LMFDB - Embedded newform 273.2.j.c.172.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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, 2, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (of order $3$, 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 $\Q(\zeta_{3})$
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} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.2
Root			$1.14017 + 1.97483i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.c.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14017 + 1.97483i) q^{2} +1.00000 q^{3} +(-1.59997 - 2.77124i) q^{4} +(-1.46862 - 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(-2.34076 + 1.23322i) q^{7} +2.73629 q^{8} +1.00000 q^{9} +6.69792 q^{10} -5.16954 q^{11} +(-1.59997 - 2.77124i) q^{12} +(-0.364757 - 3.58705i) q^{13} +(0.233457 - 6.02869i) q^{14} +(-1.46862 - 2.54373i) q^{15} +(0.0801172 - 0.138767i) q^{16} +(-2.52646 - 4.37595i) q^{17} +(-1.14017 + 1.97483i) q^{18} +2.25859 q^{19} +(-4.69952 + 8.13980i) q^{20} +(-2.34076 + 1.23322i) q^{21} +(5.89416 - 10.2090i) q^{22} +(-2.61602 + 4.53108i) q^{23} +2.73629 q^{24} +(-1.81371 + 3.14143i) q^{25} +(7.49971 + 3.36952i) q^{26} +1.00000 q^{27} +(7.16271 + 4.51367i) q^{28} +(0.216901 + 0.375683i) q^{29} +6.69792 q^{30} +(-1.34122 + 2.32306i) q^{31} +(2.91898 + 5.05582i) q^{32} -5.16954 q^{33} +11.5224 q^{34} +(6.57468 + 4.14312i) q^{35} +(-1.59997 - 2.77124i) q^{36} +(2.12386 - 3.67863i) q^{37} +(-2.57517 + 4.46033i) q^{38} +(-0.364757 - 3.58705i) q^{39} +(-4.01857 - 6.96037i) q^{40} +(0.269622 + 0.466999i) q^{41} +(0.233457 - 6.02869i) q^{42} +(-4.66348 + 8.07739i) q^{43} +(8.27113 + 14.3260i) q^{44} +(-1.46862 - 2.54373i) q^{45} +(-5.96541 - 10.3324i) q^{46} +(-4.87054 - 8.43603i) q^{47} +(0.0801172 - 0.138767i) q^{48} +(3.95832 - 5.77336i) q^{49} +(-4.13587 - 7.16354i) q^{50} +(-2.52646 - 4.37595i) q^{51} +(-9.35697 + 6.75002i) q^{52} +(0.377571 - 0.653972i) q^{53} +(-1.14017 + 1.97483i) q^{54} +(7.59211 + 13.1499i) q^{55} +(-6.40499 + 3.37445i) q^{56} +2.25859 q^{57} -0.989214 q^{58} +(1.82385 + 3.15901i) q^{59} +(-4.69952 + 8.13980i) q^{60} +6.95468 q^{61} +(-3.05843 - 5.29736i) q^{62} +(-2.34076 + 1.23322i) q^{63} -12.9921 q^{64} +(-8.58881 + 6.19587i) q^{65} +(5.89416 - 10.2090i) q^{66} -13.3602 q^{67} +(-8.08453 + 14.0028i) q^{68} +(-2.61602 + 4.53108i) q^{69} +(-15.6782 + 8.26003i) q^{70} +(3.90487 - 6.76343i) q^{71} +2.73629 q^{72} +(-7.94401 + 13.7594i) q^{73} +(4.84312 + 8.38853i) q^{74} +(-1.81371 + 3.14143i) q^{75} +(-3.61368 - 6.25908i) q^{76} +(12.1007 - 6.37520i) q^{77} +(7.49971 + 3.36952i) q^{78} +(-7.79235 - 13.4967i) q^{79} -0.470648 q^{80} +1.00000 q^{81} -1.22966 q^{82} +13.2349 q^{83} +(7.16271 + 4.51367i) q^{84} +(-7.42083 + 12.8532i) q^{85} +(-10.6343 - 18.4192i) q^{86} +(0.216901 + 0.375683i) q^{87} -14.1453 q^{88} +(2.00143 - 3.46658i) q^{89} +6.69792 q^{90} +(5.27744 + 7.94661i) q^{91} +16.7423 q^{92} +(-1.34122 + 2.32306i) q^{93} +22.2130 q^{94} +(-3.31701 - 5.74523i) q^{95} +(2.91898 + 5.05582i) q^{96} +(2.69653 - 4.67053i) q^{97} +(6.88826 + 14.3996i) q^{98} -5.16954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.14017	+	1.97483i	−0.806222	+	1.39642i	0.109242	+	0.994015i	$0.465158\pi$
$2$	−1.14017	+	1.97483i	−0.806222	+	1.39642i	−0.915463	+	0.402402i	$0.868176\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.59997	−	2.77124i	−0.799987	−	1.38562i
$5$	−1.46862	−	2.54373i	−0.656788	−	1.13759i	−0.981442	−	0.191758i	$-0.938581\pi$
$5$	−1.46862	−	2.54373i	−0.656788	−	1.13759i	0.324654	−	0.945833i	$-0.394752\pi$
$6$	−1.14017	+	1.97483i	−0.465472	+	0.806222i
$7$	−2.34076	+	1.23322i	−0.884724	+	0.466114i
$7$	−2.34076	+	1.23322i	−0.884724	+	0.466114i
$8$	2.73629			0.967423
$9$	1.00000			0.333333
$10$	6.69792			2.11807
$11$	−5.16954			−1.55868			−0.779338	−	0.626604i	$-0.784444\pi$
$11$	−5.16954			−1.55868			−0.779338	+	0.626604i	$0.784444\pi$
$12$	−1.59997	−	2.77124i	−0.461873	−	0.799987i
$13$	−0.364757	−	3.58705i	−0.101165	−	0.994870i
$13$	−0.364757	−	3.58705i	−0.101165	−	0.994870i
$14$	0.233457	−	6.02869i	0.0623939	−	1.61124i
$15$	−1.46862	−	2.54373i	−0.379197	−	0.656788i
$16$	0.0801172	−	0.138767i	0.0200293	−	0.0346918i
$17$	−2.52646	−	4.37595i	−0.612756	−	1.06132i	−0.990774	−	0.135526i	$-0.956728\pi$
$17$	−2.52646	−	4.37595i	−0.612756	−	1.06132i	0.378018	−	0.925798i	$-0.376606\pi$
$18$	−1.14017	+	1.97483i	−0.268741	+	0.465472i
$19$	2.25859			0.518155			0.259078	−	0.965856i	$-0.416581\pi$
$19$	2.25859			0.518155			0.259078	+	0.965856i	$0.416581\pi$
$20$	−4.69952	+	8.13980i	−1.05084	+	1.82011i
$21$	−2.34076	+	1.23322i	−0.510796	+	0.269111i
$22$	5.89416	−	10.2090i	1.25664	−	2.17656i
$23$	−2.61602	+	4.53108i	−0.545478	+	0.944796i	0.453099	+	0.891460i	$0.350319\pi$
$23$	−2.61602	+	4.53108i	−0.545478	+	0.944796i	−0.998577	+	0.0533353i	$0.983015\pi$
$24$	2.73629			0.558542
$25$	−1.81371	+	3.14143i	−0.362742	+	0.628287i
$26$	7.49971	+	3.36952i	1.47081	+	0.660817i
$27$	1.00000			0.192450
$28$	7.16271	+	4.51367i	1.35362	+	0.853004i
$29$	0.216901	+	0.375683i	0.0402775	+	0.0697626i	0.885461	−	0.464713i	$-0.153842\pi$
$29$	0.216901	+	0.375683i	0.0402775	+	0.0697626i	−0.845184	+	0.534476i	$0.820509\pi$
$30$	6.69792			1.22287
$31$	−1.34122	+	2.32306i	−0.240890	+	0.417234i	−0.960968	−	0.276659i	$-0.910773\pi$
$31$	−1.34122	+	2.32306i	−0.240890	+	0.417234i	0.720078	+	0.693893i	$0.244106\pi$
$32$	2.91898	+	5.05582i	0.516008	+	0.893751i
$33$	−5.16954			−0.899902
$34$	11.5224			1.97607
$35$	6.57468	+	4.14312i	1.11132	+	0.700316i
$36$	−1.59997	−	2.77124i	−0.266662	−	0.461873i
$37$	2.12386	−	3.67863i	0.349160	−	0.604764i	−0.636940	−	0.770913i	$-0.719800\pi$
$37$	2.12386	−	3.67863i	0.349160	−	0.604764i	0.986101	+	0.166150i	$0.0531335\pi$
$38$	−2.57517	+	4.46033i	−0.417748	+	0.723561i
$39$	−0.364757	−	3.58705i	−0.0584078	−	0.574388i
$40$	−4.01857	−	6.96037i	−0.635392	−	1.10053i
$41$	0.269622	+	0.466999i	0.0421079	+	0.0729330i	0.886311	−	0.463090i	$-0.153259\pi$
$41$	0.269622	+	0.466999i	0.0421079	+	0.0729330i	−0.844203	+	0.536023i	$0.819926\pi$
$42$	0.233457	−	6.02869i	0.0360231	−	0.930247i
$43$	−4.66348	+	8.07739i	−0.711175	+	1.23179i	0.253242	+	0.967403i	$0.418503\pi$
$43$	−4.66348	+	8.07739i	−0.711175	+	1.23179i	−0.964416	+	0.264388i	$0.914830\pi$
$44$	8.27113	+	14.3260i	1.24692	+	2.15973i
$45$	−1.46862	−	2.54373i	−0.218929	−	0.379197i
$46$	−5.96541	−	10.3324i	−0.879552	−	1.52343i
$47$	−4.87054	−	8.43603i	−0.710442	−	1.23052i	−0.964691	−	0.263383i	$-0.915162\pi$
$47$	−4.87054	−	8.43603i	−0.710442	−	1.23052i	0.254250	−	0.967139i	$-0.418172\pi$
$48$	0.0801172	−	0.138767i	0.0115639	−	0.0200293i
$49$	3.95832	−	5.77336i	0.565475	−	0.824766i
$50$	−4.13587	−	7.16354i	−0.584900	−	1.01308i
$51$	−2.52646	−	4.37595i	−0.353775	−	0.612756i
$52$	−9.35697	+	6.75002i	−1.29758	+	0.936059i
$53$	0.377571	−	0.653972i	0.0518634	−	0.0898300i	−0.838928	−	0.544242i	$-0.816817\pi$
$53$	0.377571	−	0.653972i	0.0518634	−	0.0898300i	0.890792	+	0.454412i	$0.150151\pi$
$54$	−1.14017	+	1.97483i	−0.155157	+	0.268741i
$55$	7.59211	+	13.1499i	1.02372	+	1.77313i
$56$	−6.40499	+	3.37445i	−0.855903	+	0.450930i
$57$	2.25859			0.299157
$58$	−0.989214			−0.129890
$59$	1.82385	+	3.15901i	0.237445	+	0.411267i	0.959981	−	0.280067i	$-0.0903566\pi$
$59$	1.82385	+	3.15901i	0.237445	+	0.411267i	−0.722535	+	0.691334i	$0.757023\pi$
$60$	−4.69952	+	8.13980i	−0.606705	+	1.05084i
$61$	6.95468			0.890455			0.445228	−	0.895417i	$-0.353123\pi$
$61$	6.95468			0.890455			0.445228	+	0.895417i	$0.353123\pi$
$62$	−3.05843	−	5.29736i	−0.388422	−	0.672766i
$63$	−2.34076	+	1.23322i	−0.294908	+	0.155371i
$64$	−12.9921			−1.62401
$65$	−8.58881	+	6.19587i	−1.06531	+	0.768503i
$66$	5.89416	−	10.2090i	0.725520	−	1.25664i
$67$	−13.3602			−1.63221			−0.816107	−	0.577901i	$-0.803872\pi$
$67$	−13.3602			−1.63221			−0.816107	+	0.577901i	$0.803872\pi$
$68$	−8.08453	+	14.0028i	−0.980393	+	1.69809i
$69$	−2.61602	+	4.53108i	−0.314932	+	0.545478i
$70$	−15.6782	+	8.26003i	−1.87391	+	0.987262i
$71$	3.90487	−	6.76343i	0.463423	−	0.802672i	−0.535706	−	0.844404i	$-0.679955\pi$
$71$	3.90487	−	6.76343i	0.463423	−	0.802672i	0.999129	+	0.0417329i	$0.0132879\pi$
$72$	2.73629			0.322474
$73$	−7.94401	+	13.7594i	−0.929776	+	1.61042i	−0.146083	+	0.989272i	$0.546667\pi$
$73$	−7.94401	+	13.7594i	−0.929776	+	1.61042i	−0.783694	+	0.621147i	$0.786667\pi$
$74$	4.84312	+	8.38853i	0.563001	+	0.975147i
$75$	−1.81371	+	3.14143i	−0.209429	+	0.362742i
$76$	−3.61368	−	6.25908i	−0.414517	−	0.717965i
$77$	12.1007	−	6.37520i	1.37900	−	0.726521i
$78$	7.49971	+	3.36952i	0.849175	+	0.381523i
$79$	−7.79235	−	13.4967i	−0.876708	−	1.51850i	−0.854932	−	0.518740i	$-0.826401\pi$
$79$	−7.79235	−	13.4967i	−0.876708	−	1.51850i	−0.0217756	−	0.999763i	$-0.506932\pi$
$80$	−0.470648			−0.0526200
$81$	1.00000			0.111111
$82$	−1.22966			−0.135793
$83$	13.2349			1.45272			0.726360	−	0.687315i	$-0.241211\pi$
$83$	13.2349			1.45272			0.726360	+	0.687315i	$0.241211\pi$
$84$	7.16271	+	4.51367i	0.781515	+	0.492482i
$85$	−7.42083	+	12.8532i	−0.804902	+	1.39413i
$86$	−10.6343	−	18.4192i	−1.14673	−	1.98619i
$87$	0.216901	+	0.375683i	0.0232542	+	0.0402775i
$88$	−14.1453			−1.50790
$89$	2.00143	−	3.46658i	0.212151	−	0.367457i	−0.740236	−	0.672347i	$-0.765286\pi$
$89$	2.00143	−	3.46658i	0.212151	−	0.367457i	0.952388	+	0.304890i	$0.0986197\pi$
$90$	6.69792			0.706023
$91$	5.27744	+	7.94661i	0.553227	+	0.833031i
$92$	16.7423			1.74550
$93$	−1.34122	+	2.32306i	−0.139078	+	0.240890i
$94$	22.2130			2.29109
$95$	−3.31701	−	5.74523i	−0.340318	−	0.589449i
$96$	2.91898	+	5.05582i	0.297917	+	0.516008i
$97$	2.69653	−	4.67053i	0.273791	−	0.474220i	−0.696038	−	0.718005i	$-0.745056\pi$
$97$	2.69653	−	4.67053i	0.273791	−	0.474220i	0.969829	+	0.243784i	$0.0783889\pi$
$98$	6.88826	+	14.3996i	0.695819	+	1.45458i
$99$	−5.16954			−0.519559
$100$	11.6075			1.16075
$101$	−3.15240			−0.313676			−0.156838	−	0.987624i	$-0.550130\pi$
$101$	−3.15240			−0.313676			−0.156838	+	0.987624i	$0.550130\pi$
$102$	11.5224			1.14088
$103$	−6.59727	−	11.4268i	−0.650048	−	1.12592i	−0.983111	−	0.183012i	$-0.941415\pi$
$103$	−6.59727	−	11.4268i	−0.650048	−	1.12592i	0.333062	−	0.942905i	$-0.391918\pi$
$104$	−0.998078	−	9.81520i	−0.0978696	−	0.962460i
$105$	6.57468	+	4.14312i	0.641623	+	0.404327i
$106$	0.860990	+	1.49128i	0.0836267	+	0.144846i
$107$	−2.93351	+	5.08098i	−0.283593	+	0.491197i	−0.972267	−	0.233874i	$-0.924860\pi$
$107$	−2.93351	+	5.08098i	−0.283593	+	0.491197i	0.688674	+	0.725071i	$0.258193\pi$
$108$	−1.59997	−	2.77124i	−0.153958	−	0.266662i
$109$	2.74399	−	4.75273i	0.262826	−	0.455229i	−0.704166	−	0.710036i	$-0.748679\pi$
$109$	2.74399	−	4.75273i	0.262826	−	0.455229i	0.966992	+	0.254807i	$0.0820120\pi$
$110$	−34.6252			−3.30138
$111$	2.12386	−	3.67863i	0.201588	−	0.349160i
$112$	−0.0164045	+	0.423623i	−0.00155008	+	0.0400286i
$113$	0.794808	−	1.37665i	0.0747692	−	0.129504i	−0.826217	−	0.563352i	$-0.809511\pi$
$113$	0.794808	−	1.37665i	0.0747692	−	0.129504i	0.900986	+	0.433848i	$0.142845\pi$
$114$	−2.57517	+	4.46033i	−0.241187	+	0.417748i
$115$	15.3678			1.43305
$116$	0.694071	−	1.20217i	0.0644428	−	0.111618i
$117$	−0.364757	−	3.58705i	−0.0337218	−	0.331623i
$118$	−8.31800			−0.765734
$119$	11.3104	+	7.12737i	1.03682	+	0.653365i
$120$	−4.01857	−	6.96037i	−0.366844	−	0.635392i
$121$	15.7242			1.42947
$122$	−7.92951	+	13.7343i	−0.717904	+	1.24345i
$123$	0.269622	+	0.466999i	0.0243110	+	0.0421079i
$124$	8.58366			0.770835
$125$	−4.03162			−0.360599
$126$	0.233457	−	6.02869i	0.0207980	−	0.537079i
$127$	0.348278	+	0.603236i	0.0309047	+	0.0535285i	0.881064	−	0.472997i	$-0.156828\pi$
$127$	0.348278	+	0.603236i	0.0309047	+	0.0535285i	−0.850159	+	0.526525i	$0.823494\pi$
$128$	8.97519	−	15.5455i	0.793302	−	1.37404i
$129$	−4.66348	+	8.07739i	−0.410597	+	0.711175i
$130$	−2.44311	−	24.0258i	−0.214275	−	2.10720i
$131$	3.35469	+	5.81049i	0.293101	+	0.507665i	0.974541	−	0.224208i	$-0.0719796\pi$
$131$	3.35469	+	5.81049i	0.293101	+	0.507665i	−0.681441	+	0.731873i	$0.738646\pi$
$132$	8.27113	+	14.3260i	0.719910	+	1.24692i
$133$	−5.28681	+	2.78534i	−0.458425	+	0.241520i
$134$	15.2329	−	26.3842i	1.31593	−	2.27925i
$135$	−1.46862	−	2.54373i	−0.126399	−	0.218929i
$136$	−6.91311	−	11.9739i	−0.592794	−	1.02675i
$137$	−6.24965	−	10.8247i	−0.533944	−	0.924818i	−0.999214	−	0.0396491i	$-0.987376\pi$
$137$	−6.24965	−	10.8247i	−0.533944	−	0.924818i	0.465270	−	0.885169i	$-0.345957\pi$
$138$	−5.96541	−	10.3324i	−0.507810	−	0.879552i
$139$	−0.657614	+	1.13902i	−0.0557781	+	0.0966105i	−0.892566	−	0.450916i	$-0.851097\pi$
$139$	−0.657614	+	1.13902i	−0.0557781	+	0.0966105i	0.836788	+	0.547527i	$0.184431\pi$
$140$	0.962254	−	24.8489i	0.0813253	−	2.10011i
$141$	−4.87054	−	8.43603i	−0.410174	−	0.710442i
$142$	8.90442	+	15.4229i	0.747243	+	1.29426i
$143$	1.88563	+	18.5434i	0.157684	+	1.55068i
$144$	0.0801172	−	0.138767i	0.00667643	−	0.0115639i
$145$	0.637091	−	1.10347i	0.0529075	−	0.0916385i
$146$	−18.1150	−	31.3762i	−1.49921	−	2.59671i
$147$	3.95832	−	5.77336i	0.326477	−	0.476179i
$148$	−13.5925			−1.11729
$149$	21.1927			1.73618			0.868088	−	0.496411i	$-0.165349\pi$
$149$	21.1927			1.73618			0.868088	+	0.496411i	$0.165349\pi$
$150$	−4.13587	−	7.16354i	−0.337692	−	0.584900i
$151$	7.90358	−	13.6894i	0.643185	−	1.11403i	−0.341533	−	0.939870i	$-0.610946\pi$
$151$	7.90358	−	13.6894i	0.643185	−	1.11403i	0.984718	−	0.174159i	$-0.0557205\pi$
$152$	6.18014			0.501275
$153$	−2.52646	−	4.37595i	−0.204252	−	0.353775i
$154$	−1.20686	+	31.1656i	−0.0972518	+	2.51139i
$155$	7.87898			0.632855
$156$	−9.35697	+	6.75002i	−0.749157	+	0.540434i
$157$	−2.76205	+	4.78402i	−0.220436	+	0.381806i	−0.954940	−	0.296798i	$-0.904081\pi$
$157$	−2.76205	+	4.78402i	−0.220436	+	0.381806i	0.734505	+	0.678604i	$0.237415\pi$
$158$	35.5384			2.82728
$159$	0.377571	−	0.653972i	0.0299433	−	0.0518634i
$160$	8.57376	−	14.8502i	0.677815	−	1.17401i
$161$	0.535646	−	13.8323i	0.0422148	−	1.09014i
$162$	−1.14017	+	1.97483i	−0.0895802	+	0.155157i
$163$	−3.14870			−0.246625			−0.123313	−	0.992368i	$-0.539352\pi$
$163$	−3.14870			−0.246625			−0.123313	+	0.992368i	$0.539352\pi$
$164$	0.862777	−	1.49437i	0.0673715	−	0.116691i
$165$	7.59211	+	13.1499i	0.591045	+	1.02372i
$166$	−15.0900	+	26.1367i	−1.17121	+	2.02860i
$167$	6.71152	+	11.6247i	0.519353	+	0.899546i	0.999747	+	0.0224932i	$0.00716043\pi$
$167$	6.71152	+	11.6247i	0.519353	+	0.899546i	−0.480394	+	0.877053i	$0.659506\pi$
$168$	−6.40499	+	3.37445i	−0.494156	+	0.260344i
$169$	−12.7339	+	2.61680i	−0.979531	+	0.201293i
$170$	−16.9220	−	29.3098i	−1.29786	−	2.24796i
$171$	2.25859			0.172718
$172$	29.8458			2.27572
$173$	−12.8488			−0.976879			−0.488439	−	0.872598i	$-0.662434\pi$
$173$	−12.8488			−0.976879			−0.488439	+	0.872598i	$0.662434\pi$
$174$	−0.989214			−0.0749921
$175$	0.371368	−	9.59005i	0.0280728	−	0.724940i
$176$	−0.414169	+	0.717362i	−0.0312192	+	0.0540732i
$177$	1.82385	+	3.15901i	0.137089	+	0.237445i
$178$	4.56394	+	7.90498i	0.342082	+	0.592503i
$179$	18.6663			1.39518			0.697591	−	0.716496i	$-0.254255\pi$
$179$	18.6663			1.39518			0.697591	+	0.716496i	$0.254255\pi$
$180$	−4.69952	+	8.13980i	−0.350281	+	0.606705i
$181$	0.878433			0.0652934			0.0326467	−	0.999467i	$-0.489606\pi$
$181$	0.878433			0.0652934			0.0326467	+	0.999467i	$0.489606\pi$
$182$	−21.7104	+	1.36158i	−1.60928	+	0.100927i
$183$	6.95468			0.514104
$184$	−7.15818	+	12.3983i	−0.527708	+	0.914017i
$185$	−12.4766			−0.917298
$186$	−3.05843	−	5.29736i	−0.224255	−	0.388422i
$187$	13.0606	+	22.6217i	0.955088	+	1.65426i
$188$	−15.5855	+	26.9948i	−1.13669	+	1.96880i
$189$	−2.34076	+	1.23322i	−0.170265	+	0.0897038i
$190$	15.1278			1.09749
$191$	−15.9513			−1.15419			−0.577097	−	0.816675i	$-0.695815\pi$
$191$	−15.9513			−1.15419			−0.577097	+	0.816675i	$0.695815\pi$
$192$	−12.9921			−0.937621
$193$	3.95066			0.284375			0.142187	−	0.989840i	$-0.454586\pi$
$193$	3.95066			0.284375			0.142187	+	0.989840i	$0.454586\pi$
$194$	6.14900	+	10.6504i	0.441473	+	0.764653i
$195$	−8.58881	+	6.19587i	−0.615057	+	0.443696i
$196$	−22.3325	−	1.73222i	−1.59518	−	0.123730i
$197$	−6.72353	−	11.6455i	−0.479032	−	0.829708i	0.520679	−	0.853753i	$-0.325679\pi$
$197$	−6.72353	−	11.6455i	−0.479032	−	0.829708i	−0.999711	+	0.0240448i	$0.992346\pi$
$198$	5.89416	−	10.2090i	0.418879	−	0.725520i
$199$	−10.4145	−	18.0385i	−0.738268	−	1.27872i	−0.953275	−	0.302105i	$-0.902311\pi$
$199$	−10.4145	−	18.0385i	−0.738268	−	1.27872i	0.215007	−	0.976612i	$-0.431023\pi$
$200$	−4.96282	+	8.59586i	−0.350925	+	0.607819i
$201$	−13.3602			−0.942359
$202$	3.59427	−	6.22546i	0.252892	−	0.438022i
$203$	−0.971014	−	0.611897i	−0.0681518	−	0.0429468i
$204$	−8.08453	+	14.0028i	−0.566030	+	0.980393i
$205$	0.791947	−	1.37169i	0.0553120	−	0.0958031i
$206$	30.0880			2.09633
$207$	−2.61602	+	4.53108i	−0.181826	+	0.314932i
$208$	−0.526988	−	0.236769i	−0.0365401	−	0.0164169i
$209$	−11.6759			−0.807636
$210$	−15.6782	+	8.26003i	−1.08190	+	0.569996i
$211$	7.17814	+	12.4329i	0.494164	+	0.855917i	0.999977	−	0.00672604i	$-0.00214098\pi$
$211$	7.17814	+	12.4329i	0.494164	+	0.855917i	−0.505814	+	0.862643i	$0.668808\pi$
$212$	−2.41641			−0.165960
$213$	3.90487	−	6.76343i	0.267557	−	0.463423i
$214$	−6.68939	−	11.5864i	−0.457277	−	0.792027i
$215$	27.3956			1.86836
$216$	2.73629			0.186181
$217$	0.274623	−	7.09175i	0.0186426	−	0.481419i
$218$	6.25722	+	10.8378i	0.423793	+	0.734030i
$219$	−7.94401	+	13.7594i	−0.536807	+	0.929776i
$220$	24.2943	−	42.0790i	1.63792	−	2.83697i
$221$	−14.7752	+	10.6587i	−0.993890	+	0.716981i
$222$	4.84312	+	8.38853i	0.325049	+	0.563001i
$223$	0.596931	+	1.03392i	0.0399735	+	0.0692361i	0.885320	−	0.464982i	$-0.153939\pi$
$223$	0.596931	+	1.03392i	0.0399735	+	0.0692361i	−0.845346	+	0.534218i	$0.820606\pi$
$224$	−13.0676	−	8.23472i	−0.873115	−	0.550205i
$225$	−1.81371	+	3.14143i	−0.120914	+	0.209429i
$226$	1.81243	+	3.13922i	0.120561	+	0.208818i
$227$	7.94437	+	13.7600i	0.527286	+	0.913286i	0.999494	+	0.0317993i	$0.0101237\pi$
$227$	7.94437	+	13.7600i	0.527286	+	0.913286i	−0.472208	+	0.881487i	$0.656543\pi$
$228$	−3.61368	−	6.25908i	−0.239322	−	0.414517i
$229$	−4.39323	−	7.60931i	−0.290313	−	0.502837i	0.683571	−	0.729884i	$-0.260426\pi$
$229$	−4.39323	−	7.60931i	−0.290313	−	0.502837i	−0.973884	+	0.227047i	$0.927093\pi$
$230$	−17.5219	+	30.3488i	−1.15536	+	2.00114i
$231$	12.1007	−	6.37520i	0.796165	−	0.419457i
$232$	0.593502	+	1.02798i	0.0389653	+	0.0674899i
$233$	2.86714	+	4.96604i	0.187833	+	0.325336i	0.944527	−	0.328432i	$-0.106520\pi$
$233$	2.86714	+	4.96604i	0.187833	+	0.325336i	−0.756695	+	0.653769i	$0.773187\pi$
$234$	7.49971	+	3.36952i	0.490271	+	0.220272i
$235$	−14.3060	+	24.7787i	−0.933220	+	1.61638i
$236$	5.83623	−	10.1086i	0.379906	−	0.658017i
$237$	−7.79235	−	13.4967i	−0.506168	−	0.876708i
$238$	−26.9711	+	14.2096i	−1.74828	+	0.921074i
$239$	−11.5411			−0.746532			−0.373266	−	0.927724i	$-0.621762\pi$
$239$	−11.5411			−0.746532			−0.373266	+	0.927724i	$0.621762\pi$
$240$	−0.470648			−0.0303802
$241$	2.83030	+	4.90223i	0.182316	+	0.315780i	0.942669	−	0.333730i	$-0.108307\pi$
$241$	2.83030	+	4.90223i	0.182316	+	0.315780i	−0.760353	+	0.649510i	$0.774974\pi$
$242$	−17.9282	+	31.0526i	−1.15247	+	1.99614i
$243$	1.00000			0.0641500
$244$	−11.1273	−	19.2730i	−0.712352	−	1.23383i
$245$	−20.4992	−	1.59001i	−1.30964	−	0.101582i
$246$	−1.22966			−0.0784003
$247$	−0.823835	−	8.10167i	−0.0524193	−	0.515497i
$248$	−3.66996	+	6.35655i	−0.233043	+	0.403642i
$249$	13.2349			0.838728
$250$	4.59673	−	7.96177i	0.290723	−	0.503546i
$251$	12.1872	−	21.1088i	0.769249	−	1.33238i	−0.168721	−	0.985664i	$-0.553964\pi$
$251$	12.1872	−	21.1088i	0.769249	−	1.33238i	0.937971	−	0.346715i	$-0.112703\pi$
$252$	7.16271	+	4.51367i	0.451208	+	0.284335i
$253$	13.5236	−	23.4236i	0.850223	−	1.47263i
$254$	−1.58839			−0.0996641
$255$	−7.42083	+	12.8532i	−0.464710	+	0.804902i
$256$	7.47442	+	12.9461i	0.467151	+	0.809130i
$257$	−2.30268	+	3.98836i	−0.143637	+	0.248787i	−0.928864	−	0.370422i	$-0.879213\pi$
$257$	−2.30268	+	3.98836i	−0.143637	+	0.248787i	0.785226	+	0.619209i	$0.212547\pi$
$258$	−10.6343	−	18.4192i	−0.662064	−	1.14673i
$259$	−0.434873	+	11.2300i	−0.0270217	+	0.697798i
$260$	30.9121	+	13.8884i	1.91709	+	0.861320i
$261$	0.216901	+	0.375683i	0.0134258	+	0.0232542i
$262$	−15.2997			−0.945216
$263$	22.9824			1.41715			0.708576	−	0.705634i	$-0.249338\pi$
$263$	22.9824			1.41715			0.708576	+	0.705634i	$0.249338\pi$
$264$	−14.1453			−0.870586
$265$	−2.21804			−0.136253
$266$	0.527282	−	13.6163i	0.0323297	−	0.834870i
$267$	2.00143	−	3.46658i	0.122486	−	0.212151i
$268$	21.3760	+	37.0244i	1.30575	+	2.26162i
$269$	−7.00246	−	12.1286i	−0.426948	−	0.739495i	0.569652	−	0.821886i	$-0.307078\pi$
$269$	−7.00246	−	12.1286i	−0.426948	−	0.739495i	−0.996600	+	0.0823905i	$0.973745\pi$
$270$	6.69792			0.407622
$271$	9.55299	−	16.5463i	0.580303	−	1.00511i	−0.415141	−	0.909757i	$-0.636268\pi$
$271$	9.55299	−	16.5463i	0.580303	−	1.00511i	0.995443	−	0.0953563i	$-0.0303990\pi$
$272$	−0.809651			−0.0490923
$273$	5.27744	+	7.94661i	0.319405	+	0.480951i
$274$	28.5027			1.72191
$275$	9.37604	−	16.2398i	0.565397	−	0.979296i
$276$	16.7423			1.00777
$277$	−6.45998	−	11.1890i	−0.388142	−	0.672282i	0.604057	−	0.796941i	$-0.293550\pi$
$277$	−6.45998	−	11.1890i	−0.388142	−	0.672282i	−0.992200	+	0.124658i	$0.960216\pi$
$278$	−1.49958	−	2.59735i	−0.0899390	−	0.155779i
$279$	−1.34122	+	2.32306i	−0.0802967	+	0.139078i
$280$	17.9902	+	11.3368i	1.07512	+	0.677502i
$281$	−19.6264			−1.17082			−0.585408	−	0.810739i	$-0.699066\pi$
$281$	−19.6264			−1.17082			−0.585408	+	0.810739i	$0.699066\pi$
$282$	22.2130			1.32276
$283$	3.26727			0.194219			0.0971095	−	0.995274i	$-0.469040\pi$
$283$	3.26727			0.194219			0.0971095	+	0.995274i	$0.469040\pi$
$284$	−24.9907			−1.48293
$285$	−3.31701	−	5.74523i	−0.196483	−	0.340318i
$286$	−38.7701	−	17.4189i	−2.29252	−	1.03000i
$287$	−1.20704	−	0.760629i	−0.0712490	−	0.0448985i
$288$	2.91898	+	5.05582i	0.172003	+	0.297917i
$289$	−4.26597	+	7.38888i	−0.250939	+	0.434640i
$290$	1.45278	+	2.51629i	0.0853104	+	0.147762i
$291$	2.69653	−	4.67053i	0.158073	−	0.273791i
$292$	50.8408			2.97523
$293$	9.50947	−	16.4709i	0.555549	−	0.962239i	−0.442311	−	0.896862i	$-0.645841\pi$
$293$	9.50947	−	16.4709i	0.555549	−	0.962239i	0.997861	−	0.0653778i	$-0.0208252\pi$
$294$	6.88826	+	14.3996i	0.401731	+	0.839803i
$295$	5.35710	−	9.27878i	0.311903	−	0.540231i
$296$	5.81149	−	10.0658i	0.337786	−	0.585062i
$297$	−5.16954			−0.299967
$298$	−24.1633	+	41.8521i	−1.39974	+	2.42442i
$299$	17.2074	+	7.73106i	0.995132	+	0.447099i
$300$	11.6075			0.670162
$301$	0.954876	−	24.6584i	0.0550382	−	1.42128i
$302$	18.0229	+	31.2165i	1.03710	+	1.79631i
$303$	−3.15240			−0.181101
$304$	0.180952	−	0.313418i	0.0103783	−	0.0179757i
$305$	−10.2138	−	17.6908i	−0.584840	−	1.01297i
$306$	11.5224			0.658689
$307$	−8.30660			−0.474083			−0.237041	−	0.971500i	$-0.576178\pi$
$307$	−8.30660			−0.474083			−0.237041	+	0.971500i	$0.576178\pi$
$308$	−37.0279	−	23.3336i	−2.10986	−	1.32956i
$309$	−6.59727	−	11.4268i	−0.375306	−	0.650048i
$310$	−8.98338	+	15.5597i	−0.510221	+	0.883729i
$311$	5.42853	−	9.40250i	0.307824	−	0.533167i	−0.670062	−	0.742305i	$-0.733733\pi$
$311$	5.42853	−	9.40250i	0.307824	−	0.533167i	0.977886	+	0.209138i	$0.0670659\pi$
$312$	−0.998078	−	9.81520i	−0.0565051	−	0.555676i
$313$	0.566928	+	0.981949i	0.0320447	+	0.0555030i	0.881603	−	0.471992i	$-0.156465\pi$
$313$	0.566928	+	0.981949i	0.0320447	+	0.0555030i	−0.849558	+	0.527495i	$0.823131\pi$
$314$	−6.29842	−	10.9092i	−0.355440	−	0.615641i
$315$	6.57468	+	4.14312i	0.370441	+	0.233439i
$316$	−24.9351	+	43.1889i	−1.40271	+	2.42956i
$317$	−4.98712	−	8.63795i	−0.280105	−	0.485155i	0.691306	−	0.722562i	$-0.257036\pi$
$317$	−4.98712	−	8.63795i	−0.280105	−	0.485155i	−0.971410	+	0.237407i	$0.923702\pi$
$318$	0.860990	+	1.49128i	0.0482819	+	0.0836267i
$319$	−1.12128	−	1.94211i	−0.0627795	−	0.108737i
$320$	19.0804	+	33.0483i	1.06663	+	1.84746i
$321$	−2.93351	+	5.08098i	−0.163732	+	0.283593i
$322$	26.7058	+	16.8290i	1.48825	+	0.937843i
$323$	−5.70622	−	9.88347i	−0.317503	−	0.549931i
$324$	−1.59997	−	2.77124i	−0.0888874	−	0.153958i
$325$	11.9301	+	5.36001i	0.661760	+	0.297320i
$326$	3.59005	−	6.21815i	0.198835	−	0.344392i
$327$	2.74399	−	4.75273i	0.151743	−	0.262826i
$328$	0.737763	+	1.27784i	0.0407362	+	0.0705571i
$329$	21.8043	+	13.7403i	1.20211	+	0.757525i
$330$	−34.6252			−1.90605
$331$	−1.65514			−0.0909746			−0.0454873	−	0.998965i	$-0.514484\pi$
$331$	−1.65514			−0.0909746			−0.0454873	+	0.998965i	$0.514484\pi$
$332$	−21.1755	−	36.6770i	−1.16216	−	2.01291i
$333$	2.12386	−	3.67863i	0.116387	−	0.201588i
$334$	−30.6091			−1.67486
$335$	19.6212	+	33.9849i	1.07202	+	1.85679i
$336$	−0.0164045	+	0.423623i	−0.000894938	+	0.0231105i
$337$	−12.4081			−0.675913			−0.337956	−	0.941162i	$-0.609736\pi$
$337$	−12.4081			−0.675913			−0.337956	+	0.941162i	$0.609736\pi$
$338$	9.35107	−	28.1309i	0.508631	−	1.53012i
$339$	0.794808	−	1.37665i	0.0431680	−	0.0747692i
$340$	47.4925			2.57564
$341$	6.93349	−	12.0092i	0.375469	−	0.650332i
$342$	−2.57517	+	4.46033i	−0.139249	+	0.241187i
$343$	−2.14565	+	18.3955i	−0.115854	+	0.993266i
$344$	−12.7606	+	22.1021i	−0.688007	+	1.19166i
$345$	15.3678			0.827374
$346$	14.6498	−	25.3743i	0.787581	−	1.36413i
$347$	−6.62262	−	11.4707i	−0.355521	−	0.615780i	0.631686	−	0.775224i	$-0.282363\pi$
$347$	−6.62262	−	11.4707i	−0.355521	−	0.615780i	−0.987207	+	0.159444i	$0.949030\pi$
$348$	0.694071	−	1.20217i	0.0372061	−	0.0644428i
$349$	17.5068	+	30.3227i	0.937119	+	1.62314i	0.770812	+	0.637063i	$0.219851\pi$
$349$	17.5068	+	30.3227i	0.937119	+	1.62314i	0.166307	+	0.986074i	$0.446816\pi$
$350$	18.5153	+	11.6677i	0.989685	+	0.623663i
$351$	−0.364757	−	3.58705i	−0.0194693	−	0.191463i
$352$	−15.0898	−	26.1363i	−0.804289	−	1.39307i
$353$	23.1083			1.22993			0.614964	−	0.788555i	$-0.289171\pi$
$353$	23.1083			1.22993			0.614964	+	0.788555i	$0.289171\pi$
$354$	−8.31800			−0.442097
$355$	−22.9391			−1.21748
$356$	−12.8089			−0.678873
$357$	11.3104	+	7.12737i	0.598608	+	0.377221i
$358$	−21.2827	+	36.8628i	−1.12483	+	1.94826i
$359$	−6.44458	−	11.1623i	−0.340132	−	0.589126i	0.644325	−	0.764752i	$-0.277138\pi$
$359$	−6.44458	−	11.1623i	−0.340132	−	0.589126i	−0.984457	+	0.175626i	$0.943805\pi$
$360$	−4.01857	−	6.96037i	−0.211797	−	0.366844i
$361$	−13.8988			−0.731515
$362$	−1.00156	+	1.73476i	−0.0526409	+	0.0911768i
$363$	15.7242			0.825305
$364$	13.5781	−	27.3394i	0.711688	−	1.43297i
$365$	46.6670			2.44266
$366$	−7.92951	+	13.7343i	−0.414482	+	0.717904i
$367$	−26.4929			−1.38292			−0.691460	−	0.722415i	$-0.743032\pi$
$367$	−26.4929			−1.38292			−0.691460	+	0.722415i	$0.743032\pi$
$368$	0.419177	+	0.726035i	0.0218511	+	0.0378472i
$369$	0.269622	+	0.466999i	0.0140360	+	0.0243110i
$370$	14.2254	−	24.6392i	0.739545	−	1.28093i
$371$	−0.0773099	+	1.99642i	−0.00401373	+	0.103649i
$372$	8.58366			0.445042
$373$	−12.3710			−0.640545			−0.320273	−	0.947325i	$-0.603775\pi$
$373$	−12.3710			−0.640545			−0.320273	+	0.947325i	$0.603775\pi$
$374$	−59.5653			−3.08005
$375$	−4.03162			−0.208192
$376$	−13.3272	−	23.0834i	−0.687298	−	1.19043i
$377$	1.26848	−	0.915067i	0.0653300	−	0.0471284i
$378$	0.233457	−	6.02869i	0.0120077	−	0.310082i
$379$	−14.0179	−	24.2797i	−0.720050	−	1.24716i	−0.960979	−	0.276621i	$-0.910785\pi$
$379$	−14.0179	−	24.2797i	−0.720050	−	1.24716i	0.240929	−	0.970543i	$-0.422548\pi$
$380$	−10.6143	+	18.3844i	−0.544500	+	0.943102i
$381$	0.348278	+	0.603236i	0.0178428	+	0.0309047i
$382$	18.1872	−	31.5011i	0.930537	−	1.61174i
$383$	−26.2903			−1.34337			−0.671687	−	0.740835i	$-0.734430\pi$
$383$	−26.2903			−1.34337			−0.671687	+	0.740835i	$0.734430\pi$
$384$	8.97519	−	15.5455i	0.458013	−	0.793302i
$385$	−33.9881	−	21.4181i	−1.73219	−	1.09157i
$386$	−4.50442	+	7.80188i	−0.229269	+	0.397105i
$387$	−4.66348	+	8.07739i	−0.237058	+	0.410597i
$388$	−17.2575			−0.876117
$389$	−13.4205	+	23.2449i	−0.680445	+	1.17856i	0.294400	+	0.955682i	$0.404880\pi$
$389$	−13.4205	+	23.2449i	−0.680445	+	1.17856i	−0.974845	+	0.222883i	$0.928453\pi$
$390$	−2.44311	−	24.0258i	−0.123712	−	1.21659i
$391$	26.4371			1.33698
$392$	10.8311	−	15.7976i	0.547053	−	0.797897i
$393$	3.35469	+	5.81049i	0.169222	+	0.293101i
$394$	30.6639			1.54482
$395$	−22.8881	+	39.6433i	−1.15162	+	1.99467i
$396$	8.27113	+	14.3260i	0.415640	+	0.719910i
$397$	24.5243			1.23084			0.615419	−	0.788200i	$-0.288987\pi$
$397$	24.5243			1.23084			0.615419	+	0.788200i	$0.288987\pi$
$398$	47.4974			2.38083
$399$	−5.28681	+	2.78534i	−0.264672	+	0.139441i
$400$	0.290618	+	0.503366i	0.0145309	+	0.0251683i
$401$	−1.58285	+	2.74158i	−0.0790438	+	0.136908i	−0.902838	−	0.429982i	$-0.858520\pi$
$401$	−1.58285	+	2.74158i	−0.0790438	+	0.136908i	0.823794	+	0.566889i	$0.191853\pi$
$402$	15.2329	−	26.3842i	0.759750	−	1.31593i
$403$	8.82216	+	3.96367i	0.439463	+	0.197445i
$404$	5.04376	+	8.73605i	0.250936	+	0.434635i
$405$	−1.46862	−	2.54373i	−0.0729765	−	0.126399i
$406$	2.31551	−	1.21992i	0.114917	−	0.0605437i
$407$	−10.9794	+	19.0169i	−0.544228	+	0.942630i
$408$	−6.91311	−	11.9739i	−0.342250	−	0.592794i
$409$	−9.53424	−	16.5138i	−0.471438	−	0.816555i	0.528028	−	0.849227i	$-0.322932\pi$
$409$	−9.53424	−	16.5138i	−0.471438	−	0.816555i	−0.999466	+	0.0326723i	$0.989598\pi$
$410$	1.80591	+	3.12792i	0.0891874	+	0.154477i
$411$	−6.24965	−	10.8247i	−0.308273	−	0.533944i
$412$	−21.1109	+	36.5652i	−1.04006	+	1.80144i
$413$	−8.16496	−	5.14526i	−0.401771	−	0.253182i
$414$	−5.96541	−	10.3324i	−0.293184	−	0.507810i
$415$	−19.4371	−	33.6660i	−0.954129	−	1.65260i
$416$	17.0708	−	12.3147i	0.836964	−	0.603777i
$417$	−0.657614	+	1.13902i	−0.0322035	+	0.0557781i
$418$	13.3125	−	23.0579i	0.651134	−	1.12780i
$419$	7.80534	+	13.5192i	0.381316	+	0.660458i	0.991251	−	0.131993i	$-0.0421377\pi$
$419$	7.80534	+	13.5192i	0.381316	+	0.660458i	−0.609935	+	0.792452i	$0.708804\pi$
$420$	0.962254	−	24.8489i	0.0469532	−	1.21250i
$421$	−18.0525			−0.879827			−0.439913	−	0.898040i	$-0.644991\pi$
$421$	−18.0525			−0.879827			−0.439913	+	0.898040i	$0.644991\pi$
$422$	−32.7372			−1.59362
$423$	−4.87054	−	8.43603i	−0.236814	−	0.410174i
$424$	1.03314	−	1.78945i	0.0501738	−	0.0869036i
$425$	18.3290			0.889088
$426$	8.90442	+	15.4229i	0.431421	+	0.747243i
$427$	−16.2792	+	8.57667i	−0.787807	+	0.415054i
$428$	18.7741			0.907481
$429$	1.88563	+	18.5434i	0.0910388	+	0.895285i
$430$	−31.2356	+	54.1017i	−1.50632	+	2.60902i
$431$	−17.5165			−0.843741			−0.421871	−	0.906656i	$-0.638626\pi$
$431$	−17.5165			−0.843741			−0.421871	+	0.906656i	$0.638626\pi$
$432$	0.0801172	−	0.138767i	0.00385464	−	0.00667643i
$433$	−3.02961	+	5.24744i	−0.145594	+	0.252176i	−0.929594	−	0.368584i	$-0.879843\pi$
$433$	−3.02961	+	5.24744i	−0.145594	+	0.252176i	0.784001	+	0.620760i	$0.213176\pi$
$434$	13.6919	+	8.62813i	0.657232	+	0.414163i
$435$	0.637091	−	1.10347i	0.0305462	−	0.0529075i
$436$	−17.5612			−0.841030
$437$	−5.90851	+	10.2338i	−0.282642	+	0.489551i
$438$	−18.1150	−	31.3762i	−0.865570	−	1.49921i
$439$	−11.6912	+	20.2497i	−0.557990	+	0.966467i	0.439674	+	0.898157i	$0.355094\pi$
$439$	−11.6912	+	20.2497i	−0.557990	+	0.966467i	−0.997664	+	0.0683098i	$0.978239\pi$
$440$	20.7742	+	35.9819i	0.990370	+	1.71537i
$441$	3.95832	−	5.77336i	0.188492	−	0.274922i
$442$	−4.20286	−	41.3313i	−0.199910	−	1.96593i
$443$	4.44712	+	7.70264i	0.211289	+	0.365963i	0.952118	−	0.305730i	$-0.0989005\pi$
$443$	4.44712	+	7.70264i	0.211289	+	0.365963i	−0.740829	+	0.671693i	$0.765567\pi$
$444$	−13.5925			−0.645070
$445$	−11.7574			−0.557354
$446$	−2.72241			−0.128910
$447$	21.1927			1.00238
$448$	30.4113	−	16.0221i	1.43680	−	0.756973i
$449$	−19.3671	+	33.5448i	−0.913989	+	1.58308i	−0.105614	+	0.994407i	$0.533681\pi$
$449$	−19.3671	+	33.5448i	−0.913989	+	1.58308i	−0.808375	+	0.588668i	$0.799652\pi$
$450$	−4.13587	−	7.16354i	−0.194967	−	0.337692i
$451$	−1.39382	−	2.41417i	−0.0656326	−	0.113679i
$452$	−5.08668			−0.239258
$453$	7.90358	−	13.6894i	0.371343	−	0.643185i
$454$	−36.2317			−1.70044
$455$	12.4634	−	25.0950i	0.584295	−	1.17647i
$456$	6.18014			0.289411
$457$	−11.2001	+	19.3992i	−0.523920	+	0.907457i	0.475692	+	0.879612i	$0.342198\pi$
$457$	−11.2001	+	19.3992i	−0.523920	+	0.907457i	−0.999612	+	0.0278448i	$0.991136\pi$
$458$	20.0361			0.936227
$459$	−2.52646	−	4.37595i	−0.117925	−	0.204252i
$460$	−24.5881	−	42.5878i	−1.14642	−	1.98567i
$461$	−1.40367	+	2.43123i	−0.0653755	+	0.113234i	−0.896860	−	0.442314i	$-0.854158\pi$
$461$	−1.40367	+	2.43123i	−0.0653755	+	0.113234i	0.831485	+	0.555547i	$0.187491\pi$
$462$	−1.20686	+	31.1656i	−0.0561484	+	1.44995i
$463$	37.7530			1.75453			0.877266	−	0.480004i	$-0.159365\pi$
$463$	37.7530			1.75453			0.877266	+	0.480004i	$0.159365\pi$
$464$	0.0695099			0.00322692
$465$	7.87898			0.365379
$466$	−13.0761			−0.605740
$467$	−8.04389	−	13.9324i	−0.372227	−	0.644716i	0.617681	−	0.786429i	$-0.288072\pi$
$467$	−8.04389	−	13.9324i	−0.372227	−	0.644716i	−0.989908	+	0.141713i	$0.954739\pi$
$468$	−9.35697	+	6.75002i	−0.432526	+	0.312020i
$469$	31.2731	−	16.4762i	1.44406	−	0.760798i
$470$	−32.6225	−	56.5038i	−1.50476	−	2.60633i
$471$	−2.76205	+	4.78402i	−0.127269	+	0.220436i
$472$	4.99058	+	8.64394i	0.229710	+	0.397870i
$473$	24.1081	−	41.7564i	1.10849	−	1.91996i
$474$	35.5384			1.63233
$475$	−4.09642	+	7.09520i	−0.187956	+	0.325550i
$476$	1.65536	−	42.7473i	0.0758731	−	1.95932i
$477$	0.377571	−	0.653972i	0.0172878	−	0.0299433i
$478$	13.1588	−	22.7917i	0.601870	−	1.04247i
$479$	8.54850			0.390591			0.195295	−	0.980744i	$-0.437433\pi$
$479$	8.54850			0.390591			0.195295	+	0.980744i	$0.437433\pi$
$480$	8.57376	−	14.8502i	0.391337	−	0.677815i
$481$	−13.9701	−	6.27659i	−0.636984	−	0.286188i
$482$	−12.9081			−0.587948
$483$	0.535646	−	13.8323i	0.0243727	−	0.629392i
$484$	−25.1583	−	43.5754i	−1.14356	−	1.98070i
$485$	−15.8407			−0.719291
$486$	−1.14017	+	1.97483i	−0.0517191	+	0.0895802i
$487$	17.7881	+	30.8098i	0.806054	+	1.39613i	0.915577	+	0.402142i	$0.131734\pi$
$487$	17.7881	+	30.8098i	0.806054	+	1.39613i	−0.109524	+	0.993984i	$0.534932\pi$
$488$	19.0300			0.861447
$489$	−3.14870			−0.142389
$490$	26.5125	−	38.6695i	1.19771	−	1.74691i
$491$	15.6990	+	27.1914i	0.708485	+	1.22713i	0.965419	+	0.260703i	$0.0839544\pi$
$491$	15.6990	+	27.1914i	0.708485	+	1.22713i	−0.256934	+	0.966429i	$0.582712\pi$
$492$	0.862777	−	1.49437i	0.0388970	−	0.0673715i
$493$	1.09598	−	1.89829i	0.0493605	−	0.0854949i
$494$	16.9387	+	7.61034i	0.762110	+	0.342406i
$495$	7.59211	+	13.1499i	0.341240	+	0.591045i
$496$	0.214909	+	0.372234i	0.00964972	+	0.0167138i
$497$	−0.799545	+	20.6471i	−0.0358645	+	0.926151i
$498$	−15.0900	+	26.1367i	−0.676200	+	1.17121i
$499$	2.14606	+	3.71708i	0.0960708	+	0.166399i	0.910055	−	0.414488i	$-0.136039\pi$
$499$	2.14606	+	3.71708i	0.0960708	+	0.166399i	−0.813984	+	0.580887i	$0.802706\pi$
$500$	6.45048	+	11.1726i	0.288474	+	0.499652i
$501$	6.71152	+	11.6247i	0.299849	+	0.519353i
$502$	27.7909	+	48.1353i	1.24037	+	2.14839i
$503$	7.83439	−	13.5696i	0.349318	−	0.605037i	−0.636810	−	0.771021i	$-0.719747\pi$
$503$	7.83439	−	13.5696i	0.349318	−	0.605037i	0.986129	+	0.165984i	$0.0530799\pi$
$504$	−6.40499	+	3.37445i	−0.285301	+	0.150310i
$505$	4.62969	+	8.01886i	0.206019	+	0.356835i
$506$	30.8385	+	53.4138i	1.37094	+	2.37453i
$507$	−12.7339	+	2.61680i	−0.565533	+	0.116216i
$508$	1.11447	−	1.93032i	0.0494467	−	0.0856442i
$509$	−0.851865	+	1.47547i	−0.0377583	+	0.0653992i	−0.884287	−	0.466944i	$-0.845355\pi$
$509$	−0.851865	+	1.47547i	−0.0377583	+	0.0653992i	0.846529	+	0.532343i	$0.178688\pi$
$510$	−16.9220	−	29.3098i	−0.749319	−	1.29786i
$511$	1.62658	−	42.0043i	0.0719558	−	1.85816i
$512$	1.81234			0.0800947
$513$	2.25859			0.0997190
$514$	−5.25089	−	9.09481i	−0.231607	−	0.401155i
$515$	−19.3778	+	33.5633i	−0.853888	+	1.47898i
$516$	29.8458			1.31389
$517$	25.1785	+	43.6104i	1.10735	+	1.91798i
$518$	−21.6815	−	13.6629i	−0.952631	−	0.600313i
$519$	−12.8488			−0.564001
$520$	−23.5014	+	16.9537i	−1.03061	+	0.743468i
$521$	8.39696	−	14.5440i	0.367878	−	0.637183i	−0.621356	−	0.783528i	$-0.713418\pi$
$521$	8.39696	−	14.5440i	0.367878	−	0.637183i	0.989234	+	0.146346i	$0.0467512\pi$
$522$	−0.989214			−0.0432967
$523$	3.74526	−	6.48697i	0.163769	−	0.283656i	−0.772449	−	0.635077i	$-0.780968\pi$
$523$	3.74526	−	6.48697i	0.163769	−	0.283656i	0.936217	+	0.351422i	$0.114302\pi$
$524$	10.7348	−	18.5933i	0.468953	−	0.812251i
$525$	0.371368	−	9.59005i	0.0162078	−	0.418544i
$526$	−26.2038	+	45.3863i	−1.14254	+	1.97894i
$527$	13.5541			0.590427
$528$	−0.414169	+	0.717362i	−0.0180244	+	0.0312192i
$529$	−2.18713	−	3.78822i	−0.0950926	−	0.164705i
$530$	2.52894	−	4.38025i	0.109850	−	0.190266i
$531$	1.82385	+	3.15901i	0.0791485	+	0.137089i
$532$	16.1776	+	10.1945i	0.701388	+	0.441989i
$533$	1.57681	−	1.13749i	0.0682990	−	0.0492702i
$534$	4.56394	+	7.90498i	0.197501	+	0.342082i
$535$	17.2329			0.745041
$536$	−36.5574			−1.57904
$537$	18.6663			0.805509
$538$	31.9360			1.37686
$539$	−20.4627	+	29.8456i	−0.881392	+	1.28554i
$540$	−4.69952	+	8.13980i	−0.202235	+	0.350281i
$541$	4.78963	+	8.29588i	0.205922	+	0.356668i	0.950426	−	0.310950i	$-0.100647\pi$
$541$	4.78963	+	8.29588i	0.205922	+	0.356668i	−0.744504	+	0.667618i	$0.767314\pi$
$542$	21.7840	+	37.7311i	0.935705	+	1.62069i
$543$	0.878433			0.0376972
$544$	14.7494	−	25.5466i	0.632373	−	1.09530i
$545$	−16.1195			−0.690485
$546$	−21.7104	+	1.36158i	−0.929119	+	0.0582704i
$547$	−30.1843			−1.29059			−0.645293	−	0.763935i	$-0.723265\pi$
$547$	−30.1843			−1.29059			−0.645293	+	0.763935i	$0.723265\pi$
$548$	−19.9986	+	34.6385i	−0.854296	+	1.47968i
$549$	6.95468			0.296818
$550$	21.3806	+	37.0322i	0.911670	+	1.57906i
$551$	0.489889	+	0.848513i	0.0208700	+	0.0361479i
$552$	−7.15818	+	12.3983i	−0.304672	+	0.527708i
$553$	34.8845	+	21.9829i	1.48344	+	0.934810i
$554$	29.4619			1.25172
$555$	−12.4766			−0.529602
$556$	4.20866			0.178487
$557$	−4.67142			−0.197935			−0.0989673	−	0.995091i	$-0.531554\pi$
$557$	−4.67142			−0.197935			−0.0989673	+	0.995091i	$0.531554\pi$
$558$	−3.05843	−	5.29736i	−0.129474	−	0.224255i
$559$	30.6751	+	13.7819i	1.29742	+	0.582912i
$560$	1.10167	−	0.580414i	0.0465542	−	0.0245270i
$561$	13.0606	+	22.6217i	0.551420	+	0.955088i
$562$	22.3775	−	38.7589i	0.943937	−	1.63495i
$563$	7.19090	+	12.4550i	0.303060	+	0.524915i	0.976828	−	0.214028i	$-0.0686584\pi$
$563$	7.19090	+	12.4550i	0.303060	+	0.524915i	−0.673767	+	0.738943i	$0.735325\pi$
$564$	−15.5855	+	26.9948i	−0.656267	+	1.13669i
$565$	−4.66909			−0.196430
$566$	−3.72524	+	6.45231i	−0.156584	+	0.271211i
$567$	−2.34076	+	1.23322i	−0.0983027	+	0.0517905i
$568$	10.6848	−	18.5067i	0.448326	−	0.776523i
$569$	7.28779	−	12.6228i	0.305520	−	0.529176i	−0.671857	−	0.740681i	$-0.734503\pi$
$569$	7.28779	−	12.6228i	0.305520	−	0.529176i	0.977377	+	0.211505i	$0.0678364\pi$
$570$	15.1278			0.633635
$571$	−12.9575	+	22.4430i	−0.542254	+	0.939211i	0.456520	+	0.889713i	$0.349096\pi$
$571$	−12.9575	+	22.4430i	−0.542254	+	0.939211i	−0.998774	+	0.0494981i	$0.984238\pi$
$572$	48.3712	−	34.8945i	2.02250	−	1.45901i
$573$	−15.9513			−0.666375
$574$	2.87834	−	1.51645i	0.120140	−	0.0632952i
$575$	−9.48940	−	16.4361i	−0.395735	−	0.685433i
$576$	−12.9921			−0.541336
$577$	11.7875	−	20.4165i	0.490719	−	0.849950i	−0.509224	−	0.860634i	$-0.670068\pi$
$577$	11.7875	−	20.4165i	0.490719	−	0.849950i	0.999943	+	0.0106839i	$0.00340085\pi$
$578$	−9.72786	−	16.8491i	−0.404626	−	0.700832i
$579$	3.95066			0.164184
$580$	−4.07731			−0.169301
$581$	−30.9797	+	16.3216i	−1.28526	+	0.677133i
$582$	6.14900	+	10.6504i	0.254884	+	0.441473i
$583$	−1.95187	+	3.38074i	−0.0808382	+	0.140016i
$584$	−21.7371	+	37.6497i	−0.899487	+	1.55796i
$585$	−8.58881	+	6.19587i	−0.355103	+	0.256168i
$586$	21.6848	+	37.5592i	0.895791	+	1.55156i
$587$	−23.7561	−	41.1468i	−0.980521	−	1.69831i	−0.660361	−	0.750948i	$-0.729597\pi$
$587$	−23.7561	−	41.1468i	−0.980521	−	1.69831i	−0.320160	−	0.947364i	$-0.603737\pi$
$588$	−22.3325	−	1.73222i	−0.920979	−	0.0714355i
$589$	−3.02926	+	5.24683i	−0.124818	+	0.216192i
$590$	12.2160	+	21.1588i	0.502925	+	0.871092i
$591$	−6.72353	−	11.6455i	−0.276569	−	0.479032i
$592$	−0.340316	−	0.589444i	−0.0139869	−	0.0242260i
$593$	−2.36887	−	4.10300i	−0.0972779	−	0.168490i	0.813279	−	0.581874i	$-0.197680\pi$
$593$	−2.36887	−	4.10300i	−0.0972779	−	0.168490i	−0.910557	+	0.413384i	$0.864347\pi$
$594$	5.89416	−	10.2090i	0.241840	−	0.418879i
$595$	1.51946	−	39.2379i	0.0622917	−	1.60860i
$596$	−33.9078	−	58.7300i	−1.38892	−	2.40568i
$597$	−10.4145	−	18.0385i	−0.426239	−	0.738268i
$598$	−34.8870	+	25.1671i	−1.42663	+	1.02916i
$599$	1.07453	−	1.86114i	0.0439041	−	0.0760441i	−0.843238	−	0.537540i	$-0.819354\pi$
$599$	1.07453	−	1.86114i	0.0439041	−	0.0760441i	0.887142	+	0.461496i	$0.152687\pi$
$600$	−4.96282	+	8.59586i	−0.202606	+	0.350925i
$601$	0.736182	+	1.27511i	0.0300295	+	0.0520126i	0.880650	−	0.473768i	$-0.157107\pi$
$601$	0.736182	+	1.27511i	0.0300295	+	0.0520126i	−0.850620	+	0.525781i	$0.823773\pi$
$602$	47.6074	+	30.0004i	1.94033	+	1.22273i
$603$	−13.3602			−0.544071
$604$	−50.5821			−2.05816
$605$	−23.0929	−	39.9980i	−0.938859	−	1.62615i
$606$	3.59427	−	6.22546i	0.146007	−	0.252892i
$607$	−12.9859			−0.527082			−0.263541	−	0.964648i	$-0.584890\pi$
$607$	−12.9859			−0.527082			−0.263541	+	0.964648i	$0.584890\pi$
$608$	6.59277	+	11.4190i	0.267372	+	0.463102i
$609$	−0.971014	−	0.611897i	−0.0393475	−	0.0247953i
$610$	46.5818			1.88604
$611$	−28.4839	+	20.5480i	−1.15234	+	0.831283i
$612$	−8.08453	+	14.0028i	−0.326798	+	0.566030i
$613$	−40.1092			−1.61999			−0.809997	−	0.586433i	$-0.800532\pi$
$613$	−40.1092			−1.61999			−0.809997	+	0.586433i	$0.800532\pi$
$614$	9.47093	−	16.4041i	0.382216	−	0.662017i
$615$	0.791947	−	1.37169i	0.0319344	−	0.0553120i
$616$	33.1109	−	17.4444i	1.33407	−	0.702853i
$617$	8.82052	−	15.2776i	0.355101	−	0.615052i	−0.632035	−	0.774940i	$-0.717780\pi$
$617$	8.82052	−	15.2776i	0.355101	−	0.615052i	0.987135	+	0.159888i	$0.0511133\pi$
$618$	30.0880			1.21032
$619$	13.3825	−	23.1792i	0.537890	−	0.931652i	−0.461128	−	0.887334i	$-0.652555\pi$
$619$	13.3825	−	23.1792i	0.537890	−	0.931652i	0.999017	−	0.0443184i	$-0.0141116\pi$
$620$	−12.6062	−	21.8345i	−0.506276	−	0.876895i
$621$	−2.61602	+	4.53108i	−0.104977	+	0.181826i
$622$	12.3789	+	21.4409i	0.496349	+	0.859701i
$623$	−0.409805	+	10.5826i	−0.0164185	+	0.423985i
$624$	−0.526988	−	0.236769i	−0.0210964	−	0.00947833i
$625$	14.9895	+	25.9625i	0.599579	+	1.03850i
$626$	−2.58558			−0.103340
$627$	−11.6759			−0.466289
$628$	17.6768			0.705383
$629$	−21.4634			−0.855800
$630$	−15.6782	+	8.26003i	−0.624635	+	0.329087i
$631$	10.1224	−	17.5324i	0.402964	−	0.697955i	−0.591118	−	0.806585i	$-0.701313\pi$
$631$	10.1224	−	17.5324i	0.402964	−	0.697955i	0.994082	+	0.108630i	$0.0346465\pi$
$632$	−21.3221	−	36.9309i	−0.848147	−	1.46903i
$633$	7.17814	+	12.4329i	0.285306	+	0.494164i
$634$	22.7447			0.903306
$635$	1.02298	−	1.77185i	0.0405957	−	0.0703138i
$636$	−2.41641			−0.0958170
$637$	−22.1532	−	12.0928i	−0.877741	−	0.479136i
$638$	5.11379			0.202457
$639$	3.90487	−	6.76343i	0.154474	−	0.267557i
$640$	−52.7247			−2.08413
$641$	7.38825	+	12.7968i	0.291819	+	0.505445i	0.974240	−	0.225515i	$-0.0724063\pi$
$641$	7.38825	+	12.7968i	0.291819	+	0.505445i	−0.682421	+	0.730959i	$0.739073\pi$
$642$	−6.68939	−	11.5864i	−0.264009	−	0.457277i
$643$	4.74073	−	8.21118i	0.186956	−	0.323817i	−0.757278	−	0.653093i	$-0.773471\pi$
$643$	4.74073	−	8.21118i	0.186956	−	0.323817i	0.944234	+	0.329276i	$0.106804\pi$
$644$	−39.1896	+	20.6469i	−1.54429	+	0.813603i
$645$	27.3956			1.07870
$646$	26.0242			1.02391
$647$	−49.9026			−1.96187			−0.980937	−	0.194327i	$-0.937748\pi$
$647$	−49.9026			−1.96187			−0.980937	+	0.194327i	$0.937748\pi$
$648$	2.73629			0.107491
$649$	−9.42848	−	16.3306i	−0.370100	−	0.641033i
$650$	−24.1874	+	17.4485i	−0.948708	+	0.684388i
$651$	0.274623	−	7.09175i	0.0107633	−	0.277948i
$652$	5.03784	+	8.72579i	0.197297	+	0.341728i
$653$	−20.7019	+	35.8568i	−0.810128	+	1.40318i	0.102645	+	0.994718i	$0.467269\pi$
$653$	−20.7019	+	35.8568i	−0.810128	+	1.40318i	−0.912774	+	0.408466i	$0.866064\pi$
$654$	6.25722	+	10.8378i	0.244677	+	0.423793i
$655$	9.85355	−	17.0668i	0.385010	−	0.666857i
$656$	0.0864055			0.00337357
$657$	−7.94401	+	13.7594i	−0.309925	+	0.536807i
$658$	−51.9953	+	27.3936i	−2.02699	+	1.06791i
$659$	1.08993	−	1.88781i	0.0424576	−	0.0735387i	−0.844016	−	0.536318i	$-0.819815\pi$
$659$	1.08993	−	1.88781i	0.0424576	−	0.0735387i	0.886473	+	0.462780i	$0.153148\pi$
$660$	24.2943	−	42.0790i	0.945656	−	1.63792i
$661$	32.8566			1.27797			0.638986	−	0.769218i	$-0.279354\pi$
$661$	32.8566			1.27797			0.638986	+	0.769218i	$0.279354\pi$
$662$	1.88714	−	3.26862i	0.0733457	−	0.127038i
$663$	−14.7752	+	10.6587i	−0.573822	+	0.413949i
$664$	36.2145			1.40539
$665$	14.8495	+	9.35760i	0.575838	+	0.362872i
$666$	4.84312	+	8.38853i	0.187667	+	0.325049i
$667$	−2.26967			−0.0878819
$668$	21.4765	−	37.1984i	0.830951	−	1.43925i
$669$	0.596931	+	1.03392i	0.0230787	+	0.0399735i
$670$	−89.4858			−3.45714
$671$	−35.9525			−1.38793
$672$	−13.0676	−	8.23472i	−0.504093	−	0.317661i
$673$	−5.61199	−	9.72024i	−0.216326	−	0.374688i	0.737356	−	0.675505i	$-0.236074\pi$
$673$	−5.61199	−	9.72024i	−0.216326	−	0.374688i	−0.953682	+	0.300817i	$0.902741\pi$
$674$	14.1473	−	24.5039i	0.544936	−	0.943856i
$675$	−1.81371	+	3.14143i	−0.0698097	+	0.120914i
$676$	27.6257	+	31.1018i	1.06253	+	1.19622i
$677$	10.0207	+	17.3564i	0.385127	+	0.667059i	0.991787	−	0.127902i	$-0.0408244\pi$
$677$	10.0207	+	17.3564i	0.385127	+	0.667059i	−0.606660	+	0.794961i	$0.707491\pi$
$678$	1.81243	+	3.13922i	0.0696060	+	0.120561i
$679$	−0.552131	+	14.2580i	−0.0211888	+	0.547172i
$680$	−20.3055	+	35.1702i	−0.778680	+	1.34871i
$681$	7.94437	+	13.7600i	0.304429	+	0.527286i
$682$	15.8107	+	27.3849i	0.605423	+	1.04862i
$683$	−7.33004	−	12.6960i	−0.280476	−	0.485799i	0.691026	−	0.722830i	$-0.257159\pi$
$683$	−7.33004	−	12.6960i	−0.280476	−	0.485799i	−0.971502	+	0.237031i	$0.923826\pi$
$684$	−3.61368	−	6.25908i	−0.138172	−	0.239322i
$685$	−18.3568	+	31.7949i	−0.701376	+	1.21482i
$686$	−33.8817	−	25.2113i	−1.29361	−	0.962573i
$687$	−4.39323	−	7.60931i	−0.167612	−	0.290313i
$688$	0.747251	+	1.29428i	0.0284887	+	0.0493438i
$689$	−2.48355	−	1.11583i	−0.0946159	−	0.0425096i
$690$	−17.5219	+	30.3488i	−0.667047	+	1.15536i
$691$	−14.4726	+	25.0673i	−0.550565	+	0.953606i	0.447669	+	0.894199i	$0.352254\pi$
$691$	−14.4726	+	25.0673i	−0.550565	+	0.953606i	−0.998234	+	0.0594069i	$0.981079\pi$
$692$	20.5578	+	35.6071i	0.781490	+	1.35358i
$693$	12.1007	−	6.37520i	0.459666	−	0.242174i
$694$	30.2036			1.14651
$695$	3.86315			0.146538
$696$	0.593502	+	1.02798i	0.0224966	+	0.0389653i
$697$	1.36238	−	2.35971i	0.0516037	−	0.0893803i
$698$	−79.8430			−3.02210
$699$	2.86714	+	4.96604i	0.108445	+	0.187833i
$700$	−27.1705	+	14.3147i	−1.02695	+	0.541044i
$701$	−37.6521			−1.42210			−0.711051	−	0.703141i	$-0.751780\pi$
$701$	−37.6521			−1.42210			−0.711051	+	0.703141i	$0.751780\pi$
$702$	7.49971	+	3.36952i	0.283058	+	0.127174i
$703$	4.79692	−	8.30851i	0.180919	−	0.313362i
$704$	67.1630			2.53130
$705$	−14.3060	+	24.7787i	−0.538795	+	0.933220i
$706$	−26.3473	+	45.6349i	−0.991595	+	1.71749i
$707$	7.37902	−	3.88761i	0.277517	−	0.146209i
$708$	5.83623	−	10.1086i	0.219339	−	0.379906i
$709$	22.4214			0.842053			0.421026	−	0.907048i	$-0.361670\pi$
$709$	22.4214			0.842053			0.421026	+	0.907048i	$0.361670\pi$
$710$	26.1545	−	45.3009i	0.981560	−	1.70011i
$711$	−7.79235	−	13.4967i	−0.292236	−	0.506168i
$712$	5.47649	−	9.48555i	0.205240	−	0.355486i
$713$	−7.01731	−	12.1543i	−0.262800	−	0.455184i
$714$	−26.9711	+	14.2096i	−1.00937	+	0.531782i
$715$	44.4002	−	32.0298i	1.66047	−	1.19785i
$716$	−29.8655	−	51.7286i	−1.11613	−	1.93319i
$717$	−11.5411			−0.431010
$718$	29.3917			1.09689
$719$	8.37217			0.312229			0.156115	−	0.987739i	$-0.450103\pi$
$719$	8.37217			0.312229			0.156115	+	0.987739i	$0.450103\pi$
$720$	−0.470648			−0.0175400
$721$	29.5344	+	18.6115i	1.09992	+	0.693129i
$722$	15.8470	−	27.4478i	0.589763	−	1.02150i
$723$	2.83030	+	4.90223i	0.105260	+	0.182316i
$724$	−1.40547	−	2.43434i	−0.0522338	−	0.0904717i
$725$	−1.57358			−0.0584412
$726$	−17.9282	+	31.0526i	−0.665379	+	1.15247i
$727$	20.0990			0.745432			0.372716	−	0.927945i	$-0.378427\pi$
$727$	20.0990			0.745432			0.372716	+	0.927945i	$0.378427\pi$
$728$	14.4406	+	21.7442i	0.535204	+	0.805893i
$729$	1.00000			0.0370370
$730$	−53.2083	+	92.1596i	−1.96933	+	3.41098i
$731$	47.1284			1.74311
$732$	−11.1273	−	19.2730i	−0.411277	−	0.712352i
$733$	5.77804	+	10.0079i	0.213417	+	0.369649i	0.952782	−	0.303656i	$-0.0982074\pi$
$733$	5.77804	+	10.0079i	0.213417	+	0.369649i	−0.739365	+	0.673305i	$0.764874\pi$
$734$	30.2064	−	52.3191i	1.11494	−	1.93113i
$735$	−20.4992	−	1.59001i	−0.756123	−	0.0586485i
$736$	−30.5444			−1.12588
$737$	69.0664			2.54409
$738$	−1.22966			−0.0452644
$739$	24.2650			0.892601			0.446300	−	0.894883i	$-0.352741\pi$
$739$	24.2650			0.892601			0.446300	+	0.894883i	$0.352741\pi$
$740$	19.9622	+	34.5756i	0.733826	+	1.27102i
$741$	−0.823835	−	8.10167i	−0.0302643	−	0.297622i
$742$	−3.85445	−	2.42893i	−0.141501	−	0.0891689i
$743$	0.777681	+	1.34698i	0.0285303	+	0.0494160i	0.879938	−	0.475088i	$-0.157584\pi$
$743$	0.777681	+	1.34698i	0.0285303	+	0.0494160i	−0.851408	+	0.524504i	$0.824251\pi$
$744$	−3.66996	+	6.35655i	−0.134547	+	0.233043i
$745$	−31.1241	−	53.9086i	−1.14030	−	1.97506i
$746$	14.1050	−	24.4306i	0.516422	−	0.894468i
$747$	13.2349			0.484240
$748$	41.7933	−	72.3881i	1.52811	−	2.64677i
$749$	0.600653	−	15.5110i	0.0219474	−	0.566761i
$750$	4.59673	−	7.96177i	0.167849	−	0.290723i
$751$	17.6793	−	30.6214i	0.645125	−	1.11739i	−0.339148	−	0.940733i	$-0.610139\pi$
$751$	17.6793	−	30.6214i	0.645125	−	1.11739i	0.984273	−	0.176656i	$-0.0565281\pi$
$752$	−1.56086			−0.0569186
$753$	12.1872	−	21.1088i	0.444126	−	0.769249i
$754$	0.360823	+	3.54836i	0.0131404	+	0.129224i
$755$	−46.4295			−1.68974
$756$	7.16271	+	4.51367i	0.260505	+	0.164161i
$757$	9.73684	+	16.8647i	0.353891	+	0.612958i	0.986928	−	0.161164i	$-0.0515249\pi$
$757$	9.73684	+	16.8647i	0.353891	+	0.612958i	−0.633036	+	0.774122i	$0.718192\pi$
$758$	63.9310			2.32208
$759$	13.5236	−	23.4236i	0.490877	−	0.850223i
$760$	−9.07629	−	15.7206i	−0.329232	−	0.570246i
$761$	17.6396			0.639434			0.319717	−	0.947513i	$-0.396412\pi$
$761$	17.6396			0.639434			0.319717	+	0.947513i	$0.396412\pi$
$762$	−1.58839			−0.0575411
$763$	−0.561848	+	14.5089i	−0.0203403	+	0.525259i
$764$	25.5216	+	44.2048i	0.923341	+	1.59927i
$765$	−7.42083	+	12.8532i	−0.268301	+	0.464710i
$766$	29.9754	−	51.9190i	1.08306	−	1.87591i
$767$	10.6663	−	7.69452i	0.385136	−	0.277833i
$768$	7.47442	+	12.9461i	0.269710	+	0.467151i
$769$	−2.32077	−	4.01969i	−0.0836890	−	0.144954i	0.821143	−	0.570723i	$-0.193337\pi$
$769$	−2.32077	−	4.01969i	−0.0836890	−	0.144954i	−0.904832	+	0.425769i	$0.860004\pi$
$770$	81.0492	−	42.7006i	2.92081	−	1.53882i
$771$	−2.30268	+	3.98836i	−0.0829290	+	0.143637i
$772$	−6.32095	−	10.9482i	−0.227496	−	0.394034i
$773$	−10.0222	−	17.3590i	−0.360475	−	0.624360i	0.627564	−	0.778565i	$-0.284052\pi$
$773$	−10.0222	−	17.3590i	−0.360475	−	0.624360i	−0.988039	+	0.154204i	$0.950719\pi$
$774$	−10.6343	−	18.4192i	−0.382243	−	0.662064i
$775$	−4.86516	−	8.42670i	−0.174762	−	0.302696i
$776$	7.37848	−	12.7799i	0.264872	−	0.458772i
$777$	−0.434873	+	11.2300i	−0.0156010	+	0.402874i
$778$	−30.6032	−	53.0063i	−1.09718	−	1.90037i
$779$	0.608965	+	1.05476i	0.0218184	+	0.0377906i
$780$	30.9121	+	13.8884i	1.10683	+	0.497283i
$781$	−20.1864	+	34.9638i	−0.722326	+	1.25110i
$782$	−30.1427	+	52.2087i	−1.07790	+	1.86698i
$783$	0.216901	+	0.375683i	0.00775140	+	0.0134258i
$784$	−0.484023	−	1.01183i	−0.0172865	−	0.0361368i
$785$	16.2257			0.579119
$786$	−15.2997			−0.545721
$787$	5.05832	+	8.76128i	0.180310	+	0.312306i	0.941986	−	0.335652i	$-0.108957\pi$
$787$	5.05832	+	8.76128i	0.180310	+	0.312306i	−0.761676	+	0.647958i	$0.775623\pi$
$788$	−21.5150	+	37.2650i	−0.766438	+	1.32751i
$789$	22.9824			0.818193
$790$	−52.1925	−	90.4001i	−1.85693	−	3.21629i
$791$	−0.162742	+	4.20258i	−0.00578643	+	0.149426i
$792$	−14.1453			−0.502633
$793$	−2.53676	−	24.9468i	−0.0900831	−	0.885887i
$794$	−27.9618	+	48.4313i	−0.992328	+	1.71876i
$795$	−2.21804			−0.0786657
$796$	−33.3260	+	57.7223i	−1.18121	+	2.04591i
$797$	−4.44188	+	7.69357i	−0.157340	+	0.272520i	−0.933908	−	0.357512i	$-0.883625\pi$
$797$	−4.44188	+	7.69357i	−0.157340	+	0.272520i	0.776569	+	0.630032i	$0.216958\pi$
$798$	0.527282	−	13.6163i	0.0186656	−	0.482013i
$799$	−24.6104	+	42.6265i	−0.870655	+	1.50802i
$800$	−21.1767			−0.748710
$801$	2.00143	−	3.46658i	0.0707171	−	0.122486i
$802$	−3.60944	−	6.25172i	−0.127454	−	0.220756i
$803$	41.0669	−	71.1300i	1.44922	−	2.51012i
$804$	21.3760	+	37.0244i	0.753875	+	1.30575i
$805$	−35.9723	+	18.9519i	−1.26786	+	0.667967i
$806$	−17.8863	+	12.9030i	−0.630020	+	0.454489i
$807$	−7.00246	−	12.1286i	−0.246498	−	0.426948i
$808$	−8.62587			−0.303457
$809$	−41.7569			−1.46809			−0.734047	−	0.679099i	$-0.762371\pi$
$809$	−41.7569			−1.46809			−0.734047	+	0.679099i	$0.762371\pi$
$810$	6.69792			0.235341
$811$	−31.3690			−1.10151			−0.550757	−	0.834666i	$-0.685661\pi$
$811$	−31.3690			−1.10151			−0.550757	+	0.834666i	$0.685661\pi$
$812$	−0.142115	+	3.66993i	−0.00498726	+	0.128789i
$813$	9.55299	−	16.5463i	0.335038	−	0.580303i
$814$	−25.0367	−	43.3649i	−0.877537	−	1.51994i
$815$	4.62425	+	8.00944i	0.161981	+	0.280559i
$816$	−0.809651			−0.0283434
$817$	−10.5329	+	18.2435i	−0.368499	+	0.638259i
$818$	43.4826			1.52033
$819$	5.27744	+	7.94661i	0.184409	+	0.277677i
$820$	−5.06838			−0.176995
$821$	−15.2754	+	26.4577i	−0.533114	+	0.923381i	0.466138	+	0.884712i	$0.345645\pi$
$821$	−15.2754	+	26.4577i	−0.533114	+	0.923381i	−0.999252	+	0.0386690i	$0.987688\pi$
$822$	28.5027			0.994144
$823$	−1.67437	−	2.90010i	−0.0583650	−	0.101091i	0.835367	−	0.549693i	$-0.185255\pi$
$823$	−1.67437	−	2.90010i	−0.0583650	−	0.101091i	−0.893732	+	0.448602i	$0.851922\pi$
$824$	−18.0520	−	31.2670i	−0.628872	−	1.08924i
$825$	9.37604	−	16.2398i	0.326432	−	0.565397i
$826$	19.4705	−	10.2580i	0.677464	−	0.356920i
$827$	−48.2646			−1.67833			−0.839163	−	0.543880i	$-0.816955\pi$
$827$	−48.2646			−1.67833			−0.839163	+	0.543880i	$0.816955\pi$
$828$	16.7423			0.581834
$829$	49.8292			1.73064			0.865320	−	0.501219i	$-0.167115\pi$
$829$	49.8292			1.73064			0.865320	+	0.501219i	$0.167115\pi$
$830$	88.6463			3.07696
$831$	−6.45998	−	11.1890i	−0.224094	−	0.388142i
$832$	4.73894	+	46.6032i	0.164293	+	1.61568i
$833$	−35.2645	−	2.73528i	−1.22184	−	0.0947719i
$834$	−1.49958	−	2.59735i	−0.0519263	−	0.0899390i
$835$	19.7134	−	34.1446i	0.682210	−	1.18162i
$836$	18.6811	+	32.3566i	0.646098	+	1.11907i
$837$	−1.34122	+	2.32306i	−0.0463593	+	0.0802967i
$838$	−35.5976			−1.22970
$839$	16.4441	−	28.4819i	0.567712	−	0.983305i	−0.429080	−	0.903266i	$-0.641162\pi$
$839$	16.4441	−	28.4819i	0.567712	−	0.983305i	0.996792	−	0.0800390i	$-0.0255045\pi$
$840$	17.9902	+	11.3368i	0.620721	+	0.391156i
$841$	14.4059	−	24.9518i	0.496755	−	0.860406i
$842$	20.5830	−	35.6507i	0.709335	−	1.22860i
$843$	−19.6264			−0.675971
$844$	22.9697	−	39.7846i	0.790649	−	1.36944i
$845$	25.3577	+	28.5485i	0.872333	+	0.982099i
$846$	22.2130			0.763698
$847$	−36.8065	+	19.3914i	−1.26469	+	0.666297i
$848$	−0.0604999	−	0.104789i	−0.00207757	−	0.00359846i
$849$	3.26727			0.112132
$850$	−20.8982	+	36.1967i	−0.716802	+	1.24154i
$851$	11.1121	+	19.2468i	0.380919	+	0.659771i
$852$	−24.9907			−0.856169
$853$	−17.9823			−0.615701			−0.307850	−	0.951435i	$-0.599610\pi$
$853$	−17.9823			−0.615701			−0.307850	+	0.951435i	$0.599610\pi$
$854$	1.62361	−	41.9276i	0.0555590	−	1.43473i
$855$	−3.31701	−	5.74523i	−0.113439	−	0.196483i
$856$	−8.02691	+	13.9030i	−0.274354	+	0.475195i
$857$	23.5502	−	40.7901i	0.804459	−	1.39336i	−0.112196	−	0.993686i	$-0.535789\pi$
$857$	23.5502	−	40.7901i	0.804459	−	1.39336i	0.916656	−	0.399678i	$-0.130878\pi$
$858$	−38.7701	−	17.4189i	−1.32359	−	0.594670i
$859$	−13.8486	−	23.9866i	−0.472510	−	0.818411i	0.526995	−	0.849868i	$-0.323319\pi$
$859$	−13.8486	−	23.9866i	−0.472510	−	0.818411i	−0.999505	+	0.0314573i	$0.989985\pi$
$860$	−43.8322	−	75.9197i	−1.49467	−	2.58884i
$861$	−1.20704	−	0.760629i	−0.0411357	−	0.0259222i
$862$	19.9718	−	34.5922i	0.680242	−	1.17821i
$863$	18.5569	+	32.1414i	0.631683	+	1.09411i	0.987208	+	0.159440i	$0.0509689\pi$
$863$	18.5569	+	32.1414i	0.631683	+	1.09411i	−0.355525	+	0.934667i	$0.615698\pi$
$864$	2.91898	+	5.05582i	0.0993057	+	0.172003i
$865$	18.8701	+	32.6840i	0.641602	+	1.11129i
$866$	−6.90854	−	11.9659i	−0.234762	−	0.406619i
$867$	−4.26597	+	7.38888i	−0.144880	+	0.250939i
$868$	−20.0923	+	10.5856i	−0.681977	+	0.359298i
$869$	40.2829	+	69.7720i	1.36650	+	2.36685i
$870$	1.45278	+	2.51629i	0.0492540	+	0.0853104i
$871$	4.87324	+	47.9239i	0.165123	+	1.62384i
$872$	7.50833	−	13.0048i	0.254264	−	0.440399i
$873$	2.69653	−	4.67053i	0.0912637	−	0.158073i
$874$	−13.4734	−	23.3366i	−0.455745	−	0.789373i
$875$	9.43705	−	4.97188i	0.319031	−	0.168080i
$876$	50.8408			1.71775
$877$	28.2981			0.955559			0.477780	−	0.878480i	$-0.341442\pi$
$877$	28.2981			0.955559			0.477780	+	0.878480i	$0.341442\pi$
$878$	−26.6599	−	46.1763i	−0.899727	−	1.55837i
$879$	9.50947	−	16.4709i	0.320746	−	0.555549i
$880$	2.43303			0.0820176
$881$	−9.74919	−	16.8861i	−0.328458	−	0.568907i	0.653748	−	0.756713i	$-0.273196\pi$
$881$	−9.74919	−	16.8861i	−0.328458	−	0.568907i	−0.982206	+	0.187806i	$0.939862\pi$
$882$	6.88826	+	14.3996i	0.231940	+	0.484861i
$883$	36.8164			1.23897			0.619485	−	0.785009i	$-0.287342\pi$
$883$	36.8164			1.23897			0.619485	+	0.785009i	$0.287342\pi$
$884$	53.1777	+	23.8920i	1.78856	+	0.803575i
$885$	5.35710	−	9.27878i	0.180077	−	0.311903i
$886$	−20.2819			−0.681383
$887$	11.0920	−	19.2118i	0.372432	−	0.645070i	−0.617507	−	0.786565i	$-0.711857\pi$
$887$	11.0920	−	19.2118i	0.372432	−	0.645070i	0.989939	+	0.141495i	$0.0451908\pi$
$888$	5.81149	−	10.0658i	0.195021	−	0.337786i
$889$	−1.55916	−	0.982526i	−0.0522926	−	0.0329529i
$890$	13.4054	−	23.2189i	0.449351	−	0.778298i
$891$	−5.16954			−0.173186
$892$	1.91015	−	3.30847i	0.0639565	−	0.110776i
$893$	−11.0005	−	19.0535i	−0.368119	−	0.637601i
$894$	−24.1633	+	41.8521i	−0.808142	+	1.39974i
$895$	−27.4137	−	47.4820i	−0.916340	−	1.58715i
$896$	−1.83772	+	47.4567i	−0.0613941	+	1.58542i
$897$	17.2074	+	7.73106i	0.574540	+	0.258133i
$898$	−44.1635	−	76.4935i	−1.47376	−	2.55262i
$899$	−1.16365			−0.0388098
$900$	11.6075			0.386918
$901$	−3.81567			−0.127118
$902$	6.35678			0.211658
$903$	0.954876	−	24.6584i	0.0317763	−	0.820579i
$904$	2.17482	−	3.76690i	0.0723335	−	0.125285i
$905$	−1.29009	−	2.23450i	−0.0428839	−	0.0742771i
$906$	18.0229	+	31.2165i	0.598769	+	1.03710i
$907$	−46.6084			−1.54761			−0.773803	−	0.633427i	$-0.781648\pi$
$907$	−46.6084			−1.54761			−0.773803	+	0.633427i	$0.781648\pi$
$908$	25.4215	−	44.0314i	0.843644	−	1.46123i
$909$	−3.15240			−0.104559
$910$	35.3479	+	53.2257i	1.17177	+	1.76442i
$911$	0.542513			0.0179743			0.00898714	−	0.999960i	$-0.497139\pi$
$911$	0.542513			0.0179743			0.00898714	+	0.999960i	$0.497139\pi$
$912$	0.180952	−	0.313418i	0.00599191	−	0.0103783i
$913$	−68.4184			−2.26432
$914$	−25.5401	−	44.2368i	−0.844792	−	1.46322i
$915$	−10.2138	−	17.6908i	−0.337658	−	0.584840i
$916$	−14.0581	+	24.3494i	−0.464493	+	0.804526i
$917$	−15.0182	−	9.46389i	−0.495943	−	0.312525i
$918$	11.5224			0.380294
$919$	33.6621			1.11041			0.555205	−	0.831713i	$-0.312640\pi$
$919$	33.6621			1.11041			0.555205	+	0.831713i	$0.312640\pi$
$920$	42.0507			1.38637
$921$	−8.30660			−0.273712
$922$	−3.20085	−	5.54403i	−0.105414	−	0.182583i
$923$	−25.6851	−	11.5400i	−0.845436	−	0.379843i
$924$	−37.0279	−	23.3336i	−1.21813	−	0.767620i
$925$	7.70412	+	13.3439i	0.253310	+	0.438746i
$926$	−43.0449	+	74.5559i	−1.41454	+	2.45006i
$927$	−6.59727	−	11.4268i	−0.216683	−	0.375306i
$928$	−1.26626	+	2.19322i	−0.0415669	+	0.0719961i
$929$	−42.6784			−1.40023			−0.700116	−	0.714029i	$-0.746869\pi$
$929$	−42.6784			−1.40023			−0.700116	+	0.714029i	$0.746869\pi$
$930$	−8.98338	+	15.5597i	−0.294576	+	0.510221i
$931$	8.94021	−	13.0396i	0.293004	−	0.427357i
$932$	9.17471	−	15.8911i	0.300528	−	0.520529i
$933$	5.42853	−	9.40250i	0.177722	−	0.307824i
$934$	36.6856			1.20039
$935$	38.3623	−	66.4454i	1.25458	−	2.17300i
$936$	−0.998078	−	9.81520i	−0.0326232	−	0.320820i
$937$	−10.2859			−0.336026			−0.168013	−	0.985785i	$-0.553735\pi$
$937$	−10.2859			−0.336026			−0.168013	+	0.985785i	$0.553735\pi$
$938$	−3.11904	+	80.5448i	−0.101840	+	2.62988i
$939$	0.566928	+	0.981949i	0.0185010	+	0.0320447i
$940$	91.5568			2.98625
$941$	5.84119	−	10.1172i	0.190417	−	0.329813i	−0.754971	−	0.655758i	$-0.772349\pi$
$941$	5.84119	−	10.1172i	0.190417	−	0.329813i	0.945389	+	0.325945i	$0.105683\pi$
$942$	−6.29842	−	10.9092i	−0.205214	−	0.355440i
$943$	−2.82135			−0.0918758
$944$	0.584488			0.0190235
$945$	6.57468	+	4.14312i	0.213874	+	0.134776i
$946$	54.9746	+	95.2188i	1.78738	+	3.09583i
$947$	−15.9404	+	27.6096i	−0.517993	+	0.897190i	0.481789	+	0.876287i	$0.339987\pi$
$947$	−15.9404	+	27.6096i	−0.517993	+	0.897190i	−0.999782	+	0.0209026i	$0.993346\pi$
$948$	−24.9351	+	43.1889i	−0.809855	+	1.40271i
$949$	52.2535	+	23.4768i	1.69622	+	0.762088i
$950$	−9.34122	−	16.1795i	−0.303069	−	0.524931i
$951$	−4.98712	−	8.63795i	−0.161718	−	0.280105i
$952$	30.9484	+	19.5025i	1.00304	+	0.632080i
$953$	3.72492	−	6.45175i	0.120662	−	0.208993i	−0.799367	−	0.600843i	$-0.794832\pi$
$953$	3.72492	−	6.45175i	0.120662	−	0.208993i	0.920029	+	0.391850i	$0.128165\pi$
$954$	0.860990	+	1.49128i	0.0278756	+	0.0482819i
$955$	23.4264	+	40.5758i	0.758062	+	1.31300i
$956$	18.4655	+	31.9831i	0.597215	+	1.03441i
$957$	−1.12128	−	1.94211i	−0.0362458	−	0.0627795i
$958$	−9.74674	+	16.8818i	−0.314903	+	0.545428i
$959$	27.9782	+	17.6309i	0.903464	+	0.569330i
$960$	19.0804	+	33.0483i	0.615819	+	1.06663i
$961$	11.9023	+	20.6153i	0.383944	+	0.665010i
$962$	28.3236	−	20.4323i	0.913188	−	0.658764i
$963$	−2.93351	+	5.08098i	−0.0945309	+	0.163732i
$964$	9.05681	−	15.6869i	0.291700	−	0.505240i
$965$	−5.80203	−	10.0494i	−0.186774	−	0.323502i
$966$	26.7058	+	16.8290i	0.859244	+	0.541464i
$967$	−51.0981			−1.64320			−0.821602	−	0.570061i	$-0.806920\pi$
$967$	−51.0981			−1.64320			−0.821602	+	0.570061i	$0.806920\pi$
$968$	43.0258			1.38290
$969$	−5.70622	−	9.88347i	−0.183310	−	0.317503i
$970$	18.0611	−	31.2828i	0.579908	−	1.00443i
$971$	5.01835			0.161046			0.0805232	−	0.996753i	$-0.474341\pi$
$971$	5.01835			0.161046			0.0805232	+	0.996753i	$0.474341\pi$
$972$	−1.59997	−	2.77124i	−0.0513192	−	0.0888874i
$973$	0.134650	−	3.47716i	0.00431669	−	0.111473i
$974$	−81.1256			−2.59943
$975$	11.9301	+	5.36001i	0.382068	+	0.171658i
$976$	0.557189	−	0.965080i	0.0178352	−	0.0308915i
$977$	−27.6611			−0.884958			−0.442479	−	0.896779i	$-0.645901\pi$
$977$	−27.6611			−0.884958			−0.442479	+	0.896779i	$0.645901\pi$
$978$	3.59005	−	6.21815i	0.114797	−	0.198835i
$979$	−10.3465	+	17.9206i	−0.330675	+	0.572746i
$980$	28.3918	+	59.3519i	0.906943	+	1.89593i
$981$	2.74399	−	4.75273i	0.0876088	−	0.151743i
$982$	−71.5980			−2.28478
$983$	2.23464	−	3.87050i	0.0712738	−	0.123450i	−0.828186	−	0.560453i	$-0.810627\pi$
$983$	2.23464	−	3.87050i	0.0712738	−	0.123450i	0.899460	+	0.437003i	$0.143960\pi$
$984$	0.737763	+	1.27784i	0.0235190	+	0.0407362i
$985$	−19.7487	+	34.2057i	−0.629245	+	1.08988i
$986$	2.49921	+	4.32875i	0.0795910	+	0.137856i
$987$	21.8043	+	13.7403i	0.694038	+	0.437357i
$988$	−21.1335	+	15.2455i	−0.672347	+	0.485024i
$989$	−24.3995	−	42.2613i	−0.775860	−	1.34383i
$990$	−34.6252			−1.10046
$991$	10.4243			0.331139			0.165570	−	0.986198i	$-0.447054\pi$
$991$	10.4243			0.331139			0.165570	+	0.986198i	$0.447054\pi$
$992$	−15.6600			−0.497204
$993$	−1.65514			−0.0525242
$994$	−39.8630	−	25.1202i	−1.26438	−	0.796765i
$995$	−30.5901	+	52.9836i	−0.969771	+	1.67969i
$996$	−21.1755	−	36.6770i	−0.670971	−	1.16216i
$997$	7.25600	+	12.5678i	0.229800	+	0.398025i	0.957749	−	0.287607i	$-0.0928596\pi$
$997$	7.25600	+	12.5678i	0.229800	+	0.398025i	−0.727949	+	0.685631i	$0.759526\pi$
$998$	−9.78748			−0.309817
$999$	2.12386	−	3.67863i	0.0671960	−	0.116387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.172.2	yes	20
3.2	odd	2		819.2.n.f.172.9		20
7.2	even	3		273.2.l.c.16.9	yes	20
13.9	even	3		273.2.l.c.256.9	yes	20
21.2	odd	6		819.2.s.f.289.2		20
39.35	odd	6		819.2.s.f.802.2		20
91.9	even	3	inner	273.2.j.c.100.2	✓	20
273.191	odd	6		819.2.n.f.100.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.2	✓	20	91.9	even	3	inner
273.2.j.c.172.2	yes	20	1.1	even	1	trivial
273.2.l.c.16.9	yes	20	7.2	even	3
273.2.l.c.256.9	yes	20	13.9	even	3
819.2.n.f.100.9		20	273.191	odd	6
819.2.n.f.172.9		20	3.2	odd	2
819.2.s.f.289.2		20	21.2	odd	6
819.2.s.f.802.2		20	39.35	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14017 + 1.97483i) q^{2} +1.00000 q^{3} +(-1.59997 - 2.77124i) q^{4} +(-1.46862 - 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(-2.34076 + 1.23322i) q^{7} +2.73629 q^{8} +1.00000 q^{9} +6.69792 q^{10} -5.16954 q^{11} +(-1.59997 - 2.77124i) q^{12} +(-0.364757 - 3.58705i) q^{13} +(0.233457 - 6.02869i) q^{14} +(-1.46862 - 2.54373i) q^{15} +(0.0801172 - 0.138767i) q^{16} +(-2.52646 - 4.37595i) q^{17} +(-1.14017 + 1.97483i) q^{18} +2.25859 q^{19} +(-4.69952 + 8.13980i) q^{20} +(-2.34076 + 1.23322i) q^{21} +(5.89416 - 10.2090i) q^{22} +(-2.61602 + 4.53108i) q^{23} +2.73629 q^{24} +(-1.81371 + 3.14143i) q^{25} +(7.49971 + 3.36952i) q^{26} +1.00000 q^{27} +(7.16271 + 4.51367i) q^{28} +(0.216901 + 0.375683i) q^{29} +6.69792 q^{30} +(-1.34122 + 2.32306i) q^{31} +(2.91898 + 5.05582i) q^{32} -5.16954 q^{33} +11.5224 q^{34} +(6.57468 + 4.14312i) q^{35} +(-1.59997 - 2.77124i) q^{36} +(2.12386 - 3.67863i) q^{37} +(-2.57517 + 4.46033i) q^{38} +(-0.364757 - 3.58705i) q^{39} +(-4.01857 - 6.96037i) q^{40} +(0.269622 + 0.466999i) q^{41} +(0.233457 - 6.02869i) q^{42} +(-4.66348 + 8.07739i) q^{43} +(8.27113 + 14.3260i) q^{44} +(-1.46862 - 2.54373i) q^{45} +(-5.96541 - 10.3324i) q^{46} +(-4.87054 - 8.43603i) q^{47} +(0.0801172 - 0.138767i) q^{48} +(3.95832 - 5.77336i) q^{49} +(-4.13587 - 7.16354i) q^{50} +(-2.52646 - 4.37595i) q^{51} +(-9.35697 + 6.75002i) q^{52} +(0.377571 - 0.653972i) q^{53} +(-1.14017 + 1.97483i) q^{54} +(7.59211 + 13.1499i) q^{55} +(-6.40499 + 3.37445i) q^{56} +2.25859 q^{57} -0.989214 q^{58} +(1.82385 + 3.15901i) q^{59} +(-4.69952 + 8.13980i) q^{60} +6.95468 q^{61} +(-3.05843 - 5.29736i) q^{62} +(-2.34076 + 1.23322i) q^{63} -12.9921 q^{64} +(-8.58881 + 6.19587i) q^{65} +(5.89416 - 10.2090i) q^{66} -13.3602 q^{67} +(-8.08453 + 14.0028i) q^{68} +(-2.61602 + 4.53108i) q^{69} +(-15.6782 + 8.26003i) q^{70} +(3.90487 - 6.76343i) q^{71} +2.73629 q^{72} +(-7.94401 + 13.7594i) q^{73} +(4.84312 + 8.38853i) q^{74} +(-1.81371 + 3.14143i) q^{75} +(-3.61368 - 6.25908i) q^{76} +(12.1007 - 6.37520i) q^{77} +(7.49971 + 3.36952i) q^{78} +(-7.79235 - 13.4967i) q^{79} -0.470648 q^{80} +1.00000 q^{81} -1.22966 q^{82} +13.2349 q^{83} +(7.16271 + 4.51367i) q^{84} +(-7.42083 + 12.8532i) q^{85} +(-10.6343 - 18.4192i) q^{86} +(0.216901 + 0.375683i) q^{87} -14.1453 q^{88} +(2.00143 - 3.46658i) q^{89} +6.69792 q^{90} +(5.27744 + 7.94661i) q^{91} +16.7423 q^{92} +(-1.34122 + 2.32306i) q^{93} +22.2130 q^{94} +(-3.31701 - 5.74523i) q^{95} +(2.91898 + 5.05582i) q^{96} +(2.69653 - 4.67053i) q^{97} +(6.88826 + 14.3996i) q^{98} -5.16954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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