LMFDB - Embedded newform 45.4.e.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, 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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.1
Root			$-2.69252 + 4.66357i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.4.e.c.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.69252 - 4.66357i) q^{2} +(-4.09553 - 3.19791i) q^{3} +(-10.4993 + 18.1853i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-3.88642 + 27.7102i) q^{6} +(-6.28510 - 10.8861i) q^{7} +69.9976 q^{8} +(6.54673 + 26.1943i) q^{9} -26.9252 q^{10} +(-6.41534 - 11.1117i) q^{11} +(101.155 - 40.9026i) q^{12} +(-29.9322 + 51.8442i) q^{13} +(-33.8455 + 58.6220i) q^{14} +(-24.0862 + 9.73939i) q^{15} +(-104.475 - 180.957i) q^{16} -110.011 q^{17} +(104.532 - 101.060i) q^{18} -12.0872 q^{19} +(52.4964 + 90.9264i) q^{20} +(-9.07201 + 64.6836i) q^{21} +(-34.5468 + 59.8368i) q^{22} +(33.8608 - 58.6485i) q^{23} +(-286.677 - 223.846i) q^{24} +(-12.5000 - 21.6506i) q^{25} +322.372 q^{26} +(56.9547 - 128.215i) q^{27} +263.956 q^{28} +(-99.9790 - 173.169i) q^{29} +(110.273 + 86.1042i) q^{30} +(-38.3143 + 66.3624i) q^{31} +(-282.613 + 489.500i) q^{32} +(-9.26000 + 66.0240i) q^{33} +(296.206 + 513.044i) q^{34} -62.8510 q^{35} +(-545.086 - 155.967i) q^{36} -22.4815 q^{37} +(32.5449 + 56.3694i) q^{38} +(288.381 - 116.609i) q^{39} +(174.994 - 303.099i) q^{40} +(-43.8807 + 76.0037i) q^{41} +(326.083 - 131.854i) q^{42} +(-59.7050 - 103.412i) q^{43} +269.426 q^{44} +(129.791 + 37.1375i) q^{45} -364.682 q^{46} +(-121.578 - 210.579i) q^{47} +(-150.801 + 1075.22i) q^{48} +(92.4951 - 160.206i) q^{49} +(-67.3129 + 116.589i) q^{50} +(450.553 + 351.805i) q^{51} +(-628.534 - 1088.65i) q^{52} -293.518 q^{53} +(-751.293 + 79.6094i) q^{54} -64.1534 q^{55} +(-439.942 - 762.002i) q^{56} +(49.5034 + 38.6537i) q^{57} +(-538.390 + 932.519i) q^{58} +(290.692 - 503.493i) q^{59} +(75.7741 - 540.271i) q^{60} +(386.847 + 670.038i) q^{61} +412.648 q^{62} +(244.007 - 235.902i) q^{63} +1372.15 q^{64} +(149.661 + 259.221i) q^{65} +(332.840 - 134.586i) q^{66} +(115.719 - 200.431i) q^{67} +(1155.03 - 2000.58i) q^{68} +(-326.231 + 131.913i) q^{69} +(169.227 + 293.110i) q^{70} -744.342 q^{71} +(458.255 + 1833.54i) q^{72} -264.839 q^{73} +(60.5317 + 104.844i) q^{74} +(-18.0427 + 128.645i) q^{75} +(126.907 - 219.809i) q^{76} +(-80.6421 + 139.676i) q^{77} +(-1320.28 - 1030.92i) q^{78} +(-279.858 - 484.729i) q^{79} -1044.75 q^{80} +(-643.281 + 342.974i) q^{81} +472.598 q^{82} +(610.443 + 1057.32i) q^{83} +(-1081.04 - 844.108i) q^{84} +(-275.027 + 476.361i) q^{85} +(-321.513 + 556.878i) q^{86} +(-144.311 + 1028.94i) q^{87} +(-449.059 - 777.792i) q^{88} -255.905 q^{89} +(-176.272 - 705.285i) q^{90} +752.509 q^{91} +(711.027 + 1231.53i) q^{92} +(369.138 - 149.263i) q^{93} +(-654.699 + 1133.97i) q^{94} +(-30.2179 + 52.3390i) q^{95} +(2722.83 - 1100.99i) q^{96} +(-524.759 - 908.909i) q^{97} -996.177 q^{98} +(249.064 - 240.791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18}+ \cdots + 2320 q^{99}+O(q^{100}) $ 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.69252	−	4.66357i	−0.951948	−	1.64882i	−0.741203	−	0.671281i	$-0.765744\pi$
$2$	−2.69252	−	4.66357i	−0.951948	−	1.64882i	−0.210745	−	0.977541i	$-0.567589\pi$
$3$	−4.09553	−	3.19791i	−0.788185	−	0.615438i
$3$	−4.09553	−	3.19791i	−0.788185	−	0.615438i
$4$	−10.4993	+	18.1853i	−1.31241	+	2.27316i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	−3.88642	+	27.7102i	−0.264437	+	1.88544i
$7$	−6.28510	−	10.8861i	−0.339363	−	0.587795i	0.644950	−	0.764225i	$-0.276878\pi$
$7$	−6.28510	−	10.8861i	−0.339363	−	0.587795i	−0.984313	+	0.176430i	$0.943545\pi$
$8$	69.9976			3.09349
$9$	6.54673	+	26.1943i	0.242471	+	0.970159i
$10$	−26.9252			−0.851448
$11$	−6.41534	−	11.1117i	−0.175845	−	0.304573i	0.764608	−	0.644495i	$-0.222933\pi$
$11$	−6.41534	−	11.1117i	−0.175845	−	0.304573i	−0.940454	+	0.339922i	$0.889599\pi$
$12$	101.155	−	40.9026i	2.43341	−	0.983964i
$13$	−29.9322	+	51.8442i	−0.638593	+	1.10608i	0.347148	+	0.937810i	$0.387150\pi$
$13$	−29.9322	+	51.8442i	−0.638593	+	1.10608i	−0.985742	+	0.168266i	$0.946183\pi$
$14$	−33.8455	+	58.6220i	−0.646113	+	1.11910i
$15$	−24.0862	+	9.73939i	−0.414602	+	0.167647i
$16$	−104.475	−	180.957i	−1.63243	−	2.82745i
$17$	−110.011			−1.56950			−0.784752	−	0.619810i	$-0.787210\pi$
$17$	−110.011			−1.56950			−0.784752	+	0.619810i	$0.787210\pi$
$18$	104.532	−	101.060i	1.36880	−	1.32333i
$19$	−12.0872			−0.145947			−0.0729733	−	0.997334i	$-0.523249\pi$
$19$	−12.0872			−0.145947			−0.0729733	+	0.997334i	$0.523249\pi$
$20$	52.4964	+	90.9264i	0.586927	+	1.01659i
$21$	−9.07201	+	64.6836i	−0.0942702	+	0.672148i
$22$	−34.5468	+	59.8368i	−0.334791	+	0.579875i
$23$	33.8608	−	58.6485i	0.306976	−	0.531699i	−0.670723	−	0.741708i	$-0.734016\pi$
$23$	33.8608	−	58.6485i	0.306976	−	0.531699i	0.977699	+	0.210009i	$0.0673494\pi$
$24$	−286.677	−	223.846i	−2.43824	−	1.90385i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	322.372			2.43163
$27$	56.9547	−	128.215i	0.405960	−	0.913891i
$28$	263.956			1.78154
$29$	−99.9790	−	173.169i	−0.640194	−	1.10885i	−0.985389	−	0.170318i	$-0.945521\pi$
$29$	−99.9790	−	173.169i	−0.640194	−	1.10885i	0.345195	−	0.938531i	$-0.387813\pi$
$30$	110.273	+	86.1042i	0.671099	+	0.524014i
$31$	−38.3143	+	66.3624i	−0.221982	+	0.384485i	−0.955410	−	0.295283i	$-0.904586\pi$
$31$	−38.3143	+	66.3624i	−0.221982	+	0.384485i	0.733427	+	0.679768i	$0.237919\pi$
$32$	−282.613	+	489.500i	−1.56123	+	2.70413i
$33$	−9.26000	+	66.0240i	−0.0488473	+	0.348282i
$34$	296.206	+	513.044i	1.49409	+	2.58783i
$35$	−62.8510			−0.303536
$36$	−545.086	−	155.967i	−2.52355	−	0.722069i
$37$	−22.4815			−0.0998900			−0.0499450	−	0.998752i	$-0.515905\pi$
$37$	−22.4815			−0.0998900			−0.0499450	+	0.998752i	$0.515905\pi$
$38$	32.5449	+	56.3694i	0.138934	+	0.240640i
$39$	288.381	−	116.609i	1.18405	−	0.478778i
$40$	174.994	−	303.099i	0.691725	−	1.19810i
$41$	−43.8807	+	76.0037i	−0.167147	+	0.289507i	−0.937416	−	0.348213i	$-0.886789\pi$
$41$	−43.8807	+	76.0037i	−0.167147	+	0.289507i	0.770269	+	0.637719i	$0.220122\pi$
$42$	326.083	−	131.854i	1.19799	−	0.484415i
$43$	−59.7050	−	103.412i	−0.211743	−	0.366749i	0.740517	−	0.672037i	$-0.234581\pi$
$43$	−59.7050	−	103.412i	−0.211743	−	0.366749i	−0.952260	+	0.305288i	$0.901247\pi$
$44$	269.426			0.923124
$45$	129.791	+	37.1375i	0.429959	+	0.123025i
$46$	−364.682			−1.16890
$47$	−121.578	−	210.579i	−0.377317	−	0.653533i	0.613354	−	0.789808i	$-0.289820\pi$
$47$	−121.578	−	210.579i	−0.377317	−	0.653533i	−0.990671	+	0.136276i	$0.956487\pi$
$48$	−150.801	+	1075.22i	−0.453465	+	3.23321i
$49$	92.4951	−	160.206i	0.269665	−	0.467073i
$50$	−67.3129	+	116.589i	−0.190390	+	0.329764i
$51$	450.553	+	351.805i	1.23706	+	0.965932i
$52$	−628.534	−	1088.65i	−1.67619	−	2.90325i
$53$	−293.518			−0.760712			−0.380356	−	0.924840i	$-0.624199\pi$
$53$	−293.518			−0.760712			−0.380356	+	0.924840i	$0.624199\pi$
$54$	−751.293	+	79.6094i	−1.89330	+	0.200620i
$55$	−64.1534			−0.157281
$56$	−439.942	−	762.002i	−1.04982	−	1.81834i
$57$	49.5034	+	38.6537i	0.115033	+	0.0898212i
$58$	−538.390	+	932.519i	−1.21886	+	2.11113i
$59$	290.692	−	503.493i	0.641438	−	1.11100i	−0.343674	−	0.939089i	$-0.611672\pi$
$59$	290.692	−	503.493i	0.641438	−	1.11100i	0.985112	−	0.171914i	$-0.0549951\pi$
$60$	75.7741	−	540.271i	0.163040	−	1.16248i
$61$	386.847	+	670.038i	0.811977	+	1.40639i	0.911478	+	0.411349i	$0.134942\pi$
$61$	386.847	+	670.038i	0.811977	+	1.40639i	−0.0995008	+	0.995037i	$0.531725\pi$
$62$	412.648			0.845263
$63$	244.007	−	235.902i	0.487968	−	0.471760i
$64$	1372.15			2.67998
$65$	149.661	+	259.221i	0.285588	+	0.494652i
$66$	332.840	−	134.586i	0.620755	−	0.251006i
$67$	115.719	−	200.431i	0.211005	−	0.365471i	−0.741024	−	0.671478i	$-0.765660\pi$
$67$	115.719	−	200.431i	0.211005	−	0.365471i	0.952029	+	0.306007i	$0.0989931\pi$
$68$	1155.03	−	2000.58i	2.05983	−	3.56773i
$69$	−326.231	+	131.913i	−0.569182	+	0.230152i
$70$	169.227	+	293.110i	0.288950	+	0.500477i
$71$	−744.342			−1.24418			−0.622092	−	0.782944i	$-0.713717\pi$
$71$	−744.342			−1.24418			−0.622092	+	0.782944i	$0.713717\pi$
$72$	458.255	+	1833.54i	0.750082	+	3.00117i
$73$	−264.839			−0.424616			−0.212308	−	0.977203i	$-0.568098\pi$
$73$	−264.839			−0.424616			−0.212308	+	0.977203i	$0.568098\pi$
$74$	60.5317	+	104.844i	0.0950901	+	0.164701i
$75$	−18.0427	+	128.645i	−0.0277785	+	0.198061i
$76$	126.907	−	219.809i	0.191542	−	0.331760i
$77$	−80.6421	+	139.676i	−0.119351	+	0.206722i
$78$	−1320.28	−	1030.92i	−1.91657	−	1.49652i
$79$	−279.858	−	484.729i	−0.398564	−	0.690333i	0.594985	−	0.803737i	$-0.297158\pi$
$79$	−279.858	−	484.729i	−0.398564	−	0.690333i	−0.993549	+	0.113404i	$0.963825\pi$
$80$	−1044.75			−1.46009
$81$	−643.281	+	342.974i	−0.882415	+	0.470471i
$82$	472.598			0.636460
$83$	610.443	+	1057.32i	0.807288	+	1.39826i	0.914736	+	0.404052i	$0.132399\pi$
$83$	610.443	+	1057.32i	0.807288	+	1.39826i	−0.107448	+	0.994211i	$0.534268\pi$
$84$	−1081.04	−	844.108i	−1.40418	−	1.09643i
$85$	−275.027	+	476.361i	−0.350952	+	0.607866i
$86$	−321.513	+	556.878i	−0.403136	+	0.698252i
$87$	−144.311	+	1028.94i	−0.177837	+	1.26798i
$88$	−449.059	−	777.792i	−0.543975	−	0.942193i
$89$	−255.905			−0.304785			−0.152392	−	0.988320i	$-0.548698\pi$
$89$	−255.905			−0.304785			−0.152392	+	0.988320i	$0.548698\pi$
$90$	−176.272	−	705.285i	−0.206452	−	0.826040i
$91$	752.509			0.866861
$92$	711.027	+	1231.53i	0.805757	+	1.39561i
$93$	369.138	−	149.263i	0.411590	−	0.166429i
$94$	−654.699	+	1133.97i	−0.718373	+	1.24426i
$95$	−30.2179	+	52.3390i	−0.0326347	+	0.0565249i
$96$	2722.83	−	1100.99i	2.89476	−	1.17051i
$97$	−524.759	−	908.909i	−0.549291	−	0.951400i	−0.998323	−	0.0578842i	$-0.981565\pi$
$97$	−524.759	−	908.909i	−0.549291	−	0.951400i	0.449032	−	0.893515i	$-0.351769\pi$
$98$	−996.177			−1.02683
$99$	249.064	−	240.791i	0.252847	−	0.244448i
$100$	524.964			0.524964
$101$	−44.3635	−	76.8398i	−0.0437062	−	0.0757014i	0.843345	−	0.537373i	$-0.180583\pi$
$101$	−44.3635	−	76.8398i	−0.0437062	−	0.0757014i	−0.887051	+	0.461671i	$0.847250\pi$
$102$	427.548	−	3048.43i	0.415035	−	2.95921i
$103$	772.035	−	1337.20i	0.738552	−	1.27921i	−0.214595	−	0.976703i	$-0.568843\pi$
$103$	772.035	−	1337.20i	0.738552	−	1.27921i	0.953147	−	0.302507i	$-0.0978236\pi$
$104$	−2095.19	+	3628.97i	−1.97548	+	3.42163i
$105$	257.408	+	200.992i	0.239242	+	0.186808i
$106$	790.301	+	1368.84i	0.724158	+	1.25428i
$107$	−585.772			−0.529240			−0.264620	−	0.964353i	$-0.585247\pi$
$107$	−585.772			−0.529240			−0.264620	+	0.964353i	$0.585247\pi$
$108$	1733.65	+	2381.90i	1.54463	+	2.12221i
$109$	1367.04			1.20127			0.600634	−	0.799524i	$-0.294915\pi$
$109$	1367.04			1.20127			0.600634	+	0.799524i	$0.294915\pi$
$110$	172.734	+	299.184i	0.149723	+	0.259328i
$111$	92.0735	+	71.8937i	0.0787318	+	0.0614761i
$112$	−1313.28	+	2274.66i	−1.10797	+	1.91907i
$113$	−85.2146	+	147.596i	−0.0709408	+	0.122873i	−0.899314	−	0.437304i	$-0.855933\pi$
$113$	−85.2146	+	147.596i	−0.0709408	+	0.122873i	0.828373	+	0.560177i	$0.189267\pi$
$114$	46.9758	−	334.938i	0.0385937	−	0.275174i
$115$	−169.304	−	293.243i	−0.137284	−	0.237783i
$116$	4198.83			3.36079
$117$	−1553.98	−	444.644i	−1.22791	−	0.351345i
$118$	−3130.77			−2.44246
$119$	691.429	+	1197.59i	0.532632	+	0.922546i
$120$	−1685.98	+	681.734i	−1.28256	+	0.518612i
$121$	583.187	−	1010.11i	0.438157	−	0.758910i
$122$	2083.18	−	3608.17i	1.54592	−	2.67761i
$123$	422.768	−	170.949i	0.309916	−	0.125316i
$124$	−804.545	−	1393.51i	−0.582664	−	1.00920i
$125$	−125.000			−0.0894427
$126$	−1757.14	−	502.775i	−1.24237	−	0.355482i
$127$	1809.74			1.26447			0.632237	−	0.774775i	$-0.282137\pi$
$127$	1809.74			1.26447			0.632237	+	0.774775i	$0.282137\pi$
$128$	−1433.63	−	2483.13i	−0.989973	−	1.71468i
$129$	−86.1791	+	614.459i	−0.0588190	+	0.419381i
$130$	805.930	−	1395.91i	0.543729	−	0.941766i
$131$	619.147	−	1072.39i	0.412940	−	0.715232i	−0.582270	−	0.812995i	$-0.697835\pi$
$131$	619.147	−	1072.39i	0.412940	−	0.715232i	0.995210	+	0.0977630i	$0.0311687\pi$
$132$	−1103.44	−	861.600i	−0.727593	−	0.568126i
$133$	75.9691	+	131.582i	0.0495290	+	0.0857867i
$134$	−1246.30			−0.803462
$135$	−412.802	−	567.159i	−0.263173	−	0.361580i
$136$	−7700.50			−4.85524
$137$	−253.091	−	438.367i	−0.157832	−	0.273374i	0.776254	−	0.630420i	$-0.217117\pi$
$137$	−253.091	−	438.367i	−0.157832	−	0.273374i	−0.934087	+	0.357046i	$0.883784\pi$
$138$	1493.57	+	1166.22i	0.921311	+	0.719387i
$139$	106.840	−	185.052i	0.0651946	−	0.112920i	−0.831586	−	0.555396i	$-0.812567\pi$
$139$	106.840	−	185.052i	0.0651946	−	0.112920i	0.896780	+	0.442476i	$0.145900\pi$
$140$	659.890	−	1142.96i	0.398363	−	0.689986i
$141$	−175.487	+	1251.23i	−0.104813	+	0.747320i
$142$	2004.15	+	3471.29i	1.18440	+	2.05144i
$143$	768.103			0.449175
$144$	4056.06	−	3921.33i	2.34726	−	2.26929i
$145$	−999.790			−0.572607
$146$	713.082	+	1235.09i	0.404213	+	0.700117i
$147$	−891.141	+	360.338i	−0.500001	+	0.202178i
$148$	236.039	−	408.832i	0.131097	−	0.227066i
$149$	452.655	−	784.022i	0.248879	−	0.431071i	−0.714336	−	0.699803i	$-0.753271\pi$
$149$	452.655	−	784.022i	0.248879	−	0.431071i	0.963215	+	0.268732i	$0.0866046\pi$
$150$	648.524	−	262.234i	0.353012	−	0.142742i
$151$	−679.335	−	1176.64i	−0.366116	−	0.634131i	0.622839	−	0.782350i	$-0.285979\pi$
$151$	−679.335	−	1176.64i	−0.366116	−	0.634131i	−0.988955	+	0.148219i	$0.952646\pi$
$152$	−846.073			−0.451484
$153$	−720.211	−	2881.66i	−0.380560	−	1.52267i
$154$	868.521			0.454464
$155$	191.572	+	331.812i	0.0992736	+	0.171947i
$156$	−907.235	+	6468.60i	−0.465622	+	3.31989i
$157$	−950.670	+	1646.61i	−0.483259	+	0.837030i	−0.999815	−	0.0192236i	$-0.993881\pi$
$157$	−950.670	+	1646.61i	−0.483259	+	0.837030i	0.516556	+	0.856254i	$0.327214\pi$
$158$	−1507.05	+	2610.28i	−0.758824	+	1.31432i
$159$	1202.11	+	938.643i	0.599582	+	0.468172i
$160$	1413.06	+	2447.50i	0.698203	+	1.20932i
$161$	−851.273			−0.416706
$162$	3331.53	+	2076.53i	1.61574	+	1.00708i
$163$	−2325.15			−1.11730			−0.558649	−	0.829404i	$-0.688680\pi$
$163$	−2325.15			−1.11730			−0.558649	+	0.829404i	$0.688680\pi$
$164$	−921.432	−	1595.97i	−0.438730	−	0.759903i
$165$	262.742	+	205.157i	0.123966	+	0.0967967i
$166$	3287.26	−	5693.69i	1.53699	−	2.66215i
$167$	−982.901	+	1702.43i	−0.455444	+	0.788853i	−0.998714	−	0.0507059i	$-0.983853\pi$
$167$	−982.901	+	1702.43i	−0.455444	+	0.788853i	0.543269	+	0.839558i	$0.317186\pi$
$168$	−635.019	+	4527.70i	−0.291624	+	2.07928i
$169$	−693.379	−	1200.97i	−0.315603	−	0.546640i
$170$	2962.06			1.33635
$171$	−79.1314	−	316.615i	−0.0353879	−	0.141591i
$172$	2507.44			1.11157
$173$	1148.95	+	1990.04i	0.504932	+	0.874567i	0.999984	+	0.00570381i	$0.00181559\pi$
$173$	1148.95	+	1990.04i	0.504932	+	0.874567i	−0.495052	+	0.868863i	$0.664851\pi$
$174$	5187.10	−	2097.43i	2.25996	−	0.913828i
$175$	−157.127	+	272.153i	−0.0678727	+	0.117559i
$176$	−1340.49	+	2321.80i	−0.574110	+	0.994387i
$177$	−2800.66	+	1132.46i	−1.18933	+	0.480911i
$178$	689.027	+	1193.43i	0.290139	+	0.502536i
$179$	−873.696			−0.364822			−0.182411	−	0.983222i	$-0.558390\pi$
$179$	−873.696			−0.364822			−0.182411	+	0.983222i	$0.558390\pi$
$180$	−2038.07	+	1970.38i	−0.843939	+	0.815906i
$181$	1494.20			0.613609			0.306805	−	0.951772i	$-0.400740\pi$
$181$	1494.20			0.613609			0.306805	+	0.951772i	$0.400740\pi$
$182$	−2026.14	−	3509.38i	−0.825206	−	1.42930i
$183$	558.380	−	3981.26i	0.225555	−	1.60821i
$184$	2370.17	−	4105.26i	0.949627	−	1.64480i
$185$	−56.2037	+	97.3476i	−0.0223361	+	0.0386872i
$186$	−1690.01	−	1319.61i	−0.666224	−	0.520207i
$187$	705.758	+	1222.41i	0.275990	+	0.478028i
$188$	5105.91			1.98078
$189$	−1753.73	+	185.831i	−0.674948	+	0.0715196i
$190$	325.449			0.124266
$191$	−2525.13	−	4373.65i	−0.956607	−	1.65689i	−0.730648	−	0.682754i	$-0.760782\pi$
$191$	−2525.13	−	4373.65i	−0.956607	−	1.65689i	−0.225959	−	0.974137i	$-0.572551\pi$
$192$	−5619.68	−	4388.02i	−2.11232	−	1.64936i
$193$	−2580.80	+	4470.08i	−0.962539	+	1.66717i	−0.246452	+	0.969155i	$0.579265\pi$
$193$	−2580.80	+	4470.08i	−0.962539	+	1.66717i	−0.716087	+	0.698011i	$0.754069\pi$
$194$	−2825.84	+	4894.50i	−1.04579	+	1.81137i
$195$	216.023	−	1540.25i	0.0793321	−	0.565639i
$196$	1942.26	+	3364.10i	0.707822	+	1.22598i
$197$	374.025			0.135270			0.0676350	−	0.997710i	$-0.478455\pi$
$197$	374.025			0.135270			0.0676350	+	0.997710i	$0.478455\pi$
$198$	−1793.55	−	513.194i	−0.643748	−	0.184197i
$199$	603.342			0.214924			0.107462	−	0.994209i	$-0.465728\pi$
$199$	603.342			0.214924			0.107462	+	0.994209i	$0.465728\pi$
$200$	−874.970	−	1515.49i	−0.309349	−	0.535808i
$201$	−1114.89	+	450.813i	−0.391236	+	0.158198i
$202$	−238.899	+	413.785i	−0.0832121	+	0.144128i
$203$	−1256.76	+	2176.76i	−0.434517	+	0.752606i
$204$	−11128.2	+	4499.73i	−3.81925	+	1.54433i
$205$	219.404	+	380.018i	0.0747504	+	0.129471i
$206$	−8314.87			−2.81225
$207$	1757.93	+	503.002i	0.590265	+	0.168894i
$208$	12508.7			4.16983
$209$	77.5434	+	134.309i	0.0256640	+	0.0444514i
$210$	244.265	−	1741.62i	0.0802662	−	0.572299i
$211$	−1205.91	+	2088.69i	−0.393450	+	0.681476i	−0.992902	−	0.118935i	$-0.962052\pi$
$211$	−1205.91	+	2088.69i	−0.393450	+	0.681476i	0.599452	+	0.800411i	$0.295385\pi$
$212$	3081.72	−	5337.70i	0.998366	−	1.72922i
$213$	3048.47	+	2380.34i	0.980648	+	0.765719i
$214$	1577.20	+	2731.79i	0.503809	+	0.872623i
$215$	−597.050			−0.189388
$216$	3986.69	−	8974.76i	1.25583	−	2.82711i
$217$	963.237			0.301331
$218$	−3680.76	−	6375.27i	−1.14354	−	1.98068i
$219$	1084.65	+	846.930i	0.334676	+	0.261325i
$220$	673.565	−	1166.65i	0.206417	−	0.357525i
$221$	3292.87	−	5703.42i	1.00227	−	1.73599i
$222$	87.3724	−	622.966i	0.0264146	−	0.188337i
$223$	−2740.64	−	4746.93i	−0.822990	−	1.42546i	−0.903446	−	0.428703i	$-0.858971\pi$
$223$	−2740.64	−	4746.93i	−0.822990	−	1.42546i	0.0804554	−	0.996758i	$-0.474363\pi$
$224$	7105.00			2.11930
$225$	485.289	−	469.169i	0.143789	−	0.139013i
$226$	917.766			0.270128
$227$	2736.24	+	4739.30i	0.800046	+	1.38572i	0.919585	+	0.392891i	$0.128525\pi$
$227$	2736.24	+	4739.30i	0.800046	+	1.38572i	−0.119539	+	0.992830i	$0.538142\pi$
$228$	−1222.68	+	494.397i	−0.355148	+	0.143606i
$229$	−1637.99	+	2837.08i	−0.472670	+	0.818689i	−0.999511	−	0.0312750i	$-0.990043\pi$
$229$	−1637.99	+	2837.08i	−0.472670	+	0.818689i	0.526840	+	0.849964i	$0.323377\pi$
$230$	−911.706	+	1579.12i	−0.261374	+	0.452714i
$231$	776.945	−	314.162i	0.221295	−	0.0894820i
$232$	−6998.29	−	12121.4i	−1.98043	−	3.43021i
$233$	3446.21			0.968965			0.484483	−	0.874801i	$-0.339008\pi$
$233$	3446.21			0.968965			0.484483	+	0.874801i	$0.339008\pi$
$234$	2110.48	+	8444.31i	0.589601	+	2.35907i
$235$	−1215.78			−0.337483
$236$	6104.11	+	10572.6i	1.68366	+	2.91618i
$237$	−403.952	+	2880.18i	−0.110715	+	0.789401i
$238$	3723.37	−	6449.06i	1.01408	−	1.75643i
$239$	862.406	−	1493.73i	0.233408	−	0.404274i	−0.725401	−	0.688326i	$-0.758346\pi$
$239$	862.406	−	1493.73i	0.233408	−	0.404274i	0.958809	+	0.284053i	$0.0916790\pi$
$240$	4278.82	+	3341.03i	1.15082	+	0.898594i
$241$	2787.86	+	4828.71i	0.745152	+	1.29064i	0.950124	+	0.311873i	$0.100956\pi$
$241$	2787.86	+	4828.71i	0.745152	+	1.29064i	−0.204972	+	0.978768i	$0.565710\pi$
$242$	−6280.96			−1.66841
$243$	3731.37	+	652.496i	0.985053	+	0.172254i
$244$	−16246.4			−4.26259
$245$	−462.475	−	801.031i	−0.120598	−	0.208882i
$246$	−1935.54	−	1511.33i	−0.501649	−	0.391702i
$247$	361.796	−	626.649i	0.0932006	−	0.161428i
$248$	−2681.91	+	4645.21i	−0.686700	+	1.18940i
$249$	881.123	−	6282.42i	0.224253	−	1.59893i
$250$	336.564	+	582.947i	0.0851448	+	0.147475i
$251$	−1356.38			−0.341090			−0.170545	−	0.985350i	$-0.554553\pi$
$251$	−1356.38			−0.341090			−0.170545	+	0.985350i	$0.554553\pi$
$252$	1728.05	+	6914.14i	0.431971	+	1.72837i
$253$	−868.913			−0.215921
$254$	−4872.75	−	8439.84i	−1.20371	−	2.08489i
$255$	2649.74	−	1071.44i	0.650719	−	0.263122i
$256$	−2231.56	+	3865.18i	−0.544815	+	0.943647i
$257$	2043.91	−	3540.16i	0.496092	−	0.859256i	−0.503898	−	0.863763i	$-0.668101\pi$
$257$	2043.91	−	3540.16i	0.496092	−	0.859256i	0.999990	+	0.00450688i	$0.00143459\pi$
$258$	3097.61	−	1252.54i	0.747476	−	0.302246i
$259$	141.298	+	244.736i	0.0338990	+	0.0587148i
$260$	−6285.34			−1.49923
$261$	3881.49	−	3752.57i	0.920530	−	0.889954i
$262$	−6668.25			−1.57239
$263$	215.130	+	372.616i	0.0504391	+	0.0873631i	0.890143	−	0.455682i	$-0.150605\pi$
$263$	215.130	+	372.616i	0.0504391	+	0.0873631i	−0.839704	+	0.543045i	$0.817271\pi$
$264$	−648.178	+	4621.52i	−0.151108	+	1.07741i
$265$	−733.794	+	1270.97i	−0.170100	+	0.294623i
$266$	409.096	−	708.575i	0.0942980	−	0.163329i
$267$	1048.06	+	818.360i	0.240227	+	0.187576i
$268$	2429.93	+	4208.76i	0.553849	+	0.959295i
$269$	3467.85			0.786017			0.393008	−	0.919535i	$-0.371434\pi$
$269$	3467.85			0.786017			0.393008	+	0.919535i	$0.371434\pi$
$270$	−1533.51	+	3452.22i	−0.345654	+	0.778130i
$271$	−55.4415			−0.0124274			−0.00621371	−	0.999981i	$-0.501978\pi$
$271$	−55.4415			−0.0124274			−0.00621371	+	0.999981i	$0.501978\pi$
$272$	11493.4	+	19907.2i	2.56210	+	4.43769i
$273$	−3081.92	−	2406.46i	−0.683247	−	0.533499i
$274$	−1362.90	+	2360.62i	−0.300497	+	0.520475i
$275$	−160.384	+	277.793i	−0.0351691	+	0.0609146i
$276$	1026.31	−	7317.59i	0.223828	−	1.59589i
$277$	786.769	+	1362.72i	0.170658	+	0.295589i	0.938650	−	0.344871i	$-0.112077\pi$
$277$	786.769	+	1362.72i	0.170658	+	0.295589i	−0.767992	+	0.640460i	$0.778744\pi$
$278$	−1150.67			−0.248247
$279$	−1989.15	−	569.160i	−0.426836	−	0.122132i
$280$	−4399.42			−0.938984
$281$	−4073.23	−	7055.04i	−0.864727	−	1.49775i	−0.867318	−	0.497755i	$-0.834158\pi$
$281$	−4073.23	−	7055.04i	−0.864727	−	1.49775i	0.00259078	−	0.999997i	$-0.499175\pi$
$282$	6307.68	−	2550.55i	1.33198	−	0.538592i
$283$	−1549.15	+	2683.21i	−0.325398	+	0.563605i	−0.981593	−	0.190986i	$-0.938832\pi$
$283$	−1549.15	+	2683.21i	−0.325398	+	0.563605i	0.656195	+	0.754591i	$0.272165\pi$
$284$	7815.05	−	13536.1i	1.63288	−	2.82823i
$285$	291.134	−	117.722i	0.0605098	−	0.0244675i
$286$	−2068.13	−	3582.10i	−0.427591	−	0.740609i
$287$	1103.18			0.226894
$288$	−14672.3	−	4198.22i	−3.00199	−	0.858967i
$289$	7189.39			1.46334
$290$	2691.95	+	4662.59i	0.545092	+	0.944127i
$291$	−757.445	+	5400.60i	−0.152585	+	1.08793i
$292$	2780.61	−	4816.16i	0.557271	−	0.965221i
$293$	−61.0799	+	105.794i	−0.0121786	+	0.0210939i	−0.872050	−	0.489416i	$-0.837210\pi$
$293$	−61.0799	+	105.794i	−0.0121786	+	0.0210939i	0.859872	+	0.510510i	$0.170543\pi$
$294$	4079.87	+	3185.69i	0.809330	+	0.631949i
$295$	−1453.46	−	2517.46i	−0.286860	−	0.496856i
$296$	−1573.65			−0.309008
$297$	−1790.07	+	189.682i	−0.349733	+	0.0370588i
$298$	−4875.12			−0.947679
$299$	2027.06	+	3510.97i	0.392066	+	0.679078i
$300$	−2150.00	−	1678.79i	−0.413769	−	0.323083i
$301$	−750.504	+	1299.91i	−0.143715	+	0.248922i
$302$	−3658.24	+	6336.25i	−0.697046	+	1.20732i
$303$	−64.0349	+	456.570i	−0.0121410	+	0.0865652i
$304$	1262.81	+	2187.25i	0.238247	+	0.412657i
$305$	3868.47			0.726255
$306$	−11499.6	+	11117.7i	−2.14833	+	2.07697i
$307$	−1928.53			−0.358525			−0.179263	−	0.983801i	$-0.557371\pi$
$307$	−1928.53			−0.358525			−0.179263	+	0.983801i	$0.557371\pi$
$308$	−1693.37	−	2933.00i	−0.313275	−	0.542608i
$309$	−7438.15	+	3007.66i	−1.36939	+	0.553721i
$310$	1031.62	−	1786.82i	0.189007	−	0.327369i
$311$	−3969.65	+	6875.63i	−0.723788	+	1.25364i	0.235683	+	0.971830i	$0.424267\pi$
$311$	−3969.65	+	6875.63i	−0.723788	+	1.25364i	−0.959471	+	0.281807i	$0.909066\pi$
$312$	20186.0	−	8162.33i	3.66285	−	1.48109i
$313$	3379.44	+	5853.37i	0.610279	+	1.05703i	0.991193	+	0.132424i	$0.0422762\pi$
$313$	3379.44	+	5853.37i	0.610279	+	1.05703i	−0.380914	+	0.924611i	$0.624391\pi$
$314$	10238.8			1.84015
$315$	−411.468	−	1646.34i	−0.0735988	−	0.294478i
$316$	11753.2			2.09232
$317$	−4212.12	−	7295.60i	−0.746297	−	1.29262i	−0.949587	−	0.313505i	$-0.898497\pi$
$317$	−4212.12	−	7295.60i	−0.746297	−	1.29262i	0.203290	−	0.979119i	$-0.434837\pi$
$318$	1140.73	−	8133.44i	0.201161	−	1.43428i
$319$	−1282.80	+	2221.87i	−0.225150	+	0.389972i
$320$	3430.38	−	5941.59i	0.599262	−	1.03795i
$321$	2399.05	+	1873.25i	0.417139	+	0.325715i
$322$	2292.06	+	3969.97i	0.396683	+	0.687074i
$323$	1329.72			0.229064
$324$	516.912	−	15299.2i	0.0886337	−	2.62332i
$325$	1496.61			0.255437
$326$	6260.49	+	10843.5i	1.06361	+	1.84222i
$327$	−5598.73	−	4371.66i	−0.946822	−	0.739307i
$328$	−3071.55	+	5320.08i	−0.517067	+	0.895586i
$329$	−1528.25	+	2647.01i	−0.256095	+	0.443570i
$330$	249.327	−	1777.71i	0.0415909	−	0.296544i
$331$	−128.837	−	223.153i	−0.0213944	−	0.0370562i	0.855130	−	0.518414i	$-0.173477\pi$
$331$	−128.837	−	223.153i	−0.0213944	−	0.0370562i	−0.876524	+	0.481357i	$0.840144\pi$
$332$	−25636.9			−4.23797
$333$	−147.180	−	588.886i	−0.0242205	−	0.0969091i
$334$	10585.9			1.73424
$335$	−578.595	−	1002.16i	−0.0943642	−	0.163444i
$336$	12652.7	−	5116.20i	2.05435	−	0.830690i
$337$	5549.76	−	9612.47i	0.897077	−	1.55378i	0.0658636	−	0.997829i	$-0.479020\pi$
$337$	5549.76	−	9612.47i	0.897077	−	1.55378i	0.831213	−	0.555954i	$-0.187647\pi$
$338$	−3733.87	+	6467.25i	−0.600874	+	1.04075i
$339$	820.997	−	331.975i	0.131535	−	0.0531870i
$340$	−5775.17	−	10002.9i	−0.921184	−	1.59554i
$341$	983.198			0.156138
$342$	−1263.49	+	1221.53i	−0.199772	+	0.193136i
$343$	−6636.94			−1.04478
$344$	−4179.21	−	7238.60i	−0.655023	−	1.13453i
$345$	−244.376	+	1742.40i	−0.0381355	+	0.271907i
$346$	6187.14	−	10716.4i	0.961337	−	1.66508i
$347$	−4943.28	+	8562.02i	−0.764753	+	1.32459i	0.175624	+	0.984457i	$0.443806\pi$
$347$	−4943.28	+	8562.02i	−0.764753	+	1.32459i	−0.940377	+	0.340134i	$0.889528\pi$
$348$	−17196.4	−	13427.5i	−2.64892	−	2.06836i
$349$	−3029.60	−	5247.42i	−0.464673	−	0.804837i	0.534514	−	0.845160i	$-0.320495\pi$
$349$	−3029.60	−	5247.42i	−0.464673	−	0.804837i	−0.999187	+	0.0403230i	$0.987161\pi$
$350$	1692.27			0.258445
$351$	4942.43	+	6790.54i	0.751589	+	1.03263i
$352$	7252.23			1.09814
$353$	4548.34	+	7877.96i	0.685790	+	1.18782i	0.973188	+	0.230012i	$0.0738765\pi$
$353$	4548.34	+	7877.96i	0.685790	+	1.18782i	−0.287398	+	0.957811i	$0.592790\pi$
$354$	12822.2	+	10011.9i	1.92511	+	1.50318i
$355$	−1860.85	+	3223.10i	−0.278208	+	0.481871i
$356$	2686.81	−	4653.70i	0.400002	−	0.692824i
$357$	998.020	−	7115.90i	0.147957	−	1.05494i
$358$	2352.44	+	4074.55i	0.347291	+	0.601527i
$359$	−8804.63			−1.29440			−0.647201	−	0.762319i	$-0.724061\pi$
$359$	−8804.63			−1.29440			−0.647201	+	0.762319i	$0.724061\pi$
$360$	9085.09	+	2599.54i	1.33007	+	0.380577i
$361$	−6712.90			−0.978700
$362$	−4023.17	−	6968.33i	−0.584124	−	1.01173i
$363$	−5618.70	+	2271.95i	−0.812411	+	0.328503i
$364$	−7900.80	+	13684.6i	−1.13768	+	1.97051i
$365$	−662.096	+	1146.78i	−0.0949471	+	0.164453i
$366$	−20070.3	+	8115.56i	−2.86638	+	1.15904i
$367$	−4326.18	−	7493.17i	−0.615326	−	1.06578i	−0.990327	−	0.138752i	$-0.955691\pi$
$367$	−4326.18	−	7493.17i	−0.615326	−	1.06578i	0.375001	−	0.927025i	$-0.377642\pi$
$368$	−14150.5			−2.00447
$369$	−2278.14	−	651.849i	−0.321396	−	0.0919619i
$370$	605.317			0.0850511
$371$	1844.79	+	3195.27i	0.258158	+	0.447143i
$372$	−1161.29	+	8280.04i	−0.161855	+	1.15403i
$373$	5959.31	−	10321.8i	0.827243	−	1.43283i	−0.0729500	−	0.997336i	$-0.523241\pi$
$373$	5959.31	−	10321.8i	0.827243	−	1.43283i	0.900193	−	0.435491i	$-0.143425\pi$
$374$	3800.53	−	6582.70i	0.525456	−	0.910116i
$375$	511.941	+	399.739i	0.0704974	+	0.0550465i
$376$	−8510.14	−	14740.0i	−1.16723	−	2.02170i
$377$	11970.4			1.63529
$378$	5588.59	+	7678.30i	0.760439	+	1.04479i
$379$	5052.23			0.684738			0.342369	−	0.939566i	$-0.388771\pi$
$379$	5052.23			0.684738			0.342369	+	0.939566i	$0.388771\pi$
$380$	−634.533	−	1099.04i	−0.0856601	−	0.148368i
$381$	−7411.83	−	5787.38i	−0.996640	−	0.778206i
$382$	−13597.9	+	23552.2i	−1.82128	+	3.15455i
$383$	2665.19	−	4616.24i	0.355573	−	0.615871i	−0.631642	−	0.775260i	$-0.717619\pi$
$383$	2665.19	−	4616.24i	0.355573	−	0.615871i	0.987216	+	0.159388i	$0.0509522\pi$
$384$	−2069.33	+	14754.4i	−0.275000	+	1.96076i
$385$	403.211	+	698.381i	0.0533754	+	0.0924489i
$386$	27795.4			3.66515
$387$	2317.93	−	2240.94i	0.304463	−	0.294350i
$388$	22038.4			2.88358
$389$	−1669.76	−	2892.11i	−0.217635	−	0.376955i	0.736449	−	0.676493i	$-0.236501\pi$
$389$	−1669.76	−	2892.11i	−0.217635	−	0.376955i	−0.954085	+	0.299537i	$0.903168\pi$
$390$	−7764.72	+	3139.71i	−1.00816	+	0.407654i
$391$	−3725.05	+	6451.98i	−0.481800	+	0.834503i
$392$	6474.43	−	11214.0i	0.834205	−	1.44488i
$393$	−5965.15	+	2412.04i	−0.765654	+	0.309597i
$394$	−1007.07	−	1744.29i	−0.128770	−	0.223036i
$395$	−2798.58			−0.356486
$396$	1763.86	+	7057.42i	0.223831	+	0.895577i
$397$	9041.65			1.14304			0.571520	−	0.820588i	$-0.306354\pi$
$397$	9041.65			1.14304			0.571520	+	0.820588i	$0.306354\pi$
$398$	−1624.51	−	2813.73i	−0.204596	−	0.354371i
$399$	109.655	−	781.842i	0.0137584	−	0.0980978i
$400$	−2611.89	+	4523.92i	−0.326486	+	0.565490i
$401$	835.978	−	1447.96i	0.104107	−	0.180318i	−0.809266	−	0.587442i	$-0.800135\pi$
$401$	835.978	−	1447.96i	0.104107	−	0.180318i	0.913373	+	0.407124i	$0.133468\pi$
$402$	5104.26	+	3985.56i	0.633277	+	0.494482i
$403$	−2293.67	−	3972.75i	−0.283513	−	0.491059i
$404$	1863.14			0.229442
$405$	−123.083	+	3642.92i	−0.0151013	+	0.446959i
$406$	13535.3			1.65455
$407$	144.226	+	249.807i	0.0175652	+	0.0304238i
$408$	31537.6	+	24625.5i	3.82683	+	2.98810i
$409$	−236.363	+	409.393i	−0.0285755	+	0.0494943i	−0.879960	−	0.475049i	$-0.842430\pi$
$409$	−236.363	+	409.393i	−0.0285755	+	0.0494943i	0.851384	+	0.524543i	$0.175764\pi$
$410$	1181.50	−	2046.41i	0.142317	−	0.246500i
$411$	−365.316	+	2604.71i	−0.0438436	+	0.312605i
$412$	16211.6	+	28079.4i	1.93857	+	3.35770i
$413$	−7308.11			−0.870722
$414$	−2387.48	−	9552.59i	−0.283425	−	1.13402i
$415$	6104.43			0.722060
$416$	−16918.5	−	29303.7i	−1.99398	−	3.45368i
$417$	−1029.35	+	416.222i	−0.120881	+	0.0488789i
$418$	417.573	−	723.258i	0.0488617	−	0.0846309i
$419$	−6269.65	+	10859.3i	−0.731008	+	1.26614i	0.225445	+	0.974256i	$0.427616\pi$
$419$	−6269.65	+	10859.3i	−0.731008	+	1.26614i	−0.956453	+	0.291887i	$0.905717\pi$
$420$	−6357.69	+	2570.77i	−0.738628	+	0.298668i
$421$	3375.88	+	5847.19i	0.390808	+	0.676900i	0.992556	−	0.121786i	$-0.0388623\pi$
$421$	3375.88	+	5847.19i	0.390808	+	0.676900i	−0.601748	+	0.798686i	$0.705529\pi$
$422$	12987.7			1.49818
$423$	4720.02	−	4563.24i	0.542542	−	0.524521i
$424$	−20545.5			−2.35325
$425$	1375.14	+	2381.81i	0.156950	+	0.271846i
$426$	2892.82	−	20625.9i	0.329009	−	2.34584i
$427$	4862.74	−	8422.51i	0.551111	−	0.954552i
$428$	6150.18	−	10652.4i	0.694580	−	1.20305i
$429$	−3145.79	−	2456.32i	−0.354033	−	0.276439i
$430$	1607.57	+	2784.39i	0.180288	+	0.312268i
$431$	7535.06			0.842114			0.421057	−	0.907034i	$-0.361659\pi$
$431$	7535.06			0.842114			0.421057	+	0.907034i	$0.361659\pi$
$432$	−29151.8	+	3089.01i	−3.24668	+	0.344028i
$433$	−5135.13			−0.569928			−0.284964	−	0.958538i	$-0.591982\pi$
$433$	−5135.13			−0.569928			−0.284964	+	0.958538i	$0.591982\pi$
$434$	−2593.53	−	4492.13i	−0.286851	−	0.496841i
$435$	4094.67	+	3197.24i	0.451320	+	0.352404i
$436$	−14352.9	+	24859.9i	−1.57656	+	2.73068i
$437$	−409.281	+	708.895i	−0.0448022	+	0.0775996i
$438$	1029.27	−	7338.74i	0.112284	−	0.800590i
$439$	−8486.60	−	14699.2i	−0.922650	−	1.59808i	−0.795297	−	0.606220i	$-0.792685\pi$
$439$	−8486.60	−	14699.2i	−0.922650	−	1.59808i	−0.127353	−	0.991857i	$-0.540648\pi$
$440$	−4490.59			−0.486546
$441$	4802.02	+	1374.02i	0.518521	+	0.148366i
$442$	−35464.4			−3.81645
$443$	−5676.15	−	9831.39i	−0.608763	−	1.05441i	−0.991445	−	0.130529i	$-0.958333\pi$
$443$	−5676.15	−	9831.39i	−0.608763	−	1.05441i	0.382681	−	0.923880i	$-0.375001\pi$
$444$	−2274.11	+	919.550i	−0.243073	+	0.0982881i
$445$	−639.762	+	1108.10i	−0.0681519	+	0.118043i
$446$	−14758.4	+	25562.3i	−1.56689	+	2.71393i
$447$	−4361.09	+	1763.43i	−0.461460	+	0.186594i
$448$	−8624.10	−	14937.4i	−0.909488	−	1.57528i
$449$	11059.8			1.16246			0.581230	−	0.813740i	$-0.302572\pi$
$449$	11059.8			1.16246			0.581230	+	0.813740i	$0.302572\pi$
$450$	−3494.65	−	999.934i	−0.366088	−	0.104750i
$451$	1126.04			0.117568
$452$	−1789.38	−	3099.30i	−0.186207	−	0.322520i
$453$	−980.562	+	6991.42i	−0.101702	+	0.725134i
$454$	14734.7	−	25521.3i	1.52320	−	2.63827i
$455$	1881.27	−	3258.46i	0.193836	−	0.335734i
$456$	3465.12	+	2705.67i	0.355853	+	0.277861i
$457$	−178.342	−	308.897i	−0.0182549	−	0.0316184i	0.856754	−	0.515726i	$-0.172478\pi$
$457$	−178.342	−	308.897i	−0.0182549	−	0.0316184i	−0.875009	+	0.484107i	$0.839144\pi$
$458$	17641.3			1.79983
$459$	−6265.63	+	14105.1i	−0.637156	+	1.43435i
$460$	7110.27			0.720691
$461$	−5159.88	−	8937.17i	−0.521300	−	0.902918i	−0.999693	−	0.0247726i	$-0.992114\pi$
$461$	−5159.88	−	8937.17i	−0.521300	−	0.902918i	0.478393	−	0.878146i	$-0.341219\pi$
$462$	−3557.05	−	2777.45i	−0.358201	−	0.279694i
$463$	9084.27	−	15734.4i	0.911839	−	1.57935i	0.100376	−	0.994950i	$-0.467996\pi$
$463$	9084.27	−	15734.4i	0.911839	−	1.57935i	0.811464	−	0.584403i	$-0.198671\pi$
$464$	−20890.7	+	36183.7i	−2.09014	+	3.62023i
$465$	276.517	−	1971.57i	0.0275767	−	0.196623i
$466$	−9278.98	−	16071.7i	−0.922404	−	1.59765i
$467$	3817.15			0.378237			0.189118	−	0.981954i	$-0.439437\pi$
$467$	3817.15			0.378237			0.189118	+	0.981954i	$0.439437\pi$
$468$	24401.6	−	23591.1i	2.41018	−	2.33013i
$469$	−2909.22			−0.286429
$470$	3273.50	+	5669.86i	0.321266	+	0.556449i
$471$	9159.21	−	3703.58i	0.896038	−	0.362318i
$472$	20347.7	−	35243.3i	1.98428	−	3.43687i
$473$	−766.056	+	1326.85i	−0.0744679	+	0.128982i
$474$	14519.6	−	5871.08i	1.40698	−	0.568919i
$475$	151.090	+	261.695i	0.0145947	+	0.0252787i
$476$	−29038.0			−2.79613
$477$	−1921.58	−	7688.48i	−0.184451	−	0.738012i
$478$	−9288.17			−0.888768
$479$	−1453.28	−	2517.16i	−0.138627	−	0.240109i	0.788350	−	0.615227i	$-0.210936\pi$
$479$	−1453.28	−	2517.16i	−0.138627	−	0.240109i	−0.926977	+	0.375118i	$0.877602\pi$
$480$	2039.64	−	14542.7i	0.193951	−	1.38287i
$481$	672.921	−	1165.53i	0.0637891	−	0.110486i
$482$	15012.7	−	26002.7i	1.41869	−	2.45725i
$483$	3486.41	+	2722.29i	0.328442	+	0.256457i
$484$	12246.1	+	21210.8i	1.15008	+	1.99200i
$485$	−5247.59			−0.491301
$486$	−7003.82	−	19158.4i	−0.653703	−	1.78815i
$487$	10411.1			0.968734			0.484367	−	0.874865i	$-0.339050\pi$
$487$	10411.1			0.968734			0.484367	+	0.874865i	$0.339050\pi$
$488$	27078.3	+	46901.0i	2.51184	+	4.35064i
$489$	9522.70	+	7435.61i	0.880637	+	0.687628i
$490$	−2490.44	+	4313.57i	−0.229606	+	0.397689i
$491$	−7316.26	+	12672.1i	−0.672460	+	1.16474i	0.304744	+	0.952434i	$0.401429\pi$
$491$	−7316.26	+	12672.1i	−0.672460	+	1.16474i	−0.977204	+	0.212301i	$0.931904\pi$
$492$	−1330.01	+	9482.99i	−0.121873	+	0.868956i
$493$	10998.8	+	19050.4i	1.00479	+	1.74034i
$494$	−3896.57			−0.354888
$495$	−419.995	−	1680.45i	−0.0381361	−	0.152587i
$496$	16011.6			1.44948
$497$	4678.26	+	8102.99i	0.422231	+	0.731325i
$498$	−31671.0	+	12806.3i	−2.84982	+	1.15234i
$499$	−4083.42	+	7072.69i	−0.366330	+	0.634503i	−0.988989	−	0.147991i	$-0.952719\pi$
$499$	−4083.42	+	7072.69i	−0.366330	+	0.634503i	0.622658	+	0.782494i	$0.286053\pi$
$500$	1312.41	−	2273.16i	0.117385	−	0.203318i
$501$	9469.74	−	3829.14i	0.844464	−	0.341464i
$502$	3652.06	+	6325.56i	0.324700	+	0.562397i
$503$	−8080.38			−0.716275			−0.358137	−	0.933669i	$-0.616588\pi$
$503$	−8080.38			−0.716275			−0.358137	+	0.933669i	$0.616588\pi$
$504$	17079.9	−	16512.6i	1.50952	−	1.45938i
$505$	−443.635			−0.0390921
$506$	2339.56	+	4052.24i	0.205546	+	0.356016i
$507$	−1000.83	+	7135.96i	−0.0876698	+	0.625087i
$508$	−19000.9	+	32910.6i	−1.65951	+	2.87435i
$509$	−58.0903	+	100.615i	−0.00505856	+	0.00876169i	−0.868544	−	0.495613i	$-0.834944\pi$
$509$	−58.0903	+	100.615i	−0.00505856	+	0.00876169i	0.863485	+	0.504374i	$0.168277\pi$
$510$	−12131.2	−	9472.40i	−1.05329	−	0.822441i
$511$	1664.54	+	2883.06i	0.144099	+	0.249587i
$512$	1095.90			0.0945947
$513$	−688.421	+	1549.76i	−0.0592486	+	0.133379i
$514$	−22013.0			−1.88901
$515$	−3860.18	−	6686.02i	−0.330291	−	0.572080i
$516$	−10269.3	−	8018.57i	−0.876124	−	0.684104i
$517$	−1559.92	+	2701.87i	−0.132699	+	0.229841i
$518$	760.895	−	1317.91i	0.0645402	−	0.111787i
$519$	1658.41	−	11824.5i	0.140263	−	1.00007i
$520$	10475.9	+	18144.8i	0.883461	+	1.53020i
$521$	−14479.3			−1.21756			−0.608780	−	0.793339i	$-0.708341\pi$
$521$	−14479.3			−1.21756			−0.608780	+	0.793339i	$0.708341\pi$
$522$	−27951.3	−	7997.79i	−2.34367	−	0.670601i
$523$	6841.05			0.571966			0.285983	−	0.958235i	$-0.407680\pi$
$523$	6841.05			0.571966			0.285983	+	0.958235i	$0.407680\pi$
$524$	13001.2	+	22518.7i	1.08389	+	1.87736i
$525$	1513.84	−	612.130i	0.125847	−	0.0508868i
$526$	1158.48	−	2006.55i	0.0960308	−	0.166330i
$527$	4214.99	−	7300.58i	0.348402	−	0.603450i
$528$	12914.9	−	5222.22i	1.06449	−	0.430432i
$529$	3790.40	+	6565.16i	0.311531	+	0.539588i
$530$	7903.01			0.647707
$531$	15091.7	+	4318.23i	1.23338	+	0.352910i
$532$	−3190.48			−0.260009
$533$	−2626.90	−	4549.92i	−0.213478	−	0.369754i
$534$	994.552	−	7091.17i	0.0805964	−	0.574654i
$535$	−1464.43	+	2536.47i	−0.118342	+	0.204974i
$536$	8100.05	−	14029.7i	0.652741	−	1.13058i
$537$	3578.25	+	2794.00i	0.287547	+	0.224525i
$538$	−9337.24	−	16172.6i	−0.748247	−	1.29600i
$539$	−2373.55			−0.189677
$540$	14648.1	−	1552.16i	1.16732	−	0.123693i
$541$	−12746.0			−1.01293			−0.506465	−	0.862261i	$-0.669048\pi$
$541$	−12746.0			−1.01293			−0.506465	+	0.862261i	$0.669048\pi$
$542$	149.277	+	258.555i	0.0118303	+	0.0204906i
$543$	−6119.56	−	4778.33i	−0.483638	−	0.377639i
$544$	31090.5	−	53850.3i	2.45036	−	4.24414i
$545$	3417.59	−	5919.44i	0.268612	−	0.465249i
$546$	−2924.56	+	20852.2i	−0.229230	+	1.63442i
$547$	−2490.27	−	4313.28i	−0.194655	−	0.337152i	0.752132	−	0.659012i	$-0.229025\pi$
$547$	−2490.27	−	4313.28i	−0.194655	−	0.337152i	−0.946787	+	0.321860i	$0.895692\pi$
$548$	10629.1			0.828563
$549$	−15018.6	+	14519.7i	−1.16754	+	1.12876i
$550$	1727.34			0.133916
$551$	1208.46	+	2093.12i	0.0934342	+	0.161833i
$552$	−22835.4	+	9233.61i	−1.76076	+	0.711972i
$553$	−3517.88	+	6093.14i	−0.270516	+	0.468547i
$554$	4236.77	−	7338.31i	0.324916	−	0.562771i
$555$	541.493	−	218.956i	0.0414146	−	0.0167462i
$556$	2243.48	+	3885.83i	0.171124	+	0.296395i
$557$	−635.610			−0.0483513			−0.0241756	−	0.999708i	$-0.507696\pi$
$557$	−635.610			−0.0483513			−0.0241756	+	0.999708i	$0.507696\pi$
$558$	2701.49	+	10809.0i	0.204952	+	0.820039i
$559$	7148.42			0.540869
$560$	6566.38	+	11373.3i	0.495501	+	0.858232i
$561$	1018.70	−	7263.36i	0.0766660	−	0.546630i
$562$	−21934.4	+	37991.6i	−1.64635	+	2.85156i
$563$	3768.84	−	6527.82i	0.282127	−	0.488659i	−0.689781	−	0.724018i	$-0.742293\pi$
$563$	3768.84	−	6527.82i	0.282127	−	0.488659i	0.971908	+	0.235359i	$0.0756266\pi$
$564$	−20911.4	−	16328.2i	−1.56122	−	1.21905i
$565$	426.073	+	737.980i	0.0317257	+	0.0549505i
$566$	16684.5			1.23905
$567$	7776.73	+	4847.20i	0.576000	+	0.359018i
$568$	−52102.2			−3.84887
$569$	1129.18	+	1955.79i	0.0831943	+	0.144097i	0.904620	−	0.426218i	$-0.140154\pi$
$569$	1129.18	+	1955.79i	0.0831943	+	0.144097i	−0.821426	+	0.570315i	$0.806821\pi$
$570$	−1332.89	−	1040.76i	−0.0979446	−	0.0764781i
$571$	−5688.66	+	9853.06i	−0.416923	+	0.722132i	−0.995628	−	0.0934047i	$-0.970225\pi$
$571$	−5688.66	+	9853.06i	−0.416923	+	0.722132i	0.578705	+	0.815537i	$0.303558\pi$
$572$	−8064.52	+	13968.2i	−0.589501	+	1.02105i
$573$	−3644.81	+	25987.5i	−0.265731	+	1.89467i
$574$	−2970.33	−	5144.76i	−0.215991	−	0.374108i
$575$	−1693.04			−0.122791
$576$	8983.10	+	35942.5i	0.649819	+	2.60001i
$577$	−25027.9			−1.80576			−0.902881	−	0.429890i	$-0.858553\pi$
$577$	−25027.9			−1.80576			−0.902881	+	0.429890i	$0.858553\pi$
$578$	−19357.5	−	33528.3i	−1.39302	−	2.41279i
$579$	24864.6	−	10054.2i	1.78470	−	0.721652i
$580$	10497.1	−	18181.5i	0.751495	−	1.30163i
$581$	7673.39	−	13290.7i	0.547928	−	0.949039i
$582$	27225.5	−	11008.8i	1.93906	−	0.784071i
$583$	1883.02	+	3261.48i	0.133768	+	0.231692i
$584$	−18538.1			−1.31355
$585$	−5810.31	+	5617.32i	−0.410644	+	0.397004i
$586$	657.835			0.0463736
$587$	−74.1295	−	128.396i	−0.00521235	−	0.00902806i	0.863407	−	0.504507i	$-0.168326\pi$
$587$	−74.1295	−	128.396i	−0.00521235	−	0.00902806i	−0.868620	+	0.495479i	$0.834992\pi$
$588$	2803.49	−	19988.9i	0.196622	−	1.40192i
$589$	463.112	−	802.133i	0.0323976	−	0.0561143i
$590$	−7826.92	+	13556.6i	−0.546151	+	0.945961i
$591$	−1531.83	−	1196.10i	−0.106618	−	0.0832503i
$592$	2348.76	+	4068.17i	0.163063	+	0.282434i
$593$	−27452.6			−1.90109			−0.950544	−	0.310590i	$-0.899473\pi$
$593$	−27452.6			−1.90109			−0.950544	+	0.310590i	$0.899473\pi$
$594$	5704.40	+	7837.42i	0.394031	+	0.541369i
$595$	6914.29			0.476401
$596$	9505.10	+	16463.3i	0.653262	+	1.13148i
$597$	−2471.01	−	1929.43i	−0.169400	−	0.132272i
$598$	10915.8	−	18906.7i	0.746453	−	1.29289i
$599$	1906.00	−	3301.29i	0.130012	−	0.225187i	−0.793669	−	0.608350i	$-0.791832\pi$
$599$	1906.00	−	3301.29i	0.130012	−	0.225187i	0.923681	+	0.383163i	$0.125165\pi$
$600$	−1262.95	+	9004.82i	−0.0859325	+	0.612700i
$601$	−11584.3	−	20064.6i	−0.786247	−	1.36182i	−0.928251	−	0.371954i	$-0.878688\pi$
$601$	−11584.3	−	20064.6i	−0.786247	−	1.36182i	0.142004	−	0.989866i	$-0.454646\pi$
$602$	8082.97			0.547238
$603$	6007.73	+	1719.01i	0.405728	+	0.116092i
$604$	28530.1			1.92197
$605$	−2915.93	−	5050.55i	−0.195950	−	0.339395i
$606$	2301.66	−	930.691i	0.154288	−	0.0623873i
$607$	−3676.39	+	6367.69i	−0.245832	+	0.425794i	−0.962365	−	0.271759i	$-0.912395\pi$
$607$	−3676.39	+	6367.69i	−0.245832	+	0.425794i	0.716533	+	0.697553i	$0.245728\pi$
$608$	3415.99	−	5916.67i	0.227856	−	0.394659i
$609$	12108.2	−	4896.01i	0.805662	−	0.325774i
$610$	−10415.9	−	18040.9i	−0.691357	−	1.19746i
$611$	14556.4			0.963809
$612$	59965.4	+	17158.1i	3.96072	+	1.13329i
$613$	19902.6			1.31135			0.655676	−	0.755043i	$-0.272384\pi$
$613$	19902.6			1.31135			0.655676	+	0.755043i	$0.272384\pi$
$614$	5192.61	+	8993.86i	0.341297	+	0.591144i
$615$	316.691	−	2258.01i	0.0207646	−	0.148052i
$616$	−5644.76	+	9777.01i	−0.369211	+	0.639492i
$617$	−12542.6	+	21724.4i	−0.818390	+	1.41749i	0.0884785	+	0.996078i	$0.471800\pi$
$617$	−12542.6	+	21724.4i	−0.818390	+	1.41749i	−0.906868	+	0.421414i	$0.861534\pi$
$618$	34053.8	+	26590.2i	2.21658	+	1.73077i
$619$	1565.52	+	2711.56i	0.101654	+	0.176069i	0.912366	−	0.409375i	$-0.134253\pi$
$619$	1565.52	+	2711.56i	0.101654	+	0.176069i	−0.810712	+	0.585445i	$0.800920\pi$
$620$	−8045.45			−0.521150
$621$	−5591.11	−	7681.78i	−0.361294	−	0.496391i
$622$	42753.3			2.75603
$623$	1608.39	+	2785.81i	0.103433	+	0.179151i
$624$	−51229.9	−	40001.8i	−3.28660	−	2.56627i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	18198.4	−	31520.6i	1.16191	−	2.01248i
$627$	111.927	−	798.043i	0.00712910	−	0.0508306i
$628$	−19962.7	−	34576.4i	−1.26847	−	2.19705i
$629$	2473.21			0.156778
$630$	−6569.93	+	6351.70i	−0.415480	+	0.401679i
$631$	−22527.2			−1.42123			−0.710614	−	0.703582i	$-0.751583\pi$
$631$	−22527.2			−1.42123			−0.710614	+	0.703582i	$0.751583\pi$
$632$	−19589.4	−	33929.9i	−1.23295	−	2.13553i
$633$	11618.3	−	4697.92i	0.729518	−	0.294985i
$634$	−22682.4	+	39287.0i	−1.42087	+	2.46102i
$635$	4524.34	−	7836.39i	0.282745	−	0.489729i
$636$	−29690.8	+	12005.6i	−1.85113	+	0.748513i
$637$	5537.17	+	9590.66i	0.344412	+	0.596540i
$638$	13815.8			0.857325
$639$	−4873.00	−	19497.5i	−0.301679	−	1.20706i
$640$	−14336.3			−0.885459
$641$	3462.88	+	5997.88i	0.213378	+	0.369582i	0.952770	−	0.303694i	$-0.0982200\pi$
$641$	3462.88	+	5997.88i	0.213378	+	0.369582i	−0.739391	+	0.673276i	$0.764887\pi$
$642$	2276.55	−	16231.9i	0.139951	−	0.997852i
$643$	7482.26	−	12959.7i	0.458898	−	0.794835i	−0.540005	−	0.841662i	$-0.681578\pi$
$643$	7482.26	−	12959.7i	0.458898	−	0.794835i	0.998903	+	0.0468271i	$0.0149110\pi$
$644$	8937.75	−	15480.6i	0.546889	−	0.947240i
$645$	2445.24	+	1909.31i	0.149273	+	0.116557i
$646$	−3580.29	−	6201.25i	−0.218057	−	0.377685i
$647$	−2371.74			−0.144115			−0.0720577	−	0.997400i	$-0.522957\pi$
$647$	−2371.74			−0.144115			−0.0720577	+	0.997400i	$0.522957\pi$
$648$	−45028.1	+	24007.3i	−2.72974	+	1.45540i
$649$	−7459.55			−0.451176
$650$	−4029.65	−	6979.56i	−0.243163	−	0.421171i
$651$	−3944.97	−	3080.35i	−0.237505	−	0.185451i
$652$	24412.4	−	42283.4i	1.46635	−	2.53980i
$653$	7985.85	−	13831.9i	0.478577	−	0.828919i	−0.521122	−	0.853482i	$-0.674486\pi$
$653$	7985.85	−	13831.9i	0.478577	−	0.828919i	0.999698	+	0.0245632i	$0.00781950\pi$
$654$	−5312.87	+	37880.9i	−0.317660	+	2.26492i
$655$	−3095.73	−	5361.97i	−0.184672	−	0.319862i
$656$	18337.8			1.09142
$657$	−1733.83	−	6937.25i	−0.102957	−	0.411945i
$658$	16459.4			0.975158
$659$	3421.46	+	5926.15i	0.202248	+	0.350304i	0.949252	−	0.314515i	$-0.101842\pi$
$659$	3421.46	+	5926.15i	0.202248	+	0.350304i	−0.747005	+	0.664819i	$0.768509\pi$
$660$	−6489.44	+	2624.04i	−0.382729	+	0.154759i
$661$	6695.50	−	11597.0i	0.393986	−	0.682404i	−0.598985	−	0.800760i	$-0.704429\pi$
$661$	6695.50	−	11597.0i	0.393986	−	0.682404i	0.992971	+	0.118356i	$0.0377624\pi$
$662$	−693.793	+	1201.68i	−0.0407327	+	0.0705511i
$663$	−31725.1	+	12828.2i	−1.85837	+	0.751443i
$664$	42729.6	+	74009.8i	2.49733	+	4.32551i
$665$	759.691			0.0443001
$666$	−2350.03	+	2271.97i	−0.136729	+	0.132188i
$667$	−13541.5			−0.786098
$668$	−20639.5	−	35748.7i	−1.19546	−	2.07060i
$669$	−3955.88	+	28205.5i	−0.228615	+	1.63003i
$670$	−3115.75	+	5396.64i	−0.179660	+	0.311180i
$671$	4963.51	−	8597.05i	0.285565	−	0.494613i
$672$	−29098.7	−	22721.2i	−1.67040	−	1.30430i
$673$	15951.1	+	27628.1i	0.913624	+	1.58244i	0.808904	+	0.587941i	$0.200061\pi$
$673$	15951.1	+	27628.1i	0.913624	+	1.58244i	0.104720	+	0.994502i	$0.466605\pi$
$674$	−59771.3			−3.41588
$675$	−3487.88	+	369.586i	−0.198887	+	0.0210746i
$676$	29119.9			1.65680
$677$	5930.38	+	10271.7i	0.336666	+	0.583123i	0.983803	−	0.179251i	$-0.0573673\pi$
$677$	5930.38	+	10271.7i	0.336666	+	0.583123i	−0.647137	+	0.762373i	$0.724034\pi$
$678$	−3758.74	−	2934.93i	−0.212911	−	0.166247i
$679$	−6596.33	+	11425.2i	−0.372818	+	0.645741i
$680$	−19251.2	+	33344.1i	−1.08566	+	1.88043i
$681$	3949.53	−	28160.2i	0.222241	−	1.58458i
$682$	−2647.28	−	4585.22i	−0.148636	−	0.257444i
$683$	7639.34			0.427981			0.213991	−	0.976836i	$-0.431354\pi$
$683$	7639.34			0.427981			0.213991	+	0.976836i	$0.431354\pi$
$684$	6588.55	+	1885.20i	0.368303	+	0.105384i
$685$	−2530.91			−0.141170
$686$	17870.1	+	30951.9i	0.994580	+	1.72266i
$687$	15781.2	−	6381.21i	0.876405	−	0.354379i
$688$	−12475.4	+	21608.0i	−0.691309	+	1.19738i
$689$	8785.64	−	15217.2i	0.485786	−	0.841406i
$690$	8783.81	−	3551.78i	0.484629	−	0.195962i
$691$	7863.00	+	13619.1i	0.432883	+	0.749776i	0.997120	−	0.0758369i	$-0.0241628\pi$
$691$	7863.00	+	13619.1i	0.432883	+	0.749776i	−0.564237	+	0.825613i	$0.690829\pi$
$692$	−48252.6			−2.65071
$693$	−4186.66	−	1197.94i	−0.229492	−	0.0656652i
$694$	53239.5			2.91202
$695$	−534.200	−	925.261i	−0.0291559	−	0.0504995i
$696$	−10101.4	+	72023.4i	−0.550135	+	3.92247i
$697$	4827.36	−	8361.23i	0.262338	−	0.454382i
$698$	−16314.5	+	28257.5i	−0.884688	+	1.53232i
$699$	−14114.1	−	11020.7i	−0.763724	−	0.596338i
$700$	−3299.45	−	5714.81i	−0.178154	−	0.308571i
$701$	−6338.17			−0.341497			−0.170748	−	0.985315i	$-0.554619\pi$
$701$	−6338.17			−0.341497			−0.170748	+	0.985315i	$0.554619\pi$
$702$	18360.6	−	41333.0i	0.987146	−	2.22224i
$703$	271.737			0.0145786
$704$	−8802.82	−	15246.9i	−0.471262	−	0.816250i
$705$	4979.25	+	3887.94i	0.265999	+	0.207700i
$706$	24493.0	−	42423.1i	1.30567	−	2.26149i
$707$	−557.658	+	965.892i	−0.0296646	+	0.0513806i
$708$	8810.76	−	62820.9i	0.467696	−	3.33468i
$709$	−17191.8	−	29777.1i	−0.910651	−	1.57729i	−0.813147	−	0.582059i	$-0.802247\pi$
$709$	−17191.8	−	29777.1i	−0.910651	−	1.57729i	−0.0975047	−	0.995235i	$-0.531086\pi$
$710$	20041.5			1.05936
$711$	10865.0	−	10504.1i	0.573092	−	0.554056i
$712$	−17912.7			−0.942847
$713$	2594.70	+	4494.16i	0.136287	+	0.236055i
$714$	−35872.7	+	14505.3i	−1.88025	+	0.760292i
$715$	1920.26	−	3325.98i	0.100438	−	0.173965i
$716$	9173.18	−	15888.4i	0.478796	−	0.829299i
$717$	−8308.83	+	3359.72i	−0.432774	+	0.174995i
$718$	23706.6	+	41061.0i	1.23220	+	2.13424i
$719$	−988.886			−0.0512924			−0.0256462	−	0.999671i	$-0.508164\pi$
$719$	−988.886			−0.0512924			−0.0256462	+	0.999671i	$0.508164\pi$
$720$	−6839.72	−	27366.6i	−0.354030	−	1.41652i
$721$	−19409.3			−1.00255
$722$	18074.6	+	31306.1i	0.931671	+	1.61370i
$723$	4024.03	−	28691.4i	0.206992	−	1.47586i
$724$	−15688.1	+	27172.5i	−0.805307	+	1.39483i
$725$	−2499.47	+	4329.22i	−0.128039	+	0.221770i
$726$	25723.8	+	20085.9i	1.31502	+	1.02680i
$727$	6845.92	+	11857.5i	0.349245	+	0.604910i	0.986116	−	0.166061i	$-0.0531048\pi$
$727$	6845.92	+	11857.5i	0.349245	+	0.604910i	−0.636871	+	0.770971i	$0.719771\pi$
$728$	52673.8			2.68162
$729$	−13195.3	−	14604.9i	−0.670392	−	0.742007i
$730$	7130.82			0.361539
$731$	6568.20	+	11376.5i	0.332331	+	0.575614i
$732$	66537.8	+	51954.7i	3.35971	+	2.62336i
$733$	1250.97	−	2166.74i	0.0630363	−	0.109182i	−0.832785	−	0.553597i	$-0.813255\pi$
$733$	1250.97	−	2166.74i	0.0630363	−	0.109182i	0.895821	+	0.444415i	$0.146588\pi$
$734$	−23296.6	+	40350.9i	−1.17152	+	2.02913i
$735$	−667.544	+	4759.60i	−0.0335003	+	0.238858i
$736$	19139.0	+	33149.7i	0.958521	+	1.66021i
$737$	−2969.51			−0.148417
$738$	3093.97	+	12379.4i	0.154323	+	0.617468i
$739$	26453.1			1.31677			0.658384	−	0.752682i	$-0.271240\pi$
$739$	26453.1			1.31677			0.658384	+	0.752682i	$0.271240\pi$
$740$	−1180.20	−	2044.16i	−0.0586282	−	0.101547i
$741$	−3485.72	+	1409.47i	−0.172808	+	0.0698760i
$742$	9934.24	−	17206.6i	0.491506	−	0.851313i
$743$	10441.4	−	18085.0i	0.515555	−	0.892967i	−0.484282	−	0.874912i	$-0.660919\pi$
$743$	10441.4	−	18085.0i	0.515555	−	0.892967i	0.999837	−	0.0180555i	$-0.00574755\pi$
$744$	25838.8	−	10448.1i	1.27325	−	0.514845i
$745$	−2263.28	−	3920.11i	−0.111302	−	0.192781i
$746$	−64182.2			−3.14997
$747$	−23699.3	+	22912.1i	−1.16079	+	1.12224i
$748$	−29639.8			−1.44885
$749$	3681.64	+	6376.78i	0.179605	+	0.311085i
$750$	485.802	−	3463.78i	0.0236520	−	0.168639i
$751$	8847.65	−	15324.6i	0.429901	−	0.744610i	−0.566963	−	0.823743i	$-0.691882\pi$
$751$	8847.65	−	15324.6i	0.429901	−	0.744610i	0.996864	+	0.0791332i	$0.0252152\pi$
$752$	−25403.7	+	44000.6i	−1.23189	+	2.13369i
$753$	5555.08	+	4337.57i	0.268842	+	0.209920i
$754$	−32230.4	−	55824.8i	−1.55672	−	2.69631i
$755$	−6793.35			−0.327464
$756$	15033.5	−	33843.2i	0.723233	−	1.62813i
$757$	7755.61			0.372368			0.186184	−	0.982515i	$-0.440388\pi$
$757$	7755.61			0.372368			0.186184	+	0.982515i	$0.440388\pi$
$758$	−13603.2	−	23561.4i	−0.651835	−	1.12901i
$759$	3558.66	+	2778.71i	0.170186	+	0.132886i
$760$	−2115.18	+	3663.60i	−0.100955	+	0.174859i
$761$	−8527.15	+	14769.5i	−0.406188	+	0.703538i	−0.994459	−	0.105126i	$-0.966476\pi$
$761$	−8527.15	+	14769.5i	−0.406188	+	0.703538i	0.588271	+	0.808664i	$0.299809\pi$
$762$	−7033.40	+	50148.2i	−0.334374	+	2.38409i
$763$	−8591.95	−	14881.7i	−0.407667	−	0.706099i
$764$	106048.			5.02184
$765$	−14278.5	−	4085.53i	−0.674822	−	0.193089i
$766$	−28704.2			−1.35395
$767$	17402.1	+	30141.3i	0.819236	+	1.41896i
$768$	21499.9	−	8693.61i	1.01017	−	0.408468i
$769$	5024.16	−	8702.11i	0.235599	−	0.408070i	−0.723847	−	0.689960i	$-0.757628\pi$
$769$	5024.16	−	8702.11i	0.235599	−	0.408070i	0.959447	+	0.281890i	$0.0909613\pi$
$770$	2171.30	−	3760.81i	0.101621	−	0.176013i
$771$	−19692.0	+	7962.57i	−0.919831	+	0.371939i
$772$	−54193.0	−	93865.1i	−2.52649	−	4.37601i
$773$	7293.24			0.339352			0.169676	−	0.985500i	$-0.445728\pi$
$773$	7293.24			0.339352			0.169676	+	0.985500i	$0.445728\pi$
$774$	−16691.9	−	4776.09i	−0.775164	−	0.221800i
$775$	1915.72			0.0887930
$776$	−36731.9	−	63621.5i	−1.69922	−	2.94314i
$777$	203.952	−	1454.18i	0.00941665	−	0.0671409i
$778$	−8991.70	+	15574.1i	−0.414355	+	0.717684i
$779$	530.394	−	918.670i	0.0243945	−	0.0422526i
$780$	25741.8	+	20100.0i	1.18167	+	0.922684i
$781$	4775.21	+	8270.90i	0.218784	+	0.378945i
$782$	40119.0			1.83460
$783$	−27897.1	+	2956.07i	−1.27326	+	0.134919i
$784$	−38653.8			−1.76083
$785$	4753.35	+	8233.04i	0.216120	+	0.374331i
$786$	27310.0	+	21324.5i	1.23933	+	0.967708i
$787$	−14228.1	+	24643.8i	−0.644445	+	1.11621i	0.339985	+	0.940431i	$0.389578\pi$
$787$	−14228.1	+	24643.8i	−0.644445	+	1.11621i	−0.984429	+	0.175780i	$0.943755\pi$
$788$	−3926.99	+	6801.75i	−0.177530	+	0.307490i
$789$	310.522	−	2214.03i	0.0140112	−	0.0999004i
$790$	7535.23	+	13051.4i	0.339356	+	0.587782i
$791$	2142.33			0.0962989
$792$	17433.9	−	16854.8i	0.782178	−	0.756197i
$793$	−46316.7			−2.07409
$794$	−24344.8	−	42166.4i	−1.08812	−	1.88467i
$795$	7069.72	−	2858.68i	0.315393	−	0.127531i
$796$	−6334.66	+	10971.9i	−0.282068	+	0.488556i
$797$	−2040.73	+	3534.65i	−0.0906981	+	0.157094i	−0.907805	−	0.419392i	$-0.862243\pi$
$797$	−2040.73	+	3534.65i	−0.0906981	+	0.157094i	0.817107	+	0.576486i	$0.195576\pi$
$798$	−3941.42	+	1593.74i	−0.174843	+	0.0706988i
$799$	13374.9	+	23165.9i	0.592201	+	1.02572i
$800$	14130.6			0.624492
$801$	−1675.34	−	6703.24i	−0.0739015	−	0.295689i
$802$	−9003.54			−0.396416
$803$	1699.03	+	2942.81i	0.0746668	+	0.129327i
$804$	3507.40	−	25007.8i	0.153851	−	1.09696i
$805$	−2128.18	+	3686.12i	−0.0931783	+	0.161390i
$806$	−12351.5	+	21393.4i	−0.539779	+	0.934925i
$807$	−14202.7	−	11089.9i	−0.619527	−	0.483745i
$808$	−3105.34	−	5378.60i	−0.135205	−	0.234181i
$809$	14209.7			0.617536			0.308768	−	0.951137i	$-0.400083\pi$
$809$	14209.7			0.617536			0.308768	+	0.951137i	$0.400083\pi$
$810$	17320.4	−	9234.62i	0.751331	−	0.400582i
$811$	4901.79			0.212238			0.106119	−	0.994353i	$-0.466158\pi$
$811$	4901.79			0.212238			0.106119	+	0.994353i	$0.466158\pi$
$812$	−26390.0	−	45708.9i	−1.14053	−	1.97545i
$813$	227.062	+	177.297i	0.00979511	+	0.00764831i
$814$	776.663	−	1345.22i	0.0334423	−	0.0579237i
$815$	−5812.87	+	10068.2i	−0.249835	+	0.432727i
$816$	16589.8	−	118286.i	0.711714	−	5.07454i
$817$	721.665	+	1249.96i	0.0309031	+	0.0535258i
$818$	2545.64			0.108810
$819$	4926.47	+	19711.4i	0.210189	+	0.840992i
$820$	−9214.32			−0.392412
$821$	7259.82	+	12574.4i	0.308611	+	0.534530i	0.978059	−	0.208329i	$-0.0668026\pi$
$821$	7259.82	+	12574.4i	0.308611	+	0.534530i	−0.669448	+	0.742859i	$0.733469\pi$
$822$	13130.9	−	5309.54i	0.557167	−	0.225294i
$823$	19203.2	−	33260.9i	0.813344	−	1.40875i	−0.0971672	−	0.995268i	$-0.530978\pi$
$823$	19203.2	−	33260.9i	0.813344	−	1.40875i	0.910511	−	0.413485i	$-0.135688\pi$
$824$	54040.6	−	93601.1i	2.28470	−	3.95722i
$825$	1545.21	−	624.815i	0.0652089	−	0.0263676i
$826$	19677.2	+	34081.9i	0.828882	+	1.43567i
$827$	−10446.4			−0.439248			−0.219624	−	0.975585i	$-0.570483\pi$
$827$	−10446.4			−0.439248			−0.219624	+	0.975585i	$0.570483\pi$
$828$	−27604.3	+	26687.4i	−1.15859	+	1.12011i
$829$	−6474.00			−0.271232			−0.135616	−	0.990761i	$-0.543301\pi$
$829$	−6474.00			−0.271232			−0.135616	+	0.990761i	$0.543301\pi$
$830$	−16436.3	−	28468.5i	−0.687363	−	1.19055i
$831$	1135.63	−	8097.09i	0.0474064	−	0.338008i
$832$	−41071.6	+	71138.0i	−1.71142	+	2.96426i
$833$	−10175.5	+	17624.4i	−0.423240	+	0.733073i
$834$	4712.61	+	3679.75i	0.195665	+	0.152781i
$835$	4914.51	+	8512.17i	0.203681	+	0.352786i
$836$	−3256.60			−0.134727
$837$	6326.49	+	8692.13i	0.261261	+	0.358953i
$838$	67524.5			2.78353
$839$	−7919.71	−	13717.3i	−0.325886	−	0.564452i	0.655805	−	0.754930i	$-0.272329\pi$
$839$	−7919.71	−	13717.3i	−0.325886	−	0.564452i	−0.981691	+	0.190478i	$0.938996\pi$
$840$	18018.0	+	14069.0i	0.740093	+	0.577887i
$841$	−7797.09	+	13505.0i	−0.319697	+	0.553731i
$842$	18179.2	−	31487.3i	0.744058	−	1.28875i
$843$	−5879.36	+	41919.9i	−0.240209	+	1.71269i
$844$	−25322.3	−	43859.5i	−1.03274	−	1.78875i
$845$	−6933.79			−0.282284
$846$	−33989.7	−	9725.57i	−1.38131	−	0.395239i
$847$	−14661.5			−0.594778
$848$	30665.4	+	53114.0i	1.24181	+	2.15087i
$849$	14925.3	−	6035.12i	0.603338	−	0.243963i
$850$	7405.15	−	12826.1i	0.298817	−	0.517566i
$851$	−761.239	+	1318.51i	−0.0306639	+	0.0531114i
$852$	−75293.9	+	30445.5i	−3.02761	+	1.22423i
$853$	9420.17	+	16316.2i	0.378125	+	0.654931i	0.990789	−	0.135412i	$-0.0432357\pi$
$853$	9420.17	+	16316.2i	0.378125	+	0.654931i	−0.612665	+	0.790343i	$0.709902\pi$
$854$	−52372.0			−2.09852
$855$	−1568.81	−	448.888i	−0.0627511	−	0.0179551i
$856$	−41002.6			−1.63720
$857$	−4528.11	−	7842.91i	−0.180487	−	0.312612i	0.761560	−	0.648095i	$-0.224434\pi$
$857$	−4528.11	−	7842.91i	−0.180487	−	0.312612i	−0.942046	+	0.335483i	$0.891101\pi$
$858$	−2985.17	+	21284.3i	−0.118778	+	0.846893i
$859$	−11027.7	+	19100.6i	−0.438022	+	0.758676i	−0.997537	−	0.0701440i	$-0.977654\pi$
$859$	−11027.7	+	19100.6i	−0.438022	+	0.758676i	0.559515	+	0.828820i	$0.310987\pi$
$860$	6268.60	−	10857.5i	0.248555	−	0.430510i
$861$	−4518.10	−	3527.87i	−0.178835	−	0.139639i
$862$	−20288.3	−	35140.3i	−0.801649	−	1.38850i
$863$	13105.6			0.516941			0.258471	−	0.966019i	$-0.416781\pi$
$863$	13105.6			0.516941			0.258471	+	0.966019i	$0.416781\pi$
$864$	46665.2	+	64114.6i	1.83748	+	2.52456i
$865$	11489.5			0.451624
$866$	13826.4	+	23948.1i	0.542542	+	0.939710i
$867$	−29444.4	−	22991.0i	−1.15338	−	0.900596i
$868$	−10113.3	+	17516.7i	−0.395470	+	0.684973i
$869$	−3590.78	+	6219.41i	−0.140171	+	0.242784i
$870$	3885.60	−	27704.4i	0.151419	−	1.07962i
$871$	6927.46	+	11998.7i	0.269492	+	0.466775i
$872$	95689.2			3.71611
$873$	20372.8	−	19696.1i	0.789821	−	0.763586i
$874$	4407.98			0.170597
$875$	785.637	+	1360.76i	0.0303536	+	0.0525740i
$876$	−26789.7	+	10832.6i	−1.03327	+	0.417807i
$877$	18361.1	−	31802.4i	0.706967	−	1.22450i	−0.259010	−	0.965875i	$-0.583396\pi$
$877$	18361.1	−	31802.4i	0.706967	−	1.22450i	0.965977	−	0.258628i	$-0.0832705\pi$
$878$	−45700.6	+	79155.8i	−1.75663	+	3.04257i
$879$	588.473	−	237.952i	0.0225810	−	0.00913076i
$880$	6702.46	+	11609.0i	0.256750	+	0.444704i
$881$	36054.4			1.37878			0.689390	−	0.724390i	$-0.257879\pi$
$881$	36054.4			1.37878			0.689390	+	0.724390i	$0.257879\pi$
$882$	−6521.70	−	26094.1i	−0.248976	−	0.996186i
$883$	13524.6			0.515446			0.257723	−	0.966219i	$-0.417028\pi$
$883$	13524.6			0.515446			0.257723	+	0.966219i	$0.417028\pi$
$884$	69145.6	+	119764.i	2.63079	+	4.55666i
$885$	−2097.94	+	14958.4i	−0.0796855	+	0.568159i
$886$	−30566.3	+	52942.3i	−1.15902	+	2.00749i
$887$	19865.1	−	34407.4i	0.751978	−	1.30246i	−0.194884	−	0.980826i	$-0.562433\pi$
$887$	19865.1	−	34407.4i	0.751978	−	1.30246i	0.946863	−	0.321639i	$-0.104234\pi$
$888$	6444.92	+	5032.39i	0.243556	+	0.190176i
$889$	−11374.4	−	19701.0i	−0.429116	−	0.743251i
$890$	6890.27			0.259508
$891$	7937.89	+	4947.65i	0.298462	+	0.186030i
$892$	115099.			4.32040
$893$	1469.53	+	2545.30i	0.0550682	+	0.0953810i
$894$	19966.2	+	15590.2i	0.746946	+	0.583238i
$895$	−2184.24	+	3783.22i	−0.0815767	+	0.141295i
$896$	−18021.1	+	31213.4i	−0.671921	+	1.16380i
$897$	2925.88	−	20861.6i	0.108910	−	0.776532i
$898$	−29778.7	−	51578.2i	−1.10660	−	1.91669i
$899$	15322.5			0.568447
$900$	3436.79	+	13751.1i	0.127289	+	0.509298i
$901$	32290.1			1.19394
$902$	−3031.88	−	5251.37i	−0.111919	−	0.193849i
$903$	7230.71	−	2923.78i	0.266471	−	0.107749i
$904$	−5964.81	+	10331.4i	−0.219454	+	0.380106i
$905$	3735.51	−	6470.09i	0.137207	−	0.237650i
$906$	35245.2	−	14251.6i	1.29243	−	0.522602i
$907$	−11511.2	−	19938.0i	−0.421415	−	0.729912i	0.574663	−	0.818390i	$-0.305133\pi$
$907$	−11511.2	−	19938.0i	−0.421415	−	0.729912i	−0.996078	+	0.0884783i	$0.971800\pi$
$908$	−114914.			−4.19995
$909$	1722.33	−	1665.12i	0.0628449	−	0.0607574i
$910$	−20261.4			−0.738087
$911$	−15940.1	−	27609.1i	−0.579714	−	1.00409i	−0.995512	−	0.0946365i	$-0.969831\pi$
$911$	−15940.1	−	27609.1i	−0.579714	−	1.00409i	0.415798	−	0.909457i	$-0.363502\pi$
$912$	1822.76	−	12996.3i	0.0661817	−	0.471877i
$913$	7832.41	−	13566.1i	0.283916	−	0.491756i
$914$	−960.376	+	1663.42i	−0.0347554	+	0.0601981i
$915$	−15843.4	−	12371.0i	−0.572423	−	0.446965i
$916$	−34395.5	−	59574.7i	−1.24067	−	2.14891i
$917$	−15565.6			−0.560547
$918$	82650.4	−	8757.89i	2.97153	−	0.314873i
$919$	38459.6			1.38049			0.690243	−	0.723578i	$-0.257504\pi$
$919$	38459.6			1.38049			0.690243	+	0.723578i	$0.257504\pi$
$920$	−11850.9	−	20526.3i	−0.424686	−	0.735578i
$921$	7898.37	+	6167.28i	0.282584	+	0.220650i
$922$	−27786.1	+	48126.9i	−0.992501	+	1.71906i
$923$	22279.8	−	38589.8i	0.794528	−	1.37616i
$924$	−2444.23	+	17427.4i	−0.0870231	+	0.620477i
$925$	281.018	+	486.738i	0.00998900	+	0.0173015i
$926$	−97838.1			−3.47209
$927$	40081.4	+	11468.6i	1.42011	+	0.406341i
$928$	113021.			3.99796
$929$	18600.5	+	32217.1i	0.656903	+	1.13779i	0.981413	+	0.191908i	$0.0614675\pi$
$929$	18600.5	+	32217.1i	0.656903	+	1.13779i	−0.324509	+	0.945882i	$0.605199\pi$
$930$	−9939.11	+	4018.93i	−0.350447	+	0.141705i
$931$	−1118.00	+	1936.44i	−0.0393567	+	0.0681678i
$932$	−36182.7	+	62670.3i	−1.27168	+	2.20261i
$933$	38245.5	−	15464.8i	1.34201	−	0.542651i
$934$	−10277.7	−	17801.5i	−0.360062	−	0.623645i
$935$	7057.58			0.246853
$936$	−108775.	−	31124.0i	−3.79852	−	1.08688i
$937$	−23593.7			−0.822595			−0.411298	−	0.911501i	$-0.634924\pi$
$937$	−23593.7			−0.822595			−0.411298	+	0.911501i	$0.634924\pi$
$938$	7833.12	+	13567.4i	0.272666	+	0.472271i
$939$	4877.94	−	34779.8i	0.169527	−	1.20873i
$940$	12764.8	−	22109.2i	0.442916	−	0.767153i
$941$	−18285.8	+	31672.0i	−0.633477	+	1.09721i	0.353359	+	0.935488i	$0.385039\pi$
$941$	−18285.8	+	31672.0i	−0.633477	+	1.09721i	−0.986836	+	0.161726i	$0.948294\pi$
$942$	−41933.2	−	32742.7i	−1.45038	−	1.13250i
$943$	2971.67	+	5147.08i	0.102620	+	0.177744i
$944$	−121481.			−4.18841
$945$	−3579.66	+	8058.46i	−0.123224	+	0.277399i
$946$	8250.48			0.283558
$947$	−16455.9	−	28502.4i	−0.564671	−	0.978039i	−0.997080	−	0.0763615i	$-0.975670\pi$
$947$	−16455.9	−	28502.4i	−0.564671	−	0.978039i	0.432409	−	0.901678i	$-0.357664\pi$
$948$	−48135.8	−	37585.8i	−1.64913	−	1.28769i
$949$	7927.21	−	13730.3i	0.271157	−	0.469658i
$950$	813.622	−	1409.24i	0.0277867	−	0.0481280i
$951$	−6079.83	+	43349.3i	−0.207310	+	1.47813i
$952$	48398.4	+	83828.5i	1.64769	+	2.85388i
$953$	−21564.5			−0.732993			−0.366497	−	0.930419i	$-0.619443\pi$
$953$	−21564.5			−0.732993			−0.366497	+	0.930419i	$0.619443\pi$
$954$	−30681.9	+	29662.8i	−1.04126	+	1.00668i
$955$	−25251.3			−0.855615
$956$	18109.3	+	31366.2i	0.612653	+	1.06115i
$957$	12359.1	−	4997.47i	0.417464	−	0.168804i
$958$	−7825.98	+	13555.0i	−0.263931	+	0.457142i
$959$	−3181.41	+	5510.36i	−0.107125	+	0.185546i
$960$	−33049.9	+	13363.9i	−1.11113	+	0.449290i
$961$	11959.5	+	20714.5i	0.401448	+	0.695328i
$962$	−7247.40			−0.242895
$963$	−3834.89	−	15343.9i	−0.128326	−	0.513447i
$964$	−117082.			−3.91178
$965$	12904.0	+	22350.4i	0.430460	+	0.745579i
$966$	3308.40	−	23589.0i	0.110193	−	0.785675i
$967$	−14881.9	+	25776.2i	−0.494901	+	0.857193i	−0.999983	−	0.00587841i	$-0.998129\pi$
$967$	−14881.9	+	25776.2i	−0.494901	+	0.857193i	0.505082	+	0.863071i	$0.331462\pi$
$968$	40821.7	−	70705.2i	1.35543	−	2.34768i
$969$	−5445.91	−	4252.33i	−0.180545	−	0.140975i
$970$	14129.2	+	24472.5i	0.467693	+	0.810067i
$971$	29812.3			0.985297			0.492648	−	0.870228i	$-0.336029\pi$
$971$	29812.3			0.985297			0.492648	+	0.870228i	$0.336029\pi$
$972$	−51042.6	+	61005.4i	−1.68435	+	2.01311i
$973$	−2686.00			−0.0884986
$974$	−28032.1	−	48553.1i	−0.922184	−	1.59727i
$975$	−6129.42	−	4786.03i	−0.201332	−	0.157206i
$976$	80831.9	−	140005.i	2.65099	−	4.59165i
$977$	2879.87	−	4988.07i	0.0943041	−	0.163339i	−0.815014	−	0.579441i	$-0.803271\pi$
$977$	2879.87	−	4988.07i	0.0943041	−	0.163339i	0.909318	+	0.416102i	$0.136604\pi$
$978$	9036.49	−	64430.3i	0.295455	−	2.10660i
$979$	1641.72	+	2843.54i	0.0535950	+	0.0928292i
$980$	19422.6			0.633095
$981$	8949.61	+	35808.5i	0.291273	+	1.16542i
$982$	78796.5			2.56059
$983$	8825.70	+	15286.6i	0.286364	+	0.495998i	0.972939	−	0.231062i	$-0.0742199\pi$
$983$	8825.70	+	15286.6i	0.286364	+	0.495998i	−0.686575	+	0.727059i	$0.740887\pi$
$984$	29592.7	−	11966.0i	0.958722	−	0.387665i
$985$	935.063	−	1619.58i	0.0302473	−	0.0523898i
$986$	59228.7	−	102587.i	1.91301	−	3.31343i
$987$	14723.9	−	5953.70i	0.474841	−	0.192005i
$988$	7597.20	+	13158.7i	0.244635	+	0.423720i
$989$	−8086.63			−0.260000
$990$	−6706.07	+	6483.32i	−0.215286	+	0.208135i
$991$	−5186.45			−0.166249			−0.0831246	−	0.996539i	$-0.526490\pi$
$991$	−5186.45			−0.166249			−0.0831246	+	0.996539i	$0.526490\pi$
$992$	−21656.2	−	37509.7i	−0.693131	−	1.20054i
$993$	−185.966	+	1325.94i	−0.00594305	+	0.0423740i
$994$	25192.6	−	43634.8i	0.803884	−	1.39237i
$995$	1508.36	−	2612.55i	0.0480584	−	0.0832395i
$996$	104996.	+	81984.4i	3.34030	+	2.60821i
$997$	8055.12	+	13951.9i	0.255876	+	0.443190i	0.965133	−	0.261760i	$-0.0843028\pi$
$997$	8055.12	+	13951.9i	0.255876	+	0.443190i	−0.709257	+	0.704950i	$0.750970\pi$
$998$	43978.6			1.39491
$999$	−1280.42	+	2882.47i	−0.0405514	+	0.0912885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.c.31.1	yes	14
3.2	odd	2		135.4.e.c.91.7		14
5.2	odd	4		225.4.k.d.49.14		28
5.3	odd	4		225.4.k.d.49.1		28
5.4	even	2		225.4.e.d.76.7		14
9.2	odd	6		135.4.e.c.46.7		14
9.4	even	3		405.4.a.m.1.7		7
9.5	odd	6		405.4.a.n.1.1		7
9.7	even	3	inner	45.4.e.c.16.1	✓	14
45.4	even	6		2025.4.a.bb.1.1		7
45.7	odd	12		225.4.k.d.124.1		28
45.14	odd	6		2025.4.a.ba.1.7		7
45.34	even	6		225.4.e.d.151.7		14
45.43	odd	12		225.4.k.d.124.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.1	✓	14	9.7	even	3	inner
45.4.e.c.31.1	yes	14	1.1	even	1	trivial
135.4.e.c.46.7		14	9.2	odd	6
135.4.e.c.91.7		14	3.2	odd	2
225.4.e.d.76.7		14	5.4	even	2
225.4.e.d.151.7		14	45.34	even	6
225.4.k.d.49.1		28	5.3	odd	4
225.4.k.d.49.14		28	5.2	odd	4
225.4.k.d.124.1		28	45.7	odd	12
225.4.k.d.124.14		28	45.43	odd	12
405.4.a.m.1.7		7	9.4	even	3
405.4.a.n.1.1		7	9.5	odd	6
2025.4.a.ba.1.7		7	45.14	odd	6
2025.4.a.bb.1.1		7	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69252 - 4.66357i) q^{2} +(-4.09553 - 3.19791i) q^{3} +(-10.4993 + 18.1853i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-3.88642 + 27.7102i) q^{6} +(-6.28510 - 10.8861i) q^{7} +69.9976 q^{8} +(6.54673 + 26.1943i) q^{9} -26.9252 q^{10} +(-6.41534 - 11.1117i) q^{11} +(101.155 - 40.9026i) q^{12} +(-29.9322 + 51.8442i) q^{13} +(-33.8455 + 58.6220i) q^{14} +(-24.0862 + 9.73939i) q^{15} +(-104.475 - 180.957i) q^{16} -110.011 q^{17} +(104.532 - 101.060i) q^{18} -12.0872 q^{19} +(52.4964 + 90.9264i) q^{20} +(-9.07201 + 64.6836i) q^{21} +(-34.5468 + 59.8368i) q^{22} +(33.8608 - 58.6485i) q^{23} +(-286.677 - 223.846i) q^{24} +(-12.5000 - 21.6506i) q^{25} +322.372 q^{26} +(56.9547 - 128.215i) q^{27} +263.956 q^{28} +(-99.9790 - 173.169i) q^{29} +(110.273 + 86.1042i) q^{30} +(-38.3143 + 66.3624i) q^{31} +(-282.613 + 489.500i) q^{32} +(-9.26000 + 66.0240i) q^{33} +(296.206 + 513.044i) q^{34} -62.8510 q^{35} +(-545.086 - 155.967i) q^{36} -22.4815 q^{37} +(32.5449 + 56.3694i) q^{38} +(288.381 - 116.609i) q^{39} +(174.994 - 303.099i) q^{40} +(-43.8807 + 76.0037i) q^{41} +(326.083 - 131.854i) q^{42} +(-59.7050 - 103.412i) q^{43} +269.426 q^{44} +(129.791 + 37.1375i) q^{45} -364.682 q^{46} +(-121.578 - 210.579i) q^{47} +(-150.801 + 1075.22i) q^{48} +(92.4951 - 160.206i) q^{49} +(-67.3129 + 116.589i) q^{50} +(450.553 + 351.805i) q^{51} +(-628.534 - 1088.65i) q^{52} -293.518 q^{53} +(-751.293 + 79.6094i) q^{54} -64.1534 q^{55} +(-439.942 - 762.002i) q^{56} +(49.5034 + 38.6537i) q^{57} +(-538.390 + 932.519i) q^{58} +(290.692 - 503.493i) q^{59} +(75.7741 - 540.271i) q^{60} +(386.847 + 670.038i) q^{61} +412.648 q^{62} +(244.007 - 235.902i) q^{63} +1372.15 q^{64} +(149.661 + 259.221i) q^{65} +(332.840 - 134.586i) q^{66} +(115.719 - 200.431i) q^{67} +(1155.03 - 2000.58i) q^{68} +(-326.231 + 131.913i) q^{69} +(169.227 + 293.110i) q^{70} -744.342 q^{71} +(458.255 + 1833.54i) q^{72} -264.839 q^{73} +(60.5317 + 104.844i) q^{74} +(-18.0427 + 128.645i) q^{75} +(126.907 - 219.809i) q^{76} +(-80.6421 + 139.676i) q^{77} +(-1320.28 - 1030.92i) q^{78} +(-279.858 - 484.729i) q^{79} -1044.75 q^{80} +(-643.281 + 342.974i) q^{81} +472.598 q^{82} +(610.443 + 1057.32i) q^{83} +(-1081.04 - 844.108i) q^{84} +(-275.027 + 476.361i) q^{85} +(-321.513 + 556.878i) q^{86} +(-144.311 + 1028.94i) q^{87} +(-449.059 - 777.792i) q^{88} -255.905 q^{89} +(-176.272 - 705.285i) q^{90} +752.509 q^{91} +(711.027 + 1231.53i) q^{92} +(369.138 - 149.263i) q^{93} +(-654.699 + 1133.97i) q^{94} +(-30.2179 + 52.3390i) q^{95} +(2722.83 - 1100.99i) q^{96} +(-524.759 - 908.909i) q^{97} -996.177 q^{98} +(249.064 - 240.791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18}+ \cdots + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Introduction

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