LMFDB - Embedded newform 845.2.n.e.484.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(484,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("845.484");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.6
Root			$2.20467 + 1.27287i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.e.529.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20467 - 1.27287i) q^{2} +(1.86449 - 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(-2.54486 - 1.46928i) q^{7} -6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +O(q^{10})$	\(q+(2.20467 - 1.27287i) q^{2} +(1.86449 - 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(-2.54486 - 1.46928i) q^{7} -6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +(4.45158 + 3.54786i) q^{10} +(-0.317544 - 0.550003i) q^{11} -9.64680i q^{12} -7.48079 q^{14} +(3.76470 + 3.00042i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(1.05998 + 0.611979i) q^{17} -4.16251i q^{18} +(-0.682456 + 1.18205i) q^{19} +(9.90788 + 1.49037i) q^{20} -6.32648 q^{21} +(-1.40016 - 0.808385i) q^{22} +(-1.86449 + 1.07646i) q^{23} +(-6.79833 - 11.7751i) q^{24} +(-3.66324 + 3.40304i) q^{25} +2.93855i q^{27} +(-11.4030 + 6.58351i) q^{28} +(1.50000 + 2.59808i) q^{29} +(12.1191 + 1.82298i) q^{30} +8.96157 q^{31} +(-4.74954 - 2.74215i) q^{32} +(-1.18412 - 0.683650i) q^{33} +3.11588 q^{34} +(0.977401 - 6.49770i) q^{35} +(-3.66324 - 6.34492i) q^{36} +(-1.05998 + 0.611979i) q^{37} +3.47471i q^{38} +(13.1440 - 5.16315i) q^{40} +(-4.98079 - 8.62698i) q^{41} +(-13.9478 + 8.05279i) q^{42} +(-1.18412 - 0.683650i) q^{43} -2.84570 q^{44} +(3.61549 + 0.543852i) q^{45} +(-2.74039 + 4.74650i) q^{46} +6.16379i q^{47} +(-13.2675 - 7.65998i) q^{48} +(0.817544 + 1.41603i) q^{49} +(-3.74464 + 12.1654i) q^{50} +2.63509 q^{51} -0.642285i q^{53} +(3.74039 + 6.47855i) q^{54} +(0.885090 - 1.11054i) q^{55} +(-9.27912 + 16.0719i) q^{56} +2.93855i q^{57} +(6.61402 + 3.81861i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(20.0774 - 7.88669i) q^{60} +(1.13509 - 1.96603i) q^{61} +(19.7574 - 11.4069i) q^{62} +(-4.16107 + 2.40240i) q^{63} +0.270178 q^{64} -3.48079 q^{66} +(-6.95421 + 4.01502i) q^{67} +(4.74954 - 2.74215i) q^{68} +(-2.31754 + 4.01410i) q^{69} +(-6.11588 - 15.5694i) q^{70} +(1.31754 - 2.28205i) q^{71} +(-8.94284 - 5.16315i) q^{72} -10.3263i q^{73} +(-1.55794 + 2.69843i) q^{74} +(-3.16683 + 10.2883i) q^{75} +(3.05794 + 5.29650i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(9.91702 - 12.4431i) q^{80} +(5.61588 + 9.72698i) q^{81} +(-21.9620 - 12.6798i) q^{82} +11.8452i q^{83} +(-14.1738 + 24.5498i) q^{84} +(-0.407104 + 2.70640i) q^{85} -3.48079 q^{86} +(5.59346 + 3.22939i) q^{87} +(-3.47351 + 2.00543i) q^{88} +(6.27912 + 10.8758i) q^{89} +(8.66324 - 3.40304i) q^{90} +9.64680i q^{92} +(16.7087 - 9.64680i) q^{93} +(7.84570 + 13.5891i) q^{94} +(-3.01808 - 0.453987i) q^{95} -11.8073 q^{96} +(-12.8031 - 7.39190i) q^{97} +(3.60484 + 2.08125i) q^{98} -1.03843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 + 4 * q^15 - 16 * q^16 - 12 * q^19 + q^20 + 8 * q^21 - 32 * q^24 - 2 * q^25 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 29 * q^45 - 10 * q^46 + 6 * q^49 + 31 * q^50 + 24 * q^51 + 22 * q^54 - 26 * q^55 - 16 * q^56 + 4 * q^59 + 96 * q^60 + 6 * q^61 - 12 * q^64 + 4 * q^66 - 24 * q^69 - 20 * q^70 + 12 * q^71 + 8 * q^74 + 2 * q^75 + 10 * q^76 - 104 * q^79 - 33 * q^80 + 14 * q^81 - 90 * q^84 - 21 * q^85 + 4 * q^86 - 20 * q^89 + 62 * q^90 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	2.20467	−	1.27287i	1.55894	−	0.900055i	0.561582	−	0.827421i	$-0.310193\pi$
$2$	2.20467	−	1.27287i	1.55894	−	0.900055i	0.997359	−	0.0726333i	$-0.0231403\pi$
$3$	1.86449	−	1.07646i	1.07646	−	0.621496i	0.146523	−	0.989207i	$-0.453192\pi$
$3$	1.86449	−	1.07646i	1.07646	−	0.621496i	0.929940	+	0.367711i	$0.119858\pi$
$4$	2.24039	−	3.88048i	1.12020	−	1.94024i
$5$	0.817544	+	2.08125i	0.365617	+	0.930765i
$5$	0.817544	+	2.08125i	0.365617	+	0.930765i
$6$	2.74039	−	4.74650i	1.11876	−	1.93775i
$7$	−2.54486	−	1.46928i	−0.961867	−	0.555334i	−0.0651198	−	0.997877i	$-0.520743\pi$
$7$	−2.54486	−	1.46928i	−0.961867	−	0.555334i	−0.896747	+	0.442543i	$0.854076\pi$
$8$		−	6.31544i		−	2.23284i
$9$	0.817544	−	1.41603i	0.272515	−	0.472010i
$10$	4.45158	+	3.54786i	1.40771	+	1.12193i
$11$	−0.317544	−	0.550003i	−0.0957433	−	0.165832i	0.814175	−	0.580619i	$-0.197189\pi$
$11$	−0.317544	−	0.550003i	−0.0957433	−	0.165832i	−0.909919	+	0.414787i	$0.863856\pi$
$12$		−	9.64680i		−	2.78479i
$13$		0			0
$13$		0			0
$14$	−7.48079			−1.99932
$15$	3.76470	+	3.00042i	0.972040	+	0.774705i
$16$	−3.55794	−	6.16253i	−0.889484	−	1.54063i
$17$	1.05998	+	0.611979i	0.257082	+	0.148427i	0.623003	−	0.782220i	$-0.285912\pi$
$17$	1.05998	+	0.611979i	0.257082	+	0.148427i	−0.365920	+	0.930646i	$0.619246\pi$
$18$		−	4.16251i		−	0.981113i
$19$	−0.682456	+	1.18205i	−0.156566	+	0.271180i	−0.933628	−	0.358244i	$-0.883376\pi$
$19$	−0.682456	+	1.18205i	−0.156566	+	0.271180i	0.777062	+	0.629424i	$0.216709\pi$
$20$	9.90788	+	1.49037i	2.21547	+	0.333256i
$21$	−6.32648			−1.38055
$22$	−1.40016	−	0.808385i	−0.298516	−	0.172348i
$23$	−1.86449	+	1.07646i	−0.388773	+	0.224458i	−0.681628	−	0.731699i	$-0.738728\pi$
$23$	−1.86449	+	1.07646i	−0.388773	+	0.224458i	0.292856	+	0.956157i	$0.405394\pi$
$24$	−6.79833	−	11.7751i	−1.38770	−	2.40357i
$25$	−3.66324	+	3.40304i	−0.732648	+	0.680607i
$26$		0			0
$27$			2.93855i			0.565525i
$28$	−11.4030	+	6.58351i	−2.15496	+	1.24417i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	12.1191	+	1.82298i	2.21263	+	0.332829i
$31$	8.96157			1.60955			0.804773	−	0.593583i	$-0.202287\pi$
$31$	8.96157			1.60955			0.804773	+	0.593583i	$0.202287\pi$
$32$	−4.74954	−	2.74215i	−0.839607	−	0.484747i
$33$	−1.18412	−	0.683650i	−0.206128	−	0.119008i
$34$	3.11588			0.534368
$35$	0.977401	−	6.49770i	0.165211	−	1.09831i
$36$	−3.66324	−	6.34492i	−0.610540	−	1.05749i
$37$	−1.05998	+	0.611979i	−0.174259	+	0.100609i	−0.584593	−	0.811327i	$-0.698746\pi$
$37$	−1.05998	+	0.611979i	−0.174259	+	0.100609i	0.410333	+	0.911936i	$0.365412\pi$
$38$			3.47471i			0.563672i
$39$		0			0
$40$	13.1440	−	5.16315i	2.07825	−	0.816366i
$41$	−4.98079	−	8.62698i	−0.777868	−	1.34731i	−0.933168	−	0.359440i	$-0.882968\pi$
$41$	−4.98079	−	8.62698i	−0.777868	−	1.34731i	0.155300	−	0.987867i	$-0.450366\pi$
$42$	−13.9478	+	8.05279i	−2.15220	+	1.24257i
$43$	−1.18412	−	0.683650i	−0.180576	−	0.104256i	0.406987	−	0.913434i	$-0.366579\pi$
$43$	−1.18412	−	0.683650i	−0.180576	−	0.104256i	−0.587563	+	0.809178i	$0.699913\pi$
$44$	−2.84570			−0.429005
$45$	3.61549	+	0.543852i	0.538966	+	0.0810727i
$46$	−2.74039	+	4.74650i	−0.404049	+	0.699833i
$47$			6.16379i			0.899081i	0.893260	+	0.449540i	$0.148412\pi$
$47$			6.16379i			0.899081i	−0.893260	+	0.449540i	$0.851588\pi$
$48$	−13.2675	−	7.65998i	−1.91499	−	1.10562i
$49$	0.817544	+	1.41603i	0.116792	+	0.202290i
$50$	−3.74464	+	12.1654i	−0.529571	+	1.72045i
$51$	2.63509			0.368986
$52$		0			0
$53$		−	0.642285i		−	0.0882246i	−0.999027	−	0.0441123i	$-0.985954\pi$
$53$		−	0.642285i		−	0.0882246i	0.999027	−	0.0441123i	$-0.0140459\pi$
$54$	3.74039	+	6.47855i	0.509003	+	0.881619i
$55$	0.885090	−	1.11054i	0.119345	−	0.149746i
$56$	−9.27912	+	16.0719i	−1.23997	+	2.14770i
$57$			2.93855i			0.389221i
$58$	6.61402	+	3.81861i	0.868464	+	0.501408i
$59$	−3.79833	+	6.57890i	−0.494501	+	0.856500i	−0.999980	−	0.00633858i	$-0.997982\pi$
$59$	−3.79833	+	6.57890i	−0.494501	+	0.856500i	0.505479	+	0.862839i	$0.331316\pi$
$60$	20.0774	−	7.88669i	2.59199	−	1.01817i
$61$	1.13509	−	1.96603i	0.145333	−	0.251725i	−0.784164	−	0.620554i	$-0.786908\pi$
$61$	1.13509	−	1.96603i	0.145333	−	0.251725i	0.929497	+	0.368829i	$0.120241\pi$
$62$	19.7574	−	11.4069i	2.50919	−	1.44868i
$63$	−4.16107	+	2.40240i	−0.524246	+	0.302674i
$64$	0.270178			0.0337722
$65$		0			0
$66$	−3.48079			−0.428455
$67$	−6.95421	+	4.01502i	−0.849592	+	0.490512i	−0.860513	−	0.509428i	$-0.829857\pi$
$67$	−6.95421	+	4.01502i	−0.849592	+	0.490512i	0.0109212	+	0.999940i	$0.496524\pi$
$68$	4.74954	−	2.74215i	0.575966	−	0.332534i
$69$	−2.31754	+	4.01410i	−0.279000	+	0.483241i
$70$	−6.11588	−	15.5694i	−0.730987	−	1.86090i
$71$	1.31754	−	2.28205i	0.156364	−	0.270830i	−0.777191	−	0.629265i	$-0.783356\pi$
$71$	1.31754	−	2.28205i	0.156364	−	0.270830i	0.933555	+	0.358435i	$0.116689\pi$
$72$	−8.94284	−	5.16315i	−1.05392	−	0.608483i
$73$		−	10.3263i		−	1.20860i	−0.796756	−	0.604301i	$-0.793453\pi$
$73$		−	10.3263i		−	1.20860i	0.796756	−	0.604301i	$-0.206547\pi$
$74$	−1.55794	+	2.69843i	−0.181107	+	0.313686i
$75$	−3.16683	+	10.2883i	−0.365674	+	1.18799i
$76$	3.05794	+	5.29650i	0.350770	+	0.607551i
$77$			1.86624i			0.212678i
$78$		0			0
$79$	−1.03843			−0.116832			−0.0584161	−	0.998292i	$-0.518605\pi$
$79$	−1.03843			−0.116832			−0.0584161	+	0.998292i	$0.518605\pi$
$80$	9.91702	−	12.4431i	1.10876	−	1.39118i
$81$	5.61588	+	9.72698i	0.623986	+	1.08078i
$82$	−21.9620	−	12.6798i	−2.42530	−	1.40025i
$83$			11.8452i			1.30018i	0.759855	+	0.650092i	$0.225270\pi$
$83$			11.8452i			1.30018i	−0.759855	+	0.650092i	$0.774730\pi$
$84$	−14.1738	+	24.5498i	−1.54649	+	2.67860i
$85$	−0.407104	+	2.70640i	−0.0441566	+	0.293551i
$86$	−3.48079			−0.375343
$87$	5.59346	+	3.22939i	0.599682	+	0.346227i
$88$	−3.47351	+	2.00543i	−0.370277	+	0.213780i
$89$	6.27912	+	10.8758i	0.665585	+	1.15283i	0.979126	+	0.203253i	$0.0651513\pi$
$89$	6.27912	+	10.8758i	0.665585	+	1.15283i	−0.313541	+	0.949575i	$0.601515\pi$
$90$	8.66324	−	3.40304i	0.913186	−	0.358712i
$91$		0			0
$92$			9.64680i			1.00575i
$93$	16.7087	−	9.64680i	1.73262	−	1.00033i
$94$	7.84570	+	13.5891i	0.809222	+	1.40161i
$95$	−3.01808	−	0.453987i	−0.309648	−	0.0465781i
$96$	−11.8073			−1.20507
$97$	−12.8031	−	7.39190i	−1.29996	−	0.750534i	−0.319565	−	0.947564i	$-0.603537\pi$
$97$	−12.8031	−	7.39190i	−1.29996	−	0.750534i	−0.980397	+	0.197031i	$0.936870\pi$
$98$	3.60484	+	2.08125i	0.364144	+	0.210238i
$99$	−1.03843			−0.104366
$100$	4.99829	+	21.8393i	0.499829	+	2.18393i
$101$	−6.61588	−	11.4590i	−0.658304	−	1.14022i	−0.981054	−	0.193732i	$-0.937941\pi$
$101$	−6.61588	−	11.4590i	−0.658304	−	1.14022i	0.322750	−	0.946484i	$-0.395393\pi$
$102$	5.80951	−	3.35412i	0.575228	−	0.332108i
$103$		−	10.9686i		−	1.08077i	−0.841419	−	0.540383i	$-0.818279\pi$
$103$		−	10.9686i		−	1.08077i	0.841419	−	0.540383i	$-0.181721\pi$
$104$		0			0
$105$	−5.17218	−	13.1670i	−0.504753	−	1.28497i
$106$	−0.817544	−	1.41603i	−0.0794069	−	0.137537i
$107$	−9.24360	+	5.33680i	−0.893613	+	0.515928i	−0.875123	−	0.483901i	$-0.839219\pi$
$107$	−9.24360	+	5.33680i	−0.893613	+	0.515928i	−0.0184903	+	0.999829i	$0.505886\pi$
$108$	11.4030	+	6.58351i	1.09725	+	0.633499i
$109$	−3.27018			−0.313226			−0.156613	−	0.987660i	$-0.550058\pi$
$109$	−3.27018			−0.313226			−0.156613	+	0.987660i	$0.550058\pi$
$110$	0.537759	−	3.57499i	0.0512733	−	0.340862i
$111$	−1.31754	+	2.28205i	−0.125056	+	0.216603i
$112$			20.9104i			1.97584i
$113$	−4.78895	−	2.76490i	−0.450507	−	0.260100i	0.257537	−	0.966268i	$-0.417089\pi$
$113$	−4.78895	−	2.76490i	−0.450507	−	0.260100i	−0.708044	+	0.706168i	$0.750422\pi$
$114$	3.74039	+	6.47855i	0.350320	+	0.606772i
$115$	−3.76470	−	3.00042i	−0.351060	−	0.279790i
$116$	13.4424			1.24809
$117$		0			0
$118$			19.3391i			1.78031i
$119$	−1.79833	−	3.11480i	−0.164853	−	0.285533i
$120$	18.9490	−	23.7757i	1.72979	−	2.17041i
$121$	5.29833	−	9.17698i	0.481666	−	0.834271i
$122$		−	5.77928i		−	0.523231i
$123$	−18.5732	−	10.7233i	−1.67469	−	0.966884i
$124$	20.0774	−	34.7752i	1.80301	−	3.12290i
$125$	−10.0774	−	4.84201i	−0.901354	−	0.433082i
$126$	−6.11588	+	10.5930i	−0.544845	+	0.943700i
$127$	−14.9231	+	8.61586i	−1.32421	+	0.764534i	−0.984397	−	0.175959i	$-0.943697\pi$
$127$	−14.9231	+	8.61586i	−1.32421	+	0.764534i	−0.339813	+	0.940493i	$0.610364\pi$
$128$	10.0947	−	5.82819i	0.892256	−	0.515144i
$129$	−2.94369			−0.259178
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−5.30577	+	3.06329i	−0.461808	+	0.266625i
$133$	3.47351	−	2.00543i	0.301191	−	0.173893i
$134$	−10.2212	+	17.7036i	−0.882975	+	1.52936i
$135$	−6.11588	+	2.40240i	−0.526371	+	0.206765i
$136$	3.86491	−	6.69422i	0.331413	−	0.574025i
$137$	−7.51044	−	4.33616i	−0.641661	−	0.370463i	0.143593	−	0.989637i	$-0.454134\pi$
$137$	−7.51044	−	4.33616i	−0.641661	−	0.370463i	−0.785254	+	0.619174i	$0.787468\pi$
$138$			11.7997i			1.00446i
$139$	7.16324	−	12.4071i	0.607578	−	1.05236i	−0.384060	−	0.923308i	$-0.625474\pi$
$139$	7.16324	−	12.4071i	0.607578	−	1.05236i	0.991638	−	0.129048i	$-0.0411922\pi$
$140$	−23.0244	−	18.3502i	−1.94592	−	1.55087i
$141$	6.63509	+	11.4923i	0.558775	+	0.967827i
$142$		−	6.70825i		−	0.562944i
$143$		0			0
$144$	−11.6351			−0.969591
$145$	−4.18094	+	5.24592i	−0.347208	+	0.435650i
$146$	−13.1440	−	22.7661i	−1.08781	−	1.88414i
$147$	3.04860	+	1.76011i	0.251445	+	0.145172i
$148$			5.48429i			0.450806i
$149$	8.57745	−	14.8566i	0.702692	−	1.21710i	−0.264826	−	0.964296i	$-0.585315\pi$
$149$	8.57745	−	14.8566i	0.702692	−	1.21710i	0.967518	−	0.252802i	$-0.0813521\pi$
$150$	6.11379	+	26.7132i	0.499189	+	2.18113i
$151$	21.3828			1.74011			0.870053	−	0.492957i	$-0.164084\pi$
$151$	21.3828			1.74011			0.870053	+	0.492957i	$0.164084\pi$
$152$	7.46515	+	4.31000i	0.605503	+	0.349587i
$153$	1.73316	−	1.00064i	0.140118	−	0.0808969i
$154$	2.37548	+	4.11446i	0.191422	+	0.331552i
$155$	7.32648	+	18.6513i	0.588477	+	1.49811i
$156$		0			0
$157$		−	18.3646i		−	1.46566i	−0.680413	−	0.732829i	$-0.738200\pi$
$157$		−	18.3646i		−	1.46566i	0.680413	−	0.732829i	$-0.261800\pi$
$158$	−2.28939	+	1.32178i	−0.182134	+	0.105155i
$159$	−0.691395	−	1.19753i	−0.0548312	−	0.0949705i
$160$	1.82415	−	12.1268i	0.144211	−	0.958709i
$161$	6.32648			0.498597
$162$	24.7624	+	14.2966i	1.94551	+	1.12324i
$163$	3.47351	+	2.00543i	0.272066	+	0.157078i	0.629826	−	0.776736i	$-0.283126\pi$
$163$	3.47351	+	2.00543i	0.272066	+	0.157078i	−0.357760	+	0.933814i	$0.616459\pi$
$164$	−44.6357			−3.48546
$165$	0.454782	−	3.02336i	0.0354047	−	0.235368i
$166$	15.0774	+	26.1149i	1.17024	+	2.02691i
$167$	−2.54486	+	1.46928i	−0.196927	+	0.113696i	−0.595221	−	0.803562i	$-0.702936\pi$
$167$	−2.54486	+	1.46928i	−0.196927	+	0.113696i	0.398294	+	0.917258i	$0.369602\pi$
$168$			39.9545i			3.08256i
$169$		0			0
$170$	2.54737	+	6.48493i	0.195374	+	0.497371i
$171$	1.11588	+	1.93275i	0.0853331	+	0.147801i
$172$	−5.30577	+	3.06329i	−0.404561	+	0.233574i
$173$	1.18412	+	0.683650i	0.0900267	+	0.0519769i	0.544337	−	0.838866i	$-0.316781\pi$
$173$	1.18412	+	0.683650i	0.0900267	+	0.0519769i	−0.454311	+	0.890843i	$0.650114\pi$
$174$	16.4424			1.24649
$175$	14.3224	−	3.27794i	1.08267	−	0.247789i
$176$	−2.25961	+	3.91375i	−0.170324	+	0.295010i
$177$			16.3550i			1.22932i
$178$	27.6868	+	15.9850i	2.07522	+	1.19813i
$179$	3.89306	+	6.74299i	0.290981	+	0.503994i	0.974042	−	0.226367i	$-0.0726849\pi$
$179$	3.89306	+	6.74299i	0.290981	+	0.503994i	−0.683061	+	0.730362i	$0.739352\pi$
$180$	10.2105	−	12.8114i	0.761048	−	0.954905i
$181$	−3.86684			−0.287420			−0.143710	−	0.989620i	$-0.545903\pi$
$181$	−3.86684			−0.287420			−0.143710	+	0.989620i	$0.545903\pi$
$182$		0			0
$183$		−	4.88752i		−	0.361296i
$184$	6.79833	+	11.7751i	0.501180	+	0.868069i
$185$	−2.14026	−	1.70576i	−0.157355	−	0.125410i
$186$	24.5582	−	42.5361i	1.80070	−	3.11890i
$187$		−	0.777322i		−	0.0568434i
$188$	23.9184	+	13.8093i	1.74443	+	1.00715i
$189$	4.31754	−	7.47821i	0.314055	−	0.543959i
$190$	−7.23175	+	2.84073i	−0.524646	+	0.206088i
$191$	−2.47185	+	4.28136i	−0.178857	+	0.309789i	−0.941489	−	0.337043i	$-0.890573\pi$
$191$	−2.47185	+	4.28136i	−0.178857	+	0.309789i	0.762633	+	0.646832i	$0.223906\pi$
$192$	0.503743	−	0.290836i	0.0363545	−	0.0209893i
$193$	4.29240	−	2.47822i	0.308974	−	0.178386i	−0.337493	−	0.941328i	$-0.609579\pi$
$193$	4.29240	−	2.47822i	0.308974	−	0.178386i	0.646467	+	0.762942i	$0.276246\pi$
$194$	−37.6357			−2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	−5.84174	+	3.37273i	−0.416207	+	0.240297i	−0.693453	−	0.720502i	$-0.743912\pi$
$197$	−5.84174	+	3.37273i	−0.416207	+	0.240297i	0.277246	+	0.960799i	$0.410578\pi$
$198$	−2.28939	+	1.32178i	−0.162700	+	0.0939349i
$199$	2.58772	−	4.48207i	0.183439	−	0.317725i	−0.759611	−	0.650378i	$-0.774610\pi$
$199$	2.58772	−	4.48207i	0.183439	−	0.317725i	0.943049	+	0.332653i	$0.107944\pi$
$200$	21.4917	+	23.1350i	1.51969	+	1.63589i
$201$	−8.64403	+	14.9719i	−0.609703	+	1.05604i
$202$	−29.1717	−	16.8423i	−2.05251	−	1.18502i
$203$		−	8.81566i		−	0.618738i
$204$	5.90364	−	10.2254i	0.413337	−	0.715921i
$205$	13.8829	−	17.4192i	0.969625	−	1.21661i
$206$	−13.9616	−	24.1822i	−0.972749	−	1.68485i
$207$			3.52022i			0.244673i
$208$		0			0
$209$	0.866840			0.0599606
$210$	−28.1629	−	22.4455i	−1.94342	−	1.54889i
$211$	7.00894	+	12.1398i	0.482515	+	0.835741i	0.999799	−	0.0200732i	$-0.00638994\pi$
$211$	7.00894	+	12.1398i	0.482515	+	0.835741i	−0.517283	+	0.855814i	$0.673057\pi$
$212$	−2.49237	−	1.43897i	−0.171177	−	0.0988289i
$213$		−	5.67315i		−	0.388718i
$214$	−13.5861	+	23.5318i	−0.928726	+	1.60860i
$215$	0.454782	−	3.02336i	0.0310158	−	0.206191i
$216$	18.5582			1.26273
$217$	−22.8060	−	13.1670i	−1.54817	−	0.893836i
$218$	−7.20968	+	4.16251i	−0.488301	+	0.281921i
$219$	−11.1159	−	19.2533i	−0.751141	−	1.30101i
$220$	−2.32648	−	5.92262i	−0.156852	−	0.399303i
$221$		0			0
$222$			6.70825i			0.450228i
$223$	−0.00719226	+	0.00415245i	−0.000481629	+	0.000278069i	−0.500241	−	0.865886i	$-0.666755\pi$
$223$	−0.00719226	+	0.00415245i	−0.000481629	+	0.000278069i	0.499759	+	0.866164i	$0.333422\pi$
$224$	8.05794	+	13.9568i	0.538394	+	0.932525i
$225$	1.82393	+	7.96939i	0.121596	+	0.531293i
$226$	−14.0774			−0.936418
$227$	9.75454	+	5.63179i	0.647431	+	0.373795i	0.787471	−	0.616351i	$-0.211390\pi$
$227$	9.75454	+	5.63179i	0.647431	+	0.373795i	−0.140040	+	0.990146i	$0.544723\pi$
$228$	11.4030	+	6.58351i	0.755181	+	0.436004i
$229$	−16.5404			−1.09302			−0.546509	−	0.837453i	$-0.684043\pi$
$229$	−16.5404			−1.09302			−0.546509	+	0.837453i	$0.684043\pi$
$230$	−12.1191	−	1.82298i	−0.799108	−	0.120204i
$231$	2.00894	+	3.47959i	0.132179	+	0.228940i
$232$	16.4080	−	9.47315i	1.07724	−	0.621943i
$233$		−	6.94941i		−	0.455271i	−0.973746	−	0.227636i	$-0.926900\pi$
$233$		−	6.94941i		−	0.455271i	0.973746	−	0.227636i	$-0.0730995\pi$
$234$		0			0
$235$	−12.8284	+	5.03917i	−0.836833	+	0.328719i
$236$	17.0195	+	29.4787i	1.10788	+	1.91890i
$237$	−1.93613	+	1.11783i	−0.125765	+	0.0726107i
$238$	−7.92947	−	4.57808i	−0.513991	−	0.296753i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	5.09562	−	33.8753i	0.328921	−	2.18664i
$241$	9.88605	−	17.1231i	0.636817	−	1.10300i	−0.349310	−	0.937007i	$-0.613584\pi$
$241$	9.88605	−	17.1231i	0.636817	−	1.10300i	0.986127	−	0.165992i	$-0.0530825\pi$
$242$		−	26.9763i		−	1.73410i
$243$	13.3069	+	7.68273i	0.853637	+	0.492848i
$244$	−5.08609	−	8.80937i	−0.325604	−	0.563962i
$245$	−2.27874	+	2.85918i	−0.145583	+	0.182667i
$246$	−54.5973			−3.48099
$247$		0			0
$248$		−	56.5962i		−	3.59386i
$249$	12.7510	+	22.0853i	0.808060	+	1.39960i
$250$	−28.3807	+	2.15223i	−1.79496	+	0.136119i
$251$	−1.83676	+	3.18136i	−0.115935	+	0.200806i	−0.918153	−	0.396226i	$-0.870320\pi$
$251$	−1.83676	+	3.18136i	−0.115935	+	0.200806i	0.802218	+	0.597031i	$0.203653\pi$
$252$			21.5293i			1.35622i
$253$	1.18412	+	0.683650i	0.0744447	+	0.0429807i
$254$	−21.9337	+	37.9903i	−1.37624	+	2.38372i
$255$	2.15430	+	5.48429i	0.134908	+	0.343440i
$256$	14.5669	−	25.2306i	0.910430	−	1.57691i
$257$	−11.4877	+	6.63242i	−0.716583	+	0.413719i	−0.813494	−	0.581574i	$-0.802437\pi$
$257$	−11.4877	+	6.63242i	−0.716583	+	0.413719i	0.0969108	+	0.995293i	$0.469104\pi$
$258$	−6.48989	+	3.74694i	−0.404043	+	0.233274i
$259$	3.59666			0.223486
$260$		0			0
$261$	4.90527			0.303628
$262$	22.0467	−	12.7287i	1.36205	−	0.786381i
$263$	26.2150	−	15.1352i	1.61649	−	0.933279i	0.628667	−	0.777674i	$-0.283601\pi$
$263$	26.2150	−	15.1352i	1.61649	−	0.933279i	0.987819	−	0.155605i	$-0.0497327\pi$
$264$	−4.31754	+	7.47821i	−0.265726	+	0.460252i
$265$	1.33676	−	0.525096i	0.0821164	−	0.0322564i
$266$	5.10530	−	8.84265i	0.313026	−	0.542177i
$267$	23.4147	+	13.5185i	1.43296	+	0.827317i
$268$			35.9809i			2.19788i
$269$	−11.1248	+	19.2687i	−0.678292	+	1.17484i	0.297203	+	0.954814i	$0.403946\pi$
$269$	−11.1248	+	19.2687i	−0.678292	+	1.17484i	−0.975495	+	0.220022i	$0.929387\pi$
$270$	−10.4256	+	13.0812i	−0.634480	+	0.796097i
$271$	−5.91421	−	10.2437i	−0.359262	−	0.622261i	0.628575	−	0.777749i	$-0.283638\pi$
$271$	−5.91421	−	10.2437i	−0.359262	−	0.622261i	−0.987838	+	0.155488i	$0.950305\pi$
$272$		−	8.70953i		−	0.528093i
$273$		0			0
$274$	−22.0774			−1.33375
$275$	3.03492	+	0.934179i	0.183013	+	0.0563331i
$276$	10.3844	+	17.9863i	0.625069	+	1.08265i
$277$	14.5363	+	8.39254i	0.873402	+	0.504259i	0.868477	−	0.495729i	$-0.165099\pi$
$277$	14.5363	+	8.39254i	0.873402	+	0.504259i	0.00492452	+	0.999988i	$0.498432\pi$
$278$		−	36.4715i		−	2.18741i
$279$	7.32648	−	12.6898i	0.438625	−	0.759721i
$280$	−41.0358	−	6.17271i	−2.45236	−	0.368890i
$281$	10.5967			0.632144			0.316072	−	0.948735i	$-0.397636\pi$
$281$	10.5967			0.632144			0.316072	+	0.948735i	$0.397636\pi$
$282$	29.2564	+	16.8912i	1.74219	+	1.00586i
$283$	−7.63458	+	4.40783i	−0.453829	+	0.262018i	−0.709446	−	0.704760i	$-0.751055\pi$
$283$	−7.63458	+	4.40783i	−0.453829	+	0.262018i	0.255617	+	0.966778i	$0.417721\pi$
$284$	−5.90364	−	10.2254i	−0.350316	−	0.606766i
$285$	−6.11588	+	2.40240i	−0.362273	+	0.142306i
$286$		0			0
$287$			29.2726i			1.72791i
$288$	−7.76591	+	4.48365i	−0.457611	+	0.264202i
$289$	−7.75096	−	13.4251i	−0.455939	−	0.789710i
$290$	−2.54024	+	16.8873i	−0.149168	+	0.991659i
$291$	−31.8284			−1.86581
$292$	−40.0709	−	23.1350i	−2.34497	−	1.35387i
$293$	−24.4675	−	14.1263i	−1.42940	−	0.825267i	−0.432331	−	0.901715i	$-0.642309\pi$
$293$	−24.4675	−	14.1263i	−1.42940	−	0.825267i	−0.997074	+	0.0764476i	$0.975642\pi$
$294$	8.96157			0.522650
$295$	−16.7977	−	2.52675i	−0.977999	−	0.147113i
$296$	3.86491	+	6.69422i	0.224643	+	0.389094i
$297$	1.61621	−	0.933121i	0.0937822	−	0.0541452i
$298$		−	43.6719i		−	2.52984i
$299$		0			0
$300$	32.8284	+	35.3386i	1.89535	+	2.04027i
$301$	2.00894	+	3.47959i	0.115793	+	0.200560i
$302$	47.1421	−	27.2175i	2.71272	−	1.56619i
$303$	−24.6704	−	14.2435i	−1.41728	−	0.818267i
$304$	9.71254			0.557052
$305$	5.01980	+	0.755091i	0.287433	+	0.0432364i
$306$	2.54737	−	4.41217i	0.145623	−	0.252227i
$307$			12.7219i			0.726077i	0.931774	+	0.363039i	$0.118261\pi$
$307$			12.7219i			0.726077i	−0.931774	+	0.363039i	$0.881739\pi$
$308$	7.24190	+	4.18112i	0.412646	+	0.238241i
$309$	−11.8073	−	20.4508i	−0.671692	−	1.16340i
$310$	39.8932	+	31.7944i	2.26578	+	1.80580i
$311$	27.9231			1.58338			0.791688	−	0.610925i	$-0.209202\pi$
$311$	27.9231			1.58338			0.791688	+	0.610925i	$0.209202\pi$
$312$		0			0
$313$			24.5807i			1.38938i	0.719307	+	0.694692i	$0.244460\pi$
$313$			24.5807i			1.38938i	−0.719307	+	0.694692i	$0.755540\pi$
$314$	−23.3758	−	40.4880i	−1.31917	−	2.28487i
$315$	−8.40186	−	6.69619i	−0.473391	−	0.377287i
$316$	−2.32648	+	4.02959i	−0.130875	+	0.226682i
$317$		−	0.234377i		−	0.0131639i	−0.999978	−	0.00658196i	$-0.997905\pi$
$317$		−	0.234377i		−	0.0131639i	0.999978	−	0.00658196i	$-0.00209512\pi$
$318$	−3.04860	−	1.76011i	−0.170957	−	0.0987022i
$319$	0.952633	−	1.65001i	0.0533372	−	0.0923828i
$320$	0.220882	+	0.562309i	0.0123477	+	0.0314340i
$321$	−11.4897	+	19.9008i	−0.641294	+	1.11075i
$322$	13.9478	−	8.05279i	0.777283	−	0.448764i
$323$	−1.44678	+	0.835296i	−0.0805008	+	0.0464771i
$324$	50.3271			2.79595
$325$		0			0
$326$	10.2106			0.565513
$327$	−6.09721	+	3.52022i	−0.337176	+	0.194669i
$328$	−54.4831	+	31.4558i	−3.00833	+	1.73686i
$329$	9.05631	−	15.6860i	0.499290	−	0.864796i
$330$	−2.84570	−	7.24440i	−0.156651	−	0.398791i
$331$	−9.16324	+	15.8712i	−0.503657	+	0.872360i	0.496334	+	0.868132i	$0.334679\pi$
$331$	−9.16324	+	15.8712i	−0.503657	+	0.872360i	−0.999991	+	0.00422829i	$0.998654\pi$
$332$	45.9652	+	26.5380i	2.52267	+	1.45646i
$333$			2.00128i			0.109669i
$334$	−3.74039	+	6.47855i	−0.204665	+	0.354491i
$335$	−14.0416	−	11.1910i	−0.767177	−	0.611431i
$336$	22.5092	+	38.9871i	1.22798	+	2.12692i
$337$			21.2949i			1.16001i	0.814614	+	0.580003i	$0.196949\pi$
$337$			21.2949i			1.16001i	−0.814614	+	0.580003i	$0.803051\pi$
$338$		0			0
$339$	−11.9053			−0.646605
$340$	9.59006	+	7.64317i	0.520094	+	0.414509i
$341$	−2.84570	−	4.92889i	−0.154103	−	0.266915i
$342$	4.92028	+	2.84073i	0.266059	+	0.153609i
$343$			15.7651i			0.851234i
$344$	−4.31754	+	7.47821i	−0.232786	+	0.403198i
$345$	−10.2491	−	1.54169i	−0.551791	−	0.0830019i
$346$	3.48079			0.187128
$347$	−3.30407	−	1.90761i	−0.177372	−	0.102406i	0.408685	−	0.912675i	$-0.365987\pi$
$347$	−3.30407	−	1.90761i	−0.177372	−	0.102406i	−0.586057	+	0.810270i	$0.699321\pi$
$348$	25.0631	−	14.4702i	1.34352	−	0.775684i
$349$	−12.1632	−	21.0674i	−0.651083	−	1.12771i	−0.982860	−	0.184352i	$-0.940981\pi$
$349$	−12.1632	−	21.0674i	−0.651083	−	1.12771i	0.331777	−	0.943358i	$-0.392352\pi$
$350$	27.4039	−	25.4574i	1.46480	−	1.36075i
$351$		0			0
$352$			3.48301i			0.185645i
$353$	23.4338	−	13.5295i	1.24726	−	0.720104i	0.276696	−	0.960958i	$-0.410761\pi$
$353$	23.4338	−	13.5295i	1.24726	−	0.720104i	0.970562	+	0.240853i	$0.0774272\pi$
$354$	20.8178	+	36.0576i	1.10646	+	1.91644i
$355$	5.82669	+	0.876465i	0.309248	+	0.0465179i
$356$	56.2708			2.98235
$357$	−6.70593	−	3.87167i	−0.354916	−	0.204911i
$358$	17.1659	+	9.91073i	0.907245	+	0.523798i
$359$	27.0039			1.42521			0.712605	−	0.701566i	$-0.247515\pi$
$359$	27.0039			1.42521			0.712605	+	0.701566i	$0.247515\pi$
$360$	3.43466	−	22.8334i	0.181023	−	1.20343i
$361$	8.56851	+	14.8411i	0.450974	+	0.781110i
$362$	−8.52512	+	4.92198i	−0.448071	+	0.258694i
$363$		−	22.8138i		−	1.19742i
$364$		0			0
$365$	21.4917	−	8.44221i	1.12492	−	0.441885i
$366$	−6.22118	−	10.7754i	−0.325186	−	0.563239i
$367$	6.01118	−	3.47055i	0.313781	−	0.181161i	−0.334836	−	0.942276i	$-0.608681\pi$
$367$	6.01118	−	3.47055i	0.313781	−	0.181161i	0.648617	+	0.761115i	$0.275348\pi$
$368$	13.2675	+	7.65998i	0.691615	+	0.399304i
$369$	−16.2881			−0.847922
$370$	−6.88980	−	1.03638i	−0.358184	−	0.0538789i
$371$	−0.943693	+	1.63452i	−0.0489941	+	0.0848603i
$372$		−	86.4505i		−	4.48225i
$373$	−2.00301	−	1.15644i	−0.103712	−	0.0598781i	0.447247	−	0.894411i	$-0.352405\pi$
$373$	−2.00301	−	1.15644i	−0.103712	−	0.0598781i	−0.550959	+	0.834532i	$0.685738\pi$
$374$	−0.989429	−	1.71374i	−0.0511622	−	0.0886154i
$375$	−24.0015	+	1.82013i	−1.23943	+	0.0939913i
$376$	38.9270			2.00751
$377$		0			0
$378$		−	21.9827i		−	1.13067i
$379$	−2.58772	−	4.48207i	−0.132922	−	0.230228i	0.791880	−	0.610677i	$-0.209103\pi$
$379$	−2.58772	−	4.48207i	−0.132922	−	0.230228i	−0.924802	+	0.380449i	$0.875769\pi$
$380$	−8.52337	+	10.6945i	−0.437240	+	0.548615i
$381$	−18.5493	+	32.1283i	−0.950309	+	1.64598i
$382$			12.5854i			0.643923i
$383$	−17.8929	−	10.3305i	−0.914283	−	0.527861i	−0.0324760	−	0.999473i	$-0.510339\pi$
$383$	−17.8929	−	10.3305i	−0.914283	−	0.527861i	−0.881807	+	0.471611i	$0.843673\pi$
$384$	12.5477	−	21.7332i	0.640320	−	1.10907i
$385$	−3.88412	+	1.52574i	−0.197953	+	0.0777587i
$386$	6.30890	−	10.9273i	0.321115	−	0.556187i
$387$	−1.93613	+	1.11783i	−0.0984193	+	0.0568224i
$388$	−57.3682	+	33.1215i	−2.91243	+	1.68149i
$389$	−19.7477			−1.00125			−0.500624	−	0.865665i	$-0.666896\pi$
$389$	−19.7477			−1.00125			−0.500624	+	0.865665i	$0.666896\pi$
$390$		0			0
$391$	−2.63509			−0.133262
$392$	8.94284	−	5.16315i	0.451681	−	0.260778i
$393$	18.6449	−	10.7646i	0.940510	−	0.543004i
$394$	−8.58609	+	14.8715i	−0.432561	+	0.749218i
$395$	−0.848960	−	2.16123i	−0.0427158	−	0.108743i
$396$	−2.32648	+	4.02959i	−0.116910	+	0.202494i
$397$	8.13113	+	4.69451i	0.408090	+	0.235611i	0.689969	−	0.723839i	$-0.257624\pi$
$397$	8.13113	+	4.69451i	0.408090	+	0.235611i	−0.281879	+	0.959450i	$0.590958\pi$
$398$		−	13.1753i		−	0.660420i
$399$	4.31754	−	7.47821i	0.216148	−	0.374379i
$400$	34.0049	+	10.4670i	1.70024	+	0.523352i
$401$	12.2510	+	21.2193i	0.611784	+	1.05964i	0.990940	+	0.134308i	$0.0428812\pi$
$401$	12.2510	+	21.2193i	0.611784	+	1.05964i	−0.379156	+	0.925333i	$0.623786\pi$
$402$			44.0109i			2.19506i
$403$		0			0
$404$	−59.2887			−2.94972
$405$	−15.6531	+	19.6403i	−0.777809	+	0.975935i
$406$	−11.2212	−	19.4357i	−0.556898	−	0.964575i
$407$	0.673180	+	0.388661i	0.0333683	+	0.0192652i
$408$		−	16.6417i		−	0.823889i
$409$	−18.0582	+	31.2778i	−0.892922	+	1.54659i	−0.0565671	+	0.998399i	$0.518015\pi$
$409$	−18.0582	+	31.2778i	−0.892922	+	1.54659i	−0.836355	+	0.548188i	$0.815318\pi$
$410$	8.43492	−	56.0749i	0.416571	−	2.76934i
$411$	−18.6708			−0.920965
$412$	−42.5633	−	24.5739i	−2.09694	−	1.21067i
$413$	19.3324	−	11.1616i	0.951288	−	0.549226i
$414$	4.48079	+	7.76095i	0.220219	+	0.381430i
$415$	−24.6530	+	9.68401i	−1.21017	+	0.475370i
$416$		0			0
$417$		−	30.8439i		−	1.51043i
$418$	1.91110	−	1.10337i	0.0934749	−	0.0539678i
$419$	−3.43342	−	5.94686i	−0.167734	−	0.290523i	0.769889	−	0.638178i	$-0.220311\pi$
$419$	−3.43342	−	5.94686i	−0.167734	−	0.290523i	−0.937623	+	0.347655i	$0.886978\pi$
$420$	−62.6820	−	9.42879i	−3.05857	−	0.460078i
$421$	−33.9795			−1.65606			−0.828029	−	0.560686i	$-0.810538\pi$
$421$	−33.9795			−1.65606			−0.828029	+	0.560686i	$0.810538\pi$
$422$	30.9049	+	17.8429i	1.50443	+	0.868580i
$423$	8.72810	+	5.03917i	0.424375	+	0.245013i
$424$	−4.05631			−0.196992
$425$	−5.96554	+	1.36532i	−0.289371	+	0.0662277i
$426$	−7.22118	−	12.5075i	−0.349867	−	0.605988i
$427$	−5.77729	+	3.33552i	−0.279582	+	0.161417i
$428$			47.8261i			2.31176i
$429$		0			0
$430$	−2.84570	−	7.24440i	−0.137232	−	0.349356i
$431$	−8.12482	−	14.0726i	−0.391359	−	0.677853i	0.601270	−	0.799046i	$-0.294661\pi$
$431$	−8.12482	−	14.0726i	−0.391359	−	0.677853i	−0.992629	+	0.121193i	$0.961328\pi$
$432$	18.1089	−	10.4552i	0.871265	−	0.503025i
$433$	−0.221929	−	0.128130i	−0.0106652	−	0.00615756i	0.494658	−	0.869088i	$-0.335293\pi$
$433$	−0.221929	−	0.128130i	−0.0106652	−	0.00615756i	−0.505323	+	0.862930i	$0.668627\pi$
$434$	−67.0396			−3.21800
$435$	−2.14827	+	14.2816i	−0.103002	+	0.684750i
$436$	−7.32648	+	12.6898i	−0.350875	+	0.607733i
$437$		−	2.93855i		−	0.140570i
$438$	−49.0138	−	28.2981i	−2.34197	−	1.35214i
$439$	−3.79833	−	6.57890i	−0.181284	−	0.313994i	0.761034	−	0.648712i	$-0.224692\pi$
$439$	−3.79833	−	6.57890i	−0.181284	−	0.313994i	−0.942318	+	0.334718i	$0.891359\pi$
$440$	−7.01356	−	5.58973i	−0.334358	−	0.266480i
$441$	2.67352			0.127310
$442$		0			0
$443$			4.32246i			0.205366i	0.994714	+	0.102683i	$0.0327428\pi$
$443$			4.32246i			0.205366i	−0.994714	+	0.102683i	$0.967257\pi$
$444$	5.90364	+	10.2254i	0.280174	+	0.485276i
$445$	−17.5017	+	21.9599i	−0.829663	+	1.04100i
$446$	−0.0105711	+	0.0183096i	−0.000500554	+	0.000866986i
$447$		−	36.9332i		−	1.74688i
$448$	−0.687565	−	0.396966i	−0.0324844	−	0.0187549i
$449$	−1.64403	+	2.84754i	−0.0775865	+	0.134384i	−0.902208	−	0.431301i	$-0.858055\pi$
$449$	−1.64403	+	2.84754i	−0.0775865	+	0.134384i	0.824622	+	0.565685i	$0.191388\pi$
$450$	14.1652	+	15.2483i	0.667753	+	0.718811i
$451$	−3.16324	+	5.47890i	−0.148951	+	0.257991i
$452$	−21.4583	+	12.3889i	−1.00931	+	0.582727i
$453$	39.8680	−	23.0178i	1.87316	−	1.08147i
$454$	28.6741			1.34574
$455$		0			0
$456$	18.5582			0.869069
$457$	−13.3594	+	7.71304i	−0.624925	+	0.360801i	−0.778784	−	0.627292i	$-0.784163\pi$
$457$	−13.3594	+	7.71304i	−0.624925	+	0.360801i	0.153859	+	0.988093i	$0.450830\pi$
$458$	−36.4661	+	21.0537i	−1.70395	+	0.983775i
$459$	−1.79833	+	3.11480i	−0.0839389	+	0.145386i
$460$	−20.0774	+	7.88669i	−0.936116	+	0.367719i
$461$	12.9424	−	22.4168i	0.602786	−	1.04406i	−0.389611	−	0.920979i	$-0.627391\pi$
$461$	12.9424	−	22.4168i	0.602786	−	1.04406i	0.992397	−	0.123076i	$-0.0392760\pi$
$462$	8.85812	+	5.11424i	0.412117	+	0.237936i
$463$		−	7.04045i		−	0.327197i	−0.986527	−	0.163599i	$-0.947690\pi$
$463$		−	7.04045i		−	0.327197i	0.986527	−	0.163599i	$-0.0523102\pi$
$464$	10.6738	−	18.4876i	0.495519	−	0.858265i
$465$	33.7376	+	26.8885i	1.56454	+	1.24692i
$466$	−8.84570	−	15.3212i	−0.409769	−	0.709741i
$467$		−	18.8113i		−	0.870482i	−0.900314	−	0.435241i	$-0.856663\pi$
$467$		−	18.8113i		−	0.870482i	0.900314	−	0.435241i	$-0.143337\pi$
$468$		0			0
$469$	23.5967			1.08959
$470$	−21.8683	+	27.4386i	−1.00871	+	1.26565i
$471$	−19.7688	−	34.2406i	−0.910900	−	1.57773i
$472$	41.5486	+	23.9881i	1.91243	+	1.10414i
$473$			0.868356i			0.0399271i
$474$	−2.84570	+	4.92889i	−0.130707	+	0.226392i
$475$	−1.52255	−	6.65255i	−0.0698594	−	0.305240i
$476$	−16.1159			−0.738670
$477$	−0.909493	−	0.525096i	−0.0416428	−	0.0240425i
$478$	8.81870	−	5.09148i	0.403358	−	0.232879i
$479$	9.73876	+	16.8680i	0.444975	+	0.770720i	0.998051	−	0.0624114i	$-0.0198791\pi$
$479$	9.73876	+	16.8680i	0.444975	+	0.770720i	−0.553075	+	0.833131i	$0.686546\pi$
$480$	−9.65297	−	24.5739i	−0.440596	−	1.12164i
$481$		0			0
$482$		−	50.3346i		−	2.29268i
$483$	11.7957	−	6.81023i	0.536721	−	0.309876i
$484$	−23.7407	−	41.1201i	−1.07912	−	1.86909i
$485$	4.91728	−	32.6898i	0.223282	−	1.48437i
$486$	39.1165			1.77436
$487$	27.9935	+	16.1620i	1.26851	+	0.732372i	0.974705	−	0.223495i	$-0.0717467\pi$
$487$	27.9935	+	16.1620i	1.26851	+	0.732372i	0.293800	+	0.955867i	$0.405080\pi$
$488$	−12.4163	−	7.16858i	−0.562062	−	0.324506i
$489$	8.63509			0.390492
$490$	−1.38451	+	9.20411i	−0.0625456	+	0.415799i
$491$	−14.3354	−	24.8297i	−0.646949	−	1.12055i	−0.983848	−	0.179007i	$-0.942711\pi$
$491$	−14.3354	−	24.8297i	−0.646949	−	1.12055i	0.336899	−	0.941541i	$-0.390622\pi$
$492$	−83.2227	+	48.0487i	−3.75197	+	2.16620i
$493$			3.67187i			0.165373i
$494$		0			0
$495$	−0.848960	−	2.16123i	−0.0381579	−	0.0971401i
$496$	−31.8847	−	55.2260i	−1.43167	−	2.47972i
$497$	−6.70593	+	3.87167i	−0.300802	+	0.173668i
$498$	56.2235	+	32.4606i	2.51943	+	1.45460i
$499$	28.9616			1.29650			0.648249	−	0.761428i	$-0.275502\pi$
$499$	28.9616			1.29650			0.648249	+	0.761428i	$0.275502\pi$
$500$	−41.3667	+	28.2573i	−1.84998	+	1.26370i
$501$	−3.16324	+	5.47890i	−0.141323	+	0.244779i
$502$			9.35181i			0.417392i
$503$	24.3433	+	14.0546i	1.08542	+	0.626665i	0.932352	−	0.361551i	$-0.117753\pi$
$503$	24.3433	+	14.0546i	1.08542	+	0.626665i	0.153063	+	0.988216i	$0.451086\pi$
$504$	15.1722	+	26.2790i	0.675823	+	1.17056i
$505$	18.4404	−	23.1376i	0.820587	−	1.02961i
$506$	3.48079			0.154740
$507$		0			0
$508$			77.2116i			3.42571i
$509$	−10.5563	−	18.2841i	−0.467900	−	0.810427i	0.531427	−	0.847104i	$-0.321656\pi$
$509$	−10.5563	−	18.2841i	−0.467900	−	0.810427i	−0.999327	+	0.0366773i	$0.988323\pi$
$510$	11.7303	+	9.34893i	0.519427	+	0.413978i
$511$	−15.1722	+	26.2790i	−0.671178	+	1.16251i
$512$		−	50.8542i		−	2.24746i
$513$	−3.47351	−	2.00543i	−0.153359	−	0.0885420i
$514$	−16.8844	+	29.2447i	−0.744740	+	1.28993i
$515$	22.8284	−	8.96730i	1.00594	−	0.395147i
$516$	−6.59503	+	11.4229i	−0.290330	+	0.502866i
$517$	3.39010	−	1.95728i	0.149097	−	0.0860809i
$518$	7.92947	−	4.57808i	0.348401	−	0.201149i
$519$	2.94369			0.129214
$520$		0			0
$521$	0.673516			0.0295073			0.0147536	−	0.999891i	$-0.495304\pi$
$521$	0.673516			0.0295073			0.0147536	+	0.999891i	$0.495304\pi$
$522$	10.8145	−	6.24376i	0.473339	−	0.273282i
$523$	−25.8618	+	14.9313i	−1.13086	+	0.652900i	−0.944150	−	0.329516i	$-0.893114\pi$
$523$	−25.8618	+	14.9313i	−1.13086	+	0.652900i	−0.186706	+	0.982416i	$0.559781\pi$
$524$	22.4039	−	38.8048i	0.978720	−	1.69519i
$525$	23.1754	−	21.5293i	1.01146	−	0.939614i
$526$	38.5304	−	66.7366i	1.68000	−	2.90985i
$527$	9.49907	+	5.48429i	0.413786	+	0.238899i
$528$			9.72953i			0.423423i
$529$	−9.18246	+	15.9045i	−0.399237	+	0.691499i
$530$	2.27874	−	2.85918i	0.0989820	−	0.124195i
$531$	6.21061	+	10.7571i	0.269517	+	0.466818i
$532$		−	17.9718i		−	0.779177i
$533$		0			0
$534$	68.8290			2.97852
$535$	−18.6643	−	14.8752i	−0.806928	−	0.643112i
$536$	25.3566	+	43.9189i	1.09524	+	1.89701i
$537$	14.5171	+	8.38148i	0.626461	+	0.361687i
$538$			56.6418i			2.44200i
$539$	0.519213	−	0.899304i	0.0223641	−	0.0387358i
$540$	−4.37953	+	29.1148i	−0.188465	+	1.25290i
$541$	−6.28806			−0.270345			−0.135172	−	0.990822i	$-0.543159\pi$
$541$	−6.28806			−0.270345			−0.135172	+	0.990822i	$0.543159\pi$
$542$	−26.0778	−	15.0560i	−1.12014	−	0.646712i
$543$	−7.20968	+	4.16251i	−0.309397	+	0.178630i
$544$	−3.35627	−	5.81323i	−0.143899	−	0.249240i
$545$	−2.67352	−	6.80607i	−0.114521	−	0.291540i
$546$		0			0
$547$			3.03789i			0.129891i	0.997889	+	0.0649454i	$0.0206873\pi$
$547$			3.03789i			0.129891i	−0.997889	+	0.0649454i	$0.979313\pi$
$548$	−33.6527	+	19.4294i	−1.43757	+	0.829983i
$549$	−1.85597	−	3.21464i	−0.0792109	−	0.137197i
$550$	7.88011	−	1.80350i	0.336009	−	0.0769015i
$551$	−4.09473			−0.174442
$552$	25.3508	+	14.6363i	1.07900	+	0.622962i
$553$	2.64265	+	1.52574i	0.112377	+	0.0648809i
$554$	42.7304			1.81544
$555$	−5.82669	−	0.876465i	−0.247329	−	0.0372039i
$556$	−32.0970	−	55.5936i	−1.36121	−	2.35769i
$557$	17.9264	−	10.3498i	0.759566	−	0.438536i	−0.0695738	−	0.997577i	$-0.522164\pi$
$557$	17.9264	−	10.3498i	0.759566	−	0.438536i	0.829140	+	0.559041i	$0.188831\pi$
$558$		−	37.3026i		−	1.57915i
$559$		0			0
$560$	−43.5198	+	17.0952i	−1.83905	+	0.722402i
$561$	−0.836758	−	1.44931i	−0.0353279	−	0.0611898i
$562$	23.3622	−	13.4882i	0.985475	−	0.568964i
$563$	−9.49188	−	5.48014i	−0.400035	−	0.230960i	0.286464	−	0.958091i	$-0.407520\pi$
$563$	−9.49188	−	5.48014i	−0.400035	−	0.230960i	−0.686499	+	0.727131i	$0.740853\pi$
$564$	59.4608			2.50375
$565$	1.83929	−	12.2275i	0.0773794	−	0.514413i
$566$	−11.2212	+	19.4357i	−0.471661	+	0.816941i
$567$		−	33.0051i		−	1.38608i
$568$	−14.4122	−	8.32087i	−0.604721	−	0.349136i
$569$	21.3566	+	36.9907i	0.895314	+	1.55073i	0.833416	+	0.552647i	$0.186382\pi$
$569$	21.3566	+	36.9907i	0.895314	+	1.55073i	0.0618981	+	0.998082i	$0.480285\pi$
$570$	−10.4256	+	13.0812i	−0.436679	+	0.547912i
$571$	−23.6145			−0.988238			−0.494119	−	0.869394i	$-0.664509\pi$
$571$	−23.6145			−0.988238			−0.494119	+	0.869394i	$0.664509\pi$
$572$		0			0
$573$			10.6434i			0.444635i
$574$	37.2602	+	64.5366i	1.55521	+	2.69370i
$575$	3.16683	−	10.2883i	0.132066	−	0.429050i
$576$	0.220882	−	0.382579i	0.00920343	−	0.0159408i
$577$		−	18.3646i		−	0.764530i	−0.924053	−	0.382265i	$-0.875144\pi$
$577$		−	18.3646i		−	0.764530i	0.924053	−	0.382265i	$-0.124856\pi$
$578$	−34.1767	−	19.7319i	−1.42156	−	0.820740i
$579$	5.33542	−	9.24123i	0.221733	−	0.384052i
$580$	10.9897	+	27.9770i	0.456324	+	1.16168i
$581$	17.4039	−	30.1445i	0.722037	−	1.25060i
$582$	−70.1713	+	40.5134i	−2.90869	+	1.67934i
$583$	−0.353259	+	0.203954i	−0.0146305	+	0.00844691i
$584$	−65.2151			−2.69862
$585$		0			0
$586$	−71.9237			−2.97114
$587$	−0.608726	+	0.351448i	−0.0251248	+	0.0145058i	−0.512510	−	0.858681i	$-0.671284\pi$
$587$	−0.608726	+	0.351448i	−0.0251248	+	0.0145058i	0.487385	+	0.873187i	$0.337951\pi$
$588$	13.6601	−	7.88669i	0.563335	−	0.325242i
$589$	−6.11588	+	10.5930i	−0.252000	+	0.436477i
$590$	−40.2496	+	15.8106i	−1.65705	+	0.650912i
$591$	−7.26124	+	12.5768i	−0.298687	+	0.517342i
$592$	7.54267	+	4.35476i	0.310002	+	0.178980i
$593$			37.1593i			1.52595i	0.646428	+	0.762975i	$0.276262\pi$
$593$			37.1593i			1.52595i	−0.646428	+	0.762975i	$0.723738\pi$
$594$	2.37548	−	4.11446i	0.0974672	−	0.168818i
$595$	5.01248	−	6.28927i	0.205492	−	0.257835i
$596$	−38.4337	−	66.5692i	−1.57431	−	2.72678i
$597$		−	11.1423i		−	0.456026i
$598$		0			0
$599$	15.6914			0.641133			0.320567	−	0.947226i	$-0.396127\pi$
$599$	15.6914			0.641133			0.320567	+	0.947226i	$0.396127\pi$
$600$	64.9749	+	19.9999i	2.65259	+	0.816493i
$601$	−6.00193	−	10.3956i	−0.244824	−	0.424047i	0.717258	−	0.696807i	$-0.245397\pi$
$601$	−6.00193	−	10.3956i	−0.244824	−	0.424047i	−0.962082	+	0.272760i	$0.912063\pi$
$602$	8.85812	+	5.11424i	0.361030	+	0.208441i
$603$			13.1298i			0.534687i
$604$	47.9059	−	82.9754i	1.94926	−	3.37622i
$605$	23.4313	+	3.52459i	0.952616	+	0.143295i
$606$	−72.5204			−2.94594
$607$	33.5035	+	19.3433i	1.35987	+	0.785119i	0.989606	−	0.143809i	$-0.0459350\pi$
$607$	33.5035	+	19.3433i	1.35987	+	0.785119i	0.370261	+	0.928928i	$0.379268\pi$
$608$	6.48269	−	3.74278i	0.262908	−	0.151790i
$609$	−9.48973	−	16.4367i	−0.384543	−	0.666048i
$610$	12.0282	−	4.72482i	0.487006	−	0.191302i
$611$		0			0
$612$		−	8.96730i		−	0.362482i
$613$	14.9684	−	8.64201i	0.604568	−	0.349047i	−0.166269	−	0.986081i	$-0.553172\pi$
$613$	14.9684	−	8.64201i	0.604568	−	0.349047i	0.770836	+	0.637033i	$0.219839\pi$
$614$	16.1933	+	28.0477i	0.653509	+	1.13191i
$615$	7.13340	−	47.4224i	0.287646	−	1.91225i
$616$	11.7861			0.474877
$617$	−22.9229	−	13.2345i	−0.922841	−	0.532803i	−0.0383009	−	0.999266i	$-0.512195\pi$
$617$	−22.9229	−	13.2345i	−0.922841	−	0.532803i	−0.884540	+	0.466464i	$0.845528\pi$
$618$	−52.0624	−	30.0582i	−2.09426	−	1.20912i
$619$	−31.0039			−1.24615			−0.623075	−	0.782162i	$-0.714117\pi$
$619$	−31.0039			−1.24615			−0.623075	+	0.782162i	$0.714117\pi$
$620$	88.7902	+	13.3560i	3.56590	+	0.536392i
$621$	−3.16324	−	5.47890i	−0.126937	−	0.219861i
$622$	61.5615	−	35.5425i	2.46839	−	1.42513i
$623$		−	36.9030i		−	1.47849i
$624$		0			0
$625$	1.83869	−	24.9323i	0.0735475	−	0.997292i
$626$	31.2881	+	54.1925i	1.25052	+	2.16597i
$627$	1.61621	−	0.933121i	0.0645453	−	0.0372653i
$628$	−71.2635	−	41.1440i	−2.84372	−	1.64182i
$629$	−1.49807			−0.0597320
$630$	−27.0467	−	4.06844i	−1.07757	−	0.162091i
$631$	−10.3566	+	17.9381i	−0.412288	+	0.714104i	−0.995140	−	0.0984745i	$-0.968604\pi$
$631$	−10.3566	+	17.9381i	−0.412288	+	0.714104i	0.582851	+	0.812579i	$0.301937\pi$
$632$			6.55812i			0.260868i
$633$	26.1362	+	15.0897i	1.03882	+	0.599763i
$634$	−0.298331	−	0.516725i	−0.0118482	−	0.0205218i
$635$	−30.1321	−	24.0149i	−1.19576	−	0.953003i
$636$	−6.19599			−0.245687
$637$		0			0
$638$		−	4.85031i		−	0.192026i
$639$	−2.15430	−	3.73136i	−0.0852229	−	0.147610i
$640$	20.3828	+	16.2449i	0.805702	+	0.642136i
$641$	−10.5947	+	18.3506i	−0.418467	+	0.724806i	−0.995785	−	0.0917132i	$-0.970766\pi$
$641$	−10.5947	+	18.3506i	−0.418467	+	0.724806i	0.577319	+	0.816519i	$0.304099\pi$
$642$			58.4997i			2.30880i
$643$	−9.98843	−	5.76682i	−0.393905	−	0.227421i	0.289946	−	0.957043i	$-0.406363\pi$
$643$	−9.98843	−	5.76682i	−0.393905	−	0.227421i	−0.683851	+	0.729622i	$0.739696\pi$
$644$	14.1738	−	24.5498i	0.558526	−	0.967396i
$645$	−2.40660	−	6.12658i	−0.0947598	−	0.241234i
$646$	−2.12645	+	3.68311i	−0.0836639	+	0.144910i
$647$	30.1779	−	17.4232i	1.18641	−	0.684977i	0.228925	−	0.973444i	$-0.426479\pi$
$647$	30.1779	−	17.4232i	1.18641	−	0.684977i	0.957490	+	0.288467i	$0.0931456\pi$
$648$	61.4301	−	35.4667i	2.41320	−	1.39326i
$649$	4.82456			0.189380
$650$		0			0
$651$	−56.6953			−2.22206
$652$	15.5641	−	8.98591i	0.609535	−	0.351915i
$653$	19.3324	−	11.1616i	0.756537	−	0.436787i	−0.0715139	−	0.997440i	$-0.522783\pi$
$653$	19.3324	−	11.1616i	0.756537	−	0.436787i	0.828051	+	0.560653i	$0.189450\pi$
$654$	−8.96157	+	15.5219i	−0.350425	+	0.606954i
$655$	8.17544	+	20.8125i	0.319441	+	0.813214i
$656$	−35.4427	+	61.3885i	−1.38380	+	2.39682i
$657$	−14.6223	−	8.44221i	−0.570471	−	0.329362i
$658$		−	46.1100i		−	1.79755i
$659$	−0.433420	+	0.750705i	−0.0168836	+	0.0292433i	−0.874344	−	0.485307i	$-0.838708\pi$
$659$	−0.433420	+	0.750705i	−0.0168836	+	0.0292433i	0.857460	+	0.514550i	$0.172041\pi$
$660$	−10.7132	−	8.53829i	−0.417010	−	0.332352i
$661$	6.65430	+	11.5256i	0.258822	+	0.448293i	0.965927	−	0.258816i	$-0.0833322\pi$
$661$	6.65430	+	11.5256i	0.258822	+	0.448293i	−0.707104	+	0.707109i	$0.749999\pi$
$662$			46.6544i			1.81328i
$663$		0			0
$664$	74.8079			2.90311
$665$	7.01356	+	5.58973i	0.271974	+	0.216760i
$666$	2.54737	+	4.41217i	0.0987085	+	0.170968i
$667$	−5.59346	−	3.22939i	−0.216580	−	0.125042i
$668$			13.1670i			0.509448i
$669$	−0.00893993	+	0.0154844i	−0.000345637	+	0.000598662i
$670$	−45.2020	−	6.79940i	−1.74630	−	0.262684i
$671$	−1.44176			−0.0556587
$672$	30.0479	+	17.3481i	1.15912	+	0.669219i
$673$	−4.77457	+	2.75660i	−0.184046	+	0.106259i	−0.589192	−	0.807993i	$-0.700554\pi$
$673$	−4.77457	+	2.75660i	−0.184046	+	0.106259i	0.405146	+	0.914252i	$0.367221\pi$
$674$	27.1056	+	46.9483i	1.04407	+	1.80838i
$675$	−10.0000	−	10.7646i	−0.384900	−	0.414331i
$676$		0			0
$677$			4.80479i			0.184663i	0.995728	+	0.0923316i	$0.0294320\pi$
$677$			4.80479i			0.184663i	−0.995728	+	0.0923316i	$0.970568\pi$
$678$	−26.2472	+	15.1539i	−1.00802	+	0.581980i
$679$	21.7215	+	37.6227i	0.833594	+	1.44383i
$680$	17.0921	+	2.57104i	0.655453	+	0.0985949i
$681$	24.2496			0.929248
$682$	−12.5477	−	7.24440i	−0.480475	−	0.277403i
$683$	10.1866	+	5.88126i	0.389781	+	0.225040i	0.682065	−	0.731291i	$-0.261082\pi$
$683$	10.1866	+	5.88126i	0.389781	+	0.225040i	−0.292284	+	0.956331i	$0.594415\pi$
$684$	10.0000			0.382360
$685$	2.88453	−	19.1761i	0.110212	−	0.732683i
$686$	20.0669	+	34.7569i	0.766157	+	1.32702i
$687$	−30.8393	+	17.8051i	−1.17659	+	0.679306i
$688$			9.72953i			0.370935i
$689$		0			0
$690$	−24.5582	+	9.64680i	−0.934916	+	0.367247i
$691$	2.43342	+	4.21481i	0.0925717	+	0.160339i	0.908593	−	0.417684i	$-0.137158\pi$
$691$	2.43342	+	4.21481i	0.0925717	+	0.160339i	−0.816021	+	0.578022i	$0.803825\pi$
$692$	5.30577	−	3.06329i	0.201695	−	0.116449i
$693$	2.64265	+	1.52574i	0.100386	+	0.0579579i
$694$	−9.71254			−0.368683
$695$	31.6786	+	4.76518i	1.20164	+	0.180753i
$696$	20.3950	−	35.3252i	0.773070	−	1.33900i
$697$		−	12.1925i		−	0.461825i
$698$	−53.6320	−	30.9644i	−2.03000	−	1.17202i
$699$	−7.48079	−	12.9571i	−0.282949	−	0.490083i
$700$	19.3679	−	62.9218i	0.732039	−	2.37822i
$701$	21.3828			0.807617			0.403808	−	0.914844i	$-0.367686\pi$
$701$	21.3828			0.807617			0.403808	+	0.914844i	$0.367686\pi$
$702$		0			0
$703$		−	1.67059i		−	0.0630076i
$704$	−0.0857934	−	0.148599i	−0.00323346	−	0.00560052i
$705$	−18.4939	+	23.2048i	−0.696522	+	0.873943i
$706$	34.4427	−	59.6564i	1.29627	−	2.24520i
$707$			38.8822i			1.46232i
$708$	63.4654	+	36.6417i	2.38517	+	1.37708i
$709$	13.0582	−	22.6175i	0.490412	−	0.849419i	−0.509527	−	0.860455i	$-0.670180\pi$
$709$	13.0582	−	22.6175i	0.490412	−	0.849419i	0.999939	+	0.0110357i	$0.00351286\pi$
$710$	13.9616	−	5.48429i	0.523969	−	0.205822i
$711$	−0.848960	+	1.47044i	−0.0318385	+	0.0551459i
$712$	68.6851	−	39.6554i	2.57408	−	1.48615i
$713$	−16.7087	+	9.64680i	−0.625748	+	0.361276i
$714$	−19.7125			−0.737723
$715$		0			0
$716$	34.8880			1.30383
$717$	7.45795	−	4.30585i	0.278522	−	0.160805i
$718$	59.5347	−	34.3724i	2.22182	−	1.28277i
$719$	18.3387	−	31.7635i	0.683918	−	1.18458i	−0.289858	−	0.957070i	$-0.593608\pi$
$719$	18.3387	−	31.7635i	0.683918	−	1.18458i	0.973776	−	0.227510i	$-0.0730586\pi$
$720$	−9.51220	−	24.2156i	−0.354499	−	0.902462i
$721$	−16.1159	+	27.9135i	−0.600187	+	1.03955i
$722$	37.7815	+	21.8132i	1.40608	+	0.811803i
$723$		−	42.5679i		−	1.58312i
$724$	−8.66324	+	15.0052i	−0.321967	+	0.557663i
$725$	−14.3362	−	4.41283i	−0.532434	−	0.163888i
$726$	−29.0390	−	50.2971i	−1.07774	−	1.86670i
$727$			26.2596i			0.973916i	0.873425	+	0.486958i	$0.161893\pi$
$727$			26.2596i			0.973916i	−0.873425	+	0.486958i	$0.838107\pi$
$728$		0			0
$729$	−0.614542			−0.0227608
$730$	36.6363	−	45.9684i	1.35597	−	1.70137i
$731$	−0.836758	−	1.44931i	−0.0309486	−	0.0536046i
$732$	−18.9659	−	10.9500i	−0.701000	−	0.404723i
$733$		−	31.7811i		−	1.17386i	−0.809637	−	0.586931i	$-0.800336\pi$
$733$		−	31.7811i		−	1.17386i	0.809637	−	0.586931i	$-0.199664\pi$
$734$	8.83513	−	15.3029i	0.326110	−	0.564840i
$735$	−1.17087	+	7.78389i	−0.0431883	+	0.287113i
$736$	11.8073			0.435222
$737$	4.41654	+	2.54989i	0.162685	+	0.0939265i
$738$	−35.9099	+	20.7326i	−1.32186	+	0.763176i
$739$	17.0685	+	29.5635i	0.627875	+	1.08751i	0.987977	+	0.154599i	$0.0494085\pi$
$739$	17.0685	+	29.5635i	0.627875	+	1.08751i	−0.360102	+	0.932913i	$0.617258\pi$
$740$	−11.4142	+	4.48365i	−0.419595	+	0.164822i
$741$		0			0
$742$			4.80479i			0.176390i
$743$	−2.70254	+	1.56031i	−0.0991465	+	0.0572423i	−0.548753	−	0.835984i	$-0.684897\pi$
$743$	−2.70254	+	1.56031i	−0.0991465	+	0.0572423i	0.449607	+	0.893227i	$0.351564\pi$
$744$	−60.9237	−	105.523i	−2.23357	−	3.86866i
$745$	37.9328	+	5.70594i	1.38975	+	0.209050i
$746$	−5.88798			−0.215574
$747$	16.7732	+	9.68401i	0.613699	+	0.354320i
$748$	−3.01638	−	1.74151i	−0.110290	−	0.0636758i
$749$	31.3649			1.14605
$750$	−50.5988	+	34.5636i	−1.84761	+	1.26208i
$751$	−0.742024	−	1.28522i	−0.0270769	−	0.0468985i	0.852169	−	0.523266i	$-0.175287\pi$
$751$	−0.742024	−	1.28522i	−0.0270769	−	0.0468985i	−0.879246	+	0.476367i	$0.841953\pi$
$752$	37.9845	−	21.9304i	1.38515	−	0.799718i
$753$			7.90881i			0.288213i
$754$		0			0
$755$	17.4814	+	44.5030i	0.636213	+	1.61963i
$756$	−19.3460	−	33.5082i	−0.703607	−	1.21868i
$757$	−4.41654	+	2.54989i	−0.160522	+	0.0926774i	−0.578109	−	0.815960i	$-0.696209\pi$
$757$	−4.41654	+	2.54989i	−0.160522	+	0.0926774i	0.417587	+	0.908637i	$0.362876\pi$
$758$	−11.4102	−	6.58767i	−0.414436	−	0.239275i
$759$	2.94369			0.106849
$760$	−2.86713	+	19.0605i	−0.104002	+	0.691397i
$761$	−14.8931	+	25.7955i	−0.539873	+	0.935088i	0.459037	+	0.888417i	$0.348194\pi$
$761$	−14.8931	+	25.7955i	−0.539873	+	0.935088i	−0.998910	+	0.0466707i	$0.985139\pi$
$762$			94.4433i			3.42132i
$763$	8.32215	+	4.80479i	0.301282	+	0.173945i
$764$	11.0758	+	19.1839i	0.400709	+	0.694048i
$765$	3.49952	+	2.78908i	0.126525	+	0.100839i
$766$	−52.5973			−1.90042
$767$		0			0
$768$		−	62.7228i		−	2.26331i
$769$	−9.54930	−	16.5399i	−0.344356	−	0.596443i	0.640880	−	0.767641i	$-0.278570\pi$
$769$	−9.54930	−	16.5399i	−0.344356	−	0.596443i	−0.985237	+	0.171198i	$0.945236\pi$
$770$	−6.62117	+	8.30773i	−0.238610	+	0.299390i
$771$	−14.2791	+	24.7322i	−0.514250	+	0.890707i
$772$		−	22.2088i		−	0.799311i
$773$	42.6350	+	24.6153i	1.53347	+	0.885351i	0.999198	+	0.0400400i	$0.0127485\pi$
$773$	42.6350	+	24.6153i	1.53347	+	0.885351i	0.534275	+	0.845311i	$0.320585\pi$
$774$	−2.84570	+	4.92889i	−0.102286	+	0.177165i
$775$	−32.8284	+	30.4966i	−1.17923	+	1.09547i
$776$	−46.6831	+	80.8574i	−1.67582	+	2.90261i
$777$	6.70593	−	3.87167i	0.240574	−	0.138895i
$778$	−43.5373	+	25.1362i	−1.56089	+	0.901178i
$779$	13.5967			0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$	−5.80951	+	3.35412i	−0.207748	+	0.119943i
$783$	−7.63458	+	4.40783i	−0.272838	+	0.157523i
$784$	5.81754	−	10.0763i	0.207769	−	0.359867i
$785$	38.2215	−	15.0139i	1.36418	−	0.535869i
$786$	27.4039	−	47.4650i	0.977466	−	1.69302i
$787$	8.47263	+	4.89168i	0.302017	+	0.174369i	0.643349	−	0.765573i	$-0.277545\pi$
$787$	8.47263	+	4.89168i	0.302017	+	0.174369i	−0.341332	+	0.939943i	$0.610878\pi$
$788$			30.2250i			1.07672i
$789$	32.5851	−	56.4390i	1.16006	−	2.00928i
$790$	−4.62264	−	3.68419i	−0.164466	−	0.131078i
$791$	8.12482	+	14.0726i	0.288885	+	0.500364i
$792$			6.55812i			0.233033i
$793$		0			0
$794$	23.9020			0.848250
$795$	1.92712	−	2.41801i	0.0683480	−	0.0857578i
$796$	−11.5950	−	20.0832i	−0.410975	−	0.711830i
$797$	14.3216	+	8.26856i	0.507296	+	0.292887i	0.731721	−	0.681604i	$-0.238717\pi$
$797$	14.3216	+	8.26856i	0.507296	+	0.292887i	−0.224426	+	0.974491i	$0.572051\pi$
$798$		−	21.9827i		−	0.778178i
$799$	−3.77211	+	6.53348i	−0.133448	+	0.231138i
$800$	26.7303	−	6.11770i	0.945060	−	0.216293i
$801$	20.5338			0.725527
$802$	54.0188	+	31.1878i	1.90747	+	1.10128i
$803$	−5.67950	+	3.27906i	−0.200425	+	0.115715i
$804$	38.7320	+	67.0859i	1.36597	+	2.36594i
$805$	5.17218	+	13.1670i	0.182295	+	0.464077i
$806$		0			0
$807$			47.9018i			1.68622i
$808$	−72.3688	+	41.7821i	−2.54592	+	1.46989i
$809$	−15.9212	−	27.5764i	−0.559760	−	0.969533i	−0.997516	−	0.0704392i	$-0.977560\pi$
$809$	−15.9212	−	27.5764i	−0.559760	−	0.969533i	0.437756	−	0.899094i	$-0.355773\pi$
$810$	−9.51044	+	63.2248i	−0.334163	+	2.22149i
$811$	−13.3470			−0.468678			−0.234339	−	0.972155i	$-0.575293\pi$
$811$	−13.3470			−0.468678			−0.234339	+	0.972155i	$0.575293\pi$
$812$	−34.2089	−	19.7505i	−1.20050	−	0.693108i
$813$	−22.0539	−	12.7328i	−0.773465	−	0.446560i
$814$	1.97886			0.0693589
$815$	−1.33407	+	8.86879i	−0.0467303	+	0.310660i
$816$	−9.37548	−	16.2388i	−0.328208	−	0.568472i
$817$	1.61621	−	0.933121i	0.0565441	−	0.0326458i
$818$			91.9431i			3.21472i
$819$		0			0
$820$	−36.4917	−	92.8982i	−1.27434	−	3.24415i
$821$	5.83676	+	10.1096i	0.203704	+	0.352826i	0.949719	−	0.313103i	$-0.101369\pi$
$821$	5.83676	+	10.1096i	0.203704	+	0.352826i	−0.746015	+	0.665929i	$0.768035\pi$
$822$	−41.1631	+	23.7656i	−1.43573	+	0.828919i
$823$	−28.0867	−	16.2159i	−0.979041	−	0.565249i	−0.0770602	−	0.997026i	$-0.524553\pi$
$823$	−28.0867	−	16.2159i	−0.979041	−	0.565249i	−0.901980	+	0.431777i	$0.857887\pi$
$824$	−69.2714			−2.41318
$825$	6.66419	−	1.52522i	0.232017	−	0.0531012i
$826$	28.4145	−	49.2154i	0.988667	−	1.71242i
$827$			27.3319i			0.950425i	0.879871	+	0.475212i	$0.157629\pi$
$827$			27.3319i			0.950425i	−0.879871	+	0.475212i	$0.842371\pi$
$828$	13.6601	+	7.88669i	0.474723	+	0.274081i
$829$	1.77018	+	3.06604i	0.0614808	+	0.106488i	0.895128	−	0.445810i	$-0.147084\pi$
$829$	1.77018	+	3.06604i	0.0614808	+	0.106488i	−0.833647	+	0.552298i	$0.813751\pi$
$830$	−42.0253	+	52.7301i	−1.45872	+	1.83029i
$831$	36.1370			1.25358
$832$		0			0
$833$			2.00128i			0.0693402i
$834$	−39.2602	−	68.0007i	−1.35947	−	2.35467i
$835$	−5.13847	−	4.09531i	−0.177824	−	0.141724i
$836$	1.94206	−	3.36375i	0.0671676	−	0.116338i
$837$			26.3341i			0.910238i
$838$	−15.1391	−	8.74059i	−0.522973	−	0.301939i
$839$	−22.3950	+	38.7893i	−0.773161	+	1.33915i	0.162661	+	0.986682i	$0.447992\pi$
$839$	−22.3950	+	38.7893i	−0.773161	+	1.33915i	−0.935822	+	0.352472i	$0.885341\pi$
$840$	−83.1555	+	32.6646i	−2.86914	+	1.12704i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−74.9136	+	43.2514i	−2.58169	+	1.49054i
$843$	19.7574	−	11.4069i	0.680479	−	0.392875i
$844$	62.8111			2.16205
$845$		0			0
$846$	25.6568			0.882100
$847$	−26.9670	+	15.5694i	−0.926598	+	0.534972i
$848$	−3.95810	+	2.28521i	−0.135922	+	0.0784744i
$849$	−9.48973	+	16.4367i	−0.325687	+	0.564106i
$850$	−11.4142	+	10.6034i	−0.391504	+	0.363695i
$851$	1.31754	−	2.28205i	0.0451648	−	0.0782278i
$852$	−22.0145	−	12.7101i	−0.754205	−	0.435440i
$853$			31.3732i			1.07420i	0.843519	+	0.537099i	$0.180480\pi$
$853$			31.3732i			1.07420i	−0.843519	+	0.537099i	$0.819520\pi$
$854$	−8.49136	+	14.7075i	−0.290568	+	0.503279i
$855$	−3.11027	+	3.90253i	−0.106369	+	0.133464i
$856$	33.7042	+	58.3774i	1.15199	+	1.99530i
$857$			21.2813i			0.726955i	0.931603	+	0.363478i	$0.118411\pi$
$857$			21.2813i			0.726955i	−0.931603	+	0.363478i	$0.881589\pi$
$858$		0			0
$859$	−56.8502			−1.93970			−0.969851	−	0.243698i	$-0.921639\pi$
$859$	−56.8502			−1.93970			−0.969851	+	0.243698i	$0.921639\pi$
$860$	−10.7132	−	8.53829i	−0.365317	−	0.291153i
$861$	31.5109	+	54.5784i	1.07389	+	1.86003i
$862$	−35.8251	−	20.6837i	−1.22021	−	0.704488i
$863$		−	32.8011i		−	1.11656i	−0.829651	−	0.558282i	$-0.811461\pi$
$863$		−	32.8011i		−	1.11656i	0.829651	−	0.558282i	$-0.188539\pi$
$864$	8.05794	−	13.9568i	0.274137	−	0.474819i
$865$	−0.454782	+	3.02336i	−0.0154630	+	0.102797i
$866$	−0.652374			−0.0221686
$867$	−28.9032	−	16.6873i	−0.981603	−	0.566729i
$868$	−102.189	+	58.9986i	−3.46851	+	2.00254i
$869$	0.329747	+	0.571138i	0.0111859	+	0.0193745i
$870$	13.4424	+	34.2207i	0.455739	+	1.16019i
$871$		0			0
$872$			20.6526i			0.699385i
$873$	−20.9343	+	12.0864i	−0.708518	+	0.409063i
$874$	−3.74039	−	6.47855i	−0.126521	−	0.219140i
$875$	18.5315	+	27.1288i	0.626478	+	0.917120i
$876$	−99.6157			−3.36570
$877$	31.2333	+	18.0325i	1.05467	+	0.608916i	0.923954	−	0.382504i	$-0.124938\pi$
$877$	31.2333	+	18.0325i	1.05467	+	0.608916i	0.130719	+	0.991419i	$0.458271\pi$
$878$	−16.7482	−	9.66956i	−0.565223	−	0.326332i
$879$	−60.8257			−2.05160
$880$	−9.99285	−	1.50315i	−0.336859	−	0.0506712i
$881$	23.0198	+	39.8715i	0.775557	+	1.34330i	0.934481	+	0.356013i	$0.115864\pi$
$881$	23.0198	+	39.8715i	0.775557	+	1.34330i	−0.158924	+	0.987291i	$0.550802\pi$
$882$	5.89423	−	3.40304i	0.198469	−	0.114586i
$883$			0.802236i			0.0269974i	0.999909	+	0.0134987i	$0.00429690\pi$
$883$			0.802236i			0.0269974i	−0.999909	+	0.0134987i	$0.995703\pi$
$884$		0			0
$885$	−34.0390	+	13.3710i	−1.14421	+	0.449461i
$886$	5.50193	+	9.52962i	0.184841	+	0.320154i
$887$	−7.12365	+	4.11284i	−0.239189	+	0.138096i	−0.614804	−	0.788680i	$-0.710765\pi$
$887$	−7.12365	+	4.11284i	−0.239189	+	0.138096i	0.375615	+	0.926776i	$0.377431\pi$
$888$	14.4122	+	8.32087i	0.483641	+	0.279230i
$889$	50.6363			1.69829
$890$	−10.6336	+	70.6918i	−0.356440	+	2.36959i
$891$	3.56658	−	6.17750i	0.119485	−	0.206954i
$892$			0.0372125i			0.00124597i
$893$	−7.28589	−	4.20651i	−0.243813	−	0.140766i
$894$	−47.0112	−	81.4257i	−1.57229	−	2.72328i
$895$	−10.8511	+	13.6151i	−0.362713	+	0.455104i
$896$	−34.2529			−1.14431
$897$		0			0
$898$			8.37054i			0.279328i
$899$	13.4424	+	23.2829i	0.448328	+	0.776527i
$900$	35.0113	+	10.7768i	1.16704	+	0.359228i
$901$	0.393064	−	0.680808i	0.0130949	−	0.0226810i
$902$			16.1056i			0.536257i
$903$	7.49129	+	4.32510i	0.249295	+	0.143930i
$904$	−17.4616	+	30.2443i	−0.580763	+	1.00591i
$905$	−3.16131	−	8.04788i	−0.105086	−	0.267521i
$906$	58.5973	−	101.493i	1.94676	−	3.37189i
$907$	26.3583	−	15.2180i	0.875213	−	0.505305i	0.00613601	−	0.999981i	$-0.498047\pi$
$907$	26.3583	−	15.2180i	0.875213	−	0.505305i	0.869077	+	0.494677i	$0.164714\pi$
$908$	43.7080	−	25.2348i	1.45050	−	0.837447i
$909$	−21.6351			−0.717591
$910$		0			0
$911$	43.6145			1.44501			0.722507	−	0.691363i	$-0.242990\pi$
$911$	43.6145			1.44501			0.722507	+	0.691363i	$0.242990\pi$
$912$	18.1089	−	10.4552i	0.599646	−	0.346206i
$913$	6.51492	−	3.76139i	0.215612	−	0.124484i
$914$	−19.6354	+	34.0095i	−0.649481	+	1.12493i
$915$	10.1722	−	3.99577i	0.336282	−	0.132096i
$916$	−37.0569	+	64.1844i	−1.22439	+	2.12071i
$917$	−25.4486	−	14.6928i	−0.840387	−	0.485198i
$918$			9.15616i			0.302198i
$919$	−18.5109	+	32.0618i	−0.610617	+	1.05762i	0.380519	+	0.924773i	$0.375745\pi$
$919$	−18.5109	+	32.0618i	−0.610617	+	1.05762i	−0.991137	+	0.132847i	$0.957588\pi$
$920$	−18.9490	+	23.7757i	−0.624728	+	0.783861i
$921$	13.6947	+	23.7198i	0.451254	+	0.781595i
$922$		−	65.8957i		−	2.17016i
$923$		0			0
$924$	18.0033			0.592264
$925$	1.80037	−	5.84897i	0.0591958	−	0.192313i
$926$	−8.96157	−	15.5219i	−0.294496	−	0.510081i
$927$	−15.5318	−	8.96730i	−0.510132	−	0.294525i
$928$		−	16.4529i		−	0.540092i
$929$	2.38412	−	4.12942i	0.0782206	−	0.135482i	−0.824262	−	0.566209i	$-0.808409\pi$
$929$	2.38412	−	4.12942i	0.0782206	−	0.135482i	0.902482	+	0.430727i	$0.141743\pi$
$930$	108.606	+	16.3368i	3.56133	+	0.535704i
$931$	−2.23175			−0.0731427
$932$	−26.9670	−	15.5694i	−0.883334	−	0.509993i
$933$	52.0624	−	30.0582i	1.70445	−	0.984062i
$934$	−23.9443	−	41.4727i	−0.783481	−	1.35703i
$935$	1.61780	−	0.635495i	0.0529079	−	0.0207829i
$936$		0			0
$937$		−	43.6264i		−	1.42521i	−0.701565	−	0.712606i	$-0.747515\pi$
$937$		−	43.6264i		−	1.42521i	0.701565	−	0.712606i	$-0.252485\pi$
$938$	52.0230	−	30.0355i	1.69861	−	0.980693i
$939$	26.4602	+	45.8305i	0.863497	+	1.49562i
$940$	−9.18631	+	61.0701i	−0.299625	+	1.99189i
$941$	−18.2675			−0.595504			−0.297752	−	0.954643i	$-0.596237\pi$
$941$	−18.2675			−0.595504			−0.297752	+	0.954643i	$0.596237\pi$
$942$	−87.1677	−	50.3263i	−2.84008	−	1.63972i
$943$	18.5732	+	10.7233i	0.604828	+	0.349197i
$944$	54.0569			1.75940
$945$	19.0938	+	2.87214i	0.621123	+	0.0934308i
$946$	1.10530	+	1.91444i	0.0359365	+	0.0622439i
$947$	−17.3057	+	9.99146i	−0.562360	+	0.324679i	−0.754092	−	0.656769i	$-0.771923\pi$
$947$	−17.3057	+	9.99146i	−0.562360	+	0.324679i	0.191732	+	0.981447i	$0.438590\pi$
$948$			10.0175i			0.325353i
$949$		0			0
$950$	−11.8246	−	12.7287i	−0.383639	−	0.412973i
$951$	−0.252298	−	0.436993i	−0.00818132	−	0.0141705i
$952$	−19.6713	+	11.3572i	−0.637551	+	0.368090i
$953$	34.5228	+	19.9317i	1.11830	+	0.645652i	0.940967	−	0.338498i	$-0.109919\pi$
$953$	34.5228	+	19.9317i	1.11830	+	0.645652i	0.177335	+	0.984150i	$0.443252\pi$
$954$	−2.67352			−0.0865583
$955$	−10.9315	−	1.64434i	−0.353734	−	0.0532095i
$956$	8.96157	−	15.5219i	0.289838	−	0.502014i
$957$		−	4.10190i		−	0.132596i
$958$	42.9416	+	24.7923i	1.38738	+	0.801004i
$959$	12.7420	+	22.0698i	0.411461	+	0.712672i
$960$	1.01714	+	0.810646i	0.0328280	+	0.0261635i
$961$	49.3098			1.59064
$962$		0			0
$963$			17.4523i			0.562392i
$964$	−44.2973	−	76.7252i	−1.42672	−	2.47115i
$965$	8.66704	+	6.90753i	0.279002	+	0.222361i
$966$	17.3371	−	30.0287i	0.557811	−	0.966156i
$967$		−	43.8607i		−	1.41047i	−0.708975	−	0.705233i	$-0.750842\pi$
$967$		−	43.8607i		−	1.41047i	0.708975	−	0.705233i	$-0.249158\pi$
$968$	−57.9566	−	33.4613i	−1.86280	−	1.07549i
$969$	−1.79833	+	3.11480i	−0.0577707	+	0.100062i
$970$	−30.7688	−	78.3294i	−0.987928	−	2.51501i
$971$	−30.4897	+	52.8098i	−0.978462	+	1.69475i	−0.310459	+	0.950587i	$0.600483\pi$
$971$	−30.4897	+	52.8098i	−0.978462	+	1.69475i	−0.668002	+	0.744159i	$0.732850\pi$
$972$	59.6253	−	34.4247i	1.91248	−	1.10417i
$973$	−36.4589	+	21.0496i	−1.16882	+	0.674818i
$974$	82.2887			2.63670
$975$		0			0
$976$	−16.1543			−0.517087
$977$	44.4875	−	25.6849i	1.42328	−	0.821731i	0.426703	−	0.904392i	$-0.359675\pi$
$977$	44.4875	−	25.6849i	1.42328	−	0.821731i	0.996578	+	0.0826604i	$0.0263417\pi$
$978$	19.0376	−	10.9913i	0.608754	−	0.351464i
$979$	3.98780	−	6.90707i	0.127451	−	0.220751i
$980$	5.98973	+	15.2483i	0.191335	+	0.487088i
$981$	−2.67352	+	4.63066i	−0.0853588	+	0.147846i
$982$	−63.2099	−	36.4942i	−2.01711	−	1.16458i
$983$		−	37.3026i		−	1.18977i	−0.803811	−	0.594885i	$-0.797198\pi$
$983$		−	37.3026i		−	1.18977i	0.803811	−	0.594885i	$-0.202802\pi$
$984$	−67.7221	+	117.298i	−2.15890	+	3.73933i
$985$	−11.7954	−	9.40079i	−0.375832	−	0.299534i
$986$	4.67381	+	8.09528i	0.148845	+	0.257806i
$987$		−	38.9951i		−	1.24123i
$988$		0			0
$989$	2.94369			0.0936040
$990$	−4.62264	−	3.68419i	−0.146917	−	0.117091i
$991$	25.7810	+	44.6541i	0.818962	+	1.41848i	0.906448	+	0.422318i	$0.138783\pi$
$991$	25.7810	+	44.6541i	0.818962	+	1.41848i	−0.0874859	+	0.996166i	$0.527883\pi$
$992$	−42.5633	−	24.5739i	−1.35139	−	0.780223i
$993$			39.4556i			1.25208i
$994$	−9.85627	+	17.0716i	−0.312622	+	0.541477i
$995$	11.4439	+	1.72142i	0.362796	+	0.0545727i
$996$	114.269			3.62074
$997$	19.8743	+	11.4744i	0.629425	+	0.363399i	0.780529	−	0.625119i	$-0.214950\pi$
$997$	19.8743	+	11.4744i	0.629425	+	0.363399i	−0.151104	+	0.988518i	$0.548283\pi$
$998$	63.8508	−	36.8643i	2.02116	−	1.16692i
$999$	−1.79833	−	3.11480i	−0.0568967	−	0.0985479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.e.484.6		12
5.4	even	2	inner	845.2.n.e.484.1		12
13.2	odd	12		845.2.d.d.844.12		12
13.3	even	3		845.2.b.e.339.6		6
13.4	even	6		65.2.n.a.9.6	yes	12
13.5	odd	4		845.2.l.f.699.2		24
13.6	odd	12		845.2.l.f.654.1		24
13.7	odd	12		845.2.l.f.654.11		24
13.8	odd	4		845.2.l.f.699.12		24
13.9	even	3	inner	845.2.n.e.529.1		12
13.10	even	6		845.2.b.d.339.1		6
13.11	odd	12		845.2.d.d.844.2		12
13.12	even	2		65.2.n.a.29.1	yes	12
39.17	odd	6		585.2.bs.a.334.1		12
39.38	odd	2		585.2.bs.a.289.6		12
52.43	odd	6		1040.2.dh.a.529.5		12
52.51	odd	2		1040.2.dh.a.289.2		12
65.3	odd	12		4225.2.a.bq.1.6		6
65.4	even	6		65.2.n.a.9.1	✓	12
65.9	even	6	inner	845.2.n.e.529.6		12
65.12	odd	4		325.2.e.e.276.1		12
65.17	odd	12		325.2.e.e.126.1		12
65.19	odd	12		845.2.l.f.654.12		24
65.23	odd	12		4225.2.a.br.1.1		6
65.24	odd	12		845.2.d.d.844.11		12
65.29	even	6		845.2.b.e.339.1		6
65.34	odd	4		845.2.l.f.699.1		24
65.38	odd	4		325.2.e.e.276.6		12
65.42	odd	12		4225.2.a.bq.1.1		6
65.43	odd	12		325.2.e.e.126.6		12
65.44	odd	4		845.2.l.f.699.11		24
65.49	even	6		845.2.b.d.339.6		6
65.54	odd	12		845.2.d.d.844.1		12
65.59	odd	12		845.2.l.f.654.2		24
65.62	odd	12		4225.2.a.br.1.6		6
65.64	even	2		65.2.n.a.29.6	yes	12
195.134	odd	6		585.2.bs.a.334.6		12
195.194	odd	2		585.2.bs.a.289.1		12
260.199	odd	6		1040.2.dh.a.529.2		12
260.259	odd	2		1040.2.dh.a.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	65.4	even	6
65.2.n.a.9.6	yes	12	13.4	even	6
65.2.n.a.29.1	yes	12	13.12	even	2
65.2.n.a.29.6	yes	12	65.64	even	2
325.2.e.e.126.1		12	65.17	odd	12
325.2.e.e.126.6		12	65.43	odd	12
325.2.e.e.276.1		12	65.12	odd	4
325.2.e.e.276.6		12	65.38	odd	4
585.2.bs.a.289.1		12	195.194	odd	2
585.2.bs.a.289.6		12	39.38	odd	2
585.2.bs.a.334.1		12	39.17	odd	6
585.2.bs.a.334.6		12	195.134	odd	6
845.2.b.d.339.1		6	13.10	even	6
845.2.b.d.339.6		6	65.49	even	6
845.2.b.e.339.1		6	65.29	even	6
845.2.b.e.339.6		6	13.3	even	3
845.2.d.d.844.1		12	65.54	odd	12
845.2.d.d.844.2		12	13.11	odd	12
845.2.d.d.844.11		12	65.24	odd	12
845.2.d.d.844.12		12	13.2	odd	12
845.2.l.f.654.1		24	13.6	odd	12
845.2.l.f.654.2		24	65.59	odd	12
845.2.l.f.654.11		24	13.7	odd	12
845.2.l.f.654.12		24	65.19	odd	12
845.2.l.f.699.1		24	65.34	odd	4
845.2.l.f.699.2		24	13.5	odd	4
845.2.l.f.699.11		24	65.44	odd	4
845.2.l.f.699.12		24	13.8	odd	4
845.2.n.e.484.1		12	5.4	even	2	inner
845.2.n.e.484.6		12	1.1	even	1	trivial
845.2.n.e.529.1		12	13.9	even	3	inner
845.2.n.e.529.6		12	65.9	even	6	inner
1040.2.dh.a.289.2		12	52.51	odd	2
1040.2.dh.a.289.5		12	260.259	odd	2
1040.2.dh.a.529.2		12	260.199	odd	6
1040.2.dh.a.529.5		12	52.43	odd	6
4225.2.a.bq.1.1		6	65.42	odd	12
4225.2.a.bq.1.6		6	65.3	odd	12
4225.2.a.br.1.1		6	65.23	odd	12
4225.2.a.br.1.6		6	65.62	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.20467 - 1.27287i) q^{2} +(1.86449 - 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(-2.54486 - 1.46928i) q^{7} -6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +O(q^{10})\)	\(q+(2.20467 - 1.27287i) q^{2} +(1.86449 - 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(-2.54486 - 1.46928i) q^{7} -6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +(4.45158 + 3.54786i) q^{10} +(-0.317544 - 0.550003i) q^{11} -9.64680i q^{12} -7.48079 q^{14} +(3.76470 + 3.00042i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(1.05998 + 0.611979i) q^{17} -4.16251i q^{18} +(-0.682456 + 1.18205i) q^{19} +(9.90788 + 1.49037i) q^{20} -6.32648 q^{21} +(-1.40016 - 0.808385i) q^{22} +(-1.86449 + 1.07646i) q^{23} +(-6.79833 - 11.7751i) q^{24} +(-3.66324 + 3.40304i) q^{25} +2.93855i q^{27} +(-11.4030 + 6.58351i) q^{28} +(1.50000 + 2.59808i) q^{29} +(12.1191 + 1.82298i) q^{30} +8.96157 q^{31} +(-4.74954 - 2.74215i) q^{32} +(-1.18412 - 0.683650i) q^{33} +3.11588 q^{34} +(0.977401 - 6.49770i) q^{35} +(-3.66324 - 6.34492i) q^{36} +(-1.05998 + 0.611979i) q^{37} +3.47471i q^{38} +(13.1440 - 5.16315i) q^{40} +(-4.98079 - 8.62698i) q^{41} +(-13.9478 + 8.05279i) q^{42} +(-1.18412 - 0.683650i) q^{43} -2.84570 q^{44} +(3.61549 + 0.543852i) q^{45} +(-2.74039 + 4.74650i) q^{46} +6.16379i q^{47} +(-13.2675 - 7.65998i) q^{48} +(0.817544 + 1.41603i) q^{49} +(-3.74464 + 12.1654i) q^{50} +2.63509 q^{51} -0.642285i q^{53} +(3.74039 + 6.47855i) q^{54} +(0.885090 - 1.11054i) q^{55} +(-9.27912 + 16.0719i) q^{56} +2.93855i q^{57} +(6.61402 + 3.81861i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(20.0774 - 7.88669i) q^{60} +(1.13509 - 1.96603i) q^{61} +(19.7574 - 11.4069i) q^{62} +(-4.16107 + 2.40240i) q^{63} +0.270178 q^{64} -3.48079 q^{66} +(-6.95421 + 4.01502i) q^{67} +(4.74954 - 2.74215i) q^{68} +(-2.31754 + 4.01410i) q^{69} +(-6.11588 - 15.5694i) q^{70} +(1.31754 - 2.28205i) q^{71} +(-8.94284 - 5.16315i) q^{72} -10.3263i q^{73} +(-1.55794 + 2.69843i) q^{74} +(-3.16683 + 10.2883i) q^{75} +(3.05794 + 5.29650i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(9.91702 - 12.4431i) q^{80} +(5.61588 + 9.72698i) q^{81} +(-21.9620 - 12.6798i) q^{82} +11.8452i q^{83} +(-14.1738 + 24.5498i) q^{84} +(-0.407104 + 2.70640i) q^{85} -3.48079 q^{86} +(5.59346 + 3.22939i) q^{87} +(-3.47351 + 2.00543i) q^{88} +(6.27912 + 10.8758i) q^{89} +(8.66324 - 3.40304i) q^{90} +9.64680i q^{92} +(16.7087 - 9.64680i) q^{93} +(7.84570 + 13.5891i) q^{94} +(-3.01808 - 0.453987i) q^{95} -11.8073 q^{96} +(-12.8031 - 7.39190i) q^{97} +(3.60484 + 2.08125i) q^{98} -1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 + 4 * q^15 - 16 * q^16 - 12 * q^19 + q^20 + 8 * q^21 - 32 * q^24 - 2 * q^25 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 29 * q^45 - 10 * q^46 + 6 * q^49 + 31 * q^50 + 24 * q^51 + 22 * q^54 - 26 * q^55 - 16 * q^56 + 4 * q^59 + 96 * q^60 + 6 * q^61 - 12 * q^64 + 4 * q^66 - 24 * q^69 - 20 * q^70 + 12 * q^71 + 8 * q^74 + 2 * q^75 + 10 * q^76 - 104 * q^79 - 33 * q^80 + 14 * q^81 - 90 * q^84 - 21 * q^85 + 4 * q^86 - 20 * q^89 + 62 * q^90 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

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