.0282826	−	0.0489869i
$559$	−18.5512	−	11.4413i	−0.784631	−	0.483914i
$560$	7.61680	−	17.4428i	0.321869	−	0.737094i
$561$		−	1.08760i		−	0.0459185i
$562$	2.96797	−	5.14067i	0.125196	−	0.216846i
$563$	23.3803	+	40.4959i	0.985363	+	1.70670i	0.640311	+	0.768116i	$0.278805\pi$
$563$	23.3803	+	40.4959i	0.985363	+	1.70670i	0.345052	+	0.938584i	$0.387861\pi$
$564$	−1.46516	+	0.845910i	−0.0616944	+	0.0356193i
$565$	48.6860	+	28.1089i	2.04824	+	1.18255i
$566$		−	3.44596i		−	0.144844i
$567$	2.42466	+	1.05878i	0.101826	+	0.0444647i
$568$	19.8501			0.832891
$569$	9.13720	−	15.8261i	0.383051	−	0.663464i	−0.608446	−	0.793596i	$-0.708207\pi$
$569$	9.13720	−	15.8261i	0.383051	−	0.663464i	0.991497	+	0.130131i	$0.0415399\pi$
$570$	6.72739	−	3.88406i	0.281779	−	0.162685i
$571$	1.65070	+	2.85909i	0.0690795	+	0.119649i	0.898496	−	0.438981i	$-0.144660\pi$
$571$	1.65070	+	2.85909i	0.0690795	+	0.119649i	−0.829417	+	0.558630i	$0.811327\pi$
$572$	−0.522655	−	0.969210i	−0.0218533	−	0.0405247i
$573$	−7.48173			−0.312554
$574$	−1.00570	−	8.95129i	−0.0419770	−	0.373620i
$575$	−14.7109			−0.613485
$576$	0.157729	−	0.273195i	0.00657206	−	0.0113831i
$577$	35.4863	−	20.4880i	1.47731	−	0.852928i	0.477643	−	0.878554i	$-0.341491\pi$
$577$	35.4863	−	20.4880i	1.47731	−	0.852928i	0.999672	+	0.0256259i	$0.00815788\pi$
$578$	8.28554	−	4.78366i	0.344633	−	0.198974i
$579$	15.6952	+	9.06162i	0.652270	+	0.376588i
$580$		−	60.6681i		−	2.51911i
$581$	14.6895	+	19.9168i	0.609425	+	0.826289i
$582$	4.14851			0.171961
$583$	−1.42847	−	0.824726i	−0.0591610	−	0.0341566i
$584$	−1.35112	−	2.34022i	−0.0559099	−	0.0968388i
$585$	−15.4306	−	0.448221i	−0.637978	−	0.0185317i
$586$	5.79790	−	10.0423i	0.239509	−	0.414842i
$587$		−	32.5142i		−	1.34200i	−0.741456	−	0.671002i	$-0.765864\pi$
$587$		−	32.5142i		−	1.34200i	0.741456	−	0.671002i	$-0.234136\pi$
$588$	−7.53953	−	8.13601i	−0.310925	−	0.335524i
$589$	5.83629			0.240480
$590$	11.6818	+	6.74449i	0.480932	+	0.277666i
$591$	−5.21578	+	3.01133i	−0.214549	+	0.123870i
$592$	11.0134	−	6.35862i	0.452650	−	0.261338i
$593$	−32.0213	−	18.4875i	−1.31496	−	0.759191i	−0.332045	−	0.943263i	$-0.607739\pi$
$593$	−32.0213	−	18.4875i	−1.31496	−	0.759191i	−0.982913	+	0.184072i	$0.941072\pi$
$594$	0.124216			0.00509664
$595$	37.9429	+	51.4448i	1.55551	+	2.10903i
$596$		−	3.38364i		−	0.138599i
$597$	−2.67876	+	4.63974i	−0.109634	+	0.189892i
$598$	2.56320	+	0.0744545i	0.104817	+	0.00304467i
$599$	−9.83321	−	17.0316i	−0.401774	−	0.695893i	0.592166	−	0.805816i	$-0.298273\pi$
$599$	−9.83321	−	17.0316i	−0.401774	−	0.695893i	−0.993940	+	0.109923i	$0.964940\pi$
$600$	−26.6727	−	15.3995i	−1.08891	−	0.628682i
$601$	−47.3029			−1.92952			−0.964762	−	0.263125i	$-0.915247\pi$
$601$	−47.3029			−1.92952			−0.964762	+	0.263125i	$0.915247\pi$
$602$	−10.2435	+	1.15088i	−0.417493	+	0.0469063i
$603$		−	15.2078i		−	0.619310i
$604$	−20.7972	−	12.0072i	−0.846225	−	0.488568i
$605$	−40.6490	+	23.4687i	−1.65262	+	0.954138i
$606$	2.68768	−	1.55173i	0.109180	−	0.0630348i
$607$	−11.2295	+	19.4500i	−0.455791	+	0.789453i	−0.998733	−	0.0503169i	$-0.983977\pi$
$607$	−11.2295	+	19.4500i	−0.455791	+	0.789453i	0.542942	+	0.839770i	$0.317310\pi$
$608$	16.0560			0.651158
$609$	−21.6816	−	9.46777i	−0.878584	−	0.383654i
$610$	−23.8800			−0.966871
$611$	−1.82713	−	3.38823i	−0.0739179	−	0.137073i
$612$	−4.47106	−	7.74411i	−0.180732	−	0.313037i
$613$	−28.7231	+	16.5833i	−1.16011	+	0.669792i	−0.951331	−	0.308170i	$-0.900284\pi$
$613$	−28.7231	+	16.5833i	−1.16011	+	0.669792i	−0.208783	+	0.977962i	$0.566950\pi$
$614$	4.61742	−	7.99760i	0.186344	−	0.322757i
$615$	22.6168			0.911996
$616$	−1.07962	−	0.471440i	−0.0434991	−	0.0189949i
$617$			37.2085i			1.49796i	0.662595	+	0.748978i	$0.269455\pi$
$617$			37.2085i			1.49796i	−0.662595	+	0.748978i	$0.730545\pi$
$618$	6.25525	+	3.61147i	0.251623	+	0.145275i
$619$	21.6184	−	12.4814i	0.868918	−	0.501670i	0.00192925	−	0.999998i	$-0.499386\pi$
$619$	21.6184	−	12.4814i	0.868918	−	0.501670i	0.866988	+	0.498328i	$0.166053\pi$
$620$	−7.03283	−	12.1812i	−0.282445	−	0.489210i
$621$	0.551746	−	0.955651i	0.0221408	−	0.0383490i
$622$			9.28716i			0.372381i
$623$	0.0752525	−	0.00845479i	0.00301493	−	0.000338734i
$624$	−5.15638	−	3.18015i	−0.206420	−	0.127308i
$625$	−43.0324	+	74.5343i	−1.72130	+	2.98137i
$626$	−2.49107	+	1.43822i	−0.0995632	+	0.0574828i
$627$	0.271280	+	0.469871i	0.0108339	+	0.0187648i
$628$	0.503291	−	0.871726i	0.0200835	−	0.0347857i
$629$			42.7110i			1.70300i
$630$	−5.87557	+	4.33349i	−0.234088	+	0.172651i
$631$		−	8.02717i		−	0.319556i	−0.987153	−	0.159778i	$-0.948922\pi$
$631$		−	8.02717i		−	0.319556i	0.987153	−	0.159778i	$-0.0510779\pi$
$632$	7.68739	+	4.43832i	0.305788	+	0.176547i
$633$	−8.22276	−	14.2422i	−0.326825	−	0.566078i
$634$	1.63458	+	2.83117i	0.0649174	+	0.112440i
$635$	35.6579	+	20.5871i	1.41504	+	0.816974i
$636$	−13.5616			−0.537753
$637$	19.0026	−	16.6103i	0.752909	−	0.658125i
$638$	−1.11075			−0.0439752
$639$	7.44089	+	4.29600i	0.294357	+	0.169947i
$640$	−23.9843	−	41.5420i	−0.948063	−	1.64209i
$641$	1.62243	+	2.81014i	0.0640823	+	0.110994i	0.896287	−	0.443475i	$-0.146255\pi$
$641$	1.62243	+	2.81014i	0.0640823	+	0.110994i	−0.832204	+	0.554469i	$0.812921\pi$
$642$	−6.24773	−	3.60713i	−0.246578	−	0.142362i
$643$			24.8373i			0.979487i	0.871867	+	0.489743i	$0.162910\pi$
$643$			24.8373i			0.979487i	−0.871867	+	0.489743i	$0.837090\pi$
$644$	−3.72325	+	2.74606i	−0.146717	+	0.108210i
$645$		−	25.8817i		−	1.01909i
$646$	−5.11927	+	8.86683i	−0.201415	+	0.348861i
$647$	−20.3448	−	35.2383i	−0.799838	−	1.38536i	−0.919722	−	0.392571i	$-0.871586\pi$
$647$	−20.3448	−	35.2383i	−0.799838	−	1.38536i	0.119884	−	0.992788i	$-0.461748\pi$
$648$	2.00078	−	1.15515i	0.0785979	−	0.0453785i
$649$	−0.471065	+	0.815908i	−0.0184909	+	0.0320272i
$650$	16.2619	−	26.3675i	0.637844	−	1.03422i
$651$	−5.45087	+	0.612418i	−0.213637	+	0.0240025i
$652$		−	12.5827i		−	0.492775i
$653$	9.31697	−	16.1375i	0.364601	−	0.631508i	−0.624111	−	0.781336i	$-0.714539\pi$
$653$	9.31697	−	16.1375i	0.364601	−	0.631508i	0.988712	+	0.149828i	$0.0478720\pi$
$654$	0.842271	+	1.45886i	0.0329354	+	0.0570458i
$655$	45.7226	−	26.3980i	1.78653	−	1.03145i
$656$	7.68664	+	4.43788i	0.300113	+	0.173270i
$657$		−	1.16965i		−	0.0456326i
$658$	−1.66842	−	0.728555i	−0.0650420	−	0.0284020i
$659$	−41.9643			−1.63470			−0.817349	−	0.576143i	$-0.804557\pi$
$659$	−41.9643			−1.63470			−0.817349	+	0.576143i	$0.804557\pi$
$660$	0.653795	−	1.13241i	0.0254489	−	0.0440788i
$661$	−31.0575	+	17.9311i	−1.20800	+	0.697437i	−0.962321	−	0.271915i	$-0.912343\pi$
$661$	−31.0575	+	17.9311i	−1.20800	+	0.697437i	−0.245676	+	0.969352i	$0.579010\pi$
$662$	−7.63589	−	13.2258i	−0.296777	−	0.514034i
$663$	17.9085	−	9.65732i	0.695509	−	0.375059i
$664$	21.6102			0.838638
$665$	−29.2242	−	12.7614i	−1.13326	−	0.494865i
$666$	−4.87806			−0.189021
$667$	−4.93378	+	8.54556i	−0.191037	+	0.330885i
$668$	−20.6635	+	11.9301i	−0.799494	+	0.461588i
$669$	7.17640	−	4.14330i	0.277456	−	0.160189i
$670$	36.3428	+	20.9825i	1.40404	+	0.810626i
$671$		−	1.66788i		−	0.0643878i
$672$	−14.9957	+	1.68480i	−0.578473	+	0.0649927i
$673$	−9.54544			−0.367950			−0.183975	−	0.982931i	$-0.558897\pi$
$673$	−9.54544			−0.367950			−0.183975	+	0.982931i	$0.558897\pi$
$674$	6.50858	+	3.75773i	0.250701	+	0.144742i
$675$	−6.66560	−	11.5452i	−0.256559	−	0.444373i
$676$	11.3182	−	17.2122i	0.435315	−	0.662007i
$677$	−4.98834	+	8.64005i	−0.191717	+	0.332064i	−0.945819	−	0.324693i	$-0.894739\pi$
$677$	−4.98834	+	8.64005i	−0.191717	+	0.332064i	0.754102	+	0.656757i	$0.228072\pi$
$678$		−	8.46260i		−	0.325004i
$679$	−10.1084	−	13.7055i	−0.387926	−	0.525970i
$680$	55.8188			2.14055
$681$	0.256975	+	0.148365i	0.00984730	+	0.00568534i
$682$	−0.223023	+	0.128762i	−0.00853997	+	0.00493056i
$683$	−20.9587	+	12.1005i	−0.801963	+	0.463013i	−0.844157	−	0.536096i	$-0.819898\pi$
$683$	−20.9587	+	12.1005i	−0.801963	+	0.463013i	0.0421943	+	0.999109i	$0.486565\pi$
$684$	3.86323	+	2.23043i	0.147714	+	0.0852828i
$685$	−4.74362			−0.181245
$686$	2.23025	−	11.7262i	0.0851514	−	0.447707i
$687$		−	6.53615i		−	0.249370i
$688$	5.07853	−	8.79627i	0.193617	−	0.335355i
$689$	0.895951	−	30.8444i	0.0341330	−	1.17508i
$690$	1.52251	+	2.63706i	0.0579609	+	0.100391i
$691$	−22.0497	−	12.7304i	−0.838812	−	0.484288i	0.0180485	−	0.999837i	$-0.494255\pi$
$691$	−22.0497	−	12.7304i	−0.838812	−	0.484288i	−0.856860	+	0.515549i	$0.827588\pi$
$692$	3.54722			0.134845
$693$	−0.302670	−	0.410375i	−0.0114975	−	0.0155889i
$694$			5.68318i			0.215730i
$695$	−28.8978	−	16.6842i	−1.09616	−	0.632867i
$696$	−17.8912	+	10.3295i	−0.678164	+	0.391538i
$697$	−25.8156	+	14.9047i	−0.977837	+	0.564555i
$698$	−1.21823	+	2.11004i	−0.0461108	+	0.0798662i
$699$	−7.71146			−0.291674
$700$	6.24022	+	55.5416i	0.235858	+	2.09927i
$701$	−29.8645			−1.12797			−0.563983	−	0.825787i	$-0.690732\pi$
$701$	−29.8645			−1.12797			−0.563983	+	0.825787i	$0.690732\pi$
$702$	1.10297	+	2.04535i	0.0416290	+	0.0771967i
$703$	−10.6534	−	18.4522i	−0.401800	−	0.695938i
$704$	−0.0526533	+	0.0303994i	−0.00198444	+	0.00114572i
$705$	2.28558	−	3.95874i	0.0860798	−	0.149095i
$706$	9.70562			0.365276
$707$	−11.6754	−	5.09834i	−0.439100	−	0.191743i
$708$			7.74609i			0.291116i
$709$	23.4308	+	13.5278i	0.879962	+	0.508046i	0.870646	−	0.491910i	$-0.163701\pi$
$709$	23.4308	+	13.5278i	0.879962	+	0.508046i	0.00931619	+	0.999957i	$0.497035\pi$
$710$	−20.5327	+	11.8545i	−0.770578	+	0.444893i
$711$	1.92110	+	3.32745i	0.0720470	+	0.124789i
$712$	0.0330623	−	0.0572657i	0.00123906	−	0.00214612i
$713$			2.28776i			0.0856771i
$714$	3.85078	−	8.81847i	0.144112	−	0.330023i
$715$	2.53234	+	1.56180i	0.0947040	+	0.0584078i
$716$	1.76663	−	3.05990i	0.0660222	−	0.114354i
$717$	−3.14939	+	1.81830i	−0.117616	+	0.0679057i
$718$	0.287537	+	0.498028i	0.0107308	+	0.0185863i
$719$	12.6736	−	21.9514i	0.472647	−	0.818649i	−0.526863	−	0.849950i	$-0.676632\pi$
$719$	12.6736	−	21.9514i	0.472647	−	0.818649i	0.999510	+	0.0313014i	$0.00996516\pi$
$720$		−	7.19393i		−	0.268102i
$721$	−3.31052	−	29.4655i	−0.123290	−	1.09735i
$722$			7.13797i			0.265648i
$723$	4.68275	+	2.70359i	0.174153	+	0.100547i
$724$	11.8744	+	20.5671i	0.441310	+	0.764371i
$725$	59.6047	+	103.238i	2.21366	+	3.83417i
$726$	6.11899	+	3.53280i	0.227097	+	0.131114i
$727$	26.4047			0.979295			0.489648	−	0.871920i	$-0.337125\pi$
$727$	26.4047			0.979295			0.489648	+	0.871920i	$0.337125\pi$
$728$	−1.82369	−	21.9632i	−0.0675905	−	0.814012i
$729$	1.00000			0.0370370
$730$	2.79517	+	1.61379i	0.103454	+	0.0597292i
$731$	17.0563	+	29.5424i	0.630850	+	1.09266i
$732$	−6.85657	−	11.8759i	−0.253426	−	0.438947i
$733$	−37.9361	−	21.9024i	−1.40120	−	0.808984i	−0.406686	−	0.913568i	$-0.633316\pi$
$733$	−37.9361	−	21.9024i	−1.40120	−	0.808984i	−0.994516	+	0.104584i	$0.966649\pi$
$734$		−	21.9881i		−	0.811594i
$735$	28.6334	+	8.85209i	1.05616	+	0.326514i
$736$			6.29377i			0.231992i
$737$	−1.46551	+	2.53834i	−0.0539828	+	0.0935009i
$738$	−1.70228	−	2.94843i	−0.0626617	−	0.108533i
$739$	43.5810	−	25.1615i	1.60315	−	0.925582i	0.612303	−	0.790623i	$-0.290243\pi$
$739$	43.5810	−	25.1615i	1.60315	−	0.925582i	0.990851	−	0.134958i	$-0.0430901\pi$
$740$	−25.6751	+	44.4705i	−0.943834	+	1.63477i
$741$	−5.32810	+	8.63912i	−0.195733	+	0.317366i
$742$	−8.66224	−	11.7447i	−0.318001	−	0.431162i
$743$		−	21.4547i		−	0.787098i	−0.919304	−	0.393549i	$-0.871247\pi$
$743$		−	21.4547i		−	0.787098i	0.919304	−	0.393549i	$-0.128753\pi$
$744$	−2.39485	+	4.14801i	−0.0877995	+	0.152073i
$745$	4.57115	+	7.91747i	0.167474	+	0.290074i
$746$	6.19291	−	3.57548i	0.226738	−	0.130908i
$747$	8.10068	+	4.67693i	0.296388	+	0.171120i
$748$			1.72343i			0.0630147i
$749$	3.30654	+	29.4301i	0.120818	+	1.07535i
$750$	22.9894			0.839455
$751$	13.2217	−	22.9006i	0.482466	−	0.835656i	−0.517331	−	0.855785i	$-0.673074\pi$
$751$	13.2217	−	22.9006i	0.482466	−	0.835656i	0.999797	+	0.0201293i	$0.00640779\pi$
$752$	1.55357	−	0.896956i	0.0566530	−	0.0327086i
$753$	2.96797	+	5.14067i	0.108159	+	0.187336i
$754$	−9.86293	−	18.2898i	−0.359187	−	0.666074i
$755$	64.8851			2.36141
$756$	−3.84215	−	1.67776i	−0.139738	−	0.0610197i
$757$	−19.3762			−0.704240			−0.352120	−	0.935955i	$-0.614539\pi$
$757$	−19.3762			−0.704240			−0.352120	+	0.935955i	$0.614539\pi$
$758$	−4.39604	+	7.61417i	−0.159671	+	0.276559i
$759$	−0.184184	+	0.106339i	−0.00668545	+	0.00385985i
$760$	−24.1151	+	13.9229i	−0.874747	+	0.505036i
$761$	9.01174	+	5.20293i	0.326675	+	0.188606i	0.654364	−	0.756180i	$-0.272936\pi$
$761$	9.01174	+	5.20293i	0.326675	+	0.188606i	−0.327689	+	0.944786i	$0.606270\pi$
$762$		−	6.19804i		−	0.224531i
$763$	2.76735	−	6.33735i	0.100185	−	0.229427i
$764$	11.8557			0.428923
$765$	20.9239	+	12.0804i	0.756506	+	0.436769i
$766$	9.39048	+	16.2648i	0.339292	+	0.587671i
$767$	−17.6176	−	0.511747i	−0.636135	−	0.0184781i
$768$	−3.92587	+	6.79981i	−0.141663	+	0.245367i
$769$			21.8053i			0.786319i	0.919470	+	0.393160i	$0.128618\pi$
$769$			21.8053i			0.786319i	−0.919470	+	0.393160i	$0.871382\pi$
$770$	1.39829	−	0.157101i	0.0503909	−	0.00566153i
$771$	3.17745			0.114433
$772$	−24.8708	−	14.3592i	−0.895121	−	0.516798i
$773$	−35.7653	+	20.6491i	−1.28639	+	0.742697i	−0.978008	−	0.208566i	$-0.933120\pi$
$773$	−35.7653	+	20.6491i	−1.28639	+	0.742697i	−0.308380	+	0.951263i	$0.599787\pi$
$774$	−3.37406	+	1.94802i	−0.121278	+	0.0700200i
$775$	23.9354	+	13.8191i	0.859785	+	0.496397i
$776$	−14.8708			−0.533831
$777$	11.8861	+	16.1158i	0.426412	+	0.578151i
$778$		−	16.2371i		−	0.582128i
$779$	7.43534	−	12.8784i	0.266399	−	0.461416i
$780$	24.4516	+	0.710258i	0.875509	+	0.0254313i
$781$	−0.827973	−	1.43409i	−0.0296272	−	0.0513158i
$782$	−3.47570	−	2.00669i	−0.124291	−	0.0717592i
$783$	−8.94213			−0.319566
$784$	7.99450	+	8.62697i	0.285518	+	0.308106i
$785$			2.71970i			0.0970702i
$786$	−6.88274	−	3.97375i	−0.245499	−	0.141739i
$787$	41.0800	−	23.7176i	1.46435	−	0.845440i	0.465138	−	0.885238i	$-0.346005\pi$
$787$	41.0800	−	23.7176i	1.46435	−	0.845440i	0.999208	+	0.0397981i	$0.0126715\pi$
$788$	8.26501	−	4.77180i	0.294429	−	0.169988i
$789$	−13.4383	+	23.2759i	−0.478417	+	0.828642i
$790$	−10.6023			−0.377214
$791$	−27.9581	+	20.6203i	−0.994076	+	0.733175i
$792$	−0.445266			−0.0158218
$793$	27.4634	−	14.8099i	0.975256	−	0.525915i
$794$	4.52238	+	7.83299i	0.160493	+	0.277983i
$795$	31.7332	−	18.3212i	1.12546	−	0.649784i
$796$	4.24480	−	7.35221i	0.150453	−	0.260592i
$797$	34.2594			1.21353			0.606765	−	0.794881i	$-0.292467\pi$
$797$	34.2594			1.21353			0.606765	+	0.794881i	$0.292467\pi$
$798$	0.535954	+	4.77030i	0.0189726	+	0.168867i
$799$			6.02487i			0.213145i
$800$	65.8479	+	38.0173i	2.32808	+	1.34412i
$801$	0.0247871	−	0.0143109i	0.000875811	−	0.000505650i
$802$	−9.12068	−	15.7975i	−0.322062	−	0.557829i
$803$	−0.112714	+	0.195227i	−0.00397761	+	0.00688942i
$804$			24.0986i			0.849890i
$805$	5.00232	−	11.4555i	0.176308	−	0.403754i
$806$	−4.10053	−	2.52897i	−0.144435	−	0.0890790i
$807$	−1.51184	+	2.61859i	−0.0532194	+	0.0921786i
$808$	−9.63430	+	5.56236i	−0.338933	+	0.195683i
$809$	2.27028	+	3.93224i	0.0798188	+	0.138250i	0.903172	−	0.429280i	$-0.141232\pi$
$809$	2.27028	+	3.93224i	0.0798188	+	0.138250i	−0.823353	+	0.567530i	$0.807899\pi$
$810$	−1.37972	+	2.38974i	−0.0484784	+	0.0839670i
$811$			33.9839i			1.19333i	0.802489	+	0.596667i	$0.203509\pi$
$811$			33.9839i			1.19333i	−0.802489	+	0.596667i	$0.796491\pi$
$812$	34.3570	+	15.0028i	1.20570	+	0.526494i
$813$		−	23.9018i		−	0.838274i
$814$	0.814198	+	0.470077i	0.0285376	+	0.0164762i
$815$	16.9986	+	29.4425i	0.595437	+	1.03133i
$816$	4.74087	+	8.21142i	0.165963	+	0.287457i
$817$	−14.7375	−	8.50869i	−0.515600	−	0.297682i
$818$	3.79584			0.132719
$819$	4.06972	−	8.62771i	0.142207	−	0.301477i
$820$	−35.8389			−1.25155
$821$	32.4170	+	18.7159i	1.13136	+	0.653191i	0.944277	−	0.329153i	$-0.106763\pi$
$821$	32.4170	+	18.7159i	1.13136	+	0.653191i	0.187084	+	0.982344i	$0.440097\pi$
$822$	0.357034	+	0.618402i	0.0124530	+	0.0215692i
$823$	−14.0565	−	24.3466i	−0.489979	−	0.848669i	0.509954	−	0.860202i	$-0.329662\pi$
$823$	−14.0565	−	24.3466i	−0.489979	−	0.848669i	−0.999933	+	0.0115324i	$0.996329\pi$
$824$	−22.4227	−	12.9457i	−0.781130	−	0.450986i
$825$			2.56934i			0.0894529i
$826$	−6.70831	+	4.94768i	−0.233412	+	0.172152i
$827$		−	24.0959i		−	0.837895i	−0.908010	−	0.418948i	$-0.862399\pi$
$827$		−	24.0959i		−	0.837895i	0.908010	−	0.418948i	$-0.137601\pi$
$828$	−0.874304	+	1.51434i	−0.0303842	+	0.0526269i
$829$	−22.2586	−	38.5530i	−0.773072	−	1.33900i	−0.935872	−	0.352341i	$-0.885386\pi$
$829$	−22.2586	−	38.5530i	−0.773072	−	1.33900i	0.162800	−	0.986659i	$-0.447947\pi$
$830$	−22.3533	+	12.9057i	−0.775895	+	0.447963i
$831$	7.32155	−	12.6813i	0.253982	−	0.439909i
$832$	−0.968092	−	0.597062i	−0.0335626	−	0.0206994i
$833$	−38.5168	+	8.76555i	−1.33453	+	0.303708i
$834$			5.02302i			0.173933i
$835$	32.2340	−	55.8310i	1.11550	−	1.93211i
$836$	−0.429874	−	0.744564i	−0.0148675	−	0.0257513i
$837$	−1.79544	+	1.03660i	−0.0620596	+	0.0358301i
$838$	8.84829	+	5.10856i	0.305659	+	0.176472i
$839$			47.9803i			1.65647i	0.560384	+	0.828233i	$0.310653\pi$
$839$			47.9803i			1.65647i	−0.560384	+	0.828233i	$0.689347\pi$
$840$	21.0617	−	15.5339i	0.726696	−	0.535971i
$841$	50.9617			1.75730
$842$	6.12049	−	10.6010i	0.210926	−	0.365334i
$843$	−7.97617	+	4.60504i	−0.274714	+	0.158606i
$844$	13.0299	+	22.5685i	0.448508	+	0.776839i
$845$	−3.23080	+	55.5656i	−0.111143	+	1.91151i
$846$	−0.688106			−0.0236576
$847$	−3.23840	−	28.8236i	−0.111273	−	0.990392i
$848$	14.3800			0.493810
$849$	−2.67334	+	4.63037i	−0.0917489	+	0.158914i
$850$	−41.9896	+	24.2427i	−1.44023	+	0.831519i
$851$	7.23305	−	4.17600i	0.247946	−	0.143152i
$852$	−11.7910	−	6.80751i	−0.403951	−	0.233221i
$853$		−	45.2649i		−	1.54984i	−0.632058	−	0.774921i	$-0.717790\pi$
$853$		−	45.2649i		−	1.54984i	0.632058	−	0.774921i	$-0.282210\pi$
$854$	5.90534	−	13.5235i	0.202077	−	0.462765i
$855$	−12.0529			−0.412200
$856$	22.3957	+	12.9302i	0.765470	+	0.441944i
$857$	3.14719	+	5.45109i	0.107506	+	0.186206i	0.914759	−	0.403999i	$-0.132380\pi$
$857$	3.14719	+	5.45109i	0.107506	+	0.186206i	−0.807253	+	0.590205i	$0.799047\pi$
$858$	0.0130039	−	0.447678i	0.000443946	−	0.0152835i
$859$	4.35048	−	7.53525i	0.148436	−	0.257100i	−0.782213	−	0.623011i	$-0.785909\pi$
$859$	4.35048	−	7.53525i	0.148436	−	0.257100i	0.930650	+	0.365911i	$0.119243\pi$
$860$			41.0125i			1.39852i
$861$	−5.59297	+	12.8081i	−0.190608	+	0.436500i
$862$	−12.9896			−0.442428
$863$	−30.2077	−	17.4404i	−1.02828	−	0.593678i	−0.111789	−	0.993732i	$-0.535658\pi$
$863$	−30.2077	−	17.4404i	−1.02828	−	0.593678i	−0.916492	+	0.400054i	$0.868991\pi$
$864$	−4.93939	+	2.85176i	−0.168041	+	0.0970187i
$865$	−8.30023	+	4.79214i	−0.282216	+	0.162938i
$866$	0.814536	+	0.470273i	0.0276791	+	0.0159805i
$867$	−14.8445			−0.504145
$868$	8.63754	−	0.970447i	0.293177	−	0.0329391i
$869$		−	0.740513i		−	0.0251202i
$870$	12.3376	−	21.3694i	0.418285	−	0.724490i
$871$	−54.8095	−	1.59208i	−1.85715	−	0.0539454i
$872$	−3.01922	−	5.22944i	−0.102244	−	0.177091i
$873$	−5.57439	−	3.21837i	−0.188664	−	0.108925i
$874$	2.00212			0.0677226
$875$	−56.0171	−	75.9508i	−1.89372	−	2.56760i
$876$			1.85345i			0.0626224i
$877$	32.5892	+	18.8154i	1.10046	+	0.635351i	0.936342	−	0.351090i	$-0.114189\pi$
$877$	32.5892	+	18.8154i	1.10046	+	0.635351i	0.164118	+	0.986441i	$0.447522\pi$
$878$	7.46369	−	4.30916i	0.251887	−	0.145427i
$879$	−15.5814	+	8.99592i	−0.525547	+	0.303425i
$880$	−0.693247	+	1.20074i	−0.0233693	+	0.0404769i
$881$	−24.9268			−0.839804			−0.419902	−	0.907569i	$-0.637936\pi$
$881$	−24.9268			−0.839804			−0.419902	+	0.907569i	$0.637936\pi$
$882$	−1.00112	−	4.39905i	−0.0337095	−	0.148124i
$883$	54.9685			1.84984			0.924918	−	0.380166i	$-0.124133\pi$
$883$	54.9685			1.84984			0.924918	+	0.380166i	$0.124133\pi$
$884$	−28.3781	+	15.3031i	−0.954458	+	0.514700i
$885$	−10.4646	−	18.1253i	−0.351765	−	0.609275i
$886$	17.0237	−	9.82862i	0.571921	−	0.330199i
$887$	−12.9288	+	22.3933i	−0.434106	+	0.751894i	−0.997222	−	0.0744836i	$-0.976269\pi$
$887$	−12.9288	+	22.3933i	−0.434106	+	0.751894i	0.563116	+	0.826378i	$0.309602\pi$
$888$	17.4860			0.586791
$889$	−20.4766	+	15.1024i	−0.686765	+	0.506519i
$890$			0.0789799i			0.00264741i
$891$	−0.166910	−	0.0963656i	−0.00559170	−	0.00322837i
$892$	−11.3718	+	6.56553i	−0.380757	+	0.219830i
$893$	−1.50278	−	2.60290i	−0.0502887	−	0.0871026i
$894$	0.688106	−	1.19184i	0.0230137	−	0.0398609i
$895$			9.54659i			0.319107i
$896$	29.4569	−	3.30955i	0.984086	−	0.110564i
$897$	−3.38644	−	2.08855i	−0.113070	−	0.0697348i
$898$	1.41419	−	2.44946i	0.0471923	−	0.0817394i
$899$	16.0551	−	9.26941i	0.535467	−	0.309152i
$900$	10.5624	+	18.2946i	0.352080	+	0.609821i
$901$	−24.1476	+	41.8249i	−0.804474	+	1.39339i
$902$			0.656164i			0.0218479i
$903$	14.6571	+	6.40036i	0.487758	+	0.212991i
$904$			30.3352i			1.00893i
$905$	−55.5706	−	32.0837i	−1.84723	−	1.06650i
$906$	−4.88365	−	8.45874i	−0.162249	−	0.281023i
$907$	8.59164	+	14.8811i	0.285281	+	0.494120i	0.972677	−	0.232162i	$-0.0745799\pi$
$907$	8.59164	+	14.8811i	0.285281	+	0.494120i	−0.687397	+	0.726282i	$0.741247\pi$
$908$	−0.407206	−	0.235101i	−0.0135136	−	0.00780209i
$909$	−4.81528			−0.159713
$910$	15.0029	+	21.6294i	0.497343	+	0.717008i
$911$	−6.41300			−0.212472			−0.106236	−	0.994341i	$-0.533880\pi$
$911$	−6.41300			−0.212472			−0.106236	+	0.994341i	$0.533880\pi$
$912$	−4.09635	−	2.36503i	−0.135644	−	0.0783139i
$913$	−0.901390	−	1.56125i	−0.0298317	−	0.0516700i
$914$	5.91575	+	10.2464i	0.195676	+	0.338920i
$915$	32.0877	+	18.5259i	1.06079	+	0.612446i
$916$			10.3573i			0.342215i
$917$	3.64261	+	32.4213i	0.120289	+	1.07065i
$918$		−	3.63699i		−	0.120039i
$919$	11.3628	−	19.6809i	0.374823	−	0.649213i	−0.615477	−	0.788154i	$-0.711037\pi$
$919$	11.3628	−	19.6809i	0.374823	−	0.649213i	0.990301	+	0.138942i	$0.0443701\pi$
$920$	−5.45760	−	9.45285i	−0.179932	−	0.311651i
$921$	−12.4089	+	7.16431i	−0.408888	+	0.236072i
$922$	−10.2847	+	17.8137i	−0.338710	+	0.586663i
$923$	16.2619	−	26.3675i	0.535267	−	0.867896i
$924$	0.479616	+	0.650287i	0.0157782	+	0.0213929i
$925$		−	100.900i		−	3.31757i
$926$	2.74010	−	4.74599i	0.0900451	−	0.155963i
$927$	−5.60349	−	9.70553i	−0.184043	−	0.318771i
$928$	44.1686	−	25.5008i	1.44991	−	0.837104i
$929$	17.4910	+	10.0984i	0.573860	+	0.331318i	0.758690	−	0.651452i	$-0.225840\pi$
$929$	17.4910	+	10.0984i	0.573860	+	0.331318i	−0.184830	+	0.982771i	$0.559173\pi$
$930$		−	5.72086i		−	0.187594i
$931$	14.4538	−	13.3942i	0.473706	−	0.438977i
$932$	12.2197			0.400270
$933$	7.20490	−	12.4792i	0.235878	−	0.408552i
$934$	−7.10336	+	4.10112i	−0.232429	+	0.134193i
$935$	−2.32828	−	4.03269i	−0.0761428	−	0.131883i
$936$	−3.95373	−	7.33179i	−0.129232	−	0.239647i
$937$	37.9736			1.24054			0.620272	−	0.784387i	$-0.287022\pi$
$937$	37.9736			1.24054			0.620272	+	0.784387i	$0.287022\pi$
$938$	−20.8700	+	15.3925i	−0.681428	+	0.502584i
$939$	4.46303			0.145646
$940$	−3.62176	+	6.27307i	−0.118129	+	0.204605i
$941$	−1.64382	+	0.949060i	−0.0535870	+	0.0309385i	−0.526554	−	0.850142i	$-0.676516\pi$
$941$	−1.64382	+	0.949060i	−0.0535870	+	0.0309385i	0.472967	+	0.881080i	$0.343183\pi$
$942$	0.354553	−	0.204701i	0.0115520	−	0.00666953i
$943$	5.04818	+	2.91457i	0.164391	+	0.0949114i
$944$		−	8.21352i		−	0.267327i
$945$	11.2569	−	1.26474i	0.366188	−	0.0411421i
$946$	0.750887			0.0244134
$947$	20.1070	+	11.6088i	0.653389	+	0.377234i	0.789754	−	0.613424i	$-0.210208\pi$
$947$	20.1070	+	11.6088i	0.653389	+	0.377234i	−0.136364	+	0.990659i	$0.543542\pi$
$948$	−3.04421	−	5.27272i	−0.0988713	−	0.171250i
$949$	−4.21547	−	0.122449i	−0.136840	−	0.00397485i
$950$	12.0937	−	20.9469i	0.392372	−	0.679608i
$951$		−	5.07237i		−	0.164483i
$952$	−13.8036	+	31.6108i	−0.447377	+	1.02451i
$953$	−39.5254			−1.28035			−0.640176	−	0.768228i	$-0.721139\pi$
$953$	−39.5254			−1.28035			−0.640176	+	0.768228i	$0.721139\pi$
$954$	−4.77687	−	2.75793i	−0.154657	−	0.0892912i
$955$	−27.7414	+	16.0165i	−0.897690	+	0.518282i
$956$	4.99057	−	2.88131i	0.161407	−	0.0931881i
$957$	1.49253	+	0.861714i	0.0482467	+	0.0278552i
$958$	2.21232			0.0714769
$959$	1.17306	−	2.68637i	0.0378802	−	0.0867474i
$960$		−	1.35064i		−	0.0435916i
$961$	−13.3509	+	23.1245i	−0.430675	+	0.745951i
$962$	−0.510674	+	17.5807i	−0.0164648	+	0.566824i
$963$	5.59676	+	9.69387i	0.180353	+	0.312381i
$964$	−7.42036	−	4.28414i	−0.238994	−	0.137983i
$965$	77.5946			2.49786
$966$	−1.86990	+	0.210088i	−0.0601631	+	0.00675947i
$967$		−	30.9135i		−	0.994111i	−0.867719	−	0.497055i	$-0.834415\pi$
$967$		−	30.9135i		−	0.994111i	0.867719	−	0.497055i	$-0.165585\pi$
$968$	−21.9342	−	12.6637i	−0.704992	−	0.407027i
$969$	13.7576	−	7.94297i	0.441958	−	0.255165i
$970$	15.3822	−	8.88090i	0.493892	−	0.285149i
$971$	−8.47382	+	14.6771i	−0.271938	+	0.471010i	−0.969358	−	0.245652i	$-0.920998\pi$
$971$	−8.47382	+	14.6771i	−0.271938	+	0.471010i	0.697420	+	0.716663i	$0.254331\pi$
$972$	−1.58462			−0.0508266
$973$	16.5947	−	12.2393i	0.532001	−	0.392374i
$974$	25.7517			0.825139
$975$	−42.3069	+	22.8144i	−1.35491	+	0.730645i
$976$	7.27032	+	12.5926i	0.232717	+	0.403078i
$977$	35.5892	−	20.5474i	1.13860	−	0.657371i	0.192517	−	0.981294i	$-0.438335\pi$
$977$	35.5892	−	20.5474i	1.13860	−	0.657371i	0.946084	+	0.323923i	$0.105002\pi$
$978$	2.55885	−	4.43205i	0.0818229	−	0.141721i
$979$	−0.00551630			−0.000176302
$980$	−45.3729	−	14.0272i	−1.44938	−	0.448081i
$981$		−	2.61370i		−	0.0834492i
$982$	−18.4595	−	10.6576i	−0.589065	−	0.340097i
$983$	24.5823	−	14.1926i	0.784055	−	0.452674i	−0.0538106	−	0.998551i	$-0.517137\pi$
$983$	24.5823	−	14.1926i	0.784055	−	0.452674i	0.837865	+	0.545877i	$0.183803\pi$
$984$	6.10201	+	10.5690i	0.194525	+	0.336927i
$985$	−12.8930	+	22.3313i	−0.410805	+	0.711536i
$986$			32.5224i			1.03573i
$987$	1.67667	+	2.27332i	0.0533690	+	0.0723604i
$988$	8.44299	−	13.6897i	0.268607	−	0.435527i
$989$	3.33531	−	5.77693i	0.106057	−	0.183696i
$990$	0.460578	−	0.265915i	0.0146381	−	0.00845133i
$991$	22.1694	+	38.3985i	0.704233	+	1.21977i	0.966968	+	0.254900i	$0.0820424\pi$
$991$	22.1694	+	38.3985i	0.704233	+	1.21977i	−0.262734	+	0.964868i	$0.584624\pi$
$992$	5.91226	−	10.2403i	0.187714	−	0.325131i
$993$			23.6954i			0.751952i
$994$	−1.63579	−	14.5594i	−0.0518840	−	0.461797i
$995$			22.9382i			0.727189i
$996$	−12.8365	−	7.41114i	−0.406739	−	0.234831i
$997$	−19.7068	−	34.1332i	−0.624121	−	1.08101i	−0.988710	−	0.149841i	$-0.952124\pi$
$997$	−19.7068	−	34.1332i	−0.624121	−	1.08101i	0.364589	−	0.931169i	$-0.381210\pi$
$998$	6.03062	+	10.4453i	0.190896	+	0.330642i
$999$	6.55470	+	3.78436i	0.207382	+	0.119732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.d.142.3	yes	16
3.2	odd	2		819.2.dl.g.415.6		16
7.2	even	3		1911.2.c.j.883.6		8
7.4	even	3	inner	273.2.bj.d.25.6	yes	16
7.5	odd	6		1911.2.c.m.883.6		8
13.12	even	2	inner	273.2.bj.d.142.6	yes	16
21.11	odd	6		819.2.dl.g.298.3		16
39.38	odd	2		819.2.dl.g.415.3		16
91.12	odd	6		1911.2.c.m.883.3		8
91.25	even	6	inner	273.2.bj.d.25.3	✓	16
91.51	even	6		1911.2.c.j.883.3		8
273.116	odd	6		819.2.dl.g.298.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.d.25.3	✓	16	91.25	even	6	inner
273.2.bj.d.25.6	yes	16	7.4	even	3	inner
273.2.bj.d.142.3	yes	16	1.1	even	1	trivial
273.2.bj.d.142.6	yes	16	13.12	even	2	inner
819.2.dl.g.298.3		16	21.11	odd	6
819.2.dl.g.298.6		16	273.116	odd	6
819.2.dl.g.415.3		16	39.38	odd	2
819.2.dl.g.415.6		16	3.2	odd	2
1911.2.c.j.883.3		8	91.51	even	6
1911.2.c.j.883.6		8	7.2	even	3
1911.2.c.m.883.3		8	91.12	odd	6
1911.2.c.m.883.6		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.558156 - 0.322252i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.792308 - 1.37232i) q^{4} +(3.70788 + 2.14075i) q^{5} -0.644503i q^{6} +(-2.12926 + 1.57043i) q^{7} +2.31030i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.558156 - 0.322252i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.792308 - 1.37232i) q^{4} +(3.70788 + 2.14075i) q^{5} -0.644503i q^{6} +(-2.12926 + 1.57043i) q^{7} +2.31030i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.37972 - 2.38974i) q^{10} +(0.166910 - 0.0963656i) q^{11} +(0.792308 - 1.37232i) q^{12} +(3.06884 + 1.89268i) q^{13} +(1.69453 - 0.190385i) q^{14} +4.28149i q^{15} +(-0.840118 + 1.45513i) q^{16} +(-2.82155 - 4.88706i) q^{17} +(0.558156 - 0.322252i) q^{18} +(2.43796 + 1.40756i) q^{19} -6.78452i q^{20} +(-2.42466 - 1.05878i) q^{21} -0.124216 q^{22} +(-0.551746 + 0.955651i) q^{23} +(-2.00078 + 1.15515i) q^{24} +(6.66560 + 11.5452i) q^{25} +(-1.10297 - 2.04535i) q^{26} -1.00000 q^{27} +(3.84215 + 1.67776i) q^{28} +8.94213 q^{29} +(1.37972 - 2.38974i) q^{30} +(1.79544 - 1.03660i) q^{31} +(4.93939 - 2.85176i) q^{32} +(0.166910 + 0.0963656i) q^{33} +3.63699i q^{34} +(-11.2569 + 1.26474i) q^{35} +1.58462 q^{36} +(-6.55470 - 3.78436i) q^{37} +(-0.907174 - 1.57127i) q^{38} +(-0.104688 + 3.60403i) q^{39} +(-4.94576 + 8.56631i) q^{40} -5.28245i q^{41} +(1.01215 + 1.37232i) q^{42} -6.04501 q^{43} +(-0.264488 - 0.152702i) q^{44} +(-3.70788 + 2.14075i) q^{45} +(0.615920 - 0.355602i) q^{46} +(-0.924615 - 0.533827i) q^{47} -1.68024 q^{48} +(2.06752 - 6.68770i) q^{49} -8.59200i q^{50} +(2.82155 - 4.88706i) q^{51} +(0.165890 - 5.71100i) q^{52} +(-4.27915 - 7.41170i) q^{53} +(0.558156 + 0.322252i) q^{54} +0.825178 q^{55} +(-3.62815 - 4.91923i) q^{56} +2.81511i q^{57} +(-4.99111 - 2.88162i) q^{58} +(-4.23340 + 2.44416i) q^{59} +(5.87557 - 3.39226i) q^{60} +(4.32696 - 7.49451i) q^{61} -1.33618 q^{62} +(-0.295398 - 2.62921i) q^{63} -0.315459 q^{64} +(7.32715 + 13.5874i) q^{65} +(-0.0621080 - 0.107574i) q^{66} +(-13.1704 + 7.60391i) q^{67} +(-4.47106 + 7.74411i) q^{68} -1.10349 q^{69} +(6.69070 + 2.92165i) q^{70} -8.59200i q^{71} +(-2.00078 - 1.15515i) q^{72} +(-1.01295 + 0.584827i) q^{73} +(2.43903 + 4.22453i) q^{74} +(-6.66560 + 11.5452i) q^{75} -4.46087i q^{76} +(-0.204060 + 0.467308i) q^{77} +(1.21984 - 1.97788i) q^{78} +(1.92110 - 3.32745i) q^{79} +(-6.23012 + 3.59696i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.70228 + 2.94843i) q^{82} -9.35386i q^{83} +(0.468092 + 4.16629i) q^{84} -24.1609i q^{85} +(3.37406 + 1.94802i) q^{86} +(4.47106 + 7.74411i) q^{87} +(0.222633 + 0.385612i) q^{88} +(-0.0247871 - 0.0143109i) q^{89} +2.75944 q^{90} +(-9.50668 + 0.789375i) q^{91} +1.74861 q^{92} +(1.79544 + 1.03660i) q^{93} +(0.344053 + 0.595918i) q^{94} +(6.02644 + 10.4381i) q^{95} +(4.93939 + 2.85176i) q^{96} +6.43675i q^{97} +(-3.30912 + 3.06652i) q^{98} +0.192731i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

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