LMFDB - Embedded newform 80.4.l.a.21.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,4,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	80.l (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:	$4.72015280046$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.7
Character	$\chi$	$=$	80.21
Dual form			80.4.l.a.61.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87695 - 2.11591i) q^{2} +(1.30312 - 1.30312i) q^{3} +(-0.954112 + 7.94290i) q^{4} +(3.53553 + 3.53553i) q^{5} +(-5.20319 - 0.311388i) q^{6} +17.9744i q^{7} +(18.5972 - 12.8896i) q^{8} +23.6037i q^{9} +(0.844833 - 14.1169i) q^{10} +(9.66542 + 9.66542i) q^{11} +(9.10726 + 11.5939i) q^{12} +(19.1969 - 19.1969i) q^{13} +(38.0322 - 33.7371i) q^{14} +9.21448 q^{15} +(-62.1793 - 15.1568i) q^{16} +103.565 q^{17} +(49.9433 - 44.3031i) q^{18} +(16.2553 - 16.2553i) q^{19} +(-31.4557 + 24.7091i) q^{20} +(23.4229 + 23.4229i) q^{21} +(2.30960 - 38.5926i) q^{22} +49.6583i q^{23} +(7.43774 - 41.0313i) q^{24} +25.0000i q^{25} +(-76.6503 - 4.58718i) q^{26} +(65.9429 + 65.9429i) q^{27} +(-142.769 - 17.1496i) q^{28} +(-68.7899 + 68.7899i) q^{29} +(-17.2951 - 19.4970i) q^{30} -249.904 q^{31} +(84.6371 + 160.014i) q^{32} +25.1905 q^{33} +(-194.386 - 219.134i) q^{34} +(-63.5492 + 63.5492i) q^{35} +(-187.482 - 22.5206i) q^{36} +(210.860 + 210.860i) q^{37} +(-64.9051 - 3.88428i) q^{38} -50.0318i q^{39} +(111.323 + 20.1795i) q^{40} -129.785i q^{41} +(5.59701 - 93.5242i) q^{42} +(-344.071 - 344.071i) q^{43} +(-85.9934 + 67.5496i) q^{44} +(-83.4518 + 83.4518i) q^{45} +(105.072 - 93.2063i) q^{46} -174.483 q^{47} +(-100.779 + 61.2761i) q^{48} +19.9202 q^{49} +(52.8976 - 46.9238i) q^{50} +(134.958 - 134.958i) q^{51} +(134.163 + 170.795i) q^{52} +(322.832 + 322.832i) q^{53} +(15.7574 - 263.301i) q^{54} +68.3448i q^{55} +(231.683 + 334.275i) q^{56} -42.3653i q^{57} +(274.668 + 16.4377i) q^{58} +(-21.0376 - 21.0376i) q^{59} +(-8.79164 + 73.1897i) q^{60} +(489.653 - 489.653i) q^{61} +(469.058 + 528.774i) q^{62} -424.264 q^{63} +(179.715 - 479.423i) q^{64} +135.742 q^{65} +(-47.2813 - 53.3007i) q^{66} +(261.470 - 261.470i) q^{67} +(-98.8126 + 822.606i) q^{68} +(64.7110 + 64.7110i) q^{69} +(253.743 + 15.1854i) q^{70} +218.795i q^{71} +(304.243 + 438.965i) q^{72} -1085.01i q^{73} +(50.3860 - 841.934i) q^{74} +(32.5781 + 32.5781i) q^{75} +(113.605 + 144.624i) q^{76} +(-173.730 + 173.730i) q^{77} +(-105.862 + 93.9071i) q^{78} -1155.60 q^{79} +(-166.250 - 273.425i) q^{80} -465.437 q^{81} +(-274.613 + 243.600i) q^{82} +(777.042 - 777.042i) q^{83} +(-208.394 + 163.698i) q^{84} +(366.157 + 366.157i) q^{85} +(-82.2175 + 1373.83i) q^{86} +179.283i q^{87} +(304.334 + 55.1666i) q^{88} +15.9331i q^{89} +(333.211 + 19.9412i) q^{90} +(345.052 + 345.052i) q^{91} +(-394.431 - 47.3796i) q^{92} +(-325.656 + 325.656i) q^{93} +(327.497 + 369.190i) q^{94} +114.942 q^{95} +(318.811 + 98.2257i) q^{96} -923.624 q^{97} +(-37.3892 - 42.1492i) q^{98} +(-228.140 + 228.140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 20 q^{4} + 60 q^{6} + 60 q^{10} - 40 q^{11} - 156 q^{12} - 244 q^{14} + 120 q^{15} - 432 q^{16} - 320 q^{18} + 24 q^{19} + 40 q^{20} + 740 q^{22} + 1096 q^{24} + 272 q^{26} - 264 q^{27} - 308 q^{28}+ \cdots - 4456 q^{99}+O(q^{100}) $ 48 * q - 20 * q^4 + 60 * q^6 + 60 * q^10 - 40 * q^11 - 156 * q^12 - 244 * q^14 + 120 * q^15 - 432 * q^16 - 320 * q^18 + 24 * q^19 + 40 * q^20 + 740 * q^22 + 1096 * q^24 + 272 * q^26 - 264 * q^27 - 308 * q^28 + 400 * q^29 - 1600 * q^32 - 848 * q^34 + 1452 * q^36 + 16 * q^37 + 220 * q^38 + 900 * q^42 + 808 * q^43 - 1656 * q^44 - 2188 * q^46 + 1880 * q^47 - 40 * q^48 - 2352 * q^49 + 100 * q^50 + 2144 * q^51 + 792 * q^52 + 752 * q^53 + 1696 * q^54 + 2512 * q^56 - 2036 * q^58 - 2728 * q^59 + 980 * q^60 - 912 * q^61 - 344 * q^62 - 2520 * q^63 - 1040 * q^64 - 1920 * q^66 - 2040 * q^67 + 16 * q^68 - 528 * q^69 - 1240 * q^70 + 1240 * q^72 + 1928 * q^74 - 1024 * q^76 + 1904 * q^77 + 7568 * q^78 + 2832 * q^79 + 2320 * q^80 - 3888 * q^81 + 876 * q^82 + 2440 * q^83 + 896 * q^84 - 240 * q^85 + 244 * q^86 - 8320 * q^88 - 2340 * q^90 - 4448 * q^91 + 2524 * q^92 + 4272 * q^93 + 6676 * q^94 - 3040 * q^95 - 1080 * q^96 - 1436 * q^98 - 4456 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.87695	−	2.11591i	−0.663602	−	0.748086i
$2$	−1.87695	−	2.11591i	−0.663602	−	0.748086i
$3$	1.30312	−	1.30312i	0.250786	−	0.250786i	−0.570507	−	0.821293i	$-0.693253\pi$
$3$	1.30312	−	1.30312i	0.250786	−	0.250786i	0.821293	+	0.570507i	$0.193253\pi$
$4$	−0.954112	+	7.94290i	−0.119264	+	0.992863i
$5$	3.53553	+	3.53553i	0.316228	+	0.316228i
$5$	3.53553	+	3.53553i	0.316228	+	0.316228i
$6$	−5.20319	−	0.311388i	−0.354032	−	0.0211872i
$7$			17.9744i			0.970528i	0.874368	+	0.485264i	$0.161276\pi$
$7$			17.9744i			0.970528i	−0.874368	+	0.485264i	$0.838724\pi$
$8$	18.5972	−	12.8896i	0.821890	−	0.569646i
$9$			23.6037i			0.874213i
$10$	0.844833	−	14.1169i	0.0267160	−	0.446415i
$11$	9.66542	+	9.66542i	0.264930	+	0.264930i	0.827054	−	0.562123i	$-0.190015\pi$
$11$	9.66542	+	9.66542i	0.264930	+	0.264930i	−0.562123	+	0.827054i	$0.690015\pi$
$12$	9.10726	+	11.5939i	0.219087	+	0.278906i
$13$	19.1969	−	19.1969i	0.409558	−	0.409558i	−0.472027	−	0.881584i	$-0.656477\pi$
$13$	19.1969	−	19.1969i	0.409558	−	0.409558i	0.881584	+	0.472027i	$0.156477\pi$
$14$	38.0322	−	33.7371i	0.726038	−	0.644044i
$15$	9.21448			0.158611
$16$	−62.1793	−	15.1568i	−0.971552	−	0.236826i
$17$	103.565			1.47754			0.738770	−	0.673957i	$-0.235407\pi$
$17$	103.565			1.47754			0.738770	+	0.673957i	$0.235407\pi$
$18$	49.9433	−	44.3031i	0.653986	−	0.580129i
$19$	16.2553	−	16.2553i	0.196275	−	0.196275i	−0.602126	−	0.798401i	$-0.705680\pi$
$19$	16.2553	−	16.2553i	0.196275	−	0.196275i	0.798401	+	0.602126i	$0.205680\pi$
$20$	−31.4557	+	24.7091i	−0.351685	+	0.276256i
$21$	23.4229	+	23.4229i	0.243395	+	0.243395i
$22$	2.30960	−	38.5926i	0.0223822	−	0.373999i
$23$			49.6583i			0.450195i	0.974336	+	0.225097i	$0.0722700\pi$
$23$			49.6583i			0.450195i	−0.974336	+	0.225097i	$0.927730\pi$
$24$	7.43774	−	41.0313i	0.0632593	−	0.348978i
$25$			25.0000i			0.200000i
$26$	−76.6503	−	4.58718i	−0.578168	−	0.0346008i
$27$	65.9429	+	65.9429i	0.470027	+	0.470027i
$28$	−142.769	−	17.1496i	−0.963600	−	0.115749i
$29$	−68.7899	+	68.7899i	−0.440481	+	0.440481i	−0.892174	−	0.451692i	$-0.850820\pi$
$29$	−68.7899	+	68.7899i	−0.440481	+	0.440481i	0.451692	+	0.892174i	$0.350820\pi$
$30$	−17.2951	−	19.4970i	−0.105255	−	0.118655i
$31$	−249.904			−1.44787			−0.723937	−	0.689866i	$-0.757670\pi$
$31$	−249.904			−1.44787			−0.723937	+	0.689866i	$0.757670\pi$
$32$	84.6371	+	160.014i	0.467558	+	0.883962i
$33$	25.1905			0.132882
$34$	−194.386	−	219.134i	−0.980499	−	1.10533i
$35$	−63.5492	+	63.5492i	−0.306908	+	0.306908i
$36$	−187.482	−	22.5206i	−0.867973	−	0.104262i
$37$	210.860	+	210.860i	0.936897	+	0.936897i	0.998124	−	0.0612269i	$-0.0195013\pi$
$37$	210.860	+	210.860i	0.936897	+	0.936897i	−0.0612269	+	0.998124i	$0.519501\pi$
$38$	−64.9051	−	3.88428i	−0.277079	−	0.0165819i
$39$		−	50.0318i		−	0.205423i
$40$	111.323	+	20.1795i	0.440042	+	0.0797665i
$41$		−	129.785i		−	0.494367i	−0.968969	−	0.247183i	$-0.920495\pi$
$41$		−	129.785i		−	0.494367i	0.968969	−	0.247183i	$-0.0795050\pi$
$42$	5.59701	−	93.5242i	0.0205628	−	0.343598i
$43$	−344.071	−	344.071i	−1.22024	−	1.22024i	−0.967546	−	0.252696i	$-0.918683\pi$
$43$	−344.071	−	344.071i	−1.22024	−	1.22024i	−0.252696	−	0.967546i	$-0.581317\pi$
$44$	−85.9934	+	67.5496i	−0.294636	+	0.231443i
$45$	−83.4518	+	83.4518i	−0.276450	+	0.276450i
$46$	105.072	−	93.2063i	0.336784	−	0.298750i
$47$	−174.483			−0.541511			−0.270755	−	0.962648i	$-0.587273\pi$
$47$	−174.483			−0.541511			−0.270755	+	0.962648i	$0.587273\pi$
$48$	−100.779	+	61.2761i	−0.303045	+	0.184259i
$49$	19.9202			0.0580764
$50$	52.8976	−	46.9238i	0.149617	−	0.132720i
$51$	134.958	−	134.958i	0.370547	−	0.370547i
$52$	134.163	+	170.795i	0.357789	+	0.455480i
$53$	322.832	+	322.832i	0.836687	+	0.836687i	0.988421	−	0.151735i	$-0.0484859\pi$
$53$	322.832	+	322.832i	0.836687	+	0.836687i	−0.151735	+	0.988421i	$0.548486\pi$
$54$	15.7574	−	263.301i	0.0397094	−	0.663531i
$55$			68.3448i			0.167557i
$56$	231.683	+	334.275i	0.552857	+	0.797667i
$57$		−	42.3653i		−	0.0984461i
$58$	274.668	+	16.4377i	0.621822	+	0.0372133i
$59$	−21.0376	−	21.0376i	−0.0464213	−	0.0464213i	0.683515	−	0.729936i	$-0.260450\pi$
$59$	−21.0376	−	21.0376i	−0.0464213	−	0.0464213i	−0.729936	+	0.683515i	$0.760450\pi$
$60$	−8.79164	+	73.1897i	−0.0189166	+	0.157479i
$61$	489.653	−	489.653i	1.02777	−	1.02777i	0.0281617	−	0.999603i	$-0.491035\pi$
$61$	489.653	−	489.653i	1.02777	−	1.02777i	0.999603	−	0.0281617i	$-0.00896533\pi$
$62$	469.058	+	528.774i	0.960813	+	1.08313i
$63$	−424.264			−0.848447
$64$	179.715	−	479.423i	0.351006	−	0.936373i
$65$	135.742			0.259027
$66$	−47.2813	−	53.3007i	−0.0881806	−	0.0994069i
$67$	261.470	−	261.470i	0.476771	−	0.476771i	−0.427327	−	0.904097i	$-0.640545\pi$
$67$	261.470	−	261.470i	0.476771	−	0.476771i	0.904097	+	0.427327i	$0.140545\pi$
$68$	−98.8126	+	822.606i	−0.176217	+	1.46700i
$69$	64.7110	+	64.7110i	0.112903	+	0.112903i
$70$	253.743	+	15.1854i	0.433258	+	0.0259286i
$71$			218.795i			0.365720i	0.983139	+	0.182860i	$0.0585356\pi$
$71$			218.795i			0.365720i	−0.983139	+	0.182860i	$0.941464\pi$
$72$	304.243	+	438.965i	0.497992	+	0.718507i
$73$		−	1085.01i		−	1.73960i	−0.493401	−	0.869802i	$-0.664246\pi$
$73$		−	1085.01i		−	1.73960i	0.493401	−	0.869802i	$-0.335754\pi$
$74$	50.3860	−	841.934i	0.0791521	−	1.32261i
$75$	32.5781	+	32.5781i	0.0501573	+	0.0501573i
$76$	113.605	+	144.624i	0.171465	+	0.218282i
$77$	−173.730	+	173.730i	−0.257122	+	0.257122i
$78$	−105.862	+	93.9071i	−0.153674	+	0.136319i
$79$	−1155.60			−1.64576			−0.822880	−	0.568215i	$-0.807634\pi$
$79$	−1155.60			−1.64576			−0.822880	+	0.568215i	$0.807634\pi$
$80$	−166.250	−	273.425i	−0.232341	−	0.382123i
$81$	−465.437			−0.638460
$82$	−274.613	+	243.600i	−0.369829	+	0.328063i
$83$	777.042	−	777.042i	1.02761	−	1.02761i	0.0280004	−	0.999608i	$-0.491086\pi$
$83$	777.042	−	777.042i	1.02761	−	1.02761i	0.999608	−	0.0280004i	$-0.00891397\pi$
$84$	−208.394	+	163.698i	−0.270686	+	0.212629i
$85$	366.157	+	366.157i	0.467239	+	0.467239i
$86$	−82.2175	+	1373.83i	−0.103090	+	1.72260i
$87$			179.283i			0.220933i
$88$	304.334	+	55.1666i	0.368660	+	0.0668271i
$89$			15.9331i			0.0189765i	0.999955	+	0.00948823i	$0.00302024\pi$
$89$			15.9331i			0.0189765i	−0.999955	+	0.00948823i	$0.996980\pi$
$90$	333.211	+	19.9412i	0.390261	+	0.0233554i
$91$	345.052	+	345.052i	0.397487	+	0.397487i
$92$	−394.431	−	47.3796i	−0.446982	−	0.0536921i
$93$	−325.656	+	325.656i	−0.363107	+	0.363107i
$94$	327.497	+	369.190i	0.359348	+	0.405096i
$95$	114.942			0.124135
$96$	318.811	+	98.2257i	0.338943	+	0.104428i
$97$	−923.624			−0.966802			−0.483401	−	0.875399i	$-0.660599\pi$
$97$	−923.624			−0.966802			−0.483401	+	0.875399i	$0.660599\pi$
$98$	−37.3892	−	42.1492i	−0.0385396	−	0.0434461i
$99$	−228.140	+	228.140i	−0.231605	+	0.231605i
$100$	−198.573	−	23.8528i	−0.198573	−	0.0238528i
$101$	−385.353	−	385.353i	−0.379644	−	0.379644i	0.491330	−	0.870974i	$-0.336511\pi$
$101$	−385.353	−	385.353i	−0.379644	−	0.379644i	−0.870974	+	0.491330i	$0.836511\pi$
$102$	−538.868	−	32.2489i	−0.523097	−	0.0313050i
$103$		−	1445.05i		−	1.38238i	−0.722672	−	0.691191i	$-0.757086\pi$
$103$		−	1445.05i		−	1.38238i	0.722672	−	0.691191i	$-0.242914\pi$
$104$	109.569	−	604.449i	0.103308	−	0.569914i
$105$			165.625i			0.153936i
$106$	77.1423	−	1289.02i	0.0706861	−	1.18114i
$107$	488.994	+	488.994i	0.441802	+	0.441802i	0.892617	−	0.450815i	$-0.148867\pi$
$107$	488.994	+	488.994i	0.441802	+	0.441802i	−0.450815	+	0.892617i	$0.648867\pi$
$108$	−586.695	+	460.861i	−0.522729	+	0.410615i
$109$	−640.953	+	640.953i	−0.563231	+	0.563231i	−0.930224	−	0.366993i	$-0.880387\pi$
$109$	−640.953	+	640.953i	−0.563231	+	0.563231i	0.366993	+	0.930224i	$0.380387\pi$
$110$	144.611	−	128.280i	0.125347	−	0.111191i
$111$	549.554			0.469922
$112$	272.435	−	1117.64i	0.229846	−	0.942918i
$113$	214.312			0.178414			0.0892069	−	0.996013i	$-0.471567\pi$
$113$	214.312			0.178414			0.0892069	+	0.996013i	$0.471567\pi$
$114$	−89.6411	+	79.5177i	−0.0736461	+	0.0653290i
$115$	−175.569	+	175.569i	−0.142364	+	0.142364i
$116$	−480.758	−	612.025i	−0.384804	−	0.489871i
$117$	453.118	+	453.118i	0.358040	+	0.358040i
$118$	−5.02702	+	83.9999i	−0.00392182	+	0.0655324i
$119$			1861.52i			1.43399i
$120$	171.364	−	118.771i	0.130361	−	0.0903522i
$121$		−	1144.16i		−	0.859624i
$122$	−1955.11	−	117.005i	−1.45088	−	0.0868290i
$123$	−169.126	−	169.126i	−0.123980	−	0.123980i
$124$	238.437	−	1984.96i	0.172679	−	1.43754i
$125$	−88.3883	+	88.3883i	−0.0632456	+	0.0632456i
$126$	796.322	+	897.702i	0.563032	+	0.634711i
$127$	68.9099			0.0481478			0.0240739	−	0.999710i	$-0.492336\pi$
$127$	68.9099			0.0481478			0.0240739	+	0.999710i	$0.492336\pi$
$128$	−1351.73	+	519.593i	−0.933416	+	0.358796i
$129$	−896.735			−0.612040
$130$	−254.782	−	287.218i	−0.171891	−	0.193774i
$131$	488.197	−	488.197i	0.325603	−	0.325603i	−0.525309	−	0.850912i	$-0.676050\pi$
$131$	488.197	−	488.197i	0.325603	−	0.325603i	0.850912	+	0.525309i	$0.176050\pi$
$132$	−24.0345	+	200.085i	−0.0158480	+	0.131933i
$133$	292.180	+	292.180i	0.190490	+	0.190490i
$134$	−1044.01	−	62.4795i	−0.673051	−	0.0402792i
$135$			466.287i			0.297271i
$136$	1926.02	−	1334.91i	1.21438	−	0.841675i
$137$		−	2605.52i		−	1.62485i	−0.583066	−	0.812425i	$-0.698147\pi$
$137$		−	2605.52i		−	1.62485i	0.583066	−	0.812425i	$-0.301853\pi$
$138$	15.4630	−	258.382i	0.00953839	−	0.159383i
$139$	2138.54	+	2138.54i	1.30495	+	1.30495i	0.925009	+	0.379944i	$0.124057\pi$
$139$	2138.54	+	2138.54i	1.30495	+	1.30495i	0.379944	+	0.925009i	$0.375943\pi$
$140$	−444.132	−	565.398i	−0.268114	−	0.341320i
$141$	−227.373	+	227.373i	−0.135803	+	0.135803i
$142$	462.949	−	410.667i	0.273590	−	0.242693i
$143$	371.091			0.217009
$144$	357.758	−	1467.66i	0.207036	−	0.849343i
$145$	−486.418			−0.278585
$146$	−2295.78	+	2036.52i	−1.30137	+	1.15441i
$147$	25.9585	−	25.9585i	0.0145648	−	0.0145648i
$148$	−1876.03	+	1473.66i	−1.04195	+	0.818472i
$149$	1394.57	+	1394.57i	0.766764	+	0.766764i	0.977535	−	0.210771i	$-0.0675976\pi$
$149$	1394.57	+	1394.57i	0.766764	+	0.766764i	−0.210771	+	0.977535i	$0.567598\pi$
$150$	7.78469	−	130.080i	0.00423745	−	0.0708064i
$151$			1946.09i			1.04881i	0.851469	+	0.524405i	$0.175712\pi$
$151$			1946.09i			1.04881i	−0.851469	+	0.524405i	$0.824288\pi$
$152$	92.7792	−	511.829i	0.0495091	−	0.273124i
$153$			2444.52i			1.29168i
$154$	693.680	+	41.5137i	0.362976	+	0.0217225i
$155$	−883.545	−	883.545i	−0.457858	−	0.457858i
$156$	397.397	+	47.7359i	0.203957	+	0.0244996i
$157$	−514.931	+	514.931i	−0.261758	+	0.261758i	−0.825768	−	0.564010i	$-0.809258\pi$
$157$	−514.931	+	514.931i	−0.261758	+	0.261758i	0.564010	+	0.825768i	$0.309258\pi$
$158$	2169.00	+	2445.14i	1.09213	+	1.23117i
$159$	841.380			0.419659
$160$	−266.498	+	864.973i	−0.131678	+	0.427388i
$161$	−892.580			−0.436926
$162$	873.603	+	984.821i	0.423684	+	0.477623i
$163$	1228.72	−	1228.72i	0.590433	−	0.590433i	−0.347316	−	0.937748i	$-0.612907\pi$
$163$	1228.72	−	1228.72i	0.590433	−	0.590433i	0.937748	+	0.347316i	$0.112907\pi$
$164$	1030.87	+	123.830i	0.490838	+	0.0589602i
$165$	89.0618	+	89.0618i	0.0420209	+	0.0420209i
$166$	−3102.62	−	185.678i	−1.45066	−	0.0868157i
$167$		−	587.588i		−	0.272269i	−0.990690	−	0.136135i	$-0.956532\pi$
$167$		−	587.588i		−	0.272269i	0.990690	−	0.136135i	$-0.0434679\pi$
$168$	737.514	+	133.689i	0.338693	+	0.0613949i
$169$			1459.96i			0.664525i
$170$	87.4951	−	1462.01i	0.0394739	−	0.659596i
$171$	383.686	+	383.686i	0.171586	+	0.171586i
$172$	3061.21	−	2404.64i	1.35706	−	1.06600i
$173$	1062.06	−	1062.06i	0.466744	−	0.466744i	−0.434114	−	0.900858i	$-0.642938\pi$
$173$	1062.06	−	1062.06i	0.466744	−	0.466744i	0.900858	+	0.434114i	$0.142938\pi$
$174$	379.347	−	336.506i	0.165277	−	0.146612i
$175$	−449.361			−0.194106
$176$	−454.492	−	747.487i	−0.194651	−	0.320136i
$177$	−54.8291			−0.0232836
$178$	33.7129	−	29.9056i	0.0141960	−	0.0125928i
$179$	1954.76	−	1954.76i	0.816234	−	0.816234i	−0.169326	−	0.985560i	$-0.554159\pi$
$179$	1954.76	−	1954.76i	0.816234	−	0.816234i	0.985560	+	0.169326i	$0.0541590\pi$
$180$	−583.227	−	742.472i	−0.241507	−	0.307448i
$181$	−2384.68	−	2384.68i	−0.979293	−	0.979293i	0.0204973	−	0.999790i	$-0.493475\pi$
$181$	−2384.68	−	2384.68i	−0.979293	−	0.979293i	−0.999790	+	0.0204973i	$0.993475\pi$
$182$	82.4519	−	1377.74i	0.0335810	−	0.561128i
$183$		−	1276.16i		−	0.515499i
$184$	640.077	+	923.509i	0.256452	+	0.370011i
$185$			1491.01i			0.592546i
$186$	1300.30	+	77.8171i	0.512594	+	0.0306765i
$187$	1001.00	+	1001.00i	0.391445	+	0.391445i
$188$	166.477	−	1385.90i	0.0645828	−	0.537646i
$189$	−1185.29	+	1185.29i	−0.456174	+	0.456174i
$190$	−215.741	−	243.207i	−0.0823764	−	0.0928637i
$191$	3326.75			1.26029			0.630145	−	0.776478i	$-0.282996\pi$
$191$	3326.75			1.26029			0.630145	+	0.776478i	$0.282996\pi$
$192$	−390.556	−	858.939i	−0.146802	−	0.322857i
$193$	2489.93			0.928648			0.464324	−	0.885665i	$-0.346297\pi$
$193$	2489.93			0.928648			0.464324	+	0.885665i	$0.346297\pi$
$194$	1733.60	+	1954.30i	0.641572	+	0.723250i
$195$	176.889	−	176.889i	0.0649604	−	0.0649604i
$196$	−19.0061	+	158.224i	−0.00692642	+	0.0576618i
$197$	−1788.50	−	1788.50i	−0.646829	−	0.646829i	0.305396	−	0.952225i	$-0.401211\pi$
$197$	−1788.50	−	1788.50i	−0.646829	−	0.646829i	−0.952225	+	0.305396i	$0.901211\pi$
$198$	910.930	+	54.5152i	0.326955	+	0.0195668i
$199$			1891.36i			0.673743i	0.941551	+	0.336872i	$0.109369\pi$
$199$			1891.36i			0.673743i	−0.941551	+	0.336872i	$0.890631\pi$
$200$	322.241	+	464.931i	0.113929	+	0.164378i
$201$		−	681.455i		−	0.239135i
$202$	−92.0819	+	1538.66i	−0.0320736	+	0.535939i
$203$	−1236.46	−	1236.46i	−0.427499	−	0.427499i
$204$	943.193	+	1200.72i	0.323709	+	0.412095i
$205$	458.860	−	458.860i	0.156333	−	0.156333i
$206$	−3057.60	+	2712.29i	−1.03414	+	0.917352i
$207$	−1172.12			−0.393566
$208$	−1484.61	+	902.684i	−0.494900	+	0.300913i
$209$	314.229			0.103998
$210$	350.447	−	310.870i	0.115158	−	0.102153i
$211$	−3007.32	+	3007.32i	−0.981197	+	0.981197i	−0.999826	−	0.0186292i	$-0.994070\pi$
$211$	−3007.32	+	3007.32i	−0.981197	+	0.981197i	0.0186292	+	0.999826i	$0.494070\pi$
$212$	−2872.24	+	2256.21i	−0.930502	+	0.730928i
$213$	285.116	+	285.116i	0.0917176	+	0.0917176i
$214$	116.847	−	1952.48i	0.0373249	−	0.623687i
$215$		−	2432.95i		−	0.771749i
$216$	2076.34	+	376.378i	0.654059	+	0.118561i
$217$		−	4491.88i		−	1.40520i
$218$	2559.23	+	153.159i	0.795106	+	0.0475836i
$219$	−1413.91	−	1413.91i	−0.436269	−	0.436269i
$220$	−542.856	−	65.2086i	−0.166361	−	0.0199835i
$221$	1988.12	−	1988.12i	0.605138	−	0.605138i
$222$	−1031.48	−	1162.80i	−0.311841	−	0.351542i
$223$	−5155.90			−1.54827			−0.774136	−	0.633019i	$-0.781815\pi$
$223$	−5155.90			−1.54827			−0.774136	+	0.633019i	$0.781815\pi$
$224$	−2876.16	+	1521.30i	−0.857910	+	0.453778i
$225$	−590.093			−0.174843
$226$	−402.253	−	453.464i	−0.118396	−	0.133469i
$227$	−363.535	+	363.535i	−0.106294	+	0.106294i	−0.758254	−	0.651960i	$-0.773947\pi$
$227$	−363.535	+	363.535i	−0.106294	+	0.106294i	0.651960	+	0.758254i	$0.273947\pi$
$228$	336.504	+	40.4213i	0.0977434	+	0.0117411i
$229$	−2227.85	−	2227.85i	−0.642884	−	0.642884i	0.308380	−	0.951263i	$-0.400213\pi$
$229$	−2227.85	−	2227.85i	−0.642884	−	0.642884i	−0.951263	+	0.308380i	$0.900213\pi$
$230$	701.021	+	41.9530i	0.200974	+	0.0120274i
$231$			452.784i			0.128965i
$232$	−392.627	+	2165.98i	−0.111109	+	0.612946i
$233$			3753.04i			1.05524i	0.849482	+	0.527618i	$0.176915\pi$
$233$			3753.04i			1.05524i	−0.849482	+	0.527618i	$0.823085\pi$
$234$	108.275	−	1809.23i	0.0302484	−	0.505441i
$235$	−616.892	−	616.892i	−0.171241	−	0.171241i
$236$	187.171	−	147.027i	0.0516264	−	0.0405536i
$237$	−1505.89	+	1505.89i	−0.412734	+	0.412734i
$238$	3938.80	−	3493.98i	1.07275	−	0.951602i
$239$	−1005.32			−0.272088			−0.136044	−	0.990703i	$-0.543439\pi$
$239$	−1005.32			−0.272088			−0.136044	+	0.990703i	$0.543439\pi$
$240$	−572.950	−	139.662i	−0.154099	−	0.0375632i
$241$	−1393.93			−0.372576			−0.186288	−	0.982495i	$-0.559646\pi$
$241$	−1393.93			−0.372576			−0.186288	+	0.982495i	$0.559646\pi$
$242$	−2420.93	+	2147.53i	−0.643072	+	0.570448i
$243$	−2386.98	+	2386.98i	−0.630144	+	0.630144i
$244$	3422.08	+	4356.45i	0.897854	+	1.14300i
$245$	70.4285	+	70.4285i	0.0183654	+	0.0183654i
$246$	−40.4135	+	675.296i	−0.0104743	+	0.175022i
$247$		−	624.101i		−	0.160772i
$248$	−4647.53	+	3221.17i	−1.18999	+	0.824776i
$249$		−	2025.16i		−	0.515420i
$250$	352.922	+	21.1208i	0.0892830	+	0.00534319i
$251$	−4032.99	−	4032.99i	−1.01418	−	1.01418i	−0.999898	−	0.0142864i	$-0.995452\pi$
$251$	−4032.99	−	4032.99i	−1.01418	−	1.01418i	−0.0142864	−	0.999898i	$-0.504548\pi$
$252$	404.795	−	3369.88i	0.101189	−	0.842392i
$253$	−479.969	+	479.969i	−0.119270	+	0.119270i
$254$	−129.341	−	145.807i	−0.0319510	−	0.0360187i
$255$	954.297			0.234354
$256$	3636.54	+	1884.88i	0.887827	+	0.460177i
$257$	2814.94			0.683234			0.341617	−	0.939839i	$-0.389025\pi$
$257$	2814.94			0.683234			0.341617	+	0.939839i	$0.389025\pi$
$258$	1683.13	+	1897.41i	0.406151	+	0.457858i
$259$	−3790.09	+	3790.09i	−0.909284	+	0.909284i
$260$	−129.513	+	1078.19i	−0.0308926	+	0.257178i
$261$	−1623.70	−	1623.70i	−0.385074	−	0.385074i
$262$	−1949.30	−	116.657i	−0.459650	−	0.0275080i
$263$		−	5568.12i		−	1.30549i	−0.757576	−	0.652747i	$-0.773616\pi$
$263$		−	5568.12i		−	1.30549i	0.757576	−	0.652747i	$-0.226384\pi$
$264$	468.474	−	324.696i	0.109214	−	0.0756956i
$265$			2282.77i			0.529167i
$266$	69.8177	−	1166.63i	0.0160932	−	0.268913i
$267$	20.7628	+	20.7628i	0.00475904	+	0.00475904i
$268$	1827.36	+	2326.30i	0.416506	+	0.530229i
$269$	3381.13	−	3381.13i	0.766362	−	0.766362i	−0.211102	−	0.977464i	$-0.567705\pi$
$269$	3381.13	−	3381.13i	0.766362	−	0.766362i	0.977464	+	0.211102i	$0.0677052\pi$
$270$	986.619	−	875.198i	0.222384	−	0.197270i
$271$	8497.20			1.90468			0.952339	−	0.305040i	$-0.0986699\pi$
$271$	8497.20			1.90468			0.952339	+	0.305040i	$0.0986699\pi$
$272$	−6439.60	−	1569.72i	−1.43551	−	0.349919i
$273$	899.292			0.199369
$274$	−5513.03	+	4890.43i	−1.21553	+	1.07825i
$275$	−241.635	+	241.635i	−0.0529861	+	0.0529861i
$276$	−575.734	+	452.251i	−0.125562	+	0.0986316i
$277$	776.937	+	776.937i	0.168526	+	0.168526i	0.786331	−	0.617805i	$-0.211978\pi$
$277$	776.937	+	776.937i	0.168526	+	0.168526i	−0.617805	+	0.786331i	$0.711978\pi$
$278$	511.014	−	8538.88i	0.110247	−	1.84219i
$279$		−	5898.67i		−	1.26575i
$280$	−362.715	+	2000.96i	−0.0774156	+	0.427073i
$281$			8079.78i			1.71530i	0.514234	+	0.857650i	$0.328076\pi$
$281$			8079.78i			1.71530i	−0.514234	+	0.857650i	$0.671924\pi$
$282$	907.869	+	54.3319i	0.191712	+	0.0114731i
$283$	−2189.72	−	2189.72i	−0.459949	−	0.459949i	0.438690	−	0.898639i	$-0.355443\pi$
$283$	−2189.72	−	2189.72i	−0.459949	−	0.459949i	−0.898639	+	0.438690i	$0.855443\pi$
$284$	−1737.86	−	208.755i	−0.363110	−	0.0436173i
$285$	149.784	−	149.784i	0.0311314	−	0.0311314i
$286$	−696.520	−	785.194i	−0.144007	−	0.162341i
$287$	2332.81			0.479797
$288$	−3776.93	+	1997.75i	−0.772771	+	0.408745i
$289$	5812.70			1.18313
$290$	912.983	+	1029.21i	0.184870	+	0.208405i
$291$	−1203.60	+	1203.60i	−0.242461	+	0.242461i
$292$	8618.15	+	1035.22i	1.72719	+	0.207472i
$293$	5552.61	+	5552.61i	1.10712	+	1.10712i	0.993527	+	0.113596i	$0.0362369\pi$
$293$	5552.61	+	5552.61i	1.10712	+	1.10712i	0.113596	+	0.993527i	$0.463763\pi$
$294$	−103.648	−	6.20290i	−0.0205609	−	0.00123048i
$295$		−	148.758i		−	0.0293594i
$296$	6639.32	+	1203.51i	1.30373	+	0.236327i
$297$			1274.73i			0.249049i
$298$	333.240	−	5568.33i	0.0647787	−	1.08243i
$299$	953.284	+	953.284i	0.184381	+	0.184381i
$300$	−289.848	+	227.681i	−0.0557812	+	0.0438173i
$301$	6184.48	−	6184.48i	1.18428	−	1.18428i
$302$	4117.74	−	3652.71i	0.784600	−	0.695993i
$303$	−1004.32			−0.190419
$304$	−1257.12	+	764.365i	−0.237174	+	0.144208i
$305$	3462.37			0.650016
$306$	5172.37	−	4588.24i	0.966291	−	0.857165i
$307$	−4301.90	+	4301.90i	−0.799747	+	0.799747i	−0.983055	−	0.183309i	$-0.941319\pi$
$307$	−4301.90	+	4301.90i	−0.799747	+	0.799747i	0.183309	+	0.983055i	$0.441319\pi$
$308$	−1214.16	−	1545.68i	−0.224622	−	0.285952i
$309$	−1883.08	−	1883.08i	−0.346682	−	0.346682i
$310$	−211.127	+	3527.87i	−0.0386814	+	0.646353i
$311$			4756.88i			0.867325i	0.901075	+	0.433663i	$0.142779\pi$
$311$			4756.88i			0.867325i	−0.901075	+	0.433663i	$0.857221\pi$
$312$	−644.890	−	930.453i	−0.117018	−	0.168835i
$313$			5433.84i			0.981274i	0.871364	+	0.490637i	$0.163236\pi$
$313$			5433.84i			0.981274i	−0.871364	+	0.490637i	$0.836764\pi$
$314$	2056.04	+	123.045i	0.369520	+	0.0221141i
$315$	−1500.00	−	1500.00i	−0.268303	−	0.268303i
$316$	1102.57	−	9178.81i	0.196280	−	1.63401i
$317$	−728.663	+	728.663i	−0.129103	+	0.129103i	−0.768706	−	0.639602i	$-0.779099\pi$
$317$	−728.663	+	728.663i	−0.129103	+	0.129103i	0.639602	+	0.768706i	$0.279099\pi$
$318$	−1579.23	−	1780.28i	−0.278487	−	0.313941i
$319$	−1329.77			−0.233394
$320$	2330.41	−	1059.63i	0.407105	−	0.185109i
$321$	1274.44			0.221596
$322$	1675.33	+	1888.62i	0.289945	+	0.326858i
$323$	1683.48	−	1683.48i	0.290004	−	0.290004i
$324$	444.079	−	3696.92i	0.0761453	−	0.633903i
$325$	479.921	+	479.921i	0.0819115	+	0.0819115i
$326$	−4906.09	−	293.608i	−0.833507	−	0.0498817i
$327$			1670.48i			0.282501i
$328$	−1672.88	−	2413.65i	−0.281614	−	0.406315i
$329$		−	3136.24i		−	0.525551i
$330$	21.2817	−	355.611i	0.00355006	−	0.0593204i
$331$	2514.44	+	2514.44i	0.417541	+	0.417541i	0.884355	−	0.466814i	$-0.154598\pi$
$331$	2514.44	+	2514.44i	0.417541	+	0.417541i	−0.466814	+	0.884355i	$0.654598\pi$
$332$	5430.59	+	6913.36i	0.897717	+	1.14283i
$333$	−4977.09	+	4977.09i	−0.819047	+	0.819047i
$334$	−1243.28	+	1102.87i	−0.203681	+	0.180678i
$335$	1848.87			0.301536
$336$	−1101.40	−	1811.44i	−0.178829	−	0.294113i
$337$	82.5425			0.0133424			0.00667118	−	0.999978i	$-0.497876\pi$
$337$	82.5425			0.0133424			0.00667118	+	0.999978i	$0.497876\pi$
$338$	3089.14	−	2740.28i	0.497122	−	0.440980i
$339$	279.275	−	279.275i	0.0447438	−	0.0447438i
$340$	−3257.71	+	2559.00i	−0.519629	+	0.408180i
$341$	−2415.43	−	2415.43i	−0.383586	−	0.383586i
$342$	91.6836	−	1532.00i	0.0144961	−	0.242226i
$343$			6523.28i			1.02689i
$344$	−10833.7	−	1963.83i	−1.69801	−	0.307799i
$345$			457.576i			0.0714059i
$346$	−4240.64	−	253.784i	−0.658897	−	0.0394321i
$347$	7202.76	+	7202.76i	1.11431	+	1.11431i	0.992561	+	0.121745i	$0.0388490\pi$
$347$	7202.76	+	7202.76i	1.11431	+	1.11431i	0.121745	+	0.992561i	$0.461151\pi$
$348$	−1424.03	−	171.057i	−0.219356	−	0.0263494i
$349$	−2134.41	+	2134.41i	−0.327370	+	0.327370i	−0.851586	−	0.524215i	$-0.824359\pi$
$349$	−2134.41	+	2134.41i	−0.327370	+	0.327370i	0.524215	+	0.851586i	$0.324359\pi$
$350$	843.428	+	950.804i	0.128809	+	0.145208i
$351$	2531.79			0.385006
$352$	−728.552	+	2364.66i	−0.110318	+	0.358059i
$353$	705.357			0.106352			0.0531761	−	0.998585i	$-0.483066\pi$
$353$	705.357			0.106352			0.0531761	+	0.998585i	$0.483066\pi$
$354$	102.911	+	116.013i	0.0154511	+	0.0174182i
$355$	−773.556	+	773.556i	−0.115651	+	0.115651i
$356$	−126.555	−	15.2020i	−0.0188410	−	0.00226321i
$357$	2425.79	+	2425.79i	0.359626	+	0.359626i
$358$	−7805.09	−	467.100i	−1.15227	−	0.0689582i
$359$		−	11015.7i		−	1.61946i	−0.586803	−	0.809730i	$-0.699614\pi$
$359$		−	11015.7i		−	1.61946i	0.586803	−	0.809730i	$-0.300386\pi$
$360$	−476.312	+	2627.64i	−0.0697329	+	0.384691i
$361$			6330.53i			0.922952i
$362$	−569.831	+	9521.69i	−0.0827339	+	1.38246i
$363$	−1490.98	−	1490.98i	−0.215582	−	0.215582i
$364$	−3069.94	+	2411.50i	−0.442056	+	0.347244i
$365$	3836.10	−	3836.10i	0.550111	−	0.550111i
$366$	−2700.23	+	2395.28i	−0.385637	+	0.342086i
$367$	−12269.4			−1.74512			−0.872560	−	0.488506i	$-0.837542\pi$
$367$	−12269.4			−1.74512			−0.872560	+	0.488506i	$0.837542\pi$
$368$	752.663	−	3087.72i	0.106618	−	0.437388i
$369$	3063.42			0.432182
$370$	3154.83	−	2798.54i	0.443275	−	0.393215i
$371$	−5802.72	+	5802.72i	−0.812028	+	0.812028i
$372$	−2275.94	−	2897.37i	−0.317210	−	0.403821i
$373$	−1651.92	−	1651.92i	−0.229312	−	0.229312i	0.583093	−	0.812405i	$-0.301842\pi$
$373$	−1651.92	−	1651.92i	−0.229312	−	0.229312i	−0.812405	+	0.583093i	$0.801842\pi$
$374$	239.194	−	3996.84i	0.0330706	−	0.552599i
$375$			230.362i			0.0317222i
$376$	−3244.91	+	2249.02i	−0.445062	+	0.308470i
$377$			2641.10i			0.360805i
$378$	4732.68	+	283.230i	0.643975	+	0.0385391i
$379$	−2757.81	−	2757.81i	−0.373771	−	0.373771i	0.495078	−	0.868849i	$-0.335140\pi$
$379$	−2757.81	−	2757.81i	−0.373771	−	0.373771i	−0.868849	+	0.495078i	$0.835140\pi$
$380$	−109.668	+	912.976i	−0.0148049	+	0.123249i
$381$	89.7982	−	89.7982i	0.0120748	−	0.0120748i
$382$	−6244.15	−	7039.09i	−0.836331	−	0.942804i
$383$	10375.4			1.38423			0.692116	−	0.721787i	$-0.256679\pi$
$383$	10375.4			1.38423			0.692116	+	0.721787i	$0.256679\pi$
$384$	−1084.38	+	2438.57i	−0.144107	+	0.324069i
$385$	−1228.46			−0.162618
$386$	−4673.48	−	5268.46i	−0.616253	−	0.694708i
$387$	8121.37	−	8121.37i	1.06675	−	1.06675i
$388$	881.241	−	7336.25i	0.115305	−	0.959901i
$389$	−2933.34	−	2933.34i	−0.382330	−	0.382330i	0.489611	−	0.871941i	$-0.337139\pi$
$389$	−2933.34	−	2933.34i	−0.382330	−	0.382330i	−0.871941	+	0.489611i	$0.837139\pi$
$390$	−706.292	−	42.2685i	−0.0917038	−	0.00548807i
$391$			5142.87i			0.665181i
$392$	370.461	−	256.764i	0.0477324	−	0.0330830i
$393$		−	1272.36i		−	0.163313i
$394$	−427.371	+	7141.22i	−0.0546462	+	0.913121i
$395$	−4085.66	−	4085.66i	−0.520435	−	0.520435i
$396$	−1594.42	−	2029.76i	−0.202330	−	0.257575i
$397$	−2310.28	+	2310.28i	−0.292065	+	0.292065i	−0.837895	−	0.545831i	$-0.816214\pi$
$397$	−2310.28	+	2310.28i	−0.292065	+	0.292065i	0.545831	+	0.837895i	$0.316214\pi$
$398$	4001.94	−	3549.99i	0.504018	−	0.447098i
$399$	761.492			0.0955446
$400$	378.921	−	1554.48i	0.0473651	−	0.194310i
$401$	−15396.7			−1.91740			−0.958698	−	0.284427i	$-0.908197\pi$
$401$	−15396.7			−1.91740			−0.958698	+	0.284427i	$0.908197\pi$
$402$	−1441.89	+	1279.06i	−0.178893	+	0.158691i
$403$	−4797.37	+	4797.37i	−0.592988	+	0.592988i
$404$	3428.49	−	2693.15i	0.422212	−	0.331656i
$405$	−1645.57	−	1645.57i	−0.201899	−	0.201899i
$406$	−295.458	+	4937.00i	−0.0361166	+	0.603496i
$407$			4076.10i			0.496425i
$408$	770.290	−	4249.40i	0.0934682	−	0.515629i
$409$		−	12575.6i		−	1.52036i	−0.649715	−	0.760178i	$-0.725112\pi$
$409$		−	12575.6i		−	1.52036i	0.649715	−	0.760178i	$-0.274888\pi$
$410$	−1832.16	−	109.647i	−0.220693	−	0.0132075i
$411$	−3395.31	−	3395.31i	−0.407490	−	0.407490i
$412$	11477.9	+	1378.74i	1.37252	+	0.164868i
$413$	378.138	−	378.138i	0.0450531	−	0.0450531i
$414$	2200.02	+	2480.10i	0.261171	+	0.294421i
$415$	5494.52			0.649917
$416$	4696.54	+	1447.00i	0.553526	+	0.170541i
$417$	5573.56			0.654529
$418$	−589.792	−	664.878i	−0.0690135	−	0.0777997i
$419$	8665.37	−	8665.37i	1.01034	−	1.01034i	0.0103906	−	0.999946i	$-0.496693\pi$
$419$	8665.37	−	8665.37i	1.01034	−	1.01034i	0.999946	−	0.0103906i	$-0.00330748\pi$
$420$	−1315.54	−	158.025i	−0.152838	−	0.0183591i
$421$	−7662.55	−	7662.55i	−0.887054	−	0.887054i	0.107185	−	0.994239i	$-0.465816\pi$
$421$	−7662.55	−	7662.55i	−0.887054	−	0.887054i	−0.994239	+	0.107185i	$0.965816\pi$
$422$	12007.8	+	718.614i	1.38514	+	0.0828948i
$423$		−	4118.46i		−	0.473395i
$424$	10165.0	+	1842.61i	1.16428	+	0.211049i
$425$			2589.12i			0.295508i
$426$	68.1299	−	1138.43i	0.00774861	−	0.129477i
$427$	8801.23	+	8801.23i	0.997474	+	0.997474i
$428$	−4350.59	+	3417.47i	−0.491340	+	0.385958i
$429$	483.578	−	483.578i	0.0544228	−	0.0544228i
$430$	−5147.90	+	4566.53i	−0.577334	+	0.512134i
$431$	−1895.81			−0.211874			−0.105937	−	0.994373i	$-0.533784\pi$
$431$	−1895.81			−0.211874			−0.105937	+	0.994373i	$0.533784\pi$
$432$	−3100.80	−	5099.77i	−0.345341	−	0.567970i
$433$	−2200.34			−0.244207			−0.122104	−	0.992517i	$-0.538964\pi$
$433$	−2200.34			−0.244207			−0.122104	+	0.992517i	$0.538964\pi$
$434$	−9504.40	+	8431.04i	−1.05121	+	0.932495i
$435$	−633.863	+	633.863i	−0.0698653	+	0.0698653i
$436$	−4479.48	−	5702.56i	−0.492037	−	0.626384i
$437$	807.211	+	807.211i	0.0883619	+	0.0883619i
$438$	−337.860	+	5645.52i	−0.0368574	+	0.615875i
$439$			6043.58i			0.657049i	0.944495	+	0.328524i	$0.106551\pi$
$439$			6043.58i			0.657049i	−0.944495	+	0.328524i	$0.893449\pi$
$440$	880.939	+	1271.03i	0.0954480	+	0.137713i
$441$			470.191i			0.0507711i
$442$	−7938.28	−	475.071i	−0.854266	−	0.0511241i
$443$	−2766.30	−	2766.30i	−0.296684	−	0.296684i	0.543030	−	0.839714i	$-0.317277\pi$
$443$	−2766.30	−	2766.30i	−0.296684	−	0.296684i	−0.839714	+	0.543030i	$0.817277\pi$
$444$	−524.336	+	4365.05i	−0.0560448	+	0.466568i
$445$	−56.3320	+	56.3320i	−0.00600088	+	0.00600088i
$446$	9677.37	+	10909.4i	1.02744	+	1.15824i
$447$	3634.60			0.384588
$448$	8617.35	+	3230.28i	0.908776	+	0.340661i
$449$	−17830.6			−1.87411			−0.937056	−	0.349179i	$-0.886461\pi$
$449$	−17830.6			−1.87411			−0.937056	+	0.349179i	$0.886461\pi$
$450$	1107.58	+	1248.58i	0.116026	+	0.130797i
$451$	1254.43	−	1254.43i	0.130973	−	0.130973i
$452$	−204.478	+	1702.26i	−0.0212784	+	0.177140i
$453$	2535.99	+	2535.99i	0.263027	+	0.263027i
$454$	1451.54	+	86.8685i	0.150054	+	0.00898004i
$455$			2439.89i			0.251393i
$456$	−546.073	−	787.879i	−0.0560794	−	0.0809119i
$457$		−	14018.4i		−	1.43491i	−0.696606	−	0.717454i	$-0.745307\pi$
$457$		−	14018.4i		−	1.43491i	0.696606	−	0.717454i	$-0.254693\pi$
$458$	−532.355	+	8895.48i	−0.0543129	+	0.907551i
$459$	6829.38	+	6829.38i	0.694484	+	0.694484i
$460$	−1227.01	−	1562.04i	−0.124369	−	0.158327i
$461$	2477.06	−	2477.06i	0.250256	−	0.250256i	−0.570819	−	0.821076i	$-0.693374\pi$
$461$	2477.06	−	2477.06i	0.250256	−	0.250256i	0.821076	+	0.570819i	$0.193374\pi$
$462$	958.049	−	849.854i	0.0964772	−	0.0855817i
$463$	−6279.68			−0.630327			−0.315163	−	0.949037i	$-0.602059\pi$
$463$	−6279.68			−0.630327			−0.315163	+	0.949037i	$0.602059\pi$
$464$	5319.95	−	3234.67i	0.532268	−	0.323633i
$465$	−2302.74			−0.229649
$466$	7941.08	−	7044.27i	0.789406	−	0.700257i
$467$	5797.97	−	5797.97i	0.574514	−	0.574514i	−0.358873	−	0.933386i	$-0.616839\pi$
$467$	5797.97	−	5797.97i	0.574514	−	0.574514i	0.933386	+	0.358873i	$0.116839\pi$
$468$	−4031.39	+	3166.74i	−0.398186	+	0.312784i
$469$	4699.77	+	4699.77i	0.462719	+	0.462719i
$470$	−147.409	+	2463.16i	−0.0144670	+	0.241738i
$471$			1342.04i			0.131290i
$472$	−662.407	−	120.075i	−0.0645969	−	0.0117095i
$473$		−	6651.19i		−	0.646558i
$474$	6012.80	+	359.839i	0.582652	+	0.0348691i
$475$	406.383	+	406.383i	0.0392550	+	0.0392550i
$476$	−14785.9	−	1776.10i	−1.42376	−	0.171024i
$477$	−7620.04	+	7620.04i	−0.731442	+	0.731442i
$478$	1886.94	+	2127.17i	0.180558	+	0.203545i
$479$	965.448			0.0920927			0.0460464	−	0.998939i	$-0.485338\pi$
$479$	965.448			0.0920927			0.0460464	+	0.998939i	$0.485338\pi$
$480$	779.887	+	1474.45i	0.0741600	+	0.140206i
$481$	8095.70			0.767427
$482$	2616.33	+	2949.42i	0.247242	+	0.278718i
$483$	−1163.14	+	1163.14i	−0.109575	+	0.109575i
$484$	9087.94	+	1091.66i	0.853488	+	0.102522i
$485$	−3265.50	−	3265.50i	−0.305730	−	0.305730i
$486$	9530.87	+	570.381i	0.889566	+	0.0532366i
$487$		−	13452.2i		−	1.25170i	−0.779942	−	0.625852i	$-0.784752\pi$
$487$		−	13452.2i		−	1.25170i	0.779942	−	0.625852i	$-0.215248\pi$
$488$	2794.76	−	15417.6i	0.259247	−	1.43017i
$489$		−	3202.34i		−	0.296145i
$490$	16.8292	−	281.211i	0.00155157	−	0.0259261i
$491$	−7716.82	−	7716.82i	−0.709277	−	0.709277i	0.257106	−	0.966383i	$-0.417231\pi$
$491$	−7716.82	−	7716.82i	−0.709277	−	0.709277i	−0.966383	+	0.257106i	$0.917231\pi$
$492$	1504.72	−	1181.99i	0.137882	−	0.108309i
$493$	−7124.22	+	7124.22i	−0.650829	+	0.650829i
$494$	−1320.54	+	1171.41i	−0.120271	+	0.106689i
$495$	−1613.19			−0.146480
$496$	15538.9	+	3787.76i	1.40669	+	0.342894i
$497$	−3932.71			−0.354942
$498$	−4285.06	+	3801.13i	−0.385578	+	0.342034i
$499$	3025.88	−	3025.88i	0.271457	−	0.271457i	−0.558230	−	0.829686i	$-0.688519\pi$
$499$	3025.88	−	3025.88i	0.271457	−	0.271457i	0.829686	+	0.558230i	$0.188519\pi$
$500$	−617.727	−	786.392i	−0.0552512	−	0.0703371i
$501$	−765.700	−	765.700i	−0.0682813	−	0.0682813i
$502$	−963.703	+	16103.2i	−0.0856816	+	1.43171i
$503$			7264.11i			0.643918i	0.946754	+	0.321959i	$0.104341\pi$
$503$			7264.11i			0.643918i	−0.946754	+	0.321959i	$0.895659\pi$
$504$	−7890.13	+	5468.60i	−0.697330	+	0.483315i
$505$		−	2724.86i		−	0.240108i
$506$	1916.45	+	114.691i	0.168372	+	0.0100763i
$507$	1902.51	+	1902.51i	0.166654	+	0.166654i
$508$	−65.7478	+	547.345i	−0.00574230	+	0.0478041i
$509$	−6106.12	+	6106.12i	−0.531727	+	0.531727i	−0.921086	−	0.389359i	$-0.872697\pi$
$509$	−6106.12	+	6106.12i	−0.531727	+	0.531727i	0.389359	+	0.921086i	$0.372697\pi$
$510$	−1791.17	−	2019.20i	−0.155518	−	0.175317i
$511$	19502.5			1.68833
$512$	−2837.37	−	11232.4i	−0.244913	−	0.969545i
$513$	2143.84			0.184509
$514$	−5283.50	−	5956.15i	−0.453396	−	0.511118i
$515$	5109.04	−	5109.04i	0.437148	−	0.437148i
$516$	855.586	−	7122.68i	0.0729943	−	0.607671i
$517$	−1686.45	−	1686.45i	−0.143463	−	0.143463i
$518$	15133.3	+	905.660i	1.28363	+	0.0768193i
$519$		−	2767.98i		−	0.234106i
$520$	2524.43	−	1749.67i	0.212892	−	0.147554i
$521$			15120.8i			1.27151i	0.771893	+	0.635753i	$0.219310\pi$
$521$			15120.8i			1.27151i	−0.771893	+	0.635753i	$0.780690\pi$
$522$	−387.991	+	6483.19i	−0.0325324	+	0.543605i
$523$	15970.5	+	15970.5i	1.33526	+	1.33526i	0.900589	+	0.434671i	$0.143135\pi$
$523$	15970.5	+	15970.5i	1.33526	+	1.33526i	0.434671	+	0.900589i	$0.356865\pi$
$524$	3411.91	+	4343.50i	0.284446	+	0.362112i
$525$	−585.572	+	585.572i	−0.0486790	+	0.0486790i
$526$	−11781.6	+	10451.1i	−0.976621	+	0.866329i
$527$	−25881.3			−2.13929
$528$	−1566.33	−	381.808i	−0.129102	−	0.0314698i
$529$	9701.05			0.797325
$530$	4830.12	−	4284.64i	0.395862	−	0.351157i
$531$	496.565	−	496.565i	0.0405821	−	0.0405821i
$532$	−2599.53	+	2041.98i	−0.211849	+	0.166412i
$533$	−2491.47	−	2491.47i	−0.202472	−	0.202472i
$534$	4.96137	−	82.9029i	0.000402059	−	0.00671827i
$535$			3457.71i			0.279420i
$536$	1492.37	−	8232.87i	0.120262	−	0.663444i
$537$		−	5094.60i		−	0.409401i
$538$	−13500.4	−	807.938i	−1.08186	−	0.0647448i
$539$	192.537	+	192.537i	0.0153862	+	0.0153862i
$540$	−3703.67	−	444.890i	−0.295149	−	0.0354537i
$541$	16156.7	−	16156.7i	1.28398	−	1.28398i	0.345592	−	0.938385i	$-0.387678\pi$
$541$	16156.7	−	16156.7i	1.28398	−	1.28398i	0.938385	−	0.345592i	$-0.112322\pi$
$542$	−15948.8	−	17979.3i	−1.26395	−	1.42486i
$543$	−6215.07			−0.491186
$544$	8765.44	+	16571.9i	0.690837	+	1.30609i
$545$	−4532.22			−0.356218
$546$	−1687.93	−	1902.82i	−0.132301	−	0.149145i
$547$	6368.79	−	6368.79i	0.497824	−	0.497824i	−0.412936	−	0.910760i	$-0.635497\pi$
$547$	6368.79	−	6368.79i	0.497824	−	0.497824i	0.910760	+	0.412936i	$0.135497\pi$
$548$	20695.4	+	2485.96i	1.61325	+	0.193786i
$549$	11557.6	+	11557.6i	0.898485	+	0.898485i
$550$	964.816	+	57.7400i	0.0747998	+	0.00447644i
$551$			2236.40i			0.172911i
$552$	2037.55	+	369.346i	0.157108	+	0.0284790i
$553$		−	20771.2i		−	1.59726i
$554$	185.653	−	3102.20i	0.0142376	−	0.237906i
$555$	1942.97	+	1942.97i	0.148602	+	0.148602i
$556$	−19026.6	+	14945.8i	−1.45127	+	1.14001i
$557$	−9746.29	+	9746.29i	−0.741407	+	0.741407i	−0.972849	−	0.231442i	$-0.925656\pi$
$557$	−9746.29	+	9746.29i	−0.741407	+	0.741407i	0.231442	+	0.972849i	$0.425656\pi$
$558$	−12481.0	+	11071.5i	−0.946889	+	0.839955i
$559$	−13210.2			−0.999519
$560$	4914.65	−	2988.24i	0.370860	−	0.225493i
$561$	2608.85			0.196338
$562$	17096.1	−	15165.3i	1.28319	−	1.13828i
$563$	7196.60	−	7196.60i	0.538722	−	0.538722i	−0.384431	−	0.923154i	$-0.625602\pi$
$563$	7196.60	−	7196.60i	0.538722	−	0.538722i	0.923154	+	0.384431i	$0.125602\pi$
$564$	−1589.06	−	2022.94i	−0.118638	−	0.151031i
$565$	757.707	+	757.707i	0.0564194	+	0.0564194i
$566$	−523.245	+	8743.25i	−0.0388580	+	0.649305i
$567$		−	8365.97i		−	0.619643i
$568$	2820.18	+	4068.98i	0.208331	+	0.300582i
$569$			5236.83i			0.385834i	0.981215	+	0.192917i	$0.0617948\pi$
$569$			5236.83i			0.385834i	−0.981215	+	0.192917i	$0.938205\pi$
$570$	−598.066	−	35.7916i	−0.0439478	−	0.00263008i
$571$	−7407.25	−	7407.25i	−0.542879	−	0.542879i	0.381493	−	0.924372i	$-0.375410\pi$
$571$	−7407.25	−	7407.25i	−0.542879	−	0.542879i	−0.924372	+	0.381493i	$0.875410\pi$
$572$	−354.063	+	2947.54i	−0.0258813	+	0.215460i
$573$	4335.17	−	4335.17i	0.316063	−	0.316063i
$574$	−4378.58	−	4936.01i	−0.318394	−	0.358929i
$575$	−1241.46			−0.0900390
$576$	11316.2	+	4241.95i	0.818589	+	0.306854i
$577$	−7726.80			−0.557488			−0.278744	−	0.960365i	$-0.589918\pi$
$577$	−7726.80			−0.557488			−0.278744	+	0.960365i	$0.589918\pi$
$578$	−10910.2	−	12299.1i	−0.785126	−	0.885080i
$579$	3244.69	−	3244.69i	0.232892	−	0.232892i
$580$	464.097	−	3863.57i	0.0332252	−	0.276597i
$581$	13966.9	+	13966.9i	0.997322	+	0.997322i
$582$	4805.78	+	287.605i	0.342279	+	0.0204839i
$583$			6240.62i			0.443327i
$584$	−13985.4	−	20178.2i	−0.990959	−	1.42976i
$585$			3204.03i			0.226445i
$586$	1326.82	−	22170.8i	0.0935334	−	1.56291i
$587$	−8359.85	−	8359.85i	−0.587816	−	0.587816i	0.349224	−	0.937039i	$-0.386445\pi$
$587$	−8359.85	−	8359.85i	−0.587816	−	0.587816i	−0.937039	+	0.349224i	$0.886445\pi$
$588$	181.418	+	230.953i	0.0127237	+	0.0161978i
$589$	−4062.27	+	4062.27i	−0.284181	+	0.284181i
$590$	−314.758	+	279.211i	−0.0219633	+	0.0194830i
$591$	−4661.27			−0.324432
$592$	−9915.17	−	16307.1i	−0.688363	−	1.13213i
$593$	−8292.91			−0.574281			−0.287141	−	0.957888i	$-0.592705\pi$
$593$	−8292.91			−0.574281			−0.287141	+	0.957888i	$0.592705\pi$
$594$	2697.21	−	2392.61i	0.186310	−	0.165269i
$595$	−6581.47	+	6581.47i	−0.453469	+	0.453469i
$596$	−12407.5	+	9746.37i	−0.852739	+	0.669844i
$597$	2464.68	+	2464.68i	0.168966	+	0.168966i
$598$	227.792	−	3806.33i	0.0155771	−	0.260288i
$599$			27431.8i			1.87117i	0.353097	+	0.935587i	$0.385129\pi$
$599$			27431.8i			1.87117i	−0.353097	+	0.935587i	$0.614871\pi$
$600$	1025.78	+	185.944i	0.0697956	+	0.0126519i
$601$			2790.89i			0.189422i	0.995505	+	0.0947112i	$0.0301928\pi$
$601$			2790.89i			0.189422i	−0.995505	+	0.0947112i	$0.969807\pi$
$602$	−24693.8	−	1477.81i	−1.67183	−	0.100052i
$603$	6171.67	+	6171.67i	0.416799	+	0.416799i
$604$	−15457.6	−	1856.79i	−1.04132	−	0.125085i
$605$	4045.21	−	4045.21i	0.271837	−	0.271837i
$606$	1885.07	+	2125.06i	0.126362	+	0.142450i
$607$	−10317.1			−0.689882			−0.344941	−	0.938624i	$-0.612101\pi$
$607$	−10317.1			−0.689882			−0.344941	+	0.938624i	$0.612101\pi$
$608$	3976.88	+	1225.28i	0.265270	+	0.0817296i
$609$	−3222.52			−0.214422
$610$	−6498.70	−	7326.05i	−0.431352	−	0.486267i
$611$	−3349.53	+	3349.53i	−0.221780	+	0.221780i
$612$	−19416.6	−	2332.35i	−1.28247	−	0.154052i
$613$	−2563.99	−	2563.99i	−0.168938	−	0.168938i	0.617575	−	0.786512i	$-0.288115\pi$
$613$	−2563.99	−	2563.99i	−0.168938	−	0.168938i	−0.786512	+	0.617575i	$0.788115\pi$
$614$	17176.9	+	1027.96i	1.12899	+	0.0675652i
$615$		−	1195.90i		−	0.0784121i
$616$	−991.588	+	5470.22i	−0.0648575	+	0.357795i
$617$		−	9519.59i		−	0.621141i	−0.950550	−	0.310571i	$-0.899480\pi$
$617$		−	9519.59i		−	0.621141i	0.950550	−	0.310571i	$-0.100520\pi$
$618$	−449.972	+	7518.88i	−0.0292889	+	0.489407i
$619$	5737.81	+	5737.81i	0.372572	+	0.372572i	0.868413	−	0.495841i	$-0.165140\pi$
$619$	5737.81	+	5737.81i	0.372572	+	0.372572i	−0.495841	+	0.868413i	$0.665140\pi$
$620$	7860.91	−	6174.91i	0.509196	−	0.399984i
$621$	−3274.62	+	3274.62i	−0.211604	+	0.211604i
$622$	10065.1	−	8928.44i	0.648834	−	0.575559i
$623$	−286.388			−0.0184172
$624$	−758.323	+	3110.94i	−0.0486494	+	0.199579i
$625$	−625.000			−0.0400000
$626$	11497.5	−	10199.1i	0.734077	−	0.651176i
$627$	409.479	−	409.479i	0.0260814	−	0.0260814i
$628$	−3598.74	−	4581.34i	−0.228671	−	0.291108i
$629$	21837.7	+	21837.7i	1.38430	+	1.38430i
$630$	−358.432	+	5989.28i	−0.0226671	+	0.378760i
$631$		−	2962.42i		−	0.186897i	−0.995624	−	0.0934485i	$-0.970211\pi$
$631$		−	2962.42i		−	0.186897i	0.995624	−	0.0934485i	$-0.0297890\pi$
$632$	−21491.0	+	14895.2i	−1.35263	+	0.937501i
$633$			7837.83i			0.492142i
$634$	2909.45	+	174.118i	0.182254	+	0.0109071i
$635$	243.633	+	243.633i	0.0152257	+	0.0152257i
$636$	−802.771	+	6683.00i	−0.0500502	+	0.416664i
$637$	382.405	−	382.405i	0.0237856	−	0.0237856i
$638$	2495.91	+	2813.66i	0.154881	+	0.174599i
$639$	−5164.37			−0.319717
$640$	−6616.13	−	2942.05i	−0.408633	−	0.181711i
$641$	−14378.2			−0.885964			−0.442982	−	0.896530i	$-0.646079\pi$
$641$	−14378.2			−0.885964			−0.442982	+	0.896530i	$0.646079\pi$
$642$	−2392.06	−	2696.59i	−0.147051	−	0.165773i
$643$	6022.70	−	6022.70i	0.369381	−	0.369381i	−0.497870	−	0.867251i	$-0.665884\pi$
$643$	6022.70	−	6022.70i	0.369381	−	0.369381i	0.867251	+	0.497870i	$0.165884\pi$
$644$	851.622	−	7089.67i	0.0521096	−	0.433808i
$645$	−3170.44	−	3170.44i	−0.193544	−	0.193544i
$646$	−6721.89	−	402.276i	−0.409395	−	0.0245005i
$647$			14764.5i			0.897147i	0.893746	+	0.448573i	$0.148068\pi$
$647$			14764.5i			0.897147i	−0.893746	+	0.448573i	$0.851932\pi$
$648$	−8655.85	+	5999.31i	−0.524744	+	0.363696i
$649$		−	406.674i		−	0.0245968i
$650$	114.680	−	1916.26i	0.00692016	−	0.115634i
$651$	−5853.48	−	5853.48i	−0.352405	−	0.352405i
$652$	8587.24	+	10931.9i	0.515801	+	0.656636i
$653$	9815.04	−	9815.04i	0.588197	−	0.588197i	−0.348946	−	0.937143i	$-0.613460\pi$
$653$	9815.04	−	9815.04i	0.588197	−	0.588197i	0.937143	+	0.348946i	$0.113460\pi$
$654$	3534.58	−	3135.41i	0.211335	−	0.187468i
$655$	3452.08			0.205929
$656$	−1967.13	+	8069.96i	−0.117079	+	0.480303i
$657$	25610.4			1.52078
$658$	−6635.98	+	5886.56i	−0.393157	+	0.348757i
$659$	−19820.3	+	19820.3i	−1.17161	+	1.17161i	−0.189783	+	0.981826i	$0.560779\pi$
$659$	−19820.3	+	19820.3i	−1.17161	+	1.17161i	−0.981826	+	0.189783i	$0.939221\pi$
$660$	−792.384	+	622.434i	−0.0467326	+	0.0367094i
$661$	12939.4	+	12939.4i	0.761397	+	0.761397i	0.976575	−	0.215178i	$-0.0690331\pi$
$661$	12939.4	+	12939.4i	0.761397	+	0.761397i	−0.215178	+	0.976575i	$0.569033\pi$
$662$	600.838	−	10039.8i	0.0352752	−	0.589438i
$663$		−	5181.54i		−	0.303521i
$664$	4435.07	−	24466.6i	0.259208	−	1.42995i
$665$			2066.02i			0.120477i
$666$	19872.8	+	1189.30i	1.15624	+	0.0691958i
$667$	−3415.99	−	3415.99i	−0.198302	−	0.198302i
$668$	4667.15	+	560.625i	0.270326	+	0.0324719i
$669$	−6718.78	+	6718.78i	−0.388285	+	0.388285i
$670$	−3470.24	−	3912.04i	−0.200100	−	0.225575i
$671$	9465.41			0.544572
$672$	−1765.55	+	5730.44i	−0.101351	+	0.328953i
$673$	−3822.26			−0.218926			−0.109463	−	0.993991i	$-0.534913\pi$
$673$	−3822.26			−0.218926			−0.109463	+	0.993991i	$0.534913\pi$
$674$	−154.928	−	174.652i	−0.00885402	−	0.00998122i
$675$	−1648.57	+	1648.57i	−0.0940053	+	0.0940053i
$676$	−11596.3	−	1392.97i	−0.659782	−	0.0792539i
$677$	20574.4	+	20574.4i	1.16800	+	1.16800i	0.982677	+	0.185324i	$0.0593336\pi$
$677$	20574.4	+	20574.4i	1.16800	+	1.16800i	0.185324	+	0.982677i	$0.440666\pi$
$678$	−1115.10	−	66.7341i	−0.0631642	−	0.00378010i
$679$		−	16601.6i		−	0.938308i
$680$	11529.2	+	2089.89i	0.650181	+	0.117858i
$681$			947.463i			0.0533140i
$682$	−577.178	+	9644.46i	−0.0324066	+	0.541504i
$683$	5442.92	+	5442.92i	0.304931	+	0.304931i	0.842939	−	0.538009i	$-0.180823\pi$
$683$	5442.92	+	5442.92i	0.304931	+	0.304931i	−0.538009	+	0.842939i	$0.680823\pi$
$684$	−3413.66	+	2681.50i	−0.190825	+	0.149897i
$685$	9211.90	−	9211.90i	0.513823	−	0.513823i
$686$	13802.6	−	12243.9i	0.768203	−	0.681448i
$687$	−5806.33			−0.322453
$688$	16179.1	+	26609.2i	0.896544	+	1.47451i
$689$	12394.7			0.685343
$690$	968.187	−	858.847i	0.0534177	−	0.0473851i
$691$	7826.48	−	7826.48i	0.430873	−	0.430873i	−0.458052	−	0.888925i	$-0.651453\pi$
$691$	7826.48	−	7826.48i	0.430873	−	0.430873i	0.888925	+	0.458052i	$0.151453\pi$
$692$	7422.50	+	9449.14i	0.407747	+	0.519079i
$693$	−4100.69	−	4100.69i	−0.224779	−	0.224779i
$694$	1721.13	−	28759.6i	0.0941403	−	1.57305i
$695$			15121.8i			0.825325i
$696$	2310.90	+	3334.18i	0.125854	+	0.181583i
$697$		−	13441.2i		−	0.730447i
$698$	8522.38	+	510.027i	0.462145	+	0.0276573i
$699$	4890.68	+	4890.68i	0.264639	+	0.264639i
$700$	428.740	−	3569.23i	0.0231498	−	0.192720i
$701$	−5762.25	+	5762.25i	−0.310467	+	0.310467i	−0.845090	−	0.534624i	$-0.820453\pi$
$701$	−5762.25	+	5762.25i	−0.310467	+	0.310467i	0.534624	+	0.845090i	$0.320453\pi$
$702$	−4752.05	−	5357.04i	−0.255491	−	0.288018i
$703$	6855.19			0.367779
$704$	6370.85	−	2896.80i	0.341066	−	0.155081i
$705$	−1607.77			−0.0858896
$706$	−1323.92	−	1492.47i	−0.0705756	−	0.0795606i
$707$	6926.49	−	6926.49i	0.368455	−	0.368455i
$708$	52.3131	−	435.502i	0.00277690	−	0.0231175i
$709$	−16981.3	−	16981.3i	−0.899502	−	0.899502i	0.0958899	−	0.995392i	$-0.469430\pi$
$709$	−16981.3	−	16981.3i	−0.899502	−	0.899502i	−0.995392	+	0.0958899i	$0.969430\pi$
$710$	3088.70	+	184.845i	0.163263	+	0.00977057i
$711$		−	27276.5i		−	1.43874i
$712$	205.372	+	296.312i	0.0108099	+	0.0155966i
$713$		−	12409.8i		−	0.651826i
$714$	579.655	−	9685.84i	0.0303824	−	0.507680i
$715$	1312.01	+	1312.01i	0.0686241	+	0.0686241i
$716$	13661.4	+	17391.6i	0.713061	+	0.907756i
$717$	−1310.06	+	1310.06i	−0.0682359	+	0.0682359i
$718$	−23308.2	+	20675.9i	−1.21149	+	1.07468i
$719$	−1795.42			−0.0931262			−0.0465631	−	0.998915i	$-0.514827\pi$
$719$	−1795.42			−0.0931262			−0.0465631	+	0.998915i	$0.514827\pi$
$720$	6453.84	−	3924.11i	0.334056	−	0.203115i
$721$	25974.0			1.34164
$722$	13394.8	−	11882.1i	0.690447	−	0.612473i
$723$	−1816.46	+	1816.46i	−0.0934368	+	0.0934368i
$724$	21216.5	−	16666.0i	1.08910	−	0.855509i
$725$	−1719.75	−	1719.75i	−0.0880963	−	0.0880963i
$726$	−356.277	+	5953.27i	−0.0182131	+	0.304334i
$727$		−	15599.8i		−	0.795825i	−0.917423	−	0.397912i	$-0.869735\pi$
$727$		−	15599.8i		−	0.795825i	0.917423	−	0.397912i	$-0.130265\pi$
$728$	10864.6	+	1969.43i	0.553118	+	0.100264i
$729$		−	6345.74i		−	0.322397i
$730$	−15317.0	−	916.654i	−0.776585	−	0.0464752i
$731$	−35633.7	−	35633.7i	−1.80296	−	1.80296i
$732$	10136.4	+	1217.60i	0.511819	+	0.0614805i
$733$	12450.9	−	12450.9i	0.627401	−	0.627401i	−0.320013	−	0.947413i	$-0.603687\pi$
$733$	12450.9	−	12450.9i	0.627401	−	0.627401i	0.947413	+	0.320013i	$0.103687\pi$
$734$	23029.1	+	25961.0i	1.15807	+	1.30550i
$735$	183.554			0.00921156
$736$	−7946.04	+	4202.94i	−0.397955	+	0.210492i
$737$	5054.43			0.252622
$738$	−5749.88	−	6481.90i	−0.286797	−	0.323309i
$739$	637.719	−	637.719i	0.0317441	−	0.0317441i	−0.691057	−	0.722801i	$-0.742854\pi$
$739$	637.719	−	637.719i	0.0317441	−	0.0317441i	0.722801	+	0.691057i	$0.242854\pi$
$740$	−11842.9	−	1422.59i	−0.588316	−	0.0706694i
$741$	−813.281	−	813.281i	−0.0403193	−	0.0403193i
$742$	23169.4	+	1386.59i	1.14633	+	0.0686028i
$743$		−	1952.47i		−	0.0964053i	−0.998838	−	0.0482026i	$-0.984651\pi$
$743$		−	1952.47i		−	0.0964053i	0.998838	−	0.0482026i	$-0.0153493\pi$
$744$	−1858.72	+	10253.9i	−0.0915915	+	0.505277i
$745$			9861.12i			0.484944i
$746$	−394.735	+	6595.89i	−0.0193730	+	0.323717i
$747$	18341.1	+	18341.1i	0.898348	+	0.898348i
$748$	−8905.90	+	6995.77i	−0.435337	+	0.341966i
$749$	−8789.38	+	8789.38i	−0.428781	+	0.428781i
$750$	487.424	−	432.378i	0.0237309	−	0.0210509i
$751$	−13710.1			−0.666161			−0.333081	−	0.942898i	$-0.608088\pi$
$751$	−13710.1			−0.666161			−0.333081	+	0.942898i	$0.608088\pi$
$752$	10849.3	+	2644.61i	0.526106	+	0.128244i
$753$	−10511.0			−0.508687
$754$	5588.32	−	4957.21i	0.269913	−	0.239431i
$755$	−6880.46	+	6880.46i	−0.331663	+	0.331663i
$756$	−8283.71	−	10545.5i	−0.398513	−	0.507323i
$757$	5425.87	+	5425.87i	0.260510	+	0.260510i	0.825261	−	0.564751i	$-0.191028\pi$
$757$	5425.87	+	5425.87i	0.260510	+	0.260510i	−0.564751	+	0.825261i	$0.691028\pi$
$758$	−658.992	+	11011.5i	−0.0315774	+	0.527648i
$759$			1250.92i			0.0598227i
$760$	2137.61	−	1481.56i	0.102025	−	0.0707131i
$761$			18568.0i			0.884481i	0.896896	+	0.442241i	$0.145816\pi$
$761$			18568.0i			0.884481i	−0.896896	+	0.442241i	$0.854184\pi$
$762$	−358.551	−	21.4577i	−0.0170459	−	0.00102012i
$763$	−11520.8	−	11520.8i	−0.546631	−	0.546631i
$764$	−3174.09	+	26424.1i	−0.150307	+	1.25129i
$765$	−8642.68	+	8642.68i	−0.408467	+	0.408467i
$766$	−19474.2	−	21953.5i	−0.918579	−	1.03552i
$767$	−807.710			−0.0380244
$768$	7195.10	−	2282.62i	0.338061	−	0.107249i
$769$	13501.1			0.633110			0.316555	−	0.948574i	$-0.397474\pi$
$769$	13501.1			0.633110			0.316555	+	0.948574i	$0.397474\pi$
$770$	2305.76	+	2599.30i	0.107914	+	0.121652i
$771$	3668.22	−	3668.22i	0.171346	−	0.171346i
$772$	−2375.67	+	19777.3i	−0.110754	+	0.922020i
$773$	−19002.7	−	19002.7i	−0.884191	−	0.884191i	0.109767	−	0.993957i	$-0.464990\pi$
$773$	−19002.7	−	19002.7i	−0.884191	−	0.884191i	−0.993957	+	0.109767i	$0.964990\pi$
$774$	−32427.5	−	1940.64i	−1.50592	−	0.0901226i
$775$		−	6247.60i		−	0.289575i
$776$	−17176.9	+	11905.2i	−0.794605	+	0.550735i
$777$			9877.91i			0.456072i
$778$	−700.936	+	11712.4i	−0.0323005	+	0.539731i
$779$	−2109.70	−	2109.70i	−0.0970318	−	0.0970318i
$780$	1236.24	+	1573.78i	0.0567493	+	0.0722442i
$781$	−2114.74	+	2114.74i	−0.0968904	+	0.0968904i
$782$	10881.8	−	9652.90i	0.497612	−	0.441416i
$783$	−9072.41			−0.414076
$784$	−1238.62	−	301.927i	−0.0564242	−	0.0137540i
$785$	−3641.11			−0.165550
$786$	−2692.20	+	2388.16i	−0.122172	+	0.108375i
$787$	−18237.9	+	18237.9i	−0.826061	+	0.826061i	−0.986969	−	0.160908i	$-0.948558\pi$
$787$	−18237.9	+	18237.9i	−0.826061	+	0.826061i	0.160908	+	0.986969i	$0.448558\pi$
$788$	15912.3	−	12499.4i	0.719356	−	0.565069i
$789$	−7255.95	−	7255.95i	−0.327400	−	0.327400i
$790$	−976.289	+	16313.5i	−0.0439681	+	0.734692i
$791$			3852.13i			0.173156i
$792$	−1302.14	+	7183.42i	−0.0584210	+	0.322287i
$793$		−	18799.6i		−	0.841858i
$794$	9224.62	+	552.053i	0.412304	+	0.0246746i
$795$	2974.73	+	2974.73i	0.132708	+	0.132708i
$796$	−15022.9	−	1804.57i	−0.668934	−	0.0803533i
$797$	14529.0	−	14529.0i	0.645727	−	0.645727i	−0.306230	−	0.951958i	$-0.599068\pi$
$797$	14529.0	−	14529.0i	0.645727	−	0.645727i	0.951958	+	0.306230i	$0.0990677\pi$
$798$	−1429.28	−	1611.25i	−0.0634036	−	0.0714756i
$799$	−18070.4			−0.800104
$800$	−4000.36	+	2115.93i	−0.176792	+	0.0935117i
$801$	−376.081			−0.0165895
$802$	28898.9	+	32578.0i	1.27239	+	1.43438i
$803$	10487.1	−	10487.1i	0.460874	−	0.460874i
$804$	5412.73	+	650.185i	0.237428	+	0.0285202i
$805$	−3155.75	−	3155.75i	−0.138168	−	0.138168i
$806$	19155.2	+	1146.36i	0.837114	+	0.0500976i
$807$		−	8812.07i		−	0.384386i
$808$	−12133.6	−	2199.45i	−0.528288	−	0.0957628i
$809$			35390.4i			1.53802i	0.639234	+	0.769012i	$0.279252\pi$
$809$			35390.4i			1.53802i	−0.639234	+	0.769012i	$0.720748\pi$
$810$	−393.217	+	6570.52i	−0.0170571	+	0.285018i
$811$	3671.23	+	3671.23i	0.158957	+	0.158957i	0.782104	−	0.623147i	$-0.214146\pi$
$811$	3671.23	+	3671.23i	0.158957	+	0.158957i	−0.623147	+	0.782104i	$0.714146\pi$
$812$	11000.8	−	8641.35i	0.475433	−	0.373463i
$813$	11072.9	−	11072.9i	0.477667	−	0.477667i
$814$	8624.65	−	7650.64i	0.371368	−	0.329429i
$815$	8688.34			0.373422
$816$	−10437.1	+	6346.06i	−0.447761	+	0.272251i
$817$	−11186.0			−0.479006
$818$	−26608.9	+	23603.9i	−1.13736	+	1.00891i
$819$	−8144.53	+	8144.53i	−0.347488	+	0.347488i
$820$	3206.87	+	4082.48i	0.136572	+	0.173862i
$821$	−32787.6	−	32787.6i	−1.39378	−	1.39378i	−0.816652	−	0.577131i	$-0.804172\pi$
$821$	−32787.6	−	32787.6i	−1.39378	−	1.39378i	−0.577131	−	0.816652i	$-0.695828\pi$
$822$	−811.326	+	13557.0i	−0.0344261	+	0.575249i
$823$			24158.6i			1.02323i	0.859216	+	0.511613i	$0.170952\pi$
$823$			24158.6i			1.02323i	−0.859216	+	0.511613i	$0.829048\pi$
$824$	−18626.2	−	26874.0i	−0.787469	−	1.13617i
$825$			629.762i			0.0265764i
$826$	−1509.85	−	90.3579i	−0.0636010	−	0.00380624i
$827$	−24624.9	−	24624.9i	−1.03542	−	1.03542i	−0.999349	−	0.0360706i	$-0.988516\pi$
$827$	−24624.9	−	24624.9i	−1.03542	−	1.03542i	−0.0360706	−	0.999349i	$-0.511484\pi$
$828$	1118.34	−	9310.05i	0.0469383	−	0.390757i
$829$	2211.20	−	2211.20i	0.0926394	−	0.0926394i	−0.659268	−	0.751908i	$-0.729134\pi$
$829$	2211.20	−	2211.20i	0.0926394	−	0.0926394i	0.751908	+	0.659268i	$0.229134\pi$
$830$	−10312.9	−	11625.9i	−0.431286	−	0.486193i
$831$	2024.89			0.0845279
$832$	−5753.45	−	12653.4i	−0.239741	−	0.527256i
$833$	2063.03			0.0858102
$834$	−10461.3	−	11793.1i	−0.434347	−	0.489644i
$835$	2077.44	−	2077.44i	0.0860990	−	0.0860990i
$836$	−299.809	+	2495.89i	−0.0124033	+	0.103256i
$837$	−16479.4	−	16479.4i	−0.680540	−	0.680540i
$838$	−34599.6	−	2070.63i	−1.42628	−	0.0853566i
$839$		−	14313.9i		−	0.589001i	−0.955651	−	0.294501i	$-0.904847\pi$
$839$		−	14313.9i		−	0.589001i	0.955651	−	0.294501i	$-0.0951533\pi$
$840$	2134.84	+	3080.17i	0.0876893	+	0.126519i
$841$			14924.9i			0.611952i
$842$	−1831.00	+	30595.5i	−0.0749412	+	1.25224i
$843$	10529.0	+	10529.0i	0.430174	+	0.430174i
$844$	−21017.5	−	26756.2i	−0.857173	−	1.09122i
$845$	−5161.74	+	5161.74i	−0.210141	+	0.210141i
$846$	−8714.27	+	7730.14i	−0.354140	+	0.314146i
$847$	20565.6			0.834289
$848$	−15180.4	−	24966.6i	−0.614736	−	1.01103i
$849$	−5706.96			−0.230698
$850$	5478.34	−	4859.66i	0.221065	−	0.196100i
$851$	−10471.0	+	10471.0i	−0.421786	+	0.421786i
$852$	−2536.68	+	1992.62i	−0.102002	+	0.0801244i
$853$	−21680.6	−	21680.6i	−0.870257	−	0.870257i	0.122243	−	0.992500i	$-0.460991\pi$
$853$	−21680.6	−	21680.6i	−0.870257	−	0.870257i	−0.992500	+	0.122243i	$0.960991\pi$
$854$	2103.10	−	35142.1i	0.0842699	−	1.40812i
$855$			2713.07i			0.108520i
$856$	15396.9	+	2791.00i	0.614784	+	0.111442i
$857$			19741.2i			0.786870i	0.919352	+	0.393435i	$0.128713\pi$
$857$			19741.2i			0.786870i	−0.919352	+	0.393435i	$0.871287\pi$
$858$	−1930.86	−	115.553i	−0.0768279	−	0.00459781i
$859$	−4986.65	−	4986.65i	−0.198070	−	0.198070i	0.601102	−	0.799172i	$-0.294729\pi$
$859$	−4986.65	−	4986.65i	−0.198070	−	0.198070i	−0.799172	+	0.601102i	$0.794729\pi$
$860$	19324.7	+	2321.31i	0.766240	+	0.0920419i
$861$	3039.94	−	3039.94i	0.120326	−	0.120326i
$862$	3558.34	+	4011.35i	0.140600	+	0.158500i
$863$	38207.3			1.50706			0.753529	−	0.657415i	$-0.228350\pi$
$863$	38207.3			1.50706			0.753529	+	0.657415i	$0.228350\pi$
$864$	−4970.59	+	16133.0i	−0.195721	+	0.635251i
$865$	7509.88			0.295195
$866$	4129.94	+	4655.72i	0.162056	+	0.182688i
$867$	7574.67	−	7574.67i	0.296712	−	0.296712i
$868$	35678.6	+	4285.76i	1.39517	+	0.167590i
$869$	−11169.4	−	11169.4i	−0.436012	−	0.436012i
$870$	2530.92	+	151.465i	0.0986280	+	0.00590245i
$871$		−	10038.8i		−	0.390530i
$872$	−3658.32	+	20181.6i	−0.142071	+	0.783756i
$873$		−	21801.0i		−	0.845190i
$874$	192.887	−	3223.08i	0.00746511	−	0.124739i
$875$	−1588.73	−	1588.73i	−0.0613815	−	0.0613815i
$876$	12579.5	−	9881.49i	0.485186	−	0.381124i
$877$	−24917.7	+	24917.7i	−0.959421	+	0.959421i	−0.999208	−	0.0397868i	$-0.987332\pi$
$877$	−24917.7	+	24917.7i	−0.959421	+	0.959421i	0.0397868	+	0.999208i	$0.487332\pi$
$878$	12787.6	−	11343.5i	0.491529	−	0.436019i
$879$	14471.5			0.555302
$880$	1035.89	−	4249.64i	0.0396817	−	0.162790i
$881$	−28327.0			−1.08327			−0.541635	−	0.840614i	$-0.682195\pi$
$881$	−28327.0			−1.08327			−0.541635	+	0.840614i	$0.682195\pi$
$882$	994.880	−	882.525i	0.0379811	−	0.0336918i
$883$	−18768.9	+	18768.9i	−0.715314	+	0.715314i	−0.967642	−	0.252328i	$-0.918804\pi$
$883$	−18768.9	+	18768.9i	−0.715314	+	0.715314i	0.252328	+	0.967642i	$0.418804\pi$
$884$	13894.6	+	17688.3i	0.528648	+	0.672990i
$885$	−193.850	−	193.850i	−0.00736293	−	0.00736293i
$886$	−661.021	+	11045.5i	−0.0250648	+	0.418825i
$887$			26017.3i			0.984865i	0.870351	+	0.492433i	$0.163892\pi$
$887$			26017.3i			0.984865i	−0.870351	+	0.492433i	$0.836108\pi$
$888$	10220.2	−	7083.54i	0.386224	−	0.267689i
$889$			1238.62i			0.0467288i
$890$	224.926	+	13.4608i	0.00847137	+	0.000506974i
$891$	−4498.65	−	4498.65i	−0.169147	−	0.169147i
$892$	4919.31	−	40952.8i	0.184653	−	1.53722i
$893$	−2836.28	+	2836.28i	−0.106285	+	0.106285i
$894$	−6821.97	−	7690.47i	−0.255213	−	0.287705i
$895$	13822.3			0.516232
$896$	−9339.38	−	24296.6i	−0.348222	−	0.905906i
$897$	2484.49			0.0924803
$898$	33467.1	+	37727.8i	1.24367	+	1.40200i
$899$	17190.9	−	17190.9i	0.637762	−	0.637762i
$900$	563.015	−	4687.05i	0.0208524	−	0.173595i
$901$	33434.1	+	33434.1i	1.23624	+	1.23624i
$902$	−5008.75	−	299.752i	−0.184893	−	0.0110650i
$903$		−	16118.3i		−	0.594001i
$904$	3985.61	−	2762.40i	0.146637	−	0.101633i
$905$		−	16862.2i		−	0.619359i
$906$	605.988	−	10125.9i	0.0222214	−	0.371312i
$907$	26216.3	+	26216.3i	0.959757	+	0.959757i	0.999221	−	0.0394644i	$-0.0125652\pi$
$907$	26216.3	+	26216.3i	0.959757	+	0.959757i	−0.0394644	+	0.999221i	$0.512565\pi$
$908$	−2540.67	−	3234.38i	−0.0928581	−	0.118212i
$909$	9095.77	−	9095.77i	0.331889	−	0.331889i
$910$	5162.57	−	4579.55i	0.188063	−	0.166825i
$911$	1507.54			0.0548265			0.0274132	−	0.999624i	$-0.491273\pi$
$911$	1507.54			0.0548265			0.0274132	+	0.999624i	$0.491273\pi$
$912$	−642.125	+	2634.25i	−0.0233146	+	0.0956455i
$913$	15020.9			0.544489
$914$	−29661.6	+	26311.8i	−1.07343	+	0.952208i
$915$	4511.90	−	4511.90i	0.163015	−	0.163015i
$916$	19821.2	−	15570.0i	0.714968	−	0.561622i
$917$	8775.06	+	8775.06i	0.316007	+	0.316007i
$918$	1631.91	−	27268.7i	0.0586723	−	0.980394i
$919$			2424.43i			0.0870236i	0.999053	+	0.0435118i	$0.0138546\pi$
$919$			2424.43i			0.0870236i	−0.999053	+	0.0435118i	$0.986145\pi$
$920$	−1002.08	+	5528.11i	−0.0359105	+	0.198105i
$921$			11211.8i			0.401131i
$922$	−9890.55	−	591.906i	−0.353284	−	0.0211425i
$923$	4200.17	+	4200.17i	0.149784	+	0.149784i
$924$	−3596.42	−	432.007i	−0.128045	−	0.0153809i
$925$	−5271.50	+	5271.50i	−0.187379	+	0.187379i
$926$	11786.6	+	13287.2i	0.418286	+	0.471538i
$927$	34108.7			1.20850
$928$	−16829.5	−	5185.18i	−0.595320	−	0.183418i
$929$	−31265.1			−1.10417			−0.552086	−	0.833787i	$-0.686168\pi$
$929$	−31265.1			−1.10417			−0.552086	+	0.833787i	$0.686168\pi$
$930$	4322.12	+	4872.37i	0.152396	+	0.171797i
$931$	323.809	−	323.809i	0.0113989	−	0.0113989i
$932$	−29810.0	−	3580.82i	−1.04770	−	0.125852i
$933$	6198.81	+	6198.81i	0.217513	+	0.217513i
$934$	−23150.4	−	1385.45i	−0.811034	−	0.0485368i
$935$			7078.13i			0.247572i
$936$	14267.3	+	2586.23i	0.498226	+	0.0903135i
$937$			24317.7i			0.847839i	0.905700	+	0.423919i	$0.139346\pi$
$937$			24317.7i			0.847839i	−0.905700	+	0.423919i	$0.860654\pi$
$938$	1123.03	−	18765.5i	0.0390920	−	0.653215i
$939$	7080.97	+	7080.97i	0.246090	+	0.246090i
$940$	5488.49	−	4311.32i	0.190441	−	0.149596i
$941$	26684.6	−	26684.6i	0.924433	−	0.924433i	−0.0729055	−	0.997339i	$-0.523227\pi$
$941$	26684.6	−	26684.6i	0.924433	−	0.924433i	0.997339	+	0.0729055i	$0.0232271\pi$
$942$	2839.62	−	2518.94i	0.0982165	−	0.0871246i
$943$	6444.92			0.222561
$944$	989.238	+	1626.96i	0.0341070	+	0.0560945i
$945$	−8381.24			−0.288510
$946$	−14073.3	+	12484.0i	−0.483681	+	0.429057i
$947$	−12759.1	+	12759.1i	−0.437819	+	0.437819i	−0.891278	−	0.453458i	$-0.850190\pi$
$947$	−12759.1	+	12759.1i	−0.437819	+	0.437819i	0.453458	+	0.891278i	$0.350190\pi$
$948$	−10524.3	−	13397.9i	−0.360564	−	0.459013i
$949$	−20828.8	−	20828.8i	−0.712468	−	0.712468i
$950$	97.1071	−	1622.63i	0.00331639	−	0.0554158i
$951$			1899.08i			0.0647547i
$952$	23994.3	+	34619.2i	0.816869	+	1.17859i
$953$			4436.11i			0.150787i	0.997154	+	0.0753933i	$0.0240212\pi$
$953$			4436.11i			0.150787i	−0.997154	+	0.0753933i	$0.975979\pi$
$954$	30425.7	+	1820.85i	1.03257	+	0.0617946i
$955$	11761.8	+	11761.8i	0.398539	+	0.398539i
$956$	959.191	−	7985.18i	0.0324503	−	0.270146i
$957$	−1732.85	+	1732.85i	−0.0585320	+	0.0585320i
$958$	−1812.10	−	2042.80i	−0.0611130	−	0.0688933i
$959$	46832.7			1.57696
$960$	1655.98	−	4417.63i	0.0556735	−	0.148519i
$961$	32661.1			1.09634
$962$	−15195.2	−	17129.7i	−0.509266	−	0.574101i
$963$	−11542.1	+	11542.1i	−0.386229	+	0.386229i
$964$	1329.96	−	11071.8i	0.0444349	−	0.369916i
$965$	8803.23	+	8803.23i	0.293664	+	0.293664i
$966$	4644.26	+	277.938i	0.154686	+	0.00925727i
$967$		−	37242.9i		−	1.23852i	−0.785185	−	0.619261i	$-0.787432\pi$
$967$		−	37242.9i		−	1.23852i	0.785185	−	0.619261i	$-0.212568\pi$
$968$	−14747.8	−	21278.2i	−0.489681	−	0.706516i
$969$		−	4387.57i		−	0.145458i
$970$	−780.308	+	13038.7i	−0.0258290	+	0.431595i
$971$	28061.0	+	28061.0i	0.927414	+	0.927414i	0.997538	−	0.0701242i	$-0.0223396\pi$
$971$	28061.0	+	28061.0i	0.927414	+	0.927414i	−0.0701242	+	0.997538i	$0.522340\pi$
$972$	−16682.1	−	21237.0i	−0.550493	−	0.700800i
$973$	−38439.0	+	38439.0i	−1.26649	+	1.26649i
$974$	−28463.7	+	25249.2i	−0.936381	+	0.830633i
$975$	1250.79			0.0410846
$976$	−37867.9	+	23024.7i	−1.24193	+	0.755126i
$977$	11806.4			0.386611			0.193306	−	0.981139i	$-0.438079\pi$
$977$	11806.4			0.386611			0.193306	+	0.981139i	$0.438079\pi$
$978$	−6775.85	+	6010.63i	−0.221542	+	0.196522i
$979$	−154.000	+	154.000i	−0.00502744	+	0.00502744i
$980$	−626.603	+	492.210i	−0.0204246	+	0.0160439i
$981$	−15128.9	−	15128.9i	−0.492383	−	0.492383i
$982$	−1843.97	+	30812.2i	−0.0599221	+	1.00128i
$983$			28865.2i			0.936579i	0.883575	+	0.468290i	$0.155130\pi$
$983$			28865.2i			0.936579i	−0.883575	+	0.468290i	$0.844870\pi$
$984$	−5325.25	−	965.309i	−0.172523	−	0.0312733i
$985$		−	12646.6i		−	0.409091i
$986$	28446.0	+	1702.37i	0.918768	+	0.0549842i
$987$	−4086.90	−	4086.90i	−0.131801	−	0.131801i
$988$	4957.18	+	595.463i	0.159624	+	0.0191743i
$989$	17086.0	−	17086.0i	0.549347	−	0.549347i
$990$	3027.88	+	3413.37i	0.0972045	+	0.109580i
$991$	37756.7			1.21027			0.605137	−	0.796121i	$-0.293118\pi$
$991$	37756.7			1.21027			0.605137	+	0.796121i	$0.293118\pi$
$992$	−21151.2	−	39988.2i	−0.676966	−	1.27987i
$993$	6553.25			0.209427
$994$	7381.50	+	8321.23i	0.235540	+	0.265527i
$995$	−6686.97	+	6686.97i	−0.213056	+	0.213056i
$996$	16085.7	+	1932.23i	0.511741	+	0.0614711i
$997$	−11348.0	−	11348.0i	−0.360478	−	0.360478i	0.503511	−	0.863989i	$-0.332041\pi$
$997$	−11348.0	−	11348.0i	−0.360478	−	0.360478i	−0.863989	+	0.503511i	$0.832041\pi$
$998$	−12081.9	−	723.048i	−0.383212	−	0.0229335i
$999$			27809.5i			0.880733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.4.l.a.21.7	✓	48
4.3	odd	2		320.4.l.a.241.10		48
8.3	odd	2		640.4.l.a.481.15		48
8.5	even	2		640.4.l.b.481.10		48
16.3	odd	4		320.4.l.a.81.10		48
16.5	even	4		640.4.l.b.161.10		48
16.11	odd	4		640.4.l.a.161.15		48
16.13	even	4	inner	80.4.l.a.61.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.4.l.a.21.7	✓	48	1.1	even	1	trivial
80.4.l.a.61.7	yes	48	16.13	even	4	inner
320.4.l.a.81.10		48	16.3	odd	4
320.4.l.a.241.10		48	4.3	odd	2
640.4.l.a.161.15		48	16.11	odd	4
640.4.l.a.481.15		48	8.3	odd	2
640.4.l.b.161.10		48	16.5	even	4
640.4.l.b.481.10		48	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87695 - 2.11591i) q^{2} +(1.30312 - 1.30312i) q^{3} +(-0.954112 + 7.94290i) q^{4} +(3.53553 + 3.53553i) q^{5} +(-5.20319 - 0.311388i) q^{6} +17.9744i q^{7} +(18.5972 - 12.8896i) q^{8} +23.6037i q^{9} +(0.844833 - 14.1169i) q^{10} +(9.66542 + 9.66542i) q^{11} +(9.10726 + 11.5939i) q^{12} +(19.1969 - 19.1969i) q^{13} +(38.0322 - 33.7371i) q^{14} +9.21448 q^{15} +(-62.1793 - 15.1568i) q^{16} +103.565 q^{17} +(49.9433 - 44.3031i) q^{18} +(16.2553 - 16.2553i) q^{19} +(-31.4557 + 24.7091i) q^{20} +(23.4229 + 23.4229i) q^{21} +(2.30960 - 38.5926i) q^{22} +49.6583i q^{23} +(7.43774 - 41.0313i) q^{24} +25.0000i q^{25} +(-76.6503 - 4.58718i) q^{26} +(65.9429 + 65.9429i) q^{27} +(-142.769 - 17.1496i) q^{28} +(-68.7899 + 68.7899i) q^{29} +(-17.2951 - 19.4970i) q^{30} -249.904 q^{31} +(84.6371 + 160.014i) q^{32} +25.1905 q^{33} +(-194.386 - 219.134i) q^{34} +(-63.5492 + 63.5492i) q^{35} +(-187.482 - 22.5206i) q^{36} +(210.860 + 210.860i) q^{37} +(-64.9051 - 3.88428i) q^{38} -50.0318i q^{39} +(111.323 + 20.1795i) q^{40} -129.785i q^{41} +(5.59701 - 93.5242i) q^{42} +(-344.071 - 344.071i) q^{43} +(-85.9934 + 67.5496i) q^{44} +(-83.4518 + 83.4518i) q^{45} +(105.072 - 93.2063i) q^{46} -174.483 q^{47} +(-100.779 + 61.2761i) q^{48} +19.9202 q^{49} +(52.8976 - 46.9238i) q^{50} +(134.958 - 134.958i) q^{51} +(134.163 + 170.795i) q^{52} +(322.832 + 322.832i) q^{53} +(15.7574 - 263.301i) q^{54} +68.3448i q^{55} +(231.683 + 334.275i) q^{56} -42.3653i q^{57} +(274.668 + 16.4377i) q^{58} +(-21.0376 - 21.0376i) q^{59} +(-8.79164 + 73.1897i) q^{60} +(489.653 - 489.653i) q^{61} +(469.058 + 528.774i) q^{62} -424.264 q^{63} +(179.715 - 479.423i) q^{64} +135.742 q^{65} +(-47.2813 - 53.3007i) q^{66} +(261.470 - 261.470i) q^{67} +(-98.8126 + 822.606i) q^{68} +(64.7110 + 64.7110i) q^{69} +(253.743 + 15.1854i) q^{70} +218.795i q^{71} +(304.243 + 438.965i) q^{72} -1085.01i q^{73} +(50.3860 - 841.934i) q^{74} +(32.5781 + 32.5781i) q^{75} +(113.605 + 144.624i) q^{76} +(-173.730 + 173.730i) q^{77} +(-105.862 + 93.9071i) q^{78} -1155.60 q^{79} +(-166.250 - 273.425i) q^{80} -465.437 q^{81} +(-274.613 + 243.600i) q^{82} +(777.042 - 777.042i) q^{83} +(-208.394 + 163.698i) q^{84} +(366.157 + 366.157i) q^{85} +(-82.2175 + 1373.83i) q^{86} +179.283i q^{87} +(304.334 + 55.1666i) q^{88} +15.9331i q^{89} +(333.211 + 19.9412i) q^{90} +(345.052 + 345.052i) q^{91} +(-394.431 - 47.3796i) q^{92} +(-325.656 + 325.656i) q^{93} +(327.497 + 369.190i) q^{94} +114.942 q^{95} +(318.811 + 98.2257i) q^{96} -923.624 q^{97} +(-37.3892 - 42.1492i) q^{98} +(-228.140 + 228.140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{4} + 60 q^{6} + 60 q^{10} - 40 q^{11} - 156 q^{12} - 244 q^{14} + 120 q^{15} - 432 q^{16} - 320 q^{18} + 24 q^{19} + 40 q^{20} + 740 q^{22} + 1096 q^{24} + 272 q^{26} - 264 q^{27} - 308 q^{28}+ \cdots - 4456 q^{99}+O(q^{100}) \) 48 * q - 20 * q^4 + 60 * q^6 + 60 * q^10 - 40 * q^11 - 156 * q^12 - 244 * q^14 + 120 * q^15 - 432 * q^16 - 320 * q^18 + 24 * q^19 + 40 * q^20 + 740 * q^22 + 1096 * q^24 + 272 * q^26 - 264 * q^27 - 308 * q^28 + 400 * q^29 - 1600 * q^32 - 848 * q^34 + 1452 * q^36 + 16 * q^37 + 220 * q^38 + 900 * q^42 + 808 * q^43 - 1656 * q^44 - 2188 * q^46 + 1880 * q^47 - 40 * q^48 - 2352 * q^49 + 100 * q^50 + 2144 * q^51 + 792 * q^52 + 752 * q^53 + 1696 * q^54 + 2512 * q^56 - 2036 * q^58 - 2728 * q^59 + 980 * q^60 - 912 * q^61 - 344 * q^62 - 2520 * q^63 - 1040 * q^64 - 1920 * q^66 - 2040 * q^67 + 16 * q^68 - 528 * q^69 - 1240 * q^70 + 1240 * q^72 + 1928 * q^74 - 1024 * q^76 + 1904 * q^77 + 7568 * q^78 + 2832 * q^79 + 2320 * q^80 - 3888 * q^81 + 876 * q^82 + 2440 * q^83 + 896 * q^84 - 240 * q^85 + 244 * q^86 - 8320 * q^88 - 2340 * q^90 - 4448 * q^91 + 2524 * q^92 + 4272 * q^93 + 6676 * q^94 - 3040 * q^95 - 1080 * q^96 - 1436 * q^98 - 4456 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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