LMFDB - Embedded newform 845.2.l.f.699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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, 1]))

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

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

chi := DirichletCharacter("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			699.1
Character	$\chi$	$=$	845.699
Dual form			845.2.l.f.654.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27287 - 2.20467i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(-2.24039 + 3.88048i) q^{4} +(2.08125 + 0.817544i) q^{5} +(4.74650 + 2.74039i) q^{6} +(1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(0.817544 - 1.41603i) q^{9} +O(q^{10})$	\(q+(-1.27287 - 2.20467i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(-2.24039 + 3.88048i) q^{4} +(2.08125 + 0.817544i) q^{5} +(4.74650 + 2.74039i) q^{6} +(1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(0.817544 - 1.41603i) q^{9} +(-0.846746 - 5.62912i) q^{10} +(-0.550003 + 0.317544i) q^{11} -9.64680i q^{12} -7.48079 q^{14} +(-4.76053 + 0.716091i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(1.05998 + 0.611979i) q^{17} -4.16251 q^{18} +(-1.18205 - 0.682456i) q^{19} +(-7.83529 + 6.24464i) q^{20} +6.32648i q^{21} +(1.40016 + 0.808385i) q^{22} +(-1.86449 + 1.07646i) q^{23} +(-11.7751 + 6.79833i) q^{24} +(3.66324 + 3.40304i) q^{25} -2.93855i q^{27} +(6.58351 + 11.4030i) q^{28} +(1.50000 + 2.59808i) q^{29} +(7.63828 + 9.58393i) q^{30} +8.96157i q^{31} +(-2.74215 + 4.74954i) q^{32} +(0.683650 - 1.18412i) q^{33} -3.11588i q^{34} +(5.13847 - 4.09531i) q^{35} +(3.66324 + 6.34492i) q^{36} +(-0.611979 - 1.05998i) q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(8.62698 - 4.98079i) q^{41} +(13.9478 - 8.05279i) q^{42} +(-1.18412 - 0.683650i) q^{43} -2.84570i q^{44} +(2.85918 - 2.27874i) q^{45} +(4.74650 + 2.74039i) q^{46} -6.16379 q^{47} +(13.2675 + 7.65998i) q^{48} +(-0.817544 - 1.41603i) q^{49} +(2.83976 - 12.4079i) q^{50} -2.63509 q^{51} +0.642285i q^{53} +(-6.47855 + 3.74039i) q^{54} +(-1.40430 + 0.211239i) q^{55} +(9.27912 - 16.0719i) q^{56} +2.93855 q^{57} +(3.81861 - 6.61402i) q^{58} +(6.57890 + 3.79833i) q^{59} +(7.88669 - 20.0774i) q^{60} +(1.13509 - 1.96603i) q^{61} +(19.7574 - 11.4069i) q^{62} +(-2.40240 - 4.16107i) q^{63} -0.270178 q^{64} -3.48079 q^{66} +(4.01502 + 6.95421i) q^{67} +(-4.74954 + 2.74215i) q^{68} +(2.31754 - 4.01410i) q^{69} +(-15.5694 - 6.11588i) q^{70} +(2.28205 + 1.31754i) q^{71} +(5.16315 - 8.94284i) q^{72} +10.3263 q^{73} +(-1.55794 + 2.69843i) q^{74} +(-10.4933 - 2.40158i) q^{75} +(5.29650 - 3.05794i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(-2.36683 - 15.7346i) q^{80} +(5.61588 + 9.72698i) q^{81} +(-21.9620 - 12.6798i) q^{82} +11.8452 q^{83} +(-24.5498 - 14.1738i) q^{84} +(1.70576 + 2.14026i) q^{85} +3.48079i q^{86} +(-5.59346 - 3.22939i) q^{87} +(-3.47351 + 2.00543i) q^{88} +(10.8758 - 6.27912i) q^{89} +(-8.66324 - 3.40304i) q^{90} -9.64680i q^{92} +(-9.64680 - 16.7087i) q^{93} +(7.84570 + 13.5891i) q^{94} +(-1.90220 - 2.38674i) q^{95} -11.8073i q^{96} +(-7.39190 + 12.8031i) q^{97} +(-2.08125 + 3.60484i) q^{98} +1.03843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^4 + 12 * q^9	$ 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) $ 24 * q - 8 * q^4 + 12 * q^9 - 14 * q^10 - 88 * q^14 - 32 * q^16 + 4 * q^25 + 36 * q^29 - 8 * q^30 + 20 * q^35 + 4 * q^36 + 140 * q^40 - 12 * q^49 - 48 * q^51 - 52 * q^55 + 32 * q^56 + 12 * q^61 + 24 * q^64 + 8 * q^66 + 48 * q^69 + 16 * q^74 - 4 * q^75 - 208 * q^79 + 28 * q^81 - 124 * q^90 + 112 * q^94 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.27287	−	2.20467i	−0.900055	−	1.55894i	−0.827421	−	0.561582i	$-0.810193\pi$
$2$	−1.27287	−	2.20467i	−0.900055	−	1.55894i	−0.0726333	−	0.997359i	$-0.523140\pi$
$3$	−1.86449	+	1.07646i	−1.07646	+	0.621496i	−0.929940	−	0.367711i	$-0.880142\pi$
$3$	−1.86449	+	1.07646i	−1.07646	+	0.621496i	−0.146523	+	0.989207i	$0.546808\pi$
$4$	−2.24039	+	3.88048i	−1.12020	+	1.94024i
$5$	2.08125	+	0.817544i	0.930765	+	0.365617i
$5$	2.08125	+	0.817544i	0.930765	+	0.365617i
$6$	4.74650	+	2.74039i	1.93775	+	1.11876i
$7$	1.46928	−	2.54486i	0.555334	−	0.961867i	−0.442543	−	0.896747i	$-0.645924\pi$
$7$	1.46928	−	2.54486i	0.555334	−	0.961867i	0.997877	−	0.0651198i	$-0.0207430\pi$
$8$	6.31544			2.23284
$9$	0.817544	−	1.41603i	0.272515	−	0.472010i
$10$	−0.846746	−	5.62912i	−0.267765	−	1.78008i
$11$	−0.550003	+	0.317544i	−0.165832	+	0.0957433i	−0.580619	−	0.814175i	$-0.697189\pi$
$11$	−0.550003	+	0.317544i	−0.165832	+	0.0957433i	0.414787	+	0.909919i	$0.363856\pi$
$12$		−	9.64680i		−	2.78479i
$13$		0			0
$13$		0			0
$14$	−7.48079			−1.99932
$15$	−4.76053	+	0.716091i	−1.22916	+	0.184894i
$16$	−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	$0.619246\pi$
$18$	−4.16251			−0.981113
$19$	−1.18205	−	0.682456i	−0.271180	−	0.156566i	0.358244	−	0.933628i	$-0.383376\pi$
$19$	−1.18205	−	0.682456i	−0.271180	−	0.156566i	−0.629424	+	0.777062i	$0.716709\pi$
$20$	−7.83529	+	6.24464i	−1.75202	+	1.39634i
$21$			6.32648i			1.38055i
$22$	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	$0.405394\pi$
$24$	−11.7751	+	6.79833i	−2.40357	+	1.38770i
$25$	3.66324	+	3.40304i	0.732648	+	0.680607i
$26$		0			0
$27$		−	2.93855i		−	0.565525i
$28$	6.58351	+	11.4030i	1.24417	+	2.15496i
$29$	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	$0.743482\pi$
$30$	7.63828	+	9.58393i	1.39455	+	1.74978i
$31$			8.96157i			1.60955i	0.593583	+	0.804773i	$0.297713\pi$
$31$			8.96157i			1.60955i	−0.593583	+	0.804773i	$0.702287\pi$
$32$	−2.74215	+	4.74954i	−0.484747	+	0.839607i
$33$	0.683650	−	1.18412i	0.119008	−	0.206128i
$34$		−	3.11588i		−	0.534368i
$35$	5.13847	−	4.09531i	0.868561	−	0.692233i
$36$	3.66324	+	6.34492i	0.610540	+	1.05749i
$37$	−0.611979	−	1.05998i	−0.100609	−	0.174259i	0.811327	−	0.584593i	$-0.198746\pi$
$37$	−0.611979	−	1.05998i	−0.100609	−	0.174259i	−0.911936	+	0.410333i	$0.865412\pi$
$38$			3.47471i			0.563672i
$39$		0			0
$40$	13.1440	+	5.16315i	2.07825	+	0.816366i
$41$	8.62698	−	4.98079i	1.34731	−	0.777868i	0.359440	−	0.933168i	$-0.382968\pi$
$41$	8.62698	−	4.98079i	1.34731	−	0.777868i	0.987867	+	0.155300i	$0.0496344\pi$
$42$	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	$0.699913\pi$
$44$		−	2.84570i		−	0.429005i
$45$	2.85918	−	2.27874i	0.426222	−	0.339694i
$46$	4.74650	+	2.74039i	0.699833	+	0.404049i
$47$	−6.16379			−0.899081			−0.449540	−	0.893260i	$-0.648412\pi$
$47$	−6.16379			−0.899081			−0.449540	+	0.893260i	$0.648412\pi$
$48$	13.2675	+	7.65998i	1.91499	+	1.10562i
$49$	−0.817544	−	1.41603i	−0.116792	−	0.202290i
$50$	2.83976	−	12.4079i	0.401603	−	1.75474i
$51$	−2.63509			−0.368986
$52$		0			0
$53$			0.642285i			0.0882246i	0.999027	+	0.0441123i	$0.0140459\pi$
$53$			0.642285i			0.0882246i	−0.999027	+	0.0441123i	$0.985954\pi$
$54$	−6.47855	+	3.74039i	−0.881619	+	0.509003i
$55$	−1.40430	+	0.211239i	−0.189356	+	0.0284834i
$56$	9.27912	−	16.0719i	1.23997	−	2.14770i
$57$	2.93855			0.389221
$58$	3.81861	−	6.61402i	0.501408	−	0.868464i
$59$	6.57890	+	3.79833i	0.856500	+	0.494501i	0.862839	−	0.505479i	$-0.168684\pi$
$59$	6.57890	+	3.79833i	0.856500	+	0.494501i	−0.00633858	+	0.999980i	$0.502018\pi$
$60$	7.88669	−	20.0774i	1.01817	−	2.59199i
$61$	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
$63$	−2.40240	−	4.16107i	−0.302674	−	0.524246i
$64$	−0.270178			−0.0337722
$65$		0			0
$66$	−3.48079			−0.428455
$67$	4.01502	+	6.95421i	0.490512	+	0.849592i	0.999940	−	0.0109212i	$-0.00347639\pi$
$67$	4.01502	+	6.95421i	0.490512	+	0.849592i	−0.509428	+	0.860513i	$0.670143\pi$
$68$	−4.74954	+	2.74215i	−0.575966	+	0.332534i
$69$	2.31754	−	4.01410i	0.279000	−	0.483241i
$70$	−15.5694	−	6.11588i	−1.86090	−	0.730987i
$71$	2.28205	+	1.31754i	0.270830	+	0.156364i	0.629265	−	0.777191i	$-0.283356\pi$
$71$	2.28205	+	1.31754i	0.270830	+	0.156364i	−0.358435	+	0.933555i	$0.616689\pi$
$72$	5.16315	−	8.94284i	0.608483	−	1.05392i
$73$	10.3263			1.20860			0.604301	−	0.796756i	$-0.293453\pi$
$73$	10.3263			1.20860			0.604301	+	0.796756i	$0.293453\pi$
$74$	−1.55794	+	2.69843i	−0.181107	+	0.313686i
$75$	−10.4933	−	2.40158i	−1.21166	−	0.277310i
$76$	5.29650	−	3.05794i	0.607551	−	0.350770i
$77$			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	$0.518605\pi$
$80$	−2.36683	−	15.7346i	−0.264620	−	1.75918i
$81$	5.61588	+	9.72698i	0.623986	+	1.08078i
$82$	−21.9620	−	12.6798i	−2.42530	−	1.40025i
$83$	11.8452			1.30018			0.650092	−	0.759855i	$-0.274730\pi$
$83$	11.8452			1.30018			0.650092	+	0.759855i	$0.274730\pi$
$84$	−24.5498	−	14.1738i	−2.67860	−	1.54649i
$85$	1.70576	+	2.14026i	0.185016	+	0.232144i
$86$			3.48079i			0.375343i
$87$	−5.59346	−	3.22939i	−0.599682	−	0.346227i
$88$	−3.47351	+	2.00543i	−0.370277	+	0.213780i
$89$	10.8758	−	6.27912i	1.15283	−	0.665585i	0.203253	−	0.979126i	$-0.434849\pi$
$89$	10.8758	−	6.27912i	1.15283	−	0.665585i	0.949575	+	0.313541i	$0.101515\pi$
$90$	−8.66324	−	3.40304i	−0.913186	−	0.358712i
$91$		0			0
$92$		−	9.64680i		−	1.00575i
$93$	−9.64680	−	16.7087i	−1.00033	−	1.73262i
$94$	7.84570	+	13.5891i	0.809222	+	1.40161i
$95$	−1.90220	−	2.38674i	−0.195162	−	0.244874i
$96$		−	11.8073i		−	1.20507i
$97$	−7.39190	+	12.8031i	−0.750534	+	1.29996i	0.197031	+	0.980397i	$0.436870\pi$
$97$	−7.39190	+	12.8031i	−0.750534	+	1.29996i	−0.947564	+	0.319565i	$0.896463\pi$
$98$	−2.08125	+	3.60484i	−0.210238	+	0.364144i
$99$			1.03843i			0.104366i
$100$	−21.4125	+	6.59098i	−2.14125	+	0.659098i
$101$	6.61588	+	11.4590i	0.658304	+	1.14022i	0.981054	+	0.193732i	$0.0620593\pi$
$101$	6.61588	+	11.4590i	0.658304	+	1.14022i	−0.322750	+	0.946484i	$0.604607\pi$
$102$	3.35412	+	5.80951i	0.332108	+	0.575228i
$103$		−	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
$106$	1.41603	−	0.817544i	0.137537	−	0.0794069i
$107$	9.24360	−	5.33680i	0.893613	−	0.515928i	0.0184903	−	0.999829i	$-0.494114\pi$
$107$	9.24360	−	5.33680i	0.893613	−	0.515928i	0.875123	+	0.483901i	$0.160781\pi$
$108$	11.4030	+	6.58351i	1.09725	+	0.633499i
$109$		−	3.27018i		−	0.313226i	−0.987660	−	0.156613i	$-0.949942\pi$
$109$		−	3.27018i		−	0.313226i	0.987660	−	0.156613i	$-0.0500576\pi$
$110$	2.25321	+	2.82715i	0.214835	+	0.269558i
$111$	2.28205	+	1.31754i	0.216603	+	0.125056i
$112$	−20.9104			−1.97584
$113$	4.78895	+	2.76490i	0.450507	+	0.260100i	0.708044	−	0.706168i	$-0.249578\pi$
$113$	4.78895	+	2.76490i	0.450507	+	0.260100i	−0.257537	+	0.966268i	$0.582911\pi$
$114$	−3.74039	−	6.47855i	−0.350320	−	0.606772i
$115$	−4.76053	+	0.716091i	−0.443922	+	0.0667759i
$116$	−13.4424			−1.24809
$117$		0			0
$118$		−	19.3391i		−	1.78031i
$119$	3.11480	−	1.79833i	0.285533	−	0.164853i
$120$	−30.0648	+	4.52243i	−2.74453	+	0.412839i
$121$	−5.29833	+	9.17698i	−0.481666	+	0.834271i
$122$	−5.77928			−0.523231
$123$	−10.7233	+	18.5732i	−0.966884	+	1.67469i
$124$	−34.7752	−	20.0774i	−3.12290	−	1.80301i
$125$	4.84201	+	10.0774i	0.433082	+	0.901354i
$126$	−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	$0.610364\pi$
$128$	5.82819	+	10.0947i	0.515144	+	0.892256i
$129$	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	$0.356093\pi$
$132$	3.06329	+	5.30577i	0.266625	+	0.461808i
$133$	−3.47351	+	2.00543i	−0.301191	+	0.173893i
$134$	10.2212	−	17.7036i	0.882975	−	1.52936i
$135$	2.40240	−	6.11588i	0.206765	−	0.526371i
$136$	6.69422	+	3.86491i	0.574025	+	0.331413i
$137$	4.33616	−	7.51044i	0.370463	−	0.641661i	−0.619174	−	0.785254i	$-0.712532\pi$
$137$	4.33616	−	7.51044i	0.370463	−	0.641661i	0.989637	+	0.143593i	$0.0458657\pi$
$138$	−11.7997			−1.00446
$139$	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	$-0.0411922\pi$
$140$	4.37953	+	29.1148i	0.370137	+	2.46065i
$141$	11.4923	−	6.63509i	0.967827	−	0.558775i
$142$		−	6.70825i		−	0.562944i
$143$		0			0
$144$	−11.6351			−0.969591
$145$	0.997839	+	6.63357i	0.0828660	+	0.550888i
$146$	−13.1440	−	22.7661i	−1.08781	−	1.88414i
$147$	3.04860	+	1.76011i	0.251445	+	0.145172i
$148$	5.48429			0.450806
$149$	14.8566	+	8.57745i	1.21710	+	0.702692i	0.964296	−	0.264826i	$-0.0853145\pi$
$149$	14.8566	+	8.57745i	1.21710	+	0.702692i	0.252802	+	0.967518i	$0.418648\pi$
$150$	8.06192	+	26.1912i	0.658253	+	2.13851i
$151$		−	21.3828i		−	1.74011i	−0.492957	−	0.870053i	$-0.664084\pi$
$151$		−	21.3828i		−	1.74011i	0.492957	−	0.870053i	$-0.335916\pi$
$152$	−7.46515	−	4.31000i	−0.605503	−	0.349587i
$153$	1.73316	−	1.00064i	0.140118	−	0.0808969i
$154$	4.11446	−	2.37548i	0.331552	−	0.191422i
$155$	−7.32648	+	18.6513i	−0.588477	+	1.49811i
$156$		0			0
$157$			18.3646i			1.46566i	0.680413	+	0.732829i	$0.261800\pi$
$157$			18.3646i			1.46566i	−0.680413	+	0.732829i	$0.738200\pi$
$158$	1.32178	+	2.28939i	0.105155	+	0.182134i
$159$	−0.691395	−	1.19753i	−0.0548312	−	0.0949705i
$160$	−9.59006	+	7.64317i	−0.758161	+	0.604245i
$161$			6.32648i			0.498597i
$162$	14.2966	−	24.7624i	1.12324	−	1.94551i
$163$	−2.00543	+	3.47351i	−0.157078	+	0.272066i	−0.933814	−	0.357760i	$-0.883541\pi$
$163$	−2.00543	+	3.47351i	−0.157078	+	0.272066i	0.776736	+	0.629826i	$0.216874\pi$
$164$			44.6357i			3.48546i
$165$	2.39092	−	1.90553i	0.186133	−	0.148346i
$166$	−15.0774	−	26.1149i	−1.17024	−	2.02691i
$167$	−1.46928	−	2.54486i	−0.113696	−	0.196927i	0.803562	−	0.595221i	$-0.202936\pi$
$167$	−1.46928	−	2.54486i	−0.113696	−	0.196927i	−0.917258	+	0.398294i	$0.869602\pi$
$168$			39.9545i			3.08256i
$169$		0			0
$170$	2.54737	−	6.48493i	0.195374	−	0.497371i
$171$	−1.93275	+	1.11588i	−0.147801	+	0.0853331i
$172$	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	$0.650114\pi$
$174$			16.4424i			1.24649i
$175$	14.0426	−	4.32244i	1.06152	−	0.326746i
$176$	3.91375	+	2.25961i	0.295010	+	0.170324i
$177$	−16.3550			−1.22932
$178$	−27.6868	−	15.9850i	−2.07522	−	1.19813i
$179$	−3.89306	−	6.74299i	−0.290981	−	0.503994i	0.683061	−	0.730362i	$-0.260648\pi$
$179$	−3.89306	−	6.74299i	−0.290981	−	0.503994i	−0.974042	+	0.226367i	$0.927315\pi$
$180$	2.43688	+	16.2003i	0.181635	+	1.20750i
$181$	3.86684			0.287420			0.143710	−	0.989620i	$-0.454097\pi$
$181$	3.86684			0.287420			0.143710	+	0.989620i	$0.454097\pi$
$182$		0			0
$183$			4.88752i			0.361296i
$184$	−11.7751	+	6.79833i	−0.868069	+	0.501180i
$185$	−0.407104	−	2.70640i	−0.0299309	−	0.198979i
$186$	−24.5582	+	42.5361i	−1.80070	+	3.11890i
$187$	−0.777322			−0.0568434
$188$	13.8093	−	23.9184i	1.00715	−	1.74443i
$189$	−7.47821	−	4.31754i	−0.543959	−	0.314055i
$190$	−2.84073	+	7.23175i	−0.206088	+	0.524646i
$191$	−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
$193$	2.47822	+	4.29240i	0.178386	+	0.308974i	0.941328	−	0.337493i	$-0.109579\pi$
$193$	2.47822	+	4.29240i	0.178386	+	0.308974i	−0.762942	+	0.646467i	$0.776246\pi$
$194$	37.6357			2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	3.37273	+	5.84174i	0.240297	+	0.416207i	0.960799	−	0.277246i	$-0.0894218\pi$
$197$	3.37273	+	5.84174i	0.240297	+	0.416207i	−0.720502	+	0.693453i	$0.756088\pi$
$198$	2.28939	−	1.32178i	0.162700	−	0.0939349i
$199$	−2.58772	+	4.48207i	−0.183439	+	0.317725i	−0.943049	−	0.332653i	$-0.892056\pi$
$199$	−2.58772	+	4.48207i	−0.183439	+	0.317725i	0.759611	+	0.650378i	$0.225390\pi$
$200$	23.1350	+	21.4917i	1.63589	+	1.51969i
$201$	−14.9719	−	8.64403i	−1.05604	−	0.609703i
$202$	16.8423	−	29.1717i	1.18502	−	2.05251i
$203$	8.81566			0.618738
$204$	5.90364	−	10.2254i	0.413337	−	0.715921i
$205$	22.0269	−	3.31335i	1.53843	−	0.231414i
$206$	−24.1822	+	13.9616i	−1.68485	+	0.972749i
$207$			3.52022i			0.244673i
$208$		0			0
$209$	0.866840			0.0599606
$210$	35.6125	−	5.35693i	2.45750	−	0.369663i
$211$	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
$213$	−5.67315			−0.388718
$214$	−23.5318	−	13.5861i	−1.60860	−	0.928726i
$215$	−1.90553	−	2.39092i	−0.129956	−	0.163059i
$216$		−	18.5582i		−	1.26273i
$217$	22.8060	+	13.1670i	1.54817	+	0.893836i
$218$	−7.20968	+	4.16251i	−0.488301	+	0.281921i
$219$	−19.2533	+	11.1159i	−1.30101	+	0.751141i
$220$	2.32648	−	5.92262i	0.156852	−	0.399303i
$221$		0			0
$222$		−	6.70825i		−	0.450228i
$223$	0.00415245	+	0.00719226i	0.000278069	+	0.000481629i	0.866164	−	0.499759i	$-0.166578\pi$
$223$	0.00415245	+	0.00719226i	0.000278069	+	0.000481629i	−0.865886	+	0.500241i	$0.833245\pi$
$224$	8.05794	+	13.9568i	0.538394	+	0.932525i
$225$	7.81366	−	2.40512i	0.520911	−	0.160341i
$226$		−	14.0774i		−	0.936418i
$227$	5.63179	−	9.75454i	0.373795	−	0.647431i	−0.616351	−	0.787471i	$-0.711390\pi$
$227$	5.63179	−	9.75454i	0.373795	−	0.647431i	0.990146	+	0.140040i	$0.0447231\pi$
$228$	−6.58351	+	11.4030i	−0.436004	+	0.755181i
$229$			16.5404i			1.09302i	0.837453	+	0.546509i	$0.184043\pi$
$229$			16.5404i			1.09302i	−0.837453	+	0.546509i	$0.815957\pi$
$230$	7.63828	+	9.58393i	0.503653	+	0.631946i
$231$	−2.00894	−	3.47959i	−0.132179	−	0.228940i
$232$	9.47315	+	16.4080i	0.621943	+	1.07724i
$233$		−	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
$236$	−29.4787	+	17.0195i	−1.91890	+	1.10788i
$237$	1.93613	−	1.11783i	0.125765	−	0.0726107i
$238$	−7.92947	−	4.57808i	−0.513991	−	0.296753i
$239$			4.00000i			0.258738i	0.991596	+	0.129369i	$0.0412952\pi$
$239$			4.00000i			0.258738i	−0.991596	+	0.129369i	$0.958705\pi$
$240$	21.3506	+	26.7891i	1.37818	+	1.72923i
$241$	−17.1231	−	9.88605i	−1.10300	−	0.636817i	−0.165992	−	0.986127i	$-0.553083\pi$
$241$	−17.1231	−	9.88605i	−1.10300	−	0.636817i	−0.937007	+	0.349310i	$0.886416\pi$
$242$	26.9763			1.73410
$243$	−13.3069	−	7.68273i	−0.853637	−	0.492848i
$244$	5.08609	+	8.80937i	0.325604	+	0.563962i
$245$	−0.543852	−	3.61549i	−0.0347454	−	0.230985i
$246$	54.5973			3.48099
$247$		0			0
$248$			56.5962i			3.59386i
$249$	−22.0853	+	12.7510i	−1.39960	+	0.808060i
$250$	16.0543	−	23.5023i	1.01536	−	1.48642i
$251$	1.83676	−	3.18136i	0.115935	−	0.200806i	−0.802218	−	0.597031i	$-0.796347\pi$
$251$	1.83676	−	3.18136i	0.115935	−	0.200806i	0.918153	+	0.396226i	$0.129680\pi$
$252$	21.5293			1.35622
$253$	0.683650	−	1.18412i	0.0429807	−	0.0744447i
$254$	37.9903	+	21.9337i	2.38372	+	1.37624i
$255$	−5.48429	−	2.15430i	−0.343440	−	0.134908i
$256$	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	$0.469104\pi$
$258$	−3.74694	−	6.48989i	−0.233274	−	0.404043i
$259$	−3.59666			−0.223486
$260$		0			0
$261$	4.90527			0.303628
$262$	−12.7287	−	22.0467i	−0.786381	−	1.36205i
$263$	−26.2150	+	15.1352i	−1.61649	+	0.933279i	−0.628667	+	0.777674i	$0.716399\pi$
$263$	−26.2150	+	15.1352i	−1.61649	+	0.933279i	−0.987819	+	0.155605i	$0.950267\pi$
$264$	4.31754	−	7.47821i	0.265726	−	0.460252i
$265$	−0.525096	+	1.33676i	−0.0322564	+	0.0821164i
$266$	8.84265	+	5.10530i	0.542177	+	0.313026i
$267$	−13.5185	+	23.4147i	−0.827317	+	1.43296i
$268$	−35.9809			−2.19788
$269$	−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	$0.929387\pi$
$270$	−16.5415	+	2.48821i	−1.00668	+	0.151427i
$271$	−10.2437	+	5.91421i	−0.622261	+	0.359262i	−0.777749	−	0.628575i	$-0.783638\pi$
$271$	−10.2437	+	5.91421i	−0.622261	+	0.359262i	0.155488	+	0.987838i	$0.450305\pi$
$272$		−	8.70953i		−	0.528093i
$273$		0			0
$274$	−22.0774			−1.33375
$275$	−3.09541	−	0.708438i	−0.186660	−	0.0427204i
$276$	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	$0.498432\pi$
$278$	−36.4715			−2.18741
$279$	12.6898	+	7.32648i	0.759721	+	0.438625i
$280$	32.4517	−	25.8636i	1.93936	−	1.54565i
$281$		−	10.5967i		−	0.632144i	−0.948735	−	0.316072i	$-0.897636\pi$
$281$		−	10.5967i		−	0.632144i	0.948735	−	0.316072i	$-0.102364\pi$
$282$	−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	$0.417721\pi$
$284$	−10.2254	+	5.90364i	−0.606766	+	0.350316i
$285$	6.11588	+	2.40240i	0.362273	+	0.142306i
$286$		0			0
$287$		−	29.2726i		−	1.72791i
$288$	4.48365	+	7.76591i	0.264202	+	0.457611i
$289$	−7.75096	−	13.4251i	−0.455939	−	0.789710i
$290$	13.3548	−	10.6436i	0.784218	−	0.625013i
$291$		−	31.8284i		−	1.86581i
$292$	−23.1350	+	40.0709i	−1.35387	+	2.34497i
$293$	14.1263	−	24.4675i	0.825267	−	1.42940i	−0.0764476	−	0.997074i	$-0.524358\pi$
$293$	14.1263	−	24.4675i	0.825267	−	1.42940i	0.901715	−	0.432331i	$-0.142309\pi$
$294$		−	8.96157i		−	0.522650i
$295$	10.5871	+	13.2838i	0.616403	+	0.773415i
$296$	−3.86491	−	6.69422i	−0.224643	−	0.389094i
$297$	0.933121	+	1.61621i	0.0541452	+	0.0937822i
$298$		−	43.6719i		−	2.52984i
$299$		0			0
$300$	32.8284	−	35.3386i	1.89535	−	2.04027i
$301$	−3.47959	+	2.00894i	−0.200560	+	0.115793i
$302$	−47.1421	+	27.2175i	−2.71272	+	1.56619i
$303$	−24.6704	−	14.2435i	−1.41728	−	0.818267i
$304$			9.71254i			0.557052i
$305$	3.96973	−	3.16383i	0.227306	−	0.181160i
$306$	−4.41217	−	2.54737i	−0.252227	−	0.145623i
$307$	−12.7219			−0.726077			−0.363039	−	0.931774i	$-0.618261\pi$
$307$	−12.7219			−0.726077			−0.363039	+	0.931774i	$0.618261\pi$
$308$	−7.24190	−	4.18112i	−0.412646	−	0.238241i
$309$	11.8073	+	20.4508i	0.671692	+	1.16340i
$310$	50.4457	−	7.58818i	2.86513	−	0.430980i
$311$	−27.9231			−1.58338			−0.791688	−	0.610925i	$-0.790798\pi$
$311$	−27.9231			−1.58338			−0.791688	+	0.610925i	$0.790798\pi$
$312$		0			0
$313$		−	24.5807i		−	1.38938i	−0.719307	−	0.694692i	$-0.755540\pi$
$313$		−	24.5807i		−	1.38938i	0.719307	−	0.694692i	$-0.244460\pi$
$314$	40.4880	−	23.3758i	2.28487	−	1.31917i
$315$	−1.59814	−	10.6243i	−0.0900448	−	0.598613i
$316$	2.32648	−	4.02959i	0.130875	−	0.226682i
$317$	−0.234377			−0.0131639			−0.00658196	−	0.999978i	$-0.502095\pi$
$317$	−0.234377			−0.0131639			−0.00658196	+	0.999978i	$0.502095\pi$
$318$	−1.76011	+	3.04860i	−0.0987022	+	0.170957i
$319$	−1.65001	−	0.952633i	−0.0923828	−	0.0533372i
$320$	−0.562309	−	0.220882i	−0.0314340	−	0.0123477i
$321$	−11.4897	+	19.9008i	−0.641294	+	1.11075i
$322$	13.9478	−	8.05279i	0.777283	−	0.448764i
$323$	−0.835296	−	1.44678i	−0.0464771	−	0.0805008i
$324$	−50.3271			−2.79595
$325$		0			0
$326$	10.2106			0.565513
$327$	3.52022	+	6.09721i	0.194669	+	0.337176i
$328$	54.4831	−	31.4558i	3.00833	−	1.73686i
$329$	−9.05631	+	15.6860i	−0.499290	+	0.864796i
$330$	−7.24440	−	2.84570i	−0.398791	−	0.156651i
$331$	−15.8712	−	9.16324i	−0.872360	−	0.503657i	−0.00422829	−	0.999991i	$-0.501346\pi$
$331$	−15.8712	−	9.16324i	−0.872360	−	0.503657i	−0.868132	+	0.496334i	$0.834679\pi$
$332$	−26.5380	+	45.9652i	−1.45646	+	2.52267i
$333$	−2.00128			−0.109669
$334$	−3.74039	+	6.47855i	−0.204665	+	0.354491i
$335$	2.67089	+	17.7559i	0.145926	+	0.970110i
$336$	38.9871	−	22.5092i	2.12692	−	1.22798i
$337$			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
$340$	−12.1268	+	1.82415i	−0.657669	+	0.0989283i
$341$	−2.84570	−	4.92889i	−0.154103	−	0.266915i
$342$	4.92028	+	2.84073i	0.266059	+	0.153609i
$343$	15.7651			0.851234
$344$	−7.47821	−	4.31754i	−0.403198	−	0.232786i
$345$	8.10511	−	6.45968i	0.436364	−	0.347777i
$346$		−	3.48079i		−	0.187128i
$347$	3.30407	+	1.90761i	0.177372	+	0.102406i	0.586057	−	0.810270i	$-0.300679\pi$
$347$	3.30407	+	1.90761i	0.177372	+	0.102406i	−0.408685	+	0.912675i	$0.634013\pi$
$348$	25.0631	−	14.4702i	1.34352	−	0.775684i
$349$	−21.0674	+	12.1632i	−1.12771	+	0.651083i	−0.943358	−	0.331777i	$-0.892352\pi$
$349$	−21.0674	+	12.1632i	−1.12771	+	0.651083i	−0.184352	+	0.982860i	$0.559019\pi$
$350$	−27.4039	−	25.4574i	−1.46480	−	1.36075i
$351$		0			0
$352$		−	3.48301i		−	0.185645i
$353$	−13.5295	−	23.4338i	−0.720104	−	1.24726i	−0.960958	−	0.276696i	$-0.910761\pi$
$353$	−13.5295	−	23.4338i	−0.720104	−	1.24726i	0.240853	−	0.970562i	$-0.422573\pi$
$354$	20.8178	+	36.0576i	1.10646	+	1.91644i
$355$	3.67238	+	4.60783i	0.194910	+	0.244558i
$356$			56.2708i			2.98235i
$357$	−3.87167	+	6.70593i	−0.204911	+	0.354916i
$358$	−9.91073	+	17.1659i	−0.523798	+	0.907245i
$359$		−	27.0039i		−	1.42521i	−0.701566	−	0.712605i	$-0.747515\pi$
$359$		−	27.0039i		−	1.42521i	0.701566	−	0.712605i	$-0.252485\pi$
$360$	18.0570	−	14.3912i	0.951687	−	0.758484i
$361$	−8.56851	−	14.8411i	−0.450974	−	0.781110i
$362$	−4.92198	−	8.52512i	−0.258694	−	0.448071i
$363$		−	22.8138i		−	1.19742i
$364$		0			0
$365$	21.4917	+	8.44221i	1.12492	+	0.441885i
$366$	10.7754	−	6.22118i	0.563239	−	0.325186i
$367$	−6.01118	+	3.47055i	−0.313781	+	0.181161i	−0.648617	−	0.761115i	$-0.724652\pi$
$367$	−6.01118	+	3.47055i	−0.313781	+	0.181161i	0.334836	+	0.942276i	$0.391319\pi$
$368$	13.2675	+	7.65998i	0.691615	+	0.399304i
$369$		−	16.2881i		−	0.847922i
$370$	−5.44855	+	4.34243i	−0.283257	+	0.225752i
$371$	1.63452	+	0.943693i	0.0848603	+	0.0489941i
$372$	86.4505			4.48225
$373$	2.00301	+	1.15644i	0.103712	+	0.0598781i	0.550959	−	0.834532i	$-0.314262\pi$
$373$	2.00301	+	1.15644i	0.103712	+	0.0598781i	−0.447247	+	0.894411i	$0.647595\pi$
$374$	0.989429	+	1.71374i	0.0511622	+	0.0886154i
$375$	−19.8759	−	13.5770i	−1.02639	−	0.701116i
$376$	−38.9270			−2.00751
$377$		0			0
$378$			21.9827i			1.13067i
$379$	4.48207	−	2.58772i	0.230228	−	0.132922i	−0.380449	−	0.924802i	$-0.624231\pi$
$379$	4.48207	−	2.58772i	0.230228	−	0.132922i	0.610677	+	0.791880i	$0.290897\pi$
$380$	13.5234	−	2.03422i	0.693734	−	0.104353i
$381$	18.5493	−	32.1283i	0.950309	−	1.64598i
$382$	12.5854			0.643923
$383$	−10.3305	+	17.8929i	−0.527861	+	0.914283i	0.471611	+	0.881807i	$0.343673\pi$
$383$	−10.3305	+	17.8929i	−0.527861	+	0.914283i	−0.999473	+	0.0324760i	$0.989661\pi$
$384$	−21.7332	−	12.5477i	−1.10907	−	0.640320i
$385$	−1.52574	+	3.88412i	−0.0777587	+	0.197953i
$386$	6.30890	−	10.9273i	0.321115	−	0.556187i
$387$	−1.93613	+	1.11783i	−0.0984193	+	0.0568224i
$388$	−33.1215	−	57.3682i	−1.68149	−	2.91243i
$389$	19.7477			1.00125			0.500624	−	0.865665i	$-0.333104\pi$
$389$	19.7477			1.00125			0.500624	+	0.865665i	$0.333104\pi$
$390$		0			0
$391$	−2.63509			−0.133262
$392$	−5.16315	−	8.94284i	−0.260778	−	0.451681i
$393$	−18.6449	+	10.7646i	−0.940510	+	0.543004i
$394$	8.58609	−	14.8715i	0.432561	−	0.749218i
$395$	−2.16123	−	0.848960i	−0.108743	−	0.0427158i
$396$	−4.02959	−	2.32648i	−0.202494	−	0.116910i
$397$	−4.69451	+	8.13113i	−0.235611	+	0.408090i	−0.959450	−	0.281879i	$-0.909042\pi$
$397$	−4.69451	+	8.13113i	−0.235611	+	0.408090i	0.723839	+	0.689969i	$0.242376\pi$
$398$	13.1753			0.660420
$399$	4.31754	−	7.47821i	0.216148	−	0.374379i
$400$	7.93772	−	34.6826i	0.396886	−	1.73413i
$401$	21.2193	−	12.2510i	1.05964	−	0.611784i	0.134308	−	0.990940i	$-0.457119\pi$
$401$	21.2193	−	12.2510i	1.05964	−	0.611784i	0.925333	+	0.379156i	$0.123786\pi$
$402$			44.0109i			2.19506i
$403$		0			0
$404$	−59.2887			−2.94972
$405$	3.73583	+	24.8356i	0.185635	+	1.23409i
$406$	−11.2212	−	19.4357i	−0.556898	−	0.964575i
$407$	0.673180	+	0.388661i	0.0333683	+	0.0192652i
$408$	−16.6417			−0.823889
$409$	−31.2778	−	18.0582i	−1.54659	−	0.892922i	−0.998399	−	0.0565671i	$-0.981985\pi$
$409$	−31.2778	−	18.0582i	−1.54659	−	0.892922i	−0.548188	−	0.836355i	$-0.684682\pi$
$410$	−35.3423	−	44.3448i	−1.74543	−	2.19003i
$411$			18.6708i			0.920965i
$412$	42.5633	+	24.5739i	2.09694	+	1.21067i
$413$	19.3324	−	11.1616i	0.951288	−	0.549226i
$414$	7.76095	−	4.48079i	0.381430	−	0.220219i
$415$	24.6530	+	9.68401i	1.21017	+	0.475370i
$416$		0			0
$417$			30.8439i			1.51043i
$418$	−1.10337	−	1.91110i	−0.0539678	−	0.0934749i
$419$	−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	$0.886978\pi$
$420$	−39.5066	−	49.5698i	−1.92772	−	2.41876i
$421$		−	33.9795i		−	1.65606i	−0.560686	−	0.828029i	$-0.689462\pi$
$421$		−	33.9795i		−	1.65606i	0.560686	−	0.828029i	$-0.310538\pi$
$422$	17.8429	−	30.9049i	0.868580	−	1.50443i
$423$	−5.03917	+	8.72810i	−0.245013	+	0.424375i
$424$			4.05631i			0.196992i
$425$	1.80037	+	5.84897i	0.0873308	+	0.283717i
$426$	7.22118	+	12.5075i	0.349867	+	0.605988i
$427$	−3.33552	−	5.77729i	−0.161417	−	0.279582i
$428$			47.8261i			2.31176i
$429$		0			0
$430$	−2.84570	+	7.24440i	−0.137232	+	0.349356i
$431$	14.0726	−	8.12482i	0.677853	−	0.391359i	−0.121193	−	0.992629i	$-0.538672\pi$
$431$	14.0726	−	8.12482i	0.677853	−	0.391359i	0.799046	+	0.601270i	$0.205339\pi$
$432$	−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	$0.668627\pi$
$434$		−	67.0396i		−	3.21800i
$435$	−9.00126	−	11.2941i	−0.431577	−	0.541510i
$436$	12.6898	+	7.32648i	0.607733	+	0.350875i
$437$	2.93855			0.140570
$438$	49.0138	+	28.2981i	2.34197	+	1.35214i
$439$	3.79833	+	6.57890i	0.181284	+	0.313994i	0.942318	−	0.334718i	$-0.108641\pi$
$439$	3.79833	+	6.57890i	0.181284	+	0.313994i	−0.761034	+	0.648712i	$0.775308\pi$
$440$	−8.86879	+	1.33407i	−0.422803	+	0.0635991i
$441$	−2.67352			−0.127310
$442$		0			0
$443$		−	4.32246i		−	0.205366i	−0.994714	−	0.102683i	$-0.967257\pi$
$443$		−	4.32246i		−	0.205366i	0.994714	−	0.102683i	$-0.0327428\pi$
$444$	−10.2254	+	5.90364i	−0.485276	+	0.280174i
$445$	27.7687	−	4.17703i	1.31636	−	0.198010i
$446$	0.0105711	−	0.0183096i	0.000500554	−	0.000866986i
$447$	−36.9332			−1.74688
$448$	−0.396966	+	0.687565i	−0.0187549	+	0.0324844i
$449$	2.84754	+	1.64403i	0.134384	+	0.0775865i	0.565685	−	0.824622i	$-0.308612\pi$
$449$	2.84754	+	1.64403i	0.134384	+	0.0775865i	−0.431301	+	0.902208i	$0.641945\pi$
$450$	−15.2483	−	14.1652i	−0.718811	−	0.667753i
$451$	−3.16324	+	5.47890i	−0.148951	+	0.257991i
$452$	−21.4583	+	12.3889i	−1.00931	+	0.582727i
$453$	23.0178	+	39.8680i	1.08147	+	1.87316i
$454$	−28.6741			−1.34574
$455$		0			0
$456$	18.5582			0.869069
$457$	7.71304	+	13.3594i	0.360801	+	0.624925i	0.988093	−	0.153859i	$-0.0491701\pi$
$457$	7.71304	+	13.3594i	0.360801	+	0.624925i	−0.627292	+	0.778784i	$0.715837\pi$
$458$	36.4661	−	21.0537i	1.70395	−	0.983775i
$459$	1.79833	−	3.11480i	0.0839389	−	0.145386i
$460$	7.88669	−	20.0774i	0.367719	−	0.936116i
$461$	22.4168	+	12.9424i	1.04406	+	0.602786i	0.920979	−	0.389611i	$-0.127391\pi$
$461$	22.4168	+	12.9424i	1.04406	+	0.602786i	0.123076	+	0.992397i	$0.460724\pi$
$462$	−5.11424	+	8.85812i	−0.237936	+	0.412117i
$463$	7.04045			0.327197			0.163599	−	0.986527i	$-0.447690\pi$
$463$	7.04045			0.327197			0.163599	+	0.986527i	$0.447690\pi$
$464$	10.6738	−	18.4876i	0.495519	−	0.858265i
$465$	−6.41730	−	42.6618i	−0.297595	−	1.97840i
$466$	−15.3212	+	8.84570i	−0.709741	+	0.409769i
$467$		−	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
$470$	5.21916	+	34.6967i	0.240742	+	1.60044i
$471$	−19.7688	−	34.2406i	−0.910900	−	1.57773i
$472$	41.5486	+	23.9881i	1.91243	+	1.10414i
$473$	0.868356			0.0399271
$474$	−4.92889	−	2.84570i	−0.226392	−	0.130707i
$475$	−2.00771	−	6.52255i	−0.0921199	−	0.299275i
$476$			16.1159i			0.738670i
$477$	0.909493	+	0.525096i	0.0416428	+	0.0240425i
$478$	8.81870	−	5.09148i	0.403358	−	0.232879i
$479$	16.8680	−	9.73876i	0.770720	−	0.444975i	−0.0624114	−	0.998051i	$-0.519879\pi$
$479$	16.8680	−	9.73876i	0.770720	−	0.444975i	0.833131	+	0.553075i	$0.186546\pi$
$480$	9.65297	−	24.5739i	0.440596	−	1.12164i
$481$		0			0
$482$			50.3346i			2.29268i
$483$	−6.81023	−	11.7957i	−0.309876	−	0.536721i
$484$	−23.7407	−	41.1201i	−1.07912	−	1.86909i
$485$	−25.8516	+	20.6034i	−1.17386	+	0.935552i
$486$			39.1165i			1.77436i
$487$	16.1620	−	27.9935i	0.732372	−	1.26851i	−0.223495	−	0.974705i	$-0.571747\pi$
$487$	16.1620	−	27.9935i	0.732372	−	1.26851i	0.955867	−	0.293800i	$-0.0949200\pi$
$488$	7.16858	−	12.4163i	0.324506	−	0.562062i
$489$		−	8.63509i		−	0.390492i
$490$	−7.27874	+	5.80107i	−0.328820	+	0.262066i
$491$	14.3354	+	24.8297i	0.646949	+	1.12055i	0.983848	+	0.179007i	$0.0572885\pi$
$491$	14.3354	+	24.8297i	0.646949	+	1.12055i	−0.336899	+	0.941541i	$0.609378\pi$
$492$	−48.0487	−	83.2227i	−2.16620	−	3.75197i
$493$			3.67187i			0.165373i
$494$		0			0
$495$	−0.848960	+	2.16123i	−0.0381579	+	0.0971401i
$496$	55.2260	−	31.8847i	2.47972	−	1.43167i
$497$	6.70593	−	3.87167i	0.300802	−	0.173668i
$498$	56.2235	+	32.4606i	2.51943	+	1.45460i
$499$			28.9616i			1.29650i	0.761428	+	0.648249i	$0.224498\pi$
$499$			28.9616i			1.29650i	−0.761428	+	0.648249i	$0.775502\pi$
$500$	−49.9533	−	3.78816i	−2.23398	−	0.169412i
$501$	5.47890	+	3.16324i	0.244779	+	0.141323i
$502$	−9.35181			−0.417392
$503$	−24.3433	−	14.0546i	−1.08542	−	0.626665i	−0.153063	−	0.988216i	$-0.548914\pi$
$503$	−24.3433	−	14.0546i	−1.08542	−	0.626665i	−0.932352	+	0.361551i	$0.882247\pi$
$504$	−15.1722	−	26.2790i	−0.675823	−	1.17056i
$505$	4.40105	+	29.2579i	0.195844	+	1.30196i
$506$	−3.48079			−0.154740
$507$		0			0
$508$		−	77.2116i		−	3.42571i
$509$	18.2841	−	10.5563i	0.810427	−	0.467900i	−0.0366773	−	0.999327i	$-0.511677\pi$
$509$	18.2841	−	10.5563i	0.810427	−	0.467900i	0.847104	+	0.531427i	$0.178344\pi$
$510$	2.23125	+	14.8332i	0.0988015	+	0.656826i
$511$	15.1722	−	26.2790i	0.671178	−	1.16251i
$512$	−50.8542			−2.24746
$513$	−2.00543	+	3.47351i	−0.0885420	+	0.153359i
$514$	29.2447	+	16.8844i	1.28993	+	0.744740i
$515$	8.96730	−	22.8284i	0.395147	−	1.00594i
$516$	−6.59503	+	11.4229i	−0.290330	+	0.502866i
$517$	3.39010	−	1.95728i	0.149097	−	0.0860809i
$518$	4.57808	+	7.92947i	0.201149	+	0.348401i
$519$	−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	$0.495304\pi$
$522$	−6.24376	−	10.8145i	−0.273282	−	0.473339i
$523$	25.8618	−	14.9313i	1.13086	−	0.652900i	0.186706	−	0.982416i	$-0.440219\pi$
$523$	25.8618	−	14.9313i	1.13086	−	0.652900i	0.944150	+	0.329516i	$0.106886\pi$
$524$	−22.4039	+	38.8048i	−0.978720	+	1.69519i
$525$	−21.5293	+	23.1754i	−0.939614	+	1.01146i
$526$	66.7366	+	38.5304i	2.90985	+	1.68000i
$527$	−5.48429	+	9.49907i	−0.238899	+	0.413786i
$528$	−9.72953			−0.423423
$529$	−9.18246	+	15.9045i	−0.399237	+	0.691499i
$530$	3.61549	−	0.543852i	0.157047	−	0.0236234i
$531$	10.7571	−	6.21061i	0.466818	−	0.269517i
$532$		−	17.9718i		−	0.779177i
$533$		0			0
$534$	68.8290			2.97852
$535$	23.6014	−	3.55018i	1.02038	−	0.153488i
$536$	25.3566	+	43.9189i	1.09524	+	1.89701i
$537$	14.5171	+	8.38148i	0.626461	+	0.361687i
$538$	56.6418			2.44200
$539$	0.899304	+	0.519213i	0.0387358	+	0.0223641i
$540$	18.3502	+	23.0244i	0.789666	+	0.990813i
$541$			6.28806i			0.270345i	0.990822	+	0.135172i	$0.0431588\pi$
$541$			6.28806i			0.270345i	−0.990822	+	0.135172i	$0.956841\pi$
$542$	26.0778	+	15.0560i	1.12014	+	0.646712i
$543$	−7.20968	+	4.16251i	−0.309397	+	0.178630i
$544$	−5.81323	+	3.35627i	−0.249240	+	0.143899i
$545$	2.67352	−	6.80607i	0.114521	−	0.291540i
$546$		0			0
$547$		−	3.03789i		−	0.129891i	−0.997889	−	0.0649454i	$-0.979313\pi$
$547$		−	3.03789i		−	0.129891i	0.997889	−	0.0649454i	$-0.0206873\pi$
$548$	19.4294	+	33.6527i	0.829983	+	1.43757i
$549$	−1.85597	−	3.21464i	−0.0792109	−	0.137197i
$550$	2.37818	+	7.72612i	0.101406	+	0.329443i
$551$		−	4.09473i		−	0.174442i
$552$	14.6363	−	25.3508i	0.622962	−	1.07900i
$553$	−1.52574	+	2.64265i	−0.0648809	+	0.112377i
$554$		−	42.7304i		−	1.81544i
$555$	3.67238	+	4.60783i	0.155884	+	0.195591i
$556$	32.0970	+	55.5936i	1.36121	+	2.35769i
$557$	10.3498	+	17.9264i	0.438536	+	0.759566i	0.997577	−	0.0695738i	$-0.0221639\pi$
$557$	10.3498	+	17.9264i	0.438536	+	0.759566i	−0.559041	+	0.829140i	$0.688831\pi$
$558$		−	37.3026i		−	1.57915i
$559$		0			0
$560$	−43.5198	−	17.0952i	−1.83905	−	0.722402i
$561$	1.44931	−	0.836758i	0.0611898	−	0.0353279i
$562$	−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	$0.740853\pi$
$564$			59.4608i			2.50375i
$565$	7.70660	+	9.66965i	0.324219	+	0.406805i
$566$	19.4357	+	11.2212i	0.816941	+	0.471661i
$567$	33.0051			1.38608
$568$	14.4122	+	8.32087i	0.604721	+	0.349136i
$569$	−21.3566	−	36.9907i	−0.895314	−	1.55073i	−0.833416	−	0.552647i	$-0.813618\pi$
$569$	−21.3566	−	36.9907i	−0.895314	−	1.55073i	−0.0618981	−	0.998082i	$-0.519715\pi$
$570$	−2.48821	−	16.5415i	−0.104220	−	0.692845i
$571$	23.6145			0.988238			0.494119	−	0.869394i	$-0.335491\pi$
$571$	23.6145			0.988238			0.494119	+	0.869394i	$0.335491\pi$
$572$		0			0
$573$		−	10.6434i		−	0.444635i
$574$	−64.5366	+	37.2602i	−2.69370	+	1.55521i
$575$	−10.4933	−	2.40158i	−0.437601	−	0.100153i
$576$	−0.220882	+	0.382579i	−0.00920343	+	0.0159408i
$577$	−18.3646			−0.764530			−0.382265	−	0.924053i	$-0.624856\pi$
$577$	−18.3646			−0.764530			−0.382265	+	0.924053i	$0.624856\pi$
$578$	−19.7319	+	34.1767i	−0.820740	+	1.42156i
$579$	−9.24123	−	5.33542i	−0.384052	−	0.221733i
$580$	−27.9770	−	10.9897i	−1.16168	−	0.456324i
$581$	17.4039	−	30.1445i	0.722037	−	1.25060i
$582$	−70.1713	+	40.5134i	−2.90869	+	1.67934i
$583$	−0.203954	−	0.353259i	−0.00844691	−	0.0146305i
$584$	65.2151			2.69862
$585$		0			0
$586$	−71.9237			−2.97114
$587$	0.351448	+	0.608726i	0.0145058	+	0.0251248i	0.873187	−	0.487385i	$-0.162049\pi$
$587$	0.351448	+	0.608726i	0.0145058	+	0.0251248i	−0.858681	+	0.512510i	$0.828716\pi$
$588$	−13.6601	+	7.88669i	−0.563335	+	0.325242i
$589$	6.11588	−	10.5930i	0.252000	−	0.436477i
$590$	15.8106	−	40.2496i	0.650912	−	1.65705i
$591$	−12.5768	−	7.26124i	−0.517342	−	0.298687i
$592$	−4.35476	+	7.54267i	−0.178980	+	0.310002i
$593$	−37.1593			−1.52595			−0.762975	−	0.646428i	$-0.776262\pi$
$593$	−37.1593			−1.52595			−0.762975	+	0.646428i	$0.776262\pi$
$594$	2.37548	−	4.11446i	0.0974672	−	0.168818i
$595$	7.95291	−	1.19630i	0.326037	−	0.0490434i
$596$	−66.5692	+	38.4337i	−2.72678	+	1.57431i
$597$		−	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	$0.396127\pi$
$600$	−66.2698	−	15.1670i	−2.70546	−	0.619190i
$601$	−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
$603$	13.1298			0.534687
$604$	82.9754	+	47.9059i	3.37622	+	1.94926i
$605$	−18.5298	+	14.7680i	−0.753342	+	0.600405i
$606$			72.5204i			2.94594i
$607$	−33.5035	−	19.3433i	−1.35987	−	0.785119i	−0.370261	−	0.928928i	$-0.620732\pi$
$607$	−33.5035	−	19.3433i	−1.35987	−	0.785119i	−0.989606	+	0.143809i	$0.954065\pi$
$608$	6.48269	−	3.74278i	0.262908	−	0.151790i
$609$	−16.4367	+	9.48973i	−0.666048	+	0.384543i
$610$	−12.0282	−	4.72482i	−0.487006	−	0.191302i
$611$		0			0
$612$			8.96730i			0.362482i
$613$	−8.64201	−	14.9684i	−0.349047	−	0.604568i	0.637033	−	0.770836i	$-0.280161\pi$
$613$	−8.64201	−	14.9684i	−0.349047	−	0.604568i	−0.986081	+	0.166269i	$0.946828\pi$
$614$	16.1933	+	28.0477i	0.653509	+	1.13191i
$615$	−37.5023	+	29.8889i	−1.51224	+	1.20524i
$616$			11.7861i			0.474877i
$617$	−13.2345	+	22.9229i	−0.532803	+	0.922841i	0.466464	+	0.884540i	$0.345528\pi$
$617$	−13.2345	+	22.9229i	−0.532803	+	0.922841i	−0.999266	+	0.0383009i	$0.987805\pi$
$618$	30.0582	−	52.0624i	1.20912	−	2.09426i
$619$			31.0039i			1.24615i	0.782162	+	0.623075i	$0.214117\pi$
$619$			31.0039i			1.24615i	−0.782162	+	0.623075i	$0.785883\pi$
$620$	−55.9618	−	70.2165i	−2.24748	−	2.81996i
$621$	3.16324	+	5.47890i	0.126937	+	0.219861i
$622$	35.5425	+	61.5615i	1.42513	+	2.46839i
$623$		−	36.9030i		−	1.47849i
$624$		0			0
$625$	1.83869	+	24.9323i	0.0735475	+	0.997292i
$626$	−54.1925	+	31.2881i	−2.16597	+	1.25052i
$627$	−1.61621	+	0.933121i	−0.0645453	+	0.0372653i
$628$	−71.2635	−	41.1440i	−2.84372	−	1.64182i
$629$		−	1.49807i		−	0.0597320i
$630$	−21.3889	+	17.0467i	−0.852156	+	0.679159i
$631$	17.9381	+	10.3566i	0.714104	+	0.412288i	0.812579	−	0.582851i	$-0.198063\pi$
$631$	17.9381	+	10.3566i	0.714104	+	0.412288i	−0.0984745	+	0.995140i	$0.531396\pi$
$632$	−6.55812			−0.260868
$633$	−26.1362	−	15.0897i	−1.03882	−	0.599763i
$634$	0.298331	+	0.516725i	0.0118482	+	0.0205218i
$635$	−38.1026	+	5.73149i	−1.51206	+	0.227447i
$636$	6.19599			0.245687
$637$		0			0
$638$			4.85031i			0.192026i
$639$	3.73136	−	2.15430i	0.147610	−	0.0852229i
$640$	3.87707	+	25.7745i	0.153254	+	1.01883i
$641$	10.5947	−	18.3506i	0.418467	−	0.724806i	−0.577319	−	0.816519i	$-0.695901\pi$
$641$	10.5947	−	18.3506i	0.418467	−	0.724806i	0.995785	+	0.0917132i	$0.0292343\pi$
$642$	58.4997			2.30880
$643$	−5.76682	+	9.98843i	−0.227421	+	0.393905i	−0.957043	−	0.289946i	$-0.906363\pi$
$643$	−5.76682	+	9.98843i	−0.227421	+	0.393905i	0.729622	+	0.683851i	$0.239696\pi$
$644$	−24.5498	−	14.1738i	−0.967396	−	0.558526i
$645$	6.12658	+	2.40660i	0.241234	+	0.0947598i
$646$	−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	$0.0931456\pi$
$648$	35.4667	+	61.4301i	1.39326	+	2.41320i
$649$	−4.82456			−0.189380
$650$		0			0
$651$	−56.6953			−2.22206
$652$	−8.98591	−	15.5641i	−0.351915	−	0.609535i
$653$	−19.3324	+	11.1616i	−0.756537	+	0.436787i	−0.828051	−	0.560653i	$-0.810550\pi$
$653$	−19.3324	+	11.1616i	−0.756537	+	0.436787i	0.0715139	+	0.997440i	$0.477217\pi$
$654$	8.96157	−	15.5219i	0.350425	−	0.606954i
$655$	20.8125	+	8.17544i	0.813214	+	0.319441i
$656$	−61.3885	−	35.4427i	−2.39682	−	1.38380i
$657$	8.44221	−	14.6223i	0.329362	−	0.570471i
$658$	46.1100			1.79755
$659$	−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	$0.172041\pi$
$660$	2.03778	+	13.5470i	0.0793205	+	0.527318i
$661$	11.5256	−	6.65430i	0.448293	−	0.258822i	−0.258816	−	0.965927i	$-0.583332\pi$
$661$	11.5256	−	6.65430i	0.448293	−	0.258822i	0.707109	+	0.707104i	$0.249999\pi$
$662$			46.6544i			1.81328i
$663$		0			0
$664$	74.8079			2.90311
$665$	−8.86879	+	1.33407i	−0.343917	+	0.0517328i
$666$	2.54737	+	4.41217i	0.0987085	+	0.170968i
$667$	−5.59346	−	3.22939i	−0.216580	−	0.125042i
$668$	13.1670			0.509448
$669$	−0.0154844	−	0.00893993i	−0.000598662	−	0.000345637i
$670$	35.7464	−	28.4894i	1.38100	−	1.10064i
$671$			1.44176i			0.0556587i
$672$	−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	$0.367221\pi$
$674$	46.9483	−	27.1056i	1.80838	−	1.04407i
$675$	10.0000	−	10.7646i	0.384900	−	0.414331i
$676$		0			0
$677$		−	4.80479i		−	0.184663i	−0.995728	−	0.0923316i	$-0.970568\pi$
$677$		−	4.80479i		−	0.184663i	0.995728	−	0.0923316i	$-0.0294320\pi$
$678$	15.1539	+	26.2472i	0.581980	+	1.00802i
$679$	21.7215	+	37.6227i	0.833594	+	1.44383i
$680$	10.7726	+	13.5167i	0.413112	+	0.518341i
$681$			24.2496i			0.929248i
$682$	−7.24440	+	12.5477i	−0.277403	+	0.480475i
$683$	−5.88126	+	10.1866i	−0.225040	+	0.389781i	−0.956331	−	0.292284i	$-0.905585\pi$
$683$	−5.88126	+	10.1866i	−0.225040	+	0.389781i	0.731291	+	0.682065i	$0.238918\pi$
$684$		−	10.0000i		−	0.382360i
$685$	15.1648	−	12.0861i	0.579416	−	0.461788i
$686$	−20.0669	−	34.7569i	−0.766157	−	1.32702i
$687$	−17.8051	−	30.8393i	−0.679306	−	1.17659i
$688$			9.72953i			0.370935i
$689$		0			0
$690$	−24.5582	−	9.64680i	−0.934916	−	0.367247i
$691$	−4.21481	+	2.43342i	−0.160339	+	0.0925717i	−0.578022	−	0.816021i	$-0.696175\pi$
$691$	−4.21481	+	2.43342i	−0.160339	+	0.0925717i	0.417684	+	0.908593i	$0.362842\pi$
$692$	−5.30577	+	3.06329i	−0.201695	+	0.116449i
$693$	2.64265	+	1.52574i	0.100386	+	0.0579579i
$694$		−	9.71254i		−	0.368683i
$695$	25.0519	−	19.9661i	0.950272	−	0.757356i
$696$	−35.3252	−	20.3950i	−1.33900	−	0.773070i
$697$	12.1925			0.461825
$698$	53.6320	+	30.9644i	2.03000	+	1.17202i
$699$	7.48079	+	12.9571i	0.282949	+	0.490083i
$700$	−14.6877	+	64.1758i	−0.555145	+	2.42562i
$701$	−21.3828			−0.807617			−0.403808	−	0.914844i	$-0.632314\pi$
$701$	−21.3828			−0.807617			−0.403808	+	0.914844i	$0.632314\pi$
$702$		0			0
$703$			1.67059i			0.0630076i
$704$	0.148599	−	0.0857934i	0.00560052	−	0.00323346i
$705$	29.3429	−	4.41383i	1.10512	−	0.166235i
$706$	−34.4427	+	59.6564i	−1.29627	+	2.24520i
$707$	38.8822			1.46232
$708$	36.6417	−	63.4654i	1.37708	−	2.38517i
$709$	−22.6175	−	13.0582i	−0.849419	−	0.490412i	0.0110357	−	0.999939i	$-0.496487\pi$
$709$	−22.6175	−	13.0582i	−0.849419	−	0.490412i	−0.860455	+	0.509527i	$0.829820\pi$
$710$	5.48429	−	13.9616i	0.205822	−	0.523969i
$711$	−0.848960	+	1.47044i	−0.0318385	+	0.0551459i
$712$	68.6851	−	39.6554i	2.57408	−	1.48615i
$713$	−9.64680	−	16.7087i	−0.361276	−	0.625748i
$714$	19.7125			0.737723
$715$		0			0
$716$	34.8880			1.30383
$717$	−4.30585	−	7.45795i	−0.160805	−	0.278522i
$718$	−59.5347	+	34.3724i	−2.22182	+	1.28277i
$719$	−18.3387	+	31.7635i	−0.683918	+	1.18458i	0.289858	+	0.957070i	$0.406392\pi$
$719$	−18.3387	+	31.7635i	−0.683918	+	1.18458i	−0.973776	+	0.227510i	$0.926941\pi$
$720$	−24.2156	−	9.51220i	−0.902462	−	0.354499i
$721$	−27.9135	−	16.1159i	−1.03955	−	0.600187i
$722$	−21.8132	+	37.7815i	−0.811803	+	1.40608i
$723$	42.5679			1.58312
$724$	−8.66324	+	15.0052i	−0.321967	+	0.557663i
$725$	−3.34648	+	14.6219i	−0.124285	+	0.543045i
$726$	−50.2971	+	29.0390i	−1.86670	+	1.07774i
$727$			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
$730$	−8.74375	−	58.1279i	−0.323621	−	2.15141i
$731$	−0.836758	−	1.44931i	−0.0309486	−	0.0536046i
$732$	−18.9659	−	10.9500i	−0.701000	−	0.404723i
$733$	−31.7811			−1.17386			−0.586931	−	0.809637i	$-0.699664\pi$
$733$	−31.7811			−1.17386			−0.586931	+	0.809637i	$0.699664\pi$
$734$	15.3029	+	8.83513i	0.564840	+	0.326110i
$735$	4.90595	+	6.15561i	0.180959	+	0.227053i
$736$		−	11.8073i		−	0.435222i
$737$	−4.41654	−	2.54989i	−0.162685	−	0.0939265i
$738$	−35.9099	+	20.7326i	−1.32186	+	0.763176i
$739$	29.5635	−	17.0685i	1.08751	−	0.627875i	0.154599	−	0.987977i	$-0.450591\pi$
$739$	29.5635	−	17.0685i	1.08751	−	0.627875i	0.932913	+	0.360102i	$0.117258\pi$
$740$	11.4142	+	4.48365i	0.419595	+	0.164822i
$741$		0			0
$742$		−	4.80479i		−	0.176390i
$743$	1.56031	+	2.70254i	0.0572423	+	0.0991465i	0.893227	−	0.449607i	$-0.148436\pi$
$743$	1.56031	+	2.70254i	0.0572423	+	0.0991465i	−0.835984	+	0.548753i	$0.815103\pi$
$744$	−60.9237	−	105.523i	−2.23357	−	3.86866i
$745$	23.9079	+	29.9978i	0.875917	+	1.09903i
$746$		−	5.88798i		−	0.215574i
$747$	9.68401	−	16.7732i	0.354320	−	0.613699i
$748$	1.74151	−	3.01638i	0.0636758	−	0.110290i
$749$		−	31.3649i		−	1.14605i
$750$	−4.63359	+	61.1016i	−0.169195	+	2.23112i
$751$	0.742024	+	1.28522i	0.0270769	+	0.0468985i	0.879246	−	0.476367i	$-0.158047\pi$
$751$	0.742024	+	1.28522i	0.0270769	+	0.0468985i	−0.852169	+	0.523266i	$0.824713\pi$
$752$	21.9304	+	37.9845i	0.799718	+	1.38515i
$753$			7.90881i			0.288213i
$754$		0			0
$755$	17.4814	−	44.5030i	0.636213	−	1.61963i
$756$	33.5082	−	19.3460i	1.21868	−	0.703607i
$757$	4.41654	−	2.54989i	0.160522	−	0.0926774i	−0.417587	−	0.908637i	$-0.637124\pi$
$757$	4.41654	−	2.54989i	0.160522	−	0.0926774i	0.578109	+	0.815960i	$0.303791\pi$
$758$	−11.4102	−	6.58767i	−0.414436	−	0.239275i
$759$			2.94369i			0.106849i
$760$	−12.0132	−	15.0733i	−0.435766	−	0.546766i
$761$	25.7955	+	14.8931i	0.935088	+	0.539873i	0.888417	−	0.459037i	$-0.151806\pi$
$761$	25.7955	+	14.8931i	0.935088	+	0.539873i	0.0466707	+	0.998910i	$0.485139\pi$
$762$	−94.4433			−3.42132
$763$	−8.32215	−	4.80479i	−0.301282	−	0.173945i
$764$	−11.0758	−	19.1839i	−0.400709	−	0.694048i
$765$	4.42521	−	0.665652i	0.159994	−	0.0240667i
$766$	52.5973			1.90042
$767$		0			0
$768$			62.7228i			2.26331i
$769$	16.5399	−	9.54930i	0.596443	−	0.344356i	−0.171198	−	0.985237i	$-0.554764\pi$
$769$	16.5399	−	9.54930i	0.596443	−	0.344356i	0.767641	+	0.640880i	$0.221430\pi$
$770$	10.5053	−	1.58023i	0.378584	−	0.0569476i
$771$	14.2791	−	24.7322i	0.514250	−	0.890707i
$772$	−22.2088			−0.799311
$773$	24.6153	−	42.6350i	0.885351	−	1.53347i	0.0400400	−	0.999198i	$-0.487251\pi$
$773$	24.6153	−	42.6350i	0.885351	−	1.53347i	0.845311	−	0.534275i	$-0.179415\pi$
$774$	4.92889	+	2.84570i	0.177165	+	0.102286i
$775$	−30.4966	+	32.8284i	−1.09547	+	1.17923i
$776$	−46.6831	+	80.8574i	−1.67582	+	2.90261i
$777$	6.70593	−	3.87167i	0.240574	−	0.138895i
$778$	−25.1362	−	43.5373i	−0.901178	−	1.56089i
$779$	−13.5967			−0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$	3.35412	+	5.80951i	0.119943	+	0.207748i
$783$	7.63458	−	4.40783i	0.272838	−	0.157523i
$784$	−5.81754	+	10.0763i	−0.207769	+	0.359867i
$785$	−15.0139	+	38.2215i	−0.535869	+	1.36418i
$786$	47.4650	+	27.4039i	1.69302	+	0.977466i
$787$	−4.89168	+	8.47263i	−0.174369	+	0.302017i	−0.939943	−	0.341332i	$-0.889122\pi$
$787$	−4.89168	+	8.47263i	−0.174369	+	0.302017i	0.765573	+	0.643349i	$0.222455\pi$
$788$	−30.2250			−1.07672
$789$	32.5851	−	56.4390i	1.16006	−	2.00928i
$790$	0.879284	+	5.84543i	0.0312835	+	0.207971i
$791$	14.0726	−	8.12482i	0.500364	−	0.288885i
$792$			6.55812i			0.233033i
$793$		0			0
$794$	23.9020			0.848250
$795$	−0.459934	−	3.05762i	−0.0163122	−	0.108442i
$796$	−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	$0.572051\pi$
$798$	−21.9827			−0.778178
$799$	−6.53348	−	3.77211i	−0.231138	−	0.133448i
$800$	−26.2080	+	8.06708i	−0.926592	+	0.285214i
$801$		−	20.5338i		−	0.725527i
$802$	−54.0188	−	31.1878i	−1.90747	−	1.10128i
$803$	−5.67950	+	3.27906i	−0.200425	+	0.115715i
$804$	67.0859	−	38.7320i	2.36594	−	1.36597i
$805$	−5.17218	+	13.1670i	−0.182295	+	0.464077i
$806$		0			0
$807$		−	47.9018i		−	1.68622i
$808$	41.7821	+	72.3688i	1.46989	+	2.54592i
$809$	−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	$-0.355773\pi$
$810$	49.9991	−	39.8487i	1.75679	−	1.40014i
$811$		−	13.3470i		−	0.468678i	−0.972155	−	0.234339i	$-0.924707\pi$
$811$		−	13.3470i		−	0.468678i	0.972155	−	0.234339i	$-0.0752925\pi$
$812$	−19.7505	+	34.2089i	−0.693108	+	1.20050i
$813$	12.7328	−	22.0539i	0.446560	−	0.773465i
$814$		−	1.97886i		−	0.0693589i
$815$	−7.01356	+	5.58973i	−0.245674	+	0.195800i
$816$	9.37548	+	16.2388i	0.328208	+	0.568472i
$817$	0.933121	+	1.61621i	0.0326458	+	0.0565441i
$818$			91.9431i			3.21472i
$819$		0			0
$820$	−36.4917	+	92.8982i	−1.27434	+	3.24415i
$821$	−10.1096	+	5.83676i	−0.352826	+	0.203704i	−0.665929	−	0.746015i	$-0.731965\pi$
$821$	−10.1096	+	5.83676i	−0.352826	+	0.203704i	0.313103	+	0.949719i	$0.398631\pi$
$822$	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	$0.857887\pi$
$824$		−	69.2714i		−	2.41318i
$825$	6.53396	−	2.01122i	0.227483	−	0.0700216i
$826$	−49.2154	−	28.4145i	−1.71242	−	0.988667i
$827$	−27.3319			−0.950425			−0.475212	−	0.879871i	$-0.657629\pi$
$827$	−27.3319			−0.950425			−0.475212	+	0.879871i	$0.657629\pi$
$828$	−13.6601	−	7.88669i	−0.474723	−	0.274081i
$829$	−1.77018	−	3.06604i	−0.0614808	−	0.106488i	0.833647	−	0.552298i	$-0.186249\pi$
$829$	−1.77018	−	3.06604i	−0.0614808	−	0.106488i	−0.895128	+	0.445810i	$0.852916\pi$
$830$	−10.0299	−	66.6783i	−0.348143	−	2.31444i
$831$	−36.1370			−1.25358
$832$		0			0
$833$		−	2.00128i		−	0.0693402i
$834$	68.0007	−	39.2602i	2.35467	−	1.35947i
$835$	−0.977401	−	6.49770i	−0.0338244	−	0.224862i
$836$	−1.94206	+	3.36375i	−0.0671676	+	0.116338i
$837$	26.3341			0.910238
$838$	−8.74059	+	15.1391i	−0.301939	+	0.522973i
$839$	38.7893	+	22.3950i	1.33915	+	0.773161i	0.986682	−	0.162661i	$-0.0520078\pi$
$839$	38.7893	+	22.3950i	1.33915	+	0.773161i	0.352472	+	0.935822i	$0.385341\pi$
$840$	−32.6646	+	83.1555i	−1.12704	+	2.86914i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−74.9136	+	43.2514i	−2.58169	+	1.49054i
$843$	11.4069	+	19.7574i	0.392875	+	0.680479i
$844$	−62.8111			−2.16205
$845$		0			0
$846$	25.6568			0.882100
$847$	15.5694	+	26.9670i	0.534972	+	0.926598i
$848$	3.95810	−	2.28521i	0.135922	−	0.0784744i
$849$	9.48973	−	16.4367i	0.325687	−	0.564106i
$850$	10.6034	−	11.4142i	0.363695	−	0.391504i
$851$	2.28205	+	1.31754i	0.0782278	+	0.0451648i
$852$	12.7101	−	22.0145i	0.435440	−	0.754205i
$853$	−31.3732			−1.07420			−0.537099	−	0.843519i	$-0.680480\pi$
$853$	−31.3732			−1.07420			−0.537099	+	0.843519i	$0.680480\pi$
$854$	−8.49136	+	14.7075i	−0.290568	+	0.503279i
$855$	−4.93483	+	0.742310i	−0.168768	+	0.0253865i
$856$	58.3774	−	33.7042i	1.99530	−	1.15199i
$857$			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	$0.921639\pi$
$860$	13.5470	−	2.03778i	0.461950	−	0.0694877i
$861$	31.5109	+	54.5784i	1.07389	+	1.86003i
$862$	−35.8251	−	20.6837i	−1.22021	−	0.704488i
$863$	−32.8011			−1.11656			−0.558282	−	0.829651i	$-0.688539\pi$
$863$	−32.8011			−1.11656			−0.558282	+	0.829651i	$0.688539\pi$
$864$	13.9568	+	8.05794i	0.474819	+	0.274137i
$865$	1.90553	+	2.39092i	0.0647901	+	0.0812936i
$866$			0.652374i			0.0221686i
$867$	28.9032	+	16.6873i	0.981603	+	0.566729i
$868$	−102.189	+	58.9986i	−3.46851	+	2.00254i
$869$	0.571138	−	0.329747i	0.0193745	−	0.0111859i
$870$	−13.4424	+	34.2207i	−0.455739	+	1.16019i
$871$		0			0
$872$		−	20.6526i		−	0.699385i
$873$	12.0864	+	20.9343i	0.409063	+	0.708518i
$874$	−3.74039	−	6.47855i	−0.126521	−	0.219140i
$875$	32.7599	+	2.48432i	1.10749	+	0.0839854i
$876$		−	99.6157i		−	3.36570i
$877$	18.0325	−	31.2333i	0.608916	−	1.05467i	−0.382504	−	0.923954i	$-0.624938\pi$
$877$	18.0325	−	31.2333i	0.608916	−	1.05467i	0.991419	−	0.130719i	$-0.0417286\pi$
$878$	9.66956	−	16.7482i	0.326332	−	0.565223i
$879$			60.8257i			2.05160i
$880$	6.29819	+	7.90248i	0.212312	+	0.266393i
$881$	−23.0198	−	39.8715i	−0.775557	−	1.34330i	−0.934481	−	0.356013i	$-0.884136\pi$
$881$	−23.0198	−	39.8715i	−0.775557	−	1.34330i	0.158924	−	0.987291i	$-0.449198\pi$
$882$	3.40304	+	5.89423i	0.114586	+	0.198469i
$883$			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
$886$	−9.52962	+	5.50193i	−0.320154	+	0.184841i
$887$	7.12365	−	4.11284i	0.239189	−	0.138096i	−0.375615	−	0.926776i	$-0.622569\pi$
$887$	7.12365	−	4.11284i	0.239189	−	0.138096i	0.614804	+	0.788680i	$0.289235\pi$
$888$	14.4122	+	8.32087i	0.483641	+	0.279230i
$889$			50.6363i			1.69829i
$890$	−44.5549	−	55.9041i	−1.49348	−	1.87391i
$891$	−6.17750	−	3.56658i	−0.206954	−	0.119485i
$892$	−0.0372125			−0.00124597
$893$	7.28589	+	4.20651i	0.243813	+	0.140766i
$894$	47.0112	+	81.4257i	1.57229	+	2.72328i
$895$	−2.58977	−	17.2166i	−0.0865664	−	0.575488i
$896$	34.2529			1.14431
$897$		0			0
$898$		−	8.37054i		−	0.279328i
$899$	−23.2829	+	13.4424i	−0.776527	+	0.448328i
$900$	−8.17266	+	35.7091i	−0.272422	+	1.19030i
$901$	−0.393064	+	0.680808i	−0.0130949	+	0.0226810i
$902$	16.1056			0.536257
$903$	4.32510	−	7.49129i	0.143930	−	0.249295i
$904$	30.2443	+	17.4616i	1.00591	+	0.580763i
$905$	8.04788	+	3.16131i	0.267521	+	0.105086i
$906$	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	$0.164714\pi$
$908$	25.2348	+	43.7080i	0.837447	+	1.45050i
$909$	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	$0.242990\pi$
$912$	−10.4552	−	18.1089i	−0.346206	−	0.599646i
$913$	−6.51492	+	3.76139i	−0.215612	+	0.124484i
$914$	19.6354	−	34.0095i	0.649481	−	1.12493i
$915$	−3.99577	+	10.1722i	−0.132096	+	0.336282i
$916$	−64.1844	−	37.0569i	−2.12071	−	1.22439i
$917$	14.6928	−	25.4486i	0.485198	−	0.840387i
$918$	−9.15616			−0.302198
$919$	−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	$0.957588\pi$
$920$	−30.0648	+	4.52243i	−0.991208	+	0.149100i
$921$	23.7198	−	13.6947i	0.781595	−	0.451254i
$922$		−	65.8957i		−	2.17016i
$923$		0			0
$924$	18.0033			0.592264
$925$	1.36532	−	5.96554i	0.0448914	−	0.196146i
$926$	−8.96157	−	15.5219i	−0.294496	−	0.510081i
$927$	−15.5318	−	8.96730i	−0.510132	−	0.294525i
$928$	−16.4529			−0.540092
$929$	4.12942	+	2.38412i	0.135482	+	0.0782206i	0.566209	−	0.824262i	$-0.308409\pi$
$929$	4.12942	+	2.38412i	0.135482	+	0.0782206i	−0.430727	+	0.902482i	$0.641743\pi$
$930$	−85.8871	+	68.4510i	−2.81635	+	2.24460i
$931$			2.23175i			0.0731427i
$932$	26.9670	+	15.5694i	0.883334	+	0.509993i
$933$	52.0624	−	30.0582i	1.70445	−	0.984062i
$934$	−41.4727	+	23.9443i	−1.35703	+	0.783481i
$935$	−1.61780	−	0.635495i	−0.0529079	−	0.0207829i
$936$		0			0
$937$			43.6264i			1.42521i	0.701565	+	0.712606i	$0.252485\pi$
$937$			43.6264i			1.42521i	−0.701565	+	0.712606i	$0.747515\pi$
$938$	−30.0355	−	52.0230i	−0.980693	−	1.69861i
$939$	26.4602	+	45.8305i	0.863497	+	1.49562i
$940$	48.2951	−	38.4906i	1.57521	−	1.25543i
$941$		−	18.2675i		−	0.595504i	−0.954643	−	0.297752i	$-0.903763\pi$
$941$		−	18.2675i		−	0.595504i	0.954643	−	0.297752i	$-0.0962368\pi$
$942$	−50.3263	+	87.1677i	−1.63972	+	2.84008i
$943$	−10.7233	+	18.5732i	−0.349197	+	0.604828i
$944$		−	54.0569i		−	1.75940i
$945$	−12.0343	−	15.0997i	−0.391475	−	0.491192i
$946$	−1.10530	−	1.91444i	−0.0359365	−	0.0622439i
$947$	−9.99146	−	17.3057i	−0.324679	−	0.562360i	0.656769	−	0.754092i	$-0.271923\pi$
$947$	−9.99146	−	17.3057i	−0.324679	−	0.562360i	−0.981447	+	0.191732i	$0.938590\pi$
$948$			10.0175i			0.325353i
$949$		0			0
$950$	−11.8246	+	12.7287i	−0.383639	+	0.412973i
$951$	0.436993	−	0.252298i	0.0141705	−	0.00818132i
$952$	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	$0.443252\pi$
$954$		−	2.67352i		−	0.0865583i
$955$	−8.64475	+	6.88976i	−0.279737	+	0.222948i
$956$	−15.5219	−	8.96157i	−0.502014	−	0.289838i
$957$	4.10190			0.132596
$958$	−42.9416	−	24.7923i	−1.38738	−	0.801004i
$959$	−12.7420	−	22.0698i	−0.411461	−	0.712672i
$960$	1.28619	−	0.193472i	0.0415116	−	0.00624428i
$961$	−49.3098			−1.59064
$962$		0			0
$963$		−	17.4523i		−	0.562392i
$964$	76.7252	−	44.2973i	2.47115	−	1.42672i
$965$	1.64858	+	10.9596i	0.0530696	+	0.352803i
$966$	−17.3371	+	30.0287i	−0.557811	+	0.966156i
$967$	−43.8607			−1.41047			−0.705233	−	0.708975i	$-0.749158\pi$
$967$	−43.8607			−1.41047			−0.705233	+	0.708975i	$0.749158\pi$
$968$	−33.4613	+	57.9566i	−1.07549	+	1.86280i
$969$	3.11480	+	1.79833i	0.100062	+	0.0577707i
$970$	78.3294	+	30.7688i	2.51501	+	0.987928i
$971$	−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
$973$	−21.0496	−	36.4589i	−0.674818	−	1.16882i
$974$	−82.2887			−2.63670
$975$		0			0
$976$	−16.1543			−0.517087
$977$	−25.6849	−	44.4875i	−0.821731	−	1.42328i	−0.904392	−	0.426703i	$-0.859675\pi$
$977$	−25.6849	−	44.4875i	−0.821731	−	1.42328i	0.0826604	−	0.996578i	$-0.473658\pi$
$978$	−19.0376	+	10.9913i	−0.608754	+	0.351464i
$979$	−3.98780	+	6.90707i	−0.127451	+	0.220751i
$980$	15.2483	+	5.98973i	0.487088	+	0.191335i
$981$	−4.63066	−	2.67352i	−0.147846	−	0.0853588i
$982$	36.4942	−	63.2099i	1.16458	−	2.01711i
$983$	37.3026			1.18977			0.594885	−	0.803811i	$-0.297198\pi$
$983$	37.3026			1.18977			0.594885	+	0.803811i	$0.297198\pi$
$984$	−67.7221	+	117.298i	−2.15890	+	3.73933i
$985$	2.24363	+	14.9155i	0.0714880	+	0.475248i
$986$	8.09528	−	4.67381i	0.257806	−	0.148845i
$987$		−	38.9951i		−	1.24123i
$988$		0			0
$989$	2.94369			0.0936040
$990$	5.84543	−	0.879284i	0.185780	−	0.0279455i
$991$	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
$993$	39.4556			1.25208
$994$	−17.0716	−	9.85627i	−0.541477	−	0.312622i
$995$	−9.05000	+	7.21274i	−0.286904	+	0.228659i
$996$		−	114.269i		−	3.62074i
$997$	−19.8743	−	11.4744i	−0.629425	−	0.363399i	0.151104	−	0.988518i	$-0.451717\pi$
$997$	−19.8743	−	11.4744i	−0.629425	−	0.363399i	−0.780529	+	0.625119i	$0.785050\pi$
$998$	63.8508	−	36.8643i	2.02116	−	1.16692i
$999$	−3.11480	+	1.79833i	−0.0985479	+	0.0568967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.l.f.699.1		24
5.4	even	2	inner	845.2.l.f.699.12		24
13.2	odd	12		845.2.b.e.339.1		6
13.3	even	3		845.2.d.d.844.11		12
13.4	even	6	inner	845.2.l.f.654.12		24
13.5	odd	4		845.2.n.e.484.1		12
13.6	odd	12		845.2.n.e.529.6		12
13.7	odd	12		65.2.n.a.9.1	✓	12
13.8	odd	4		65.2.n.a.29.6	yes	12
13.9	even	3	inner	845.2.l.f.654.2		24
13.10	even	6		845.2.d.d.844.1		12
13.11	odd	12		845.2.b.d.339.6		6
13.12	even	2	inner	845.2.l.f.699.11		24
39.8	even	4		585.2.bs.a.289.1		12
39.20	even	12		585.2.bs.a.334.6		12
52.7	even	12		1040.2.dh.a.529.2		12
52.47	even	4		1040.2.dh.a.289.5		12
65.2	even	12		4225.2.a.bq.1.6		6
65.4	even	6	inner	845.2.l.f.654.1		24
65.7	even	12		325.2.e.e.126.6		12
65.8	even	4		325.2.e.e.276.1		12
65.9	even	6	inner	845.2.l.f.654.11		24
65.19	odd	12		845.2.n.e.529.1		12
65.24	odd	12		845.2.b.d.339.1		6
65.28	even	12		4225.2.a.bq.1.1		6
65.29	even	6		845.2.d.d.844.2		12
65.33	even	12		325.2.e.e.126.1		12
65.34	odd	4		65.2.n.a.29.1	yes	12
65.37	even	12		4225.2.a.br.1.1		6
65.44	odd	4		845.2.n.e.484.6		12
65.47	even	4		325.2.e.e.276.6		12
65.49	even	6		845.2.d.d.844.12		12
65.54	odd	12		845.2.b.e.339.6		6
65.59	odd	12		65.2.n.a.9.6	yes	12
65.63	even	12		4225.2.a.br.1.6		6
65.64	even	2	inner	845.2.l.f.699.2		24
195.59	even	12		585.2.bs.a.334.1		12
195.164	even	4		585.2.bs.a.289.6		12
260.59	even	12		1040.2.dh.a.529.5		12
260.99	even	4		1040.2.dh.a.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	13.7	odd	12
65.2.n.a.9.6	yes	12	65.59	odd	12
65.2.n.a.29.1	yes	12	65.34	odd	4
65.2.n.a.29.6	yes	12	13.8	odd	4
325.2.e.e.126.1		12	65.33	even	12
325.2.e.e.126.6		12	65.7	even	12
325.2.e.e.276.1		12	65.8	even	4
325.2.e.e.276.6		12	65.47	even	4
585.2.bs.a.289.1		12	39.8	even	4
585.2.bs.a.289.6		12	195.164	even	4
585.2.bs.a.334.1		12	195.59	even	12
585.2.bs.a.334.6		12	39.20	even	12
845.2.b.d.339.1		6	65.24	odd	12
845.2.b.d.339.6		6	13.11	odd	12
845.2.b.e.339.1		6	13.2	odd	12
845.2.b.e.339.6		6	65.54	odd	12
845.2.d.d.844.1		12	13.10	even	6
845.2.d.d.844.2		12	65.29	even	6
845.2.d.d.844.11		12	13.3	even	3
845.2.d.d.844.12		12	65.49	even	6
845.2.l.f.654.1		24	65.4	even	6	inner
845.2.l.f.654.2		24	13.9	even	3	inner
845.2.l.f.654.11		24	65.9	even	6	inner
845.2.l.f.654.12		24	13.4	even	6	inner
845.2.l.f.699.1		24	1.1	even	1	trivial
845.2.l.f.699.2		24	65.64	even	2	inner
845.2.l.f.699.11		24	13.12	even	2	inner
845.2.l.f.699.12		24	5.4	even	2	inner
845.2.n.e.484.1		12	13.5	odd	4
845.2.n.e.484.6		12	65.44	odd	4
845.2.n.e.529.1		12	65.19	odd	12
845.2.n.e.529.6		12	13.6	odd	12
1040.2.dh.a.289.2		12	260.99	even	4
1040.2.dh.a.289.5		12	52.47	even	4
1040.2.dh.a.529.2		12	52.7	even	12
1040.2.dh.a.529.5		12	260.59	even	12
4225.2.a.bq.1.1		6	65.28	even	12
4225.2.a.bq.1.6		6	65.2	even	12
4225.2.a.br.1.1		6	65.37	even	12
4225.2.a.br.1.6		6	65.63	even	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27287 - 2.20467i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(-2.24039 + 3.88048i) q^{4} +(2.08125 + 0.817544i) q^{5} +(4.74650 + 2.74039i) q^{6} +(1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(0.817544 - 1.41603i) q^{9} +O(q^{10})\)	\(q+(-1.27287 - 2.20467i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(-2.24039 + 3.88048i) q^{4} +(2.08125 + 0.817544i) q^{5} +(4.74650 + 2.74039i) q^{6} +(1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(0.817544 - 1.41603i) q^{9} +(-0.846746 - 5.62912i) q^{10} +(-0.550003 + 0.317544i) q^{11} -9.64680i q^{12} -7.48079 q^{14} +(-4.76053 + 0.716091i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(1.05998 + 0.611979i) q^{17} -4.16251 q^{18} +(-1.18205 - 0.682456i) q^{19} +(-7.83529 + 6.24464i) q^{20} +6.32648i q^{21} +(1.40016 + 0.808385i) q^{22} +(-1.86449 + 1.07646i) q^{23} +(-11.7751 + 6.79833i) q^{24} +(3.66324 + 3.40304i) q^{25} -2.93855i q^{27} +(6.58351 + 11.4030i) q^{28} +(1.50000 + 2.59808i) q^{29} +(7.63828 + 9.58393i) q^{30} +8.96157i q^{31} +(-2.74215 + 4.74954i) q^{32} +(0.683650 - 1.18412i) q^{33} -3.11588i q^{34} +(5.13847 - 4.09531i) q^{35} +(3.66324 + 6.34492i) q^{36} +(-0.611979 - 1.05998i) q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(8.62698 - 4.98079i) q^{41} +(13.9478 - 8.05279i) q^{42} +(-1.18412 - 0.683650i) q^{43} -2.84570i q^{44} +(2.85918 - 2.27874i) q^{45} +(4.74650 + 2.74039i) q^{46} -6.16379 q^{47} +(13.2675 + 7.65998i) q^{48} +(-0.817544 - 1.41603i) q^{49} +(2.83976 - 12.4079i) q^{50} -2.63509 q^{51} +0.642285i q^{53} +(-6.47855 + 3.74039i) q^{54} +(-1.40430 + 0.211239i) q^{55} +(9.27912 - 16.0719i) q^{56} +2.93855 q^{57} +(3.81861 - 6.61402i) q^{58} +(6.57890 + 3.79833i) q^{59} +(7.88669 - 20.0774i) q^{60} +(1.13509 - 1.96603i) q^{61} +(19.7574 - 11.4069i) q^{62} +(-2.40240 - 4.16107i) q^{63} -0.270178 q^{64} -3.48079 q^{66} +(4.01502 + 6.95421i) q^{67} +(-4.74954 + 2.74215i) q^{68} +(2.31754 - 4.01410i) q^{69} +(-15.5694 - 6.11588i) q^{70} +(2.28205 + 1.31754i) q^{71} +(5.16315 - 8.94284i) q^{72} +10.3263 q^{73} +(-1.55794 + 2.69843i) q^{74} +(-10.4933 - 2.40158i) q^{75} +(5.29650 - 3.05794i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(-2.36683 - 15.7346i) q^{80} +(5.61588 + 9.72698i) q^{81} +(-21.9620 - 12.6798i) q^{82} +11.8452 q^{83} +(-24.5498 - 14.1738i) q^{84} +(1.70576 + 2.14026i) q^{85} +3.48079i q^{86} +(-5.59346 - 3.22939i) q^{87} +(-3.47351 + 2.00543i) q^{88} +(10.8758 - 6.27912i) q^{89} +(-8.66324 - 3.40304i) q^{90} -9.64680i q^{92} +(-9.64680 - 16.7087i) q^{93} +(7.84570 + 13.5891i) q^{94} +(-1.90220 - 2.38674i) q^{95} -11.8073i q^{96} +(-7.39190 + 12.8031i) q^{97} +(-2.08125 + 3.60484i) q^{98} +1.03843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^4 + 12 * q^9	\( 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) \) 24 * q - 8 * q^4 + 12 * q^9 - 14 * q^10 - 88 * q^14 - 32 * q^16 + 4 * q^25 + 36 * q^29 - 8 * q^30 + 20 * q^35 + 4 * q^36 + 140 * q^40 - 12 * q^49 - 48 * q^51 - 52 * q^55 + 32 * q^56 + 12 * q^61 + 24 * q^64 + 8 * q^66 + 48 * q^69 + 16 * q^74 - 4 * q^75 - 208 * q^79 + 28 * q^81 - 124 * q^90 + 112 * q^94 - 40 * q^95

Introduction

L-functions

Modular forms

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