LMFDB - Embedded newform 197.4.e.a.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(6,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("197.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.e (of order $14$, degree $6$, 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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.3
Character	$\chi$	$=$	197.33
Dual form			197.4.e.a.6.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.98986 - 1.13890i) q^{2} +(5.41261 - 1.23539i) q^{3} +(16.3939 + 7.89487i) q^{4} +(-8.43757 - 17.5208i) q^{5} -28.4152 q^{6} +(-6.51769 - 28.5559i) q^{7} +(-40.7992 - 32.5362i) q^{8} +(3.44396 - 1.65853i) q^{9} +O(q^{10})$	\(q+(-4.98986 - 1.13890i) q^{2} +(5.41261 - 1.23539i) q^{3} +(16.3939 + 7.89487i) q^{4} +(-8.43757 - 17.5208i) q^{5} -28.4152 q^{6} +(-6.51769 - 28.5559i) q^{7} +(-40.7992 - 32.5362i) q^{8} +(3.44396 - 1.65853i) q^{9} +(22.1478 + 97.0359i) q^{10} +(-13.7841 - 3.14613i) q^{11} +(98.4868 + 22.4790i) q^{12} +(-37.6611 + 30.0337i) q^{13} +149.913i q^{14} +(-67.3143 - 84.4094i) q^{15} +(75.7673 + 95.0092i) q^{16} +(-6.71202 - 13.9376i) q^{17} +(-19.0738 + 4.35347i) q^{18} +102.106 q^{19} -353.847i q^{20} +(-70.5554 - 146.510i) q^{21} +(65.1976 + 31.3975i) q^{22} +(-0.195533 + 0.856684i) q^{23} +(-261.025 - 125.703i) q^{24} +(-157.849 + 197.937i) q^{25} +(222.129 - 106.972i) q^{26} +(-100.604 + 80.2287i) q^{27} +(118.595 - 519.597i) q^{28} +(37.5596 - 164.559i) q^{29} +(239.755 + 497.856i) q^{30} +(323.958 + 73.9412i) q^{31} +(-88.7273 - 184.244i) q^{32} -78.4947 q^{33} +(17.6184 + 77.1913i) q^{34} +(-445.328 + 355.137i) q^{35} +69.5537 q^{36} +(-91.9794 + 115.339i) q^{37} +(-509.495 - 116.289i) q^{38} +(-166.741 + 209.087i) q^{39} +(-225.815 + 989.360i) q^{40} +(183.728 - 88.4787i) q^{41} +(185.201 + 811.419i) q^{42} +(-62.7192 + 274.791i) q^{43} +(-201.136 - 160.401i) q^{44} +(-58.1174 - 46.3470i) q^{45} +(1.95136 - 4.05204i) q^{46} +(-68.3567 + 85.7166i) q^{47} +(527.472 + 420.645i) q^{48} +(-463.925 + 223.415i) q^{49} +(1013.08 - 807.902i) q^{50} +(-53.5480 - 67.1470i) q^{51} +(-854.523 + 195.039i) q^{52} +(-506.443 - 243.890i) q^{53} +(593.371 - 285.752i) q^{54} +(61.1816 + 268.054i) q^{55} +(-663.185 + 1377.12i) q^{56} +(552.660 - 126.141i) q^{57} +(-374.834 + 778.352i) q^{58} +(162.756 - 713.079i) q^{59} +(-437.140 - 1915.23i) q^{60} +(-74.6854 + 327.218i) q^{61} +(-1532.29 - 737.913i) q^{62} +(-69.8073 - 87.5356i) q^{63} +(16.5726 + 72.6091i) q^{64} +(843.983 + 406.441i) q^{65} +(391.677 + 89.3978i) q^{66} +(-153.486 - 122.401i) q^{67} -281.482i q^{68} +4.87846i q^{69} +(2626.59 - 1264.90i) q^{70} +(198.649 + 412.498i) q^{71} +(-194.473 - 44.3872i) q^{72} +(-572.814 - 456.804i) q^{73} +(590.324 - 470.768i) q^{74} +(-609.847 + 1266.36i) q^{75} +(1673.91 + 806.114i) q^{76} +414.123i q^{77} +(1070.15 - 853.413i) q^{78} +(390.390 - 810.653i) q^{79} +(1025.34 - 2129.15i) q^{80} +(-509.763 + 639.222i) q^{81} +(-1017.55 + 232.248i) q^{82} -1307.56 q^{83} -2958.89i q^{84} +(-187.566 + 235.200i) q^{85} +(625.921 - 1299.74i) q^{86} -937.096i q^{87} +(460.017 + 576.843i) q^{88} +(-1382.17 + 315.472i) q^{89} +(237.213 + 297.455i) q^{90} +(1103.10 + 879.695i) q^{91} +(-9.96895 + 12.5007i) q^{92} +1844.80 q^{93} +(438.713 - 349.862i) q^{94} +(-861.526 - 1788.98i) q^{95} +(-707.860 - 887.628i) q^{96} +(-561.127 + 270.224i) q^{97} +(2569.37 - 586.442i) q^{98} +(-52.6899 + 12.0261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9}+O(q^{10}) $ 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19} - 7 q^{21} + 807 q^{22} + 413 q^{23} - 1425 q^{24} + 1195 q^{25} - 543 q^{26} + 455 q^{27} + 174 q^{28} - 906 q^{29} + 798 q^{30} + 917 q^{31} + 945 q^{32} + 894 q^{33} - 219 q^{34} - 7 q^{35} + 3250 q^{36} + 1734 q^{37} - 63 q^{38} - 825 q^{39} + 141 q^{40} + 563 q^{41} + 432 q^{42} - 423 q^{43} + 2149 q^{44} - 3808 q^{45} - 2569 q^{46} - 289 q^{47} - 3703 q^{48} - 3747 q^{49} - 4963 q^{50} - 87 q^{51} + 3654 q^{52} - 1573 q^{53} - 1228 q^{54} + 2825 q^{55} + 98 q^{56} - 518 q^{57} - 5103 q^{58} + 2045 q^{59} + 3375 q^{60} + 287 q^{61} - 2547 q^{62} + 1453 q^{63} + 6475 q^{64} + 1268 q^{65} + 4634 q^{66} - 3577 q^{67} - 814 q^{70} - 273 q^{71} - 1008 q^{72} - 679 q^{73} - 315 q^{74} - 1281 q^{75} + 6078 q^{76} + 4739 q^{78} + 1463 q^{79} + 441 q^{80} - 4427 q^{81} - 7 q^{82} + 4900 q^{83} - 3351 q^{85} + 3472 q^{86} + 3738 q^{88} + 147 q^{89} + 7133 q^{90} - 14133 q^{91} - 803 q^{92} - 4894 q^{93} - 7833 q^{94} - 7700 q^{95} - 16450 q^{96} + 1233 q^{97} - 2030 q^{98} + 2464 q^{99}+O(q^{100}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−4.98986	−	1.13890i	−1.76418	−	0.402663i	−0.787322	−	0.616542i	$-0.788533\pi$
$2$	−4.98986	−	1.13890i	−1.76418	−	0.402663i	−0.976860	+	0.213879i	$0.931390\pi$
$3$	5.41261	−	1.23539i	1.04166	−	0.237751i	0.332722	−	0.943025i	$-0.392033\pi$
$3$	5.41261	−	1.23539i	1.04166	−	0.237751i	0.708935	+	0.705274i	$0.249176\pi$
$4$	16.3939	+	7.89487i	2.04923	+	0.986859i
$5$	−8.43757	−	17.5208i	−0.754679	−	1.56711i	−0.822074	−	0.569381i	$-0.807183\pi$
$5$	−8.43757	−	17.5208i	−0.754679	−	1.56711i	0.0673949	−	0.997726i	$-0.478531\pi$
$6$	−28.4152			−1.93341
$7$	−6.51769	−	28.5559i	−0.351922	−	1.54187i	−0.772737	−	0.634726i	$-0.781113\pi$
$7$	−6.51769	−	28.5559i	−0.351922	−	1.54187i	0.420815	−	0.907146i	$-0.361744\pi$
$8$	−40.7992	−	32.5362i	−1.80309	−	1.43791i
$9$	3.44396	−	1.65853i	0.127554	−	0.0614269i
$10$	22.1478	+	97.0359i	0.700375	+	3.06854i
$11$	−13.7841	−	3.14613i	−0.377824	−	0.0862359i	0.0293915	−	0.999568i	$-0.490643\pi$
$11$	−13.7841	−	3.14613i	−0.377824	−	0.0862359i	−0.407215	+	0.913332i	$0.633500\pi$
$12$	98.4868	+	22.4790i	2.36922	+	0.540760i
$13$	−37.6611	+	30.0337i	−0.803485	+	0.640758i	−0.936623	−	0.350339i	$-0.886066\pi$
$13$	−37.6611	+	30.0337i	−0.803485	+	0.640758i	0.133137	+	0.991098i	$0.457495\pi$
$14$			149.913i			2.86185i
$15$	−67.3143	−	84.4094i	−1.15870	−	1.45296i
$16$	75.7673	+	95.0092i	1.18386	+	1.48452i
$17$	−6.71202	−	13.9376i	−0.0957590	−	0.198846i	0.847587	−	0.530657i	$-0.178055\pi$
$17$	−6.71202	−	13.9376i	−0.0957590	−	0.198846i	−0.943346	+	0.331811i	$0.892340\pi$
$18$	−19.0738	+	4.35347i	−0.249763	+	0.0570068i
$19$	102.106			1.23288			0.616440	−	0.787402i	$-0.288574\pi$
$19$	102.106			1.23288			0.616440	+	0.787402i	$0.288574\pi$
$20$		−	353.847i		−	3.95613i
$21$	−70.5554	−	146.510i	−0.733164	−	1.52243i
$22$	65.1976	+	31.3975i	0.631826	+	0.304272i
$23$	−0.195533	+	0.856684i	−0.00177267	+	0.00776657i	−0.975807	−	0.218636i	$-0.929839\pi$
$23$	−0.195533	+	0.856684i	−0.00177267	+	0.00776657i	0.974034	+	0.226402i	$0.0726965\pi$
$24$	−261.025	−	125.703i	−2.22006	−	1.06913i
$25$	−157.849	+	197.937i	−1.26279	+	1.58349i
$26$	222.129	−	106.972i	1.67550	−	0.806880i
$27$	−100.604	+	80.2287i	−0.717080	+	0.571853i
$28$	118.595	−	519.597i	0.800439	−	3.50695i
$29$	37.5596	−	164.559i	0.240505	−	1.05372i	−0.700054	−	0.714090i	$-0.746841\pi$
$29$	37.5596	−	164.559i	0.240505	−	1.05372i	0.940559	−	0.339631i	$-0.110302\pi$
$30$	239.755	+	497.856i	1.45910	+	3.02985i
$31$	323.958	+	73.9412i	1.87692	+	0.428395i	0.998751	−	0.0499574i	$-0.0159086\pi$
$31$	323.958	+	73.9412i	1.87692	+	0.428395i	0.878168	+	0.478352i	$0.158766\pi$
$32$	−88.7273	−	184.244i	−0.490154	−	1.01782i
$33$	−78.4947			−0.414066
$34$	17.6184	+	77.1913i	0.0888686	+	0.389359i
$35$	−445.328	+	355.137i	−2.15069	+	1.71512i
$36$	69.5537			0.322008
$37$	−91.9794	+	115.339i	−0.408685	+	0.512474i	−0.942992	−	0.332816i	$-0.892001\pi$
$37$	−91.9794	+	115.339i	−0.408685	+	0.512474i	0.534307	+	0.845290i	$0.320573\pi$
$38$	−509.495	−	116.289i	−2.17503	−	0.496435i
$39$	−166.741	+	209.087i	−0.684615	+	0.858480i
$40$	−225.815	+	989.360i	−0.892612	+	3.91079i
$41$	183.728	−	88.4787i	0.699841	−	0.337026i	−0.0499028	−	0.998754i	$-0.515891\pi$
$41$	183.728	−	88.4787i	0.699841	−	0.337026i	0.749744	+	0.661729i	$0.230177\pi$
$42$	185.201	+	811.419i	0.680409	+	2.98107i
$43$	−62.7192	+	274.791i	−0.222432	+	0.974540i	0.733208	+	0.680004i	$0.238022\pi$
$43$	−62.7192	+	274.791i	−0.222432	+	0.974540i	−0.955640	+	0.294536i	$0.904835\pi$
$44$	−201.136	−	160.401i	−0.689147	−	0.549576i
$45$	−58.1174	−	46.3470i	−0.192525	−	0.153534i
$46$	1.95136	−	4.05204i	0.00625462	−	0.0129879i
$47$	−68.3567	+	85.7166i	−0.212146	+	0.266022i	−0.876507	−	0.481389i	$-0.840132\pi$
$47$	−68.3567	+	85.7166i	−0.212146	+	0.266022i	0.664361	+	0.747412i	$0.268704\pi$
$48$	527.472	+	420.645i	1.58613	+	1.26489i
$49$	−463.925	+	223.415i	−1.35255	+	0.651355i
$50$	1013.08	−	807.902i	2.86541	−	2.28509i
$51$	−53.5480	−	67.1470i	−0.147024	−	0.184362i
$52$	−854.523	+	195.039i	−2.27887	+	0.520136i
$53$	−506.443	−	243.890i	−1.31255	−	0.632093i	−0.359006	−	0.933335i	$-0.616884\pi$
$53$	−506.443	−	243.890i	−1.31255	−	0.632093i	−0.953548	+	0.301243i	$0.902599\pi$
$54$	593.371	−	285.752i	1.49532	−	0.720110i
$55$	61.1816	+	268.054i	0.149995	+	0.657171i
$56$	−663.185	+	1377.12i	−1.58253	+	3.28616i
$57$	552.660	−	126.141i	1.28424	−	0.293119i
$58$	−374.834	+	778.352i	−0.848589	+	1.76211i
$59$	162.756	−	713.079i	0.359135	−	1.57348i	−0.396217	−	0.918157i	$-0.629677\pi$
$59$	162.756	−	713.079i	0.359135	−	1.57348i	0.755353	−	0.655318i	$-0.227466\pi$
$60$	−437.140	−	1915.23i	−0.940575	−	4.12093i
$61$	−74.6854	+	327.218i	−0.156762	+	0.686820i	0.834063	+	0.551669i	$0.186009\pi$
$61$	−74.6854	+	327.218i	−0.156762	+	0.686820i	−0.990825	+	0.135150i	$0.956848\pi$
$62$	−1532.29	−	737.913i	−3.13873	−	1.51153i
$63$	−69.8073	−	87.5356i	−0.139602	−	0.175055i
$64$	16.5726	+	72.6091i	0.0323683	+	0.141815i
$65$	843.983	+	406.441i	1.61051	+	0.775581i
$66$	391.677	+	89.3978i	0.730487	+	0.166729i
$67$	−153.486	−	122.401i	−0.279870	−	0.223189i	0.473487	−	0.880801i	$-0.342995\pi$
$67$	−153.486	−	122.401i	−0.279870	−	0.223189i	−0.753357	+	0.657612i	$0.771567\pi$
$68$		−	281.482i		−	0.501982i
$69$			4.87846i			0.00851155i
$70$	2626.59	−	1264.90i	4.48483	−	2.15978i
$71$	198.649	+	412.498i	0.332046	+	0.689501i	0.998424	−	0.0561131i	$-0.0178707\pi$
$71$	198.649	+	412.498i	0.332046	+	0.689501i	−0.666378	+	0.745614i	$0.732156\pi$
$72$	−194.473	−	44.3872i	−0.318318	−	0.0726539i
$73$	−572.814	−	456.804i	−0.918395	−	0.732396i	0.0454196	−	0.998968i	$-0.485538\pi$
$73$	−572.814	−	456.804i	−0.918395	−	0.732396i	−0.963815	+	0.266572i	$0.914109\pi$
$74$	590.324	−	470.768i	0.927348	−	0.739536i
$75$	−609.847	+	1266.36i	−0.938921	+	1.94969i
$76$	1673.91	+	806.114i	2.52646	+	1.21668i
$77$			414.123i			0.612905i
$78$	1070.15	−	853.413i	1.55346	−	1.23885i
$79$	390.390	−	810.653i	0.555978	−	1.15450i	−0.413767	−	0.910383i	$-0.635787\pi$
$79$	390.390	−	810.653i	0.555978	−	1.15450i	0.969746	−	0.244118i	$-0.0784984\pi$
$80$	1025.34	−	2129.15i	1.43296	−	2.97558i
$81$	−509.763	+	639.222i	−0.699263	+	0.876848i
$82$	−1017.55	+	232.248i	−1.37035	+	0.312774i
$83$	−1307.56			−1.72919			−0.864597	−	0.502466i	$-0.832426\pi$
$83$	−1307.56			−1.72919			−0.864597	+	0.502466i	$0.832426\pi$
$84$		−	2958.89i		−	3.84335i
$85$	−187.566	+	235.200i	−0.239345	+	0.300129i
$86$	625.921	−	1299.74i	0.784823	−	1.62970i
$87$		−	937.096i		−	1.15480i
$88$	460.017	+	576.843i	0.557249	+	0.698768i
$89$	−1382.17	+	315.472i	−1.64618	+	0.375730i	−0.942348	−	0.334635i	$-0.891387\pi$
$89$	−1382.17	+	315.472i	−1.64618	+	0.375730i	−0.703834	+	0.710365i	$0.748530\pi$
$90$	237.213	+	297.455i	0.277827	+	0.348384i
$91$	1103.10	+	879.695i	1.27073	+	1.01337i
$92$	−9.96895	+	12.5007i	−0.0112971	+	0.0141661i
$93$	1844.80			2.05696
$94$	438.713	−	349.862i	0.481381	−	0.383889i
$95$	−861.526	−	1788.98i	−0.930429	−	1.93206i
$96$	−707.860	−	887.628i	−0.752559	−	0.943679i
$97$	−561.127	+	270.224i	−0.587358	+	0.282857i	−0.703866	−	0.710333i	$-0.748544\pi$
$97$	−561.127	+	270.224i	−0.587358	+	0.282857i	0.116507	+	0.993190i	$0.462830\pi$
$98$	2569.37	−	586.442i	2.64842	−	0.604486i
$99$	−52.6899	+	12.0261i	−0.0534902	+	0.0122088i
$100$	−4150.45	+	1998.75i	−4.15045	+	1.99875i
$101$	−62.8771	−	78.8453i	−0.0619456	−	0.0776773i	0.749893	−	0.661559i	$-0.230105\pi$
$101$	−62.8771	−	78.8453i	−0.0619456	−	0.0776773i	−0.811839	+	0.583881i	$0.801533\pi$
$102$	190.723	+	396.040i	0.185141	+	0.384449i
$103$	467.112	−	372.510i	0.446854	−	0.356354i	−0.374062	−	0.927404i	$-0.622035\pi$
$103$	467.112	−	372.510i	0.446854	−	0.356354i	0.820915	+	0.571050i	$0.193464\pi$
$104$	2513.73			2.37011
$105$	−1971.65	+	2472.37i	−1.83251	+	2.29789i
$106$	2249.31	+	1793.77i	2.06106	+	1.64364i
$107$	746.289	+	935.817i	0.674266	+	0.845503i	0.994812	−	0.101730i	$-0.0324378\pi$
$107$	746.289	+	935.817i	0.674266	+	0.845503i	−0.320546	+	0.947233i	$0.603866\pi$
$108$	−2282.68	+	521.006i	−2.03380	+	0.464202i
$109$	−1374.38	−	1723.42i	−1.20773	−	1.51444i	−0.798484	−	0.602015i	$-0.794365\pi$
$109$	−1374.38	−	1723.42i	−1.20773	−	1.51444i	−0.409242	−	0.912426i	$-0.634207\pi$
$110$		−	1407.23i		−	1.21977i
$111$	−355.360	+	737.913i	−0.303868	+	0.630987i
$112$	2219.24	−	2782.84i	1.87231	−	2.34780i
$113$		−	315.056i		−	0.262283i	−0.991364	−	0.131142i	$-0.958136\pi$
$113$		−	315.056i		−	0.262283i	0.991364	−	0.131142i	$-0.0418643\pi$
$114$	−2901.36			−2.38366
$115$	16.6596	−	3.80245i	0.0135088	−	0.00308330i
$116$	1914.92	−	2401.24i	1.53272	−	1.92198i
$117$	−79.8918	+	165.897i	−0.0631282	+	0.131087i
$118$	−1624.26	+	3372.80i	−1.26716	+	2.63129i
$119$	−354.255	+	282.509i	−0.272895	+	0.217626i
$120$			5633.99i			4.28592i
$121$	−1019.09	−	490.766i	−0.765655	−	0.368720i
$122$	745.340	−	1547.71i	0.553114	−	1.14855i
$123$	885.141	−	705.876i	0.648866	−	0.517453i
$124$	4727.16	+	3769.79i	3.42348	+	2.73013i
$125$	2429.99	+	554.630i	1.73876	+	0.396861i
$126$	248.634	+	516.294i	0.175794	+	0.365041i
$127$	1265.87	−	609.611i	0.884471	−	0.425939i	0.0642156	−	0.997936i	$-0.479545\pi$
$127$	1265.87	−	609.611i	0.884471	−	0.425939i	0.820256	+	0.571997i	$0.193831\pi$
$128$			1254.78i			0.866469i
$129$			1564.82i			1.06802i
$130$	−3748.46	−	2989.30i	−2.52894	−	2.01676i
$131$	1831.20	+	417.959i	1.22132	+	0.278758i	0.784121	−	0.620609i	$-0.213114\pi$
$131$	1831.20	+	417.959i	1.22132	+	0.278758i	0.437196	+	0.899366i	$0.355972\pi$
$132$	−1286.83	−	619.705i	−0.848517	−	0.408624i
$133$	−665.495	−	2915.73i	−0.433878	−	1.90094i
$134$	626.471	+	785.569i	0.403872	+	0.506439i
$135$	2254.52	+	1085.72i	1.43732	+	0.692177i
$136$	−179.634	+	787.028i	−0.113261	+	0.496229i
$137$	−218.459	−	957.131i	−0.136235	−	0.596885i	−0.996243	−	0.0866038i	$-0.972399\pi$
$137$	−218.459	−	957.131i	−0.136235	−	0.596885i	0.860008	−	0.510281i	$-0.170459\pi$
$138$	5.55609	−	24.3428i	0.00342729	−	0.0150159i
$139$	557.860	−	1158.41i	0.340410	−	0.706869i	−0.658546	−	0.752540i	$-0.728828\pi$
$139$	557.860	−	1158.41i	0.340410	−	0.706869i	0.998957	+	0.0456710i	$0.0145426\pi$
$140$	−10104.4	+	2306.27i	−6.09985	+	1.39225i
$141$	−264.094	+	548.398i	−0.157736	+	0.327542i
$142$	−521.434	−	2284.55i	−0.308153	−	1.35011i
$143$	613.615	−	295.501i	0.358832	−	0.172805i
$144$	418.515	+	201.546i	0.242196	+	0.116635i
$145$	−3200.12	+	730.407i	−1.83280	+	0.418324i
$146$	2338.01	+	2931.77i	1.32531	+	1.66188i
$147$	−2235.04	+	1782.39i	−1.25403	+	1.00006i
$148$	−2418.48	+	1164.68i	−1.34323	+	0.646865i
$149$	1047.43	+	835.297i	0.575897	+	0.459263i	0.867611	−	0.497243i	$-0.165654\pi$
$149$	1047.43	+	835.297i	0.575897	+	0.459263i	−0.291714	+	0.956506i	$0.594226\pi$
$150$	4485.31	−	5624.40i	2.44149	−	3.06154i
$151$	385.622	−	800.752i	0.207824	−	0.431552i	−0.770837	−	0.637033i	$-0.780162\pi$
$151$	385.622	−	800.752i	0.207824	−	0.431552i	0.978661	+	0.205481i	$0.0658759\pi$
$152$	−4165.84	−	3322.15i	−2.22299	−	1.77277i
$153$	−46.2319	−	36.8687i	−0.0244289	−	0.0194814i
$154$	471.646	−	2066.41i	0.246794	−	1.08128i
$155$	−1437.91	−	6299.88i	−0.745131	−	3.26463i
$156$	−4384.25	+	2111.34i	−2.25013	+	1.08361i
$157$	−83.2541	+	364.760i	−0.0423210	+	0.185421i	−0.991670	−	0.128802i	$-0.958887\pi$
$157$	−83.2541	+	364.760i	−0.0423210	+	0.185421i	0.949349	+	0.314223i	$0.101744\pi$
$158$	−2871.25	+	3600.43i	−1.44572	+	1.81288i
$159$	−3042.48	−	694.426i	−1.51751	−	0.346362i
$160$	−2479.46	+	3109.15i	−1.22512	+	1.53625i
$161$	25.7378			0.0125989
$162$	3271.66	−	2609.06i	1.58670	−	1.26535i
$163$	−355.134	−	1555.94i	−0.170652	−	0.747673i	−0.985732	−	0.168325i	$-0.946164\pi$
$163$	−355.134	−	1555.94i	−0.170652	−	0.747673i	0.815080	−	0.579348i	$-0.196693\pi$
$164$	3710.54			1.76673
$165$	662.304	+	1375.29i	0.312487	+	0.648885i
$166$	6524.53	+	1489.18i	3.05061	+	0.696283i
$167$	238.713	+	495.693i	0.110612	+	0.229688i	0.948925	−	0.315501i	$-0.102172\pi$
$167$	238.713	+	495.693i	0.110612	+	0.229688i	−0.838314	+	0.545188i	$0.816458\pi$
$168$	−1888.28	+	8273.09i	−0.867165	+	3.79930i
$169$	27.4554	−	120.290i	0.0124968	−	0.0547519i
$170$	1203.80	−	959.995i	0.543100	−	0.433107i
$171$	351.649	−	169.345i	0.157259	−	0.0757320i
$172$	−3197.65	+	4009.73i	−1.41755	+	1.77755i
$173$	1225.51	+	590.176i	0.538578	+	0.259366i	0.683339	−	0.730101i	$-0.260527\pi$
$173$	1225.51	+	590.176i	0.538578	+	0.259366i	−0.144761	+	0.989467i	$0.546241\pi$
$174$	−1067.26	+	4675.98i	−0.464994	+	2.03727i
$175$	6681.07	+	3217.43i	2.88595	+	1.38980i
$176$	−745.473	−	1547.99i	−0.319273	−	0.662978i
$177$		−	4060.69i		−	1.72441i
$178$	7256.15			3.05546
$179$	−4181.96	+	954.506i	−1.74623	+	0.398565i	−0.972119	−	0.234489i	$-0.924658\pi$
$179$	−4181.96	+	954.506i	−1.74623	+	0.398565i	−0.774108	+	0.633053i	$0.781801\pi$
$180$	−586.864	−	1218.64i	−0.243013	−	0.504621i
$181$	1103.99	+	1384.36i	0.453365	+	0.568502i	0.955011	−	0.296571i	$-0.0958432\pi$
$181$	1103.99	+	1384.36i	0.453365	+	0.568502i	−0.501646	+	0.865073i	$0.667272\pi$
$182$	−4502.44	−	5645.88i	−1.83375	−	2.29945i
$183$			1863.37i			0.752701i
$184$	35.8509	−	28.5901i	0.0143639	−	0.0114548i
$185$	2796.91	+	638.375i	1.11153	+	0.253699i
$186$	−9205.31	−	2101.05i	−3.62885	−	0.828261i
$187$	48.6695	+	213.235i	0.0190324	+	0.0833865i
$188$	−1797.35	+	865.559i	−0.697263	+	0.335784i
$189$	2946.70	+	2349.92i	1.13408	+	0.904399i
$190$	2261.42	+	9907.95i	0.863479	+	3.78315i
$191$	−126.464			−0.0479088			−0.0239544	−	0.999713i	$-0.507626\pi$
$191$	−126.464			−0.0479088			−0.0239544	+	0.999713i	$0.507626\pi$
$192$	179.401	+	372.531i	0.0674332	+	0.140027i
$193$	2392.21	+	1152.03i	0.892203	+	0.429662i	0.823067	−	0.567945i	$-0.192261\pi$
$193$	2392.21	+	1152.03i	0.892203	+	0.429662i	0.0691363	+	0.997607i	$0.477976\pi$
$194$	3107.70	−	709.313i	1.15010	−	0.262504i
$195$	5070.26	+	1157.25i	1.86199	+	0.424988i
$196$	−9369.36			−3.41449
$197$	837.936	−	2635.00i	0.303048	−	0.952975i
$197$	837.936	−	2635.00i	0.303048	−	0.952975i
$198$	276.612			0.0992826
$199$	−2944.16	−	671.985i	−1.04877	−	0.239376i	−0.336795	−	0.941578i	$-0.609343\pi$
$199$	−2944.16	−	671.985i	−1.04877	−	0.239376i	−0.711977	+	0.702202i	$0.752200\pi$
$200$	12880.2	−	2939.83i	4.55385	−	1.03939i
$201$	−981.972	−	472.893i	−0.344592	−	0.165947i
$202$	223.951	+	465.038i	0.0780055	+	0.161980i
$203$	−4943.94			−1.70934
$204$	−347.741	−	1523.55i	−0.119347	−	0.522893i
$205$	−3100.43	−	2472.51i	−1.05631	−	0.842379i
$206$	−2755.08	+	1326.78i	−0.931822	+	0.448742i
$207$	0.747426	+	3.27469i	0.000250965	+	0.00109955i
$208$	−5706.96	−	1302.58i	−1.90243	−	0.434218i
$209$	−1407.44	−	321.239i	−0.465812	−	0.106318i
$210$	12654.1	−	10091.3i	4.15816	−	3.31602i
$211$		−	2199.21i		−	0.717535i	−0.933427	−	0.358768i	$-0.883197\pi$
$211$		−	2199.21i		−	0.717535i	0.933427	−	0.358768i	$-0.116803\pi$
$212$	−6377.08	−	7996.61i	−2.06594	−	2.59061i
$213$	1584.80	+	1987.28i	0.509808	+	0.639279i
$214$	−2658.07	−	5519.55i	−0.849076	−	1.76312i
$215$	5343.75	−	1219.68i	1.69507	−	0.386890i
$216$	6714.88			2.11523
$217$		−	9732.82i		−	3.04473i
$218$	4895.18	+	10164.9i	1.52084	+	3.15806i
$219$	−3664.75	−	1764.85i	−1.13078	−	0.544555i
$220$	−1113.25	+	4877.46i	−0.341160	+	1.49472i
$221$	671.382	+	323.320i	0.204353	+	0.0984112i
$222$	2613.61	−	3277.36i	0.790153	−	0.990821i
$223$	−208.304	+	100.314i	−0.0625517	+	0.0301233i	−0.464898	−	0.885364i	$-0.653909\pi$
$223$	−208.304	+	100.314i	−0.0625517	+	0.0301233i	0.402346	+	0.915488i	$0.368195\pi$
$224$	−4682.96	+	3734.53i	−1.39684	+	1.11395i
$225$	−215.344	+	943.484i	−0.0638057	+	0.279551i
$226$	−358.819	+	1572.09i	−0.105612	+	0.462716i
$227$	−218.713	−	454.161i	−0.0639492	−	0.132792i	0.866544	−	0.499100i	$-0.166336\pi$
$227$	−218.713	−	454.161i	−0.0639492	−	0.132792i	−0.930494	+	0.366308i	$0.880622\pi$
$228$	10056.1	+	2295.24i	2.92097	+	0.666692i
$229$	242.853	+	504.289i	0.0700793	+	0.145521i	0.933066	−	0.359706i	$-0.117123\pi$
$229$	242.853	+	504.289i	0.0700793	+	0.145521i	−0.862986	+	0.505227i	$0.831409\pi$
$230$	−87.4598			−0.0250736
$231$	511.604	+	2241.48i	0.145719	+	0.638436i
$232$	−6886.54	+	5491.83i	−1.94881	+	1.55412i
$233$	−3979.54			−1.11892			−0.559460	−	0.828857i	$-0.688992\pi$
$233$	−3979.54			−1.11892			−0.559460	+	0.828857i	$0.688992\pi$
$234$	587.589	−	736.814i	0.164154	−	0.205842i
$235$	2078.59	+	474.424i	0.576987	+	0.131694i
$236$	8297.86	−	10405.2i	2.28875	−	2.87000i
$237$	1111.55	−	4870.03i	0.304654	−	1.33478i
$238$	2089.43	−	1006.22i	0.569066	−	0.274048i
$239$	426.251	+	1867.53i	0.115364	+	0.505441i	0.999285	+	0.0378056i	$0.0120368\pi$
$239$	426.251	+	1867.53i	0.115364	+	0.505441i	−0.883922	+	0.467635i	$0.845106\pi$
$240$	2919.45	−	12790.9i	0.785207	−	3.44022i
$241$	−2597.80	−	2071.67i	−0.694352	−	0.553727i	0.211470	−	0.977384i	$-0.432175\pi$
$241$	−2597.80	−	2071.67i	−0.694352	−	0.553727i	−0.905823	+	0.423657i	$0.860746\pi$
$242$	4526.16	+	3609.50i	1.20228	+	0.958790i
$243$	−462.025	+	959.404i	−0.121971	+	0.253275i
$244$	−3807.73	+	4774.74i	−0.999036	+	1.25275i
$245$	7828.80	+	6243.26i	2.04148	+	1.62803i
$246$	−5220.66	+	2514.13i	−1.35308	+	0.651607i
$247$	−3845.42	+	3066.62i	−0.990601	+	0.789978i
$248$	−10811.4	−	13557.1i	−2.76825	−	3.47128i
$249$	−7077.30	+	1615.35i	−1.80123	+	0.411118i
$250$	−11493.7	−	5535.05i	−2.90769	−	1.40027i
$251$	−5529.55	+	2662.89i	−1.39053	+	0.669642i	−0.971216	−	0.238201i	$-0.923442\pi$
$251$	−5529.55	+	2662.89i	−1.39053	+	0.669642i	−0.419310	+	0.907843i	$0.637728\pi$
$252$	−453.330	−	1986.17i	−0.113322	−	0.496495i
$253$	5.39048	−	11.1935i	0.00133951	−	0.00278153i
$254$	−7010.81	+	1600.17i	−1.73188	+	0.395290i
$255$	−724.655	+	1504.76i	−0.177959	+	0.369536i
$256$	1561.65	−	6842.06i	0.381263	−	1.67042i
$257$	727.609	+	3187.86i	0.176603	+	0.773749i	0.983183	+	0.182623i	$0.0584589\pi$
$257$	727.609	+	3187.86i	0.176603	+	0.773749i	−0.806580	+	0.591125i	$0.798684\pi$
$258$	1782.18	−	7808.23i	0.430052	−	1.88418i
$259$	3893.09	+	1874.81i	0.933995	+	0.449788i
$260$	10627.3	+	13326.3i	2.53492	+	3.17869i
$261$	−143.572	−	629.030i	−0.0340494	−	0.149180i
$262$	−8661.41	−	4171.11i	−2.04238	−	0.983558i
$263$	5237.10	+	1195.33i	1.22788	+	0.280257i	0.786800	−	0.617209i	$-0.211737\pi$
$263$	5237.10	+	1195.33i	1.22788	+	0.280257i	0.441085	+	0.897465i	$0.354594\pi$
$264$	3202.52	+	2553.92i	0.746596	+	0.595390i
$265$			10931.1i			2.53394i
$266$			15307.0i			3.52832i
$267$	−7091.43	+	3415.05i	−1.62543	+	0.782764i
$268$	−1549.89	−	3218.38i	−0.353263	−	0.733558i
$269$	−89.8931	−	20.5175i	−0.0203750	−	0.00465046i	0.212321	−	0.977200i	$-0.431898\pi$
$269$	−89.8931	−	20.5175i	−0.0203750	−	0.00465046i	−0.232696	+	0.972549i	$0.574755\pi$
$270$	−10013.2	−	7985.27i	−2.25698	−	1.79988i
$271$	4617.30	−	3682.18i	1.03499	−	0.825374i	0.0501287	−	0.998743i	$-0.484037\pi$
$271$	4617.30	−	3682.18i	1.03499	−	0.825374i	0.984857	+	0.173369i	$0.0554654\pi$
$272$	815.653	−	1693.72i	0.181824	−	0.377562i
$273$	7057.43	+	3398.68i	1.56460	+	0.753470i
$274$			5024.75i			1.10787i
$275$	2798.55	−	2231.77i	0.613668	−	0.489384i
$276$	−38.5148	+	79.9768i	−0.00839970	+	0.0174422i
$277$	−566.071	+	1175.46i	−0.122787	+	0.254969i	−0.953297	−	0.302034i	$-0.902335\pi$
$277$	−566.071	+	1175.46i	−0.122787	+	0.254969i	0.830511	+	0.557003i	$0.188049\pi$
$278$	−4102.96	+	5144.94i	−0.885176	+	1.10998i
$279$	1238.33	−	282.641i	0.265724	−	0.0606497i
$280$	29723.8			6.34407
$281$		−	604.652i		−	0.128365i	−0.997938	−	0.0641824i	$-0.979556\pi$
$281$		−	604.652i		−	0.128365i	0.997938	−	0.0641824i	$-0.0204439\pi$
$282$	1942.37	−	2435.65i	0.410164	−	0.514329i
$283$	−71.6768	+	148.838i	−0.0150556	+	0.0312633i	−0.908361	−	0.418187i	$-0.862666\pi$
$283$	−71.6768	+	148.838i	−0.0150556	+	0.0312633i	0.893305	+	0.449450i	$0.148380\pi$
$284$			8330.75i			1.74063i
$285$	−6873.19	−	8618.71i	−1.42854	−	1.79133i
$286$	−3398.40	+	775.662i	−0.702628	+	0.160370i
$287$	−3724.07	−	4669.83i	−0.765940	−	0.960458i
$288$	−611.147	−	487.374i	−0.125042	−	0.0997180i
$289$	2914.00	−	3654.04i	0.593120	−	0.743749i
$290$	16800.0			3.40183
$291$	−2703.32	+	2155.83i	−0.544576	+	0.434285i
$292$	−5784.23	−	12011.1i	−1.15924	−	2.40718i
$293$	−4296.90	−	5388.14i	−0.856749	−	1.07433i	−0.996454	−	0.0841360i	$-0.973187\pi$
$293$	−4296.90	−	5388.14i	−0.856749	−	1.07433i	0.139705	−	0.990193i	$-0.455384\pi$
$294$	13182.5	−	6348.36i	2.61503	−	1.25933i
$295$	−13867.0	+	3165.05i	−2.73684	+	0.624665i
$296$	7505.37	−	1713.05i	1.47379	−	0.336382i
$297$	1639.14	−	789.369i	0.320244	−	0.154222i
$298$	−4275.20	−	5360.94i	−0.831060	−	1.04212i
$299$	−18.3655	−	38.1363i	−0.00355218	−	0.00737618i
$300$	−19995.5	+	15945.9i	−3.84813	+	3.06878i
$301$	8255.68			1.58090
$302$	−2836.18	+	3556.46i	−0.540410	+	0.677653i
$303$	−437.734	−	349.081i	−0.0829939	−	0.0661854i
$304$	7736.29	+	9701.01i	1.45956	+	1.83023i
$305$	6363.29	−	1452.38i	1.19463	−	0.272665i
$306$	188.701	+	236.623i	0.0352526	+	0.0442054i
$307$			1766.06i			0.328320i	0.986434	+	0.164160i	$0.0524914\pi$
$307$			1766.06i			0.328320i	−0.986434	+	0.164160i	$0.947509\pi$
$308$	−3269.44	+	6789.07i	−0.604850	+	1.25598i
$309$	2068.10	−	2593.31i	0.380745	−	0.477439i
$310$			33073.2i			6.05945i
$311$	−7181.14			−1.30934			−0.654670	−	0.755915i	$-0.727193\pi$
$311$	−7181.14			−1.30934			−0.654670	+	0.755915i	$0.727193\pi$
$312$	13605.8	−	3105.44i	2.46884	−	0.563496i
$313$	−4985.22	+	6251.26i	−0.900259	+	1.12889i	0.0908537	+	0.995864i	$0.471040\pi$
$313$	−4985.22	+	6251.26i	−0.900259	+	1.12889i	−0.991113	+	0.133025i	$0.957531\pi$
$314$	830.853	−	1725.28i	0.149324	−	0.310075i
$315$	−944.689	+	1961.67i	−0.168975	+	0.350881i
$316$	12800.0	−	10207.7i	2.27866	−	1.81717i
$317$		−	2801.26i		−	0.496324i	−0.968719	−	0.248162i	$-0.920174\pi$
$317$		−	2801.26i		−	0.496324i	0.968719	−	0.248162i	$-0.0798265\pi$
$318$	14390.7	+	6930.18i	2.53770	+	1.22209i
$319$	−1035.45	+	2150.14i	−0.181737	+	0.377381i
$320$	1132.34	−	903.008i	0.197811	−	0.157749i
$321$	5195.47	+	4143.25i	0.903373	+	0.720416i
$322$	−128.428	−	29.3129i	−0.0222268	−	0.00507311i
$323$	−685.337	−	1423.12i	−0.118059	−	0.245153i
$324$	−13403.6	+	6454.82i	−2.29828	+	1.10679i
$325$		−	12195.3i		−	2.08146i
$326$			8168.40i			1.38775i
$327$	−9568.11	−	7630.31i	−1.61810	−	1.29039i
$328$	−10374.7	−	2367.96i	−1.74649	−	0.398624i
$329$	2893.24	+	1393.31i	0.484831	+	0.233482i
$330$	−1738.48	−	7616.80i	−0.290001	−	1.27058i
$331$	1558.19	+	1953.91i	0.258749	+	0.324461i	0.894189	−	0.447689i	$-0.147753\pi$
$331$	1558.19	+	1953.91i	0.258749	+	0.324461i	−0.635441	+	0.772150i	$0.719181\pi$
$332$	−21435.9	−	10323.0i	−3.54352	−	1.70647i
$333$	−125.482	+	549.772i	−0.0206497	+	0.0904724i
$334$	−626.599	−	2745.31i	−0.102653	−	0.449751i
$335$	−849.513	+	3721.96i	−0.138549	+	0.607022i
$336$	8573.98	−	17804.1i	1.39211	−	2.89075i
$337$	4295.12	−	980.333i	0.694273	−	0.158463i	0.139199	−	0.990264i	$-0.455547\pi$
$337$	4295.12	−	980.333i	0.694273	−	0.158463i	0.555074	+	0.831801i	$0.312690\pi$
$338$	−273.997	+	568.961i	−0.0440931	+	0.0915603i
$339$	−389.218	−	1705.28i	−0.0623582	−	0.273209i
$340$	−4931.80	+	2375.03i	−0.786659	+	0.378835i
$341$	−4232.84	−	2038.43i	−0.672202	−	0.323716i
$342$	−1947.55	+	444.516i	−0.307928	+	0.0702826i
$343$	3139.60	+	3936.93i	0.494234	+	0.619750i
$344$	11499.6	−	9170.59i	1.80237	−	1.43734i
$345$	85.4744	−	41.1623i	0.0133385	−	0.00642349i
$346$	−5442.99	−	4340.64i	−0.845713	−	0.674434i
$347$	2918.88	−	3660.16i	0.451567	−	0.566247i	−0.502984	−	0.864296i	$-0.667764\pi$
$347$	2918.88	−	3660.16i	0.451567	−	0.566247i	0.954551	+	0.298049i	$0.0963359\pi$
$348$	7398.25	−	15362.6i	1.13962	−	2.36645i
$349$	4697.80	+	3746.37i	0.720537	+	0.574609i	0.913618	−	0.406574i	$-0.133277\pi$
$349$	4697.80	+	3746.37i	0.720537	+	0.574609i	−0.193081	+	0.981183i	$0.561848\pi$
$350$	−29673.3	−	23663.6i	−4.53172	−	3.61393i
$351$	1379.28	−	6043.00i	0.209744	−	0.918950i
$352$	643.370	+	2818.79i	0.0974197	+	0.426824i
$353$	−655.047	+	315.454i	−0.0987667	+	0.0475635i	−0.482615	−	0.875833i	$-0.660313\pi$
$353$	−655.047	+	315.454i	−0.0987667	+	0.0475635i	0.383848	+	0.923396i	$0.374599\pi$
$354$	−4624.73	+	20262.3i	−0.694355	+	3.04217i
$355$	5551.18	−	6960.97i	0.829933	−	1.04070i
$356$	−25149.8	−	5740.27i	−3.74420	−	0.854590i
$357$	−1568.43	+	1966.75i	−0.232522	+	0.291573i
$358$	21954.5			3.24115
$359$	10141.8	−	8087.79i	1.49098	−	1.18902i	0.557609	−	0.830104i	$-0.311719\pi$
$359$	10141.8	−	8087.79i	1.49098	−	1.18902i	0.933371	−	0.358913i	$-0.116853\pi$
$360$	863.181	+	3781.84i	0.126371	+	0.553668i
$361$	3566.64			0.519994
$362$	−3932.11	−	8165.12i	−0.570904	−	1.18549i
$363$	−6122.20	−	1397.35i	−0.885213	−	0.202044i
$364$	11139.0	+	23130.5i	1.60397	+	3.33067i
$365$	−3170.41	+	13890.5i	−0.454649	+	1.99195i
$366$	2122.20	−	9297.96i	0.303085	−	1.32790i
$367$	2647.41	−	2111.24i	0.376550	−	0.300289i	−0.416866	−	0.908968i	$-0.636872\pi$
$367$	2647.41	−	2111.24i	0.376550	−	0.300289i	0.793417	+	0.608679i	$0.208300\pi$
$368$	−96.2078	+	46.3313i	−0.0136282	+	0.00656300i
$369$	486.008	−	609.435i	0.0685652	−	0.0859780i
$370$	−13229.1	−	6370.81i	−1.85878	−	0.895142i
$371$	−3663.66	+	16051.5i	−0.512689	+	2.24624i
$372$	30243.4	+	14564.5i	4.21519	+	2.02993i
$373$	−1941.04	−	4030.61i	−0.269446	−	0.559510i	0.721713	−	0.692193i	$-0.243355\pi$
$373$	−1941.04	−	4030.61i	−0.269446	−	0.559510i	−0.991159	+	0.132683i	$0.957641\pi$
$374$		−	1119.44i		−	0.154773i
$375$	13837.8			1.90555
$376$	5577.79	−	1273.09i	0.765034	−	0.174614i
$377$	3527.79	+	7325.54i	0.481938	+	1.00075i
$378$	−12027.3	−	15081.8i	−1.63656	−	2.05218i
$379$	4823.43	+	6048.39i	0.653729	+	0.819750i	0.992644	−	0.121067i	$-0.0386316\pi$
$379$	4823.43	+	6048.39i	0.653729	+	0.819750i	−0.338916	+	0.940817i	$0.610060\pi$
$380$		−	36129.9i		−	4.87743i
$381$	6098.55	−	4863.43i	0.820048	−	0.653966i
$382$	631.036	+	144.030i	0.0845199	+	0.0192911i
$383$	4435.75	+	1012.43i	0.591791	+	0.135073i	0.507920	−	0.861404i	$-0.330414\pi$
$383$	4435.75	+	1012.43i	0.591791	+	0.135073i	0.0838712	+	0.996477i	$0.473272\pi$
$384$	1550.15	+	6791.64i	0.206004	+	0.902563i
$385$	7255.76	−	3494.19i	0.960487	−	0.462546i
$386$	−10624.8	−	8472.96i	−1.40100	−	1.11726i
$387$	239.745	+	1050.39i	0.0314908	+	0.137970i
$388$	−11332.4			−1.48277
$389$	−1693.09	−	3515.75i	−0.220677	−	0.458240i	0.761010	−	0.648740i	$-0.224704\pi$
$389$	−1693.09	−	3515.75i	−0.220677	−	0.458240i	−0.981687	+	0.190499i	$0.938989\pi$
$390$	−23981.9	−	11549.1i	−3.11377	−	1.49951i
$391$	13.2526	−	3.02482i	0.00171410	−	0.000391232i
$392$	26196.8	+	5979.26i	3.37536	+	0.770403i
$393$	10427.9			1.33847
$394$	−7182.20	+	12194.0i	−0.918360	+	1.55920i
$395$	−17497.2			−2.22881
$396$	−958.736	−	218.825i	−0.121662	−	0.0277686i
$397$	5061.02	−	1155.14i	0.639812	−	0.146033i	0.109706	−	0.993964i	$-0.465009\pi$
$397$	5061.02	−	1155.14i	0.639812	−	0.146033i	0.530106	+	0.847931i	$0.322152\pi$
$398$	13925.6	+	6706.22i	1.75384	+	0.844604i
$399$	−7204.13	−	14959.5i	−0.903904	−	1.87698i
$400$	−30765.6			−3.84570
$401$	−132.596	−	580.940i	−0.0165125	−	0.0723460i	0.966000	−	0.258541i	$-0.0832416\pi$
$401$	−132.596	−	580.940i	−0.0165125	−	0.0723460i	−0.982513	+	0.186195i	$0.940384\pi$
$402$	4361.33	+	3478.04i	0.541102	+	0.431515i
$403$	−14421.3	+	6944.95i	−1.78257	+	0.858443i
$404$	−408.324	−	1788.99i	−0.0502844	−	0.220310i
$405$	15500.8	+	3537.97i	1.90183	+	0.434081i
$406$	24669.6	+	5630.67i	3.01559	+	0.688289i
$407$	1630.72	−	1300.46i	0.198604	−	0.158382i
$408$			4481.79i			0.543828i
$409$	−970.547	−	1217.03i	−0.117336	−	0.147135i	0.719695	−	0.694291i	$-0.244282\pi$
$409$	−970.547	−	1217.03i	−0.117336	−	0.147135i	−0.837031	+	0.547156i	$0.815710\pi$
$410$	12654.8	+	15868.6i	1.52433	+	1.91145i
$411$	−2364.86	−	4910.69i	−0.283820	−	0.589359i
$412$	10598.7	−	2419.08i	1.26738	−	0.289271i
$413$	−21423.4			−2.55249
$414$		−	17.1915i		−	0.00204086i
$415$	11032.6	+	22909.4i	1.30499	+	2.70983i
$416$	8875.11	+	4274.03i	1.04600	+	0.503729i
$417$	1588.39	−	6959.18i	0.186532	−	0.817248i
$418$	6657.07	+	3205.88i	0.778966	+	0.375130i
$419$	−4186.16	+	5249.28i	−0.488084	+	0.612038i	−0.963495	−	0.267726i	$-0.913728\pi$
$419$	−4186.16	+	5249.28i	−0.488084	+	0.612038i	0.475411	+	0.879764i	$0.342299\pi$
$420$	−51842.1	+	24965.8i	−6.02294	+	2.90049i
$421$	5521.81	−	4403.49i	0.639231	−	0.509770i	−0.249395	−	0.968402i	$-0.580232\pi$
$421$	5521.81	−	4403.49i	0.639231	−	0.509770i	0.888626	+	0.458632i	$0.151660\pi$
$422$	−2504.69	+	10973.8i	−0.288925	+	1.26586i
$423$	−93.2548	+	408.576i	−0.0107192	+	0.0469637i
$424$	12727.2	+	26428.3i	1.45775	+	3.02705i
$425$	3818.26	+	871.493i	0.435795	+	0.0994674i
$426$	−5644.63	−	11721.2i	−0.641980	−	1.33308i
$427$	9830.78			1.11416
$428$	4846.41	+	21233.5i	0.547337	+	2.39804i
$429$	2956.20	−	2357.49i	0.332696	−	0.265316i
$430$	−28053.7			−3.14621
$431$	−8490.82	+	10647.2i	−0.948930	+	1.18992i	0.0327660	+	0.999463i	$0.489568\pi$
$431$	−8490.82	+	10647.2i	−0.948930	+	1.18992i	−0.981696	+	0.190457i	$0.939003\pi$
$432$	−15244.9	−	3479.55i	−1.69785	−	0.387523i
$433$	7888.60	−	9891.99i	0.875524	−	1.09787i	−0.118951	−	0.992900i	$-0.537953\pi$
$433$	7888.60	−	9891.99i	0.875524	−	1.09787i	0.994475	−	0.104973i	$-0.0334755\pi$
$434$	−11084.7	+	48565.4i	−1.22600	+	5.37146i
$435$	−16418.7	+	7906.81i	−1.80969	+	0.871500i
$436$	−8925.27	−	39104.2i	−0.980374	−	4.29530i
$437$	−19.9651	+	87.4726i	−0.00218549	+	0.00957525i
$438$	16276.6	+	12980.2i	1.77563	+	1.41602i
$439$	−12230.3	−	9753.31i	−1.32966	−	1.06037i	−0.992922	−	0.118765i	$-0.962106\pi$
$439$	−12230.3	−	9753.31i	−1.32966	−	1.06037i	−0.336733	−	0.941600i	$-0.609322\pi$
$440$	6225.32	−	12927.0i	0.674501	−	1.40062i
$441$	−1227.20	+	1538.86i	−0.132513	+	0.166166i
$442$	−2981.87	−	2377.96i	−0.320889	−	0.255901i
$443$	−877.620	+	422.639i	−0.0941241	+	0.0453278i	−0.480353	−	0.877075i	$-0.659492\pi$
$443$	−877.620	+	422.639i	−0.0941241	+	0.0453278i	0.386229	+	0.922403i	$0.373777\pi$
$444$	−11651.5	+	9291.73i	−1.24539	+	0.993166i
$445$	17189.5	+	21555.0i	1.83115	+	2.29619i
$446$	1153.65	−	263.314i	0.122482	−	0.0279558i
$447$	6701.24	+	3227.15i	0.709078	+	0.341474i
$448$	1965.40	−	946.487i	0.207269	−	0.0998155i
$449$	−1767.19	−	7742.56i	−0.185743	−	0.813795i	−0.978828	−	0.204684i	$-0.934383\pi$
$449$	−1767.19	−	7742.56i	−0.185743	−	0.813795i	0.793085	−	0.609111i	$-0.208474\pi$
$450$	2149.07	−	4462.60i	0.225130	−	0.467487i
$451$	−2810.89	+	641.567i	−0.293480	+	0.0669850i
$452$	2487.33	−	5164.99i	0.258837	−	0.537480i
$453$	1097.98	−	4810.55i	0.113880	−	0.498939i
$454$	574.100	+	2515.29i	0.0593476	+	0.260019i
$455$	6105.45	−	26749.7i	0.629072	−	2.75615i
$456$	−26652.2	−	12835.0i	−2.73707	−	1.31810i
$457$	4204.72	+	5272.56i	0.430391	+	0.539693i	0.948982	−	0.315329i	$-0.102115\pi$
$457$	4204.72	+	5272.56i	0.430391	+	0.539693i	−0.518592	+	0.855022i	$0.673543\pi$
$458$	−637.466	−	2792.92i	−0.0650367	−	0.284944i
$459$	1793.45	+	863.681i	0.182377	+	0.0878283i
$460$	303.135	+	69.1886i	0.0307255	+	0.00701291i
$461$	9234.99	+	7364.66i	0.933007	+	0.744048i	0.966841	−	0.255379i	$-0.0822003\pi$
$461$	9234.99	+	7364.66i	0.933007	+	0.744048i	−0.0338338	+	0.999427i	$0.510772\pi$
$462$		−	11767.4i		−	1.18499i
$463$		−	11613.2i		−	1.16569i	−0.812585	−	0.582843i	$-0.801940\pi$
$463$		−	11613.2i		−	1.16569i	0.812585	−	0.582843i	$-0.198060\pi$
$464$	18480.4	−	8899.71i	1.84899	−	0.890428i
$465$	−15565.6	−	32322.4i	−1.55234	−	3.22347i
$466$	19857.4	+	4532.32i	1.97398	+	0.450548i
$467$	9626.68	+	7677.02i	0.953896	+	0.760707i	0.970983	−	0.239147i	$-0.0768678\pi$
$467$	9626.68	+	7677.02i	0.953896	+	0.760707i	−0.0170872	+	0.999854i	$0.505439\pi$
$468$	−2619.47	+	2088.96i	−0.258729	+	0.206329i
$469$	−2494.89	+	5180.70i	−0.245636	+	0.510069i
$470$	−9831.54	−	4734.62i	−0.964883	−	0.464663i
$471$			2077.15i			0.203206i
$472$	−29841.2	+	23797.6i	−2.91007	+	2.32070i
$473$	1729.06	−	3590.42i	0.168081	−	0.349023i
$474$	−11093.0	+	23034.8i	−1.07493	+	2.23212i
$475$	−16117.4	+	20210.5i	−1.55687	+	1.95226i
$476$	−8037.98	+	1834.62i	−0.773992	+	0.176659i
$477$	−2148.67			−0.206249
$478$		−	9804.17i		−	0.938142i
$479$	6582.01	−	8253.57i	0.627849	−	0.787297i	−0.361576	−	0.932342i	$-0.617761\pi$
$479$	6582.01	−	8253.57i	0.627849	−	0.787297i	0.989425	+	0.145045i	$0.0463328\pi$
$480$	−9579.33	+	19891.7i	−0.910906	+	1.89152i
$481$		−	7106.26i		−	0.673633i
$482$	10603.2	+	13296.0i	1.00200	+	1.25647i
$483$	139.309	−	31.7963i	0.0131237	−	0.00299540i
$484$	−12832.2	−	16091.1i	−1.20513	−	1.51119i
$485$	9469.09	+	7551.34i	0.886534	+	0.706987i
$486$	3398.11	−	4261.09i	0.317163	−	0.397710i
$487$	−15597.5			−1.45131			−0.725655	−	0.688059i	$-0.758463\pi$
$487$	−15597.5			−1.45131			−0.725655	+	0.688059i	$0.758463\pi$
$488$	13693.6	−	10920.2i	1.27024	−	1.01298i
$489$	−3844.40	−	7982.97i	−0.355521	−	0.738246i
$490$	−31954.2	−	40069.3i	−2.94600	−	3.69417i
$491$	−10643.3	+	5125.53i	−0.978256	+	0.471103i	−0.853505	−	0.521085i	$-0.825528\pi$
$491$	−10643.3	+	5125.53i	−0.978256	+	0.471103i	−0.124751	+	0.992188i	$0.539813\pi$
$492$	20083.7	−	4583.97i	1.84033	−	0.420043i
$493$	−2545.67	+	581.033i	−0.232558	+	0.0530799i
$494$	22680.7	−	10922.5i	2.06570	−	0.994787i
$495$	655.282	+	821.697i	0.0595005	+	0.0746112i
$496$	17520.3	+	36381.3i	1.58606	+	3.29348i
$497$	10484.5	−	8361.12i	0.946268	−	0.754623i
$498$	37154.4			3.34323
$499$	−9829.54	+	12325.9i	−0.881825	+	1.10577i	0.111877	+	0.993722i	$0.464314\pi$
$499$	−9829.54	+	12325.9i	−0.881825	+	1.10577i	−0.993702	+	0.112052i	$0.964258\pi$
$500$	35458.2	+	28277.0i	3.17148	+	2.52917i
$501$	1904.44	+	2388.09i	0.169828	+	0.212958i
$502$	30624.5	−	6989.83i	2.72278	−	0.621457i
$503$	−10224.9	−	12821.6i	−0.906372	−	1.13655i	−0.990142	−	0.140069i	$-0.955268\pi$
$503$	−10224.9	−	12821.6i	−0.906372	−	1.13655i	0.0837700	−	0.996485i	$-0.473304\pi$
$504$			5842.65i			0.516374i
$505$	−850.903	+	1766.92i	−0.0749796	+	0.155697i
$506$	−39.6460	+	49.7146i	−0.00348316	+	0.00436775i
$507$		−	685.000i		−	0.0600038i
$508$	25565.3			2.23283
$509$	−446.226	+	101.848i	−0.0388578	+	0.00886903i	−0.241906	−	0.970300i	$-0.577772\pi$
$509$	−446.226	+	101.848i	−0.0388578	+	0.00886903i	0.203048	+	0.979169i	$0.434915\pi$
$510$	5329.70	−	6683.24i	0.462751	−	0.580272i
$511$	−9311.02	+	19334.5i	−0.806057	+	1.67379i
$512$	−11229.4	+	23318.2i	−0.969290	+	2.01275i
$513$	−10272.2	+	8191.83i	−0.884074	+	0.705026i
$514$		−	16735.7i		−	1.43615i
$515$	−10468.0	−	5041.10i	−0.895676	−	0.431335i
$516$	−12354.0	+	25653.4i	−1.05398	+	2.18862i
$517$	1211.91	−	966.467i	0.103094	−	0.0822151i
$518$	−17290.7	−	13788.9i	−1.46662	−	1.16959i
$519$	7362.32	+	1680.40i	0.622678	+	0.142122i
$520$	−21209.7	−	44042.5i	−1.78867	−	3.71421i
$521$	−6460.49	+	3111.21i	−0.543261	+	0.261621i	−0.685326	−	0.728237i	$-0.740340\pi$
$521$	−6460.49	+	3111.21i	−0.543261	+	0.261621i	0.142065	+	0.989857i	$0.454626\pi$
$522$			3302.29i			0.276891i
$523$		−	18643.4i		−	1.55873i	−0.626569	−	0.779366i	$-0.715541\pi$
$523$		−	18643.4i		−	1.55873i	0.626569	−	0.779366i	$-0.284459\pi$
$524$	26720.7	+	21309.0i	2.22767	+	1.77651i
$525$	40136.8	+	9160.96i	3.33660	+	0.761557i
$526$	−24771.1	−	11929.1i	−2.05336	−	0.988848i
$527$	−1143.84	−	5011.50i	−0.0945476	−	0.414240i
$528$	−5947.33	−	7457.71i	−0.490197	−	0.614688i
$529$	10961.4	+	5278.73i	0.900912	+	0.433856i
$530$	12449.5	−	54544.8i	1.02032	−	4.47033i
$531$	−622.136	−	2725.75i	−0.0508444	−	0.222764i
$532$	12109.2	−	53054.0i	0.986846	−	4.32365i
$533$	−4262.05	+	8850.24i	−0.346360	+	0.719224i
$534$	39274.7	−	8964.19i	3.18274	−	0.726439i
$535$	10099.4	−	20971.6i	0.816139	−	1.69473i
$536$	2279.63	+	9987.71i	0.183703	+	0.804857i
$537$	−21456.1	+	10332.7i	−1.72421	+	0.830336i
$538$	425.187	+	204.759i	0.0340727	+	0.0164085i
$539$	7097.69	−	1620.00i	0.567197	−	0.129459i
$540$	28388.7	+	35598.3i	2.26232	+	2.83686i
$541$	3093.07	−	2466.64i	0.245807	−	0.196024i	−0.492835	−	0.870123i	$-0.664039\pi$
$541$	3093.07	−	2466.64i	0.245807	−	0.196024i	0.738641	+	0.674099i	$0.235468\pi$
$542$	−27233.3	+	13114.9i	−2.15825	+	1.03936i
$543$	7685.71	+	6129.15i	0.607413	+	0.484396i
$544$	−1972.39	+	2473.30i	−0.155451	+	0.194930i
$545$	−18599.3	+	38621.8i	−1.46185	+	3.03555i
$546$	−31344.8	−	24996.7i	−2.45684	−	1.95927i
$547$	−19165.7	−	15284.2i	−1.49811	−	1.19470i	−0.927690	−	0.373352i	$-0.878208\pi$
$547$	−19165.7	−	15284.2i	−1.49811	−	1.19470i	−0.570422	−	0.821352i	$-0.693220\pi$
$548$	3975.04	−	17415.8i	0.309863	−	1.35760i
$549$	285.486	+	1250.80i	0.0221935	+	0.0972361i
$550$	−16506.1	+	7948.93i	−1.27968	+	0.616261i
$551$	3835.06	−	16802.5i	0.296514	−	1.29911i
$552$	158.727	−	199.037i	0.0122389	−	0.0153471i
$553$	−25693.3	−	5864.34i	−1.97575	−	0.450953i
$554$	4163.35	−	5220.68i	0.319285	−	0.400371i
$555$	15927.2			1.21815
$556$	18291.0	−	14586.5i	1.39516	−	1.11260i
$557$	−3820.79	−	16740.0i	−0.290650	−	1.27342i	−0.883623	−	0.468199i	$-0.844903\pi$
$557$	−3820.79	−	16740.0i	−0.290650	−	1.27342i	0.592973	−	0.805222i	$-0.297954\pi$
$558$	−6501.00			−0.493207
$559$	−5890.92	−	12232.6i	−0.445723	−	0.925554i
$560$	−67482.6	−	15402.5i	−5.09225	−	1.16227i
$561$	526.858	+	1094.03i	0.0396505	+	0.0823352i
$562$	−688.640	+	3017.13i	−0.0516878	+	0.226459i
$563$	−2060.13	+	9026.03i	−0.154217	+	0.675669i	0.837414	+	0.546569i	$0.184066\pi$
$563$	−2060.13	+	9026.03i	−0.154217	+	0.675669i	−0.991631	+	0.129101i	$0.958791\pi$
$564$	−8659.06	+	6905.37i	−0.646475	+	0.515547i
$565$	−5520.04	+	2658.31i	−0.411026	+	0.197940i
$566$	527.170	−	661.050i	0.0391495	−	0.0490919i
$567$	21576.0	+	10390.5i	1.59807	+	0.769592i
$568$	5316.45	−	23292.9i	0.392734	−	1.72068i
$569$	18536.6	+	8926.77i	1.36572	+	0.657697i	0.965905	−	0.258898i	$-0.0833594\pi$
$569$	18536.6	+	8926.77i	1.36572	+	0.657697i	0.399817	+	0.916595i	$0.369074\pi$
$570$	24480.4	+	50834.1i	1.79890	+	3.73545i
$571$			13393.3i			0.981594i	0.871274	+	0.490797i	$0.163294\pi$
$571$			13393.3i			0.981594i	−0.871274	+	0.490797i	$0.836706\pi$
$572$	12392.5			0.905865
$573$	−684.498	+	156.232i	−0.0499045	+	0.0113904i
$574$	13264.1	+	27543.2i	0.964517	+	2.00284i
$575$	−138.705	−	173.930i	−0.0100598	−	0.0126146i
$576$	177.499	+	222.577i	0.0128399	+	0.0161008i
$577$		−	25876.5i		−	1.86699i	−0.358589	−	0.933496i	$-0.616742\pi$
$577$		−	25876.5i		−	1.86699i	0.358589	−	0.933496i	$-0.383258\pi$
$578$	−18702.0	+	14914.4i	−1.34585	+	1.07328i
$579$	14371.3	+	3280.16i	1.03152	+	0.235438i
$580$	−58228.8	−	13290.3i	−4.16866	−	0.951468i
$581$	8522.26	+	37338.4i	0.608542	+	2.66620i
$582$	15944.5	−	7678.46i	1.13560	−	0.546877i
$583$	6213.56	+	4955.15i	0.441405	+	0.352009i
$584$	8507.65	+	37274.5i	0.602824	+	2.64114i
$585$	3580.74			0.253069
$586$	15304.4	+	31779.8i	1.07887	+	2.24029i
$587$	5863.42	+	2823.67i	0.412281	+	0.198544i	0.628515	−	0.777797i	$-0.283663\pi$
$587$	5863.42	+	2823.67i	0.412281	+	0.198544i	−0.216234	+	0.976342i	$0.569377\pi$
$588$	−50712.7	+	11574.8i	−3.55673	+	0.811799i
$589$	33078.0	+	7549.84i	2.31402	+	0.528159i
$590$	72799.0			5.07981
$591$	1280.15	−	15297.4i	0.0891007	−	1.06472i
$592$	−17927.3			−1.24460
$593$	10458.4	+	2387.05i	0.724238	+	0.165303i	0.568721	−	0.822531i	$-0.307439\pi$
$593$	10458.4	+	2387.05i	0.724238	+	0.165303i	0.155517	+	0.987833i	$0.450296\pi$
$594$	−9078.10	+	2072.02i	−0.627069	+	0.143124i
$595$	7938.83	+	3823.14i	0.546992	+	0.263417i
$596$	10576.9	+	21963.1i	0.726921	+	1.50947i
$597$	−16765.7			−1.14937
$598$	48.2076	+	211.211i	0.00329658	+	0.0144433i
$599$	−11100.9	−	8852.66i	−0.757212	−	0.603857i	0.166902	−	0.985974i	$-0.446624\pi$
$599$	−11100.9	−	8852.66i	−0.757212	−	0.603857i	−0.924114	+	0.382117i	$0.875195\pi$
$600$	66083.8	−	31824.3i	4.49644	−	2.16537i
$601$	1006.44	+	4409.51i	0.0683089	+	0.299281i	0.997530	−	0.0702438i	$-0.0223777\pi$
$601$	1006.44	+	4409.51i	0.0683089	+	0.299281i	−0.929221	+	0.369524i	$0.879521\pi$
$602$	−41194.7	−	9402.42i	−2.78899	−	0.636568i
$603$	−731.605	−	166.984i	−0.0494084	−	0.0112771i
$604$	12643.7	−	10083.0i	0.851761	−	0.679257i
$605$			21996.1i			1.47813i
$606$	1786.66	+	2240.40i	0.119766	+	0.150182i
$607$	−674.160	−	845.370i	−0.0450796	−	0.0565280i	0.758781	−	0.651346i	$-0.225795\pi$
$607$	−674.160	−	845.370i	−0.0450796	−	0.0565280i	−0.803860	+	0.594818i	$0.797224\pi$
$608$	−9059.59	−	18812.4i	−0.604301	−	1.25484i
$609$	−26759.6	+	6107.70i	−1.78055	+	0.406398i
$610$	−33406.0			−2.21733
$611$		−	5281.19i		−	0.349679i
$612$	−466.846	−	969.415i	−0.0308352	−	0.0640299i
$613$	−12970.0	−	6246.05i	−0.854576	−	0.411542i	−0.0453022	−	0.998973i	$-0.514425\pi$
$613$	−12970.0	−	6246.05i	−0.854576	−	0.411542i	−0.809274	+	0.587431i	$0.800139\pi$
$614$	2011.37	−	8812.39i	0.132202	−	0.579217i
$615$	−19835.9	−	9552.49i	−1.30059	−	0.626331i
$616$	13474.0	−	16895.9i	0.881303	−	1.10512i
$617$	−2306.66	+	1110.83i	−0.150507	+	0.0724803i	−0.507621	−	0.861580i	$-0.669475\pi$
$617$	−2306.66	+	1110.83i	−0.150507	+	0.0724803i	0.357114	+	0.934061i	$0.383761\pi$
$618$	−13273.1	+	10584.9i	−0.863950	+	0.688977i
$619$	4345.34	−	19038.2i	0.282155	−	1.23620i	−0.612870	−	0.790184i	$-0.709985\pi$
$619$	4345.34	−	19038.2i	0.282155	−	1.23620i	0.895024	−	0.446017i	$-0.147158\pi$
$620$	26163.9	−	114631.i	1.69478	−	7.42534i
$621$	−49.0594	−	101.873i	−0.00317019	−	0.00658296i
$622$	35832.9	+	8178.62i	2.30992	+	0.527223i
$623$	18017.2	+	37413.0i	1.15866	+	2.40597i
$624$	−32498.7			−2.08492
$625$	−3743.70	−	16402.2i	−0.239597	−	1.04974i
$626$	31995.1	−	25515.3i	2.04278	−	1.62907i
$627$	−8014.78			−0.510493
$628$	−4244.59	+	5322.55i	−0.269709	+	0.338205i
$629$	2224.92	+	507.823i	0.141039	+	0.0321911i
$630$	6948.02	−	8712.54i	0.439390	−	0.550978i
$631$	2080.73	−	9116.26i	0.131272	−	0.575139i	−0.865916	−	0.500190i	$-0.833263\pi$
$631$	2080.73	−	9116.26i	0.131272	−	0.575139i	0.997187	−	0.0749490i	$-0.0238794\pi$
$632$	−42303.2	+	20372.1i	−2.66255	+	1.28222i
$633$	−2716.89	−	11903.5i	−0.170595	−	0.747425i
$634$	−3190.37	+	13977.9i	−0.199851	+	0.875606i
$635$	−21361.7	−	17035.4i	−1.33498	−	1.06461i
$636$	−44395.6	−	35404.3i	−2.76792	−	2.20735i
$637$	10762.0	−	22347.4i	0.669395	−	1.39001i
$638$	7615.55	−	9549.60i	0.472575	−	0.592590i
$639$	1368.28	+	1091.17i	0.0847077	+	0.0675522i
$640$	21984.8	−	10587.3i	1.35785	−	0.653906i
$641$	15611.6	−	12449.9i	0.961969	−	0.767145i	−0.0105558	−	0.999944i	$-0.503360\pi$
$641$	15611.6	−	12449.9i	0.961969	−	0.767145i	0.972525	+	0.232800i	$0.0747887\pi$
$642$	−21205.9	−	26591.4i	−1.30363	−	1.63470i
$643$	20032.8	−	4572.36i	1.22864	−	0.280429i	0.441534	−	0.897245i	$-0.354435\pi$
$643$	20032.8	−	4572.36i	1.22864	−	0.280429i	0.787108	+	0.616815i	$0.211577\pi$
$644$	421.942	+	203.197i	0.0258181	+	0.0124333i
$645$	27416.9	−	13203.3i	1.67370	−	0.806012i
$646$	1798.95	+	7881.69i	0.109564	+	0.480033i
$647$	−4212.36	+	8747.06i	−0.255958	+	0.531503i	−0.988863	−	0.148828i	$-0.952450\pi$
$647$	−4212.36	+	8747.06i	−0.255958	+	0.531503i	0.732905	+	0.680331i	$0.238164\pi$
$648$	41595.8	−	9493.97i	2.52166	−	0.575553i
$649$	−4486.88	+	9317.11i	−0.271380	+	0.563526i
$650$	−13889.3	+	60853.0i	−0.838127	+	3.67208i
$651$	−12023.8	−	52679.9i	−0.723889	−	3.17157i
$652$	6461.95	−	28311.6i	0.388143	−	1.70057i
$653$	16742.1	+	8062.58i	1.00332	+	0.483175i	0.862065	−	0.506798i	$-0.169171\pi$
$653$	16742.1	+	8062.58i	1.00332	+	0.483175i	0.141258	+	0.989973i	$0.454885\pi$
$654$	39053.4	+	48971.4i	2.33503	+	2.92803i
$655$	−8127.88	−	35610.6i	−0.484859	−	2.12431i
$656$	22326.8	+	10752.0i	1.32884	+	0.639934i
$657$	−2730.37	−	623.190i	−0.162134	−	0.0370060i
$658$	−12850.0	−	10247.5i	−0.761316	−	0.607129i
$659$		−	25700.4i		−	1.51919i	−0.650396	−	0.759596i	$-0.725397\pi$
$659$		−	25700.4i		−	1.51919i	0.650396	−	0.759596i	$-0.274603\pi$
$660$			27775.1i			1.63810i
$661$	−14546.6	+	7005.26i	−0.855970	+	0.412214i	−0.809790	−	0.586720i	$-0.800419\pi$
$661$	−14546.6	+	7005.26i	−0.855970	+	0.412214i	−0.0461801	+	0.998933i	$0.514705\pi$
$662$	−5549.84	−	11524.4i	−0.325832	−	0.676596i
$663$	4033.35	+	920.586i	0.236263	+	0.0539255i
$664$	53347.3	+	42543.0i	3.11788	+	2.48643i
$665$	−45470.7	+	36261.6i	−2.65154	+	2.11454i
$666$	1252.27	−	2600.37i	0.0728598	−	0.151295i
$667$	133.631	+	64.3534i	0.00775746	+	0.00373579i
$668$			10010.9i			0.579842i
$669$	−1003.54	+	800.295i	−0.0579956	+	0.0462499i
$670$	8477.91	−	17604.6i	0.488851	−	1.01511i
$671$	2058.94	−	4275.44i	0.118457	−	0.245978i
$672$	−20733.4	+	25998.8i	−1.19019	+	1.49245i
$673$	16480.3	−	3761.53i	0.943938	−	0.215448i	0.277261	−	0.960795i	$-0.410573\pi$
$673$	16480.3	−	3761.53i	0.943938	−	0.215448i	0.666677	+	0.745347i	$0.267716\pi$
$674$	−22548.6			−1.28863
$675$		−	32577.2i		−	1.85763i
$676$	1399.77	−	1755.26i	0.0796411	−	0.0998668i
$677$	−10609.0	+	22029.9i	−0.602273	+	1.25063i	0.347496	+	0.937681i	$0.387032\pi$
$677$	−10609.0	+	22029.9i	−0.602273	+	1.25063i	−0.949769	+	0.312951i	$0.898682\pi$
$678$			8952.38i			0.507100i
$679$	11373.7	+	14262.2i	0.642834	+	0.806088i
$680$	15305.0	−	3493.27i	0.863119	−	0.197001i
$681$	−1744.87	−	2188.00i	−0.0981845	−	0.123120i
$682$	18799.7	+	14992.3i	1.05554	+	0.841764i
$683$	−193.636	+	242.811i	−0.0108481	+	0.0136031i	−0.787226	−	0.616665i	$-0.788483\pi$
$683$	−193.636	+	242.811i	−0.0108481	+	0.0136031i	0.776378	+	0.630268i	$0.217055\pi$
$684$	7101.85			0.396997
$685$	−14926.4	+	11903.4i	−0.832568	+	0.663951i
$686$	−11182.4	−	23220.4i	−0.622369	−	1.29236i
$687$	1937.46	+	2429.50i	0.107596	+	0.134922i
$688$	−30859.7	+	14861.3i	−1.71005	+	0.823518i
$689$	26398.2	−	6025.21i	1.45964	−	0.333152i
$690$	−473.385	+	108.047i	−0.0261181	+	0.00596128i
$691$	4200.05	−	2022.64i	0.231226	−	0.111353i	−0.314684	−	0.949197i	$-0.601898\pi$
$691$	4200.05	−	2022.64i	0.231226	−	0.111353i	0.545910	+	0.837844i	$0.316184\pi$
$692$	15431.5	+	19350.5i	0.847715	+	1.06300i
$693$	686.833	+	1426.22i	0.0376488	+	0.0781786i
$694$	−18733.4	+	14939.4i	−1.02465	+	0.817133i
$695$	−25003.2			−1.36464
$696$	−30489.6	+	38232.7i	−1.66050	+	2.08220i
$697$	−2466.37	−	1966.86i	−0.134032	−	0.106887i
$698$	−19174.6	−	24044.2i	−1.03978	−	1.30385i
$699$	−21539.7	+	4916.30i	−1.16553	+	0.266025i
$700$	84127.4	+	105492.i	4.54245	+	5.69605i
$701$		−	17802.0i		−	0.959163i	−0.877497	−	0.479582i	$-0.840788\pi$
$701$		−	17802.0i		−	0.959163i	0.877497	−	0.479582i	$-0.159212\pi$
$702$	−13764.8	+	28582.9i	−0.740055	+	1.53674i
$703$	−9391.65	+	11776.8i	−0.503859	+	0.631819i
$704$		−	1052.99i		−	0.0563723i
$705$	11836.7			0.632333
$706$	3627.87	−	828.037i	0.193395	−	0.0441411i
$707$	−1841.68	+	2309.40i	−0.0979684	+	0.122849i
$708$	32058.6	−	66570.3i	1.70174	−	3.53371i
$709$	−5866.36	+	12181.6i	−0.310741	+	0.645261i	−0.996593	−	0.0824805i	$-0.973716\pi$
$709$	−5866.36	+	12181.6i	−0.310741	+	0.645261i	0.685851	+	0.727742i	$0.259430\pi$
$710$	−35627.5	+	28412.0i	−1.88321	+	1.50181i
$711$		−	3439.33i		−	0.181413i
$712$	66655.8	+	32099.8i	3.50847	+	1.68959i
$713$	−126.689	+	263.072i	−0.00665431	+	0.0138178i
$714$	10066.2	−	8027.53i	0.527617	−	0.420760i
$715$	−10354.8	−	8257.70i	−0.541607	−	0.431917i
$716$	−76094.2	−	17368.0i	−3.97175	−	0.906527i
$717$	4614.26	+	9581.61i	0.240338	+	0.499068i
$718$	−59817.2	+	28806.4i	−3.10913	+	1.49728i
$719$			27741.8i			1.43894i	0.694526	+	0.719468i	$0.255614\pi$
$719$			27741.8i			1.43894i	−0.694526	+	0.719468i	$0.744386\pi$
$720$		−	9033.27i		−	0.467570i
$721$	−13681.8	−	10910.9i	−0.706710	−	0.563582i
$722$	−17797.0	−	4062.06i	−0.917364	−	0.209382i
$723$	−16620.2	−	8003.86i	−0.854926	−	0.411711i
$724$	7169.34	+	31410.9i	0.368020	+	1.61240i
$725$	26643.6	+	33410.0i	1.36485	+	1.71147i
$726$	28957.5	+	13945.2i	1.48032	+	0.712885i
$727$	−747.477	+	3274.91i	−0.0381326	+	0.167070i	−0.990409	−	0.138168i	$-0.955879\pi$
$727$	−747.477	+	3274.91i	−0.0381326	+	0.167070i	0.952276	+	0.305238i	$0.0987359\pi$
$728$	−16383.7	−	71781.6i	−0.834093	−	3.65440i
$729$	3596.65	−	15758.0i	0.182729	−	0.800588i
$730$	31639.8	−	65700.8i	1.60417	−	3.33109i
$731$	4250.91	−	970.243i	0.215083	−	0.0490913i
$732$	−14711.1	+	30547.8i	−0.742809	+	1.54246i
$733$	−5618.44	−	24616.0i	−0.283113	−	1.24040i	−0.893778	−	0.448509i	$-0.851955\pi$
$733$	−5618.44	−	24616.0i	−0.283113	−	1.24040i	0.610665	−	0.791889i	$-0.290902\pi$
$734$	−15614.7	+	7519.66i	−0.785218	+	0.378141i
$735$	50087.1	+	24120.7i	2.51359	+	1.21048i
$736$	175.188	−	39.9856i	0.00877381	−	0.00200256i
$737$	1730.58	+	2170.07i	0.0864947	+	0.108461i
$738$	−3119.20	+	2487.48i	−0.155582	+	0.124072i
$739$	−7826.15	+	3768.88i	−0.389567	+	0.187605i	−0.618406	−	0.785859i	$-0.712221\pi$
$739$	−7826.15	+	3768.88i	−0.389567	+	0.187605i	0.228839	+	0.973464i	$0.426507\pi$
$740$	40812.2	+	32546.6i	2.02741	+	1.61681i
$741$	−17025.3	+	21349.0i	−0.844048	+	1.05840i
$742$	36562.3	−	75922.4i	1.80895	−	3.75633i
$743$	7727.37	+	6162.37i	0.381548	+	0.304274i	0.795417	−	0.606062i	$-0.207252\pi$
$743$	7727.37	+	6162.37i	0.381548	+	0.304274i	−0.413870	+	0.910336i	$0.635823\pi$
$744$	−75266.4	−	60022.9i	−3.70887	−	2.95772i
$745$	5797.31	−	25399.7i	0.285096	−	1.24909i
$746$	5095.04	+	22322.8i	0.250057	+	1.09557i
$747$	−4503.18	+	2168.62i	−0.220566	+	0.106219i
$748$	−885.581	+	3879.98i	−0.0432888	+	0.189661i
$749$	21859.0	−	27410.3i	1.06637	−	1.33718i
$750$	−69048.6	−	15759.9i	−3.36173	−	0.767293i
$751$	−612.748	+	768.362i	−0.0297730	+	0.0373341i	−0.796495	−	0.604645i	$-0.793315\pi$
$751$	−612.748	+	768.362i	−0.0297730	+	0.0373341i	0.766722	+	0.641979i	$0.221886\pi$
$752$	−13323.1			−0.646067
$753$	−26639.6	+	21244.3i	−1.28924	+	1.02814i
$754$	−9260.12	−	40571.2i	−0.447260	−	1.95957i
$755$	−17283.5			−0.833128
$756$	29755.6	+	61788.1i	1.43148	+	2.97250i
$757$	−23838.1	−	5440.88i	−1.14453	−	0.261231i	−0.392112	−	0.919918i	$-0.628255\pi$
$757$	−23838.1	−	5440.88i	−1.14453	−	0.261231i	−0.752418	+	0.658686i	$0.771113\pi$
$758$	−17179.7	−	35674.1i	−0.823214	−	1.70942i
$759$	15.3483	−	67.2451i	0.000734001	−	0.00321587i
$760$	−23057.1	+	101020.i	−1.10048	+	4.82154i
$761$	3585.59	−	2859.41i	0.170798	−	0.136207i	−0.534360	−	0.845257i	$-0.679447\pi$
$761$	3585.59	−	2859.41i	0.170798	−	0.136207i	0.705158	+	0.709050i	$0.250876\pi$
$762$	−35969.9	+	17322.2i	−1.71004	+	0.823513i
$763$	−40256.1	+	50479.5i	−1.91005	+	2.39513i
$764$	−2073.23	−	998.413i	−0.0981763	−	0.0472792i
$765$	−255.884	+	1121.10i	−0.0120935	+	0.0529850i
$766$	−20980.7	−	10103.8i	−0.989639	−	0.476585i
$767$	15286.9	+

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.98986 - 1.13890i) q^{2} +(5.41261 - 1.23539i) q^{3} +(16.3939 + 7.89487i) q^{4} +(-8.43757 - 17.5208i) q^{5} -28.4152 q^{6} +(-6.51769 - 28.5559i) q^{7} +(-40.7992 - 32.5362i) q^{8} +(3.44396 - 1.65853i) q^{9} +O(q^{10})\)	\(q+(-4.98986 - 1.13890i) q^{2} +(5.41261 - 1.23539i) q^{3} +(16.3939 + 7.89487i) q^{4} +(-8.43757 - 17.5208i) q^{5} -28.4152 q^{6} +(-6.51769 - 28.5559i) q^{7} +(-40.7992 - 32.5362i) q^{8} +(3.44396 - 1.65853i) q^{9} +(22.1478 + 97.0359i) q^{10} +(-13.7841 - 3.14613i) q^{11} +(98.4868 + 22.4790i) q^{12} +(-37.6611 + 30.0337i) q^{13} +149.913i q^{14} +(-67.3143 - 84.4094i) q^{15} +(75.7673 + 95.0092i) q^{16} +(-6.71202 - 13.9376i) q^{17} +(-19.0738 + 4.35347i) q^{18} +102.106 q^{19} -353.847i q^{20} +(-70.5554 - 146.510i) q^{21} +(65.1976 + 31.3975i) q^{22} +(-0.195533 + 0.856684i) q^{23} +(-261.025 - 125.703i) q^{24} +(-157.849 + 197.937i) q^{25} +(222.129 - 106.972i) q^{26} +(-100.604 + 80.2287i) q^{27} +(118.595 - 519.597i) q^{28} +(37.5596 - 164.559i) q^{29} +(239.755 + 497.856i) q^{30} +(323.958 + 73.9412i) q^{31} +(-88.7273 - 184.244i) q^{32} -78.4947 q^{33} +(17.6184 + 77.1913i) q^{34} +(-445.328 + 355.137i) q^{35} +69.5537 q^{36} +(-91.9794 + 115.339i) q^{37} +(-509.495 - 116.289i) q^{38} +(-166.741 + 209.087i) q^{39} +(-225.815 + 989.360i) q^{40} +(183.728 - 88.4787i) q^{41} +(185.201 + 811.419i) q^{42} +(-62.7192 + 274.791i) q^{43} +(-201.136 - 160.401i) q^{44} +(-58.1174 - 46.3470i) q^{45} +(1.95136 - 4.05204i) q^{46} +(-68.3567 + 85.7166i) q^{47} +(527.472 + 420.645i) q^{48} +(-463.925 + 223.415i) q^{49} +(1013.08 - 807.902i) q^{50} +(-53.5480 - 67.1470i) q^{51} +(-854.523 + 195.039i) q^{52} +(-506.443 - 243.890i) q^{53} +(593.371 - 285.752i) q^{54} +(61.1816 + 268.054i) q^{55} +(-663.185 + 1377.12i) q^{56} +(552.660 - 126.141i) q^{57} +(-374.834 + 778.352i) q^{58} +(162.756 - 713.079i) q^{59} +(-437.140 - 1915.23i) q^{60} +(-74.6854 + 327.218i) q^{61} +(-1532.29 - 737.913i) q^{62} +(-69.8073 - 87.5356i) q^{63} +(16.5726 + 72.6091i) q^{64} +(843.983 + 406.441i) q^{65} +(391.677 + 89.3978i) q^{66} +(-153.486 - 122.401i) q^{67} -281.482i q^{68} +4.87846i q^{69} +(2626.59 - 1264.90i) q^{70} +(198.649 + 412.498i) q^{71} +(-194.473 - 44.3872i) q^{72} +(-572.814 - 456.804i) q^{73} +(590.324 - 470.768i) q^{74} +(-609.847 + 1266.36i) q^{75} +(1673.91 + 806.114i) q^{76} +414.123i q^{77} +(1070.15 - 853.413i) q^{78} +(390.390 - 810.653i) q^{79} +(1025.34 - 2129.15i) q^{80} +(-509.763 + 639.222i) q^{81} +(-1017.55 + 232.248i) q^{82} -1307.56 q^{83} -2958.89i q^{84} +(-187.566 + 235.200i) q^{85} +(625.921 - 1299.74i) q^{86} -937.096i q^{87} +(460.017 + 576.843i) q^{88} +(-1382.17 + 315.472i) q^{89} +(237.213 + 297.455i) q^{90} +(1103.10 + 879.695i) q^{91} +(-9.96895 + 12.5007i) q^{92} +1844.80 q^{93} +(438.713 - 349.862i) q^{94} +(-861.526 - 1788.98i) q^{95} +(-707.860 - 887.628i) q^{96} +(-561.127 + 270.224i) q^{97} +(2569.37 - 586.442i) q^{98} +(-52.6899 + 12.0261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9}+O(q^{10}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19} - 7 q^{21} + 807 q^{22} + 413 q^{23} - 1425 q^{24} + 1195 q^{25} - 543 q^{26} + 455 q^{27} + 174 q^{28} - 906 q^{29} + 798 q^{30} + 917 q^{31} + 945 q^{32} + 894 q^{33} - 219 q^{34} - 7 q^{35} + 3250 q^{36} + 1734 q^{37} - 63 q^{38} - 825 q^{39} + 141 q^{40} + 563 q^{41} + 432 q^{42} - 423 q^{43} + 2149 q^{44} - 3808 q^{45} - 2569 q^{46} - 289 q^{47} - 3703 q^{48} - 3747 q^{49} - 4963 q^{50} - 87 q^{51} + 3654 q^{52} - 1573 q^{53} - 1228 q^{54} + 2825 q^{55} + 98 q^{56} - 518 q^{57} - 5103 q^{58} + 2045 q^{59} + 3375 q^{60} + 287 q^{61} - 2547 q^{62} + 1453 q^{63} + 6475 q^{64} + 1268 q^{65} + 4634 q^{66} - 3577 q^{67} - 814 q^{70} - 273 q^{71} - 1008 q^{72} - 679 q^{73} - 315 q^{74} - 1281 q^{75} + 6078 q^{76} + 4739 q^{78} + 1463 q^{79} + 441 q^{80} - 4427 q^{81} - 7 q^{82} + 4900 q^{83} - 3351 q^{85} + 3472 q^{86} + 3738 q^{88} + 147 q^{89} + 7133 q^{90} - 14133 q^{91} - 803 q^{92} - 4894 q^{93} - 7833 q^{94} - 7700 q^{95} - 16450 q^{96} + 1233 q^{97} - 2030 q^{98} + 2464 q^{99}+O(q^{100}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

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