LMFDB - Embedded newform 273.2.bt.a.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(136,273)]

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, 5]))

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

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

chi := DirichletCharacter("273.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bt (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			271.2
Character	$\chi$	$=$	273.271
Dual form			273.2.bt.a.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48267 - 1.48267i) q^{2} +(0.866025 + 0.500000i) q^{3} +2.39661i q^{4} +(0.507149 + 1.89270i) q^{5} +(-0.542694 - 2.02536i) q^{6} +(-0.313052 - 2.62717i) q^{7} +(0.588043 - 0.588043i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.48267 - 1.48267i) q^{2} +(0.866025 + 0.500000i) q^{3} +2.39661i q^{4} +(0.507149 + 1.89270i) q^{5} +(-0.542694 - 2.02536i) q^{6} +(-0.313052 - 2.62717i) q^{7} +(0.588043 - 0.588043i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.05432 - 3.55819i) q^{10} +(0.648767 + 2.42123i) q^{11} +(-1.19831 + 2.07553i) q^{12} +(3.33753 - 1.36415i) q^{13} +(-3.43106 + 4.35937i) q^{14} +(-0.507149 + 1.89270i) q^{15} +3.04948 q^{16} +7.32088 q^{17} +(0.542694 - 2.02536i) q^{18} +(0.930935 + 0.249443i) q^{19} +(-4.53608 + 1.21544i) q^{20} +(1.04247 - 2.43172i) q^{21} +(2.62798 - 4.55179i) q^{22} +6.63818i q^{23} +(0.803282 - 0.215239i) q^{24} +(1.00500 - 0.580235i) q^{25} +(-6.97103 - 2.92587i) q^{26} +1.00000i q^{27} +(6.29629 - 0.750265i) q^{28} +(-5.21743 - 9.03685i) q^{29} +(3.55819 - 2.05432i) q^{30} +(-2.92062 - 0.782577i) q^{31} +(-5.69745 - 5.69745i) q^{32} +(-0.648767 + 2.42123i) q^{33} +(-10.8544 - 10.8544i) q^{34} +(4.81368 - 1.92488i) q^{35} +(-2.07553 + 1.19831i) q^{36} +(-0.974084 + 0.974084i) q^{37} +(-1.01043 - 1.75011i) q^{38} +(3.57246 + 0.487377i) q^{39} +(1.41122 + 0.814767i) q^{40} +(0.710011 + 0.190247i) q^{41} +(-5.15107 + 2.05979i) q^{42} +(10.1261 + 5.84633i) q^{43} +(-5.80275 + 1.55484i) q^{44} +(-1.38556 + 1.38556i) q^{45} +(9.84223 - 9.84223i) q^{46} +(-3.62699 + 0.971849i) q^{47} +(2.64092 + 1.52474i) q^{48} +(-6.80400 + 1.64488i) q^{49} +(-2.35037 - 0.629781i) q^{50} +(6.34007 + 3.66044i) q^{51} +(3.26933 + 7.99876i) q^{52} +(-1.15862 - 2.00679i) q^{53} +(1.48267 - 1.48267i) q^{54} +(-4.25365 + 2.45585i) q^{55} +(-1.72898 - 1.36080i) q^{56} +(0.681492 + 0.681492i) q^{57} +(-5.66294 + 21.1344i) q^{58} +(-3.35900 - 3.35900i) q^{59} +(-4.53608 - 1.21544i) q^{60} +(-8.18748 + 4.72704i) q^{61} +(3.17000 + 5.49061i) q^{62} +(2.11867 - 1.58469i) q^{63} +10.7959i q^{64} +(4.27455 + 5.62513i) q^{65} +(4.55179 - 2.62798i) q^{66} +(-6.06032 + 1.62386i) q^{67} +17.5453i q^{68} +(-3.31909 + 5.74884i) q^{69} +(-9.99105 - 4.28314i) q^{70} +(8.32895 - 2.23174i) q^{71} +(0.803282 + 0.215239i) q^{72} +(2.01139 - 7.50661i) q^{73} +2.88849 q^{74} +1.16047 q^{75} +(-0.597819 + 2.23109i) q^{76} +(6.15788 - 2.46239i) q^{77} +(-4.57415 - 6.01939i) q^{78} +(-2.31642 + 4.01217i) q^{79} +(1.54654 + 5.77176i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.770638 - 1.33478i) q^{82} +(-10.1090 + 10.1090i) q^{83} +(5.82788 + 2.49840i) q^{84} +(3.71277 + 13.8563i) q^{85} +(-6.34554 - 23.6819i) q^{86} -10.4349i q^{87} +(1.80529 + 1.04229i) q^{88} +(-2.89859 - 2.89859i) q^{89} +4.10864 q^{90} +(-4.62866 - 8.34119i) q^{91} -15.9091 q^{92} +(-2.13804 - 2.13804i) q^{93} +(6.81855 + 3.93669i) q^{94} +1.88849i q^{95} +(-2.08541 - 7.78286i) q^{96} +(-2.63968 - 9.85141i) q^{97} +(12.5269 + 7.64926i) q^{98} +(-1.77246 + 1.77246i) 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} - 8 q^{11} - 16 q^{12} + 42 q^{14} - 24 q^{16} - 8 q^{17} - 18 q^{19} + 14 q^{20} - 4 q^{21} + 4 q^{22} + 18 q^{24} + 24 q^{25} - 50 q^{26} + 34 q^{28} + 8 q^{29} + 6 q^{31} - 50 q^{32} + 8 q^{33} - 24 q^{34} + 14 q^{35} - 14 q^{37} - 8 q^{38} - 2 q^{39} - 30 q^{40} + 34 q^{41} - 18 q^{42} + 30 q^{43} + 28 q^{44} - 32 q^{46} - 10 q^{47} + 24 q^{48} + 6 q^{49} - 20 q^{50} - 24 q^{51} + 4 q^{52} - 8 q^{53} - 30 q^{55} - 92 q^{56} - 24 q^{57} + 72 q^{58} - 70 q^{59} + 14 q^{60} - 60 q^{61} - 48 q^{62} + 6 q^{63} - 44 q^{65} + 18 q^{66} - 46 q^{67} + 4 q^{69} + 80 q^{70} + 42 q^{71} + 18 q^{72} - 56 q^{73} + 40 q^{74} - 20 q^{75} + 12 q^{76} + 24 q^{77} - 16 q^{78} + 170 q^{80} - 18 q^{81} + 24 q^{82} - 60 q^{83} + 2 q^{85} + 12 q^{86} + 84 q^{88} + 64 q^{89} - 86 q^{91} - 100 q^{92} + 12 q^{93} - 66 q^{94} + 46 q^{96} + 36 q^{97} - 22 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 6 * q^7 + 18 * q^9 - 8 * q^11 - 16 * q^12 + 42 * q^14 - 24 * q^16 - 8 * q^17 - 18 * q^19 + 14 * q^20 - 4 * q^21 + 4 * q^22 + 18 * q^24 + 24 * q^25 - 50 * q^26 + 34 * q^28 + 8 * q^29 + 6 * q^31 - 50 * q^32 + 8 * q^33 - 24 * q^34 + 14 * q^35 - 14 * q^37 - 8 * q^38 - 2 * q^39 - 30 * q^40 + 34 * q^41 - 18 * q^42 + 30 * q^43 + 28 * q^44 - 32 * q^46 - 10 * q^47 + 24 * q^48 + 6 * q^49 - 20 * q^50 - 24 * q^51 + 4 * q^52 - 8 * q^53 - 30 * q^55 - 92 * q^56 - 24 * q^57 + 72 * q^58 - 70 * q^59 + 14 * q^60 - 60 * q^61 - 48 * q^62 + 6 * q^63 - 44 * q^65 + 18 * q^66 - 46 * q^67 + 4 * q^69 + 80 * q^70 + 42 * q^71 + 18 * q^72 - 56 * q^73 + 40 * q^74 - 20 * q^75 + 12 * q^76 + 24 * q^77 - 16 * q^78 + 170 * q^80 - 18 * q^81 + 24 * q^82 - 60 * q^83 + 2 * q^85 + 12 * q^86 + 84 * q^88 + 64 * q^89 - 86 * q^91 - 100 * q^92 + 12 * q^93 - 66 * q^94 + 46 * q^96 + 36 * q^97 - 22 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.48267	−	1.48267i	−1.04840	−	1.04840i	−0.998767	−	0.0496376i	$-0.984193\pi$
$2$	−1.48267	−	1.48267i	−1.04840	−	1.04840i	−0.0496376	−	0.998767i	$-0.515807\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$			2.39661i			1.19831i
$5$	0.507149	+	1.89270i	0.226804	+	0.846443i	0.981674	+	0.190569i	$0.0610332\pi$
$5$	0.507149	+	1.89270i	0.226804	+	0.846443i	−0.754870	+	0.655874i	$0.772300\pi$
$6$	−0.542694	−	2.02536i	−0.221554	−	0.826851i
$7$	−0.313052	−	2.62717i	−0.118323	−	0.992975i
$7$	−0.313052	−	2.62717i	−0.118323	−	0.992975i
$8$	0.588043	−	0.588043i	0.207905	−	0.207905i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.05432	−	3.55819i	0.649633	−	1.12520i
$11$	0.648767	+	2.42123i	0.195611	+	0.730029i	0.992108	+	0.125387i	$0.0400172\pi$
$11$	0.648767	+	2.42123i	0.195611	+	0.730029i	−0.796497	+	0.604642i	$0.793316\pi$
$12$	−1.19831	+	2.07553i	−0.345921	+	0.599153i
$13$	3.33753	−	1.36415i	0.925664	−	0.378347i
$13$	3.33753	−	1.36415i	0.925664	−	0.378347i
$14$	−3.43106	+	4.35937i	−0.916990	+	1.16509i
$15$	−0.507149	+	1.89270i	−0.130945	+	0.488694i
$16$	3.04948			0.762369
$17$	7.32088			1.77557			0.887787	−	0.460254i	$-0.152242\pi$
$17$	7.32088			1.77557			0.887787	+	0.460254i	$0.152242\pi$
$18$	0.542694	−	2.02536i	0.127914	−	0.477383i
$19$	0.930935	+	0.249443i	0.213571	+	0.0572262i	0.364018	−	0.931392i	$-0.381405\pi$
$19$	0.930935	+	0.249443i	0.213571	+	0.0572262i	−0.150447	+	0.988618i	$0.548071\pi$
$20$	−4.53608	+	1.21544i	−1.01430	+	0.271780i
$21$	1.04247	−	2.43172i	0.227486	−	0.530644i
$22$	2.62798	−	4.55179i	0.560287	−	0.970445i
$23$			6.63818i			1.38416i	0.721822	+	0.692079i	$0.243305\pi$
$23$			6.63818i			1.38416i	−0.721822	+	0.692079i	$0.756695\pi$
$24$	0.803282	−	0.215239i	0.163969	−	0.0439354i
$25$	1.00500	−	0.580235i	0.200999	−	0.116047i
$26$	−6.97103	−	2.92587i	−1.36713	−	0.573810i
$27$			1.00000i			0.192450i
$28$	6.29629	−	0.750265i	1.18989	−	0.141787i
$29$	−5.21743	−	9.03685i	−0.968852	−	1.67810i	−0.698888	−	0.715232i	$-0.746321\pi$
$29$	−5.21743	−	9.03685i	−0.968852	−	1.67810i	−0.269965	−	0.962870i	$-0.587012\pi$
$30$	3.55819	−	2.05432i	0.649633	−	0.375066i
$31$	−2.92062	−	0.782577i	−0.524558	−	0.140555i	−0.0131839	−	0.999913i	$-0.504197\pi$
$31$	−2.92062	−	0.782577i	−0.524558	−	0.140555i	−0.511374	+	0.859358i	$0.670863\pi$
$32$	−5.69745	−	5.69745i	−1.00718	−	1.00718i
$33$	−0.648767	+	2.42123i	−0.112936	+	0.421482i
$34$	−10.8544	−	10.8544i	−1.86152	−	1.86152i
$35$	4.81368	−	1.92488i	0.813661	−	0.325364i
$36$	−2.07553	+	1.19831i	−0.345921	+	0.199718i
$37$	−0.974084	+	0.974084i	−0.160138	+	0.160138i	−0.782628	−	0.622490i	$-0.786121\pi$
$37$	−0.974084	+	0.974084i	−0.160138	+	0.160138i	0.622490	+	0.782628i	$0.286121\pi$
$38$	−1.01043	−	1.75011i	−0.163913	−	0.283905i
$39$	3.57246	+	0.487377i	0.572051	+	0.0780428i
$40$	1.41122	+	0.814767i	0.223133	+	0.128826i
$41$	0.710011	+	0.190247i	0.110885	+	0.0297116i	0.313835	−	0.949478i	$-0.398386\pi$
$41$	0.710011	+	0.190247i	0.110885	+	0.0297116i	−0.202950	+	0.979189i	$0.565053\pi$
$42$	−5.15107	+	2.05979i	−0.794828	+	0.317833i
$43$	10.1261	+	5.84633i	1.54422	+	0.891556i	0.998565	+	0.0535470i	$0.0170527\pi$
$43$	10.1261	+	5.84633i	1.54422	+	0.891556i	0.545656	+	0.838009i	$0.316281\pi$
$44$	−5.80275	+	1.55484i	−0.874798	+	0.234401i
$45$	−1.38556	+	1.38556i	−0.206546	+	0.206546i
$46$	9.84223	−	9.84223i	1.45116	−	1.45116i
$47$	−3.62699	+	0.971849i	−0.529051	+	0.141759i	−0.513450	−	0.858120i	$-0.671633\pi$
$47$	−3.62699	+	0.971849i	−0.529051	+	0.141759i	−0.0156008	+	0.999878i	$0.504966\pi$
$48$	2.64092	+	1.52474i	0.381185	+	0.220077i
$49$	−6.80400	+	1.64488i	−0.972000	+	0.234983i
$50$	−2.35037	−	0.629781i	−0.332393	−	0.0890645i
$51$	6.34007	+	3.66044i	0.887787	+	0.512564i
$52$	3.26933	+	7.99876i	0.453375	+	1.10923i
$53$	−1.15862	−	2.00679i	−0.159149	−	0.275654i	0.775413	−	0.631454i	$-0.217542\pi$
$53$	−1.15862	−	2.00679i	−0.159149	−	0.275654i	−0.934562	+	0.355800i	$0.884208\pi$
$54$	1.48267	−	1.48267i	0.201766	−	0.201766i
$55$	−4.25365	+	2.45585i	−0.573563	+	0.331147i
$56$	−1.72898	−	1.36080i	−0.231044	−	0.181844i
$57$	0.681492	+	0.681492i	0.0902658	+	0.0902658i
$58$	−5.66294	+	21.1344i	−0.743580	+	2.77508i
$59$	−3.35900	−	3.35900i	−0.437305	−	0.437305i	0.453799	−	0.891104i	$-0.350068\pi$
$59$	−3.35900	−	3.35900i	−0.437305	−	0.437305i	−0.891104	+	0.453799i	$0.850068\pi$
$60$	−4.53608	−	1.21544i	−0.585605	−	0.156912i
$61$	−8.18748	+	4.72704i	−1.04830	+	0.605236i	−0.922173	−	0.386778i	$-0.873588\pi$
$61$	−8.18748	+	4.72704i	−1.04830	+	0.605236i	−0.126126	+	0.992014i	$0.540254\pi$
$62$	3.17000	+	5.49061i	0.402591	+	0.697308i
$63$	2.11867	−	1.58469i	0.266927	−	0.199653i
$64$			10.7959i			1.34949i
$65$	4.27455	+	5.62513i	0.530193	+	0.697711i
$66$	4.55179	−	2.62798i	0.560287	−	0.323482i
$67$	−6.06032	+	1.62386i	−0.740386	+	0.198386i	−0.609249	−	0.792979i	$-0.708529\pi$
$67$	−6.06032	+	1.62386i	−0.740386	+	0.198386i	−0.131136	+	0.991364i	$0.541863\pi$
$68$			17.5453i			2.12768i
$69$	−3.31909	+	5.74884i	−0.399572	+	0.692079i
$70$	−9.99105	−	4.28314i	−1.19416	−	0.511933i
$71$	8.32895	−	2.23174i	0.988465	−	0.264858i	0.271859	−	0.962337i	$-0.412361\pi$
$71$	8.32895	−	2.23174i	0.988465	−	0.264858i	0.716606	+	0.697479i	$0.245695\pi$
$72$	0.803282	+	0.215239i	0.0946677	+	0.0253661i
$73$	2.01139	−	7.50661i	0.235415	−	0.878583i	−0.742546	−	0.669795i	$-0.766382\pi$
$73$	2.01139	−	7.50661i	0.235415	−	0.878583i	0.977961	−	0.208787i	$-0.0669516\pi$
$74$	2.88849			0.335780
$75$	1.16047			0.134000
$76$	−0.597819	+	2.23109i	−0.0685745	+	0.255923i
$77$	6.15788	−	2.46239i	0.701755	−	0.280615i
$78$	−4.57415	−	6.01939i	−0.517921	−	0.681562i
$79$	−2.31642	+	4.01217i	−0.260618	+	0.451404i	−0.966406	−	0.257019i	$-0.917260\pi$
$79$	−2.31642	+	4.01217i	−0.260618	+	0.451404i	0.705788	+	0.708423i	$0.250593\pi$
$80$	1.54654	+	5.77176i	0.172908	+	0.645302i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.770638	−	1.33478i	−0.0851028	−	0.147402i
$83$	−10.1090	+	10.1090i	−1.10961	+	1.10961i	−0.116405	+	0.993202i	$0.537137\pi$
$83$	−10.1090	+	10.1090i	−1.10961	+	1.10961i	−0.993202	+	0.116405i	$0.962863\pi$
$84$	5.82788	+	2.49840i	0.635874	+	0.272598i
$85$	3.71277	+	13.8563i	0.402707	+	1.50292i
$86$	−6.34554	−	23.6819i	−0.684257	−	2.55368i
$87$		−	10.4349i		−	1.11873i
$88$	1.80529	+	1.04229i	0.192445	+	0.111108i
$89$	−2.89859	−	2.89859i	−0.307250	−	0.307250i	0.536592	−	0.843842i	$-0.319711\pi$
$89$	−2.89859	−	2.89859i	−0.307250	−	0.307250i	−0.843842	+	0.536592i	$0.819711\pi$
$90$	4.10864			0.433089
$91$	−4.62866	−	8.34119i	−0.485216	−	0.874394i
$92$	−15.9091			−1.65864
$93$	−2.13804	−	2.13804i	−0.221704	−	0.221704i
$94$	6.81855	+	3.93669i	0.703280	+	0.406039i
$95$			1.88849i			0.193755i
$96$	−2.08541	−	7.78286i	−0.212841	−	0.794335i
$97$	−2.63968	−	9.85141i	−0.268019	−	1.00026i	−0.960377	−	0.278705i	$-0.910095\pi$
$97$	−2.63968	−	9.85141i	−0.268019	−	1.00026i	0.692358	−	0.721554i	$-0.256572\pi$
$98$	12.5269	+	7.64926i	1.26541	+	0.772692i
$99$	−1.77246	+	1.77246i	−0.178139	+	0.178139i
$100$	1.39060	+	2.40859i	0.139060	+	0.240859i
$101$	−1.90282	+	3.29578i	−0.189337	+	0.327942i	−0.945030	−	0.326985i	$-0.893967\pi$
$101$	−1.90282	+	3.29578i	−0.189337	+	0.327942i	0.755692	+	0.654927i	$0.227301\pi$
$102$	−3.97300	−	14.8274i	−0.393386	−	1.46814i
$103$	−4.75097	+	8.22892i	−0.468127	+	0.810819i	−0.999337	−	0.0364211i	$-0.988404\pi$
$103$	−4.75097	+	8.22892i	−0.468127	+	0.810819i	0.531210	+	0.847240i	$0.321738\pi$
$104$	1.16043	−	2.76479i	0.113790	−	0.271110i
$105$	5.13121	+	0.739848i	0.500755	+	0.0722018i
$106$	−1.25755	+	4.69325i	−0.122144	+	0.455849i
$107$	−9.75503			−0.943055			−0.471527	−	0.881851i	$-0.656297\pi$
$107$	−9.75503			−0.943055			−0.471527	+	0.881851i	$0.656297\pi$
$108$	−2.39661			−0.230614
$109$	1.54206	−	5.75506i	0.147703	−	0.551235i	−0.851917	−	0.523676i	$-0.824560\pi$
$109$	1.54206	−	5.75506i	0.147703	−	0.551235i	0.999620	−	0.0275585i	$-0.00877324\pi$
$110$	9.94797	+	2.66555i	0.948501	+	0.254150i
$111$	−1.33062	+	0.356539i	−0.126297	+	0.0338412i
$112$	−0.954645	−	8.01148i	−0.0902055	−	0.757014i
$113$	5.65861	−	9.80099i	0.532317	−	0.922000i	−0.466971	−	0.884273i	$-0.654655\pi$
$113$	5.65861	−	9.80099i	0.532317	−	0.922000i	0.999288	−	0.0377273i	$-0.0120118\pi$
$114$		−	2.02085i		−	0.189270i
$115$	−12.5641	+	3.36655i	−1.17161	+	0.313932i
$116$	21.6578	−	12.5042i	2.01088	−	1.16098i
$117$	2.85015	+	2.20831i	0.263497	+	0.204158i
$118$			9.96057i			0.916945i
$119$	−2.29182	−	19.2332i	−0.210091	−	1.76310i
$120$	0.814767	+	1.41122i	0.0743777	+	0.128826i
$121$	4.08482	−	2.35837i	0.371347	−	0.214397i
$122$	19.1479	+	5.13068i	1.73357	+	0.464510i
$123$	0.519764	+	0.519764i	0.0468656	+	0.0468656i
$124$	1.87553	−	6.99958i	0.168428	−	0.628581i
$125$	8.53568	+	8.53568i	0.763454	+	0.763454i
$126$	−5.49085	−	0.791703i	−0.489164	−	0.0705305i
$127$	9.81199	−	5.66496i	0.870673	−	0.502684i	0.00310144	−	0.999995i	$-0.499013\pi$
$127$	9.81199	−	5.66496i	0.870673	−	0.502684i	0.867572	+	0.497312i	$0.165679\pi$
$128$	4.61185	−	4.61185i	0.407634	−	0.407634i
$129$	5.84633	+	10.1261i	0.514740	+	0.891556i
$130$	2.00246	−	14.6779i	0.175627	−	1.28734i
$131$	−12.3925	−	7.15480i	−1.08274	−	0.625118i	−0.151102	−	0.988518i	$-0.548282\pi$
$131$	−12.3925	−	7.15480i	−1.08274	−	0.625118i	−0.931633	+	0.363401i	$0.881616\pi$
$132$	−5.80275	−	1.55484i	−0.505065	−	0.135332i
$133$	0.363897	−	2.52381i	0.0315539	−	0.218842i
$134$	11.3931	+	6.57780i	0.984213	+	0.568235i
$135$	−1.89270	+	0.507149i	−0.162898	+	0.0436484i
$136$	4.30500	−	4.30500i	0.369150	−	0.369150i
$137$	−4.02745	+	4.02745i	−0.344089	+	0.344089i	−0.857902	−	0.513813i	$-0.828232\pi$
$137$	−4.02745	+	4.02745i	−0.344089	+	0.344089i	0.513813	+	0.857902i	$0.328232\pi$
$138$	13.4447	−	3.60251i	1.14449	−	0.306666i
$139$	9.38055	+	5.41586i	0.795648	+	0.459368i	0.841947	−	0.539560i	$-0.181409\pi$
$139$	9.38055	+	5.41586i	0.795648	+	0.459368i	−0.0462992	+	0.998928i	$0.514743\pi$
$140$	4.61319	+	11.5365i	0.389885	+	0.975015i
$141$	−3.62699	−	0.971849i	−0.305448	−	0.0818444i
$142$	−15.6580	−	9.04015i	−1.31399	−	0.758633i
$143$	5.46820	+	7.19592i	0.457274	+	0.601753i
$144$	1.52474	+	2.64092i	0.127062	+	0.220077i
$145$	14.4581	−	14.4581i	1.20068	−	1.20068i
$146$	−14.1120	+	8.14759i	−1.16792	+	0.674300i
$147$	−6.71487	−	1.97749i	−0.553833	−	0.163101i
$148$	−2.33450	−	2.33450i	−0.191895	−	0.191895i
$149$	2.30894	−	8.61708i	0.189156	−	0.705939i	−0.804547	−	0.593889i	$-0.797592\pi$
$149$	2.30894	−	8.61708i	0.189156	−	0.705939i	0.993703	−	0.112050i	$-0.0357416\pi$
$150$	−1.72059	−	1.72059i	−0.140486	−	0.140486i
$151$	−12.4233	−	3.32882i	−1.01100	−	0.270896i	−0.284951	−	0.958542i	$-0.591977\pi$
$151$	−12.4233	−	3.32882i	−1.01100	−	0.270896i	−0.726046	+	0.687647i	$0.758644\pi$
$152$	0.694113	−	0.400747i	0.0563000	−	0.0325048i
$153$	3.66044	+	6.34007i	0.295929	+	0.512564i
$154$	−12.7810	−	5.47918i	−1.02992	−	0.441525i
$155$		−	5.92474i		−	0.475887i
$156$	−1.16805	+	8.56180i	−0.0935192	+	0.685492i
$157$	−3.95550	+	2.28371i	−0.315683	+	0.182260i	−0.649467	−	0.760390i	$-0.725008\pi$
$157$	−3.95550	+	2.28371i	−0.315683	+	0.182260i	0.333784	+	0.942650i	$0.391675\pi$
$158$	9.38320	−	2.51422i	0.746487	−	0.200021i
$159$		−	2.31724i		−	0.183769i
$160$	7.89413	−	13.6730i	0.624086	−	1.08095i
$161$	17.4396	−	2.07810i	1.37443	−	0.163777i
$162$	2.02536	−	0.542694i	0.159128	−	0.0426381i
$163$	2.47798	+	0.663973i	0.194091	+	0.0520064i	0.354555	−	0.935035i	$-0.384632\pi$
$163$	2.47798	+	0.663973i	0.194091	+	0.0520064i	−0.160464	+	0.987042i	$0.551299\pi$
$164$	−0.455948	+	1.70162i	−0.0356036	+	0.132874i
$165$	−4.91170			−0.382375
$166$	29.9766			2.32664
$167$	1.90396	−	7.10569i	0.147333	−	0.549855i	−0.852307	−	0.523041i	$-0.824797\pi$
$167$	1.90396	−	7.10569i	0.147333	−	0.549855i	0.999640	−	0.0268134i	$-0.00853598\pi$
$168$	−0.816937	−	2.04297i	−0.0630281	−	0.157619i
$169$	9.27820	−	9.10577i	0.713708	−	0.700444i
$170$	15.0394	−	26.0491i	1.15347	−	1.99787i
$171$	0.249443	+	0.930935i	0.0190754	+	0.0711904i
$172$	−14.0114	+	24.2684i	−1.06836	+	1.85045i
$173$	−9.17077	−	15.8842i	−0.697241	−	1.20766i	−0.969419	−	0.245410i	$-0.921077\pi$
$173$	−9.17077	−	15.8842i	−0.697241	−	1.20766i	0.272178	−	0.962247i	$-0.412256\pi$
$174$	−15.4714	+	15.4714i	−1.17289	+	1.17289i
$175$	−1.83899	−	2.45865i	−0.139015	−	0.185856i
$176$	1.97840	+	7.38349i	0.149127	+	0.556551i
$177$	−1.22948	−	4.58848i	−0.0924134	−	0.344891i
$178$			8.59529i			0.644244i
$179$	−1.65369	−	0.954758i	−0.123603	−	0.0713620i	0.436924	−	0.899498i	$-0.356068\pi$
$179$	−1.65369	−	0.954758i	−0.123603	−	0.0713620i	−0.560527	+	0.828136i	$0.689401\pi$
$180$	−3.32064	−	3.32064i	−0.247506	−	0.247506i
$181$	−18.9344			−1.40738			−0.703691	−	0.710506i	$-0.748466\pi$
$181$	−18.9344			−1.40738			−0.703691	+	0.710506i	$0.748466\pi$
$182$	−5.50445	+	19.2300i	−0.408017	+	1.42542i
$183$	−9.45408			−0.698866
$184$	3.90354	+	3.90354i	0.287773	+	0.287773i
$185$	−2.33766	−	1.34965i	−0.171868	−	0.0992281i
$186$			6.34001i			0.464872i
$187$	4.74955	+	17.7255i	0.347321	+	1.29622i
$188$	−2.32914	−	8.69248i	−0.169870	−	0.633965i
$189$	2.62717	−	0.313052i	0.191098	−	0.0227712i
$190$	2.80000	−	2.80000i	0.203134	−	0.203134i
$191$	−5.39449	−	9.34352i	−0.390331	−	0.676074i	0.602162	−	0.798374i	$-0.294306\pi$
$191$	−5.39449	−	9.34352i	−0.390331	−	0.676074i	−0.992493	+	0.122300i	$0.960973\pi$
$192$	−5.39795	+	9.34953i	−0.389564	+	0.674744i
$193$	5.08690	+	18.9846i	0.366163	+	1.36654i	0.865837	+	0.500326i	$0.166786\pi$
$193$	5.08690	+	18.9846i	0.366163	+	1.36654i	−0.499674	+	0.866213i	$0.666547\pi$
$194$	−10.6926	+	18.5201i	−0.767685	+	1.32967i
$195$	0.889307	+	7.00878i	0.0636846	+	0.501909i
$196$	−3.94214	−	16.3065i	−0.281581	−	1.16475i
$197$	−2.96842	+	11.0783i	−0.211491	+	0.789295i	0.775881	+	0.630879i	$0.217306\pi$
$197$	−2.96842	+	11.0783i	−0.211491	+	0.789295i	−0.987372	+	0.158417i	$0.949361\pi$
$198$	5.25595			0.373524
$199$	−5.55472			−0.393764			−0.196882	−	0.980427i	$-0.563082\pi$
$199$	−5.55472			−0.393764			−0.196882	+	0.980427i	$0.563082\pi$
$200$	0.249778	−	0.932185i	0.0176620	−	0.0659155i
$201$	−6.06032	−	1.62386i	−0.427462	−	0.114538i
$202$	7.70779	−	2.06530i	0.542318	−	0.145314i
$203$	−22.1080	+	16.5361i	−1.55168	+	1.16060i
$204$	−8.77265	+	15.1947i	−0.614209	+	1.06384i
$205$			1.44032i			0.100597i
$206$	19.2449	−	5.15665i	1.34085	−	0.359281i
$207$	−5.74884	+	3.31909i	−0.399572	+	0.230693i
$208$	10.1777	−	4.15994i	0.705698	−	0.288440i
$209$			2.41584i			0.167107i
$210$	−6.51094	−	8.70483i	−0.449297	−	0.600691i
$211$	−8.06339	−	13.9662i	−0.555106	−	0.961473i	−0.997895	−	0.0648467i	$-0.979344\pi$
$211$	−8.06339	−	13.9662i	−0.555106	−	0.961473i	0.442789	−	0.896626i	$-0.353989\pi$
$212$	4.80949	−	2.77676i	0.330317	−	0.190709i
$213$	8.32895	+	2.23174i	0.570690	+	0.152916i
$214$	14.4635	+	14.4635i	0.988703	+	0.988703i
$215$	−5.92991	+	22.1307i	−0.404417	+	1.50930i
$216$	0.588043	+	0.588043i	0.0400113	+	0.0400113i
$217$	−1.14165	+	7.91793i	−0.0775004	+	0.537504i
$218$	−10.8192	+	6.24648i	−0.732770	+	0.423065i
$219$	5.49522	−	5.49522i	0.371333	−	0.371333i
$220$	−5.88571	−	10.1944i	−0.396815	−	0.687303i
$221$	24.4337	−	9.98677i	1.64359	−	0.671783i
$222$	2.50150	+	1.44424i	0.167890	+	0.0969313i
$223$	25.6580	+	6.87505i	1.71819	+	0.460387i	0.977408	−	0.211359i	$-0.0677890\pi$
$223$	25.6580	+	6.87505i	1.71819	+	0.460387i	0.740781	+	0.671747i	$0.234456\pi$
$224$	−13.1845	+	16.7517i	−0.880929	+	1.11927i
$225$	1.00500	+	0.580235i	0.0669998	+	0.0386824i
$226$	−22.9215	+	6.14179i	−1.52471	+	0.408546i
$227$	1.25693	−	1.25693i	0.0834252	−	0.0834252i	−0.664163	−	0.747588i	$-0.731212\pi$
$227$	1.25693	−	1.25693i	0.0834252	−	0.0834252i	0.747588	+	0.664163i	$0.231212\pi$
$228$	−1.63327	+	1.63327i	−0.108166	+	0.108166i
$229$	−8.68390	+	2.32685i	−0.573849	+	0.153762i	−0.534061	−	0.845446i	$-0.679335\pi$
$229$	−8.68390	+	2.32685i	−0.573849	+	0.153762i	−0.0397875	+	0.999208i	$0.512668\pi$
$230$	23.6199	+	13.6370i	1.55745	+	0.899194i
$231$	6.56407	+	0.946446i	0.431884	+	0.0622716i
$232$	−8.38214	−	2.24599i	−0.550314	−	0.147456i
$233$	0.891738	+	0.514845i	0.0584197	+	0.0337286i	0.528925	−	0.848668i	$-0.322595\pi$
$233$	0.891738	+	0.514845i	0.0584197	+	0.0337286i	−0.470506	+	0.882397i	$0.655928\pi$
$234$	−0.951638	−	7.50002i	−0.0622105	−	0.490292i
$235$	−3.67884	−	6.37195i	−0.239981	−	0.415660i
$236$	8.05022	−	8.05022i	0.524025	−	0.524025i
$237$	−4.01217	+	2.31642i	−0.260618	+	0.150468i
$238$	−25.1184	+	31.9144i	−1.62818	+	2.06870i
$239$	−13.2347	−	13.2347i	−0.856079	−	0.856079i	0.134795	−	0.990874i	$-0.456962\pi$
$239$	−13.2347	−	13.2347i	−0.856079	−	0.856079i	−0.990874	+	0.134795i	$0.956962\pi$
$240$	−1.54654	+	5.77176i	−0.0998286	+	0.372565i
$241$	2.07666	+	2.07666i	0.133769	+	0.133769i	0.770821	−	0.637052i	$-0.219846\pi$
$241$	2.07666	+	2.07666i	0.133769	+	0.133769i	−0.637052	+	0.770821i	$0.719846\pi$
$242$	−9.55311	−	2.55975i	−0.614097	−	0.164547i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−11.3289	−	19.6222i	−0.725257	−	1.25618i
$245$	−6.56391	−	12.0438i	−0.419353	−	0.769447i
$246$		−	1.54128i		−	0.0982682i
$247$	3.44730	−	0.437409i	0.219346	−	0.0278317i
$248$	−2.17764	+	1.25726i	−0.138280	+	0.0798361i
$249$	−13.8092	+	3.70015i	−0.875120	+	0.234488i
$250$		−	25.3112i		−	1.60082i
$251$	0.244838	−	0.424072i	0.0154540	−	0.0267672i	−0.858195	−	0.513324i	$-0.828414\pi$
$251$	0.244838	−	0.424072i	0.0154540	−	0.0267672i	0.873649	+	0.486557i	$0.161747\pi$
$252$	3.79790	+	5.07762i	0.239245	+	0.319860i
$253$	−16.0726	+	4.30664i	−1.01047	+	0.270756i
$254$	−22.9472	−	6.14868i	−1.43983	−	0.385802i
$255$	−3.71277	+	13.8563i	−0.232503	+	0.867713i
$256$	7.91613			0.494758
$257$	18.7117			1.16720			0.583602	−	0.812040i	$-0.301643\pi$
$257$	18.7117			1.16720			0.583602	+	0.812040i	$0.301643\pi$
$258$	6.34554	−	23.6819i	0.395056	−	1.47437i
$259$	2.86402	+	2.25414i	0.177961	+	0.140065i
$260$	−13.4812	+	10.2444i	−0.836072	+	0.635333i
$261$	5.21743	−	9.03685i	0.322951	−	0.559367i
$262$	7.76574	+	28.9821i	0.479769	+	1.79052i
$263$	1.72119	−	2.98119i	0.106133	−	0.183828i	−0.808067	−	0.589090i	$-0.799486\pi$
$263$	1.72119	−	2.98119i	0.106133	−	0.183828i	0.914201	+	0.405262i	$0.132820\pi$
$264$	1.04229	+	1.80529i	0.0641483	+	0.111108i
$265$	3.21067	−	3.21067i	0.197230	−	0.197230i
$266$	−4.28151	+	3.20243i	−0.262516	+	0.196354i
$267$	−1.06096	−	3.95954i	−0.0649295	−	0.242320i
$268$	−3.89176	−	14.5242i	−0.237727	−	0.887208i
$269$			9.04672i			0.551588i	0.961217	+	0.275794i	$0.0889408\pi$
$269$			9.04672i			0.551588i	−0.961217	+	0.275794i	$0.911059\pi$
$270$	3.55819	+	2.05432i	0.216544	+	0.125022i
$271$	−5.53295	−	5.53295i	−0.336103	−	0.336103i	0.518796	−	0.854898i	$-0.326381\pi$
$271$	−5.53295	−	5.53295i	−0.336103	−	0.336103i	−0.854898	+	0.518796i	$0.826381\pi$
$272$	22.3249			1.35364
$273$	0.162054	−	9.53802i	0.00980797	−	0.577267i
$274$	11.9428			0.721488
$275$	2.05689	+	2.05689i	0.124035	+	0.124035i
$276$	−13.7777	−	7.95457i	−0.829322	−	0.478809i
$277$			1.54911i			0.0930772i	0.998916	+	0.0465386i	$0.0148190\pi$
$277$			1.54911i			0.0930772i	−0.998916	+	0.0465386i	$0.985181\pi$
$278$	−5.87832	−	21.9382i	−0.352558	−	1.31576i
$279$	−0.782577	−	2.92062i	−0.0468516	−	0.174853i
$280$	1.69874	−	3.96257i	0.101519	−	0.236809i
$281$	4.20181	−	4.20181i	0.250659	−	0.250659i	−0.570582	−	0.821241i	$-0.693282\pi$
$281$	4.20181	−	4.20181i	0.250659	−	0.250659i	0.821241	+	0.570582i	$0.193282\pi$
$282$	3.93669	+	6.81855i	0.234427	+	0.406039i
$283$	−2.32807	+	4.03233i	−0.138389	+	0.239697i	−0.926887	−	0.375340i	$-0.877526\pi$
$283$	−2.32807	+	4.03233i	−0.138389	+	0.239697i	0.788498	+	0.615038i	$0.210859\pi$
$284$	5.34860	+	19.9613i	0.317381	+	1.18448i
$285$	−0.944245	+	1.63548i	−0.0559322	+	0.0968775i
$286$	2.56163	−	18.7767i	0.151473	−	1.11029i
$287$	0.277540	−	1.92487i	0.0163826	−	0.113622i
$288$	2.08541	−	7.78286i	0.122884	−	0.458609i
$289$	36.5953			2.15266
$290$	−42.8731			−2.51759
$291$	2.63968	−	9.85141i	0.154741	−	0.577500i
$292$	17.9904	+	4.82052i	1.05281	+	0.282100i
$293$	10.8009	−	2.89410i	0.630997	−	0.169075i	0.0708751	−	0.997485i	$-0.477421\pi$
$293$	10.8009	−	2.89410i	0.630997	−	0.169075i	0.560122	+	0.828410i	$0.310754\pi$
$294$	7.02397	+	12.8879i	0.409646	+	0.751637i
$295$	4.65408	−	8.06111i	0.270971	−	0.469336i
$296$			1.14561i			0.0665871i
$297$	−2.42123	+	0.648767i	−0.140494	+	0.0376453i
$298$	−16.1997	+	9.35289i	−0.938422	+	0.541798i
$299$	9.05547	+	22.1551i	0.523691	+	1.28126i
$300$			2.78120i			0.160573i
$301$	12.1893	−	28.4332i	0.702577	−	1.63886i
$302$	13.4841	+	23.3552i	0.775925	+	1.34394i
$303$	−3.29578	+	1.90282i	−0.189337	+	0.109314i
$304$	2.83886	+	0.760671i	0.162820	+	0.0436275i
$305$	−13.0992	−	13.0992i	−0.750056	−	0.750056i
$306$	3.97300	−	14.8274i	0.227121	−	0.847628i
$307$	2.63969	+	2.63969i	0.150655	+	0.150655i	0.778411	−	0.627756i	$-0.216026\pi$
$307$	2.63969	+	2.63969i	0.150655	+	0.150655i	−0.627756	+	0.778411i	$0.716026\pi$
$308$	5.90139	+	14.7580i	0.336263	+	0.840917i
$309$	−8.22892	+	4.75097i	−0.468127	+	0.270273i
$310$	−8.78443	+	8.78443i	−0.498922	+	0.498922i
$311$	−16.2833	−	28.2035i	−0.923341	−	1.59927i	−0.794208	−	0.607646i	$-0.792114\pi$
$311$	−16.2833	−	28.2035i	−0.923341	−	1.59927i	−0.129133	−	0.991627i	$-0.541220\pi$
$312$	2.38736	−	1.81416i	0.135158	−	0.102707i
$313$	−12.7123	−	7.33945i	−0.718541	−	0.414850i	0.0956743	−	0.995413i	$-0.469499\pi$
$313$	−12.7123	−	7.33945i	−0.718541	−	0.414850i	−0.814216	+	0.580563i	$0.802833\pi$
$314$	9.25067	+	2.47871i	0.522046	+	0.139882i
$315$	4.07384	+	3.20633i	0.229535	+	0.180656i
$316$	−9.61560	−	5.55157i	−0.540920	−	0.312300i
$317$	9.92063	−	2.65822i	0.557198	−	0.149301i	0.0307793	−	0.999526i	$-0.490201\pi$
$317$	9.92063	−	2.65822i	0.557198	−	0.149301i	0.526419	+	0.850225i	$0.323534\pi$
$318$	−3.43570	+	3.43570i	−0.192664	+	0.192664i
$319$	18.4954	−	18.4954i	1.03554	−	1.03554i
$320$	−20.4335	+	5.47513i	−1.14226	+	0.306069i
$321$	−8.44811	−	4.87752i	−0.471527	−	0.272236i
$322$	−28.9383	−	22.7760i	−1.61267	−	1.26926i
$323$	6.81526	+	1.82614i	0.379211	+	0.101609i
$324$	−2.07553	−	1.19831i	−0.115307	−	0.0665725i
$325$	2.56268	−	3.30752i	0.142152	−	0.183468i
$326$	−2.68957	−	4.65848i	−0.148962	−	0.258009i
$327$	4.21300	−	4.21300i	0.232979	−	0.232979i
$328$	0.529391	−	0.305644i	0.0292307	−	0.0168764i
$329$	3.68864	+	9.22446i	0.203362	+	0.508561i
$330$	7.28242	+	7.28242i	0.400884	+	0.400884i
$331$	−6.55085	+	24.4481i	−0.360068	+	1.34379i	0.513918	+	0.857839i	$0.328193\pi$
$331$	−6.55085	+	24.4481i	−0.360068	+	1.34379i	−0.873986	+	0.485951i	$0.838473\pi$
$332$	−24.2274	−	24.2274i	−1.32965	−	1.32965i
$333$	−1.33062	−	0.356539i	−0.0729177	−	0.0195382i
$334$	−13.3583	+	7.71243i	−0.730935	+	0.422006i
$335$	−6.14696	−	10.6469i	−0.335845	−	0.581700i
$336$	3.17899	−	7.41547i	0.173428	−	0.404547i
$337$			0.741618i			0.0403985i	0.999796	+	0.0201993i	$0.00643006\pi$
$337$			0.741618i			0.0403985i	−0.999796	+	0.0201993i	$0.993570\pi$
$338$	−27.2573	−	0.255654i	−1.48260	−	0.0139058i
$339$	9.80099	−	5.65861i	0.532317	−	0.307333i
$340$	−33.2081	+	8.89808i	−1.80096	+	0.482566i
$341$		−	7.57920i		−	0.410436i
$342$	1.01043	−	1.75011i	0.0546376	−	0.0946351i
$343$	6.45138	+	17.3603i	0.348342	+	0.937368i
$344$	9.39250	−	2.51671i	0.506410	−	0.135692i
$345$	−12.5641	−	3.36655i	−0.676430	−	0.181249i
$346$	−9.95385	+	37.1483i	−0.535122	+	1.99710i
$347$	34.1772			1.83473			0.917364	−	0.398048i	$-0.130312\pi$
$347$	34.1772			1.83473			0.917364	+	0.398048i	$0.130312\pi$
$348$	25.0083			1.34059
$349$	7.26033	−	27.0959i	0.388636	−	1.45041i	−0.443718	−	0.896167i	$-0.646341\pi$
$349$	7.26033	−	27.0959i	0.388636	−	1.45041i	0.832354	−	0.554244i	$-0.186993\pi$
$350$	−0.918749	+	6.37198i	−0.0491092	+	0.340596i
$351$	1.36415	+	3.33753i	0.0728129	+	0.178144i
$352$	10.0985	−	17.4912i	0.538253	−	0.932282i
$353$	−2.49904	−	9.32655i	−0.133011	−	0.496402i	0.866988	−	0.498330i	$-0.166053\pi$
$353$	−2.49904	−	9.32655i	−0.133011	−	0.496402i	−0.999998	+	0.00192769i	$0.999386\pi$
$354$	−4.98029	+	8.62611i	−0.264699	+	0.458472i
$355$	8.44803	+	14.6324i	0.448375	+	0.776608i
$356$	6.94679	−	6.94679i	0.368179	−	0.368179i
$357$	7.63181	−	17.8023i	0.403918	−	0.942199i
$358$	1.03628	+	3.86746i	0.0547693	+	0.204402i
$359$	8.84959	+	33.0271i	0.467064	+	1.74311i	0.649955	+	0.759973i	$0.274788\pi$
$359$	8.84959	+	33.0271i	0.467064	+	1.74311i	−0.182891	+	0.983133i	$0.558546\pi$
$360$			1.62953i			0.0858840i
$361$	−15.6501	−	9.03557i	−0.823688	−	0.475556i
$362$	28.0734	+	28.0734i	1.47551	+	1.47551i
$363$	4.71674			0.247565
$364$	19.9906	−	11.0931i	1.04779	−	0.581437i
$365$	15.2279			0.797063
$366$	14.0173	+	14.0173i	0.732695	+	0.732695i
$367$	−23.1967	−	13.3926i	−1.21086	−	0.699090i	−0.247913	−	0.968782i	$-0.579745\pi$
$367$	−23.1967	−	13.3926i	−1.21086	−	0.699090i	−0.962947	+	0.269692i	$0.913078\pi$
$368$			20.2430i			1.05524i
$369$	0.190247	+	0.710011i	0.00990386	+	0.0369617i
$370$	1.46489	+	5.46705i	0.0761561	+	0.284218i
$371$	−4.90946	+	3.67212i	−0.254886	+	0.190647i
$372$	5.12405	−	5.12405i	0.265670	−	0.265670i
$373$	−1.83233	−	3.17370i	−0.0948747	−	0.164328i	0.814682	−	0.579908i	$-0.196912\pi$
$373$	−1.83233	−	3.17370i	−0.0948747	−	0.164328i	−0.909556	+	0.415581i	$0.863578\pi$
$374$	19.2391	−	33.3231i	0.994831	−	1.72310i
$375$	3.12427	+	11.6599i	0.161337	+	0.602117i
$376$	−1.56134	+	2.70432i	−0.0805198	+	0.139464i
$377$	−29.7409	−	23.0434i	−1.53174	−	1.18680i
$378$	−4.35937	−	3.43106i	−0.224222	−	0.176475i
$379$	−6.16351	+	23.0025i	−0.316598	+	1.18156i	0.605894	+	0.795545i	$0.292816\pi$
$379$	−6.16351	+	23.0025i	−0.316598	+	1.18156i	−0.922492	+	0.386016i	$0.873851\pi$
$380$	−4.52597			−0.232178
$381$	11.3299			0.580449
$382$	−5.85511	+	21.8516i	−0.299574	+	1.11802i
$383$	−29.5578	−	7.91998i	−1.51033	−	0.404692i	−0.593786	−	0.804623i	$-0.702368\pi$
$383$	−29.5578	−	7.91998i	−1.51033	−	0.404692i	−0.916545	+	0.399931i	$0.869034\pi$
$384$	6.29990	−	1.68805i	0.321490	−	0.0861431i
$385$	7.78354	+	10.4062i	0.396686	+	0.530351i
$386$	20.6056	−	35.6900i	1.04880	−	1.81657i
$387$			11.6927i			0.594371i
$388$	23.6100	−	6.32628i	1.19862	−	0.321168i
$389$	−1.02102	+	0.589484i	−0.0517676	+	0.0298880i	−0.525660	−	0.850694i	$-0.676182\pi$
$389$	−1.02102	+	0.589484i	−0.0517676	+	0.0298880i	0.473893	+	0.880583i	$0.342848\pi$
$390$	9.07315	−	11.7102i	0.459437	−	0.592971i
$391$			48.5974i			2.45767i
$392$	−3.03378	+	4.96831i	−0.153229	+	0.250937i
$393$	−7.15480	−	12.3925i	−0.360912	−	0.625118i
$394$	20.8266	−	12.0242i	1.04923	−	0.605773i
$395$	−8.76861	−	2.34954i	−0.441197	−	0.118218i
$396$	−4.24791	−	4.24791i	−0.213465	−	0.213465i
$397$	−3.14500	+	11.7373i	−0.157843	+	0.589078i	0.841002	+	0.541032i	$0.181966\pi$
$397$	−3.14500	+	11.7373i	−0.157843	+	0.589078i	−0.998845	+	0.0480464i	$0.984700\pi$
$398$	8.23581	+	8.23581i	0.412824	+	0.412824i
$399$	1.57705	−	2.00373i	0.0789512	−	0.100312i
$400$	3.06471	−	1.76941i	0.153236	−	0.0884707i
$401$	−1.52505	+	1.52505i	−0.0761573	+	0.0761573i	−0.744159	−	0.668002i	$-0.767150\pi$
$401$	−1.52505	+	1.52505i	−0.0761573	+	0.0761573i	0.668002	+	0.744159i	$0.267150\pi$
$402$	6.57780	+	11.3931i	0.328071	+	0.568235i
$403$	−10.8152	+	1.37228i	−0.538743	+	0.0683582i
$404$	−7.89869	−	4.56031i	−0.392975	−	0.226884i
$405$	−1.89270	−	0.507149i	−0.0940492	−	0.0252004i
$406$	57.2963	+	8.26131i	2.84357	+	0.410002i
$407$	−2.99044	−	1.72653i	−0.148230	−	0.0855809i
$408$	5.88073	−	1.57574i	0.291140	−	0.0780106i
$409$	−3.39607	+	3.39607i	−0.167925	+	0.167925i	−0.786067	−	0.618142i	$-0.787886\pi$
$409$	−3.39607	+	3.39607i	−0.167925	+	0.167925i	0.618142	+	0.786067i	$0.287886\pi$
$410$	2.13552	−	2.13552i	0.105466	−	0.105466i
$411$	−5.50160	+	1.47415i	−0.271374	+	0.0727145i
$412$	−19.7215	−	11.3862i	−0.971609	−	0.560959i
$413$	−7.77311	+	9.87620i	−0.382490	+	0.485976i
$414$	13.4447	+	3.60251i	0.660773	+	0.177053i
$415$	−24.2601	−	14.0066i	−1.19088	−	0.687556i
$416$	−26.7876	−	11.2432i	−1.31337	−	0.551245i
$417$	5.41586	+	9.38055i	0.265216	+	0.459368i
$418$	3.58189	−	3.58189i	0.175196	−	0.175196i
$419$	−18.2738	+	10.5504i	−0.892733	+	0.515420i	−0.874836	−	0.484420i	$-0.839031\pi$
$419$	−18.2738	+	10.5504i	−0.892733	+	0.515420i	−0.0178978	+	0.999840i	$0.505697\pi$
$420$	−1.77313	+	12.2975i	−0.0865198	+	0.600058i
$421$	24.4128	+	24.4128i	1.18981	+	1.18981i	0.977120	+	0.212688i	$0.0682218\pi$
$421$	24.4128	+	24.4128i	1.18981	+	1.18981i	0.212688	+	0.977120i	$0.431778\pi$
$422$	−8.75191	+	32.6626i	−0.426036	+	1.58999i
$423$	−2.65514	−	2.65514i	−0.129097	−	0.129097i
$424$	−1.86140	−	0.498760i	−0.0903975	−	0.0242219i
$425$	7.35746	−	4.24783i	0.356889	−	0.206050i
$426$	−9.04015	−	15.6580i	−0.437997	−	0.758633i
$427$	14.9818	+	20.0300i	0.725022	+	0.969322i
$428$		−	23.3790i		−	1.13007i
$429$	1.13764	+	8.96594i	0.0549258	+	0.432880i
$430$	41.6046	−	24.0204i	2.00635	−	1.15837i
$431$	−7.96117	+	2.13319i	−0.383476	+	0.102752i	−0.445407	−	0.895328i	$-0.646941\pi$
$431$	−7.96117	+	2.13319i	−0.383476	+	0.102752i	0.0619308	+	0.998080i	$0.480274\pi$
$432$			3.04948i			0.146718i
$433$	−13.2942	+	23.0262i	−0.638878	+	1.10657i	0.346801	+	0.937939i	$0.387268\pi$
$433$	−13.2942	+	23.0262i	−0.638878	+	1.10657i	−0.985679	+	0.168631i	$0.946065\pi$
$434$	13.4324	−	10.0470i	0.644774	−	0.482270i
$435$	19.7501	−	5.29202i	0.946945	−	0.253733i
$436$	13.7926	+	3.69573i	0.660548	+	0.176993i
$437$	−1.65585	+	6.17972i	−0.0792101	+	0.295616i
$438$	−16.2952			−0.778614
$439$	−17.8799			−0.853362			−0.426681	−	0.904402i	$-0.640317\pi$
$439$	−17.8799			−0.853362			−0.426681	+	0.904402i	$0.640317\pi$
$440$	−1.05719	+	3.94548i	−0.0503994	+	0.188093i
$441$	−4.82651	−	5.06999i	−0.229834	−	0.241428i
$442$	−51.0341	−	21.4199i	−2.42744	−	1.01884i
$443$	10.8928	−	18.8669i	0.517532	−	0.896392i	−0.482261	−	0.876028i	$-0.660184\pi$
$443$	10.8928	−	18.8669i	0.517532	−	0.896392i	0.999793	−	0.0203640i	$-0.00648252\pi$
$444$	−0.854486	−	3.18899i	−0.0405521	−	0.151343i
$445$	4.01615	−	6.95618i	0.190384	−	0.329755i
$446$	−27.8489	−	48.2358i	−1.31869	−	2.28403i
$447$	6.30814	−	6.30814i	0.298365	−	0.298365i
$448$	28.3626	−	3.37968i	1.34001	−	0.159675i
$449$	−0.850694	−	3.17483i	−0.0401467	−	0.149830i	0.942943	−	0.332954i	$-0.108045\pi$
$449$	−0.850694	−	3.17483i	−0.0401467	−	0.149830i	−0.983090	+	0.183125i	$0.941379\pi$
$450$	−0.629781	−	2.35037i	−0.0296882	−	0.110798i
$451$			1.84253i			0.0867612i
$452$	23.4892	+	13.5615i	1.10484	+	0.637878i
$453$	−9.09451	−	9.09451i	−0.427297	−	0.427297i
$454$	−3.72721			−0.174927
$455$	13.4400	−	12.9909i	0.630076	−	0.609024i
$456$	0.801493			0.0375334
$457$	25.5511	+	25.5511i	1.19523	+	1.19523i	0.975578	+	0.219653i	$0.0704925\pi$
$457$	25.5511	+	25.5511i	1.19523	+	1.19523i	0.219653	+	0.975578i	$0.429507\pi$
$458$	16.3253	+	9.42541i	0.762831	+	0.440421i
$459$			7.32088i			0.341709i
$460$	−8.06830	−	30.1113i	−0.376187	−	1.40395i
$461$	3.32485	+	12.4085i	0.154854	+	0.577922i	0.999118	+	0.0419948i	$0.0133713\pi$
$461$	3.32485	+	12.4085i	0.154854	+	0.577922i	−0.844264	+	0.535927i	$0.819962\pi$
$462$	−8.32908	−	11.1356i	−0.387504	−	0.518076i
$463$	22.2200	−	22.2200i	1.03265	−	1.03265i	0.0332014	−	0.999449i	$-0.489430\pi$
$463$	22.2200	−	22.2200i	1.03265	−	1.03265i	0.999449	−	0.0332014i	$-0.0105703\pi$
$464$	−15.9104	−	27.5577i	−0.738623	−	1.27933i
$465$	2.96237	−	5.13098i	0.137377	−	0.237943i
$466$	−0.558807	−	2.08550i	−0.0258862	−	0.0966087i
$467$	−17.1486	+	29.7023i	−0.793543	+	1.37446i	0.130217	+	0.991486i	$0.458433\pi$
$467$	−17.1486	+	29.7023i	−0.793543	+	1.37446i	−0.923760	+	0.382972i	$0.874901\pi$
$468$	−5.29246	+	6.83071i	−0.244644	+	0.315750i
$469$	6.16334	+	15.4131i	0.284597	+	0.711711i
$470$	−3.99298	+	14.9020i	−0.184182	+	0.687378i
$471$	−4.56742			−0.210455
$472$	−3.95048			−0.181835
$473$	−7.58581	+	28.3106i	−0.348796	+	1.30172i
$474$	9.38320	+	2.51422i	0.430985	+	0.115482i
$475$	1.08032	−	0.289472i	0.0495686	−	0.0132819i
$476$	46.0944	−	5.49260i	2.11273	−	0.251753i
$477$	1.15862	−	2.00679i	0.0530496	−	0.0918846i
$478$			39.2452i			1.79503i
$479$	2.30910	−	0.618722i	0.105505	−	0.0282701i	−0.205680	−	0.978619i	$-0.565941\pi$
$479$	2.30910	−	0.618722i	0.105505	−	0.0282701i	0.311186	+	0.950349i	$0.399274\pi$
$480$	13.6730	−	7.89413i	0.624086	−	0.360316i
$481$	−1.92224	+	4.57983i	−0.0876465	+	0.208822i
$482$		−	6.15798i		−	0.280489i
$483$	16.1422	+	6.92012i	0.734495	+	0.314876i
$484$	5.65210	+	9.78972i	0.256913	+	0.444987i
$485$	17.3071	−	9.99226i	0.785875	−	0.453725i
$486$	2.02536	+	0.542694i	0.0918723	+	0.0246171i
$487$	−5.93438	−	5.93438i	−0.268912	−	0.268912i	0.559749	−	0.828662i	$-0.310897\pi$
$487$	−5.93438	−	5.93438i	−0.268912	−	0.268912i	−0.828662	+	0.559749i	$0.810897\pi$
$488$	−2.03489	+	7.59430i	−0.0921149	+	0.343778i
$489$	1.81401	+	1.81401i	0.0820323	+	0.0820323i
$490$	−8.12479	+	27.5890i	−0.367041	+	1.24634i
$491$	−5.46870	+	3.15735i	−0.246799	+	0.142489i	−0.618298	−	0.785944i	$-0.712177\pi$
$491$	−5.46870	+	3.15735i	−0.246799	+	0.142489i	0.371499	+	0.928433i	$0.378844\pi$
$492$	−1.24567	+	1.24567i	−0.0561593	+	0.0561593i
$493$	−38.1962	−	66.1577i	−1.72027	−	2.97959i
$494$	−5.75974	−	4.46267i	−0.259143	−	0.200785i
$495$	−4.25365	−	2.45585i	−0.191188	−	0.110382i
$496$	−8.90635	−	2.38645i	−0.399907	−	0.107155i
$497$	−8.47054	−	21.1829i	−0.379956	−	0.950182i
$498$	25.9605	+	14.9883i	1.16332	+	0.671642i
$499$	33.9532	−	9.09774i	1.51996	−	0.407271i	0.600228	−	0.799829i	$-0.295077\pi$
$499$	33.9532	−	9.09774i	1.51996	−	0.407271i	0.919727	+	0.392558i	$0.128410\pi$
$500$	−20.4567	+	20.4567i	−0.914851	+	0.914851i
$501$	5.20172	−	5.20172i	0.232396	−	0.232396i
$502$	−0.991772	+	0.265744i	−0.0442649	+	0.0118608i
$503$	−8.32980	−	4.80921i	−0.371408	−	0.214432i	0.302666	−	0.953097i	$-0.402123\pi$
$503$	−8.32980	−	4.80921i	−0.371408	−	0.214432i	−0.674073	+	0.738665i	$0.735457\pi$
$504$	0.313999	−	2.17774i	0.0139866	−	0.0970041i
$505$	−7.20294	−	1.93002i	−0.320527	−	0.0858849i
$506$	30.2156	+	17.4450i	1.34325	+	0.775525i
$507$	12.5880	−	3.24673i	0.559054	−	0.144192i
$508$	13.5767	+	23.5155i	0.602369	+	1.04333i
$509$	−9.11455	+	9.11455i	−0.403995	+	0.403995i	−0.879638	−	0.475643i	$-0.842215\pi$
$509$	−9.11455	+	9.11455i	−0.403995	+	0.403995i	0.475643	+	0.879638i	$0.342215\pi$
$510$	26.0491	−	15.0394i	1.15347	−	0.665957i
$511$	−20.3508	−	2.93429i	−0.900266	−	0.129806i
$512$	−20.9607	−	20.9607i	−0.926340	−	0.926340i
$513$	−0.249443	+	0.930935i	−0.0110132	+	0.0411018i
$514$	−27.7432	−	27.7432i	−1.22370	−	1.22370i
$515$	−17.9844	−	4.81889i	−0.792485	−	0.212346i
$516$	−24.2684	+	14.0114i	−1.06836	+	0.616816i
$517$	−4.70614	−	8.15128i	−0.206976	−	0.358493i
$518$	−0.904247	−	7.58853i	−0.0397303	−	0.333421i
$519$		−	18.3415i		−	0.805104i
$520$	5.82144	+	0.794198i	0.255287	+	0.0348279i
$521$	−9.09809	+	5.25278i	−0.398594	+	0.230129i	−0.685877	−	0.727717i	$-0.740581\pi$
$521$	−9.09809	+	5.25278i	−0.398594	+	0.230129i	0.287283	+	0.957846i	$0.407248\pi$
$522$	−21.1344	+	5.66294i	−0.925027	+	0.247860i
$523$		−	0.571212i		−	0.0249773i	−0.999922	−	0.0124887i	$-0.996025\pi$
$523$		−	0.571212i		−	0.0249773i	0.999922	−	0.0124887i	$-0.00397537\pi$
$524$	17.1473	−	29.6999i	0.749082	−	1.29745i
$525$	−0.363288	−	3.04875i	−0.0158552	−	0.133058i
$526$	−6.97208	+	1.86816i	−0.303997	+	0.0814558i
$527$	−21.3815	−	5.72915i	−0.931392	−	0.249566i
$528$	−1.97840	+	7.38349i	−0.0860988	+	0.321325i
$529$	−21.0655			−0.915891
$530$	−9.52071			−0.413553
$531$	1.22948	−	4.58848i	0.0533549	−	0.199123i
$532$	6.04859	+	0.872121i	0.262240	+	0.0378112i
$533$	2.62921	−	0.333606i	0.113884	−	0.0144501i
$534$	−4.29764	+	7.44374i	−0.185977	+	0.322122i
$535$	−4.94725	−	18.4634i	−0.213888	−	0.798242i
$536$	−2.60883	+	4.51863i	−0.112684	+	0.195175i
$537$	−0.954758	−	1.65369i	−0.0412008	−	0.0713620i
$538$	13.4133	−	13.4133i	0.578288	−	0.578288i
$539$	−8.39684	−	15.4069i	−0.361678	−	0.663622i
$540$	−1.21544	−	4.53608i	−0.0523041	−	0.195202i
$541$	−3.18970	−	11.9041i	−0.137136	−	0.511798i	−0.999980	−	0.00632795i	$-0.997986\pi$
$541$	−3.18970	−	11.9041i	−0.137136	−	0.511798i	0.862844	−	0.505470i	$-0.168681\pi$
$542$			16.4070i			0.704743i
$543$	−16.3977	−	9.46719i	−0.703691	−	0.406276i
$544$	−41.7103	−	41.7103i	−1.78832	−	1.78832i
$545$	11.6747			0.500089
$546$	−14.3820	+	13.9014i	−0.615492	+	0.594927i
$547$	−16.2110			−0.693132			−0.346566	−	0.938026i	$-0.612652\pi$
$547$	−16.2110			−0.693132			−0.346566	+	0.938026i	$0.612652\pi$
$548$	−9.65224	−	9.65224i	−0.412323	−	0.412323i
$549$	−8.18748	−	4.72704i	−0.349433	−	0.201745i
$550$		−	6.09938i		−	0.260078i
$551$	−2.60291	−	9.71418i	−0.110887	−	0.413838i
$552$	1.42879	+	5.33234i	0.0608135	+	0.226959i
$553$	11.2658	+	4.82961i	0.479070	+	0.205376i
$554$	2.29682	−	2.29682i	0.0975826	−	0.0975826i
$555$	−1.34965	−	2.33766i	−0.0572893	−	0.0992281i
$556$	−12.9797	+	22.4815i	−0.550463	+	0.953429i
$557$	8.66766	+	32.3481i	0.367260	+	1.37063i	0.864330	+	0.502924i	$0.167743\pi$
$557$	8.66766	+	32.3481i	0.367260	+	1.37063i	−0.497070	+	0.867710i	$0.665591\pi$
$558$	−3.17000	+	5.49061i	−0.134197	+	0.232436i
$559$	41.7715	+	5.69873i	1.76675	+	0.241031i
$560$	14.6792	−	5.86987i	0.620310	−	0.248047i
$561$	−4.74955	+	17.7255i	−0.200526	+	0.748373i
$562$	−12.4598			−0.525584
$563$	−0.157014			−0.00661736			−0.00330868	−	0.999995i	$-0.501053\pi$
$563$	−0.157014			−0.00661736			−0.00330868	+	0.999995i	$0.501053\pi$
$564$	2.32914	−	8.69248i	0.0980747	−	0.366020i
$565$	21.4201	+	5.73951i	0.901152	+	0.241463i
$566$	9.43036	−	2.52686i	0.396388	−	0.106212i
$567$	2.43172	+	1.04247i	0.102123	+	0.0437797i
$568$	3.58543	−	6.21014i	0.150441	−	0.260572i
$569$			42.2556i			1.77145i	0.464213	+	0.885724i	$0.346337\pi$
$569$			42.2556i			1.77145i	−0.464213	+	0.885724i	$0.653663\pi$
$570$	3.82488	−	1.02487i	0.160206	−	0.0429272i
$571$	28.4747	−	16.4399i	1.19163	−	0.687987i	0.232952	−	0.972488i	$-0.425161\pi$
$571$	28.4747	−	16.4399i	1.19163	−	0.687987i	0.958676	+	0.284502i	$0.0918281\pi$
$572$	−17.2458	+	13.1051i	−0.721084	+	0.547954i
$573$		−	10.7890i		−	0.450716i
$574$	−3.26545	+	2.44245i	−0.136297	+	0.101946i
$575$	3.85171	+	6.67136i	0.160627	+	0.278215i
$576$	−9.34953	+	5.39795i	−0.389564	+	0.224915i
$577$	41.6112	+	11.1497i	1.73230	+	0.464167i	0.980710	−	0.195467i	$-0.0626223\pi$
$577$	41.6112	+	11.1497i	1.73230	+	0.464167i	0.751586	+	0.659635i	$0.229289\pi$
$578$	−54.2587	−	54.2587i	−2.25686	−	2.25686i
$579$	−5.08690	+	18.9846i	−0.211404	+	0.788972i
$580$	34.6504	+	34.6504i	1.43878	+	1.43878i
$581$	29.7227	+	23.3934i	1.23310	+	0.970521i
$582$	−18.5201	+	10.6926i	−0.767685	+	0.443223i
$583$	4.10723	−	4.10723i	0.170104	−	0.170104i
$584$	−3.23143	−	5.59700i	−0.133717	−	0.231605i
$585$	−2.73423	+	6.51444i	−0.113046	+	0.269339i
$586$	−20.3052	−	11.7232i	−0.838800	−	0.484281i
$587$	−15.3441	−	4.11144i	−0.633318	−	0.169697i	−0.0721432	−	0.997394i	$-0.522984\pi$
$587$	−15.3441	−	4.11144i	−0.633318	−	0.169697i	−0.561175	+	0.827697i	$0.689651\pi$
$588$	4.73928	−	16.0929i	0.195444	−	0.663662i
$589$	−2.52369	−	1.45706i	−0.103987	−	0.0600369i
$590$	−18.8524	+	5.05149i	−0.776142	+	0.207967i
$591$	−8.10987	+	8.10987i	−0.333595	+	0.333595i
$592$	−2.97045	+	2.97045i	−0.122085	+	0.122085i
$593$	18.7597	−	5.02665i	0.770369	−	0.206420i	0.147834	−	0.989012i	$-0.452770\pi$
$593$	18.7597	−	5.02665i	0.770369	−	0.206420i	0.622534	+	0.782592i	$0.286103\pi$
$594$	4.55179	+	2.62798i	0.186762	+	0.107827i
$595$	35.2404	−	14.0918i	1.44472	−	0.577708i
$596$	20.6518	+	5.53363i	0.845931	+	0.226666i
$597$	−4.81053	−	2.77736i	−0.196882	−	0.113670i
$598$	19.4225	−	46.2750i	0.794243	−	1.89232i
$599$	22.3885	+	38.7780i	0.914770	+	1.58443i	0.807238	+	0.590226i	$0.200961\pi$
$599$	22.3885	+	38.7780i	0.914770	+	1.58443i	0.107531	+	0.994202i	$0.465705\pi$
$600$	0.682407	−	0.682407i	0.0278592	−	0.0278592i
$601$	−33.7722	+	19.4984i	−1.37760	+	0.795355i	−0.991870	−	0.127258i	$-0.959382\pi$
$601$	−33.7722	+	19.4984i	−1.37760	+	0.795355i	−0.385726	+	0.922613i	$0.626049\pi$
$602$	−60.2297	+	24.0844i	−2.45478	+	0.981608i
$603$	−4.43646	−	4.43646i	−0.180667	−	0.180667i
$604$	7.97789	−	29.7739i	0.324616	−	1.21148i
$605$	6.53531	+	6.53531i	0.265698	+	0.265698i
$606$	7.70779	+	2.06530i	0.313108	+	0.0838969i
$607$	27.6946	−	15.9895i	1.12409	−	0.648992i	0.181646	−	0.983364i	$-0.441857\pi$
$607$	27.6946	−	15.9895i	1.12409	−	0.648992i	0.942441	+	0.334372i	$0.108524\pi$
$608$	−3.88276	−	6.72514i	−0.157467	−	0.272741i
$609$	−27.4141	+	3.26666i	−1.11088	+	0.132372i
$610$			38.8434i			1.57272i
$611$	−10.7794	+	8.19132i	−0.436089	+	0.331386i
$612$	−15.1947	+	8.77265i	−0.614209	+	0.354613i
$613$	−21.4241	+	5.74057i	−0.865311	+	0.231859i	−0.664059	−	0.747680i	$-0.731168\pi$
$613$	−21.4241	+	5.74057i	−0.865311	+	0.231859i	−0.201252	+	0.979540i	$0.564501\pi$
$614$		−	7.82757i		−	0.315895i
$615$	−0.720162	+	1.24736i	−0.0290398	+	0.0502983i
$616$	2.17311	−	5.06909i	0.0875570	−	0.204239i
$617$	19.7363	−	5.28833i	0.794554	−	0.212900i	0.161363	−	0.986895i	$-0.448411\pi$
$617$	19.7363	−	5.28833i	0.794554	−	0.212900i	0.633192	+	0.773995i	$0.281744\pi$
$618$	19.2449	+	5.15665i	0.774142	+	0.207431i
$619$	−7.46806	+	27.8712i	−0.300167	+	1.12024i	0.636860	+	0.770980i	$0.280233\pi$
$619$	−7.46806	+	27.8712i	−0.300167	+	1.12024i	−0.937027	+	0.349258i	$0.886434\pi$
$620$	14.1993			0.570258
$621$	−6.63818			−0.266381
$622$	−17.6737	+	65.9592i	−0.708651	+	2.64472i
$623$	−6.70766	+	8.52248i	−0.268737	+	0.341446i
$624$	10.8941	+	1.48625i	0.436114	+	0.0594974i
$625$	−8.92548	+	15.4594i	−0.357019	+	0.618375i
$626$	7.96615	+	29.7301i	0.318391	+	1.18825i
$627$	−1.20792	+	2.09218i	−0.0482397	+	0.0835535i
$628$	−5.47316	−	9.47979i	−0.218403	−	0.378285i
$629$	−7.13115	+	7.13115i	−0.284338	+	0.284338i
$630$	−1.28622	−	10.7941i	−0.0512442	−	0.430046i
$631$	−0.897330	−	3.34888i	−0.0357221	−	0.133317i	0.945762	−	0.324860i	$-0.105317\pi$
$631$	−0.897330	−	3.34888i	−0.0357221	−	0.133317i	−0.981484	+	0.191544i	$0.938651\pi$
$632$	0.997169	+	3.72148i	0.0396652	+	0.148033i
$633$		−	16.1268i		−	0.640982i
$634$	−18.6503	−	10.7677i	−0.740697	−	0.427641i
$635$	15.6982	+	15.6982i	0.622965	+	0.622965i
$636$	5.55353			0.220212
$637$	−20.4647	+	14.7715i	−0.810840	+	0.585268i
$638$	−54.8451			−2.17134
$639$	6.09722	+	6.09722i	0.241202	+	0.241202i
$640$	11.0678	+	6.38997i	0.437491	+	0.252586i
$641$			6.69397i			0.264396i	0.991223	+	0.132198i	$0.0422035\pi$
$641$			6.69397i			0.264396i	−0.991223	+	0.132198i	$0.957797\pi$
$642$	5.29400	+	19.7575i	0.208938	+	0.779766i
$643$	−11.3176	−	42.2380i	−0.446324	−	1.66570i	−0.712416	−	0.701757i	$-0.752399\pi$
$643$	−11.3176	−	42.2380i	−0.446324	−	1.66570i	0.266092	−	0.963948i	$-0.414268\pi$
$644$	4.98040	+	41.7960i	0.196255	+	1.64699i
$645$	−16.2008	+	16.2008i	−0.637907	+	0.637907i
$646$	−7.39721	−	12.8123i	−0.291039	−	0.504095i
$647$	1.21242	−	2.09997i	0.0476652	−	0.0825585i	−0.841208	−	0.540711i	$-0.818155\pi$
$647$	1.21242	−	2.09997i	0.0476652	−	0.0825585i	0.888874	+	0.458152i	$0.151489\pi$
$648$	0.215239	+	0.803282i	0.00845538	+	0.0315559i
$649$	5.95371	−	10.3121i	0.233704	−	0.404787i
$650$	−8.70356	+	1.10435i	−0.341382	+	0.0433161i
$651$	−4.94766	+	6.28630i	−0.193914	+	0.246380i
$652$	−1.59129	+	5.93876i	−0.0623196	+	0.232580i
$653$	18.9747			0.742539			0.371269	−	0.928525i	$-0.378923\pi$
$653$	18.9747			0.742539			0.371269	+	0.928525i	$0.378923\pi$
$654$	−12.4930			−0.488513
$655$	7.25709	−	27.0838i	0.283558	−	1.05825i
$656$	2.16516	+	0.580154i	0.0845354	+	0.0226512i
$657$	7.50661	−	2.01139i	0.292861	−	0.0784718i
$658$	8.20778	−	19.1459i	0.319973	−	0.746383i
$659$	−1.16446	+	2.01691i	−0.0453610	+	0.0785676i	−0.887814	−	0.460202i	$-0.847777\pi$
$659$	−1.16446	+	2.01691i	−0.0453610	+	0.0785676i	0.842453	+	0.538769i	$0.181110\pi$
$660$		−	11.7714i		−	0.458202i
$661$	−24.8482	+	6.65805i	−0.966482	+	0.258968i	−0.707342	−	0.706872i	$-0.750106\pi$
$661$	−24.8482	+	6.65805i	−0.966482	+	0.258968i	−0.259140	+	0.965840i	$0.583439\pi$
$662$	45.9612	−	26.5357i	1.78633	−	1.03134i
$663$	26.1535	+	3.56803i	1.01572	+	0.138571i
$664$			11.8891i			0.461385i
$665$	4.96137	−	0.591196i	0.192394	−	0.0229256i
$666$	1.44424	+	2.50150i	0.0559633	+	0.0969313i
$667$	59.9883	−	34.6343i	2.32276	−	1.34104i
$668$	17.0296	+	4.56306i	0.658894	+	0.176550i
$669$	18.7830	+	18.7830i	0.726192	+	0.726192i
$670$	−6.67184	+	24.8997i	−0.257756	+	0.961958i
$671$	−16.7570	−	16.7570i	−0.646898	−	0.646898i
$672$	−19.7940	+	7.91516i	−0.763571	+	0.305334i
$673$	−24.9952	+	14.4310i	−0.963493	+	0.556273i	−0.897246	−	0.441530i	$-0.854436\pi$
$673$	−24.9952	+	14.4310i	−0.963493	+	0.556273i	−0.0662467	+	0.997803i	$0.521102\pi$
$674$	1.09957	−	1.09957i	0.0423540	−	0.0423540i
$675$	0.580235	+	1.00500i	0.0223333	+	0.0386824i
$676$	21.8230	+	22.2362i	0.839346	+	0.855240i
$677$	13.4814	+	7.78352i	0.518134	+	0.299145i	0.736171	−	0.676796i	$-0.236632\pi$
$677$	13.4814	+	7.78352i	0.518134	+	0.299145i	−0.218037	+	0.975941i	$0.569965\pi$
$678$	−22.9215	−	6.14179i	−0.880293	−	0.235874i
$679$	−25.0549	+	10.0189i	−0.961520	+	0.384489i
$680$	10.3314	+	5.96481i	0.396189	+	0.228740i
$681$	1.71699	−	0.460067i	0.0657954	−	0.0176298i
$682$	−11.2374	+	11.2374i	−0.430304	+	0.430304i
$683$	−29.7469	+	29.7469i	−1.13823	+	1.13823i	−0.149467	+	0.988767i	$0.547756\pi$
$683$	−29.7469	+	29.7469i	−1.13823	+	1.13823i	−0.988767	+	0.149467i	$0.952244\pi$
$684$	−2.23109	+	0.597819i	−0.0853078	+	0.0228582i
$685$	−9.66529	−	5.58026i	−0.369292	−	0.213211i
$686$	16.1743	−	35.3048i	0.617538	−	1.34794i
$687$	−8.68390	−	2.32685i	−0.331312	−	0.0887747i
$688$	30.8794	+	17.8282i	1.17727	+	0.679695i
$689$	−6.60449	−	5.11719i	−0.251611	−	0.194949i
$690$	13.6370	+	23.6199i	0.519150	+	0.899194i
$691$	15.4899	−	15.4899i	0.589263	−	0.589263i	−0.348169	−	0.937432i	$-0.613197\pi$
$691$	15.4899	−	15.4899i	0.589263	−	0.589263i	0.937432	+	0.348169i	$0.113197\pi$
$692$	38.0684	−	21.9788i	1.44714	−	0.835508i
$693$	5.21143	+	4.10168i	0.197966	+	0.155810i
$694$	−50.6735	−	50.6735i	−1.92354	−	1.92354i
$695$	−5.49329	+	20.5013i	−0.208373	+	0.777657i
$696$	−6.13615	−	6.13615i	−0.232590	−	0.232590i
$697$	5.19791	+	1.39278i	0.196885	+	0.0527551i
$698$	−50.9389	+	29.4096i	−1.92807	+	1.11317i
$699$	0.514845	+	0.891738i	0.0194732	+	0.0337286i
$700$	5.89243	−	4.40735i	0.222713	−	0.166582i
$701$			15.8478i			0.598564i	0.954165	+	0.299282i	$0.0967471\pi$
$701$			15.8478i			0.598564i	−0.954165	+	0.299282i	$0.903253\pi$
$702$	2.92587	−	6.97103i	0.110430	−	0.263105i
$703$	−1.14979	+	0.663830i	−0.0433650	+	0.0250368i
$704$	−26.1394	+	7.00403i	−0.985165	+	0.263974i
$705$		−	7.35769i		−	0.277107i
$706$	−10.1229	+	17.5334i	−0.380981	+	0.659879i
$707$	9.25423	+	3.96727i	0.348041	+	0.149204i
$708$	10.9968	−	2.94659i	0.413285	−	0.110739i
$709$	−46.6694	−	12.5050i	−1.75271	−	0.469637i	−0.767507	−	0.641041i	$-0.778503\pi$
$709$	−46.6694	−	12.5050i	−1.75271	−	0.469637i	−0.985201	+	0.171404i	$0.945170\pi$
$710$	9.16940	−	34.2207i	0.344121	−	1.28428i
$711$	−4.63285			−0.173745
$712$	−3.40899			−0.127757
$713$	5.19489	−	19.3876i	0.194550	−	0.726071i
$714$	−37.7104	+	15.0795i	−1.41128	+	0.564336i
$715$	−10.8466	+	13.9991i	−0.405638	+	0.523536i
$716$	2.28818	−	3.96325i	0.0855134	−	0.148114i
$717$	−4.84422	−	18.0789i	−0.180911	−	0.675168i
$718$	35.8473	−	62.0893i	1.33781	−	2.31715i
$719$	5.32163	+	9.21734i	0.198463	+	0.343749i	0.948030	−	0.318180i	$-0.103072\pi$
$719$	5.32163	+	9.21734i	0.198463	+	0.343749i	−0.749567	+	0.661928i	$0.769738\pi$
$720$	−4.22522	+	4.22522i	−0.157465	+	0.157465i
$721$	23.1060	+	9.90549i	0.860513	+	0.368900i
$722$	9.80710	+	36.6006i	0.364983	+	1.36213i
$723$	0.760109	+	2.83676i	0.0282688	+	0.105500i
$724$		−	45.3784i		−	1.68647i
$725$	−10.4870	−	6.05467i	−0.389478	−	0.224865i
$726$	−6.99336	−	6.99336i	−0.259548	−	0.259548i
$727$	5.89296			0.218558			0.109279	−	0.994011i	$-0.465146\pi$
$727$	5.89296			0.218558			0.109279	+	0.994011i	$0.465146\pi$
$728$	−7.62684	−	2.18313i	−0.282669	−	0.0809120i
$729$	−1.00000			−0.0370370
$730$	−22.5779	−	22.5779i	−0.835645	−	0.835645i
$731$	74.1322	+	42.8003i	2.74188	+	1.58302i
$732$		−	22.6578i		−	0.837455i
$733$	9.93532	+	37.0791i	0.366970	+	1.36955i	0.864731	+	0.502235i	$0.167489\pi$
$733$	9.93532	+	37.0791i	0.366970	+	1.36955i	−0.497762	+	0.867314i	$0.665845\pi$
$734$	14.5362	+	54.2499i	0.536542	+	2.00240i
$735$	0.337366	−	13.7122i	0.0124439	−	0.505780i
$736$	37.8207	−	37.8207i	1.39409	−	1.39409i
$737$	−7.86347	−	13.6199i	−0.289655	−	0.501696i
$738$	0.770638	−	1.33478i	0.0283676	−	0.0491341i
$739$	−5.34503	−	19.9479i	−0.196620	−	0.733796i	−0.991842	−	0.127477i	$-0.959312\pi$
$739$	−5.34503	−	19.9479i	−0.196620	−	0.733796i	0.795221	−	0.606319i	$-0.207355\pi$
$740$	3.23458	−	5.60246i	0.118906	−	0.205950i
$741$	3.20415	+	1.34484i	0.117708	+	0.0494040i
$742$	12.7236	+	1.83457i	0.467099	+	0.0673491i
$743$	8.72671	−	32.5685i	0.320152	−	1.19482i	−0.598945	−	0.800790i	$-0.704413\pi$
$743$	8.72671	−	32.5685i	0.320152	−	1.19482i	0.919097	−	0.394033i	$-0.128920\pi$
$744$	−2.51452			−0.0921867
$745$	17.4806			0.640439
$746$	−1.98879	+	7.42228i	−0.0728150	+	0.271749i
$747$	−13.8092	−	3.70015i	−0.505251	−	0.135381i
$748$	−42.4812	+	11.3828i	−1.55327	+	0.416197i
$749$	3.05384	+	25.6281i	0.111585	+	0.936430i
$750$	12.6556	−	21.9201i	0.462116	−	0.800409i
$751$		−	31.7749i		−	1.15948i	−0.814801	−	0.579741i	$-0.803154\pi$
$751$		−	31.7749i		−	1.15948i	0.814801	−	0.579741i	$-0.196846\pi$
$752$	−11.0604	+	2.96363i	−0.403332	+	0.108072i
$753$	0.424072	−	0.244838i	0.0154540	−	0.00892240i
$754$	9.93020	+	78.2617i	0.361637	+	2.85012i
$755$		−	25.2019i		−	0.917191i
$756$	0.750265	+	6.29629i	0.0272869	+	0.228994i
$757$	−13.6215	−	23.5930i	−0.495080	−	0.857504i	0.504904	−	0.863176i	$-0.331528\pi$
$757$	−13.6215	−	23.5930i	−0.495080	−	0.857504i	−0.999984	+	0.00567171i	$0.998195\pi$
$758$	43.2436	−	24.9667i	1.57068	−	0.906831i
$759$	−16.0726	−	4.30664i	−0.583398	−	0.156321i
$760$	1.11051	+	1.11051i	0.0402826	+	0.0402826i
$761$	7.38152	−	27.5482i	0.267580	−	0.998622i	−0.693072	−	0.720868i	$-0.743743\pi$
$761$	7.38152	−	27.5482i	0.267580	−	0.998622i	0.960652	−	0.277754i	$-0.0895900\pi$
$762$	−16.7985	−	16.7985i	−0.608546	−	0.608546i
$763$	−15.6022	−	2.24962i	−0.564839	−	0.0814418i
$764$	22.3928	−	12.9285i	0.810143	−	0.467736i
$765$	−10.1435	+	10.1435i	−0.366739	+	0.366739i
$766$	32.0817	+	55.5671i	1.15916	+	2.00772i
$767$	−15.7929	−	6.62859i	−0.570250	−	0.239344i
$768$	6.85557	+	3.95806i	0.247379	+	0.142824i
$769$	−27.2629	−	7.30506i	−0.983124	−	0.263427i	−0.268764	−	0.963206i	$-0.586615\pi$
$769$	−27.2629	−	7.30506i	−0.983124	−	0.263427i	−0.714360	+	0.699779i	$0.753282\pi$
$770$	3.88861	−	26.9694i	0.140136	−	0.971910i
$771$	16.2048	+	9.35585i	0.583602	+	0.336943i
$772$	−45.4986	+	12.1913i	−1.63753	+	0.438775i
$773$	8.57861	−	8.57861i	0.308551	−	0.308551i	−0.535796	−	0.844347i	$-0.679989\pi$
$773$	8.57861	−	8.57861i	0.308551	−	0.308551i	0.844347	+	0.535796i	$0.179989\pi$
$774$	17.3363	−	17.3363i	0.623141	−	0.623141i
$775$	−3.38929	+	0.908157i	−0.121747	+	0.0326220i
$776$	−7.34530	−	4.24081i	−0.263681	−	0.152236i
$777$	1.35324	+	3.38415i	0.0485473	+	0.121406i
$778$	2.38784	+	0.639819i	0.0856082	+	0.0229386i
$779$	0.613518	+	0.354215i	0.0219816	+	0.0126911i
$780$	−16.7973	+	2.13132i	−0.601441	+	0.0763136i
$781$	10.8071	+	18.7184i	0.386708	+	0.669799i
$782$	72.0538	−	72.0538i	2.57664	−	2.57664i
$783$	9.03685	−	5.21743i	0.322951	−	0.186456i
$784$	−20.7486	+	5.01602i	−0.741022	+	0.179144i
$785$	−6.32841	−	6.32841i	−0.225871	−	0.225871i
$786$	−7.76574	+	28.9821i	−0.276995	+	1.03376i
$787$	13.1589	+	13.1589i	0.469063	+	0.469063i	0.901611	−	0.432548i	$-0.142385\pi$
$787$	13.1589	+	13.1589i	0.469063	+	0.469063i	−0.432548	+	0.901611i	$0.642385\pi$
$788$	−26.5504	−	7.11415i	−0.945817	−	0.253431i
$789$	2.98119	−	1.72119i	0.106133	−	0.0612761i
$790$	9.51735	+	16.4845i	0.338612	+	0.586494i
$791$	−27.5203	−	11.7979i	−0.978508	−	0.419484i
$792$			2.08457i			0.0740720i
$793$	−20.8776	+	26.9456i	−0.741384	+	0.956865i
$794$	22.0655	−	12.7395i	0.783076	−	0.452109i
$795$	4.38585	−	1.17519i	0.155550	−	0.0416795i
$796$		−	13.3125i		−	0.471849i
$797$	16.8639	−	29.2091i	0.597350	−	1.03464i	−0.395861	−	0.918311i	$-0.629554\pi$
$797$	16.8639	−	29.2091i	0.597350	−	1.03464i	0.993211	−	0.116330i	$-0.0371130\pi$
$798$	−5.30911	+	0.632632i	−0.187941	+	0.0223949i
$799$	−26.5528	+	7.11479i	−0.939369	+	0.251703i
$800$	−9.03178	−	2.42006i	−0.319322	−	0.0855620i
$801$	1.06096	−	3.95954i	0.0374871	−	0.139904i
$802$	4.52228			0.159687
$803$	19.4802			0.687440
$804$	3.89176	−	14.5242i	0.137252	−	0.512230i
$805$	12.7777	+	31.9541i	0.450355	+	1.12623i
$806$	18.0700	+	14.0007i	0.636488	+	0.493154i
$807$	−4.52336	+	7.83469i	−0.159230	+	0.275794i
$808$	0.819120	+	3.05700i	0.0288165	+	0.107545i
$809$	22.6796	−	39.2823i	0.797373	−	1.38109i	−0.123948	−	0.992289i	$-0.539556\pi$
$809$	22.6796	−	39.2823i	0.797373	−	1.38109i	0.921321	−	0.388802i	$-0.127111\pi$
$810$	2.05432	+	3.55819i	0.0721814	+	0.125022i
$811$	11.6911	−	11.6911i	0.410531	−	0.410531i	−0.471392	−	0.881924i	$-0.656248\pi$
$811$	11.6911	−	11.6911i	0.410531	−	0.410531i	0.881924	+	0.471392i	$0.156248\pi$
$812$	−39.6305	−	52.9842i	−1.39076	−	1.85938i
$813$	−2.02520	−	7.55815i	−0.0710268	−	0.265076i
$814$	1.87395	+	6.99369i	0.0656821	+	0.245129i
$815$			5.02682i			0.176082i
$816$	19.3339	+	11.1624i	0.676822	+	0.390763i
$817$	7.96844	+	7.96844i	0.278781	+	0.278781i
$818$	10.0705			0.352106
$819$	4.90935	−	8.17914i	0.171547	−	0.285802i
$820$	−3.45190			−0.120546
$821$	12.7335	+	12.7335i	0.444402	+	0.444402i	0.893488	−	0.449086i	$-0.148250\pi$
$821$	12.7335	+	12.7335i	0.444402	+	0.444402i	−0.449086	+	0.893488i	$0.648250\pi$
$822$	10.3427	+	5.97138i	0.360744	+	0.208276i
$823$		−	22.4156i		−	0.781358i	−0.920527	−	0.390679i	$-0.872240\pi$
$823$		−	22.4156i		−	0.781358i	0.920527	−	0.390679i	$-0.127760\pi$
$824$	2.04518	+	7.63273i	0.0712474	+	0.265899i
$825$	0.752875	+	2.80977i	0.0262117	+	0.0978236i
$826$	26.1681	−	3.11818i	0.910504	−	0.108495i
$827$	21.3413	−	21.3413i	0.742110	−	0.742110i	−0.230873	−	0.972984i	$-0.574158\pi$
$827$	21.3413	−	21.3413i	0.742110	−	0.742110i	0.972984	+	0.230873i	$0.0741584\pi$
$828$	−7.95457	−	13.7777i	−0.276441	−	0.478809i
$829$	−1.16634	+	2.02016i	−0.0405086	+	0.0701629i	−0.885569	−	0.464508i	$-0.846231\pi$
$829$	−1.16634	+	2.02016i	−0.0405086	+	0.0701629i	0.845060	+	0.534671i	$0.179564\pi$
$830$	15.2026	+	56.7368i	0.527690	+	1.96936i
$831$	−0.774557	+	1.34157i	−0.0268691	+	0.0465386i
$832$	14.7272	+	36.0316i	0.510574	+	1.24917i
$833$	−49.8112	+	12.0420i	−1.72586	+	0.417230i
$834$	5.87832	−	21.9382i	0.203549	−	0.759657i
$835$	14.4146			0.498836
$836$	−5.78983			−0.200245
$837$	0.782577	−	2.92062i	0.0270498	−	0.100951i
$838$	42.7367	+	11.4513i	1.47631	+	0.395577i
$839$	32.4718	−	8.70079i	1.12105	−	0.300385i	0.349742	−	0.936846i	$-0.386269\pi$
$839$	32.4718	−	8.70079i	1.12105	−	0.300385i	0.771308	+	0.636462i	$0.219603\pi$
$840$	3.45244	−	2.58231i	0.119120	−	0.0890982i
$841$	−39.9432	+	69.1836i	−1.37735	+	2.38564i
$842$		−	72.3923i		−	2.49480i
$843$	5.73978	−	1.53797i	0.197689	−	0.0529705i
$844$	33.4715	−	19.3248i	1.15214	−	0.665187i
$845$	21.9400	+	12.9429i	0.754757	+	0.445250i
$846$			7.87339i			0.270693i
$847$	−7.47459	−	9.99320i	−0.256830	−	0.343370i
$848$	−3.53319	−	6.11966i	−0.121330	−	0.210150i
$849$	−4.03233	+	2.32807i	−0.138389	+	0.0798991i
$850$	−17.2068	−	4.61055i	−0.590189	−	0.158141i
$851$	−6.46615	−	6.46615i	−0.221657	−	0.221657i
$852$	−5.34860	+	19.9613i	−0.183240	+	0.683862i
$853$	4.02453	+	4.02453i	0.137797	+	0.137797i	0.772641	−	0.634844i	$-0.218935\pi$
$853$	4.02453	+	4.02453i	0.137797	+	0.137797i	−0.634844	+	0.772641i	$0.718935\pi$
$854$	7.48483	−	51.9110i	0.256126	−	1.77636i
$855$	−1.63548	+	0.944245i	−0.0559322	+	0.0322925i
$856$	−5.73638	+	5.73638i	−0.196066	+	0.196066i
$857$	7.66605	+	13.2780i	0.261867	+	0.453567i	0.966738	−	0.255768i	$-0.0823284\pi$
$857$	7.66605	+	13.2780i	0.261867	+	0.453567i	−0.704871	+	0.709336i	$0.748995\pi$
$858$	11.6068	−	14.9803i	0.396249	−	0.511418i
$859$	−27.5049	−	15.8800i	−0.938455	−	0.541817i	−0.0489791	−	0.998800i	$-0.515597\pi$
$859$	−27.5049	−	15.8800i	−0.938455	−	0.541817i	−0.889476	+	0.456983i	$0.848930\pi$
$860$	−53.0388	−	14.2117i	−1.80861	−	0.484615i
$861$	1.20279	−	1.52822i	0.0409911	−	0.0520816i
$862$	14.9666	+	8.64096i	0.509764	+	0.294312i
$863$	−1.30949	+	0.350876i	−0.0445754	+	0.0119439i	−0.281038	−	0.959697i	$-0.590679\pi$
$863$	−1.30949	+	0.350876i	−0.0445754	+	0.0119439i	0.236462	+	0.971641i	$0.424012\pi$
$864$	5.69745	−	5.69745i	0.193831	−	0.193831i
$865$	25.4132	−	25.4132i	0.864076	−	0.864076i
$866$	53.8511	−	14.4294i	1.82994	−	0.490330i
$867$	31.6925	+	18.2976i	1.07633	+	0.621421i
$868$	−18.9762	−	2.73610i	−0.644094	−	0.0928692i
$869$	−11.2172	−	3.00564i	−0.380517	−	0.101959i
$870$	−37.1292	−	21.4365i	−1.25880	−	0.726767i
$871$	−18.0113	+	13.6868i	−0.610290	+	0.463761i
$872$	−2.47742	−	4.29103i	−0.0838962	−	0.145312i
$873$	7.21173	−	7.21173i	0.244080	−	0.244080i
$874$	11.6175	−	6.70740i	0.392969	−	0.226881i
$875$	19.7525	−	25.0967i	0.667757	−	0.848425i
$876$	13.1699	+	13.1699i	0.444970	+	0.444970i
$877$	12.1476	−	45.3356i	0.410197	−	1.53088i	−0.384069	−	0.923305i	$-0.625477\pi$
$877$	12.1476	−	45.3356i	0.410197	−	1.53088i	0.794265	−	0.607571i	$-0.207856\pi$
$878$	26.5100	+	26.5100i	0.894669	+	0.894669i
$879$	10.8009	+	2.89410i	0.364306	+	0.0976156i
$880$	−12.9714	+	7.48905i	−0.437266	+	0.252456i
$881$	3.74445	+	6.48558i	0.126154	+	0.218505i	0.922183	−	0.386753i	$-0.126403\pi$
$881$	3.74445	+	6.48558i	0.126154	+	0.218505i	−0.796030	+	0.605258i	$0.793070\pi$
$882$	−0.361011	+	14.6732i	−0.0121559	+	0.494073i
$883$			21.6436i			0.728364i	0.931328	+	0.364182i	$0.118651\pi$
$883$			21.6436i			0.728364i	−0.931328	+	0.364182i	$0.881349\pi$
$884$	23.9344	+	58.5580i	0.805001	+	1.96952i
$885$	8.06111	−	4.65408i	0.270971	−	0.156445i
$886$	−44.1237	+	11.8229i	−1.48236	+	0.397198i
$887$			9.93222i			0.333491i	0.986000	+	0.166746i	$0.0533259\pi$
$887$			9.93222i			0.333491i	−0.986000	+	0.166746i	$0.946674\pi$
$888$	−0.572804	+	0.992125i	−0.0192220	+	0.0332935i
$889$	−17.9544	−	24.0043i	−0.602173	−	0.805078i
$890$	−16.2683	+	4.35909i	−0.545316	+	0.146117i
$891$	−2.42123	−	0.648767i	−0.0811143	−	0.0217345i
$892$	−16.4768	+	61.4923i	−0.551685	+	2.05892i
$893$	−3.61891			−0.121102
$894$	−18.7058			−0.625615
$895$	0.968408	−	3.61415i	0.0323703	−	0.120808i
$896$	−13.5598	−	10.6723i	−0.453002	−	0.356538i
$897$	−3.23530	+	23.7146i	−0.108024	+	0.791809i
$898$	−3.44593	+	5.96852i	−0.114992	+	0.199172i
$899$	8.16608	+	30.4762i	0.272354	+	1.01644i
$900$	−1.39060	+	2.40859i	−0.0463533	+	0.0802863i
$901$	−8.48212	−	14.6915i	−0.282580	−	0.489444i
$902$	2.73186	−	2.73186i	0.0909609	−	0.0909609i
$903$	24.7728	−	18.5293i	0.824388	−	0.616616i
$904$	−2.43590	−	9.09091i	−0.0810169	−	0.302359i
$905$	−9.60255	−	35.8372i	−0.319199	−	1.19127i
$906$			26.9683i			0.895961i
$907$	34.7910	+	20.0866i	1.15522	+	0.666965i	0.950153	−	0.311784i	$-0.100926\pi$
$907$	34.7910	+	20.0866i	1.15522	+	0.666965i	0.205064	+	0.978749i	$0.434260\pi$
$908$	3.01237	+	3.01237i	0.0999689	+	0.0999689i
$909$	−3.80563			−0.126225
$910$	−39.1883	−	0.665823i	−1.29908	−	0.0220718i
$911$	15.0163			0.497513			0.248757	−	0.968566i	$-0.419978\pi$
$911$	15.0163			0.497513			0.248757	+	0.968566i	$0.419978\pi$
$912$	2.07819	+	2.07819i	0.0688158	+	0.0688158i
$913$	−31.0346	−	17.9178i	−1.02710	−	0.592994i
$914$		−	75.7677i		−	2.50617i
$915$	−4.79463	−	17.8938i	−0.158505	−	0.591550i
$916$	−5.57654	−	20.8119i	−0.184254	−	0.687646i
$917$	−14.9173	+	34.7969i	−0.492614	+	1.14910i
$918$	10.8544	−	10.8544i	0.358250	−	0.358250i
$919$	−9.43771	−	16.3466i	−0.311321	−	0.539224i	0.667327	−	0.744765i	$-0.267438\pi$
$919$	−9.43771	−	16.3466i	−0.311321	−	0.539224i	−0.978649	+	0.205540i	$0.934105\pi$
$920$	−5.40857	+	9.36792i	−0.178315	+	0.308851i
$921$	0.966193	+	3.60588i	0.0318371	+	0.118818i
$922$	13.4681	−	23.3274i	0.443547	−	0.768246i
$923$	24.7537	−	18.8104i	0.814778	−	0.619152i
$924$	−2.26826	+	15.7315i	−0.0746204	+	0.517529i
$925$	−0.413754	+	1.54415i	−0.0136041	+	0.0507713i
$926$	−65.8897			−2.16527
$927$	−9.50193			−0.312084
$928$	−21.7610	+	81.2131i	−0.714339	+	2.66595i
$929$	45.2763	+	12.1317i	1.48547	+	0.398029i	0.908203	−	0.418529i	$-0.137454\pi$
$929$	45.2763	+	12.1317i	1.48547	+	0.398029i	0.577262	+	0.816559i	$0.304121\pi$
$930$	−11.9998	+	3.21533i	−0.393488	+	0.105435i
$931$	−6.74438	−	0.165935i	−0.221038	−	0.00543829i
$932$	−1.23388	+	2.13715i	−0.0404172	+	0.0700046i
$933$		−	32.5666i		−	1.06618i
$934$	69.4643	−	18.6129i	2.27294	−	0.609033i
$935$	−31.1405	+	17.9790i	−1.01840	+	0.587975i
$936$	2.97459	−	0.377430i	0.0972277	−	0.0123367i
$937$		−	17.9722i		−	0.587126i	−0.955940	−	0.293563i	$-0.905159\pi$
$937$		−	17.9722i		−	0.587126i	0.955940	−	0.293563i	$-0.0948411\pi$
$938$	13.7143	−	31.9907i	0.447789	−	1.04453i
$939$	−7.33945	−	12.7123i	−0.239514	−	0.414850i
$940$	15.2711	−	8.81676i	0.498088	−	0.287571i
$941$	−34.1628	−	9.15389i	−1.11367	−	0.298408i	−0.345353	−	0.938473i	$-0.612241\pi$
$941$	−34.1628	−	9.15389i	−1.11367	−	0.298408i	−0.768321	+	0.640065i	$0.778908\pi$
$942$	6.77196	+	6.77196i	0.220642	+	0.220642i
$943$	−1.26289	+	4.71319i	−0.0411255	+	0.153482i
$944$	−10.2432	−	10.2432i	−0.333388	−	0.333388i
$945$	1.92488	+	4.81368i	0.0626163	+	0.156589i
$946$	53.2225	−	30.7280i	1.73041	−	0.999054i
$947$	−0.0932783	+	0.0932783i	−0.00303114	+	0.00303114i	−0.708621	−	0.705590i	$-0.750682\pi$
$947$	−0.0932783	+	0.0932783i	−0.00303114	+	0.00303114i	0.705590	+	0.708621i	$0.250682\pi$
$948$	−5.55157	−	9.61560i	−0.180307	−	0.312300i
$949$	−3.52706	−	27.7974i	−0.114493	−	0.902341i
$950$	−2.03095	−	1.17257i	−0.0658927	−	0.0380432i
$951$	9.92063	+	2.65822i	0.321698	+	0.0861988i
$952$	−12.6576	−	9.96225i	−0.410236	−	0.322878i
$953$	30.3290	+	17.5105i	0.982454	+	0.567220i	0.903010	−	0.429619i	$-0.141352\pi$
$953$	30.3290	+	17.5105i	0.982454	+	0.567220i	0.0794437	+	0.996839i	$0.474686\pi$
$954$	−4.69325	+	1.25755i	−0.151950	+	0.0407148i
$955$	14.9487	−	14.9487i	0.483729	−	0.483729i
$956$	31.7183	−	31.7183i	1.02584	−	1.02584i
$957$	25.2652	−	6.76979i	0.816708	−	0.218836i
$958$	−4.34099	−	2.50627i	−0.140251	−	0.0809740i
$959$	11.8416	+	9.31998i	0.382385	+	0.300958i
$960$	−20.4335	−	5.47513i	−0.659487	−	0.176709i
$961$	−18.9292	−	10.9288i	−0.610620	−	0.352542i
$962$	9.64041	−	3.94032i	0.310819	−	0.127041i
$963$	−4.87752	−	8.44811i	−0.157176	−	0.272236i
$964$	−4.97694	+	4.97694i	−0.160296	+	0.160296i
$965$	−33.3524	+	19.2560i	−1.07365	+	0.619872i
$966$	−13.6733	−	34.1938i	−0.439931	−	1.10017i
$967$	−13.6207	−	13.6207i	−0.438014	−	0.438014i	0.453329	−	0.891343i	$-0.350236\pi$
$967$	−13.6207	−	13.6207i	−0.438014	−	0.438014i	−0.891343	+	0.453329i	$0.850236\pi$
$968$	1.01523	−	3.78887i	0.0326306	−	0.121779i
$969$	4.98912	+	4.98912i	0.160274	+	0.160274i
$970$	−40.4759	−	10.8455i	−1.29960	−	0.348228i
$971$	2.95070	−	1.70359i	0.0946923	−	0.0546707i	−0.451906	−	0.892066i	$-0.649256\pi$
$971$	2.95070	−	1.70359i	0.0946923	−	0.0546707i	0.546598	+	0.837395i	$0.315922\pi$
$972$	−1.19831	−	2.07553i	−0.0384357	−	0.0665725i
$973$	11.2918	−	26.3397i	0.361997	−	0.844412i
$974$			17.5974i			0.563858i
$975$	3.87310	−	1.58305i	0.124039	−	0.0506983i
$976$	−24.9675	+	14.4150i	−0.799191	+	0.461413i
$977$	−11.5654	+	3.09893i	−0.370009	+	0.0991436i	−0.439032	−	0.898471i	$-0.644679\pi$
$977$	−11.5654	+	3.09893i	−0.370009	+	0.0991436i	0.0690229	+	0.997615i	$0.478012\pi$
$978$		−	5.37915i		−	0.172006i
$979$	5.13764	−	8.89866i	0.164200	−	0.284402i
$980$	28.8642	−	15.7311i	0.922033	−	0.502513i
$981$	5.75506	−	1.54206i	0.183745	−	0.0492343i
$982$	12.7896	+	3.42696i	0.408132	+	0.109359i
$983$	−2.94720	+	10.9991i	−0.0940010	+	0.350817i	−0.996866	−	0.0791074i	$-0.974793\pi$
$983$	−2.94720	+	10.9991i	−0.0940010	+	0.350817i	0.902865	+	0.429924i	$0.141460\pi$
$984$	0.611288			0.0194871
$985$	−22.4734			−0.716061
$986$	−41.4577	+	154.722i	−1.32028	+	4.92736i
$987$	−1.41777	+	9.83294i	−0.0451281	+	0.312986i
$988$	1.04830	+	8.26184i	0.0333509	+	0.262844i
$989$	−38.8090	+	67.2192i	−1.23405	+	2.13744i
$990$	2.66555	+	9.94797i	0.0847167	+	0.316167i
$991$	−16.9431	+	29.3463i	−0.538216	+	0.932217i	0.460785	+	0.887512i	$0.347568\pi$
$991$	−16.9431	+	29.3463i	−0.538216	+	0.932217i	−0.999000	+	0.0447048i	$0.985765\pi$
$992$	12.1814	+	21.0987i	0.386759	+	0.669886i
$993$	−17.8973	+	17.8973i	−0.567953	+	0.567953i
$994$	−18.8482	+	43.9662i	−0.597829	+	1.39452i
$995$	−2.81707	−	10.5134i	−0.0893071	−	0.333299i
$996$	−8.86783	−	33.0952i	−0.280988	−	1.04866i
$997$			36.5027i			1.15605i	0.816018	+	0.578026i	$0.196177\pi$
$997$			36.5027i			1.15605i	−0.816018	+	0.578026i	$0.803823\pi$
$998$	−63.8303	−	36.8524i	−2.02051	−	1.16654i
$999$	−0.974084	−	0.974084i	−0.0308186	−	0.0308186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bt.a.271.2	yes	36
3.2	odd	2		819.2.et.c.271.8		36
7.3	odd	6		273.2.cg.a.115.8	yes	36
13.6	odd	12		273.2.cg.a.19.8	yes	36
21.17	even	6		819.2.gh.c.388.2		36
39.32	even	12		819.2.gh.c.19.2		36
91.45	even	12	inner	273.2.bt.a.136.2	✓	36
273.227	odd	12		819.2.et.c.136.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.2	✓	36	91.45	even	12	inner
273.2.bt.a.271.2	yes	36	1.1	even	1	trivial
273.2.cg.a.19.8	yes	36	13.6	odd	12
273.2.cg.a.115.8	yes	36	7.3	odd	6
819.2.et.c.136.8		36	273.227	odd	12
819.2.et.c.271.8		36	3.2	odd	2
819.2.gh.c.19.2		36	39.32	even	12
819.2.gh.c.388.2		36	21.17	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.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48267 - 1.48267i) q^{2} +(0.866025 + 0.500000i) q^{3} +2.39661i q^{4} +(0.507149 + 1.89270i) q^{5} +(-0.542694 - 2.02536i) q^{6} +(-0.313052 - 2.62717i) q^{7} +(0.588043 - 0.588043i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.48267 - 1.48267i) q^{2} +(0.866025 + 0.500000i) q^{3} +2.39661i q^{4} +(0.507149 + 1.89270i) q^{5} +(-0.542694 - 2.02536i) q^{6} +(-0.313052 - 2.62717i) q^{7} +(0.588043 - 0.588043i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.05432 - 3.55819i) q^{10} +(0.648767 + 2.42123i) q^{11} +(-1.19831 + 2.07553i) q^{12} +(3.33753 - 1.36415i) q^{13} +(-3.43106 + 4.35937i) q^{14} +(-0.507149 + 1.89270i) q^{15} +3.04948 q^{16} +7.32088 q^{17} +(0.542694 - 2.02536i) q^{18} +(0.930935 + 0.249443i) q^{19} +(-4.53608 + 1.21544i) q^{20} +(1.04247 - 2.43172i) q^{21} +(2.62798 - 4.55179i) q^{22} +6.63818i q^{23} +(0.803282 - 0.215239i) q^{24} +(1.00500 - 0.580235i) q^{25} +(-6.97103 - 2.92587i) q^{26} +1.00000i q^{27} +(6.29629 - 0.750265i) q^{28} +(-5.21743 - 9.03685i) q^{29} +(3.55819 - 2.05432i) q^{30} +(-2.92062 - 0.782577i) q^{31} +(-5.69745 - 5.69745i) q^{32} +(-0.648767 + 2.42123i) q^{33} +(-10.8544 - 10.8544i) q^{34} +(4.81368 - 1.92488i) q^{35} +(-2.07553 + 1.19831i) q^{36} +(-0.974084 + 0.974084i) q^{37} +(-1.01043 - 1.75011i) q^{38} +(3.57246 + 0.487377i) q^{39} +(1.41122 + 0.814767i) q^{40} +(0.710011 + 0.190247i) q^{41} +(-5.15107 + 2.05979i) q^{42} +(10.1261 + 5.84633i) q^{43} +(-5.80275 + 1.55484i) q^{44} +(-1.38556 + 1.38556i) q^{45} +(9.84223 - 9.84223i) q^{46} +(-3.62699 + 0.971849i) q^{47} +(2.64092 + 1.52474i) q^{48} +(-6.80400 + 1.64488i) q^{49} +(-2.35037 - 0.629781i) q^{50} +(6.34007 + 3.66044i) q^{51} +(3.26933 + 7.99876i) q^{52} +(-1.15862 - 2.00679i) q^{53} +(1.48267 - 1.48267i) q^{54} +(-4.25365 + 2.45585i) q^{55} +(-1.72898 - 1.36080i) q^{56} +(0.681492 + 0.681492i) q^{57} +(-5.66294 + 21.1344i) q^{58} +(-3.35900 - 3.35900i) q^{59} +(-4.53608 - 1.21544i) q^{60} +(-8.18748 + 4.72704i) q^{61} +(3.17000 + 5.49061i) q^{62} +(2.11867 - 1.58469i) q^{63} +10.7959i q^{64} +(4.27455 + 5.62513i) q^{65} +(4.55179 - 2.62798i) q^{66} +(-6.06032 + 1.62386i) q^{67} +17.5453i q^{68} +(-3.31909 + 5.74884i) q^{69} +(-9.99105 - 4.28314i) q^{70} +(8.32895 - 2.23174i) q^{71} +(0.803282 + 0.215239i) q^{72} +(2.01139 - 7.50661i) q^{73} +2.88849 q^{74} +1.16047 q^{75} +(-0.597819 + 2.23109i) q^{76} +(6.15788 - 2.46239i) q^{77} +(-4.57415 - 6.01939i) q^{78} +(-2.31642 + 4.01217i) q^{79} +(1.54654 + 5.77176i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.770638 - 1.33478i) q^{82} +(-10.1090 + 10.1090i) q^{83} +(5.82788 + 2.49840i) q^{84} +(3.71277 + 13.8563i) q^{85} +(-6.34554 - 23.6819i) q^{86} -10.4349i q^{87} +(1.80529 + 1.04229i) q^{88} +(-2.89859 - 2.89859i) q^{89} +4.10864 q^{90} +(-4.62866 - 8.34119i) q^{91} -15.9091 q^{92} +(-2.13804 - 2.13804i) q^{93} +(6.81855 + 3.93669i) q^{94} +1.88849i q^{95} +(-2.08541 - 7.78286i) q^{96} +(-2.63968 - 9.85141i) q^{97} +(12.5269 + 7.64926i) q^{98} +(-1.77246 + 1.77246i) 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	\( 36 q + 6 q^{7} + 18 q^{9} - 8 q^{11} - 16 q^{12} + 42 q^{14} - 24 q^{16} - 8 q^{17} - 18 q^{19} + 14 q^{20} - 4 q^{21} + 4 q^{22} + 18 q^{24} + 24 q^{25} - 50 q^{26} + 34 q^{28} + 8 q^{29} + 6 q^{31} - 50 q^{32} + 8 q^{33} - 24 q^{34} + 14 q^{35} - 14 q^{37} - 8 q^{38} - 2 q^{39} - 30 q^{40} + 34 q^{41} - 18 q^{42} + 30 q^{43} + 28 q^{44} - 32 q^{46} - 10 q^{47} + 24 q^{48} + 6 q^{49} - 20 q^{50} - 24 q^{51} + 4 q^{52} - 8 q^{53} - 30 q^{55} - 92 q^{56} - 24 q^{57} + 72 q^{58} - 70 q^{59} + 14 q^{60} - 60 q^{61} - 48 q^{62} + 6 q^{63} - 44 q^{65} + 18 q^{66} - 46 q^{67} + 4 q^{69} + 80 q^{70} + 42 q^{71} + 18 q^{72} - 56 q^{73} + 40 q^{74} - 20 q^{75} + 12 q^{76} + 24 q^{77} - 16 q^{78} + 170 q^{80} - 18 q^{81} + 24 q^{82} - 60 q^{83} + 2 q^{85} + 12 q^{86} + 84 q^{88} + 64 q^{89} - 86 q^{91} - 100 q^{92} + 12 q^{93} - 66 q^{94} + 46 q^{96} + 36 q^{97} - 22 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 6 * q^7 + 18 * q^9 - 8 * q^11 - 16 * q^12 + 42 * q^14 - 24 * q^16 - 8 * q^17 - 18 * q^19 + 14 * q^20 - 4 * q^21 + 4 * q^22 + 18 * q^24 + 24 * q^25 - 50 * q^26 + 34 * q^28 + 8 * q^29 + 6 * q^31 - 50 * q^32 + 8 * q^33 - 24 * q^34 + 14 * q^35 - 14 * q^37 - 8 * q^38 - 2 * q^39 - 30 * q^40 + 34 * q^41 - 18 * q^42 + 30 * q^43 + 28 * q^44 - 32 * q^46 - 10 * q^47 + 24 * q^48 + 6 * q^49 - 20 * q^50 - 24 * q^51 + 4 * q^52 - 8 * q^53 - 30 * q^55 - 92 * q^56 - 24 * q^57 + 72 * q^58 - 70 * q^59 + 14 * q^60 - 60 * q^61 - 48 * q^62 + 6 * q^63 - 44 * q^65 + 18 * q^66 - 46 * q^67 + 4 * q^69 + 80 * q^70 + 42 * q^71 + 18 * q^72 - 56 * q^73 + 40 * q^74 - 20 * q^75 + 12 * q^76 + 24 * q^77 - 16 * q^78 + 170 * q^80 - 18 * q^81 + 24 * q^82 - 60 * q^83 + 2 * q^85 + 12 * q^86 + 84 * q^88 + 64 * q^89 - 86 * q^91 - 100 * q^92 + 12 * q^93 - 66 * q^94 + 46 * q^96 + 36 * q^97 - 22 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more