LMFDB - Embedded newform 48.4.k.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.668281 - 2.74835i) q^{2} +(-4.66767 + 2.28317i) q^{3} +(-7.10680 - 3.67333i) q^{4} +(-11.5146 + 11.5146i) q^{5} +(3.15562 + 14.3542i) q^{6} +0.829117 q^{7} +(-14.8449 + 17.0771i) q^{8} +(16.5743 - 21.3142i) q^{9} +O(q^{10})$	\(q+(0.668281 - 2.74835i) q^{2} +(-4.66767 + 2.28317i) q^{3} +(-7.10680 - 3.67333i) q^{4} +(-11.5146 + 11.5146i) q^{5} +(3.15562 + 14.3542i) q^{6} +0.829117 q^{7} +(-14.8449 + 17.0771i) q^{8} +(16.5743 - 21.3142i) q^{9} +(23.9512 + 39.3412i) q^{10} +(-38.2302 - 38.2302i) q^{11} +(41.5590 + 0.919870i) q^{12} +(-20.0189 + 20.0189i) q^{13} +(0.554083 - 2.27870i) q^{14} +(27.4566 - 80.0363i) q^{15} +(37.0133 + 52.2113i) q^{16} +77.9578i q^{17} +(-47.5024 - 59.7957i) q^{18} +(-37.6931 - 37.6931i) q^{19} +(124.129 - 39.5351i) q^{20} +(-3.87005 + 1.89301i) q^{21} +(-130.618 + 79.5214i) q^{22} -159.603i q^{23} +(30.3012 - 113.604i) q^{24} -140.173i q^{25} +(41.6406 + 68.3971i) q^{26} +(-28.6995 + 137.329i) q^{27} +(-5.89237 - 3.04562i) q^{28} +(26.6150 + 26.6150i) q^{29} +(-201.619 - 128.947i) q^{30} +226.344i q^{31} +(168.230 - 66.8335i) q^{32} +(265.732 + 91.1601i) q^{33} +(214.255 + 52.0977i) q^{34} +(-9.54698 + 9.54698i) q^{35} +(-196.084 + 90.5927i) q^{36} +(176.815 + 176.815i) q^{37} +(-128.783 + 78.4041i) q^{38} +(47.7351 - 139.148i) q^{39} +(-25.7030 - 367.571i) q^{40} -301.571 q^{41} +(2.61638 + 11.9013i) q^{42} +(-96.1344 + 96.1344i) q^{43} +(131.262 + 412.127i) q^{44} +(54.5779 + 436.271i) q^{45} +(-438.645 - 106.660i) q^{46} -122.486 q^{47} +(-291.973 - 159.197i) q^{48} -342.313 q^{49} +(-385.245 - 93.6751i) q^{50} +(-177.991 - 363.881i) q^{51} +(215.807 - 68.7343i) q^{52} +(138.452 - 138.452i) q^{53} +(358.249 + 170.651i) q^{54} +880.414 q^{55} +(-12.3082 + 14.1589i) q^{56} +(261.999 + 89.8792i) q^{57} +(90.9335 - 55.3609i) q^{58} +(-168.375 - 168.375i) q^{59} +(-489.129 + 467.945i) q^{60} +(-178.364 + 178.364i) q^{61} +(622.071 + 151.261i) q^{62} +(13.7420 - 17.6719i) q^{63} +(-71.2566 - 507.017i) q^{64} -461.021i q^{65} +(428.123 - 669.403i) q^{66} +(-233.257 - 233.257i) q^{67} +(286.365 - 554.030i) q^{68} +(364.402 + 744.976i) q^{69} +(19.8583 + 32.6185i) q^{70} +668.427i q^{71} +(117.941 + 599.448i) q^{72} -1216.50i q^{73} +(604.110 - 367.786i) q^{74} +(320.039 + 654.283i) q^{75} +(129.418 + 406.337i) q^{76} +(-31.6974 - 31.6974i) q^{77} +(-350.527 - 224.183i) q^{78} -39.4578i q^{79} +(-1027.39 - 174.999i) q^{80} +(-179.586 - 706.534i) q^{81} +(-201.534 + 828.820i) q^{82} +(-293.710 + 293.710i) q^{83} +(34.4573 + 0.762680i) q^{84} +(-897.655 - 897.655i) q^{85} +(199.966 + 328.455i) q^{86} +(-184.997 - 63.4635i) q^{87} +(1220.39 - 85.3379i) q^{88} -732.996 q^{89} +(1235.50 + 141.553i) q^{90} +(-16.5980 + 16.5980i) q^{91} +(-586.276 + 1134.27i) q^{92} +(-516.781 - 1056.50i) q^{93} +(-81.8547 + 336.633i) q^{94} +868.044 q^{95} +(-632.649 + 696.054i) q^{96} +451.695 q^{97} +(-228.761 + 940.793i) q^{98} +(-1448.48 + 181.207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.668281	−	2.74835i	0.236273	−	0.971687i
$2$	0.668281	−	2.74835i	0.236273	−	0.971687i
$3$	−4.66767	+	2.28317i	−0.898293	+	0.439396i
$3$	−4.66767	+	2.28317i	−0.898293	+	0.439396i
$4$	−7.10680	−	3.67333i	−0.888350	−	0.459166i
$5$	−11.5146	+	11.5146i	−1.02990	+	1.02990i	−0.0303606	+	0.999539i	$0.509666\pi$
$5$	−11.5146	+	11.5146i	−1.02990	+	1.02990i	−0.999539	+	0.0303606i	$0.990334\pi$
$6$	3.15562	+	14.3542i	0.214713	+	0.976677i
$7$	0.829117			0.0447681			0.0223841	−	0.999749i	$-0.492874\pi$
$7$	0.829117			0.0447681			0.0223841	+	0.999749i	$0.492874\pi$
$8$	−14.8449	+	17.0771i	−0.656059	+	0.754710i
$9$	16.5743	−	21.3142i	0.613862	−	0.789413i
$10$	23.9512	+	39.3412i	0.757402	+	1.24408i
$11$	−38.2302	−	38.2302i	−1.04790	−	1.04790i	−0.998794	−	0.0491019i	$-0.984364\pi$
$11$	−38.2302	−	38.2302i	−1.04790	−	1.04790i	−0.0491019	−	0.998794i	$-0.515636\pi$
$12$	41.5590	+	0.919870i	0.999755	+	0.0221286i
$13$	−20.0189	+	20.0189i	−0.427096	+	0.427096i	−0.887638	−	0.460542i	$-0.847655\pi$
$13$	−20.0189	+	20.0189i	−0.427096	+	0.427096i	0.460542	+	0.887638i	$0.347655\pi$
$14$	0.554083	−	2.27870i	0.0105775	−	0.0435006i
$15$	27.4566	−	80.0363i	0.472618	−	1.37769i
$16$	37.0133	+	52.2113i	0.578332	+	0.815801i
$17$			77.9578i			1.11221i	0.831113	+	0.556104i	$0.187704\pi$
$17$			77.9578i			1.11221i	−0.831113	+	0.556104i	$0.812296\pi$
$18$	−47.5024	−	59.7957i	−0.622023	−	0.782999i
$19$	−37.6931	−	37.6931i	−0.455126	−	0.455126i	0.441926	−	0.897052i	$-0.354295\pi$
$19$	−37.6931	−	37.6931i	−0.455126	−	0.455126i	−0.897052	+	0.441926i	$0.854295\pi$
$20$	124.129	−	39.5351i	1.38781	−	0.442016i
$21$	−3.87005	+	1.89301i	−0.0402149	+	0.0196709i
$22$	−130.618	+	79.5214i	−1.26582	+	0.770637i
$23$		−	159.603i		−	1.44694i	−0.690356	−	0.723470i	$-0.742546\pi$
$23$		−	159.603i		−	1.44694i	0.690356	−	0.723470i	$-0.257454\pi$
$24$	30.3012	−	113.604i	0.257717	−	0.966220i
$25$		−	140.173i		−	1.12139i
$26$	41.6406	+	68.3971i	0.314092	+	0.515915i
$27$	−28.6995	+	137.329i	−0.204563	+	0.978853i
$28$	−5.89237	−	3.04562i	−0.0397698	−	0.0205560i
$29$	26.6150	+	26.6150i	0.170424	+	0.170424i	0.787165	−	0.616742i	$-0.211548\pi$
$29$	26.6150	+	26.6150i	0.170424	+	0.170424i	−0.616742	+	0.787165i	$0.711548\pi$
$30$	−201.619	−	128.947i	−1.22701	−	0.784747i
$31$			226.344i			1.31137i	0.755034	+	0.655686i	$0.227621\pi$
$31$			226.344i			1.31137i	−0.755034	+	0.655686i	$0.772379\pi$
$32$	168.230	−	66.8335i	0.929348	−	0.369206i
$33$	265.732	+	91.1601i	1.40176	+	0.480877i
$34$	214.255	+	52.0977i	1.08072	+	0.262785i
$35$	−9.54698	+	9.54698i	−0.0461067	+	0.0461067i
$36$	−196.084	+	90.5927i	−0.907797	+	0.419410i
$37$	176.815	+	176.815i	0.785626	+	0.785626i	0.980774	−	0.195148i	$-0.0625188\pi$
$37$	176.815	+	176.815i	0.785626	+	0.785626i	−0.195148	+	0.980774i	$0.562519\pi$
$38$	−128.783	+	78.4041i	−0.549773	+	0.334706i
$39$	47.7351	−	139.148i	0.195993	−	0.571322i
$40$	−25.7030	−	367.571i	−0.101600	−	1.45295i
$41$	−301.571			−1.14872			−0.574359	−	0.818604i	$-0.694749\pi$
$41$	−301.571			−1.14872			−0.574359	+	0.818604i	$0.694749\pi$
$42$	2.61638	+	11.9013i	0.00961230	+	0.0437240i
$43$	−96.1344	+	96.1344i	−0.340938	+	0.340938i	−0.856720	−	0.515782i	$-0.827502\pi$
$43$	−96.1344	+	96.1344i	−0.340938	+	0.340938i	0.515782	+	0.856720i	$0.327502\pi$
$44$	131.262	+	412.127i	0.449740	+	1.41206i
$45$	54.5779	+	436.271i	0.180800	+	1.44523i
$46$	−438.645	−	106.660i	−1.40597	−	0.341873i
$47$	−122.486			−0.380135			−0.190068	−	0.981771i	$-0.560871\pi$
$47$	−122.486			−0.380135			−0.190068	+	0.981771i	$0.560871\pi$
$48$	−291.973	−	159.197i	−0.877972	−	0.478712i
$49$	−342.313			−0.997996
$50$	−385.245	−	93.6751i	−1.08964	−	0.264953i
$51$	−177.991	−	363.881i	−0.488700	−	0.999089i
$52$	215.807	−	68.7343i	0.575519	−	0.183303i
$53$	138.452	−	138.452i	0.358828	−	0.358828i	−0.504553	−	0.863381i	$-0.668343\pi$
$53$	138.452	−	138.452i	0.358828	−	0.358828i	0.863381	+	0.504553i	$0.168343\pi$
$54$	358.249	+	170.651i	0.902806	+	0.430048i
$55$	880.414			2.15845
$56$	−12.3082	+	14.1589i	−0.0293705	+	0.0337869i
$57$	261.999	+	89.8792i	0.608817	+	0.208856i
$58$	90.9335	−	55.3609i	0.205865	−	0.125332i
$59$	−168.375	−	168.375i	−0.371535	−	0.371535i	0.496501	−	0.868036i	$-0.334618\pi$
$59$	−168.375	−	168.375i	−0.371535	−	0.371535i	−0.868036	+	0.496501i	$0.834618\pi$
$60$	−489.129	+	467.945i	−1.05244	+	1.00686i
$61$	−178.364	+	178.364i	−0.374379	+	0.374379i	−0.869069	−	0.494690i	$-0.835282\pi$
$61$	−178.364	+	178.364i	−0.374379	+	0.374379i	0.494690	+	0.869069i	$0.335282\pi$
$62$	622.071	+	151.261i	1.27424	+	0.309842i
$63$	13.7420	−	17.6719i	0.0274815	−	0.0353406i
$64$	−71.2566	−	507.017i	−0.139173	−	0.990268i
$65$		−	461.021i		−	0.879732i
$66$	428.123	−	669.403i	0.798459	−	1.24845i
$67$	−233.257	−	233.257i	−0.425326	−	0.425326i	0.461707	−	0.887033i	$-0.347237\pi$
$67$	−233.257	−	233.257i	−0.425326	−	0.425326i	−0.887033	+	0.461707i	$0.847237\pi$
$68$	286.365	−	554.030i	0.510689	−	0.988030i
$69$	364.402	+	744.976i	0.635780	+	1.29978i
$70$	19.8583	+	32.6185i	0.0339075	+	0.0556950i
$71$			668.427i			1.11729i	0.829406	+	0.558646i	$0.188679\pi$
$71$			668.427i			1.11729i	−0.829406	+	0.558646i	$0.811321\pi$
$72$	117.941	+	599.448i	0.193048	+	0.981189i
$73$		−	1216.50i		−	1.95041i	−0.221297	−	0.975207i	$-0.571029\pi$
$73$		−	1216.50i		−	1.95041i	0.221297	−	0.975207i	$-0.428971\pi$
$74$	604.110	−	367.786i	0.949004	−	0.577760i
$75$	320.039	+	654.283i	0.492733	+	1.00733i
$76$	129.418	+	406.337i	0.195333	+	0.613289i
$77$	−31.6974	−	31.6974i	−0.0469123	−	0.0469123i
$78$	−350.527	−	224.183i	−0.508838	−	0.325432i
$79$		−	39.4578i		−	0.0561943i	−0.999605	−	0.0280971i	$-0.991055\pi$
$79$		−	39.4578i		−	0.0561943i	0.999605	−	0.0280971i	$-0.00894478\pi$
$80$	−1027.39	−	174.999i	−1.43582	−	0.244569i
$81$	−179.586	−	706.534i	−0.246346	−	0.969182i
$82$	−201.534	+	828.820i	−0.271411	+	1.11619i
$83$	−293.710	+	293.710i	−0.388419	+	0.388419i	−0.874123	−	0.485704i	$-0.838563\pi$
$83$	−293.710	+	293.710i	−0.388419	+	0.388419i	0.485704	+	0.874123i	$0.338563\pi$
$84$	34.4573	+	0.762680i	0.0447572	+	0.000990657i
$85$	−897.655	−	897.655i	−1.14546	−	1.14546i
$86$	199.966	+	328.455i	0.250731	+	0.411840i
$87$	−184.997	−	63.4635i	−0.227974	−	0.0782069i
$88$	1220.39	−	85.3379i	1.47834	−	0.103376i
$89$	−732.996			−0.873004			−0.436502	−	0.899703i	$-0.643783\pi$
$89$	−732.996			−0.873004			−0.436502	+	0.899703i	$0.643783\pi$
$90$	1235.50	+	141.553i	1.44703	+	0.165789i
$91$	−16.5980	+	16.5980i	−0.0191203	+	0.0191203i
$92$	−586.276	+	1134.27i	−0.664386	+	1.28539i
$93$	−516.781	−	1056.50i	−0.576212	−	1.17800i
$94$	−81.8547	+	336.633i	−0.0898156	+	0.369372i
$95$	868.044			0.937467
$96$	−632.649	+	696.054i	−0.672599	+	0.740007i
$97$	451.695			0.472811			0.236406	−	0.971654i	$-0.424031\pi$
$97$	451.695			0.472811			0.236406	+	0.971654i	$0.424031\pi$
$98$	−228.761	+	940.793i	−0.235799	+	0.969739i
$99$	−1448.48	+	181.207i	−1.47049	+	0.183959i
$100$	−514.903	+	996.184i	−0.514903	+	0.996184i
$101$	991.920	−	991.920i	0.977225	−	0.977225i	−0.0225216	−	0.999746i	$-0.507169\pi$
$101$	991.920	−	991.920i	0.977225	−	0.977225i	0.999746	+	0.0225216i	$0.00716945\pi$
$102$	−1119.02	+	246.005i	−1.08627	+	0.238805i
$103$	173.550			0.166023			0.0830114	−	0.996549i	$-0.473546\pi$
$103$	173.550			0.166023			0.0830114	+	0.996549i	$0.473546\pi$
$104$	−44.6864	−	639.045i	−0.0421333	−	0.602534i
$105$	22.7648	−	66.3595i	0.0211582	−	0.0616764i
$106$	−287.990	−	473.040i	−0.263887	−	0.433450i
$107$	216.201	+	216.201i	0.195336	+	0.195336i	0.797997	−	0.602661i	$-0.205893\pi$
$107$	216.201	+	216.201i	0.195336	+	0.195336i	−0.602661	+	0.797997i	$0.705893\pi$
$108$	708.417	−	870.550i	0.631181	−	0.775636i
$109$	−883.171	+	883.171i	−0.776078	+	0.776078i	−0.979161	−	0.203084i	$-0.934904\pi$
$109$	−883.171	+	883.171i	−0.776078	+	0.776078i	0.203084	+	0.979161i	$0.434904\pi$
$110$	588.364	−	2419.68i	0.509984	−	2.09734i
$111$	−1229.01	−	421.615i	−1.05092	−	0.360522i
$112$	30.6883	+	43.2893i	0.0258909	+	0.0365219i
$113$			1915.77i			1.59487i	0.603403	+	0.797437i	$0.293811\pi$
$113$			1915.77i			1.59487i	−0.603403	+	0.797437i	$0.706189\pi$
$114$	422.108	−	659.998i	0.346789	−	0.542232i
$115$	1837.77	+	1837.77i	1.49020	+	1.49020i
$116$	−91.3819	−	286.913i	−0.0731430	−	0.229649i
$117$	94.8871	+	758.485i	0.0749771	+	0.599333i
$118$	−575.275	+	350.231i	−0.448799	+	0.273232i
$119$			64.6361i			0.0497915i
$120$	959.199	+	1657.01i	0.729687	+	1.26053i
$121$			1592.10i			1.19617i
$122$	371.008	+	609.402i	0.275324	+	0.452235i
$123$	1407.63	−	688.537i	1.03189	−	0.504742i
$124$	831.436	−	1608.58i	0.602138	−	1.16496i
$125$	174.715	+	174.715i	0.125016	+	0.125016i
$126$	−39.3851	−	49.5776i	−0.0278468	−	0.0350534i
$127$			42.9875i			0.0300357i	0.999887	+	0.0150178i	$0.00478050\pi$
$127$			42.9875i			0.0300357i	−0.999887	+	0.0150178i	$0.995219\pi$
$128$	−1441.08	−	142.992i	−0.995113	−	0.0987408i
$129$	229.232	−	668.214i	0.156456	−	0.456070i
$130$	−1267.04	−	308.091i	−0.854824	−	0.207857i
$131$	556.534	−	556.534i	0.371180	−	0.371180i	−0.496727	−	0.867907i	$-0.665465\pi$
$131$	556.534	−	556.534i	0.371180	−	0.371180i	0.867907	+	0.496727i	$0.165465\pi$
$132$	−1553.65	−	1623.98i	−1.02445	−	1.07083i
$133$	−31.2520	−	31.2520i	−0.0203751	−	0.0203751i
$134$	−796.950	+	485.189i	−0.513776	+	0.312790i
$135$	−1250.83	−	1911.76i	−0.797441	−	1.21880i
$136$	−1331.29	−	1157.28i	−0.839394	−	0.729674i
$137$	1557.02			0.970988			0.485494	−	0.874240i	$-0.338640\pi$
$137$	1557.02			0.970988			0.485494	+	0.874240i	$0.338640\pi$
$138$	2290.97	−	503.648i	1.41319	−	0.310677i
$139$	−682.898	+	682.898i	−0.416710	+	0.416710i	−0.884068	−	0.467358i	$-0.845206\pi$
$139$	−682.898	+	682.898i	−0.416710	+	0.416710i	0.467358	+	0.884068i	$0.345206\pi$
$140$	102.918	−	32.7793i	0.0621295	−	0.0197882i
$141$	571.722	−	279.655i	0.341473	−	0.167030i
$142$	1837.07	+	446.697i	1.08566	+	0.263986i
$143$	1530.66			0.895104
$144$	1726.31	+	76.4578i	0.999021	+	0.0442464i
$145$	−612.924			−0.351038
$146$	−3343.35	−	812.961i	−1.89519	−	0.460830i
$147$	1597.80	−	781.557i	0.896493	−	0.438515i
$148$	−607.088	−	1906.09i	−0.337178	−	1.05864i
$149$	143.722	−	143.722i	0.0790215	−	0.0790215i	−0.666491	−	0.745513i	$-0.732205\pi$
$149$	143.722	−	143.722i	0.0790215	−	0.0790215i	0.745513	+	0.666491i	$0.232205\pi$
$150$	2012.07	−	442.334i	1.09523	−	0.240776i
$151$	−1427.53			−0.769340			−0.384670	−	0.923054i	$-0.625685\pi$
$151$	−1427.53			−0.769340			−0.384670	+	0.923054i	$0.625685\pi$
$152$	1203.24	−	84.1388i	0.642077	−	0.0448984i
$153$	1661.60	+	1292.09i	0.877992	+	0.682742i
$154$	−108.298	+	65.9326i	−0.0566682	+	0.0345000i
$155$	−2606.26	−	2606.26i	−1.35058	−	1.35058i
$156$	−850.382	+	813.552i	−0.436442	+	0.417540i
$157$	2228.30	−	2228.30i	1.13273	−	1.13273i	0.143003	−	0.989722i	$-0.454324\pi$
$157$	2228.30	−	2228.30i	1.13273	−	1.13273i	0.989722	−	0.143003i	$-0.0456760\pi$
$158$	−108.444	−	26.3689i	−0.0546032	−	0.0132772i
$159$	−330.140	+	962.360i	−0.164665	+	0.480000i
$160$	−1167.54	+	2706.67i	−0.576889	+	1.33738i
$161$		−	132.330i		−	0.0647768i
$162$	−2061.81	+	21.4028i	−0.999946	+	0.0103800i
$163$	−418.032	−	418.032i	−0.200876	−	0.200876i	0.599499	−	0.800375i	$-0.295366\pi$
$163$	−418.032	−	418.032i	−0.200876	−	0.200876i	−0.800375	+	0.599499i	$0.795366\pi$
$164$	2143.20	+	1107.77i	1.02046	+	0.527453i
$165$	−4109.48	+	2010.13i	−1.93893	+	0.948416i
$166$	610.935	+	1003.50i	0.285649	+	0.469195i
$167$			3870.40i			1.79342i	0.442623	+	0.896708i	$0.354048\pi$
$167$			3870.40i			1.79342i	−0.442623	+	0.896708i	$0.645952\pi$
$168$	25.1233	−	94.1909i	0.0115375	−	0.0432559i
$169$			1395.49i			0.635178i
$170$	−3066.95	+	1867.18i	−1.38367	+	0.842389i
$171$	−1428.13	+	178.660i	−0.638667	+	0.0798977i
$172$	1036.34	−	330.075i	0.459420	−	0.146325i
$173$	1289.55	+	1289.55i	0.566721	+	0.566721i	0.931208	−	0.364487i	$-0.118756\pi$
$173$	1289.55	+	1289.55i	0.566721	+	0.566721i	−0.364487	+	0.931208i	$0.618756\pi$
$174$	−298.049	+	466.023i	−0.129857	+	0.203041i
$175$		−	116.220i		−	0.0502024i
$176$	581.024	−	3411.08i	0.248843	−	1.46091i
$177$	1170.35	+	401.491i	0.496999	+	0.170496i
$178$	−489.847	+	2014.52i	−0.206267	+	0.848287i
$179$	1767.33	−	1767.33i	0.737970	−	0.737970i	−0.234215	−	0.972185i	$-0.575252\pi$
$179$	1767.33	−	1767.33i	0.737970	−	0.737970i	0.972185	+	0.234215i	$0.0752520\pi$
$180$	1214.69	−	3300.98i	0.502989	−	1.36689i
$181$	417.552	+	417.552i	0.171472	+	0.171472i	0.787626	−	0.616154i	$-0.211310\pi$
$181$	417.552	+	417.552i	0.171472	+	0.171472i	−0.616154	+	0.787626i	$0.711310\pi$
$182$	34.5250	+	56.7093i	0.0140613	+	0.0230965i
$183$	425.308	−	1239.78i	0.171802	−	0.500803i
$184$	2725.57	+	2369.30i	1.09202	+	0.949278i
$185$	−4071.91			−1.61823
$186$	−3248.98	+	714.256i	−1.28079	+	0.281569i
$187$	2980.34	−	2980.34i	1.16548	−	1.16548i
$188$	870.481	+	449.930i	0.337693	+	0.174545i
$189$	−23.7952	+	113.862i	−0.00915792	+	0.0438214i
$190$	580.097	−	2385.68i	0.221498	−	0.910925i
$191$	−1181.47			−0.447580			−0.223790	−	0.974637i	$-0.571843\pi$
$191$	−1181.47			−0.447580			−0.223790	+	0.974637i	$0.571843\pi$
$192$	1490.21	+	2203.90i	0.560138	+	0.828399i
$193$	−1794.87			−0.669417			−0.334709	−	0.942322i	$-0.608638\pi$
$193$	−1794.87			−0.669417			−0.334709	+	0.942322i	$0.608638\pi$
$194$	301.859	−	1241.41i	0.111713	−	0.459425i
$195$	1052.59	+	2151.89i	0.386551	+	0.790257i
$196$	2432.75	+	1257.43i	0.886570	+	0.458246i
$197$	31.7151	−	31.7151i	0.0114701	−	0.0114701i	−0.701348	−	0.712819i	$-0.747418\pi$
$197$	31.7151	−	31.7151i	0.0114701	−	0.0114701i	0.712819	+	0.701348i	$0.247418\pi$
$198$	−469.976	+	4102.03i	−0.168685	+	1.47232i
$199$	−4332.32			−1.54327			−0.771634	−	0.636067i	$-0.780560\pi$
$199$	−4332.32			−1.54327			−0.771634	+	0.636067i	$0.780560\pi$
$200$	2393.76	+	2080.86i	0.846321	+	0.735696i
$201$	1621.33	+	556.200i	0.568954	+	0.195181i
$202$	−2063.26	−	3389.02i	−0.718665	−	1.18045i
$203$	22.0670	+	22.0670i	0.00762955	+	0.00762955i
$204$	−71.7110	+	3239.85i	−0.0246116	+	1.11194i
$205$	3472.47	−	3472.47i	1.18306	−	1.18306i
$206$	115.980	−	476.974i	0.0392267	−	0.161322i
$207$	−3401.81	−	2645.31i	−1.14223	−	0.888222i
$208$	−1786.18	−	304.248i	−0.595429	−	0.101422i
$209$			2882.03i			0.953848i
$210$	−167.166	−	106.912i	−0.0549310	−	0.0351316i
$211$	−2291.21	−	2291.21i	−0.747553	−	0.747553i	0.226466	−	0.974019i	$-0.427283\pi$
$211$	−2291.21	−	2291.21i	−0.747553	−	0.747553i	−0.974019	+	0.226466i	$0.927283\pi$
$212$	−1492.53	+	475.372i	−0.483527	+	0.154003i
$213$	−1526.13	−	3120.00i	−0.490934	−	1.00366i
$214$	738.678	−	449.712i	0.235958	−	0.143653i
$215$		−	2213.90i		−	0.702265i
$216$	−1919.15	−	2528.75i	−0.604544	−	0.796572i
$217$			187.666i			0.0587077i
$218$	1837.05	+	3017.47i	0.570738	+	0.937471i
$219$	2777.47	+	5678.20i	0.857004	+	1.75204i
$220$	−6256.93	−	3234.05i	−1.91746	−	0.991090i
$221$	−1560.63	−	1560.63i	−0.475020	−	0.475020i
$222$	−1980.07	+	3095.99i	−0.598619	+	0.935987i
$223$			1012.13i			0.303933i	0.988386	+	0.151966i	$0.0485605\pi$
$223$			1012.13i			0.303933i	−0.988386	+	0.151966i	$0.951439\pi$
$224$	139.482	−	55.4128i	0.0416052	−	0.0165287i
$225$	−2987.68	−	2323.27i	−0.885237	−	0.688377i
$226$	5265.20	+	1280.27i	1.54972	+	0.376825i
$227$	−218.272	+	218.272i	−0.0638202	+	0.0638202i	−0.738297	−	0.674476i	$-0.764369\pi$
$227$	−218.272	+	218.272i	−0.0638202	+	0.0638202i	0.674476	+	0.738297i	$0.264369\pi$
$228$	−1531.82	−	1601.16i	−0.444943	−	0.465086i
$229$	−563.164	−	563.164i	−0.162510	−	0.162510i	0.621167	−	0.783678i	$-0.286659\pi$
$229$	−563.164	−	563.164i	−0.162510	−	0.162510i	−0.783678	+	0.621167i	$0.786659\pi$
$230$	6278.99	−	3822.69i	1.80010	−	1.09592i
$231$	220.323	+	75.5824i	0.0627541	+	0.0215279i
$232$	−849.606	+	59.4102i	−0.240428	+	0.0168124i
$233$	646.432			0.181756			0.0908781	−	0.995862i	$-0.471033\pi$
$233$	646.432			0.181756			0.0908781	+	0.995862i	$0.471033\pi$
$234$	2147.99	+	246.098i	0.600079	+	0.0687520i
$235$	1410.38	−	1410.38i	0.391501	−	0.391501i
$236$	578.111	+	1815.11i	0.159457	+	0.500650i
$237$	90.0888	+	184.176i	0.0246915	+	0.0504790i
$238$	177.642	+	43.1951i	0.0483817	+	0.0117644i
$239$	996.350			0.269659			0.134830	−	0.990869i	$-0.456951\pi$
$239$	996.350			0.269659			0.134830	+	0.990869i	$0.456951\pi$
$240$	5195.06	−	1528.86i	1.39725	−	0.411198i
$241$	4528.91			1.21051			0.605255	−	0.796032i	$-0.293071\pi$
$241$	4528.91			1.21051			0.605255	+	0.796032i	$0.293071\pi$
$242$	4375.65	+	1063.97i	1.16230	+	0.282623i
$243$	2451.39	+	2887.84i	0.647146	+	0.762366i
$244$	1922.78	−	612.407i	0.504482	−	0.160678i
$245$	3941.60	−	3941.60i	1.02784	−	1.02784i
$246$	−951.643	−	4328.80i	−0.246645	−	1.12193i
$247$	1509.15			0.388765
$248$	−3865.30	−	3360.06i	−0.989705	−	0.860338i
$249$	700.351	−	2041.53i	0.178245	−	0.519585i
$250$	596.936	−	363.418i	0.151014	−	0.0919384i
$251$	−3612.53	−	3612.53i	−0.908449	−	0.908449i	0.0876984	−	0.996147i	$-0.472049\pi$
$251$	−3612.53	−	3612.53i	−0.908449	−	0.908449i	−0.996147	+	0.0876984i	$0.972049\pi$
$252$	−162.577	+	75.1119i	−0.0406404	+	0.0187762i
$253$	−6101.68	+	6101.68i	−1.51624	+	1.51624i
$254$	118.145	+	28.7277i	0.0291852	+	0.00709661i
$255$	6239.45	+	2140.46i	1.53227	+	0.525650i
$256$	−1356.04	+	3865.02i	−0.331063	+	0.943609i
$257$		−	1679.73i		−	0.407699i	−0.979002	−	0.203850i	$-0.934655\pi$
$257$		−	1679.73i		−	0.407699i	0.979002	−	0.203850i	$-0.0653453\pi$
$258$	−1683.29	−	1076.56i	−0.406191	−	0.259783i
$259$	146.600	+	146.600i	0.0351710	+	0.0351710i
$260$	−1693.48	+	3276.38i	−0.403943	+	0.781510i
$261$	1008.40	−	126.152i	0.239151	−	0.0299180i
$262$	−1157.63	−	1901.47i	−0.272971	−	0.448371i
$263$			1574.43i			0.369139i	0.982819	+	0.184569i	$0.0590890\pi$
$263$			1574.43i			0.369139i	−0.982819	+	0.184569i	$0.940911\pi$
$264$	−5501.53	+	3184.68i	−1.28256	+	0.742438i
$265$			3188.45i			0.739114i
$266$	−106.776	+	65.0062i	−0.0246123	+	0.0149841i
$267$	3421.38	−	1673.55i	0.784214	−	0.383595i
$268$	800.879	+	2514.54i	0.182543	+	0.573133i
$269$	−1316.04	−	1316.04i	−0.298290	−	0.298290i	0.542054	−	0.840344i	$-0.317647\pi$
$269$	−1316.04	−	1316.04i	−0.298290	−	0.298290i	−0.840344	+	0.542054i	$0.817647\pi$
$270$	−6090.08	+	2160.13i	−1.37271	+	0.486893i
$271$		−	4047.05i		−	0.907162i	−0.891215	−	0.453581i	$-0.850146\pi$
$271$		−	4047.05i		−	0.907162i	0.891215	−	0.453581i	$-0.149854\pi$
$272$	−4070.27	+	2885.47i	−0.907341	+	0.643226i
$273$	39.5780	−	115.370i	0.00877425	−	0.0255770i
$274$	1040.53	−	4279.23i	0.229418	−	0.943496i
$275$	−5358.86	+	5358.86i	−1.17510	+	1.17510i
$276$	146.814	−	6632.97i	0.0320188	−	1.44659i
$277$	4498.76	+	4498.76i	0.975829	+	0.975829i	0.999715	−	0.0238859i	$-0.00760383\pi$
$277$	4498.76	+	4498.76i	0.975829	+	0.975829i	−0.0238859	+	0.999715i	$0.507604\pi$
$278$	1420.47	+	2333.21i	0.306454	+	0.503368i
$279$	4824.33	+	3751.49i	1.03521	+	0.805002i
$280$	−21.3108	−	304.759i	−0.00454845	−	0.0650459i
$281$	−2856.76			−0.606476			−0.303238	−	0.952915i	$-0.598068\pi$
$281$	−2856.76			−0.606476			−0.303238	+	0.952915i	$0.598068\pi$
$282$	−386.518	−	1758.18i	−0.0816199	−	0.371269i
$283$	−5461.16	+	5461.16i	−1.14711	+	1.14711i	−0.159992	+	0.987118i	$0.551147\pi$
$283$	−5461.16	+	5461.16i	−1.14711	+	1.14711i	−0.987118	+	0.159992i	$0.948853\pi$
$284$	2455.36	−	4750.38i	0.513023	−	0.992547i
$285$	−4051.74	+	1981.89i	−0.842121	+	0.411919i
$286$	1022.91	−	4206.77i	0.211489	−	0.869761i
$287$	−250.038			−0.0514260
$288$	1363.79	−	4693.39i	0.279035	−	0.960281i
$289$	−1164.41			−0.237006
$290$	−409.605	+	1684.53i	−0.0829408	+	0.341099i
$291$	−2108.36	+	1031.30i	−0.424723	+	0.207751i
$292$	−4468.60	+	8645.40i	−0.895564	+	1.73265i
$293$	−4624.96	+	4624.96i	−0.922162	+	0.922162i	−0.997182	−	0.0750205i	$-0.976098\pi$
$293$	−4624.96	+	4624.96i	−0.922162	+	0.922162i	0.0750205	+	0.997182i	$0.476098\pi$
$294$	−1080.21	−	4913.61i	−0.214283	−	0.974720i
$295$	3877.55			0.765288
$296$	−5644.29	+	394.687i	−1.10834	+	0.0775024i
$297$	6347.32	−	4152.95i	1.24010	−	0.811375i
$298$	−298.952	−	491.046i	−0.0581135	−	0.0954548i
$299$	3195.09	+	3195.09i	0.617982	+	0.617982i
$300$	128.941	−	5825.47i	0.0248147	−	1.12111i
$301$	−79.7067	+	79.7067i	−0.0152632	+	0.0152632i
$302$	−953.988	+	3923.33i	−0.181774	+	0.747558i
$303$	−2365.23	+	6894.67i	−0.448446	+	1.30722i
$304$	572.860	−	3363.15i	0.108078	−	0.634506i
$305$		−	4107.58i		−	0.771146i
$306$	4661.54	−	3703.18i	0.870857	−	0.691819i
$307$	1372.35	+	1372.35i	0.255128	+	0.255128i	0.823069	−	0.567941i	$-0.192260\pi$
$307$	1372.35	+	1372.35i	0.255128	+	0.255128i	−0.567941	+	0.823069i	$0.692260\pi$
$308$	108.832	+	341.702i	0.0201340	+	0.0632152i
$309$	−810.073	+	396.243i	−0.149137	+	0.0729498i
$310$	−8904.63	+	5421.20i	−1.63145	+	0.993237i
$311$			3244.39i			0.591551i	0.955258	+	0.295775i	$0.0955780\pi$
$311$			3244.39i			0.591551i	−0.955258	+	0.295775i	$0.904422\pi$
$312$	1667.63	+	2880.82i	0.302599	+	0.522739i
$313$		−	6287.66i		−	1.13546i	−0.823214	−	0.567731i	$-0.807822\pi$
$313$		−	6287.66i		−	1.13546i	0.823214	−	0.567731i	$-0.192178\pi$
$314$	−4635.01	−	7613.28i	−0.833022	−	1.36829i
$315$	45.2515	+	361.720i	0.00809407	+	0.0647004i
$316$	−144.942	+	280.419i	−0.0258025	+	0.0499202i
$317$	−4723.19	−	4723.19i	−0.836848	−	0.836848i	0.151595	−	0.988443i	$-0.451559\pi$
$317$	−4723.19	−	4723.19i	−0.836848	−	0.836848i	−0.988443	+	0.151595i	$0.951559\pi$
$318$	2424.27	+	1550.46i	0.427504	+	0.273414i
$319$		−	2035.00i		−	0.357172i
$320$	6658.61	+	5017.62i	1.16321	+	0.876542i
$321$	−1502.78	−	515.532i	−0.261299	−	0.0896392i
$322$	−363.688	−	88.4336i	−0.0629427	−	0.0153050i
$323$	2938.47	−	2938.47i	0.506194	−	0.506194i
$324$	−1319.05	+	5680.87i	−0.226174	+	0.974087i
$325$	2806.12	+	2806.12i	0.478940	+	0.478940i
$326$	−1428.26	+	869.534i	−0.242650	+	0.147727i
$327$	2105.92	−	6138.78i	0.356140	−	1.03815i
$328$	4476.79	−	5149.96i	0.753627	−	0.866948i
$329$	−101.555			−0.0170179
$330$	2778.25	+	12637.6i	0.463448	+	2.10811i
$331$	−6112.31	+	6112.31i	−1.01499	+	1.01499i	−0.0151076	+	0.999886i	$0.504809\pi$
$331$	−6112.31	+	6112.31i	−1.01499	+	1.01499i	−0.999886	+	0.0151076i	$0.995191\pi$
$332$	3166.23	−	1008.44i	0.523402	−	0.166703i
$333$	6699.23	−	838.079i	1.10245	−	0.137917i
$334$	10637.2	+	2586.51i	1.74264	+	0.423735i
$335$	5371.72			0.876086
$336$	−242.080	−	131.993i	−0.0393052	−	0.0214310i
$337$	5377.59			0.869246			0.434623	−	0.900613i	$-0.356882\pi$
$337$	5377.59			0.869246			0.434623	+	0.900613i	$0.356882\pi$
$338$	3835.28	+	932.576i	0.617194	+	0.150075i
$339$	−4374.03	−	8942.19i	−0.700781	−	1.43266i
$340$	3082.07	+	9676.84i	0.491614	+	1.54353i
$341$	8653.18	−	8653.18i	1.37418	−	1.37418i
$342$	−463.372	+	4044.40i	−0.0732640	+	0.639462i
$343$	−568.205			−0.0894465
$344$	−214.592	−	3068.81i	−0.0336338	−	0.480985i
$345$	−12774.1	−	4382.17i	−1.99343	−	0.683850i
$346$	4405.91	−	2682.35i	0.684576	−	0.416774i
$347$	3586.40	+	3586.40i	0.554835	+	0.554835i	0.927832	−	0.372997i	$-0.121670\pi$
$347$	3586.40	+	3586.40i	0.554835	+	0.554835i	−0.372997	+	0.927832i	$0.621670\pi$
$348$	1081.61	+	1130.58i	0.166611	+	0.174153i
$349$	−3892.45	+	3892.45i	−0.597015	+	0.597015i	−0.939517	−	0.342502i	$-0.888726\pi$
$349$	−3892.45	+	3892.45i	−0.597015	+	0.597015i	0.342502	+	0.939517i	$0.388726\pi$
$350$	−319.413	−	77.6677i	−0.0487810	−	0.0118615i
$351$	−2174.65	−	3323.72i	−0.330696	−	0.505433i
$352$	−8986.53	−	3876.41i	−1.36075	−	0.586970i
$353$		−	2306.40i		−	0.347754i	−0.984767	−	0.173877i	$-0.944370\pi$
$353$		−	2306.40i		−	0.347754i	0.984767	−	0.173877i	$-0.0556296\pi$
$354$	1885.56	−	2948.21i	0.283096	−	0.442643i
$355$	−7696.69	−	7696.69i	−1.15070	−	1.15070i
$356$	5209.25	+	2692.54i	0.775534	+	0.400854i
$357$	−147.575	−	301.700i	−0.0218782	−	0.0447274i
$358$	−3676.16	−	6038.31i	−0.542713	−	0.891438i
$359$		−	3997.53i		−	0.587693i	−0.955853	−	0.293846i	$-0.905065\pi$
$359$		−	3997.53i		−	0.587693i	0.955853	−	0.293846i	$-0.0949354\pi$
$360$	−8260.46	−	5544.38i	−1.20935	−	0.811707i
$361$		−	4017.46i		−	0.585721i
$362$	1426.62	−	868.535i	0.207131	−	0.126103i
$363$	−3635.04	−	7431.41i	−0.525593	−	1.07451i
$364$	178.929	−	56.9888i	0.0257649	−	0.00820612i
$365$	14007.5	+	14007.5i	2.00873	+	2.00873i
$366$	−3123.11	−	1997.41i	−0.446032	−	0.285264i
$367$			4404.23i			0.626428i	0.949683	+	0.313214i	$0.101406\pi$
$367$			4404.23i			0.626428i	−0.949683	+	0.313214i	$0.898594\pi$
$368$	8333.10	−	5907.44i	1.18042	−	0.836812i
$369$	−4998.32	+	6427.73i	−0.705155	+	0.906813i
$370$	−2721.18	+	11191.0i	−0.382344	+	1.57241i
$371$	114.793	−	114.793i	0.0160641	−	0.0160641i
$372$	−208.207	+	9406.63i	−0.0290189	+	1.31105i
$373$	−6347.59	−	6347.59i	−0.881141	−	0.881141i	0.112509	−	0.993651i	$-0.464111\pi$
$373$	−6347.59	−	6347.59i	−0.881141	−	0.881141i	−0.993651	+	0.112509i	$0.964111\pi$
$374$	−6199.31	−	10182.7i	−0.857109	−	1.40785i
$375$	−1214.42	−	416.608i	−0.167232	−	0.0573694i
$376$	1818.29	−	2091.70i	0.249391	−	0.286892i
$377$	−1065.61			−0.145574
$378$	297.031	+	141.489i	0.0404169	+	0.0192524i
$379$	7494.33	−	7494.33i	1.01572	−	1.01572i	0.0158460	−	0.999874i	$-0.494956\pi$
$379$	7494.33	−	7494.33i	1.01572	−	1.01572i	0.999874	−	0.0158460i	$-0.00504414\pi$
$380$	−6169.01	−	3188.61i	−0.832799	−	0.430454i
$381$	−98.1478	−	200.652i	−0.0131975	−	0.0269808i
$382$	−789.550	+	3247.07i	−0.105751	+	0.434908i
$383$	−14197.9			−1.89420			−0.947100	−	0.320940i	$-0.896001\pi$
$383$	−14197.9			−1.89420			−0.947100	+	0.320940i	$0.896001\pi$
$384$	7052.95	−	2622.78i	0.937290	−	0.348551i
$385$	729.967			0.0966300
$386$	−1199.48	+	4932.92i	−0.158165	+	0.650464i
$387$	455.665	+	3642.38i	0.0598521	+	0.478431i
$388$	−3210.11	−	1659.23i	−0.420022	−	0.217099i
$389$	−9377.75	+	9377.75i	−1.22229	+	1.22229i	−0.255475	+	0.966816i	$0.582232\pi$
$389$	−9377.75	+	9377.75i	−1.22229	+	1.22229i	−0.966816	+	0.255475i	$0.917768\pi$
$390$	6617.57	−	1454.81i	0.859214	−	0.188890i
$391$	12442.3			1.60930
$392$	5081.60	−	5845.72i	0.654744	−	0.753197i
$393$	−1327.06	+	3868.38i	−0.170334	+	0.496524i
$394$	−65.9695	−	108.359i	−0.00843527	−	0.0138554i
$395$	454.342	+	454.342i	0.0578745	+	0.0578745i
$396$	10959.7	+	4032.96i	1.39077	+	0.511778i
$397$	303.909	−	303.909i	0.0384201	−	0.0384201i	−0.687636	−	0.726056i	$-0.741351\pi$
$397$	303.909	−	303.909i	0.0384201	−	0.0384201i	0.726056	+	0.687636i	$0.241351\pi$
$398$	−2895.21	+	11906.7i	−0.364632	+	1.49957i
$399$	217.228	+	74.5204i	0.0272556	+	0.00935009i
$400$	7318.63	−	5188.27i	0.914828	−	0.648534i
$401$			13634.6i			1.69795i	0.528432	+	0.848976i	$0.322780\pi$
$401$			13634.6i			1.69795i	−0.528432	+	0.848976i	$0.677220\pi$
$402$	2612.13	−	4084.27i	0.324083	−	0.506729i
$403$	−4531.16	−	4531.16i	−0.560082	−	0.560082i
$404$	−10693.0	+	3405.73i	−1.31683	+	0.419409i
$405$	10203.3	+	6067.60i	1.25187	+	0.744448i
$406$	75.3946	−	45.9007i	0.00921618	−	0.00561087i
$407$		−	13519.3i		−	1.64651i
$408$	8856.30	+	2362.22i	1.07464	+	0.286635i
$409$			3759.45i			0.454506i	0.973836	+	0.227253i	$0.0729744\pi$
$409$			3759.45i			0.454506i	−0.973836	+	0.227253i	$0.927026\pi$
$410$	−7222.97	−	11864.1i	−0.870042	−	1.42909i
$411$	−7267.66	+	3554.94i	−0.872232	+	0.426648i
$412$	−1233.38	−	637.505i	−0.147486	−	0.0762321i
$413$	−139.603	−	139.603i	−0.0166329	−	0.0166329i
$414$	−9543.60	+	7581.54i	−1.13295	+	0.900030i
$415$		−	6763.91i		−	0.800066i
$416$	−2029.85	+	4705.71i	−0.239234	+	0.554607i
$417$	1628.37	−	4746.71i	0.191227	−	0.557428i
$418$	7920.82	+	1926.01i	0.926842	+	0.225369i
$419$	4010.59	−	4010.59i	0.467614	−	0.467614i	−0.433527	−	0.901141i	$-0.642731\pi$
$419$	4010.59	−	4010.59i	0.467614	−	0.467614i	0.901141	+	0.433527i	$0.142731\pi$
$420$	−405.545	+	387.981i	−0.0471157	+	0.0450751i
$421$	909.573	+	909.573i	0.105297	+	0.105297i	0.757792	−	0.652496i	$-0.226278\pi$
$421$	909.573	+	909.573i	0.105297	+	0.105297i	−0.652496	+	0.757792i	$0.726278\pi$
$422$	−7828.22	+	4765.87i	−0.903014	+	0.549761i
$423$	−2030.11	+	2610.68i	−0.233351	+	0.300084i
$424$	309.054	+	4419.68i	0.0353986	+	0.506223i
$425$	10927.6			1.24721
$426$	−9594.72	+	2109.30i	−1.09123	+	0.239897i
$427$	−147.884	+	147.884i	−0.0167603	+	0.0167603i
$428$	−742.320	−	2330.68i	−0.0838351	−	0.263219i
$429$	−7144.60	+	3494.75i	−0.804066	+	0.393305i
$430$	−6084.57	−	1479.51i	−0.682381	−	0.165926i
$431$	4734.20			0.529092			0.264546	−	0.964373i	$-0.414778\pi$
$431$	4734.20			0.529092			0.264546	+	0.964373i	$0.414778\pi$
$432$	−8232.40	+	3584.57i	−0.916855	+	0.399219i
$433$	−4314.42			−0.478841			−0.239420	−	0.970916i	$-0.576957\pi$
$433$	−4314.42			−0.478841			−0.239420	+	0.970916i	$0.576957\pi$
$434$	515.770	+	125.413i	0.0570455	+	0.0138710i
$435$	2860.93	−	1399.41i	0.315335	−	0.154245i
$436$	9520.71	−	3032.34i	1.04578	−	0.333080i
$437$	−6015.95	+	6015.95i	−0.658539	+	0.658539i
$438$	17461.8	−	3838.80i	1.90492	−	0.418779i
$439$	−12834.1			−1.39531			−0.697654	−	0.716435i	$-0.745773\pi$
$439$	−12834.1			−1.39531			−0.697654	+	0.716435i	$0.745773\pi$
$440$	−13069.7	+	15034.9i	−1.41607	+	1.62901i
$441$	−5673.58	+	7296.10i	−0.612632	+	0.787831i
$442$	−5332.09	+	3246.21i	−0.573804	+	0.349336i
$443$	1859.08	+	1859.08i	0.199385	+	0.199385i	0.799736	−	0.600351i	$-0.204973\pi$
$443$	1859.08	+	1859.08i	0.199385	+	0.199385i	−0.600351	+	0.799736i	$0.704973\pi$
$444$	7185.60	+	7510.89i	0.768048	+	0.802818i
$445$	8440.17	−	8440.17i	0.899107	−	0.899107i
$446$	2781.67	+	676.384i	0.295327	+	0.0718111i
$447$	−342.706	+	998.991i	−0.0362628	+	0.105706i
$448$	−59.0801	−	420.377i	−0.00623052	−	0.0443325i
$449$		−	8018.01i		−	0.842747i	−0.906887	−	0.421373i	$-0.861548\pi$
$449$		−	8018.01i		−	0.842747i	0.906887	−	0.421373i	$-0.138452\pi$
$450$	−8381.76	+	6658.57i	−0.878044	+	0.697528i
$451$	11529.1	+	11529.1i	1.20374	+	1.20374i
$452$	7037.27	−	13615.0i	0.732312	−	1.41681i
$453$	6663.22	−	3259.28i	0.691093	−	0.338045i
$454$	454.019	+	745.752i	0.0469343	+	0.0770923i
$455$		−	382.240i		−	0.0393840i
$456$	−5424.23	+	3139.93i	−0.557045	+	0.322458i
$457$		−	15869.1i		−	1.62434i	−0.583420	−	0.812171i	$-0.698286\pi$
$457$		−	15869.1i		−	1.62434i	0.583420	−	0.812171i	$-0.301714\pi$
$458$	−1924.12	+	1171.42i	−0.196306	+	0.119512i
$459$	−10705.9	−	2237.35i	−1.08869	−	0.227517i
$460$	−6309.94	−	19811.4i	−0.639571	−	2.00807i
$461$	−2986.52	−	2986.52i	−0.301727	−	0.301727i	0.539962	−	0.841689i	$-0.318438\pi$
$461$	−2986.52	−	2986.52i	−0.301727	−	0.301727i	−0.841689	+	0.539962i	$0.818438\pi$
$462$	354.964	−	555.014i	0.0357455	−	0.0558909i
$463$			18753.3i			1.88238i	0.337883	+	0.941188i	$0.390289\pi$
$463$			18753.3i			1.88238i	−0.337883	+	0.941188i	$0.609711\pi$
$464$	−404.495	+	2374.71i	−0.0404703	+	0.237593i
$465$	18115.7	+	6214.64i	1.80666	+	0.619779i
$466$	431.998	−	1776.62i	0.0429440	−	0.176610i
$467$	−1865.17	+	1865.17i	−0.184817	+	0.184817i	−0.793451	−	0.608634i	$-0.791718\pi$
$467$	−1865.17	+	1865.17i	−0.184817	+	0.184817i	0.608634	+	0.793451i	$0.291718\pi$
$468$	2111.82	−	5738.96i	0.208588	−	0.566845i
$469$	−193.397	−	193.397i	−0.0190410	−	0.0190410i
$470$	−2933.67	−	4818.73i	−0.287915	−	0.472918i
$471$	−5313.39	+	15488.6i	−0.519805	+	1.51524i
$472$	5374.88	−	375.848i	0.524150	−	0.0366521i
$473$	7350.48			0.714536
$474$	566.384	−	124.514i	0.0548837	−	0.0120656i
$475$	−5283.56	+	5283.56i	−0.510372	+	0.510372i
$476$	237.430	−	459.356i	0.0228626	−	0.0442323i
$477$	−656.246	−	5245.74i	−0.0629926	−	0.503535i
$478$	665.842	−	2738.31i	0.0637132	−	0.262024i
$479$	15505.8			1.47907			0.739536	−	0.673117i	$-0.235045\pi$
$479$	15505.8			1.47907			0.739536	+	0.673117i	$0.235045\pi$
$480$	−730.077	−	15299.5i	−0.0694235	−	1.45484i
$481$	−7079.27			−0.671075
$482$	3026.58	−	12447.0i	0.286011	−	1.17624i
$483$	302.132	+	617.673i	0.0284627	+	0.0581886i
$484$	5848.32	−	11314.8i	0.549241	−	1.06262i
$485$	−5201.10	+	5201.10i	−0.486948	+	0.486948i
$486$	9574.99	−	4807.37i	0.893684	−	0.448697i
$487$	3905.87			0.363433			0.181716	−	0.983351i	$-0.441835\pi$
$487$	3905.87			0.363433			0.181716	+	0.983351i	$0.441835\pi$
$488$	−398.145	−	5693.74i	−0.0369327	−	0.528163i
$489$	2905.67	+	996.798i	0.268710	+	0.0921815i
$490$	−8198.79	−	13467.0i	−0.755884	−	1.24158i
$491$	394.762	+	394.762i	0.0362839	+	0.0362839i	0.725016	−	0.688732i	$-0.241832\pi$
$491$	394.762	+	394.762i	0.0362839	+	0.0362839i	−0.688732	+	0.725016i	$0.741832\pi$
$492$	−12533.0	−	277.406i	−1.14844	−	0.0254196i
$493$	−2074.85	+	2074.85i	−0.189546	+	0.189546i
$494$	1008.54	−	4147.66i	0.0918545	−	0.377757i
$495$	14592.2	−	18765.3i	1.32499	−	1.70391i
$496$	−11817.7	+	8377.72i	−1.06982	+	0.758409i
$497$			554.205i			0.0500191i
$498$	−5142.79	−	3289.12i	−0.462759	−	0.295962i
$499$	10139.9	+	10139.9i	0.909665	+	0.909665i	0.996245	−	0.0865797i	$-0.0275937\pi$
$499$	10139.9	+	10139.9i	0.909665	+	0.909665i	−0.0865797	+	0.996245i	$0.527594\pi$
$500$	−599.879	−	1883.45i	−0.0536548	−	0.168461i
$501$	−8836.77	−	18065.7i	−0.788020	−	1.61101i
$502$	−12342.6	+	7514.29i	−1.09737	+	0.668086i
$503$			4295.85i			0.380800i	0.981707	+	0.190400i	$0.0609785\pi$
$503$			4295.85i			0.380800i	−0.981707	+	0.190400i	$0.939022\pi$
$504$	97.7867	+	497.013i	0.00864239	+	0.0439260i
$505$			22843.2i			2.01289i
$506$	12691.9	+	20847.2i	1.11507	+	1.83156i
$507$	−3186.13	−	6513.67i	−0.279095	−	0.570576i
$508$	157.908	−	305.504i	0.0137914	−	0.0266822i
$509$	−10770.7	−	10770.7i	−0.937927	−	0.937927i	0.0602555	−	0.998183i	$-0.480808\pi$
$509$	−10770.7	−	10770.7i	−0.937927	−	0.937927i	−0.998183	+	0.0602555i	$0.980808\pi$
$510$	10052.4	−	15717.7i	0.872802	−	1.36469i
$511$		−	1008.62i		−	0.0873163i
$512$	9716.20	+	6309.77i	0.838671	+	0.544639i
$513$	6258.14	−	4094.59i	0.538603	−	0.352399i
$514$	−4616.48	−	1122.53i	−0.396156	−	0.0963283i
$515$	−1998.36	+	1998.36i	−0.170987	+	0.170987i
$516$	−4083.68	+	3906.82i	−0.348399	+	0.333310i
$517$	4682.65	+	4682.65i	0.398342	+	0.398342i
$518$	500.878	−	304.938i	0.0424851	−	0.0258652i
$519$	−8963.46	−	3074.93i	−0.758097	−	0.260067i
$520$	7872.91	+	6843.82i	0.663942	+	0.577156i
$521$	16048.6			1.34952			0.674761	−	0.738036i	$-0.264247\pi$
$521$	16048.6			1.34952			0.674761	+	0.738036i	$0.264247\pi$
$522$	327.186	−	2855.74i	0.0274340	−	0.239449i
$523$	16568.1	−	16568.1i	1.38523	−	1.38523i	0.550185	−	0.835043i	$-0.314557\pi$
$523$	16568.1	−	16568.1i	1.38523	−	1.38523i	0.835043	−	0.550185i	$-0.185443\pi$
$524$	−5999.51	+	1910.84i	−0.500171	+	0.159304i
$525$	265.350	+	542.477i	0.0220587	+	0.0450965i
$526$	4327.08	+	1052.16i	0.358687	+	0.0872175i
$527$	−17645.3			−1.45852
$528$	5076.04	+	17248.4i	0.418383	+	1.42166i
$529$	−13306.3			−1.09363
$530$	8762.97	+	2130.78i	0.718187	+	0.174633i
$531$	−6379.47	+	798.077i	−0.521366	+	0.0652233i
$532$	107.303	+	336.901i	0.00874467	+	0.0274558i
$533$	6037.12	−	6037.12i	0.490613	−	0.490613i
$534$	−2313.06	−	10521.5i	−0.187445	−	0.852643i
$535$	−4978.95			−0.402353
$536$	7446.03	−	520.677i	0.600036	−	0.0419586i
$537$	−4214.20	+	12284.4i	−0.338652	+	0.987174i
$538$	−4496.40	+	2737.44i	−0.360323	+	0.219367i
$539$	13086.7	+	13086.7i	1.04580	+	1.04580i
$540$	1866.89	+	18181.2i	0.148775	+	1.44888i
$541$	−212.644	+	212.644i	−0.0168988	+	0.0168988i	−0.715506	−	0.698607i	$-0.753804\pi$
$541$	−212.644	+	212.644i	−0.0168988	+	0.0168988i	0.698607	+	0.715506i	$0.253804\pi$
$542$	−11122.7	−	2704.57i	−0.881478	−	0.214338i
$543$	−2902.34	−	995.653i	−0.229376	−	0.0786880i
$544$	5210.19	+	13114.8i	0.410634	+	1.03363i
$545$		−	20338.8i		−	1.59856i
$546$	−290.628	−	185.874i	−0.0227797	−	0.0145690i
$547$	6455.68	+	6455.68i	0.504616	+	0.504616i	0.912869	−	0.408253i	$-0.133862\pi$
$547$	6455.68	+	6455.68i	0.504616	+	0.504616i	−0.408253	+	0.912869i	$0.633862\pi$
$548$	−11065.4	−	5719.45i	−0.862577	−	0.445845i
$549$	845.422	+	6757.92i	0.0657226	+	0.525357i
$550$	11146.8	+	18309.2i	0.864182	+	1.41947i
$551$		−	2006.40i		−	0.155128i
$552$	−18131.6	−	4836.18i	−1.39806	−	0.372901i
$553$		−	32.7151i		−	0.00251571i
$554$	15370.6	−	9357.72i	1.17876	−	0.717638i
$555$	19006.3	−	9296.86i	1.45365	−	0.711044i
$556$	7361.73	−	2344.71i	0.561523	−	0.178845i
$557$	2281.17	+	2281.17i	0.173530	+	0.173530i	0.788528	−	0.614998i	$-0.210843\pi$
$557$	2281.17	+	2281.17i	0.173530	+	0.173530i	−0.614998	+	0.788528i	$0.710843\pi$
$558$	13534.4	−	10751.9i	1.02680	−	0.815704i
$559$		−	3849.01i		−	0.291227i
$560$	−851.825	−	145.095i	−0.0642789	−	0.0109489i
$561$	−7106.63	+	20715.9i	−0.534835	+	1.55905i
$562$	−1909.11	+	7851.35i	−0.143294	+	0.589305i
$563$	−8170.55	+	8170.55i	−0.611630	+	0.611630i	−0.943371	−	0.331741i	$-0.892364\pi$
$563$	−8170.55	+	8170.55i	−0.611630	+	0.611630i	0.331741	+	0.943371i	$0.392364\pi$
$564$	−5090.38	−	112.671i	−0.380042	−	0.00841187i
$565$	−22059.4	−	22059.4i	−1.64256	−	1.64256i
$566$	11359.6	+	18658.7i	0.843601	+	1.38566i
$567$	−148.898	−	585.799i	−0.0110285	−	0.0433885i
$568$	−11414.8	−	9922.75i	−0.843231	−	0.733010i
$569$	−17007.4			−1.25305			−0.626526	−	0.779400i	$-0.715524\pi$
$569$	−17007.4			−1.25305			−0.626526	+	0.779400i	$0.715524\pi$
$570$	2739.22	+	12460.0i	0.201286	+	0.915603i
$571$	1588.50	−	1588.50i	0.116421	−	0.116421i	−0.646496	−	0.762917i	$-0.723766\pi$
$571$	1588.50	−	1588.50i	0.116421	−	0.116421i	0.762917	+	0.646496i	$0.223766\pi$
$572$	−10878.1	−	5622.61i	−0.795166	−	0.411002i
$573$	5514.69	−	2697.49i	0.402058	−	0.196665i
$574$	−167.095	+	687.189i	−0.0121506	+	0.0499699i
$575$	−22372.1			−1.62258
$576$	−11987.7	−	6884.67i	−0.867164	−	0.498023i
$577$	−9412.03			−0.679078			−0.339539	−	0.940592i	$-0.610271\pi$
$577$	−9412.03			−0.679078			−0.339539	+	0.940592i	$0.610271\pi$
$578$	−778.154	+	3200.21i	−0.0559982	+	0.230296i
$579$	8377.86	−	4097.99i	0.601333	−	0.294139i
$580$	4355.93	+	2251.47i	0.311845	+	0.161185i
$581$	−243.520	+	243.520i	−0.0173888	+	0.0173888i
$582$	1425.38	+	6483.71i	0.101519	+	0.461784i
$583$	−10586.1			−0.752029
$584$	20774.3	+	18058.8i	1.47200	+	1.27959i
$585$	−9826.27	−	7641.09i	−0.694472	−	0.540034i
$586$	9620.23	+	15801.8i	0.678170	+	1.11393i
$587$	1526.76	+	1526.76i	0.107353	+	0.107353i	0.758743	−	0.651390i	$-0.225814\pi$
$587$	1526.76	+	1526.76i	0.107353	+	0.107353i	−0.651390	+	0.758743i	$0.725814\pi$
$588$	−14226.2	−	314.883i	−0.997751	−	0.0220843i
$589$	8531.60	−	8531.60i	0.596839	−	0.596839i
$590$	2591.29	−	10656.9i	0.180817	−	0.743620i
$591$	−75.6247	+	220.447i	−0.00526360	+	0.0153434i
$592$	−2687.23	+	15776.2i	−0.186562	+	1.09527i
$593$		−	4477.09i		−	0.310037i	−0.987912	−	0.155019i	$-0.950456\pi$
$593$		−	4477.09i		−	0.310037i	0.987912	−	0.155019i	$-0.0495437\pi$
$594$	−7171.94	−	20220.0i	−0.495401	−	1.39669i
$595$	−744.261	−	744.261i	−0.0512802	−	0.0512802i
$596$	−1549.35	+	493.467i	−0.106483	+	0.0339147i
$597$	20221.9	−	9891.43i	1.38631	−	0.678106i
$598$	10916.4	−	6645.99i	0.746497	−	0.454473i
$599$			15005.4i			1.02354i	0.859121	+	0.511772i	$0.171011\pi$
$599$			15005.4i			1.02354i	−0.859121	+	0.511772i	$0.828989\pi$
$600$	−15924.2	−	4247.42i	−1.08351	−	0.289000i
$601$			2400.70i			0.162939i	0.996676	+	0.0814696i	$0.0259613\pi$
$601$			2400.70i			0.162939i	−0.996676	+	0.0814696i	$0.974039\pi$
$602$	165.795	+	272.328i	0.0112248	+	0.0184373i
$603$	−8837.73	+	1105.61i	−0.596849	+	0.0746663i
$604$	10145.1	+	5243.77i	0.683444	+	0.353255i
$605$	−18332.5	−	18332.5i	−1.23194	−	1.23194i
$606$	17368.3	+	11108.1i	1.16426	+	0.744610i
$607$		−	6723.04i		−	0.449555i	−0.974410	−	0.224777i	$-0.927835\pi$
$607$		−	6723.04i		−	0.449555i	0.974410	−	0.224777i	$-0.0721655\pi$
$608$	−8860.26	−	3821.94i	−0.591005	−	0.254935i
$609$	−153.384	−	52.6187i	−0.0102060	−	0.00350118i
$610$	−11289.1	−	2745.02i	−0.749312	−	0.182201i
$611$	2452.03	−	2452.03i	0.162354	−	0.162354i
$612$	−7062.40	−	15286.3i	−0.466472	−	1.00966i
$613$	−9705.73	−	9705.73i	−0.639495	−	0.639495i	0.310936	−	0.950431i	$-0.399358\pi$
$613$	−9705.73	−	9705.73i	−0.639495	−	0.639495i	−0.950431	+	0.310936i	$0.899358\pi$
$614$	4688.81	−	2854.58i	0.308184	−	0.187625i
$615$	−8280.12	+	24136.6i	−0.542905	+	1.58257i
$616$	1011.84	−	70.7551i	0.0661824	−	0.00462793i
$617$	−3612.89			−0.235737			−0.117868	−	0.993029i	$-0.537606\pi$
$617$	−3612.89			−0.235737			−0.117868	+	0.993029i	$0.537606\pi$
$618$	547.657	+	2491.16i	0.0356473	+	0.162151i
$619$	−7079.67	+	7079.67i	−0.459703	+	0.459703i	−0.898558	−	0.438855i	$-0.855384\pi$
$619$	−7079.67	+	7079.67i	−0.459703	+	0.459703i	0.438855	+	0.898558i	$0.355384\pi$
$620$	8948.53	+	28095.9i	0.579648	+	1.81993i
$621$	21918.2	+	4580.53i	1.41634	+	0.295991i
$622$	8916.69	+	2168.16i	0.574802	+	0.139767i
$623$	−607.739			−0.0390828
$624$	9031.94	−	2658.02i	0.579434	−	0.170522i
$625$	13498.1			0.863879
$626$	−17280.6	−	4201.92i	−1.10331	−	0.268279i
$627$	−6580.17	−	13452.4i	−0.419117	−	0.856836i
$628$	−24021.4	+	7650.81i	−1.52637	+	0.486147i
$629$	−13784.1	+	13784.1i	−0.873779	+	0.873779i
$630$	1024.37	+	117.364i	0.0647809	+	0.00742204i
$631$	11384.1			0.718217			0.359108	−	0.933296i	$-0.383081\pi$
$631$	11384.1			0.718217			0.359108	+	0.933296i	$0.383081\pi$
$632$	673.826	+	585.748i	0.0424104	+	0.0368668i
$633$	15925.9	+	5463.40i	0.999994	+	0.343050i
$634$	−16137.4	+	9824.54i	−1.01088	+	0.615430i
$635$	−494.986	−	494.986i	−0.0309337	−	0.0309337i
$636$	5881.30	−	5626.59i	0.366681	−	0.350800i
$637$	6852.73	−	6852.73i	0.426240	−	0.426240i
$638$	−5592.87	−	1359.95i	−0.347060	−	0.0843901i
$639$	14247.0	+	11078.7i	0.882005	+	0.685863i
$640$	18240.0	−	14947.0i	1.12656	−	0.923174i
$641$		−	7632.61i		−	0.470312i	−0.971958	−	0.235156i	$-0.924440\pi$
$641$		−	7632.61i		−	0.470312i	0.971958	−	0.235156i	$-0.0755601\pi$
$642$	−2421.14	+	3785.64i	−0.148839	+	0.232721i
$643$	−4357.38	−	4357.38i	−0.267245	−	0.267245i	0.560744	−	0.827989i	$-0.310515\pi$
$643$	−4357.38	−	4357.38i	−0.267245	−	0.267245i	−0.827989	+	0.560744i	$0.810515\pi$
$644$	−486.092	+	940.443i	−0.0297433	+	0.0575445i
$645$	5054.71	+	10333.8i	0.308572	+	0.630840i
$646$	−6112.20	−	10039.6i	−0.372262	−	0.611462i
$647$		−	15886.6i		−	0.965326i	−0.875806	−	0.482663i	$-0.839670\pi$
$647$		−	15886.6i		−	0.965326i	0.875806	−	0.482663i	$-0.160330\pi$
$648$	14731.5	+	7421.61i	0.893069	+	0.449921i
$649$			12874.0i			0.778660i
$650$	9587.45	−	5836.90i	0.578540	−	0.352219i
$651$	−428.472	−	875.961i	−0.0257959	−	0.0527367i
$652$	1435.30	+	4506.44i	0.0862127	+	0.270684i
$653$	8850.83	+	8850.83i	0.530413	+	0.530413i	0.920695	−	0.390282i	$-0.127622\pi$
$653$	8850.83	+	8850.83i	0.530413	+	0.530413i	−0.390282	+	0.920695i	$0.627622\pi$
$654$	−15464.1	−	9890.23i	−0.924611	−	0.591344i
$655$			12816.6i			0.764556i
$656$	−11162.1	−	15745.4i	−0.664341	−	0.937126i
$657$	−25928.6	−	20162.6i	−1.53968	−	1.19728i
$658$	−67.8672	+	279.108i	−0.00402088	+	0.0165361i
$659$	8224.56	−	8224.56i	0.486166	−	0.486166i	−0.420928	−	0.907094i	$-0.638295\pi$
$659$	8224.56	−	8224.56i	0.486166	−	0.486166i	0.907094	+	0.420928i	$0.138295\pi$
$660$	36589.2	+	809.866i	2.15793	+	0.0477636i
$661$	8586.18	+	8586.18i	0.505240	+	0.505240i	0.913062	−	0.407822i	$-0.133711\pi$
$661$	8586.18	+	8586.18i	0.505240	+	0.505240i	−0.407822	+	0.913062i	$0.633711\pi$
$662$	12714.0	+	20883.5i	0.746440	+	1.22607i
$663$	10847.7	+	3721.32i	0.635429	+	0.217985i
$664$	−655.621	−	9375.81i	−0.0383178	−	0.547970i
$665$	719.710			0.0419687
$666$	2173.63	−	18971.9i	0.126466	−	1.10382i
$667$	4247.85	−	4247.85i	0.246593	−	0.246593i
$668$	14217.3	−	27506.1i	0.823476	−	1.59318i
$669$	−2310.86	−	4724.27i	−0.133547	−	0.273021i
$670$	3589.82	−	14763.4i	0.206995	−	0.851281i
$671$	13637.8			0.784621
$672$	−524.541	+	577.110i	−0.0301110	+	0.0331287i
$673$	24087.3			1.37964			0.689821	−	0.723980i	$-0.257689\pi$
$673$	24087.3			1.37964			0.689821	+	0.723980i	$0.257689\pi$
$674$	3593.74	−	14779.5i	0.205379	−	0.844635i
$675$	19249.9	+	4022.90i	1.09767	+	0.229395i
$676$	5126.08	−	9917.44i	0.291652	−	0.564261i
$677$	−11065.3	+	11065.3i	−0.628174	+	0.628174i	−0.947608	−	0.319434i	$-0.896507\pi$
$677$	−11065.3	+	11065.3i	−0.628174	+	0.628174i	0.319434	+	0.947608i	$0.396507\pi$
$678$	−27499.3	+	6045.45i	−1.55768	+	0.342440i
$679$	374.508			0.0211669
$680$	28655.0	−	2003.75i	1.61598	−	0.113001i
$681$	520.469	−	1517.17i	0.0292869	−	0.0853717i
$682$	−17999.2	−	29564.7i	−1.01059	−	1.65996i
$683$	−13547.1	−	13547.1i	−0.758955	−	0.758955i	0.217177	−	0.976132i	$-0.430315\pi$
$683$	−13547.1	−	13547.1i	−0.758955	−	0.758955i	−0.976132	+	0.217177i	$0.930315\pi$
$684$	10805.7	+	3976.30i	0.604046	+	0.222277i
$685$	−17928.5	+	17928.5i	−1.00002	+	1.00002i
$686$	−379.720	+	1561.62i	−0.0211338	+	0.0869140i
$687$	3914.46	+	1342.86i	0.217389	+	0.0745756i
$688$	−8577.55	−	1461.05i	−0.475314	−	0.0809623i
$689$			5543.33i			0.306508i
$690$	−20580.4	+	32179.0i	−1.13548	+	1.77541i
$691$	5857.82	+	5857.82i	0.322492	+	0.322492i	0.849722	−	0.527230i	$-0.176770\pi$
$691$	5857.82	+	5857.82i	0.322492	+	0.322492i	−0.527230	+	0.849722i	$0.676770\pi$
$692$	−4427.63	−	13901.5i	−0.243227	−	0.763666i
$693$	−1200.96	+	150.242i	−0.0658309	+	0.00823550i
$694$	12253.4	−	7459.94i	0.670219	−	0.408034i
$695$		−	15726.6i		−	0.858338i
$696$	3830.04	−	2217.10i	0.208588	−	0.120746i
$697$		−	23509.8i		−	1.27761i
$698$	8096.55	+	13299.1i	0.439053	+	0.721170i
$699$	−3017.33	+	1475.91i	−0.163270	+	0.0798629i
$700$	−426.915	+	825.953i	−0.0230512	+	0.0445973i
$701$	16142.4	+	16142.4i	0.869743	+	0.869743i	0.992444	−	0.122701i	$-0.0391555\pi$
$701$	16142.4	+	16142.4i	0.869743	+	0.869743i	−0.122701	+	0.992444i	$0.539156\pi$
$702$	−10588.0	+	3755.52i	−0.569257	+	0.201913i
$703$		−	13329.4i		−	0.715117i
$704$	−16659.2	+	22107.6i	−0.891859	+	1.18354i
$705$	−3363.04	+	9803.29i	−0.179659	+	0.523707i
$706$	−6338.79	−	1541.32i	−0.337908	−	0.0821649i
$707$	822.418	−	822.418i	0.0437485	−	0.0437485i
$708$	−6842.62	−	7152.39i	−0.363223	−	0.379666i
$709$	12454.7	+	12454.7i	0.659729	+	0.659729i	0.955316	−	0.295587i	$-0.0955153\pi$
$709$	12454.7	+	12454.7i	0.659729	+	0.659729i	−0.295587	+	0.955316i	$0.595515\pi$
$710$	−26296.7	+	16009.6i	−1.39000	+	0.846240i
$711$	−841.010	−	653.985i	−0.0443605	−	0.0344956i
$712$	10881.3	−	12517.5i	0.572742	−	0.658865i
$713$	36125.2			1.89748
$714$	−927.798	+	203.967i	−0.0486302	+	0.0106909i
$715$	−17624.9	+	17624.9i	−0.921867	+	0.921867i
$716$	−19052.1	+	6068.08i	−0.994427	+	0.316725i
$717$	−4650.63	+	2274.84i	−0.242233	+	0.118487i
$718$	−10986.6	−	2671.47i	−0.571053	−	0.138856i
$719$	−6194.00			−0.321276			−0.160638	−	0.987013i	$-0.551355\pi$
$719$	−6194.00			−0.321276			−0.160638	+	0.987013i	$0.551355\pi$
$720$	−20758.2	+	18997.4i	−1.07446	+	0.983322i
$721$	143.893			0.00743253
$722$	−11041.4	−	2684.79i	−0.569138	−	0.138390i
$723$	−21139.5	+	10340.3i	−1.08739	+	0.531893i
$724$	−1433.65	−	4501.27i	−0.0735929	−	0.231061i
$725$	3730.71	−	3730.71i	0.191111	−	0.191111i
$726$	−22853.3	+	5024.08i	−1.16827	+	0.256833i
$727$	−9470.69			−0.483148			−0.241574	−	0.970382i	$-0.577664\pi$
$727$	−9470.69			−0.483148			−0.241574	+	0.970382i	$0.577664\pi$
$728$	−37.0503	−	529.843i	−0.00188623	−	0.0269743i
$729$	−18035.7	−	7882.55i	−0.916308	−	0.400475i
$730$	47858.4	−	29136.5i	2.42646	−	1.47725i
$731$	−7494.42	−	7494.42i	−0.379194	−	0.379194i
$732$	−7576.70	+	7248.55i	−0.382572	+	0.366003i
$733$	−12537.1	+	12537.1i	−0.631744	+	0.631744i	−0.948505	−	0.316761i	$-0.897405\pi$
$733$	−12537.1	+	12537.1i	−0.631744	+	0.631744i	0.316761	+	0.948505i	$0.397405\pi$
$734$	12104.3	+	2943.26i	0.608691	+	0.148008i
$735$	−9398.75	+	27397.4i	−0.471671	+	1.37492i
$736$	−10666.8	−	26850.1i	−0.534219	−	1.34471i
$737$			17834.9i			0.891394i
$738$	14325.3	+	18032.6i	0.714529	+	0.899445i
$739$	−25128.2	−	25128.2i	−1.25082	−	1.25082i	−0.955354	−	0.295464i	$-0.904526\pi$
$739$	−25128.2	−	25128.2i	−1.25082	−	1.25082i	−0.295464	−	0.955354i	$-0.595474\pi$
$740$	28938.3	+	14957.5i	1.43756	+	0.743037i
$741$	−7044.21	+	3445.64i	−0.349225	+	0.170822i
$742$	−238.777	−	392.205i	−0.0118137	−	0.0194047i
$743$		−	11784.5i		−	0.581875i	−0.956742	−	0.290937i	$-0.906033\pi$
$743$		−	11784.5i		−	0.581875i	0.956742	−	0.290937i	$-0.0939672\pi$
$744$	25713.5	+	6858.49i	1.26707	+	0.337963i
$745$			3309.82i			0.162768i
$746$	−21687.3	+	13203.4i	−1.06438	+	0.648004i
$747$	1392.15	+	11128.2i	0.0681874	+	0.545060i
$748$	−32128.5	+	10232.9i	−1.57050	+	0.500204i
$749$	179.256	+	179.256i	0.00874483	+	0.00874483i
$750$	−1956.55	+	3059.22i	−0.0952576	+	0.148943i
$751$		−	18414.2i		−	0.894734i	−0.894351	−	0.447367i	$-0.852362\pi$
$751$		−	18414.2i		−	0.894734i	0.894351	−	0.447367i	$-0.147638\pi$
$752$	−4533.59	−	6395.13i	−0.219845	−	0.310115i
$753$	25110.1	+	8614.07i	1.21522	+	0.416885i
$754$	−712.125	+	2928.66i	−0.0343953	+	0.141453i
$755$	16437.4	−	16437.4i	0.792343	−	0.792343i
$756$	587.361	−	721.788i	0.0282568	−	0.0347238i
$757$	17074.1	+	17074.1i	0.819774	+	0.819774i	0.986075	−	0.166301i	$-0.0531825\pi$
$757$	17074.1	+	17074.1i	0.819774	+	0.819774i	−0.166301	+	0.986075i	$0.553182\pi$
$758$	−15588.7	−	25605.3i	−0.746975	−	1.22695i
$759$	14549.5	−	42411.8i	0.695800	−	2.02826i
$760$	−12886.0	+	14823.7i	−0.615034	+	0.707516i
$761$	−24788.6			−1.18080			−0.590399	−	0.807112i	$-0.701030\pi$
$761$	−24788.6			−1.18080			−0.590399	+	0.807112i	$0.701030\pi$
$762$	−617.050	+	135.652i	−0.0293351	+	0.00644904i
$763$	−732.253	+	732.253i	−0.0347436	+	0.0347436i
$764$	8396.44	+	4339.91i	0.397608	+	0.205514i
$765$	−34010.7	+	4254.77i	−1.60740	+	0.201087i
$766$	−9488.17	+	39020.7i	−0.447548	+	1.84057i
$767$	6741.37			0.317362
$768$	−2494.97	−	21136.7i	−0.117226	−	0.993105i
$769$	8902.84			0.417483			0.208742	−	0.977971i	$-0.433063\pi$
$769$	8902.84			0.417483			0.208742	+	0.977971i	$0.433063\pi$
$770$	487.823	−	2006.20i	0.0228310	−	0.0938941i
$771$	3835.11	+	7840.43i	0.179141	+	0.366233i
$772$	12755.8	+	6593.15i	0.594677	+	0.307374i
$773$	12931.4	−	12931.4i	0.601694	−	0.601694i	−0.339068	−	0.940762i	$-0.610112\pi$
$773$	12931.4	−	12931.4i	0.601694	−	0.601694i	0.940762	+	0.339068i	$0.110112\pi$
$774$	10315.0	+	1181.81i	0.479026	+	0.0548827i
$775$	31727.4			1.47056
$776$	−6705.38	+	7713.66i	−0.310192	+	0.356835i
$777$	−1018.99	−	349.568i	−0.0470479	−	0.0161399i
$778$	19506.3	+	32040.3i	0.898889	+	1.47648i
$779$	11367.1	+	11367.1i	0.522811	+	0.522811i
$780$	424.079	−	19159.6i	0.0194673	−	0.879517i
$781$	25554.1	−	25554.1i	1.17081	−	1.17081i
$782$	8314.97	−	34195.8i	0.380233	−	1.56373i
$783$	−4418.86	+	2891.19i	−0.201682	+	0.131957i
$784$	−12670.1	−	17872.6i	−0.577173	−	0.814166i
$785$			51316.2i			2.33319i
$786$	9744.79	+	6232.37i	0.442220	+	0.282826i
$787$	18783.4	+	18783.4i	0.850770	+	0.850770i	0.990228	−	0.139458i	$-0.0445360\pi$
$787$	18783.4	+	18783.4i	0.850770	+	0.850770i	−0.139458	+	0.990228i	$0.544536\pi$
$788$	−341.893	+	108.893i	−0.0154561	+	0.00492278i
$789$	−3594.69	−	7348.92i	−0.162198	−	0.331595i
$790$	1552.32	−	945.060i	0.0699100	−	0.0425617i
$791$			1588.40i			0.0713995i
$792$	18408.1	−	27425.9i	0.825890	−	1.23048i
$793$		−	7141.30i		−	0.319792i
$794$	−632.151	−	1038.34i	−0.0282547	−	0.0464099i
$795$	−7279.78	−	14882.6i	−0.324764	−	0.663941i
$796$	30789.0	+	15914.1i	1.37096	+	0.708617i
$797$	14788.0	+	14788.0i	0.657237	+	0.657237i	0.954725	−	0.297488i	$-0.0961489\pi$
$797$	14788.0	+	14788.0i	0.657237	+	0.657237i	−0.297488	+	0.954725i	$0.596149\pi$
$798$	349.977	−	547.216i	0.0155251	−	0.0242747i
$799$		−	9548.70i		−	0.422789i
$800$	−9368.27	−	23581.3i	−0.414023	−	1.04216i
$801$	−12148.9	+	15623.2i	−0.535904	+	0.689161i
$802$	37472.5	+	9111.73i	1.64988	+	0.401180i
$803$	−46507.0	+	46507.0i	−2.04383	+	2.04383i
$804$	−9479.35	−	9908.48i	−0.415810	−	0.434633i
$805$	1523.73	+	1523.73i	0.0667136	+	0.0667136i
$806$	−15481.3	+	9425.10i	−0.676556	+	0.411892i
$807$	9147.55	+	3138.09i	0.399020	+	0.136885i
$808$	2214.17	+	31664.1i	0.0964038	+	1.37864i
$809$	−34139.0			−1.48364			−0.741820	−	0.670600i	$-0.766037\pi$
$809$	−34139.0			−1.48364			−0.741820	+	0.670600i	$0.766037\pi$
$810$	23494.6	−	23987.4i	1.01915	−	1.04053i
$811$	−18395.6	+	18395.6i	−0.796494	+	0.796494i	−0.982541	−	0.186047i	$-0.940432\pi$
$811$	−18395.6	+	18395.6i	−0.796494	+	0.796494i	0.186047	+	0.982541i	$0.440432\pi$
$812$	−75.7663	−	237.885i	−0.00327448	−	0.0102809i
$813$	9240.11	+	18890.3i	0.398604	+	0.814898i
$814$	−37155.8	−	9034.71i	−1.59989	−	0.389025i
$815$	9626.97			0.413764
$816$	12410.7	−	22761.6i	0.532427	−	0.976487i
$817$	7247.20			0.310340
$818$	10332.3	+	2512.37i	0.441638	+	0.107387i
$819$	78.6726	+	628.873i	0.00335658	+	0.0268310i
$820$	−37433.7	+	11922.6i	−1.59420	+	0.507752i
$821$	22428.5	−	22428.5i	0.953423	−	0.953423i	−0.0455394	−	0.998963i	$-0.514501\pi$
$821$	22428.5	−	22428.5i	0.953423	−	0.953423i	0.998963	+	0.0455394i	$0.0145007\pi$
$822$	4913.37	+	22349.7i	0.208484	+	0.948341i
$823$	−34300.0			−1.45276			−0.726381	−	0.687293i	$-0.758799\pi$
$823$	−34300.0			−1.45276			−0.726381	+	0.687293i	$0.758799\pi$
$824$	−2576.33	+	2963.73i	−0.108921	+	0.125299i
$825$	12778.2	−	37248.6i	0.539249	−	1.57191i
$826$	−476.970	+	290.383i	−0.0200919	+	0.0122321i
$827$	12181.0	+	12181.0i	0.512182	+	0.512182i	0.915194	−	0.403013i	$-0.132037\pi$
$827$	12181.0	+	12181.0i	0.512182	+	0.512182i	−0.403013	+	0.915194i	$0.632037\pi$
$828$	14458.9	+	31295.7i	0.606862	+	1.31353i
$829$	−29681.5	+	29681.5i	−1.24352	+	1.24352i	−0.284992	+	0.958530i	$0.591991\pi$
$829$	−29681.5	+	29681.5i	−1.24352	+	1.24352i	−0.958530	+	0.284992i	$0.908009\pi$
$830$	−18589.6	−	4520.19i	−0.777414	−	0.189034i
$831$	−31270.2	−	10727.3i	−1.30536	−	0.447805i
$832$	11576.4	+	8723.45i	0.482380	+	0.363499i
$833$		−	26685.9i		−	1.10998i
$834$	−11957.4	−	7647.46i	−0.496464	−	0.317518i
$835$	−44566.2	−	44566.2i	−1.84704	−	1.84704i
$836$	10586.7	−	20482.0i	0.437975	−	0.847351i
$837$	−31083.6	−	6495.94i	−1.28364	−	0.268259i
$838$	−8342.29	−	13702.7i	−0.343890	−	0.564859i
$839$		−	5645.20i		−	0.232293i	−0.993232	−	0.116147i	$-0.962946\pi$
$839$		−	5645.20i		−	0.232293i	0.993232	−	0.116147i	$-0.0370543\pi$
$840$	795.288	+	1373.86i	0.0326667	+	0.0564317i
$841$		−	22972.3i		−	0.941912i
$842$	3107.67	−	1891.97i	0.127194	−	0.0774366i
$843$	13334.4	−	6522.46i	0.544793	−	0.266483i
$844$	7866.82	+	24699.6i	0.320838	+	1.00734i
$845$	−16068.5	−	16068.5i	−0.654170	−	0.654170i
$846$	5818.36	+	7324.11i	0.236453	+	0.297645i
$847$			1320.04i			0.0535503i
$848$	12353.3	+	2104.20i	0.500254	+	0.0852105i
$849$	13022.1	−	37959.6i	0.526406	−	1.53448i
$850$	7302.70	−	30032.8i	0.294683	−	1.21190i
$851$	28220.2	−	28220.2i	1.13675	−	1.13675i
$852$	−614.866	+	27779.2i	−0.0247241	+	1.11702i
$853$	8393.54	+	8393.54i	0.336916	+	0.336916i	0.855205	−	0.518289i	$-0.173431\pi$
$853$	8393.54	+	8393.54i	0.336916	+	0.336916i	−0.518289	+	0.855205i	$0.673431\pi$
$854$	307.609	+	505.266i	0.0123257	+	0.0202457i
$855$	14387.2	−	18501.6i	0.575476	−	0.740049i
$856$	−6901.58	+	482.606i	−0.275574	+	0.0192700i
$857$	22054.9			0.879092			0.439546	−	0.898220i	$-0.355139\pi$
$857$	22054.9			0.879092			0.439546	+	0.898220i	$0.355139\pi$
$858$	4830.17	+	21971.3i	0.192190	+	0.874228i
$859$	33958.2	−	33958.2i	1.34882	−	1.34882i	0.461884	−	0.886941i	$-0.347174\pi$
$859$	33958.2	−	33958.2i	1.34882	−	1.34882i	0.886941	−	0.461884i	$-0.152826\pi$
$860$	−8132.40	+	15733.8i	−0.322456	+	0.623857i
$861$	1167.09	−	570.878i	0.0461956	−	0.0225964i
$862$	3163.78	−	13011.2i	0.125010	−	0.514112i
$863$	35981.7			1.41927			0.709635	−	0.704569i	$-0.248860\pi$
$863$	35981.7			1.41927			0.709635	+	0.704569i	$0.248860\pi$
$864$	4350.09	+	25021.0i	0.171288	+	0.985221i
$865$	−29697.4			−1.16733
$866$	−2883.25	+	11857.5i	−0.113137	+	0.465283i
$867$	5435.09	−	2658.55i	0.212901	−	0.104140i
$868$	689.358	−	1333.70i	0.0269566	−	0.0521530i
$869$	−1508.48	+	1508.48i	−0.0588858	+	0.0588858i
$870$	−1934.16	−	8798.01i	−0.0753725	−	0.342851i
$871$	9339.08			0.363310
$872$	−1971.42	−	28192.6i	−0.0765605	−	1.09487i
$873$	7486.52	−	9627.50i	0.290241	−	0.373244i
$874$	12513.6	+	20554.2i	0.484299	+	0.795489i
$875$	144.859	+	144.859i	0.00559672	+	0.00559672i
$876$	1119.02	−	50556.4i	0.0431600	−	1.94994i
$877$	−9471.30	+	9471.30i	−0.364679	+	0.364679i	−0.865532	−	0.500854i	$-0.833020\pi$
$877$	−9471.30	+	9471.30i	−0.364679	+	0.364679i	0.500854	+	0.865532i	$0.333020\pi$
$878$	−8576.81	+	35272.6i	−0.329673	+	1.35580i
$879$	11028.2	−	32147.4i	0.423178	−	1.23357i
$880$	32587.0	+	45967.5i	1.24830	+	1.76087i
$881$		−	47824.3i		−	1.82888i	−0.404723	−	0.914439i	$-0.632632\pi$
$881$		−	47824.3i		−	1.82888i	0.404723	−	0.914439i	$-0.367368\pi$
$882$	16260.7	+	20468.8i	0.620777	+	0.781429i
$883$	−25305.1	−	25305.1i	−0.964421	−	0.964421i	0.0349671	−	0.999388i	$-0.488867\pi$
$883$	−25305.1	−	25305.1i	−0.964421	−	0.964421i	−0.999388	+	0.0349671i	$0.988867\pi$
$884$	5358.38	+	16823.8i	0.203871	+	0.640097i
$885$	−18099.1	+	8853.11i	−0.687453	+	0.336264i
$886$	6351.79	−	3867.01i	0.240849	−	0.146631i
$887$			43498.3i			1.64659i	0.567611	+	0.823297i	$0.307868\pi$
$887$			43498.3i			1.64659i	−0.567611	+	0.823297i	$0.692132\pi$
$888$	25444.5	−	14729.1i	0.961557	−	0.556618i
$889$			35.6417i			0.00134464i
$890$	−17556.1	−	28836.9i	−0.661216	−	1.08608i
$891$	−20145.3	+	33876.6i	−0.757456	+	1.27375i
$892$	3717.88	−	7192.98i	0.139556	−	0.269999i
$893$	4616.86	+	4616.86i	0.173009	+	0.173009i
$894$	2516.55	+	1609.48i	0.0941454	+	0.0602115i
$895$			40700.3i			1.52007i
$896$	−1194.82	−	118.557i	−0.0445494	−	0.00442044i
$897$	−22208.5	−	7618.69i	−0.826668	−	0.283590i
$898$	−22036.3	−	5358.28i	−0.818886	−	0.199118i
$899$	−6024.14	+	6024.14i	−0.223489	+	0.223489i
$900$	12698.7	+	27485.8i	0.470321	+	1.01799i
$901$	10793.4	+	10793.4i	0.399091	+	0.399091i
$902$	39390.7	−	23981.3i	1.45407	−	0.885245i
$903$	190.061	−	554.028i	0.00700423	−	0.0204174i
$904$	−32715.9	−	28439.5i	−1.20367	−	1.04633i
$905$	−9615.91			−0.353198
$906$	−4504.73	−	20490.9i	−0.165187	−	0.751397i
$907$	−23466.1	+	23466.1i	−0.859074	+	0.859074i	−0.991229	−	0.132155i	$-0.957810\pi$
$907$	−23466.1	+	23466.1i	−0.859074	+	0.859074i	0.132155	+	0.991229i	$0.457810\pi$
$908$	2353.00	−	749.429i	0.0859988	−	0.0273906i
$909$	−4701.57	−	37582.3i	−0.171553	−	1.37132i
$910$	−1050.53	−	255.444i	−0.0382689	−	0.00930536i
$911$	−18223.3			−0.662749			−0.331375	−	0.943499i	$-0.607512\pi$
$911$	−18223.3			−0.662749			−0.331375	+	0.943499i	$0.607512\pi$
$912$	5004.72	+	17006.0i	0.181713	+	0.617462i
$913$	22457.2			0.814046
$914$	−43613.7	−	10605.0i	−1.57835	−	0.383788i
$915$	9378.31	+	19172.8i	0.338839	+	0.692715i
$916$	1933.61	+	6070.98i	0.0697469	+	0.218986i
$917$	461.432	−	461.432i	0.0166170	−	0.0166170i
$918$	−13303.5	+	27928.3i	−0.478303	+	1.00411i
$919$	44782.9			1.60746			0.803729	−	0.594996i	$-0.202846\pi$
$919$	44782.9			1.60746			0.803729	+	0.594996i	$0.202846\pi$
$920$	−58665.5	+	4102.29i	−2.10233	+	0.147009i
$921$	−9539.00	−	3272.37i	−0.341282	−	0.117078i
$922$	−10203.8	+	6212.16i	−0.364474	+	0.221894i
$923$	−13381.2	−	13381.2i	−0.477191	−	0.477191i
$924$	−1288.15	−	1346.47i	−0.0458627	−	0.0479390i
$925$	24784.7	−	24784.7i	0.880990	−	0.880990i
$926$	51540.6	+	12532.5i	1.82908	+	0.444754i
$927$	2876.46	−	3699.06i	0.101915	−	0.131061i
$928$	6256.21	+	2698.67i	0.221304	+	0.0954613i
$929$			16925.2i			0.597737i	0.954294	+	0.298868i	$0.0966092\pi$
$929$			16925.2i			0.597737i	−0.954294	+	0.298868i	$0.903391\pi$
$930$	29186.4	−	45635.1i	1.02910	−	1.60907i
$931$	12902.8	+	12902.8i	0.454213	+	0.454213i
$932$	−4594.07	−	2374.56i	−0.161463	−	0.0834563i
$933$	−7407.48	−	15143.7i	−0.259925	−	0.531386i
$934$	3879.67	+	6372.59i	0.135917	+	0.223252i
$935$			68635.1i			2.40065i
$936$	−14361.3	−	9639.25i	−0.501512	−	0.336612i
$937$			31660.1i			1.10383i	0.833900	+	0.551916i	$0.186103\pi$
$937$			31660.1i			1.10383i	−0.833900	+	0.551916i	$0.813897\pi$
$938$	−660.765	+	402.278i	−0.0230008	+	0.0140030i
$939$	14355.8	+	29348.7i	0.498917	+	1.01998i
$940$	−15204.0	+	4842.48i	−0.527554	+	0.168026i
$941$	−2381.85	−	2381.85i	−0.0825143	−	0.0825143i	0.664645	−	0.747159i	$-0.268583\pi$
$941$	−2381.85	−	2381.85i	−0.0825143	−	0.0825143i	−0.747159	+	0.664645i	$0.768583\pi$
$942$	39017.1	+	24953.7i	1.34952	+	0.863096i
$943$			48131.7i			1.66213i
$944$	2558.97	−	15023.2i	0.0882280	−	0.517969i
$945$	−1037.09	−	1585.07i	−0.0356999	−	0.0545634i
$946$	4912.18	−	20201.7i	0.168825	−	0.694305i
$947$	−21792.3	+	21792.3i	−0.747786	+	0.747786i	−0.974063	−	0.226277i	$-0.927345\pi$
$947$	−21792.3	+	21792.3i	−0.747786	+	0.747786i	0.226277	+	0.974063i	$0.427345\pi$
$948$	36.2960	−	1639.83i	0.00124350	−	0.0561805i
$949$	24352.9	+	24352.9i	0.833014	+	0.833014i
$950$	10990.2	+	18052.0i	0.375334	+	0.616508i
$951$	32830.1	+	11262.5i	1.11944	+	0.384027i
$952$	−1103.80	−	959.518i	−0.0375781	−	0.0326661i
$953$	−17854.6			−0.606893			−0.303446	−	0.952849i	$-0.598137\pi$
$953$	−17854.6			−0.606893			−0.303446	+	0.952849i	$0.598137\pi$
$954$	−14855.7	−	1702.04i	−0.504161	−	0.0577625i
$955$	13604.1	−	13604.1i	0.460963	−	0.460963i
$956$	−7080.87	−	3659.93i	−0.239552	−	0.123818i
$957$	4646.24	+	9498.69i	0.156940	+	0.320846i
$958$	10362.2	−	42615.2i	0.349465	−	1.43720i
$959$	1290.95			0.0434693
$960$	−42536.3	−	8217.87i	−1.43005	−	0.276282i
$961$	−21440.5			−0.719697
$962$	−4730.94	+	19456.3i	−0.158557	+	0.652075i
$963$	8191.52	−	1024.77i	0.274110	−	0.0342914i
$964$	−32186.1	−	16636.2i	−1.07536	−	0.555825i
$965$	20667.3	−	20667.3i	0.689433	−	0.689433i
$966$	1899.49	−	417.583i	0.0632660	−	0.0139084i
$967$	−47141.7			−1.56771			−0.783854	−	0.620945i	$-0.786749\pi$
$967$	−47141.7			−1.56771			−0.783854	+	0.620945i	$0.786749\pi$
$968$	−27188.6	−	23634.6i	−0.902762	−	0.784759i
$969$	−7006.78	+	20424.8i	−0.232291	+	0.677131i
$970$	10818.6	+	17770.2i	0.358108	+	0.588214i
$971$	−11615.6	−	11615.6i	−0.383896	−	0.383896i	0.488607	−	0.872504i	$-0.337505\pi$
$971$	−11615.6	−	11615.6i	−0.383896	−	0.383896i	−0.872504	+	0.488607i	$0.837505\pi$
$972$	−6813.52	−	29528.1i	−0.224839	−	0.974396i
$973$	−566.202	+	566.202i	−0.0186553	+	0.0186553i
$974$	2610.21	−	10734.7i	0.0858693	−	0.353143i
$975$	−19504.9	−	6691.19i	−0.640672	−	0.219784i
$976$	−15914.4	−	2710.77i	−0.521935	−	0.0889034i
$977$		−	4822.57i		−	0.157920i	−0.996878	−	0.0789600i	$-0.974840\pi$
$977$		−	4822.57i		−	0.157920i	0.996878	−	0.0789600i	$-0.0251599\pi$
$978$	4681.35	−	7319.65i	0.153060	−	0.239322i
$979$	28022.6	+	28022.6i	0.914817	+	0.914817i
$980$	−42491.0	+	13533.4i	−1.38503	+	0.441130i
$981$	4186.12	+	33462.0i	0.136241	+	1.08905i
$982$	1348.76	−	821.131i	0.0438294	−	0.0266837i
$983$			3987.14i			0.129369i	0.997906	+	0.0646846i	$0.0206041\pi$
$983$			3987.14i			0.129369i	−0.997906	+	0.0646846i	$0.979396\pi$
$984$	−9137.96	+	34259.6i	−0.296044	+	1.10991i
$985$			730.376i			0.0236261i
$986$	4315.82	+	7088.98i	0.139395	+	0.228964i
$987$	474.025	−	231.867i	0.0152871	−	0.00747762i
$988$	−10725.2	−	5543.61i	−0.345359	−	0.178508i
$989$	15343.4	+	15343.4i	0.493317	+	0.493317i
$990$	−41821.8	−	52645.0i	−1.34261	−	1.69007i
$991$		−	42114.2i		−	1.34995i	−0.737840	−	0.674976i	$-0.764154\pi$
$991$		−	42114.2i		−	1.34995i	0.737840	−	0.674976i	$-0.235846\pi$
$992$	15127.3	+	38077.8i	0.484167	+	1.21872i
$993$	14574.8	−	42485.7i	0.465778	−	1.35775i
$994$	1523.15	+	370.364i	0.0486029	+	0.0118182i
$995$	49885.1	−	49885.1i	1.58941	−	1.58941i
$996$	−12476.5	+	11936.1i	−0.396920	+	0.379729i
$997$	−19496.0	−	19496.0i	−0.619304	−	0.619304i	0.326049	−	0.945353i	$-0.394283\pi$
$997$	−19496.0	−	19496.0i	−0.619304	−	0.619304i	−0.945353	+	0.326049i	$0.894283\pi$
$998$	34644.1	−	21091.6i	1.09884	−	0.668980i
$999$	−29356.3	+	19207.4i	−0.929723	+	0.608302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.11.12	yes	44
3.2	odd	2	inner	48.4.k.a.11.11	✓	44
4.3	odd	2		192.4.k.a.143.19		44
8.3	odd	2		384.4.k.a.287.4		44
8.5	even	2		384.4.k.b.287.19		44
12.11	even	2		192.4.k.a.143.8		44
16.3	odd	4	inner	48.4.k.a.35.11	yes	44
16.5	even	4		384.4.k.a.95.15		44
16.11	odd	4		384.4.k.b.95.8		44
16.13	even	4		192.4.k.a.47.8		44
24.5	odd	2		384.4.k.b.287.8		44
24.11	even	2		384.4.k.a.287.15		44
48.5	odd	4		384.4.k.a.95.4		44
48.11	even	4		384.4.k.b.95.19		44
48.29	odd	4		192.4.k.a.47.19		44
48.35	even	4	inner	48.4.k.a.35.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.11	✓	44	3.2	odd	2	inner
48.4.k.a.11.12	yes	44	1.1	even	1	trivial
48.4.k.a.35.11	yes	44	16.3	odd	4	inner
48.4.k.a.35.12	yes	44	48.35	even	4	inner
192.4.k.a.47.8		44	16.13	even	4
192.4.k.a.47.19		44	48.29	odd	4
192.4.k.a.143.8		44	12.11	even	2
192.4.k.a.143.19		44	4.3	odd	2
384.4.k.a.95.4		44	48.5	odd	4
384.4.k.a.95.15		44	16.5	even	4
384.4.k.a.287.4		44	8.3	odd	2
384.4.k.a.287.15		44	24.11	even	2
384.4.k.b.95.8		44	16.11	odd	4
384.4.k.b.95.19		44	48.11	even	4
384.4.k.b.287.8		44	24.5	odd	2
384.4.k.b.287.19		44	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.668281 - 2.74835i) q^{2} +(-4.66767 + 2.28317i) q^{3} +(-7.10680 - 3.67333i) q^{4} +(-11.5146 + 11.5146i) q^{5} +(3.15562 + 14.3542i) q^{6} +0.829117 q^{7} +(-14.8449 + 17.0771i) q^{8} +(16.5743 - 21.3142i) q^{9} +O(q^{10})\)	\(q+(0.668281 - 2.74835i) q^{2} +(-4.66767 + 2.28317i) q^{3} +(-7.10680 - 3.67333i) q^{4} +(-11.5146 + 11.5146i) q^{5} +(3.15562 + 14.3542i) q^{6} +0.829117 q^{7} +(-14.8449 + 17.0771i) q^{8} +(16.5743 - 21.3142i) q^{9} +(23.9512 + 39.3412i) q^{10} +(-38.2302 - 38.2302i) q^{11} +(41.5590 + 0.919870i) q^{12} +(-20.0189 + 20.0189i) q^{13} +(0.554083 - 2.27870i) q^{14} +(27.4566 - 80.0363i) q^{15} +(37.0133 + 52.2113i) q^{16} +77.9578i q^{17} +(-47.5024 - 59.7957i) q^{18} +(-37.6931 - 37.6931i) q^{19} +(124.129 - 39.5351i) q^{20} +(-3.87005 + 1.89301i) q^{21} +(-130.618 + 79.5214i) q^{22} -159.603i q^{23} +(30.3012 - 113.604i) q^{24} -140.173i q^{25} +(41.6406 + 68.3971i) q^{26} +(-28.6995 + 137.329i) q^{27} +(-5.89237 - 3.04562i) q^{28} +(26.6150 + 26.6150i) q^{29} +(-201.619 - 128.947i) q^{30} +226.344i q^{31} +(168.230 - 66.8335i) q^{32} +(265.732 + 91.1601i) q^{33} +(214.255 + 52.0977i) q^{34} +(-9.54698 + 9.54698i) q^{35} +(-196.084 + 90.5927i) q^{36} +(176.815 + 176.815i) q^{37} +(-128.783 + 78.4041i) q^{38} +(47.7351 - 139.148i) q^{39} +(-25.7030 - 367.571i) q^{40} -301.571 q^{41} +(2.61638 + 11.9013i) q^{42} +(-96.1344 + 96.1344i) q^{43} +(131.262 + 412.127i) q^{44} +(54.5779 + 436.271i) q^{45} +(-438.645 - 106.660i) q^{46} -122.486 q^{47} +(-291.973 - 159.197i) q^{48} -342.313 q^{49} +(-385.245 - 93.6751i) q^{50} +(-177.991 - 363.881i) q^{51} +(215.807 - 68.7343i) q^{52} +(138.452 - 138.452i) q^{53} +(358.249 + 170.651i) q^{54} +880.414 q^{55} +(-12.3082 + 14.1589i) q^{56} +(261.999 + 89.8792i) q^{57} +(90.9335 - 55.3609i) q^{58} +(-168.375 - 168.375i) q^{59} +(-489.129 + 467.945i) q^{60} +(-178.364 + 178.364i) q^{61} +(622.071 + 151.261i) q^{62} +(13.7420 - 17.6719i) q^{63} +(-71.2566 - 507.017i) q^{64} -461.021i q^{65} +(428.123 - 669.403i) q^{66} +(-233.257 - 233.257i) q^{67} +(286.365 - 554.030i) q^{68} +(364.402 + 744.976i) q^{69} +(19.8583 + 32.6185i) q^{70} +668.427i q^{71} +(117.941 + 599.448i) q^{72} -1216.50i q^{73} +(604.110 - 367.786i) q^{74} +(320.039 + 654.283i) q^{75} +(129.418 + 406.337i) q^{76} +(-31.6974 - 31.6974i) q^{77} +(-350.527 - 224.183i) q^{78} -39.4578i q^{79} +(-1027.39 - 174.999i) q^{80} +(-179.586 - 706.534i) q^{81} +(-201.534 + 828.820i) q^{82} +(-293.710 + 293.710i) q^{83} +(34.4573 + 0.762680i) q^{84} +(-897.655 - 897.655i) q^{85} +(199.966 + 328.455i) q^{86} +(-184.997 - 63.4635i) q^{87} +(1220.39 - 85.3379i) q^{88} -732.996 q^{89} +(1235.50 + 141.553i) q^{90} +(-16.5980 + 16.5980i) q^{91} +(-586.276 + 1134.27i) q^{92} +(-516.781 - 1056.50i) q^{93} +(-81.8547 + 336.633i) q^{94} +868.044 q^{95} +(-632.649 + 696.054i) q^{96} +451.695 q^{97} +(-228.761 + 940.793i) q^{98} +(-1448.48 + 181.207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

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