LMFDB - Embedded newform 273.2.i.c.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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, 0]))

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

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

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.i (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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	273.79
Dual form			273.2.i.c.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12349 - 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 - 2.64044i) q^{4} +(-0.178448 + 0.309081i) q^{5} -2.24698 q^{6} +(-2.37047 - 1.17511i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.12349 - 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 - 2.64044i) q^{4} +(-0.178448 + 0.309081i) q^{5} -2.24698 q^{6} +(-2.37047 - 1.17511i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.400969 + 0.694498i) q^{10} +(-2.59299 - 4.49119i) q^{11} +(-1.52446 + 2.64044i) q^{12} +1.00000 q^{13} +(-4.94989 + 3.29257i) q^{14} +0.356896 q^{15} +(0.400969 - 0.694498i) q^{16} +(3.82640 + 6.62751i) q^{17} +(1.12349 + 1.94594i) q^{18} +(3.74698 - 6.48996i) q^{19} +1.08815 q^{20} +(0.167563 + 2.64044i) q^{21} -11.6528 q^{22} +(0.524459 - 0.908389i) q^{23} +(1.17845 + 2.04113i) q^{24} +(2.43631 + 4.21982i) q^{25} +(1.12349 - 1.94594i) q^{26} +1.00000 q^{27} +(0.510885 + 8.05048i) q^{28} -0.246980 q^{29} +(0.400969 - 0.694498i) q^{30} +(4.12349 + 7.14209i) q^{31} +(-3.25786 - 5.64279i) q^{32} +(-2.59299 + 4.49119i) q^{33} +17.1957 q^{34} +(0.786208 - 0.522971i) q^{35} +3.04892 q^{36} +(4.57942 - 7.93178i) q^{37} +(-8.41939 - 14.5828i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(0.420583 - 0.728471i) q^{40} -5.75302 q^{41} +(5.32640 + 2.64044i) q^{42} +1.54288 q^{43} +(-7.90581 + 13.6933i) q^{44} +(-0.178448 - 0.309081i) q^{45} +(-1.17845 - 2.04113i) q^{46} +(-0.780167 + 1.35129i) q^{47} -0.801938 q^{48} +(4.23825 + 5.57111i) q^{49} +10.9487 q^{50} +(3.82640 - 6.62751i) q^{51} +(-1.52446 - 2.64044i) q^{52} +(-4.50484 - 7.80262i) q^{53} +(1.12349 - 1.94594i) q^{54} +1.85086 q^{55} +(5.58695 + 2.76960i) q^{56} -7.49396 q^{57} +(-0.277479 + 0.480608i) q^{58} +(2.67241 + 4.62874i) q^{59} +(-0.544073 - 0.942362i) q^{60} +(-0.914542 + 1.58403i) q^{61} +18.5308 q^{62} +(2.20291 - 1.46533i) q^{63} -13.0368 q^{64} +(-0.178448 + 0.309081i) q^{65} +(5.82640 + 10.0916i) q^{66} +(5.73005 + 9.92474i) q^{67} +(11.6664 - 20.2067i) q^{68} -1.04892 q^{69} +(-0.134375 - 2.11747i) q^{70} -10.4547 q^{71} +(1.17845 - 2.04113i) q^{72} +(-3.08426 - 5.34210i) q^{73} +(-10.2899 - 17.8226i) q^{74} +(2.43631 - 4.21982i) q^{75} -22.8485 q^{76} +(0.868977 + 13.6933i) q^{77} -2.24698 q^{78} +(0.370469 - 0.641672i) q^{79} +(0.143104 + 0.247864i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.46346 + 11.1950i) q^{82} +2.80194 q^{83} +(6.71648 - 4.46768i) q^{84} -2.73125 q^{85} +(1.73341 - 3.00235i) q^{86} +(0.123490 + 0.213891i) q^{87} +(6.11141 + 10.5853i) q^{88} +(-1.99880 + 3.46203i) q^{89} -0.801938 q^{90} +(-2.37047 - 1.17511i) q^{91} -3.19806 q^{92} +(4.12349 - 7.14209i) q^{93} +(1.75302 + 3.03632i) q^{94} +(1.33728 + 2.31624i) q^{95} +(-3.25786 + 5.64279i) q^{96} +6.36658 q^{97} +(15.6027 - 1.98831i) q^{98} +5.18598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + 6 q^{13} - 7 q^{14} - 6 q^{15} - 2 q^{16} + 5 q^{17} + 2 q^{18} + 13 q^{19} + 14 q^{20} - 34 q^{22} - 6 q^{23} + 3 q^{24} - 2 q^{25} + 2 q^{26} + 6 q^{27} + 8 q^{29} - 2 q^{30} + 20 q^{31} - 7 q^{32} - q^{33} + 30 q^{34} + 21 q^{35} + 19 q^{37} - 18 q^{38} - 3 q^{39} + 11 q^{40} - 44 q^{41} + 14 q^{42} - 28 q^{43} - 21 q^{44} + 3 q^{45} - 3 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{50} + 5 q^{51} - 5 q^{53} + 2 q^{54} - 16 q^{55} - 26 q^{57} - 2 q^{58} - 7 q^{59} - 7 q^{60} + 5 q^{61} + 36 q^{62} - 22 q^{64} + 3 q^{65} + 17 q^{66} + 9 q^{67} + 28 q^{68} + 12 q^{69} + 7 q^{70} - 18 q^{71} + 3 q^{72} + 12 q^{73} - 15 q^{74} - 2 q^{75} - 28 q^{76} + 35 q^{77} - 4 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 10 q^{82} + 8 q^{83} + 21 q^{84} - 32 q^{85} + 7 q^{86} - 4 q^{87} - 6 q^{88} + 29 q^{89} + 4 q^{90} - 28 q^{92} + 20 q^{93} + 20 q^{94} - 13 q^{95} - 7 q^{96} - 14 q^{97} + 35 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + 6 * q^13 - 7 * q^14 - 6 * q^15 - 2 * q^16 + 5 * q^17 + 2 * q^18 + 13 * q^19 + 14 * q^20 - 34 * q^22 - 6 * q^23 + 3 * q^24 - 2 * q^25 + 2 * q^26 + 6 * q^27 + 8 * q^29 - 2 * q^30 + 20 * q^31 - 7 * q^32 - q^33 + 30 * q^34 + 21 * q^35 + 19 * q^37 - 18 * q^38 - 3 * q^39 + 11 * q^40 - 44 * q^41 + 14 * q^42 - 28 * q^43 - 21 * q^44 + 3 * q^45 - 3 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^50 + 5 * q^51 - 5 * q^53 + 2 * q^54 - 16 * q^55 - 26 * q^57 - 2 * q^58 - 7 * q^59 - 7 * q^60 + 5 * q^61 + 36 * q^62 - 22 * q^64 + 3 * q^65 + 17 * q^66 + 9 * q^67 + 28 * q^68 + 12 * q^69 + 7 * q^70 - 18 * q^71 + 3 * q^72 + 12 * q^73 - 15 * q^74 - 2 * q^75 - 28 * q^76 + 35 * q^77 - 4 * q^78 - 12 * q^79 + 9 * q^80 - 3 * q^81 - 10 * q^82 + 8 * q^83 + 21 * q^84 - 32 * q^85 + 7 * q^86 - 4 * q^87 - 6 * q^88 + 29 * q^89 + 4 * q^90 - 28 * q^92 + 20 * q^93 + 20 * q^94 - 13 * q^95 - 7 * q^96 - 14 * q^97 + 35 * q^98 + 2 * q^99

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 $

$2$	1.12349	−	1.94594i	0.794427	−	1.37599i	−0.128775	−	0.991674i	$-0.541104\pi$
$2$	1.12349	−	1.94594i	0.794427	−	1.37599i	0.923202	−	0.384315i	$-0.125562\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.52446	−	2.64044i	−0.762229	−	1.32022i
$5$	−0.178448	+	0.309081i	−0.0798043	+	0.138225i	−0.903165	−	0.429293i	$-0.858763\pi$
$5$	−0.178448	+	0.309081i	−0.0798043	+	0.138225i	0.823361	+	0.567518i	$0.192096\pi$
$6$	−2.24698			−0.917326
$7$	−2.37047	−	1.17511i	−0.895953	−	0.444148i
$7$	−2.37047	−	1.17511i	−0.895953	−	0.444148i
$8$	−2.35690			−0.833289
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.400969	+	0.694498i	0.126797	+	0.219620i
$11$	−2.59299	−	4.49119i	−0.781816	−	1.35415i	−0.930883	−	0.365318i	$-0.880960\pi$
$11$	−2.59299	−	4.49119i	−0.781816	−	1.35415i	0.149067	−	0.988827i	$-0.452373\pi$
$12$	−1.52446	+	2.64044i	−0.440073	+	0.762229i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−4.94989	+	3.29257i	−1.32291	+	0.879978i
$15$	0.356896			0.0921501
$16$	0.400969	−	0.694498i	0.100242	−	0.173625i
$17$	3.82640	+	6.62751i	0.928037	+	1.60741i	0.786602	+	0.617461i	$0.211838\pi$
$17$	3.82640	+	6.62751i	0.928037	+	1.60741i	0.141436	+	0.989947i	$0.454828\pi$
$18$	1.12349	+	1.94594i	0.264809	+	0.458663i
$19$	3.74698	−	6.48996i	0.859616	−	1.48890i	−0.0126794	−	0.999920i	$-0.504036\pi$
$19$	3.74698	−	6.48996i	0.859616	−	1.48890i	0.872295	−	0.488979i	$-0.162631\pi$
$20$	1.08815			0.243317
$21$	0.167563	+	2.64044i	0.0365652	+	0.576191i
$22$	−11.6528			−2.48438
$23$	0.524459	−	0.908389i	0.109357	−	0.189412i	−0.806153	−	0.591707i	$-0.798454\pi$
$23$	0.524459	−	0.908389i	0.109357	−	0.189412i	0.915510	+	0.402295i	$0.131787\pi$
$24$	1.17845	+	2.04113i	0.240550	+	0.416644i
$25$	2.43631	+	4.21982i	0.487263	+	0.843963i
$26$	1.12349	−	1.94594i	0.220334	−	0.381631i
$27$	1.00000			0.192450
$28$	0.510885	+	8.05048i	0.0965482	+	1.52140i
$29$	−0.246980			−0.0458630			−0.0229315	−	0.999737i	$-0.507300\pi$
$29$	−0.246980			−0.0458630			−0.0229315	+	0.999737i	$0.507300\pi$
$30$	0.400969	−	0.694498i	0.0732066	−	0.126797i
$31$	4.12349	+	7.14209i	0.740601	+	1.28276i	0.952222	+	0.305406i	$0.0987923\pi$
$31$	4.12349	+	7.14209i	0.740601	+	1.28276i	−0.211622	+	0.977352i	$0.567874\pi$
$32$	−3.25786	−	5.64279i	−0.575915	−	0.997513i
$33$	−2.59299	+	4.49119i	−0.451382	+	0.781816i
$34$	17.1957			2.94903
$35$	0.786208	−	0.522971i	0.132893	−	0.0883983i
$36$	3.04892			0.508153
$37$	4.57942	−	7.93178i	0.752851	−	1.30398i	−0.193584	−	0.981084i	$-0.562011\pi$
$37$	4.57942	−	7.93178i	0.752851	−	1.30398i	0.946435	−	0.322893i	$-0.104655\pi$
$38$	−8.41939	−	14.5828i	−1.36580	−	2.36564i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	0.420583	−	0.728471i	0.0665000	−	0.115181i
$41$	−5.75302			−0.898471			−0.449235	−	0.893413i	$-0.648304\pi$
$41$	−5.75302			−0.898471			−0.449235	+	0.893413i	$0.648304\pi$
$42$	5.32640	+	2.64044i	0.821881	+	0.407429i
$43$	1.54288			0.235286			0.117643	−	0.993056i	$-0.462466\pi$
$43$	1.54288			0.235286			0.117643	+	0.993056i	$0.462466\pi$
$44$	−7.90581	+	13.6933i	−1.19185	+	2.06434i
$45$	−0.178448	−	0.309081i	−0.0266014	−	0.0460751i
$46$	−1.17845	−	2.04113i	−0.173753	−	0.300948i
$47$	−0.780167	+	1.35129i	−0.113799	+	0.197106i	−0.917299	−	0.398199i	$-0.869635\pi$
$47$	−0.780167	+	1.35129i	−0.113799	+	0.197106i	0.803500	+	0.595305i	$0.202969\pi$
$48$	−0.801938			−0.115750
$49$	4.23825	+	5.57111i	0.605464	+	0.795872i
$50$	10.9487			1.54838
$51$	3.82640	−	6.62751i	0.535803	−	0.928037i
$52$	−1.52446	−	2.64044i	−0.211404	−	0.366163i
$53$	−4.50484	−	7.80262i	−0.618788	−	1.07177i	−0.989707	−	0.143107i	$-0.954291\pi$
$53$	−4.50484	−	7.80262i	−0.618788	−	1.07177i	0.370919	−	0.928665i	$-0.379043\pi$
$54$	1.12349	−	1.94594i	0.152888	−	0.264809i
$55$	1.85086			0.249569
$56$	5.58695	+	2.76960i	0.746588	+	0.370104i
$57$	−7.49396			−0.992599
$58$	−0.277479	+	0.480608i	−0.0364348	+	0.0631069i
$59$	2.67241	+	4.62874i	0.347918	+	0.602611i	0.985879	−	0.167457i	$-0.0535555\pi$
$59$	2.67241	+	4.62874i	0.347918	+	0.602611i	−0.637962	+	0.770068i	$0.720222\pi$
$60$	−0.544073	−	0.942362i	−0.0702395	−	0.121658i
$61$	−0.914542	+	1.58403i	−0.117095	+	0.202815i	−0.918615	−	0.395153i	$-0.870692\pi$
$61$	−0.914542	+	1.58403i	−0.117095	+	0.202815i	0.801520	+	0.597968i	$0.204025\pi$
$62$	18.5308			2.35341
$63$	2.20291	−	1.46533i	0.277540	−	0.184615i
$64$	−13.0368			−1.62960
$65$	−0.178448	+	0.309081i	−0.0221337	+	0.0383368i
$66$	5.82640	+	10.0916i	0.717180	+	1.24219i
$67$	5.73005	+	9.92474i	0.700037	+	1.21250i	0.968453	+	0.249197i	$0.0801667\pi$
$67$	5.73005	+	9.92474i	0.700037	+	1.21250i	−0.268415	+	0.963303i	$0.586500\pi$
$68$	11.6664	−	20.2067i	1.41475	−	2.45043i
$69$	−1.04892			−0.126275
$70$	−0.134375	−	2.11747i	−0.0160609	−	0.253086i
$71$	−10.4547			−1.24075			−0.620374	−	0.784306i	$-0.713019\pi$
$71$	−10.4547			−1.24075			−0.620374	+	0.784306i	$0.713019\pi$
$72$	1.17845	−	2.04113i	0.138881	−	0.240550i
$73$	−3.08426	−	5.34210i	−0.360985	−	0.625245i	0.627138	−	0.778908i	$-0.284226\pi$
$73$	−3.08426	−	5.34210i	−0.360985	−	0.625245i	−0.988123	+	0.153663i	$0.950893\pi$
$74$	−10.2899	−	17.8226i	−1.19617	−	2.07183i
$75$	2.43631	−	4.21982i	0.281321	−	0.487263i
$76$	−22.8485			−2.62090
$77$	0.868977	+	13.6933i	0.0990292	+	1.56049i
$78$	−2.24698			−0.254420
$79$	0.370469	−	0.641672i	0.0416811	−	0.0721937i	−0.844432	−	0.535662i	$-0.820062\pi$
$79$	0.370469	−	0.641672i	0.0416811	−	0.0721937i	0.886113	+	0.463469i	$0.153395\pi$
$80$	0.143104	+	0.247864i	0.0159995	+	0.0277120i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.46346	+	11.1950i	−0.713770	+	1.23629i
$83$	2.80194			0.307553			0.153776	−	0.988106i	$-0.450856\pi$
$83$	2.80194			0.307553			0.153776	+	0.988106i	$0.450856\pi$
$84$	6.71648	−	4.46768i	0.732828	−	0.487464i
$85$	−2.73125			−0.296246
$86$	1.73341	−	3.00235i	0.186918	−	0.323751i
$87$	0.123490	+	0.213891i	0.0132395	+	0.0229315i
$88$	6.11141	+	10.5853i	0.651478	+	1.12839i
$89$	−1.99880	+	3.46203i	−0.211873	+	0.366974i	−0.952301	−	0.305161i	$-0.901290\pi$
$89$	−1.99880	+	3.46203i	−0.211873	+	0.366974i	0.740428	+	0.672136i	$0.234623\pi$
$90$	−0.801938			−0.0845317
$91$	−2.37047	−	1.17511i	−0.248493	−	0.123185i
$92$	−3.19806			−0.333421
$93$	4.12349	−	7.14209i	0.427586	−	0.740601i
$94$	1.75302	+	3.03632i	0.180810	+	0.313173i
$95$	1.33728	+	2.31624i	0.137202	+	0.237641i
$96$	−3.25786	+	5.64279i	−0.332504	+	0.575915i
$97$	6.36658			0.646429			0.323214	−	0.946326i	$-0.395237\pi$
$97$	6.36658			0.646429			0.323214	+	0.946326i	$0.395237\pi$
$98$	15.6027	−	1.98831i	1.57611	−	0.200849i
$99$	5.18598			0.521211
$100$	7.42812	−	12.8659i	0.742812	−	1.28659i
$101$	2.06853	+	3.58280i	0.205827	+	0.356502i	0.950396	−	0.311043i	$-0.100678\pi$
$101$	2.06853	+	3.58280i	0.205827	+	0.356502i	−0.744569	+	0.667545i	$0.767345\pi$
$102$	−8.59783	−	14.8919i	−0.851312	−	1.47452i
$103$	1.72521	−	2.98815i	0.169990	−	0.294431i	−0.768426	−	0.639938i	$-0.778960\pi$
$103$	1.72521	−	2.98815i	0.169990	−	0.294431i	0.938416	+	0.345507i	$0.112293\pi$
$104$	−2.35690			−0.231113
$105$	−0.846011	−	0.419391i	−0.0825622	−	0.0409283i
$106$	−20.2446			−1.96633
$107$	−6.32640	+	10.9576i	−0.611596	+	1.05932i	0.379376	+	0.925243i	$0.376139\pi$
$107$	−6.32640	+	10.9576i	−0.611596	+	1.05932i	−0.990972	+	0.134072i	$0.957195\pi$
$108$	−1.52446	−	2.64044i	−0.146691	−	0.254076i
$109$	4.16972	+	7.22216i	0.399387	+	0.691758i	0.993650	−	0.112512i	$-0.0358898\pi$
$109$	4.16972	+	7.22216i	0.399387	+	0.691758i	−0.594264	+	0.804270i	$0.702556\pi$
$110$	2.07942	−	3.60166i	0.198265	−	0.343404i
$111$	−9.15883			−0.869318
$112$	−1.76659	+	1.17511i	−0.166927	+	0.111037i
$113$	11.9825			1.12722			0.563611	−	0.826040i	$-0.309412\pi$
$113$	11.9825			1.12722			0.563611	+	0.826040i	$0.309412\pi$
$114$	−8.41939	+	14.5828i	−0.788548	+	1.36580i
$115$	0.187177	+	0.324200i	0.0174544	+	0.0302318i
$116$	0.376510	+	0.652135i	0.0349581	+	0.0605492i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	12.0097			1.10558
$119$	−1.28232	−	20.2067i	−0.117550	−	1.85235i
$120$	−0.841166			−0.0767876
$121$	−7.94720	+	13.7650i	−0.722473	+	1.25136i
$122$	2.05496	+	3.55929i	0.186047	+	0.322243i
$123$	2.87651	+	4.98226i	0.259366	+	0.449235i
$124$	12.5722	−	21.7757i	1.12902	−	1.95551i
$125$	−3.52350			−0.315151
$126$	−0.376510	−	5.93301i	−0.0335422	−	0.528555i
$127$	11.9976			1.06462			0.532308	−	0.846551i	$-0.321325\pi$
$127$	11.9976			1.06462			0.532308	+	0.846551i	$0.321325\pi$
$128$	−8.13102	+	14.0833i	−0.718688	+	1.24480i
$129$	−0.771438	−	1.33617i	−0.0679214	−	0.117643i
$130$	0.400969	+	0.694498i	0.0351673	+	0.0609115i
$131$	−7.09515	+	12.2892i	−0.619906	+	1.07371i	0.369597	+	0.929192i	$0.379496\pi$
$131$	−7.09515	+	12.2892i	−0.619906	+	1.07371i	−0.989502	+	0.144516i	$0.953837\pi$
$132$	15.8116			1.37623
$133$	−16.5085	+	10.9812i	−1.43147	+	0.952186i
$134$	25.7506			2.22452
$135$	−0.178448	+	0.309081i	−0.0153584	+	0.0266014i
$136$	−9.01842	−	15.6204i	−0.773323	−	1.33943i
$137$	6.73221	+	11.6605i	0.575171	+	0.996226i	0.996023	+	0.0890967i	$0.0283980\pi$
$137$	6.73221	+	11.6605i	0.575171	+	0.996226i	−0.420851	+	0.907130i	$0.638269\pi$
$138$	−1.17845	+	2.04113i	−0.100316	+	0.173753i
$139$	−12.1685			−1.03212			−0.516060	−	0.856552i	$-0.672602\pi$
$139$	−12.1685			−1.03212			−0.516060	+	0.856552i	$0.672602\pi$
$140$	−2.57942	−	1.27869i	−0.218001	−	0.108069i
$141$	1.56033			0.131404
$142$	−11.7458	+	20.3443i	−0.985684	+	1.70726i
$143$	−2.59299	−	4.49119i	−0.216837	−	0.375572i
$144$	0.400969	+	0.694498i	0.0334141	+	0.0578749i
$145$	0.0440730	−	0.0763367i	0.00366006	−	0.00633942i
$146$	−13.8605			−1.14711
$147$	2.70560	−	6.45599i	0.223154	−	0.532481i
$148$	−27.9245			−2.29538
$149$	−3.33513	+	5.77661i	−0.273224	+	0.473238i	−0.969686	−	0.244356i	$-0.921423\pi$
$149$	−3.33513	+	5.77661i	−0.273224	+	0.473238i	0.696461	+	0.717594i	$0.254757\pi$
$150$	−5.47434	−	9.48184i	−0.446978	−	0.774189i
$151$	0.670251	+	1.16091i	0.0545443	+	0.0944734i	0.892008	−	0.452019i	$-0.149296\pi$
$151$	0.670251	+	1.16091i	0.0545443	+	0.0944734i	−0.837464	+	0.546492i	$0.815963\pi$
$152$	−8.83124	+	15.2962i	−0.716308	+	1.24068i
$153$	−7.65279			−0.618692
$154$	27.6226	+	13.6933i	2.22589	+	1.10344i
$155$	−2.94331			−0.236413
$156$	−1.52446	+	2.64044i	−0.122054	+	0.211404i
$157$	−4.09568	−	7.09392i	−0.326871	−	0.566157i	0.655018	−	0.755613i	$-0.272661\pi$
$157$	−4.09568	−	7.09392i	−0.326871	−	0.566157i	−0.981889	+	0.189456i	$0.939328\pi$
$158$	−0.832437	−	1.44182i	−0.0662251	−	0.114705i
$159$	−4.50484	+	7.80262i	−0.357257	+	0.618788i
$160$	2.32544			0.183842
$161$	−2.31067	+	1.53701i	−0.182106	+	0.121134i
$162$	−2.24698			−0.176539
$163$	7.09030	−	12.2808i	0.555355	−	0.961904i	−0.442520	−	0.896758i	$-0.645916\pi$
$163$	7.09030	−	12.2808i	0.555355	−	0.961904i	0.997876	−	0.0651452i	$-0.0207511\pi$
$164$	8.77024	+	15.1905i	0.684841	+	1.18618i
$165$	−0.925428	−	1.60289i	−0.0720444	−	0.124785i
$166$	3.14795	−	5.45241i	0.244328	−	0.423189i
$167$	−13.2741			−1.02718			−0.513591	−	0.858035i	$-0.671685\pi$
$167$	−13.2741			−1.02718			−0.513591	+	0.858035i	$0.671685\pi$
$168$	−0.394928	−	6.22324i	−0.0304694	−	0.480134i
$169$	1.00000			0.0769231
$170$	−3.06853	+	5.31485i	−0.235346	+	0.407631i
$171$	3.74698	+	6.48996i	0.286539	+	0.496300i
$172$	−2.35205	−	4.07387i	−0.179342	−	0.310630i
$173$	1.91789	−	3.32189i	0.145815	−	0.252559i	−0.783862	−	0.620935i	$-0.786753\pi$
$173$	1.91789	−	3.32189i	0.145815	−	0.252559i	0.929677	+	0.368377i	$0.120086\pi$
$174$	0.554958			0.0420713
$175$	−0.816471	−	12.8659i	−0.0617194	−	0.972569i
$176$	−4.15883			−0.313484
$177$	2.67241	−	4.62874i	0.200870	−	0.347918i
$178$	4.49127	+	7.77911i	0.336635	+	0.583069i
$179$	−0.708947	−	1.22793i	−0.0529892	−	0.0917800i	0.838314	−	0.545188i	$-0.183542\pi$
$179$	−0.708947	−	1.22793i	−0.0529892	−	0.0917800i	−0.891303	+	0.453408i	$0.850208\pi$
$180$	−0.544073	+	0.942362i	−0.0405528	+	0.0702395i
$181$	−19.4373			−1.44476			−0.722381	−	0.691496i	$-0.756952\pi$
$181$	−19.4373			−1.44476			−0.722381	+	0.691496i	$0.756952\pi$
$182$	−4.94989	+	3.29257i	−0.366910	+	0.244062i
$183$	1.82908			0.135210
$184$	−1.23609	+	2.14098i	−0.0911261	+	0.157835i
$185$	1.63437	+	2.83082i	0.120162	+	0.208126i
$186$	−9.26540	−	16.0481i	−0.679372	−	1.17671i
$187$	19.8436	−	34.3702i	1.45111	−	2.51339i
$188$	4.75733			0.346964
$189$	−2.37047	−	1.17511i	−0.172426	−	0.0854764i
$190$	6.00969			0.435989
$191$	3.15668	−	5.46753i	0.228409	−	0.395616i	−0.728928	−	0.684591i	$-0.759981\pi$
$191$	3.15668	−	5.46753i	0.228409	−	0.395616i	0.957337	+	0.288974i	$0.0933143\pi$
$192$	6.51842	+	11.2902i	0.470426	+	0.814802i
$193$	−11.8768	−	20.5712i	−0.854911	−	1.48075i	−0.876727	−	0.480988i	$-0.840278\pi$
$193$	−11.8768	−	20.5712i	−0.854911	−	1.48075i	0.0218162	−	0.999762i	$-0.493055\pi$
$194$	7.15279	−	12.3890i	0.513541	−	0.889478i
$195$	0.356896			0.0255578
$196$	8.24914	−	19.6838i	0.589224	−	1.40598i
$197$	11.7530			0.837368			0.418684	−	0.908132i	$-0.362491\pi$
$197$	11.7530			0.837368			0.418684	+	0.908132i	$0.362491\pi$
$198$	5.82640	−	10.0916i	0.414064	−	0.717180i
$199$	3.95593	+	6.85187i	0.280428	+	0.485716i	0.971490	−	0.237080i	$-0.0761902\pi$
$199$	3.95593	+	6.85187i	0.280428	+	0.485716i	−0.691062	+	0.722795i	$0.742857\pi$
$200$	−5.74214	−	9.94567i	−0.406030	−	0.703265i
$201$	5.73005	−	9.92474i	0.404167	−	0.700037i
$202$	9.29590			0.654057
$203$	0.585458	+	0.290227i	0.0410911	+	0.0203700i
$204$	−23.3327			−1.63362
$205$	1.02661	−	1.77815i	0.0717019	−	0.124191i
$206$	−3.87651	−	6.71431i	−0.270089	−	0.467808i
$207$	0.524459	+	0.908389i	0.0364524	+	0.0631374i
$208$	0.400969	−	0.694498i	0.0278022	−	0.0481548i
$209$	−38.8635			−2.68825
$210$	−1.76659	+	1.17511i	−0.121907	+	0.0810900i
$211$	11.7681			0.810148			0.405074	−	0.914284i	$-0.367246\pi$
$211$	11.7681			0.810148			0.405074	+	0.914284i	$0.367246\pi$
$212$	−13.7349	+	23.7895i	−0.943317	+	1.63387i
$213$	5.22737	+	9.05406i	0.358173	+	0.620374i
$214$	14.2153	+	24.6216i	0.971737	+	1.68310i
$215$	−0.275323	+	0.476874i	−0.0187769	+	0.0325225i
$216$	−2.35690			−0.160366
$217$	−1.38189	−	21.7757i	−0.0938086	−	1.47823i
$218$	18.7385			1.26913
$219$	−3.08426	+	5.34210i	−0.208415	+	0.360985i
$220$	−2.82155	−	4.88707i	−0.190229	−	0.329486i
$221$	3.82640	+	6.62751i	0.257391	+	0.445815i
$222$	−10.2899	+	17.8226i	−0.690610	+	1.19617i
$223$	14.2664			0.955346			0.477673	−	0.878538i	$-0.341480\pi$
$223$	14.2664			0.955346			0.477673	+	0.878538i	$0.341480\pi$
$224$	1.09179	+	17.2044i	0.0729485	+	1.14952i
$225$	−4.87263			−0.324842
$226$	13.4623	−	23.3173i	0.895496	−	1.55105i
$227$	−1.81402	−	3.14197i	−0.120401	−	0.208540i	0.799525	−	0.600633i	$-0.205085\pi$
$227$	−1.81402	−	3.14197i	−0.120401	−	0.208540i	−0.919926	+	0.392093i	$0.871751\pi$
$228$	11.4242	+	19.7873i	0.756588	+	1.31045i
$229$	6.88404	−	11.9235i	0.454910	−	0.787928i	−0.543773	−	0.839233i	$-0.683005\pi$
$229$	6.88404	−	11.9235i	0.454910	−	0.787928i	0.998683	+	0.0513047i	$0.0163380\pi$
$230$	0.841166			0.0554649
$231$	11.4242	−	7.59919i	0.751659	−	0.499990i
$232$	0.582105			0.0382171
$233$	3.76540	−	6.52186i	0.246679	−	0.427261i	−0.715923	−	0.698179i	$-0.753994\pi$
$233$	3.76540	−	6.52186i	0.246679	−	0.427261i	0.962602	+	0.270918i	$0.0873272\pi$
$234$	1.12349	+	1.94594i	0.0734448	+	0.127210i
$235$	−0.278439	−	0.482270i	−0.0181633	−	0.0314598i
$236$	8.14795	−	14.1127i	0.530386	−	0.918656i
$237$	−0.740939			−0.0481291
$238$	−40.7618	−	20.2067i	−2.64220	−	1.30981i
$239$	−12.2446			−0.792036			−0.396018	−	0.918243i	$-0.629608\pi$
$239$	−12.2446			−0.792036			−0.396018	+	0.918243i	$0.629608\pi$
$240$	0.143104	−	0.247864i	0.00923733	−	0.0159995i
$241$	14.6875	+	25.4394i	0.946103	+	1.63870i	0.753527	+	0.657417i	$0.228351\pi$
$241$	14.6875	+	25.4394i	0.946103	+	1.63870i	0.192576	+	0.981282i	$0.438316\pi$
$242$	17.8572	+	30.9296i	1.14790	+	1.98823i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.57673			0.357013
$245$	−2.47823	+	0.315810i	−0.158328	+	0.0201763i
$246$	12.9269			0.824190
$247$	3.74698	−	6.48996i	0.238415	−	0.412946i
$248$	−9.71864	−	16.8332i	−0.617134	−	1.06891i
$249$	−1.40097	−	2.42655i	−0.0887828	−	0.153776i
$250$	−3.95862	+	6.85652i	−0.250365	+	0.433645i
$251$	0.522434			0.0329758			0.0164879	−	0.999864i	$-0.494752\pi$
$251$	0.522434			0.0329758			0.0164879	+	0.999864i	$0.494752\pi$
$252$	−7.22737	−	3.58280i	−0.455281	−	0.225695i
$253$	−5.43967			−0.341989
$254$	13.4792	−	23.3466i	0.845760	−	1.46490i
$255$	1.36563	+	2.36533i	0.0855188	+	0.148123i
$256$	5.23341	+	9.06453i	0.327088	+	0.566533i
$257$	1.59903	−	2.76960i	0.0997448	−	0.172763i	−0.811834	−	0.583888i	$-0.801531\pi$
$257$	1.59903	−	2.76960i	0.0997448	−	0.172763i	0.911579	+	0.411125i	$0.134864\pi$
$258$	−3.46681			−0.215834
$259$	−20.1761	+	13.4207i	−1.25368	+	0.833925i
$260$	1.08815			0.0674840
$261$	0.123490	−	0.213891i	0.00764383	−	0.0132395i
$262$	15.9426	+	27.6135i	0.984940	+	1.70597i
$263$	−6.03415	−	10.4514i	−0.372081	−	0.644464i	0.617804	−	0.786332i	$-0.288022\pi$
$263$	−6.03415	−	10.4514i	−0.372081	−	0.644464i	−0.989886	+	0.141868i	$0.954689\pi$
$264$	6.11141	−	10.5853i	0.376131	−	0.651478i
$265$	3.21552			0.197528
$266$	2.82155	+	44.4618i	0.173000	+	2.72613i
$267$	3.99761			0.244650
$268$	17.4705	−	30.2597i	1.06718	−	1.84841i
$269$	5.04772	+	8.74291i	0.307765	+	0.533065i	0.977873	−	0.209199i	$-0.0670856\pi$
$269$	5.04772	+	8.74291i	0.307765	+	0.533065i	−0.670108	+	0.742263i	$0.733752\pi$
$270$	0.400969	+	0.694498i	0.0244022	+	0.0422658i
$271$	−0.522967	+	0.905805i	−0.0317680	+	0.0550237i	−0.881472	−	0.472236i	$-0.843447\pi$
$271$	−0.522967	+	0.905805i	−0.0317680	+	0.0550237i	0.849704	+	0.527260i	$0.176780\pi$
$272$	6.13706			0.372114
$273$	0.167563	+	2.64044i	0.0101414	+	0.159807i
$274$	30.2543			1.82773
$275$	12.6347	−	21.8839i	0.761899	−	1.31965i
$276$	1.59903	+	2.76960i	0.0962504	+	0.166711i
$277$	1.10656	+	1.91662i	0.0664870	+	0.115159i	0.897353	−	0.441314i	$-0.145488\pi$
$277$	1.10656	+	1.91662i	0.0664870	+	0.115159i	−0.830866	+	0.556473i	$0.812154\pi$
$278$	−13.6712	+	23.6792i	−0.819945	+	1.42019i
$279$	−8.24698			−0.493734
$280$	−1.85301	+	1.23259i	−0.110739	+	0.0736613i
$281$	21.3666			1.27462			0.637312	−	0.770606i	$-0.280046\pi$
$281$	21.3666			1.27462			0.637312	+	0.770606i	$0.280046\pi$
$282$	1.75302	−	3.03632i	0.104391	−	0.180810i
$283$	−0.605072	−	1.04802i	−0.0359678	−	0.0622980i	0.847481	−	0.530825i	$-0.178118\pi$
$283$	−0.605072	−	1.04802i	−0.0359678	−	0.0622980i	−0.883449	+	0.468527i	$0.844785\pi$
$284$	15.9378	+	27.6051i	0.945735	+	1.63806i
$285$	1.33728	−	2.31624i	0.0792137	−	0.137202i
$286$	−11.6528			−0.689044
$287$	13.6374	+	6.76041i	0.804988	+	0.399054i
$288$	6.51573			0.383943
$289$	−20.7826	+	35.9966i	−1.22251	+	2.11744i
$290$	−0.0990311	−	0.171527i	−0.00581531	−	0.0100724i
$291$	−3.18329	−	5.51362i	−0.186608	−	0.323214i
$292$	−9.40366	+	16.2876i	−0.550307	+	0.953160i
$293$	−17.7181			−1.03510			−0.517551	−	0.855652i	$-0.673156\pi$
$293$	−17.7181			−1.03510			−0.517551	+	0.855652i	$0.673156\pi$
$294$	−9.52326	−	12.5182i	−0.555408	−	0.730074i
$295$	−1.90754			−0.111061
$296$	−10.7932	+	18.6944i	−0.627343	+	1.08659i
$297$	−2.59299	−	4.49119i	−0.150461	−	0.260605i
$298$	7.49396	+	12.9799i	0.434113	+	0.751906i
$299$	0.524459	−	0.908389i	0.0303302	−	0.0525335i
$300$	−14.8562			−0.857725
$301$	−3.65734	−	1.81304i	−0.210806	−	0.104502i
$302$	3.01208			0.173326
$303$	2.06853	−	3.58280i	0.118834	−	0.205827i
$304$	−3.00484	−	5.20454i	−0.172340	−	0.298501i
$305$	−0.326396	−	0.565335i	−0.0186894	−	0.0323710i
$306$	−8.59783	+	14.8919i	−0.491505	+	0.851312i
$307$	−6.93900			−0.396030			−0.198015	−	0.980199i	$-0.563449\pi$
$307$	−6.93900			−0.396030			−0.198015	+	0.980199i	$0.563449\pi$
$308$	34.8315	−	23.1693i	1.98471	−	1.32019i
$309$	−3.45042			−0.196287
$310$	−3.30678	+	5.72751i	−0.187813	+	0.325301i
$311$	−11.9221	−	20.6496i	−0.676039	−	1.17093i	−0.976164	−	0.217034i	$-0.930362\pi$
$311$	−11.9221	−	20.6496i	−0.676039	−	1.17093i	0.300125	−	0.953900i	$-0.402972\pi$
$312$	1.17845	+	2.04113i	0.0667165	+	0.115556i
$313$	−1.17725	+	2.03906i	−0.0665422	+	0.115254i	−0.897377	−	0.441265i	$-0.854530\pi$
$313$	−1.17725	+	2.03906i	−0.0665422	+	0.115254i	0.830835	+	0.556519i	$0.187863\pi$
$314$	−18.4058			−1.03870
$315$	0.0598025	+	0.942362i	0.00336949	+	0.0530961i
$316$	−2.25906			−0.127082
$317$	11.1712	−	19.3491i	0.627438	−	1.08675i	−0.360626	−	0.932710i	$-0.617437\pi$
$317$	11.1712	−	19.3491i	0.627438	−	1.08675i	0.988064	−	0.154044i	$-0.0492296\pi$
$318$	10.1223	+	17.5323i	0.567630	+	0.983164i
$319$	0.640416	+	1.10923i	0.0358564	+	0.0621051i
$320$	2.32640	−	4.02944i	0.130050	−	0.225252i
$321$	12.6528			0.706210
$322$	0.394928	+	6.22324i	0.0220085	+	0.346808i
$323$	57.3497			3.19102
$324$	−1.52446	+	2.64044i	−0.0846921	+	0.146691i
$325$	2.43631	+	4.21982i	0.135142	+	0.234073i
$326$	−15.9318	−	27.5946i	−0.882379	−	1.52832i
$327$	4.16972	−	7.22216i	0.230586	−	0.399387i
$328$	13.5593			0.748685
$329$	3.43727	−	2.28641i	0.189503	−	0.126054i
$330$	−4.15883			−0.228936
$331$	1.09903	−	1.90358i	0.0604082	−	0.104630i	−0.834240	−	0.551402i	$-0.814093\pi$
$331$	1.09903	−	1.90358i	0.0604082	−	0.104630i	0.894648	+	0.446772i	$0.147426\pi$
$332$	−4.27144	−	7.39835i	−0.234426	−	0.406037i
$333$	4.57942	+	7.93178i	0.250950	+	0.434659i
$334$	−14.9133	+	25.8307i	−0.816022	+	1.41339i
$335$	−4.09006			−0.223464
$336$	1.90097	+	0.942362i	0.103706	+	0.0514101i
$337$	3.29052			0.179246			0.0896230	−	0.995976i	$-0.471434\pi$
$337$	3.29052			0.179246			0.0896230	+	0.995976i	$0.471434\pi$
$338$	1.12349	−	1.94594i	0.0611098	−	0.105845i
$339$	−5.99127	−	10.3772i	−0.325401	−	0.563611i
$340$	4.16368	+	7.21170i	0.225807	+	0.391109i
$341$	21.3843	−	37.0388i	1.15803	−	2.00576i
$342$	16.8388			0.910537
$343$	−3.50000	−	18.1865i	−0.188982	−	0.981981i
$344$	−3.63640			−0.196062
$345$	0.187177	−	0.324200i	0.0100773	−	0.0174544i
$346$	−4.30947	−	7.46422i	−0.231679	−	0.401279i
$347$	16.1576	+	27.9858i	0.867387	+	1.50236i	0.864657	+	0.502363i	$0.167536\pi$
$347$	16.1576	+	27.9858i	0.867387	+	1.50236i	0.00273047	+	0.999996i	$0.499131\pi$
$348$	0.376510	−	0.652135i	0.0201831	−	0.0349581i
$349$	16.9855			0.909214			0.454607	−	0.890692i	$-0.349780\pi$
$349$	16.9855			0.909214			0.454607	+	0.890692i	$0.349780\pi$
$350$	−25.9535	−	12.8659i	−1.38727	−	0.687710i
$351$	1.00000			0.0533761
$352$	−16.8952	+	29.2634i	−0.900518	+	1.55974i
$353$	4.05280	+	7.01966i	0.215709	+	0.373619i	0.953492	−	0.301419i	$-0.0974604\pi$
$353$	4.05280	+	7.01966i	0.215709	+	0.373619i	−0.737783	+	0.675038i	$0.764127\pi$
$354$	−6.00484	−	10.4007i	−0.319154	−	0.552791i
$355$	1.86563	−	3.23136i	0.0990171	−	0.171503i
$356$	12.1884			0.645983
$357$	−16.8584	+	11.2139i	−0.892240	+	0.593502i
$358$	−3.18598			−0.168384
$359$	−9.55376	+	16.5476i	−0.504228	+	0.873349i	0.495760	+	0.868460i	$0.334890\pi$
$359$	−9.55376	+	16.5476i	−0.504228	+	0.873349i	−0.999988	+	0.00488927i	$0.998444\pi$
$360$	0.420583	+	0.728471i	0.0221667	+	0.0383938i
$361$	−18.5797	−	32.1810i	−0.977880	−	1.69374i
$362$	−21.8376	+	37.8238i	−1.14776	+	1.98797i
$363$	15.8944			0.834239
$364$	0.510885	+	8.05048i	0.0267777	+	0.421960i
$365$	2.20152			0.115233
$366$	2.05496	−	3.55929i	0.107414	−	0.186047i
$367$	−8.00753	−	13.8695i	−0.417990	−	0.723980i	0.577747	−	0.816216i	$-0.303932\pi$
$367$	−8.00753	−	13.8695i	−0.417990	−	0.723980i	−0.995737	+	0.0922361i	$0.970599\pi$
$368$	−0.420583	−	0.728471i	−0.0219244	−	0.0379742i
$369$	2.87651	−	4.98226i	0.149745	−	0.259366i
$370$	7.34481			0.381839
$371$	1.50969	+	23.7895i	0.0783791	+	1.23509i
$372$	−25.1444			−1.30367
$373$	−6.15279	+	10.6569i	−0.318580	+	0.551796i	−0.980192	−	0.198050i	$-0.936539\pi$
$373$	−6.15279	+	10.6569i	−0.318580	+	0.551796i	0.661612	+	0.749846i	$0.269872\pi$
$374$	−44.5882	−	77.2290i	−2.30560	−	3.99342i
$375$	1.76175	+	3.05144i	0.0909764	+	0.157576i
$376$	1.83877	−	3.18485i	0.0948275	−	0.164246i
$377$	−0.246980			−0.0127201
$378$	−4.94989	+	3.29257i	−0.254595	+	0.169352i
$379$	−25.2131			−1.29511			−0.647556	−	0.762018i	$-0.724209\pi$
$379$	−25.2131			−1.29511			−0.647556	+	0.762018i	$0.724209\pi$
$380$	4.07726	−	7.06202i	0.209159	−	0.362274i
$381$	−5.99880	−	10.3902i	−0.307328	−	0.532308i
$382$	−7.09299	−	12.2854i	−0.362909	−	0.628577i
$383$	−3.16219	+	5.47707i	−0.161580	+	0.279865i	−0.935436	−	0.353497i	$-0.884992\pi$
$383$	−3.16219	+	5.47707i	−0.161580	+	0.279865i	0.773855	+	0.633362i	$0.218326\pi$
$384$	16.2620			0.829869
$385$	−4.38740	−	2.17495i	−0.223602	−	0.110846i
$386$	−53.3739			−2.71666
$387$	−0.771438	+	1.33617i	−0.0392144	+	0.0679214i
$388$	−9.70560	−	16.8106i	−0.492727	−	0.853428i
$389$	10.9438	+	18.9553i	0.554875	+	0.961072i	0.997913	+	0.0645690i	$0.0205672\pi$
$389$	10.9438	+	18.9553i	0.554875	+	0.961072i	−0.443038	+	0.896503i	$0.646099\pi$
$390$	0.400969	−	0.694498i	0.0203038	−	0.0351673i
$391$	8.02715			0.405950
$392$	−9.98911	−	13.1305i	−0.504526	−	0.663191i
$393$	14.1903			0.715806
$394$	13.2044	−	22.8707i	0.665228	−	1.15221i
$395$	0.132219	+	0.229010i	0.00665266	+	0.0115227i
$396$	−7.90581	−	13.6933i	−0.397282	−	0.688113i
$397$	−18.4840	+	32.0153i	−0.927687	+	1.60680i	−0.140505	+	0.990080i	$0.544873\pi$
$397$	−18.4840	+	32.0153i	−0.927687	+	1.60680i	−0.787182	+	0.616721i	$0.788461\pi$
$398$	17.7778			0.891119
$399$	17.7642	+	8.80620i	0.889322	+	0.440861i
$400$	3.90754			0.195377
$401$	8.56100	−	14.8281i	0.427516	−	0.740479i	−0.569136	−	0.822244i	$-0.692722\pi$
$401$	8.56100	−	14.8281i	0.427516	−	0.740479i	0.996652	+	0.0817643i	$0.0260555\pi$
$402$	−12.8753	−	22.3007i	−0.642162	−	1.11226i
$403$	4.12349	+	7.14209i	0.205406	+	0.355773i
$404$	6.30678	−	10.9237i	0.313774	−	0.543473i
$405$	0.356896			0.0177343
$406$	1.22252	−	0.813199i	0.0606727	−	0.0403584i
$407$	−47.4975			−2.35437
$408$	−9.01842	+	15.6204i	−0.446478	+	0.773323i
$409$	−7.11625	−	12.3257i	−0.351876	−	0.609467i	0.634702	−	0.772757i	$-0.281123\pi$
$409$	−7.11625	−	12.3257i	−0.351876	−	0.609467i	−0.986578	+	0.163290i	$0.947789\pi$
$410$	−2.30678	−	3.99546i	−0.113924	−	0.197322i
$411$	6.73221	−	11.6605i	0.332075	−	0.575171i
$412$	−10.5200			−0.518285
$413$	−0.895592	−	14.1127i	−0.0440692	−	0.694439i
$414$	2.35690			0.115835
$415$	−0.500000	+	0.866025i	−0.0245440	+	0.0425115i
$416$	−3.25786	−	5.64279i	−0.159730	−	0.276660i
$417$	6.08426	+	10.5382i	0.297948	+	0.516060i
$418$	−43.6628	+	75.6261i	−2.13562	+	3.69900i
$419$	−16.3297			−0.797760			−0.398880	−	0.917003i	$-0.630601\pi$
$419$	−16.3297			−0.797760			−0.398880	+	0.917003i	$0.630601\pi$
$420$	0.182333	+	2.87318i	0.00889693	+	0.140197i
$421$	−12.7754			−0.622634			−0.311317	−	0.950306i	$-0.600770\pi$
$421$	−12.7754			−0.622634			−0.311317	+	0.950306i	$0.600770\pi$
$422$	13.2213	−	22.9000i	0.643604	−	1.11475i
$423$	−0.780167	−	1.35129i	−0.0379330	−	0.0657020i
$424$	10.6174	+	18.3900i	0.515629	+	0.893095i
$425$	−18.6446	+	32.2934i	−0.904396	+	1.56646i
$426$	23.4916			1.13817
$427$	4.02930	−	2.68022i	0.194992	−	0.129705i
$428$	38.5773			1.86471
$429$	−2.59299	+	4.49119i	−0.125191	+	0.216837i
$430$	0.618645	+	1.07153i	0.0298337	+	0.0516735i
$431$	−12.4170	−	21.5069i	−0.598106	−	1.03595i	−0.993101	−	0.117266i	$-0.962587\pi$
$431$	−12.4170	−	21.5069i	−0.598106	−	1.03595i	0.394995	−	0.918683i	$-0.370746\pi$
$432$	0.400969	−	0.694498i	0.0192916	−	0.0334141i
$433$	−8.30021			−0.398883			−0.199441	−	0.979910i	$-0.563913\pi$
$433$	−8.30021			−0.398883			−0.199441	+	0.979910i	$0.563913\pi$
$434$	−43.9267	−	21.7757i	−2.10855	−	1.04526i
$435$	−0.0881460			−0.00422628
$436$	12.7131	−	22.0198i	0.608848	−	1.05456i
$437$	−3.93027	−	6.80743i	−0.188010	−	0.325644i
$438$	6.93027	+	12.0036i	0.331141	+	0.573553i
$439$	−7.01022	+	12.1421i	−0.334580	+	0.579509i	−0.983404	−	0.181429i	$-0.941928\pi$
$439$	−7.01022	+	12.1421i	−0.334580	+	0.579509i	0.648824	+	0.760938i	$0.275261\pi$
$440$	−4.36227			−0.207963
$441$	−6.94385	+	0.884879i	−0.330659	+	0.0421371i
$442$	17.1957			0.817915
$443$	6.30612	−	10.9225i	0.299613	−	0.518944i	−0.676435	−	0.736503i	$-0.736476\pi$
$443$	6.30612	−	10.9225i	0.299613	−	0.518944i	0.976047	+	0.217558i	$0.0698092\pi$
$444$	13.9623	+	24.1833i	0.662620	+	1.14769i
$445$	−0.713365	−	1.23558i	−0.0338167	−	0.0585723i
$446$	16.0281	−	27.7615i	0.758953	−	1.31454i
$447$	6.67025			0.315492
$448$	30.9034	+	15.3197i	1.46005	+	0.723786i
$449$	−19.6437			−0.927043			−0.463522	−	0.886086i	$-0.653414\pi$
$449$	−19.6437			−0.927043			−0.463522	+	0.886086i	$0.653414\pi$
$450$	−5.47434	+	9.48184i	−0.258063	+	0.446978i
$451$	14.9175	+	25.8379i	0.702439	+	1.21666i
$452$	−18.2669	−	31.6392i	−0.859202	−	1.48818i
$453$	0.670251	−	1.16091i	0.0314911	−	0.0545443i
$454$	−8.15213			−0.382598
$455$	0.786208	−	0.522971i	0.0368580	−	0.0245173i
$456$	17.6625			0.827121
$457$	3.63557	−	6.29699i	0.170065	−	0.294561i	−0.768377	−	0.639997i	$-0.778936\pi$
$457$	3.63557	−	6.29699i	0.170065	−	0.294561i	0.938442	+	0.345436i	$0.112269\pi$
$458$	−15.4683	−	26.7919i	−0.722786	−	1.25190i
$459$	3.82640	+	6.62751i	0.178601	+	0.309346i
$460$	0.570688	−	0.988460i	0.0266084	−	0.0460872i
$461$	−4.25368			−0.198114			−0.0990569	−	0.995082i	$-0.531583\pi$
$461$	−4.25368			−0.198114			−0.0990569	+	0.995082i	$0.531583\pi$
$462$	−1.95257	−	30.7685i	−0.0908420	−	1.43148i
$463$	−35.8678			−1.66692			−0.833460	−	0.552580i	$-0.813643\pi$
$463$	−35.8678			−1.66692			−0.833460	+	0.552580i	$0.813643\pi$
$464$	−0.0990311	+	0.171527i	−0.00459740	+	0.00796294i
$465$	1.47166	+	2.54898i	0.0682464	+	0.118206i
$466$	−8.46077	−	14.6545i	−0.391938	−	0.678856i
$467$	5.62349	−	9.74017i	0.260224	−	0.450721i	−0.706077	−	0.708135i	$-0.749537\pi$
$467$	5.62349	−	9.74017i	0.260224	−	0.450721i	0.966301	+	0.257413i	$0.0828702\pi$
$468$	3.04892			0.140936
$469$	−1.92029	−	30.2597i	−0.0886706	−	1.39726i
$470$	−1.25129			−0.0577178
$471$	−4.09568	+	7.09392i	−0.188719	+	0.326871i
$472$	−6.29859	−	10.9095i	−0.289916	−	0.502149i
$473$	−4.00066	−	6.92935i	−0.183951	−	0.318612i
$474$	−0.832437	+	1.44182i	−0.0382351	+	0.0662251i
$475$	36.5153			1.67543
$476$	−51.3998	+	34.1902i	−2.35591	+	1.56711i
$477$	9.00969			0.412525
$478$	−13.7567	+	23.8272i	−0.629215	+	1.08983i
$479$	−4.83177	−	8.36888i	−0.220769	−	0.382384i	0.734272	−	0.678855i	$-0.237523\pi$
$479$	−4.83177	−	8.36888i	−0.220769	−	0.382384i	−0.955042	+	0.296471i	$0.904190\pi$
$480$	−1.16272	−	2.01389i	−0.0530706	−	0.0919210i
$481$	4.57942	−	7.93178i	0.208803	−	0.361658i
$482$	66.0049			3.00644
$483$	2.48643	+	1.23259i	0.113136	+	0.0560848i
$484$	48.4607			2.20276
$485$	−1.13610	+	1.96779i	−0.0515878	+	0.0893527i
$486$	1.12349	+	1.94594i	0.0509625	+	0.0882697i
$487$	7.09419	+	12.2875i	0.321468	+	0.556799i	0.980791	−	0.195060i	$-0.0624903\pi$
$487$	7.09419	+	12.2875i	0.321468	+	0.556799i	−0.659323	+	0.751860i	$0.729157\pi$
$488$	2.15548	−	3.73340i	0.0975741	−	0.169003i
$489$	−14.1806			−0.641269
$490$	−2.16972	+	5.17730i	−0.0980179	+	0.233887i
$491$	40.5338			1.82926			0.914632	−	0.404288i	$-0.132481\pi$
$491$	40.5338			1.82926			0.914632	+	0.404288i	$0.132481\pi$
$492$	8.77024	−	15.1905i	0.395393	−	0.684841i
$493$	−0.945042	−	1.63686i	−0.0425625	−	0.0737205i
$494$	−8.41939	−	14.5828i	−0.378806	−	0.656111i
$495$	−0.925428	+	1.60289i	−0.0415949	+	0.0720444i
$496$	6.61356			0.296958
$497$	24.7826	+	12.2854i	1.11165	+	0.551076i
$498$	−6.29590			−0.282126
$499$	−13.8901	+	24.0583i	−0.621806	+	1.07700i	0.367344	+	0.930085i	$0.380267\pi$
$499$	−13.8901	+	24.0583i	−0.621806	+	1.07700i	−0.989149	+	0.146914i	$0.953066\pi$
$500$	5.37143	+	9.30359i	0.240218	+	0.416069i
$501$	6.63706	+	11.4957i	0.296522	+	0.513591i
$502$	0.586950	−	1.01663i	0.0261968	−	0.0453743i
$503$	3.40880			0.151991			0.0759954	−	0.997108i	$-0.475787\pi$
$503$	3.40880			0.151991			0.0759954	+	0.997108i	$0.475787\pi$
$504$	−5.19202	+	3.45364i	−0.231271	+	0.153837i
$505$	−1.47650			−0.0657034
$506$	−6.11141	+	10.5853i	−0.271685	+	0.470573i
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	−18.2899	−	31.6790i	−0.811481	−	1.40553i
$509$	−16.4095	+	28.4220i	−0.727337	+	1.25978i	0.230668	+	0.973032i	$0.425909\pi$
$509$	−16.4095	+	28.4220i	−0.727337	+	1.25978i	−0.958005	+	0.286751i	$0.907425\pi$
$510$	6.13706			0.271754
$511$	1.03361	+	16.2876i	0.0457244	+	0.720522i
$512$	−9.00538			−0.397985
$513$	3.74698	−	6.48996i	0.165433	−	0.286539i
$514$	−3.59299	−	6.22324i	−0.158480	−	0.274495i
$515$	0.615720	+	1.06646i	0.0271319	+	0.0469938i
$516$	−2.35205	+	4.07387i	−0.103543	+	0.179342i
$517$	8.09187			0.355880
$518$	3.44839	+	54.3395i	0.151514	+	2.38754i
$519$	−3.83579			−0.168372
$520$	0.420583	−	0.728471i	0.0184438	−	0.0319456i
$521$	18.6869	+	32.3667i	0.818690	+	1.41801i	0.906648	+	0.421888i	$0.138632\pi$
$521$	18.6869	+	32.3667i	0.818690	+	1.41801i	−0.0879582	+	0.996124i	$0.528034\pi$
$522$	−0.277479	−	0.480608i	−0.0121449	−	0.0210356i
$523$	−7.54825	+	13.0740i	−0.330062	+	0.571684i	−0.982524	−	0.186137i	$-0.940403\pi$
$523$	−7.54825	+	13.0740i	−0.330062	+	0.571684i	0.652462	+	0.757822i	$0.273736\pi$
$524$	43.2650			1.89004
$525$	−10.7339	+	7.14002i	−0.468467	+	0.311616i
$526$	−27.1172			−1.18237
$527$	−31.5562	+	54.6570i	−1.37461	+	2.38089i
$528$	2.07942	+	3.60166i	0.0904950	+	0.156742i
$529$	10.9499	+	18.9658i	0.476082	+	0.824598i
$530$	3.61260	−	6.25721i	0.156922	−	0.271796i
$531$	−5.34481			−0.231945
$532$	54.1616	+	26.8494i	2.34820	+	1.16407i
$533$	−5.75302			−0.249191
$534$	4.49127	−	7.77911i	0.194356	−	0.336635i
$535$	−2.25786	−	3.91074i	−0.0976160	−	0.169076i
$536$	−13.5051	−	23.3916i	−0.583333	−	1.01036i
$537$	−0.708947	+	1.22793i	−0.0305933	+	0.0529892i
$538$	22.6843			0.977988
$539$	14.0312	−	33.4806i	0.604365	−	1.44211i
$540$	1.08815			0.0468263
$541$	12.5543	−	21.7447i	0.539751	−	0.934877i	−0.459166	−	0.888351i	$-0.651852\pi$
$541$	12.5543	−	21.7447i	0.539751	−	0.934877i	0.998917	−	0.0465260i	$-0.0148150\pi$
$542$	1.17510	+	2.03533i	0.0504747	+	0.0874247i
$543$	9.71864	+	16.8332i	0.417067	+	0.722381i
$544$	24.9318	−	43.1831i	1.06894	−	1.85146i
$545$	−2.97631			−0.127491
$546$	5.32640	+	2.64044i	0.227949	+	0.113000i
$547$	−3.83685			−0.164052			−0.0820260	−	0.996630i	$-0.526139\pi$
$547$	−3.83685			−0.164052			−0.0820260	+	0.996630i	$0.526139\pi$
$548$	20.5260	−	35.5520i	0.876825	−	1.51871i
$549$	−0.914542	−	1.58403i	−0.0390317	−	0.0676049i
$550$	−28.3898	−	49.1727i	−1.21055	−	2.09673i
$551$	−0.925428	+	1.60289i	−0.0394245	+	0.0682853i
$552$	2.47219			0.105223
$553$	−1.63222	+	1.08572i	−0.0694090	+	0.0461696i
$554$	4.97285			0.211276
$555$	1.63437	−	2.83082i	0.0693754	−	0.120162i
$556$	18.5504	+	32.1303i	0.786713	+	1.36263i
$557$	−4.07673	−	7.06110i	−0.172737	−	0.299188i	0.766639	−	0.642078i	$-0.221928\pi$
$557$	−4.07673	−	7.06110i	−0.172737	−	0.299188i	−0.939376	+	0.342890i	$0.888594\pi$
$558$	−9.26540	+	16.0481i	−0.392236	+	0.679372i
$559$	1.54288			0.0652567
$560$	−0.0479579	−	0.755716i	−0.00202659	−	0.0319348i
$561$	−39.6872			−1.67560
$562$	24.0051	−	41.5781i	1.01260	−	1.75387i
$563$	−4.42274	−	7.66041i	−0.186396	−	0.322848i	0.757650	−	0.652661i	$-0.226347\pi$
$563$	−4.42274	−	7.66041i	−0.186396	−	0.322848i	−0.944046	+	0.329813i	$0.893014\pi$
$564$	−2.37867	−	4.11997i	−0.100160	−	0.173482i
$565$	−2.13826	+	3.70357i	−0.0899573	+	0.155811i
$566$	−2.71917			−0.114295
$567$	0.167563	+	2.64044i	0.00703698	+	0.110888i
$568$	24.6407			1.03390
$569$	−10.7726	+	18.6588i	−0.451612	+	0.782216i	−0.998486	−	0.0549994i	$-0.982484\pi$
$569$	−10.7726	+	18.6588i	−0.451612	+	0.782216i	0.546874	+	0.837215i	$0.315818\pi$
$570$	−3.00484	−	5.20454i	−0.125859	−	0.217994i
$571$	−2.42543	−	4.20096i	−0.101501	−	0.175805i	0.810802	−	0.585320i	$-0.199031\pi$
$571$	−2.42543	−	4.20096i	−0.101501	−	0.175805i	−0.912303	+	0.409515i	$0.865698\pi$
$572$	−7.90581	+	13.6933i	−0.330559	+	0.572544i
$573$	−6.31336			−0.263744
$574$	28.4768	−	18.9422i	1.18860	−	0.790634i
$575$	5.11098			0.213143
$576$	6.51842	−	11.2902i	0.271601	−	0.470426i
$577$	15.6141	+	27.0444i	0.650023	+	1.12587i	0.983117	+	0.182980i	$0.0585742\pi$
$577$	15.6141	+	27.0444i	0.650023	+	1.12587i	−0.333093	+	0.942894i	$0.608092\pi$
$578$	46.6981	+	80.8835i	1.94239	+	3.36431i
$579$	−11.8768	+	20.5712i	−0.493583	+	0.854911i
$580$	−0.268750			−0.0111592
$581$	−6.64191	−	3.29257i	−0.275553	−	0.136599i
$582$	−14.3056			−0.592986
$583$	−23.3620	+	40.4642i	−0.967557	+	1.67586i
$584$	7.26928	+	12.5908i	0.300805	+	0.521010i
$585$	−0.178448	−	0.309081i	−0.00737791	−	0.0127789i
$586$	−19.9061	+	34.4784i	−0.822314	+	1.42429i
$587$	5.49502			0.226804			0.113402	−	0.993549i	$-0.463825\pi$
$587$	5.49502			0.226804			0.113402	+	0.993549i	$0.463825\pi$
$588$	−21.1712	+	2.69792i	−0.873086	+	0.111260i
$589$	61.8025			2.54653
$590$	−2.14310	+	3.71197i	−0.0882302	+	0.152819i
$591$	−5.87651	−	10.1784i	−0.241727	−	0.418684i
$592$	−3.67241	−	6.36080i	−0.150935	−	0.261427i
$593$	2.02930	−	3.51486i	0.0833335	−	0.144338i	−0.821346	−	0.570430i	$-0.806777\pi$
$593$	2.02930	−	3.51486i	0.0833335	−	0.144338i	0.904680	+	0.426092i	$0.140110\pi$
$594$	−11.6528			−0.478120
$595$	6.47434	+	3.20951i	0.265422	+	0.131577i
$596$	20.3370			0.833038
$597$	3.95593	−	6.85187i	0.161905	−	0.280428i
$598$	−1.17845	−	2.04113i	−0.0481903	−	0.0834681i
$599$	−17.6664	−	30.5990i	−0.721828	−	1.25024i	−0.960266	−	0.279085i	$-0.909969\pi$
$599$	−17.6664	−	30.5990i	−0.721828	−	1.25024i	0.238438	−	0.971158i	$-0.423365\pi$
$600$	−5.74214	+	9.94567i	−0.234422	+	0.406030i
$601$	−47.8974			−1.95377			−0.976887	−	0.213754i	$-0.931431\pi$
$601$	−47.8974			−1.95377			−0.976887	+	0.213754i	$0.931431\pi$
$602$	−7.63706	+	5.08004i	−0.311263	+	0.207047i
$603$	−11.4601			−0.466692
$604$	2.04354	−	3.53952i	0.0831505	−	0.144021i
$605$	−2.83632	−	4.91265i	−0.115313	−	0.199728i
$606$	−4.64795	−	8.05048i	−0.188810	−	0.327029i
$607$	−10.8204	+	18.7414i	−0.439185	+	0.760690i	−0.997627	−	0.0688533i	$-0.978066\pi$
$607$	−10.8204	+	18.7414i	−0.439185	+	0.760690i	0.558442	+	0.829543i	$0.311399\pi$
$608$	−48.8286			−1.98026
$609$	−0.0413846	−	0.652135i	−0.00167699	−	0.0264258i
$610$	−1.46681			−0.0593895
$611$	−0.780167	+	1.35129i	−0.0315622	+	0.0546673i
$612$	11.6664	+	20.2067i	0.471585	+	0.816809i
$613$	−6.62229	−	11.4701i	−0.267472	−	0.463275i	0.700736	−	0.713420i	$-0.252855\pi$
$613$	−6.62229	−	11.4701i	−0.267472	−	0.463275i	−0.968208	+	0.250145i	$0.919522\pi$
$614$	−7.79590	+	13.5029i	−0.314617	+	0.544932i
$615$	−2.05323			−0.0827942
$616$	−2.04809	−	32.2736i	−0.0825199	−	1.30034i
$617$	49.1081			1.97702			0.988509	−	0.151161i	$-0.0483013\pi$
$617$	49.1081			1.97702			0.988509	+	0.151161i	$0.0483013\pi$
$618$	−3.87651	+	6.71431i	−0.155936	+	0.270089i
$619$	3.35301	+	5.80759i	0.134769	+	0.233427i	0.925509	−	0.378725i	$-0.123637\pi$
$619$	3.35301	+	5.80759i	0.134769	+	0.233427i	−0.790740	+	0.612152i	$0.790304\pi$
$620$	4.48696	+	7.77164i	0.180201	+	0.312117i
$621$	0.524459	−	0.908389i	0.0210458	−	0.0364524i
$622$	−53.5773			−2.14825
$623$	8.80636	−	5.85783i	0.352819	−	0.234689i
$624$	−0.801938			−0.0321032
$625$	−11.5528	+	20.0100i	−0.462112	+	0.800402i
$626$	2.64526	+	4.58172i	0.105726	+	0.183123i
$627$	19.4318	+	33.6568i	0.776030	+	1.34412i
$628$	−12.4874	+	21.6288i	−0.498301	+	0.863083i
$629$	70.0907			2.79470
$630$	1.90097	+	0.942362i	0.0757364	+	0.0375446i
$631$	23.9390			0.952997			0.476498	−	0.879175i	$-0.341906\pi$
$631$	23.9390			0.952997			0.476498	+	0.879175i	$0.341906\pi$
$632$	−0.873158	+	1.51235i	−0.0347324	+	0.0601582i
$633$	−5.88404	−	10.1915i	−0.233870	−	0.405074i
$634$	−25.1015	−	43.4770i	−0.996907	−	1.72669i
$635$	−2.14095	+	3.70823i	−0.0849609	+	0.147157i
$636$	27.4698			1.08925
$637$	4.23825	+	5.57111i	0.167926	+	0.220735i
$638$	2.87800			0.113941
$639$	5.22737	−	9.05406i	0.206791	−	0.358173i
$640$	−2.90193	−	5.02629i	−0.114709	−	0.198681i
$641$	18.9882	+	32.8886i	0.749989	+	1.29902i	0.947827	+	0.318785i	$0.103275\pi$
$641$	18.9882	+	32.8886i	0.749989	+	1.29902i	−0.197838	+	0.980235i	$0.563392\pi$
$642$	14.2153	−	24.6216i	0.561032	−	0.971737i
$643$	17.6045			0.694252			0.347126	−	0.937818i	$-0.387158\pi$
$643$	17.6045			0.694252			0.347126	+	0.937818i	$0.387158\pi$
$644$	7.58091	+	3.75806i	0.298730	+	0.148088i
$645$	0.550646			0.0216817
$646$	64.4318	−	111.599i	2.53504	−	4.39081i
$647$	1.73407	+	3.00350i	0.0681733	+	0.118080i	0.898097	−	0.439797i	$-0.144950\pi$
$647$	1.73407	+	3.00350i	0.0681733	+	0.118080i	−0.829924	+	0.557877i	$0.811616\pi$
$648$	1.17845	+	2.04113i	0.0462938	+	0.0801832i
$649$	13.8591	−	24.0046i	0.544015	−	0.942262i
$650$	10.9487			0.429443
$651$	−18.1673	+	12.0846i	−0.712034	+	0.473632i
$652$	−43.2355			−1.69323
$653$	−5.42476	+	9.39597i	−0.212287	+	0.367693i	−0.952430	−	0.304757i	$-0.901425\pi$
$653$	−5.42476	+	9.39597i	−0.212287	+	0.367693i	0.740143	+	0.672450i	$0.234758\pi$
$654$	−9.36927	−	16.2281i	−0.366368	−	0.634567i
$655$	−2.53223	−	4.38595i	−0.0989424	−	0.171373i
$656$	−2.30678	+	3.99546i	−0.0900647	+	0.155997i
$657$	6.16852			0.240657
$658$	−0.587482	−	9.25749i	−0.0229024	−	0.360895i
$659$	−34.7982			−1.35555			−0.677773	−	0.735271i	$-0.737055\pi$
$659$	−34.7982			−1.35555			−0.677773	+	0.735271i	$0.737055\pi$
$660$	−2.82155	+	4.88707i	−0.109829	+	0.190229i
$661$	8.65279	+	14.9871i	0.336555	+	0.582930i	0.983782	−	0.179367i	$-0.0574050\pi$
$661$	8.65279	+	14.9871i	0.336555	+	0.582930i	−0.647228	+	0.762297i	$0.724072\pi$
$662$	−2.46950	−	4.27730i	−0.0959799	−	0.166242i
$663$	3.82640	−	6.62751i	0.148605	−	0.257391i
$664$	−6.60388			−0.256280
$665$	−0.448157	−	7.06202i	−0.0173788	−	0.273854i
$666$	20.5797			0.797448
$667$	−0.129531	+	0.224354i	−0.00501544	+	0.00868700i
$668$	20.2359	+	35.0495i	0.782949	+	1.35611i
$669$	−7.13318	−	12.3550i	−0.275785	−	0.477673i
$670$	−4.59515	+	7.95903i	−0.177526	+	0.307484i
$671$	9.48560			0.366187
$672$	14.3535	−	9.54772i	0.553700	−	0.368311i
$673$	12.5797			0.484912			0.242456	−	0.970162i	$-0.422047\pi$
$673$	12.5797			0.484912			0.242456	+	0.970162i	$0.422047\pi$
$674$	3.69687	−	6.40316i	0.142398	−	0.246640i
$675$	2.43631	+	4.21982i	0.0937737	+	0.162421i
$676$	−1.52446	−	2.64044i	−0.0586330	−	0.101555i
$677$	18.4022	−	31.8736i	0.707255	−	1.22500i	−0.258617	−	0.965980i	$-0.583267\pi$
$677$	18.4022	−	31.8736i	0.707255	−	1.22500i	0.965872	−	0.259021i	$-0.0834000\pi$
$678$	−26.9245			−1.03403
$679$	−15.0918	−	7.48141i	−0.579170	−	0.287110i
$680$	6.43727			0.246858
$681$	−1.81402	+	3.14197i	−0.0695134	+	0.120401i
$682$	−48.0502	−	83.2253i	−1.83994	−	3.18686i
$683$	−24.8240	−	42.9964i	−0.949864	−	1.64521i	−0.745706	−	0.666275i	$-0.767888\pi$
$683$	−24.8240	−	42.9964i	−0.949864	−	1.64521i	−0.204158	−	0.978938i	$-0.565446\pi$
$684$	11.4242	−	19.7873i	0.436816	−	0.756588i
$685$	−4.80540			−0.183605
$686$	−39.3221	−	13.6216i	−1.50133	−	0.520075i
$687$	−13.7681			−0.525285
$688$	0.618645	−	1.07153i	0.0235856	−	0.0408515i
$689$	−4.50484	−	7.80262i	−0.171621	−	0.297256i
$690$	−0.420583	−	0.728471i	−0.0160113	−	0.0277324i
$691$	16.2419	−	28.1318i	0.617871	−	1.07018i	−0.372003	−	0.928232i	$-0.621329\pi$
$691$	16.2419	−	28.1318i	0.617871	−	1.07018i	0.989874	−	0.141952i	$-0.0453379\pi$
$692$	−11.6950			−0.444577
$693$	−12.2932	−	6.09408i	−0.466980	−	0.231495i
$694$	72.6118			2.75630
$695$	2.17145	−	3.76106i	0.0823677	−	0.142665i
$696$	−0.291053	−	0.504118i	−0.0110323	−	0.0191085i
$697$	−22.0133	−	38.1282i	−0.833815	−	1.44421i
$698$	19.0831	−	33.0528i	0.722305	−	1.25107i
$699$	−7.53079			−0.284841
$700$	−32.7269	+	21.7693i	−1.23696	+	0.822804i
$701$	−15.5362			−0.586793			−0.293397	−	0.955991i	$-0.594786\pi$
$701$	−15.5362			−0.586793			−0.293397	+	0.955991i	$0.594786\pi$
$702$	1.12349	−	1.94594i	0.0424034	−	0.0734448i
$703$	−34.3180	−	59.4405i	−1.29433	−	2.24184i
$704$	33.8044	+	58.5509i	1.27405	+	2.20672i
$705$	−0.278439	+	0.482270i	−0.0104866	+	0.0181633i
$706$	18.2131			0.685460
$707$	−0.693218	−	10.9237i	−0.0260711	−	0.410827i
$708$	−16.2959			−0.612437
$709$	3.90366	−	6.76133i	0.146605	−	0.253927i	−0.783366	−	0.621561i	$-0.786499\pi$
$709$	3.90366	−	6.76133i	0.146605	−	0.253927i	0.929971	+	0.367634i	$0.119832\pi$
$710$	−4.19202	−	7.26079i	−0.157324	−	0.272493i
$711$	0.370469	+	0.641672i	0.0138937	+	0.0240646i
$712$	4.71097	−	8.15964i	0.176551	−	0.305796i
$713$	8.65040			0.323960
$714$	2.88135	+	45.4041i	0.107832	+	1.69921i
$715$	1.85086			0.0692181
$716$	−2.16152	+	3.74387i	−0.0807799	+	0.139915i
$717$	6.12229	+	10.6041i	0.228641	+	0.396018i
$718$	21.4671	+	37.1821i	0.801145	+	1.38762i
$719$	−16.2690	+	28.1788i	−0.606733	+	1.05089i	0.385042	+	0.922899i	$0.374187\pi$
$719$	−16.2690	+	28.1788i	−0.606733	+	1.05089i	−0.991775	+	0.127993i	$0.959146\pi$
$720$	−0.286208			−0.0106664
$721$	−7.60095	+	5.05601i	−0.283074	+	0.188296i
$722$	−83.4965			−3.10742
$723$	14.6875	−	25.4394i	0.546233	−	0.946103i
$724$	29.6313	+	51.3229i	1.10124	+	1.90740i
$725$	−0.601720	−	1.04221i	−0.0223473	−	0.0387067i
$726$	17.8572	−	30.9296i	0.662743	−	1.14790i
$727$	37.0814			1.37527			0.687637	−	0.726054i	$-0.258648\pi$
$727$	37.0814			1.37527			0.687637	+	0.726054i	$0.258648\pi$
$728$	5.58695	+	2.76960i	0.207066	+	0.102648i
$729$	1.00000			0.0370370
$730$	2.47339	−	4.28403i	0.0915441	−	0.158559i
$731$	5.90366	+	10.2254i	0.218355	+	0.378201i
$732$	−2.78836	−	4.82959i	−0.103061	−	0.178507i
$733$	−1.69136	+	2.92952i	−0.0624717	+	0.108204i	−0.895570	−	0.444921i	$-0.853232\pi$
$733$	−1.69136	+	2.92952i	−0.0624717	+	0.108204i	0.833098	+	0.553125i	$0.186565\pi$
$734$	−35.9855			−1.32825
$735$	1.51261	+	1.98831i	0.0557936	+	0.0733397i
$736$	−6.83446			−0.251922
$737$	29.7159	−	51.4695i	1.09460	−	1.89590i
$738$	−6.46346	−	11.1950i	−0.237923	−	0.412095i
$739$	9.50820	+	16.4687i	0.349765	+	0.605810i	0.986207	−	0.165514i	$-0.0529282\pi$
$739$	9.50820	+	16.4687i	0.349765	+	0.605810i	−0.636443	+	0.771324i	$0.719595\pi$
$740$	4.98307	−	8.63094i	0.183181	−	0.317280i
$741$	−7.49396			−0.275297
$742$	47.9892	+	23.7895i	1.76174	+	0.873342i
$743$	−21.9511			−0.805307			−0.402654	−	0.915352i	$-0.631912\pi$
$743$	−21.9511			−0.805307			−0.402654	+	0.915352i	$0.631912\pi$
$744$	−9.71864	+	16.8332i	−0.356302	+	0.617134i
$745$	−1.19029	−	2.06165i	−0.0436089	−	0.0755329i
$746$	13.8252	+	23.9459i	0.506177	+	0.876723i
$747$	−1.40097	+	2.42655i	−0.0512588	+	0.0887828i
$748$	−121.003			−4.42431
$749$	27.8729	−	18.5406i	1.01845	−	0.677457i
$750$	7.91723			0.289096
$751$	−0.362937	+	0.628625i	−0.0132437	+	0.0229388i	−0.872571	−	0.488487i	$-0.837549\pi$
$751$	−0.362937	+	0.628625i	−0.0132437	+	0.0229388i	0.859328	+	0.511426i	$0.170882\pi$
$752$	0.625646	+	1.08365i	0.0228150	+	0.0395167i
$753$	−0.261217	−	0.452441i	−0.00951928	−	0.0164879i
$754$	−0.277479	+	0.480608i	−0.0101052	+	0.0175027i
$755$	−0.478420			−0.0174115
$756$	0.510885	+	8.05048i	0.0185807	+	0.292793i
$757$	17.4383			0.633807			0.316904	−	0.948458i	$-0.397357\pi$
$757$	17.4383			0.633807			0.316904	+	0.948458i	$0.397357\pi$
$758$	−28.3267	+	49.0633i	−1.02887	+	1.78206i
$759$	2.71983	+	4.71089i	0.0987237	+	0.170994i
$760$	−3.15183	−	5.45914i	−0.114329	−	0.198024i
$761$	14.1930	−	24.5830i	0.514495	−	0.891132i	−0.485363	−	0.874313i	$-0.661313\pi$
$761$	14.1930	−	24.5830i	0.514495	−	0.891132i	0.999859	−	0.0168192i	$-0.00535398\pi$
$762$	−26.9584			−0.976599
$763$	−1.39738	−	22.0198i	−0.0505885	−	0.797170i
$764$	−19.2489			−0.696401
$765$	1.36563	−	2.36533i	0.0493743	−	0.0855188i
$766$	7.10537	+	12.3069i	0.256727	+	0.444665i
$767$	2.67241	+	4.62874i	0.0964950	+	0.167134i
$768$	5.23341	−	9.06453i	0.188844	−	0.327088i
$769$	−5.48380			−0.197751			−0.0988754	−	0.995100i	$-0.531525\pi$
$769$	−5.48380			−0.197751			−0.0988754	+	0.995100i	$0.531525\pi$
$770$	−9.16152	+	6.09408i	−0.330158	+	0.219615i
$771$	−3.19806			−0.115175
$772$	−36.2114	+	62.7200i	−1.30328	+	2.25734i
$773$	−13.3138	−	23.0601i	−0.478863	−	0.829416i	0.520843	−	0.853653i	$-0.325618\pi$
$773$	−13.3138	−	23.0601i	−0.478863	−	0.829416i	−0.999706	+	0.0242368i	$0.992284\pi$
$774$	1.73341	+	3.00235i	0.0623060	+	0.107917i
$775$	−20.0922	+	34.8007i	−0.721734	+	1.25008i
$776$	−15.0054			−0.538662
$777$	21.7107	+	10.7626i	0.778868	+	0.386106i
$778$	49.1812			1.76323
$779$	−21.5565	+	37.3369i	−0.772340	+	1.33773i
$780$	−0.544073	−	0.942362i	−0.0194809	−	0.0337420i
$781$	27.1090	+	46.9542i	0.970037	+	1.68015i
$782$	9.01842	−	15.6204i	0.322498	−	0.558583i
$783$	−0.246980			−0.00882633
$784$	5.56853	−	0.709618i	0.198876	−	0.0253435i
$785$	2.92346			0.104343
$786$	15.9426	−	27.6135i	0.568655	−	0.984940i
$787$	7.83244	+	13.5662i	0.279196	+	0.483582i	0.971185	−	0.238326i	$-0.0765987\pi$
$787$	7.83244	+	13.5662i	0.279196	+	0.483582i	−0.691989	+	0.721908i	$0.743265\pi$
$788$	−17.9170	−	31.0331i	−0.638266	−	1.10551i
$789$	−6.03415	+	10.4514i	−0.214821	+	0.372081i
$790$	0.594187			0.0211402
$791$	−28.4042	−	14.0808i	−1.00994	−	0.500654i
$792$	−12.2228			−0.434319
$793$	−0.914542	+	1.58403i	−0.0324764	+	0.0562507i
$794$	41.5332	+	71.9377i	1.47396	+	2.55297i
$795$	−1.60776	−	2.78472i	−0.0570214	−	0.0987639i
$796$	12.0613	−	20.8908i	0.427501	−	0.740454i
$797$	−23.2360			−0.823060			−0.411530	−	0.911396i	$-0.635005\pi$
$797$	−23.2360			−0.823060			−0.411530	+	0.911396i	$0.635005\pi$
$798$	37.0942	−	24.6744i	1.31312	−	0.873465i
$799$	−11.9409			−0.422439
$800$	15.8744	−	27.4952i	0.561243	−	0.972102i
$801$	−1.99880	−	3.46203i	−0.0706243	−	0.122325i
$802$	−19.2364	−	33.3184i	−0.679261	−	1.17651i
$803$	−15.9949	+	27.7040i	−0.564448	+	0.977653i
$804$	−34.9409			−1.23227
$805$	−0.0627278	−	0.988460i	−0.00221087	−	0.0348386i
$806$	18.5308			0.652719
$807$	5.04772	−	8.74291i	0.177688	−	0.307765i
$808$	−4.87531	−	8.44429i	−0.171513	−	0.297069i
$809$	−2.11811	−	3.66868i	−0.0744689	−	0.128984i	0.826386	−	0.563104i	$-0.190393\pi$
$809$	−2.11811	−	3.66868i	−0.0744689	−	0.128984i	−0.900855	+	0.434120i	$0.857059\pi$
$810$	0.400969	−	0.694498i	0.0140886	−	0.0244022i
$811$	1.84548			0.0648035			0.0324018	−	0.999475i	$-0.489684\pi$
$811$	1.84548			0.0648035			0.0324018	+	0.999475i	$0.489684\pi$
$812$	−0.126178	−	1.98831i	−0.00442799	−	0.0697758i
$813$	1.04593			0.0366825
$814$	−53.3630	+	92.4274i	−1.87037	+	3.23958i
$815$	2.53050	+	4.38295i	0.0886395	+	0.153528i
$816$	−3.06853	−	5.31485i	−0.107420	−	0.186057i
$817$	5.78113	−	10.0132i	0.202256	−	0.350318i
$818$	−31.9801			−1.11816
$819$	2.20291	−	1.46533i	0.0769758	−	0.0512029i
$820$	−6.26013			−0.218613
$821$	10.7098	−	18.5499i	0.373774	−	0.647395i	−0.616369	−	0.787458i	$-0.711397\pi$
$821$	10.7098	−	18.5499i	0.373774	−	0.647395i	0.990143	+	0.140062i	$0.0447303\pi$
$822$	−15.1271	−	26.2010i	−0.527620	−	0.913864i
$823$	10.8971	+	18.8743i	0.379848	+	0.657917i	0.991040	−	0.133566i	$-0.0426428\pi$
$823$	10.8971	+	18.8743i	0.379848	+	0.657917i	−0.611191	+	0.791483i	$0.709309\pi$
$824$	−4.06614	+	7.04276i	−0.141651	+	0.245346i
$825$	−25.2693			−0.879766
$826$	−28.4686	−	14.1127i	−0.990549	−	0.491042i
$827$	−24.4166			−0.849047			−0.424524	−	0.905417i	$-0.639558\pi$
$827$	−24.4166			−0.849047			−0.424524	+	0.905417i	$0.639558\pi$
$828$	1.59903	−	2.76960i	0.0555702	−	0.0962504i
$829$	10.3896	+	17.9952i	0.360844	+	0.625000i	0.988100	−	0.153813i	$-0.0491553\pi$
$829$	10.3896	+	17.9952i	0.360844	+	0.625000i	−0.627256	+	0.778813i	$0.715822\pi$
$830$	1.12349	+	1.94594i	0.0389969	+	0.0675446i
$831$	1.10656	−	1.91662i	0.0383863	−	0.0664870i
$832$	−13.0368			−0.451971
$833$	−20.7054	+	49.4063i	−0.717398	+	1.71183i
$834$	27.3424			0.946791
$835$	2.36874	−	4.10278i	0.0819736	−	0.141983i
$836$	59.2458	+	102.617i	2.04906	+	3.54908i
$837$	4.12349	+	7.14209i	0.142529	+	0.246867i
$838$	−18.3463	+	31.7767i	−0.633763	+	1.09771i
$839$	33.6668			1.16231			0.581153	−	0.813794i	$-0.302602\pi$
$839$	33.6668			1.16231			0.581153	+	0.813794i	$0.302602\pi$
$840$	1.99396	+	0.988460i	0.0687981	+	0.0341051i
$841$	−28.9390			−0.997897
$842$	−14.3530	+	24.8601i	−0.494637	+	0.856737i
$843$	−10.6833	−	18.5040i	−0.367952	−	0.637312i
$844$	−17.9400	−	31.0729i	−0.617519	−	1.06957i
$845$	−0.178448	+	0.309081i	−0.00613880	+	0.0106327i
$846$	−3.50604			−0.120540
$847$	35.0139	−	23.2906i	1.20309	−	0.800274i
$848$	−7.22521			−0.248115
$849$	−0.605072	+	1.04802i	−0.0207660	+	0.0359678i
$850$	41.8940	+	72.5626i	1.43695	+	2.48888i
$851$	−4.80343	−	8.31978i	−0.164659	−	0.285199i
$852$	15.9378	−	27.6051i	0.546020	−	0.945735i
$853$	−15.0358			−0.514815			−0.257407	−	0.966303i	$-0.582868\pi$
$853$	−15.0358			−0.514815			−0.257407	+	0.966303i	$0.582868\pi$
$854$	−0.688669	−	10.8520i	−0.0235658	−	0.371347i
$855$	−2.67456			−0.0914681
$856$	14.9107	−	25.8260i	0.509636	−	0.882715i
$857$	6.46346	+	11.1950i	0.220788	+	0.382415i	0.955047	−	0.296453i	$-0.0958039\pi$
$857$	6.46346	+	11.1950i	0.220788	+	0.382415i	−0.734260	+	0.678869i	$0.762471\pi$
$858$	5.82640	+	10.0916i	0.198910	+	0.344522i
$859$	8.44385	−	14.6252i	0.288100	−	0.499004i	−0.685256	−	0.728302i	$-0.740310\pi$
$859$	8.44385	−	14.6252i	0.288100	−	0.499004i	0.973356	+	0.229298i	$0.0736430\pi$
$860$	1.67887			0.0572492
$861$	−0.963992	−	15.1905i	−0.0328528	−	0.517691i
$862$	−55.8015			−1.90061
$863$	3.99157	−	6.91360i	0.135874	−	0.235342i	−0.790057	−	0.613034i	$-0.789949\pi$
$863$	3.99157	−	6.91360i	0.135874	−	0.235342i	0.925931	+	0.377692i	$0.123282\pi$
$864$	−3.25786	−	5.64279i	−0.110835	−	0.191972i
$865$	0.684489	+	1.18557i	0.0232733	+	0.0403106i
$866$	−9.32520	+	16.1517i	−0.316883	+	0.548858i
$867$	41.5652			1.41163
$868$	−55.3907	+	36.8449i	−1.88008	+	1.25060i
$869$	−3.84249			−0.130348
$870$	−0.0990311	+	0.171527i	−0.00335747	+	0.00581531i
$871$	5.73005	+	9.92474i	0.194155	+	0.336287i
$872$	−9.82759	−	17.0219i	−0.332804	−	0.576434i
$873$	−3.18329	+	5.51362i	−0.107738	+	0.186608i
$874$	−17.6625			−0.597442
$875$	8.35235	+	4.14049i	0.282361	+	0.139974i
$876$	18.8073			0.635440
$877$	−11.6945	+	20.2554i	−0.394894	+	0.683977i	−0.993088	−	0.117375i	$-0.962552\pi$
$877$	−11.6945	+	20.2554i	−0.394894	+	0.683977i	0.598193	+	0.801352i	$0.295885\pi$
$878$	15.7518	+	27.2830i	0.531598	+	0.920755i
$879$	8.85905	+	15.3443i	0.298808	+	0.517551i
$880$	0.742135	−	1.28542i	0.0250174	−	0.0433314i
$881$	−2.63342			−0.0887220			−0.0443610	−	0.999016i	$-0.514125\pi$
$881$	−2.63342			−0.0887220			−0.0443610	+	0.999016i	$0.514125\pi$
$882$	−6.07942	+	14.5065i	−0.204705	+	0.488458i
$883$	17.1570			0.577380			0.288690	−	0.957423i	$-0.406780\pi$
$883$	17.1570			0.577380			0.288690	+	0.957423i	$0.406780\pi$
$884$	11.6664	−	20.2067i	0.392382	−	0.679626i
$885$	0.953771	+	1.65198i	0.0320607	+	0.0555307i
$886$	−14.1697	−	24.5427i	−0.476041	−	0.824527i
$887$	6.55041	−	11.3456i	0.219941	−	0.380949i	−0.734849	−	0.678231i	$-0.762747\pi$
$887$	6.55041	−	11.3456i	0.219941	−	0.380949i	0.954790	+	0.297282i	$0.0960801\pi$
$888$	21.5864			0.724393
$889$	−28.4400	−	14.0985i	−0.953846	−	0.472847i
$890$	−3.20583			−0.107460
$891$	−2.59299	+	4.49119i	−0.0868684	+	0.150461i
$892$	−21.7485	−	37.6695i	−0.728193	−	1.26127i
$893$	5.84654	+	10.1265i	0.195647	+	0.338871i
$894$	7.49396	−	12.9799i	0.250635	−	0.434113i
$895$	0.506041			0.0169151
$896$	35.8238	−	23.8293i	1.19679	−	0.796082i
$897$	−1.04892			−0.0350223
$898$	−22.0695	+	38.2255i	−0.736468	+	1.27560i
$899$	−1.01842	−	1.76395i	−0.0339661	−	0.0588311i
$900$	7.42812	+	12.8659i	0.247604	+	0.428862i
$901$	34.4746	−	59.7118i	1.14852	−	1.98929i
$902$	67.0388			2.23215
$903$	0.258529	+	4.07387i	0.00860330	+	0.135570i
$904$	−28.2416			−0.939302
$905$	3.46854	−	6.00769i	0.115298	−	0.199702i
$906$	−1.50604	−	2.60854i	−0.0500349	−	0.0866629i
$907$	10.6984	+	18.5301i	0.355233	+	0.615282i	0.987158	−	0.159748i	$-0.0510681\pi$
$907$	10.6984	+	18.5301i	0.355233	+	0.615282i	−0.631925	+	0.775030i	$0.717735\pi$
$908$	−5.53079	+	9.57962i	−0.183546	+	0.317911i
$909$	−4.13706			−0.137218
$910$	−0.134375	−	2.11747i	−0.00445449	−	0.0701934i
$911$	−3.20344			−0.106135			−0.0530673	−	0.998591i	$-0.516900\pi$
$911$	−3.20344			−0.106135			−0.0530673	+	0.998591i	$0.516900\pi$
$912$	−3.00484	+	5.20454i	−0.0995003	+	0.172340i
$913$	−7.26540	−	12.5840i	−0.240450	−	0.416471i
$914$	−8.16905	−	14.1492i	−0.270208	−	0.468015i
$915$	−0.326396	+	0.565335i	−0.0107903	+	0.0186894i
$916$	−41.9778			−1.38698
$917$	31.2599	−	20.7935i	1.03229	−	0.686662i
$918$	17.1957			0.567542
$919$	6.61380	−	11.4554i	0.218169	−	0.377880i	−0.736079	−	0.676896i	$-0.763325\pi$
$919$	6.61380	−	11.4554i	0.218169	−	0.377880i	0.954248	+	0.299015i	$0.0966582\pi$
$920$	−0.441157	−	0.764106i	−0.0145445	−	0.0251918i
$921$	3.46950	+	6.00935i	0.114324	+	0.198015i
$922$	−4.77897	+	8.27742i	−0.157387	+	0.272602i
$923$	−10.4547			−0.344122
$924$	−37.4810	−	18.5803i	−1.23303	−	0.611248i
$925$	44.6276			1.46735
$926$	−40.2972	+	69.7967i	−1.32425	+	2.29366i
$927$	1.72521	+	2.98815i	0.0566633	+	0.0981437i
$928$	0.804626	+	1.39365i	0.0264131	+	0.0457489i
$929$	22.9252	−	39.7076i	0.752151	−	1.30276i	−0.194627	−	0.980877i	$-0.562350\pi$
$929$	22.9252	−	39.7076i	0.752151	−	1.30276i	0.946778	−	0.321887i	$-0.104317\pi$
$930$	6.61356			0.216867
$931$	52.0369	−	6.63125i	1.70544	−	0.217330i
$932$	−22.9608			−0.752105
$933$	−11.9221	+	20.6496i	−0.390311	+	0.676039i
$934$	−12.6359	−	21.8860i	−0.413458	−	0.716131i
$935$	7.08211	+	12.2666i	0.231610	+	0.401160i
$936$	1.17845	−	2.04113i	0.0385188	−	0.0667165i
$937$	25.0680			0.818937			0.409468	−	0.912324i	$-0.365714\pi$
$937$	25.0680			0.818937			0.409468	+	0.912324i	$0.365714\pi$
$938$	−61.0411	−	30.2597i	−1.99306	−	0.988015i
$939$	2.35450			0.0768363
$940$	−0.848936	+	1.47040i	−0.0276892	+	0.0479592i
$941$	−27.6405	−	47.8747i	−0.901054	−	1.56067i	−0.826129	−	0.563482i	$-0.809462\pi$
$941$	−27.6405	−	47.8747i	−0.901054	−	1.56067i	−0.0749251	−	0.997189i	$-0.523872\pi$
$942$	9.20291	+	15.9399i	0.299847	+	0.519350i
$943$	−3.01722	+	5.22598i	−0.0982542	+	0.170181i
$944$	4.28621			0.139504
$945$	0.786208	−	0.522971i	0.0255754	−	0.0170123i
$946$	−17.9788			−0.584542
$947$	3.26510	−	5.65532i	0.106102	−	0.183773i	−0.808086	−	0.589064i	$-0.799496\pi$
$947$	3.26510	−	5.65532i	0.106102	−	0.183773i	0.914188	+	0.405291i	$0.132830\pi$
$948$	1.12953	+	1.95640i	0.0366854	+	0.0635411i
$949$	−3.08426	−	5.34210i	−0.100119	−	0.173412i
$950$	41.0245	−	71.0565i	1.33101	−	2.30538i
$951$	−22.3424			−0.724503
$952$	3.02230	+	47.6252i	0.0979534	+	1.54354i
$953$	44.7741			1.45037			0.725187	−	0.688552i	$-0.241753\pi$
$953$	44.7741			1.45037			0.725187	+	0.688552i	$0.241753\pi$
$954$	10.1223	−	17.5323i	0.327721	−	0.567630i
$955$	1.12661	+	1.95134i	0.0364561	+	0.0631438i
$956$	18.6664	+	32.3311i	0.603713	+	1.04566i
$957$	0.640416	−	1.10923i	0.0207017	−	0.0358564i
$958$	−21.7138			−0.701541
$959$	−2.25614	−	35.5520i	−0.0728544	−	1.14803i
$960$	−4.65279			−0.150168
$961$	−18.5063	+	32.0539i	−0.596979	+	1.03400i
$962$	−10.2899	−	17.8226i	−0.331758	−	0.574622i
$963$	−6.32640	−	10.9576i	−0.203865	−	0.353105i
$964$	44.7809	−	77.5628i	1.44230	−	2.49813i
$965$	8.47757			0.272902
$966$	5.19202	−	3.45364i	0.167051	−	0.111119i
$967$	−54.5763			−1.75505			−0.877527	−	0.479527i	$-0.840808\pi$
$967$	−54.5763			−1.75505			−0.877527	+	0.479527i	$0.840808\pi$
$968$	18.7307	−	32.4426i	0.602028	−	1.04274i
$969$	−28.6749	−	49.6663i	−0.921169	−	1.59551i
$970$	2.55280	+	4.42158i	0.0819655	+	0.141968i
$971$	23.2017	−	40.1865i	0.744578	−	1.28965i	−0.205813	−	0.978591i	$-0.565984\pi$
$971$	23.2017	−	40.1865i	0.744578	−	1.28965i	0.950392	−	0.311056i	$-0.100683\pi$
$972$	3.04892			0.0977941
$973$	28.8451	+	14.2993i	0.924732	+	0.458415i
$974$	31.8810			1.02153
$975$	2.43631	−	4.21982i	0.0780244	−	0.135142i
$976$	0.733406	+	1.27030i	0.0234758	+	0.0406612i
$977$	−6.13491	−	10.6260i	−0.196273	−	0.339955i	0.751044	−	0.660252i	$-0.229551\pi$
$977$	−6.13491	−	10.6260i	−0.196273	−	0.339955i	−0.947317	+	0.320297i	$0.896217\pi$
$978$	−15.9318	+	27.5946i	−0.509442	+	0.882379i
$979$	20.7315			0.662582
$980$	4.61184	+	6.06218i	0.147320	+	0.193649i
$981$	−8.33944			−0.266258
$982$	45.5393	−	78.8764i	1.45322	−	2.51705i
$983$	16.5196	+	28.6128i	0.526894	+	0.912607i	0.999509	+	0.0313379i	$0.00997681\pi$
$983$	16.5196	+	28.6128i	0.526894	+	0.912607i	−0.472615	+	0.881269i	$0.656690\pi$
$984$	−6.77963	−	11.7427i	−0.216127	−	0.374343i
$985$	−2.09730	+	3.63263i	−0.0668256	+	0.115745i
$986$	−4.24698			−0.135251
$987$	−3.69873	−	1.83356i	−0.117732	−	0.0583628i
$988$	−22.8485			−0.726906
$989$	0.809175	−	1.40153i	0.0257303	−	0.0445661i
$990$	2.07942	+	3.60166i	0.0660882	+	0.114468i
$991$	−9.39373	−	16.2704i	−0.298402	−	0.516847i	0.677369	−	0.735644i	$-0.263120\pi$
$991$	−9.39373	−	16.2704i	−0.298402	−	0.516847i	−0.975770	+	0.218797i	$0.929787\pi$
$992$	26.8675	−	46.5360i	0.853045	−	1.47752i
$993$	−2.19806			−0.0697534
$994$	51.7497	−	34.4230i	1.64140	−	1.09183i
$995$	−2.82371			−0.0895176
$996$	−4.27144	+	7.39835i	−0.135346	+	0.234426i
$997$	−2.45497	−	4.25213i	−0.0777496	−	0.134666i	0.824529	−	0.565820i	$-0.191440\pi$
$997$	−2.45497	−	4.25213i	−0.0777496	−	0.134666i	−0.902279	+	0.431153i	$0.858107\pi$
$998$	31.2107	+	54.0586i	0.987959	+	1.71119i
$999$	4.57942	−	7.93178i	0.144886	−	0.250950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.c.79.3	✓	6
3.2	odd	2		819.2.j.d.352.1		6
7.2	even	3		1911.2.a.m.1.1		3
7.4	even	3	inner	273.2.i.c.235.3	yes	6
7.5	odd	6		1911.2.a.l.1.1		3
21.2	odd	6		5733.2.a.bb.1.3		3
21.5	even	6		5733.2.a.ba.1.3		3
21.11	odd	6		819.2.j.d.235.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.c.79.3	✓	6	1.1	even	1	trivial
273.2.i.c.235.3	yes	6	7.4	even	3	inner
819.2.j.d.235.1		6	21.11	odd	6
819.2.j.d.352.1		6	3.2	odd	2
1911.2.a.l.1.1		3	7.5	odd	6
1911.2.a.m.1.1		3	7.2	even	3
5733.2.a.ba.1.3		3	21.5	even	6
5733.2.a.bb.1.3		3	21.2	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12349 - 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 - 2.64044i) q^{4} +(-0.178448 + 0.309081i) q^{5} -2.24698 q^{6} +(-2.37047 - 1.17511i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.12349 - 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 - 2.64044i) q^{4} +(-0.178448 + 0.309081i) q^{5} -2.24698 q^{6} +(-2.37047 - 1.17511i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.400969 + 0.694498i) q^{10} +(-2.59299 - 4.49119i) q^{11} +(-1.52446 + 2.64044i) q^{12} +1.00000 q^{13} +(-4.94989 + 3.29257i) q^{14} +0.356896 q^{15} +(0.400969 - 0.694498i) q^{16} +(3.82640 + 6.62751i) q^{17} +(1.12349 + 1.94594i) q^{18} +(3.74698 - 6.48996i) q^{19} +1.08815 q^{20} +(0.167563 + 2.64044i) q^{21} -11.6528 q^{22} +(0.524459 - 0.908389i) q^{23} +(1.17845 + 2.04113i) q^{24} +(2.43631 + 4.21982i) q^{25} +(1.12349 - 1.94594i) q^{26} +1.00000 q^{27} +(0.510885 + 8.05048i) q^{28} -0.246980 q^{29} +(0.400969 - 0.694498i) q^{30} +(4.12349 + 7.14209i) q^{31} +(-3.25786 - 5.64279i) q^{32} +(-2.59299 + 4.49119i) q^{33} +17.1957 q^{34} +(0.786208 - 0.522971i) q^{35} +3.04892 q^{36} +(4.57942 - 7.93178i) q^{37} +(-8.41939 - 14.5828i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(0.420583 - 0.728471i) q^{40} -5.75302 q^{41} +(5.32640 + 2.64044i) q^{42} +1.54288 q^{43} +(-7.90581 + 13.6933i) q^{44} +(-0.178448 - 0.309081i) q^{45} +(-1.17845 - 2.04113i) q^{46} +(-0.780167 + 1.35129i) q^{47} -0.801938 q^{48} +(4.23825 + 5.57111i) q^{49} +10.9487 q^{50} +(3.82640 - 6.62751i) q^{51} +(-1.52446 - 2.64044i) q^{52} +(-4.50484 - 7.80262i) q^{53} +(1.12349 - 1.94594i) q^{54} +1.85086 q^{55} +(5.58695 + 2.76960i) q^{56} -7.49396 q^{57} +(-0.277479 + 0.480608i) q^{58} +(2.67241 + 4.62874i) q^{59} +(-0.544073 - 0.942362i) q^{60} +(-0.914542 + 1.58403i) q^{61} +18.5308 q^{62} +(2.20291 - 1.46533i) q^{63} -13.0368 q^{64} +(-0.178448 + 0.309081i) q^{65} +(5.82640 + 10.0916i) q^{66} +(5.73005 + 9.92474i) q^{67} +(11.6664 - 20.2067i) q^{68} -1.04892 q^{69} +(-0.134375 - 2.11747i) q^{70} -10.4547 q^{71} +(1.17845 - 2.04113i) q^{72} +(-3.08426 - 5.34210i) q^{73} +(-10.2899 - 17.8226i) q^{74} +(2.43631 - 4.21982i) q^{75} -22.8485 q^{76} +(0.868977 + 13.6933i) q^{77} -2.24698 q^{78} +(0.370469 - 0.641672i) q^{79} +(0.143104 + 0.247864i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.46346 + 11.1950i) q^{82} +2.80194 q^{83} +(6.71648 - 4.46768i) q^{84} -2.73125 q^{85} +(1.73341 - 3.00235i) q^{86} +(0.123490 + 0.213891i) q^{87} +(6.11141 + 10.5853i) q^{88} +(-1.99880 + 3.46203i) q^{89} -0.801938 q^{90} +(-2.37047 - 1.17511i) q^{91} -3.19806 q^{92} +(4.12349 - 7.14209i) q^{93} +(1.75302 + 3.03632i) q^{94} +(1.33728 + 2.31624i) q^{95} +(-3.25786 + 5.64279i) q^{96} +6.36658 q^{97} +(15.6027 - 1.98831i) q^{98} +5.18598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + 6 q^{13} - 7 q^{14} - 6 q^{15} - 2 q^{16} + 5 q^{17} + 2 q^{18} + 13 q^{19} + 14 q^{20} - 34 q^{22} - 6 q^{23} + 3 q^{24} - 2 q^{25} + 2 q^{26} + 6 q^{27} + 8 q^{29} - 2 q^{30} + 20 q^{31} - 7 q^{32} - q^{33} + 30 q^{34} + 21 q^{35} + 19 q^{37} - 18 q^{38} - 3 q^{39} + 11 q^{40} - 44 q^{41} + 14 q^{42} - 28 q^{43} - 21 q^{44} + 3 q^{45} - 3 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{50} + 5 q^{51} - 5 q^{53} + 2 q^{54} - 16 q^{55} - 26 q^{57} - 2 q^{58} - 7 q^{59} - 7 q^{60} + 5 q^{61} + 36 q^{62} - 22 q^{64} + 3 q^{65} + 17 q^{66} + 9 q^{67} + 28 q^{68} + 12 q^{69} + 7 q^{70} - 18 q^{71} + 3 q^{72} + 12 q^{73} - 15 q^{74} - 2 q^{75} - 28 q^{76} + 35 q^{77} - 4 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 10 q^{82} + 8 q^{83} + 21 q^{84} - 32 q^{85} + 7 q^{86} - 4 q^{87} - 6 q^{88} + 29 q^{89} + 4 q^{90} - 28 q^{92} + 20 q^{93} + 20 q^{94} - 13 q^{95} - 7 q^{96} - 14 q^{97} + 35 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + 6 * q^13 - 7 * q^14 - 6 * q^15 - 2 * q^16 + 5 * q^17 + 2 * q^18 + 13 * q^19 + 14 * q^20 - 34 * q^22 - 6 * q^23 + 3 * q^24 - 2 * q^25 + 2 * q^26 + 6 * q^27 + 8 * q^29 - 2 * q^30 + 20 * q^31 - 7 * q^32 - q^33 + 30 * q^34 + 21 * q^35 + 19 * q^37 - 18 * q^38 - 3 * q^39 + 11 * q^40 - 44 * q^41 + 14 * q^42 - 28 * q^43 - 21 * q^44 + 3 * q^45 - 3 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^50 + 5 * q^51 - 5 * q^53 + 2 * q^54 - 16 * q^55 - 26 * q^57 - 2 * q^58 - 7 * q^59 - 7 * q^60 + 5 * q^61 + 36 * q^62 - 22 * q^64 + 3 * q^65 + 17 * q^66 + 9 * q^67 + 28 * q^68 + 12 * q^69 + 7 * q^70 - 18 * q^71 + 3 * q^72 + 12 * q^73 - 15 * q^74 - 2 * q^75 - 28 * q^76 + 35 * q^77 - 4 * q^78 - 12 * q^79 + 9 * q^80 - 3 * q^81 - 10 * q^82 + 8 * q^83 + 21 * q^84 - 32 * q^85 + 7 * q^86 - 4 * q^87 - 6 * q^88 + 29 * q^89 + 4 * q^90 - 28 * q^92 + 20 * q^93 + 20 * q^94 - 13 * q^95 - 7 * q^96 - 14 * q^97 + 35 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more