LMFDB - Embedded newform 177.4.e.a.7.4

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			7.4
Character	$\chi$	$=$	177.7
Dual form			177.4.e.a.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93104 - 2.84807i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-1.42147 + 3.56762i) q^{4} +(-12.2161 + 5.65175i) q^{5} +(8.84530 - 5.32204i) q^{6} +(8.68646 - 31.2858i) q^{7} +(-13.9786 + 3.07691i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})$	\(q+(-1.93104 - 2.84807i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-1.42147 + 3.56762i) q^{4} +(-12.2161 + 5.65175i) q^{5} +(8.84530 - 5.32204i) q^{6} +(8.68646 - 31.2858i) q^{7} +(-13.9786 + 3.07691i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(39.6862 + 23.8784i) q^{10} +(25.9292 - 24.5614i) q^{11} +(-10.4563 - 4.83760i) q^{12} +(-8.20288 + 0.892117i) q^{13} +(-105.878 + 35.6744i) q^{14} +(-14.9463 - 37.5124i) q^{15} +(58.0611 + 54.9984i) q^{16} +(29.2819 + 105.464i) q^{17} +(14.5061 + 27.3614i) q^{18} +(-86.3444 + 65.6373i) q^{19} +(-2.79854 - 51.6161i) q^{20} +(92.3089 + 31.1025i) q^{21} +(-120.023 - 26.4190i) q^{22} +(-81.9564 + 154.586i) q^{23} +(-6.94685 - 42.3739i) q^{24} +(36.3665 - 42.8139i) q^{25} +(18.3809 + 21.6396i) q^{26} +(4.36811 - 26.6443i) q^{27} +(99.2684 + 75.4619i) q^{28} +(-45.9129 + 67.7164i) q^{29} +(-77.9758 + 115.006i) q^{30} +(-80.9959 - 61.5715i) q^{31} +(25.9960 - 158.569i) q^{32} +(69.3648 + 81.6626i) q^{33} +(243.824 - 287.051i) q^{34} +(70.7052 + 431.283i) q^{35} +(16.1898 - 30.5372i) q^{36} +(257.448 + 56.6685i) q^{37} +(353.674 + 119.167i) q^{38} +(-1.34014 - 24.7174i) q^{39} +(153.373 - 116.591i) q^{40} +(154.205 + 290.861i) q^{41} +(-89.6699 - 322.962i) q^{42} +(-23.7248 - 22.4733i) q^{43} +(50.7683 + 127.419i) q^{44} +(114.800 - 38.6805i) q^{45} +(598.532 - 65.0943i) q^{46} +(-362.060 - 167.507i) q^{47} +(-174.183 + 164.995i) q^{48} +(-609.444 - 366.690i) q^{49} +(-192.162 - 20.8989i) q^{50} +(-320.684 + 70.5878i) q^{51} +(8.47742 - 30.5329i) q^{52} +(517.422 - 311.322i) q^{53} +(-84.3198 + 39.0105i) q^{54} +(-177.937 + 446.589i) q^{55} +(-25.1605 + 464.058i) q^{56} +(-182.599 - 269.314i) q^{57} +281.520 q^{58} +(-452.557 + 23.8903i) q^{59} +155.076 q^{60} +(416.119 + 613.730i) q^{61} +(-18.9536 + 349.578i) q^{62} +(-108.163 + 271.469i) q^{63} +(78.8494 - 36.4796i) q^{64} +(95.1648 - 57.2588i) q^{65} +(98.6344 - 355.249i) q^{66} +(-400.175 + 88.0852i) q^{67} +(-417.879 - 45.4471i) q^{68} +(-449.767 - 270.616i) q^{69} +(1091.79 - 1034.20i) q^{70} +(-691.863 - 320.090i) q^{71} +(128.064 - 13.9278i) q^{72} +(146.073 - 49.2179i) q^{73} +(-335.745 - 842.657i) q^{74} +(122.347 + 115.893i) q^{75} +(-111.433 - 401.346i) q^{76} +(-543.191 - 1024.57i) q^{77} +(-67.8090 + 51.5471i) q^{78} +(37.0535 + 683.411i) q^{79} +(-1020.12 - 343.717i) q^{80} +(79.1063 + 17.4126i) q^{81} +(530.617 - 1000.85i) q^{82} +(-108.716 - 663.136i) q^{83} +(-242.176 + 285.112i) q^{84} +(-953.765 - 1122.86i) q^{85} +(-18.1920 + 110.967i) q^{86} +(-195.394 - 148.535i) q^{87} +(-286.879 + 423.115i) q^{88} +(-244.086 + 360.000i) q^{89} +(-331.847 - 252.263i) q^{90} +(-43.3434 + 264.383i) q^{91} +(-435.007 - 512.129i) q^{92} +(197.599 - 232.631i) q^{93} +(222.081 + 1354.63i) q^{94} +(683.823 - 1289.83i) q^{95} +(470.787 + 103.628i) q^{96} +(109.738 + 36.9749i) q^{97} +(132.501 + 2443.83i) q^{98} +(-255.895 + 194.526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

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 $

$2$	−1.93104	−	2.84807i	−0.682725	−	1.00694i	−0.998314	−	0.0580474i	$-0.981513\pi$
$2$	−1.93104	−	2.84807i	−0.682725	−	1.00694i	0.315589	−	0.948896i	$-0.397798\pi$
$3$	−0.162417	+	2.99560i	−0.0312571	+	0.576504i
$3$	−0.162417	+	2.99560i	−0.0312571	+	0.576504i
$4$	−1.42147	+	3.56762i	−0.177684	+	0.445953i
$5$	−12.2161	+	5.65175i	−1.09264	+	0.505508i	−0.881613	−	0.471973i	$-0.843542\pi$
$5$	−12.2161	+	5.65175i	−1.09264	+	0.505508i	−0.211024	+	0.977481i	$0.567680\pi$
$6$	8.84530	−	5.32204i	0.601846	−	0.362119i
$7$	8.68646	−	31.2858i	0.469025	−	1.68927i	−0.229187	−	0.973382i	$-0.573607\pi$
$7$	8.68646	−	31.2858i	0.469025	−	1.68927i	0.698212	−	0.715891i	$-0.253979\pi$
$8$	−13.9786	+	3.07691i	−0.617771	+	0.135982i
$9$	−8.94724	−	0.973071i	−0.331379	−	0.0360397i
$10$	39.6862	+	23.8784i	1.25499	+	0.755101i
$11$	25.9292	−	24.5614i	0.710722	−	0.673231i	−0.244323	−	0.969694i	$-0.578566\pi$
$11$	25.9292	−	24.5614i	0.710722	−	0.673231i	0.955044	+	0.296463i	$0.0958070\pi$
$12$	−10.4563	−	4.83760i	−0.251540	−	0.116375i
$13$	−8.20288	+	0.892117i	−0.175005	+	0.0190330i	−0.195202	−	0.980763i	$-0.562536\pi$
$13$	−8.20288	+	0.892117i	−0.175005	+	0.0190330i	0.0201967	+	0.999796i	$0.493571\pi$
$14$	−105.878	+	35.6744i	−2.02122	+	0.681027i
$15$	−14.9463	−	37.5124i	−0.257274	−	0.645710i
$16$	58.0611	+	54.9984i	0.907205	+	0.859351i
$17$	29.2819	+	105.464i	0.417759	+	1.50463i	0.810917	+	0.585161i	$0.198969\pi$
$17$	29.2819	+	105.464i	0.417759	+	1.50463i	−0.393158	+	0.919471i	$0.628617\pi$
$18$	14.5061	+	27.3614i	0.189951	+	0.358285i
$19$	−86.3444	+	65.6373i	−1.04257	+	0.792539i	−0.978674	−	0.205418i	$-0.934145\pi$
$19$	−86.3444	+	65.6373i	−1.04257	+	0.792539i	−0.0638924	+	0.997957i	$0.520351\pi$
$20$	−2.79854	−	51.6161i	−0.0312887	−	0.577086i
$21$	92.3089	+	31.1025i	0.959212	+	0.323196i
$22$	−120.023	−	26.4190i	−1.16313	−	0.256025i
$23$	−81.9564	+	154.586i	−0.743004	+	1.40145i	0.166620	+	0.986021i	$0.446715\pi$
$23$	−81.9564	+	154.586i	−0.743004	+	1.40145i	−0.909624	+	0.415433i	$0.863630\pi$
$24$	−6.94685	−	42.3739i	−0.0590842	−	0.360397i
$25$	36.3665	−	42.8139i	0.290932	−	0.342511i
$26$	18.3809	+	21.6396i	0.138646	+	0.163226i
$27$	4.36811	−	26.6443i	0.0311350	−	0.189915i
$28$	99.2684	+	75.4619i	0.669999	+	0.509320i
$29$	−45.9129	+	67.7164i	−0.293993	+	0.433608i	−0.945786	−	0.324789i	$-0.894707\pi$
$29$	−45.9129	+	67.7164i	−0.293993	+	0.433608i	0.651793	+	0.758397i	$0.274017\pi$
$30$	−77.9758	+	115.006i	−0.474546	+	0.699903i
$31$	−80.9959	−	61.5715i	−0.469267	−	0.356728i	0.343659	−	0.939095i	$-0.388334\pi$
$31$	−80.9959	−	61.5715i	−0.469267	−	0.356728i	−0.812926	+	0.582367i	$0.802127\pi$
$32$	25.9960	−	158.569i	0.143609	−	0.875977i
$33$	69.3648	+	81.6626i	0.365905	+	0.430777i
$34$	243.824	−	287.051i	1.22987	−	1.44791i
$35$	70.7052	+	431.283i	0.341467	+	2.08286i
$36$	16.1898	−	30.5372i	0.0749528	−	0.141376i
$37$	257.448	+	56.6685i	1.14390	+	0.251790i	0.746197	−	0.665726i	$-0.231878\pi$
$37$	257.448	+	56.6685i	1.14390	+	0.251790i	0.397699	+	0.917516i	$0.369809\pi$
$38$	353.674	+	119.167i	1.50983	+	0.508720i
$39$	−1.34014	−	24.7174i	−0.00550242	−	0.101486i
$40$	153.373	−	116.591i	0.606260	−	0.460867i
$41$	154.205	+	290.861i	0.587384	+	1.10792i	0.981965	+	0.189063i	$0.0605451\pi$
$41$	154.205	+	290.861i	0.587384	+	1.10792i	−0.394581	+	0.918861i	$0.629110\pi$
$42$	−89.6699	−	322.962i	−0.329437	−	1.18653i
$43$	−23.7248	−	22.4733i	−0.0841394	−	0.0797011i	0.644474	−	0.764626i	$-0.277076\pi$
$43$	−23.7248	−	22.4733i	−0.0841394	−	0.0797011i	−0.728614	+	0.684925i	$0.759835\pi$
$44$	50.7683	+	127.419i	0.173946	+	0.436571i
$45$	114.800	−	38.6805i	0.380296	−	0.128137i
$46$	598.532	−	65.0943i	1.91845	−	0.208644i
$47$	−362.060	−	167.507i	−1.12366	−	0.519860i	−0.232067	−	0.972700i	$-0.574549\pi$
$47$	−362.060	−	167.507i	−1.12366	−	0.519860i	−0.891592	+	0.452840i	$0.850411\pi$
$48$	−174.183	+	164.995i	−0.523775	+	0.496146i
$49$	−609.444	−	366.690i	−1.77680	−	1.06907i
$50$	−192.162	−	20.8989i	−0.543516	−	0.0591109i
$51$	−320.684	+	70.5878i	−0.880484	+	0.193809i
$52$	8.47742	−	30.5329i	0.0226078	−	0.0814260i
$53$	517.422	−	311.322i	1.34101	−	0.806857i	0.349503	−	0.936935i	$-0.386350\pi$
$53$	517.422	−	311.322i	1.34101	−	0.806857i	0.991504	+	0.130078i	$0.0415228\pi$
$54$	−84.3198	+	39.0105i	−0.212490	+	0.0983084i
$55$	−177.937	+	446.589i	−0.436237	+	1.09487i
$56$	−25.1605	+	464.058i	−0.0600395	+	1.10736i
$57$	−182.599	−	269.314i	−0.424314	−	0.625816i
$58$	281.520			0.637335
$59$	−452.557	+	23.8903i	−0.998610	+	0.0527161i
$59$	−452.557	+	23.8903i	−0.998610	+	0.0527161i
$60$	155.076			0.333670
$61$	416.119	+	613.730i	0.873419	+	1.28820i	0.956523	+	0.291656i	$0.0942063\pi$
$61$	416.119	+	613.730i	0.873419	+	1.28820i	−0.0831038	+	0.996541i	$0.526483\pi$
$62$	−18.9536	+	349.578i	−0.0388243	+	0.716073i
$63$	−108.163	+	271.469i	−0.216306	+	0.542887i
$64$	78.8494	−	36.4796i	0.154003	−	0.0712493i
$65$	95.1648	−	57.2588i	0.181596	−	0.109263i
$66$	98.6344	−	355.249i	0.183955	−	0.662548i
$67$	−400.175	+	88.0852i	−0.729689	+	0.160617i	−0.564251	−	0.825603i	$-0.690835\pi$
$67$	−400.175	+	88.0852i	−0.729689	+	0.160617i	−0.165438	+	0.986220i	$0.552904\pi$
$68$	−417.879	−	45.4471i	−0.745224	−	0.0810480i
$69$	−449.767	−	270.616i	−0.784719	−	0.472150i
$70$	1091.79	−	1034.20i	1.86419	−	1.76586i
$71$	−691.863	−	320.090i	−1.15646	−	0.535038i	−0.254596	−	0.967047i	$-0.581943\pi$
$71$	−691.863	−	320.090i	−1.15646	−	0.535038i	−0.901869	+	0.432010i	$0.857805\pi$
$72$	128.064	−	13.9278i	0.209617	−	0.0227972i
$73$	146.073	−	49.2179i	0.234200	−	0.0789111i	−0.199754	−	0.979846i	$-0.564014\pi$
$73$	146.073	−	49.2179i	0.234200	−	0.0789111i	0.433954	+	0.900935i	$0.357118\pi$
$74$	−335.745	−	842.657i	−0.527427	−	1.32374i
$75$	122.347	+	115.893i	0.188365	+	0.178429i
$76$	−111.433	−	401.346i	−0.168188	−	0.605757i
$77$	−543.191	−	1024.57i	−0.803926	−	1.51637i
$78$	−67.8090	+	51.5471i	−0.0984341	+	0.0748277i
$79$	37.0535	+	683.411i	0.0527701	+	0.973288i	0.898306	+	0.439370i	$0.144798\pi$
$79$	37.0535	+	683.411i	0.0527701	+	0.973288i	−0.845536	+	0.533918i	$0.820719\pi$
$80$	−1020.12	−	343.717i	−1.42565	−	0.480359i
$81$	79.1063	+	17.4126i	0.108513	+	0.0238856i
$82$	530.617	−	1000.85i	0.714595	−	1.34787i
$83$	−108.716	−	663.136i	−0.143772	−	0.876972i	−0.955943	−	0.293552i	$-0.905163\pi$
$83$	−108.716	−	663.136i	−0.143772	−	0.876972i	0.812171	−	0.583420i	$-0.198286\pi$
$84$	−242.176	+	285.112i	−0.314567	+	0.370337i
$85$	−953.765	−	1122.86i	−1.21706	−	1.43284i
$86$	−18.1920	+	110.967i	−0.0228104	+	0.139138i
$87$	−195.394	−	148.535i	−0.240787	−	0.183041i
$88$	−286.879	+	423.115i	−0.347516	+	0.512548i
$89$	−244.086	+	360.000i	−0.290709	+	0.428763i	−0.944798	−	0.327654i	$-0.893742\pi$
$89$	−244.086	+	360.000i	−0.290709	+	0.428763i	0.654089	+	0.756418i	$0.273052\pi$
$90$	−331.847	−	252.263i	−0.388663	−	0.295454i
$91$	−43.3434	+	264.383i	−0.0499299	+	0.304559i
$92$	−435.007	−	512.129i	−0.492963	−	0.580361i
$93$	197.599	−	232.631i	0.220323	−	0.259384i
$94$	222.081	+	1354.63i	0.243680	+	1.48638i
$95$	683.823	−	1289.83i	0.738513	−	1.39298i
$96$	470.787	+	103.628i	0.500515	+	0.110172i
$97$	109.738	+	36.9749i	0.114868	+	0.0387034i	0.376148	−	0.926559i	$-0.377248\pi$
$97$	109.738	+	36.9749i	0.114868	+	0.0387034i	−0.261281	+	0.965263i	$0.584145\pi$
$98$	132.501	+	2443.83i	0.136577	+	2.51902i
$99$	−255.895	+	194.526i	−0.259782	+	0.197481i
$100$	101.050	+	190.601i	0.101050	+	0.190601i
$101$	354.913	+	1278.28i	0.349655	+	1.25934i	0.904171	+	0.427170i	$0.140489\pi$
$101$	354.913	+	1278.28i	0.349655	+	1.25934i	−0.554516	+	0.832173i	$0.687097\pi$
$102$	820.290	+	777.020i	0.796283	+	0.754279i
$103$	18.2399	+	45.7788i	0.0174489	+	0.0437934i	0.937443	−	0.348139i	$-0.113186\pi$
$103$	18.2399	+	45.7788i	0.0174489	+	0.0437934i	−0.919994	+	0.391932i	$0.871807\pi$
$104$	111.919	−	37.7100i	0.105525	−	0.0355555i
$105$	−1303.43	+	141.757i	−1.21145	+	0.131753i
$106$	−1885.83	−	872.477i	−1.72800	−	0.799457i
$107$	−523.483	+	495.869i	−0.472963	+	0.448014i	−0.886675	−	0.462394i	$-0.846991\pi$
$107$	−523.483	+	495.869i	−0.472963	+	0.448014i	0.413712	+	0.910408i	$0.364232\pi$
$108$	88.8478	+	53.4579i	0.0791609	+	0.0476295i
$109$	−679.495	−	73.8995i	−0.597099	−	0.0649385i	−0.195421	−	0.980719i	$-0.562607\pi$
$109$	−679.495	−	73.8995i	−0.597099	−	0.0649385i	−0.401678	+	0.915781i	$0.631573\pi$
$110$	1615.52	−	355.602i	1.40031	−	0.308230i
$111$	−211.570	+	762.006i	−0.180913	+	0.651590i
$112$	2225.01	−	1338.75i	1.87718	−	1.12946i
$113$	−352.542	+	163.103i	−0.293490	+	0.135783i	−0.561109	−	0.827742i	$-0.689625\pi$
$113$	−352.542	+	163.103i	−0.293490	+	0.135783i	0.267619	+	0.963525i	$0.413763\pi$
$114$	−414.418	+	1040.11i	−0.340472	+	0.854520i
$115$	127.502	−	2351.63i	0.103388	−	1.90688i
$116$	−176.323	−	260.057i	−0.141131	−	0.208152i
$117$	74.2612			0.0586791
$118$	941.946	+	1242.78i	0.734857	+	0.969553i
$119$	3553.88			2.73768
$120$	324.350	+	478.380i	0.246741	+	0.363916i
$121$	−3.00011	+	55.3337i	−0.00225403	+	0.0415731i
$122$	944.401	−	2370.27i	0.700837	−	1.75897i
$123$	−896.350	+	414.696i	−0.657082	+	0.303999i
$124$	334.797	−	201.441i	0.242465	−	0.145886i
$125$	247.838	−	892.633i	0.177339	−	0.638717i
$126$	982.028	−	216.161i	0.694334	−	0.152834i
$127$	2193.41	+	238.548i	1.53255	+	0.166675i	0.835156	−	0.550013i	$-0.185377\pi$
$127$	2193.41	+	238.548i	1.53255	+	0.166675i	0.697394	+	0.716688i	$0.254343\pi$
$128$	−1357.63	−	816.862i	−0.937493	−	0.564071i
$129$	71.1743	−	67.4199i	0.0485779	−	0.0460155i
$130$	−346.843	−	160.467i	−0.234001	−	0.108261i
$131$	−1196.59	+	130.137i	−0.798065	+	0.0867948i	−0.498060	−	0.867143i	$-0.665954\pi$
$131$	−1196.59	+	130.137i	−0.798065	+	0.0867948i	−0.300005	+	0.953938i	$0.596988\pi$
$132$	−389.942	+	131.387i	−0.257122	+	0.0866344i
$133$	1303.49	+	3271.51i	0.849825	+	2.13290i
$134$	1023.63	+	969.630i	0.659909	+	0.625099i
$135$	97.2259	+	350.176i	0.0619842	+	0.223247i
$136$	−733.822	−	1384.13i	−0.462682	−	0.872710i
$137$	−1373.64	+	1044.21i	−0.856628	+	0.651192i	−0.938435	−	0.345457i	$-0.887724\pi$
$137$	−1373.64	+	1044.21i	−0.856628	+	0.651192i	0.0818067	+	0.996648i	$0.473931\pi$
$138$	97.7849	+	1803.54i	0.0603189	+	1.11252i
$139$	1327.88	+	447.415i	0.810284	+	0.273016i	0.693792	−	0.720175i	$-0.255939\pi$
$139$	1327.88	+	447.415i	0.810284	+	0.273016i	0.116492	+	0.993192i	$0.462835\pi$
$140$	−1639.16	−	360.806i	−0.989531	−	0.217812i
$141$	560.589	−	1057.38i	0.334823	−	0.631544i
$142$	424.376	+	2588.58i	0.250794	+	1.52978i
$143$	−190.782	+	224.606i	−0.111566	+	0.131346i
$144$	−465.970	−	548.582i	−0.269658	−	0.317466i
$145$	178.158	−	1086.72i	0.102036	−	0.622392i
$146$	−422.249	−	320.985i	−0.239353	−	0.181951i
$147$	1197.44	−	1766.09i	0.671859	−	0.990918i
$148$	−568.126	+	837.924i	−0.315539	+	0.465385i
$149$	−793.071	−	602.877i	−0.436046	−	0.331474i	0.364014	−	0.931394i	$-0.381406\pi$
$149$	−793.071	−	602.877i	−0.436046	−	0.331474i	−0.800060	+	0.599920i	$0.795199\pi$
$150$	93.8149	−	572.246i	0.0510664	−	0.311491i
$151$	−1689.70	−	1989.27i	−0.910637	−	1.07208i	−0.997121	−	0.0758313i	$-0.975839\pi$
$151$	−1689.70	−	1989.27i	−0.910637	−	1.07208i	0.0864839	−	0.996253i	$-0.472437\pi$
$152$	1005.01	−	1183.19i	0.536296	−	0.631377i
$153$	−159.368	−	972.104i	−0.0842103	−	0.513660i
$154$	−1869.11	+	3525.52i	−0.978034	+	1.84477i
$155$	1337.44	+	294.392i	0.693068	+	0.152556i
$156$	90.0875	+	30.3540i	0.0462357	+	0.0155786i
$157$	73.8766	+	1362.57i	0.0375541	+	0.692645i	0.955329	+	0.295544i	$0.0955009\pi$
$157$	73.8766	+	1362.57i	0.0375541	+	0.692645i	−0.917775	+	0.397101i	$0.870016\pi$
$158$	1874.85	−	1425.22i	0.944018	−	0.717624i
$159$	848.560	+	1600.55i	0.423240	+	0.798315i
$160$	578.622	+	2084.01i	0.285901	+	1.02972i
$161$	4124.44	+	3906.88i	2.01895	+	1.91245i
$162$	−103.165	−	258.924i	−0.0500333	−	0.125574i
$163$	−75.4613	+	25.4259i	−0.0362613	+	0.0122178i	−0.337374	−	0.941371i	$-0.609539\pi$
$163$	−75.4613	+	25.4259i	−0.0362613	+	0.0122178i	0.301112	+	0.953589i	$0.402642\pi$
$164$	−1256.88	+	136.694i	−0.598451	+	0.0650855i
$165$	−1308.90	−	605.562i	−0.617563	−	0.285715i
$166$	−1678.72	+	1590.17i	−0.784904	+	0.743501i
$167$	−16.9946	−	10.2253i	−0.00787475	−	0.00473808i	0.511611	−	0.859217i	$-0.329049\pi$
$167$	−16.9946	−	10.2253i	−0.00787475	−	0.00473808i	−0.519486	+	0.854479i	$0.673876\pi$
$168$	−1386.04	−	150.741i	−0.636522	−	0.0692259i
$169$	−2079.14	+	457.654i	−0.946356	+	0.208309i
$170$	−1356.22	+	4884.67i	−0.611867	+	2.20375i
$171$	836.414	−	503.254i	0.374048	−	0.225057i
$172$	113.900	−	52.6959i	0.0504932	−	0.0233606i
$173$	−123.936	+	311.055i	−0.0544663	+	0.136700i	−0.953692	−	0.300785i	$-0.902751\pi$
$173$	−123.936	+	311.055i	−0.0544663	+	0.136700i	0.899226	+	0.437485i	$0.144131\pi$
$174$	−45.7236	+	843.322i	−0.0199212	+	0.367426i
$175$	−1023.57	−	1509.66i	−0.442141	−	0.652110i
$176$	2856.32			1.22331
$177$	1.93719	−	1359.56i	0.000822644	−	0.577350i
$178$	1496.64			0.630214
$179$	−2429.12	−	3582.68i	−1.01431	−	1.49599i	−0.861516	−	0.507730i	$-0.830485\pi$
$179$	−2429.12	−	3582.68i	−1.01431	−	1.49599i	−0.152789	−	0.988259i	$-0.548826\pi$
$180$	−25.1869	+	464.545i	−0.0104296	+	0.192362i
$181$	−776.844	+	1949.73i	−0.319018	+	0.800676i	0.678779	+	0.734343i	$0.262509\pi$
$181$	−776.844	+	1949.73i	−0.319018	+	0.800676i	−0.997798	+	0.0663334i	$0.978870\pi$
$182$	836.677	−	387.088i	0.340762	−	0.157653i
$183$	−1906.07	+	1146.85i	−0.769951	+	0.463264i
$184$	669.984	−	2413.06i	0.268434	−	0.966812i
$185$	−3465.27	+	762.764i	−1.37715	+	0.303133i
$186$	−1044.12	−	113.555i	−0.411605	−	0.0447647i
$187$	3349.60	+	2015.39i	1.30988	+	0.788126i
$188$	1112.26	−	1053.59i	0.431489	−	0.408728i
$189$	−795.645	−	368.105i	−0.306215	−	0.141670i
$190$	−4994.00	+	543.130i	−1.90686	+	0.207383i
$191$	61.5340	−	20.7332i	0.0233112	−	0.00785447i	−0.307622	−	0.951509i	$-0.599533\pi$
$191$	61.5340	−	20.7332i	0.0233112	−	0.00785447i	0.330933	+	0.943654i	$0.392637\pi$
$192$	96.4719	+	242.126i	0.0362618	+	0.0910102i
$193$	−243.623	−	230.772i	−0.0908618	−	0.0860689i	0.640921	−	0.767607i	$-0.278553\pi$
$193$	−243.623	−	230.772i	−0.0908618	−	0.0860689i	−0.731783	+	0.681538i	$0.761311\pi$
$194$	−106.600	−	383.940i	−0.0394508	−	0.142089i
$195$	156.068	+	294.375i	0.0573142	+	0.108106i
$196$	2174.52	−	1653.03i	0.792464	−	0.602415i
$197$	−266.297	−	4911.57i	−0.0963091	−	1.77632i	−0.504491	−	0.863417i	$-0.668320\pi$
$197$	−266.297	−	4911.57i	−0.0963091	−	1.77632i	0.408182	−	0.912901i	$-0.366163\pi$
$198$	1048.16	+	353.168i	0.376211	+	0.126760i
$199$	−4566.85	−	1005.24i	−1.62681	−	0.358088i	−0.694429	−	0.719561i	$-0.744343\pi$
$199$	−4566.85	−	1005.24i	−1.62681	−	0.358088i	−0.932383	+	0.361473i	$0.882274\pi$
$200$	−376.616	+	710.373i	−0.133154	+	0.251155i
$201$	−198.873	−	1213.07i	−0.0697882	−	0.425689i
$202$	2955.28	−	3479.22i	1.02937	−	1.21187i
$203$	1719.74	+	2024.64i	0.594592	+	0.700008i
$204$	204.012	−	1244.42i	0.0700180	−	0.427091i
$205$	−3527.65	−	2681.65i	−1.20186	−	0.913632i
$206$	95.1590	−	140.349i	0.0321847	−	0.0474688i
$207$	883.707	−	1303.37i	0.296724	−	0.437635i
$208$	−525.333	−	399.348i	−0.175122	−	0.133124i
$209$	−626.694	+	3822.66i	−0.207413	+	1.26516i
$210$	2920.71	+	3438.53i	0.959754	+	1.12991i
$211$	409.680	−	482.313i	0.133666	−	0.157364i	−0.691257	−	0.722609i	$-0.742943\pi$
$211$	409.680	−	482.313i	0.133666	−	0.157364i	0.824923	+	0.565245i	$0.191219\pi$
$212$	375.181	+	2288.50i	0.121545	+	0.741392i
$213$	1071.23	−	2020.56i	0.344599	−	0.649982i
$214$	2423.13	+	533.372i	0.774028	+	0.170376i
$215$	416.837	+	140.449i	0.132223	+	0.0445513i
$216$	20.9223	+	385.889i	0.00659066	+	0.121558i
$217$	−2629.88	+	1999.18i	−0.822709	+	0.625407i
$218$	1101.66	+	2077.95i	0.342265	+	0.645580i
$219$	123.712	+	445.571i	0.0381721	+	0.137484i
$220$	−1340.33	−	1269.63i	−0.410750	−	0.389083i
$221$	−334.282	−	838.984i	−0.101748	−	0.255367i
$222$	2578.79	−	868.897i	0.779628	−	0.262687i
$223$	2707.09	−	294.413i	0.812914	−	0.0884098i	0.307788	−	0.951455i	$-0.400411\pi$
$223$	2707.09	−	294.413i	0.812914	−	0.0884098i	0.505127	+	0.863045i	$0.331446\pi$
$224$	−4735.14	−	2190.71i	−1.41241	−	0.653450i
$225$	−367.041	+	347.679i	−0.108753	+	0.103016i
$226$	1145.30	+	689.105i	0.337099	+	0.202825i
$227$	−3292.83	−	358.117i	−0.962787	−	0.104709i	−0.386796	−	0.922165i	$-0.626418\pi$
$227$	−3292.83	−	358.117i	−0.962787	−	0.104709i	−0.575991	+	0.817456i	$0.695384\pi$
$228$	1220.37	−	268.624i	0.354478	−	0.0780266i
$229$	946.457	−	3408.83i	0.273116	−	0.983676i	−0.692009	−	0.721888i	$-0.743274\pi$
$229$	946.457	−	3408.83i	0.273116	−	0.983676i	0.965126	−	0.261787i	$-0.0843119\pi$
$230$	−6943.81	+	4177.95i	−1.99070	+	1.19776i
$231$	3157.41	−	1460.78i	0.899319	−	0.416069i
$232$	433.438	−	1087.85i	0.122658	−	0.307848i
$233$	133.043	−	2453.84i	0.0374075	−	0.689941i	−0.918347	−	0.395776i	$-0.870476\pi$
$233$	133.043	−	2453.84i	0.0374075	−	0.689941i	0.955755	−	0.294165i	$-0.0950416\pi$
$234$	−143.401	−	211.501i	−0.0400616	−	0.0590865i
$235$	5369.66			1.49054
$236$	558.066	−	1648.51i	0.153928	−	0.454700i
$237$	−2053.24			−0.562753
$238$	−6862.67	−	10121.7i	−1.86908	−	2.75668i
$239$	−190.253	+	3509.00i	−0.0514913	+	0.949701i	0.852654	+	0.522476i	$0.174992\pi$
$239$	−190.253	+	3509.00i	−0.0514913	+	0.949701i	−0.904145	+	0.427225i	$0.859491\pi$
$240$	1195.32	−	3000.03i	0.321491	−	0.806880i
$241$	−5464.95	+	2528.36i	−1.46070	+	0.675792i	−0.979615	−	0.200883i	$-0.935619\pi$
$241$	−5464.95	+	2528.36i	−1.46070	+	0.675792i	−0.481084	+	0.876674i	$0.659757\pi$
$242$	163.387	−	98.3069i	0.0434006	−	0.0261133i
$243$	−65.0094	+	234.143i	−0.0171620	+	0.0618118i
$244$	−2781.06	+	612.157i	−0.729668	+	0.160612i
$245$	9517.44	+	1035.08i	2.48182	+	0.269915i
$246$	2911.96	+	1752.07i	0.754716	+	0.454097i
$247$	649.716	−	615.444i	0.167370	−	0.158542i
$248$	1321.66	+	611.463i	0.338408	+	0.156564i
$249$	2004.15	−	217.964i	0.510071	−	0.0554736i
$250$	−3020.86	+	1017.85i	−0.764225	+	0.257497i
$251$	−331.269	−	831.422i	−0.0833048	−	0.209079i	0.881424	−	0.472327i	$-0.156586\pi$
$251$	−331.269	−	831.422i	−0.0833048	−	0.209079i	−0.964728	+	0.263247i	$0.915206\pi$
$252$	−814.748	−	771.771i	−0.203668	−	0.192925i
$253$	1671.79	+	6021.26i	0.415434	+	1.49626i
$254$	−3556.16	−	6707.63i	−0.878477	−	1.65698i
$255$	3518.54	−	2674.73i	0.864077	−	0.656855i
$256$	257.538	+	4750.01i	0.0628755	+	1.15967i
$257$	3165.16	+	1066.47i	0.768237	+	0.258849i	0.676014	−	0.736889i	$-0.263706\pi$
$257$	3165.16	+	1066.47i	0.768237	+	0.258849i	0.0922236	+	0.995738i	$0.470603\pi$
$258$	−329.457	−	72.5189i	−0.0795003	−	0.0174993i
$259$	4009.23	−	7562.20i	0.961858	−	1.81426i
$260$	69.0037	+	420.904i	0.0164593	+	0.100398i
$261$	476.686	−	561.199i	0.113050	−	0.133093i
$262$	2681.30	+	3156.67i	0.632256	+	0.744349i
$263$	−490.535	+	2992.13i	−0.115010	+	0.701531i	0.864878	+	0.501982i	$0.167396\pi$
$263$	−490.535	+	2992.13i	−0.115010	+	0.701531i	−0.979888	+	0.199548i	$0.936052\pi$
$264$	−1220.89	−	928.096i	−0.284623	−	0.216365i
$265$	−4561.34	+	6727.47i	−1.05736	+	1.55949i
$266$	6800.39	−	10029.8i	1.56751	−	2.31191i
$267$	−1038.77	−	789.654i	−0.238097	−	0.180996i
$268$	254.583	−	1552.89i	0.0580265	−	0.353946i
$269$	4769.54	+	5615.14i	1.08106	+	1.27272i	0.959978	+	0.280074i	$0.0903591\pi$
$269$	4769.54	+	5615.14i	1.08106	+	1.27272i	0.121077	+	0.992643i	$0.461365\pi$
$270$	809.577	−	953.108i	0.182479	−	0.214831i
$271$	607.640	+	3706.44i	0.136205	+	0.830813i	0.963236	+	0.268657i	$0.0865797\pi$
$271$	607.640	+	3706.44i	0.136205	+	0.830813i	−0.827031	+	0.562156i	$0.809972\pi$
$272$	−4100.21	+	7733.81i	−0.914013	+	1.72401i
$273$	−784.945	−	172.780i	−0.174019	−	0.0383044i
$274$	5626.54	+	1895.80i	1.24055	+	0.417991i
$275$	−108.618	−	2003.34i	−0.0238179	−	0.439295i
$276$	1604.79	−	1219.93i	0.349989	−	0.266054i
$277$	−2004.95	−	3781.74i	−0.434895	−	0.820299i	0.565094	−	0.825027i	$-0.308840\pi$
$277$	−2004.95	−	3781.74i	−0.434895	−	0.820299i	−0.999989	+	0.00472775i	$0.998495\pi$
$278$	−1289.92	−	4645.87i	−0.278289	−	1.00230i
$279$	664.776	+	629.710i	0.142649	+	0.135124i
$280$	−2315.38	−	5811.15i	−0.494179	−	1.24030i
$281$	1031.22	−	347.459i	0.218924	−	0.0737640i	−0.207702	−	0.978192i	$-0.566599\pi$
$281$	1031.22	−	347.459i	0.218924	−	0.0737640i	0.426626	+	0.904428i	$0.359702\pi$
$282$	−4094.01	+	445.251i	−0.864521	+	0.0940223i
$283$	−4276.78	−	1978.65i	−0.898332	−	0.415613i	−0.0843052	−	0.996440i	$-0.526867\pi$
$283$	−4276.78	−	1978.65i	−0.898332	−	0.415613i	−0.814027	+	0.580827i	$0.802729\pi$
$284$	2125.42	−	2013.31i	0.444087	−	0.420661i
$285$	3752.74	+	2257.95i	0.779976	+	0.469296i
$286$	1008.10	+	109.638i	0.208427	+	0.0226678i
$287$	10439.3	−	2297.87i	2.14709	−	0.472609i
$288$	−386.892	+	1393.46i	−0.0791591	+	0.285105i
$289$	−6055.46	+	3643.45i	−1.23254	+	0.741594i
$290$	−3439.07	+	1591.08i	−0.696376	+	0.322178i
$291$	−128.585	+	322.725i	−0.0259031	+	0.0650119i
$292$	−32.0483	+	591.097i	−0.00642290	+	0.118463i
$293$	−1625.93	−	2398.06i	−0.324190	−	0.478145i	0.630315	−	0.776340i	$-0.282926\pi$
$293$	−1625.93	−	2398.06i	−0.324190	−	0.478145i	−0.954505	+	0.298195i	$0.903615\pi$
$294$	−7342.25			−1.45649
$295$	5393.45	−	2849.59i	1.06447	−	0.562405i
$296$	−3773.11			−0.740904
$297$	−541.161	−	798.152i	−0.105728	−	0.155938i
$298$	−185.584	+	3422.90i	−0.0360758	+	0.665379i
$299$	534.369	−	1341.17i	0.103356	−	0.259403i
$300$	−587.376	+	271.749i	−0.113041	+	0.0522981i
$301$	−909.179	+	547.035i	−0.174100	+	0.104753i
$302$	−2402.70	+	8653.75i	−0.457814	+	1.64890i
$303$	−3886.86	+	855.563i	−0.736945	+	0.162214i
$304$	−8623.21	−	937.830i	−1.62689	−	0.176935i
$305$	−8551.98	−	5145.56i	−1.60552	−	0.966012i
$306$	−2460.87	+	2331.06i	−0.459734	+	0.435483i
$307$	−765.789	−	354.292i	−0.142365	−	0.0658648i	0.347413	−	0.937712i	$-0.387060\pi$
$307$	−765.789	−	354.292i	−0.142365	−	0.0658648i	−0.489778	+	0.871847i	$0.662922\pi$
$308$	4427.40	−	481.508i	0.819073	−	0.0890795i
$309$	−140.097	+	47.2043i	−0.0257924	+	0.00869048i
$310$	−1744.19	−	4377.59i	−0.319559	−	0.802034i
$311$	3818.57	+	3617.14i	0.696241	+	0.659515i	0.951603	−	0.307331i	$-0.0994359\pi$
$311$	3818.57	+	3617.14i	0.696241	+	0.659515i	−0.255362	+	0.966846i	$0.582195\pi$
$312$	94.7866	+	341.391i	0.0171995	+	0.0619469i
$313$	4602.97	+	8682.12i	0.831231	+	1.56787i	0.823097	+	0.567901i	$0.192244\pi$
$313$	4602.97	+	8682.12i	0.831231	+	1.56787i	0.00813376	+	0.999967i	$0.497411\pi$
$314$	3738.04	−	2841.58i	0.671815	−	0.510700i
$315$	−212.948	−	3927.59i	−0.0380897	−	0.702523i
$316$	−2490.82	−	839.256i	−0.443417	−	0.149405i
$317$	3634.06	+	799.917i	0.643877	+	0.141728i	0.524893	−	0.851168i	$-0.324105\pi$
$317$	3634.06	+	799.917i	0.643877	+	0.141728i	0.118984	+	0.992896i	$0.462036\pi$
$318$	2919.88	−	5507.48i	0.514902	−	0.971208i
$319$	472.728	+	2883.52i	0.0829709	+	0.506100i
$320$	−757.055	+	891.274i	−0.132252	+	0.155699i
$321$	−1400.40	−	1648.68i	−0.243498	−	0.286668i
$322$	3162.60	−	19291.0i	0.547344	−	3.33865i
$323$	−9450.70	−	7184.23i	−1.62802	−	1.23759i
$324$	−174.569	+	257.470i	−0.0299329	+	0.0441478i
$325$	−260.115	+	383.640i	−0.0443956	+	0.0654786i
$326$	218.133	+	165.820i	0.0370591	+	0.0281716i
$327$	331.735	−	2023.49i	0.0561008	−	0.342200i
$328$	−3050.52	−	3591.35i	−0.513526	−	0.604570i
$329$	−8385.61	+	9872.30i	−1.40521	+	1.65434i
$330$	802.855	+	4897.20i	0.133926	+	0.816915i
$331$	−3525.52	+	6649.83i	−0.585438	+	1.10425i	0.397027	+	0.917807i	$0.370042\pi$
$331$	−3525.52	+	6649.83i	−0.585438	+	1.10425i	−0.982465	+	0.186446i	$0.940303\pi$
$332$	2520.36	+	554.772i	0.416634	+	0.0917081i
$333$	−2248.30	−	757.542i	−0.369989	−	0.124664i
$334$	3.69484	+	68.1472i	0.000605307	+	0.0111642i
$335$	4390.73	−	3337.74i	0.716093	−	0.544360i
$336$	3648.97	+	6882.69i	0.592463	+	1.11750i
$337$	2199.86	+	7923.19i	0.355591	+	1.28072i	0.897772	+	0.440461i	$0.145185\pi$
$337$	2199.86	+	7923.19i	0.355591	+	1.28072i	−0.542181	+	0.840262i	$0.682401\pi$
$338$	5318.33	+	5037.79i	0.855855	+	0.810709i
$339$	−431.334	−	1082.57i	−0.0691057	−	0.173442i
$340$	5361.69	−	1806.56i	0.855230	−	0.288161i
$341$	−3612.44	+	392.876i	−0.573679	+	0.0623913i
$342$	−3048.45	−	1410.36i	−0.481991	−	0.222993i
$343$	−8680.71	+	8222.81i	−1.36651	+	1.29443i
$344$	400.787	+	241.145i	0.0628168	+	0.0377956i
$345$	7023.84	+	763.888i	1.09609	+	0.119207i
$346$	1125.23	−	247.682i	0.174835	−	0.0384840i
$347$	1703.86	−	6136.76i	0.263597	−	0.949391i	−0.706708	−	0.707506i	$-0.749820\pi$
$347$	1703.86	−	6136.76i	0.263597	−	0.949391i	0.970305	−	0.241885i	$-0.0777658\pi$
$348$	807.664	−	485.955i	0.124412	−	0.0748561i
$349$	1621.11	−	750.006i	0.248642	−	0.115034i	−0.291610	−	0.956537i	$-0.594191\pi$
$349$	1621.11	−	750.006i	0.248642	−	0.115034i	0.540252	+	0.841503i	$0.318329\pi$
$350$	−2323.04	+	5830.40i	−0.354777	+	0.890423i
$351$	−12.0613	+	222.457i	−0.00183414	+	0.0338287i
$352$	−3220.62	−	4750.06i	−0.487669	−	0.719258i
$353$	13097.4			1.97480			0.987399	−	0.158253i	$-0.0505861\pi$
$353$	13097.4			1.97480			0.987399	+	0.158253i	$0.0505861\pi$
$354$	−3875.86	+	2619.85i	−0.581920	+	0.393342i
$355$	10260.9			1.53406
$356$	−937.383	−	1382.54i	−0.139554	−	0.205827i
$357$	−577.209	+	10646.0i	−0.0855718	+	1.57828i
$358$	−5512.99	+	13836.6i	−0.813885	+	2.04270i
$359$	−4827.99	+	2233.67i	−0.709782	+	0.328380i	−0.741347	−	0.671122i	$-0.765813\pi$
$359$	−4827.99	+	2233.67i	−0.709782	+	0.328380i	0.0315653	+	0.999502i	$0.489951\pi$
$360$	−1485.72	+	893.925i	−0.217511	+	0.130872i
$361$	1312.12	−	4725.84i	0.191300	−	0.688999i
$362$	7053.08	−	1552.50i	1.02404	−	0.225408i
$363$	−165.270	−	17.9742i	−0.0238966	−	0.00259891i
$364$	−881.607	−	530.445i	−0.126947	−	0.0763816i
$365$	−1506.27	+	1426.82i	−0.216005	+	0.204611i
$366$	6946.99	+	3214.02i	0.992145	+	0.459015i
$367$	−5770.73	+	627.605i	−0.820789	+	0.0892662i	−0.508871	−	0.860843i	$-0.669937\pi$
$367$	−5770.73	+	627.605i	−0.820789	+	0.0892662i	−0.311918	+	0.950109i	$0.600971\pi$
$368$	−13260.5	+	4467.98i	−1.87840	+	0.632906i
$369$	−1096.68	−	2752.46i	−0.154718	−	0.388312i
$370$	8863.97	+	8396.40i	1.24545	+	1.17975i
$371$	−5245.41	−	18892.2i	−0.734037	−	2.64376i
$372$	549.059	+	1035.64i	0.0765253	+	0.144342i
$373$	9793.73	−	7445.00i	1.35952	−	1.03348i	0.364773	−	0.931097i	$-0.381147\pi$
$373$	9793.73	−	7445.00i	1.35952	−	1.03348i	0.994745	−	0.102382i	$-0.0326464\pi$
$374$	−728.243	−	13431.7i	−0.100686	−	1.85704i
$375$	2633.72	+	887.404i	0.362679	+	0.122201i
$376$	5576.49	+	1227.48i	0.764855	+	0.168357i
$377$	316.207	−	596.429i	0.0431975	−	0.0814792i
$378$	488.033	+	2976.87i	0.0664067	+	0.405063i
$379$	−2942.73	+	3464.45i	−0.398834	+	0.469543i	−0.924519	−	0.381136i	$-0.875533\pi$
$379$	−2942.73	+	3464.45i	−0.398834	+	0.469543i	0.525685	+	0.850679i	$0.323809\pi$
$380$	3629.58	+	4273.07i	0.489983	+	0.576853i
$381$	−1070.84	+	6531.84i	−0.143992	+	0.878311i
$382$	−177.874	−	135.216i	−0.0238242	−	0.0181107i
$383$	−2035.37	+	3001.94i	−0.271547	+	0.400501i	−0.938873	−	0.344264i	$-0.888128\pi$
$383$	−2035.37	+	3001.94i	−0.271547	+	0.400501i	0.667326	+	0.744766i	$0.267439\pi$
$384$	2667.49	−	3934.26i	0.354492	−	0.522837i
$385$	12426.2	+	9446.18i	1.64493	+	1.25045i
$386$	−186.808	+	1139.48i	−0.0246329	+	0.150254i
$387$	190.403	+	224.160i	0.0250097	+	0.0294437i
$388$	−287.901	+	338.944i	−0.0376700	+	0.0443486i
$389$	−1700.57	−	10373.0i	−0.221651	−	1.35201i	−0.829743	−	0.558146i	$-0.811513\pi$
$389$	−1700.57	−	10373.0i	−0.221651	−	1.35201i	0.608091	−	0.793867i	$-0.291935\pi$
$390$	537.028	−	1012.94i	0.0697268	−	0.131519i
$391$	−18703.1	−	4116.86i	−2.41907	−	0.532477i
$392$	9647.42	+	3250.59i	1.24303	+	0.418826i
$393$	−195.492	−	3605.64i	−0.0250923	−	0.462800i
$394$	−13474.2	+	10242.8i	−1.72290	+	1.30971i
$395$	−4315.12	−	8139.17i	−0.549663	−	1.03677i
$396$	−330.249	−	1189.45i	−0.0419082	−	0.150940i
$397$	4307.43	+	4080.22i	0.544544	+	0.515819i	0.909777	−	0.415097i	$-0.136252\pi$
$397$	4307.43	+	4080.22i	0.544544	+	0.515819i	−0.365234	+	0.930916i	$0.619011\pi$
$398$	5955.77	+	14947.8i	0.750090	+	1.88258i
$399$	−10011.8	+	3373.38i	−1.25619	+	0.423259i
$400$	4466.18	−	485.726i	0.558272	−	0.0607158i
$401$	2024.88	+	936.810i	0.252164	+	0.116664i	0.541900	−	0.840443i	$-0.317705\pi$
$401$	2024.88	+	936.810i	0.252164	+	0.116664i	−0.289736	+	0.957107i	$0.593567\pi$
$402$	−3070.88	+	2908.89i	−0.380999	+	0.360901i
$403$	719.328	+	432.805i	0.0889139	+	0.0534977i
$404$	−5064.92	−	550.843i	−0.623736	−	0.0678354i
$405$	−1064.78	+	234.375i	−0.130640	+	0.0287561i
$406$	2445.41	−	8807.58i	0.298926	−	1.07663i
$407$	8067.26	−	4853.91i	0.982505	−	0.591153i
$408$	4265.50	−	1973.43i	0.517583	−	0.239459i
$409$	2692.64	−	6758.02i	0.325532	−	0.817023i	−0.671570	−	0.740941i	$-0.734380\pi$
$409$	2692.64	−	6758.02i	0.325532	−	0.817023i	0.997102	−	0.0760817i	$-0.0242410\pi$
$410$	−825.494	+	15225.3i	−0.0994348	+	1.83397i
$411$	−2904.95	−	4284.48i	−0.348639	−	0.514203i
$412$	−189.249			−0.0226302
$413$	−3183.69	+	14366.1i	−0.379320	+	1.71165i
$414$	−5418.55			−0.643255
$415$	5075.96	+	7486.47i	0.600407	+	0.885534i
$416$	−71.7804	+	1323.91i	−0.00845992	+	0.156034i
$417$	−1555.95	+	3905.13i	−0.182722	+	0.458598i
$418$	12097.4	−	5596.84i	1.41555	−	0.654905i
$419$	−7983.82	+	4803.70i	−0.930871	+	0.560086i	−0.898300	−	0.439383i	$-0.855197\pi$
$419$	−7983.82	+	4803.70i	−0.930871	+	0.560086i	−0.0325711	+	0.999469i	$0.510370\pi$
$420$	1347.06	−	4851.67i	0.156499	−	0.563660i
$421$	2706.34	−	595.710i	0.313299	−	0.0689623i	−0.0555376	−	0.998457i	$-0.517687\pi$
$421$	2706.34	−	595.710i	0.313299	−	0.0689623i	0.368837	+	0.929494i	$0.379756\pi$
$422$	−2164.77	−	235.432i	−0.249714	−	0.0271580i
$423$	3076.45	+	1851.04i	0.353622	+	0.212767i
$424$	−6274.90	+	5943.90i	−0.718717	+	0.680805i
$425$	5580.20	+	2581.68i	0.636893	+	0.294658i
$426$	−7823.26	+	850.831i	−0.889762	+	0.0967674i
$427$	22815.6	−	7687.48i	2.58577	−	0.871248i
$428$	−1024.96	−	2572.45i	−0.115755	−	0.290524i
$429$	−641.844	−	607.987i	−0.0722343	−	0.0684240i
$430$	−404.920	−	1458.39i	−0.0454116	−	0.163558i
$431$	−1971.92	−	3719.44i	−0.220381	−	0.415682i	0.748527	−	0.663104i	$-0.230761\pi$
$431$	−1971.92	−	3719.44i	−0.220381	−	0.415682i	−0.968908	+	0.247422i	$0.920417\pi$
$432$	1719.01	−	1306.76i	0.191449	−	0.145536i
$433$	−69.4612	−	1281.14i	−0.00770922	−	0.142188i	−0.999854	−	0.0170926i	$-0.994559\pi$
$433$	−69.4612	−	1281.14i	−0.00770922	−	0.142188i	0.992145	−	0.125096i	$-0.0399238\pi$
$434$	10772.2	+	3629.58i	1.19143	+	0.401440i
$435$	3226.43	+	710.191i	0.355622	+	0.0782783i
$436$	1229.53	−	2319.14i	0.135054	−	0.254740i
$437$	−3070.14	−	18727.0i	−0.336075	−	2.04997i
$438$	1030.12	−	1212.75i	0.112377	−	0.132301i
$439$	−4898.81	−	5767.33i	−0.532591	−	0.627015i	0.428401	−	0.903589i	$-0.359077\pi$
$439$	−4898.81	−	5767.33i	−0.532591	−	0.627015i	−0.960993	+	0.276573i	$0.910801\pi$
$440$	1113.19	−	6790.16i	0.120612	−	0.735701i
$441$	5096.03	+	3873.90i	0.550267	+	0.418302i
$442$	−1743.97	+	2572.17i	−0.187675	+	0.276800i
$443$	5183.54	−	7645.15i	0.555931	−	0.819937i	−0.441058	−	0.897478i	$-0.645397\pi$
$443$	5183.54	−	7645.15i	0.555931	−	0.819937i	0.996989	+	0.0775419i	$0.0247072\pi$
$444$	−2417.81	−	1837.97i	−0.258433	−	0.196456i
$445$	947.139	−	5777.29i	0.100896	−	0.615438i
$446$	−6065.99	−	7141.44i	−0.644020	−	0.758199i
$447$	1934.79	−	2277.81i	0.204725	−	0.241021i
$448$	−456.372	−	2783.75i	−0.0481284	−	0.293571i
$449$	−2500.28	+	4716.02i	−0.262796	+	0.495686i	−0.979435	−	0.201758i	$-0.935335\pi$
$449$	−2500.28	+	4716.02i	−0.262796	+	0.495686i	0.716639	+	0.697444i	$0.245679\pi$
$450$	1698.98	+	373.974i	0.177980	+	0.0391763i
$451$	11142.4	+	3754.30i	1.16336	+	0.391980i
$452$	−80.7629	−	1489.58i	−0.00840436	−	0.155009i
$453$	6233.50	−	4738.59i	0.646524	−	0.491475i
$454$	5338.63	+	10069.7i	0.551882	+	1.04096i
$455$	−964.740	−	3474.68i	−0.0994016	−	0.358012i
$456$	3381.13	+	3202.78i	0.347228	+	0.328912i
$457$	−2512.87	−	6306.83i	−0.257215	−	0.645560i	0.742490	−	0.669857i	$-0.233645\pi$
$457$	−2512.87	−	6306.83i	−0.257215	−	0.645560i	−0.999705	+	0.0242969i	$0.992265\pi$
$458$	−11536.2	+	3887.00i	−1.17697	+	0.396567i
$459$	2937.92	−	319.518i	0.298759	−	0.0324920i
$460$	8208.49	+	3797.65i	0.832006	+	0.384927i
$461$	−1996.84	+	1891.51i	−0.201740	+	0.191099i	−0.781899	−	0.623405i	$-0.785749\pi$
$461$	−1996.84	+	1891.51i	−0.201740	+	0.191099i	0.580159	+	0.814503i	$0.302990\pi$
$462$	−10257.5	−	6171.71i	−1.03294	−	0.621502i
$463$	14959.6	+	1626.95i	1.50158	+	0.163307i	0.821659	−	0.569979i	$-0.193049\pi$
$463$	14959.6	+	1626.95i	1.50158	+	0.163307i	0.679921	+	0.733285i	$0.262014\pi$
$464$	−6390.05	+	1406.56i	−0.639333	+	0.140728i
$465$	−1099.10	+	3958.61i	−0.109612	+	0.394788i
$466$	−7245.60	+	4359.54i	−0.720271	+	0.433372i
$467$	−5513.28	+	2550.71i	−0.546304	+	0.252747i	−0.673573	−	0.739121i	$-0.735241\pi$
$467$	−5513.28	+	2550.71i	−0.546304	+	0.252747i	0.127268	+	0.991868i	$0.459379\pi$
$468$	−105.560	+	264.936i	−0.0104263	+	0.0261681i
$469$	−720.289	+	13284.9i	−0.0709165	+	1.30798i
$470$	−10369.0	−	15293.1i	−1.01763	−	1.50089i
$471$	−4093.72			−0.400486
$472$	6252.59	−	1726.43i	0.609743	−	0.168359i
$473$	−1167.14			−0.113457
$474$	3964.89	+	5847.77i	0.384206	+	0.566661i
$475$	−329.851	+	6083.74i	−0.0318623	+	0.587666i
$476$	−5051.73	+	12678.9i	−0.486441	+	1.22087i
$477$	−4932.44	+	2281.99i	−0.473461	+	0.219046i
$478$	10361.3	−	6234.16i	0.991449	−	0.596535i
$479$	−71.6386	+	258.019i	−0.00683351	+	0.0246121i	−0.966888	−	0.255200i	$-0.917859\pi$
$479$	−71.6386	+	258.019i	−0.00683351	+	0.0246121i	0.960055	+	0.279813i	$0.0902723\pi$
$480$	−6336.84	+	1394.84i	−0.602574	+	0.132637i
$481$	−2162.37	−	235.172i	−0.204980	−	0.0222929i
$482$	17753.9	+	10682.2i	1.67774	+	1.00946i
$483$	−12373.3	+	11720.6i	−1.16564	+	1.10416i
$484$	−193.145	−	89.3586i	−0.0181391	−	0.00839205i
$485$	−1549.53	+	168.522i	−0.145074	+	0.0157777i
$486$	792.389	−	266.987i	0.0739578	−	0.0249193i
$487$	4483.13	+	11251.8i	0.417146	+	1.04696i	0.976015	+	0.217701i	$0.0698559\pi$
$487$	4483.13	+	11251.8i	0.417146	+	1.04696i	−0.558870	+	0.829255i	$0.688765\pi$
$488$	−7705.14	−	7298.69i	−0.714744	−	0.677041i
$489$	−63.9096	−	230.181i	−0.00591021	−	0.0212866i
$490$	−15430.5	−	29105.1i	−1.42261	−	2.68333i
$491$	−1474.61	+	1120.97i	−0.135536	+	0.103032i	−0.670746	−	0.741688i	$-0.734026\pi$
$491$	−1474.61	+	1120.97i	−0.135536	+	0.103032i	0.535210	+	0.844719i	$0.320233\pi$
$492$	−205.342	−	3787.32i	−0.0188162	−	0.347044i
$493$	−8486.05	−	2859.28i	−0.775238	−	0.261208i
$494$	−3007.45	−	661.990i	−0.273910	−	0.0602922i
$495$	2026.61	−	3822.59i	0.184019	−	0.347096i
$496$	−1316.38	−	8029.56i	−0.119168	−	0.726891i
$497$	−16024.1	+	18865.0i	−1.44624	+	1.70264i
$498$	−4490.86	−	5287.05i	−0.404097	−	0.475740i
$499$	−1314.64	+	8018.95i	−0.117939	+	0.719394i	0.859967	+	0.510349i	$0.170484\pi$
$499$	−1314.64	+	8018.95i	−0.117939	+	0.719394i	−0.977906	+	0.209045i	$0.932965\pi$
$500$	2832.29	+	2153.05i	0.253327	+	0.192574i
$501$	33.3912	−	49.2483i	0.00297766	−	0.00439172i
$502$	−1728.25	+	2548.98i	−0.153657	+	0.226627i
$503$	12142.0	+	9230.12i	1.07631	+	0.818192i	0.984112	−	0.177548i	$-0.0568166\pi$
$503$	12142.0	+	9230.12i	1.07631	+	0.818192i	0.0922013	+	0.995740i	$0.470610\pi$
$504$	676.678	−	4127.55i	0.0598048	−	0.364793i
$505$	−11560.2	−	13609.7i	−1.01865	−	1.19925i
$506$	13920.6	−	16388.6i	1.22302	−	1.43985i
$507$	−1033.26	−	6302.62i	−0.0905103	−	0.552089i
$508$	−3968.92	+	7486.18i	−0.346639	+	0.653830i
$509$	16669.7	+	3669.29i	1.45162	+	0.319525i	0.869643	−	0.493682i	$-0.164349\pi$
$509$	16669.7	+	3669.29i	1.45162	+	0.319525i	0.581975	+	0.813207i	$0.302280\pi$
$510$	−14412.2	−	4856.05i	−1.25134	−	0.421626i
$511$	−270.959	−	4997.55i	−0.0234570	−	0.432639i
$512$	2940.16	−	2235.05i	0.253785	−	0.192922i
$513$	1371.70	+	2587.30i	0.118055	+	0.222675i
$514$	−3074.67	−	11074.0i	−0.263848	−	0.950294i
$515$	−481.550	−	456.149i	−0.0412032	−	0.0390297i
$516$	139.357	+	349.759i	0.0118892	+	0.0298397i
$517$	−13502.1	+	4549.40i	−1.14859	+	0.387006i
$518$	−29279.6	+	3184.35i	−2.48354	+	0.270101i
$519$	−911.668	−	421.783i	−0.0771056	−	0.0356728i
$520$	−1154.09	+	1093.21i	−0.0973270	+	0.0921930i
$521$	3653.36	+	2198.15i	0.307210	+	0.184842i	0.660807	−	0.750556i	$-0.270214\pi$
$521$	3653.36	+	2198.15i	0.307210	+	0.184842i	−0.353597	+	0.935398i	$0.615042\pi$
$522$	−2518.83	−	273.939i	−0.211200	−	0.0229693i
$523$	17489.4	−	3849.71i	1.46225	−	0.321866i	0.588603	−	0.808422i	$-0.299678\pi$
$523$	17489.4	−	3849.71i	1.46225	−	0.321866i	0.873650	+	0.486556i	$0.161747\pi$
$524$	1236.64	−	4453.97i	0.103097	−	0.371321i
$525$	4688.57	−	2821.02i	0.389764	−	0.234513i
$526$	9469.02	−	4380.84i	0.784922	−	0.363144i
$527$	4121.85	−	10345.1i	0.340703	−	0.855101i
$528$	−463.914	+	8556.38i	−0.0382372	+	0.705244i
$529$	−10352.1	−	15268.2i	−0.850831	−	1.25488i
$530$	27968.4			2.29221
$531$	4072.39	+	226.619i	0.332818	+	0.0185205i
$532$	−13524.4			−1.10217
$533$	−1524.41	−	2248.33i	−0.123882	−	0.182713i
$534$	−243.080	+	4483.34i	−0.0196987	+	0.363321i
$535$	3592.37	−	9016.16i	0.290302	−	0.728603i
$536$	5322.84	−	2462.61i	0.428940	−	0.198449i
$537$	11126.8	−	6694.77i	0.894147	−	0.537990i
$538$	6782.12	−	24427.0i	0.543491	−	1.95748i
$539$	−24808.8	+	5460.83i	−1.98254	+	0.436391i
$540$	−1387.50	−	150.900i	−0.110571	−	0.0120254i
$541$	−10298.8	−	6196.59i	−0.818448	−	0.492444i	0.0437336	−	0.999043i	$-0.486075\pi$
$541$	−10298.8	−	6196.59i	−0.818448	−	0.492444i	−0.862182	+	0.506599i	$0.830902\pi$
$542$	9382.81	−	8887.87i	0.743591	−	0.704367i
$543$	−5714.44	−	2643.78i	−0.451621	−	0.208942i
$544$	17484.5	−	1901.55i	1.37802	−	0.149868i
$545$	8718.41	−	2937.57i	0.685240	−	0.230884i
$546$	1023.67	+	2569.22i	0.0802364	+	0.201378i
$547$	−14268.3	−	13515.7i	−1.11530	−	1.05647i	−0.997990	−	0.0633720i	$-0.979815\pi$
$547$	−14268.3	−	13515.7i	−1.11530	−	1.05647i	−0.117309	−	0.993095i	$-0.537427\pi$
$548$	−1772.77	−	6384.95i	−0.138192	−	0.497722i
$549$	−3125.91	−	5896.10i	−0.243007	−	0.458360i
$550$	−5495.90	+	4177.88i	−0.426084	+	0.323900i
$551$	−480.404	−	8860.53i	−0.0371432	−	0.685066i
$552$	7119.76	+	2398.93i	0.548980	+	0.184973i
$553$	21702.9	+	4777.17i	1.66890	+	0.367353i
$554$	−6899.01	+	13012.9i	−0.529081	+	0.997953i
$555$	−1722.12	−	10504.5i	−0.131711	−	0.803404i
$556$	−3483.76	+	4101.39i	−0.265727	+	0.312838i
$557$	−3750.70	−	4415.67i	−0.285318	−	0.335903i	0.600768	−	0.799424i	$-0.294862\pi$
$557$	−3750.70	−	4415.67i	−0.285318	−	0.335903i	−0.886086	+	0.463521i	$0.846586\pi$
$558$	509.747	−	3109.32i	0.0386726	−	0.235892i
$559$	214.660	+	163.181i	0.0162418	+	0.0123467i
$560$	−19614.6	+	28929.4i	−1.48013	+	2.18302i
$561$	−6581.32	+	9706.72i	−0.495301	+	0.730514i
$562$	−2980.91	−	2266.03i	−0.223741	−	0.170083i
$563$	277.305	−	1691.48i	0.0207584	−	0.126621i	−0.974414	−	0.224759i	$-0.927840\pi$
$563$	277.305	−	1691.48i	0.0207584	−	0.126621i	0.995173	+	0.0981383i	$0.0312887\pi$
$564$	2975.48	+	3503.01i	0.222146	+	0.261531i
$565$	3384.86	−	3984.96i	0.252039	−	0.296723i
$566$	2623.29	+	16001.4i	0.194815	+	1.18832i
$567$	1231.92	−	2323.65i	0.0912448	−	0.172106i
$568$	10656.1	+	2345.59i	0.787185	+	0.173273i
$569$	−1423.32	−	479.572i	−0.104866	−	0.0353334i	0.266379	−	0.963868i	$-0.414173\pi$
$569$	−1423.32	−	479.572i	−0.104866	−	0.0353334i	−0.371245	+	0.928535i	$0.621069\pi$
$570$	−815.891	−	15048.2i	−0.0599543	−	1.10579i
$571$	−6241.07	+	4744.34i	−0.457409	+	0.347713i	−0.808368	−	0.588678i	$-0.799649\pi$
$571$	−6241.07	+	4744.34i	−0.457409	+	0.347713i	0.350959	+	0.936391i	$0.385856\pi$
$572$	−530.119	−	999.910i	−0.0387507	−	0.0730915i
$573$	52.1143	+	187.699i	0.00379949	+	0.0136845i
$574$	−26703.2	−	25294.6i	−1.94176	−	1.83933i
$575$	3637.97	+	9130.63i	0.263850	+	0.662215i
$576$	−740.982	+	249.666i	−0.0536011	+	0.0180603i
$577$	−18831.1	+	2048.01i	−1.35867	+	0.147764i	−0.758271	−	0.651940i	$-0.773955\pi$
$577$	−18831.1	+	2048.01i	−1.35867	+	0.147764i	−0.600395	+	0.799704i	$0.704990\pi$
$578$	22070.1	+	10210.7i	1.58823	+	0.734792i
$579$	730.868	−	692.315i	0.0524591	−	0.0496919i
$580$	3623.75	+	2180.34i	0.259427	+	0.156092i
$581$	−21691.1	−	2359.05i	−1.54888	−	0.168451i
$582$	1167.44	−	256.974i	0.0831479	−	0.0183022i
$583$	5769.80	−	20780.9i	0.409881	−	1.47626i
$584$	−1890.46	+	1137.45i	−0.133951	+	0.0805959i
$585$	−907.179	+	419.706i	−0.0641149	+	0.0296627i
$586$	−3690.12	+	9261.50i	−0.260132	+	0.652882i
$587$	865.331	−	15960.1i	0.0608450	−	1.12222i	−0.795546	−	0.605893i	$-0.792816\pi$
$587$	865.331	−	15960.1i	0.0608450	−	1.12222i	0.856391	−	0.516328i	$-0.172701\pi$
$588$	4598.63	+	6782.47i	0.322524	+	0.475688i
$589$	11034.9			0.771963
$590$	−18530.7	−	9858.23i	−1.29305	−	0.687893i
$591$	14756.3			1.02706
$592$	11831.0	+	17449.5i	0.821372	+	1.21143i
$593$	−490.296	+	9042.97i	−0.0339528	+	0.626223i	0.931196	+	0.364520i	$0.118767\pi$
$593$	−490.296	+	9042.97i	−0.0339528	+	0.626223i	−0.965148	+	0.261703i	$0.915716\pi$
$594$	−1228.19	+	3082.52i	−0.0848370	+	0.212925i
$595$	−43414.4	+	20085.6i	−2.99129	+	1.38392i
$596$	3278.17	−	1972.41i	0.225300	−	0.135559i
$597$	3753.03	−	13517.2i	0.257289	−	0.926670i
$598$	−4851.62	+	1067.92i	−0.331768	+	0.0730277i
$599$	−21277.1	−	2314.02i	−1.45135	−	0.157844i	−0.651776	−	0.758412i	$-0.725976\pi$
$599$	−21277.1	−	2314.02i	−1.45135	−	0.157844i	−0.799574	+	0.600568i	$0.794941\pi$
$600$	−2066.83	−	1243.57i	−0.140630	−	0.0846141i
$601$	16075.9	−	15227.9i	1.09110	−	1.03354i	0.0918099	−	0.995777i	$-0.470735\pi$
$601$	16075.9	−	15227.9i	1.09110	−	1.03354i	0.999287	−	0.0377650i	$-0.0120238\pi$
$602$	3313.65	+	1533.06i	0.224343	+	0.103792i
$603$	3666.18	−	398.721i	0.247593	−	0.0269273i
$604$	9498.85	−	3200.53i	0.639905	−	0.215609i
$605$	−276.083	−	692.916i	−0.0185527	−	0.0465637i
$606$	9942.37	+	9417.91i	0.666470	+	0.631314i
$607$	5107.99	+	18397.3i	0.341560	+	1.23019i	0.912459	+	0.409168i	$0.134181\pi$
$607$	5107.99	+	18397.3i	0.341560	+	1.23019i	−0.570899	+	0.821020i	$0.693405\pi$
$608$	8163.42	+	15397.8i	0.544524	+	1.02708i
$609$	−6344.31	+	4822.82i	−0.422142	+	0.320904i
$610$	1859.30	+	34292.9i	0.123412	+	2.27619i
$611$	3119.37	+	1051.04i	0.206541	+	0.0695916i
$612$	3694.64	+	813.252i	0.244031	+	0.0537153i
$613$	−32.3353	+	60.9908i	−0.00213052	+	0.00401859i	−0.884575	−	0.466398i	$-0.845551\pi$
$613$	−32.3353	+	60.9908i	−0.00213052	+	0.00401859i	0.882444	+	0.470417i	$0.155896\pi$
$614$	469.721	+	2865.17i	0.0308736	+	0.188321i
$615$	8606.10	−	10131.9i	0.564279	−	0.664321i
$616$	10745.5	+	12650.6i	0.702840	+	0.827447i
$617$	−2412.16	+	14713.5i	−0.157391	+	0.960040i	0.783515	+	0.621372i	$0.213425\pi$
$617$	−2412.16	+	14713.5i	−0.157391	+	0.960040i	−0.940906	+	0.338668i	$0.890024\pi$
$618$	404.974	+	307.853i	0.0263599	+	0.0200383i
$619$	7102.06	−	10474.8i	0.461157	−	0.680155i	−0.524019	−	0.851707i	$-0.675568\pi$
$619$	7102.06	−	10474.8i	0.461157	−	0.680155i	0.985175	+	0.171552i	$0.0548781\pi$
$620$	−2951.41	+	4353.00i	−0.191180	+	0.281969i
$621$	3760.85	+	2858.92i	0.243024	+	0.184742i
$622$	2928.06	−	17860.3i	0.188753	−	1.15134i
$623$	9142.64	+	10763.5i	0.587949	+	0.692187i
$624$	1281.61	−	1508.83i	0.0822203	−	0.0967972i
$625$	3153.33	+	19234.5i	0.201813	+	1.23101i
$626$	15838.8	−	29875.1i	1.01125	−	1.90742i
$627$	−11349.4	−	2498.19i	−0.722888	−	0.159120i
$628$	−4966.16	−	1673.30i	−0.315560	−	0.106324i
$629$	1562.08	+	28810.8i	0.0990207	+	1.82633i
$630$	−10774.8	+	8190.81i	−0.681396	+	0.517984i
$631$	10741.2	+	20260.1i	0.677658	+	1.27820i	0.948866	+	0.315678i	$0.102232\pi$
$631$	10741.2	+	20260.1i	0.677658	+	1.27820i	−0.271208	+	0.962521i	$0.587423\pi$
$632$	−2620.75	−	9439.09i	−0.164949	−	0.594093i
$633$	1378.28	+	1305.57i	0.0865428	+	0.0819777i
$634$	−4739.29	−	11894.7i	−0.296879	−	0.745109i
$635$	−28143.1	+	9482.50i	−1.75878	+	0.592601i
$636$	−6916.38	+	752.201i	−0.431214	+	0.0468974i
$637$	5326.32	+	2464.22i	0.331298	+	0.153275i
$638$	7299.59	−	6914.53i	0.452968	−	0.429074i
$639$	5878.79	+	3537.15i	0.363946	+	0.218979i
$640$	21201.6	+	2305.82i	1.30948	+	0.142415i
$641$	−10543.3	+	2320.76i	−0.649665	+	0.143002i	−0.527564	−	0.849516i	$-0.676894\pi$
$641$	−10543.3	+	2320.76i	−0.649665	+	0.143002i	−0.122101	+	0.992518i	$0.538963\pi$
$642$	−1991.33	+	7172.11i	−0.122416	+	0.440904i
$643$	11469.2	−	6900.77i	0.703422	−	0.423235i	−0.118410	−	0.992965i	$-0.537780\pi$
$643$	11469.2	−	6900.77i	0.703422	−	0.423235i	0.821832	+	0.569730i	$0.192952\pi$
$644$	−19801.0	+	9160.94i	−1.21160	+	0.560546i
$645$	−488.429	+	1225.87i	−0.0298169	+	0.0748347i
$646$	−2211.53	+	40789.2i	−0.134693	+	2.48426i
$647$	−4299.01	−	6340.57i	−0.261223	−	0.385276i	0.674348	−	0.738414i	$-0.264425\pi$
$647$	−4299.01	−	6340.57i	−0.261223	−	0.385276i	−0.935571	+	0.353138i	$0.885115\pi$
$648$	−1159.37			−0.0702844
$649$	−11147.7	+	11734.9i	−0.674243	+	0.709762i
$650$	1594.92			0.0962432
$651$	−5561.61	−	8202.77i	−0.334834	−	0.493843i
$652$	16.5561	−	305.360i	0.000994460	−	0.0183417i
$653$	5986.60	−	15025.2i	0.358765	−	0.900432i	−0.633208	−	0.773982i	$-0.718262\pi$
$653$	5986.60	−	15025.2i	0.358765	−	0.900432i	0.991973	−	0.126451i	$-0.0403585\pi$
$654$	−6403.63	+	2962.64i	−0.382877	+	0.177138i
$655$	13882.1	−	8352.58i	0.828120	−	0.498263i
$656$	−7043.60	+	25368.8i	−0.419217	+	1.50988i
$657$	−1354.85	+	298.224i	−0.0804529	+	0.0177090i
$658$	44309.9	+	4818.99i	2.62520	+	0.285507i
$659$	7438.99	+	4475.89i	0.439730	+	0.264576i	0.718157	−	0.695881i	$-0.244986\pi$
$659$	7438.99	+	4475.89i	0.439730	+	0.264576i	−0.278428	+	0.960457i	$0.589813\pi$
$660$	4020.99	−	3808.88i	0.237146	−	0.224637i
$661$	2726.38	+	1261.36i	0.160429	+	0.0742225i	0.498461	−	0.866912i	$-0.333899\pi$
$661$	2726.38	+	1261.36i	0.160429	+	0.0742225i	−0.338031	+	0.941135i	$0.609761\pi$
$662$	25747.1	−	2800.16i	1.51161	−	0.164398i
$663$	2567.55	−	865.110i	0.150401	−	0.0506758i
$664$	3560.10	+	8935.18i	0.208070	+	0.522217i
$665$	−34413.2	−	32597.9i	−2.00675	−	1.90089i
$666$	2184.03	+	7866.16i	0.127071	+	0.457669i
$667$	−6705.17	−	12647.3i	−0.389243	−	0.734190i
$668$	60.6375	−	46.0954i	0.00351218	−	0.00266989i
$669$	442.269	+	8157.17i	0.0255592	+	0.471411i
$670$	−17984.8	−	6059.77i	−1.03703	−	0.349417i
$671$	25863.7	+	5693.03i	1.48801	+	0.327536i
$672$	7331.55	−	13828.8i	0.420864	−	0.793834i
$673$	−1860.45	−	11348.2i	−0.106560	−	0.649988i	−0.985056	−	0.172237i	$-0.944900\pi$
$673$	−1860.45	−	11348.2i	−0.106560	−	0.649988i	0.878495	−	0.477751i	$-0.158548\pi$
$674$	18317.8	−	21565.3i	1.04684	−	1.23244i
$675$	−981.895	−	1155.98i	−0.0559898	−	0.0659163i
$676$	1322.71	−	8068.15i	0.0752563	−	0.459043i
$677$	12640.2	+	9608.83i	0.717581	+	0.545491i	0.899018	−	0.437912i	$-0.144282\pi$
$677$	12640.2	+	9608.83i	0.717581	+	0.545491i	−0.181437	+	0.983403i	$0.558075\pi$
$678$	−2250.30	+	3318.94i	−0.127466	+	0.187999i
$679$	2110.02	−	3112.05i	0.119256	−	0.175890i
$680$	16787.2	+	12761.3i	0.946705	+	0.719666i
$681$	1607.58	−	9805.83i	0.0904593	−	0.551777i
$682$	8094.69	+	9529.80i	0.454489	+	0.535066i
$683$	2957.98	−	3482.40i	0.165716	−	0.195096i	−0.673036	−	0.739610i	$-0.735010\pi$
$683$	2957.98	−	3482.40i	0.165716	−	0.195096i	0.838752	+	0.544514i	$0.183286\pi$
$684$	606.481	+	3699.37i	0.0339026	+	0.206797i
$685$	10878.8	−	20519.7i	0.606801	−	1.14455i
$686$	40181.9	+	8844.70i	2.23637	+	0.492263i
$687$	10057.8	+	3388.86i	0.558556	+	0.188199i
$688$	−141.491	−	2609.65i	−0.00784056	−	0.144611i
$689$	−3966.61	+	3015.34i	−0.219326	+	0.166728i
$690$	−11387.7	−	21479.4i	−0.628292	−	1.18508i
$691$	8159.05	+	29386.3i	0.449182	+	1.61781i	0.748139	+	0.663542i	$0.230948\pi$
$691$	8159.05	+	29386.3i	0.449182	+	1.61781i	−0.298957	+	0.954267i	$0.596639\pi$
$692$	−933.557	−	884.313i	−0.0512840	−	0.0485788i
$693$	3863.08	+	9695.60i	0.211755	+	0.531465i
$694$	−20768.1	+	6997.60i	−1.13595	+	0.382745i
$695$	−18750.2	+	2039.20i	−1.02336	+	0.111297i
$696$	3188.36	+	1475.09i	0.173641	+	0.0803351i
$697$	−26160.0	+	24780.0i	−1.42163	+	1.34664i
$698$	−5266.49	−	3168.74i	−0.285587	−	0.171832i
$699$	7329.11	+	797.089i	0.396584	+	0.0431311i
$700$	6840.86	−	1505.79i	0.369372	−	0.0813049i
$701$	6686.88	−	24084.0i	0.360285	−	1.29763i	−0.532225	−	0.846603i	$-0.678644\pi$
$701$	6686.88	−	24084.0i	0.360285	−	1.29763i	0.892510	−	0.451027i	$-0.148942\pi$
$702$	656.863	−	395.221i	0.0353158	−	0.0212488i
$703$	−25948.7	+	12005.2i	−1.39214	+	0.644073i
$704$	1148.51	−	2882.54i	0.0614859	−	0.154318i
$705$	−872.122	+	16085.3i	−0.0465901	+	0.859304i
$706$	−25291.5	−	37302.2i	−1.34824	−	1.98851i
$707$	43074.9			2.29137
$708$	4847.65	+	1939.49i	0.257325	+	0.102953i
$709$	−15091.4			−0.799392			−0.399696	−	0.916648i	$-0.630884\pi$
$709$	−15091.4			−0.799392			−0.399696	+	0.916648i	$0.630884\pi$
$710$	−19814.2	−	29223.7i	−1.04734	−	1.54471i
$711$	333.481	−	6150.70i	0.0175900	−	0.324429i
$712$	2304.28	−	5783.31i	0.121287	−	0.304408i
$713$	16156.2	−	7474.67i	0.848605	−	0.392607i
$714$	31435.1	−	18913.9i	1.64766	−	0.991364i
$715$	1061.19	−	3822.05i	0.0555051	−	0.199911i
$716$	16234.6	−	3573.50i	0.847366	−	0.186519i
$717$	−10480.7	−	1139.84i	−0.545896	−	0.0593698i
$718$	15684.7	+	9437.15i	0.815246	+	0.490517i
$719$	2586.82	−	2450.36i	0.134175	−	0.127097i	−0.617669	−	0.786438i	$-0.711923\pi$
$719$	2586.82	−	2450.36i	0.134175	−	0.127097i	0.751845	+	0.659340i	$0.229164\pi$
$720$	8792.76	+	4067.96i	0.455121	+	0.210561i
$721$	1590.67	−	172.995i	0.0821629	−	0.00893576i
$722$	−15993.3	+	5388.76i	−0.824388	+	0.277769i
$723$	−6686.35	−	16781.5i	−0.343939	−	0.863222i
$724$	−5851.65	−	5542.97i	−0.300379	−	0.284535i
$725$	1229.52	+	4428.32i	0.0629836	+	0.226846i
$726$	267.951	+	505.410i	0.0136978	+	0.0258368i
$727$	−3195.04	+	2428.81i	−0.162995	+	0.123906i	−0.683492	−	0.729958i	$-0.739540\pi$
$727$	−3195.04	+	2428.81i	−0.162995	+	0.123906i	0.520497	+	0.853863i	$0.325747\pi$
$728$	−207.605	−	3829.05i	−0.0105692	−	0.194937i
$729$	−690.839	−	232.771i	−0.0350983	−	0.0118260i
$730$	6972.34	+	1534.73i	0.353504	+	0.0778121i
$731$	1675.42	−	3160.17i	0.0847708	−	0.159895i
$732$	−1382.09	−	8430.36i	−0.0697861	−	0.425676i
$733$	−18756.0	+	22081.3i	−0.945114	+	1.11267i	0.0483849	+	0.998829i	$0.484593\pi$
$733$	−18756.0	+	22081.3i	−0.945114	+	1.11267i	−0.993499	+	0.113845i	$0.963683\pi$
$734$	12930.9	+	15223.5i	0.650259	+	0.765544i
$735$	−4646.49	+	28342.3i	−0.233181	+	1.42234i
$736$	22382.0	+	17014.4i	1.12094	+	0.852116i
$737$	−8212.71	+	12112.8i	−0.410474	+	0.605404i
$738$	−5721.45	+	8438.51i	−0.285379	+	0.420902i
$739$	−4430.46	−	3367.95i	−0.220537	−	0.167648i	0.489072	−	0.872243i	$-0.337336\pi$
$739$	−4430.46	−	3367.95i	−0.220537	−	0.167648i	−0.709609	+	0.704595i	$0.751129\pi$
$740$	2204.53	−	13447.0i	0.109514	−	0.668004i
$741$	1738.10	+	2046.25i	0.0861683	+	0.101445i
$742$	−43677.3	+	51420.9i	−2.16097	+	2.54410i
$743$	−1398.14	−	8528.28i	−0.0690347	−	0.421093i	−0.998621	−	0.0524897i	$-0.983284\pi$
$743$	−1398.14	−	8528.28i	−0.0690347	−	0.421093i	0.929587	−	0.368603i	$-0.120164\pi$
$744$	−2046.36	+	3859.84i	−0.100838	+	0.190200i
$745$	13095.5	+	2882.54i	0.644003	+	0.141756i
$746$	−40115.9	−	13516.6i	−1.96883	−	0.663376i
$747$	327.427	+	6039.03i	0.0160374	+	0.295792i
$748$	−11951.5	+	9085.29i	−0.584211	+	0.444106i
$749$	10966.5	+	20684.9i	0.534987	+	1.00909i
$750$	−2558.43	−	9214.62i	−0.124561	−	0.448627i
$751$	−3635.34	−	3443.58i	−0.176639	−	0.167321i	0.594272	−	0.804264i	$-0.297440\pi$
$751$	−3635.34	−	3443.58i	−0.176639	−	0.167321i	−0.770911	+	0.636943i	$0.780199\pi$
$752$	−11809.0	−	29638.4i	−0.572647	−	1.43724i
$753$	2544.41	−	857.312i	0.123139	−	0.0414903i
$754$	−2309.28	+	251.149i	−0.111537	+	0.0121304i
$755$	31884.4	+	14751.3i	1.53694	+	0.711065i
$756$	2444.25	−	2315.31i	0.117588	−	0.111385i
$757$	−7160.31	−	4308.22i	−0.343786	−	0.206849i	0.333180	−	0.942863i	$-0.391878\pi$
$757$	−7160.31	−	4308.22i	−0.343786	−	0.206849i	−0.676966	+	0.736014i	$0.736706\pi$
$758$	15549.5	+	1691.11i	0.745097	+	0.0810342i
$759$	−18308.8	+	4030.07i	−0.875583	+	0.192730i
$760$	−5590.17	+	20134.0i	−0.266811	+	0.960968i
$761$	−34958.1	+	21033.6i	−1.66522	+	1.00193i	−0.710824	+	0.703370i	$0.751678\pi$
$761$	−34958.1	+	21033.6i	−1.66522	+	1.00193i	−0.954392	+	0.298557i	$0.903495\pi$
$762$	20671.0	−	9563.40i	0.982716	−	0.454653i
$763$	−8214.41	+	20616.6i	−0.389753	+	0.978206i
$764$	−13.5005	+	249.002i	−0.000639307	+	0.0117913i
$765$	7440.94	+	10974.6i	0.351670	+	0.518675i
$766$	12480.1			0.588674
$767$	3690.96	−	599.703i	0.173759	−	0.0282321i
$768$	−14271.0			−0.670519
$769$	−11563.5	−	17054.9i	−0.542251	−	0.799760i	0.453557	−	0.891227i	$-0.350155\pi$
$769$	−11563.5	−	17054.9i	−0.542251	−	0.799760i	−0.995808	+	0.0914668i	$0.970844\pi$
$770$	2907.82	−	53631.7i	0.136092	−	2.51007i
$771$	−3708.78	+	9308.33i	−0.173240	+	0.434801i
$772$	1169.61	−	541.118i	0.0545274	−	0.0252270i
$773$	13856.0	−	8336.89i	0.644717	−	0.387914i	−0.155320	−	0.987864i	$-0.549641\pi$
$773$	13856.0	−	8336.89i	0.644717	−	0.387914i	0.800037	+	0.599951i	$0.204813\pi$
$774$	270.747	−	975.142i	0.0125734	−	0.0452852i
$775$	−5581.65	+	1228.61i	−0.258708	+	0.0569460i
$776$	−1647.74	−	179.203i	−0.0762248	−	0.00828995i
$777$	22002.2	+	13238.3i	1.01586	+	0.611223i
$778$	−26259.2	+	24874.0i	−1.21007	+	1.14624i
$779$	−32406.1	−	14992.7i	−1.49046	−	0.689560i
$780$	−1272.07	+	138.346i	−0.0583940	+	0.00635073i
$781$	−25801.3	+	8693.47i	−1.18213	+	0.398306i
$782$	24391.3	+	61217.5i	1.11538	+	2.79940i
$783$	1603.70	+	1519.11i	0.0731951	+	0.0693340i
$784$	−15217.6	−	54808.9i	−0.693223	−	2.49676i
$785$	−8603.41	−	16227.7i	−0.391170	−	0.737825i
$786$	−9891.60	+	7519.40i	−0.448882	+	0.341232i
$787$	−1745.15	−	32187.4i	−0.0790444	−	1.45789i	−0.721951	−	0.691944i	$-0.756754\pi$
$787$	−1745.15	−	32187.4i	−0.0790444	−	1.45789i	0.642907	−	0.765945i	$-0.277728\pi$
$788$	17901.2	+	6031.60i	0.809267	+	0.272674i
$789$	−8883.55	−	1955.42i	−0.400840	−	0.0882316i
$790$	−14848.2	+	28006.8i	−0.668705	+	1.26131i
$791$	2040.48	+	12446.3i	0.0917205	+	0.559471i
$792$	2978.50	−	3506.56i	0.133632	−	0.157323i
$793$	−3960.89	−	4663.12i	−0.177371	−	0.208818i
$794$	3302.92	−	20146.9i	0.147627	−	0.900487i
$795$	−19412.0	−	14756.6i	−0.866002	−	0.658318i
$796$	10078.0	−	14863.9i	0.448749	−	0.661855i
$797$	−20023.4	+	29532.3i	−0.889919	+	1.31253i	0.0594052	+	0.998234i	$0.481080\pi$
$797$	−20023.4	+	29532.3i	−0.889919	+	1.31253i	−0.949324	+	0.314298i	$0.898231\pi$
$798$	28940.8	+	22000.3i	1.28383	+	0.975941i
$799$	7064.12	−	43089.2i	0.312779	−	1.90787i
$800$	−5843.57	−	6879.58i	−0.258252	−	0.304037i
$801$	2534.20	−	2983.49i	0.111787	−	0.131606i
$802$	−1242.02	−	7576.01i	−0.0546850	−	0.333564i
$803$	2578.70	−	4863.95i	0.113326	−	0.213755i
$804$	4610.48	+	1014.84i	0.202237	+	0.0445158i
$805$	−72465.1	−	24416.3i	−3.17274	−	1.06902i
$806$	−156.391	−	2884.46i	−0.00683453	−	0.126055i
$807$	−17595.4	+	13375.6i	−0.767517	+	0.583451i
$808$	−8894.32	−	16776.5i	−0.387254	−	0.730438i
$809$	6131.80	+	22084.7i	0.266480	+	0.959775i	0.968786	+	0.247900i	$0.0797403\pi$
$809$	6131.80	+	22084.7i	0.266480	+	0.959775i	−0.702305	+	0.711876i	$0.747846\pi$
$810$	2723.64	+	2579.97i	0.118147	+	0.111915i
$811$	−79.9803	−	200.735i	−0.00346300	−	0.00869146i	0.927235	−	0.374480i	$-0.122179\pi$
$811$	−79.9803	−	200.735i	−0.00346300	−	0.00869146i	−0.930698	+	0.365788i	$0.880799\pi$
$812$	−9667.70	+	3257.43i	−0.417820	+	0.140780i
$813$	−11201.7	+	1218.26i	−0.483224	+	0.0525538i
$814$	−29402.4	−	13603.0i	−1.26604	−	0.585732i
$815$	778.139	−	737.092i	0.0334442	−	0.0316800i
$816$	−22501.5	−	13538.7i	−0.965330	−	0.580820i
$817$	3523.59	+	383.214i	0.150887	+	0.0164100i
$818$	−24446.9	+	5381.16i	−1.04494	+	0.230010i
$819$	645.067	−	2323.32i	0.0275219	−	0.0991250i
$820$	14581.6	−	8773.44i	0.620989	−	0.373637i
$821$	11656.6	−	5392.89i	0.495513	−	0.229249i	−0.156184	−	0.987728i	$-0.549919\pi$
$821$	11656.6	−	5392.89i	0.495513	−	0.229249i	0.651697	+	0.758479i	$0.274057\pi$
$822$	−6592.91	+	16547.0i	−0.279750	+	0.702119i
$823$	485.954	−	8962.90i	0.0205824	−	0.379620i	−0.970036	−	0.242962i	$-0.921881\pi$
$823$	485.954	−	8962.90i	0.0205824	−	0.379620i	0.990618	−	0.136658i	$-0.0436361\pi$
$824$	−395.825	−	583.798i	−0.0167345	−	0.0246815i
$825$	6018.85			0.253999
$826$	47063.5	−	18674.2i	1.98251	−	0.786631i
$827$	−1118.13			−0.0470147			−0.0235074	−	0.999724i	$-0.507483\pi$
$827$	−1118.13			−0.0470147			−0.0235074	+	0.999724i	$0.507483\pi$
$828$	3393.77	+	5005.44i	0.142442	+	0.210086i
$829$	427.576	−	7886.17i	0.0179135	−	0.330396i	−0.975817	−	0.218591i	$-0.929854\pi$
$829$	427.576	−	7886.17i	0.0179135	−	0.330396i	0.993730	−	0.111805i	$-0.0356632\pi$
$830$	11520.1	−	28913.3i	0.481770	−	1.20915i
$831$	11654.2	−	5391.82i	0.486499	−	0.225078i
$832$	−614.248	+	369.581i	−0.0255952	+	0.0154001i
$833$	20826.9	−	75011.7i	0.866278	−	3.12005i
$834$	14126.7	−	3109.52i	0.586531	−	0.129105i
$835$	265.398	+	28.8638i	0.0109994	+	0.00119625i
$836$	−12747.0	−	7669.61i	−0.527349	−	0.317296i
$837$	−1994.33	+	1889.13i	−0.0823585	+	0.0780141i
$838$	29098.3	+	13462.3i	1.19950	+	0.554950i
$839$	28140.4	−	3060.46i	1.15794	−	0.125934i	0.491081	−	0.871114i	$-0.336602\pi$
$839$	28140.4	−	3060.46i	1.15794	−	0.125934i	0.666863	+	0.745180i	$0.267636\pi$
$840$	17783.9	−	5992.11i	0.730482	−	0.246128i
$841$	6549.78	+	16438.7i	0.268555	+	0.674021i
$842$	−6922.66	−	6557.49i	−0.283338	−	0.268392i
$843$	873.361	+	3145.56i	0.0356823	+	0.128516i
$844$	1138.36	+	2147.18i	0.0464266	+	0.0875698i
$845$	22812.4	−	17341.5i	0.928722	−	0.705996i
$846$	−668.857	−	12336.3i	−0.0271818	−	0.501338i
$847$	1705.10	+	574.515i	0.0691711	+	0.0233064i
$848$	47164.4	+	10381.7i	1.90994	+	0.420410i
$849$	6621.86	−	12490.1i	0.267681	−	0.504901i
$850$	−3422.79	−	20878.1i	−0.138118	−	0.842486i
$851$	−29859.6	+	35153.5i	−1.20279	+	1.41604i
$852$	5685.86	+	6693.91i	0.228632	+	0.269166i
$853$	−6307.48	+	38473.9i	−0.253182	+	1.54434i	0.487885	+	0.872908i	$0.337769\pi$
$853$	−6307.48	+	38473.9i	−0.253182	+	1.54434i	−0.741066	+	0.671432i	$0.765680\pi$
$854$	−65952.2	−	50135.6i	−2.64267	−	2.00890i
$855$	−7373.42	+	10875.0i	−0.294931	+	0.434990i
$856$	5791.79	−	8542.25i	0.231261	−	0.341084i
$857$	29549.5	+	22463.0i	1.17782	+	0.895357i	0.996121	−	0.0879974i	$-0.0280467\pi$
$857$	29549.5	+	22463.0i	1.17782	+	0.895357i	0.181701	+	0.983354i	$0.441840\pi$
$858$	−492.162	+	3002.06i	−0.0195829	+	0.119451i
$859$	15240.5	+	17942.5i	0.605354	+	0.712678i	0.976408	−	0.215933i	$-0.0692793\pi$
$859$	15240.5	+	17942.5i	0.605354	+	0.712678i	−0.371054	+	0.928611i	$0.621003\pi$
$860$	−1093.59	+	1287.47i	−0.0433617	+	0.0510494i
$861$	5187.97	+	31645.2i	0.205349	+	1.25257i
$862$	−6785.36	+	12798.5i	−0.268109	+	0.505708i
$863$	22859.9	+	5031.83i	0.901690	+	0.198477i	0.641539	−	0.767091i	$-0.278296\pi$
$863$	22859.9	+	5031.83i	0.901690	+	0.198477i	0.260152	+	0.965568i	$0.416227\pi$
$864$	−4111.41	−	1385.29i	−0.161890	−	0.0545470i
$865$	−244.000	−	4500.32i	−0.00959106	−	0.176897i
$866$	−3514.63	+	2671.75i	−0.137912	+	0.104838i
$867$	−9930.81	−	18731.5i	−0.389006	−	0.733743i
$868$	−3394.03	−	12224.2i	−0.132720	−	0.478014i
$869$	17746.3	+	16810.2i	0.692753	+	0.656210i
$870$	−4207.68	−	10560.5i	−0.163970	−	0.411533i
$871$	3204.01	−	1079.56i	0.124642	−	0.0419969i
$872$	9725.74	−	1057.74i	0.377701	−	0.0410774i
$873$	−945.869	−	437.606i	−0.0366699	−	0.0169653i
$874$	−47407.3	+	44906.6i	−1.83476	+	1.73797i
$875$	−25773.9	−	15507.6i	−0.995791	−	0.599147i
$876$	−1765.48	−	192.008i	−0.0680938	−	0.00740565i
$877$	−6482.31	+	1426.86i	−0.249592	+	0.0549393i	−0.338004	−	0.941145i	$-0.609752\pi$
$877$	−6482.31	+	1426.86i	−0.249592	+	0.0549393i	0.0884123	+	0.996084i	$0.471821\pi$
$878$	−6965.95	+	25089.1i	−0.267755	+	0.964368i
$879$	7447.72	−	4481.14i	0.285785	−	0.171951i
$880$	−34892.9	+	16143.2i	−1.33664	+	0.618394i
$881$	5965.15	−	14971.4i	0.228117	−	0.572530i	−0.769712	−	0.638392i	$-0.779600\pi$
$881$	5965.15	−	14971.4i	0.228117	−	0.572530i	0.997829	+	0.0658610i	$0.0209794\pi$
$882$	1192.50	−	21994.5i	0.0455258	−	0.839673i
$883$	−16641.1	−	24543.8i	−0.634223	−	0.935409i	−0.999989	−	0.00470179i	$-0.998503\pi$
$883$	−16641.1	−	24543.8i	−0.634223	−	0.935409i	0.365766	−	0.930707i	$-0.380807\pi$
$884$	3468.35			0.131961
$885$	7660.24	+	16619.4i	0.290956	+	0.631250i
$886$	−31783.5			−1.20518
$887$	−8541.63	−	12598.0i	−0.323337	−	0.476886i	0.630931	−	0.775839i	$-0.282673\pi$
$887$	−8541.63	−	12598.0i	−0.323337	−	0.476886i	−0.954268	+	0.298953i	$0.903363\pi$
$888$	612.816	−	11302.7i	0.0231585	−	0.427134i
$889$	26516.1	−	66550.5i	1.00036	−	2.51072i
$890$	−18283.1	+	8458.65i	−0.688595	+	0.318578i
$891$	2478.84	−	1491.47i	0.0932034	−	0.0560786i
$892$	−2797.69	+	10076.4i	−0.105015	+	0.378231i
$893$	42256.6	−	9301.38i	1.58350	−	0.348554i
$894$	−10223.5	−	1111.87i	−0.382466	−	0.0415957i
$895$	49922.6	+	30037.4i	1.86450	+	1.12183i
$896$	−37349.2	+	35379.0i	−1.39258	+	1.31912i
$897$	3930.81	+	1818.58i	0.146316	+	0.0676932i
$898$	18259.7	−	1985.86i	0.678545	−	0.0737962i
$899$	7888.15	−	2657.83i	0.292641	−	0.0986024i
$900$	−718.652	−	1803.68i	−0.0266167	−	0.0668029i
$901$	47984.4	+	45453.2i	1.77424	+	1.68065i
$902$	−10823.8	−	38983.9i	−0.399550	−	1.43905i
$903$	−1491.03	−	2812.39i	−0.0549485	−	0.103644i
$904$	4426.17	−	3364.69i	0.162846	−	0.123792i
$905$	−1529.42	−	28208.5i	−0.0561765	−	1.03611i
$906$	−25532.9	−	8603.05i	−0.936286	−	0.315471i
$907$	44116.2	+	9710.71i	1.61506	+	0.355501i	0.928429	−	0.371510i	$-0.121160\pi$
$907$	44116.2	+	9710.71i	1.61506	+	0.355501i	0.686626	+	0.727011i	$0.259091\pi$
$908$	5958.29	−	11238.5i	0.217767	−	0.410753i
$909$	−1931.63	−	11782.4i	−0.0704821	−	0.429922i
$910$	−8033.17	+	9457.38i	−0.292634	+	0.344515i
$911$	1941.85	+	2286.13i	0.0706218	+	0.0831424i	0.796338	−	0.604851i	$-0.206767\pi$
$911$	1941.85	+	2286.13i	0.0706218	+	0.0831424i	−0.725717	+	0.687994i	$0.758492\pi$
$912$	4209.92	−	25679.4i	0.152856	−	0.932378i
$913$	−19106.5	−	14524.4i	−0.692587	−	0.526491i
$914$	−13109.8	+	19335.5i	−0.474436	+	0.699740i
$915$	16803.0	−	24782.6i	0.607093	−	0.895396i
$916$	10816.1	+	8222.15i	0.390145	+	0.296580i
$917$	−6322.68	+	38566.7i	−0.227692	+	1.38886i
$918$	−6583.24	−	7750.39i	−0.236688	−	0.278650i
$919$	30589.1	−	36012.3i	1.09798	−	1.29264i	0.145057	−	0.989423i	$-0.453663\pi$
$919$	30589.1	−	36012.3i	1.09798	−	1.29264i	0.952921	−	0.303217i	$-0.0980608\pi$
$920$	5453.47	+	33264.7i	0.195430	+	1.19207i
$921$	1185.69	−	2236.46i	0.0424212	−	0.0800149i
$922$	9243.13	+	2034.57i	0.330159	+	0.0726734i
$923$	5960.82	+	2008.44i	0.212571	+	0.0716235i
$924$	723.323	+	13340.9i	0.0257528	+	0.474983i
$925$	11788.7	−	8961.51i	0.419037	−	0.318543i
$926$	−24253.9	−	45747.6i	−0.860725	−	1.62350i
$927$	−118.651	−	427.342i	−0.00420390	−	0.0151411i
$928$	9544.16	+	9040.71i	0.337610	+	0.319802i
$929$	−9838.68	−	24693.2i	−0.347467	−	0.872076i	−0.994019	−	0.109206i	$-0.965169\pi$
$929$	−9838.68	−	24693.2i	−0.347467	−	0.872076i	0.646552	−	0.762870i	$-0.276210\pi$
$930$	13396.8	−	4513.91i	0.472364	−	0.159158i
$931$	76690.6	−	8340.61i	2.69971	−	0.293612i
$932$	8565.26	+	3962.71i	0.301035	+	0.139273i
$933$	−11455.7	+	10851.4i	−0.401975	+	0.380771i
$934$	17910.9	+	10776.7i	0.627478	+	0.377541i
$935$	−52309.3	−	5688.98i	−1.82962	−	0.198984i
$936$	−1038.06	+	228.495i	−0.0362502	+	0.00797927i
$937$	7796.91	−	28081.9i	0.271840	−	0.979079i	−0.694008	−	0.719968i	$-0.744157\pi$
$937$	7796.91	−	28081.9i	0.271840	−	0.979079i	0.965847	−	0.259111i	$-0.0834296\pi$
$938$	39227.3	−	23602.3i	1.36548	−	0.821580i
$939$	−26755.8	+	12378.5i	−0.929863	+	0.430200i
$940$	−7632.82	+	19156.9i	−0.264846	+	0.664713i
$941$	601.159	−	11087.7i	0.0208259	−	0.384112i	−0.969477	−	0.245184i	$-0.921152\pi$
$941$	601.159	−	11087.7i	0.0208259	−	0.384112i	0.990302	−	0.138928i	$-0.0443656\pi$
$942$	7905.13	+	11659.2i	0.273422	+	0.403267i
$943$	−57601.2			−1.98913
$944$	−27589.9	−	23502.9i	−0.951246	−	0.810331i
$945$	11800.1			0.406197
$946$	2253.79	+	3324.09i	0.0774599	+	0.114245i
$947$	−2607.71	+	48096.4i	−0.0894818	+	1.65039i	0.517503	+	0.855681i	$0.326861\pi$
$947$	−2607.71	+	48096.4i	−0.0894818	+	1.65039i	−0.606985	+	0.794713i	$0.707621\pi$
$948$	2918.63	−	7325.20i	0.0999922	−	0.250962i
$949$	−1154.31	+	534.042i	−0.0394843	+	0.0182674i
$950$	17963.8	−	10808.5i	0.613499	−	0.369130i
$951$	−2986.46	+	10756.3i	−0.101833	+	0.366768i
$952$	−49678.1	+	10935.0i	−1.69126	+	0.372273i
$953$	−50356.9	−	5476.64i	−1.71167	−	0.186155i	−0.800822	−	0.598903i	$-0.795604\pi$
$953$	−50356.9	−	5476.64i	−1.71167	−	0.186155i	−0.910845	+	0.412748i	$0.864569\pi$
$954$	16024.0	+	9641.30i	0.543811	+	0.327200i
$955$	−634.524	+	601.053i	−0.0215002	+	0.0203661i
$956$	−12248.4	−	5666.70i	−0.414373	−	0.191709i
$957$	−8714.64	+	947.774i	−0.294362	+	0.0320138i
$958$	873.191	−	294.212i	0.0294484	−	0.00992231i
$959$	20737.0	+	52046.0i	0.698261	+	1.75250i
$960$	−2546.94	−	2412.59i	−0.0856273	−	0.0811105i
$961$	−5200.65	−	18731.0i	−0.174571	−	0.628748i
$962$	3505.82	+	6612.69i	0.117497	+	0.221623i
$963$	5166.24	−	3927.28i	0.172876	−	0.131417i
$964$	−1251.95	−	23090.9i	−0.0418285	−	0.771481i
$965$	4280.37	+	1442.22i	0.142788	+	0.0481107i
$966$	57274.4	+	12607.1i	1.90763	+	0.419902i
$967$	−13121.2	+	24749.2i	−0.436349	+	0.823042i	−0.999996	−	0.00297451i	$-0.999053\pi$
$967$	−13121.2	+	24749.2i	−0.436349	+	0.823042i	0.563647	+	0.826016i	$0.309398\pi$
$968$	−128.320	−	782.717i	−0.00426070	−	0.0259891i
$969$	23056.0	−	27143.7i	0.764362	−	0.899876i
$970$	3472.17	+	4087.75i	0.114933	+	0.135309i
$971$	−90.8242	+	554.003i	−0.00300174	+	0.0183098i	−0.988285	−	0.152620i	$-0.951229\pi$
$971$	−90.8242	+	554.003i	−0.00300174	+	0.0183098i	0.985283	+	0.170930i	$0.0546772\pi$
$972$	−742.924	−	564.756i	−0.0245157	−	0.0186364i
$973$	25532.3	−	37657.4i	0.841242	−	1.24074i
$974$	23388.8	−	34495.9i	0.769431	−	1.13483i
$975$	−1106.99	−	841.509i	−0.0363610	−	0.0276409i
$976$	−9593.82	+	58519.7i	−0.314642	+	1.91923i
$977$	6696.70	+	7883.96i	0.219290	+	0.258168i	0.860796	−	0.508950i	$-0.169966\pi$
$977$	6696.70	+	7883.96i	0.219290	+	0.258168i	−0.641506	+	0.767118i	$0.721690\pi$
$978$	−532.160	+	626.508i	−0.0173994	+	0.0204842i
$979$	2513.16	+	15329.6i	0.0820439	+	0.500445i
$980$	−17221.6	+	32483.3i	−0.561350	+	1.05882i
$981$	6007.70	+	1322.39i	0.195526	+	0.0430385i
$982$	6040.11	+	2035.15i	0.196281	+	0.0661347i
$983$	−45.0072	−	830.109i	−0.00146033	−	0.0269342i	0.997712	−	0.0676011i	$-0.0215345\pi$
$983$	−45.0072	−	830.109i	−0.00146033	−	0.0269342i	−0.999173	+	0.0406669i	$0.987052\pi$
$984$	11253.7	−	8554.83i	0.364588	−	0.277153i
$985$	31012.0	+	58494.9i	1.00317	+	1.89219i
$986$	8243.45	+	29690.2i	0.266252	+	0.958954i
$987$	−28211.5	−	26723.4i	−0.909810	−	0.861818i
$988$	1272.12	+	3192.78i	0.0409631	+	0.102810i
$989$	5418.46	−	1825.69i	0.174213	−	0.0586993i
$990$	−14800.5	+	1609.65i	−0.475141	+	0.0516747i
$991$	15430.6	+	7138.96i	0.494621	+	0.228836i	0.651310	−	0.758812i	$-0.274220\pi$
$991$	15430.6	+	7138.96i	0.494621	+	0.228836i	−0.156689	+	0.987648i	$0.550082\pi$
$992$	−11868.9	+	11242.8i	−0.379877	+	0.359838i
$993$	−19347.6	−	11641.1i	−0.618307	−	0.372023i
$994$	84672.0	+	9208.63i	2.70184	+	0.293843i
$995$	61470.3	−	13530.6i	1.95853	−	0.431105i
$996$	−2071.22	+	7459.88i	−0.0658928	+	0.237325i
$997$	−19748.9	+	11882.5i	−0.627335	+	0.377455i	−0.793436	−	0.608654i	$-0.791710\pi$
$997$	−19748.9	+	11882.5i	−0.627335	+	0.377455i	0.166101	+	0.986109i	$0.446882\pi$
$998$	25377.1	−	11740.7i	0.804908	−	0.372390i
$999$	2634.45	−	6611.98i	0.0834339	−	0.209403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.7.4	✓	420
59.17	even	29	inner	177.4.e.a.76.4	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.7.4	✓	420	1.1	even	1	trivial
177.4.e.a.76.4	yes	420	59.17	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.93104 - 2.84807i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-1.42147 + 3.56762i) q^{4} +(-12.2161 + 5.65175i) q^{5} +(8.84530 - 5.32204i) q^{6} +(8.68646 - 31.2858i) q^{7} +(-13.9786 + 3.07691i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})\)	\(q+(-1.93104 - 2.84807i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-1.42147 + 3.56762i) q^{4} +(-12.2161 + 5.65175i) q^{5} +(8.84530 - 5.32204i) q^{6} +(8.68646 - 31.2858i) q^{7} +(-13.9786 + 3.07691i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(39.6862 + 23.8784i) q^{10} +(25.9292 - 24.5614i) q^{11} +(-10.4563 - 4.83760i) q^{12} +(-8.20288 + 0.892117i) q^{13} +(-105.878 + 35.6744i) q^{14} +(-14.9463 - 37.5124i) q^{15} +(58.0611 + 54.9984i) q^{16} +(29.2819 + 105.464i) q^{17} +(14.5061 + 27.3614i) q^{18} +(-86.3444 + 65.6373i) q^{19} +(-2.79854 - 51.6161i) q^{20} +(92.3089 + 31.1025i) q^{21} +(-120.023 - 26.4190i) q^{22} +(-81.9564 + 154.586i) q^{23} +(-6.94685 - 42.3739i) q^{24} +(36.3665 - 42.8139i) q^{25} +(18.3809 + 21.6396i) q^{26} +(4.36811 - 26.6443i) q^{27} +(99.2684 + 75.4619i) q^{28} +(-45.9129 + 67.7164i) q^{29} +(-77.9758 + 115.006i) q^{30} +(-80.9959 - 61.5715i) q^{31} +(25.9960 - 158.569i) q^{32} +(69.3648 + 81.6626i) q^{33} +(243.824 - 287.051i) q^{34} +(70.7052 + 431.283i) q^{35} +(16.1898 - 30.5372i) q^{36} +(257.448 + 56.6685i) q^{37} +(353.674 + 119.167i) q^{38} +(-1.34014 - 24.7174i) q^{39} +(153.373 - 116.591i) q^{40} +(154.205 + 290.861i) q^{41} +(-89.6699 - 322.962i) q^{42} +(-23.7248 - 22.4733i) q^{43} +(50.7683 + 127.419i) q^{44} +(114.800 - 38.6805i) q^{45} +(598.532 - 65.0943i) q^{46} +(-362.060 - 167.507i) q^{47} +(-174.183 + 164.995i) q^{48} +(-609.444 - 366.690i) q^{49} +(-192.162 - 20.8989i) q^{50} +(-320.684 + 70.5878i) q^{51} +(8.47742 - 30.5329i) q^{52} +(517.422 - 311.322i) q^{53} +(-84.3198 + 39.0105i) q^{54} +(-177.937 + 446.589i) q^{55} +(-25.1605 + 464.058i) q^{56} +(-182.599 - 269.314i) q^{57} +281.520 q^{58} +(-452.557 + 23.8903i) q^{59} +155.076 q^{60} +(416.119 + 613.730i) q^{61} +(-18.9536 + 349.578i) q^{62} +(-108.163 + 271.469i) q^{63} +(78.8494 - 36.4796i) q^{64} +(95.1648 - 57.2588i) q^{65} +(98.6344 - 355.249i) q^{66} +(-400.175 + 88.0852i) q^{67} +(-417.879 - 45.4471i) q^{68} +(-449.767 - 270.616i) q^{69} +(1091.79 - 1034.20i) q^{70} +(-691.863 - 320.090i) q^{71} +(128.064 - 13.9278i) q^{72} +(146.073 - 49.2179i) q^{73} +(-335.745 - 842.657i) q^{74} +(122.347 + 115.893i) q^{75} +(-111.433 - 401.346i) q^{76} +(-543.191 - 1024.57i) q^{77} +(-67.8090 + 51.5471i) q^{78} +(37.0535 + 683.411i) q^{79} +(-1020.12 - 343.717i) q^{80} +(79.1063 + 17.4126i) q^{81} +(530.617 - 1000.85i) q^{82} +(-108.716 - 663.136i) q^{83} +(-242.176 + 285.112i) q^{84} +(-953.765 - 1122.86i) q^{85} +(-18.1920 + 110.967i) q^{86} +(-195.394 - 148.535i) q^{87} +(-286.879 + 423.115i) q^{88} +(-244.086 + 360.000i) q^{89} +(-331.847 - 252.263i) q^{90} +(-43.3434 + 264.383i) q^{91} +(-435.007 - 512.129i) q^{92} +(197.599 - 232.631i) q^{93} +(222.081 + 1354.63i) q^{94} +(683.823 - 1289.83i) q^{95} +(470.787 + 103.628i) q^{96} +(109.738 + 36.9749i) q^{97} +(132.501 + 2443.83i) q^{98} +(-255.895 + 194.526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Introduction

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