LMFDB - Embedded newform 177.4.e.a.133.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			133.11
Character	$\chi$	$=$	177.133
Dual form			177.4.e.a.4.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.45810 - 0.267335i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-1.84216 + 0.405491i) q^{4} +(7.30295 - 5.55156i) q^{5} +(-5.38528 - 5.10121i) q^{6} +(-2.79914 - 7.02531i) q^{7} +(-23.1651 + 7.80525i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})$	\(q+(2.45810 - 0.267335i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-1.84216 + 0.405491i) q^{4} +(7.30295 - 5.55156i) q^{5} +(-5.38528 - 5.10121i) q^{6} +(-2.79914 - 7.02531i) q^{7} +(-23.1651 + 7.80525i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(16.4673 - 15.5986i) q^{10} +(-29.6784 - 13.7307i) q^{11} +(4.50492 + 3.42455i) q^{12} +(-9.95264 - 60.7084i) q^{13} +(-8.75869 - 16.5206i) q^{14} +(-26.8771 - 5.91609i) q^{15} +(-41.1603 + 19.0428i) q^{16} +(12.2307 - 30.6967i) q^{17} +(-1.20477 + 22.2207i) q^{18} +(-79.9088 + 117.857i) q^{19} +(-11.2021 + 13.1882i) q^{20} +(-10.6269 + 20.0445i) q^{21} +(-76.6233 - 25.8174i) q^{22} +(-9.44781 - 174.255i) q^{23} +(62.8370 + 37.8078i) q^{24} +(-10.9277 + 39.3582i) q^{25} +(-40.6941 - 146.567i) q^{26} +(23.1351 - 13.9200i) q^{27} +(8.00518 + 11.8068i) q^{28} +(-86.9923 - 9.46098i) q^{29} +(-67.6481 - 7.35718i) q^{30} +(-124.267 - 183.281i) q^{31} +(71.4799 - 43.0080i) q^{32} +(26.2451 + 94.5265i) q^{33} +(21.8580 - 78.7252i) q^{34} +(-59.4434 - 35.7659i) q^{35} +(-0.919082 - 16.9515i) q^{36} +(142.006 + 47.8474i) q^{37} +(-164.917 + 311.066i) q^{38} +(-119.479 + 140.662i) q^{39} +(-125.843 + 185.604i) q^{40} +(4.32733 - 79.8129i) q^{41} +(-20.7634 + 52.1123i) q^{42} +(275.947 - 127.667i) q^{43} +(60.2402 + 13.2599i) q^{44} +(38.6725 + 72.9440i) q^{45} +(-69.8080 - 425.810i) q^{46} +(263.317 + 200.168i) q^{47} +(123.481 + 57.1283i) q^{48} +(207.497 - 196.551i) q^{49} +(-16.3397 + 99.6678i) q^{50} +(-93.9414 + 31.6525i) q^{51} +(42.9511 + 107.799i) q^{52} +(534.609 + 506.409i) q^{53} +(53.1473 - 40.4015i) q^{54} +(-292.967 + 64.4869i) q^{55} +(119.677 + 140.894i) q^{56} +(424.673 - 46.1860i) q^{57} -216.365 q^{58} +(-395.079 - 222.017i) q^{59} +51.9109 q^{60} +(203.036 - 22.0815i) q^{61} +(-354.460 - 417.302i) q^{62} +(66.4705 - 14.6313i) q^{63} +(453.042 - 344.394i) q^{64} +(-409.710 - 388.098i) q^{65} +(89.7835 + 225.339i) q^{66} +(129.930 - 43.7786i) q^{67} +(-10.0837 + 61.5077i) q^{68} +(-380.082 + 360.032i) q^{69} +(-155.680 - 72.0250i) q^{70} +(609.418 + 463.267i) q^{71} +(-35.5925 - 217.105i) q^{72} +(-340.622 - 642.481i) q^{73} +(361.857 + 79.6507i) q^{74} +(111.215 - 51.4537i) q^{75} +(99.4154 - 249.514i) q^{76} +(-13.3884 + 246.934i) q^{77} +(-256.089 + 377.702i) q^{78} +(-664.206 + 781.963i) q^{79} +(-194.874 + 367.572i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-10.6997 - 197.345i) q^{82} +(-343.457 - 206.652i) q^{83} +(11.4487 - 41.2343i) q^{84} +(-81.0944 - 292.076i) q^{85} +(644.176 - 387.588i) q^{86} +(147.320 + 217.281i) q^{87} +(794.676 + 86.4262i) q^{88} +(-251.325 - 27.3333i) q^{89} +(114.561 + 168.965i) q^{90} +(-398.637 + 239.852i) q^{91} +(88.0631 + 317.175i) q^{92} +(-177.722 + 640.096i) q^{93} +(700.771 + 421.640i) q^{94} +(70.7182 + 1304.32i) q^{95} +(-237.163 - 79.9094i) q^{96} +(817.476 - 1541.92i) q^{97} +(457.503 - 538.614i) q^{98} +(165.161 - 243.595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.45810	−	0.267335i	0.869071	−	0.0945171i	0.337291	−	0.941400i	$-0.390489\pi$
$2$	2.45810	−	0.267335i	0.869071	−	0.0945171i	0.531779	+	0.846883i	$0.321524\pi$
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$4$	−1.84216	+	0.405491i	−0.230271	+	0.0506864i
$5$	7.30295	−	5.55156i	0.653196	−	0.496547i	−0.225304	−	0.974288i	$-0.572338\pi$
$5$	7.30295	−	5.55156i	0.653196	−	0.496547i	0.878500	+	0.477742i	$0.158545\pi$
$6$	−5.38528	−	5.10121i	−0.366422	−	0.347093i
$7$	−2.79914	−	7.02531i	−0.151139	−	0.379331i	0.833839	−	0.552007i	$-0.186138\pi$
$7$	−2.79914	−	7.02531i	−0.151139	−	0.379331i	−0.984979	+	0.172676i	$0.944759\pi$
$8$	−23.1651	+	7.80525i	−1.02376	+	0.344946i
$9$	−1.45604	+	8.88144i	−0.0539273	+	0.328942i
$10$	16.4673	−	15.5986i	0.520741	−	0.493272i
$11$	−29.6784	−	13.7307i	−0.813489	−	0.376360i	−0.0313844	−	0.999507i	$-0.509992\pi$
$11$	−29.6784	−	13.7307i	−0.813489	−	0.376360i	−0.782104	+	0.623147i	$0.785854\pi$
$12$	4.50492	+	3.42455i	0.108372	+	0.0823820i
$13$	−9.95264	−	60.7084i	−0.212336	−	1.29519i	−0.850780	−	0.525523i	$-0.823870\pi$
$13$	−9.95264	−	60.7084i	−0.212336	−	1.29519i	0.638444	−	0.769668i	$-0.279578\pi$
$14$	−8.75869	−	16.5206i	−0.167204	−	0.315380i
$15$	−26.8771	−	5.91609i	−0.462642	−	0.101835i
$16$	−41.1603	+	19.0428i	−0.643129	+	0.297543i
$17$	12.2307	−	30.6967i	0.174493	−	0.437943i	−0.815554	−	0.578680i	$-0.803568\pi$
$17$	12.2307	−	30.6967i	0.174493	−	0.437943i	0.990047	+	0.140737i	$0.0449472\pi$
$18$	−1.20477	+	22.2207i	−0.0157760	+	0.290971i
$19$	−79.9088	+	117.857i	−0.964860	+	1.42306i	−0.0595917	+	0.998223i	$0.518980\pi$
$19$	−79.9088	+	117.857i	−0.964860	+	1.42306i	−0.905269	+	0.424840i	$0.860330\pi$
$20$	−11.2021	+	13.1882i	−0.125244	+	0.147448i
$21$	−10.6269	+	20.0445i	−0.110428	+	0.208289i
$22$	−76.6233	−	25.8174i	−0.742552	−	0.250195i
$23$	−9.44781	−	174.255i	−0.0856524	−	1.57977i	−0.653690	−	0.756763i	$-0.726780\pi$
$23$	−9.44781	−	174.255i	−0.0856524	−	1.57977i	0.568037	−	0.823003i	$-0.307703\pi$
$24$	62.8370	+	37.8078i	0.534439	+	0.321561i
$25$	−10.9277	+	39.3582i	−0.0874220	+	0.314866i
$26$	−40.6941	−	146.567i	−0.306953	−	1.10554i
$27$	23.1351	−	13.9200i	0.164902	−	0.0992184i
$28$	8.00518	+	11.8068i	0.0540299	+	0.0796881i
$29$	−86.9923	−	9.46098i	−0.557037	−	0.0605814i	−0.174729	−	0.984617i	$-0.555905\pi$
$29$	−86.9923	−	9.46098i	−0.557037	−	0.0605814i	−0.382308	+	0.924035i	$0.624871\pi$
$30$	−67.6481	−	7.35718i	−0.411693	−	0.0447744i
$31$	−124.267	−	183.281i	−0.719971	−	1.06188i	−0.994945	−	0.100426i	$-0.967979\pi$
$31$	−124.267	−	183.281i	−0.719971	−	1.06188i	0.274974	−	0.961452i	$-0.411331\pi$
$32$	71.4799	−	43.0080i	0.394874	−	0.237588i
$33$	26.2451	+	94.5265i	0.138445	+	0.498635i
$34$	21.8580	−	78.7252i	0.110253	−	0.397096i
$35$	−59.4434	−	35.7659i	−0.287079	−	0.172730i
$36$	−0.919082	−	16.9515i	−0.00425501	−	0.0784791i
$37$	142.006	+	47.8474i	0.630964	+	0.212596i	0.616570	−	0.787300i	$-0.288522\pi$
$37$	142.006	+	47.8474i	0.630964	+	0.212596i	0.0143936	+	0.999896i	$0.495418\pi$
$38$	−164.917	+	311.066i	−0.704028	+	1.32794i
$39$	−119.479	+	140.662i	−0.490564	+	0.577537i
$40$	−125.843	+	185.604i	−0.497437	+	0.733664i
$41$	4.32733	−	79.8129i	0.0164833	−	0.304016i	−0.978654	−	0.205516i	$-0.934113\pi$
$41$	4.32733	−	79.8129i	0.0164833	−	0.304016i	0.995137	−	0.0985003i	$-0.0314046\pi$
$42$	−20.7634	+	52.1123i	−0.0762826	+	0.191455i
$43$	275.947	−	127.667i	0.978639	−	0.452767i	0.135685	−	0.990752i	$-0.456676\pi$
$43$	275.947	−	127.667i	0.978639	−	0.452767i	0.842954	+	0.537985i	$0.180814\pi$
$44$	60.2402	+	13.2599i	0.206399	+	0.0454318i
$45$	38.6725	+	72.9440i	0.128110	+	0.241641i
$46$	−69.8080	−	425.810i	−0.223753	−	1.36483i
$47$	263.317	+	200.168i	0.817206	+	0.621224i	0.927984	−	0.372621i	$-0.121541\pi$
$47$	263.317	+	200.168i	0.817206	+	0.621224i	−0.110777	+	0.993845i	$0.535334\pi$
$48$	123.481	+	57.1283i	0.371311	+	0.171787i
$49$	207.497	−	196.551i	0.604946	−	0.573036i
$50$	−16.3397	+	99.6678i	−0.0462157	+	0.281903i
$51$	−93.9414	+	31.6525i	−0.257930	+	0.0869067i
$52$	42.9511	+	107.799i	0.114543	+	0.287482i
$53$	534.609	+	506.409i	1.38555	+	1.31246i	0.898422	+	0.439134i	$0.144715\pi$
$53$	534.609	+	506.409i	1.38555	+	1.31246i	0.487130	+	0.873330i	$0.338044\pi$
$54$	53.1473	−	40.4015i	0.133934	−	0.101814i
$55$	−292.967	+	64.4869i	−0.718248	+	0.158098i
$56$	119.677	+	140.894i	0.285580	+	0.336211i
$57$	424.673	−	46.1860i	0.986831	−	0.107324i
$58$	−216.365			−0.489830
$59$	−395.079	−	222.017i	−0.871778	−	0.489901i
$59$	−395.079	−	222.017i	−0.871778	−	0.489901i
$60$	51.9109			0.111694
$61$	203.036	−	22.0815i	0.426166	−	0.0463484i	0.107477	−	0.994208i	$-0.465723\pi$
$61$	203.036	−	22.0815i	0.426166	−	0.0463484i	0.318689	+	0.947859i	$0.396757\pi$
$62$	−354.460	−	417.302i	−0.726071	−	0.854797i
$63$	66.4705	−	14.6313i	0.132929	−	0.0292598i
$64$	453.042	−	344.394i	0.884848	−	0.672644i
$65$	−409.710	−	388.098i	−0.781820	−	0.740579i
$66$	89.7835	+	225.339i	0.167448	+	0.420263i
$67$	129.930	−	43.7786i	0.236918	−	0.0798269i	−0.198338	−	0.980134i	$-0.563554\pi$
$67$	129.930	−	43.7786i	0.236918	−	0.0798269i	0.435256	+	0.900307i	$0.356658\pi$
$68$	−10.0837	+	61.5077i	−0.0179827	+	0.109690i
$69$	−380.082	+	360.032i	−0.663137	+	0.628157i
$70$	−155.680	−	72.0250i	−0.265818	−	0.122981i
$71$	609.418	+	463.267i	1.01866	+	0.774362i	0.974437	−	0.224659i	$-0.0721269\pi$
$71$	609.418	+	463.267i	1.01866	+	0.774362i	0.0442191	+	0.999022i	$0.485920\pi$
$72$	−35.5925	−	217.105i	−0.0582585	−	0.355361i
$73$	−340.622	−	642.481i	−0.546120	−	1.03009i	−0.990919	−	0.134462i	$-0.957070\pi$
$73$	−340.622	−	642.481i	−0.546120	−	1.03009i	0.444798	−	0.895631i	$-0.353275\pi$
$74$	361.857	+	79.6507i	0.568446	+	0.125124i
$75$	111.215	−	51.4537i	0.171227	−	0.0792182i
$76$	99.4154	−	249.514i	0.150049	−	0.376595i
$77$	−13.3884	+	246.934i	−0.0198149	+	0.365465i
$78$	−256.089	+	377.702i	−0.371748	+	0.548287i
$79$	−664.206	+	781.963i	−0.945936	+	1.11364i	0.0474559	+	0.998873i	$0.484889\pi$
$79$	−664.206	+	781.963i	−0.945936	+	1.11364i	−0.993392	+	0.114769i	$0.963387\pi$
$80$	−194.874	+	367.572i	−0.272345	+	0.513698i
$81$	−76.7599	−	25.8634i	−0.105295	−	0.0354779i
$82$	−10.6997	−	197.345i	−0.0144096	−	0.265770i
$83$	−343.457	−	206.652i	−0.454209	−	0.273289i	0.270011	−	0.962857i	$-0.412973\pi$
$83$	−343.457	−	206.652i	−0.454209	−	0.273289i	−0.724220	+	0.689569i	$0.757800\pi$
$84$	11.4487	−	41.2343i	0.0148708	−	0.0535599i
$85$	−81.0944	−	292.076i	−0.103481	−	0.372706i
$86$	644.176	−	387.588i	0.807712	−	0.485984i
$87$	147.320	+	217.281i	0.181545	+	0.267759i
$88$	794.676	+	86.4262i	0.962645	+	0.104694i
$89$	−251.325	−	27.3333i	−0.299331	−	0.0325542i	−0.0427786	−	0.999085i	$-0.513621\pi$
$89$	−251.325	−	27.3333i	−0.299331	−	0.0325542i	−0.256552	+	0.966530i	$0.582587\pi$
$90$	114.561	+	168.965i	0.134176	+	0.197895i
$91$	−398.637	+	239.852i	−0.459214	+	0.276300i
$92$	88.0631	+	317.175i	0.0997958	+	0.359432i
$93$	−177.722	+	640.096i	−0.198160	+	0.713709i
$94$	700.771	+	421.640i	0.768926	+	0.462647i
$95$	70.7182	+	1304.32i	0.0763741	+	1.40864i
$96$	−237.163	−	79.9094i	−0.252139	−	0.0849554i
$97$	817.476	−	1541.92i	0.855691	−	1.61401i	0.0682065	−	0.997671i	$-0.478272\pi$
$97$	817.476	−	1541.92i	0.855691	−	1.61401i	0.787485	−	0.616334i	$-0.211383\pi$
$98$	457.503	−	538.614i	0.471579	−	0.555186i
$99$	165.161	−	243.595i	0.167670	−	0.247295i
$100$	4.17131	−	76.9353i	0.00417131	−	0.0769353i
$101$	307.730	−	772.343i	0.303171	−	0.760901i	−0.695914	−	0.718125i	$-0.745000\pi$
$101$	307.730	−	772.343i	0.303171	−	0.760901i	0.999085	−	0.0427761i	$-0.0136202\pi$
$102$	−222.456	+	102.919i	−0.215945	+	0.0999069i
$103$	−1935.27	−	425.985i	−1.85134	−	0.407510i	−0.857141	−	0.515082i	$-0.827762\pi$
$103$	−1935.27	−	425.985i	−1.85134	−	0.407510i	−0.994197	+	0.107571i	$0.965693\pi$
$104$	704.398	+	1328.64i	0.664153	+	1.25273i
$105$	33.6703	+	205.380i	0.0312941	+	0.190886i
$106$	1449.50	+	1101.88i	1.32819	+	1.00967i
$107$	350.807	+	162.301i	0.316951	+	0.146637i	0.571914	−	0.820314i	$-0.306201\pi$
$107$	350.807	+	162.301i	0.316951	+	0.146637i	−0.254963	+	0.966951i	$0.582063\pi$
$108$	−36.9743	+	35.0239i	−0.0329431	+	0.0312054i
$109$	−25.0319	+	152.688i	−0.0219965	+	0.134173i	−0.995542	−	0.0943214i	$-0.969932\pi$
$109$	−25.0319	+	152.688i	−0.0219965	+	0.134173i	0.973545	+	0.228494i	$0.0733801\pi$
$110$	−702.903	+	236.836i	−0.609265	+	0.205285i
$111$	−166.396	−	417.622i	−0.142285	−	0.357108i
$112$	248.995	+	235.860i	0.210070	+	0.198988i
$113$	−31.5856	+	24.0108i	−0.0262949	+	0.0199889i	−0.618239	−	0.785990i	$-0.712154\pi$
$113$	−31.5856	+	24.0108i	−0.0262949	+	0.0199889i	0.591944	+	0.805979i	$0.298361\pi$
$114$	1031.54	−	227.060i	0.847482	−	0.186545i
$115$	−1036.38	−	1220.12i	−0.840375	−	0.989366i
$116$	164.090	−	17.8459i	0.131340	−	0.0142841i
$117$	553.669			0.437494
$118$	−1030.50	−	440.122i	−0.803941	−	0.343360i
$119$	−249.889			−0.192498
$120$	668.787	−	72.7350i	0.508764	−	0.0553314i
$121$	−169.395	−	199.427i	−0.127269	−	0.149833i
$122$	493.181	−	108.557i	0.365988	−	0.0805601i
$123$	−190.895	+	145.115i	−0.139939	+	0.106379i
$124$	303.240	+	287.244i	0.219611	+	0.208026i
$125$	563.127	+	1413.34i	0.402941	+	1.01131i
$126$	159.480	−	53.7351i	0.112759	−	0.0379929i
$127$	217.848	−	1328.81i	0.152211	−	0.928449i	−0.794711	−	0.606988i	$-0.792378\pi$
$127$	217.848	−	1328.81i	0.152211	−	0.928449i	0.946923	−	0.321461i	$-0.104174\pi$
$128$	537.049	−	508.720i	0.370851	−	0.351288i
$129$	−827.840	−	383.000i	−0.565018	−	0.261405i
$130$	−1110.86	−	844.455i	−0.749454	−	0.569720i
$131$	79.9286	+	487.543i	0.0533084	+	0.325167i	0.999995	+	0.00301208i	$0.000958777\pi$
$131$	79.9286	+	487.543i	0.0533084	+	0.325167i	−0.946687	+	0.322154i	$0.895593\pi$
$132$	−86.6775	−	163.491i	−0.0571538	−	0.107804i
$133$	1051.66	+	231.487i	0.685640	+	0.150921i
$134$	307.678	−	142.347i	0.198353	−	0.0917680i
$135$	91.6774	−	230.093i	0.0584469	−	0.146691i
$136$	−43.7302	+	806.556i	−0.0275723	+	0.508541i
$137$	−1547.46	+	2282.34i	−0.965027	+	1.42331i	−0.0598814	+	0.998206i	$0.519072\pi$
$137$	−1547.46	+	2282.34i	−0.965027	+	1.42331i	−0.905145	+	0.425102i	$0.860238\pi$
$138$	−838.031	+	986.606i	−0.516941	+	0.608590i
$139$	680.212	−	1283.02i	0.415071	−	0.782907i	−0.584524	−	0.811377i	$-0.698719\pi$
$139$	680.212	−	1283.02i	0.415071	−	0.782907i	0.999595	+	0.0284697i	$0.00906343\pi$
$140$	124.007	+	41.7829i	0.0748609	+	0.0252236i
$141$	−53.7212	−	990.828i	−0.0320861	−	0.591793i
$142$	1621.86	+	975.840i	0.958475	+	0.576695i
$143$	−538.190	+	1938.39i	−0.314725	+	1.13354i
$144$	−109.196	−	393.289i	−0.0631923	−	0.227598i
$145$	−687.824	+	413.850i	−0.393936	+	0.237023i
$146$	−1009.04	−	1488.22i	−0.571978	−	0.843605i
$147$	−852.403	−	92.7044i	−0.478265	−	0.0520145i
$148$	−281.000	−	30.5606i	−0.156068	−	0.0169734i
$149$	−833.465	−	1229.27i	−0.458256	−	0.675877i	0.526429	−	0.850219i	$-0.323531\pi$
$149$	−833.465	−	1229.27i	−0.458256	−	0.675877i	−0.984685	+	0.174342i	$0.944220\pi$
$150$	259.623	−	156.210i	0.141321	−	0.0850301i
$151$	−118.764	−	427.749i	−0.0640058	−	0.230528i	0.924628	−	0.380871i	$-0.124376\pi$
$151$	−118.764	−	427.749i	−0.0640058	−	0.230528i	−0.988634	+	0.150343i	$0.951962\pi$
$152$	931.199	−	3353.88i	0.496909	−	1.78971i
$153$	254.822	+	153.321i	0.134648	+	0.0810151i
$154$	33.1041	+	610.569i	0.0173221	+	0.319487i
$155$	−1925.01	−	648.613i	−0.997554	−	0.336115i
$156$	163.063	−	307.570i	0.0836892	−	0.157855i
$157$	207.584	−	244.386i	0.105522	−	0.124230i	−0.706866	−	0.707348i	$-0.749891\pi$
$157$	207.584	−	244.386i	0.105522	−	0.124230i	0.812388	+	0.583118i	$0.198167\pi$
$158$	−1423.64	+	2099.71i	−0.716827	+	1.05724i
$159$	119.601	−	2205.90i	0.0596537	−	1.10025i
$160$	283.253	−	710.910i	0.139957	−	0.351265i
$161$	−1197.75	+	554.137i	−0.586309	+	0.271255i
$162$	−195.598	−	43.0544i	−0.0948619	−	0.0208807i
$163$	−1169.66	−	2206.21i	−0.562053	−	1.06014i	−0.987862	−	0.155332i	$-0.950355\pi$
$163$	−1169.66	−	2206.21i	−0.562053	−	1.06014i	0.425809	−	0.904813i	$-0.359989\pi$
$164$	24.3917	+	148.783i	0.0116139	+	0.0708415i
$165$	716.436	+	544.621i	0.338027	+	0.256962i
$166$	−899.499	−	416.152i	−0.420570	−	0.194576i
$167$	−954.191	+	903.858i	−0.442141	+	0.418818i	−0.876111	−	0.482109i	$-0.839871\pi$
$167$	−954.191	+	903.858i	−0.442141	+	0.418818i	0.433970	+	0.900927i	$0.357112\pi$
$168$	89.7218	−	547.279i	0.0412035	−	0.251330i
$169$	−1504.46	+	506.912i	−0.684780	+	0.230729i
$170$	−277.420	−	696.273i	−0.125160	−	0.314127i
$171$	−930.387	−	881.309i	−0.416073	−	0.394125i
$172$	−456.572	+	347.077i	−0.202403	+	0.153863i
$173$	1228.99	−	270.521i	0.540107	−	0.118887i	0.0634650	−	0.997984i	$-0.479785\pi$
$173$	1228.99	−	270.521i	0.540107	−	0.118887i	0.476642	+	0.879098i	$0.341854\pi$
$174$	420.216	+	494.716i	0.183083	+	0.215542i
$175$	307.092	−	33.3983i	0.132651	−	0.0144267i
$176$	1483.04			0.635162
$177$	259.668	+	1334.54i	0.110270	+	0.566722i
$178$	−625.091			−0.263216
$179$	−2797.34	+	304.229i	−1.16806	+	0.127034i	−0.671525	−	0.740982i	$-0.734360\pi$
$179$	−2797.34	+	304.229i	−1.16806	+	0.127034i	−0.496536	+	0.868016i	$0.665395\pi$
$180$	−100.819	−	118.693i	−0.0417479	−	0.0491494i
$181$	−2118.46	+	466.309i	−0.869967	+	0.191494i	−0.627454	−	0.778654i	$-0.715903\pi$
$181$	−2118.46	+	466.309i	−0.869967	+	0.191494i	−0.242513	+	0.970148i	$0.577972\pi$
$182$	−915.769	+	696.150i	−0.372974	+	0.283528i
$183$	−444.818	−	421.354i	−0.179683	−	0.170204i
$184$	1578.96	+	3962.89i	0.632622	+	1.58776i
$185$	1302.69	−	438.928i	0.517707	−	0.174436i
$186$	−265.739	+	1620.93i	−0.104758	+	0.638993i
$187$	−784.473	+	743.093i	−0.306772	+	0.290590i
$188$	−566.239	−	261.970i	−0.219666	−	0.101628i
$189$	−162.551	−	123.568i	−0.0625599	−	0.0475568i
$190$	522.523	+	3187.25i	0.199515	+	1.21699i
$191$	344.489	+	649.775i	0.130504	+	0.246157i	0.940149	−	0.340762i	$-0.110685\pi$
$191$	344.489	+	649.775i	0.130504	+	0.246157i	−0.809645	+	0.586920i	$0.800340\pi$
$192$	−1667.33	−	367.007i	−0.626715	−	0.137950i
$193$	1667.46	−	771.448i	0.621897	−	0.287720i	−0.0835272	−	0.996506i	$-0.526619\pi$
$193$	1667.46	−	771.448i	0.621897	−	0.287720i	0.705424	+	0.708785i	$0.250756\pi$
$194$	1597.23	−	4008.74i	0.591105	−	1.48356i
$195$	−91.6586	+	1690.54i	−0.0336606	+	0.620833i
$196$	−302.543	+	446.218i	−0.110256	+	0.162616i
$197$	3425.95	−	4033.34i	1.23903	−	1.45870i	0.398287	−	0.917261i	$-0.369605\pi$
$197$	3425.95	−	4033.34i	1.23903	−	1.45870i	0.840742	−	0.541436i	$-0.182119\pi$
$198$	340.862	−	642.934i	0.122343	−	0.230764i
$199$	−3295.95	−	1110.54i	−1.17409	−	0.395597i	−0.336387	−	0.941724i	$-0.609205\pi$
$199$	−3295.95	−	1110.54i	−1.17409	−	0.395597i	−0.837702	+	0.546127i	$0.816102\pi$
$200$	−54.0575	−	997.032i	−0.0191122	−	0.352504i
$201$	−352.444	−	212.059i	−0.123679	−	0.0744152i
$202$	549.957	−	1980.77i	0.191559	−	0.689932i
$203$	177.037	+	637.631i	0.0612098	+	0.220458i
$204$	160.221	−	96.4016i	0.0549887	−	0.0330856i
$205$	−411.484	−	606.893i	−0.140192	−	0.206767i
$206$	−4870.97	−	529.750i	−1.64746	−	0.179172i
$207$	1561.39	+	169.811i	0.524270	+	0.0570178i
$208$	1565.71	+	2309.25i	0.521935	+	0.769796i
$209$	3989.82	−	2400.60i	1.32049	−	0.794511i
$210$	137.670	+	495.843i	0.0452388	+	0.162935i
$211$	676.636	−	2437.02i	0.220765	−	0.795125i	−0.767326	−	0.641257i	$-0.778413\pi$
$211$	676.636	−	2437.02i	0.220765	−	0.795125i	0.988091	−	0.153868i	$-0.0491731\pi$
$212$	−1190.18	−	716.109i	−0.385576	−	0.231993i
$213$	−124.332	−	2293.16i	−0.0399956	−	0.737676i
$214$	905.708	+	305.168i	0.289313	+	0.0974808i
$215$	1306.48	−	2464.28i	0.414423	−	0.781686i
$216$	−427.280	+	503.033i	−0.134596	+	0.158459i
$217$	−939.763	+	1386.05i	−0.293987	+	0.433599i
$218$	−20.7122	+	382.014i	−0.00643489	+	0.118684i
$219$	−807.482	+	2026.63i	−0.249153	+	0.625328i
$220$	513.544	−	237.591i	0.157378	−	0.0728108i
$221$	−1985.27	−	436.992i	−0.604271	−	0.133010i
$222$	−520.663	−	982.075i	−0.157408	−	0.296903i
$223$	939.643	+	5731.57i	0.282167	+	1.72114i	0.624038	+	0.781394i	$0.285491\pi$
$223$	939.643	+	5731.57i	0.282167	+	1.72114i	−0.341872	+	0.939747i	$0.611061\pi$
$224$	−502.227	−	381.783i	−0.149806	−	0.113879i
$225$	−333.646	−	154.361i	−0.0988581	−	0.0457366i
$226$	−71.2218	+	67.4648i	−0.0209628	+	0.0198571i
$227$	−7.59538	+	46.3298i	−0.00222081	+	0.0135463i	−0.987914	−	0.155005i	$-0.950461\pi$
$227$	−7.59538	+	46.3298i	−0.00222081	+	0.0135463i	0.985693	+	0.168551i	$0.0539089\pi$
$228$	−763.590	+	257.283i	−0.221798	+	0.0747325i
$229$	419.525	+	1052.93i	0.121061	+	0.303840i	0.977001	−	0.213235i	$-0.0684000\pi$
$229$	419.525	+	1052.93i	0.121061	+	0.303840i	−0.855940	+	0.517075i	$0.827021\pi$
$230$	−2873.71	−	2722.13i	−0.823857	−	0.780399i
$231$	590.614	−	448.973i	0.168223	−	0.127880i
$232$	2089.03	−	459.831i	0.591172	−	0.130127i
$233$	2482.23	+	2922.31i	0.697924	+	0.821659i	0.990920	−	0.134454i	$-0.0429282\pi$
$233$	2482.23	+	2922.31i	0.697924	+	0.821659i	−0.292996	+	0.956114i	$0.594652\pi$
$234$	1360.98	−	148.015i	0.380213	−	0.0413506i
$235$	3034.23			0.842262
$236$	817.826	+	248.791i	0.225576	+	0.0686224i
$237$	3077.94			0.843602
$238$	−614.253	+	66.8040i	−0.167295	+	0.0181944i
$239$	617.803	+	727.334i	0.167207	+	0.196851i	0.839383	−	0.543540i	$-0.182916\pi$
$239$	617.803	+	727.334i	0.167207	+	0.196851i	−0.672177	+	0.740391i	$0.734640\pi$
$240$	1218.93	−	268.306i	0.327839	−	0.0721628i
$241$	−2458.85	+	1869.17i	−0.657214	+	0.499601i	−0.879820	−	0.475307i	$-0.842337\pi$
$241$	−2458.85	+	1869.17i	−0.657214	+	0.499601i	0.222606	+	0.974909i	$0.428544\pi$
$242$	−469.705	−	444.928i	−0.124768	−	0.118186i
$243$	89.9436	+	225.741i	0.0237444	+	0.0595939i
$244$	−365.073	+	123.007i	−0.0957843	+	0.0322735i
$245$	424.172	−	2587.33i	0.110610	−	0.674689i
$246$	−430.446	+	407.740i	−0.111562	+	0.105677i
$247$	7950.20	+	3678.15i	2.04801	+	0.947511i
$248$	4309.23	+	3275.79i	1.10337	+	0.838761i
$249$	194.543	+	1186.66i	0.0495127	+	0.302014i
$250$	1762.06	+	3323.60i	0.445770	+	0.840811i
$251$	7264.01	+	1598.93i	1.82669	+	0.402086i	0.989466	−	0.144768i	$-0.0462434\pi$
$251$	7264.01	+	1598.93i	1.82669	+	0.402086i	0.837228	+	0.546853i	$0.184174\pi$
$252$	−116.517	+	53.9064i	−0.0291265	+	0.0134753i
$253$	−2112.24	+	5301.33i	−0.524883	+	1.31736i
$254$	180.254	−	3324.59i	0.0445282	−	0.821274i
$255$	−510.329	+	752.679i	−0.125326	+	0.184841i
$256$	−1763.20	+	2075.80i	−0.430469	+	0.506788i
$257$	478.384	−	902.329i	0.116112	−	0.219011i	−0.818644	−	0.574302i	$-0.805274\pi$
$257$	478.384	−	902.329i	0.116112	−	0.219011i	0.934756	+	0.355291i	$0.115618\pi$
$258$	−2137.31	−	720.142i	−0.515748	−	0.173776i
$259$	−61.3519	−	1131.57i	−0.0147190	−	0.271476i
$260$	912.123	+	548.806i	0.217567	+	0.130906i
$261$	210.691	−	758.841i	0.0499673	−	0.179966i
$262$	326.810	+	1177.06i	0.0770625	+	0.277554i
$263$	−5432.38	+	3268.55i	−1.27367	+	0.766341i	−0.981764	−	0.190106i	$-0.939117\pi$
$263$	−5432.38	+	3268.55i	−1.27367	+	0.766341i	−0.291905	+	0.956447i	$0.594289\pi$
$264$	−1345.77	−	1984.87i	−0.313737	−	0.462728i
$265$	6715.58	+	730.364i	1.55674	+	0.169305i
$266$	2646.96	+	287.875i	0.610135	+	0.0663561i
$267$	425.617	+	627.738i	0.0975555	+	0.143884i
$268$	−221.601	+	133.333i	−0.0505091	+	0.0303903i
$269$	−352.023	−	1267.87i	−0.0797890	−	0.287374i	0.912882	−	0.408224i	$-0.133852\pi$
$269$	−352.023	−	1267.87i	−0.0797890	−	0.287374i	−0.992671	+	0.120850i	$0.961438\pi$
$270$	163.841	−	590.101i	0.0369297	−	0.133009i
$271$	3807.95	+	2291.17i	0.853566	+	0.513574i	0.873836	−	0.486221i	$-0.161625\pi$
$271$	3807.95	+	2291.17i	0.853566	+	0.513574i	−0.0202699	+	0.999795i	$0.506453\pi$
$272$	81.1319	+	1496.39i	0.0180858	+	0.333573i
$273$	1322.63	+	445.647i	0.293221	+	0.0987978i
$274$	−3193.67	+	6023.91i	−0.704149	+	1.32817i
$275$	864.733	−	1018.04i	0.189620	−	0.223237i
$276$	554.183	−	817.359i	0.120862	−	0.178258i
$277$	438.178	−	8081.71i	0.0950453	−	1.75301i	−0.430819	−	0.902438i	$-0.641775\pi$
$277$	438.178	−	8081.71i	0.0950453	−	1.75301i	0.525864	−	0.850569i	$-0.323742\pi$
$278$	1329.04	−	3335.63i	0.286728	−	0.719633i
$279$	1808.74	−	836.810i	0.388122	−	0.179565i
$280$	1656.18	+	364.552i	0.353484	+	0.0778077i
$281$	2792.87	+	5267.91i	0.592913	+	1.11835i	0.980500	+	0.196519i	$0.0629638\pi$
$281$	2792.87	+	5267.91i	0.592913	+	1.11835i	−0.387587	+	0.921833i	$0.626691\pi$
$282$	−396.935	−	2421.20i	−0.0838196	−	0.511277i
$283$	1081.79	+	822.353i	0.227228	+	0.172734i	0.712594	−	0.701577i	$-0.247520\pi$
$283$	1081.79	+	822.353i	0.227228	+	0.172734i	−0.485366	+	0.874311i	$0.661313\pi$
$284$	−1310.50	−	606.301i	−0.273816	−	0.126681i
$285$	2844.97	−	2694.89i	0.591303	−	0.560111i
$286$	−804.729	+	4908.63i	−0.166380	+	1.01487i
$287$	−572.823	+	193.007i	−0.117814	+	0.0396962i
$288$	277.896	+	697.466i	0.0568582	+	0.142703i
$289$	2774.12	+	2627.79i	0.564649	+	0.534864i
$290$	−1580.11	+	1201.16i	−0.319955	+	0.243224i
$291$	−5113.25	+	1125.51i	−1.03005	+	0.226731i
$292$	888.002	+	1045.44i	0.177967	+	0.209519i
$293$	1799.70	−	195.729i	0.358839	−	0.0390260i	0.0730757	−	0.997326i	$-0.476719\pi$
$293$	1799.70	−	195.729i	0.358839	−	0.0390260i	0.285763	+	0.958300i	$0.407753\pi$
$294$	−2120.08			−0.420563
$295$	−4117.78	+	571.926i	−0.812701	+	0.112877i
$296$	−3663.05			−0.719293
$297$	−877.745	+	95.4605i	−0.171488	+	0.0186504i
$298$	−2377.37	−	2798.86i	−0.462139	−	0.544072i
$299$	−10484.7	+	2307.86i	−2.02791	+	0.446377i
$300$	−184.013	+	139.883i	−0.0354133	+	0.0269205i
$301$	−1669.31	−	1581.26i	−0.319660	−	0.302798i
$302$	−406.286	−	1019.70i	−0.0774144	−	0.194295i
$303$	−2363.61	+	796.394i	−0.448139	+	0.150995i
$304$	1044.75	−	6372.70i	0.197107	−	1.20230i
$305$	1360.18	−	1288.43i	0.255356	−	0.241886i
$306$	667.367	+	308.757i	0.124676	+	0.0576813i
$307$	−7166.11	−	5447.53i	−1.33222	−	1.01273i	−0.997519	−	0.0704020i	$-0.977572\pi$
$307$	−7166.11	−	5447.53i	−1.33222	−	1.01273i	−0.334700	−	0.942325i	$-0.608635\pi$
$308$	−75.4660	−	460.322i	−0.0139613	−	0.0851600i
$309$	2784.59	+	5252.30i	0.512654	+	0.966967i
$310$	−4905.28	−	1079.73i	−0.898713	−	0.197822i
$311$	−1117.21	+	516.877i	−0.203702	+	0.0942425i	−0.519088	−	0.854721i	$-0.673728\pi$
$311$	−1117.21	+	516.877i	−0.203702	+	0.0942425i	0.315386	+	0.948964i	$0.397866\pi$
$312$	1669.85	−	4191.02i	0.303003	−	0.760480i
$313$	34.9588	−	644.778i	0.00631307	−	0.116438i	−0.993678	−	0.112266i	$-0.964189\pi$
$313$	34.9588	−	644.778i	0.00631307	−	0.116438i	0.999991	−	0.00417201i	$-0.00132800\pi$
$314$	444.929	−	656.221i	0.0799643	−	0.117939i
$315$	404.205	−	475.867i	0.0722996	−	0.0851176i
$316$	906.497	−	1709.83i	0.161375	−	0.304385i
$317$	1861.26	+	627.132i	0.329775	+	0.111114i	0.479319	−	0.877641i	$-0.340884\pi$
$317$	1861.26	+	627.132i	0.329775	+	0.111114i	−0.149543	+	0.988755i	$0.547780\pi$
$318$	−295.724	−	5454.31i	−0.0521490	−	0.961831i
$319$	2451.89	+	1475.25i	0.430343	+	0.258929i
$320$	1396.62	−	5030.18i	0.243980	−	0.878736i
$321$	−310.225	−	1117.33i	−0.0539410	−	0.194278i
$322$	−2796.05	+	1682.33i	−0.483906	+	0.291156i
$323$	2640.47	+	3894.40i	0.454860	+	0.670868i
$324$	151.892	+	16.5192i	0.0260445	+	0.00283251i
$325$	2498.13	+	271.688i	0.426374	+	0.0463710i
$326$	−3464.93	−	5110.40i	−0.588666	−	0.868217i
$327$	397.734	−	239.308i	0.0672622	−	0.0404703i
$328$	522.716	+	1882.65i	0.0879944	+	0.316927i
$329$	669.183	−	2410.18i	0.112138	−	0.403883i
$330$	1906.67	+	1147.21i	0.318057	+	0.191368i
$331$	−11.2874	−	208.184i	−0.00187435	−	0.0345704i	0.997447	−	0.0714160i	$-0.0227518\pi$
$331$	−11.2874	−	208.184i	−0.00187435	−	0.0345704i	−0.999321	+	0.0368456i	$0.988269\pi$
$332$	716.500	+	241.417i	0.118443	+	0.0399081i
$333$	−631.720	+	1191.55i	−0.103958	+	0.196086i
$334$	−2103.87	+	2476.86i	−0.344666	+	0.405772i
$335$	705.834	−	1041.03i	0.115116	−	0.169783i
$336$	55.7041	−	1027.40i	0.00904437	−	0.166814i
$337$	1887.58	−	4737.47i	0.305113	−	0.765775i	−0.693845	−	0.720125i	$-0.744085\pi$
$337$	1887.58	−	4737.47i	0.305113	−	0.765775i	0.998957	−	0.0456505i	$-0.0145361\pi$
$338$	−3562.61	+	1648.24i	−0.573315	+	0.265244i
$339$	116.245	+	25.5874i	0.0186240	+	0.00409945i
$340$	267.823	+	505.168i	0.0427199	+	0.0805782i
$341$	1171.49	+	7145.76i	0.186040	+	1.13479i
$342$	−2522.59	−	1917.62i	−0.398848	−	0.303197i
$343$	−4315.82	−	1996.71i	−0.679394	−	0.314321i
$344$	−5395.88	+	5111.25i	−0.845716	+	0.801105i
$345$	−776.976	+	4739.35i	−0.121249	+	0.739588i
$346$	2948.67	−	993.522i	0.458154	−	0.154370i
$347$	−3857.46	−	9681.51i	−0.596771	−	1.49778i	−0.848076	−	0.529875i	$-0.822239\pi$
$347$	−3857.46	−	9681.51i	−0.596771	−	1.49778i	0.251305	−	0.967908i	$-0.419140\pi$
$348$	−359.494	−	340.531i	−0.0553762	−	0.0524551i
$349$	3180.07	−	2417.43i	0.487752	−	0.370779i	−0.332203	−	0.943208i	$-0.607792\pi$
$349$	3180.07	−	2417.43i	0.487752	−	0.370779i	0.819954	+	0.572429i	$0.193999\pi$
$350$	745.935	−	164.193i	0.113920	−	0.0250756i
$351$	−1075.31	−	1265.96i	−0.163521	−	0.192512i
$352$	−2711.94	+	294.941i	−0.410644	+	0.0446603i
$353$	−1065.42			−0.160642			−0.0803210	−	0.996769i	$-0.525595\pi$
$353$	−1065.42			−0.160642			−0.0803210	+	0.996769i	$0.525595\pi$
$354$	995.057	+	3211.01i	0.149397	+	0.482099i
$355$	7022.41			1.04989
$356$	474.066	−	51.5578i	0.0705771	−	0.00767572i
$357$	485.324	+	571.368i	0.0719498	+	0.0847059i
$358$	−6794.81	+	1495.65i	−1.00312	+	0.220803i
$359$	1453.96	−	1105.27i	0.213753	−	0.162491i	−0.492819	−	0.870132i	$-0.664034\pi$
$359$	1453.96	−	1105.27i	0.213753	−	0.162491i	0.706572	+	0.707641i	$0.250241\pi$
$360$	−1465.20	−	1387.91i	−0.214508	−	0.203192i
$361$	−4966.01	−	12463.7i	−0.724013	−	1.81714i
$362$	−5082.73	+	1712.57i	−0.737963	+	0.248649i
$363$	−126.996	+	774.640i	−0.0183624	+	0.112006i
$364$	637.097	−	603.490i	0.0917388	−	0.0868996i
$365$	−6054.32	−	2801.03i	−0.868212	−	0.401678i
$366$	−1206.05	−	916.816i	−0.172244	−	0.130937i
$367$	−412.563	−	2516.52i	−0.0586801	−	0.357933i	−0.999803	−	0.0198671i	$-0.993676\pi$
$367$	−412.563	−	2516.52i	−0.0586801	−	0.357933i	0.941123	−	0.338066i	$-0.109773\pi$
$368$	3707.17	+	6992.46i	0.525134	+	0.990508i
$369$	702.552	+	154.643i	0.0991149	+	0.0218168i
$370$	3084.81	−	1427.18i	0.433437	−	0.200529i
$371$	2061.23	−	5173.31i	0.288447	−	0.723948i
$372$	67.8396	−	1251.23i	0.00945516	−	0.174390i
$373$	−3431.42	+	5060.97i	−0.476333	+	0.702539i	−0.987619	−	0.156872i	$-0.949859\pi$
$373$	−3431.42	+	5060.97i	−0.476333	+	0.702539i	0.511286	+	0.859411i	$0.329169\pi$
$374$	−1729.66	+	2036.32i	−0.239141	+	0.281538i
$375$	2137.90	−	4032.52i	0.294402	−	0.555302i
$376$	−7662.13	−	2581.67i	−1.05092	−	0.354095i
$377$	291.442	+	5375.33i	0.0398144	+	0.734333i
$378$	−432.600	−	260.287i	−0.0588639	−	0.0354172i
$379$	1701.69	−	6128.94i	0.230633	−	0.830666i	−0.754124	−	0.656732i	$-0.771938\pi$
$379$	1701.69	−	6128.94i	0.230633	−	0.830666i	0.984757	−	0.173934i	$-0.0556480\pi$
$380$	−659.165	−	2374.10i	−0.0889854	−	0.320496i
$381$	−3461.40	+	2082.66i	−0.465441	+	0.280047i
$382$	1020.50	+	1505.12i	0.136684	+	0.201593i
$383$	12668.5	+	1377.78i	1.69016	+	0.183816i	0.902024	−	0.431687i	$-0.142081\pi$
$383$	12668.5	+	1377.78i	1.69016	+	0.183816i	0.788135	+	0.615503i	$0.211047\pi$
$384$	−2206.22	−	239.940i	−0.293191	−	0.0318865i
$385$	1273.10	+	1877.68i	0.168527	+	0.248559i
$386$	3892.54	−	2342.07i	0.513278	−	0.308829i
$387$	732.074	+	2636.69i	0.0961587	+	0.346332i
$388$	−880.688	+	3171.95i	−0.115232	+	0.415030i
$389$	5861.51	+	3526.76i	0.763986	+	0.459675i	0.843480	−	0.537160i	$-0.180503\pi$
$389$	5861.51	+	3526.76i	0.763986	+	0.459675i	−0.0794943	+	0.996835i	$0.525331\pi$
$390$	226.635	+	4180.03i	0.0294259	+	0.542729i
$391$	−5464.59	−	1841.23i	−0.706793	−	0.238146i
$392$	−3272.56	+	6172.70i	−0.421656	+	0.795328i
$393$	959.526	−	1129.64i	0.123160	−	0.144995i
$394$	7343.08	−	10830.2i	0.938931	−	1.38482i
$395$	−509.546	+	9398.02i	−0.0649064	+	1.19713i
$396$	−205.479	+	515.712i	−0.0260750	+	0.0654433i
$397$	272.377	−	126.015i	0.0344338	−	0.0159308i	−0.402597	−	0.915377i	$-0.631892\pi$
$397$	272.377	−	126.015i	0.0344338	−	0.0159308i	0.437030	+	0.899447i	$0.356030\pi$
$398$	−8398.67	−	1848.69i	−1.05776	−	0.232830i
$399$	−1513.19	−	2854.18i	−0.189861	−	0.358115i
$400$	−299.700	−	1828.09i	−0.0374625	−	0.228511i
$401$	−2945.56	−	2239.16i	−0.366819	−	0.278848i	0.405485	−	0.914102i	$-0.367103\pi$
$401$	−2945.56	−	2239.16i	−0.366819	−	0.278848i	−0.772304	+	0.635253i	$0.780896\pi$
$402$	−923.034	−	427.041i	−0.114519	−	0.0529823i
$403$	−9889.90	+	9368.21i	−1.22246	+	1.15797i
$404$	−253.710	+	1547.56i	−0.0312440	+	0.190580i
$405$	−704.156	+	237.258i	−0.0863946	+	0.0291097i
$406$	605.637	+	1520.03i	0.0740326	+	0.185808i
$407$	−3557.54	−	3369.88i	−0.433269	−	0.410414i
$408$	1929.11	−	1466.47i	0.234081	−	0.177944i
$409$	2102.40	−	462.773i	0.254173	−	0.0559478i	−0.0860559	−	0.996290i	$-0.527426\pi$
$409$	2102.40	−	462.773i	0.254173	−	0.0559478i	0.340229	+	0.940343i	$0.389495\pi$
$410$	−1173.71	−	1381.80i	−0.141379	−	0.166445i
$411$	8223.95	−	894.408i	0.987001	−	0.107343i
$412$	3737.82			0.446964
$413$	−453.857	+	3397.01i	−0.0540747	+	0.404736i
$414$	3883.45			0.461017
$415$	−3655.49	+	397.559i	−0.432388	+	0.0470250i
$416$	−3322.36	−	3911.39i	−0.391568	−	0.460989i
$417$	−4254.68	+	936.526i	−0.499647	+	0.109981i
$418$	9165.63	−	6967.53i	1.07250	−	0.815294i
$419$	3703.49	+	3508.14i	0.431808	+	0.409030i	0.872489	−	0.488634i	$-0.162504\pi$
$419$	3703.49	+	3508.14i	0.431808	+	0.409030i	−0.440681	+	0.897664i	$0.645263\pi$
$420$	−145.306	−	364.690i	−0.0168814	−	0.0423692i
$421$	−2238.04	+	754.084i	−0.259087	+	0.0872965i	−0.445848	−	0.895109i	$-0.647098\pi$
$421$	−2238.04	+	754.084i	−0.259087	+	0.0872965i	0.186761	+	0.982405i	$0.440201\pi$
$422$	1011.74	−	6171.34i	0.116708	−	0.711886i
$423$	−2161.18	+	2047.18i	−0.248417	+	0.235313i
$424$	−16336.9	−	7558.27i	−1.87121	−	0.865713i
$425$	1074.51	+	816.823i	0.122639	+	0.0932276i
$426$	−918.663	−	5603.60i	−0.104482	−	0.637312i
$427$	−723.457	−	1364.59i	−0.0819919	−	0.154653i
$428$	−712.055	−	156.735i	−0.0804170	−	0.0177011i
$429$	5477.34	−	2534.09i	0.616430	−	0.285191i
$430$	2552.67	−	6406.72i	0.286281	−	0.718510i
$431$	−198.114	+	3654.00i	−0.0221411	+	0.408368i	0.966364	+	0.257179i	$0.0827930\pi$
$431$	−198.114	+	3654.00i	−0.0221411	+	0.408368i	−0.988505	+	0.151189i	$0.951690\pi$
$432$	−687.174	+	1013.51i	−0.0765317	+	0.112876i
$433$	−10.0472	+	11.8285i	−0.00111510	+	0.00131280i	−0.762719	−	0.646730i	$-0.776136\pi$
$433$	−10.0472	+	11.8285i	−0.00111510	+	0.00131280i	0.761604	+	0.648042i	$0.224412\pi$
$434$	−1939.50	+	3658.28i	−0.214513	+	0.404615i
$435$	2282.13	+	768.938i	0.251539	+	0.0847534i
$436$	−15.8006	−	291.426i	−0.00173558	−	0.0320109i
$437$	21292.0	+	12811.0i	2.33075	+	1.40236i
$438$	−1443.09	+	5197.53i	−0.157428	+	0.567003i
$439$	−2888.76	−	10404.4i	−0.314061	−	1.13115i	−0.937130	−	0.348979i	$-0.886528\pi$
$439$	−2888.76	−	10404.4i	−0.314061	−	1.13115i	0.623069	−	0.782167i	$-0.285885\pi$
$440$	6283.28	−	3780.52i	0.680781	−	0.409612i
$441$	1443.53	+	2129.05i	0.155872	+	0.229895i
$442$	−4996.83	−	543.438i	−0.537726	−	0.0584812i
$443$	−17809.6	−	1936.91i	−1.91007	−	0.207732i	−0.925007	−	0.379951i	$-0.875941\pi$
$443$	−17809.6	−	1936.91i	−1.91007	−	0.207732i	−0.985059	+	0.172219i	$0.944906\pi$
$444$	475.871	+	701.857i	0.0508645	+	0.0750195i
$445$	−1987.16	+	1195.63i	−0.211686	+	0.127367i
$446$	3841.99	+	13837.6i	0.407900	+	1.46912i
$447$	−1191.99	+	4293.14i	−0.126127	+	0.454270i
$448$	−3687.60	−	2218.76i	−0.388890	−	0.233987i
$449$	6.96801	+	128.517i	0.000732384	+	0.0135080i	0.998877	−	0.0473837i	$-0.0150883\pi$
$449$	6.96801	+	128.517i	0.000732384	+	0.0135080i	−0.998144	+	0.0608917i	$0.980606\pi$
$450$	−861.403	−	290.240i	−0.0902376	−	0.0304046i
$451$	−1224.31	+	2309.30i	−0.127829	+	0.241110i
$452$	48.4497	−	57.0394i	0.00504178	−	0.00593564i
$453$	−747.384	+	1102.31i	−0.0775169	+	0.114329i
$454$	−6.28467	+	115.914i	−0.000649678	+	0.0119826i
$455$	−1579.67	+	3964.68i	−0.162761	+	0.408499i
$456$	−9477.13	+	4384.59i	−0.973261	+	0.450279i
$457$	15755.9	+	3468.13i	1.61275	+	0.354994i	0.927650	−	0.373451i	$-0.121826\pi$
$457$	15755.9	+	3468.13i	1.61275	+	0.354994i	0.685104	+	0.728445i	$0.259757\pi$
$458$	1312.72	+	2476.05i	0.133929	+	0.252616i
$459$	−144.338	−	880.422i	−0.0146778	−	0.0895307i
$460$	2403.93	+	1827.42i	0.243661	+	0.185226i
$461$	7792.25	+	3605.08i	0.787248	+	0.364220i	0.771966	−	0.635664i	$-0.219273\pi$
$461$	7792.25	+	3605.08i	0.787248	+	0.364220i	0.0152816	+	0.999883i	$0.495136\pi$
$462$	1331.76	−	1261.51i	0.134111	−	0.127037i
$463$	−1323.59	+	8073.54i	−0.132856	+	0.810387i	0.833375	+	0.552709i	$0.186406\pi$
$463$	−1323.59	+	8073.54i	−0.132856	+	0.810387i	−0.966231	+	0.257678i	$0.917043\pi$
$464$	3760.79	−	1267.16i	0.376272	−	0.126781i
$465$	2255.64	+	5661.23i	0.224952	+	0.564587i
$466$	6882.81	+	6519.74i	0.684206	+	0.648114i
$467$	6249.92	−	4751.06i	0.619297	−	0.470777i	−0.247871	−	0.968793i	$-0.579731\pi$
$467$	6249.92	−	4751.06i	0.619297	−	0.470777i	0.867168	+	0.498016i	$0.165938\pi$
$468$	−1019.95	+	224.508i	−0.100742	+	0.0221750i
$469$	−671.251	−	790.258i	−0.0660885	−	0.0778054i
$470$	7458.46	−	811.156i	0.731985	−	0.0796082i
$471$	−961.946			−0.0941065
$472$	10885.0	+	2059.37i	1.06148	+	0.200826i
$473$	−9942.61			−0.966516
$474$	7565.89	−	822.841i	0.733150	−	0.0797349i
$475$	−3765.40	−	4432.98i	−0.363723	−	0.428208i
$476$	460.337	−	101.328i	0.0443267	−	0.00975704i
$477$	−5276.05	+	4010.75i	−0.506444	+	0.384989i
$478$	1713.07	+	1622.70i	0.163920	+	0.155273i
$479$	−3309.50	−	8306.22i	−0.315689	−	0.792319i	−0.998115	−	0.0613650i	$-0.980455\pi$
$479$	−3309.50	−	8306.22i	−0.315689	−	0.792319i	0.682427	−	0.730954i	$-0.260925\pi$
$480$	−2175.61	+	733.048i	−0.206880	+	0.0697060i
$481$	1491.41	−	9097.17i	0.141377	−	0.862360i
$482$	−5544.42	+	5251.95i	−0.523944	+	0.496307i
$483$	3593.24	+	1662.41i	0.338506	+	0.156609i
$484$	392.920	+	298.690i	0.0369008	+	0.0280513i
$485$	−2590.09	−	15798.9i	−0.242495	−	1.47915i
$486$	281.439	+	530.850i	0.0262682	+	0.0495470i
$487$	2542.22	+	559.585i	0.236548	+	0.0520682i	0.331662	−	0.943398i	$-0.392391\pi$
$487$	2542.22	+	559.585i	0.236548	+	0.0520682i	−0.0951140	+	0.995466i	$0.530322\pi$
$488$	−4531.02	+	2096.27i	−0.420306	+	0.194454i
$489$	−2772.80	+	6959.21i	−0.256422	+	0.643572i
$490$	350.974	−	6473.33i	0.0323579	−	0.596807i
$491$	1528.22	−	2253.96i	0.140464	−	0.207169i	−0.750950	−	0.660359i	$-0.770404\pi$
$491$	1528.22	−	2253.96i	0.140464	−	0.207169i	0.891414	+	0.453191i	$0.149714\pi$
$492$	292.818	−	344.732i	0.0268318	−	0.0315888i
$493$	−1354.40	+	2554.66i	−0.123730	+	0.233380i
$494$	20525.7	+	6915.91i	1.86942	+	0.629882i
$495$	−146.165	−	2695.86i	−0.0132720	−	0.244788i
$496$	8605.06	+	5177.49i	0.778989	+	0.468702i
$497$	1548.75	−	5578.10i	0.139781	−	0.503445i
$498$	795.443	+	2864.93i	0.0715756	+	0.257792i
$499$	14958.1	−	9000.01i	1.34192	−	0.807406i	0.350305	−	0.936636i	$-0.386078\pi$
$499$	14958.1	−	9000.01i	1.34192	−	0.807406i	0.991615	+	0.129230i	$0.0412504\pi$
$500$	−1610.47	−	2375.26i	−0.144045	−	0.212450i
$501$	3919.85	+	426.309i	0.349553	+	0.0380162i
$502$	18283.1	+	1988.41i	1.62553	+	0.176787i
$503$	−11358.9	−	16753.1i	−1.00690	−	1.48506i	−0.869122	−	0.494597i	$-0.835316\pi$
$503$	−11358.9	−	16753.1i	−1.00690	−	1.48506i	−0.137774	−	0.990464i	$-0.543995\pi$
$504$	−1425.60	+	857.754i	−0.125994	+	0.0758084i
$505$	−2040.38	−	7348.77i	−0.179793	−	0.647556i
$506$	−3774.88	+	13595.9i	−0.331648	+	1.19449i
$507$	4080.95	+	2455.43i	0.357478	+	0.215088i
$508$	137.510	+	2536.22i	0.0120099	+	0.221509i
$509$	10261.1	+	3457.38i	0.893550	+	0.301072i	0.728364	−	0.685190i	$-0.240281\pi$
$509$	10261.1	+	3457.38i	0.893550	+	0.301072i	0.165186	+	0.986262i	$0.447178\pi$
$510$	−1053.22	+	1986.59i	−0.0914461	+	0.172486i
$511$	−3560.18	+	4191.37i	−0.308206	+	0.362848i
$512$	−7100.27	+	10472.1i	−0.612872	+	0.903918i
$513$	−208.142	+	3838.96i	−0.0179137	+	0.330398i
$514$	934.694	−	2345.90i	0.0802093	−	0.201310i
$515$	−16498.1	+	7632.82i	−1.41163	+	0.653092i
$516$	1680.32	+	369.867i	0.143357	+	0.0315552i
$517$	−5066.37	−	9556.19i	−0.430984	−	0.812922i
$518$	−453.317	−	2765.11i	−0.0384510	−	0.234541i
$519$	−3005.44	−	2284.68i	−0.254189	−	0.193230i
$520$	12520.2	+	5792.46i	1.05586	+	0.488492i
$521$	8960.71	−	8488.04i	0.753505	−	0.713758i	−0.211098	−	0.977465i	$-0.567704\pi$
$521$	8960.71	−	8488.04i	0.753505	−	0.713758i	0.964603	+	0.263707i	$0.0849453\pi$
$522$	315.036	−	1921.63i	0.0264152	−	0.161126i
$523$	−13179.6	+	4440.71i	−1.10192	+	0.371278i	−0.810749	−	0.585394i	$-0.800940\pi$
$523$	−13179.6	+	4440.71i	−1.10192	+	0.371278i	−0.291166	+	0.956672i	$0.594043\pi$
$524$	−344.936	−	865.724i	−0.0287569	−	0.0721743i
$525$	−672.786	−	637.297i	−0.0559291	−	0.0529789i
$526$	−12479.5	+	9486.70i	−1.03448	+	0.786388i
$527$	−7145.99	+	1572.95i	−0.590672	+	0.130017i
$528$	−2880.30	−	3390.95i	−0.237404	−	0.279493i
$529$	−18179.7	+	1977.17i	−1.49418	+	0.162502i
$530$	16702.8			1.36892
$531$	2547.08	−	3185.61i	0.208162	−	0.260346i
$532$	−2031.19			−0.165532
$533$	−4888.38	+	531.643i	−0.397259	+	0.0432046i
$534$	1214.03	+	1429.26i	0.0983821	+	0.115824i
$535$	3462.95	−	762.252i	0.279843	−	0.0615982i
$536$	−2668.15	+	2028.27i	−0.215012	+	0.163448i
$537$	6128.49	+	5805.21i	0.492484	+	0.466505i
$538$	−1204.26	−	3022.45i	−0.0965040	−	0.242207i
$539$	−8856.95	+	2984.26i	−0.707785	+	0.238480i
$540$	−75.5842	+	461.043i	−0.00602338	+	0.0367410i
$541$	−1271.35	+	1204.29i	−0.101034	+	0.0957049i	−0.736550	−	0.676383i	$-0.763546\pi$
$541$	−1271.35	+	1204.29i	−0.101034	+	0.0957049i	0.635515	+	0.772088i	$0.280788\pi$
$542$	9972.84	+	4613.93i	0.790350	+	0.365655i
$543$	5180.60	+	3938.19i	0.409430	+	0.311241i
$544$	−445.956	−	2720.21i	−0.0351474	−	0.214390i
$545$	664.848	+	1254.04i	0.0522549	+	0.0985633i
$546$	3370.31	+	741.861i	0.264168	+	0.0581478i
$547$	3073.83	−	1422.10i	0.240269	−	0.111160i	−0.296060	−	0.955169i	$-0.595673\pi$
$547$	3073.83	−	1422.10i	0.240269	−	0.111160i	0.536329	+	0.844009i	$0.319811\pi$
$548$	1925.21	−	4831.92i	0.150075	−	0.376660i
$549$	−99.5129	+	1835.41i	−0.00773608	+	0.142684i
$550$	1853.45	−	2733.63i	0.143693	−	0.211931i
$551$	8066.50	−	9496.61i	0.623674	−	0.734246i
$552$	5994.50	−	11306.8i	0.462216	−	0.871831i
$553$	7352.74	+	2477.43i	0.565408	+	0.190508i
$554$	−1083.44	−	19982.8i	−0.0830881	−	1.53247i
$555$	−3533.64	−	2126.12i	−0.270260	−	0.162610i
$556$	−732.811	+	2639.35i	−0.0558959	+	0.201319i
$557$	−389.175	−	1401.68i	−0.0296048	−	0.106627i	0.947272	−	0.320432i	$-0.103828\pi$
$557$	−389.175	−	1401.68i	−0.0296048	−	0.106627i	−0.976876	+	0.213805i	$0.931414\pi$
$558$	4222.35	−	2540.50i	0.320334	−	0.192738i
$559$	−10496.8	−	15481.7i	−0.794220	−	1.17139i
$560$	3127.79	+	340.168i	0.236024	+	0.0256691i
$561$	3222.64	+	350.484i	0.242531	+	0.0263769i
$562$	8273.45	+	12202.4i	0.620987	+	0.915887i
$563$	6362.25	−	3828.04i	0.476265	−	0.286559i	−0.257112	−	0.966382i	$-0.582771\pi$
$563$	6362.25	−	3828.04i	0.476265	−	0.286559i	0.733376	+	0.679823i	$0.237943\pi$
$564$	500.735	+	1803.48i	0.0373843	+	0.134646i
$565$	−97.3710	+	350.699i	−0.00725032	+	0.0261133i
$566$	2878.99	+	1732.23i	0.213804	+	0.128641i
$567$	33.1631	+	611.658i	0.00245630	+	0.0453037i
$568$	−17733.2	−	5975.00i	−1.30998	−	0.441383i
$569$	−8045.64	+	15175.7i	−0.592778	+	1.11810i	0.387758	+	0.921761i	$0.373250\pi$
$569$	−8045.64	+	15175.7i	−0.592778	+	1.11810i	−0.980536	+	0.196337i	$0.937095\pi$
$570$	6272.78	−	7384.89i	0.460943	−	0.542665i
$571$	−11263.4	+	16612.3i	−0.825500	+	1.21752i	0.148035	+	0.988982i	$0.452705\pi$
$571$	−11263.4	+	16612.3i	−0.825500	+	1.21752i	−0.973535	+	0.228539i	$0.926605\pi$
$572$	205.437	−	3789.06i	0.0150170	−	0.276973i
$573$	816.649	−	2049.63i	0.0595393	−	0.149432i
$574$	−1356.46	+	627.566i	−0.0986369	+	0.0456343i
$575$	6961.59	+	1532.36i	0.504902	+	0.111137i
$576$	2399.06	+	4525.11i	0.173543	+	0.327338i
$577$	525.698	+	3206.61i	0.0379291	+	0.231357i	0.998988	−	0.0449880i	$-0.0143250\pi$
$577$	525.698	+	3206.61i	0.0379291	+	0.231357i	−0.961058	+	0.276345i	$0.910877\pi$
$578$	7521.57	+	5717.75i	0.541273	+	0.411465i
$579$	−5002.37	−	2314.34i	−0.359052	−	0.166115i
$580$	1099.27	−	1041.29i	0.0786979	−	0.0745466i
$581$	−490.406	+	2991.34i	−0.0350180	+	0.213600i
$582$	−12268.0	+	4133.57i	−0.873755	+	0.294402i
$583$	−8913.01	−	22370.0i	−0.633171	−	1.58914i
$584$	12905.3	+	12224.5i	0.914425	+	0.866190i
$585$	4043.42	−	3073.73i	0.285769	−	0.217236i
$586$	4371.53	−	962.246i	0.308167	−	0.0678328i
$587$	−3913.42	−	4607.23i	−0.275169	−	0.323954i	0.607167	−	0.794574i	$-0.292306\pi$
$587$	−3913.42	−	4607.23i	−0.275169	−	0.323954i	−0.882336	+	0.470621i	$0.844030\pi$
$588$	1607.86	−	174.865i	0.112767	−	0.0122641i
$589$	31531.0			2.20579
$590$	−9969.04	+	2506.68i	−0.695625	+	0.174912i
$591$	−15875.9			−1.10499
$592$	−6756.16	+	734.776i	−0.469048	+	0.0510120i
$593$	−5314.87	−	6257.15i	−0.368053	−	0.433306i	0.546694	−	0.837333i	$-0.315886\pi$
$593$	−5314.87	−	6257.15i	−0.368053	−	0.433306i	−0.914747	+	0.404027i	$0.867610\pi$
$594$	−2132.07	+	469.303i	−0.147272	+	0.0324171i
$595$	−1824.93	+	1387.27i	−0.125739	+	0.0955844i
$596$	2033.84	+	1926.55i	0.139781	+	0.132407i
$597$	3862.04	+	9692.99i	0.264762	+	0.664502i
$598$	−25155.5	+	8475.87i	−1.72021	+	0.579605i
$599$	−784.913	+	4787.76i	−0.0535404	+	0.326582i	0.946453	+	0.322843i	$0.104638\pi$
$599$	−784.913	+	4787.76i	−0.0535404	+	0.326582i	−0.999993	+	0.00373907i	$0.998810\pi$
$600$	−2174.71	+	2060.00i	−0.147970	+	0.140165i
$601$	4523.03	+	2092.57i	0.306985	+	0.142026i	0.567333	−	0.823488i	$-0.307975\pi$
$601$	4523.03	+	2092.57i	0.306985	+	0.142026i	−0.260348	+	0.965515i	$0.583837\pi$
$602$	−4526.06	−	3440.62i	−0.306426	−	0.232939i
$603$	199.633	+	1217.71i	0.0134821	+	0.0822371i
$604$	392.231	+	739.826i	0.0264233	+	0.0498396i
$605$	−2344.22	−	516.002i	−0.157531	−	0.0346751i
$606$	−5597.10	+	2589.49i	−0.375192	+	0.173582i
$607$	134.863	−	338.481i	0.00901800	−	0.0226335i	−0.924399	−	0.381427i	$-0.875433\pi$
$607$	134.863	−	338.481i	0.00901800	−	0.0226335i	0.933417	+	0.358794i	$0.116812\pi$
$608$	−643.091	+	11861.1i	−0.0428960	+	0.791170i
$609$	1114.10	−	1643.17i	0.0741307	−	0.109335i
$610$	2999.02	−	3530.72i	0.199060	−	0.234352i
$611$	9531.20	−	17977.7i	0.631082	−	1.19035i
$612$	−531.595	−	179.115i	−0.0351118	−	0.0118306i
$613$	−797.868	−	14715.8i	−0.0525703	−	0.969601i	−0.899233	−	0.437471i	$-0.855874\pi$
$613$	−797.868	−	14715.8i	−0.0525703	−	0.969601i	0.846662	−	0.532131i	$-0.178608\pi$
$614$	−19071.3	−	11474.8i	−1.25351	−	0.754213i
$615$	−588.486	+	2119.53i	−0.0385854	+	0.138972i
$616$	−1617.24	−	5824.77i	−0.105780	−	0.380985i
$617$	−17334.5	+	10429.8i	−1.13106	+	0.680534i	−0.952845	−	0.303458i	$-0.901859\pi$
$617$	−17334.5	+	10429.8i	−1.13106	+	0.680534i	−0.178211	+	0.983992i	$0.557031\pi$
$618$	8248.94	+	12166.3i	0.536927	+	0.791908i
$619$	17725.2	+	1927.73i	1.15094	+	0.125173i	0.663635	−	0.748057i	$-0.269013\pi$
$619$	17725.2	+	1927.73i	1.15094	+	0.125173i	0.487309	+	0.873230i	$0.337979\pi$
$620$	3809.20	+	414.275i	0.246744	+	0.0268350i
$621$	−2644.19	−	3899.89i	−0.170866	−	0.252009i
$622$	−2608.04	+	1569.21i	−0.168124	+	0.101157i
$623$	511.470	+	1842.15i	0.0328918	+	0.118466i
$624$	2239.21	−	8064.90i	0.143654	−	0.517395i
$625$	7583.73	+	4562.98i	0.485359	+	0.292031i
$626$	−86.4391	−	1594.28i	−0.00551885	−	0.101789i
$627$	−13237.8	−	4460.33i	−0.843169	−	0.284097i
$628$	−283.307	+	534.373i	−0.0180019	+	0.0339551i
$629$	3205.59	−	3773.91i	0.203204	−	0.239230i
$630$	866.361	−	1277.79i	0.0547883	−	0.0808068i
$631$	−1514.03	+	27924.7i	−0.0955193	+	1.76175i	0.422483	+	0.906371i	$0.361158\pi$
$631$	−1514.03	+	27924.7i	−0.0955193	+	1.76175i	−0.518003	+	0.855379i	$0.673324\pi$
$632$	9283.00	−	23298.6i	0.584269	−	1.46640i
$633$	−6886.35	+	3185.96i	−0.432398	+	0.200049i
$634$	4742.82	+	1043.97i	0.297100	+	0.0653967i
$635$	−5786.05	−	10913.6i	−0.361594	−	0.682039i
$636$	674.150	+	4112.13i	0.0420311	+	0.256378i
$637$	−13997.5	−	10640.6i	−0.870643	−	0.661845i
$638$	6421.38	+	2970.85i	0.398471	+	0.184352i
$639$	−5001.82	+	4737.97i	−0.309654	+	0.293320i
$640$	1097.85	−	6696.62i	0.0678071	−	0.413605i
$641$	−11842.1	+	3990.06i	−0.729694	+	0.245863i	−0.659536	−	0.751673i	$-0.729247\pi$
$641$	−11842.1	+	3990.06i	−0.729694	+	0.245863i	−0.0701585	+	0.997536i	$0.522351\pi$
$642$	−1061.26	−	2663.57i	−0.0652411	−	0.163743i
$643$	5105.15	+	4835.86i	0.313107	+	0.296590i	0.828073	−	0.560620i	$-0.189437\pi$
$643$	5105.15	+	4835.86i	0.313107	+	0.296590i	−0.514967	+	0.857210i	$0.672196\pi$
$644$	1981.75	−	1506.49i	0.121261	−	0.0921800i
$645$	−8171.93	+	1798.78i	−0.498867	+	0.109809i
$646$	7531.66	+	8866.95i	0.458714	+	0.540040i
$647$	−12355.2	+	1343.71i	−0.750746	+	0.0816485i	−0.475488	−	0.879722i	$-0.657729\pi$
$647$	−12355.2	+	1343.71i	−0.750746	+	0.0816485i	−0.275257	+	0.961371i	$0.588763\pi$
$648$	1980.02			0.120035
$649$	8676.87	+	12013.8i	0.524803	+	0.726631i
$650$	6213.30			0.374932
$651$	4994.35	−	543.168i	0.300682	−	0.0327011i
$652$	3049.30	+	3589.91i	0.183159	+	0.215632i
$653$	−8406.83	+	1850.48i	−0.503805	+	0.110896i	−0.459599	−	0.888127i	$-0.652007\pi$
$653$	−8406.83	+	1850.48i	−0.503805	+	0.110896i	−0.0442061	+	0.999022i	$0.514076\pi$
$654$	913.695	−	694.573i	0.0546304	−	0.0415290i
$655$	3290.34	+	3116.77i	0.196281	+	0.185927i
$656$	1341.74	+	3367.52i	0.0798572	+	0.200426i
$657$	6202.12	−	2089.74i	0.368292	−	0.124092i
$658$	1000.60	−	6103.37i	0.0592816	−	0.361602i
$659$	−7428.04	+	7036.21i	−0.439082	+	0.415921i	−0.875043	−	0.484045i	$-0.839167\pi$
$659$	−7428.04	+	7036.21i	−0.439082	+	0.415921i	0.435961	+	0.899966i	$0.356409\pi$
$660$	−1540.63	−	712.772i	−0.0908622	−	0.0420373i
$661$	−17692.3	−	13449.3i	−1.04107	−	0.791403i	−0.0626544	−	0.998035i	$-0.519957\pi$
$661$	−17692.3	−	13449.3i	−1.04107	−	0.791403i	−0.978419	+	0.206632i	$0.933750\pi$
$662$	−83.4003	−	508.719i	−0.00489644	−	0.0298670i
$663$	2856.54	+	5388.01i	0.167329	+	0.315615i
$664$	9569.21	+	2106.34i	0.559273	+	0.123105i
$665$	8965.31	−	4147.80i	0.522797	−	0.241872i
$666$	−1234.29	+	3097.83i	−0.0718135	+	0.180238i
$667$	−826.733	+	15248.2i	−0.0479929	+	0.885176i
$668$	1391.27	−	2051.97i	0.0805836	−	0.118852i
$669$	11280.2	−	13280.1i	0.651896	−	0.767471i
$670$	1456.71	−	2747.65i	0.0839965	−	0.158434i
$671$	−6328.99	−	2132.49i	−0.364125	−	0.122688i
$672$	102.463	+	1889.82i	0.00588184	+	0.108484i
$673$	11649.9	+	7009.50i	0.667266	+	0.401481i	0.808500	−	0.588496i	$-0.200280\pi$
$673$	11649.9	+	7009.50i	0.667266	+	0.401481i	−0.141234	+	0.989976i	$0.545107\pi$
$674$	3373.37	−	12149.8i	0.192786	−	0.694351i
$675$	295.049	+	1062.67i	0.0168244	+	0.0605959i
$676$	2565.92	−	1543.86i	0.145990	−	0.0878392i
$677$	565.792	+	834.480i	0.0321199	+	0.0473732i	0.843410	−	0.537271i	$-0.180545\pi$
$677$	565.792	+	834.480i	0.0321199	+	0.0473732i	−0.811290	+	0.584644i	$0.801234\pi$
$678$	292.581	+	31.8201i	0.0165730	+	0.00180243i
$679$	−13120.7	−	1426.96i	−0.741571	−	0.0806507i
$680$	4158.29	+	6133.01i	0.234504	+	0.345868i
$681$	120.684	−	72.6131i	0.00679092	−	0.00408596i
$682$	4789.95	+	17251.8i	0.268939	+	0.968632i
$683$	−1718.78	+	6190.50i	−0.0962920	+	0.346812i	−0.995964	−	0.0897542i	$-0.971392\pi$
$683$	−1718.78	+	6190.50i	−0.0962920	+	0.346812i	0.899672	+	0.436567i	$0.143806\pi$
$684$	2071.29	+	1246.25i	0.115786	+	0.0696662i
$685$	1369.48	+	25258.6i	0.0763872	+	1.40888i
$686$	−11142.5	−	3754.35i	−0.620150	−	0.208953i
$687$	1592.72	−	3004.19i	0.0884514	−	0.166837i
$688$	−8926.92	+	10509.6i	−0.494674	+	0.582375i
$689$	25422.5	−	37495.4i	1.40569	−	2.07324i
$690$	−642.896	+	11857.5i	−0.0354705	+	0.654214i
$691$	9956.30	−	24988.4i	0.548127	−	1.37569i	−0.350328	−	0.936627i	$-0.613930\pi$
$691$	9956.30	−	24988.4i	0.548127	−	1.37569i	0.898454	−	0.439067i	$-0.144691\pi$
$692$	−2154.31	+	996.690i	−0.118345	+	0.0547521i
$693$	−2173.64	−	478.454i	−0.119148	−	0.0262265i
$694$	−12070.2	−	22766.9i	−0.660202	−	1.24527i
$695$	−2155.19	−	13146.1i	−0.117627	−	0.717494i
$696$	−5108.63	−	3883.48i	−0.278222	−	0.211499i
$697$	−2397.06	−	1109.00i	−0.130266	−	0.0602674i
$698$	7170.68	−	6792.43i	0.388846	−	0.368334i
$699$	1860.93	−	11351.2i	0.100696	−	0.614221i
$700$	−552.171	+	186.048i	−0.0298144	+	0.0100457i
$701$	4392.02	+	11023.1i	0.236640	+	0.593921i	0.998554	−	0.0537569i	$-0.0171196\pi$
$701$	4392.02	+	11023.1i	0.236640	+	0.593921i	−0.761914	+	0.647678i	$0.775740\pi$
$702$	−2981.67	−	2824.38i	−0.160307	−	0.151851i
$703$	−16986.7	+	12912.9i	−0.911330	+	0.692775i
$704$	−18174.3	+	4000.47i	−0.972970	+	0.214167i
$705$	−5892.97	−	6937.74i	−0.314811	−	0.370624i
$706$	−2618.91	+	284.824i	−0.139609	+	0.0151834i
$707$	−6287.33			−0.334455
$708$	−1019.49	−	2353.14i	−0.0541170	−	0.124910i
$709$	−22317.9			−1.18218			−0.591091	−	0.806605i	$-0.701302\pi$
$709$	−22317.9			−1.18218			−0.591091	+	0.806605i	$0.701302\pi$
$710$	17261.8	−	1877.33i	0.912428	−	0.0992325i
$711$	−5977.85	−	7037.67i	−0.315312	−	0.371214i
$712$	6035.33	−	1328.48i	0.317674	−	0.0699252i
$713$	−30763.5	+	23385.8i	−1.61585	+	1.22834i
$714$	1345.72	+	1274.74i	0.0705356	+	0.0668149i
$715$	6830.69	+	17143.7i	0.357277	+	0.896698i
$716$	5029.79	−	1694.73i	0.262531	−	0.0884570i
$717$	463.168	−	2825.20i	0.0241246	−	0.147153i
$718$	3278.51	−	3105.57i	0.170408	−	0.161419i
$719$	11101.8	+	5136.25i	0.575839	+	0.266412i	0.686119	−	0.727489i	$-0.259313\pi$
$719$	11101.8	+	5136.25i	0.575839	+	0.266412i	−0.110280	+	0.993901i	$0.535175\pi$
$720$	−2980.82	−	2265.96i	−0.154290	−	0.117288i
$721$	2424.41	+	14788.3i	0.125229	+	0.763861i
$722$	−15538.9	−	29309.6i	−0.800969	−	1.51079i
$723$	9049.31	+	1991.90i	0.465488	+	0.102462i
$724$	3713.47	−	1718.03i	0.190622	−	0.0881909i
$725$	1323.00	−	3320.47i	0.0677722	−	0.170096i
$726$	−105.080	+	1938.09i	−0.00537176	+	0.0990763i
$727$	−17271.8	+	25474.0i	−0.881123	+	1.29956i	0.0721324	+	0.997395i	$0.477020\pi$
$727$	−17271.8	+	25474.0i	−0.881123	+	1.29956i	−0.953256	+	0.302165i	$0.902291\pi$
$728$	7362.38	−	8667.66i	0.374818	−	0.441270i
$729$	341.470	−	644.080i	0.0173485	−	0.0327227i
$730$	−15630.9	−	5266.68i	−0.792503	−	0.267025i
$731$	−543.924	−	10032.1i	−0.0275209	−	0.507593i
$732$	990.283	+	595.834i	0.0500026	+	0.0300856i
$733$	9400.80	−	33858.6i	0.473706	−	1.70613i	−0.211148	−	0.977454i	$-0.567720\pi$
$733$	9400.80	−	33858.6i	0.473706	−	1.70613i	0.684854	−	0.728680i	$-0.259866\pi$
$734$	−1686.87	−	6075.57i	−0.0848279	−	0.305522i
$735$	−6739.71	+	4055.15i	−0.338229	+	0.203505i
$736$	−8169.68	−	12049.4i	−0.409155	−	0.603459i
$737$	−4457.23	−	484.753i	−0.222774	−	0.0242281i
$738$	1768.29	+	192.313i	0.0881999	+	0.00959232i
$739$	12419.7	+	18317.7i	0.618223	+	0.911810i	0.999922	−	0.0124762i	$-0.00397139\pi$
$739$	12419.7	+	18317.7i	0.618223	+	0.911810i	−0.381699	+	0.924287i	$0.624661\pi$
$740$	−2221.79	+	1336.81i	−0.110371	+	0.0664081i
$741$	−7030.50	−	25321.6i	−0.348545	−	1.25535i
$742$	3683.72	−	13267.6i	0.182255	−	0.656425i
$743$	21204.1	+	12758.1i	1.04698	+	0.629945i	0.931640	−	0.363382i	$-0.118378\pi$
$743$	21204.1	+	12758.1i	1.04698	+	0.629945i	0.115336	+	0.993327i	$0.463206\pi$
$744$	−879.156	−	16215.1i	−0.0433218	−	0.799024i
$745$	−12911.1	−	4350.26i	−0.634935	−	0.213935i
$746$	−7081.81	+	13357.7i	−0.347565	+	0.655577i
$747$	2335.45	−	2749.50i	0.114390	−	0.134671i
$748$	1143.81	−	1687.00i	0.0559116	−	0.0824635i
$749$	158.254	−	2918.83i	0.00772028	−	0.142392i
$750$	4177.16	−	10483.9i	0.203371	−	0.510423i
$751$	−8437.88	+	3903.78i	−0.409990	+	0.189682i	−0.614033	−	0.789280i	$-0.710454\pi$
$751$	−8437.88	+	3903.78i	−0.409990	+	0.189682i	0.204043	+	0.978962i	$0.434592\pi$
$752$	−14649.9	−	3224.70i	−0.710410	−	0.156373i
$753$	−10451.9	−	19714.4i	−0.505829	−	0.954095i
$754$	2153.41	+	13135.2i	0.104008	+	0.634424i
$755$	−3242.00	−	2464.51i	−0.156276	−	0.118798i
$756$	349.550	+	161.719i	0.0168162	+	0.00777999i
$757$	19493.2	−	18464.9i	0.935919	−	0.886550i	−0.0578138	−	0.998327i	$-0.518413\pi$
$757$	19493.2	−	18464.9i	0.935919	−	0.886550i	0.993733	+	0.111777i	$0.0356544\pi$
$758$	2544.45	−	15520.5i	0.121924	−	0.743706i
$759$	16223.7	−	5466.41i	0.775868	−	0.261420i
$760$	−11818.7	−	29662.8i	−0.564093	−	1.41577i
$761$	16944.5	+	16050.7i	0.807145	+	0.764568i	0.975227	−	0.221205i	$-0.0709988\pi$
$761$	16944.5	+	16050.7i	0.807145	+	0.764568i	−0.168082	+	0.985773i	$0.553757\pi$
$762$	−7951.72	+	6044.74i	−0.378032	+	0.287373i
$763$	1142.75	−	251.537i	0.0542204	−	0.0119348i
$764$	−898.083	−	1057.30i	−0.0425281	−	0.0500680i
$765$	2712.13	−	294.962i	0.128179	−	0.0139403i
$766$	31508.8			1.48624
$767$	−9546.22	+	26194.3i	−0.449405	+	1.23314i
$768$	8170.71			0.383900
$769$	−17386.5	+	1890.90i	−0.815310	+	0.0886703i	−0.506266	−	0.862377i	$-0.668975\pi$
$769$	−17386.5	+	1890.90i	−0.815310	+	0.0886703i	−0.309044	+	0.951048i	$0.600009\pi$
$770$	3631.37	+	4275.18i	0.169955	+	0.200087i
$771$	−2992.26	+	658.646i	−0.139771	+	0.0307660i
$772$	−2758.91	+	2097.27i	−0.128621	+	0.0977752i
$773$	23070.4	+	21853.5i	1.07346	+	1.01684i	0.999809	+	0.0195520i	$0.00622400\pi$
$773$	23070.4	+	21853.5i	1.07346	+	1.01684i	0.0736519	+	0.997284i	$0.476535\pi$
$774$	2504.39	+	6285.55i	0.116303	+	0.291899i
$775$	8571.57	−	2888.10i	0.397290	−	0.133863i
$776$	−6901.85	+	42099.4i	−0.319281	+	1.94753i
$777$	−2468.16	+	2337.97i	−0.113957	+	0.107946i
$778$	15351.0	+	7102.14i	0.707405	+	0.327280i
$779$	9060.69	+	6887.76i	0.416730	+	0.316790i
$780$	−516.650	−	3151.43i	−0.0237167	−	0.144666i
$781$	−11725.6	−	22116.8i	−0.537227	−	1.01332i
$782$	−13924.7	−	3065.07i	−0.636762	−	0.140162i
$783$	−2144.28	+	992.048i	−0.0978674	+	0.0452783i
$784$	−4797.74	+	12041.4i	−0.218556	+	0.548534i
$785$	159.248	−	2937.15i	0.00724051	−	0.133543i
$786$	2056.62	−	3033.29i	0.0933298	−	0.137651i
$787$	−730.554	+	860.075i	−0.0330895	+	0.0389560i	−0.778458	−	0.627697i	$-0.783998\pi$
$787$	−730.554	+	860.075i	−0.0330895	+	0.0389560i	0.745368	+	0.666653i	$0.232274\pi$
$788$	−4675.68	+	8819.26i	−0.211376	+	0.398697i
$789$	18024.0	+	6073.01i	0.813274	+	0.274024i
$790$	1259.90	+	23237.5i	0.0567409	+	1.04652i
$791$	257.096	+	154.689i	0.0115566	+	0.00695337i
$792$	−1924.67	+	6932.03i	−0.0863511	+	0.311009i
$793$	−3361.28	−	12106.3i	−0.150520	−	0.542126i
$794$	635.843	−	382.574i	0.0284197	−	0.0170995i
$795$	−11372.8	−	16773.6i	−0.507359	−	0.748298i
$796$	6522.00	+	709.310i	0.290410	+	0.0315839i
$797$	−43439.4	−	4724.32i	−1.93062	−	0.209968i	−0.939462	−	0.342654i	$-0.888674\pi$
$797$	−43439.4	−	4724.32i	−1.93062	−	0.209968i	−0.991158	+	0.132686i	$0.957640\pi$
$798$	−4482.60	−	6611.35i	−0.198850	−	0.293282i
$799$	9365.04	−	5634.76i	0.414657	−	0.249491i
$800$	911.604	+	3283.30i	0.0402876	+	0.145103i
$801$	608.698	−	2192.33i	0.0268506	−	0.0967069i
$802$	−7839.10	−	4716.63i	−0.345147	−	0.207668i
$803$	1287.41	+	23744.8i	0.0565773	+	1.04351i
$804$	735.248	+	247.734i	0.0322515	+	0.0108668i
$805$	−5670.77	+	10696.2i	−0.248284	+	0.468313i
$806$	−21805.9	+	25671.9i	−0.952955	+	1.12190i
$807$	−2215.29	+	3267.31i	−0.0966318	+	0.142521i
$808$	−1100.27	+	20293.3i	−0.0479053	+	0.883561i
$809$	8086.88	−	20296.5i	0.351446	−	0.882062i	−0.641889	−	0.766797i	$-0.721849\pi$
$809$	8086.88	−	20296.5i	0.351446	−	0.882062i	0.993335	−	0.115265i	$-0.0367716\pi$
$810$	−1667.46	+	771.450i	−0.0723316	+	0.0334642i
$811$	20668.1	+	4549.40i	0.894891	+	0.196980i	0.638527	−	0.769600i	$-0.279544\pi$
$811$	20668.1	+	4549.40i	0.894891	+	0.196980i	0.256365	+	0.966580i	$0.417475\pi$
$812$	−584.685	−	1102.83i	−0.0252690	−	0.0476624i
$813$	−2156.92	−	13156.6i	−0.0930461	−	0.567556i
$814$	−9645.68	−	7332.45i	−0.415333	−	0.315728i
$815$	−20789.9	−	9618.41i	−0.893542	−	0.413397i
$816$	3263.90	−	3091.73i	0.140024	−	0.132638i
$817$	−7004.22	+	42723.9i	−0.299935	+	1.82952i
$818$	5044.19	−	1699.59i	0.215606	−	0.0726463i
$819$	−1549.80	−	3889.70i	−0.0661225	−	0.165955i
$820$	1004.11	+	951.144i	0.0427622	+	0.0405066i
$821$	4081.70	−	3102.83i	0.173511	−	0.131899i	−0.514815	−	0.857301i	$-0.672139\pi$
$821$	4081.70	−	3102.83i	0.173511	−	0.131899i	0.688325	+	0.725402i	$0.258346\pi$
$822$	19976.2	−	4397.10i	0.847628	−	0.186577i
$823$	19414.9	+	22857.0i	0.822311	+	0.968099i	0.999872	−	0.0160105i	$-0.00509653\pi$
$823$	19414.9	+	22857.0i	0.822311	+	0.968099i	−0.177561	+	0.984110i	$0.556821\pi$
$824$	48155.7	−	5237.25i	2.03590	−	0.221418i
$825$	−4007.19			−0.169106
$826$	−207.488	+	8471.53i	−0.00874022	+	0.356855i
$827$	30776.3			1.29407			0.647035	−	0.762460i	$-0.276009\pi$
$827$	30776.3			1.29407			0.647035	+	0.762460i	$0.276009\pi$
$828$	−2945.19	+	320.309i	−0.123614	+	0.0134438i
$829$	9974.40	+	11742.8i	0.417883	+	0.491970i	0.930317	−	0.366757i	$-0.119532\pi$
$829$	9974.40	+	11742.8i	0.417883	+	0.491970i	−0.512434	+	0.858727i	$0.671256\pi$
$830$	−8879.29	+	1954.48i	−0.371331	+	0.0817361i
$831$	−19329.7	+	14694.1i	−0.806908	+	0.613396i
$832$	−25416.6	−	24075.8i	−1.05909	−	1.00322i
$833$	−3495.65	−	8773.41i	−0.145398	−	0.364923i
$834$	−10208.1	+	3439.50i	−0.423833	+	0.142806i
$835$	−1950.59	+	11898.1i	−0.0808419	+	0.493114i
$836$	−6376.49	+	6040.13i	−0.263798	+	0.249883i
$837$	−5426.21	−	2510.43i	−0.224083	−	0.103672i
$838$	10041.4	+	7633.28i	0.413932	+	0.314663i
$839$	−2904.78	−	17718.4i	−0.119528	−	0.729089i	−0.976788	−	0.214206i	$-0.931284\pi$
$839$	−2904.78	−	17718.4i	−0.119528	−	0.729089i	0.857260	−	0.514883i	$-0.172165\pi$
$840$	−2383.02	−	4494.85i	−0.0978832	−	0.184627i
$841$	−16340.6	−	3596.85i	−0.670001	−	0.147478i
$842$	−5299.75	+	2451.92i	−0.216914	+	0.100355i
$843$	6620.80	−	16617.0i	0.270501	−	0.678907i
$844$	−258.284	+	4763.76i	−0.0105338	+	0.194284i
$845$	−8172.86	+	12054.1i	−0.332728	+	0.490737i
$846$	−4765.12	+	5609.93i	−0.193650	+	0.227983i
$847$	−926.879	+	1748.28i	−0.0376009	+	0.0709228i
$848$	−31648.1	−	10663.5i	−1.28160	−	0.431822i
$849$	−220.703	−	4070.63i	−0.00892169	−	0.164551i
$850$	2859.63	+	1720.58i	0.115393	+	0.0694299i
$851$	6995.99	−	25197.3i	0.281809	−	1.01498i
$852$	1158.90	+	4173.97i	0.0466000	+	0.167838i
$853$	23494.0	−	14135.9i	0.943047	−	0.567413i	0.0410511	−	0.999157i	$-0.486929\pi$
$853$	23494.0	−	14135.9i	0.943047	−	0.567413i	0.901996	+	0.431744i	$0.142102\pi$
$854$	−2143.13	−	3160.89i	−0.0858741	−	0.126655i
$855$	−11687.2	−	1271.06i	−0.467479	−	0.0508414i
$856$	−9393.28	−	1021.58i	−0.375065	−	0.0407908i
$857$	21257.9	+	31353.1i	0.847325	+	1.24971i	0.966456	+	0.256832i	$0.0826788\pi$
$857$	21257.9	+	31353.1i	0.847325	+	1.24971i	−0.119131	+	0.992879i	$0.538011\pi$
$858$	12786.4	−	7693.33i	0.508766	−	0.306114i
$859$	−3218.19	−	11590.9i	−0.127827	−	0.460390i	0.871736	−	0.489977i	$-0.162995\pi$
$859$	−3218.19	−	11590.9i	−0.127827	−	0.460390i	−0.999562	+	0.0295866i	$0.990581\pi$
$860$	−1407.50	+	5069.37i	−0.0558087	+	0.201005i
$861$	1553.82	+	934.903i	0.0615030	+	0.0370051i
$862$	489.856	+	9034.86i	0.0193556	+	0.356994i
$863$	−9837.64	−	3314.69i	−0.388039	−	0.130745i	0.118519	−	0.992952i	$-0.462186\pi$
$863$	−9837.64	−	3314.69i	−0.388039	−	0.130745i	−0.506557	+	0.862206i	$0.669082\pi$
$864$	1055.03	−	1989.99i	0.0415426	−	0.0783576i
$865$	7473.45	−	8798.43i	0.293763	−	0.345844i
$866$	−21.5349	+	31.7616i	−0.000845019	+	0.00124631i
$867$	620.615	−	11446.6i	0.0243105	−	0.448380i
$868$	1169.17	−	2934.39i	0.0457191	−	0.114746i
$869$	30449.5	−	14087.4i	1.18864	−	0.549923i
$870$	5815.26	+	1280.04i	0.226616	+	0.0498819i
$871$	−3950.88	−	7452.14i	−0.153697	−	0.289904i
$872$	−611.897	−	3732.41i	−0.0237631	−	0.144949i
$873$	12504.2	+	9505.46i	0.484769	+	0.368512i
$874$	55762.9	+	25798.6i	2.15813	+	0.998458i
$875$	8352.90	−	7912.29i	0.322719	−	0.305696i
$876$	665.736	−	4060.81i	0.0256771	−	0.156623i
$877$	15442.0	−	5203.00i	0.594570	−	0.200334i	−0.00589806	−	0.999983i	$-0.501877\pi$
$877$	15442.0	−	5203.00i	0.594570	−	0.200334i	0.600468	+	0.799649i	$0.294981\pi$
$878$	−9882.31	−	24802.7i	−0.379854	−	0.953361i
$879$	−3942.84	−	3734.86i	−0.151295	−	0.143315i
$880$	10830.6	−	8233.19i	0.414885	−	0.315387i
$881$	29130.8	−	6412.16i	1.11401	−	0.245211i	0.380424	−	0.924812i	$-0.375778\pi$
$881$	29130.8	−	6412.16i	1.11401	−	0.245211i	0.733582	+	0.679601i	$0.237847\pi$
$882$	4117.53	+	4847.53i	0.157193	+	0.185062i
$883$	39685.8	−	4316.10i	1.51250	−	0.164494i	0.686069	−	0.727536i	$-0.259335\pi$
$883$	39685.8	−	4316.10i	1.51250	−	0.164494i	0.826428	+	0.563042i	$0.190369\pi$
$884$	3834.40			0.145888
$885$	9305.09	+	8304.49i	0.353432	+	0.315426i
$886$	−44295.6			−1.67962
$887$	50785.3	−	5523.23i	1.92244	−	0.209078i	0.933627	−	0.358247i	$-0.116625\pi$
$887$	50785.3	−	5523.23i	1.92244	−	0.209078i	0.988812	+	0.149169i	$0.0476599\pi$
$888$	7114.23	+	8375.52i	0.268849	+	0.316514i
$889$	−9945.10	+	2189.08i	−0.375195	+	0.0825866i
$890$	−4565.01	+	3470.23i	−0.171932	+	0.130699i
$891$	1922.99	+	1821.55i	0.0723037	+	0.0684897i
$892$	−4055.08	−	10177.5i	−0.152213	−	0.382026i
$893$	−44632.5	+	15038.4i	−1.67253	+	0.563541i
$894$	−1782.32	+	10871.6i	−0.0666774	+	0.406714i
$895$	−18739.9	+	17751.4i	−0.699894	+	0.662975i
$896$	−5077.19	−	2348.96i	−0.189305	−	0.0875817i
$897$	25639.8	+	19490.9i	0.954391	+	0.725509i
$898$	51.4852	+	314.046i	0.00191323	+	0.0116702i
$899$	9076.30	+	17119.7i	0.336720	+	0.635122i
$900$	677.223	+	149.068i	0.0250823	+	0.00552104i
$901$	22083.7	−	10217.0i	0.816553	−	0.377778i
$902$	−2392.13	+	6003.80i	−0.0883030	+	0.221624i
$903$	−373.452	+	6887.91i	−0.0137627	+	0.253837i
$904$	544.275	−	802.746i	0.0200247	−	0.0295342i
$905$	−12882.3	+	15166.2i	−0.473173	+	0.557062i
$906$	−1542.46	+	2909.39i	−0.0565616	+	0.106687i
$907$	37546.9	+	12651.0i	1.37456	+	0.463143i	0.907116	−	0.420881i	$-0.138279\pi$
$907$	37546.9	+	12651.0i	1.37456	+	0.463143i	0.467443	+	0.884023i	$0.345175\pi$
$908$	−4.79437	−	88.4269i	−0.000175228	−	0.00323188i
$909$	6411.45	+	3857.64i	0.233943	+	0.140759i
$910$	−2823.10	+	10167.9i	−0.102841	+	0.370398i
$911$	−7584.94	−	27318.5i	−0.275851	−	0.993526i	−0.963550	−	0.267530i	$-0.913793\pi$
$911$	−7584.94	−	27318.5i	−0.275851	−	0.993526i	0.687699	−	0.725996i	$-0.258621\pi$
$912$	−16600.2	+	9987.99i	−0.602726	+	0.362648i
$913$	7355.80	+	10849.0i	0.266639	+	0.393263i
$914$	39656.7	+	4312.93i	1.43515	+	0.156082i
$915$	−5587.66	−	607.695i	−0.201882	−	0.0219560i
$916$	−1199.79	−	1769.55i	−0.0432774	−	0.0638294i
$917$	3201.41	−	1926.22i	0.115289	−	0.0693670i
$918$	−590.165	−	2125.58i	−0.0212182	−	0.0764212i
$919$	5412.29	−	19493.3i	0.194271	−	0.699700i	−0.800658	−	0.599121i	$-0.795517\pi$
$919$	5412.29	−	19493.3i	0.194271	−	0.699700i	0.994929	−	0.100579i	$-0.0320695\pi$
$920$	33531.3	+	20175.1i	1.20162	+	0.722993i
$921$	1462.01	+	26965.2i	0.0523071	+	0.964748i
$922$	20117.9	+	6778.51i	0.718599	+	0.242124i
$923$	22058.9	−	41607.5i	0.786650	−	1.48378i
$924$	−905.953	+	1066.57i	−0.0322551	+	0.0379736i
$925$	−3434.99	+	5066.24i	−0.122099	+	0.180083i
$926$	−1095.18	+	20199.4i	−0.0388660	+	0.716841i
$927$	6601.19	−	16567.7i	0.233885	−	0.587007i
$928$	−6625.10	+	3065.10i	−0.234353	+	0.108423i
$929$	−6096.01	−	1341.83i	−0.215289	−	0.0473888i	0.106016	−	0.994364i	$-0.466191\pi$
$929$	−6096.01	−	1341.83i	−0.215289	−	0.0473888i	−0.321305	+	0.946976i	$0.604122\pi$
$930$	7058.04	+	13312.9i	0.248862	+	0.469404i
$931$	6584.07	+	40161.1i	0.231777	+	1.41378i
$932$	−5757.64	−	4376.84i	−0.202358	−	0.153829i
$933$	3351.64	+	1550.63i	0.117607	+	0.0544109i
$934$	14092.8	−	13349.4i	0.493716	−	0.467673i
$935$	−1603.65	+	9781.82i	−0.0560908	+	0.342139i
$936$	−12825.8	+	4321.53i	−0.447890	+	0.150912i
$937$	1387.67	+	3482.78i	0.0483811	+	0.121427i	0.951181	−	0.308633i	$-0.0998715\pi$
$937$	1387.67	+	3482.78i	0.0483811	+	0.121427i	−0.902800	+	0.430061i	$0.858492\pi$
$938$	−1861.27	−	1763.09i	−0.0647895	−	0.0613719i
$939$	−1542.17	+	1172.33i	−0.0535962	+	0.0407428i
$940$	−5589.56	+	1230.35i	−0.193948	+	0.0426912i
$941$	23783.3	+	27999.8i	0.823924	+	0.969998i	0.999896	−	0.0143969i	$-0.00458283\pi$
$941$	23783.3	+	27999.8i	0.823924	+	0.969998i	−0.175972	+	0.984395i	$0.556307\pi$
$942$	−2364.56	+	257.162i	−0.0817852	+	0.00889467i
$943$	−13948.6			−0.481687
$944$	20489.4	+	1614.88i	0.706433	+	0.0556778i
$945$	−1873.09			−0.0644780
$946$	−24440.0	+	2658.01i	−0.839970	+	0.0913523i
$947$	−22169.8	−	26100.4i	−0.760742	−	0.895615i	0.236362	−	0.971665i	$-0.424045\pi$
$947$	−22169.8	−	26100.4i	−0.760742	−	0.895615i	−0.997104	+	0.0760500i	$0.975769\pi$
$948$	−5670.07	+	1248.08i	−0.194257	+	0.0427591i
$949$	−35613.9	+	27073.0i	−1.21821	+	0.926056i
$950$	−10440.8	−	9890.09i	−0.356574	−	0.337765i
$951$	−2180.94	−	5473.74i	−0.0743656	−	0.186644i
$952$	5788.72	−	1950.45i	0.197073	−	0.0664016i
$953$	1471.02	−	8972.82i	0.0500010	−	0.304993i	−0.949972	−	0.312335i	$-0.898889\pi$
$953$	1471.02	−	8972.82i	0.0500010	−	0.304993i	0.999973	+	0.00734229i	$0.00233715\pi$
$954$	−11896.9	+	11269.3i	−0.403747	+	0.382450i
$955$	6123.05	+	2832.82i	0.207474	+	0.0959875i
$956$	−1433.02	−	1089.36i	−0.0484804	−	0.0368538i
$957$	−1388.81	−	8471.38i	−0.0469111	−	0.286145i
$958$	−10355.6	−	19532.8i	−0.349244	−	0.658743i
$959$	20365.7	+	4482.83i	0.685759	+	0.150947i
$960$	−14213.9	+	6576.05i	−0.477866	+	0.221084i
$961$	−7122.67	+	17876.6i	−0.239088	+	0.600066i
$962$	1234.04	−	22760.5i	0.0413586	−	0.762815i
$963$	−1952.25	+	2879.35i	−0.0653275	+	0.0963508i
$964$	3771.68	−	4440.36i	0.126014	−	0.148355i
$965$	7894.62	−	14890.8i	0.263354	−	0.496739i
$966$	9276.98	+	3125.78i	0.308988	+	0.104110i
$967$	2892.57	+	53350.4i	0.0961933	+	1.77418i	0.506507	+	0.862236i	$0.330936\pi$
$967$	2892.57	+	53350.4i	0.0961933	+	1.77418i	−0.410314	+	0.911944i	$0.634581\pi$
$968$	5480.64	+	3297.59i	0.181978	+	0.109492i
$969$	3776.28	−	13600.9i	0.125193	−	0.450903i
$970$	−10590.3	−	38142.8i	−0.350550	−	1.26257i
$971$	28269.1	−	17009.0i	0.934293	−	0.562146i	0.0349500	−	0.999389i	$-0.488873\pi$
$971$	28269.1	−	17009.0i	0.934293	−	0.562146i	0.899343	+	0.437244i	$0.144045\pi$
$972$	−257.227	−	379.381i	−0.00848823	−	0.0125192i
$973$	−10917.6	−	1187.36i	−0.359715	−	0.0391213i
$974$	6398.64	+	695.894i	0.210499	+	0.0228931i
$975$	−4230.56	−	6239.61i	−0.138960	−	0.204951i
$976$	−7936.54	+	4775.26i	−0.260289	+	0.156611i
$977$	5658.49	+	20380.0i	0.185293	+	0.667365i	0.996574	+	0.0827081i	$0.0263569\pi$
$977$	5658.49	+	20380.0i	0.185293	+	0.667365i	−0.811281	+	0.584657i	$0.801229\pi$
$978$	−4955.40	+	17847.7i	−0.162021	+	0.583545i
$979$	7083.63	+	4262.08i	0.231250	+	0.139139i
$980$	267.746	+	4938.29i	0.00872739	+	0.160967i
$981$	−1319.64	−	444.638i	−0.0429488	−	0.0144711i
$982$	3153.97	−	5949.02i	0.102492	−	0.193321i
$983$	−21567.6	+	25391.4i	−0.699797	+	0.823864i	−0.991149	−	0.132751i	$-0.957619\pi$
$983$	−21567.6	+	25391.4i	−0.699797	+	0.823864i	0.291353	+	0.956616i	$0.405895\pi$
$984$	3289.46	−	4851.59i	0.106569	−	0.157178i
$985$	2628.22	−	48474.6i	0.0850172	−	1.56805i
$986$	−2646.29	+	6641.69i	−0.0854717	+	0.214518i
$987$	−6810.51	+	3150.88i	−0.219636	+	0.101614i
$988$	−16137.0	−	3552.03i	−0.519623	−	0.114378i
$989$	−24853.6	−	46878.8i	−0.799088	−	1.50724i
$990$	−1079.99	−	6587.63i	−0.0346710	−	0.211483i
$991$	24742.7	+	18808.9i	0.793114	+	0.602910i	0.921305	−	0.388840i	$-0.127124\pi$
$991$	24742.7	+	18808.9i	0.793114	+	0.602910i	−0.128191	+	0.991749i	$0.540917\pi$
$992$	−16765.2	−	7756.39i	−0.536587	−	0.248252i
$993$	−454.087	+	430.134i	−0.0145116	+	0.0137461i
$994$	2315.77	−	14125.6i	0.0738952	−	0.450741i
$995$	−30235.4	+	10187.5i	−0.963343	+	0.324588i
$996$	−839.561	−	2107.14i	−0.0267093	−	0.0670354i
$997$	5865.49	+	5556.08i	0.186321	+	0.176492i	0.775174	−	0.631747i	$-0.217662\pi$
$997$	5865.49	+	5556.08i	0.186321	+	0.176492i	−0.588854	+	0.808240i	$0.700421\pi$
$998$	34362.6	−	26121.8i	1.08991	−	0.828527i
$999$	3951.37	−	869.761i	0.125141	−	0.0275456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.133.11	yes	420
59.4	even	29	inner	177.4.e.a.4.11	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.4.11	✓	420	59.4	even	29	inner
177.4.e.a.133.11	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)

\(f(q)\)	\(=\)	\(q+(2.45810 - 0.267335i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-1.84216 + 0.405491i) q^{4} +(7.30295 - 5.55156i) q^{5} +(-5.38528 - 5.10121i) q^{6} +(-2.79914 - 7.02531i) q^{7} +(-23.1651 + 7.80525i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})\)	\(q+(2.45810 - 0.267335i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(-1.84216 + 0.405491i) q^{4} +(7.30295 - 5.55156i) q^{5} +(-5.38528 - 5.10121i) q^{6} +(-2.79914 - 7.02531i) q^{7} +(-23.1651 + 7.80525i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(16.4673 - 15.5986i) q^{10} +(-29.6784 - 13.7307i) q^{11} +(4.50492 + 3.42455i) q^{12} +(-9.95264 - 60.7084i) q^{13} +(-8.75869 - 16.5206i) q^{14} +(-26.8771 - 5.91609i) q^{15} +(-41.1603 + 19.0428i) q^{16} +(12.2307 - 30.6967i) q^{17} +(-1.20477 + 22.2207i) q^{18} +(-79.9088 + 117.857i) q^{19} +(-11.2021 + 13.1882i) q^{20} +(-10.6269 + 20.0445i) q^{21} +(-76.6233 - 25.8174i) q^{22} +(-9.44781 - 174.255i) q^{23} +(62.8370 + 37.8078i) q^{24} +(-10.9277 + 39.3582i) q^{25} +(-40.6941 - 146.567i) q^{26} +(23.1351 - 13.9200i) q^{27} +(8.00518 + 11.8068i) q^{28} +(-86.9923 - 9.46098i) q^{29} +(-67.6481 - 7.35718i) q^{30} +(-124.267 - 183.281i) q^{31} +(71.4799 - 43.0080i) q^{32} +(26.2451 + 94.5265i) q^{33} +(21.8580 - 78.7252i) q^{34} +(-59.4434 - 35.7659i) q^{35} +(-0.919082 - 16.9515i) q^{36} +(142.006 + 47.8474i) q^{37} +(-164.917 + 311.066i) q^{38} +(-119.479 + 140.662i) q^{39} +(-125.843 + 185.604i) q^{40} +(4.32733 - 79.8129i) q^{41} +(-20.7634 + 52.1123i) q^{42} +(275.947 - 127.667i) q^{43} +(60.2402 + 13.2599i) q^{44} +(38.6725 + 72.9440i) q^{45} +(-69.8080 - 425.810i) q^{46} +(263.317 + 200.168i) q^{47} +(123.481 + 57.1283i) q^{48} +(207.497 - 196.551i) q^{49} +(-16.3397 + 99.6678i) q^{50} +(-93.9414 + 31.6525i) q^{51} +(42.9511 + 107.799i) q^{52} +(534.609 + 506.409i) q^{53} +(53.1473 - 40.4015i) q^{54} +(-292.967 + 64.4869i) q^{55} +(119.677 + 140.894i) q^{56} +(424.673 - 46.1860i) q^{57} -216.365 q^{58} +(-395.079 - 222.017i) q^{59} +51.9109 q^{60} +(203.036 - 22.0815i) q^{61} +(-354.460 - 417.302i) q^{62} +(66.4705 - 14.6313i) q^{63} +(453.042 - 344.394i) q^{64} +(-409.710 - 388.098i) q^{65} +(89.7835 + 225.339i) q^{66} +(129.930 - 43.7786i) q^{67} +(-10.0837 + 61.5077i) q^{68} +(-380.082 + 360.032i) q^{69} +(-155.680 - 72.0250i) q^{70} +(609.418 + 463.267i) q^{71} +(-35.5925 - 217.105i) q^{72} +(-340.622 - 642.481i) q^{73} +(361.857 + 79.6507i) q^{74} +(111.215 - 51.4537i) q^{75} +(99.4154 - 249.514i) q^{76} +(-13.3884 + 246.934i) q^{77} +(-256.089 + 377.702i) q^{78} +(-664.206 + 781.963i) q^{79} +(-194.874 + 367.572i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-10.6997 - 197.345i) q^{82} +(-343.457 - 206.652i) q^{83} +(11.4487 - 41.2343i) q^{84} +(-81.0944 - 292.076i) q^{85} +(644.176 - 387.588i) q^{86} +(147.320 + 217.281i) q^{87} +(794.676 + 86.4262i) q^{88} +(-251.325 - 27.3333i) q^{89} +(114.561 + 168.965i) q^{90} +(-398.637 + 239.852i) q^{91} +(88.0631 + 317.175i) q^{92} +(-177.722 + 640.096i) q^{93} +(700.771 + 421.640i) q^{94} +(70.7182 + 1304.32i) q^{95} +(-237.163 - 79.9094i) q^{96} +(817.476 - 1541.92i) q^{97} +(457.503 - 538.614i) q^{98} +(165.161 - 243.595i) 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

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