LMFDB - Embedded newform 177.4.e.b.76.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			76.2
Character	$\chi$	$=$	177.76
Dual form			177.4.e.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57971 + 3.80479i) q^{2} +(0.162417 + 2.99560i) q^{3} +(-4.86039 - 12.1987i) q^{4} +(-1.87335 - 0.866706i) q^{5} +(-11.8166 - 7.10982i) q^{6} +(0.688121 + 2.47839i) q^{7} +(23.0364 + 5.07071i) q^{8} +(-8.94724 + 0.973071i) q^{9} +O(q^{10})$	\(q+(-2.57971 + 3.80479i) q^{2} +(0.162417 + 2.99560i) q^{3} +(-4.86039 - 12.1987i) q^{4} +(-1.87335 - 0.866706i) q^{5} +(-11.8166 - 7.10982i) q^{6} +(0.688121 + 2.47839i) q^{7} +(23.0364 + 5.07071i) q^{8} +(-8.94724 + 0.973071i) q^{9} +(8.13034 - 4.89186i) q^{10} +(-48.9029 - 46.3233i) q^{11} +(35.7529 - 16.5411i) q^{12} +(57.6303 + 6.26768i) q^{13} +(-11.2049 - 3.77537i) q^{14} +(2.29204 - 5.75259i) q^{15} +(-2.45420 + 2.32474i) q^{16} +(24.6960 - 88.9470i) q^{17} +(19.3789 - 36.5526i) q^{18} +(85.5643 + 65.0443i) q^{19} +(-1.46742 + 27.0650i) q^{20} +(-7.31250 + 2.46387i) q^{21} +(302.405 - 66.5644i) q^{22} +(-55.8834 - 105.407i) q^{23} +(-11.4483 + 69.8315i) q^{24} +(-78.1650 - 92.0230i) q^{25} +(-172.517 + 203.102i) q^{26} +(-4.36811 - 26.6443i) q^{27} +(26.8885 - 20.4401i) q^{28} +(143.576 + 211.759i) q^{29} +(15.9746 + 23.5607i) q^{30} +(-150.448 + 114.367i) q^{31} +(28.0148 + 170.883i) q^{32} +(130.823 - 154.017i) q^{33} +(274.716 + 323.421i) q^{34} +(0.858940 - 5.23930i) q^{35} +(55.3573 + 104.415i) q^{36} +(-209.484 + 46.1110i) q^{37} +(-468.210 + 157.758i) q^{38} +(-9.41532 + 173.655i) q^{39} +(-38.7606 - 29.4651i) q^{40} +(124.589 - 235.000i) q^{41} +(9.48963 - 34.1786i) q^{42} +(384.303 - 364.031i) q^{43} +(-327.395 + 821.699i) q^{44} +(17.6047 + 5.93172i) q^{45} +(545.215 + 59.2957i) q^{46} +(-295.213 + 136.580i) q^{47} +(-7.36261 - 6.97423i) q^{48} +(288.233 - 173.424i) q^{49} +(551.771 - 60.0087i) q^{50} +(270.461 + 59.5329i) q^{51} +(-203.649 - 733.476i) q^{52} +(205.327 + 123.541i) q^{53} +(112.644 + 52.1148i) q^{54} +(51.4638 + 129.164i) q^{55} +(3.28469 + 60.5825i) q^{56} +(-180.950 + 266.881i) q^{57} -1176.08 q^{58} +(12.0188 - 453.028i) q^{59} -81.3141 q^{60} +(282.636 - 416.857i) q^{61} +(-47.0321 - 867.456i) q^{62} +(-8.56843 - 21.5051i) q^{63} +(-746.986 - 345.592i) q^{64} +(-102.530 - 61.6902i) q^{65} +(248.516 + 895.074i) q^{66} +(122.606 + 26.9877i) q^{67} +(-1205.07 + 131.059i) q^{68} +(306.682 - 184.524i) q^{69} +(17.7186 + 16.7839i) q^{70} +(-255.374 + 118.149i) q^{71} +(-211.047 - 22.9527i) q^{72} +(-328.165 - 110.572i) q^{73} +(364.966 - 915.996i) q^{74} +(262.969 - 249.097i) q^{75} +(377.577 - 1359.91i) q^{76} +(81.1560 - 153.076i) q^{77} +(-636.433 - 483.804i) q^{78} +(29.1124 - 536.946i) q^{79} +(6.61246 - 2.22800i) q^{80} +(79.1063 - 17.4126i) q^{81} +(572.720 + 1080.26i) q^{82} +(128.203 - 782.001i) q^{83} +(65.5975 + 77.2273i) q^{84} +(-123.355 + 145.225i) q^{85} +(393.671 + 2401.28i) q^{86} +(-611.027 + 464.491i) q^{87} +(-891.657 - 1315.10i) q^{88} +(-132.412 - 195.293i) q^{89} +(-67.9840 + 51.6801i) q^{90} +(24.1229 + 147.143i) q^{91} +(-1014.21 + 1194.02i) q^{92} +(-367.034 - 432.106i) q^{93} +(241.906 - 1475.56i) q^{94} +(-103.918 - 196.010i) q^{95} +(-507.346 + 111.675i) q^{96} +(-117.215 + 39.4945i) q^{97} +(-83.7159 + 1544.05i) q^{98} +(482.622 + 366.880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{20}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.57971	+	3.80479i	−0.912065	+	1.34519i	0.0263386	+	0.999653i	$0.491615\pi$
$2$	−2.57971	+	3.80479i	−0.912065	+	1.34519i	−0.938403	+	0.345542i	$0.887695\pi$
$3$	0.162417	+	2.99560i	0.0312571	+	0.576504i
$3$	0.162417	+	2.99560i	0.0312571	+	0.576504i
$4$	−4.86039	−	12.1987i	−0.607549	−	1.52483i
$5$	−1.87335	−	0.866706i	−0.167558	−	0.0775206i	0.334317	−	0.942461i	$-0.391494\pi$
$5$	−1.87335	−	0.866706i	−0.167558	−	0.0775206i	−0.501875	+	0.864940i	$0.667356\pi$
$6$	−11.8166	−	7.10982i	−0.804018	−	0.483762i
$7$	0.688121	+	2.47839i	0.0371551	+	0.133820i	0.979802	−	0.199972i	$-0.0640852\pi$
$7$	0.688121	+	2.47839i	0.0371551	+	0.133820i	−0.942646	+	0.333793i	$0.891671\pi$
$8$	23.0364	+	5.07071i	1.01808	+	0.224096i
$9$	−8.94724	+	0.973071i	−0.331379	+	0.0360397i
$10$	8.13034	−	4.89186i	0.257104	−	0.154694i
$11$	−48.9029	−	46.3233i	−1.34043	−	1.26973i	−0.934564	−	0.355796i	$-0.884210\pi$
$11$	−48.9029	−	46.3233i	−1.34043	−	1.26973i	−0.405870	−	0.913931i	$-0.633032\pi$
$12$	35.7529	−	16.5411i	0.860081	−	0.397916i
$13$	57.6303	+	6.26768i	1.22952	+	0.133719i	0.699729	−	0.714409i	$-0.253304\pi$
$13$	57.6303	+	6.26768i	1.22952	+	0.133719i	0.529793	+	0.848127i	$0.322270\pi$
$14$	−11.2049	−	3.77537i	−0.213902	−	0.0720721i
$15$	2.29204	−	5.75259i	0.0394535	−	0.0990208i
$16$	−2.45420	+	2.32474i	−0.0383469	+	0.0363241i
$17$	24.6960	−	88.9470i	0.352333	−	1.26899i	−0.548985	−	0.835832i	$-0.684986\pi$
$17$	24.6960	−	88.9470i	0.352333	−	1.26899i	0.901318	−	0.433158i	$-0.142601\pi$
$18$	19.3789	−	36.5526i	0.253759	−	0.478640i
$19$	85.5643	+	65.0443i	1.03315	+	0.785378i	0.977042	−	0.213047i	$-0.0683388\pi$
$19$	85.5643	+	65.0443i	1.03315	+	0.785378i	0.0561049	+	0.998425i	$0.482132\pi$
$20$	−1.46742	+	27.0650i	−0.0164062	+	0.302595i
$21$	−7.31250	+	2.46387i	−0.0759866	+	0.0256029i
$22$	302.405	−	66.5644i	2.93059	−	0.645072i
$23$	−55.8834	−	105.407i	−0.506630	−	0.955606i	−0.996483	−	0.0838006i	$-0.973294\pi$
$23$	−55.8834	−	105.407i	−0.506630	−	0.955606i	0.489852	−	0.871805i	$-0.337051\pi$
$24$	−11.4483	+	69.8315i	−0.0973698	+	0.593929i
$25$	−78.1650	−	92.0230i	−0.625320	−	0.736184i
$26$	−172.517	+	203.102i	−1.30128	+	1.53199i
$27$	−4.36811	−	26.6443i	−0.0311350	−	0.189915i
$28$	26.8885	−	20.4401i	0.181480	−	0.137958i
$29$	143.576	+	211.759i	0.919361	+	1.35596i	0.934459	+	0.356070i	$0.115883\pi$
$29$	143.576	+	211.759i	0.919361	+	1.35596i	−0.0150984	+	0.999886i	$0.504806\pi$
$30$	15.9746	+	23.5607i	0.0972181	+	0.143386i
$31$	−150.448	+	114.367i	−0.871652	+	0.662613i	−0.942257	−	0.334891i	$-0.891300\pi$
$31$	−150.448	+	114.367i	−0.871652	+	0.662613i	0.0706043	+	0.997504i	$0.477507\pi$
$32$	28.0148	+	170.883i	0.154761	+	0.944002i
$33$	130.823	−	154.017i	0.690104	−	0.812453i
$34$	274.716	+	323.421i	1.38569	+	1.63136i
$35$	0.858940	−	5.23930i	0.00414821	−	0.0253029i
$36$	55.3573	+	104.415i	0.256284	+	0.483402i
$37$	−209.484	+	46.1110i	−0.930784	+	0.204881i	−0.654385	−	0.756162i	$-0.727072\pi$
$37$	−209.484	+	46.1110i	−0.930784	+	0.204881i	−0.276399	+	0.961043i	$0.589141\pi$
$38$	−468.210	+	157.758i	−1.99878	+	0.673468i
$39$	−9.41532	+	173.655i	−0.0386579	+	0.713003i
$40$	−38.7606	−	29.4651i	−0.153215	−	0.116471i
$41$	124.589	−	235.000i	0.474573	−	0.895141i	−0.524471	−	0.851429i	$-0.675737\pi$
$41$	124.589	−	235.000i	0.474573	−	0.895141i	0.999044	−	0.0437121i	$-0.0139184\pi$
$42$	9.48963	−	34.1786i	0.0348638	−	0.125568i
$43$	384.303	−	364.031i	1.36292	−	1.29103i	0.444307	−	0.895874i	$-0.353450\pi$
$43$	384.303	−	364.031i	1.36292	−	1.29103i	0.918615	−	0.395154i	$-0.129309\pi$
$44$	−327.395	+	821.699i	−1.12174	+	2.81536i
$45$	17.6047	+	5.93172i	0.0583190	+	0.0196500i
$46$	545.215	+	59.2957i	1.74756	+	0.190058i
$47$	−295.213	+	136.580i	−0.916197	+	0.423878i	−0.820574	−	0.571540i	$-0.806346\pi$
$47$	−295.213	+	136.580i	−0.916197	+	0.423878i	−0.0956229	+	0.995418i	$0.530484\pi$
$48$	−7.36261	−	6.97423i	−0.0221396	−	0.0209717i
$49$	288.233	−	173.424i	0.840330	−	0.505610i
$50$	551.771	−	60.0087i	1.56064	−	0.169730i
$51$	270.461	+	59.5329i	0.742590	+	0.163456i
$52$	−203.649	−	733.476i	−0.543096	−	1.95606i
$53$	205.327	+	123.541i	0.532147	+	0.320182i	0.756141	−	0.654408i	$-0.227082\pi$
$53$	205.327	+	123.541i	0.532147	+	0.320182i	−0.223995	+	0.974590i	$0.571910\pi$
$54$	112.644	+	52.1148i	0.283870	+	0.131332i
$55$	51.4638	+	129.164i	0.126170	+	0.316664i
$56$	3.28469	+	60.5825i	0.00783812	+	0.144566i
$57$	−180.950	+	266.881i	−0.420480	+	0.620161i
$58$	−1176.08			−2.66254
$59$	12.0188	−	453.028i	0.0265205	−	0.999648i
$59$	12.0188	−	453.028i	0.0265205	−	0.999648i
$60$	−81.3141			−0.174960
$61$	282.636	−	416.857i	0.593244	−	0.874969i	−0.405999	−	0.913873i	$-0.633076\pi$
$61$	282.636	−	416.857i	0.593244	−	0.874969i	0.999243	+	0.0389043i	$0.0123867\pi$
$62$	−47.0321	−	867.456i	−0.0963401	−	1.77689i
$63$	−8.56843	−	21.5051i	−0.0171353	−	0.0430063i
$64$	−746.986	−	345.592i	−1.45896	−	0.674985i
$65$	−102.530	−	61.6902i	−0.195650	−	0.117719i
$66$	248.516	+	895.074i	0.463488	+	1.66933i
$67$	122.606	+	26.9877i	0.223563	+	0.0492100i	0.325339	−	0.945597i	$-0.394522\pi$
$67$	122.606	+	26.9877i	0.223563	+	0.0492100i	−0.101776	+	0.994807i	$0.532453\pi$
$68$	−1205.07	+	131.059i	−2.14906	+	0.233724i
$69$	306.682	−	184.524i	0.535074	−	0.321944i
$70$	17.7186	+	16.7839i	0.0302540	+	0.0286581i
$71$	−255.374	+	118.149i	−0.426864	+	0.197488i	−0.621545	−	0.783378i	$-0.713495\pi$
$71$	−255.374	+	118.149i	−0.426864	+	0.197488i	0.194681	+	0.980867i	$0.437633\pi$
$72$	−211.047	−	22.9527i	−0.345446	−	0.0375695i
$73$	−328.165	−	110.572i	−0.526147	−	0.177280i	0.0436778	−	0.999046i	$-0.486093\pi$
$73$	−328.165	−	110.572i	−0.526147	−	0.177280i	−0.569825	+	0.821766i	$0.692989\pi$
$74$	364.966	−	915.996i	0.573330	−	1.43895i
$75$	262.969	−	249.097i	0.404867	−	0.383510i
$76$	377.577	−	1359.91i	0.569883	−	2.05253i
$77$	81.1560	−	153.076i	0.120111	−	0.226554i
$78$	−636.433	−	483.804i	−0.923870	−	0.702308i
$79$	29.1124	−	536.946i	0.0414607	−	0.764698i	−0.901700	−	0.432362i	$-0.857680\pi$
$79$	29.1124	−	536.946i	0.0414607	−	0.764698i	0.943161	−	0.332336i	$-0.107837\pi$
$80$	6.61246	−	2.22800i	0.00924119	−	0.00311372i
$81$	79.1063	−	17.4126i	0.108513	−	0.0238856i
$82$	572.720	+	1080.26i	0.771297	+	1.45482i
$83$	128.203	−	782.001i	0.169543	−	1.03417i	−0.755736	−	0.654877i	$-0.772720\pi$
$83$	128.203	−	782.001i	0.169543	−	1.03417i	0.925278	−	0.379289i	$-0.123831\pi$
$84$	65.5975	+	77.2273i	0.0852056	+	0.100312i
$85$	−123.355	+	145.225i	−0.157409	+	0.185316i
$86$	393.671	+	2401.28i	0.493612	+	3.01090i
$87$	−611.027	+	464.491i	−0.752977	+	0.572398i
$88$	−891.657	−	1315.10i	−1.08012	−	1.59306i
$89$	−132.412	−	195.293i	−0.157704	−	0.232596i	0.740626	−	0.671918i	$-0.234529\pi$
$89$	−132.412	−	195.293i	−0.157704	−	0.232596i	−0.898330	+	0.439322i	$0.855219\pi$
$90$	−67.9840	+	51.6801i	−0.0796238	+	0.0605284i
$91$	24.1229	+	147.143i	0.0277887	+	0.169503i
$92$	−1014.21	+	1194.02i	−1.14934	+	1.35310i
$93$	−367.034	−	432.106i	−0.409244	−	0.481799i
$94$	241.906	−	1475.56i	0.265433	−	1.61907i
$95$	−103.918	−	196.010i	−0.112229	−	0.211686i
$96$	−507.346	+	111.675i	−0.539383	+	0.118727i
$97$	−117.215	+	39.4945i	−0.122695	+	0.0413408i	−0.379979	−	0.924995i	$-0.624069\pi$
$97$	−117.215	+	39.4945i	−0.122695	+	0.0413408i	0.257284	+	0.966336i	$0.417172\pi$
$98$	−83.7159	+	1544.05i	−0.0862917	+	1.59156i
$99$	482.622	+	366.880i	0.489953	+	0.372452i
$100$	−742.645	+	1400.78i	−0.742645	+	1.40078i
$101$	216.205	−	778.702i	0.213002	−	0.767166i	−0.777406	−	0.628999i	$-0.783465\pi$
$101$	216.205	−	778.702i	0.213002	−	0.767166i	0.990409	−	0.138167i	$-0.0441211\pi$
$102$	−924.220	+	875.468i	−0.897171	+	0.849846i
$103$	645.125	−	1619.14i	0.617146	−	1.54892i	−0.204466	−	0.978874i	$-0.565546\pi$
$103$	645.125	−	1619.14i	0.617146	−	1.54892i	0.821612	−	0.570047i	$-0.193075\pi$
$104$	1295.82	+	436.611i	1.22178	+	0.411666i
$105$	15.8344	+	1.72209i	0.0147169	+	0.00160056i
$106$	−999.729	+	462.524i	−0.916060	+	0.423814i
$107$	−834.561	−	790.538i	−0.754019	−	0.714245i	0.210693	−	0.977552i	$-0.432428\pi$
$107$	−834.561	−	790.538i	−0.754019	−	0.714245i	−0.964712	+	0.263308i	$0.915187\pi$
$108$	−303.794	+	182.787i	−0.270672	+	0.162858i
$109$	−343.987	+	37.4108i	−0.302275	+	0.0328744i	−0.258000	−	0.966145i	$-0.583063\pi$
$109$	−343.987	+	37.4108i	−0.302275	+	0.0328744i	−0.0442752	+	0.999019i	$0.514098\pi$
$110$	−624.204	−	137.398i	−0.541050	−	0.119094i
$111$	−172.154	−	620.042i	−0.147208	−	0.530196i
$112$	−7.45041	−	4.48276i	−0.00628569	−	0.00378197i
$113$	−88.1038	−	40.7612i	−0.0733461	−	0.0339335i	0.382873	−	0.923801i	$-0.374935\pi$
$113$	−88.1038	−	40.7612i	−0.0733461	−	0.0339335i	−0.456219	+	0.889867i	$0.650797\pi$
$114$	−548.626	−	1376.95i	−0.450733	−	1.13125i
$115$	13.3323	+	245.900i	0.0108108	+	0.199394i
$116$	1885.34	−	2780.67i	1.50905	−	2.22568i
$117$	−521.731			−0.412257
$118$	1692.67	+	1214.41i	1.32053	+	0.947419i
$119$	237.439			0.182908
$120$	81.9702	−	120.897i	0.0623568	−	0.0919694i
$121$	173.588	+	3201.64i	0.130419	+	2.40544i
$122$	856.934	+	2150.74i	0.635927	+	1.59606i
$123$	724.200	+	335.051i	0.530886	+	0.245614i
$124$	2126.37	+	1279.39i	1.53995	+	0.926555i
$125$	135.701	+	488.749i	0.0970995	+	0.349721i
$126$	103.927	+	22.8760i	0.0734803	+	0.0161742i
$127$	−611.766	+	66.5336i	−0.427444	+	0.0464874i	−0.319313	−	0.947649i	$-0.603452\pi$
$127$	−611.766	+	66.5336i	−0.427444	+	0.0464874i	−0.108131	+	0.994137i	$0.534487\pi$
$128$	2054.90	−	1236.39i	1.41898	−	0.853770i
$129$	1152.91	+	1092.09i	0.786884	+	0.745376i
$130$	499.215	−	230.961i	0.336800	−	0.155820i
$131$	2581.17	+	280.719i	1.72151	+	0.187225i	0.914850	−	0.403794i	$-0.132309\pi$
$131$	2581.17	+	280.719i	1.72151	+	0.187225i	0.806658	+	0.591019i	$0.201274\pi$
$132$	−2514.66	−	847.286i	−1.65813	−	0.558688i
$133$	−102.326	+	256.820i	−0.0667129	+	0.167437i
$134$	−418.970	+	396.870i	−0.270101	+	0.255853i
$135$	−14.9098	+	53.7001i	−0.00950540	+	0.0342353i
$136$	1019.93	−	1923.80i	0.643077	−	1.21297i
$137$	166.582	+	126.632i	0.103883	+	0.0789701i	0.655826	−	0.754912i	$-0.272320\pi$
$137$	166.582	+	126.632i	0.103883	+	0.0789701i	−0.551943	+	0.833882i	$0.686113\pi$
$138$	−89.0742	+	1642.88i	−0.0549456	+	1.01341i
$139$	−935.072	+	315.063i	−0.570589	+	0.192254i	−0.589783	−	0.807562i	$-0.700787\pi$
$139$	−935.072	+	315.063i	−0.570589	+	0.192254i	0.0191940	+	0.999816i	$0.493890\pi$
$140$	−68.0872	+	14.9871i	−0.0411030	+	0.00904746i
$141$	−457.087	−	862.158i	−0.273005	−	0.514942i
$142$	209.261	−	1276.43i	0.123667	−	0.754337i
$143$	−2527.95	−	2976.13i	−1.47831	−	1.74040i
$144$	19.6962	−	23.1882i	0.0113983	−	0.0134191i
$145$	−85.4364	−	521.139i	−0.0489318	−	0.298471i
$146$	1267.27	−	963.354i	0.718356	−	0.546080i
$147$	566.323	+	835.264i	0.317752	+	0.468649i
$148$	1580.67	+	2331.31i	0.877906	+	1.29481i
$149$	−679.307	+	516.396i	−0.373497	+	0.283925i	−0.775036	−	0.631917i	$-0.782268\pi$
$149$	−679.307	+	516.396i	−0.373497	+	0.283925i	0.401539	+	0.915842i	$0.368475\pi$
$150$	269.379	+	1643.14i	0.146631	+	0.894411i
$151$	−2.34457	+	2.76024i	−0.00126357	+	0.00148758i	−0.762793	−	0.646642i	$-0.776173\pi$
$151$	−2.34457	+	2.76024i	−0.00126357	+	0.00148758i	0.761530	+	0.648130i	$0.224449\pi$
$152$	1641.28	+	1932.26i	0.875823	+	1.03110i
$153$	−134.410	+	819.862i	−0.0710220	+	0.433215i
$154$	373.064	+	703.673i	0.195210	+	0.368205i
$155$	380.965	−	83.8568i	0.197418	−	0.0434551i
$156$	2164.13	−	729.179i	1.11070	−	0.374238i
$157$	−50.4668	+	930.806i	−0.0256541	+	0.473162i	0.957275	+	0.289178i	$0.0933821\pi$
$157$	−50.4668	+	930.806i	−0.0256541	+	0.473162i	−0.982929	+	0.183983i	$0.941101\pi$
$158$	1967.86	+	1495.93i	0.990853	+	0.753227i
$159$	−336.731	+	635.141i	−0.167953	+	0.316792i
$160$	95.6234	−	344.404i	0.0472481	−	0.170172i
$161$	222.786	−	211.034i	0.109056	−	0.103303i
$162$	−137.820	+	345.902i	−0.0668404	+	0.167757i
$163$	−3435.61	−	1157.59i	−1.65090	−	0.556254i	−0.668612	−	0.743611i	$-0.733111\pi$
$163$	−3435.61	−	1157.59i	−1.65090	−	0.556254i	−0.982292	+	0.187357i	$0.940008\pi$
$164$	−3472.23	−	377.628i	−1.65327	−	0.179804i
$165$	−378.566	+	175.143i	−0.178614	+	0.0826357i
$166$	2644.62	+	2505.12i	1.23652	+	1.17129i
$167$	1307.97	−	786.977i	0.606068	−	0.364659i	−0.179202	−	0.983812i	$-0.557352\pi$
$167$	1307.97	−	786.977i	0.606068	−	0.364659i	0.785270	+	0.619153i	$0.212524\pi$
$168$	−180.948	+	19.6792i	−0.0830976	+	0.00903741i
$169$	1136.34	+	250.127i	0.517222	+	0.113849i
$170$	−234.330	−	843.979i	−0.105719	−	0.380766i
$171$	−828.857	−	498.707i	−0.370668	−	0.223024i
$172$	−6308.56	−	2918.65i	−2.79664	−	1.29387i
$173$	541.340	+	1358.66i	0.237904	+	0.597093i	0.998649	−	0.0519571i	$-0.0165459\pi$
$173$	541.340	+	1358.66i	0.237904	+	0.597093i	−0.760746	+	0.649050i	$0.775167\pi$
$174$	−191.016	−	3523.08i	−0.0832234	−	1.53496i
$175$	174.282	−	257.046i	0.0752826	−	0.111034i
$176$	227.707			0.0975232
$177$	1359.04	−	37.5759i	0.577130	−	0.0159569i
$178$	1084.63			0.456723
$179$	−1774.52	+	2617.22i	−0.740970	+	1.09285i	0.251198	+	0.967936i	$0.419176\pi$
$179$	−1774.52	+	2617.22i	−0.740970	+	1.09285i	−0.992168	+	0.124913i	$0.960135\pi$
$180$	−13.2068	−	243.585i	−0.00546875	−	0.100865i
$181$	−232.019	−	582.323i	−0.0952808	−	0.239137i	0.873609	−	0.486628i	$-0.161773\pi$
$181$	−232.019	−	582.323i	−0.0952808	−	0.239137i	−0.968890	+	0.247491i	$0.920394\pi$
$182$	−622.079	−	287.804i	−0.253360	−	0.117217i
$183$	1294.64	+	778.961i	0.522966	+	0.314658i
$184$	−752.866	−	2711.58i	−0.301641	−	1.08641i
$185$	432.403	+	95.1791i	0.171843	+	0.0378254i
$186$	2590.91	−	281.779i	1.02137	−	0.111081i
$187$	−5328.03	+	3205.77i	−2.08355	+	1.25363i
$188$	3100.95	+	2937.37i	1.20298	+	1.13952i
$189$	63.0292	−	29.1604i	0.0242577	−	0.0112228i
$190$	1013.85	+	110.263i	0.387120	+	0.0421018i
$191$	−3099.04	−	1044.19i	−1.17403	−	0.395575i	−0.336347	−	0.941738i	$-0.609191\pi$
$191$	−3099.04	−	1044.19i	−1.17403	−	0.395575i	−0.837679	+	0.546163i	$0.816088\pi$
$192$	913.934	−	2293.80i	0.343529	−	0.862192i
$193$	3542.10	−	3355.25i	1.32107	−	1.25138i	0.375153	−	0.926963i	$-0.377590\pi$
$193$	3542.10	−	3355.25i	1.32107	−	1.25138i	0.945914	−	0.324418i	$-0.105168\pi$
$194$	152.114	−	547.864i	0.0562944	−	0.202754i
$195$	168.146	−	317.158i	0.0617498	−	0.116473i
$196$	−3516.47	−	2673.15i	−1.28151	−	0.974180i
$197$	7.55129	−	139.275i	0.00273100	−	0.0503703i	−0.996850	−	0.0793068i	$-0.974729\pi$
$197$	7.55129	−	139.275i	0.00273100	−	0.0503703i	0.999581	+	0.0289365i	$0.00921207\pi$
$198$	−2640.92	+	889.830i	−0.947889	+	0.319381i
$199$	−621.527	+	136.808i	−0.221401	+	0.0487342i	−0.324286	−	0.945959i	$-0.605124\pi$
$199$	−621.527	+	136.808i	−0.221401	+	0.0487342i	0.102884	+	0.994693i	$0.467193\pi$
$200$	−1334.02	−	2516.23i	−0.471648	−	0.889623i
$201$	−60.9309	+	371.662i	−0.0213818	+	0.130423i
$202$	2405.05	+	2831.44i	0.837715	+	0.986234i
$203$	−426.024	+	501.554i	−0.147296	+	0.173410i
$204$	−588.323	−	3588.61i	−0.201916	−	1.23163i
$205$	−437.075	+	332.256i	−0.148910	+	0.113199i
$206$	4496.25	+	6631.48i	1.52072	+	2.24290i
$207$	602.571	+	888.726i	0.202327	+	0.298409i
$208$	−156.007	+	118.594i	−0.0520056	+	0.0395336i
$209$	−1171.28	−	7144.47i	−0.387650	−	2.36456i
$210$	−47.4002	+	55.8038i	−0.0155758	+	0.0183373i
$211$	1350.27	+	1589.67i	0.440553	+	0.518659i	0.936963	−	0.349429i	$-0.113624\pi$
$211$	1350.27	+	1589.67i	0.440553	+	0.518659i	−0.496410	+	0.868088i	$0.665349\pi$
$212$	509.066	−	3105.17i	0.164919	−	1.00596i
$213$	−395.403	−	745.810i	−0.127195	−	0.239916i
$214$	5160.75	−	1135.97i	1.64851	−	0.362865i
$215$	−1035.44	+	348.882i	−0.328450	+	0.110668i
$216$	34.4797	−	635.940i	0.0108613	−	0.200325i
$217$	−386.973	−	294.169i	−0.121057	−	0.0920255i
$218$	745.046	−	1405.31i	0.231472	−	0.436602i
$219$	277.929	−	1001.01i	0.0857565	−	0.308867i
$220$	1325.50	−	1255.58i	0.406205	−	0.384778i
$221$	1980.73	−	4971.26i	0.602889	−	1.51314i
$222$	2803.23	+	944.519i	0.847481	+	0.285550i
$223$	−2349.75	−	255.550i	−0.705609	−	0.0767396i	−0.251723	−	0.967799i	$-0.580997\pi$
$223$	−2349.75	−	255.550i	−0.705609	−	0.0767396i	−0.453886	+	0.891060i	$0.649963\pi$
$224$	−404.236	+	187.019i	−0.120577	+	0.0557846i
$225$	788.906	+	747.292i	0.233750	+	0.221420i
$226$	382.370	−	230.064i	0.112544	−	0.0677152i
$227$	−5616.51	+	610.832i	−1.64221	+	0.178601i	−0.882056	−	0.471145i	$-0.843841\pi$
$227$	−5616.51	+	610.832i	−1.64221	+	0.178601i	−0.760151	+	0.649746i	$0.774875\pi$
$228$	4135.07	+	910.198i	1.20110	+	0.264383i
$229$	−1754.15	−	6317.88i	−0.506190	−	1.82313i	−0.565307	−	0.824881i	$-0.691242\pi$
$229$	−1754.15	−	6317.88i	−0.506190	−	1.82313i	0.0591171	−	0.998251i	$-0.481171\pi$
$230$	−969.989	−	583.623i	−0.278083	−	0.167317i
$231$	471.737	+	218.249i	0.134364	+	0.0621632i
$232$	2233.72	+	5606.22i	0.632116	+	1.58649i
$233$	152.768	+	2817.64i	0.0429535	+	0.792231i	0.938080	+	0.346419i	$0.112602\pi$
$233$	152.768	+	2817.64i	0.0429535	+	0.792231i	−0.895126	+	0.445812i	$0.852915\pi$
$234$	1345.92	−	1985.08i	0.376005	−	0.554566i
$235$	671.414			0.186375
$236$	−5584.75	+	2055.28i	−1.54041	+	0.566896i
$237$	1613.20			0.442147
$238$	−612.524	+	903.405i	−0.166824	+	0.246046i
$239$	360.046	+	6640.67i	0.0974455	+	1.79728i	0.484060	+	0.875035i	$0.339162\pi$
$239$	360.046	+	6640.67i	0.0974455	+	1.79728i	−0.386615	+	0.922241i	$0.626356\pi$
$240$	7.74816	+	19.4464i	0.00208392	+	0.00523025i
$241$	5114.78	+	2366.35i	1.36710	+	0.632489i	0.959769	−	0.280791i	$-0.0905966\pi$
$241$	5114.78	+	2366.35i	1.36710	+	0.632489i	0.407333	+	0.913280i	$0.366459\pi$
$242$	−12629.3	−	7598.82i	−3.35473	−	2.01847i
$243$	65.0094	+	234.143i	0.0171620	+	0.0618118i
$244$	−6458.83	−	1421.70i	−1.69461	−	0.373011i
$245$	−690.271	+	75.0714i	−0.179999	+	0.0195761i
$246$	−3143.02	+	1891.09i	−0.814600	+	0.490129i
$247$	4523.42	+	4284.81i	1.16526	+	1.10379i
$248$	−4045.71	+	1871.74i	−1.03590	+	0.479257i
$249$	2363.38	+	257.034i	0.601500	+	0.0654170i
$250$	−2209.65	−	744.519i	−0.559003	−	0.188350i
$251$	2258.91	−	5669.43i	0.568051	−	1.42570i	−0.311660	−	0.950194i	$-0.600885\pi$
$251$	2258.91	−	5669.43i	0.568051	−	1.42570i	0.879711	−	0.475508i	$-0.157736\pi$
$252$	−220.688	+	209.047i	−0.0551668	+	0.0522568i
$253$	−2149.95	+	7743.42i	−0.534254	+	1.92421i
$254$	1325.03	−	2499.28i	0.327322	−	0.617396i
$255$	−455.072	−	345.936i	−0.111756	−	0.0849544i
$256$	−240.360	+	4433.18i	−0.0586817	+	1.08232i
$257$	3124.54	−	1052.78i	0.758380	−	0.255528i	0.0865644	−	0.996246i	$-0.472411\pi$
$257$	3124.54	−	1052.78i	0.758380	−	0.255528i	0.671816	+	0.740718i	$0.265515\pi$
$258$	−7129.35	+	1569.29i	−1.72036	+	0.378681i
$259$	−258.432	−	487.454i	−0.0620006	−	0.116946i
$260$	−254.202	+	1550.57i	−0.0606344	+	0.369854i
$261$	−1490.67	−	1754.95i	−0.353525	−	0.416202i
$262$	−7726.73	+	9096.61i	−1.82198	+	2.14500i
$263$	723.094	+	4410.68i	0.169536	+	1.03412i	0.925288	+	0.379265i	$0.123823\pi$
$263$	723.094	+	4410.68i	0.169536	+	1.03412i	−0.755752	+	0.654858i	$0.772729\pi$
$264$	3794.68	−	2884.64i	0.884646	−	0.672490i
$265$	−277.576	−	409.394i	−0.0643447	−	0.0949014i
$266$	−713.172	−	1051.85i	−0.164389	−	0.242455i
$267$	563.515	−	428.373i	0.129163	−	0.0981872i
$268$	−266.701	−	1626.80i	−0.0607886	−	0.370794i
$269$	−1909.53	+	2248.07i	−0.432810	+	0.509544i	−0.934724	−	0.355374i	$-0.884354\pi$
$269$	−1909.53	+	2248.07i	−0.432810	+	0.509544i	0.501914	+	0.864918i	$0.332629\pi$
$270$	−165.855	−	195.259i	−0.0373837	−	0.0440115i
$271$	−45.6397	+	278.390i	−0.0102303	+	0.0624021i	−0.991448	−	0.130500i	$-0.958342\pi$
$271$	−45.6397	+	278.390i	−0.0102303	+	0.0624021i	0.981218	+	0.192902i	$0.0617900\pi$
$272$	146.170	+	275.706i	0.0325840	+	0.0614600i
$273$	−436.865	+	96.1612i	−0.0968507	+	0.0213185i
$274$	−911.540	+	307.134i	−0.200979	+	0.0677176i
$275$	−440.310	+	8121.05i	−0.0965517	+	1.78079i
$276$	−3741.54	−	2844.25i	−0.815994	−	0.620303i
$277$	−3504.25	+	6609.73i	−0.760109	+	1.43372i	0.136382	+	0.990656i	$0.456453\pi$
$277$	−3504.25	+	6609.73i	−0.760109	+	1.43372i	−0.896491	+	0.443062i	$0.853892\pi$
$278$	1213.47	−	4370.52i	0.261795	−	0.942901i
$279$	1234.81	−	1169.67i	0.264967	−	0.250990i
$280$	46.3539	−	116.339i	0.00989347	−	0.0248307i
$281$	858.643	+	289.311i	0.182286	+	0.0614193i	0.408964	−	0.912550i	$-0.365890\pi$
$281$	858.643	+	289.311i	0.182286	+	0.0614193i	−0.226678	+	0.973970i	$0.572787\pi$
$282$	4459.48	+	484.997i	0.941695	+	0.102416i
$283$	2280.61	−	1055.12i	0.479039	−	0.221627i	−0.165483	−	0.986213i	$-0.552918\pi$
$283$	2280.61	−	1055.12i	0.479039	−	0.221627i	0.644522	+	0.764585i	$0.277056\pi$
$284$	2682.47	+	2540.97i	0.560477	+	0.530912i
$285$	570.290	−	343.132i	0.118530	−	0.0713171i
$286$	17844.9	−	1940.75i	3.68948	−	0.401256i
$287$	668.152	+	147.071i	0.137421	+	0.0302486i
$288$	−416.936	−	1501.67i	−0.0853062	−	0.307245i
$289$	−3091.94	−	1860.36i	−0.629339	−	0.378661i
$290$	2203.22	+	1019.32i	0.446130	+	0.206402i
$291$	−137.347	−	344.716i	−0.0276682	−	0.0694419i
$292$	246.184	+	4540.59i	0.0493384	+	0.909993i
$293$	1306.04	−	1926.26i	0.260408	−	0.384073i	−0.674899	−	0.737910i	$-0.735813\pi$
$293$	1306.04	−	1926.26i	0.260408	−	0.384073i	0.935307	+	0.353837i	$0.115123\pi$
$294$	−4638.95			−0.920235
$295$	−415.158	+	838.266i	−0.0819370	+	0.165443i
$296$	−5059.59			−0.993522
$297$	−1020.64	+	1505.33i	−0.199406	+	0.294101i
$298$	−212.361	−	3916.77i	−0.0412810	−	0.761384i
$299$	−2559.92	−	6424.92i	−0.495131	−	1.24268i
$300$	−4316.78	−	1997.16i	−0.830765	−	0.384353i
$301$	1166.66	+	701.955i	0.223405	+	0.134419i
$302$	−4.45382	−	16.0412i	−0.000848637	−	0.00305651i
$303$	2367.79	+	521.191i	0.448931	+	0.0988173i
$304$	−361.203	+	39.2832i	−0.0681461	+	0.00741134i
$305$	−890.771	+	535.959i	−0.167231	+	0.100619i
$306$	−2772.66	−	2626.40i	−0.517982	−	0.490659i
$307$	−4357.57	+	2016.03i	−0.810097	+	0.374791i	−0.780801	−	0.624780i	$-0.785189\pi$
$307$	−4357.57	+	2016.03i	−0.810097	+	0.374791i	−0.0292960	+	0.999571i	$0.509327\pi$
$308$	−2261.78	−	245.983i	−0.418431	−	0.0455071i
$309$	4955.08	+	1669.56i	0.912249	+	0.307372i
$310$	−663.722	+	1665.82i	−0.121603	+	0.305200i
$311$	−4399.13	+	4167.08i	−0.802096	+	0.759786i	−0.974295	−	0.225276i	$-0.927672\pi$
$311$	−4399.13	+	4167.08i	−0.802096	+	0.759786i	0.172199	+	0.985062i	$0.444913\pi$
$312$	−1097.45	+	3952.66i	−0.199138	+	0.717229i
$313$	816.426	−	1539.94i	0.147435	−	0.278092i	−0.798785	−	0.601617i	$-0.794523\pi$
$313$	816.426	−	1539.94i	0.147435	−	0.278092i	0.946220	+	0.323525i	$0.104868\pi$
$314$	−3411.33	−	2593.22i	−0.613097	−	0.466064i
$315$	−2.58693	+	47.7131i	−0.000462720	+	0.00853437i
$316$	−6691.52	+	2254.64i	−1.19123	+	0.401371i
$317$	3047.71	−	670.851i	0.539989	−	0.118860i	0.0634021	−	0.997988i	$-0.479805\pi$
$317$	3047.71	−	670.851i	0.539989	−	0.118860i	0.476586	+	0.879128i	$0.341874\pi$
$318$	−1547.91	−	2919.67i	−0.272964	−	0.514864i
$319$	2788.09	−	17006.6i	0.489351	−	2.98491i
$320$	1099.84	+	1294.83i	0.192135	+	0.226198i
$321$	2232.59	−	2628.41i	0.388196	−	0.457020i
$322$	228.216	+	1392.06i	0.0394969	+	0.240920i
$323$	7898.59	−	6004.35i	1.36065	−	1.03434i
$324$	−596.898	−	880.359i	−0.102349	−	0.150953i
$325$	−3927.91	−	5793.23i	−0.670403	−	0.988771i
$326$	13267.2	−	10085.5i	2.25400	−	1.71345i
$327$	−167.937	−	1024.37i	−0.0284004	−	0.173235i
$328$	4061.70	−	4781.80i	0.683749	−	0.804972i
$329$	−541.641	−	637.669i	−0.0907649	−	0.106857i
$330$	310.207	−	1892.18i	0.0517465	−	0.315640i
$331$	2365.30	+	4461.42i	0.392775	+	0.740852i	0.998496	−	0.0548250i	$-0.0174601\pi$
$331$	2365.30	+	4461.42i	0.392775	+	0.740852i	−0.605721	+	0.795677i	$0.707115\pi$
$332$	−10162.5	+	2236.93i	−1.67994	+	0.369782i
$333$	1829.44	−	616.409i	0.301059	−	0.101438i
$334$	−379.892	+	7006.70i	−0.0622359	+	1.14787i
$335$	−206.294	−	156.821i	−0.0336450	−	0.0255762i
$336$	12.2185	−	23.0465i	0.00198385	−	0.00374194i
$337$	−16.3602	+	58.9240i	−0.00264450	+	0.00952461i	−0.964860	−	0.262763i	$-0.915366\pi$
$337$	−16.3602	+	58.9240i	−0.00264450	+	0.00952461i	0.962216	+	0.272287i	$0.0877801\pi$
$338$	−3883.10	+	3678.27i	−0.624890	+	0.591927i
$339$	107.795	−	270.544i	0.0172702	−	0.0433449i
$340$	2371.11	+	798.919i	0.378210	+	0.127434i
$341$	12655.2	+	1376.34i	2.00973	+	0.218571i
$342$	4035.68	−	1867.10i	0.638084	−	0.295209i
$343$	1268.66	+	1201.74i	0.199712	+	0.189177i
$344$	10698.9	−	6437.30i	1.67687	−	1.00894i
$345$	−734.452	+	79.8765i	−0.114613	+	0.0124649i
$346$	−6565.91	−	1445.27i	−1.02019	−	0.224561i
$347$	−1545.47	−	5566.29i	−0.239093	−	0.861136i	−0.981544	−	0.191236i	$-0.938750\pi$
$347$	−1545.47	−	5566.29i	−0.239093	−	0.861136i	0.742451	−	0.669901i	$-0.233663\pi$
$348$	8636.00	+	5196.11i	1.33028	+	0.800404i
$349$	8312.37	+	3845.71i	1.27493	+	0.589846i	0.936342	−	0.351088i	$-0.114188\pi$
$349$	8312.37	+	3845.71i	1.27493	+	0.589846i	0.338589	+	0.940934i	$0.390050\pi$
$350$	528.410	+	1326.21i	0.0806991	+	0.202540i
$351$	−84.7379	−	1562.90i	−0.0128860	−	0.237668i
$352$	6545.84	−	9654.39i	0.991177	−	1.46188i
$353$	−941.280			−0.141924			−0.0709622	−	0.997479i	$-0.522607\pi$
$353$	−941.280			−0.141924			−0.0709622	+	0.997479i	$0.522607\pi$
$354$	−3362.97	+	5267.80i	−0.504914	+	0.790906i
$355$	580.807			0.0868338
$356$	−1738.74	+	2564.45i	−0.258857	+	0.381786i
$357$	38.5641	+	711.273i	0.00571717	+	0.105447i
$358$	−5380.21	−	13503.3i	−0.794282	−	1.99350i
$359$	9328.09	+	4315.64i	1.37136	+	0.634458i	0.960766	−	0.277360i	$-0.0894595\pi$
$359$	9328.09	+	4315.64i	1.37136	+	0.634458i	0.410593	+	0.911819i	$0.365322\pi$
$360$	375.472	+	225.914i	0.0549698	+	0.0330742i
$361$	1255.51	+	4521.94i	0.183046	+	0.659271i
$362$	2814.16	+	619.443i	0.408588	+	0.0899370i
$363$	−9562.63	+	1040.00i	−1.38267	+	0.150374i
$364$	1677.70	−	1009.44i	0.241581	−	0.145355i
$365$	518.936	+	491.562i	0.0744173	+	0.0704919i
$366$	−6303.58	+	2916.35i	−0.900255	+	0.416502i
$367$	−13244.5	−	1440.42i	−1.88380	−	0.204876i	−0.907316	−	0.420449i	$-0.861872\pi$
$367$	−13244.5	−	1440.42i	−1.88380	−	0.204876i	−0.976488	+	0.215573i	$0.930838\pi$
$368$	382.194	+	128.776i	0.0541392	+	0.0182416i
$369$	−886.055	+	2223.83i	−0.125003	+	0.313735i
$370$	−1477.61	+	1399.67i	−0.207614	+	0.196663i
$371$	−164.893	+	593.890i	−0.0230750	+	0.0831085i
$372$	−3487.19	+	6577.54i	−0.486028	+	0.916746i
$373$	−3376.41	−	2566.68i	−0.468697	−	0.356294i	0.344011	−	0.938966i	$-0.388214\pi$
$373$	−3376.41	−	2566.68i	−0.468697	−	0.356294i	−0.812708	+	0.582672i	$0.802007\pi$
$374$	1547.50	−	28541.9i	0.213955	−	3.94617i
$375$	−1442.06	+	485.886i	−0.198580	+	0.0669094i
$376$	−7493.22	+	1649.38i	−1.02775	+	0.226225i
$377$	6947.12	+	13103.7i	0.949058	+	1.79011i
$378$	−51.6478	+	315.038i	−0.00702772	+	0.0428672i
$379$	3234.29	+	3807.70i	0.438349	+	0.516064i	0.936329	−	0.351124i	$-0.114201\pi$
$379$	3234.29	+	3807.70i	0.438349	+	0.516064i	−0.497980	+	0.867189i	$0.665925\pi$
$380$	−1885.98	+	2220.35i	−0.254602	+	0.299740i
$381$	−298.669	−	1821.80i	−0.0401608	−	0.244970i
$382$	11967.5	−	9097.49i	1.60291	−	1.21850i
$383$	3418.42	+	5041.79i	0.456065	+	0.672646i	0.984310	−	0.176446i	$-0.0564601\pi$
$383$	3418.42	+	5041.79i	0.456065	+	0.672646i	−0.528245	+	0.849092i	$0.677150\pi$
$384$	4037.48	+	5954.84i	0.536555	+	0.791359i
$385$	−284.706	+	216.428i	−0.0376882	+	0.0286498i
$386$	3628.44	+	22132.5i	0.478453	+	2.91843i
$387$	−3084.22	+	3631.03i	−0.405116	+	0.476939i
$388$	1051.49	+	1237.91i	0.137581	+	0.161973i
$389$	657.783	−	4012.30i	0.0857351	−	0.522961i	−0.908686	−	0.417480i	$-0.862913\pi$
$389$	657.783	−	4012.30i	0.0857351	−	0.522961i	0.994421	−	0.105481i	$-0.0336383\pi$
$390$	772.949	+	1457.94i	0.100358	+	0.189296i
$391$	−10755.8	+	2367.52i	−1.39116	+	0.306217i
$392$	7519.25	−	2533.53i	0.968825	−	0.326435i
$393$	−421.697	+	7777.73i	−0.0541267	+	0.998307i
$394$	510.432	+	388.021i	0.0652670	+	0.0496147i
$395$	−519.912	+	980.659i	−0.0662269	+	0.124917i
$396$	2129.71	−	7670.52i	0.270257	−	0.973379i
$397$	1289.74	−	1221.71i	0.163048	−	0.154447i	−0.601826	−	0.798627i	$-0.705560\pi$
$397$	1289.74	−	1221.71i	0.163048	−	0.154447i	0.764874	+	0.644180i	$0.222801\pi$
$398$	1082.83	−	2717.70i	0.136376	−	0.342277i
$399$	−785.949	−	264.817i	−0.0986132	−	0.0332267i
$400$	405.762	+	44.1293i	0.0507203	+	0.00551617i
$401$	224.110	−	103.684i	0.0279090	−	0.0129121i	−0.405885	−	0.913924i	$-0.633037\pi$
$401$	224.110	−	103.684i	0.0279090	−	0.0129121i	0.433794	+	0.901012i	$0.357175\pi$
$402$	−1256.91	−	1190.61i	−0.155943	−	0.147717i
$403$	−9387.18	+	5648.08i	−1.16032	+	0.698141i
$404$	−10550.0	+	1147.38i	−1.29921	+	0.141297i
$405$	−163.286	−	35.9419i	−0.0200339	−	0.00440980i
$406$	−809.288	−	2914.79i	−0.0989269	−	0.356302i
$407$	12380.4	+	7449.04i	1.50780	+	0.907212i
$408$	5928.58	+	2742.85i	0.719384	+	0.332822i
$409$	−2203.61	−	5530.65i	−0.266410	−	0.668638i	0.733529	−	0.679658i	$-0.237872\pi$
$409$	−2203.61	−	5530.65i	−0.266410	−	0.668638i	−0.999939	+	0.0110194i	$0.996492\pi$
$410$	−136.636	−	2520.10i	−0.0164584	−	0.303558i
$411$	−352.283	+	519.579i	−0.0422795	+	0.0623575i
$412$	−22886.9			−2.73679
$413$	1131.05	−	281.951i	0.134759	−	0.0335930i
$414$	−4935.87			−0.585954
$415$	−917.934	+	1353.85i	−0.108577	+	0.160140i
$416$	543.464	+	10023.6i	0.0640518	+	1.18137i
$417$	−1095.67	−	2749.93i	−0.128670	−	0.322937i
$418$	30204.7	+	13974.2i	3.53436	+	1.63517i
$419$	7994.70	+	4810.25i	0.932140	+	0.560850i	0.898687	−	0.438590i	$-0.144522\pi$
$419$	7994.70	+	4810.25i	0.932140	+	0.560850i	0.0334529	+	0.999440i	$0.489350\pi$
$420$	−55.9540	−	201.528i	−0.00650065	−	0.0234132i
$421$	1595.00	+	351.086i	0.184645	+	0.0406435i	0.306330	−	0.951925i	$-0.400899\pi$
$421$	1595.00	+	351.086i	0.184645	+	0.0406435i	−0.121685	+	0.992569i	$0.538830\pi$
$422$	−9531.65	+	1036.63i	−1.09951	+	0.119579i
$423$	2508.44	−	1509.28i	0.288332	−	0.173484i
$424$	4103.56	+	3887.09i	0.470015	+	0.445222i
$425$	−10115.5	+	4679.95i	−1.15453	+	0.534143i
$426$	3857.67	+	419.547i	0.438744	+	0.0477162i
$427$	1227.62	+	413.634i	0.139131	+	0.0468786i
$428$	−5587.21	+	14022.8i	−0.631000	+	1.58369i
$429$	8504.72	−	8056.10i	0.957138	−	0.906649i
$430$	1343.72	−	4839.65i	0.150698	−	0.542765i
$431$	3905.14	−	7365.88i	0.436437	−	0.823207i	−0.563559	−	0.826076i	$-0.690568\pi$
$431$	3905.14	−	7365.88i	0.436437	−	0.823207i	0.999996	+	0.00286884i	$0.000913182\pi$
$432$	72.6614	+	55.2358i	0.00809242	+	0.00615170i
$433$	253.652	−	4678.34i	0.0281518	−	0.519230i	−0.950118	−	0.311892i	$-0.899037\pi$
$433$	253.652	−	4678.34i	0.0281518	−	0.519230i	0.978269	−	0.207338i	$-0.0664800\pi$
$434$	2117.53	−	713.479i	0.234204	−	0.0789126i
$435$	1547.25	−	340.575i	0.170540	−	0.0375387i
$436$	2128.27	+	4014.35i	0.233775	+	0.440946i
$437$	2074.52	−	12654.0i	0.227088	−	1.38518i
$438$	3091.65	+	3639.77i	0.337271	+	0.397066i
$439$	−5533.53	+	6514.57i	−0.601596	+	0.708254i	−0.975695	−	0.219135i	$-0.929676\pi$
$439$	−5533.53	+	6514.57i	−0.601596	+	0.708254i	0.374098	+	0.927389i	$0.377952\pi$
$440$	530.588	+	3236.45i	0.0574882	+	0.350662i
$441$	−2410.14	+	1832.14i	−0.260246	+	0.197834i
$442$	13804.9	+	20360.7i	1.48559	+	2.19108i
$443$	4283.36	+	6317.49i	0.459388	+	0.677546i	0.984877	−	0.173254i	$-0.0554281\pi$
$443$	4283.36	+	6317.49i	0.459388	+	0.677546i	−0.525489	+	0.850800i	$0.676118\pi$
$444$	−6726.95	+	5113.69i	−0.719025	+	0.546588i
$445$	78.7930	+	480.616i	0.00839359	+	0.0511986i
$446$	7033.98	−	8281.04i	0.746791	−	0.879190i
$447$	−1657.25	−	1951.06i	−0.175358	−	0.206447i
$448$	342.496	−	2089.13i	0.0361192	−	0.220317i
$449$	18.9365	+	35.7181i	0.00199035	+	0.00375421i	0.884505	−	0.466530i	$-0.154496\pi$
$449$	18.9365	+	35.7181i	0.00199035	+	0.00375421i	−0.882515	+	0.470284i	$0.844151\pi$
$450$	−4878.43	+	1073.82i	−0.511048	+	0.112490i
$451$	−16978.7	+	5720.79i	−1.77272	+	0.597298i
$452$	−69.0127	+	1272.86i	−0.00718160	+	0.132457i
$453$	−8.64938	−	6.57508i	−0.000897093	−	0.000681952i
$454$	12164.9	−	22945.4i	1.25755	−	2.37198i
$455$	82.3392	−	296.559i	0.00848378	−	0.0305558i
$456$	−5521.71	+	5230.44i	−0.567056	+	0.537144i
$457$	5110.70	−	12826.9i	0.523125	−	1.31295i	−0.395736	−	0.918364i	$-0.629510\pi$
$457$	5110.70	−	12826.9i	0.523125	−	1.31295i	0.918861	−	0.394581i	$-0.129110\pi$
$458$	28563.4	+	9624.12i	2.91415	+	0.981890i
$459$	−2477.81	−	269.478i	−0.251970	−	0.0274034i
$460$	2934.85	−	1357.81i	0.297474	−	0.137626i
$461$	8479.83	+	8032.53i	0.856714	+	0.811523i	0.983594	−	0.180395i	$-0.0577377\pi$
$461$	8479.83	+	8032.53i	0.856714	+	0.811523i	−0.126880	+	0.991918i	$0.540496\pi$
$462$	−2047.33	+	1231.84i	−0.206170	+	0.124048i
$463$	−1528.34	+	166.217i	−0.153408	+	0.0166842i	−0.184501	−	0.982832i	$-0.559067\pi$
$463$	−1528.34	+	166.217i	−0.153408	+	0.0166842i	0.0310926	+	0.999517i	$0.490101\pi$
$464$	−844.652	−	185.922i	−0.0845085	−	0.0186017i
$465$	313.076	+	1127.60i	0.0312227	+	0.112454i
$466$	−11114.6	−	6687.44i	−1.10488	−	0.664785i
$467$	−6613.14	−	3059.56i	−0.655288	−	0.303169i	0.0639285	−	0.997954i	$-0.479637\pi$
$467$	−6613.14	−	3059.56i	−0.655288	−	0.303169i	−0.719217	+	0.694786i	$0.755499\pi$
$468$	2535.82	+	6364.43i	0.250466	+	0.628623i
$469$	17.4820	+	322.436i	0.00172120	+	0.0317457i
$470$	−1732.05	+	2554.59i	−0.169986	+	0.250711i
$471$	−2796.52			−0.273581
$472$	2574.04	−	10375.2i	0.251017	−	1.01178i
$473$	−35656.6			−3.46616
$474$	−4161.60	+	6137.90i	−0.403267	+	0.594774i
$475$	−702.566	−	12958.1i	−0.0678651	−	1.25170i
$476$	−1154.05	−	2896.44i	−0.111125	−	0.278904i
$477$	−1957.32	−	905.553i	−0.187882	−	0.0869233i
$478$	−26195.1	−	15761.1i	−2.50656	−	1.50815i
$479$	−622.259	−	2241.18i	−0.0593565	−	0.213783i	0.927924	−	0.372768i	$-0.121591\pi$
$479$	−622.259	−	2241.18i	−0.0593565	−	0.213783i	−0.987281	+	0.158986i	$0.949178\pi$
$480$	1047.23	+	230.512i	0.0995817	+	0.0219196i
$481$	−12361.7	+	1344.41i	−1.17182	+	0.127443i
$482$	−22198.1	+	13356.1i	−2.09771	+	1.26215i
$483$	668.357	+	633.101i	0.0629633	+	0.0596420i
$484$	38212.0	−	17678.7i	3.58865	−	1.66029i
$485$	253.816	+	27.6042i	0.0237633	+	0.00258441i
$486$	−1058.57	−	356.673i	−0.0988017	−	0.0332902i
$487$	−6609.69	+	16589.1i	−0.615018	+	1.54358i	0.209539	+	0.977800i	$0.432804\pi$
$487$	−6609.69	+	16589.1i	−0.615018	+	1.54358i	−0.824557	+	0.565778i	$0.808576\pi$
$488$	8624.70	−	8169.75i	0.800044	−	0.757842i
$489$	2909.68	−	10479.7i	0.269080	−	0.969139i
$490$	1495.07	−	2819.99i	0.137837	−	0.259988i
$491$	−6598.86	−	5016.32i	−0.606522	−	0.461066i	0.256284	−	0.966602i	$-0.417502\pi$
$491$	−6598.86	−	5016.32i	−0.606522	−	0.461066i	−0.862806	+	0.505536i	$0.831295\pi$
$492$	567.274	−	10462.7i	0.0519811	−	0.958734i
$493$	22381.1	−	7541.08i	2.04462	−	0.688911i
$494$	−27971.9	+	6157.08i	−2.54760	+	0.560770i
$495$	−586.145	−	1105.59i	−0.0532227	−	0.100389i
$496$	103.354	−	630.433i	0.00935634	−	0.0570712i
$497$	−468.547	−	551.616i	−0.0422881	−	0.0497854i
$498$	−7074.80	+	8329.10i	−0.636605	+	0.749470i
$499$	−1952.51	−	11909.8i	−0.175163	−	1.06845i	−0.917299	−	0.398200i	$-0.869635\pi$
$499$	−1952.51	−	11909.8i	−0.175163	−	1.06845i	0.742135	−	0.670250i	$-0.233813\pi$
$500$	5302.53	−	4030.88i	0.474273	−	0.360533i
$501$	2569.90	+	3790.32i	0.229171	+	0.338002i
$502$	15743.6	+	23220.1i	1.39975	+	2.06447i
$503$	−17066.1	+	12973.3i	−1.51280	+	1.15000i	−0.567700	+	0.823235i	$0.692167\pi$
$503$	−17066.1	+	12973.3i	−1.51280	+	1.15000i	−0.945104	+	0.326769i	$0.894040\pi$
$504$	−88.3400	−	538.850i	−0.00780749	−	0.0476236i
$505$	−1079.94	+	1271.40i	−0.0951613	+	0.112033i
$506$	−23915.8	−	28155.9i	−2.10116	−	2.47368i
$507$	−564.720	+	3444.64i	−0.0494676	+	0.301739i
$508$	3785.04	+	7139.35i	0.330579	+	0.623538i
$509$	3182.85	−	700.597i	0.277165	−	0.0610087i	−0.0742124	−	0.997242i	$-0.523644\pi$
$509$	3182.85	−	700.597i	0.277165	−	0.0610087i	0.351378	+	0.936234i	$0.385713\pi$
$510$	2490.17	−	839.035i	0.216209	−	0.0728492i
$511$	48.2222	−	889.406i	0.00417461	−	0.0769961i
$512$	−973.844	−	740.297i	−0.0840590	−	0.0639000i
$513$	1359.31	−	2563.92i	0.116988	−	0.220663i
$514$	−4054.81	+	14604.1i	−0.347957	+	1.25323i
$515$	−2611.87	+	2474.09i	−0.223481	+	0.211692i
$516$	7718.49	−	19371.9i	0.658503	−	1.65272i
$517$	20763.6	+	6996.08i	1.76631	+	0.595140i
$518$	2521.33	+	274.212i	0.213863	+	0.0232590i
$519$	−3982.08	+	1842.31i	−0.336790	+	0.155816i
$520$	−2049.11	−	1941.02i	−0.172807	−	0.163691i
$521$	11445.9	−	6886.76i	0.962483	−	0.579107i	0.0546801	−	0.998504i	$-0.482586\pi$
$521$	11445.9	−	6886.76i	0.962483	−	0.579107i	0.907803	+	0.419397i	$0.137759\pi$
$522$	10522.7	−	1144.41i	0.882311	−	0.0959571i
$523$	−3417.48	−	752.244i	−0.285728	−	0.0628936i	0.0697937	−	0.997561i	$-0.477766\pi$
$523$	−3417.48	−	752.244i	−0.285728	−	0.0628936i	−0.355522	+	0.934668i	$0.615697\pi$
$524$	−9121.08	−	32851.2i	−0.760413	−	2.73876i
$525$	798.314	+	480.330i	0.0663643	+	0.0399301i
$526$	−18647.1	−	8627.05i	−1.54572	−	0.715128i
$527$	6457.18	+	16206.3i	0.533737	+	1.33958i
$528$	36.9835	+	682.120i	0.00304829	+	0.0562225i
$529$	−1159.78	+	1710.55i	−0.0953217	+	0.140589i
$530$	2273.72			0.186347
$531$	333.294	+	4065.05i	0.0272386	+	0.332219i
$532$	3630.20			0.295845
$533$	8653.00	−	12762.2i	0.703195	−	1.03714i
$534$	176.163	+	3249.13i	0.0142758	+	0.263303i
$535$	878.264	+	2204.28i	0.0709732	+	0.178129i
$536$	2687.56	+	1243.40i	0.216577	+	0.100199i
$537$	−8128.35	−	4890.66i	−0.653192	−	0.393012i
$538$	−3627.40	−	13064.7i	−0.290685	−	1.04695i
$539$	−22129.0	−	4870.96i	−1.76839	−	0.389253i
$540$	727.537	−	79.1244i	0.0579782	−	0.00630551i
$541$	−11984.0	+	7210.55i	−0.952372	+	0.573023i	−0.904796	−	0.425844i	$-0.859977\pi$
$541$	−11984.0	+	7210.55i	−0.952372	+	0.573023i	−0.0475756	+	0.998868i	$0.515150\pi$
$542$	−941.476	−	891.814i	−0.0746123	−	0.0706765i
$543$	1706.72	−	789.615i	0.134885	−	0.0624044i
$544$	15891.4	+	1728.29i	1.25246	+	0.136213i
$545$	676.834	+	228.052i	0.0531970	+	0.0179242i
$546$	761.111	−	1910.24i	0.0596566	−	0.149727i
$547$	420.846	−	398.647i	0.0328960	−	0.0311607i	−0.671075	−	0.741390i	$-0.734167\pi$
$547$	420.846	−	398.647i	0.0328960	−	0.0311607i	0.703971	+	0.710229i	$0.251409\pi$
$548$	735.090	−	2647.55i	0.0573020	−	0.206383i
$549$	−2123.18	+	4004.75i	−0.165055	+	0.311327i
$550$	−29763.0	−	22625.2i	−2.30745	−	1.75408i
$551$	−1488.72	+	27457.9i	−0.115103	+	2.12295i
$552$	8000.52	−	2695.69i	0.616893	−	0.207855i
$553$	1350.79	−	297.332i	0.103873	−	0.0228641i
$554$	−16108.6	−	30384.1i	−1.23536	−	2.33014i
$555$	−214.889	+	1310.77i	−0.0164352	+	0.100250i
$556$	8388.16	+	9875.31i	0.639815	+	0.753249i
$557$	2863.84	−	3371.57i	0.217854	−	0.256478i	−0.642369	−	0.766396i	$-0.722048\pi$
$557$	2863.84	−	3371.57i	0.217854	−	0.256478i	0.860223	+	0.509918i	$0.170324\pi$
$558$	1264.90	+	7715.58i	0.0959636	+	0.585352i
$559$	24429.1	−	18570.6i	1.84838	−	1.40510i
$560$	10.0720	+	14.8551i	0.000760036	+	0.00112097i
$561$	−10468.6	−	15440.0i	−0.787848	−	1.16199i
$562$	−3315.81	+	2520.62i	−0.248878	+	0.189192i
$563$	−1481.12	−	9034.44i	−0.110874	−	0.676299i	−0.982519	−	0.186162i	$-0.940395\pi$
$563$	−1481.12	−	9034.44i	−0.110874	−	0.676299i	0.871646	−	0.490137i	$-0.163053\pi$
$564$	−8295.55	+	9766.28i	−0.619336	+	0.729139i
$565$	129.722	+	152.720i	0.00965918	+	0.0113717i
$566$	−1868.79	+	11399.1i	−0.138783	+	0.846540i
$567$	97.5899	+	184.074i	0.00722820	+	0.0136338i
$568$	−6482.01	+	1426.80i	−0.478836	+	0.105400i
$569$	−7218.07	+	2432.05i	−0.531805	+	0.179186i	−0.572377	−	0.819991i	$-0.693979\pi$
$569$	−7218.07	+	2432.05i	−0.531805	+	0.179186i	0.0405719	+	0.999177i	$0.487082\pi$
$570$	−165.638	+	3055.01i	−0.0121716	+	0.224492i
$571$	−12915.9	−	9818.41i	−0.946608	−	0.719593i	0.0132986	−	0.999912i	$-0.495767\pi$
$571$	−12915.9	−	9818.41i	−0.946608	−	0.719593i	−0.959907	+	0.280319i	$0.909560\pi$
$572$	−24018.0	+	45302.8i	−1.75567	+	3.31155i
$573$	2624.64	−	9453.09i	0.191354	−	0.689195i
$574$	−2283.21	+	2162.78i	−0.166027	+	0.157269i
$575$	−5331.76	+	13381.7i	−0.386696	+	0.970533i
$576$	7019.75	+	2365.23i	0.507794	+	0.171096i
$577$	9661.48	+	1050.75i	0.697075	+	0.0758115i	0.449794	−	0.893132i	$-0.351497\pi$
$577$	9661.48	+	1050.75i	0.697075	+	0.0758115i	0.247281	+	0.968944i	$0.420463\pi$
$578$	15054.6	−	6965.00i	1.08337	−	0.501221i
$579$	10626.3	+	10065.8i	0.762718	+	0.722485i
$580$	−5941.94	+	3575.15i	−0.425389	+	0.255948i
$581$	2026.32	−	220.376i	0.144692	−	0.0157362i
$582$	1665.89	+	366.689i	0.118648	+	0.0261164i
$583$	−4318.24	−	15552.9i	−0.306764	−	1.10486i
$584$	−6999.07	−	4211.20i	−0.495931	−	0.298392i
$585$	977.388	+	452.188i	0.0690770	+	0.0319584i
$586$	3959.82	+	9938.40i	0.279144	+	0.700600i
$587$	−0.137147	−	2.52952i	−9.64337e−6	−	0.000177861i	0.998529	−	0.0542278i	$-0.0172697\pi$
$587$	−0.137147	−	2.52952i	−9.64337e−6	−	0.000177861i	−0.998538	+	0.0540500i	$0.982787\pi$
$588$	7436.55	−	10968.1i	0.521562	−	0.769246i
$589$	−20311.9			−1.42095
$590$	−2118.44	−	3742.07i	−0.147821	−	0.261116i
$591$	418.440			0.0291240
$592$	406.921	−	600.163i	0.0282506	−	0.0416665i
$593$	−356.824	−	6581.22i	−0.0247099	−	0.455748i	−0.984539	−	0.175164i	$-0.943955\pi$
$593$	−356.824	−	6581.22i	−0.0247099	−	0.455748i	0.959829	−	0.280584i	$-0.0905282\pi$
$594$	−3094.50	−	7766.62i	−0.213753	−	0.536479i
$595$	−444.808	−	205.790i	−0.0306476	−	0.0141791i
$596$	9601.04	+	5776.75i	0.659855	+	0.397022i
$597$	−510.770	−	1839.63i	−0.0350158	−	0.126115i
$598$	31049.3	+	6834.46i	2.12324	+	0.467361i
$599$	16600.6	−	1805.43i	1.13236	−	0.123152i	0.477309	−	0.878736i	$-0.341612\pi$
$599$	16600.6	−	1805.43i	1.13236	−	0.123152i	0.655052	+	0.755584i	$0.272647\pi$
$600$	7320.96	−	4404.88i	0.498128	−	0.299714i
$601$	15210.8	+	14408.5i	1.03238	+	0.977926i	0.999768	−	0.0215422i	$-0.00685763\pi$
$601$	15210.8	+	14408.5i	1.03238	+	0.977926i	0.0326157	+	0.999468i	$0.489616\pi$
$602$	−5680.42	+	2628.04i	−0.384579	+	0.177925i
$603$	−1123.25	−	122.161i	−0.0758577	−	0.00825002i
$604$	45.0668	+	15.1848i	0.00303600	+	0.00102295i
$605$	2449.69	−	6148.25i	0.164618	−	0.413160i
$606$	−8091.24	+	7664.43i	−0.542383	+	0.513773i
$607$	1021.17	−	3677.92i	0.0682833	−	0.245934i	−0.921530	−	0.388308i	$-0.873060\pi$
$607$	1021.17	−	3677.92i	0.0682833	−	0.245934i	0.989813	+	0.142374i	$0.0454735\pi$
$608$	−8717.87	+	16443.6i	−0.581507	+	1.09684i
$609$	−1571.65	−	1194.74i	−0.104575	−	0.0794962i
$610$	258.720	−	4771.81i	0.0171726	−	0.316729i
$611$	−17869.3	+	6020.86i	−1.18316	+	0.398655i
$612$	10654.5	−	2345.23i	0.703730	−	0.154903i
$613$	−2580.15	−	4866.68i	−0.170002	−	0.320658i	0.783842	−	0.620960i	$-0.213257\pi$
$613$	−2580.15	−	4866.68i	−0.170002	−	0.320658i	−0.953844	+	0.300303i	$0.902912\pi$
$614$	3570.71	−	21780.4i	0.234694	−	1.43157i
$615$	−1066.29	−	1255.34i	−0.0699140	−	0.0823091i
$616$	2645.75	−	3114.82i	0.173052	−	0.203733i
$617$	−1366.87	−	8337.53i	−0.0891865	−	0.544013i	−0.993192	−	0.116492i	$-0.962835\pi$
$617$	−1366.87	−	8337.53i	−0.0891865	−	0.544013i	0.904005	−	0.427521i	$-0.140613\pi$
$618$	−19135.0	+	14546.0i	−1.24551	+	0.946809i
$619$	−8850.74	−	13053.9i	−0.574703	−	0.847624i	0.423600	−	0.905849i	$-0.360766\pi$
$619$	−8850.74	−	13053.9i	−0.574703	−	0.847624i	−0.998303	+	0.0582256i	$0.981456\pi$
$620$	−2874.58	−	4239.69i	−0.186203	−	0.274629i
$621$	−2564.40	+	1949.41i	−0.165710	+	0.125969i
$622$	−4506.37	−	27487.6i	−0.290496	−	1.77195i
$623$	392.897	−	462.554i	0.0252666	−	0.0297461i
$624$	−380.597	−	448.074i	−0.0244168	−	0.0287457i
$625$	−2272.30	+	13860.4i	−0.145427	+	0.887065i
$626$	3753.01	+	7078.93i	0.239618	+	0.451967i
$627$	21211.7	−	4669.06i	1.35106	−	0.297391i
$628$	11599.9	−	3908.45i	0.737079	−	0.248351i
$629$	−1071.99	+	19771.8i	−0.0679542	+	1.25334i
$630$	−174.865	−	132.929i	−0.0110584	−	0.00840635i
$631$	−2563.41	+	4835.10i	−0.161724	+	0.305043i	−0.951109	−	0.308854i	$-0.900054\pi$
$631$	−2563.41	+	4835.10i	−0.161724	+	0.305043i	0.789386	+	0.613898i	$0.210399\pi$
$632$	3393.34	−	12221.7i	0.213576	−	0.769230i
$633$	−4542.70	+	4303.07i	−0.285239	+	0.270192i
$634$	−5309.75	+	13326.5i	−0.332614	+	0.834798i
$635$	1203.72	+	405.580i	0.0752254	+	0.0253464i
$636$	9384.52	+	1020.63i	0.585095	+	0.0636329i
$637$	17697.9	−	8187.94i	1.10081	−	0.509290i
$638$	57513.9	+	54480.1i	3.56896	+	3.38070i
$639$	2169.93	−	1305.60i	0.134336	−	0.0808276i
$640$	−4921.14	+	535.206i	−0.303946	+	0.0330561i
$641$	23367.2	+	5143.51i	1.43986	+	0.316937i	0.865188	−	0.501448i	$-0.167199\pi$
$641$	23367.2	+	5143.51i	1.43986	+	0.316937i	0.574670	+	0.818385i	$0.305130\pi$
$642$	4241.10	+	15275.0i	0.260721	+	0.939031i
$643$	5787.30	+	3482.11i	0.354944	+	0.213563i	0.681846	−	0.731495i	$-0.261177\pi$
$643$	5787.30	+	3482.11i	0.354944	+	0.213563i	−0.326902	+	0.945058i	$0.606005\pi$
$644$	−3657.16	−	1691.98i	−0.223777	−	0.103530i
$645$	−1213.28	−	3045.11i	−0.0740666	−	0.185893i
$646$	2469.21	+	45541.9i	0.150387	+	2.77372i
$647$	8107.68	−	11957.9i	0.492652	−	0.726608i	−0.497367	−	0.867540i	$-0.665700\pi$
$647$	8107.68	−	11957.9i	0.492652	−	0.726608i	0.990019	+	0.140933i	$0.0450101\pi$
$648$	1910.62			0.115828
$649$	−21573.5	+	21597.6i	−1.30483	+	1.30629i
$650$	32174.8			1.94154
$651$	818.363	−	1207.00i	0.0492691	−	0.0726665i
$652$	2577.33	+	47536.1i	0.154810	+	2.85530i
$653$	1337.47	+	3356.80i	0.0801520	+	0.201166i	0.963591	−	0.267379i	$-0.0861576\pi$
$653$	1337.47	+	3356.80i	0.0801520	+	0.201166i	−0.883439	+	0.468545i	$0.844778\pi$
$654$	4330.74	+	2003.61i	0.258938	+	0.119797i
$655$	−4592.14	−	2763.00i	−0.273938	−	0.164823i
$656$	240.547	+	866.373i	0.0143168	+	0.0515643i
$657$	3043.76	+	669.983i	0.180743	+	0.0397846i
$658$	3823.47	−	415.828i	0.226527	−	0.0246362i
$659$	24612.5	−	14808.9i	1.45488	−	0.875373i	0.454996	−	0.890493i	$-0.349641\pi$
$659$	24612.5	−	14808.9i	1.45488	−	0.875373i	0.999886	+	0.0151200i	$0.00481302\pi$
$660$	3976.49	+	3766.74i	0.234522	+	0.222152i
$661$	8309.95	−	3844.59i	0.488986	−	0.226229i	−0.159873	−	0.987138i	$-0.551109\pi$
$661$	8309.95	−	3844.59i	0.488986	−	0.226229i	0.648859	+	0.760909i	$0.275246\pi$
$662$	−23076.5	−	2509.72i	−1.35483	−	0.147346i
$663$	15213.6	+	5126.06i	0.891173	+	0.300271i
$664$	6918.63	−	17364.4i	0.404360	−	1.01487i
$665$	414.281	−	392.428i	0.0241581	−	0.0228838i
$666$	−2374.11	+	8550.77i	−0.138131	+	0.497501i
$667$	14297.4	−	26967.8i	0.829984	−	1.56552i
$668$	−15957.3	−	12130.4i	−0.924261	−	0.702605i
$669$	383.889	−	7080.41i	0.0221853	−	0.409185i
$670$	1128.85	−	380.354i	0.0650914	−	0.0219319i
$671$	−33131.9	+	7292.89i	−1.90618	+	0.419581i
$672$	−625.890	−	1180.55i	−0.0359289	−	0.0677691i
$673$	−856.156	+	5222.32i	−0.0490377	+	0.299117i	−0.999946	−	0.0103547i	$-0.996704\pi$
$673$	−856.156	+	5222.32i	−0.0490377	+	0.299117i	0.950909	+	0.309472i	$0.100152\pi$
$674$	−181.989	−	214.254i	−0.0104005	−	0.0122444i
$675$	−2110.46	+	2484.62i	−0.120343	+	0.141679i
$676$	−2471.83	−	15077.5i	−0.140637	−	0.857846i
$677$	4293.62	−	3263.93i	0.243748	−	0.185292i	−0.476167	−	0.879355i	$-0.657974\pi$
$677$	4293.62	−	3263.93i	0.243748	−	0.185292i	0.719915	+	0.694063i	$0.244181\pi$
$678$	751.284	+	1108.06i	0.0425559	+	0.0627652i
$679$	−178.541	−	263.328i	−0.0100910	−	0.0148831i
$680$	−3578.06	+	2719.97i	−0.201783	+	0.153391i
$681$	−2742.03	−	16725.6i	−0.154295	−	0.941156i
$682$	−37883.4	+	44599.8i	−2.12702	+	2.50413i
$683$	−4615.86	−	5434.20i	−0.258596	−	0.304442i	0.617509	−	0.786564i	$-0.288142\pi$
$683$	−4615.86	−	5434.20i	−0.258596	−	0.304442i	−0.876104	+	0.482122i	$0.839866\pi$
$684$	−2054.99	+	12534.9i	−0.114875	+	0.700705i
$685$	−202.314	−	381.604i	−0.0112847	−	0.0212852i
$686$	−7845.12	+	1726.84i	−0.436630	+	0.0961094i
$687$	18640.9	−	6280.86i	1.03522	−	0.348806i
$688$	−96.8781	+	1786.81i	−0.00536838	+	0.0990139i
$689$	11058.7	+	8406.63i	0.611472	+	0.464829i
$690$	1590.76	−	3000.49i	0.0877669	−	0.165546i
$691$	2082.16	−	7499.26i	0.114630	−	0.412858i	−0.883863	−	0.467746i	$-0.845066\pi$
$691$	2082.16	−	7499.26i	0.114630	−	0.412858i	0.998493	+	0.0548875i	$0.0174800\pi$
$692$	13942.7	−	13207.2i	0.765929	−	0.725526i
$693$	−577.168	+	1448.58i	−0.0316375	+	0.0794041i
$694$	25165.4	+	8479.22i	1.37646	+	0.463785i
$695$	2024.79	+	220.209i	0.110510	+	0.0120187i
$696$	−16431.2	+	7601.88i	−0.894860	+	0.414006i
$697$	−17825.7	−	16885.4i	−0.968716	−	0.917617i
$698$	−36075.6	+	21706.0i	−1.95628	+	1.17705i
$699$	−8415.72	+	915.264i	−0.455381	+	0.0495257i
$700$	−3982.70	−	876.658i	−0.215045	−	0.0473351i
$701$	1774.06	+	6389.59i	0.0955854	+	0.344268i	0.995843	−	0.0910910i	$-0.0290354\pi$
$701$	1774.06	+	6389.59i	0.0955854	+	0.344268i	−0.900257	+	0.435359i	$0.856622\pi$
$702$	6165.09	+	3709.41i	0.331462	+	0.199434i
$703$	−20923.6	−	9680.30i	−1.12255	−	0.519345i
$704$	20520.8	+	51503.3i	1.09859	+	2.75725i
$705$	109.049	+	2011.29i	0.00582556	+	0.107446i
$706$	2428.23	−	3581.37i	0.129444	−	0.190916i
$707$	2078.70			0.110577
$708$	−7063.86	−	16395.9i	−0.374966	−	0.870332i
$709$	−9531.00			−0.504858			−0.252429	−	0.967615i	$-0.581229\pi$
$709$	−9531.00			−0.504858			−0.252429	+	0.967615i	$0.581229\pi$
$710$	−1498.31	+	2209.84i	−0.0791981	+	0.116808i
$711$	262.011	+	4832.52i	0.0138202	+	0.254899i
$712$	−2060.03	−	5170.29i	−0.108431	−	0.272141i
$713$	20462.7	+	9467.05i	1.07480	+	0.497257i
$714$	−2805.73	−	1688.15i	−0.147061	−	0.0884837i
$715$	2156.31	+	7766.34i	0.112785	+	0.406216i
$716$	40551.4	+	8926.04i	2.11659	+	0.465896i
$717$	−19834.3	+	2157.11i	−1.03309	+	0.112355i
$718$	−40483.8	+	24358.3i	−2.10424	+	1.26608i
$719$	6798.20	+	6439.60i	0.352615	+	0.334015i	0.843420	−	0.537255i	$-0.180539\pi$
$719$	6798.20	+	6439.60i	0.352615	+	0.334015i	−0.490805	+	0.871269i	$0.663297\pi$
$720$	−56.9953	+	26.3688i	−0.00295012	+	0.00136487i
$721$	4456.79	+	484.705i	0.230207	+	0.0250366i
$722$	−20443.9	−	6888.34i	−1.05380	−	0.355066i
$723$	−6257.91	+	15706.2i	−0.321900	+	0.807909i
$724$	−5975.86	+	5660.64i	−0.306756	+	0.290575i
$725$	8264.07	−	29764.5i	0.423338	−	1.52472i
$726$	20711.8	−	39066.6i	1.05880	−	1.99711i
$727$	16848.1	+	12807.6i	0.859505	+	0.653379i	0.939174	−	0.343443i	$-0.111593\pi$
$727$	16848.1	+	12807.6i	0.859505	+	0.653379i	−0.0796686	+	0.996821i	$0.525386\pi$
$728$	−190.414	+	3511.98i	−0.00969397	+	0.178795i
$729$	−690.839	+	232.771i	−0.0350983	+	0.0118260i
$730$	−3208.99	+	706.352i	−0.162699	+	0.0358127i
$731$	−22888.7	−	43172.7i	−1.15810	−	2.18441i
$732$	3209.81	−	19579.0i	0.162074	−	0.988606i
$733$	7319.99	+	8617.76i	0.368854	+	0.434249i	0.915008	−	0.403436i	$-0.132184\pi$
$733$	7319.99	+	8617.76i	0.368854	+	0.434249i	−0.546154	+	0.837685i	$0.683908\pi$
$734$	39647.4	−	46676.5i	1.99375	−	2.34722i
$735$	−336.996	−	2055.58i	−0.0169119	−	0.103158i
$736$	16446.7	−	12502.5i	0.823687	−	0.626151i
$737$	−4745.64	−	6999.29i	−0.237188	−	0.349827i
$738$	−6175.44	−	9108.09i	−0.308023	−	0.454300i
$739$	−4601.90	+	3498.27i	−0.229071	+	0.174135i	−0.713414	−	0.700743i	$-0.752852\pi$
$739$	−4601.90	+	3498.27i	−0.229071	+	0.174135i	0.484343	+	0.874878i	$0.339059\pi$
$740$	−940.590	−	5737.35i	−0.0467254	−	0.285012i
$741$	−12100.9	+	14246.3i	−0.599916	+	0.706276i
$742$	−1834.25	−	2159.45i	−0.0907512	−	0.106841i
$743$	3616.28	−	22058.3i	0.178558	−	1.08916i	−0.733680	−	0.679495i	$-0.762199\pi$
$743$	3616.28	−	22058.3i	0.178558	−	1.08916i	0.912238	−	0.409660i	$-0.134353\pi$
$744$	−6264.08	−	11815.3i	−0.308673	−	0.582218i
$745$	1720.15	−	378.633i	0.0845923	−	0.0186202i
$746$	18475.8	−	6225.23i	0.906766	−	0.305525i
$747$	−386.117	+	7121.50i	−0.0189120	+	0.348811i
$748$	65002.4	+	49413.5i	3.17744	+	2.41542i
$749$	1384.98	−	2612.35i	0.0675649	−	0.127441i
$750$	1871.40	−	6740.16i	0.0911117	−	0.328155i
$751$	15910.5	−	15071.2i	0.773077	−	0.732298i	−0.195583	−	0.980687i	$-0.562660\pi$
$751$	15910.5	−	15071.2i	0.773077	−	0.732298i	0.968660	+	0.248389i	$0.0799012\pi$
$752$	406.999	−	1021.49i	0.0197363	−	0.0495345i
$753$	17350.2	+	5845.97i	0.839678	+	0.282920i
$754$	−67778.1	−	7371.32i	−3.27365	−	0.356031i
$755$	6.78453	−	3.13886i	0.000327039	−	0.000151304i
$756$	−662.064	−	627.141i	−0.0318506	−	0.0301705i
$757$	11337.0	−	6821.23i	0.544319	−	0.327506i	−0.216697	−	0.976239i	$-0.569528\pi$
$757$	11337.0	−	6821.23i	0.544319	−	0.327506i	0.761016	+	0.648733i	$0.224701\pi$
$758$	−22831.0	+	2483.02i	−1.09401	+	0.118981i
$759$	−23545.4	−	5182.73i	−1.12601	−	0.247854i
$760$	−1399.99	−	5042.31i	−0.0668198	−	0.240663i
$761$	26405.4	+	15887.6i	1.25781	+	0.756801i	0.979062	−	0.203563i	$-0.0652521\pi$
$761$	26405.4	+	15887.6i	1.25781	+	0.756801i	0.278751	+	0.960363i	$0.410080\pi$
$762$	7702.04	+	3563.34i	0.366162	+	0.169405i
$763$	−329.423	−	826.790i	−0.0156303	−	0.0392291i
$764$	2324.85	+	42879.4i	0.110092	+	2.03052i
$765$	962.376	−	1419.40i	0.0454834	−	0.0670829i
$766$	−28001.4			−1.32080
$767$	3532.08	−	26032.8i	0.166279	−	1.22554i
$768$	−13319.1			−0.625795
$769$	−4335.00	+	6393.64i	−0.203282	+	0.299819i	−0.915641	−	0.401996i	$-0.868316\pi$
$769$	−4335.00	+	6393.64i	−0.203282	+	0.299819i	0.712359	+	0.701815i	$0.247627\pi$
$770$	−89.0032	−	1641.57i	−0.00416552	−	0.0768285i
$771$	3661.19	+	9188.90i	0.171018	+	0.429222i
$772$	−58145.6	−	26901.0i	−2.71076	−	1.25413i
$773$	−26772.5	−	16108.5i	−1.24572	−	0.749522i	−0.268810	−	0.963193i	$-0.586630\pi$
$773$	−26772.5	−	16108.5i	−1.24572	−	0.749522i	−0.976906	+	0.213671i	$0.931458\pi$
$774$	−5858.89	−	21101.8i	−0.272084	−	0.979960i
$775$	22284.2	+	4905.12i	1.03287	+	0.227351i
$776$	−2900.49	+	315.447i	−0.134177	+	0.0145927i
$777$	1418.24	−	853.328i	0.0654815	−	0.0393989i
$778$	13569.1	+	12853.3i	0.625288	+	0.592305i
$779$	25945.7	−	12003.8i	1.19333	−	0.552092i
$780$	−4686.16	−	509.651i	−0.215117	−	0.0233954i
$781$	17961.6	+	6051.96i	0.822939	+	0.277280i
$782$	18738.8	−	47030.9i	0.856904	−	2.15067i
$783$	5015.02	−	4750.48i	0.228892	−	0.216818i
$784$	−304.216	+	1095.69i	−0.0138582	+	0.0499128i
$785$	901.278	−	1699.99i	0.0409783	−	0.0772933i
$786$	−28504.8	−	21668.8i	−1.29355	−	0.983332i
$787$	−588.483	+	10853.9i	−0.0266546	+	0.491614i	0.954478	+	0.298280i	$0.0964130\pi$
$787$	−588.483	+	10853.9i	−0.0266546	+	0.491614i	−0.981133	+	0.193334i	$0.938070\pi$
$788$	−1735.67	+	584.817i	−0.0784655	+	0.0264381i
$789$	−13095.2	+	2882.47i	−0.590876	+	0.130062i
$790$	−2389.97	−	4507.97i	−0.107635	−	0.203021i
$791$	40.3959	−	246.404i	0.00181582	−	0.0110760i
$792$	9257.55	+	10898.8i	0.415344	+	0.488981i
$793$	18901.2	−	22252.2i	0.846406	−	0.996466i
$794$	1321.18	+	8058.82i	0.0590514	+	0.360198i
$795$	1181.30	−	897.999i	0.0526997	−	0.0400613i
$796$	4689.75	+	6916.86i	0.208824	+	0.307992i
$797$	−16911.0	−	24941.8i	−0.751589	−	1.10851i	−0.990506	−	0.137471i	$-0.956103\pi$
$797$	−16911.0	−	24941.8i	−0.751589	−	1.10851i	0.238917	−	0.971040i	$-0.423208\pi$
$798$	3035.09	−	2307.22i	0.134638	−	0.102349i
$799$	4857.81	+	29631.3i	0.215090	+	1.31199i
$800$	13535.3	−	15935.0i	0.598183	−	0.704236i
$801$	1374.76	+	1618.49i	0.0606425	+	0.0713939i
$802$	−183.642	+	1120.16i	−0.00808555	+	0.0493197i
$803$	10926.2	+	20608.9i	0.480169	+	0.905695i
$804$	4829.93	−	1063.15i	0.211864	−	0.0466348i
$805$	−600.261	+	202.251i	−0.0262813	+	0.00885519i
$806$	2726.46	−	50286.6i	0.119151	−	2.19761i
$807$	−7044.46	−	5355.06i	−0.307282	−	0.233590i
$808$	8929.17	−	16842.2i	0.388771	−	0.733300i
$809$	5457.14	−	19654.8i	0.237160	−	0.854174i	−0.745147	−	0.666900i	$-0.767621\pi$
$809$	5457.14	−	19654.8i	0.237160	−	0.854174i	0.982308	−	0.187274i	$-0.0599654\pi$
$810$	557.981	−	528.547i	0.0242043	−	0.0229275i
$811$	−4994.96	+	12536.4i	−0.216272	+	0.542802i	−0.996584	−	0.0825886i	$-0.973681\pi$
$811$	−4994.96	+	12536.4i	−0.216272	+	0.542802i	0.780311	+	0.625391i	$0.215061\pi$
$812$	8188.93	+	2759.17i	0.353910	+	0.119246i
$813$	−841.357	−	91.5031i	−0.0362948	−	0.00394730i
$814$	−60279.8	+	27888.4i	−2.59559	+	1.20085i
$815$	5432.82	+	5146.24i	0.233501	+	0.221184i
$816$	−802.164	+	482.646i	−0.0344134	+	0.0207059i
$817$	56560.7	−	6151.35i	2.42204	−	0.263413i
$818$	26727.6	+	5883.19i	1.14243	+	0.251468i
$819$	−359.014	−	1293.05i	−0.0153174	−	0.0551684i
$820$	6177.43	+	3716.83i	0.263079	+	0.158290i
$821$	16271.1	+	7527.83i	0.691677	+	0.320004i	0.734048	−	0.679098i	$-0.237629\pi$
$821$	16271.1	+	7527.83i	0.691677	+	0.320004i	−0.0423705	+	0.999102i	$0.513491\pi$
$822$	−1068.10	−	2680.73i	−0.0453214	−	0.113748i
$823$	−96.3064	−	1776.27i	−0.00407901	−	0.0752330i	0.995785	−	0.0917170i	$-0.0292355\pi$
$823$	−96.3064	−	1776.27i	−0.00407901	−	0.0752330i	−0.999864	+	0.0164840i	$0.994753\pi$
$824$	23071.6	−	34028.0i	0.975409	−	1.43862i
$825$	−24398.9			−1.02965
$826$	−1845.02	+	5030.76i	−0.0777195	+	0.211916i
$827$	−6723.28			−0.282698			−0.141349	−	0.989960i	$-0.545144\pi$
$827$	−6723.28			−0.282698			−0.141349	+	0.989960i	$0.545144\pi$
$828$	7912.54	−	11670.1i	0.332101	−	0.489812i
$829$	382.190	+	7049.08i	0.0160121	+	0.295325i	0.995561	+	0.0941189i	$0.0300034\pi$
$829$	382.190	+	7049.08i	0.0160121	+	0.295325i	−0.979549	+	0.201206i	$0.935514\pi$
$830$	−2783.11	−	6985.08i	−0.116389	−	0.292115i
$831$	−20369.2	−	9423.82i	−0.850302	−	0.393392i
$832$	−40883.0	−	24598.5i	−1.70356	−	1.02500i
$833$	−8307.35	−	29920.4i	−0.345537	−	1.24451i
$834$	13289.4	+	2925.22i	0.551768	+	0.121453i
$835$	−3132.36	+	340.665i	−0.129820	+	0.0141188i
$836$	−81460.1	+	49012.9i	−3.37004	+	2.02769i
$837$	3704.42	+	3509.01i	0.152979	+	0.144909i
$838$	−38926.0	+	18009.1i	−1.60462	+	0.742378i
$839$	−21830.8	−	2374.24i	−0.898312	−	0.0976973i	−0.352701	−	0.935736i	$-0.614737\pi$
$839$	−21830.8	−	2374.24i	−0.898312	−	0.0976973i	−0.545611	+	0.838039i	$0.683702\pi$
$840$	356.035	+	119.962i	0.0146243	+	0.00492749i
$841$	−15200.5	+	38150.5i	−0.623254	+	1.56425i
$842$	−5450.45	+	5162.94i	−0.223082	+	0.211314i
$843$	−727.201	+	2619.14i	−0.0297107	+	0.107008i
$844$	12828.9	−	24197.9i	0.523211	−	0.986881i
$845$	−1911.98	−	1453.45i	−0.0778390	−	0.0591717i
$846$	−728.565	+	13437.6i	−0.0296082	+	0.546092i
$847$	−7815.45	+	2633.33i	−0.317051	+	0.106827i
$848$	−791.114	+	174.137i	−0.0320365	+	0.00705177i
$849$	3531.13	+	6660.42i	0.142742	+	0.269240i
$850$	8288.95	−	50560.3i	0.334481	−	2.04024i
$851$	16567.1	+	19504.3i	0.667349	+	0.785664i
$852$	−7176.07	+	8448.32i	−0.288554	+	0.339712i
$853$	2936.00	+	17908.8i	0.117851	+	0.718858i	0.977967	+	0.208760i	$0.0669426\pi$
$853$	2936.00	+	17908.8i	0.117851	+	0.718858i	−0.860116	+	0.510098i	$0.829609\pi$
$854$	−4740.70	+	3603.78i	−0.189957	+	0.144402i
$855$	1120.51	+	1652.63i	0.0448195	+	0.0661038i
$856$	−15216.7	−	22443.0i	−0.607590	−	0.896128i
$857$	−6860.32	+	5215.08i	−0.273447	+	0.207869i	−0.732906	−	0.680330i	$-0.761836\pi$
$857$	−6860.32	+	5215.08i	−0.273447	+	0.207869i	0.459459	+	0.888199i	$0.348043\pi$
$858$	8712.03	+	53141.1i	0.346648	+	2.11446i
$859$	22530.9	−	26525.5i	0.894931	−	1.05359i	−0.103330	−	0.994647i	$-0.532950\pi$
$859$	22530.9	−	26525.5i	0.894931	−	1.05359i	0.998261	−	0.0589476i	$-0.0187745\pi$
$860$	9288.55	+	10935.3i	0.368299	+	0.433595i
$861$	−332.048	+	2025.40i	−0.0131431	+	0.0801691i
$862$	17951.5	+	33860.1i	0.709315	+	1.33791i
$863$	−37087.7	+	8163.62i	−1.46290	+	0.322008i	−0.873891	−	0.486122i	$-0.838411\pi$
$863$	−37087.7	+	8163.62i	−1.46290	+	0.322008i	−0.589005	+	0.808129i	$0.700480\pi$
$864$	4430.68	−	1492.87i	0.174461	−	0.0587829i
$865$	163.438	−	3014.44i	0.00642434	−	0.118490i
$866$	17145.7	+	13033.8i	0.672790	+	0.511441i
$867$	5070.72	−	9564.38i	0.198628	−	0.374652i
$868$	−1707.63	+	6150.34i	−0.0667751	+	0.240502i
$869$	−26296.8	+	24909.6i	−1.02653	+	0.972384i
$870$	−2695.63	+	6765.53i	−0.105047	+	0.263647i
$871$	6896.68	+	2323.76i	0.268295	+	0.0903992i
$872$	−8113.93	−	882.444i	−0.315106	−	0.0342698i
$873$	1010.32	−	467.425i	0.0391687	−	0.0181214i
$874$	42794.1	+	40536.7i	1.65621	+	1.56885i
$875$	−1117.93	+	672.638i	−0.0431920	+	0.0259878i
$876$	−13561.8	+	1474.94i	−0.523072	+	0.0568875i
$877$	−27433.0	−	6038.45i	−1.05627	−	0.232502i	−0.347307	−	0.937751i	$-0.612904\pi$
$877$	−27433.0	−	6038.45i	−1.05627	−	0.232502i	−0.708959	+	0.705250i	$0.750835\pi$
$878$	−10511.7	−	37859.6i	−0.404045	−	1.45524i
$879$	5982.44	+	3599.51i	0.229559	+	0.138121i
$880$	−426.576	−	197.355i	−0.0163408	−	0.00756005i
$881$	8314.64	+	20868.2i	0.317965	+	0.798032i	0.997901	+	0.0647605i	$0.0206283\pi$
$881$	8314.64	+	20868.2i	0.317965	+	0.798032i	−0.679936	+	0.733272i	$0.737992\pi$
$882$	−753.443	−	13896.4i	−0.0287639	−	0.530519i
$883$	13794.5	−	20345.4i	0.525733	−	0.775399i	−0.468405	−	0.883514i	$-0.655171\pi$
$883$	13794.5	−	20345.4i	0.525733	−	0.775399i	0.994138	+	0.108115i	$0.0344815\pi$
$884$	−70269.9			−2.67357
$885$	−2578.54	−	1107.50i	−0.0979397	−	0.0420657i
$886$	−35086.5			−1.33042
$887$	−11741.9	+	17318.0i	−0.444480	+	0.655559i	−0.982260	−	0.187527i	$-0.939953\pi$
$887$	−11741.9	+	17318.0i	−0.444480	+	0.655559i	0.537780	+	0.843086i	$0.319263\pi$
$888$	−821.762	−	15156.5i	−0.0310546	−	0.572769i
$889$	−585.865	−	1470.41i	−0.0221027	−	0.0554735i
$890$	−2031.90	−	940.059i	−0.0765276	−	0.0354054i
$891$	−4675.13	−	2812.93i	−0.175783	−	0.105765i
$892$	8303.32	+	29905.9i	0.311677	+	1.12256i
$893$	−34143.5	−	7515.54i	−1.27947	−	0.281633i
$894$	11698.6	−	1272.30i	0.437650	−	0.0475973i
$895$	5592.66	−	3364.99i	0.208874	−	0.125675i
$896$	4478.28	+	4242.05i	0.166974	+	0.158166i
$897$	18830.7	−	8712.01i	0.700935	−	0.324287i
$898$	−184.750	−	20.0928i	−0.00686547	−	0.000746665i
$899$	−45819.1	−	15438.3i	−1.69984	−	0.572742i
$900$	5281.57	−	13255.7i	0.195614	−	0.490953i
$901$	16059.4	−	15212.2i	0.593801	−	0.562478i
$902$	22033.7	−	79358.3i	0.813351	−	2.92943i
$903$	−1913.29	+	3608.85i	−0.0705098	+	0.132996i
$904$	−1822.91	−	1385.74i	−0.0670676	−	0.0509835i
$905$	−70.0497	+	1291.99i	−0.00257296	+	0.0474555i
$906$	47.3297	−	15.9472i	0.00173557	−	0.000584780i
$907$	−25751.2	+	5668.27i	−0.942729	+	0.207510i	−0.659639	−	0.751583i	$-0.729291\pi$
$907$	−25751.2	+	5668.27i	−0.942729	+	0.207510i	−0.283090	+	0.959093i	$0.591360\pi$
$908$	34749.8	+	65545.1i	1.27006	+	2.39558i
$909$	−1176.71	+	7177.62i	−0.0429362	+	0.261899i
$910$	915.932	+	1078.32i	0.0333658	+	0.0392812i
$911$	10211.4	−	12021.7i	0.371370	−	0.437210i	−0.544454	−	0.838791i	$-0.683263\pi$
$911$	10211.4	−	12021.7i	0.371370	−	0.437210i	0.915824	+	0.401581i	$0.131539\pi$
$912$	−176.342	−	1075.64i	−0.00640271	−	0.0390548i
$913$	−42494.3	+	32303.3i	−1.54037	+	1.17096i
$914$	35619.4	+	52534.7i	1.28904	+	1.90120i
$915$	−1750.20	−	2581.34i	−0.0632346	−	0.0932641i
$916$	−68543.8	+	52105.6i	−2.47244	+	1.87950i
$917$	1080.42	+	6590.30i	0.0389081	+	0.237329i
$918$	7417.33	−	8732.36i	0.266676	−	0.313955i
$919$	17780.9	+	20933.3i	0.638236	+	0.751389i	0.982250	−	0.187575i	$-0.0600628\pi$
$919$	17780.9	+	20933.3i	0.638236	+	0.751389i	−0.344014	+	0.938964i	$0.611787\pi$
$920$	−939.756	+	5732.26i	−0.0336770	+	0.205421i
$921$	−6746.95	−	12726.1i	−0.241389	−	0.455309i
$922$	−52437.5	+	11542.4i	−1.87304	+	0.412286i
$923$	−15457.8	+	5208.35i	−0.551246	+	0.185737i
$924$	369.516	−	6815.33i	0.0131561	−	0.242649i
$925$	20617.6	+	15673.1i	0.732868	+	0.557112i
$926$	3310.25	−	6243.80i	0.117475	−	0.221581i
$927$	−4196.55	+	15114.6i	−0.148687	+	0.535522i
$928$	−32163.7	+	30467.1i	−1.13774	+	1.07773i
$929$	−238.598	+	598.836i	−0.00842643	+	0.0211487i	−0.933130	−	0.359540i	$-0.882934\pi$
$929$	−238.598	+	598.836i	−0.00842643	+	0.0211487i	0.924703	+	0.380689i	$0.124313\pi$
$930$	−5097.92	−	1717.69i	−0.179750	−	0.0605648i
$931$	35942.7	+	3909.00i	1.26528	+	0.137607i
$932$	33628.9	−	15558.4i	1.18192	−	0.546816i
$933$	−13197.4	−	12501.2i	−0.463091	−	0.438663i
$934$	28701.0	−	17268.8i	1.00549	−	0.604981i
$935$	12759.7	−	1387.71i	0.446297	−	0.0485378i
$936$	−12018.8	−	2645.55i	−0.419709	−	0.0923850i
$937$	6467.32	+	23293.2i	0.225483	+	0.812118i	0.986552	+	0.163447i	$0.0522612\pi$
$937$	6467.32	+	23293.2i	0.225483	+	0.812118i	−0.761069	+	0.648671i	$0.775325\pi$
$938$	−1271.90	−	765.277i	−0.0442740	−	0.0266388i
$939$	4745.66	+	2195.57i	0.164929	+	0.0763044i
$940$	−3263.33	−	8190.35i	−0.113232	−	0.284191i
$941$	2653.60	+	48942.8i	0.0919287	+	1.69553i	0.573570	+	0.819157i	$0.305558\pi$
$941$	2653.60	+	48942.8i	0.0919287	+	1.69553i	−0.481641	+	0.876369i	$0.659959\pi$
$942$	7214.20	−	10640.2i	0.249524	−	0.368020i
$943$	−31733.1			−1.09584
$944$	1023.68	+	1139.76i	0.0352944	+	0.0392967i
$945$	−143.349			−0.00493456
$946$	91983.7	−	135666.i	3.16136	−	4.66266i
$947$	1663.52	+	30681.8i	0.0570824	+	1.05282i	0.877046	+	0.480407i	$0.159511\pi$
$947$	1663.52	+	30681.8i	0.0570824	+	1.05282i	−0.819963	+	0.572416i	$0.806006\pi$
$948$	−7840.81	−	19678.9i	−0.268626	−	0.674201i
$949$	−18219.2	−	8429.10i	−0.623204	−	0.288325i
$950$	51115.1	+	30754.9i	1.74568	+	1.05034i
$951$	2504.60	+	9020.76i	0.0854020	+	0.307590i
$952$	5469.76	+	1203.98i	0.186214	+	0.0409888i
$953$	14809.6	−	1610.64i	0.503390	−	0.0547470i	0.147099	−	0.989122i	$-0.453007\pi$
$953$	14809.6	−	1610.64i	0.503390	−	0.0547470i	0.356292	+	0.934375i	$0.384041\pi$
$954$	8494.75	−	5111.12i	0.288289	−	0.173458i
$955$	4900.60	+	4642.10i	0.166052	+	0.157293i
$956$	79257.3	−	36668.3i	2.68134	−	1.24052i
$957$	51397.7	+	5589.84i	1.73610	+	0.188813i
$958$	10132.4	+	3414.02i	0.341716	+	0.115138i
$959$	−199.215	+	499.992i	−0.00670802	+	0.0168359i
$960$	−3700.17	+	3504.99i	−0.124399	+	0.117837i
$961$	1584.69	−	5707.55i	0.0531937	−	0.191586i
$962$	26774.3	−	50501.7i	0.897336	−	1.69256i
$963$	8236.27	+	6261.05i	0.275607	+	0.209511i
$964$	4006.46	−	73894.8i	0.133858	−	2.46887i
$965$	−9543.63	+	3215.62i	−0.318363	+	0.107269i
$966$	−4132.98	+	909.738i	−0.137657	+	0.0303006i
$967$	−16188.4	−	30534.5i	−0.538348	−	1.01543i	−0.992235	−	0.124373i	$-0.960308\pi$
$967$	−16188.4	−	30534.5i	−0.538348	−	1.01543i	0.453887	−	0.891059i	$-0.350037\pi$
$968$	−12235.7	+	74634.5i	−0.406271	+	2.47814i
$969$	19269.5	+	22685.8i	0.638830	+	0.752088i
$970$	−759.799	+	894.505i	−0.0251502	+	0.0296091i
$971$	6208.12	+	37867.8i	0.205178	+	1.25153i	0.865638	+	0.500670i	$0.166913\pi$
$971$	6208.12	+	37867.8i	0.205178	+	1.25153i	−0.660460	+	0.750861i	$0.729639\pi$
$972$	2540.26	−	1931.05i	0.0838259	−	0.0637228i
$973$	−1424.29	−	2100.67i	−0.0469277	−	0.0692132i
$974$	−46066.8	−	67943.4i	−1.51548	−	2.23516i
$975$	16716.2	−	12707.4i	0.549075	−	0.417396i
$976$	275.440	+	1680.11i	0.00903342	+	0.0551014i
$977$	−29378.1	+	34586.5i	−0.962014	+	1.13257i	0.0291027	+	0.999576i	$0.490735\pi$
$977$	−29378.1	+	34586.5i	−0.962014	+	1.13257i	−0.991117	+	0.132994i	$0.957541\pi$
$978$	32366.9	+	38105.3i	1.05826	+	1.24588i
$979$	−2571.29	+	15684.2i	−0.0839415	+	0.512021i
$980$	4270.76	+	8055.50i	0.139208	+	0.262575i
$981$	3041.33	−	669.447i	0.0989829	−	0.0217878i
$982$	36109.1	−	12166.6i	1.17341	−	0.395368i
$983$	959.466	−	17696.3i	0.0311315	−	0.574186i	−0.940806	−	0.338946i	$-0.889930\pi$
$983$	959.466	−	17696.3i	0.0311315	−	0.574186i	0.971937	−	0.235240i	$-0.0755876\pi$
$984$	14984.1	+	11390.6i	0.485441	+	0.369023i
$985$	−134.857	+	254.367i	−0.00436234	+	0.00822824i
$986$	−29044.6	+	104609.i	−0.938102	+	3.37874i
$987$	1822.23	−	1726.11i	0.0587662	−	0.0556663i
$988$	30283.4	−	76005.6i	0.975145	−	2.44743i
$989$	−59847.7	−	20165.0i	−1.92421	−	0.648343i
$990$	5718.60	+	621.936i	0.183585	+	0.0199661i
$991$	10966.3	−	5073.55i	0.351520	−	0.162630i	−0.236180	−	0.971709i	$-0.575896\pi$
$991$	10966.3	−	5073.55i	0.351520	−	0.162630i	0.587700	+	0.809079i	$0.300034\pi$
$992$	−23758.2	−	22504.9i	−0.760406	−	0.720295i
$993$	−12980.5	+	7810.09i	−0.414827	+	0.249593i
$994$	3307.49	−	359.712i	0.105541	−	0.0114782i
$995$	1282.91	+	282.391i	0.0408755	+	0.00899737i
$996$	−8351.51	−	30079.4i	−0.265690	−	0.956930i
$997$	4294.38	+	2583.85i	0.136414	+	0.0820774i	0.582125	−	0.813099i	$-0.302222\pi$
$997$	4294.38	+	2583.85i	0.136414	+	0.0820774i	−0.445711	+	0.895177i	$0.647049\pi$
$998$	50351.2	+	23294.9i	1.59703	+	0.738866i
$999$	2143.65	+	5380.15i	0.0678899	+	0.170391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.b.76.2	yes	420
59.7	even	29	inner	177.4.e.b.7.2	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.b.7.2	✓	420	59.7	even	29	inner
177.4.e.b.76.2	yes	420	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.57971 + 3.80479i) q^{2} +(0.162417 + 2.99560i) q^{3} +(-4.86039 - 12.1987i) q^{4} +(-1.87335 - 0.866706i) q^{5} +(-11.8166 - 7.10982i) q^{6} +(0.688121 + 2.47839i) q^{7} +(23.0364 + 5.07071i) q^{8} +(-8.94724 + 0.973071i) q^{9} +O(q^{10})\)	\(q+(-2.57971 + 3.80479i) q^{2} +(0.162417 + 2.99560i) q^{3} +(-4.86039 - 12.1987i) q^{4} +(-1.87335 - 0.866706i) q^{5} +(-11.8166 - 7.10982i) q^{6} +(0.688121 + 2.47839i) q^{7} +(23.0364 + 5.07071i) q^{8} +(-8.94724 + 0.973071i) q^{9} +(8.13034 - 4.89186i) q^{10} +(-48.9029 - 46.3233i) q^{11} +(35.7529 - 16.5411i) q^{12} +(57.6303 + 6.26768i) q^{13} +(-11.2049 - 3.77537i) q^{14} +(2.29204 - 5.75259i) q^{15} +(-2.45420 + 2.32474i) q^{16} +(24.6960 - 88.9470i) q^{17} +(19.3789 - 36.5526i) q^{18} +(85.5643 + 65.0443i) q^{19} +(-1.46742 + 27.0650i) q^{20} +(-7.31250 + 2.46387i) q^{21} +(302.405 - 66.5644i) q^{22} +(-55.8834 - 105.407i) q^{23} +(-11.4483 + 69.8315i) q^{24} +(-78.1650 - 92.0230i) q^{25} +(-172.517 + 203.102i) q^{26} +(-4.36811 - 26.6443i) q^{27} +(26.8885 - 20.4401i) q^{28} +(143.576 + 211.759i) q^{29} +(15.9746 + 23.5607i) q^{30} +(-150.448 + 114.367i) q^{31} +(28.0148 + 170.883i) q^{32} +(130.823 - 154.017i) q^{33} +(274.716 + 323.421i) q^{34} +(0.858940 - 5.23930i) q^{35} +(55.3573 + 104.415i) q^{36} +(-209.484 + 46.1110i) q^{37} +(-468.210 + 157.758i) q^{38} +(-9.41532 + 173.655i) q^{39} +(-38.7606 - 29.4651i) q^{40} +(124.589 - 235.000i) q^{41} +(9.48963 - 34.1786i) q^{42} +(384.303 - 364.031i) q^{43} +(-327.395 + 821.699i) q^{44} +(17.6047 + 5.93172i) q^{45} +(545.215 + 59.2957i) q^{46} +(-295.213 + 136.580i) q^{47} +(-7.36261 - 6.97423i) q^{48} +(288.233 - 173.424i) q^{49} +(551.771 - 60.0087i) q^{50} +(270.461 + 59.5329i) q^{51} +(-203.649 - 733.476i) q^{52} +(205.327 + 123.541i) q^{53} +(112.644 + 52.1148i) q^{54} +(51.4638 + 129.164i) q^{55} +(3.28469 + 60.5825i) q^{56} +(-180.950 + 266.881i) q^{57} -1176.08 q^{58} +(12.0188 - 453.028i) q^{59} -81.3141 q^{60} +(282.636 - 416.857i) q^{61} +(-47.0321 - 867.456i) q^{62} +(-8.56843 - 21.5051i) q^{63} +(-746.986 - 345.592i) q^{64} +(-102.530 - 61.6902i) q^{65} +(248.516 + 895.074i) q^{66} +(122.606 + 26.9877i) q^{67} +(-1205.07 + 131.059i) q^{68} +(306.682 - 184.524i) q^{69} +(17.7186 + 16.7839i) q^{70} +(-255.374 + 118.149i) q^{71} +(-211.047 - 22.9527i) q^{72} +(-328.165 - 110.572i) q^{73} +(364.966 - 915.996i) q^{74} +(262.969 - 249.097i) q^{75} +(377.577 - 1359.91i) q^{76} +(81.1560 - 153.076i) q^{77} +(-636.433 - 483.804i) q^{78} +(29.1124 - 536.946i) q^{79} +(6.61246 - 2.22800i) q^{80} +(79.1063 - 17.4126i) q^{81} +(572.720 + 1080.26i) q^{82} +(128.203 - 782.001i) q^{83} +(65.5975 + 77.2273i) q^{84} +(-123.355 + 145.225i) q^{85} +(393.671 + 2401.28i) q^{86} +(-611.027 + 464.491i) q^{87} +(-891.657 - 1315.10i) q^{88} +(-132.412 - 195.293i) q^{89} +(-67.9840 + 51.6801i) q^{90} +(24.1229 + 147.143i) q^{91} +(-1014.21 + 1194.02i) q^{92} +(-367.034 - 432.106i) q^{93} +(241.906 - 1475.56i) q^{94} +(-103.918 - 196.010i) q^{95} +(-507.346 + 111.675i) q^{96} +(-117.215 + 39.4945i) q^{97} +(-83.7159 + 1544.05i) q^{98} +(482.622 + 366.880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Introduction

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