LMFDB - Embedded newform 177.4.e.a.133.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			133.6
Character	$\chi$	$=$	177.133
Dual form			177.4.e.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03313 + 0.221116i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-3.72826 + 0.820651i) q^{4} +(16.1269 - 12.2594i) q^{5} +(4.45423 + 4.21927i) q^{6} +(-2.36180 - 5.92767i) q^{7} +(22.9030 - 7.71693i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})$	\(q+(-2.03313 + 0.221116i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-3.72826 + 0.820651i) q^{4} +(16.1269 - 12.2594i) q^{5} +(4.45423 + 4.21927i) q^{6} +(-2.36180 - 5.92767i) q^{7} +(22.9030 - 7.71693i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-30.0773 + 28.4907i) q^{10} +(9.15701 + 4.23648i) q^{11} +(9.11727 + 6.93077i) q^{12} +(4.88429 + 29.7928i) q^{13} +(6.11253 + 11.5295i) q^{14} +(-59.3519 - 13.0643i) q^{15} +(-17.1410 + 7.93027i) q^{16} +(13.2050 - 33.1420i) q^{17} +(0.996482 - 18.3790i) q^{18} +(24.5922 - 36.2708i) q^{19} +(-50.0646 + 58.9406i) q^{20} +(-8.96654 + 16.9127i) q^{21} +(-19.5541 - 6.58855i) q^{22} +(-4.67865 - 86.2927i) q^{23} +(-62.1260 - 37.3800i) q^{24} +(76.3443 - 274.967i) q^{25} +(-16.5180 - 59.4926i) q^{26} +(23.1351 - 13.9200i) q^{27} +(13.6699 + 20.1616i) q^{28} +(-80.0540 - 8.70639i) q^{29} +(123.559 + 13.4378i) q^{30} +(-183.374 - 270.457i) q^{31} +(-132.573 + 79.7665i) q^{32} +(-8.09771 - 29.1653i) q^{33} +(-19.5191 + 70.3016i) q^{34} +(-110.758 - 66.6408i) q^{35} +(-1.86008 - 34.3072i) q^{36} +(-11.7771 - 3.96816i) q^{37} +(-41.9790 + 79.1808i) q^{38} +(58.6349 - 69.0303i) q^{39} +(274.750 - 405.227i) q^{40} +(-10.8283 + 199.716i) q^{41} +(14.4904 - 36.3683i) q^{42} +(-17.4299 + 8.06392i) q^{43} +(-37.6164 - 8.27999i) q^{44} +(85.3993 + 161.080i) q^{45} +(28.5930 + 174.409i) q^{46} +(-49.3229 - 37.4943i) q^{47} +(51.4230 + 23.7908i) q^{48} +(219.457 - 207.881i) q^{49} +(-94.4180 + 575.924i) q^{50} +(-101.425 + 34.1740i) q^{51} +(-42.6594 - 107.067i) q^{52} +(-161.287 - 152.779i) q^{53} +(-43.9587 + 33.4166i) q^{54} +(199.611 - 43.9377i) q^{55} +(-99.8357 - 117.536i) q^{56} +(-130.695 + 14.2139i) q^{57} +164.685 q^{58} +(-448.795 + 62.9462i) q^{59} +232.000 q^{60} +(-28.2997 + 3.07777i) q^{61} +(432.625 + 509.326i) q^{62} +(56.0851 - 12.3453i) q^{63} +(372.184 - 282.927i) q^{64} +(444.010 + 420.588i) q^{65} +(22.9126 + 57.5062i) q^{66} +(-157.146 + 52.9486i) q^{67} +(-22.0335 + 134.398i) q^{68} +(-188.220 + 178.292i) q^{69} +(239.920 + 110.999i) q^{70} +(-365.568 - 277.898i) q^{71} +(35.1897 + 214.648i) q^{72} +(263.714 + 497.417i) q^{73} +(24.8217 + 5.46367i) q^{74} +(-776.982 + 359.470i) q^{75} +(-61.9204 + 155.409i) q^{76} +(3.48545 - 64.2854i) q^{77} +(-103.948 + 153.312i) q^{78} +(520.229 - 612.461i) q^{79} +(-179.211 + 338.028i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-22.1451 - 408.442i) q^{82} +(451.620 + 271.731i) q^{83} +(19.5501 - 70.4132i) q^{84} +(-193.344 - 696.362i) q^{85} +(33.6541 - 20.2490i) q^{86} +(135.570 + 199.951i) q^{87} +(242.416 + 26.3643i) q^{88} +(1223.98 + 133.116i) q^{89} +(-209.245 - 308.613i) q^{90} +(165.066 - 99.3171i) q^{91} +(88.2595 + 317.882i) q^{92} +(-262.254 + 944.553i) q^{93} +(108.570 + 65.3246i) q^{94} +(-48.0603 - 886.421i) q^{95} +(439.863 + 148.207i) q^{96} +(-745.126 + 1405.46i) q^{97} +(-400.219 + 471.174i) q^{98} +(-50.9590 + 75.1589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{28}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.03313	+	0.221116i	−0.718818	+	0.0781762i	−0.460215	−	0.887807i	$-0.652228\pi$
$2$	−2.03313	+	0.221116i	−0.718818	+	0.0781762i	−0.258603	+	0.965984i	$0.583262\pi$
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$4$	−3.72826	+	0.820651i	−0.466032	+	0.102581i
$5$	16.1269	−	12.2594i	1.44243	−	1.09651i	0.464991	−	0.885316i	$-0.346058\pi$
$5$	16.1269	−	12.2594i	1.44243	−	1.09651i	0.977444	−	0.211195i	$-0.0677354\pi$
$6$	4.45423	+	4.21927i	0.303072	+	0.287085i
$7$	−2.36180	−	5.92767i	−0.127525	−	0.320064i	0.851326	−	0.524637i	$-0.175799\pi$
$7$	−2.36180	−	5.92767i	−0.127525	−	0.320064i	−0.978851	+	0.204573i	$0.934419\pi$
$8$	22.9030	−	7.71693i	1.01218	−	0.341043i
$9$	−1.45604	+	8.88144i	−0.0539273	+	0.328942i
$10$	−30.0773	+	28.4907i	−0.951128	+	0.900956i
$11$	9.15701	+	4.23648i	0.250995	+	0.116123i	0.541353	−	0.840796i	$-0.317912\pi$
$11$	9.15701	+	4.23648i	0.250995	+	0.116123i	−0.290358	+	0.956918i	$0.593774\pi$
$12$	9.11727	+	6.93077i	0.219328	+	0.166728i
$13$	4.88429	+	29.7928i	0.104204	+	0.635619i	0.986353	+	0.164647i	$0.0526485\pi$
$13$	4.88429	+	29.7928i	0.104204	+	0.635619i	−0.882148	+	0.470972i	$0.843903\pi$
$14$	6.11253	+	11.5295i	0.116689	+	0.220098i
$15$	−59.3519	−	13.0643i	−1.02164	−	0.224880i
$16$	−17.1410	+	7.93027i	−0.267828	+	0.123910i
$17$	13.2050	−	33.1420i	0.188393	−	0.472830i	−0.804194	−	0.594366i	$-0.797403\pi$
$17$	13.2050	−	33.1420i	0.188393	−	0.472830i	0.992587	+	0.121537i	$0.0387822\pi$
$18$	0.996482	−	18.3790i	0.0130485	−	0.240666i
$19$	24.5922	−	36.2708i	0.296939	−	0.437952i	−0.649727	−	0.760167i	$-0.725117\pi$
$19$	24.5922	−	36.2708i	0.296939	−	0.437952i	0.946667	+	0.322215i	$0.104427\pi$
$20$	−50.0646	+	58.9406i	−0.559739	+	0.658976i
$21$	−8.96654	+	16.9127i	−0.0931743	+	0.175745i
$22$	−19.5541	−	6.58855i	−0.189498	−	0.0638492i
$23$	−4.67865	−	86.2927i	−0.0424160	−	0.782316i	−0.939938	−	0.341346i	$-0.889117\pi$
$23$	−4.67865	−	86.2927i	−0.0424160	−	0.782316i	0.897522	−	0.440970i	$-0.145366\pi$
$24$	−62.1260	−	37.3800i	−0.528392	−	0.317923i
$25$	76.3443	−	274.967i	0.610754	−	2.19974i
$26$	−16.5180	−	59.4926i	−0.124594	−	0.448748i
$27$	23.1351	−	13.9200i	0.164902	−	0.0992184i
$28$	13.6699	+	20.1616i	0.0922634	+	0.136078i
$29$	−80.0540	−	8.70639i	−0.512609	−	0.0557495i	−0.151840	−	0.988405i	$-0.548520\pi$
$29$	−80.0540	−	8.70639i	−0.512609	−	0.0557495i	−0.360768	+	0.932655i	$0.617485\pi$
$30$	123.559	+	13.4378i	0.751953	+	0.0817799i
$31$	−183.374	−	270.457i	−1.06242	−	1.56695i	−0.798109	−	0.602513i	$-0.794166\pi$
$31$	−183.374	−	270.457i	−1.06242	−	1.56695i	−0.264310	−	0.964438i	$-0.585144\pi$
$32$	−132.573	+	79.7665i	−0.732369	+	0.440652i
$33$	−8.09771	−	29.1653i	−0.0427161	−	0.153849i
$34$	−19.5191	+	70.3016i	−0.0984560	+	0.354607i
$35$	−110.758	−	66.6408i	−0.534900	−	0.321839i
$36$	−1.86008	−	34.3072i	−0.00861149	−	0.158830i
$37$	−11.7771	−	3.96816i	−0.0523281	−	0.0176314i	0.293016	−	0.956108i	$-0.405341\pi$
$37$	−11.7771	−	3.96816i	−0.0523281	−	0.0176314i	−0.345344	+	0.938476i	$0.612238\pi$
$38$	−41.9790	+	79.1808i	−0.179208	+	0.338022i
$39$	58.6349	−	69.0303i	0.240746	−	0.283428i
$40$	274.750	−	405.227i	1.08605	−	1.60180i
$41$	−10.8283	+	199.716i	−0.0412462	+	0.760742i	0.902625	+	0.430428i	$0.141637\pi$
$41$	−10.8283	+	199.716i	−0.0412462	+	0.760742i	−0.943871	+	0.330314i	$0.892845\pi$
$42$	14.4904	−	36.3683i	0.0532363	−	0.133613i
$43$	−17.4299	+	8.06392i	−0.0618147	+	0.0285985i	−0.450553	−	0.892750i	$-0.648773\pi$
$43$	−17.4299	+	8.06392i	−0.0618147	+	0.0285985i	0.388738	+	0.921348i	$0.372911\pi$
$44$	−37.6164	−	8.27999i	−0.128884	−	0.0283694i
$45$	85.3993	+	161.080i	0.282902	+	0.533609i
$46$	28.5930	+	174.409i	0.0916479	+	0.559027i
$47$	−49.3229	−	37.4943i	−0.153074	−	0.116364i	0.525834	−	0.850587i	$-0.323753\pi$
$47$	−49.3229	−	37.4943i	−0.153074	−	0.116364i	−0.678908	+	0.734223i	$0.737546\pi$
$48$	51.4230	+	23.7908i	0.154631	+	0.0715397i
$49$	219.457	−	207.881i	0.639817	−	0.606067i
$50$	−94.4180	+	575.924i	−0.267054	+	1.62896i
$51$	−101.425	+	34.1740i	−0.278477	+	0.0938297i
$52$	−42.6594	−	107.067i	−0.113765	−	0.285529i
$53$	−161.287	−	152.779i	−0.418009	−	0.395959i	0.449581	−	0.893240i	$-0.351573\pi$
$53$	−161.287	−	152.779i	−0.418009	−	0.395959i	−0.867590	+	0.497281i	$0.834332\pi$
$54$	−43.9587	+	33.4166i	−0.110778	+	0.0842114i
$55$	199.611	−	43.9377i	0.489373	−	0.107719i
$56$	−99.8357	−	117.536i	−0.238234	−	0.280471i
$57$	−130.695	+	14.2139i	−0.303701	+	0.0330294i
$58$	164.685			0.372831
$59$	−448.795	+	62.9462i	−0.990307	+	0.138897i
$59$	−448.795	+	62.9462i	−0.990307	+	0.138897i
$60$	232.000			0.499185
$61$	−28.2997	+	3.07777i	−0.0594000	+	0.00646014i	−0.137771	−	0.990464i	$-0.543994\pi$
$61$	−28.2997	+	3.07777i	−0.0594000	+	0.00646014i	0.0783708	+	0.996924i	$0.475028\pi$
$62$	432.625	+	509.326i	0.886185	+	1.04330i
$63$	56.0851	−	12.3453i	0.112160	−	0.0246882i
$64$	372.184	−	282.927i	0.726921	−	0.552591i
$65$	444.010	+	420.588i	0.847271	+	0.802578i
$66$	22.9126	+	57.5062i	0.0427324	+	0.107250i
$67$	−157.146	+	52.9486i	−0.286544	+	0.0965478i	−0.458903	−	0.888486i	$-0.651758\pi$
$67$	−157.146	+	52.9486i	−0.286544	+	0.0965478i	0.172359	+	0.985034i	$0.444861\pi$
$68$	−22.0335	+	134.398i	−0.0392934	+	0.239679i
$69$	−188.220	+	178.292i	−0.328392	+	0.311070i
$70$	239.920	+	110.999i	0.409656	+	0.189527i
$71$	−365.568	−	277.898i	−0.611056	−	0.464512i	0.253304	−	0.967387i	$-0.418483\pi$
$71$	−365.568	−	277.898i	−0.611056	−	0.464512i	−0.864360	+	0.502874i	$0.832276\pi$
$72$	35.1897	+	214.648i	0.0575993	+	0.351340i
$73$	263.714	+	497.417i	0.422813	+	0.797510i	0.999815	−	0.0192328i	$-0.00612235\pi$
$73$	263.714	+	497.417i	0.422813	+	0.797510i	−0.577002	+	0.816743i	$0.695778\pi$
$74$	24.8217	+	5.46367i	0.0389928	+	0.00858296i
$75$	−776.982	+	359.470i	−1.19624	+	0.553440i
$76$	−61.9204	+	155.409i	−0.0934574	+	0.234560i
$77$	3.48545	−	64.2854i	0.00515850	−	0.0951429i
$78$	−103.948	+	153.312i	−0.150895	+	0.222554i
$79$	520.229	−	612.461i	0.740890	−	0.872244i	−0.254606	−	0.967045i	$-0.581946\pi$
$79$	520.229	−	612.461i	0.740890	−	0.872244i	0.995496	+	0.0948013i	$0.0302216\pi$
$80$	−179.211	+	338.028i	−0.250455	+	0.472409i
$81$	−76.7599	−	25.8634i	−0.105295	−	0.0354779i
$82$	−22.1451	−	408.442i	−0.0298234	−	0.550060i
$83$	451.620	+	271.731i	0.597250	+	0.359353i	0.781856	−	0.623459i	$-0.214273\pi$
$83$	451.620	+	271.731i	0.597250	+	0.359353i	−0.184606	+	0.982813i	$0.559101\pi$
$84$	19.5501	−	70.4132i	0.0253940	−	0.0914609i
$85$	−193.344	−	696.362i	−0.246719	−	0.888600i
$86$	33.6541	−	20.2490i	0.0421978	−	0.0253896i
$87$	135.570	+	199.951i	0.167065	+	0.246403i
$88$	242.416	+	26.3643i	0.293655	+	0.0319369i
$89$	1223.98	+	133.116i	1.45778	+	0.158543i	0.802412	−	0.596771i	$-0.203550\pi$
$89$	1223.98	+	133.116i	1.45778	+	0.158543i	0.655363	+	0.755314i	$0.272515\pi$
$90$	−209.245	−	308.613i	−0.245071	−	0.361452i
$91$	165.066	−	99.3171i	0.190150	−	0.114409i
$92$	88.2595	+	317.882i	0.100018	+	0.360233i
$93$	−262.254	+	944.553i	−0.292413	+	1.05318i
$94$	108.570	+	65.3246i	0.119129	+	0.0716778i
$95$	−48.0603	−	886.421i	−0.0519041	−	0.957314i
$96$	439.863	+	148.207i	0.467639	+	0.157566i
$97$	−745.126	+	1405.46i	−0.779960	+	1.47116i	0.0994232	+	0.995045i	$0.468300\pi$
$97$	−745.126	+	1405.46i	−0.779960	+	1.47116i	−0.879383	+	0.476115i	$0.842045\pi$
$98$	−400.219	+	471.174i	−0.412532	+	0.485671i
$99$	−50.9590	+	75.1589i	−0.0517331	+	0.0763006i
$100$	−58.9788	+	1087.80i	−0.0589788	+	1.08780i
$101$	−394.654	+	990.507i	−0.388807	+	0.975833i	0.596125	+	0.802892i	$0.296706\pi$
$101$	−394.654	+	990.507i	−0.388807	+	0.975833i	−0.984932	+	0.172941i	$0.944673\pi$
$102$	198.653	−	91.9066i	0.192839	−	0.0892168i
$103$	−926.836	−	204.012i	−0.886640	−	0.195164i	−0.251774	−	0.967786i	$-0.581014\pi$
$103$	−926.836	−	204.012i	−0.886640	−	0.195164i	−0.634866	+	0.772622i	$0.718945\pi$
$104$	341.774	+	644.655i	0.322247	+	0.607823i
$105$	62.7361	+	382.673i	0.0583087	+	0.355668i
$106$	361.698	+	274.956i	0.331427	+	0.251944i
$107$	142.618	+	65.9821i	0.128854	+	0.0596143i	0.483257	−	0.875479i	$-0.339454\pi$
$107$	142.618	+	65.9821i	0.128854	+	0.0596143i	−0.354403	+	0.935093i	$0.615316\pi$
$108$	−74.8303	+	70.8830i	−0.0666718	+	0.0631549i
$109$	−81.0291	+	494.256i	−0.0712035	+	0.434322i	0.927034	+	0.374977i	$0.122349\pi$
$109$	−81.0291	+	494.256i	−0.0712035	+	0.434322i	−0.998238	+	0.0593450i	$0.981099\pi$
$110$	−396.119	+	133.468i	−0.343349	+	0.115688i
$111$	13.7998	+	34.6349i	0.0118002	+	0.0296162i
$112$	87.4915	+	82.8764i	0.0738140	+	0.0699204i
$113$	1502.13	−	1141.89i	1.25052	−	0.950620i	0.250672	−	0.968072i	$-0.419348\pi$
$113$	1502.13	−	1141.89i	1.25052	−	0.950620i	0.999848	+	0.0174517i	$0.00555534\pi$
$114$	262.576	−	57.7973i	0.215724	−	0.0474843i
$115$	−1133.35	−	1334.28i	−0.919000	−	1.08193i
$116$	305.607	−	33.2367i	0.244611	−	0.0266030i
$117$	−271.715			−0.214701
$118$	898.538	−	227.213i	0.700992	−	0.177260i
$119$	−227.642			−0.175361
$120$	−1460.15	+	158.801i	−1.11078	+	0.120804i
$121$	−795.768	−	936.851i	−0.597872	−	0.703870i
$122$	56.8562	−	12.5150i	0.0421928	−	0.00928733i
$123$	477.678	−	363.122i	0.350169	−	0.266192i
$124$	905.617	+	857.846i	0.655861	+	0.621265i
$125$	−1202.46	−	3017.95i	−0.860412	−	2.15947i
$126$	−111.298	+	37.5008i	−0.0786924	+	0.0265145i
$127$	200.706	−	1224.25i	0.140234	−	0.855392i	−0.819210	−	0.573494i	$-0.805588\pi$
$127$	200.706	−	1224.25i	0.140234	−	0.855392i	0.959444	−	0.281898i	$-0.0909641\pi$
$128$	204.472	−	193.686i	0.141195	−	0.133747i
$129$	52.2897	+	24.1918i	0.0356887	+	0.0165114i
$130$	−995.726	−	756.931i	−0.671776	−	0.510671i
$131$	−274.580	−	1674.86i	−0.183131	−	1.11705i	−0.905124	−	0.425148i	$-0.860222\pi$
$131$	−274.580	−	1674.86i	−0.183131	−	1.11705i	0.721993	−	0.691900i	$-0.243226\pi$
$132$	54.1249	+	102.090i	0.0356891	+	0.0673168i
$133$	−273.083	−	60.1101i	−0.178040	−	0.0391896i
$134$	307.790	−	142.399i	0.198425	−	0.0918013i
$135$	202.449	−	508.108i	0.129067	−	0.323933i
$136$	46.6795	−	860.953i	0.0294319	−	0.542839i
$137$	897.826	−	1324.19i	0.559901	−	0.825792i	−0.437396	−	0.899269i	$-0.644099\pi$
$137$	897.826	−	1324.19i	0.559901	−	0.825792i	0.997297	+	0.0734767i	$0.0234095\pi$
$138$	343.253	−	404.108i	0.211736	−	0.249275i
$139$	1317.17	−	2484.45i	0.803750	−	1.51603i	−0.0520026	−	0.998647i	$-0.516560\pi$
$139$	1317.17	−	2484.45i	0.803750	−	1.51603i	0.855752	−	0.517386i	$-0.173095\pi$
$140$	467.623	+	157.560i	0.282295	+	0.0951163i
$141$	10.0627	+	185.596i	0.00601018	+	0.110851i
$142$	804.693	+	484.168i	0.475552	+	0.286130i
$143$	−81.4914	+	293.506i	−0.0476549	+	0.171638i
$144$	−45.4742	−	163.783i	−0.0263161	−	0.0947821i
$145$	−1397.76	+	841.003i	−0.800534	+	0.481666i
$146$	−646.150	−	953.000i	−0.366272	−	0.540211i
$147$	−901.538	−	98.0482i	−0.505834	−	0.0550128i
$148$	47.1644	+	5.12944i	0.0261952	+	0.00284890i
$149$	1983.71	+	2925.75i	1.09068	+	1.60864i	0.740639	+	0.671903i	$0.234523\pi$
$149$	1983.71	+	2925.75i	1.09068	+	1.60864i	0.350043	+	0.936734i	$0.386167\pi$
$150$	1500.22	−	902.651i	0.816615	−	0.491341i
$151$	−28.0497	−	101.026i	−0.0151169	−	0.0544462i	0.955607	−	0.294645i	$-0.0952013\pi$
$151$	−28.0497	−	101.026i	−0.0151169	−	0.0544462i	−0.970724	+	0.240198i	$0.922787\pi$
$152$	283.337	−	1020.49i	0.151195	−	0.544556i
$153$	275.121	+	165.535i	0.145374	+	0.0874687i
$154$	7.12815	+	131.471i	0.00372989	+	0.0687938i
$155$	−6272.89	−	2113.58i	−3.25065	−	1.09527i
$156$	−161.956	+	305.481i	−0.0831209	+	0.156783i
$157$	2196.32	−	2585.70i	1.11647	−	1.31441i	0.172259	−	0.985052i	$-0.444893\pi$
$157$	2196.32	−	2585.70i	1.11647	−	1.31441i	0.944207	−	0.329353i	$-0.106831\pi$
$158$	−922.266	+	1360.24i	−0.464377	+	0.684905i
$159$	−36.0824	+	665.501i	−0.0179970	+	0.331935i
$160$	−1160.11	+	2911.65i	−0.573215	+	1.43866i
$161$	−500.464	+	231.539i	−0.244982	+	0.113341i
$162$	161.781	+	35.6108i	0.0784614	+	0.0172707i
$163$	1392.02	+	2625.62i	0.668903	+	1.26168i	0.953024	+	0.302896i	$0.0979534\pi$
$163$	1392.02	+	2625.62i	0.668903	+	1.26168i	−0.284121	+	0.958788i	$0.591702\pi$
$164$	−123.527	−	753.479i	−0.0588159	−	0.358761i
$165$	−488.139	−	371.074i	−0.230312	−	0.175079i
$166$	−978.284	−	452.603i	−0.457407	−	0.211619i
$167$	−2702.20	+	2559.66i	−1.25211	+	1.18606i	−0.277853	+	0.960624i	$0.589623\pi$
$167$	−2702.20	+	2559.66i	−1.25211	+	1.18606i	−0.974257	+	0.225439i	$0.927618\pi$
$168$	−74.8469	+	456.546i	−0.0343724	+	0.209662i
$169$	1218.24	−	410.472i	0.554500	−	0.186833i
$170$	547.069	+	1373.04i	0.246813	+	0.619455i
$171$	286.330	+	271.226i	0.128048	+	0.121293i
$172$	58.3654	−	44.3682i	0.0258740	−	0.0196689i
$173$	311.213	−	68.5032i	0.136769	−	0.0301052i	−0.146058	−	0.989276i	$-0.546659\pi$
$173$	311.213	−	68.5032i	0.136769	−	0.0301052i	0.282827	+	0.959171i	$0.408728\pi$
$174$	−319.844	−	376.550i	−0.139352	−	0.164058i
$175$	−1810.22	+	196.874i	−0.781943	+	0.0850415i
$176$	−190.557			−0.0816122
$177$	1015.56	+	903.912i	0.431265	+	0.383854i
$178$	−2517.95			−1.06027
$179$	1190.40	−	129.463i	0.497064	−	0.0540590i	0.143846	−	0.989600i	$-0.454053\pi$
$179$	1190.40	−	129.463i	0.497064	−	0.0540590i	0.353218	+	0.935541i	$0.385087\pi$
$180$	−450.581	−	530.465i	−0.186580	−	0.219659i
$181$	2207.57	−	485.924i	0.906562	−	0.199549i	0.262867	−	0.964832i	$-0.415332\pi$
$181$	2207.57	−	485.924i	0.906562	−	0.199549i	0.643694	+	0.765283i	$0.277401\pi$
$182$	−313.640	+	238.423i	−0.127739	+	0.0971048i
$183$	61.9997	+	58.7292i	0.0250445	+	0.0237234i
$184$	−773.070	−	1940.26i	−0.309736	−	0.777379i
$185$	−238.575	+	80.3853i	−0.0948129	+	0.0319462i
$186$	324.339	−	1978.38i	0.127859	−	0.779904i
$187$	261.323	−	247.539i	0.102192	−	0.0968012i
$188$	214.658	+	99.3115i	0.0832743	+	0.0385268i
$189$	−137.153	−	104.261i	−0.0527854	−	0.0401264i
$190$	293.714	+	1791.58i	0.112149	+	0.684078i
$191$	2289.65	+	4318.73i	0.867398	+	1.63609i	0.767464	+	0.641092i	$0.221518\pi$
$191$	2289.65	+	4318.73i	0.867398	+	1.63609i	0.0999342	+	0.994994i	$0.468137\pi$
$192$	−1369.75	−	301.504i	−0.514859	−	0.113329i
$193$	−3631.54	+	1680.13i	−1.35442	+	0.626623i	−0.956752	−	0.290905i	$-0.906044\pi$
$193$	−3631.54	+	1680.13i	−1.35442	+	0.626623i	−0.397671	+	0.917528i	$0.630181\pi$
$194$	1204.17	−	3022.23i	0.445640	−	1.11847i
$195$	99.3320	−	1832.07i	0.0364785	−	0.672807i
$196$	−647.595	+	955.132i	−0.236004	+	0.348080i
$197$	−672.066	+	791.217i	−0.243059	+	0.286152i	−0.870142	−	0.492801i	$-0.835973\pi$
$197$	−672.066	+	791.217i	−0.243059	+	0.286152i	0.627083	+	0.778953i	$0.284249\pi$
$198$	86.9873	−	164.075i	0.0312218	−	0.0588906i
$199$	1409.87	+	475.040i	0.502225	+	0.169219i	0.559000	−	0.829168i	$-0.311185\pi$
$199$	1409.87	+	475.040i	0.502225	+	0.169219i	−0.0567748	+	0.998387i	$0.518082\pi$
$200$	−373.388	−	6886.73i	−0.132012	−	2.43483i
$201$	426.269	+	256.477i	0.149585	+	0.0900026i
$202$	583.364	−	2101.09i	0.203195	−	0.731842i
$203$	137.463	+	495.096i	0.0475270	+	0.171177i
$204$	350.093	−	210.644i	0.120154	−	0.0722942i
$205$	2273.76	+	3353.55i	0.774666	+	1.14255i
$206$	1929.49	+	209.844i	0.652590	+	0.0709735i
$207$	773.216	+	84.0923i	0.259624	+	0.0282358i
$208$	−319.987	−	471.945i	−0.106669	−	0.157325i
$209$	378.852	−	227.948i	0.125386	−	0.0754424i
$210$	−212.166	−	764.151i	−0.0697182	−	0.251102i
$211$	163.149	−	587.608i	0.0532304	−	0.191719i	−0.932155	−	0.362060i	$-0.882073\pi$
$211$	163.149	−	587.608i	0.0532304	−	0.191719i	0.985385	+	0.170342i	$0.0544872\pi$
$212$	726.697	+	437.239i	0.235423	+	0.141650i
$213$	74.5822	+	1375.59i	0.0239920	+	0.442506i
$214$	−304.550	−	102.615i	−0.0972832	−	0.0327785i
$215$	−182.232	+	343.725i	−0.0578051	+	0.109032i
$216$	422.446	−	497.341i	0.133073	−	0.156666i
$217$	−1170.08	+	1725.75i	−0.366039	+	0.539867i
$218$	55.4547	−	1022.80i	0.0172287	−	0.317765i
$219$	625.163	−	1569.04i	0.192898	−	0.484137i
$220$	−708.143	+	327.622i	−0.217014	+	0.100401i
$221$	1051.89	+	231.538i	0.320171	+	0.0704749i
$222$	−35.7151	−	67.3658i	−0.0107975	−	0.0203662i
$223$	274.777	+	1676.06i	0.0825130	+	0.503307i	0.995456	+	0.0952204i	$0.0303556\pi$
$223$	274.777	+	1676.06i	0.0825130	+	0.503307i	−0.912943	+	0.408087i	$0.866196\pi$
$224$	785.940	+	597.456i	0.234432	+	0.178211i
$225$	2330.95	+	1078.41i	0.690650	+	0.319529i
$226$	−2801.53	+	2653.75i	−0.824581	+	0.781084i
$227$	−15.2640	+	93.1064i	−0.00446303	+	0.0272233i	−0.988964	−	0.148155i	$-0.952667\pi$
$227$	−15.2640	+	93.1064i	−0.00446303	+	0.0272233i	0.984501	+	0.175378i	$0.0561148\pi$
$228$	475.599	−	160.248i	0.138146	−	0.0465468i
$229$	−745.711	−	1871.59i	−0.215188	−	0.540080i	0.781268	−	0.624195i	$-0.214573\pi$
$229$	−745.711	−	1871.59i	−0.215188	−	0.540080i	−0.996456	+	0.0841150i	$0.973194\pi$
$230$	2599.26	+	2462.15i	0.745175	+	0.705868i
$231$	−153.757	+	116.883i	−0.0437942	+	0.0332915i
$232$	−1900.66	+	418.368i	−0.537865	+	0.118393i
$233$	2716.30	+	3197.88i	0.763738	+	0.899141i	0.997318	−	0.0731961i	$-0.0233199\pi$
$233$	2716.30	+	3197.88i	0.763738	+	0.899141i	−0.233580	+	0.972338i	$0.575044\pi$
$234$	552.431	−	60.0805i	0.154331	−	0.0167845i
$235$	−1255.08			−0.348394
$236$	1621.57	−	602.984i	0.447267	−	0.166317i
$237$	−2410.75			−0.660739
$238$	462.825	−	50.3352i	0.126052	−	0.0137090i
$239$	2504.15	+	2948.12i	0.677742	+	0.797899i	0.988278	−	0.152662i	$-0.0487846\pi$
$239$	2504.15	+	2948.12i	0.677742	+	0.797899i	−0.310537	+	0.950561i	$0.600509\pi$
$240$	1120.95	−	246.740i	0.301488	−	0.0663626i
$241$	3260.89	−	2478.86i	0.871586	−	0.662563i	−0.0706537	−	0.997501i	$-0.522509\pi$
$241$	3260.89	−	2478.86i	0.871586	−	0.662563i	0.942240	+	0.334938i	$0.108715\pi$
$242$	1825.05	+	1728.78i	0.484788	+	0.459215i
$243$	89.9436	+	225.741i	0.0237444	+	0.0595939i
$244$	102.983	−	34.6989i	0.0270196	−	0.00910397i
$245$	990.681	−	6042.88i	0.258336	−	1.57578i
$246$	−890.888	+	843.894i	−0.230898	+	0.218718i
$247$	1200.73	+	555.515i	0.309313	+	0.143104i
$248$	−6286.92	−	4779.19i	−1.60976	−	1.22371i
$249$	−255.809	−	1560.37i	−0.0651054	−	0.397126i
$250$	3112.08	+	5870.00i	0.787300	+	1.48500i
$251$	−1592.10	−	350.447i	−0.400368	−	0.0881277i	0.0102220	−	0.999948i	$-0.496746\pi$
$251$	−1592.10	−	350.447i	−0.400368	−	0.0881277i	−0.410590	+	0.911820i	$0.634677\pi$
$252$	−198.968	+	92.0526i	−0.0497374	+	0.0230110i
$253$	322.735	−	810.004i	0.0801984	−	0.201283i
$254$	−137.359	+	2533.44i	−0.0339318	+	0.625835i
$255$	−1216.72	+	1794.52i	−0.298799	+	0.440696i
$256$	−2794.18	+	3289.56i	−0.682173	+	0.803116i
$257$	1203.76	−	2270.54i	0.292174	−	0.551098i	−0.693357	−	0.720594i	$-0.743869\pi$
$257$	1203.76	−	2270.54i	0.292174	−	0.551098i	0.985531	+	0.169496i	$0.0542140\pi$
$258$	−111.661	−	37.6228i	−0.0269445	−	0.00907867i
$259$	4.29315	+	79.1826i	0.00102998	+	0.0189968i
$260$	−2000.54	−	1203.68i	−0.477185	−	0.287113i
$261$	193.887	−	698.318i	0.0459820	−	0.165612i
$262$	928.593	+	3344.49i	0.218964	+	0.788638i
$263$	−5609.45	+	3375.09i	−1.31518	+	0.791320i	−0.988120	−	0.153683i	$-0.950887\pi$
$263$	−5609.45	+	3375.09i	−1.31518	+	0.791320i	−0.327063	+	0.945002i	$0.606059\pi$
$264$	−410.529	−	605.484i	−0.0957056	−	0.141155i
$265$	−4474.03	−	486.580i	−1.03712	−	0.112794i
$266$	568.504	+	61.8285i	0.131042	+	0.0142517i
$267$	−2072.80	−	3057.15i	−0.475106	−	0.700730i
$268$	542.428	−	326.368i	0.123635	−	0.0743884i
$269$	1779.37	+	6408.71i	0.403309	+	1.45259i	0.834842	+	0.550490i	$0.185559\pi$
$269$	1779.37	+	6408.71i	0.403309	+	1.45259i	−0.431533	+	0.902097i	$0.642027\pi$
$270$	−299.253	+	1077.81i	−0.0674517	+	0.242939i
$271$	6049.51	+	3639.87i	1.35602	+	0.815891i	0.993251	−	0.115988i	$-0.0370034\pi$
$271$	6049.51	+	3639.87i	1.35602	+	0.815891i	0.362770	+	0.931879i	$0.381831\pi$
$272$	36.4784	+	672.805i	0.00813172	+	0.149981i
$273$	−547.672	−	184.532i	−0.121416	−	0.0409099i
$274$	−1532.59	+	2890.78i	−0.337910	+	0.637366i
$275$	1863.98	−	2194.45i	0.408735	−	0.481201i
$276$	555.419	−	819.181i	0.121131	−	0.178655i
$277$	−45.5218	+	839.599i	−0.00987414	+	0.182118i	0.989436	+	0.144972i	$0.0463093\pi$
$277$	−45.5218	+	839.599i	−0.00987414	+	0.182118i	−0.999310	+	0.0371456i	$0.988173\pi$
$278$	−2128.63	+	5342.45i	−0.459232	+	1.15259i
$279$	2669.05	−	1234.83i	0.572730	−	0.264973i
$280$	−3050.95	−	671.566i	−0.651176	−	0.143335i
$281$	−2780.56	−	5244.69i	−0.590299	−	1.11342i	−0.981201	−	0.192990i	$-0.938181\pi$
$281$	−2780.56	−	5244.69i	−0.590299	−	1.11342i	0.390901	−	0.920433i	$-0.372163\pi$
$282$	−61.4970	−	375.115i	−0.0129862	−	0.0792120i
$283$	−774.844	−	589.021i	−0.162755	−	0.123723i	0.520627	−	0.853785i	$-0.325698\pi$
$283$	−774.844	−	589.021i	−0.162755	−	0.123723i	−0.683382	+	0.730061i	$0.739491\pi$
$284$	1590.99	+	736.070i	0.332422	+	0.153795i
$285$	−1933.45	+	1831.46i	−0.401851	+	0.380654i
$286$	100.784	−	614.753i	0.0208373	−	0.127102i
$287$	1209.42	−	407.502i	0.248746	−	0.0838122i
$288$	−515.410	−	1293.58i	−0.105454	−	0.264670i
$289$	2642.80	+	2503.39i	0.537919	+	0.509544i
$290$	2655.86	−	2018.93i	0.537784	−	0.408813i
$291$	4660.71	−	1025.90i	0.938886	−	0.206664i
$292$	−1391.40	−	1638.08i	−0.278854	−	0.328292i
$293$	3259.88	−	354.534i	0.649981	−	0.0706897i	0.222812	−	0.974861i	$-0.428476\pi$
$293$	3259.88	−	354.534i	0.649981	−	0.0706897i	0.427169	+	0.904172i	$0.359511\pi$
$294$	1854.62			0.367904
$295$	−6465.99	+	6517.06i	−1.27615	+	1.28623i
$296$	−300.353			−0.0589785
$297$	270.820	−	29.4535i	0.0529111	−	0.00575443i
$298$	−4680.06	−	5509.79i	−0.909760	−	1.07105i
$299$	2548.05	−	560.869i	0.492835	−	0.108481i
$300$	2601.79	−	1977.83i	0.500714	−	0.380633i
$301$	88.9661	+	84.2732i	0.0170363	+	0.0161376i
$302$	79.3670	+	199.196i	0.0151227	+	0.0379551i
$303$	3031.26	−	1021.35i	0.574724	−	0.193647i
$304$	−133.898	+	816.740i	−0.0252617	+	0.154090i
$305$	−418.654	+	396.571i	−0.0785970	+	0.0744510i
$306$	−595.959	−	275.720i	−0.111336	−	0.0515093i
$307$	−3436.40	−	2612.28i	−0.638846	−	0.485638i	0.234901	−	0.972019i	$-0.424524\pi$
$307$	−3436.40	−	2612.28i	−0.638846	−	0.485638i	−0.873747	+	0.486381i	$0.838317\pi$
$308$	39.7612	+	242.533i	0.00735587	+	0.0448688i
$309$	1333.59	+	2515.42i	0.245519	+	0.463098i
$310$	13220.9	+	2910.14i	2.42225	+	0.533177i
$311$	−6185.44	+	2861.69i	−1.12779	+	0.521773i	−0.892903	−	0.450249i	$-0.851335\pi$
$311$	−6185.44	+	2861.69i	−1.12779	+	0.521773i	−0.234891	+	0.972022i	$0.575473\pi$
$312$	810.214	−	2033.48i	0.147017	−	0.368985i
$313$	556.956	−	10272.4i	0.100578	−	1.85506i	−0.319522	−	0.947579i	$-0.603522\pi$
$313$	556.956	−	10272.4i	0.100578	−	1.85506i	0.420100	−	0.907478i	$-0.361995\pi$
$314$	−3893.65	+	5742.70i	−0.699781	+	1.03210i
$315$	753.134	−	886.658i	0.134712	−	0.158595i
$316$	−1436.93	+	2710.34i	−0.255803	+	0.482495i
$317$	−7904.04	−	2663.18i	−1.40043	−	0.471859i	−0.485060	−	0.874481i	$-0.661202\pi$
$317$	−7904.04	−	2663.18i	−1.40043	−	0.471859i	−0.915366	+	0.402622i	$0.868099\pi$
$318$	−73.7927	−	1361.03i	−0.0130129	−	0.240008i
$319$	−696.171	−	418.872i	−0.122188	−	0.0735183i
$320$	2533.67	−	9125.46i	0.442614	−	1.59415i
$321$	−126.120	−	454.242i	−0.0219293	−	0.0789823i
$322$	966.310	−	581.409i	0.167237	−	0.100623i
$323$	−877.346	−	1293.99i	−0.151136	−	0.222909i
$324$	307.405	+	33.4324i	0.0527101	+	0.00573257i
$325$	8564.95	+	931.494i	1.46184	+	0.158985i
$326$	−3410.71	−	5030.42i	−0.579453	−	0.854630i
$327$	1287.48	−	774.651i	0.217730	−	0.131004i
$328$	1293.19	+	4657.66i	0.217697	+	0.784074i
$329$	−105.763	+	380.924i	−0.0177231	+	0.0638329i
$330$	1074.50	+	646.504i	0.179240	+	0.107845i
$331$	−350.504	−	6464.67i	−0.0582038	−	1.07351i	−0.871102	−	0.491101i	$-0.836594\pi$
$331$	−350.504	−	6464.67i	−0.0582038	−	1.07351i	0.812899	−	0.582405i	$-0.197888\pi$
$332$	−1906.75	−	642.459i	−0.315201	−	0.106203i
$333$	52.3908	−	98.8196i	0.00862162	−	0.0162621i
$334$	4927.93	−	5801.61i	0.807318	−	0.950449i
$335$	−1885.16	+	2780.41i	−0.307455	+	0.453462i
$336$	19.5732	−	361.007i	0.00317800	−	0.0586148i
$337$	−2100.85	+	5272.74i	−0.339587	+	0.852298i	0.655673	+	0.755045i	$0.272385\pi$
$337$	−2100.85	+	5272.74i	−0.339587	+	0.852298i	−0.995260	+	0.0972530i	$0.968994\pi$
$338$	−2386.07	+	1103.91i	−0.383979	+	0.177648i
$339$	−5528.30	−	1216.87i	−0.885711	−	0.194960i
$340$	1292.31	+	2437.55i	0.206133	+	0.388808i
$341$	−533.374	−	3253.44i	−0.0847033	−	0.516667i
$342$	−642.117	−	488.124i	−0.101525	−	0.0771776i
$343$	−3736.91	−	1728.88i	−0.588263	−	0.272160i
$344$	−336.968	+	319.193i	−0.0528143	+	0.0500284i
$345$	−849.670	+	5182.76i	−0.132593	+	0.808783i
$346$	−617.588	+	208.090i	−0.0959588	+	0.0323323i
$347$	3792.30	+	9517.95i	0.586689	+	1.47248i	0.859868	+	0.510516i	$0.170546\pi$
$347$	3792.30	+	9517.95i	0.586689	+	1.47248i	−0.273179	+	0.961963i	$0.588075\pi$
$348$	−669.532	−	634.214i	−0.103134	−	0.0976938i
$349$	1777.07	−	1350.89i	0.272563	−	0.207197i	−0.459960	−	0.887940i	$-0.652136\pi$
$349$	1777.07	−	1350.89i	0.272563	−	0.207197i	0.732522	+	0.680743i	$0.238343\pi$
$350$	3636.88	−	800.538i	0.555427	−	0.122259i
$351$	527.714	+	621.273i	0.0802486	+	0.0944760i
$352$	−1551.90	+	168.779i	−0.234990	+	0.0255568i
$353$	3331.16			0.502265			0.251133	−	0.967953i	$-0.419197\pi$
$353$	3331.16			0.502265			0.251133	+	0.967953i	$0.419197\pi$
$354$	−2264.62	−	1613.21i	−0.340009	−	0.242207i
$355$	−9302.33			−1.39075
$356$	−4672.57	+	508.172i	−0.695633	+	0.0756547i
$357$	442.117	+	520.500i	0.0655443	+	0.0771647i
$358$	−2391.60	+	526.431i	−0.353073	+	0.0777172i
$359$	10242.2	−	7785.92i	1.50575	−	1.14464i	0.556184	−	0.831059i	$-0.312265\pi$
$359$	10242.2	−	7785.92i	1.50575	−	1.14464i	0.949562	−	0.313580i	$-0.101528\pi$
$360$	3198.95	+	3030.20i	0.468332	+	0.443627i
$361$	1827.98	+	4587.89i	0.266509	+	0.668886i
$362$	−4380.83	+	1476.07i	−0.636053	+	0.214311i
$363$	−596.588	+	3639.03i	−0.0862610	+	0.526169i
$364$	−533.905	+	505.742i	−0.0768797	+	0.0728243i
$365$	10350.9	+	4788.83i	1.48436	+	0.686737i
$366$	−139.039	−	105.695i	−0.0198571	−	0.0150950i
$367$	−1047.60	−	6390.06i	−0.149003	−	0.908878i	−0.950465	−	0.310832i	$-0.899392\pi$
$367$	−1047.60	−	6390.06i	−0.149003	−	0.908878i	0.801462	−	0.598046i	$-0.204056\pi$
$368$	764.521	+	1442.04i	0.108297	+	0.204270i
$369$	−1758.00	−	386.965i	−0.248016	−	0.0545924i
$370$	467.278	−	216.186i	0.0656558	−	0.0303756i
$371$	−524.696	+	1316.89i	−0.0734255	+	0.184284i
$372$	202.601	−	3736.75i	0.0282375	−	0.520811i
$373$	−3140.82	+	4632.36i	−0.435993	+	0.643041i	−0.980685	−	0.195595i	$-0.937336\pi$
$373$	−3140.82	+	4632.36i	−0.435993	+	0.643041i	0.544692	+	0.838636i	$0.316647\pi$
$374$	−476.569	+	561.060i	−0.0658898	+	0.0775714i
$375$	−4565.14	+	8610.76i	−0.628647	+	1.18575i
$376$	−1418.99	−	478.112i	−0.194624	−	0.0655764i
$377$	−131.618	−	2427.56i	−0.0179806	−	0.331633i
$378$	301.904	+	181.650i	0.0410801	+	0.0247170i
$379$	970.843	−	3496.66i	0.131580	−	0.473909i	−0.868170	−	0.496267i	$-0.834704\pi$
$379$	970.843	−	3496.66i	0.131580	−	0.473909i	0.999750	+	0.0223584i	$0.00711750\pi$
$380$	906.624	+	3265.36i	0.122392	+	0.440815i
$381$	−3189.04	+	1918.78i	−0.428817	+	0.258011i
$382$	−5610.08	−	8274.25i	−0.751405	−	1.10824i
$383$	−11388.0	−	1238.52i	−1.51932	−	0.165236i	−0.689915	−	0.723890i	$-0.742352\pi$
$383$	−11388.0	−	1238.52i	−1.51932	−	0.165236i	−0.829400	+	0.558655i	$0.811318\pi$
$384$	−839.977	−	91.3530i	−0.111627	−	0.0121402i
$385$	−731.888	−	1079.45i	−0.0968844	−	0.142894i
$386$	7011.86	−	4218.90i	0.924597	−	0.556312i
$387$	−46.2407	−	166.544i	−0.00607376	−	0.0218757i
$388$	1624.63	−	5851.39i	0.212573	−	0.765617i
$389$	9677.75	+	5822.91i	1.26139	+	0.758954i	0.979684	−	0.200546i	$-0.0642716\pi$
$389$	9677.75	+	5822.91i	1.26139	+	0.758954i	0.281708	+	0.959500i	$0.409099\pi$
$390$	203.145	+	3746.79i	0.0263761	+	0.486478i
$391$	−2921.69	−	984.432i	−0.377893	−	0.127327i
$392$	3422.03	−	6454.64i	0.440915	−	0.831655i
$393$	−3296.27	+	3880.67i	−0.423091	+	0.498101i
$394$	1191.44	−	1757.25i	0.152345	−	0.224693i
$395$	881.308	−	16254.8i	0.112262	−	2.07055i
$396$	128.309	−	322.031i	0.0162823	−	0.0408654i
$397$	−3527.35	+	1631.92i	−0.445926	+	0.206307i	−0.629984	−	0.776608i	$-0.716939\pi$
$397$	−3527.35	+	1631.92i	−0.445926	+	0.206307i	0.184058	+	0.982915i	$0.441076\pi$
$398$	−2971.48	−	654.071i	−0.374238	−	0.0823760i
$399$	392.930	+	741.144i	0.0493010	+	0.0929915i
$400$	871.947	+	5318.64i	0.108993	+	0.664830i
$401$	6793.44	+	5164.24i	0.846005	+	0.643116i	0.935678	−	0.352855i	$-0.114789\pi$
$401$	6793.44	+	5164.24i	0.846005	+	0.643116i	−0.0896731	+	0.995971i	$0.528582\pi$
$402$	−923.369	−	427.196i	−0.114561	−	0.0530015i
$403$	7162.02	−	6784.23i	0.885275	−	0.838577i
$404$	658.510	−	4016.74i	0.0810944	−	0.494654i
$405$	−1554.97	+	523.930i	−0.190783	+	0.0642822i
$406$	−388.952	−	976.197i	−0.0475453	−	0.119330i
$407$	−91.0318	−	86.2299i	−0.0110867	−	0.0105019i
$408$	−2059.22	+	1565.38i	−0.249869	+	0.189945i
$409$	11560.1	−	2544.57i	1.39758	−	0.307631i	0.548613	−	0.836076i	$-0.315156\pi$
$409$	11560.1	−	2544.57i	1.39758	−	0.307631i	0.848967	+	0.528446i	$0.177225\pi$
$410$	−5364.37	−	6315.42i	−0.646164	−	0.760723i
$411$	−4771.47	+	518.929i	−0.572651	+	0.0622795i
$412$	3622.91			0.433223
$413$	1433.09	+	2511.64i	0.170745	+	0.299249i
$414$	−1590.64			−0.188830
$415$	10614.5	−	1154.39i	1.25553	−	0.136547i
$416$	−3024.00	−	3560.12i	−0.356403	−	0.419590i
$417$	−8238.83	+	1813.50i	−0.967523	+	0.212968i
$418$	−719.851	+	547.216i	−0.0842322	+	0.0640316i
$419$	−78.1337	−	74.0122i	−0.00910998	−	0.00862943i	0.683131	−	0.730296i	$-0.260618\pi$
$419$	−78.1337	−	74.0122i	−0.00910998	−	0.00862943i	−0.692241	+	0.721666i	$0.743376\pi$
$420$	−547.938	−	1375.22i	−0.0636586	−	0.159771i
$421$	−9997.16	+	3368.44i	−1.15732	+	0.389947i	−0.831522	−	0.555493i	$-0.812530\pi$
$421$	−9997.16	+	3368.44i	−1.15732	+	0.389947i	−0.325799	+	0.945439i	$0.605633\pi$
$422$	−201.772	+	1230.76i	−0.0232752	+	0.141972i
$423$	404.820	−	383.465i	0.0465319	−	0.0440774i
$424$	−4872.94	−	2254.46i	−0.558139	−	0.258223i
$425$	−8104.83	−	6161.13i	−0.925040	−	0.703197i
$426$	−455.799	−	2780.25i	−0.0518393	−	0.316206i
$427$	85.0821	+	160.482i	0.00964265	+	0.0181880i
$428$	−585.865	−	128.959i	−0.0661655	−	0.0145641i
$429$	829.366	−	383.705i	0.0933384	−	0.0431829i
$430$	294.497	−	739.131i	0.0330277	−	0.0828932i
$431$	430.956	−	7948.52i	0.0481634	−	0.888322i	−0.870228	−	0.492649i	$-0.836029\pi$
$431$	430.956	−	7948.52i	0.0481634	−	0.888322i	0.918391	−	0.395673i	$-0.129489\pi$
$432$	−286.170	+	422.070i	−0.0318712	+	0.0470066i
$433$	−3129.23	+	3684.01i	−0.347300	+	0.408874i	−0.907882	−	0.419225i	$-0.862302\pi$
$433$	−3129.23	+	3684.01i	−0.347300	+	0.408874i	0.560582	+	0.828099i	$0.310578\pi$
$434$	1997.34	−	3767.38i	0.220911	−	0.416682i
$435$	4637.61	+	1562.59i	0.511164	+	0.172231i
$436$	−103.514	−	1909.21i	−0.0113703	−	0.209712i
$437$	−3244.97	−	1952.43i	−0.355212	−	0.213724i
$438$	−924.095	+	3328.29i	−0.100810	+	0.363086i
$439$	−3349.60	−	12064.2i	−0.364163	−	1.31160i	−0.888026	−	0.459794i	$-0.847923\pi$
$439$	−3349.60	−	12064.2i	−0.364163	−	1.31160i	0.523863	−	0.851803i	$-0.324490\pi$
$440$	4232.63	−	2546.69i	0.458597	−	0.275929i
$441$	1526.74	+	2251.78i	0.164857	+	0.243146i
$442$	−2189.82	−	238.157i	−0.235654	−	0.0256289i
$443$	1032.80	+	112.324i	0.110767	+	0.0120467i	0.163335	−	0.986571i	$-0.447775\pi$
$443$	1032.80	+	112.324i	0.110767	+	0.0120467i	−0.0525675	+	0.998617i	$0.516740\pi$
$444$	−79.8725	−	117.803i	−0.00853734	−	0.0125916i
$445$	21371.0	−	12858.5i	2.27659	−	1.36978i
$446$	−929.259	−	3346.89i	−0.0986585	−	0.355336i
$447$	2837.01	−	10218.0i	0.300193	−	1.08120i
$448$	−2556.12	−	1537.96i	−0.269565	−	0.162192i
$449$	386.983	+	7137.48i	0.0406745	+	0.750197i	0.945740	+	0.324924i	$0.105339\pi$
$449$	386.983	+	7137.48i	0.0406745	+	0.750197i	−0.905065	+	0.425272i	$0.860178\pi$
$450$	−4977.56	−	1677.13i	−0.521432	−	0.175691i
$451$	−945.249	+	1782.93i	−0.0986918	+	0.186153i
$452$	−4663.24	+	5489.99i	−0.485266	+	0.571300i
$453$	−176.517	+	260.344i	−0.0183080	+	0.0270022i
$454$	10.4464	−	192.672i	0.00107990	−	0.0199175i
$455$	1444.45	−	3625.28i	0.148828	−	0.373530i
$456$	−2883.62	+	1334.10i	−0.296135	+	0.137007i
$457$	−10618.4	−	2337.29i	−1.08689	−	0.239242i	−0.364830	−	0.931074i	$-0.618873\pi$
$457$	−10618.4	−	2337.29i	−1.08689	−	0.239242i	−0.722059	+	0.691832i	$0.756804\pi$
$458$	1929.96	+	3640.30i	0.196902	+	0.371397i
$459$	−155.836	−	950.556i	−0.0158470	−	0.0966627i
$460$	5320.38	+	4044.45i	0.539269	+	0.409942i
$461$	−279.804	−	129.451i	−0.0282685	−	0.0130784i	0.405704	−	0.914005i	$-0.367026\pi$
$461$	−279.804	−	129.451i	−0.0282685	−	0.0130784i	−0.433972	+	0.900926i	$0.642888\pi$
$462$	286.763	−	271.636i	0.0288775	−	0.0273542i
$463$	−376.657	+	2297.50i	−0.0378072	+	0.230614i	−0.998970	−	0.0453670i	$-0.985554\pi$
$463$	−376.657	+	2297.50i	−0.0378072	+	0.230614i	0.961163	+	0.275981i	$0.0890025\pi$
$464$	1441.25	−	485.613i	0.144199	−	0.0485862i
$465$	7350.27	+	18447.8i	0.733033	+	1.83977i
$466$	−6229.69	−	5901.07i	−0.619280	−	0.586613i
$467$	−9451.26	+	7184.66i	−0.936514	+	0.711919i	−0.957673	−	0.287857i	$-0.907057\pi$
$467$	−9451.26	+	7184.66i	−0.936514	+	0.711919i	0.0211596	+	0.999776i	$0.493264\pi$
$468$	1013.02	−	222.983i	0.100058	−	0.0220244i
$469$	685.009	+	806.455i	0.0674430	+	0.0794000i
$470$	2551.74	−	277.519i	0.250432	−	0.0272361i
$471$	−10177.8			−0.995683
$472$	−9793.01	+	4904.98i	−0.954999	+	0.478326i
$473$	−193.768			−0.0188361
$474$	4901.36	−	533.055i	0.474951	−	0.0516541i
$475$	−8095.81	−	9531.13i	−0.782024	−	0.920670i
$476$	848.707	−	186.815i	0.0817236	−	0.0179887i
$477$	1591.74	−	1210.01i	0.152790	−	0.116148i
$478$	−5743.14	−	5440.19i	−0.549550	−	0.520562i
$479$	3257.93	+	8176.79i	0.310770	+	0.779973i	0.998539	+	0.0540432i	$0.0172109\pi$
$479$	3257.93	+	8176.79i	0.310770	+	0.779973i	−0.687769	+	0.725930i	$0.741410\pi$
$480$	8910.55	−	3002.31i	0.847311	−	0.285492i
$481$	60.7001	−	370.254i	0.00575403	−	0.0350980i
$482$	−6081.68	+	5760.87i	−0.574716	+	0.544400i
$483$	1501.39	+	694.618i	0.141440	+	0.0654373i
$484$	3735.66	+	2839.77i	0.350832	+	0.266695i
$485$	5213.42	+	31800.4i	0.488101	+	2.97729i
$486$	−232.782	−	439.073i	−0.0217267	−	0.0409809i
$487$	13172.0	+	2899.37i	1.22563	+	0.269781i	0.780195	−	0.625536i	$-0.215120\pi$
$487$	13172.0	+	2899.37i	1.22563	+	0.269781i	0.445430	+	0.895317i	$0.353051\pi$
$488$	−624.397	+	288.877i	−0.0579203	+	0.0267968i
$489$	3299.93	−	8282.20i	0.305170	−	0.765918i
$490$	−678.001	+	12505.0i	−0.0625081	+	1.15289i
$491$	−4217.67	+	6220.60i	−0.387660	+	0.571755i	−0.970581	−	0.240773i	$-0.922599\pi$
$491$	−4217.67	+	6220.60i	−0.387660	+	0.571755i	0.582922	+	0.812528i	$0.301909\pi$
$492$	−1482.91	+	1745.82i	−0.135884	+	0.159975i
$493$	−1345.66	+	2538.18i	−0.122932	+	0.231874i
$494$	−2564.06	−	863.932i	−0.233527	−	0.0786845i
$495$	99.5888	+	1836.81i	0.00904279	+	0.166784i
$496$	5288.01	+	3181.69i	0.478707	+	0.288028i
$497$	−783.886	+	2823.30i	−0.0707487	+	0.254814i
$498$	865.114	+	3115.86i	0.0778448	+	0.280372i
$499$	7284.08	−	4382.68i	0.653467	−	0.393178i	−0.149867	−	0.988706i	$-0.547885\pi$
$499$	7284.08	−	4382.68i	0.653467	−	0.393178i	0.803335	+	0.595528i	$0.203057\pi$
$500$	6959.78	+	10264.9i	0.622501	+	0.918121i
$501$	11100.7	+	1207.28i	0.989908	+	0.107659i
$502$	3314.43	+	360.466i	0.294681	+	0.0320485i
$503$	4917.00	+	7252.03i	0.435861	+	0.642847i	0.980660	−	0.195720i	$-0.0627043\pi$
$503$	4917.00	+	7252.03i	0.435861	+	0.642847i	−0.544799	+	0.838567i	$0.683394\pi$
$504$	1189.25	−	715.548i	0.105106	−	0.0632402i
$505$	5778.43	+	20812.0i	0.509181	+	1.83391i
$506$	−477.057	+	1718.20i	−0.0419126	+	0.150955i
$507$	−3304.55	−	1988.28i	−0.289468	−	0.174167i
$508$	256.401	+	4729.04i	0.0223936	+	0.413026i
$509$	−3639.73	−	1226.37i	−0.316951	−	0.106793i	0.156330	−	0.987705i	$-0.450034\pi$
$509$	−3639.73	−	1226.37i	−0.316951	−	0.106793i	−0.473281	+	0.880912i	$0.656930\pi$
$510$	2076.94	−	3917.53i	0.180330	−	0.340139i
$511$	2325.68	−	2738.00i	0.201335	−	0.237030i
$512$	3689.11	−	5441.03i	0.318432	−	0.469652i
$513$	64.0565	−	1181.45i	0.00551299	−	0.101681i
$514$	−1945.35	+	4882.46i	−0.166937	+	0.418980i
$515$	−17448.1	+	8072.33i	−1.49292	+	0.690698i
$516$	−214.802	−	47.2816i	−0.0183259	−	0.00403383i
$517$	−292.807	−	552.292i	−0.0249084	−	0.0469821i
$518$	−26.2370	−	160.039i	−0.00222546	−	0.0135747i
$519$	−761.057	−	578.541i	−0.0643674	−	0.0489309i
$520$	13414.8	+	6206.35i	1.13130	+	0.523397i
$521$	−9983.65	+	9457.02i	−0.839523	+	0.795239i	−0.980858	−	0.194723i	$-0.937619\pi$
$521$	−9983.65	+	9457.02i	−0.839523	+	0.795239i	0.141335	+	0.989962i	$0.454861\pi$
$522$	−239.787	+	1462.64i	−0.0201058	+	0.122640i
$523$	16325.4	−	5500.66i	1.36493	−	0.459899i	0.460933	−	0.887435i	$-0.347515\pi$
$523$	16325.4	−	5500.66i	1.36493	−	0.459899i	0.903998	+	0.427536i	$0.140618\pi$
$524$	2398.18	+	6018.98i	0.199933	+	0.501794i
$525$	3965.89	+	3756.69i	0.329687	+	0.312296i
$526$	10658.4	−	8102.32i	0.883516	−	0.671631i
$527$	−11384.9	+	2506.01i	−0.941053	+	0.207141i
$528$	370.091	+	435.705i	0.0305041	+	0.0359122i
$529$	4671.13	−	508.016i	0.383918	−	0.0417536i
$530$	9203.86			0.754321
$531$	94.4095	−	4077.60i	0.00771568	−	0.333244i
$532$	1067.45			0.0869924
$533$	−6003.00	+	652.865i	−0.487840	+	0.0530558i
$534$	4890.25	+	5757.25i	0.396296	+	0.466555i
$535$	3108.89	−	684.318i	0.251232	−	0.0553002i
$536$	−3190.52	+	2425.37i	−0.257107	+	0.195448i
$537$	−2607.96	−	2470.39i	−0.209575	−	0.198520i
$538$	−5034.75	−	12636.3i	−0.403464	−	1.01262i
$539$	2890.26	−	973.841i	0.230969	−	0.0778225i
$540$	−337.801	+	2060.50i	−0.0269197	+	0.164203i
$541$	10234.1	−	9694.27i	0.813307	−	0.770405i	−0.163039	−	0.986620i	$-0.552130\pi$
$541$	10234.1	−	9694.27i	0.813307	−	0.770405i	0.976346	+	0.216215i	$0.0693711\pi$
$542$	−13104.3	−	6062.67i	−1.03852	−	0.480469i
$543$	−5398.52	−	4103.85i	−0.426653	−	0.324333i
$544$	892.997	+	5447.04i	0.0703804	+	0.429301i
$545$	4752.51	+	8964.18i	0.373532	+	0.704557i
$546$	1154.29	+	254.078i	0.0904744	+	0.0199149i
$547$	3318.46	−	1535.28i	0.259391	−	0.120007i	−0.285884	−	0.958264i	$-0.592287\pi$
$547$	3318.46	−	1535.28i	0.259391	−	0.120007i	0.545275	+	0.838257i	$0.316425\pi$
$548$	−2260.62	+	5673.74i	−0.176221	+	0.442281i
$549$	13.8703	−	255.823i	0.00107827	−	0.0198875i
$550$	−3304.48	+	4873.74i	−0.256188	+	0.377849i
$551$	−2284.49	+	2689.51i	−0.176629	+	0.207944i
$552$	−2934.95	+	5535.91i	−0.226304	+	0.426855i
$553$	−4859.14	−	1637.23i	−0.373656	−	0.125899i
$554$	−93.0972	−	1717.08i	−0.00713957	−	0.131682i
$555$	647.150	+	389.377i	0.0494955	+	0.0297805i
$556$	−2871.89	+	10343.6i	−0.219056	+	0.788970i
$557$	5582.92	+	20107.8i	0.424696	+	1.52962i	0.798434	+	0.602083i	$0.205662\pi$
$557$	5582.92	+	20107.8i	0.424696	+	1.52962i	−0.373738	+	0.927534i	$0.621924\pi$
$558$	−5153.46	+	3100.74i	−0.390974	+	0.235241i
$559$	−325.380	−	479.899i	−0.0246191	−	0.0363105i
$560$	2426.98	+	263.950i	0.183140	+	0.0199177i
$561$	−1073.53	−	116.753i	−0.0807919	−	0.00878665i
$562$	6812.91	+	10048.3i	0.511361	+	0.754202i
$563$	20516.6	−	12344.4i	1.53583	−	0.924077i	0.539187	−	0.842186i	$-0.318732\pi$
$563$	20516.6	−	12344.4i	1.53583	−	0.924077i	0.996641	−	0.0818911i	$-0.0260960\pi$
$564$	−189.826	−	683.692i	−0.0141722	−	0.0510437i
$565$	10225.9	−	36830.4i	0.761428	−	2.74242i
$566$	1705.60	+	1026.22i	0.126664	+	0.0762110i
$567$	27.9817	+	516.091i	0.00207252	+	0.0382254i
$568$	−10517.1	−	3543.63i	−0.776917	−	0.261774i
$569$	7427.89	−	14010.5i	0.547264	−	1.03225i	−0.443451	−	0.896298i	$-0.646246\pi$
$569$	7427.89	−	14010.5i	0.547264	−	1.03225i	0.990716	−	0.135951i	$-0.0434091\pi$
$570$	3525.98	−	4151.10i	0.259100	−	0.305036i
$571$	−3814.12	+	5625.40i	−0.279537	+	0.412287i	−0.941376	−	0.337360i	$-0.890466\pi$
$571$	−3814.12	+	5625.40i	−0.279537	+	0.412287i	0.661838	+	0.749647i	$0.269777\pi$
$572$	62.9552	−	1161.14i	0.00460190	−	0.0848771i
$573$	5427.86	−	13622.9i	0.395728	−	0.993203i
$574$	−2368.81	+	1095.93i	−0.172251	+	0.0796918i
$575$	−24084.9	−	5301.48i	−1.74680	−	0.384499i
$576$	1970.88	+	3717.48i	0.142570	+	0.268915i
$577$	−1154.73	−	7043.52i	−0.0833135	−	0.508190i	−0.995209	−	0.0977681i	$-0.968830\pi$
$577$	−1154.73	−	7043.52i	−0.0833135	−	0.508190i	0.911896	−	0.410422i	$-0.134619\pi$
$578$	−5926.68	−	4505.34i	−0.426501	−	0.324217i
$579$	10894.6	+	5040.38i	0.781976	+	0.361781i
$580$	4521.03	−	4282.55i	0.323665	−	0.306592i
$581$	544.094	−	3318.83i	0.0388517	−	0.236985i
$582$	−9248.97	+	3116.34i	−0.658732	+	0.221953i
$583$	−829.660	−	2082.29i	−0.0589382	−	0.147924i
$584$	9878.37	+	9357.29i	0.699948	+	0.663026i
$585$	−4381.92	+	3331.05i	−0.309693	+	0.235422i
$586$	−6549.36	+	1441.62i	−0.461692	+	0.101626i
$587$	−3708.48	−	4365.96i	−0.260759	−	0.306989i	0.616166	−	0.787616i	$-0.288685\pi$
$587$	−3708.48	−	4365.96i	−0.260759	−	0.306989i	−0.876925	+	0.480627i	$0.840409\pi$
$588$	3441.63	−	374.300i	0.241378	−	0.0262515i
$589$	−14319.3			−1.00172
$590$	11705.2	−	14679.7i	0.816769	−	1.02433i
$591$	3114.37			0.216765
$592$	233.339	−	25.3772i	0.0161996	−	0.00176182i
$593$	11546.3	+	13593.3i	0.799577	+	0.941335i	0.999258	−	0.0385263i	$-0.0122663\pi$
$593$	11546.3	+	13593.3i	0.799577	+	0.941335i	−0.199681	+	0.979861i	$0.563990\pi$
$594$	−544.099	+	119.765i	−0.0375836	+	0.00827278i
$595$	−3671.16	+	2790.74i	−0.252946	+	0.192285i
$596$	−9796.79	−	9280.02i	−0.673309	−	0.637792i
$597$	−1652.01	−	4146.24i	−0.113254	−	0.284245i
$598$	−5056.50	+	1703.73i	−0.345778	+	0.116506i
$599$	1865.23	−	11377.4i	0.127231	−	0.776073i	−0.843718	−	0.536786i	$-0.819638\pi$
$599$	1865.23	−	11377.4i	0.127231	−	0.776073i	0.970949	−	0.239287i	$-0.0769135\pi$
$600$	−15021.2	+	14228.9i	−1.02207	+	0.968152i
$601$	−1704.40	−	788.541i	−0.115681	−	0.0535196i	0.361195	−	0.932490i	$-0.382369\pi$
$601$	−1704.40	−	788.541i	−0.115681	−	0.0535196i	−0.476876	+	0.878971i	$0.658231\pi$
$602$	−199.513	−	151.666i	−0.0135076	−	0.0102682i
$603$	−241.450	−	1472.78i	−0.0163061	−	0.0994629i
$604$	187.484	+	353.632i	0.0126301	+	0.0238230i
$605$	−24318.5	−	5352.90i	−1.63419	−	0.359713i
$606$	−5937.10	+	2746.79i	−0.397984	+	0.184127i
$607$	−7364.37	+	18483.2i	−0.492439	+	1.23593i	0.447407	+	0.894331i	$0.352348\pi$
$607$	−7364.37	+	18483.2i	−0.492439	+	1.23593i	−0.939846	+	0.341599i	$0.889032\pi$
$608$	−367.068	+	6770.16i	−0.0244845	+	0.451590i
$609$	865.056	−	1275.86i	0.0575596	−	0.0848941i
$610$	763.489	−	898.849i	0.0506767	−	0.0596612i
$611$	876.155	−	1652.60i	0.0580122	−	0.109423i
$612$	−1161.57	−	391.378i	−0.0767217	−	0.0258505i
$613$	1120.31	+	20663.0i	0.0738157	+	1.36145i	0.767443	+	0.641117i	$0.221529\pi$
$613$	1120.31	+	20663.0i	0.0738157	+	1.36145i	−0.693628	+	0.720334i	$0.743989\pi$
$614$	7564.25	+	4551.26i	0.497180	+	0.299143i
$615$	3251.84	−	11712.1i	0.213214	−	0.767928i
$616$	−416.259	−	1499.23i	−0.0272265	−	0.0980611i
$617$	2924.80	−	1759.79i	0.190840	−	0.114824i	−0.416927	−	0.908940i	$-0.636893\pi$
$617$	2924.80	−	1759.79i	0.190840	−	0.114824i	0.607767	+	0.794115i	$0.292065\pi$
$618$	−3267.56	−	4819.29i	−0.212687	−	0.313690i
$619$	−10181.5	−	1107.30i	−0.661111	−	0.0719002i	−0.228588	−	0.973523i	$-0.573411\pi$
$619$	−10181.5	−	1107.30i	−0.661111	−	0.0719002i	−0.432523	+	0.901623i	$0.642376\pi$
$620$	25121.4	+	2732.12i	1.62726	+	0.176975i
$621$	−1309.43	−	1931.27i	−0.0846146	−	0.124797i
$622$	11943.0	−	7185.87i	0.769889	−	0.463227i
$623$	−2101.73	−	7569.76i	−0.135159	−	0.486799i
$624$	−457.631	+	1648.24i	−0.0293588	+	0.105741i
$625$	−25825.1	−	15538.5i	−1.65281	−	0.994461i
$626$	1139.04	+	21008.3i	0.0727238	+	1.34131i
$627$	−1256.99	−	423.529i	−0.0800627	−	0.0269763i
$628$	−6066.47	+	11442.6i	−0.385475	+	0.727084i
$629$	−287.028	+	337.916i	−0.0181949	+	0.0214207i
$630$	−1335.16	+	1969.22i	−0.0844351	+	0.124532i
$631$	−735.661	+	13568.5i	−0.0464124	+	0.856026i	0.878943	+	0.476926i	$0.158249\pi$
$631$	−735.661	+	13568.5i	−0.0464124	+	0.856026i	−0.925356	+	0.379100i	$0.876234\pi$
$632$	7188.50	−	18041.8i	0.452442	−	1.13554i
$633$	−1660.42	+	768.192i	−0.104259	+	0.0482352i
$634$	16658.8	+	3666.87i	1.04354	+	0.229701i
$635$	−11771.8	−	22203.9i	−0.735667	−	1.38762i
$636$	−411.620	−	2510.77i	−0.0256632	−	0.156539i
$637$	7265.26	+	5522.91i	0.451900	+	0.343525i
$638$	1508.02	+	697.685i	0.0935786	+	0.0432941i
$639$	3000.41	−	2842.14i	0.185750	−	0.175952i
$640$	923.033	−	5630.25i	0.0570095	−	0.347742i
$641$	−10913.6	+	3677.22i	−0.672483	+	0.226586i	−0.634768	−	0.772703i	$-0.718904\pi$
$641$	−10913.6	+	3677.22i	−0.672483	+	0.226586i	−0.0377146	+	0.999289i	$0.512008\pi$
$642$	356.857	+	895.644i	0.0219377	+	0.0550596i
$643$	−14909.4	−	14122.9i	−0.914414	−	0.866179i	0.0769876	−	0.997032i	$-0.475470\pi$
$643$	−14909.4	−	14122.9i	−0.914414	−	0.866179i	−0.991402	+	0.130853i	$0.958228\pi$
$644$	1675.85	−	1273.95i	0.102543	−	0.0779510i
$645$	1139.85	−	250.899i	0.0695836	−	0.0153165i
$646$	2069.88	+	2436.85i	0.126065	+	0.148416i
$647$	23269.8	−	2530.74i	1.41395	−	0.153777i	0.630965	−	0.775811i	$-0.282659\pi$
$647$	23269.8	−	2530.74i	1.41395	−	0.153777i	0.782990	+	0.622034i	$0.213694\pi$
$648$	−1957.62			−0.118677
$649$	−4376.29	−	1324.91i	−0.264691	−	0.0801347i
$650$	−17619.6			−1.06323
$651$	6218.38	−	676.290i	0.374374	−	0.0407157i
$652$	−7344.51	−	8646.63i	−0.441155	−	0.519368i
$653$	−7974.10	+	1755.23i	−0.477872	+	0.105188i	−0.447374	−	0.894347i	$-0.647641\pi$
$653$	−7974.10	+	1755.23i	−0.477872	+	0.105188i	−0.0304986	+	0.999535i	$0.509710\pi$
$654$	−2446.32	+	1859.65i	−0.146267	+	0.111189i
$655$	−24960.8	−	23644.2i	−1.48901	−	1.41046i
$656$	−1398.19	−	3509.20i	−0.0832169	−	0.208859i
$657$	−4801.75	+	1617.90i	−0.285136	+	0.0960735i
$658$	130.801	−	797.852i	0.00774949	−	0.0472698i
$659$	9915.07	−	9392.05i	0.586095	−	0.555178i	−0.336139	−	0.941813i	$-0.609121\pi$
$659$	9915.07	−	9392.05i	0.586095	−	0.555178i	0.922233	+	0.386634i	$0.126362\pi$
$660$	2124.43	+	982.865i	0.125293	+	0.0579666i
$661$	5247.43	+	3989.00i	0.308777	+	0.234726i	0.748073	−	0.663616i	$-0.230979\pi$
$661$	5247.43	+	3989.00i	0.308777	+	0.234726i	−0.439296	+	0.898342i	$0.644772\pi$
$662$	2142.06	+	13066.0i	0.125761	+	0.767106i
$663$	−1513.53	−	2854.82i	−0.0886584	−	0.167228i
$664$	12440.4	+	2738.34i	0.727080	+	0.160042i
$665$	−5140.90	+	2378.43i	−0.299783	+	0.138694i
$666$	−84.6666	+	212.497i	−0.00492607	+	0.0123635i
$667$	−376.753	+	6948.81i	−0.0218710	+	0.403387i
$668$	7973.91	−	11760.6i	0.461856	−	0.681186i
$669$	3298.63	−	3883.45i	0.190632	−	0.224429i
$670$	3217.98	−	6069.75i	0.185554	−	0.349993i
$671$	−272.179	−	91.7079i	−0.0156593	−	0.00527622i
$672$	−160.345	−	2957.39i	−0.00920454	−	0.169768i
$673$	−10702.3	−	6439.34i	−0.612989	−	0.368823i	0.174949	−	0.984577i	$-0.444024\pi$
$673$	−10702.3	−	6439.34i	−0.612989	−	0.368823i	−0.787938	+	0.615754i	$0.788851\pi$
$674$	3105.41	−	11184.7i	0.177472	−	0.639195i
$675$	−2061.30	−	7424.12i	−0.117540	−	0.423340i
$676$	−4205.05	+	2530.09i	−0.239249	+	0.143952i
$677$	8860.95	+	13068.9i	0.503034	+	0.741919i	0.991421	−	0.130708i	$-0.0417250\pi$
$677$	8860.95	+	13068.9i	0.503034	+	0.741919i	−0.488387	+	0.872627i	$0.662415\pi$
$678$	11508.8	+	1251.66i	0.651906	+	0.0708991i
$679$	10090.9	+	1097.45i	0.570330	+	0.0620271i
$680$	−9801.93	−	14456.8i	−0.552775	−	0.815282i
$681$	242.532	−	145.926i	0.0136473	−	0.00821132i
$682$	1803.80	+	6496.71i	0.101277	+	0.364768i
$683$	277.506	−	999.485i	0.0155468	−	0.0559945i	−0.955370	−	0.295413i	$-0.904543\pi$
$683$	277.506	−	999.485i	0.0155468	−	0.0559945i	0.970917	+	0.239418i	$0.0769567\pi$
$684$	−1290.09	−	776.223i	−0.0721169	−	0.0433913i
$685$	−1754.61	−	32361.9i	−0.0978691	−	1.80509i
$686$	7979.90	+	2688.74i	0.444131	+	0.149645i
$687$	−2831.08	+	5339.99i	−0.157224	+	0.296555i
$688$	234.816	−	276.447i	0.0130121	−	0.0153190i
$689$	3763.95	−	5551.41i	0.208121	−	0.306955i
$690$	581.497	−	10725.1i	0.0320829	−	0.591734i
$691$	−9254.62	+	23227.3i	−0.509497	+	1.27874i	0.419198	+	0.907895i	$0.362311\pi$
$691$	−9254.62	+	23227.3i	−0.509497	+	1.27874i	−0.928694	+	0.370846i	$0.879068\pi$
$692$	−1104.07	+	510.795i	−0.0606507	+	0.0280600i
$693$	565.872	+	124.558i	0.0310183	+	0.00682765i
$694$	−9814.79	−	18512.7i	−0.536836	−	1.01258i
$695$	−9215.86	−	56214.2i	−0.502989	−	3.06810i
$696$	4647.99	+	3533.31i	0.253134	+	0.192428i
$697$	6475.99	+	2996.11i	0.351931	+	0.162820i
$698$	−3314.30	+	3139.48i	−0.179725	+	0.170245i
$699$	2036.41	−	12421.6i	0.110192	−	0.672142i
$700$	6587.42	−	2219.56i	0.355687	−	0.119845i
$701$	−7475.71	−	18762.6i	−0.402787	−	1.01092i	−0.980822	−	0.194907i	$-0.937559\pi$
$701$	−7475.71	−	18762.6i	−0.402787	−	1.01092i	0.578034	−	0.816012i	$-0.303820\pi$
$702$	−1210.28	−	1146.44i	−0.0650700	−	0.0616376i
$703$	−433.553	+	329.578i	−0.0232600	+	0.0176818i
$704$	4606.70	−	1014.01i	0.246622	−	0.0542855i
$705$	2437.57	+	2869.73i	0.130219	+	0.153305i
$706$	−6772.66	+	736.572i	−0.361038	+	0.0392652i
$707$	6803.48			0.361911
$708$	−4528.05	−	2536.60i	−0.240360	−	0.134649i
$709$	3848.80			0.203871			0.101936	−	0.994791i	$-0.467496\pi$
$709$	3848.80			0.203871			0.101936	+	0.994791i	$0.467496\pi$
$710$	18912.8	−	2056.89i	0.999697	−	0.108724i
$711$	4682.06	+	5512.15i	0.246963	+	0.290748i
$712$	29060.2	−	6396.63i	1.52960	−	0.336691i
$713$	−22480.5	+	17089.2i	−1.18079	+	0.897611i
$714$	−1013.97	−	960.483i	−0.0531469	−	0.0503434i
$715$	2283.99	+	5732.37i	0.119463	+	0.299830i
$716$	−4331.86	+	1459.57i	−0.226102	+	0.0761827i
$717$	1877.37	−	11451.4i	0.0977846	−	0.596460i
$718$	−19102.1	+	18094.5i	−0.992875	+	0.940501i
$719$	21073.7	+	9749.74i	1.09307	+	0.505708i	0.881754	−	0.471710i	$-0.156363\pi$
$719$	21073.7	+	9749.74i	1.09307	+	0.505708i	0.211316	+	0.977418i	$0.432225\pi$
$720$	−2741.24	−	2083.84i	−0.141889	−	0.107861i
$721$	979.685	+	5975.81i	0.0506038	+	0.308670i
$722$	−4730.97	−	8923.56i	−0.243862	−	0.459973i
$723$	−12001.1	−	2641.63i	−0.617322	−	0.135883i
$724$	−7831.63	+	3623.30i	−0.402017	+	0.185993i
$725$	−8505.64	+	21347.5i	−0.435712	+	1.09356i
$726$	408.292	−	7530.51i	0.0208721	−	0.384963i
$727$	−17829.4	+	26296.4i	−0.909567	+	1.34151i	0.0301454	+	0.999546i	$0.490403\pi$
$727$	−17829.4	+	26296.4i	−0.909567	+	1.34151i	−0.939712	+	0.341966i	$0.888907\pi$
$728$	3014.10	−	3548.47i	0.153448	−	0.180652i
$729$	341.470	−	644.080i	0.0173485	−	0.0327227i
$730$	−22103.6	−	7447.56i	−1.12067	−	0.377598i
$731$	37.0932	+	684.144i	0.00187680	+	0.0346156i
$732$	−279.347	−	168.078i	−0.0141051	−	0.00848678i
$733$	4358.51	−	15697.9i	0.219625	−	0.791018i	−0.768824	−	0.639461i	$-0.779158\pi$
$733$	4358.51	−	15697.9i	0.219625	−	0.791018i	0.988449	−	0.151557i	$-0.0484286\pi$
$734$	3542.84	+	12760.1i	0.178159	+	0.641670i
$735$	−15741.0	+	9471.06i	−0.789955	+	0.475300i
$736$	7503.53	+	11066.9i	0.375793	+	0.554254i
$737$	−1663.30	−	180.895i	−0.0831324	−	0.00904119i
$738$	3659.80	+	398.027i	0.182546	+	0.0198531i
$739$	18223.6	+	26877.7i	0.907124	+	1.33791i	0.940973	+	0.338481i	$0.109913\pi$
$739$	18223.6	+	26877.7i	0.907124	+	1.33791i	−0.0338496	+	0.999427i	$0.510777\pi$
$740$	823.500	−	495.484i	0.0409088	−	0.0246140i
$741$	−1061.82	−	3824.34i	−0.0526411	−	0.189596i
$742$	775.588	−	2793.42i	0.0383730	−	0.138207i
$743$	−19013.6	−	11440.1i	−0.938819	−	0.564869i	−0.0381017	−	0.999274i	$-0.512131\pi$
$743$	−19013.6	−	11440.1i	−0.938819	−	0.564869i	−0.900718	+	0.434405i	$0.856959\pi$
$744$	1282.64	+	23656.9i	0.0632041	+	1.16573i
$745$	67858.9	+	22864.3i	3.33712	+	1.12441i
$746$	5361.39	−	10112.6i	0.263129	−	0.496314i
$747$	−3070.94	+	3615.39i	−0.150415	+	0.177082i
$748$	−771.138	+	1137.34i	−0.0376946	+	0.0555954i
$749$	54.2850	−	1001.23i	0.00264824	−	0.0488439i
$750$	7377.52	−	18516.2i	0.359185	−	0.901487i
$751$	491.599	−	227.438i	0.0238864	−	0.0110510i	−0.407910	−	0.913022i	$-0.633742\pi$
$751$	491.599	−	227.438i	0.0238864	−	0.0110510i	0.431796	+	0.901971i	$0.357880\pi$
$752$	1142.78	+	251.546i	0.0554163	+	0.0121980i
$753$	2290.81	+	4320.94i	0.110866	+	0.209115i
$754$	804.369	+	4906.43i	0.0388506	+	0.236978i
$755$	−1690.87	−	1285.36i	−0.0815060	−	0.0619592i
$756$	596.905	+	276.158i	0.0287159	+	0.0132854i
$757$	−6393.10	+	6055.87i	−0.306950	+	0.290759i	−0.825632	−	0.564208i	$-0.809181\pi$
$757$	−6393.10	+	6055.87i	−0.306950	+	0.290759i	0.518682	+	0.854967i	$0.326423\pi$
$758$	−1200.68	+	7323.82i	−0.0575338	+	0.350941i
$759$	−2478.87	+	835.227i	−0.118547	+	0.0399431i
$760$	−7941.17	−	19930.8i	−0.379022	−	0.951273i
$761$	−4753.50	−	4502.76i	−0.226431	−	0.214487i	0.566070	−	0.824357i	$-0.308463\pi$
$761$	−4753.50	−	4502.76i	−0.226431	−	0.214487i	−0.792502	+	0.609870i	$0.791222\pi$
$762$	6059.44	−	4606.27i	0.288071	−	0.218986i
$763$	3121.16	−	687.019i	0.148091	−	0.0325973i
$764$	−12080.6	−	14222.3i	−0.572067	−	0.673490i
$765$	6466.21	−	703.243i	0.305603	−	0.0332363i
$766$	23427.0			1.10503
$767$	−4067.39	−	13063.4i	−0.191480	−	0.614984i
$768$	12948.3			0.608374
$769$	21049.4	−	2289.26i	0.987077	−	0.107351i	0.399684	−	0.916653i	$-0.369120\pi$
$769$	21049.4	−	2289.26i	0.987077	−	0.107351i	0.587393	+	0.809302i	$0.300154\pi$
$770$	1726.71	+	2032.83i	0.0808132	+	0.0951406i
$771$	−7529.45	+	1657.36i	−0.351707	+	0.0774166i
$772$	12160.5	−	9244.17i	0.566925	−	0.430965i
$773$	19210.2	+	18196.9i	0.893847	+	0.846697i	0.988871	−	0.148778i	$-0.0475341\pi$
$773$	19210.2	+	18196.9i	0.893847	+	0.846697i	−0.0950237	+	0.995475i	$0.530293\pi$
$774$	130.839	+	328.380i	0.00607609	+	0.0152498i
$775$	−88366.4	+	29774.1i	−4.09576	+	1.38002i
$776$	−6219.83	+	37939.3i	−0.287731	+	1.75508i
$777$	172.712	−	163.601i	0.00797427	−	0.00755363i
$778$	−20963.6	−	9698.80i	−0.966044	−	0.446940i
$779$	6977.57	+	5304.21i	0.320921	+	0.243958i
$780$	1133.16	+	6911.95i	0.0520173	+	0.317292i
$781$	−2170.20	−	4093.43i	−0.0994314	−	0.187548i
$782$	6157.84	+	1355.44i	0.281591	+	0.0619828i
$783$	−1973.25	+	912.924i	−0.0900617	+	0.0416670i
$784$	−2113.16	+	5303.64i	−0.0962629	+	0.241602i
$785$	3720.73	−	68624.8i	0.169170	−	3.12016i
$786$	5843.65	−	8618.74i	0.265186	−	0.391120i
$787$	−15014.5	+	17676.4i	−0.680061	+	0.800629i	−0.988597	−	0.150583i	$-0.951885\pi$
$787$	−15014.5	+	17676.4i	−0.680061	+	0.800629i	0.308537	+	0.951212i	$0.400161\pi$
$788$	1856.32	−	3501.39i	0.0839197	−	0.158289i
$789$	18611.5	+	6270.96i	0.839782	+	0.282956i
$790$	1802.38	+	33242.9i	0.0811717	+	1.49712i
$791$	−10316.5	−	6207.22i	−0.463732	−	0.279018i
$792$	−587.120	+	2114.61i	−0.0263414	+	0.0948732i
$793$	−229.919	−	828.094i	−0.0102959	−	0.0370826i
$794$	6810.69	−	4097.86i	0.304411	−	0.183158i
$795$	7576.72	+	11174.8i	0.338011	+	0.498529i
$796$	−5646.19	−	614.060i	−0.251412	−	0.0273427i
$797$	−24297.4	−	2642.50i	−1.07987	−	0.117443i	−0.449153	−	0.893455i	$-0.648274\pi$
$797$	−24297.4	−	2642.50i	−1.07987	−	0.117443i	−0.630719	+	0.776011i	$0.717240\pi$
$798$	−962.754	−	1419.96i	−0.0427082	−	0.0629899i
$799$	−1893.94	+	1139.55i	−0.0838584	+	0.0504559i
$800$	11812.0	+	42543.0i	0.522021	+	1.88015i
$801$	−2964.43	+	10676.9i	−0.130765	+	0.470974i
$802$	−14953.8	−	8997.40i	−0.658400	−	0.396146i
$803$	307.531	+	5672.07i	0.0135150	+	0.249269i
$804$	−1799.72	−	606.395i	−0.0789442	−	0.0265994i
$805$	−5232.42	+	9869.39i	−0.229091	+	0.432112i
$806$	−13061.2	+	15376.8i	−0.570795	+	0.671992i
$807$	11197.6	−	16515.2i	0.488444	−	0.720401i
$808$	−1395.10	+	25731.1i	−0.0607419	+	1.12032i
$809$	6149.22	−	15433.4i	0.267237	−	0.670715i	−0.732714	−	0.680536i	$-0.761747\pi$
$809$	6149.22	−	15433.4i	0.267237	−	0.670715i	0.999952	+	0.00982116i	$0.00312622\pi$
$810$	3045.60	−	1409.04i	0.132113	−	0.0611219i
$811$	31718.7	+	6981.81i	1.37336	+	0.302299i	0.839539	−	0.543300i	$-0.182825\pi$
$811$	31718.7	+	6981.81i	1.37336	+	0.302299i	0.533819	+	0.845599i	$0.320756\pi$
$812$	−918.797	−	1733.04i	−0.0397087	−	0.0748986i
$813$	−3426.60	−	20901.3i	−0.147818	−	0.901650i
$814$	204.146	+	155.188i	0.00879031	+	0.00668222i
$815$	54637.3	+	25277.9i	2.34830	+	1.08644i
$816$	1467.51	−	1390.10i	0.0629573	−	0.0596364i
$817$	−136.155	+	830.506i	−0.00583041	+	0.0355639i
$818$	−22940.5	+	7729.55i	−0.980557	+	0.330388i
$819$	641.736	+	1610.64i	0.0273798	+	0.0687182i
$820$	−11229.3	−	10636.9i	−0.478223	−	0.452997i
$821$	9853.64	−	7490.54i	0.418872	−	0.318419i	−0.374420	−	0.927259i	$-0.622158\pi$
$821$	9853.64	−	7490.54i	0.418872	−	0.318419i	0.793293	+	0.608841i	$0.208365\pi$
$822$	9586.26	−	2110.10i	0.406763	−	0.0895353i
$823$	−15887.3	−	18703.9i	−0.672899	−	0.792198i	0.314701	−	0.949191i	$-0.398096\pi$
$823$	−15887.3	−	18703.9i	−0.672899	−	0.792198i	−0.987600	+	0.156993i	$0.949820\pi$
$824$	−22801.7	+	2479.83i	−0.963999	+	0.104841i
$825$	−8637.72			−0.364517
$826$	−3469.01	−	4789.60i	−0.146129	−	0.201757i
$827$	37334.8			1.56984			0.784921	−	0.619596i	$-0.212704\pi$
$827$	37334.8			1.56984			0.784921	+	0.619596i	$0.212704\pi$
$828$	−2951.76	+	321.023i	−0.123890	+	0.0134738i
$829$	−16317.1	−	19209.9i	−0.683613	−	0.804811i	0.305465	−	0.952203i	$-0.401188\pi$
$829$	−16317.1	−	19209.9i	−0.683613	−	0.804811i	−0.989078	+	0.147392i	$0.952912\pi$
$830$	−21325.3	+	4694.06i	−0.891822	+	0.196305i
$831$	2008.14	−	1526.55i	0.0838288	−	0.0637250i
$832$	10247.0	+	9706.51i	0.426986	+	0.404462i
$833$	−3991.66	−	10018.3i	−0.166030	−	0.416703i
$834$	16349.6	−	5508.81i	0.678824	−	0.228723i
$835$	−12198.3	+	74406.6i	−0.505558	+	3.08377i
$836$	−1225.39	+	1160.75i	−0.0506950	+	0.0480209i
$837$	−8007.14	−	3704.50i	−0.330666	−	0.152982i
$838$	175.221	+	133.200i	0.00722304	+	0.00549081i
$839$	198.726	+	1212.18i	0.00817735	+	0.0498796i	0.990600	−	0.136791i	$-0.0436787\pi$
$839$	198.726	+	1212.18i	0.00817735	+	0.0498796i	−0.982423	+	0.186670i	$0.940230\pi$
$840$	4389.91	+	8280.25i	0.180317	+	0.340114i
$841$	−17486.0	−	3848.95i	−0.716961	−	0.157815i
$842$	19580.7	−	9058.98i	0.801419	−	0.370776i
$843$	−6591.62	+	16543.7i	−0.269309	+	0.675915i
$844$	−126.038	+	2324.64i	−0.00514031	+	0.0948075i
$845$	14614.3	−	21554.4i	0.594966	−	0.877509i
$846$	−738.259	+	869.145i	−0.0300022	+	0.0353213i
$847$	−3673.89	+	6929.70i	−0.149040	+	0.281118i
$848$	3976.19	+	1339.74i	0.161018	+	0.0542532i
$849$	158.082	+	2915.64i	0.00639028	+	0.117862i
$850$	17840.5	+	10734.3i	0.719909	+	0.433155i
$851$	−287.322	+	1034.84i	−0.0115738	+	0.0416850i
$852$	−1406.94	−	5067.34i	−0.0565739	−	0.203761i
$853$	9649.11	−	5805.68i	0.387314	−	0.233039i	−0.308557	−	0.951206i	$-0.599846\pi$
$853$	9649.11	−	5805.68i	0.387314	−	0.233039i	0.695871	+	0.718167i	$0.255018\pi$
$854$	−208.468	−	307.467i	−0.00835318	−	0.0123200i
$855$	7942.67	+	863.817i	0.317700	+	0.0345520i
$856$	3775.56	+	410.617i	0.150755	+	0.0163956i
$857$	−1652.33	−	2437.01i	−0.0658607	−	0.0971373i	0.793332	−	0.608789i	$-0.208344\pi$
$857$	−1652.33	−	2437.01i	−0.0658607	−	0.0971373i	−0.859193	+	0.511651i	$0.829034\pi$
$858$	−1601.36	+	963.507i	−0.0637175	+	0.0383375i
$859$	4979.09	+	17933.1i	0.197770	+	0.712303i	0.994198	+	0.107569i	$0.0343068\pi$
$859$	4979.09	+	17933.1i	0.197770	+	0.712303i	−0.796428	+	0.604734i	$0.793279\pi$
$860$	397.328	−	1431.04i	0.0157544	−	0.0567421i
$861$	−3280.64	−	1973.90i	−0.129854	−	0.0781304i
$862$	881.355	+	16255.6i	0.0348249	+	0.642308i
$863$	−4499.49	−	1516.06i	−0.177479	−	0.0597997i	0.229159	−	0.973389i	$-0.426402\pi$
$863$	−4499.49	−	1516.06i	−0.177479	−	0.0597997i	−0.406638	+	0.913589i	$0.633299\pi$
$864$	−1956.75	+	3690.82i	−0.0770485	+	0.145329i
$865$	4179.10	−	4920.02i	0.164270	−	0.193394i
$866$	5547.52	−	8181.98i	0.217682	−	0.321057i
$867$	591.236	−	10904.7i	0.0231597	−	0.427155i
$868$	2946.14	−	7394.25i	0.115206	−	0.289144i
$869$	7358.42	−	3404.37i	0.287247	−	0.132895i
$870$	−9774.36	−	2151.50i	−0.380899	−	0.0838421i
$871$	−2345.04	−	4423.21i	−0.0912268	−	0.172072i
$872$	1958.32	+	11945.3i	0.0760519	+	0.463896i
$873$	−11397.5	−	8664.19i	−0.441866	−	0.335897i
$874$	7029.14	+	3252.02i	0.272041	+	0.125860i
$875$	−15049.4	+	14255.6i	−0.581445	+	0.550774i
$876$	−1043.13	+	6362.82i	−0.0402331	+	0.245411i
$877$	17738.6	−	5976.82i	0.682997	−	0.230129i	0.0436502	−	0.999047i	$-0.486101\pi$
$877$	17738.6	−	5976.82i	0.682997	−	0.230129i	0.639347	+	0.768918i	$0.279205\pi$
$878$	9477.73	+	23787.3i	0.364303	+	0.914331i
$879$	−7141.84	−	6765.11i	−0.274048	−	0.259592i
$880$	−3073.09	+	2336.10i	−0.117720	+	0.0894886i
$881$	4707.63	−	1036.23i	0.180027	−	0.0396270i	−0.124042	−	0.992277i	$-0.539586\pi$
$881$	4707.63	−	1036.23i	0.180027	−	0.0396270i	0.304069	+	0.952650i	$0.401655\pi$
$882$	−3601.97	−	4240.56i	−0.137511	−	0.161890i
$883$	−25850.2	+	2811.38i	−0.985196	+	0.107147i	−0.586511	−	0.809941i	$-0.699499\pi$
$883$	−25850.2	+	2811.38i	−0.985196	+	0.107147i	−0.398685	+	0.917088i	$0.630533\pi$
$884$	−4111.73			−0.156439
$885$	27459.2	+	2127.23i	1.04297	+	0.0807978i
$886$	−2124.65			−0.0805634
$887$	27627.1	−	3004.63i	1.04580	−	0.113738i	0.430947	−	0.902377i	$-0.358180\pi$
$887$	27627.1	−	3004.63i	1.04580	−	0.113738i	0.614856	+	0.788640i	$0.289214\pi$
$888$	583.333	+	686.752i	0.0220443	+	0.0259526i
$889$	−7730.98	+	1701.72i	−0.291664	+	0.0642000i
$890$	−40606.7	+	30868.4i	−1.52937	+	1.16260i
$891$	−593.321	−	562.024i	−0.0223087	−	0.0211319i
$892$	−2399.90	−	6023.30i	−0.0900837	−	0.226093i
$893$	−2572.91	+	866.914i	−0.0964156	+	0.0324862i
$894$	−3508.64	+	21401.8i	−0.131260	+	0.800651i
$895$	17610.3	−	16681.3i	0.657706	−	0.623012i
$896$	−1631.03	−	754.593i	−0.0608134	−	0.0281353i
$897$	−6231.14	−	4736.79i	−0.231942	−	0.176318i
$898$	−2364.99	−	14425.8i	−0.0878851	−	0.536075i
$899$	12325.1	+	23247.7i	0.457248	+	0.862462i
$900$	−9575.36	−	2107.70i	−0.354643	−	0.0780628i
$901$	−7193.18	+	3327.92i	−0.265971	+	0.123051i
$902$	1527.58	−	3833.93i	0.0563888	−	0.141525i
$903$	19.9031	−	367.092i	0.000733483	−	0.0135283i
$904$	25591.5	−	37744.6i	0.941549	−	1.38868i
$905$	29644.2	−	34899.9i	1.08885	−	1.28189i
$906$	301.316	−	568.342i	0.0110492	−	0.0208410i
$907$	30088.6	+	10138.0i	1.10151	+	0.371144i	0.810597	−	0.585604i	$-0.199143\pi$
$907$	30088.6	+	10138.0i	1.10151	+	0.371144i	0.290918	+	0.956748i	$0.406039\pi$
$908$	−19.4997	−	359.651i	−0.000712688	−	0.0131447i
$909$	−8222.49	−	4947.31i	−0.300025	−	0.180519i
$910$	−2135.13	+	7690.05i	−0.0777790	+	0.280135i
$911$	−12823.9	−	46187.4i	−0.466382	−	1.67976i	−0.705456	−	0.708754i	$-0.749258\pi$
$911$	−12823.9	−	46187.4i	−0.466382	−	1.67976i	0.239074	−	0.971001i	$-0.423156\pi$
$912$	2127.52	−	1280.08i	0.0772468	−	0.0464779i
$913$	2984.31	+	4401.52i	0.108178	+	0.159550i
$914$	22105.4	+	2404.10i	0.799979	+	0.0870029i
$915$	1719.85	+	187.045i	0.0621381	+	0.00675793i
$916$	4316.13	+	6365.81i	0.155687	+	0.229620i
$917$	−9279.52	+	5583.30i	−0.334173	+	0.201065i
$918$	527.017	+	1898.14i	0.0189479	+	0.0682441i
$919$	27.1476	−	97.7767i	0.000974446	−	0.00350964i	−0.963061	−	0.269283i	$-0.913213\pi$
$919$	27.1476	−	97.7767i	0.000974446	−	0.00350964i	0.964036	+	0.265773i	$0.0856272\pi$
$920$	−36253.6	−	21813.0i	−1.29918	−	0.781690i
$921$	701.085	+	12930.8i	0.0250831	+	0.462631i
$922$	597.501	+	201.322i	0.0213424	+	0.00719108i
$923$	6493.82	−	12248.6i	0.231578	−	0.436803i
$924$	477.325	−	561.951i	0.0169944	−	0.0200074i
$925$	−1990.23	+	2935.37i	−0.0707441	+	0.104340i
$926$	257.776	−	4754.40i	0.00914800	−	0.168725i
$927$	3161.43	−	7934.59i	0.112012	−	0.281129i
$928$	11307.5	−	5231.39i	0.399985	−	0.185053i
$929$	12375.2	+	2723.98i	0.437047	+	0.0962012i	0.428043	−	0.903758i	$-0.359203\pi$
$929$	12375.2	+	2723.98i	0.437047	+	0.0962012i	0.00900327	+	0.999959i	$0.497134\pi$
$930$	−19023.1	−	35881.4i	−0.670744	−	1.26516i
$931$	−2143.07	−	13072.2i	−0.0754418	−	0.460174i
$932$	−12751.4	−	9693.37i	−0.448161	−	0.340683i
$933$	18556.3	+	8585.06i	0.651132	+	0.301246i
$934$	17627.0	−	16697.1i	0.617528	−	0.584954i
$935$	1179.67	−	7195.69i	0.0412614	−	0.251684i
$936$	−6223.10	+	2096.81i	−0.217317	+	0.0732225i
$937$	−20568.0	−	51621.9i	−0.717106	−	1.79980i	−0.589153	−	0.808021i	$-0.700539\pi$
$937$	−20568.0	−	51621.9i	−0.717106	−	1.79980i	−0.127953	−	0.991780i	$-0.540841\pi$
$938$	−1571.03	−	1488.16i	−0.0546865	−	0.0518018i
$939$	−24569.5	+	18677.2i	−0.853882	+	0.649104i
$940$	4679.27	−	1029.99i	0.162363	−	0.0357387i
$941$	13866.1	+	16324.5i	0.480365	+	0.565529i	0.947950	−	0.318419i	$-0.103152\pi$
$941$	13866.1	+	16324.5i	0.480365	+	0.565529i	−0.467585	+	0.883948i	$0.654876\pi$
$942$	20692.7	−	2250.47i	0.715716	−	0.0778388i
$943$	17284.7			0.596890
$944$	7193.61	−	4638.02i	0.248021	−	0.159910i
$945$	−3490.04			−0.120139
$946$	393.955	−	42.8452i	0.0135397	−	0.00147254i
$947$	22944.7	+	27012.6i	0.787331	+	0.926917i	0.998725	−	0.0504837i	$-0.0160763\pi$
$947$	22944.7	+	27012.6i	0.787331	+	0.926917i	−0.211394	+	0.977401i	$0.567800\pi$
$948$	8987.90	−	1978.39i	0.307925	−	0.0677795i
$949$	−13531.4	+	10286.3i	−0.462854	+	0.351852i
$950$	18567.3	+	17587.9i	0.634108	+	0.600659i
$951$	9261.58	+	23244.8i	0.315801	+	0.792602i
$952$	−5213.69	+	1756.70i	−0.177496	+	0.0598055i
$953$	−2368.46	+	14447.0i	−0.0805058	+	0.491064i	0.915540	+	0.402226i	$0.131763\pi$
$953$	−2368.46	+	14447.0i	−0.0805058	+	0.491064i	−0.996046	+	0.0888375i	$0.971685\pi$
$954$	−2968.65	+	2812.05i	−0.100748	+	0.0954336i
$955$	89869.8	+	41578.2i	3.04515	+	1.40884i
$956$	−11755.5	−	8936.31i	−0.397699	−	0.302323i
$957$	394.329	+	2405.30i	0.0133196	+	0.0812459i
$958$	−8431.80	−	15904.1i	−0.284362	−	0.536364i
$959$	−9969.86	−	2194.53i	−0.335708	−	0.0738949i
$960$	−25786.0	+	11929.9i	−0.866918	+	0.401079i
$961$	−28494.0	+	71514.5i	−0.956462	+	2.40054i
$962$	−41.5419	+	766.195i	−0.00139227	+	0.0256789i
$963$	−793.674	+	1170.58i	−0.0265584	+	0.0391708i
$964$	−10123.1	+	11917.9i	−0.338221	+	0.398184i
$965$	−37968.2	+	71615.5i	−1.26657	+	2.38900i
$966$	−3206.11	−	1080.26i	−0.106786	−	0.0359803i
$967$	772.154	+	14241.5i	0.0256782	+	0.473606i	0.982887	+	0.184209i	$0.0589722\pi$
$967$	772.154	+	14241.5i	0.0256782	+	0.473606i	−0.957209	+	0.289398i	$0.906545\pi$
$968$	−25455.1	−	15315.8i	−0.845205	−	0.508543i
$969$	−1254.74	+	4519.17i	−0.0415977	+	0.149821i
$970$	−17631.1	−	63501.5i	−0.583609	−	2.10197i
$971$	−11283.1	+	6788.83i	−0.372907	+	0.224371i	−0.689653	−	0.724140i	$-0.742237\pi$
$971$	−11283.1	+	6788.83i	−0.372907	+	0.224371i	0.316747	+	0.948510i	$0.397410\pi$
$972$	−520.588	−	767.809i	−0.0171789	−	0.0253369i
$973$	−17837.9	−	1939.99i	−0.587726	−	0.0639190i
$974$	−27421.4	−	2982.26i	−0.902092	−	0.0981085i
$975$	−14504.6	−	21392.7i	−0.476431	−	0.702683i
$976$	460.677	−	277.180i	0.0151085	−	0.00909048i
$977$	8393.73	+	30231.5i	0.274861	+	0.989960i	0.964125	+	0.265449i	$0.0855203\pi$
$977$	8393.73	+	30231.5i	0.274861	+	0.989960i	−0.689264	+	0.724510i	$0.742066\pi$
$978$	−4877.85	+	17568.4i	−0.159485	+	0.574413i
$979$	10644.1	+	6404.33i	0.347484	+	0.209074i
$980$	1265.59	+	23342.4i	0.0412528	+	0.760864i
$981$	−4271.72	−	1439.31i	−0.139027	−	0.0468437i
$982$	7199.58	−	13579.9i	0.233959	−	0.441294i
$983$	14593.6	−	17181.0i	0.473514	−	0.557464i	−0.472608	−	0.881273i	$-0.656687\pi$
$983$	14593.6	−	17181.0i	0.473514	−	0.557464i	0.946123	+	0.323808i	$0.104963\pi$
$984$	8138.09	−	12002.8i	0.263651	−	0.388857i
$985$	−1138.53	+	20999.0i	−0.0368291	+	0.679272i
$986$	2174.66	−	5457.98i	0.0702386	−	0.176285i
$987$	1076.39	−	497.989i	0.0347130	−	0.0160599i
$988$	−4932.50	−	1085.73i	−0.158830	−	0.0349611i
$989$	777.406	+	1466.34i	0.0249950	+	0.0471456i
$990$	−608.623	−	3712.44i	−0.0195387	−	0.119181i
$991$	−13535.8	−	10289.6i	−0.433883	−	0.329829i	0.365329	−	0.930878i	$-0.380956\pi$
$991$	−13535.8	−	10289.6i	−0.433883	−	0.329829i	−0.799212	+	0.601049i	$0.794750\pi$
$992$	45883.9	+	21228.1i	1.46856	+	0.679429i
$993$	−14100.7	+	13356.8i	−0.450625	+	0.426855i
$994$	969.463	−	5913.46i	0.0309351	−	0.188696i
$995$	28560.5	−	9623.14i	0.909978	−	0.306607i
$996$	2234.24	+	5607.52i	0.0710789	+	0.178395i
$997$	6249.28	+	5919.63i	0.198512	+	0.188041i	0.780498	−	0.625158i	$-0.214966\pi$
$997$	6249.28	+	5919.63i	0.198512	+	0.188041i	−0.581986	+	0.813199i	$0.697724\pi$
$998$	−13840.4	+	10521.2i	−0.438987	+	0.333709i
$999$	−327.701	+	72.1324i	−0.0103784	+	0.00228445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.133.6	yes	420
59.4	even	29	inner	177.4.e.a.4.6	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.4.6	✓	420	59.4	even	29	inner
177.4.e.a.133.6	yes	420	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03313 + 0.221116i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-3.72826 + 0.820651i) q^{4} +(16.1269 - 12.2594i) q^{5} +(4.45423 + 4.21927i) q^{6} +(-2.36180 - 5.92767i) q^{7} +(22.9030 - 7.71693i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})\)	\(q+(-2.03313 + 0.221116i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-3.72826 + 0.820651i) q^{4} +(16.1269 - 12.2594i) q^{5} +(4.45423 + 4.21927i) q^{6} +(-2.36180 - 5.92767i) q^{7} +(22.9030 - 7.71693i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-30.0773 + 28.4907i) q^{10} +(9.15701 + 4.23648i) q^{11} +(9.11727 + 6.93077i) q^{12} +(4.88429 + 29.7928i) q^{13} +(6.11253 + 11.5295i) q^{14} +(-59.3519 - 13.0643i) q^{15} +(-17.1410 + 7.93027i) q^{16} +(13.2050 - 33.1420i) q^{17} +(0.996482 - 18.3790i) q^{18} +(24.5922 - 36.2708i) q^{19} +(-50.0646 + 58.9406i) q^{20} +(-8.96654 + 16.9127i) q^{21} +(-19.5541 - 6.58855i) q^{22} +(-4.67865 - 86.2927i) q^{23} +(-62.1260 - 37.3800i) q^{24} +(76.3443 - 274.967i) q^{25} +(-16.5180 - 59.4926i) q^{26} +(23.1351 - 13.9200i) q^{27} +(13.6699 + 20.1616i) q^{28} +(-80.0540 - 8.70639i) q^{29} +(123.559 + 13.4378i) q^{30} +(-183.374 - 270.457i) q^{31} +(-132.573 + 79.7665i) q^{32} +(-8.09771 - 29.1653i) q^{33} +(-19.5191 + 70.3016i) q^{34} +(-110.758 - 66.6408i) q^{35} +(-1.86008 - 34.3072i) q^{36} +(-11.7771 - 3.96816i) q^{37} +(-41.9790 + 79.1808i) q^{38} +(58.6349 - 69.0303i) q^{39} +(274.750 - 405.227i) q^{40} +(-10.8283 + 199.716i) q^{41} +(14.4904 - 36.3683i) q^{42} +(-17.4299 + 8.06392i) q^{43} +(-37.6164 - 8.27999i) q^{44} +(85.3993 + 161.080i) q^{45} +(28.5930 + 174.409i) q^{46} +(-49.3229 - 37.4943i) q^{47} +(51.4230 + 23.7908i) q^{48} +(219.457 - 207.881i) q^{49} +(-94.4180 + 575.924i) q^{50} +(-101.425 + 34.1740i) q^{51} +(-42.6594 - 107.067i) q^{52} +(-161.287 - 152.779i) q^{53} +(-43.9587 + 33.4166i) q^{54} +(199.611 - 43.9377i) q^{55} +(-99.8357 - 117.536i) q^{56} +(-130.695 + 14.2139i) q^{57} +164.685 q^{58} +(-448.795 + 62.9462i) q^{59} +232.000 q^{60} +(-28.2997 + 3.07777i) q^{61} +(432.625 + 509.326i) q^{62} +(56.0851 - 12.3453i) q^{63} +(372.184 - 282.927i) q^{64} +(444.010 + 420.588i) q^{65} +(22.9126 + 57.5062i) q^{66} +(-157.146 + 52.9486i) q^{67} +(-22.0335 + 134.398i) q^{68} +(-188.220 + 178.292i) q^{69} +(239.920 + 110.999i) q^{70} +(-365.568 - 277.898i) q^{71} +(35.1897 + 214.648i) q^{72} +(263.714 + 497.417i) q^{73} +(24.8217 + 5.46367i) q^{74} +(-776.982 + 359.470i) q^{75} +(-61.9204 + 155.409i) q^{76} +(3.48545 - 64.2854i) q^{77} +(-103.948 + 153.312i) q^{78} +(520.229 - 612.461i) q^{79} +(-179.211 + 338.028i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-22.1451 - 408.442i) q^{82} +(451.620 + 271.731i) q^{83} +(19.5501 - 70.4132i) q^{84} +(-193.344 - 696.362i) q^{85} +(33.6541 - 20.2490i) q^{86} +(135.570 + 199.951i) q^{87} +(242.416 + 26.3643i) q^{88} +(1223.98 + 133.116i) q^{89} +(-209.245 - 308.613i) q^{90} +(165.066 - 99.3171i) q^{91} +(88.2595 + 317.882i) q^{92} +(-262.254 + 944.553i) q^{93} +(108.570 + 65.3246i) q^{94} +(-48.0603 - 886.421i) q^{95} +(439.863 + 148.207i) q^{96} +(-745.126 + 1405.46i) q^{97} +(-400.219 + 471.174i) q^{98} +(-50.9590 + 75.1589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Introduction

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