LMFDB - Embedded newform 225.4.p.b.32.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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([10, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.9
Character	$\chi$	$=$	225.32
Dual form			225.4.p.b.218.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.471331 + 0.126293i) q^{2} +(-3.69630 + 3.65204i) q^{3} +(-6.72200 - 3.88095i) q^{4} +(-2.20341 + 1.25450i) q^{6} +(1.53228 - 5.71856i) q^{7} +(-5.43846 - 5.43846i) q^{8} +(0.325220 - 26.9980i) q^{9} +O(q^{10})$	\(q+(0.471331 + 0.126293i) q^{2} +(-3.69630 + 3.65204i) q^{3} +(-6.72200 - 3.88095i) q^{4} +(-2.20341 + 1.25450i) q^{6} +(1.53228 - 5.71856i) q^{7} +(-5.43846 - 5.43846i) q^{8} +(0.325220 - 26.9980i) q^{9} +(36.3372 - 20.9793i) q^{11} +(39.0199 - 10.2039i) q^{12} +(1.34093 + 5.00442i) q^{13} +(1.44443 - 2.50182i) q^{14} +(29.1711 + 50.5258i) q^{16} +(-70.8600 + 70.8600i) q^{17} +(3.56294 - 12.6839i) q^{18} +136.976i q^{19} +(15.2206 + 26.7334i) q^{21} +(19.7764 - 5.29906i) q^{22} +(2.67644 - 0.717150i) q^{23} +(39.9636 + 0.240693i) q^{24} +2.52809i q^{26} +(97.3958 + 100.980i) q^{27} +(-32.4934 + 32.4934i) q^{28} +(14.4814 + 25.0825i) q^{29} +(93.7536 - 162.386i) q^{31} +(23.2931 + 86.9311i) q^{32} +(-57.6958 + 210.250i) q^{33} +(-42.3476 + 24.4494i) q^{34} +(-106.964 + 180.219i) q^{36} +(223.324 + 223.324i) q^{37} +(-17.2990 + 64.5608i) q^{38} +(-23.2328 - 13.6007i) q^{39} +(226.624 + 130.841i) q^{41} +(3.79771 + 14.5226i) q^{42} +(-187.643 - 50.2787i) q^{43} -325.678 q^{44} +1.35206 q^{46} +(251.467 + 67.3803i) q^{47} +(-292.347 - 80.2245i) q^{48} +(266.693 + 153.975i) q^{49} +(3.13609 - 520.703i) q^{51} +(10.4082 - 38.8438i) q^{52} +(24.8198 + 24.8198i) q^{53} +(33.1526 + 59.8956i) q^{54} +(-39.4334 + 22.7669i) q^{56} +(-500.240 - 506.302i) q^{57} +(3.65779 + 13.6510i) q^{58} +(-26.6691 + 46.1922i) q^{59} +(27.2731 + 47.2385i) q^{61} +(64.6971 - 64.6971i) q^{62} +(-153.892 - 43.2284i) q^{63} -422.823i q^{64} +(-53.7469 + 91.8110i) q^{66} +(-292.789 + 78.4527i) q^{67} +(751.325 - 201.317i) q^{68} +(-7.27386 + 12.4253i) q^{69} +1148.16i q^{71} +(-148.596 + 145.059i) q^{72} +(719.489 - 719.489i) q^{73} +(77.0552 + 133.463i) q^{74} +(531.595 - 920.750i) q^{76} +(-64.2924 - 239.942i) q^{77} +(-9.23268 - 9.34457i) q^{78} +(685.820 - 395.959i) q^{79} +(-728.788 - 17.5606i) q^{81} +(90.2906 + 90.2906i) q^{82} +(-204.035 + 761.471i) q^{83} +(1.43808 - 238.773i) q^{84} +(-82.0919 - 47.3958i) q^{86} +(-145.130 - 39.8257i) q^{87} +(-311.713 - 83.5233i) q^{88} -488.019 q^{89} +30.6728 q^{91} +(-20.7743 - 5.56645i) q^{92} +(246.499 + 942.618i) q^{93} +(110.014 + 63.5169i) q^{94} +(-403.574 - 236.256i) q^{96} +(330.884 - 1234.88i) q^{97} +(106.255 + 106.255i) q^{98} +(-554.582 - 987.855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.471331	+	0.126293i	0.166641	+	0.0446512i	0.341175	−	0.940000i	$-0.389175\pi$
$2$	0.471331	+	0.126293i	0.166641	+	0.0446512i	−0.174534	+	0.984651i	$0.555842\pi$
$3$	−3.69630	+	3.65204i	−0.711353	+	0.702835i
$3$	−3.69630	+	3.65204i	−0.711353	+	0.702835i
$4$	−6.72200	−	3.88095i	−0.840250	−	0.485119i
$5$		0			0
$5$		0			0
$6$	−2.20341	+	1.25450i	−0.149923	+	0.0853582i
$7$	1.53228	−	5.71856i	0.0827355	−	0.308773i	−0.912140	−	0.409878i	$-0.865571\pi$
$7$	1.53228	−	5.71856i	0.0827355	−	0.308773i	0.994876	+	0.101105i	$0.0322378\pi$
$8$	−5.43846	−	5.43846i	−0.240348	−	0.240348i
$9$	0.325220	−	26.9980i	0.0120452	−	0.999927i
$10$		0			0
$11$	36.3372	−	20.9793i	0.996006	−	0.575045i	0.0889422	−	0.996037i	$-0.471651\pi$
$11$	36.3372	−	20.9793i	0.996006	−	0.575045i	0.907064	+	0.420992i	$0.138318\pi$
$12$	39.0199	−	10.2039i	0.938673	−	0.245467i
$13$	1.34093	+	5.00442i	0.0286083	+	0.106767i	0.978754	−	0.205040i	$-0.0657324\pi$
$13$	1.34093	+	5.00442i	0.0286083	+	0.106767i	−0.950145	+	0.311807i	$0.899066\pi$
$14$	1.44443	−	2.50182i	0.0275742	−	0.0477599i
$15$		0			0
$16$	29.1711	+	50.5258i	0.455799	+	0.789466i
$17$	−70.8600	+	70.8600i	−1.01095	+	1.01095i	−0.0110058	+	0.999939i	$0.503503\pi$
$17$	−70.8600	+	70.8600i	−1.01095	+	1.01095i	−0.999939	+	0.0110058i	$0.996497\pi$
$18$	3.56294	−	12.6839i	0.0466552	−	0.166091i
$19$			136.976i			1.65391i	0.562266	+	0.826956i	$0.309930\pi$
$19$			136.976i			1.65391i	−0.562266	+	0.826956i	$0.690070\pi$
$20$		0			0
$21$	15.2206	+	26.7334i	0.158163	+	0.277796i
$22$	19.7764	−	5.29906i	0.191652	−	0.0513529i
$23$	2.67644	−	0.717150i	0.0242642	−	0.00650157i	−0.246667	−	0.969100i	$-0.579335\pi$
$23$	2.67644	−	0.717150i	0.0242642	−	0.00650157i	0.270931	+	0.962599i	$0.412669\pi$
$24$	39.9636	+	0.240693i	0.339897	+	0.00204714i
$25$		0			0
$26$			2.52809i			0.0190692i
$27$	97.3958	+	100.980i	0.694216	+	0.719767i
$28$	−32.4934	+	32.4934i	−0.219310	+	0.219310i
$29$	14.4814	+	25.0825i	0.0927284	+	0.160610i	0.908658	−	0.417541i	$-0.137108\pi$
$29$	14.4814	+	25.0825i	0.0927284	+	0.160610i	−0.815930	+	0.578151i	$0.803775\pi$
$30$		0			0
$31$	93.7536	−	162.386i	0.543182	−	0.940819i	−0.455537	−	0.890217i	$-0.650553\pi$
$31$	93.7536	−	162.386i	0.543182	−	0.940819i	0.998719	−	0.0506018i	$-0.0161139\pi$
$32$	23.2931	+	86.9311i	0.128677	+	0.480231i
$33$	−57.6958	+	210.250i	−0.304350	+	1.10909i
$34$	−42.3476	+	24.4494i	−0.213605	+	0.123325i
$35$		0			0
$36$	−106.964	+	180.219i	−0.495204	+	0.834346i
$37$	223.324	+	223.324i	0.992275	+	0.992275i	0.999970	−	0.00769584i	$-0.00244969\pi$
$37$	223.324	+	223.324i	0.992275	+	0.992275i	−0.00769584	+	0.999970i	$0.502450\pi$
$38$	−17.2990	+	64.5608i	−0.0738493	+	0.275609i
$39$	−23.2328	−	13.6007i	−0.0953905	−	0.0558424i
$40$		0			0
$41$	226.624	+	130.841i	0.863237	+	0.498390i	0.865095	−	0.501608i	$-0.167258\pi$
$41$	226.624	+	130.841i	0.863237	+	0.498390i	−0.00185777	+	0.999998i	$0.500591\pi$
$42$	3.79771	+	14.5226i	0.0139524	+	0.0533543i
$43$	−187.643	−	50.2787i	−0.665470	−	0.178312i	−0.0897568	−	0.995964i	$-0.528609\pi$
$43$	−187.643	−	50.2787i	−0.665470	−	0.178312i	−0.575714	+	0.817651i	$0.695276\pi$
$44$	−325.678			−1.11586
$45$		0			0
$46$	1.35206			0.00433371
$47$	251.467	+	67.3803i	0.780430	+	0.209115i	0.626974	−	0.779040i	$-0.284293\pi$
$47$	251.467	+	67.3803i	0.780430	+	0.209115i	0.153455	+	0.988156i	$0.450960\pi$
$48$	−292.347	−	80.2245i	−0.879098	−	0.241238i
$49$	266.693	+	153.975i	0.777530	+	0.448907i
$50$		0			0
$51$	3.13609	−	520.703i	0.00861061	−	1.42967i
$52$	10.4082	−	38.8438i	0.0277568	−	0.103590i
$53$	24.8198	+	24.8198i	0.0643256	+	0.0643256i	0.738538	−	0.674212i	$-0.235517\pi$
$53$	24.8198	+	24.8198i	0.0643256	+	0.0643256i	−0.674212	+	0.738538i	$0.735517\pi$
$54$	33.1526	+	59.8956i	0.0835461	+	0.150940i
$55$		0			0
$56$	−39.4334	+	22.7669i	−0.0940984	+	0.0543277i
$57$	−500.240	−	506.302i	−1.16243	−	1.17652i
$58$	3.65779	+	13.6510i	0.00828087	+	0.0309046i
$59$	−26.6691	+	46.1922i	−0.0588478	+	0.101927i	−0.893948	−	0.448170i	$-0.852076\pi$
$59$	−26.6691	+	46.1922i	−0.0588478	+	0.101927i	0.835101	+	0.550097i	$0.185409\pi$
$60$		0			0
$61$	27.2731	+	47.2385i	0.0572454	+	0.0991519i	0.893228	−	0.449604i	$-0.148435\pi$
$61$	27.2731	+	47.2385i	0.0572454	+	0.0991519i	−0.835983	+	0.548756i	$0.815102\pi$
$62$	64.6971	−	64.6971i	0.132525	−	0.132525i
$63$	−153.892	−	43.2284i	−0.307754	−	0.0864487i
$64$		−	422.823i		−	0.825826i
$65$		0			0
$66$	−53.7469	+	91.8110i	−0.100239	+	0.171230i
$67$	−292.789	+	78.4527i	−0.533879	+	0.143053i	−0.515679	−	0.856782i	$-0.672460\pi$
$67$	−292.789	+	78.4527i	−0.533879	+	0.143053i	−0.0182002	+	0.999834i	$0.505794\pi$
$68$	751.325	−	201.317i	1.33988	−	0.359018i
$69$	−7.27386	+	12.4253i	−0.0126909	+	0.0216787i
$70$		0			0
$71$			1148.16i			1.91917i	0.281418	+	0.959585i	$0.409195\pi$
$71$			1148.16i			1.91917i	−0.281418	+	0.959585i	$0.590805\pi$
$72$	−148.596	+	145.059i	−0.243226	+	0.237436i
$73$	719.489	−	719.489i	1.15356	−	1.15356i	0.167725	−	0.985834i	$-0.446358\pi$
$73$	719.489	−	719.489i	1.15356	−	1.15356i	0.985834	−	0.167725i	$-0.0536421\pi$
$74$	77.0552	+	133.463i	0.121047	+	0.209660i
$75$		0			0
$76$	531.595	−	920.750i	0.802344	−	1.38970i
$77$	−64.2924	−	239.942i	−0.0951532	−	0.355117i
$78$	−9.23268	−	9.34457i	−0.0134025	−	0.0135649i
$79$	685.820	−	395.959i	0.976719	−	0.563909i	0.0754413	−	0.997150i	$-0.475963\pi$
$79$	685.820	−	395.959i	0.976719	−	0.563909i	0.901278	+	0.433241i	$0.142630\pi$
$80$		0			0
$81$	−728.788	−	17.5606i	−0.999710	−	0.0240886i
$82$	90.2906	+	90.2906i	0.121597	+	0.121597i
$83$	−204.035	+	761.471i	−0.269829	+	1.00702i	0.689399	+	0.724382i	$0.257875\pi$
$83$	−204.035	+	761.471i	−0.269829	+	1.00702i	−0.959228	+	0.282634i	$0.908792\pi$
$84$	1.43808	−	238.773i	0.00186795	−	0.310146i
$85$		0			0
$86$	−82.0919	−	47.3958i	−0.102933	−	0.0594282i
$87$	−145.130	−	39.8257i	−0.178845	−	0.0490778i
$88$	−311.713	−	83.5233i	−0.377599	−	0.101177i
$89$	−488.019			−0.581235			−0.290618	−	0.956839i	$-0.593861\pi$
$89$	−488.019			−0.581235			−0.290618	+	0.956839i	$0.593861\pi$
$90$		0			0
$91$	30.6728			0.0353338
$92$	−20.7743	−	5.56645i	−0.0235420	−	0.00630807i
$93$	246.499	+	942.618i	0.274847	+	1.05102i
$94$	110.014	+	63.5169i	0.120714	+	0.0696943i
$95$		0			0
$96$	−403.574	−	236.256i	−0.429058	−	0.251174i
$97$	330.884	−	1234.88i	0.346353	−	1.29261i	−0.544672	−	0.838649i	$-0.683346\pi$
$97$	330.884	−	1234.88i	0.346353	−	1.29261i	0.891024	−	0.453956i	$-0.149988\pi$
$98$	106.255	+	106.255i	0.109524	+	0.109524i
$99$	−554.582	−	987.855i	−0.563006	−	1.00286i
$100$		0			0
$101$	−290.425	+	167.677i	−0.286122	+	0.165193i	−0.636192	−	0.771531i	$-0.719491\pi$
$101$	−290.425	+	167.677i	−0.286122	+	0.165193i	0.350070	+	0.936724i	$0.386158\pi$
$102$	67.2392	−	245.027i	0.0652713	−	0.237856i
$103$	−152.239	−	568.164i	−0.145636	−	0.543523i	−0.999726	−	0.0233970i	$-0.992552\pi$
$103$	−152.239	−	568.164i	−0.145636	−	0.543523i	0.854090	−	0.520126i	$-0.174115\pi$
$104$	19.9237	−	34.5089i	0.0187854	−	0.0325373i
$105$		0			0
$106$	8.56377	+	14.8329i	0.00784705	+	0.0135915i
$107$	−971.379	+	971.379i	−0.877634	+	0.877634i	−0.993289	−	0.115656i	$-0.963103\pi$
$107$	−971.379	+	971.379i	−0.877634	+	0.877634i	0.115656	+	0.993289i	$0.463103\pi$
$108$	−262.794	−	1056.78i	−0.234143	−	0.941561i
$109$			1394.99i			1.22583i	0.790148	+	0.612916i	$0.210004\pi$
$109$			1394.99i			1.22583i	−0.790148	+	0.612916i	$0.789996\pi$
$110$		0			0
$111$	−1641.06	−	9.88377i	−1.40326	−	0.00845158i
$112$	333.633	−	89.3968i	0.281477	−	0.0754215i
$113$	993.280	−	266.148i	0.826902	−	0.221568i	0.179540	−	0.983751i	$-0.442539\pi$
$113$	993.280	−	266.148i	0.826902	−	0.221568i	0.647362	+	0.762183i	$0.275872\pi$
$114$	−171.836	−	301.813i	−0.141175	−	0.247959i
$115$		0			0
$116$		−	224.806i		−	0.179937i
$117$	135.546	−	34.5750i	0.107104	−	0.0273201i
$118$	−18.4037	+	18.4037i	−0.0143576	+	0.0143576i
$119$	296.639	+	513.795i	0.228512	+	0.395794i
$120$		0			0
$121$	214.760	−	371.976i	0.161352	−	0.279471i
$122$	6.88880	+	25.7094i	0.00511215	+	0.0190788i
$123$	−1315.51	+	344.011i	−0.964352	+	0.252182i
$124$	−1260.42	+	727.706i	−0.912817	+	0.527015i
$125$		0			0
$126$	−67.0744	−	39.8103i	−0.0474243	−	0.0281475i
$127$	−577.252	−	577.252i	−0.403329	−	0.403329i	0.476075	−	0.879405i	$-0.342059\pi$
$127$	−577.252	−	577.252i	−0.403329	−	0.403329i	−0.879405	+	0.476075i	$0.842059\pi$
$128$	239.744	−	894.738i	0.165552	−	0.617847i
$129$	877.202	−	499.433i	0.598708	−	0.340873i
$130$		0			0
$131$	678.256	+	391.591i	0.452363	+	0.261172i	0.708828	−	0.705382i	$-0.249224\pi$
$131$	678.256	+	391.591i	0.452363	+	0.261172i	−0.256465	+	0.966554i	$0.582558\pi$
$132$	1203.80	−	1189.39i	0.793769	−	0.784265i
$133$	783.303	+	209.885i	0.510684	+	0.136837i
$134$	−147.909			−0.0953535
$135$		0			0
$136$	770.738			0.485958
$137$	−2023.48	−	542.190i	−1.26188	−	0.338120i	−0.434966	−	0.900447i	$-0.643240\pi$
$137$	−2023.48	−	542.190i	−1.26188	−	0.338120i	−0.826915	+	0.562327i	$0.809906\pi$
$138$	−4.99762	+	4.93778i	−0.00308279	+	0.00304588i
$139$	446.372	+	257.713i	0.272380	+	0.157258i	0.629969	−	0.776621i	$-0.283068\pi$
$139$	446.372	+	257.713i	0.272380	+	0.157258i	−0.357589	+	0.933879i	$0.616401\pi$
$140$		0			0
$141$	−1175.57	+	669.309i	−0.702134	+	0.399759i
$142$	−145.004	+	541.162i	−0.0856933	+	0.319812i
$143$	153.715	+	153.715i	0.0898900	+	0.0898900i
$144$	1373.59	−	771.131i	0.794899	−	0.446256i
$145$		0			0
$146$	429.984	−	248.251i	0.243738	−	0.140722i
$147$	−1548.10	+	404.834i	−0.868605	+	0.227144i
$148$	−634.474	−	2367.89i	−0.352388	−	1.31513i
$149$	5.67890	−	9.83614i	0.00312237	−	0.00540811i	−0.864460	−	0.502702i	$-0.832339\pi$
$149$	5.67890	−	9.83614i	0.00312237	−	0.00540811i	0.867582	+	0.497294i	$0.165673\pi$
$150$		0			0
$151$	−582.335	−	1008.63i	−0.313839	−	0.543586i	0.665351	−	0.746531i	$-0.268282\pi$
$151$	−582.335	−	1008.63i	−0.313839	−	0.543586i	−0.979190	+	0.202945i	$0.934949\pi$
$152$	744.936	−	744.936i	0.397515	−	0.397515i
$153$	1890.04	+	1936.13i	0.998695	+	1.02305i
$154$		−	121.212i		−	0.0634256i
$155$		0			0
$156$	103.387	+	181.589i	0.0530617	+	0.0931973i
$157$	1985.99	−	532.146i	1.00955	−	0.270509i	0.284110	−	0.958792i	$-0.408302\pi$
$157$	1985.99	−	532.146i	1.00955	−	0.270509i	0.725442	+	0.688283i	$0.241635\pi$
$158$	373.255	−	100.013i	0.187940	−	0.0503585i
$159$	−182.384	−	1.09846i	−0.0909686	−	0.000547886i
$160$		0			0
$161$		−	16.4043i		−	0.00803005i
$162$	−341.283	−	100.318i	−0.165517	−	0.0486524i
$163$	−1397.14	+	1397.14i	−0.671367	+	0.671367i	−0.958031	−	0.286664i	$-0.907454\pi$
$163$	−1397.14	+	1397.14i	−0.671367	+	0.671367i	0.286664	+	0.958031i	$0.407454\pi$
$164$	−1015.58	−	1759.03i	−0.483557	−	0.837545i
$165$		0			0
$166$	−192.336	+	333.137i	−0.0899290	+	0.155762i
$167$	823.744	+	3074.25i	0.381696	+	1.42451i	0.843310	+	0.537427i	$0.180604\pi$
$167$	823.744	+	3074.25i	0.381696	+	1.42451i	−0.461614	+	0.887081i	$0.652730\pi$
$168$	62.6120	−	228.165i	0.0287537	−	0.104782i
$169$	1879.41	−	1085.08i	0.855445	−	0.493891i
$170$		0			0
$171$	3698.07	+	44.5472i	1.65379	+	0.0199217i
$172$	1066.20	+	1066.20i	0.472659	+	0.472659i
$173$	−860.618	+	3211.87i	−0.378217	+	1.41153i	0.470369	+	0.882470i	$0.344121\pi$
$173$	−860.618	+	3211.87i	−0.378217	+	1.41153i	−0.848587	+	0.529057i	$0.822546\pi$
$174$	−63.3744	−	37.0999i	−0.0276115	−	0.0161640i
$175$		0			0
$176$	2119.99	+	1223.98i	0.907957	+	0.524209i
$177$	−70.1189	−	268.137i	−0.0297766	−	0.113867i
$178$	−230.019	−	61.6333i	−0.0968574	−	0.0259529i
$179$	−2843.77			−1.18745			−0.593724	−	0.804669i	$-0.702343\pi$
$179$	−2843.77			−1.18745			−0.593724	+	0.804669i	$0.702343\pi$
$180$		0			0
$181$	1354.23			0.556127			0.278064	−	0.960563i	$-0.410307\pi$
$181$	1354.23			0.556127			0.278064	+	0.960563i	$0.410307\pi$
$182$	14.4570	+	3.87375i	0.00588806	+	0.00157770i
$183$	−273.326	−	75.0048i	−0.110409	−	0.0302979i
$184$	−18.4559	−	10.6555i	−0.00739450	−	0.00426922i
$185$		0			0
$186$	−2.86334	+	475.416i	−0.00112877	+	0.187415i
$187$	−1088.26	+	4061.44i	−0.425569	+	1.58825i
$188$	−1428.86	−	1428.86i	−0.554310	−	0.554310i
$189$	726.701	−	402.233i	0.279681	−	0.154805i
$190$		0			0
$191$	−2327.94	+	1344.03i	−0.881903	+	0.509167i	−0.871285	−	0.490777i	$-0.836713\pi$
$191$	−2327.94	+	1344.03i	−0.881903	+	0.509167i	−0.0106177	+	0.999944i	$0.503380\pi$
$192$	1544.17	+	1562.88i	0.580419	+	0.587453i
$193$	443.701	+	1655.91i	0.165483	+	0.617592i	0.997978	+	0.0635591i	$0.0202451\pi$
$193$	443.701	+	1655.91i	0.165483	+	0.617592i	−0.832495	+	0.554033i	$0.813088\pi$
$194$	311.912	−	540.247i	0.115433	−	0.199936i
$195$		0			0
$196$	−1195.14	−	2070.04i	−0.435546	−	0.754388i
$197$	2756.63	−	2756.63i	0.996964	−	0.996964i	−0.00303165	−	0.999995i	$-0.500965\pi$
$197$	2756.63	−	2756.63i	0.996964	−	0.996964i	0.999995	+	0.00303165i	$0.000965005\pi$
$198$	−136.633	−	535.647i	−0.0490407	−	0.192256i
$199$			485.479i			0.172938i	0.996255	+	0.0864691i	$0.0275584\pi$
$199$			485.479i			0.172938i	−0.996255	+	0.0864691i	$0.972442\pi$
$200$		0			0
$201$	795.724	−	1359.26i	0.279234	−	0.476990i
$202$	−158.063	+	42.3528i	−0.0550557	+	0.0147521i
$203$	165.625	−	44.3791i	0.0572641	−	0.0153439i
$204$	−2041.90	+	3487.99i	−0.700793	+	1.19710i
$205$		0			0
$206$		−	287.020i		−	0.0970758i
$207$	−18.4912	−	72.4919i	−0.00620884	−	0.0243408i
$208$	−213.736	+	213.736i	−0.0712497	+	0.0712497i
$209$	2873.65	+	4977.30i	0.951074	+	1.64731i
$210$		0			0
$211$	−933.004	+	1616.01i	−0.304411	+	0.527254i	−0.977130	−	0.212643i	$-0.931793\pi$
$211$	−933.004	+	1616.01i	−0.304411	+	0.527254i	0.672719	+	0.739898i	$0.265126\pi$
$212$	−70.5143	−	263.163i	−0.0228441	−	0.0852552i
$213$	−4193.11	−	4243.93i	−1.34886	−	1.36521i
$214$	−580.520	+	335.163i	−0.185437	+	0.107062i
$215$		0			0
$216$	19.4952	−	1078.86i	0.00614112	−	0.339848i
$217$	−784.957	−	784.957i	−0.245559	−	0.245559i
$218$	−176.177	+	657.502i	−0.0547350	+	0.204274i
$219$	−31.8429	+	5287.05i	−0.00982530	+	1.63135i
$220$		0			0
$221$	−449.632	−	259.595i	−0.136857	−	0.0790147i
$222$	−772.232	−	211.912i	−0.233463	−	0.0640658i
$223$	−56.7455	−	15.2049i	−0.0170402	−	0.00456590i	0.250289	−	0.968171i	$-0.419474\pi$
$223$	−56.7455	−	15.2049i	−0.0170402	−	0.00456590i	−0.267329	+	0.963605i	$0.586141\pi$
$224$	532.812			0.158929
$225$		0			0
$226$	501.776			0.147689
$227$	2577.66	+	690.683i	0.753681	+	0.201948i	0.615150	−	0.788410i	$-0.289095\pi$
$227$	2577.66	+	690.683i	0.753681	+	0.201948i	0.138531	+	0.990358i	$0.455762\pi$
$228$	1397.68	+	5344.77i	0.405981	+	1.55248i
$229$	−2556.44	−	1475.96i	−0.737706	−	0.425914i	0.0835289	−	0.996505i	$-0.473381\pi$
$229$	−2556.44	−	1475.96i	−0.737706	−	0.425914i	−0.821234	+	0.570591i	$0.806714\pi$
$230$		0			0
$231$	1113.92	+	652.100i	0.317276	+	0.185736i
$232$	57.6536	−	215.166i	0.0163153	−	0.0608895i
$233$	−1491.42	−	1491.42i	−0.419340	−	0.419340i	0.465636	−	0.884976i	$-0.345826\pi$
$233$	−1491.42	−	1491.42i	−0.419340	−	0.419340i	−0.884976	+	0.465636i	$0.845826\pi$
$234$	68.2535	+	0.822185i	0.0190678	+	0.000229692i
$235$		0			0
$236$	358.539	−	207.003i	0.0988937	−	0.0570963i
$237$	−1088.94	+	3968.22i	−0.298457	+	1.08761i
$238$	74.9268	+	279.631i	0.0204067	+	0.0761587i
$239$	−171.393	+	296.862i	−0.0463870	+	0.0803447i	−0.888287	−	0.459289i	$-0.848104\pi$
$239$	−171.393	+	296.862i	−0.0463870	+	0.0803447i	0.841900	+	0.539634i	$0.181437\pi$
$240$		0			0
$241$	2323.76	+	4024.86i	0.621105	+	1.07579i	0.989280	+	0.146029i	$0.0466493\pi$
$241$	2323.76	+	4024.86i	0.621105	+	1.07579i	−0.368175	+	0.929756i	$0.620017\pi$
$242$	148.201	−	148.201i	0.0393666	−	0.0393666i
$243$	2757.95	−	2596.65i	0.728077	−	0.685496i
$244$		−	423.383i		−	0.111083i
$245$		0			0
$246$	−663.486	−	3.99605i	−0.171961	−	0.00103569i
$247$	−685.483	+	183.675i	−0.176584	+	0.0473156i
$248$	−1393.00	+	373.254i	−0.356677	+	0.0955713i
$249$	−2026.75	−	3559.77i	−0.515822	−	0.905988i
$250$		0			0
$251$		−	6326.15i		−	1.59085i	−0.606053	−	0.795424i	$-0.707248\pi$
$251$		−	6326.15i		−	1.59085i	0.606053	−	0.795424i	$-0.292752\pi$
$252$	866.692	+	887.827i	0.216653	+	0.221936i
$253$	82.2090	−	82.2090i	0.0204286	−	0.0204286i
$254$	−199.174	−	344.980i	−0.0492019	−	0.0852203i
$255$		0			0
$256$	−1465.29	+	2537.96i	−0.357738	+	0.619620i
$257$	629.092	+	2347.80i	0.152691	+	0.569852i	0.999292	+	0.0376231i	$0.0119786\pi$
$257$	629.092	+	2347.80i	0.152691	+	0.569852i	−0.846601	+	0.532229i	$0.821355\pi$
$258$	476.528	−	124.614i	0.114990	−	0.0300703i
$259$	1619.28	−	934.894i	0.388484	−	0.224291i
$260$		0			0
$261$	681.887	−	382.811i	0.161716	−	0.0907871i
$262$	270.228	+	270.228i	0.0637204	+	0.0637204i
$263$	181.061	−	675.727i	0.0424512	−	0.158430i	−0.941447	−	0.337162i	$-0.890533\pi$
$263$	181.061	−	675.727i	0.0424512	−	0.158430i	0.983898	+	0.178732i	$0.0571996\pi$
$264$	1457.21	−	829.662i	0.339717	−	0.193417i
$265$		0			0
$266$	342.688	+	197.851i	0.0789908	+	0.0456053i
$267$	1803.86	−	1782.27i	0.413463	−	0.408513i
$268$	2272.60	+	608.942i	0.517990	+	0.138795i
$269$	4742.28			1.07488			0.537438	−	0.843303i	$-0.319392\pi$
$269$	4742.28			1.07488			0.537438	+	0.843303i	$0.319392\pi$
$270$		0			0
$271$	−1142.59			−0.256116			−0.128058	−	0.991767i	$-0.540874\pi$
$271$	−1142.59			−0.256116			−0.128058	+	0.991767i	$0.540874\pi$
$272$	−5647.32	−	1513.20i	−1.25889	−	0.337320i
$273$	−113.376	+	112.018i	−0.0251348	+	0.0248339i
$274$	−885.255	−	511.102i	−0.195183	−	0.112689i
$275$		0			0
$276$	97.1167	−	55.2932i	0.0211802	−	0.0120589i
$277$	2132.03	−	7956.83i	0.462459	−	1.72592i	−0.202721	−	0.979237i	$-0.564978\pi$
$277$	2132.03	−	7956.83i	0.462459	−	1.72592i	0.665180	−	0.746683i	$-0.268355\pi$
$278$	177.842	+	177.842i	0.0383677	+	0.0383677i
$279$	−4353.61	−	2583.97i	−0.934208	−	0.554475i
$280$		0			0
$281$	−1119.69	+	646.452i	−0.237704	+	0.137239i	−0.614121	−	0.789212i	$-0.710489\pi$
$281$	−1119.69	+	646.452i	−0.237704	+	0.137239i	0.376417	+	0.926450i	$0.377156\pi$
$282$	−638.612	+	167.000i	−0.134854	+	0.0352649i
$283$	1511.67	+	5641.62i	0.317524	+	1.18502i	0.921616	+	0.388102i	$0.126869\pi$
$283$	1511.67	+	5641.62i	0.317524	+	1.18502i	−0.604092	+	0.796914i	$0.706464\pi$
$284$	4455.94	−	7717.91i	0.931025	−	1.61258i
$285$		0			0
$286$	53.0375	+	91.8636i	0.0109656	+	0.0189930i
$287$	1095.48	−	1095.48i	0.225310	−	0.225310i
$288$	2354.54	−	600.597i	0.481746	−	0.122884i
$289$		−	5129.27i		−	1.04402i
$290$		0			0
$291$	3286.77	+	5772.87i	0.662110	+	1.16293i
$292$	−7628.70	+	2044.10i	−1.52889	+	0.409665i
$293$	4784.30	−	1281.95i	0.953931	−	0.255605i	0.251901	−	0.967753i	$-0.418944\pi$
$293$	4784.30	−	1281.95i	0.953931	−	0.255605i	0.702029	+	0.712148i	$0.252278\pi$
$294$	−780.795	−	4.70258i	−0.154887	−	0.000932857i
$295$		0			0
$296$		−	2429.07i		−	0.476983i
$297$	5657.59	+	1626.05i	1.10534	+	0.317687i
$298$	3.91887	−	3.91887i	0.000761793	−	0.000761793i
$299$	7.17785	+	12.4324i	0.00138831	+	0.00240463i
$300$		0			0
$301$	−575.043	+	996.004i	−0.110116	+	0.190727i
$302$	−147.089	−	548.945i	−0.0280266	−	0.104597i
$303$	461.134	−	1680.43i	0.0874305	−	0.318607i
$304$	−6920.81	+	3995.73i	−1.30571	+	0.753851i
$305$		0			0
$306$	646.314	+	1151.25i	0.120743	+	0.215075i
$307$	−4710.15	−	4710.15i	−0.875644	−	0.875644i	0.117437	−	0.993080i	$-0.462532\pi$
$307$	−4710.15	−	4710.15i	−0.875644	−	0.875644i	−0.993080	+	0.117437i	$0.962532\pi$
$308$	−499.031	+	1862.41i	−0.0923212	+	0.344547i
$309$	2637.68	+	1544.12i	0.485606	+	0.284278i
$310$		0			0
$311$	−6261.22	−	3614.92i	−1.14161	−	0.659110i	−0.194783	−	0.980846i	$-0.562400\pi$
$311$	−6261.22	−	3614.92i	−1.14161	−	0.659110i	−0.946829	+	0.321736i	$0.895734\pi$
$312$	52.3839	+	200.318i	0.00950530	+	0.0363485i
$313$	−792.984	−	212.480i	−0.143202	−	0.0383708i	0.186506	−	0.982454i	$-0.440284\pi$
$313$	−792.984	−	212.480i	−0.143202	−	0.0383708i	−0.329708	+	0.944083i	$0.606950\pi$
$314$	1003.27			0.180311
$315$		0			0
$316$	−6146.78			−1.09425
$317$	−6609.48	−	1771.00i	−1.17106	−	0.313784i	−0.379684	−	0.925116i	$-0.623967\pi$
$317$	−6609.48	−	1771.00i	−1.17106	−	0.313784i	−0.791374	+	0.611332i	$0.790634\pi$
$318$	−85.8246	−	23.5515i	−0.0151346	−	0.00415316i
$319$	1052.42	+	607.617i	0.184716	+	0.106646i
$320$		0			0
$321$	42.9909	−	7138.02i	0.00747514	−	1.24114i
$322$	2.07174	−	7.73184i	0.000358552	−	0.00133813i
$323$	−9706.08	−	9706.08i	−1.67202	−	1.67202i
$324$	4830.76	+	2946.43i	0.828320	+	0.505218i
$325$		0			0
$326$	−834.967	+	482.068i	−0.141854	+	0.0818997i
$327$	−5094.56	−	5156.30i	−0.861559	−	0.871999i
$328$	−520.910	−	1944.06i	−0.0876903	−	0.327265i
$329$	770.636	−	1334.78i	0.129138	−	0.223674i
$330$		0			0
$331$	1573.67	+	2725.68i	0.261320	+	0.452619i	0.966593	−	0.256317i	$-0.0825090\pi$
$331$	1573.67	+	2725.68i	0.261320	+	0.452619i	−0.705273	+	0.708936i	$0.749176\pi$
$332$	4326.76	−	4326.76i	0.715246	−	0.715246i
$333$	6101.93	−	5956.67i	1.00415	−	0.980250i
$334$			1553.02i			0.254424i
$335$		0			0
$336$	−906.728	+	1548.88i	−0.147220	+	0.251483i
$337$	2268.47	−	607.833i	0.366680	−	0.0982516i	−0.0707740	−	0.997492i	$-0.522547\pi$
$337$	2268.47	−	607.833i	0.366680	−	0.0982516i	0.437454	+	0.899241i	$0.355880\pi$
$338$	1022.86	−	274.075i	0.164605	−	0.0441057i
$339$	−2699.47	+	4611.26i	−0.432493	+	0.738788i
$340$		0			0
$341$		−	7867.53i		−	1.24942i
$342$	1737.39	+	488.036i	0.274700	+	0.0771637i
$343$	2725.06	−	2725.06i	0.428977	−	0.428977i
$344$	747.048	+	1293.92i	0.117088	+	0.202802i
$345$		0			0
$346$	−811.272	+	1405.16i	−0.126053	+	0.218330i
$347$	−477.316	−	1781.37i	−0.0738434	−	0.275587i	0.919125	−	0.393966i	$-0.128897\pi$
$347$	−477.316	−	1781.37i	−0.0738434	−	0.275587i	−0.992969	+	0.118378i	$0.962230\pi$
$348$	821.000	+	830.949i	0.126466	+	0.127999i
$349$	2408.12	−	1390.33i	0.369351	−	0.213245i	−0.303824	−	0.952728i	$-0.598263\pi$
$349$	2408.12	−	1390.33i	0.369351	−	0.213245i	0.673175	+	0.739483i	$0.264930\pi$
$350$		0			0
$351$	−374.748	+	622.817i	−0.0569874	+	0.0947109i
$352$	2670.16	+	2670.16i	0.404318	+	0.404318i
$353$	−524.320	+	1956.79i	−0.0790559	+	0.295041i	−0.994122	−	0.108263i	$-0.965471\pi$
$353$	−524.320	+	1956.79i	−0.0790559	+	0.295041i	0.915066	+	0.403303i	$0.132138\pi$
$354$	0.814504	−	135.237i	0.000122289	−	0.0203044i
$355$		0			0
$356$	3280.47	+	1893.98i	0.488383	+	0.281968i
$357$	−2972.86	−	815.798i	−0.440730	−	0.120943i
$358$	−1340.36	−	359.147i	−0.197877	−	0.0530210i
$359$	−11693.7			−1.71914			−0.859572	−	0.511015i	$-0.829270\pi$
$359$	−11693.7			−1.71914			−0.859572	+	0.511015i	$0.829270\pi$
$360$		0			0
$361$	−11903.3			−1.73543
$362$	638.290	+	171.029i	0.0926734	+	0.0248318i
$363$	564.652	+	2159.24i	0.0816434	+	0.312206i
$364$	−206.182	−	119.039i	−0.0296893	−	0.0171411i
$365$		0			0
$366$	−119.355	−	69.8712i	−0.0170458	−	0.00997876i
$367$	−2113.84	+	7888.96i	−0.300658	+	1.12207i	0.635961	+	0.771722i	$0.280604\pi$
$367$	−2113.84	+	7888.96i	−0.300658	+	1.12207i	−0.936619	+	0.350350i	$0.886063\pi$
$368$	114.309	+	114.309i	0.0161924	+	0.0161924i
$369$	3606.17	−	6075.85i	0.508752	−	0.857171i
$370$		0			0
$371$	179.964	−	103.902i	0.0251840	−	0.0145400i
$372$	2001.29	−	7292.93i	0.278930	−	1.01645i
$373$	2015.68	+	7522.61i	0.279806	+	1.04425i	0.952552	+	0.304377i	$0.0984483\pi$
$373$	2015.68	+	7522.61i	0.279806	+	1.04425i	−0.672745	+	0.739874i	$0.734885\pi$
$374$	−1025.86	+	1776.84i	−0.141834	+	0.245664i
$375$		0			0
$376$	−1001.15	−	1734.04i	−0.137314	−	0.237835i
$377$	−106.105	+	106.105i	−0.0144952	+	0.0144952i
$378$	393.316	−	97.8078i	0.0535185	−	0.0133087i
$379$		−	989.896i		−	0.134162i	−0.997748	−	0.0670812i	$-0.978631\pi$
$379$		−	989.896i		−	0.134162i	0.997748	−	0.0670812i	$-0.0213687\pi$
$380$		0			0
$381$	4241.84	+	25.5478i	0.570384	+	0.00343531i
$382$	−1266.97	+	339.484i	−0.169696	+	0.0454699i
$383$	−833.905	+	223.444i	−0.111255	+	0.0298106i	−0.314017	−	0.949417i	$-0.601675\pi$
$383$	−833.905	+	223.444i	−0.111255	+	0.0298106i	0.202762	+	0.979228i	$0.435008\pi$
$384$	2381.45	+	4182.77i	0.316479	+	0.555863i
$385$		0			0
$386$			836.520i			0.110305i
$387$	−1418.45	+	5049.63i	−0.186315	+	0.663274i
$388$	−7016.70	+	7016.70i	−0.918090	+	0.918090i
$389$	82.6486	+	143.152i	0.0107724	+	0.0186583i	0.871361	−	0.490642i	$-0.163238\pi$
$389$	82.6486	+	143.152i	0.0107724	+	0.0186583i	−0.860589	+	0.509300i	$0.829904\pi$
$390$		0			0
$391$	−138.835	+	240.470i	−0.0179570	+	0.0311025i
$392$	−613.010	−	2287.78i	−0.0789839	−	0.294772i
$393$	−3937.14	+	1029.58i	−0.505350	+	0.132151i
$394$	1647.43	−	951.143i	0.210650	−	0.121619i
$395$		0			0
$396$	−105.917	+	8792.67i	−0.0134407	+	1.11578i
$397$	5029.27	+	5029.27i	0.635798	+	0.635798i	0.949516	−	0.313718i	$-0.101575\pi$
$397$	5029.27	+	5029.27i	0.635798	+	0.635798i	−0.313718	+	0.949516i	$0.601575\pi$
$398$	−61.3125	+	228.821i	−0.00772191	+	0.0288186i
$399$	−3661.83	+	2084.85i	−0.459450	+	0.261587i
$400$		0			0
$401$	−2100.87	−	1212.94i	−0.261627	−	0.151050i	0.363450	−	0.931614i	$-0.381599\pi$
$401$	−2100.87	−	1212.94i	−0.261627	−	0.151050i	−0.625076	+	0.780564i	$0.714932\pi$
$402$	546.715	−	540.168i	0.0678300	−	0.0670178i
$403$	938.365	+	251.434i	0.115988	+	0.0310790i
$404$	2602.98			0.320552
$405$		0			0
$406$	83.6690			0.0102276
$407$	12800.1	+	3429.78i	1.55891	+	0.417710i
$408$	−2848.88	+	2814.77i	−0.345687	+	0.341548i
$409$	−3256.06	−	1879.89i	−0.393647	−	0.227272i	0.290092	−	0.956999i	$-0.406314\pi$
$409$	−3256.06	−	1879.89i	−0.393647	−	0.227272i	−0.683739	+	0.729726i	$0.739647\pi$
$410$		0			0
$411$	9459.49	−	5385.74i	1.13529	−	0.646372i
$412$	−1181.66	+	4410.03i	−0.141302	+	0.527346i
$413$	223.288	+	223.288i	0.0266036	+	0.0266036i
$414$	0.439717	−	36.5030i	5.22003e−5	−	0.00433339i
$415$		0			0
$416$	−403.805	+	233.137i	−0.0475918	+	0.0274771i
$417$	−2591.10	+	677.584i	−0.304285	+	0.0795718i
$418$	725.842	+	2708.88i	0.0849332	+	0.316975i
$419$	4357.50	−	7547.42i	0.508062	−	0.879989i	−0.491894	−	0.870655i	$-0.663695\pi$
$419$	4357.50	−	7547.42i	0.508062	−	0.879989i	0.999956	−	0.00933453i	$-0.00297132\pi$
$420$		0			0
$421$	3301.73	+	5718.76i	0.382224	+	0.662031i	0.991380	−	0.131019i	$-0.0418250\pi$
$421$	3301.73	+	5718.76i	0.382224	+	0.662031i	−0.609156	+	0.793050i	$0.708492\pi$
$422$	−643.844	+	643.844i	−0.0742697	+	0.0742697i
$423$	1900.92	−	6767.20i	0.218501	−	0.777854i
$424$		−	269.963i		−	0.0309211i
$425$		0			0
$426$	−1440.37	−	2529.85i	−0.163817	−	0.287727i
$427$	311.926	−	83.5803i	0.0353517	−	0.00947245i
$428$	10299.5	−	2759.74i	1.16319	−	0.311675i
$429$	−1129.55	−	6.80305i	−0.127121	−	0.000765628i
$430$		0			0
$431$			13342.2i			1.49112i	0.666439	+	0.745559i	$0.267817\pi$
$431$			13342.2i			1.49112i	−0.666439	+	0.745559i	$0.732183\pi$
$432$	−2260.98	+	7866.72i	−0.251809	+	0.876129i
$433$	5872.34	−	5872.34i	0.651748	−	0.651748i	−0.301666	−	0.953414i	$-0.597543\pi$
$433$	5872.34	−	5872.34i	0.651748	−	0.651748i	0.953414	+	0.301666i	$0.0975428\pi$
$434$	−270.840	−	469.109i	−0.0299556	−	0.0518847i
$435$		0			0
$436$	5413.88	−	9377.12i	0.594674	−	1.03001i
$437$	98.2321	+	366.607i	0.0107530	+	0.0401309i
$438$	−682.724	+	2487.93i	−0.0744790	+	0.271410i
$439$	3389.85	−	1957.13i	0.368539	−	0.212776i	−0.304281	−	0.952582i	$-0.598416\pi$
$439$	3389.85	−	1957.13i	0.368539	−	0.212776i	0.672820	+	0.739806i	$0.265083\pi$
$440$		0			0
$441$	4243.76	−	7150.10i	0.458240	−	0.772066i
$442$	−179.140	−	179.140i	−0.0192779	−	0.0192779i
$443$	−3230.55	+	12056.6i	−0.346475	+	1.29306i	0.544406	+	0.838822i	$0.316755\pi$
$443$	−3230.55	+	12056.6i	−0.346475	+	1.29306i	−0.890880	+	0.454239i	$0.849911\pi$
$444$	10992.8	+	6435.29i	1.17499	+	0.687850i
$445$		0			0
$446$	−24.8257	−	14.3331i	−0.00263572	−	0.00152173i
$447$	14.9311	+	57.0969i	0.00157990	+	0.00604159i
$448$	−2417.94	−	647.884i	−0.254993	−	0.0683251i
$449$	−4009.66			−0.421442			−0.210721	−	0.977546i	$-0.567581\pi$
$449$	−4009.66			−0.421442			−0.210721	+	0.977546i	$0.567581\pi$
$450$		0			0
$451$	10979.8			1.14639
$452$	−7709.73	−	2065.82i	−0.802291	−	0.214973i
$453$	5836.05	+	1601.50i	0.605301	+	0.166104i
$454$	1127.70	+	651.081i	0.116577	+	0.0673056i
$455$		0			0
$456$	−32.9691	+	5474.04i	−0.00338579	+	0.562161i
$457$	2764.21	−	10316.2i	0.282942	−	1.05595i	−0.667389	−	0.744709i	$-0.732588\pi$
$457$	2764.21	−	10316.2i	0.282942	−	1.05595i	0.950330	−	0.311243i	$-0.100745\pi$
$458$	−1018.53	−	1018.53i	−0.103914	−	0.103914i
$459$	−14056.9	−	254.011i	−1.42946	−	0.0258306i
$460$		0			0
$461$	4629.56	−	2672.88i	0.467723	−	0.270040i	−0.247563	−	0.968872i	$-0.579630\pi$
$461$	4629.56	−	2672.88i	0.467723	−	0.270040i	0.715286	+	0.698832i	$0.246296\pi$
$462$	442.671	+	448.036i	0.0445777	+	0.0451180i
$463$	−4883.83	−	18226.7i	−0.490217	−	1.82952i	−0.555319	−	0.831638i	$-0.687404\pi$
$463$	−4883.83	−	18226.7i	−0.490217	−	1.82952i	0.0651012	−	0.997879i	$-0.479263\pi$
$464$	−844.875	+	1463.37i	−0.0845309	+	0.146412i
$465$		0			0
$466$	−514.597	−	891.309i	−0.0511551	−	0.0886032i
$467$	−1782.80	+	1782.80i	−0.176656	+	0.176656i	−0.789896	−	0.613241i	$-0.789866\pi$
$467$	−1782.80	+	1782.80i	−0.176656	+	0.176656i	0.613241	+	0.789896i	$0.289866\pi$
$468$	−1045.32	−	293.633i	−0.103248	−	0.0290025i
$469$			1794.54i			0.176683i
$470$		0			0
$471$	−5397.41	+	9219.90i	−0.528024	+	0.901976i
$472$	396.253	−	106.176i	0.0386420	−	0.0103541i
$473$	−7873.21	+	2109.62i	−0.765350	+	0.205075i
$474$	−1014.41	+	1732.82i	−0.0982982	+	0.167914i
$475$		0			0
$476$		−	4604.97i		−	0.443421i
$477$	678.157	−	662.014i	0.0650958	−	0.0635462i
$478$	−118.274	+	118.274i	−0.0113175	+	0.0113175i
$479$	9007.84	+	15602.0i	0.859245	+	1.48826i	0.872650	+	0.488346i	$0.162400\pi$
$479$	9007.84	+	15602.0i	0.859245	+	1.48826i	−0.0134045	+	0.999910i	$0.504267\pi$
$480$		0			0
$481$	−818.144	+	1417.07i	−0.0775554	+	0.134330i
$482$	586.947	+	2190.52i	0.0554662	+	0.207003i
$483$	59.9090	+	60.6350i	0.00564380	+	0.00571220i
$484$	−2887.24	+	1666.95i	−0.271153	+	0.156550i
$485$		0			0
$486$	1627.85	−	875.575i	0.151935	−	0.0817220i
$487$	−1062.70	−	1062.70i	−0.0988823	−	0.0988823i	0.655935	−	0.754817i	$-0.272275\pi$
$487$	−1062.70	−	1062.70i	−0.0988823	−	0.0988823i	−0.754817	+	0.655935i	$0.772275\pi$
$488$	108.581	−	405.228i	0.0100722	−	0.0375898i
$489$	61.8343	−	10266.7i	0.00571829	−	0.949439i
$490$		0			0
$491$	7535.78	+	4350.79i	0.692638	+	0.399895i	0.804599	−	0.593818i	$-0.202380\pi$
$491$	7535.78	+	4350.79i	0.692638	+	0.399895i	−0.111962	+	0.993713i	$0.535713\pi$
$492$	10177.9	+	2792.98i	0.932635	+	0.255929i
$493$	−2803.49	−	751.194i	−0.256112	−	0.0686249i
$494$	−346.286			−0.0315388
$495$		0			0
$496$	10939.6			0.990326
$497$	6565.80	+	1759.30i	0.592588	+	0.158784i
$498$	−505.695	−	1933.79i	−0.0455035	−	0.174007i
$499$	7621.49	+	4400.27i	0.683737	+	0.394756i	0.801262	−	0.598314i	$-0.204163\pi$
$499$	7621.49	+	4400.27i	0.683737	+	0.394756i	−0.117525	+	0.993070i	$0.537496\pi$
$500$		0			0
$501$	−14272.1	−	8355.01i	−1.27271	−	0.745058i
$502$	798.947	−	2981.71i	0.0710333	−	0.265100i
$503$	−2500.57	−	2500.57i	−0.221660	−	0.221660i	0.587537	−	0.809197i	$-0.300098\pi$
$503$	−2500.57	−	2500.57i	−0.221660	−	0.221660i	−0.809197	+	0.587537i	$0.800098\pi$
$504$	601.837	+	1072.03i	0.0531904	+	0.0947459i
$505$		0			0
$506$	49.1301	−	28.3653i	0.00431640	−	0.00249207i
$507$	−2984.11	+	10874.5i	−0.261399	+	0.952567i
$508$	1640.00	+	6120.57i	0.143235	+	0.534560i
$509$	−7173.58	+	12425.0i	−0.624683	+	1.08198i	0.363920	+	0.931430i	$0.381438\pi$
$509$	−7173.58	+	12425.0i	−0.624683	+	1.08198i	−0.988602	+	0.150551i	$0.951895\pi$
$510$		0			0
$511$	−3011.98	−	5216.90i	−0.260748	−	0.451628i
$512$	−6251.11	+	6251.11i	−0.539576	+	0.539576i
$513$	−13831.9	+	13340.8i	−1.19043	+	1.14817i
$514$			1186.04i			0.101778i
$515$		0			0
$516$	−7834.83	−	47.1877i	−0.668429	−	0.00402582i
$517$	10551.2	−	2827.18i	0.897564	−	0.240501i
$518$	881.289	−	236.141i	0.0747521	−	0.0200298i
$519$	−8548.78	−	15015.0i	−0.723025	−	1.26992i
$520$		0			0
$521$			7742.56i			0.651071i	0.945530	+	0.325535i	$0.105545\pi$
$521$			7742.56i			0.651071i	−0.945530	+	0.325535i	$0.894455\pi$
$522$	369.741	−	94.3134i	0.0310021	−	0.00790802i
$523$	−4506.88	+	4506.88i	−0.376811	+	0.376811i	−0.869950	−	0.493139i	$-0.835849\pi$
$523$	−4506.88	+	4506.88i	−0.376811	+	0.376811i	0.493139	+	0.869950i	$0.335849\pi$
$524$	−3039.49	−	5264.56i	−0.253399	−	0.438899i
$525$		0			0
$526$	170.679	−	295.624i	0.0141482	−	0.0245054i
$527$	4863.29	+	18150.0i	0.401989	+	1.50024i
$528$	−12306.1	+	3218.11i	−1.01431	+	0.265246i
$529$	−10530.3	+	6079.66i	−0.865479	+	0.499684i
$530$		0			0
$531$	1238.43	+	735.036i	0.101211	+	0.0600712i
$532$	−4450.81	−	4450.81i	−0.362720	−	0.362720i
$533$	−350.899	+	1309.57i	−0.0285161	+	0.106424i
$534$	1075.30	−	612.222i	0.0871404	−	0.0496132i
$535$		0			0
$536$	2018.98	+	1165.66i	0.162699	+	0.0939345i
$537$	10511.4	−	10385.5i	0.844694	−	0.834580i
$538$	2235.18	+	598.915i	0.179118	+	0.0479946i
$539$	12921.1			1.03257
$540$		0			0
$541$	16576.9			1.31737			0.658683	−	0.752421i	$-0.271114\pi$
$541$	16576.9			1.31737			0.658683	+	0.752421i	$0.271114\pi$
$542$	−538.537	−	144.301i	−0.0426793	−	0.0114359i
$543$	−5005.63	+	4945.70i	−0.395603	+	0.390866i
$544$	−7810.48	−	4509.38i	−0.615573	−	0.355401i
$545$		0			0
$546$	−67.5845	+	38.4791i	−0.00529735	+	0.00301603i
$547$	421.476	−	1572.97i	0.0329452	−	0.122953i	−0.947495	−	0.319771i	$-0.896394\pi$
$547$	421.476	−	1572.97i	0.0329452	−	0.122953i	0.980440	+	0.196818i	$0.0630607\pi$
$548$	11497.6	+	11497.6i	0.896267	+	0.896267i
$549$	1284.22	−	720.958i	0.0998342	−	0.0560469i
$550$		0			0
$551$	−3435.69	+	1983.59i	−0.265635	+	0.153365i
$552$	107.133	−	28.0157i	0.00826065	−	0.00216020i
$553$	−1213.44	−	4528.63i	−0.0933106	−	0.348240i
$554$	2009.78	−	3481.04i	0.154129	−	0.266959i
$555$		0			0
$556$	−2000.34	−	3464.69i	−0.152578	−	0.264273i
$557$	−1176.10	+	1176.10i	−0.0894671	+	0.0894671i	−0.750424	−	0.660957i	$-0.770151\pi$
$557$	−1176.10	+	1176.10i	−0.0894671	+	0.0894671i	0.660957	+	0.750424i	$0.270151\pi$
$558$	−1725.66	−	1767.74i	−0.130919	−	0.134112i
$559$		−	1006.46i		−	0.0761518i
$560$		0			0
$561$	−10810.0	−	18986.7i	−0.813546	−	1.42891i
$562$	−609.385	+	163.284i	−0.0457391	+	0.0122558i
$563$	13347.9	−	3576.55i	0.999193	−	0.267733i	0.278086	−	0.960556i	$-0.410300\pi$
$563$	13347.9	−	3576.55i	0.999193	−	0.267733i	0.721107	+	0.692823i	$0.243633\pi$
$564$	10499.7	+	63.2379i	0.783899	+	0.00472127i
$565$		0			0
$566$			2849.98i			0.211650i
$567$	−1217.13	+	4140.71i	−0.0901494	+	0.306691i
$568$	6244.20	−	6244.20i	0.461269	−	0.461269i
$569$	−597.719	−	1035.28i	−0.0440381	−	0.0762762i	0.843166	−	0.537653i	$-0.180689\pi$
$569$	−597.719	−	1035.28i	−0.0440381	−	0.0762762i	−0.887204	+	0.461377i	$0.847356\pi$
$570$		0			0
$571$	−4009.75	+	6945.09i	−0.293875	+	0.509007i	−0.974723	−	0.223418i	$-0.928278\pi$
$571$	−4009.75	+	6945.09i	−0.293875	+	0.509007i	0.680847	+	0.732425i	$0.261612\pi$
$572$	−436.712	−	1629.83i	−0.0319228	−	0.119137i
$573$	3696.27	−	13469.7i	0.269484	−	0.982030i
$574$	654.683	−	377.981i	0.0476062	−	0.0274854i
$575$		0			0
$576$	−11415.4	−	137.510i	−0.825766	−	0.00994722i
$577$	654.061	+	654.061i	0.0471905	+	0.0471905i	0.730308	−	0.683118i	$-0.239376\pi$
$577$	654.061	+	654.061i	0.0471905	+	0.0471905i	−0.683118	+	0.730308i	$0.739376\pi$
$578$	647.790	−	2417.59i	0.0466168	−	0.173976i
$579$	−7687.51	−	4500.34i	−0.551782	−	0.323018i
$580$		0			0
$581$	4041.88	+	2333.58i	0.288615	+	0.166632i
$582$	820.085	+	3136.03i	0.0584083	+	0.223355i
$583$	1422.58	+	381.180i	0.101059	+	0.0270786i
$584$	−7825.82			−0.554511
$585$		0			0
$586$	2416.89			0.170377
$587$	−8859.34	−	2373.85i	−0.622937	−	0.166915i	−0.0664744	−	0.997788i	$-0.521175\pi$
$587$	−8859.34	−	2373.85i	−0.622937	−	0.166915i	−0.556463	+	0.830873i	$0.687842\pi$
$588$	11977.5	+	3286.79i	0.840038	+	0.230519i
$589$	22242.9	+	12841.9i	1.55603	+	0.898376i
$590$		0			0
$591$	−122.002	+	20256.7i	−0.00849152	+	1.40989i
$592$	−4769.01	+	17798.2i	−0.331090	+	1.23564i
$593$	2028.49	+	2028.49i	0.140473	+	0.140473i	0.773846	−	0.633374i	$-0.218330\pi$
$593$	2028.49	+	2028.49i	0.140473	+	0.140473i	−0.633374	+	0.773846i	$0.718330\pi$
$594$	2461.24	+	1480.92i	0.170010	+	0.102294i
$595$		0			0
$596$	−76.3471	+	44.0790i	−0.00524715	+	0.00302944i
$597$	−1772.99	−	1794.48i	−0.121547	−	0.123020i
$598$	1.81302	+	6.76628i	0.000123980	+	0.000462699i
$599$	−1508.22	+	2612.31i	−0.102878	+	0.178191i	−0.912869	−	0.408252i	$-0.866139\pi$
$599$	−1508.22	+	2612.31i	−0.102878	+	0.178191i	0.809991	+	0.586442i	$0.199472\pi$
$600$		0			0
$601$	−11257.7	−	19498.9i	−0.764079	−	1.32342i	−0.940732	−	0.339151i	$-0.889860\pi$
$601$	−11257.7	−	19498.9i	−0.764079	−	1.32342i	0.176653	−	0.984273i	$-0.443473\pi$
$602$	−396.824	+	396.824i	−0.0268660	+	0.0268660i
$603$	2022.85	+	7930.25i	0.136611	+	0.535564i
$604$			9040.04i			0.608997i
$605$		0			0
$606$	429.572	−	733.799i	0.0287957	−	0.0491890i
$607$	11599.7	−	3108.12i	0.775645	−	0.207833i	0.150781	−	0.988567i	$-0.451821\pi$
$607$	11599.7	−	3108.12i	0.775645	−	0.207833i	0.624864	+	0.780734i	$0.285155\pi$
$608$	−11907.4	+	3190.59i	−0.794260	+	0.212821i
$609$	−450.125	+	768.908i	−0.0299507	+	0.0511621i
$610$		0			0
$611$			1348.80i			0.0893069i
$612$	−5190.81	−	20349.8i	−0.342853	−	1.34410i
$613$	10049.6	−	10049.6i	0.662152	−	0.662152i	−0.293735	−	0.955887i	$-0.594898\pi$
$613$	10049.6	−	10049.6i	0.662152	−	0.662152i	0.955887	+	0.293735i	$0.0948982\pi$
$614$	−1625.18	−	2814.90i	−0.106819	−	0.185016i
$615$		0			0
$616$	−955.266	+	1654.57i	−0.0624817	+	0.108222i
$617$	−6719.22	−	25076.5i	−0.438421	−	1.63621i	−0.732745	−	0.680503i	$-0.761761\pi$
$617$	−6719.22	−	25076.5i	−0.438421	−	1.63621i	0.294324	−	0.955706i	$-0.404905\pi$
$618$	1048.21	+	1060.91i	0.0682283	+	0.0690551i
$619$	18043.0	−	10417.1i	1.17158	−	0.676414i	0.217531	−	0.976053i	$-0.430200\pi$
$619$	18043.0	−	10417.1i	1.17158	−	0.676414i	0.954052	+	0.299639i	$0.0968664\pi$
$620$		0			0
$621$	333.092	+	200.421i	0.0215242	+	0.0129511i
$622$	−2494.57	−	2494.57i	−0.160809	−	0.160809i
$623$	−747.784	+	2790.77i	−0.0480888	+	0.179470i
$624$	9.45946	−	1570.61i	0.000606861	−	0.100760i
$625$		0			0
$626$	−346.923	−	200.296i	−0.0221499	−	0.0127883i
$627$	−28799.2	−	7902.92i	−1.83433	−	0.503369i
$628$	−15415.1	−	4130.46i	−0.979505	−	0.262457i
$629$	−31649.4			−2.00627
$630$		0			0
$631$	−82.2965			−0.00519203			−0.00259601	−	0.999997i	$-0.500826\pi$
$631$	−82.2965			−0.00519203			−0.00259601	+	0.999997i	$0.500826\pi$
$632$	−5883.21	−	1576.40i	−0.370287	−	0.0992182i
$633$	−2453.07	−	9380.62i	−0.154030	−	0.589014i
$634$	−2891.59	−	1669.46i	−0.181135	−	0.104578i
$635$		0			0
$636$	1221.72	+	715.207i	0.0761705	+	0.0445909i
$637$	−412.940	+	1541.11i	−0.0256849	+	0.0958573i
$638$	419.303	+	419.303i	0.0260194	+	0.0260194i
$639$	30998.0	+	373.403i	1.91903	+	0.0231168i
$640$		0			0
$641$	−12303.0	+	7103.15i	−0.758096	+	0.437687i	−0.828612	−	0.559824i	$-0.810869\pi$
$641$	−12303.0	+	7103.15i	−0.758096	+	0.437687i	0.0705156	+	0.997511i	$0.477536\pi$
$642$	921.744	−	3358.94i	0.0566641	−	0.206490i
$643$	−4357.53	−	16262.5i	−0.267254	−	0.997405i	−0.960856	−	0.277047i	$-0.910644\pi$
$643$	−4357.53	−	16262.5i	−0.267254	−	0.997405i	0.693603	−	0.720358i	$-0.256022\pi$
$644$	−63.6641	+	110.270i	−0.00389552	+	0.00674725i
$645$		0			0
$646$	−3348.97	−	5800.59i	−0.203968	−	0.353283i
$647$	−6061.72	+	6061.72i	−0.368332	+	0.368332i	−0.866869	−	0.498537i	$-0.833871\pi$
$647$	−6061.72	+	6061.72i	−0.368332	+	0.368332i	0.498537	+	0.866869i	$0.333871\pi$
$648$	3867.98	+	4058.99i	0.234489	+	0.246068i
$649$			2237.99i			0.135360i
$650$		0			0
$651$	5768.13	+	34.7403i	0.347267	+	0.00209152i
$652$	14813.8	−	3969.36i	0.889808	−	0.238423i
$653$	22408.3	−	6004.30i	1.34289	−	0.359826i	0.485384	−	0.874301i	$-0.338680\pi$
$653$	22408.3	−	6004.30i	1.34289	−	0.359826i	0.857505	+	0.514475i	$0.172013\pi$
$654$	−1750.02	−	3073.73i	−0.104635	−	0.183780i
$655$		0			0
$656$			15267.2i			0.908662i
$657$	−19190.8	−	19658.8i	−1.13958	−	1.16737i
$658$	531.798	−	531.798i	0.0315071	−	0.0315071i
$659$	−10607.4	−	18372.5i	−0.627017	−	1.08603i	−0.988147	−	0.153510i	$-0.950942\pi$
$659$	−10607.4	−	18372.5i	−0.627017	−	1.08603i	0.361130	−	0.932516i	$-0.382391\pi$
$660$		0			0
$661$	13457.5	−	23309.2i	0.791888	−	1.37159i	−0.132908	−	0.991128i	$-0.542432\pi$
$661$	13457.5	−	23309.2i	0.791888	−	1.37159i	0.924797	−	0.380462i	$-0.124235\pi$
$662$	397.487	+	1483.44i	0.0233365	+	0.0870930i
$663$	2610.02	−	682.532i	0.152888	−	0.0399809i
$664$	5250.86	−	3031.59i	0.306887	−	0.177181i
$665$		0			0
$666$	3628.31	−	2036.93i	0.211102	−	0.118513i
$667$	56.7465	+	56.7465i	0.00329420	+	0.00329420i
$668$	6393.81	−	23862.0i	0.370335	−	1.38211i
$669$	265.277	−	151.035i	0.0153307	−	0.00872848i
$670$		0			0
$671$	1982.06	+	1144.34i	0.114034	+	0.0658373i
$672$	−1969.43	+	1945.85i	−0.113054	+	0.111701i
$673$	26968.7	+	7226.24i	1.54467	+	0.413894i	0.927773	−	0.373146i	$-0.121721\pi$
$673$	26968.7	+	7226.24i	1.54467	+	0.413894i	0.616902	+	0.787040i	$0.288387\pi$
$674$	1145.96			0.0654909
$675$		0			0
$676$	−16844.5			−0.958383
$677$	10091.6	+	2704.04i	0.572899	+	0.153508i	0.533626	−	0.845721i	$-0.320829\pi$
$677$	10091.6	+	2704.04i	0.572899	+	0.153508i	0.0392732	+	0.999229i	$0.487496\pi$
$678$	−1854.71	+	1832.51i	−0.105059	+	0.103801i
$679$	−6554.71	−	3784.36i	−0.370466	−	0.213889i
$680$		0			0
$681$	−12050.2	+	6860.76i	−0.678069	+	0.386057i
$682$	993.612	−	3708.21i	0.0557879	−	0.208203i
$683$	6573.66	+	6573.66i	0.368278	+	0.368278i	0.866849	−	0.498571i	$-0.166142\pi$
$683$	6573.66	+	6573.66i	0.368278	+	0.368278i	−0.498571	+	0.866849i	$0.666142\pi$
$684$	−24685.6	−	14651.5i	−1.37994	−	0.819025i
$685$		0			0
$686$	1628.56	−	940.249i	0.0906395	−	0.0523307i
$687$	14839.7	−	3880.63i	0.824116	−	0.215510i
$688$	−2933.37	−	10947.5i	−0.162549	−	0.606641i
$689$	−90.9270	+	157.490i	−0.00502764	+	0.00870813i
$690$		0			0
$691$	1964.11	+	3401.94i	0.108131	+	0.187288i	0.915013	−	0.403424i	$-0.132180\pi$
$691$	1964.11	+	3401.94i	0.108131	+	0.187288i	−0.806882	+	0.590712i	$0.798847\pi$
$692$	18250.2	−	18250.2i	1.00255	−	1.00255i
$693$	−6498.89	+	1657.73i	−0.356237	+	0.0908689i
$694$		−	899.895i		−	0.0492212i
$695$		0			0
$696$	572.691	+	1005.87i	0.0311894	+	0.0547809i
$697$	−25330.0	+	6787.15i	−1.37653	+	0.368840i
$698$	1310.61	−	351.177i	0.0710706	−	0.0190433i
$699$	10959.5	+	66.0068i	0.593026	+	0.00357168i
$700$		0			0
$701$		−	1942.50i		−	0.104661i	−0.998630	−	0.0523305i	$-0.983335\pi$
$701$		−	1942.50i		−	0.104661i	0.998630	−	0.0523305i	$-0.0166649\pi$
$702$	−255.288	+	246.225i	−0.0137254	+	0.0132381i
$703$	−30589.9	+	30589.9i	−1.64114	+	1.64114i
$704$	−8870.52	−	15364.2i	−0.474887	−	0.822528i
$705$		0			0
$706$	−494.256	+	856.077i	−0.0263479	+	0.0456358i
$707$	513.857	+	1917.74i	0.0273346	+	0.102014i
$708$	−569.285	+	2074.54i	−0.0302190	+	0.110122i
$709$	−1476.94	+	852.712i	−0.0782336	+	0.0451682i	−0.538607	−	0.842557i	$-0.681049\pi$
$709$	−1476.94	+	852.712i	−0.0782336	+	0.0451682i	0.460373	+	0.887726i	$0.347716\pi$
$710$		0			0
$711$	−10467.1	−	18644.6i	−0.552104	−	0.983441i
$712$	2654.07	+	2654.07i	0.139699	+	0.139699i
$713$	134.471	−	501.852i	0.00706308	−	0.0263598i
$714$	−1298.17	−	759.962i	−0.0680433	−	0.0398332i
$715$		0			0
$716$	19115.8	+	11036.5i	0.997753	+	0.576053i
$717$	−450.630	−	1723.22i	−0.0234715	−	0.0897558i
$718$	−5511.63	−	1476.84i	−0.286479	−	0.0767619i
$719$	13850.6			0.718415			0.359207	−	0.933258i	$-0.383047\pi$
$719$	13850.6			0.718415			0.359207	+	0.933258i	$0.383047\pi$
$720$		0			0
$721$	−3482.35			−0.179874
$722$	−5610.39	−	1503.30i	−0.289193	−	0.0774890i
$723$	−23288.3	−	6390.64i	−1.19792	−	0.328728i
$724$	−9103.13	−	5255.69i	−0.467286	−	0.269788i
$725$		0			0
$726$	−6.55902	+	1089.03i	−0.000335300	+	0.0556718i
$727$	−1022.15	+	3814.73i	−0.0521452	+	0.194609i	−0.987085	−	0.160198i	$-0.948787\pi$
$727$	−1022.15	+	3814.73i	−0.0521452	+	0.194609i	0.934940	+	0.354807i	$0.115453\pi$
$728$	−166.813	−	166.813i	−0.00849242	−	0.00849242i
$729$	−711.118	+	19670.1i	−0.0361286	+	0.999347i
$730$		0			0
$731$	16859.1	−	9733.60i	0.853018	−	0.492490i
$732$	1546.21	+	1564.95i	0.0780732	+	0.0790193i
$733$	2077.08	+	7751.76i	0.104664	+	0.390611i	0.998307	−	0.0581677i	$-0.0185258\pi$
$733$	2077.08	+	7751.76i	0.104664	+	0.390611i	−0.893643	+	0.448779i	$0.851859\pi$
$734$	−1992.64	+	3451.35i	−0.100204	+	0.173558i
$735$		0			0
$736$	124.685	+	215.961i	0.00624451	+	0.0108158i
$737$	−8993.26	+	8993.26i	−0.449486	+	0.449486i
$738$	2467.03	−	2408.31i	0.123053	−	0.120123i
$739$		−	6687.71i		−	0.332898i	−0.986050	−	0.166449i	$-0.946770\pi$
$739$		−	6687.71i		−	0.332898i	0.986050	−	0.166449i	$-0.0532301\pi$
$740$		0			0
$741$	1862.96	−	3182.33i	0.0923585	−	0.157768i
$742$	97.9449	−	26.2443i	0.00484592	−	0.00129846i
$743$	−23178.0	+	6210.54i	−1.14444	+	0.306652i	−0.780735	−	0.624862i	$-0.785155\pi$
$743$	−23178.0	+	6210.54i	−1.14444	+	0.306652i	−0.363706	+	0.931514i	$0.618489\pi$
$744$	3785.82	−	6466.96i	0.186552	−	0.318670i
$745$		0			0
$746$			3800.20i			0.186508i
$747$	20491.9	+	5756.20i	1.00369	+	0.281939i
$748$	23077.5	−	23077.5i	1.12807	−	1.12807i
$749$	4066.46	+	7043.32i	0.198378	+	0.343601i
$750$		0			0
$751$	−5405.41	+	9362.45i	−0.262645	+	0.454914i	−0.966944	−	0.254989i	$-0.917928\pi$
$751$	−5405.41	+	9362.45i	−0.262645	+	0.454914i	0.704299	+	0.709904i	$0.251261\pi$
$752$	3931.12	+	14671.1i	0.190629	+	0.711437i
$753$	23103.3	+	23383.3i	1.11810	+	1.13165i
$754$	−63.4107	+	36.6102i	−0.00306271	+	0.00176826i
$755$		0			0
$756$	−6445.93	−	116.479i	−0.310101	−	0.00560357i
$757$	4054.07	+	4054.07i	0.194647	+	0.194647i	0.797700	−	0.603054i	$-0.206050\pi$
$757$	4054.07	+	4054.07i	0.194647	+	0.194647i	−0.603054	+	0.797700i	$0.706050\pi$
$758$	125.017	−	466.569i	0.00599052	−	0.0223569i
$759$	−3.63838	+	604.100i	−0.000173998	+	0.0288899i
$760$		0			0
$761$	−26529.1	−	15316.6i	−1.26370	−	0.729599i	−0.289914	−	0.957053i	$-0.593627\pi$
$761$	−26529.1	−	15316.6i	−1.26370	−	0.729599i	−0.973789	+	0.227453i	$0.926960\pi$
$762$	1996.09	+	547.756i	0.0948957	+	0.0260408i
$763$	7977.33	+	2137.52i	0.378504	+	0.101420i
$764$	20864.5			0.988025
$765$		0			0
$766$	−421.265			−0.0198706
$767$	−266.927	−	71.5228i	−0.0125661	−	0.00336706i
$768$	−3852.58	−	14732.4i	−0.181013	−	0.692199i
$769$	14879.3	+	8590.59i	0.697740	+	0.402841i	0.806505	−	0.591227i	$-0.201356\pi$
$769$	14879.3	+	8590.59i	0.697740	+	0.402841i	−0.108765	+	0.994068i	$0.534690\pi$
$770$		0			0
$771$	−10899.6	−	6380.71i	−0.509129	−	0.298049i
$772$	3443.96	−	12853.0i	0.160558	−	0.599211i
$773$	25722.7	+	25722.7i	1.19687	+	1.19687i	0.975099	+	0.221772i	$0.0711840\pi$
$773$	25722.7	+	25722.7i	1.19687	+	1.19687i	0.221772	+	0.975099i	$0.428816\pi$
$774$	−1306.29	+	2200.91i	−0.0606637	+	0.102209i
$775$		0			0
$776$	−8515.32	+	4916.32i	−0.393921	+	0.227430i
$777$	−2571.08	+	9369.33i	−0.118709	+	0.432591i
$778$	20.8759	+	77.9097i	0.000961999	+	0.00359023i
$779$	−17922.1	+	31041.9i	−0.824294	+	1.42772i
$780$		0			0
$781$	24087.5	+	41720.8i	1.10361	+	1.91151i
$782$	−95.8070	+	95.8070i	−0.00438114	+	0.00438114i
$783$	−1122.42	+	3905.26i	−0.0512284	+	0.178241i
$784$			17966.5i			0.818445i
$785$		0			0
$786$	−1985.73	−	11.9597i	−0.0901126	−	0.000542731i
$787$	−5971.71	+	1600.12i	−0.270481	+	0.0724752i	−0.391510	−	0.920174i	$-0.628047\pi$
$787$	−5971.71	+	1600.12i	−0.270481	+	0.0724752i	0.121029	+	0.992649i	$0.461381\pi$
$788$	−29228.4	+	7831.73i	−1.32134	+	0.354053i
$789$	1798.53	+	3158.93i	0.0811525	+	0.142536i
$790$		0			0
$791$		−	6087.94i		−	0.273657i
$792$	−2356.34	+	8388.48i	−0.105718	+	0.376353i
$793$	−199.830	+	199.830i	−0.00894850	+	0.00894850i
$794$	1735.29	+	3005.61i	0.0775606	+	0.134339i
$795$		0			0
$796$	1884.12	−	3263.39i	0.0838956	−	0.145311i
$797$	2697.77	+	10068.2i	0.119900	+	0.447472i	0.999607	−	0.0280444i	$-0.00892798\pi$
$797$	2697.77	+	10068.2i	0.119900	+	0.447472i	−0.879707	+	0.475516i	$0.842261\pi$
$798$	−1989.24	+	520.194i	−0.0882433	+	0.0230760i
$799$	−22593.5	+	13044.4i	−1.00038	+	0.577567i
$800$		0			0
$801$	−158.714	+	13175.6i	−0.00700108	+	0.581193i
$802$	−837.019	−	837.019i	−0.0368531	−	0.0368531i
$803$	11049.8	−	41238.5i	0.485604	−	1.81230i
$804$	−10624.1	+	6048.80i	−0.466023	+	0.265329i
$805$		0			0
$806$	410.526	+	237.017i	0.0179407	+	0.0103580i
$807$	−17528.9	+	17319.0i	−0.764616	+	0.755461i
$808$	2491.37	+	667.560i	0.108473	+	0.0290652i
$809$	39011.6			1.69540			0.847698	−	0.530478i	$-0.177988\pi$
$809$	39011.6			1.69540			0.847698	+	0.530478i	$0.177988\pi$
$810$		0			0
$811$	−7036.87			−0.304683			−0.152341	−	0.988328i	$-0.548681\pi$
$811$	−7036.87			−0.304683			−0.152341	+	0.988328i	$0.548681\pi$
$812$	−1285.57	−	344.466i	−0.0555597	−	0.0148872i
$813$	4223.35	−	4172.78i	0.182188	−	0.180007i
$814$	5599.93	+	3233.12i	0.241127	+	0.139215i
$815$		0			0
$816$	26400.4	−	15031.0i	1.13260	−	0.644842i
$817$	6886.95	−	25702.4i	0.294913	−	1.10063i
$818$	−1297.27	−	1297.27i	−0.0554497	−	0.0554497i
$819$	9.97539	−	828.105i	0.000425602	−	0.0353313i
$820$		0			0
$821$	−5998.79	+	3463.40i	−0.255005	+	0.147227i	−0.622054	−	0.782974i	$-0.713702\pi$
$821$	−5998.79	+	3463.40i	−0.255005	+	0.147227i	0.367049	+	0.930202i	$0.380368\pi$
$822$	5138.73	−	1343.80i	0.218046	−	0.0570200i
$823$	6367.67	+	23764.5i	0.269700	+	1.00653i	0.959310	+	0.282353i	$0.0911151\pi$
$823$	6367.67	+	23764.5i	0.269700	+	1.00653i	−0.689611	+	0.724180i	$0.742218\pi$
$824$	−2261.99	+	3917.88i	−0.0956312	+	0.165638i
$825$		0			0
$826$	77.0430	+	133.442i	0.00324536	+	0.00562113i
$827$	−15154.8	+	15154.8i	−0.637222	+	0.637222i	−0.949869	−	0.312647i	$-0.898784\pi$
$827$	−15154.8	+	15154.8i	−0.637222	+	0.637222i	0.312647	+	0.949869i	$0.398784\pi$
$828$	−157.039	+	559.054i	−0.00659118	+	0.0234643i
$829$		−	19437.6i		−	0.814350i	−0.913350	−	0.407175i	$-0.866514\pi$
$829$		−	19437.6i		−	0.814350i	0.913350	−	0.407175i	$-0.133486\pi$
$830$		0			0
$831$	21178.1	+	37197.1i	0.884066	+	1.55277i
$832$	2115.98	−	566.976i	0.0881713	−	0.0236254i
$833$	−29808.5	+	7987.17i	−1.23986	+	0.332220i
$834$	−1306.84	−	7.87085i	−0.0542592	−	0.000326793i
$835$		0			0
$836$		−	44609.9i		−	1.84553i
$837$	25529.0	−	6348.43i	1.05426	−	0.262167i
$838$	3007.01	−	3007.01i	0.123956	−	0.123956i
$839$	7918.88	+	13715.9i	0.325852	+	0.564392i	0.981684	−	0.190514i	$-0.0610155\pi$
$839$	7918.88	+	13715.9i	0.325852	+	0.564392i	−0.655832	+	0.754907i	$0.727682\pi$
$840$		0			0
$841$	11775.1	−	20395.0i	0.482803	−	0.836239i
$842$	833.968	+	3112.41i	0.0341335	+	0.127388i
$843$	1777.83	−	6478.62i	0.0726354	−	0.264692i
$844$	12543.3	−	7241.88i	0.511562	−	0.295350i
$845$		0			0
$846$	1750.61	−	2949.52i	0.0711433	−	0.119866i
$847$	−1798.09	−	1798.09i	−0.0729435	−	0.0729435i
$848$	−530.020	+	1978.06i	−0.0214634	+	0.0801025i
$849$	−26191.0	−	15332.4i	−1.05874	−	0.619797i
$850$		0			0
$851$	757.869	+	437.556i	0.0305281	+	0.0176254i
$852$	11715.6	+	44800.9i	0.471093	+	1.80147i
$853$	−37612.9	−	10078.3i	−1.50978	−	0.404544i	−0.593416	−	0.804896i	$-0.702221\pi$
$853$	−37612.9	−	10078.3i	−1.50978	−	0.404544i	−0.916361	+	0.400352i	$0.868888\pi$
$854$	157.576			0.00631398
$855$		0			0
$856$	10565.6			0.421875
$857$	25206.0	+	6753.94i	1.00469	+	0.269207i	0.723410	−	0.690418i	$-0.242574\pi$
$857$	25206.0	+	6753.94i	1.00469	+	0.269207i	0.281283	+	0.959625i	$0.409240\pi$
$858$	−531.532	−	145.860i	−0.0211494	−	0.00580371i
$859$	−27394.6	−	15816.3i	−1.08812	−	0.628224i	−0.155041	−	0.987908i	$-0.549551\pi$
$859$	−27394.6	−	15816.3i	−1.08812	−	0.628224i	−0.933074	+	0.359684i	$0.882884\pi$
$860$		0			0
$861$	−48.4832	+	8049.93i	−0.00191905	+	0.318631i
$862$	−1685.03	+	6288.60i	−0.0665803	+	0.248481i
$863$	3712.77	+	3712.77i	0.146447	+	0.146447i	0.776529	−	0.630082i	$-0.216979\pi$
$863$	3712.77	+	3712.77i	0.146447	+	0.146447i	−0.630082	+	0.776529i	$0.716979\pi$
$864$	−6509.69	+	10818.9i	−0.256324	+	0.426002i
$865$		0			0
$866$	3509.45	−	2026.18i	0.137709	−	0.0795063i
$867$	18732.3	+	18959.3i	0.733774	+	0.742667i
$868$	2230.10	+	8322.86i	0.0872058	+	0.325456i
$869$	16613.9	−	28776.0i	0.648546	−	1.12331i
$870$		0			0
$871$	−785.220	−	1360.04i	−0.0305467	−	0.0529084i
$872$	7586.59	−	7586.59i	0.294627	−	0.294627i
$873$	−33231.6	−	9334.83i	−1.28834	−	0.361897i
$874$			185.199i			0.00716757i
$875$		0			0
$876$	20732.8	−	35415.9i	0.799653	−	1.36597i
$877$	−17442.2	+	4673.61i	−0.671585	+	0.179951i	−0.578469	−	0.815705i	$-0.696349\pi$
$877$	−17442.2	+	4673.61i	−0.671585	+	0.179951i	−0.0931161	+	0.995655i	$0.529683\pi$
$878$	1844.91	−	494.343i	0.0709143	−	0.0190014i
$879$	−13002.5	+	22210.9i	−0.498933	+	0.852281i
$880$		0			0
$881$			37257.2i			1.42478i	0.701786	+	0.712388i	$0.252386\pi$
$881$			37257.2i			1.42478i	−0.701786	+	0.712388i	$0.747614\pi$
$882$	2903.22	−	2834.11i	0.110835	−	0.108197i
$883$	−3681.13	+	3681.13i	−0.140294	+	0.140294i	−0.773766	−	0.633472i	$-0.781629\pi$
$883$	−3681.13	+	3681.13i	−0.140294	+	0.140294i	0.633472	+	0.773766i	$0.281629\pi$
$884$	2014.95	+	3489.99i	0.0766630	+	0.132784i
$885$		0			0
$886$	−3045.32	+	5274.65i	−0.115474	+	0.200006i
$887$	−11837.4	−	44177.9i	−0.448097	−	1.67232i	−0.707628	−	0.706585i	$-0.750235\pi$
$887$	−11837.4	−	44177.9i	−0.448097	−	1.67232i	0.259531	−	0.965735i	$-0.416432\pi$
$888$	8871.06	+	8978.57i	0.335240	+	0.339303i
$889$	−4185.56	+	2416.54i	−0.157907	+	0.0911676i
$890$		0			0
$891$	−26850.5	+	14651.4i	−1.00957	+	0.550885i
$892$	322.434	+	322.434i	0.0121030	+	0.0121030i
$893$	−9229.45	+	34444.8i	−0.345859	+	1.29076i
$894$	−0.173440	+	28.7972i	−6.48848e−6	+	0.00107732i
$895$		0			0
$896$	−4749.26	−	2741.98i	−0.177078	−	0.102236i
$897$	−71.9350	−	19.7400i	−0.00267764	−	0.000734784i
$898$	−1889.88	−	506.391i	−0.0702293	−	0.0188179i
$899$	5430.72			0.201474
$900$		0			0
$901$	−3517.46			−0.130059
$902$	5175.14	+	1386.67i	0.191035	+	0.0511876i
$903$	−1511.92	−	5781.61i	−0.0557180	−	0.213067i
$904$	−6849.35	−	3954.47i	−0.251998	−	0.145491i
$905$		0			0
$906$	2548.45	+	1491.89i	0.0934511	+	0.0547071i
$907$	−1347.01	+	5027.10i	−0.0493128	+	0.184038i	−0.986189	−	0.165623i	$-0.947036\pi$
$907$	−1347.01	+	5027.10i	−0.0493128	+	0.184038i	0.936876	+	0.349661i	$0.113703\pi$
$908$	−14646.6	−	14646.6i	−0.535311	−	0.535311i
$909$	4432.49	+	7895.43i	0.161734	+	0.288091i
$910$		0			0
$911$	37253.9	−	21508.5i	1.35486	−	0.782228i	0.365933	−	0.930641i	$-0.380750\pi$
$911$	37253.9	−	21508.5i	1.35486	−	0.782228i	0.988925	+	0.148413i	$0.0474166\pi$
$912$	10988.8	−	40044.5i	0.398986	−	1.45395i
$913$	8561.03	+	31950.2i	0.310327	+	1.15816i
$914$	2605.72	−	4513.23i	0.0942991	−	0.163331i
$915$		0			0
$916$	11456.3	+	19842.9i	0.413238	+	0.715749i
$917$	3278.62	−	3278.62i	0.118069	−	0.118069i
$918$	−6593.39	−	1895.01i	−0.237053	−	0.0681315i
$919$		−	4433.60i		−	0.159141i	−0.996829	−	0.0795707i	$-0.974645\pi$
$919$		−	4433.60i		−	0.159141i	0.996829	−	0.0795707i	$-0.0253549\pi$
$920$		0			0
$921$	34611.8	+	208.460i	1.23832	+	0.00745819i
$922$	2519.62	−	675.131i	0.0899993	−	0.0241152i
$923$	−5745.86	+	1539.60i	−0.204905	+	0.0549041i
$924$	−4957.02	−	8706.50i	−0.176487	−	0.309981i
$925$		0			0
$926$		−	9207.60i		−	0.326761i
$927$	−15388.8	+	3925.38i	−0.545237	+	0.139079i
$928$	−1843.13	+	1843.13i	−0.0651980	+	0.0651980i
$929$	−18443.1	−	31944.5i	−0.651346	−	1.12816i	−0.982797	−	0.184691i	$-0.940871\pi$
$929$	−18443.1	−	31944.5i	−0.651346	−	1.12816i	0.331451	−	0.943472i	$-0.392462\pi$
$930$		0			0
$931$	−21090.8	+	36530.4i	−0.742453	+	1.28597i
$932$	4237.21	+	15813.5i	0.148921	+	0.555780i
$933$	36345.2	−	9504.42i	1.27533	−	0.333506i
$934$	−1065.44	+	615.134i	−0.0373259	+	0.0215501i
$935$		0			0
$936$	−925.194	−	549.125i	−0.0323087	−	0.0191760i
$937$	21727.1	+	21727.1i	0.757517	+	0.757517i	0.975870	−	0.218353i	$-0.0700684\pi$
$937$	21727.1	+	21727.1i	0.757517	+	0.757517i	−0.218353	+	0.975870i	$0.570068\pi$
$938$	−226.638	+	845.825i	−0.00788912	+	0.0294426i
$939$	3707.09	−	2110.62i	0.128835	−	0.0733520i
$940$		0			0
$941$	−36326.4	−	20973.0i	−1.25845	−	0.726569i	−0.285680	−	0.958325i	$-0.592220\pi$
$941$	−36326.4	−	20973.0i	−1.25845	−	0.726569i	−0.972774	+	0.231756i	$0.925553\pi$
$942$	−3708.37	+	3663.97i	−0.128265	+	0.126729i
$943$	700.379	+	187.666i	0.0241861	+	0.00648064i
$944$	−3111.87			−0.107291
$945$		0			0
$946$	−3977.32			−0.136695
$947$	13154.9	+	3524.84i	0.451400	+	0.120952i	0.477355	−	0.878711i	$-0.341596\pi$
$947$	13154.9	+	3524.84i	0.451400	+	0.120952i	−0.0259542	+	0.999663i	$0.508262\pi$
$948$	22720.3	−	22448.3i	0.778399	−	0.769078i
$949$	4565.41	+	2635.84i	0.156164	+	0.0901612i
$950$		0			0
$951$	30898.4	−	17591.9i	1.05357	−	0.599850i
$952$	1180.99	−	4407.51i	0.0402060	−	0.150051i
$953$	−17271.0	−	17271.0i	−0.587055	−	0.587055i	0.349778	−	0.936833i	$-0.386257\pi$
$953$	−17271.0	−	17271.0i	−0.587055	−	0.587055i	−0.936833	+	0.349778i	$0.886257\pi$
$954$	403.244	−	226.381i	0.0136850	−	0.00768277i
$955$		0			0
$956$	2304.21	−	1330.34i	0.0779534	−	0.0450064i
$957$	−6109.12	+	1597.56i	−0.206353	+	0.0539622i
$958$	2275.25	+	8491.35i	0.0767327	+	0.286370i
$959$	−6201.09	+	10740.6i	−0.208805	+	0.361661i
$960$		0			0
$961$	−2683.97	−	4648.77i	−0.0900932	−	0.156046i
$962$	−564.582	+	564.582i	−0.0189219	+	0.0189219i
$963$	25909.4	+	26541.3i	0.866999	+	0.888141i
$964$		−	36073.5i		−	1.20524i
$965$		0			0
$966$	20.5792	+	36.1453i	0.000685430	+	0.00120389i
$967$	−22985.8	+	6159.02i	−0.764397	+	0.204820i	−0.619895	−	0.784685i	$-0.712825\pi$
$967$	−22985.8	+	6159.02i	−0.764397	+	0.204820i	−0.144502	+	0.989504i	$0.546158\pi$
$968$	−3190.94	+	855.009i	−0.105951	+	0.0283895i
$969$	71323.6	+	429.568i	2.36454	+	0.0142412i
$970$		0			0
$971$		−	1752.77i		−	0.0579291i	−0.999580	−	0.0289645i	$-0.990779\pi$
$971$		−	1752.77i		−	0.0579291i	0.999580	−	0.0289645i	$-0.00922099\pi$
$972$	−28616.4	+	6751.25i	−0.944313	+	0.222784i
$973$	2157.71	−	2157.71i	0.0710927	−	0.0710927i
$974$	−366.673	−	635.097i	−0.0120626	−	0.0208930i
$975$		0			0
$976$	−1591.18	+	2756.00i	−0.0521847	+	0.0903866i
$977$	−8487.73	−	31676.6i	−0.277939	−	1.03728i	−0.953846	−	0.300296i	$-0.902915\pi$
$977$	−8487.73	−	31676.6i	−0.277939	−	1.03728i	0.675907	−	0.736987i	$-0.263752\pi$
$978$	1325.75	−	4831.20i	0.0433465	−	0.157960i
$979$	−17733.2	+	10238.3i	−0.578914	+	0.334236i
$980$		0			0
$981$	37662.0	+	453.678i	1.22574	+	0.0147654i
$982$	3002.38	+	3002.38i	0.0975659	+	0.0975659i
$983$	9064.56	−	33829.4i	0.294114	−	1.09765i	−0.647804	−	0.761807i	$-0.724312\pi$
$983$	9064.56	−	33829.4i	0.294114	−	1.09765i	0.941918	−	0.335843i	$-0.109021\pi$
$984$	9025.22	+	5283.44i	0.292392	+	0.171169i
$985$		0			0
$986$	−1226.50	−	708.122i	−0.0396144	−	0.0228714i
$987$	2026.17	+	7748.14i	0.0653433	+	0.249874i
$988$	5320.65	+	1425.66i	0.171328	+	0.0459073i
$989$	−538.272			−0.0173064
$990$		0			0
$991$	−56528.0			−1.81198			−0.905989	−	0.423301i	$-0.860871\pi$
$991$	−56528.0			−1.81198			−0.905989	+	0.423301i	$0.860871\pi$
$992$	16300.2	+	4367.63i	0.521705	+	0.139791i
$993$	−15771.1	−	4327.81i	−0.504007	−	0.138307i
$994$	2872.48	+	1658.43i	0.0916594	+	0.0529196i
$995$		0			0
$996$	−191.492	+	31794.5i	−0.00609202	+	1.01149i
$997$	−10153.3	+	37892.5i	−0.322525	+	1.20368i	0.594251	+	0.804279i	$0.297448\pi$
$997$	−10153.3	+	37892.5i	−0.322525	+	1.20368i	−0.916776	+	0.399401i	$0.869218\pi$
$998$	3036.52	+	3036.52i	0.0963121	+	0.0963121i
$999$	−800.546	+	44302.1i	−0.0253535	+	1.40306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.32.9		64
5.2	odd	4		45.4.l.a.23.8	yes	64
5.3	odd	4	inner	225.4.p.b.68.9		64
5.4	even	2		45.4.l.a.32.8	yes	64
9.2	odd	6	inner	225.4.p.b.182.9		64
15.2	even	4		135.4.m.a.98.9		64
15.14	odd	2		135.4.m.a.17.9		64
45.2	even	12		45.4.l.a.38.8	yes	64
45.7	odd	12		135.4.m.a.8.9		64
45.29	odd	6		45.4.l.a.2.8	✓	64
45.34	even	6		135.4.m.a.62.9		64
45.38	even	12	inner	225.4.p.b.218.9		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.8	✓	64	45.29	odd	6
45.4.l.a.23.8	yes	64	5.2	odd	4
45.4.l.a.32.8	yes	64	5.4	even	2
45.4.l.a.38.8	yes	64	45.2	even	12
135.4.m.a.8.9		64	45.7	odd	12
135.4.m.a.17.9		64	15.14	odd	2
135.4.m.a.62.9		64	45.34	even	6
135.4.m.a.98.9		64	15.2	even	4
225.4.p.b.32.9		64	1.1	even	1	trivial
225.4.p.b.68.9		64	5.3	odd	4	inner
225.4.p.b.182.9		64	9.2	odd	6	inner
225.4.p.b.218.9		64	45.38	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.471331 + 0.126293i) q^{2} +(-3.69630 + 3.65204i) q^{3} +(-6.72200 - 3.88095i) q^{4} +(-2.20341 + 1.25450i) q^{6} +(1.53228 - 5.71856i) q^{7} +(-5.43846 - 5.43846i) q^{8} +(0.325220 - 26.9980i) q^{9} +O(q^{10})\)	\(q+(0.471331 + 0.126293i) q^{2} +(-3.69630 + 3.65204i) q^{3} +(-6.72200 - 3.88095i) q^{4} +(-2.20341 + 1.25450i) q^{6} +(1.53228 - 5.71856i) q^{7} +(-5.43846 - 5.43846i) q^{8} +(0.325220 - 26.9980i) q^{9} +(36.3372 - 20.9793i) q^{11} +(39.0199 - 10.2039i) q^{12} +(1.34093 + 5.00442i) q^{13} +(1.44443 - 2.50182i) q^{14} +(29.1711 + 50.5258i) q^{16} +(-70.8600 + 70.8600i) q^{17} +(3.56294 - 12.6839i) q^{18} +136.976i q^{19} +(15.2206 + 26.7334i) q^{21} +(19.7764 - 5.29906i) q^{22} +(2.67644 - 0.717150i) q^{23} +(39.9636 + 0.240693i) q^{24} +2.52809i q^{26} +(97.3958 + 100.980i) q^{27} +(-32.4934 + 32.4934i) q^{28} +(14.4814 + 25.0825i) q^{29} +(93.7536 - 162.386i) q^{31} +(23.2931 + 86.9311i) q^{32} +(-57.6958 + 210.250i) q^{33} +(-42.3476 + 24.4494i) q^{34} +(-106.964 + 180.219i) q^{36} +(223.324 + 223.324i) q^{37} +(-17.2990 + 64.5608i) q^{38} +(-23.2328 - 13.6007i) q^{39} +(226.624 + 130.841i) q^{41} +(3.79771 + 14.5226i) q^{42} +(-187.643 - 50.2787i) q^{43} -325.678 q^{44} +1.35206 q^{46} +(251.467 + 67.3803i) q^{47} +(-292.347 - 80.2245i) q^{48} +(266.693 + 153.975i) q^{49} +(3.13609 - 520.703i) q^{51} +(10.4082 - 38.8438i) q^{52} +(24.8198 + 24.8198i) q^{53} +(33.1526 + 59.8956i) q^{54} +(-39.4334 + 22.7669i) q^{56} +(-500.240 - 506.302i) q^{57} +(3.65779 + 13.6510i) q^{58} +(-26.6691 + 46.1922i) q^{59} +(27.2731 + 47.2385i) q^{61} +(64.6971 - 64.6971i) q^{62} +(-153.892 - 43.2284i) q^{63} -422.823i q^{64} +(-53.7469 + 91.8110i) q^{66} +(-292.789 + 78.4527i) q^{67} +(751.325 - 201.317i) q^{68} +(-7.27386 + 12.4253i) q^{69} +1148.16i q^{71} +(-148.596 + 145.059i) q^{72} +(719.489 - 719.489i) q^{73} +(77.0552 + 133.463i) q^{74} +(531.595 - 920.750i) q^{76} +(-64.2924 - 239.942i) q^{77} +(-9.23268 - 9.34457i) q^{78} +(685.820 - 395.959i) q^{79} +(-728.788 - 17.5606i) q^{81} +(90.2906 + 90.2906i) q^{82} +(-204.035 + 761.471i) q^{83} +(1.43808 - 238.773i) q^{84} +(-82.0919 - 47.3958i) q^{86} +(-145.130 - 39.8257i) q^{87} +(-311.713 - 83.5233i) q^{88} -488.019 q^{89} +30.6728 q^{91} +(-20.7743 - 5.56645i) q^{92} +(246.499 + 942.618i) q^{93} +(110.014 + 63.5169i) q^{94} +(-403.574 - 236.256i) q^{96} +(330.884 - 1234.88i) q^{97} +(106.255 + 106.255i) q^{98} +(-554.582 - 987.855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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