LMFDB - Embedded newform 627.2.k.a.274.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(274,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("627.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			274.15
Character	$\chi$	$=$	627.274
Dual form			627.2.k.a.373.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.460857 + 0.798227i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.575222 + 0.996315i) q^{4} +(-0.869775 + 1.50649i) q^{5} +(-0.798227 + 0.460857i) q^{6} +3.56103i q^{7} -2.90381 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.801683 - 1.38856i) q^{10} +(3.27069 + 0.550103i) q^{11} +1.15044i q^{12} +(-0.380210 - 0.658543i) q^{13} +(-2.84251 - 1.64112i) q^{14} +(-1.50649 + 0.869775i) q^{15} +(0.187793 - 0.325267i) q^{16} +(-2.52364 - 1.45702i) q^{17} -0.921713 q^{18} +(2.89874 - 3.25535i) q^{19} -2.00126 q^{20} +(-1.78051 + 3.08394i) q^{21} +(-1.94642 + 2.35723i) q^{22} +(-1.34795 - 2.33472i) q^{23} +(-2.51477 - 1.45190i) q^{24} +(0.986983 + 1.70950i) q^{25} +0.700889 q^{26} +1.00000i q^{27} +(-3.54790 + 2.04838i) q^{28} +(-1.70480 - 2.95280i) q^{29} -1.60337i q^{30} -8.14745i q^{31} +(-2.73071 - 4.72974i) q^{32} +(2.55745 + 2.11175i) q^{33} +(2.32607 - 1.34296i) q^{34} +(-5.36467 - 3.09729i) q^{35} +(-0.575222 + 0.996315i) q^{36} +9.58163i q^{37} +(1.26260 + 3.81410i) q^{38} -0.760419i q^{39} +(2.52566 - 4.37457i) q^{40} +(-3.08801 + 5.34859i) q^{41} +(-1.64112 - 2.84251i) q^{42} +(9.39702 + 5.42537i) q^{43} +(1.33330 + 3.57506i) q^{44} -1.73955 q^{45} +2.48484 q^{46} +(1.86741 + 3.23445i) q^{47} +(0.325267 - 0.187793i) q^{48} -5.68092 q^{49} -1.81943 q^{50} +(-1.45702 - 2.52364i) q^{51} +(0.437410 - 0.757617i) q^{52} +(8.50900 - 4.91267i) q^{53} +(-0.798227 - 0.460857i) q^{54} +(-3.67349 + 4.44880i) q^{55} -10.3405i q^{56} +(4.13806 - 1.36985i) q^{57} +3.14267 q^{58} +(-6.31940 - 3.64851i) q^{59} +(-1.73314 - 1.00063i) q^{60} +(2.07815 - 1.19982i) q^{61} +(6.50351 + 3.75481i) q^{62} +(-3.08394 + 1.78051i) q^{63} +5.78504 q^{64} +1.32279 q^{65} +(-2.86427 + 1.06821i) q^{66} +(-11.6810 + 6.74403i) q^{67} -3.35245i q^{68} -2.69590i q^{69} +(4.94469 - 2.85482i) q^{70} +(-7.97377 - 4.60366i) q^{71} +(-1.45190 - 2.51477i) q^{72} +(12.3555 + 7.13345i) q^{73} +(-7.64831 - 4.41576i) q^{74} +1.97397i q^{75} +(4.91077 + 1.01551i) q^{76} +(-1.95893 + 11.6470i) q^{77} +(0.606987 + 0.350444i) q^{78} +(-6.17631 + 10.6977i) q^{79} +(0.326676 + 0.565819i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.84626 - 4.92986i) q^{82} +0.382821i q^{83} -4.09677 q^{84} +(4.39000 - 2.53457i) q^{85} +(-8.66136 + 5.00064i) q^{86} -3.40960i q^{87} +(-9.49744 - 1.59739i) q^{88} +(12.0854 - 6.97752i) q^{89} +(0.801683 - 1.38856i) q^{90} +(2.34509 - 1.35394i) q^{91} +(1.55074 - 2.68596i) q^{92} +(4.07372 - 7.05590i) q^{93} -3.44243 q^{94} +(2.38292 + 7.19836i) q^{95} -5.46143i q^{96} +(-12.8826 - 7.43780i) q^{97} +(2.61809 - 4.53467i) q^{98} +(1.15894 + 3.10755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 40 q^{4} + 4 q^{5} + 40 q^{9} + 4 q^{11} - 24 q^{14} + 12 q^{15} - 40 q^{16} + 48 q^{20} - 24 q^{23} - 56 q^{25} + 80 q^{26} + 6 q^{33} - 48 q^{34} + 40 q^{36} + 60 q^{38} - 4 q^{42} + 14 q^{44}+ \cdots + 2 q^{99}+O(q^{100}) $ 80 * q - 40 * q^4 + 4 * q^5 + 40 * q^9 + 4 * q^11 - 24 * q^14 + 12 * q^15 - 40 * q^16 + 48 * q^20 - 24 * q^23 - 56 * q^25 + 80 * q^26 + 6 * q^33 - 48 * q^34 + 40 * q^36 + 60 * q^38 - 4 * q^42 + 14 * q^44 + 8 * q^45 - 16 * q^47 - 48 * q^48 - 80 * q^49 - 108 * q^53 - 24 * q^55 + 152 * q^58 - 48 * q^60 + 104 * q^64 - 36 * q^66 + 96 * q^67 - 60 * q^70 + 84 * q^71 - 60 * q^77 + 96 * q^78 - 32 * q^80 - 40 * q^81 - 20 * q^82 - 48 * q^86 + 72 * q^89 + 24 * q^91 - 104 * q^92 + 48 * q^93 + 36 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.460857	+	0.798227i	−0.325875	+	0.564432i	−0.981689	−	0.190491i	$-0.938992\pi$
$2$	−0.460857	+	0.798227i	−0.325875	+	0.564432i	0.655814	+	0.754922i	$0.272325\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.575222	+	0.996315i	0.287611	+	0.498157i
$5$	−0.869775	+	1.50649i	−0.388975	+	0.673725i	−0.992312	−	0.123762i	$-0.960504\pi$
$5$	−0.869775	+	1.50649i	−0.388975	+	0.673725i	0.603337	+	0.797487i	$0.293837\pi$
$6$	−0.798227	+	0.460857i	−0.325875	+	0.188144i
$7$			3.56103i			1.34594i	0.739669	+	0.672971i	$0.234982\pi$
$7$			3.56103i			1.34594i	−0.739669	+	0.672971i	$0.765018\pi$
$8$	−2.90381			−1.02665
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.801683	−	1.38856i	−0.253514	−	0.439100i
$11$	3.27069	+	0.550103i	0.986149	+	0.165862i
$11$	3.27069	+	0.550103i	0.986149	+	0.165862i
$12$			1.15044i			0.332105i
$13$	−0.380210	−	0.658543i	−0.105451	−	0.182647i	0.808471	−	0.588536i	$-0.200295\pi$
$13$	−0.380210	−	0.658543i	−0.105451	−	0.182647i	−0.913922	+	0.405889i	$0.866962\pi$
$14$	−2.84251	−	1.64112i	−0.759693	−	0.438609i
$15$	−1.50649	+	0.869775i	−0.388975	+	0.224575i
$16$	0.187793	−	0.325267i	0.0469483	−	0.0813169i
$17$	−2.52364	−	1.45702i	−0.612073	−	0.353380i	0.161704	−	0.986839i	$-0.448301\pi$
$17$	−2.52364	−	1.45702i	−0.612073	−	0.353380i	−0.773776	+	0.633459i	$0.781634\pi$
$18$	−0.921713			−0.217250
$19$	2.89874	−	3.25535i	0.665017	−	0.746829i
$19$	2.89874	−	3.25535i	0.665017	−	0.746829i
$20$	−2.00126			−0.447495
$21$	−1.78051	+	3.08394i	−0.388540	+	0.672971i
$22$	−1.94642	+	2.35723i	−0.414979	+	0.502563i
$23$	−1.34795	−	2.33472i	−0.281067	−	0.486822i	0.690581	−	0.723255i	$-0.257355\pi$
$23$	−1.34795	−	2.33472i	−0.281067	−	0.486822i	−0.971648	+	0.236433i	$0.924022\pi$
$24$	−2.51477	−	1.45190i	−0.513325	−	0.296368i
$25$	0.986983	+	1.70950i	0.197397	+	0.341901i
$26$	0.700889			0.137456
$27$			1.00000i			0.192450i
$28$	−3.54790	+	2.04838i	−0.670491	+	0.387108i
$29$	−1.70480	−	2.95280i	−0.316574	−	0.548322i	0.663197	−	0.748445i	$-0.269199\pi$
$29$	−1.70480	−	2.95280i	−0.316574	−	0.548322i	−0.979771	+	0.200123i	$0.935866\pi$
$30$		−	1.60337i		−	0.292733i
$31$		−	8.14745i		−	1.46332i	−0.681667	−	0.731662i	$-0.738745\pi$
$31$		−	8.14745i		−	1.46332i	0.681667	−	0.731662i	$-0.261255\pi$
$32$	−2.73071	−	4.72974i	−0.482727	−	0.836107i
$33$	2.55745	+	2.11175i	0.445194	+	0.367608i
$34$	2.32607	−	1.34296i	0.398918	−	0.230315i
$35$	−5.36467	−	3.09729i	−0.906795	−	0.523538i
$36$	−0.575222	+	0.996315i	−0.0958704	+	0.166052i
$37$			9.58163i			1.57521i	0.616180	+	0.787605i	$0.288679\pi$
$37$			9.58163i			1.57521i	−0.616180	+	0.787605i	$0.711321\pi$
$38$	1.26260	+	3.81410i	0.204822	+	0.618729i
$39$		−	0.760419i		−	0.121765i
$40$	2.52566	−	4.37457i	0.399342	−	0.691680i
$41$	−3.08801	+	5.34859i	−0.482266	+	0.835309i	−0.999793	−	0.0203579i	$-0.993519\pi$
$41$	−3.08801	+	5.34859i	−0.482266	+	0.835309i	0.517527	+	0.855667i	$0.326853\pi$
$42$	−1.64112	−	2.84251i	−0.253231	−	0.438609i
$43$	9.39702	+	5.42537i	1.43303	+	0.827362i	0.997351	−	0.0727391i	$-0.0231741\pi$
$43$	9.39702	+	5.42537i	1.43303	+	0.827362i	0.435682	+	0.900101i	$0.356507\pi$
$44$	1.33330	+	3.57506i	0.201002	+	0.538961i
$45$	−1.73955			−0.259317
$46$	2.48484			0.366370
$47$	1.86741	+	3.23445i	0.272390	+	0.471792i	0.969473	−	0.245197i	$-0.0788527\pi$
$47$	1.86741	+	3.23445i	0.272390	+	0.471792i	−0.697084	+	0.716990i	$0.745519\pi$
$48$	0.325267	−	0.187793i	0.0469483	−	0.0271056i
$49$	−5.68092			−0.811561
$50$	−1.81943			−0.257306
$51$	−1.45702	−	2.52364i	−0.204024	−	0.353380i
$52$	0.437410	−	0.757617i	0.0606579	−	0.105063i
$53$	8.50900	−	4.91267i	1.16880	−	0.674808i	0.215404	−	0.976525i	$-0.430893\pi$
$53$	8.50900	−	4.91267i	1.16880	−	0.674808i	0.953397	+	0.301717i	$0.0975599\pi$
$54$	−0.798227	−	0.460857i	−0.108625	−	0.0627146i
$55$	−3.67349	+	4.44880i	−0.495333	+	0.599877i
$56$		−	10.3405i		−	1.38181i
$57$	4.13806	−	1.36985i	0.548099	−	0.181441i
$58$	3.14267			0.412653
$59$	−6.31940	−	3.64851i	−0.822716	−	0.474995i	0.0286360	−	0.999590i	$-0.490884\pi$
$59$	−6.31940	−	3.64851i	−0.822716	−	0.474995i	−0.851352	+	0.524594i	$0.824217\pi$
$60$	−1.73314	−	1.00063i	−0.223747	−	0.129181i
$61$	2.07815	−	1.19982i	0.266080	−	0.153622i	−0.361025	−	0.932556i	$-0.617573\pi$
$61$	2.07815	−	1.19982i	0.266080	−	0.153622i	0.627105	+	0.778935i	$0.284240\pi$
$62$	6.50351	+	3.75481i	0.825947	+	0.476861i
$63$	−3.08394	+	1.78051i	−0.388540	+	0.224324i
$64$	5.78504			0.723131
$65$	1.32279			0.164072
$66$	−2.86427	+	1.06821i	−0.352567	+	0.131488i
$67$	−11.6810	+	6.74403i	−1.42706	+	0.823914i	−0.996888	−	0.0788324i	$-0.974881\pi$
$67$	−11.6810	+	6.74403i	−1.42706	+	0.823914i	−0.430173	+	0.902746i	$0.641547\pi$
$68$		−	3.35245i		−	0.406544i
$69$		−	2.69590i		−	0.324548i
$70$	4.94469	−	2.85482i	0.591003	−	0.341216i
$71$	−7.97377	−	4.60366i	−0.946313	−	0.546354i	−0.0543791	−	0.998520i	$-0.517318\pi$
$71$	−7.97377	−	4.60366i	−0.946313	−	0.546354i	−0.891934	+	0.452167i	$0.850651\pi$
$72$	−1.45190	−	2.51477i	−0.171108	−	0.296368i
$73$	12.3555	+	7.13345i	1.44610	+	0.834907i	0.998246	−	0.0591997i	$-0.0188549\pi$
$73$	12.3555	+	7.13345i	1.44610	+	0.834907i	0.447855	+	0.894106i	$0.352188\pi$
$74$	−7.64831	−	4.41576i	−0.889098	−	0.513321i
$75$			1.97397i			0.227934i
$76$	4.91077	+	1.01551i	0.563304	+	0.116487i
$77$	−1.95893	+	11.6470i	−0.223241	+	1.32730i
$78$	0.606987	+	0.350444i	0.0687278	+	0.0396800i
$79$	−6.17631	+	10.6977i	−0.694889	+	1.20358i	0.275329	+	0.961350i	$0.411213\pi$
$79$	−6.17631	+	10.6977i	−0.694889	+	1.20358i	−0.970218	+	0.242233i	$0.922120\pi$
$80$	0.326676	+	0.565819i	0.0365235	+	0.0632605i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.84626	−	4.92986i	−0.314317	−	0.544412i
$83$			0.382821i			0.0420200i	0.999779	+	0.0210100i	$0.00668819\pi$
$83$			0.382821i			0.0420200i	−0.999779	+	0.0210100i	$0.993312\pi$
$84$	−4.09677			−0.446994
$85$	4.39000	−	2.53457i	0.476162	−	0.274912i
$86$	−8.66136	+	5.00064i	−0.933978	+	0.539233i
$87$		−	3.40960i		−	0.365548i
$88$	−9.49744	−	1.59739i	−1.01243	−	0.170283i
$89$	12.0854	−	6.97752i	1.28105	−	0.739616i	0.304011	−	0.952668i	$-0.401674\pi$
$89$	12.0854	−	6.97752i	1.28105	−	0.739616i	0.977041	+	0.213053i	$0.0683406\pi$
$90$	0.801683	−	1.38856i	0.0845048	−	0.146367i
$91$	2.34509	−	1.35394i	0.245832	−	0.141931i
$92$	1.55074	−	2.68596i	0.161676	−	0.280031i
$93$	4.07372	−	7.05590i	0.422426	−	0.731662i
$94$	−3.44243			−0.355060
$95$	2.38292	+	7.19836i	0.244482	+	0.738536i
$96$		−	5.46143i		−	0.557405i
$97$	−12.8826	−	7.43780i	−1.30803	−	0.755194i	−0.326266	−	0.945278i	$-0.605791\pi$
$97$	−12.8826	−	7.43780i	−1.30803	−	0.755194i	−0.981768	+	0.190084i	$0.939124\pi$
$98$	2.61809	−	4.53467i	0.264467	−	0.458071i
$99$	1.15894	+	3.10755i	0.116478	+	0.312320i
$100$	−1.13547	+	1.96669i	−0.113547	+	0.196669i
$101$	−10.1873	+	5.88162i	−1.01367	+	0.585243i	−0.912264	−	0.409602i	$-0.865667\pi$
$101$	−10.1873	+	5.88162i	−1.01367	+	0.585243i	−0.101406	+	0.994845i	$0.532334\pi$
$102$	2.68592			0.265945
$103$		−	7.63869i		−	0.752662i	−0.926485	−	0.376331i	$-0.877186\pi$
$103$		−	7.63869i		−	0.752662i	0.926485	−	0.376331i	$-0.122814\pi$
$104$	1.10406	+	1.91228i	0.108262	+	0.187514i
$105$	−3.09729	−	5.36467i	−0.302265	−	0.523538i
$106$			9.05615i			0.879611i
$107$	16.5490			1.59986			0.799928	−	0.600096i	$-0.204871\pi$
$107$	16.5490			1.59986			0.799928	+	0.600096i	$0.204871\pi$
$108$	−0.996315	+	0.575222i	−0.0958704	+	0.0553508i
$109$	5.29689	−	9.17448i	0.507350	−	0.878756i	−0.492614	−	0.870248i	$-0.663959\pi$
$109$	5.29689	−	9.17448i	0.507350	−	0.878756i	0.999964	−	0.00850765i	$-0.00270810\pi$
$110$	−1.85820	−	4.98254i	−0.177173	−	0.475066i
$111$	−4.79081	+	8.29793i	−0.454724	+	0.787605i
$112$	1.15829	+	0.668737i	0.109448	+	0.0631897i
$113$			11.6205i			1.09317i	0.837404	+	0.546585i	$0.184072\pi$
$113$			11.6205i			1.09317i	−0.837404	+	0.546585i	$0.815928\pi$
$114$	−0.813603	+	3.93441i	−0.0762009	+	0.368491i
$115$	4.68965			0.437312
$116$	1.96128	−	3.39704i	0.182100	−	0.315407i
$117$	0.380210	−	0.658543i	0.0351504	−	0.0608823i
$118$	5.82468	−	3.36288i	0.536205	−	0.309578i
$119$	5.18850	−	8.98675i	0.475629	−	0.823814i
$120$	4.37457	−	2.52566i	0.399342	−	0.230560i
$121$	10.3948	+	3.59843i	0.944979	+	0.327130i
$122$			2.21178i			0.200246i
$123$	−5.34859	+	3.08801i	−0.482266	+	0.278436i
$124$	8.11742	−	4.68660i	0.728966	−	0.420869i
$125$	−12.1316			−1.08508
$126$		−	3.28225i		−	0.292406i
$127$	0.110261	+	0.190978i	0.00978409	+	0.0169465i	0.870876	−	0.491503i	$-0.163552\pi$
$127$	0.110261	+	0.190978i	0.00978409	+	0.0169465i	−0.861092	+	0.508449i	$0.830219\pi$
$128$	2.79535	−	4.84170i	0.247077	−	0.427949i
$129$	5.42537	+	9.39702i	0.477678	+	0.827362i
$130$	−0.609615	+	1.05588i	−0.0534668	+	0.0926072i
$131$	13.7070	+	7.91373i	1.19758	+	0.691425i	0.960016	−	0.279946i	$-0.0903164\pi$
$131$	13.7070	+	7.91373i	1.19758	+	0.691425i	0.237568	+	0.971371i	$0.423650\pi$
$132$	−0.632864	+	3.76274i	−0.0550837	+	0.327505i
$133$	11.5924	+	10.3225i	1.00519	+	0.895074i
$134$		−	12.4321i		−	1.07397i
$135$	−1.50649	−	0.869775i	−0.129658	−	0.0748583i
$136$	7.32816	+	4.23092i	0.628385	+	0.362798i
$137$	6.82870	+	11.8277i	0.583415	+	1.01051i	0.995071	+	0.0991657i	$0.0316174\pi$
$137$	6.82870	+	11.8277i	0.583415	+	1.01051i	−0.411655	+	0.911340i	$0.635049\pi$
$138$	2.15194	+	1.24242i	0.183185	+	0.105762i
$139$	16.8645	−	9.73670i	1.43042	−	0.825856i	0.433272	−	0.901263i	$-0.357359\pi$
$139$	16.8645	−	9.73670i	1.43042	−	0.825856i	0.997153	+	0.0754075i	$0.0240258\pi$
$140$		−	7.12653i		−	0.602302i
$141$			3.73482i			0.314528i
$142$	7.34953	−	4.24325i	0.616759	−	0.356086i
$143$	−0.881280	−	2.36304i	−0.0736963	−	0.197607i
$144$	0.375586			0.0312989
$145$	5.93117			0.492557
$146$	−11.3882	+	6.57499i	−0.942496	+	0.544150i
$147$	−4.91983	−	2.84046i	−0.405780	−	0.234277i
$148$	−9.54632	+	5.51157i	−0.784702	+	0.453048i
$149$	−8.64191	−	4.98941i	−0.707973	−	0.408748i	0.102337	−	0.994750i	$-0.467368\pi$
$149$	−8.64191	−	4.98941i	−0.707973	−	0.408748i	−0.810310	+	0.586002i	$0.800701\pi$
$150$	−1.57567	−	0.909715i	−0.128653	−	0.0742779i
$151$	−0.581930			−0.0473568			−0.0236784	−	0.999720i	$-0.507538\pi$
$151$	−0.581930			−0.0473568			−0.0236784	+	0.999720i	$0.507538\pi$
$152$	−8.41738	+	9.45291i	−0.682740	+	0.766732i
$153$		−	2.91405i		−	0.235587i
$154$	−8.39417	−	6.93127i	−0.676421	−	0.558538i
$155$	12.2741	+	7.08645i	0.985878	+	0.569197i
$156$	0.757617	−	0.437410i	0.0606579	−	0.0350209i
$157$	2.10322	−	3.64289i	0.167856	−	0.290734i	−0.769810	−	0.638273i	$-0.779649\pi$
$157$	2.10322	−	3.64289i	0.167856	−	0.290734i	0.937666	+	0.347539i	$0.112982\pi$
$158$	−5.69278	−	9.86019i	−0.452894	−	0.784435i
$159$	9.82535			0.779201
$160$	9.50043			0.751075
$161$	8.31399	−	4.80009i	0.655234	−	0.378300i
$162$	−0.460857	−	0.798227i	−0.0362083	−	0.0627146i
$163$	−0.700790			−0.0548901			−0.0274450	−	0.999623i	$-0.508737\pi$
$163$	−0.700790			−0.0548901			−0.0274450	+	0.999623i	$0.508737\pi$
$164$	−7.10517			−0.554820
$165$	−5.40574	+	2.01603i	−0.420836	+	0.156948i
$166$	−0.305578	−	0.176425i	−0.0237174	−	0.0136933i
$167$	3.80474	+	6.58999i	0.294419	+	0.509949i	0.974850	−	0.222864i	$-0.0715405\pi$
$167$	3.80474	+	6.58999i	0.294419	+	0.509949i	−0.680430	+	0.732813i	$0.738207\pi$
$168$	5.17027	−	8.95517i	0.398895	−	0.690906i
$169$	6.21088	−	10.7576i	0.477760	−	0.827505i
$170$			4.67229i			0.358348i
$171$	4.26859	+	0.882707i	0.326427	+	0.0675023i
$172$			12.4832i			0.951834i
$173$	−3.35033	+	5.80294i	−0.254721	+	0.441189i	−0.964820	−	0.262913i	$-0.915317\pi$
$173$	−3.35033	+	5.80294i	−0.254721	+	0.441189i	0.710099	+	0.704102i	$0.248650\pi$
$174$	2.72164	+	1.57134i	0.206327	+	0.119123i
$175$	−6.08759	+	3.51467i	−0.460179	+	0.265684i
$176$	0.793143	−	0.960542i	0.0597854	−	0.0724036i
$177$	−3.64851	−	6.31940i	−0.274239	−	0.474995i
$178$			12.8625i			0.964088i
$179$			14.1949i			1.06098i	0.847691	+	0.530490i	$0.177992\pi$
$179$			14.1949i			1.06098i	−0.847691	+	0.530490i	$0.822008\pi$
$180$	−1.00063	−	1.73314i	−0.0745824	−	0.129181i
$181$	16.5699	−	9.56662i	1.23163	−	0.711081i	0.264260	−	0.964452i	$-0.414872\pi$
$181$	16.5699	−	9.56662i	1.23163	−	0.711081i	0.967369	+	0.253370i	$0.0815390\pi$
$182$			2.49588i			0.185007i
$183$	2.39964			0.177387
$184$	3.91418	+	6.77956i	0.288557	+	0.499796i
$185$	−14.4347	−	8.33386i	−1.06126	−	0.612718i
$186$	3.75481	+	6.50351i	0.275316	+	0.476861i
$187$	−7.45252	−	6.15373i	−0.544982	−	0.450005i
$188$	−2.14835	+	3.72105i	−0.156685	+	0.271386i
$189$	−3.56103			−0.259027
$190$	−6.84411	−	1.41530i	−0.496524	−	0.102677i
$191$	6.73902			0.487619			0.243809	−	0.969823i	$-0.421603\pi$
$191$	6.73902			0.487619			0.243809	+	0.969823i	$0.421603\pi$
$192$	5.01000	+	2.89252i	0.361565	+	0.208750i
$193$	3.86243	−	6.68993i	0.278024	−	0.481552i	−0.692870	−	0.721063i	$-0.743654\pi$
$193$	3.86243	−	6.68993i	0.278024	−	0.481552i	0.970894	+	0.239511i	$0.0769872\pi$
$194$	11.8741	−	6.85551i	0.852511	−	0.492197i
$195$	1.14557	+	0.661394i	0.0820358	+	0.0473634i
$196$	−3.26780	−	5.65999i	−0.233414	−	0.404285i
$197$		−	10.8986i		−	0.776496i	−0.921555	−	0.388248i	$-0.873080\pi$
$197$		−	10.8986i		−	0.776496i	0.921555	−	0.388248i	$-0.126920\pi$
$198$	−3.01463	−	0.507037i	−0.214241	−	0.0360336i
$199$	0.119894	+	0.207662i	0.00849903	+	0.0147208i	0.870244	−	0.492622i	$-0.163961\pi$
$199$	0.119894	+	0.207662i	0.00849903	+	0.0147208i	−0.861745	+	0.507342i	$0.830628\pi$
$200$	−2.86601	−	4.96407i	−0.202657	−	0.351013i
$201$	−13.4881			−0.951374
$202$		−	10.8423i		−	0.762863i
$203$	10.5150	−	6.07085i	0.738009	−	0.426090i
$204$	1.67623	−	2.90331i	0.117359	−	0.203272i
$205$	−5.37175	−	9.30414i	−0.375179	−	0.649829i
$206$	6.09741	+	3.52034i	0.424826	+	0.245274i
$207$	1.34795	−	2.33472i	0.0936889	−	0.162274i
$208$	−0.285603			−0.0198030
$209$	11.2716	−	9.05262i	0.779676	−	0.626183i
$210$	5.70963			0.394002
$211$	−2.47356	+	4.28433i	−0.170287	+	0.294946i	−0.938520	−	0.345224i	$-0.887803\pi$
$211$	−2.47356	+	4.28433i	−0.170287	+	0.294946i	0.768233	+	0.640170i	$0.221136\pi$
$212$	9.78914	+	5.65176i	0.672321	+	0.388165i
$213$	−4.60366	−	7.97377i	−0.315438	−	0.546354i
$214$	−7.62673	+	13.2099i	−0.521353	+	0.903009i
$215$	−16.3466	+	9.43771i	−1.11483	+	0.643646i
$216$		−	2.90381i		−	0.197579i
$217$	29.0133			1.96955
$218$	4.88221	+	8.45624i	0.330665	+	0.572729i
$219$	7.13345	+	12.3555i	0.482034	+	0.834907i
$220$	−6.54548	−	1.10090i	−0.441296	−	0.0742225i
$221$			2.21590i			0.149057i
$222$	−4.41576	−	7.64831i	−0.296366	−	0.513321i
$223$	0.0411307	+	0.0237468i	0.00275432	+	0.00159020i	0.501377	−	0.865229i	$-0.332827\pi$
$223$	0.0411307	+	0.0237468i	0.00275432	+	0.00159020i	−0.498622	+	0.866819i	$0.666160\pi$
$224$	16.8427	−	9.72415i	1.12535	−	0.649722i
$225$	−0.986983	+	1.70950i	−0.0657989	+	0.113967i
$226$	−9.27583	−	5.35541i	−0.617019	−	0.356236i
$227$	23.8084			1.58022			0.790110	−	0.612965i	$-0.210023\pi$
$227$	23.8084			1.58022			0.790110	+	0.612965i	$0.210023\pi$
$228$	3.74510	+	3.33484i	0.248025	+	0.220855i
$229$	−13.7094			−0.905943			−0.452972	−	0.891525i	$-0.649636\pi$
$229$	−13.7094			−0.905943			−0.452972	+	0.891525i	$0.649636\pi$
$230$	−2.16126	+	3.74341i	−0.142509	+	0.246833i
$231$	−7.51999	+	9.10714i	−0.494779	+	0.599206i
$232$	4.95041	+	8.57437i	0.325010	+	0.562935i
$233$	−16.7872	−	9.69209i	−1.09977	−	0.634950i	−0.163606	−	0.986526i	$-0.552313\pi$
$233$	−16.7872	−	9.69209i	−1.09977	−	0.634950i	−0.936159	+	0.351576i	$0.885646\pi$
$234$	0.350444	+	0.606987i	0.0229093	+	0.0396800i
$235$	−6.49690			−0.423811
$236$		−	8.39482i		−	0.546456i
$237$	−10.6977	+	6.17631i	−0.694889	+	0.401194i
$238$	4.78231	+	8.28321i	0.309991	+	0.536921i
$239$			6.51378i			0.421342i	0.977557	+	0.210671i	$0.0675648\pi$
$239$			6.51378i			0.421342i	−0.977557	+	0.210671i	$0.932435\pi$
$240$			0.653352i			0.0421737i
$241$	−4.77370	−	8.26830i	−0.307501	−	0.532608i	0.670314	−	0.742078i	$-0.266160\pi$
$241$	−4.77370	−	8.26830i	−0.307501	−	0.532608i	−0.977815	+	0.209470i	$0.932826\pi$
$242$	−7.66286	+	6.63903i	−0.492587	+	0.426773i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	2.39080	+	1.38033i	0.153055	+	0.0883666i
$245$	4.94113	−	8.55828i	0.315677	−	0.546769i
$246$		−	5.69252i		−	0.362942i
$247$	−3.24592	−	0.671228i	−0.206533	−	0.0427092i
$248$			23.6586i			1.50232i
$249$	−0.191410	+	0.331532i	−0.0121301	+	0.0210100i
$250$	5.59091	−	9.68374i	0.353600	−	0.612453i
$251$	10.3954	+	18.0054i	0.656153	+	1.13649i	0.981603	+	0.190931i	$0.0611508\pi$
$251$	10.3954	+	18.0054i	0.656153	+	1.13649i	−0.325450	+	0.945559i	$0.605516\pi$
$252$	−3.54790	−	2.04838i	−0.223497	−	0.129036i
$253$	−3.12438	−	8.37764i	−0.196428	−	0.526697i
$254$	−0.203258			−0.0127536
$255$	5.06913			0.317441
$256$	8.36156	+	14.4826i	0.522597	+	0.905165i
$257$	1.24210	−	0.717125i	0.0774799	−	0.0447330i	−0.460760	−	0.887525i	$-0.652423\pi$
$257$	1.24210	−	0.717125i	0.0774799	−	0.0447330i	0.538239	+	0.842792i	$0.319090\pi$
$258$	−10.0013			−0.622652
$259$	−34.1205			−2.12014
$260$	0.760897	+	1.31791i	0.0471888	+	0.0817335i
$261$	1.70480	−	2.95280i	0.105525	−	0.182774i
$262$	−12.6339	+	7.29418i	−0.780525	+	0.450636i
$263$	−20.4430	−	11.8028i	−1.26057	−	0.727789i	−0.287384	−	0.957816i	$-0.592786\pi$
$263$	−20.4430	−	11.8028i	−1.26057	−	0.727789i	−0.973184	+	0.230026i	$0.926119\pi$
$264$	−7.42633	−	6.13210i	−0.457059	−	0.377405i
$265$			17.0917i			1.04993i
$266$	−13.5821	+	4.49617i	−0.832774	+	0.275678i
$267$	13.9550			0.854035
$268$	−13.4383	−	7.75863i	−0.820878	−	0.473934i
$269$	−15.0418	−	8.68439i	−0.917115	−	0.529496i	−0.0344012	−	0.999408i	$-0.510952\pi$
$269$	−15.0418	−	8.68439i	−0.917115	−	0.529496i	−0.882713	+	0.469912i	$0.844286\pi$
$270$	1.38856	−	0.801683i	0.0845048	−	0.0487889i
$271$	−27.8457	−	16.0767i	−1.69150	−	0.976590i	−0.953306	−	0.302005i	$-0.902344\pi$
$271$	−27.8457	−	16.0767i	−1.69150	−	0.976590i	−0.738197	−	0.674585i	$-0.764322\pi$
$272$	−0.947845	+	0.547239i	−0.0574715	+	0.0331812i
$273$	2.70788			0.163888
$274$	−12.5882			−0.760482
$275$	2.28771	+	6.13419i	0.137954	+	0.369906i
$276$	2.68596	−	1.55074i	0.161676	−	0.0933437i
$277$		−	2.81009i		−	0.168842i	−0.996430	−	0.0844209i	$-0.973096\pi$
$277$		−	2.81009i		−	0.168842i	0.996430	−	0.0844209i	$-0.0269040\pi$
$278$			17.9489i			1.07650i
$279$	7.05590	−	4.07372i	0.422426	−	0.243887i
$280$	15.5780	+	8.99394i	0.930961	+	0.537491i
$281$	5.39343	+	9.34170i	0.321745	+	0.557279i	0.980848	−	0.194774i	$-0.0623972\pi$
$281$	5.39343	+	9.34170i	0.321745	+	0.557279i	−0.659103	+	0.752053i	$0.729064\pi$
$282$	−2.98123	−	1.72121i	−0.177530	−	0.102497i
$283$	−12.7052	−	7.33533i	−0.755244	−	0.436040i	0.0723415	−	0.997380i	$-0.476953\pi$
$283$	−12.7052	−	7.33533i	−0.755244	−	0.436040i	−0.827586	+	0.561340i	$0.810286\pi$
$284$		−	10.5925i		−	0.628550i
$285$	−1.53551	+	7.42542i	−0.0909560	+	0.439844i
$286$	2.29239	+	0.385561i	0.135552	+	0.0227987i
$287$	−19.0465	−	10.9965i	−1.12428	−	0.649102i
$288$	2.73071	−	4.72974i	0.160909	−	0.278702i
$289$	−4.25416	−	7.36843i	−0.250245	−	0.433437i
$290$	−2.73342	+	4.73442i	−0.160512	+	0.278015i
$291$	−7.43780	−	12.8826i	−0.436011	−	0.755194i
$292$			16.4133i			0.960514i
$293$	24.6753			1.44154			0.720772	−	0.693172i	$-0.243787\pi$
$293$	24.6753			1.44154			0.720772	+	0.693172i	$0.243787\pi$
$294$	4.53467	−	2.61809i	0.264467	−	0.152690i
$295$	10.9929	−	6.34676i	0.640032	−	0.369523i
$296$		−	27.8232i		−	1.61719i
$297$	−0.550103	+	3.27069i	−0.0319202	+	0.189784i
$298$	7.96536	−	4.59880i	0.461421	−	0.266402i
$299$	−1.02501	+	1.77536i	−0.0592777	+	0.102672i
$300$	−1.96669	+	1.13547i	−0.113547	+	0.0655564i
$301$	−19.3199	+	33.4631i	−1.11358	+	1.92878i
$302$	0.268186	−	0.464512i	0.0154324	−	0.0267297i
$303$	−11.7632			−0.675780
$304$	−0.514496	−	1.55420i	−0.0295083	−	0.0891394i
$305$			4.17430i			0.239020i
$306$	2.32607	+	1.34296i	0.132973	+	0.0767718i
$307$	−11.3606	+	19.6771i	−0.648382	+	1.12303i	0.335127	+	0.942173i	$0.391221\pi$
$307$	−11.3606	+	19.6771i	−0.648382	+	1.12303i	−0.983509	+	0.180858i	$0.942113\pi$
$308$	−12.7309	+	4.74791i	−0.725411	+	0.270537i
$309$	3.81934	−	6.61530i	0.217275	−	0.376331i
$310$	−11.3132	+	6.53167i	−0.642546	+	0.370974i
$311$	15.6415			0.886949			0.443474	−	0.896287i	$-0.353746\pi$
$311$	15.6415			0.886949			0.443474	+	0.896287i	$0.353746\pi$
$312$			2.20811i			0.125010i
$313$	−0.911080	−	1.57804i	−0.0514973	−	0.0891959i	0.839128	−	0.543935i	$-0.183066\pi$
$313$	−0.911080	−	1.57804i	−0.0514973	−	0.0891959i	−0.890625	+	0.454739i	$0.849733\pi$
$314$	1.93857	+	3.35770i	0.109400	+	0.189486i
$315$		−	6.19459i		−	0.349025i
$316$	−14.2110			−0.799431
$317$	−6.44615	+	3.72169i	−0.362052	+	0.209031i	−0.669981	−	0.742379i	$-0.733698\pi$
$317$	−6.44615	+	3.72169i	−0.362052	+	0.209031i	0.307929	+	0.951409i	$0.400364\pi$
$318$	−4.52808	+	7.84286i	−0.253922	+	0.439806i
$319$	−3.95152	−	10.5955i	−0.221243	−	0.593234i
$320$	−5.03169	+	8.71514i	−0.281280	+	0.487191i
$321$	14.3319	+	8.27452i	0.799928	+	0.461839i
$322$			8.84860i			0.493113i
$323$	−12.0585	+	3.99180i	−0.670953	+	0.222110i
$324$	−1.15044			−0.0639136
$325$	0.750521	−	1.29994i	0.0416314	−	0.0721077i
$326$	0.322963	−	0.559389i	0.0178873	−	0.0309817i
$327$	9.17448	−	5.29689i	0.507350	−	0.292919i
$328$	8.96698	−	15.5313i	0.495119	−	0.857570i
$329$	−11.5180	+	6.64989i	−0.635005	+	0.366621i
$330$	0.882017	−	5.24411i	0.0485534	−	0.288679i
$331$		−	11.4878i		−	0.631429i	−0.948854	−	0.315715i	$-0.897756\pi$
$331$		−	11.4878i		−	0.631429i	0.948854	−	0.315715i	$-0.102244\pi$
$332$	−0.381410	+	0.220207i	−0.0209326	+	0.0120854i
$333$	−8.29793	+	4.79081i	−0.454724	+	0.262535i
$334$	−7.01375			−0.383775
$335$		−	23.4631i		−	1.28193i
$336$	0.668737	+	1.15829i	0.0364826	+	0.0631897i
$337$	1.35777	−	2.35172i	0.0739624	−	0.128107i	−0.826672	−	0.562684i	$-0.809769\pi$
$337$	1.35777	−	2.35172i	0.0739624	−	0.128107i	0.900635	+	0.434577i	$0.143102\pi$
$338$	5.72465	+	9.91539i	0.311380	+	0.539326i
$339$	−5.81027	+	10.0637i	−0.315571	+	0.546585i
$340$	5.05045	+	2.91588i	0.273899	+	0.158136i
$341$	4.48194	−	26.6477i	0.242711	−	1.44306i
$342$	−2.67181	+	3.00050i	−0.144475	+	0.162248i
$343$			4.69726i			0.253628i
$344$	−27.2871	−	15.7542i	−1.47122	−	0.849411i
$345$	4.06136	+	2.34483i	0.218656	+	0.126241i
$346$	−3.08804	−	5.34864i	−0.166014	−	0.287545i
$347$	−21.3494	−	12.3261i	−1.14610	−	0.661700i	−0.198164	−	0.980169i	$-0.563498\pi$
$347$	−21.3494	−	12.3261i	−1.14610	−	0.661700i	−0.947933	+	0.318469i	$0.896831\pi$
$348$	3.39704	−	1.96128i	0.182100	−	0.105136i
$349$		−	21.1011i		−	1.12952i	−0.825256	−	0.564759i	$-0.808969\pi$
$349$		−	21.1011i		−	1.12952i	0.825256	−	0.564759i	$-0.191031\pi$
$350$		−	6.47904i		−	0.346319i
$351$	0.658543	−	0.380210i	0.0351504	−	0.0202941i
$352$	−6.32947	−	16.9717i	−0.337362	−	0.904592i
$353$	−12.7521			−0.678727			−0.339364	−	0.940655i	$-0.610212\pi$
$353$	−12.7521			−0.678727			−0.339364	+	0.940655i	$0.610212\pi$
$354$	6.72576			0.357470
$355$	13.8708	−	8.00830i	0.736184	−	0.425036i
$356$	13.9036	+	8.02725i	0.736890	+	0.425444i
$357$	8.98675	−	5.18850i	0.475629	−	0.274605i
$358$	−11.3308	−	6.54183i	−0.598850	−	0.345746i
$359$	9.75636	+	5.63284i	0.514921	+	0.297290i	0.734854	−	0.678225i	$-0.237251\pi$
$359$	9.75636	+	5.63284i	0.514921	+	0.297290i	−0.219933	+	0.975515i	$0.570584\pi$
$360$	5.05132			0.266228
$361$	−2.19461	−	18.8728i	−0.115506	−	0.993307i
$362$			17.6354i			0.926894i
$363$	7.20292	+	8.31372i	0.378055	+	0.436357i
$364$	2.69790	+	1.55763i	0.141408	+	0.0816420i
$365$	−21.4930	+	12.4090i	−1.12499	+	0.649516i
$366$	−1.10589	+	1.91546i	−0.0578059	+	0.100123i
$367$	0.313272	+	0.542603i	0.0163527	+	0.0283237i	0.874086	−	0.485771i	$-0.161461\pi$
$367$	0.313272	+	0.542603i	0.0163527	+	0.0283237i	−0.857733	+	0.514095i	$0.828128\pi$
$368$	−1.01254			−0.0527825
$369$	−6.17602			−0.321511
$370$	13.3046	−	7.68143i	0.691675	−	0.399338i
$371$	17.4942	+	30.3008i	0.908252	+	1.57314i
$372$	9.37319			0.485977
$373$	−7.00152			−0.362525			−0.181262	−	0.983435i	$-0.558018\pi$
$373$	−7.00152			−0.362525			−0.181262	+	0.983435i	$0.558018\pi$
$374$	8.34662	−	3.11281i	0.431593	−	0.160960i
$375$	−10.5062	−	6.06578i	−0.542540	−	0.313236i
$376$	−5.42259	−	9.39221i	−0.279649	−	0.484366i
$377$	−1.29636	+	2.24537i	−0.0667661	+	0.115642i
$378$	1.64112	−	2.84251i	0.0844103	−	0.146203i
$379$			8.96742i			0.460625i	0.973117	+	0.230313i	$0.0739749\pi$
$379$			8.96742i			0.460625i	−0.973117	+	0.230313i	$0.926025\pi$
$380$	−5.80112	+	6.51479i	−0.297591	+	0.334202i
$381$			0.220522i			0.0112977i
$382$	−3.10572	+	5.37927i	−0.158903	+	0.275227i
$383$	17.6276	+	10.1773i	0.900730	+	0.520037i	0.877437	−	0.479692i	$-0.159252\pi$
$383$	17.6276	+	10.1773i	0.900730	+	0.520037i	0.0232929	+	0.999729i	$0.492585\pi$
$384$	4.84170	−	2.79535i	0.247077	−	0.142650i
$385$	−15.8423	−	13.0814i	−0.807399	−	0.666690i
$386$	3.56005	+	6.16619i	0.181202	+	0.313851i
$387$			10.8507i			0.551574i
$388$		−	17.1135i		−	0.868809i
$389$	5.34578	+	9.25916i	0.271042	+	0.469458i	0.969129	−	0.246555i	$-0.0792985\pi$
$389$	5.34578	+	9.25916i	0.271042	+	0.469458i	−0.698087	+	0.716013i	$0.745965\pi$
$390$	−1.05588	+	0.609615i	−0.0534668	+	0.0308691i
$391$			7.85598i			0.397294i
$392$	16.4963			0.833189
$393$	7.91373	+	13.7070i	0.399195	+	0.691425i
$394$	8.69959	+	5.02271i	0.438279	+	0.253040i
$395$	−10.7440	−	18.6091i	−0.540589	−	0.936328i
$396$	−2.42945	+	2.94220i	−0.122084	+	0.147851i
$397$	−8.85962	+	15.3453i	−0.444651	+	0.770159i	−0.998028	−	0.0627725i	$-0.980006\pi$
$397$	−8.85962	+	15.3453i	−0.444651	+	0.770159i	0.553377	+	0.832931i	$0.313339\pi$
$398$	−0.221015			−0.0110785
$399$	4.87806	+	14.7357i	0.244208	+	0.737710i
$400$	0.741395			0.0370697
$401$	−2.18175	−	1.25963i	−0.108951	−	0.0629032i	0.444534	−	0.895762i	$-0.353369\pi$
$401$	−2.18175	−	1.25963i	−0.108951	−	0.0629032i	−0.553486	+	0.832859i	$0.686703\pi$
$402$	6.21606	−	10.7665i	0.310029	−	0.536986i
$403$	−5.36544	+	3.09774i	−0.267272	+	0.154309i
$404$	−11.7199	−	6.76648i	−0.583086	−	0.336645i
$405$	−0.869775	−	1.50649i	−0.0432195	−	0.0748583i
$406$			11.1912i			0.555408i
$407$	−5.27089	+	31.3385i	−0.261268	+	1.55339i
$408$	4.23092	+	7.32816i	0.209462	+	0.362798i
$409$	−5.76427	−	9.98401i	−0.285025	−	0.493678i	0.687590	−	0.726099i	$-0.258669\pi$
$409$	−5.76427	−	9.98401i	−0.285025	−	0.493678i	−0.972615	+	0.232421i	$0.925335\pi$
$410$	9.90242			0.489045
$411$			13.6574i			0.673670i
$412$	7.61054	−	4.39395i	0.374944	−	0.216474i
$413$	12.9924	−	22.5036i	0.639316	−	1.10733i
$414$	1.24242	+	2.15194i	0.0610617	+	0.105762i
$415$	−0.576717	−	0.332968i	−0.0283099	−	0.0163447i
$416$	−2.07649	+	3.59658i	−0.101808	+	0.176337i
$417$	19.4734			0.953616
$418$	2.03143	+	13.1693i	0.0993607	+	0.644131i
$419$	3.35421			0.163864			0.0819320	−	0.996638i	$-0.473891\pi$
$419$	3.35421			0.163864			0.0819320	+	0.996638i	$0.473891\pi$
$420$	3.56327	−	6.17176i	0.173870	−	0.301151i
$421$	5.32185	+	3.07257i	0.259371	+	0.149748i	0.624048	−	0.781386i	$-0.285487\pi$
$421$	5.32185	+	3.07257i	0.259371	+	0.149748i	−0.364677	+	0.931134i	$0.618820\pi$
$422$	−2.27991	−	3.94893i	−0.110984	−	0.192231i
$423$	−1.86741	+	3.23445i	−0.0907965	+	0.157264i
$424$	−24.7085	+	14.2655i	−1.19995	+	0.692792i
$425$		−	5.75223i		−	0.279024i
$426$	8.48651			0.411173
$427$	4.27260	+	7.40036i	0.206766	+	0.358129i
$428$	9.51938	+	16.4880i	0.460137	+	0.796980i
$429$	0.418309	−	2.48709i	0.0201962	−	0.120078i
$430$		−	17.3977i		−	0.838993i
$431$	7.72284	+	13.3764i	0.371996	+	0.644317i	0.989873	−	0.141959i	$-0.0453401\pi$
$431$	7.72284	+	13.3764i	0.371996	+	0.644317i	−0.617876	+	0.786275i	$0.712007\pi$
$432$	0.325267	+	0.187793i	0.0156494	+	0.00903521i
$433$	13.3342	−	7.69849i	0.640800	−	0.369966i	−0.144123	−	0.989560i	$-0.546036\pi$
$433$	13.3342	−	7.69849i	0.640800	−	0.369966i	0.784923	+	0.619594i	$0.212703\pi$
$434$	−13.3710	+	23.1592i	−0.641827	+	1.11168i
$435$	5.13655	+	2.96559i	0.246279	+	0.142189i
$436$	12.1876			0.583678
$437$	−11.5077	−	2.37969i	−0.550487	−	0.113836i
$438$	−13.1500			−0.628330
$439$	0.808369	−	1.40014i	0.0385814	−	0.0668249i	−0.846090	−	0.533040i	$-0.821049\pi$
$439$	0.808369	−	1.40014i	0.0385814	−	0.0668249i	0.884671	+	0.466215i	$0.154383\pi$
$440$	10.6671	−	12.9185i	0.508534	−	0.615864i
$441$	−2.84046	−	4.91983i	−0.135260	−	0.234277i
$442$	−1.76879	−	1.02121i	−0.0841328	−	0.0485741i
$443$	−15.5582	−	26.9477i	−0.739195	−	1.28032i	−0.952858	−	0.303416i	$-0.901873\pi$
$443$	−15.5582	−	26.9477i	−0.739195	−	1.28032i	0.213664	−	0.976907i	$-0.431460\pi$
$444$	−11.0231			−0.523135
$445$			24.2755i			1.15077i
$446$	−0.0379107	+	0.0218878i	−0.00179512	+	0.00103642i
$447$	−4.98941	−	8.64191i	−0.235991	−	0.408748i
$448$			20.6007i			0.973292i
$449$		−	23.2893i		−	1.09909i	−0.835465	−	0.549544i	$-0.814801\pi$
$449$		−	23.2893i		−	1.09909i	0.835465	−	0.549544i	$-0.185199\pi$
$450$	−0.909715	−	1.57567i	−0.0428844	−	0.0742779i
$451$	−13.0422	+	15.7948i	−0.614132	+	0.743749i
$452$	−11.5777	+	6.68440i	−0.544570	+	0.314408i
$453$	−0.503966	−	0.290965i	−0.0236784	−	0.0136707i
$454$	−10.9723	+	19.0045i	−0.514954	+	0.891927i
$455$			4.71048i			0.220831i
$456$	−12.0161	+	3.97777i	−0.562706	+	0.186276i
$457$		−	20.0009i		−	0.935603i	−0.883833	−	0.467802i	$-0.845046\pi$
$457$		−	20.0009i		−	0.935603i	0.883833	−	0.467802i	$-0.154954\pi$
$458$	6.31807	−	10.9432i	0.295224	−	0.511343i
$459$	1.45702	−	2.52364i	0.0680081	−	0.117793i
$460$	2.69759	+	4.67237i	0.125776	+	0.217850i
$461$	−4.35044	−	2.51173i	−0.202620	−	0.116983i	0.395257	−	0.918571i	$-0.370656\pi$
$461$	−4.35044	−	2.51173i	−0.202620	−	0.116983i	−0.597877	+	0.801588i	$0.703989\pi$
$462$	−3.80393	−	10.1997i	−0.176975	−	0.474535i
$463$	−18.3132			−0.851087			−0.425544	−	0.904938i	$-0.639917\pi$
$463$	−18.3132			−0.851087			−0.425544	+	0.904938i	$0.639917\pi$
$464$	−1.28060			−0.0594504
$465$	7.08645	+	12.2741i	0.328626	+	0.569197i
$466$	15.4730	−	8.93332i	0.716771	−	0.413828i
$467$	5.86763			0.271521			0.135761	−	0.990742i	$-0.456652\pi$
$467$	5.86763			0.271521			0.135761	+	0.990742i	$0.456652\pi$
$468$	0.874821			0.0404386
$469$	−24.0157	−	41.5964i	−1.10894	−	1.92074i
$470$	2.99414	−	5.18600i	0.138109	−	0.239212i
$471$	3.64289	−	2.10322i	0.167856	−	0.0969115i
$472$	18.3503	+	10.5946i	0.844642	+	0.487654i
$473$	27.7502	+	22.9140i	1.27596	+	1.05359i
$474$		−	11.3856i		−	0.522956i
$475$	8.42604	+	1.74243i	0.386613	+	0.0799484i
$476$	11.9382			0.547185
$477$	8.50900	+	4.91267i	0.389600	+	0.224936i
$478$	−5.19948	−	3.00192i	−0.237819	−	0.137305i
$479$	1.68573	−	0.973257i	0.0770230	−	0.0444692i	−0.460994	−	0.887403i	$-0.652507\pi$
$479$	1.68573	−	0.973257i	0.0770230	−	0.0444692i	0.538017	+	0.842934i	$0.319174\pi$
$480$	8.22761	+	4.75022i	0.375537	+	0.216817i
$481$	6.30991	−	3.64303i	0.287707	−	0.166108i
$482$	8.79997			0.400828
$483$	9.60017			0.436823
$484$	2.39414	+	12.4264i	0.108824	+	0.564835i
$485$	22.4100	−	12.9384i	1.01759	−	0.587503i
$486$		−	0.921713i		−	0.0418098i
$487$		−	19.8947i		−	0.901515i	−0.892646	−	0.450758i	$-0.851154\pi$
$487$		−	19.8947i		−	0.901515i	0.892646	−	0.450758i	$-0.148846\pi$
$488$	−6.03456	+	3.48405i	−0.273171	+	0.157716i
$489$	−0.606902	−	0.350395i	−0.0274450	−	0.0158454i
$490$	4.55430	+	7.88828i	0.205742	+	0.356356i
$491$	11.5059	+	6.64296i	0.519256	+	0.299792i	0.736630	−	0.676296i	$-0.236416\pi$
$491$	11.5059	+	6.64296i	0.519256	+	0.299792i	−0.217374	+	0.976088i	$0.569749\pi$
$492$	−6.15326	−	3.55258i	−0.277410	−	0.160163i
$493$			9.93574i			0.447483i
$494$	2.03169	−	2.28164i	0.0914102	−	0.102656i
$495$	−5.68952	−	0.956932i	−0.255725	−	0.0430109i
$496$	−2.65010	−	1.53004i	−0.118993	−	0.0687006i
$497$	16.3938	−	28.3948i	0.735361	−	1.27368i
$498$	−0.176425	−	0.305578i	−0.00790581	−	0.0136933i
$499$	−9.65043	+	16.7150i	−0.432012	+	0.748268i	−0.997047	−	0.0768000i	$-0.975530\pi$
$499$	−9.65043	+	16.7150i	−0.432012	+	0.748268i	0.565034	+	0.825068i	$0.308863\pi$
$500$	−6.97835	−	12.0869i	−0.312081	−	0.540540i
$501$			7.60947i			0.339966i
$502$	−19.1632			−0.855295
$503$	25.6498	−	14.8089i	1.14367	−	0.660296i	0.196331	−	0.980538i	$-0.437097\pi$
$503$	25.6498	−	14.8089i	1.14367	−	0.660296i	0.947336	+	0.320241i	$0.103764\pi$
$504$	8.95517	−	5.17027i	0.398895	−	0.230302i
$505$		−	20.4627i		−	0.910580i
$506$	8.12715	+	1.36692i	0.361296	+	0.0607671i
$507$	10.7576	−	6.21088i	0.477760	−	0.275835i
$508$	−0.126849	+	0.219710i	−0.00562803	+	0.00974803i
$509$	14.1179	−	8.15098i	0.625765	−	0.361286i	−0.153345	−	0.988173i	$-0.549005\pi$
$509$	14.1179	−	8.15098i	0.625765	−	0.361286i	0.779110	+	0.626887i	$0.215671\pi$
$510$	−2.33614	+	4.04632i	−0.103446	+	0.179174i
$511$	−25.4024	+	43.9983i	−1.12374	+	1.94637i
$512$	−4.23250			−0.187052
$513$	3.25535	+	2.89874i	0.143727	+	0.127983i
$514$			1.32197i			0.0583095i
$515$	11.5076	+	6.64394i	0.507087	+	0.292767i
$516$	−6.24159	+	10.8108i	−0.274771	+	0.475917i
$517$	4.32843	+	11.6061i	0.190364	+	0.510437i
$518$	15.7246	−	27.2359i	0.690901	−	1.19668i
$519$	−5.80294	+	3.35033i	−0.254721	+	0.147063i
$520$	−3.84112			−0.168444
$521$		−	8.06667i		−	0.353407i	−0.984264	−	0.176704i	$-0.943457\pi$
$521$		−	8.06667i		−	0.353407i	0.984264	−	0.176704i	$-0.0565434\pi$
$522$	1.57134	+	2.72164i	0.0687756	+	0.119123i
$523$	−13.2304	−	22.9157i	−0.578525	−	1.00204i	−0.995649	−	0.0931853i	$-0.970295\pi$
$523$	−13.2304	−	22.9157i	−0.578525	−	1.00204i	0.417124	−	0.908850i	$-0.363038\pi$
$524$			18.2086i			0.795447i
$525$	−7.02935			−0.306786
$526$	18.8426	−	10.8788i	0.821575	−	0.474336i
$527$	−11.8710	+	20.5612i	−0.517110	+	0.895661i
$528$	1.16715	−	0.435282i	0.0507938	−	0.0189432i
$529$	7.86607	−	13.6244i	0.342003	−	0.592366i
$530$	−13.6430	−	7.87682i	−0.592616	−	0.342147i
$531$		−	7.29702i		−	0.316664i
$532$	−3.61625	+	17.4874i	−0.156784	+	0.758175i
$533$	4.69636			0.203422
$534$	−6.43127	+	11.1393i	−0.278308	+	0.482044i
$535$	−14.3939	+	24.9310i	−0.622304	+	1.07786i
$536$	33.9194	−	19.5833i	1.46509	−	0.845872i
$537$	−7.09747	+	12.2932i	−0.306278	+	0.530490i
$538$	13.8642	−	8.00451i	0.597729	−	0.345099i
$539$	−18.5805	−	3.12510i	−0.800320	−	0.134607i
$540$		−	2.00126i		−	0.0861204i
$541$	8.95945	−	5.17274i	0.385197	−	0.222393i	−0.294880	−	0.955534i	$-0.595280\pi$
$541$	8.95945	−	5.17274i	0.385197	−	0.222393i	0.680077	+	0.733141i	$0.261946\pi$
$542$	25.6657	−	14.8181i	1.10244	−	0.636492i
$543$	19.1332			0.821086
$544$			15.9149i			0.682344i
$545$	9.21420	+	15.9595i	0.394693	+	0.683628i
$546$	−1.24794	+	2.16150i	−0.0534070	+	0.0925036i
$547$	7.58218	+	13.1327i	0.324191	+	0.561515i	0.981348	−	0.192238i	$-0.0615747\pi$
$547$	7.58218	+	13.1327i	0.324191	+	0.561515i	−0.657158	+	0.753753i	$0.728241\pi$
$548$	−7.85605	+	13.6071i	−0.335594	+	0.581265i
$549$	2.07815	+	1.19982i	0.0886934	+	0.0512072i
$550$	−5.95078	−	1.00087i	−0.253742	−	0.0426774i
$551$	−14.5542	−	3.00968i	−0.620029	−	0.128217i
$552$			7.82837i			0.333197i
$553$	−38.0947	−	21.9940i	−1.61995	−	0.935280i
$554$	2.24309	+	1.29505i	0.0952997	+	0.0550213i
$555$	−8.33386	−	14.4347i	−0.353753	−	0.612718i
$556$	19.4016	+	11.2015i	0.822812	+	0.475051i
$557$	29.3386	−	16.9387i	1.24312	−	0.717715i	0.273390	−	0.961903i	$-0.411855\pi$
$557$	29.3386	−	16.9387i	1.24312	−	0.717715i	0.969728	+	0.244189i	$0.0785216\pi$
$558$			7.50961i			0.317907i
$559$		−	8.25112i		−	0.348985i
$560$	−2.01490	+	1.16330i	−0.0851450	+	0.0491585i
$561$	−3.37721	−	9.05555i	−0.142586	−	0.382325i
$562$	−9.94239			−0.419395
$563$	−24.4907			−1.03216			−0.516080	−	0.856541i	$-0.672609\pi$
$563$	−24.4907			−1.03216			−0.516080	+	0.856541i	$0.672609\pi$
$564$	−3.72105	+	2.14835i	−0.156685	+	0.0904619i
$565$	−17.5063	−	10.1073i	−0.736495	−	0.425216i
$566$	11.7105	−	6.76107i	0.492230	−	0.284189i
$567$	−3.08394	−	1.78051i	−0.129513	−	0.0747746i
$568$	23.1543	+	13.3681i	0.971532	+	0.560914i
$569$	1.27774			0.0535658			0.0267829	−	0.999641i	$-0.491474\pi$
$569$	1.27774			0.0535658			0.0267829	+	0.999641i	$0.491474\pi$
$570$	−5.21952	−	4.64774i	−0.218622	−	0.194672i
$571$		−	0.409674i		−	0.0171443i	−0.999963	−	0.00857215i	$-0.997271\pi$
$571$		−	0.409674i		−	0.0171443i	0.999963	−	0.00857215i	$-0.00272863\pi$
$572$	1.84740	−	2.23731i	0.0772436	−	0.0935465i
$573$	5.83617	+	3.36951i	0.243809	+	0.140763i
$574$	17.5554	−	10.1356i	0.732748	−	0.423052i
$575$	2.66081	−	4.60865i	0.110963	−	0.192194i
$576$	2.89252	+	5.01000i	0.120522	+	0.208750i
$577$	44.2314			1.84138			0.920689	−	0.390296i	$-0.127627\pi$
$577$	44.2314			1.84138			0.920689	+	0.390296i	$0.127627\pi$
$578$	7.84223			0.326194
$579$	6.68993	−	3.86243i	0.278024	−	0.160517i
$580$	3.41174	+	5.90931i	0.141665	+	0.245371i
$581$	−1.36324			−0.0565565
$582$	13.7110			0.568340
$583$	30.5327	−	11.3870i	1.26454	−	0.471601i
$584$	−35.8780	−	20.7141i	−1.48464	−	0.857157i
$585$	0.661394	+	1.14557i	0.0273453	+	0.0473634i
$586$	−11.3718	+	19.6965i	−0.469763	+	0.813654i
$587$	4.34110	−	7.51901i	0.179176	−	0.310343i	−0.762422	−	0.647080i	$-0.775990\pi$
$587$	4.34110	−	7.51901i	0.179176	−	0.310343i	0.941599	+	0.336737i	$0.109323\pi$
$588$		−	6.53559i		−	0.269523i
$589$	−26.5228	−	23.6173i	−1.09285	−	0.973135i
$590$			11.6998i			0.481673i
$591$	5.44932	−	9.43850i	0.224155	−	0.388248i
$592$	3.11659	+	1.79937i	0.128091	+	0.0739535i
$593$	−26.3345	+	15.2042i	−1.08143	+	0.624362i	−0.931281	−	0.364302i	$-0.881308\pi$
$593$	−26.3345	+	15.2042i	−1.08143	+	0.624362i	−0.150146	+	0.988664i	$0.547974\pi$
$594$	−2.35723	−	1.94642i	−0.0967184	−	0.0798628i
$595$	9.02566	+	15.6329i	0.370016	+	0.640887i
$596$		−	11.4801i		−	0.470242i
$597$			0.239787i			0.00981384i
$598$	−0.944762	−	1.63638i	−0.0386342	−	0.0669164i
$599$	3.20926	−	1.85287i	0.131127	−	0.0757061i	−0.433002	−	0.901393i	$-0.642546\pi$
$599$	3.20926	−	1.85287i	0.131127	−	0.0757061i	0.564129	+	0.825687i	$0.309212\pi$
$600$		−	5.73201i		−	0.234008i
$601$	45.8624			1.87077			0.935383	−	0.353637i	$-0.115055\pi$
$601$	45.8624			1.87077			0.935383	+	0.353637i	$0.115055\pi$
$602$	−17.8074	−	30.8433i	−0.725776	−	1.25708i
$603$	−11.6810	−	6.74403i	−0.475687	−	0.274638i
$604$	−0.334739	−	0.579785i	−0.0136203	−	0.0235911i
$605$	−14.4621	+	12.5298i	−0.587969	+	0.509411i
$606$	5.42116	−	9.38973i	0.220220	−	0.381432i
$607$	−19.5511			−0.793557			−0.396778	−	0.917914i	$-0.629872\pi$
$607$	−19.5511			−0.793557			−0.396778	+	0.917914i	$0.629872\pi$
$608$	−23.3126	−	4.82084i	−0.945450	−	0.195511i
$609$	12.1417			0.492006
$610$	−3.33204	−	1.92375i	−0.134910	−	0.0778905i
$611$	1.42001	−	2.45954i	0.0574476	−	0.0995022i
$612$	2.90331	−	1.67623i	0.117359	−	0.0677574i
$613$	19.1210	+	11.0395i	0.772288	+	0.445881i	0.833690	−	0.552232i	$-0.186224\pi$
$613$	19.1210	+	11.0395i	0.772288	+	0.445881i	−0.0614021	+	0.998113i	$0.519557\pi$
$614$	−10.4712	−	18.1366i	−0.422583	−	0.731935i
$615$		−	10.7435i		−	0.433219i
$616$	5.68836	−	33.8207i	0.229191	−	1.36267i
$617$	13.2725	+	22.9887i	0.534331	+	0.925488i	0.999195	+	0.0401065i	$0.0127697\pi$
$617$	13.2725	+	22.9887i	0.534331	+	0.925488i	−0.464864	+	0.885382i	$0.653897\pi$
$618$	3.52034	+	6.09741i	0.141609	+	0.245274i
$619$	−27.2310			−1.09451			−0.547254	−	0.836967i	$-0.684327\pi$
$619$	−27.2310			−1.09451			−0.547254	+	0.836967i	$0.684327\pi$
$620$			16.3051i			0.654830i
$621$	2.33472	−	1.34795i	0.0936889	−	0.0540913i
$622$	−7.20849	+	12.4855i	−0.289034	+	0.500622i
$623$	24.8471	+	43.0365i	0.995480	+	1.72422i
$624$	−0.247340	−	0.142802i	−0.00990151	−	0.00571664i
$625$	5.61682	−	9.72861i	0.224673	−	0.389144i
$626$	1.67951			0.0671267
$627$	14.2878	−	2.20398i	0.570602	−	0.0880184i
$628$	4.83929			0.193109
$629$	13.9607	−	24.1806i	0.556648	−	0.964143i
$630$	4.94469	+	2.85482i	0.197001	+	0.113739i
$631$	13.0878	+	22.6688i	0.521018	+	0.902430i	0.999701	+	0.0244424i	$0.00778102\pi$
$631$	13.0878	+	22.6688i	0.521018	+	0.902430i	−0.478683	+	0.877988i	$0.658886\pi$
$632$	17.9348	−	31.0640i	0.713408	−	1.23566i
$633$	−4.28433	+	2.47356i	−0.170287	+	0.0983153i
$634$		−	6.86066i		−	0.272471i
$635$	−0.383609			−0.0152231
$636$	5.65176	+	9.78914i	0.224107	+	0.388165i
$637$	2.15994	+	3.74113i	0.0855800	+	0.148229i
$638$	10.2787	+	1.72880i	0.406938	+	0.0684437i
$639$		−	9.20732i		−	0.364236i
$640$	4.86266	+	8.42237i	0.192213	+	0.332923i
$641$	5.07826	+	2.93193i	0.200579	+	0.115804i	0.596926	−	0.802297i	$-0.296389\pi$
$641$	5.07826	+	2.93193i	0.200579	+	0.115804i	−0.396346	+	0.918101i	$0.629722\pi$
$642$	−13.2099	+	7.62673i	−0.521353	+	0.301003i
$643$	−13.7171	+	23.7588i	−0.540951	+	0.936954i	0.457899	+	0.889004i	$0.348602\pi$
$643$	−13.7171	+	23.7588i	−0.540951	+	0.936954i	−0.998850	+	0.0479501i	$0.984731\pi$
$644$	9.56479	+	5.52223i	0.376906	+	0.217607i
$645$	−18.8754			−0.743219
$646$	2.37088	−	11.4651i	0.0932810	−	0.451087i
$647$	−8.38224			−0.329540			−0.164770	−	0.986332i	$-0.552688\pi$
$647$	−8.38224			−0.329540			−0.164770	+	0.986332i	$0.552688\pi$
$648$	1.45190	−	2.51477i	0.0570361	−	0.0987895i
$649$	−18.6617	−	15.4095i	−0.732537	−	0.604874i
$650$	0.691765	+	1.19817i	0.0271333	+	0.0469962i
$651$	25.1263	+	14.5066i	0.984775	+	0.568560i
$652$	−0.403110	−	0.698207i	−0.0157870	−	0.0273439i
$653$	15.8771			0.621321			0.310660	−	0.950521i	$-0.399450\pi$
$653$	15.8771			0.621321			0.310660	+	0.950521i	$0.399450\pi$
$654$			9.76442i			0.381819i
$655$	−23.8440	+	13.7663i	−0.931661	+	0.537895i
$656$	1.15981	+	2.00886i	0.0452831	+	0.0784327i
$657$			14.2669i			0.556604i
$658$		−	12.2586i		−	0.477890i
$659$	−23.0867	−	39.9873i	−0.899330	−	1.55769i	−0.828352	−	0.560208i	$-0.810721\pi$
$659$	−23.0867	−	39.9873i	−0.899330	−	1.55769i	−0.0709779	−	0.997478i	$-0.522612\pi$
$660$	−5.11810	−	4.22615i	−0.199222	−	0.164503i
$661$	−18.1760	+	10.4939i	−0.706966	+	0.408167i	−0.809937	−	0.586518i	$-0.800499\pi$
$661$	−18.1760	+	10.4939i	−0.706966	+	0.408167i	0.102971	+	0.994684i	$0.467165\pi$
$662$	9.16991	+	5.29425i	0.356399	+	0.205767i
$663$	−1.10795	+	1.91902i	−0.0430292	+	0.0745287i
$664$		−	1.11164i		−	0.0431399i
$665$	−25.6336	+	8.48563i	−0.994027	+	0.329059i
$666$		−	8.83151i		−	0.342214i
$667$	−4.59597	+	7.96045i	−0.177957	+	0.308230i
$668$	−4.37714	+	7.58143i	−0.169357	+	0.293334i
$669$	0.0237468	+	0.0411307i	0.000918105	+	0.00159020i
$670$	18.7289	+	10.8131i	0.723561	+	0.417748i
$671$	7.45701	−	2.78104i	0.287875	−	0.107361i
$672$	19.4483			0.750235
$673$	20.6869			0.797420			0.398710	−	0.917077i	$-0.369458\pi$
$673$	20.6869			0.797420			0.398710	+	0.917077i	$0.369458\pi$
$674$	1.25147	+	2.16762i	0.0482050	+	0.0834934i
$675$	−1.70950	+	0.986983i	−0.0657989	+	0.0379890i
$676$	14.2906			0.549637
$677$	−16.0938			−0.618535			−0.309268	−	0.950975i	$-0.600084\pi$
$677$	−16.0938			−0.618535			−0.309268	+	0.950975i	$0.600084\pi$
$678$	−5.35541	−	9.27583i	−0.205673	−	0.356236i
$679$	26.4862	−	45.8754i	1.01645	−	1.76054i
$680$	−12.7477	+	7.35989i	−0.488852	+	0.282239i
$681$	20.6187	+	11.9042i	0.790110	+	0.456170i
$682$	19.2054	+	15.8584i	0.735413	+	0.607249i
$683$			1.75157i			0.0670218i	0.999438	+	0.0335109i	$0.0106689\pi$
$683$			1.75157i			0.0670218i	−0.999438	+	0.0335109i	$0.989331\pi$
$684$	1.57593	+	4.76061i	0.0602573	+	0.182026i
$685$	−23.7577			−0.907737
$686$	−3.74948	−	2.16476i	−0.143156	−	0.0826511i
$687$	−11.8727	−	6.85471i	−0.452972	−	0.261523i
$688$	3.52939	−	2.03770i	0.134557	−	0.0776865i
$689$	−6.47041	−	3.73569i	−0.246503	−	0.142319i
$690$	−3.74341	+	2.16126i	−0.142509	+	0.0822776i
$691$	−7.03102			−0.267473			−0.133736	−	0.991017i	$-0.542698\pi$
$691$	−7.03102			−0.267473			−0.133736	+	0.991017i	$0.542698\pi$
$692$	−7.70874			−0.293042
$693$	−11.0661	+	4.12702i	−0.420365	+	0.156772i
$694$	19.6780	−	11.3611i	0.746968	−	0.431262i
$695$			33.8749i			1.28495i
$696$			9.90082i			0.375290i
$697$	15.5860	−	8.99860i	0.590363	−	0.340846i
$698$	16.8435	+	9.72459i	0.637536	+	0.368081i
$699$	−9.69209	−	16.7872i	−0.366588	−	0.634950i
$700$	−7.00344	−	4.04344i	−0.264705	−	0.152828i
$701$	−42.6064	−	24.5988i	−1.60922	−	0.929085i	−0.989544	−	0.144228i	$-0.953930\pi$
$701$	−42.6064	−	24.5988i	−1.60922	−	0.929085i	−0.619678	−	0.784857i	$-0.712737\pi$
$702$			0.700889i			0.0264533i
$703$	31.1916	+	27.7747i	1.17641	+	1.04754i
$704$	18.9211	+	3.18237i	0.713114	+	0.119940i
$705$	−5.62648	−	3.24845i	−0.211906	−	0.122344i
$706$	5.87690	−	10.1791i	0.221180	−	0.383095i
$707$	−20.9446	−	36.2771i	−0.787703	−	1.36434i
$708$	4.19741	−	7.27013i	0.157748	−	0.273228i
$709$	−8.84136	−	15.3137i	−0.332044	−	0.575117i	0.650868	−	0.759191i	$-0.274405\pi$
$709$	−8.84136	−	15.3137i	−0.332044	−	0.575117i	−0.982913	+	0.184073i	$0.941072\pi$
$710$			14.7627i			0.554034i
$711$	−12.3526			−0.463259
$712$	−35.0937	+	20.2614i	−1.31519	+	0.759327i
$713$	−19.0220	+	10.9823i	−0.712379	+	0.411292i
$714$			9.56462i			0.357947i
$715$	4.32642	+	0.727670i	0.161799	+	0.0272133i
$716$	−14.1426	+	8.16525i	−0.528535	+	0.305150i
$717$	−3.25689	+	5.64110i	−0.121631	+	0.210671i
$718$	−8.99256	+	5.19186i	−0.335599	+	0.193758i
$719$	−4.53413	+	7.85334i	−0.169094	+	0.292880i	−0.938102	−	0.346360i	$-0.887418\pi$
$719$	−4.53413	+	7.85334i	−0.169094	+	0.292880i	0.769007	+	0.639240i	$0.220751\pi$
$720$	−0.326676	+	0.565819i	−0.0121745	+	0.0210868i
$721$	27.2016			1.01304
$722$	16.0762	+	6.94587i	0.598294	+	0.258498i
$723$		−	9.54741i		−	0.355072i
$724$	19.0627	+	11.0059i	0.708461	+	0.409030i
$725$	3.36522	−	5.82873i	0.124981	−	0.216474i
$726$	−9.95575	+	1.91814i	−0.369492	+	0.0711887i
$727$	15.3944	−	26.6639i	0.570948	−	0.988911i	−0.425521	−	0.904948i	$-0.639909\pi$
$727$	15.3944	−	26.6639i	0.570948	−	0.988911i	0.996469	−	0.0839621i	$-0.0267575\pi$
$728$	−6.80968	+	3.93157i	−0.252384	+	0.145714i
$729$	−1.00000			−0.0370370
$730$		−	22.8751i		−	0.846644i
$731$	−15.8098	−	27.3834i	−0.584747	−	1.01281i
$732$	1.38033	+	2.39080i	0.0510185	+	0.0883666i
$733$		−	30.4920i		−	1.12625i	−0.826373	−	0.563123i	$-0.809600\pi$
$733$		−	30.4920i		−	1.12625i	0.826373	−	0.563123i	$-0.190400\pi$
$734$	−0.577494			−0.0213157
$735$	8.55828	−	4.94113i	0.315677	−	0.182256i
$736$	−7.36173	+	12.7509i	−0.271357	+	0.470004i
$737$	−41.9148	+	15.6318i	−1.54395	+	0.575806i
$738$	2.84626	−	4.92986i	0.104772	−	0.181471i
$739$	−19.5991	−	11.3156i	−0.720965	−	0.416249i	0.0941426	−	0.995559i	$-0.469989\pi$
$739$	−19.5991	−	11.3156i	−0.720965	−	0.416249i	−0.815108	+	0.579309i	$0.803322\pi$
$740$		−	19.1753i		−	0.704898i
$741$	−2.47543	−	2.20426i	−0.0909373	−	0.0809755i
$742$	−32.2492			−1.18391
$743$	−22.5162	+	38.9992i	−0.826039	+	1.43074i	0.0750840	+	0.997177i	$0.476078\pi$
$743$	−22.5162	+	38.9992i	−0.826039	+	1.43074i	−0.901123	+	0.433564i	$0.857256\pi$
$744$	−11.8293	+	20.4890i	−0.433683	+	0.751162i
$745$	15.0330	−	8.67933i	0.550768	−	0.317986i
$746$	3.22670	−	5.58880i	0.118138	−	0.204621i
$747$	−0.331532	+	0.191410i	−0.0121301	+	0.00700334i
$748$	1.84419	−	10.9648i	0.0674304	−	0.400913i
$749$			58.9316i			2.15331i
$750$	9.68374	−	5.59091i	0.353600	−	0.204151i
$751$	13.8390	−	7.98994i	0.504991	−	0.291557i	−0.225781	−	0.974178i	$-0.572493\pi$
$751$	13.8390	−	7.98994i	0.504991	−	0.291557i	0.730772	+	0.682621i	$0.239160\pi$
$752$	1.40275			0.0511529
$753$			20.7908i			0.757660i
$754$	−1.19488	−	2.06959i	−0.0435148	−	0.0753698i
$755$	0.506148	−	0.876674i	0.0184206	−	0.0319054i
$756$	−2.04838	−	3.54790i	−0.0744990	−	0.129036i
$757$	−11.5239	+	19.9601i	−0.418845	+	0.725460i	−0.995824	−	0.0912987i	$-0.970898\pi$
$757$	−11.5239	+	19.9601i	−0.418845	+	0.725460i	0.576979	+	0.816759i	$0.304232\pi$
$758$	−7.15804	−	4.13269i	−0.259992	−	0.150106i
$759$	1.48302	−	8.81744i	0.0538303	−	0.320053i
$760$	−6.91953	−	20.9026i	−0.250998	−	0.758218i
$761$		−	3.20452i		−	0.116164i	−0.998312	−	0.0580819i	$-0.981502\pi$
$761$		−	3.20452i		−	0.116164i	0.998312	−	0.0580819i	$-0.0184985\pi$
$762$	−0.176027	−	0.101629i	−0.00637678	−	0.00368163i
$763$	32.6706	+	18.8624i	1.18275	+	0.682863i
$764$	3.87644	+	6.71419i	0.140245	+	0.242911i
$765$	4.39000	+	2.53457i	0.158721	+	0.0916374i
$766$	−16.2476	+	9.38057i	−0.587050	+	0.338934i
$767$			5.54879i			0.200355i
$768$			16.7231i			0.603444i
$769$	23.4919	−	13.5631i	0.847140	−	0.489096i	−0.0125450	−	0.999921i	$-0.503993\pi$
$769$	23.4919	−	13.5631i	0.847140	−	0.489096i	0.859685	+	0.510825i	$0.170660\pi$
$770$	17.7430	−	6.61712i	0.639412	−	0.238464i
$771$	1.43425			0.0516533
$772$	8.88703			0.319851
$773$	11.8135	−	6.82050i	0.424900	−	0.245316i	−0.272271	−	0.962221i	$-0.587775\pi$
$773$	11.8135	−	6.82050i	0.424900	−	0.245316i	0.697172	+	0.716904i	$0.254441\pi$
$774$	−8.66136	−	5.00064i	−0.311326	−	0.179744i
$775$	13.9281	−	8.04139i	0.500312	−	0.288855i
$776$	37.4087	+	21.5979i	1.34289	+	0.775320i
$777$	−29.5492	−	17.0602i	−1.06007	−	0.612032i
$778$	−9.85455			−0.353303
$779$	8.46019	+	25.5567i	0.303118	+	0.915664i
$780$			1.52179i			0.0544890i
$781$	−23.5472	−	19.4435i	−0.842586	−	0.695744i
$782$	−6.27085	−	3.62048i	−0.224245	−	0.129468i
$783$	2.95280	−	1.70480i	0.105525	−	0.0609246i
$784$	−1.06684	+	1.84782i	−0.0381014	+	0.0659936i
$785$	3.65866	+	6.33699i	0.130583	+	0.226177i
$786$	−14.5884			−0.520350
$787$	−22.6377			−0.806948			−0.403474	−	0.914991i	$-0.632197\pi$
$787$	−22.6377			−0.806948			−0.403474	+	0.914991i	$0.632197\pi$
$788$	10.8585	−	6.26914i	0.386817	−	0.223329i
$789$	−11.8028	−	20.4430i	−0.420189	−	0.727789i
$790$	19.8058			0.704657
$791$	−41.3811			−1.47134
$792$	−3.36534	−	9.02372i	−0.119582	−	0.320644i
$793$	−1.58027	−	0.912368i	−0.0561170	−	0.0323991i
$794$	−8.16602	−	14.1440i	−0.289801	−	0.501951i
$795$	−8.54584	+	14.8018i	−0.303090	+	0.524967i
$796$	−0.137931	+	0.238903i	−0.00488883	+	0.00846771i
$797$		−	26.0393i		−	0.922359i	−0.887307	−	0.461179i	$-0.847427\pi$
$797$		−	26.0393i		−	0.922359i	0.887307	−	0.461179i	$-0.152573\pi$
$798$	−14.0106	−	2.89726i	−0.495968	−	0.102562i
$799$		−	10.8834i		−	0.385028i
$800$	5.39034	−	9.33634i	0.190577	−	0.330089i
$801$	12.0854	+	6.97752i	0.427017	+	0.246539i
$802$	2.01095	−	1.16102i	0.0710091	−	0.0409971i
$803$	36.4868	+	30.1281i	1.28759	+	1.06320i
$804$	−7.75863	−	13.4383i	−0.273626	−	0.473934i
$805$			16.7000i			0.588597i
$806$		−	5.71045i		−	0.201142i
$807$	−8.68439	−	15.0418i	−0.305705	−	0.529496i
$808$	29.5818	−	17.0791i	1.04068	−	0.600840i
$809$		−	41.4286i		−	1.45655i	−0.685284	−	0.728276i	$-0.740322\pi$
$809$		−	41.4286i		−	1.45655i	0.685284	−	0.728276i	$-0.259678\pi$
$810$	1.60337			0.0563365
$811$	6.24712	+	10.8203i	0.219366	+	0.379953i	0.954614	−	0.297845i	$-0.0962677\pi$
$811$	6.24712	+	10.8203i	0.219366	+	0.379953i	−0.735248	+	0.677798i	$0.762934\pi$
$812$	12.0969	+	6.98417i	0.424519	+	0.245096i
$813$	−16.0767	−	27.8457i	−0.563834	−	0.976590i
$814$	−22.5861	−	18.6499i	−0.791643	−	0.653679i
$815$	0.609529	−	1.05574i	0.0213509	−	0.0369808i
$816$	−1.09448			−0.0383144
$817$	44.9010	−	14.8639i	1.57089	−	0.520020i
$818$	10.6260			0.371530
$819$	2.34509	+	1.35394i	0.0819440	+	0.0473104i
$820$	6.17990	−	10.7039i	0.215811	−	0.373796i
$821$	−34.8303	+	20.1093i	−1.21559	+	0.701819i	−0.963971	−	0.266008i	$-0.914295\pi$
$821$	−34.8303	+	20.1093i	−1.21559	+	0.701819i	−0.251616	+	0.967827i	$0.580962\pi$
$822$	−10.9017	−	6.29411i	−0.380241	−	0.219532i
$823$	14.5960	+	25.2809i	0.508783	+	0.881238i	0.999948	+	0.0101715i	$0.00323774\pi$
$823$	14.5960	+	25.2809i	0.508783	+	0.881238i	−0.491165	+	0.871066i	$0.663429\pi$
$824$			22.1813i			0.772721i
$825$	−1.08588	+	6.45622i	−0.0378057	+	0.224777i
$826$	11.9753	+	20.7418i	0.416674	+	0.721701i
$827$	−14.6809	−	25.4281i	−0.510505	−	0.884221i	−0.999926	−	0.0121734i	$-0.996125\pi$
$827$	−14.6809	−	25.4281i	−0.510505	−	0.884221i	0.489420	−	0.872048i	$-0.337208\pi$
$828$	3.10148			0.107784
$829$		−	43.5967i		−	1.51417i	−0.653314	−	0.757087i	$-0.726622\pi$
$829$		−	43.5967i		−	1.51417i	0.653314	−	0.757087i	$-0.273378\pi$
$830$	0.531568	−	0.306901i	0.0184510	−	0.0106527i
$831$	1.40504	−	2.43361i	0.0487404	−	0.0844209i
$832$	−2.19953	−	3.80970i	−0.0762550	−	0.132078i
$833$	14.3366	+	8.27724i	0.496734	+	0.286790i
$834$	−8.97444	+	15.5442i	−0.310760	+	0.538251i
$835$	−13.2371			−0.458087
$836$	15.5030	+	6.02283i	0.536181	+	0.208304i
$837$	8.14745			0.281617
$838$	−1.54581	+	2.67742i	−0.0533991	+	0.0924900i
$839$	−7.27332	−	4.19925i	−0.251103	−	0.144974i	0.369166	−	0.929363i	$-0.379643\pi$
$839$	−7.27332	−	4.19925i	−0.251103	−	0.144974i	−0.620269	+	0.784389i	$0.712977\pi$
$840$	8.99394	+	15.5780i	0.310320	+	0.537491i
$841$	8.68731	−	15.0469i	0.299562	−	0.518857i
$842$	−4.90522	+	2.83203i	−0.169045	+	0.0975981i
$843$			10.7869i			0.371519i
$844$	−5.69139			−0.195906
$845$	10.8041	+	18.7133i	0.371674	+	0.643758i
$846$	−1.72121	−	2.98123i	−0.0591766	−	0.102497i
$847$	−12.8141	+	37.0161i	−0.440298	+	1.27189i
$848$		−	3.69027i		−	0.126724i
$849$	−7.33533	−	12.7052i	−0.251748	−	0.436040i
$850$	4.59159	+	2.65095i	0.157490	+	0.0909269i
$851$	22.3704	−	12.9155i	0.766847	−	0.442739i
$852$	5.29626	−	9.17339i	0.181447	−	0.314275i
$853$	−1.78074	−	1.02811i	−0.0609715	−	0.0352019i	0.469204	−	0.883090i	$-0.344541\pi$
$853$	−1.78074	−	1.02811i	−0.0609715	−	0.0352019i	−0.530176	+	0.847888i	$0.677874\pi$
$854$	−7.87623			−0.269519
$855$	−5.04250	+	5.66284i	−0.172450	+	0.193665i
$856$	−48.0552			−1.64249
$857$	25.1045	−	43.4822i	0.857553	−	1.48533i	−0.0167033	−	0.999860i	$-0.505317\pi$
$857$	25.1045	−	43.4822i	0.857553	−	1.48533i	0.874256	−	0.485465i	$-0.161350\pi$
$858$	1.79248	+	1.48010i	0.0611944	+	0.0505297i
$859$	−0.524915	−	0.909180i	−0.0179099	−	0.0310208i	0.856932	−	0.515430i	$-0.172368\pi$
$859$	−0.524915	−	0.909180i	−0.0179099	−	0.0310208i	−0.874841	+	0.484409i	$0.839035\pi$
$860$	−18.8059	−	10.8576i	−0.641274	−	0.370240i
$861$	−10.9965	−	19.0465i	−0.374759	−	0.649102i
$862$	−14.2365			−0.484897
$863$			37.9950i			1.29336i	0.762760	+	0.646682i	$0.223844\pi$
$863$			37.9950i			1.29336i	−0.762760	+	0.646682i	$0.776156\pi$
$864$	4.72974	−	2.73071i	0.160909	−	0.0929008i
$865$	−5.82806	−	10.0945i	−0.198160	−	0.343223i
$866$			14.1916i			0.482250i
$867$		−	8.50832i		−	0.288958i
$868$	16.6891	+	28.9064i	0.566465	+	0.981146i
$869$	−26.0856	+	31.5911i	−0.884893	+	1.07166i
$870$	−4.73442	+	2.73342i	−0.160512	+	0.0926716i
$871$	8.88246	+	5.12829i	0.300971	+	0.173765i
$872$	−15.3811	+	26.6409i	−0.520871	+	0.902175i
$873$		−	14.8756i		−	0.503462i
$874$	7.20292	−	8.08904i	0.243642	−	0.273616i
$875$		−	43.2008i		−	1.46045i
$876$	−8.20664	+	14.2143i	−0.277277	+	0.480257i
$877$	−15.0434	+	26.0560i	−0.507980	+	0.879848i	0.491977	+	0.870608i	$0.336274\pi$
$877$	−15.0434	+	26.0560i	−0.507980	+	0.879848i	−0.999957	+	0.00923952i	$0.997059\pi$
$878$	0.745085	+	1.29052i	0.0251454	+	0.0435531i
$879$	21.3694	+	12.3376i	0.720772	+	0.416138i
$880$	0.757195	+	2.03032i	0.0255250	+	0.0684421i
$881$	32.9899			1.11146			0.555729	−	0.831364i	$-0.312439\pi$
$881$	32.9899			1.11146			0.555729	+	0.831364i	$0.312439\pi$
$882$	5.23618			0.176311
$883$	−0.678521	−	1.17523i	−0.0228340	−	0.0395497i	0.854383	−	0.519644i	$-0.173936\pi$
$883$	−0.678521	−	1.17523i	−0.0228340	−	0.0395497i	−0.877217	+	0.480095i	$0.840602\pi$
$884$	−2.20773	+	1.27463i	−0.0742541	+	0.0428706i
$885$	12.6935			0.426688
$886$	28.6805			0.963540
$887$	16.9999	+	29.4447i	0.570801	+	0.988657i	0.996484	+	0.0837841i	$0.0267006\pi$
$887$	16.9999	+	29.4447i	0.570801	+	0.988657i	−0.425683	+	0.904872i	$0.639966\pi$
$888$	13.9116	−	24.0956i	0.466843	−	0.808595i
$889$	−0.680078	+	0.392643i	−0.0228091	+	0.0131688i
$890$	−19.3774	−	11.1875i	−0.649530	−	0.375006i
$891$	−2.11175	+	2.55745i	−0.0707462	+	0.0856776i
$892$			0.0546388i			0.00182944i
$893$	15.9424	+	3.29675i	0.533492	+	0.110322i
$894$	9.19761			0.307614
$895$	−21.3846	−	12.3464i	−0.714808	−	0.412695i
$896$	17.2414	+	9.95434i	0.575995	+	0.332551i
$897$	−1.77536	+	1.02501i	−0.0592777	+	0.0342240i
$898$	18.5901	+	10.7330i	0.620360	+	0.358165i
$899$	−24.0578	+	13.8898i	−0.802373	+	0.463250i
$900$	−2.27094			−0.0756980
$901$	−28.6315			−0.953855
$902$	−6.59728	−	17.6898i	−0.219665	−	0.589005i
$903$	−33.4631	+	19.3199i	−1.11358	+	0.642926i
$904$		−	33.7438i		−	1.12230i
$905$			33.2832i			1.10637i
$906$	0.464512	−	0.268186i	0.0154324	−	0.00890989i
$907$	−14.4855	−	8.36322i	−0.480984	−	0.277696i	0.239842	−	0.970812i	$-0.422904\pi$
$907$	−14.4855	−	8.36322i	−0.480984	−	0.277696i	−0.720826	+	0.693116i	$0.756238\pi$
$908$	13.6951	+	23.7207i	0.454489	+	0.787198i
$909$	−10.1873	−	5.88162i	−0.337890	−	0.195081i
$910$	−3.76004	−	2.17086i	−0.124644	−	0.0719632i
$911$			22.9652i			0.760870i	0.924808	+	0.380435i	$0.124226\pi$
$911$			22.9652i			0.760870i	−0.924808	+	0.380435i	$0.875774\pi$
$912$	0.331533	−	1.60322i	0.0109782	−	0.0530880i
$913$	−0.210591	+	1.25209i	−0.00696954	+	0.0414380i
$914$	15.9653	+	9.21755i	0.528084	+	0.304890i
$915$	−2.08715	+	3.61505i	−0.0689991	+	0.119510i
$916$	−7.88596	−	13.6589i	−0.260559	−	0.451302i
$917$	−28.1810	+	48.8109i	−0.930619	+	1.61188i
$918$	1.34296	+	2.32607i	0.0443242	+	0.0767718i
$919$		−	27.3889i		−	0.903478i	−0.892150	−	0.451739i	$-0.850804\pi$
$919$		−	27.3889i		−	0.903478i	0.892150	−	0.451739i	$-0.149196\pi$
$920$	−13.6178			−0.448967
$921$	−19.6771	+	11.3606i	−0.648382	+	0.374344i
$922$	4.00986	−	2.31509i	0.132058	−	0.0762436i
$923$			7.00142i			0.230455i
$924$	−13.3992	−	2.25365i	−0.440803	−	0.0741395i
$925$	−16.3798	+	9.45690i	−0.538566	+	0.310941i
$926$	8.43976	−	14.6181i	0.277348	−	0.480381i
$927$	6.61530	−	3.81934i	0.217275	−	0.125444i
$928$	−9.31065	+	16.1265i	−0.305637	+	0.529379i
$929$	14.2065	−	24.6064i	0.466101	−	0.807311i	−0.533149	−	0.846021i	$-0.678992\pi$
$929$	14.2065	−	24.6064i	0.466101	−	0.807311i	0.999250	+	0.0387104i	$0.0123250\pi$
$930$	−13.0633			−0.428364
$931$	−16.4675	+	18.4934i	−0.539701	+	0.606097i
$932$		−	22.3004i		−	0.730475i
$933$	13.5459	+	7.82076i	0.443474	+	0.256040i
$934$	−2.70413	+	4.68370i	−0.0884820	+	0.153255i
$935$	15.7526	−	5.87482i	0.515164	−	0.192127i
$936$	−1.10406	+	1.91228i	−0.0360872	+	0.0625048i
$937$	27.5277	−	15.8931i	0.899289	−	0.519205i	0.0223196	−	0.999751i	$-0.492895\pi$
$937$	27.5277	−	15.8931i	0.899289	−	0.519205i	0.876969	+	0.480546i	$0.159562\pi$
$938$	44.2711			1.44550
$939$		−	1.82216i		−	0.0594639i
$940$	−3.73716	−	6.47296i	−0.121893	−	0.211125i
$941$	0.191016	+	0.330850i	0.00622696	+	0.0107854i	0.869122	−	0.494598i	$-0.164685\pi$
$941$	0.191016	+	0.330850i	0.00622696	+	0.0107854i	−0.862895	+	0.505383i	$0.831351\pi$
$942$			3.87714i			0.126324i
$943$	16.6499			0.542196
$944$	−2.37348	+	1.37033i	−0.0772503	+	0.0446005i
$945$	3.09729	−	5.36467i	0.100755	−	0.174513i
$946$	−31.0795	+	11.5909i	−1.01048	+	0.376852i
$947$	−11.5767	+	20.0514i	−0.376191	+	0.651583i	−0.990505	−	0.137480i	$-0.956100\pi$
$947$	−11.5767	+	20.0514i	−0.376191	+	0.651583i	0.614313	+	0.789062i	$0.289433\pi$
$948$	−12.3071	−	7.10550i	−0.399716	−	0.230776i
$949$		−	10.8488i		−	0.352168i
$950$	−5.27405	+	5.92288i	−0.171113	+	0.192164i
$951$	−7.44338			−0.241368
$952$	−15.0664	+	26.0958i	−0.488305	+	0.845769i
$953$	−6.84988	+	11.8643i	−0.221889	+	0.384324i	−0.955382	−	0.295374i	$-0.904556\pi$
$953$	−6.84988	+	11.8643i	−0.221889	+	0.384324i	0.733492	+	0.679698i	$0.237889\pi$
$954$	−7.84286	+	4.52808i	−0.253922	+	0.146602i
$955$	−5.86144	+	10.1523i	−0.189672	+	0.328521i
$956$	−6.48978	+	3.74687i	−0.209894	+	0.121183i
$957$	1.87563	−	11.1517i	0.0606306	−	0.360484i
$958$			1.79413i			0.0579656i
$959$	−42.1186	+	24.3172i	−1.36008	+	0.785244i
$960$	−8.71514	+	5.03169i	−0.281280	+	0.162397i
$961$	−35.3809			−1.14132
$962$			6.71565i			0.216521i
$963$	8.27452	+	14.3319i	0.266643	+	0.461839i
$964$	5.49188	−	9.51222i	0.176882	−	0.306368i
$965$	6.71889	+	11.6375i	0.216289	+	0.374623i
$966$	−4.42430	+	7.66312i	−0.142350	+	0.246557i
$967$	21.9309	+	12.6618i	0.705251	+	0.407177i	0.809300	−	0.587395i	$-0.199847\pi$
$967$	21.9309	+	12.6618i	0.705251	+	0.407177i	−0.104049	+	0.994572i	$0.533180\pi$
$968$	−30.1844	−	10.4491i	−0.970164	−	0.335848i
$969$	−12.4389	−	2.57225i	−0.399594	−	0.0826326i
$970$			23.8510i			0.765810i
$971$	18.1277	+	10.4660i	0.581745	+	0.335871i	0.761827	−	0.647781i	$-0.224303\pi$
$971$	18.1277	+	10.4660i	0.581745	+	0.335871i	−0.180082	+	0.983652i	$0.557636\pi$
$972$	−0.996315	−	0.575222i	−0.0319568	−	0.0184503i
$973$	34.6727	+	60.0548i	1.11155	+	1.92527i
$974$	15.8805	+	9.16861i	0.508844	+	0.293781i
$975$	1.29994	−	0.750521i	0.0416314	−	0.0240359i
$976$		−	0.901274i		−	0.0288491i
$977$			18.7966i			0.601356i	0.953726	+	0.300678i	$0.0972130\pi$
$977$			18.7966i			0.601356i	−0.953726	+	0.300678i	$0.902787\pi$
$978$	0.559389	−	0.322963i	0.0178873	−	0.0103272i
$979$	43.3660	−	16.1730i	1.38598	−	0.516893i
$980$	11.3690			0.363169
$981$	10.5938			0.338233
$982$	−10.6052	+	6.12290i	−0.338425	+	0.195390i
$983$	−32.1895	−	18.5846i	−1.02669	−	0.592758i	−0.110653	−	0.993859i	$-0.535294\pi$
$983$	−32.1895	−	18.5846i	−1.02669	−	0.592758i	−0.916034	+	0.401102i	$0.868627\pi$
$984$	15.5313	−	8.96698i	0.495119	−	0.285857i
$985$	16.4187	+	9.47937i	0.523145	+	0.302038i
$986$	−7.93098	−	4.57895i	−0.252574	−	0.145824i
$987$	−13.2998			−0.423337
$988$	−1.19837	−	3.62006i	−0.0381252	−	0.115169i
$989$		−	29.2525i		−	0.930176i
$990$	3.38590	−	4.10052i	0.107611	−	0.130323i
$991$	45.9133	+	26.5080i	1.45848	+	0.842056i	0.998937	−	0.0460983i	$-0.0146788\pi$
$991$	45.9133	+	26.5080i	1.45848	+	0.842056i	0.459546	+	0.888154i	$0.348012\pi$
$992$	−38.5353	+	22.2484i	−1.22350	+	0.706386i
$993$	5.74392	−	9.94877i	0.182278	−	0.315715i
$994$	15.1103	+	26.1719i	0.479271	+	0.830122i
$995$	−0.417122			−0.0132237
$996$	−0.440414			−0.0139551
$997$	−28.1440	+	16.2489i	−0.891328	+	0.514608i	−0.874377	−	0.485248i	$-0.838729\pi$
$997$	−28.1440	+	16.2489i	−0.891328	+	0.514608i	−0.0169514	+	0.999856i	$0.505396\pi$
$998$	−8.89493	−	15.4065i	−0.281564	−	0.487683i
$999$	−9.58163			−0.303149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.k.a.274.15	✓	80
11.10	odd	2	inner	627.2.k.a.274.26	yes	80
19.12	odd	6	inner	627.2.k.a.373.26	yes	80
209.164	even	6	inner	627.2.k.a.373.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.k.a.274.15	✓	80	1.1	even	1	trivial
627.2.k.a.274.26	yes	80	11.10	odd	2	inner
627.2.k.a.373.15	yes	80	209.164	even	6	inner
627.2.k.a.373.26	yes	80	19.12	odd	6	inner

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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.460857 + 0.798227i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.575222 + 0.996315i) q^{4} +(-0.869775 + 1.50649i) q^{5} +(-0.798227 + 0.460857i) q^{6} +3.56103i q^{7} -2.90381 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.801683 - 1.38856i) q^{10} +(3.27069 + 0.550103i) q^{11} +1.15044i q^{12} +(-0.380210 - 0.658543i) q^{13} +(-2.84251 - 1.64112i) q^{14} +(-1.50649 + 0.869775i) q^{15} +(0.187793 - 0.325267i) q^{16} +(-2.52364 - 1.45702i) q^{17} -0.921713 q^{18} +(2.89874 - 3.25535i) q^{19} -2.00126 q^{20} +(-1.78051 + 3.08394i) q^{21} +(-1.94642 + 2.35723i) q^{22} +(-1.34795 - 2.33472i) q^{23} +(-2.51477 - 1.45190i) q^{24} +(0.986983 + 1.70950i) q^{25} +0.700889 q^{26} +1.00000i q^{27} +(-3.54790 + 2.04838i) q^{28} +(-1.70480 - 2.95280i) q^{29} -1.60337i q^{30} -8.14745i q^{31} +(-2.73071 - 4.72974i) q^{32} +(2.55745 + 2.11175i) q^{33} +(2.32607 - 1.34296i) q^{34} +(-5.36467 - 3.09729i) q^{35} +(-0.575222 + 0.996315i) q^{36} +9.58163i q^{37} +(1.26260 + 3.81410i) q^{38} -0.760419i q^{39} +(2.52566 - 4.37457i) q^{40} +(-3.08801 + 5.34859i) q^{41} +(-1.64112 - 2.84251i) q^{42} +(9.39702 + 5.42537i) q^{43} +(1.33330 + 3.57506i) q^{44} -1.73955 q^{45} +2.48484 q^{46} +(1.86741 + 3.23445i) q^{47} +(0.325267 - 0.187793i) q^{48} -5.68092 q^{49} -1.81943 q^{50} +(-1.45702 - 2.52364i) q^{51} +(0.437410 - 0.757617i) q^{52} +(8.50900 - 4.91267i) q^{53} +(-0.798227 - 0.460857i) q^{54} +(-3.67349 + 4.44880i) q^{55} -10.3405i q^{56} +(4.13806 - 1.36985i) q^{57} +3.14267 q^{58} +(-6.31940 - 3.64851i) q^{59} +(-1.73314 - 1.00063i) q^{60} +(2.07815 - 1.19982i) q^{61} +(6.50351 + 3.75481i) q^{62} +(-3.08394 + 1.78051i) q^{63} +5.78504 q^{64} +1.32279 q^{65} +(-2.86427 + 1.06821i) q^{66} +(-11.6810 + 6.74403i) q^{67} -3.35245i q^{68} -2.69590i q^{69} +(4.94469 - 2.85482i) q^{70} +(-7.97377 - 4.60366i) q^{71} +(-1.45190 - 2.51477i) q^{72} +(12.3555 + 7.13345i) q^{73} +(-7.64831 - 4.41576i) q^{74} +1.97397i q^{75} +(4.91077 + 1.01551i) q^{76} +(-1.95893 + 11.6470i) q^{77} +(0.606987 + 0.350444i) q^{78} +(-6.17631 + 10.6977i) q^{79} +(0.326676 + 0.565819i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.84626 - 4.92986i) q^{82} +0.382821i q^{83} -4.09677 q^{84} +(4.39000 - 2.53457i) q^{85} +(-8.66136 + 5.00064i) q^{86} -3.40960i q^{87} +(-9.49744 - 1.59739i) q^{88} +(12.0854 - 6.97752i) q^{89} +(0.801683 - 1.38856i) q^{90} +(2.34509 - 1.35394i) q^{91} +(1.55074 - 2.68596i) q^{92} +(4.07372 - 7.05590i) q^{93} -3.44243 q^{94} +(2.38292 + 7.19836i) q^{95} -5.46143i q^{96} +(-12.8826 - 7.43780i) q^{97} +(2.61809 - 4.53467i) q^{98} +(1.15894 + 3.10755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 40 q^{4} + 4 q^{5} + 40 q^{9} + 4 q^{11} - 24 q^{14} + 12 q^{15} - 40 q^{16} + 48 q^{20} - 24 q^{23} - 56 q^{25} + 80 q^{26} + 6 q^{33} - 48 q^{34} + 40 q^{36} + 60 q^{38} - 4 q^{42} + 14 q^{44}+ \cdots + 2 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 4 * q^5 + 40 * q^9 + 4 * q^11 - 24 * q^14 + 12 * q^15 - 40 * q^16 + 48 * q^20 - 24 * q^23 - 56 * q^25 + 80 * q^26 + 6 * q^33 - 48 * q^34 + 40 * q^36 + 60 * q^38 - 4 * q^42 + 14 * q^44 + 8 * q^45 - 16 * q^47 - 48 * q^48 - 80 * q^49 - 108 * q^53 - 24 * q^55 + 152 * q^58 - 48 * q^60 + 104 * q^64 - 36 * q^66 + 96 * q^67 - 60 * q^70 + 84 * q^71 - 60 * q^77 + 96 * q^78 - 32 * q^80 - 40 * q^81 - 20 * q^82 - 48 * q^86 + 72 * q^89 + 24 * q^91 - 104 * q^92 + 48 * q^93 + 36 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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