LMFDB - Embedded newform 1520.2.q.o.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, degree $2$, not 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:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$0.689667 - 1.19454i$ of defining polynomial
Character	$\chi$	$=$	1520.961
Dual form			1520.2.q.o.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.189667 + 0.328513i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.89307 q^{7} +(1.42805 + 2.47346i) q^{9} +O(q^{10})$	\(q+(-0.189667 + 0.328513i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.89307 q^{7} +(1.42805 + 2.47346i) q^{9} -0.134400 q^{11} +(-1.75687 - 3.04298i) q^{13} +(-0.189667 - 0.328513i) q^{15} +(0.830615 - 1.43867i) q^{17} +(-2.10596 + 3.81640i) q^{19} +(0.359052 - 0.621897i) q^{21} +(2.68492 + 4.65042i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.22142 q^{27} +(-2.48530 - 4.30466i) q^{29} -6.56472 q^{31} +(0.0254912 - 0.0441521i) q^{33} +(0.946534 - 1.63944i) q^{35} -1.69819 q^{37} +1.33288 q^{39} +(-5.31637 + 9.20823i) q^{41} +(4.25392 - 7.36801i) q^{43} -2.85611 q^{45} +(-5.55771 - 9.62623i) q^{47} -3.41630 q^{49} +(0.315080 + 0.545735i) q^{51} +(0.132424 + 0.229365i) q^{53} +(0.0672000 - 0.116394i) q^{55} +(-0.854305 - 1.41568i) q^{57} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(-2.70340 - 4.68243i) q^{63} +3.51373 q^{65} +(-1.47677 - 2.55784i) q^{67} -2.03696 q^{69} +(0.664176 - 1.15039i) q^{71} +(3.17119 - 5.49266i) q^{73} +0.379334 q^{75} +0.254428 q^{77} +(-0.733639 + 1.27070i) q^{79} +(-3.86283 + 6.69062i) q^{81} -7.44736 q^{83} +(0.830615 + 1.43867i) q^{85} +1.88551 q^{87} +(-4.86804 - 8.43169i) q^{89} +(3.32587 + 5.76057i) q^{91} +(1.24511 - 2.15659i) q^{93} +(-2.25212 - 3.73202i) q^{95} +(-8.73447 + 15.1285i) q^{97} +(-0.191930 - 0.332433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9	$ 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.189667	+	0.328513i	−0.109504	+	0.189667i	−0.915570	−	0.402160i	$-0.868260\pi$
$3$	−0.189667	+	0.328513i	−0.109504	+	0.189667i	0.806065	+	0.591827i	$0.201593\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.89307			−0.715512			−0.357756	−	0.933815i	$-0.616458\pi$
$7$	−1.89307			−0.715512			−0.357756	+	0.933815i	$0.616458\pi$
$8$		0			0
$9$	1.42805	+	2.47346i	0.476018	+	0.824487i
$10$		0			0
$11$	−0.134400			−0.0405231			−0.0202615	−	0.999795i	$-0.506450\pi$
$11$	−0.134400			−0.0405231			−0.0202615	+	0.999795i	$0.506450\pi$
$12$		0			0
$13$	−1.75687	−	3.04298i	−0.487267	−	0.843972i	0.512626	−	0.858612i	$-0.328673\pi$
$13$	−1.75687	−	3.04298i	−0.487267	−	0.843972i	−0.999893	+	0.0146407i	$0.995340\pi$
$14$		0			0
$15$	−0.189667	−	0.328513i	−0.0489718	−	0.0848216i
$16$		0			0
$17$	0.830615	−	1.43867i	0.201454	−	0.348928i	−0.747543	−	0.664213i	$-0.768767\pi$
$17$	0.830615	−	1.43867i	0.201454	−	0.348928i	0.948997	+	0.315285i	$0.102100\pi$
$18$		0			0
$19$	−2.10596	+	3.81640i	−0.483141	+	0.875543i
$19$	−2.10596	+	3.81640i	−0.483141	+	0.875543i
$20$		0			0
$21$	0.359052	−	0.621897i	0.0783516	−	0.135709i
$22$		0			0
$23$	2.68492	+	4.65042i	0.559844	+	0.969679i	0.997509	+	0.0705407i	$0.0224725\pi$
$23$	2.68492	+	4.65042i	0.559844	+	0.969679i	−0.437664	+	0.899138i	$0.644194\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−2.22142			−0.427512
$28$		0			0
$29$	−2.48530	−	4.30466i	−0.461508	−	0.799355i	0.537528	−	0.843246i	$-0.319358\pi$
$29$	−2.48530	−	4.30466i	−0.461508	−	0.799355i	−0.999036	+	0.0438905i	$0.986025\pi$
$30$		0			0
$31$	−6.56472			−1.17906			−0.589529	−	0.807747i	$-0.700687\pi$
$31$	−6.56472			−1.17906			−0.589529	+	0.807747i	$0.700687\pi$
$32$		0			0
$33$	0.0254912	−	0.0441521i	0.00443745	−	0.00768589i
$34$		0			0
$35$	0.946534	−	1.63944i	0.159993	−	0.277117i
$36$		0			0
$37$	−1.69819			−0.279181			−0.139590	−	0.990209i	$-0.544579\pi$
$37$	−1.69819			−0.279181			−0.139590	+	0.990209i	$0.544579\pi$
$38$		0			0
$39$	1.33288			0.213431
$40$		0			0
$41$	−5.31637	+	9.20823i	−0.830278	+	1.43808i	0.0675398	+	0.997717i	$0.478485\pi$
$41$	−5.31637	+	9.20823i	−0.830278	+	1.43808i	−0.897818	+	0.440367i	$0.854848\pi$
$42$		0			0
$43$	4.25392	−	7.36801i	0.648717	−	1.12361i	−0.334713	−	0.942320i	$-0.608639\pi$
$43$	4.25392	−	7.36801i	0.648717	−	1.12361i	0.983430	−	0.181290i	$-0.0580274\pi$
$44$		0			0
$45$	−2.85611			−0.425763
$46$		0			0
$47$	−5.55771	−	9.62623i	−0.810675	−	1.40413i	−0.912392	−	0.409316i	$-0.865767\pi$
$47$	−5.55771	−	9.62623i	−0.810675	−	1.40413i	0.101718	−	0.994813i	$-0.467566\pi$
$48$		0			0
$49$	−3.41630			−0.488042
$50$		0			0
$51$	0.315080	+	0.545735i	0.0441201	+	0.0764182i
$52$		0			0
$53$	0.132424	+	0.229365i	0.0181898	+	0.0315057i	0.874977	−	0.484164i	$-0.160876\pi$
$53$	0.132424	+	0.229365i	0.0181898	+	0.0315057i	−0.856787	+	0.515670i	$0.827543\pi$
$54$		0			0
$55$	0.0672000	−	0.116394i	0.00906124	−	0.0156945i
$56$		0			0
$57$	−0.854305	−	1.41568i	−0.113155	−	0.187511i
$58$		0			0
$59$	−3.44833	+	5.97269i	−0.448935	+	0.777578i	−0.998317	−	0.0579932i	$-0.981530\pi$
$59$	−3.44833	+	5.97269i	−0.448935	+	0.777578i	0.549382	+	0.835571i	$0.314863\pi$
$60$		0			0
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	−0.994568	−	0.104087i	$-0.966808\pi$
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	0.407142	−	0.913365i	$-0.366525\pi$
$62$		0			0
$63$	−2.70340	−	4.68243i	−0.340596	−	0.589930i
$64$		0			0
$65$	3.51373			0.435825
$66$		0			0
$67$	−1.47677	−	2.55784i	−0.180416	−	0.312490i	0.761606	−	0.648040i	$-0.224411\pi$
$67$	−1.47677	−	2.55784i	−0.180416	−	0.312490i	−0.942022	+	0.335550i	$0.891078\pi$
$68$		0			0
$69$	−2.03696			−0.245221
$70$		0			0
$71$	0.664176	−	1.15039i	0.0788232	−	0.136526i	−0.823919	−	0.566707i	$-0.808217\pi$
$71$	0.664176	−	1.15039i	0.0788232	−	0.136526i	0.902742	+	0.430181i	$0.141550\pi$
$72$		0			0
$73$	3.17119	−	5.49266i	0.371159	−	0.642867i	−0.618585	−	0.785718i	$-0.712294\pi$
$73$	3.17119	−	5.49266i	0.371159	−	0.642867i	0.989744	+	0.142851i	$0.0456271\pi$
$74$		0			0
$75$	0.379334			0.0438017
$76$		0			0
$77$	0.254428			0.0289948
$78$		0			0
$79$	−0.733639	+	1.27070i	−0.0825408	+	0.142965i	−0.904341	−	0.426811i	$-0.859637\pi$
$79$	−0.733639	+	1.27070i	−0.0825408	+	0.142965i	0.821800	+	0.569776i	$0.192970\pi$
$80$		0			0
$81$	−3.86283	+	6.69062i	−0.429203	+	0.743402i
$82$		0			0
$83$	−7.44736			−0.817454			−0.408727	−	0.912657i	$-0.634027\pi$
$83$	−7.44736			−0.817454			−0.408727	+	0.912657i	$0.634027\pi$
$84$		0			0
$85$	0.830615	+	1.43867i	0.0900928	+	0.156045i
$86$		0			0
$87$	1.88551			0.202148
$88$		0			0
$89$	−4.86804	−	8.43169i	−0.516011	−	0.893757i	−0.999827	−	0.0185878i	$-0.994083\pi$
$89$	−4.86804	−	8.43169i	−0.516011	−	0.893757i	0.483816	−	0.875170i	$-0.339250\pi$
$90$		0			0
$91$	3.32587	+	5.76057i	0.348646	+	0.603872i
$92$		0			0
$93$	1.24511	−	2.15659i	0.129112	−	0.223628i
$94$		0			0
$95$	−2.25212	−	3.73202i	−0.231063	−	0.382897i
$96$		0			0
$97$	−8.73447	+	15.1285i	−0.886851	+	1.53607i	−0.0432737	+	0.999063i	$0.513779\pi$
$97$	−8.73447	+	15.1285i	−0.886851	+	1.53607i	−0.843577	+	0.537008i	$0.819555\pi$
$98$		0			0
$99$	−0.191930	−	0.332433i	−0.0192897	−	0.0334108i
$100$		0			0
$101$	−2.69865	−	4.67420i	−0.268526	−	0.465101i	0.699955	−	0.714187i	$-0.253203\pi$
$101$	−2.69865	−	4.67420i	−0.268526	−	0.465101i	−0.968481	+	0.249086i	$0.919870\pi$
$102$		0			0
$103$	−2.14750			−0.211599			−0.105800	−	0.994387i	$-0.533740\pi$
$103$	−2.14750			−0.211599			−0.105800	+	0.994387i	$0.533740\pi$
$104$		0			0
$105$	0.359052	+	0.621897i	0.0350399	+	0.0606909i
$106$		0			0
$107$	1.00093			0.0967631			0.0483815	−	0.998829i	$-0.484594\pi$
$107$	1.00093			0.0967631			0.0483815	+	0.998829i	$0.484594\pi$
$108$		0			0
$109$	−8.13145	+	14.0841i	−0.778852	+	1.34901i	0.153752	+	0.988109i	$0.450864\pi$
$109$	−8.13145	+	14.0841i	−0.778852	+	1.34901i	−0.932604	+	0.360902i	$0.882469\pi$
$110$		0			0
$111$	0.322091	−	0.557877i	0.0305715	−	0.0529514i
$112$		0			0
$113$	0.843010			0.0793037			0.0396519	−	0.999214i	$-0.487375\pi$
$113$	0.843010			0.0793037			0.0396519	+	0.999214i	$0.487375\pi$
$114$		0			0
$115$	−5.36984			−0.500740
$116$		0			0
$117$	5.01780	−	8.69108i	0.463896	−	0.803491i
$118$		0			0
$119$	−1.57241	+	2.72349i	−0.144143	+	0.249662i
$120$		0			0
$121$	−10.9819			−0.998358
$122$		0			0
$123$	−2.01668	−	3.49299i	−0.181838	−	0.314953i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.36984	+	16.2290i	0.831439	+	1.44009i	0.896897	+	0.442239i	$0.145816\pi$
$127$	9.36984	+	16.2290i	0.831439	+	1.44009i	−0.0654584	+	0.997855i	$0.520851\pi$
$128$		0			0
$129$	1.61366	+	2.79493i	0.142074	+	0.246080i
$130$		0			0
$131$	1.44322	−	2.49973i	0.126095	−	0.218402i	−0.796066	−	0.605210i	$-0.793089\pi$
$131$	1.44322	−	2.49973i	0.126095	−	0.218402i	0.922160	+	0.386808i	$0.126422\pi$
$132$		0			0
$133$	3.98673	−	7.22471i	0.345693	−	0.626461i
$134$		0			0
$135$	1.11071	−	1.92381i	0.0955946	−	0.165575i
$136$		0			0
$137$	9.41579	+	16.3086i	0.804445	+	1.39334i	0.916665	+	0.399656i	$0.130871\pi$
$137$	9.41579	+	16.3086i	0.804445	+	1.39334i	−0.112220	+	0.993683i	$0.535796\pi$
$138$		0			0
$139$	−9.08974	−	15.7439i	−0.770982	−	1.33538i	−0.937025	−	0.349262i	$-0.886432\pi$
$139$	−9.08974	−	15.7439i	−0.770982	−	1.33538i	0.166043	−	0.986118i	$-0.446901\pi$
$140$		0			0
$141$	4.21645			0.355089
$142$		0			0
$143$	0.236123	+	0.408977i	0.0197456	+	0.0342003i
$144$		0			0
$145$	4.97059			0.412785
$146$		0			0
$147$	0.647958	−	1.12230i	0.0534427	−	0.0925655i
$148$		0			0
$149$	11.1272	−	19.2728i	0.911573	−	1.57889i	0.0997308	−	0.995014i	$-0.468202\pi$
$149$	11.1272	−	19.2728i	0.911573	−	1.57889i	0.811842	−	0.583877i	$-0.198465\pi$
$150$		0			0
$151$	−3.33482			−0.271384			−0.135692	−	0.990751i	$-0.543326\pi$
$151$	−3.33482			−0.271384			−0.135692	+	0.990751i	$0.543326\pi$
$152$		0			0
$153$	4.74465			0.383582
$154$		0			0
$155$	3.28236	−	5.68521i	0.263645	−	0.456647i
$156$		0			0
$157$	−3.63145	+	6.28986i	−0.289822	+	0.501986i	−0.973767	−	0.227548i	$-0.926929\pi$
$157$	−3.63145	+	6.28986i	−0.289822	+	0.501986i	0.683945	+	0.729533i	$0.260263\pi$
$158$		0			0
$159$	−0.100466			−0.00796744
$160$		0			0
$161$	−5.08273	−	8.80355i	−0.400576	−	0.693817i
$162$		0			0
$163$	19.7783			1.54916			0.774578	−	0.632478i	$-0.217962\pi$
$163$	19.7783			1.54916			0.774578	+	0.632478i	$0.217962\pi$
$164$		0			0
$165$	0.0254912	+	0.0441521i	0.00198449	+	0.00343723i
$166$		0			0
$167$	−1.70160	−	2.94726i	−0.131674	−	0.228066i	0.792648	−	0.609679i	$-0.208702\pi$
$167$	−1.70160	−	2.94726i	−0.131674	−	0.228066i	−0.924322	+	0.381614i	$0.875368\pi$
$168$		0			0
$169$	0.326838	−	0.566100i	0.0251414	−	0.0435461i
$170$		0			0
$171$	−12.4471	+	0.241010i	−0.951857	+	0.0184305i
$172$		0			0
$173$	5.29286	−	9.16750i	0.402409	−	0.696992i	−0.591607	−	0.806226i	$-0.701506\pi$
$173$	5.29286	−	9.16750i	0.402409	−	0.696992i	0.994016	+	0.109234i	$0.0348398\pi$
$174$		0			0
$175$	0.946534	+	1.63944i	0.0715512	+	0.123930i
$176$		0			0
$177$	−1.30807	−	2.26564i	−0.0983205	−	0.170296i
$178$		0			0
$179$	14.6024			1.09144			0.545718	−	0.837969i	$-0.316257\pi$
$179$	14.6024			1.09144			0.545718	+	0.837969i	$0.316257\pi$
$180$		0			0
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	0.949141	−	0.314851i	$-0.101955\pi$
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	−0.747240	+	0.664555i	$0.768621\pi$
$182$		0			0
$183$	3.48072			0.257303
$184$		0			0
$185$	0.849095	−	1.47068i	0.0624267	−	0.108126i
$186$		0			0
$187$	−0.111635	+	0.193357i	−0.00816353	+	0.0141396i
$188$		0			0
$189$	4.20530			0.305890
$190$		0			0
$191$	−20.4758			−1.48157			−0.740787	−	0.671740i	$-0.765547\pi$
$191$	−20.4758			−1.48157			−0.740787	+	0.671740i	$0.765547\pi$
$192$		0			0
$193$	−5.51176	+	9.54664i	−0.396745	+	0.687182i	−0.993322	−	0.115373i	$-0.963194\pi$
$193$	−5.51176	+	9.54664i	−0.396745	+	0.687182i	0.596577	+	0.802556i	$0.296527\pi$
$194$		0			0
$195$	−0.666439	+	1.15431i	−0.0477247	+	0.0826616i
$196$		0			0
$197$	−19.8532			−1.41448			−0.707242	−	0.706971i	$-0.750061\pi$
$197$	−19.8532			−1.41448			−0.707242	+	0.706971i	$0.750061\pi$
$198$		0			0
$199$	10.5013	+	18.1888i	0.744417	+	1.28937i	0.950467	+	0.310826i	$0.100606\pi$
$199$	10.5013	+	18.1888i	0.744417	+	1.28937i	−0.206050	+	0.978542i	$0.566061\pi$
$200$		0			0
$201$	1.12038			0.0790254
$202$		0			0
$203$	4.70483	+	8.14901i	0.330215	+	0.571948i
$204$		0			0
$205$	−5.31637	−	9.20823i	−0.371312	−	0.643131i
$206$		0			0
$207$	−7.66842	+	13.2821i	−0.532992	+	0.923169i
$208$		0			0
$209$	0.283041	−	0.512924i	0.0195784	−	0.0354797i
$210$		0			0
$211$	−6.41284	+	11.1074i	−0.441478	+	0.764663i	−0.997799	−	0.0663046i	$-0.978879\pi$
$211$	−6.41284	+	11.1074i	−0.441478	+	0.764663i	0.556321	+	0.830967i	$0.312212\pi$
$212$		0			0
$213$	0.251944	+	0.436380i	0.0172629	+	0.0299003i
$214$		0			0
$215$	4.25392	+	7.36801i	0.290115	+	0.502494i
$216$		0			0
$217$	12.4275			0.843630
$218$		0			0
$219$	1.20294	+	2.08355i	0.0812870	+	0.140793i
$220$		0			0
$221$	−5.83712			−0.392647
$222$		0			0
$223$	10.1972	−	17.6621i	0.682856	−	1.18274i	−0.291249	−	0.956647i	$-0.594071\pi$
$223$	10.1972	−	17.6621i	0.682856	−	1.18274i	0.974105	−	0.226095i	$-0.0725959\pi$
$224$		0			0
$225$	1.42805	−	2.47346i	0.0952035	−	0.164897i
$226$		0			0
$227$	−25.4172			−1.68700			−0.843500	−	0.537129i	$-0.819509\pi$
$227$	−25.4172			−1.68700			−0.843500	+	0.537129i	$0.819509\pi$
$228$		0			0
$229$	2.21553			0.146406			0.0732030	−	0.997317i	$-0.476678\pi$
$229$	2.21553			0.146406			0.0732030	+	0.997317i	$0.476678\pi$
$230$		0			0
$231$	−0.0482566	+	0.0835829i	−0.00317505	+	0.00549935i
$232$		0			0
$233$	7.07882	−	12.2609i	0.463749	−	0.803236i	−0.535395	−	0.844602i	$-0.679837\pi$
$233$	7.07882	−	12.2609i	0.463749	−	0.803236i	0.999144	+	0.0413652i	$0.0131707\pi$
$234$		0			0
$235$	11.1154			0.725089
$236$		0			0
$237$	−0.278294	−	0.482019i	−0.0180771	−	0.0313105i
$238$		0			0
$239$	−3.01476			−0.195008			−0.0975042	−	0.995235i	$-0.531086\pi$
$239$	−3.01476			−0.195008			−0.0975042	+	0.995235i	$0.531086\pi$
$240$		0			0
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	0.939781	+	0.341776i	$0.111028\pi$
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	−0.173904	+	0.984763i	$0.555638\pi$
$242$		0			0
$243$	−4.79743	−	8.30939i	−0.307755	−	0.533048i
$244$		0			0
$245$	1.70815	−	2.95860i	0.109130	−	0.189018i
$246$		0			0
$247$	15.3131	−	0.296503i	0.974352	−	0.0188660i
$248$		0			0
$249$	1.41252	−	2.44655i	0.0895147	−	0.155044i
$250$		0			0
$251$	8.59495	+	14.8869i	0.542509	+	0.939653i	0.998759	+	0.0498012i	$0.0158588\pi$
$251$	8.59495	+	14.8869i	0.542509	+	0.939653i	−0.456250	+	0.889851i	$0.650808\pi$
$252$		0			0
$253$	−0.360853	−	0.625016i	−0.0226866	−	0.0392944i
$254$		0			0
$255$	−0.630160			−0.0394622
$256$		0			0
$257$	9.77143	+	16.9246i	0.609525	+	1.05573i	0.991319	+	0.131481i	$0.0419732\pi$
$257$	9.77143	+	16.9246i	0.609525	+	1.05573i	−0.381794	+	0.924248i	$0.624693\pi$
$258$		0			0
$259$	3.21479			0.199757
$260$		0			0
$261$	7.09827	−	12.2946i	0.439372	−	0.761014i
$262$		0			0
$263$	4.40680	−	7.63280i	0.271735	−	0.470659i	−0.697571	−	0.716515i	$-0.745736\pi$
$263$	4.40680	−	7.63280i	0.271735	−	0.470659i	0.969306	+	0.245857i	$0.0790692\pi$
$264$		0			0
$265$	−0.264847			−0.0162694
$266$		0			0
$267$	3.69322			0.226022
$268$		0			0
$269$	−0.144181	+	0.249729i	−0.00879088	+	0.0152263i	−0.870387	−	0.492368i	$-0.836132\pi$
$269$	−0.144181	+	0.249729i	−0.00879088	+	0.0152263i	0.861596	+	0.507594i	$0.169465\pi$
$270$		0			0
$271$	−12.4356	+	21.5391i	−0.755409	+	1.30841i	0.189761	+	0.981830i	$0.439229\pi$
$271$	−12.4356	+	21.5391i	−0.755409	+	1.30841i	−0.945171	+	0.326577i	$0.894105\pi$
$272$		0			0
$273$	−2.52323			−0.152713
$274$		0			0
$275$	0.0672000	+	0.116394i	0.00405231	+	0.00701881i
$276$		0			0
$277$	−4.40486			−0.264662			−0.132331	−	0.991206i	$-0.542246\pi$
$277$	−4.40486			−0.264662			−0.132331	+	0.991206i	$0.542246\pi$
$278$		0			0
$279$	−9.37476	−	16.2376i	−0.561252	−	0.972118i
$280$		0			0
$281$	16.3607	+	28.3376i	0.975998	+	1.69048i	0.676600	+	0.736350i	$0.263452\pi$
$281$	16.3607	+	28.3376i	0.975998	+	1.69048i	0.299398	+	0.954128i	$0.403214\pi$
$282$		0			0
$283$	−0.664463	+	1.15088i	−0.0394982	+	0.0684129i	−0.885099	−	0.465403i	$-0.845909\pi$
$283$	−0.664463	+	1.15088i	−0.0394982	+	0.0684129i	0.845600	+	0.533816i	$0.179243\pi$
$284$		0			0
$285$	1.65317	−	0.0320097i	0.0979252	−	0.00189609i
$286$		0			0
$287$	10.0643	−	17.4318i	0.594074	−	1.02897i
$288$		0			0
$289$	7.12016	+	12.3325i	0.418833	+	0.725440i
$290$		0			0
$291$	−3.31328	−	5.73877i	−0.194228	−	0.336413i
$292$		0			0
$293$	−7.72365			−0.451220			−0.225610	−	0.974218i	$-0.572438\pi$
$293$	−7.72365			−0.451220			−0.225610	+	0.974218i	$0.572438\pi$
$294$		0			0
$295$	−3.44833	−	5.97269i	−0.200770	−	0.347743i
$296$		0			0
$297$	0.298558			0.0173241
$298$		0			0
$299$	9.43409	−	16.3403i	0.545588	−	0.944986i
$300$		0			0
$301$	−8.05296	+	13.9481i	−0.464165	+	0.803957i
$302$		0			0
$303$	2.04738			0.117619
$304$		0			0
$305$	9.17589			0.525410
$306$		0			0
$307$	−4.55001	+	7.88085i	−0.259683	+	0.449784i	−0.966157	−	0.257955i	$-0.916951\pi$
$307$	−4.55001	+	7.88085i	−0.259683	+	0.449784i	0.706474	+	0.707739i	$0.250285\pi$
$308$		0			0
$309$	0.407309	−	0.705480i	0.0231710	−	0.0401333i
$310$		0			0
$311$	12.4569			0.706364			0.353182	−	0.935555i	$-0.385100\pi$
$311$	12.4569			0.706364			0.353182	+	0.935555i	$0.385100\pi$
$312$		0			0
$313$	−1.02277	−	1.77148i	−0.0578101	−	0.100130i	0.835672	−	0.549229i	$-0.185078\pi$
$313$	−1.02277	−	1.77148i	−0.0578101	−	0.100130i	−0.893482	+	0.449099i	$0.851745\pi$
$314$		0			0
$315$	5.40680			0.304639
$316$		0			0
$317$	−11.7856	−	20.4133i	−0.661947	−	1.14653i	−0.980103	−	0.198487i	$-0.936397\pi$
$317$	−11.7856	−	20.4133i	−0.661947	−	1.14653i	0.318157	−	0.948038i	$-0.396936\pi$
$318$		0			0
$319$	0.334024	+	0.578546i	0.0187017	+	0.0323923i
$320$		0			0
$321$	−0.189842	+	0.328817i	−0.0105960	+	0.0183528i
$322$		0			0
$323$	3.74129	+	6.19974i	0.208171	+	0.344963i
$324$		0			0
$325$	−1.75687	+	3.04298i	−0.0974534	+	0.168794i
$326$		0			0
$327$	−3.08454	−	5.34257i	−0.170575	−	0.295445i
$328$		0			0
$329$	10.5211	+	18.2231i	0.580048	+	1.00467i
$330$		0			0
$331$	18.7175			1.02881			0.514403	−	0.857549i	$-0.328014\pi$
$331$	18.7175			1.02881			0.514403	+	0.857549i	$0.328014\pi$
$332$		0			0
$333$	−2.42511	−	4.20041i	−0.132895	−	0.230181i
$334$		0			0
$335$	2.95354			0.161369
$336$		0			0
$337$	16.3440	−	28.3087i	0.890316	−	1.54207i	0.0508197	−	0.998708i	$-0.483817\pi$
$337$	16.3440	−	28.3087i	0.890316	−	1.54207i	0.839497	−	0.543365i	$-0.182850\pi$
$338$		0			0
$339$	−0.159891	+	0.276940i	−0.00868409	+	0.0150413i
$340$		0			0
$341$	0.882297			0.0477791
$342$		0			0
$343$	19.7188			1.06471
$344$		0			0
$345$	1.01848	−	1.76406i	0.0548332	−	0.0949738i
$346$		0			0
$347$	−1.28333	+	2.22279i	−0.0688927	+	0.119326i	−0.898414	−	0.439149i	$-0.855280\pi$
$347$	−1.28333	+	2.22279i	−0.0688927	+	0.119326i	0.829521	+	0.558475i	$0.188613\pi$
$348$		0			0
$349$	16.6195			0.889619			0.444810	−	0.895625i	$-0.353271\pi$
$349$	16.6195			0.889619			0.444810	+	0.895625i	$0.353271\pi$
$350$		0			0
$351$	3.90274	+	6.75974i	0.208313	+	0.360808i
$352$		0			0
$353$	28.3629			1.50961			0.754803	−	0.655951i	$-0.227732\pi$
$353$	28.3629			1.50961			0.754803	+	0.655951i	$0.227732\pi$
$354$		0			0
$355$	0.664176	+	1.15039i	0.0352508	+	0.0610562i
$356$		0			0
$357$	−0.596468	−	1.03311i	−0.0315684	−	0.0546781i
$358$		0			0
$359$	8.69427	−	15.0589i	0.458866	−	0.794780i	−0.540035	−	0.841643i	$-0.681589\pi$
$359$	8.69427	−	15.0589i	0.458866	−	0.794780i	0.998901	+	0.0468628i	$0.0149224\pi$
$360$		0			0
$361$	−10.1298	−	16.0744i	−0.533150	−	0.846021i
$362$		0			0
$363$	2.08291	−	3.60771i	0.109324	−	0.189355i
$364$		0			0
$365$	3.17119	+	5.49266i	0.165987	+	0.287499i
$366$		0			0
$367$	12.9024	+	22.3477i	0.673501	+	1.16654i	0.976905	+	0.213676i	$0.0685436\pi$
$367$	12.9024	+	22.3477i	0.673501	+	1.16654i	−0.303404	+	0.952862i	$0.598123\pi$
$368$		0			0
$369$	−30.3683			−1.58091
$370$		0			0
$371$	−0.250687	−	0.434203i	−0.0130150	−	0.0225427i
$372$		0			0
$373$	27.0663			1.40144			0.700719	−	0.713437i	$-0.252862\pi$
$373$	27.0663			1.40144			0.700719	+	0.713437i	$0.252862\pi$
$374$		0			0
$375$	−0.189667	+	0.328513i	−0.00979436	+	0.0169643i
$376$		0			0
$377$	−8.73267	+	15.1254i	−0.449755	+	0.778999i
$378$		0			0
$379$	−12.4028			−0.637092			−0.318546	−	0.947907i	$-0.603194\pi$
$379$	−12.4028			−0.637092			−0.318546	+	0.947907i	$0.603194\pi$
$380$		0			0
$381$	−7.10859			−0.364184
$382$		0			0
$383$	−2.67971	+	4.64139i	−0.136927	+	0.237164i	−0.926332	−	0.376709i	$-0.877056\pi$
$383$	−2.67971	+	4.64139i	−0.136927	+	0.237164i	0.789405	+	0.613873i	$0.210389\pi$
$384$		0			0
$385$	−0.127214	+	0.220341i	−0.00648343	+	0.0112296i
$386$		0			0
$387$	24.2993			1.23520
$388$		0			0
$389$	−4.28467	−	7.42126i	−0.217241	−	0.376273i	0.736722	−	0.676195i	$-0.236372\pi$
$389$	−4.28467	−	7.42126i	−0.217241	−	0.376273i	−0.953964	+	0.299923i	$0.903039\pi$
$390$		0			0
$391$	8.92053			0.451131
$392$		0			0
$393$	0.547462	+	0.948232i	0.0276158	+	0.0478320i
$394$		0			0
$395$	−0.733639	−	1.27070i	−0.0369134	−	0.0639359i
$396$		0			0
$397$	5.32227	−	9.21844i	0.267117	−	0.462660i	−0.700999	−	0.713162i	$-0.747262\pi$
$397$	5.32227	−	9.21844i	0.267117	−	0.462660i	0.968116	+	0.250502i	$0.0805957\pi$
$398$		0			0
$399$	1.61726	+	2.67998i	0.0809641	+	0.134167i
$400$		0			0
$401$	−3.82604	+	6.62690i	−0.191063	+	0.330932i	−0.945603	−	0.325323i	$-0.894527\pi$
$401$	−3.82604	+	6.62690i	−0.191063	+	0.330932i	0.754539	+	0.656255i	$0.227860\pi$
$402$		0			0
$403$	11.5333	+	19.9763i	0.574516	+	0.995091i
$404$		0			0
$405$	−3.86283	−	6.69062i	−0.191946	−	0.332459i
$406$		0			0
$407$	0.228237			0.0113133
$408$		0			0
$409$	8.84435	+	15.3189i	0.437325	+	0.757469i	0.997482	−	0.0709173i	$-0.0225927\pi$
$409$	8.84435	+	15.3189i	0.437325	+	0.757469i	−0.560157	+	0.828386i	$0.689259\pi$
$410$		0			0
$411$	−7.14345			−0.352361
$412$		0			0
$413$	6.52793	−	11.3067i	0.321218	−	0.556367i
$414$		0			0
$415$	3.72368	−	6.44961i	0.182788	−	0.316599i
$416$		0			0
$417$	6.89609			0.337703
$418$		0			0
$419$	−1.18732			−0.0580045			−0.0290023	−	0.999579i	$-0.509233\pi$
$419$	−1.18732			−0.0580045			−0.0290023	+	0.999579i	$0.509233\pi$
$420$		0			0
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	0.0975661	+	0.995229i	$0.468894\pi$
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	−0.910677	+	0.413120i	$0.864439\pi$
$422$		0			0
$423$	15.8734	−	27.4935i	0.771791	−	1.33678i
$424$		0			0
$425$	−1.66123			−0.0805815
$426$		0			0
$427$	8.68529	+	15.0434i	0.420311	+	0.727999i
$428$		0			0
$429$	−0.179139			−0.00864890
$430$		0			0
$431$	−3.08799	−	5.34855i	−0.148743	−	0.257631i	0.782020	−	0.623253i	$-0.214189\pi$
$431$	−3.08799	−	5.34855i	−0.148743	−	0.257631i	−0.930763	+	0.365623i	$0.880856\pi$
$432$		0			0
$433$	9.27761	+	16.0693i	0.445854	+	0.772241i	0.998111	−	0.0614325i	$-0.0195669\pi$
$433$	9.27761	+	16.0693i	0.445854	+	0.772241i	−0.552258	+	0.833673i	$0.686234\pi$
$434$		0			0
$435$	−0.942757	+	1.63290i	−0.0452017	+	0.0782917i
$436$		0			0
$437$	−23.4022	+	0.453129i	−1.11948	+	0.0216761i
$438$		0			0
$439$	−0.113656	+	0.196858i	−0.00542450	+	0.00939550i	−0.868725	−	0.495295i	$-0.835060\pi$
$439$	−0.113656	+	0.196858i	−0.00542450	+	0.00939550i	0.863300	+	0.504690i	$0.168393\pi$
$440$		0			0
$441$	−4.87865	−	8.45007i	−0.232317	−	0.402384i
$442$		0			0
$443$	−17.4913	−	30.2959i	−0.831038	−	1.43940i	−0.897216	−	0.441593i	$-0.854414\pi$
$443$	−17.4913	−	30.2959i	−0.831038	−	1.43940i	0.0661770	−	0.997808i	$-0.478920\pi$
$444$		0			0
$445$	9.73608			0.461534
$446$		0			0
$447$	4.22091	+	7.31083i	0.199642	+	0.345791i
$448$		0			0
$449$	−16.9509			−0.799961			−0.399980	−	0.916524i	$-0.630983\pi$
$449$	−16.9509			−0.799961			−0.399980	+	0.916524i	$0.630983\pi$
$450$		0			0
$451$	0.714520	−	1.23759i	0.0336454	−	0.0582756i
$452$		0			0
$453$	0.632505	−	1.09553i	0.0297177	−	0.0514725i
$454$		0			0
$455$	−6.65174			−0.311838
$456$		0			0
$457$	1.60241			0.0749578			0.0374789	−	0.999297i	$-0.488067\pi$
$457$	1.60241			0.0749578			0.0374789	+	0.999297i	$0.488067\pi$
$458$		0			0
$459$	−1.84514	+	3.19588i	−0.0861239	+	0.149171i
$460$		0			0
$461$	4.37081	−	7.57046i	0.203569	−	0.352592i	−0.746107	−	0.665826i	$-0.768079\pi$
$461$	4.37081	−	7.57046i	0.203569	−	0.352592i	0.949676	+	0.313234i	$0.101413\pi$
$462$		0			0
$463$	−21.1886			−0.984718			−0.492359	−	0.870392i	$-0.663865\pi$
$463$	−21.1886			−0.984718			−0.492359	+	0.870392i	$0.663865\pi$
$464$		0			0
$465$	1.24511	+	2.15659i	0.0577406	+	0.100010i
$466$		0			0
$467$	−20.4516			−0.946388			−0.473194	−	0.880958i	$-0.656899\pi$
$467$	−20.4516			−0.946388			−0.473194	+	0.880958i	$0.656899\pi$
$468$		0			0
$469$	2.79563	+	4.84217i	0.129090	+	0.223591i
$470$		0			0
$471$	−1.37753	−	2.38596i	−0.0634734	−	0.109939i
$472$		0			0
$473$	−0.571727	+	0.990259i	−0.0262880	+	0.0455322i
$474$		0			0
$475$	4.35808	−	0.0843840i	0.199963	−	0.00387180i
$476$		0			0
$477$	−0.378216	+	0.655090i	−0.0173173	+	0.0299945i
$478$		0			0
$479$	11.7746	+	20.3942i	0.537994	+	0.931833i	0.999012	+	0.0444419i	$0.0141510\pi$
$479$	11.7746	+	20.3942i	0.537994	+	0.931833i	−0.461018	+	0.887391i	$0.652516\pi$
$480$		0			0
$481$	2.98350	+	5.16757i	0.136036	+	0.235621i
$482$		0			0
$483$	3.85611			0.175459
$484$		0			0
$485$	−8.73447	−	15.1285i	−0.396612	−	0.686952i
$486$		0			0
$487$	−36.0392			−1.63309			−0.816546	−	0.577280i	$-0.804114\pi$
$487$	−36.0392			−1.63309			−0.816546	+	0.577280i	$0.804114\pi$
$488$		0			0
$489$	−3.75129	+	6.49742i	−0.169639	+	0.293824i
$490$		0			0
$491$	10.0297	−	17.3720i	0.452635	−	0.783988i	−0.545913	−	0.837842i	$-0.683817\pi$
$491$	10.0297	−	17.3720i	0.452635	−	0.783988i	0.998549	+	0.0538541i	$0.0171506\pi$
$492$		0			0
$493$	−8.25729			−0.371890
$494$		0			0
$495$	0.383860			0.0172532
$496$		0			0
$497$	−1.25733	+	2.17776i	−0.0563989	+	0.0976858i
$498$		0			0
$499$	−18.4364	+	31.9328i	−0.825328	+	1.42951i	0.0763399	+	0.997082i	$0.475677\pi$
$499$	−18.4364	+	31.9328i	−0.825328	+	1.42951i	−0.901668	+	0.432429i	$0.857657\pi$
$500$		0			0
$501$	1.29095			0.0576753
$502$		0			0
$503$	−10.8244	−	18.7483i	−0.482634	−	0.835947i	0.517167	−	0.855884i	$-0.326987\pi$
$503$	−10.8244	−	18.7483i	−0.482634	−	0.835947i	−0.999801	+	0.0199377i	$0.993653\pi$
$504$		0			0
$505$	5.39731			0.240177
$506$		0			0
$507$	0.123981	+	0.214741i	0.00550617	+	0.00953697i
$508$		0			0
$509$	18.2279	+	31.5717i	0.807938	+	1.39939i	0.914289	+	0.405062i	$0.132750\pi$
$509$	18.2279	+	31.5717i	0.807938	+	1.39939i	−0.106351	+	0.994329i	$0.533917\pi$
$510$		0			0
$511$	−6.00327	+	10.3980i	−0.265569	+	0.459979i
$512$		0			0
$513$	4.67822	−	8.47783i	0.206549	−	0.374305i
$514$		0			0
$515$	1.07375	−	1.85979i	0.0473150	−	0.0819520i
$516$		0			0
$517$	0.746955	+	1.29376i	0.0328511	+	0.0568997i
$518$		0			0
$519$	2.00776	+	3.47754i	0.0881309	+	0.152647i
$520$		0			0
$521$	−22.6092			−0.990528			−0.495264	−	0.868742i	$-0.664929\pi$
$521$	−22.6092			−0.990528			−0.495264	+	0.868742i	$0.664929\pi$
$522$		0			0
$523$	0.266456	+	0.461515i	0.0116513	+	0.0201806i	0.871792	−	0.489876i	$-0.162958\pi$
$523$	0.266456	+	0.461515i	0.0116513	+	0.0201806i	−0.860141	+	0.510056i	$0.829625\pi$
$524$		0			0
$525$	−0.718104			−0.0313406
$526$		0			0
$527$	−5.45275	+	9.44444i	−0.237525	+	0.411406i
$528$		0			0
$529$	−2.91759	+	5.05341i	−0.126852	+	0.219714i
$530$		0			0
$531$	−19.6976			−0.854804
$532$		0			0
$533$	37.3606			1.61827
$534$		0			0
$535$	−0.500463	+	0.866827i	−0.0216369	+	0.0374762i
$536$		0			0
$537$	−2.76959	+	4.79708i	−0.119517	+	0.207009i
$538$		0			0
$539$	0.459150			0.0197770
$540$		0			0
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	0.807057	−	0.590473i	$-0.201059\pi$
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	−0.914893	+	0.403696i	$0.867725\pi$
$542$		0			0
$543$	−2.06077			−0.0884362
$544$		0			0
$545$	−8.13145	−	14.0841i	−0.348313	−	0.603296i
$546$		0			0
$547$	11.3149	+	19.5981i	0.483792	+	0.837952i	0.999827	−	0.0186154i	$-0.00592582\pi$
$547$	11.3149	+	19.5981i	0.483792	+	0.837952i	−0.516035	+	0.856568i	$0.672592\pi$
$548$		0			0
$549$	13.1037	−	22.6962i	0.559250	−	0.968650i
$550$		0			0
$551$	21.6622	−	0.419439i	0.922843	−	0.0178687i
$552$		0			0
$553$	1.38883	−	2.40552i	0.0590590	−	0.102293i
$554$		0			0
$555$	0.322091	+	0.557877i	0.0136720	+	0.0236806i
$556$		0			0
$557$	−17.6277	−	30.5321i	−0.746910	−	1.29369i	−0.949297	−	0.314381i	$-0.898203\pi$
$557$	−17.6277	−	30.5321i	−0.746910	−	1.29369i	0.202387	−	0.979306i	$-0.435130\pi$
$558$		0			0
$559$	−29.8943			−1.26439
$560$		0			0
$561$	−0.0423468	−	0.0733467i	−0.00178788	−	0.00309670i
$562$		0			0
$563$	24.6295			1.03801			0.519005	−	0.854771i	$-0.326302\pi$
$563$	24.6295			1.03801			0.519005	+	0.854771i	$0.326302\pi$
$564$		0			0
$565$	−0.421505	+	0.730068i	−0.0177329	+	0.0307142i
$566$		0			0
$567$	7.31260	−	12.6658i	0.307100	−	0.531913i
$568$		0			0
$569$	−20.0193			−0.839252			−0.419626	−	0.907697i	$-0.637839\pi$
$569$	−20.0193			−0.839252			−0.419626	+	0.907697i	$0.637839\pi$
$570$		0			0
$571$	16.6121			0.695195			0.347597	−	0.937644i	$-0.386998\pi$
$571$	16.6121			0.695195			0.347597	+	0.937644i	$0.386998\pi$
$572$		0			0
$573$	3.88357	−	6.72655i	0.162239	−	0.281006i
$574$		0			0
$575$	2.68492	−	4.65042i	0.111969	−	0.193936i
$576$		0			0
$577$	12.4486			0.518244			0.259122	−	0.965845i	$-0.416567\pi$
$577$	12.4486			0.518244			0.259122	+	0.965845i	$0.416567\pi$
$578$		0			0
$579$	−2.09080	−	3.62136i	−0.0868905	−	0.150499i
$580$		0			0
$581$	14.0984			0.584899
$582$		0			0
$583$	−0.0177977	−	0.0308266i	−0.000737107	−	0.00127671i
$584$		0			0
$585$	5.01780	+	8.69108i	0.207460	+	0.359332i
$586$		0			0
$587$	2.25572	−	3.90702i	0.0931036	−	0.161260i	−0.815712	−	0.578458i	$-0.803655\pi$
$587$	2.25572	−	3.90702i	0.0931036	−	0.161260i	0.908816	+	0.417198i	$0.136988\pi$
$588$		0			0
$589$	13.8250	−	25.0536i	0.569651	−	1.03232i
$590$		0			0
$591$	3.76550	−	6.52204i	0.154892	−	0.268281i
$592$		0			0
$593$	−9.80411	−	16.9812i	−0.402606	−	0.697335i	0.591433	−	0.806354i	$-0.298562\pi$
$593$	−9.80411	−	16.9812i	−0.402606	−	0.697335i	−0.994040	+	0.109019i	$0.965229\pi$
$594$		0			0
$595$	−1.57241	−	2.72349i	−0.0644625	−	0.111652i
$596$		0			0
$597$	−7.96699			−0.326067
$598$		0			0
$599$	5.38795	+	9.33221i	0.220146	+	0.381304i	0.954852	−	0.297082i	$-0.0960134\pi$
$599$	5.38795	+	9.33221i	0.220146	+	0.381304i	−0.734706	+	0.678385i	$0.762680\pi$
$600$		0			0
$601$	15.0244			0.612860			0.306430	−	0.951893i	$-0.400866\pi$
$601$	15.0244			0.612860			0.306430	+	0.951893i	$0.400866\pi$
$602$		0			0
$603$	4.21782	−	7.30547i	0.171763	−	0.297502i
$604$		0			0
$605$	5.49097	−	9.51064i	0.223240	−	0.386662i
$606$		0			0
$607$	−25.1901			−1.02243			−0.511217	−	0.859452i	$-0.670805\pi$
$607$	−25.1901			−1.02243			−0.511217	+	0.859452i	$0.670805\pi$
$608$		0			0
$609$	−3.56940			−0.144640
$610$		0			0
$611$	−19.5283	+	33.8240i	−0.790030	+	1.36837i
$612$		0			0
$613$	−8.11753	+	14.0600i	−0.327864	+	0.567877i	−0.982088	−	0.188424i	$-0.939662\pi$
$613$	−8.11753	+	14.0600i	−0.327864	+	0.567877i	0.654224	+	0.756301i	$0.272995\pi$
$614$		0			0
$615$	4.03336			0.162641
$616$		0			0
$617$	−3.25913	−	5.64498i	−0.131208	−	0.227258i	0.792935	−	0.609307i	$-0.208552\pi$
$617$	−3.25913	−	5.64498i	−0.131208	−	0.227258i	−0.924142	+	0.382048i	$0.875219\pi$
$618$		0			0
$619$	4.39112			0.176494			0.0882470	−	0.996099i	$-0.471874\pi$
$619$	4.39112			0.176494			0.0882470	+	0.996099i	$0.471874\pi$
$620$		0			0
$621$	−5.96433	−	10.3305i	−0.239340	−	0.414550i
$622$		0			0
$623$	9.21553	+	15.9618i	0.369212	+	0.639494i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	0.114819	+	0.190267i	0.00458541	+	0.00759855i
$628$		0			0
$629$	−1.41054	+	2.44313i	−0.0562420	+	0.0974140i
$630$		0			0
$631$	−17.3104	−	29.9826i	−0.689118	−	1.19359i	−0.972124	−	0.234469i	$-0.924665\pi$
$631$	−17.3104	−	29.9826i	−0.689118	−	1.19359i	0.283006	−	0.959118i	$-0.408668\pi$
$632$		0			0
$633$	−2.43261	−	4.21340i	−0.0966875	−	0.167468i
$634$		0			0
$635$	−18.7397			−0.743661
$636$		0			0
$637$	6.00198	+	10.3957i	0.237807	+	0.411894i
$638$		0			0
$639$	3.79391			0.150085
$640$		0			0
$641$	−3.70621	+	6.41934i	−0.146386	+	0.253549i	−0.929889	−	0.367839i	$-0.880098\pi$
$641$	−3.70621	+	6.41934i	−0.146386	+	0.253549i	0.783503	+	0.621388i	$0.213431\pi$
$642$		0			0
$643$	−8.27294	+	14.3292i	−0.326253	+	0.565087i	−0.981765	−	0.190098i	$-0.939120\pi$
$643$	−8.27294	+	14.3292i	−0.326253	+	0.565087i	0.655512	+	0.755185i	$0.272453\pi$
$644$		0			0
$645$	−3.22731			−0.127075
$646$		0			0
$647$	−29.4822			−1.15907			−0.579533	−	0.814949i	$-0.696765\pi$
$647$	−29.4822			−1.15907			−0.579533	+	0.814949i	$0.696765\pi$
$648$		0			0
$649$	0.463456	−	0.802729i	0.0181922	−	0.0315099i
$650$		0			0
$651$	−2.35708	+	4.08258i	−0.0923811	+	0.160009i
$652$		0			0
$653$	6.57421			0.257269			0.128634	−	0.991692i	$-0.458941\pi$
$653$	6.57421			0.257269			0.128634	+	0.991692i	$0.458941\pi$
$654$		0			0
$655$	1.44322	+	2.49973i	0.0563912	+	0.0976725i
$656$		0			0
$657$	18.1145			0.706713
$658$		0			0
$659$	−13.1685	−	22.8085i	−0.512972	−	0.888494i	−0.999887	−	0.0150445i	$-0.995211\pi$
$659$	−13.1685	−	22.8085i	−0.512972	−	0.888494i	0.486915	−	0.873450i	$-0.338122\pi$
$660$		0			0
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	0.826880	−	0.562378i	$-0.190114\pi$
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	−0.900474	+	0.434910i	$0.856780\pi$
$662$		0			0
$663$	1.10711	−	1.91757i	0.0429965	−	0.0744721i
$664$		0			0
$665$	4.26341	+	7.06496i	0.165328	+	0.273967i
$666$		0			0
$667$	13.3456	−	23.1153i	0.516745	−	0.895029i
$668$		0			0
$669$	3.86815	+	6.69983i	0.149551	+	0.259031i
$670$		0			0
$671$	0.616619	+	1.06802i	0.0238043	+	0.0412303i
$672$		0			0
$673$	−21.0431			−0.811150			−0.405575	−	0.914062i	$-0.632929\pi$
$673$	−21.0431			−0.811150			−0.405575	+	0.914062i	$0.632929\pi$
$674$		0			0
$675$	1.11071	+	1.92381i	0.0427512	+	0.0740473i
$676$		0			0
$677$	−15.2744			−0.587043			−0.293522	−	0.955952i	$-0.594827\pi$
$677$	−15.2744			−0.587043			−0.293522	+	0.955952i	$0.594827\pi$
$678$		0			0
$679$	16.5349	−	28.6394i	0.634553	−	1.09908i
$680$		0			0
$681$	4.82081	−	8.34988i	0.184734	−	0.319968i
$682$		0			0
$683$	8.60225			0.329156			0.164578	−	0.986364i	$-0.447374\pi$
$683$	8.60225			0.329156			0.164578	+	0.986364i	$0.447374\pi$
$684$		0			0
$685$	−18.8316			−0.719518
$686$		0			0
$687$	−0.420212	+	0.727828i	−0.0160321	+	0.0277684i
$688$		0			0
$689$	0.465302	−	0.805926i	0.0177266	−	0.0307033i
$690$		0			0
$691$	−34.1079			−1.29753			−0.648763	−	0.760990i	$-0.724714\pi$
$691$	−34.1079			−1.29753			−0.648763	+	0.760990i	$0.724714\pi$
$692$		0			0
$693$	0.363337	+	0.629318i	0.0138020	+	0.0239058i
$694$		0			0
$695$	18.1795			0.689587
$696$		0			0
$697$	8.83172	+	15.2970i	0.334525	+	0.579414i
$698$		0			0
$699$	2.68523	+	4.65096i	0.101565	+	0.175916i
$700$		0			0
$701$	−5.36463	+	9.29181i	−0.202619	+	0.350947i	−0.949372	−	0.314155i	$-0.898279\pi$
$701$	−5.36463	+	9.29181i	−0.202619	+	0.350947i	0.746752	+	0.665102i	$0.231612\pi$
$702$		0			0
$703$	3.57633	−	6.48098i	0.134884	−	0.244435i
$704$		0			0
$705$	−2.10823	+	3.65155i	−0.0794004	+	0.137525i
$706$		0			0
$707$	5.10873	+	8.84859i	0.192134	+	0.332785i
$708$		0			0
$709$	14.4238	+	24.9828i	0.541697	+	0.938247i	0.998807	+	0.0488369i	$0.0155514\pi$
$709$	14.4238	+	24.9828i	0.541697	+	0.938247i	−0.457109	+	0.889410i	$0.651115\pi$
$710$		0			0
$711$	−4.19070			−0.157164
$712$		0			0
$713$	−17.6257	−	30.5287i	−0.660089	−	1.14331i
$714$		0			0
$715$	−0.472245			−0.0176610
$716$		0			0
$717$	0.571800	−	0.990386i	0.0213542	−	0.0369866i
$718$		0			0
$719$	−10.0278	+	17.3686i	−0.373972	+	0.647739i	−0.990173	−	0.139851i	$-0.955338\pi$
$719$	−10.0278	+	17.3686i	−0.373972	+	0.647739i	0.616200	+	0.787589i	$0.288671\pi$
$720$		0			0
$721$	4.06535			0.151402
$722$		0			0
$723$	−9.02026			−0.335467
$724$		0			0
$725$	−2.48530	+	4.30466i	−0.0923016	+	0.159871i
$726$		0			0
$727$	−0.390261	+	0.675951i	−0.0144740	+	0.0250697i	−0.873172	−	0.487413i	$-0.837941\pi$
$727$	−0.390261	+	0.675951i	−0.0144740	+	0.0250697i	0.858698	+	0.512482i	$0.171274\pi$
$728$		0			0
$729$	−19.5373			−0.723604
$730$		0			0
$731$	−7.06674	−	12.2399i	−0.261373	−	0.452711i
$732$		0			0
$733$	−26.8391			−0.991326			−0.495663	−	0.868515i	$-0.665075\pi$
$733$	−26.8391			−0.991326			−0.495663	+	0.868515i	$0.665075\pi$
$734$		0			0
$735$	0.647958	+	1.12230i	0.0239003	+	0.0413965i
$736$		0			0
$737$	0.198478	+	0.343774i	0.00731103	+	0.0126631i
$738$		0			0
$739$	10.3265	−	17.8861i	0.379867	−	0.657949i	−0.611175	−	0.791495i	$-0.709303\pi$
$739$	10.3265	−	17.8861i	0.379867	−	0.657949i	0.991043	+	0.133546i	$0.0426363\pi$
$740$		0			0
$741$	−2.80699	+	5.08680i	−0.103117	+	0.186868i
$742$		0			0
$743$	0.736585	−	1.27580i	0.0270227	−	0.0468047i	−0.852198	−	0.523220i	$-0.824731\pi$
$743$	0.736585	−	1.27580i	0.0270227	−	0.0468047i	0.879220	+	0.476415i	$0.158064\pi$
$744$		0			0
$745$	11.1272	+	19.2728i	0.407668	+	0.706102i
$746$		0			0
$747$	−10.6352	−	18.4208i	−0.389123	−	0.673980i
$748$		0			0
$749$	−1.89482			−0.0692352
$750$		0			0
$751$	7.78121	+	13.4775i	0.283940	+	0.491799i	0.972352	−	0.233521i	$-0.0750249\pi$
$751$	7.78121	+	13.4775i	0.283940	+	0.491799i	−0.688411	+	0.725321i	$0.741692\pi$
$752$		0			0
$753$	−6.52071			−0.237628
$754$		0			0
$755$	1.66741	−	2.88804i	0.0606832	−	0.105106i
$756$		0			0
$757$	−10.0878	+	17.4726i	−0.366647	+	0.635052i	−0.989039	−	0.147654i	$-0.952828\pi$
$757$	−10.0878	+	17.4726i	−0.366647	+	0.635052i	0.622392	+	0.782706i	$0.286161\pi$
$758$		0			0
$759$	0.273767			0.00993713
$760$		0			0
$761$	−15.1076			−0.547649			−0.273825	−	0.961780i	$-0.588289\pi$
$761$	−15.1076			−0.547649			−0.273825	+	0.961780i	$0.588289\pi$
$762$		0			0
$763$	15.3934	−	26.6621i	0.557278	−	0.965234i
$764$		0			0
$765$	−2.37232	+	4.10898i	−0.0857715	+	0.148561i
$766$		0			0
$767$	24.2331			0.875005
$768$		0			0
$769$	−25.8290	−	44.7372i	−0.931418	−	1.61326i	−0.780900	−	0.624656i	$-0.785239\pi$
$769$	−25.8290	−	44.7372i	−0.931418	−	1.61326i	−0.150518	−	0.988607i	$-0.548094\pi$
$770$		0			0
$771$	−7.41327			−0.266982
$772$		0			0
$773$	−15.0779	−	26.1157i	−0.542314	−	0.939316i	−0.998771	−	0.0495699i	$-0.984215\pi$
$773$	−15.0779	−	26.1157i	−0.542314	−	0.939316i	0.456457	−	0.889746i	$-0.349118\pi$
$774$		0			0
$775$	3.28236	+	5.68521i	0.117906	+	0.204219i
$776$		0			0
$777$	−0.609739	+	1.05610i	−0.0218743	+	0.0378874i
$778$		0			0
$779$	−23.9462	−	39.6816i	−0.857962	−	1.42174i
$780$		0			0
$781$	−0.0892652	+	0.154612i	−0.00319416	+	0.00553244i
$782$		0			0
$783$	5.52088	+	9.56245i	0.197300	+	0.341734i
$784$		0			0
$785$	−3.63145	−	6.28986i	−0.129612	−	0.224495i
$786$		0			0
$787$	−43.0969			−1.53624			−0.768119	−	0.640307i	$-0.778807\pi$
$787$	−43.0969			−1.53624			−0.768119	+	0.640307i	$0.778807\pi$
$788$		0			0
$789$	1.67165	+	2.89538i	0.0595123	+	0.103078i
$790$		0			0
$791$	−1.59588			−0.0567428
$792$		0			0
$793$	−16.1208	+	27.9221i	−0.572467	+	0.991542i
$794$		0			0
$795$	0.0502328	−	0.0870057i	0.00178157	−	0.00308578i
$796$		0			0
$797$	−50.5062			−1.78902			−0.894510	−	0.447048i	$-0.852475\pi$
$797$	−50.5062			−1.78902			−0.894510	+	0.447048i	$0.852475\pi$
$798$		0			0
$799$	−18.4652			−0.653253
$800$		0			0
$801$	13.9036	−	24.0818i	0.491261	−	0.850889i
$802$		0			0
$803$	−0.426207	+	0.738212i	−0.0150405	+	0.0260509i
$804$		0			0
$805$	10.1655			0.358286
$806$		0			0
$807$	−0.0546928	−	0.0947307i	−0.00192528	−	0.00333468i
$808$		0			0
$809$	−30.0872			−1.05781			−0.528905	−	0.848681i	$-0.677397\pi$
$809$	−30.0872			−1.05781			−0.528905	+	0.848681i	$0.677397\pi$
$810$		0			0
$811$	11.4755	+	19.8761i	0.402958	+	0.697944i	0.994081	−	0.108637i	$-0.0346486\pi$
$811$	11.4755	+	19.8761i	0.402958	+	0.697944i	−0.591123	+	0.806581i	$0.701315\pi$
$812$		0			0
$813$	−4.71725	−	8.17051i	−0.165441	−	0.286552i
$814$		0			0
$815$	−9.88915	+	17.1285i	−0.346402	+	0.599986i
$816$		0			0
$817$	19.1607	+	31.7514i	0.670347	+	1.11084i
$818$		0			0
$819$	−9.49903	+	16.4528i	−0.331923	+	0.574907i
$820$		0			0
$821$	19.0403	+	32.9788i	0.664513	+	1.15097i	0.979417	+	0.201846i	$0.0646941\pi$
$821$	19.0403	+	32.9788i	0.664513	+	1.15097i	−0.314905	+	0.949123i	$0.601973\pi$
$822$		0			0
$823$	26.8966	+	46.5862i	0.937556	+	1.62389i	0.770012	+	0.638030i	$0.220250\pi$
$823$	26.8966	+	46.5862i	0.937556	+	1.62389i	0.167544	+	0.985865i	$0.446416\pi$
$824$		0			0
$825$	−0.0509824			−0.00177498
$826$		0			0
$827$	16.2046	+	28.0672i	0.563490	+	0.975993i	0.997188	+	0.0749347i	$0.0238748\pi$
$827$	16.2046	+	28.0672i	0.563490	+	0.975993i	−0.433699	+	0.901058i	$0.642792\pi$
$828$		0			0
$829$	−18.5305			−0.643592			−0.321796	−	0.946809i	$-0.604287\pi$
$829$	−18.5305			−0.643592			−0.321796	+	0.946809i	$0.604287\pi$
$830$		0			0
$831$	0.835456	−	1.44705i	0.0289817	−	0.0501977i
$832$		0			0
$833$	−2.83763	+	4.91491i	−0.0983179	+	0.170292i
$834$		0			0
$835$	3.40320			0.117773
$836$		0			0
$837$	14.5830			0.504062
$838$		0			0
$839$	0.413304	−	0.715864i	0.0142688	−	0.0247144i	−0.858803	−	0.512306i	$-0.828791\pi$
$839$	0.413304	−	0.715864i	0.0142688	−	0.0247144i	0.873072	+	0.487592i	$0.162125\pi$
$840$		0			0
$841$	2.14661	−	3.71803i	0.0740209	−	0.128208i
$842$		0			0
$843$	−12.4123			−0.427504
$844$		0			0
$845$	0.326838	+	0.566100i	0.0112436	+	0.0194744i
$846$		0			0
$847$	20.7895			0.714337
$848$		0			0
$849$	−0.252053	−	0.436569i	−0.00865044	−	0.0149830i
$850$		0			0
$851$	−4.55951	−	7.89730i	−0.156298	−	0.270716i
$852$		0			0
$853$	3.67469	−	6.36475i	0.125819	−	0.217925i	−0.796234	−	0.604989i	$-0.793177\pi$
$853$	3.67469	−	6.36475i	0.125819	−	0.217925i	0.922053	+	0.387064i	$0.126511\pi$
$854$		0			0
$855$	6.01485	−	10.9000i	0.205704	−	0.372774i
$856$		0			0
$857$	22.6748	−	39.2739i	0.774556	−	1.34157i	−0.160488	−	0.987038i	$-0.551307\pi$
$857$	22.6748	−	39.2739i	0.774556	−	1.34157i	0.935044	−	0.354532i	$-0.115360\pi$
$858$		0			0
$859$	14.8143	+	25.6590i	0.505456	+	0.875475i	0.999980	+	0.00631148i	$0.00200902\pi$
$859$	14.8143	+	25.6590i	0.505456	+	0.875475i	−0.494524	+	0.869164i	$0.664658\pi$
$860$		0			0
$861$	3.81771	+	6.61247i	0.130107	+	0.225352i
$862$		0			0
$863$	−41.0807			−1.39840			−0.699201	−	0.714925i	$-0.746461\pi$
$863$	−41.0807			−1.39840			−0.699201	+	0.714925i	$0.746461\pi$
$864$		0			0
$865$	5.29286	+	9.16750i	0.179963	+	0.311704i
$866$		0			0
$867$	−5.40183			−0.183456
$868$		0			0
$869$	0.0986010	−	0.170782i	0.00334481	−	0.00579338i
$870$		0			0
$871$	−5.18898	+	8.98758i	−0.175822	+	0.304533i
$872$		0			0
$873$	−49.8931			−1.68863
$874$		0			0
$875$	−1.89307			−0.0639974
$876$		0			0
$877$	−27.3154	+	47.3116i	−0.922374	+	1.59760i	−0.126643	+	0.991948i	$0.540420\pi$
$877$	−27.3154	+	47.3116i	−0.922374	+	1.59760i	−0.795731	+	0.605650i	$0.792913\pi$
$878$		0			0
$879$	1.46492	−	2.53732i	0.0494105	−	0.0855815i
$880$		0			0
$881$	−15.4805			−0.521552			−0.260776	−	0.965399i	$-0.583978\pi$
$881$	−15.4805			−0.521552			−0.260776	+	0.965399i	$0.583978\pi$
$882$		0			0
$883$	−22.6747	−	39.2738i	−0.763066	−	1.32167i	−0.941263	−	0.337674i	$-0.890360\pi$
$883$	−22.6747	−	39.2738i	−0.763066	−	1.32167i	0.178197	−	0.983995i	$-0.442973\pi$
$884$		0			0
$885$	2.61614			0.0879406
$886$		0			0
$887$	−15.5700	−	26.9680i	−0.522788	−	0.905496i	−0.999648	−	0.0265165i	$-0.991559\pi$
$887$	−15.5700	−	26.9680i	−0.522788	−	0.905496i	0.476860	−	0.878979i	$-0.341775\pi$
$888$		0			0
$889$	−17.7377	−	30.7227i	−0.594905	−	1.03041i
$890$		0			0
$891$	0.519164	−	0.899218i	0.0173926	−	0.0301249i
$892$		0			0
$893$	48.4419	−	0.937963i	1.62105	−	0.0313877i
$894$		0			0
$895$	−7.30121	+	12.6461i	−0.244052	+	0.422711i
$896$		0			0
$897$	3.57867	+	6.19844i	0.119488	+	0.206960i
$898$		0			0
$899$	16.3153	+	28.2589i	0.544145	+	0.942486i
$900$		0			0
$901$	0.439972			0.0146576
$902$		0			0
$903$	−3.05476	−	5.29100i	−0.101656	−	0.176073i
$904$		0			0
$905$	−5.43261			−0.180586
$906$		0			0
$907$	21.7707	−	37.7080i	0.722886	−	1.25207i	−0.236952	−	0.971521i	$-0.576149\pi$
$907$	21.7707	−	37.7080i	0.722886	−	1.25207i	0.959838	−	0.280554i	$-0.0905181\pi$
$908$		0			0
$909$	7.70764	−	13.3500i	0.255646	−	0.442792i
$910$		0			0
$911$	−5.72789			−0.189774			−0.0948868	−	0.995488i	$-0.530249\pi$
$911$	−5.72789			−0.189774			−0.0948868	+	0.995488i	$0.530249\pi$
$912$		0			0
$913$	1.00093			0.0331258
$914$		0			0
$915$	−1.74036	+	3.01440i	−0.0575346	+	0.0996529i
$916$		0			0
$917$	−2.73211	+	4.73216i	−0.0902223	+	0.156270i
$918$		0			0
$919$	−7.93860			−0.261870			−0.130935	−	0.991391i	$-0.541798\pi$
$919$	−7.93860			−0.261870			−0.130935	+	0.991391i	$0.541798\pi$
$920$		0			0
$921$	−1.72597	−	2.98947i	−0.0568728	−	0.0985065i
$922$		0			0
$923$	−4.66747			−0.153632
$924$		0			0
$925$	0.849095	+	1.47068i	0.0279181	+	0.0483555i
$926$		0			0
$927$	−3.06674	−	5.31174i	−0.100725	−	0.174461i
$928$		0			0
$929$	14.4784	−	25.0772i	0.475019	−	0.822758i	−0.524571	−	0.851366i	$-0.675774\pi$
$929$	14.4784	−	25.0772i	0.475019	−	0.822758i	0.999591	+	0.0286089i	$0.00910773\pi$
$930$		0			0
$931$	7.19459	−	13.0380i	0.235793	−	0.427302i
$932$		0			0
$933$	−2.36265	+	4.09224i	−0.0773498	+	0.133974i
$934$		0			0
$935$	−0.111635	−	0.193357i	−0.00365084	−	0.00632344i
$936$		0			0
$937$	7.34080	+	12.7146i	0.239813	+	0.415369i	0.960661	−	0.277725i	$-0.0895804\pi$
$937$	7.34080	+	12.7146i	0.239813	+	0.415369i	−0.720847	+	0.693094i	$0.756247\pi$
$938$		0			0
$939$	0.775939			0.0253218
$940$		0			0
$941$	0.0773773	+	0.134021i	0.00252243	+	0.00436897i	0.867284	−	0.497814i	$-0.165864\pi$
$941$	0.0773773	+	0.134021i	0.00252243	+	0.00436897i	−0.864761	+	0.502183i	$0.832530\pi$
$942$		0			0
$943$	−57.0961			−1.85931
$944$		0			0
$945$	−2.10265	+	3.64189i	−0.0683991	+	0.118471i
$946$		0			0
$947$	−3.75904	+	6.51084i	−0.122152	+	0.211574i	−0.920616	−	0.390469i	$-0.872313\pi$
$947$	−3.75904	+	6.51084i	−0.122152	+	0.211574i	0.798464	+	0.602043i	$0.205646\pi$
$948$		0			0
$949$	−22.2854			−0.723415
$950$		0			0
$951$	8.94137			0.289944
$952$		0			0
$953$	−11.3372	+	19.6365i	−0.367247	+	0.636090i	−0.989134	−	0.147017i	$-0.953033\pi$
$953$	−11.3372	+	19.6365i	−0.367247	+	0.636090i	0.621887	+	0.783107i	$0.286366\pi$
$954$		0			0
$955$	10.2379	−	17.7325i	0.331290	−	0.573811i
$956$		0			0
$957$	−0.253413			−0.00819167
$958$		0			0
$959$	−17.8247	−	30.8733i	−0.575590	−	0.996952i
$960$		0			0
$961$	12.0955			0.390177
$962$		0			0
$963$	1.42937	+	2.47575i	0.0460609	+	0.0797799i
$964$		0			0
$965$	−5.51176	−	9.54664i	−0.177430	−	0.307317i
$966$		0			0
$967$	14.4172	−	24.9714i	0.463627	−	0.803025i	−0.535512	−	0.844528i	$-0.679881\pi$
$967$	14.4172	−	24.9714i	0.463627	−	0.803025i	0.999138	+	0.0415030i	$0.0132146\pi$
$968$		0			0
$969$	−2.74629	+	0.0531755i	−0.0882236	+	0.00170824i
$970$		0			0
$971$	13.1831	−	22.8338i	0.423065	−	0.732770i	−0.573173	−	0.819435i	$-0.694288\pi$
$971$	13.1831	−	22.8338i	0.423065	−	0.732770i	0.996238	+	0.0866647i	$0.0276209\pi$
$972$		0			0
$973$	17.2075	+	29.8043i	0.551647	+	0.955481i
$974$		0			0
$975$	−0.666439	−	1.15431i	−0.0213431	−	0.0369674i
$976$		0			0
$977$	4.59218			0.146917			0.0734585	−	0.997298i	$-0.476596\pi$
$977$	4.59218			0.146917			0.0734585	+	0.997298i	$0.476596\pi$
$978$		0			0
$979$	0.654264	+	1.13322i	0.0209104	+	0.0362178i
$980$		0			0
$981$	−46.4486			−1.48299
$982$		0			0
$983$	3.45737	−	5.98833i	0.110273	−	0.190998i	−0.805607	−	0.592450i	$-0.798161\pi$
$983$	3.45737	−	5.98833i	0.110273	−	0.190998i	0.915880	+	0.401452i	$0.131494\pi$
$984$		0			0
$985$	9.92662	−	17.1934i	0.316288	−	0.547828i
$986$		0			0
$987$	−7.98203			−0.254071
$988$		0			0
$989$	45.6857			1.45272
$990$		0			0
$991$	−19.0035	+	32.9150i	−0.603666	+	1.04558i	0.388594	+	0.921409i	$0.372961\pi$
$991$	−19.0035	+	32.9150i	−0.603666	+	1.04558i	−0.992261	+	0.124172i	$0.960373\pi$
$992$		0			0
$993$	−3.55009	+	6.14893i	−0.112659	+	0.195130i
$994$		0			0
$995$	−21.0026			−0.665827
$996$		0			0
$997$	−8.11326	−	14.0526i	−0.256950	−	0.445050i	0.708474	−	0.705737i	$-0.249384\pi$
$997$	−8.11326	−	14.0526i	−0.256950	−	0.445050i	−0.965423	+	0.260688i	$0.916051\pi$
$998$		0			0
$999$	3.77239			0.119353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.o.961.2		8
4.3	odd	2		95.2.e.c.11.2	✓	8
12.11	even	2		855.2.k.h.676.3		8
19.7	even	3	inner	1520.2.q.o.881.2		8
20.3	even	4		475.2.j.c.49.5		16
20.7	even	4		475.2.j.c.49.4		16
20.19	odd	2		475.2.e.e.201.3		8
76.7	odd	6		95.2.e.c.26.2	yes	8
76.11	odd	6		1805.2.a.o.1.3		4
76.27	even	6		1805.2.a.i.1.2		4
228.83	even	6		855.2.k.h.406.3		8
380.7	even	12		475.2.j.c.349.5		16
380.83	even	12		475.2.j.c.349.4		16
380.159	odd	6		475.2.e.e.26.3		8
380.179	even	6		9025.2.a.bp.1.3		4
380.239	odd	6		9025.2.a.bg.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.2	✓	8	4.3	odd	2
95.2.e.c.26.2	yes	8	76.7	odd	6
475.2.e.e.26.3		8	380.159	odd	6
475.2.e.e.201.3		8	20.19	odd	2
475.2.j.c.49.4		16	20.7	even	4
475.2.j.c.49.5		16	20.3	even	4
475.2.j.c.349.4		16	380.83	even	12
475.2.j.c.349.5		16	380.7	even	12
855.2.k.h.406.3		8	228.83	even	6
855.2.k.h.676.3		8	12.11	even	2
1520.2.q.o.881.2		8	19.7	even	3	inner
1520.2.q.o.961.2		8	1.1	even	1	trivial
1805.2.a.i.1.2		4	76.27	even	6
1805.2.a.o.1.3		4	76.11	odd	6
9025.2.a.bg.1.2		4	380.239	odd	6
9025.2.a.bp.1.3		4	380.179	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.189667 + 0.328513i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.89307 q^{7} +(1.42805 + 2.47346i) q^{9} +O(q^{10})\)	\(q+(-0.189667 + 0.328513i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.89307 q^{7} +(1.42805 + 2.47346i) q^{9} -0.134400 q^{11} +(-1.75687 - 3.04298i) q^{13} +(-0.189667 - 0.328513i) q^{15} +(0.830615 - 1.43867i) q^{17} +(-2.10596 + 3.81640i) q^{19} +(0.359052 - 0.621897i) q^{21} +(2.68492 + 4.65042i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.22142 q^{27} +(-2.48530 - 4.30466i) q^{29} -6.56472 q^{31} +(0.0254912 - 0.0441521i) q^{33} +(0.946534 - 1.63944i) q^{35} -1.69819 q^{37} +1.33288 q^{39} +(-5.31637 + 9.20823i) q^{41} +(4.25392 - 7.36801i) q^{43} -2.85611 q^{45} +(-5.55771 - 9.62623i) q^{47} -3.41630 q^{49} +(0.315080 + 0.545735i) q^{51} +(0.132424 + 0.229365i) q^{53} +(0.0672000 - 0.116394i) q^{55} +(-0.854305 - 1.41568i) q^{57} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(-2.70340 - 4.68243i) q^{63} +3.51373 q^{65} +(-1.47677 - 2.55784i) q^{67} -2.03696 q^{69} +(0.664176 - 1.15039i) q^{71} +(3.17119 - 5.49266i) q^{73} +0.379334 q^{75} +0.254428 q^{77} +(-0.733639 + 1.27070i) q^{79} +(-3.86283 + 6.69062i) q^{81} -7.44736 q^{83} +(0.830615 + 1.43867i) q^{85} +1.88551 q^{87} +(-4.86804 - 8.43169i) q^{89} +(3.32587 + 5.76057i) q^{91} +(1.24511 - 2.15659i) q^{93} +(-2.25212 - 3.73202i) q^{95} +(-8.73447 + 15.1285i) q^{97} +(-0.191930 - 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9	\( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

Introduction

L-functions

Modular forms

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