LMFDB - Embedded newform 126.3.q.a.29.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(29,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.29"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.q (of order $6$, degree $2$, 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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	126.29
Dual form			126.3.q.a.113.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +(-1.41155 + 2.64717i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.60855 + 2.08340i) q^{5} +(-3.60062 + 2.24400i) q^{6} +(-1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(-5.01506 - 7.47323i) q^{9} -5.89274 q^{10} +(-5.60663 - 3.23699i) q^{11} +(-5.99659 + 0.202301i) q^{12} +(7.36010 + 12.7481i) q^{13} +(-3.24037 + 1.87083i) q^{14} +(-0.421473 - 12.4933i) q^{15} +(-2.00000 + 3.46410i) q^{16} +18.6466i q^{17} +(-0.857802 - 12.6990i) q^{18} +15.6987 q^{19} +(-7.21710 - 4.16679i) q^{20} +(-4.19814 - 6.73615i) q^{21} +(-4.57780 - 7.92898i) q^{22} +(17.1145 - 9.88106i) q^{23} +(-7.48734 - 3.99246i) q^{24} +(-3.81892 + 6.61456i) q^{25} +20.8175i q^{26} +(26.8619 - 2.72692i) q^{27} -5.29150 q^{28} +(-9.30724 - 5.37354i) q^{29} +(8.31788 - 15.5991i) q^{30} +(11.1508 + 19.3137i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(16.4829 - 10.2726i) q^{33} +(-13.1851 + 22.8373i) q^{34} -11.0243i q^{35} +(7.92895 - 16.1596i) q^{36} +70.8586 q^{37} +(19.2269 + 11.1006i) q^{38} +(-44.1355 + 1.48896i) q^{39} +(-5.89274 - 10.2065i) q^{40} +(-7.29137 + 4.20968i) q^{41} +(-0.378470 - 11.2186i) q^{42} +(24.9486 - 43.2123i) q^{43} -12.9480i q^{44} +(33.6668 + 16.5191i) q^{45} +27.9479 q^{46} +(-62.5123 - 36.0915i) q^{47} +(-6.34698 - 10.1841i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-9.35440 + 5.40077i) q^{50} +(-49.3607 - 26.3205i) q^{51} +(-14.7202 + 25.4961i) q^{52} +80.3093i q^{53} +(34.8273 + 15.6545i) q^{54} +26.9757 q^{55} +(-6.48074 - 3.74166i) q^{56} +(-22.1594 + 41.5571i) q^{57} +(-7.59933 - 13.1624i) q^{58} +(-22.8843 + 13.2122i) q^{59} +(21.2175 - 13.2233i) q^{60} +(32.7902 - 56.7944i) q^{61} +31.5391i q^{62} +(23.7576 - 1.60480i) q^{63} -8.00000 q^{64} +(-53.1186 - 30.6680i) q^{65} +(27.4512 - 0.926092i) q^{66} +(-11.9038 - 20.6181i) q^{67} +(-32.2968 + 18.6466i) q^{68} +(1.99895 + 59.2527i) q^{69} +(7.79536 - 13.5020i) q^{70} -111.926i q^{71} +(21.1375 - 14.1847i) q^{72} +13.3109 q^{73} +(86.7837 + 50.1046i) q^{74} +(-12.1193 - 19.4461i) q^{75} +(15.6987 + 27.1909i) q^{76} +(14.8338 - 8.56427i) q^{77} +(-55.1076 - 29.3849i) q^{78} +(-59.8755 + 103.707i) q^{79} -16.6672i q^{80} +(-30.6983 + 74.9574i) q^{81} -11.9068 q^{82} +(10.0716 + 5.81486i) q^{83} +(7.46921 - 14.0075i) q^{84} +(-38.8482 - 67.2871i) q^{85} +(61.1114 - 35.2827i) q^{86} +(27.3623 - 17.0529i) q^{87} +(9.15559 - 15.8580i) q^{88} +83.5516i q^{89} +(29.5524 + 44.0378i) q^{90} -38.9460 q^{91} +(34.2290 + 19.7621i) q^{92} +(-66.8665 + 2.25581i) q^{93} +(-51.0411 - 88.4058i) q^{94} +(-56.6494 + 32.7065i) q^{95} +(-0.572193 - 16.9609i) q^{96} +(-84.0615 + 145.599i) q^{97} -9.89949i q^{98} +(3.92684 + 58.1334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30}+ \cdots - 440 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	−1.41155	+	2.64717i	−0.470516	+	0.882391i
$3$	−1.41155	+	2.64717i	−0.470516	+	0.882391i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−3.60855	+	2.08340i	−0.721710	+	0.416679i	−0.815382	−	0.578924i	$-0.803473\pi$
$5$	−3.60855	+	2.08340i	−0.721710	+	0.416679i	0.0936719	+	0.995603i	$0.470140\pi$
$6$	−3.60062	+	2.24400i	−0.600104	+	0.374000i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$			2.82843i			0.353553i
$9$	−5.01506	−	7.47323i	−0.557229	−	0.830359i
$10$	−5.89274			−0.589274
$11$	−5.60663	−	3.23699i	−0.509694	−	0.294272i	0.223014	−	0.974815i	$-0.428410\pi$
$11$	−5.60663	−	3.23699i	−0.509694	−	0.294272i	−0.732708	+	0.680543i	$0.761744\pi$
$12$	−5.99659	+	0.202301i	−0.499716	+	0.0168584i
$13$	7.36010	+	12.7481i	0.566162	+	0.980621i	0.996941	+	0.0781633i	$0.0249056\pi$
$13$	7.36010	+	12.7481i	0.566162	+	0.980621i	−0.430779	+	0.902458i	$0.641761\pi$
$14$	−3.24037	+	1.87083i	−0.231455	+	0.133631i
$15$	−0.421473	−	12.4933i	−0.0280982	−	0.832885i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			18.6466i			1.09686i	0.836197	+	0.548428i	$0.184774\pi$
$17$			18.6466i			1.09686i	−0.836197	+	0.548428i	$0.815226\pi$
$18$	−0.857802	−	12.6990i	−0.0476557	−	0.705499i
$19$	15.6987			0.826245			0.413123	−	0.910675i	$-0.364438\pi$
$19$	15.6987			0.826245			0.413123	+	0.910675i	$0.364438\pi$
$20$	−7.21710	−	4.16679i	−0.360855	−	0.208340i
$21$	−4.19814	−	6.73615i	−0.199911	−	0.320769i
$22$	−4.57780	−	7.92898i	−0.208082	−	0.360408i
$23$	17.1145	−	9.88106i	0.744109	−	0.429611i	−0.0794526	−	0.996839i	$-0.525317\pi$
$23$	17.1145	−	9.88106i	0.744109	−	0.429611i	0.823561	+	0.567227i	$0.191984\pi$
$24$	−7.48734	−	3.99246i	−0.311972	−	0.166353i
$25$	−3.81892	+	6.61456i	−0.152757	+	0.264582i
$26$			20.8175i			0.800674i
$27$	26.8619	−	2.72692i	0.994887	−	0.100997i
$28$	−5.29150			−0.188982
$29$	−9.30724	−	5.37354i	−0.320939	−	0.185294i	0.330872	−	0.943676i	$-0.392657\pi$
$29$	−9.30724	−	5.37354i	−0.320939	−	0.185294i	−0.651811	+	0.758381i	$0.725991\pi$
$30$	8.31788	−	15.5991i	0.277263	−	0.519970i
$31$	11.1508	+	19.3137i	0.359702	+	0.623022i	0.987911	−	0.155023i	$-0.0495451\pi$
$31$	11.1508	+	19.3137i	0.359702	+	0.623022i	−0.628209	+	0.778044i	$0.716212\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	16.4829	−	10.2726i	0.499482	−	0.311290i
$34$	−13.1851	+	22.8373i	−0.387798	+	0.671685i
$35$		−	11.0243i		−	0.314980i
$36$	7.92895	−	16.1596i	0.220249	−	0.448877i
$37$	70.8586			1.91510			0.957548	−	0.288273i	$-0.0930810\pi$
$37$	70.8586			1.91510			0.957548	+	0.288273i	$0.0930810\pi$
$38$	19.2269	+	11.1006i	0.505970	+	0.292122i
$39$	−44.1355	+	1.48896i	−1.13168	+	0.0381783i
$40$	−5.89274	−	10.2065i	−0.147318	−	0.255163i
$41$	−7.29137	+	4.20968i	−0.177838	+	0.102675i	−0.586277	−	0.810111i	$-0.699407\pi$
$41$	−7.29137	+	4.20968i	−0.177838	+	0.102675i	0.408438	+	0.912786i	$0.366074\pi$
$42$	−0.378470	−	11.2186i	−0.00901120	−	0.267109i
$43$	24.9486	−	43.2123i	0.580201	−	1.00494i	−0.415254	−	0.909705i	$-0.636307\pi$
$43$	24.9486	−	43.2123i	0.580201	−	1.00494i	0.995455	−	0.0952318i	$-0.0303592\pi$
$44$		−	12.9480i		−	0.294272i
$45$	33.6668	+	16.5191i	0.748151	+	0.367092i
$46$	27.9479			0.607562
$47$	−62.5123	−	36.0915i	−1.33005	−	0.767904i	−0.344743	−	0.938697i	$-0.612034\pi$
$47$	−62.5123	−	36.0915i	−1.33005	−	0.767904i	−0.985307	+	0.170793i	$0.945367\pi$
$48$	−6.34698	−	10.1841i	−0.132229	−	0.212169i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	−9.35440	+	5.40077i	−0.187088	+	0.108015i
$51$	−49.3607	−	26.3205i	−0.967857	−	0.516089i
$52$	−14.7202	+	25.4961i	−0.283081	+	0.490310i
$53$			80.3093i			1.51527i	0.652679	+	0.757635i	$0.273645\pi$
$53$			80.3093i			1.51527i	−0.652679	+	0.757635i	$0.726355\pi$
$54$	34.8273	+	15.6545i	0.644949	+	0.289898i
$55$	26.9757			0.490468
$56$	−6.48074	−	3.74166i	−0.115728	−	0.0668153i
$57$	−22.1594	+	41.5571i	−0.388762	+	0.729072i
$58$	−7.59933	−	13.1624i	−0.131023	−	0.226938i
$59$	−22.8843	+	13.2122i	−0.387869	+	0.223936i	−0.681236	−	0.732064i	$-0.738557\pi$
$59$	−22.8843	+	13.2122i	−0.387869	+	0.223936i	0.293368	+	0.956000i	$0.405224\pi$
$60$	21.2175	−	13.2233i	0.353625	−	0.220388i
$61$	32.7902	−	56.7944i	0.537545	−	0.931055i	−0.461491	−	0.887145i	$-0.652685\pi$
$61$	32.7902	−	56.7944i	0.537545	−	0.931055i	0.999035	−	0.0439099i	$-0.0139815\pi$
$62$			31.5391i			0.508695i
$63$	23.7576	−	1.60480i	0.377105	−	0.0254730i
$64$	−8.00000			−0.125000
$65$	−53.1186	−	30.6680i	−0.817209	−	0.471816i
$66$	27.4512	−	0.926092i	0.415927	−	0.0140317i
$67$	−11.9038	−	20.6181i	−0.177669	−	0.307732i	0.763413	−	0.645911i	$-0.223522\pi$
$67$	−11.9038	−	20.6181i	−0.177669	−	0.307732i	−0.941082	+	0.338179i	$0.890189\pi$
$68$	−32.2968	+	18.6466i	−0.474953	+	0.274214i
$69$	1.99895	+	59.2527i	0.0289702	+	0.858734i
$70$	7.79536	−	13.5020i	0.111362	−	0.192885i
$71$		−	111.926i		−	1.57643i	−0.615403	−	0.788213i	$-0.711007\pi$
$71$		−	111.926i		−	1.57643i	0.615403	−	0.788213i	$-0.288993\pi$
$72$	21.1375	−	14.1847i	0.293576	−	0.197010i
$73$	13.3109			0.182342			0.0911709	−	0.995835i	$-0.470939\pi$
$73$	13.3109			0.182342			0.0911709	+	0.995835i	$0.470939\pi$
$74$	86.7837	+	50.1046i	1.17275	+	0.677089i
$75$	−12.1193	−	19.4461i	−0.161591	−	0.259281i
$76$	15.6987	+	27.1909i	0.206561	+	0.357775i
$77$	14.8338	−	8.56427i	0.192646	−	0.111224i
$78$	−55.1076	−	29.3849i	−0.706507	−	0.376730i
$79$	−59.8755	+	103.707i	−0.757917	+	1.31275i	0.185994	+	0.982551i	$0.440450\pi$
$79$	−59.8755	+	103.707i	−0.757917	+	1.31275i	−0.943911	+	0.330200i	$0.892884\pi$
$80$		−	16.6672i		−	0.208340i
$81$	−30.6983	+	74.9574i	−0.378991	+	0.925400i
$82$	−11.9068			−0.145204
$83$	10.0716	+	5.81486i	0.121345	+	0.0700586i	0.559444	−	0.828868i	$-0.311015\pi$
$83$	10.0716	+	5.81486i	0.121345	+	0.0700586i	−0.438099	+	0.898927i	$0.644348\pi$
$84$	7.46921	−	14.0075i	0.0889192	−	0.166756i
$85$	−38.8482	−	67.2871i	−0.457038	−	0.791612i
$86$	61.1114	−	35.2827i	0.710598	−	0.410264i
$87$	27.3623	−	17.0529i	0.314509	−	0.196010i
$88$	9.15559	−	15.8580i	0.104041	−	0.180204i
$89$			83.5516i			0.938782i	0.882990	+	0.469391i	$0.155527\pi$
$89$			83.5516i			0.938782i	−0.882990	+	0.469391i	$0.844473\pi$
$90$	29.5524	+	44.0378i	0.328360	+	0.489308i
$91$	−38.9460			−0.427978
$92$	34.2290	+	19.7621i	0.372054	+	0.214806i
$93$	−66.8665	+	2.25581i	−0.718994	+	0.0242560i
$94$	−51.0411	−	88.4058i	−0.542990	−	0.940487i
$95$	−56.6494	+	32.7065i	−0.596309	+	0.344279i
$96$	−0.572193	−	16.9609i	−0.00596035	−	0.176676i
$97$	−84.0615	+	145.599i	−0.866613	+	1.50102i	−0.00117642	+	0.999999i	$0.500374\pi$
$97$	−84.0615	+	145.599i	−0.866613	+	1.50102i	−0.865437	+	0.501018i	$0.832959\pi$
$98$		−	9.89949i		−	0.101015i
$99$	3.92684	+	58.1334i	0.0396651	+	0.587206i
$100$	−15.2757			−0.152757
$101$	−19.0956	−	11.0248i	−0.189065	−	0.109157i	0.402480	−	0.915429i	$-0.368148\pi$
$101$	−19.0956	−	11.0248i	−0.189065	−	0.109157i	−0.591545	+	0.806272i	$0.701482\pi$
$102$	−41.8429	−	67.1392i	−0.410224	−	0.658228i
$103$	−63.2562	−	109.563i	−0.614138	−	1.06372i	−0.990535	−	0.137260i	$-0.956170\pi$
$103$	−63.2562	−	109.563i	−0.614138	−	1.06372i	0.376397	−	0.926459i	$-0.377163\pi$
$104$	−36.0570	+	20.8175i	−0.346702	+	0.200168i
$105$	29.1832	+	15.5613i	0.277936	+	0.148203i
$106$	−56.7872	+	98.3584i	−0.535729	+	0.927909i
$107$		−	39.7026i		−	0.371053i	−0.982639	−	0.185526i	$-0.940601\pi$
$107$		−	39.7026i		−	0.371053i	0.982639	−	0.185526i	$-0.0593990\pi$
$108$	31.5851	+	43.7993i	0.292455	+	0.405549i
$109$	93.2221			0.855249			0.427624	−	0.903957i	$-0.359351\pi$
$109$	93.2221			0.855249			0.427624	+	0.903957i	$0.359351\pi$
$110$	33.0384	+	19.0747i	0.300349	+	0.173407i
$111$	−100.020	+	187.575i	−0.901084	+	1.68986i
$112$	−5.29150	−	9.16515i	−0.0472456	−	0.0818317i
$113$	69.6562	−	40.2160i	0.616427	−	0.355894i	−0.159050	−	0.987271i	$-0.550843\pi$
$113$	69.6562	−	40.2160i	0.616427	−	0.355894i	0.775476	+	0.631376i	$0.217510\pi$
$114$	−56.5249	+	35.2278i	−0.495833	+	0.309015i
$115$	−41.1723	+	71.3126i	−0.358020	+	0.620109i
$116$		−	21.4941i		−	0.185294i
$117$	58.3579	−	118.936i	0.498785	−	1.01655i
$118$	−37.3698			−0.316693
$119$	−42.7247	−	24.6671i	−0.359031	−	0.207286i
$120$	35.3363	−	1.19211i	0.294469	−	0.00993421i
$121$	−39.5438	−	68.4918i	−0.326808	−	0.566048i
$122$	80.3193	−	46.3724i	0.658355	−	0.380102i
$123$	−0.851621	−	25.2437i	−0.00692375	−	0.205233i
$124$	−22.3015	+	38.6273i	−0.179851	+	0.311511i
$125$		−	135.995i		−	1.08796i
$126$	30.2318	+	14.8337i	0.239935	+	0.117728i
$127$	−22.5391			−0.177473			−0.0887367	−	0.996055i	$-0.528283\pi$
$127$	−22.5391			−0.177473			−0.0887367	+	0.996055i	$0.528283\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	79.1743	+	127.040i	0.613754	+	0.984803i
$130$	−43.3711	−	75.1210i	−0.333624	−	0.577854i
$131$	205.316	−	118.539i	1.56729	−	0.904878i	0.570811	−	0.821081i	$-0.306629\pi$
$131$	205.316	−	118.539i	1.56729	−	0.904878i	0.996483	−	0.0837963i	$-0.0267045\pi$
$132$	34.2755	+	18.2767i	0.259663	+	0.138460i
$133$	−20.7674	+	35.9702i	−0.156146	+	0.270452i
$134$		−	33.6691i		−	0.251262i
$135$	−91.2514	+	65.8043i	−0.675936	+	0.487439i
$136$	−52.7405			−0.387798
$137$	168.003	+	96.9965i	1.22630	+	0.708004i	0.966254	−	0.257593i	$-0.0829294\pi$
$137$	168.003	+	96.9965i	1.22630	+	0.708004i	0.260045	+	0.965597i	$0.416263\pi$
$138$	−39.4498	+	73.9829i	−0.285868	+	0.536108i
$139$	79.4617	+	137.632i	0.571667	+	0.990156i	0.996395	+	0.0848352i	$0.0270364\pi$
$139$	79.4617	+	137.632i	0.571667	+	0.990156i	−0.424728	+	0.905321i	$0.639630\pi$
$140$	19.0946	−	11.0243i	0.136390	−	0.0787450i
$141$	183.780	−	114.536i	1.30340	−	0.812313i
$142$	79.1438	−	137.081i	0.557351	−	0.965360i
$143$		−	95.2983i		−	0.666422i
$144$	35.9181	−	2.42623i	0.249432	−	0.0168488i
$145$	44.7808			0.308833
$146$	16.3025	+	9.41226i	0.111661	+	0.0644675i
$147$	20.9881	−	0.708053i	0.142776	−	0.00481669i
$148$	70.8586	+	122.731i	0.478774	+	0.829261i
$149$	88.2118	−	50.9291i	0.592026	−	0.341806i	−0.173872	−	0.984768i	$-0.555628\pi$
$149$	88.2118	−	50.9291i	0.592026	−	0.341806i	0.765898	+	0.642962i	$0.222295\pi$
$150$	−1.09258	−	32.3862i	−0.00728386	−	0.215908i
$151$	70.2311	−	121.644i	0.465106	−	0.805588i	−0.534100	−	0.845421i	$-0.679349\pi$
$151$	70.2311	−	121.644i	0.465106	−	0.805588i	0.999206	+	0.0398334i	$0.0126827\pi$
$152$			44.4025i			0.292122i
$153$	139.350	−	93.5137i	0.910785	−	0.611201i
$154$	24.2234			0.157295
$155$	−80.4761	−	46.4629i	−0.519200	−	0.299760i
$156$	−46.7144	−	74.9560i	−0.299452	−	0.480487i
$157$	−124.454	−	215.560i	−0.792700	−	1.37300i	−0.924290	−	0.381692i	$-0.875342\pi$
$157$	−124.454	−	215.560i	−0.792700	−	1.37300i	0.131590	−	0.991304i	$-0.457992\pi$
$158$	−146.664	+	84.6767i	−0.928255	+	0.535928i
$159$	−212.593	−	113.360i	−1.33706	−	0.712959i
$160$	11.7855	−	20.4130i	0.0736592	−	0.127581i
$161$			52.2857i			0.324756i
$162$	−90.6005	+	70.0967i	−0.559262	+	0.432696i
$163$	168.569			1.03417			0.517083	−	0.855935i	$-0.327018\pi$
$163$	168.569			1.03417			0.517083	+	0.855935i	$0.327018\pi$
$164$	−14.5827	−	8.41935i	−0.0889192	−	0.0513375i
$165$	−38.0776	+	71.4095i	−0.230773	+	0.432785i
$166$	8.22346	+	14.2434i	0.0495389	+	0.0858039i
$167$	252.089	−	145.544i	1.50952	−	0.871519i	0.509577	−	0.860425i	$-0.329802\pi$
$167$	252.089	−	145.544i	1.50952	−	0.871519i	0.999938	−	0.0110940i	$-0.00353140\pi$
$168$	19.0527	−	11.8741i	0.113409	−	0.0706793i
$169$	−23.8422	+	41.2959i	−0.141078	+	0.244354i
$170$		−	109.879i		−	0.646349i
$171$	−78.7298	−	117.320i	−0.460408	−	0.686080i
$172$	99.7945			0.580201
$173$	119.791	+	69.1612i	0.692432	+	0.399776i	0.804522	−	0.593922i	$-0.202421\pi$
$173$	119.791	+	69.1612i	0.692432	+	0.399776i	−0.112091	+	0.993698i	$0.535755\pi$
$174$	45.5700	−	1.53735i	0.261897	−	0.00883535i
$175$	−10.1039	−	17.5005i	−0.0577366	−	0.100003i
$176$	22.4265	−	12.9480i	0.127423	−	0.0735680i
$177$	−2.67285	−	79.2283i	−0.0151008	−	0.447617i
$178$	−59.0799	+	102.329i	−0.331910	+	0.574884i
$179$			304.532i			1.70130i	0.525735	+	0.850649i	$0.323790\pi$
$179$			304.532i			1.70130i	−0.525735	+	0.850649i	$0.676210\pi$
$180$	5.05480	+	74.8317i	0.0280822	+	0.415732i
$181$	−260.720			−1.44044			−0.720221	−	0.693745i	$-0.755960\pi$
$181$	−260.720			−1.44044			−0.720221	+	0.693745i	$0.755960\pi$
$182$	−47.6989	−	27.5390i	−0.262082	−	0.151313i
$183$	104.060	+	166.969i	0.568631	+	0.912401i
$184$	27.9479	+	48.4071i	0.151891	+	0.263082i
$185$	−255.697	+	147.627i	−1.38214	+	0.797981i
$186$	−83.4895	−	44.5189i	−0.448868	−	0.239349i
$187$	60.3588	−	104.544i	0.322774	−	0.559061i
$188$		−	144.366i		−	0.767904i
$189$	−29.2868	+	65.1558i	−0.154957	+	0.344740i
$190$	−92.5081			−0.486885
$191$	49.9914	+	28.8626i	0.261735	+	0.151113i	0.625126	−	0.780524i	$-0.285048\pi$
$191$	49.9914	+	28.8626i	0.261735	+	0.151113i	−0.363391	+	0.931637i	$0.618381\pi$
$192$	11.2924	−	21.1774i	0.0588145	−	0.110299i
$193$	−44.7554	−	77.5186i	−0.231893	−	0.401651i	0.726472	−	0.687196i	$-0.241159\pi$
$193$	−44.7554	−	77.5186i	−0.231893	−	0.401651i	−0.958365	+	0.285545i	$0.907825\pi$
$194$	−205.908	+	118.881i	−1.06138	+	0.612788i
$195$	156.163	−	97.3247i	0.800836	−	0.499101i
$196$	7.00000	−	12.1244i	0.0357143	−	0.0618590i
$197$		−	1.87709i		−	0.00952838i	−0.999989	−	0.00476419i	$-0.998484\pi$
$197$		−	1.87709i		−	0.00952838i	0.999989	−	0.00476419i	$-0.00151650\pi$
$198$	−36.2971	+	73.9752i	−0.183319	+	0.373612i
$199$	−80.1938			−0.402984			−0.201492	−	0.979490i	$-0.564579\pi$
$199$	−80.1938			−0.402984			−0.201492	+	0.979490i	$0.564579\pi$
$200$	−18.7088	−	10.8015i	−0.0935440	−	0.0540077i
$201$	71.3824	−	2.40816i	0.355136	−	0.0119809i
$202$	−15.5915	−	27.0052i	−0.0771855	−	0.133689i
$203$	24.6246	−	14.2170i	0.121304	−	0.0700347i
$204$	−3.77222	−	111.816i	−0.0184913	−	0.548117i
$205$	17.5409	−	30.3816i	0.0855651	−	0.148203i
$206$		−	178.916i		−	0.868523i
$207$	−159.674	−	78.3464i	−0.771371	−	0.378485i
$208$	−58.8808			−0.283081
$209$	−88.0166	−	50.8164i	−0.421132	−	0.243141i
$210$	24.7385	+	39.6943i	0.117802	+	0.189021i
$211$	80.5551	+	139.526i	0.381778	+	0.661259i	0.991316	−	0.131498i	$-0.0419786\pi$
$211$	80.5551	+	139.526i	0.381778	+	0.661259i	−0.609539	+	0.792756i	$0.708645\pi$
$212$	−139.100	+	80.3093i	−0.656131	+	0.378817i
$213$	296.288	+	157.989i	1.39102	+	0.741734i
$214$	28.0740	−	48.6256i	0.131187	−	0.227222i
$215$			207.912i			0.967031i
$216$	7.71290	+	75.9770i	0.0357079	+	0.351746i
$217$	−59.0042			−0.271909
$218$	114.173	+	65.9180i	0.523731	+	0.302376i
$219$	−18.7890	+	35.2364i	−0.0857947	+	0.160897i
$220$	26.9757	+	46.7234i	0.122617	+	0.212379i
$221$	−237.708	+	137.241i	−1.07560	+	0.620998i
$222$	−255.135	+	159.006i	−1.14926	+	0.716245i
$223$	10.2489	−	17.7515i	0.0459590	−	0.0796033i	−0.842131	−	0.539273i	$-0.818699\pi$
$223$	10.2489	−	17.7515i	0.0459590	−	0.0796033i	0.888090	+	0.459670i	$0.152032\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	68.5842	−	4.63279i	0.304819	−	0.0205902i
$226$	113.748			0.503310
$227$	−130.615	−	75.4107i	−0.575397	−	0.332206i	0.183905	−	0.982944i	$-0.441126\pi$
$227$	−130.615	−	75.4107i	−0.575397	−	0.332206i	−0.759302	+	0.650738i	$0.774459\pi$
$228$	−94.1384	+	3.17585i	−0.412888	+	0.0139292i
$229$	148.880	+	257.868i	0.650133	+	1.12606i	0.983090	+	0.183121i	$0.0586200\pi$
$229$	148.880	+	257.868i	0.650133	+	1.12606i	−0.332958	+	0.942942i	$0.608047\pi$
$230$	−100.851	+	58.2265i	−0.438484	+	0.253159i
$231$	1.73256	+	51.3564i	0.00750026	+	0.222322i
$232$	15.1987	−	26.3248i	0.0655115	−	0.113469i
$233$			386.415i			1.65843i	0.558928	+	0.829216i	$0.311213\pi$
$233$			386.415i			1.65843i	−0.558928	+	0.829216i	$0.688787\pi$
$234$	155.574	−	104.401i	0.664846	−	0.446159i
$235$	300.772			1.27988
$236$	−45.7685	−	26.4245i	−0.193934	−	0.111968i
$237$	−190.014	−	304.889i	−0.801748	−	1.28645i
$238$	−34.8845	−	60.4218i	−0.146574	−	0.253873i
$239$	−180.122	+	103.994i	−0.753649	+	0.435119i	−0.827011	−	0.562186i	$-0.809960\pi$
$239$	−180.122	+	103.994i	−0.753649	+	0.435119i	0.0733620	+	0.997305i	$0.476627\pi$
$240$	44.1209	+	23.5265i	0.183837	+	0.0980272i
$241$	−161.733	+	280.130i	−0.671092	+	1.16236i	0.306503	+	0.951870i	$0.400841\pi$
$241$	−161.733	+	280.130i	−0.671092	+	1.16236i	−0.977595	+	0.210495i	$0.932492\pi$
$242$		−	111.847i		−	0.462176i
$243$	−155.093	−	187.070i	−0.638244	−	0.769834i
$244$	131.161			0.537545
$245$	25.2598	+	14.5838i	0.103101	+	0.0595256i
$246$	16.8070	−	31.5193i	0.0683210	−	0.128127i
$247$	115.544	+	200.128i	0.467789	+	0.810234i
$248$	−54.6273	+	31.5391i	−0.220271	+	0.127174i
$249$	−29.6096	+	18.4534i	−0.118914	+	0.0741101i
$250$	96.1631	−	166.559i	0.384652	−	0.666237i
$251$		−	288.081i		−	1.14773i	−0.818948	−	0.573867i	$-0.805442\pi$
$251$		−	288.081i		−	1.14773i	0.818948	−	0.573867i	$-0.194558\pi$
$252$	26.5372	+	39.5446i	0.105306	+	0.156923i
$253$	−127.940			−0.505690
$254$	−27.6047	−	15.9376i	−0.108680	−	0.0627463i
$255$	232.957	−	7.85902i	0.913556	−	0.0308197i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−111.683	+	64.4799i	−0.434562	+	0.250895i	−0.701288	−	0.712878i	$-0.747391\pi$
$257$	−111.683	+	64.4799i	−0.434562	+	0.250895i	0.266726	+	0.963772i	$0.414058\pi$
$258$	7.13772	+	211.576i	0.0276656	+	0.820061i
$259$	−93.7371	+	162.357i	−0.361919	+	0.626863i
$260$		−	122.672i		−	0.471816i
$261$	6.51872	+	96.5038i	0.0249759	+	0.369746i
$262$	335.279			1.27969
$263$	−27.4385	−	15.8417i	−0.104329	−	0.0602344i	0.446928	−	0.894570i	$-0.352518\pi$
$263$	−27.4385	−	15.8417i	−0.104329	−	0.0602344i	−0.551257	+	0.834336i	$0.685851\pi$
$264$	29.0552	+	46.6207i	0.110058	+	0.176594i
$265$	−167.316	−	289.800i	−0.631381	−	1.09358i
$266$	−50.8695	+	29.3695i	−0.191239	+	0.110412i
$267$	−221.176	−	117.937i	−0.828373	−	0.441712i
$268$	23.8077	−	41.2361i	0.0888346	−	0.153866i
$269$		−	154.678i		−	0.575011i	−0.957779	−	0.287505i	$-0.907174\pi$
$269$		−	154.678i		−	0.575011i	0.957779	−	0.287505i	$-0.0928260\pi$
$270$	−158.290	+	16.0690i	−0.586260	+	0.0595149i
$271$	−170.350			−0.628598			−0.314299	−	0.949324i	$-0.601769\pi$
$271$	−170.350			−0.628598			−0.314299	+	0.949324i	$0.601769\pi$
$272$	−64.5936	−	37.2931i	−0.237477	−	0.137107i
$273$	54.9742	−	103.097i	0.201371	−	0.377644i
$274$	137.174	+	237.592i	0.500634	+	0.867124i
$275$	42.8225	−	24.7236i	0.155718	−	0.0899040i
$276$	−100.630	+	62.7149i	−0.364600	+	0.227228i
$277$	263.888	−	457.068i	0.952665	−	1.65007i	0.213043	−	0.977043i	$-0.431662\pi$
$277$	263.888	−	457.068i	0.952665	−	1.65007i	0.739622	−	0.673022i	$-0.235004\pi$
$278$			224.752i			0.808459i
$279$	88.4137	−	180.191i	0.316895	−	0.645847i
$280$	31.1814			0.111362
$281$	−349.542	−	201.808i	−1.24392	−	0.718179i	−0.274032	−	0.961721i	$-0.588357\pi$
$281$	−349.542	−	201.808i	−1.24392	−	0.718179i	−0.969890	+	0.243542i	$0.921691\pi$
$282$	306.073	−	10.3257i	1.08536	−	0.0366158i
$283$	110.981	+	192.224i	0.392158	+	0.679238i	0.992734	−	0.120330i	$-0.0383951\pi$
$283$	110.981	+	192.224i	0.392158	+	0.679238i	−0.600576	+	0.799568i	$0.705062\pi$
$284$	193.862	−	111.926i	0.682612	−	0.394106i
$285$	−6.61656	−	196.128i	−0.0232160	−	0.688167i
$286$	67.3861	−	116.716i	0.235616	−	0.408098i
$287$		−	22.2755i		−	0.0776150i
$288$	45.7062	+	22.4265i	0.158702	+	0.0778696i
$289$	−58.6945			−0.203095
$290$	54.8451	+	31.6648i	0.189121	+	0.109189i
$291$	−266.768	−	428.045i	−0.916730	−	1.47094i
$292$	13.3109	+	23.0552i	0.0455854	+	0.0789563i
$293$	−226.579	+	130.815i	−0.773306	+	0.446469i	−0.834053	−	0.551685i	$-0.813985\pi$
$293$	−226.579	+	130.815i	−0.773306	+	0.446469i	0.0607464	+	0.998153i	$0.480652\pi$
$294$	26.2057	+	13.9736i	0.0891350	+	0.0475293i
$295$	55.0526	−	95.3539i	0.186619	−	0.323234i
$296$			200.418i			0.677089i
$297$	−159.432	−	71.6630i	−0.536808	−	0.241290i
$298$	144.049			0.483387
$299$	251.929	+	145.451i	0.842572	+	0.486459i
$300$	21.5623	−	40.4374i	0.0718745	−	0.134791i
$301$	66.0079	+	114.329i	0.219295	+	0.379831i
$302$	172.030	−	99.3217i	0.569637	−	0.328880i
$303$	56.1390	−	34.9872i	0.185277	−	0.115469i
$304$	−31.3973	+	54.3818i	−0.103281	+	0.178887i
$305$			273.260i			0.895935i
$306$	236.792	−	15.9951i	0.773832	−	0.0522714i
$307$	−137.772			−0.448769			−0.224384	−	0.974501i	$-0.572037\pi$
$307$	−137.772			−0.448769			−0.224384	+	0.974501i	$0.572037\pi$
$308$	29.6675	+	17.1285i	0.0963231	+	0.0556122i
$309$	379.322	−	12.7968i	1.22758	−	0.0414136i
$310$	−65.7084	−	113.810i	−0.211963	−	0.367130i
$311$	296.994	−	171.469i	0.954964	−	0.551349i	0.0603446	−	0.998178i	$-0.480780\pi$
$311$	296.994	−	171.469i	0.954964	−	0.551349i	0.894619	+	0.446829i	$0.147447\pi$
$312$	−4.21140	−	124.834i	−0.0134981	−	0.400109i
$313$	176.129	−	305.064i	0.562711	−	0.974644i	−0.434548	−	0.900649i	$-0.643092\pi$
$313$	176.129	−	305.064i	0.562711	−	0.974644i	0.997259	−	0.0739953i	$-0.0235750\pi$
$314$		−	352.009i		−	1.12105i
$315$	−82.3871	+	55.2875i	−0.261546	+	0.175516i
$316$	−239.502			−0.757917
$317$	128.074	+	73.9438i	0.404020	+	0.233261i	0.688217	−	0.725505i	$-0.258394\pi$
$317$	128.074	+	73.9438i	0.404020	+	0.233261i	−0.284197	+	0.958766i	$0.591727\pi$
$318$	−180.214	−	289.163i	−0.566710	−	0.909319i
$319$	34.7882	+	60.2549i	0.109054	+	0.188887i
$320$	28.8684	−	16.6672i	0.0902137	−	0.0520849i
$321$	105.100	+	56.0422i	0.327414	+	0.174586i
$322$	−36.9715	+	64.0366i	−0.114818	+	0.198871i
$323$			292.726i			0.906273i
$324$	−160.528	+	21.7864i	−0.495458	+	0.0672420i
$325$	−112.430			−0.345940
$326$	206.454	+	119.196i	0.633295	+	0.365633i
$327$	−131.588	+	246.775i	−0.402408	+	0.754664i
$328$	−11.9068	−	20.6231i	−0.0363011	−	0.0628754i
$329$	165.392	−	95.4892i	0.502711	−	0.290241i
$330$	−97.1294	+	60.5335i	−0.294332	+	0.183435i
$331$	−280.028	+	485.023i	−0.846006	+	1.46533i	0.0387387	+	0.999249i	$0.487666\pi$
$331$	−280.028	+	485.023i	−0.846006	+	1.46533i	−0.884745	+	0.466076i	$0.845667\pi$
$332$			23.2594i			0.0700586i
$333$	−355.360	−	529.542i	−1.06715	−	1.59022i
$334$	411.660			1.23251
$335$	85.9112	+	49.6008i	0.256451	+	0.148062i
$336$	31.7310	−	1.07048i	0.0944374	−	0.00318594i
$337$	11.9600	+	20.7154i	0.0354897	+	0.0614699i	0.883225	−	0.468950i	$-0.155368\pi$
$337$	11.9600	+	20.7154i	0.0354897	+	0.0614699i	−0.847735	+	0.530420i	$0.822034\pi$
$338$	−58.4012	+	33.7180i	−0.172785	+	0.0997573i
$339$	8.13574	+	241.159i	0.0239992	+	0.711383i
$340$	77.6964	−	134.574i	0.228519	−	0.395806i
$341$		−	144.380i		−	0.423400i
$342$	−13.4663	−	199.357i	−0.0393753	−	0.582915i
$343$	18.5203			0.0539949
$344$	122.223	+	70.5654i	0.355299	+	0.205132i
$345$	−130.660	−	209.651i	−0.378725	−	0.607685i
$346$	97.8087	+	169.410i	0.282684	+	0.489623i
$347$	209.628	−	121.029i	0.604115	−	0.348786i	−0.166544	−	0.986034i	$-0.553261\pi$
$347$	209.628	−	121.029i	0.604115	−	0.348786i	0.770659	+	0.637248i	$0.219927\pi$
$348$	56.8988	+	30.3400i	0.163502	+	0.0871840i
$349$	−17.9763	+	31.1358i	−0.0515079	+	0.0892143i	−0.890630	−	0.454729i	$-0.849736\pi$
$349$	−17.9763	+	31.1358i	−0.0515079	+	0.0892143i	0.839122	+	0.543943i	$0.183069\pi$
$350$		−	28.5782i		−	0.0816519i
$351$	232.470	+	322.368i	0.662307	+	0.918426i
$352$	36.6224			0.104041
$353$	266.093	+	153.629i	0.753806	+	0.435210i	0.827067	−	0.562103i	$-0.190008\pi$
$353$	266.093	+	153.629i	0.753806	+	0.435210i	−0.0732617	+	0.997313i	$0.523341\pi$
$354$	52.7493	−	98.9244i	0.149009	−	0.279448i
$355$	233.187	+	403.891i	0.656864	+	1.13772i
$356$	−144.716	+	83.5516i	−0.406505	+	0.234695i
$357$	125.606	−	78.2808i	0.351838	−	0.219274i
$358$	−215.337	+	372.974i	−0.601499	+	1.04183i
$359$			529.049i			1.47368i	0.676070	+	0.736838i	$0.263682\pi$
$359$			529.049i			1.47368i	−0.676070	+	0.736838i	$0.736318\pi$
$360$	−46.7232	+	95.2241i	−0.129787	+	0.264511i
$361$	−114.552			−0.317318
$362$	−319.316	−	184.357i	−0.882087	−	0.509273i
$363$	237.128	−	7.99974i	0.653245	−	0.0220379i
$364$	−38.9460	−	67.4564i	−0.106995	−	0.185320i
$365$	−48.0332	+	27.7320i	−0.131598	+	0.0759780i
$366$	9.38118	+	278.076i	0.0256316	+	0.759771i
$367$	169.534	−	293.642i	0.461946	−	0.800115i	−0.537112	−	0.843511i	$-0.680485\pi$
$367$	169.534	−	293.642i	0.461946	−	0.800115i	0.999058	+	0.0433966i	$0.0138179\pi$
$368$			79.0485i			0.214806i
$369$	68.0266	+	33.3783i	0.184354	+	0.0904561i
$370$	−417.551			−1.12852
$371$	−184.012	−	106.239i	−0.495988	−	0.286359i
$372$	−70.7736	−	113.560i	−0.190252	−	0.305270i
$373$	−247.394	−	428.499i	−0.663255	−	1.14879i	−0.979755	−	0.200199i	$-0.935841\pi$
$373$	−247.394	−	428.499i	−0.663255	−	1.14879i	0.316500	−	0.948593i	$-0.397492\pi$
$374$	147.848	−	85.3602i	0.395316	−	0.228236i
$375$	360.003	+	191.964i	0.960007	+	0.511903i
$376$	102.082	−	176.812i	0.271495	−	0.470244i
$377$		−	158.199i		−	0.419626i
$378$	−81.9410	+	59.0903i	−0.216775	+	0.156324i
$379$	−14.4703			−0.0381802			−0.0190901	−	0.999818i	$-0.506077\pi$
$379$	−14.4703			−0.0381802			−0.0190901	+	0.999818i	$0.506077\pi$
$380$	−113.299	−	65.4131i	−0.298155	−	0.172140i
$381$	31.8150	−	59.6650i	0.0835041	−	0.156601i
$382$	40.8178	+	70.6985i	0.106853	+	0.185075i
$383$	258.762	−	149.397i	0.675620	−	0.390069i	−0.122583	−	0.992458i	$-0.539118\pi$
$383$	258.762	−	149.397i	0.675620	−	0.390069i	0.798203	+	0.602389i	$0.205784\pi$
$384$	28.8050	−	17.9520i	0.0750129	−	0.0467500i
$385$	−35.6856	+	61.8092i	−0.0926898	+	0.160543i
$386$		−	126.587i		−	0.327947i
$387$	−448.054	+	30.2656i	−1.15776	+	0.0782056i
$388$	−336.246			−0.866613
$389$	−77.0026	−	44.4575i	−0.197950	−	0.114287i	0.397749	−	0.917494i	$-0.369792\pi$
$389$	−77.0026	−	44.4575i	−0.197950	−	0.114287i	−0.595699	+	0.803208i	$0.703125\pi$
$390$	260.079	−	8.77402i	0.666869	−	0.0224975i
$391$	184.248	+	319.127i	0.471222	+	0.816181i
$392$	17.1464	−	9.89949i	0.0437409	−	0.0252538i
$393$	23.9805	+	710.829i	0.0610192	+	1.80873i
$394$	1.32730	−	2.29896i	0.00336879	−	0.00583492i
$395$		−	498.977i		−	1.26323i
$396$	−96.7631	+	64.9349i	−0.244351	+	0.163977i
$397$	−537.580			−1.35411			−0.677053	−	0.735935i	$-0.736743\pi$
$397$	−537.580			−1.35411			−0.677053	+	0.735935i	$0.736743\pi$
$398$	−98.2169	−	56.7056i	−0.246776	−	0.142476i
$399$	−65.9051	−	105.748i	−0.165176	−	0.265034i
$400$	−15.2757	−	26.4582i	−0.0381892	−	0.0661456i
$401$	151.261	−	87.3304i	0.377209	−	0.217782i	−0.299394	−	0.954129i	$-0.596785\pi$
$401$	151.261	−	87.3304i	0.377209	−	0.217782i	0.676603	+	0.736348i	$0.263451\pi$
$402$	89.1281	+	47.5256i	0.221712	+	0.118223i
$403$	−164.141	+	284.301i	−0.407299	+	0.705462i
$404$		−	44.0993i		−	0.109157i
$405$	−45.3898	−	334.444i	−0.112073	−	0.825788i
$406$	40.2119			0.0990440
$407$	−397.278	−	229.369i	−0.976113	−	0.563559i
$408$	74.4457	−	139.613i	0.182465	−	0.342189i
$409$	−107.632	−	186.423i	−0.263158	−	0.455803i	0.703922	−	0.710278i	$-0.251431\pi$
$409$	−107.632	−	186.423i	−0.263158	−	0.455803i	−0.967079	+	0.254475i	$0.918097\pi$
$410$	42.9661	−	24.8065i	0.104795	−	0.0605037i
$411$	−493.911	+	307.818i	−1.20173	+	0.748948i
$412$	126.512	−	219.126i	0.307069	−	0.531859i
$413$		−	69.9125i		−	0.169280i
$414$	−140.160	−	208.861i	−0.338551	−	0.504495i
$415$	−48.4587			−0.116768
$416$	−72.1140	−	41.6350i	−0.173351	−	0.100084i
$417$	−476.499	+	16.0752i	−1.14268	+	0.0385496i
$418$	−71.8653	−	124.474i	−0.171927	−	0.297785i
$419$	202.288	−	116.791i	0.482788	−	0.278738i	−0.238790	−	0.971071i	$-0.576751\pi$
$419$	202.288	−	116.791i	0.482788	−	0.278738i	0.721578	+	0.692334i	$0.243417\pi$
$420$	2.23023	+	66.1082i	0.00531006	+	0.157400i
$421$	407.164	−	705.229i	0.967136	−	1.67513i	0.263372	−	0.964694i	$-0.415165\pi$
$421$	407.164	−	705.229i	0.967136	−	1.67513i	0.703764	−	0.710434i	$-0.251501\pi$
$422$			227.844i			0.539915i
$423$	43.7832	+	648.170i	0.103506	+	1.53232i
$424$	−227.149			−0.535729
$425$	−123.339	−	71.2097i	−0.290209	−	0.167552i
$426$	251.162	+	403.004i	0.589583	+	0.946019i
$427$	86.7548	+	150.264i	0.203173	+	0.351906i
$428$	68.7670	−	39.7026i	0.160670	−	0.0927631i
$429$	252.271	+	134.518i	0.588045	+	0.313562i
$430$	−147.016	+	254.639i	−0.341897	+	0.592183i
$431$		−	317.979i		−	0.737770i	−0.929475	−	0.368885i	$-0.879740\pi$
$431$		−	317.979i		−	0.737770i	0.929475	−	0.368885i	$-0.120260\pi$
$432$	−44.2775	+	98.5063i	−0.102494	+	0.228024i
$433$	−344.299			−0.795148			−0.397574	−	0.917570i	$-0.630148\pi$
$433$	−344.299			−0.795148			−0.397574	+	0.917570i	$0.630148\pi$
$434$	−72.2651	−	41.7223i	−0.166510	−	0.0961343i
$435$	−63.2103	+	118.543i	−0.145311	+	0.272512i
$436$	93.2221	+	161.465i	0.213812	+	0.370334i
$437$	268.675	−	155.119i	0.614816	−	0.354964i
$438$	−47.9277	+	29.8697i	−0.109424	+	0.0681957i
$439$	135.682	−	235.008i	0.309071	−	0.535326i	−0.669089	−	0.743183i	$-0.733315\pi$
$439$	135.682	−	235.008i	0.309071	−	0.535326i	0.978159	+	0.207856i	$0.0666487\pi$
$440$			76.2989i			0.173407i
$441$	−27.7513	+	56.5585i	−0.0629282	+	0.128251i
$442$	−388.175			−0.878224
$443$	−164.368	−	94.8980i	−0.371034	−	0.214217i	0.302876	−	0.953030i	$-0.402053\pi$
$443$	−164.368	−	94.8980i	−0.371034	−	0.214217i	−0.673910	+	0.738813i	$0.735387\pi$
$444$	−424.910	+	14.3348i	−0.957004	+	0.0322855i
$445$	−174.071	−	301.500i	−0.391171	−	0.677528i
$446$	25.1045	−	14.4941i	0.0562881	−	0.0324979i
$447$	10.3030	+	305.401i	0.0230492	+	0.683224i
$448$	10.5830	−	18.3303i	0.0236228	−	0.0409159i
$449$			601.830i			1.34038i	0.742190	+	0.670190i	$0.233787\pi$
$449$			601.830i			1.34038i	−0.742190	+	0.670190i	$0.766213\pi$
$450$	87.2741	+	42.8224i	0.193942	+	0.0951609i
$451$	54.5067			0.120858
$452$	139.312	+	80.4321i	0.308213	+	0.177947i
$453$	222.878	+	357.620i	0.492004	+	0.789448i
$454$	−106.647	−	184.718i	−0.234905	−	0.406867i
$455$	140.539	−	81.1400i	0.308876	−	0.178330i
$456$	−117.541	−	62.6763i	−0.257766	−	0.137448i
$457$	88.5414	−	153.358i	0.193745	−	0.335576i	−0.752743	−	0.658314i	$-0.771270\pi$
$457$	88.5414	−	153.358i	0.193745	−	0.335576i	0.946488	+	0.322738i	$0.104603\pi$
$458$			421.097i			0.919426i
$459$	50.8477	+	500.883i	0.110779	+	1.09125i
$460$	−164.689			−0.358020
$461$	173.407	+	100.117i	0.376154	+	0.217173i	0.676144	−	0.736770i	$-0.263650\pi$
$461$	173.407	+	100.117i	0.376154	+	0.217173i	−0.299990	+	0.953942i	$0.596983\pi$
$462$	−34.1925	+	64.1236i	−0.0740098	+	0.138796i
$463$	−237.254	−	410.935i	−0.512427	−	0.887549i	−0.999896	−	0.0144092i	$-0.995413\pi$
$463$	−237.254	−	410.935i	−0.512427	−	0.887549i	0.487469	−	0.873140i	$-0.337920\pi$
$464$	37.2290	−	21.4941i	0.0802348	−	0.0463236i
$465$	236.591	−	147.450i	0.508798	−	0.317096i
$466$	−273.236	+	473.259i	−0.586344	+	1.01558i
$467$			253.035i			0.541832i	0.962603	+	0.270916i	$0.0873265\pi$
$467$			253.035i			0.541832i	−0.962603	+	0.270916i	$0.912673\pi$
$468$	264.361	−	17.8573i	0.564874	−	0.0381566i
$469$	62.9892			0.134305
$470$	368.369	+	212.678i	0.783763	+	0.452506i
$471$	746.298	−	25.1771i	1.58450	−	0.0534546i
$472$	−37.3698	−	64.7264i	−0.0791734	−	0.137132i
$473$	−279.756	+	161.517i	−0.591450	+	0.341474i
$474$	−17.1302	−	507.771i	−0.0361396	−	1.07125i
$475$	−59.9519	+	103.840i	−0.126215	+	0.218610i
$476$		−	98.6684i		−	0.207286i
$477$	600.170	−	402.756i	1.25822	−	0.844352i
$478$	−294.138			−0.615352
$479$	−633.064	−	365.500i	−1.32164	−	0.763048i	−0.337648	−	0.941273i	$-0.609631\pi$
$479$	−633.064	−	365.500i	−1.32164	−	0.763048i	−0.983990	+	0.178225i	$0.942965\pi$
$480$	37.4011	+	60.0122i	0.0779190	+	0.125025i
$481$	521.526	+	903.310i	1.08425	+	1.87798i
$482$	−396.164	+	228.725i	−0.821916	+	0.474533i
$483$	−138.409	−	73.8037i	−0.286562	−	0.152803i
$484$	79.0876	−	136.984i	0.163404	−	0.283024i
$485$		−	700.533i		−	1.44440i
$486$	−57.6714	−	338.780i	−0.118665	−	0.697079i
$487$	638.705			1.31151			0.655754	−	0.754974i	$-0.272351\pi$
$487$	638.705			1.31151			0.655754	+	0.754974i	$0.272351\pi$
$488$	160.639	+	92.7448i	0.329178	+	0.190051i
$489$	−237.943	+	446.232i	−0.486592	+	0.912539i
$490$	20.6246	+	35.7228i	0.0420910	+	0.0729037i
$491$	487.319	−	281.354i	0.992504	−	0.573022i	0.0864820	−	0.996253i	$-0.472437\pi$
$491$	487.319	−	281.354i	0.992504	−	0.573022i	0.906022	+	0.423231i	$0.139104\pi$
$492$	42.8717	−	26.7188i	0.0871377	−	0.0543064i
$493$	100.198	−	173.548i	0.203241	−	0.352024i
$494$			326.807i			0.661553i
$495$	−135.285	−	201.596i	−0.273303	−	0.407264i
$496$	−89.2060			−0.179851
$497$	256.455	+	148.064i	0.516006	+	0.297916i
$498$	−49.3127	+	1.66361i	−0.0990215	+	0.00334059i
$499$	−379.091	−	656.605i	−0.759701	−	1.31584i	−0.943003	−	0.332785i	$-0.892012\pi$
$499$	−379.091	−	656.605i	−0.759701	−	1.31584i	0.183302	−	0.983057i	$-0.441322\pi$
$500$	235.550	−	135.995i	0.471101	−	0.271990i
$501$	29.4436	+	872.766i	0.0587697	+	1.74205i
$502$	203.704	−	352.826i	0.405786	−	0.702841i
$503$		−	367.332i		−	0.730283i	−0.930952	−	0.365142i	$-0.881021\pi$
$503$		−	367.332i		−	0.730283i	0.930952	−	0.365142i	$-0.118979\pi$
$504$	4.53906	+	67.1967i	0.00900607	+	0.133327i
$505$	91.8764			0.181933
$506$	−156.693	−	90.4670i	−0.309671	−	0.178788i
$507$	−75.6630	−	121.406i	−0.149237	−	0.239459i
$508$	−22.5391	−	39.0389i	−0.0443683	−	0.0768482i
$509$	−254.904	+	147.169i	−0.500794	+	0.289134i	−0.729042	−	0.684469i	$-0.760034\pi$
$509$	−254.904	+	147.169i	−0.500794	+	0.289134i	0.228247	+	0.973603i	$0.426701\pi$
$510$	290.870	+	155.100i	0.570333	+	0.304118i
$511$	−17.6087	+	30.4992i	−0.0344593	+	0.0596853i
$512$		−	22.6274i		−	0.0441942i
$513$	421.697	−	42.8090i	0.822021	−	0.0834484i
$514$	−182.377			−0.354819
$515$	456.526	+	263.576i	0.886459	+	0.511797i
$516$	−140.865	+	264.174i	−0.272994	+	0.511964i
$517$	233.656	+	404.704i	0.451945	+	0.782792i
$518$	−229.608	+	132.564i	−0.443259	+	0.255916i
$519$	−352.172	+	219.483i	−0.678559	+	0.422895i
$520$	86.7423	−	150.242i	0.166812	−	0.288927i
$521$		−	53.1458i		−	0.102007i	−0.998698	−	0.0510037i	$-0.983758\pi$
$521$		−	53.1458i		−	0.102007i	0.998698	−	0.0510037i	$-0.0162420\pi$
$522$	−60.2547	+	122.802i	−0.115430	+	0.235253i
$523$	−776.112			−1.48396			−0.741981	−	0.670421i	$-0.766113\pi$
$523$	−776.112			−1.48396			−0.741981	+	0.670421i	$0.766113\pi$
$524$	410.631	+	237.078i	0.783647	+	0.452439i
$525$	60.5890	−	2.04403i	0.115408	−	0.00389339i
$526$	−22.4035	−	38.8040i	−0.0425922	−	0.0737718i
$527$	−360.134	+	207.923i	−0.683365	+	0.394541i
$528$	2.61938	+	77.6436i	0.00496096	+	0.147052i
$529$	−69.2293	+	119.909i	−0.130868	+	0.226670i
$530$		−	473.241i		−	0.892908i
$531$	213.504	+	104.759i	0.402079	+	0.197286i
$532$	−83.0695			−0.156146
$533$	−107.331	−	61.9673i	−0.201371	−	0.116261i
$534$	−187.490	−	300.838i	−0.351104	−	0.563366i
$535$	82.7163	+	143.269i	0.154610	+	0.267792i
$536$	58.3167	−	33.6691i	0.108800	−	0.0628156i
$537$	−806.150	−	429.862i	−1.50121	−	0.800488i
$538$	109.374	−	189.441i	0.203297	−	0.352121i
$539$			45.3179i			0.0840777i
$540$	−205.228	−	92.2477i	−0.380051	−	0.170829i
$541$	414.383			0.765958			0.382979	−	0.923757i	$-0.374898\pi$
$541$	414.383			0.765958			0.382979	+	0.923757i	$0.374898\pi$
$542$	−208.635	−	120.456i	−0.384936	−	0.222243i
$543$	368.019	−	690.171i	0.677751	−	1.27103i
$544$	−52.7405	−	91.3492i	−0.0969494	−	0.167921i
$545$	−336.397	+	194.219i	−0.617241	+	0.356364i
$546$	140.230	−	87.3947i	0.256831	−	0.160064i
$547$	194.595	−	337.048i	0.355749	−	0.616175i	−0.631497	−	0.775378i	$-0.717559\pi$
$547$	194.595	−	337.048i	0.355749	−	0.616175i	0.987246	+	0.159203i	$0.0508925\pi$
$548$			387.986i			0.708004i
$549$	−588.882	+	39.7783i	−1.07265	+	0.0724560i
$550$	69.9289			0.127143
$551$	−146.111	−	84.3574i	−0.265175	−	0.153099i
$552$	−167.592	+	5.65388i	−0.303608	+	0.0102425i
$553$	−158.416	−	274.384i	−0.286466	−	0.496173i
$554$	646.392	−	373.194i	1.16677	−	0.673636i
$555$	−29.8650	−	885.255i	−0.0538108	−	1.59505i
$556$	−158.923	+	275.263i	−0.285833	+	0.495078i
$557$		−	752.828i		−	1.35158i	−0.737096	−	0.675788i	$-0.763803\pi$
$557$		−	752.828i		−	1.35158i	0.737096	−	0.675788i	$-0.236197\pi$
$558$	235.699	−	158.170i	0.422399	−	0.283460i
$559$	734.498			1.31395
$560$	38.1893	+	22.0486i	0.0681952	+	0.0393725i
$561$	191.548	+	307.350i	0.341440	+	0.547861i
$562$	−285.400	−	494.327i	−0.507829	−	0.879586i
$563$	−574.864	+	331.898i	−1.02107	+	0.589517i	−0.914415	−	0.404779i	$-0.867349\pi$
$563$	−574.864	+	331.898i	−1.02107	+	0.589517i	−0.106659	+	0.994296i	$0.534015\pi$
$564$	382.162	+	203.780i	0.677592	+	0.361311i
$565$	−167.572	+	290.243i	−0.296587	+	0.513704i
$566$			313.901i			0.554596i
$567$	−131.139	−	169.498i	−0.231286	−	0.298938i
$568$	316.575			0.557351
$569$	496.119	+	286.435i	0.871914	+	0.503400i	0.867984	−	0.496592i	$-0.165416\pi$
$569$	496.119	+	286.435i	0.871914	+	0.503400i	0.00393041	+	0.999992i	$0.498749\pi$
$570$	130.580	−	244.885i	0.229087	−	0.429623i
$571$	−179.597	−	311.072i	−0.314531	−	0.544784i	0.664806	−	0.747016i	$-0.268514\pi$
$571$	−179.597	−	311.072i	−0.314531	−	0.544784i	−0.979338	+	0.202231i	$0.935181\pi$
$572$	165.062	−	95.2983i	0.288569	−	0.166605i
$573$	−146.969	+	91.5951i	−0.256491	+	0.159852i
$574$	15.7512	−	27.2818i	0.0274411	−	0.0475293i
$575$			150.940i			0.262504i
$576$	40.1205	+	59.7858i	0.0696537	+	0.103795i
$577$	327.352			0.567334			0.283667	−	0.958923i	$-0.408449\pi$
$577$	327.352			0.567334			0.283667	+	0.958923i	$0.408449\pi$
$578$	−71.8858	−	41.5033i	−0.124370	−	0.0718050i
$579$	268.380	−	9.05406i	0.463523	−	0.0156374i
$580$	44.7808	+	77.5627i	0.0772083	+	0.133729i
$581$	−26.6470	+	15.3847i	−0.0458641	+	0.0264797i
$582$	−24.0497	−	712.880i	−0.0413225	−	1.22488i
$583$	259.960	−	450.265i	0.445901	−	0.772324i
$584$			37.6490i			0.0644675i
$585$	37.2038	+	550.769i	0.0635963	+	0.941486i
$586$	−370.002			−0.631402
$587$	702.685	+	405.696i	1.19708	+	0.691134i	0.959903	−	0.280333i	$-0.0904449\pi$
$587$	702.685	+	405.696i	1.19708	+	0.691134i	0.237176	+	0.971467i	$0.423778\pi$
$588$	22.2144	+	35.6443i	0.0377797	+	0.0606196i
$589$	175.052	+	303.199i	0.297202	+	0.514769i
$590$	134.851	−	77.8562i	0.228561	−	0.131960i
$591$	4.96899	+	2.64961i	0.00840776	+	0.00448326i
$592$	−141.717	+	245.461i	−0.239387	+	0.414631i
$593$		−	1078.74i		−	1.81912i	−0.415576	−	0.909559i	$-0.636420\pi$
$593$		−	1078.74i		−	1.81912i	0.415576	−	0.909559i	$-0.363580\pi$
$594$	−144.590	−	200.504i	−0.243418	−	0.337550i
$595$	205.565			0.345488
$596$	176.424	+	101.858i	0.296013	+	0.170903i
$597$	113.197	−	212.287i	0.189610	−	0.355589i
$598$	205.699	+	356.281i	0.343978	+	0.595788i
$599$	95.0263	−	54.8635i	0.158642	−	0.0915918i	−0.418578	−	0.908181i	$-0.637471\pi$
$599$	95.0263	−	54.8635i	0.158642	−	0.0915918i	0.577219	+	0.816589i	$0.304138\pi$
$600$	55.0019	−	34.2786i	0.0916698	−	0.0571309i
$601$	−402.166	+	696.572i	−0.669161	+	1.15902i	0.308978	+	0.951069i	$0.400013\pi$
$601$	−402.166	+	696.572i	−0.669161	+	1.15902i	−0.978139	+	0.207952i	$0.933320\pi$
$602$			186.698i			0.310130i
$603$	−94.3849	+	192.361i	−0.156526	+	0.319007i
$604$	280.924			0.465106
$605$	285.391	+	164.771i	0.471721	+	0.272348i
$606$	93.4956	−	3.15417i	0.154283	−	0.00520489i
$607$	109.545	+	189.738i	0.180470	+	0.312584i	0.942041	−	0.335498i	$-0.108905\pi$
$607$	109.545	+	189.738i	0.180470	+	0.312584i	−0.761571	+	0.648082i	$0.775571\pi$
$608$	−76.9074	+	44.4025i	−0.126492	+	0.0730305i
$609$	2.87612	+	85.2538i	0.00472269	+	0.139990i
$610$	−193.224	+	334.674i	−0.316761	+	0.548646i
$611$		−	1062.55i		−	1.73903i
$612$	301.321	+	147.848i	0.492354	+	0.241581i
$613$	897.371			1.46390			0.731951	−	0.681358i	$-0.238610\pi$
$613$	897.371			1.46390			0.731951	+	0.681358i	$0.238610\pi$
$614$	−168.736	−	97.4195i	−0.274814	−	0.158664i
$615$	55.6658	+	89.3189i	0.0905134	+	0.145234i
$616$	24.2234	+	41.9562i	0.0393237	+	0.0681107i
$617$	−617.603	+	356.573i	−1.00098	+	0.577915i	−0.908537	−	0.417804i	$-0.862800\pi$
$617$	−617.603	+	356.573i	−1.00098	+	0.577915i	−0.0924400	+	0.995718i	$0.529467\pi$
$618$	473.621	+	252.548i	0.766377	+	0.408654i
$619$	210.975	−	365.420i	0.340832	−	0.590339i	−0.643755	−	0.765231i	$-0.722625\pi$
$619$	210.975	−	365.420i	0.340832	−	0.590339i	0.984588	+	0.174893i	$0.0559579\pi$
$620$		−	185.851i		−	0.299760i
$621$	432.784	−	312.094i	0.696914	−	0.502567i
$622$	484.989			0.779725
$623$	−191.441	−	110.528i	−0.307289	−	0.177413i
$624$	83.1131	−	155.868i	0.133194	−	0.249788i
$625$	187.859	+	325.381i	0.300574	+	0.520610i
$626$	431.425	−	249.083i	0.689177	−	0.397897i
$627$	258.760	−	161.266i	0.412695	−	0.257202i
$628$	248.908	−	431.121i	0.396350	−	0.686498i
$629$			1321.27i			2.10059i
$630$	−139.997	+	9.45666i	−0.222218	+	0.0150106i
$631$	−601.037			−0.952515			−0.476257	−	0.879306i	$-0.658007\pi$
$631$	−601.037			−0.952515			−0.476257	+	0.879306i	$0.658007\pi$
$632$	−293.329	−	169.353i	−0.464128	−	0.267964i
$633$	−483.056	+	16.2964i	−0.763121	+	0.0257447i
$634$	104.572	+	181.125i	0.164941	+	0.285685i
$635$	81.3335	−	46.9579i	0.128084	−	0.0739495i
$636$	−16.2466	−	481.582i	−0.0255450	−	0.757204i
$637$	51.5207	−	89.2365i	0.0808802	−	0.140089i
$638$			98.3958i			0.154225i
$639$	−836.450	+	561.317i	−1.30900	+	0.878430i
$640$	47.1419			0.0736592
$641$	−809.038	−	467.098i	−1.26215	−	0.728702i	−0.288660	−	0.957432i	$-0.593210\pi$
$641$	−809.038	−	467.098i	−1.26215	−	0.728702i	−0.973490	+	0.228729i	$0.926543\pi$
$642$	89.0926	+	142.954i	0.138774	+	0.222670i
$643$	10.0042	+	17.3277i	0.0155586	+	0.0269482i	0.873700	−	0.486465i	$-0.161714\pi$
$643$	10.0042	+	17.3277i	0.0155586	+	0.0269482i	−0.858141	+	0.513414i	$0.828381\pi$
$644$	−90.5614	+	52.2857i	−0.140623	+	0.0811889i
$645$	−550.378	−	293.477i	−0.853299	−	0.455003i
$646$	−206.989	+	358.515i	−0.320416	+	0.554977i
$647$			724.799i			1.12025i	0.828410	+	0.560123i	$0.189246\pi$
$647$			724.799i			1.12025i	−0.828410	+	0.560123i	$0.810754\pi$
$648$	−212.012	−	86.8279i	−0.327178	−	0.133994i
$649$	171.071			0.263592
$650$	−137.699	−	79.5004i	−0.211844	−	0.122308i
$651$	83.2873	−	156.194i	0.127938	−	0.239930i
$652$	168.569	+	291.970i	0.258541	+	0.447807i
$653$	68.1776	−	39.3624i	0.104407	−	0.0602793i	−0.446887	−	0.894590i	$-0.647468\pi$
$653$	68.1776	−	39.3624i	0.104407	−	0.0602793i	0.551294	+	0.834311i	$0.314134\pi$
$654$	−335.658	+	209.190i	−0.513238	+	0.319863i
$655$	−493.927	+	855.507i	−0.754088	+	1.30612i
$656$		−	33.6774i		−	0.0513375i
$657$	−66.7552	−	99.4757i	−0.101606	−	0.151409i
$658$	270.084			0.410462
$659$	−822.374	−	474.798i	−1.24791	−	0.720483i	−0.277220	−	0.960806i	$-0.589413\pi$
$659$	−822.374	−	474.798i	−1.24791	−	0.720483i	−0.970693	+	0.240324i	$0.922746\pi$
$660$	−161.762	+	5.45722i	−0.245095	+	0.00826851i
$661$	−192.159	−	332.828i	−0.290709	−	0.503523i	0.683269	−	0.730167i	$-0.260558\pi$
$661$	−192.159	−	332.828i	−0.290709	−	0.503523i	−0.973978	+	0.226644i	$0.927224\pi$
$662$	−685.926	+	396.019i	−1.03614	+	0.598217i
$663$	−27.7639	−	822.976i	−0.0418762	−	1.24129i
$664$	−16.4469	+	28.4869i	−0.0247694	+	0.0429019i
$665$		−	173.067i		−	0.260251i
$666$	−60.7826	−	899.832i	−0.0912652	−	1.35110i
$667$	−212.385			−0.318418
$668$	504.178	+	291.087i	0.754758	+	0.435760i
$669$	32.5247	+	52.1877i	0.0486168	+	0.0780085i
$670$	70.1462	+	121.497i	0.104696	+	0.181338i
$671$	−367.686	+	212.283i	−0.547967	+	0.316369i
$672$	39.6193	+	21.1261i	0.0589573	+	0.0314377i
$673$	−99.9437	+	173.108i	−0.148505	+	0.257218i	−0.930675	−	0.365847i	$-0.880779\pi$
$673$	−99.9437	+	173.108i	−0.148505	+	0.257218i	0.782170	+	0.623065i	$0.214113\pi$
$674$			33.8281i			0.0501900i
$675$	−84.5462	+	188.094i	−0.125254	+	0.278657i
$676$	−95.3688			−0.141078
$677$	856.490	+	494.495i	1.26513	+	0.730420i	0.974062	−	0.226283i	$-0.0726575\pi$
$677$	856.490	+	494.495i	1.26513	+	0.730420i	0.291064	+	0.956704i	$0.405991\pi$
$678$	−160.561	+	301.111i	−0.236816	+	0.444117i
$679$	−222.406	−	385.218i	−0.327549	−	0.567331i
$680$	190.317	−	109.879i	0.279877	−	0.161587i
$681$	383.995	−	239.315i	0.563869	−	0.351417i
$682$	102.092	−	176.828i	0.149695	−	0.259279i
$683$			472.371i			0.691612i	0.938306	+	0.345806i	$0.112394\pi$
$683$			472.371i			0.691612i	−0.938306	+	0.345806i	$0.887606\pi$
$684$	124.474	−	253.684i	0.181979	−	0.370883i
$685$	−808.329			−1.18004
$686$	22.6826	+	13.0958i	0.0330650	+	0.0190901i
$687$	−892.774	+	30.1186i	−1.29953	+	0.0438408i
$688$	99.7945	+	172.849i	0.145050	+	0.251234i
$689$	−1023.79	+	591.085i	−1.48590	+	0.857888i
$690$	−11.7793	−	349.160i	−0.0170714	−	0.506029i
$691$	−379.591	+	657.471i	−0.549336	+	0.951478i	0.448984	+	0.893540i	$0.351786\pi$
$691$	−379.591	+	657.471i	−0.549336	+	0.951478i	−0.998320	+	0.0579384i	$0.981547\pi$
$692$			276.645i			0.399776i
$693$	−138.395	−	67.9057i	−0.199704	−	0.0979880i
$694$	342.321			0.493258
$695$	−573.483	−	331.100i	−0.825155	−	0.476404i
$696$	48.2328	+	77.3923i	0.0693000	+	0.111196i
$697$	−78.4960	−	135.959i	−0.112620	−	0.195063i
$698$	−44.0326	+	25.4223i	−0.0630840	+	0.0364216i
$699$	−1022.91	−	545.443i	−1.46339	−	0.780319i
$700$	20.2078	−	35.0010i	0.0288683	−	0.0500014i
$701$		−	590.449i		−	0.842295i	−0.906992	−	0.421147i	$-0.861628\pi$
$701$		−	590.449i		−	0.842295i	0.906992	−	0.421147i	$-0.138372\pi$
$702$	56.7677	+	559.199i	0.0808657	+	0.796579i
$703$	1112.38			1.58234
$704$	44.8531	+	25.8959i	0.0637117	+	0.0367840i
$705$	−424.554	+	796.195i	−0.602204	+	1.12935i
$706$	217.264	+	376.313i	0.307740	+	0.533021i
$707$	50.5221	−	29.1690i	0.0714598	−	0.0412574i
$708$	134.555	−	83.8578i	0.190049	−	0.118443i
$709$	−375.204	+	649.872i	−0.529201	+	0.916603i	0.470219	+	0.882550i	$0.344175\pi$
$709$	−375.204	+	649.872i	−0.529201	+	0.916603i	−0.999420	+	0.0340534i	$0.989158\pi$
$710$			659.552i			0.928946i
$711$	1075.31	−	72.6358i	1.51239	−	0.102160i
$712$	−236.320			−0.331910
$713$	381.679	+	220.362i	0.535314	+	0.309064i
$714$	209.188	−	7.05717i	0.292981	−	0.00988399i
$715$	198.544	+	343.889i	0.277684	+	0.480963i
$716$	−527.465	+	304.532i	−0.736683	+	0.425324i
$717$	−21.0380	−	623.606i	−0.0293417	−	0.869744i
$718$	−374.094	+	647.951i	−0.521023	+	0.902438i
$719$			528.232i			0.734676i	0.930088	+	0.367338i	$0.119731\pi$
$719$			528.232i			0.734676i	−0.930088	+	0.367338i	$0.880269\pi$
$720$	−124.558	+	83.5869i	−0.172997	+	0.116093i
$721$	334.721			0.464245
$722$	−140.297	−	81.0005i	−0.194317	−	0.112189i
$723$	−513.259	−	823.553i	−0.709901	−	1.13908i
$724$	−260.720	−	451.580i	−0.360111	−	0.623730i
$725$	71.0872	−	41.0422i	0.0980513	−	0.0566099i
$726$	296.078	+	157.877i	0.407821	+	0.217461i
$727$	337.899	−	585.259i	0.464786	−	0.805033i	−0.534406	−	0.845228i	$-0.679465\pi$
$727$	337.899	−	585.259i	0.464786	−	0.805033i	0.999192	+	0.0401952i	$0.0127980\pi$
$728$		−	110.156i		−	0.151313i
$729$	714.128	−	146.501i	0.979599	−	0.200961i
$730$	−78.4379			−0.107449
$731$	805.761	+	465.206i	1.10227	+	0.636397i
$732$	−185.140	+	347.206i	−0.252924	+	0.474325i
$733$	83.9702	+	145.441i	0.114557	+	0.198418i	0.917603	−	0.397499i	$-0.130122\pi$
$733$	83.9702	+	145.441i	0.114557	+	0.198418i	−0.803046	+	0.595918i	$0.796789\pi$
$734$	415.273	−	239.758i	0.565766	−	0.326645i
$735$	−74.2613	+	46.2815i	−0.101036	+	0.0629680i
$736$	−55.8957	+	96.8142i	−0.0759453	+	0.131541i
$737$			154.130i			0.209132i
$738$	59.7132	+	88.9820i	0.0809122	+	0.120572i
$739$	−832.894			−1.12706			−0.563528	−	0.826097i	$-0.690556\pi$
$739$	−832.894			−1.12706			−0.563528	+	0.826097i	$0.690556\pi$
$740$	−511.393	−	295.253i	−0.691072	−	0.398991i
$741$	−692.868	+	23.3746i	−0.935045	+	0.0315447i
$742$	−150.245	−	260.232i	−0.202486	−	0.350717i
$743$	−698.782	+	403.442i	−0.940487	+	0.542990i	−0.890113	−	0.455740i	$-0.849375\pi$
$743$	−698.782	+	403.442i	−0.940487	+	0.542990i	−0.0503738	+	0.998730i	$0.516041\pi$
$744$	−6.38038	−	189.127i	−0.00857579	−	0.254203i
$745$	−212.211	+	367.560i	−0.284847	+	0.493370i
$746$		−	699.737i		−	0.937985i
$747$	−7.05410	−	104.430i	−0.00944324	−	0.139799i
$748$	241.435			0.322774
$749$	90.9701	+	52.5216i	0.121455	+	0.0701223i
$750$	305.173	+	489.667i	0.406897	+	0.652889i
$751$	−203.868	−	353.110i	−0.271462	−	0.470187i	0.697774	−	0.716318i	$-0.254174\pi$
$751$	−203.868	−	353.110i	−0.271462	−	0.470187i	−0.969237	+	0.246131i	$0.920841\pi$
$752$	250.049	−	144.366i	0.332512	−	0.191976i
$753$	762.602	+	406.641i	1.01275	+	0.540028i
$754$	111.864	−	193.754i	0.148360	−	0.256968i
$755$			585.277i			0.775201i
$756$	−142.140	+	14.4295i	−0.188016	+	0.0190867i
$757$	709.798			0.937646			0.468823	−	0.883292i	$-0.344678\pi$
$757$	709.798			0.937646			0.468823	+	0.883292i	$0.344678\pi$
$758$	−17.7224	−	10.2321i	−0.0233805	−	0.0134988i
$759$	180.593	−	338.678i	0.237935	−	0.446217i
$760$	−92.5081	−	160.229i	−0.121721	−	0.210827i
$761$	454.599	−	262.463i	0.597370	−	0.344892i	−0.170636	−	0.985334i	$-0.554582\pi$
$761$	454.599	−	262.463i	0.597370	−	0.344892i	0.768006	+	0.640442i	$0.221249\pi$
$762$	81.1548	−	50.5777i	0.106502	−	0.0663750i
$763$	−123.321	+	213.599i	−0.161627	+	0.279946i
$764$			115.450i			0.151113i
$765$	−308.025	+	627.770i	−0.402648	+	0.820615i
$766$	422.557			0.551641
$767$	−336.861	−	194.487i	−0.439193	−	0.253568i
$768$	47.9727	−	1.61841i	0.0624645	−	0.00210730i
$769$	164.387	+	284.726i	0.213767	+	0.370255i	0.952890	−	0.303315i	$-0.0980933\pi$
$769$	164.387	+	284.726i	0.213767	+	0.370255i	−0.739123	+	0.673570i	$0.764760\pi$
$770$	−87.4114	+	50.4670i	−0.113521	+	0.0655416i
$771$	−13.0443	−	386.660i	−0.0169187	−	0.501504i
$772$	89.5108	−	155.037i	0.115947	−	0.200825i
$773$		−	343.076i		−	0.443824i	−0.975067	−	0.221912i	$-0.928770\pi$
$773$		−	343.076i		−	0.443824i	0.975067	−	0.221912i	$-0.0712298\pi$
$774$	−570.153	−	279.755i	−0.736632	−	0.361440i
$775$	−170.335			−0.219787
$776$	−411.815	−	237.762i	−0.530690	−	0.306394i
$777$	−297.474	−	477.314i	−0.382849	−	0.614303i
$778$	−62.8723	−	108.898i	−0.0808128	−	0.139972i
$779$	−114.465	+	66.0863i	−0.146938	+	0.0848348i
$780$	324.734	+	173.158i	0.416326	+	0.221997i
$781$	−362.304	+	627.529i	−0.463898	+	0.803495i
$782$			521.132i			0.666409i
$783$	−264.664	−	118.964i	−0.338012	−	0.151933i
$784$	28.0000			0.0357143
$785$	898.195	+	518.573i	1.14420	+	0.660603i
$786$	−473.262	+	887.542i	−0.602115	+	1.12919i
$787$	−165.233	−	286.191i	−0.209952	−	0.363648i	0.741747	−	0.670680i	$-0.233998\pi$
$787$	−165.233	−	286.191i	−0.209952	−	0.363648i	−0.951699	+	0.307032i	$0.900664\pi$
$788$	3.25122	−	1.87709i	0.00412591	−	0.00238210i
$789$	80.6664	−	50.2734i	0.102239	−	0.0637178i
$790$	352.830	−	611.120i	0.446621	−	0.773570i
$791$			212.803i			0.269031i
$792$	−164.426	+	11.1068i	−0.207609	+	0.0140237i
$793$	965.358			1.21735
$794$	−658.398	−	380.126i	−0.829217	−	0.478749i
$795$	1003.33	−	33.8482i	1.26204	−	0.0425763i
$796$	−80.1938	−	138.900i	−0.100746	−	0.174497i
$797$	−199.933	+	115.431i	−0.250856	+	0.144832i	−0.620156	−	0.784478i	$-0.712931\pi$
$797$	−199.933	+	115.431i	−0.250856	+	0.144832i	0.369300	+	0.929310i	$0.379598\pi$
$798$	−5.94148	−	176.117i	−0.00744546	−	0.220698i
$799$	672.983	−	1165.64i	0.842281	−	1.45887i
$800$		−	43.2061i		−	0.0540077i
$801$	624.400	−	419.017i	0.779526	−	0.523117i
$802$	247.008			0.307990
$803$	−74.6296	−	43.0874i	−0.0929385	−	0.0536581i
$804$	75.5535	+	121.230i	0.0939720	+	0.150783i
$805$	−108.932	−	188.675i	−0.135319	−	0.234379i
$806$	−402.062	+	232.131i	−0.498837	+	0.288004i
$807$	409.459	+	218.335i	0.507385	+	0.270552i
$808$	31.1829	−	54.0104i	0.0385927	−	0.0668446i
$809$		−	1138.49i		−	1.40729i	−0.710554	−	0.703643i	$-0.751556\pi$
$809$		−	1138.49i		−	1.40729i	0.710554	−	0.703643i	$-0.248444\pi$
$810$	180.897	−	441.704i	0.223330	−	0.545314i
$811$	1346.08			1.65977			0.829887	−	0.557931i	$-0.188405\pi$
$811$	1346.08			1.65977			0.829887	+	0.557931i	$0.188405\pi$
$812$	49.2493	+	28.4341i	0.0606518	+	0.0350173i
$813$	240.457	−	450.946i	0.295766	−	0.554670i
$814$	−324.376	−	561.836i	−0.398496	−	0.690216i
$815$	−608.289	+	351.196i	−0.746367	+	0.430915i
$816$	189.898	−	118.349i	0.232719	−	0.145036i
$817$	391.660	−	678.375i	0.479388	−	0.830325i
$818$		−	304.428i		−	0.372161i
$819$	195.317	+	291.052i	0.238482	+	0.355375i
$820$	70.1634			0.0855651
$821$	415.276	+	239.760i	0.505817	+	0.292034i	0.731113	−	0.682257i	$-0.239001\pi$
$821$	415.276	+	239.760i	0.505817	+	0.292034i	−0.225295	+	0.974291i	$0.572335\pi$
$822$	−822.575	+	27.7504i	−1.00070	+	0.0337596i
$823$	−623.100	−	1079.24i	−0.757109	−	1.31135i	−0.944319	−	0.329031i	$-0.893278\pi$
$823$	−623.100	−	1079.24i	−0.757109	−	1.31135i	0.187210	−	0.982320i	$-0.440055\pi$
$824$	309.891	−	178.916i	0.376081	−	0.217131i
$825$	5.00161	+	148.257i	0.00606255	+	0.179706i
$826$	49.4356	−	85.6250i	0.0598494	−	0.103662i
$827$			464.446i			0.561603i	0.959766	+	0.280802i	$0.0906003\pi$
$827$			464.446i			0.561603i	−0.959766	+	0.280802i	$0.909400\pi$
$828$	−23.9737	−	354.909i	−0.0289538	−	0.428635i
$829$	479.856			0.578837			0.289418	−	0.957203i	$-0.406538\pi$
$829$	479.856			0.578837			0.289418	+	0.957203i	$0.406538\pi$
$830$	−59.3495	−	34.2654i	−0.0715054	−	0.0412837i
$831$	837.448	+	1343.73i	1.00776	+	1.61701i
$832$	−58.8808	−	101.985i	−0.0707702	−	0.122578i
$833$	113.039	−	65.2630i	0.135701	−	0.0783469i
$834$	−594.957	−	317.248i	−0.713377	−	0.380393i
$835$	−606.450	+	1050.40i	−0.726288	+	1.25797i
$836$		−	203.266i		−	0.243141i
$837$	352.198	+	488.395i	0.420786	+	0.583507i
$838$	330.335			0.394195
$839$	−249.072	−	143.802i	−0.296868	−	0.171397i	0.344167	−	0.938908i	$-0.388161\pi$
$839$	−249.072	−	143.802i	−0.296868	−	0.171397i	−0.641035	+	0.767512i	$0.721495\pi$
$840$	−44.0141	+	82.5427i	−0.0523977	+	0.0982651i
$841$	−362.750	−	628.302i	−0.431332	−	0.747089i
$842$	997.344	−	575.817i	1.18449	−	0.683868i
$843$	1027.62	−	640.437i	1.21900	−	0.759712i
$844$	−161.110	+	279.051i	−0.190889	+	0.330629i
$845$		−	198.691i		−	0.235137i
$846$	−404.702	+	824.802i	−0.478372	+	0.974944i
$847$	209.246			0.247044
$848$	−278.200	−	160.619i	−0.328065	−	0.189409i
$849$	−665.507	+	22.4515i	−0.783871	+	0.0264447i
$850$	−100.706	−	174.427i	−0.118477	−	0.205209i
$851$	1212.71	−	700.158i	1.42504	−	0.822747i
$852$	22.6428	+	671.176i	0.0265760	+	0.787765i
$853$	339.982	−	588.866i	0.398572	−	0.690347i	−0.594978	−	0.803742i	$-0.702839\pi$
$853$	339.982	−	588.866i	0.398572	−	0.690347i	0.993550	+	0.113395i	$0.0361725\pi$
$854$			245.380i			0.287330i
$855$	528.524	+	259.328i	0.618156	+	0.303308i
$856$	112.296			0.131187
$857$	725.061	+	418.614i	0.846045	+	0.488464i	0.859314	−	0.511448i	$-0.170891\pi$
$857$	725.061	+	418.614i	0.846045	+	0.488464i	−0.0132695	+	0.999912i	$0.504224\pi$
$858$	213.849	+	343.133i	0.249242	+	0.399922i
$859$	−173.311	−	300.184i	−0.201759	−	0.349457i	0.747336	−	0.664446i	$-0.231332\pi$
$859$	−173.311	−	300.184i	−0.201759	−	0.349457i	−0.949095	+	0.314989i	$0.897999\pi$
$860$	−360.113	+	207.912i	−0.418737	+	0.241758i
$861$	58.9672	+	31.4430i	0.0684868	+	0.0365191i
$862$	224.845	−	389.443i	0.260841	−	0.451790i
$863$		−	62.3236i		−	0.0722174i	−0.999348	−	0.0361087i	$-0.988504\pi$
$863$		−	62.3236i		−	0.0722174i	0.999348	−	0.0361087i	$-0.0114962\pi$
$864$	−123.883	+	89.3362i	−0.143383	+	0.103398i
$865$	−576.361			−0.666313
$866$	−421.679	−	243.456i	−0.486927	−	0.281127i
$867$	82.8502	−	155.375i	0.0955596	−	0.179210i
$868$	−59.0042	−	102.198i	−0.0679772	−	0.117740i
$869$	671.399	−	387.633i	0.772612	−	0.446068i
$870$	−161.239	+	100.488i	−0.185332	+	0.115504i
$871$	175.227	−	303.502i	0.201179	−	0.348452i
$872$			263.672i			0.302376i
$873$	1509.67	−	101.976i	1.72929	−	0.116811i
$874$	438.744			0.501995
$875$	311.604	+	179.905i	0.356119	+	0.205605i
$876$	−79.8203	+	2.69282i	−0.0911190	+	0.00307399i
$877$	845.076	+	1463.71i	0.963598	+	1.66900i	0.713334	+	0.700824i	$0.247184\pi$
$877$	845.076	+	1463.71i	0.963598	+	1.66900i	0.250264	+	0.968178i	$0.419483\pi$
$878$	332.352	−	191.883i	0.378533	−	0.218546i
$879$	−26.4641	−	784.446i	−0.0301070	−	0.892430i
$880$	−53.9515	+	93.4467i	−0.0613085	+	0.106189i
$881$		−	1480.43i		−	1.68040i	−0.542280	−	0.840198i	$-0.682439\pi$
$881$		−	1480.43i		−	1.68040i	0.542280	−	0.840198i	$-0.317561\pi$
$882$	−73.9812	+	49.6466i	−0.0838789	+	0.0562886i
$883$	−688.171			−0.779356			−0.389678	−	0.920951i	$-0.627414\pi$
$883$	−688.171			−0.779356			−0.389678	+	0.920951i	$0.627414\pi$
$884$	−475.416	−	274.481i	−0.537800	−	0.310499i
$885$	174.709	+	280.331i	0.197411	+	0.316758i
$886$	−134.206	−	232.452i	−0.151474	−	0.262361i
$887$	−541.722	+	312.763i	−0.610735	+	0.352608i	−0.773253	−	0.634098i	$-0.781372\pi$
$887$	−541.722	+	312.763i	−0.610735	+	0.352608i	0.162518	+	0.986706i	$0.448038\pi$
$888$	−530.542	−	282.900i	−0.597457	−	0.318581i
$889$	29.8164	−	51.6436i	0.0335393	−	0.0580918i
$890$		−	492.347i		−	0.553199i
$891$	414.751	−	320.889i	0.465489	−	0.360144i
$892$	40.9954			0.0459590
$893$	−981.360	−	566.589i	−1.09895	−	0.634478i
$894$	−203.333	+	381.324i	−0.227441	+	0.426536i
$895$	−634.461	−	1098.92i	−0.708895	−	1.22784i
$896$	25.9230	−	14.9666i	0.0289319	−	0.0167038i
$897$	−740.645	+	461.588i	−0.825691	+	0.514591i
$898$	−425.558	+	737.088i	−0.473896	+	0.820811i
$899$		−	239.676i		−	0.266603i
$900$	76.6084	+	114.159i	0.0851205	+	0.126843i
$901$	−1497.49			−1.66203
$902$	66.7569	+	38.5421i	0.0740098	+	0.0427296i
$903$	−395.822	+	13.3535i	−0.438341	+	0.0147879i
$904$	113.748	+	197.018i	0.125828	+	0.217940i
$905$	940.821	−	543.183i	1.03958	−	0.600203i
$906$	20.0929	+	595.592i	0.0221776	+	0.657386i
$907$	−503.987	+	872.931i	−0.555664	+	0.962438i	0.442188	+	0.896922i	$0.354202\pi$
$907$	−503.987	+	872.931i	−0.555664	+	0.962438i	−0.997852	+	0.0655154i	$0.979131\pi$
$908$		−	301.643i		−	0.332206i
$909$	13.3744	+	197.996i	0.0147133	+	0.217817i
$910$	229.498			0.252196
$911$	−331.886	−	191.614i	−0.364309	−	0.210334i	0.306660	−	0.951819i	$-0.400788\pi$
$911$	−331.886	−	191.614i	−0.364309	−	0.210334i	−0.670969	+	0.741485i	$0.734122\pi$
$912$	−99.6392	−	159.877i	−0.109253	−	0.175303i
$913$	−37.6453	−	65.2036i	−0.0412325	−	0.0714169i
$914$	216.881	−	125.217i	0.237288	−	0.136998i
$915$	−723.368	−	385.720i	−0.790566	−	0.421552i
$916$	−297.761	+	515.737i	−0.325066	+	0.563031i
$917$			627.249i			0.684023i
$918$	−291.902	+	649.409i	−0.317976	+	0.707417i
$919$	−769.956			−0.837819			−0.418910	−	0.908028i	$-0.637588\pi$
$919$	−769.956			−0.837819			−0.418910	+	0.908028i	$0.637588\pi$
$920$	−201.702	−	116.453i	−0.219242	−	0.126579i
$921$	194.472	−	364.706i	0.211153	−	0.395990i
$922$	141.586	+	245.234i	0.153564	+	0.265981i
$923$	1426.84	−	823.788i	1.54588	−	0.892512i
$924$	−87.2194	+	54.3573i	−0.0943933	+	0.0588283i
$925$	−270.603	+	468.698i	−0.292544	+	0.506701i
$926$		−	671.055i		−	0.724681i
$927$	−501.555	+	1022.19i	−0.541052	+	1.10269i
$928$	60.7946			0.0655115
$929$	−323.085	−	186.533i	−0.347778	−	0.200789i	0.315928	−	0.948783i	$-0.397684\pi$
$929$	−323.085	−	186.533i	−0.347778	−	0.200789i	−0.663706	+	0.747994i	$0.731017\pi$
$930$	394.026	−	13.2929i	0.423684	−	0.0142934i
$931$	−54.9453	−	95.1681i	−0.0590175	−	0.102221i
$932$	−669.290	+	386.415i	−0.718122	+	0.414608i
$933$	34.6884	+	1028.23i	0.0371794	+	1.10207i
$934$	−178.923	+	309.904i	−0.191566	+	0.331803i
$935$			503.005i			0.537973i
$936$	336.402	+	165.061i	0.359404	+	0.176347i
$937$	−987.512			−1.05391			−0.526954	−	0.849894i	$-0.676666\pi$
$937$	−987.512			−1.05391			−0.526954	+	0.849894i	$0.676666\pi$
$938$	77.1457	+	44.5401i	0.0822449	+	0.0474841i
$939$	558.943	+	896.855i	0.595253	+	0.955117i
$940$	300.772	+	520.952i	0.319970	+	0.554204i
$941$	−1178.37	+	680.335i	−1.25226	+	0.722991i	−0.971557	−	0.236804i	$-0.923900\pi$
$941$	−1178.37	+	680.335i	−1.25226	+	0.722991i	−0.280700	+	0.959795i	$0.590567\pi$
$942$	931.828	+	496.877i	0.989202	+	0.527470i
$943$	−83.1921	+	144.093i	−0.0882207	+	0.152803i
$944$		−	105.698i		−	0.111968i
$945$	−30.0624	−	296.134i	−0.0318121	−	0.313369i
$946$	−456.839			−0.482917
$947$	1344.82	+	776.431i	1.42008	+	0.819884i	0.996305	−	0.0858826i	$-0.0273710\pi$
$947$	1344.82	+	776.431i	1.42008	+	0.819884i	0.423776	+	0.905767i	$0.360704\pi$
$948$	338.068	−	634.003i	0.356612	−	0.668780i
$949$	97.9699	+	169.689i	0.103235	+	0.178808i
$950$	−146.852	+	84.7848i	−0.154581	+	0.0892472i
$951$	−376.525	+	234.660i	−0.395926	+	0.246751i
$952$	69.7691	−	120.844i	0.0732868	−	0.126937i
$953$			756.704i			0.794023i	0.917814	+	0.397012i	$0.129953\pi$
$953$			756.704i			0.794023i	−0.917814	+	0.397012i	$0.870047\pi$
$954$	1019.85	−	68.8895i	1.06902	−	0.0722112i
$955$	−240.529			−0.251862
$956$	−360.244	−	207.987i	−0.376824	−	0.217560i
$957$	−208.610	+	7.03768i	−0.217984	+	0.00735390i
$958$	−516.895	−	895.288i	−0.539556	−	0.934539i
$959$	−444.494	+	256.629i	−0.463497	+	0.267600i
$960$	3.37178	+	99.9462i	0.00351227	+	0.104111i
$961$	231.822	−	401.527i	0.241229	−	0.417822i
$962$			1475.10i			1.53337i
$963$	−296.707	+	199.111i	−0.308107	+	0.206761i
$964$	−646.932			−0.671092
$965$	323.004	+	186.486i	0.334719	+	0.193250i
$966$	−117.329	−	188.261i	−0.121458	−	0.194887i
$967$	49.6997	+	86.0824i	0.0513958	+	0.0890201i	0.890579	−	0.454829i	$-0.150300\pi$
$967$	49.6997	+	86.0824i	0.0513958	+	0.0890201i	−0.839183	+	0.543849i	$0.816966\pi$
$968$	193.724	−	111.847i	0.200128	−	0.115544i
$969$	−774.897	−	413.197i	−0.799688	−	0.426416i
$970$	495.352	−	857.975i	0.510672	−	0.884510i
$971$			24.0392i			0.0247571i	0.999923	+	0.0123786i	$0.00394032\pi$
$971$			24.0392i			0.0247571i	−0.999923	+	0.0123786i	$0.996060\pi$
$972$	168.921	−	455.699i	0.173787	−	0.468826i
$973$	−420.472			−0.432140
$974$	782.250	+	451.632i	0.803132	+	0.463688i
$975$	158.701	−	297.623i	0.162770	−	0.305254i
$976$	131.161	+	227.177i	0.134386	+	0.232764i
$977$	1101.39	−	635.889i	1.12732	−	0.650859i	0.184061	−	0.982915i	$-0.441076\pi$
$977$	1101.39	−	635.889i	1.12732	−	0.650859i	0.943260	+	0.332056i	$0.107742\pi$
$978$	−606.953	+	378.268i	−0.620607	+	0.386778i
$979$	270.456	−	468.443i	0.276257	−	0.478491i
$980$			58.3351i			0.0595256i
$981$	−467.515	−	696.670i	−0.476570	−	0.710163i
$982$	795.789			0.810376
$983$	881.017	+	508.656i	0.896254	+	0.517452i	0.875983	−	0.482342i	$-0.160214\pi$
$983$	881.017	+	508.656i	0.896254	+	0.517452i	0.0202708	+	0.999795i	$0.493547\pi$
$984$	71.4000	−	2.40875i	0.0725609	−	0.00244792i
$985$	3.91073	+	6.77358i	0.00397028	+	0.00687673i
$986$	245.434	−	141.701i	0.248919	−	0.143713i
$987$	19.3175	+	572.609i	0.0195720	+	0.580151i
$988$	−231.088	+	400.255i	−0.233894	+	0.405117i
$989$		−	986.076i		−	0.997043i
$990$	−23.1398	−	342.565i	−0.0233736	−	0.346025i
$991$	−1748.26			−1.76414			−0.882070	−	0.471118i	$-0.843851\pi$
$991$	−1748.26			−1.76414			−0.882070	+	0.471118i	$0.843851\pi$
$992$	−109.255	−	63.0782i	−0.110136	−	0.0635869i
$993$	−888.667	−	1425.92i	−0.894931	−	1.43597i
$994$	209.395	+	362.682i	0.210659	+	0.364872i
$995$	289.383	−	167.075i	0.290837	−	0.167915i
$996$	−61.5718	−	32.8318i	−0.0618191	−	0.0329637i
$997$	−123.758	+	214.355i	−0.124130	+	0.215000i	−0.921393	−	0.388633i	$-0.872947\pi$
$997$	−123.758	+	214.355i	−0.124130	+	0.215000i	0.797262	+	0.603633i	$0.206281\pi$
$998$		−	1072.23i		−	1.07438i
$999$	1903.40	−	193.226i	1.90530	−	0.193419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.q.a.29.8	✓	24
3.2	odd	2		378.3.q.a.197.5		24
9.2	odd	6		1134.3.b.c.323.21		24
9.4	even	3		378.3.q.a.71.5		24
9.5	odd	6	inner	126.3.q.a.113.8	yes	24
9.7	even	3		1134.3.b.c.323.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.8	✓	24	1.1	even	1	trivial
126.3.q.a.113.8	yes	24	9.5	odd	6	inner
378.3.q.a.71.5		24	9.4	even	3
378.3.q.a.197.5		24	3.2	odd	2
1134.3.b.c.323.4		24	9.7	even	3
1134.3.b.c.323.21		24	9.2	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-1.41155 + 2.64717i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.60855 + 2.08340i) q^{5} +(-3.60062 + 2.24400i) q^{6} +(-1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(-5.01506 - 7.47323i) q^{9} -5.89274 q^{10} +(-5.60663 - 3.23699i) q^{11} +(-5.99659 + 0.202301i) q^{12} +(7.36010 + 12.7481i) q^{13} +(-3.24037 + 1.87083i) q^{14} +(-0.421473 - 12.4933i) q^{15} +(-2.00000 + 3.46410i) q^{16} +18.6466i q^{17} +(-0.857802 - 12.6990i) q^{18} +15.6987 q^{19} +(-7.21710 - 4.16679i) q^{20} +(-4.19814 - 6.73615i) q^{21} +(-4.57780 - 7.92898i) q^{22} +(17.1145 - 9.88106i) q^{23} +(-7.48734 - 3.99246i) q^{24} +(-3.81892 + 6.61456i) q^{25} +20.8175i q^{26} +(26.8619 - 2.72692i) q^{27} -5.29150 q^{28} +(-9.30724 - 5.37354i) q^{29} +(8.31788 - 15.5991i) q^{30} +(11.1508 + 19.3137i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(16.4829 - 10.2726i) q^{33} +(-13.1851 + 22.8373i) q^{34} -11.0243i q^{35} +(7.92895 - 16.1596i) q^{36} +70.8586 q^{37} +(19.2269 + 11.1006i) q^{38} +(-44.1355 + 1.48896i) q^{39} +(-5.89274 - 10.2065i) q^{40} +(-7.29137 + 4.20968i) q^{41} +(-0.378470 - 11.2186i) q^{42} +(24.9486 - 43.2123i) q^{43} -12.9480i q^{44} +(33.6668 + 16.5191i) q^{45} +27.9479 q^{46} +(-62.5123 - 36.0915i) q^{47} +(-6.34698 - 10.1841i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-9.35440 + 5.40077i) q^{50} +(-49.3607 - 26.3205i) q^{51} +(-14.7202 + 25.4961i) q^{52} +80.3093i q^{53} +(34.8273 + 15.6545i) q^{54} +26.9757 q^{55} +(-6.48074 - 3.74166i) q^{56} +(-22.1594 + 41.5571i) q^{57} +(-7.59933 - 13.1624i) q^{58} +(-22.8843 + 13.2122i) q^{59} +(21.2175 - 13.2233i) q^{60} +(32.7902 - 56.7944i) q^{61} +31.5391i q^{62} +(23.7576 - 1.60480i) q^{63} -8.00000 q^{64} +(-53.1186 - 30.6680i) q^{65} +(27.4512 - 0.926092i) q^{66} +(-11.9038 - 20.6181i) q^{67} +(-32.2968 + 18.6466i) q^{68} +(1.99895 + 59.2527i) q^{69} +(7.79536 - 13.5020i) q^{70} -111.926i q^{71} +(21.1375 - 14.1847i) q^{72} +13.3109 q^{73} +(86.7837 + 50.1046i) q^{74} +(-12.1193 - 19.4461i) q^{75} +(15.6987 + 27.1909i) q^{76} +(14.8338 - 8.56427i) q^{77} +(-55.1076 - 29.3849i) q^{78} +(-59.8755 + 103.707i) q^{79} -16.6672i q^{80} +(-30.6983 + 74.9574i) q^{81} -11.9068 q^{82} +(10.0716 + 5.81486i) q^{83} +(7.46921 - 14.0075i) q^{84} +(-38.8482 - 67.2871i) q^{85} +(61.1114 - 35.2827i) q^{86} +(27.3623 - 17.0529i) q^{87} +(9.15559 - 15.8580i) q^{88} +83.5516i q^{89} +(29.5524 + 44.0378i) q^{90} -38.9460 q^{91} +(34.2290 + 19.7621i) q^{92} +(-66.8665 + 2.25581i) q^{93} +(-51.0411 - 88.4058i) q^{94} +(-56.6494 + 32.7065i) q^{95} +(-0.572193 - 16.9609i) q^{96} +(-84.0615 + 145.599i) q^{97} -9.89949i q^{98} +(3.92684 + 58.1334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30}+ \cdots - 440 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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