LMFDB - Embedded newform 1045.2.f.b.626.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (of order $2$, degree $1$, 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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.7
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17500 q^{2} +1.39639i q^{3} +2.73061 q^{4} +1.00000 q^{5} -3.03714i q^{6} -0.972912i q^{7} -1.58909 q^{8} +1.05010 q^{9} +O(q^{10})$	\(q-2.17500 q^{2} +1.39639i q^{3} +2.73061 q^{4} +1.00000 q^{5} -3.03714i q^{6} -0.972912i q^{7} -1.58909 q^{8} +1.05010 q^{9} -2.17500 q^{10} +(-1.20844 - 3.08864i) q^{11} +3.81299i q^{12} -5.65178 q^{13} +2.11608i q^{14} +1.39639i q^{15} -2.00497 q^{16} +4.67880i q^{17} -2.28397 q^{18} +(4.31293 + 0.631362i) q^{19} +2.73061 q^{20} +1.35856 q^{21} +(2.62835 + 6.71778i) q^{22} -1.62223 q^{23} -2.21898i q^{24} +1.00000 q^{25} +12.2926 q^{26} +5.65551i q^{27} -2.65665i q^{28} -6.29460 q^{29} -3.03714i q^{30} +8.09635i q^{31} +7.53898 q^{32} +(4.31293 - 1.68745i) q^{33} -10.1764i q^{34} -0.972912i q^{35} +2.86743 q^{36} -4.08553i q^{37} +(-9.38062 - 1.37321i) q^{38} -7.89208i q^{39} -1.58909 q^{40} +10.2227 q^{41} -2.95487 q^{42} +9.06878i q^{43} +(-3.29978 - 8.43388i) q^{44} +1.05010 q^{45} +3.52835 q^{46} +4.98078 q^{47} -2.79972i q^{48} +6.05344 q^{49} -2.17500 q^{50} -6.53341 q^{51} -15.4328 q^{52} +1.30811i q^{53} -12.3007i q^{54} +(-1.20844 - 3.08864i) q^{55} +1.54604i q^{56} +(-0.881625 + 6.02252i) q^{57} +13.6907 q^{58} +3.03892i q^{59} +3.81299i q^{60} +12.2024i q^{61} -17.6095i q^{62} -1.02166i q^{63} -12.3873 q^{64} -5.65178 q^{65} +(-9.38062 + 3.67019i) q^{66} +8.46997i q^{67} +12.7760i q^{68} -2.26527i q^{69} +2.11608i q^{70} -15.6680i q^{71} -1.66870 q^{72} +3.75996i q^{73} +8.88603i q^{74} +1.39639i q^{75} +(11.7770 + 1.72401i) q^{76} +(-3.00497 + 1.17570i) q^{77} +17.1652i q^{78} +0.484850 q^{79} -2.00497 q^{80} -4.74697 q^{81} -22.2344 q^{82} +7.80143i q^{83} +3.70971 q^{84} +4.67880i q^{85} -19.7246i q^{86} -8.78970i q^{87} +(1.92031 + 4.90811i) q^{88} -7.55029i q^{89} -2.28397 q^{90} +5.49869i q^{91} -4.42970 q^{92} -11.3056 q^{93} -10.8332 q^{94} +(4.31293 + 0.631362i) q^{95} +10.5273i q^{96} +9.02220i q^{97} -13.1662 q^{98} +(-1.26899 - 3.24339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.17500			−1.53796			−0.768978	−	0.639275i	$-0.779234\pi$
$2$	−2.17500			−1.53796			−0.768978	+	0.639275i	$0.779234\pi$
$3$			1.39639i			0.806204i	0.915155	+	0.403102i	$0.132068\pi$
$3$			1.39639i			0.806204i	−0.915155	+	0.403102i	$0.867932\pi$
$4$	2.73061			1.36531
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		−	3.03714i		−	1.23991i
$7$		−	0.972912i		−	0.367726i	−0.982952	−	0.183863i	$-0.941140\pi$
$7$		−	0.972912i		−	0.367726i	0.982952	−	0.183863i	$-0.0588603\pi$
$8$	−1.58909			−0.561827
$9$	1.05010			0.350035
$10$	−2.17500			−0.687795
$11$	−1.20844	−	3.08864i	−0.364358	−	0.931259i
$11$	−1.20844	−	3.08864i	−0.364358	−	0.931259i
$12$			3.81299i			1.10072i
$13$	−5.65178			−1.56752			−0.783761	−	0.621062i	$-0.786701\pi$
$13$	−5.65178			−1.56752			−0.783761	+	0.621062i	$0.786701\pi$
$14$			2.11608i			0.565547i
$15$			1.39639i			0.360546i
$16$	−2.00497			−0.501243
$17$			4.67880i			1.13477i	0.823451	+	0.567387i	$0.192046\pi$
$17$			4.67880i			1.13477i	−0.823451	+	0.567387i	$0.807954\pi$
$18$	−2.28397			−0.538338
$19$	4.31293	+	0.631362i	0.989454	+	0.144844i
$19$	4.31293	+	0.631362i	0.989454	+	0.144844i
$20$	2.73061			0.610584
$21$	1.35856			0.296462
$22$	2.62835	+	6.71778i	0.560366	+	1.43224i
$23$	−1.62223			−0.338259			−0.169130	−	0.985594i	$-0.554096\pi$
$23$	−1.62223			−0.338259			−0.169130	+	0.985594i	$0.554096\pi$
$24$		−	2.21898i		−	0.452947i
$25$	1.00000			0.200000
$26$	12.2926			2.41078
$27$			5.65551i			1.08840i
$28$		−	2.65665i		−	0.502059i
$29$	−6.29460			−1.16888			−0.584439	−	0.811438i	$-0.698685\pi$
$29$	−6.29460			−1.16888			−0.584439	+	0.811438i	$0.698685\pi$
$30$		−	3.03714i		−	0.554503i
$31$			8.09635i			1.45415i	0.686560	+	0.727073i	$0.259120\pi$
$31$			8.09635i			1.45415i	−0.686560	+	0.727073i	$0.740880\pi$
$32$	7.53898			1.33272
$33$	4.31293	−	1.68745i	0.750785	−	0.293747i
$34$		−	10.1764i		−	1.74523i
$35$		−	0.972912i		−	0.164452i
$36$	2.86743			0.477905
$37$		−	4.08553i		−	0.671658i	−0.941923	−	0.335829i	$-0.890984\pi$
$37$		−	4.08553i		−	0.671658i	0.941923	−	0.335829i	$-0.109016\pi$
$38$	−9.38062	−	1.37321i	−1.52174	−	0.222764i
$39$		−	7.89208i		−	1.26374i
$40$	−1.58909			−0.251257
$41$	10.2227			1.59652			0.798262	−	0.602311i	$-0.205753\pi$
$41$	10.2227			1.59652			0.798262	+	0.602311i	$0.205753\pi$
$42$	−2.95487			−0.455946
$43$			9.06878i			1.38298i	0.722388	+	0.691488i	$0.243044\pi$
$43$			9.06878i			1.38298i	−0.722388	+	0.691488i	$0.756956\pi$
$44$	−3.29978	−	8.43388i	−0.497460	−	1.27145i
$45$	1.05010			0.156540
$46$	3.52835			0.520228
$47$	4.98078			0.726522			0.363261	−	0.931687i	$-0.381663\pi$
$47$	4.98078			0.726522			0.363261	+	0.931687i	$0.381663\pi$
$48$		−	2.79972i		−	0.404104i
$49$	6.05344			0.864777
$50$	−2.17500			−0.307591
$51$	−6.53341			−0.914860
$52$	−15.4328			−2.14015
$53$			1.30811i			0.179683i	0.995956	+	0.0898415i	$0.0286361\pi$
$53$			1.30811i			0.179683i	−0.995956	+	0.0898415i	$0.971364\pi$
$54$		−	12.3007i		−	1.67392i
$55$	−1.20844	−	3.08864i	−0.162946	−	0.416472i
$56$			1.54604i			0.206598i
$57$	−0.881625	+	6.02252i	−0.116774	+	0.797702i
$58$	13.6907			1.79768
$59$			3.03892i			0.395634i	0.980239	+	0.197817i	$0.0633851\pi$
$59$			3.03892i			0.395634i	−0.980239	+	0.197817i	$0.936615\pi$
$60$			3.81299i			0.492256i
$61$			12.2024i			1.56235i	0.624309	+	0.781177i	$0.285381\pi$
$61$			12.2024i			1.56235i	−0.624309	+	0.781177i	$0.714619\pi$
$62$		−	17.6095i		−	2.23641i
$63$		−	1.02166i		−	0.128717i
$64$	−12.3873			−1.54842
$65$	−5.65178			−0.701017
$66$	−9.38062	+	3.67019i	−1.15467	+	0.451769i
$67$			8.46997i			1.03477i	0.855752	+	0.517386i	$0.173095\pi$
$67$			8.46997i			1.03477i	−0.855752	+	0.517386i	$0.826905\pi$
$68$			12.7760i			1.54932i
$69$		−	2.26527i		−	0.272706i
$70$			2.11608i			0.252920i
$71$		−	15.6680i		−	1.85944i	−0.368262	−	0.929722i	$-0.620047\pi$
$71$		−	15.6680i		−	1.85944i	0.368262	−	0.929722i	$-0.379953\pi$
$72$	−1.66870			−0.196659
$73$			3.75996i			0.440070i	0.975492	+	0.220035i	$0.0706172\pi$
$73$			3.75996i			0.440070i	−0.975492	+	0.220035i	$0.929383\pi$
$74$			8.88603i			1.03298i
$75$			1.39639i			0.161241i
$76$	11.7770	+	1.72401i	1.35091	+	0.197757i
$77$	−3.00497	+	1.17570i	−0.342448	+	0.133984i
$78$			17.1652i			1.94358i
$79$	0.484850			0.0545499			0.0272749	−	0.999628i	$-0.491317\pi$
$79$	0.484850			0.0545499			0.0272749	+	0.999628i	$0.491317\pi$
$80$	−2.00497			−0.224163
$81$	−4.74697			−0.527441
$82$	−22.2344			−2.45538
$83$			7.80143i			0.856318i	0.903703	+	0.428159i	$0.140838\pi$
$83$			7.80143i			0.856318i	−0.903703	+	0.428159i	$0.859162\pi$
$84$	3.70971			0.404762
$85$			4.67880i			0.507487i
$86$		−	19.7246i		−	2.12695i
$87$		−	8.78970i		−	0.942354i
$88$	1.92031	+	4.90811i	0.204706	+	0.523206i
$89$		−	7.55029i		−	0.800329i	−0.916443	−	0.400165i	$-0.868953\pi$
$89$		−	7.55029i		−	0.800329i	0.916443	−	0.400165i	$-0.131047\pi$
$90$	−2.28397			−0.240752
$91$			5.49869i			0.576419i
$92$	−4.42970			−0.461828
$93$	−11.3056			−1.17234
$94$	−10.8332			−1.11736
$95$	4.31293	+	0.631362i	0.442497	+	0.0647763i
$96$			10.5273i			1.07444i
$97$			9.02220i			0.916065i	0.888935	+	0.458033i	$0.151446\pi$
$97$			9.02220i			0.916065i	−0.888935	+	0.458033i	$0.848554\pi$
$98$	−13.1662			−1.32999
$99$	−1.26899	−	3.24339i	−0.127538	−	0.325973i
$100$	2.73061			0.273061
$101$			9.56775i			0.952027i	0.879438	+	0.476014i	$0.157919\pi$
$101$			9.56775i			0.952027i	−0.879438	+	0.476014i	$0.842081\pi$
$102$	14.2101			1.40701
$103$			12.5103i			1.23268i	0.787480	+	0.616340i	$0.211385\pi$
$103$			12.5103i			1.23268i	−0.787480	+	0.616340i	$0.788615\pi$
$104$	8.98117			0.880676
$105$	1.35856			0.132582
$106$		−	2.84514i		−	0.276345i
$107$	12.6741			1.22525			0.612627	−	0.790372i	$-0.290113\pi$
$107$	12.6741			1.22525			0.612627	+	0.790372i	$0.290113\pi$
$108$			15.4430i			1.48601i
$109$	6.06357			0.580785			0.290392	−	0.956908i	$-0.406214\pi$
$109$	6.06357			0.580785			0.290392	+	0.956908i	$0.406214\pi$
$110$	2.62835	+	6.71778i	0.250603	+	0.640515i
$111$	5.70499			0.541493
$112$			1.95066i			0.184320i
$113$		−	1.86280i		−	0.175238i	−0.996154	−	0.0876188i	$-0.972074\pi$
$113$		−	1.86280i		−	0.175238i	0.996154	−	0.0876188i	$-0.0279257\pi$
$114$	1.91753	−	13.0990i	0.179593	−	1.22683i
$115$	−1.62223			−0.151274
$116$	−17.1881			−1.59588
$117$	−5.93496			−0.548687
$118$		−	6.60964i		−	0.608467i
$119$	4.55206			0.417286
$120$		−	2.21898i		−	0.202564i
$121$	−8.07936	+	7.46485i	−0.734487	+	0.678623i
$122$		−	26.5402i		−	2.40283i
$123$			14.2749i			1.28712i
$124$			22.1080i			1.98536i
$125$	1.00000			0.0894427
$126$			2.22211i			0.197961i
$127$	−8.92689			−0.792133			−0.396067	−	0.918222i	$-0.629625\pi$
$127$	−8.92689			−0.792133			−0.396067	+	0.918222i	$0.629625\pi$
$128$	11.8644			1.04868
$129$	−12.6635			−1.11496
$130$	12.2926			1.07813
$131$			21.0267i			1.83711i	0.395288	+	0.918557i	$0.370645\pi$
$131$			21.0267i			1.83711i	−0.395288	+	0.918557i	$0.629355\pi$
$132$	11.7770	−	4.60777i	1.02505	−	0.401055i
$133$	0.614259	−	4.19610i	0.0532630	−	0.363848i
$134$		−	18.4222i		−	1.59143i
$135$			5.65551i			0.486749i
$136$		−	7.43501i		−	0.637547i
$137$	−2.18431			−0.186619			−0.0933093	−	0.995637i	$-0.529745\pi$
$137$	−2.18431			−0.186619			−0.0933093	+	0.995637i	$0.529745\pi$
$138$			4.92695i			0.419410i
$139$			8.03228i			0.681289i	0.940192	+	0.340644i	$0.110645\pi$
$139$			8.03228i			0.681289i	−0.940192	+	0.340644i	$0.889355\pi$
$140$		−	2.65665i		−	0.224528i
$141$			6.95510i			0.585725i
$142$			34.0778i			2.85974i
$143$	6.82983	+	17.4563i	0.571139	+	1.45977i
$144$	−2.10543			−0.175452
$145$	−6.29460			−0.522738
$146$		−	8.17791i		−	0.676809i
$147$			8.45295i			0.697187i
$148$		−	11.1560i		−	0.917019i
$149$		−	24.0698i		−	1.97187i	−0.167125	−	0.985936i	$-0.553448\pi$
$149$		−	24.0698i		−	1.97187i	0.167125	−	0.985936i	$-0.446552\pi$
$150$		−	3.03714i		−	0.247981i
$151$	−6.76413			−0.550457			−0.275229	−	0.961379i	$-0.588754\pi$
$151$	−6.76413			−0.550457			−0.275229	+	0.961379i	$0.588754\pi$
$152$	−6.85362	−	1.00329i	−0.555902	−	0.0813774i
$153$			4.91322i			0.397210i
$154$	6.53581	−	2.55715i	0.526670	−	0.206061i
$155$			8.09635i			0.650314i
$156$		−	21.5502i		−	1.72540i
$157$	2.33432			0.186299			0.0931497	−	0.995652i	$-0.470306\pi$
$157$	2.33432			0.186299			0.0931497	+	0.995652i	$0.470306\pi$
$158$	−1.05455			−0.0838953
$159$	−1.82663			−0.144861
$160$	7.53898			0.596009
$161$			1.57829i			0.124387i
$162$	10.3247			0.811181
$163$	−22.6656			−1.77531			−0.887654	−	0.460512i	$-0.847666\pi$
$163$	−22.6656			−1.77531			−0.887654	+	0.460512i	$0.847666\pi$
$164$	27.9144			2.17975
$165$	4.31293	−	1.68745i	0.335761	−	0.131368i
$166$		−	16.9681i		−	1.31698i
$167$	−14.8876			−1.15204			−0.576019	−	0.817437i	$-0.695394\pi$
$167$	−14.8876			−1.15204			−0.576019	+	0.817437i	$0.695394\pi$
$168$	−2.15887			−0.166561
$169$	18.9427			1.45713
$170$		−	10.1764i		−	0.780492i
$171$	4.52903	+	0.662995i	0.346343	+	0.0507005i
$172$			24.7633i			1.88819i
$173$	4.88973			0.371759			0.185880	−	0.982573i	$-0.440487\pi$
$173$	4.88973			0.371759			0.185880	+	0.982573i	$0.440487\pi$
$174$			19.1176i			1.44930i
$175$		−	0.972912i		−	0.0735452i
$176$	2.42288	+	6.19263i	0.182632	+	0.466787i
$177$	−4.24351			−0.318961
$178$			16.4219i			1.23087i
$179$		−	10.7774i		−	0.805538i	−0.915302	−	0.402769i	$-0.868048\pi$
$179$		−	10.7774i		−	0.805538i	0.915302	−	0.402769i	$-0.131952\pi$
$180$	2.86743			0.213726
$181$			5.35025i			0.397681i	0.980032	+	0.198840i	$0.0637176\pi$
$181$			5.35025i			0.397681i	−0.980032	+	0.198840i	$0.936282\pi$
$182$		−	11.9596i		−	0.886507i
$183$	−17.0392			−1.25958
$184$	2.57787			0.190043
$185$		−	4.08553i		−	0.300374i
$186$	24.5897			1.80301
$187$	14.4511	−	5.65403i	1.05677	−	0.413464i
$188$	13.6006			0.991926
$189$	5.50232			0.400235
$190$	−9.38062	−	1.37321i	−0.680541	−	0.0996231i
$191$	10.8963			0.788430			0.394215	−	0.919018i	$-0.371016\pi$
$191$	10.8963			0.788430			0.394215	+	0.919018i	$0.371016\pi$
$192$		−	17.2975i		−	1.24834i
$193$	3.15789			0.227310			0.113655	−	0.993520i	$-0.463744\pi$
$193$	3.15789			0.227310			0.113655	+	0.993520i	$0.463744\pi$
$194$		−	19.6233i		−	1.40887i
$195$		−	7.89208i		−	0.565163i
$196$	16.5296			1.18069
$197$		−	15.8323i		−	1.12801i	−0.825773	−	0.564003i	$-0.809261\pi$
$197$		−	15.8323i		−	1.12801i	0.825773	−	0.564003i	$-0.190739\pi$
$198$	2.76004	+	7.05436i	0.196147	+	0.501332i
$199$	−11.4899			−0.814501			−0.407250	−	0.913317i	$-0.633512\pi$
$199$	−11.4899			−0.814501			−0.407250	+	0.913317i	$0.633512\pi$
$200$	−1.58909			−0.112365
$201$	−11.8274			−0.834237
$202$		−	20.8098i		−	1.46418i
$203$			6.12409i			0.429827i
$204$	−17.8402			−1.24907
$205$	10.2227			0.713987
$206$		−	27.2099i		−	1.89581i
$207$	−1.70351			−0.118402
$208$	11.3317			0.785710
$209$	−3.26186	−	14.0840i	−0.225628	−	0.974214i
$210$	−2.95487			−0.203905
$211$	−13.9424			−0.959836			−0.479918	−	0.877313i	$-0.659334\pi$
$211$	−13.9424			−0.959836			−0.479918	+	0.877313i	$0.659334\pi$
$212$			3.57195i			0.245323i
$213$	21.8785			1.49909
$214$	−27.5662			−1.88439
$215$			9.06878i			0.618485i
$216$		−	8.98709i		−	0.611494i
$217$	7.87703			0.534728
$218$	−13.1882			−0.893221
$219$	−5.25036			−0.354787
$220$	−3.29978	−	8.43388i	−0.222471	−	0.568612i
$221$		−	26.4435i		−	1.77878i
$222$	−12.4083			−0.832793
$223$		−	28.3718i		−	1.89992i	−0.312375	−	0.949959i	$-0.601124\pi$
$223$		−	28.3718i		−	1.89992i	0.312375	−	0.949959i	$-0.398876\pi$
$224$		−	7.33477i		−	0.490075i
$225$	1.05010			0.0700069
$226$			4.05159i			0.269508i
$227$	17.7816			1.18021			0.590103	−	0.807328i	$-0.299087\pi$
$227$	17.7816			1.18021			0.590103	+	0.807328i	$0.299087\pi$
$228$	−2.40738	+	16.4452i	−0.159433	+	1.08911i
$229$	25.8689			1.70946			0.854732	−	0.519069i	$-0.173721\pi$
$229$	25.8689			1.70946			0.854732	+	0.519069i	$0.173721\pi$
$230$	3.52835			0.232653
$231$	−1.64174	−	4.19610i	−0.108018	−	0.276083i
$232$	10.0027			0.656707
$233$		−	28.4609i		−	1.86453i	−0.361771	−	0.932267i	$-0.617828\pi$
$233$		−	28.4609i		−	1.86453i	0.361771	−	0.932267i	$-0.382172\pi$
$234$	12.9085			0.843856
$235$	4.98078			0.324910
$236$			8.29812i			0.540161i
$237$			0.677038i			0.0439783i
$238$	−9.90071			−0.641768
$239$			5.55577i			0.359373i	0.983724	+	0.179686i	$0.0575083\pi$
$239$			5.55577i			0.359373i	−0.983724	+	0.179686i	$0.942492\pi$
$240$		−	2.79972i		−	0.180721i
$241$	9.28244			0.597935			0.298967	−	0.954263i	$-0.403358\pi$
$241$	9.28244			0.597935			0.298967	+	0.954263i	$0.403358\pi$
$242$	17.5726	−	16.2360i	1.12961	−	1.04369i
$243$			10.3379i			0.663178i
$244$			33.3200i			2.13309i
$245$	6.05344			0.386740
$246$		−	31.0479i		−	1.97954i
$247$	−24.3758	−	3.56832i	−1.55099	−	0.227047i
$248$		−	12.8658i		−	0.816978i
$249$	−10.8938			−0.690367
$250$	−2.17500			−0.137559
$251$	−29.8106			−1.88163			−0.940813	−	0.338926i	$-0.889937\pi$
$251$	−29.8106			−1.88163			−0.940813	+	0.338926i	$0.889937\pi$
$252$		−	2.78976i		−	0.175738i
$253$	1.96037	+	5.01049i	0.123247	+	0.315007i
$254$	19.4160			1.21827
$255$	−6.53341			−0.409138
$256$	−1.03047			−0.0644047
$257$		−	5.55860i		−	0.346736i	−0.984857	−	0.173368i	$-0.944535\pi$
$257$		−	5.55860i		−	0.346736i	0.984857	−	0.173368i	$-0.0554650\pi$
$258$	27.5431			1.71476
$259$	−3.97486			−0.246986
$260$	−15.4328			−0.957104
$261$	−6.60998			−0.409148
$262$		−	45.7331i		−	2.82540i
$263$		−	9.27150i		−	0.571705i	−0.958274	−	0.285853i	$-0.907723\pi$
$263$		−	9.27150i		−	0.571705i	0.958274	−	0.285853i	$-0.0922768\pi$
$264$	−6.85362	+	2.68150i	−0.421811	+	0.165035i
$265$			1.30811i			0.0803567i
$266$	−1.33601	+	9.12652i	−0.0819162	+	0.559583i
$267$	10.5431			0.645229
$268$			23.1282i			1.41278i
$269$			14.5893i			0.889527i	0.895648	+	0.444764i	$0.146712\pi$
$269$			14.5893i			0.889527i	−0.895648	+	0.444764i	$0.853288\pi$
$270$		−	12.3007i		−	0.748598i
$271$			0.391130i			0.0237595i	0.999929	+	0.0118797i	$0.00378152\pi$
$271$			0.391130i			0.0237595i	−0.999929	+	0.0118797i	$0.996218\pi$
$272$		−	9.38085i		−	0.568798i
$273$	−7.67830			−0.464712
$274$	4.75088			0.287011
$275$	−1.20844	−	3.08864i	−0.0728715	−	0.186252i
$276$		−	6.18557i		−	0.372327i
$277$		−	27.3177i		−	1.64136i	−0.571385	−	0.820682i	$-0.693594\pi$
$277$		−	27.3177i		−	1.64136i	0.571385	−	0.820682i	$-0.306406\pi$
$278$		−	17.4702i		−	1.04779i
$279$			8.50200i			0.509002i
$280$			1.54604i			0.0923936i
$281$	−14.9188			−0.889981			−0.444990	−	0.895535i	$-0.646793\pi$
$281$	−14.9188			−0.889981			−0.444990	+	0.895535i	$0.646793\pi$
$282$		−	15.1273i		−	0.900819i
$283$		−	6.61985i		−	0.393509i	−0.980453	−	0.196755i	$-0.936960\pi$
$283$		−	6.61985i		−	0.393509i	0.980453	−	0.196755i	$-0.0630402\pi$
$284$		−	42.7832i		−	2.53871i
$285$	−0.881625	+	6.02252i	−0.0522230	+	0.356743i
$286$	−14.8549	−	37.9674i	−0.878386	−	2.24506i
$287$		−	9.94582i		−	0.587083i
$288$	7.91671			0.466497
$289$	−4.89113			−0.287713
$290$	13.6907			0.803948
$291$	−12.5985			−0.738536
$292$			10.2670i			0.600832i
$293$	−5.50397			−0.321545			−0.160773	−	0.986991i	$-0.551399\pi$
$293$	−5.50397			−0.321545			−0.160773	+	0.986991i	$0.551399\pi$
$294$		−	18.3851i		−	1.07224i
$295$			3.03892i			0.176933i
$296$			6.49226i			0.377355i
$297$	17.4678	−	6.83433i	1.01359	−	0.396568i
$298$			52.3517i			3.03265i
$299$	9.16851			0.530229
$300$			3.81299i			0.220143i
$301$	8.82312			0.508556
$302$	14.7120			0.846579
$303$	−13.3603			−0.767528
$304$	−8.64731	−	1.26586i	−0.495957	−	0.0726022i
$305$			12.2024i			0.698706i
$306$		−	10.6862i		−	0.610892i
$307$	−17.0723			−0.974370			−0.487185	−	0.873299i	$-0.661976\pi$
$307$	−17.0723			−0.974370			−0.487185	+	0.873299i	$0.661976\pi$
$308$	−8.20542	+	3.21039i	−0.467547	+	0.182929i
$309$	−17.4693			−0.993792
$310$		−	17.6095i		−	1.00015i
$311$	−15.6920			−0.889811			−0.444905	−	0.895578i	$-0.646763\pi$
$311$	−15.6920			−0.889811			−0.444905	+	0.895578i	$0.646763\pi$
$312$			12.5412i			0.710005i
$313$	−12.6657			−0.715907			−0.357953	−	0.933739i	$-0.616525\pi$
$313$	−12.6657			−0.715907			−0.357953	+	0.933739i	$0.616525\pi$
$314$	−5.07715			−0.286520
$315$		−	1.02166i		−	0.0575639i
$316$	1.32394			0.0744773
$317$			22.0274i			1.23718i	0.785713	+	0.618591i	$0.212296\pi$
$317$			22.0274i			1.23718i	−0.785713	+	0.618591i	$0.787704\pi$
$318$	3.97292			0.222790
$319$	7.60663	+	19.4417i	0.425890	+	1.08853i
$320$	−12.3873			−0.692472
$321$			17.6980i			0.987805i
$322$		−	3.43278i		−	0.191301i
$323$	−2.95401	+	20.1793i	−0.164366	+	1.12281i
$324$	−12.9621			−0.720119
$325$	−5.65178			−0.313505
$326$	49.2976			2.73034
$327$			8.46709i			0.468231i
$328$	−16.2448			−0.896969
$329$		−	4.84586i		−	0.267161i
$330$	−9.38062	+	3.67019i	−0.516386	+	0.202037i
$331$			24.8878i			1.36796i	0.729503	+	0.683978i	$0.239752\pi$
$331$			24.8878i			1.36796i	−0.729503	+	0.683978i	$0.760248\pi$
$332$			21.3027i			1.16914i
$333$		−	4.29023i		−	0.235103i
$334$	32.3805			1.77178
$335$			8.46997i			0.462764i
$336$	−2.72388			−0.148600
$337$	30.4875			1.66076			0.830381	−	0.557196i	$-0.188123\pi$
$337$	30.4875			1.66076			0.830381	+	0.557196i	$0.188123\pi$
$338$	−41.2002			−2.24100
$339$	2.60119			0.141277
$340$			12.7760i			0.692875i
$341$	25.0067	−	9.78393i	1.35419	−	0.529830i
$342$	−9.85062	−	1.44201i	−0.532661	−	0.0779751i
$343$		−	12.6999i		−	0.685727i
$344$		−	14.4111i		−	0.776992i
$345$		−	2.26527i		−	0.121958i
$346$	−10.6352			−0.571749
$347$		−	7.58202i		−	0.407024i	−0.979072	−	0.203512i	$-0.934764\pi$
$347$		−	7.58202i		−	0.407024i	0.979072	−	0.203512i	$-0.0652356\pi$
$348$		−	24.0013i		−	1.28660i
$349$		−	6.12605i		−	0.327920i	−0.986467	−	0.163960i	$-0.947573\pi$
$349$		−	6.12605i		−	0.327920i	0.986467	−	0.163960i	$-0.0524268\pi$
$350$			2.11608i			0.113109i
$351$		−	31.9637i		−	1.70610i
$352$	−9.11039	−	23.2852i	−0.485585	−	1.24110i
$353$	21.3055			1.13398			0.566989	−	0.823726i	$-0.308108\pi$
$353$	21.3055			1.13398			0.566989	+	0.823726i	$0.308108\pi$
$354$	9.22962			0.490549
$355$		−	15.6680i		−	0.831569i
$356$		−	20.6169i		−	1.09270i
$357$			6.35643i			0.336418i
$358$			23.4407i			1.23888i
$359$			15.5529i			0.820850i	0.911894	+	0.410425i	$0.134620\pi$
$359$			15.5529i			0.820850i	−0.911894	+	0.410425i	$0.865380\pi$
$360$	−1.66870			−0.0879485
$361$	18.2028	+	5.44604i	0.958040	+	0.286634i
$362$		−	11.6368i		−	0.611616i
$363$	−10.4238	−	11.2819i	−0.547109	−	0.592147i
$364$			15.0148i			0.786989i
$365$			3.75996i			0.196806i
$366$	37.0603			1.93717
$367$	20.2864			1.05894			0.529471	−	0.848328i	$-0.322390\pi$
$367$	20.2864			1.05894			0.529471	+	0.848328i	$0.322390\pi$
$368$	3.25253			0.169550
$369$	10.7349			0.558838
$370$			8.88603i			0.461962i
$371$	1.27268			0.0660742
$372$	−30.8713			−1.60060
$373$	30.8771			1.59876			0.799378	−	0.600828i	$-0.205163\pi$
$373$	30.8771			1.59876			0.799378	+	0.600828i	$0.205163\pi$
$374$	−31.4311	+	12.2975i	−1.62526	+	0.635889i
$375$			1.39639i			0.0721091i
$376$	−7.91489			−0.408179
$377$	35.5757			1.83224
$378$	−11.9675			−0.615543
$379$			21.3201i			1.09514i	0.836760	+	0.547570i	$0.184447\pi$
$379$			21.3201i			1.09514i	−0.836760	+	0.547570i	$0.815553\pi$
$380$	11.7770	+	1.72401i	0.604145	+	0.0884396i
$381$		−	12.4654i		−	0.638621i
$382$	−23.6995			−1.21257
$383$			21.8821i			1.11812i	0.829126	+	0.559062i	$0.188838\pi$
$383$			21.8821i			1.11812i	−0.829126	+	0.559062i	$0.811162\pi$
$384$			16.5673i			0.845449i
$385$	−3.00497	+	1.17570i	−0.153148	+	0.0599194i
$386$	−6.86840			−0.349592
$387$			9.52315i			0.484089i
$388$			24.6361i			1.25071i
$389$	−1.08492			−0.0550076			−0.0275038	−	0.999622i	$-0.508756\pi$
$389$	−1.08492			−0.0550076			−0.0275038	+	0.999622i	$0.508756\pi$
$390$			17.1652i			0.869196i
$391$		−	7.59010i		−	0.383848i
$392$	−9.61944			−0.485855
$393$	−29.3615			−1.48109
$394$			34.4352i			1.73482i
$395$	0.484850			0.0243954
$396$	−3.46511	−	8.85645i	−0.174128	−	0.445053i
$397$	−24.6349			−1.23639			−0.618196	−	0.786024i	$-0.712136\pi$
$397$	−24.6349			−1.23639			−0.618196	+	0.786024i	$0.712136\pi$
$398$	24.9906			1.25267
$399$	5.85938	+	0.857744i	0.293336	+	0.0429409i
$400$	−2.00497			−0.100249
$401$			33.6227i			1.67904i	0.543331	+	0.839518i	$0.317163\pi$
$401$			33.6227i			1.67904i	−0.543331	+	0.839518i	$0.682837\pi$
$402$	25.7245			1.28302
$403$		−	45.7588i		−	2.27941i
$404$			26.1259i			1.29981i
$405$	−4.74697			−0.235879
$406$		−	13.3199i		−	0.661055i
$407$	−12.6187	+	4.93711i	−0.625487	+	0.244724i
$408$	10.3821			0.513993
$409$	−13.4178			−0.663467			−0.331734	−	0.943373i	$-0.607634\pi$
$409$	−13.4178			−0.663467			−0.331734	+	0.943373i	$0.607634\pi$
$410$	−22.2344			−1.09808
$411$		−	3.05015i		−	0.150453i
$412$			34.1609i			1.68299i
$413$	2.95660			0.145485
$414$	3.70514			0.182098
$415$			7.80143i			0.382957i
$416$	−42.6087			−2.08906
$417$	−11.2162			−0.549258
$418$	7.09454	+	30.6328i	0.347006	+	1.49830i
$419$	3.60679			0.176203			0.0881017	−	0.996111i	$-0.471920\pi$
$419$	3.60679			0.176203			0.0881017	+	0.996111i	$0.471920\pi$
$420$	3.70971			0.181015
$421$			18.1941i			0.886727i	0.896342	+	0.443363i	$0.146215\pi$
$421$			18.1941i			0.886727i	−0.896342	+	0.443363i	$0.853785\pi$
$422$	30.3247			1.47618
$423$	5.23034			0.254308
$424$		−	2.07870i		−	0.100951i
$425$			4.67880i			0.226955i
$426$	−47.5857			−2.30554
$427$	11.8718			0.574519
$428$	34.6082			1.67285
$429$	−24.3758	+	9.53708i	−1.17687	+	0.460455i
$430$		−	19.7246i		−	0.951203i
$431$	19.6594			0.946962			0.473481	−	0.880804i	$-0.342997\pi$
$431$	19.6594			0.946962			0.473481	+	0.880804i	$0.342997\pi$
$432$		−	11.3391i		−	0.545555i
$433$		−	14.7215i		−	0.707469i	−0.935346	−	0.353734i	$-0.884912\pi$
$433$		−	14.7215i		−	0.707469i	0.935346	−	0.353734i	$-0.115088\pi$
$434$	−17.1325			−0.822388
$435$		−	8.78970i		−	0.421434i
$436$	16.5573			0.792949
$437$	−6.99658	−	1.02422i	−0.334692	−	0.0489949i
$438$	11.4195			0.545646
$439$	14.7126			0.702194			0.351097	−	0.936339i	$-0.385809\pi$
$439$	14.7126			0.702194			0.351097	+	0.936339i	$0.385809\pi$
$440$	1.92031	+	4.90811i	0.0915473	+	0.233985i
$441$	6.35674			0.302702
$442$			57.5146i			2.73569i
$443$	31.9332			1.51719			0.758596	−	0.651562i	$-0.225886\pi$
$443$	31.9332			1.51719			0.758596	+	0.651562i	$0.225886\pi$
$444$	15.5781			0.739305
$445$		−	7.55029i		−	0.357918i
$446$			61.7087i			2.92199i
$447$	33.6107			1.58973
$448$			12.0518i			0.569393i
$449$		−	20.7939i		−	0.981324i	−0.871350	−	0.490662i	$-0.836755\pi$
$449$		−	20.7939i		−	0.981324i	0.871350	−	0.490662i	$-0.163245\pi$
$450$	−2.28397			−0.107668
$451$	−12.3535	−	31.5743i	−0.581706	−	1.48678i
$452$		−	5.08659i		−	0.239253i
$453$		−	9.44535i		−	0.443781i
$454$	−38.6749			−1.81510
$455$			5.49869i			0.257782i
$456$	1.40098	−	9.57030i	0.0656068	−	0.448171i
$457$		−	40.8753i		−	1.91206i	−0.293263	−	0.956032i	$-0.594741\pi$
$457$		−	40.8753i		−	1.91206i	0.293263	−	0.956032i	$-0.405259\pi$
$458$	−56.2648			−2.62908
$459$	−26.4610			−1.23509
$460$	−4.42970			−0.206536
$461$			16.6649i			0.776163i	0.921625	+	0.388082i	$0.126862\pi$
$461$			16.6649i			0.776163i	−0.921625	+	0.388082i	$0.873138\pi$
$462$	3.57077	+	9.12652i	0.166127	+	0.424604i
$463$	1.66981			0.0776028			0.0388014	−	0.999247i	$-0.487646\pi$
$463$	1.66981			0.0776028			0.0388014	+	0.999247i	$0.487646\pi$
$464$	12.6205			0.585892
$465$	−11.3056			−0.524286
$466$			61.9023i			2.86757i
$467$	−25.9860			−1.20249			−0.601244	−	0.799066i	$-0.705328\pi$
$467$	−25.9860			−1.20249			−0.601244	+	0.799066i	$0.705328\pi$
$468$	−16.2061			−0.749127
$469$	8.24053			0.380513
$470$	−10.8332			−0.499698
$471$			3.25962i			0.150195i
$472$		−	4.82910i		−	0.222277i
$473$	28.0102	−	10.9591i	1.28791	−	0.503898i
$474$		−	1.47256i		−	0.0676367i
$475$	4.31293	+	0.631362i	0.197891	+	0.0289689i
$476$	12.4299			0.569724
$477$			1.37365i			0.0628953i
$478$		−	12.0838i		−	0.552699i
$479$			8.36708i			0.382302i	0.981561	+	0.191151i	$0.0612220\pi$
$479$			8.36708i			0.382302i	−0.981561	+	0.191151i	$0.938778\pi$
$480$			10.5273i			0.480505i
$481$			23.0905i			1.05284i
$482$	−20.1893			−0.919597
$483$	−2.20390			−0.100281
$484$	−22.0616	+	20.3836i	−1.00280	+	0.926529i
$485$			9.02220i			0.409677i
$486$		−	22.4850i		−	1.01994i
$487$			9.22400i			0.417979i	0.977918	+	0.208990i	$0.0670175\pi$
$487$			9.22400i			0.417979i	−0.977918	+	0.208990i	$0.932983\pi$
$488$		−	19.3906i		−	0.877773i
$489$		−	31.6500i		−	1.43126i
$490$	−13.1662			−0.594789
$491$			12.4210i			0.560552i	0.959920	+	0.280276i	$0.0904259\pi$
$491$			12.4210i			0.560552i	−0.959920	+	0.280276i	$0.909574\pi$
$492$			38.9792i			1.75732i
$493$		−	29.4511i		−	1.32641i
$494$	53.0172	+	7.76109i	2.38536	+	0.349188i
$495$	−1.26899	−	3.24339i	−0.0570366	−	0.145780i
$496$		−	16.2329i		−	0.728881i
$497$	−15.2435			−0.683766
$498$	23.6940			1.06175
$499$	28.9039			1.29392			0.646958	−	0.762525i	$-0.276041\pi$
$499$	28.9039			1.29392			0.646958	+	0.762525i	$0.276041\pi$
$500$	2.73061			0.122117
$501$		−	20.7889i		−	0.928777i
$502$	64.8379			2.89386
$503$			9.43977i			0.420898i	0.977605	+	0.210449i	$0.0674927\pi$
$503$			9.43977i			0.420898i	−0.977605	+	0.210449i	$0.932507\pi$
$504$			1.62350i			0.0723166i
$505$			9.56775i			0.425759i
$506$	−4.26380	−	10.8978i	−0.189549	−	0.484467i
$507$			26.4513i			1.17474i
$508$	−24.3759			−1.08151
$509$		−	8.32455i		−	0.368979i	−0.982834	−	0.184490i	$-0.940937\pi$
$509$		−	8.32455i		−	0.368979i	0.982834	−	0.184490i	$-0.0590632\pi$
$510$	14.2101			0.629236
$511$	3.65811			0.161825
$512$	−21.4876			−0.949626
$513$	−3.57067	+	24.3918i	−0.157649	+	1.07693i
$514$			12.0899i			0.533264i
$515$			12.5103i			0.551271i
$516$	−34.5792			−1.52226
$517$	−6.01897	−	15.3838i	−0.264714	−	0.676580i
$518$	8.64532			0.379854
$519$			6.82796i			0.299714i
$520$	8.98117			0.393850
$521$		−	33.5533i		−	1.47000i	−0.678068	−	0.734999i	$-0.737183\pi$
$521$		−	33.5533i		−	1.47000i	0.678068	−	0.734999i	$-0.262817\pi$
$522$	14.3767			0.629251
$523$	−6.04714			−0.264423			−0.132212	−	0.991222i	$-0.542208\pi$
$523$	−6.04714			−0.264423			−0.132212	+	0.991222i	$0.542208\pi$
$524$			57.4159i			2.50823i
$525$	1.35856			0.0592925
$526$			20.1655i			0.879258i
$527$	−37.8812			−1.65013
$528$	−8.64731	+	3.38328i	−0.376326	+	0.147239i
$529$	−20.3684			−0.885581
$530$		−	2.84514i		−	0.123585i
$531$			3.19118i			0.138485i
$532$	1.67731	−	11.4579i	0.0727204	−	0.496765i
$533$	−57.7767			−2.50259
$534$	−22.9313			−0.992333
$535$	12.6741			0.547950
$536$		−	13.4595i		−	0.581362i
$537$	15.0494			0.649428
$538$		−	31.7318i		−	1.36805i
$539$	−7.31521	−	18.6969i	−0.315088	−	0.805332i
$540$			15.4430i			0.664562i
$541$		−	3.72092i		−	0.159975i	−0.996796	−	0.0799874i	$-0.974512\pi$
$541$		−	3.72092i		−	0.159975i	0.996796	−	0.0799874i	$-0.0254880\pi$
$542$		−	0.850707i		−	0.0365410i
$543$	−7.47102			−0.320612
$544$			35.2733i			1.51233i
$545$	6.06357			0.259735
$546$	16.7003			0.714706
$547$	−21.9076			−0.936700			−0.468350	−	0.883543i	$-0.655151\pi$
$547$	−21.9076			−0.936700			−0.468350	+	0.883543i	$0.655151\pi$
$548$	−5.96452			−0.254792
$549$			12.8138i			0.546878i
$550$	2.62835	+	6.71778i	0.112073	+	0.286447i
$551$	−27.1482	−	3.97417i	−1.15655	−	0.169305i
$552$			3.59970i			0.153213i
$553$		−	0.471716i		−	0.0200594i
$554$			59.4160i			2.52435i
$555$	5.70499			0.242163
$556$			21.9331i			0.930169i
$557$		−	15.4884i		−	0.656265i	−0.944632	−	0.328133i	$-0.893581\pi$
$557$		−	15.4884i		−	0.656265i	0.944632	−	0.328133i	$-0.106419\pi$
$558$		−	18.4918i		−	0.782822i
$559$		−	51.2547i		−	2.16784i
$560$			1.95066i			0.0824305i
$561$	7.89522	+	20.1793i	0.333336	+	0.851972i
$562$	32.4484			1.36875
$563$	18.8626			0.794966			0.397483	−	0.917610i	$-0.369884\pi$
$563$	18.8626			0.794966			0.397483	+	0.917610i	$0.369884\pi$
$564$			18.9917i			0.799695i
$565$		−	1.86280i		−	0.0783686i
$566$			14.3982i			0.605200i
$567$			4.61838i			0.193954i
$568$			24.8977i			1.04469i
$569$	−1.49572			−0.0627040			−0.0313520	−	0.999508i	$-0.509981\pi$
$569$	−1.49572			−0.0627040			−0.0313520	+	0.999508i	$0.509981\pi$
$570$	1.91753	−	13.0990i	0.0803166	−	0.548655i
$571$		−	4.86506i		−	0.203597i	−0.994805	−	0.101798i	$-0.967540\pi$
$571$		−	4.86506i		−	0.203597i	0.994805	−	0.101798i	$-0.0324596\pi$
$572$	18.6496	+	47.6664i	0.779780	+	1.99303i
$573$			15.2155i			0.635636i
$574$			21.6321i			0.902908i
$575$	−1.62223			−0.0676518
$576$	−13.0080			−0.541999
$577$	31.4094			1.30759			0.653795	−	0.756672i	$-0.273176\pi$
$577$	31.4094			1.30759			0.653795	+	0.756672i	$0.273176\pi$
$578$	10.6382			0.442490
$579$			4.40963i			0.183258i
$580$	−17.1881			−0.713698
$581$	7.59010			0.314891
$582$	27.4017			1.13584
$583$	4.04028	−	1.58077i	0.167331	−	0.0654689i
$584$		−	5.97491i		−	0.247243i
$585$	−5.93496			−0.245380
$586$	11.9711			0.494522
$587$	−25.0613			−1.03439			−0.517195	−	0.855868i	$-0.673024\pi$
$587$	−25.0613			−1.03439			−0.517195	+	0.855868i	$0.673024\pi$
$588$			23.0817i			0.951875i
$589$	−5.11172	+	34.9190i	−0.210625	+	1.43881i
$590$		−	6.60964i		−	0.272115i
$591$	22.1080			0.909403
$592$			8.19138i			0.336664i
$593$		−	15.6595i		−	0.643059i	−0.946900	−	0.321530i	$-0.895803\pi$
$593$		−	15.6595i		−	0.643059i	0.946900	−	0.321530i	$-0.104197\pi$
$594$	−37.9925	+	14.8647i	−1.55885	+	0.609904i
$595$	4.55206			0.186616
$596$		−	65.7252i		−	2.69221i
$597$		−	16.0444i		−	0.656654i
$598$	−19.9415			−0.815468
$599$		−	23.6006i		−	0.964294i	−0.876090	−	0.482147i	$-0.839857\pi$
$599$		−	23.6006i		−	0.964294i	0.876090	−	0.482147i	$-0.160143\pi$
$600$		−	2.21898i		−	0.0905894i
$601$	22.1292			0.902669			0.451335	−	0.892355i	$-0.350948\pi$
$601$	22.1292			0.902669			0.451335	+	0.892355i	$0.350948\pi$
$602$	−19.1903			−0.782137
$603$			8.89435i			0.362206i
$604$	−18.4702			−0.751544
$605$	−8.07936	+	7.46485i	−0.328473	+	0.303489i
$606$	29.0586			1.18042
$607$	−42.9701			−1.74410			−0.872050	−	0.489416i	$-0.837210\pi$
$607$	−42.9701			−1.74410			−0.872050	+	0.489416i	$0.837210\pi$
$608$	32.5151	+	4.75982i	1.31866	+	0.193036i
$609$	−8.55160			−0.346528
$610$		−	26.5402i		−	1.07458i
$611$	−28.1503			−1.13884
$612$			13.4161i			0.542314i
$613$		−	11.0445i		−	0.446085i	−0.974809	−	0.223042i	$-0.928401\pi$
$613$		−	11.0445i		−	0.446085i	0.974809	−	0.223042i	$-0.0715989\pi$
$614$	37.1323			1.49854
$615$			14.2749i			0.575619i
$616$	4.77516	−	1.86829i	0.192397	−	0.0752757i
$617$	20.7355			0.834779			0.417390	−	0.908728i	$-0.362945\pi$
$617$	20.7355			0.834779			0.417390	+	0.908728i	$0.362945\pi$
$618$	37.9956			1.52841
$619$	32.5035			1.30643			0.653213	−	0.757174i	$-0.273421\pi$
$619$	32.5035			1.30643			0.653213	+	0.757174i	$0.273421\pi$
$620$			22.1080i			0.887879i
$621$		−	9.17456i		−	0.368162i
$622$	34.1300			1.36849
$623$	−7.34577			−0.294302
$624$			15.8234i			0.633443i
$625$	1.00000			0.0400000
$626$	27.5478			1.10103
$627$	19.6668	−	4.55482i	0.785415	−	0.181902i
$628$	6.37414			0.254356
$629$	19.1154			0.762180
$630$			2.22211i			0.0885308i
$631$	−20.4278			−0.813218			−0.406609	−	0.913602i	$-0.633289\pi$
$631$	−20.4278			−0.813218			−0.406609	+	0.913602i	$0.633289\pi$
$632$	−0.770468			−0.0306476
$633$		−	19.4690i		−	0.773824i
$634$		−	47.9095i		−	1.90273i
$635$	−8.92689			−0.354253
$636$	−4.98782			−0.197780
$637$	−34.2127			−1.35556
$638$	−16.5444	−	42.2857i	−0.654999	−	1.67411i
$639$		−	16.4530i		−	0.650870i
$640$	11.8644			0.468983
$641$		−	16.2148i		−	0.640448i	−0.947342	−	0.320224i	$-0.896242\pi$
$641$		−	16.2148i		−	0.640448i	0.947342	−	0.320224i	$-0.103758\pi$
$642$		−	38.4931i		−	1.51920i
$643$	−25.0822			−0.989145			−0.494572	−	0.869136i	$-0.664675\pi$
$643$	−25.0822			−0.989145			−0.494572	+	0.869136i	$0.664675\pi$
$644$			4.30970i			0.169826i
$645$	−12.6635			−0.498626
$646$	6.42497	−	43.8900i	0.252787	−	1.72683i
$647$	31.2539			1.22872			0.614359	−	0.789026i	$-0.289415\pi$
$647$	31.2539			1.22872			0.614359	+	0.789026i	$0.289415\pi$
$648$	7.54334			0.296331
$649$	9.38612	−	3.67234i	0.368437	−	0.144152i
$650$	12.2926			0.482156
$651$			10.9994i			0.431100i
$652$	−61.8910			−2.42384
$653$	−34.4492			−1.34810			−0.674052	−	0.738684i	$-0.735447\pi$
$653$	−34.4492			−1.34810			−0.674052	+	0.738684i	$0.735447\pi$
$654$		−	18.4159i		−	0.720119i
$655$			21.0267i			0.821583i
$656$	−20.4963			−0.800246
$657$			3.94835i			0.154040i
$658$			10.5397i			0.410882i
$659$	23.9110			0.931442			0.465721	−	0.884932i	$-0.345795\pi$
$659$	23.9110			0.931442			0.465721	+	0.884932i	$0.345795\pi$
$660$	11.7770	−	4.60777i	0.458417	−	0.179357i
$661$			21.4808i			0.835507i	0.908560	+	0.417753i	$0.137182\pi$
$661$			21.4808i			0.835507i	−0.908560	+	0.417753i	$0.862818\pi$
$662$		−	54.1308i		−	2.10386i
$663$	36.9254			1.43406
$664$		−	12.3971i		−	0.481102i
$665$	0.614259	−	4.19610i	0.0238200	−	0.162718i
$666$			9.33125i			0.361579i
$667$	10.2113			0.395384
$668$	−40.6523			−1.57289
$669$	39.6180			1.53172
$670$		−	18.4222i		−	0.711710i
$671$	37.6887	−	14.7458i	1.45496	−	0.569256i
$672$	10.2422			0.395100
$673$	20.3173			0.783173			0.391587	−	0.920141i	$-0.371926\pi$
$673$	20.3173			0.783173			0.391587	+	0.920141i	$0.371926\pi$
$674$	−66.3103			−2.55418
$675$			5.65551i			0.217681i
$676$	51.7251			1.98943
$677$	−4.84776			−0.186315			−0.0931573	−	0.995651i	$-0.529696\pi$
$677$	−4.84776			−0.186315			−0.0931573	+	0.995651i	$0.529696\pi$
$678$	−5.65758			−0.217278
$679$	8.77780			0.336861
$680$		−	7.43501i		−	0.285120i
$681$			24.8300i			0.951487i
$682$	−54.3895	+	21.2800i	−2.08268	+	0.814854i
$683$		−	6.25656i		−	0.239401i	−0.992810	−	0.119700i	$-0.961807\pi$
$683$		−	6.25656i		−	0.239401i	0.992810	−	0.119700i	$-0.0381934\pi$
$684$	12.3670	+	1.81038i	0.472865	+	0.0692218i
$685$	−2.18431			−0.0834584
$686$			27.6221i			1.05462i
$687$			36.1230i			1.37818i
$688$		−	18.1826i		−	0.693207i
$689$		−	7.39317i		−	0.281657i
$690$			4.92695i			0.187566i
$691$	6.23907			0.237345			0.118673	−	0.992933i	$-0.462136\pi$
$691$	6.23907			0.237345			0.118673	+	0.992933i	$0.462136\pi$
$692$	13.3520			0.507566
$693$	−3.15553	+	1.23461i	−0.119869	+	0.0468990i
$694$			16.4909i			0.625985i
$695$			8.03228i			0.304682i
$696$			13.9676i			0.529440i
$697$			47.8301i			1.81169i
$698$			13.3241i			0.504326i
$699$	39.7424			1.50320
$700$		−	2.65665i		−	0.100412i
$701$		−	2.81580i		−	0.106351i	−0.998585	−	0.0531756i	$-0.983066\pi$
$701$		−	2.81580i		−	0.106351i	0.998585	−	0.0531756i	$-0.0169343\pi$
$702$			69.5210i			2.62390i
$703$	2.57945	−	17.6206i	0.0972858	−	0.664575i
$704$	14.9693	+	38.2599i	0.564177	+	1.44198i
$705$			6.95510i			0.261944i
$706$	−46.3394			−1.74401
$707$	9.30858			0.350085
$708$	−11.5874			−0.435480
$709$	20.2900			0.762007			0.381003	−	0.924574i	$-0.375579\pi$
$709$	20.2900			0.762007			0.381003	+	0.924574i	$0.375579\pi$
$710$			34.0778i			1.27892i
$711$	0.509143			0.0190943
$712$			11.9981i			0.449646i
$713$		−	13.1342i		−	0.491878i
$714$		−	13.8252i		−	0.517396i
$715$	6.82983	+	17.4563i	0.255421	+	0.652829i
$716$		−	29.4288i		−	1.09981i
$717$	−7.75800			−0.289728
$718$		−	33.8275i		−	1.26243i
$719$	−26.7102			−0.996124			−0.498062	−	0.867141i	$-0.665955\pi$
$719$	−26.7102			−0.996124			−0.498062	+	0.867141i	$0.665955\pi$
$720$	−2.10543			−0.0784647
$721$	12.1715			0.453289
$722$	−39.5910	−	11.8451i	−1.47342	−	0.440830i
$723$			12.9619i			0.482057i
$724$			14.6095i			0.542957i
$725$	−6.29460			−0.233776
$726$	22.6718	+	24.5381i	0.841429	+	0.910695i
$727$	−0.681569			−0.0252780			−0.0126390	−	0.999920i	$-0.504023\pi$
$727$	−0.681569			−0.0252780			−0.0126390	+	0.999920i	$0.504023\pi$
$728$		−	8.73789i		−	0.323848i
$729$	−28.6767			−1.06210
$730$		−	8.17791i		−	0.302678i
$731$	−42.4309			−1.56937
$732$	−46.5276			−1.71971
$733$			53.2039i			1.96513i	0.185917	+	0.982565i	$0.440474\pi$
$733$			53.2039i			1.96513i	−0.185917	+	0.982565i	$0.559526\pi$
$734$	−44.1229			−1.62861
$735$			8.45295i			0.311792i
$736$	−12.2300			−0.450803
$737$	26.1607	−	10.2354i	0.963640	−	0.377027i
$738$	−23.3485			−0.859469
$739$		−	29.8894i		−	1.09950i	−0.835330	−	0.549749i	$-0.814723\pi$
$739$		−	29.8894i		−	1.09950i	0.835330	−	0.549749i	$-0.185277\pi$
$740$		−	11.1560i		−	0.410103i
$741$	4.98275	−	34.0380i	0.183046	−	1.25042i
$742$	−2.76807			−0.101619
$743$	29.6484			1.08770			0.543848	−	0.839184i	$-0.316967\pi$
$743$	29.6484			1.08770			0.543848	+	0.839184i	$0.316967\pi$
$744$	17.9656			0.658652
$745$		−	24.0698i		−	0.881848i
$746$	−67.1576			−2.45882
$747$			8.19231i			0.299741i
$748$	39.4604	−	15.4390i	1.44281	−	0.564505i
$749$		−	12.3308i		−	0.450558i
$750$		−	3.03714i		−	0.110901i
$751$			17.3604i			0.633491i	0.948511	+	0.316745i	$0.102590\pi$
$751$			17.3604i			0.633491i	−0.948511	+	0.316745i	$0.897410\pi$
$752$	−9.98633			−0.364164
$753$		−	41.6271i		−	1.51698i
$754$	−77.3771			−2.81791
$755$	−6.76413			−0.246172
$756$	15.0247			0.546443
$757$	−1.54332			−0.0560930			−0.0280465	−	0.999607i	$-0.508929\pi$
$757$	−1.54332			−0.0560930			−0.0280465	+	0.999607i	$0.508929\pi$
$758$		−	46.3712i		−	1.68428i
$759$	−6.99658	+	2.73743i	−0.253960	+	0.0993625i
$760$	−6.85362	−	1.00329i	−0.248607	−	0.0363931i
$761$			16.6916i			0.605069i	0.953138	+	0.302535i	$0.0978328\pi$
$761$			16.6916i			0.605069i	−0.953138	+	0.302535i	$0.902167\pi$
$762$			27.1122i			0.982171i
$763$		−	5.89932i		−	0.213570i
$764$	29.7537			1.07645
$765$			4.91322i			0.177638i
$766$		−	47.5935i		−	1.71962i
$767$		−	17.1753i		−	0.620164i
$768$		−	1.43894i		−	0.0519233i
$769$		−	22.8156i		−	0.822751i	−0.911466	−	0.411375i	$-0.865049\pi$
$769$		−	22.8156i		−	0.822751i	0.911466	−	0.411375i	$-0.134951\pi$
$770$	6.53581	−	2.55715i	0.235534	−	0.0921534i
$771$	7.76195			0.279540
$772$	8.62297			0.310348
$773$		−	19.0830i		−	0.686369i	−0.939268	−	0.343185i	$-0.888494\pi$
$773$		−	19.0830i		−	0.686369i	0.939268	−	0.343185i	$-0.111506\pi$
$774$		−	20.7128i		−	0.744508i
$775$			8.09635i			0.290829i
$776$		−	14.3370i		−	0.514670i
$777$		−	5.55045i		−	0.199121i
$778$	2.35970			0.0845993
$779$	44.0900	+	6.45424i	1.57969	+	0.231247i
$780$		−	21.5502i		−	0.771622i
$781$	−48.3926	+	18.9337i	−1.73162	+	0.677503i
$782$			16.5084i			0.590341i
$783$		−	35.5992i		−	1.27221i
$784$	−12.1370			−0.433464
$785$	2.33432			0.0833156
$786$	63.8611			2.27785
$787$	−29.9926			−1.06912			−0.534560	−	0.845130i	$-0.679523\pi$
$787$	−29.9926			−1.06912			−0.534560	+	0.845130i	$0.679523\pi$
$788$		−	43.2319i		−	1.54007i
$789$	12.9466			0.460911
$790$	−1.05455			−0.0375191
$791$	−1.81234			−0.0644394
$792$	2.01653	+	5.15402i	0.0716541	+	0.183140i
$793$		−	68.9652i		−	2.44903i
$794$	53.5809			1.90152
$795$	−1.82663			−0.0647839
$796$	−31.3746			−1.11204
$797$		−	32.9837i		−	1.16834i	−0.811631	−	0.584171i	$-0.801420\pi$
$797$		−	32.9837i		−	1.16834i	0.811631	−	0.584171i	$-0.198580\pi$
$798$	−12.7441	−	1.86559i	−0.451138	−	0.0660412i
$799$			23.3041i			0.824438i
$800$	7.53898			0.266543
$801$		−	7.92859i		−	0.280143i
$802$		−	73.1293i		−	2.58228i
$803$	11.6132	−	4.54368i	0.409820	−	0.160343i
$804$	−32.2959			−1.13899
$805$			1.57829i			0.0556274i
$806$			99.5253i			3.50563i
$807$	−20.3724			−0.717141
$808$		−	15.2040i		−	0.534874i
$809$		−	14.3804i		−	0.505589i	−0.967520	−	0.252795i	$-0.918650\pi$
$809$		−	14.3804i		−	0.505589i	0.967520	−	0.252795i	$-0.0813497\pi$
$810$	10.3247			0.362771
$811$	−20.8631			−0.732602			−0.366301	−	0.930496i	$-0.619376\pi$
$811$	−20.8631			−0.732602			−0.366301	+	0.930496i	$0.619376\pi$
$812$			16.7225i			0.586846i
$813$	−0.546169			−0.0191550
$814$	27.4457	−	10.7382i	0.961972	−	0.376374i
$815$	−22.6656			−0.793941
$816$	13.0993			0.458567
$817$	−5.72568	+	39.1130i	−0.200316	+	1.36839i
$818$	29.1837			1.02038
$819$			5.77419i			0.201767i
$820$	27.9144			0.974812
$821$			46.1822i			1.61177i	0.592073	+	0.805884i	$0.298310\pi$
$821$			46.1822i			1.61177i	−0.592073	+	0.805884i	$0.701690\pi$
$822$			6.63407i			0.231390i
$823$	2.49801			0.0870750			0.0435375	−	0.999052i	$-0.486137\pi$
$823$	2.49801			0.0870750			0.0435375	+	0.999052i	$0.486137\pi$
$824$		−	19.8800i		−	0.692552i
$825$	4.31293	−	1.68745i	0.150157	−	0.0587494i
$826$	−6.43060			−0.223749
$827$	−7.78584			−0.270740			−0.135370	−	0.990795i	$-0.543222\pi$
$827$	−7.78584			−0.270740			−0.135370	+	0.990795i	$0.543222\pi$
$828$	−4.65164			−0.161656
$829$		−	11.6526i		−	0.404713i	−0.979312	−	0.202356i	$-0.935140\pi$
$829$		−	11.6526i		−	0.404713i	0.979312	−	0.202356i	$-0.0648599\pi$
$830$		−	16.9681i		−	0.588971i
$831$	38.1461			1.32327
$832$	70.0105			2.42718
$833$			28.3228i			0.981327i
$834$	24.3951			0.844735
$835$	−14.8876			−0.515207
$836$	−8.90689	−	38.4581i	−0.308051	−	1.33010i
$837$	−45.7890			−1.58270
$838$	−7.84476			−0.270993
$839$		−	8.48629i		−	0.292979i	−0.989212	−	0.146490i	$-0.953202\pi$
$839$		−	8.48629i		−	0.292979i	0.989212	−	0.146490i	$-0.0467975\pi$
$840$	−2.15887			−0.0744881
$841$	10.6220			0.366275
$842$		−	39.5721i		−	1.36375i
$843$		−	20.8324i		−	0.717506i
$844$	−38.0714			−1.31047
$845$	18.9427			0.651647
$846$	−11.3760			−0.391114
$847$	7.26264	+	7.86050i	0.249547	+	0.270090i
$848$		−	2.62273i		−	0.0900649i
$849$	9.24387			0.317249
$850$		−	10.1764i		−	0.349047i
$851$			6.62769i			0.227194i
$852$	59.7418			2.04672
$853$		−	44.3202i		−	1.51749i	−0.651385	−	0.758747i	$-0.725812\pi$
$853$		−	44.3202i		−	1.51749i	0.651385	−	0.758747i	$-0.274188\pi$
$854$	−25.8212			−0.883584
$855$	4.52903	+	0.662995i	0.154889	+	0.0226740i
$856$	−20.1403			−0.688381
$857$	−18.2932			−0.624883			−0.312441	−	0.949937i	$-0.601147\pi$
$857$	−18.2932			−0.624883			−0.312441	+	0.949937i	$0.601147\pi$
$858$	53.0172	−	20.7431i	1.80998	−	0.708159i
$859$	−55.4093			−1.89054			−0.945270	−	0.326290i	$-0.894202\pi$
$859$	−55.4093			−1.89054			−0.945270	+	0.326290i	$0.894202\pi$
$860$			24.7633i			0.844423i
$861$	13.8882			0.473309
$862$	−42.7592			−1.45639
$863$		−	6.31916i		−	0.215107i	−0.994199	−	0.107553i	$-0.965698\pi$
$863$		−	6.31916i		−	0.215107i	0.994199	−	0.107553i	$-0.0343017\pi$
$864$			42.6368i			1.45053i
$865$	4.88973			0.166256
$866$			32.0192i			1.08806i
$867$		−	6.82990i		−	0.231956i
$868$	21.5091			0.730068
$869$	−0.585911	−	1.49753i	−0.0198757	−	0.0508001i
$870$			19.1176i			0.648146i
$871$		−	47.8704i		−	1.62203i
$872$	−9.63553			−0.326300
$873$			9.47424i			0.320655i
$874$	15.2176	+	2.22767i	0.514741	+	0.0753520i
$875$		−	0.972912i		−	0.0328904i
$876$	−14.3367			−0.484393
$877$	−44.3324			−1.49700			−0.748499	−	0.663135i	$-0.769225\pi$
$877$	−44.3324			−1.49700			−0.748499	+	0.663135i	$0.769225\pi$
$878$	−31.9999			−1.07994
$879$		−	7.68567i		−	0.259231i
$880$	2.42288	+	6.19263i	0.0816754	+	0.208754i
$881$	47.3061			1.59378			0.796891	−	0.604123i	$-0.206477\pi$
$881$	47.3061			1.59378			0.796891	+	0.604123i	$0.206477\pi$
$882$	−13.8259			−0.465542
$883$	35.0364			1.17907			0.589535	−	0.807743i	$-0.299311\pi$
$883$	35.0364			1.17907			0.589535	+	0.807743i	$0.299311\pi$
$884$		−	72.2071i		−	2.42859i
$885$	−4.24351			−0.142644
$886$	−69.4546			−2.33337
$887$	16.1611			0.542637			0.271319	−	0.962490i	$-0.412540\pi$
$887$	16.1611			0.542637			0.271319	+	0.962490i	$0.412540\pi$
$888$	−9.06571			−0.304225
$889$			8.68508i			0.291288i
$890$			16.4219i			0.550462i
$891$	5.73642	+	14.6617i	0.192177	+	0.491184i
$892$		−	77.4725i		−	2.59397i
$893$	21.4818	+	3.14468i	0.718860	+	0.105233i
$894$	−73.1032			−2.44494
$895$		−	10.7774i		−	0.360247i
$896$		−	11.5431i		−	0.385626i
$897$			12.8028i			0.427473i
$898$			45.2267i			1.50923i
$899$		−	50.9633i		−	1.69972i
$900$	2.86743			0.0955810
$901$	−6.12039			−0.203900
$902$	26.8689	+	68.6741i	0.894637	+	2.28660i
$903$			12.3205i			0.410000i
$904$			2.96015i			0.0984531i
$905$			5.35025i			0.177848i
$906$			20.5436i			0.682516i
$907$			10.8480i			0.360203i	0.983648	+	0.180102i	$0.0576426\pi$
$907$			10.8480i			0.360203i	−0.983648	+	0.180102i	$0.942357\pi$
$908$	48.5547			1.61134
$909$			10.0471i			0.333242i
$910$		−	11.9596i		−	0.396458i
$911$		−	0.810612i		−	0.0268568i	−0.999910	−	0.0134284i	$-0.995725\pi$
$911$		−	0.810612i		−	0.0268568i	0.999910	−	0.0134284i	$-0.00427452\pi$
$912$	1.76763	−	12.0750i	0.0585322	−	0.399843i
$913$	24.0958	−	9.42754i	0.797454	−	0.312006i
$914$			88.9036i			2.94067i
$915$	−17.0392			−0.563300
$916$	70.6380			2.33394
$917$	20.4572			0.675555
$918$	57.5526			1.89952
$919$		−	13.5017i		−	0.445381i	−0.974889	−	0.222691i	$-0.928516\pi$
$919$		−	13.5017i		−	0.445381i	0.974889	−	0.222691i	$-0.0714840\pi$
$920$	2.57787			0.0849898
$921$		−	23.8396i		−	0.785541i
$922$		−	36.2462i		−	1.19370i
$923$			88.5519i			2.91472i
$924$	−4.48295	−	11.4579i	−0.147478	−	0.376939i
$925$		−	4.08553i		−	0.134332i
$926$	−3.63184			−0.119350
$927$			13.1371i			0.431481i
$928$	−47.4549			−1.55778
$929$	−26.1312			−0.857336			−0.428668	−	0.903462i	$-0.641017\pi$
$929$	−26.1312			−0.857336			−0.428668	+	0.903462i	$0.641017\pi$
$930$	24.5897			0.806329
$931$	26.1081	+	3.82191i	0.855658	+	0.125258i
$932$		−	77.7157i		−	2.54566i
$933$		−	21.9121i		−	0.717369i
$934$	56.5194			1.84937
$935$	14.4511	−	5.65403i	0.472602	−	0.184907i
$936$	9.43116			0.308267
$937$			18.8189i			0.614788i	0.951582	+	0.307394i	$0.0994569\pi$
$937$			18.8189i			0.614788i	−0.951582	+	0.307394i	$0.900543\pi$
$938$	−17.9231			−0.585211
$939$		−	17.6862i		−	0.577167i
$940$	13.6006			0.443603
$941$	41.9359			1.36707			0.683536	−	0.729917i	$-0.260441\pi$
$941$	41.9359			1.36707			0.683536	+	0.729917i	$0.260441\pi$
$942$		−	7.08966i		−	0.230994i
$943$	−16.5837			−0.540039
$944$		−	6.09295i		−	0.198309i
$945$	5.50232			0.178990
$946$	−60.9220	+	23.8359i	−1.98075	+	0.774972i
$947$	18.6697			0.606684			0.303342	−	0.952882i	$-0.401897\pi$
$947$	18.6697			0.606684			0.303342	+	0.952882i	$0.401897\pi$
$948$			1.84873i			0.0600440i
$949$		−	21.2505i		−	0.689820i
$950$	−9.38062	−	1.37321i	−0.304347	−	0.0445528i
$951$	−30.7588			−0.997421
$952$	−7.23361			−0.234443
$953$	21.7799			0.705519			0.352759	−	0.935714i	$-0.385243\pi$
$953$	21.7799			0.705519			0.352759	+	0.935714i	$0.385243\pi$
$954$		−	2.98769i		−	0.0967301i
$955$	10.8963			0.352597
$956$			15.1707i			0.490654i
$957$	−27.1482	+	10.6218i	−0.877576	+	0.343354i
$958$		−	18.1984i		−	0.587963i
$959$			2.12515i			0.0686245i
$960$		−	17.2975i		−	0.558274i
$961$	−34.5508			−1.11454
$962$		−	50.2219i		−	1.61922i
$963$	13.3092			0.428881
$964$	25.3468			0.816365
$965$	3.15789			0.101656
$966$	4.79349			0.154228
$967$			8.75238i			0.281458i	0.990048	+	0.140729i	$0.0449446\pi$
$967$			8.75238i			0.281458i	−0.990048	+	0.140729i	$0.955055\pi$
$968$	12.8388	−	11.8623i	0.412654	−	0.381268i
$969$	−28.1781	−	4.12494i	−0.905212	−	0.132512i
$970$		−	19.6233i		−	0.630065i
$971$		−	36.4552i		−	1.16990i	−0.811068	−	0.584952i	$-0.801113\pi$
$971$		−	36.4552i		−	1.16990i	0.811068	−	0.584952i	$-0.198887\pi$
$972$			28.2289i			0.905442i
$973$	7.81470			0.250528
$974$		−	20.0622i		−	0.642834i
$975$		−	7.89208i		−	0.252749i
$976$		−	24.4654i		−	0.783119i
$977$		−	41.1046i		−	1.31505i	−0.753432	−	0.657526i	$-0.771603\pi$
$977$		−	41.1046i		−	1.31505i	0.753432	−	0.657526i	$-0.228397\pi$
$978$			68.8386i			2.20121i
$979$	−23.3201	+	9.12406i	−0.745314	+	0.291606i
$980$	16.5296			0.528019
$981$	6.36738			0.203295
$982$		−	27.0156i		−	0.862103i
$983$			14.8911i			0.474954i	0.971393	+	0.237477i	$0.0763204\pi$
$983$			14.8911i			0.474954i	−0.971393	+	0.237477i	$0.923680\pi$
$984$		−	22.6840i		−	0.723141i
$985$		−	15.8323i		−	0.504459i
$986$			64.0562i			2.03996i
$987$	6.76670			0.215386
$988$	−66.5608	−	9.74371i	−2.11758	−	0.309989i
$989$		−	14.7117i		−	0.467804i
$990$	2.76004	+	7.05436i	0.0877198	+	0.224202i
$991$		−	49.8061i		−	1.58214i	−0.611725	−	0.791071i	$-0.709524\pi$
$991$		−	49.8061i		−	1.58214i	0.611725	−	0.791071i	$-0.290476\pi$
$992$			61.0382i			1.93796i
$993$	−34.7530			−1.10285
$994$	33.1547			1.05160
$995$	−11.4899			−0.364256
$996$	−29.7468			−0.942564
$997$		−	37.5057i		−	1.18782i	−0.804532	−	0.593909i	$-0.797584\pi$
$997$		−	37.5057i		−	1.18782i	0.804532	−	0.593909i	$-0.202416\pi$
$998$	−62.8659			−1.98999
$999$	23.1058			0.731035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.7	✓	40
11.10	odd	2	inner	1045.2.f.b.626.33	yes	40
19.18	odd	2	inner	1045.2.f.b.626.34	yes	40
209.208	even	2	inner	1045.2.f.b.626.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.7	✓	40	1.1	even	1	trivial
1045.2.f.b.626.8	yes	40	209.208	even	2	inner
1045.2.f.b.626.33	yes	40	11.10	odd	2	inner
1045.2.f.b.626.34	yes	40	19.18	odd	2	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.17500 q^{2} +1.39639i q^{3} +2.73061 q^{4} +1.00000 q^{5} -3.03714i q^{6} -0.972912i q^{7} -1.58909 q^{8} +1.05010 q^{9} +O(q^{10})\)	\(q-2.17500 q^{2} +1.39639i q^{3} +2.73061 q^{4} +1.00000 q^{5} -3.03714i q^{6} -0.972912i q^{7} -1.58909 q^{8} +1.05010 q^{9} -2.17500 q^{10} +(-1.20844 - 3.08864i) q^{11} +3.81299i q^{12} -5.65178 q^{13} +2.11608i q^{14} +1.39639i q^{15} -2.00497 q^{16} +4.67880i q^{17} -2.28397 q^{18} +(4.31293 + 0.631362i) q^{19} +2.73061 q^{20} +1.35856 q^{21} +(2.62835 + 6.71778i) q^{22} -1.62223 q^{23} -2.21898i q^{24} +1.00000 q^{25} +12.2926 q^{26} +5.65551i q^{27} -2.65665i q^{28} -6.29460 q^{29} -3.03714i q^{30} +8.09635i q^{31} +7.53898 q^{32} +(4.31293 - 1.68745i) q^{33} -10.1764i q^{34} -0.972912i q^{35} +2.86743 q^{36} -4.08553i q^{37} +(-9.38062 - 1.37321i) q^{38} -7.89208i q^{39} -1.58909 q^{40} +10.2227 q^{41} -2.95487 q^{42} +9.06878i q^{43} +(-3.29978 - 8.43388i) q^{44} +1.05010 q^{45} +3.52835 q^{46} +4.98078 q^{47} -2.79972i q^{48} +6.05344 q^{49} -2.17500 q^{50} -6.53341 q^{51} -15.4328 q^{52} +1.30811i q^{53} -12.3007i q^{54} +(-1.20844 - 3.08864i) q^{55} +1.54604i q^{56} +(-0.881625 + 6.02252i) q^{57} +13.6907 q^{58} +3.03892i q^{59} +3.81299i q^{60} +12.2024i q^{61} -17.6095i q^{62} -1.02166i q^{63} -12.3873 q^{64} -5.65178 q^{65} +(-9.38062 + 3.67019i) q^{66} +8.46997i q^{67} +12.7760i q^{68} -2.26527i q^{69} +2.11608i q^{70} -15.6680i q^{71} -1.66870 q^{72} +3.75996i q^{73} +8.88603i q^{74} +1.39639i q^{75} +(11.7770 + 1.72401i) q^{76} +(-3.00497 + 1.17570i) q^{77} +17.1652i q^{78} +0.484850 q^{79} -2.00497 q^{80} -4.74697 q^{81} -22.2344 q^{82} +7.80143i q^{83} +3.70971 q^{84} +4.67880i q^{85} -19.7246i q^{86} -8.78970i q^{87} +(1.92031 + 4.90811i) q^{88} -7.55029i q^{89} -2.28397 q^{90} +5.49869i q^{91} -4.42970 q^{92} -11.3056 q^{93} -10.8332 q^{94} +(4.31293 + 0.631362i) q^{95} +10.5273i q^{96} +9.02220i q^{97} -13.1662 q^{98} +(-1.26899 - 3.24339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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