LMFDB - Embedded newform 352.3.bd.a.3.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,3,Mod(3,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 15, 32])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	352.bd (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.59130530548$
Analytic rank:	$0$
Dimension:	$1504$
Relative dimension:	$94$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	352.3
Dual form			352.3.bd.a.235.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.84943 - 0.761328i) q^{2} +(0.815381 + 0.0641719i) q^{3} +(2.84076 + 2.81604i) q^{4} +(1.73462 - 7.22523i) q^{5} +(-1.45913 - 0.739454i) q^{6} +(-10.4618 + 5.33054i) q^{7} +(-3.10984 - 7.37081i) q^{8} +(-8.22847 - 1.30326i) q^{9} +(-8.70883 + 12.0419i) q^{10} +(8.20714 + 7.32413i) q^{11} +(2.13559 + 2.47844i) q^{12} +(3.15722 + 13.1508i) q^{13} +(23.4066 - 1.89360i) q^{14} +(1.87804 - 5.78000i) q^{15} +(0.139816 + 15.9994i) q^{16} +(3.26132 - 4.48883i) q^{17} +(14.2257 + 8.67485i) q^{18} +(-2.18501 + 27.7631i) q^{19} +(25.2742 - 15.6404i) q^{20} +(-8.87240 + 3.67507i) q^{21} +(-9.60243 - 19.7938i) q^{22} +(-2.50983 + 2.50983i) q^{23} +(-2.06271 - 6.20959i) q^{24} +(-26.9198 - 13.7163i) q^{25} +(4.17300 - 26.7250i) q^{26} +(-13.7834 - 3.30911i) q^{27} +(-44.7304 - 14.3180i) q^{28} +(20.7600 - 24.3068i) q^{29} +(-7.87377 + 9.25988i) q^{30} +(17.5965 + 24.2195i) q^{31} +(11.9222 - 29.6961i) q^{32} +(6.22194 + 6.49863i) q^{33} +(-9.44905 + 5.81882i) q^{34} +(20.3671 + 84.8352i) q^{35} +(-19.7050 - 26.8740i) q^{36} +(19.6744 - 1.54841i) q^{37} +(25.1779 - 49.6824i) q^{38} +(1.73043 + 10.9255i) q^{39} +(-58.6502 + 9.68373i) q^{40} +(-29.5162 + 57.9287i) q^{41} +(19.2068 - 0.0419602i) q^{42} +(10.4299 + 25.1800i) q^{43} +(2.68943 + 43.9177i) q^{44} +(-23.6897 + 57.1919i) q^{45} +(6.55256 - 2.73095i) q^{46} +(-9.86630 - 30.3654i) q^{47} +(-0.912708 + 13.0546i) q^{48} +(52.2326 - 71.8920i) q^{49} +(39.3436 + 45.8622i) q^{50} +(2.94728 - 3.45082i) q^{51} +(-28.0642 + 46.2490i) q^{52} +(-27.5736 + 44.9961i) q^{53} +(22.9721 + 16.6137i) q^{54} +(67.1548 - 46.5938i) q^{55} +(71.8249 + 60.5346i) q^{56} +(-3.56323 + 22.4973i) q^{57} +(-56.8996 + 29.1486i) q^{58} +(6.84365 + 86.9568i) q^{59} +(21.6118 - 11.1310i) q^{60} +(20.0798 + 32.7672i) q^{61} +(-14.1044 - 58.1888i) q^{62} +(93.0314 - 30.2277i) q^{63} +(-44.6578 + 45.8441i) q^{64} +100.494 q^{65} +(-6.55943 - 16.7557i) q^{66} +(13.7871 - 33.2850i) q^{67} +(21.9054 - 3.56765i) q^{68} +(-2.20753 + 1.88541i) q^{69} +(26.9199 - 172.403i) q^{70} +(-14.8968 - 94.0548i) q^{71} +(15.9831 + 64.7034i) q^{72} +(-70.7779 + 36.0631i) q^{73} +(-37.5652 - 12.1150i) q^{74} +(-21.0697 - 12.9115i) q^{75} +(-84.3893 + 72.7153i) q^{76} +(-124.903 - 32.8749i) q^{77} +(5.11758 - 21.5233i) q^{78} +(-112.664 + 81.8551i) q^{79} +(115.842 + 26.7427i) q^{80} +(60.2832 + 19.5872i) q^{81} +(98.6907 - 84.6634i) q^{82} +(11.0343 + 18.0063i) q^{83} +(-35.5535 - 14.5451i) q^{84} +(-26.7756 - 31.3502i) q^{85} +(-0.119083 - 54.5090i) q^{86} +(18.4871 - 18.4871i) q^{87} +(28.4619 - 83.2702i) q^{88} +(-70.0253 + 70.0253i) q^{89} +(87.3541 - 87.7366i) q^{90} +(-103.131 - 120.751i) q^{91} +(-14.1976 + 0.0620341i) q^{92} +(12.7936 + 20.8773i) q^{93} +(-4.87100 + 63.6700i) q^{94} +(196.805 + 63.9458i) q^{95} +(11.6268 - 23.4486i) q^{96} +(9.24533 - 6.71713i) q^{97} +(-151.334 + 93.1928i) q^{98} +(-57.9869 - 70.9624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1504 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} + 64 q^{12} - 12 q^{13} + 4 q^{14} - 24 q^{15} - 52 q^{16} + 168 q^{18} - 12 q^{19}+ \cdots - 236 q^{99}+O(q^{100}) $ 1504 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 + 64 * q^12 - 12 * q^13 + 4 * q^14 - 24 * q^15 - 52 * q^16 + 168 * q^18 - 12 * q^19 - 92 * q^20 - 32 * q^21 - 164 * q^22 + 96 * q^23 - 12 * q^24 - 12 * q^25 + 288 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 + 20 * q^30 + 8 * q^32 - 32 * q^33 + 56 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 348 * q^40 - 12 * q^41 + 188 * q^42 - 224 * q^43 + 168 * q^44 + 40 * q^45 + 52 * q^46 - 24 * q^47 - 12 * q^48 - 12 * q^50 - 84 * q^51 - 860 * q^52 - 492 * q^53 - 648 * q^54 - 272 * q^55 + 1016 * q^56 - 12 * q^57 - 12 * q^58 - 140 * q^59 - 28 * q^60 - 12 * q^61 - 44 * q^62 - 156 * q^64 - 64 * q^65 + 560 * q^66 + 288 * q^67 + 476 * q^68 - 12 * q^69 + 324 * q^70 + 244 * q^71 - 1272 * q^72 - 12 * q^73 + 1044 * q^74 - 964 * q^75 - 32 * q^76 - 240 * q^77 + 688 * q^78 - 24 * q^79 + 1388 * q^80 - 132 * q^82 - 12 * q^83 - 1244 * q^84 - 212 * q^85 - 948 * q^86 - 32 * q^87 - 692 * q^88 - 32 * q^89 - 1044 * q^90 - 588 * q^91 - 316 * q^92 - 84 * q^93 + 2096 * q^94 - 1100 * q^96 - 24 * q^97 - 64 * q^98 - 236 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.84943	−	0.761328i	−0.924713	−	0.380664i
$2$	−1.84943	−	0.761328i	−0.924713	−	0.380664i
$3$	0.815381	+	0.0641719i	0.271794	+	0.0213906i	0.213624	−	0.976916i	$-0.431473\pi$
$3$	0.815381	+	0.0641719i	0.271794	+	0.0213906i	0.0581701	+	0.998307i	$0.481473\pi$
$4$	2.84076	+	2.81604i	0.710190	+	0.704010i
$5$	1.73462	−	7.22523i	0.346925	−	1.44505i	−0.477279	−	0.878752i	$-0.658377\pi$
$5$	1.73462	−	7.22523i	0.346925	−	1.44505i	0.824203	−	0.566294i	$-0.191623\pi$
$6$	−1.45913	−	0.739454i	−0.243189	−	0.123242i
$7$	−10.4618	+	5.33054i	−1.49454	+	0.761506i	−0.994524	−	0.104511i	$-0.966672\pi$
$7$	−10.4618	+	5.33054i	−1.49454	+	0.761506i	−0.500015	+	0.866017i	$0.666672\pi$
$8$	−3.10984	−	7.37081i	−0.388730	−	0.921352i
$9$	−8.22847	−	1.30326i	−0.914274	−	0.144807i
$10$	−8.70883	+	12.0419i	−0.870883	+	1.20419i
$11$	8.20714	+	7.32413i	0.746103	+	0.665830i
$11$	8.20714	+	7.32413i	0.746103	+	0.665830i
$12$	2.13559	+	2.47844i	0.177966	+	0.206537i
$13$	3.15722	+	13.1508i	0.242863	+	1.01160i	0.951896	+	0.306421i	$0.0991317\pi$
$13$	3.15722	+	13.1508i	0.242863	+	1.01160i	−0.709033	+	0.705175i	$0.750868\pi$
$14$	23.4066	−	1.89360i	1.67190	−	0.135257i
$15$	1.87804	−	5.78000i	0.125202	−	0.385333i
$16$	0.139816	+	15.9994i	0.00873849	+	0.999962i
$17$	3.26132	−	4.48883i	0.191843	−	0.264049i	−0.702250	−	0.711930i	$-0.747821\pi$
$17$	3.26132	−	4.48883i	0.191843	−	0.264049i	0.894093	+	0.447881i	$0.147821\pi$
$18$	14.2257	+	8.67485i	0.790319	+	0.481936i
$19$	−2.18501	+	27.7631i	−0.115000	+	1.46122i	0.620773	+	0.783990i	$0.286819\pi$
$19$	−2.18501	+	27.7631i	−0.115000	+	1.46122i	−0.735773	+	0.677228i	$0.763181\pi$
$20$	25.2742	−	15.6404i	1.26371	−	0.782018i
$21$	−8.87240	+	3.67507i	−0.422495	+	0.175003i
$22$	−9.60243	−	19.7938i	−0.436474	−	0.899717i
$23$	−2.50983	+	2.50983i	−0.109123	+	0.109123i	−0.759560	−	0.650437i	$-0.774586\pi$
$23$	−2.50983	+	2.50983i	−0.109123	+	0.109123i	0.650437	+	0.759560i	$0.274586\pi$
$24$	−2.06271	−	6.20959i	−0.0859461	−	0.258733i
$25$	−26.9198	−	13.7163i	−1.07679	−	0.548654i
$26$	4.17300	−	26.7250i	0.160500	−	1.02789i
$27$	−13.7834	−	3.30911i	−0.510498	−	0.122560i
$28$	−44.7304	−	14.3180i	−1.59751	−	0.511358i
$29$	20.7600	−	24.3068i	0.715862	−	0.838167i	−0.276566	−	0.960995i	$-0.589196\pi$
$29$	20.7600	−	24.3068i	0.715862	−	0.838167i	0.992428	+	0.122828i	$0.0391963\pi$
$30$	−7.87377	+	9.25988i	−0.262459	+	0.308663i
$31$	17.5965	+	24.2195i	0.567628	+	0.781273i	0.992271	−	0.124088i	$-0.0396005\pi$
$31$	17.5965	+	24.2195i	0.567628	+	0.781273i	−0.424643	+	0.905361i	$0.639601\pi$
$32$	11.9222	−	29.6961i	0.372569	−	0.928004i
$33$	6.22194	+	6.49863i	0.188544	+	0.196928i
$34$	−9.44905	+	5.81882i	−0.277913	+	0.171142i
$35$	20.3671	+	84.8352i	0.581918	+	2.42386i
$36$	−19.7050	−	26.8740i	−0.547362	−	0.746499i
$37$	19.6744	−	1.54841i	0.531740	−	0.0418488i	0.190253	−	0.981735i	$-0.439069\pi$
$37$	19.6744	−	1.54841i	0.531740	−	0.0418488i	0.341487	+	0.939886i	$0.389069\pi$
$38$	25.1779	−	49.6824i	0.662576	−	1.30743i
$39$	1.73043	+	10.9255i	0.0443699	+	0.280141i
$40$	−58.6502	+	9.68373i	−1.46626	+	0.242093i
$41$	−29.5162	+	57.9287i	−0.719906	+	1.41290i	0.183024	+	0.983108i	$0.441411\pi$
$41$	−29.5162	+	57.9287i	−0.719906	+	1.41290i	−0.902930	+	0.429787i	$0.858589\pi$
$42$	19.2068	−	0.0419602i	0.457305	−	0.000999053i
$43$	10.4299	+	25.1800i	0.242555	+	0.585580i	0.997535	−	0.0701676i	$-0.0223534\pi$
$43$	10.4299	+	25.1800i	0.242555	+	0.585580i	−0.754980	+	0.655748i	$0.772353\pi$
$44$	2.68943	+	43.9177i	0.0611233	+	0.998130i
$45$	−23.6897	+	57.1919i	−0.526437	+	1.27093i
$46$	6.55256	−	2.73095i	0.142447	−	0.0593684i
$47$	−9.86630	−	30.3654i	−0.209921	−	0.646071i	−0.999475	−	0.0323903i	$-0.989688\pi$
$47$	−9.86630	−	30.3654i	−0.209921	−	0.646071i	0.789554	−	0.613681i	$-0.210312\pi$
$48$	−0.912708	+	13.0546i	−0.0190147	+	0.271970i
$49$	52.2326	−	71.8920i	1.06597	−	1.46718i
$50$	39.3436	+	45.8622i	0.786873	+	0.917244i
$51$	2.94728	−	3.45082i	0.0577898	−	0.0676631i
$52$	−28.0642	+	46.2490i	−0.539696	+	0.889403i
$53$	−27.5736	+	44.9961i	−0.520257	+	0.848982i	−0.999589	−	0.0286511i	$-0.990879\pi$
$53$	−27.5736	+	44.9961i	−0.520257	+	0.848982i	0.479332	+	0.877633i	$0.340879\pi$
$54$	22.9721	+	16.6137i	0.425410	+	0.307661i
$55$	67.1548	−	46.5938i	1.22100	−	0.847160i
$56$	71.8249	+	60.5346i	1.28259	+	1.08098i
$57$	−3.56323	+	22.4973i	−0.0625127	+	0.394690i
$58$	−56.8996	+	29.1486i	−0.981028	+	0.502561i
$59$	6.84365	+	86.9568i	0.115994	+	1.47384i	0.729406	+	0.684081i	$0.239797\pi$
$59$	6.84365	+	86.9568i	0.115994	+	1.47384i	−0.613412	+	0.789763i	$0.710203\pi$
$60$	21.6118	−	11.1310i	0.360196	−	0.185516i
$61$	20.0798	+	32.7672i	0.329177	+	0.537168i	0.973821	−	0.227315i	$-0.0729946\pi$
$61$	20.0798	+	32.7672i	0.329177	+	0.537168i	−0.644645	+	0.764482i	$0.722995\pi$
$62$	−14.1044	−	58.1888i	−0.227490	−	0.938529i
$63$	93.0314	−	30.2277i	1.47669	−	0.479806i
$64$	−44.6578	+	45.8441i	−0.697778	+	0.716314i
$65$	100.494			1.54606
$66$	−6.55943	−	16.7557i	−0.0993854	−	0.253874i
$67$	13.7871	−	33.2850i	0.205778	−	0.496791i	−0.786972	−	0.616988i	$-0.788353\pi$
$67$	13.7871	−	33.2850i	0.205778	−	0.496791i	0.992750	+	0.120197i	$0.0383526\pi$
$68$	21.9054	−	3.56765i	0.322138	−	0.0524654i
$69$	−2.20753	+	1.88541i	−0.0319932	+	0.0273248i
$70$	26.9199	−	172.403i	0.384570	−	2.46289i
$71$	−14.8968	−	94.0548i	−0.209814	−	1.32472i	−0.837581	−	0.546314i	$-0.816031\pi$
$71$	−14.8968	−	94.0548i	−0.209814	−	1.32472i	0.627766	−	0.778402i	$-0.283969\pi$
$72$	15.9831	+	64.7034i	0.221988	+	0.898659i
$73$	−70.7779	+	36.0631i	−0.969560	+	0.494016i	−0.865693	−	0.500576i	$-0.833122\pi$
$73$	−70.7779	+	36.0631i	−0.969560	+	0.494016i	−0.103867	+	0.994591i	$0.533122\pi$
$74$	−37.5652	−	12.1150i	−0.507637	−	0.163716i
$75$	−21.0697	−	12.9115i	−0.280930	−	0.172154i
$76$	−84.3893	+	72.7153i	−1.11039	+	0.956781i
$77$	−124.903	−	32.8749i	−1.62211	−	0.426947i
$78$	5.11758	−	21.5233i	0.0656100	−	0.275940i
$79$	−112.664	+	81.8551i	−1.42613	+	1.03614i	−0.435404	+	0.900235i	$0.643394\pi$
$79$	−112.664	+	81.8551i	−1.42613	+	1.03614i	−0.990722	+	0.135906i	$0.956606\pi$
$80$	115.842	+	26.7427i	1.44802	+	0.334284i
$81$	60.2832	+	19.5872i	0.744237	+	0.241817i
$82$	98.6907	−	84.6634i	1.20355	−	1.03248i
$83$	11.0343	+	18.0063i	0.132943	+	0.216944i	0.912184	−	0.409781i	$-0.134395\pi$
$83$	11.0343	+	18.0063i	0.132943	+	0.216944i	−0.779241	+	0.626725i	$0.784395\pi$
$84$	−35.5535	−	14.5451i	−0.423256	−	0.173156i
$85$	−26.7756	−	31.3502i	−0.315007	−	0.368826i
$86$	−0.119083	−	54.5090i	−0.00138469	−	0.633826i
$87$	18.4871	−	18.4871i	0.212496	−	0.212496i
$88$	28.4619	−	83.2702i	0.323431	−	0.946252i
$89$	−70.0253	+	70.0253i	−0.786801	+	0.786801i	−0.980968	−	0.194167i	$-0.937800\pi$
$89$	−70.0253	+	70.0253i	−0.786801	+	0.786801i	0.194167	+	0.980968i	$0.437800\pi$
$90$	87.3541	−	87.7366i	0.970601	−	0.974851i
$91$	−103.131	−	120.751i	−1.13330	−	1.32693i
$92$	−14.1976	+	0.0620341i	−0.154322	+	0.000674284i
$93$	12.7936	+	20.8773i	0.137566	+	0.224487i
$94$	−4.87100	+	63.6700i	−0.0518192	+	0.677340i
$95$	196.805	+	63.9458i	2.07163	+	0.673114i
$96$	11.6268	−	23.4486i	0.121112	−	0.244256i
$97$	9.24533	−	6.71713i	0.0953127	−	0.0692487i	−0.539108	−	0.842237i	$-0.681239\pi$
$97$	9.24533	−	6.71713i	0.0953127	−	0.0692487i	0.634421	+	0.772988i	$0.281239\pi$
$98$	−151.334	+	93.1928i	−1.54422	+	0.950947i
$99$	−57.9869	−	70.9624i	−0.585726	−	0.716792i
$100$	−37.8470	−	114.772i	−0.378470	−	1.14772i
$101$	−52.8980	−	32.4159i	−0.523742	−	0.320950i	0.235374	−	0.971905i	$-0.424369\pi$
$101$	−52.8980	−	32.4159i	−0.523742	−	0.320950i	−0.759116	+	0.650955i	$0.774369\pi$
$102$	−8.07798	+	4.13819i	−0.0791959	+	0.0405705i
$103$	−81.5375	+	41.5454i	−0.791627	+	0.403354i	−0.802549	−	0.596586i	$-0.796523\pi$
$103$	−81.5375	+	41.5454i	−0.791627	+	0.403354i	0.0109222	+	0.999940i	$0.496523\pi$
$104$	87.1133	−	64.1680i	0.837628	−	0.617000i
$105$	11.1629	+	70.4800i	0.106314	+	0.671238i
$106$	85.2522	−	62.2243i	0.804266	−	0.587022i
$107$	41.6218	−	35.5484i	0.388989	−	0.332228i	−0.433350	−	0.901226i	$-0.642669\pi$
$107$	41.6218	−	35.5484i	0.388989	−	0.332228i	0.822339	+	0.568998i	$0.192669\pi$
$108$	−29.8368	−	48.2151i	−0.276267	−	0.446436i
$109$	34.2137	−	82.5992i	0.313887	−	0.757791i	−0.685666	−	0.727916i	$-0.740489\pi$
$109$	34.2137	−	82.5992i	0.313887	−	0.757791i	0.999554	−	0.0298750i	$-0.00951093\pi$
$110$	−159.671	+	35.0450i	−1.45156	+	0.318591i
$111$	16.1415			0.145419
$112$	−86.7481	−	166.637i	−0.774537	−	1.48783i
$113$	−204.259	+	66.3676i	−1.80760	+	0.587324i	−0.999997	−	0.00240462i	$-0.999235\pi$
$113$	−204.259	+	66.3676i	−1.80760	+	0.587324i	−0.807601	+	0.589729i	$0.799235\pi$
$114$	23.7178	−	38.8944i	0.208051	−	0.341179i
$115$	13.7805	+	22.4877i	0.119830	+	0.195546i
$116$	127.423	−	10.5888i	1.09848	−	0.0912830i
$117$	−8.84019	−	112.325i	−0.0755572	−	0.960045i
$118$	53.5458	−	166.030i	0.453778	−	1.40704i
$119$	−10.1914	+	64.3457i	−0.0856417	+	0.540720i
$120$	−48.4437	+	4.13224i	−0.403697	+	0.0344353i
$121$	13.7142	+	120.220i	0.113340	+	0.993556i
$122$	−12.1895	−	75.8879i	−0.0999137	−	0.622032i
$123$	−27.7843	+	45.3399i	−0.225889	+	0.368617i
$124$	−18.2157	+	118.354i	−0.146901	+	0.954468i
$125$	−25.1559	+	29.4538i	−0.201247	+	0.235630i
$126$	−195.068	−	14.9235i	−1.54816	−	0.118440i
$127$	75.2549	−	103.580i	0.592559	−	0.815587i	−0.402443	−	0.915445i	$-0.631839\pi$
$127$	75.2549	−	103.580i	0.592559	−	0.815587i	0.995002	+	0.0998580i	$0.0318389\pi$
$128$	117.494	−	50.7861i	0.917920	−	0.396767i
$129$	6.88848	+	21.2006i	0.0533991	+	0.164345i
$130$	−185.856	−	76.5088i	−1.42966	−	0.588529i
$131$	−64.2853	+	155.199i	−0.490728	+	1.18472i	0.463623	+	0.886033i	$0.346549\pi$
$131$	−64.2853	+	155.199i	−0.490728	+	1.18472i	−0.954351	+	0.298689i	$0.903451\pi$
$132$	−0.625375	+	35.9823i	−0.00473769	+	0.272593i
$133$	−125.134	−	302.099i	−0.940854	−	2.27142i
$134$	−50.8391	+	51.0617i	−0.379396	+	0.381057i
$135$	−47.8182	+	93.8484i	−0.354209	+	0.695173i
$136$	−43.2285	−	10.0791i	−0.317857	−	0.0741108i
$137$	−14.1269	−	89.1935i	−0.103116	−	0.651048i	−0.984061	−	0.177830i	$-0.943092\pi$
$137$	−14.1269	−	89.1935i	−0.103116	−	0.651048i	0.880945	−	0.473218i	$-0.156908\pi$
$138$	5.51808	−	1.80627i	0.0399861	−	0.0130889i
$139$	45.1661	−	3.55465i	0.324936	−	0.0255730i	0.0850578	−	0.996376i	$-0.472892\pi$
$139$	45.1661	−	3.55465i	0.324936	−	0.0255730i	0.239878	+	0.970803i	$0.422892\pi$
$140$	−181.041	+	298.351i	−1.29315	+	2.13108i
$141$	−6.09619	−	25.3925i	−0.0432354	−	0.180088i
$142$	−44.0560	+	185.289i	−0.310254	+	1.30485i
$143$	−70.4062	+	131.054i	−0.492351	+	0.916461i
$144$	19.7009	−	131.833i	0.136812	−	0.915505i
$145$	−139.612	−	192.159i	−0.962840	−	1.32523i
$146$	158.354	−	12.8109i	1.08462	−	0.0877460i
$147$	47.2029	−	55.2675i	0.321108	−	0.375969i
$148$	60.2505	+	51.0052i	0.407098	+	0.344630i
$149$	−94.2452	−	22.6263i	−0.632518	−	0.151854i	−0.0955062	−	0.995429i	$-0.530447\pi$
$149$	−94.2452	−	22.6263i	−0.632518	−	0.151854i	−0.537012	+	0.843575i	$0.680447\pi$
$150$	29.1370	+	39.9199i	0.194247	+	0.266133i
$151$	100.793	+	51.3568i	0.667506	+	0.340111i	0.754691	−	0.656081i	$-0.227787\pi$
$151$	100.793	+	51.3568i	0.667506	+	0.340111i	−0.0871844	+	0.996192i	$0.527787\pi$
$152$	211.432	−	70.2337i	1.39100	−	0.462064i
$153$	−32.6858	+	32.6858i	−0.213633	+	0.213633i
$154$	205.970	+	155.892i	1.33747	+	1.01228i
$155$	205.514	−	85.1268i	1.32590	−	0.549205i
$156$	−25.8509	+	35.9096i	−0.165711	+	0.230190i
$157$	13.1745	−	167.398i	0.0839142	−	1.06623i	−0.800440	−	0.599414i	$-0.795401\pi$
$157$	13.1745	−	167.398i	0.0839142	−	1.06623i	0.884354	−	0.466817i	$-0.154599\pi$
$158$	270.682	−	65.6108i	1.71318	−	0.415258i
$159$	−25.3705	+	34.9195i	−0.159563	+	0.219619i
$160$	−193.881	−	137.652i	−1.21176	−	0.860327i
$161$	12.8785	−	39.6361i	0.0799910	−	0.246187i
$162$	−96.5770	−	82.1204i	−0.596155	−	0.506916i
$163$	1.06317	+	4.42843i	0.00652253	+	0.0271683i	0.975536	−	0.219838i	$-0.0705530\pi$
$163$	1.06317	+	4.42843i	0.00652253	+	0.0271683i	−0.969014	+	0.247007i	$0.920553\pi$
$164$	−246.978	+	81.4427i	−1.50596	+	0.496602i
$165$	57.7468	−	33.6823i	0.349980	−	0.204135i
$166$	−6.69839	−	41.7021i	−0.0403517	−	0.251217i
$167$	294.480	+	46.6411i	1.76335	+	0.279288i	0.952185	−	0.305523i	$-0.0988312\pi$
$167$	294.480	+	46.6411i	1.76335	+	0.279288i	0.811170	+	0.584811i	$0.198831\pi$
$168$	54.6800	+	53.9679i	0.325476	+	0.321238i
$169$	−12.3943	+	6.31521i	−0.0733391	+	0.0373681i
$170$	25.6517	+	78.3650i	0.150893	+	0.460971i
$171$	54.1619	−	225.601i	0.316736	−	1.31930i
$172$	−41.2790	+	100.901i	−0.239994	+	0.586635i
$173$	−200.486	−	15.7786i	−1.15888	−	0.0912056i	−0.515593	−	0.856834i	$-0.672428\pi$
$173$	−200.486	−	15.7786i	−1.15888	−	0.0912056i	−0.643284	+	0.765628i	$0.722428\pi$
$174$	−48.2654	+	20.1158i	−0.277387	+	0.115608i
$175$	354.745			2.02711
$176$	−116.034	+	132.333i	−0.659285	+	0.751893i
$177$			71.3421i			0.403063i
$178$	182.819	−	76.1944i	1.02707	−	0.428059i
$179$	17.9136	−	227.614i	0.100076	−	1.27159i	−0.717822	−	0.696227i	$-0.754861\pi$
$179$	17.9136	−	227.614i	0.100076	−	1.27159i	0.817898	−	0.575363i	$-0.195139\pi$
$180$	−228.351	+	95.7573i	−1.26862	+	0.531985i
$181$	270.968	+	65.0536i	1.49706	+	0.359412i	0.897535	−	0.440944i	$-0.145356\pi$
$181$	270.968	+	65.0536i	1.49706	+	0.359412i	0.599525	+	0.800356i	$0.295356\pi$
$182$	98.8019	+	301.836i	0.542868	+	1.65844i
$183$	14.2699	+	28.0063i	0.0779778	+	0.153040i
$184$	26.3047	+	10.6943i	0.142960	+	0.0581214i
$185$	22.9401	−	144.838i	0.124000	−	0.782907i
$186$	−7.76638	−	48.3511i	−0.0417548	−	0.259952i
$187$	59.6429	−	12.9540i	0.318946	−	0.0692730i
$188$	57.4823	−	114.045i	0.305757	−	0.606620i
$189$	161.839	−	38.8540i	0.856288	−	0.205577i
$190$	−315.293	−	268.096i	−1.65943	−	1.41103i
$191$	11.8645	+	3.85500i	0.0621177	+	0.0201833i	0.339911	−	0.940458i	$-0.389603\pi$
$191$	11.8645	+	3.85500i	0.0621177	+	0.0201833i	−0.277793	+	0.960641i	$0.589603\pi$
$192$	−39.3550	+	34.5147i	−0.204974	+	0.179764i
$193$	23.2433	+	16.8872i	0.120431	+	0.0874985i	0.646371	−	0.763024i	$-0.276286\pi$
$193$	23.2433	+	16.8872i	0.120431	+	0.0874985i	−0.525939	+	0.850522i	$0.676286\pi$
$194$	−22.2125	+	5.38410i	−0.114497	+	0.0277531i
$195$	81.9407	+	6.44888i	0.420209	+	0.0330712i
$196$	350.831	−	57.1386i	1.78995	−	0.291523i
$197$	−59.2464	−	143.034i	−0.300743	−	0.726059i	−0.999938	−	0.0111274i	$-0.996458\pi$
$197$	−59.2464	−	143.034i	−0.300743	−	0.726059i	0.699195	−	0.714931i	$-0.253542\pi$
$198$	53.2168	+	175.387i	0.268772	+	0.885792i
$199$	−30.6797	−	30.6797i	−0.154169	−	0.154169i	0.625808	−	0.779977i	$-0.284769\pi$
$199$	−30.6797	−	30.6797i	−0.154169	−	0.154169i	−0.779977	+	0.625808i	$0.784769\pi$
$200$	−17.3842	+	241.077i	−0.0869208	+	1.20538i
$201$	13.3777	−	26.2552i	0.0665558	−	0.130623i
$202$	73.1518	+	100.224i	0.362137	+	0.496156i
$203$	−87.6179	+	364.955i	−0.431615	+	1.79781i
$204$	18.0902	−	1.50328i	0.0886772	−	0.00736904i
$205$	367.349	+	313.745i	1.79195	+	1.53047i
$206$	182.427	−	14.7584i	0.885570	−	0.0716429i
$207$	23.9231	−	17.3811i	0.115570	−	0.0839667i
$208$	−209.963	+	52.3522i	−1.00944	+	0.251693i
$209$	−221.274	+	211.853i	−1.05873	+	1.01365i
$210$	33.0134	−	138.846i	0.157207	−	0.661173i
$211$	−256.944	+	61.6867i	−1.21774	+	0.292354i	−0.790885	−	0.611965i	$-0.790379\pi$
$211$	−256.944	+	61.6867i	−1.21774	+	0.292354i	−0.426858	+	0.904319i	$0.640379\pi$
$212$	−205.041	+	50.1745i	−0.967174	+	0.236672i
$213$	−6.11091	−	77.6465i	−0.0286897	−	0.364537i
$214$	−104.040	+	34.0562i	−0.486170	+	0.159141i
$215$	200.023	−	31.6805i	0.930339	−	0.147351i
$216$	18.4735	+	111.886i	0.0855253	+	0.517990i
$217$	−313.193	−	159.580i	−1.44329	−	0.735391i
$218$	−126.161	+	126.713i	−0.578720	+	0.581254i
$219$	−60.0252	+	24.8632i	−0.274088	+	0.113531i
$220$	321.981	+	56.7490i	1.46355	+	0.257950i
$221$	69.3282	+	28.7167i	0.313702	+	0.129940i
$222$	−29.8525	−	12.2890i	−0.134471	−	0.0553557i
$223$	−177.352	+	57.6251i	−0.795299	+	0.258408i	−0.678359	−	0.734731i	$-0.737309\pi$
$223$	−177.352	+	57.6251i	−0.795299	+	0.258408i	−0.116940	+	0.993139i	$0.537309\pi$
$224$	33.5690	+	374.226i	0.149862	+	1.67065i
$225$	203.633	+	147.948i	0.905036	+	0.657547i
$226$	428.289	+	32.7658i	1.89508	+	0.144981i
$227$	−178.957	−	152.844i	−0.788357	−	0.673321i	0.161197	−	0.986922i	$-0.448464\pi$
$227$	−178.957	−	152.844i	−0.788357	−	0.673321i	−0.949555	+	0.313601i	$0.898464\pi$
$228$	−73.4757	+	53.8753i	−0.322262	+	0.236295i
$229$	116.372	+	71.3130i	0.508176	+	0.311411i	0.752847	−	0.658195i	$-0.228680\pi$
$229$	116.372	+	71.3130i	0.508176	+	0.311411i	−0.244671	+	0.969606i	$0.578680\pi$
$230$	−8.36548	−	52.0809i	−0.0363717	−	0.226439i
$231$	−99.7337	−	34.8209i	−0.431748	−	0.150740i
$232$	−243.722	−	77.4277i	−1.05052	−	0.333740i
$233$	91.1572	+	14.4379i	0.391233	+	0.0619652i	0.348952	−	0.937141i	$-0.386538\pi$
$233$	91.1572	+	14.4379i	0.391233	+	0.0619652i	0.0422808	+	0.999106i	$0.486538\pi$
$234$	−69.1671	+	214.468i	−0.295586	+	0.916528i
$235$	−236.511	+	18.6138i	−1.00643	+	0.0792077i
$236$	−225.433	+	266.295i	−0.955224	+	1.12837i
$237$	−97.1168	+	59.5133i	−0.409776	+	0.251111i
$238$	67.8364	−	111.244i	0.285027	−	0.467410i
$239$	73.6672	+	226.724i	0.308231	+	0.948637i	0.978452	+	0.206475i	$0.0661994\pi$
$239$	73.6672	+	226.724i	0.308231	+	0.948637i	−0.670221	+	0.742162i	$0.733801\pi$
$240$	92.7390	+	29.2393i	0.386413	+	0.121830i
$241$		−	80.5238i		−	0.334124i	−0.985946	−	0.167062i	$-0.946572\pi$
$241$		−	80.5238i		−	0.334124i	0.985946	−	0.167062i	$-0.0534280\pi$
$242$	66.1638	−	232.780i	0.273404	−	0.961899i
$243$	165.762	+	68.6607i	0.682146	+	0.282554i
$244$	−35.2321	+	149.629i	−0.144394	+	0.613235i
$245$	−428.832	−	502.098i	−1.75033	−	2.04938i
$246$	85.9036	−	62.6998i	0.349201	−	0.254877i
$247$	−372.005	+	58.9198i	−1.50609	+	0.238542i
$248$	123.795	−	205.019i	0.499173	−	0.826689i
$249$	7.84165	+	15.3901i	0.0314926	+	0.0618077i
$250$	68.9480	−	35.3207i	0.275792	−	0.141283i
$251$	−106.618	+	173.985i	−0.424773	+	0.693167i	−0.991409	−	0.130802i	$-0.958245\pi$
$251$	−106.618	+	173.985i	−0.424773	+	0.693167i	0.566635	+	0.823969i	$0.308245\pi$
$252$	349.402	+	176.111i	1.38652	+	0.698852i
$253$	−38.9809	+	2.21619i	−0.154075	+	0.00875966i
$254$	−218.037	+	134.269i	−0.858412	+	0.528618i
$255$	−19.8205	−	27.2806i	−0.0777276	−	0.106983i
$256$	−255.961	+	4.47394i	−0.999847	+	0.0174763i
$257$	−72.9189	+	224.421i	−0.283731	+	0.873234i	0.703045	+	0.711145i	$0.251823\pi$
$257$	−72.9189	+	224.421i	−0.283731	+	0.873234i	−0.986776	+	0.162089i	$0.948177\pi$
$258$	3.40085	−	44.4533i	0.0131816	−	0.172300i
$259$	−197.575	+	121.074i	−0.762838	+	0.467468i
$260$	285.479	+	282.995i	1.09799	+	1.08844i
$261$	−202.501	+	172.952i	−0.775867	+	0.662653i
$262$	237.048	−	238.086i	0.904764	−	0.908725i
$263$	−58.3235	−	58.3235i	−0.221762	−	0.221762i	0.587478	−	0.809240i	$-0.300121\pi$
$263$	−58.3235	−	58.3235i	−0.221762	−	0.221762i	−0.809240	+	0.587478i	$0.800121\pi$
$264$	28.5509	−	66.0704i	0.108147	−	0.250267i
$265$	277.277	+	277.277i	1.04633	+	1.04633i
$266$	1.42872	+	653.978i	0.00537111	+	2.45856i
$267$	−61.5910	+	52.6037i	−0.230678	+	0.197017i
$268$	132.898	−	55.7296i	0.495888	−	0.207946i
$269$	326.678	−	200.188i	1.21442	−	0.744195i	0.240400	−	0.970674i	$-0.422721\pi$
$269$	326.678	−	200.188i	1.21442	−	0.744195i	0.974016	+	0.226479i	$0.0727214\pi$
$270$	159.886	−	137.160i	0.592169	−	0.508002i
$271$	41.5161	−	127.773i	0.153196	−	0.471489i	−0.844778	−	0.535117i	$-0.820267\pi$
$271$	41.5161	−	127.773i	0.153196	−	0.471489i	0.997974	+	0.0636287i	$0.0202673\pi$
$272$	72.2745	+	51.5516i	0.265715	+	0.189528i
$273$	−76.3420	−	105.076i	−0.279641	−	0.384893i
$274$	−41.7790	+	175.712i	−0.152478	+	0.641285i
$275$	−120.475	−	309.736i	−0.438089	−	1.12631i
$276$	−11.5805	−	0.860507i	−0.0419582	−	0.00311778i
$277$	34.1409	−	55.7128i	0.123252	−	0.201129i	−0.785063	−	0.619416i	$-0.787369\pi$
$277$	34.1409	−	55.7128i	0.123252	−	0.201129i	0.908315	+	0.418287i	$0.137369\pi$
$278$	−86.2377	−	27.8122i	−0.310207	−	0.100044i
$279$	−113.228	−	222.222i	−0.405834	−	0.796494i
$280$	561.966	−	413.946i	2.00702	−	1.47838i
$281$	−24.1934	+	3.83186i	−0.0860976	+	0.0136365i	−0.199335	−	0.979931i	$-0.563878\pi$
$281$	−24.1934	+	3.83186i	−0.0860976	+	0.0136365i	0.113237	+	0.993568i	$0.463878\pi$
$282$	−8.05755	+	51.6027i	−0.0285729	+	0.182988i
$283$	116.879	+	136.847i	0.412999	+	0.483560i	0.927443	−	0.373964i	$-0.122002\pi$
$283$	116.879	+	136.847i	0.412999	+	0.483560i	−0.514444	+	0.857524i	$0.672002\pi$
$284$	222.544	−	309.137i	0.783606	−	1.08851i
$285$	156.367	+	64.7695i	0.548658	+	0.227262i
$286$	229.986	−	188.772i	0.804147	−	0.660043i
$287$		−	763.374i		−	2.65984i
$288$	−136.803	+	228.816i	−0.475012	+	0.794500i
$289$	79.7926	+	245.576i	0.276099	+	0.849745i
$290$	111.906	+	461.674i	0.385881	+	1.59198i
$291$	7.96952	−	4.88373i	0.0273867	−	0.0167826i
$292$	−302.618	−	96.8669i	−1.03636	−	0.331736i
$293$	562.493	−	44.2691i	1.91977	−	0.151089i	0.938699	−	0.344737i	$-0.112032\pi$
$293$	562.493	−	44.2691i	1.91977	−	0.151089i	0.981071	+	0.193648i	$0.0620319\pi$
$294$	−129.375	+	66.2763i	−0.440051	+	0.225429i
$295$	640.154	+	101.390i	2.17001	+	0.343696i
$296$	−72.5972	−	140.201i	−0.245261	−	0.473652i
$297$	−88.8862	−	128.110i	−0.299280	−	0.431347i
$298$	157.074	+	113.597i	0.527092	+	0.381199i
$299$	−40.9303	−	25.0821i	−0.136891	−	0.0838867i
$300$	−23.4946	−	96.0118i	−0.0783152	−	0.320039i
$301$	−243.338	−	207.830i	−0.808431	−	0.690466i
$302$	−147.311	−	171.718i	−0.487784	−	0.568601i
$303$	−41.0518	−	29.8259i	−0.135484	−	0.0984352i
$304$	−444.499	−	31.0771i	−1.46217	−	0.102227i
$305$	271.582	−	88.2422i	0.890432	−	0.289319i
$306$	85.3346	−	35.5654i	0.278871	−	0.116227i
$307$	−374.080	−	154.949i	−1.21850	−	0.504720i	−0.321569	−	0.946886i	$-0.604210\pi$
$307$	−374.080	−	154.949i	−1.21850	−	0.504720i	−0.896933	+	0.442166i	$0.854210\pi$
$308$	−262.241	−	445.121i	−0.851433	−	1.44520i
$309$	−69.1502	+	28.6430i	−0.223787	+	0.0926956i
$310$	−444.893	+	0.971938i	−1.43514	+	0.00313528i
$311$	359.890	+	183.373i	1.15720	+	0.589624i	0.923845	−	0.382768i	$-0.125029\pi$
$311$	359.890	+	183.373i	1.15720	+	0.589624i	0.233357	+	0.972391i	$0.425029\pi$
$312$	75.1483	−	46.7312i	0.240860	−	0.149779i
$313$	6.62186	−	1.04880i	0.0211561	−	0.00335080i	−0.145847	−	0.989307i	$-0.546591\pi$
$313$	6.62186	−	1.04880i	0.0211561	−	0.00335080i	0.167004	+	0.985956i	$0.446591\pi$
$314$	−151.810	+	299.561i	−0.483473	+	0.954015i
$315$	−57.0278	−	724.607i	−0.181041	−	2.30034i
$316$	−550.559	−	84.7357i	−1.74227	−	0.268151i
$317$	−327.147	+	78.5411i	−1.03201	+	0.247764i	−0.713869	−	0.700279i	$-0.753059\pi$
$317$	−327.147	+	78.5411i	−1.03201	+	0.247764i	−0.318142	+	0.948043i	$0.603059\pi$
$318$	73.5060	−	45.2657i	0.231151	−	0.142345i
$319$	348.407	−	47.4406i	1.09218	−	0.148716i
$320$	253.770	+	402.185i	0.793031	+	1.25683i
$321$	36.2188	−	26.3145i	0.112831	−	0.0819767i
$322$	−53.9940	+	63.4992i	−0.167683	+	0.197203i
$323$	117.498	+	100.353i	0.363771	+	0.310690i
$324$	116.092	+	225.402i	0.358307	+	0.695686i
$325$	95.3885	−	397.322i	0.293503	−	1.22253i
$326$	1.40523	−	8.99949i	0.00431053	−	0.0276058i
$327$	33.1978	−	65.1543i	0.101522	−	0.199249i
$328$	518.772	+	37.4089i	1.58162	+	0.114052i
$329$	265.083	+	265.083i	0.805723	+	0.805723i
$330$	−132.442	+	18.3286i	−0.401338	+	0.0555413i
$331$	131.081	+	316.458i	0.396016	+	0.956067i	0.988601	+	0.150559i	$0.0481074\pi$
$331$	131.081	+	316.458i	0.396016	+	0.956067i	−0.592585	+	0.805508i	$0.701893\pi$
$332$	−19.3608	+	82.2246i	−0.0583157	+	0.247665i
$333$	−163.908	−	12.8998i	−0.492216	−	0.0387382i
$334$	−509.110	−	310.455i	−1.52428	−	0.929507i
$335$	−216.576	−	157.352i	−0.646497	−	0.469707i
$336$	−60.0394	−	141.439i	−0.178689	−	0.420950i
$337$	−299.863	−	97.4314i	−0.889801	−	0.289114i	−0.171780	−	0.985135i	$-0.554952\pi$
$337$	−299.863	−	97.4314i	−0.889801	−	0.289114i	−0.718021	+	0.696022i	$0.754952\pi$
$338$	27.7303	−	2.24339i	0.0820423	−	0.00663724i
$339$	−170.808	+	41.0073i	−0.503857	+	0.120965i
$340$	12.2205	−	164.460i	0.0359426	−	0.483705i
$341$	−32.9699	+	327.651i	−0.0966860	+	0.960854i
$342$	−271.925	+	375.997i	−0.795101	+	1.09941i
$343$	−73.2202	+	462.294i	−0.213470	+	1.34780i
$344$	153.161	−	155.182i	0.445237	−	0.451112i
$345$	9.79328	+	19.2204i	0.0283863	+	0.0557113i
$346$	358.771	+	181.817i	1.03691	+	0.525482i
$347$	103.808	+	24.9220i	0.299157	+	0.0718213i	0.380246	−	0.924886i	$-0.375839\pi$
$347$	103.808	+	24.9220i	0.299157	+	0.0718213i	−0.0810880	+	0.996707i	$0.525839\pi$
$348$	104.578	−	0.456936i	0.300512	−	0.00131303i
$349$	−21.3741	+	271.584i	−0.0612439	+	0.778178i	0.887231	+	0.461326i	$0.152626\pi$
$349$	−21.3741	+	271.584i	−0.0612439	+	0.778178i	−0.948475	+	0.316852i	$0.897374\pi$
$350$	−656.075	−	270.077i	−1.87450	−	0.771649i
$351$		−	191.710i		−	0.546183i
$352$	315.346	−	156.400i	0.895868	−	0.444319i
$353$	398.172			1.12797			0.563983	−	0.825786i	$-0.309268\pi$
$353$	398.172			1.12797			0.563983	+	0.825786i	$0.309268\pi$
$354$	54.3148	−	131.942i	0.153432	−	0.372717i
$355$	−705.408	−	55.5168i	−1.98706	−	0.156385i
$356$	−396.119	+	1.73078i	−1.11269	+	0.00486173i
$357$	−12.4390	+	51.8123i	−0.0348432	+	0.145132i
$358$	−206.419	+	407.318i	−0.576590	+	1.13776i
$359$	190.185	−	96.9041i	0.529763	−	0.269928i	−0.168583	−	0.985687i	$-0.553919\pi$
$359$	190.185	−	96.9041i	0.529763	−	0.269928i	0.698347	+	0.715759i	$0.253919\pi$
$360$	495.222	−	3.24571i	1.37562	−	0.00901585i
$361$	−409.463	−	64.8525i	−1.13425	−	0.179647i
$362$	−451.608	−	326.607i	−1.24754	−	0.902230i
$363$	3.46751	+	98.9054i	0.00955237	+	0.272467i
$364$	47.0692	−	633.444i	0.129311	−	1.74023i
$365$	137.791	+	573.942i	0.377511	+	1.57245i
$366$	−5.06919	−	62.6598i	−0.0138503	−	0.171202i
$367$	42.7155	−	131.465i	0.116391	−	0.358215i	−0.875844	−	0.482595i	$-0.839694\pi$
$367$	42.7155	−	131.465i	0.116391	−	0.358215i	0.992235	+	0.124380i	$0.0396942\pi$
$368$	−40.5067	−	39.8049i	−0.110073	−	0.108165i
$369$	318.369	−	438.197i	0.862788	−	1.18753i
$370$	−152.695	+	250.402i	−0.412689	+	0.676762i
$371$	48.6157	−	617.721i	0.131040	−	1.66502i
$372$	−22.4477	+	95.3346i	−0.0603434	+	0.256276i
$373$	−637.346	+	263.997i	−1.70870	+	0.707768i	−0.708706	+	0.705504i	$0.750721\pi$
$373$	−637.346	+	263.997i	−1.70870	+	0.707768i	−0.999997	+	0.00226352i	$0.999279\pi$
$374$	−120.167	−	21.4503i	−0.321303	−	0.0573536i
$375$	−22.4017	+	22.4017i	−0.0597380	+	0.0597380i
$376$	−193.135	+	167.154i	−0.513656	+	0.444559i
$377$	385.197	+	196.268i	1.02174	+	0.520604i
$378$	−328.889	−	51.3546i	−0.870077	−	0.135859i
$379$	491.268	+	117.943i	1.29622	+	0.311195i	0.822140	−	0.569286i	$-0.192780\pi$
$379$	491.268	+	117.943i	1.29622	+	0.311195i	0.474082	+	0.880481i	$0.342780\pi$
$380$	379.001	+	735.866i	0.997372	+	1.93649i
$381$	68.0083	−	79.6275i	0.178500	−	0.208996i
$382$	−19.0076	−	16.1623i	−0.0497580	−	0.0423097i
$383$	−286.284	−	394.036i	−0.747477	−	1.02881i	−0.998153	−	0.0607433i	$-0.980653\pi$
$383$	−286.284	−	394.036i	−0.747477	−	1.02881i	0.250676	−	0.968071i	$-0.419347\pi$
$384$	99.0612	−	33.8703i	0.257972	−	0.0882038i
$385$	−454.188	+	845.425i	−1.17971	+	2.19591i
$386$	−30.1300	−	48.9274i	−0.0780570	−	0.126755i
$387$	−53.0059	−	220.785i	−0.136966	−	0.570505i
$388$	45.1795	+	6.95351i	0.116442	+	0.0179214i
$389$	−19.9817	+	1.57260i	−0.0513669	+	0.00404266i	−0.104117	−	0.994565i	$-0.533201\pi$
$389$	−19.9817	+	1.57260i	−0.0513669	+	0.00404266i	0.0527496	+	0.998608i	$0.483201\pi$
$390$	−146.634	−	74.3105i	−0.375984	−	0.190540i
$391$	3.08083	+	19.4516i	0.00787936	+	0.0497483i
$392$	−692.337	−	161.424i	−1.76617	−	0.411796i
$393$	−62.3764	+	122.421i	−0.158719	+	0.311503i
$394$	0.676448	+	309.636i	0.00171687	+	0.785878i
$395$	395.993	+	956.011i	1.00251	+	2.42028i
$396$	35.1064	−	364.881i	0.0886525	−	0.921416i
$397$	92.5927	−	223.539i	0.233231	−	0.563070i	−0.763323	−	0.646017i	$-0.776433\pi$
$397$	92.5927	−	223.539i	0.233231	−	0.563070i	0.996554	+	0.0829477i	$0.0264334\pi$
$398$	33.3825	+	80.0971i	0.0838756	+	0.201249i
$399$	−82.6452	−	254.356i	−0.207131	−	0.637483i
$400$	215.689	−	432.619i	0.539223	−	1.08155i
$401$	312.731	−	430.437i	0.779878	−	1.07341i	−0.215417	−	0.976522i	$-0.569111\pi$
$401$	312.731	−	430.437i	0.779878	−	1.07341i	0.995295	−	0.0968880i	$-0.0308889\pi$
$402$	−44.7299	+	38.3723i	−0.111269	+	0.0954535i
$403$	−262.948	+	307.873i	−0.652477	+	0.763953i
$404$	−58.9858	−	241.049i	−0.146004	−	0.596655i
$405$	246.091	−	401.583i	0.607631	−	0.991564i
$406$	439.893	−	608.251i	1.08348	−	1.49816i
$407$	172.811	+	131.390i	0.424597	+	0.322825i
$408$	−34.6009	−	10.9923i	−0.0848061	−	0.0269420i
$409$	84.7458	−	535.064i	0.207202	−	1.30822i	−0.636443	−	0.771324i	$-0.719595\pi$
$409$	84.7458	−	535.064i	0.207202	−	1.30822i	0.843645	−	0.536901i	$-0.180405\pi$
$410$	−440.521	−	859.922i	−1.07444	−	2.09737i
$411$	−5.79506	−	73.6333i	−0.0140999	−	0.179156i
$412$	−348.622	−	111.593i	−0.846170	−	0.270856i
$413$	−535.123	−	873.242i	−1.29570	−	2.11439i
$414$	−57.4767	+	13.9318i	−0.138833	+	0.0336517i
$415$	149.240	−	48.4911i	0.359615	−	0.116846i
$416$	428.168	+	63.0289i	1.02925	+	0.151512i
$417$	37.0557			0.0888626
$418$	570.519	−	223.344i	1.36488	−	0.534316i
$419$	19.0548	−	46.0025i	0.0454770	−	0.109791i	−0.899509	−	0.436903i	$-0.856075\pi$
$419$	19.0548	−	46.0025i	0.0454770	−	0.109791i	0.944986	+	0.327112i	$0.106075\pi$
$420$	−166.763	+	231.652i	−0.397056	+	0.551552i
$421$	304.776	−	260.303i	0.723932	−	0.618297i	−0.209182	−	0.977877i	$-0.567080\pi$
$421$	304.776	−	260.303i	0.723932	−	0.618297i	0.933114	+	0.359580i	$0.117080\pi$
$422$	522.162	+	81.5335i	1.23735	+	0.193207i
$423$	41.6106	+	262.719i	0.0983701	+	0.621084i
$424$	417.407	+	63.3094i	0.984451	+	0.149315i
$425$	−149.365	+	76.1051i	−0.351446	+	0.179071i
$426$	−47.8128	+	148.254i	−0.112237	+	0.348014i
$427$	−384.737	−	235.767i	−0.901024	−	0.552148i
$428$	218.343	+	16.2244i	0.510147	+	0.0379074i
$429$	−65.8178	+	102.341i	−0.153422	+	0.238557i
$430$	−394.047	−	93.6923i	−0.916388	−	0.217889i
$431$	−396.635	+	288.172i	−0.920266	+	0.668613i	−0.943590	−	0.331115i	$-0.892575\pi$
$431$	−396.635	+	288.172i	−0.920266	+	0.668613i	0.0233240	+	0.999728i	$0.492575\pi$
$432$	51.0166	−	220.989i	0.118094	−	0.511549i
$433$	436.554	+	141.845i	1.00821	+	0.327587i	0.766141	−	0.642673i	$-0.222175\pi$
$433$	436.554	+	141.845i	1.00821	+	0.327587i	0.242067	+	0.970260i	$0.422175\pi$
$434$	457.735	+	533.574i	1.05469	+	1.22943i
$435$	−101.506	−	165.642i	−0.233346	−	0.380786i
$436$	329.796	−	138.297i	0.756412	−	0.317195i
$437$	−64.1969	−	75.1649i	−0.146904	−	0.172002i
$438$	129.941	−	0.283877i	0.296670	−	0.000648121i
$439$	−492.799	+	492.799i	−1.12255	+	1.12255i	−0.131193	+	0.991357i	$0.541881\pi$
$439$	−492.799	+	492.799i	−1.12255	+	1.12255i	−0.991357	+	0.131193i	$0.958119\pi$
$440$	−552.275	−	350.086i	−1.25517	−	0.795651i
$441$	−523.488	+	523.488i	−1.18705	+	1.18705i
$442$	−106.355	−	105.891i	−0.240621	−	0.239572i
$443$	411.533	+	481.844i	0.928969	+	1.08768i	0.995948	+	0.0899290i	$0.0286640\pi$
$443$	411.533	+	481.844i	0.928969	+	1.08768i	−0.0669788	+	0.997754i	$0.521336\pi$
$444$	45.8540	+	45.4551i	0.103275	+	0.102376i
$445$	384.481	+	627.417i	0.864003	+	1.40993i
$446$	371.871	+	28.4496i	0.833791	+	0.0637882i
$447$	−75.3938	−	24.4969i	−0.168666	−	0.0548030i
$448$	222.826	−	717.661i	0.497378	−	1.60192i
$449$	579.420	−	420.973i	1.29047	−	0.937579i	0.290652	−	0.956829i	$-0.406128\pi$
$449$	579.420	−	420.973i	1.29047	−	0.937579i	0.999815	+	0.0192495i	$0.00612770\pi$
$450$	−263.967	−	428.651i	−0.586594	−	0.952557i
$451$	−666.521	+	259.249i	−1.47787	+	0.574831i
$452$	−767.143	−	386.666i	−1.69722	−	0.855457i
$453$	78.8894	+	48.3435i	0.174149	+	0.106719i
$454$	214.604	+	418.919i	0.472695	+	0.922728i
$455$	−1051.34	+	535.686i	−2.31065	+	1.17733i
$456$	176.905	−	43.6993i	0.387949	−	0.0958317i
$457$	128.212	+	809.496i	0.280550	+	1.77133i	0.577459	+	0.816420i	$0.304044\pi$
$457$	128.212	+	809.496i	0.280550	+	1.77133i	−0.296908	+	0.954906i	$0.595956\pi$
$458$	−160.929	−	220.486i	−0.351374	−	0.481410i
$459$	−59.8063	+	51.0794i	−0.130297	+	0.111284i
$460$	−24.1793	+	102.689i	−0.0525638	+	0.223236i
$461$	55.6670	−	134.392i	0.120753	−	0.291523i	−0.851932	−	0.523652i	$-0.824569\pi$
$461$	55.6670	−	134.392i	0.120753	−	0.291523i	0.972685	+	0.232129i	$0.0745693\pi$
$462$	157.940	+	140.329i	0.341862	+	0.303742i
$463$	704.384			1.52135			0.760674	−	0.649135i	$-0.224869\pi$
$463$	704.384			1.52135			0.760674	+	0.649135i	$0.224869\pi$
$464$	391.797	+	328.749i	0.844391	+	0.708511i
$465$	173.035	−	56.2225i	0.372119	−	0.120909i
$466$	−157.597	−	96.1024i	−0.338190	−	0.206228i
$467$	75.7068	+	123.542i	0.162113	+	0.264544i	0.923374	−	0.383901i	$-0.125420\pi$
$467$	75.7068	+	123.542i	0.162113	+	0.264544i	−0.761261	+	0.648445i	$0.775420\pi$
$468$	291.200	−	343.983i	0.622222	−	0.735007i
$469$	33.1895	+	421.713i	0.0707666	+	0.899175i
$470$	451.581	+	145.638i	0.960810	+	0.309867i
$471$	21.4845	−	135.648i	0.0456147	−	0.288000i
$472$	619.660	−	320.865i	1.31284	−	0.679799i
$473$	−98.8219	+	283.045i	−0.208926	+	0.598404i
$474$	224.920	−	36.1276i	0.474514	−	0.0762186i
$475$	439.629	−	717.409i	0.925535	−	1.51034i
$476$	−210.151	+	154.091i	−0.441495	+	0.323721i
$477$	285.530	−	334.313i	0.598596	−	0.700866i
$478$	36.3696	−	475.395i	0.0760869	−	0.994550i
$479$	197.733	−	272.157i	0.412805	−	0.568177i	−0.551095	−	0.834442i	$-0.685790\pi$
$479$	197.733	−	272.157i	0.412805	−	0.568177i	0.963900	+	0.266266i	$0.0857899\pi$
$480$	−149.253	−	124.681i	−0.310945	−	0.259752i
$481$	82.4790	+	253.844i	0.171474	+	0.527743i
$482$	−61.3051	+	148.923i	−0.127189	+	0.308969i
$483$	13.0444	−	31.4921i	0.0270071	−	0.0652010i
$484$	−299.587	+	380.137i	−0.618981	+	0.785406i
$485$	−32.4956	−	78.4513i	−0.0670012	−	0.161755i
$486$	−254.290	−	253.182i	−0.523231	−	0.520950i
$487$	−218.738	+	429.297i	−0.449153	+	0.881513i	0.549779	+	0.835310i	$0.314712\pi$
$487$	−218.738	+	429.297i	−0.449153	+	0.881513i	−0.998932	+	0.0462027i	$0.985288\pi$
$488$	179.076	−	249.905i	0.366959	−	0.512101i
$489$	0.582710	+	3.67909i	0.00119164	+	0.00752369i
$490$	410.832	+	1255.08i	0.838433	+	2.56138i
$491$	−841.081	+	66.1945i	−1.71300	+	0.134816i	−0.896648	−	0.442745i	$-0.854005\pi$
$491$	−841.081	+	66.1945i	−1.71300	+	0.134816i	−0.816348	+	0.577561i	$0.804005\pi$
$492$	−206.607	+	50.5578i	−0.419934	+	0.102760i
$493$	−41.4041	−	172.461i	−0.0839840	−	0.349819i
$494$	732.853	+	174.250i	1.48351	+	0.352733i
$495$	−613.305	+	295.875i	−1.23900	+	0.597728i
$496$	−385.036	+	284.919i	−0.776283	+	0.574433i
$497$	657.210	+	904.572i	1.32235	+	1.82006i
$498$	−2.78563	−	34.4329i	−0.00559364	−	0.0691425i
$499$	−516.650	+	604.919i	−1.03537	+	1.21226i	−0.0585323	+	0.998286i	$0.518642\pi$
$499$	−516.650	+	604.919i	−1.03537	+	1.21226i	−0.976839	+	0.213978i	$0.931358\pi$
$500$	−154.405	+	12.8310i	−0.308810	+	0.0256620i
$501$	237.121	+	56.9276i	0.473294	+	0.113628i
$502$	329.642	−	240.601i	0.656657	−	0.479285i
$503$	−611.133	−	311.388i	−1.21498	−	0.619061i	−0.275377	−	0.961336i	$-0.588803\pi$
$503$	−611.133	−	311.388i	−1.21498	−	0.619061i	−0.939600	+	0.342275i	$0.888803\pi$
$504$	−512.116	−	591.714i	−1.01610	−	1.17404i
$505$	−325.970	+	325.970i	−0.645486	+	0.645486i
$506$	73.7796	+	25.5786i	0.145809	+	0.0505506i
$507$	−10.5113	+	4.35394i	−0.0207324	+	0.00858765i
$508$	505.465	−	82.3234i	0.995011	−	0.162054i
$509$	−51.7258	+	657.238i	−0.101622	+	1.29123i	0.708809	+	0.705400i	$0.249233\pi$
$509$	−51.7258	+	657.238i	−0.101622	+	1.29123i	−0.810431	+	0.585834i	$0.800767\pi$
$510$	15.8871	+	65.5435i	0.0311512	+	0.128517i
$511$	548.226	−	754.569i	1.07285	−	1.47665i
$512$	476.787	+	186.596i	0.931225	+	0.364445i
$513$	121.988	−	375.441i	0.237794	−	0.731854i
$514$	305.716	−	359.535i	0.594779	−	0.699485i
$515$	158.738	+	661.193i	0.308230	+	1.28387i
$516$	−40.1332	+	79.6239i	−0.0777775	+	0.154310i
$517$	141.426	−	321.475i	0.273551	−	0.621808i
$518$	457.578	−	73.4983i	0.883355	−	0.141889i
$519$	−162.460	−	25.7311i	−0.313024	−	0.0495782i
$520$	−312.520	−	740.721i	−0.601000	−	1.42446i
$521$	349.435	−	178.046i	0.670701	−	0.341739i	−0.0852571	−	0.996359i	$-0.527171\pi$
$521$	349.435	−	178.046i	0.670701	−	0.341739i	0.755959	+	0.654620i	$0.227171\pi$
$522$	506.185	−	165.693i	0.969703	−	0.317419i
$523$	107.019	−	445.766i	0.204625	−	0.852325i	−0.771695	−	0.635993i	$-0.780591\pi$
$523$	107.019	−	445.766i	0.204625	−	0.852325i	0.976320	−	0.216332i	$-0.0694094\pi$
$524$	−619.665	+	259.851i	−1.18257	+	0.495899i
$525$	289.252	+	22.7646i	0.550957	+	0.0433612i
$526$	63.4617	+	152.268i	0.120650	+	0.289484i
$527$	166.105			0.315189
$528$	−103.104	+	100.456i	−0.195273	+	0.190257i
$529$			516.401i			0.976184i
$530$	−301.705	−	723.902i	−0.569254	−	1.36585i
$531$	57.0147	−	724.440i	0.107372	−	1.36429i
$532$	495.249	−	1210.57i	0.930920	−	2.27551i
$533$	−854.995	−	205.266i	−1.60412	−	0.385115i
$534$	153.957	−	50.3957i	0.288308	−	0.0943739i
$535$	−184.647	−	362.390i	−0.345134	−	0.677364i
$536$	−288.213	+	1.88896i	−0.537712	+	0.00352419i
$537$	29.2129	−	184.443i	0.0544002	−	0.343469i
$538$	−756.576	+	121.525i	−1.40628	+	0.225882i
$539$	955.226	−	207.469i	1.77222	−	0.384914i
$540$	−400.121	+	131.943i	−0.740965	+	0.244338i
$541$	−112.242	+	26.9468i	−0.207471	+	0.0498093i	−0.335848	−	0.941916i	$-0.609023\pi$
$541$	−112.242	+	26.9468i	−0.207471	+	0.0498093i	0.128378	+	0.991725i	$0.459023\pi$
$542$	−174.059	+	204.700i	−0.321141	+	0.377676i
$543$	216.767	+	70.4320i	0.399203	+	0.129709i
$544$	−94.4187	−	150.365i	−0.173564	−	0.276407i
$545$	−537.450	−	390.481i	−0.986147	−	0.716478i
$546$	61.1918	+	252.451i	0.112073	+	0.462365i
$547$	69.9277	+	5.50343i	0.127839	+	0.0100611i	0.142217	−	0.989836i	$-0.454577\pi$
$547$	69.9277	+	5.50343i	0.127839	+	0.0100611i	−0.0143783	+	0.999897i	$0.504577\pi$
$548$	211.042	−	293.159i	0.385113	−	0.534962i
$549$	−122.522	−	295.793i	−0.223172	−	0.538786i
$550$	−13.0024	+	664.556i	−0.0236406	+	1.20828i
$551$	629.474	+	629.474i	1.14242	+	1.14242i
$552$	20.7621	+	10.4080i	0.0376125	+	0.0188550i
$553$	742.332	−	1456.91i	1.34237	−	2.63456i
$554$	−105.557	+	77.0444i	−0.190536	+	0.139069i
$555$	27.9994	−	116.626i	0.0504494	−	0.210137i
$556$	138.316	+	117.092i	0.248770	+	0.210597i
$557$	121.654	+	103.902i	0.218409	+	0.186539i	0.751920	−	0.659254i	$-0.229128\pi$
$557$	121.654	+	103.902i	0.218409	+	0.186539i	−0.533511	+	0.845793i	$0.679128\pi$
$558$	40.2225	+	497.186i	0.0720833	+	0.891015i
$559$	−298.206	+	216.659i	−0.533464	+	0.387584i
$560$	−1354.46	+	337.723i	−2.41868	+	0.603077i
$561$	49.4630	−	6.73509i	0.0881693	−	0.0120055i
$562$	47.6613	+	11.3324i	0.0848065	+	0.0201644i
$563$	27.9569	−	6.71186i	0.0496570	−	0.0119216i	−0.208541	−	0.978014i	$-0.566871\pi$
$563$	27.9569	−	6.71186i	0.0496570	−	0.0119216i	0.258198	+	0.966092i	$0.416871\pi$
$564$	54.1885	−	89.3010i	0.0960788	−	0.158335i
$565$	125.210	+	1590.94i	0.221610	+	2.81582i
$566$	−111.973	−	342.073i	−0.197832	−	0.604368i
$567$	−735.079	+	116.425i	−1.29644	+	0.205335i
$568$	−646.934	+	402.297i	−1.13897	+	0.708270i
$569$	900.398	+	458.776i	1.58242	+	0.806284i	0.999978	−	0.00658672i	$-0.00209663\pi$
$569$	900.398	+	458.776i	1.58242	+	0.806284i	0.582444	+	0.812871i	$0.302097\pi$
$570$	−239.879	−	238.833i	−0.420841	−	0.419006i
$571$	−876.514	+	363.064i	−1.53505	+	0.635839i	−0.980537	−	0.196336i	$-0.937096\pi$
$571$	−876.514	+	363.064i	−1.53505	+	0.635839i	−0.554514	+	0.832175i	$0.687096\pi$
$572$	−569.060	+	174.026i	−0.994861	+	0.304241i
$573$	9.42669	+	3.90466i	0.0164515	+	0.00681442i
$574$	−581.178	+	1411.80i	−1.01251	+	2.45959i
$575$	101.990	−	33.1386i	0.177374	−	0.0576323i
$576$	427.212	−	319.026i	0.741687	−	0.553865i
$577$	−297.397	−	216.071i	−0.515419	−	0.374474i	0.299457	−	0.954110i	$-0.403195\pi$
$577$	−297.397	−	216.071i	−0.515419	−	0.374474i	−0.814875	+	0.579636i	$0.803195\pi$
$578$	39.3937	−	514.924i	0.0681551	−	0.890871i
$579$	17.8684	+	15.2611i	0.0308608	+	0.0263576i
$580$	144.525	−	939.030i	0.249181	−	1.61902i
$581$	−211.422	−	129.559i	−0.363893	−	0.222994i
$582$	−18.4572	+	2.96468i	−0.0317133	+	0.00509394i
$583$	−555.858	+	167.336i	−0.953444	+	0.287026i
$584$	485.923	+	409.540i	0.832059	+	0.701267i
$585$	−826.910	−	130.970i	−1.41352	−	0.223880i
$586$	−1073.99	−	346.369i	−1.83275	−	0.591074i
$587$	753.634	−	59.3122i	1.28387	−	0.101043i	0.581908	−	0.813255i	$-0.302306\pi$
$587$	753.634	−	59.3122i	1.28387	−	0.101043i	0.701965	+	0.712212i	$0.252306\pi$
$588$	289.728	−	24.0762i	0.492734	−	0.0409460i
$589$	−710.857	+	435.613i	−1.20689	+	0.739581i
$590$	−1106.73	−	674.881i	−1.87581	−	1.14387i
$591$	−39.1297	−	120.429i	−0.0662093	−	0.203771i
$592$	27.5244	+	314.562i	0.0464938	+	0.531354i
$593$		−	334.214i		−	0.563599i	−0.959473	−	0.281799i	$-0.909069\pi$
$593$		−	334.214i		−	0.563599i	0.959473	−	0.281799i	$-0.0909313\pi$
$594$	66.8547	+	304.602i	0.112550	+	0.512797i
$595$	447.234	+	185.250i	0.751654	+	0.311345i
$596$	−204.011	−	329.674i	−0.342301	−	0.553145i
$597$	−23.0468	−	26.9844i	−0.0386044	−	0.0452000i
$598$	56.6019	+	77.5490i	0.0946520	+	0.129681i
$599$	−223.865	+	35.4567i	−0.373731	+	0.0591932i	−0.340475	−	0.940254i	$-0.610588\pi$
$599$	−223.865	+	35.4567i	−0.373731	+	0.0591932i	−0.0332565	+	0.999447i	$0.510588\pi$
$600$	−29.6451	+	195.454i	−0.0494084	+	0.325756i
$601$	−51.7683	−	101.601i	−0.0861369	−	0.169053i	0.843920	−	0.536470i	$-0.180242\pi$
$601$	−51.7683	−	101.601i	−0.0861369	−	0.169053i	−0.930057	+	0.367416i	$0.880242\pi$
$602$	291.808	+	569.627i	0.484732	+	0.946223i
$603$	−156.826	+	255.916i	−0.260076	+	0.424405i
$604$	141.707	+	429.731i	0.234614	+	0.711475i
$605$	892.408	+	109.449i	1.47505	+	0.180907i
$606$	53.2150	+	86.4147i	0.0878136	+	0.142598i
$607$	−24.8895	−	34.2574i	−0.0410041	−	0.0564373i	0.788023	−	0.615646i	$-0.211105\pi$
$607$	−24.8895	−	34.2574i	−0.0410041	−	0.0564373i	−0.829027	+	0.559209i	$0.811105\pi$
$608$	798.408	+	395.884i	1.31317	+	0.651126i
$609$	−94.8618	+	291.955i	−0.155767	+	0.479400i
$610$	−569.452	−	43.5653i	−0.933527	−	0.0714185i
$611$	368.177	−	225.619i	0.602582	−	0.369262i
$612$	−184.897	+	0.807876i	−0.302119	+	0.00132006i
$613$	360.656	−	308.029i	0.588346	−	0.502495i	−0.304707	−	0.952446i	$-0.598559\pi$
$613$	360.656	−	308.029i	0.588346	−	0.502495i	0.893053	+	0.449951i	$0.148559\pi$
$614$	573.867	+	571.365i	0.934637	+	0.930562i
$615$	279.396	+	279.396i	0.454302	+	0.454302i
$616$	146.113	+	1022.87i	0.237196	+	1.66050i
$617$	−164.735	−	164.735i	−0.266993	−	0.266993i	0.560894	−	0.827887i	$-0.310457\pi$
$617$	−164.735	−	164.735i	−0.266993	−	0.266993i	−0.827887	+	0.560894i	$0.810457\pi$
$618$	149.695	−	0.327032i	0.242225	−	0.000529178i
$619$	516.155	−	440.838i	0.833852	−	0.712177i	−0.126198	−	0.992005i	$-0.540277\pi$
$619$	516.155	−	440.838i	0.833852	−	0.712177i	0.960050	+	0.279828i	$0.0902774\pi$
$620$	823.537	+	336.912i	1.32829	+	0.543407i
$621$	42.8994	−	26.2888i	0.0690812	−	0.0423330i
$622$	−525.983	−	613.129i	−0.845631	−	0.985738i
$623$	359.316	−	1105.86i	0.576752	−	1.77506i
$624$	−174.559	+	29.2133i	−0.279742	+	0.0468162i
$625$	−274.793	−	378.219i	−0.439668	−	0.605151i
$626$	−13.0451	−	3.10173i	−0.0208389	−	0.00495484i
$627$	−194.017	+	158.541i	−0.309437	+	0.252857i
$628$	508.826	−	438.438i	0.810233	−	0.698150i
$629$	57.2140	−	93.3647i	0.0909602	−	0.148434i
$630$	−446.195	+	1383.52i	−0.708246	+	2.19607i
$631$	−83.3553	−	163.594i	−0.132100	−	0.259261i	0.815476	−	0.578791i	$-0.196475\pi$
$631$	−83.3553	−	163.594i	−0.132100	−	0.259261i	−0.947576	+	0.319529i	$0.896475\pi$
$632$	953.706	+	575.868i	1.50903	+	0.911184i
$633$	−213.466	+	33.8096i	−0.337228	+	0.0534117i
$634$	664.831	+	103.810i	1.04863	+	0.163739i
$635$	−617.847	−	723.406i	−0.972987	−	1.13922i
$636$	−170.406	+	27.7534i	−0.267934	+	0.0436375i
$637$	1110.34	+	459.919i	1.74308	+	0.722008i
$638$	−680.471	−	177.514i	−1.06657	−	0.278235i
$639$			793.341i			1.24154i
$640$	−163.134	−	937.014i	−0.254897	−	1.46408i
$641$	−23.5425	−	72.4564i	−0.0367278	−	0.113037i	0.931012	−	0.364989i	$-0.118927\pi$
$641$	−23.5425	−	72.4564i	−0.0367278	−	0.113037i	−0.967740	+	0.251953i	$0.918927\pi$
$642$	−87.0180	+	21.0923i	−0.135542	+	0.0328541i
$643$	−123.285	+	75.5493i	−0.191734	+	0.117495i	−0.615053	−	0.788486i	$-0.710865\pi$
$643$	−123.285	+	75.5493i	−0.191734	+	0.117495i	0.423318	+	0.905981i	$0.360865\pi$
$644$	148.202	−	76.3300i	0.230127	−	0.118525i
$645$	165.128	−	12.9958i	0.256012	−	0.0201486i
$646$	−140.902	−	275.050i	−0.218115	−	0.425773i
$647$	237.082	+	37.5501i	0.366433	+	0.0580373i	0.336936	−	0.941528i	$-0.390609\pi$
$647$	237.082	+	37.5501i	0.366433	+	0.0580373i	0.0294972	+	0.999565i	$0.490609\pi$
$648$	−43.0976	−	505.249i	−0.0665087	−	0.779705i
$649$	−580.716	+	763.790i	−0.894786	+	1.17687i
$650$	−478.907	+	662.196i	−0.736779	+	1.01876i
$651$	−245.131	−	150.216i	−0.376545	−	0.230747i
$652$	−9.45044	+	15.5740i	−0.0144945	+	0.0238866i
$653$	−173.733	−	148.382i	−0.266054	−	0.227231i	0.506406	−	0.862295i	$-0.330974\pi$
$653$	−173.733	−	148.382i	−0.266054	−	0.227231i	−0.772460	+	0.635064i	$0.780974\pi$
$654$	−111.001	+	95.2237i	−0.169726	+	0.145602i
$655$	1009.83	+	733.687i	1.54173	+	1.12013i
$656$	−930.951	−	464.141i	−1.41913	−	0.707532i
$657$	629.393	−	204.502i	0.957981	−	0.311267i
$658$	−288.436	−	692.066i	−0.438353	−	1.05177i
$659$	−465.932	−	192.995i	−0.707029	−	0.292861i	4.56217e−5	−	1.00000i	$-0.499985\pi$
$659$	−465.932	−	192.995i	−0.707029	−	0.292861i	−0.707075	+	0.707139i	$0.749985\pi$
$660$	258.895	+	66.9342i	0.392266	+	0.101415i
$661$	950.116	−	393.551i	1.43739	−	0.595387i	0.478227	−	0.878236i	$-0.341280\pi$
$661$	950.116	−	393.551i	1.43739	−	0.595387i	0.959164	+	0.282849i	$0.0912796\pi$
$662$	−1.49662	−	685.062i	−0.00226076	−	1.03484i
$663$	54.6861	+	27.8639i	0.0824828	+	0.0420271i
$664$	98.4064	−	137.329i	0.148202	−	0.206820i
$665$	−2399.79	+	380.090i	−3.60871	+	0.571564i
$666$	293.315	+	148.645i	0.440412	+	0.223191i
$667$	8.90198	+	113.110i	0.0133463	+	0.169581i
$668$	705.204	+	961.765i	1.05569	+	1.43977i
$669$	−148.307	+	35.6054i	−0.221685	+	0.0532218i
$670$	280.746	+	455.897i	0.419023	+	0.680443i
$671$	−75.1940	+	415.992i	−0.112063	+	0.619958i
$672$	3.35675	+	307.291i	0.00499517	+	0.457278i
$673$	536.239	−	389.601i	0.796790	−	0.578902i	−0.113181	−	0.993574i	$-0.536104\pi$
$673$	536.239	−	389.601i	0.796790	−	0.578902i	0.909971	+	0.414673i	$0.136104\pi$
$674$	480.397	+	408.486i	0.712755	+	0.606063i
$675$	325.659	+	278.139i	0.482458	+	0.412058i
$676$	−52.9931	−	16.9629i	−0.0783922	−	0.0250930i
$677$	121.798	−	507.326i	0.179909	−	0.749374i	−0.807326	−	0.590105i	$-0.799086\pi$
$677$	121.798	−	507.326i	0.179909	−	0.749374i	0.987235	−	0.159269i	$-0.0509137\pi$
$678$	347.116	+	54.2007i	0.511970	+	0.0799420i
$679$	−60.9167	+	119.556i	−0.0897152	+	0.176076i
$680$	−147.809	+	294.852i	−0.217366	+	0.433607i
$681$	−136.110	−	136.110i	−0.199868	−	0.199868i
$682$	310.426	−	580.866i	0.455169	−	0.851709i
$683$	24.1728	+	58.3584i	0.0353921	+	0.0854442i	0.940587	−	0.339552i	$-0.110275\pi$
$683$	24.1728	+	58.3584i	0.0353921	+	0.0854442i	−0.905195	+	0.424996i	$0.860275\pi$
$684$	789.161	−	488.354i	1.15374	−	0.713968i
$685$	−668.949	−	52.6474i	−0.976567	−	0.0768575i
$686$	487.373	−	799.234i	0.710456	−	1.16506i
$687$	90.3115	+	65.6151i	0.131458	+	0.0955096i
$688$	−401.406	+	170.392i	−0.583438	+	0.247663i
$689$	−678.788	−	220.552i	−0.985179	−	0.320104i
$690$	−3.47892	−	43.0026i	−0.00504192	−	0.0623226i
$691$	−126.192	+	30.2961i	−0.182623	+	0.0438438i	−0.323725	−	0.946151i	$-0.604935\pi$
$691$	−126.192	+	30.2961i	−0.182623	+	0.0438438i	0.141102	+	0.989995i	$0.454935\pi$
$692$	−525.098	−	609.399i	−0.758812	−	0.880634i
$693$	984.914	+	433.291i	1.42123	+	0.625240i
$694$	−173.011	−	125.123i	−0.249295	−	0.180293i
$695$	52.6631	−	332.501i	0.0757742	−	0.478419i
$696$	−193.757	−	78.7731i	−0.278387	−	0.113180i
$697$	163.770	+	321.417i	0.234964	+	0.461144i
$698$	246.295	−	486.002i	0.352858	−	0.696278i
$699$	73.4014	+	17.6221i	0.105009	+	0.0252105i
$700$	1007.74	+	998.976i	1.43963	+	1.42711i
$701$	−87.2397	+	1108.49i	−0.124450	+	1.58129i	0.545001	+	0.838436i	$0.316529\pi$
$701$	−87.2397	+	1108.49i	−0.124450	+	1.58129i	−0.669451	+	0.742856i	$0.733471\pi$
$702$	−145.954	+	354.554i	−0.207912	+	0.505063i
$703$			549.606i			0.781801i
$704$	−702.281	+	49.1696i	−0.997558	+	0.0698432i
$705$	−194.041			−0.275236
$706$	−736.390	−	303.140i	−1.04305	−	0.429377i
$707$	726.201	+	57.1532i	1.02716	+	0.0808391i
$708$	−200.902	+	202.666i	−0.283760	+	0.286251i
$709$	−49.7270	+	207.128i	−0.0701368	+	0.292141i	−0.996404	−	0.0847259i	$-0.972999\pi$
$709$	−49.7270	+	207.128i	−0.0701368	+	0.292141i	0.926267	+	0.376867i	$0.122999\pi$
$710$	1262.33	+	639.721i	1.77793	+	0.901016i
$711$	1033.73	−	526.712i	1.45391	−	0.740804i
$712$	733.911	+	298.376i	1.03077	+	0.419067i
$713$	−104.951	−	16.6226i	−0.147196	−	0.0233136i
$714$	62.4512	−	86.3528i	0.0874667	−	0.120942i
$715$	824.766	+	736.030i	1.15352	+	1.02941i
$716$	691.860	−	596.152i	0.966285	−	0.832615i
$717$	45.5175	+	189.594i	0.0634833	+	0.264427i
$718$	−425.509	+	34.4238i	−0.592631	+	0.0479440i
$719$	−129.668	+	399.077i	−0.180345	+	0.555045i	−0.999837	−	0.0180456i	$-0.994256\pi$
$719$	−129.668	+	399.077i	−0.180345	+	0.555045i	0.819492	+	0.573090i	$0.194256\pi$
$720$	−918.347	−	371.024i	−1.27548	−	0.515311i
$721$	631.568	−	869.278i	0.875961	−	1.20566i
$722$	707.897	+	431.676i	0.980467	+	0.597889i
$723$	5.16737	−	65.6576i	0.00714712	−	0.0908127i
$724$	586.560	+	947.858i	0.810166	+	1.30920i
$725$	−892.257	+	369.585i	−1.23070	+	0.509773i
$726$	68.8866	−	185.558i	0.0948851	−	0.255590i
$727$	−121.031	+	121.031i	−0.166480	+	0.166480i	−0.785430	−	0.618950i	$-0.787558\pi$
$727$	−121.031	+	121.031i	−0.166480	+	0.166480i	0.618950	+	0.785430i	$0.287558\pi$
$728$	−569.310	+	1135.67i	−0.782019	+	1.55999i
$729$	−377.539	−	192.366i	−0.517886	−	0.263876i
$730$	182.124	−	1166.37i	0.249484	−	1.59777i
$731$	147.044	+	35.3021i	0.201154	+	0.0482928i
$732$	−38.3296	+	119.744i	−0.0523628	+	0.163585i
$733$	466.051	−	545.676i	0.635813	−	0.744442i	−0.345169	−	0.938541i	$-0.612178\pi$
$733$	466.051	−	545.676i	0.635813	−	0.744442i	0.980982	+	0.194099i	$0.0621783\pi$
$734$	−179.087	+	210.614i	−0.243988	+	0.286940i
$735$	−317.441	−	436.920i	−0.431892	−	0.594449i
$736$	44.6096	+	104.455i	0.0606109	+	0.141923i
$737$	356.937	−	172.196i	0.484310	−	0.233645i
$738$	−922.412	+	568.030i	−1.24988	+	0.769689i
$739$	−20.4441	−	85.1558i	−0.0276645	−	0.115231i	0.956829	−	0.290651i	$-0.0938718\pi$
$739$	−20.4441	−	85.1558i	−0.0276645	−	0.115231i	−0.984494	+	0.175420i	$0.943872\pi$
$740$	473.036	−	346.849i	0.639238	−	0.468715i
$741$	−307.107	+	24.1698i	−0.414449	+	0.0326179i
$742$	−560.200	+	1105.42i	−0.754986	+	1.48978i
$743$	−47.2271	−	298.180i	−0.0635627	−	0.401319i	−0.998872	−	0.0474874i	$-0.984879\pi$
$743$	−47.2271	−	298.180i	−0.0635627	−	0.401319i	0.935309	−	0.353832i	$-0.115121\pi$
$744$	114.096	−	159.224i	0.153355	−	0.214011i
$745$	−326.960	+	641.695i	−0.438872	+	0.861336i
$746$	1379.71	−	3.01420i	1.84948	−	0.00404048i
$747$	−67.3283	−	162.545i	−0.0901317	−	0.217597i
$748$	205.910	+	131.158i	0.275281	+	0.175344i
$749$	−245.946	+	593.766i	−0.328365	+	0.792744i
$750$	58.4855	−	24.3753i	0.0779806	−	0.0325004i
$751$	−132.130	−	406.654i	−0.175938	−	0.541483i	0.823737	−	0.566973i	$-0.191885\pi$
$751$	−132.130	−	406.654i	−0.175938	−	0.541483i	−0.999675	+	0.0254898i	$0.991885\pi$
$752$	484.448	−	162.100i	0.644212	−	0.215559i
$753$	−98.0993	+	135.022i	−0.130278	+	0.179312i
$754$	−562.970	−	656.245i	−0.746645	−	0.870351i
$755$	545.904	−	639.171i	0.723051	−	0.846584i
$756$	569.159	+	345.369i	0.752855	+	0.456838i
$757$	237.990	−	388.365i	0.314386	−	0.513032i	−0.655946	−	0.754808i	$-0.727730\pi$
$757$	237.990	−	388.365i	0.314386	−	0.513032i	0.970332	+	0.241776i	$0.0777300\pi$
$758$	−818.771	−	592.143i	−1.08017	−	0.781191i
$759$	−31.9265	−	0.694436i	−0.0420639	−	0.000914935i
$760$	−140.700	−	1649.47i	−0.185131	−	2.17036i
$761$	46.5558	−	293.942i	0.0611772	−	0.386258i	−0.938034	−	0.346544i	$-0.887355\pi$
$761$	46.5558	−	293.942i	0.0611772	−	0.386258i	0.999211	−	0.0397141i	$-0.0126447\pi$
$762$	−186.399	+	95.4886i	−0.244618	+	0.125313i
$763$	82.3623	+	1046.51i	0.107945	+	1.37158i
$764$	22.8483	+	44.3620i	0.0299061	+	0.0580655i
$765$	179.465	+	292.860i	0.234595	+	0.382824i
$766$	229.470	+	946.696i	0.299570	+	1.23590i
$767$	−1121.94	+	364.541i	−1.46277	+	0.475281i
$768$	−208.993	−	12.7775i	−0.272126	−	0.0166374i
$769$	1228.16			1.59709			0.798546	−	0.601934i	$-0.205603\pi$
$769$	1228.16			1.59709			0.798546	+	0.601934i	$0.205603\pi$
$770$	1483.63	−	1217.77i	1.92680	−	1.58151i
$771$	−73.8582	+	178.309i	−0.0957953	+	0.231270i
$772$	18.4734	+	113.426i	0.0239292	+	0.146926i
$773$	−583.825	+	498.634i	−0.755272	+	0.645063i	−0.941334	−	0.337475i	$-0.890427\pi$
$773$	−583.825	+	498.634i	−0.755272	+	0.645063i	0.186063	+	0.982538i	$0.440427\pi$
$774$	−70.0597	+	448.681i	−0.0905163	+	0.579691i
$775$	−141.492	−	893.343i	−0.182570	−	1.15270i
$776$	−78.2622	−	47.2564i	−0.100853	−	0.0608974i
$777$	−168.868	+	86.0428i	−0.217334	+	0.110737i
$778$	38.1520	+	12.3043i	0.0490386	+	0.0158152i
$779$	−1543.79	−	946.036i	−1.98176	−	1.21442i
$780$	214.614	+	249.068i	0.275146	+	0.319318i
$781$	566.610	−	881.027i	0.725493	−	1.12808i
$782$	9.11128	−	38.3198i	0.0116513	−	0.0490023i
$783$	−366.578	+	266.335i	−0.468172	+	0.340147i
$784$	1157.53	+	825.638i	1.47644	+	1.05311i
$785$	−1186.64	−	385.562i	−1.51164	−	0.491162i
$786$	208.563	−	178.919i	0.265347	−	0.227632i
$787$	−185.127	−	302.099i	−0.235231	−	0.383862i	0.713142	−	0.701020i	$-0.247271\pi$
$787$	−185.127	−	302.099i	−0.235231	−	0.383862i	−0.948373	+	0.317158i	$0.897271\pi$
$788$	234.484	−	573.164i	0.297568	−	0.727366i
$789$	−43.8131	−	51.2986i	−0.0555300	−	0.0650172i
$790$	−4.52126	−	2069.55i	−0.00572311	−	2.61969i
$791$	1783.13	−	1783.13i	2.25428	−	2.25428i
$792$	−342.721	+	648.092i	−0.432728	+	0.818299i
$793$	−367.518	+	367.518i	−0.463452	+	0.463452i
$794$	−341.430	+	342.925i	−0.430012	+	0.431895i
$795$	208.293	+	243.880i	0.262004	+	0.306767i
$796$	−0.758291	−	173.549i	−0.000952627	−	0.218026i
$797$	522.672	+	852.924i	0.655800	+	1.07017i	0.991738	+	0.128284i	$0.0409468\pi$
$797$	522.672	+	852.924i	0.655800	+	1.07017i	−0.335938	+	0.941884i	$0.609053\pi$
$798$	−40.8020	+	533.333i	−0.0511304	+	0.668337i
$799$	−168.482	−	54.7431i	−0.210866	−	0.0685146i
$800$	−728.267	+	635.886i	−0.910333	+	0.794858i
$801$	667.462	−	484.940i	0.833286	−	0.605418i
$802$	−906.078	+	557.971i	−1.12977	+	0.695725i
$803$	−845.015	−	222.412i	−1.05232	−	0.276976i
$804$	111.939	−	36.9126i	0.139227	−	0.0459112i
$805$	−264.040	−	161.804i	−0.328000	−	0.200999i
$806$	720.696	−	369.198i	0.894164	−	0.458062i
$807$	279.213	−	142.266i	0.345989	−	0.176290i
$808$	−74.4273	+	490.709i	−0.0921130	+	0.607314i
$809$	−153.289	−	967.830i	−0.189480	−	1.19633i	−0.880697	−	0.473681i	$-0.842925\pi$
$809$	−153.289	−	967.830i	−0.189480	−	1.19633i	0.691217	−	0.722648i	$-0.257075\pi$
$810$	−760.863	+	555.343i	−0.939337	+	0.685609i
$811$	50.1124	−	42.8000i	0.0617908	−	0.0527744i	−0.618016	−	0.786165i	$-0.712063\pi$
$811$	50.1124	−	42.8000i	0.0617908	−	0.0527744i	0.679807	+	0.733391i	$0.262063\pi$
$812$	−1276.63	+	790.013i	−1.57220	+	0.972922i
$813$	42.0509	−	101.520i	0.0517231	−	0.124871i
$814$	−219.571	−	374.562i	−0.269743	−	0.460149i
$815$	33.8407			0.0415223
$816$	55.6231	+	46.6722i	0.0681655	+	0.0571963i
$817$	−721.864	+	234.548i	−0.883555	+	0.287084i
$818$	−564.090	+	925.042i	−0.689597	+	1.13086i
$819$	691.238	+	1128.00i	0.844003	+	1.37729i
$820$	160.029	+	1925.74i	0.195157	+	2.34847i
$821$	−80.6382	−	1024.61i	−0.0982195	−	1.24800i	−0.826586	−	0.562810i	$-0.809720\pi$
$821$	−80.6382	−	1024.61i	−0.0982195	−	1.24800i	0.728367	−	0.685187i	$-0.240280\pi$
$822$	−45.3415	+	140.591i	−0.0551600	+	0.171036i
$823$	−199.389	+	1258.89i	−0.242271	+	1.52964i	0.503829	+	0.863803i	$0.331924\pi$
$823$	−199.389	+	1258.89i	−0.242271	+	1.52964i	−0.746100	+	0.665834i	$0.768076\pi$
$824$	559.793	+	471.798i	0.679360	+	0.572571i
$825$	−78.3563	−	260.284i	−0.0949773	−	0.315496i
$826$	324.848	+	2022.40i	0.393278	+	2.44843i
$827$	−439.544	+	717.271i	−0.531492	+	0.867317i	−0.999869	−	0.0162123i	$-0.994839\pi$
$827$	−439.544	+	717.271i	−0.531492	+	0.867317i	0.468376	+	0.883529i	$0.344839\pi$
$828$	116.906	+	17.9928i	0.141190	+	0.0217304i
$829$	−396.439	+	464.170i	−0.478214	+	0.559916i	−0.946101	−	0.323872i	$-0.895015\pi$
$829$	−396.439	+	464.170i	−0.478214	+	0.559916i	0.467887	+	0.883788i	$0.345015\pi$
$830$	−312.926	−	23.9401i	−0.377020	−	0.0288435i
$831$	31.4130	−	43.2363i	0.0378014	−	0.0520292i
$832$	−743.879	−	442.544i	−0.894086	−	0.531903i
$833$	−152.363	−	468.926i	−0.182909	−	0.562936i
$834$	−68.5318	−	28.2115i	−0.0821724	−	0.0338268i
$835$	847.805	−	2046.78i	1.01534	−	2.45124i
$836$	−1225.17	−	21.2936i	−1.46552	−	0.0254708i
$837$	−162.395	−	392.056i	−0.194020	−	0.468406i
$838$	−70.2635	+	70.5712i	−0.0838467	+	0.0842138i
$839$	−394.538	+	774.324i	−0.470248	+	0.922913i	0.527077	+	0.849817i	$0.323288\pi$
$839$	−394.538	+	774.324i	−0.470248	+	0.922913i	−0.997325	+	0.0730956i	$0.976712\pi$
$840$	484.780	−	301.462i	0.577119	−	0.358883i
$841$	−28.2835	−	178.575i	−0.0336308	−	0.212336i
$842$	−761.836	+	249.377i	−0.904793	+	0.296172i
$843$	−19.9727	+	1.57189i	−0.0236925	+	0.00186464i
$844$	−903.627	−	548.327i	−1.07065	−	0.649677i
$845$	24.1294	+	100.506i	0.0285555	+	0.118942i
$846$	123.060	−	517.558i	0.145460	−	0.611771i
$847$	−784.314	−	1184.61i	−0.925990	−	1.39860i
$848$	−723.765	−	434.870i	−0.853496	−	0.512818i
$849$	86.5190	+	119.083i	0.101907	+	0.140263i
$850$	334.180	−	27.0352i	0.393153	−	0.0318062i
$851$	−45.4932	+	53.2657i	−0.0534585	+	0.0625919i
$852$	201.296	−	237.783i	0.236263	−	0.279089i
$853$	−82.9153	−	19.9062i	−0.0972044	−	0.0233367i	0.184551	−	0.982823i	$-0.440917\pi$
$853$	−82.9153	−	19.9062i	−0.0972044	−	0.0233367i	−0.281756	+	0.959486i	$0.590917\pi$
$854$	532.047	+	728.946i	0.623006	+	0.853566i
$855$	−1536.06	−	782.664i	−1.79657	−	0.915397i
$856$	−391.458	−	196.237i	−0.457310	−	0.229248i
$857$	805.176	−	805.176i	0.939528	−	0.939528i	−0.0587450	−	0.998273i	$-0.518710\pi$
$857$	805.176	−	805.176i	0.939528	−	0.939528i	0.998273	+	0.0587450i	$0.0187099\pi$
$858$	199.640	−	139.163i	0.232681	−	0.162194i
$859$	475.511	−	196.963i	0.553564	−	0.229294i	−0.0883245	−	0.996092i	$-0.528151\pi$
$859$	475.511	−	196.963i	0.553564	−	0.229294i	0.641888	+	0.766798i	$0.278151\pi$
$860$	657.430	+	473.276i	0.764454	+	0.550321i
$861$	48.9871	−	622.441i	0.0568956	−	0.722928i
$862$	952.940	−	230.984i	1.10550	−	0.267963i
$863$	398.757	−	548.841i	0.462059	−	0.635969i	−0.512876	−	0.858463i	$-0.671420\pi$
$863$	398.757	−	548.841i	0.462059	−	0.635969i	0.974934	+	0.222494i	$0.0714198\pi$
$864$	−262.597	+	369.863i	−0.303931	+	0.428082i
$865$	−461.771	+	1421.18i	−0.533839	+	1.64299i
$866$	−699.384	−	594.693i	−0.807603	−	0.686712i
$867$	49.3023	+	205.359i	0.0568653	+	0.236861i
$868$	−440.322	−	1335.29i	−0.507284	−	1.53835i
$869$	−1524.17	−	153.369i	−1.75393	−	0.176489i
$870$	61.6191	+	383.622i	0.0708266	+	0.440945i
$871$	481.252	+	76.2229i	0.552528	+	0.0875119i
$872$	−715.223	+	4.68760i	−0.820209	+	0.00537569i
$873$	−84.8291	+	43.2226i	−0.0971696	+	0.0495104i
$874$	61.5023	+	187.887i	0.0703687	+	0.214974i
$875$	106.171	−	442.233i	0.121338	−	0.505409i
$876$	−240.533	−	98.4030i	−0.274581	−	0.112332i
$877$	257.610	+	20.2743i	0.293740	+	0.0231178i	0.224473	−	0.974480i	$-0.427934\pi$
$877$	257.610	+	20.2743i	0.293740	+	0.0231178i	0.0692670	+	0.997598i	$0.477934\pi$
$878$	1286.58	−	536.214i	1.46535	−	0.610722i
$879$	461.487			0.525013
$880$	754.862	+	1067.92i	0.857798	+	1.21355i
$881$		−	1006.53i		−	1.14249i	−0.820780	−	0.571245i	$-0.806461\pi$
$881$		−	1006.53i		−	1.14249i	0.820780	−	0.571245i	$-0.193539\pi$
$882$	1366.70	−	569.606i	1.54955	−	0.645812i
$883$	98.4393	−	1250.79i	0.111483	−	1.41652i	−0.645836	−	0.763477i	$-0.723491\pi$
$883$	98.4393	−	1250.79i	0.111483	−	1.41652i	0.757318	−	0.653046i	$-0.226509\pi$
$884$	116.077	+	276.808i	0.131309	+	0.313131i
$885$	515.463	+	123.752i	0.582444	+	0.139832i
$886$	−394.260	−	1204.45i	−0.444988	−	1.35942i
$887$	−95.0346	−	186.516i	−0.107142	−	0.210277i	0.831211	−	0.555957i	$-0.187648\pi$
$887$	−95.0346	−	186.516i	−0.107142	−	0.210277i	−0.938352	+	0.345680i	$0.887648\pi$
$888$	−50.1974	−	118.976i	−0.0565287	−	0.133982i
$889$	−235.165	+	1484.78i	−0.264528	+	1.67016i
$890$	−233.400	−	1453.08i	−0.262247	−	1.63267i
$891$	351.293	+	602.277i	0.394268	+	0.675956i
$892$	−666.088	−	335.731i	−0.746735	−	0.376380i
$893$	864.596	−	207.571i	0.968192	−	0.232442i
$894$	120.785	+	102.705i	0.135106	+	0.114882i
$895$	−1613.49	−	524.256i	−1.80279	−	0.585761i
$896$	−958.475	+	1157.62i	−1.06973	+	1.29198i
$897$	−31.7642	−	23.0781i	−0.0354116	−	0.0257281i
$898$	−1392.09	+	337.430i	−1.55021	+	0.375757i
$899$	954.001	+	75.0815i	1.06118	+	0.0835167i
$900$	161.844	+	993.724i	0.179827	+	1.10414i
$901$	112.053	+	270.520i	0.124365	+	0.300244i
$902$	1430.05	+	27.9797i	1.58543	+	0.0310196i
$903$	−185.076	−	185.076i	−0.204957	−	0.204957i
$904$	1124.40	+	1299.16i	1.24380	+	1.43712i
$905$	940.054	−	1844.96i	1.03873	−	2.03863i
$906$	−109.095	−	149.468i	−0.120414	−	0.164976i
$907$	150.668	−	627.578i	0.166117	−	0.691927i	−0.825684	−	0.564133i	$-0.809210\pi$
$907$	150.668	−	627.578i	0.166117	−	0.691927i	0.991801	−	0.127794i	$-0.0407895\pi$
$908$	−77.9593	−	938.143i	−0.0858583	−	1.03320i
$909$	393.023	+	335.673i	0.432368	+	0.369277i
$910$	2352.22	−	190.295i	2.58485	−	0.209115i
$911$	−996.918	+	724.303i	−1.09431	+	0.795064i	−0.980122	−	0.198395i	$-0.936427\pi$
$911$	−996.918	+	724.303i	−1.09431	+	0.795064i	−0.114189	+	0.993459i	$0.536427\pi$
$912$	−360.442	−	53.8640i	−0.395221	−	0.0590614i
$913$	−41.3208	+	228.597i	−0.0452583	+	0.250380i
$914$	379.174	−	1594.71i	0.414852	−	1.74476i
$915$	227.105	−	54.5231i	0.248202	−	0.0595881i
$916$	129.765	+	530.292i	0.141665	+	0.578922i
$917$	−154.753	−	1966.33i	−0.168760	−	2.14430i
$918$	149.495	−	48.9354i	0.162849	−	0.0533065i
$919$	−597.083	+	94.5686i	−0.649709	+	0.102904i	−0.472586	−	0.881285i	$-0.656679\pi$
$919$	−597.083	+	94.5686i	−0.649709	+	0.102904i	−0.177124	+	0.984189i	$0.556679\pi$
$920$	122.898	−	171.507i	0.133585	−	0.186420i
$921$	−295.075	−	150.348i	−0.320385	−	0.163244i
$922$	−205.268	+	206.167i	−0.222634	+	0.223609i
$923$	1189.86	−	492.856i	1.28912	−	0.533972i
$924$	−185.262	−	379.772i	−0.200500	−	0.411009i
$925$	−550.870	−	228.178i	−0.595535	−	0.246679i
$926$	−1302.71	−	536.267i	−1.40681	−	0.579122i
$927$	725.073	−	235.591i	0.782172	−	0.254143i
$928$	−474.314	−	906.284i	−0.511115	−	0.976599i
$929$	−151.008	−	109.714i	−0.162549	−	0.118099i	0.503537	−	0.863974i	$-0.332032\pi$
$929$	−151.008	−	109.714i	−0.162549	−	0.118099i	−0.666086	+	0.745875i	$0.732032\pi$
$930$	−362.820	−	27.7571i	−0.390129	−	0.0298464i
$931$	1881.82	+	1607.23i	2.02129	+	1.72634i
$932$	218.298	+	297.717i	0.234225	+	0.319439i
$933$	281.680	+	172.614i	0.301908	+	0.185009i
$934$	−45.9579	−	286.120i	−0.0492055	−	0.306338i
$935$	9.86202	−	453.404i	0.0105476	−	0.484924i
$936$	−800.437	+	414.473i	−0.855168	+	0.442813i
$937$	1345.75	+	213.146i	1.43624	+	0.227477i	0.825520	−	0.564372i	$-0.190882\pi$
$937$	1345.75	+	213.146i	1.43624	+	0.227477i	0.610716	+	0.791850i	$0.290882\pi$
$938$	259.680	−	805.196i	0.276845	−	0.858417i
$939$	5.46664	−	0.430234i	0.00582177	−	0.000458183i
$940$	−724.288	−	613.147i	−0.770519	−	0.652285i
$941$	−1057.67	+	648.142i	−1.12399	+	0.688780i	−0.954931	−	0.296826i	$-0.904072\pi$
$941$	−1057.67	+	648.142i	−1.12399	+	0.688780i	−0.169056	+	0.985607i	$0.554072\pi$
$942$	−143.007	+	234.514i	−0.151812	+	0.248953i
$943$	−71.3108	−	219.472i	−0.0756212	−	0.232738i
$944$	−1390.30	+	121.652i	−1.47277	+	0.128869i
$945$		−	1236.72i		−	1.30870i
$946$	398.254	−	448.235i	0.420987	−	0.473822i
$947$	1327.58	+	549.902i	1.40188	+	0.580678i	0.950239	−	0.311522i	$-0.100839\pi$
$947$	1327.58	+	549.902i	1.40188	+	0.580678i	0.451641	+	0.892200i	$0.350839\pi$
$948$	−443.477	−	104.422i	−0.467803	−	0.110150i
$949$	−697.719	−	816.924i	−0.735215	−	0.860826i
$950$	−1359.25	+	992.094i	−1.43079	+	1.04431i
$951$	−271.790	+	43.0473i	−0.285794	+	0.0452653i
$952$	505.974	−	124.986i	0.531485	−	0.131288i
$953$	−687.906	−	1350.09i	−0.721832	−	1.41668i	−0.901425	−	0.432934i	$-0.857478\pi$
$953$	−687.906	−	1350.09i	−0.721832	−	1.41668i	0.179593	−	0.983741i	$-0.442522\pi$
$954$	−782.589	+	400.905i	−0.820324	+	0.420236i
$955$	48.4337	−	79.0366i	0.0507159	−	0.0827609i
$956$	−429.194	+	851.519i	−0.448948	+	0.890710i
$957$	287.129	−	16.3242i	0.300030	−	0.0170577i
$958$	−572.894	+	352.794i	−0.598010	+	0.368261i
$959$	623.242	+	857.819i	0.649887	+	0.894493i
$960$	181.110	+	344.219i	0.188656	+	0.358561i
$961$	20.0190	−	61.6121i	0.0208314	−	0.0641125i
$962$	40.7200	−	532.260i	0.0423285	−	0.553285i
$963$	−388.812	+	238.264i	−0.403751	+	0.247419i
$964$	226.758	−	228.749i	0.235227	−	0.237291i
$965$	162.332	−	138.645i	0.168220	−	0.143673i
$966$	−48.1005	+	48.3112i	−0.0497935	+	0.0500116i
$967$	−124.916	−	124.916i	−0.129179	−	0.129179i	0.639561	−	0.768740i	$-0.279116\pi$
$967$	−124.916	−	124.916i	−0.129179	−	0.129179i	−0.768740	+	0.639561i	$0.779116\pi$
$968$	843.472	−	474.951i	0.871356	−	0.490652i
$969$	89.3658	+	89.3658i	0.0922247	+	0.0922247i
$970$	0.371020	+	169.830i	0.000382494	+	0.175082i
$971$	−1001.01	+	854.944i	−1.03091	+	0.880478i	−0.992918	−	0.118801i	$-0.962095\pi$
$971$	−1001.01	+	854.944i	−1.03091	+	0.880478i	−0.0379886	+	0.999278i	$0.512095\pi$
$972$	277.537	+	661.840i	0.285532	+	0.680905i
$973$	−453.569	+	277.948i	−0.466156	+	0.285660i
$974$	731.375	−	627.422i	0.750898	−	0.644170i
$975$	103.275	−	317.847i	0.105923	−	0.325997i
$976$	−521.448	+	325.846i	−0.534271	+	0.333858i
$977$	584.634	+	804.680i	0.598397	+	0.823623i	0.995560	−	0.0941248i	$-0.0300053\pi$
$977$	584.634	+	804.680i	0.598397	+	0.823623i	−0.397163	+	0.917748i	$0.630005\pi$
$978$	1.72331	−	7.24783i	0.00176208	−	0.00741087i
$979$	−1087.58	+	61.8326i	−1.11091	+	0.0631590i
$980$	195.720	−	2633.95i	0.199715	−	2.68770i
$981$	−389.175	+	635.076i	−0.396712	+	0.647376i
$982$	1605.91	+	517.917i	1.63535	+	0.527410i
$983$	555.720	+	1090.66i	0.565331	+	1.10952i	0.979897	+	0.199505i	$0.0639335\pi$
$983$	555.720	+	1090.66i	0.565331	+	1.10952i	−0.414566	+	0.910019i	$0.636067\pi$
$984$	420.596	+	63.7931i	0.427435	+	0.0648304i
$985$	−1136.22	+	179.960i	−1.15352	+	0.182700i
$986$	−54.7252	+	350.475i	−0.0555023	+	0.355452i
$987$	199.133	+	233.154i	0.201755	+	0.236225i
$988$	−1222.70	−	880.205i	−1.23755	−	0.890895i
$989$	−89.3748	−	37.0202i	−0.0903688	−	0.0374320i
$990$	1359.52	−	80.2733i	1.37325	−	0.0810842i
$991$		−	652.016i		−	0.657938i	−0.944341	−	0.328969i	$-0.893299\pi$
$991$		−	652.016i		−	0.657938i	0.944341	−	0.328969i	$-0.106701\pi$
$992$	929.013	−	233.798i	0.936505	−	0.235683i
$993$	86.5734	+	266.446i	0.0871837	+	0.268324i
$994$	−526.786	−	2173.29i	−0.529965	−	2.18641i
$995$	−274.885	+	168.450i	−0.276266	+	0.169296i
$996$	−21.0629	+	65.8020i	−0.0211475	+	0.0660663i
$997$	−1629.50	+	128.245i	−1.63441	+	0.128631i	−0.862140	−	0.506670i	$-0.830876\pi$
$997$	−1629.50	+	128.245i	−1.63441	+	0.128631i	−0.772265	+	0.635300i	$0.780876\pi$
$998$	1416.05	−	725.414i	1.41889	−	0.726868i
$999$	−276.304	−	43.7623i	−0.276581	−	0.0438061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.3.bd.a.3.13	✓	1504
11.4	even	5	inner	352.3.bd.a.323.51	yes	1504
32.11	odd	8	inner	352.3.bd.a.267.51	yes	1504
352.235	odd	40	inner	352.3.bd.a.235.13	yes	1504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.3.bd.a.3.13	✓	1504	1.1	even	1	trivial
352.3.bd.a.235.13	yes	1504	352.235	odd	40	inner
352.3.bd.a.267.51	yes	1504	32.11	odd	8	inner
352.3.bd.a.323.51	yes	1504	11.4	even	5	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	352.bd (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84943 - 0.761328i) q^{2} +(0.815381 + 0.0641719i) q^{3} +(2.84076 + 2.81604i) q^{4} +(1.73462 - 7.22523i) q^{5} +(-1.45913 - 0.739454i) q^{6} +(-10.4618 + 5.33054i) q^{7} +(-3.10984 - 7.37081i) q^{8} +(-8.22847 - 1.30326i) q^{9} +(-8.70883 + 12.0419i) q^{10} +(8.20714 + 7.32413i) q^{11} +(2.13559 + 2.47844i) q^{12} +(3.15722 + 13.1508i) q^{13} +(23.4066 - 1.89360i) q^{14} +(1.87804 - 5.78000i) q^{15} +(0.139816 + 15.9994i) q^{16} +(3.26132 - 4.48883i) q^{17} +(14.2257 + 8.67485i) q^{18} +(-2.18501 + 27.7631i) q^{19} +(25.2742 - 15.6404i) q^{20} +(-8.87240 + 3.67507i) q^{21} +(-9.60243 - 19.7938i) q^{22} +(-2.50983 + 2.50983i) q^{23} +(-2.06271 - 6.20959i) q^{24} +(-26.9198 - 13.7163i) q^{25} +(4.17300 - 26.7250i) q^{26} +(-13.7834 - 3.30911i) q^{27} +(-44.7304 - 14.3180i) q^{28} +(20.7600 - 24.3068i) q^{29} +(-7.87377 + 9.25988i) q^{30} +(17.5965 + 24.2195i) q^{31} +(11.9222 - 29.6961i) q^{32} +(6.22194 + 6.49863i) q^{33} +(-9.44905 + 5.81882i) q^{34} +(20.3671 + 84.8352i) q^{35} +(-19.7050 - 26.8740i) q^{36} +(19.6744 - 1.54841i) q^{37} +(25.1779 - 49.6824i) q^{38} +(1.73043 + 10.9255i) q^{39} +(-58.6502 + 9.68373i) q^{40} +(-29.5162 + 57.9287i) q^{41} +(19.2068 - 0.0419602i) q^{42} +(10.4299 + 25.1800i) q^{43} +(2.68943 + 43.9177i) q^{44} +(-23.6897 + 57.1919i) q^{45} +(6.55256 - 2.73095i) q^{46} +(-9.86630 - 30.3654i) q^{47} +(-0.912708 + 13.0546i) q^{48} +(52.2326 - 71.8920i) q^{49} +(39.3436 + 45.8622i) q^{50} +(2.94728 - 3.45082i) q^{51} +(-28.0642 + 46.2490i) q^{52} +(-27.5736 + 44.9961i) q^{53} +(22.9721 + 16.6137i) q^{54} +(67.1548 - 46.5938i) q^{55} +(71.8249 + 60.5346i) q^{56} +(-3.56323 + 22.4973i) q^{57} +(-56.8996 + 29.1486i) q^{58} +(6.84365 + 86.9568i) q^{59} +(21.6118 - 11.1310i) q^{60} +(20.0798 + 32.7672i) q^{61} +(-14.1044 - 58.1888i) q^{62} +(93.0314 - 30.2277i) q^{63} +(-44.6578 + 45.8441i) q^{64} +100.494 q^{65} +(-6.55943 - 16.7557i) q^{66} +(13.7871 - 33.2850i) q^{67} +(21.9054 - 3.56765i) q^{68} +(-2.20753 + 1.88541i) q^{69} +(26.9199 - 172.403i) q^{70} +(-14.8968 - 94.0548i) q^{71} +(15.9831 + 64.7034i) q^{72} +(-70.7779 + 36.0631i) q^{73} +(-37.5652 - 12.1150i) q^{74} +(-21.0697 - 12.9115i) q^{75} +(-84.3893 + 72.7153i) q^{76} +(-124.903 - 32.8749i) q^{77} +(5.11758 - 21.5233i) q^{78} +(-112.664 + 81.8551i) q^{79} +(115.842 + 26.7427i) q^{80} +(60.2832 + 19.5872i) q^{81} +(98.6907 - 84.6634i) q^{82} +(11.0343 + 18.0063i) q^{83} +(-35.5535 - 14.5451i) q^{84} +(-26.7756 - 31.3502i) q^{85} +(-0.119083 - 54.5090i) q^{86} +(18.4871 - 18.4871i) q^{87} +(28.4619 - 83.2702i) q^{88} +(-70.0253 + 70.0253i) q^{89} +(87.3541 - 87.7366i) q^{90} +(-103.131 - 120.751i) q^{91} +(-14.1976 + 0.0620341i) q^{92} +(12.7936 + 20.8773i) q^{93} +(-4.87100 + 63.6700i) q^{94} +(196.805 + 63.9458i) q^{95} +(11.6268 - 23.4486i) q^{96} +(9.24533 - 6.71713i) q^{97} +(-151.334 + 93.1928i) q^{98} +(-57.9869 - 70.9624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1504 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} + 64 q^{12} - 12 q^{13} + 4 q^{14} - 24 q^{15} - 52 q^{16} + 168 q^{18} - 12 q^{19}+ \cdots - 236 q^{99}+O(q^{100}) \) 1504 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 + 64 * q^12 - 12 * q^13 + 4 * q^14 - 24 * q^15 - 52 * q^16 + 168 * q^18 - 12 * q^19 - 92 * q^20 - 32 * q^21 - 164 * q^22 + 96 * q^23 - 12 * q^24 - 12 * q^25 + 288 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 + 20 * q^30 + 8 * q^32 - 32 * q^33 + 56 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 348 * q^40 - 12 * q^41 + 188 * q^42 - 224 * q^43 + 168 * q^44 + 40 * q^45 + 52 * q^46 - 24 * q^47 - 12 * q^48 - 12 * q^50 - 84 * q^51 - 860 * q^52 - 492 * q^53 - 648 * q^54 - 272 * q^55 + 1016 * q^56 - 12 * q^57 - 12 * q^58 - 140 * q^59 - 28 * q^60 - 12 * q^61 - 44 * q^62 - 156 * q^64 - 64 * q^65 + 560 * q^66 + 288 * q^67 + 476 * q^68 - 12 * q^69 + 324 * q^70 + 244 * q^71 - 1272 * q^72 - 12 * q^73 + 1044 * q^74 - 964 * q^75 - 32 * q^76 - 240 * q^77 + 688 * q^78 - 24 * q^79 + 1388 * q^80 - 132 * q^82 - 12 * q^83 - 1244 * q^84 - 212 * q^85 - 948 * q^86 - 32 * q^87 - 692 * q^88 - 32 * q^89 - 1044 * q^90 - 588 * q^91 - 316 * q^92 - 84 * q^93 + 2096 * q^94 - 1100 * q^96 - 24 * q^97 - 64 * q^98 - 236 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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