LMFDB - Embedded newform 847.2.e.i.606.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(485,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("847.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 15 x^{18} - 14 x^{17} + 149 x^{16} - 131 x^{15} + 825 x^{14} - 595 x^{13} + 3197 x^{12} + \cdots + 1 $ x^20 - x^19 + 15x^18 - 14x^17 + 149x^16 - 131x^15 + 825x^14 - 595x^13 + 3197x^12 - 1997x^11 + 6915x^10 - 2406x^9 + 9021x^8 - 3913x^7 + 4916x^6 - 1317x^5 + 1429x^4 - 426x^3 + 205x^2 - 15x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			606.6
Root			$0.218609 + 0.378642i$ of defining polynomial
Character	$\chi$	$=$	847.606
Dual form			847.2.e.i.485.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.218609 + 0.378642i) q^{2} +(1.29176 - 2.23740i) q^{3} +(0.904420 - 1.56650i) q^{4} +(0.607894 + 1.05290i) q^{5} +1.12957 q^{6} +(-2.54037 - 0.739259i) q^{7} +1.66530 q^{8} +(-1.83731 - 3.18231i) q^{9} +O(q^{10})$	\(q+(0.218609 + 0.378642i) q^{2} +(1.29176 - 2.23740i) q^{3} +(0.904420 - 1.56650i) q^{4} +(0.607894 + 1.05290i) q^{5} +1.12957 q^{6} +(-2.54037 - 0.739259i) q^{7} +1.66530 q^{8} +(-1.83731 - 3.18231i) q^{9} +(-0.265782 + 0.460348i) q^{10} +(-2.33659 - 4.04710i) q^{12} -4.24812 q^{13} +(-0.275434 - 1.12350i) q^{14} +3.14102 q^{15} +(-1.44479 - 2.50245i) q^{16} +(2.42099 - 4.19328i) q^{17} +(0.803306 - 1.39137i) q^{18} +(1.09416 + 1.89515i) q^{19} +2.19916 q^{20} +(-4.93558 + 4.72889i) q^{21} +(-3.26652 - 5.65778i) q^{23} +(2.15117 - 3.72593i) q^{24} +(1.76093 - 3.05002i) q^{25} +(-0.928677 - 1.60852i) q^{26} -1.74290 q^{27} +(-3.45562 + 3.31090i) q^{28} +1.65791 q^{29} +(0.686656 + 1.18932i) q^{30} +(-0.0243293 + 0.0421396i) q^{31} +(2.29698 - 3.97849i) q^{32} +2.11701 q^{34} +(-0.765908 - 3.12416i) q^{35} -6.64680 q^{36} +(4.54852 + 7.87826i) q^{37} +(-0.478389 + 0.828594i) q^{38} +(-5.48756 + 9.50474i) q^{39} +(1.01232 + 1.75339i) q^{40} +0.0947390 q^{41} +(-2.86952 - 0.835042i) q^{42} +5.77210 q^{43} +(2.23378 - 3.86902i) q^{45} +(1.42818 - 2.47369i) q^{46} +(1.68230 + 2.91383i) q^{47} -7.46532 q^{48} +(5.90699 + 3.75599i) q^{49} +1.53982 q^{50} +(-6.25471 - 10.8335i) q^{51} +(-3.84208 + 6.65468i) q^{52} +(-0.141461 + 0.245018i) q^{53} +(-0.381013 - 0.659935i) q^{54} +(-4.23047 - 1.23109i) q^{56} +5.65361 q^{57} +(0.362434 + 0.627754i) q^{58} +(-5.12783 + 8.88165i) q^{59} +(2.84080 - 4.92041i) q^{60} +(2.19797 + 3.80700i) q^{61} -0.0212744 q^{62} +(2.31490 + 9.44251i) q^{63} -3.77060 q^{64} +(-2.58240 - 4.47285i) q^{65} +(-4.56257 + 7.90259i) q^{67} +(-4.37919 - 7.58498i) q^{68} -16.8783 q^{69} +(1.01550 - 0.972975i) q^{70} -5.00931 q^{71} +(-3.05966 - 5.29949i) q^{72} +(3.79948 - 6.58089i) q^{73} +(-1.98870 + 3.44452i) q^{74} +(-4.54942 - 7.87982i) q^{75} +3.95834 q^{76} -4.79853 q^{78} +(-1.75918 - 3.04700i) q^{79} +(1.75656 - 3.04245i) q^{80} +(3.26052 - 5.64738i) q^{81} +(0.0207108 + 0.0358722i) q^{82} +13.6125 q^{83} +(2.94397 + 12.0085i) q^{84} +5.88683 q^{85} +(1.26183 + 2.18556i) q^{86} +(2.14163 - 3.70941i) q^{87} +(2.34726 + 4.06558i) q^{89} +1.95330 q^{90} +(10.7918 + 3.14046i) q^{91} -11.8172 q^{92} +(0.0628554 + 0.108869i) q^{93} +(-0.735533 + 1.27398i) q^{94} +(-1.33027 + 2.30410i) q^{95} +(-5.93432 - 10.2786i) q^{96} +18.0218 q^{97} +(-0.130854 + 3.05773i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} - 18 q^{6} - 11 q^{7} + 6 q^{8} - 9 q^{9}+O(q^{10}) $ 20 * q + q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 - 18 * q^6 - 11 * q^7 + 6 * q^8 - 9 * q^9	\( 20 q + q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} - 18 q^{6} - 11 q^{7} + 6 q^{8} - 9 q^{9} + 7 q^{10} - 9 q^{12} - 2 q^{13} - 19 q^{14} - 2 q^{15} - 15 q^{16} + 19 q^{17} + 17 q^{18} + 28 q^{19} - 10 q^{20} - q^{21} - 7 q^{23} + 19 q^{24} + 8 q^{25} + 5 q^{26} + 12 q^{27} + 8 q^{28} + 30 q^{29} - 22 q^{30} + 14 q^{31} - 15 q^{32} + 24 q^{34} + 8 q^{35} + 32 q^{36} - 13 q^{37} - 24 q^{38} + 4 q^{39} + 10 q^{40} - 70 q^{41} + 25 q^{42} - 36 q^{43} - 8 q^{45} + 9 q^{46} - 16 q^{47} - 66 q^{48} - 25 q^{49} - 12 q^{50} - 21 q^{51} - 4 q^{52} + 9 q^{53} + 17 q^{54} + 12 q^{56} - 8 q^{57} + 9 q^{58} - 12 q^{59} + 21 q^{60} + 20 q^{61} - 76 q^{62} + 12 q^{63} - 58 q^{64} - 20 q^{65} - 19 q^{67} + 56 q^{68} + 18 q^{69} + 21 q^{70} + 30 q^{71} - 4 q^{72} + 3 q^{73} + 42 q^{74} + 27 q^{75} - 48 q^{76} - 50 q^{78} - 32 q^{79} + 6 q^{80} + 46 q^{81} + 18 q^{82} - 58 q^{83} + 73 q^{84} + 46 q^{85} - 9 q^{86} + 24 q^{87} - 5 q^{89} - 24 q^{90} + 28 q^{91} + 30 q^{92} + q^{93} - 19 q^{94} + q^{95} + 46 q^{96} + 8 q^{97} + 58 q^{98}+O(q^{100}) \) 20 * q + q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 - 18 * q^6 - 11 * q^7 + 6 * q^8 - 9 * q^9 + 7 * q^10 - 9 * q^12 - 2 * q^13 - 19 * q^14 - 2 * q^15 - 15 * q^16 + 19 * q^17 + 17 * q^18 + 28 * q^19 - 10 * q^20 - q^21 - 7 * q^23 + 19 * q^24 + 8 * q^25 + 5 * q^26 + 12 * q^27 + 8 * q^28 + 30 * q^29 - 22 * q^30 + 14 * q^31 - 15 * q^32 + 24 * q^34 + 8 * q^35 + 32 * q^36 - 13 * q^37 - 24 * q^38 + 4 * q^39 + 10 * q^40 - 70 * q^41 + 25 * q^42 - 36 * q^43 - 8 * q^45 + 9 * q^46 - 16 * q^47 - 66 * q^48 - 25 * q^49 - 12 * q^50 - 21 * q^51 - 4 * q^52 + 9 * q^53 + 17 * q^54 + 12 * q^56 - 8 * q^57 + 9 * q^58 - 12 * q^59 + 21 * q^60 + 20 * q^61 - 76 * q^62 + 12 * q^63 - 58 * q^64 - 20 * q^65 - 19 * q^67 + 56 * q^68 + 18 * q^69 + 21 * q^70 + 30 * q^71 - 4 * q^72 + 3 * q^73 + 42 * q^74 + 27 * q^75 - 48 * q^76 - 50 * q^78 - 32 * q^79 + 6 * q^80 + 46 * q^81 + 18 * q^82 - 58 * q^83 + 73 * q^84 + 46 * q^85 - 9 * q^86 + 24 * q^87 - 5 * q^89 - 24 * q^90 + 28 * q^91 + 30 * q^92 + q^93 - 19 * q^94 + q^95 + 46 * q^96 + 8 * q^97 + 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.218609	+	0.378642i	0.154580	+	0.267741i	0.932906	−	0.360120i	$-0.117264\pi$
$2$	0.218609	+	0.378642i	0.154580	+	0.267741i	−0.778326	+	0.627860i	$0.783931\pi$
$3$	1.29176	−	2.23740i	0.745800	−	1.29176i	−0.204019	−	0.978967i	$-0.565401\pi$
$3$	1.29176	−	2.23740i	0.745800	−	1.29176i	0.949820	−	0.312797i	$-0.101266\pi$
$4$	0.904420	−	1.56650i	0.452210	−	0.783251i
$5$	0.607894	+	1.05290i	0.271858	+	0.470872i	0.969338	−	0.245733i	$-0.0790285\pi$
$5$	0.607894	+	1.05290i	0.271858	+	0.470872i	−0.697479	+	0.716605i	$0.745695\pi$
$6$	1.12957			0.461143
$7$	−2.54037	−	0.739259i	−0.960171	−	0.279414i
$7$	−2.54037	−	0.739259i	−0.960171	−	0.279414i
$8$	1.66530			0.588771
$9$	−1.83731	−	3.18231i	−0.612436	−	1.06077i
$10$	−0.265782	+	0.460348i	−0.0840477	+	0.145575i
$11$		0			0
$11$		0			0
$12$	−2.33659	−	4.04710i	−0.674517	−	1.16830i
$13$	−4.24812			−1.17822			−0.589108	−	0.808055i	$-0.700521\pi$
$13$	−4.24812			−1.17822			−0.589108	+	0.808055i	$0.700521\pi$
$14$	−0.275434	−	1.12350i	−0.0736129	−	0.300268i
$15$	3.14102			0.811008
$16$	−1.44479	−	2.50245i	−0.361198	−	0.625613i
$17$	2.42099	−	4.19328i	0.587177	−	1.01702i	−0.407423	−	0.913240i	$-0.633572\pi$
$17$	2.42099	−	4.19328i	0.587177	−	1.01702i	0.994600	−	0.103781i	$-0.0330942\pi$
$18$	0.803306	−	1.39137i	0.189341	−	0.327948i
$19$	1.09416	+	1.89515i	0.251018	+	0.434777i	0.963806	−	0.266603i	$-0.0859012\pi$
$19$	1.09416	+	1.89515i	0.251018	+	0.434777i	−0.712788	+	0.701380i	$0.752568\pi$
$20$	2.19916			0.491748
$21$	−4.93558	+	4.72889i	−1.07703	+	1.03193i
$22$		0			0
$23$	−3.26652	−	5.65778i	−0.681117	−	1.17973i	−0.974640	−	0.223777i	$-0.928161\pi$
$23$	−3.26652	−	5.65778i	−0.681117	−	1.17973i	0.293524	−	0.955952i	$-0.405172\pi$
$24$	2.15117	−	3.72593i	0.439105	−	0.760553i
$25$	1.76093	−	3.05002i	0.352186	−	0.610004i
$26$	−0.928677	−	1.60852i	−0.182129	−	0.315456i
$27$	−1.74290			−0.335421
$28$	−3.45562	+	3.31090i	−0.653050	+	0.625701i
$29$	1.65791			0.307866			0.153933	−	0.988081i	$-0.450806\pi$
$29$	1.65791			0.307866			0.153933	+	0.988081i	$0.450806\pi$
$30$	0.686656	+	1.18932i	0.125366	+	0.217140i
$31$	−0.0243293	+	0.0421396i	−0.00436967	+	0.00756849i	−0.868202	−	0.496211i	$-0.834724\pi$
$31$	−0.0243293	+	0.0421396i	−0.00436967	+	0.00756849i	0.863832	+	0.503779i	$0.168058\pi$
$32$	2.29698	−	3.97849i	0.406053	−	0.703305i
$33$		0			0
$34$	2.11701			0.363064
$35$	−0.765908	−	3.12416i	−0.129462	−	0.528079i
$36$	−6.64680			−1.10780
$37$	4.54852	+	7.87826i	0.747772	+	1.29518i	0.948889	+	0.315611i	$0.102210\pi$
$37$	4.54852	+	7.87826i	0.747772	+	1.29518i	−0.201117	+	0.979567i	$0.564457\pi$
$38$	−0.478389	+	0.828594i	−0.0776049	+	0.134416i
$39$	−5.48756	+	9.50474i	−0.878713	+	1.52198i
$40$	1.01232	+	1.75339i	0.160062	+	0.277236i
$41$	0.0947390			0.0147957			0.00739787	−	0.999973i	$-0.497645\pi$
$41$	0.0947390			0.0147957			0.00739787	+	0.999973i	$0.497645\pi$
$42$	−2.86952	−	0.835042i	−0.442776	−	0.128850i
$43$	5.77210			0.880237			0.440118	−	0.897940i	$-0.354936\pi$
$43$	5.77210			0.880237			0.440118	+	0.897940i	$0.354936\pi$
$44$		0			0
$45$	2.23378	−	3.86902i	0.332992	−	0.576759i
$46$	1.42818	−	2.47369i	0.210574	−	0.364725i
$47$	1.68230	+	2.91383i	0.245389	+	0.425026i	0.962241	−	0.272199i	$-0.0877510\pi$
$47$	1.68230	+	2.91383i	0.245389	+	0.425026i	−0.716852	+	0.697225i	$0.754418\pi$
$48$	−7.46532			−1.07753
$49$	5.90699	+	3.75599i	0.843856	+	0.536570i
$50$	1.53982			0.217764
$51$	−6.25471	−	10.8335i	−0.875834	−	1.51699i
$52$	−3.84208	+	6.65468i	−0.532801	+	0.922838i
$53$	−0.141461	+	0.245018i	−0.0194312	+	0.0336559i	−0.875578	−	0.483078i	$-0.839519\pi$
$53$	−0.141461	+	0.245018i	−0.0194312	+	0.0336559i	0.856146	+	0.516734i	$0.172852\pi$
$54$	−0.381013	−	0.659935i	−0.0518494	−	0.0898057i
$55$		0			0
$56$	−4.23047	−	1.23109i	−0.565320	−	0.164511i
$57$	5.65361			0.748839
$58$	0.362434	+	0.627754i	0.0475899	+	0.0824282i
$59$	−5.12783	+	8.88165i	−0.667586	+	1.15629i	0.310991	+	0.950413i	$0.399339\pi$
$59$	−5.12783	+	8.88165i	−0.667586	+	1.15629i	−0.978577	+	0.205880i	$0.933994\pi$
$60$	2.84080	−	4.92041i	0.366746	−	0.635223i
$61$	2.19797	+	3.80700i	0.281421	+	0.487436i	0.971735	−	0.236074i	$-0.0758608\pi$
$61$	2.19797	+	3.80700i	0.281421	+	0.487436i	−0.690314	+	0.723510i	$0.742528\pi$
$62$	−0.0212744			−0.00270185
$63$	2.31490	+	9.44251i	0.291650	+	1.18964i
$64$	−3.77060			−0.471325
$65$	−2.58240	−	4.47285i	−0.320308	−	0.554789i
$66$		0			0
$67$	−4.56257	+	7.90259i	−0.557406	+	0.965456i	0.440306	+	0.897848i	$0.354870\pi$
$67$	−4.56257	+	7.90259i	−0.557406	+	0.965456i	−0.997712	+	0.0676078i	$0.978463\pi$
$68$	−4.37919	−	7.58498i	−0.531055	−	0.919814i
$69$	−16.8783			−2.03191
$70$	1.01550	−	0.972975i	0.121376	−	0.116293i
$71$	−5.00931			−0.594496			−0.297248	−	0.954800i	$-0.596069\pi$
$71$	−5.00931			−0.594496			−0.297248	+	0.954800i	$0.596069\pi$
$72$	−3.05966	−	5.29949i	−0.360585	−	0.624551i
$73$	3.79948	−	6.58089i	0.444696	−	0.770235i	−0.553335	−	0.832959i	$-0.686645\pi$
$73$	3.79948	−	6.58089i	0.444696	−	0.770235i	0.998031	+	0.0627232i	$0.0199785\pi$
$74$	−1.98870	+	3.44452i	−0.231181	+	0.400418i
$75$	−4.54942	−	7.87982i	−0.525321	−	0.909883i
$76$	3.95834			0.454052
$77$		0			0
$78$	−4.79853			−0.543326
$79$	−1.75918	−	3.04700i	−0.197924	−	0.342814i	0.749931	−	0.661516i	$-0.230086\pi$
$79$	−1.75918	−	3.04700i	−0.197924	−	0.342814i	−0.947855	+	0.318702i	$0.896753\pi$
$80$	1.75656	−	3.04245i	0.196389	−	0.340156i
$81$	3.26052	−	5.64738i	0.362280	−	0.627487i
$82$	0.0207108	+	0.0358722i	0.00228713	+	0.00396142i
$83$	13.6125			1.49417			0.747085	−	0.664729i	$-0.231453\pi$
$83$	13.6125			1.49417			0.747085	+	0.664729i	$0.231453\pi$
$84$	2.94397	+	12.0085i	0.321213	+	1.31023i
$85$	5.88683			0.638516
$86$	1.26183	+	2.18556i	0.136067	+	0.235675i
$87$	2.14163	−	3.70941i	0.229607	−	0.397690i
$88$		0			0
$89$	2.34726	+	4.06558i	0.248810	+	0.430951i	0.963196	−	0.268801i	$-0.0866274\pi$
$89$	2.34726	+	4.06558i	0.248810	+	0.430951i	−0.714386	+	0.699752i	$0.753294\pi$
$90$	1.95330			0.205896
$91$	10.7918	+	3.14046i	1.13129	+	0.329210i
$92$	−11.8172			−1.23203
$93$	0.0628554	+	0.108869i	0.00651780	+	0.0112892i
$94$	−0.735533	+	1.27398i	−0.0758645	+	0.131401i
$95$	−1.33027	+	2.30410i	−0.136483	+	0.236395i
$96$	−5.93432	−	10.2786i	−0.605669	−	1.04905i
$97$	18.0218			1.82983			0.914917	−	0.403642i	$-0.132256\pi$
$97$	18.0218			1.82983			0.914917	+	0.403642i	$0.132256\pi$
$98$	−0.130854	+	3.05773i	−0.0132182	+	0.308877i
$99$		0			0
$100$	−3.18524	−	5.51700i	−0.318524	−	0.551700i
$101$	−7.77994	+	13.4753i	−0.774133	+	1.34084i	0.161147	+	0.986930i	$0.448481\pi$
$101$	−7.77994	+	13.4753i	−0.774133	+	1.34084i	−0.935280	+	0.353908i	$0.884853\pi$
$102$	2.73467	−	4.73659i	0.270773	−	0.468993i
$103$	−2.15152	−	3.72654i	−0.211996	−	0.367187i	0.740343	−	0.672229i	$-0.234663\pi$
$103$	−2.15152	−	3.72654i	−0.211996	−	0.367187i	−0.952339	+	0.305042i	$0.901330\pi$
$104$	−7.07437			−0.693699
$105$	−7.97936	−	2.32203i	−0.778706	−	0.226607i
$106$	−0.123699			−0.0120147
$107$	−2.92337	−	5.06342i	−0.282613	−	0.489500i	0.689415	−	0.724367i	$-0.257868\pi$
$107$	−2.92337	−	5.06342i	−0.282613	−	0.489500i	−0.972027	+	0.234867i	$0.924534\pi$
$108$	−1.57631	+	2.73025i	−0.151681	+	0.262719i
$109$	−2.76027	+	4.78093i	−0.264386	+	0.457930i	−0.967403	−	0.253244i	$-0.918503\pi$
$109$	−2.76027	+	4.78093i	−0.264386	+	0.457930i	0.703017	+	0.711173i	$0.251836\pi$
$110$		0			0
$111$	23.5024			2.23075
$112$	1.82035	+	7.42524i	0.172007	+	0.701619i
$113$	12.1237			1.14050			0.570250	−	0.821471i	$-0.306846\pi$
$113$	12.1237			1.14050			0.570250	+	0.821471i	$0.306846\pi$
$114$	1.23593	+	2.14069i	0.115756	+	0.200494i
$115$	3.97139	−	6.87866i	0.370334	−	0.641438i
$116$	1.49945	−	2.59712i	0.139220	−	0.241136i
$117$	7.80510	+	13.5188i	0.721582	+	1.24982i
$118$	−4.48396			−0.412782
$119$	−9.25015	+	8.86277i	−0.847960	+	0.812448i
$120$	5.23073			0.477498
$121$		0			0
$122$	−0.960993	+	1.66449i	−0.0870042	+	0.150696i
$123$	0.122380	−	0.211969i	0.0110347	−	0.0191126i
$124$	0.0440078	+	0.0762237i	0.00395202	+	0.00684509i
$125$	10.3608			0.926695
$126$	−3.06928	+	2.94074i	−0.273433	+	0.261982i
$127$	10.7484			0.953768			0.476884	−	0.878966i	$-0.341766\pi$
$127$	10.7484			0.953768			0.476884	+	0.878966i	$0.341766\pi$
$128$	−5.41826	−	9.38469i	−0.478911	−	0.829498i
$129$	7.45619	−	12.9145i	0.656481	−	1.13706i
$130$	1.12907	−	1.95561i	0.0990263	−	0.171519i
$131$	2.57533	+	4.46059i	0.225007	+	0.389724i	0.956322	−	0.292317i	$-0.0944261\pi$
$131$	2.57533	+	4.46059i	0.225007	+	0.389724i	−0.731314	+	0.682040i	$0.761093\pi$
$132$		0			0
$133$	−1.37858	−	5.62325i	−0.119538	−	0.487598i
$134$	−3.98967			−0.344655
$135$	−1.05950	−	1.83510i	−0.0911869	−	0.157940i
$136$	4.03167	−	6.98306i	0.345713	−	0.598792i
$137$	−2.90245	+	5.02718i	−0.247973	+	0.429501i	−0.962963	−	0.269633i	$-0.913098\pi$
$137$	−2.90245	+	5.02718i	−0.247973	+	0.429501i	0.714990	+	0.699134i	$0.246431\pi$
$138$	−3.68975	−	6.39084i	−0.314093	−	0.544024i
$139$	−12.6510			−1.07304			−0.536522	−	0.843887i	$-0.680262\pi$
$139$	−12.6510			−1.07304			−0.536522	+	0.843887i	$0.680262\pi$
$140$	−5.58670	−	1.62575i	−0.472162	−	0.137401i
$141$	8.69255			0.732045
$142$	−1.09508	−	1.89674i	−0.0918972	−	0.159171i
$143$		0			0
$144$	−5.30906	+	9.19556i	−0.442421	+	0.766296i
$145$	1.00783	+	1.74562i	0.0836959	+	0.144966i
$146$	3.32241			0.274964
$147$	16.0341	−	8.36446i	1.32247	−	0.689889i
$148$	16.4551			1.35260
$149$	−7.56130	−	13.0966i	−0.619446	−	1.07291i	−0.989587	−	0.143936i	$-0.954024\pi$
$149$	−7.56130	−	13.0966i	−0.619446	−	1.07291i	0.370141	−	0.928976i	$-0.379309\pi$
$150$	1.98909	−	3.44520i	0.162408	−	0.281300i
$151$	10.4489	−	18.0981i	0.850322	−	1.47280i	−0.0305954	−	0.999532i	$-0.509740\pi$
$151$	10.4489	−	18.0981i	0.850322	−	1.47280i	0.880918	−	0.473270i	$-0.156926\pi$
$152$	1.82211	+	3.15598i	0.147792	+	0.255984i
$153$	−17.7925			−1.43844
$154$		0			0
$155$	−0.0591584			−0.00475172
$156$	9.92612	+	17.1926i	0.794726	+	1.37651i
$157$	−3.55324	+	6.15439i	−0.283579	+	0.491173i	−0.972264	−	0.233888i	$-0.924855\pi$
$157$	−3.55324	+	6.15439i	−0.283579	+	0.491173i	0.688685	+	0.725061i	$0.258189\pi$
$158$	0.769148	−	1.33220i	0.0611901	−	0.105984i
$159$	0.365470	+	0.633012i	0.0289836	+	0.0502011i
$160$	5.58529			0.441556
$161$	4.11562	+	16.7877i	0.324356	+	1.32305i
$162$	2.85112			0.224005
$163$	−2.39164	−	4.14244i	−0.187328	−	0.324461i	0.757031	−	0.653379i	$-0.226649\pi$
$163$	−2.39164	−	4.14244i	−0.187328	−	0.324461i	−0.944358	+	0.328918i	$0.893316\pi$
$164$	0.0856838	−	0.148409i	0.00669078	−	0.0115888i
$165$		0			0
$166$	2.97582	+	5.15428i	0.230969	+	0.400050i
$167$	0.210556			0.0162933			0.00814667	−	0.999967i	$-0.497407\pi$
$167$	0.210556			0.0162933			0.00814667	+	0.999967i	$0.497407\pi$
$168$	−8.21920	+	7.87499i	−0.634125	+	0.607569i
$169$	5.04649			0.388191
$170$	1.28691	+	2.22900i	0.0987018	+	0.170957i
$171$	4.02064	−	6.96395i	0.307466	−	0.532546i
$172$	5.22040	−	9.04200i	0.398052	−	0.689446i
$173$	8.97585	+	15.5466i	0.682422	+	1.18199i	0.974240	+	0.225515i	$0.0724065\pi$
$173$	8.97585	+	15.5466i	0.682422	+	1.18199i	−0.291818	+	0.956474i	$0.594260\pi$
$174$	1.87272			0.141970
$175$	−6.72818	+	6.44641i	−0.508603	+	0.487303i
$176$		0			0
$177$	13.2479	+	22.9460i	0.995772	+	1.72473i
$178$	−1.02627	+	1.77755i	−0.0769220	+	0.133233i
$179$	1.97205	−	3.41569i	0.147398	−	0.255301i	−0.782867	−	0.622189i	$-0.786244\pi$
$179$	1.97205	−	3.41569i	0.147398	−	0.255301i	0.930265	+	0.366888i	$0.119577\pi$
$180$	−4.04055	−	6.99843i	−0.301164	−	0.521632i
$181$	−4.72727			−0.351375			−0.175688	−	0.984446i	$-0.556215\pi$
$181$	−4.72727			−0.351375			−0.175688	+	0.984446i	$0.556215\pi$
$182$	1.17008	+	4.77276i	0.0867318	+	0.353781i
$183$	11.3570			0.839536
$184$	−5.43972	−	9.42187i	−0.401022	−	0.694590i
$185$	−5.53003	+	9.57829i	−0.406576	+	0.704210i
$186$	−0.0274815	+	0.0475994i	−0.00201504	+	0.00349016i
$187$		0			0
$188$	6.08603			0.443869
$189$	4.42761	+	1.28845i	0.322061	+	0.0937212i
$190$	−1.16324			−0.0843901
$191$	−8.34025	−	14.4457i	−0.603479	−	1.04526i	−0.992290	−	0.123939i	$-0.960447\pi$
$191$	−8.34025	−	14.4457i	−0.603479	−	1.04526i	0.388810	−	0.921318i	$-0.372886\pi$
$192$	−4.87072	+	8.43634i	−0.351514	+	0.608840i
$193$	−5.56973	+	9.64706i	−0.400918	+	0.694410i	−0.993837	−	0.110852i	$-0.964642\pi$
$193$	−5.56973	+	9.64706i	−0.400918	+	0.694410i	0.592919	+	0.805262i	$0.297975\pi$
$194$	3.93973	+	6.82380i	0.282856	+	0.489921i
$195$	−13.3434			−0.955542
$196$	11.2262	−	5.85632i	0.801869	−	0.418308i
$197$	−3.23277			−0.230325			−0.115163	−	0.993347i	$-0.536739\pi$
$197$	−3.23277			−0.230325			−0.115163	+	0.993347i	$0.536739\pi$
$198$		0			0
$199$	0.736849	−	1.27626i	0.0522338	−	0.0904716i	−0.838726	−	0.544553i	$-0.816699\pi$
$199$	0.736849	−	1.27626i	0.0522338	−	0.0904716i	0.890960	+	0.454082i	$0.150033\pi$
$200$	2.93247	−	5.07919i	0.207357	−	0.359153i
$201$	11.7875	+	20.4166i	0.831427	+	1.44007i
$202$	−6.80307			−0.478662
$203$	−4.21171	−	1.22562i	−0.295604	−	0.0860220i
$204$	−22.6275			−1.58424
$205$	0.0575912	+	0.0997509i	0.00402234	+	0.00696690i
$206$	0.940684	−	1.62931i	0.0655406	−	0.113520i
$207$	−12.0032	+	20.7902i	−0.834282	+	1.44502i
$208$	6.13764	+	10.6307i	0.425569	+	0.737107i
$209$		0			0
$210$	−0.865144	−	3.52894i	−0.0597006	−	0.243520i
$211$	−0.173168			−0.0119214			−0.00596070	−	0.999982i	$-0.501897\pi$
$211$	−0.173168			−0.0119214			−0.00596070	+	0.999982i	$0.501897\pi$
$212$	0.255881	+	0.443199i	0.0175740	+	0.0304390i
$213$	−6.47085	+	11.2078i	−0.443375	+	0.767948i
$214$	1.27815	−	2.21382i	0.0873726	−	0.151334i
$215$	3.50882	+	6.07746i	0.239300	+	0.414479i
$216$	−2.90244			−0.197486
$217$	0.0929575	−	0.0890645i	0.00631037	−	0.00604609i
$218$	−2.41368			−0.163475
$219$	−9.81607	−	17.0019i	−0.663308	−	1.14888i
$220$		0			0
$221$	−10.2847	+	17.8136i	−0.691821	+	1.19827i
$222$	5.13785	+	8.89902i	0.344830	+	0.597263i
$223$	−5.12899			−0.343462			−0.171731	−	0.985144i	$-0.554936\pi$
$223$	−5.12899			−0.343462			−0.171731	+	0.985144i	$0.554936\pi$
$224$	−8.77634	+	8.40879i	−0.586394	+	0.561836i
$225$	−12.9415			−0.862767
$226$	2.65035	+	4.59054i	0.176298	+	0.305358i
$227$	−12.7096	+	22.0137i	−0.843568	+	1.46110i	0.0432915	+	0.999062i	$0.486216\pi$
$227$	−12.7096	+	22.0137i	−0.843568	+	1.46110i	−0.886859	+	0.462040i	$0.847118\pi$
$228$	5.11324	−	8.85639i	0.338632	−	0.586528i
$229$	5.79873	+	10.0437i	0.383191	+	0.663706i	0.991516	−	0.129982i	$-0.0414918\pi$
$229$	5.79873	+	10.0437i	0.383191	+	0.663706i	−0.608326	+	0.793688i	$0.708158\pi$
$230$	3.47273			0.228985
$231$		0			0
$232$	2.76091			0.181262
$233$	−5.98576	−	10.3676i	−0.392140	−	0.679207i	0.600591	−	0.799556i	$-0.294932\pi$
$233$	−5.98576	−	10.3676i	−0.392140	−	0.679207i	−0.992732	+	0.120349i	$0.961599\pi$
$234$	−3.41253	+	5.91068i	−0.223084	+	0.386393i
$235$	−2.04532	+	3.54260i	−0.133422	+	0.231094i
$236$	9.27542	+	16.0655i	0.603778	+	1.04577i
$237$	−9.08980			−0.590446
$238$	−5.37799	−	1.56502i	−0.348603	−	0.101445i
$239$	−15.9932			−1.03452			−0.517258	−	0.855829i	$-0.673047\pi$
$239$	−15.9932			−1.03452			−0.517258	+	0.855829i	$0.673047\pi$
$240$	−4.53812	−	7.86025i	−0.292934	−	0.507377i
$241$	3.89795	−	6.75145i	0.251089	−	0.434899i	−0.712737	−	0.701432i	$-0.752545\pi$
$241$	3.89795	−	6.75145i	0.251089	−	0.434899i	0.963826	+	0.266532i	$0.0858779\pi$
$242$		0			0
$243$	−11.0380	−	19.1183i	−0.708087	−	1.22644i
$244$	7.95155			0.509046
$245$	−0.363869	+	8.50273i	−0.0232467	+	0.543219i
$246$	0.107014			0.00682296
$247$	−4.64814	−	8.05081i	−0.295754	−	0.512261i
$248$	−0.0405154	+	0.0701748i	−0.00257273	+	0.00445610i
$249$	17.5842	−	30.4567i	1.11435	−	1.93011i
$250$	2.26496	+	3.92303i	0.143249	+	0.248114i
$251$	−13.4311			−0.847764			−0.423882	−	0.905717i	$-0.639333\pi$
$251$	−13.4311			−0.847764			−0.423882	+	0.905717i	$0.639333\pi$
$252$	16.8853	+	4.91371i	1.06368	+	0.309535i
$253$		0			0
$254$	2.34970	+	4.06980i	0.147433	+	0.255362i
$255$	7.60439	−	13.1712i	0.476205	−	0.824812i
$256$	−1.40164	+	2.42770i	−0.0876022	+	0.151732i
$257$	5.49788	+	9.52260i	0.342948	+	0.594004i	0.984979	−	0.172675i	$-0.0552411\pi$
$257$	5.49788	+	9.52260i	0.342948	+	0.594004i	−0.642031	+	0.766679i	$0.721908\pi$
$258$	6.51997			0.405916
$259$	−5.73085	−	23.3763i	−0.356098	−	1.45253i
$260$	−9.34230			−0.579385
$261$	−3.04609	−	5.27599i	−0.188548	−	0.326575i
$262$	−1.12598	+	1.95025i	−0.0695633	+	0.120487i
$263$	15.1005	−	26.1548i	0.931136	−	1.61278i	0.149753	−	0.988723i	$-0.452152\pi$
$263$	15.1005	−	26.1548i	0.931136	−	1.61278i	0.781383	−	0.624052i	$-0.214515\pi$
$264$		0			0
$265$	−0.343974			−0.0211302
$266$	1.82783	−	1.75128i	0.112072	−	0.107378i
$267$	12.1284			0.742249
$268$	8.25295	+	14.2945i	0.504129	+	0.873177i
$269$	−2.35137	+	4.07269i	−0.143365	+	0.248316i	−0.928762	−	0.370677i	$-0.879126\pi$
$269$	−2.35137	+	4.07269i	−0.143365	+	0.248316i	0.785396	+	0.618993i	$0.212459\pi$
$270$	0.463231	−	0.802340i	0.0281914	−	0.0488289i
$271$	4.61243	+	7.98896i	0.280185	+	0.485295i	0.971430	−	0.237326i	$-0.0762709\pi$
$271$	4.61243	+	7.98896i	0.280185	+	0.485295i	−0.691245	+	0.722620i	$0.742938\pi$
$272$	−13.9913			−0.848349
$273$	20.9669	−	20.0889i	1.26898	−	1.21583i
$274$	−2.53801			−0.153327
$275$		0			0
$276$	−15.2651	+	26.4399i	−0.918849	+	1.59149i
$277$	−4.59581	+	7.96018i	−0.276136	+	0.478281i	−0.970421	−	0.241419i	$-0.922387\pi$
$277$	−4.59581	+	7.96018i	−0.276136	+	0.478281i	0.694285	+	0.719700i	$0.255721\pi$
$278$	−2.76562	−	4.79020i	−0.165871	−	0.287297i
$279$	0.178802			0.0107046
$280$	−1.27546	−	5.20264i	−0.0762235	−	0.310917i
$281$	5.45750			0.325567			0.162783	−	0.986662i	$-0.447953\pi$
$281$	5.45750			0.325567			0.162783	+	0.986662i	$0.447953\pi$
$282$	1.90027	+	3.29137i	0.113160	+	0.195998i
$283$	−8.31216	+	14.3971i	−0.494106	+	0.855817i	−0.999977	−	0.00679200i	$-0.997838\pi$
$283$	−8.31216	+	14.3971i	−0.494106	+	0.855817i	0.505871	+	0.862609i	$0.331171\pi$
$284$	−4.53052	+	7.84709i	−0.268837	+	0.465639i
$285$	3.43679	+	5.95270i	0.203578	+	0.352607i
$286$		0			0
$287$	−0.240672	−	0.0700367i	−0.0142064	−	0.00413413i
$288$	−16.8811			−0.994727
$289$	−3.22243	−	5.58141i	−0.189554	−	0.328318i
$290$	−0.440643	+	0.763216i	−0.0258754	+	0.0448176i
$291$	23.2799	−	40.3219i	1.36469	−	2.36371i
$292$	−6.87265	−	11.9038i	−0.402192	−	0.696616i
$293$	−28.9378			−1.69056			−0.845282	−	0.534320i	$-0.820568\pi$
$293$	−28.9378			−1.69056			−0.845282	+	0.534320i	$0.820568\pi$
$294$	6.67234	+	4.24264i	0.389139	+	0.247436i
$295$	−12.4687			−0.725955
$296$	7.57462	+	13.1196i	0.440266	+	0.762563i
$297$		0			0
$298$	3.30594	−	5.72606i	0.191508	−	0.331702i
$299$	13.8766	+	24.0349i	0.802502	+	1.38997i
$300$	−16.4583			−0.950222
$301$	−14.6633	−	4.26708i	−0.845178	−	0.245950i
$302$	9.13693			0.525771
$303$	20.0997	+	34.8137i	1.15470	+	2.00000i
$304$	3.16168	−	5.47619i	0.181335	−	0.314081i
$305$	−2.67226	+	4.62850i	−0.153013	+	0.265027i
$306$	−3.88960	−	6.73698i	−0.222353	−	0.385127i
$307$	−19.8610			−1.13353			−0.566764	−	0.823880i	$-0.691805\pi$
$307$	−19.8610			−1.13353			−0.566764	+	0.823880i	$0.691805\pi$
$308$		0			0
$309$	−11.1170			−0.632425
$310$	−0.0129326	−	0.0223999i	−0.000734521	−	0.00127223i
$311$	−0.0860813	+	0.149097i	−0.00488122	+	0.00845452i	−0.868456	−	0.495767i	$-0.834887\pi$
$311$	−0.0860813	+	0.149097i	−0.00488122	+	0.00845452i	0.863574	+	0.504221i	$0.168220\pi$
$312$	−9.13841	+	15.8282i	−0.517361	+	0.896095i
$313$	−0.174666	−	0.302531i	−0.00987272	−	0.0171001i	0.861047	−	0.508526i	$-0.169809\pi$
$313$	−0.174666	−	0.302531i	−0.00987272	−	0.0171001i	−0.870920	+	0.491426i	$0.836476\pi$
$314$	−3.10708			−0.175343
$315$	−8.53483	+	8.17740i	−0.480883	+	0.460744i
$316$	−6.36417			−0.358012
$317$	11.7931	+	20.4263i	0.662369	+	1.14726i	0.979991	+	0.199040i	$0.0637823\pi$
$317$	11.7931	+	20.4263i	0.662369	+	1.14726i	−0.317622	+	0.948217i	$0.602884\pi$
$318$	−0.159790	+	0.276765i	−0.00896058	+	0.0155202i
$319$		0			0
$320$	−2.29212	−	3.97007i	−0.128133	−	0.221934i
$321$	−15.1052			−0.843091
$322$	−5.45681	+	5.22829i	−0.304096	+	0.291361i
$323$	10.5959			0.589569
$324$	−5.89775	−	10.2152i	−0.327653	−	0.567511i
$325$	−7.48064	+	12.9568i	−0.414951	+	0.718716i
$326$	1.04567	−	1.81115i	0.0579143	−	0.100310i
$327$	7.13123	+	12.3517i	0.394358	+	0.683048i
$328$	0.157768			0.00871130
$329$	−2.11960	−	8.64588i	−0.116857	−	0.476663i
$330$		0			0
$331$	5.45719	+	9.45213i	0.299954	+	0.519536i	0.976125	−	0.217209i	$-0.0696952\pi$
$331$	5.45719	+	9.45213i	0.299954	+	0.519536i	−0.676171	+	0.736745i	$0.736362\pi$
$332$	12.3114	−	21.3240i	0.675678	−	1.17031i
$333$	16.7141	−	28.9496i	0.915925	−	1.58643i
$334$	0.0460296	+	0.0797256i	0.00251863	+	0.00436239i
$335$	−11.0942			−0.606142
$336$	18.9647	+	5.51881i	1.03461	+	0.301076i
$337$	31.2495			1.70227			0.851133	−	0.524950i	$-0.175916\pi$
$337$	31.2495			1.70227			0.851133	+	0.524950i	$0.175916\pi$
$338$	1.10321	+	1.91081i	0.0600066	+	0.103935i
$339$	15.6609	−	27.1255i	0.850585	−	1.47326i
$340$	5.32416	−	9.22172i	0.288743	−	0.500118i
$341$		0			0
$342$	3.51579			0.190112
$343$	−12.2293	−	13.9084i	−0.660321	−	0.750984i
$344$	9.61225			0.518258
$345$	−10.2602	−	17.7712i	−0.552391	−	0.956770i
$346$	−3.92441	+	6.79728i	−0.210978	+	0.365424i
$347$	12.1789	−	21.0945i	0.653799	−	1.13241i	−0.328394	−	0.944541i	$-0.606507\pi$
$347$	12.1789	−	21.0945i	0.653799	−	1.13241i	0.982193	−	0.187873i	$-0.0601593\pi$
$348$	−3.87386	−	6.70973i	−0.207661	−	0.359679i
$349$	23.0111			1.23176			0.615879	−	0.787841i	$-0.288801\pi$
$349$	23.0111			1.23176			0.615879	+	0.787841i	$0.288801\pi$
$350$	−3.91172	−	1.13833i	−0.209090	−	0.0608462i
$351$	7.40403			0.395198
$352$		0			0
$353$	6.05269	−	10.4836i	0.322152	−	0.557984i	−0.658779	−	0.752336i	$-0.728927\pi$
$353$	6.05269	−	10.4836i	0.322152	−	0.557984i	0.980932	+	0.194352i	$0.0622603\pi$
$354$	−5.79222	+	10.0324i	−0.307853	+	0.533217i
$355$	−3.04513	−	5.27432i	−0.161619	−	0.279932i
$356$	8.49165			0.450057
$357$	7.88054	+	32.1449i	0.417083	+	1.70129i
$358$	1.72443			0.0911391
$359$	4.59894	+	7.96559i	0.242723	+	0.420408i	0.961489	−	0.274844i	$-0.0886262\pi$
$359$	4.59894	+	7.96559i	0.242723	+	0.420408i	−0.718766	+	0.695252i	$0.755293\pi$
$360$	3.71990	−	6.44305i	0.196056	−	0.339579i
$361$	7.10561	−	12.3073i	0.373979	−	0.647751i
$362$	−1.03343	−	1.78994i	−0.0543156	−	0.0940774i
$363$		0			0
$364$	14.6799	−	14.0651i	0.769433	−	0.737210i
$365$	9.23872			0.483577
$366$	2.48275	+	4.30025i	0.129776	+	0.224778i
$367$	15.0319	−	26.0360i	0.784658	−	1.35907i	−0.144545	−	0.989498i	$-0.546172\pi$
$367$	15.0319	−	26.0360i	0.784658	−	1.35907i	0.929203	−	0.369569i	$-0.120495\pi$
$368$	−9.43888	+	16.3486i	−0.492036	+	0.852231i
$369$	−0.174065	−	0.301489i	−0.00906145	−	0.0156949i
$370$	−4.83566			−0.251394
$371$	0.540497	−	0.517862i	0.0280612	−	0.0268860i
$372$	0.227391			0.0117897
$373$	7.35958	+	12.7472i	0.381065	+	0.660023i	0.991215	−	0.132263i	$-0.0422242\pi$
$373$	7.35958	+	12.7472i	0.381065	+	0.660023i	−0.610150	+	0.792286i	$0.708891\pi$
$374$		0			0
$375$	13.3837	−	23.1812i	0.691130	−	1.19707i
$376$	2.80153	+	4.85239i	0.144478	+	0.250243i
$377$	−7.04299			−0.362732
$378$	0.480053	+	1.95815i	0.0246913	+	0.100716i
$379$	−2.06187			−0.105911			−0.0529555	−	0.998597i	$-0.516864\pi$
$379$	−2.06187			−0.105911			−0.0529555	+	0.998597i	$0.516864\pi$
$380$	2.40625	+	4.16774i	0.123438	+	0.213801i
$381$	13.8844	−	24.0485i	0.711320	−	1.23204i
$382$	3.64651	−	6.31594i	0.186572	−	0.323152i
$383$	−4.26361	−	7.38479i	−0.217860	−	0.377345i	0.736293	−	0.676663i	$-0.236574\pi$
$383$	−4.26361	−	7.38479i	−0.217860	−	0.377345i	−0.954154	+	0.299317i	$0.903241\pi$
$384$	−27.9964			−1.42869
$385$		0			0
$386$	−4.87038			−0.247896
$387$	−10.6051	−	18.3686i	−0.539089	−	0.933730i
$388$	16.2993	−	28.2311i	0.827469	−	1.43322i
$389$	−4.86924	+	8.43378i	−0.246880	+	0.427609i	−0.962659	−	0.270718i	$-0.912739\pi$
$389$	−4.86924	+	8.43378i	−0.246880	+	0.427609i	0.715778	+	0.698328i	$0.246072\pi$
$390$	−2.91699	−	5.05238i	−0.147708	−	0.255837i
$391$	−31.6329			−1.59975
$392$	9.83688	+	6.25483i	0.496838	+	0.315917i
$393$	13.3069			0.671242
$394$	−0.706712	−	1.22406i	−0.0356037	−	0.0616673i
$395$	2.13879	−	3.70450i	0.107614	−	0.186394i
$396$		0			0
$397$	−12.2809	−	21.2712i	−0.616362	−	1.06757i	−0.990144	−	0.140053i	$-0.955273\pi$
$397$	−12.2809	−	21.2712i	−0.616362	−	1.06757i	0.373782	−	0.927516i	$-0.378061\pi$
$398$	0.644328			0.0322972
$399$	−14.3623	−	4.17948i	−0.719013	−	0.209236i
$400$	−10.1767			−0.508836
$401$	0.613864	+	1.06324i	0.0306549	+	0.0530959i	0.880946	−	0.473217i	$-0.156907\pi$
$401$	0.613864	+	1.06324i	0.0306549	+	0.0530959i	−0.850291	+	0.526313i	$0.823574\pi$
$402$	−5.15372	+	8.92650i	−0.257044	+	0.445214i
$403$	0.103354	−	0.179014i	0.00514841	−	0.00891731i
$404$	14.0727	+	24.3746i	0.700142	+	1.21268i
$405$	7.92819			0.393955
$406$	−0.456645	−	1.86266i	−0.0226629	−	0.0924424i
$407$		0			0
$408$	−10.4159	−	18.0409i	−0.515666	−	0.893159i
$409$	−4.99747	+	8.65588i	−0.247109	+	0.428006i	−0.962722	−	0.270491i	$-0.912814\pi$
$409$	−4.99747	+	8.65588i	−0.247109	+	0.428006i	0.715613	+	0.698497i	$0.246147\pi$
$410$	−0.0251799	+	0.0436129i	−0.00124355	+	0.00215389i
$411$	7.49855	+	12.9879i	0.369876	+	0.640645i
$412$	−7.78351			−0.383466
$413$	19.5924	−	18.7719i	0.964081	−	0.923706i
$414$	−10.4961			−0.515853
$415$	8.27497	+	14.3327i	0.406202	+	0.703563i
$416$	−9.75786	+	16.9011i	−0.478418	+	0.828645i
$417$	−16.3421	+	28.3054i	−0.800276	+	1.38612i
$418$		0			0
$419$	−0.981491			−0.0479490			−0.0239745	−	0.999713i	$-0.507632\pi$
$419$	−0.981491			−0.0479490			−0.0239745	+	0.999713i	$0.507632\pi$
$420$	−10.8542	+	10.3996i	−0.529629	+	0.507448i
$421$	−3.66723			−0.178730			−0.0893649	−	0.995999i	$-0.528484\pi$
$421$	−3.66723			−0.178730			−0.0893649	+	0.995999i	$0.528484\pi$
$422$	−0.0378562	−	0.0655688i	−0.00184281	−	0.00319184i
$423$	6.18182	−	10.7072i	0.300570	−	0.520603i
$424$	−0.235575	+	0.408028i	−0.0114405	+	0.0198156i
$425$	−8.52641	−	14.7682i	−0.413592	−	0.716361i
$426$	−5.65835			−0.274148
$427$	−2.76931	−	11.2961i	−0.134016	−	0.546655i
$428$	−10.5758			−0.511201
$429$		0			0
$430$	−1.53412	+	2.65718i	−0.0739819	+	0.128140i
$431$	5.64898	−	9.78433i	0.272102	−	0.471294i	−0.697298	−	0.716781i	$-0.745615\pi$
$431$	5.64898	−	9.78433i	0.272102	−	0.471294i	0.969400	+	0.245487i	$0.0789479\pi$
$432$	2.51812	+	4.36152i	0.121153	+	0.209844i
$433$	17.2031			0.826730			0.413365	−	0.910566i	$-0.364353\pi$
$433$	17.2031			0.826730			0.413365	+	0.910566i	$0.364353\pi$
$434$	0.0540450	+	0.0157273i	0.00259424	+	0.000754935i
$435$	5.20753			0.249682
$436$	4.99289	+	8.64793i	0.239116	+	0.414161i
$437$	7.14822	−	12.3811i	0.341946	−	0.592267i
$438$	4.29177	−	7.43356i	0.205068	−	0.355189i
$439$	15.2909	+	26.4845i	0.729793	+	1.26404i	0.956971	+	0.290185i	$0.0937167\pi$
$439$	15.2909	+	26.4845i	0.729793	+	1.26404i	−0.227178	+	0.973853i	$0.572950\pi$
$440$		0			0
$441$	1.09976	−	25.6988i	0.0523698	−	1.22375i
$442$	−8.99329			−0.427767
$443$	−18.1493	−	31.4356i	−0.862300	−	1.49355i	−0.869703	−	0.493575i	$-0.835690\pi$
$443$	−18.1493	−	31.4356i	−0.862300	−	1.49355i	0.00740256	−	0.999973i	$-0.497644\pi$
$444$	21.2561	−	36.8166i	1.00877	−	1.74724i
$445$	−2.85377	+	4.94288i	−0.135282	+	0.234315i
$446$	−1.12124	−	1.94205i	−0.0530924	−	0.0919588i
$447$	−39.0697			−1.84793
$448$	9.57872	+	2.78745i	0.452552	+	0.131695i
$449$	−36.2315			−1.70987			−0.854934	−	0.518737i	$-0.826403\pi$
$449$	−36.2315			−1.70987			−0.854934	+	0.518737i	$0.826403\pi$
$450$	−2.82913	−	4.90020i	−0.133367	−	0.230998i
$451$		0			0
$452$	10.9649	−	18.9918i	0.515745	−	0.893297i
$453$	−26.9951	−	46.7569i	−1.26834	−	2.19683i
$454$	−11.1138			−0.521595
$455$	3.25367	+	13.2718i	0.152534	+	0.622190i
$456$	9.41493			0.440894
$457$	11.5039	+	19.9253i	0.538129	+	0.932067i	0.999005	+	0.0446020i	$0.0142020\pi$
$457$	11.5039	+	19.9253i	0.538129	+	0.932067i	−0.460876	+	0.887465i	$0.652465\pi$
$458$	−2.53531	+	4.39129i	−0.118467	+	0.205191i
$459$	−4.21954	+	7.30847i	−0.196951	+	0.341130i
$460$	−7.18362	−	12.4424i	−0.334938	−	0.580129i
$461$	−0.514925			−0.0239825			−0.0119912	−	0.999928i	$-0.503817\pi$
$461$	−0.514925			−0.0239825			−0.0119912	+	0.999928i	$0.503817\pi$
$462$		0			0
$463$	−11.8353			−0.550031			−0.275016	−	0.961440i	$-0.588683\pi$
$463$	−11.8353			−0.550031			−0.275016	+	0.961440i	$0.588683\pi$
$464$	−2.39533	−	4.14884i	−0.111201	−	0.192605i
$465$	−0.0764188	+	0.132361i	−0.00354384	+	0.00613810i
$466$	2.61708	−	4.53292i	0.121234	−	0.209984i
$467$	1.95982	+	3.39451i	0.0906896	+	0.157079i	0.907802	−	0.419400i	$-0.137760\pi$
$467$	1.95982	+	3.39451i	0.0906896	+	0.157079i	−0.817112	+	0.576479i	$0.804426\pi$
$468$	28.2364			1.30523
$469$	17.4327	−	16.7026i	0.804967	−	0.771255i
$470$	−1.78850			−0.0824975
$471$	9.17989	+	15.9000i	0.422987	+	0.732635i
$472$	−8.53934	+	14.7906i	−0.393055	+	0.680791i
$473$		0			0
$474$	−1.98712	−	3.44178i	−0.0912712	−	0.158086i
$475$	7.70699			0.353621
$476$	5.51751	+	22.5060i	0.252895	+	1.03156i
$477$	1.03963			0.0476016
$478$	−3.49627	−	6.05571i	−0.159916	−	0.276982i
$479$	1.40937	−	2.44109i	0.0643956	−	0.111536i	−0.832030	−	0.554730i	$-0.812821\pi$
$479$	1.40937	−	2.44109i	0.0643956	−	0.111536i	0.896426	+	0.443194i	$0.146155\pi$
$480$	7.21487	−	12.4965i	0.329312	−	0.570386i
$481$	−19.3226	−	33.4678i	−0.881036	−	1.52600i
$482$	3.40851			0.155254
$483$	42.8772	+	12.4774i	1.95098	+	0.567743i
$484$		0			0
$485$	10.9553	+	18.9752i	0.497455	+	0.861618i
$486$	4.82601	−	8.35889i	0.218912	−	0.379167i
$487$	−14.8731	+	25.7609i	−0.673963	+	1.16734i	0.302808	+	0.953052i	$0.402076\pi$
$487$	−14.8731	+	25.7609i	−0.673963	+	1.16734i	−0.976771	+	0.214286i	$0.931257\pi$
$488$	3.66027	+	6.33977i	0.165693	+	0.286988i
$489$	−12.3577			−0.558836
$490$	−3.29904	+	1.72100i	−0.149035	+	0.0777468i
$491$	−15.7344			−0.710082			−0.355041	−	0.934851i	$-0.615533\pi$
$491$	−15.7344			−0.710082			−0.355041	+	0.934851i	$0.615533\pi$
$492$	−0.221367	−	0.383418i	−0.00997997	−	0.0172858i
$493$	4.01379	−	6.95208i	0.180772	−	0.313106i
$494$	2.03225	−	3.51996i	0.0914353	−	0.158371i
$495$		0			0
$496$	0.140603			0.00631326
$497$	12.7255	+	3.70318i	0.570818	+	0.166110i
$498$	15.3763			0.689026
$499$	−12.7231	−	22.0371i	−0.569566	−	0.986518i	−0.996609	−	0.0822861i	$-0.973778\pi$
$499$	−12.7231	−	22.0371i	−0.569566	−	0.986518i	0.427042	−	0.904232i	$-0.359555\pi$
$500$	9.37049	−	16.2302i	0.419061	−	0.725835i
$501$	0.271989	−	0.471099i	0.0121516	−	0.0210472i
$502$	−2.93616	−	5.08558i	−0.131047	−	0.226981i
$503$	−24.6798			−1.10042			−0.550208	−	0.835027i	$-0.685452\pi$
$503$	−24.6798			−1.10042			−0.550208	+	0.835027i	$0.685452\pi$
$504$	3.85499	+	15.7246i	0.171715	+	0.700428i
$505$	−18.9175			−0.841818
$506$		0			0
$507$	6.51887	−	11.2910i	0.289513	−	0.501452i
$508$	9.72108	−	16.8374i	0.431303	−	0.747039i
$509$	−12.7747	−	22.1265i	−0.566229	−	0.980738i	−0.996934	−	0.0782449i	$-0.975068\pi$
$509$	−12.7747	−	22.1265i	−0.566229	−	0.980738i	0.430705	−	0.902493i	$-0.358265\pi$
$510$	6.64956			0.294447
$511$	−14.5171	+	13.9091i	−0.642198	+	0.615303i
$512$	−22.8987			−1.01199
$513$	−1.90702	−	3.30305i	−0.0841968	−	0.145833i
$514$	−2.40377	+	4.16346i	−0.106026	+	0.183642i
$515$	2.61579	−	4.53068i	0.115265	−	0.199646i
$516$	−13.4871	−	23.3603i	−0.593735	−	1.02838i
$517$		0			0
$518$	7.59842	−	7.28021i	0.333856	−	0.319874i
$519$	46.3787			2.03580
$520$	−4.30046	−	7.44862i	−0.188588	−	0.326643i
$521$	−22.8052	+	39.4998i	−0.999116	+	1.73052i	−0.463148	+	0.886281i	$0.653280\pi$
$521$	−22.8052	+	39.4998i	−0.999116	+	1.73052i	−0.535968	+	0.844238i	$0.680053\pi$
$522$	1.33181	−	2.30676i	0.0582916	−	0.100964i
$523$	3.30392	+	5.72256i	0.144471	+	0.250230i	0.929175	−	0.369639i	$-0.120519\pi$
$523$	3.30392	+	5.72256i	0.144471	+	0.250230i	−0.784705	+	0.619870i	$0.787185\pi$
$524$	9.31670			0.407002
$525$	5.73198	+	23.3809i	0.250164	+	1.02043i
$526$	13.2044			0.575740
$527$	0.117802	+	0.204039i	0.00513154	+	0.00888809i
$528$		0			0
$529$	−9.84032	+	17.0439i	−0.427840	+	0.741041i
$530$	−0.0751959	−	0.130243i	−0.00326630	−	0.00565740i
$531$	37.6856			1.63542
$532$	−10.0556	−	2.92624i	−0.435968	−	0.126868i
$533$	−0.402462			−0.0174326
$534$	2.65139	+	4.59234i	0.114737	+	0.198730i
$535$	3.55419	−	6.15604i	0.153661	−	0.266149i
$536$	−7.59802	+	13.1602i	−0.328184	+	0.568432i
$537$	−5.09485	−	8.82453i	−0.219859	−	0.380807i
$538$	−2.05612			−0.0886458
$539$		0			0
$540$	−3.83292			−0.164943
$541$	0.789671	+	1.36775i	0.0339506	+	0.0588042i	0.882501	−	0.470310i	$-0.155858\pi$
$541$	0.789671	+	1.36775i	0.0339506	+	0.0588042i	−0.848551	+	0.529114i	$0.822524\pi$
$542$	−2.01664	+	3.49292i	−0.0866220	+	0.150034i
$543$	−6.10652	+	10.5768i	−0.262056	+	0.453894i
$544$	−11.1220	−	19.2638i	−0.476851	−	0.825929i
$545$	−6.71180			−0.287502
$546$	12.1901	+	3.54736i	0.521686	+	0.151813i
$547$	14.9843			0.640682			0.320341	−	0.947302i	$-0.396203\pi$
$547$	14.9843			0.640682			0.320341	+	0.947302i	$0.396203\pi$
$548$	5.25006	+	9.09337i	0.224272	+	0.388450i
$549$	8.07670	−	13.9893i	0.344705	−	0.597047i
$550$		0			0
$551$	1.81402	+	3.14198i	0.0772800	+	0.133853i
$552$	−28.1074			−1.19633
$553$	2.21646	+	9.04100i	0.0942536	+	0.384462i
$554$	−4.01875			−0.170740
$555$	14.2870	+	24.7458i	0.606449	+	1.05040i
$556$	−11.4418	+	19.8178i	−0.485241	+	0.840462i
$557$	3.56041	−	6.16681i	0.150860	−	0.261296i	−0.780684	−	0.624926i	$-0.785129\pi$
$557$	3.56041	−	6.16681i	0.150860	−	0.261296i	0.931544	+	0.363629i	$0.118463\pi$
$558$	0.0390877	+	0.0677019i	0.00165471	+	0.00286605i
$559$	−24.5205			−1.03711
$560$	−6.71147	+	6.43040i	−0.283611	+	0.271734i
$561$		0			0
$562$	1.19306	+	2.06644i	0.0503262	+	0.0871675i
$563$	−17.8721	+	30.9554i	−0.753219	+	1.30461i	0.193036	+	0.981192i	$0.438167\pi$
$563$	−17.8721	+	30.9554i	−0.753219	+	1.30461i	−0.946255	+	0.323422i	$0.895167\pi$
$564$	7.86172	−	13.6169i	0.331038	−	0.573375i
$565$	7.36990	+	12.7650i	0.310054	+	0.537030i
$566$	−7.26846			−0.305516
$567$	−12.4578	+	11.9361i	−0.523179	+	0.501268i
$568$	−8.34198			−0.350022
$569$	4.70754	+	8.15370i	0.197350	+	0.341821i	0.947668	−	0.319256i	$-0.103433\pi$
$569$	4.70754	+	8.15370i	0.197350	+	0.341821i	−0.750318	+	0.661077i	$0.770100\pi$
$570$	−1.50263	+	2.60263i	−0.0629382	+	0.109012i
$571$	18.8476	−	32.6450i	0.788748	−	1.36615i	−0.137986	−	0.990434i	$-0.544063\pi$
$571$	18.8476	−	32.6450i	0.788748	−	1.36615i	0.926734	−	0.375718i	$-0.122604\pi$
$572$		0			0
$573$	−43.0945			−1.80030
$574$	−0.0260943	−	0.106439i	−0.00108916	−	0.00444269i
$575$	−23.0085			−0.959520
$576$	6.92775	+	11.9992i	0.288656	+	0.499968i
$577$	4.53288	−	7.85118i	0.188706	−	0.326849i	−0.756113	−	0.654441i	$-0.772904\pi$
$577$	4.53288	−	7.85118i	0.188706	−	0.326849i	0.944819	+	0.327592i	$0.106237\pi$
$578$	1.40890	−	2.44029i	0.0586027	−	0.101503i
$579$	14.3896	+	24.9234i	0.598010	+	1.03578i
$580$	3.64601			0.151392
$581$	−34.5809	−	10.0632i	−1.43466	−	0.417492i
$582$	20.3568			0.843816
$583$		0			0
$584$	6.32726	−	10.9591i	0.261824	−	0.453492i
$585$	−9.48934	+	16.4360i	−0.392336	+	0.679546i
$586$	−6.32607	−	10.9571i	−0.261328	−	0.452633i
$587$	−8.33134			−0.343871			−0.171936	−	0.985108i	$-0.555002\pi$
$587$	−8.33134			−0.343871			−0.171936	+	0.985108i	$0.555002\pi$
$588$	1.39862	−	32.6824i	0.0576783	−	1.34780i
$589$	−0.106481			−0.00438747
$590$	−2.72577	−	4.72117i	−0.112218	−	0.194368i
$591$	−4.17597	+	7.23299i	−0.171776	+	0.297526i
$592$	13.1433	−	22.7649i	0.540187	−	0.935631i
$593$	2.85183	+	4.93952i	0.117111	+	0.202842i	0.918622	−	0.395139i	$-0.129303\pi$
$593$	2.85183	+	4.93952i	0.117111	+	0.202842i	−0.801511	+	0.597980i	$0.795970\pi$
$594$		0			0
$595$	−14.9547	−	4.35189i	−0.613084	−	0.178410i
$596$	−27.3544			−1.12048
$597$	−1.90367	−	3.29725i	−0.0779120	−	0.134948i
$598$	−6.06709	+	10.5085i	−0.248102	+	0.429725i
$599$	−9.93090	+	17.2008i	−0.405766	+	0.702807i	−0.994410	−	0.105585i	$-0.966328\pi$
$599$	−9.93090	+	17.2008i	−0.405766	+	0.702807i	0.588645	+	0.808392i	$0.299662\pi$
$600$	−7.57612	−	13.1222i	−0.309294	−	0.535712i
$601$	−16.0095			−0.653041			−0.326521	−	0.945190i	$-0.605876\pi$
$601$	−16.0095			−0.653041			−0.326521	+	0.945190i	$0.605876\pi$
$602$	−1.58983	−	6.48496i	−0.0647968	−	0.264307i
$603$	33.5314			1.36550
$604$	−18.9005	−	32.7365i	−0.769048	−	1.33203i
$605$		0			0
$606$	−8.78796	+	15.2212i	−0.356987	+	0.618319i
$607$	9.34314	+	16.1828i	0.379226	+	0.656839i	0.990950	−	0.134232i	$-0.0428569\pi$
$607$	9.34314	+	16.1828i	0.379226	+	0.656839i	−0.611724	+	0.791072i	$0.709524\pi$
$608$	10.0531			0.407708
$609$	−8.18275	+	7.84006i	−0.331582	+	0.317695i
$610$	−2.33673			−0.0946113
$611$	−7.14661	−	12.3783i	−0.289121	−	0.500772i
$612$	−16.0919	+	27.8719i	−0.650475	+	1.12666i
$613$	−6.47275	+	11.2111i	−0.261432	+	0.452813i	−0.966623	−	0.256204i	$-0.917528\pi$
$613$	−6.47275	+	11.2111i	−0.261432	+	0.452813i	0.705191	+	0.709018i	$0.250861\pi$
$614$	−4.34180	−	7.52022i	−0.175221	−	0.303492i
$615$	0.297577			0.0119995
$616$		0			0
$617$	3.04683			0.122661			0.0613304	−	0.998118i	$-0.480466\pi$
$617$	3.04683			0.122661			0.0613304	+	0.998118i	$0.480466\pi$
$618$	−2.43028	−	4.20938i	−0.0977604	−	0.169326i
$619$	−9.55764	+	16.5543i	−0.384154	+	0.665374i	−0.991651	−	0.128947i	$-0.958840\pi$
$619$	−9.55764	+	16.5543i	−0.384154	+	0.665374i	0.607497	+	0.794322i	$0.292173\pi$
$620$	−0.0535041	+	0.0926718i	−0.00214878	+	0.00372179i
$621$	5.69321	+	9.86093i	0.228461	+	0.395706i
$622$	−0.0752727			−0.00301816
$623$	−2.95741	−	12.0633i	−0.118486	−	0.483307i
$624$	31.7135			1.26956
$625$	−2.50641	−	4.34123i	−0.100256	−	0.173649i
$626$	0.0763673	−	0.132272i	0.00305225	−	0.00528665i
$627$		0			0
$628$	6.42724	+	11.1323i	0.256475	+	0.444227i
$629$	44.0477			1.75630
$630$	−4.96210	−	1.44399i	−0.197695	−	0.0575301i
$631$	−18.1136			−0.721091			−0.360546	−	0.932742i	$-0.617409\pi$
$631$	−18.1136			−0.721091			−0.360546	+	0.932742i	$0.617409\pi$
$632$	−2.92956	−	5.07415i	−0.116532	−	0.201839i
$633$	−0.223693	+	0.387447i	−0.00889098	+	0.0153996i
$634$	−5.15618	+	8.93077i	−0.204778	+	0.354686i
$635$	6.53389	+	11.3170i	0.259290	+	0.449103i
$636$	1.32215			0.0524268
$637$	−25.0936	−	15.9559i	−0.994244	−	0.632195i
$638$		0			0
$639$	9.20365	+	15.9412i	0.364091	+	0.630624i
$640$	6.58745	−	11.4098i	0.260392	−	0.451012i
$641$	−1.54317	+	2.67284i	−0.0609515	+	0.105571i	−0.894891	−	0.446285i	$-0.852747\pi$
$641$	−1.54317	+	2.67284i	−0.0609515	+	0.105571i	0.833940	+	0.551856i	$0.186080\pi$
$642$	−3.30214	−	5.71947i	−0.130325	−	0.225730i
$643$	41.6974			1.64439			0.822193	−	0.569208i	$-0.192750\pi$
$643$	41.6974			1.64439			0.822193	+	0.569208i	$0.192750\pi$
$644$	30.0202	+	8.73600i	1.18296	+	0.344247i
$645$	18.1303			0.713879
$646$	2.31635	+	4.01204i	0.0911357	+	0.157852i
$647$	−3.83458	+	6.64168i	−0.150753	+	0.261112i	−0.931504	−	0.363730i	$-0.881503\pi$
$647$	−3.83458	+	6.64168i	−0.150753	+	0.261112i	0.780752	+	0.624842i	$0.214836\pi$
$648$	5.42972	−	9.40455i	0.213300	−	0.369446i
$649$		0			0
$650$	−6.54135			−0.256573
$651$	−0.0791939	−	0.323034i	−0.00310385	−	0.0126607i
$652$	−8.65219			−0.338846
$653$	−4.95937	−	8.58989i	−0.194075	−	0.336148i	0.752522	−	0.658567i	$-0.228837\pi$
$653$	−4.95937	−	8.58989i	−0.194075	−	0.336148i	−0.946597	+	0.322419i	$0.895504\pi$
$654$	−3.11791	+	5.40037i	−0.121920	+	0.211171i
$655$	−3.13105	+	5.42313i	−0.122340	+	0.211899i
$656$	−0.136878	−	0.237080i	−0.00534419	−	0.00925641i
$657$	−27.9233			−1.08939
$658$	2.81033	−	2.69264i	0.109558	−	0.104970i
$659$	13.0070			0.506683			0.253341	−	0.967377i	$-0.418470\pi$
$659$	13.0070			0.506683			0.253341	+	0.967377i	$0.418470\pi$
$660$		0			0
$661$	−13.9690	+	24.1951i	−0.543332	+	0.941079i	0.455377	+	0.890299i	$0.349504\pi$
$661$	−13.9690	+	24.1951i	−0.543332	+	0.941079i	−0.998710	+	0.0507809i	$0.983829\pi$
$662$	−2.38598	+	4.13265i	−0.0927339	+	0.160620i
$663$	26.5707	+	46.0218i	1.03192	+	1.78734i
$664$	22.6689			0.879723
$665$	5.08271	−	4.86985i	0.197099	−	0.188845i
$666$	14.6154			0.566335
$667$	−5.41560	−	9.38009i	−0.209693	−	0.363198i
$668$	0.190431	−	0.329837i	0.00736801	−	0.0127618i
$669$	−6.62544	+	11.4756i	−0.256154	+	0.443673i
$670$	−2.42530	−	4.20074i	−0.0936974	−	0.162289i
$671$		0			0
$672$	7.47688	+	30.4984i	0.288427	+	1.17650i
$673$	9.03118			0.348127			0.174063	−	0.984734i	$-0.444310\pi$
$673$	9.03118			0.348127			0.174063	+	0.984734i	$0.444310\pi$
$674$	6.83142	+	11.8324i	0.263136	+	0.455766i
$675$	−3.06912	+	5.31588i	−0.118131	+	0.204608i
$676$	4.56414	−	7.90533i	0.175544	−	0.304051i
$677$	−15.4570	−	26.7723i	−0.594060	−	1.02894i	−0.993679	−	0.112261i	$-0.964191\pi$
$677$	−15.4570	−	26.7723i	−0.594060	−	1.02894i	0.399619	−	0.916681i	$-0.369142\pi$
$678$	13.6945			0.525934
$679$	−45.7820	−	13.3228i	−1.75695	−	0.511281i
$680$	9.80330			0.375940
$681$	32.8357	+	56.8731i	1.25827	+	2.17938i
$682$		0			0
$683$	−7.36701	+	12.7600i	−0.281891	+	0.488249i	−0.971850	−	0.235599i	$-0.924295\pi$
$683$	−7.36701	+	12.7600i	−0.281891	+	0.488249i	0.689960	+	0.723848i	$0.257628\pi$
$684$	−7.27269	−	12.5967i	−0.278078	−	0.481646i
$685$	−7.05751			−0.269654
$686$	2.59287	−	7.67104i	0.0989964	−	0.292882i
$687$	29.9624			1.14314
$688$	−8.33948	−	14.4444i	−0.317940	−	0.550688i
$689$	0.600945	−	1.04087i	0.0228942	−	0.0396539i
$690$	4.48595	−	7.76990i	0.170777	−	0.295795i
$691$	21.5811	+	37.3796i	0.820984	+	1.42199i	0.904951	+	0.425517i	$0.139908\pi$
$691$	21.5811	+	37.3796i	0.820984	+	1.42199i	−0.0839669	+	0.996469i	$0.526759\pi$
$692$	32.4718			1.23439
$693$		0			0
$694$	10.6497			0.404257
$695$	−7.69046	−	13.3203i	−0.291716	−	0.505266i
$696$	3.56644	−	6.17726i	0.135186	−	0.234148i
$697$	0.229362	−	0.397267i	0.00868772	−	0.0150476i
$698$	5.03045	+	8.71299i	0.190405	+	0.329792i
$699$	−30.9288			−1.16983
$700$	4.01321	+	16.3700i	0.151685	+	0.618726i
$701$	−25.3038			−0.955710			−0.477855	−	0.878439i	$-0.658586\pi$
$701$	−25.3038			−0.955710			−0.477855	+	0.878439i	$0.658586\pi$
$702$	1.61859	+	2.80348i	0.0610897	+	0.105810i
$703$	−9.95365	+	17.2402i	−0.375409	+	0.650227i
$704$		0			0
$705$	5.28414	+	9.15241i	0.199012	+	0.344700i
$706$	5.29270			0.199193
$707$	29.7257	−	28.4808i	1.11795	−	1.07113i
$708$	47.9266			1.80119
$709$	2.35209	+	4.07395i	0.0883348	+	0.153000i	0.906807	−	0.421545i	$-0.138512\pi$
$709$	2.35209	+	4.07395i	0.0883348	+	0.153000i	−0.818473	+	0.574546i	$0.805179\pi$
$710$	1.33139	−	2.30603i	0.0499660	−	0.0865437i
$711$	−6.46433	+	11.1966i	−0.242431	+	0.419903i
$712$	3.90889	+	6.77039i	0.146492	+	0.253731i
$713$	0.317888			0.0119050
$714$	−10.4487	+	10.0111i	−0.391031	+	0.374655i
$715$		0			0
$716$	−3.56712	−	6.17844i	−0.133310	−	0.230899i
$717$	−20.6595	+	35.7833i	−0.771543	+	1.33635i
$718$	−2.01074	+	3.48270i	−0.0750402	+	0.129973i
$719$	−12.7529	−	22.0888i	−0.475605	−	0.823772i	0.524005	−	0.851715i	$-0.324437\pi$
$719$	−12.7529	−	22.0888i	−0.475605	−	0.823772i	−0.999609	+	0.0279437i	$0.991104\pi$
$720$	−12.9094			−0.481104
$721$	2.71078	+	11.0573i	0.100955	+	0.411797i
$722$	6.21341			0.231239
$723$	−10.0705	−	17.4426i	−0.374525	−	0.648696i
$724$	−4.27544	+	7.40528i	−0.158895	+	0.275215i
$725$	2.91946	−	5.05666i	0.108426	−	0.187800i
$726$		0			0
$727$	27.4481			1.01799			0.508997	−	0.860769i	$-0.330017\pi$
$727$	27.4481			1.01799			0.508997	+	0.860769i	$0.330017\pi$
$728$	17.9715	+	5.22979i	0.666069	+	0.193829i
$729$	−37.4708			−1.38781
$730$	2.01967	+	3.49817i	0.0747513	+	0.129473i
$731$	13.9742	−	24.2041i	0.516855	−	0.895219i
$732$	10.2715	−	17.7908i	0.379647	−	0.657568i
$733$	1.05206	+	1.82223i	0.0388589	+	0.0673056i	0.884801	−	0.465970i	$-0.154294\pi$
$733$	1.05206	+	1.82223i	0.0388589	+	0.0673056i	−0.845942	+	0.533275i	$0.820961\pi$
$734$	13.1444			0.485170
$735$	18.5540	+	11.7976i	0.684374	+	0.435162i
$736$	−30.0126			−1.10628
$737$		0			0
$738$	0.0761043	−	0.131817i	0.00280144	−	0.00485223i
$739$	8.97875	−	15.5516i	0.330289	−	0.572077i	−0.652280	−	0.757978i	$-0.726187\pi$
$739$	8.97875	−	15.5516i	0.330289	−	0.572077i	0.982568	+	0.185902i	$0.0595206\pi$
$740$	10.0029	+	17.3256i	0.367715	+	0.636902i
$741$	−24.0172			−0.882293
$742$	0.314242	+	0.0914457i	0.0115362	+	0.00335708i
$743$	−34.7957			−1.27653			−0.638265	−	0.769817i	$-0.720348\pi$
$743$	−34.7957			−1.27653			−0.638265	+	0.769817i	$0.720348\pi$
$744$	0.104673	+	0.181299i	0.00383749	+	0.00664673i
$745$	9.19293	−	15.9226i	0.336803	−	0.583360i
$746$	−3.21774	+	5.57329i	−0.117810	+	0.204053i
$747$	−25.0104	−	43.3193i	−0.915084	−	1.58497i
$748$		0			0
$749$	3.68326	+	15.0241i	0.134584	+	0.548969i
$750$	11.7032			0.427340
$751$	8.99156	+	15.5738i	0.328107	+	0.568298i	0.982136	−	0.188171i	$-0.0602561\pi$
$751$	8.99156	+	15.5738i	0.328107	+	0.568298i	−0.654029	+	0.756469i	$0.726923\pi$
$752$	4.86115	−	8.41976i	0.177268	−	0.307037i
$753$	−17.3498	+	30.0508i	−0.632263	+	1.09511i
$754$	−1.53966	−	2.66677i	−0.0560712	−	0.0971182i
$755$	25.4074			0.924668
$756$	6.02278	−	5.77055i	0.219046	−	0.209873i
$757$	−3.20050			−0.116324			−0.0581621	−	0.998307i	$-0.518524\pi$
$757$	−3.20050			−0.116324			−0.0581621	+	0.998307i	$0.518524\pi$
$758$	−0.450743	−	0.780711i	−0.0163717	−	0.0283567i
$759$		0			0
$760$	−2.21529	+	3.83700i	−0.0803571	+	0.139183i
$761$	9.41607	+	16.3091i	0.341332	+	0.591205i	0.984680	−	0.174369i	$-0.0557885\pi$
$761$	9.41607	+	16.3091i	0.341332	+	0.591205i	−0.643348	+	0.765574i	$0.722455\pi$
$762$	12.1410			0.439824
$763$	10.5465	−	10.1048i	0.381807	−	0.365818i
$764$	−30.1724			−1.09160
$765$	−10.8159	−	18.7337i	−0.391051	−	0.677319i
$766$	1.86413	−	3.22877i	0.0673537	−	0.116660i
$767$	21.7836	−	37.7303i	0.786560	−	1.36236i
$768$	3.62117	+	6.27204i	0.130668	+	0.226323i
$769$	20.1946			0.728235			0.364118	−	0.931353i	$-0.381371\pi$
$769$	20.1946			0.728235			0.364118	+	0.931353i	$0.381371\pi$
$770$		0			0
$771$	28.4078			1.02308
$772$	10.0748	+	17.4500i	0.362598	+	0.628039i
$773$	−1.81606	+	3.14550i	−0.0653190	+	0.113136i	−0.896835	−	0.442364i	$-0.854140\pi$
$773$	−1.81606	+	3.14550i	−0.0653190	+	0.113136i	0.831516	+	0.555500i	$0.187473\pi$
$774$	4.63676	−	8.03110i	0.166665	−	0.288672i
$775$	0.0856844	+	0.148410i	0.00307787	+	0.00533103i
$776$	30.0116			1.07735
$777$	−59.7050	−	17.3744i	−2.14190	−	0.623303i
$778$	−4.25784			−0.152651
$779$	0.103660	+	0.179544i	0.00371400	+	0.00643284i
$780$	−12.0681	+	20.9025i	−0.432106	+	0.748429i
$781$		0			0
$782$	−6.91525	−	11.9776i	−0.247289	−	0.428317i
$783$	−2.88957			−0.103265
$784$	0.864814	−	20.2086i	0.0308862	−	0.721735i
$785$	−8.63996			−0.308373
$786$	2.90900	+	5.03854i	0.103761	+	0.179719i
$787$	10.5110	−	18.2057i	0.374678	−	0.648962i	−0.615601	−	0.788058i	$-0.711087\pi$
$787$	10.5110	−	18.2057i	0.374678	−	0.648962i	0.990279	+	0.139097i	$0.0444199\pi$
$788$	−2.92378	+	5.06413i	−0.104155	+	0.180402i
$789$	−39.0126	−	67.5717i	−1.38888	−	2.40562i
$790$	1.87024			0.0665401
$791$	−30.7987	−	8.96254i	−1.09507	−	0.318671i
$792$		0			0
$793$	−9.33723	−	16.1726i	−0.331575	−	0.574305i
$794$	5.36944	−	9.30015i	0.190554	−	0.330050i
$795$	−0.444333	+	0.769608i	−0.0157589	+	0.0272952i
$796$	−1.33284	−	2.30855i	−0.0472413	−	0.0818244i
$797$	−34.0730			−1.20693			−0.603464	−	0.797390i	$-0.706213\pi$
$797$	−34.0730			−1.20693			−0.603464	+	0.797390i	$0.706213\pi$
$798$	−1.55720	−	6.35184i	−0.0551242	−	0.224853i
$799$	16.2914			0.576347
$800$	−8.08966	−	14.0117i	−0.286013	−	0.495389i
$801$	8.62530	−	14.9395i	0.304760	−	0.527860i
$802$	−0.268393	+	0.464870i	−0.00947728	+	0.0164151i
$803$		0			0
$804$	42.6435			1.50392
$805$	−15.1739	+	14.5385i	−0.534811	+	0.512414i
$806$	0.0903762			0.00318337
$807$	6.07483	+	10.5219i	0.213844	+	0.370389i
$808$	−12.9559	+	22.4403i	−0.455787	+	0.789446i
$809$	−12.6317	+	21.8787i	−0.444106	+	0.769214i	−0.997989	−	0.0633804i	$-0.979812\pi$
$809$	−12.6317	+	21.8787i	−0.444106	+	0.769214i	0.553884	+	0.832594i	$0.313145\pi$
$810$	1.73317	+	3.00195i	0.0608975	+	0.105478i
$811$	28.5947			1.00410			0.502048	−	0.864840i	$-0.332580\pi$
$811$	28.5947			1.00410			0.502048	+	0.864840i	$0.332580\pi$
$812$	−5.72910	+	5.48917i	−0.201052	+	0.192632i
$813$	23.8327			0.835848
$814$		0			0
$815$	2.90773	−	5.03633i	0.101853	−	0.176415i
$816$	−18.0735	+	31.3042i	−0.632699	+	1.09587i
$817$	6.31562	+	10.9390i	0.220956	+	0.382707i
$818$	−4.36997			−0.152793
$819$	−9.83395	−	40.1129i	−0.343626	−	1.40166i
$820$	0.208347			0.00727578
$821$	21.4863	+	37.2154i	0.749877	+	1.29883i	0.947881	+	0.318624i	$0.103221\pi$
$821$	21.4863	+	37.2154i	0.749877	+	1.29883i	−0.198004	+	0.980201i	$0.563446\pi$
$822$	−3.27851	+	5.67854i	−0.114351	+	0.198062i
$823$	−15.1057	+	26.1638i	−0.526551	+	0.912013i	0.472970	+	0.881078i	$0.343182\pi$
$823$	−15.1057	+	26.1638i	−0.526551	+	0.912013i	−0.999521	+	0.0309348i	$0.990152\pi$
$824$	−3.58292	−	6.20579i	−0.124817	−	0.216189i
$825$		0			0
$826$	11.3909	+	3.31481i	0.396341	+	0.115337i
$827$	−48.0217			−1.66988			−0.834938	−	0.550344i	$-0.814497\pi$
$827$	−48.0217			−1.66988			−0.834938	+	0.550344i	$0.814497\pi$
$828$	21.7119	+	37.6061i	0.754541	+	1.30690i
$829$	−7.77647	+	13.4692i	−0.270088	+	0.467806i	−0.968884	−	0.247515i	$-0.920386\pi$
$829$	−7.77647	+	13.4692i	−0.270088	+	0.467806i	0.698796	+	0.715321i	$0.253719\pi$
$830$	−3.61797	+	6.26651i	−0.125582	+	0.217514i
$831$	11.8734	+	20.5654i	0.411884	+	0.713405i
$832$	16.0179			0.555322
$833$	30.0507	−	15.6765i	1.04120	−	0.543157i
$834$	−14.2901			−0.494827
$835$	0.127996	+	0.221695i	0.00442948	+	0.00767208i
$836$		0			0
$837$	0.0424034	−	0.0734449i	0.00146568	−	0.00253863i
$838$	−0.214563	−	0.371634i	−0.00741196	−	0.0128379i
$839$	−42.9015			−1.48112			−0.740562	−	0.671988i	$-0.765441\pi$
$839$	−42.9015			−1.48112			−0.740562	+	0.671988i	$0.765441\pi$
$840$	−13.2880	−	3.86686i	−0.458479	−	0.133419i
$841$	−26.2513			−0.905219
$842$	−0.801690	−	1.38857i	−0.0276281	−	0.0478532i
$843$	7.04980	−	12.2106i	0.242808	−	0.420556i
$844$	−0.156617	+	0.271268i	−0.00539097	+	0.00933744i
$845$	3.06773	+	5.31346i	0.105533	+	0.182789i
$846$	5.40561			0.185849
$847$		0			0
$848$	0.817529			0.0280741
$849$	21.4747	+	37.1953i	0.737010	+	1.27654i
$850$	3.72790	−	6.45692i	0.127866	−	0.221470i
$851$	29.7157	−	51.4690i	1.01864	−	1.76434i
$852$	11.7047	+	20.2732i	0.400997	+	0.694548i
$853$	29.0168			0.993518			0.496759	−	0.867889i	$-0.334523\pi$
$853$	29.0168			0.993518			0.496759	+	0.867889i	$0.334523\pi$
$854$	3.67177	−	3.51800i	0.125645	−	0.120383i
$855$	9.77647			0.334348
$856$	−4.86827	−	8.43209i	−0.166394	−	0.288203i
$857$	−14.4841	+	25.0872i	−0.494768	+	0.856963i	−0.999982	−	0.00603088i	$-0.998080\pi$
$857$	−14.4841	+	25.0872i	−0.494768	+	0.856963i	0.505214	+	0.862994i	$0.331414\pi$
$858$		0			0
$859$	7.81527	+	13.5364i	0.266654	+	0.461858i	0.967996	−	0.250967i	$-0.0807487\pi$
$859$	7.81527	+	13.5364i	0.266654	+	0.461858i	−0.701342	+	0.712825i	$0.747415\pi$
$860$	12.6938			0.432855
$861$	−0.467592	+	0.448010i	−0.0159355	+	0.0152681i
$862$	4.93968			0.168246
$863$	2.02916	+	3.51461i	0.0690735	+	0.119639i	0.898494	−	0.438986i	$-0.144662\pi$
$863$	2.02916	+	3.51461i	0.0690735	+	0.119639i	−0.829420	+	0.558625i	$0.811329\pi$
$864$	−4.00341	+	6.93411i	−0.136199	+	0.235903i
$865$	−10.9127	+	18.9014i	−0.371044	+	0.642667i
$866$	3.76076	+	6.51383i	0.127796	+	0.221349i
$867$	−16.6505			−0.565479
$868$	−0.0554471	−	0.226170i	−0.00188200	−	0.00767670i
$869$		0			0
$870$	1.13841	+	1.97179i	0.0385958	+	0.0668499i
$871$	19.3823	−	33.5711i	0.656744	−	1.13751i
$872$	−4.59666	+	7.96165i	−0.155663	+	0.269616i
$873$	−33.1116	−	57.3509i	−1.12066	−	1.94103i
$874$	6.25067			0.211432
$875$	−26.3202	−	7.65930i	−0.889786	−	0.258931i
$876$	−35.5114			−1.19982
$877$	0.925497	+	1.60301i	0.0312518	+	0.0541297i	0.881228	−	0.472691i	$-0.156717\pi$
$877$	0.925497	+	1.60301i	0.0312518	+	0.0541297i	−0.849976	+	0.526821i	$0.823384\pi$
$878$	−6.68544	+	11.5795i	−0.225623	+	0.390790i
$879$	−37.3808	+	64.7455i	−1.26082	+	2.18381i
$880$		0			0
$881$	−18.0162			−0.606981			−0.303490	−	0.952835i	$-0.598152\pi$
$881$	−18.0162			−0.606981			−0.303490	+	0.952835i	$0.598152\pi$
$882$	9.97107	−	5.20158i	0.335744	−	0.175146i
$883$	36.8405			1.23978			0.619891	−	0.784688i	$-0.287177\pi$
$883$	36.8405			1.23978			0.619891	+	0.784688i	$0.287177\pi$
$884$	18.6033	+	32.2219i	0.625697	+	1.08374i
$885$	−16.1066	+	27.8975i	−0.541418	+	0.937763i
$886$	7.93522	−	13.7442i	0.266589	−	0.461745i
$887$	9.08201	+	15.7305i	0.304944	+	0.528179i	0.977249	−	0.212096i	$-0.0680289\pi$
$887$	9.08201	+	15.7305i	0.304944	+	0.528179i	−0.672305	+	0.740274i	$0.734696\pi$
$888$	39.1385			1.31340
$889$	−27.3050	−	7.94587i	−0.915780	−	0.266496i
$890$	−2.49544			−0.0836475
$891$		0			0
$892$	−4.63876	+	8.03457i	−0.155317	+	0.269017i
$893$	−3.68143	+	6.37642i	−0.123194	+	0.213379i
$894$	−8.54099	−	14.7934i	−0.285653	−	0.494766i
$895$	4.79518			0.160285
$896$	6.82667	+	27.8461i	0.228063	+	0.930274i
$897$	71.7010			2.39403
$898$	−7.92053	−	13.7188i	−0.264312	−	0.457801i
$899$	−0.0403357	+	0.0698635i	−0.00134527	+	0.00233008i
$900$	−11.7046	+	20.2729i	−0.390152	+	0.675763i
$901$	0.684955	+	1.18638i	0.0228192	+	0.0395239i
$902$		0			0
$903$	−28.4887	+	27.2956i	−0.948044	+	0.908341i
$904$	20.1895			0.671493
$905$	−2.87368	−	4.97736i	−0.0955243	−	0.165453i
$906$	11.8028	−	20.4430i	0.392121	−	0.679173i
$907$	17.1820	−	29.7602i	0.570520	−	0.988170i	−0.425992	−	0.904727i	$-0.640075\pi$
$907$	17.1820	−	29.7602i	0.570520	−	0.988170i	0.996513	−	0.0834435i	$-0.0265918\pi$
$908$	22.9897	+	39.8193i	0.762940	+	1.32145i
$909$	57.1767			1.89643
$910$	−4.31397	+	4.13331i	−0.143007	+	0.137018i
$911$	52.0506			1.72451			0.862256	−	0.506472i	$-0.169051\pi$
$911$	52.0506			1.72451			0.862256	+	0.506472i	$0.169051\pi$
$912$	−8.16828	−	14.1479i	−0.270479	−	0.468483i
$913$		0			0
$914$	−5.02971	+	8.71171i	−0.166368	+	0.288158i
$915$	6.90387	+	11.9579i	0.228235	+	0.395314i
$916$	20.9780			0.693131
$917$	−3.24475	−	13.2354i	−0.107151	−	0.437072i
$918$	−3.68973			−0.121779
$919$	−14.9655	−	25.9210i	−0.493666	−	0.855054i	0.506308	−	0.862353i	$-0.331010\pi$
$919$	−14.9655	−	25.9210i	−0.493666	−	0.855054i	−0.999973	+	0.00729870i	$0.997677\pi$
$920$	6.61354	−	11.4550i	0.218042	−	0.377660i
$921$	−25.6558	+	44.4371i	−0.845386	+	1.46425i
$922$	−0.112567	−	0.194972i	−0.00370721	−	0.00642108i
$923$	21.2801			0.700444
$924$		0			0
$925$	32.0385			1.05342
$926$	−2.58730	−	4.48133i	−0.0850239	−	0.147266i
$927$	−7.90602	+	13.6936i	−0.259668	+	0.449757i
$928$	3.80819	−	6.59598i	0.125010	−	0.216524i
$929$	−10.2131	−	17.6896i	−0.335081	−	0.580377i	0.648420	−	0.761283i	$-0.275430\pi$
$929$	−10.2131	−	17.6896i	−0.335081	−	0.580377i	−0.983500	+	0.180906i	$0.942097\pi$
$930$	−0.0668234			−0.00219123
$931$	−0.654938	+	15.3043i	−0.0214647	+	0.501578i
$932$	−21.6546			−0.709319
$933$	0.222393	+	0.385197i	0.00728084	+	0.0126108i
$934$	−0.856869	+	1.48414i	−0.0280376	+	0.0485626i
$935$		0			0
$936$	12.9978	+	22.5128i	0.424846	+	0.735856i
$937$	−38.4905			−1.25743			−0.628715	−	0.777636i	$-0.716419\pi$
$937$	−38.4905			−1.25743			−0.628715	+	0.777636i	$0.716419\pi$
$938$	10.1353	+	2.94940i	0.330928	+	0.0963015i
$939$	−0.902510			−0.0294523
$940$	3.69966	+	6.40800i	0.120670	+	0.209006i
$941$	16.5822	−	28.7213i	0.540565	−	0.936287i	−0.458306	−	0.888794i	$-0.651544\pi$
$941$	16.5822	−	28.7213i	0.540565	−	0.936287i	0.998872	−	0.0474924i	$-0.0151230\pi$
$942$	−4.01362	+	6.95179i	−0.130771	+	0.226501i
$943$	−0.309467	−	0.536012i	−0.0100776	−	0.0174550i
$944$	29.6345			0.964522
$945$	1.33490	+	5.44508i	0.0434243	+	0.177129i
$946$		0			0
$947$	−5.78522	−	10.0203i	−0.187994	−	0.325616i	0.756587	−	0.653893i	$-0.226865\pi$
$947$	−5.78522	−	10.0203i	−0.187994	−	0.325616i	−0.944581	+	0.328277i	$0.893532\pi$
$948$	−8.22100	+	14.2392i	−0.267006	+	0.462467i
$949$	−16.1406	+	27.9564i	−0.523947	+	0.907503i
$950$	1.68482	+	2.91819i	0.0546627	+	0.0946787i
$951$	60.9359			1.97598
$952$	−15.4042	+	14.7591i	−0.499254	+	0.478346i
$953$	−16.3894			−0.530904			−0.265452	−	0.964124i	$-0.585521\pi$
$953$	−16.3894			−0.530904			−0.265452	+	0.964124i	$0.585521\pi$
$954$	0.227274	+	0.393649i	0.00735825	+	0.0127449i
$955$	10.1400	−	17.5629i	0.328122	−	0.568323i
$956$	−14.4646	+	25.0534i	−0.467819	+	0.810285i
$957$		0			0
$958$	1.23240			0.0398171
$959$	11.0897	−	10.6253i	0.358105	−	0.343108i
$960$	−11.8435			−0.382248
$961$	15.4988	+	26.8447i	0.499962	+	0.865959i
$962$	8.44821	−	14.6327i	0.272381	−	0.471778i
$963$	−10.7423	+	18.6061i	−0.346165	+	0.599575i
$964$	−7.05077	−	12.2123i	−0.227090	−	0.393332i
$965$	−13.5432			−0.435971
$966$	4.64886	+	18.9628i	0.149575	+	0.610118i
$967$	52.7001			1.69472			0.847361	−	0.531017i	$-0.178190\pi$
$967$	52.7001			1.69472			0.847361	+	0.531017i	$0.178190\pi$
$968$		0			0
$969$	13.6874	−	23.7072i	0.439701	−	0.761585i
$970$	−4.78987	+	8.29629i	−0.153793	+	0.266378i
$971$	−18.3046	−	31.7046i	−0.587424	−	1.01745i	−0.994568	−	0.104084i	$-0.966809\pi$
$971$	−18.3046	−	31.7046i	−0.587424	−	1.01745i	0.407145	−	0.913364i	$-0.366525\pi$
$972$	−39.9319			−1.28082
$973$	32.1382	+	9.35237i	1.03030	+	0.299823i
$974$	−13.0056			−0.416725
$975$	19.3264	+	33.4744i	0.618941	+	1.07204i
$976$	6.35122	−	11.0006i	0.203298	−	0.352122i
$977$	25.0740	−	43.4294i	0.802187	−	1.38943i	−0.115987	−	0.993251i	$-0.537003\pi$
$977$	25.0740	−	43.4294i	0.802187	−	1.38943i	0.918174	−	0.396178i	$-0.129664\pi$
$978$	−2.70152	−	4.67916i	−0.0863850	−	0.149623i
$979$		0			0
$980$	12.9904	+	8.26004i	0.414964	+	0.263857i
$981$	20.2859			0.647678
$982$	−3.43968	−	5.95769i	−0.109764	−	0.190118i
$983$	−4.26365	+	7.38486i	−0.135989	+	0.235541i	−0.925975	−	0.377585i	$-0.876755\pi$
$983$	−4.26365	+	7.38486i	−0.135989	+	0.235541i	0.789986	+	0.613125i	$0.210088\pi$
$984$	0.203799	−	0.352991i	0.00649689	−	0.0112529i
$985$	−1.96518	−	3.40379i	−0.0626158	−	0.108454i
$986$	3.50980			0.111775
$987$	−22.0823	−	6.42605i	−0.702888	−	0.204543i
$988$	−16.8155			−0.534971
$989$	−18.8547	−	32.6573i	−0.599544	−	1.03844i
$990$		0			0
$991$	25.2969	−	43.8155i	0.803582	−	1.39185i	−0.113662	−	0.993520i	$-0.536258\pi$
$991$	25.2969	−	43.8155i	0.803582	−	1.39185i	0.917244	−	0.398326i	$-0.130409\pi$
$992$	0.111768	+	0.193588i	0.00354864	+	0.00614642i
$993$	28.1976			0.894824
$994$	1.37974	+	5.62797i	0.0437625	+	0.178508i
$995$	1.79170			0.0568008
$996$	−31.8070	−	55.0913i	−1.00784	−	1.74563i
$997$	−3.39043	+	5.87240i	−0.107376	+	0.185981i	−0.914707	−	0.404119i	$-0.867578\pi$
$997$	−3.39043	+	5.87240i	−0.107376	+	0.185981i	0.807330	+	0.590100i	$0.200912\pi$
$998$	5.56279	−	9.63504i	0.176087	−	0.304992i
$999$	−7.92760	−	13.7310i	−0.250818	−	0.434430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.e.i.606.6		20
7.2	even	3	inner	847.2.e.i.485.6		20
7.3	odd	6		5929.2.a.bx.1.5		10
7.4	even	3		5929.2.a.bw.1.5		10
11.2	odd	10		847.2.n.j.81.3		40
11.3	even	5		847.2.n.i.130.3		40
11.4	even	5		847.2.n.i.753.3		40
11.5	even	5		77.2.m.b.25.3	yes	40
11.6	odd	10		847.2.n.j.487.3		40
11.7	odd	10		847.2.n.h.753.3		40
11.8	odd	10		847.2.n.h.130.3		40
11.9	even	5		77.2.m.b.4.3	✓	40
11.10	odd	2		847.2.e.h.606.5		20
33.5	odd	10		693.2.by.b.487.3		40
33.20	odd	10		693.2.by.b.235.3		40
77.2	odd	30		847.2.n.j.807.3		40
77.5	odd	30		539.2.q.h.520.3		40
77.9	even	15		77.2.m.b.37.3	yes	40
77.10	even	6		5929.2.a.bz.1.6		10
77.16	even	15		77.2.m.b.58.3	yes	40
77.20	odd	10		539.2.q.h.312.3		40
77.27	odd	10		539.2.q.h.410.3		40
77.30	odd	30		847.2.n.h.9.3		40
77.31	odd	30		539.2.f.g.246.3		20
77.32	odd	6		5929.2.a.by.1.6		10
77.37	even	15		847.2.n.i.632.3		40
77.38	odd	30		539.2.f.g.344.3		20
77.51	odd	30		847.2.n.h.632.3		40
77.53	even	15		539.2.f.h.246.3		20
77.58	even	15		847.2.n.i.9.3		40
77.60	even	15		539.2.f.h.344.3		20
77.65	odd	6		847.2.e.h.485.5		20
77.72	odd	30		847.2.n.j.366.3		40
77.75	odd	30		539.2.q.h.422.3		40
231.86	odd	30		693.2.by.b.37.3		40
231.170	odd	30		693.2.by.b.289.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.3	✓	40	11.9	even	5
77.2.m.b.25.3	yes	40	11.5	even	5
77.2.m.b.37.3	yes	40	77.9	even	15
77.2.m.b.58.3	yes	40	77.16	even	15
539.2.f.g.246.3		20	77.31	odd	30
539.2.f.g.344.3		20	77.38	odd	30
539.2.f.h.246.3		20	77.53	even	15
539.2.f.h.344.3		20	77.60	even	15
539.2.q.h.312.3		40	77.20	odd	10
539.2.q.h.410.3		40	77.27	odd	10
539.2.q.h.422.3		40	77.75	odd	30
539.2.q.h.520.3		40	77.5	odd	30
693.2.by.b.37.3		40	231.86	odd	30
693.2.by.b.235.3		40	33.20	odd	10
693.2.by.b.289.3		40	231.170	odd	30
693.2.by.b.487.3		40	33.5	odd	10
847.2.e.h.485.5		20	77.65	odd	6
847.2.e.h.606.5		20	11.10	odd	2
847.2.e.i.485.6		20	7.2	even	3	inner
847.2.e.i.606.6		20	1.1	even	1	trivial
847.2.n.h.9.3		40	77.30	odd	30
847.2.n.h.130.3		40	11.8	odd	10
847.2.n.h.632.3		40	77.51	odd	30
847.2.n.h.753.3		40	11.7	odd	10
847.2.n.i.9.3		40	77.58	even	15
847.2.n.i.130.3		40	11.3	even	5
847.2.n.i.632.3		40	77.37	even	15
847.2.n.i.753.3		40	11.4	even	5
847.2.n.j.81.3		40	11.2	odd	10
847.2.n.j.366.3		40	77.72	odd	30
847.2.n.j.487.3		40	11.6	odd	10
847.2.n.j.807.3		40	77.2	odd	30
5929.2.a.bw.1.5		10	7.4	even	3
5929.2.a.bx.1.5		10	7.3	odd	6
5929.2.a.by.1.6		10	77.32	odd	6
5929.2.a.bz.1.6		10	77.10	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.218609 + 0.378642i) q^{2} +(1.29176 - 2.23740i) q^{3} +(0.904420 - 1.56650i) q^{4} +(0.607894 + 1.05290i) q^{5} +1.12957 q^{6} +(-2.54037 - 0.739259i) q^{7} +1.66530 q^{8} +(-1.83731 - 3.18231i) q^{9} +O(q^{10})\)	\(q+(0.218609 + 0.378642i) q^{2} +(1.29176 - 2.23740i) q^{3} +(0.904420 - 1.56650i) q^{4} +(0.607894 + 1.05290i) q^{5} +1.12957 q^{6} +(-2.54037 - 0.739259i) q^{7} +1.66530 q^{8} +(-1.83731 - 3.18231i) q^{9} +(-0.265782 + 0.460348i) q^{10} +(-2.33659 - 4.04710i) q^{12} -4.24812 q^{13} +(-0.275434 - 1.12350i) q^{14} +3.14102 q^{15} +(-1.44479 - 2.50245i) q^{16} +(2.42099 - 4.19328i) q^{17} +(0.803306 - 1.39137i) q^{18} +(1.09416 + 1.89515i) q^{19} +2.19916 q^{20} +(-4.93558 + 4.72889i) q^{21} +(-3.26652 - 5.65778i) q^{23} +(2.15117 - 3.72593i) q^{24} +(1.76093 - 3.05002i) q^{25} +(-0.928677 - 1.60852i) q^{26} -1.74290 q^{27} +(-3.45562 + 3.31090i) q^{28} +1.65791 q^{29} +(0.686656 + 1.18932i) q^{30} +(-0.0243293 + 0.0421396i) q^{31} +(2.29698 - 3.97849i) q^{32} +2.11701 q^{34} +(-0.765908 - 3.12416i) q^{35} -6.64680 q^{36} +(4.54852 + 7.87826i) q^{37} +(-0.478389 + 0.828594i) q^{38} +(-5.48756 + 9.50474i) q^{39} +(1.01232 + 1.75339i) q^{40} +0.0947390 q^{41} +(-2.86952 - 0.835042i) q^{42} +5.77210 q^{43} +(2.23378 - 3.86902i) q^{45} +(1.42818 - 2.47369i) q^{46} +(1.68230 + 2.91383i) q^{47} -7.46532 q^{48} +(5.90699 + 3.75599i) q^{49} +1.53982 q^{50} +(-6.25471 - 10.8335i) q^{51} +(-3.84208 + 6.65468i) q^{52} +(-0.141461 + 0.245018i) q^{53} +(-0.381013 - 0.659935i) q^{54} +(-4.23047 - 1.23109i) q^{56} +5.65361 q^{57} +(0.362434 + 0.627754i) q^{58} +(-5.12783 + 8.88165i) q^{59} +(2.84080 - 4.92041i) q^{60} +(2.19797 + 3.80700i) q^{61} -0.0212744 q^{62} +(2.31490 + 9.44251i) q^{63} -3.77060 q^{64} +(-2.58240 - 4.47285i) q^{65} +(-4.56257 + 7.90259i) q^{67} +(-4.37919 - 7.58498i) q^{68} -16.8783 q^{69} +(1.01550 - 0.972975i) q^{70} -5.00931 q^{71} +(-3.05966 - 5.29949i) q^{72} +(3.79948 - 6.58089i) q^{73} +(-1.98870 + 3.44452i) q^{74} +(-4.54942 - 7.87982i) q^{75} +3.95834 q^{76} -4.79853 q^{78} +(-1.75918 - 3.04700i) q^{79} +(1.75656 - 3.04245i) q^{80} +(3.26052 - 5.64738i) q^{81} +(0.0207108 + 0.0358722i) q^{82} +13.6125 q^{83} +(2.94397 + 12.0085i) q^{84} +5.88683 q^{85} +(1.26183 + 2.18556i) q^{86} +(2.14163 - 3.70941i) q^{87} +(2.34726 + 4.06558i) q^{89} +1.95330 q^{90} +(10.7918 + 3.14046i) q^{91} -11.8172 q^{92} +(0.0628554 + 0.108869i) q^{93} +(-0.735533 + 1.27398i) q^{94} +(-1.33027 + 2.30410i) q^{95} +(-5.93432 - 10.2786i) q^{96} +18.0218 q^{97} +(-0.130854 + 3.05773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} - 18 q^{6} - 11 q^{7} + 6 q^{8} - 9 q^{9}+O(q^{10}) \) 20 * q + q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 - 18 * q^6 - 11 * q^7 + 6 * q^8 - 9 * q^9	\( 20 q + q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} - 18 q^{6} - 11 q^{7} + 6 q^{8} - 9 q^{9} + 7 q^{10} - 9 q^{12} - 2 q^{13} - 19 q^{14} - 2 q^{15} - 15 q^{16} + 19 q^{17} + 17 q^{18} + 28 q^{19} - 10 q^{20} - q^{21} - 7 q^{23} + 19 q^{24} + 8 q^{25} + 5 q^{26} + 12 q^{27} + 8 q^{28} + 30 q^{29} - 22 q^{30} + 14 q^{31} - 15 q^{32} + 24 q^{34} + 8 q^{35} + 32 q^{36} - 13 q^{37} - 24 q^{38} + 4 q^{39} + 10 q^{40} - 70 q^{41} + 25 q^{42} - 36 q^{43} - 8 q^{45} + 9 q^{46} - 16 q^{47} - 66 q^{48} - 25 q^{49} - 12 q^{50} - 21 q^{51} - 4 q^{52} + 9 q^{53} + 17 q^{54} + 12 q^{56} - 8 q^{57} + 9 q^{58} - 12 q^{59} + 21 q^{60} + 20 q^{61} - 76 q^{62} + 12 q^{63} - 58 q^{64} - 20 q^{65} - 19 q^{67} + 56 q^{68} + 18 q^{69} + 21 q^{70} + 30 q^{71} - 4 q^{72} + 3 q^{73} + 42 q^{74} + 27 q^{75} - 48 q^{76} - 50 q^{78} - 32 q^{79} + 6 q^{80} + 46 q^{81} + 18 q^{82} - 58 q^{83} + 73 q^{84} + 46 q^{85} - 9 q^{86} + 24 q^{87} - 5 q^{89} - 24 q^{90} + 28 q^{91} + 30 q^{92} + q^{93} - 19 q^{94} + q^{95} + 46 q^{96} + 8 q^{97} + 58 q^{98}+O(q^{100}) \) 20 * q + q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 - 18 * q^6 - 11 * q^7 + 6 * q^8 - 9 * q^9 + 7 * q^10 - 9 * q^12 - 2 * q^13 - 19 * q^14 - 2 * q^15 - 15 * q^16 + 19 * q^17 + 17 * q^18 + 28 * q^19 - 10 * q^20 - q^21 - 7 * q^23 + 19 * q^24 + 8 * q^25 + 5 * q^26 + 12 * q^27 + 8 * q^28 + 30 * q^29 - 22 * q^30 + 14 * q^31 - 15 * q^32 + 24 * q^34 + 8 * q^35 + 32 * q^36 - 13 * q^37 - 24 * q^38 + 4 * q^39 + 10 * q^40 - 70 * q^41 + 25 * q^42 - 36 * q^43 - 8 * q^45 + 9 * q^46 - 16 * q^47 - 66 * q^48 - 25 * q^49 - 12 * q^50 - 21 * q^51 - 4 * q^52 + 9 * q^53 + 17 * q^54 + 12 * q^56 - 8 * q^57 + 9 * q^58 - 12 * q^59 + 21 * q^60 + 20 * q^61 - 76 * q^62 + 12 * q^63 - 58 * q^64 - 20 * q^65 - 19 * q^67 + 56 * q^68 + 18 * q^69 + 21 * q^70 + 30 * q^71 - 4 * q^72 + 3 * q^73 + 42 * q^74 + 27 * q^75 - 48 * q^76 - 50 * q^78 - 32 * q^79 + 6 * q^80 + 46 * q^81 + 18 * q^82 - 58 * q^83 + 73 * q^84 + 46 * q^85 - 9 * q^86 + 24 * q^87 - 5 * q^89 - 24 * q^90 + 28 * q^91 + 30 * q^92 + q^93 - 19 * q^94 + q^95 + 46 * q^96 + 8 * q^97 + 58 * q^98

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