LMFDB - Embedded newform 845.2.n.e.484.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("845.484");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			484.1
Root			$-2.20467 - 1.27287i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.e.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20467 + 1.27287i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(2.54486 + 1.46928i) q^{7} +6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +O(q^{10})$	\(q+(-2.20467 + 1.27287i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(2.54486 + 1.46928i) q^{7} +6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +(0.846746 + 5.62912i) q^{10} +(-0.317544 - 0.550003i) q^{11} +9.64680i q^{12} -7.48079 q^{14} +(0.716091 + 4.76053i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(-1.05998 - 0.611979i) q^{17} +4.16251i q^{18} +(-0.682456 + 1.18205i) q^{19} +(-6.24464 - 7.83529i) q^{20} -6.32648 q^{21} +(1.40016 + 0.808385i) q^{22} +(1.86449 - 1.07646i) q^{23} +(-6.79833 - 11.7751i) q^{24} +(-3.66324 - 3.40304i) q^{25} -2.93855i q^{27} +(11.4030 - 6.58351i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-7.63828 - 9.58393i) q^{30} +8.96157 q^{31} +(4.74954 + 2.74215i) q^{32} +(1.18412 + 0.683650i) q^{33} +3.11588 q^{34} +(5.13847 - 4.09531i) q^{35} +(-3.66324 - 6.34492i) q^{36} +(1.05998 - 0.611979i) q^{37} -3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(-4.98079 - 8.62698i) q^{41} +(13.9478 - 8.05279i) q^{42} +(1.18412 + 0.683650i) q^{43} -2.84570 q^{44} +(-2.27874 - 2.85918i) q^{45} +(-2.74039 + 4.74650i) q^{46} -6.16379i q^{47} +(13.2675 + 7.65998i) q^{48} +(0.817544 + 1.41603i) q^{49} +(12.4079 + 2.83976i) q^{50} +2.63509 q^{51} +0.642285i q^{53} +(3.74039 + 6.47855i) q^{54} +(-1.40430 + 0.211239i) q^{55} +(-9.27912 + 16.0719i) q^{56} -2.93855i q^{57} +(-6.61402 - 3.81861i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(20.0774 + 7.88669i) q^{60} +(1.13509 - 1.96603i) q^{61} +(-19.7574 + 11.4069i) q^{62} +(4.16107 - 2.40240i) q^{63} +0.270178 q^{64} -3.48079 q^{66} +(6.95421 - 4.01502i) q^{67} +(-4.74954 + 2.74215i) q^{68} +(-2.31754 + 4.01410i) q^{69} +(-6.11588 + 15.5694i) q^{70} +(1.31754 - 2.28205i) q^{71} +(8.94284 + 5.16315i) q^{72} +10.3263i q^{73} +(-1.55794 + 2.69843i) q^{74} +(10.4933 + 2.40158i) q^{75} +(3.05794 + 5.29650i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(-15.7346 + 2.36683i) q^{80} +(5.61588 + 9.72698i) q^{81} +(21.9620 + 12.6798i) q^{82} -11.8452i q^{83} +(-14.1738 + 24.5498i) q^{84} +(-2.14026 + 1.70576i) q^{85} -3.48079 q^{86} +(-5.59346 - 3.22939i) q^{87} +(3.47351 - 2.00543i) q^{88} +(6.27912 + 10.8758i) q^{89} +(8.66324 + 3.40304i) q^{90} -9.64680i q^{92} +(-16.7087 + 9.64680i) q^{93} +(7.84570 + 13.5891i) q^{94} +(1.90220 + 2.38674i) q^{95} -11.8073 q^{96} +(12.8031 + 7.39190i) q^{97} +(-3.60484 - 2.08125i) q^{98} -1.03843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 + 4 * q^15 - 16 * q^16 - 12 * q^19 + q^20 + 8 * q^21 - 32 * q^24 - 2 * q^25 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 29 * q^45 - 10 * q^46 + 6 * q^49 + 31 * q^50 + 24 * q^51 + 22 * q^54 - 26 * q^55 - 16 * q^56 + 4 * q^59 + 96 * q^60 + 6 * q^61 - 12 * q^64 + 4 * q^66 - 24 * q^69 - 20 * q^70 + 12 * q^71 + 8 * q^74 + 2 * q^75 + 10 * q^76 - 104 * q^79 - 33 * q^80 + 14 * q^81 - 90 * q^84 - 21 * q^85 + 4 * q^86 - 20 * q^89 + 62 * q^90 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.20467	+	1.27287i	−1.55894	+	0.900055i	−0.561582	+	0.827421i	$0.689807\pi$
$2$	−2.20467	+	1.27287i	−1.55894	+	0.900055i	−0.997359	+	0.0726333i	$0.976860\pi$
$3$	−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
$5$	0.817544	−	2.08125i	0.365617	−	0.930765i
$5$	0.817544	−	2.08125i	0.365617	−	0.930765i
$6$	2.74039	−	4.74650i	1.11876	−	1.93775i
$7$	2.54486	+	1.46928i	0.961867	+	0.555334i	0.896747	−	0.442543i	$-0.145924\pi$
$7$	2.54486	+	1.46928i	0.961867	+	0.555334i	0.0651198	+	0.997877i	$0.479257\pi$
$8$			6.31544i			2.23284i
$9$	0.817544	−	1.41603i	0.272515	−	0.472010i
$10$	0.846746	+	5.62912i	0.267765	+	1.78008i
$11$	−0.317544	−	0.550003i	−0.0957433	−	0.165832i	0.814175	−	0.580619i	$-0.197189\pi$
$11$	−0.317544	−	0.550003i	−0.0957433	−	0.165832i	−0.909919	+	0.414787i	$0.863856\pi$
$12$			9.64680i			2.78479i
$13$		0			0
$13$		0			0
$14$	−7.48079			−1.99932
$15$	0.716091	+	4.76053i	0.184894	+	1.22916i
$16$	−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	$0.714088\pi$
$18$			4.16251i			0.981113i
$19$	−0.682456	+	1.18205i	−0.156566	+	0.271180i	−0.933628	−	0.358244i	$-0.883376\pi$
$19$	−0.682456	+	1.18205i	−0.156566	+	0.271180i	0.777062	+	0.629424i	$0.216709\pi$
$20$	−6.24464	−	7.83529i	−1.39634	−	1.75202i
$21$	−6.32648			−1.38055
$22$	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	$0.261272\pi$
$24$	−6.79833	−	11.7751i	−1.38770	−	2.40357i
$25$	−3.66324	−	3.40304i	−0.732648	−	0.680607i
$26$		0			0
$27$		−	2.93855i		−	0.565525i
$28$	11.4030	−	6.58351i	2.15496	−	1.24417i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−7.63828	−	9.58393i	−1.39455	−	1.74978i
$31$	8.96157			1.60955			0.804773	−	0.593583i	$-0.202287\pi$
$31$	8.96157			1.60955			0.804773	+	0.593583i	$0.202287\pi$
$32$	4.74954	+	2.74215i	0.839607	+	0.484747i
$33$	1.18412	+	0.683650i	0.206128	+	0.119008i
$34$	3.11588			0.534368
$35$	5.13847	−	4.09531i	0.868561	−	0.692233i
$36$	−3.66324	−	6.34492i	−0.610540	−	1.05749i
$37$	1.05998	−	0.611979i	0.174259	−	0.100609i	−0.410333	−	0.911936i	$-0.634588\pi$
$37$	1.05998	−	0.611979i	0.174259	−	0.100609i	0.584593	+	0.811327i	$0.301254\pi$
$38$		−	3.47471i		−	0.563672i
$39$		0			0
$40$	13.1440	+	5.16315i	2.07825	+	0.816366i
$41$	−4.98079	−	8.62698i	−0.777868	−	1.34731i	−0.933168	−	0.359440i	$-0.882968\pi$
$41$	−4.98079	−	8.62698i	−0.777868	−	1.34731i	0.155300	−	0.987867i	$-0.450366\pi$
$42$	13.9478	−	8.05279i	2.15220	−	1.24257i
$43$	1.18412	+	0.683650i	0.180576	+	0.104256i	0.587563	−	0.809178i	$-0.300087\pi$
$43$	1.18412	+	0.683650i	0.180576	+	0.104256i	−0.406987	+	0.913434i	$0.633421\pi$
$44$	−2.84570			−0.429005
$45$	−2.27874	−	2.85918i	−0.339694	−	0.426222i
$46$	−2.74039	+	4.74650i	−0.404049	+	0.699833i
$47$		−	6.16379i		−	0.899081i	−0.893260	−	0.449540i	$-0.851588\pi$
$47$		−	6.16379i		−	0.899081i	0.893260	−	0.449540i	$-0.148412\pi$
$48$	13.2675	+	7.65998i	1.91499	+	1.10562i
$49$	0.817544	+	1.41603i	0.116792	+	0.202290i
$50$	12.4079	+	2.83976i	1.75474	+	0.401603i
$51$	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	$0.985954\pi$
$54$	3.74039	+	6.47855i	0.509003	+	0.881619i
$55$	−1.40430	+	0.211239i	−0.189356	+	0.0284834i
$56$	−9.27912	+	16.0719i	−1.23997	+	2.14770i
$57$		−	2.93855i		−	0.389221i
$58$	−6.61402	−	3.81861i	−0.868464	−	0.501408i
$59$	−3.79833	+	6.57890i	−0.494501	+	0.856500i	−0.999980	−	0.00633858i	$-0.997982\pi$
$59$	−3.79833	+	6.57890i	−0.494501	+	0.856500i	0.505479	+	0.862839i	$0.331316\pi$
$60$	20.0774	+	7.88669i	2.59199	+	1.01817i
$61$	1.13509	−	1.96603i	0.145333	−	0.251725i	−0.784164	−	0.620554i	$-0.786908\pi$
$61$	1.13509	−	1.96603i	0.145333	−	0.251725i	0.929497	+	0.368829i	$0.120241\pi$
$62$	−19.7574	+	11.4069i	−2.50919	+	1.44868i
$63$	4.16107	−	2.40240i	0.524246	−	0.302674i
$64$	0.270178			0.0337722
$65$		0			0
$66$	−3.48079			−0.428455
$67$	6.95421	−	4.01502i	0.849592	−	0.490512i	−0.0109212	−	0.999940i	$-0.503476\pi$
$67$	6.95421	−	4.01502i	0.849592	−	0.490512i	0.860513	+	0.509428i	$0.170143\pi$
$68$	−4.74954	+	2.74215i	−0.575966	+	0.332534i
$69$	−2.31754	+	4.01410i	−0.279000	+	0.483241i
$70$	−6.11588	+	15.5694i	−0.730987	+	1.86090i
$71$	1.31754	−	2.28205i	0.156364	−	0.270830i	−0.777191	−	0.629265i	$-0.783356\pi$
$71$	1.31754	−	2.28205i	0.156364	−	0.270830i	0.933555	+	0.358435i	$0.116689\pi$
$72$	8.94284	+	5.16315i	1.05392	+	0.608483i
$73$			10.3263i			1.20860i	0.796756	+	0.604301i	$0.206547\pi$
$73$			10.3263i			1.20860i	−0.796756	+	0.604301i	$0.793453\pi$
$74$	−1.55794	+	2.69843i	−0.181107	+	0.313686i
$75$	10.4933	+	2.40158i	1.21166	+	0.277310i
$76$	3.05794	+	5.29650i	0.350770	+	0.607551i
$77$		−	1.86624i		−	0.212678i
$78$		0			0
$79$	−1.03843			−0.116832			−0.0584161	−	0.998292i	$-0.518605\pi$
$79$	−1.03843			−0.116832			−0.0584161	+	0.998292i	$0.518605\pi$
$80$	−15.7346	+	2.36683i	−1.75918	+	0.264620i
$81$	5.61588	+	9.72698i	0.623986	+	1.08078i
$82$	21.9620	+	12.6798i	2.42530	+	1.40025i
$83$		−	11.8452i		−	1.30018i	−0.759855	−	0.650092i	$-0.774730\pi$
$83$		−	11.8452i		−	1.30018i	0.759855	−	0.650092i	$-0.225270\pi$
$84$	−14.1738	+	24.5498i	−1.54649	+	2.67860i
$85$	−2.14026	+	1.70576i	−0.232144	+	0.185016i
$86$	−3.48079			−0.375343
$87$	−5.59346	−	3.22939i	−0.599682	−	0.346227i
$88$	3.47351	−	2.00543i	0.370277	−	0.213780i
$89$	6.27912	+	10.8758i	0.665585	+	1.15283i	0.979126	+	0.203253i	$0.0651513\pi$
$89$	6.27912	+	10.8758i	0.665585	+	1.15283i	−0.313541	+	0.949575i	$0.601515\pi$
$90$	8.66324	+	3.40304i	0.913186	+	0.358712i
$91$		0			0
$92$		−	9.64680i		−	1.00575i
$93$	−16.7087	+	9.64680i	−1.73262	+	1.00033i
$94$	7.84570	+	13.5891i	0.809222	+	1.40161i
$95$	1.90220	+	2.38674i	0.195162	+	0.244874i
$96$	−11.8073			−1.20507
$97$	12.8031	+	7.39190i	1.29996	+	0.750534i	0.980397	−	0.197031i	$-0.0631299\pi$
$97$	12.8031	+	7.39190i	1.29996	+	0.750534i	0.319565	+	0.947564i	$0.396463\pi$
$98$	−3.60484	−	2.08125i	−0.364144	−	0.210238i
$99$	−1.03843			−0.104366
$100$	−21.4125	+	6.59098i	−2.14125	+	0.659098i
$101$	−6.61588	−	11.4590i	−0.658304	−	1.14022i	−0.981054	−	0.193732i	$-0.937941\pi$
$101$	−6.61588	−	11.4590i	−0.658304	−	1.14022i	0.322750	−	0.946484i	$-0.395393\pi$
$102$	−5.80951	+	3.35412i	−0.575228	+	0.332108i
$103$			10.9686i			1.08077i	0.841419	+	0.540383i	$0.181721\pi$
$103$			10.9686i			1.08077i	−0.841419	+	0.540383i	$0.818279\pi$
$104$		0			0
$105$	−5.17218	+	13.1670i	−0.504753	+	1.28497i
$106$	−0.817544	−	1.41603i	−0.0794069	−	0.137537i
$107$	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
$109$	−3.27018			−0.313226			−0.156613	−	0.987660i	$-0.550058\pi$
$109$	−3.27018			−0.313226			−0.156613	+	0.987660i	$0.550058\pi$
$110$	2.82715	−	2.25321i	0.269558	−	0.214835i
$111$	−1.31754	+	2.28205i	−0.125056	+	0.216603i
$112$		−	20.9104i		−	1.97584i
$113$	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
$115$	−0.716091	−	4.76053i	−0.0667759	−	0.443922i
$116$	13.4424			1.24809
$117$		0			0
$118$		−	19.3391i		−	1.78031i
$119$	−1.79833	−	3.11480i	−0.164853	−	0.285533i
$120$	−30.0648	+	4.52243i	−2.74453	+	0.412839i
$121$	5.29833	−	9.17698i	0.481666	−	0.834271i
$122$			5.77928i			0.523231i
$123$	18.5732	+	10.7233i	1.67469	+	0.966884i
$124$	20.0774	−	34.7752i	1.80301	−	3.12290i
$125$	−10.0774	+	4.84201i	−0.901354	+	0.433082i
$126$	−6.11588	+	10.5930i	−0.544845	+	0.943700i
$127$	14.9231	−	8.61586i	1.32421	−	0.764534i	0.339813	−	0.940493i	$-0.389636\pi$
$127$	14.9231	−	8.61586i	1.32421	−	0.764534i	0.984397	+	0.175959i	$0.0563027\pi$
$128$	−10.0947	+	5.82819i	−0.892256	+	0.515144i
$129$	−2.94369			−0.259178
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	5.30577	−	3.06329i	0.461808	−	0.266625i
$133$	−3.47351	+	2.00543i	−0.301191	+	0.173893i
$134$	−10.2212	+	17.7036i	−0.882975	+	1.52936i
$135$	−6.11588	−	2.40240i	−0.526371	−	0.206765i
$136$	3.86491	−	6.69422i	0.331413	−	0.574025i
$137$	7.51044	+	4.33616i	0.641661	+	0.370463i	0.785254	−	0.619174i	$-0.212532\pi$
$137$	7.51044	+	4.33616i	0.641661	+	0.370463i	−0.143593	+	0.989637i	$0.545866\pi$
$138$		−	11.7997i		−	1.00446i
$139$	7.16324	−	12.4071i	0.607578	−	1.05236i	−0.384060	−	0.923308i	$-0.625474\pi$
$139$	7.16324	−	12.4071i	0.607578	−	1.05236i	0.991638	−	0.129048i	$-0.0411922\pi$
$140$	−4.37953	−	29.1148i	−0.370137	−	2.46065i
$141$	6.63509	+	11.4923i	0.558775	+	0.967827i
$142$			6.70825i			0.562944i
$143$		0			0
$144$	−11.6351			−0.969591
$145$	6.63357	−	0.997839i	0.550888	−	0.0828660i
$146$	−13.1440	−	22.7661i	−1.08781	−	1.88414i
$147$	−3.04860	−	1.76011i	−0.251445	−	0.145172i
$148$		−	5.48429i		−	0.450806i
$149$	8.57745	−	14.8566i	0.702692	−	1.21710i	−0.264826	−	0.964296i	$-0.585315\pi$
$149$	8.57745	−	14.8566i	0.702692	−	1.21710i	0.967518	−	0.252802i	$-0.0813521\pi$
$150$	−26.1912	+	8.06192i	−2.13851	+	0.658253i
$151$	21.3828			1.74011			0.870053	−	0.492957i	$-0.164084\pi$
$151$	21.3828			1.74011			0.870053	+	0.492957i	$0.164084\pi$
$152$	−7.46515	−	4.31000i	−0.605503	−	0.349587i
$153$	−1.73316	+	1.00064i	−0.140118	+	0.0808969i
$154$	2.37548	+	4.11446i	0.191422	+	0.331552i
$155$	7.32648	−	18.6513i	0.588477	−	1.49811i
$156$		0			0
$157$			18.3646i			1.46566i	0.680413	+	0.732829i	$0.261800\pi$
$157$			18.3646i			1.46566i	−0.680413	+	0.732829i	$0.738200\pi$
$158$	2.28939	−	1.32178i	0.182134	−	0.105155i
$159$	−0.691395	−	1.19753i	−0.0548312	−	0.0949705i
$160$	9.59006	−	7.64317i	0.758161	−	0.604245i
$161$	6.32648			0.498597
$162$	−24.7624	−	14.2966i	−1.94551	−	1.12324i
$163$	−3.47351	−	2.00543i	−0.272066	−	0.157078i	0.357760	−	0.933814i	$-0.383541\pi$
$163$	−3.47351	−	2.00543i	−0.272066	−	0.157078i	−0.629826	+	0.776736i	$0.716874\pi$
$164$	−44.6357			−3.48546
$165$	2.39092	−	1.90553i	0.186133	−	0.148346i
$166$	15.0774	+	26.1149i	1.17024	+	2.02691i
$167$	2.54486	−	1.46928i	0.196927	−	0.113696i	−0.398294	−	0.917258i	$-0.630398\pi$
$167$	2.54486	−	1.46928i	0.196927	−	0.113696i	0.595221	+	0.803562i	$0.297064\pi$
$168$		−	39.9545i		−	3.08256i
$169$		0			0
$170$	2.54737	−	6.48493i	0.195374	−	0.497371i
$171$	1.11588	+	1.93275i	0.0853331	+	0.147801i
$172$	5.30577	−	3.06329i	0.404561	−	0.233574i
$173$	−1.18412	−	0.683650i	−0.0900267	−	0.0519769i	0.454311	−	0.890843i	$-0.349886\pi$
$173$	−1.18412	−	0.683650i	−0.0900267	−	0.0519769i	−0.544337	+	0.838866i	$0.683219\pi$
$174$	16.4424			1.24649
$175$	−4.32244	−	14.0426i	−0.326746	−	1.06152i
$176$	−2.25961	+	3.91375i	−0.170324	+	0.295010i
$177$		−	16.3550i		−	1.22932i
$178$	−27.6868	−	15.9850i	−2.07522	−	1.19813i
$179$	3.89306	+	6.74299i	0.290981	+	0.503994i	0.974042	−	0.226367i	$-0.0726849\pi$
$179$	3.89306	+	6.74299i	0.290981	+	0.503994i	−0.683061	+	0.730362i	$0.739352\pi$
$180$	−16.2003	+	2.43688i	−1.20750	+	0.181635i
$181$	−3.86684			−0.287420			−0.143710	−	0.989620i	$-0.545903\pi$
$181$	−3.86684			−0.287420			−0.143710	+	0.989620i	$0.545903\pi$
$182$		0			0
$183$			4.88752i			0.361296i
$184$	6.79833	+	11.7751i	0.501180	+	0.868069i
$185$	−0.407104	−	2.70640i	−0.0299309	−	0.198979i
$186$	24.5582	−	42.5361i	1.80070	−	3.11890i
$187$			0.777322i			0.0568434i
$188$	−23.9184	−	13.8093i	−1.74443	−	1.00715i
$189$	4.31754	−	7.47821i	0.314055	−	0.543959i
$190$	−7.23175	−	2.84073i	−0.524646	−	0.206088i
$191$	−2.47185	+	4.28136i	−0.178857	+	0.309789i	−0.941489	−	0.337043i	$-0.890573\pi$
$191$	−2.47185	+	4.28136i	−0.178857	+	0.309789i	0.762633	+	0.646832i	$0.223906\pi$
$192$	−0.503743	+	0.290836i	−0.0363545	+	0.0209893i
$193$	−4.29240	+	2.47822i	−0.308974	+	0.178386i	−0.646467	−	0.762942i	$-0.723754\pi$
$193$	−4.29240	+	2.47822i	−0.308974	+	0.178386i	0.337493	+	0.941328i	$0.390421\pi$
$194$	−37.6357			−2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	5.84174	−	3.37273i	0.416207	−	0.240297i	−0.277246	−	0.960799i	$-0.589422\pi$
$197$	5.84174	−	3.37273i	0.416207	−	0.240297i	0.693453	+	0.720502i	$0.256088\pi$
$198$	2.28939	−	1.32178i	0.162700	−	0.0939349i
$199$	2.58772	−	4.48207i	0.183439	−	0.317725i	−0.759611	−	0.650378i	$-0.774610\pi$
$199$	2.58772	−	4.48207i	0.183439	−	0.317725i	0.943049	+	0.332653i	$0.107944\pi$
$200$	21.4917	−	23.1350i	1.51969	−	1.63589i
$201$	−8.64403	+	14.9719i	−0.609703	+	1.05604i
$202$	29.1717	+	16.8423i	2.05251	+	1.18502i
$203$			8.81566i			0.618738i
$204$	5.90364	−	10.2254i	0.413337	−	0.715921i
$205$	−22.0269	+	3.31335i	−1.53843	+	0.231414i
$206$	−13.9616	−	24.1822i	−0.972749	−	1.68485i
$207$		−	3.52022i		−	0.244673i
$208$		0			0
$209$	0.866840			0.0599606
$210$	−5.35693	−	35.6125i	−0.369663	−	2.45750i
$211$	7.00894	+	12.1398i	0.482515	+	0.835741i	0.999799	−	0.0200732i	$-0.00638994\pi$
$211$	7.00894	+	12.1398i	0.482515	+	0.835741i	−0.517283	+	0.855814i	$0.673057\pi$
$212$	2.49237	+	1.43897i	0.171177	+	0.0988289i
$213$			5.67315i			0.388718i
$214$	−13.5861	+	23.5318i	−0.928726	+	1.60860i
$215$	2.39092	−	1.90553i	0.163059	−	0.129956i
$216$	18.5582			1.26273
$217$	22.8060	+	13.1670i	1.54817	+	0.893836i
$218$	7.20968	−	4.16251i	0.488301	−	0.281921i
$219$	−11.1159	−	19.2533i	−0.751141	−	1.30101i
$220$	−2.32648	+	5.92262i	−0.156852	+	0.399303i
$221$		0			0
$222$		−	6.70825i		−	0.450228i
$223$	0.00719226	−	0.00415245i	0.000481629	−	0.000278069i	−0.499759	−	0.866164i	$-0.666578\pi$
$223$	0.00719226	−	0.00415245i	0.000481629	−	0.000278069i	0.500241	+	0.865886i	$0.333245\pi$
$224$	8.05794	+	13.9568i	0.538394	+	0.932525i
$225$	−7.81366	+	2.40512i	−0.520911	+	0.160341i
$226$	−14.0774			−0.936418
$227$	−9.75454	−	5.63179i	−0.647431	−	0.373795i	0.140040	−	0.990146i	$-0.455277\pi$
$227$	−9.75454	−	5.63179i	−0.647431	−	0.373795i	−0.787471	+	0.616351i	$0.788610\pi$
$228$	−11.4030	−	6.58351i	−0.755181	−	0.436004i
$229$	−16.5404			−1.09302			−0.546509	−	0.837453i	$-0.684043\pi$
$229$	−16.5404			−1.09302			−0.546509	+	0.837453i	$0.684043\pi$
$230$	7.63828	+	9.58393i	0.503653	+	0.631946i
$231$	2.00894	+	3.47959i	0.132179	+	0.228940i
$232$	−16.4080	+	9.47315i	−1.07724	+	0.621943i
$233$			6.94941i			0.455271i	0.973746	+	0.227636i	$0.0730995\pi$
$233$			6.94941i			0.455271i	−0.973746	+	0.227636i	$0.926900\pi$
$234$		0			0
$235$	−12.8284	−	5.03917i	−0.836833	−	0.328719i
$236$	17.0195	+	29.4787i	1.10788	+	1.91890i
$237$	1.93613	−	1.11783i	0.125765	−	0.0726107i
$238$	7.92947	+	4.57808i	0.513991	+	0.296753i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	26.7891	−	21.3506i	1.72923	−	1.37818i
$241$	9.88605	−	17.1231i	0.636817	−	1.10300i	−0.349310	−	0.937007i	$-0.613584\pi$
$241$	9.88605	−	17.1231i	0.636817	−	1.10300i	0.986127	−	0.165992i	$-0.0530825\pi$
$242$			26.9763i			1.73410i
$243$	−13.3069	−	7.68273i	−0.853637	−	0.492848i
$244$	−5.08609	−	8.80937i	−0.325604	−	0.563962i
$245$	3.61549	−	0.543852i	0.230985	−	0.0347454i
$246$	−54.5973			−3.48099
$247$		0			0
$248$			56.5962i			3.59386i
$249$	12.7510	+	22.0853i	0.808060	+	1.39960i
$250$	16.0543	−	23.5023i	1.01536	−	1.48642i
$251$	−1.83676	+	3.18136i	−0.115935	+	0.200806i	−0.918153	−	0.396226i	$-0.870320\pi$
$251$	−1.83676	+	3.18136i	−0.115935	+	0.200806i	0.802218	+	0.597031i	$0.203653\pi$
$252$		−	21.5293i		−	1.35622i
$253$	−1.18412	−	0.683650i	−0.0744447	−	0.0429807i
$254$	−21.9337	+	37.9903i	−1.37624	+	2.38372i
$255$	2.15430	−	5.48429i	0.134908	−	0.343440i
$256$	14.5669	−	25.2306i	0.910430	−	1.57691i
$257$	11.4877	−	6.63242i	0.716583	−	0.413719i	−0.0969108	−	0.995293i	$-0.530896\pi$
$257$	11.4877	−	6.63242i	0.716583	−	0.413719i	0.813494	+	0.581574i	$0.197563\pi$
$258$	6.48989	−	3.74694i	0.404043	−	0.233274i
$259$	3.59666			0.223486
$260$		0			0
$261$	4.90527			0.303628
$262$	−22.0467	+	12.7287i	−1.36205	+	0.786381i
$263$	−26.2150	+	15.1352i	−1.61649	+	0.933279i	−0.628667	+	0.777674i	$0.716399\pi$
$263$	−26.2150	+	15.1352i	−1.61649	+	0.933279i	−0.987819	+	0.155605i	$0.950267\pi$
$264$	−4.31754	+	7.47821i	−0.265726	+	0.460252i
$265$	1.33676	+	0.525096i	0.0821164	+	0.0322564i
$266$	5.10530	−	8.84265i	0.313026	−	0.542177i
$267$	−23.4147	−	13.5185i	−1.43296	−	0.827317i
$268$		−	35.9809i		−	2.19788i
$269$	−11.1248	+	19.2687i	−0.678292	+	1.17484i	0.297203	+	0.954814i	$0.403946\pi$
$269$	−11.1248	+	19.2687i	−0.678292	+	1.17484i	−0.975495	+	0.220022i	$0.929387\pi$
$270$	16.5415	−	2.48821i	1.00668	−	0.151427i
$271$	−5.91421	−	10.2437i	−0.359262	−	0.622261i	0.628575	−	0.777749i	$-0.283638\pi$
$271$	−5.91421	−	10.2437i	−0.359262	−	0.622261i	−0.987838	+	0.155488i	$0.950305\pi$
$272$			8.70953i			0.528093i
$273$		0			0
$274$	−22.0774			−1.33375
$275$	−0.708438	+	3.09541i	−0.0427204	+	0.186660i
$276$	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	$0.834901\pi$
$278$			36.4715i			2.18741i
$279$	7.32648	−	12.6898i	0.438625	−	0.759721i
$280$	25.8636	+	32.4517i	1.54565	+	1.93936i
$281$	10.5967			0.632144			0.316072	−	0.948735i	$-0.397636\pi$
$281$	10.5967			0.632144			0.316072	+	0.948735i	$0.397636\pi$
$282$	−29.2564	−	16.8912i	−1.74219	−	1.00586i
$283$	7.63458	−	4.40783i	0.453829	−	0.262018i	−0.255617	−	0.966778i	$-0.582279\pi$
$283$	7.63458	−	4.40783i	0.453829	−	0.262018i	0.709446	+	0.704760i	$0.248945\pi$
$284$	−5.90364	−	10.2254i	−0.350316	−	0.606766i
$285$	−6.11588	−	2.40240i	−0.362273	−	0.142306i
$286$		0			0
$287$		−	29.2726i		−	1.72791i
$288$	7.76591	−	4.48365i	0.457611	−	0.264202i
$289$	−7.75096	−	13.4251i	−0.455939	−	0.789710i
$290$	−13.3548	+	10.6436i	−0.784218	+	0.625013i
$291$	−31.8284			−1.86581
$292$	40.0709	+	23.1350i	2.34497	+	1.35387i
$293$	24.4675	+	14.1263i	1.42940	+	0.825267i	0.997074	−	0.0764476i	$-0.0243578\pi$
$293$	24.4675	+	14.1263i	1.42940	+	0.825267i	0.432331	+	0.901715i	$0.357691\pi$
$294$	8.96157			0.522650
$295$	10.5871	+	13.2838i	0.616403	+	0.773415i
$296$	3.86491	+	6.69422i	0.224643	+	0.389094i
$297$	−1.61621	+	0.933121i	−0.0937822	+	0.0541452i
$298$			43.6719i			2.52984i
$299$		0			0
$300$	32.8284	−	35.3386i	1.89535	−	2.04027i
$301$	2.00894	+	3.47959i	0.115793	+	0.200560i
$302$	−47.1421	+	27.2175i	−2.71272	+	1.56619i
$303$	24.6704	+	14.2435i	1.41728	+	0.818267i
$304$	9.71254			0.557052
$305$	−3.16383	−	3.96973i	−0.181160	−	0.227306i
$306$	2.54737	−	4.41217i	0.145623	−	0.252227i
$307$		−	12.7219i		−	0.726077i	−0.931774	−	0.363039i	$-0.881739\pi$
$307$		−	12.7219i		−	0.726077i	0.931774	−	0.363039i	$-0.118261\pi$
$308$	−7.24190	−	4.18112i	−0.412646	−	0.238241i
$309$	−11.8073	−	20.4508i	−0.671692	−	1.16340i
$310$	7.58818	+	50.4457i	0.430980	+	2.86513i
$311$	27.9231			1.58338			0.791688	−	0.610925i	$-0.209202\pi$
$311$	27.9231			1.58338			0.791688	+	0.610925i	$0.209202\pi$
$312$		0			0
$313$		−	24.5807i		−	1.38938i	−0.719307	−	0.694692i	$-0.755540\pi$
$313$		−	24.5807i		−	1.38938i	0.719307	−	0.694692i	$-0.244460\pi$
$314$	−23.3758	−	40.4880i	−1.31917	−	2.28487i
$315$	−1.59814	−	10.6243i	−0.0900448	−	0.598613i
$316$	−2.32648	+	4.02959i	−0.130875	+	0.226682i
$317$			0.234377i			0.0131639i	0.999978	+	0.00658196i	$0.00209512\pi$
$317$			0.234377i			0.0131639i	−0.999978	+	0.00658196i	$0.997905\pi$
$318$	3.04860	+	1.76011i	0.170957	+	0.0987022i
$319$	0.952633	−	1.65001i	0.0533372	−	0.0923828i
$320$	0.220882	−	0.562309i	0.0123477	−	0.0314340i
$321$	−11.4897	+	19.9008i	−0.641294	+	1.11075i
$322$	−13.9478	+	8.05279i	−0.777283	+	0.448764i
$323$	1.44678	−	0.835296i	0.0805008	−	0.0464771i
$324$	50.3271			2.79595
$325$		0			0
$326$	10.2106			0.565513
$327$	6.09721	−	3.52022i	0.337176	−	0.194669i
$328$	54.4831	−	31.4558i	3.00833	−	1.73686i
$329$	9.05631	−	15.6860i	0.499290	−	0.864796i
$330$	−2.84570	+	7.24440i	−0.156651	+	0.398791i
$331$	−9.16324	+	15.8712i	−0.503657	+	0.872360i	0.496334	+	0.868132i	$0.334679\pi$
$331$	−9.16324	+	15.8712i	−0.503657	+	0.872360i	−0.999991	+	0.00422829i	$0.998654\pi$
$332$	−45.9652	−	26.5380i	−2.52267	−	1.45646i
$333$		−	2.00128i		−	0.109669i
$334$	−3.74039	+	6.47855i	−0.204665	+	0.354491i
$335$	−2.67089	−	17.7559i	−0.145926	−	0.970110i
$336$	22.5092	+	38.9871i	1.22798	+	2.12692i
$337$		−	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
$340$	1.82415	+	12.1268i	0.0989283	+	0.657669i
$341$	−2.84570	−	4.92889i	−0.154103	−	0.266915i
$342$	−4.92028	−	2.84073i	−0.266059	−	0.153609i
$343$		−	15.7651i		−	0.851234i
$344$	−4.31754	+	7.47821i	−0.232786	+	0.403198i
$345$	6.45968	+	8.10511i	0.347777	+	0.436364i
$346$	3.48079			0.187128
$347$	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
$349$	−12.1632	−	21.0674i	−0.651083	−	1.12771i	−0.982860	−	0.184352i	$-0.940981\pi$
$349$	−12.1632	−	21.0674i	−0.651083	−	1.12771i	0.331777	−	0.943358i	$-0.392352\pi$
$350$	27.4039	+	25.4574i	1.46480	+	1.36075i
$351$		0			0
$352$		−	3.48301i		−	0.185645i
$353$	−23.4338	+	13.5295i	−1.24726	+	0.720104i	−0.970562	−	0.240853i	$-0.922573\pi$
$353$	−23.4338	+	13.5295i	−1.24726	+	0.720104i	−0.276696	+	0.960958i	$0.589239\pi$
$354$	20.8178	+	36.0576i	1.10646	+	1.91644i
$355$	−3.67238	−	4.60783i	−0.194910	−	0.244558i
$356$	56.2708			2.98235
$357$	6.70593	+	3.87167i	0.354916	+	0.204911i
$358$	−17.1659	−	9.91073i	−0.907245	−	0.523798i
$359$	27.0039			1.42521			0.712605	−	0.701566i	$-0.247515\pi$
$359$	27.0039			1.42521			0.712605	+	0.701566i	$0.247515\pi$
$360$	18.0570	−	14.3912i	0.951687	−	0.758484i
$361$	8.56851	+	14.8411i	0.450974	+	0.781110i
$362$	8.52512	−	4.92198i	0.448071	−	0.258694i
$363$			22.8138i			1.19742i
$364$		0			0
$365$	21.4917	+	8.44221i	1.12492	+	0.441885i
$366$	−6.22118	−	10.7754i	−0.325186	−	0.563239i
$367$	−6.01118	+	3.47055i	−0.313781	+	0.181161i	−0.648617	−	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
$369$	−16.2881			−0.847922
$370$	4.34243	+	5.44855i	0.225752	+	0.283257i
$371$	−0.943693	+	1.63452i	−0.0489941	+	0.0848603i
$372$			86.4505i			4.48225i
$373$	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
$375$	13.5770	−	19.8759i	0.701116	−	1.02639i
$376$	38.9270			2.00751
$377$		0			0
$378$			21.9827i			1.13067i
$379$	−2.58772	−	4.48207i	−0.132922	−	0.230228i	0.791880	−	0.610677i	$-0.209103\pi$
$379$	−2.58772	−	4.48207i	−0.132922	−	0.230228i	−0.924802	+	0.380449i	$0.875769\pi$
$380$	13.5234	−	2.03422i	0.693734	−	0.104353i
$381$	−18.5493	+	32.1283i	−0.950309	+	1.64598i
$382$		−	12.5854i		−	0.643923i
$383$	17.8929	+	10.3305i	0.914283	+	0.527861i	0.881807	−	0.471611i	$-0.156327\pi$
$383$	17.8929	+	10.3305i	0.914283	+	0.527861i	0.0324760	+	0.999473i	$0.489661\pi$
$384$	12.5477	−	21.7332i	0.640320	−	1.10907i
$385$	−3.88412	−	1.52574i	−0.197953	−	0.0777587i
$386$	6.30890	−	10.9273i	0.321115	−	0.556187i
$387$	1.93613	−	1.11783i	0.0984193	−	0.0568224i
$388$	57.3682	−	33.1215i	2.91243	−	1.68149i
$389$	−19.7477			−1.00125			−0.500624	−	0.865665i	$-0.666896\pi$
$389$	−19.7477			−1.00125			−0.500624	+	0.865665i	$0.666896\pi$
$390$		0			0
$391$	−2.63509			−0.133262
$392$	−8.94284	+	5.16315i	−0.451681	+	0.260778i
$393$	−18.6449	+	10.7646i	−0.940510	+	0.543004i
$394$	−8.58609	+	14.8715i	−0.432561	+	0.749218i
$395$	−0.848960	+	2.16123i	−0.0427158	+	0.108743i
$396$	−2.32648	+	4.02959i	−0.116910	+	0.202494i
$397$	−8.13113	−	4.69451i	−0.408090	−	0.235611i	0.281879	−	0.959450i	$-0.409042\pi$
$397$	−8.13113	−	4.69451i	−0.408090	−	0.235611i	−0.689969	+	0.723839i	$0.742376\pi$
$398$			13.1753i			0.660420i
$399$	4.31754	−	7.47821i	0.216148	−	0.374379i
$400$	−7.93772	+	34.6826i	−0.396886	+	1.73413i
$401$	12.2510	+	21.2193i	0.611784	+	1.05964i	0.990940	+	0.134308i	$0.0428812\pi$
$401$	12.2510	+	21.2193i	0.611784	+	1.05964i	−0.379156	+	0.925333i	$0.623786\pi$
$402$		−	44.0109i		−	2.19506i
$403$		0			0
$404$	−59.2887			−2.94972
$405$	24.8356	−	3.73583i	1.23409	−	0.185635i
$406$	−11.2212	−	19.4357i	−0.556898	−	0.964575i
$407$	−0.673180	−	0.388661i	−0.0333683	−	0.0192652i
$408$			16.6417i			0.823889i
$409$	−18.0582	+	31.2778i	−0.892922	+	1.54659i	−0.0565671	+	0.998399i	$0.518015\pi$
$409$	−18.0582	+	31.2778i	−0.892922	+	1.54659i	−0.836355	+	0.548188i	$0.815318\pi$
$410$	44.3448	−	35.3423i	2.19003	−	1.74543i
$411$	−18.6708			−0.920965
$412$	42.5633	+	24.5739i	2.09694	+	1.21067i
$413$	−19.3324	+	11.1616i	−0.951288	+	0.549226i
$414$	4.48079	+	7.76095i	0.220219	+	0.381430i
$415$	−24.6530	−	9.68401i	−1.21017	−	0.475370i
$416$		0			0
$417$			30.8439i			1.51043i
$418$	−1.91110	+	1.10337i	−0.0934749	+	0.0539678i
$419$	−3.43342	−	5.94686i	−0.167734	−	0.290523i	0.769889	−	0.638178i	$-0.220311\pi$
$419$	−3.43342	−	5.94686i	−0.167734	−	0.290523i	−0.937623	+	0.347655i	$0.886978\pi$
$420$	39.5066	+	49.5698i	1.92772	+	2.41876i
$421$	−33.9795			−1.65606			−0.828029	−	0.560686i	$-0.810538\pi$
$421$	−33.9795			−1.65606			−0.828029	+	0.560686i	$0.810538\pi$
$422$	−30.9049	−	17.8429i	−1.50443	−	0.868580i
$423$	−8.72810	−	5.03917i	−0.424375	−	0.245013i
$424$	−4.05631			−0.196992
$425$	1.80037	+	5.84897i	0.0873308	+	0.283717i
$426$	−7.22118	−	12.5075i	−0.349867	−	0.605988i
$427$	5.77729	−	3.33552i	0.279582	−	0.161417i
$428$		−	47.8261i		−	2.31176i
$429$		0			0
$430$	−2.84570	+	7.24440i	−0.137232	+	0.349356i
$431$	−8.12482	−	14.0726i	−0.391359	−	0.677853i	0.601270	−	0.799046i	$-0.294661\pi$
$431$	−8.12482	−	14.0726i	−0.391359	−	0.677853i	−0.992629	+	0.121193i	$0.961328\pi$
$432$	−18.1089	+	10.4552i	−0.871265	+	0.503025i
$433$	0.221929	+	0.128130i	0.0106652	+	0.00615756i	0.505323	−	0.862930i	$-0.331373\pi$
$433$	0.221929	+	0.128130i	0.0106652	+	0.00615756i	−0.494658	+	0.869088i	$0.664707\pi$
$434$	−67.0396			−3.21800
$435$	−11.2941	+	9.00126i	−0.541510	+	0.431577i
$436$	−7.32648	+	12.6898i	−0.350875	+	0.607733i
$437$			2.93855i			0.140570i
$438$	49.0138	+	28.2981i	2.34197	+	1.35214i
$439$	−3.79833	−	6.57890i	−0.181284	−	0.313994i	0.761034	−	0.648712i	$-0.224692\pi$
$439$	−3.79833	−	6.57890i	−0.181284	−	0.313994i	−0.942318	+	0.334718i	$0.891359\pi$
$440$	−1.33407	−	8.86879i	−0.0635991	−	0.422803i
$441$	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	$-0.0327428\pi$
$444$	5.90364	+	10.2254i	0.280174	+	0.485276i
$445$	27.7687	−	4.17703i	1.31636	−	0.198010i
$446$	−0.0105711	+	0.0183096i	−0.000500554	+	0.000866986i
$447$			36.9332i			1.74688i
$448$	0.687565	+	0.396966i	0.0324844	+	0.0187549i
$449$	−1.64403	+	2.84754i	−0.0775865	+	0.134384i	−0.902208	−	0.431301i	$-0.858055\pi$
$449$	−1.64403	+	2.84754i	−0.0775865	+	0.134384i	0.824622	+	0.565685i	$0.191388\pi$
$450$	14.1652	−	15.2483i	0.667753	−	0.718811i
$451$	−3.16324	+	5.47890i	−0.148951	+	0.257991i
$452$	21.4583	−	12.3889i	1.00931	−	0.582727i
$453$	−39.8680	+	23.0178i	−1.87316	+	1.08147i
$454$	28.6741			1.34574
$455$		0			0
$456$	18.5582			0.869069
$457$	13.3594	−	7.71304i	0.624925	−	0.360801i	−0.153859	−	0.988093i	$-0.549170\pi$
$457$	13.3594	−	7.71304i	0.624925	−	0.360801i	0.778784	+	0.627292i	$0.215837\pi$
$458$	36.4661	−	21.0537i	1.70395	−	0.983775i
$459$	−1.79833	+	3.11480i	−0.0839389	+	0.145386i
$460$	−20.0774	−	7.88669i	−0.936116	−	0.367719i
$461$	12.9424	−	22.4168i	0.602786	−	1.04406i	−0.389611	−	0.920979i	$-0.627391\pi$
$461$	12.9424	−	22.4168i	0.602786	−	1.04406i	0.992397	−	0.123076i	$-0.0392760\pi$
$462$	−8.85812	−	5.11424i	−0.412117	−	0.237936i
$463$			7.04045i			0.327197i	0.986527	+	0.163599i	$0.0523102\pi$
$463$			7.04045i			0.327197i	−0.986527	+	0.163599i	$0.947690\pi$
$464$	10.6738	−	18.4876i	0.495519	−	0.858265i
$465$	6.41730	+	42.6618i	0.297595	+	1.97840i
$466$	−8.84570	−	15.3212i	−0.409769	−	0.709741i
$467$			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
$470$	34.6967	−	5.21916i	1.60044	−	0.240742i
$471$	−19.7688	−	34.2406i	−0.910900	−	1.57773i
$472$	−41.5486	−	23.9881i	−1.91243	−	1.10414i
$473$		−	0.868356i		−	0.0399271i
$474$	−2.84570	+	4.92889i	−0.130707	+	0.226392i
$475$	6.52255	−	2.00771i	0.299275	−	0.0921199i
$476$	−16.1159			−0.738670
$477$	0.909493	+	0.525096i	0.0416428	+	0.0240425i
$478$	−8.81870	+	5.09148i	−0.403358	+	0.232879i
$479$	9.73876	+	16.8680i	0.444975	+	0.770720i	0.998051	−	0.0624114i	$-0.0198791\pi$
$479$	9.73876	+	16.8680i	0.444975	+	0.770720i	−0.553075	+	0.833131i	$0.686546\pi$
$480$	−9.65297	+	24.5739i	−0.440596	+	1.12164i
$481$		0			0
$482$			50.3346i			2.29268i
$483$	−11.7957	+	6.81023i	−0.536721	+	0.309876i
$484$	−23.7407	−	41.1201i	−1.07912	−	1.86909i
$485$	25.8516	−	20.6034i	1.17386	−	0.935552i
$486$	39.1165			1.77436
$487$	−27.9935	−	16.1620i	−1.26851	−	0.732372i	−0.293800	−	0.955867i	$-0.594920\pi$
$487$	−27.9935	−	16.1620i	−1.26851	−	0.732372i	−0.974705	+	0.223495i	$0.928253\pi$
$488$	12.4163	+	7.16858i	0.562062	+	0.324506i
$489$	8.63509			0.390492
$490$	−7.27874	+	5.80107i	−0.328820	+	0.262066i
$491$	−14.3354	−	24.8297i	−0.646949	−	1.12055i	−0.983848	−	0.179007i	$-0.942711\pi$
$491$	−14.3354	−	24.8297i	−0.646949	−	1.12055i	0.336899	−	0.941541i	$-0.390622\pi$
$492$	83.2227	−	48.0487i	3.75197	−	2.16620i
$493$		−	3.67187i		−	0.165373i
$494$		0			0
$495$	−0.848960	+	2.16123i	−0.0381579	+	0.0971401i
$496$	−31.8847	−	55.2260i	−1.43167	−	2.47972i
$497$	6.70593	−	3.87167i	0.300802	−	0.173668i
$498$	−56.2235	−	32.4606i	−2.51943	−	1.45460i
$499$	28.9616			1.29650			0.648249	−	0.761428i	$-0.275502\pi$
$499$	28.9616			1.29650			0.648249	+	0.761428i	$0.275502\pi$
$500$	−3.78816	+	49.9533i	−0.169412	+	2.23398i
$501$	−3.16324	+	5.47890i	−0.141323	+	0.244779i
$502$		−	9.35181i		−	0.417392i
$503$	−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
$505$	−29.2579	+	4.40105i	−1.30196	+	0.195844i
$506$	3.48079			0.154740
$507$		0			0
$508$		−	77.2116i		−	3.42571i
$509$	−10.5563	−	18.2841i	−0.467900	−	0.810427i	0.531427	−	0.847104i	$-0.321656\pi$
$509$	−10.5563	−	18.2841i	−0.467900	−	0.810427i	−0.999327	+	0.0366773i	$0.988323\pi$
$510$	2.23125	+	14.8332i	0.0988015	+	0.656826i
$511$	−15.1722	+	26.2790i	−0.671178	+	1.16251i
$512$			50.8542i			2.24746i
$513$	3.47351	+	2.00543i	0.153359	+	0.0885420i
$514$	−16.8844	+	29.2447i	−0.744740	+	1.28993i
$515$	22.8284	+	8.96730i	1.00594	+	0.395147i
$516$	−6.59503	+	11.4229i	−0.290330	+	0.502866i
$517$	−3.39010	+	1.95728i	−0.149097	+	0.0860809i
$518$	−7.92947	+	4.57808i	−0.348401	+	0.201149i
$519$	2.94369			0.129214
$520$		0			0
$521$	0.673516			0.0295073			0.0147536	−	0.999891i	$-0.495304\pi$
$521$	0.673516			0.0295073			0.0147536	+	0.999891i	$0.495304\pi$
$522$	−10.8145	+	6.24376i	−0.473339	+	0.273282i
$523$	25.8618	−	14.9313i	1.13086	−	0.652900i	0.186706	−	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
$525$	23.1754	+	21.5293i	1.01146	+	0.939614i
$526$	38.5304	−	66.7366i	1.68000	−	2.90985i
$527$	−9.49907	−	5.48429i	−0.413786	−	0.238899i
$528$		−	9.72953i		−	0.423423i
$529$	−9.18246	+	15.9045i	−0.399237	+	0.691499i
$530$	−3.61549	+	0.543852i	−0.157047	+	0.0236234i
$531$	6.21061	+	10.7571i	0.269517	+	0.466818i
$532$			17.9718i			0.779177i
$533$		0			0
$534$	68.8290			2.97852
$535$	−3.55018	−	23.6014i	−0.153488	−	1.02038i
$536$	25.3566	+	43.9189i	1.09524	+	1.89701i
$537$	−14.5171	−	8.38148i	−0.626461	−	0.361687i
$538$		−	56.6418i		−	2.44200i
$539$	0.519213	−	0.899304i	0.0223641	−	0.0387358i
$540$	−23.0244	+	18.3502i	−0.990813	+	0.789666i
$541$	−6.28806			−0.270345			−0.135172	−	0.990822i	$-0.543159\pi$
$541$	−6.28806			−0.270345			−0.135172	+	0.990822i	$0.543159\pi$
$542$	26.0778	+	15.0560i	1.12014	+	0.646712i
$543$	7.20968	−	4.16251i	0.309397	−	0.178630i
$544$	−3.35627	−	5.81323i	−0.143899	−	0.249240i
$545$	−2.67352	+	6.80607i	−0.114521	+	0.291540i
$546$		0			0
$547$		−	3.03789i		−	0.129891i	−0.997889	−	0.0649454i	$-0.979313\pi$
$547$		−	3.03789i		−	0.129891i	0.997889	−	0.0649454i	$-0.0206873\pi$
$548$	33.6527	−	19.4294i	1.43757	−	0.829983i
$549$	−1.85597	−	3.21464i	−0.0792109	−	0.137197i
$550$	−2.37818	−	7.72612i	−0.101406	−	0.329443i
$551$	−4.09473			−0.174442
$552$	−25.3508	−	14.6363i	−1.07900	−	0.622962i
$553$	−2.64265	−	1.52574i	−0.112377	−	0.0648809i
$554$	42.7304			1.81544
$555$	3.67238	+	4.60783i	0.155884	+	0.195591i
$556$	−32.0970	−	55.5936i	−1.36121	−	2.35769i
$557$	−17.9264	+	10.3498i	−0.759566	+	0.438536i	−0.829140	−	0.559041i	$-0.811169\pi$
$557$	−17.9264	+	10.3498i	−0.759566	+	0.438536i	0.0695738	+	0.997577i	$0.477836\pi$
$558$			37.3026i			1.57915i
$559$		0			0
$560$	−43.5198	−	17.0952i	−1.83905	−	0.722402i
$561$	−0.836758	−	1.44931i	−0.0353279	−	0.0611898i
$562$	−23.3622	+	13.4882i	−0.985475	+	0.568964i
$563$	9.49188	+	5.48014i	0.400035	+	0.230960i	0.686499	−	0.727131i	$-0.259147\pi$
$563$	9.49188	+	5.48014i	0.400035	+	0.230960i	−0.286464	+	0.958091i	$0.592480\pi$
$564$	59.4608			2.50375
$565$	9.66965	−	7.70660i	0.406805	−	0.324219i
$566$	−11.2212	+	19.4357i	−0.471661	+	0.816941i
$567$			33.0051i			1.38608i
$568$	14.4122	+	8.32087i	0.604721	+	0.349136i
$569$	21.3566	+	36.9907i	0.895314	+	1.55073i	0.833416	+	0.552647i	$0.186382\pi$
$569$	21.3566	+	36.9907i	0.895314	+	1.55073i	0.0618981	+	0.998082i	$0.480285\pi$
$570$	16.5415	−	2.48821i	0.692845	−	0.104220i
$571$	−23.6145			−0.988238			−0.494119	−	0.869394i	$-0.664509\pi$
$571$	−23.6145			−0.988238			−0.494119	+	0.869394i	$0.664509\pi$
$572$		0			0
$573$		−	10.6434i		−	0.444635i
$574$	37.2602	+	64.5366i	1.55521	+	2.69370i
$575$	−10.4933	−	2.40158i	−0.437601	−	0.100153i
$576$	0.220882	−	0.382579i	0.00920343	−	0.0159408i
$577$			18.3646i			0.764530i	0.924053	+	0.382265i	$0.124856\pi$
$577$			18.3646i			0.764530i	−0.924053	+	0.382265i	$0.875144\pi$
$578$	34.1767	+	19.7319i	1.42156	+	0.820740i
$579$	5.33542	−	9.24123i	0.221733	−	0.384052i
$580$	10.9897	−	27.9770i	0.456324	−	1.16168i
$581$	17.4039	−	30.1445i	0.722037	−	1.25060i
$582$	70.1713	−	40.5134i	2.90869	−	1.67934i
$583$	0.353259	−	0.203954i	0.0146305	−	0.00844691i
$584$	−65.2151			−2.69862
$585$		0			0
$586$	−71.9237			−2.97114
$587$	0.608726	−	0.351448i	0.0251248	−	0.0145058i	−0.487385	−	0.873187i	$-0.662049\pi$
$587$	0.608726	−	0.351448i	0.0251248	−	0.0145058i	0.512510	+	0.858681i	$0.328716\pi$
$588$	−13.6601	+	7.88669i	−0.563335	+	0.325242i
$589$	−6.11588	+	10.5930i	−0.252000	+	0.436477i
$590$	−40.2496	−	15.8106i	−1.65705	−	0.650912i
$591$	−7.26124	+	12.5768i	−0.298687	+	0.517342i
$592$	−7.54267	−	4.35476i	−0.310002	−	0.178980i
$593$		−	37.1593i		−	1.52595i	−0.646428	−	0.762975i	$-0.723738\pi$
$593$		−	37.1593i		−	1.52595i	0.646428	−	0.762975i	$-0.276262\pi$
$594$	2.37548	−	4.11446i	0.0974672	−	0.168818i
$595$	−7.95291	+	1.19630i	−0.326037	+	0.0490434i
$596$	−38.4337	−	66.5692i	−1.57431	−	2.72678i
$597$			11.1423i			0.456026i
$598$		0			0
$599$	15.6914			0.641133			0.320567	−	0.947226i	$-0.396127\pi$
$599$	15.6914			0.641133			0.320567	+	0.947226i	$0.396127\pi$
$600$	−15.1670	+	66.2698i	−0.619190	+	2.70546i
$601$	−6.00193	−	10.3956i	−0.244824	−	0.424047i	0.717258	−	0.696807i	$-0.245397\pi$
$601$	−6.00193	−	10.3956i	−0.244824	−	0.424047i	−0.962082	+	0.272760i	$0.912063\pi$
$602$	−8.85812	−	5.11424i	−0.361030	−	0.208441i
$603$		−	13.1298i		−	0.534687i
$604$	47.9059	−	82.9754i	1.94926	−	3.37622i
$605$	−14.7680	−	18.5298i	−0.600405	−	0.753342i
$606$	−72.5204			−2.94594
$607$	−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
$609$	−9.48973	−	16.4367i	−0.384543	−	0.666048i
$610$	12.0282	+	4.72482i	0.487006	+	0.191302i
$611$		0			0
$612$			8.96730i			0.362482i
$613$	−14.9684	+	8.64201i	−0.604568	+	0.349047i	−0.770836	−	0.637033i	$-0.780161\pi$
$613$	−14.9684	+	8.64201i	−0.604568	+	0.349047i	0.166269	+	0.986081i	$0.446828\pi$
$614$	16.1933	+	28.0477i	0.653509	+	1.13191i
$615$	37.5023	−	29.8889i	1.51224	−	1.20524i
$616$	11.7861			0.474877
$617$	22.9229	+	13.2345i	0.922841	+	0.532803i	0.884540	−	0.466464i	$-0.154472\pi$
$617$	22.9229	+	13.2345i	0.922841	+	0.532803i	0.0383009	+	0.999266i	$0.487805\pi$
$618$	52.0624	+	30.0582i	2.09426	+	1.20912i
$619$	−31.0039			−1.24615			−0.623075	−	0.782162i	$-0.714117\pi$
$619$	−31.0039			−1.24615			−0.623075	+	0.782162i	$0.714117\pi$
$620$	−55.9618	−	70.2165i	−2.24748	−	2.81996i
$621$	−3.16324	−	5.47890i	−0.126937	−	0.219861i
$622$	−61.5615	+	35.5425i	−2.46839	+	1.42513i
$623$			36.9030i			1.47849i
$624$		0			0
$625$	1.83869	+	24.9323i	0.0735475	+	0.997292i
$626$	31.2881	+	54.1925i	1.25052	+	2.16597i
$627$	−1.61621	+	0.933121i	−0.0645453	+	0.0372653i
$628$	71.2635	+	41.1440i	2.84372	+	1.64182i
$629$	−1.49807			−0.0597320
$630$	17.0467	+	21.3889i	0.679159	+	0.852156i
$631$	−10.3566	+	17.9381i	−0.412288	+	0.714104i	−0.995140	−	0.0984745i	$-0.968604\pi$
$631$	−10.3566	+	17.9381i	−0.412288	+	0.714104i	0.582851	+	0.812579i	$0.301937\pi$
$632$		−	6.55812i		−	0.260868i
$633$	−26.1362	−	15.0897i	−1.03882	−	0.599763i
$634$	−0.298331	−	0.516725i	−0.0118482	−	0.0205218i
$635$	−5.73149	−	38.1026i	−0.227447	−	1.51206i
$636$	−6.19599			−0.245687
$637$		0			0
$638$			4.85031i			0.192026i
$639$	−2.15430	−	3.73136i	−0.0852229	−	0.147610i
$640$	3.87707	+	25.7745i	0.153254	+	1.01883i
$641$	−10.5947	+	18.3506i	−0.418467	+	0.724806i	−0.995785	−	0.0917132i	$-0.970766\pi$
$641$	−10.5947	+	18.3506i	−0.418467	+	0.724806i	0.577319	+	0.816519i	$0.304099\pi$
$642$		−	58.4997i		−	2.30880i
$643$	9.98843	+	5.76682i	0.393905	+	0.227421i	0.683851	−	0.729622i	$-0.260304\pi$
$643$	9.98843	+	5.76682i	0.393905	+	0.227421i	−0.289946	+	0.957043i	$0.593637\pi$
$644$	14.1738	−	24.5498i	0.558526	−	0.967396i
$645$	−2.40660	+	6.12658i	−0.0947598	+	0.241234i
$646$	−2.12645	+	3.68311i	−0.0836639	+	0.144910i
$647$	−30.1779	+	17.4232i	−1.18641	+	0.684977i	−0.957490	−	0.288467i	$-0.906854\pi$
$647$	−30.1779	+	17.4232i	−1.18641	+	0.684977i	−0.228925	+	0.973444i	$0.573521\pi$
$648$	−61.4301	+	35.4667i	−2.41320	+	1.39326i
$649$	4.82456			0.189380
$650$		0			0
$651$	−56.6953			−2.22206
$652$	−15.5641	+	8.98591i	−0.609535	+	0.351915i
$653$	−19.3324	+	11.1616i	−0.756537	+	0.436787i	−0.828051	−	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
$655$	8.17544	−	20.8125i	0.319441	−	0.813214i
$656$	−35.4427	+	61.3885i	−1.38380	+	2.39682i
$657$	14.6223	+	8.44221i	0.570471	+	0.329362i
$658$			46.1100i			1.79755i
$659$	−0.433420	+	0.750705i	−0.0168836	+	0.0292433i	−0.874344	−	0.485307i	$-0.838708\pi$
$659$	−0.433420	+	0.750705i	−0.0168836	+	0.0292433i	0.857460	+	0.514550i	$0.172041\pi$
$660$	−2.03778	−	13.5470i	−0.0793205	−	0.527318i
$661$	6.65430	+	11.5256i	0.258822	+	0.448293i	0.965927	−	0.258816i	$-0.0833322\pi$
$661$	6.65430	+	11.5256i	0.258822	+	0.448293i	−0.707104	+	0.707109i	$0.749999\pi$
$662$		−	46.6544i		−	1.81328i
$663$		0			0
$664$	74.8079			2.90311
$665$	1.33407	+	8.86879i	0.0517328	+	0.343917i
$666$	2.54737	+	4.41217i	0.0987085	+	0.170968i
$667$	5.59346	+	3.22939i	0.216580	+	0.125042i
$668$		−	13.1670i		−	0.509448i
$669$	−0.00893993	+	0.0154844i	−0.000345637	+	0.000598662i
$670$	28.4894	+	35.7464i	1.10064	+	1.38100i
$671$	−1.44176			−0.0556587
$672$	−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	$0.299446\pi$
$674$	27.1056	+	46.9483i	1.04407	+	1.80838i
$675$	−10.0000	+	10.7646i	−0.384900	+	0.414331i
$676$		0			0
$677$		−	4.80479i		−	0.184663i	−0.995728	−	0.0923316i	$-0.970568\pi$
$677$		−	4.80479i		−	0.184663i	0.995728	−	0.0923316i	$-0.0294320\pi$
$678$	26.2472	−	15.1539i	1.00802	−	0.581980i
$679$	21.7215	+	37.6227i	0.833594	+	1.44383i
$680$	−10.7726	−	13.5167i	−0.413112	−	0.518341i
$681$	24.2496			0.929248
$682$	12.5477	+	7.24440i	0.480475	+	0.277403i
$683$	−10.1866	−	5.88126i	−0.389781	−	0.225040i	0.292284	−	0.956331i	$-0.405585\pi$
$683$	−10.1866	−	5.88126i	−0.389781	−	0.225040i	−0.682065	+	0.731291i	$0.738918\pi$
$684$	10.0000			0.382360
$685$	15.1648	−	12.0861i	0.579416	−	0.461788i
$686$	20.0669	+	34.7569i	0.766157	+	1.32702i
$687$	30.8393	−	17.8051i	1.17659	−	0.679306i
$688$		−	9.72953i		−	0.370935i
$689$		0			0
$690$	−24.5582	−	9.64680i	−0.934916	−	0.367247i
$691$	2.43342	+	4.21481i	0.0925717	+	0.160339i	0.908593	−	0.417684i	$-0.137158\pi$
$691$	2.43342	+	4.21481i	0.0925717	+	0.160339i	−0.816021	+	0.578022i	$0.803825\pi$
$692$	−5.30577	+	3.06329i	−0.201695	+	0.116449i
$693$	−2.64265	−	1.52574i	−0.100386	−	0.0579579i
$694$	−9.71254			−0.368683
$695$	−19.9661	−	25.0519i	−0.757356	−	0.950272i
$696$	20.3950	−	35.3252i	0.773070	−	1.33900i
$697$			12.1925i			0.461825i
$698$	53.6320	+	30.9644i	2.03000	+	1.17202i
$699$	−7.48079	−	12.9571i	−0.282949	−	0.490083i
$700$	−64.1758	−	14.6877i	−2.42562	−	0.555145i
$701$	21.3828			0.807617			0.403808	−	0.914844i	$-0.367686\pi$
$701$	21.3828			0.807617			0.403808	+	0.914844i	$0.367686\pi$
$702$		0			0
$703$			1.67059i			0.0630076i
$704$	−0.0857934	−	0.148599i	−0.00323346	−	0.00560052i
$705$	29.3429	−	4.41383i	1.10512	−	0.166235i
$706$	34.4427	−	59.6564i	1.29627	−	2.24520i
$707$		−	38.8822i		−	1.46232i
$708$	−63.4654	−	36.6417i	−2.38517	−	1.37708i
$709$	13.0582	−	22.6175i	0.490412	−	0.849419i	−0.509527	−	0.860455i	$-0.670180\pi$
$709$	13.0582	−	22.6175i	0.490412	−	0.849419i	0.999939	+	0.0110357i	$0.00351286\pi$
$710$	13.9616	+	5.48429i	0.523969	+	0.205822i
$711$	−0.848960	+	1.47044i	−0.0318385	+	0.0551459i
$712$	−68.6851	+	39.6554i	−2.57408	+	1.48615i
$713$	16.7087	−	9.64680i	0.625748	−	0.361276i
$714$	−19.7125			−0.737723
$715$		0			0
$716$	34.8880			1.30383
$717$	−7.45795	+	4.30585i	−0.278522	+	0.160805i
$718$	−59.5347	+	34.3724i	−2.22182	+	1.28277i
$719$	18.3387	−	31.7635i	0.683918	−	1.18458i	−0.289858	−	0.957070i	$-0.593608\pi$
$719$	18.3387	−	31.7635i	0.683918	−	1.18458i	0.973776	−	0.227510i	$-0.0730586\pi$
$720$	−9.51220	+	24.2156i	−0.354499	+	0.902462i
$721$	−16.1159	+	27.9135i	−0.600187	+	1.03955i
$722$	−37.7815	−	21.8132i	−1.40608	−	0.811803i
$723$			42.5679i			1.58312i
$724$	−8.66324	+	15.0052i	−0.321967	+	0.557663i
$725$	3.34648	−	14.6219i	0.124285	−	0.543045i
$726$	−29.0390	−	50.2971i	−1.07774	−	1.86670i
$727$		−	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
$730$	−58.1279	+	8.74375i	−2.15141	+	0.323621i
$731$	−0.836758	−	1.44931i	−0.0309486	−	0.0536046i
$732$	18.9659	+	10.9500i	0.701000	+	0.404723i
$733$			31.7811i			1.17386i	0.809637	+	0.586931i	$0.199664\pi$
$733$			31.7811i			1.17386i	−0.809637	+	0.586931i	$0.800336\pi$
$734$	8.83513	−	15.3029i	0.326110	−	0.564840i
$735$	−6.15561	+	4.90595i	−0.227053	+	0.180959i
$736$	11.8073			0.435222
$737$	−4.41654	−	2.54989i	−0.162685	−	0.0939265i
$738$	35.9099	−	20.7326i	1.32186	−	0.763176i
$739$	17.0685	+	29.5635i	0.627875	+	1.08751i	0.987977	+	0.154599i	$0.0494085\pi$
$739$	17.0685	+	29.5635i	0.627875	+	1.08751i	−0.360102	+	0.932913i	$0.617258\pi$
$740$	−11.4142	−	4.48365i	−0.419595	−	0.164822i
$741$		0			0
$742$		−	4.80479i		−	0.176390i
$743$	2.70254	−	1.56031i	0.0991465	−	0.0572423i	−0.449607	−	0.893227i	$-0.648436\pi$
$743$	2.70254	−	1.56031i	0.0991465	−	0.0572423i	0.548753	+	0.835984i	$0.315103\pi$
$744$	−60.9237	−	105.523i	−2.23357	−	3.86866i
$745$	−23.9079	−	29.9978i	−0.875917	−	1.09903i
$746$	−5.88798			−0.215574
$747$	−16.7732	−	9.68401i	−0.613699	−	0.354320i
$748$	3.01638	+	1.74151i	0.110290	+	0.0636758i
$749$	31.3649			1.14605
$750$	−4.63359	+	61.1016i	−0.169195	+	2.23112i
$751$	−0.742024	−	1.28522i	−0.0270769	−	0.0468985i	0.852169	−	0.523266i	$-0.175287\pi$
$751$	−0.742024	−	1.28522i	−0.0270769	−	0.0468985i	−0.879246	+	0.476367i	$0.841953\pi$
$752$	−37.9845	+	21.9304i	−1.38515	+	0.799718i
$753$		−	7.90881i		−	0.288213i
$754$		0			0
$755$	17.4814	−	44.5030i	0.636213	−	1.61963i
$756$	−19.3460	−	33.5082i	−0.703607	−	1.21868i
$757$	4.41654	−	2.54989i	0.160522	−	0.0926774i	−0.417587	−	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
$759$	2.94369			0.106849
$760$	−15.0733	+	12.0132i	−0.546766	+	0.435766i
$761$	−14.8931	+	25.7955i	−0.539873	+	0.935088i	0.459037	+	0.888417i	$0.348194\pi$
$761$	−14.8931	+	25.7955i	−0.539873	+	0.935088i	−0.998910	+	0.0466707i	$0.985139\pi$
$762$		−	94.4433i		−	3.42132i
$763$	−8.32215	−	4.80479i	−0.301282	−	0.173945i
$764$	11.0758	+	19.1839i	0.400709	+	0.694048i
$765$	0.665652	+	4.42521i	0.0240667	+	0.159994i
$766$	−52.5973			−1.90042
$767$		0			0
$768$			62.7228i			2.26331i
$769$	−9.54930	−	16.5399i	−0.344356	−	0.596443i	0.640880	−	0.767641i	$-0.278570\pi$
$769$	−9.54930	−	16.5399i	−0.344356	−	0.596443i	−0.985237	+	0.171198i	$0.945236\pi$
$770$	10.5053	−	1.58023i	0.378584	−	0.0569476i
$771$	−14.2791	+	24.7322i	−0.514250	+	0.890707i
$772$			22.2088i			0.799311i
$773$	−42.6350	−	24.6153i	−1.53347	−	0.885351i	−0.999198	−	0.0400400i	$-0.987251\pi$
$773$	−42.6350	−	24.6153i	−1.53347	−	0.885351i	−0.534275	−	0.845311i	$-0.679415\pi$
$774$	−2.84570	+	4.92889i	−0.102286	+	0.177165i
$775$	−32.8284	−	30.4966i	−1.17923	−	1.09547i
$776$	−46.6831	+	80.8574i	−1.67582	+	2.90261i
$777$	−6.70593	+	3.87167i	−0.240574	+	0.138895i
$778$	43.5373	−	25.1362i	1.56089	−	0.901178i
$779$	13.5967			0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$	5.80951	−	3.35412i	0.207748	−	0.119943i
$783$	7.63458	−	4.40783i	0.272838	−	0.157523i
$784$	5.81754	−	10.0763i	0.207769	−	0.359867i
$785$	38.2215	+	15.0139i	1.36418	+	0.535869i
$786$	27.4039	−	47.4650i	0.977466	−	1.69302i
$787$	−8.47263	−	4.89168i	−0.302017	−	0.174369i	0.341332	−	0.939943i	$-0.389122\pi$
$787$	−8.47263	−	4.89168i	−0.302017	−	0.174369i	−0.643349	+	0.765573i	$0.722455\pi$
$788$		−	30.2250i		−	1.07672i
$789$	32.5851	−	56.4390i	1.16006	−	2.00928i
$790$	−0.879284	−	5.84543i	−0.0312835	−	0.207971i
$791$	8.12482	+	14.0726i	0.288885	+	0.500364i
$792$		−	6.55812i		−	0.233033i
$793$		0			0
$794$	23.9020			0.848250
$795$	−3.05762	+	0.459934i	−0.108442	+	0.0163122i
$796$	−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	$0.761283\pi$
$798$			21.9827i			0.778178i
$799$	−3.77211	+	6.53348i	−0.133448	+	0.231138i
$800$	−8.06708	−	26.2080i	−0.285214	−	0.926592i
$801$	20.5338			0.725527
$802$	−54.0188	−	31.1878i	−1.90747	−	1.10128i
$803$	5.67950	−	3.27906i	0.200425	−	0.115715i
$804$	38.7320	+	67.0859i	1.36597	+	2.36594i
$805$	5.17218	−	13.1670i	0.182295	−	0.464077i
$806$		0			0
$807$		−	47.9018i		−	1.68622i
$808$	72.3688	−	41.7821i	2.54592	−	1.46989i
$809$	−15.9212	−	27.5764i	−0.559760	−	0.969533i	−0.997516	−	0.0704392i	$-0.977560\pi$
$809$	−15.9212	−	27.5764i	−0.559760	−	0.969533i	0.437756	−	0.899094i	$-0.355773\pi$
$810$	−49.9991	+	39.8487i	−1.75679	+	1.40014i
$811$	−13.3470			−0.468678			−0.234339	−	0.972155i	$-0.575293\pi$
$811$	−13.3470			−0.468678			−0.234339	+	0.972155i	$0.575293\pi$
$812$	34.2089	+	19.7505i	1.20050	+	0.693108i
$813$	22.0539	+	12.7328i	0.773465	+	0.446560i
$814$	1.97886			0.0693589
$815$	−7.01356	+	5.58973i	−0.245674	+	0.195800i
$816$	−9.37548	−	16.2388i	−0.328208	−	0.568472i
$817$	−1.61621	+	0.933121i	−0.0565441	+	0.0326458i
$818$		−	91.9431i		−	3.21472i
$819$		0			0
$820$	−36.4917	+	92.8982i	−1.27434	+	3.24415i
$821$	5.83676	+	10.1096i	0.203704	+	0.352826i	0.949719	−	0.313103i	$-0.101369\pi$
$821$	5.83676	+	10.1096i	0.203704	+	0.352826i	−0.746015	+	0.665929i	$0.768035\pi$
$822$	41.1631	−	23.7656i	1.43573	−	0.828919i
$823$	28.0867	+	16.2159i	0.979041	+	0.565249i	0.901980	−	0.431777i	$-0.142113\pi$
$823$	28.0867	+	16.2159i	0.979041	+	0.565249i	0.0770602	+	0.997026i	$0.475447\pi$
$824$	−69.2714			−2.41318
$825$	−2.01122	−	6.53396i	−0.0700216	−	0.227483i
$826$	28.4145	−	49.2154i	0.988667	−	1.71242i
$827$		−	27.3319i		−	0.950425i	−0.879871	−	0.475212i	$-0.842371\pi$
$827$		−	27.3319i		−	0.950425i	0.879871	−	0.475212i	$-0.157629\pi$
$828$	−13.6601	−	7.88669i	−0.474723	−	0.274081i
$829$	1.77018	+	3.06604i	0.0614808	+	0.106488i	0.895128	−	0.445810i	$-0.147084\pi$
$829$	1.77018	+	3.06604i	0.0614808	+	0.106488i	−0.833647	+	0.552298i	$0.813751\pi$
$830$	66.6783	−	10.0299i	2.31444	−	0.348143i
$831$	36.1370			1.25358
$832$		0			0
$833$		−	2.00128i		−	0.0693402i
$834$	−39.2602	−	68.0007i	−1.35947	−	2.35467i
$835$	−0.977401	−	6.49770i	−0.0338244	−	0.224862i
$836$	1.94206	−	3.36375i	0.0671676	−	0.116338i
$837$		−	26.3341i		−	0.910238i
$838$	15.1391	+	8.74059i	0.522973	+	0.301939i
$839$	−22.3950	+	38.7893i	−0.773161	+	1.33915i	0.162661	+	0.986682i	$0.447992\pi$
$839$	−22.3950	+	38.7893i	−0.773161	+	1.33915i	−0.935822	+	0.352472i	$0.885341\pi$
$840$	−83.1555	−	32.6646i	−2.86914	−	1.12704i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	74.9136	−	43.2514i	2.58169	−	1.49054i
$843$	−19.7574	+	11.4069i	−0.680479	+	0.392875i
$844$	62.8111			2.16205
$845$		0			0
$846$	25.6568			0.882100
$847$	26.9670	−	15.5694i	0.926598	−	0.534972i
$848$	3.95810	−	2.28521i	0.135922	−	0.0784744i
$849$	−9.48973	+	16.4367i	−0.325687	+	0.564106i
$850$	−11.4142	−	10.6034i	−0.391504	−	0.363695i
$851$	1.31754	−	2.28205i	0.0451648	−	0.0782278i
$852$	22.0145	+	12.7101i	0.754205	+	0.435440i
$853$		−	31.3732i		−	1.07420i	−0.843519	−	0.537099i	$-0.819520\pi$
$853$		−	31.3732i		−	1.07420i	0.843519	−	0.537099i	$-0.180480\pi$
$854$	−8.49136	+	14.7075i	−0.290568	+	0.503279i
$855$	4.93483	−	0.742310i	0.168768	−	0.0253865i
$856$	33.7042	+	58.3774i	1.15199	+	1.99530i
$857$		−	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	$0.921639\pi$
$860$	−2.03778	−	13.5470i	−0.0694877	−	0.461950i
$861$	31.5109	+	54.5784i	1.07389	+	1.86003i
$862$	35.8251	+	20.6837i	1.22021	+	0.704488i
$863$			32.8011i			1.11656i	0.829651	+	0.558282i	$0.188539\pi$
$863$			32.8011i			1.11656i	−0.829651	+	0.558282i	$0.811461\pi$
$864$	8.05794	−	13.9568i	0.274137	−	0.474819i
$865$	−2.39092	+	1.90553i	−0.0812936	+	0.0647901i
$866$	−0.652374			−0.0221686
$867$	28.9032	+	16.6873i	0.981603	+	0.566729i
$868$	102.189	−	58.9986i	3.46851	−	2.00254i
$869$	0.329747	+	0.571138i	0.0111859	+	0.0193745i
$870$	13.4424	−	34.2207i	0.455739	−	1.16019i
$871$		0			0
$872$		−	20.6526i		−	0.699385i
$873$	20.9343	−	12.0864i	0.708518	−	0.409063i
$874$	−3.74039	−	6.47855i	−0.126521	−	0.219140i
$875$	−32.7599	−	2.48432i	−1.10749	−	0.0839854i
$876$	−99.6157			−3.36570
$877$	−31.2333	−	18.0325i	−1.05467	−	0.608916i	−0.130719	−	0.991419i	$-0.541729\pi$
$877$	−31.2333	−	18.0325i	−1.05467	−	0.608916i	−0.923954	+	0.382504i	$0.875062\pi$
$878$	16.7482	+	9.66956i	0.565223	+	0.326332i
$879$	−60.8257			−2.05160
$880$	6.29819	+	7.90248i	0.212312	+	0.266393i
$881$	23.0198	+	39.8715i	0.775557	+	1.34330i	0.934481	+	0.356013i	$0.115864\pi$
$881$	23.0198	+	39.8715i	0.775557	+	1.34330i	−0.158924	+	0.987291i	$0.550802\pi$
$882$	−5.89423	+	3.40304i	−0.198469	+	0.114586i
$883$		−	0.802236i		−	0.0269974i	−0.999909	−	0.0134987i	$-0.995703\pi$
$883$		−	0.802236i		−	0.0269974i	0.999909	−	0.0134987i	$-0.00429690\pi$
$884$		0			0
$885$	−34.0390	−	13.3710i	−1.14421	−	0.449461i
$886$	5.50193	+	9.52962i	0.184841	+	0.320154i
$887$	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
$889$	50.6363			1.69829
$890$	−55.9041	+	44.5549i	−1.87391	+	1.49348i
$891$	3.56658	−	6.17750i	0.119485	−	0.206954i
$892$		−	0.0372125i		−	0.00124597i
$893$	7.28589	+	4.20651i	0.243813	+	0.140766i
$894$	−47.0112	−	81.4257i	−1.57229	−	2.72328i
$895$	17.2166	−	2.58977i	0.575488	−	0.0865664i
$896$	−34.2529			−1.14431
$897$		0			0
$898$		−	8.37054i		−	0.279328i
$899$	13.4424	+	23.2829i	0.448328	+	0.776527i
$900$	−8.17266	+	35.7091i	−0.272422	+	1.19030i
$901$	0.393064	−	0.680808i	0.0130949	−	0.0226810i
$902$		−	16.1056i		−	0.536257i
$903$	−7.49129	−	4.32510i	−0.249295	−	0.143930i
$904$	−17.4616	+	30.2443i	−0.580763	+	1.00591i
$905$	−3.16131	+	8.04788i	−0.105086	+	0.267521i
$906$	58.5973	−	101.493i	1.94676	−	3.37189i
$907$	−26.3583	+	15.2180i	−0.875213	+	0.505305i	−0.869077	−	0.494677i	$-0.835286\pi$
$907$	−26.3583	+	15.2180i	−0.875213	+	0.505305i	−0.00613601	+	0.999981i	$0.501953\pi$
$908$	−43.7080	+	25.2348i	−1.45050	+	0.837447i
$909$	−21.6351			−0.717591
$910$		0			0
$911$	43.6145			1.44501			0.722507	−	0.691363i	$-0.242990\pi$
$911$	43.6145			1.44501			0.722507	+	0.691363i	$0.242990\pi$
$912$	−18.1089	+	10.4552i	−0.599646	+	0.346206i
$913$	−6.51492	+	3.76139i	−0.215612	+	0.124484i
$914$	−19.6354	+	34.0095i	−0.649481	+	1.12493i
$915$	10.1722	+	3.99577i	0.336282	+	0.132096i
$916$	−37.0569	+	64.1844i	−1.22439	+	2.12071i
$917$	25.4486	+	14.6928i	0.840387	+	0.485198i
$918$		−	9.15616i		−	0.302198i
$919$	−18.5109	+	32.0618i	−0.610617	+	1.05762i	0.380519	+	0.924773i	$0.375745\pi$
$919$	−18.5109	+	32.0618i	−0.610617	+	1.05762i	−0.991137	+	0.132847i	$0.957588\pi$
$920$	30.0648	−	4.52243i	0.991208	−	0.149100i
$921$	13.6947	+	23.7198i	0.451254	+	0.781595i
$922$			65.8957i			2.17016i
$923$		0			0
$924$	18.0033			0.592264
$925$	−5.96554	−	1.36532i	−0.196146	−	0.0448914i
$926$	−8.96157	−	15.5219i	−0.294496	−	0.510081i
$927$	15.5318	+	8.96730i	0.510132	+	0.294525i
$928$			16.4529i			0.540092i
$929$	2.38412	−	4.12942i	0.0782206	−	0.135482i	−0.824262	−	0.566209i	$-0.808409\pi$
$929$	2.38412	−	4.12942i	0.0782206	−	0.135482i	0.902482	+	0.430727i	$0.141743\pi$
$930$	−68.4510	−	85.8871i	−2.24460	−	2.81635i
$931$	−2.23175			−0.0731427
$932$	26.9670	+	15.5694i	0.883334	+	0.509993i
$933$	−52.0624	+	30.0582i	−1.70445	+	0.984062i
$934$	−23.9443	−	41.4727i	−0.783481	−	1.35703i
$935$	1.61780	+	0.635495i	0.0529079	+	0.0207829i
$936$		0			0
$937$			43.6264i			1.42521i	0.701565	+	0.712606i	$0.252485\pi$
$937$			43.6264i			1.42521i	−0.701565	+	0.712606i	$0.747515\pi$
$938$	−52.0230	+	30.0355i	−1.69861	+	0.980693i
$939$	26.4602	+	45.8305i	0.863497	+	1.49562i
$940$	−48.2951	+	38.4906i	−1.57521	+	1.25543i
$941$	−18.2675			−0.595504			−0.297752	−	0.954643i	$-0.596237\pi$
$941$	−18.2675			−0.595504			−0.297752	+	0.954643i	$0.596237\pi$
$942$	87.1677	+	50.3263i	2.84008	+	1.63972i
$943$	−18.5732	−	10.7233i	−0.604828	−	0.349197i
$944$	54.0569			1.75940
$945$	−12.0343	−	15.0997i	−0.391475	−	0.491192i
$946$	1.10530	+	1.91444i	0.0359365	+	0.0622439i
$947$	17.3057	−	9.99146i	0.562360	−	0.324679i	−0.191732	−	0.981447i	$-0.561410\pi$
$947$	17.3057	−	9.99146i	0.562360	−	0.324679i	0.754092	+	0.656769i	$0.228077\pi$
$948$		−	10.0175i		−	0.325353i
$949$		0			0
$950$	−11.8246	+	12.7287i	−0.383639	+	0.412973i
$951$	−0.252298	−	0.436993i	−0.00818132	−	0.0141705i
$952$	19.6713	−	11.3572i	0.637551	−	0.368090i
$953$	−34.5228	−	19.9317i	−1.11830	−	0.645652i	−0.177335	−	0.984150i	$-0.556748\pi$
$953$	−34.5228	−	19.9317i	−1.11830	−	0.645652i	−0.940967	+	0.338498i	$0.890081\pi$
$954$	−2.67352			−0.0865583
$955$	6.88976	+	8.64475i	0.222948	+	0.279737i
$956$	8.96157	−	15.5219i	0.289838	−	0.502014i
$957$			4.10190i			0.132596i
$958$	−42.9416	−	24.7923i	−1.38738	−	0.801004i
$959$	12.7420	+	22.0698i	0.411461	+	0.712672i
$960$	0.193472	+	1.28619i	0.00624428	+	0.0415116i
$961$	49.3098			1.59064
$962$		0			0
$963$		−	17.4523i		−	0.562392i
$964$	−44.2973	−	76.7252i	−1.42672	−	2.47115i
$965$	1.64858	+	10.9596i	0.0530696	+	0.352803i
$966$	17.3371	−	30.0287i	0.557811	−	0.966156i
$967$			43.8607i			1.41047i	0.708975	+	0.705233i	$0.249158\pi$
$967$			43.8607i			1.41047i	−0.708975	+	0.705233i	$0.750842\pi$
$968$	57.9566	+	33.4613i	1.86280	+	1.07549i
$969$	−1.79833	+	3.11480i	−0.0577707	+	0.100062i
$970$	−30.7688	+	78.3294i	−0.987928	+	2.51501i
$971$	−30.4897	+	52.8098i	−0.978462	+	1.69475i	−0.310459	+	0.950587i	$0.600483\pi$
$971$	−30.4897	+	52.8098i	−0.978462	+	1.69475i	−0.668002	+	0.744159i	$0.732850\pi$
$972$	−59.6253	+	34.4247i	−1.91248	+	1.10417i
$973$	36.4589	−	21.0496i	1.16882	−	0.674818i
$974$	82.2887			2.63670
$975$		0			0
$976$	−16.1543			−0.517087
$977$	−44.4875	+	25.6849i	−1.42328	+	0.821731i	−0.996578	−	0.0826604i	$-0.973658\pi$
$977$	−44.4875	+	25.6849i	−1.42328	+	0.821731i	−0.426703	+	0.904392i	$0.640325\pi$
$978$	−19.0376	+	10.9913i	−0.608754	+	0.351464i
$979$	3.98780	−	6.90707i	0.127451	−	0.220751i
$980$	5.98973	−	15.2483i	0.191335	−	0.487088i
$981$	−2.67352	+	4.63066i	−0.0853588	+	0.147846i
$982$	63.2099	+	36.4942i	2.01711	+	1.16458i
$983$			37.3026i			1.18977i	0.803811	+	0.594885i	$0.202802\pi$
$983$			37.3026i			1.18977i	−0.803811	+	0.594885i	$0.797198\pi$
$984$	−67.7221	+	117.298i	−2.15890	+	3.73933i
$985$	−2.24363	−	14.9155i	−0.0714880	−	0.475248i
$986$	4.67381	+	8.09528i	0.148845	+	0.257806i
$987$			38.9951i			1.24123i
$988$		0			0
$989$	2.94369			0.0936040
$990$	−0.879284	−	5.84543i	−0.0279455	−	0.185780i
$991$	25.7810	+	44.6541i	0.818962	+	1.41848i	0.906448	+	0.422318i	$0.138783\pi$
$991$	25.7810	+	44.6541i	0.818962	+	1.41848i	−0.0874859	+	0.996166i	$0.527883\pi$
$992$	42.5633	+	24.5739i	1.35139	+	0.780223i
$993$		−	39.4556i		−	1.25208i
$994$	−9.85627	+	17.0716i	−0.312622	+	0.541477i
$995$	−7.21274	−	9.05000i	−0.228659	−	0.286904i
$996$	114.269			3.62074
$997$	−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
$999$	−1.79833	−	3.11480i	−0.0568967	−	0.0985479i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.20467 + 1.27287i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(2.54486 + 1.46928i) q^{7} +6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +O(q^{10})\)	\(q+(-2.20467 + 1.27287i) q^{2} +(-1.86449 + 1.07646i) q^{3} +(2.24039 - 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.74039 - 4.74650i) q^{6} +(2.54486 + 1.46928i) q^{7} +6.31544i q^{8} +(0.817544 - 1.41603i) q^{9} +(0.846746 + 5.62912i) q^{10} +(-0.317544 - 0.550003i) q^{11} +9.64680i q^{12} -7.48079 q^{14} +(0.716091 + 4.76053i) q^{15} +(-3.55794 - 6.16253i) q^{16} +(-1.05998 - 0.611979i) q^{17} +4.16251i q^{18} +(-0.682456 + 1.18205i) q^{19} +(-6.24464 - 7.83529i) q^{20} -6.32648 q^{21} +(1.40016 + 0.808385i) q^{22} +(1.86449 - 1.07646i) q^{23} +(-6.79833 - 11.7751i) q^{24} +(-3.66324 - 3.40304i) q^{25} -2.93855i q^{27} +(11.4030 - 6.58351i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-7.63828 - 9.58393i) q^{30} +8.96157 q^{31} +(4.74954 + 2.74215i) q^{32} +(1.18412 + 0.683650i) q^{33} +3.11588 q^{34} +(5.13847 - 4.09531i) q^{35} +(-3.66324 - 6.34492i) q^{36} +(1.05998 - 0.611979i) q^{37} -3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(-4.98079 - 8.62698i) q^{41} +(13.9478 - 8.05279i) q^{42} +(1.18412 + 0.683650i) q^{43} -2.84570 q^{44} +(-2.27874 - 2.85918i) q^{45} +(-2.74039 + 4.74650i) q^{46} -6.16379i q^{47} +(13.2675 + 7.65998i) q^{48} +(0.817544 + 1.41603i) q^{49} +(12.4079 + 2.83976i) q^{50} +2.63509 q^{51} +0.642285i q^{53} +(3.74039 + 6.47855i) q^{54} +(-1.40430 + 0.211239i) q^{55} +(-9.27912 + 16.0719i) q^{56} -2.93855i q^{57} +(-6.61402 - 3.81861i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(20.0774 + 7.88669i) q^{60} +(1.13509 - 1.96603i) q^{61} +(-19.7574 + 11.4069i) q^{62} +(4.16107 - 2.40240i) q^{63} +0.270178 q^{64} -3.48079 q^{66} +(6.95421 - 4.01502i) q^{67} +(-4.74954 + 2.74215i) q^{68} +(-2.31754 + 4.01410i) q^{69} +(-6.11588 + 15.5694i) q^{70} +(1.31754 - 2.28205i) q^{71} +(8.94284 + 5.16315i) q^{72} +10.3263i q^{73} +(-1.55794 + 2.69843i) q^{74} +(10.4933 + 2.40158i) q^{75} +(3.05794 + 5.29650i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(-15.7346 + 2.36683i) q^{80} +(5.61588 + 9.72698i) q^{81} +(21.9620 + 12.6798i) q^{82} -11.8452i q^{83} +(-14.1738 + 24.5498i) q^{84} +(-2.14026 + 1.70576i) q^{85} -3.48079 q^{86} +(-5.59346 - 3.22939i) q^{87} +(3.47351 - 2.00543i) q^{88} +(6.27912 + 10.8758i) q^{89} +(8.66324 + 3.40304i) q^{90} -9.64680i q^{92} +(-16.7087 + 9.64680i) q^{93} +(7.84570 + 13.5891i) q^{94} +(1.90220 + 2.38674i) q^{95} -11.8073 q^{96} +(12.8031 + 7.39190i) q^{97} +(-3.60484 - 2.08125i) q^{98} -1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 + 4 * q^15 - 16 * q^16 - 12 * q^19 + q^20 + 8 * q^21 - 32 * q^24 - 2 * q^25 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 29 * q^45 - 10 * q^46 + 6 * q^49 + 31 * q^50 + 24 * q^51 + 22 * q^54 - 26 * q^55 - 16 * q^56 + 4 * q^59 + 96 * q^60 + 6 * q^61 - 12 * q^64 + 4 * q^66 - 24 * q^69 - 20 * q^70 + 12 * q^71 + 8 * q^74 + 2 * q^75 + 10 * q^76 - 104 * q^79 - 33 * q^80 + 14 * q^81 - 90 * q^84 - 21 * q^85 + 4 * q^86 - 20 * q^89 + 62 * q^90 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

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