LMFDB - Embedded newform 225.3.o.b.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,3,Mod(7,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage: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")

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:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			7.2
Character	$\chi$	$=$	225.7
Dual form			225.3.o.b.193.2

$q$-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} +(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} + 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}+ \cdots + 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.804008	−	0.594619i	$-0.797303\pi$
$2$	−2.40598	+	0.644680i	−1.20299	+	0.322340i	−0.398981	+	0.916959i	$0.630636\pi$
$3$	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	−0.254115	−	0.967174i	$-0.581784\pi$
$7$	0.0658171	−	0.0176356i	0.00940244	−	0.00251938i	0.263517	+	0.964655i	$0.415117\pi$
$8$	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	−0.575700	−	0.817661i	$-0.695270\pi$
$11$	4.62292	−	8.00713i	0.420265	−	0.727921i	0.995965	+	0.0897404i	$0.0286037\pi$
$12$	−2.66465	−	6.05242i	−0.222054	−	0.504368i
$13$	12.6403	+	3.38696i	0.972331	+	0.260535i	0.709812	−	0.704391i	$-0.248780\pi$
$13$	12.6403	+	3.38696i	0.972331	+	0.260535i	0.262519	+	0.964927i	$0.415447\pi$
$14$	−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	0.182952	−	0.983122i	$-0.441435\pi$
$17$	−13.6029	−	13.6029i	−0.800170	−	0.800170i	−0.983122	+	0.182952i	$0.941435\pi$
$18$	22.3959	−	0.987258i	1.24422	−	0.0548477i
$19$			5.80704i			0.305634i	0.988255	+	0.152817i	$0.0488345\pi$
$19$			5.80704i			0.305634i	−0.988255	+	0.152817i	$0.951166\pi$
$20$		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	−0.995676	−	0.0928936i	$-0.970388\pi$
$23$	−43.8013	−	11.7365i	−1.90440	−	0.510283i	−0.908728	−	0.417390i	$-0.862945\pi$
$24$	−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	0.386094	−	0.922459i	$-0.373824\pi$
$29$	−6.37222	−	3.67900i	−0.219732	−	0.126862i	−0.605826	+	0.795597i	$0.707157\pi$
$30$		0			0
$31$	−8.35363	−	14.4689i	−0.269472	−	0.466739i	0.699254	−	0.714874i	$-0.253516\pi$
$31$	−8.35363	−	14.4689i	−0.269472	−	0.466739i	−0.968726	+	0.248135i	$0.920183\pi$
$32$	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	0.0248806	−	0.999690i	$-0.492079\pi$
$37$	−36.0680	−	36.0680i	−0.974810	−	0.974810i	−0.999690	+	0.0248806i	$0.992079\pi$
$38$	−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	−0.942892	−	0.333100i	$-0.891905\pi$
$41$	−31.1567	−	53.9649i	−0.759919	−	1.31622i	0.182973	−	0.983118i	$-0.441428\pi$
$42$	0.205165	+	0.466007i	0.00488488	+	0.0110954i
$43$	2.59980	+	9.70259i	0.0604605	+	0.225642i	0.989545	−	0.144227i	$-0.0460694\pi$
$43$	2.59980	+	9.70259i	0.0604605	+	0.225642i	−0.929084	+	0.369868i	$0.879403\pi$
$44$		−	20.3810i		−	0.463204i
$45$		0			0
$46$	112.951			2.45546
$47$	44.6476	−	11.9633i	0.949948	−	0.254538i	0.249608	−	0.968347i	$-0.419698\pi$
$47$	44.6476	−	11.9633i	0.949948	−	0.254538i	0.700340	+	0.713809i	$0.253032\pi$
$48$	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	−0.920211	−	0.391423i	$-0.871983\pi$
$53$	−28.0258	+	28.0258i	−0.528789	+	0.528789i	0.391423	+	0.920211i	$0.371983\pi$
$54$	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	−0.632126	−	0.774866i	$-0.717817\pi$
$59$	−16.3509	+	9.44022i	−0.277135	+	0.160004i	0.354991	+	0.934870i	$0.384484\pi$
$60$		0			0
$61$	2.69547	−	4.66870i	0.0441881	−	0.0765360i	−0.843085	−	0.537780i	$-0.819263\pi$
$61$	2.69547	−	4.66870i	0.0441881	−	0.0765360i	0.887274	+	0.461244i	$0.152597\pi$
$62$	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	0.801508	+	0.597984i	$0.204031\pi$
$67$	−12.8379	+	47.9117i	−0.191610	+	0.715100i	−0.993118	+	0.117116i	$0.962635\pi$
$68$	−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	−0.224885	−	0.974385i	$-0.572201\pi$
$73$	54.7135	−	54.7135i	0.749500	−	0.749500i	0.974385	+	0.224885i	$0.0722007\pi$
$74$	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	0.736361	−	0.676589i	$-0.236543\pi$
$79$	40.9692	+	23.6536i	0.518597	+	0.299412i	−0.217763	+	0.976002i	$0.569876\pi$
$80$		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	0.992578	+	0.121608i	$0.0388052\pi$
$83$	16.0841	+	60.0267i	0.193784	+	0.723213i	−0.798794	+	0.601605i	$0.794528\pi$
$84$	−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	$-0.892156\pi$
$89$		−	59.1599i		−	0.664718i	0.943153	−	0.332359i	$-0.107844\pi$
$90$		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	0.619823	−	0.784742i	$-0.287204\pi$
$97$	150.251	−	40.2595i	1.54898	−	0.415047i	0.929153	+	0.369695i	$0.120538\pi$
$98$	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	−0.696390	−	0.717663i	$-0.745212\pi$
$101$	27.6053	−	47.8137i	0.273319	−	0.473403i	0.969710	+	0.244260i	$0.0785451\pi$
$102$	84.9779	−	115.946i	0.833116	−	1.13673i
$103$	−88.3218	−	23.6658i	−0.857493	−	0.229765i	−0.196821	−	0.980439i	$-0.563062\pi$
$103$	−88.3218	−	23.6658i	−0.857493	−	0.229765i	−0.660672	+	0.750675i	$0.729729\pi$
$104$	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	0.772174	−	0.635411i	$-0.219169\pi$
$107$	14.6336	+	14.6336i	0.136762	+	0.136762i	−0.635411	+	0.772174i	$0.719169\pi$
$108$	11.6480	+	58.3663i	0.107852	+	0.540429i
$109$		−	112.055i		−	1.02803i	−0.857781	−	0.514015i	$-0.828157\pi$
$109$		−	112.055i		−	1.02803i	0.857781	−	0.514015i	$-0.171843\pi$
$110$		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	0.413803	−	0.910366i	$-0.364200\pi$
$113$	35.8191	+	9.59771i	0.316984	+	0.0849355i	−0.0968194	+	0.995302i	$0.530867\pi$
$114$	−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	−0.975580	−	0.219643i	$-0.929511\pi$
$127$	−151.793	−	151.793i	−1.19522	−	1.19522i	−0.219643	−	0.975580i	$-0.570489\pi$
$128$	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	0.863143	−	0.504960i	$-0.168493\pi$
$131$	−0.751448	−	1.30155i	−0.00573624	−	0.00993547i	−0.868879	+	0.495024i	$0.835159\pi$
$132$	−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	−0.496508	−	0.868032i	$-0.665385\pi$
$137$	−67.4699	+	18.0785i	−0.492481	+	0.131960i	0.00402717	+	0.999992i	$0.498718\pi$
$138$	36.8192	−	336.847i	0.266805	−	2.44092i
$139$	106.332	−	61.3909i	0.764980	−	0.441661i	−0.0661012	−	0.997813i	$-0.521056\pi$
$139$	106.332	−	61.3909i	0.764980	−	0.441661i	0.831081	+	0.556152i	$0.187723\pi$
$140$		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	−0.420797	−	0.907155i	$-0.638250\pi$
$149$	23.0090	−	13.2842i	0.154423	−	0.0891560i	0.575220	+	0.817999i	$0.304916\pi$
$150$		0			0
$151$	−49.2414	+	85.2887i	−0.326102	+	0.564826i	−0.981735	−	0.190254i	$-0.939069\pi$
$151$	−49.2414	+	85.2887i	−0.326102	+	0.564826i	0.655633	+	0.755080i	$0.272402\pi$
$152$	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	−0.664370	−	0.747404i	$-0.731300\pi$
$157$	44.6968	−	166.811i	0.284693	−	1.06249i	0.949063	−	0.315086i	$-0.102033\pi$
$158$	−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	−0.478700	−	0.877978i	$-0.658892\pi$
$163$	65.0824	−	65.0824i	0.399278	−	0.399278i	0.877978	+	0.478700i	$0.158892\pi$
$164$	−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	−0.619311	−	0.785146i	$-0.712588\pi$
$167$	51.7034	−	192.960i	0.309601	−	1.15545i	0.928912	−	0.370301i	$-0.120745\pi$
$168$	−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	0.935224	−	0.354056i	$-0.115198\pi$
$173$	−8.94958	−	33.4003i	−0.0517317	−	0.193065i	−0.986956	+	0.160991i	$0.948531\pi$
$174$	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	$0.173862\pi$
$179$			185.962i			1.03890i	−0.854502	+	0.519448i	$0.826138\pi$
$180$		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	−0.987478	−	0.157759i	$-0.949573\pi$
$191$	−68.2090	+	118.141i	−0.357115	+	0.618542i	0.630362	+	0.776301i	$0.282906\pi$
$192$	−1.69598	−	0.185379i	−0.00883321	−	0.000965515i
$193$	89.2148	+	23.9050i	0.462253	+	0.123860i	0.482427	−	0.875936i	$-0.339755\pi$
$193$	89.2148	+	23.9050i	0.462253	+	0.123860i	−0.0201740	+	0.999796i	$0.506422\pi$
$194$	−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	0.992039	−	0.125932i	$-0.0401920\pi$
$197$	170.623	+	170.623i	0.866107	+	0.866107i	−0.125932	+	0.992039i	$0.540192\pi$
$198$	95.6294	−	183.891i	0.482977	−	0.928742i
$199$		−	36.4196i		−	0.183013i	−0.995804	−	0.0915066i	$-0.970832\pi$
$199$		−	36.4196i		−	0.183013i	0.995804	−	0.0915066i	$-0.0291683\pi$
$200$		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	0.998897	−	0.0469559i	$-0.0149520\pi$
$211$	96.8033	+	167.668i	0.458784	+	0.794636i	−0.540113	+	0.841592i	$0.681619\pi$
$212$	−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	0.998968	−	0.0454290i	$-0.0144655\pi$
$223$	24.7802	+	92.4808i	0.111122	+	0.414712i	−0.887846	+	0.460141i	$0.847799\pi$
$224$		−	2.16833i		−	0.00968002i
$225$		0			0
$226$	−92.3675			−0.408706
$227$	−318.219	+	85.2664i	−1.40184	+	0.375623i	−0.879007	−	0.476810i	$-0.841793\pi$
$227$	−318.219	+	85.2664i	−1.40184	+	0.375623i	−0.522837	+	0.852433i	$0.675126\pi$
$228$	35.1467	−	15.4737i	0.154152	−	0.0678672i
$229$	360.256	−	207.994i	1.57317	−	0.908269i	0.577391	−	0.816468i	$-0.304071\pi$
$229$	360.256	−	207.994i	1.57317	−	0.908269i	0.995777	−	0.0918017i	$-0.0292626\pi$
$230$		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	−0.658270	−	0.752782i	$-0.728711\pi$
$233$	22.0213	−	22.0213i	0.0945121	−	0.0945121i	0.752782	+	0.658270i	$0.228711\pi$
$234$	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	−0.941264	−	0.337672i	$-0.890361\pi$
$239$	−267.552	+	154.471i	−1.11946	+	0.646323i	−0.178200	+	0.983994i	$0.557027\pi$
$240$		0			0
$241$	−12.8569	+	22.2688i	−0.0533481	+	0.0924016i	−0.891466	−	0.453087i	$-0.850323\pi$
$241$	−12.8569	+	22.2688i	−0.0533481	+	0.0924016i	0.838118	+	0.545489i	$0.183656\pi$
$242$	−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	−0.969073	−	0.246776i	$-0.920629\pi$
$257$	−1.65593	+	6.18001i	−0.00644330	+	0.0240467i	0.962629	+	0.270822i	$0.0872956\pi$
$258$	−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	−0.988157	−	0.153448i	$-0.950962\pi$
$263$	−54.9964	−	205.249i	−0.209112	−	0.780416i	0.779045	−	0.626968i	$-0.215704\pi$
$264$	−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	$-0.775278\pi$
$269$		−	349.046i		−	1.29757i	0.760973	−	0.648784i	$-0.224722\pi$
$270$		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	0.190381	−	0.981710i	$-0.439028\pi$
$277$	234.373	−	62.8000i	0.846112	−	0.226715i	0.655730	+	0.754995i	$0.272361\pi$
$278$	−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	−0.501210	−	0.865326i	$-0.667111\pi$
$281$	140.160	−	242.764i	0.498789	−	0.863929i	0.999999	+	0.00139729i	$0.000444772\pi$
$282$	139.175	+	316.120i	0.493530	+	1.12099i
$283$	372.686	+	99.8610i	1.31691	+	0.352866i	0.847820	−	0.530283i	$-0.177914\pi$
$283$	372.686	+	99.8610i	1.31691	+	0.352866i	0.469092	+	0.883149i	$0.344581\pi$
$284$	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	0.188512	−	0.982071i	$-0.439633\pi$
$293$	−40.8052	−	10.9337i	−0.139267	−	0.0373164i	−0.327779	+	0.944754i	$0.606300\pi$
$294$	−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	0.832004	−	0.554769i	$-0.187194\pi$
$307$	85.1111	+	85.1111i	0.277235	+	0.277235i	−0.554769	+	0.832004i	$0.687194\pi$
$308$	−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	0.956797	+	0.290758i	$0.0939074\pi$
$311$	227.093	+	393.336i	0.730202	+	1.26475i	−0.226595	+	0.973989i	$0.572759\pi$
$312$	−70.7531	−	160.707i	−0.226773	−	0.515087i
$313$	−76.9018	−	287.001i	−0.245693	−	0.916937i	−0.973034	−	0.230661i	$-0.925911\pi$
$313$	−76.9018	−	287.001i	−0.245693	−	0.916937i	0.727342	−	0.686276i	$-0.240756\pi$
$314$			430.158i			1.36993i
$315$		0			0
$316$	104.281			0.330004
$317$	−85.3965	+	22.8819i	−0.269389	+	0.0721827i	−0.390985	−	0.920397i	$-0.627866\pi$
$317$	−85.3965	+	22.8819i	−0.269389	+	0.0721827i	0.121596	+	0.992580i	$0.461199\pi$
$318$	−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	−0.302535	−	0.953138i	$-0.597833\pi$
$331$	223.152	−	386.510i	0.674175	−	1.16770i	0.976709	−	0.214566i	$-0.0688338\pi$
$332$	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	−0.976262	−	0.216593i	$-0.930506\pi$
$337$	−7.58184	+	28.2958i	−0.0224980	+	0.0839638i	0.953764	+	0.300556i	$0.0971724\pi$
$338$	−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	0.717956	+	0.696089i	$0.245078\pi$
$347$	−87.3943	+	326.160i	−0.251857	+	0.939942i	−0.969812	+	0.243853i	$0.921589\pi$
$348$	−5.28716	+	48.3706i	−0.0151930	+	0.138996i
$349$	51.4915	+	29.7286i	0.147540	+	0.0851823i	0.571953	−	0.820287i	$-0.306186\pi$
$349$	51.4915	+	29.7286i	0.147540	+	0.0851823i	−0.424413	+	0.905469i	$0.639519\pi$
$350$		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	0.829342	+	0.558742i	$0.188716\pi$
$353$	137.840	+	514.426i	0.390482	+	1.45730i	−0.438860	+	0.898555i	$0.644618\pi$
$354$	−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	$-0.841870\pi$
$359$		−	342.196i		−	0.953192i	0.879122	−	0.476596i	$-0.158130\pi$
$360$		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	−0.708275	−	0.705937i	$-0.750526\pi$
$367$	−355.509	+	95.2584i	−0.968690	+	0.259560i	−0.260416	+	0.965497i	$0.583860\pi$
$368$	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	0.662596	−	0.748977i	$-0.269455\pi$
$373$	321.501	+	86.1459i	0.861933	+	0.230954i	0.199337	+	0.979931i	$0.436121\pi$
$374$	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	$-0.913395\pi$
$379$		−	203.700i		−	0.537466i	0.963215	−	0.268733i	$-0.0866049\pi$
$380$		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	0.232633	−	0.972565i	$-0.425266\pi$
$383$	−19.9865	−	5.35538i	−0.0521842	−	0.0139827i	−0.284817	+	0.958582i	$0.591933\pi$
$384$	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	0.691838	−	0.722053i	$-0.256801\pi$
$389$	160.439	+	92.6297i	0.412440	+	0.238123i	−0.279397	+	0.960176i	$0.590135\pi$
$390$		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	0.939152	−	0.343501i	$-0.111613\pi$
$397$	236.474	+	236.474i	0.595652	+	0.595652i	−0.343501	+	0.939152i	$0.611613\pi$
$398$	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	0.820459	−	0.571705i	$-0.193718\pi$
$401$	−34.0375	−	58.9547i	−0.0848816	−	0.147019i	−0.905341	+	0.424686i	$0.860385\pi$
$402$	−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	−0.842882	−	0.538099i	$-0.819143\pi$
$409$	−326.511	+	188.511i	−0.798315	+	0.460907i	0.0445668	+	0.999006i	$0.485809\pi$
$410$		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	−0.244720	−	0.969594i	$-0.578696\pi$
$419$	198.025	−	114.330i	0.472613	−	0.272863i	0.717333	+	0.696731i	$0.245363\pi$
$420$		0			0
$421$	204.894	−	354.887i	0.486684	−	0.842961i	−0.513199	−	0.858270i	$-0.671540\pi$
$421$	204.894	−	354.887i	0.486684	−	0.842961i	0.999883	+	0.0153086i	$0.00487306\pi$
$422$	−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	−0.00544093	−	0.999985i	$-0.501732\pi$
$433$	430.638	−	430.638i	0.994544	−	0.994544i	0.999985	+	0.00544093i	$0.00173191\pi$
$434$	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	0.0668232	−	0.997765i	$-0.478714\pi$
$439$	−335.332	−	193.604i	−0.763855	−	0.441012i	−0.830678	+	0.556753i	$0.812047\pi$
$440$		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	−0.755874	−	0.654717i	$-0.772788\pi$
$443$	−189.882	−	708.648i	−0.428627	−	1.59966i	0.327247	−	0.944939i	$-0.393879\pi$
$444$	−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	$0.0502226\pi$
$449$			141.098i			0.314250i	−0.987579	+	0.157125i	$0.949777\pi$
$450$		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	0.621865	−	0.783124i	$-0.286375\pi$
$457$	709.254	−	190.044i	1.55198	−	0.415851i	0.930113	+	0.367273i	$0.119709\pi$
$458$	−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	0.273304	+	0.961928i	$0.411883\pi$
$461$	−321.041	+	556.060i	−0.696402	+	1.20620i	−0.969706	+	0.244275i	$0.921450\pi$
$462$	4.67984	+	0.511530i	0.0101295	+	0.00110721i
$463$	−268.091	−	71.8346i	−0.579029	−	0.155150i	−0.0425948	−	0.999092i	$-0.513562\pi$
$463$	−268.091	−	71.8346i	−0.579029	−	0.155150i	−0.536434	+	0.843942i	$0.680229\pi$
$464$	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	0.765930	−	0.642924i	$-0.222279\pi$
$467$	57.4439	+	57.4439i	0.123006	+	0.123006i	−0.642924	+	0.765930i	$0.722279\pi$
$468$	−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	0.869147	−	0.494554i	$-0.164669\pi$
$479$	419.328	+	242.099i	0.875423	+	0.505426i	0.00627671	+	0.999980i	$0.498002\pi$
$480$		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	0.853731	−	0.520714i	$-0.174334\pi$
$487$	162.179	+	162.179i	0.333017	+	0.333017i	−0.520714	+	0.853731i	$0.674334\pi$
$488$	−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	−0.916610	−	0.399783i	$-0.869086\pi$
$491$	−395.023	−	684.199i	−0.804527	−	1.39348i	0.112083	−	0.993699i	$-0.464248\pi$
$492$	−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	−0.859441	−	0.511236i	$-0.829188\pi$
$499$	−422.362	+	243.851i	−0.846418	+	0.488680i	0.0130228	+	0.999915i	$0.495855\pi$
$500$		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	−0.961882	−	0.273465i	$-0.911830\pi$
$503$	−346.274	+	346.274i	−0.688418	+	0.688418i	0.273465	+	0.961882i	$0.411830\pi$
$504$	−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	−0.100080	−	0.994979i	$-0.531910\pi$
$509$	362.182	−	209.106i	0.711557	−	0.410818i	0.811637	+	0.584162i	$0.198577\pi$
$510$		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	−0.110462	+	0.993880i	$0.535233\pi$
$523$	−577.571	+	577.571i	−1.10434	+	1.10434i	−0.993880	+	0.110462i	$0.964767\pi$
$524$	−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	−0.318677	−	0.947863i	$-0.603239\pi$
$547$	−66.0385	+	17.6950i	−0.120728	+	0.0323491i	0.197949	+	0.980212i	$0.436572\pi$
$548$	−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	0.296225	−	0.955118i	$-0.404272\pi$
$557$	−367.003	−	367.003i	−0.658893	−	0.658893i	−0.955118	+	0.296225i	$0.904272\pi$
$558$	−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	0.518448	−	0.855109i	$-0.326510\pi$
$563$	303.953	+	81.4441i	0.539882	+	0.144661i	0.0214341	+	0.999770i	$0.493177\pi$
$564$	−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	−0.998022	−	0.0628645i	$-0.979976\pi$
$569$	−882.789	−	509.679i	−1.55148	−	0.895745i	−0.553453	−	0.832880i	$-0.686690\pi$
$570$		0			0
$571$	443.096	+	767.465i	0.776000	+	1.34407i	0.934231	+	0.356669i	$0.116088\pi$
$571$	443.096	+	767.465i	0.776000	+	1.34407i	−0.158231	+	0.987402i	$0.550579\pi$
$572$	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	0.518172	−	0.855277i	$-0.326613\pi$
$577$	−194.509	−	194.509i	−0.337105	−	0.337105i	−0.855277	+	0.518172i	$0.826613\pi$
$578$	−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	0.471960	−	0.881620i	$-0.343547\pi$
$587$	775.720	−	207.853i	1.32150	−	0.354095i	0.849539	+	0.527526i	$0.176880\pi$
$588$	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	−0.999411	−	0.0343049i	$-0.989078\pi$
$593$	−572.308	+	572.308i	−0.965106	+	0.965106i	0.0343049	+	0.999411i	$0.489078\pi$
$594$	−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	−0.263945	−	0.964538i	$-0.585024\pi$
$599$	263.198	−	151.957i	0.439396	−	0.253685i	0.703341	+	0.710852i	$0.251691\pi$
$600$		0			0
$601$	−52.0948	+	90.2308i	−0.0866801	+	0.150134i	−0.906106	−	0.423051i	$-0.860959\pi$
$601$	−52.0948	+	90.2308i	−0.0866801	+	0.150134i	0.819426	+	0.573185i	$0.194292\pi$
$602$	−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	−0.999844	−	0.0176696i	$-0.994375\pi$
$607$	−75.9472	+	283.439i	−0.125119	+	0.466950i	0.874725	+	0.484620i	$0.161042\pi$
$608$	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	−0.999993	−	0.00363596i	$-0.998843\pi$
$613$	−610.767	+	610.767i	−0.996357	+	0.996357i	0.00363596	+	0.999993i	$0.498843\pi$
$614$	−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	−0.346908	−	0.937899i	$-0.612768\pi$
$617$	260.666	−	972.818i	0.422473	−	1.57669i	0.769381	−	0.638791i	$-0.220565\pi$
$618$	74.2429	−	679.226i	0.120134	−	1.09907i
$619$	189.444	+	109.376i	0.306049	+	0.176697i	0.645157	−	0.764050i	$-0.276792\pi$
$619$	189.444	+	109.376i	0.306049	+	0.176697i	−0.339108	+	0.940747i	$0.610125\pi$
$620$		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	−0.993822	−	0.110982i	$-0.964600\pi$
$641$	−256.912	+	444.984i	−0.400798	+	0.694203i	0.593024	+	0.805185i	$0.297934\pi$
$642$	−91.4165	+	124.731i	−0.142393	+	0.194286i
$643$	−187.988	−	50.3713i	−0.292361	−	0.0783379i	0.109657	−	0.993969i	$-0.465025\pi$
$643$	−187.988	−	50.3713i	−0.292361	−	0.0783379i	−0.402019	+	0.915632i	$0.631691\pi$
$644$	−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	0.806794	−	0.590833i	$-0.201201\pi$
$647$	139.726	+	139.726i	0.215960	+	0.215960i	−0.590833	+	0.806794i	$0.701201\pi$
$648$	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	−0.251503	−	0.967856i	$-0.580925\pi$
$653$	−622.466	−	166.789i	−0.953240	−	0.255420i	−0.701737	+	0.712437i	$0.747592\pi$
$654$	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	0.331965	−	0.943292i	$-0.392289\pi$
$659$	−210.200	−	121.359i	−0.318968	−	0.184156i	−0.650932	+	0.759136i	$0.725622\pi$
$660$		0			0
$661$	−331.364	−	573.939i	−0.501307	−	0.868288i	−0.999999	−	0.00150927i	$-0.999520\pi$
$661$	−331.364	−	573.939i	−0.501307	−	0.868288i	0.498692	−	0.866779i	$-0.333814\pi$
$662$	−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	−0.994373	−	0.105935i	$-0.966216\pi$
$673$	−125.305	−	467.643i	−0.186188	−	0.694864i	0.808185	−	0.588929i	$-0.200450\pi$
$674$		−	72.9670i		−	0.108260i
$675$		0			0
$676$	4.95712			0.00733302
$677$	−425.004	+	113.880i	−0.627776	+	0.168212i	−0.558660	−	0.829397i	$-0.688684\pi$
$677$	−425.004	+	113.880i	−0.627776	+	0.168212i	−0.0691156	+	0.997609i	$0.522018\pi$
$678$	−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	−0.416938	−	0.908935i	$-0.636897\pi$
$683$	336.034	−	336.034i	0.491998	−	0.491998i	0.908935	+	0.416938i	$0.136897\pi$
$684$	−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	0.304029	+	0.952663i	$0.401668\pi$
$691$	−465.054	+	805.496i	−0.673015	+	1.16570i	−0.977045	+	0.213034i	$0.931665\pi$
$692$	−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	0.147223	−	0.989103i	$-0.452966\pi$
$709$	−450.749	−	260.240i	−0.635754	−	0.367053i	−0.782977	+	0.622051i	$0.786300\pi$
$710$		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	$0.319072\pi$
$719$			1211.89i			1.68553i	−0.538285	+	0.842763i	$0.680928\pi$
$720$		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	−0.117707	−	0.993048i	$-0.537554\pi$
$727$	201.292	−	53.9360i	0.276880	−	0.0741899i	0.394587	+	0.918859i	$0.370888\pi$
$728$	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	−0.258502	−	0.966011i	$-0.583229\pi$
$733$	−707.621	−	189.606i	−0.965376	−	0.258672i	−0.706874	+	0.707339i	$0.749895\pi$
$734$	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	$-0.681597\pi$
$739$		−	1243.93i		−	1.68326i	0.540056	−	0.841629i	$-0.318403\pi$
$740$		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	0.964687	−	0.263400i	$-0.0848440\pi$
$743$	1239.64	+	332.161i	1.66843	+	0.447054i	0.703743	+	0.710455i	$0.251511\pi$
$744$	−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	−0.988308	−	0.152471i	$-0.951277\pi$
$751$	−470.274	−	814.539i	−0.626198	−	1.08461i	0.362110	−	0.932135i	$-0.382056\pi$
$752$	−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	−0.986123	−	0.166015i	$-0.946910\pi$
$757$	−872.169	−	872.169i	−1.15214	−	1.15214i	−0.166015	−	0.986123i	$-0.553090\pi$
$758$	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	0.674605	−	0.738179i	$-0.264314\pi$
$761$	−229.806	−	398.036i	−0.301979	−	0.523043i	−0.976584	+	0.215136i	$0.930981\pi$
$762$	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	−0.910689	−	0.413092i	$-0.864449\pi$
$769$	−775.372	+	447.661i	−1.00829	+	0.582134i	−0.0975969	+	0.995226i	$0.531116\pi$
$770$		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	−0.765316	−	0.643654i	$-0.777417\pi$
$773$	−94.0446	+	94.0446i	−0.121662	+	0.121662i	0.643654	+	0.765316i	$0.277417\pi$
$774$	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	−0.625315	−	0.780372i	$-0.715030\pi$
$787$	241.144	−	899.963i	0.306410	−	1.14354i	0.931725	−	0.363164i	$-0.118304\pi$
$788$	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	−0.932945	−	0.360019i	$-0.882770\pi$
$797$	43.8496	−	163.649i	0.0550183	−	0.205331i	0.987963	+	0.154687i	$0.0494370\pi$
$798$	−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	$-0.598715\pi$
$809$		−	1540.82i		−	1.90459i	0.305175	−	0.952296i	$-0.401285\pi$
$810$		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	−0.992783	−	0.119927i	$-0.961734\pi$
$821$	−322.268	+	558.185i	−0.392531	+	0.679884i	0.600251	+	0.799811i	$0.295067\pi$
$822$	−210.317	−	477.710i	−0.255860	−	0.581156i
$823$	−211.257	−	56.6061i	−0.256691	−	0.0687802i	0.128179	−	0.991751i	$-0.459087\pi$
$823$	−211.257	−	56.6061i	−0.256691	−	0.0687802i	−0.384870	+	0.922971i	$0.625754\pi$
$824$	−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	0.977522	+	0.210831i	$0.0676170\pi$
$827$	982.768	+	982.768i	1.18835	+	1.18835i	0.210831	+	0.977522i	$0.432383\pi$
$828$	898.759	−	39.6191i	1.08546	−	0.0478492i
$829$		−	763.031i		−	0.920424i	−0.887809	−	0.460212i	$-0.847773\pi$
$829$		−	763.031i		−	0.920424i	0.887809	−	0.460212i	$-0.152227\pi$
$830$		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	0.943457	−	0.331496i	$-0.107553\pi$
$839$	946.477	+	546.449i	1.12810	+	0.651309i	0.184644	+	0.982805i	$0.440887\pi$
$840$		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	−0.507369	−	0.861729i	$-0.669382\pi$
$853$	−425.510	−	1588.02i	−0.498839	−	1.86169i	0.00853057	−	0.999964i	$-0.497285\pi$
$854$			0.914971i			0.00107140i
$855$		0			0
$856$	92.5628			0.108134
$857$	318.230	−	85.2695i	0.371330	−	0.0994977i	−0.0683276	−	0.997663i	$-0.521766\pi$
$857$	318.230	−	85.2695i	0.371330	−	0.0994977i	0.439658	+	0.898165i	$0.355100\pi$
$858$	729.240	+	534.465i	0.849930	+	0.622920i
$859$	−1361.73	+	786.197i	−1.58525	+	0.915247i	−0.591180	+	0.806540i	$0.701338\pi$
$859$	−1361.73	+	786.197i	−1.58525	+	0.915247i	−0.994074	+	0.108707i	$0.965329\pi$
$860$		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	−0.920957	−	0.389665i	$-0.872591\pi$
$863$	−458.505	+	458.505i	−0.531292	+	0.531292i	0.389665	+	0.920957i	$0.372591\pi$
$864$	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	0.602623	+	0.798026i	$0.294122\pi$
$877$	−279.129	+	1041.72i	−0.318277	+	1.18783i	−0.920900	+	0.389800i	$0.872544\pi$
$878$	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	0.148657	−	0.988889i	$-0.452505\pi$
$883$	1004.45	−	1004.45i	1.13755	−	1.13755i	0.988889	−	0.148657i	$-0.0474951\pi$
$884$	−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	−0.996441	−	0.0842901i	$-0.973138\pi$
$887$	−81.0299	+	302.408i	−0.0913528	+	0.340933i	0.905088	+	0.425223i	$0.139804\pi$
$888$	−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	−0.0560100	−	0.998430i	$-0.517838\pi$
$907$	357.992	−	95.9237i	0.394699	−	0.105759i	0.450709	+	0.892671i	$0.351171\pi$
$908$	−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	−0.461051	−	0.887374i	$-0.652527\pi$
$911$	490.084	−	848.851i	0.537963	−	0.931779i	0.999014	−	0.0444052i	$-0.0141393\pi$
$912$	−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	$0.255313\pi$
$919$			1321.17i			1.43762i	−0.695205	+	0.718811i	$0.744687\pi$
$920$		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	0.816105	−	0.577904i	$-0.196129\pi$
$929$	672.297	+	388.151i	0.723678	+	0.417816i	−0.0924267	+	0.995719i	$0.529462\pi$
$930$		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	0.531561	−	0.847020i	$-0.321606\pi$
$937$	−295.586	−	295.586i	−0.315459	−	0.315459i	−0.847020	+	0.531561i	$0.821606\pi$
$938$	−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	0.838929	−	0.544241i	$-0.183182\pi$
$941$	−48.8020	−	84.5275i	−0.0518618	−	0.0898273i	−0.890791	+	0.454413i	$0.849849\pi$
$942$	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	−0.164099	−	0.986444i	$-0.552472\pi$
$947$	177.098	−	47.4532i	0.187009	−	0.0501090i	0.351108	+	0.936335i	$0.385805\pi$
$948$	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	−0.698195	−	0.715908i	$-0.746013\pi$
$953$	16.8810	−	16.8810i	0.0177135	−	0.0177135i	0.715908	+	0.698195i	$0.246013\pi$
$954$	−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	−0.595772	−	0.803153i	$-0.703154\pi$
$967$	311.140	−	1161.19i	0.321758	−	1.20082i	0.917531	−	0.397665i	$-0.130179\pi$
$968$	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	−0.953250	−	0.302183i	$-0.902285\pi$
$977$	22.8425	−	85.2493i	0.0233802	−	0.0872562i	0.976630	+	0.214927i	$0.0689513\pi$
$978$	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	0.852049	+	0.523461i	$0.175360\pi$
$983$	369.494	+	1378.97i	0.375884	+	1.40282i	−0.476166	+	0.879356i	$0.657974\pi$
$984$	−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	−0.368796	−	0.929510i	$-0.620230\pi$
$997$	−222.758	+	59.6878i	−0.223428	+	0.0598674i	0.145368	+	0.989378i	$0.453563\pi$
$998$	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.7.2		40
5.2	odd	4		45.3.k.a.43.2	yes	40
5.3	odd	4	inner	225.3.o.b.43.9		40
5.4	even	2		45.3.k.a.7.9	✓	40
9.4	even	3	inner	225.3.o.b.157.9		40
15.2	even	4		135.3.l.a.73.9		40
15.14	odd	2		135.3.l.a.127.2		40
45.2	even	12		405.3.g.g.163.9		20
45.4	even	6		45.3.k.a.22.2	yes	40
45.7	odd	12		405.3.g.h.163.2		20
45.13	odd	12	inner	225.3.o.b.193.2		40
45.14	odd	6		135.3.l.a.37.9		40
45.22	odd	12		45.3.k.a.13.9	yes	40
45.29	odd	6		405.3.g.g.82.9		20
45.32	even	12		135.3.l.a.118.2		40
45.34	even	6		405.3.g.h.82.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	5.4	even	2
45.3.k.a.13.9	yes	40	45.22	odd	12
45.3.k.a.22.2	yes	40	45.4	even	6
45.3.k.a.43.2	yes	40	5.2	odd	4
135.3.l.a.37.9		40	45.14	odd	6
135.3.l.a.73.9		40	15.2	even	4
135.3.l.a.118.2		40	45.32	even	12
135.3.l.a.127.2		40	15.14	odd	2
225.3.o.b.7.2		40	1.1	even	1	trivial
225.3.o.b.43.9		40	5.3	odd	4	inner
225.3.o.b.157.9		40	9.4	even	3	inner
225.3.o.b.193.2		40	45.13	odd	12	inner
405.3.g.g.82.9		20	45.29	odd	6
405.3.g.g.163.9		20	45.2	even	12
405.3.g.h.82.2		20	45.34	even	6
405.3.g.h.163.2		20	45.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) \) 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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