LMFDB - Embedded newform 225.3.o.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(7,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	225.193
Dual form			225.3.o.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40598 - 0.644680i) q^{2} +(0.325974 + 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(1.13830 - 7.38535i) q^{6} +(0.0658171 + 0.0176356i) q^{7} +(3.16269 + 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +O(q^{10})$	\(q+(-2.40598 - 0.644680i) q^{2} +(0.325974 + 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(1.13830 - 7.38535i) q^{6} +(0.0658171 + 0.0176356i) q^{7} +(3.16269 + 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +(4.62292 + 8.00713i) q^{11} +(-2.66465 + 6.05242i) q^{12} +(12.6403 - 3.38696i) q^{13} +(-0.146985 - 0.0848619i) q^{14} +(-9.97912 - 17.2843i) q^{16} +(-13.6029 + 13.6029i) q^{17} +(22.3959 + 0.987258i) q^{18} -5.80704i q^{19} +(-0.0311390 + 0.202031i) q^{21} +(-5.96060 - 22.2453i) q^{22} +(-43.8013 + 11.7365i) q^{23} +(-8.40093 + 10.4628i) q^{24} -32.5958 q^{26} +(-8.66274 - 25.5726i) q^{27} +(0.106208 + 0.106208i) q^{28} +(-6.37222 + 3.67900i) q^{29} +(-8.35363 + 14.4689i) q^{31} +(8.23618 + 30.7378i) q^{32} +(-22.3722 + 16.3967i) q^{33} +(41.4978 - 23.9587i) q^{34} +(-18.9184 - 5.97368i) q^{36} +(-36.0680 + 36.0680i) q^{37} +(-3.74368 + 13.9716i) q^{38} +(14.2211 + 36.5923i) q^{39} +(-31.1567 + 53.9649i) q^{41} +(0.205165 - 0.466007i) q^{42} +(2.59980 - 9.70259i) q^{43} +20.3810i q^{44} +112.951 q^{46} +(44.6476 + 11.9633i) q^{47} +(48.2931 - 35.3944i) q^{48} +(-42.4312 - 24.4977i) q^{49} +(-45.0012 - 36.1329i) q^{51} +(27.8636 + 7.46602i) q^{52} +(-28.0258 - 28.0258i) q^{53} +(4.35625 + 67.1118i) q^{54} +(0.152383 + 0.263935i) q^{56} +(17.3180 - 1.89294i) q^{57} +(17.7032 - 4.74356i) q^{58} +(-16.3509 - 9.44022i) q^{59} +(2.69547 + 4.66870i) q^{61} +(29.4265 - 29.4265i) q^{62} +(-0.612655 - 0.0270071i) q^{63} +0.568692i q^{64} +(64.3977 - 25.0273i) q^{66} +(-12.8379 - 47.9117i) q^{67} +(-40.9609 + 10.9754i) q^{68} +(-49.2792 - 126.800i) q^{69} +56.4200 q^{71} +(-33.9412 - 21.6430i) q^{72} +(54.7135 + 54.7135i) q^{73} +(110.031 - 63.5264i) q^{74} +(6.40036 - 11.0857i) q^{76} +(0.163056 + 0.608534i) q^{77} +(-10.6254 - 97.2084i) q^{78} +(40.9692 - 23.6536i) q^{79} +(73.4397 - 34.1704i) q^{81} +(109.752 - 109.752i) q^{82} +(16.0841 - 60.0267i) q^{83} +(-0.282117 + 0.351360i) q^{84} +(-12.5101 + 21.6682i) q^{86} +(-13.0488 - 17.8042i) q^{87} +(-10.7032 + 39.9449i) q^{88} +59.1599i q^{89} +0.891679 q^{91} +(-96.5530 - 25.8713i) q^{92} +(-45.8728 - 20.1960i) q^{93} +(-99.7085 - 57.5668i) q^{94} +(-88.9828 + 34.5820i) q^{96} +(150.251 + 40.2595i) q^{97} +(86.2954 + 86.2954i) q^{98} +(-56.1918 - 61.3743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8}+O(q^{10}) $ 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8	$ 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31} + 14 q^{32} - 96 q^{33} + 264 q^{36} + 92 q^{37} - 330 q^{38} - 28 q^{41} - 498 q^{42} + 2 q^{43} - 136 q^{46} - 64 q^{47} + 510 q^{48} - 396 q^{51} + 74 q^{52} + 608 q^{53} - 192 q^{56} + 114 q^{57} - 30 q^{58} + 92 q^{61} + 100 q^{62} - 24 q^{63} + 588 q^{66} + 80 q^{67} - 626 q^{68} + 248 q^{71} + 162 q^{72} + 8 q^{73} - 96 q^{76} - 338 q^{77} - 1062 q^{78} + 204 q^{81} - 104 q^{82} - 370 q^{83} - 328 q^{86} - 534 q^{87} + 210 q^{88} + 152 q^{91} - 388 q^{92} + 1062 q^{93} - 876 q^{96} - 292 q^{97} + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.40598	−	0.644680i	−1.20299	−	0.322340i	−0.398981	−	0.916959i	$-0.630636\pi$
$2$	−2.40598	−	0.644680i	−1.20299	−	0.322340i	−0.804008	+	0.594619i	$0.797303\pi$
$3$	0.325974	+	2.98224i	0.108658	+	0.994079i
$3$	0.325974	+	2.98224i	0.108658	+	0.994079i
$4$	1.90902	+	1.10217i	0.477254	+	0.275543i
$5$		0			0
$5$		0			0
$6$	1.13830	−	7.38535i	0.189717	−	1.23089i
$7$	0.0658171	+	0.0176356i	0.00940244	+	0.00251938i	0.263517	−	0.964655i	$-0.415117\pi$
$7$	0.0658171	+	0.0176356i	0.00940244	+	0.00251938i	−0.254115	+	0.967174i	$0.581784\pi$
$8$	3.16269	+	3.16269i	0.395336	+	0.395336i
$9$	−8.78748	+	1.94426i	−0.976387	+	0.216029i
$10$		0			0
$11$	4.62292	+	8.00713i	0.420265	+	0.727921i	0.995965	−	0.0897404i	$-0.0286037\pi$
$11$	4.62292	+	8.00713i	0.420265	+	0.727921i	−0.575700	+	0.817661i	$0.695270\pi$
$12$	−2.66465	+	6.05242i	−0.222054	+	0.504368i
$13$	12.6403	−	3.38696i	0.972331	−	0.260535i	0.262519	−	0.964927i	$-0.415447\pi$
$13$	12.6403	−	3.38696i	0.972331	−	0.260535i	0.709812	+	0.704391i	$0.248780\pi$
$14$	−0.146985	−	0.0848619i	−0.0104989	−	0.00606156i
$15$		0			0
$16$	−9.97912	−	17.2843i	−0.623695	−	1.08027i
$17$	−13.6029	+	13.6029i	−0.800170	+	0.800170i	−0.983122	−	0.182952i	$-0.941435\pi$
$17$	−13.6029	+	13.6029i	−0.800170	+	0.800170i	0.182952	+	0.983122i	$0.441435\pi$
$18$	22.3959	+	0.987258i	1.24422	+	0.0548477i
$19$		−	5.80704i		−	0.305634i	−0.988255	−	0.152817i	$-0.951166\pi$
$19$		−	5.80704i		−	0.305634i	0.988255	−	0.152817i	$-0.0488345\pi$
$20$		0			0
$21$	−0.0311390	+	0.202031i	−0.00148281	+	0.00962052i
$22$	−5.96060	−	22.2453i	−0.270936	−	1.01115i
$23$	−43.8013	+	11.7365i	−1.90440	+	0.510283i	−0.908728	+	0.417390i	$0.862945\pi$
$23$	−43.8013	+	11.7365i	−1.90440	+	0.510283i	−0.995676	+	0.0928936i	$0.970388\pi$
$24$	−8.40093	+	10.4628i	−0.350039	+	0.435952i
$25$		0			0
$26$	−32.5958			−1.25368
$27$	−8.66274	−	25.5726i	−0.320842	−	0.947133i
$28$	0.106208	+	0.106208i	0.00379316	+	0.00379316i
$29$	−6.37222	+	3.67900i	−0.219732	+	0.126862i	−0.605826	−	0.795597i	$-0.707157\pi$
$29$	−6.37222	+	3.67900i	−0.219732	+	0.126862i	0.386094	+	0.922459i	$0.373824\pi$
$30$		0			0
$31$	−8.35363	+	14.4689i	−0.269472	+	0.466739i	−0.968726	−	0.248135i	$-0.920183\pi$
$31$	−8.35363	+	14.4689i	−0.269472	+	0.466739i	0.699254	+	0.714874i	$0.253516\pi$
$32$	8.23618	+	30.7378i	0.257381	+	0.960558i
$33$	−22.3722	+	16.3967i	−0.677946	+	0.496871i
$34$	41.4978	−	23.9587i	1.22052	−	0.704669i
$35$		0			0
$36$	−18.9184	−	5.97368i	−0.525510	−	0.165936i
$37$	−36.0680	+	36.0680i	−0.974810	+	0.974810i	−0.999690	−	0.0248806i	$-0.992079\pi$
$37$	−36.0680	+	36.0680i	−0.974810	+	0.974810i	0.0248806	+	0.999690i	$0.492079\pi$
$38$	−3.74368	+	13.9716i	−0.0985180	+	0.367674i
$39$	14.2211	+	36.5923i	0.364644	+	0.938265i
$40$		0			0
$41$	−31.1567	+	53.9649i	−0.759919	+	1.31622i	0.182973	+	0.983118i	$0.441428\pi$
$41$	−31.1567	+	53.9649i	−0.759919	+	1.31622i	−0.942892	+	0.333100i	$0.891905\pi$
$42$	0.205165	−	0.466007i	0.00488488	−	0.0110954i
$43$	2.59980	−	9.70259i	0.0604605	−	0.225642i	−0.929084	−	0.369868i	$-0.879403\pi$
$43$	2.59980	−	9.70259i	0.0604605	−	0.225642i	0.989545	+	0.144227i	$0.0460694\pi$
$44$			20.3810i			0.463204i
$45$		0			0
$46$	112.951			2.45546
$47$	44.6476	+	11.9633i	0.949948	+	0.254538i	0.700340	−	0.713809i	$-0.253032\pi$
$47$	44.6476	+	11.9633i	0.949948	+	0.254538i	0.249608	+	0.968347i	$0.419698\pi$
$48$	48.2931	−	35.3944i	1.00611	−	0.737382i
$49$	−42.4312	−	24.4977i	−0.865943	−	0.499953i
$50$		0			0
$51$	−45.0012	−	36.1329i	−0.882377	−	0.708488i
$52$	27.8636	+	7.46602i	0.535838	+	0.143577i
$53$	−28.0258	−	28.0258i	−0.528789	−	0.528789i	0.391423	−	0.920211i	$-0.371983\pi$
$53$	−28.0258	−	28.0258i	−0.528789	−	0.528789i	−0.920211	+	0.391423i	$0.871983\pi$
$54$	4.35625	+	67.1118i	0.0806712	+	1.24281i
$55$		0			0
$56$	0.152383	+	0.263935i	0.00272112	+	0.00471312i
$57$	17.3180	−	1.89294i	0.303824	−	0.0332096i
$58$	17.7032	−	4.74356i	0.305228	−	0.0817855i
$59$	−16.3509	−	9.44022i	−0.277135	−	0.160004i	0.354991	−	0.934870i	$-0.384484\pi$
$59$	−16.3509	−	9.44022i	−0.277135	−	0.160004i	−0.632126	+	0.774866i	$0.717817\pi$
$60$		0			0
$61$	2.69547	+	4.66870i	0.0441881	+	0.0765360i	0.887274	−	0.461244i	$-0.152597\pi$
$61$	2.69547	+	4.66870i	0.0441881	+	0.0765360i	−0.843085	+	0.537780i	$0.819263\pi$
$62$	29.4265	−	29.4265i	0.474621	−	0.474621i
$63$	−0.612655	−	0.0270071i	−0.00972468	−	0.000428684i
$64$			0.568692i			0.00888582i
$65$		0			0
$66$	64.3977	−	25.0273i	0.975722	−	0.379202i
$67$	−12.8379	−	47.9117i	−0.191610	−	0.715100i	−0.993118	−	0.117116i	$-0.962635\pi$
$67$	−12.8379	−	47.9117i	−0.191610	−	0.715100i	0.801508	−	0.597984i	$-0.204031\pi$
$68$	−40.9609	+	10.9754i	−0.602366	+	0.161403i
$69$	−49.2792	−	126.800i	−0.714191	−	1.83768i
$70$		0			0
$71$	56.4200			0.794648			0.397324	−	0.917678i	$-0.369939\pi$
$71$	56.4200			0.794648			0.397324	+	0.917678i	$0.369939\pi$
$72$	−33.9412	−	21.6430i	−0.471405	−	0.300597i
$73$	54.7135	+	54.7135i	0.749500	+	0.749500i	0.974385	−	0.224885i	$-0.0722007\pi$
$73$	54.7135	+	54.7135i	0.749500	+	0.749500i	−0.224885	+	0.974385i	$0.572201\pi$
$74$	110.031	−	63.5264i	1.48691	−	0.858465i
$75$		0			0
$76$	6.40036	−	11.0857i	0.0842152	−	0.145865i
$77$	0.163056	+	0.608534i	0.00211761	+	0.00790303i
$78$	−10.6254	−	97.2084i	−0.136223	−	1.24626i
$79$	40.9692	−	23.6536i	0.518597	−	0.299412i	−0.217763	−	0.976002i	$-0.569876\pi$
$79$	40.9692	−	23.6536i	0.518597	−	0.299412i	0.736361	+	0.676589i	$0.236543\pi$
$80$		0			0
$81$	73.4397	−	34.1704i	0.906663	−	0.421856i
$82$	109.752	−	109.752i	1.33844	−	1.33844i
$83$	16.0841	−	60.0267i	0.193784	−	0.723213i	−0.798794	−	0.601605i	$-0.794528\pi$
$83$	16.0841	−	60.0267i	0.193784	−	0.723213i	0.992578	−	0.121608i	$-0.0388052\pi$
$84$	−0.282117	+	0.351360i	−0.00335854	+	0.00418285i
$85$		0			0
$86$	−12.5101	+	21.6682i	−0.145467	+	0.251956i
$87$	−13.0488	−	17.8042i	−0.149987	−	0.204646i
$88$	−10.7032	+	39.9449i	−0.121627	+	0.453919i
$89$			59.1599i			0.664718i	0.943153	+	0.332359i	$0.107844\pi$
$89$			59.1599i			0.664718i	−0.943153	+	0.332359i	$0.892156\pi$
$90$		0			0
$91$	0.891679			0.00979867
$92$	−96.5530	−	25.8713i	−1.04949	−	0.281210i
$93$	−45.8728	−	20.1960i	−0.493256	−	0.217162i
$94$	−99.7085	−	57.5668i	−1.06073	−	0.612412i
$95$		0			0
$96$	−88.9828	+	34.5820i	−0.926904	+	0.360229i
$97$	150.251	+	40.2595i	1.54898	+	0.415047i	0.929153	−	0.369695i	$-0.120538\pi$
$97$	150.251	+	40.2595i	1.54898	+	0.415047i	0.619823	+	0.784742i	$0.287204\pi$
$98$	86.2954	+	86.2954i	0.880566	+	0.880566i
$99$	−56.1918	−	61.3743i	−0.567594	−	0.619943i
$100$		0			0
$101$	27.6053	+	47.8137i	0.273319	+	0.473403i	0.969710	−	0.244260i	$-0.0785451\pi$
$101$	27.6053	+	47.8137i	0.273319	+	0.473403i	−0.696390	+	0.717663i	$0.745212\pi$
$102$	84.9779	+	115.946i	0.833116	+	1.13673i
$103$	−88.3218	+	23.6658i	−0.857493	+	0.229765i	−0.660672	−	0.750675i	$-0.729729\pi$
$103$	−88.3218	+	23.6658i	−0.857493	+	0.229765i	−0.196821	+	0.980439i	$0.563062\pi$
$104$	50.6892	+	29.2654i	0.487397	+	0.281399i
$105$		0			0
$106$	49.3618	+	85.4971i	0.465677	+	0.806576i
$107$	14.6336	−	14.6336i	0.136762	−	0.136762i	−0.635411	−	0.772174i	$-0.719169\pi$
$107$	14.6336	−	14.6336i	0.136762	−	0.136762i	0.772174	+	0.635411i	$0.219169\pi$
$108$	11.6480	−	58.3663i	0.107852	−	0.540429i
$109$			112.055i			1.02803i	0.857781	+	0.514015i	$0.171843\pi$
$109$			112.055i			1.02803i	−0.857781	+	0.514015i	$0.828157\pi$
$110$		0			0
$111$	−119.320	−	95.8060i	−1.07496	−	0.863117i
$112$	−0.351976	−	1.31359i	−0.00314264	−	0.0117285i
$113$	35.8191	−	9.59771i	0.316984	−	0.0849355i	−0.0968194	−	0.995302i	$-0.530867\pi$
$113$	35.8191	−	9.59771i	0.316984	−	0.0849355i	0.413803	+	0.910366i	$0.364200\pi$
$114$	−42.8870	−	6.61017i	−0.376202	−	0.0579840i
$115$		0			0
$116$	−16.2196			−0.139824
$117$	−104.491	+	54.3389i	−0.893088	+	0.464435i
$118$	33.2541	+	33.2541i	0.281814	+	0.281814i
$119$	−1.13520	+	0.655407i	−0.00953948	+	0.00550762i
$120$		0			0
$121$	17.7573	−	30.7565i	0.146754	−	0.254186i
$122$	−3.47543	−	12.9705i	−0.0284872	−	0.106316i
$123$	−171.092	−	75.3254i	−1.39100	−	0.612402i
$124$	−31.8944	+	18.4143i	−0.257213	+	0.148502i
$125$		0			0
$126$	1.45662	+	0.459945i	0.0115605	+	0.00365035i
$127$	−151.793	+	151.793i	−1.19522	+	1.19522i	−0.219643	+	0.975580i	$0.570489\pi$
$127$	−151.793	+	151.793i	−1.19522	+	1.19522i	−0.975580	+	0.219643i	$0.929511\pi$
$128$	33.3113	−	124.320i	0.260245	−	0.971247i
$129$	29.7829	+	4.59044i	0.230875	+	0.0355848i
$130$		0			0
$131$	−0.751448	+	1.30155i	−0.00573624	+	0.00993547i	−0.868879	−	0.495024i	$-0.835159\pi$
$131$	−0.751448	+	1.30155i	−0.00573624	+	0.00993547i	0.863143	+	0.504960i	$0.168493\pi$
$132$	−60.7809	+	6.64367i	−0.460462	+	0.0503308i
$133$	0.102411	−	0.382203i	0.000770006	−	0.00287370i
$134$			123.551i			0.922021i
$135$		0			0
$136$	−86.0434			−0.632672
$137$	−67.4699	−	18.0785i	−0.492481	−	0.131960i	0.00402717	−	0.999992i	$-0.498718\pi$
$137$	−67.4699	−	18.0785i	−0.492481	−	0.131960i	−0.496508	+	0.868032i	$0.665385\pi$
$138$	36.8192	+	336.847i	0.266805	+	2.44092i
$139$	106.332	+	61.3909i	0.764980	+	0.441661i	0.831081	−	0.556152i	$-0.187723\pi$
$139$	106.332	+	61.3909i	0.764980	+	0.441661i	−0.0661012	+	0.997813i	$0.521056\pi$
$140$		0			0
$141$	−21.1234	+	137.049i	−0.149811	+	0.971981i
$142$	−135.745	−	36.3728i	−0.955953	−	0.256147i
$143$	85.5549	+	85.5549i	0.598286	+	0.598286i
$144$	121.297	+	132.484i	0.842338	+	0.920027i
$145$		0			0
$146$	−96.3668	−	166.912i	−0.660047	−	1.14323i
$147$	59.2264	−	134.526i	0.402901	−	0.915140i
$148$	−108.607	+	29.1013i	−0.733834	+	0.196630i
$149$	23.0090	+	13.2842i	0.154423	+	0.0891560i	0.575220	−	0.817999i	$-0.304916\pi$
$149$	23.0090	+	13.2842i	0.154423	+	0.0891560i	−0.420797	+	0.907155i	$0.638250\pi$
$150$		0			0
$151$	−49.2414	−	85.2887i	−0.326102	−	0.564826i	0.655633	−	0.755080i	$-0.272402\pi$
$151$	−49.2414	−	85.2887i	−0.326102	−	0.564826i	−0.981735	+	0.190254i	$0.939069\pi$
$152$	18.3659	−	18.3659i	0.120828	−	0.120828i
$153$	93.0876	−	145.983i	0.608415	−	0.954136i
$154$		−	1.56924i		−	0.0101899i
$155$		0			0
$156$	−13.1826	+	85.5295i	−0.0845042	+	0.548266i
$157$	44.6968	+	166.811i	0.284693	+	1.06249i	0.949063	+	0.315086i	$0.102033\pi$
$157$	44.6968	+	166.811i	0.284693	+	1.06249i	−0.664370	+	0.747404i	$0.731300\pi$
$158$	−113.820	+	30.4980i	−0.720379	+	0.193025i
$159$	74.4439	−	92.7152i	0.468201	−	0.583115i
$160$		0			0
$161$	−3.08985			−0.0191916
$162$	−198.723	+	34.8680i	−1.22669	+	0.215235i
$163$	65.0824	+	65.0824i	0.399278	+	0.399278i	0.877978	−	0.478700i	$-0.158892\pi$
$163$	65.0824	+	65.0824i	0.399278	+	0.399278i	−0.478700	+	0.877978i	$0.658892\pi$
$164$	−118.957	+	68.6800i	−0.725349	+	0.418780i
$165$		0			0
$166$	−77.3960	+	134.054i	−0.466241	+	0.807553i
$167$	51.7034	+	192.960i	0.309601	+	1.15545i	0.928912	+	0.370301i	$0.120745\pi$
$167$	51.7034	+	192.960i	0.309601	+	1.15545i	−0.619311	+	0.785146i	$0.712588\pi$
$168$	−0.737444	+	0.540478i	−0.00438955	+	0.00321713i
$169$	1.94752	−	1.12440i	0.0115238	−	0.00665325i
$170$		0			0
$171$	11.2904	+	51.0293i	0.0660258	+	0.298417i
$172$	15.6570	−	15.6570i	0.0910290	−	0.0910290i
$173$	−8.94958	+	33.4003i	−0.0517317	+	0.193065i	−0.986956	−	0.160991i	$-0.948531\pi$
$173$	−8.94958	+	33.4003i	−0.0517317	+	0.193065i	0.935224	+	0.354056i	$0.115198\pi$
$174$	19.9172	+	51.2489i	0.114467	+	0.294534i
$175$		0			0
$176$	92.2653	−	159.808i	0.524235	−	0.908001i
$177$	22.8230	−	51.8397i	0.128944	−	0.292879i
$178$	38.1392	−	142.337i	0.214265	−	0.799648i
$179$		−	185.962i		−	1.03890i	−0.854502	−	0.519448i	$-0.826138\pi$
$179$		−	185.962i		−	1.03890i	0.854502	−	0.519448i	$-0.173862\pi$
$180$		0			0
$181$	−97.7851			−0.540249			−0.270125	−	0.962825i	$-0.587065\pi$
$181$	−97.7851			−0.540249			−0.270125	+	0.962825i	$0.587065\pi$
$182$	−2.14536	−	0.574847i	−0.0117877	−	0.00315850i
$183$	−13.0445	+	9.56041i	−0.0712814	+	0.0522427i
$184$	−175.649	−	101.411i	−0.954613	−	0.551146i
$185$		0			0
$186$	97.3490	+	78.1645i	0.523382	+	0.420239i
$187$	−171.805	−	46.0350i	−0.918744	−	0.246177i
$188$	72.0473	+	72.0473i	0.383231	+	0.383231i
$189$	−0.119168	−	1.83589i	−0.000630518	−	0.00971368i
$190$		0			0
$191$	−68.2090	−	118.141i	−0.357115	−	0.618542i	0.630362	−	0.776301i	$-0.282906\pi$
$191$	−68.2090	−	118.141i	−0.357115	−	0.618542i	−0.987478	+	0.157759i	$0.949573\pi$
$192$	−1.69598	+	0.185379i	−0.00883321	+	0.000965515i
$193$	89.2148	−	23.9050i	0.462253	−	0.123860i	−0.0201740	−	0.999796i	$-0.506422\pi$
$193$	89.2148	−	23.9050i	0.462253	−	0.123860i	0.482427	+	0.875936i	$0.339755\pi$
$194$	−335.545	−	193.727i	−1.72961	−	0.998594i
$195$		0			0
$196$	−54.0013	−	93.5329i	−0.275517	−	0.477209i
$197$	170.623	−	170.623i	0.866107	−	0.866107i	−0.125932	−	0.992039i	$-0.540192\pi$
$197$	170.623	−	170.623i	0.866107	−	0.866107i	0.992039	+	0.125932i	$0.0401920\pi$
$198$	95.6294	+	183.891i	0.482977	+	0.928742i
$199$			36.4196i			0.183013i	0.995804	+	0.0915066i	$0.0291683\pi$
$199$			36.4196i			0.183013i	−0.995804	+	0.0915066i	$0.970832\pi$
$200$		0			0
$201$	138.699	−	53.9036i	0.690046	−	0.268177i
$202$	−35.5931	−	132.835i	−0.176204	−	0.657601i
$203$	−0.484283	+	0.129763i	−0.00238563	+	0.000639227i
$204$	−46.0835	−	118.577i	−0.225900	−	0.581261i
$205$		0			0
$206$	227.757			1.10562
$207$	362.084	−	188.296i	1.74920	−	0.909641i
$208$	−184.681	−	184.681i	−0.887887	−	0.887887i
$209$	46.4977	−	26.8455i	0.222477	−	0.128447i
$210$		0			0
$211$	96.8033	−	167.668i	0.458784	−	0.794636i	−0.540113	−	0.841592i	$-0.681619\pi$
$211$	96.8033	−	167.668i	0.458784	−	0.794636i	0.998897	+	0.0469559i	$0.0149520\pi$
$212$	−22.6125	−	84.3909i	−0.106663	−	0.398070i
$213$	18.3914	+	168.258i	0.0863448	+	0.789943i
$214$	−44.6420	+	25.7741i	−0.208607	+	0.120440i
$215$		0			0
$216$	53.4805	−	108.276i	0.247595	−	0.501276i
$217$	−0.804980	+	0.804980i	−0.00370959	+	0.00370959i
$218$	72.2398	−	269.603i	0.331375	−	1.23671i
$219$	−145.334	+	181.004i	−0.663623	+	0.826502i
$220$		0			0
$221$	−125.872	+	218.017i	−0.569558	+	0.986503i
$222$	225.318	+	307.431i	1.01495	+	1.38482i
$223$	24.7802	−	92.4808i	0.111122	−	0.414712i	−0.887846	−	0.460141i	$-0.847799\pi$
$223$	24.7802	−	92.4808i	0.111122	−	0.414712i	0.998968	+	0.0454290i	$0.0144655\pi$
$224$			2.16833i			0.00968002i
$225$		0			0
$226$	−92.3675			−0.408706
$227$	−318.219	−	85.2664i	−1.40184	−	0.375623i	−0.522837	−	0.852433i	$-0.675126\pi$
$227$	−318.219	−	85.2664i	−1.40184	−	0.375623i	−0.879007	+	0.476810i	$0.841793\pi$
$228$	35.1467	+	15.4737i	0.154152	+	0.0678672i
$229$	360.256	+	207.994i	1.57317	+	0.908269i	0.995777	+	0.0918017i	$0.0292626\pi$
$229$	360.256	+	207.994i	1.57317	+	0.908269i	0.577391	+	0.816468i	$0.304071\pi$
$230$		0			0
$231$	−1.76164	+	0.684638i	−0.00762615	+	0.00296380i
$232$	−31.7889	−	8.51781i	−0.137021	−	0.0367147i
$233$	22.0213	+	22.0213i	0.0945121	+	0.0945121i	0.752782	−	0.658270i	$-0.228711\pi$
$233$	22.0213	+	22.0213i	0.0945121	+	0.0945121i	−0.658270	+	0.752782i	$0.728711\pi$
$234$	286.435	−	63.3748i	1.22408	−	0.270833i
$235$		0			0
$236$	−20.8095	−	36.0431i	−0.0881758	−	0.152725i
$237$	83.8955	+	114.469i	0.353989	+	0.482993i
$238$	3.15379	−	0.845055i	0.0132512	−	0.00355065i
$239$	−267.552	−	154.471i	−1.11946	−	0.646323i	−0.178200	−	0.983994i	$-0.557027\pi$
$239$	−267.552	−	154.471i	−1.11946	−	0.646323i	−0.941264	+	0.337672i	$0.890361\pi$
$240$		0			0
$241$	−12.8569	−	22.2688i	−0.0533481	−	0.0924016i	0.838118	−	0.545489i	$-0.183656\pi$
$241$	−12.8569	−	22.2688i	−0.0533481	−	0.0924016i	−0.891466	+	0.453087i	$0.850323\pi$
$242$	−62.5517	+	62.5517i	−0.258478	+	0.258478i
$243$	125.844	+	207.876i	0.517875	+	0.855457i
$244$			11.8835i			0.0487028i
$245$		0			0
$246$	363.084	+	291.531i	1.47595	+	1.18509i
$247$	−19.6682	−	73.4028i	−0.0796284	−	0.297177i
$248$	−72.1806	+	19.3407i	−0.291051	+	0.0779868i
$249$	184.257	+	28.3995i	0.739987	+	0.114054i
$250$		0			0
$251$	275.877			1.09911			0.549556	−	0.835457i	$-0.314797\pi$
$251$	275.877			1.09911			0.549556	+	0.835457i	$0.314797\pi$
$252$	−1.13980	−	0.726807i	−0.00452302	−	0.00288416i
$253$	−296.465	−	296.465i	−1.17180	−	1.17180i
$254$	463.070	−	267.353i	1.82311	−	1.05257i
$255$		0			0
$256$	−159.155	+	275.665i	−0.621701	+	1.07682i
$257$	−1.65593	−	6.18001i	−0.00644330	−	0.0240467i	0.962629	−	0.270822i	$-0.0872956\pi$
$257$	−1.65593	−	6.18001i	−0.00644330	−	0.0240467i	−0.969073	+	0.246776i	$0.920629\pi$
$258$	−68.6977	−	30.2449i	−0.266270	−	0.117228i
$259$	−3.00997	+	1.73781i	−0.0116215	+	0.00670968i
$260$		0			0
$261$	48.8428	−	44.7185i	0.187137	−	0.171335i
$262$	2.64705	−	2.64705i	0.0101032	−	0.0101032i
$263$	−54.9964	+	205.249i	−0.209112	+	0.780416i	0.779045	+	0.626968i	$0.215704\pi$
$263$	−54.9964	+	205.249i	−0.209112	+	0.780416i	−0.988157	+	0.153448i	$0.950962\pi$
$264$	−122.614	−	18.8985i	−0.464447	−	0.0715852i
$265$		0			0
$266$	−0.492797	+	0.853549i	−0.00185262	+	0.00320883i
$267$	−176.429	+	19.2846i	−0.660782	+	0.0722269i
$268$	28.2991	−	105.614i	0.105594	−	0.394081i
$269$			349.046i			1.29757i	0.760973	+	0.648784i	$0.224722\pi$
$269$			349.046i			1.29757i	−0.760973	+	0.648784i	$0.775278\pi$
$270$		0			0
$271$	−202.277			−0.746409			−0.373205	−	0.927749i	$-0.621741\pi$
$271$	−202.277			−0.746409			−0.373205	+	0.927749i	$0.621741\pi$
$272$	370.862	+	99.3722i	1.36346	+	0.365339i
$273$	0.290664	+	2.65920i	0.00106470	+	0.00974065i
$274$	150.676	+	86.9930i	0.549913	+	0.317493i
$275$		0			0
$276$	45.6806	−	296.377i	0.165509	−	1.07383i
$277$	234.373	+	62.8000i	0.846112	+	0.226715i	0.655730	−	0.754995i	$-0.272361\pi$
$277$	234.373	+	62.8000i	0.846112	+	0.226715i	0.190381	+	0.981710i	$0.439028\pi$
$278$	−216.255	−	216.255i	−0.777897	−	0.777897i
$279$	45.2760	−	143.387i	0.162280	−	0.513932i
$280$		0			0
$281$	140.160	+	242.764i	0.498789	+	0.863929i	0.999999	−	0.00139729i	$-0.000444772\pi$
$281$	140.160	+	242.764i	0.498789	+	0.863929i	−0.501210	+	0.865326i	$0.667111\pi$
$282$	139.175	−	316.120i	0.493530	−	1.12099i
$283$	372.686	−	99.8610i	1.31691	−	0.352866i	0.469092	−	0.883149i	$-0.344581\pi$
$283$	372.686	−	99.8610i	1.31691	−	0.352866i	0.847820	+	0.530283i	$0.177914\pi$
$284$	107.707	+	62.1845i	0.379249	+	0.218959i
$285$		0			0
$286$	−150.688	−	260.999i	−0.526880	−	0.912583i
$287$	−3.00235	+	3.00235i	−0.0104611	+	0.0104611i
$288$	−132.138	−	254.095i	−0.458812	−	0.882274i
$289$		−	81.0774i		−	0.280545i
$290$		0			0
$291$	−71.0857	+	461.207i	−0.244281	+	1.58490i
$292$	44.1453	+	164.753i	0.151183	+	0.564222i
$293$	−40.8052	+	10.9337i	−0.139267	+	0.0373164i	−0.327779	−	0.944754i	$-0.606300\pi$
$293$	−40.8052	+	10.9337i	−0.139267	+	0.0373164i	0.188512	+	0.982071i	$0.439633\pi$
$294$	−229.223	+	285.484i	−0.779672	+	0.971032i
$295$		0			0
$296$	−228.143			−0.770755
$297$	164.716	−	187.584i	0.554598	−	0.631595i
$298$	−46.7950	−	46.7950i	−0.157030	−	0.157030i
$299$	−513.910	+	296.706i	−1.71876	+	0.992329i
$300$		0			0
$301$	0.342223	−	0.592747i	0.00113695	−	0.00196926i
$302$	63.4899	+	236.948i	0.210232	+	0.784595i
$303$	−133.593	+	97.9115i	−0.440902	+	0.323140i
$304$	−100.371	+	57.9492i	−0.330168	+	0.190622i
$305$		0			0
$306$	−318.079	+	291.220i	−1.03947	+	0.951698i
$307$	85.1111	−	85.1111i	0.277235	−	0.277235i	−0.554769	−	0.832004i	$-0.687194\pi$
$307$	85.1111	−	85.1111i	0.277235	−	0.277235i	0.832004	+	0.554769i	$0.187194\pi$
$308$	−0.359431	+	1.34142i	−0.00116699	+	0.00435525i
$309$	−99.3675	−	255.682i	−0.321578	−	0.827450i
$310$		0			0
$311$	227.093	−	393.336i	0.730202	−	1.26475i	−0.226595	−	0.973989i	$-0.572759\pi$
$311$	227.093	−	393.336i	0.730202	−	1.26475i	0.956797	−	0.290758i	$-0.0939074\pi$
$312$	−70.7531	+	160.707i	−0.226773	+	0.515087i
$313$	−76.9018	+	287.001i	−0.245693	+	0.916937i	0.727342	+	0.686276i	$0.240756\pi$
$313$	−76.9018	+	287.001i	−0.245693	+	0.916937i	−0.973034	+	0.230661i	$0.925911\pi$
$314$		−	430.158i		−	1.36993i
$315$		0			0
$316$	104.281			0.330004
$317$	−85.3965	−	22.8819i	−0.269389	−	0.0721827i	0.121596	−	0.992580i	$-0.461199\pi$
$317$	−85.3965	−	22.8819i	−0.269389	−	0.0721827i	−0.390985	+	0.920397i	$0.627866\pi$
$318$	−238.882	+	175.078i	−0.751201	+	0.550561i
$319$	−58.9165	−	34.0155i	−0.184691	−	0.106632i
$320$		0			0
$321$	48.4109	+	38.8706i	0.150813	+	0.121092i
$322$	7.43412	+	1.99197i	0.0230873	+	0.00618623i
$323$	78.9926	+	78.9926i	0.244559	+	0.244559i
$324$	177.859	+	15.7113i	0.548948	+	0.0484917i
$325$		0			0
$326$	−114.629	−	198.544i	−0.351624	−	0.609031i
$327$	−334.176	+	36.5271i	−1.02194	+	0.111704i
$328$	−269.213	+	72.1354i	−0.820771	+	0.219925i
$329$	2.72759	+	1.57478i	0.00829055	+	0.00478655i
$330$		0			0
$331$	223.152	+	386.510i	0.674175	+	1.16770i	0.976709	+	0.214566i	$0.0688338\pi$
$331$	223.152	+	386.510i	0.674175	+	1.16770i	−0.302535	+	0.953138i	$0.597833\pi$
$332$	96.8645	−	96.8645i	0.291761	−	0.291761i
$333$	246.821	−	387.072i	0.741204	−	1.16238i
$334$		−	497.589i		−	1.48979i
$335$		0			0
$336$	3.80271	−	1.47787i	0.0113176	−	0.00439843i
$337$	−7.58184	−	28.2958i	−0.0224980	−	0.0839638i	0.953764	−	0.300556i	$-0.0971724\pi$
$337$	−7.58184	−	28.2958i	−0.0224980	−	0.0839638i	−0.976262	+	0.216593i	$0.930506\pi$
$338$	−5.41056	+	1.44975i	−0.0160076	+	0.00428921i
$339$	40.2988	+	103.693i	0.118875	+	0.305878i
$340$		0			0
$341$	−154.473			−0.452999
$342$	5.73305	−	130.054i	0.0167633	−	0.380275i
$343$	−4.72156	−	4.72156i	−0.0137655	−	0.0137655i
$344$	38.9086	−	22.4639i	0.113107	−	0.0653021i
$345$		0			0
$346$	43.0650	−	74.5907i	0.124465	−	0.215580i
$347$	−87.3943	−	326.160i	−0.251857	−	0.939942i	−0.969812	−	0.243853i	$-0.921589\pi$
$347$	−87.3943	−	326.160i	−0.251857	−	0.939942i	0.717956	−	0.696089i	$-0.245078\pi$
$348$	−5.28716	−	48.3706i	−0.0151930	−	0.138996i
$349$	51.4915	−	29.7286i	0.147540	−	0.0851823i	−0.424413	−	0.905469i	$-0.639519\pi$
$349$	51.4915	−	29.7286i	0.147540	−	0.0851823i	0.571953	+	0.820287i	$0.306186\pi$
$350$		0			0
$351$	−196.113	−	293.905i	−0.558727	−	0.837336i
$352$	−208.047	+	208.047i	−0.591042	+	0.591042i
$353$	137.840	−	514.426i	0.390482	−	1.45730i	−0.438860	−	0.898555i	$-0.644618\pi$
$353$	137.840	−	514.426i	0.390482	−	1.45730i	0.829342	−	0.558742i	$-0.188716\pi$
$354$	−88.3316	+	110.012i	−0.249524	+	0.310767i
$355$		0			0
$356$	−65.2043	+	112.937i	−0.183158	+	0.317239i
$357$	−2.32462	−	3.17178i	−0.00651155	−	0.00888455i
$358$	−119.886	+	447.421i	−0.334878	+	1.24978i
$359$			342.196i			0.953192i	0.879122	+	0.476596i	$0.158130\pi$
$359$			342.196i			0.953192i	−0.879122	+	0.476596i	$0.841870\pi$
$360$		0			0
$361$	327.278			0.906588
$362$	235.269	+	63.0401i	0.649914	+	0.174144i
$363$	97.5117	+	42.9306i	0.268627	+	0.118266i
$364$	1.70223	+	0.982783i	0.00467646	+	0.00269995i
$365$		0			0
$366$	37.5482	−	14.5926i	0.102591	−	0.0398705i
$367$	−355.509	−	95.2584i	−0.968690	−	0.259560i	−0.260416	−	0.965497i	$-0.583860\pi$
$367$	−355.509	−	95.2584i	−0.968690	−	0.259560i	−0.708275	+	0.705937i	$0.750526\pi$
$368$	639.956	+	639.956i	1.73901	+	1.73901i
$369$	168.867	−	534.793i	0.457633	−	1.44930i
$370$		0			0
$371$	−1.35032	−	2.33883i	−0.00363968	−	0.00630412i
$372$	−65.3125	−	89.1142i	−0.175571	−	0.239554i
$373$	321.501	−	86.1459i	0.861933	−	0.230954i	0.199337	−	0.979931i	$-0.436121\pi$
$373$	321.501	−	86.1459i	0.861933	−	0.230954i	0.662596	+	0.748977i	$0.269455\pi$
$374$	383.681	+	221.519i	1.02589	+	0.592296i
$375$		0			0
$376$	103.370	+	179.042i	0.274921	+	0.476177i
$377$	−68.0862	+	68.0862i	−0.180600	+	0.180600i
$378$	−0.896843	+	4.49392i	−0.00237260	+	0.0118887i
$379$			203.700i			0.537466i	0.963215	+	0.268733i	$0.0866049\pi$
$379$			203.700i			0.537466i	−0.963215	+	0.268733i	$0.913395\pi$
$380$		0			0
$381$	−502.164	−	403.203i	−1.31802	−	1.05828i
$382$	87.9460	+	328.219i	0.230225	+	0.859212i
$383$	−19.9865	+	5.35538i	−0.0521842	+	0.0139827i	−0.284817	−	0.958582i	$-0.591933\pi$
$383$	−19.9865	+	5.35538i	−0.0521842	+	0.0139827i	0.232633	+	0.972565i	$0.425266\pi$
$384$	381.609	+	58.8174i	0.993774	+	0.153170i
$385$		0			0
$386$	−230.060			−0.596010
$387$	−3.98132	+	90.3161i	−0.0102876	+	0.233375i
$388$	242.458	+	242.458i	0.624892	+	0.624892i
$389$	160.439	−	92.6297i	0.412440	−	0.238123i	−0.279397	−	0.960176i	$-0.590135\pi$
$389$	160.439	−	92.6297i	0.412440	−	0.238123i	0.691838	+	0.722053i	$0.256801\pi$
$390$		0			0
$391$	436.174	−	755.475i	1.11553	−	1.93216i
$392$	−56.7182	−	211.675i	−0.144689	−	0.539988i
$393$	−4.12647	−	1.81673i	−0.0104999	−	0.00462271i
$394$	−520.513	+	300.518i	−1.32110	+	0.762737i
$395$		0			0
$396$	−39.6260	−	179.098i	−0.100066	−	0.452266i
$397$	236.474	−	236.474i	0.595652	−	0.595652i	−0.343501	−	0.939152i	$-0.611613\pi$
$397$	236.474	−	236.474i	0.595652	−	0.595652i	0.939152	+	0.343501i	$0.111613\pi$
$398$	23.4790	−	87.6248i	0.0589925	−	0.220163i
$399$	1.17320	+	0.180825i	0.00294036	+	0.000453197i
$400$		0			0
$401$	−34.0375	+	58.9547i	−0.0848816	+	0.147019i	−0.905341	−	0.424686i	$-0.860385\pi$
$401$	−34.0375	+	58.9547i	−0.0848816	+	0.147019i	0.820459	+	0.571705i	$0.193718\pi$
$402$	−368.458	+	40.2743i	−0.916562	+	0.100185i
$403$	−56.5868	+	211.185i	−0.140414	+	0.524032i
$404$			121.703i			0.301245i
$405$		0			0
$406$	1.24883			0.00307593
$407$	−455.540	−	122.062i	−1.11926	−	0.299906i
$408$	−28.0479	−	256.602i	−0.0687449	−	0.628926i
$409$	−326.511	−	188.511i	−0.798315	−	0.460907i	0.0445668	−	0.999006i	$-0.485809\pi$
$409$	−326.511	−	188.511i	−0.798315	−	0.460907i	−0.842882	+	0.538099i	$0.819143\pi$
$410$		0			0
$411$	31.9210	−	207.104i	0.0776666	−	0.503904i
$412$	−194.691	−	52.1674i	−0.472552	−	0.126620i
$413$	−0.909687	−	0.909687i	−0.00220263	−	0.00220263i
$414$	−992.557	+	219.607i	−2.39748	+	0.530451i
$415$		0			0
$416$	208.216	+	360.640i	0.500518	+	0.866923i
$417$	−148.421	+	337.120i	−0.355925	+	0.808440i
$418$	−129.179	+	34.6135i	−0.309041	+	0.0828074i
$419$	198.025	+	114.330i	0.472613	+	0.272863i	0.717333	−	0.696731i	$-0.245363\pi$
$419$	198.025	+	114.330i	0.472613	+	0.272863i	−0.244720	+	0.969594i	$0.578696\pi$
$420$		0			0
$421$	204.894	+	354.887i	0.486684	+	0.842961i	0.999883	−	0.0153086i	$-0.00487306\pi$
$421$	204.894	+	354.887i	0.486684	+	0.842961i	−0.513199	+	0.858270i	$0.671540\pi$
$422$	−340.999	+	340.999i	−0.808055	+	0.808055i
$423$	−415.599	−	18.3205i	−0.982504	−	0.0433108i
$424$		−	177.274i		−	0.418098i
$425$		0			0
$426$	64.2230	−	416.681i	0.150758	−	0.978125i
$427$	0.0950727	+	0.354816i	0.000222653	+	0.000830951i
$428$	44.0644	−	11.8070i	0.102954	−	0.0275865i
$429$	−227.256	+	283.034i	−0.529735	+	0.659752i
$430$		0			0
$431$	46.4787			0.107839			0.0539196	−	0.998545i	$-0.482829\pi$
$431$	46.4787			0.107839			0.0539196	+	0.998545i	$0.482829\pi$
$432$	−355.559	+	404.922i	−0.823053	+	0.937319i
$433$	430.638	+	430.638i	0.994544	+	0.994544i	0.999985	−	0.00544093i	$-0.00173191\pi$
$433$	430.638	+	430.638i	0.994544	+	0.994544i	−0.00544093	+	0.999985i	$0.501732\pi$
$434$	2.45572	−	1.41781i	0.00565834	−	0.00326684i
$435$		0			0
$436$	−123.504	+	213.916i	−0.283266	+	0.490632i
$437$	68.1545	+	254.356i	0.155960	+	0.582050i
$438$	466.359	−	341.798i	1.06475	−	0.780360i
$439$	−335.332	+	193.604i	−0.763855	+	0.441012i	−0.830678	−	0.556753i	$-0.812047\pi$
$439$	−335.332	+	193.604i	−0.763855	+	0.441012i	0.0668232	+	0.997765i	$0.478714\pi$
$440$		0			0
$441$	420.494	+	132.775i	0.953500	+	0.301078i
$442$	443.397	−	443.397i	1.00316	−	1.00316i
$443$	−189.882	+	708.648i	−0.428627	+	1.59966i	0.327247	+	0.944939i	$0.393879\pi$
$443$	−189.882	+	708.648i	−0.428627	+	1.59966i	−0.755874	+	0.654717i	$0.772788\pi$
$444$	−122.190	−	314.407i	−0.275203	−	0.708124i
$445$		0			0
$446$	−119.241	+	206.531i	−0.267357	+	0.463075i
$447$	−32.1164	+	72.9486i	−0.0718489	+	0.163196i
$448$	−0.0100292	+	0.0374297i	−2.23867e−5	+	8.35483e-5i
$449$		−	141.098i		−	0.314250i	−0.987579	−	0.157125i	$-0.949777\pi$
$449$		−	141.098i		−	0.314250i	0.987579	−	0.157125i	$-0.0502226\pi$
$450$		0			0
$451$	−576.139			−1.27747
$452$	78.9577	+	21.1566i	0.174685	+	0.0468067i
$453$	238.300	−	174.652i	0.526048	−	0.385544i
$454$	710.657	+	410.298i	1.56532	+	0.903740i
$455$		0			0
$456$	60.7582	+	48.7846i	0.133242	+	0.106984i
$457$	709.254	+	190.044i	1.55198	+	0.415851i	0.930113	−	0.367273i	$-0.119709\pi$
$457$	709.254	+	190.044i	1.55198	+	0.415851i	0.621865	+	0.783124i	$0.286375\pi$
$458$	−732.678	−	732.678i	−1.59973	−	1.59973i
$459$	465.699	+	230.023i	1.01460	+	0.501139i
$460$		0			0
$461$	−321.041	−	556.060i	−0.696402	−	1.20620i	−0.969706	−	0.244275i	$-0.921450\pi$
$461$	−321.041	−	556.060i	−0.696402	−	1.20620i	0.273304	−	0.961928i	$-0.411883\pi$
$462$	4.67984	−	0.511530i	0.0101295	−	0.00110721i
$463$	−268.091	+	71.8346i	−0.579029	+	0.155150i	−0.536434	−	0.843942i	$-0.680229\pi$
$463$	−268.091	+	71.8346i	−0.579029	+	0.155150i	−0.0425948	+	0.999092i	$0.513562\pi$
$464$	127.178	+	73.4265i	0.274091	+	0.158247i
$465$		0			0
$466$	−38.7861	−	67.1795i	−0.0832320	−	0.144162i
$467$	57.4439	−	57.4439i	0.123006	−	0.123006i	−0.642924	−	0.765930i	$-0.722279\pi$
$467$	57.4439	−	57.4439i	0.123006	−	0.123006i	0.765930	+	0.642924i	$0.222279\pi$
$468$	−259.366	−	11.4334i	−0.554202	−	0.0244304i
$469$		−	3.37981i		−	0.00720642i
$470$		0			0
$471$	−482.900	+	187.673i	−1.02526	+	0.398456i
$472$	−21.8565	−	81.5694i	−0.0463061	−	0.172817i
$473$	89.7086	−	24.0373i	0.189659	−	0.0508189i
$474$	−128.055	−	329.497i	−0.270157	−	0.695140i
$475$		0			0
$476$	−2.88948			−0.00607034
$477$	300.766	+	191.787i	0.630536	+	0.402068i
$478$	544.139	+	544.139i	1.13837	+	1.13837i
$479$	419.328	−	242.099i	0.875423	−	0.505426i	0.00627671	−	0.999980i	$-0.498002\pi$
$479$	419.328	−	242.099i	0.875423	−	0.505426i	0.869147	+	0.494554i	$0.164669\pi$
$480$		0			0
$481$	−333.749	+	578.071i	−0.693866	+	1.20181i
$482$	16.5771	+	61.8668i	0.0343924	+	0.128354i
$483$	−1.00721	−	9.21467i	−0.00208532	−	0.0190780i
$484$	67.7979	−	39.1431i	0.140078	−	0.0808742i
$485$		0			0
$486$	−168.763	−	581.274i	−0.347250	−	1.19604i
$487$	162.179	−	162.179i	0.333017	−	0.333017i	−0.520714	−	0.853731i	$-0.674334\pi$
$487$	162.179	−	162.179i	0.333017	−	0.333017i	0.853731	+	0.520714i	$0.174334\pi$
$488$	−6.24069	+	23.2906i	−0.0127883	+	0.0477266i
$489$	−172.876	+	215.306i	−0.353530	+	0.440299i
$490$		0			0
$491$	−395.023	+	684.199i	−0.804527	+	1.39348i	0.112083	+	0.993699i	$0.464248\pi$
$491$	−395.023	+	684.199i	−0.804527	+	1.39348i	−0.916610	+	0.399783i	$0.869086\pi$
$492$	−243.597	−	332.371i	−0.495116	−	0.675550i
$493$	36.6356	−	136.726i	0.0743115	−	0.277334i
$494$			189.285i			0.383168i
$495$		0			0
$496$	333.448			0.672274
$497$	3.71340	+	0.995002i	0.00747163	+	0.00200202i
$498$	−425.009	−	187.115i	−0.853433	−	0.375733i
$499$	−422.362	−	243.851i	−0.846418	−	0.488680i	0.0130228	−	0.999915i	$-0.495855\pi$
$499$	−422.362	−	243.851i	−0.846418	−	0.488680i	−0.859441	+	0.511236i	$0.829188\pi$
$500$		0			0
$501$	−558.597	+	217.091i	−1.11496	+	0.433316i
$502$	−663.754	−	177.852i	−1.32222	−	0.354288i
$503$	−346.274	−	346.274i	−0.688418	−	0.688418i	0.273465	−	0.961882i	$-0.411830\pi$
$503$	−346.274	−	346.274i	−0.688418	−	0.688418i	−0.961882	+	0.273465i	$0.911830\pi$
$504$	−1.85222	−	2.02305i	−0.00367504	−	0.00401399i
$505$		0			0
$506$	522.164	+	904.415i	1.03194	+	1.78738i
$507$	3.98806	+	5.44143i	0.00786600	+	0.0107326i
$508$	−457.078	+	122.474i	−0.899760	+	0.241090i
$509$	362.182	+	209.106i	0.711557	+	0.410818i	0.811637	−	0.584162i	$-0.198577\pi$
$509$	362.182	+	209.106i	0.711557	+	0.410818i	−0.100080	+	0.994979i	$0.531910\pi$
$510$		0			0
$511$	2.63618	+	4.56599i	0.00515886	+	0.00893540i
$512$	196.607	−	196.607i	0.383998	−	0.383998i
$513$	−148.501	+	50.3049i	−0.289476	+	0.0980603i
$514$			15.9365i			0.0310049i
$515$		0			0
$516$	51.7966	+	41.5891i	0.100381	+	0.0805990i
$517$	110.610	+	412.804i	0.213947	+	0.798460i
$518$	8.36225	−	2.24066i	0.0161433	−	0.00432559i
$519$	−102.525	−	15.8022i	−0.197543	−	0.0304473i
$520$		0			0
$521$	−17.3149			−0.0332341			−0.0166170	−	0.999862i	$-0.505290\pi$
$521$	−17.3149			−0.0332341			−0.0166170	+	0.999862i	$0.505290\pi$
$522$	−146.344	+	76.1036i	−0.280352	+	0.145792i
$523$	−577.571	−	577.571i	−1.10434	−	1.10434i	−0.993880	−	0.110462i	$-0.964767\pi$
$523$	−577.571	−	577.571i	−1.10434	−	1.10434i	−0.110462	−	0.993880i	$-0.535233\pi$
$524$	−2.86905	+	1.65645i	−0.00547529	+	0.00316116i
$525$		0			0
$526$	264.640	−	458.370i	0.503118	−	0.871427i
$527$	−83.1855	−	310.453i	−0.157847	−	0.589094i
$528$	506.662	+	223.064i	0.959587	+	0.422469i
$529$	1322.68	−	763.649i	2.50034	−	1.44357i
$530$		0			0
$531$	162.038	+	51.1652i	0.305156	+	0.0963564i
$532$	0.616757	−	0.616757i	0.00115932	−	0.00115932i
$533$	−211.053	+	787.659i	−0.395971	+	1.47778i
$534$	436.916	+	67.3418i	0.818195	+	0.126108i
$535$		0			0
$536$	110.927	−	192.132i	0.206954	−	0.358455i
$537$	554.584	−	60.6189i	1.03274	−	0.112884i
$538$	225.023	−	839.797i	0.418258	−	1.56096i
$539$		−	453.003i		−	0.840451i
$540$		0			0
$541$	846.162			1.56407			0.782035	−	0.623234i	$-0.214182\pi$
$541$	846.162			1.56407			0.782035	+	0.623234i	$0.214182\pi$
$542$	486.674	+	130.404i	0.897922	+	0.240598i
$543$	−31.8754	−	291.618i	−0.0587024	−	0.537050i
$544$	−530.160	−	306.088i	−0.974558	−	0.562661i
$545$		0			0
$546$	1.01500	−	6.58536i	0.00185897	−	0.0120611i
$547$	−66.0385	−	17.6950i	−0.120728	−	0.0323491i	0.197949	−	0.980212i	$-0.436572\pi$
$547$	−66.0385	−	17.6950i	−0.120728	−	0.0323491i	−0.318677	+	0.947863i	$0.603239\pi$
$548$	−108.876	−	108.876i	−0.198678	−	0.198678i
$549$	−32.7636	−	35.7854i	−0.0596787	−	0.0651828i
$550$		0			0
$551$	21.3641	+	37.0038i	0.0387734	+	0.0671575i
$552$	245.174	−	556.884i	0.444156	−	1.00885i
$553$	3.11362	−	0.834291i	0.00563041	−	0.00150866i
$554$	−523.410	−	302.191i	−0.944784	−	0.545471i
$555$		0			0
$556$	135.327	+	234.392i	0.243393	+	0.421569i
$557$	−367.003	+	367.003i	−0.658893	+	0.658893i	−0.955118	−	0.296225i	$-0.904272\pi$
$557$	−367.003	+	367.003i	−0.658893	+	0.658893i	0.296225	+	0.955118i	$0.404272\pi$
$558$	−201.372	+	315.797i	−0.360881	+	0.565945i
$559$		−	131.449i		−	0.235151i
$560$		0			0
$561$	81.2835	−	527.370i	0.144890	−	0.940053i
$562$	−180.716	−	674.443i	−0.321560	−	1.20008i
$563$	303.953	−	81.4441i	0.539882	−	0.144661i	0.0214341	−	0.999770i	$-0.493177\pi$
$563$	303.953	−	81.4441i	0.539882	−	0.144661i	0.518448	+	0.855109i	$0.326510\pi$
$564$	−191.377	+	238.348i	−0.339320	+	0.422603i
$565$		0			0
$566$	−961.053			−1.69797
$567$	5.43620	−	0.953838i	0.00958765	−	0.00168225i
$568$	178.439	+	178.439i	0.314153	+	0.314153i
$569$	−882.789	+	509.679i	−1.55148	+	0.895745i	−0.553453	+	0.832880i	$0.686690\pi$
$569$	−882.789	+	509.679i	−1.55148	+	0.895745i	−0.998022	+	0.0628645i	$0.979976\pi$
$570$		0			0
$571$	443.096	−	767.465i	0.776000	−	1.34407i	−0.158231	−	0.987402i	$-0.550579\pi$
$571$	443.096	−	767.465i	0.776000	−	1.34407i	0.934231	−	0.356669i	$-0.116088\pi$
$572$	69.0296	+	257.622i	0.120681	+	0.450388i
$573$	330.092	−	241.927i	0.576076	−	0.422210i
$574$	9.15913	−	5.28803i	0.0159567	−	0.00921259i
$575$		0			0
$576$	−1.10569	−	4.99737i	−0.00191960	−	0.00867600i
$577$	−194.509	+	194.509i	−0.337105	+	0.337105i	−0.855277	−	0.518172i	$-0.826613\pi$
$577$	−194.509	+	194.509i	−0.337105	+	0.337105i	0.518172	+	0.855277i	$0.326613\pi$
$578$	−52.2689	+	195.070i	−0.0904307	+	0.337492i
$579$	100.372	+	258.267i	0.173354	+	0.446058i
$580$		0			0
$581$	2.11722	−	3.66713i	0.00364409	−	0.00631175i
$582$	468.361	−	1063.83i	0.804745	−	1.82788i
$583$	94.8452	−	353.967i	0.162685	−	0.607147i
$584$			346.084i			0.592609i
$585$		0			0
$586$	105.225			0.179565
$587$	775.720	+	207.853i	1.32150	+	0.354095i	0.849539	−	0.527526i	$-0.176880\pi$
$587$	775.720	+	207.853i	1.32150	+	0.354095i	0.471960	+	0.881620i	$0.343547\pi$
$588$	261.334	−	191.534i	0.444446	−	0.325738i
$589$	84.0216	+	48.5099i	0.142651	+	0.0823598i
$590$		0			0
$591$	564.457	+	453.220i	0.955089	+	0.766870i
$592$	983.338	+	263.485i	1.66104	+	0.445075i
$593$	−572.308	−	572.308i	−0.965106	−	0.965106i	0.0343049	−	0.999411i	$-0.489078\pi$
$593$	−572.308	−	572.308i	−0.965106	−	0.965106i	−0.999411	+	0.0343049i	$0.989078\pi$
$594$	−517.234	+	345.133i	−0.870764	+	0.581032i
$595$		0			0
$596$	29.2830	+	50.7197i	0.0491326	+	0.0851001i
$597$	−108.612	+	11.8718i	−0.181930	+	0.0198858i
$598$	1427.74	−	382.561i	2.38752	−	0.639734i
$599$	263.198	+	151.957i	0.439396	+	0.253685i	0.703341	−	0.710852i	$-0.251691\pi$
$599$	263.198	+	151.957i	0.439396	+	0.253685i	−0.263945	+	0.964538i	$0.585024\pi$
$600$		0			0
$601$	−52.0948	−	90.2308i	−0.0866801	−	0.150134i	0.819426	−	0.573185i	$-0.194292\pi$
$601$	−52.0948	−	90.2308i	−0.0866801	−	0.150134i	−0.906106	+	0.423051i	$0.860959\pi$
$602$	−1.20551	+	1.20551i	−0.00200251	+	0.00200251i
$603$	205.966	+	396.063i	0.341568	+	0.656821i
$604$		−	217.090i		−	0.359420i
$605$		0			0
$606$	384.544	−	149.448i	0.634561	−	0.246614i
$607$	−75.9472	−	283.439i	−0.125119	−	0.466950i	0.874725	−	0.484620i	$-0.161042\pi$
$607$	−75.9472	−	283.439i	−0.125119	−	0.466950i	−0.999844	+	0.0176696i	$0.994375\pi$
$608$	178.496	−	47.8279i	0.293579	−	0.0786642i
$609$	−0.544848	−	1.40195i	−0.000894660	−	0.00230205i
$610$		0			0
$611$	604.878			0.989980
$612$	338.604	−	176.085i	0.553274	−	0.287721i
$613$	−610.767	−	610.767i	−0.996357	−	0.996357i	0.00363596	−	0.999993i	$-0.498843\pi$
$613$	−610.767	−	610.767i	−0.996357	−	0.996357i	−0.999993	+	0.00363596i	$0.998843\pi$
$614$	−259.645	+	149.906i	−0.422874	+	0.244147i
$615$		0			0
$616$	−1.40891	+	2.44030i	−0.00228719	+	0.00396152i
$617$	260.666	+	972.818i	0.422473	+	1.57669i	0.769381	+	0.638791i	$0.220565\pi$
$617$	260.666	+	972.818i	0.422473	+	1.57669i	−0.346908	+	0.937899i	$0.612768\pi$
$618$	74.2429	+	679.226i	0.120134	+	1.09907i
$619$	189.444	−	109.376i	0.306049	−	0.176697i	−0.339108	−	0.940747i	$-0.610125\pi$
$619$	189.444	−	109.376i	0.306049	−	0.176697i	0.645157	+	0.764050i	$0.276792\pi$
$620$		0			0
$621$	679.572	+	1018.44i	1.09432	+	1.64000i
$622$	−799.956	+	799.956i	−1.28610	+	1.28610i
$623$	−1.04332	+	3.89373i	−0.00167467	+	0.00624997i
$624$	490.560	−	610.962i	0.786154	−	0.979106i
$625$		0			0
$626$	370.048	−	640.942i	0.591131	−	1.02387i
$627$	95.2166	+	129.916i	0.151861	+	0.207203i
$628$	−98.5271	+	367.708i	−0.156890	+	0.585523i
$629$		−	981.257i		−	1.56003i
$630$		0			0
$631$	−427.714			−0.677835			−0.338917	−	0.940816i	$-0.610061\pi$
$631$	−427.714			−0.677835			−0.338917	+	0.940816i	$0.610061\pi$
$632$	204.382	+	54.7639i	0.323389	+	0.0866517i
$633$	531.582	+	234.035i	0.839782	+	0.369724i
$634$	190.711	+	110.107i	0.300805	+	0.173670i
$635$		0			0
$636$	244.303	−	94.9450i	0.384124	−	0.149285i
$637$	−619.316	−	165.945i	−0.972239	−	0.260511i
$638$	119.823	+	119.823i	0.187810	+	0.187810i
$639$	−495.790	+	109.695i	−0.775884	+	0.171667i
$640$		0			0
$641$	−256.912	−	444.984i	−0.400798	−	0.694203i	0.593024	−	0.805185i	$-0.297934\pi$
$641$	−256.912	−	444.984i	−0.400798	−	0.694203i	−0.993822	+	0.110982i	$0.964600\pi$
$642$	−91.4165	−	124.731i	−0.142393	−	0.194286i
$643$	−187.988	+	50.3713i	−0.292361	+	0.0783379i	−0.402019	−	0.915632i	$-0.631691\pi$
$643$	−187.988	+	50.3713i	−0.292361	+	0.0783379i	0.109657	+	0.993969i	$0.465025\pi$
$644$	−5.89858	−	3.40555i	−0.00915929	−	0.00528812i
$645$		0			0
$646$	−139.129	−	240.979i	−0.215371	−	0.373033i
$647$	139.726	−	139.726i	0.215960	−	0.215960i	−0.590833	−	0.806794i	$-0.701201\pi$
$647$	139.726	−	139.726i	0.215960	−	0.215960i	0.806794	+	0.590833i	$0.201201\pi$
$648$	340.337	+	124.197i	0.525211	+	0.191661i
$649$		−	174.565i		−	0.268976i
$650$		0			0
$651$	−2.66304	−	2.13824i	−0.00409070	−	0.00328455i
$652$	52.5114	+	195.975i	0.0805390	+	0.300576i
$653$	−622.466	+	166.789i	−0.953240	+	0.255420i	−0.701737	−	0.712437i	$-0.747592\pi$
$653$	−622.466	+	166.789i	−0.953240	+	0.255420i	−0.251503	+	0.967856i	$0.580925\pi$
$654$	827.568	+	127.553i	1.26539	+	0.195035i
$655$		0			0
$656$	1243.66			1.89583
$657$	−587.172	−	374.417i	−0.893716	−	0.569888i
$658$	−5.54730	−	5.54730i	−0.00843054	−	0.00843054i
$659$	−210.200	+	121.359i	−0.318968	+	0.184156i	−0.650932	−	0.759136i	$-0.725622\pi$
$659$	−210.200	+	121.359i	−0.318968	+	0.184156i	0.331965	+	0.943292i	$0.392289\pi$
$660$		0			0
$661$	−331.364	+	573.939i	−0.501307	+	0.868288i	0.498692	+	0.866779i	$0.333814\pi$
$661$	−331.364	+	573.939i	−0.501307	+	0.868288i	−0.999999	+	0.00150927i	$0.999520\pi$
$662$	−287.723	−	1073.80i	−0.434627	−	1.62205i
$663$	−691.210	−	304.313i	−1.04255	−	0.458994i
$664$	240.715	−	138.977i	0.362522	−	0.209302i
$665$		0			0
$666$	−843.384	+	772.167i	−1.26634	+	1.15941i
$667$	235.933	−	235.933i	0.353722	−	0.353722i
$668$	−113.972	+	425.349i	−0.170617	+	0.636750i
$669$	283.877	+	43.7540i	0.424331	+	0.0654021i
$670$		0			0
$671$	−24.9219	+	43.1660i	−0.0371414	+	0.0643308i
$672$	−6.46646	+	0.706817i	−0.00962271	+	0.00105181i
$673$	−125.305	+	467.643i	−0.186188	+	0.694864i	0.808185	+	0.588929i	$0.200450\pi$
$673$	−125.305	+	467.643i	−0.186188	+	0.694864i	−0.994373	+	0.105935i	$0.966216\pi$
$674$			72.9670i			0.108260i
$675$		0			0
$676$	4.95712			0.00733302
$677$	−425.004	−	113.880i	−0.627776	−	0.168212i	−0.0691156	−	0.997609i	$-0.522018\pi$
$677$	−425.004	−	113.880i	−0.627776	−	0.168212i	−0.558660	+	0.829397i	$0.688684\pi$
$678$	−30.1094	−	275.462i	−0.0444091	−	0.406286i
$679$	9.17906	+	5.29953i	0.0135185	+	0.00780490i
$680$		0			0
$681$	150.554	−	976.798i	0.221077	−	1.43436i
$682$	371.658	+	99.5854i	0.544953	+	0.146020i
$683$	336.034	+	336.034i	0.491998	+	0.491998i	0.908935	−	0.416938i	$-0.136897\pi$
$683$	336.034	+	336.034i	0.491998	+	0.491998i	−0.416938	+	0.908935i	$0.636897\pi$
$684$	−34.6894	+	109.860i	−0.0507155	+	0.160614i
$685$		0			0
$686$	8.31607	+	14.4039i	0.0121226	+	0.0209969i
$687$	−502.853	+	1142.17i	−0.731954	+	1.66254i
$688$	−193.647	+	51.8875i	−0.281463	+	0.0754179i
$689$	−449.177	−	259.332i	−0.651926	−	0.376389i
$690$		0			0
$691$	−465.054	−	805.496i	−0.673015	−	1.16570i	−0.977045	−	0.213034i	$-0.931665\pi$
$691$	−465.054	−	805.496i	−0.673015	−	1.16570i	0.304029	−	0.952663i	$-0.401668\pi$
$692$	−53.8977	+	53.8977i	−0.0778869	+	0.0778869i
$693$	−2.61600	−	5.03045i	−0.00377489	−	0.00725895i
$694$			841.075i			1.21192i
$695$		0			0
$696$	15.0398	−	97.5786i	0.0216089	−	0.140199i
$697$	−310.258	−	1157.90i	−0.445134	−	1.66126i
$698$	−143.053	+	38.3309i	−0.204947	+	0.0549153i
$699$	−58.4944	+	72.8512i	−0.0836830	+	0.104222i
$700$		0			0
$701$	−1057.58			−1.50868			−0.754338	−	0.656486i	$-0.772042\pi$
$701$	−1057.58			−1.50868			−0.754338	+	0.656486i	$0.772042\pi$
$702$	282.369	+	833.559i	0.402235	+	1.18741i
$703$	209.448	+	209.448i	0.297935	+	0.297935i
$704$	−4.55359	+	2.62902i	−0.00646817	+	0.00373440i
$705$		0			0
$706$	−663.280	+	1148.83i	−0.939490	+	1.62724i
$707$	0.973672	+	3.63379i	0.00137719	+	0.00513974i
$708$	100.706	−	73.8079i	0.142240	−	0.104248i
$709$	−450.749	+	260.240i	−0.635754	+	0.367053i	−0.782977	−	0.622051i	$-0.786300\pi$
$709$	−450.749	+	260.240i	−0.635754	+	0.367053i	0.147223	+	0.989103i	$0.452966\pi$
$710$		0			0
$711$	−314.027	+	287.510i	−0.441670	+	0.404374i
$712$	−187.104	+	187.104i	−0.262787	+	0.262787i
$713$	196.085	−	731.800i	0.275014	−	1.02637i
$714$	3.54821	+	9.12988i	0.00496948	+	0.0127870i
$715$		0			0
$716$	204.962	−	355.005i	0.286260	−	0.495817i
$717$	373.455	−	848.257i	0.520857	−	1.18306i
$718$	220.607	−	823.316i	0.307252	−	1.14668i
$719$		−	1211.89i		−	1.68553i	−0.538285	−	0.842763i	$-0.680928\pi$
$719$		−	1211.89i		−	1.68553i	0.538285	−	0.842763i	$-0.319072\pi$
$720$		0			0
$721$	−6.23044			−0.00864139
$722$	−787.424	−	210.990i	−1.09062	−	0.292230i
$723$	62.2198	−	45.6013i	0.0860578	−	0.0630724i
$724$	−186.673	−	107.776i	−0.257836	−	0.148862i
$725$		0			0
$726$	−206.934	−	166.154i	−0.285034	−	0.228862i
$727$	201.292	+	53.9360i	0.276880	+	0.0741899i	0.394587	−	0.918859i	$-0.370888\pi$
$727$	201.292	+	53.9360i	0.276880	+	0.0741899i	−0.117707	+	0.993048i	$0.537554\pi$
$728$	2.82010	+	2.82010i	0.00387377	+	0.00387377i
$729$	−578.914	+	443.057i	−0.794120	+	0.607761i
$730$		0			0
$731$	96.6185	+	167.348i	0.132173	+	0.228930i
$732$	−35.4394	+	3.87371i	−0.0484145	+	0.00529195i
$733$	−707.621	+	189.606i	−0.965376	+	0.258672i	−0.706874	−	0.707339i	$-0.749895\pi$
$733$	−707.621	+	189.606i	−0.965376	+	0.258672i	−0.258502	+	0.966011i	$0.583229\pi$
$734$	793.936	+	458.379i	1.08166	+	0.624495i
$735$		0			0
$736$	−721.511	−	1249.69i	−0.980313	−	1.69795i
$737$	324.286	−	324.286i	0.440009	−	0.440009i
$738$	−751.059	+	1177.83i	−1.01770	+	1.59598i
$739$			1243.93i			1.68326i	0.540056	+	0.841629i	$0.318403\pi$
$739$			1243.93i			1.68326i	−0.540056	+	0.841629i	$0.681597\pi$
$740$		0			0
$741$	212.493	−	82.5827i	0.286766	−	0.111448i
$742$	1.74105	+	6.49769i	0.00234643	+	0.00875700i
$743$	1239.64	−	332.161i	1.66843	−	0.447054i	0.703743	−	0.710455i	$-0.251511\pi$
$743$	1239.64	−	332.161i	1.66843	−	0.447054i	0.964687	+	0.263400i	$0.0848440\pi$
$744$	−81.2077	−	208.955i	−0.109150	−	0.280854i
$745$		0			0
$746$	−829.060			−1.11134
$747$	−24.6311	+	558.755i	−0.0329733	+	0.747999i
$748$	−277.240	−	277.240i	−0.370642	−	0.370642i
$749$	1.22121	−	0.705066i	0.00163045	−	0.000941343i
$750$		0			0
$751$	−470.274	+	814.539i	−0.626198	+	1.08461i	0.362110	+	0.932135i	$0.382056\pi$
$751$	−470.274	+	814.539i	−0.626198	+	1.08461i	−0.988308	+	0.152471i	$0.951277\pi$
$752$	−238.766	−	891.087i	−0.317508	−	1.18496i
$753$	89.9287	+	822.731i	0.119427	+	1.09260i
$754$	207.708	−	119.920i	0.275474	−	0.159045i
$755$		0			0
$756$	1.79597	−	3.63608i	0.00237562	−	0.00480963i
$757$	−872.169	+	872.169i	−1.15214	+	1.15214i	−0.166015	+	0.986123i	$0.553090\pi$
$757$	−872.169	+	872.169i	−1.15214	+	1.15214i	−0.986123	+	0.166015i	$0.946910\pi$
$758$	131.321	−	490.097i	0.173247	−	0.646566i
$759$	787.490	−	980.770i	1.03754	−	1.29219i
$760$		0			0
$761$	−229.806	+	398.036i	−0.301979	+	0.523043i	−0.976584	−	0.215136i	$-0.930981\pi$
$761$	−229.806	+	398.036i	−0.301979	+	0.523043i	0.674605	+	0.738179i	$0.264314\pi$
$762$	948.260	+	1293.83i	1.24444	+	1.69794i
$763$	−1.97617	+	7.37515i	−0.00259000	+	0.00966599i
$764$		−	300.712i		−	0.393602i
$765$		0			0
$766$	51.5397			0.0672842
$767$	−238.655	−	63.9473i	−0.311153	−	0.0833733i
$768$	−873.980	−	384.779i	−1.13799	−	0.501015i
$769$	−775.372	−	447.661i	−1.00829	−	0.582134i	−0.0975969	−	0.995226i	$-0.531116\pi$
$769$	−775.372	−	447.661i	−1.00829	−	0.582134i	−0.910689	+	0.413092i	$0.864449\pi$
$770$		0			0
$771$	17.8905	−	6.95289i	0.0232042	−	0.00901802i
$772$	196.660	+	52.6949i	0.254741	+	0.0682576i
$773$	−94.0446	−	94.0446i	−0.121662	−	0.121662i	0.643654	−	0.765316i	$-0.277417\pi$
$773$	−94.0446	−	94.0446i	−0.121662	−	0.121662i	−0.765316	+	0.643654i	$0.777417\pi$
$774$	67.8039	−	214.732i	0.0876020	−	0.277431i
$775$		0			0
$776$	347.868	+	602.524i	0.448283	+	0.776449i
$777$	−6.16372	−	8.40996i	−0.00793272	−	0.0108236i
$778$	−445.730	+	119.433i	−0.572918	+	0.153513i
$779$	313.377	+	180.928i	0.402281	+	0.232257i
$780$		0			0
$781$	260.825	+	451.762i	0.333963	+	0.578441i
$782$	−1536.46	+	1536.46i	−1.96479	+	1.96479i
$783$	149.283	+	131.084i	0.190655	+	0.167412i
$784$			977.861i			1.24727i
$785$		0			0
$786$	8.75699	+	7.03126i	0.0111412	+	0.00894562i
$787$	241.144	+	899.963i	0.306410	+	1.14354i	0.931725	+	0.363164i	$0.118304\pi$
$787$	241.144	+	899.963i	0.306410	+	1.14354i	−0.625315	+	0.780372i	$0.715030\pi$
$788$	513.778	−	137.666i	0.652003	−	0.174704i
$789$	−630.030	−	97.1064i	−0.798517	−	0.123075i
$790$		0			0
$791$	2.52677			0.00319440
$792$	16.3908	−	371.825i	0.0206955	−	0.469476i
$793$	49.8843	+	49.8843i	0.0629058	+	0.0629058i
$794$	−721.400	+	416.501i	−0.908565	+	0.524560i
$795$		0			0
$796$	−40.1407	+	69.5257i	−0.0504280	+	0.0873438i
$797$	43.8496	+	163.649i	0.0550183	+	0.205331i	0.987963	−	0.154687i	$-0.0494370\pi$
$797$	43.8496	+	163.649i	0.0550183	+	0.205331i	−0.932945	+	0.360019i	$0.882770\pi$
$798$	−2.70612	−	1.19140i	−0.00339113	−	0.00149298i
$799$	−770.071	+	444.601i	−0.963793	+	0.556446i
$800$		0			0
$801$	−115.022	−	519.866i	−0.143598	−	0.649022i
$802$	119.900	−	119.900i	0.149502	−	0.149502i
$803$	−185.162	+	691.034i	−0.230588	+	0.860565i
$804$	324.190	+	49.9674i	0.403222	+	0.0621485i
$805$		0			0
$806$	272.293	−	471.626i	0.337833	−	0.585144i
$807$	−1040.94	+	113.780i	−1.28989	+	0.140991i
$808$	−63.9130	+	238.527i	−0.0791003	+	0.295206i
$809$			1540.82i			1.90459i	0.305175	+	0.952296i	$0.401285\pi$
$809$			1540.82i			1.90459i	−0.305175	+	0.952296i	$0.598715\pi$
$810$		0			0
$811$	−895.419			−1.10409			−0.552046	−	0.833813i	$-0.686153\pi$
$811$	−895.419			−1.10409			−0.552046	+	0.833813i	$0.686153\pi$
$812$	−1.06752	−	0.286042i	−0.00131469	−	0.000352269i
$813$	−65.9370	−	603.238i	−0.0811033	−	0.741990i
$814$	1017.33	+	587.355i	1.24979	+	0.721566i
$815$		0			0
$816$	−175.460	+	1138.39i	−0.215025	+	1.39509i
$817$	−56.3434	−	15.0972i	−0.0689637	−	0.0184788i
$818$	664.048	+	664.048i	0.811795	+	0.811795i
$819$	−7.83561	+	1.73366i	−0.00956729	+	0.00211680i
$820$		0			0
$821$	−322.268	−	558.185i	−0.392531	−	0.679884i	0.600251	−	0.799811i	$-0.295067\pi$
$821$	−322.268	−	558.185i	−0.392531	−	0.679884i	−0.992783	+	0.119927i	$0.961734\pi$
$822$	−210.317	+	477.710i	−0.255860	+	0.581156i
$823$	−211.257	+	56.6061i	−0.256691	+	0.0687802i	−0.384870	−	0.922971i	$-0.625754\pi$
$823$	−211.257	+	56.6061i	−0.256691	+	0.0687802i	0.128179	+	0.991751i	$0.459087\pi$
$824$	−354.182	−	204.487i	−0.429832	−	0.248164i
$825$		0			0
$826$	1.60223	+	2.77514i	0.00193975	+	0.00335974i
$827$	982.768	−	982.768i	1.18835	−	1.18835i	0.210831	−	0.977522i	$-0.432383\pi$
$827$	982.768	−	982.768i	1.18835	−	1.18835i	0.977522	−	0.210831i	$-0.0676170\pi$
$828$	898.759	+	39.6191i	1.08546	+	0.0478492i
$829$			763.031i			0.920424i	0.887809	+	0.460212i	$0.152227\pi$
$829$			763.031i			0.920424i	−0.887809	+	0.460212i	$0.847773\pi$
$830$		0			0
$831$	−110.885	+	719.427i	−0.133436	+	0.865736i
$832$	1.92614	+	7.18844i	0.00231507	+	0.00863996i
$833$	910.427	−	243.948i	1.09295	−	0.292855i
$834$	574.431	−	715.418i	0.688766	−	0.857816i
$835$		0			0
$836$	118.353			0.141571
$837$	442.373	+	88.2834i	0.528522	+	0.105476i
$838$	−402.737	−	402.737i	−0.480593	−	0.480593i
$839$	946.477	−	546.449i	1.12810	−	0.651309i	0.184644	−	0.982805i	$-0.440887\pi$
$839$	946.477	−	546.449i	1.12810	−	0.651309i	0.943457	+	0.331496i	$0.107553\pi$
$840$		0			0
$841$	−393.430	+	681.440i	−0.467812	+	0.810274i
$842$	−264.182	−	985.940i	−0.313755	−	1.17095i
$843$	−678.291	+	497.125i	−0.804616	+	0.589709i
$844$	369.598	−	213.388i	0.437913	−	0.252829i
$845$		0			0
$846$	988.112	+	312.007i	1.16798	+	0.368803i
$847$	1.71114	−	1.71114i	0.00202024	−	0.00202024i
$848$	−204.735	+	764.080i	−0.241432	+	0.901038i
$849$	419.295	+	1078.89i	0.493870	+	1.27077i
$850$		0			0
$851$	1156.51	−	2003.14i	1.35900	−	2.35386i
$852$	−150.339	+	341.478i	−0.176455	+	0.400795i
$853$	−425.510	+	1588.02i	−0.498839	+	1.86169i	0.00853057	+	0.999964i	$0.497285\pi$
$853$	−425.510	+	1588.02i	−0.498839	+	1.86169i	−0.507369	+	0.861729i	$0.669382\pi$
$854$		−	0.914971i		−	0.00107140i
$855$		0			0
$856$	92.5628			0.108134
$857$	318.230	+	85.2695i	0.371330	+	0.0994977i	0.439658	−	0.898165i	$-0.355100\pi$
$857$	318.230	+	85.2695i	0.371330	+	0.0994977i	−0.0683276	+	0.997663i	$0.521766\pi$
$858$	729.240	−	534.465i	0.849930	−	0.622920i
$859$	−1361.73	−	786.197i	−1.58525	−	0.915247i	−0.994074	−	0.108707i	$-0.965329\pi$
$859$	−1361.73	−	786.197i	−1.58525	−	0.915247i	−0.591180	−	0.806540i	$-0.701338\pi$
$860$		0			0
$861$	−9.93239	−	7.97502i	−0.0115359	−	0.00926251i
$862$	−111.827	−	29.9639i	−0.129729	−	0.0347609i
$863$	−458.505	−	458.505i	−0.531292	−	0.531292i	0.389665	−	0.920957i	$-0.372591\pi$
$863$	−458.505	−	458.505i	−0.531292	−	0.531292i	−0.920957	+	0.389665i	$0.872591\pi$
$864$	714.698	−	476.895i	0.827197	−	0.551961i
$865$		0			0
$866$	−758.481	−	1313.73i	−0.875844	−	1.51701i
$867$	241.792	−	26.4291i	0.278883	−	0.0304834i
$868$	−2.42395	+	0.649494i	−0.00279256	+	0.000748265i
$869$	378.794	+	218.697i	0.435897	+	0.251665i
$870$		0			0
$871$	−324.550	−	562.137i	−0.372618	−	0.645393i
$872$	−354.396	+	354.396i	−0.406418	+	0.406418i
$873$	−1398.60	−	61.6532i	−1.60206	−	0.0706222i
$874$		−	655.913i		−	0.750472i
$875$		0			0
$876$	−476.941	+	185.357i	−0.544454	+	0.211595i
$877$	−279.129	−	1041.72i	−0.318277	−	1.18783i	−0.920900	−	0.389800i	$-0.872544\pi$
$877$	−279.129	−	1041.72i	−0.318277	−	1.18783i	0.602623	−	0.798026i	$-0.294122\pi$
$878$	931.615	−	249.625i	1.06106	−	0.284311i
$879$	−45.9083	−	118.127i	−0.0522279	−	0.134387i
$880$		0			0
$881$	1585.15			1.79927			0.899633	−	0.436647i	$-0.143834\pi$
$881$	1585.15			1.79927			0.899633	+	0.436647i	$0.143834\pi$
$882$	−926.101	−	590.539i	−1.05000	−	0.669545i
$883$	1004.45	+	1004.45i	1.13755	+	1.13755i	0.988889	+	0.148657i	$0.0474951\pi$
$883$	1004.45	+	1004.45i	1.13755	+	1.13755i	0.148657	+	0.988889i	$0.452505\pi$
$884$	−480.584	+	277.466i	−0.543648	+	0.313875i
$885$		0			0
$886$	913.702	−	1582.58i	1.03127	−	1.78621i
$887$	−81.0299	−	302.408i	−0.0913528	−	0.340933i	0.905088	−	0.425223i	$-0.139804\pi$
$887$	−81.0299	−	302.408i	−0.0913528	−	0.340933i	−0.996441	+	0.0842901i	$0.973138\pi$
$888$	−74.3688	−	680.378i	−0.0837487	−	0.766191i
$889$	−12.6676	+	7.31362i	−0.0142492	+	0.00822680i
$890$		0			0
$891$	613.112	+	430.074i	0.688117	+	0.482687i
$892$	149.235	−	149.235i	0.167304	−	0.167304i
$893$	69.4713	−	259.270i	0.0777954	−	0.290336i
$894$	124.300	−	154.808i	0.139038	−	0.173163i
$895$		0			0
$896$	4.38491	−	7.59489i	0.00489387	−	0.00847644i
$897$	−1052.37	−	1435.88i	−1.17321	−	1.60076i
$898$	−90.9632	+	339.479i	−0.101295	+	0.378039i
$899$		−	122.932i		−	0.136743i
$900$		0			0
$901$	762.464			0.846242
$902$	1386.18	+	371.425i	1.53678	+	0.411779i
$903$	1.87927	+	0.827369i	0.00208114	+	0.000916245i
$904$	143.639	+	82.9302i	0.158893	+	0.0917370i
$905$		0			0
$906$	−685.938	+	266.581i	−0.757106	+	0.294239i
$907$	357.992	+	95.9237i	0.394699	+	0.105759i	0.450709	−	0.892671i	$-0.351171\pi$
$907$	357.992	+	95.9237i	0.394699	+	0.105759i	−0.0560100	+	0.998430i	$0.517838\pi$
$908$	−513.506	−	513.506i	−0.565536	−	0.565536i
$909$	−335.543	−	366.490i	−0.369134	−	0.403180i
$910$		0			0
$911$	490.084	+	848.851i	0.537963	+	0.931779i	0.999014	+	0.0444052i	$0.0141393\pi$
$911$	490.084	+	848.851i	0.537963	+	0.931779i	−0.461051	+	0.887374i	$0.652527\pi$
$912$	−205.537	−	280.440i	−0.225369	−	0.307500i
$913$	554.997	−	148.711i	0.607883	−	0.162882i
$914$	−1583.93	−	914.484i	−1.73297	−	1.00053i
$915$		0			0
$916$	458.489	+	794.127i	0.500534	+	0.866951i
$917$	−0.0724117	+	0.0724117i	−7.89659e−5	+	7.89659e-5i
$918$	−972.172	−	853.657i	−1.05901	−	0.929909i
$919$		−	1321.17i		−	1.43762i	−0.695205	−	0.718811i	$-0.744687\pi$
$919$		−	1321.17i		−	1.43762i	0.695205	−	0.718811i	$-0.255313\pi$
$920$		0			0
$921$	281.565	+	226.077i	0.305717	+	0.245470i
$922$	413.938	+	1544.84i	0.448956	+	1.67553i
$923$	713.166	−	191.092i	0.772661	−	0.207034i
$924$	−4.11759	−	0.634643i	−0.00445626	−	0.000686843i
$925$		0			0
$926$	691.330			0.746577
$927$	730.114	−	379.683i	0.787609	−	0.409583i
$928$	−165.567	−	165.567i	−0.178413	−	0.178413i
$929$	672.297	−	388.151i	0.723678	−	0.417816i	−0.0924267	−	0.995719i	$-0.529462\pi$
$929$	672.297	−	388.151i	0.723678	−	0.417816i	0.816105	+	0.577904i	$0.196129\pi$
$930$		0			0
$931$	−142.259	+	246.400i	−0.152802	+	0.264662i
$932$	17.7678	+	66.3103i	0.0190642	+	0.0711484i
$933$	1247.05	+	549.027i	1.33660	+	0.588454i
$934$	−175.242	+	101.176i	−0.187625	+	0.108325i
$935$		0			0
$936$	−502.331	−	158.616i	−0.536678	−	0.169462i
$937$	−295.586	+	295.586i	−0.315459	+	0.315459i	−0.847020	−	0.531561i	$-0.821606\pi$
$937$	−295.586	+	295.586i	−0.315459	+	0.315459i	0.531561	+	0.847020i	$0.321606\pi$
$938$	−2.17890	+	8.13175i	−0.00232292	+	0.00866925i
$939$	−880.974	−	135.784i	−0.938205	−	0.144605i
$940$		0			0
$941$	−48.8020	+	84.5275i	−0.0518618	+	0.0898273i	−0.890791	−	0.454413i	$-0.849849\pi$
$941$	−48.8020	+	84.5275i	−0.0518618	+	0.0898273i	0.838929	+	0.544241i	$0.183182\pi$
$942$	1282.83	−	140.220i	1.36182	−	0.148854i
$943$	731.341	−	2729.40i	0.775548	−	2.89438i
$944$			376.820i			0.399174i
$945$		0			0
$946$	−231.333			−0.244538
$947$	177.098	+	47.4532i	0.187009	+	0.0501090i	0.351108	−	0.936335i	$-0.385805\pi$
$947$	177.098	+	47.4532i	0.187009	+	0.0501090i	−0.164099	+	0.986444i	$0.552472\pi$
$948$	33.9929	+	310.991i	0.0358575	+	0.328050i
$949$	876.908	+	506.283i	0.924034	+	0.533491i
$950$		0			0
$951$	40.4023	−	262.131i	0.0424840	−	0.275638i
$952$	−5.66313	−	1.51743i	−0.00594866	−	0.00159394i
$953$	16.8810	+	16.8810i	0.0177135	+	0.0177135i	0.715908	−	0.698195i	$-0.246013\pi$
$953$	16.8810	+	16.8810i	0.0177135	+	0.0177135i	−0.698195	+	0.715908i	$0.746013\pi$
$954$	−599.995	−	655.332i	−0.628925	−	0.686931i
$955$		0			0
$956$	−340.507	−	589.776i	−0.356179	−	0.616920i
$957$	82.2369	−	186.791i	0.0859320	−	0.195184i
$958$	−1164.97	+	312.153i	−1.21604	+	0.325838i
$959$	−4.12185	−	2.37975i	−0.00429807	−	0.00248149i
$960$		0			0
$961$	340.934	+	590.514i	0.354770	+	0.614479i
$962$	1175.66	−	1175.66i	1.22210	−	1.22210i
$963$	−100.141	+	157.044i	−0.103988	+	0.163078i
$964$		−	56.6819i		−	0.0587987i
$965$		0			0
$966$	−3.51719	+	22.8196i	−0.00364098	+	0.0236228i
$967$	311.140	+	1161.19i	0.321758	+	1.20082i	0.917531	+	0.397665i	$0.130179\pi$
$967$	311.140	+	1161.19i	0.321758	+	1.20082i	−0.595772	+	0.803153i	$0.703154\pi$
$968$	153.434	−	41.1125i	0.158506	−	0.0424716i
$969$	−209.825	+	261.324i	−0.216538	+	0.269684i
$970$		0			0
$971$	−608.975			−0.627163			−0.313582	−	0.949561i	$-0.601529\pi$
$971$	−608.975			−0.627163			−0.313582	+	0.949561i	$0.601529\pi$
$972$	11.1225	+	535.540i	0.0114429	+	0.550967i
$973$	5.91580	+	5.91580i	0.00607996	+	0.00607996i
$974$	−494.753	+	285.646i	−0.507960	+	0.293271i
$975$		0			0
$976$	53.7969	−	93.1790i	0.0551198	−	0.0954702i
$977$	22.8425	+	85.2493i	0.0233802	+	0.0872562i	0.976630	−	0.214927i	$-0.0689513\pi$
$977$	22.8425	+	85.2493i	0.0233802	+	0.0872562i	−0.953250	+	0.302183i	$0.902285\pi$
$978$	554.739	−	406.572i	0.567218	−	0.415718i
$979$	−473.701	+	273.491i	−0.483862	+	0.279358i
$980$		0			0
$981$	−217.865	−	984.684i	−0.222085	−	1.00376i
$982$	1391.51	−	1391.51i	1.41701	−	1.41701i
$983$	369.494	−	1378.97i	0.375884	−	1.40282i	−0.476166	−	0.879356i	$-0.657974\pi$
$983$	369.494	−	1378.97i	0.375884	−	1.40282i	0.852049	−	0.523461i	$-0.175360\pi$
$984$	−302.881	−	779.343i	−0.307806	−	0.792015i
$985$		0			0
$986$	−176.289	+	305.341i	−0.178792	+	0.309676i
$987$	−3.80723	+	8.64766i	−0.00385738	+	0.00876156i
$988$	43.3555	−	161.805i	0.0438821	−	0.163770i
$989$			455.499i			0.460565i
$990$		0			0
$991$	14.7275			0.0148613			0.00743063	−	0.999972i	$-0.497635\pi$
$991$	14.7275			0.0148613			0.00743063	+	0.999972i	$0.497635\pi$
$992$	−513.545	−	137.604i	−0.517687	−	0.138714i
$993$	−1079.92	+	791.484i	−1.08754	+	0.797063i
$994$	−8.29290	−	4.78791i	−0.00834296	−	0.00481681i
$995$		0			0
$996$	320.448	+	257.298i	0.321735	+	0.258331i
$997$	−222.758	−	59.6878i	−0.223428	−	0.0598674i	0.145368	−	0.989378i	$-0.453563\pi$
$997$	−222.758	−	59.6878i	−0.223428	−	0.0598674i	−0.368796	+	0.929510i	$0.620230\pi$
$998$	858.989	+	858.989i	0.860710	+	0.860710i
$999$	1234.80	+	609.903i	1.23603	+	0.610514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.o.b.193.2		40
5.2	odd	4	inner	225.3.o.b.157.9		40
5.3	odd	4		45.3.k.a.22.2	yes	40
5.4	even	2		45.3.k.a.13.9	yes	40
9.7	even	3	inner	225.3.o.b.43.9		40
15.8	even	4		135.3.l.a.37.9		40
15.14	odd	2		135.3.l.a.118.2		40
45.4	even	6		405.3.g.h.163.2		20
45.7	odd	12	inner	225.3.o.b.7.2		40
45.13	odd	12		405.3.g.h.82.2		20
45.14	odd	6		405.3.g.g.163.9		20
45.23	even	12		405.3.g.g.82.9		20
45.29	odd	6		135.3.l.a.73.9		40
45.34	even	6		45.3.k.a.43.2	yes	40
45.38	even	12		135.3.l.a.127.2		40
45.43	odd	12		45.3.k.a.7.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	45.43	odd	12
45.3.k.a.13.9	yes	40	5.4	even	2
45.3.k.a.22.2	yes	40	5.3	odd	4
45.3.k.a.43.2	yes	40	45.34	even	6
135.3.l.a.37.9		40	15.8	even	4
135.3.l.a.73.9		40	45.29	odd	6
135.3.l.a.118.2		40	15.14	odd	2
135.3.l.a.127.2		40	45.38	even	12
225.3.o.b.7.2		40	45.7	odd	12	inner
225.3.o.b.43.9		40	9.7	even	3	inner
225.3.o.b.157.9		40	5.2	odd	4	inner
225.3.o.b.193.2		40	1.1	even	1	trivial
405.3.g.g.82.9		20	45.23	even	12
405.3.g.g.163.9		20	45.14	odd	6
405.3.g.h.82.2		20	45.13	odd	12
405.3.g.h.163.2		20	45.4	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.40598 - 0.644680i) q^{2} +(0.325974 + 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(1.13830 - 7.38535i) q^{6} +(0.0658171 + 0.0176356i) q^{7} +(3.16269 + 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +O(q^{10})\)	\(q+(-2.40598 - 0.644680i) q^{2} +(0.325974 + 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(1.13830 - 7.38535i) q^{6} +(0.0658171 + 0.0176356i) q^{7} +(3.16269 + 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +(4.62292 + 8.00713i) q^{11} +(-2.66465 + 6.05242i) q^{12} +(12.6403 - 3.38696i) q^{13} +(-0.146985 - 0.0848619i) q^{14} +(-9.97912 - 17.2843i) q^{16} +(-13.6029 + 13.6029i) q^{17} +(22.3959 + 0.987258i) q^{18} -5.80704i q^{19} +(-0.0311390 + 0.202031i) q^{21} +(-5.96060 - 22.2453i) q^{22} +(-43.8013 + 11.7365i) q^{23} +(-8.40093 + 10.4628i) q^{24} -32.5958 q^{26} +(-8.66274 - 25.5726i) q^{27} +(0.106208 + 0.106208i) q^{28} +(-6.37222 + 3.67900i) q^{29} +(-8.35363 + 14.4689i) q^{31} +(8.23618 + 30.7378i) q^{32} +(-22.3722 + 16.3967i) q^{33} +(41.4978 - 23.9587i) q^{34} +(-18.9184 - 5.97368i) q^{36} +(-36.0680 + 36.0680i) q^{37} +(-3.74368 + 13.9716i) q^{38} +(14.2211 + 36.5923i) q^{39} +(-31.1567 + 53.9649i) q^{41} +(0.205165 - 0.466007i) q^{42} +(2.59980 - 9.70259i) q^{43} +20.3810i q^{44} +112.951 q^{46} +(44.6476 + 11.9633i) q^{47} +(48.2931 - 35.3944i) q^{48} +(-42.4312 - 24.4977i) q^{49} +(-45.0012 - 36.1329i) q^{51} +(27.8636 + 7.46602i) q^{52} +(-28.0258 - 28.0258i) q^{53} +(4.35625 + 67.1118i) q^{54} +(0.152383 + 0.263935i) q^{56} +(17.3180 - 1.89294i) q^{57} +(17.7032 - 4.74356i) q^{58} +(-16.3509 - 9.44022i) q^{59} +(2.69547 + 4.66870i) q^{61} +(29.4265 - 29.4265i) q^{62} +(-0.612655 - 0.0270071i) q^{63} +0.568692i q^{64} +(64.3977 - 25.0273i) q^{66} +(-12.8379 - 47.9117i) q^{67} +(-40.9609 + 10.9754i) q^{68} +(-49.2792 - 126.800i) q^{69} +56.4200 q^{71} +(-33.9412 - 21.6430i) q^{72} +(54.7135 + 54.7135i) q^{73} +(110.031 - 63.5264i) q^{74} +(6.40036 - 11.0857i) q^{76} +(0.163056 + 0.608534i) q^{77} +(-10.6254 - 97.2084i) q^{78} +(40.9692 - 23.6536i) q^{79} +(73.4397 - 34.1704i) q^{81} +(109.752 - 109.752i) q^{82} +(16.0841 - 60.0267i) q^{83} +(-0.282117 + 0.351360i) q^{84} +(-12.5101 + 21.6682i) q^{86} +(-13.0488 - 17.8042i) q^{87} +(-10.7032 + 39.9449i) q^{88} +59.1599i q^{89} +0.891679 q^{91} +(-96.5530 - 25.8713i) q^{92} +(-45.8728 - 20.1960i) q^{93} +(-99.7085 - 57.5668i) q^{94} +(-88.9828 + 34.5820i) q^{96} +(150.251 + 40.2595i) q^{97} +(86.2954 + 86.2954i) q^{98} +(-56.1918 - 61.3743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8}+O(q^{10}) \) 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31} + 14 q^{32} - 96 q^{33} + 264 q^{36} + 92 q^{37} - 330 q^{38} - 28 q^{41} - 498 q^{42} + 2 q^{43} - 136 q^{46} - 64 q^{47} + 510 q^{48} - 396 q^{51} + 74 q^{52} + 608 q^{53} - 192 q^{56} + 114 q^{57} - 30 q^{58} + 92 q^{61} + 100 q^{62} - 24 q^{63} + 588 q^{66} + 80 q^{67} - 626 q^{68} + 248 q^{71} + 162 q^{72} + 8 q^{73} - 96 q^{76} - 338 q^{77} - 1062 q^{78} + 204 q^{81} - 104 q^{82} - 370 q^{83} - 328 q^{86} - 534 q^{87} + 210 q^{88} + 152 q^{91} - 388 q^{92} + 1062 q^{93} - 876 q^{96} - 292 q^{97} + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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