LMFDB - Embedded newform 700.2.be.e.443.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(107,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("700.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			443.1
Character	$\chi$	$=$	700.443
Dual form			700.2.be.e.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41374 + 0.0366689i) q^{2} +(-0.402205 - 0.107770i) q^{3} +(1.99731 - 0.103680i) q^{4} +(0.572564 + 0.137611i) q^{6} +(-2.30240 - 1.30345i) q^{7} +(-2.81987 + 0.219816i) q^{8} +(-2.44792 - 1.41331i) q^{9} +O(q^{10})$	\(q+(-1.41374 + 0.0366689i) q^{2} +(-0.402205 - 0.107770i) q^{3} +(1.99731 - 0.103680i) q^{4} +(0.572564 + 0.137611i) q^{6} +(-2.30240 - 1.30345i) q^{7} +(-2.81987 + 0.219816i) q^{8} +(-2.44792 - 1.41331i) q^{9} +(-0.725638 + 0.418947i) q^{11} +(-0.814501 - 0.173550i) q^{12} +(1.16367 + 1.16367i) q^{13} +(3.30278 + 1.75831i) q^{14} +(3.97850 - 0.414164i) q^{16} +(4.94841 + 1.32592i) q^{17} +(3.51255 + 1.90829i) q^{18} +(-2.91741 + 5.05309i) q^{19} +(0.785561 + 0.772382i) q^{21} +(1.01050 - 0.618890i) q^{22} +(0.896861 + 3.34713i) q^{23} +(1.15786 + 0.215488i) q^{24} +(-1.68779 - 1.60245i) q^{26} +(1.71555 + 1.71555i) q^{27} +(-4.73374 - 2.36468i) q^{28} +5.00172i q^{29} +(7.03267 - 4.06031i) q^{31} +(-5.60937 + 0.731407i) q^{32} +(0.337005 - 0.0903002i) q^{33} +(-7.04437 - 1.69305i) q^{34} +(-5.03579 - 2.56901i) q^{36} +(0.190621 + 0.711408i) q^{37} +(3.93916 - 7.25073i) q^{38} +(-0.342623 - 0.593441i) q^{39} +0.0958388 q^{41} +(-1.13890 - 1.06314i) q^{42} +(4.87975 - 4.87975i) q^{43} +(-1.40589 + 0.912002i) q^{44} +(-1.39066 - 4.69908i) q^{46} +(-5.28468 + 1.41603i) q^{47} +(-1.64481 - 0.262186i) q^{48} +(3.60205 + 6.00210i) q^{49} +(-1.84738 - 1.06658i) q^{51} +(2.44486 + 2.20356i) q^{52} +(-3.43436 + 12.8172i) q^{53} +(-2.48825 - 2.36244i) q^{54} +(6.77898 + 3.16945i) q^{56} +(1.71797 - 1.71797i) q^{57} +(-0.183407 - 7.07112i) q^{58} +(4.46933 + 7.74111i) q^{59} +(0.919379 - 1.59241i) q^{61} +(-9.79346 + 5.99810i) q^{62} +(3.79391 + 6.44473i) q^{63} +(7.90336 - 1.23971i) q^{64} +(-0.473126 + 0.140018i) q^{66} +(0.138137 - 0.515535i) q^{67} +(10.0210 + 2.13522i) q^{68} -1.44289i q^{69} +13.6494i q^{71} +(7.21350 + 3.44726i) q^{72} +(-1.55074 + 5.78744i) q^{73} +(-0.295575 - 0.998755i) q^{74} +(-5.30306 + 10.3951i) q^{76} +(2.21678 - 0.0187518i) q^{77} +(0.506141 + 0.826407i) q^{78} +(5.30723 - 9.19239i) q^{79} +(3.73481 + 6.46888i) q^{81} +(-0.135491 + 0.00351430i) q^{82} +(-4.36830 + 4.36830i) q^{83} +(1.64909 + 1.46124i) q^{84} +(-6.71975 + 7.07762i) q^{86} +(0.539037 - 2.01171i) q^{87} +(1.95412 - 1.34088i) q^{88} +(-2.50474 - 1.44611i) q^{89} +(-1.16244 - 4.19600i) q^{91} +(2.13834 + 6.59227i) q^{92} +(-3.26615 + 0.875163i) q^{93} +(7.41923 - 2.19567i) q^{94} +(2.33494 + 0.310349i) q^{96} +(-4.24461 + 4.24461i) q^{97} +(-5.31245 - 8.35332i) q^{98} +2.36841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.41374	+	0.0366689i	−0.999664	+	0.0259288i
$2$	−1.41374	+	0.0366689i	−0.999664	+	0.0259288i
$3$	−0.402205	−	0.107770i	−0.232213	−	0.0622213i	0.140836	−	0.990033i	$-0.455021\pi$
$3$	−0.402205	−	0.107770i	−0.232213	−	0.0622213i	−0.373049	+	0.927812i	$0.621688\pi$
$4$	1.99731	−	0.103680i	0.998655	−	0.0518402i
$5$		0			0
$5$		0			0
$6$	0.572564	+	0.137611i	0.233748	+	0.0561793i
$7$	−2.30240	−	1.30345i	−0.870224	−	0.492657i
$7$	−2.30240	−	1.30345i	−0.870224	−	0.492657i
$8$	−2.81987	+	0.219816i	−0.996975	+	0.0777167i
$9$	−2.44792	−	1.41331i	−0.815974	−	0.471103i
$10$		0			0
$11$	−0.725638	+	0.418947i	−0.218788	+	0.126317i	−0.605389	−	0.795930i	$-0.706982\pi$
$11$	−0.725638	+	0.418947i	−0.218788	+	0.126317i	0.386601	+	0.922247i	$0.373649\pi$
$12$	−0.814501	−	0.173550i	−0.235126	−	0.0500996i
$13$	1.16367	+	1.16367i	0.322743	+	0.322743i	0.849819	−	0.527075i	$-0.176711\pi$
$13$	1.16367	+	1.16367i	0.322743	+	0.322743i	−0.527075	+	0.849819i	$0.676711\pi$
$14$	3.30278	+	1.75831i	0.882705	+	0.469927i
$15$		0			0
$16$	3.97850	−	0.414164i	0.994625	−	0.103541i
$17$	4.94841	+	1.32592i	1.20016	+	0.321583i	0.802896	−	0.596119i	$-0.203291\pi$
$17$	4.94841	+	1.32592i	1.20016	+	0.321583i	0.397269	+	0.917702i	$0.369958\pi$
$18$	3.51255	+	1.90829i	0.827915	+	0.449787i
$19$	−2.91741	+	5.05309i	−0.669299	+	1.15926i	0.308802	+	0.951126i	$0.400072\pi$
$19$	−2.91741	+	5.05309i	−0.669299	+	1.15926i	−0.978101	+	0.208133i	$0.933261\pi$
$20$		0			0
$21$	0.785561	+	0.772382i	0.171423	+	0.168548i
$22$	1.01050	−	0.618890i	0.215439	−	0.131948i
$23$	0.896861	+	3.34713i	0.187008	+	0.697925i	0.994192	+	0.107624i	$0.0343242\pi$
$23$	0.896861	+	3.34713i	0.187008	+	0.697925i	−0.807183	+	0.590301i	$0.799009\pi$
$24$	1.15786	+	0.215488i	0.236346	+	0.0439862i
$25$		0			0
$26$	−1.68779	−	1.60245i	−0.331003	−	0.314266i
$27$	1.71555	+	1.71555i	0.330159	+	0.330159i
$28$	−4.73374	−	2.36468i	−0.894593	−	0.446882i
$29$			5.00172i			0.928795i	0.885627	+	0.464398i	$0.153729\pi$
$29$			5.00172i			0.928795i	−0.885627	+	0.464398i	$0.846271\pi$
$30$		0			0
$31$	7.03267	−	4.06031i	1.26310	−	0.729254i	0.289430	−	0.957199i	$-0.406534\pi$
$31$	7.03267	−	4.06031i	1.26310	−	0.729254i	0.973674	+	0.227945i	$0.0732008\pi$
$32$	−5.60937	+	0.731407i	−0.991606	+	0.129296i
$33$	0.337005	−	0.0903002i	0.0586650	−	0.0157192i
$34$	−7.04437	−	1.69305i	−1.20810	−	0.290356i
$35$		0			0
$36$	−5.03579	−	2.56901i	−0.839299	−	0.428169i
$37$	0.190621	+	0.711408i	0.0313379	+	0.116955i	0.979823	−	0.199867i	$-0.0640510\pi$
$37$	0.190621	+	0.711408i	0.0313379	+	0.116955i	−0.948485	+	0.316822i	$0.897384\pi$
$38$	3.93916	−	7.25073i	0.639015	−	1.17622i
$39$	−0.342623	−	0.593441i	−0.0548637	−	0.0950266i
$40$		0			0
$41$	0.0958388			0.0149675			0.00748375	−	0.999972i	$-0.497618\pi$
$41$	0.0958388			0.0149675			0.00748375	+	0.999972i	$0.497618\pi$
$42$	−1.13890	−	1.06314i	−0.175736	−	0.164046i
$43$	4.87975	−	4.87975i	0.744155	−	0.744155i	−0.229220	−	0.973375i	$-0.573617\pi$
$43$	4.87975	−	4.87975i	0.744155	−	0.744155i	0.973375	+	0.229220i	$0.0736174\pi$
$44$	−1.40589	+	0.912002i	−0.211946	+	0.137490i
$45$		0			0
$46$	−1.39066	−	4.69908i	−0.205042	−	0.692841i
$47$	−5.28468	+	1.41603i	−0.770850	+	0.206549i	−0.622747	−	0.782423i	$-0.713983\pi$
$47$	−5.28468	+	1.41603i	−0.770850	+	0.206549i	−0.148103	+	0.988972i	$0.547317\pi$
$48$	−1.64481	−	0.262186i	−0.237407	−	0.0378433i
$49$	3.60205	+	6.00210i	0.514579	+	0.857443i
$50$		0			0
$51$	−1.84738	−	1.06658i	−0.258684	−	0.149352i
$52$	2.44486	+	2.20356i	0.339040	+	0.305578i
$53$	−3.43436	+	12.8172i	−0.471745	+	1.76058i	0.161752	+	0.986832i	$0.448286\pi$
$53$	−3.43436	+	12.8172i	−0.471745	+	1.76058i	−0.633497	+	0.773745i	$0.718381\pi$
$54$	−2.48825	−	2.36244i	−0.338608	−	0.321487i
$55$		0			0
$56$	6.77898	+	3.16945i	0.905879	+	0.423536i
$57$	1.71797	−	1.71797i	0.227550	−	0.227550i
$58$	−0.183407	−	7.07112i	−0.0240826	−	0.928483i
$59$	4.46933	+	7.74111i	0.581858	+	1.00781i	0.995259	+	0.0972582i	$0.0310073\pi$
$59$	4.46933	+	7.74111i	0.581858	+	1.00781i	−0.413402	+	0.910549i	$0.635659\pi$
$60$		0			0
$61$	0.919379	−	1.59241i	0.117714	−	0.203887i	−0.801147	−	0.598467i	$-0.795777\pi$
$61$	0.919379	−	1.59241i	0.117714	−	0.203887i	0.918862	+	0.394580i	$0.129110\pi$
$62$	−9.79346	+	5.99810i	−1.24377	+	0.761759i
$63$	3.79391	+	6.44473i	0.477988	+	0.811960i
$64$	7.90336	−	1.23971i	0.987920	−	0.154963i
$65$		0			0
$66$	−0.473126	+	0.140018i	−0.0582377	+	0.0172351i
$67$	0.138137	−	0.515535i	0.0168761	−	0.0629826i	−0.956974	−	0.290173i	$-0.906287\pi$
$67$	0.138137	−	0.515535i	0.0168761	−	0.0629826i	0.973850	+	0.227190i	$0.0729539\pi$
$68$	10.0210	+	2.13522i	1.21522	+	0.258934i
$69$		−	1.44289i		−	0.173703i
$70$		0			0
$71$			13.6494i			1.61989i	0.586505	+	0.809946i	$0.300503\pi$
$71$			13.6494i			1.61989i	−0.586505	+	0.809946i	$0.699497\pi$
$72$	7.21350	+	3.44726i	0.850119	+	0.406263i
$73$	−1.55074	+	5.78744i	−0.181500	+	0.677368i	0.813852	+	0.581072i	$0.197366\pi$
$73$	−1.55074	+	5.78744i	−0.181500	+	0.677368i	−0.995353	+	0.0962967i	$0.969300\pi$
$74$	−0.295575	−	0.998755i	−0.0343599	−	0.116103i
$75$		0			0
$76$	−5.30306	+	10.3951i	−0.608303	+	1.19240i
$77$	2.21678	−	0.0187518i	0.252626	−	0.00213696i
$78$	0.506141	+	0.826407i	0.0573091	+	0.0935721i
$79$	5.30723	−	9.19239i	0.597110	−	1.03422i	−0.396136	−	0.918192i	$-0.629649\pi$
$79$	5.30723	−	9.19239i	0.597110	−	1.03422i	0.993245	−	0.116033i	$-0.0370177\pi$
$80$		0			0
$81$	3.73481	+	6.46888i	0.414979	+	0.718764i
$82$	−0.135491	+	0.00351430i	−0.0149625	+	0.000388090i
$83$	−4.36830	+	4.36830i	−0.479483	+	0.479483i	−0.904966	−	0.425483i	$-0.860104\pi$
$83$	−4.36830	+	4.36830i	−0.479483	+	0.479483i	0.425483	+	0.904966i	$0.360104\pi$
$84$	1.64909	+	1.46124i	0.179931	+	0.159434i
$85$		0			0
$86$	−6.71975	+	7.07762i	−0.724610	+	0.763200i
$87$	0.539037	−	2.01171i	0.0577908	−	0.215678i
$88$	1.95412	−	1.34088i	0.208309	−	0.142939i
$89$	−2.50474	−	1.44611i	−0.265502	−	0.153288i	0.361340	−	0.932434i	$-0.382319\pi$
$89$	−2.50474	−	1.44611i	−0.265502	−	0.153288i	−0.626842	+	0.779147i	$0.715653\pi$
$90$		0			0
$91$	−1.16244	−	4.19600i	−0.121857	−	0.439860i
$92$	2.13834	+	6.59227i	0.222937	+	0.687292i
$93$	−3.26615	+	0.875163i	−0.338684	+	0.0907502i
$94$	7.41923	−	2.19567i	0.765235	−	0.226466i
$95$		0			0
$96$	2.33494	+	0.310349i	0.238309	+	0.0316749i
$97$	−4.24461	+	4.24461i	−0.430975	+	0.430975i	−0.888960	−	0.457985i	$-0.848571\pi$
$97$	−4.24461	+	4.24461i	−0.430975	+	0.430975i	0.457985	+	0.888960i	$0.348571\pi$
$98$	−5.31245	−	8.35332i	−0.536638	−	0.843812i
$99$	2.36841			0.238034
$100$		0			0
$101$	−0.859895	−	1.48938i	−0.0855628	−	0.148199i	0.820068	−	0.572266i	$-0.193935\pi$
$101$	−0.859895	−	1.48938i	−0.0855628	−	0.148199i	−0.905631	+	0.424067i	$0.860602\pi$
$102$	2.65082	+	1.44013i	0.262470	+	0.142594i
$103$	−4.06549	−	15.1726i	−0.400584	−	1.49500i	−0.812057	−	0.583579i	$-0.801652\pi$
$103$	−4.06549	−	15.1726i	−0.400584	−	1.49500i	0.411472	−	0.911422i	$-0.365015\pi$
$104$	−3.53719	−	3.02560i	−0.346850	−	0.296685i
$105$		0			0
$106$	4.38529	−	18.2461i	0.425937	−	1.77222i
$107$	13.4365	−	3.60029i	1.29895	−	0.348053i	0.457899	−	0.889004i	$-0.348602\pi$
$107$	13.4365	−	3.60029i	1.29895	−	0.348053i	0.841054	+	0.540951i	$0.181936\pi$
$108$	3.60437	+	3.24863i	0.346830	+	0.312599i
$109$	−9.23440	+	5.33148i	−0.884495	+	0.510664i	−0.872138	−	0.489260i	$-0.837267\pi$
$109$	−9.23440	+	5.33148i	−0.884495	+	0.510664i	−0.0123573	+	0.999924i	$0.503934\pi$
$110$		0			0
$111$		−	0.306675i		−	0.0291083i
$112$	−9.69992	−	4.23220i	−0.916557	−	0.399905i
$113$	5.62032	+	5.62032i	0.528715	+	0.528715i	0.920189	−	0.391474i	$-0.128035\pi$
$113$	5.62032	+	5.62032i	0.528715	+	0.528715i	−0.391474	+	0.920189i	$0.628035\pi$
$114$	−2.36576	+	2.49175i	−0.221574	+	0.233374i
$115$		0			0
$116$	0.518580	+	9.98998i	0.0481490	+	0.927547i
$117$	−1.20395	−	4.49319i	−0.111305	−	0.415395i
$118$	−6.60233	−	10.7800i	−0.607793	−	0.992381i
$119$	−9.66492	−	9.50278i	−0.885982	−	0.871119i
$120$		0			0
$121$	−5.14897	+	8.91827i	−0.468088	+	0.810752i
$122$	−1.24137	+	2.28496i	−0.112388	+	0.206871i
$123$	−0.0385468	−	0.0103286i	−0.00347565	−	0.000931297i
$124$	13.6254	−	8.83886i	1.22360	−	0.793753i
$125$		0			0
$126$	−5.59992	−	8.97205i	−0.498881	−	0.799293i
$127$	4.54633	+	4.54633i	0.403421	+	0.403421i	0.879437	−	0.476016i	$-0.157919\pi$
$127$	4.54633	+	4.54633i	0.403421	+	0.403421i	−0.476016	+	0.879437i	$0.657919\pi$
$128$	−11.1278	+	2.04243i	−0.983570	+	0.180527i
$129$	−2.48855	+	1.43677i	−0.219105	+	0.126500i
$130$		0			0
$131$	−11.9545	−	6.90194i	−1.04447	−	0.603025i	−0.123374	−	0.992360i	$-0.539371\pi$
$131$	−11.9545	−	6.90194i	−1.04447	−	0.603025i	−0.921096	+	0.389335i	$0.872705\pi$
$132$	0.663741	−	0.215298i	0.0577713	−	0.0187393i
$133$	13.3035	−	7.83154i	1.15356	−	0.679081i
$134$	−0.176386	+	0.733896i	−0.0152374	+	0.0633990i
$135$		0			0
$136$	−14.2453	−	2.65119i	−1.22153	−	0.227338i
$137$	13.8922	+	3.72240i	1.18689	+	0.318026i	0.797656	−	0.603112i	$-0.206073\pi$
$137$	13.8922	+	3.72240i	1.18689	+	0.318026i	0.389235	+	0.921139i	$0.372740\pi$
$138$	0.0529090	+	2.03986i	0.00450391	+	0.173645i
$139$	−1.45615			−0.123509			−0.0617544	−	0.998091i	$-0.519670\pi$
$139$	−1.45615			−0.123509			−0.0617544	+	0.998091i	$0.519670\pi$
$140$		0			0
$141$	2.27813			0.191853
$142$	−0.500510	−	19.2967i	−0.0420019	−	1.61935i
$143$	−1.33192	−	0.356886i	−0.111380	−	0.0298443i
$144$	−10.3244	−	4.60901i	−0.860367	−	0.384084i
$145$		0			0
$146$	1.98012	−	8.23879i	0.163876	−	0.681847i
$147$	−0.801913	−	2.80227i	−0.0661407	−	0.231127i
$148$	0.454489	+	1.40114i	0.0373588	+	0.115173i
$149$	−10.0147	−	5.78197i	−0.820433	−	0.473677i	0.0301327	−	0.999546i	$-0.490407\pi$
$149$	−10.0147	−	5.78197i	−0.820433	−	0.473677i	−0.850566	+	0.525869i	$0.823740\pi$
$150$		0			0
$151$	−4.17078	+	2.40800i	−0.339414	+	0.195961i	−0.660013	−	0.751254i	$-0.729449\pi$
$151$	−4.17078	+	2.40800i	−0.339414	+	0.195961i	0.320599	+	0.947215i	$0.396116\pi$
$152$	7.11596	−	14.8904i	0.577181	−	1.20777i
$153$	−10.2394	−	10.2394i	−0.827805	−	0.827805i
$154$	−3.13326	+	0.107797i	−0.252485	+	0.00868653i
$155$		0			0
$156$	−0.745854	−	1.14976i	−0.0597161	−	0.0920547i
$157$	−4.12149	−	1.10435i	−0.328931	−	0.0881368i	0.0905743	−	0.995890i	$-0.471130\pi$
$157$	−4.12149	−	1.10435i	−0.328931	−	0.0881368i	−0.419505	+	0.907753i	$0.637796\pi$
$158$	−7.16596	+	13.1902i	−0.570093	+	1.04936i
$159$	2.76263	−	4.78501i	0.219091	−	0.379476i
$160$		0			0
$161$	2.29788	−	8.87543i	0.181098	−	0.699482i
$162$	−5.51725	−	9.00835i	−0.433476	−	0.707763i
$163$	2.10452	+	7.85417i	0.164839	+	0.615186i	0.998061	+	0.0622476i	$0.0198268\pi$
$163$	2.10452	+	7.85417i	0.164839	+	0.615186i	−0.833222	+	0.552938i	$0.813506\pi$
$164$	0.191420	−	0.00993661i	0.0149474	−	0.000775919i
$165$		0			0
$166$	6.01545	−	6.33581i	0.466889	−	0.491754i
$167$	−5.50649	−	5.50649i	−0.426105	−	0.426105i	0.461194	−	0.887299i	$-0.347421\pi$
$167$	−5.50649	−	5.50649i	−0.426105	−	0.426105i	−0.887299	+	0.461194i	$0.847421\pi$
$168$	−2.38496	−	2.00534i	−0.184004	−	0.154715i
$169$		−	10.2918i		−	0.791674i
$170$		0			0
$171$	14.2832	−	8.24639i	1.09226	−	0.630617i
$172$	9.24044	−	10.2523i	0.704577	−	0.781731i
$173$	−3.02430	+	0.810358i	−0.229933	+	0.0616104i	−0.371946	−	0.928254i	$-0.621309\pi$
$173$	−3.02430	+	0.810358i	−0.229933	+	0.0616104i	0.142013	+	0.989865i	$0.454643\pi$
$174$	−0.688290	+	2.86380i	−0.0521791	+	0.217104i
$175$		0			0
$176$	−2.71344	+	1.96732i	−0.204533	+	0.148292i
$177$	−0.963323	−	3.59517i	−0.0724078	−	0.270230i
$178$	3.59408	+	1.95258i	0.269387	+	0.146352i
$179$	8.05255	+	13.9474i	0.601876	+	1.04248i	0.992537	+	0.121945i	$0.0389131\pi$
$179$	8.05255	+	13.9474i	0.601876	+	1.04248i	−0.390661	+	0.920535i	$0.627754\pi$
$180$		0			0
$181$	−3.83256			−0.284872			−0.142436	−	0.989804i	$-0.545493\pi$
$181$	−3.83256			−0.284872			−0.142436	+	0.989804i	$0.545493\pi$
$182$	1.79725	+	5.88942i	0.133221	+	0.436553i
$183$	−0.541393	+	0.541393i	−0.0400209	+	0.0400209i
$184$	−3.26479	−	9.24133i	−0.240683	−	0.681280i
$185$		0			0
$186$	4.58539	−	1.35702i	0.336217	−	0.0995013i
$187$	−4.14624	+	1.11098i	−0.303203	+	0.0812431i
$188$	−10.4083	+	3.37616i	−0.759106	+	0.246232i
$189$	−1.71375	−	6.18602i	−0.124657	−	0.449967i
$190$		0			0
$191$	−2.42531	−	1.40025i	−0.175489	−	0.101319i	0.409682	−	0.912228i	$-0.365640\pi$
$191$	−2.42531	−	1.40025i	−0.175489	−	0.101319i	−0.585172	+	0.810909i	$0.698973\pi$
$192$	−3.31237	−	0.353133i	−0.239050	−	0.0254851i
$193$	2.23839	−	8.35378i	0.161123	−	0.601318i	−0.837380	−	0.546621i	$-0.815914\pi$
$193$	2.23839	−	8.35378i	0.161123	−	0.601318i	0.998503	−	0.0546973i	$-0.0174194\pi$
$194$	5.84513	−	6.15642i	0.419656	−	0.442005i
$195$		0			0
$196$	7.81672	+	11.6146i	0.558337	+	0.829614i
$197$	4.90073	−	4.90073i	0.349162	−	0.349162i	−0.510635	−	0.859798i	$-0.670590\pi$
$197$	4.90073	−	4.90073i	0.349162	−	0.349162i	0.859798	+	0.510635i	$0.170590\pi$
$198$	−3.34831	+	0.0868469i	−0.237954	+	0.00617194i
$199$	−6.19859	−	10.7363i	−0.439406	−	0.761074i	0.558237	−	0.829681i	$-0.311478\pi$
$199$	−6.19859	−	10.7363i	−0.439406	−	0.761074i	−0.997644	+	0.0686071i	$0.978145\pi$
$200$		0			0
$201$	−0.111119	+	0.192463i	−0.00783771	+	0.0135753i
$202$	1.27028	+	2.07406i	0.0893766	+	0.145931i
$203$	6.51947	−	11.5159i	0.457577	−	0.808260i
$204$	−3.80037	−	1.93876i	−0.266079	−	0.135740i
$205$		0			0
$206$	6.30389	+	21.3010i	0.439213	+	1.48411i
$207$	2.53508	−	9.46105i	0.176200	−	0.657589i
$208$	5.11160	+	4.14770i	0.354426	+	0.287591i
$209$		−	4.88896i		−	0.338176i
$210$		0			0
$211$		−	0.877438i		−	0.0604053i	−0.999544	−	0.0302027i	$-0.990385\pi$
$211$		−	0.877438i		−	0.0604053i	0.999544	−	0.0302027i	$-0.00961527\pi$
$212$	−5.53059	+	25.9560i	−0.379842	+	1.78267i
$213$	1.47101	−	5.48987i	0.100792	−	0.376160i
$214$	−18.8636	+	5.58257i	−1.28949	+	0.381617i
$215$		0			0
$216$	−5.21475	−	4.46054i	−0.354819	−	0.303501i
$217$	−21.4844	+	0.181737i	−1.45846	+	0.0123371i
$218$	12.8595	−	7.87594i	0.870957	−	0.533426i
$219$	1.24743	−	2.16061i	0.0842934	−	0.146000i
$220$		0			0
$221$	4.21537	+	7.30123i	0.283556	+	0.491134i
$222$	0.0112454	+	0.433558i	0.000754744	+	0.0290985i
$223$	−12.6059	+	12.6059i	−0.844153	+	0.844153i	−0.989396	−	0.145243i	$-0.953604\pi$
$223$	−12.6059	+	12.6059i	−0.844153	+	0.844153i	0.145243	+	0.989396i	$0.453604\pi$
$224$	13.8683	+	5.62753i	0.926618	+	0.376005i
$225$		0			0
$226$	−8.15175	−	7.73957i	−0.542246	−	0.514828i
$227$	−2.71787	+	10.1432i	−0.180392	+	0.673230i	0.815179	+	0.579210i	$0.196639\pi$
$227$	−2.71787	+	10.1432i	−0.180392	+	0.673230i	−0.995570	+	0.0940208i	$0.970028\pi$
$228$	3.25320	−	3.60943i	0.215448	−	0.239041i
$229$	23.5981	+	13.6244i	1.55941	+	0.900324i	0.997314	+	0.0732513i	$0.0233375\pi$
$229$	23.5981	+	13.6244i	1.55941	+	0.900324i	0.562094	+	0.827073i	$0.309996\pi$
$230$		0			0
$231$	−0.893620	−	0.231361i	−0.0587959	−	0.0152225i
$232$	−1.09946	−	14.1042i	−0.0721830	−	0.925986i
$233$	−12.6865	+	3.39933i	−0.831118	+	0.222697i	−0.649201	−	0.760617i	$-0.724897\pi$
$233$	−12.6865	+	3.39933i	−0.831118	+	0.222697i	−0.181917	+	0.983314i	$0.558230\pi$
$234$	1.86682	+	6.30804i	0.122038	+	0.412370i
$235$		0			0
$236$	9.72925	+	14.9980i	0.633320	+	0.976288i
$237$	−3.12526	+	3.12526i	−0.203007	+	0.203007i
$238$	14.0121	+	13.0800i	0.908271	+	0.847853i
$239$	10.7078			0.692631			0.346315	−	0.938118i	$-0.387433\pi$
$239$	10.7078			0.692631			0.346315	+	0.938118i	$0.387433\pi$
$240$		0			0
$241$	−6.28701	−	10.8894i	−0.404982	−	0.701449i	0.589337	−	0.807887i	$-0.299389\pi$
$241$	−6.28701	−	10.8894i	−0.404982	−	0.701449i	−0.994319	+	0.106438i	$0.966056\pi$
$242$	6.95227	−	12.7969i	0.446909	−	0.822616i
$243$	−2.68881	−	10.0348i	−0.172487	−	0.643732i
$244$	1.67118	−	3.27586i	0.106987	−	0.209716i
$245$		0			0
$246$	0.0548738	+	0.0131884i	0.00349863	+	0.000840864i
$247$	−9.27501	+	2.48523i	−0.590155	+	0.158132i
$248$	−18.9387	+	12.9955i	−1.20261	+	0.825212i
$249$	2.22772	−	1.28618i	0.141176	−	0.0815080i
$250$		0			0
$251$			14.8357i			0.936420i	0.883617	+	0.468210i	$0.155101\pi$
$251$			14.8357i			0.936420i	−0.883617	+	0.468210i	$0.844899\pi$
$252$	8.24582	+	12.4788i	0.519438	+	0.786089i
$253$	−2.05307	−	2.05307i	−0.129075	−	0.129075i
$254$	−6.59403	−	6.26061i	−0.413746	−	0.392826i
$255$		0			0
$256$	15.6569	−	3.29550i	0.978559	−	0.205969i
$257$	−3.93031	−	14.6681i	−0.245166	−	0.914972i	−0.973300	−	0.229537i	$-0.926279\pi$
$257$	−3.93031	−	14.6681i	−0.245166	−	0.914972i	0.728134	−	0.685435i	$-0.240388\pi$
$258$	3.46547	−	2.12246i	0.215751	−	0.132139i
$259$	0.488397	−	1.88641i	0.0303475	−	0.117216i
$260$		0			0
$261$	7.06897	−	12.2438i	0.437558	−	0.757873i
$262$	17.1536	+	9.31917i	1.05975	+	0.575740i
$263$	−11.3208	−	3.03340i	−0.698072	−	0.187048i	−0.107705	−	0.994183i	$-0.534350\pi$
$263$	−11.3208	−	3.03340i	−0.698072	−	0.187048i	−0.590367	+	0.807135i	$0.701017\pi$
$264$	−0.930462	+	0.328714i	−0.0572659	+	0.0202310i
$265$		0			0
$266$	−18.5204	+	11.5596i	−1.13556	+	0.708763i
$267$	0.851570	+	0.851570i	0.0521153	+	0.0521153i
$268$	0.222452	−	1.04400i	0.0135884	−	0.0637727i
$269$	17.9195	−	10.3458i	1.09257	−	0.630797i	0.158313	−	0.987389i	$-0.449395\pi$
$269$	17.9195	−	10.3458i	1.09257	−	0.630797i	0.934260	+	0.356592i	$0.116061\pi$
$270$		0			0
$271$	−18.2735	−	10.5502i	−1.11003	−	0.640878i	−0.171195	−	0.985237i	$-0.554763\pi$
$271$	−18.2735	−	10.5502i	−1.11003	−	0.640878i	−0.938838	+	0.344359i	$0.888096\pi$
$272$	20.2364	+	3.22573i	1.22701	+	0.195588i
$273$	0.0153356	+	1.81293i	0.000928151	+	0.109723i
$274$	−19.7764	−	4.75309i	−1.19474	−	0.287145i
$275$		0			0
$276$	−0.149599	−	2.88189i	−0.00900480	−	0.173469i
$277$	−3.15920	−	0.846505i	−0.189818	−	0.0508616i	0.162658	−	0.986683i	$-0.447993\pi$
$277$	−3.15920	−	0.846505i	−0.189818	−	0.0508616i	−0.352476	+	0.935821i	$0.614660\pi$
$278$	2.05861	−	0.0533953i	0.123467	−	0.00320244i
$279$	−22.9539			−1.37421
$280$		0			0
$281$	2.60091			0.155157			0.0775787	−	0.996986i	$-0.475281\pi$
$281$	2.60091			0.155157			0.0775787	+	0.996986i	$0.475281\pi$
$282$	−3.22068	+	0.0835364i	−0.191788	+	0.00497452i
$283$	26.7711	+	7.17330i	1.59138	+	0.426409i	0.942424	−	0.334419i	$-0.108540\pi$
$283$	26.7711	+	7.17330i	1.59138	+	0.426409i	0.648954	+	0.760828i	$0.275207\pi$
$284$	1.41518	+	27.2622i	0.0839755	+	1.61771i
$285$		0			0
$286$	1.89607	+	0.455703i	0.112117	+	0.0269463i
$287$	−0.220659	−	0.124921i	−0.0130251	−	0.00737384i
$288$	14.7650	+	6.13735i	0.870036	+	0.361647i
$289$	8.00623	+	4.62240i	0.470955	+	0.271906i
$290$		0			0
$291$	2.16465	−	1.24976i	0.126894	−	0.0732622i
$292$	−2.49726	+	11.7201i	−0.146141	+	0.685867i
$293$	−11.9223	−	11.9223i	−0.696506	−	0.696506i	0.267149	−	0.963655i	$-0.413918\pi$
$293$	−11.9223	−	11.9223i	−0.696506	−	0.696506i	−0.963655	+	0.267149i	$0.913918\pi$
$294$	1.23645	+	3.93227i	0.0721113	+	0.229334i
$295$		0			0
$296$	−0.693906	−	1.96418i	−0.0403325	−	0.114166i
$297$	−1.96360	−	0.526145i	−0.113940	−	0.0305300i
$298$	14.3701	+	7.80696i	0.832439	+	0.452245i
$299$	−2.85130	+	4.93859i	−0.164895	+	0.285606i
$300$		0			0
$301$	−17.5956	+	4.87462i	−1.01419	+	0.280968i
$302$	5.80810	−	3.55722i	0.334218	−	0.204695i
$303$	0.185342	+	0.691707i	0.0106476	+	0.0397376i
$304$	−9.51409	+	21.3120i	−0.545670	+	1.22233i
$305$		0			0
$306$	14.8513	+	14.1003i	0.848990	+	0.806062i
$307$	13.0364	+	13.0364i	0.744028	+	0.744028i	0.973350	−	0.229323i	$-0.0736511\pi$
$307$	13.0364	+	13.0364i	0.744028	+	0.744028i	−0.229323	+	0.973350i	$0.573651\pi$
$308$	4.42566	−	0.267290i	0.252175	−	0.0152303i
$309$			6.54063i			0.372083i
$310$		0			0
$311$	−10.1447	+	5.85707i	−0.575255	+	0.332124i	−0.759246	−	0.650804i	$-0.774432\pi$
$311$	−10.1447	+	5.85707i	−0.575255	+	0.332124i	0.183990	+	0.982928i	$0.441099\pi$
$312$	1.09660	+	1.59811i	0.0620829	+	0.0904754i
$313$	18.4473	−	4.94295i	1.04270	−	0.279392i	0.303471	−	0.952841i	$-0.401855\pi$
$313$	18.4473	−	4.94295i	1.04270	−	0.279392i	0.739234	+	0.673449i	$0.235188\pi$
$314$	5.86721	+	1.41013i	0.331106	+	0.0795783i
$315$		0			0
$316$	9.64711	−	18.9103i	0.542693	−	1.06379i
$317$	0.747448	+	2.78952i	0.0419809	+	0.156675i	0.983734	−	0.179629i	$-0.0574898\pi$
$317$	0.747448	+	2.78952i	0.0419809	+	0.156675i	−0.941754	+	0.336304i	$0.890823\pi$
$318$	−3.73017	+	6.86605i	−0.209178	+	0.385029i
$319$	−2.09546	−	3.62944i	−0.117323	−	0.203209i
$320$		0			0
$321$	−5.79221			−0.323290
$322$	−2.92315	+	12.6318i	−0.162901	+	0.703942i
$323$	−21.1365	+	21.1365i	−1.17607	+	1.17607i
$324$	8.13027	+	12.5331i	0.451682	+	0.696285i
$325$		0			0
$326$	−3.26324	−	11.0266i	−0.180734	−	0.610705i
$327$	4.28869	−	1.14915i	0.237165	−	0.0635482i
$328$	−0.270253	+	0.0210669i	−0.0149222	+	0.00116323i
$329$	14.0131	+	3.62805i	0.772569	+	0.200021i
$330$		0			0
$331$	30.1984	+	17.4351i	1.65986	+	0.958318i	0.972780	+	0.231732i	$0.0744391\pi$
$331$	30.1984	+	17.4351i	1.65986	+	0.958318i	0.687075	+	0.726586i	$0.258894\pi$
$332$	−8.27194	+	9.17775i	−0.453982	+	0.503694i
$333$	0.538813	−	2.01088i	0.0295268	−	0.110195i
$334$	7.98665	+	7.58282i	0.437010	+	0.414913i
$335$		0			0
$336$	3.44525	+	2.74757i	0.187954	+	0.149892i
$337$	−15.8847	+	15.8847i	−0.865292	+	0.865292i	−0.991947	−	0.126655i	$-0.959576\pi$
$337$	−15.8847	+	15.8847i	−0.865292	+	0.865292i	0.126655	+	0.991947i	$0.459576\pi$
$338$	0.377387	+	14.5498i	0.0205272	+	0.791407i
$339$	−1.65481	−	2.86622i	−0.0898771	−	0.155672i
$340$		0			0
$341$	−3.40211	+	5.89263i	−0.184235	+	0.319104i
$342$	−19.8903	+	12.1820i	−1.07554	+	0.658726i
$343$	−0.469928	−	18.5143i	−0.0253737	−	0.999678i
$344$	−12.6876	+	14.8329i	−0.684071	+	0.799738i
$345$		0			0
$346$	4.24585	−	1.25653i	0.228258	−	0.0675516i
$347$	−6.21524	+	23.1956i	−0.333651	+	1.24520i	0.571673	+	0.820482i	$0.306295\pi$
$347$	−6.21524	+	23.1956i	−0.333651	+	1.24520i	−0.905324	+	0.424722i	$0.860372\pi$
$348$	0.868049	−	4.07390i	0.0465323	−	0.218384i
$349$		−	20.0084i		−	1.07102i	−0.844528	−	0.535512i	$-0.820119\pi$
$349$		−	20.0084i		−	1.07102i	0.844528	−	0.535512i	$-0.179881\pi$
$350$		0			0
$351$			3.99267i			0.213113i
$352$	3.76395	−	2.88077i	0.200619	−	0.153545i
$353$	6.06381	−	22.6305i	0.322744	−	1.20450i	−0.593816	−	0.804601i	$-0.702379\pi$
$353$	6.06381	−	22.6305i	0.322744	−	1.20450i	0.916560	−	0.399897i	$-0.130954\pi$
$354$	1.49372	+	5.04731i	0.0793902	+	0.268261i
$355$		0			0
$356$	−5.15268	−	2.62865i	−0.273092	−	0.139318i
$357$	2.86316	+	4.86365i	0.151534	+	0.257412i
$358$	−11.8956	−	19.4227i	−0.628704	−	1.02652i
$359$	−13.4523	+	23.3000i	−0.709984	+	1.22973i	0.254878	+	0.966973i	$0.417965\pi$
$359$	−13.4523	+	23.3000i	−0.709984	+	1.22973i	−0.964862	+	0.262756i	$0.915369\pi$
$360$		0			0
$361$	−7.52251	−	13.0294i	−0.395922	−	0.685756i
$362$	5.41824	−	0.140536i	0.284776	−	0.00738639i
$363$	3.03206	−	3.03206i	0.159142	−	0.159142i
$364$	−2.75681	−	8.26020i	−0.144496	−	0.432952i
$365$		0			0
$366$	0.745536	−	0.785240i	0.0389698	−	0.0410452i
$367$	7.09214	−	26.4682i	0.370207	−	1.38163i	−0.490017	−	0.871713i	$-0.663009\pi$
$367$	7.09214	−	26.4682i	0.370207	−	1.38163i	0.860223	−	0.509917i	$-0.170324\pi$
$368$	4.95442	+	12.9451i	0.258267	+	0.674811i
$369$	−0.234606	−	0.135450i	−0.0122131	−	0.00705123i
$370$		0			0
$371$	24.6138	−	25.0337i	1.27788	−	1.29969i
$372$	−6.43278	+	2.08661i	−0.333524	+	0.108186i
$373$	21.1806	−	5.67531i	1.09669	−	0.293857i	0.335272	−	0.942121i	$-0.391172\pi$
$373$	21.1806	−	5.67531i	1.09669	−	0.293857i	0.761415	+	0.648265i	$0.224505\pi$
$374$	5.82096	−	1.72268i	0.300995	−	0.0890775i
$375$		0			0
$376$	14.5909	−	5.15467i	0.752466	−	0.265832i
$377$	−5.82033	+	5.82033i	−0.299762	+	0.299762i
$378$	2.64963	+	8.68257i	0.136282	+	0.446583i
$379$	20.4602			1.05097			0.525484	−	0.850803i	$-0.323884\pi$
$379$	20.4602			1.05097			0.525484	+	0.850803i	$0.323884\pi$
$380$		0			0
$381$	−1.33859	−	2.31851i	−0.0685783	−	0.118781i
$382$	3.48010	+	1.89066i	0.178057	+	0.0967345i
$383$	−1.88076	−	7.01910i	−0.0961024	−	0.358659i	0.901082	−	0.433649i	$-0.142774\pi$
$383$	−1.88076	−	7.01910i	−0.0961024	−	0.358659i	−0.997184	+	0.0749899i	$0.976108\pi$
$384$	4.69577	+	0.377776i	0.239630	+	0.0192783i
$385$		0			0
$386$	−2.85817	+	11.8921i	−0.145477	+	0.605294i
$387$	−18.8418	+	5.04866i	−0.957785	+	0.256638i
$388$	−8.03773	+	8.91790i	−0.408054	+	0.452738i
$389$	4.81003	−	2.77707i	0.243878	−	0.140803i	−0.373080	−	0.927799i	$-0.621698\pi$
$389$	4.81003	−	2.77707i	0.243878	−	0.140803i	0.616958	+	0.786996i	$0.288365\pi$
$390$		0			0
$391$			17.7521i			0.897764i
$392$	−11.4767	−	16.1334i	−0.579660	−	0.814858i
$393$	4.06433	+	4.06433i	0.205018	+	0.205018i
$394$	−6.74864	+	7.10805i	−0.339992	+	0.358098i
$395$		0			0
$396$	4.73044	−	0.245557i	0.237714	−	0.0123397i
$397$	7.78865	+	29.0677i	0.390901	+	1.45886i	0.828650	+	0.559766i	$0.189109\pi$
$397$	7.78865	+	29.0677i	0.390901	+	1.45886i	−0.437749	+	0.899097i	$0.644224\pi$
$398$	9.15687	+	14.9510i	0.458992	+	0.749425i
$399$	−6.19472	+	1.71616i	−0.310124	+	0.0859155i
$400$		0			0
$401$	2.31962	−	4.01770i	0.115836	−	0.200634i	−0.802277	−	0.596951i	$-0.796379\pi$
$401$	2.31962	−	4.01770i	0.115836	−	0.200634i	0.918114	+	0.396317i	$0.129712\pi$
$402$	0.150035	−	0.276167i	0.00748308	−	0.0137740i
$403$	12.9085	+	3.45883i	0.643020	+	0.172297i
$404$	−1.87190	−	2.88560i	−0.0931304	−	0.143564i
$405$		0			0
$406$	−8.79455	+	16.5196i	−0.436466	+	0.819853i
$407$	−0.436364	−	0.436364i	−0.0216298	−	0.0216298i
$408$	5.44382	+	2.60155i	0.269509	+	0.128796i
$409$	−30.0868	+	17.3706i	−1.48770	+	0.858922i	−0.999901	−	0.0140366i	$-0.995532\pi$
$409$	−30.0868	+	17.3706i	−1.48770	+	0.858922i	−0.487795	+	0.872958i	$0.662199\pi$
$410$		0			0
$411$	−5.18634	−	2.99434i	−0.255823	−	0.147700i
$412$	−9.69314	−	29.8829i	−0.477547	−	1.47222i
$413$	−0.200044	−	23.6486i	−0.00984353	−	1.16367i
$414$	−3.23702	+	13.4684i	−0.159091	+	0.661936i
$415$		0			0
$416$	−7.37856	−	5.67633i	−0.361764	−	0.278305i
$417$	0.585669	+	0.156930i	0.0286803	+	0.00768487i
$418$	0.179273	+	6.91170i	0.00876851	+	0.338062i
$419$	28.1311			1.37429			0.687147	−	0.726518i	$-0.258863\pi$
$419$	28.1311			1.37429			0.687147	+	0.726518i	$0.258863\pi$
$420$		0			0
$421$	3.94616			0.192324			0.0961621	−	0.995366i	$-0.469343\pi$
$421$	3.94616			0.192324			0.0961621	+	0.995366i	$0.469343\pi$
$422$	0.0321747	+	1.24047i	0.00156624	+	0.0603850i
$423$	14.9378	+	4.00256i	0.726299	+	0.194611i
$424$	6.86702	−	36.8978i	0.333492	−	1.79191i
$425$		0			0
$426$	−1.87831	+	7.81518i	−0.0910044	+	0.378647i
$427$	−4.19240	+	2.46800i	−0.202884	+	0.119435i
$428$	26.4635	−	8.58400i	1.27916	−	0.414923i
$429$	0.497241	+	0.287082i	0.0240070	+	0.0138605i
$430$		0			0
$431$	−12.1350	+	7.00616i	−0.584523	+	0.337475i	−0.762929	−	0.646482i	$-0.776239\pi$
$431$	−12.1350	+	7.00616i	−0.584523	+	0.337475i	0.178406	+	0.983957i	$0.442906\pi$
$432$	7.53586	+	6.11482i	0.362569	+	0.294199i
$433$	2.21951	+	2.21951i	0.106663	+	0.106663i	0.758424	−	0.651761i	$-0.225970\pi$
$433$	2.21951	+	2.21951i	0.106663	+	0.106663i	−0.651761	+	0.758424i	$0.725970\pi$
$434$	30.3666	−	1.04474i	1.45764	−	0.0501490i
$435$		0			0
$436$	−17.8912	+	11.6061i	−0.856833	+	0.555829i
$437$	−19.5299	−	5.23301i	−0.934240	−	0.250329i
$438$	−1.68431	+	3.10028i	−0.0804795	+	0.148137i
$439$	−12.5163	+	21.6788i	−0.597369	+	1.03467i	0.395839	+	0.918320i	$0.370454\pi$
$439$	−12.5163	+	21.6788i	−0.597369	+	1.03467i	−0.993208	+	0.116354i	$0.962879\pi$
$440$		0			0
$441$	−0.334721	−	19.7835i	−0.0159391	−	0.942071i
$442$	−6.22715	−	10.1675i	−0.296196	−	0.483617i
$443$	−1.13949	−	4.25262i	−0.0541386	−	0.202048i	0.933559	−	0.358424i	$-0.116686\pi$
$443$	−1.13949	−	4.25262i	−0.0541386	−	0.202048i	−0.987698	+	0.156376i	$0.950019\pi$
$444$	−0.0317962	−	0.612525i	−0.00150898	−	0.0290691i
$445$		0			0
$446$	17.3592	−	18.2837i	0.821982	−	0.865758i
$447$	3.40482	+	3.40482i	0.161042	+	0.161042i
$448$	−19.8126	−	7.44732i	−0.936055	−	0.351853i
$449$		−	24.2255i		−	1.14327i	−0.820507	−	0.571636i	$-0.806309\pi$
$449$		−	24.2255i		−	1.14327i	0.820507	−	0.571636i	$-0.193691\pi$
$450$		0			0
$451$	−0.0695443	+	0.0401514i	−0.00327471	+	0.00189066i
$452$	11.8082	+	10.6428i	0.555413	+	0.500595i
$453$	1.93702	−	0.519023i	0.0910091	−	0.0243858i
$454$	3.47042	−	14.4395i	0.162875	−	0.677681i
$455$		0			0
$456$	−4.46681	+	5.22209i	−0.209178	+	0.244547i
$457$	2.42378	+	9.04568i	0.113380	+	0.423139i	0.999161	−	0.0409647i	$-0.0130431\pi$
$457$	2.42378	+	9.04568i	0.113380	+	0.423139i	−0.885781	+	0.464104i	$0.846376\pi$
$458$	−33.8612	−	18.3960i	−1.58223	−	0.859588i
$459$	6.21457	+	10.7640i	0.290071	+	0.502418i
$460$		0			0
$461$	12.3582			0.575580			0.287790	−	0.957693i	$-0.407079\pi$
$461$	12.3582			0.575580			0.287790	+	0.957693i	$0.407079\pi$
$462$	1.27183	+	0.294316i	0.0591708	+	0.0136928i
$463$	−29.6788	+	29.6788i	−1.37929	+	1.37929i	−0.533471	+	0.845818i	$0.679113\pi$
$463$	−29.6788	+	29.6788i	−1.37929	+	1.37929i	−0.845818	+	0.533471i	$0.820887\pi$
$464$	2.07153	+	19.8993i	0.0961684	+	0.923803i
$465$		0			0
$466$	17.8107	−	5.27096i	0.825064	−	0.244172i
$467$	−34.9600	+	9.36749i	−1.61775	+	0.433476i	−0.950341	−	0.311212i	$-0.899265\pi$
$467$	−34.9600	+	9.36749i	−1.61775	+	0.433476i	−0.667413	+	0.744687i	$0.732599\pi$
$468$	−2.87051	−	8.84947i	−0.132689	−	0.409067i
$469$	−0.990018	+	1.00691i	−0.0457148	+	0.0464948i
$470$		0			0
$471$	1.53867	+	0.888349i	0.0708980	+	0.0409330i
$472$	−14.3046	−	20.8465i	−0.658421	−	0.959539i
$473$	−1.49657	+	5.58529i	−0.0688125	+	0.256812i
$474$	4.30370	−	4.53290i	0.197675	−	0.208203i
$475$		0			0
$476$	−20.2891	−	17.9779i	−0.929950	−	0.824018i
$477$	26.5217	−	26.5217i	1.21434	−	1.21434i
$478$	−15.1380	+	0.392644i	−0.692398	+	0.0179591i
$479$	−15.9325	−	27.5959i	−0.727974	−	1.26089i	−0.957738	−	0.287642i	$-0.907129\pi$
$479$	−15.9325	−	27.5959i	−0.727974	−	1.26089i	0.229764	−	0.973246i	$-0.426205\pi$
$480$		0			0
$481$	−0.606023	+	1.04966i	−0.0276323	+	0.0478605i
$482$	9.28749	+	15.1643i	0.423034	+	0.690713i
$483$	−1.88072	+	3.32209i	−0.0855759	+	0.151160i
$484$	−9.35944	+	18.3464i	−0.425429	+	0.833928i
$485$		0			0
$486$	4.16924	+	14.0880i	0.189121	+	0.639043i
$487$	2.58469	−	9.64618i	0.117123	−	0.437110i	−0.882314	−	0.470662i	$-0.844015\pi$
$487$	2.58469	−	9.64618i	0.117123	−	0.437110i	0.999437	+	0.0335518i	$0.0106819\pi$
$488$	−2.24249	+	4.69249i	−0.101513	+	0.212419i
$489$		−	3.38579i		−	0.153111i
$490$		0			0
$491$			16.3501i			0.737871i	0.929455	+	0.368936i	$0.120278\pi$
$491$			16.3501i			0.737871i	−0.929455	+	0.368936i	$0.879722\pi$
$492$	−0.0780608	−	0.0166328i	−0.00351925	−	0.000749866i
$493$	−6.63188	+	24.7505i	−0.298685	+	1.11471i
$494$	13.0213	−	3.85357i	0.585856	−	0.173380i
$495$		0			0
$496$	26.2978	−	19.0666i	1.18081	−	0.856117i
$497$	17.7913	−	31.4264i	0.798050	−	1.40967i
$498$	−3.10225	+	1.90000i	−0.139015	+	0.0851412i
$499$	−4.74809	+	8.22393i	−0.212554	+	0.368154i	−0.952513	−	0.304498i	$-0.901511\pi$
$499$	−4.74809	+	8.22393i	−0.212554	+	0.368154i	0.739959	+	0.672652i	$0.234845\pi$
$500$		0			0
$501$	1.62130	+	2.80817i	0.0724343	+	0.125460i
$502$	−0.544008	−	20.9738i	−0.0242803	−	0.936105i
$503$	9.76866	−	9.76866i	0.435563	−	0.435563i	−0.454953	−	0.890516i	$-0.650344\pi$
$503$	9.76866	−	9.76866i	0.435563	−	0.435563i	0.890516	+	0.454953i	$0.150344\pi$
$504$	−12.1150	−	17.3394i	−0.539645	−	0.772356i
$505$		0			0
$506$	2.97778	+	2.82722i	0.132379	+	0.125685i
$507$	−1.10915	+	4.13939i	−0.0492589	+	0.183837i
$508$	9.55180	+	8.60906i	0.423792	+	0.381965i
$509$	−17.0075	−	9.81931i	−0.753846	−	0.435233i	0.0732360	−	0.997315i	$-0.476667\pi$
$509$	−17.0075	−	9.81931i	−0.753846	−	0.435233i	−0.827082	+	0.562082i	$0.810001\pi$
$510$		0			0
$511$	11.1140	−	11.3037i	0.491656	−	0.500045i
$512$	−22.0140	+	5.23310i	−0.972889	+	0.231273i
$513$	−13.6738	+	3.66389i	−0.603714	+	0.161765i
$514$	6.09429	+	20.5928i	0.268808	+	0.908308i
$515$		0			0
$516$	−4.82144	+	3.12768i	−0.212252	+	0.137688i
$517$	3.24152	−	3.24152i	0.142562	−	0.142562i
$518$	−0.621293	+	2.68480i	−0.0272981	+	0.117963i
$519$	1.30372			0.0572269
$520$		0			0
$521$	21.2862	+	36.8688i	0.932565	+	1.61525i	0.778920	+	0.627124i	$0.215768\pi$
$521$	21.2862	+	36.8688i	0.932565	+	1.61525i	0.153645	+	0.988126i	$0.450899\pi$
$522$	−9.54470	+	17.5688i	−0.417760	+	0.768964i
$523$	−0.529969	−	1.97787i	−0.0231739	−	0.0864862i	0.953370	−	0.301803i	$-0.0975884\pi$
$523$	−0.529969	−	1.97787i	−0.0231739	−	0.0864862i	−0.976544	+	0.215316i	$0.930922\pi$
$524$	−24.5925	−	12.5459i	−1.07433	−	0.548069i
$525$		0			0
$526$	16.1159	+	3.87332i	0.702687	+	0.168885i
$527$	40.1842	−	10.7673i	1.75045	−	0.469032i
$528$	1.30338	−	0.498835i	0.0567221	−	0.0217090i
$529$	9.51967	−	5.49618i	0.413899	−	0.238964i
$530$		0			0
$531$		−	25.2662i		−	1.09646i
$532$	25.7592	−	17.0213i	1.11680	−	0.737968i
$533$	0.111524	+	0.111524i	0.00483066	+	0.00483066i
$534$	−1.23512	−	1.17267i	−0.0534490	−	0.0507464i
$535$		0			0
$536$	−0.276206	+	1.48411i	−0.0119303	+	0.0641036i
$537$	−1.73565	−	6.47754i	−0.0748989	−	0.279527i
$538$	−24.9542	+	15.2834i	−1.07585	+	0.658915i
$539$	−5.12835	−	2.84628i	−0.220894	−	0.122598i
$540$		0			0
$541$	−2.22119	+	3.84722i	−0.0954965	+	0.165405i	−0.909816	−	0.415012i	$-0.863777\pi$
$541$	−2.22119	+	3.84722i	−0.0954965	+	0.165405i	0.814319	+	0.580417i	$0.197111\pi$
$542$	26.2207	+	14.2451i	1.12628	+	0.611881i
$543$	1.54147	+	0.413036i	0.0661509	+	0.0177251i
$544$	−28.7272	−	3.81829i	−1.23167	−	0.163708i
$545$		0			0
$546$	−0.0881585	−	2.56244i	−0.00377284	−	0.109662i
$547$	13.7530	+	13.7530i	0.588037	+	0.588037i	0.937099	−	0.349062i	$-0.113500\pi$
$547$	13.7530	+	13.7530i	0.588037	+	0.588037i	−0.349062	+	0.937099i	$0.613500\pi$
$548$	28.1330	+	5.99445i	1.20178	+	0.256070i
$549$	−4.50114	+	2.59873i	−0.192104	+	0.110911i
$550$		0			0
$551$	−25.2741	−	14.5920i	−1.07671	−	0.621642i
$552$	0.317170	+	4.06875i	0.0134996	+	0.173178i
$553$	−24.2011	+	14.2468i	−1.02914	+	0.605837i
$554$	4.49732	+	1.08089i	0.191073	+	0.0459227i
$555$		0			0
$556$	−2.90838	+	0.150974i	−0.123343	+	0.00640272i
$557$	−12.0723	−	3.23476i	−0.511519	−	0.137061i	−0.00617797	−	0.999981i	$-0.501967\pi$
$557$	−12.0723	−	3.23476i	−0.511519	−	0.137061i	−0.505341	+	0.862920i	$0.668633\pi$
$558$	32.4508	−	0.841694i	1.37375	−	0.0356317i
$559$	11.3568			0.480342
$560$		0			0
$561$	1.78737			0.0754628
$562$	−3.67701	+	0.0953725i	−0.155105	+	0.00402305i
$563$	−7.45322	−	1.99709i	−0.314116	−	0.0841671i	0.0983168	−	0.995155i	$-0.468654\pi$
$563$	−7.45322	−	1.99709i	−0.314116	−	0.0841671i	−0.412433	+	0.910988i	$0.635321\pi$
$564$	4.55013	−	0.236197i	0.191595	−	0.00994570i
$565$		0			0
$566$	−38.1104	−	9.15950i	−1.60190	−	0.385003i
$567$	−0.167167	−	19.7620i	−0.00702037	−	0.829928i
$568$	−3.00037	−	38.4897i	−0.125893	−	1.61499i
$569$	22.8689	+	13.2033i	0.958712	+	0.553513i	0.895776	−	0.444505i	$-0.146620\pi$
$569$	22.8689	+	13.2033i	0.958712	+	0.553513i	0.0629358	+	0.998018i	$0.479954\pi$
$570$		0			0
$571$	−4.41042	+	2.54636i	−0.184570	+	0.106562i	−0.589438	−	0.807813i	$-0.700651\pi$
$571$	−4.41042	+	2.54636i	−0.184570	+	0.106562i	0.404868	+	0.914375i	$0.367318\pi$
$572$	−2.69725	−	0.574718i	−0.112778	−	0.0240302i
$573$	0.824564	+	0.824564i	0.0344467	+	0.0344467i
$574$	0.316534	+	0.168514i	0.0132119	+	0.00703364i
$575$		0			0
$576$	−21.0989	−	8.13518i	−0.879121	−	0.338966i
$577$	19.0781	+	5.11195i	0.794230	+	0.212813i	0.633049	−	0.774111i	$-0.281803\pi$
$577$	19.0781	+	5.11195i	0.794230	+	0.212813i	0.161181	+	0.986925i	$0.448470\pi$
$578$	−11.4882	−	6.24128i	−0.477847	−	0.259603i
$579$	−1.80058	+	3.11870i	−0.0748295	+	0.129609i
$580$		0			0
$581$	15.7514	−	4.36370i	0.653478	−	0.181037i
$582$	−3.01442	+	1.84621i	−0.124952	+	0.0765278i
$583$	−2.87763	−	10.7395i	−0.119179	−	0.444783i
$584$	3.10071	−	16.6607i	0.128308	−	0.689425i
$585$		0			0
$586$	17.2921	+	16.4178i	0.714332	+	0.678213i
$587$	−8.18830	−	8.18830i	−0.337967	−	0.337967i	0.517635	−	0.855602i	$-0.326813\pi$
$587$	−8.18830	−	8.18830i	−0.337967	−	0.337967i	−0.855602	+	0.517635i	$0.826813\pi$
$588$	−1.89221	−	5.51385i	−0.0780334	−	0.227388i
$589$			47.3823i			1.95235i
$590$		0			0
$591$	−2.49925	+	1.44294i	−0.102805	+	0.0593547i
$592$	1.05303	+	2.75139i	0.0432791	+	0.113081i
$593$	−6.09096	+	1.63207i	−0.250126	+	0.0670210i	−0.381703	−	0.924285i	$-0.624662\pi$
$593$	−6.09096	+	1.63207i	−0.250126	+	0.0670210i	0.131578	+	0.991306i	$0.457996\pi$
$594$	2.79531	+	0.671828i	0.114693	+	0.0275654i
$595$		0			0
$596$	−20.6019	−	10.5101i	−0.843886	−	0.430509i
$597$	1.33605	+	4.98620i	0.0546808	+	0.204072i
$598$	3.84990	−	7.08643i	0.157434	−	0.289786i
$599$	−12.5631	−	21.7600i	−0.513315	−	0.889088i	−0.999881	−	0.0154439i	$-0.995084\pi$
$599$	−12.5631	−	21.7600i	−0.513315	−	0.889088i	0.486566	−	0.873644i	$-0.338249\pi$
$600$		0			0
$601$	−23.9702			−0.977766			−0.488883	−	0.872349i	$-0.662595\pi$
$601$	−23.9702			−0.977766			−0.488883	+	0.872349i	$0.662595\pi$
$602$	24.6968	−	7.53665i	1.00657	−	0.307171i
$603$	−1.06676	+	1.06676i	−0.0434417	+	0.0434417i
$604$	−8.08069	+	5.24196i	−0.328799	+	0.213292i
$605$		0			0
$606$	−0.287390	−	0.971097i	−0.0116744	−	0.0394481i
$607$	1.98316	−	0.531386i	0.0804940	−	0.0215683i	−0.218347	−	0.975871i	$-0.570067\pi$
$607$	1.98316	−	0.531386i	0.0804940	−	0.0215683i	0.298841	+	0.954303i	$0.403400\pi$
$608$	12.6689	−	30.4785i	0.513793	−	1.23607i
$609$	−3.86324	+	3.92915i	−0.156546	+	0.159217i
$610$		0			0
$611$	−7.79739	−	4.50183i	−0.315449	−	0.182124i
$612$	−21.5128	−	19.3896i	−0.869605	−	0.783778i
$613$	−9.48807	+	35.4100i	−0.383220	+	1.43020i	0.457735	+	0.889089i	$0.348661\pi$
$613$	−9.48807	+	35.4100i	−0.383220	+	1.43020i	−0.840954	+	0.541106i	$0.818006\pi$
$614$	−18.9081	−	17.9521i	−0.763069	−	0.724486i
$615$		0			0
$616$	−6.24692	+	0.540162i	−0.251696	+	0.0217637i
$617$	−7.99905	+	7.99905i	−0.322029	+	0.322029i	−0.849545	−	0.527516i	$-0.823124\pi$
$617$	−7.99905	+	7.99905i	−0.322029	+	0.322029i	0.527516	+	0.849545i	$0.323124\pi$
$618$	−0.239838	−	9.24673i	−0.00964768	−	0.371958i
$619$	−13.8212	−	23.9391i	−0.555523	−	0.962194i	−0.997863	−	0.0653461i	$-0.979185\pi$
$619$	−13.8212	−	23.9391i	−0.555523	−	0.962194i	0.442340	−	0.896847i	$-0.354148\pi$
$620$		0			0
$621$	−4.20357	+	7.28080i	−0.168683	+	0.292168i
$622$	14.1272	−	8.65236i	0.566450	−	0.346928i
$623$	3.88197	+	6.59432i	0.155528	+	0.264196i
$624$	−1.60891	−	2.21910i	−0.0644079	−	0.0888352i
$625$		0			0
$626$	−25.8984	+	7.66447i	−1.03511	+	0.306334i
$627$	−0.526885	+	1.96636i	−0.0210417	+	0.0785289i
$628$	−8.34640	−	1.77841i	−0.333058	−	0.0709664i
$629$			3.77309i			0.150443i
$630$		0			0
$631$			11.5488i			0.459750i	0.973220	+	0.229875i	$0.0738318\pi$
$631$			11.5488i			0.459750i	−0.973220	+	0.229875i	$0.926168\pi$
$632$	−12.9451	+	27.0880i	−0.514927	+	1.07750i
$633$	−0.0945618	+	0.352910i	−0.00375850	+	0.0140269i
$634$	−1.15898	−	3.91624i	−0.0460292	−	0.155534i
$635$		0			0
$636$	5.02171	−	9.84358i	0.199124	−	0.390324i
$637$	−2.79286	+	11.1760i	−0.110657	+	0.442811i
$638$	3.09551	+	5.05423i	0.122553	+	0.200099i
$639$	19.2909	−	33.4128i	0.763135	−	1.32179i
$640$		0			0
$641$	8.55730	+	14.8217i	0.337993	+	0.585421i	0.984055	−	0.177864i	$-0.0569186\pi$
$641$	8.55730	+	14.8217i	0.337993	+	0.585421i	−0.646062	+	0.763285i	$0.723585\pi$
$642$	8.18867	−	0.212394i	0.323181	−	0.00838253i
$643$	18.4696	−	18.4696i	0.728370	−	0.728370i	−0.241925	−	0.970295i	$-0.577779\pi$
$643$	18.4696	−	18.4696i	0.728370	−	0.728370i	0.970295	+	0.241925i	$0.0777789\pi$
$644$	3.66937	−	17.9652i	0.144593	−	0.707929i
$645$		0			0
$646$	29.1064	−	30.6566i	1.14518	−	1.20617i
$647$	8.66156	−	32.3254i	0.340521	−	1.27084i	−0.557237	−	0.830353i	$-0.688139\pi$
$647$	8.66156	−	32.3254i	0.340521	−	1.27084i	0.897758	−	0.440489i	$-0.145195\pi$
$648$	−11.9536	−	17.4204i	−0.469584	−	0.684339i
$649$	−6.48624	−	3.74483i	−0.254607	−	0.146997i
$650$		0			0
$651$	8.66070	+	2.24228i	0.339440	+	0.0878821i
$652$	5.01770	+	15.4690i	0.196508	+	0.605813i
$653$	10.2716	−	2.75226i	0.401958	−	0.107704i	−0.0521757	−	0.998638i	$-0.516616\pi$
$653$	10.2716	−	2.75226i	0.401958	−	0.107704i	0.454133	+	0.890934i	$0.349949\pi$
$654$	−6.02095	+	1.78186i	−0.235438	+	0.0696763i
$655$		0			0
$656$	0.381295	−	0.0396930i	0.0148871	−	0.00154975i
$657$	11.9755	−	11.9755i	0.467210	−	0.467210i
$658$	−19.9439	−	4.61526i	−0.777496	−	0.179922i
$659$	21.6586			0.843698			0.421849	−	0.906666i	$-0.361381\pi$
$659$	21.6586			0.843698			0.421849	+	0.906666i	$0.361381\pi$
$660$		0			0
$661$	−11.2670	−	19.5150i	−0.438236	−	0.759046i	0.559318	−	0.828953i	$-0.311063\pi$
$661$	−11.2670	−	19.5150i	−0.438236	−	0.759046i	−0.997554	+	0.0699068i	$0.977730\pi$
$662$	−43.3320	−	23.5413i	−1.68415	−	0.914957i
$663$	−0.908584	−	3.39088i	−0.0352865	−	0.131691i
$664$	11.3578	−	13.2783i	0.440769	−	0.515296i
$665$		0			0
$666$	−0.688004	+	2.86261i	−0.0266596	+	0.110924i
$667$	−16.7414	+	4.48584i	−0.648229	+	0.173693i
$668$	−11.5691	−	10.4273i	−0.447621	−	0.403443i
$669$	6.42869	−	3.71161i	0.248548	−	0.143499i
$670$		0			0
$671$			1.54069i			0.0594775i
$672$	−4.97143	−	3.75801i	−0.191777	−	0.144969i
$673$	12.3425	+	12.3425i	0.475769	+	0.475769i	0.903776	−	0.428007i	$-0.140784\pi$
$673$	12.3425	+	12.3425i	0.475769	+	0.475769i	−0.428007	+	0.903776i	$0.640784\pi$
$674$	21.8743	−	23.0392i	0.842565	−	0.887437i
$675$		0			0
$676$	−1.06705	−	20.5558i	−0.0410405	−	0.790609i
$677$	−3.54145	−	13.2169i	−0.136109	−	0.507966i	−0.999991	−	0.00427157i	$-0.998640\pi$
$677$	−3.54145	−	13.2169i	−0.136109	−	0.507966i	0.863882	−	0.503695i	$-0.168026\pi$
$678$	2.44457	+	3.99141i	0.0938833	+	0.153289i
$679$	15.3054	−	4.24015i	0.587368	−	0.162722i
$680$		0			0
$681$	2.18628	−	3.78675i	0.0837785	−	0.145109i
$682$	4.59362	−	8.45539i	0.175899	−	0.323774i
$683$	−2.13814	−	0.572913i	−0.0818137	−	0.0219219i	0.217680	−	0.976020i	$-0.430151\pi$
$683$	−2.13814	−	0.572913i	−0.0818137	−	0.0219219i	−0.299494	+	0.954098i	$0.596818\pi$
$684$	27.6729	−	17.9515i	1.05810	−	0.686392i
$685$		0			0
$686$	1.34325	+	26.1571i	0.0512856	+	0.998684i
$687$	−8.02297	−	8.02297i	−0.306095	−	0.306095i
$688$	17.3931	−	21.4351i	0.663105	−	0.817206i
$689$	−18.9114	+	10.9185i	−0.720467	+	0.415962i
$690$		0			0
$691$	−19.0959	−	11.0250i	−0.726442	−	0.419411i	0.0906771	−	0.995880i	$-0.471097\pi$
$691$	−19.0959	−	11.0250i	−0.726442	−	0.419411i	−0.817119	+	0.576469i	$0.804430\pi$
$692$	−5.95644	+	1.93210i	−0.226430	+	0.0734473i
$693$	−5.45301	−	3.08709i	−0.207143	−	0.117269i
$694$	7.93616	−	33.0204i	0.301252	−	1.25344i
$695$		0			0
$696$	−1.07781	+	5.79126i	−0.0408542	+	0.219517i
$697$	0.474249	+	0.127075i	0.0179635	+	0.00481330i
$698$	0.733685	+	28.2866i	0.0277704	+	1.07066i
$699$	5.46890			0.206853
$700$		0			0
$701$	3.86536			0.145993			0.0729964	−	0.997332i	$-0.476744\pi$
$701$	3.86536			0.145993			0.0729964	+	0.997332i	$0.476744\pi$
$702$	−0.146407	−	5.64459i	−0.00552577	−	0.213041i
$703$	−4.15093	−	1.11224i	−0.156555	−	0.0419489i
$704$	−5.21561	+	4.21067i	−0.196571	+	0.158696i
$705$		0			0
$706$	−7.74281	+	32.2159i	−0.291404	+	1.21246i
$707$	0.0384883	+	4.54997i	0.00144750	+	0.171119i
$708$	−2.29681	−	7.08080i	−0.0863192	−	0.266113i
$709$	−27.5158	−	15.8862i	−1.03338	−	0.596620i	−0.115427	−	0.993316i	$-0.536823\pi$
$709$	−27.5158	−	15.8862i	−1.03338	−	0.596620i	−0.917950	+	0.396696i	$0.870157\pi$
$710$		0			0
$711$	−25.9834	+	15.0015i	−0.974452	+	0.562600i
$712$	7.38093	+	3.52727i	0.276612	+	0.132190i
$713$	19.8977	+	19.8977i	0.745175	+	0.745175i
$714$	−4.22610	−	6.77094i	−0.158158	−	0.253396i
$715$		0			0
$716$	17.5295	+	27.0225i	0.655109	+	1.00988i
$717$	−4.30673	−	1.15398i	−0.160838	−	0.0430963i
$718$	18.1636	−	33.4334i	0.677860	−	1.24772i
$719$	−5.63438	+	9.75903i	−0.210127	+	0.363950i	−0.951754	−	0.306862i	$-0.900721\pi$
$719$	−5.63438	+	9.75903i	−0.210127	+	0.363950i	0.741627	+	0.670812i	$0.234054\pi$
$720$		0			0
$721$	−10.4163	+	40.2325i	−0.387924	+	1.49834i
$722$	11.1126	+	18.1443i	0.413569	+	0.675260i
$723$	1.35511	+	5.05733i	0.0503970	+	0.188084i
$724$	−7.65481	+	0.397361i	−0.284489	+	0.0147678i
$725$		0			0
$726$	−4.17536	+	4.39773i	−0.154962	+	0.163215i
$727$	21.9895	+	21.9895i	0.815544	+	0.815544i	0.985459	−	0.169915i	$-0.0543492\pi$
$727$	21.9895	+	21.9895i	0.815544	+	0.815544i	−0.169915	+	0.985459i	$0.554349\pi$
$728$	4.20029	+	11.5767i	0.155673	+	0.429060i
$729$		−	18.0830i		−	0.669742i
$730$		0			0
$731$	30.6172	−	17.6768i	1.13242	−	0.653801i
$732$	−1.02520	+	1.13746i	−0.0378924	+	0.0420418i
$733$	−39.0339	+	10.4591i	−1.44175	+	0.386316i	−0.893146	−	0.449766i	$-0.851507\pi$
$733$	−39.0339	+	10.4591i	−1.44175	+	0.386316i	−0.548604	+	0.836082i	$0.684841\pi$
$734$	−9.05587	+	37.6792i	−0.334258	+	1.39077i
$735$		0			0
$736$	−7.47894	−	18.1193i	−0.275677	−	0.667887i
$737$	0.115744	+	0.431964i	0.00426350	+	0.0159116i
$738$	0.336638	+	0.182888i	0.0123918	+	0.00673219i
$739$	15.6220	+	27.0581i	0.574665	+	0.995349i	0.996078	+	0.0884798i	$0.0282009\pi$
$739$	15.6220	+	27.0581i	0.574665	+	0.995349i	−0.421413	+	0.906869i	$0.638466\pi$
$740$		0			0
$741$	3.99829			0.146881
$742$	−33.8795	+	36.2937i	−1.24375	+	1.33238i
$743$	13.4261	−	13.4261i	0.492557	−	0.492557i	−0.416554	−	0.909111i	$-0.636762\pi$
$743$	13.4261	−	13.4261i	0.492557	−	0.492557i	0.909111	+	0.416554i	$0.136762\pi$
$744$	9.01776	−	3.18580i	0.330607	−	0.116797i
$745$		0			0
$746$	−29.7356	+	8.80007i	−1.08870	+	0.322194i
$747$	16.8670	−	4.51950i	0.617131	−	0.165360i
$748$	−8.16615	+	2.64886i	−0.298584	+	0.0968520i
$749$	−35.6289	−	9.22443i	−1.30185	−	0.337053i
$750$		0			0
$751$	29.3693	+	16.9564i	1.07170	+	0.618748i	0.928646	−	0.370967i	$-0.120974\pi$
$751$	29.3693	+	16.9564i	1.07170	+	0.618748i	0.143056	+	0.989715i	$0.454307\pi$
$752$	−20.4386	+	7.82238i	−0.745320	+	0.285253i
$753$	1.59885	−	5.96698i	0.0582652	−	0.217449i
$754$	8.01500	−	8.44185i	0.291889	−	0.307434i
$755$		0			0
$756$	−4.06426	−	12.1777i	−0.147816	−	0.442900i
$757$	−10.7202	+	10.7202i	−0.389633	+	0.389633i	−0.874556	−	0.484924i	$-0.838847\pi$
$757$	−10.7202	+	10.7202i	−0.389633	+	0.389633i	0.484924	+	0.874556i	$0.338847\pi$
$758$	−28.9253	+	0.750252i	−1.05061	+	0.0272504i
$759$	0.604493	+	1.04701i	0.0219417	+	0.0380041i
$760$		0			0
$761$	12.2719	−	21.2555i	0.444854	−	0.770510i	−0.553188	−	0.833057i	$-0.686589\pi$
$761$	12.2719	−	21.2555i	0.444854	−	0.770510i	0.998042	+	0.0625464i	$0.0199221\pi$
$762$	1.97744	+	3.22869i	0.0716351	+	0.116963i
$763$	28.2106	−	0.238633i	1.02129	−	0.00863911i
$764$	−4.98927	−	2.54528i	−0.180506	−	0.0920851i
$765$		0			0
$766$	2.91629	+	9.85420i	0.105370	+	0.356047i
$767$	−3.80726	+	14.2089i	−0.137472	+	0.513054i
$768$	−6.65245	−	0.361887i	−0.240050	−	0.0130585i
$769$			38.3029i			1.38124i	0.723219	+	0.690619i	$0.242662\pi$
$769$			38.3029i			1.38124i	−0.723219	+	0.690619i	$0.757338\pi$
$770$		0			0
$771$			6.32315i			0.227723i
$772$	3.60463	−	16.9172i	0.129734	−	0.608862i
$773$	−0.371576	+	1.38674i	−0.0133647	+	0.0498776i	−0.972286	−	0.233794i	$-0.924886\pi$
$773$	−0.371576	+	1.38674i	−0.0133647	+	0.0498776i	0.958922	+	0.283672i	$0.0915525\pi$
$774$	26.4523	−	7.82839i	0.950808	−	0.281386i
$775$		0			0
$776$	11.0362	−	12.9023i	0.396178	−	0.463166i
$777$	−0.399734	+	0.706087i	−0.0143404	+	0.0253307i
$778$	−6.69829	+	4.10243i	−0.240145	+	0.147079i
$779$	−0.279601	+	0.484282i	−0.0100177	+	0.0173512i
$780$		0			0
$781$	−5.71840	−	9.90456i	−0.204620	−	0.354413i
$782$	−0.650951	−	25.0969i	−0.0232780	−	0.897462i
$783$	−8.58072	+	8.58072i	−0.306650	+	0.306650i
$784$	16.8166	+	22.3875i	0.600594	+	0.799554i
$785$		0			0
$786$	−5.89493	−	5.59687i	−0.210265	−	0.199634i
$787$	3.70435	−	13.8248i	0.132046	−	0.492801i	−0.867947	−	0.496657i	$-0.834561\pi$
$787$	3.70435	−	13.8248i	0.132046	−	0.492801i	0.999993	+	0.00385583i	$0.00122735\pi$
$788$	9.28017	−	10.2964i	0.330592	−	0.366794i
$789$	4.22637	+	2.44010i	0.150463	+	0.0868698i
$790$		0			0
$791$	−5.61441	−	20.2660i	−0.199625	−	0.720575i
$792$	−6.67861	+	0.520614i	−0.237314	+	0.0184992i
$793$	2.92289	−	0.783185i	0.103795	−	0.0278117i
$794$	−12.0770	−	40.8084i	−0.428597	−	1.44824i
$795$		0			0
$796$	−13.4937	−	20.8010i	−0.478270	−	0.737272i
$797$	9.85742	−	9.85742i	0.349168	−	0.349168i	−0.510632	−	0.859800i	$-0.670588\pi$
$797$	9.85742	−	9.85742i	0.349168	−	0.349168i	0.859800	+	0.510632i	$0.170588\pi$
$798$	8.69478	−	2.65336i	0.307792	−	0.0939278i
$799$	−28.0283			−0.991569
$800$		0			0
$801$	4.08761	+	7.07995i	0.144429	+	0.250158i
$802$	−3.13201	+	5.76503i	−0.110595	+	0.203570i
$803$	−1.29936	−	4.84926i	−0.0458533	−	0.171127i
$804$	−0.201984	+	0.395930i	−0.00712342	+	0.0139634i
$805$		0			0
$806$	−18.3761	−	4.41654i	−0.647271	−	0.155566i
$807$	−8.32229	+	2.22995i	−0.292959	+	0.0784980i
$808$	2.75218	+	4.01085i	0.0968215	+	0.141101i
$809$	−30.8498	+	17.8112i	−1.08462	+	0.626207i	−0.932140	−	0.362099i	$-0.882060\pi$
$809$	−30.8498	+	17.8112i	−1.08462	+	0.626207i	−0.152483	+	0.988306i	$0.548727\pi$
$810$		0			0
$811$		−	11.1150i		−	0.390299i	−0.980774	−	0.195149i	$-0.937481\pi$
$811$		−	11.1150i		−	0.390299i	0.980774	−	0.195149i	$-0.0625192\pi$
$812$	11.8274	−	23.6768i	0.415062	−	0.830894i
$813$	6.21267	+	6.21267i	0.217888	+	0.217888i
$814$	0.632906	+	0.600904i	0.0221833	+	0.0210617i
$815$		0			0
$816$	−7.79153	−	3.47829i	−0.272758	−	0.121764i
$817$	10.4216	+	38.8940i	0.364607	+	1.36073i
$818$	41.8979	−	25.6608i	1.46493	−	0.897207i
$819$	−3.08467	+	11.9144i	−0.107787	+	0.416322i
$820$		0			0
$821$	−6.79984	+	11.7777i	−0.237316	+	0.411043i	−0.959943	−	0.280195i	$-0.909601\pi$
$821$	−6.79984	+	11.7777i	−0.237316	+	0.411043i	0.722627	+	0.691238i	$0.242934\pi$
$822$	7.44193	+	4.04303i	0.259567	+	0.141017i
$823$	−24.5214	−	6.57048i	−0.854761	−	0.229033i	−0.195274	−	0.980749i	$-0.562560\pi$
$823$	−24.5214	−	6.57048i	−0.854761	−	0.229033i	−0.659487	+	0.751716i	$0.729226\pi$
$824$	14.7993	+	41.8911i	0.515559	+	1.45935i
$825$		0			0
$826$	1.14998	+	33.4257i	0.0400129	+	1.16303i
$827$	17.3478	+	17.3478i	0.603242	+	0.603242i	0.941172	−	0.337929i	$-0.109726\pi$
$827$	17.3478	+	17.3478i	0.603242	+	0.603242i	−0.337929	+	0.941172i	$0.609726\pi$
$828$	4.08242	−	19.1595i	0.141874	−	0.665839i
$829$	16.3045	−	9.41343i	0.566280	−	0.326942i	−0.189382	−	0.981903i	$-0.560649\pi$
$829$	16.3045	−	9.41343i	0.566280	−	0.326942i	0.755662	+	0.654962i	$0.227315\pi$
$830$		0			0
$831$	1.17942	+	0.680936i	0.0409135	+	0.0236214i
$832$	10.6395	+	7.75428i	0.368858	+	0.268831i
$833$	9.86610	+	34.4769i	0.341840	+	1.19455i
$834$	−0.833737	−	0.200381i	−0.0288700	−	0.00693864i
$835$		0			0
$836$	−0.506889	−	9.76476i	−0.0175311	−	0.337721i
$837$	19.0306	+	5.09924i	0.657794	+	0.176255i
$838$	−39.7700	+	1.03154i	−1.37383	+	0.0356338i
$839$	3.21211			0.110894			0.0554472	−	0.998462i	$-0.482342\pi$
$839$	3.21211			0.110894			0.0554472	+	0.998462i	$0.482342\pi$
$840$		0			0
$841$	3.98283			0.137339
$842$	−5.57884	+	0.144701i	−0.192260	+	0.00498674i
$843$	−1.04610	−	0.280301i	−0.0360295	−	0.00965408i
$844$	−0.0909731	−	1.75252i	−0.00313142	−	0.0603241i
$845$		0			0
$846$	−21.2649	−	5.11082i	−0.731101	−	0.175714i
$847$	23.4795	−	13.8220i	0.806764	−	0.474929i
$848$	−8.35517	+	52.4156i	−0.286918	+	1.79996i
$849$	−9.99440	−	5.77027i	−0.343007	−	0.198035i
$850$		0			0
$851$	−2.21021	+	1.27607i	−0.0757652	+	0.0437430i
$852$	2.36886	−	11.1175i	0.0811559	−	0.380879i
$853$	31.7184	+	31.7184i	1.08602	+	1.08602i	0.995934	+	0.0900831i	$0.0287133\pi$
$853$	31.7184	+	31.7184i	1.08602	+	1.08602i	0.0900831	+	0.995934i	$0.471287\pi$
$854$	5.83645	−	3.64283i	0.199719	−	0.124655i
$855$		0			0
$856$	−37.0977	+	13.1059i	−1.26797	+	0.447951i
$857$	35.4579	+	9.50091i	1.21122	+	0.324545i	0.807240	−	0.590224i	$-0.200960\pi$
$857$	35.4579	+	9.50091i	1.21122	+	0.324545i	0.403978	+	0.914769i	$0.367627\pi$
$858$	−0.713496	−	0.387626i	−0.0243583	−	0.0132333i
$859$	−5.30651	+	9.19114i	−0.181056	+	0.313598i	−0.942240	−	0.334938i	$-0.891285\pi$
$859$	−5.30651	+	9.19114i	−0.181056	+	0.313598i	0.761185	+	0.648535i	$0.224618\pi$
$860$		0			0
$861$	0.0752872	+	0.0740242i	0.00256578	+	0.00252274i
$862$	16.8988	−	10.3498i	0.575576	−	0.352517i
$863$	5.67140	+	21.1660i	0.193057	+	0.720498i	0.992761	+	0.120104i	$0.0383228\pi$
$863$	5.67140	+	21.1660i	0.193057	+	0.720498i	−0.799705	+	0.600394i	$0.795011\pi$
$864$	−10.8780	−	8.36842i	−0.370075	−	0.284699i
$865$		0			0
$866$	−3.21919	−	3.05642i	−0.109393	−	0.103861i
$867$	−2.72198	−	2.72198i	−0.0924434	−	0.0924434i
$868$	−42.8922	+	2.59049i	−1.45585	+	0.0879271i
$869$			8.89379i			0.301701i
$870$		0			0
$871$	0.760656	−	0.439165i	0.0257739	−	0.0148805i
$872$	24.8679	−	17.0640i	0.842133	−	0.577859i
$873$	16.3894	−	4.39154i	0.554698	−	0.148631i
$874$	27.8020	+	6.68197i	0.940417	+	0.226021i
$875$		0			0
$876$	2.26749	−	4.44474i	0.0766114	−	0.150174i
$877$	−2.95602	−	11.0320i	−0.0998175	−	0.372524i	0.897888	−	0.440224i	$-0.145101\pi$
$877$	−2.95602	−	11.0320i	−0.0998175	−	0.372524i	−0.997706	+	0.0676994i	$0.978434\pi$
$878$	16.8998	−	31.1071i	0.570340	−	1.04981i
$879$	3.51032	+	6.08006i	0.118400	+	0.205075i
$880$		0			0
$881$	27.2610			0.918447			0.459224	−	0.888321i	$-0.348128\pi$
$881$	27.2610			0.918447			0.459224	+	0.888321i	$0.348128\pi$
$882$	1.19865	+	27.9564i	0.0403605	+	0.941341i
$883$	29.9932	−	29.9932i	1.00935	−	1.00935i	0.00939636	−	0.999956i	$-0.497009\pi$
$883$	29.9932	−	29.9932i	1.00935	−	1.00935i	0.999956	−	0.00939636i	$-0.00299100\pi$
$884$	9.17640	+	14.1458i	0.308636	+	0.475774i
$885$		0			0
$886$	1.76687	+	5.97030i	0.0593592	+	0.200576i
$887$	−21.8561	+	5.85632i	−0.733855	+	0.196636i	−0.606345	−	0.795201i	$-0.707365\pi$
$887$	−21.8561	+	5.85632i	−0.733855	+	0.196636i	−0.127510	+	0.991837i	$0.540698\pi$
$888$	0.0674121	+	0.864784i	0.00226220	+	0.0290202i
$889$	−4.54155	−	16.3933i	−0.152319	−	0.549815i
$890$		0			0
$891$	−5.42024	−	3.12937i	−0.181585	−	0.104838i
$892$	−23.8709	+	26.4849i	−0.799257	+	0.886780i
$893$	8.26224	−	30.8351i	0.276485	−	1.03186i
$894$	−4.93837	−	4.68867i	−0.165164	−	0.156813i
$895$		0			0
$896$	28.2829	+	9.80205i	0.944864	+	0.327464i
$897$	1.67904	−	1.67904i	0.0560615	−	0.0560615i
$898$	0.888322	+	34.2485i	0.0296437	+	1.14289i
$899$	20.3085	+	35.1754i	0.677327	+	1.17317i
$900$		0			0
$901$	−33.9892	+	58.8710i	−1.13234	+	1.96128i
$902$	0.0968451	−	0.0593137i	0.00322459	−	0.00197493i
$903$	7.60237	−	0.0643086i	0.252991	−	0.00214005i
$904$	−17.0840	−	14.6131i	−0.568206	−	0.486026i
$905$		0			0
$906$	−2.71941	+	0.804791i	−0.0903462	+	0.0267374i
$907$	−1.07561	+	4.01423i	−0.0357151	+	0.133290i	−0.981481	−	0.191557i	$-0.938646\pi$
$907$	−1.07561	+	4.01423i	−0.0357151	+	0.133290i	0.945766	+	0.324847i	$0.105313\pi$
$908$	−4.37678	+	20.5410i	−0.145249	+	0.681677i
$909$			4.86119i			0.161235i
$910$		0			0
$911$			29.4464i			0.975603i	0.872955	+	0.487801i	$0.162201\pi$
$911$			29.4464i			0.975603i	−0.872955	+	0.487801i	$0.837799\pi$
$912$	6.12341	−	7.54646i	0.202767	−	0.249888i
$913$	1.33972	−	4.99989i	0.0443381	−	0.165472i
$914$	−3.75829	−	12.6993i	−0.124313	−	0.420057i
$915$		0			0
$916$	48.5454	+	24.7655i	1.60398	+	0.818274i
$917$	18.5277	+	31.4731i	0.611838	+	1.03933i
$918$	−9.18048	−	14.9895i	−0.303001	−	0.494728i
$919$	4.57597	−	7.92582i	0.150947	−	0.261449i	−0.780629	−	0.624995i	$-0.785101\pi$
$919$	4.57597	−	7.92582i	0.150947	−	0.261449i	0.931576	+	0.363547i	$0.118434\pi$
$920$		0			0
$921$	−3.83837	−	6.64825i	−0.126479	−	0.219067i
$922$	−17.4713	+	0.453163i	−0.575387	+	0.0149241i
$923$	−15.8834	+	15.8834i	−0.522809	+	0.522809i
$924$	−1.80883	−	0.369449i	−0.0595060	−	0.0121540i
$925$		0			0
$926$	40.8697	−	43.0463i	1.34306	−	1.41459i
$927$	−11.4916	+	42.8871i	−0.377433	+	1.40860i
$928$	−3.65829	−	28.0565i	−0.120089	−	0.920999i
$929$	26.0531	+	15.0417i	0.854773	+	0.493504i	0.862259	−	0.506468i	$-0.169049\pi$
$929$	26.0531	+	15.0417i	0.854773	+	0.493504i	−0.00748525	+	0.999972i	$0.502383\pi$
$930$		0			0
$931$	−40.8378	+	0.690945i	−1.33841	+	0.0226448i
$932$	−24.9864	+	8.10485i	−0.818456	+	0.265483i
$933$	4.71148	−	1.26244i	0.154247	−	0.0413303i
$934$	49.0807	−	14.5251i	1.60597	−	0.475277i
$935$		0			0
$936$	4.38265	+	12.4056i	0.143251	+	0.405489i
$937$	6.79581	−	6.79581i	0.222009	−	0.222009i	−0.587335	−	0.809344i	$-0.699823\pi$
$937$	6.79581	−	6.79581i	0.222009	−	0.222009i	0.809344	+	0.587335i	$0.199823\pi$
$938$	1.36270	−	1.45981i	0.0444939	−	0.0476645i
$939$	−7.95230			−0.259514
$940$		0			0
$941$	−9.08044	−	15.7278i	−0.296014	−	0.512711i	0.679206	−	0.733947i	$-0.262324\pi$
$941$	−9.08044	−	15.7278i	−0.296014	−	0.512711i	−0.975220	+	0.221236i	$0.928991\pi$
$942$	−2.20785	−	1.19947i	−0.0719355	−	0.0390809i
$943$	0.0859540	+	0.320785i	0.00279905	+	0.0104462i
$944$	20.9873	+	28.9470i	0.683080	+	0.942144i
$945$		0			0
$946$	1.91096	−	7.95101i	0.0621306	−	0.258510i
$947$	16.9897	−	4.55237i	0.552091	−	0.147932i	0.0280205	−	0.999607i	$-0.491080\pi$
$947$	16.9897	−	4.55237i	0.552091	−	0.147932i	0.524070	+	0.851675i	$0.324413\pi$
$948$	−5.91808	+	6.56614i	−0.192210	+	0.213258i
$949$	−8.53920	+	4.93011i	−0.277194	+	0.160038i
$950$		0			0
$951$		−	1.20251i		−	0.0389940i
$952$	29.3427	+	24.6721i	0.951003	+	0.799628i
$953$	−12.8804	−	12.8804i	−0.417238	−	0.417238i	0.467013	−	0.884251i	$-0.345330\pi$
$953$	−12.8804	−	12.8804i	−0.417238	−	0.417238i	−0.884251	+	0.467013i	$0.845330\pi$
$954$	−36.5222	+	38.4672i	−1.18245	+	1.24542i
$955$		0			0
$956$	21.3868	−	1.11019i	0.691699	−	0.0359061i
$957$	0.451656	+	1.68560i	0.0146000	+	0.0544878i
$958$	23.5363	+	38.4291i	0.760423	+	1.24159i
$959$	−27.1334	−	26.6782i	−0.876183	−	0.861484i
$960$		0			0
$961$	17.4723	−	30.2629i	0.563622	−	0.976222i
$962$	0.818267	−	1.50617i	0.0263820	−	0.0485609i
$963$	−37.9798	−	10.1766i	−1.22388	−	0.327938i
$964$	−13.6861	−	21.0977i	−0.440801	−	0.679512i
$965$		0			0
$966$	2.53703	−	4.76553i	0.0816278	−	0.153329i
$967$	−21.8531	−	21.8531i	−0.702748	−	0.702748i	0.262251	−	0.965000i	$-0.415535\pi$
$967$	−21.8531	−	21.8531i	−0.702748	−	0.702748i	−0.965000	+	0.262251i	$0.915535\pi$
$968$	12.5590	−	26.2802i	0.403663	−	0.844678i
$969$	10.7791	−	6.22331i	0.346274	−	0.199922i
$970$		0			0
$971$	49.5916	+	28.6317i	1.59147	+	0.918836i	0.993055	+	0.117650i	$0.0375362\pi$
$971$	49.5916	+	28.6317i	1.59147	+	0.918836i	0.598416	+	0.801186i	$0.295797\pi$
$972$	−6.41081	−	19.7638i	−0.205627	−	0.633925i
$973$	3.35263	+	1.89801i	0.107480	+	0.0608475i
$974$	−3.30035	+	13.7319i	−0.105750	+	0.440000i
$975$		0			0
$976$	2.99823	−	6.71618i	0.0959710	−	0.214980i
$977$	−23.4116	−	6.27313i	−0.749004	−	0.200695i	−0.135928	−	0.990719i	$-0.543402\pi$
$977$	−23.4116	−	6.27313i	−0.749004	−	0.200695i	−0.613076	+	0.790024i	$0.710068\pi$
$978$	0.124153	+	4.78662i	0.00396998	+	0.153059i
$979$	2.42338			0.0774516
$980$		0			0
$981$	30.1401			0.962300
$982$	−0.599541	−	23.1148i	−0.0191321	−	0.737623i
$983$	−13.7291	−	3.67869i	−0.437889	−	0.117332i	0.0331380	−	0.999451i	$-0.489450\pi$
$983$	−13.7291	−	3.67869i	−0.437889	−	0.117332i	−0.471027	+	0.882119i	$0.656117\pi$
$984$	0.110967	+	0.0206521i	0.00353751	+	0.000658364i
$985$		0			0
$986$	8.46817	−	35.2339i	0.269682	−	1.12208i
$987$	−5.24515	−	2.96942i	−0.166955	−	0.0945176i
$988$	−18.2674	+	5.92542i	−0.581164	+	0.188513i
$989$	20.7096	+	11.9567i	0.658527	+	0.380201i
$990$		0			0
$991$	40.1223	−	23.1646i	1.27453	−	0.735848i	0.298689	−	0.954350i	$-0.403451\pi$
$991$	40.1223	−	23.1646i	1.27453	−	0.735848i	0.975836	+	0.218503i	$0.0701172\pi$
$992$	−36.4791	+	27.9195i	−1.15821	+	0.886446i
$993$	−10.2670	−	10.2670i	−0.325812	−	0.325812i
$994$	−23.9999	+	45.0811i	−0.761231	+	1.42989i
$995$		0			0
$996$	4.31610	−	2.79986i	0.136761	−	0.0887170i
$997$	−44.4512	−	11.9107i	−1.40778	−	0.377214i	−0.526649	−	0.850083i	$-0.676552\pi$
$997$	−44.4512	−	11.9107i	−1.40778	−	0.377214i	−0.881133	+	0.472869i	$0.843219\pi$
$998$	6.41099	−	11.8006i	0.202936	−	0.373541i
$999$	−0.893438	+	1.54748i	−0.0282671	+	0.0489601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.443.1		72
4.3	odd	2	inner	700.2.be.e.443.15		72
5.2	odd	4	inner	700.2.be.e.107.11		72
5.3	odd	4		140.2.w.b.107.8	yes	72
5.4	even	2		140.2.w.b.23.18	yes	72
7.4	even	3	inner	700.2.be.e.543.13		72
20.3	even	4		140.2.w.b.107.6	yes	72
20.7	even	4	inner	700.2.be.e.107.13		72
20.19	odd	2		140.2.w.b.23.4	✓	72
28.11	odd	6	inner	700.2.be.e.543.11		72
35.3	even	12		980.2.x.m.67.4		72
35.4	even	6		140.2.w.b.123.6	yes	72
35.9	even	6		980.2.k.k.883.7		36
35.13	even	4		980.2.x.m.667.8		72
35.18	odd	12		140.2.w.b.67.4	yes	72
35.19	odd	6		980.2.k.j.883.7		36
35.23	odd	12		980.2.k.k.687.15		36
35.24	odd	6		980.2.x.m.263.6		72
35.32	odd	12	inner	700.2.be.e.207.15		72
35.33	even	12		980.2.k.j.687.15		36
35.34	odd	2		980.2.x.m.863.18		72
140.3	odd	12		980.2.x.m.67.18		72
140.19	even	6		980.2.k.j.883.15		36
140.23	even	12		980.2.k.k.687.7		36
140.39	odd	6		140.2.w.b.123.8	yes	72
140.59	even	6		980.2.x.m.263.8		72
140.67	even	12	inner	700.2.be.e.207.1		72
140.79	odd	6		980.2.k.k.883.15		36
140.83	odd	4		980.2.x.m.667.6		72
140.103	odd	12		980.2.k.j.687.7		36
140.123	even	12		140.2.w.b.67.18	yes	72
140.139	even	2		980.2.x.m.863.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.4	✓	72	20.19	odd	2
140.2.w.b.23.18	yes	72	5.4	even	2
140.2.w.b.67.4	yes	72	35.18	odd	12
140.2.w.b.67.18	yes	72	140.123	even	12
140.2.w.b.107.6	yes	72	20.3	even	4
140.2.w.b.107.8	yes	72	5.3	odd	4
140.2.w.b.123.6	yes	72	35.4	even	6
140.2.w.b.123.8	yes	72	140.39	odd	6
700.2.be.e.107.11		72	5.2	odd	4	inner
700.2.be.e.107.13		72	20.7	even	4	inner
700.2.be.e.207.1		72	140.67	even	12	inner
700.2.be.e.207.15		72	35.32	odd	12	inner
700.2.be.e.443.1		72	1.1	even	1	trivial
700.2.be.e.443.15		72	4.3	odd	2	inner
700.2.be.e.543.11		72	28.11	odd	6	inner
700.2.be.e.543.13		72	7.4	even	3	inner
980.2.k.j.687.7		36	140.103	odd	12
980.2.k.j.687.15		36	35.33	even	12
980.2.k.j.883.7		36	35.19	odd	6
980.2.k.j.883.15		36	140.19	even	6
980.2.k.k.687.7		36	140.23	even	12
980.2.k.k.687.15		36	35.23	odd	12
980.2.k.k.883.7		36	35.9	even	6
980.2.k.k.883.15		36	140.79	odd	6
980.2.x.m.67.4		72	35.3	even	12
980.2.x.m.67.18		72	140.3	odd	12
980.2.x.m.263.6		72	35.24	odd	6
980.2.x.m.263.8		72	140.59	even	6
980.2.x.m.667.6		72	140.83	odd	4
980.2.x.m.667.8		72	35.13	even	4
980.2.x.m.863.4		72	140.139	even	2
980.2.x.m.863.18		72	35.34	odd	2

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41374 + 0.0366689i) q^{2} +(-0.402205 - 0.107770i) q^{3} +(1.99731 - 0.103680i) q^{4} +(0.572564 + 0.137611i) q^{6} +(-2.30240 - 1.30345i) q^{7} +(-2.81987 + 0.219816i) q^{8} +(-2.44792 - 1.41331i) q^{9} +O(q^{10})\)	\(q+(-1.41374 + 0.0366689i) q^{2} +(-0.402205 - 0.107770i) q^{3} +(1.99731 - 0.103680i) q^{4} +(0.572564 + 0.137611i) q^{6} +(-2.30240 - 1.30345i) q^{7} +(-2.81987 + 0.219816i) q^{8} +(-2.44792 - 1.41331i) q^{9} +(-0.725638 + 0.418947i) q^{11} +(-0.814501 - 0.173550i) q^{12} +(1.16367 + 1.16367i) q^{13} +(3.30278 + 1.75831i) q^{14} +(3.97850 - 0.414164i) q^{16} +(4.94841 + 1.32592i) q^{17} +(3.51255 + 1.90829i) q^{18} +(-2.91741 + 5.05309i) q^{19} +(0.785561 + 0.772382i) q^{21} +(1.01050 - 0.618890i) q^{22} +(0.896861 + 3.34713i) q^{23} +(1.15786 + 0.215488i) q^{24} +(-1.68779 - 1.60245i) q^{26} +(1.71555 + 1.71555i) q^{27} +(-4.73374 - 2.36468i) q^{28} +5.00172i q^{29} +(7.03267 - 4.06031i) q^{31} +(-5.60937 + 0.731407i) q^{32} +(0.337005 - 0.0903002i) q^{33} +(-7.04437 - 1.69305i) q^{34} +(-5.03579 - 2.56901i) q^{36} +(0.190621 + 0.711408i) q^{37} +(3.93916 - 7.25073i) q^{38} +(-0.342623 - 0.593441i) q^{39} +0.0958388 q^{41} +(-1.13890 - 1.06314i) q^{42} +(4.87975 - 4.87975i) q^{43} +(-1.40589 + 0.912002i) q^{44} +(-1.39066 - 4.69908i) q^{46} +(-5.28468 + 1.41603i) q^{47} +(-1.64481 - 0.262186i) q^{48} +(3.60205 + 6.00210i) q^{49} +(-1.84738 - 1.06658i) q^{51} +(2.44486 + 2.20356i) q^{52} +(-3.43436 + 12.8172i) q^{53} +(-2.48825 - 2.36244i) q^{54} +(6.77898 + 3.16945i) q^{56} +(1.71797 - 1.71797i) q^{57} +(-0.183407 - 7.07112i) q^{58} +(4.46933 + 7.74111i) q^{59} +(0.919379 - 1.59241i) q^{61} +(-9.79346 + 5.99810i) q^{62} +(3.79391 + 6.44473i) q^{63} +(7.90336 - 1.23971i) q^{64} +(-0.473126 + 0.140018i) q^{66} +(0.138137 - 0.515535i) q^{67} +(10.0210 + 2.13522i) q^{68} -1.44289i q^{69} +13.6494i q^{71} +(7.21350 + 3.44726i) q^{72} +(-1.55074 + 5.78744i) q^{73} +(-0.295575 - 0.998755i) q^{74} +(-5.30306 + 10.3951i) q^{76} +(2.21678 - 0.0187518i) q^{77} +(0.506141 + 0.826407i) q^{78} +(5.30723 - 9.19239i) q^{79} +(3.73481 + 6.46888i) q^{81} +(-0.135491 + 0.00351430i) q^{82} +(-4.36830 + 4.36830i) q^{83} +(1.64909 + 1.46124i) q^{84} +(-6.71975 + 7.07762i) q^{86} +(0.539037 - 2.01171i) q^{87} +(1.95412 - 1.34088i) q^{88} +(-2.50474 - 1.44611i) q^{89} +(-1.16244 - 4.19600i) q^{91} +(2.13834 + 6.59227i) q^{92} +(-3.26615 + 0.875163i) q^{93} +(7.41923 - 2.19567i) q^{94} +(2.33494 + 0.310349i) q^{96} +(-4.24461 + 4.24461i) q^{97} +(-5.31245 - 8.35332i) q^{98} +2.36841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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