LMFDB - Embedded newform 845.2.l.f.699.12

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			699.12
Character	$\chi$	$=$	845.699
Dual form			845.2.l.f.654.12

$q$-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} +(-4.45158 - 3.54786i) q^{10} +(-0.550003 + 0.317544i) q^{11} +9.64680i q^{12} -7.48079 q^{14} +(-3.00042 + 3.76470i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(-1.05998 - 0.611979i) q^{17} +4.16251 q^{18} +(-1.18205 - 0.682456i) q^{19} +(1.49037 - 9.90788i) 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} +(-12.1191 - 1.82298i) q^{30} +8.96157i q^{31} +(2.74215 - 4.74954i) q^{32} +(-0.683650 + 1.18412i) q^{33} -3.11588i q^{34} +(0.977401 - 6.49770i) 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} +(-0.543852 + 3.61549i) q^{45} +(4.74650 + 2.74039i) q^{46} +6.16379 q^{47} +(-13.2675 - 7.65998i) q^{48} +(-0.817544 - 1.41603i) q^{49} +(12.1654 + 3.74464i) q^{50} -2.63509 q^{51} -0.642285i q^{53} +(-6.47855 + 3.74039i) q^{54} +(0.885090 - 1.11054i) 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} +(3.16683 - 10.2883i) q^{75} +(5.29650 - 3.05794i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(12.4431 + 9.91702i) q^{80} +(5.61588 + 9.72698i) q^{81} +(21.9620 + 12.6798i) q^{82} -11.8452 q^{83} +(-24.5498 - 14.1738i) q^{84} +(2.70640 + 0.407104i) 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} +(3.01808 + 0.453987i) 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	$0.189807\pi$
$2$	1.27287	+	2.20467i	0.900055	+	1.55894i	0.0726333	+	0.997359i	$0.476860\pi$
$3$	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
$5$	−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	$0.354076\pi$
$7$	−1.46928	+	2.54486i	−0.555334	+	0.961867i	−0.997877	+	0.0651198i	$0.979257\pi$
$8$	−6.31544			−2.23284
$9$	0.817544	−	1.41603i	0.272515	−	0.472010i
$10$	−4.45158	−	3.54786i	−1.40771	−	1.12193i
$11$	−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
$15$	−3.00042	+	3.76470i	−0.774705	+	0.972040i
$16$	−3.55794	−	6.16253i	−0.889484	−	1.54063i
$17$	−1.05998	−	0.611979i	−0.257082	−	0.148427i	0.365920	−	0.930646i	$-0.380754\pi$
$17$	−1.05998	−	0.611979i	−0.257082	−	0.148427i	−0.623003	+	0.782220i	$0.714088\pi$
$18$	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	$0.716709\pi$
$20$	1.49037	−	9.90788i	0.333256	−	2.21547i
$21$			6.32648i			1.38055i
$22$	−1.40016	−	0.808385i	−0.298516	−	0.172348i
$23$	1.86449	−	1.07646i	0.388773	−	0.224458i	−0.292856	−	0.956157i	$-0.594606\pi$
$23$	1.86449	−	1.07646i	0.388773	−	0.224458i	0.681628	+	0.731699i	$0.261272\pi$
$24$	−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	$0.743482\pi$
$30$	−12.1191	−	1.82298i	−2.21263	−	0.332829i
$31$			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
$35$	0.977401	−	6.49770i	0.165211	−	1.09831i
$36$	3.66324	+	6.34492i	0.610540	+	1.05749i
$37$	0.611979	+	1.05998i	0.100609	+	0.174259i	0.911936	−	0.410333i	$-0.134588\pi$
$37$	0.611979	+	1.05998i	0.100609	+	0.174259i	−0.811327	+	0.584593i	$0.801254\pi$
$38$		−	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	0.587563	−	0.809178i	$-0.300087\pi$
$43$	1.18412	+	0.683650i	0.180576	+	0.104256i	−0.406987	+	0.913434i	$0.633421\pi$
$44$		−	2.84570i		−	0.429005i
$45$	−0.543852	+	3.61549i	−0.0810727	+	0.538966i
$46$	4.74650	+	2.74039i	0.699833	+	0.404049i
$47$	6.16379			0.899081			0.449540	−	0.893260i	$-0.351588\pi$
$47$	6.16379			0.899081			0.449540	+	0.893260i	$0.351588\pi$
$48$	−13.2675	−	7.65998i	−1.91499	−	1.10562i
$49$	−0.817544	−	1.41603i	−0.116792	−	0.202290i
$50$	12.1654	+	3.74464i	1.72045	+	0.529571i
$51$	−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	$-0.0140459\pi$
$54$	−6.47855	+	3.74039i	−0.881619	+	0.509003i
$55$	0.885090	−	1.11054i	0.119345	−	0.149746i
$56$	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	0.509428	−	0.860513i	$-0.329857\pi$
$67$	−4.01502	−	6.95421i	−0.490512	−	0.849592i	−0.999940	+	0.0109212i	$0.996524\pi$
$68$	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	$-0.706547\pi$
$73$	−10.3263			−1.20860			−0.604301	+	0.796756i	$0.706547\pi$
$74$	−1.55794	+	2.69843i	−0.181107	+	0.313686i
$75$	3.16683	−	10.2883i	0.365674	−	1.18799i
$76$	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	$0.518605\pi$
$80$	12.4431	+	9.91702i	1.39118	+	1.10876i
$81$	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	$-0.725270\pi$
$83$	−11.8452			−1.30018			−0.650092	+	0.759855i	$0.725270\pi$
$84$	−24.5498	−	14.1738i	−2.67860	−	1.54649i
$85$	2.70640	+	0.407104i	0.293551	+	0.0441566i
$86$			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
$95$	3.01808	+	0.453987i	0.309648	+	0.0465781i
$96$		−	11.8073i		−	1.20507i
$97$	7.39190	−	12.8031i	0.750534	−	1.29996i	−0.197031	−	0.980397i	$-0.563130\pi$
$97$	7.39190	−	12.8031i	0.750534	−	1.29996i	0.947564	−	0.319565i	$-0.103537\pi$
$98$	2.08125	−	3.60484i	0.210238	−	0.364144i
$99$			1.03843i			0.104366i
$100$	4.99829	+	21.8393i	0.499829	+	2.18393i
$101$	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	$0.181721\pi$
$103$			10.9686i			1.08077i	−0.841419	+	0.540383i	$0.818279\pi$
$104$		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	−0.875123	−	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
$109$		−	3.27018i		−	0.313226i	−0.987660	−	0.156613i	$-0.949942\pi$
$109$		−	3.27018i		−	0.313226i	0.987660	−	0.156613i	$-0.0500576\pi$
$110$	3.57499	+	0.537759i	0.340862	+	0.0512733i
$111$	2.28205	+	1.31754i	0.216603	+	0.125056i
$112$	20.9104			1.97584
$113$	−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
$115$	−3.00042	+	3.76470i	−0.279790	+	0.351060i
$116$	−13.4424			−1.24809
$117$		0			0
$118$			19.3391i			1.78031i
$119$	3.11480	−	1.79833i	0.285533	−	0.164853i
$120$	18.9490	−	23.7757i	1.72979	−	2.17041i
$121$	−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	0.339813	−	0.940493i	$-0.389636\pi$
$127$	14.9231	−	8.61586i	1.32421	−	0.764534i	0.984397	+	0.175959i	$0.0563027\pi$
$128$	−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	−0.989637	−	0.143593i	$-0.954134\pi$
$137$	−4.33616	+	7.51044i	−0.370463	+	0.641661i	0.619174	+	0.785254i	$0.287468\pi$
$138$	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	$-0.0411922\pi$
$140$	23.0244	+	18.3502i	1.94592	+	1.55087i
$141$	11.4923	−	6.63509i	0.967827	−	0.558775i
$142$			6.70825i			0.562944i
$143$		0			0
$144$	−11.6351			−0.969591
$145$	−5.24592	−	4.18094i	−0.435650	−	0.347208i
$146$	−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	$0.418648\pi$
$150$	26.7132	−	6.11379i	2.18113	−	0.499189i
$151$		−	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	$-0.738200\pi$
$157$		−	18.3646i		−	1.46566i	0.680413	−	0.732829i	$-0.261800\pi$
$158$	−1.32178	−	2.28939i	−0.105155	−	0.182134i
$159$	−0.691395	−	1.19753i	−0.0548312	−	0.0949705i
$160$	−1.82415	+	12.1268i	−0.144211	+	0.958709i
$161$			6.32648i			0.498597i
$162$	−14.2966	+	24.7624i	−1.12324	+	1.94551i
$163$	2.00543	−	3.47351i	0.157078	−	0.272066i	−0.776736	−	0.629826i	$-0.783126\pi$
$163$	2.00543	−	3.47351i	0.157078	−	0.272066i	0.933814	+	0.357760i	$0.116459\pi$
$164$			44.6357i			3.48546i
$165$	0.454782	−	3.02336i	0.0354047	−	0.235368i
$166$	−15.0774	−	26.1149i	−1.17024	−	2.02691i
$167$	1.46928	+	2.54486i	0.113696	+	0.196927i	0.917258	−	0.398294i	$-0.130398\pi$
$167$	1.46928	+	2.54486i	0.113696	+	0.196927i	−0.803562	+	0.595221i	$0.797064\pi$
$168$		−	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	0.454311	−	0.890843i	$-0.349886\pi$
$173$	−1.18412	−	0.683650i	−0.0900267	−	0.0519769i	−0.544337	+	0.838866i	$0.683219\pi$
$174$			16.4424i			1.24649i
$175$	3.27794	+	14.3224i	0.247789	+	1.08267i
$176$	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	$0.927315\pi$
$180$	−12.8114	−	10.2105i	−0.954905	−	0.761048i
$181$	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
$185$	−2.14026	−	1.70576i	−0.157355	−	0.125410i
$186$	−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	0.762942	−	0.646467i	$-0.223754\pi$
$193$	−2.47822	−	4.29240i	−0.178386	−	0.308974i	−0.941328	+	0.337493i	$0.890421\pi$
$194$	37.6357			2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	−3.37273	−	5.84174i	−0.240297	−	0.416207i	0.720502	−	0.693453i	$-0.243912\pi$
$197$	−3.37273	−	5.84174i	−0.240297	−	0.416207i	−0.960799	+	0.277246i	$0.910578\pi$
$198$	−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
$205$	−13.8829	+	17.4192i	−0.969625	+	1.21661i
$206$	−24.1822	+	13.9616i	−1.68485	+	0.972749i
$207$		−	3.52022i		−	0.244673i
$208$		0			0
$209$	0.866840			0.0599606
$210$	22.4455	−	28.1629i	1.54889	−	1.94342i
$211$	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
$215$	−3.02336	−	0.454782i	−0.206191	−	0.0310158i
$216$		−	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	0.865886	−	0.500241i	$-0.166755\pi$
$223$	−0.00415245	−	0.00719226i	−0.000278069	−	0.000481629i	−0.866164	+	0.499759i	$0.833422\pi$
$224$	8.05794	+	13.9568i	0.538394	+	0.932525i
$225$	−1.82393	−	7.96939i	−0.121596	−	0.531293i
$226$		−	14.0774i		−	0.936418i
$227$	−5.63179	+	9.75454i	−0.373795	+	0.647431i	−0.990146	−	0.140040i	$-0.955277\pi$
$227$	−5.63179	+	9.75454i	−0.373795	+	0.647431i	0.616351	+	0.787471i	$0.288610\pi$
$228$	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	$0.815957\pi$
$230$	−12.1191	−	1.82298i	−0.799108	−	0.120204i
$231$	−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	$0.0730995\pi$
$233$			6.94941i			0.455271i	−0.973746	+	0.227636i	$0.926900\pi$
$234$		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	$0.958705\pi$
$240$	33.8753	+	5.09562i	2.18664	+	0.328921i
$241$	−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
$245$	2.85918	+	2.27874i	0.182667	+	0.145583i
$246$	54.5973			3.48099
$247$		0			0
$248$		−	56.5962i		−	3.59386i
$249$	−22.0853	+	12.7510i	−1.39960	+	0.808060i
$250$	−28.3807	+	2.15223i	−1.79496	+	0.136119i
$251$	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	−0.0969108	−	0.995293i	$-0.530896\pi$
$257$	11.4877	−	6.63242i	0.716583	−	0.413719i	0.813494	+	0.581574i	$0.197563\pi$
$258$	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	$-0.283601\pi$
$263$	26.2150	−	15.1352i	1.61649	−	0.933279i	0.987819	−	0.155605i	$-0.0497327\pi$
$264$	4.31754	−	7.47821i	0.265726	−	0.460252i
$265$	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	$0.929387\pi$
$270$	10.4256	−	13.0812i	0.634480	−	0.796097i
$271$	−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
$275$	−0.934179	+	3.03492i	−0.0563331	+	0.183013i
$276$	10.3844	+	17.9863i	0.625069	+	1.08265i
$277$	−14.5363	−	8.39254i	−0.873402	−	0.504259i	−0.00492452	−	0.999988i	$-0.501568\pi$
$277$	−14.5363	−	8.39254i	−0.873402	−	0.504259i	−0.868477	+	0.495729i	$0.834901\pi$
$278$	36.4715			2.18741
$279$	12.6898	+	7.32648i	0.759721	+	0.438625i
$280$	−6.17271	+	41.0358i	−0.368890	+	2.45236i
$281$		−	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	−0.255617	−	0.966778i	$-0.582279\pi$
$283$	7.63458	−	4.40783i	0.453829	−	0.262018i	0.709446	+	0.704760i	$0.248945\pi$
$284$	−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
$290$	2.54024	−	16.8873i	0.149168	−	0.991659i
$291$		−	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	$0.475642\pi$
$293$	−14.1263	+	24.4675i	−0.825267	+	1.42940i	−0.901715	+	0.432331i	$0.857691\pi$
$294$		−	8.96157i		−	0.522650i
$295$	−16.7977	−	2.52675i	−0.977999	−	0.147113i
$296$	−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
$305$	−0.755091	+	5.01980i	−0.0432364	+	0.287433i
$306$	−4.41217	−	2.54737i	−0.252227	−	0.145623i
$307$	12.7219			0.726077			0.363039	−	0.931774i	$-0.381739\pi$
$307$	12.7219			0.726077			0.363039	+	0.931774i	$0.381739\pi$
$308$	7.24190	+	4.18112i	0.412646	+	0.238241i
$309$	11.8073	+	20.4508i	0.671692	+	1.16340i
$310$	31.7944	−	39.8932i	1.80580	−	2.26578i
$311$	−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	$0.244460\pi$
$313$			24.5807i			1.38938i	−0.719307	+	0.694692i	$0.755540\pi$
$314$	40.4880	−	23.3758i	2.28487	−	1.31917i
$315$	−8.40186	−	6.69619i	−0.473391	−	0.377287i
$316$	2.32648	−	4.02959i	0.130875	−	0.226682i
$317$	0.234377			0.0131639			0.00658196	−	0.999978i	$-0.497905\pi$
$317$	0.234377			0.0131639			0.00658196	+	0.999978i	$0.497905\pi$
$318$	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
$335$	14.0416	+	11.1910i	0.767177	+	0.611431i
$336$	38.9871	−	22.5092i	2.12692	−	1.22798i
$337$		−	21.2949i		−	1.16001i	−0.814614	−	0.580003i	$-0.803051\pi$
$337$		−	21.2949i		−	1.16001i	0.814614	−	0.580003i	$-0.196949\pi$
$338$		0			0
$339$	−11.9053			−0.646605
$340$	−7.64317	+	9.59006i	−0.414509	+	0.520094i
$341$	−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
$345$	−1.54169	+	10.2491i	−0.0830019	+	0.551791i
$346$		−	3.48079i		−	0.187128i
$347$	−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
$349$	−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	$0.0892394\pi$
$353$	13.5295	+	23.4338i	0.720104	+	1.24726i	−0.240853	+	0.970562i	$0.577427\pi$
$354$	20.8178	+	36.0576i	1.10646	+	1.91644i
$355$	−5.82669	−	0.876465i	−0.309248	−	0.0465179i
$356$			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	$-0.252485\pi$
$360$	3.43466	−	22.8334i	0.181023	−	1.20343i
$361$	−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	−0.334836	−	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
$369$		−	16.2881i		−	0.847922i
$370$	1.03638	−	6.88980i	0.0538789	−	0.358184i
$371$	1.63452	+	0.943693i	0.0848603	+	0.0489941i
$372$	−86.4505			−4.48225
$373$	−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
$375$	1.82013	+	24.0015i	0.0939913	+	1.23943i
$376$	−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	$0.290897\pi$
$380$	−8.52337	+	10.6945i	−0.437240	+	0.548615i
$381$	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	$-0.656327\pi$
$383$	10.3305	−	17.8929i	0.527861	−	0.914283i	0.999473	−	0.0324760i	$-0.0103393\pi$
$384$	−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	−0.723839	−	0.689969i	$-0.757624\pi$
$397$	4.69451	−	8.13113i	0.235611	−	0.408090i	0.959450	+	0.281879i	$0.0909576\pi$
$398$	−13.1753			−0.660420
$399$	4.31754	−	7.47821i	0.216148	−	0.374379i
$400$	−34.0049	−	10.4670i	−1.70024	−	0.523352i
$401$	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
$405$	−19.6403	−	15.6531i	−0.975935	−	0.777809i
$406$	−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	$-0.684682\pi$
$410$	−56.0749	−	8.43492i	−2.76934	−	0.416571i
$411$			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	$0.886978\pi$
$420$	62.6820	+	9.42879i	3.05857	+	0.460078i
$421$		−	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
$425$	−5.96554	+	1.36532i	−0.289371	+	0.0662277i
$426$	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	0.505323	−	0.862930i	$-0.331373\pi$
$433$	0.221929	+	0.128130i	0.0106652	+	0.00615756i	−0.494658	+	0.869088i	$0.664707\pi$
$434$		−	67.0396i		−	3.21800i
$435$	−14.2816	−	2.14827i	−0.684750	−	0.103002i
$436$	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	$0.775308\pi$
$440$	−5.58973	+	7.01356i	−0.266480	+	0.334358i
$441$	−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	$0.967257\pi$
$444$	−10.2254	+	5.90364i	−0.485276	+	0.280174i
$445$	−17.5017	+	21.9599i	−0.829663	+	1.04100i
$446$	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	0.627292	−	0.778784i	$-0.284163\pi$
$457$	−7.71304	−	13.3594i	−0.360801	−	0.624925i	−0.988093	+	0.153859i	$0.950830\pi$
$458$	−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	$-0.552310\pi$
$463$	−7.04045			−0.327197			−0.163599	+	0.986527i	$0.552310\pi$
$464$	10.6738	−	18.4876i	0.495519	−	0.858265i
$465$	−33.7376	−	26.8885i	−1.56454	−	1.24692i
$466$	−15.3212	+	8.84570i	−0.709741	+	0.409769i
$467$			18.8113i			0.870482i	0.900314	+	0.435241i	$0.143337\pi$
$467$			18.8113i			0.870482i	−0.900314	+	0.435241i	$0.856663\pi$
$468$		0			0
$469$	23.5967			1.08959
$470$	−27.4386	−	21.8683i	−1.26565	−	1.00871i
$471$	−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
$475$	−6.65255	+	1.52255i	−0.305240	+	0.0698594i
$476$			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
$485$	−4.91728	+	32.6898i	−0.223282	+	1.48437i
$486$			39.1165i			1.77436i
$487$	−16.1620	+	27.9935i	−0.732372	+	1.26851i	0.223495	+	0.974705i	$0.428253\pi$
$487$	−16.1620	+	27.9935i	−0.732372	+	1.26851i	−0.955867	+	0.293800i	$0.905080\pi$
$488$	−7.16858	+	12.4163i	−0.324506	+	0.562062i
$489$		−	8.63509i		−	0.390492i
$490$	−1.38451	+	9.20411i	−0.0625456	+	0.415799i
$491$	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	$0.775502\pi$
$500$	−28.2573	−	41.3667i	−1.26370	−	1.84998i
$501$	5.47890	+	3.16324i	0.244779	+	0.141323i
$502$	9.35181			0.417392
$503$	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
$505$	−23.1376	−	18.4404i	−1.02961	−	0.820587i
$506$	−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	$0.178344\pi$
$510$	11.7303	+	9.34893i	0.519427	+	0.413978i
$511$	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	−0.944150	−	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
$525$	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
$530$	−2.27874	+	2.85918i	−0.0989820	+	0.124195i
$531$	10.7571	−	6.21061i	0.466818	−	0.269517i
$532$			17.9718i			0.779177i
$533$		0			0
$534$	68.8290			2.97852
$535$	14.8752	−	18.6643i	0.643112	−	0.806928i
$536$	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
$540$	29.1148	+	4.37953i	1.25290	+	0.188465i
$541$			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	$0.0206873\pi$
$547$			3.03789i			0.129891i	−0.997889	+	0.0649454i	$0.979313\pi$
$548$	−19.4294	−	33.6527i	−0.829983	−	1.43757i
$549$	−1.85597	−	3.21464i	−0.0792109	−	0.137197i
$550$	−7.88011	+	1.80350i	−0.336009	+	0.0769015i
$551$		−	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
$555$	−5.82669	−	0.876465i	−0.247329	−	0.0372039i
$556$	32.0970	+	55.5936i	1.36121	+	2.35769i
$557$	−10.3498	−	17.9264i	−0.438536	−	0.759566i	0.559041	−	0.829140i	$-0.311169\pi$
$557$	−10.3498	−	17.9264i	−0.438536	−	0.759566i	−0.997577	+	0.0695738i	$0.977836\pi$
$558$			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	0.686499	−	0.727131i	$-0.259147\pi$
$563$	9.49188	+	5.48014i	0.400035	+	0.230960i	−0.286464	+	0.958091i	$0.592480\pi$
$564$			59.4608i			2.50375i
$565$	12.2275	+	1.83929i	0.514413	+	0.0773794i
$566$	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	$-0.519715\pi$
$570$	13.0812	+	10.4256i	0.547912	+	0.436679i
$571$	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
$575$	3.16683	−	10.2883i	0.132066	−	0.429050i
$576$	−0.220882	+	0.382579i	−0.00920343	+	0.0159408i
$577$	18.3646			0.764530			0.382265	−	0.924053i	$-0.375144\pi$
$577$	18.3646			0.764530			0.382265	+	0.924053i	$0.375144\pi$
$578$	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	0.858681	−	0.512510i	$-0.171284\pi$
$587$	−0.351448	−	0.608726i	−0.0145058	−	0.0251248i	−0.873187	+	0.487385i	$0.837951\pi$
$588$	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	$-0.223738\pi$
$593$	37.1593			1.52595			0.762975	+	0.646428i	$0.223738\pi$
$594$	2.37548	−	4.11446i	0.0974672	−	0.168818i
$595$	−5.01248	+	6.28927i	−0.205492	+	0.257835i
$596$	−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	$0.396127\pi$
$600$	−19.9999	+	64.9749i	−0.816493	+	2.65259i
$601$	−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
$605$	3.52459	−	23.4313i	0.143295	−	0.952616i
$606$			72.5204i			2.94594i
$607$	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
$609$	−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	0.986081	−	0.166269i	$-0.0531719\pi$
$613$	8.64201	+	14.9684i	0.349047	+	0.604568i	−0.637033	+	0.770836i	$0.719839\pi$
$614$	16.1933	+	28.0477i	0.653509	+	1.13191i
$615$	−7.13340	+	47.4224i	−0.287646	+	1.91225i
$616$			11.7861i			0.474877i
$617$	13.2345	−	22.9229i	0.532803	−	0.922841i	−0.466464	−	0.884540i	$-0.654472\pi$
$617$	13.2345	−	22.9229i	0.532803	−	0.922841i	0.999266	−	0.0383009i	$-0.0121945\pi$
$618$	−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	$0.785883\pi$
$620$	88.7902	+	13.3560i	3.56590	+	0.536392i
$621$	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
$630$	4.06844	−	27.0467i	0.162091	−	1.07757i
$631$	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
$635$	−24.0149	+	30.1321i	−0.953003	+	1.19576i
$636$	6.19599			0.245687
$637$		0			0
$638$		−	4.85031i		−	0.192026i
$639$	3.73136	−	2.15430i	0.147610	−	0.0852229i
$640$	20.3828	+	16.2449i	0.805702	+	0.642136i
$641$	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	−0.729622	−	0.683851i	$-0.760304\pi$
$643$	5.76682	−	9.98843i	0.227421	−	0.393905i	0.957043	+	0.289946i	$0.0936372\pi$
$644$	−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	−0.957490	−	0.288467i	$-0.906854\pi$
$647$	−30.1779	+	17.4232i	−1.18641	+	0.684977i	−0.228925	+	0.973444i	$0.573521\pi$
$648$	−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	−0.0715139	−	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
$655$	−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	$0.172041\pi$
$660$	10.7132	+	8.53829i	0.417010	+	0.332352i
$661$	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
$665$	−5.58973	+	7.01356i	−0.216760	+	0.271974i
$666$	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
$670$	−6.79940	+	45.2020i	−0.262684	+	1.74630i
$671$			1.44176i			0.0556587i
$672$	30.0479	+	17.3481i	1.15912	+	0.669219i
$673$	4.77457	−	2.75660i	0.184046	−	0.106259i	−0.405146	−	0.914252i	$-0.632779\pi$
$673$	4.77457	−	2.75660i	0.184046	−	0.106259i	0.589192	+	0.807993i	$0.299446\pi$
$674$	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	$0.0294320\pi$
$677$			4.80479i			0.184663i	−0.995728	+	0.0923316i	$0.970568\pi$
$678$	−15.1539	−	26.2472i	−0.581980	−	1.00802i
$679$	21.7215	+	37.6227i	0.833594	+	1.44383i
$680$	−17.0921	−	2.57104i	−0.655453	−	0.0985949i
$681$			24.2496i			0.929248i
$682$	7.24440	−	12.5477i	0.277403	−	0.480475i
$683$	5.88126	−	10.1866i	0.225040	−	0.389781i	−0.731291	−	0.682065i	$-0.761082\pi$
$683$	5.88126	−	10.1866i	0.225040	−	0.389781i	0.956331	+	0.292284i	$0.0944154\pi$
$684$		−	10.0000i		−	0.382360i
$685$	2.88453	−	19.1761i	0.110212	−	0.732683i
$686$	−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
$695$	−4.76518	+	31.6786i	−0.180753	+	1.20164i
$696$	−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
$700$	−62.9218	−	19.3679i	−2.37822	−	0.732039i
$701$	−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
$705$	−18.4939	+	23.2048i	−0.696522	+	0.873943i
$706$	−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
$725$	14.3362	+	4.41283i	0.532434	+	0.163888i
$726$	−50.2971	+	29.0390i	−1.86670	+	1.07774i
$727$		−	26.2596i		−	0.973916i	−0.873425	−	0.486958i	$-0.838107\pi$
$727$		−	26.2596i		−	0.973916i	0.873425	−	0.486958i	$-0.161893\pi$
$728$		0			0
$729$	−0.614542			−0.0227608
$730$	45.9684	+	36.6363i	1.70137	+	1.35597i
$731$	−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	$-0.300336\pi$
$733$	31.7811			1.17386			0.586931	+	0.809637i	$0.300336\pi$
$734$	15.3029	+	8.83513i	0.564840	+	0.326110i
$735$	7.78389	+	1.17087i	0.287113	+	0.0431883i
$736$		−	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	0.835984	−	0.548753i	$-0.184897\pi$
$743$	−1.56031	−	2.70254i	−0.0572423	−	0.0991465i	−0.893227	+	0.449607i	$0.851564\pi$
$744$	−60.9237	−	105.523i	−2.23357	−	3.86866i
$745$	−37.9328	−	5.70594i	−1.38975	−	0.209050i
$746$		−	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
$750$	−50.5988	+	34.5636i	−1.84761	+	1.26208i
$751$	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	−0.578109	−	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
$759$			2.94369i			0.106849i
$760$	−19.0605	−	2.86713i	−0.691397	−	0.104002i
$761$	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
$765$	2.78908	−	3.49952i	0.100839	−	0.126525i
$766$	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	$0.221430\pi$
$770$	−6.62117	+	8.30773i	−0.238610	+	0.299390i
$771$	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	$0.512749\pi$
$773$	−24.6153	+	42.6350i	−0.885351	+	1.53347i	−0.845311	+	0.534275i	$0.820585\pi$
$774$	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	−0.765573	−	0.643349i	$-0.777545\pi$
$787$	4.89168	−	8.47263i	0.174369	−	0.302017i	0.939943	+	0.341332i	$0.110878\pi$
$788$	30.2250			1.07672
$789$	32.5851	−	56.4390i	1.16006	−	2.00928i
$790$	4.62264	+	3.68419i	0.164466	+	0.131078i
$791$	14.0726	−	8.12482i	0.500364	−	0.288885i
$792$		−	6.55812i		−	0.233033i
$793$		0			0
$794$	23.9020			0.848250
$795$	2.41801	+	1.92712i	0.0857578	+	0.0683480i
$796$	−11.5950	−	20.0832i	−0.410975	−	0.711830i
$797$	−14.3216	−	8.26856i	−0.507296	−	0.292887i	0.224426	−	0.974491i	$-0.427949\pi$
$797$	−14.3216	−	8.26856i	−0.507296	−	0.292887i	−0.731721	+	0.681604i	$0.761283\pi$
$798$	21.9827			0.778178
$799$	−6.53348	−	3.77211i	−0.231138	−	0.133448i
$800$	−6.11770	−	26.7303i	−0.216293	−	0.945060i
$801$		−	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	$-0.355773\pi$
$810$	9.51044	−	63.2248i	0.334163	−	2.22149i
$811$		−	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
$815$	−1.33407	+	8.86879i	−0.0467303	+	0.310660i
$816$	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	0.901980	−	0.431777i	$-0.142113\pi$
$823$	28.0867	+	16.2159i	0.979041	+	0.565249i	0.0770602	+	0.997026i	$0.475447\pi$
$824$		−	69.2714i		−	2.41318i
$825$	1.52522	+	6.66419i	0.0531012	+	0.232017i
$826$	−49.2154	−	28.4145i	−1.71242	−	0.988667i
$827$	27.3319			0.950425			0.475212	−	0.879871i	$-0.342371\pi$
$827$	27.3319			0.950425			0.475212	+	0.879871i	$0.342371\pi$
$828$	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	$0.852916\pi$
$830$	52.7301	+	42.0253i	1.83029	+	1.45872i
$831$	−36.1370			−1.25358
$832$		0			0
$833$			2.00128i			0.0693402i
$834$	68.0007	−	39.2602i	2.35467	−	1.35947i
$835$	−5.13847	−	4.09531i	−0.177824	−	0.141724i
$836$	−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	$-0.319520\pi$
$853$	31.3732			1.07420			0.537099	+	0.843519i	$0.319520\pi$
$854$	−8.49136	+	14.7075i	−0.290568	+	0.503279i
$855$	3.11027	−	3.90253i	0.106369	−	0.133464i
$856$	58.3774	−	33.7042i	1.99530	−	1.15199i
$857$		−	21.2813i		−	0.726955i	−0.931603	−	0.363478i	$-0.881589\pi$
$857$		−	21.2813i		−	0.726955i	0.931603	−	0.363478i	$-0.118411\pi$
$858$		0			0
$859$	−56.8502			−1.93970			−0.969851	−	0.243698i	$-0.921639\pi$
$859$	−56.8502			−1.93970			−0.969851	+	0.243698i	$0.921639\pi$
$860$	8.53829	−	10.7132i	0.291153	−	0.365317i
$861$	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	$-0.311461\pi$
$863$	32.8011			1.11656			0.558282	+	0.829651i	$0.311461\pi$
$864$	13.9568	+	8.05794i	0.474819	+	0.274137i
$865$	3.02336	+	0.454782i	0.102797	+	0.0154630i
$866$			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
$875$	−18.5315	−	27.1288i	−0.626478	−	0.917120i
$876$		−	99.6157i		−	3.36570i
$877$	−18.0325	+	31.2333i	−0.608916	+	1.05467i	0.382504	+	0.923954i	$0.375062\pi$
$877$	−18.0325	+	31.2333i	−0.608916	+	1.05467i	−0.991419	+	0.130719i	$0.958271\pi$
$878$	−9.66956	+	16.7482i	−0.326332	+	0.565223i
$879$			60.8257i			2.05160i
$880$	−9.99285	−	1.50315i	−0.336859	−	0.0506712i
$881$	−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	$-0.995703\pi$
$883$		−	0.802236i		−	0.0269974i	0.999909	−	0.0134987i	$-0.00429690\pi$
$884$		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	−0.614804	−	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
$889$			50.6363i			1.69829i
$890$	−70.6918	−	10.6336i	−2.36959	−	0.356440i
$891$	−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
$895$	13.6151	+	10.8511i	0.455104	+	0.362713i
$896$	34.2529			1.14431
$897$		0			0
$898$			8.37054i			0.279328i
$899$	−23.2829	+	13.4424i	−0.776527	+	0.448328i
$900$	35.0113	+	10.7768i	1.16704	+	0.359228i
$901$	−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	−0.869077	−	0.494677i	$-0.835286\pi$
$907$	−26.3583	+	15.2180i	−0.875213	+	0.505305i	−0.00613601	+	0.999981i	$0.501953\pi$
$908$	−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	$0.957588\pi$
$920$	18.9490	−	23.7757i	0.624728	−	0.783861i
$921$	23.7198	−	13.6947i	0.781595	−	0.451254i
$922$			65.8957i			2.17016i
$923$		0			0
$924$	18.0033			0.592264
$925$	5.84897	+	1.80037i	0.192313	+	0.0591958i
$926$	−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	$0.641743\pi$
$930$	16.3368	−	108.606i	0.535704	−	3.56133i
$931$			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	$-0.747515\pi$
$937$		−	43.6264i		−	1.42521i	0.701565	−	0.712606i	$-0.252485\pi$
$938$	30.0355	+	52.0230i	0.980693	+	1.69861i
$939$	26.4602	+	45.8305i	0.863497	+	1.49562i
$940$	9.18631	−	61.0701i	0.299625	−	1.99189i
$941$		−	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
$945$	19.0938	+	2.87214i	0.621123	+	0.0934308i
$946$	−1.10530	−	1.91444i	−0.0359365	−	0.0622439i
$947$	9.99146	+	17.3057i	0.324679	+	0.562360i	0.981447	−	0.191732i	$-0.0614105\pi$
$947$	9.99146	+	17.3057i	0.324679	+	0.562360i	−0.656769	+	0.754092i	$0.728077\pi$
$948$		−	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	−0.177335	−	0.984150i	$-0.556748\pi$
$953$	−34.5228	−	19.9317i	−1.11830	−	0.645652i	−0.940967	+	0.338498i	$0.890081\pi$
$954$		−	2.67352i		−	0.0865583i
$955$	1.64434	−	10.9315i	0.0532095	−	0.353734i
$956$	−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
$960$	0.810646	−	1.01714i	0.0261635	−	0.0328280i
$961$	−49.3098			−1.59064
$962$		0			0
$963$			17.4523i			0.562392i
$964$	76.7252	−	44.2973i	2.47115	−	1.42672i
$965$	8.66704	+	6.90753i	0.279002	+	0.222361i
$966$	−17.3371	+	30.0287i	−0.557811	+	0.966156i
$967$	43.8607			1.41047			0.705233	−	0.708975i	$-0.250842\pi$
$967$	43.8607			1.41047			0.705233	+	0.708975i	$0.250842\pi$
$968$	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	$0.140325\pi$
$977$	25.6849	+	44.4875i	0.821731	+	1.42328i	−0.0826604	+	0.996578i	$0.526342\pi$
$978$	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	$-0.702802\pi$
$983$	−37.3026			−1.18977			−0.594885	+	0.803811i	$0.702802\pi$
$984$	−67.7221	+	117.298i	−2.15890	+	3.73933i
$985$	11.7954	+	9.40079i	0.375832	+	0.299534i
$986$	8.09528	−	4.67381i	0.257806	−	0.148845i
$987$			38.9951i			1.24123i
$988$		0			0
$989$	2.94369			0.0936040
$990$	3.68419	−	4.62264i	0.117091	−	0.146917i
$991$	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
$995$	1.72142	−	11.4439i	0.0545727	−	0.362796i
$996$		−	114.269i		−	3.62074i
$997$	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
$999$	−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.699.12		24
5.4	even	2	inner	845.2.l.f.699.1		24
13.2	odd	12		845.2.b.e.339.6		6
13.3	even	3		845.2.d.d.844.2		12
13.4	even	6	inner	845.2.l.f.654.1		24
13.5	odd	4		845.2.n.e.484.6		12
13.6	odd	12		845.2.n.e.529.1		12
13.7	odd	12		65.2.n.a.9.6	yes	12
13.8	odd	4		65.2.n.a.29.1	yes	12
13.9	even	3	inner	845.2.l.f.654.11		24
13.10	even	6		845.2.d.d.844.12		12
13.11	odd	12		845.2.b.d.339.1		6
13.12	even	2	inner	845.2.l.f.699.2		24
39.8	even	4		585.2.bs.a.289.6		12
39.20	even	12		585.2.bs.a.334.1		12
52.7	even	12		1040.2.dh.a.529.5		12
52.47	even	4		1040.2.dh.a.289.2		12
65.2	even	12		4225.2.a.bq.1.1		6
65.4	even	6	inner	845.2.l.f.654.12		24
65.7	even	12		325.2.e.e.126.1		12
65.8	even	4		325.2.e.e.276.6		12
65.9	even	6	inner	845.2.l.f.654.2		24
65.19	odd	12		845.2.n.e.529.6		12
65.24	odd	12		845.2.b.d.339.6		6
65.28	even	12		4225.2.a.bq.1.6		6
65.29	even	6		845.2.d.d.844.11		12
65.33	even	12		325.2.e.e.126.6		12
65.34	odd	4		65.2.n.a.29.6	yes	12
65.37	even	12		4225.2.a.br.1.6		6
65.44	odd	4		845.2.n.e.484.1		12
65.47	even	4		325.2.e.e.276.1		12
65.49	even	6		845.2.d.d.844.1		12
65.54	odd	12		845.2.b.e.339.1		6
65.59	odd	12		65.2.n.a.9.1	✓	12
65.63	even	12		4225.2.a.br.1.1		6
65.64	even	2	inner	845.2.l.f.699.11		24
195.59	even	12		585.2.bs.a.334.6		12
195.164	even	4		585.2.bs.a.289.1		12
260.59	even	12		1040.2.dh.a.529.2		12
260.99	even	4		1040.2.dh.a.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	65.59	odd	12
65.2.n.a.9.6	yes	12	13.7	odd	12
65.2.n.a.29.1	yes	12	13.8	odd	4
65.2.n.a.29.6	yes	12	65.34	odd	4
325.2.e.e.126.1		12	65.7	even	12
325.2.e.e.126.6		12	65.33	even	12
325.2.e.e.276.1		12	65.47	even	4
325.2.e.e.276.6		12	65.8	even	4
585.2.bs.a.289.1		12	195.164	even	4
585.2.bs.a.289.6		12	39.8	even	4
585.2.bs.a.334.1		12	39.20	even	12
585.2.bs.a.334.6		12	195.59	even	12
845.2.b.d.339.1		6	13.11	odd	12
845.2.b.d.339.6		6	65.24	odd	12
845.2.b.e.339.1		6	65.54	odd	12
845.2.b.e.339.6		6	13.2	odd	12
845.2.d.d.844.1		12	65.49	even	6
845.2.d.d.844.2		12	13.3	even	3
845.2.d.d.844.11		12	65.29	even	6
845.2.d.d.844.12		12	13.10	even	6
845.2.l.f.654.1		24	13.4	even	6	inner
845.2.l.f.654.2		24	65.9	even	6	inner
845.2.l.f.654.11		24	13.9	even	3	inner
845.2.l.f.654.12		24	65.4	even	6	inner
845.2.l.f.699.1		24	5.4	even	2	inner
845.2.l.f.699.2		24	13.12	even	2	inner
845.2.l.f.699.11		24	65.64	even	2	inner
845.2.l.f.699.12		24	1.1	even	1	trivial
845.2.n.e.484.1		12	65.44	odd	4
845.2.n.e.484.6		12	13.5	odd	4
845.2.n.e.529.1		12	13.6	odd	12
845.2.n.e.529.6		12	65.19	odd	12
1040.2.dh.a.289.2		12	52.47	even	4
1040.2.dh.a.289.5		12	260.99	even	4
1040.2.dh.a.529.2		12	260.59	even	12
1040.2.dh.a.529.5		12	52.7	even	12
4225.2.a.bq.1.1		6	65.2	even	12
4225.2.a.bq.1.6		6	65.28	even	12
4225.2.a.br.1.1		6	65.63	even	12
4225.2.a.br.1.6		6	65.37	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} +(-4.45158 - 3.54786i) q^{10} +(-0.550003 + 0.317544i) q^{11} +9.64680i q^{12} -7.48079 q^{14} +(-3.00042 + 3.76470i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(-1.05998 - 0.611979i) q^{17} +4.16251 q^{18} +(-1.18205 - 0.682456i) q^{19} +(1.49037 - 9.90788i) 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} +(-12.1191 - 1.82298i) q^{30} +8.96157i q^{31} +(2.74215 - 4.74954i) q^{32} +(-0.683650 + 1.18412i) q^{33} -3.11588i q^{34} +(0.977401 - 6.49770i) 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} +(-0.543852 + 3.61549i) q^{45} +(4.74650 + 2.74039i) q^{46} +6.16379 q^{47} +(-13.2675 - 7.65998i) q^{48} +(-0.817544 - 1.41603i) q^{49} +(12.1654 + 3.74464i) q^{50} -2.63509 q^{51} -0.642285i q^{53} +(-6.47855 + 3.74039i) q^{54} +(0.885090 - 1.11054i) 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} +(3.16683 - 10.2883i) q^{75} +(5.29650 - 3.05794i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(12.4431 + 9.91702i) q^{80} +(5.61588 + 9.72698i) q^{81} +(21.9620 + 12.6798i) q^{82} -11.8452 q^{83} +(-24.5498 - 14.1738i) q^{84} +(2.70640 + 0.407104i) 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} +(3.01808 + 0.453987i) 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

Varieties

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