LMFDB - Embedded newform 235.4.g.b.6.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [235,4,Mod(6,235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(235, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("235.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 235 = 5 \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	235.g (of order $23$, degree $22$, 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:	$13.8654488513$
Analytic rank:	$0$
Dimension:	$550$
Relative dimension:	$25$ over $\Q(\zeta_{23})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			6.18
Character	$\chi$	$=$	235.6
Dual form			235.4.g.b.196.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47081 - 1.07322i) q^{2} +(-0.351491 + 5.13861i) q^{3} +(-0.507353 + 0.543242i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(4.64641 + 13.0737i) q^{6} +(-4.33565 - 20.8643i) q^{7} +(-7.88740 + 22.1930i) q^{8} +(0.466704 + 0.0641470i) q^{9} +O(q^{10})$	\(q+(2.47081 - 1.07322i) q^{2} +(-0.351491 + 5.13861i) q^{3} +(-0.507353 + 0.543242i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(4.64641 + 13.0737i) q^{6} +(-4.33565 - 20.8643i) q^{7} +(-7.88740 + 22.1930i) q^{8} +(0.466704 + 0.0641470i) q^{9} +(-7.76737 + 11.0039i) q^{10} +(-23.0420 + 18.7460i) q^{11} +(-2.61318 - 2.79803i) q^{12} +(-47.4360 - 13.2909i) q^{13} +(-33.1046 - 46.8985i) q^{14} +(-11.8481 - 22.8658i) q^{15} +(3.92400 + 57.3669i) q^{16} +(63.2397 + 51.4493i) q^{17} +(1.22198 - 0.342382i) q^{18} +(-108.389 - 65.9127i) q^{19} +(0.756161 - 3.63884i) q^{20} +(108.738 - 14.9456i) q^{21} +(-36.8135 + 71.0469i) q^{22} +(-145.822 - 63.3394i) q^{23} +(-111.269 - 48.3310i) q^{24} +(11.5016 - 22.1971i) q^{25} +(-131.469 + 18.0700i) q^{26} +(-28.7876 + 138.534i) q^{27} +(13.5341 + 8.23026i) q^{28} +(-135.545 + 37.9779i) q^{29} +(-53.8145 - 43.7813i) q^{30} +(-16.2916 - 238.174i) q^{31} +(-15.4242 - 29.7674i) q^{32} +(-88.2295 - 124.993i) q^{33} +(211.470 + 59.2510i) q^{34} +(72.7261 + 77.8707i) q^{35} +(-0.271631 + 0.220988i) q^{36} +(-94.5373 + 133.929i) q^{37} +(-338.547 - 46.5321i) q^{38} +(84.9703 - 239.084i) q^{39} +(-23.9599 - 115.302i) q^{40} +(139.294 + 391.936i) q^{41} +(252.629 - 153.627i) q^{42} +(199.460 - 213.570i) q^{43} +(1.50677 - 22.0282i) q^{44} +(-2.16045 + 0.938418i) q^{45} -428.275 q^{46} +(199.917 + 252.698i) q^{47} -296.166 q^{48} +(-101.918 + 44.2693i) q^{49} +(4.59583 - 67.1886i) q^{50} +(-286.606 + 306.880i) q^{51} +(31.2870 - 19.0260i) q^{52} +(208.928 + 587.866i) q^{53} +(77.5488 + 373.185i) q^{54} +(49.7368 - 139.946i) q^{55} +(497.239 + 68.3440i) q^{56} +(376.798 - 533.801i) q^{57} +(-294.147 + 239.306i) q^{58} +(143.331 + 153.470i) q^{59} +(18.4328 + 5.16464i) q^{60} +(228.972 + 324.379i) q^{61} +(-295.867 - 570.998i) q^{62} +(-0.685085 - 10.0156i) q^{63} +(-426.890 - 347.301i) q^{64} +(237.180 - 66.4547i) q^{65} +(-352.143 - 214.143i) q^{66} +(-27.7514 + 133.547i) q^{67} +(-60.0343 + 8.25152i) q^{68} +(376.732 - 727.059i) q^{69} +(263.265 + 114.352i) q^{70} +(495.222 + 215.105i) q^{71} +(-5.10470 + 9.85162i) q^{72} +(-109.972 + 15.1154i) q^{73} +(-89.8478 + 432.371i) q^{74} +(110.020 + 66.9045i) q^{75} +(90.7979 - 25.4404i) q^{76} +(491.025 + 399.478i) q^{77} +(-46.6447 - 681.921i) q^{78} +(519.332 + 1002.26i) q^{79} +(-165.798 - 234.883i) q^{80} +(-689.505 - 193.190i) q^{81} +(764.802 + 818.903i) q^{82} +(-884.686 + 719.746i) q^{83} +(-47.0492 + 66.6536i) q^{84} +(-403.827 - 55.5048i) q^{85} +(263.619 - 741.754i) q^{86} +(-147.511 - 709.862i) q^{87} +(-234.290 - 659.228i) q^{88} +(-1209.43 + 735.470i) q^{89} +(-4.33093 + 4.63729i) q^{90} +(-71.6403 + 1047.34i) q^{91} +(108.392 - 47.0812i) q^{92} +1229.61 q^{93} +(765.157 + 409.812i) q^{94} +634.283 q^{95} +(158.385 - 68.7962i) q^{96} +(124.630 - 1822.02i) q^{97} +(-204.309 + 218.762i) q^{98} +(-11.9563 + 7.27077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9}+O(q^{10}) $ 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9} - 20 q^{10} + 74 q^{11} - 677 q^{12} + 132 q^{13} - 83 q^{14} + 10 q^{15} - 602 q^{16} - 62 q^{17} - 95 q^{18} + 590 q^{19} + 510 q^{20} - 148 q^{21} + 178 q^{22} - 2244 q^{23} + 625 q^{24} - 625 q^{25} - 2530 q^{26} + 472 q^{27} + 68 q^{28} - 40 q^{29} + 1505 q^{30} - 16 q^{31} + 301 q^{32} + 200 q^{33} + 104 q^{34} + 10 q^{35} - 778 q^{36} + 3435 q^{37} + 1724 q^{38} + 578 q^{39} + 30 q^{40} - 442 q^{41} - 3709 q^{42} - 484 q^{43} - 12170 q^{44} + 875 q^{45} + 614 q^{46} - 1743 q^{47} - 962 q^{48} - 2509 q^{49} + 100 q^{50} + 390 q^{51} - 7609 q^{52} + 758 q^{53} + 1373 q^{54} - 140 q^{55} + 106 q^{56} + 6740 q^{57} + 4800 q^{58} + 8566 q^{59} - 295 q^{60} + 1364 q^{61} - 7252 q^{62} - 3122 q^{63} - 4010 q^{64} - 660 q^{65} + 24646 q^{66} - 68 q^{67} - 905 q^{68} - 2624 q^{69} + 185 q^{70} - 318 q^{71} - 3352 q^{72} + 428 q^{73} + 506 q^{74} - 50 q^{75} + 2495 q^{76} + 18134 q^{77} + 16762 q^{78} + 4620 q^{79} - 785 q^{80} - 14403 q^{81} + 11899 q^{82} + 90 q^{83} + 15755 q^{84} + 310 q^{85} - 4050 q^{86} - 5440 q^{87} - 439 q^{88} - 2148 q^{89} + 475 q^{90} - 9933 q^{91} - 36335 q^{92} - 4472 q^{93} - 3725 q^{94} + 270 q^{95} - 1421 q^{96} - 7342 q^{97} - 39381 q^{98} - 11821 q^{99}+O(q^{100}) \) 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9 - 20 * q^10 + 74 * q^11 - 677 * q^12 + 132 * q^13 - 83 * q^14 + 10 * q^15 - 602 * q^16 - 62 * q^17 - 95 * q^18 + 590 * q^19 + 510 * q^20 - 148 * q^21 + 178 * q^22 - 2244 * q^23 + 625 * q^24 - 625 * q^25 - 2530 * q^26 + 472 * q^27 + 68 * q^28 - 40 * q^29 + 1505 * q^30 - 16 * q^31 + 301 * q^32 + 200 * q^33 + 104 * q^34 + 10 * q^35 - 778 * q^36 + 3435 * q^37 + 1724 * q^38 + 578 * q^39 + 30 * q^40 - 442 * q^41 - 3709 * q^42 - 484 * q^43 - 12170 * q^44 + 875 * q^45 + 614 * q^46 - 1743 * q^47 - 962 * q^48 - 2509 * q^49 + 100 * q^50 + 390 * q^51 - 7609 * q^52 + 758 * q^53 + 1373 * q^54 - 140 * q^55 + 106 * q^56 + 6740 * q^57 + 4800 * q^58 + 8566 * q^59 - 295 * q^60 + 1364 * q^61 - 7252 * q^62 - 3122 * q^63 - 4010 * q^64 - 660 * q^65 + 24646 * q^66 - 68 * q^67 - 905 * q^68 - 2624 * q^69 + 185 * q^70 - 318 * q^71 - 3352 * q^72 + 428 * q^73 + 506 * q^74 - 50 * q^75 + 2495 * q^76 + 18134 * q^77 + 16762 * q^78 + 4620 * q^79 - 785 * q^80 - 14403 * q^81 + 11899 * q^82 + 90 * q^83 + 15755 * q^84 + 310 * q^85 - 4050 * q^86 - 5440 * q^87 - 439 * q^88 - 2148 * q^89 + 475 * q^90 - 9933 * q^91 - 36335 * q^92 - 4472 * q^93 - 3725 * q^94 + 270 * q^95 - 1421 * q^96 - 7342 * q^97 - 39381 * q^98 - 11821 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/235\mathbb{Z}\right)^\times$.

$n$	$142$	$146$
$\chi(n)$	$1$	$e\left(\frac{19}{23}\right)$

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 $

$2$	2.47081	−	1.07322i	0.873562	−	0.379441i	0.0864531	−	0.996256i	$-0.472447\pi$
$2$	2.47081	−	1.07322i	0.873562	−	0.379441i	0.787108	+	0.616815i	$0.211577\pi$
$3$	−0.351491	+	5.13861i	−0.0676445	+	0.988927i	0.832693	+	0.553735i	$0.186798\pi$
$3$	−0.351491	+	5.13861i	−0.0676445	+	0.988927i	−0.900338	+	0.435192i	$0.856680\pi$
$4$	−0.507353	+	0.543242i	−0.0634191	+	0.0679053i
$5$	−4.27210	+	2.59792i	−0.382108	+	0.232365i
$5$	−4.27210	+	2.59792i	−0.382108	+	0.232365i
$6$	4.64641	+	13.0737i	0.316148	+	0.889556i
$7$	−4.33565	−	20.8643i	−0.234103	−	1.12657i	−0.917875	−	0.396871i	$-0.870096\pi$
$7$	−4.33565	−	20.8643i	−0.234103	−	1.12657i	0.683771	−	0.729696i	$-0.260339\pi$
$8$	−7.88740	+	22.1930i	−0.348577	+	0.980802i
$9$	0.466704	+	0.0641470i	0.0172853	+	0.00237582i
$10$	−7.76737	+	11.0039i	−0.245626	+	0.347973i
$11$	−23.0420	+	18.7460i	−0.631583	+	0.513831i	−0.892217	−	0.451607i	$-0.850851\pi$
$11$	−23.0420	+	18.7460i	−0.631583	+	0.513831i	0.260634	+	0.965438i	$0.416068\pi$
$12$	−2.61318	−	2.79803i	−0.0628634	−	0.0673103i
$13$	−47.4360	−	13.2909i	−1.01203	−	0.283557i	−0.276473	−	0.961022i	$-0.589166\pi$
$13$	−47.4360	−	13.2909i	−1.01203	−	0.283557i	−0.735555	+	0.677465i	$0.763079\pi$
$14$	−33.1046	−	46.8985i	−0.631970	−	0.895297i
$15$	−11.8481	−	22.8658i	−0.203945	−	0.393595i
$16$	3.92400	+	57.3669i	0.0613126	+	0.896358i
$17$	63.2397	+	51.4493i	0.902228	+	0.734017i	0.964511	−	0.264041i	$-0.0850556\pi$
$17$	63.2397	+	51.4493i	0.902228	+	0.734017i	−0.0622831	+	0.998059i	$0.519838\pi$
$18$	1.22198	−	0.342382i	0.0160013	−	0.00448335i
$19$	−108.389	−	65.9127i	−1.30874	−	0.795863i	−0.320278	−	0.947323i	$-0.603776\pi$
$19$	−108.389	−	65.9127i	−1.30874	−	0.795863i	−0.988463	+	0.151460i	$0.951603\pi$
$20$	0.756161	−	3.63884i	0.00845413	−	0.0406835i
$21$	108.738	−	14.9456i	1.12993	−	0.155305i
$22$	−36.8135	+	71.0469i	−0.356758	+	0.688511i
$23$	−145.822	−	63.3394i	−1.32200	−	0.574225i	−0.384793	−	0.923003i	$-0.625727\pi$
$23$	−145.822	−	63.3394i	−1.32200	−	0.574225i	−0.937205	+	0.348778i	$0.886597\pi$
$24$	−111.269	−	48.3310i	−0.946362	−	0.411063i
$25$	11.5016	−	22.1971i	0.0920130	−	0.177577i
$26$	−131.469	+	18.0700i	−0.991662	+	0.136301i
$27$	−28.7876	+	138.534i	−0.205192	+	0.987438i
$28$	13.5341	+	8.23026i	0.0913464	+	0.0555490i
$29$	−135.545	+	37.9779i	−0.867934	+	0.243184i	−0.674811	−	0.737991i	$-0.735775\pi$
$29$	−135.545	+	37.9779i	−0.867934	+	0.243184i	−0.193123	+	0.981175i	$0.561862\pi$
$30$	−53.8145	−	43.7813i	−0.327504	−	0.266445i
$31$	−16.2916	−	238.174i	−0.0943888	−	1.37992i	−0.767820	−	0.640665i	$-0.778659\pi$
$31$	−16.2916	−	238.174i	−0.0943888	−	1.37992i	0.673431	−	0.739250i	$-0.264820\pi$
$32$	−15.4242	−	29.7674i	−0.0852076	−	0.164443i
$33$	−88.2295	−	124.993i	−0.465418	−	0.659347i
$34$	211.470	+	59.2510i	1.06667	+	0.298866i
$35$	72.7261	+	77.8707i	0.351227	+	0.376073i
$36$	−0.271631	+	0.220988i	−0.00125755	+	0.00102309i
$37$	−94.5373	+	133.929i	−0.420050	+	0.595075i	−0.970887	−	0.239538i	$-0.923004\pi$
$37$	−94.5373	+	133.929i	−0.420050	+	0.595075i	0.550837	+	0.834613i	$0.314308\pi$
$38$	−338.547	−	46.5321i	−1.44525	−	0.198645i
$39$	84.9703	−	239.084i	0.348875	−	0.981641i
$40$	−23.9599	−	115.302i	−0.0947100	−	0.455770i
$41$	139.294	+	391.936i	0.530587	+	1.49293i	0.840312	+	0.542102i	$0.182372\pi$
$41$	139.294	+	391.936i	0.530587	+	1.49293i	−0.309726	+	0.950826i	$0.600237\pi$
$42$	252.629	−	153.627i	0.928133	−	0.564410i
$43$	199.460	−	213.570i	0.707381	−	0.757420i	−0.271370	−	0.962475i	$-0.587477\pi$
$43$	199.460	−	213.570i	0.707381	−	0.757420i	0.978750	+	0.205055i	$0.0657374\pi$
$44$	1.50677	−	22.0282i	0.00516260	−	0.0754745i
$45$	−2.16045	+	0.938418i	−0.00715692	+	0.00310869i
$46$	−428.275			−1.37273
$47$	199.917	+	252.698i	0.620444	+	0.784250i
$47$	199.917	+	252.698i	0.620444	+	0.784250i
$48$	−296.166			−0.890580
$49$	−101.918	+	44.2693i	−0.297137	+	0.129065i
$50$	4.59583	−	67.1886i	0.0129990	−	0.190038i
$51$	−286.606	+	306.880i	−0.786920	+	0.842586i
$52$	31.2870	−	19.0260i	0.0834369	−	0.0507391i
$53$	208.928	+	587.866i	0.541480	+	1.52358i	0.825297	+	0.564699i	$0.191008\pi$
$53$	208.928	+	587.866i	0.541480	+	1.52358i	−0.283817	+	0.958878i	$0.591601\pi$
$54$	77.5488	+	373.185i	0.195427	+	0.940446i
$55$	49.7368	−	139.946i	0.121937	−	0.343097i
$56$	497.239	+	68.3440i	1.18654	+	0.163087i
$57$	376.798	−	533.801i	0.875580	−	1.24041i
$58$	−294.147	+	239.306i	−0.665920	+	0.541766i
$59$	143.331	+	153.470i	0.316272	+	0.338645i	0.869087	−	0.494660i	$-0.164707\pi$
$59$	143.331	+	153.470i	0.316272	+	0.338645i	−0.552815	+	0.833304i	$0.686446\pi$
$60$	18.4328	+	5.16464i	0.0396612	+	0.0111125i
$61$	228.972	+	324.379i	0.480604	+	0.680861i	0.982964	−	0.183798i	$-0.0588391\pi$
$61$	228.972	+	324.379i	0.480604	+	0.680861i	−0.502360	+	0.864659i	$0.667535\pi$
$62$	−295.867	−	570.998i	−0.606051	−	1.16963i
$63$	−0.685085	−	10.0156i	−0.00137004	−	0.0200293i
$64$	−426.890	−	347.301i	−0.833770	−	0.678322i
$65$	237.180	−	66.4547i	0.452593	−	0.126811i
$66$	−352.143	−	214.143i	−0.656755	−	0.399381i
$67$	−27.7514	+	133.547i	−0.0506026	+	0.243513i	−0.996785	−	0.0801202i	$-0.974470\pi$
$67$	−27.7514	+	133.547i	−0.0506026	+	0.243513i	0.946183	+	0.323633i	$0.104904\pi$
$68$	−60.0343	+	8.25152i	−0.107062	+	0.0147153i
$69$	376.732	−	727.059i	0.657292	−	1.26852i
$70$	263.265	+	114.352i	0.449516	+	0.195253i
$71$	495.222	+	215.105i	0.827776	+	0.359554i	0.769421	−	0.638742i	$-0.220545\pi$
$71$	495.222	+	215.105i	0.827776	+	0.359554i	0.0583548	+	0.998296i	$0.481415\pi$
$72$	−5.10470	+	9.85162i	−0.00835548	+	0.0161253i
$73$	−109.972	+	15.1154i	−0.176319	+	0.0242345i	−0.223786	−	0.974638i	$-0.571842\pi$
$73$	−109.972	+	15.1154i	−0.176319	+	0.0242345i	0.0474669	+	0.998873i	$0.484885\pi$
$74$	−89.8478	+	432.371i	−0.141143	+	0.679218i
$75$	110.020	+	66.9045i	0.169387	+	0.103006i
$76$	90.7979	−	25.4404i	0.137043	−	0.0383975i
$77$	491.025	+	399.478i	0.726720	+	0.591231i
$78$	−46.6447	−	681.921i	−0.0677111	−	0.989902i
$79$	519.332	+	1002.26i	0.739612	+	1.42739i	0.897993	+	0.440009i	$0.145025\pi$
$79$	519.332	+	1002.26i	0.739612	+	1.42739i	−0.158381	+	0.987378i	$0.550627\pi$
$80$	−165.798	−	234.883i	−0.231710	−	0.328259i
$81$	−689.505	−	193.190i	−0.945823	−	0.265007i
$82$	764.802	+	818.903i	1.02998	+	1.10284i
$83$	−884.686	+	719.746i	−1.16996	+	0.951836i	−0.999438	−	0.0335177i	$-0.989329\pi$
$83$	−884.686	+	719.746i	−1.16996	+	0.951836i	−0.170525	+	0.985353i	$0.554546\pi$
$84$	−47.0492	+	66.6536i	−0.0611130	+	0.0865774i
$85$	−403.827	−	55.5048i	−0.515308	−	0.0708275i
$86$	263.619	−	741.754i	0.330544	−	0.930062i
$87$	−147.511	−	709.862i	−0.181780	−	0.874773i
$88$	−234.290	−	659.228i	−0.283811	−	0.798568i
$89$	−1209.43	+	735.470i	−1.44044	+	0.875951i	−0.999764	−	0.0217146i	$-0.993087\pi$
$89$	−1209.43	+	735.470i	−1.44044	+	0.875951i	−0.440676	+	0.897666i	$0.645261\pi$
$90$	−4.33093	+	4.63729i	−0.00507245	+	0.00543126i
$91$	−71.6403	+	1047.34i	−0.0825268	+	1.20650i
$92$	108.392	−	47.0812i	0.122833	−	0.0533538i
$93$	1229.61			1.37102
$94$	765.157	+	409.812i	0.839573	+	0.449669i
$95$	634.283			0.685011
$96$	158.385	−	68.7962i	0.168386	−	0.0731404i
$97$	124.630	−	1822.02i	0.130456	−	1.90720i	−0.228016	−	0.973657i	$-0.573224\pi$
$97$	124.630	−	1822.02i	0.130456	−	1.90720i	0.358472	−	0.933540i	$-0.383298\pi$
$98$	−204.309	+	218.762i	−0.210595	+	0.225492i
$99$	−11.9563	+	7.27077i	−0.0121379	+	0.00738121i
$100$	6.22303	+	17.5099i	0.00622303	+	0.0175099i
$101$	−282.294	−	1358.48i	−0.278112	−	1.33835i	−0.853766	−	0.520656i	$-0.825687\pi$
$101$	−282.294	−	1358.48i	−0.278112	−	1.33835i	0.575654	−	0.817693i	$-0.304748\pi$
$102$	−378.798	+	1065.83i	−0.367711	+	1.03464i
$103$	−474.235	−	65.1821i	−0.453667	−	0.0623552i	−0.0942844	−	0.995545i	$-0.530056\pi$
$103$	−474.235	−	65.1821i	−0.453667	−	0.0623552i	−0.359383	+	0.933190i	$0.617013\pi$
$104$	669.113	−	947.917i	0.630884	−	0.893758i
$105$	−425.710	+	346.341i	−0.395667	+	0.321899i
$106$	1147.13	+	1228.28i	1.05112	+	1.12548i
$107$	−97.8888	−	27.4272i	−0.0884418	−	0.0247802i	0.225291	−	0.974291i	$-0.427667\pi$
$107$	−97.8888	−	27.4272i	−0.0884418	−	0.0247802i	−0.313733	+	0.949511i	$0.601580\pi$
$108$	−60.6519	−	85.9241i	−0.0540392	−	0.0765561i
$109$	−323.578	−	624.477i	−0.284341	−	0.548753i	0.702257	−	0.711924i	$-0.252176\pi$
$109$	−323.578	−	624.477i	−0.284341	−	0.548753i	−0.986598	+	0.163171i	$0.947828\pi$
$110$	−27.3031	−	399.158i	−0.0236659	−	0.345984i
$111$	−654.980	−	532.865i	−0.560071	−	0.455652i
$112$	1179.91	−	330.595i	0.995454	−	0.278913i
$113$	−724.724	−	440.714i	−0.603330	−	0.366893i	0.184457	−	0.982841i	$-0.440947\pi$
$113$	−724.724	−	440.714i	−0.603330	−	0.366893i	−0.787787	+	0.615947i	$0.788773\pi$
$114$	358.107	−	1723.30i	0.294209	−	1.41581i
$115$	787.516	−	108.242i	0.638576	−	0.0877702i
$116$	48.1379	−	92.9020i	0.0385301	−	0.0743597i
$117$	−21.2860	−	9.24581i	−0.0168196	−	0.00730577i
$118$	518.849	+	225.368i	0.404779	+	0.175820i
$119$	799.269	−	1542.52i	0.615705	−	1.18826i
$120$	600.912	−	82.5935i	0.457129	−	0.0628310i
$121$	−91.2816	+	439.271i	−0.0685812	+	0.330031i
$122$	913.876	+	555.741i	0.678184	+	0.412413i
$123$	−2062.97	+	578.016i	−1.51229	+	0.423723i
$124$	137.652	+	111.988i	0.0996896	+	0.0811035i
$125$	8.53030	+	124.709i	0.00610379	+	0.0892342i
$126$	−12.4417	−	24.0113i	−0.00879675	−	0.0169770i
$127$	42.0087	+	59.5127i	0.0293517	+	0.0415819i	0.831381	−	0.555703i	$-0.187551\pi$
$127$	42.0087	+	59.5127i	0.0293517	+	0.0415819i	−0.802029	+	0.597284i	$0.796246\pi$
$128$	−1169.23	−	327.603i	−0.807394	−	0.226221i
$129$	1027.34	+	1100.02i	0.701182	+	0.750783i
$130$	514.705	−	418.743i	0.347251	−	0.282509i
$131$	1085.38	−	1537.64i	0.723897	−	1.02553i	−0.274065	−	0.961711i	$-0.588368\pi$
$131$	1085.38	−	1537.64i	0.723897	−	1.02553i	0.997962	−	0.0638167i	$-0.0203273\pi$
$132$	112.665	+	15.4854i	0.0742895	+	0.0102109i
$133$	−905.286	+	2547.23i	−0.590213	+	1.66070i
$134$	74.7573	+	359.752i	0.0481944	+	0.231924i
$135$	−236.916	−	666.618i	−0.151041	−	0.424987i
$136$	−1640.61	+	997.679i	−1.03442	+	0.629046i
$137$	−1786.04	+	1912.38i	−1.11381	+	1.19260i	−0.134352	+	0.990934i	$0.542895\pi$
$137$	−1786.04	+	1912.38i	−1.11381	+	1.19260i	−0.979455	+	0.201662i	$0.935366\pi$
$138$	150.535	−	2200.74i	0.0928577	−	1.35753i
$139$	−192.182	+	83.4766i	−0.117271	+	0.0509381i	−0.456222	−	0.889866i	$-0.650798\pi$
$139$	−192.182	+	83.4766i	−0.117271	+	0.0509381i	0.338951	+	0.940804i	$0.389928\pi$
$140$	−79.2004			−0.0478118
$141$	−1368.79	+	938.475i	−0.817536	+	0.560524i
$142$	1454.45			0.859542
$143$	1342.17	−	582.987i	0.784880	−	0.340922i
$144$	−1.84857	+	27.0251i	−0.00106977	+	0.0156395i
$145$	480.398	−	514.380i	0.275137	−	0.294600i
$146$	−255.498	+	155.372i	−0.144830	+	0.0880731i
$147$	−191.660	−	539.278i	−0.107536	−	0.302578i
$148$	−24.7920	−	119.306i	−0.0137695	−	0.0662627i
$149$	1142.79	−	3215.50i	0.628328	−	1.76795i	−0.0120988	−	0.999927i	$-0.503851\pi$
$149$	1142.79	−	3215.50i	0.628328	−	1.76795i	0.640427	−	0.768019i	$-0.278757\pi$
$150$	343.641	+	47.2323i	0.187054	+	0.0257100i
$151$	907.357	−	1285.43i	0.489004	−	0.692761i	−0.495403	−	0.868663i	$-0.664980\pi$
$151$	907.357	−	1285.43i	0.489004	−	0.692761i	0.984408	+	0.175902i	$0.0562841\pi$
$152$	2317.71	−	1885.59i	1.23678	−	1.00620i
$153$	26.2139	+	28.0682i	0.0138514	+	0.0148313i
$154$	1641.96	+	460.054i	0.859172	+	0.240729i
$155$	688.357	+	975.180i	0.356711	+	0.505344i
$156$	86.7703	+	167.459i	0.0445332	+	0.0859453i
$157$	116.042	+	1696.47i	0.0589882	+	0.862378i	0.929171	+	0.369649i	$0.120522\pi$
$157$	116.042	+	1696.47i	0.0589882	+	0.862378i	−0.870183	+	0.492728i	$0.836000\pi$
$158$	2358.82	+	1919.04i	1.18771	+	0.966271i
$159$	−3094.25	+	866.969i	−1.54334	+	0.432422i
$160$	143.227	+	87.0983i	0.0707694	+	0.0430358i
$161$	−689.299	+	3317.09i	−0.337419	+	1.62375i
$162$	−1910.97	+	262.657i	−0.926790	+	0.127384i
$163$	−295.179	+	569.669i	−0.141842	+	0.273742i	−0.948193	−	0.317695i	$-0.897091\pi$
$163$	−295.179	+	569.669i	−0.141842	+	0.273742i	0.806351	+	0.591437i	$0.201439\pi$
$164$	−283.587	−	123.179i	−0.135027	−	0.0586505i
$165$	701.646	+	304.768i	0.331049	+	0.143795i
$166$	−1413.44	+	2727.82i	−0.660869	+	1.27542i
$167$	368.714	−	50.6785i	0.170850	−	0.0234828i	−0.0502346	−	0.998737i	$-0.515997\pi$
$167$	368.714	−	50.6785i	0.170850	−	0.0234828i	0.221084	+	0.975255i	$0.429040\pi$
$168$	−525.968	+	2531.10i	−0.241544	+	1.16237i
$169$	196.363	+	119.411i	0.0893776	+	0.0543517i
$170$	−1057.35	+	296.255i	−0.477029	+	0.133657i
$171$	−46.3574	−	37.7145i	−0.0207312	−	0.0168661i
$172$	14.8234	+	216.710i	0.00657135	+	0.0960698i
$173$	1466.38	+	2829.98i	0.644431	+	1.24369i	0.955971	+	0.293462i	$0.0948073\pi$
$173$	1466.38	+	2829.98i	0.644431	+	1.24369i	−0.311540	+	0.950233i	$0.600845\pi$
$174$	−1126.31	−	1595.62i	−0.490721	−	0.695193i
$175$	−512.995	−	143.734i	−0.221593	−	0.0620874i
$176$	−1165.82	−	1248.29i	−0.499300	−	0.534620i
$177$	−839.000	+	682.577i	−0.356289	+	0.289862i
$178$	−2198.94	+	3115.19i	−0.925941	+	1.31176i
$179$	1333.01	+	183.218i	0.556612	+	0.0765046i	0.408989	−	0.912539i	$-0.365881\pi$
$179$	1333.01	+	183.218i	0.556612	+	0.0765046i	0.147623	+	0.989044i	$0.452838\pi$
$180$	0.586324	−	1.64976i	0.000242789	−	0.000683143i
$181$	−27.3740	−	131.731i	−0.0112414	−	0.0540965i	0.973090	−	0.230427i	$-0.0740122\pi$
$181$	−27.3740	−	131.731i	−0.0112414	−	0.0540965i	−0.984331	+	0.176330i	$0.943577\pi$
$182$	947.023	+	2664.67i	0.385703	+	1.08527i
$183$	−1747.34	+	1062.58i	−0.705832	+	0.429226i
$184$	2555.85	−	2736.64i	1.02402	−	1.09646i
$185$	55.9361	−	817.757i	0.0222298	−	0.324988i
$186$	3038.13	−	1319.65i	1.19767	−	0.520222i
$187$	−2421.64			−0.946992
$188$	−238.705	−	19.6037i	−0.0926027	−	0.00760502i
$189$	3015.22			1.16045
$190$	1567.19	−	680.727i	0.598400	−	0.259922i
$191$	248.668	−	3635.40i	0.0942041	−	1.37721i	−0.674814	−	0.737988i	$-0.735776\pi$
$191$	248.668	−	3635.40i	0.0942041	−	1.37721i	0.769018	−	0.639227i	$-0.220746\pi$
$192$	1934.69	−	2071.55i	0.727211	−	0.778653i
$193$	635.038	−	386.175i	0.236845	−	0.144029i	−0.396147	−	0.918187i	$-0.629653\pi$
$193$	635.038	−	386.175i	0.236845	−	0.144029i	0.632992	+	0.774159i	$0.281827\pi$
$194$	−1647.50	−	4635.61i	−0.609708	−	1.71555i
$195$	258.118	+	1242.13i	0.0947910	+	0.456159i
$196$	27.6595	−	77.8264i	0.0100800	−	0.0283624i
$197$	−3887.95	−	534.386i	−1.40612	−	0.193266i	−0.607123	−	0.794607i	$-0.707677\pi$
$197$	−3887.95	−	534.386i	−1.40612	−	0.193266i	−0.798992	+	0.601341i	$0.794633\pi$
$198$	−21.7385	+	30.7964i	−0.00780246	+	0.0110536i
$199$	−49.7818	+	40.5005i	−0.0177333	+	0.0144271i	−0.639913	−	0.768447i	$-0.721030\pi$
$199$	−49.7818	+	40.5005i	−0.0177333	+	0.0144271i	0.622180	+	0.782874i	$0.286247\pi$
$200$	401.903	+	430.334i	0.142094	+	0.152146i
$201$	−676.492	−	189.544i	−0.237393	−	0.0665145i
$202$	−2155.44	−	3053.56i	−0.750773	−	1.06360i
$203$	1380.06	+	2663.39i	0.477149	+	0.920855i
$204$	−21.2999	−	311.393i	−0.00731025	−	0.106872i
$205$	−1613.29	−	1312.51i	−0.549646	−	0.447170i
$206$	−1241.70	+	347.907i	−0.419967	+	0.117669i
$207$	−63.9926	−	38.9148i	−0.0214869	−	0.0130665i
$208$	576.321	−	2773.41i	0.192119	−	0.924525i
$209$	3733.09	−	513.101i	1.23552	−	0.169818i
$210$	−680.146	+	1312.62i	−0.223498	+	0.431331i
$211$	−454.911	−	197.596i	−0.148423	−	0.0644694i	0.322883	−	0.946439i	$-0.395348\pi$
$211$	−454.911	−	197.596i	−0.148423	−	0.0644694i	−0.471307	+	0.881969i	$0.656217\pi$
$212$	−425.354	−	184.757i	−0.137799	−	0.0598546i
$213$	−1279.41	+	2469.15i	−0.411567	+	0.794288i
$214$	−271.300	+	37.2893i	−0.0866620	+	0.0119114i
$215$	−297.276	+	1430.57i	−0.0942980	+	0.453787i
$216$	−2847.42	−	1731.56i	−0.896956	−	0.545451i
$217$	−4898.71	+	1372.55i	−1.53247	+	0.429378i
$218$	−1469.70	−	1195.69i	−0.456609	−	0.371479i
$219$	−39.0177	−	570.418i	−0.0120391	−	0.176006i
$220$	50.7904	+	98.0211i	0.0155650	+	0.0300390i
$221$	−2316.03	−	3281.06i	−0.704945	−	0.998679i
$222$	−2190.21	−	613.668i	−0.662150	−	0.185526i
$223$	−259.099	−	277.427i	−0.0778050	−	0.0833089i	0.690745	−	0.723098i	$-0.257283\pi$
$223$	−259.099	−	277.427i	−0.0778050	−	0.0833089i	−0.768550	+	0.639789i	$0.779022\pi$
$224$	−554.202	+	450.877i	−0.165309	+	0.134489i
$225$	6.79174	−	9.62170i	0.00201237	−	0.00285087i
$226$	−2263.64	−	311.130i	−0.666260	−	0.0915754i
$227$	722.232	−	2032.16i	0.211173	−	0.594183i	−0.788613	−	0.614890i	$-0.789200\pi$
$227$	722.232	−	2032.16i	0.211173	−	0.594183i	0.999786	+	0.0207070i	$0.00659173\pi$
$228$	98.8137	+	475.517i	0.0287022	+	0.138122i
$229$	2096.70	+	5899.54i	0.605038	+	1.70241i	0.706627	+	0.707587i	$0.250216\pi$
$229$	2096.70	+	5899.54i	0.605038	+	1.70241i	−0.101589	+	0.994826i	$0.532393\pi$
$230$	1829.63	−	1112.62i	0.524532	−	0.318975i
$231$	−2225.36	+	2382.77i	−0.633843	+	0.678680i
$232$	226.253	−	3307.70i	0.0640269	−	0.936040i
$233$	−5970.74	+	2593.46i	−1.67878	+	0.729197i	−0.999987	−	0.00513114i	$-0.998367\pi$
$233$	−5970.74	+	2593.46i	−1.67878	+	0.729197i	−0.678794	+	0.734329i	$0.737497\pi$
$234$	−62.5163			−0.0174650
$235$	−1510.55	−	560.182i	−0.419309	−	0.155499i
$236$	−156.090			−0.0430534
$237$	−5332.79	+	2316.36i	−1.46161	+	0.634868i
$238$	319.372	−	4669.06i	0.0869825	−	1.27164i
$239$	−176.302	+	188.774i	−0.0477157	+	0.0510910i	−0.754247	−	0.656591i	$-0.771998\pi$
$239$	−176.302	+	188.774i	−0.0477157	+	0.0510910i	0.706532	+	0.707682i	$0.250259\pi$
$240$	1265.25	−	769.415i	0.340298	−	0.206940i
$241$	−1371.68	−	3859.55i	−0.366630	−	1.03160i	−0.971862	−	0.235549i	$-0.924311\pi$
$241$	−1371.68	−	3859.55i	−0.366630	−	1.03160i	0.605232	−	0.796049i	$-0.293080\pi$
$242$	245.896	+	1183.32i	0.0653174	+	0.314325i
$243$	−44.2609	+	124.538i	−0.0116845	+	0.0328771i
$244$	−292.386	−	40.1875i	−0.0767135	−	0.0105440i
$245$	320.396	−	453.898i	0.0835484	−	0.118361i
$246$	−4476.85	+	3642.19i	−1.16030	+	0.943973i
$247$	4265.49	+	4567.22i	1.09881	+	1.17654i
$248$	5414.31	+	1517.02i	1.38633	+	0.388430i
$249$	−3387.54	−	4799.05i	−0.862154	−	1.22139i
$250$	154.917	+	298.976i	0.0391912	+	0.0756355i
$251$	342.456	+	5006.53i	0.0861181	+	1.25900i	0.817056	+	0.576558i	$0.195605\pi$
$251$	342.456	+	5006.53i	0.0861181	+	1.25900i	−0.730938	+	0.682444i	$0.760917\pi$
$252$	5.78846	+	4.70927i	0.00144698	+	0.00117721i
$253$	4547.38	−	1274.12i	1.13001	−	0.316613i
$254$	167.666	+	101.960i	0.0414184	+	0.0251871i
$255$	427.159	−	2055.60i	0.104901	−	0.504811i
$256$	1121.03	−	154.082i	0.273689	−	0.0376177i
$257$	−962.517	+	1857.57i	−0.233619	+	0.450865i	−0.975600	−	0.219557i	$-0.929539\pi$
$257$	−962.517	+	1857.57i	−0.233619	+	0.450865i	0.741980	+	0.670422i	$0.233887\pi$
$258$	3718.93	+	1615.36i	0.897404	+	0.389798i
$259$	3204.21	+	1391.79i	0.768726	+	0.333905i
$260$	−84.2329	+	162.562i	−0.0200919	+	0.0387756i
$261$	−65.6956	+	9.02965i	−0.0155803	+	0.00214146i
$262$	1031.54	−	4964.06i	0.243241	−	1.17054i
$263$	−5826.47	−	3543.15i	−1.36607	−	0.830723i	−0.370875	−	0.928683i	$-0.620942\pi$
$263$	−5826.47	−	3543.15i	−1.36607	−	0.830723i	−0.995190	+	0.0979598i	$0.968768\pi$
$264$	3469.87	−	972.212i	0.808923	−	0.226650i
$265$	−2419.79	−	1968.64i	−0.560930	−	0.456350i
$266$	496.959	+	7265.29i	0.114551	+	1.67467i
$267$	−3354.19	−	6473.30i	−0.768814	−	1.48374i
$268$	−58.4686	−	82.8312i	−0.0133266	−	0.0188795i
$269$	3320.02	+	930.225i	0.752510	+	0.210843i	0.624602	−	0.780943i	$-0.285261\pi$
$269$	3320.02	+	930.225i	0.752510	+	0.210843i	0.127907	+	0.991786i	$0.459174\pi$
$270$	−1300.80	−	1392.82i	−0.293201	−	0.313942i
$271$	2176.15	−	1770.43i	0.487793	−	0.396849i	−0.355186	−	0.934796i	$-0.615582\pi$
$271$	2176.15	−	1770.43i	0.487793	−	0.396849i	0.842979	+	0.537947i	$0.180800\pi$
$272$	−2703.33	+	3829.75i	−0.602624	+	0.853724i
$273$	−5356.71	−	736.264i	−1.18756	−	0.163226i
$274$	−2360.54	+	6641.93i	−0.520459	+	1.46443i
$275$	151.088	+	727.075i	0.0331307	+	0.159434i
$276$	203.833	+	573.532i	0.0444541	+	0.125082i
$277$	−3437.61	+	2090.45i	−0.745652	+	0.453441i	−0.840336	−	0.542066i	$-0.817642\pi$
$277$	−3437.61	+	2090.45i	−0.745652	+	0.453441i	0.0946834	+	0.995507i	$0.469816\pi$
$278$	−385.256	+	412.509i	−0.0831156	+	0.0889951i
$279$	7.67483	−	112.202i	0.00164688	−	0.0240766i
$280$	−2301.81	+	999.816i	−0.491283	+	0.213394i
$281$	5573.82			1.18330			0.591648	−	0.806196i	$-0.298478\pi$
$281$	5573.82			1.18330			0.591648	+	0.806196i	$0.298478\pi$
$282$	−2374.81	+	3787.80i	−0.501482	+	0.799859i
$283$	1273.82			0.267565			0.133782	−	0.991011i	$-0.457288\pi$
$283$	1273.82			0.267565			0.133782	+	0.991011i	$0.457288\pi$
$284$	−368.107	+	159.891i	−0.0769124	+	0.0334078i
$285$	−222.945	+	3259.34i	−0.0463372	+	0.677426i
$286$	2690.57	−	2880.89i	0.556281	−	0.595632i
$287$	7573.54	−	4605.57i	1.55767	−	0.947241i
$288$	−5.28906	−	14.8820i	−0.00108216	−	0.00304489i
$289$	352.648	+	1697.04i	0.0717786	+	0.345418i
$290$	634.925	−	1786.51i	0.128566	−	0.361749i
$291$	9318.86	+	1280.85i	1.87725	+	0.258023i
$292$	47.5835	−	67.4104i	0.00953634	−	0.0135099i
$293$	901.105	−	733.103i	0.179669	−	0.146172i	−0.537007	−	0.843578i	$-0.680445\pi$
$293$	901.105	−	733.103i	0.179669	−	0.146172i	0.716676	+	0.697406i	$0.245663\pi$
$294$	−1052.32	−	1126.76i	−0.208750	−	0.223517i
$295$	−1011.02	−	283.275i	−0.199539	−	0.0559083i
$296$	−2226.63	−	3154.42i	−0.437231	−	0.619415i
$297$	−1933.63	−	3731.74i	−0.377780	−	0.729083i
$298$	−627.337	−	9171.34i	−0.121948	−	1.78282i
$299$	6075.36	+	4942.67i	1.17507	+	0.955994i
$300$	−92.1642	+	25.8232i	−0.0177370	+	0.00496968i
$301$	−5320.77	−	3235.63i	−1.01888	−	0.619597i
$302$	862.348	−	4149.85i	0.164313	−	0.790718i
$303$	7079.90	−	973.110i	1.34234	−	0.184501i
$304$	3355.89	−	6476.57i	0.633136	−	1.22190i
$305$	−1820.90	−	790.929i	−0.341851	−	0.148487i
$306$	94.8929	+	41.2178i	0.0177277	+	0.00770022i
$307$	−3335.97	+	6438.13i	−0.620175	+	1.19688i	0.345815	+	0.938303i	$0.387603\pi$
$307$	−3335.97	+	6438.13i	−0.620175	+	1.19688i	−0.965990	+	0.258581i	$0.916745\pi$
$308$	−466.136	+	64.0689i	−0.0862356	+	0.0118528i
$309$	501.635	−	2414.00i	0.0923528	−	0.444426i
$310$	2747.38	+	1670.72i	0.503357	+	0.306098i
$311$	9418.90	−	2639.05i	1.71735	−	0.481180i	0.736583	−	0.676347i	$-0.236438\pi$
$311$	9418.90	−	2639.05i	1.71735	−	0.481180i	0.980770	+	0.195167i	$0.0625250\pi$
$312$	4635.79	+	3771.50i	0.841186	+	0.684355i
$313$	529.354	+	7738.88i	0.0955938	+	1.39753i	0.759885	+	0.650058i	$0.225255\pi$
$313$	529.354	+	7738.88i	0.0955938	+	1.39753i	−0.664291	+	0.747474i	$0.731266\pi$
$314$	2107.41	+	4067.12i	0.378752	+	0.730957i
$315$	28.9464	+	41.0077i	0.00517761	+	0.00733500i
$316$	−807.957	−	226.379i	−0.143833	−	0.0403000i
$317$	4344.02	+	4651.31i	0.769667	+	0.824112i	0.988432	−	0.151665i	$-0.0484636\pi$
$317$	4344.02	+	4651.31i	0.769667	+	0.824112i	−0.218765	+	0.975778i	$0.570203\pi$
$318$	−6714.85	+	5462.93i	−1.18412	+	0.963353i
$319$	2411.29	−	3416.02i	0.423217	−	0.599562i
$320$	2725.98	+	374.677i	0.476209	+	0.0654534i
$321$	175.345	−	493.373i	0.0304884	−	0.0857862i
$322$	1856.85	+	8935.65i	0.321361	+	1.54647i
$323$	−3463.31	−	9744.83i	−0.596606	−	1.67869i
$324$	454.771	−	276.553i	0.0779786	−	0.0474199i
$325$	−840.611	+	900.075i	−0.143473	+	0.153622i
$326$	−117.948	+	1724.33i	−0.0200384	+	0.292951i
$327$	3322.68	−	1443.24i	0.561911	−	0.244072i
$328$	−9796.90			−1.64922
$329$	4405.60	−	5266.74i	0.738263	−	0.882568i
$330$	2060.72			0.343753
$331$	−8508.83	+	3695.91i	−1.41295	+	0.613732i	−0.960557	−	0.278084i	$-0.910301\pi$
$331$	−8508.83	+	3695.91i	−1.41295	+	0.613732i	−0.452397	+	0.891817i	$0.649431\pi$
$332$	57.8518	−	845.764i	0.00956335	−	0.139811i
$333$	−52.7121	+	56.4409i	−0.00867449	+	0.00928811i
$334$	856.630	−	520.928i	0.140337	−	0.0853411i
$335$	−228.388	−	642.622i	−0.0372482	−	0.104806i
$336$	1284.07	+	6179.29i	0.208488	+	1.00330i
$337$	−171.434	+	482.368i	−0.0277110	+	0.0779712i	−0.955310	−	0.295607i	$-0.904478\pi$
$337$	−171.434	+	482.368i	−0.0277110	+	0.0779712i	0.927599	+	0.373578i	$0.121869\pi$
$338$	613.328	+	84.3000i	0.0987001	+	0.0135660i
$339$	2519.40	−	3569.17i	0.403642	−	0.571831i
$340$	235.035	−	191.215i	0.0374900	−	0.0305003i
$341$	4840.21	+	5182.60i	0.768657	+	0.823031i
$342$	−155.016	−	43.4335i	−0.0245097	−	0.00686729i
$343$	−2849.62	−	4037.00i	−0.448586	−	0.635502i
$344$	3166.53	+	6111.13i	0.496302	+	0.957820i
$345$	279.407	+	4084.79i	0.0436022	+	0.637442i
$346$	6660.32	+	5418.57i	1.03486	+	0.841920i
$347$	−4547.91	+	1274.26i	−0.703586	+	0.197136i	−0.602940	−	0.797787i	$-0.706004\pi$
$347$	−4547.91	+	1274.26i	−0.703586	+	0.197136i	−0.100646	+	0.994922i	$0.532091\pi$
$348$	460.467	+	280.016i	0.0709300	+	0.0431335i
$349$	582.677	−	2803.99i	0.0893696	−	0.430070i	−0.910494	−	0.413523i	$-0.864298\pi$
$349$	582.677	−	2803.99i	0.0893696	−	0.430070i	0.999863	−	0.0165466i	$-0.00526719\pi$
$350$	−1421.77	+	195.418i	−0.217134	+	0.0298443i
$351$	3206.81	−	6188.87i	0.487655	−	0.941132i
$352$	913.425	+	396.756i	0.138312	+	0.0600772i
$353$	7303.42	+	3172.32i	1.10120	+	0.478317i	0.869230	−	0.494408i	$-0.164615\pi$
$353$	7303.42	+	3172.32i	1.10120	+	0.478317i	0.231965	+	0.972724i	$0.425485\pi$
$354$	−1340.45	+	2586.95i	−0.201254	+	0.388403i
$355$	−2674.46	+	367.597i	−0.399847	+	0.0549578i
$356$	214.069	−	1030.16i	0.0318697	−	0.153366i
$357$	7645.48	+	4649.32i	1.13345	+	0.689266i
$358$	3490.23	−	977.918i	0.515264	−	0.144370i
$359$	2673.39	+	2174.96i	0.393025	+	0.319750i	0.807014	−	0.590532i	$-0.201082\pi$
$359$	2673.39	+	2174.96i	0.393025	+	0.319750i	−0.413989	+	0.910282i	$0.635865\pi$
$360$	−3.78595	−	55.3487i	−0.000554270	−	0.00810315i
$361$	4248.06	+	8198.39i	0.619341	+	1.19527i
$362$	−209.012	−	296.103i	−0.0303465	−	0.0429912i
$363$	−2225.16	−	623.461i	−0.321737	−	0.0901465i
$364$	−532.614	−	570.291i	−0.0766939	−	0.0821191i
$365$	430.544	−	350.274i	0.0617417	−	0.0502306i
$366$	−3176.96	+	4500.72i	−0.453722	+	0.642777i
$367$	4743.97	+	652.044i	0.674750	+	0.0927423i	0.465403	−	0.885099i	$-0.345910\pi$
$367$	4743.97	+	652.044i	0.674750	+	0.0927423i	0.209347	+	0.977841i	$0.432866\pi$
$368$	3061.38	−	8613.89i	0.433656	−	1.22019i
$369$	39.8676	+	191.853i	0.00562445	+	0.0270664i
$370$	−739.428	−	2080.55i	−0.103895	−	0.292332i
$371$	11359.6	−	6907.92i	1.58965	−	0.966688i
$372$	−623.847	+	667.977i	−0.0869488	+	0.0930995i
$373$	70.7514	−	1034.35i	0.00982137	−	0.143583i	−0.990172	−	0.139857i	$-0.955336\pi$
$373$	70.7514	−	1034.35i	0.00982137	−	0.143583i	0.999993	−	0.00372617i	$-0.00118608\pi$
$374$	−5983.39	+	2598.95i	−0.827256	+	0.359328i
$375$	−643.828			−0.0886590
$376$	−7184.96	+	2443.63i	−0.985467	+	0.335161i
$377$	6934.47			0.947330
$378$	7450.03	−	3236.01i	1.01373	−	0.440323i
$379$	398.424	−	5824.76i	0.0539991	−	0.789440i	−0.889264	−	0.457394i	$-0.848783\pi$
$379$	398.424	−	5824.76i	0.0539991	−	0.789440i	0.943263	−	0.332046i	$-0.107739\pi$
$380$	−321.805	+	344.569i	−0.0434428	+	0.0465159i
$381$	−320.579	+	194.948i	−0.0431069	+	0.0262139i
$382$	−3287.18	−	9249.23i	−0.440279	−	1.23883i
$383$	−1035.21	−	4981.70i	−0.138112	−	0.664630i	−0.990019	−	0.140936i	$-0.954989\pi$
$383$	−1035.21	−	4981.70i	−0.138112	−	0.664630i	0.851907	−	0.523693i	$-0.175446\pi$
$384$	2094.40	−	5893.08i	0.278332	−	0.783151i
$385$	−3135.52	−	430.967i	−0.415067	−	0.0570496i
$386$	1154.60	−	1635.70i	0.152248	−	0.215687i
$387$	106.789	−	86.8790i	0.0140268	−	0.0114117i
$388$	926.567	+	992.111i	0.121235	+	0.129811i
$389$	−4217.43	−	1181.67i	−0.549698	−	0.154018i	−0.0162761	−	0.999868i	$-0.505181\pi$
$389$	−4217.43	−	1181.67i	−0.549698	−	0.154018i	−0.533422	+	0.845849i	$0.679094\pi$
$390$	1970.85	+	2792.05i	0.255891	+	0.362516i
$391$	−5962.96	−	11508.0i	−0.771253	−	1.48845i
$392$	−178.600	−	2611.04i	−0.0230119	−	0.336422i
$393$	7519.83	+	6117.84i	0.965204	+	0.785252i
$394$	−10179.9	+	2852.27i	−1.30166	+	0.364709i
$395$	−4822.44	−	2932.59i	−0.614287	−	0.373556i
$396$	2.11626	−	10.1840i	0.000268551	−	0.00129234i
$397$	−2395.93	+	329.314i	−0.302893	+	0.0416317i	−0.286013	−	0.958226i	$-0.592330\pi$
$397$	−2395.93	+	329.314i	−0.302893	+	0.0416317i	−0.0168803	+	0.999858i	$0.505373\pi$
$398$	−79.5351	+	153.496i	−0.0100169	+	0.0193318i
$399$	−12771.0	−	5547.25i	−1.60239	−	0.696014i
$400$	1318.51	+	572.711i	0.164814	+	0.0715889i
$401$	3114.32	−	6010.36i	0.387834	−	0.748486i	−0.611243	−	0.791443i	$-0.709330\pi$
$401$	3114.32	−	6010.36i	0.387834	−	0.748486i	0.999077	+	0.0429572i	$0.0136779\pi$
$402$	−1874.90	+	257.700i	−0.232616	+	0.0319724i
$403$	−2392.75	+	11514.6i	−0.295761	+	1.42328i
$404$	881.204	+	535.872i	0.108519	+	0.0659916i
$405$	3447.53	−	965.951i	0.422985	−	0.118515i
$406$	6268.27	+	5099.62i	0.766229	+	0.623374i
$407$	−332.309	−	4858.18i	−0.0404716	−	0.591673i
$408$	−4550.03	−	8781.15i	−0.552107	−	1.06552i
$409$	391.050	+	553.991i	0.0472767	+	0.0669758i	0.839922	−	0.542708i	$-0.182601\pi$
$409$	391.050	+	553.991i	0.0472767	+	0.0669758i	−0.792645	+	0.609684i	$0.791297\pi$
$410$	−5394.75	−	1511.54i	−0.649824	−	0.182072i
$411$	−9199.21	−	9849.94i	−1.10405	−	1.18215i
$412$	276.014	−	224.554i	0.0330054	−	0.0268519i
$413$	2580.60	−	3655.88i	0.307465	−	0.435579i
$414$	−199.878	−	27.4725i	−0.0237281	−	0.00326136i
$415$	1909.62	−	5373.17i	0.225879	−	0.635562i
$416$	336.026	+	1617.05i	0.0396035	+	0.190582i
$417$	−361.404	−	1016.89i	−0.0424413	−	0.119418i
$418$	8673.07	−	5274.21i	1.01486	−	0.617153i
$419$	−5434.26	+	5818.67i	−0.633606	+	0.678426i	−0.964148	−	0.265365i	$-0.914508\pi$
$419$	−5434.26	+	5818.67i	−0.633606	+	0.678426i	0.330542	+	0.943791i	$0.392768\pi$
$420$	27.8382	−	406.981i	0.00323421	−	0.0472824i
$421$	1015.70	−	441.179i	0.117582	−	0.0510730i	−0.338791	−	0.940862i	$-0.610018\pi$
$421$	1015.70	−	441.179i	0.117582	−	0.0510730i	0.456373	+	0.889789i	$0.349148\pi$
$422$	−1336.06			−0.154119
$423$	77.0923	+	130.759i	0.00886136	+	0.0150301i
$424$	−14694.4			−1.68308
$425$	1869.39	−	811.989i	0.213361	−	0.0926759i
$426$	−511.227	+	7473.88i	−0.0581433	+	0.850025i
$427$	5775.21	−	6183.74i	0.654525	−	0.700825i
$428$	64.5638	−	39.2621i	0.00729161	−	0.00443412i
$429$	2523.98	+	7101.81i	0.284054	+	0.799250i
$430$	800.809	+	3853.71i	0.0898104	+	0.432191i
$431$	3347.64	−	9419.36i	0.374131	−	1.05270i	−0.594478	−	0.804112i	$-0.702641\pi$
$431$	3347.64	−	9419.36i	0.374131	−	1.05270i	0.968609	−	0.248591i	$-0.0799674\pi$
$432$	−8060.22	−	1107.85i	−0.897679	−	0.123383i
$433$	6956.56	−	9855.20i	0.772081	−	1.09379i	−0.220875	−	0.975302i	$-0.570891\pi$
$433$	6956.56	−	9855.20i	0.772081	−	1.09379i	0.992956	−	0.118487i	$-0.0378044\pi$
$434$	−10630.7	+	8648.72i	−1.17578	+	0.956571i
$435$	2474.35	+	2649.38i	0.272726	+	0.292018i
$436$	503.411	+	141.049i	0.0552959	+	0.0154932i
$437$	11630.6	+	16476.8i	1.27315	+	1.80364i
$438$	−708.591	−	1367.52i	−0.0773009	−	0.149184i
$439$	−48.3972	−	707.541i	−0.00526166	−	0.0769228i	0.994296	−	0.106653i	$-0.0340134\pi$
$439$	−48.3972	−	707.541i	−0.00526166	−	0.0769228i	−0.999558	+	0.0297303i	$0.990535\pi$
$440$	2713.53	+	2207.62i	0.294006	+	0.239191i
$441$	−50.4054	+	14.1229i	−0.00544276	+	0.00152499i
$442$	−9243.76	−	5621.25i	−0.994753	−	0.604923i
$443$	−2437.04	+	11727.7i	−0.261371	+	1.25778i	0.619715	+	0.784827i	$0.287248\pi$
$443$	−2437.04	+	11727.7i	−0.261371	+	1.25778i	−0.881085	+	0.472957i	$0.843187\pi$
$444$	621.781	−	85.4618i	0.0664604	−	0.00913477i
$445$	3256.11	−	6284.00i	0.346863	−	0.669416i
$446$	−937.923	−	407.397i	−0.0995783	−	0.0432530i
$447$	16121.5	+	7002.57i	1.70587	+	0.740962i
$448$	−5395.35	+	10412.6i	−0.568987	+	1.09810i
$449$	−6908.73	+	949.584i	−0.726154	+	0.0998076i	−0.489770	−	0.871852i	$-0.662919\pi$
$449$	−6908.73	+	949.584i	−0.726154	+	0.0998076i	−0.236385	+	0.971660i	$0.575963\pi$
$450$	6.45484	−	31.0624i	0.000676187	−	0.00325399i
$451$	−10556.8	−	6419.76i	−1.10222	−	0.670276i
$452$	607.105	−	170.103i	0.0631766	−	0.0177013i
$453$	6286.41	+	5114.38i	0.652012	+	0.530451i
$454$	−396.471	−	5796.20i	−0.0409852	−	0.599183i
$455$	−2414.86	−	4660.47i	−0.248814	−	0.480189i
$456$	8874.69	+	12572.6i	0.911394	+	1.29115i
$457$	−12514.2	−	3506.30i	−1.28094	−	0.358901i	−0.439004	−	0.898485i	$-0.644669\pi$
$457$	−12514.2	−	3506.30i	−1.28094	−	0.358901i	−0.841932	+	0.539584i	$0.818582\pi$
$458$	11512.0	+	12326.4i	1.17450	+	1.25759i
$459$	−8947.99	+	7279.73i	−0.909927	+	0.740280i
$460$	−340.747	+	482.728i	−0.0345378	+	0.0489290i
$461$	−10479.0	−	1440.31i	−1.05869	−	0.145514i	−0.414247	−	0.910164i	$-0.635955\pi$
$461$	−10479.0	−	1440.31i	−1.05869	−	0.145514i	−0.644445	+	0.764650i	$0.722912\pi$
$462$	−2941.17	+	8275.67i	−0.296181	+	0.833375i
$463$	63.2754	+	304.498i	0.00635131	+	0.0305642i	0.982140	−	0.188149i	$-0.0602488\pi$
$463$	63.2754	+	304.498i	0.00635131	+	0.0305642i	−0.975789	+	0.218713i	$0.929814\pi$
$464$	−2710.56	−	7626.77i	−0.271195	−	0.763069i
$465$	−5253.02	+	3194.43i	−0.523878	+	0.318577i
$466$	−11969.2	+	12815.9i	−1.18983	+	1.27400i
$467$	516.862	−	7556.26i	0.0512153	−	0.748741i	−0.899157	−	0.437626i	$-0.855819\pi$
$467$	516.862	−	7556.26i	0.0512153	−	0.748741i	0.950372	−	0.311115i	$-0.100702\pi$
$468$	15.8222	−	6.87256i	0.00156278	−	0.000678812i
$469$	2906.69			0.286180
$470$	−4333.48	+	237.060i	−0.425295	+	0.0232654i
$471$	−8758.31			−0.856819
$472$	−4536.46	+	1970.46i	−0.442389	+	0.192156i
$473$	−592.370	+	8660.14i	−0.0575839	+	0.841847i
$474$	−10690.3	+	11446.5i	−1.03591	+	1.10919i
$475$	−2709.72	+	1647.82i	−0.261748	+	0.159173i
$476$	432.450	+	1216.80i	0.0416414	+	0.117168i
$477$	59.7976	+	287.762i	0.00573992	+	0.0276220i
$478$	−233.012	+	655.634i	−0.0222965	+	0.0627364i
$479$	9037.43	+	1242.17i	0.862068	+	0.118489i	0.553637	−	0.832758i	$-0.313240\pi$
$479$	9037.43	+	1242.17i	0.862068	+	0.118489i	0.308431	+	0.951247i	$0.400196\pi$
$480$	−497.908	+	705.375i	−0.0473464	+	0.0670746i
$481$	6264.51	−	5096.55i	0.593840	−	0.483124i
$482$	−7531.31	−	8064.07i	−0.711705	−	0.762050i
$483$	−16803.0	−	4707.97i	−1.58294	−	0.443520i
$484$	−192.319	−	272.453i	−0.0180615	−	0.0255873i
$485$	4201.03	+	8107.63i	0.393318	+	0.759069i
$486$	24.2971	+	355.211i	0.00226778	+	0.0331537i
$487$	−10005.2	−	8139.87i	−0.930967	−	0.757398i	0.0393522	−	0.999225i	$-0.487471\pi$
$487$	−10005.2	−	8139.87i	−0.930967	−	0.757398i	−0.970319	+	0.241828i	$0.922253\pi$
$488$	−9004.95	+	2523.07i	−0.835318	+	0.234045i
$489$	−2823.56	−	1717.04i	−0.261116	−	0.158788i
$490$	304.503	−	1465.35i	0.0280736	−	0.135097i
$491$	−9079.48	+	1247.95i	−0.834524	+	0.114703i	−0.540762	−	0.841176i	$-0.681864\pi$
$491$	−9079.48	+	1247.95i	−0.834524	+	0.114703i	−0.293762	+	0.955879i	$0.594907\pi$
$492$	732.649	−	1413.95i	0.0671349	−	0.129564i
$493$	−10525.8	−	4571.98i	−0.961575	−	0.417671i
$494$	15440.8	+	6706.90i	1.40631	+	0.610845i
$495$	32.1895	−	62.1229i	0.00292285	−	0.00564084i
$496$	13599.4	−	1869.19i	1.23111	−	0.169212i
$497$	2340.91	−	11265.1i	0.211276	−	1.01672i
$498$	−13520.4	−	8221.93i	−1.21659	−	0.739826i
$499$	−7019.47	+	1966.76i	−0.629729	+	0.176442i	−0.569830	−	0.821763i	$-0.692991\pi$
$499$	−7019.47	+	1966.76i	−0.629729	+	0.176442i	−0.0598989	+	0.998204i	$0.519078\pi$
$500$	−72.0748	−	58.6372i	−0.00644657	−	0.00524467i
$501$	130.818	+	1912.49i	0.0116657	+	0.170546i
$502$	6219.26	+	12002.6i	0.552947	+	1.06714i
$503$	1312.13	+	1858.86i	0.116312	+	0.164777i	0.870961	−	0.491352i	$-0.163497\pi$
$503$	1312.13	+	1858.86i	0.116312	+	0.164777i	−0.754649	+	0.656129i	$0.772193\pi$
$504$	227.680	+	63.7928i	0.0201223	+	0.00563801i
$505$	4735.20	+	5070.16i	0.417255	+	0.446771i
$506$	9868.28	−	8028.44i	0.866994	−	0.705352i
$507$	−682.625	+	967.060i	−0.0597958	+	0.0847113i
$508$	−53.6430	−	7.37306i	−0.00468509	−	0.000643951i
$509$	−4115.49	+	11579.9i	−0.358381	+	1.00839i	0.616827	+	0.787098i	$0.288418\pi$
$509$	−4115.49	+	11579.9i	−0.358381	+	1.00839i	−0.975208	+	0.221289i	$0.928974\pi$
$510$	−1150.69	−	5537.43i	−0.0999088	−	0.480788i
$511$	792.173	+	2228.96i	0.0685787	+	0.192962i
$512$	10904.4	−	6631.10i	0.941230	−	0.572375i
$513$	12251.4	−	13118.0i	1.05441	−	1.12900i
$514$	−384.603	+	5622.70i	−0.0330041	+	0.482503i
$515$	2195.32	−	953.560i	0.187839	−	0.0815900i
$516$	−1118.80			−0.0954505
$517$	−9343.56	−	2075.01i	−0.794834	−	0.176516i
$518$	9410.68			0.798227
$519$	−15057.6	+	6540.43i	−1.27352	+	0.553166i
$520$	−395.903	+	5787.89i	−0.0333875	+	0.488107i
$521$	8682.66	−	9296.86i	0.730123	−	0.781771i	−0.252457	−	0.967608i	$-0.581239\pi$
$521$	8682.66	−	9296.86i	0.730123	−	0.781771i	0.982581	+	0.185837i	$0.0594996\pi$
$522$	−152.630	+	92.8165i	−0.0127978	+	0.00778250i
$523$	4902.49	+	13794.3i	0.409887	+	1.15331i	0.950144	+	0.311811i	$0.100936\pi$
$523$	4902.49	+	13794.3i	0.409887	+	1.15331i	−0.540257	+	0.841500i	$0.681673\pi$
$524$	284.638	+	1369.75i	0.0237299	+	0.114194i
$525$	918.909	−	2585.56i	0.0763895	−	0.214939i
$526$	−18198.7	−	2501.35i	−1.50855	−	0.207346i
$527$	11223.6	−	15900.3i	0.927721	−	1.31428i
$528$	6824.24	−	5551.93i	0.562475	−	0.457607i
$529$	8947.51	+	9580.45i	0.735392	+	0.787413i
$530$	−8091.62	−	2267.17i	−0.663165	−	0.185810i
$531$	57.0483	+	80.8191i	0.00466231	+	0.00660499i
$532$	−924.464	−	1784.13i	−0.0753395	−	0.145399i
$533$	−1398.35	−	20443.2i	−0.113639	−	1.66134i
$534$	−15234.9	−	12394.5i	−1.23460	−	1.00442i
$535$	489.444	−	137.136i	0.0395524	−	0.0110821i
$536$	−2744.93	−	1669.23i	−0.221199	−	0.134514i
$537$	−1410.02	+	6785.41i	−0.113309	+	0.545274i
$538$	9201.46	−	1264.71i	0.737366	−	0.101349i
$539$	1518.52	−	2930.61i	0.121349	−	0.234194i
$540$	482.335	+	209.508i	0.0384377	+	0.0166959i
$541$	−10640.5	−	4621.83i	−0.845604	−	0.367298i	−0.0692535	−	0.997599i	$-0.522062\pi$
$541$	−10640.5	−	4621.83i	−0.845604	−	0.367298i	−0.776350	+	0.630301i	$0.782931\pi$
$542$	3476.78	−	6709.89i	0.275536	−	0.531761i
$543$	686.535	−	94.3621i	0.0542579	−	0.00745758i
$544$	556.089	−	2676.05i	0.0438274	−	0.210909i
$545$	3004.70	+	1827.20i	0.236160	+	0.143612i
$546$	−14025.6	+	3929.78i	−1.09934	+	0.308020i
$547$	−14737.6	−	11989.9i	−1.15198	−	0.937204i	−0.153279	−	0.988183i	$-0.548983\pi$
$547$	−14737.6	−	11989.9i	−1.15198	−	0.937204i	−0.998700	+	0.0509786i	$0.983766\pi$
$548$	−132.734	−	1940.50i	−0.0103469	−	0.151267i
$549$	86.0542	+	166.077i	0.00668981	+	0.0129107i
$550$	1153.62	+	1634.31i	0.0894375	+	0.126704i
$551$	17194.8	+	4817.75i	1.32944	+	0.372492i
$552$	13164.2	+	14095.4i	1.01505	+	1.08685i
$553$	18659.9	−	15181.0i	1.43490	−	1.16738i
$554$	−6250.13	+	8854.42i	−0.479319	+	0.679040i
$555$	4182.48	+	574.868i	0.319885	+	0.0439672i
$556$	52.1562	−	146.754i	0.00397827	−	0.0111938i
$557$	−667.654	−	3212.93i	−0.0507889	−	0.244410i	0.946033	−	0.324070i	$-0.105051\pi$
$557$	−667.654	−	3212.93i	−0.0507889	−	0.244410i	−0.996822	+	0.0796602i	$0.974616\pi$
$558$	−101.455	−	285.466i	−0.00769699	−	0.0216572i
$559$	−12300.1	+	7479.87i	−0.930661	+	0.565948i
$560$	−4181.82	+	4477.64i	−0.315561	+	0.337884i
$561$	851.183	−	12443.9i	0.0640588	−	0.936506i
$562$	13771.8	−	5981.95i	1.03368	−	0.448991i
$563$	−17147.3			−1.28361			−0.641806	−	0.766867i	$-0.721815\pi$
$563$	−17147.3			−1.28361			−0.641806	+	0.766867i	$0.721815\pi$
$564$	184.638	−	1219.72i	0.0137849	−	0.0910629i
$565$	4241.03			0.315790
$566$	3147.37	−	1367.09i	0.233734	−	0.101525i
$567$	−1041.33	+	15223.7i	−0.0771281	+	1.12757i
$568$	−8679.86	+	9293.86i	−0.641195	+	0.686552i
$569$	−6084.43	+	3700.02i	−0.448282	+	0.272607i	−0.725528	−	0.688192i	$-0.758404\pi$
$569$	−6084.43	+	3700.02i	−0.448282	+	0.272607i	0.277246	+	0.960799i	$0.410578\pi$
$570$	2947.14	+	8292.46i	0.216565	+	0.609356i
$571$	−416.999	−	2006.71i	−0.0305620	−	0.147072i	0.961038	−	0.276417i	$-0.0891472\pi$
$571$	−416.999	−	2006.71i	−0.0305620	−	0.147072i	−0.991600	+	0.129345i	$0.958712\pi$
$572$	−364.251	+	1024.90i	−0.0266260	+	0.0749184i
$573$	18593.5	+	2555.62i	1.35559	+	0.186322i
$574$	13769.9	−	19507.6i	1.00130	−	1.41852i
$575$	−3083.14	+	2508.32i	−0.223610	+	0.181920i
$576$	−176.953	−	189.471i	−0.0128004	−	0.0137059i
$577$	14792.7	+	4144.71i	1.06729	+	0.299041i	0.758220	−	0.651998i	$-0.226069\pi$
$577$	14792.7	+	4144.71i	1.06729	+	0.299041i	0.309070	+	0.951039i	$0.399982\pi$
$578$	2692.62	+	3814.58i	0.193769	+	0.274508i
$579$	1761.20	+	3398.95i	0.126412	+	0.243965i
$580$	35.7020	+	521.945i	0.00255594	+	0.0373665i
$581$	18852.7	+	15337.8i	1.34620	+	1.09521i
$582$	24399.7	−	6836.48i	1.73780	−	0.486909i
$583$	−15834.3	−	9629.02i	−1.12485	−	0.684037i
$584$	531.941	−	2559.84i	0.0376916	−	0.181382i
$585$	114.956	−	15.8003i	0.00812450	−	0.00111669i
$586$	1439.67	−	2778.44i	0.101489	−	0.195864i
$587$	10390.8	+	4513.36i	0.730620	+	0.317353i	0.730748	−	0.682647i	$-0.239171\pi$
$587$	10390.8	+	4513.36i	0.730620	+	0.317353i	−0.000128316		1.00000i	$0.500041\pi$
$588$	390.198	+	169.487i	0.0273665	+	0.0118869i
$589$	−13932.9	+	26889.2i	−0.974694	+	1.88107i
$590$	−2802.06	+	385.134i	−0.195524	+	0.0268741i
$591$	4112.58	−	19790.8i	0.286242	−	1.37747i
$592$	−8054.05	−	4897.77i	−0.559154	−	0.340029i
$593$	−19898.8	+	5575.39i	−1.37799	+	0.386094i	−0.877470	−	0.479631i	$-0.840770\pi$
$593$	−19898.8	+	5575.39i	−1.37799	+	0.386094i	−0.500519	+	0.865726i	$0.666857\pi$
$594$	−8782.62	−	7145.19i	−0.606659	−	0.493553i
$595$	592.786	+	8666.23i	0.0408435	+	0.597110i
$596$	1167.00	+	2252.20i	0.0802048	+	0.154788i
$597$	−190.618	−	270.045i	−0.0130678	−	0.0185129i
$598$	20315.6	+	5692.17i	1.38924	+	0.389248i
$599$	770.189	+	824.671i	0.0525360	+	0.0562523i	0.756563	−	0.653921i	$-0.226877\pi$
$599$	770.189	+	824.671i	0.0525360	+	0.0562523i	−0.704027	+	0.710174i	$0.748616\pi$
$600$	−2352.58	+	1913.97i	−0.160073	+	0.130229i
$601$	−4512.89	+	6393.31i	−0.306297	+	0.433924i	−0.940783	−	0.339011i	$-0.889908\pi$
$601$	−4512.89	+	6393.31i	−0.306297	+	0.433924i	0.634485	+	0.772935i	$0.281212\pi$
$602$	−16619.1	−	2284.25i	−1.12516	−	0.154650i
$603$	−21.5183	+	60.5468i	−0.00145322	+	0.00408898i
$604$	237.951	+	1145.08i	0.0160299	+	0.0771403i
$605$	−751.227	−	2113.75i	−0.0504822	−	0.142043i
$606$	16448.7	−	10002.7i	1.10261	−	0.670513i
$607$	7004.18	−	7499.65i	0.468354	−	0.501485i	−0.452299	−	0.891866i	$-0.649396\pi$
$607$	7004.18	−	7499.65i	0.468354	−	0.501485i	0.920653	+	0.390382i	$0.127657\pi$
$608$	−290.236	+	4243.10i	−0.0193596	+	0.283027i
$609$	−14171.2	+	6155.44i	−0.942935	+	0.409574i
$610$	−5347.94			−0.354970
$611$	−6124.66	−	14644.1i	−0.405528	−	0.969615i
$612$	−28.5476			−0.00188557
$613$	−7859.78	+	3413.98i	−0.517869	+	0.224942i	−0.641130	−	0.767432i	$-0.721534\pi$
$613$	−7859.78	+	3413.98i	−0.517869	+	0.224942i	0.123262	+	0.992374i	$0.460665\pi$
$614$	−1332.99	+	19487.6i	−0.0876140	+	1.28087i
$615$	7311.56	−	7828.76i	0.479399	−	0.513311i
$616$	−12738.5	+	7746.48i	−0.833199	+	0.506679i
$617$	3564.32	+	10029.0i	0.232567	+	0.654381i	0.999914	+	0.0131484i	$0.00418540\pi$
$617$	3564.32	+	10029.0i	0.232567	+	0.654381i	−0.767346	+	0.641233i	$0.778423\pi$
$618$	−1351.32	−	6502.89i	−0.0879577	−	0.423276i
$619$	2857.29	−	8039.66i	0.185532	−	0.522037i	−0.812621	−	0.582793i	$-0.801960\pi$
$619$	2857.29	−	8039.66i	0.185532	−	0.522037i	0.998153	+	0.0607558i	$0.0193511\pi$
$620$	−878.998	−	120.816i	−0.0569378	−	0.00782592i
$621$	12972.5	−	18377.9i	0.838275	−	1.18757i
$622$	20440.0	−	16629.2i	1.31763	−	1.07197i
$623$	20588.7	+	22045.2i	1.32403	+	1.41769i
$624$	14048.9	+	3936.32i	0.901292	+	0.252530i
$625$	−360.425	−	510.606i	−0.0230672	−	0.0326788i
$626$	9613.47	+	18553.2i	0.613788	+	1.18456i
$627$	1324.48	+	19363.3i	0.0843617	+	1.23332i
$628$	−980.470	−	797.671i	−0.0623010	−	0.0506856i
$629$	−12869.1	+	3605.74i	−0.815775	+	0.228570i
$630$	115.531	+	70.2562i	0.00730616	+	0.00444297i
$631$	549.359	−	2643.66i	0.0346587	−	0.166787i	−0.958197	−	0.286110i	$-0.907638\pi$
$631$	549.359	−	2643.66i	0.0346587	−	0.166787i	0.992855	+	0.119323i	$0.0380725\pi$
$632$	−26339.5	+	3620.28i	−1.65780	+	0.227859i
$633$	1175.26	−	2268.16i	0.0737955	−	0.142419i
$634$	15725.1	+	6830.38i	0.985054	+	0.427869i
$635$	−334.074	−	145.109i	−0.0208777	−	0.00906846i
$636$	1098.90	−	2120.79i	0.0685132	−	0.132224i
$637$	5422.97	−	745.369i	0.337309	−	0.0463620i
$638$	2291.68	−	11028.2i	0.142207	−	0.684340i
$639$	217.324	+	132.158i	0.0134542	+	0.00818165i
$640$	5846.15	−	1638.02i	0.361077	−	0.101169i
$641$	13389.2	+	10892.9i	0.825026	+	0.671209i	0.946968	−	0.321328i	$-0.104129\pi$
$641$	13389.2	+	10892.9i	0.825026	+	0.671209i	−0.121941	+	0.992537i	$0.538912\pi$
$642$	−96.2559	−	1407.21i	−0.00591732	−	0.0865081i
$643$	3665.81	+	7074.68i	0.224829	+	0.433901i	0.973387	−	0.229169i	$-0.0736009\pi$
$643$	3665.81	+	7074.68i	0.224829	+	0.433901i	−0.748557	+	0.663070i	$0.769253\pi$
$644$	−1452.27	−	2057.39i	−0.0888622	−	0.125889i
$645$	−7246.66	−	2030.42i	−0.442383	−	0.123950i
$646$	−19015.5	−	20360.7i	−1.15814	−	1.24006i
$647$	−2306.72	+	1876.66i	−0.140165	+	0.114033i	−0.698590	−	0.715523i	$-0.746189\pi$
$647$	−2306.72	+	1876.66i	−0.140165	+	0.114033i	0.558425	+	0.829555i	$0.311406\pi$
$648$	9725.88	−	13778.4i	0.589612	−	0.835290i
$649$	−6179.56	−	849.361i	−0.373758	−	0.0513718i
$650$	−1111.01	+	3126.07i	−0.0670419	+	0.188638i
$651$	−5331.17	−	25655.0i	−0.320960	−	1.54455i
$652$	−159.708	−	449.376i	−0.00959304	−	0.0269922i
$653$	4735.91	−	2879.97i	0.283814	−	0.172591i	−0.370461	−	0.928848i	$-0.620800\pi$
$653$	4735.91	−	2879.97i	0.283814	−	0.172591i	0.654275	+	0.756257i	$0.272974\pi$
$654$	6660.78	−	7131.95i	0.398252	−	0.426424i
$655$	−642.204	+	9388.68i	−0.0383099	+	0.560071i
$656$	−21937.5	+	9528.82i	−1.30567	+	0.567131i
$657$	−52.2942			−0.00310531
$658$	5232.99	−	17741.3i	0.310035	−	1.05110i
$659$	24673.8			1.45851			0.729254	−	0.684243i	$-0.239867\pi$
$659$	24673.8			1.45851			0.729254	+	0.684243i	$0.239867\pi$
$660$	−521.545	+	226.539i	−0.0307593	+	0.0133606i
$661$	−641.966	+	9385.21i	−0.0377755	+	0.552258i	0.939807	+	0.341705i	$0.111005\pi$
$661$	−641.966	+	9385.21i	−0.0377755	+	0.552258i	−0.977583	+	0.210552i	$0.932474\pi$
$662$	−17057.1	+	18263.7i	−1.00143	+	1.07227i
$663$	17674.2	−	10747.9i	1.03531	−	0.629584i
$664$	−8995.46	−	25310.8i	−0.525740	−	1.47929i
$665$	−2750.03	−	13233.9i	−0.160363	−	0.771711i
$666$	−69.6677	+	196.026i	−0.00405341	+	0.0114052i
$667$	22170.9	+	3047.32i	1.28705	+	0.176901i
$668$	−159.537	+	226.013i	−0.00924054	+	0.0130909i
$669$	1516.66	−	1233.89i	0.0876495	−	0.0713081i
$670$	−1253.98	−	1342.68i	−0.0723065	−	0.0774214i
$671$	−11356.8	−	3182.02i	−0.653389	−	0.183071i
$672$	−2122.09	−	3006.31i	−0.121817	−	0.172576i
$673$	7251.13	+	13994.1i	0.415320	+	0.801532i	0.999952	−	0.00976663i	$-0.00310886\pi$
$673$	7251.13	+	13994.1i	0.415320	+	0.801532i	−0.584632	+	0.811299i	$0.698761\pi$
$674$	94.1090	+	1375.83i	0.00537825	+	0.0786273i
$675$	2743.95	+	2232.37i	0.156466	+	0.127295i
$676$	−164.494	+	46.0891i	−0.00935901	+	0.00262227i
$677$	12104.4	+	7360.82i	0.687161	+	0.417872i	0.819304	−	0.573359i	$-0.194360\pi$
$677$	12104.4	+	7360.82i	0.687161	+	0.417872i	−0.132143	+	0.991231i	$0.542186\pi$
$678$	2394.42	−	11522.6i	0.135630	−	0.652688i
$679$	−38555.6	+	5299.34i	−2.17913	+	0.299514i
$680$	4416.97	−	8524.36i	0.249093	−	0.480727i
$681$	10188.7	+	4425.56i	0.573319	+	0.249027i
$682$	17521.3	+	7610.57i	0.983761	+	0.427308i
$683$	−2726.73	+	5262.35i	−0.152761	+	0.294814i	−0.951944	−	0.306273i	$-0.900918\pi$
$683$	−2726.73	+	5262.35i	−0.152761	+	0.294814i	0.799183	+	0.601088i	$0.205266\pi$
$684$	44.0077	−	6.04872i	0.00246005	−	0.000338126i
$685$	2661.92	−	12809.9i	0.148477	−	0.714510i
$686$	−11373.5	−	6916.35i	−0.633004	−	0.384938i
$687$	−31052.4	+	8700.48i	−1.72449	+	0.483179i
$688$	13034.5	+	10604.4i	0.722291	+	0.587627i
$689$	−2097.40	−	30662.8i	−0.115972	−	1.69544i
$690$	5074.24	+	9792.84i	0.279961	+	0.540300i
$691$	14711.4	+	20841.2i	0.809908	+	1.14738i	0.986607	+	0.163113i	$0.0521535\pi$
$691$	14711.4	+	20841.2i	0.809908	+	1.14738i	−0.176700	+	0.984265i	$0.556542\pi$
$692$	−2281.33	−	639.199i	−0.125323	−	0.0351137i
$693$	203.538	+	217.936i	0.0111570	+	0.0119462i
$694$	−9869.42	+	8029.37i	−0.539824	+	0.439180i
$695$	604.156	−	855.894i	0.0329740	−	0.0467136i
$696$	16917.5	+	2325.25i	0.921344	+	0.126636i
$697$	−11355.9	+	31952.5i	−0.617125	+	1.73642i
$698$	−1569.63	−	7553.47i	−0.0851165	−	0.409603i
$699$	−11228.1	−	31592.9i	−0.607563	−	1.70952i
$700$	338.352	−	205.756i	0.0182693	−	0.0111098i
$701$	−7235.06	+	7746.86i	−0.389821	+	0.417397i	−0.895315	−	0.445434i	$-0.853049\pi$
$701$	−7235.06	+	7746.86i	−0.389821	+	0.417397i	0.505494	+	0.862830i	$0.331310\pi$
$702$	1281.38	−	18733.1i	0.0688925	−	1.00717i
$703$	19074.4	−	8285.18i	1.02333	−	0.444497i
$704$	16346.9			0.875138
$705$	3409.50	−	7565.25i	0.182141	−	0.404147i
$706$	21449.9			1.14345
$707$	−27119.7	+	11779.8i	−1.44263	+	0.626624i
$708$	54.8643	−	802.088i	0.00291233	−	0.0425767i
$709$	−4131.48	+	4423.74i	−0.218845	+	0.234326i	−0.830806	−	0.556562i	$-0.812120\pi$
$709$	−4131.48	+	4423.74i	−0.218845	+	0.234326i	0.611961	+	0.790888i	$0.290381\pi$
$710$	−6213.57	+	3778.55i	−0.328438	+	0.199728i
$711$	178.082	+	501.075i	0.00939324	+	0.0264301i
$712$	−6783.05	−	32641.8i	−0.357030	−	1.71812i
$713$	−12710.1	+	35762.9i	−0.667600	+	1.87845i
$714$	23880.2	+	3282.26i	1.25167	+	0.172039i
$715$	−4219.33	+	5977.42i	−0.220691	+	0.312648i
$716$	−775.836	+	631.190i	−0.0404949	+	0.0329451i
$717$	−908.066	−	972.301i	−0.0472976	−	0.0506433i
$718$	8939.65	+	2504.77i	0.464658	+	0.130191i
$719$	−41.0574	−	58.1651i	−0.00212960	−	0.00301696i	0.815904	−	0.578188i	$-0.196240\pi$
$719$	−41.0574	−	58.1651i	−0.00212960	−	0.00301696i	−0.818033	+	0.575171i	$0.804936\pi$
$720$	−62.3118	−	120.256i	−0.00322531	−	0.00622456i
$721$	696.139	+	10177.2i	0.0359578	+	0.525684i
$722$	19294.8	+	15697.5i	0.994569	+	0.809142i
$723$	20314.9	−	5691.96i	1.04498	−	0.292789i
$724$	85.4499	+	51.9633i	0.00438636	+	0.00266740i
$725$	−715.987	+	3445.52i	−0.0366774	+	0.176501i
$726$	−6167.05	+	847.641i	−0.315263	+	0.0433318i
$727$	4233.79	−	8170.84i	0.215987	−	0.416836i	−0.755084	−	0.655628i	$-0.772404\pi$
$727$	4233.79	−	8170.84i	0.215987	−	0.416836i	0.971071	+	0.238793i	$0.0767516\pi$
$728$	−22678.7	−	9850.74i	−1.15457	−	0.501501i
$729$	−18357.4	−	7973.73i	−0.932651	−	0.405108i
$730$	687.869	−	1327.53i	0.0348756	−	0.0673068i
$731$	23601.8	−	3243.99i	1.19418	−	0.164136i
$732$	309.279	−	1488.33i	0.0156165	−	0.0751508i
$733$	13324.0	+	8102.50i	0.671396	+	0.408285i	0.813498	−	0.581567i	$-0.197560\pi$
$733$	13324.0	+	8102.50i	0.671396	+	0.408285i	−0.142103	+	0.989852i	$0.545386\pi$
$734$	12421.2	−	3480.26i	0.624626	−	0.175012i
$735$	2219.79	+	1805.93i	0.111399	+	0.0906297i
$736$	363.741	+	5317.70i	0.0182169	+	0.266322i
$737$	−1864.03	−	3597.41i	−0.0931647	−	0.179800i
$738$	304.406	+	431.245i	0.0151834	+	0.0215100i
$739$	18636.5	+	5221.70i	0.927678	+	0.259923i	0.700271	−	0.713877i	$-0.253062\pi$
$739$	18636.5	+	5221.70i	0.927678	+	0.259923i	0.227407	+	0.973800i	$0.426975\pi$
$740$	415.861	+	445.278i	0.0206586	+	0.0221199i
$741$	−24968.5	+	20313.4i	−1.23784	+	1.00706i
$742$	20653.6	−	29259.5i	1.02186	−	1.44764i
$743$	−8792.93	−	1208.56i	−0.434160	−	0.0596740i	−0.0842228	−	0.996447i	$-0.526841\pi$
$743$	−8792.93	−	1208.56i	−0.434160	−	0.0596740i	−0.349938	+	0.936773i	$0.613797\pi$
$744$	−9698.45	+	27288.8i	−0.477906	+	1.34470i
$745$	3471.50	+	16705.8i	0.170720	+	0.821548i
$746$	−935.274	−	2631.61i	−0.0459019	−	0.129156i
$747$	−459.056	+	279.158i	−0.0224846	+	0.0136732i
$748$	1228.62	−	1315.53i	0.0600574	−	0.0643058i
$749$	−147.837	+	2161.30i	−0.00721207	+	0.105437i
$750$	−1590.77	+	690.970i	−0.0774491	+	0.0336409i
$751$	−15919.1			−0.773495			−0.386748	−	0.922186i	$-0.626402\pi$
$751$	−15919.1			−0.773495			−0.386748	+	0.922186i	$0.626402\pi$
$752$	−13712.0	+	12460.2i	−0.664928	+	0.604225i
$753$	−25847.0			−1.25089
$754$	17133.7	−	7442.23i	0.827551	−	0.359456i
$755$	−536.868	+	7848.73i	−0.0258790	+	0.378337i
$756$	−1529.78	+	1638.00i	−0.0735948	+	0.0788008i
$757$	17147.6	−	10427.7i	0.823301	−	0.500661i	−0.0436538	−	0.999047i	$-0.513900\pi$
$757$	17147.6	−	10427.7i	0.823301	−	0.500661i	0.866955	+	0.498386i	$0.166074\pi$
$758$	−5266.83	−	14819.4i	−0.252374	−	0.710114i
$759$	4948.83	+	23815.1i	0.236668	+	1.13891i
$760$	−5002.85	+	14076.7i	−0.238779	+	0.671861i
$761$	3946.36	+	542.415i	0.187984	+	0.0258377i	0.229544	−	0.973298i	$-0.426276\pi$
$761$	3946.36	+	542.415i	0.187984	+	0.0258377i	−0.0415606	+	0.999136i	$0.513233\pi$
$762$	−582.865	+	825.731i	−0.0277099	+	0.0392560i
$763$	−11626.4	+	9458.75i	−0.551642	+	0.448794i
$764$	1848.74	+	1979.51i	0.0875458	+	0.0937386i
$765$	−184.907	−	51.8086i	−0.00873901	−	0.00244856i
$766$	−7904.27	−	11197.8i	−0.372837	−	0.528190i
$767$	−4759.27	−	9184.97i	−0.224051	−	0.432399i
$768$	397.737	+	5814.71i	0.0186876	+	0.273203i
$769$	27013.4	+	21977.0i	1.26675	+	1.03057i	0.997723	+	0.0674410i	$0.0214834\pi$
$769$	27013.4	+	21977.0i	1.26675	+	1.03057i	0.269023	+	0.963134i	$0.413299\pi$
$770$	−8209.78	+	2300.27i	−0.384234	+	0.107657i
$771$	−9207.04	−	5598.93i	−0.430069	−	0.261531i
$772$	−112.402	+	540.907i	−0.00524019	+	0.0252172i
$773$	−3941.19	+	541.704i	−0.183383	+	0.0252054i	−0.227274	−	0.973831i	$-0.572981\pi$
$773$	−3941.19	+	541.704i	−0.183383	+	0.0252054i	0.0438908	+	0.999036i	$0.486025\pi$
$774$	170.614	−	329.269i	0.00792323	−	0.0152911i
$775$	−5474.17	−	2377.77i	−0.253726	−	0.110209i
$776$	39453.1	+	17136.9i	1.82511	+	0.792757i
$777$	−8278.10	+	15976.0i	−0.382208	+	0.737627i
$778$	−11688.7	+	1606.57i	−0.538636	+	0.0740338i
$779$	10735.6	−	51662.7i	0.493766	−	2.37613i
$780$	−805.737	−	489.979i	−0.0369872	−	0.0224924i
$781$	−15443.3	+	4327.00i	−0.707559	+	0.198249i
$782$	−27084.0	−	22034.4i	−1.23852	−	1.00761i
$783$	−1359.20	−	19870.9i	−0.0620357	−	0.906930i
$784$	−2939.52	−	5673.01i	−0.133907	−	0.258428i
$785$	−4903.04	−	6946.03i	−0.222926	−	0.315815i
$786$	25145.8	+	7045.53i	1.14112	+	0.319728i
$787$	2484.20	+	2659.93i	0.112519	+	0.120478i	0.784609	−	0.619992i	$-0.212864\pi$
$787$	2484.20	+	2659.93i	0.112519	+	0.120478i	−0.672090	+	0.740470i	$0.734603\pi$
$788$	2262.86	−	1840.97i	0.102298	−	0.0832259i
$789$	20254.8	−	28694.6i	0.913931	−	1.29475i
$790$	−15062.6	−	2070.31i	−0.678360	−	0.0932384i
$791$	−6053.05	+	17031.7i	−0.272088	+	0.765583i
$792$	−67.0565	−	322.693i	−0.00300852	−	0.0144778i
$793$	−6550.20	−	18430.5i	−0.293322	−	0.825330i
$794$	−5566.46	+	3385.04i	−0.248799	+	0.151298i
$795$	10966.6	−	11742.4i	0.489241	−	0.523849i
$796$	3.25535	−	47.5916i	0.000144953	−	0.00211914i
$797$	21077.4	−	9155.23i	0.936765	−	0.406894i	0.125844	−	0.992050i	$-0.459836\pi$
$797$	21077.4	−	9155.23i	0.936765	−	0.406894i	0.810921	+	0.585156i	$0.198967\pi$
$798$	−37508.2			−1.66388
$799$	−358.444	+	26266.1i	−0.0158709	+	1.16299i
$800$	−838.155			−0.0370415
$801$	−611.624	+	265.666i	−0.0269796	+	0.0117189i
$802$	1244.42	−	18192.8i	0.0547905	−	0.801009i
$803$	2250.63	−	2409.83i	0.0989076	−	0.105904i
$804$	446.189	−	271.333i	0.0195720	−	0.0119020i
$805$	−5672.78	−	15961.7i	−0.248372	−	0.698851i
$806$	6445.65	+	31018.2i	0.281685	+	1.35554i
$807$	−5947.03	+	16733.3i	−0.259412	+	0.729915i
$808$	32375.2	+	4449.87i	1.40960	+	0.193745i
$809$	3784.39	−	5361.27i	0.164465	−	0.232994i	−0.726389	−	0.687284i	$-0.758803\pi$
$809$	3784.39	−	5361.27i	0.164465	−	0.232994i	0.890854	+	0.454290i	$0.150107\pi$
$810$	7481.48	−	6086.64i	0.324534	−	0.264028i
$811$	−15027.6	−	16090.6i	−0.650667	−	0.696694i	0.317143	−	0.948378i	$-0.397277\pi$
$811$	−15027.6	−	16090.6i	−0.650667	−	0.696694i	−0.967810	+	0.251684i	$0.919016\pi$
$812$	−2147.04	−	601.574i	−0.0927913	−	0.0259989i
$813$	8332.67	+	11804.7i	0.359458	+	0.509236i
$814$	−6034.98	−	11647.0i	−0.259860	−	0.501506i
$815$	−218.922	−	3200.53i	−0.00940922	−	0.137558i
$816$	−18729.4	−	15237.5i	−0.803506	−	0.653701i
$817$	−35696.2	+	10001.6i	−1.52858	+	0.428288i
$818$	1560.76	+	949.121i	0.0667124	+	0.0405687i
$819$	−100.619	+	484.204i	−0.00429292	+	0.0206587i
$820$	1531.52	−	210.503i	0.0652232	−	0.00896473i
$821$	16890.7	−	32597.6i	0.718016	−	1.38571i	−0.196234	−	0.980557i	$-0.562871\pi$
$821$	16890.7	−	32597.6i	0.718016	−	1.38571i	0.914250	−	0.405150i	$-0.132781\pi$
$822$	−33300.6	−	14464.5i	−1.41301	−	0.613756i
$823$	−645.342	−	280.312i	−0.0273332	−	0.0118725i	0.384690	−	0.923046i	$-0.374308\pi$
$823$	−645.342	−	280.312i	−0.0273332	−	0.0118725i	−0.412023	+	0.911173i	$0.635178\pi$
$824$	5187.07	−	10010.6i	0.219296	−	0.423223i
$825$	−3789.26	+	520.822i	−0.159909	+	0.0219790i
$826$	2452.60	−	11802.5i	0.103313	−	0.497170i
$827$	−37539.7	−	22828.4i	−1.57845	−	0.959880i	−0.988288	−	0.152598i	$-0.951236\pi$
$827$	−37539.7	−	22828.4i	−1.57845	−	0.959880i	−0.590166	−	0.807282i	$-0.700938\pi$
$828$	53.6070	−	15.0200i	0.00224997	−	0.000630411i
$829$	29863.2	+	24295.5i	1.25114	+	1.01787i	0.998737	+	0.0502508i	$0.0160021\pi$
$829$	29863.2	+	24295.5i	1.25114	+	1.01787i	0.252399	+	0.967623i	$0.418781\pi$
$830$	−1048.29	−	15325.5i	−0.0438395	−	0.640911i
$831$	−9533.75	−	18399.3i	−0.397981	−	0.768069i
$832$	15634.0	+	22148.3i	0.651456	+	0.922903i
$833$	−8722.90	−	2444.04i	−0.362822	−	0.101658i
$834$	−1984.31	−	2124.68i	−0.0823873	−	0.0882153i
$835$	−1443.52	+	1174.39i	−0.0598265	+	0.0486725i
$836$	−1615.25	+	2288.30i	−0.0668239	+	0.0946679i
$837$	33464.2	+	4599.55i	1.38195	+	0.189945i
$838$	−7182.27	+	20209.0i	−0.296071	+	0.833063i
$839$	626.157	+	3013.23i	0.0257656	+	0.123991i	0.990002	−	0.141052i	$-0.0450486\pi$
$839$	626.157	+	3013.23i	0.0257656	+	0.123991i	−0.964237	+	0.265043i	$0.914614\pi$
$840$	−4328.60	−	12179.5i	−0.177799	−	0.500278i
$841$	−3908.31	+	2376.70i	−0.160249	+	0.0974495i
$842$	2036.10	−	2180.13i	0.0833358	−	0.0892309i
$843$	−1959.15	+	28641.7i	−0.0800434	+	1.17019i
$844$	338.142	−	146.876i	0.0137907	−	0.00599014i
$845$	−1149.10			−0.0467813
$846$	330.814	+	240.343i	0.0134440	+	0.00976735i
$847$	9560.85			0.387857
$848$	−32904.2	+	14292.3i	−1.33247	+	0.578774i
$849$	−447.737	+	6545.68i	−0.0180993	+	0.264602i
$850$	3747.44	−	4012.53i	0.151219	−	0.161916i
$851$	22268.6	−	13541.8i	0.897011	−	0.545485i
$852$	−692.234	−	1947.76i	−0.0278351	−	0.0783206i
$853$	−1840.38	−	8856.39i	−0.0738727	−	0.355495i	0.925878	−	0.377823i	$-0.123327\pi$
$853$	−1840.38	−	8856.39i	−0.0738727	−	0.355495i	−0.999751	+	0.0223277i	$0.992892\pi$
$854$	7632.89	−	21476.9i	0.305846	−	0.860567i
$855$	296.023	+	40.6874i	0.0118407	+	0.00162746i
$856$	1380.78	−	1956.12i	0.0551333	−	0.0781061i
$857$	−24815.8	+	20189.2i	−0.989139	+	0.804724i	−0.980755	−	0.195240i	$-0.937451\pi$
$857$	−24815.8	+	20189.2i	−0.989139	+	0.804724i	−0.00838376	+	0.999965i	$0.502669\pi$
$858$	13858.1	+	14838.4i	0.551407	+	0.590413i
$859$	−19527.2	−	5471.27i	−0.775623	−	0.217319i	−0.140863	−	0.990029i	$-0.544988\pi$
$859$	−19527.2	−	5471.27i	−0.775623	−	0.217319i	−0.634760	+	0.772710i	$0.718901\pi$
$860$	−626.323	−	887.297i	−0.0248342	−	0.0351821i
$861$	21004.2	+	40536.3i	0.831384	+	1.60450i
$862$	−1837.70	−	26866.2i	−0.0726128	−	1.06156i
$863$	−23891.4	−	19437.1i	−0.942380	−	0.766683i	0.0301299	−	0.999546i	$-0.490408\pi$
$863$	−23891.4	−	19437.1i	−0.942380	−	0.766683i	−0.972509	+	0.232863i	$0.925191\pi$
$864$	4567.82	−	1279.84i	0.179861	−	0.0503948i
$865$	−13616.6	−	8280.41i	−0.535233	−	0.325483i
$866$	6611.48	−	31816.2i	0.259431	−	1.24845i
$867$	−8844.38	+	1215.63i	−0.346448	+	0.0476182i
$868$	1739.74	−	3357.55i	0.0680308	−	0.131294i
$869$	−30754.9	−	13358.7i	−1.20056	−	0.521478i
$870$	8957.00	+	3890.58i	0.349047	+	0.151612i
$871$	3091.38	−	5966.09i	0.120261	−	0.232093i
$872$	16411.2	−	2255.67i	0.637333	−	0.0875994i
$873$	175.042	−	842.350i	0.00678612	−	0.0326566i
$874$	46420.2	+	28228.7i	1.79655	+	1.09251i
$875$	2564.97	−	718.672i	0.0990994	−	0.0277663i
$876$	329.671	+	268.207i	0.0127152	+	0.0103446i
$877$	3386.43	+	49507.8i	0.130389	+	1.90623i	0.360013	+	0.932947i	$0.382772\pi$
$877$	3386.43	+	49507.8i	0.130389	+	1.90623i	−0.229624	+	0.973279i	$0.573750\pi$
$878$	−878.929	−	1696.26i	−0.0337841	−	0.0652003i
$879$	3450.40	+	4888.11i	0.132400	+	0.187567i
$880$	8223.43	+	2304.10i	0.315014	+	0.0882627i
$881$	−3414.38	−	3655.91i	−0.130571	−	0.139808i	0.662200	−	0.749328i	$-0.269623\pi$
$881$	−3414.38	−	3655.91i	−0.130571	−	0.139808i	−0.792771	+	0.609520i	$0.791362\pi$
$882$	−109.385	+	88.9911i	−0.00417594	+	0.00339738i
$883$	−25365.6	+	35934.9i	−0.966729	+	1.36954i	−0.0377992	+	0.999285i	$0.512035\pi$
$883$	−25365.6	+	35934.9i	−0.966729	+	1.36954i	−0.928929	+	0.370257i	$0.879270\pi$
$884$	2957.45	+	406.493i	0.112523	+	0.0154659i
$885$	1811.01	−	5095.69i	0.0687869	−	0.193548i
$886$	6564.95	+	31592.3i	0.248932	+	1.19793i
$887$	5712.20	+	16072.6i	0.216231	+	0.608416i	0.999919	−	0.0127390i	$-0.00405507\pi$
$887$	5712.20	+	16072.6i	0.216231	+	0.608416i	−0.783688	+	0.621155i	$0.786664\pi$
$888$	16992.0	−	10333.1i	0.642132	−	0.390489i
$889$	1059.56	−	1134.51i	0.0399735	−	0.0428011i
$890$	1301.08	−	19021.1i	0.0490024	−	0.716390i
$891$	19509.1	−	8474.00i	0.733535	−	0.318619i
$892$	282.164			0.0105914
$893$	−5012.76	−	40566.7i	−0.187845	−	1.52017i
$894$	47348.5			1.77133
$895$	−6170.72	+	2680.32i	−0.230463	+	0.100104i
$896$	−1765.83	+	25815.6i	−0.0658397	+	0.962542i
$897$	−27533.9	+	29481.6i	−1.02490	+	1.09739i
$898$	−16051.0	+	9760.84i	−0.596469	+	0.362721i
$899$	11253.6	+	31664.6i	0.417496	+	1.17472i
$900$	1.78111	+	8.57115i	6.59669e−5	+	0.000317450i
$901$	−17032.8	+	47925.7i	−0.629794	+	1.77207i
$902$	−32973.7	−	4532.13i	−1.21719	−	0.167299i
$903$	18496.9	−	26204.1i	0.681658	−	0.965690i
$904$	15497.0	−	12607.7i	0.570157	−	0.463857i
$905$	459.170	+	491.651i	0.0168656	+	0.0180586i
$906$	21021.4	+	5889.91i	0.770848	+	0.215981i
$907$	5387.03	+	7631.69i	0.197214	+	0.279389i	0.903545	−	0.428493i	$-0.140955\pi$
$907$	5387.03	+	7631.69i	0.197214	+	0.279389i	−0.706331	+	0.707882i	$0.749651\pi$
$908$	737.531	+	1423.37i	0.0269558	+	0.0520223i
$909$	−44.6058	−	652.114i	−0.00162759	−	0.0237946i
$910$	−10968.4	−	8923.43i	−0.399558	−	0.325065i
$911$	10988.9	−	3078.95i	0.399647	−	0.111976i	−0.0641000	−	0.997943i	$-0.520418\pi$
$911$	10988.9	−	3078.95i	0.399647	−	0.111976i	0.463747	+	0.885968i	$0.346505\pi$
$912$	32101.0	+	19521.1i	1.16554	+	0.708780i
$913$	6892.53	−	33168.7i	0.249846	−	1.20233i
$914$	−34683.1	+	4767.08i	−1.25516	+	0.172518i
$915$	4704.31	−	9078.91i	0.169967	−	0.328021i
$916$	−4268.64	−	1854.13i	−0.153974	−	0.0668802i
$917$	−36787.6	−	15979.1i	−1.32479	−	0.575439i
$918$	−14296.0	+	27590.0i	−0.513984	+	0.991944i
$919$	18175.8	−	2498.21i	0.652411	−	0.0896718i	0.197632	−	0.980276i	$-0.436675\pi$
$919$	18175.8	−	2498.21i	0.652411	−	0.0896718i	0.454779	+	0.890604i	$0.349718\pi$
$920$	−3809.25	+	18331.1i	−0.136508	+	0.656911i
$921$	−31910.5	−	19405.2i	−1.14168	−	0.694270i
$922$	−27437.4	+	7687.61i	−0.980047	+	0.274596i
$923$	−20632.4	−	16785.7i	−0.735778	−	0.598600i
$924$	−165.383	−	2417.81i	−0.00588820	−	0.0860825i
$925$	1885.50	+	3638.86i	0.0670216	+	0.129346i
$926$	483.135	+	684.446i	0.0171456	+	0.0242897i
$927$	−217.146	−	60.8415i	−0.00769365	−	0.00215566i
$928$	3221.18	+	3449.04i	0.113944	+	0.122005i
$929$	−16983.9	+	13817.4i	−0.599810	+	0.487982i	−0.881919	−	0.471400i	$-0.843749\pi$
$929$	−16983.9	+	13817.4i	−0.599810	+	0.487982i	0.282109	+	0.959382i	$0.408966\pi$
$930$	−9550.86	+	13530.5i	−0.336758	+	0.477078i
$931$	13964.7	+	1919.40i	0.491594	+	0.0675681i
$932$	1620.39	−	4559.35i	0.0569504	−	0.160243i
$933$	10250.4	+	49327.7i	0.359682	+	1.73089i
$934$	−6832.48	−	19224.8i	−0.239364	−	0.673504i
$935$	10345.5	−	6291.22i	0.361853	−	0.220048i
$936$	373.084	−	399.475i	0.0130284	−	0.0139501i
$937$	1491.30	−	21802.0i	0.0519942	−	0.760129i	−0.896442	−	0.443161i	$-0.853857\pi$
$937$	1491.30	−	21802.0i	0.0519942	−	0.760129i	0.948436	−	0.316968i	$-0.102665\pi$
$938$	7181.86	−	3119.52i	0.249996	−	0.108588i
$939$	−39953.2			−1.38852
$940$	1070.70	−	536.386i	0.0371514	−	0.0186117i
$941$	−4520.44			−0.156602			−0.0783009	−	0.996930i	$-0.524949\pi$
$941$	−4520.44			−0.156602			−0.0783009	+	0.996930i	$0.524949\pi$
$942$	−21640.1	+	9399.61i	−0.748484	+	0.325112i
$943$	4512.85	−	65975.6i	0.155842	−	2.27832i
$944$	−8241.64	+	8824.64i	−0.284155	+	0.304256i
$945$	−12881.3	+	7833.31i	−0.443418	+	0.269648i
$946$	7830.63	+	22033.3i	0.269129	+	0.757255i
$947$	3011.48	+	14492.0i	0.103337	+	0.497284i	0.998655	+	0.0518558i	$0.0165136\pi$
$947$	3011.48	+	14492.0i	0.103337	+	0.497284i	−0.895318	+	0.445428i	$0.853052\pi$
$948$	1447.26	−	4072.21i	0.0495832	−	0.139514i
$949$	5417.54	+	744.624i	0.185312	+	0.0254705i
$950$	−4926.72	+	6979.57i	−0.168257	+	0.238365i
$951$	−25428.2	+	20687.4i	−0.867051	+	0.705398i
$952$	27929.0	+	29904.7i	0.950824	+	1.01808i
$953$	−32564.6	−	9124.16i	−1.10689	−	0.310137i	−0.332666	−	0.943045i	$-0.607948\pi$
$953$	−32564.6	−	9124.16i	−1.10689	−	0.310137i	−0.774227	+	0.632908i	$0.781861\pi$
$954$	456.580	+	646.827i	0.0154951	+	0.0219516i
$955$	8382.13	+	16176.8i	0.284020	+	0.548134i
$956$	−13.1023	−	191.550i	−0.000443264	−	0.00648029i
$957$	16706.0	+	13591.4i	0.564294	+	0.459087i
$958$	23662.8	−	6630.02i	0.798029	−	0.223597i
$959$	47644.1	+	28973.0i	1.60428	+	0.975587i
$960$	−2883.48	+	13876.1i	−0.0969415	+	0.466508i
$961$	−26948.1	+	3703.93i	−0.904571	+	0.124330i
$962$	10008.6	−	19315.8i	0.335438	−	0.647366i
$963$	−43.9258	−	19.0797i	−0.00146987	−	0.000638456i
$964$	2792.60	+	1213.00i	0.0933023	+	0.0405269i
$965$	−1709.69	+	3299.56i	−0.0570331	+	0.110069i
$966$	−46569.6	+	6400.84i	−1.55109	+	0.213192i
$967$	−2250.49	+	10830.0i	−0.0748407	+	0.360153i	−0.999802	−	0.0199086i	$-0.993662\pi$
$967$	−2250.49	+	10830.0i	−0.0748407	+	0.360153i	0.924961	+	0.380062i	$0.124097\pi$
$968$	−9028.78	−	5490.52i	−0.299789	−	0.182306i
$969$	51292.2	−	14371.4i	1.70046	−	0.476446i
$970$	19081.2	+	15523.7i	0.631609	+	0.513852i
$971$	2403.47	+	35137.4i	0.0794345	+	1.16129i	0.851008	+	0.525152i	$0.175992\pi$
$971$	2403.47	+	35137.4i	0.0794345	+	1.16129i	−0.771574	+	0.636140i	$0.780530\pi$
$972$	−45.1985	−	87.2292i	−0.00149151	−	0.00287847i
$973$	2574.92	+	3647.83i	0.0848387	+	0.120189i
$974$	−33456.9	−	9374.18i	−1.10065	−	0.308386i
$975$	−4329.67	−	4635.95i	−0.142216	−	0.152276i
$976$	−17710.2	+	14408.3i	−0.580828	+	0.472539i
$977$	2660.04	−	3768.42i	0.0871057	−	0.123401i	−0.771084	−	0.636734i	$-0.780285\pi$
$977$	2660.04	−	3768.42i	0.0871057	−	0.123401i	0.858190	+	0.513333i	$0.171589\pi$
$978$	−8819.23	−	1212.17i	−0.288351	−	0.0396330i
$979$	14080.5	−	39618.7i	0.459667	−	1.29338i
$980$	84.0226	+	404.339i	0.00273878	+	0.0131797i
$981$	−110.957	−	312.203i	−0.00361119	−	0.0101609i
$982$	−21094.3	+	12827.7i	−0.685485	+	0.416853i
$983$	−18327.9	+	19624.4i	−0.594678	+	0.636745i	−0.955184	−	0.296012i	$-0.904343\pi$
$983$	−18327.9	+	19624.4i	−0.594678	+	0.636745i	0.360506	+	0.932757i	$0.382604\pi$
$984$	3443.52	−	50342.5i	0.111560	−	1.63096i
$985$	17998.0	−	7817.63i	0.582196	−	0.252884i
$986$	−30913.9			−0.998477
$987$	25515.2	+	24489.9i	0.822856	+	0.789789i
$988$	−4645.21			−0.149579
$989$	−42613.0	+	18509.4i	−1.37009	+	0.595112i
$990$	12.8623	−	188.040i	0.000412920	−	0.00603667i
$991$	15135.0	−	16205.6i	0.485145	−	0.519464i	−0.440553	−	0.897727i	$-0.645218\pi$
$991$	15135.0	−	16205.6i	0.485145	−	0.519464i	0.925698	+	0.378263i	$0.123478\pi$
$992$	−6838.55	+	4158.61i	−0.218875	+	0.133101i
$993$	−16001.1	−	45022.7i	−0.511358	−	1.43882i
$994$	−6306.01	−	30346.2i	−0.201222	−	0.968332i
$995$	107.456	−	302.351i	0.00342369	−	0.00963334i
$996$	4325.72	+	594.557i	0.137616	+	0.0189149i
$997$	22936.1	−	32493.0i	0.728578	−	1.03216i	−0.269036	−	0.963130i	$-0.586705\pi$
$997$	22936.1	−	32493.0i	0.728578	−	1.03216i	0.997615	−	0.0690305i	$-0.0219906\pi$
$998$	−15233.0	+	12392.9i	−0.483157	+	0.393078i
$999$	−15832.2	−	16952.1i	−0.501409	−	0.536878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	235.4.g.b.6.18	✓	550
47.8	even	23	inner	235.4.g.b.196.18	yes	550

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.4.g.b.6.18	✓	550	1.1	even	1	trivial
235.4.g.b.196.18	yes	550	47.8	even	23	inner

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:	\( N \)	\(=\)	\( 235 = 5 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	235.g (of order \(23\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47081 - 1.07322i) q^{2} +(-0.351491 + 5.13861i) q^{3} +(-0.507353 + 0.543242i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(4.64641 + 13.0737i) q^{6} +(-4.33565 - 20.8643i) q^{7} +(-7.88740 + 22.1930i) q^{8} +(0.466704 + 0.0641470i) q^{9} +O(q^{10})\)	\(q+(2.47081 - 1.07322i) q^{2} +(-0.351491 + 5.13861i) q^{3} +(-0.507353 + 0.543242i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(4.64641 + 13.0737i) q^{6} +(-4.33565 - 20.8643i) q^{7} +(-7.88740 + 22.1930i) q^{8} +(0.466704 + 0.0641470i) q^{9} +(-7.76737 + 11.0039i) q^{10} +(-23.0420 + 18.7460i) q^{11} +(-2.61318 - 2.79803i) q^{12} +(-47.4360 - 13.2909i) q^{13} +(-33.1046 - 46.8985i) q^{14} +(-11.8481 - 22.8658i) q^{15} +(3.92400 + 57.3669i) q^{16} +(63.2397 + 51.4493i) q^{17} +(1.22198 - 0.342382i) q^{18} +(-108.389 - 65.9127i) q^{19} +(0.756161 - 3.63884i) q^{20} +(108.738 - 14.9456i) q^{21} +(-36.8135 + 71.0469i) q^{22} +(-145.822 - 63.3394i) q^{23} +(-111.269 - 48.3310i) q^{24} +(11.5016 - 22.1971i) q^{25} +(-131.469 + 18.0700i) q^{26} +(-28.7876 + 138.534i) q^{27} +(13.5341 + 8.23026i) q^{28} +(-135.545 + 37.9779i) q^{29} +(-53.8145 - 43.7813i) q^{30} +(-16.2916 - 238.174i) q^{31} +(-15.4242 - 29.7674i) q^{32} +(-88.2295 - 124.993i) q^{33} +(211.470 + 59.2510i) q^{34} +(72.7261 + 77.8707i) q^{35} +(-0.271631 + 0.220988i) q^{36} +(-94.5373 + 133.929i) q^{37} +(-338.547 - 46.5321i) q^{38} +(84.9703 - 239.084i) q^{39} +(-23.9599 - 115.302i) q^{40} +(139.294 + 391.936i) q^{41} +(252.629 - 153.627i) q^{42} +(199.460 - 213.570i) q^{43} +(1.50677 - 22.0282i) q^{44} +(-2.16045 + 0.938418i) q^{45} -428.275 q^{46} +(199.917 + 252.698i) q^{47} -296.166 q^{48} +(-101.918 + 44.2693i) q^{49} +(4.59583 - 67.1886i) q^{50} +(-286.606 + 306.880i) q^{51} +(31.2870 - 19.0260i) q^{52} +(208.928 + 587.866i) q^{53} +(77.5488 + 373.185i) q^{54} +(49.7368 - 139.946i) q^{55} +(497.239 + 68.3440i) q^{56} +(376.798 - 533.801i) q^{57} +(-294.147 + 239.306i) q^{58} +(143.331 + 153.470i) q^{59} +(18.4328 + 5.16464i) q^{60} +(228.972 + 324.379i) q^{61} +(-295.867 - 570.998i) q^{62} +(-0.685085 - 10.0156i) q^{63} +(-426.890 - 347.301i) q^{64} +(237.180 - 66.4547i) q^{65} +(-352.143 - 214.143i) q^{66} +(-27.7514 + 133.547i) q^{67} +(-60.0343 + 8.25152i) q^{68} +(376.732 - 727.059i) q^{69} +(263.265 + 114.352i) q^{70} +(495.222 + 215.105i) q^{71} +(-5.10470 + 9.85162i) q^{72} +(-109.972 + 15.1154i) q^{73} +(-89.8478 + 432.371i) q^{74} +(110.020 + 66.9045i) q^{75} +(90.7979 - 25.4404i) q^{76} +(491.025 + 399.478i) q^{77} +(-46.6447 - 681.921i) q^{78} +(519.332 + 1002.26i) q^{79} +(-165.798 - 234.883i) q^{80} +(-689.505 - 193.190i) q^{81} +(764.802 + 818.903i) q^{82} +(-884.686 + 719.746i) q^{83} +(-47.0492 + 66.6536i) q^{84} +(-403.827 - 55.5048i) q^{85} +(263.619 - 741.754i) q^{86} +(-147.511 - 709.862i) q^{87} +(-234.290 - 659.228i) q^{88} +(-1209.43 + 735.470i) q^{89} +(-4.33093 + 4.63729i) q^{90} +(-71.6403 + 1047.34i) q^{91} +(108.392 - 47.0812i) q^{92} +1229.61 q^{93} +(765.157 + 409.812i) q^{94} +634.283 q^{95} +(158.385 - 68.7962i) q^{96} +(124.630 - 1822.02i) q^{97} +(-204.309 + 218.762i) q^{98} +(-11.9563 + 7.27077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9}+O(q^{10}) \) 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9} - 20 q^{10} + 74 q^{11} - 677 q^{12} + 132 q^{13} - 83 q^{14} + 10 q^{15} - 602 q^{16} - 62 q^{17} - 95 q^{18} + 590 q^{19} + 510 q^{20} - 148 q^{21} + 178 q^{22} - 2244 q^{23} + 625 q^{24} - 625 q^{25} - 2530 q^{26} + 472 q^{27} + 68 q^{28} - 40 q^{29} + 1505 q^{30} - 16 q^{31} + 301 q^{32} + 200 q^{33} + 104 q^{34} + 10 q^{35} - 778 q^{36} + 3435 q^{37} + 1724 q^{38} + 578 q^{39} + 30 q^{40} - 442 q^{41} - 3709 q^{42} - 484 q^{43} - 12170 q^{44} + 875 q^{45} + 614 q^{46} - 1743 q^{47} - 962 q^{48} - 2509 q^{49} + 100 q^{50} + 390 q^{51} - 7609 q^{52} + 758 q^{53} + 1373 q^{54} - 140 q^{55} + 106 q^{56} + 6740 q^{57} + 4800 q^{58} + 8566 q^{59} - 295 q^{60} + 1364 q^{61} - 7252 q^{62} - 3122 q^{63} - 4010 q^{64} - 660 q^{65} + 24646 q^{66} - 68 q^{67} - 905 q^{68} - 2624 q^{69} + 185 q^{70} - 318 q^{71} - 3352 q^{72} + 428 q^{73} + 506 q^{74} - 50 q^{75} + 2495 q^{76} + 18134 q^{77} + 16762 q^{78} + 4620 q^{79} - 785 q^{80} - 14403 q^{81} + 11899 q^{82} + 90 q^{83} + 15755 q^{84} + 310 q^{85} - 4050 q^{86} - 5440 q^{87} - 439 q^{88} - 2148 q^{89} + 475 q^{90} - 9933 q^{91} - 36335 q^{92} - 4472 q^{93} - 3725 q^{94} + 270 q^{95} - 1421 q^{96} - 7342 q^{97} - 39381 q^{98} - 11821 q^{99}+O(q^{100}) \) 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9 - 20 * q^10 + 74 * q^11 - 677 * q^12 + 132 * q^13 - 83 * q^14 + 10 * q^15 - 602 * q^16 - 62 * q^17 - 95 * q^18 + 590 * q^19 + 510 * q^20 - 148 * q^21 + 178 * q^22 - 2244 * q^23 + 625 * q^24 - 625 * q^25 - 2530 * q^26 + 472 * q^27 + 68 * q^28 - 40 * q^29 + 1505 * q^30 - 16 * q^31 + 301 * q^32 + 200 * q^33 + 104 * q^34 + 10 * q^35 - 778 * q^36 + 3435 * q^37 + 1724 * q^38 + 578 * q^39 + 30 * q^40 - 442 * q^41 - 3709 * q^42 - 484 * q^43 - 12170 * q^44 + 875 * q^45 + 614 * q^46 - 1743 * q^47 - 962 * q^48 - 2509 * q^49 + 100 * q^50 + 390 * q^51 - 7609 * q^52 + 758 * q^53 + 1373 * q^54 - 140 * q^55 + 106 * q^56 + 6740 * q^57 + 4800 * q^58 + 8566 * q^59 - 295 * q^60 + 1364 * q^61 - 7252 * q^62 - 3122 * q^63 - 4010 * q^64 - 660 * q^65 + 24646 * q^66 - 68 * q^67 - 905 * q^68 - 2624 * q^69 + 185 * q^70 - 318 * q^71 - 3352 * q^72 + 428 * q^73 + 506 * q^74 - 50 * q^75 + 2495 * q^76 + 18134 * q^77 + 16762 * q^78 + 4620 * q^79 - 785 * q^80 - 14403 * q^81 + 11899 * q^82 + 90 * q^83 + 15755 * q^84 + 310 * q^85 - 4050 * q^86 - 5440 * q^87 - 439 * q^88 - 2148 * q^89 + 475 * q^90 - 9933 * q^91 - 36335 * q^92 - 4472 * q^93 - 3725 * q^94 + 270 * q^95 - 1421 * q^96 - 7342 * q^97 - 39381 * q^98 - 11821 * q^99

Introduction

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