LMFDB - Embedded newform 273.2.bz.a.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, 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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	273.73
Dual form			273.2.bz.a.187.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458633 + 1.71164i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.987324 - 0.570032i) q^{4} +(2.18934 + 0.586631i) q^{5} +(-1.25301 + 1.25301i) q^{6} +(-0.537086 - 2.59066i) q^{7} +(-1.07751 + 1.07751i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.458633 + 1.71164i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.987324 - 0.570032i) q^{4} +(2.18934 + 0.586631i) q^{5} +(-1.25301 + 1.25301i) q^{6} +(-0.537086 - 2.59066i) q^{7} +(-1.07751 + 1.07751i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.00820 + 3.47831i) q^{10} +(0.937810 + 3.49995i) q^{11} +(-0.570032 - 0.987324i) q^{12} +(1.56942 + 3.24606i) q^{13} +(4.68062 + 0.268865i) q^{14} +(1.60271 + 1.60271i) q^{15} +(-2.49019 - 4.31314i) q^{16} +(2.54394 - 4.40624i) q^{17} +(-1.71164 + 0.458633i) q^{18} +(-2.91838 - 0.781978i) q^{19} +(-1.82719 - 1.82719i) q^{20} +(0.830202 - 2.51212i) q^{21} -6.42078 q^{22} +(-2.54131 + 1.46723i) q^{23} +(-1.47190 + 0.394395i) q^{24} +(0.118928 + 0.0686633i) q^{25} +(-6.27589 + 1.19753i) q^{26} +1.00000i q^{27} +(-0.946483 + 2.86398i) q^{28} +1.91801 q^{29} +(-3.47831 + 2.00820i) q^{30} +(-0.708258 - 2.64326i) q^{31} +(5.58083 - 1.49538i) q^{32} +(-0.937810 + 3.49995i) q^{33} +(6.37517 + 6.37517i) q^{34} +(0.343901 - 5.98690i) q^{35} -1.14006i q^{36} +(-5.36332 - 1.43710i) q^{37} +(2.67693 - 4.63658i) q^{38} +(-0.263875 + 3.59588i) q^{39} +(-2.99113 + 1.72693i) q^{40} +(5.23127 - 5.23127i) q^{41} +(3.91910 + 2.57315i) q^{42} -5.01847i q^{43} +(1.06916 - 3.99017i) q^{44} +(0.586631 + 2.18934i) q^{45} +(-1.34584 - 5.02273i) q^{46} +(-1.55216 + 5.79276i) q^{47} -4.98038i q^{48} +(-6.42308 + 2.78282i) q^{49} +(-0.172072 + 0.172072i) q^{50} +(4.40624 - 2.54394i) q^{51} +(0.300835 - 4.09954i) q^{52} +(5.73961 - 9.94129i) q^{53} +(-1.71164 - 0.458633i) q^{54} +8.21272i q^{55} +(3.37017 + 2.21275i) q^{56} +(-2.13640 - 2.13640i) q^{57} +(-0.879663 + 3.28295i) q^{58} +(-1.22637 + 0.328604i) q^{59} +(-0.668797 - 2.49598i) q^{60} +(8.11798 - 4.68692i) q^{61} +4.84914 q^{62} +(1.97504 - 1.76046i) q^{63} +0.277446i q^{64} +(1.53174 + 8.02739i) q^{65} +(-5.56056 - 3.21039i) q^{66} +(7.63042 - 2.04457i) q^{67} +(-5.02340 + 2.90026i) q^{68} -2.93445 q^{69} +(10.0897 + 3.33443i) q^{70} +(1.84716 + 1.84716i) q^{71} +(-1.47190 - 0.394395i) q^{72} +(9.26691 - 2.48306i) q^{73} +(4.91960 - 8.52099i) q^{74} +(0.0686633 + 0.118928i) q^{75} +(2.43564 + 2.43564i) q^{76} +(8.56352 - 4.30933i) q^{77} +(-6.03384 - 2.10085i) q^{78} +(0.0621069 + 0.107572i) q^{79} +(-2.92165 - 10.9037i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.55482 + 11.3533i) q^{82} +(-9.88999 + 9.88999i) q^{83} +(-2.25167 + 2.00704i) q^{84} +(8.15438 - 8.15438i) q^{85} +(8.58983 + 2.30164i) q^{86} +(1.66104 + 0.959004i) q^{87} +(-4.78172 - 2.76073i) q^{88} +(-4.71305 + 17.5894i) q^{89} -4.01641 q^{90} +(7.56654 - 5.80925i) q^{91} +3.34546 q^{92} +(0.708258 - 2.64326i) q^{93} +(-9.20325 - 5.31350i) q^{94} +(-5.93058 - 3.42402i) q^{95} +(5.58083 + 1.49538i) q^{96} +(-10.0905 + 10.0905i) q^{97} +(-1.81735 - 12.2703i) q^{98} +(-2.56214 + 2.56214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q - 6 * q^7 + 18 * q^9	$ 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.458633	+	1.71164i	−0.324303	+	1.21031i	0.590708	+	0.806885i	$0.298848\pi$
$2$	−0.458633	+	1.71164i	−0.324303	+	1.21031i	−0.915011	+	0.403429i	$0.867818\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.987324	−	0.570032i	−0.493662	−	0.285016i
$5$	2.18934	+	0.586631i	0.979101	+	0.262349i	0.712666	−	0.701504i	$-0.247488\pi$
$5$	2.18934	+	0.586631i	0.979101	+	0.262349i	0.266435	+	0.963853i	$0.414154\pi$
$6$	−1.25301	+	1.25301i	−0.511539	+	0.511539i
$7$	−0.537086	−	2.59066i	−0.202999	−	0.979179i
$7$	−0.537086	−	2.59066i	−0.202999	−	0.979179i
$8$	−1.07751	+	1.07751i	−0.380957	+	0.380957i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.00820	+	3.47831i	−0.635050	+	1.09994i
$11$	0.937810	+	3.49995i	0.282760	+	1.05528i	0.950460	+	0.310845i	$0.100612\pi$
$11$	0.937810	+	3.49995i	0.282760	+	1.05528i	−0.667700	+	0.744430i	$0.732721\pi$
$12$	−0.570032	−	0.987324i	−0.164554	−	0.285016i
$13$	1.56942	+	3.24606i	0.435278	+	0.900296i
$13$	1.56942	+	3.24606i	0.435278	+	0.900296i
$14$	4.68062	+	0.268865i	1.25095	+	0.0718572i
$15$	1.60271	+	1.60271i	0.413817	+	0.413817i
$16$	−2.49019	−	4.31314i	−0.622548	−	1.07828i
$17$	2.54394	−	4.40624i	0.616997	−	1.06867i	−0.373034	−	0.927818i	$-0.621682\pi$
$17$	2.54394	−	4.40624i	0.616997	−	1.06867i	0.990031	−	0.140852i	$-0.0449843\pi$
$18$	−1.71164	+	0.458633i	−0.403438	+	0.108101i
$19$	−2.91838	−	0.781978i	−0.669522	−	0.179398i	−0.0919827	−	0.995761i	$-0.529320\pi$
$19$	−2.91838	−	0.781978i	−0.669522	−	0.179398i	−0.577540	+	0.816363i	$0.695987\pi$
$20$	−1.82719	−	1.82719i	−0.408571	−	0.408571i
$21$	0.830202	−	2.51212i	0.181165	−	0.548190i
$22$	−6.42078			−1.36891
$23$	−2.54131	+	1.46723i	−0.529900	+	0.305938i	−0.740976	−	0.671532i	$-0.765637\pi$
$23$	−2.54131	+	1.46723i	−0.529900	+	0.305938i	0.211076	+	0.977470i	$0.432303\pi$
$24$	−1.47190	+	0.394395i	−0.300451	+	0.0805056i
$25$	0.118928	+	0.0686633i	0.0237857	+	0.0137327i
$26$	−6.27589	+	1.19753i	−1.23080	+	0.234855i
$27$			1.00000i			0.192450i
$28$	−0.946483	+	2.86398i	−0.178868	+	0.541242i
$29$	1.91801			0.356165			0.178083	−	0.984016i	$-0.443011\pi$
$29$	1.91801			0.356165			0.178083	+	0.984016i	$0.443011\pi$
$30$	−3.47831	+	2.00820i	−0.635050	+	0.366646i
$31$	−0.708258	−	2.64326i	−0.127207	−	0.474743i	0.872702	−	0.488254i	$-0.162366\pi$
$31$	−0.708258	−	2.64326i	−0.127207	−	0.474743i	−0.999909	+	0.0135108i	$0.995699\pi$
$32$	5.58083	−	1.49538i	0.986560	−	0.264348i
$33$	−0.937810	+	3.49995i	−0.163252	+	0.609264i
$34$	6.37517	+	6.37517i	1.09333	+	1.09333i
$35$	0.343901	−	5.98690i	0.0581299	−	1.01197i
$36$		−	1.14006i		−	0.190011i
$37$	−5.36332	−	1.43710i	−0.881725	−	0.236258i	−0.210574	−	0.977578i	$-0.567533\pi$
$37$	−5.36332	−	1.43710i	−0.881725	−	0.236258i	−0.671151	+	0.741320i	$0.734200\pi$
$38$	2.67693	−	4.63658i	0.434256	−	0.752153i
$39$	−0.263875	+	3.59588i	−0.0422539	+	0.575802i
$40$	−2.99113	+	1.72693i	−0.472938	+	0.273051i
$41$	5.23127	−	5.23127i	0.816986	−	0.816986i	−0.168684	−	0.985670i	$-0.553952\pi$
$41$	5.23127	−	5.23127i	0.816986	−	0.816986i	0.985670	+	0.168684i	$0.0539517\pi$
$42$	3.91910	+	2.57315i	0.604730	+	0.397046i
$43$		−	5.01847i		−	0.765310i	−0.923891	−	0.382655i	$-0.875010\pi$
$43$		−	5.01847i		−	0.765310i	0.923891	−	0.382655i	$-0.124990\pi$
$44$	1.06916	−	3.99017i	0.161182	−	0.601541i
$45$	0.586631	+	2.18934i	0.0874497	+	0.326367i
$46$	−1.34584	−	5.02273i	−0.198433	−	0.740562i
$47$	−1.55216	+	5.79276i	−0.226406	+	0.844960i	0.755430	+	0.655230i	$0.227428\pi$
$47$	−1.55216	+	5.79276i	−0.226406	+	0.844960i	−0.981836	+	0.189731i	$0.939239\pi$
$48$		−	4.98038i		−	0.718856i
$49$	−6.42308	+	2.78282i	−0.917582	+	0.397546i
$50$	−0.172072	+	0.172072i	−0.0243346	+	0.0243346i
$51$	4.40624	−	2.54394i	0.616997	−	0.356223i
$52$	0.300835	−	4.09954i	0.0417183	−	0.568503i
$53$	5.73961	−	9.94129i	0.788396	−	1.36554i	−0.138553	−	0.990355i	$-0.544245\pi$
$53$	5.73961	−	9.94129i	0.788396	−	1.36554i	0.926949	−	0.375187i	$-0.122421\pi$
$54$	−1.71164	−	0.458633i	−0.232925	−	0.0624121i
$55$			8.21272i			1.10740i
$56$	3.37017	+	2.21275i	0.450359	+	0.295691i
$57$	−2.13640	−	2.13640i	−0.282973	−	0.282973i
$58$	−0.879663	+	3.28295i	−0.115505	+	0.431072i
$59$	−1.22637	+	0.328604i	−0.159659	+	0.0427805i	−0.337763	−	0.941231i	$-0.609670\pi$
$59$	−1.22637	+	0.328604i	−0.159659	+	0.0427805i	0.178104	+	0.984012i	$0.443004\pi$
$60$	−0.668797	−	2.49598i	−0.0863413	−	0.322230i
$61$	8.11798	−	4.68692i	1.03940	−	0.600099i	0.119738	−	0.992806i	$-0.461795\pi$
$61$	8.11798	−	4.68692i	1.03940	−	0.600099i	0.919664	+	0.392707i	$0.128461\pi$
$62$	4.84914			0.615842
$63$	1.97504	−	1.76046i	0.248831	−	0.221797i
$64$			0.277446i			0.0346807i
$65$	1.53174	+	8.02739i	0.189989	+	0.995675i
$66$	−5.56056	−	3.21039i	−0.684457	−	0.395172i
$67$	7.63042	−	2.04457i	0.932205	−	0.249783i	0.239410	−	0.970919i	$-0.423046\pi$
$67$	7.63042	−	2.04457i	0.932205	−	0.249783i	0.692794	+	0.721135i	$0.256379\pi$
$68$	−5.02340	+	2.90026i	−0.609176	+	0.351708i
$69$	−2.93445			−0.353267
$70$	10.0897	+	3.33443i	1.20595	+	0.398540i
$71$	1.84716	+	1.84716i	0.219218	+	0.219218i	0.808169	−	0.588951i	$-0.200459\pi$
$71$	1.84716	+	1.84716i	0.219218	+	0.219218i	−0.588951	+	0.808169i	$0.700459\pi$
$72$	−1.47190	−	0.394395i	−0.173465	−	0.0464799i
$73$	9.26691	−	2.48306i	1.08461	−	0.290620i	0.328127	−	0.944634i	$-0.393583\pi$
$73$	9.26691	−	2.48306i	1.08461	−	0.290620i	0.756483	+	0.654013i	$0.226916\pi$
$74$	4.91960	−	8.52099i	0.571892	−	0.990545i
$75$	0.0686633	+	0.118928i	0.00792856	+	0.0137327i
$76$	2.43564	+	2.43564i	0.279387	+	0.279387i
$77$	8.56352	−	4.30933i	0.975903	−	0.491093i
$78$	−6.03384	−	2.10085i	−0.683198	−	0.237875i
$79$	0.0621069	+	0.107572i	0.00698757	+	0.0121028i	0.869498	−	0.493936i	$-0.164442\pi$
$79$	0.0621069	+	0.107572i	0.00698757	+	0.0121028i	−0.862510	+	0.506039i	$0.831109\pi$
$80$	−2.92165	−	10.9037i	−0.326650	−	1.21907i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.55482	+	11.3533i	0.723859	+	1.25376i
$83$	−9.88999	+	9.88999i	−1.08557	+	1.08557i	−0.0895882	+	0.995979i	$0.528555\pi$
$83$	−9.88999	+	9.88999i	−1.08557	+	1.08557i	−0.995979	+	0.0895882i	$0.971445\pi$
$84$	−2.25167	+	2.00704i	−0.245677	+	0.218986i
$85$	8.15438	−	8.15438i	0.884467	−	0.884467i
$86$	8.58983	+	2.30164i	0.926265	+	0.248192i
$87$	1.66104	+	0.959004i	0.178083	+	0.102816i
$88$	−4.78172	−	2.76073i	−0.509734	−	0.294295i
$89$	−4.71305	+	17.5894i	−0.499583	+	1.86447i	0.00309776	+	0.999995i	$0.499014\pi$
$89$	−4.71305	+	17.5894i	−0.499583	+	1.86447i	−0.502680	+	0.864472i	$0.667653\pi$
$90$	−4.01641			−0.423367
$91$	7.56654	−	5.80925i	0.793189	−	0.608975i
$92$	3.34546			0.348789
$93$	0.708258	−	2.64326i	0.0734430	−	0.274093i
$94$	−9.20325	−	5.31350i	−0.949243	−	0.548046i
$95$	−5.93058	−	3.42402i	−0.608465	−	0.351297i
$96$	5.58083	+	1.49538i	0.569591	+	0.152621i
$97$	−10.0905	+	10.0905i	−1.02454	+	1.02454i	−0.0248466	+	0.999691i	$0.507910\pi$
$97$	−10.0905	+	10.0905i	−1.02454	+	1.02454i	−0.999691	+	0.0248466i	$0.992090\pi$
$98$	−1.81735	−	12.2703i	−0.183581	−	1.23949i
$99$	−2.56214	+	2.56214i	−0.257505	+	0.257505i
$100$	−0.0782806	−	0.135586i	−0.00782806	−	0.0135586i
$101$	−2.40929	+	4.17301i	−0.239733	+	0.415230i	−0.960638	−	0.277804i	$-0.910393\pi$
$101$	−2.40929	+	4.17301i	−0.239733	+	0.415230i	0.720904	+	0.693035i	$0.243727\pi$
$102$	2.33347	+	8.70864i	0.231048	+	0.862284i
$103$	−6.13411	−	10.6246i	−0.604412	−	1.04687i	−0.992144	−	0.125100i	$-0.960075\pi$
$103$	−6.13411	−	10.6246i	−0.604412	−	1.04687i	0.387732	−	0.921772i	$-0.373259\pi$
$104$	−5.18872	−	1.80660i	−0.508796	−	0.177151i
$105$	3.29128	−	5.01286i	0.321196	−	0.489205i
$106$	14.3836	+	14.3836i	1.39706	+	1.39706i
$107$	−6.26406	−	10.8497i	−0.605569	−	1.04888i	−0.991961	−	0.126542i	$-0.959612\pi$
$107$	−6.26406	−	10.8497i	−0.605569	−	1.04888i	0.386392	−	0.922335i	$-0.373721\pi$
$108$	0.570032	−	0.987324i	0.0548514	−	0.0950053i
$109$	15.3102	−	4.10237i	1.46646	−	0.392936i	0.564741	−	0.825268i	$-0.308976\pi$
$109$	15.3102	−	4.10237i	1.46646	−	0.392936i	0.901714	+	0.432333i	$0.142309\pi$
$110$	−14.0572	−	3.76663i	−1.34031	−	0.359134i
$111$	−3.92623	−	3.92623i	−0.372661	−	0.372661i
$112$	−9.83644	+	8.76777i	−0.929456	+	0.828477i
$113$	−13.0654			−1.22909			−0.614547	−	0.788880i	$-0.710661\pi$
$113$	−13.0654			−1.22909			−0.614547	+	0.788880i	$0.710661\pi$
$114$	4.63658	−	2.67693i	0.434256	−	0.250718i
$115$	−6.42450	+	1.72144i	−0.599088	+	0.160525i
$116$	−1.89370	−	1.09333i	−0.175825	−	0.101513i
$117$	−2.02646	+	2.98219i	−0.187347	+	0.275703i
$118$		−	2.24981i		−	0.207112i
$119$	−12.7814	−	4.22397i	−1.17167	−	0.387211i
$120$	−3.45385			−0.315292
$121$	−1.84391	+	1.06458i	−0.167628	+	0.0967801i
$122$	4.29915	+	16.0447i	0.389227	+	1.45262i
$123$	7.14604	−	1.91478i	0.644337	−	0.172650i
$124$	−0.807460	+	3.01348i	−0.0725120	+	0.270619i
$125$	−7.79343	−	7.79343i	−0.697066	−	0.697066i
$126$	2.10746	+	4.18796i	0.187748	+	0.373094i
$127$		−	22.0023i		−	1.95239i	−0.216891	−	0.976196i	$-0.569592\pi$
$127$		−	22.0023i		−	1.95239i	0.216891	−	0.976196i	$-0.430408\pi$
$128$	10.6868	+	2.86351i	0.944586	+	0.253101i
$129$	2.50924	−	4.34612i	0.220926	−	0.382655i
$130$	−14.4425	−	1.05983i	−1.26669	−	0.0929533i
$131$	2.96980	−	1.71462i	0.259473	−	0.149807i	−0.364621	−	0.931156i	$-0.618802\pi$
$131$	2.96980	−	1.71462i	0.259473	−	0.149807i	0.624094	+	0.781349i	$0.285468\pi$
$132$	2.92101	−	2.92101i	0.254241	−	0.254241i
$133$	−0.458420	+	7.98053i	−0.0397500	+	0.692000i
$134$			13.9983i			1.20927i
$135$	−0.586631	+	2.18934i	−0.0504891	+	0.188428i
$136$	2.00664	+	7.48888i	0.172068	+	0.642166i
$137$	0.0801554	+	0.299144i	0.00684814	+	0.0255576i	0.969265	−	0.246018i	$-0.0791221\pi$
$137$	0.0801554	+	0.299144i	0.00684814	+	0.0255576i	−0.962417	+	0.271575i	$0.912455\pi$
$138$	1.34584	−	5.02273i	0.114565	−	0.427563i
$139$			13.4218i			1.13842i	0.822191	+	0.569212i	$0.192752\pi$
$139$			13.4218i			1.13842i	−0.822191	+	0.569212i	$0.807248\pi$
$140$	−3.75227	+	5.71498i	−0.317125	+	0.483004i
$141$	−4.24059	+	4.24059i	−0.357122	+	0.357122i
$142$	−4.00885	+	2.31451i	−0.336415	+	0.194229i
$143$	−9.88925	+	8.53708i	−0.826981	+	0.713907i
$144$	2.49019	−	4.31314i	0.207516	−	0.359428i
$145$	4.19917	+	1.12516i	0.348722	+	0.0934397i
$146$			17.0005i			1.40697i
$147$	−6.95396	−	0.801547i	−0.573553	−	0.0661105i
$148$	4.47615	+	4.47615i	0.367937	+	0.367937i
$149$	−3.46100	+	12.9166i	−0.283536	+	1.05817i	0.666366	+	0.745624i	$0.267849\pi$
$149$	−3.46100	+	12.9166i	−0.283536	+	1.05817i	−0.949902	+	0.312547i	$0.898818\pi$
$150$	−0.235054	+	0.0629826i	−0.0191921	+	0.00514250i
$151$	2.24614	+	8.38272i	0.182788	+	0.682176i	0.995093	+	0.0989425i	$0.0315460\pi$
$151$	2.24614	+	8.38272i	0.182788	+	0.682176i	−0.812305	+	0.583233i	$0.801787\pi$
$152$	3.98716	−	2.30199i	0.323402	−	0.186716i
$153$	5.08789			0.411331
$154$	3.44851	+	16.6341i	0.277889	+	1.34041i
$155$		−	6.20246i		−	0.498194i
$156$	2.31030	−	3.39988i	0.184972	−	0.272209i
$157$	−7.07753	−	4.08622i	−0.564849	−	0.326116i	0.190241	−	0.981737i	$-0.439073\pi$
$157$	−7.07753	−	4.08622i	−0.564849	−	0.326116i	−0.755089	+	0.655622i	$0.772407\pi$
$158$	−0.212610	+	0.0569686i	−0.0169143	+	0.00453218i
$159$	9.94129	−	5.73961i	0.788396	−	0.455181i
$160$	13.0955			1.03529
$161$	5.16599	+	5.79565i	0.407137	+	0.456762i
$162$	−1.25301	−	1.25301i	−0.0984457	−	0.0984457i
$163$	−18.0124	−	4.82640i	−1.41084	−	0.378033i	−0.528614	−	0.848862i	$-0.677288\pi$
$163$	−18.0124	−	4.82640i	−1.41084	−	0.378033i	−0.882224	+	0.470829i	$0.843955\pi$
$164$	−8.14694	+	2.18297i	−0.636169	+	0.170461i
$165$	−4.10636	+	7.11243i	−0.319680	+	0.553702i
$166$	−12.3922	−	21.4640i	−0.961825	−	1.66593i
$167$	−3.50837	−	3.50837i	−0.271486	−	0.271486i	0.558212	−	0.829698i	$-0.311487\pi$
$167$	−3.50837	−	3.50837i	−0.271486	−	0.271486i	−0.829698	+	0.558212i	$0.811487\pi$
$168$	1.81228	+	3.60138i	0.139821	+	0.277853i
$169$	−8.07385	+	10.1889i	−0.621065	+	0.783759i
$170$	10.2175	+	17.6973i	0.783648	+	1.35732i
$171$	−0.781978	−	2.91838i	−0.0597993	−	0.223174i
$172$	−2.86069	+	4.95486i	−0.218125	+	0.377804i
$173$	−2.04064	−	3.53449i	−0.155147	−	0.268722i	0.777966	−	0.628307i	$-0.216252\pi$
$173$	−2.04064	−	3.53449i	−0.155147	−	0.268722i	−0.933112	+	0.359585i	$0.882918\pi$
$174$	−2.40328	+	2.40328i	−0.182192	+	0.182192i
$175$	0.114009	−	0.344982i	0.00861826	−	0.0260782i
$176$	12.7605	−	12.7605i	0.961855	−	0.961855i
$177$	−1.22637	−	0.328604i	−0.0921792	−	0.0246994i
$178$	−27.9451	−	16.1341i	−2.09458	−	1.20930i
$179$	−6.64974	−	3.83923i	−0.497025	−	0.286958i	0.230459	−	0.973082i	$-0.425977\pi$
$179$	−6.64974	−	3.83923i	−0.497025	−	0.286958i	−0.727484	+	0.686124i	$0.759311\pi$
$180$	0.668797	−	2.49598i	0.0498492	−	0.186040i
$181$	17.2079			1.27905			0.639525	−	0.768770i	$-0.279131\pi$
$181$	17.2079			1.27905			0.639525	+	0.768770i	$0.279131\pi$
$182$	6.47309	+	15.6155i	0.479817	+	1.15750i
$183$	9.37384			0.692934
$184$	1.15733	−	4.31923i	0.0853198	−	0.318418i
$185$	−10.8991	−	6.29258i	−0.801316	−	0.462640i
$186$	4.19948	+	2.42457i	0.307921	+	0.177778i
$187$	17.8074	+	4.77147i	1.30220	+	0.348924i
$188$	4.83455	−	4.83455i	0.352596	−	0.352596i
$189$	2.59066	−	0.537086i	0.188443	−	0.0390673i
$190$	8.58067	−	8.58067i	0.622507	−	0.622507i
$191$	13.5621	+	23.4903i	0.981320	+	1.69970i	0.657269	+	0.753656i	$0.271712\pi$
$191$	13.5621	+	23.4903i	0.981320	+	1.69970i	0.324051	+	0.946040i	$0.394955\pi$
$192$	−0.138723	+	0.240275i	−0.0100115	+	0.0173404i
$193$	−6.29609	−	23.4973i	−0.453202	−	1.69137i	−0.693320	−	0.720630i	$-0.743853\pi$
$193$	−6.29609	−	23.4973i	−0.453202	−	1.69137i	0.240117	−	0.970744i	$-0.422814\pi$
$194$	−12.6435	−	21.8992i	−0.907752	−	1.57227i
$195$	−2.68717	+	7.71780i	−0.192432	+	0.552683i
$196$	7.92796	+	0.913814i	0.566283	+	0.0652725i
$197$	2.73114	+	2.73114i	0.194586	+	0.194586i	0.797674	−	0.603088i	$-0.206063\pi$
$197$	2.73114	+	2.73114i	0.194586	+	0.194586i	−0.603088	+	0.797674i	$0.706063\pi$
$198$	−3.21039	−	5.56056i	−0.228152	−	0.395172i
$199$	−9.15034	+	15.8489i	−0.648650	+	1.12350i	0.334795	+	0.942291i	$0.391333\pi$
$199$	−9.15034	+	15.8489i	−0.648650	+	1.12350i	−0.983445	+	0.181205i	$0.942000\pi$
$200$	−0.202132	+	0.0541610i	−0.0142929	+	0.00382976i
$201$	7.63042	+	2.04457i	0.538209	+	0.144213i
$202$	−6.03772	−	6.03772i	−0.424813	−	0.424813i
$203$	−1.03014	−	4.96892i	−0.0723014	−	0.348750i
$204$	−5.80052			−0.406117
$205$	14.5218	−	8.38418i	1.01425	−	0.585576i
$206$	20.9988	−	5.62661i	1.46306	−	0.392025i
$207$	−2.54131	−	1.46723i	−0.176633	−	0.101979i
$208$	10.0926	−	14.8524i	0.699793	−	1.02983i
$209$		−	10.9475i		−	0.757257i
$210$	7.07073	+	7.93256i	0.487927	+	0.547398i
$211$	−6.52728			−0.449357			−0.224678	−	0.974433i	$-0.572133\pi$
$211$	−6.52728			−0.449357			−0.224678	+	0.974433i	$0.572133\pi$
$212$	−11.3337	+	6.54352i	−0.778403	+	0.449411i
$213$	0.676108	+	2.52327i	0.0463261	+	0.172892i
$214$	21.4437	−	5.74581i	1.46586	−	0.392775i
$215$	2.94399	−	10.9871i	0.200778	−	0.749315i
$216$	−1.07751	−	1.07751i	−0.0733151	−	0.0733151i
$217$	−6.46739	+	3.25452i	−0.439035	+	0.220931i
$218$			28.0871i			1.90230i
$219$	9.26691	+	2.48306i	0.626200	+	0.167790i
$220$	4.68151	−	8.10862i	0.315628	−	0.546683i
$221$	18.2954	+	1.34257i	1.23068	+	0.0903109i
$222$	8.52099	−	4.91960i	0.571892	−	0.330182i
$223$	−4.71162	+	4.71162i	−0.315513	+	0.315513i	−0.847041	−	0.531528i	$-0.821618\pi$
$223$	−4.71162	+	4.71162i	−0.315513	+	0.315513i	0.531528	+	0.847041i	$0.321618\pi$
$224$	−6.87141	−	13.6549i	−0.459115	−	0.912356i
$225$			0.137327i			0.00915511i
$226$	5.99225	−	22.3634i	0.398598	−	1.48759i
$227$	−1.41619	−	5.28529i	−0.0939959	−	0.350797i	0.902869	−	0.429915i	$-0.141456\pi$
$227$	−1.41619	−	5.28529i	−0.0939959	−	0.350797i	−0.996865	+	0.0791175i	$0.974790\pi$
$228$	0.891505	+	3.32714i	0.0590413	+	0.220345i
$229$	−2.86879	+	10.7065i	−0.189575	+	0.707504i	0.804029	+	0.594589i	$0.202685\pi$
$229$	−2.86879	+	10.7065i	−0.189575	+	0.707504i	−0.993605	+	0.112915i	$0.963981\pi$
$230$		−	11.7860i		−	0.777143i
$231$	9.57089	+	0.549773i	0.629718	+	0.0361724i
$232$	−2.06667	+	2.06667i	−0.135683	+	0.135683i
$233$	−12.5512	+	7.24643i	−0.822255	+	0.474729i	−0.851194	−	0.524852i	$-0.824121\pi$
$233$	−12.5512	+	7.24643i	−0.822255	+	0.474729i	0.0289382	+	0.999581i	$0.490787\pi$
$234$	−4.17504	−	4.83631i	−0.272931	−	0.316160i
$235$	−6.79642	+	11.7717i	−0.443349	+	0.767904i
$236$	1.39813	+	0.374629i	0.0910108	+	0.0243863i
$237$			0.124214i			0.00806856i
$238$	13.0919	−	19.9399i	0.848622	−	1.29251i
$239$	−11.7791	−	11.7791i	−0.761929	−	0.761929i	0.214742	−	0.976671i	$-0.431109\pi$
$239$	−11.7791	−	11.7791i	−0.761929	−	0.761929i	−0.976671	+	0.214742i	$0.931109\pi$
$240$	2.92165	−	10.9037i	0.188591	−	0.703833i
$241$	4.97562	−	1.33321i	0.320508	−	0.0858798i	−0.0949782	−	0.995479i	$-0.530278\pi$
$241$	4.97562	−	1.33321i	0.320508	−	0.0858798i	0.415486	+	0.909600i	$0.363611\pi$
$242$	−0.976504	−	3.64436i	−0.0627721	−	0.234268i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−10.6868			−0.684151
$245$	−15.6948	+	2.32455i	−1.00270	+	0.148510i
$246$			13.1096i			0.835841i
$247$	−2.04181	−	10.7005i	−0.129917	−	0.680856i
$248$	3.61128	+	2.08498i	0.229317	+	0.132396i
$249$	−13.5100	+	3.61999i	−0.856160	+	0.229407i
$250$	16.9139	−	9.76524i	1.06973	−	0.617608i
$251$	3.92580			0.247794			0.123897	−	0.992295i	$-0.460461\pi$
$251$	3.92580			0.247794			0.123897	+	0.992295i	$0.460461\pi$
$252$	−2.95352	+	0.612313i	−0.186054	+	0.0385721i
$253$	−7.51849	−	7.51849i	−0.472683	−	0.472683i
$254$	37.6601	+	10.0910i	2.36301	+	0.633166i
$255$	11.1391	−	2.98471i	0.697557	−	0.186910i
$256$	−10.0801	+	17.4592i	−0.630004	+	1.09120i
$257$	12.1796	+	21.0957i	0.759743	+	1.31591i	0.942981	+	0.332845i	$0.108009\pi$
$257$	12.1796	+	21.0957i	0.759743	+	1.31591i	−0.183238	+	0.983069i	$0.558658\pi$
$258$	6.28819	+	6.28819i	0.391486	+	0.391486i
$259$	−0.842472	+	14.6664i	−0.0523487	+	0.911327i
$260$	3.06354	−	8.79878i	0.189993	−	0.545677i
$261$	0.959004	+	1.66104i	0.0593609	+	0.102816i
$262$	1.57276	+	5.86962i	0.0971654	+	0.362626i
$263$	−8.06588	+	13.9705i	−0.497364	+	0.861459i	−0.999995	−	0.00304139i	$-0.999032\pi$
$263$	−8.06588	+	13.9705i	−0.497364	+	0.861459i	0.502632	+	0.864501i	$0.332365\pi$
$264$	−2.76073	−	4.78172i	−0.169911	−	0.294295i
$265$	18.3978	−	18.3978i	1.13017	−	1.13017i
$266$	−13.4496	−	4.44479i	−0.824646	−	0.272527i
$267$	−12.8763	+	12.8763i	−0.788017	+	0.788017i
$268$	−8.69917	−	2.33094i	−0.531386	−	0.142385i
$269$	6.44551	+	3.72132i	0.392990	+	0.226893i	0.683455	−	0.729993i	$-0.260477\pi$
$269$	6.44551	+	3.72132i	0.392990	+	0.226893i	−0.290465	+	0.956886i	$0.593810\pi$
$270$	−3.47831	−	2.00820i	−0.211683	−	0.122215i
$271$	−4.07517	+	15.2088i	−0.247549	+	0.923866i	0.724536	+	0.689237i	$0.242054\pi$
$271$	−4.07517	+	15.2088i	−0.247549	+	0.923866i	−0.972085	+	0.234629i	$0.924613\pi$
$272$	−25.3396			−1.53644
$273$	9.45745	−	1.24769i	0.572391	−	0.0755134i
$274$	−0.548789			−0.0331536
$275$	−0.128786	+	0.480637i	−0.00776610	+	0.0289835i
$276$	2.89726	+	1.67273i	0.174394	+	0.100687i
$277$	23.0773	+	13.3237i	1.38658	+	0.800544i	0.992928	−	0.118714i	$-0.0378772\pi$
$277$	23.0773	+	13.3237i	1.38658	+	0.800544i	0.393655	+	0.919258i	$0.371211\pi$
$278$	−22.9734	−	6.15569i	−1.37785	−	0.369194i
$279$	1.93500	−	1.93500i	0.115845	−	0.115845i
$280$	6.08038	+	6.82149i	0.363372	+	0.407662i
$281$	−2.85279	+	2.85279i	−0.170183	+	0.170183i	−0.787060	−	0.616877i	$-0.788398\pi$
$281$	−2.85279	+	2.85279i	−0.170183	+	0.170183i	0.616877	+	0.787060i	$0.288398\pi$
$282$	−5.31350	−	9.20325i	−0.316414	−	0.548046i
$283$	3.55154	−	6.15144i	0.211117	−	0.365665i	−0.740947	−	0.671563i	$-0.765623\pi$
$283$	3.55154	−	6.15144i	0.211117	−	0.365665i	0.952064	+	0.305898i	$0.0989566\pi$
$284$	−0.770806	−	2.87669i	−0.0457389	−	0.170700i
$285$	−3.42402	−	5.93058i	−0.202822	−	0.351297i
$286$	−10.0769	−	20.8423i	−0.595859	−	1.23243i
$287$	−16.3621	−	10.7428i	−0.965824	−	0.634128i
$288$	4.08545	+	4.08545i	0.240737	+	0.240737i
$289$	−4.44330	−	7.69602i	−0.261371	−	0.452707i
$290$	−3.85175	+	6.67143i	−0.226183	+	0.391760i
$291$	−13.7839	+	3.69339i	−0.808028	+	0.216510i
$292$	−10.5649	−	2.83085i	−0.618262	−	0.165663i
$293$	10.9108	+	10.9108i	0.637415	+	0.637415i	0.949917	−	0.312502i	$-0.101167\pi$
$293$	10.9108	+	10.9108i	0.637415	+	0.637415i	−0.312502	+	0.949917i	$0.601167\pi$
$294$	4.56128	−	11.5351i	0.266019	−	0.672739i
$295$	−2.87769			−0.167546
$296$	7.32751	−	4.23054i	0.425903	−	0.245895i
$297$	−3.49995	+	0.937810i	−0.203088	+	0.0544172i
$298$	−20.5213	−	11.8480i	−1.18877	−	0.686335i
$299$	−8.75109	−	5.94656i	−0.506089	−	0.343899i
$300$		−	0.156561i		−	0.00903906i
$301$	−13.0012	+	2.69535i	−0.749375	+	0.155357i
$302$	−15.3784			−0.884926
$303$	−4.17301	+	2.40929i	−0.239733	+	0.138410i
$304$	3.89455	+	14.5347i	0.223368	+	0.833619i
$305$	20.5225	−	5.49898i	1.17511	−	0.314871i
$306$	−2.33347	+	8.70864i	−0.133396	+	0.497840i
$307$	−14.8240	−	14.8240i	−0.846052	−	0.846052i	0.143586	−	0.989638i	$-0.454137\pi$
$307$	−14.8240	−	14.8240i	−0.846052	−	0.846052i	−0.989638	+	0.143586i	$0.954137\pi$
$308$	−10.9114	−	0.626777i	−0.621736	−	0.0357139i
$309$		−	12.2682i		−	0.697915i
$310$	10.6164	+	2.84466i	0.602971	+	0.161566i
$311$	8.51144	−	14.7422i	0.482639	−	0.835956i	−0.517162	−	0.855887i	$-0.673012\pi$
$311$	8.51144	−	14.7422i	0.482639	−	0.835956i	0.999801	+	0.0199318i	$0.00634490\pi$
$312$	−3.59026	−	4.15892i	−0.203259	−	0.235452i
$313$	−5.68454	+	3.28197i	−0.321309	+	0.185508i	−0.651976	−	0.758240i	$-0.726060\pi$
$313$	−5.68454	+	3.28197i	−0.321309	+	0.185508i	0.330667	+	0.943748i	$0.392726\pi$
$314$	10.2401	−	10.2401i	0.577884	−	0.577884i
$315$	5.35676	−	2.69562i	0.301819	−	0.151881i
$316$		−	0.141612i		−	0.00796628i
$317$	2.94213	−	10.9802i	0.165246	−	0.616708i	−0.832762	−	0.553631i	$-0.813242\pi$
$317$	2.94213	−	10.9802i	0.165246	−	0.616708i	0.998009	−	0.0630769i	$-0.0200914\pi$
$318$	5.26475	+	19.6483i	0.295233	+	1.10182i
$319$	1.79873	+	6.71294i	0.100709	+	0.375853i
$320$	−0.162758	+	0.607422i	−0.00909846	+	0.0339559i
$321$		−	12.5281i		−	0.699251i
$322$	−12.2894	+	6.18425i	−0.684861	+	0.344635i
$323$	−10.8698	+	10.8698i	−0.604811	+	0.604811i
$324$	0.987324	−	0.570032i	0.0548514	−	0.0316684i
$325$	−0.0362371	+	0.493810i	−0.00201007	+	0.0273917i
$326$	16.5221	−	28.6172i	0.915077	−	1.58496i
$327$	15.3102	+	4.10237i	0.846658	+	0.226861i
$328$			11.2735i			0.622473i
$329$	15.8407	+	0.909927i	0.873328	+	0.0501659i
$330$	−10.2906	−	10.2906i	−0.566480	−	0.566480i
$331$	−2.45215	+	9.15154i	−0.134782	+	0.503014i	0.865216	+	0.501398i	$0.167181\pi$
$331$	−2.45215	+	9.15154i	−0.134782	+	0.503014i	−0.999999	+	0.00161559i	$0.999486\pi$
$332$	15.4022	−	4.12702i	0.845307	−	0.226499i
$333$	−1.43710	−	5.36332i	−0.0787525	−	0.293908i
$334$	7.61413	−	4.39602i	0.416626	−	0.240539i
$335$	17.9050			0.978253
$336$	−12.9025	+	2.67489i	−0.703889	+	0.145927i
$337$		−	1.43236i		−	0.0780257i	−0.999239	−	0.0390128i	$-0.987579\pi$
$337$		−	1.43236i		−	0.0780257i	0.999239	−	0.0390128i	$-0.0124213\pi$
$338$	−13.7368	−	18.4925i	−0.747181	−	1.00586i
$339$	−11.3150	−	6.53272i	−0.614547	−	0.354809i
$340$	−12.6993	+	3.40276i	−0.688715	+	0.184541i
$341$	8.58706	−	4.95774i	0.465016	−	0.268477i
$342$	5.35386			0.289504
$343$	10.6591	+	15.1454i	0.575537	+	0.817776i
$344$	5.40744	+	5.40744i	0.291550	+	0.291550i
$345$	−6.42450	−	1.72144i	−0.345884	−	0.0926792i
$346$	6.98568	−	1.87181i	0.375553	−	0.100629i
$347$	−10.2318	+	17.7220i	−0.549272	+	0.951367i	0.449053	+	0.893505i	$0.351761\pi$
$347$	−10.2318	+	17.7220i	−0.549272	+	0.951367i	−0.998325	+	0.0578614i	$0.981572\pi$
$348$	−1.09333	−	1.89370i	−0.0586084	−	0.101513i
$349$	−10.1977	−	10.1977i	−0.545871	−	0.545871i	0.379373	−	0.925244i	$-0.376140\pi$
$349$	−10.1977	−	10.1977i	−0.545871	−	0.545871i	−0.925244	+	0.379373i	$0.876140\pi$
$350$	0.538197	+	0.353362i	0.0287678	+	0.0188880i
$351$	−3.24606	+	1.56942i	−0.173262	+	0.0837694i
$352$	10.4675	+	18.1303i	0.557920	+	0.966346i
$353$	3.02548	+	11.2913i	0.161030	+	0.600973i	0.998513	+	0.0545096i	$0.0173596\pi$
$353$	3.02548	+	11.2913i	0.161030	+	0.600973i	−0.837483	+	0.546463i	$0.815974\pi$
$354$	1.12490	−	1.94839i	0.0597879	−	0.103556i
$355$	2.96045	+	5.12766i	0.157125	+	0.272148i
$356$	14.6798	−	14.6798i	0.778028	−	0.778028i
$357$	−8.95703	−	10.0488i	−0.474056	−	0.531837i
$358$	9.62118	−	9.62118i	0.508495	−	0.508495i
$359$	−0.636918	−	0.170662i	−0.0336153	−	0.00900718i	0.241972	−	0.970283i	$-0.422206\pi$
$359$	−0.636918	−	0.170662i	−0.0336153	−	0.00900718i	−0.275587	+	0.961276i	$0.588872\pi$
$360$	−2.99113	−	1.72693i	−0.157646	−	0.0910170i
$361$	−8.54903	−	4.93578i	−0.449949	−	0.259778i
$362$	−7.89209	+	29.4537i	−0.414799	+	1.54805i
$363$	−2.12916			−0.111752
$364$	−10.7821	+	1.42244i	−0.565135	+	0.0745562i
$365$	21.7450			1.13819
$366$	−4.29915	+	16.0447i	−0.224720	+	0.838668i
$367$	23.2715	+	13.4358i	1.21476	+	0.701344i	0.963793	−	0.266651i	$-0.0859171\pi$
$367$	23.2715	+	13.4358i	1.21476	+	0.701344i	0.250970	+	0.967995i	$0.419250\pi$
$368$	12.6567	+	7.30735i	0.659776	+	0.380922i
$369$	7.14604	+	1.91478i	0.372008	+	0.0996793i
$370$	15.7693	−	15.7693i	0.819808	−	0.819808i
$371$	−28.8372	−	9.53007i	−1.49715	−	0.494776i
$372$	−2.20602	+	2.20602i	−0.114377	+	0.114377i
$373$	13.7930	+	23.8902i	0.714175	+	1.23699i	0.963277	+	0.268510i	$0.0865314\pi$
$373$	13.7930	+	23.8902i	0.714175	+	1.23699i	−0.249102	+	0.968477i	$0.580135\pi$
$374$	−16.3341	+	28.2915i	−0.844616	+	1.46292i
$375$	−2.85259	−	10.6460i	−0.147307	−	0.549758i
$376$	−4.56927	−	7.91421i	−0.235642	−	0.408144i
$377$	3.01016	+	6.22598i	0.155031	+	0.320654i
$378$	−0.268865	+	4.68062i	−0.0138289	+	0.240745i
$379$	−8.26226	−	8.26226i	−0.424404	−	0.424404i	0.462313	−	0.886717i	$-0.347020\pi$
$379$	−8.26226	−	8.26226i	−0.424404	−	0.424404i	−0.886717	+	0.462313i	$0.847020\pi$
$380$	3.90361	+	6.76124i	0.200251	+	0.346844i
$381$	11.0012	−	19.0546i	0.563607	−	0.976196i
$382$	−46.4270	+	12.4401i	−2.37541	+	0.636489i
$383$	−5.50484	−	1.47502i	−0.281284	−	0.0753698i	0.115419	−	0.993317i	$-0.463179\pi$
$383$	−5.50484	−	1.47502i	−0.281284	−	0.0753698i	−0.396703	+	0.917947i	$0.629846\pi$
$384$	7.82326	+	7.82326i	0.399229	+	0.399229i
$385$	21.2764	−	4.41094i	1.08435	−	0.224802i
$386$	43.1066			2.19407
$387$	4.34612	−	2.50924i	0.220926	−	0.127552i
$388$	15.7145	−	4.21070i	0.797785	−	0.213766i
$389$	−19.0861	−	11.0193i	−0.967702	−	0.558703i	−0.0691669	−	0.997605i	$-0.522034\pi$
$389$	−19.0861	−	11.0193i	−0.967702	−	0.558703i	−0.898535	+	0.438902i	$0.855367\pi$
$390$	−11.9777	−	8.13911i	−0.606514	−	0.412140i
$391$			14.9302i			0.755051i
$392$	3.92241	−	9.91942i	0.198111	−	0.501007i
$393$	3.42923			0.172982
$394$	−5.92733	+	3.42215i	−0.298615	+	0.172405i
$395$	0.0728677	+	0.271946i	0.00366637	+	0.0136831i
$396$	3.99017	−	1.06916i	0.200514	−	0.0537275i
$397$	−4.36019	+	16.2724i	−0.218832	+	0.816691i	0.765951	+	0.642899i	$0.222269\pi$
$397$	−4.36019	+	16.2724i	−0.218832	+	0.816691i	−0.984782	+	0.173792i	$0.944398\pi$
$398$	−22.9309	−	22.9309i	−1.14942	−	1.14942i
$399$	−4.38727	+	6.68213i	−0.219638	+	0.334525i
$400$		−	0.683939i		−	0.0341970i
$401$	−18.9983	−	5.09058i	−0.948729	−	0.254211i	−0.248906	−	0.968528i	$-0.580071\pi$
$401$	−18.9983	−	5.09058i	−0.948729	−	0.254211i	−0.699823	+	0.714316i	$0.746738\pi$
$402$	−6.99913	+	12.1229i	−0.349085	+	0.604633i
$403$	7.46862	−	6.44743i	0.372039	−	0.321169i
$404$	4.75750	−	2.74674i	0.236695	−	0.136656i
$405$	−1.60271	+	1.60271i	−0.0796391	+	0.0796391i
$406$	8.97746	+	0.515686i	0.445544	+	0.0255930i
$407$		−	20.1191i		−	0.997267i
$408$	−2.00664	+	7.48888i	−0.0993434	+	0.370755i
$409$	3.88917	+	14.5146i	0.192307	+	0.717701i	0.992947	+	0.118555i	$0.0378262\pi$
$409$	3.88917	+	14.5146i	0.192307	+	0.717701i	−0.800640	+	0.599145i	$0.795507\pi$
$410$	7.69052	+	28.7014i	0.379808	+	1.41746i
$411$	−0.0801554	+	0.299144i	−0.00395377	+	0.0147557i
$412$			13.9866i			0.689068i
$413$	1.50996	+	3.00061i	0.0743005	+	0.147650i
$414$	3.67690	−	3.67690i	0.180710	−	0.180710i
$415$	−27.4543	+	15.8507i	−1.34768	+	0.778082i
$416$	13.6127	+	15.7688i	0.667420	+	0.773131i
$417$	−6.71091	+	11.6236i	−0.328635	+	0.569212i
$418$	18.7383	+	5.02091i	0.916519	+	0.245581i
$419$			10.7242i			0.523913i	0.965080	+	0.261957i	$0.0843677\pi$
$419$			10.7242i			0.523913i	−0.965080	+	0.261957i	$0.915632\pi$
$420$	−6.10705	+	3.07318i	−0.297994	+	0.149956i
$421$	22.8079	+	22.8079i	1.11159	+	1.11159i	0.992936	+	0.118655i	$0.0378581\pi$
$421$	22.8079	+	22.8079i	1.11159	+	1.11159i	0.118655	+	0.992936i	$0.462142\pi$
$422$	2.99363	−	11.1724i	0.145728	−	0.543862i
$423$	−5.79276	+	1.55216i	−0.281653	+	0.0754688i
$424$	4.52735	+	16.8963i	0.219867	+	0.820557i
$425$	0.605094	−	0.349351i	0.0293514	−	0.0169460i
$426$	−4.62902			−0.224277
$427$	−16.5023	−	18.5137i	−0.798602	−	0.895940i
$428$			14.2829i			0.690388i
$429$	−12.8329	+	2.44870i	−0.619578	+	0.118224i
$430$	17.4558	+	10.0781i	0.841794	+	0.486010i
$431$	−32.2071	+	8.62988i	−1.55136	+	0.415687i	−0.929917	−	0.367770i	$-0.880121\pi$
$431$	−32.2071	+	8.62988i	−1.55136	+	0.415687i	−0.621446	+	0.783457i	$0.713455\pi$
$432$	4.31314	−	2.49019i	0.207516	−	0.119809i
$433$	−21.1555			−1.01667			−0.508333	−	0.861161i	$-0.669738\pi$
$433$	−21.1555			−1.01667			−0.508333	+	0.861161i	$0.669738\pi$
$434$	−2.60441	−	12.5625i	−0.125015	−	0.603019i
$435$	3.07400	+	3.07400i	0.147387	+	0.147387i
$436$	−17.4547	−	4.67696i	−0.835926	−	0.223986i
$437$	8.56385	−	2.29468i	0.409664	−	0.109769i
$438$	−8.50023	+	14.7228i	−0.406157	+	0.703484i
$439$	15.5445	+	26.9239i	0.741898	+	1.28501i	0.951630	+	0.307246i	$0.0994076\pi$
$439$	15.5445	+	26.9239i	0.741898	+	1.28501i	−0.209732	+	0.977759i	$0.567259\pi$
$440$	−8.84927	−	8.84927i	−0.421872	−	0.421872i
$441$	−5.62153	−	4.17114i	−0.267692	−	0.198626i
$442$	−10.6889	+	30.6995i	−0.508419	+	1.46023i
$443$	−1.54381	−	2.67396i	−0.0733486	−	0.127044i	0.827018	−	0.562175i	$-0.190035\pi$
$443$	−1.54381	−	2.67396i	−0.0733486	−	0.127044i	−0.900367	+	0.435131i	$0.856702\pi$
$444$	1.63838	+	6.11453i	0.0777543	+	0.290183i
$445$	−20.6369	+	35.7442i	−0.978283	+	1.69444i
$446$	−5.90370	−	10.2255i	−0.279548	−	0.484192i
$447$	−9.45562	+	9.45562i	−0.447236	+	0.447236i
$448$	0.718769	−	0.149012i	0.0339586	−	0.00704017i
$449$	25.4341	−	25.4341i	1.20031	−	1.20031i	0.226236	−	0.974073i	$-0.427358\pi$
$449$	25.4341	−	25.4341i	1.20031	−	1.20031i	0.974073	−	0.226236i	$-0.0726420\pi$
$450$	−0.235054	−	0.0629826i	−0.0110806	−	0.00296903i
$451$	23.2151	+	13.4033i	1.09316	+	0.631135i
$452$	12.8998	+	7.44772i	0.606757	+	0.350311i
$453$	−2.24614	+	8.38272i	−0.105533	+	0.393854i
$454$	9.69605			0.455058
$455$	19.9736	−	8.27963i	0.936376	−	0.388155i
$456$	4.60398			0.215601
$457$	4.93087	−	18.4023i	0.230657	−	0.860822i	−0.749402	−	0.662115i	$-0.769659\pi$
$457$	4.93087	−	18.4023i	0.230657	−	0.860822i	0.980059	−	0.198707i	$-0.0636742\pi$
$458$	−17.0099	−	9.82070i	−0.794823	−	0.458891i
$459$	4.40624	+	2.54394i	0.205666	+	0.118741i
$460$	7.32434	+	1.96255i	0.341499	+	0.0915044i
$461$	28.2657	−	28.2657i	1.31647	−	1.31647i	0.399911	−	0.916554i	$-0.369041\pi$
$461$	28.2657	−	28.2657i	1.31647	−	1.31647i	0.916554	−	0.399911i	$-0.130959\pi$
$462$	−5.33054	+	16.1298i	−0.247999	+	0.750426i
$463$	4.16596	−	4.16596i	0.193608	−	0.193608i	−0.603645	−	0.797253i	$-0.706286\pi$
$463$	4.16596	−	4.16596i	0.193608	−	0.193608i	0.797253	+	0.603645i	$0.206286\pi$
$464$	−4.77621	−	8.27264i	−0.221730	−	0.384047i
$465$	3.10123	−	5.37149i	0.143816	−	0.249097i
$466$	−6.64691	−	24.8066i	−0.307912	−	1.14914i
$467$	11.5744	+	20.0474i	0.535598	+	0.927683i	0.999134	+	0.0416048i	$0.0132470\pi$
$467$	11.5744	+	20.0474i	0.535598	+	0.927683i	−0.463536	+	0.886078i	$0.653420\pi$
$468$	3.70072	−	1.78924i	0.171066	−	0.0827075i
$469$	−9.39498	−	18.6698i	−0.433820	−	0.862089i
$470$	−17.0319	−	17.0319i	−0.785625	−	0.785625i
$471$	−4.08622	−	7.07753i	−0.188283	−	0.326116i
$472$	0.967345	−	1.67549i	0.0445257	−	0.0771207i
$473$	17.5644	−	4.70637i	0.807613	−	0.216399i
$474$	−0.212610	−	0.0569686i	−0.00976549	−	0.00261665i
$475$	−0.293385	−	0.293385i	−0.0134614	−	0.0134614i
$476$	10.2116	+	11.4562i	0.468048	+	0.525096i
$477$	11.4792			0.525597
$478$	25.5640	−	14.7594i	1.16927	−	0.675078i
$479$	22.5158	−	6.03309i	1.02877	−	0.275659i	0.295319	−	0.955399i	$-0.404574\pi$
$479$	22.5158	−	6.03309i	1.02877	−	0.275659i	0.733453	+	0.679740i	$0.237907\pi$
$480$	11.3411	+	6.54777i	0.517647	+	0.298863i
$481$	−3.75239	−	19.6651i	−0.171094	−	0.896651i
$482$			9.12794i			0.415766i
$483$	1.57605	+	7.60218i	0.0717129	+	0.345911i
$484$	2.42738			0.110335
$485$	−28.0110	+	16.1721i	−1.27191	+	0.734339i
$486$	−0.458633	−	1.71164i	−0.0208040	−	0.0776417i
$487$	27.4535	−	7.35613i	1.24403	−	0.333338i	0.424006	−	0.905660i	$-0.360624\pi$
$487$	27.4535	−	7.35613i	1.24403	−	0.333338i	0.820029	+	0.572321i	$0.193957\pi$
$488$	−3.69700	+	13.7974i	−0.167355	+	0.624578i
$489$	−13.1860	−	13.1860i	−0.596290	−	0.596290i
$490$	3.21934	−	27.9299i	0.145435	−	1.26175i
$491$		−	27.8408i		−	1.25644i	−0.778036	−	0.628220i	$-0.783784\pi$
$491$		−	27.8408i		−	1.25644i	0.778036	−	0.628220i	$-0.216216\pi$
$492$	−8.14694	−	2.18297i	−0.367293	−	0.0984158i
$493$	4.87931	−	8.45121i	0.219753	−	0.380623i
$494$	19.2519	+	1.41275i	0.866182	+	0.0635627i
$495$	−7.11243	+	4.10636i	−0.319680	+	0.184567i
$496$	−9.63703	+	9.63703i	−0.432715	+	0.432715i
$497$	3.79329	−	5.77746i	0.170152	−	0.259154i
$498$		−	24.7845i		−	1.11062i
$499$	0.886008	−	3.30663i	0.0396632	−	0.148025i	−0.943255	−	0.332071i	$-0.892253\pi$
$499$	0.886008	−	3.30663i	0.0396632	−	0.148025i	0.982918	+	0.184046i	$0.0589194\pi$
$500$	3.25214	+	12.1371i	0.145440	+	0.542790i
$501$	−1.28415	−	4.79252i	−0.0573717	−	0.214114i
$502$	−1.80050	+	6.71957i	−0.0803604	+	0.299909i
$503$			13.4085i			0.597854i	0.954276	+	0.298927i	$0.0966287\pi$
$503$			13.4085i			0.597854i	−0.954276	+	0.298927i	$0.903371\pi$
$504$	−0.231207	+	4.02503i	−0.0102988	+	0.179289i
$505$	−7.72276	+	7.72276i	−0.343658	+	0.343658i
$506$	16.3172	−	9.42074i	0.725388	−	0.418803i
$507$	−12.0866	+	4.78689i	−0.536784	+	0.212593i
$508$	−12.5420	+	21.7234i	−0.556463	+	0.963822i
$509$	−36.3876	−	9.75003i	−1.61285	−	0.432163i	−0.663962	−	0.747767i	$-0.731126\pi$
$509$	−36.3876	−	9.75003i	−1.61285	−	0.432163i	−0.948891	+	0.315604i	$0.897793\pi$
$510$			20.4350i			0.904879i
$511$	−11.4099	−	22.6738i	−0.504745	−	1.00303i
$512$	−9.61430	−	9.61430i	−0.424896	−	0.424896i
$513$	0.781978	−	2.91838i	0.0345252	−	0.128850i
$514$	−41.6943	+	11.1719i	−1.83906	+	0.492773i
$515$	−7.19692	−	26.8593i	−0.317134	−	1.18356i
$516$	−4.95486	+	2.86069i	−0.218125	+	0.125935i
$517$	−21.7300			−0.955685
$518$	−24.7173	−	8.16852i	−1.08601	−	0.358904i
$519$		−	4.08127i		−	0.179148i
$520$	−10.3000	−	6.99911i	−0.451687	−	0.306931i
$521$	18.9751	+	10.9553i	0.831312	+	0.479958i	0.854302	−	0.519777i	$-0.173985\pi$
$521$	18.9751	+	10.9553i	0.831312	+	0.479958i	−0.0229895	+	0.999736i	$0.507318\pi$
$522$	−3.28295	+	0.879663i	−0.143691	+	0.0385018i
$523$	17.4140	−	10.0540i	0.761460	−	0.439629i	−0.0683599	−	0.997661i	$-0.521777\pi$
$523$	17.4140	−	10.0540i	0.761460	−	0.439629i	0.829820	+	0.558032i	$0.188443\pi$
$524$	−3.90954			−0.170789
$525$	0.271225	−	0.241758i	0.0118372	−	0.0105512i
$526$	−20.2133	−	20.2133i	−0.881340	−	0.881340i
$527$	−13.4486	−	3.60354i	−0.585830	−	0.156973i
$528$	17.4311	−	4.67065i	0.758591	−	0.203264i
$529$	−7.19449	+	12.4612i	−0.312804	+	0.541793i
$530$	23.0526	+	39.9283i	1.00134	+	1.73437i
$531$	−0.897762	−	0.897762i	−0.0389595	−	0.0389595i
$532$	5.00177	−	7.61806i	0.216854	−	0.330285i
$533$	25.1911	+	8.77097i	1.09115	+	0.379913i
$534$	−16.1341	−	27.9451i	−0.698192	−	1.20930i
$535$	−7.34938	−	27.4283i	−0.317741	−	1.18583i
$536$	−6.01880	+	10.4249i	−0.259973	+	0.450286i
$537$	−3.83923	−	6.64974i	−0.165675	−	0.286958i
$538$	−9.32569	+	9.32569i	−0.402059	+	0.402059i
$539$	−15.7634	−	19.8707i	−0.678976	−	0.855892i
$540$	1.82719	−	1.82719i	0.0786296	−	0.0786296i
$541$	−17.0494	−	4.56838i	−0.733013	−	0.196410i	−0.127042	−	0.991897i	$-0.540548\pi$
$541$	−17.0494	−	4.56838i	−0.733013	−	0.196410i	−0.605970	+	0.795487i	$0.707215\pi$
$542$	−24.1629	−	13.9505i	−1.03789	−	0.599224i
$543$	14.9024	+	8.60393i	0.639525	+	0.369230i
$544$	7.60832	−	28.3946i	0.326204	−	1.21741i
$545$	35.9258			1.53889
$546$	−2.20191	+	16.7600i	−0.0942329	+	0.717262i
$547$	−43.6870			−1.86792			−0.933960	−	0.357378i	$-0.883671\pi$
$547$	−43.6870			−1.86792			−0.933960	+	0.357378i	$0.883671\pi$
$548$	0.0913823	−	0.341043i	0.00390366	−	0.0145686i
$549$	8.11798	+	4.68692i	0.346467	+	0.200033i
$550$	−0.763613	−	0.440872i	−0.0325606	−	0.0187988i
$551$	−5.59748	−	1.49984i	−0.238461	−	0.0638953i
$552$	3.16190	−	3.16190i	0.134579	−	0.134579i
$553$	0.245327	−	0.218674i	0.0104324	−	0.00929895i
$554$	−33.3895	+	33.3895i	−1.41858	+	1.41858i
$555$	−6.29258	−	10.8991i	−0.267105	−	0.462640i
$556$	7.65087	−	13.2517i	0.324469	−	0.561997i
$557$	−1.27518	−	4.75904i	−0.0540311	−	0.201647i	0.933634	−	0.358229i	$-0.116619\pi$
$557$	−1.27518	−	4.75904i	−0.0540311	−	0.201647i	−0.987665	+	0.156582i	$0.949953\pi$
$558$	2.42457	+	4.19948i	0.102640	+	0.177778i
$559$	16.2903	−	7.87608i	0.689005	−	0.333123i
$560$	−26.6787	+	13.4252i	−1.12738	+	0.567320i
$561$	13.0359	+	13.0359i	0.550376	+	0.550376i
$562$	−3.57457	−	6.19134i	−0.150784	−	0.261166i
$563$	4.07456	−	7.05734i	0.171722	−	0.297431i	−0.767300	−	0.641288i	$-0.778400\pi$
$563$	4.07456	−	7.05734i	0.171722	−	0.297431i	0.939022	+	0.343857i	$0.111734\pi$
$564$	6.60411	−	1.76957i	0.278083	−	0.0745122i
$565$	−28.6046	−	7.66459i	−1.20341	−	0.322452i
$566$	8.90022	+	8.90022i	0.374104	+	0.374104i
$567$	2.51212	+	0.830202i	0.105499	+	0.0348652i
$568$	−3.98066			−0.167025
$569$	9.83064	−	5.67572i	0.412122	−	0.237939i	−0.279579	−	0.960123i	$-0.590195\pi$
$569$	9.83064	−	5.67572i	0.412122	−	0.237939i	0.691701	+	0.722184i	$0.256862\pi$
$570$	11.7214	−	3.14074i	0.490956	−	0.131551i
$571$	6.99013	+	4.03575i	0.292528	+	0.168891i	0.639081	−	0.769139i	$-0.279315\pi$
$571$	6.99013	+	4.03575i	0.292528	+	0.168891i	−0.346553	+	0.938030i	$0.612648\pi$
$572$	14.6303	−	2.79168i	0.611724	−	0.116726i
$573$			27.1242i			1.13313i
$574$	25.8920	−	23.0790i	1.08071	−	0.963300i
$575$	−0.402979			−0.0168054
$576$	−0.240275	+	0.138723i	−0.0100115	+	0.00578012i
$577$	−8.07796	−	30.1474i	−0.336290	−	1.25505i	−0.902464	−	0.430765i	$-0.858244\pi$
$577$	−8.07796	−	30.1474i	−0.336290	−	1.25505i	0.566174	−	0.824286i	$-0.308423\pi$
$578$	15.2107	−	4.07569i	0.632681	−	0.169526i
$579$	6.29609	−	23.4973i	0.261656	−	0.976515i
$580$	−3.50456	−	3.50456i	−0.145519	−	0.145519i
$581$	30.9334	+	20.3099i	1.28333	+	0.842595i
$582$		−	25.2870i		−	1.04818i
$583$	40.1767	+	10.7653i	1.66395	+	0.445854i
$584$	−7.30965	+	12.6607i	−0.302476	+	0.523903i
$585$	−6.18605	+	5.34022i	−0.255762	+	0.220791i
$586$	−23.6794	+	13.6713i	−0.978188	+	0.564757i
$587$	9.12734	−	9.12734i	0.376726	−	0.376726i	−0.493194	−	0.869919i	$-0.664171\pi$
$587$	9.12734	−	9.12734i	0.376726	−	0.376726i	0.869919	+	0.493194i	$0.164171\pi$
$588$	6.40890	+	4.75536i	0.264299	+	0.196108i
$589$			8.26787i			0.340672i
$590$	1.31981	−	4.92558i	0.0543355	−	0.202783i
$591$	0.999668	+	3.73081i	0.0411208	+	0.153465i
$592$	7.15730	+	26.7114i	0.294163	+	1.09783i
$593$	−11.3771	+	42.4600i	−0.467202	+	1.74362i	0.182281	+	0.983247i	$0.441652\pi$
$593$	−11.3771	+	42.4600i	−0.467202	+	1.74362i	−0.649483	+	0.760376i	$0.725015\pi$
$594$		−	6.42078i		−	0.263448i
$595$	−25.5049	−	16.7457i	−1.04560	−	0.686505i
$596$	10.7800	−	10.7800i	0.441567	−	0.441567i
$597$	−15.8489	+	9.15034i	−0.648650	+	0.374499i
$598$	14.1919	−	12.2514i	0.580351	−	0.500999i
$599$	−10.0938	+	17.4829i	−0.412420	+	0.714332i	−0.995154	−	0.0983309i	$-0.968650\pi$
$599$	−10.0938	+	17.4829i	−0.412420	+	0.714332i	0.582734	+	0.812663i	$0.301983\pi$
$600$	−0.202132	−	0.0541610i	−0.00825198	−	0.00221111i
$601$		−	44.2929i		−	1.80674i	−0.428857	−	0.903372i	$-0.641084\pi$
$601$		−	44.2929i		−	1.80674i	0.428857	−	0.903372i	$-0.358916\pi$
$602$	1.34929	−	23.4895i	0.0549930	−	0.957362i
$603$	5.58586	+	5.58586i	0.227474	+	0.227474i
$604$	2.56075	−	9.55683i	0.104195	−	0.388862i
$605$	−4.66145	+	1.24903i	−0.189515	+	0.0507803i
$606$	−2.20996	−	8.24769i	−0.0897735	−	0.335039i
$607$	5.83160	−	3.36688i	0.236697	−	0.136657i	−0.376960	−	0.926229i	$-0.623031\pi$
$607$	5.83160	−	3.36688i	0.236697	−	0.136657i	0.613658	+	0.789572i	$0.289697\pi$
$608$	−17.4563			−0.707948
$609$	1.59233	−	4.81828i	0.0645246	−	0.195246i
$610$			37.6492i			1.52437i
$611$	−21.2396	+	4.05284i	−0.859264	+	0.163960i
$612$	−5.02340	−	2.90026i	−0.203059	−	0.117236i
$613$	21.6549	−	5.80243i	0.874635	−	0.234358i	0.206544	−	0.978437i	$-0.433778\pi$
$613$	21.6549	−	5.80243i	0.874635	−	0.234358i	0.668091	+	0.744080i	$0.267112\pi$
$614$	32.1722	−	18.5746i	1.29837	−	0.749612i
$615$	16.7684			0.676165
$616$	−4.58392	+	13.8706i	−0.184692	+	0.558862i
$617$	17.3687	+	17.3687i	0.699237	+	0.699237i	0.964246	−	0.265009i	$-0.0853749\pi$
$617$	17.3687	+	17.3687i	0.699237	+	0.699237i	−0.265009	+	0.964246i	$0.585375\pi$
$618$	20.9988	+	5.62661i	0.844696	+	0.226336i
$619$	22.5518	−	6.04273i	0.906432	−	0.242878i	0.224656	−	0.974438i	$-0.427874\pi$
$619$	22.5518	−	6.04273i	0.906432	−	0.242878i	0.681777	+	0.731560i	$0.261208\pi$
$620$	−3.53560	+	6.12384i	−0.141993	+	0.245939i
$621$	−1.46723	−	2.54131i	−0.0588778	−	0.101979i
$622$	21.3298	+	21.3298i	0.855248	+	0.855248i
$623$	48.0994	+	2.76294i	1.92706	+	0.110695i
$624$	16.1666	−	7.81630i	0.647183	−	0.312903i
$625$	−12.8339	−	22.2289i	−0.513355	−	0.889158i
$626$	−3.01044	−	11.2351i	−0.120321	−	0.449045i
$627$	5.47377	−	9.48085i	0.218601	−	0.378629i
$628$	4.65855	+	8.06884i	0.185896	+	0.321982i
$629$	−19.9762	+	19.9762i	−0.796503	+	0.796503i
$630$	2.15716	+	10.4052i	0.0859432	+	0.414552i
$631$	3.51142	−	3.51142i	0.139787	−	0.139787i	−0.633750	−	0.773538i	$-0.718485\pi$
$631$	3.51142	−	3.51142i	0.139787	−	0.139787i	0.773538	+	0.633750i	$0.218485\pi$
$632$	−0.182831	−	0.0489893i	−0.00727262	−	0.00194869i
$633$	−5.65279	−	3.26364i	−0.224678	−	0.129718i
$634$	17.4448	+	10.0717i	0.692820	+	0.400000i
$635$	12.9072	−	48.1705i	0.512208	−	1.91159i
$636$	−13.0870			−0.518935
$637$	−19.1137	−	16.4823i	−0.757312	−	0.653053i
$638$	−12.3151			−0.487560
$639$	−0.676108	+	2.52327i	−0.0267464	+	0.0998190i
$640$	21.7171	+	12.5384i	0.858444	+	0.495623i
$641$	−19.7900	−	11.4257i	−0.781657	−	0.451290i	0.0553601	−	0.998466i	$-0.482369\pi$
$641$	−19.7900	−	11.4257i	−0.781657	−	0.451290i	−0.837017	+	0.547177i	$0.815703\pi$
$642$	21.4437	+	5.74581i	0.846313	+	0.226769i
$643$	17.7070	−	17.7070i	0.698294	−	0.698294i	−0.265748	−	0.964042i	$-0.585619\pi$
$643$	17.7070	−	17.7070i	0.698294	−	0.698294i	0.964042	+	0.265748i	$0.0856190\pi$
$644$	−1.79680	−	8.66697i	−0.0708039	−	0.341527i
$645$	8.04313	−	8.04313i	0.316698	−	0.316698i
$646$	−13.6199	−	23.5904i	−0.535869	−	0.928152i
$647$	−1.63212	+	2.82692i	−0.0641653	+	0.111138i	−0.896323	−	0.443401i	$-0.853772\pi$
$647$	−1.63212	+	2.82692i	−0.0641653	+	0.111138i	0.832158	+	0.554538i	$0.187105\pi$
$648$	−0.394395	−	1.47190i	−0.0154933	−	0.0578218i
$649$	−2.30019	−	3.98405i	−0.0902905	−	0.156388i
$650$	−0.828607	−	0.288503i	−0.0325007	−	0.0113160i
$651$	−7.22818	−	0.415203i	−0.283295	−	0.0162731i
$652$	15.0329	+	15.0329i	0.588732	+	0.588732i
$653$	−23.4605	−	40.6348i	−0.918081	−	1.59016i	−0.802326	−	0.596886i	$-0.796405\pi$
$653$	−23.4605	−	40.6348i	−0.918081	−	1.59016i	−0.115755	−	0.993278i	$-0.536929\pi$
$654$	−14.0436	+	24.3242i	−0.549147	+	0.951151i
$655$	7.50774	−	2.01169i	0.293352	−	0.0786033i
$656$	−35.5900	−	9.53632i	−1.38956	−	0.372331i
$657$	6.78385	+	6.78385i	0.264663	+	0.264663i
$658$	−8.82255	+	26.6963i	−0.343939	+	1.04073i
$659$	28.5767			1.11319			0.556596	−	0.830784i	$-0.312107\pi$
$659$	28.5767			1.11319			0.556596	+	0.830784i	$0.312107\pi$
$660$	8.10862	−	4.68151i	0.315628	−	0.182228i
$661$	−6.29759	+	1.68743i	−0.244948	+	0.0656336i	−0.379204	−	0.925313i	$-0.623802\pi$
$661$	−6.29759	+	1.68743i	−0.244948	+	0.0656336i	0.134256	+	0.990947i	$0.457136\pi$
$662$	−14.5395	−	8.39440i	−0.565095	−	0.326258i
$663$	15.1730	+	10.3104i	0.589272	+	0.400424i
$664$		−	21.3131i		−	0.827108i
$665$	−5.68526	+	17.2031i	−0.220465	+	0.667109i
$666$	9.83919			0.381261
$667$	−4.87426	+	2.81415i	−0.188732	+	0.108964i
$668$	1.46402	+	5.46378i	0.0566445	+	0.211400i
$669$	−6.43619	+	1.72457i	−0.248837	+	0.0666758i
$670$	−8.21181	+	30.6469i	−0.317250	+	1.18399i
$671$	24.0171	+	24.0171i	0.927171	+	0.927171i
$672$	0.876637	−	15.2612i	0.0338170	−	0.588713i
$673$			11.2945i			0.435372i	0.976019	+	0.217686i	$0.0698509\pi$
$673$			11.2945i			0.435372i	−0.976019	+	0.217686i	$0.930149\pi$
$674$	2.45169	+	0.656928i	0.0944356	+	0.0253039i
$675$	−0.0686633	+	0.118928i	−0.00264285	+	0.00457756i
$676$	13.7795	−	5.45736i	0.529980	−	0.209898i
$677$	9.28222	−	5.35909i	0.356745	−	0.205967i	−0.310907	−	0.950440i	$-0.600633\pi$
$677$	9.28222	−	5.35909i	0.356745	−	0.205967i	0.667652	+	0.744474i	$0.267300\pi$
$678$	16.3711	−	16.3711i	0.628729	−	0.628729i
$679$	31.5606	+	20.7217i	1.21119	+	0.795225i
$680$			17.5728i			0.673887i
$681$	1.41619	−	5.28529i	0.0542685	−	0.202533i
$682$	4.54757	+	16.9718i	0.174136	+	0.649883i
$683$	−7.84710	−	29.2858i	−0.300261	−	1.12059i	−0.936949	−	0.349467i	$-0.886363\pi$
$683$	−7.84710	−	29.2858i	−0.300261	−	1.12059i	0.636688	−	0.771122i	$-0.280304\pi$
$684$	−0.891505	+	3.32714i	−0.0340875	+	0.127216i
$685$			0.701948i			0.0268201i
$686$	−30.8122	+	11.2984i	−1.17641	+	0.431374i
$687$	−7.83769	+	7.83769i	−0.299026	+	0.299026i
$688$	−21.6454	+	12.4970i	−0.825221	+	0.476442i
$689$	41.2779	+	3.02908i	1.57256	+	0.115399i
$690$	5.89298	−	10.2069i	0.224342	−	0.388572i
$691$	11.7796	+	3.15633i	0.448117	+	0.120073i	0.475818	−	0.879544i	$-0.342152\pi$
$691$	11.7796	+	3.15633i	0.448117	+	0.120073i	−0.0277012	+	0.999616i	$0.508819\pi$
$692$			4.65291i			0.176877i
$693$	8.01374	+	5.26156i	0.304417	+	0.199870i
$694$	−25.6411	−	25.6411i	−0.973322	−	0.973322i
$695$	−7.87365	+	29.3849i	−0.298665	+	1.11463i
$696$	−2.82312	+	0.756454i	−0.107010	+	0.0286733i
$697$	−9.74217	−	36.3583i	−0.369011	−	1.37717i
$698$	22.1318	−	12.7778i	0.837702	−	0.483648i
$699$	−14.4929			−0.548170
$700$	−0.309214	+	0.275620i	−0.0116872	+	0.0104175i
$701$			17.2772i			0.652550i	0.945275	+	0.326275i	$0.105794\pi$
$701$			17.2772i			0.652550i	−0.945275	+	0.326275i	$0.894206\pi$
$702$	−1.19753	−	6.27589i	−0.0451979	−	0.236868i
$703$	14.5284	+	8.38800i	0.547951	+	0.316359i
$704$	−0.971047	+	0.260191i	−0.0365977	+	0.00980633i
$705$	−11.7717	+	6.79642i	−0.443349	+	0.255968i
$706$	−20.7142			−0.779588
$707$	12.1049	+	4.00039i	0.455250	+	0.150450i
$708$	1.02351	+	1.02351i	0.0384657	+	0.0384657i
$709$	49.7679	+	13.3353i	1.86907	+	0.500817i	0.999981	+	0.00616863i	$0.00196355\pi$
$709$	49.7679	+	13.3353i	1.86907	+	0.500817i	0.869093	+	0.494648i	$0.164703\pi$
$710$	−10.1345	+	2.71553i	−0.380340	+	0.101912i
$711$	−0.0621069	+	0.107572i	−0.00232919	+	0.00403428i
$712$	−13.8743	−	24.0310i	−0.519962	−	0.900600i
$713$	5.67816	+	5.67816i	0.212649	+	0.212649i
$714$	21.3079	−	10.7225i	0.797428	−	0.401281i
$715$	−26.6590	+	12.8892i	−0.996990	+	0.482029i
$716$	4.37697	+	7.58113i	0.163575	+	0.283320i
$717$	−4.31146	−	16.0906i	−0.161015	−	0.600915i
$718$	0.584224	−	1.01191i	0.0218030	−	0.0377640i
$719$	−6.21078	−	10.7574i	−0.231623	−	0.401183i	0.726663	−	0.686994i	$-0.241070\pi$
$719$	−6.21078	−	10.7574i	−0.231623	−	0.401183i	−0.958286	+	0.285811i	$0.907737\pi$
$720$	7.98208	−	7.98208i	0.297475	−	0.297475i
$721$	−24.2302	+	21.5977i	−0.902380	+	0.804342i
$722$	12.3692	−	12.3692i	0.460333	−	0.460333i
$723$	4.97562	+	1.33321i	0.185045	+	0.0495827i
$724$	−16.9897	−	9.80903i	−0.631418	−	0.364550i
$725$	0.228106	+	0.131697i	0.00847163	+	0.00489110i
$726$	0.976504	−	3.64436i	0.0362415	−	0.135255i
$727$	32.6538			1.21106			0.605530	−	0.795822i	$-0.292961\pi$
$727$	32.6538			1.21106			0.605530	+	0.795822i	$0.292961\pi$
$728$	−1.89350	+	14.4125i	−0.0701777	+	0.534164i
$729$	−1.00000			−0.0370370
$730$	−9.97299	+	37.2197i	−0.369117	+	1.37756i
$731$	−22.1126	−	12.7667i	−0.817864	−	0.472194i
$732$	−9.25502	−	5.34339i	−0.342075	−	0.197497i
$733$	−27.6096	−	7.39797i	−1.01978	−	0.273250i	−0.290072	−	0.957005i	$-0.593679\pi$
$733$	−27.6096	−	7.39797i	−1.01978	−	0.273250i	−0.729712	+	0.683754i	$0.760346\pi$
$734$	−33.6704	+	33.6704i	−1.24280	+	1.24280i
$735$	−14.7543	−	5.83426i	−0.544222	−	0.215200i
$736$	−11.9886	+	11.9886i	−0.441904	+	0.441904i
$737$	14.3118	+	24.7887i	0.527181	+	0.913104i
$738$	−6.55482	+	11.3533i	−0.241286	+	0.417920i
$739$	−4.34269	−	16.2071i	−0.159748	−	0.596189i	−0.998652	−	0.0519089i	$-0.983469\pi$
$739$	−4.34269	−	16.2071i	−0.159748	−	0.596189i	0.838903	−	0.544280i	$-0.183197\pi$
$740$	7.17395	+	12.4256i	0.263720	+	0.456776i
$741$	3.58199	−	10.2878i	0.131588	−	0.377932i
$742$	29.5378	−	44.9882i	1.08437	−	1.65157i
$743$	8.73182	+	8.73182i	0.320339	+	0.320339i	0.848897	−	0.528558i	$-0.177267\pi$
$743$	8.73182	+	8.73182i	0.320339	+	0.320339i	−0.528558	+	0.848897i	$0.677267\pi$
$744$	2.08498	+	3.61128i	0.0764389	+	0.132396i
$745$	−15.1546	+	26.2485i	−0.555221	+	0.961670i
$746$	−47.2174	+	12.6519i	−1.72875	+	0.463218i
$747$	−13.5100	−	3.61999i	−0.494304	−	0.132448i
$748$	−14.8618	−	14.8618i	−0.543400	−	0.543400i
$749$	−24.7435	+	22.0553i	−0.904108	+	0.805882i
$750$	19.5305			0.713152
$751$	33.2670	−	19.2067i	1.21393	−	0.700863i	0.250317	−	0.968164i	$-0.419465\pi$
$751$	33.2670	−	19.2067i	1.21393	−	0.700863i	0.963613	+	0.267301i	$0.0861318\pi$
$752$	28.8501	−	7.73037i	1.05206	−	0.281898i
$753$	3.39984	+	1.96290i	0.123897	+	0.0715321i
$754$	−12.0372	+	2.29688i	−0.438369	+	0.0836473i
$755$			19.6702i			0.715873i
$756$	−2.86398	−	0.946483i	−0.104162	−	0.0344233i
$757$	−0.270595			−0.00983494			−0.00491747	−	0.999988i	$-0.501565\pi$
$757$	−0.270595			−0.00983494			−0.00491747	+	0.999988i	$0.501565\pi$
$758$	17.9314	−	10.3527i	0.651297	−	0.376027i
$759$	−2.75196	−	10.2704i	−0.0998897	−	0.372794i
$760$	10.0797	−	2.70084i	0.365628	−	0.0979697i
$761$	4.44524	−	16.5899i	0.161140	−	0.601382i	−0.837361	−	0.546650i	$-0.815903\pi$
$761$	4.44524	−	16.5899i	0.161140	−	0.601382i	0.998501	−	0.0547319i	$-0.0174304\pi$
$762$	27.5691	+	27.5691i	0.998724	+	0.998724i
$763$	−18.8508	−	37.4604i	−0.682444	−	1.35616i
$764$		−	30.9233i		−	1.11877i
$765$	11.1391	+	2.98471i	0.402735	+	0.107912i
$766$	5.04940	−	8.74582i	0.182442	−	0.315999i
$767$	−2.99135	−	3.46514i	−0.108011	−	0.125119i
$768$	−17.4592	+	10.0801i	−0.630004	+	0.363733i
$769$	−27.2014	+	27.2014i	−0.980907	+	0.980907i	−0.999821	−	0.0189145i	$-0.993979\pi$
$769$	−27.2014	+	27.2014i	−0.980907	+	0.980907i	0.0189145	+	0.999821i	$0.493979\pi$
$770$	−2.20811	+	38.4406i	−0.0795749	+	1.38530i
$771$			24.3592i			0.877276i
$772$	−7.17794	+	26.7884i	−0.258340	+	0.964137i
$773$	−4.43869	−	16.5654i	−0.159649	−	0.595817i	−0.998662	−	0.0517064i	$-0.983534\pi$
$773$	−4.43869	−	16.5654i	−0.159649	−	0.595817i	0.839014	−	0.544110i	$-0.183133\pi$
$774$	2.30164	+	8.58983i	0.0827306	+	0.308755i
$775$	0.0972628	−	0.362990i	0.00349378	−	0.0130390i
$776$		−	21.7452i		−	0.780609i
$777$	−8.06281	+	12.2803i	−0.289252	+	0.440552i
$778$	27.6147	−	27.6147i	0.990034	−	0.990034i
$779$	−19.3576	+	11.1761i	−0.693556	+	0.400425i
$780$	7.05250	−	6.08820i	0.252520	−	0.217992i
$781$	−4.73269	+	8.19726i	−0.169349	+	0.293321i
$782$	−25.5551	−	6.84747i	−0.913849	−	0.244865i
$783$			1.91801i			0.0685440i
$784$	27.9974	+	20.7739i	0.999906	+	0.741924i
$785$	−13.0980	−	13.0980i	−0.467488	−	0.467488i
$786$	−1.57276	+	5.86962i	−0.0560985	+	0.209362i
$787$	−24.3535	+	6.52551i	−0.868109	+	0.232609i	−0.665270	−	0.746603i	$-0.731684\pi$
$787$	−24.3535	+	6.52551i	−0.868109	+	0.232609i	−0.202839	+	0.979212i	$0.565017\pi$
$788$	−1.13969	−	4.25336i	−0.0405996	−	0.151520i
$789$	−13.9705	+	8.06588i	−0.497364	+	0.287153i
$790$	−0.498893			−0.0177498
$791$	7.01727	+	33.8482i	0.249505	+	1.20350i
$792$		−	5.52146i		−	0.196197i
$793$	27.9546	+	18.9957i	0.992695	+	0.674559i
$794$	−25.8529	−	14.9262i	−0.917485	−	0.529710i
$795$	25.1319	−	6.73406i	0.891335	−	0.238833i
$796$	18.0687	−	10.4320i	0.640428	−	0.369751i
$797$	−6.06034			−0.214668			−0.107334	−	0.994223i	$-0.534231\pi$
$797$	−6.06034			−0.214668			−0.107334	+	0.994223i	$0.534231\pi$
$798$	−9.42528	−	10.5741i	−0.333651	−	0.374319i
$799$	21.5757	+	21.5757i	0.763292	+	0.763292i
$800$	0.766396	+	0.205355i	0.0270962	+	0.00726041i
$801$	−17.5894	+	4.71305i	−0.621489	+	0.166528i
$802$	17.4265	−	30.1836i	0.615351	−	1.06582i
$803$	17.3812	+	30.1051i	0.613369	+	1.06239i
$804$	−6.36823	−	6.36823i	−0.224590	−	0.224590i
$805$	7.91018	+	15.7192i	0.278797	+	0.554028i
$806$	7.61033	+	15.7406i	0.268062	+	0.554440i
$807$	3.72132	+	6.44551i	0.130997	+	0.226893i
$808$	−1.90042	−	7.09248i	−0.0668567	−	0.249513i
$809$	−11.8643	+	20.5495i	−0.417126	+	0.722483i	−0.995649	−	0.0931831i	$-0.970296\pi$
$809$	−11.8643	+	20.5495i	−0.417126	+	0.722483i	0.578523	+	0.815666i	$0.303629\pi$
$810$	−2.00820	−	3.47831i	−0.0705611	−	0.122215i
$811$	9.42876	−	9.42876i	0.331088	−	0.331088i	−0.521911	−	0.853000i	$-0.674781\pi$
$811$	9.42876	−	9.42876i	0.331088	−	0.331088i	0.853000	+	0.521911i	$0.174781\pi$
$812$	−1.81536	+	5.49314i	−0.0637067	+	0.192772i
$813$	−11.1336	+	11.1336i	−0.390472	+	0.390472i
$814$	34.4367	+	9.22729i	1.20701	+	0.323416i
$815$	−36.6038	−	21.1332i	−1.28218	−	0.740265i
$816$	−21.9448	−	12.6698i	−0.768220	−	0.443532i
$817$	−3.92433	+	14.6458i	−0.137295	+	0.512392i
$818$	−26.6275			−0.931009
$819$	8.81423	+	3.64819i	0.307994	+	0.127478i
$820$	−19.1170			−0.667594
$821$	0.189047	−	0.705534i	0.00659779	−	0.0246233i	−0.962548	−	0.271110i	$-0.912609\pi$
$821$	0.189047	−	0.705534i	0.00659779	−	0.0246233i	0.969146	+	0.246486i	$0.0792761\pi$
$822$	−0.475265	−	0.274395i	−0.0165768	−	0.00957061i
$823$	11.6721	+	6.73887i	0.406863	+	0.234902i	0.689441	−	0.724342i	$-0.257856\pi$
$823$	11.6721	+	6.73887i	0.406863	+	0.234902i	−0.282578	+	0.959244i	$0.591190\pi$
$824$	18.0576	+	4.83853i	0.629068	+	0.168558i
$825$	−0.351851	+	0.351851i	−0.0122499	+	0.0122499i
$826$	−5.82849	+	1.20834i	−0.202799	+	0.0420435i
$827$	−8.01440	+	8.01440i	−0.278688	+	0.278688i	−0.832585	−	0.553897i	$-0.813140\pi$
$827$	−8.01440	+	8.01440i	−0.278688	+	0.278688i	0.553897	+	0.832585i	$0.313140\pi$
$828$	1.67273	+	2.89726i	0.0581314	+	0.100687i
$829$	−10.1091	+	17.5094i	−0.351103	+	0.608128i	−0.986443	−	0.164105i	$-0.947527\pi$
$829$	−10.1091	+	17.5094i	−0.351103	+	0.608128i	0.635340	+	0.772232i	$0.280860\pi$
$830$	−14.5393	−	54.2616i	−0.504668	−	1.88345i
$831$	13.3237	+	23.0773i	0.462194	+	0.800544i
$832$	−0.900607	+	0.435429i	−0.0312229	+	0.0150958i
$833$	−4.07818	+	35.3810i	−0.141301	+	1.22588i
$834$	−16.8177	−	16.8177i	−0.582348	−	0.582348i
$835$	−5.62288	−	9.73911i	−0.194588	−	0.337036i
$836$	−6.24045	+	10.8088i	−0.215830	+	0.373829i
$837$	2.64326	−	0.708258i	0.0913643	−	0.0244810i
$838$	−18.3561	−	4.91849i	−0.634099	−	0.169906i
$839$	−3.88791	−	3.88791i	−0.134225	−	0.134225i	0.636802	−	0.771027i	$-0.280257\pi$
$839$	−3.88791	−	3.88791i	−0.134225	−	0.134225i	−0.771027	+	0.636802i	$0.780257\pi$
$840$	1.85502	+	8.94777i	0.0640042	+	0.308728i
$841$	−25.3212			−0.873146
$842$	−49.4995	+	28.5785i	−1.70586	+	0.984881i
$843$	−3.89698	+	1.04419i	−0.134219	+	0.0359639i
$844$	6.44454	+	3.72076i	0.221830	+	0.128074i
$845$	−23.6535	+	17.5705i	−0.813704	+	0.604443i
$846$		−	10.6270i		−	0.365364i
$847$	3.74831	+	4.20517i	0.128793	+	0.144491i
$848$	−57.1709			−1.96326
$849$	6.15144	−	3.55154i	0.211117	−	0.121888i
$850$	0.320448	+	1.19593i	0.0109913	+	0.0410200i
$851$	15.7384	−	4.21710i	0.539506	−	0.144560i
$852$	0.770806	−	2.87669i	0.0264074	−	0.0985537i
$853$	2.40492	+	2.40492i	0.0823428	+	0.0823428i	0.747079	−	0.664736i	$-0.231456\pi$
$853$	2.40492	+	2.40492i	0.0823428	+	0.0823428i	−0.664736	+	0.747079i	$0.731456\pi$
$854$	39.2573	−	19.7550i	1.34336	−	0.676003i
$855$		−	6.84805i		−	0.234198i
$856$	18.4402	+	4.94103i	0.630272	+	0.168881i
$857$	6.76525	−	11.7178i	0.231097	−	0.400271i	−0.727034	−	0.686601i	$-0.759102\pi$
$857$	6.76525	−	11.7178i	0.231097	−	0.400271i	0.958131	+	0.286330i	$0.0924353\pi$
$858$	1.69428	−	23.0884i	0.0578419	−	0.788224i
$859$	8.81257	−	5.08794i	0.300681	−	0.173598i	−0.342068	−	0.939675i	$-0.611127\pi$
$859$	8.81257	−	5.08794i	0.300681	−	0.173598i	0.642749	+	0.766077i	$0.277794\pi$
$860$	−9.16968	+	9.16968i	−0.312684	+	0.312684i
$861$	−8.79858	−	17.4846i	−0.299855	−	0.595873i
$862$		−	59.0850i		−	2.01244i
$863$	8.87812	−	33.1336i	0.302215	−	1.12788i	−0.633102	−	0.774068i	$-0.718219\pi$
$863$	8.87812	−	33.1336i	0.302215	−	1.12788i	0.935317	−	0.353812i	$-0.115115\pi$
$864$	1.49538	+	5.58083i	0.0508738	+	0.189864i
$865$	−2.39420	−	8.93528i	−0.0814053	−	0.303809i
$866$	9.70259	−	36.2106i	0.329708	−	1.23049i
$867$		−	8.88660i		−	0.301805i
$868$	8.24059	+	0.473358i	0.279704	+	0.0160668i
$869$	−0.318254	+	0.318254i	−0.0107960	+	0.0107960i
$870$	−6.67143	+	3.85175i	−0.226183	+	0.130587i
$871$	18.6121	+	21.5601i	0.630648	+	0.730535i
$872$	−12.0766	+	20.9172i	−0.408964	+	0.708347i
$873$	−13.7839	−	3.69339i	−0.466515	−	0.125002i
$874$			15.7107i			0.531421i
$875$	−16.0044	+	24.3759i	−0.541048	+	0.824056i
$876$	−7.73402	−	7.73402i	−0.261308	−	0.261308i
$877$	−8.28153	+	30.9071i	−0.279647	+	1.04366i	0.673015	+	0.739629i	$0.264999\pi$
$877$	−8.28153	+	30.9071i	−0.279647	+	1.04366i	−0.952663	+	0.304030i	$0.901668\pi$
$878$	−53.2132	+	14.2584i	−1.79586	+	0.481199i
$879$	3.99363	+	14.9044i	0.134702	+	0.502713i
$880$	35.4226	−	20.4512i	1.19410	−	0.689411i
$881$	−18.4124			−0.620329			−0.310165	−	0.950683i	$-0.600384\pi$
$881$	−18.4124			−0.620329			−0.310165	+	0.950683i	$0.600384\pi$
$882$	9.71772	−	7.70903i	0.327213	−	0.259576i
$883$			44.2304i			1.48847i	0.667917	+	0.744236i	$0.267186\pi$
$883$			44.2304i			1.48847i	−0.667917	+	0.744236i	$0.732814\pi$
$884$	−17.2982	−	11.7545i	−0.581803	−	0.395348i
$885$	−2.49216	−	1.43885i	−0.0837729	−	0.0483663i
$886$	5.28490	−	1.41609i	0.177550	−	0.0475743i
$887$	32.8366	−	18.9582i	1.10255	−	0.636555i	0.165657	−	0.986183i	$-0.447025\pi$
$887$	32.8366	−	18.9582i	1.10255	−	0.636555i	0.936888	+	0.349628i	$0.113692\pi$
$888$	8.46108			0.283935
$889$	−57.0007	+	11.8171i	−1.91174	+	0.396334i
$890$	−51.7165	−	51.7165i	−1.73354	−	1.73354i
$891$	−3.49995	−	0.937810i	−0.117253	−	0.0314178i
$892$	7.33767	−	1.96612i	0.245683	−	0.0658306i
$893$	9.05961	−	15.6917i	0.303168	−	0.525103i
$894$	−11.8480	−	20.5213i	−0.396256	−	0.686335i
$895$	−12.3063	−	12.3063i	−0.411355	−	0.411355i
$896$	1.67868	−	29.2238i	0.0560807	−	0.976298i
$897$	−4.60538	−	9.52542i	−0.153769	−	0.318044i
$898$	31.8691	+	55.1990i	1.06349	+	1.84201i
$899$	−1.35845	−	5.06979i	−0.0453067	−	0.169087i
$900$	0.0782806	−	0.135586i	0.00260935	−	0.00451953i
$901$	−29.2025	−	50.5802i	−0.972876	−	1.68507i
$902$	−33.5888	+	33.5888i	−1.11838	+	1.11838i
$903$	−12.6070	−	4.16634i	−0.419535	−	0.138647i
$904$	14.0781	−	14.0781i	0.468231	−	0.468231i
$905$	37.6738	+	10.0947i	1.25232	+	0.335558i
$906$	−13.3181	−	7.68918i	−0.442463	−	0.255456i
$907$	11.4259	+	6.59673i	0.379390	+	0.219041i	0.677553	−	0.735474i	$-0.263041\pi$
$907$	11.4259	+	6.59673i	0.379390	+	0.219041i	−0.298163	+	0.954515i	$0.596374\pi$
$908$	−1.61455	+	6.02557i	−0.0535806	+	0.199966i
$909$	−4.81858			−0.159822
$910$	5.01122	+	37.9850i	0.166120	+	1.25919i
$911$	34.0993			1.12976			0.564880	−	0.825173i	$-0.308922\pi$
$911$	34.0993			1.12976			0.564880	+	0.825173i	$0.308922\pi$
$912$	−3.89455	+	14.5347i	−0.128961	+	0.481290i
$913$	−43.8894	−	25.3396i	−1.45253	−	0.838617i
$914$	29.2366	+	16.8798i	0.967062	+	0.558334i
$915$	20.5225	+	5.49898i	0.678452	+	0.181791i
$916$	8.93547	−	8.93547i	0.295236	−	0.295236i
$917$	−6.03703	−	6.77286i	−0.199360	−	0.223660i
$918$	−6.37517	+	6.37517i	−0.210412	+	0.210412i
$919$	−5.34707	−	9.26140i	−0.176384	−	0.305505i	0.764256	−	0.644913i	$-0.223107\pi$
$919$	−5.34707	−	9.26140i	−0.176384	−	0.305505i	−0.940639	+	0.339408i	$0.889773\pi$
$920$	5.06759	−	8.77732i	0.167073	−	0.289380i
$921$	−5.42597	−	20.2500i	−0.178792	−	0.667260i
$922$	35.4172	+	61.3444i	1.16640	+	2.02027i
$923$	−3.09703	+	8.89497i	−0.101940	+	0.292781i
$924$	−9.13618	−	5.99852i	−0.300558	−	0.197337i
$925$	−0.539175	−	0.539175i	−0.0177280	−	0.0177280i
$926$	5.21998	+	9.04127i	0.171539	+	0.297115i
$927$	6.13411	−	10.6246i	0.201471	−	0.348957i
$928$	10.7041	−	2.86815i	0.351379	−	0.0941516i
$929$	−11.7836	−	3.15740i	−0.386606	−	0.103591i	0.0602803	−	0.998181i	$-0.480801\pi$
$929$	−11.7836	−	3.15740i	−0.386606	−	0.103591i	−0.446887	+	0.894591i	$0.647467\pi$
$930$	7.77174	+	7.77174i	0.254845	+	0.254845i
$931$	20.9211	−	3.09862i	0.685661	−	0.101553i
$932$	16.5228			0.541222
$933$	14.7422	−	8.51144i	0.482639	−	0.278652i
$934$	−39.6224	+	10.6168i	−1.29648	+	0.347392i
$935$	36.1872	+	20.8927i	1.18345	+	0.683264i
$936$	−1.02980	−	5.39686i	−0.0336601	−	0.176402i
$937$		−	32.9237i		−	1.07557i	−0.843082	−	0.537785i	$-0.819261\pi$
$937$		−	32.9237i		−	1.07557i	0.843082	−	0.537785i	$-0.180739\pi$
$938$	36.2648	−	7.51827i	1.18409	−	0.245480i
$939$	−6.56394			−0.214206
$940$	13.4205	−	7.74835i	0.437730	−	0.252723i
$941$	−6.57596	−	24.5418i	−0.214370	−	0.800040i	−0.986387	−	0.164439i	$-0.947419\pi$
$941$	−6.57596	−	24.5418i	−0.214370	−	0.800040i	0.772017	−	0.635602i	$-0.219248\pi$
$942$	13.9883	−	3.74815i	0.455763	−	0.122121i
$943$	−5.61882	+	20.9697i	−0.182974	+	0.682868i
$944$	4.47120	+	4.47120i	0.145525	+	0.145525i
$945$	5.98690	+	0.343901i	0.194754	+	0.0111871i
$946$			32.2225i			1.04764i
$947$	27.3013	+	7.31537i	0.887175	+	0.237718i	0.673500	−	0.739187i	$-0.264790\pi$
$947$	27.3013	+	7.31537i	0.887175	+	0.237718i	0.213675	+	0.976905i	$0.431457\pi$
$948$	0.0708059	−	0.122639i	0.00229967	−	0.00398314i
$949$	22.6038	+	26.1840i	0.733752	+	0.849969i
$950$	0.636726	−	0.367614i	0.0206581	−	0.0119270i
$951$	8.03804	−	8.03804i	0.260651	−	0.260651i
$952$	18.3234	−	9.22070i	0.593866	−	0.298845i
$953$			12.5172i			0.405472i	0.979233	+	0.202736i	$0.0649833\pi$
$953$			12.5172i			0.405472i	−0.979233	+	0.202736i	$0.935017\pi$
$954$	−5.26475	+	19.6483i	−0.170453	+	0.636138i
$955$	15.9119	+	59.3840i	0.514897	+	1.92162i
$956$	4.91535	+	18.3443i	0.158974	+	0.593298i
$957$	−1.79873	+	6.71294i	−0.0581446	+	0.216999i
$958$			41.3059i			1.33453i
$959$	0.731931	−	0.368322i	0.0236353	−	0.0118937i
$960$	−0.444664	+	0.444664i	−0.0143515	+	0.0143515i
$961$	20.3616	−	11.7558i	0.656826	−	0.379219i
$962$	35.3806	+	2.59632i	1.14072	+	0.0837087i
$963$	6.26406	−	10.8497i	0.201856	−	0.349626i
$964$	−5.67253	−	1.51995i	−0.182700	−	0.0489543i
$965$		−	55.1370i		−	1.77492i
$966$	−13.7350	−	0.788972i	−0.441918	−	0.0253847i
$967$	−12.9841	−	12.9841i	−0.417541	−	0.417541i	0.466814	−	0.884355i	$-0.345402\pi$
$967$	−12.9841	−	12.9841i	−0.417541	−	0.417541i	−0.884355	+	0.466814i	$0.845402\pi$
$968$	0.839731	−	3.13392i	0.0269900	−	0.100728i
$969$	−14.8484	+	3.97861i	−0.476999	+	0.127812i
$970$	−14.8342	−	55.3618i	−0.476296	−	1.77756i
$971$	−16.7868	+	9.69187i	−0.538714	+	0.311027i	−0.744558	−	0.667558i	$-0.767340\pi$
$971$	−16.7868	+	9.69187i	−0.538714	+	0.311027i	0.205843	+	0.978585i	$0.434006\pi$
$972$	1.14006			0.0365676
$973$	34.7714	−	7.20867i	1.11472	−	0.231100i
$974$			50.3643i			1.61378i
$975$	−0.278287	+	0.409534i	−0.00891233	+	0.0131156i
$976$	−40.4307	−	23.3427i	−1.29415	−	0.747180i
$977$	−31.9558	+	8.56252i	−1.02236	+	0.273939i	−0.730783	−	0.682609i	$-0.760845\pi$
$977$	−31.9558	+	8.56252i	−1.02236	+	0.273939i	−0.291572	+	0.956549i	$0.594178\pi$
$978$	28.6172	−	16.5221i	0.915077	−	0.528320i
$979$	−65.9819			−2.10879
$980$	16.8209	+	6.65143i	0.537324	+	0.212472i
$981$	11.2079	+	11.2079i	0.357840	+	0.357840i
$982$	47.6535	+	12.7687i	1.52069	+	0.407466i
$983$	−15.5769	+	4.17382i	−0.496826	+	0.133124i	−0.498527	−	0.866874i	$-0.666125\pi$
$983$	−15.5769	+	4.17382i	−0.496826	+	0.133124i	0.00170057	+	0.999999i	$0.499459\pi$
$984$	−5.63673	+	9.76310i	−0.179692	+	0.311236i
$985$	4.37722	+	7.58156i	0.139470	+	0.241569i
$986$	12.2276	+	12.2276i	0.389407	+	0.389407i
$987$	13.2635	+	8.70839i	0.422182	+	0.277191i
$988$	−4.08370	+	11.7288i	−0.129920	+	0.373142i
$989$	7.36323	+	12.7535i	0.234137	+	0.405537i
$990$	−3.76663	−	14.0572i	−0.119711	−	0.446768i
$991$	14.0327	−	24.3054i	0.445764	−	0.772086i	−0.552341	−	0.833618i	$-0.686265\pi$
$991$	14.0327	−	24.3054i	0.445764	−	0.772086i	0.998105	+	0.0615320i	$0.0195986\pi$
$992$	−7.90534	−	13.6924i	−0.250995	−	0.434736i
$993$	−6.69939	+	6.69939i	−0.212599	+	0.212599i
$994$	8.14921	+	9.14249i	0.258477	+	0.289982i
$995$	−29.3306	+	29.3306i	−0.929842	+	0.929842i
$996$	15.4022	+	4.12702i	0.488038	+	0.130770i
$997$	−7.71874	−	4.45642i	−0.244455	−	0.141136i	0.372768	−	0.927925i	$-0.378409\pi$
$997$	−7.71874	−	4.45642i	−0.244455	−	0.141136i	−0.617223	+	0.786789i	$0.711742\pi$
$998$	5.25341	+	3.03306i	0.166294	+	0.0960097i
$999$	1.43710	−	5.36332i	0.0454678	−	0.169688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.a.73.3	✓	36
3.2	odd	2		819.2.fn.f.73.7		36
7.5	odd	6		273.2.bz.b.229.7	yes	36
13.5	odd	4		273.2.bz.b.31.7	yes	36
21.5	even	6		819.2.fn.g.775.3		36
39.5	even	4		819.2.fn.g.577.3		36
91.5	even	12	inner	273.2.bz.a.187.3	yes	36
273.5	odd	12		819.2.fn.f.460.7		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.3	✓	36	1.1	even	1	trivial
273.2.bz.a.187.3	yes	36	91.5	even	12	inner
273.2.bz.b.31.7	yes	36	13.5	odd	4
273.2.bz.b.229.7	yes	36	7.5	odd	6
819.2.fn.f.73.7		36	3.2	odd	2
819.2.fn.f.460.7		36	273.5	odd	12
819.2.fn.g.577.3		36	39.5	even	4
819.2.fn.g.775.3		36	21.5	even	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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458633 + 1.71164i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.987324 - 0.570032i) q^{4} +(2.18934 + 0.586631i) q^{5} +(-1.25301 + 1.25301i) q^{6} +(-0.537086 - 2.59066i) q^{7} +(-1.07751 + 1.07751i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.458633 + 1.71164i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.987324 - 0.570032i) q^{4} +(2.18934 + 0.586631i) q^{5} +(-1.25301 + 1.25301i) q^{6} +(-0.537086 - 2.59066i) q^{7} +(-1.07751 + 1.07751i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.00820 + 3.47831i) q^{10} +(0.937810 + 3.49995i) q^{11} +(-0.570032 - 0.987324i) q^{12} +(1.56942 + 3.24606i) q^{13} +(4.68062 + 0.268865i) q^{14} +(1.60271 + 1.60271i) q^{15} +(-2.49019 - 4.31314i) q^{16} +(2.54394 - 4.40624i) q^{17} +(-1.71164 + 0.458633i) q^{18} +(-2.91838 - 0.781978i) q^{19} +(-1.82719 - 1.82719i) q^{20} +(0.830202 - 2.51212i) q^{21} -6.42078 q^{22} +(-2.54131 + 1.46723i) q^{23} +(-1.47190 + 0.394395i) q^{24} +(0.118928 + 0.0686633i) q^{25} +(-6.27589 + 1.19753i) q^{26} +1.00000i q^{27} +(-0.946483 + 2.86398i) q^{28} +1.91801 q^{29} +(-3.47831 + 2.00820i) q^{30} +(-0.708258 - 2.64326i) q^{31} +(5.58083 - 1.49538i) q^{32} +(-0.937810 + 3.49995i) q^{33} +(6.37517 + 6.37517i) q^{34} +(0.343901 - 5.98690i) q^{35} -1.14006i q^{36} +(-5.36332 - 1.43710i) q^{37} +(2.67693 - 4.63658i) q^{38} +(-0.263875 + 3.59588i) q^{39} +(-2.99113 + 1.72693i) q^{40} +(5.23127 - 5.23127i) q^{41} +(3.91910 + 2.57315i) q^{42} -5.01847i q^{43} +(1.06916 - 3.99017i) q^{44} +(0.586631 + 2.18934i) q^{45} +(-1.34584 - 5.02273i) q^{46} +(-1.55216 + 5.79276i) q^{47} -4.98038i q^{48} +(-6.42308 + 2.78282i) q^{49} +(-0.172072 + 0.172072i) q^{50} +(4.40624 - 2.54394i) q^{51} +(0.300835 - 4.09954i) q^{52} +(5.73961 - 9.94129i) q^{53} +(-1.71164 - 0.458633i) q^{54} +8.21272i q^{55} +(3.37017 + 2.21275i) q^{56} +(-2.13640 - 2.13640i) q^{57} +(-0.879663 + 3.28295i) q^{58} +(-1.22637 + 0.328604i) q^{59} +(-0.668797 - 2.49598i) q^{60} +(8.11798 - 4.68692i) q^{61} +4.84914 q^{62} +(1.97504 - 1.76046i) q^{63} +0.277446i q^{64} +(1.53174 + 8.02739i) q^{65} +(-5.56056 - 3.21039i) q^{66} +(7.63042 - 2.04457i) q^{67} +(-5.02340 + 2.90026i) q^{68} -2.93445 q^{69} +(10.0897 + 3.33443i) q^{70} +(1.84716 + 1.84716i) q^{71} +(-1.47190 - 0.394395i) q^{72} +(9.26691 - 2.48306i) q^{73} +(4.91960 - 8.52099i) q^{74} +(0.0686633 + 0.118928i) q^{75} +(2.43564 + 2.43564i) q^{76} +(8.56352 - 4.30933i) q^{77} +(-6.03384 - 2.10085i) q^{78} +(0.0621069 + 0.107572i) q^{79} +(-2.92165 - 10.9037i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.55482 + 11.3533i) q^{82} +(-9.88999 + 9.88999i) q^{83} +(-2.25167 + 2.00704i) q^{84} +(8.15438 - 8.15438i) q^{85} +(8.58983 + 2.30164i) q^{86} +(1.66104 + 0.959004i) q^{87} +(-4.78172 - 2.76073i) q^{88} +(-4.71305 + 17.5894i) q^{89} -4.01641 q^{90} +(7.56654 - 5.80925i) q^{91} +3.34546 q^{92} +(0.708258 - 2.64326i) q^{93} +(-9.20325 - 5.31350i) q^{94} +(-5.93058 - 3.42402i) q^{95} +(5.58083 + 1.49538i) q^{96} +(-10.0905 + 10.0905i) q^{97} +(-1.81735 - 12.2703i) q^{98} +(-2.56214 + 2.56214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q - 6 * q^7 + 18 * q^9	\( 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

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