LMFDB - Embedded newform 110.4.g.d.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,4,Mod(31,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("110.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 36 x^{14} + 201 x^{13} + 7402 x^{12} + 11076 x^{11} + 759461 x^{10} + 2416768 x^{9} + \cdots + 19847025 $ x^16 - x^15 + 36x^14 + 201x^13 + 7402x^12 + 11076x^11 + 759461x^10 + 2416768x^9 + 35264614x^8 + 89458413x^7 + 558214578x^6 + 1288789920x^5 + 4043254401x^4 + 6511836240x^3 + 5366285640x^2 - 535268250x + 19847025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-1.77900 - 5.47521i$ of defining polynomial
Character	$\chi$	$=$	110.81
Dual form			110.4.g.d.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61803 - 1.17557i) q^{2} +(-1.46999 + 4.52416i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-4.04508 + 2.93893i) q^{5} +(7.69695 - 5.59216i) q^{6} +(1.62931 + 5.01451i) q^{7} +(2.47214 - 7.60845i) q^{8} +(3.53634 + 2.56930i) q^{9} +10.0000 q^{10} +(-32.0542 - 17.4221i) q^{11} -19.0279 q^{12} +(-48.2605 - 35.0633i) q^{13} +(3.25863 - 10.0290i) q^{14} +(-7.34994 - 22.6208i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(-25.8156 + 18.7561i) q^{17} +(-2.70152 - 8.31443i) q^{18} +(15.5701 - 47.9200i) q^{19} +(-16.1803 - 11.7557i) q^{20} -25.0815 q^{21} +(31.3839 + 65.8715i) q^{22} -209.392 q^{23} +(30.7878 + 22.3687i) q^{24} +(7.72542 - 23.7764i) q^{25} +(36.8677 + 113.467i) q^{26} +(-120.731 + 87.7163i) q^{27} +(-17.0624 + 12.3966i) q^{28} +(-19.1907 - 59.0630i) q^{29} +(-14.6999 + 45.2416i) q^{30} +(19.0194 + 13.8184i) q^{31} +32.0000 q^{32} +(125.940 - 119.408i) q^{33} +63.8197 q^{34} +(-21.3280 - 15.4957i) q^{35} +(-5.40304 + 16.6289i) q^{36} +(71.7803 + 220.917i) q^{37} +(-81.5263 + 59.2323i) q^{38} +(229.574 - 166.795i) q^{39} +(12.3607 + 38.0423i) q^{40} +(61.9952 - 190.802i) q^{41} +(40.5827 + 29.4851i) q^{42} +64.9004 q^{43} +(26.6564 - 143.476i) q^{44} -21.8558 q^{45} +(338.803 + 246.155i) q^{46} +(-4.55084 + 14.0061i) q^{47} +(-23.5198 - 72.3865i) q^{48} +(255.002 - 185.270i) q^{49} +(-40.4508 + 29.3893i) q^{50} +(-46.9070 - 144.365i) q^{51} +(73.7354 - 226.934i) q^{52} +(49.1688 + 35.7233i) q^{53} +298.464 q^{54} +(180.864 - 23.7310i) q^{55} +42.1806 q^{56} +(193.909 + 140.883i) q^{57} +(-38.3815 + 118.126i) q^{58} +(84.2972 + 259.440i) q^{59} +(76.9695 - 55.9216i) q^{60} +(-172.220 + 125.125i) q^{61} +(-14.5295 - 44.7173i) q^{62} +(-7.12198 + 21.9192i) q^{63} +(-51.7771 - 37.6183i) q^{64} +298.266 q^{65} +(-344.147 + 45.1552i) q^{66} -828.809 q^{67} +(-103.262 - 75.0245i) q^{68} +(307.803 - 947.320i) q^{69} +(16.2931 + 50.1451i) q^{70} +(-948.877 + 689.400i) q^{71} +(28.2907 - 20.5544i) q^{72} +(272.036 + 837.241i) q^{73} +(143.561 - 441.834i) q^{74} +(96.2119 + 69.9020i) q^{75} +201.544 q^{76} +(35.1370 - 189.122i) q^{77} -567.538 q^{78} +(1046.25 + 760.145i) q^{79} +(24.7214 - 76.0845i) q^{80} +(-182.898 - 562.904i) q^{81} +(-324.611 + 235.844i) q^{82} +(-1077.22 + 782.644i) q^{83} +(-31.0024 - 95.4157i) q^{84} +(49.3034 - 151.740i) q^{85} +(-105.011 - 76.2951i) q^{86} +295.420 q^{87} +(-211.797 + 200.813i) q^{88} -420.741 q^{89} +(35.3634 + 25.6930i) q^{90} +(97.1938 - 299.132i) q^{91} +(-258.822 - 796.573i) q^{92} +(-90.4749 + 65.7339i) q^{93} +(23.8285 - 17.3124i) q^{94} +(77.8507 + 239.600i) q^{95} +(-47.0396 + 144.773i) q^{96} +(-105.269 - 76.4821i) q^{97} -630.400 q^{98} +(-68.5918 - 143.967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 3 q^{3} - 16 q^{4} - 20 q^{5} - 16 q^{6} - 38 q^{7} - 32 q^{8} + 25 q^{9} + 160 q^{10} + 65 q^{11} + 88 q^{12} + 85 q^{13} - 76 q^{14} - 15 q^{15} - 64 q^{16} + 109 q^{17} - 280 q^{18}+ \cdots + 10702 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 3 * q^3 - 16 * q^4 - 20 * q^5 - 16 * q^6 - 38 * q^7 - 32 * q^8 + 25 * q^9 + 160 * q^10 + 65 * q^11 + 88 * q^12 + 85 * q^13 - 76 * q^14 - 15 * q^15 - 64 * q^16 + 109 * q^17 - 280 * q^18 + 12 * q^19 - 80 * q^20 - 36 * q^21 + 140 * q^22 + 432 * q^23 - 64 * q^24 - 100 * q^25 - 490 * q^26 - 507 * q^27 + 88 * q^28 + 369 * q^29 - 30 * q^30 - 334 * q^31 + 512 * q^32 - 280 * q^33 + 568 * q^34 + 110 * q^35 - 560 * q^36 - 360 * q^37 - 236 * q^38 + 279 * q^39 - 160 * q^40 - 595 * q^41 - 442 * q^42 + 612 * q^43 - 120 * q^44 + 1150 * q^45 - 206 * q^46 + 1066 * q^47 - 48 * q^48 - 1468 * q^49 - 200 * q^50 + 3404 * q^51 - 980 * q^52 - 533 * q^53 + 1556 * q^54 - 125 * q^55 + 256 * q^56 + 470 * q^57 + 738 * q^58 - 1842 * q^59 - 160 * q^60 + 1246 * q^61 - 178 * q^62 - 4622 * q^63 - 256 * q^64 + 1600 * q^65 + 920 * q^66 - 2200 * q^67 + 436 * q^68 + 4777 * q^69 - 380 * q^70 - 2158 * q^71 + 200 * q^72 - 55 * q^73 - 720 * q^74 - 200 * q^75 + 848 * q^76 + 3704 * q^77 - 1812 * q^78 + 1595 * q^79 - 320 * q^80 - 9487 * q^81 + 700 * q^82 - 486 * q^83 + 956 * q^84 - 1255 * q^85 - 1686 * q^86 - 1234 * q^87 - 640 * q^88 - 3512 * q^89 + 250 * q^90 + 3913 * q^91 - 452 * q^92 - 2423 * q^93 - 3748 * q^94 + 60 * q^95 - 96 * q^96 + 1101 * q^97 + 7224 * q^98 + 10702 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$3$	−1.46999	+	4.52416i	−0.282899	+	0.870674i	0.704121	+	0.710080i	$0.251341\pi$
$3$	−1.46999	+	4.52416i	−0.282899	+	0.870674i	−0.987020	+	0.160594i	$0.948659\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$	−4.04508	+	2.93893i	−0.361803	+	0.262866i
$5$	−4.04508	+	2.93893i	−0.361803	+	0.262866i
$6$	7.69695	−	5.59216i	0.523711	−	0.380499i
$7$	1.62931	+	5.01451i	0.0879747	+	0.270758i	0.985359	−	0.170491i	$-0.0545354\pi$
$7$	1.62931	+	5.01451i	0.0879747	+	0.270758i	−0.897385	+	0.441249i	$0.854535\pi$
$8$	2.47214	−	7.60845i	0.109254	−	0.336249i
$9$	3.53634	+	2.56930i	0.130976	+	0.0951593i
$10$	10.0000			0.316228
$11$	−32.0542	−	17.4221i	−0.878609	−	0.477542i
$11$	−32.0542	−	17.4221i	−0.878609	−	0.477542i
$12$	−19.0279			−0.457740
$13$	−48.2605	−	35.0633i	−1.02962	−	0.748062i	−0.0613863	−	0.998114i	$-0.519552\pi$
$13$	−48.2605	−	35.0633i	−1.02962	−	0.748062i	−0.968232	+	0.250052i	$0.919552\pi$
$14$	3.25863	−	10.0290i	0.0622075	−	0.191455i
$15$	−7.34994	−	22.6208i	−0.126516	−	0.389377i
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	−25.8156	+	18.7561i	−0.368306	+	0.267590i	−0.756508	−	0.653984i	$-0.773096\pi$
$17$	−25.8156	+	18.7561i	−0.368306	+	0.267590i	0.388202	+	0.921574i	$0.373096\pi$
$18$	−2.70152	−	8.31443i	−0.0353753	−	0.108874i
$19$	15.5701	−	47.9200i	0.188002	−	0.578610i	−0.811985	−	0.583678i	$-0.801613\pi$
$19$	15.5701	−	47.9200i	0.188002	−	0.578610i	0.999987	+	0.00506764i	$0.00161309\pi$
$20$	−16.1803	−	11.7557i	−0.180902	−	0.131433i
$21$	−25.0815			−0.260630
$22$	31.3839	+	65.8715i	0.304139	+	0.638357i
$23$	−209.392			−1.89831			−0.949156	−	0.314806i	$-0.898060\pi$
$23$	−209.392			−1.89831			−0.949156	+	0.314806i	$0.898060\pi$
$24$	30.7878	+	22.3687i	0.261856	+	0.190249i
$25$	7.72542	−	23.7764i	0.0618034	−	0.190211i
$26$	36.8677	+	113.467i	0.278090	+	0.855874i
$27$	−120.731	+	87.7163i	−0.860545	+	0.625223i
$28$	−17.0624	+	12.3966i	−0.115160	+	0.0836689i
$29$	−19.1907	−	59.0630i	−0.122884	−	0.378197i	0.870626	−	0.491946i	$-0.163714\pi$
$29$	−19.1907	−	59.0630i	−0.122884	−	0.378197i	−0.993510	+	0.113748i	$0.963714\pi$
$30$	−14.6999	+	45.2416i	−0.0894606	+	0.275331i
$31$	19.0194	+	13.8184i	0.110193	+	0.0800600i	0.641517	−	0.767109i	$-0.278305\pi$
$31$	19.0194	+	13.8184i	0.110193	+	0.0800600i	−0.531324	+	0.847169i	$0.678305\pi$
$32$	32.0000			0.176777
$33$	125.940	−	119.408i	0.664341	−	0.629886i
$34$	63.8197			0.321911
$35$	−21.3280	−	15.4957i	−0.103003	−	0.0748357i
$36$	−5.40304	+	16.6289i	−0.0250141	+	0.0769855i
$37$	71.7803	+	220.917i	0.318935	+	0.981582i	0.974104	+	0.226100i	$0.0725975\pi$
$37$	71.7803	+	220.917i	0.318935	+	0.981582i	−0.655169	+	0.755483i	$0.727402\pi$
$38$	−81.5263	+	59.2323i	−0.348035	+	0.252862i
$39$	229.574	−	166.795i	0.942596	−	0.684836i
$40$	12.3607	+	38.0423i	0.0488599	+	0.150375i
$41$	61.9952	−	190.802i	0.236147	−	0.726786i	−0.760820	−	0.648963i	$-0.775203\pi$
$41$	61.9952	−	190.802i	0.236147	−	0.726786i	0.996967	−	0.0778232i	$-0.0247970\pi$
$42$	40.5827	+	29.4851i	0.149096	+	0.108325i
$43$	64.9004			0.230168			0.115084	−	0.993356i	$-0.463286\pi$
$43$	64.9004			0.230168			0.115084	+	0.993356i	$0.463286\pi$
$44$	26.6564	−	143.476i	0.0913320	−	0.491588i
$45$	−21.8558			−0.0724015
$46$	338.803	+	246.155i	1.08595	+	0.788990i
$47$	−4.55084	+	14.0061i	−0.0141236	+	0.0434679i	−0.957870	−	0.287202i	$-0.907275\pi$
$47$	−4.55084	+	14.0061i	−0.0141236	+	0.0434679i	0.943746	+	0.330670i	$0.107275\pi$
$48$	−23.5198	−	72.3865i	−0.0707248	−	0.217669i
$49$	255.002	−	185.270i	0.743447	−	0.540146i
$50$	−40.4508	+	29.3893i	−0.114412	+	0.0831254i
$51$	−46.9070	−	144.365i	−0.128790	−	0.396375i
$52$	73.7354	−	226.934i	0.196640	−	0.605195i
$53$	49.1688	+	35.7233i	0.127431	+	0.0925843i	0.649675	−	0.760212i	$-0.274905\pi$
$53$	49.1688	+	35.7233i	0.127431	+	0.0925843i	−0.522244	+	0.852796i	$0.674905\pi$
$54$	298.464			0.752144
$55$	180.864	−	23.7310i	0.443413	−	0.0581798i
$56$	42.1806			0.100654
$57$	193.909	+	140.883i	0.450595	+	0.327377i
$58$	−38.3815	+	118.126i	−0.0868920	+	0.267426i
$59$	84.2972	+	259.440i	0.186009	+	0.572478i	0.999964	−	0.00844990i	$-0.00268972\pi$
$59$	84.2972	+	259.440i	0.186009	+	0.572478i	−0.813955	+	0.580928i	$0.802690\pi$
$60$	76.9695	−	55.9216i	0.165612	−	0.120324i
$61$	−172.220	+	125.125i	−0.361483	+	0.262633i	−0.753671	−	0.657252i	$-0.771719\pi$
$61$	−172.220	+	125.125i	−0.361483	+	0.262633i	0.392187	+	0.919885i	$0.371719\pi$
$62$	−14.5295	−	44.7173i	−0.0297621	−	0.0915984i
$63$	−7.12198	+	21.9192i	−0.0142426	+	0.0438343i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$	298.266			0.569159
$66$	−344.147	+	45.1552i	−0.641841	+	0.0842155i
$67$	−828.809			−1.51127			−0.755636	−	0.654992i	$-0.772672\pi$
$67$	−828.809			−1.51127			−0.755636	+	0.654992i	$0.772672\pi$
$68$	−103.262	−	75.0245i	−0.184153	−	0.133795i
$69$	307.803	−	947.320i	0.537031	−	1.65281i
$70$	16.2931	+	50.1451i	0.0278200	+	0.0856213i
$71$	−948.877	+	689.400i	−1.58607	+	1.15235i	−0.676780	+	0.736186i	$0.736625\pi$
$71$	−948.877	+	689.400i	−1.58607	+	1.15235i	−0.909291	+	0.416162i	$0.863375\pi$
$72$	28.2907	−	20.5544i	0.0463068	−	0.0336439i
$73$	272.036	+	837.241i	0.436156	+	1.34235i	0.891897	+	0.452238i	$0.149374\pi$
$73$	272.036	+	837.241i	0.436156	+	1.34235i	−0.455741	+	0.890112i	$0.650626\pi$
$74$	143.561	−	441.834i	0.225521	−	0.694084i
$75$	96.2119	+	69.9020i	0.148128	+	0.107621i
$76$	201.544			0.304193
$77$	35.1370	−	189.122i	0.0520030	−	0.279902i
$78$	−567.538			−0.823859
$79$	1046.25	+	760.145i	1.49003	+	1.08257i	0.974148	+	0.225909i	$0.0725352\pi$
$79$	1046.25	+	760.145i	1.49003	+	1.08257i	0.515881	+	0.856660i	$0.327465\pi$
$80$	24.7214	−	76.0845i	0.0345492	−	0.106331i
$81$	−182.898	−	562.904i	−0.250890	−	0.772159i
$82$	−324.611	+	235.844i	−0.437163	+	0.317617i
$83$	−1077.22	+	782.644i	−1.42458	+	1.03502i	−0.433582	+	0.901114i	$0.642751\pi$
$83$	−1077.22	+	782.644i	−1.42458	+	1.03502i	−0.990995	+	0.133901i	$0.957249\pi$
$84$	−31.0024	−	95.4157i	−0.0402696	−	0.123937i
$85$	49.3034	−	151.740i	0.0629142	−	0.193630i
$86$	−105.011	−	76.2951i	−0.131670	−	0.0956640i
$87$	295.420			0.364050
$88$	−211.797	+	200.813i	−0.256565	+	0.243258i
$89$	−420.741			−0.501106			−0.250553	−	0.968103i	$-0.580612\pi$
$89$	−420.741			−0.501106			−0.250553	+	0.968103i	$0.580612\pi$
$90$	35.3634	+	25.6930i	0.0414181	+	0.0300920i
$91$	97.1938	−	299.132i	0.111964	−	0.344588i
$92$	−258.822	−	796.573i	−0.293305	−	0.902701i
$93$	−90.4749	+	65.7339i	−0.100880	+	0.0732934i
$94$	23.8285	−	17.3124i	0.0261460	−	0.0189962i
$95$	77.8507	+	239.600i	0.0840770	+	0.258762i
$96$	−47.0396	+	144.773i	−0.0500100	+	0.153915i
$97$	−105.269	−	76.4821i	−0.110190	−	0.0800575i	0.531326	−	0.847168i	$-0.321694\pi$
$97$	−105.269	−	76.4821i	−0.110190	−	0.0800575i	−0.641516	+	0.767110i	$0.721694\pi$
$98$	−630.400			−0.649796
$99$	−68.5918	−	143.967i	−0.0696337	−	0.146154i
$100$	100.000			0.100000
$101$	−935.928	−	679.991i	−0.922062	−	0.669917i	0.0219743	−	0.999759i	$-0.493005\pi$
$101$	−935.928	−	679.991i	−0.922062	−	0.669917i	−0.944036	+	0.329841i	$0.893005\pi$
$102$	−93.8141	+	288.730i	−0.0910684	+	0.280280i
$103$	164.051	+	504.898i	0.156936	+	0.483000i	0.998352	−	0.0573882i	$-0.0182773\pi$
$103$	164.051	+	504.898i	0.156936	+	0.483000i	−0.841416	+	0.540389i	$0.818277\pi$
$104$	−386.084	+	280.506i	−0.364025	+	0.264480i
$105$	101.457	−	73.7127i	0.0942969	−	0.0685107i
$106$	−37.5617	−	115.603i	−0.0344180	−	0.105928i
$107$	127.945	−	393.775i	0.115597	−	0.355772i	−0.876474	−	0.481450i	$-0.840110\pi$
$107$	127.945	−	393.775i	0.115597	−	0.355772i	0.992071	+	0.125677i	$0.0401104\pi$
$108$	−482.925	−	350.865i	−0.430273	−	0.312611i
$109$	603.139			0.530002			0.265001	−	0.964248i	$-0.414628\pi$
$109$	603.139			0.530002			0.265001	+	0.964248i	$0.414628\pi$
$110$	−320.542	−	174.221i	−0.277841	−	0.151012i
$111$	−1104.98			−0.944865
$112$	−68.2496	−	49.5862i	−0.0575802	−	0.0418345i
$113$	437.391	−	1346.15i	0.364127	−	1.12067i	−0.586399	−	0.810022i	$-0.699455\pi$
$113$	437.391	−	1346.15i	0.364127	−	1.12067i	0.950526	−	0.310645i	$-0.100545\pi$
$114$	−148.134	−	455.909i	−0.121702	−	0.374559i
$115$	847.007	−	615.387i	0.686816	−	0.499001i
$116$	200.968	−	146.012i	0.160857	−	0.116869i
$117$	−80.5772	−	247.991i	−0.0636698	−	0.195956i
$118$	168.594	−	518.880i	0.131529	−	0.404803i
$119$	−136.115	−	98.8930i	−0.104854	−	0.0761807i
$120$	−190.279			−0.144750
$121$	723.941	+	1116.90i	0.543908	+	0.839145i
$122$	425.751			0.315948
$123$	772.085	+	560.952i	0.565988	+	0.411214i
$124$	−29.0591	+	89.4346i	−0.0210450	+	0.0647699i
$125$	38.6271	+	118.882i	0.0276393	+	0.0850651i
$126$	37.2912	−	27.0936i	0.0263664	−	0.0191563i
$127$	−546.997	+	397.417i	−0.382190	+	0.277677i	−0.762248	−	0.647285i	$-0.775904\pi$
$127$	−546.997	+	397.417i	−0.382190	+	0.277677i	0.380057	+	0.924963i	$0.375904\pi$
$128$	39.5542	+	121.735i	0.0273135	+	0.0840623i
$129$	−95.4028	+	293.620i	−0.0651143	+	0.200401i
$130$	−482.605	−	350.633i	−0.325594	−	0.236558i
$131$	1180.88			0.787588			0.393794	−	0.919199i	$-0.371162\pi$
$131$	1180.88			0.787588			0.393794	+	0.919199i	$0.371162\pi$
$132$	609.924	+	331.506i	0.402175	+	0.218590i
$133$	265.664			0.173203
$134$	1341.04	+	974.324i	0.864540	+	0.628125i
$135$	230.576	−	709.640i	0.146999	−	0.452415i
$136$	78.8854	+	242.784i	0.0497380	+	0.153078i
$137$	132.838	−	96.5122i	0.0828400	−	0.0601868i	−0.545594	−	0.838049i	$-0.683696\pi$
$137$	132.838	−	96.5122i	0.0828400	−	0.0601868i	0.628434	+	0.777863i	$0.283696\pi$
$138$	−1611.68	+	1170.95i	−0.994167	+	0.722305i
$139$	−94.8419	−	291.893i	−0.0578733	−	0.178116i	0.917941	−	0.396717i	$-0.129851\pi$
$139$	−94.8419	−	291.893i	−0.0578733	−	0.178116i	−0.975814	+	0.218601i	$0.929851\pi$
$140$	32.5863	−	100.290i	0.0196717	−	0.0605434i
$141$	−56.6759	−	41.1775i	−0.0338509	−	0.0245941i
$142$	2345.75			1.38628
$143$	936.074	+	1964.72i	0.547402	+	1.14894i
$144$	−69.9385			−0.0404737
$145$	251.210	+	182.515i	0.143875	+	0.104531i
$146$	544.072	−	1674.48i	0.308409	−	0.949185i
$147$	463.340	+	1426.01i	0.259970	+	0.800106i
$148$	−751.693	+	546.137i	−0.417492	+	0.303326i
$149$	−691.306	+	502.263i	−0.380094	+	0.276154i	−0.761384	−	0.648301i	$-0.775480\pi$
$149$	−691.306	+	502.263i	−0.380094	+	0.276154i	0.381290	+	0.924455i	$0.375480\pi$
$150$	−73.4994	−	226.208i	−0.0400080	−	0.123132i
$151$	−871.827	+	2683.21i	−0.469856	+	1.44607i	0.382915	+	0.923784i	$0.374920\pi$
$151$	−871.827	+	2683.21i	−0.469856	+	1.44607i	−0.852771	+	0.522285i	$0.825080\pi$
$152$	−326.105	−	236.929i	−0.174017	−	0.126431i
$153$	−139.483			−0.0737027
$154$	−279.179	+	264.700i	−0.146084	+	0.138507i
$155$	−117.546			−0.0609132
$156$	918.296	+	667.181i	0.471298	+	0.342418i
$157$	1070.53	−	3294.74i	0.544186	−	1.67483i	−0.178731	−	0.983898i	$-0.557199\pi$
$157$	1070.53	−	3294.74i	0.544186	−	1.67483i	0.722917	−	0.690935i	$-0.242801\pi$
$158$	−799.264	−	2459.88i	−0.402443	−	1.23859i
$159$	−233.895	+	169.935i	−0.116661	+	0.0847591i
$160$	−129.443	+	94.0456i	−0.0639584	+	0.0464685i
$161$	−341.165	−	1050.00i	−0.167003	−	0.513984i
$162$	−365.797	+	1125.81i	−0.177406	+	0.545999i
$163$	−292.966	−	212.852i	−0.140778	−	0.102281i	0.515167	−	0.857090i	$-0.327730\pi$
$163$	−292.966	−	212.852i	−0.140778	−	0.102281i	−0.655945	+	0.754808i	$0.727730\pi$
$164$	802.483			0.382094
$165$	−158.505	+	853.142i	−0.0747855	+	0.402527i
$166$	2663.03			1.24513
$167$	−922.747	−	670.415i	−0.427571	−	0.310648i	0.353106	−	0.935583i	$-0.385126\pi$
$167$	−922.747	−	670.415i	−0.427571	−	0.310648i	−0.780677	+	0.624935i	$0.785126\pi$
$168$	−62.0049	+	190.831i	−0.0284749	+	0.0876367i
$169$	420.728	+	1294.87i	0.191501	+	0.589380i
$170$	−258.156	+	187.561i	−0.116469	+	0.0846194i
$171$	178.182	−	129.457i	0.0796838	−	0.0578936i
$172$	80.2214	+	246.896i	0.0355629	+	0.109451i
$173$	495.330	−	1524.47i	0.217684	−	0.669961i	−0.781269	−	0.624195i	$-0.785427\pi$
$173$	495.330	−	1524.47i	0.217684	−	0.669961i	0.998952	−	0.0457662i	$-0.0145729\pi$
$174$	−478.000	−	347.287i	−0.208259	−	0.151309i
$175$	131.814			0.0569384
$176$	578.765	−	75.9393i	0.247875	−	0.0325235i
$177$	−1297.66			−0.551064
$178$	680.773	+	494.611i	0.286664	+	0.208273i
$179$	658.008	−	2025.14i	0.274759	−	0.845621i	−0.714524	−	0.699611i	$-0.753357\pi$
$179$	658.008	−	2025.14i	0.274759	−	0.845621i	0.989283	−	0.146010i	$-0.0466432\pi$
$180$	−27.0152	−	83.1443i	−0.0111866	−	0.0344289i
$181$	−2154.71	+	1565.49i	−0.884852	+	0.642883i	−0.934531	−	0.355882i	$-0.884180\pi$
$181$	−2154.71	+	1565.49i	−0.884852	+	0.642883i	0.0496783	+	0.998765i	$0.484180\pi$
$182$	−508.913	+	369.747i	−0.207270	+	0.150591i
$183$	−312.924	−	963.081i	−0.126404	−	0.389033i
$184$	−517.645	+	1593.15i	−0.207398	+	0.638306i
$185$	−939.617	−	682.671i	−0.373416	−	0.271303i
$186$	223.666			0.0881721
$187$	1154.27	−	151.451i	0.451382	−	0.0592255i
$188$	−58.9074			−0.0228525
$189$	−636.564	−	462.491i	−0.244990	−	0.177996i
$190$	155.701	−	479.200i	0.0594514	−	0.182973i
$191$	886.735	+	2729.09i	0.335926	+	1.03387i	0.966264	+	0.257554i	$0.0829165\pi$
$191$	886.735	+	2729.09i	0.335926	+	1.03387i	−0.630338	+	0.776321i	$0.717084\pi$
$192$	246.302	−	178.949i	0.0925800	−	0.0672633i
$193$	3463.46	−	2516.35i	1.29174	−	0.938503i	0.291900	−	0.956449i	$-0.405713\pi$
$193$	3463.46	−	2516.35i	1.29174	−	0.938503i	0.999839	+	0.0179460i	$0.00571271\pi$
$194$	80.4180	+	247.501i	0.0297612	+	0.0915956i
$195$	−438.447	+	1349.40i	−0.161015	+	0.495552i
$196$	1020.01	+	741.080i	0.371723	+	0.270073i
$197$	−26.6781			−0.00964842			−0.00482421	−	0.999988i	$-0.501536\pi$
$197$	−26.6781			−0.00964842			−0.00482421	+	0.999988i	$0.501536\pi$
$198$	−58.2597	+	313.578i	−0.0209108	+	0.112551i
$199$	398.468			0.141943			0.0709715	−	0.997478i	$-0.477390\pi$
$199$	398.468			0.141943			0.0709715	+	0.997478i	$0.477390\pi$
$200$	−161.803	−	117.557i	−0.0572061	−	0.0415627i
$201$	1218.34	−	3749.66i	0.427537	−	1.31582i
$202$	714.985	+	2200.50i	0.249040	+	0.766468i
$203$	264.904	−	192.464i	0.0915894	−	0.0665436i
$204$	491.217	−	356.890i	0.168589	−	0.122487i
$205$	309.976	+	954.009i	0.105608	+	0.325029i
$206$	328.102	−	1009.80i	0.110971	−	0.341533i
$207$	−740.480	−	537.990i	−0.248632	−	0.180642i
$208$	954.451			0.318170
$209$	−1333.95	+	1264.77i	−0.441491	+	0.418593i
$210$	−250.815			−0.0824185
$211$	−2840.87	−	2064.02i	−0.926890	−	0.673425i	0.0183391	−	0.999832i	$-0.494162\pi$
$211$	−2840.87	−	2064.02i	−0.926890	−	0.673425i	−0.945229	+	0.326407i	$0.894162\pi$
$212$	−75.1233	+	231.206i	−0.0243372	+	0.0749023i
$213$	−1724.11	−	5306.28i	−0.554621	−	1.70695i
$214$	−669.929	+	486.732i	−0.213997	+	0.155478i
$215$	−262.528	+	190.738i	−0.0832756	+	0.0605032i
$216$	368.922	+	1135.42i	0.116213	+	0.357666i
$217$	−38.3040	+	117.888i	−0.0119827	+	0.0368789i
$218$	−975.899	−	709.032i	−0.303194	−	0.220283i
$219$	−4187.70			−1.29214
$220$	313.839	+	658.715i	0.0961772	+	0.201866i
$221$	1903.52			0.579388
$222$	1787.89	+	1298.98i	0.540521	+	0.392711i
$223$	−279.902	+	861.450i	−0.0840521	+	0.258686i	−0.984246	−	0.176803i	$-0.943424\pi$
$223$	−279.902	+	861.450i	−0.0840521	+	0.258686i	0.900194	+	0.435489i	$0.143424\pi$
$224$	52.1381	+	160.464i	0.0155519	+	0.0478638i
$225$	88.4085	−	64.2325i	0.0261951	−	0.0190319i
$226$	−2290.21	+	1663.94i	−0.674082	+	0.489749i
$227$	−1070.80	−	3295.59i	−0.313091	−	0.963596i	−0.976533	−	0.215368i	$-0.930905\pi$
$227$	−1070.80	−	3295.59i	−0.313091	−	0.963596i	0.663442	−	0.748228i	$-0.269095\pi$
$228$	−296.267	+	911.817i	−0.0860561	+	0.264853i
$229$	−2546.86	−	1850.40i	−0.734940	−	0.533965i	0.156182	−	0.987728i	$-0.450081\pi$
$229$	−2546.86	−	1850.40i	−0.734940	−	0.533965i	−0.891122	+	0.453763i	$0.850081\pi$
$230$	−2093.92			−0.600299
$231$	803.967	+	436.972i	0.228992	+	0.124462i
$232$	−496.820			−0.140594
$233$	4682.01	+	3401.68i	1.31643	+	0.956444i	0.999969	+	0.00783910i	$0.00249529\pi$
$233$	4682.01	+	3401.68i	1.31643	+	0.956444i	0.316463	+	0.948605i	$0.397505\pi$
$234$	−161.154	+	495.982i	−0.0450213	+	0.138561i
$235$	−22.7542	−	70.0303i	−0.00631626	−	0.0194395i
$236$	−882.772	+	641.371i	−0.243490	+	0.176906i
$237$	−4976.99	+	3615.99i	−1.36409	+	0.991072i
$238$	103.982	+	320.025i	0.0283200	+	0.0871601i
$239$	−658.174	+	2025.65i	−0.178133	+	0.548236i	−0.999763	−	0.0217850i	$-0.993065\pi$
$239$	−658.174	+	2025.65i	−0.178133	+	0.548236i	0.821630	+	0.570021i	$0.193065\pi$
$240$	307.878	+	223.687i	0.0828060	+	0.0601621i
$241$	1811.07			0.484072			0.242036	−	0.970267i	$-0.422185\pi$
$241$	1811.07			0.484072			0.242036	+	0.970267i	$0.422185\pi$
$242$	141.635	−	2658.23i	0.0376226	−	0.706105i
$243$	−1213.74			−0.320418
$244$	−688.879	−	500.500i	−0.180742	−	0.131317i
$245$	−487.011	+	1498.87i	−0.126996	+	0.390853i
$246$	−589.820	−	1815.28i	−0.152868	−	0.470480i
$247$	−2431.65	+	1766.70i	−0.626406	+	0.455111i
$248$	152.155	−	110.547i	0.0389591	−	0.0283055i
$249$	−1957.31	−	6023.97i	−0.498150	−	1.53315i
$250$	77.2542	−	237.764i	0.0195440	−	0.0601501i
$251$	−5116.75	−	3717.54i	−1.28672	−	0.934856i	−0.286986	−	0.957935i	$-0.592653\pi$
$251$	−5116.75	−	3717.54i	−1.28672	−	0.934856i	−0.999734	+	0.0230786i	$0.992653\pi$
$252$	−92.1889			−0.0230451
$253$	6711.88	+	3648.04i	1.66787	+	0.906523i
$254$	1352.25			0.334047
$255$	614.021	+	446.112i	0.150790	+	0.109555i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	2132.10	+	6561.93i	0.517497	+	1.59269i	0.778692	+	0.627407i	$0.215884\pi$
$257$	2132.10	+	6561.93i	0.517497	+	1.59269i	−0.261195	+	0.965286i	$0.584116\pi$
$258$	499.536	−	362.934i	0.120542	−	0.0875786i
$259$	−990.839	+	719.887i	−0.237713	+	0.172709i
$260$	368.677	+	1134.67i	0.0879399	+	0.270651i
$261$	83.8857	−	258.174i	0.0198942	−	0.0612281i
$262$	−1910.70	−	1388.21i	−0.450549	−	0.327343i
$263$	2508.42			0.588121			0.294061	−	0.955787i	$-0.404993\pi$
$263$	2508.42			0.588121			0.294061	+	0.955787i	$0.404993\pi$
$264$	−597.169	−	1253.40i	−0.139217	−	0.292202i
$265$	−303.880			−0.0704423
$266$	−429.853	−	312.307i	−0.0990827	−	0.0719878i
$267$	618.484	−	1903.50i	0.141763	−	0.436300i
$268$	−1024.46	−	3152.98i	−0.233504	−	0.718652i
$269$	−5061.17	+	3677.16i	−1.14716	+	0.833458i	−0.988100	−	0.153812i	$-0.950845\pi$
$269$	−5061.17	+	3677.16i	−1.14716	+	0.833458i	−0.159056	+	0.987270i	$0.550845\pi$
$270$	−1207.31	+	877.163i	−0.272128	+	0.197713i
$271$	−1539.48	−	4738.03i	−0.345080	−	1.06205i	−0.961541	−	0.274662i	$-0.911434\pi$
$271$	−1539.48	−	4738.03i	−0.345080	−	1.06205i	0.616460	−	0.787386i	$-0.288566\pi$
$272$	157.771	−	485.569i	0.0351701	−	0.108242i
$273$	1210.44	+	879.440i	0.268350	+	0.194967i
$274$	−328.393			−0.0724048
$275$	−661.867	+	627.540i	−0.145135	+	0.137608i
$276$	3984.29			0.868934
$277$	−2554.60	−	1856.03i	−0.554120	−	0.402592i	0.275182	−	0.961392i	$-0.411262\pi$
$277$	−2554.60	−	1856.03i	−0.554120	−	0.402592i	−0.829302	+	0.558800i	$0.811262\pi$
$278$	−189.684	+	583.787i	−0.0409226	+	0.125947i
$279$	31.7554	+	97.7331i	0.00681415	+	0.0209718i
$280$	−170.624	+	123.966i	−0.0364169	+	0.0264584i
$281$	1599.68	−	1162.24i	0.339605	−	0.246737i	−0.404890	−	0.914365i	$-0.632690\pi$
$281$	1599.68	−	1162.24i	0.339605	−	0.246737i	0.744495	+	0.667628i	$0.232690\pi$
$282$	43.2965	+	133.253i	0.00914281	+	0.0281387i
$283$	82.7754	−	254.757i	0.0173869	−	0.0535113i	−0.941987	−	0.335650i	$-0.891044\pi$
$283$	82.7754	−	254.757i	0.0173869	−	0.0535113i	0.959374	+	0.282139i	$0.0910439\pi$
$284$	−3795.51	−	2757.60i	−0.793035	−	0.576174i
$285$	−1198.43			−0.249083
$286$	795.071	−	4279.41i	0.164383	−	0.884779i
$287$	1057.79			0.217558
$288$	113.163	+	82.2176i	0.0231534	+	0.0168219i
$289$	−1203.55	+	3704.14i	−0.244972	+	0.753947i
$290$	−191.907	−	590.630i	−0.0388593	−	0.119597i
$291$	500.760	−	363.824i	0.100877	−	0.0732911i
$292$	−2848.80	+	2069.77i	−0.570936	+	0.414809i
$293$	377.189	+	1160.87i	0.0752068	+	0.231463i	0.981592	−	0.190989i	$-0.0611695\pi$
$293$	377.189	+	1160.87i	0.0752068	+	0.231463i	−0.906385	+	0.422452i	$0.861170\pi$
$294$	926.680	−	2852.03i	0.183827	−	0.565761i
$295$	−1103.46	−	801.714i	−0.217784	−	0.158229i
$296$	1858.29			0.364901
$297$	5398.14	−	708.285i	1.05465	−	0.138380i
$298$	1709.00			0.332214
$299$	10105.3	+	7341.96i	1.95454	+	1.42005i
$300$	−146.999	+	452.416i	−0.0282899	+	0.0870674i
$301$	105.743	+	325.444i	0.0202490	+	0.0623199i
$302$	4564.94	−	3316.63i	0.869811	−	0.631955i
$303$	4452.19	−	3234.70i	0.844130	−	0.613297i
$304$	249.122	+	766.720i	0.0470005	+	0.144653i
$305$	328.911	−	1012.28i	0.0617487	−	0.190043i
$306$	225.688	+	163.972i	0.0421625	+	0.0306328i
$307$	−2811.48			−0.522670			−0.261335	−	0.965248i	$-0.584163\pi$
$307$	−2811.48			−0.522670			−0.261335	+	0.965248i	$0.584163\pi$
$308$	762.895	−	100.099i	0.141136	−	0.0185184i
$309$	−2525.39			−0.464933
$310$	190.194	+	138.184i	0.0348461	+	0.0253172i
$311$	−1238.78	+	3812.57i	−0.225867	+	0.695147i	0.772335	+	0.635215i	$0.219088\pi$
$311$	−1238.78	+	3812.57i	−0.225867	+	0.695147i	−0.998202	+	0.0599323i	$0.980912\pi$
$312$	−701.516	−	2159.04i	−0.127293	−	0.391768i
$313$	6367.63	−	4626.35i	1.14990	−	0.835454i	0.161435	−	0.986883i	$-0.448388\pi$
$313$	6367.63	−	4626.35i	1.14990	−	0.835454i	0.988468	+	0.151430i	$0.0483877\pi$
$314$	−5605.34	+	4072.52i	−1.00741	+	0.731929i
$315$	−35.6099	−	109.596i	−0.00636950	−	0.0196033i
$316$	−1598.53	+	4919.76i	−0.284570	+	0.875817i
$317$	8264.13	+	6004.24i	1.46423	+	1.06382i	0.982237	+	0.187645i	$0.0600855\pi$
$317$	8264.13	+	6004.24i	1.46423	+	1.06382i	0.481989	+	0.876177i	$0.339915\pi$
$318$	578.221			0.101965
$319$	−413.858	+	2227.56i	−0.0726382	+	0.390970i
$320$	320.000			0.0559017
$321$	1593.42	+	1157.69i	0.277059	+	0.201295i
$322$	−682.329	+	2099.99i	−0.118089	+	0.363441i
$323$	496.841	+	1529.12i	0.0855881	+	0.263413i
$324$	1915.34	−	1391.57i	0.328419	−	0.238610i
$325$	−1206.51	+	876.582i	−0.205924	+	0.149612i
$326$	223.806	+	688.804i	0.0380229	+	0.117022i
$327$	−886.606	+	2728.69i	−0.149937	+	0.461459i
$328$	−1298.45	−	943.376i	−0.218581	−	0.158809i
$329$	−77.6483			−0.0130118
$330$	1259.40	−	1194.08i	0.210083	−	0.199187i
$331$	2929.37			0.486444			0.243222	−	0.969971i	$-0.421796\pi$
$331$	2929.37			0.486444			0.243222	+	0.969971i	$0.421796\pi$
$332$	−4308.87	−	3130.57i	−0.712288	−	0.517508i
$333$	−313.763	+	965.663i	−0.0516339	+	0.158913i
$334$	704.916	+	2169.51i	0.115483	+	0.355420i
$335$	3352.60	−	2435.81i	0.546783	−	0.397261i
$336$	324.662	−	235.881i	0.0527136	−	0.0382986i
$337$	1275.27	+	3924.88i	0.206138	+	0.634427i	0.999665	+	0.0258918i	$0.00824254\pi$
$337$	1275.27	+	3924.88i	0.206138	+	0.634427i	−0.793527	+	0.608535i	$0.791757\pi$
$338$	841.456	−	2589.73i	0.135412	−	0.416754i
$339$	5447.24	+	3957.65i	0.872724	+	0.634071i
$340$	638.197			0.101797
$341$	−368.906	−	774.296i	−0.0585847	−	0.122963i
$342$	−440.490			−0.0696462
$343$	2807.62	+	2039.85i	0.441974	+	0.321113i
$344$	160.443	−	493.792i	0.0251468	−	0.0773938i
$345$	1539.02	+	4736.60i	0.240167	+	0.739160i
$346$	−2593.58	+	1884.35i	−0.402982	+	0.292784i
$347$	8855.10	−	6433.61i	1.36993	−	0.995315i	0.372191	−	0.928156i	$-0.378607\pi$
$347$	8855.10	−	6433.61i	1.36993	−	0.995315i	0.997742	−	0.0671583i	$-0.0213932\pi$
$348$	365.160	+	1123.85i	0.0562489	+	0.173116i
$349$	3177.20	−	9778.40i	0.487311	−	1.49979i	−0.341296	−	0.939956i	$-0.610866\pi$
$349$	3177.20	−	9778.40i	0.487311	−	1.49979i	0.828606	−	0.559832i	$-0.189134\pi$
$350$	−213.280	−	154.957i	−0.0325723	−	0.0236651i
$351$	8902.16			1.35374
$352$	−1025.73	−	557.507i	−0.155318	−	0.0844183i
$353$	−11681.5			−1.76132			−0.880658	−	0.473752i	$-0.842899\pi$
$353$	−11681.5			−1.76132			−0.880658	+	0.473752i	$0.842899\pi$
$354$	2099.66	+	1525.49i	0.315242	+	0.229037i
$355$	1812.19	−	5577.36i	0.270933	−	0.833846i
$356$	−520.065	−	1600.59i	−0.0774252	−	0.238290i
$357$	647.494	−	470.432i	0.0959916	−	0.0697420i
$358$	−3445.38	+	2503.21i	−0.508642	+	0.369550i
$359$	−1387.03	−	4268.83i	−0.203912	−	0.627577i	−0.999756	−	0.0220754i	$-0.992973\pi$
$359$	−1387.03	−	4268.83i	−0.203912	−	0.627577i	0.795844	−	0.605501i	$-0.207027\pi$
$360$	−54.0304	+	166.289i	−0.00791015	+	0.0243449i
$361$	3495.15	+	2539.38i	0.509572	+	0.370226i
$362$	5326.73			0.773389
$363$	−6117.22	+	1633.39i	−0.884493	+	0.236173i
$364$	1258.10			0.181161
$365$	−3561.00	−	2587.22i	−0.510661	−	0.371017i
$366$	−625.848	+	1926.16i	−0.0893815	+	0.275088i
$367$	−2576.82	−	7930.64i	−0.366509	−	1.12800i	−0.949031	−	0.315184i	$-0.897934\pi$
$367$	−2576.82	−	7930.64i	−0.366509	−	1.12800i	0.582521	−	0.812815i	$-0.302066\pi$
$368$	2710.42	−	1969.24i	0.383942	−	0.278950i
$369$	709.463	−	515.455i	0.100090	−	0.0727196i
$370$	717.803	+	2209.17i	0.100856	+	0.310404i
$371$	−99.0233	+	304.762i	−0.0138572	+	0.0426482i
$372$	−361.900	−	262.935i	−0.0504398	−	0.0366467i
$373$	−13794.3			−1.91486			−0.957430	−	0.288667i	$-0.906788\pi$
$373$	−13794.3			−1.91486			−0.957430	+	0.288667i	$0.906788\pi$
$374$	−2045.69	−	1111.87i	−0.282834	−	0.153726i
$375$	−594.622			−0.0818831
$376$	95.3141	+	69.2498i	0.0130730	+	0.00949809i
$377$	−1144.79	+	3523.30i	−0.156392	+	0.481324i
$378$	486.291	+	1496.65i	0.0661696	+	0.203649i
$379$	108.942	−	79.1507i	0.0147650	−	0.0107274i	−0.580378	−	0.814347i	$-0.697095\pi$
$379$	108.942	−	79.1507i	0.0147650	−	0.0107274i	0.595143	+	0.803620i	$0.297095\pi$
$380$	−815.263	+	592.323i	−0.110058	+	0.0799620i
$381$	−993.896	−	3058.90i	−0.133645	−	0.411318i
$382$	1773.47	−	5458.18i	0.237536	−	0.731060i
$383$	−5813.14	−	4223.49i	−0.775555	−	0.563473i	0.128087	−	0.991763i	$-0.459116\pi$
$383$	−5813.14	−	4223.49i	−0.775555	−	0.563473i	−0.903642	+	0.428290i	$0.859116\pi$
$384$	−608.893			−0.0809178
$385$	413.684	+	868.280i	0.0547618	+	0.114939i
$386$	−8562.15			−1.12902
$387$	229.510	+	166.749i	0.0301464	+	0.0219026i
$388$	160.836	−	495.002i	0.0210444	−	0.0647679i
$389$	2233.47	+	6873.91i	0.291109	+	0.895941i	0.984501	+	0.175380i	$0.0561154\pi$
$389$	2233.47	+	6873.91i	0.291109	+	0.895941i	−0.693392	+	0.720561i	$0.743885\pi$
$390$	2295.74	−	1667.95i	0.298075	−	0.216564i
$391$	5405.57	−	3927.38i	0.699160	−	0.507969i
$392$	−779.217	−	2398.18i	−0.100399	−	0.308996i
$393$	−1735.88	+	5342.49i	−0.222808	+	0.685732i
$394$	43.1661	+	31.3620i	0.00551949	+	0.00401014i
$395$	−6466.18			−0.823668
$396$	462.900	−	438.892i	0.0587414	−	0.0556949i
$397$	−8639.95			−1.09226			−0.546129	−	0.837701i	$-0.683899\pi$
$397$	−8639.95			−1.09226			−0.546129	+	0.837701i	$0.683899\pi$
$398$	−644.735	−	468.428i	−0.0812001	−	0.0589954i
$399$	−390.523	+	1201.91i	−0.0489990	+	0.150803i
$400$	123.607	+	380.423i	0.0154508	+	0.0475528i
$401$	−8292.46	+	6024.83i	−1.03268	+	0.750288i	−0.968844	−	0.247672i	$-0.920334\pi$
$401$	−8292.46	+	6024.83i	−1.03268	+	0.750288i	−0.0638389	+	0.997960i	$0.520334\pi$
$402$	−6379.31	+	4634.84i	−0.791470	+	0.575037i
$403$	−433.367	−	1333.76i	−0.0535671	−	0.164862i
$404$	1429.97	−	4401.00i	0.176098	−	0.541975i
$405$	2394.17	+	1739.47i	0.293747	+	0.213419i
$406$	−654.880			−0.0800521
$407$	1547.98	−	8331.88i	0.188527	−	1.01473i
$408$	−1214.36			−0.147352
$409$	−4477.27	−	3252.92i	−0.541287	−	0.393268i	0.283276	−	0.959039i	$-0.408579\pi$
$409$	−4477.27	−	3252.92i	−0.541287	−	0.393268i	−0.824563	+	0.565770i	$0.808579\pi$
$410$	619.952	−	1908.02i	0.0746763	−	0.229830i
$411$	241.366	+	742.850i	0.0289677	+	0.0891534i
$412$	−1717.97	+	1248.18i	−0.205432	+	0.149255i
$413$	−1163.62	+	845.419i	−0.138639	+	0.100727i
$414$	565.676	+	1740.97i	0.0671533	+	0.206677i
$415$	2057.30	−	6331.72i	0.243347	−	0.748944i
$416$	−1544.33	−	1122.02i	−0.182013	−	0.132240i
$417$	1459.99			0.171453
$418$	3645.21	−	478.285i	0.426539	−	0.0559657i
$419$	8259.17			0.962976			0.481488	−	0.876453i	$-0.340097\pi$
$419$	8259.17			0.962976			0.481488	+	0.876453i	$0.340097\pi$
$420$	405.827	+	294.851i	0.0471484	+	0.0342553i
$421$	−3256.88	+	10023.6i	−0.377032	+	1.16039i	0.565065	+	0.825047i	$0.308851\pi$
$421$	−3256.88	+	10023.6i	−0.377032	+	1.16039i	−0.942097	+	0.335340i	$0.891149\pi$
$422$	2170.23	+	6679.30i	0.250345	+	0.770481i
$423$	−52.0791	+	37.8377i	−0.00598622	+	0.00434925i
$424$	393.351	−	285.786i	0.0450538	−	0.0327335i
$425$	246.517	+	758.701i	0.0281361	+	0.0865939i
$426$	−3448.23	+	10612.6i	−0.392176	+	1.20699i
$427$	−908.041	−	659.731i	−0.102911	−	0.0747696i
$428$	1656.16			0.187040
$429$	−10264.7	+	1346.83i	−1.15521	+	0.151574i
$430$	649.004			0.0727855
$431$	−2366.22	−	1719.16i	−0.264447	−	0.192132i	0.447658	−	0.894205i	$-0.352258\pi$
$431$	−2366.22	−	1719.16i	−0.264447	−	0.192132i	−0.712105	+	0.702073i	$0.752258\pi$
$432$	737.843	−	2270.85i	0.0821748	−	0.252908i
$433$	−2992.11	−	9208.77i	−0.332082	−	1.02204i	−0.968141	−	0.250404i	$-0.919437\pi$
$433$	−2992.11	−	9208.77i	−0.332082	−	1.02204i	0.636059	−	0.771640i	$-0.280563\pi$
$434$	200.562	−	145.717i	0.0221827	−	0.0161167i
$435$	−1195.00	+	868.219i	−0.131715	+	0.0956963i
$436$	745.521	+	2294.48i	0.0818898	+	0.252031i
$437$	−3260.26	+	10034.0i	−0.356886	+	1.09838i
$438$	6775.83	+	4922.93i	0.739182	+	0.537047i
$439$	−14027.6			−1.52506			−0.762528	−	0.646955i	$-0.776042\pi$
$439$	−14027.6			−1.52506			−0.762528	+	0.646955i	$0.776042\pi$
$440$	266.564	−	1434.76i	0.0288817	−	0.155454i
$441$	1377.79			0.148773
$442$	−3079.97	−	2237.73i	−0.331446	−	0.240809i
$443$	−3416.04	+	10513.5i	−0.366368	+	1.12756i	0.582752	+	0.812650i	$0.301976\pi$
$443$	−3416.04	+	10513.5i	−0.366368	+	1.12756i	−0.949120	+	0.314914i	$0.898024\pi$
$444$	−1365.83	−	4203.59i	−0.145990	−	0.449310i
$445$	1701.93	−	1236.53i	0.181302	−	0.131724i
$446$	1465.59	−	1064.81i	0.155600	−	0.113050i
$447$	−1256.11	−	3865.89i	−0.132912	−	0.409062i
$448$	104.276	−	320.929i	0.0109968	−	0.0338448i
$449$	9817.24	+	7132.64i	1.03186	+	0.749688i	0.968680	−	0.248314i	$-0.0798764\pi$
$449$	9817.24	+	7132.64i	1.03186	+	0.749688i	0.0631780	+	0.998002i	$0.479876\pi$
$450$	−218.558			−0.0228954
$451$	−5311.37	+	5035.91i	−0.554552	+	0.525791i
$452$	5661.71			0.589169
$453$	−10857.7	−	7888.56i	−1.12613	−	0.818183i
$454$	−2141.61	+	6591.19i	−0.221389	+	0.681365i
$455$	485.969	+	1495.66i	0.0500716	+	0.154105i
$456$	1551.28	−	1127.07i	0.159310	−	0.115745i
$457$	68.7702	−	49.9645i	0.00703925	−	0.00511431i	−0.584260	−	0.811566i	$-0.698615\pi$
$457$	68.7702	−	49.9645i	0.00703925	−	0.00511431i	0.591299	+	0.806452i	$0.298615\pi$
$458$	1945.63	+	5988.03i	0.198501	+	0.610922i
$459$	1471.53	−	4528.90i	0.149641	−	0.460546i
$460$	3388.03	+	2461.55i	0.343408	+	0.249500i
$461$	−7350.96			−0.742665			−0.371332	−	0.928500i	$-0.621099\pi$
$461$	−7350.96			−0.742665			−0.371332	+	0.928500i	$0.621099\pi$
$462$	−787.154	−	1652.16i	−0.0792678	−	0.166375i
$463$	−12302.6			−1.23488			−0.617441	−	0.786617i	$-0.711831\pi$
$463$	−12302.6			−1.23488			−0.617441	+	0.786617i	$0.711831\pi$
$464$	803.872	+	584.047i	0.0804285	+	0.0584347i
$465$	172.792	−	531.798i	0.0172323	−	0.0530356i
$466$	−3576.74	−	11008.1i	−0.355556	−	1.09429i
$467$	7604.58	−	5525.05i	0.753529	−	0.547471i	−0.143390	−	0.989666i	$-0.545800\pi$
$467$	7604.58	−	5525.05i	0.753529	−	0.547471i	0.896919	+	0.442196i	$0.145800\pi$
$468$	843.816	−	613.068i	0.0833449	−	0.0605536i
$469$	−1350.39	−	4156.08i	−0.132954	−	0.409189i
$470$	−45.5084	+	140.061i	−0.00446627	+	0.0137458i
$471$	13332.2	+	9686.45i	1.30428	+	0.947617i
$472$	2182.33			0.212818
$473$	−2080.33	−	1130.70i	−0.202228	−	0.109915i
$474$	12303.8			1.19226
$475$	−1019.08	−	740.404i	−0.0984391	−	0.0715202i
$476$	207.965	−	640.049i	0.0200253	−	0.0616315i
$477$	82.0939	+	252.659i	0.00788013	+	0.0242525i
$478$	3446.24	−	2503.84i	0.329765	−	0.239588i
$479$	15033.1	−	10922.2i	1.43399	−	1.04185i	0.444732	−	0.895664i	$-0.353299\pi$
$479$	15033.1	−	10922.2i	1.43399	−	1.04185i	0.989257	−	0.146190i	$-0.0467010\pi$
$480$	−235.198	−	723.865i	−0.0223651	−	0.0688328i
$481$	4281.93	−	13178.4i	0.405902	−	1.24924i
$482$	−2930.38	−	2129.04i	−0.276919	−	0.201194i
$483$	5251.86			0.494757
$484$	−3354.11	+	4134.60i	−0.314999	+	0.388299i
$485$	650.595			0.0609114
$486$	1963.87	+	1426.84i	0.183299	+	0.133174i
$487$	3393.47	−	10444.0i	0.315755	−	0.971794i	−0.659687	−	0.751540i	$-0.729311\pi$
$487$	3393.47	−	10444.0i	0.315755	−	0.971794i	0.975443	−	0.220254i	$-0.0706887\pi$
$488$	526.257	+	1619.65i	0.0488167	+	0.150242i
$489$	1393.63	−	1012.53i	0.128880	−	0.0936366i
$490$	2550.02	−	1852.70i	0.235098	−	0.170809i
$491$	−2144.07	−	6598.75i	−0.197068	−	0.606512i	−0.999946	−	0.0103696i	$-0.996699\pi$
$491$	−2144.07	−	6598.75i	−0.197068	−	0.606512i	0.802878	−	0.596143i	$-0.203301\pi$
$492$	−1179.64	+	3630.56i	−0.108094	+	0.332679i
$493$	1603.21	+	1164.80i	0.146461	+	0.106410i
$494$	6011.38			0.547499
$495$	700.569	+	380.773i	0.0636126	+	0.0345747i
$496$	−376.148			−0.0340515
$497$	−5003.02	−	3634.91i	−0.451542	−	0.328064i
$498$	−3914.61	+	12047.9i	−0.352245	+	1.08410i
$499$	358.233	+	1102.53i	0.0321377	+	0.0989098i	0.965839	−	0.259144i	$-0.0834404\pi$
$499$	358.233	+	1102.53i	0.0321377	+	0.0989098i	−0.933701	+	0.358054i	$0.883440\pi$
$500$	−404.508	+	293.893i	−0.0361803	+	0.0262866i
$501$	4389.49	−	3189.15i	0.391433	−	0.284393i
$502$	3908.85	+	12030.2i	0.347531	+	1.06959i
$503$	−5400.62	+	16621.4i	−0.478731	+	1.47338i	0.362127	+	0.932129i	$0.382051\pi$
$503$	−5400.62	+	16621.4i	−0.478731	+	1.47338i	−0.840859	+	0.541255i	$0.817949\pi$
$504$	149.165	+	108.375i	0.0131832	+	0.00957815i
$505$	5784.35			0.509703
$506$	−6571.52	−	13792.9i	−0.577351	−	1.21180i
$507$	−6476.65			−0.567333
$508$	−2187.99	−	1589.67i	−0.191095	−	0.138839i
$509$	6965.85	−	21438.7i	0.606593	−	1.86690i	0.121146	−	0.992635i	$-0.461343\pi$
$509$	6965.85	−	21438.7i	0.606593	−	1.86690i	0.485447	−	0.874266i	$-0.338657\pi$
$510$	−469.070	−	1443.65i	−0.0407270	−	0.125345i
$511$	−3755.12	+	2728.26i	−0.325082	+	0.236186i
$512$	−414.217	+	300.946i	−0.0357538	+	0.0259767i
$513$	2323.56	+	7151.19i	0.199976	+	0.615463i
$514$	4264.20	−	13123.9i	0.365926	−	1.12620i
$515$	−2147.46	−	1560.22i	−0.183744	−	0.133498i
$516$	−1234.92			−0.105357
$517$	389.888	−	369.668i	0.0331669	−	0.0314467i
$518$	2449.49			0.207769
$519$	6168.81	+	4481.90i	0.521735	+	0.379063i
$520$	737.354	−	2269.34i	0.0621829	−	0.191379i
$521$	2612.43	+	8040.24i	0.219679	+	0.676102i	0.998788	+	0.0492142i	$0.0156717\pi$
$521$	2612.43	+	8040.24i	0.219679	+	0.676102i	−0.779109	+	0.626888i	$0.784328\pi$
$522$	−439.231	+	319.120i	−0.0368288	+	0.0267577i
$523$	13743.6	−	9985.28i	1.14907	−	0.834848i	0.160713	−	0.987001i	$-0.448621\pi$
$523$	13743.6	−	9985.28i	1.14907	−	0.834848i	0.988357	+	0.152153i	$0.0486206\pi$
$524$	1459.65	+	4492.34i	0.121689	+	0.374520i
$525$	−193.765	+	596.348i	−0.0161078	+	0.0495748i
$526$	−4058.71	−	2948.83i	−0.336441	−	0.244439i
$527$	−750.177			−0.0620080
$528$	−507.216	+	2730.05i	−0.0418064	+	0.225020i
$529$	31677.9			2.60359
$530$	491.688	+	357.233i	0.0402973	+	0.0292777i
$531$	−368.476	+	1134.05i	−0.0301139	+	0.0926812i
$532$	328.379	+	1010.65i	0.0267613	+	0.0823629i
$533$	−9682.05	+	7034.42i	−0.786822	+	0.571660i
$534$	−3238.42	+	2352.85i	−0.262435	+	0.190670i
$535$	639.725	+	1968.87i	0.0516967	+	0.159106i
$536$	−2048.93	+	6305.96i	−0.165112	+	0.508164i
$537$	8194.79	+	5953.86i	0.658531	+	0.478451i
$538$	12511.9			1.00265
$539$	−11401.7	+	1496.00i	−0.911141	+	0.119550i
$540$	2984.64			0.237849
$541$	−10335.0	−	7508.79i	−0.821321	−	0.596725i	0.0957696	−	0.995404i	$-0.469469\pi$
$541$	−10335.0	−	7508.79i	−0.821321	−	0.596725i	−0.917091	+	0.398679i	$0.869469\pi$
$542$	−3078.96	+	9476.07i	−0.244009	+	0.750982i
$543$	−3915.12	−	12049.5i	−0.309418	−	0.952289i
$544$	−826.099	+	600.196i	−0.0651079	+	0.0473037i
$545$	−2439.75	+	1772.58i	−0.191757	+	0.139319i
$546$	−924.698	−	2845.93i	−0.0724788	−	0.223067i
$547$	−1588.87	+	4890.05i	−0.124196	+	0.382237i	−0.993754	−	0.111595i	$-0.964404\pi$
$547$	−1588.87	+	4890.05i	−0.124196	+	0.382237i	0.869558	+	0.493832i	$0.164404\pi$
$548$	531.350	+	386.049i	0.0414200	+	0.0300934i
$549$	−930.511			−0.0723374
$550$	1808.64	−	237.310i	0.140220	−	0.0183981i
$551$	−3129.10			−0.241931
$552$	−6446.71	−	4683.81i	−0.497084	−	0.361152i
$553$	−2107.09	+	6484.95i	−0.162030	+	0.498676i
$554$	1951.54	+	6006.24i	0.149663	+	0.460615i
$555$	4469.74	−	3247.45i	0.341855	−	0.248372i
$556$	993.197	−	721.600i	0.0757571	−	0.0550407i
$557$	6460.94	+	19884.7i	0.491488	+	1.51264i	0.822359	+	0.568969i	$0.192658\pi$
$557$	6460.94	+	19884.7i	0.491488	+	1.51264i	−0.330871	+	0.943676i	$0.607342\pi$
$558$	63.5108	−	195.466i	0.00481833	−	0.0148293i
$559$	−3132.13	−	2275.62i	−0.236985	−	0.172180i
$560$	421.806			0.0318295
$561$	−1011.57	+	5444.72i	−0.0761296	+	0.409762i
$562$	−3954.62			−0.296825
$563$	1550.29	+	1126.35i	0.116052	+	0.0843164i	0.644297	−	0.764775i	$-0.277150\pi$
$563$	1550.29	+	1126.35i	0.116052	+	0.0843164i	−0.528246	+	0.849092i	$0.677150\pi$
$564$	86.5931	−	266.506i	0.00646494	−	0.0198970i
$565$	2186.96	+	6730.76i	0.162842	+	0.501177i
$566$	−433.418	+	314.896i	−0.0321871	+	0.0233853i
$567$	2524.69	−	1834.29i	0.186996	−	0.135861i
$568$	2899.51	+	8923.77i	0.214191	+	0.659214i
$569$	7480.61	−	23023.0i	0.551149	−	1.69626i	−0.154754	−	0.987953i	$-0.549459\pi$
$569$	7480.61	−	23023.0i	0.551149	−	1.69626i	0.705903	−	0.708309i	$-0.250541\pi$
$570$	1939.09	+	1408.83i	0.142491	+	0.103526i
$571$	12007.8			0.880053			0.440027	−	0.897985i	$-0.354969\pi$
$571$	12007.8			0.880053			0.440027	+	0.897985i	$0.354969\pi$
$572$	−6317.20	+	5989.57i	−0.461775	+	0.437826i
$573$	−13650.3			−0.995201
$574$	−1711.54	−	1243.50i	−0.124457	−	0.0904231i
$575$	−1617.64	+	4978.58i	−0.117322	+	0.361080i
$576$	−86.4487	−	266.062i	−0.00625352	−	0.0192464i
$577$	−4494.62	+	3265.53i	−0.324287	+	0.235608i	−0.738003	−	0.674798i	$-0.764231\pi$
$577$	−4494.62	+	3265.53i	−0.324287	+	0.235608i	0.413716	+	0.910406i	$0.364231\pi$
$578$	6301.86	−	4578.57i	0.453500	−	0.329487i
$579$	6293.13	+	19368.3i	0.451698	+	1.39018i
$580$	−383.815	+	1181.26i	−0.0274776	+	0.0845675i
$581$	−5679.70	−	4126.54i	−0.405566	−	0.294661i
$582$	−1237.95			−0.0881694
$583$	−953.693	−	2001.70i	−0.0677495	−	0.142199i
$584$	7042.62			0.499016
$585$	1054.77	+	766.335i	0.0745459	+	0.0541608i
$586$	754.378	−	2321.74i	0.0531793	−	0.163669i
$587$	4033.55	+	12414.0i	0.283616	+	0.872880i	0.986810	+	0.161882i	$0.0517564\pi$
$587$	4033.55	+	12414.0i	0.283616	+	0.872880i	−0.703194	+	0.710998i	$0.748244\pi$
$588$	−4852.16	+	3525.30i	−0.340306	+	0.247246i
$589$	958.312	−	696.255i	0.0670400	−	0.0487074i
$590$	842.972	+	2594.40i	0.0588214	+	0.181034i
$591$	39.2165	−	120.696i	0.00272953	−	0.00840063i
$592$	−3006.77	−	2184.55i	−0.208746	−	0.151663i
$593$	13129.3			0.909198			0.454599	−	0.890696i	$-0.349783\pi$
$593$	13129.3			0.909198			0.454599	+	0.890696i	$0.349783\pi$
$594$	−9567.01	−	5199.86i	−0.660841	−	0.359180i
$595$	841.234			0.0579618
$596$	−2765.22	−	2009.05i	−0.190047	−	0.138077i
$597$	−585.743	+	1802.73i	−0.0401556	+	0.123586i
$598$	−7719.79	−	23759.1i	−0.527902	−	1.62472i
$599$	5512.17	−	4004.82i	0.375995	−	0.273176i	−0.383697	−	0.923459i	$-0.625349\pi$
$599$	5512.17	−	4004.82i	0.375995	−	0.273176i	0.759693	+	0.650282i	$0.225349\pi$
$600$	769.695	−	559.216i	0.0523711	−	0.0380499i
$601$	7068.51	+	21754.6i	0.479751	+	1.47652i	0.839441	+	0.543450i	$0.182882\pi$
$601$	7068.51	+	21754.6i	0.479751	+	1.47652i	−0.359690	+	0.933072i	$0.617118\pi$
$602$	211.486	−	650.888i	0.0143182	−	0.0440668i
$603$	−2930.95	−	2129.46i	−0.197940	−	0.143811i
$604$	−11285.2			−0.760243
$605$	−6210.90	−	2390.35i	−0.417370	−	0.160631i
$606$	−11006.4			−0.737797
$607$	−23896.8	−	17362.0i	−1.59792	−	1.16096i	−0.891345	−	0.453326i	$-0.850237\pi$
$607$	−23896.8	−	17362.0i	−1.59792	−	1.16096i	−0.706579	−	0.707634i	$-0.749763\pi$
$608$	498.245	−	1533.44i	0.0332343	−	0.102285i
$609$	481.333	+	1481.39i	0.0320272	+	0.0985697i
$610$	−1722.20	+	1251.25i	−0.114311	+	0.0830519i
$611$	710.724	−	516.371i	0.0470586	−	0.0341901i
$612$	−172.410	−	530.624i	−0.0113877	−	0.0350477i
$613$	−4045.97	+	12452.2i	−0.266583	+	0.820458i	0.724742	+	0.689021i	$0.241959\pi$
$613$	−4045.97	+	12452.2i	−0.266583	+	0.820458i	−0.991325	+	0.131437i	$0.958041\pi$
$614$	4549.07	+	3305.09i	0.298999	+	0.217236i
$615$	−4771.75			−0.312870
$616$	−1352.06	−	734.874i	−0.0884354	−	0.0480664i
$617$	22439.3			1.46414			0.732069	−	0.681231i	$-0.238555\pi$
$617$	22439.3			1.46414			0.732069	+	0.681231i	$0.238555\pi$
$618$	4086.16	+	2968.77i	0.265970	+	0.193239i
$619$	−5373.58	+	16538.2i	−0.348922	+	1.07387i	0.610529	+	0.791994i	$0.290957\pi$
$619$	−5373.58	+	16538.2i	−0.348922	+	1.07387i	−0.959451	+	0.281877i	$0.909043\pi$
$620$	−145.295	−	447.173i	−0.00941161	−	0.0289660i
$621$	25280.1	−	18367.1i	1.63358	−	1.18687i
$622$	6486.33	−	4712.59i	0.418132	−	0.303790i
$623$	−685.519	−	2109.81i	−0.0440847	−	0.135679i
$624$	−1403.03	+	4318.09i	−0.0900099	+	0.277022i
$625$	−505.636	−	367.366i	−0.0323607	−	0.0235114i
$626$	−15741.6			−1.00505
$627$	−3761.12	−	7894.21i	−0.239561	−	0.502814i
$628$	13857.2			0.880512
$629$	−5996.60	−	4356.79i	−0.380127	−	0.276179i
$630$	−71.2198	+	219.192i	−0.00450392	+	0.0138616i
$631$	−1041.31	−	3204.82i	−0.0656955	−	0.202190i	0.912820	−	0.408361i	$-0.133900\pi$
$631$	−1041.31	−	3204.82i	−0.0656955	−	0.202190i	−0.978516	+	0.206171i	$0.933900\pi$
$632$	8370.00	−	6081.16i	0.526805	−	0.382746i
$633$	13514.0	−	9818.48i	0.848550	−	0.616508i
$634$	−6313.23	−	19430.1i	−0.395474	−	1.21714i
$635$	1044.67	−	3215.17i	0.0652859	−	0.200929i
$636$	−935.581	−	679.739i	−0.0583305	−	0.0423796i
$637$	−18802.7			−1.16953
$638$	3288.29	−	3117.75i	0.204051	−	0.193468i
$639$	−5126.82			−0.317393
$640$	−517.771	−	376.183i	−0.0319792	−	0.0232343i
$641$	−4688.72	+	14430.4i	−0.288913	+	0.889184i	0.696285	+	0.717765i	$0.254835\pi$
$641$	−4688.72	+	14430.4i	−0.288913	+	0.889184i	−0.985198	+	0.171418i	$0.945165\pi$
$642$	−1217.26	−	3746.35i	−0.0748311	−	0.230307i
$643$	−11710.5	+	8508.19i	−0.718224	+	0.521820i	−0.885816	−	0.464036i	$-0.846401\pi$
$643$	−11710.5	+	8508.19i	−0.718224	+	0.521820i	0.167593	+	0.985856i	$0.446401\pi$
$644$	3572.72	−	2595.74i	0.218610	−	0.158830i
$645$	−477.014	−	1468.10i	−0.0291200	−	0.0896222i
$646$	993.681	−	3058.24i	0.0605199	−	0.186261i
$647$	4190.00	+	3044.21i	0.254600	+	0.184977i	0.707763	−	0.706450i	$-0.249705\pi$
$647$	4190.00	+	3044.21i	0.254600	+	0.184977i	−0.453163	+	0.891428i	$0.649705\pi$
$648$	−4734.97			−0.287048
$649$	1817.91	−	9784.77i	0.109953	−	0.591812i
$650$	2982.66			0.179984
$651$	−477.035	−	346.586i	−0.0287196	−	0.0208660i
$652$	447.612	−	1377.61i	0.0268862	−	0.0827474i
$653$	−5716.42	−	17593.3i	−0.342574	−	1.05434i	−0.962870	−	0.269967i	$-0.912987\pi$
$653$	−5716.42	−	17593.3i	−0.342574	−	1.05434i	0.620295	−	0.784368i	$-0.287013\pi$
$654$	4642.33	−	3372.85i	0.277568	−	0.201665i
$655$	−4776.76	+	3470.52i	−0.284952	+	0.207030i
$656$	991.924	+	3052.83i	0.0590368	+	0.181697i
$657$	−1189.11	+	3659.71i	−0.0706113	+	0.217319i
$658$	125.638	+	91.2811i	0.00744356	+	0.00540806i
$659$	−26549.4			−1.56937			−0.784687	−	0.619892i	$-0.787176\pi$
$659$	−26549.4			−1.56937			−0.784687	+	0.619892i	$0.787176\pi$
$660$	−3441.47	+	451.552i	−0.202968	+	0.0266313i
$661$	−6614.64			−0.389228			−0.194614	−	0.980880i	$-0.562345\pi$
$661$	−6614.64			−0.389228			−0.194614	+	0.980880i	$0.562345\pi$
$662$	−4739.82	−	3443.68i	−0.278276	−	0.202179i
$663$	−2798.16	+	8611.84i	−0.163909	+	0.504459i
$664$	3291.68	+	10130.8i	0.192382	+	0.592092i
$665$	−1074.63	+	780.767i	−0.0626654	+	0.0455291i
$666$	1642.88	−	1193.63i	0.0955863	−	0.0694475i
$667$	4018.38	+	12367.3i	0.233272	+	0.717937i
$668$	1409.83	−	4339.02i	0.0816588	−	0.251320i
$669$	−3485.88	−	2532.64i	−0.201453	−	0.146364i
$670$	−8288.09			−0.477906
$671$	7700.31	−	1010.35i	0.443021	−	0.0581284i
$672$	−802.608			−0.0460733
$673$	−9876.97	−	7176.04i	−0.565719	−	0.411019i	0.267828	−	0.963467i	$-0.413694\pi$
$673$	−9876.97	−	7176.04i	−0.565719	−	0.411019i	−0.833548	+	0.552447i	$0.813694\pi$
$674$	2550.54	−	7849.76i	0.145761	−	0.448608i
$675$	1152.88	+	3548.20i	0.0657398	+	0.202326i
$676$	−4405.92	+	3201.09i	−0.250678	+	0.182128i
$677$	−298.572	+	216.926i	−0.0169499	+	0.0123148i	−0.596228	−	0.802815i	$-0.703335\pi$
$677$	−298.572	+	216.926i	−0.0169499	+	0.0123148i	0.579278	+	0.815130i	$0.303335\pi$
$678$	−4161.32	−	12807.2i	−0.235715	−	0.725456i
$679$	212.005	−	652.484i	0.0119823	−	0.0368778i
$680$	−1032.62	−	750.245i	−0.0582343	−	0.0423097i
$681$	16483.9			0.927551
$682$	−313.337	+	1686.51i	−0.0175928	+	0.0946919i
$683$	12318.6			0.690129			0.345065	−	0.938579i	$-0.387857\pi$
$683$	12318.6			0.690129			0.345065	+	0.938579i	$0.387857\pi$
$684$	712.728	+	517.827i	0.0398419	+	0.0289468i
$685$	−253.697	+	780.800i	−0.0141508	+	0.0435516i
$686$	−2144.83	−	6601.11i	−0.119373	−	0.367393i
$687$	12115.4	−	8802.33i	0.672824	−	0.488835i
$688$	−840.089	+	610.360i	−0.0465525	+	0.0338223i
$689$	−1120.34	−	3448.04i	−0.0619469	−	0.190653i
$690$	3078.03	−	9473.20i	0.169824	−	0.522665i
$691$	6974.30	+	5067.13i	0.383958	+	0.278962i	0.762975	−	0.646428i	$-0.223738\pi$
$691$	6974.30	+	5067.13i	0.383958	+	0.278962i	−0.379017	+	0.925390i	$0.623738\pi$
$692$	6411.69			0.352219
$693$	610.168	−	578.523i	0.0334464	−	0.0317118i
$694$	−21891.0			−1.19737
$695$	1241.50	+	902.000i	0.0677592	+	0.0492299i
$696$	730.319	−	2247.69i	0.0397740	−	0.122412i
$697$	1978.26	+	6088.45i	0.107506	+	0.330870i
$698$	−16636.0	+	12086.8i	−0.902124	+	0.655431i
$699$	−22272.2	+	16181.7i	−1.20517	+	0.875606i
$700$	162.931	+	501.451i	0.00879747	+	0.0270758i
$701$	−2087.46	+	6424.54i	−0.112471	+	0.346150i	−0.991411	−	0.130782i	$-0.958251\pi$
$701$	−2087.46	+	6424.54i	−0.112471	+	0.346150i	0.878940	+	0.476932i	$0.158251\pi$
$702$	−14404.0	−	10465.1i	−0.774422	−	0.562650i
$703$	11704.0			0.627914
$704$	1004.28	+	2107.89i	0.0537647	+	0.112847i
$705$	350.276			0.0187123
$706$	18901.1	+	13732.5i	1.00758	+	0.732051i
$707$	1884.90	−	5801.14i	0.100268	−	0.308592i
$708$	−1604.00	−	4936.60i	−0.0851441	−	0.262046i
$709$	−4913.82	+	3570.10i	−0.260286	+	0.189109i	−0.710273	−	0.703926i	$-0.751428\pi$
$709$	−4913.82	+	3570.10i	−0.260286	+	0.189109i	0.449987	+	0.893035i	$0.351428\pi$
$710$	−9488.77	+	6894.00i	−0.501559	+	0.364404i
$711$	1746.85	+	5376.26i	0.0921408	+	0.283580i
$712$	−1040.13	+	3201.19i	−0.0547479	+	0.168497i
$713$	−3982.50	−	2893.46i	−0.209181	−	0.151979i
$714$	−1600.69			−0.0838998
$715$	−9560.67	−	5196.42i	−0.500068	−	0.271797i
$716$	8517.44			0.444569
$717$	−8196.85	−	5955.36i	−0.426942	−	0.310191i
$718$	−2774.05	+	8537.65i	−0.144188	+	0.443764i
$719$	8803.72	+	27095.1i	0.456639	+	1.40539i	0.869200	+	0.494460i	$0.164634\pi$
$719$	8803.72	+	27095.1i	0.456639	+	1.40539i	−0.412561	+	0.910930i	$0.635366\pi$
$720$	282.907	−	205.544i	0.0146435	−	0.0106391i
$721$	−2264.52	+	1645.27i	−0.116970	+	0.0849836i
$722$	−2670.06	−	8217.60i	−0.137631	−	0.423584i
$723$	−2662.25	+	8193.57i	−0.136944	+	0.421469i
$724$	−8618.84	−	6261.95i	−0.442426	−	0.321441i
$725$	−1552.56			−0.0795321
$726$	11818.0	+	4548.34i	0.604144	+	0.232514i
$727$	−6806.05			−0.347211			−0.173605	−	0.984815i	$-0.555542\pi$
$727$	−6806.05			−0.347211			−0.173605	+	0.984815i	$0.555542\pi$
$728$	−2035.65	−	1478.99i	−0.103635	−	0.0752953i
$729$	6722.44	−	20689.5i	0.341535	−	1.05114i
$730$	2720.36	+	8372.41i	0.137925	+	0.424489i
$731$	−1675.44	+	1217.28i	−0.0847723	+	0.0615907i
$732$	3276.98	−	2380.87i	0.165466	−	0.120218i
$733$	−5650.99	−	17392.0i	−0.284753	−	0.876381i	−0.986472	−	0.163927i	$-0.947584\pi$
$733$	−5650.99	−	17392.0i	−0.284753	−	0.876381i	0.701719	−	0.712454i	$-0.252416\pi$
$734$	−5153.64	+	15861.3i	−0.259161	+	0.797616i
$735$	−6065.20	−	4406.62i	−0.304379	−	0.221144i
$736$	−6700.53			−0.335577
$737$	26566.8	+	14439.6i	1.32782	+	0.721695i
$738$	−1753.89			−0.0874818
$739$	25532.0	+	18550.1i	1.27092	+	0.923379i	0.999239	−	0.0390078i	$-0.0124197\pi$
$739$	25532.0	+	18550.1i	1.27092	+	0.923379i	0.271683	+	0.962387i	$0.412420\pi$
$740$	1435.61	−	4418.34i	0.0713161	−	0.219489i
$741$	−4418.32	−	13598.2i	−0.219043	−	0.674146i
$742$	518.492	−	376.707i	0.0256529	−	0.0186379i
$743$	14326.0	−	10408.5i	0.707363	−	0.513929i	−0.174959	−	0.984576i	$-0.555979\pi$
$743$	14326.0	−	10408.5i	0.707363	−	0.513929i	0.882322	+	0.470646i	$0.155979\pi$
$744$	276.467	+	850.877i	0.0136233	+	0.0419283i
$745$	1320.28	−	4063.39i	0.0649278	−	0.199827i
$746$	22319.7	+	16216.2i	1.09542	+	0.795867i
$747$	−5820.25			−0.285076
$748$	2002.91	+	4203.90i	0.0979058	+	0.205494i
$749$	2183.05			0.106498
$750$	962.119	+	699.020i	0.0468422	+	0.0340328i
$751$	−5407.84	+	16643.6i	−0.262763	+	0.808701i	0.729438	+	0.684047i	$0.239782\pi$
$751$	−5407.84	+	16643.6i	−0.262763	+	0.808701i	−0.992200	+	0.124653i	$0.960218\pi$
$752$	−72.8135	−	224.097i	−0.00353090	−	0.0108670i
$753$	24340.3	−	17684.2i	1.17797	−	0.855843i
$754$	5994.19	−	4355.03i	0.289517	−	0.210346i
$755$	−4359.13	−	13416.0i	−0.210126	−	0.646701i
$756$	972.583	−	2993.30i	0.0467890	−	0.144002i
$757$	12298.5	+	8935.35i	0.590482	+	0.429011i	0.842488	−	0.538715i	$-0.181090\pi$
$757$	12298.5	+	8935.35i	0.590482	+	0.429011i	−0.252006	+	0.967726i	$0.581090\pi$
$758$	−269.318			−0.0129051
$759$	−26370.7	+	25003.0i	−1.26113	+	1.19572i
$760$	2015.44			0.0961944
$761$	−32234.1	−	23419.4i	−1.53546	−	1.11558i	−0.953105	−	0.302639i	$-0.902132\pi$
$761$	−32234.1	−	23419.4i	−1.53546	−	1.11558i	−0.582353	−	0.812936i	$-0.697868\pi$
$762$	−1987.79	+	6117.80i	−0.0945015	+	0.290846i
$763$	982.703	+	3024.45i	0.0466268	+	0.143502i
$764$	−9286.01	+	6746.68i	−0.439733	+	0.319485i
$765$	564.220	−	409.930i	0.0266659	−	0.0193739i
$766$	4440.84	+	13667.5i	0.209470	+	0.644683i
$767$	5028.60	−	15476.4i	0.236730	−	0.728581i
$768$	985.210	+	715.797i	0.0462900	+	0.0336316i
$769$	−37129.1			−1.74110			−0.870551	−	0.492078i	$-0.836238\pi$
$769$	−37129.1			−1.74110			−0.870551	+	0.492078i	$0.836238\pi$
$770$	351.370	−	1891.22i	0.0164448	−	0.0885129i
$771$	−32821.4			−1.53312
$772$	13853.9	+	10065.4i	0.645869	+	0.469251i
$773$	−22.6041	+	69.5684i	−0.00105177	+	0.00323700i	−0.951581	−	0.307398i	$-0.900542\pi$
$773$	−22.6041	+	69.5684i	−0.00105177	+	0.00323700i	0.950529	+	0.310635i	$0.100542\pi$
$774$	−175.330	−	539.610i	−0.00814226	−	0.0250593i
$775$	475.485	−	345.460i	0.0220386	−	0.0160120i
$776$	−842.148	+	611.857i	−0.0389580	+	0.0283046i
$777$	−1800.36	−	5540.93i	−0.0831242	−	0.255830i
$778$	4466.94	−	13747.8i	0.205845	−	0.633526i
$779$	−8177.94	−	5941.62i	−0.376130	−	0.273274i
$780$	−5675.38			−0.260527
$781$	42426.3	−	5566.71i	1.94383	−	0.255048i
$782$	−13363.3			−0.611088
$783$	7497.71	+	5447.40i	0.342205	+	0.248626i
$784$	−1558.43	+	4796.37i	−0.0709928	+	0.218493i
$785$	5352.63	+	16473.7i	0.243367	+	0.749008i
$786$	9089.18	−	6603.68i	0.412469	−	0.299676i
$787$	−1126.51	+	818.460i	−0.0510240	+	0.0370711i	−0.613005	−	0.790079i	$-0.710039\pi$
$787$	−1126.51	+	818.460i	−0.0510240	+	0.0370711i	0.561981	+	0.827150i	$0.310039\pi$
$788$	−32.9760	−	101.490i	−0.00149076	−	0.00458809i
$789$	−3687.35	+	11348.5i	−0.166379	+	0.512062i
$790$	10462.5	+	7601.45i	0.471189	+	0.342339i
$791$	7462.95			0.335464
$792$	−1264.94	+	165.971i	−0.0567520	+	0.00744638i
$793$	12698.7			0.568656
$794$	13979.7	+	10156.9i	0.624839	+	0.453972i
$795$	446.700	−	1374.80i	0.0199281	−	0.0613323i
$796$	492.534	+	1515.86i	0.0219314	+	0.0674979i
$797$	2224.09	−	1615.89i	0.0988472	−	0.0718167i	−0.537264	−	0.843414i	$-0.680542\pi$
$797$	2224.09	−	1615.89i	0.0988472	−	0.0718167i	0.636111	+	0.771598i	$0.280542\pi$
$798$	2044.80	−	1485.64i	0.0907083	−	0.0659035i
$799$	−145.217	−	446.931i	−0.00642978	−	0.0197888i
$800$	247.214	−	760.845i	0.0109254	−	0.0336249i
$801$	−1487.88	−	1081.01i	−0.0656327	−	0.0476849i
$802$	20500.1			0.902598
$803$	5866.59	−	31576.5i	0.257818	−	1.38768i
$804$	15770.5			0.691770
$805$	4465.90	+	3244.67i	0.195531	+	0.142062i
$806$	−866.733	+	2667.53i	−0.0378776	+	0.116575i
$807$	−9196.17	−	28302.9i	−0.401141	−	1.23458i
$808$	−7487.42	+	5439.93i	−0.325998	+	0.236852i
$809$	−9290.96	+	6750.28i	−0.403773	+	0.293359i	−0.771076	−	0.636743i	$-0.780281\pi$
$809$	−9290.96	+	6750.28i	−0.403773	+	0.293359i	0.367303	+	0.930101i	$0.380281\pi$
$810$	−1828.98	−	5629.04i	−0.0793382	−	0.244178i
$811$	4336.85	−	13347.5i	0.187777	−	0.577919i	−0.812208	−	0.583368i	$-0.801734\pi$
$811$	4336.85	−	13347.5i	0.187777	−	0.577919i	0.999985	+	0.00544905i	$0.00173449\pi$
$812$	1059.62	+	769.857i	0.0457947	+	0.0332718i
$813$	23698.6			1.02232
$814$	−12299.4	+	11661.5i	−0.529599	+	0.502132i
$815$	1810.63			0.0778203
$816$	1964.87	+	1427.56i	0.0842943	+	0.0612434i
$817$	1010.51	−	3110.03i	0.0432720	−	0.133178i
$818$	3420.33	+	10526.7i	0.146197	+	0.449947i
$819$	1112.27	−	808.111i	0.0474552	−	0.0344783i
$820$	−3246.11	+	2358.44i	−0.138243	+	0.100439i
$821$	−9221.33	−	28380.3i	−0.391994	−	1.20643i	−0.931278	−	0.364309i	$-0.881305\pi$
$821$	−9221.33	−	28380.3i	−0.391994	−	1.20643i	0.539285	−	0.842123i	$-0.318695\pi$
$822$	482.733	−	1485.70i	0.0204833	−	0.0630410i
$823$	33302.4	+	24195.6i	1.41051	+	1.02479i	0.993248	+	0.116007i	$0.0370095\pi$
$823$	33302.4	+	24195.6i	1.41051	+	1.02479i	0.417260	+	0.908787i	$0.362991\pi$
$824$	4247.05			0.179554
$825$	−1866.15	−	3916.87i	−0.0787529	−	0.165294i
$826$	2876.62			0.121175
$827$	20078.7	+	14588.1i	0.844264	+	0.613394i	0.923558	−	0.383458i	$-0.125267\pi$
$827$	20078.7	+	14588.1i	0.844264	+	0.613394i	−0.0792947	+	0.996851i	$0.525267\pi$
$828$	1131.35	−	3481.94i	0.0474846	−	0.146142i
$829$	6024.46	+	18541.4i	0.252398	+	0.776801i	0.994331	+	0.106327i	$0.0339092\pi$
$829$	6024.46	+	18541.4i	0.252398	+	0.776801i	−0.741933	+	0.670474i	$0.766091\pi$
$830$	−10772.2	+	7826.44i	−0.450491	+	0.327301i
$831$	12152.2	−	8829.09i	0.507287	−	0.368565i
$832$	1179.77	+	3630.95i	0.0491599	+	0.151299i
$833$	−3108.09	+	9565.71i	−0.129278	+	0.397878i
$834$	−2362.31	−	1716.32i	−0.0980816	−	0.0712605i
$835$	5702.89			0.236355
$836$	−6460.33	−	3511.32i	−0.267267	−	0.145265i
$837$	−3508.33			−0.144881
$838$	−13363.6	−	9709.24i	−0.550881	−	0.400239i
$839$	−5564.94	+	17127.1i	−0.228990	+	0.704760i	0.768872	+	0.639403i	$0.220819\pi$
$839$	−5564.94	+	17127.1i	−0.228990	+	0.704760i	−0.997862	+	0.0653566i	$0.979181\pi$
$840$	−310.024	−	954.157i	−0.0127344	−	0.0391923i
$841$	16611.0	−	12068.6i	0.681084	−	0.494837i
$842$	17053.3	−	12389.9i	0.697974	−	0.507108i
$843$	2906.62	+	8945.67i	0.118754	+	0.365487i
$844$	4340.47	−	13358.6i	0.177020	−	0.544812i
$845$	−5507.40	−	4001.36i	−0.224213	−	0.162901i
$846$	128.747			0.00523215
$847$	−4421.19	+	5450.00i	−0.179355	+	0.221091i
$848$	−972.417			−0.0393784
$849$	1030.88	+	748.978i	0.0416722	+	0.0302766i
$850$	493.034	−	1517.40i	0.0198952	−	0.0612312i
$851$	−15030.2	−	46258.2i	−0.605439	−	1.86335i
$852$	18055.2	−	13117.8i	0.726009	−	0.527476i
$853$	−16569.2	+	12038.2i	−0.665085	+	0.483212i	−0.868376	−	0.495906i	$-0.834836\pi$
$853$	−16569.2	+	12038.2i	−0.665085	+	0.483212i	0.203292	+	0.979118i	$0.434836\pi$
$854$	693.682	+	2134.93i	0.0277954	+	0.0855456i
$855$	−340.298	+	1047.33i	−0.0136116	+	0.0418922i
$856$	−2679.72	−	1946.93i	−0.106999	−	0.0777391i
$857$	16879.7			0.672813			0.336406	−	0.941717i	$-0.390788\pi$
$857$	16879.7			0.672813			0.336406	+	0.941717i	$0.390788\pi$
$858$	18192.0	+	9887.70i	0.723850	+	0.393427i
$859$	14024.6			0.557058			0.278529	−	0.960428i	$-0.410153\pi$
$859$	14024.6			0.557058			0.278529	+	0.960428i	$0.410153\pi$
$860$	−1050.11	−	762.951i	−0.0416378	−	0.0302516i
$861$	−1554.93	+	4785.60i	−0.0615471	+	0.189422i
$862$	1807.63	+	5563.31i	0.0714248	+	0.219823i
$863$	−25136.4	+	18262.6i	−0.991485	+	0.720356i	−0.960246	−	0.279156i	$-0.909945\pi$
$863$	−25136.4	+	18262.6i	−0.991485	+	0.720356i	−0.0312392	+	0.999512i	$0.509945\pi$
$864$	−3863.40	+	2806.92i	−0.152124	+	0.110525i
$865$	2476.65	+	7622.35i	0.0973511	+	0.299616i
$866$	−5984.22	+	18417.5i	−0.234818	+	0.722694i
$867$	−14988.9	−	10890.1i	−0.587139	−	0.426582i
$868$	−495.817			−0.0193884
$869$	−20293.4	−	42593.7i	−0.792181	−	1.66271i
$870$	2954.20			0.115123
$871$	39998.7	+	29060.8i	1.55603	+	1.13052i
$872$	1491.04	−	4588.95i	0.0579048	−	0.178213i
$873$	−175.760	−	540.933i	−0.00681394	−	0.0209711i
$874$	17070.9	−	12402.8i	0.660678	−	0.480011i
$875$	−533.200	+	387.392i	−0.0206005	+	0.0149671i
$876$	−5176.28	−	15930.9i	−0.199646	−	0.614448i
$877$	4674.82	−	14387.6i	0.179997	−	0.553974i	−0.819829	−	0.572608i	$-0.805932\pi$
$877$	4674.82	−	14387.6i	0.179997	−	0.553974i	0.999826	+	0.0186339i	$0.00593168\pi$
$878$	22697.1	+	16490.4i	0.872426	+	0.633855i
$879$	−5806.41			−0.222805
$880$	−2117.97	+	2008.13i	−0.0811329	+	0.0769250i
$881$	−32808.2			−1.25464			−0.627319	−	0.778762i	$-0.715848\pi$
$881$	−32808.2			−1.25464			−0.627319	+	0.778762i	$0.715848\pi$
$882$	−2229.31	−	1619.69i	−0.0851074	−	0.0618341i
$883$	−1551.63	+	4775.43i	−0.0591354	+	0.182000i	−0.976261	−	0.216599i	$-0.930504\pi$
$883$	−1551.63	+	4775.43i	−0.0591354	+	0.182000i	0.917125	+	0.398599i	$0.130504\pi$
$884$	2352.88	+	7241.43i	0.0895204	+	0.275516i
$885$	5249.16	−	3813.74i	0.199377	−	0.144856i
$886$	17886.6	−	12995.4i	0.678231	−	0.492764i
$887$	−8887.86	−	27354.0i	−0.336443	−	1.03547i	−0.966007	−	0.258517i	$-0.916766\pi$
$887$	−8887.86	−	27354.0i	−0.336443	−	1.03547i	0.629564	−	0.776949i	$-0.283234\pi$
$888$	−2731.66	+	8407.18i	−0.103230	+	0.317710i
$889$	−2884.08	−	2095.41i	−0.108807	−	0.0790526i
$890$	−4207.41			−0.158464
$891$	−3944.30	+	21229.9i	−0.148304	+	0.798236i
$892$	−3623.13			−0.135999
$893$	600.313	+	436.153i	0.0224957	+	0.0163441i
$894$	−2512.21	+	7731.79i	−0.0939831	+	0.289250i
$895$	3290.04	+	10125.7i	0.122876	+	0.378173i
$896$	−545.997	+	396.690i	−0.0203577	+	0.0147907i
$897$	−48070.9	+	34925.5i	−1.78934	+	1.30003i
$898$	−7499.70	−	23081.7i	−0.278695	−	0.857736i
$899$	451.160	−	1388.53i	0.0167375	−	0.0515128i
$900$	353.634	+	256.930i	0.0130976	+	0.00951593i
$901$	−1939.35			−0.0717083
$902$	14514.0	−	1904.38i	0.535770	−	0.0702980i
$903$	−1627.80			−0.0599887
$904$	−9160.84	−	6655.74i	−0.337041	−	0.244875i
$905$	4115.13	−	12665.1i	0.151151	−	0.465194i
$906$	8294.52	+	25527.9i	0.304158	+	0.936102i
$907$	−14020.1	+	10186.2i	−0.513265	+	0.372909i	−0.814061	−	0.580780i	$-0.802748\pi$
$907$	−14020.1	+	10186.2i	−0.513265	+	0.372909i	0.300796	+	0.953689i	$0.402748\pi$
$908$	11213.6	−	8147.16i	0.409842	−	0.297768i
$909$	−1562.66	−	4809.36i	−0.0570187	−	0.175486i
$910$	971.938	−	2991.32i	0.0354060	−	0.108968i
$911$	−28018.7	−	20356.8i	−1.01899	−	0.740341i	−0.0529158	−	0.998599i	$-0.516851\pi$
$911$	−28018.7	−	20356.8i	−1.01899	−	0.740341i	−0.966076	+	0.258258i	$0.916851\pi$
$912$	−3834.96			−0.139242
$913$	48164.6	−	6319.63i	1.74591	−	0.229079i
$914$	−170.009			−0.00615253
$915$	4096.23	+	2976.09i	0.147997	+	0.107526i
$916$	3891.26	−	11976.1i	0.140361	−	0.431987i
$917$	1924.03	+	5921.54i	0.0692878	+	0.213246i
$918$	−7705.02	+	5598.03i	−0.277019	+	0.201266i
$919$	−40756.0	+	29611.0i	−1.46291	+	1.06287i	−0.480321	+	0.877093i	$0.659480\pi$
$919$	−40756.0	+	29611.0i	−1.46291	+	1.06287i	−0.982592	+	0.185776i	$0.940520\pi$
$920$	−2588.22	−	7965.73i	−0.0927513	−	0.285459i
$921$	4132.84	−	12719.6i	0.147863	−	0.455075i
$922$	11894.1	+	8641.58i	0.424850	+	0.308672i
$923$	69965.8			2.49507
$924$	−668.584	+	3598.60i	−0.0238039	+	0.128123i
$925$	5807.15			0.206419
$926$	19906.0	+	14462.6i	0.706429	+	0.513251i
$927$	−717.093	+	2206.99i	−0.0254071	+	0.0781952i
$928$	−614.103	−	1890.02i	−0.0217230	−	0.0668565i
$929$	8008.01	−	5818.16i	0.282814	−	0.205477i	−0.437330	−	0.899301i	$-0.644076\pi$
$929$	8008.01	−	5818.16i	0.282814	−	0.205477i	0.720144	+	0.693825i	$0.244076\pi$
$930$	−904.749	+	657.339i	−0.0319010	+	0.0231774i
$931$	−4907.71	−	15104.4i	−0.172764	−	0.531714i
$932$	−7153.48	+	22016.1i	−0.251416	+	0.773779i
$933$	−15427.7	−	11208.8i	−0.541349	−	0.393313i
$934$	−18799.6			−0.658608
$935$	−4224.01	+	4004.94i	−0.147743	+	0.140081i
$936$	−2086.03			−0.0728461
$937$	8699.32	+	6320.43i	0.303303	+	0.220362i	0.729017	−	0.684495i	$-0.239977\pi$
$937$	8699.32	+	6320.43i	0.303303	+	0.220362i	−0.425715	+	0.904857i	$0.639977\pi$
$938$	−2700.78	+	8312.15i	−0.0940124	+	0.289340i
$939$	11570.0	+	35608.8i	0.402101	+	1.23754i
$940$	238.285	−	173.124i	0.00826809	−	0.00600712i
$941$	−43320.4	+	31474.1i	−1.50075	+	1.09036i	−0.530668	+	0.847580i	$0.678059\pi$
$941$	−43320.4	+	31474.1i	−1.50075	+	1.09036i	−0.970082	+	0.242778i	$0.921941\pi$
$942$	−10184.9	−	31346.0i	−0.352275	−	1.08419i
$943$	−12981.3	+	39952.3i	−0.448281	+	1.37967i
$944$	−3531.09	−	2565.48i	−0.121745	−	0.0884528i
$945$	3934.18			0.135427
$946$	2036.83	+	4275.09i	0.0700031	+	0.146929i
$947$	36648.2			1.25756			0.628778	−	0.777585i	$-0.283555\pi$
$947$	36648.2			1.25756			0.628778	+	0.777585i	$0.283555\pi$
$948$	−19908.0	−	14464.0i	−0.682047	−	0.495536i
$949$	16227.8	−	49944.1i	0.555087	−	1.70838i
$950$	778.507	+	2396.00i	0.0265875	+	0.0818278i
$951$	−39312.3	+	28562.0i	−1.34047	+	0.973909i
$952$	−1088.92	+	791.144i	−0.0370714	+	0.0269340i
$953$	−10412.6	−	32046.7i	−0.353933	−	1.08929i	−0.956626	−	0.291319i	$-0.905906\pi$
$953$	−10412.6	−	32046.7i	−0.353933	−	1.08929i	0.602693	−	0.797973i	$-0.294094\pi$
$954$	164.188	−	505.318i	0.00557209	−	0.0171491i
$955$	−11607.5	−	8433.36i	−0.393309	−	0.285756i
$956$	−8519.58			−0.288225
$957$	−9469.46	−	5146.84i	−0.319858	−	0.173849i
$958$	−37163.9			−1.25335
$959$	700.396	+	508.867i	0.0235839	+	0.0171347i
$960$	−470.396	+	1447.73i	−0.0158145	+	0.0486722i
$961$	−9035.14	−	27807.3i	−0.303284	−	0.933412i
$962$	−22420.5	+	16289.4i	−0.751418	+	0.545937i
$963$	1464.18	−	1063.79i	0.0489954	−	0.0355973i
$964$	2238.61	+	6889.73i	0.0747933	+	0.230190i
$965$	−6614.63	+	20357.7i	−0.220655	+	0.679107i
$966$	−8497.68	−	6173.93i	−0.283032	−	0.205634i
$967$	−42459.9			−1.41202			−0.706008	−	0.708204i	$-0.749506\pi$
$967$	−42459.9			−1.41202			−0.706008	+	0.708204i	$0.749506\pi$
$968$	10287.6	−	2746.94i	0.341586	−	0.0912086i
$969$	−7648.32			−0.253560
$970$	−1052.69	−	764.821i	−0.0348450	−	0.0253164i
$971$	−5954.55	+	18326.2i	−0.196798	+	0.605681i	0.803153	+	0.595772i	$0.203154\pi$
$971$	−5954.55	+	18326.2i	−0.196798	+	0.605681i	−0.999951	+	0.00990831i	$0.996846\pi$
$972$	−1500.27	−	4617.34i	−0.0495072	−	0.152368i
$973$	1309.18	−	951.172i	0.0431349	−	0.0313393i
$974$	−17768.4	+	12909.5i	−0.584535	+	0.424690i
$975$	−2192.24	−	6747.01i	−0.0720079	−	0.221618i
$976$	1052.51	−	3239.30i	0.0345186	−	0.106237i
$977$	−35709.3	−	25944.3i	−1.16934	−	0.849572i	−0.178407	−	0.983957i	$-0.557094\pi$
$977$	−35709.3	−	25944.3i	−1.16934	−	0.849572i	−0.990929	+	0.134385i	$0.957094\pi$
$978$	−3445.25			−0.112645
$979$	13486.5	+	7330.19i	0.440277	+	0.239299i
$980$	−6304.00			−0.205484
$981$	2132.90	+	1549.64i	0.0694173	+	0.0504346i
$982$	−4288.13	+	13197.5i	−0.139348	+	0.428869i
$983$	−9448.53	−	29079.6i	−0.306573	−	0.943535i	−0.979086	−	0.203449i	$-0.934785\pi$
$983$	−9448.53	−	29079.6i	−0.306573	−	0.943535i	0.672513	−	0.740086i	$-0.265215\pi$
$984$	6176.68	−	4487.62i	0.200107	−	0.145386i
$985$	107.915	−	78.4051i	0.00349083	−	0.00253624i
$986$	−1224.75	−	3769.38i	−0.0395577	−	0.121746i
$987$	114.142	−	351.293i	0.00368103	−	0.0113291i
$988$	−9726.61	−	7066.80i	−0.313203	−	0.227555i
$989$	−13589.6			−0.436931
$990$	−685.918	−	1439.67i	−0.0220201	−	0.0462180i
$991$	41995.7			1.34615			0.673076	−	0.739573i	$-0.264972\pi$
$991$	41995.7			1.34615			0.673076	+	0.739573i	$0.264972\pi$
$992$	608.621	+	442.189i	0.0194796	+	0.0141527i
$993$	−4306.14	+	13252.9i	−0.137614	+	0.423534i
$994$	3821.97	+	11762.8i	0.121957	+	0.375346i
$995$	−1611.84	+	1171.07i	−0.0513555	+	0.0373119i
$996$	20497.2	−	14892.1i	0.652086	−	0.473769i
$997$	10004.1	+	30789.4i	0.317786	+	0.978044i	0.974593	+	0.223985i	$0.0719068\pi$
$997$	10004.1	+	30789.4i	0.317786	+	0.978044i	−0.656807	+	0.754059i	$0.728093\pi$
$998$	716.467	−	2205.06i	0.0227248	−	0.0699398i
$999$	−28044.2	−	20375.3i	−0.888166	−	0.645290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.g.d.81.1	✓	16
11.3	even	5	inner	110.4.g.d.91.1	yes	16
11.5	even	5		1210.4.a.bj.1.2		8
11.6	odd	10		1210.4.a.bi.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.g.d.81.1	✓	16	1.1	even	1	trivial
110.4.g.d.91.1	yes	16	11.3	even	5	inner
1210.4.a.bi.1.2		8	11.6	odd	10
1210.4.a.bj.1.2		8	11.5	even	5

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-1.46999 + 4.52416i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-4.04508 + 2.93893i) q^{5} +(7.69695 - 5.59216i) q^{6} +(1.62931 + 5.01451i) q^{7} +(2.47214 - 7.60845i) q^{8} +(3.53634 + 2.56930i) q^{9} +10.0000 q^{10} +(-32.0542 - 17.4221i) q^{11} -19.0279 q^{12} +(-48.2605 - 35.0633i) q^{13} +(3.25863 - 10.0290i) q^{14} +(-7.34994 - 22.6208i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(-25.8156 + 18.7561i) q^{17} +(-2.70152 - 8.31443i) q^{18} +(15.5701 - 47.9200i) q^{19} +(-16.1803 - 11.7557i) q^{20} -25.0815 q^{21} +(31.3839 + 65.8715i) q^{22} -209.392 q^{23} +(30.7878 + 22.3687i) q^{24} +(7.72542 - 23.7764i) q^{25} +(36.8677 + 113.467i) q^{26} +(-120.731 + 87.7163i) q^{27} +(-17.0624 + 12.3966i) q^{28} +(-19.1907 - 59.0630i) q^{29} +(-14.6999 + 45.2416i) q^{30} +(19.0194 + 13.8184i) q^{31} +32.0000 q^{32} +(125.940 - 119.408i) q^{33} +63.8197 q^{34} +(-21.3280 - 15.4957i) q^{35} +(-5.40304 + 16.6289i) q^{36} +(71.7803 + 220.917i) q^{37} +(-81.5263 + 59.2323i) q^{38} +(229.574 - 166.795i) q^{39} +(12.3607 + 38.0423i) q^{40} +(61.9952 - 190.802i) q^{41} +(40.5827 + 29.4851i) q^{42} +64.9004 q^{43} +(26.6564 - 143.476i) q^{44} -21.8558 q^{45} +(338.803 + 246.155i) q^{46} +(-4.55084 + 14.0061i) q^{47} +(-23.5198 - 72.3865i) q^{48} +(255.002 - 185.270i) q^{49} +(-40.4508 + 29.3893i) q^{50} +(-46.9070 - 144.365i) q^{51} +(73.7354 - 226.934i) q^{52} +(49.1688 + 35.7233i) q^{53} +298.464 q^{54} +(180.864 - 23.7310i) q^{55} +42.1806 q^{56} +(193.909 + 140.883i) q^{57} +(-38.3815 + 118.126i) q^{58} +(84.2972 + 259.440i) q^{59} +(76.9695 - 55.9216i) q^{60} +(-172.220 + 125.125i) q^{61} +(-14.5295 - 44.7173i) q^{62} +(-7.12198 + 21.9192i) q^{63} +(-51.7771 - 37.6183i) q^{64} +298.266 q^{65} +(-344.147 + 45.1552i) q^{66} -828.809 q^{67} +(-103.262 - 75.0245i) q^{68} +(307.803 - 947.320i) q^{69} +(16.2931 + 50.1451i) q^{70} +(-948.877 + 689.400i) q^{71} +(28.2907 - 20.5544i) q^{72} +(272.036 + 837.241i) q^{73} +(143.561 - 441.834i) q^{74} +(96.2119 + 69.9020i) q^{75} +201.544 q^{76} +(35.1370 - 189.122i) q^{77} -567.538 q^{78} +(1046.25 + 760.145i) q^{79} +(24.7214 - 76.0845i) q^{80} +(-182.898 - 562.904i) q^{81} +(-324.611 + 235.844i) q^{82} +(-1077.22 + 782.644i) q^{83} +(-31.0024 - 95.4157i) q^{84} +(49.3034 - 151.740i) q^{85} +(-105.011 - 76.2951i) q^{86} +295.420 q^{87} +(-211.797 + 200.813i) q^{88} -420.741 q^{89} +(35.3634 + 25.6930i) q^{90} +(97.1938 - 299.132i) q^{91} +(-258.822 - 796.573i) q^{92} +(-90.4749 + 65.7339i) q^{93} +(23.8285 - 17.3124i) q^{94} +(77.8507 + 239.600i) q^{95} +(-47.0396 + 144.773i) q^{96} +(-105.269 - 76.4821i) q^{97} -630.400 q^{98} +(-68.5918 - 143.967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 3 q^{3} - 16 q^{4} - 20 q^{5} - 16 q^{6} - 38 q^{7} - 32 q^{8} + 25 q^{9} + 160 q^{10} + 65 q^{11} + 88 q^{12} + 85 q^{13} - 76 q^{14} - 15 q^{15} - 64 q^{16} + 109 q^{17} - 280 q^{18}+ \cdots + 10702 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 3 * q^3 - 16 * q^4 - 20 * q^5 - 16 * q^6 - 38 * q^7 - 32 * q^8 + 25 * q^9 + 160 * q^10 + 65 * q^11 + 88 * q^12 + 85 * q^13 - 76 * q^14 - 15 * q^15 - 64 * q^16 + 109 * q^17 - 280 * q^18 + 12 * q^19 - 80 * q^20 - 36 * q^21 + 140 * q^22 + 432 * q^23 - 64 * q^24 - 100 * q^25 - 490 * q^26 - 507 * q^27 + 88 * q^28 + 369 * q^29 - 30 * q^30 - 334 * q^31 + 512 * q^32 - 280 * q^33 + 568 * q^34 + 110 * q^35 - 560 * q^36 - 360 * q^37 - 236 * q^38 + 279 * q^39 - 160 * q^40 - 595 * q^41 - 442 * q^42 + 612 * q^43 - 120 * q^44 + 1150 * q^45 - 206 * q^46 + 1066 * q^47 - 48 * q^48 - 1468 * q^49 - 200 * q^50 + 3404 * q^51 - 980 * q^52 - 533 * q^53 + 1556 * q^54 - 125 * q^55 + 256 * q^56 + 470 * q^57 + 738 * q^58 - 1842 * q^59 - 160 * q^60 + 1246 * q^61 - 178 * q^62 - 4622 * q^63 - 256 * q^64 + 1600 * q^65 + 920 * q^66 - 2200 * q^67 + 436 * q^68 + 4777 * q^69 - 380 * q^70 - 2158 * q^71 + 200 * q^72 - 55 * q^73 - 720 * q^74 - 200 * q^75 + 848 * q^76 + 3704 * q^77 - 1812 * q^78 + 1595 * q^79 - 320 * q^80 - 9487 * q^81 + 700 * q^82 - 486 * q^83 + 956 * q^84 - 1255 * q^85 - 1686 * q^86 - 1234 * q^87 - 640 * q^88 - 3512 * q^89 + 250 * q^90 + 3913 * q^91 - 452 * q^92 - 2423 * q^93 - 3748 * q^94 + 60 * q^95 - 96 * q^96 + 1101 * q^97 + 7224 * q^98 + 10702 * q^99

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