LMFDB - Embedded newform 177.4.e.b.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			4.2
Character	$\chi$	$=$	177.4
Dual form			177.4.e.b.133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.38291 - 0.476671i) q^{2} +(1.94216 - 2.28649i) q^{3} +(11.1698 + 2.45865i) q^{4} +(-11.3321 - 8.61446i) q^{5} +(-9.60221 + 9.09570i) q^{6} +(-7.94992 + 19.9528i) q^{7} +(-14.3603 - 4.83855i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(-4.38291 - 0.476671i) q^{2} +(1.94216 - 2.28649i) q^{3} +(11.1698 + 2.45865i) q^{4} +(-11.3321 - 8.61446i) q^{5} +(-9.60221 + 9.09570i) q^{6} +(-7.94992 + 19.9528i) q^{7} +(-14.3603 - 4.83855i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(45.5615 + 43.1581i) q^{10} +(27.1545 - 12.5630i) q^{11} +(27.3151 - 20.7644i) q^{12} +(-9.16870 + 55.9266i) q^{13} +(44.3547 - 83.6619i) q^{14} +(-41.7056 + 9.18010i) q^{15} +(-22.4070 - 10.3666i) q^{16} +(6.79469 + 17.0534i) q^{17} +(2.14817 + 39.6206i) q^{18} +(1.42321 + 2.09907i) q^{19} +(-105.397 - 124.083i) q^{20} +(30.1818 + 56.9289i) q^{21} +(-125.004 + 42.1188i) q^{22} +(0.0699143 - 1.28949i) q^{23} +(-38.9533 + 23.4374i) q^{24} +(20.7672 + 74.7965i) q^{25} +(66.8442 - 240.751i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-137.855 + 203.322i) q^{28} +(83.2049 - 9.04907i) q^{29} +(187.168 - 20.3558i) q^{30} +(92.4324 - 136.328i) q^{31} +(197.142 + 118.616i) q^{32} +(24.0132 - 86.4877i) q^{33} +(-21.6517 - 77.9824i) q^{34} +(261.972 - 157.623i) q^{35} +(5.57275 - 102.783i) q^{36} +(415.049 - 139.846i) q^{37} +(-5.23722 - 9.87845i) q^{38} +(110.068 + 129.582i) q^{39} +(121.051 + 178.537i) q^{40} +(-14.3068 - 263.874i) q^{41} +(-105.148 - 263.901i) q^{42} +(366.147 + 169.398i) q^{43} +(334.197 - 73.5623i) q^{44} +(-60.0088 + 113.189i) q^{45} +(-0.921092 + 5.61841i) q^{46} +(-170.485 + 129.599i) q^{47} +(-67.2211 + 31.0998i) q^{48} +(-85.8961 - 81.3651i) q^{49} +(-55.3673 - 337.726i) q^{50} +(52.1887 + 17.5844i) q^{51} +(-239.916 + 602.144i) q^{52} +(389.456 - 368.912i) q^{53} +(94.7641 + 72.0378i) q^{54} +(-415.941 - 91.5556i) q^{55} +(210.706 - 248.062i) q^{56} +(7.56359 + 0.822590i) q^{57} -368.993 q^{58} +(-361.484 + 273.329i) q^{59} -488.412 q^{60} +(474.964 + 51.6555i) q^{61} +(-470.106 + 553.452i) q^{62} +(188.785 + 41.5547i) q^{63} +(-650.278 - 494.328i) q^{64} +(585.678 - 554.784i) q^{65} +(-146.474 + 367.622i) q^{66} +(38.2631 + 12.8923i) q^{67} +(33.9667 + 207.188i) q^{68} +(-2.81263 - 2.66426i) q^{69} +(-1223.33 + 565.975i) q^{70} +(-371.141 + 282.134i) q^{71} +(-22.0641 + 134.585i) q^{72} +(-60.7073 + 114.506i) q^{73} +(-1885.78 + 415.092i) q^{74} +(211.354 + 97.7829i) q^{75} +(10.7360 + 26.9453i) q^{76} +(34.7910 + 641.683i) q^{77} +(-420.652 - 620.415i) q^{78} +(665.528 + 783.520i) q^{79} +(164.617 + 310.500i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-63.0753 + 1163.36i) q^{82} +(-114.811 + 69.0795i) q^{83} +(197.155 + 710.088i) q^{84} +(69.9074 - 251.784i) q^{85} +(-1524.04 - 916.986i) q^{86} +(140.906 - 207.822i) q^{87} +(-450.733 + 49.0202i) q^{88} +(342.833 - 37.2853i) q^{89} +(316.967 - 467.491i) q^{90} +(-1043.00 - 627.553i) q^{91} +(3.95134 - 14.2314i) q^{92} +(-132.193 - 476.115i) q^{93} +(808.996 - 486.757i) q^{94} +(1.95442 - 36.0471i) q^{95} +(654.096 - 220.390i) q^{96} +(-319.715 - 603.046i) q^{97} +(337.691 + 397.561i) q^{98} +(-151.115 - 222.879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−4.38291	−	0.476671i	−1.54959	−	0.168528i	−0.707053	−	0.707161i	$-0.749976\pi$
$2$	−4.38291	−	0.476671i	−1.54959	−	0.168528i	−0.842541	+	0.538632i	$0.818941\pi$
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$4$	11.1698	+	2.45865i	1.39622	+	0.307331i
$5$	−11.3321	−	8.61446i	−1.01358	−	0.770501i	−0.0400783	−	0.999197i	$-0.512761\pi$
$5$	−11.3321	−	8.61446i	−1.01358	−	0.770501i	−0.973498	+	0.228696i	$0.926554\pi$
$6$	−9.60221	+	9.09570i	−0.653348	+	0.618884i
$7$	−7.94992	+	19.9528i	−0.429255	+	1.07735i	0.542226	+	0.840233i	$0.317582\pi$
$7$	−7.94992	+	19.9528i	−0.429255	+	1.07735i	−0.971481	+	0.237117i	$0.923798\pi$
$8$	−14.3603	−	4.83855i	−0.634642	−	0.213836i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	45.5615	+	43.1581i	1.44078	+	1.36478i
$11$	27.1545	−	12.5630i	0.744308	−	0.344353i	−0.0108109	−	0.999942i	$-0.503441\pi$
$11$	27.1545	−	12.5630i	0.744308	−	0.344353i	0.755119	+	0.655588i	$0.227579\pi$
$12$	27.3151	−	20.7644i	0.657099	−	0.499514i
$13$	−9.16870	+	55.9266i	−0.195611	+	1.19317i	0.688268	+	0.725457i	$0.258371\pi$
$13$	−9.16870	+	55.9266i	−0.195611	+	1.19317i	−0.883879	+	0.467716i	$0.845077\pi$
$14$	44.3547	−	83.6619i	0.846735	−	1.59711i
$15$	−41.7056	+	9.18010i	−0.717890	+	0.158019i
$16$	−22.4070	−	10.3666i	−0.350110	−	0.161978i
$17$	6.79469	+	17.0534i	0.0969385	+	0.243297i	0.969447	−	0.245302i	$-0.0788872\pi$
$17$	6.79469	+	17.0534i	0.0969385	+	0.243297i	−0.872508	+	0.488600i	$0.837508\pi$
$18$	2.14817	+	39.6206i	0.0281293	+	0.518815i
$19$	1.42321	+	2.09907i	0.0171845	+	0.0253453i	0.836184	−	0.548449i	$-0.184781\pi$
$19$	1.42321	+	2.09907i	0.0171845	+	0.0253453i	−0.819000	+	0.573794i	$0.805471\pi$
$20$	−105.397	−	124.083i	−1.17838	−	1.38729i
$21$	30.1818	+	56.9289i	0.313629	+	0.591566i
$22$	−125.004	+	42.1188i	−1.21141	+	0.408171i
$23$	0.0699143	−	1.28949i	0.000633832	−	0.0116904i	−0.998199	−	0.0599832i	$-0.980895\pi$
$23$	0.0699143	−	1.28949i	0.000633832	−	0.0116904i	0.998833	+	0.0482928i	$0.0153781\pi$
$24$	−38.9533	+	23.4374i	−0.331304	+	0.199339i
$25$	20.7672	+	74.7965i	0.166137	+	0.598372i
$26$	66.8442	−	240.751i	0.504201	−	1.81597i
$27$	−23.1351	−	13.9200i	−0.164902	−	0.0992184i
$28$	−137.855	+	203.322i	−0.930437	+	1.37229i
$29$	83.2049	−	9.04907i	0.532785	−	0.0579438i	0.162227	−	0.986753i	$-0.448132\pi$
$29$	83.2049	−	9.04907i	0.532785	−	0.0579438i	0.370557	+	0.928810i	$0.379167\pi$
$30$	187.168	−	20.3558i	1.13907	−	0.123881i
$31$	92.4324	−	136.328i	0.535527	−	0.789844i	−0.459633	−	0.888109i	$-0.652019\pi$
$31$	92.4324	−	136.328i	0.535527	−	0.789844i	0.995160	+	0.0982653i	$0.0313294\pi$
$32$	197.142	+	118.616i	1.08907	+	0.655269i
$33$	24.0132	−	86.4877i	0.126672	−	0.456230i
$34$	−21.6517	−	77.9824i	−0.109213	−	0.393349i
$35$	261.972	−	157.623i	1.26518	−	0.761234i
$36$	5.57275	−	102.783i	0.0257998	−	0.475849i
$37$	415.049	−	139.846i	1.84415	−	0.621367i	0.848391	−	0.529370i	$-0.177572\pi$
$37$	415.049	−	139.846i	1.84415	−	0.621367i	0.995759	−	0.0919968i	$-0.0293250\pi$
$38$	−5.23722	−	9.87845i	−0.0223576	−	0.0421709i
$39$	110.068	+	129.582i	0.451924	+	0.532046i
$40$	121.051	+	178.537i	0.478497	+	0.705730i
$41$	−14.3068	−	263.874i	−0.0544963	−	1.00513i	−0.890092	−	0.455781i	$-0.849360\pi$
$41$	−14.3068	−	263.874i	−0.0544963	−	1.00513i	0.835596	−	0.549345i	$-0.185123\pi$
$42$	−105.148	−	263.901i	−0.386301	−	0.969543i
$43$	366.147	+	169.398i	1.29853	+	0.600765i	0.942655	−	0.333768i	$-0.108320\pi$
$43$	366.147	+	169.398i	1.29853	+	0.600765i	0.355877	+	0.934533i	$0.384182\pi$
$44$	334.197	−	73.5623i	1.14505	−	0.252044i
$45$	−60.0088	+	113.189i	−0.198791	+	0.374959i
$46$	−0.921092	+	5.61841i	−0.00295234	+	0.0180085i
$47$	−170.485	+	129.599i	−0.529101	+	0.402212i	−0.835333	−	0.549745i	$-0.814725\pi$
$47$	−170.485	+	129.599i	−0.529101	+	0.402212i	0.306231	+	0.951957i	$0.400932\pi$
$48$	−67.2211	+	31.0998i	−0.202136	+	0.0935180i
$49$	−85.8961	−	81.3651i	−0.250426	−	0.237216i
$50$	−55.3673	−	337.726i	−0.156602	−	0.955233i
$51$	52.1887	+	17.5844i	0.143292	+	0.0482806i
$52$	−239.916	+	602.144i	−0.639815	+	1.60581i
$53$	389.456	−	368.912i	1.00936	−	0.956112i	0.0103167	−	0.999947i	$-0.496716\pi$
$53$	389.456	−	368.912i	1.00936	−	0.956112i	0.999039	+	0.0438345i	$0.0139574\pi$
$54$	94.7641	+	72.0378i	0.238810	+	0.181539i
$55$	−415.941	−	91.5556i	−1.01974	−	0.224461i
$56$	210.706	−	248.062i	0.502799	−	0.591941i
$57$	7.56359	+	0.822590i	0.0175758	+	0.00191149i
$58$	−368.993			−0.835365
$59$	−361.484	+	273.329i	−0.797647	+	0.603125i
$59$	−361.484	+	273.329i	−0.797647	+	0.603125i
$60$	−488.412			−1.05090
$61$	474.964	+	51.6555i	0.996933	+	0.108423i	0.592013	−	0.805929i	$-0.298334\pi$
$61$	474.964	+	51.6555i	0.996933	+	0.108423i	0.404921	+	0.914352i	$0.367299\pi$
$62$	−470.106	+	553.452i	−0.962961	+	1.13369i
$63$	188.785	+	41.5547i	0.377534	+	0.0831016i
$64$	−650.278	−	494.328i	−1.27007	−	0.965485i
$65$	585.678	−	554.784i	1.11761	−	1.05865i
$66$	−146.474	+	367.622i	−0.273177	+	0.685623i
$67$	38.2631	+	12.8923i	0.0697699	+	0.0235082i	0.353970	−	0.935257i	$-0.384831\pi$
$67$	38.2631	+	12.8923i	0.0697699	+	0.0235082i	−0.284200	+	0.958765i	$0.591728\pi$
$68$	33.9667	+	207.188i	0.0605746	+	0.369489i
$69$	−2.81263	−	2.66426i	−0.00490725	−	0.00464840i
$70$	−1223.33	+	565.975i	−2.08881	+	0.966385i
$71$	−371.141	+	282.134i	−0.620372	+	0.471594i	−0.867533	−	0.497380i	$-0.834295\pi$
$71$	−371.141	+	282.134i	−0.620372	+	0.471594i	0.247161	+	0.968974i	$0.420502\pi$
$72$	−22.0641	+	134.585i	−0.0361150	+	0.220292i
$73$	−60.7073	+	114.506i	−0.0973322	+	0.183588i	−0.927397	−	0.374079i	$-0.877959\pi$
$73$	−60.7073	+	114.506i	−0.0973322	+	0.183588i	0.830064	+	0.557667i	$0.188304\pi$
$74$	−1885.78	+	415.092i	−2.96240	+	0.652074i
$75$	211.354	+	97.7829i	0.325401	+	0.150547i
$76$	10.7360	+	26.9453i	0.0162040	+	0.0406689i
$77$	34.7910	+	641.683i	0.0514910	+	0.949695i
$78$	−420.652	−	620.415i	−0.610634	−	0.900618i
$79$	665.528	+	783.520i	0.947819	+	1.11586i	0.993145	+	0.116887i	$0.0372915\pi$
$79$	665.528	+	783.520i	0.947819	+	1.11586i	−0.0453260	+	0.998972i	$0.514433\pi$
$80$	164.617	+	310.500i	0.230059	+	0.433937i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	−63.0753	+	1163.36i	−0.0849451	+	1.56672i
$83$	−114.811	+	69.0795i	−0.151833	+	0.0913550i	−0.589443	−	0.807810i	$-0.700653\pi$
$83$	−114.811	+	69.0795i	−0.151833	+	0.0913550i	0.437610	+	0.899165i	$0.355825\pi$
$84$	197.155	+	710.088i	0.256088	+	0.922344i
$85$	69.9074	−	251.784i	0.0892062	−	0.321292i
$86$	−1524.04	−	916.986i	−1.91095	−	1.14978i
$87$	140.906	−	207.822i	0.173641	−	0.256101i
$88$	−450.733	+	49.0202i	−0.546004	+	0.0593815i
$89$	342.833	−	37.2853i	0.408317	−	0.0444071i	0.0983437	−	0.995153i	$-0.468646\pi$
$89$	342.833	−	37.2853i	0.408317	−	0.0444071i	0.309973	+	0.950745i	$0.399680\pi$
$90$	316.967	−	467.491i	0.371236	−	0.547532i
$91$	−1043.00	−	627.553i	−1.20150	−	0.722917i
$92$	3.95134	−	14.2314i	0.00447778	−	0.0161275i
$93$	−132.193	−	476.115i	−0.147395	−	0.530869i
$94$	808.996	−	486.757i	0.887676	−	0.534097i
$95$	1.95442	−	36.0471i	0.00211072	−	0.0389300i
$96$	654.096	−	220.390i	0.695400	−	0.234307i
$97$	−319.715	−	603.046i	−0.334661	−	0.631238i	0.657884	−	0.753120i	$-0.271452\pi$
$97$	−319.715	−	603.046i	−0.334661	−	0.631238i	−0.992545	+	0.121882i	$0.961107\pi$
$98$	337.691	+	397.561i	0.348081	+	0.409793i
$99$	−151.115	−	222.879i	−0.153411	−	0.226264i
$100$	48.0656	+	886.518i	0.0480656	+	0.886518i
$101$	−299.210	−	750.960i	−0.294777	−	0.739835i	−0.999538	−	0.0303902i	$-0.990325\pi$
$101$	−299.210	−	750.960i	−0.294777	−	0.739835i	0.704761	−	0.709445i	$-0.251054\pi$
$102$	−220.357	−	101.948i	−0.213907	−	0.0989641i
$103$	690.886	−	152.075i	0.660922	−	0.145480i	0.128171	−	0.991752i	$-0.459089\pi$
$103$	690.886	−	152.075i	0.660922	−	0.145480i	0.532751	+	0.846272i	$0.321158\pi$
$104$	402.269	−	758.760i	0.379286	−	0.715409i
$105$	148.388	−	905.125i	0.137916	−	0.841249i
$106$	−1882.80	+	1431.27i	−1.72522	+	1.31148i
$107$	1400.74	−	648.052i	1.26556	−	0.585510i	0.331779	−	0.943357i	$-0.392351\pi$
$107$	1400.74	−	648.052i	1.26556	−	0.585510i	0.933780	+	0.357847i	$0.116489\pi$
$108$	−224.190	−	212.364i	−0.199747	−	0.189210i
$109$	238.996	+	1457.81i	0.210015	+	1.28103i	0.855717	+	0.517444i	$0.173117\pi$
$109$	238.996	+	1457.81i	0.210015	+	1.28103i	−0.645702	+	0.763590i	$0.723435\pi$
$110$	1779.39	+	599.548i	1.54235	+	0.519678i
$111$	486.334	−	1220.61i	0.415863	−	1.04374i
$112$	384.976	−	364.669i	0.324793	−	0.307661i
$113$	−852.595	−	648.126i	−0.709782	−	0.539562i	0.186823	−	0.982394i	$-0.440181\pi$
$113$	−852.595	−	648.126i	−0.709782	−	0.539562i	−0.896605	+	0.442831i	$0.853974\pi$
$114$	−32.7584	−	7.21068i	−0.0269132	−	0.00592405i
$115$	−11.9006	+	14.0104i	−0.00964986	+	0.0113607i
$116$	951.626	+	103.496i	0.761692	+	0.0828390i
$117$	510.059			0.403034
$118$	1714.64	−	1025.67i	1.33767	−	0.800172i
$119$	−394.280			−0.303728
$120$	643.324	+	69.9657i	0.489393	+	0.0532247i
$121$	−282.134	+	332.154i	−0.211972	+	0.249552i
$122$	−2057.10	−	452.803i	−1.52657	−	0.336023i
$123$	−631.130	−	479.772i	−0.462659	−	0.351704i
$124$	1367.63	−	1295.49i	0.990457	−	0.938210i
$125$	−249.604	+	626.459i	−0.178602	+	0.448258i
$126$	−807.620	−	272.119i	−0.571020	−	0.192399i
$127$	414.050	+	2525.60i	0.289299	+	1.76465i	0.586612	+	0.809868i	$0.300461\pi$
$127$	414.050	+	2525.60i	0.289299	+	1.76465i	−0.297312	+	0.954780i	$0.596090\pi$
$128$	1278.21	+	1210.78i	0.882647	+	0.836087i
$129$	1098.44	−	508.193i	0.749708	−	0.346852i
$130$	−2831.43	+	2152.39i	−1.91025	+	1.45213i
$131$	−316.128	+	1928.30i	−0.210842	+	1.28608i	0.643130	+	0.765757i	$0.277635\pi$
$131$	−316.128	+	1928.30i	−0.210842	+	1.28608i	−0.853972	+	0.520319i	$0.825813\pi$
$132$	480.864	−	907.006i	0.317075	−	0.598066i
$133$	−53.1967	+	11.7095i	−0.0346822	+	0.00763414i
$134$	−161.558	−	74.7449i	−0.104153	−	0.0481864i
$135$	142.258	+	357.039i	0.0906932	+	0.227623i
$136$	−15.0602	−	277.768i	−0.00949557	−	0.175136i
$137$	1348.51	+	1988.90i	0.840957	+	1.24032i	0.968631	+	0.248502i	$0.0799383\pi$
$137$	1348.51	+	1988.90i	0.840957	+	1.24032i	−0.127675	+	0.991816i	$0.540751\pi$
$138$	11.0575	+	13.0179i	0.00682086	+	0.00803014i
$139$	−604.967	−	1141.09i	−0.369155	−	0.696301i	0.627447	−	0.778659i	$-0.284100\pi$
$139$	−604.967	−	1141.09i	−0.369155	−	0.696301i	−0.996603	+	0.0823581i	$0.973755\pi$
$140$	3313.70	−	1116.52i	2.00042	−	0.674020i
$141$	−34.7818	+	641.513i	−0.0207742	+	0.383157i
$142$	1761.17	−	1059.66i	1.04080	−	0.626229i
$143$	453.635	+	1633.84i	0.265279	+	0.955447i
$144$	−59.4448	+	214.101i	−0.0344009	+	0.123901i
$145$	−1020.84	−	614.220i	−0.584664	−	0.351780i
$146$	320.657	−	472.933i	0.181765	−	0.268084i
$147$	−352.864	+	38.3763i	−0.197985	+	0.0215321i
$148$	4979.82	−	541.588i	2.76580	−	0.300799i
$149$	−655.145	+	966.267i	−0.360212	+	0.531273i	−0.964011	−	0.265864i	$-0.914343\pi$
$149$	−655.145	+	966.267i	−0.360212	+	0.531273i	0.603799	+	0.797137i	$0.293653\pi$
$150$	−879.737	−	529.320i	−0.478868	−	0.288126i
$151$	504.455	−	1816.88i	0.271868	−	0.979178i	−0.693964	−	0.720009i	$-0.744138\pi$
$151$	504.455	−	1816.88i	0.271868	−	0.979178i	0.965832	−	0.259169i	$-0.0834487\pi$
$152$	−10.2812	−	37.0295i	−0.00548629	−	0.0197598i
$153$	141.565	−	85.1770i	0.0748031	−	0.0450076i
$154$	153.385	−	2829.02i	0.0802606	−	1.48032i
$155$	−2221.84	+	748.626i	−1.15137	+	0.387943i
$156$	910.838	+	1718.02i	0.467471	+	0.881743i
$157$	884.132	+	1040.88i	0.449436	+	0.529116i	0.939490	−	0.342575i	$-0.111299\pi$
$157$	884.132	+	1040.88i	0.449436	+	0.529116i	−0.490055	+	0.871692i	$0.663023\pi$
$158$	−2543.47	−	3751.34i	−1.28068	−	1.88886i
$159$	−87.1274	−	1606.97i	−0.0434569	−	0.801516i
$160$	−1212.22	−	3042.45i	−0.598966	−	1.50329i
$161$	25.1732	+	11.6464i	0.0123225	+	0.00570100i
$162$	348.760	−	76.7680i	0.169143	−	0.0372312i
$163$	1612.22	−	3040.98i	0.774719	−	1.46127i	−0.109393	−	0.993999i	$-0.534891\pi$
$163$	1612.22	−	3040.98i	0.774719	−	1.46127i	0.884112	−	0.467276i	$-0.154765\pi$
$164$	488.969	−	2982.58i	0.232817	−	1.42012i
$165$	−1017.17	+	773.229i	−0.479916	+	0.364823i
$166$	536.135	−	248.043i	0.250676	−	0.115975i
$167$	1343.08	+	1272.23i	0.622338	+	0.589510i	0.932498	−	0.361175i	$-0.117624\pi$
$167$	1343.08	+	1272.23i	0.622338	+	0.589510i	−0.310160	+	0.950684i	$0.600383\pi$
$168$	−157.966	−	963.551i	−0.0725438	−	0.442498i
$169$	−961.727	−	324.043i	−0.437745	−	0.147494i
$170$	−426.416	+	1070.22i	−0.192380	+	0.482838i
$171$	16.5705	−	15.6964i	0.00741041	−	0.00701951i
$172$	3673.28	+	2792.35i	1.62840	+	1.23788i
$173$	3143.80	+	692.003i	1.38161	+	0.304116i	0.842762	−	0.538286i	$-0.180928\pi$
$173$	3143.80	+	692.003i	1.38161	+	0.304116i	0.538850	+	0.842402i	$0.318859\pi$
$174$	−716.643	+	843.698i	−0.312233	+	0.367589i
$175$	−1657.50	−	180.264i	−0.715971	−	0.0778665i
$176$	−738.687			−0.316367
$177$	−77.0964	+	1357.38i	−0.0327397	+	0.576421i
$178$	−1520.38			−0.640209
$179$	−1075.15	−	116.929i	−0.448940	−	0.0488252i	−0.119143	−	0.992877i	$-0.538015\pi$
$179$	−1075.15	−	116.929i	−0.448940	−	0.0488252i	−0.329797	+	0.944052i	$0.606980\pi$
$180$	−948.574	+	1116.75i	−0.392792	+	0.462430i
$181$	−2431.24	−	535.156i	−0.998411	−	0.219767i	−0.314441	−	0.949277i	$-0.601817\pi$
$181$	−2431.24	−	535.156i	−0.998411	−	0.219767i	−0.683970	+	0.729510i	$0.739748\pi$
$182$	4272.25	+	3247.68i	1.74000	+	1.32271i
$183$	1040.57	−	985.676i	0.420332	−	0.398160i
$184$	−7.24327	+	18.1792i	−0.00290207	+	0.00728365i
$185$	−5908.08	−	1990.66i	−2.34795	−	0.791117i
$186$	352.439	+	2149.78i	0.138936	+	0.847472i
$187$	398.748	+	377.714i	0.155932	+	0.147707i
$188$	−2222.91	+	1028.43i	−0.862353	+	0.398967i
$189$	461.664	−	350.948i	0.177678	−	0.135067i
$190$	−25.7486	+	157.060i	−0.00983159	+	0.0599700i
$191$	−180.431	+	340.328i	−0.0683534	+	0.128928i	−0.915334	−	0.402696i	$-0.868073\pi$
$191$	−180.431	+	340.328i	−0.0683534	+	0.128928i	0.846980	+	0.531624i	$0.178418\pi$
$192$	−2393.22	+	526.787i	−0.899561	+	0.198008i
$193$	−3978.96	−	1840.86i	−1.48400	−	0.686571i	−0.500211	−	0.865903i	$-0.666744\pi$
$193$	−3978.96	−	1840.86i	−1.48400	−	0.686571i	−0.983789	+	0.179332i	$0.942606\pi$
$194$	1113.83	+	2795.50i	0.412207	+	1.03456i
$195$	−131.026	−	2416.62i	−0.0481176	−	0.887477i
$196$	−759.390	−	1120.02i	−0.276746	−	0.408169i
$197$	2818.95	+	3318.72i	1.01950	+	1.20025i	0.979582	+	0.201047i	$0.0644344\pi$
$197$	2818.95	+	3318.72i	1.01950	+	1.20025i	0.0399197	+	0.999203i	$0.487290\pi$
$198$	556.086	+	1048.89i	0.199593	+	0.376472i
$199$	4371.75	−	1473.01i	1.55731	−	0.524720i	0.596665	−	0.802491i	$-0.296492\pi$
$199$	4371.75	−	1473.01i	1.55731	−	0.524720i	0.960647	+	0.277771i	$0.0895957\pi$
$200$	63.6840	−	1174.58i	0.0225157	−	0.415278i
$201$	103.791	−	62.4491i	0.0364222	−	0.0219145i
$202$	953.451	+	3434.02i	0.332102	+	1.19612i
$203$	−480.918	+	1732.11i	−0.166275	+	0.598868i
$204$	539.701	+	324.727i	0.185229	+	0.111448i
$205$	−2111.00	+	3113.50i	−0.719214	+	1.06076i
$206$	−3100.58	+	337.209i	−1.04868	+	0.114051i
$207$	−11.5544	+	1.25661i	−0.00387963	+	0.000421935i
$208$	785.212	−	1158.10i	0.261753	−	0.386057i
$209$	65.0170	+	39.1195i	0.0215183	+	0.0129471i
$210$	−1081.82	+	3896.35i	−0.355488	+	1.28035i
$211$	−1093.35	−	3937.88i	−0.356726	−	1.28481i	−0.896516	−	0.443011i	$-0.853910\pi$
$211$	−1093.35	−	3937.88i	−0.356726	−	1.28481i	0.539791	−	0.841799i	$-0.318503\pi$
$212$	5257.15	−	3163.12i	1.70312	−	1.02474i
$213$	−75.7192	+	1396.56i	−0.0243577	+	0.449252i
$214$	−6448.24	+	2172.66i	−2.05978	+	0.694020i
$215$	−2689.95	−	5073.79i	−0.853271	−	1.60944i
$216$	264.875	+	311.835i	0.0834374	+	0.0982301i
$217$	1985.29	+	2928.08i	0.621060	+	0.915994i
$218$	−352.602	−	6503.37i	−0.109547	−	2.02048i
$219$	143.913	+	361.195i	0.0444053	+	0.111449i
$220$	−4420.86	−	2045.31i	−1.35479	−	0.626794i
$221$	−1016.04	+	223.647i	−0.309258	+	0.0680729i
$222$	−2713.39	+	5117.99i	−0.820318	+	1.54728i
$223$	−100.620	+	613.753i	−0.0302152	+	0.184305i	−0.997622	−	0.0689227i	$-0.978044\pi$
$223$	−100.620	+	613.753i	−0.0302152	+	0.184305i	0.967407	+	0.253227i	$0.0814921\pi$
$224$	−3933.99	+	2990.54i	−1.17344	+	0.892026i
$225$	634.063	−	293.349i	0.187870	−	0.0869181i
$226$	3427.91	+	3247.08i	1.00894	+	0.955721i
$227$	−508.948	−	3104.45i	−0.148811	−	0.907707i	−0.950672	−	0.310197i	$-0.899605\pi$
$227$	−508.948	−	3104.45i	−0.148811	−	0.907707i	0.801861	−	0.597510i	$-0.203843\pi$
$228$	82.4609	+	27.7843i	0.0239522	+	0.00807045i
$229$	322.815	−	810.204i	0.0931537	−	0.233798i	−0.875015	−	0.484095i	$-0.839149\pi$
$229$	322.815	−	810.204i	0.0931537	−	0.233798i	0.968169	+	0.250297i	$0.0805282\pi$
$230$	58.8375	−	55.7339i	0.0168680	−	0.0159782i
$231$	1534.77	+	1166.70i	0.437144	+	0.332308i
$232$	−1238.63	−	272.643i	−0.350518	−	0.0771548i
$233$	1980.20	−	2331.27i	0.556769	−	0.655479i	−0.409713	−	0.912215i	$-0.634371\pi$
$233$	1980.20	−	2331.27i	0.556769	−	0.655479i	0.966482	+	0.256735i	$0.0826469\pi$
$234$	−2235.54	−	243.130i	−0.624539	−	0.0679227i
$235$	3048.38			0.846189
$236$	−4709.70	+	2164.25i	−1.29905	+	0.596953i
$237$	3084.07			0.845282
$238$	1728.10	+	187.942i	0.470655	+	0.0511868i
$239$	−2813.21	+	3311.97i	−0.761387	+	0.896374i	−0.997151	−	0.0754368i	$-0.975965\pi$
$239$	−2813.21	+	3311.97i	−0.761387	+	0.896374i	0.235764	+	0.971810i	$0.424241\pi$
$240$	1029.67	+	226.646i	0.276936	+	0.0609582i
$241$	850.754	+	646.727i	0.227394	+	0.172860i	0.712667	−	0.701502i	$-0.247487\pi$
$241$	850.754	+	646.727i	0.227394	+	0.172860i	−0.485274	+	0.874362i	$0.661280\pi$
$242$	1394.90	−	1321.32i	0.370527	−	0.350981i
$243$	−89.9436	+	225.741i	−0.0237444	+	0.0595939i
$244$	5178.23	+	1744.75i	1.35862	+	0.457771i
$245$	272.469	+	1661.99i	0.0710507	+	0.433390i
$246$	2537.49	+	2403.64i	0.657661	+	0.622970i
$247$	−130.443	+	60.3493i	−0.0336028	+	0.0155463i
$248$	−1986.98	+	1510.47i	−0.508765	+	0.386753i
$249$	−65.0320	+	396.677i	−0.0165511	+	0.100957i
$250$	1392.61	−	2626.74i	0.352305	−	0.664518i
$251$	5282.99	−	1162.87i	1.32852	−	0.292430i	0.506676	−	0.862137i	$-0.330874\pi$
$251$	5282.99	−	1162.87i	1.32852	−	0.292430i	0.821848	+	0.569706i	$0.192943\pi$
$252$	2006.51	+	928.311i	0.501581	+	0.232056i
$253$	−14.3014	−	35.8939i	−0.00355385	−	0.00891948i
$254$	−610.870	−	11266.8i	−0.150903	−	2.78324i
$255$	−439.929	−	648.847i	−0.108037	−	0.159343i
$256$	−794.665	−	935.552i	−0.194010	−	0.228406i
$257$	−903.174	−	1703.57i	−0.219216	−	0.413485i	0.749375	−	0.662146i	$-0.230354\pi$
$257$	−903.174	−	1703.57i	−0.219216	−	0.413485i	−0.968590	+	0.248661i	$0.920009\pi$
$258$	−5056.61	+	1703.77i	−1.22020	+	0.411132i
$259$	−509.281	+	9393.14i	−0.122182	+	2.25352i
$260$	7905.90	−	4756.82i	1.88578	−	1.13464i
$261$	−201.518	−	725.803i	−0.0477918	−	0.172131i
$262$	2304.72	−	8300.87i	0.543459	−	1.95736i
$263$	2146.27	+	1291.37i	0.503211	+	0.302772i	0.744432	−	0.667698i	$-0.232720\pi$
$263$	2146.27	+	1291.37i	0.503211	+	0.302772i	−0.241221	+	0.970470i	$0.577548\pi$
$264$	−763.311	+	1125.80i	−0.177949	+	0.262455i
$265$	−7591.34	+	825.608i	−1.75974	+	0.191384i
$266$	238.738	−	25.9643i	0.0550300	−	0.00598487i
$267$	580.583	−	856.296i	0.133075	−	0.196271i
$268$	395.692	+	238.080i	0.0901892	+	0.0542651i
$269$	−302.981	+	1091.24i	−0.0686731	+	0.247338i	−0.989917	−	0.141647i	$-0.954760\pi$
$269$	−302.981	+	1091.24i	−0.0686731	+	0.247338i	0.921244	+	0.388985i	$0.127174\pi$
$270$	−453.312	−	1632.68i	−0.102177	−	0.368007i
$271$	6414.27	−	3859.34i	1.43778	−	0.865085i	0.438352	−	0.898803i	$-0.355562\pi$
$271$	6414.27	−	3859.34i	1.43778	−	0.865085i	0.999431	+	0.0337180i	$0.0107348\pi$
$272$	24.5367	−	452.554i	0.00546970	−	0.100883i
$273$	−3460.57	+	1166.00i	−0.767190	+	0.258497i
$274$	−4962.35	−	9359.99i	−1.09411	−	2.06371i
$275$	1503.59	+	1770.16i	0.329709	+	0.388163i
$276$	−24.8658	−	36.6744i	−0.00542300	−	0.00799833i
$277$	191.373	+	3529.67i	0.0415108	+	0.765622i	0.942994	+	0.332809i	$0.107996\pi$
$277$	191.373	+	3529.67i	0.0415108	+	0.765622i	−0.901484	+	0.432813i	$0.857521\pi$
$278$	2107.59	+	5289.66i	0.454694	+	1.14120i
$279$	−1345.37	−	622.434i	−0.288692	−	0.133563i
$280$	−4524.66	+	995.954i	−0.965715	+	0.212570i
$281$	3524.93	−	6648.73i	0.748327	−	1.41149i	−0.157358	−	0.987542i	$-0.550298\pi$
$281$	3524.93	−	6648.73i	0.748327	−	1.41149i	0.905685	−	0.423952i	$-0.139358\pi$
$282$	458.236	−	2795.12i	0.0967644	−	0.590237i
$283$	−1911.30	+	1452.93i	−0.401467	+	0.305187i	−0.786354	−	0.617777i	$-0.788034\pi$
$283$	−1911.30	+	1452.93i	−0.401467	+	0.305187i	0.384887	+	0.922964i	$0.374240\pi$
$284$	−4839.23	+	2238.86i	−1.01111	+	0.467789i
$285$	−78.6254	−	74.4779i	−0.0163416	−	0.0154796i
$286$	−1209.44	−	7377.23i	−0.250054	−	1.52526i
$287$	5378.75	+	1812.31i	1.10626	+	0.372744i
$288$	766.438	−	1923.61i	0.156815	−	0.393576i
$289$	3322.17	−	3146.92i	0.676199	−	0.640530i
$290$	4181.48	+	3178.68i	0.846706	+	0.643649i
$291$	−1999.79	−	440.188i	−0.402852	−	0.0886745i
$292$	−959.616	+	1129.75i	−0.192319	+	0.226416i
$293$	−5485.05	−	596.535i	−1.09365	−	0.118942i	−0.456533	−	0.889707i	$-0.650909\pi$
$293$	−5485.05	−	596.535i	−1.09365	−	0.118942i	−0.637120	+	0.770765i	$0.719874\pi$
$294$	1564.87			0.310425
$295$	6450.96	+	16.5905i	1.27318	+	0.00327436i
$296$	−6636.87			−1.30324
$297$	−803.099	−	87.3423i	−0.156904	−	0.0170644i
$298$	3332.04	−	3922.78i	0.647717	−	0.762551i
$299$	71.4760	+	15.7331i	0.0138246	+	0.00304303i
$300$	2120.36	+	1611.86i	0.408064	+	0.310202i
$301$	−6290.79	+	5958.95i	−1.20464	+	1.14109i
$302$	−3077.04	+	7722.79i	−0.586304	+	1.47151i
$303$	−2298.17	−	774.345i	−0.435731	−	0.146815i
$304$	−10.1296	−	61.7877i	−0.00191109	−	0.0116571i
$305$	−4937.37	−	4676.93i	−0.926928	−	0.878033i
$306$	−661.070	+	305.844i	−0.123500	+	0.0571370i
$307$	−7852.07	+	5968.99i	−1.45974	+	1.10967i	−0.488222	+	0.872719i	$0.662354\pi$
$307$	−7852.07	+	5968.99i	−1.45974	+	1.10967i	−0.971522	+	0.236949i	$0.923853\pi$
$308$	−1189.06	+	7252.97i	−0.219978	+	1.34181i
$309$	994.091	−	1875.06i	0.183016	−	0.345204i
$310$	10095.0	−	2222.08i	1.84954	−	0.407114i
$311$	1667.87	+	771.640i	0.304104	+	0.140693i	0.566006	−	0.824401i	$-0.308488\pi$
$311$	1667.87	+	771.640i	0.304104	+	0.140693i	−0.261902	+	0.965094i	$0.584350\pi$
$312$	−953.623	−	2393.41i	−0.173039	−	0.434296i
$313$	355.756	+	6561.54i	0.0642445	+	1.18492i	0.835901	+	0.548881i	$0.184946\pi$
$313$	355.756	+	6561.54i	0.0642445	+	1.18492i	−0.771656	+	0.636040i	$0.780571\pi$
$314$	−3378.92	−	4983.53i	−0.607271	−	0.895658i
$315$	−1781.36	−	2097.18i	−0.318630	−	0.375120i
$316$	5507.38	+	10388.0i	0.980425	+	1.84928i
$317$	−5604.06	+	1888.23i	−0.992920	+	0.334554i	−0.768438	−	0.639925i	$-0.778966\pi$
$317$	−5604.06	+	1888.23i	−0.992920	+	0.334554i	−0.224482	+	0.974478i	$0.572069\pi$
$318$	−384.124	+	7084.74i	−0.0677377	+	1.24935i
$319$	2145.70	−	1291.03i	0.376603	−	0.226594i
$320$	3110.66	+	11203.6i	0.543410	+	1.95719i
$321$	1238.70	−	4461.40i	0.215382	−	0.775735i
$322$	−104.780	−	63.0443i	−0.0181341	−	0.0109109i
$323$	−26.1260	+	38.5330i	−0.00450059	+	0.00663788i
$324$	−920.978	+	100.162i	−0.157918	+	0.0171746i
$325$	−4373.52	+	475.649i	−0.746460	+	0.0811824i
$326$	−8515.78	+	12559.8i	−1.44677	+	2.13382i
$327$	3797.43	+	2284.84i	0.642196	+	0.386397i
$328$	−1071.32	+	3858.53i	−0.180346	+	0.649548i
$329$	−1230.52	−	4431.95i	−0.206204	−	0.742679i
$330$	4826.72	−	2904.14i	0.805159	−	0.484448i
$331$	14.9627	−	275.971i	0.00248467	−	0.0458270i	−0.997028	−	0.0770382i	$-0.975454\pi$
$331$	14.9627	−	275.971i	0.00248467	−	0.0458270i	0.999513	+	0.0312111i	$0.00993643\pi$
$332$	−1452.25	+	489.321i	−0.240069	+	0.0808885i
$333$	−1846.36	−	3482.61i	−0.303844	−	0.573110i
$334$	−5280.15	−	6216.28i	−0.865022	−	1.01838i
$335$	−322.542	−	475.714i	−0.0526040	−	0.0775851i
$336$	−86.1253	−	1588.49i	−0.0139837	−	0.257914i
$337$	1717.72	+	4311.15i	0.277656	+	0.696865i	0.999986	+	0.00531569i	$0.00169205\pi$
$337$	1717.72	+	4311.15i	0.277656	+	0.696865i	−0.722330	+	0.691549i	$0.756929\pi$
$338$	4060.70	+	1878.68i	0.653471	+	0.302328i
$339$	−3137.80	+	690.683i	−0.502720	+	0.110657i
$340$	1399.90	−	2640.48i	0.223294	−	0.421178i
$341$	797.270	−	4863.13i	0.126612	−	0.772297i
$342$	−80.1092	+	60.8975i	−0.0126661	+	0.00962853i
$343$	−4379.81	+	2026.32i	−0.689469	+	0.318982i
$344$	−4438.34	−	4204.22i	−0.695637	−	0.658943i
$345$	8.92187	+	54.4210i	0.00139228	+	0.00849254i
$346$	−13449.2	−	4531.55i	−2.08969	−	0.704097i
$347$	1291.98	−	3242.62i	0.199876	−	0.501651i	−0.794536	−	0.607216i	$-0.792286\pi$
$347$	1291.98	−	3242.62i	0.199876	−	0.501651i	0.994412	+	0.105566i	$0.0336654\pi$
$348$	2084.85	−	1974.88i	0.321149	−	0.304208i
$349$	−9058.06	−	6885.76i	−1.38930	−	1.05612i	−0.990266	−	0.139186i	$-0.955551\pi$
$349$	−9058.06	−	6885.76i	−1.38930	−	1.05612i	−0.399037	−	0.916935i	$-0.630656\pi$
$350$	7178.74	+	1580.16i	1.09634	+	0.241323i
$351$	990.615	−	1166.24i	0.150641	−	0.177349i
$352$	6843.46	+	744.272i	1.03624	+	0.112698i
$353$	−9112.58			−1.37398			−0.686988	−	0.726669i	$-0.741068\pi$
$353$	−9112.58			−1.37398			−0.686988	+	0.726669i	$0.741068\pi$
$354$	984.927	−	5912.51i	0.147877	−	0.887701i
$355$	6636.26			0.992157
$356$	3921.03	+	426.437i	0.583747	+	0.0634863i
$357$	−765.754	+	901.516i	−0.113524	+	0.133651i
$358$	4656.54	+	1024.98i	0.687447	+	0.151318i
$359$	4177.34	+	3175.53i	0.614126	+	0.466847i	0.865408	−	0.501067i	$-0.167059\pi$
$359$	4177.34	+	3175.53i	0.614126	+	0.466847i	−0.251282	+	0.967914i	$0.580852\pi$
$360$	1409.41	−	1335.07i	0.206340	−	0.195456i
$361$	2536.40	−	6365.88i	0.369791	−	0.928106i
$362$	10400.8	+	3504.44i	1.51009	+	0.508810i
$363$	211.516	+	1290.19i	0.0305833	+	0.186550i
$364$	−10107.1	−	9573.99i	−1.45538	−	1.37861i
$365$	1674.35	−	774.637i	0.240108	−	0.111086i
$366$	−5030.55	+	3824.13i	−0.718446	+	0.546148i
$367$	1071.44	−	6535.52i	0.152395	−	0.929568i	−0.794321	−	0.607498i	$-0.792173\pi$
$367$	1071.44	−	6535.52i	0.152395	−	0.929568i	0.946716	−	0.322070i	$-0.104379\pi$
$368$	−14.9342	+	28.1689i	−0.00211549	+	0.00399024i
$369$	−2322.75	+	511.275i	−0.327689	+	0.0721299i
$370$	24945.7	+	11541.1i	3.50504	+	1.62161i
$371$	4264.68	+	10703.5i	0.596796	+	1.49784i
$372$	−305.960	−	5643.10i	−0.0426433	−	0.786509i
$373$	−1627.97	−	2401.08i	−0.225987	−	0.333306i	0.697744	−	0.716347i	$-0.254187\pi$
$373$	−1627.97	−	2401.08i	−0.225987	−	0.333306i	−0.923731	+	0.383041i	$0.874877\pi$
$374$	−1567.63	−	1845.56i	−0.216739	−	0.255165i
$375$	947.619	+	1787.40i	0.130493	+	0.246136i
$376$	3075.28	−	1036.18i	0.421797	−	0.142120i
$377$	−256.797	+	4736.33i	−0.0350814	+	0.647039i
$378$	−2190.72	+	1318.11i	−0.298091	+	0.179356i
$379$	2163.92	+	7793.73i	0.293280	+	1.05630i	0.952547	+	0.304390i	$0.0984527\pi$
$379$	2163.92	+	7793.73i	0.293280	+	1.05630i	−0.659268	+	0.751908i	$0.729134\pi$
$380$	110.457	−	397.832i	0.0149114	−	0.0537062i
$381$	6578.89	+	3958.39i	0.884637	+	0.532269i
$382$	953.036	−	1405.62i	0.127648	−	0.188267i
$383$	5612.05	−	610.347i	0.748727	−	0.0814289i	0.274203	−	0.961672i	$-0.411586\pi$
$383$	5612.05	−	610.347i	0.748727	−	0.0814289i	0.474523	+	0.880243i	$0.342620\pi$
$384$	5250.93	−	571.073i	0.697813	−	0.0758917i
$385$	5133.49	−	7571.33i	0.679550	−	1.00226i
$386$	16562.0	+	9965.00i	2.18389	+	1.31400i
$387$	971.370	−	3498.56i	0.127591	−	0.459539i
$388$	−2088.46	−	7521.94i	−0.273261	−	0.984198i
$389$	2424.34	−	1458.68i	0.315987	−	0.190123i	−0.348720	−	0.937227i	$-0.613384\pi$
$389$	2424.34	−	1458.68i	0.315987	−	0.190123i	0.664708	+	0.747103i	$0.268556\pi$
$390$	−577.660	+	10654.3i	−0.0750024	+	1.38334i
$391$	22.4653	−	7.56944i	0.00290567	−	0.000979036i
$392$	839.805	+	1584.04i	0.108206	+	0.204097i
$393$	3795.05	+	4467.88i	0.487112	+	0.573473i
$394$	−10773.3	−	15889.4i	−1.37754	−	2.03171i
$395$	−792.245	−	14612.1i	−0.100917	−	1.86130i
$396$	−1139.94	−	2861.04i	−0.144657	−	0.363062i
$397$	−2346.02	−	1085.38i	−0.296582	−	0.137214i	0.265955	−	0.963985i	$-0.414313\pi$
$397$	−2346.02	−	1085.38i	−0.296582	−	0.137214i	−0.562537	+	0.826772i	$0.690175\pi$
$398$	−19863.1	+	4372.21i	−2.50163	+	0.550651i
$399$	−76.5429	+	144.375i	−0.00960385	+	0.0181148i
$400$	310.055	−	1891.25i	0.0387569	−	0.236406i
$401$	2789.84	−	2120.78i	0.347426	−	0.264107i	−0.416878	−	0.908963i	$-0.636876\pi$
$401$	2789.84	−	2120.78i	0.347426	−	0.264107i	0.764304	+	0.644856i	$0.223083\pi$
$402$	−484.675	+	224.235i	−0.0601329	+	0.0278204i
$403$	6776.85	+	6419.38i	0.837665	+	0.793479i
$404$	−1495.75	−	9123.69i	−0.184199	−	1.12357i
$405$	1092.65	+	368.157i	0.134060	+	0.0451701i
$406$	2933.47	−	7362.44i	0.358585	−	0.899980i
$407$	9513.54	−	9011.71i	1.15865	−	1.09753i
$408$	−664.363	−	505.035i	−0.0806148	−	0.0612818i
$409$	−15041.0	−	3310.77i	−1.81840	−	0.400261i	−0.830717	−	0.556696i	$-0.812069\pi$
$409$	−15041.0	−	3310.77i	−1.81840	−	0.400261i	−0.987688	+	0.156434i	$0.950000\pi$
$410$	10736.5	−	12639.9i	1.29326	−	1.52254i
$411$	7166.63	+	779.418i	0.860106	+	0.0935422i
$412$	8090.92			0.967503
$413$	−2579.90	−	9385.55i	−0.307382	−	1.11824i
$414$	51.2408			0.00608296
$415$	1896.14	+	206.217i	0.224284	+	0.0243923i
$416$	−8441.35	+	9937.92i	−0.994882	+	1.17127i
$417$	−3784.02	−	832.926i	−0.444375	−	0.0978143i
$418$	−266.317	−	202.449i	−0.0311627	−	0.0236892i
$419$	−9530.57	+	9027.84i	−1.11121	+	1.05260i	−0.112957	+	0.993600i	$0.536032\pi$
$419$	−9530.57	+	9027.84i	−1.11121	+	1.05260i	−0.998258	+	0.0589987i	$0.981209\pi$
$420$	3882.84	−	9745.18i	0.451102	−	1.13218i
$421$	−3837.02	−	1292.84i	−0.444192	−	0.149666i	0.0883127	−	0.996093i	$-0.471853\pi$
$421$	−3837.02	−	1292.84i	−0.444192	−	0.149666i	−0.532505	+	0.846427i	$0.678749\pi$
$422$	2914.97	+	17780.6i	0.336253	+	2.05105i
$423$	1399.26	+	1325.45i	0.160838	+	0.152353i
$424$	−7377.70	+	3413.29i	−0.845030	+	0.390952i
$425$	−1134.43	+	862.370i	−0.129477	+	0.0984261i
$426$	997.570	−	6084.91i	0.113456	−	0.692053i
$427$	−4806.60	+	9066.20i	−0.544748	+	1.02750i
$428$	17239.3	−	3794.65i	1.94694	−	0.428555i
$429$	4616.79	+	2135.96i	0.519583	+	0.240384i
$430$	9371.31	+	23520.2i	1.05099	+	2.63778i
$431$	−197.850	−	3649.13i	−0.0221116	−	0.407824i	−0.988547	−	0.150914i	$-0.951778\pi$
$431$	−197.850	−	3649.13i	−0.0221116	−	0.407824i	0.966435	−	0.256910i	$-0.0827044\pi$
$432$	374.087	+	551.737i	0.0416627	+	0.0614479i
$433$	5692.01	+	6701.15i	0.631733	+	0.743733i	0.981153	−	0.193233i	$-0.0618973\pi$
$433$	5692.01	+	6701.15i	0.631733	+	0.743733i	−0.349420	+	0.936966i	$0.613621\pi$
$434$	−7305.61	−	13779.8i	−0.808019	−	1.52409i
$435$	−3387.04	+	1141.23i	−0.373324	+	0.125788i
$436$	−914.717	+	16871.0i	−0.100475	+	1.85315i
$437$	2.80624	−	1.68846i	0.000307187	−	0.000184828i
$438$	−458.589	−	1651.69i	−0.0500279	−	0.180184i
$439$	2006.14	−	7225.45i	0.218104	−	0.785540i	−0.770812	−	0.637063i	$-0.780149\pi$
$439$	2006.14	−	7225.45i	0.218104	−	0.785540i	0.988916	−	0.148477i	$-0.0474371\pi$
$440$	5530.05	+	3327.32i	0.599170	+	0.360508i
$441$	−597.572	+	881.352i	−0.0645256	+	0.0951681i
$442$	4559.81	−	495.909i	0.490697	−	0.0533665i
$443$	−16610.4	+	1806.49i	−1.78145	+	0.193744i	−0.938740	−	0.344626i	$-0.888006\pi$
$443$	−16610.4	+	1806.49i	−1.78145	+	0.193744i	−0.842709	+	0.538370i	$0.819040\pi$
$444$	8433.27	−	12438.1i	0.901408	−	1.32948i
$445$	−4206.21	−	2530.80i	−0.448076	−	0.269598i
$446$	733.566	−	2642.06i	0.0778819	−	0.280505i
$447$	936.960	+	3374.62i	0.0991424	+	0.357079i
$448$	15032.9	−	9044.99i	1.58535	−	0.953874i
$449$	656.957	−	12116.9i	0.0690506	−	1.27356i	−0.734616	−	0.678484i	$-0.762637\pi$
$449$	656.957	−	12116.9i	0.0690506	−	1.27356i	0.803666	−	0.595080i	$-0.202880\pi$
$450$	−2918.87	+	983.483i	−0.305771	+	0.103026i
$451$	−3703.54	−	6985.62i	−0.386680	−	0.729357i
$452$	−7929.76	−	9335.63i	−0.825187	−	0.971485i
$453$	−3174.55	−	4682.11i	−0.329257	−	0.485617i
$454$	750.878	+	13849.1i	0.0776221	+	1.43166i
$455$	6413.39	+	16096.4i	0.660801	+	1.65849i
$456$	−104.635	−	48.4094i	−0.0107456	−	0.00497144i
$457$	−6786.65	+	1493.86i	−0.694674	+	0.152909i	−0.548253	−	0.836313i	$-0.684707\pi$
$457$	−6786.65	+	1493.86i	−0.694674	+	0.152909i	−0.146422	+	0.989222i	$0.546776\pi$
$458$	−1801.07	+	3397.18i	−0.183752	+	0.346593i
$459$	80.1863	−	489.115i	0.00815419	−	0.0497384i
$460$	−167.373	+	127.234i	−0.0169648	+	0.0128963i
$461$	−15860.5	+	7337.83i	−1.60237	+	0.741338i	−0.998447	−	0.0557016i	$-0.982260\pi$
$461$	−15860.5	+	7337.83i	−1.60237	+	0.741338i	−0.603928	+	0.797039i	$0.706398\pi$
$462$	−6170.62	−	5845.12i	−0.621393	−	0.588614i
$463$	858.882	+	5238.95i	0.0862109	+	0.525863i	0.994259	+	0.106998i	$0.0341238\pi$
$463$	858.882	+	5238.95i	0.0862109	+	0.525863i	−0.908048	+	0.418865i	$0.862428\pi$
$464$	−1958.18	−	659.788i	−0.195919	−	0.0660127i
$465$	−2603.45	+	6534.17i	−0.259639	+	0.651644i
$466$	−9790.29	+	9273.86i	−0.973233	+	0.921895i
$467$	6026.21	+	4581.01i	0.597130	+	0.453927i	0.859567	−	0.511022i	$-0.170733\pi$
$467$	6026.21	+	4581.01i	0.597130	+	0.453927i	−0.262437	+	0.964949i	$0.584526\pi$
$468$	5697.23	+	1254.05i	0.562723	+	0.123865i
$469$	−561.427	+	660.963i	−0.0552756	+	0.0650755i
$470$	−13360.8	−	1453.07i	−1.31125	−	0.142607i
$471$	4097.08			0.400814
$472$	6513.53	−	2176.03i	0.635189	−	0.212203i
$473$	12070.7			1.17338
$474$	−13517.2	−	1470.08i	−1.30984	−	0.142454i
$475$	−127.447	+	150.043i	−0.0123109	+	0.0144935i
$476$	−4404.01	−	969.396i	−0.424070	−	0.0933449i
$477$	−3843.53	−	2921.78i	−0.368938	−	0.280459i
$478$	13908.8	−	13175.1i	1.33090	−	1.26070i
$479$	6328.45	−	15883.2i	0.603662	−	1.51508i	−0.235879	−	0.971782i	$-0.575797\pi$
$479$	6328.45	−	15883.2i	0.603662	−	1.51508i	0.839541	−	0.543296i	$-0.182824\pi$
$480$	−9310.84	−	3137.19i	−0.885374	−	0.298317i
$481$	4015.66	+	24494.5i	0.380662	+	2.32194i
$482$	−3420.51	−	3240.08i	−0.323236	−	0.306186i
$483$	75.5196	−	34.9391i	0.00711441	−	0.00329148i
$484$	−3968.02	+	3016.41i	−0.372654	+	0.283284i
$485$	−1571.87	+	9587.97i	−0.147165	+	0.897664i
$486$	501.819	−	946.531i	0.0468374	−	0.0883447i
$487$	165.392	−	36.4055i	0.0153894	−	0.00338746i	−0.207269	−	0.978284i	$-0.566458\pi$
$487$	165.392	−	36.4055i	0.0153894	−	0.00338746i	0.222658	+	0.974897i	$0.428527\pi$
$488$	−6570.69	−	3039.92i	−0.609511	−	0.281990i
$489$	−3821.96	−	9592.39i	−0.353446	−	0.887082i
$490$	−401.988	−	7414.23i	−0.0370612	−	0.683553i
$491$	6446.24	+	9507.50i	0.592495	+	0.873864i	0.999212	−	0.0396898i	$-0.0126370\pi$
$491$	6446.24	+	9507.50i	0.592495	+	0.873864i	−0.406717	+	0.913554i	$0.633327\pi$
$492$	−5869.97	−	6910.66i	−0.537883	−	0.633245i
$493$	719.669	+	1357.44i	0.0657450	+	0.124008i
$494$	600.487	−	202.327i	0.0546906	−	0.0184274i
$495$	−207.519	+	3827.47i	−0.0188430	+	0.347539i
$496$	−3484.39	+	2096.49i	−0.315431	+	0.189788i
$497$	−2678.82	−	9648.25i	−0.241774	−	0.870791i
$498$	474.114	−	1707.60i	0.0426618	−	0.153654i
$499$	−12962.8	−	7799.48i	−1.16292	−	0.699705i	−0.202778	−	0.979225i	$-0.564997\pi$
$499$	−12962.8	−	7799.48i	−1.16292	−	0.699705i	−0.960140	+	0.279520i	$0.909825\pi$
$500$	−4328.26	+	6383.70i	−0.387131	+	0.570976i
$501$	5517.40	−	600.054i	0.492015	−	0.0535098i
$502$	−23709.2	+	2578.53i	−2.10796	+	0.229254i
$503$	4310.18	−	6357.04i	0.382071	−	0.563512i	−0.587221	−	0.809427i	$-0.699778\pi$
$503$	4310.18	−	6357.04i	0.382071	−	0.563512i	0.969291	+	0.245915i	$0.0790883\pi$
$504$	−2509.94	−	1510.18i	−0.221829	−	0.133470i
$505$	−3078.43	+	11087.5i	−0.271264	+	0.977005i
$506$	45.5724	+	164.137i	0.00400383	+	0.0144205i
$507$	−2608.75	+	1569.63i	−0.228518	+	0.137495i
$508$	−1584.71	+	29228.3i	−0.138406	+	2.55275i
$509$	10467.0	−	3526.73i	0.911473	−	0.307111i	0.175783	−	0.984429i	$-0.443754\pi$
$509$	10467.0	−	3526.73i	0.911473	−	0.307111i	0.735690	+	0.677318i	$0.236858\pi$
$510$	1618.88	+	3053.54i	0.140560	+	0.265124i
$511$	−1802.10	−	2121.59i	−0.156008	−	0.183667i
$512$	−4867.34	−	7178.79i	−0.420133	−	0.619650i
$513$	−3.70709	−	68.3733i	−0.000319049	−	0.00588451i
$514$	3146.49	+	7897.10i	0.270011	+	0.677678i
$515$	−9139.25	−	4228.27i	−0.781987	−	0.361786i
$516$	13518.8	−	2975.71i	1.15335	−	0.253872i
$517$	−3001.27	+	5661.00i	−0.255311	+	0.481567i
$518$	6709.57	−	40926.6i	0.569115	−	3.47145i
$519$	7688.02	−	5844.28i	0.650225	−	0.494288i
$520$	−11094.9	+	5133.03i	−0.935658	+	0.432881i
$521$	3142.44	+	2976.68i	0.264248	+	0.250309i	0.808339	−	0.588717i	$-0.200367\pi$
$521$	3142.44	+	2976.68i	0.264248	+	0.250309i	−0.544091	+	0.839026i	$0.683126\pi$
$522$	537.268	+	3277.19i	0.0450490	+	0.274787i
$523$	4472.57	+	1506.99i	0.373943	+	0.125996i	0.499996	−	0.866027i	$-0.333335\pi$
$523$	4472.57	+	1506.99i	0.373943	+	0.125996i	−0.126054	+	0.992023i	$0.540231\pi$
$524$	−8272.07	+	20761.3i	−0.689632	+	1.73085i
$525$	−3631.29	+	3439.74i	−0.301872	+	0.285948i
$526$	−8791.35	−	6683.01i	−0.728748	−	0.553980i
$527$	2952.90	+	649.982i	0.244080	+	0.0537261i
$528$	−1434.65	+	1689.00i	−0.118248	+	0.139212i
$529$	12094.0	+	1315.30i	0.994002	+	0.108104i
$530$	33665.7			2.75914
$531$	2953.89	+	2812.52i	0.241408	+	0.229855i
$532$	−622.983			−0.0507702
$533$	14888.7	+	1619.25i	1.20995	+	0.131590i
$534$	−2952.82	+	3476.32i	−0.239290	+	0.281714i
$535$	−21456.0	−	4722.82i	−1.73388	−	0.381655i
$536$	−487.089	−	370.276i	−0.0392520	−	0.0298386i
$537$	−2355.46	+	2231.21i	−0.189285	+	0.179300i
$538$	1848.10	−	4638.38i	0.148099	−	0.371700i
$539$	−3354.66	−	1130.32i	−0.268080	−	0.0903268i
$540$	711.147	+	4337.80i	0.0566720	+	0.345684i
$541$	2160.10	+	2046.15i	0.171663	+	0.162608i	0.768708	−	0.639600i	$-0.220900\pi$
$541$	2160.10	+	2046.15i	0.171663	+	0.162608i	−0.597045	+	0.802208i	$0.703659\pi$
$542$	−29952.8	+	13857.7i	−2.37377	+	1.09822i
$543$	−5945.47	+	4519.63i	−0.469880	+	0.357193i
$544$	−683.293	+	4167.90i	−0.0538528	+	0.328488i
$545$	9849.90	−	18578.9i	0.774171	−	1.46024i
$546$	15723.2	−	3460.93i	1.23240	−	0.271271i
$547$	21623.3	+	10004.0i	1.69021	+	0.781974i	0.998193	+	0.0600918i	$0.0191393\pi$
$547$	21623.3	+	10004.0i	1.69021	+	0.781974i	0.692016	+	0.721882i	$0.256723\pi$
$548$	10172.5	+	25531.1i	0.792971	+	1.99021i
$549$	−232.791	−	4293.58i	−0.0180970	−	0.333780i
$550$	−5746.32	−	8475.19i	−0.445498	−	0.657060i
$551$	137.412	+	161.774i	0.0106242	+	0.0125078i
$552$	27.4990	+	51.8686i	0.00212035	+	0.00399941i
$553$	−20924.3	+	7050.22i	−1.60903	+	0.542144i
$554$	843.718	−	15561.5i	0.0647042	−	1.19340i
$555$	−16026.1	+	9642.56i	−1.22571	+	0.737485i
$556$	−3951.79	−	14233.1i	−0.301427	−	1.08564i
$557$	−3303.28	+	11897.3i	−0.251283	+	0.905039i	0.725037	+	0.688709i	$0.241822\pi$
$557$	−3303.28	+	11897.3i	−0.251283	+	0.905039i	−0.976320	+	0.216330i	$0.930591\pi$
$558$	5599.94	+	3369.37i	0.424847	+	0.255622i
$559$	−12830.9	+	18924.2i	−0.970823	+	1.43186i
$560$	−7504.03	+	816.112i	−0.566255	+	0.0615840i
$561$	1638.07	−	178.151i	0.123279	−	0.0134074i
$562$	−18618.7	+	27460.6i	−1.39748	+	2.06113i
$563$	−10836.4	−	6520.04i	−0.811189	−	0.488076i	0.0485434	−	0.998821i	$-0.484542\pi$
$563$	−10836.4	−	6520.04i	−0.811189	−	0.488076i	−0.859732	+	0.510745i	$0.829370\pi$
$564$	−1965.76	+	7080.03i	−0.146761	+	0.528587i
$565$	4078.46	+	14689.3i	0.303685	+	1.09377i
$566$	9069.64	−	5457.02i	0.673543	−	0.405258i
$567$	94.1875	−	1737.19i	0.00697620	−	0.128668i
$568$	6694.82	−	2255.75i	0.494557	−	0.166636i
$569$	−9846.39	−	18572.3i	−0.725452	−	1.36835i	−0.921743	−	0.387802i	$-0.873235\pi$
$569$	−9846.39	−	18572.3i	−0.725452	−	1.36835i	0.196291	−	0.980546i	$-0.437110\pi$
$570$	309.107	+	363.909i	0.0227141	+	0.0267412i
$571$	−10546.2	−	15554.5i	−0.772935	−	1.13999i	−0.986611	−	0.163089i	$-0.947854\pi$
$571$	−10546.2	−	15554.5i	−0.772935	−	1.13999i	0.213677	−	0.976904i	$-0.431456\pi$
$572$	1049.94	+	19365.0i	0.0767484	+	1.41554i
$573$	427.731	+	1073.52i	0.0311845	+	0.0782671i
$574$	−22710.7	−	10507.1i	−1.65144	−	0.764039i
$575$	97.9016	−	21.5498i	0.00710048	−	0.00156293i
$576$	−3443.52	+	6495.16i	−0.249097	+	0.469847i
$577$	−61.4407	+	374.772i	−0.00443294	+	0.0270398i	−0.988950	−	0.148247i	$-0.952637\pi$
$577$	−61.4407	+	374.772i	−0.00443294	+	0.0270398i	0.984517	+	0.175287i	$0.0560852\pi$
$578$	−16060.8	+	12209.1i	−1.15578	+	0.878602i
$579$	−11936.9	+	5522.59i	−0.856788	+	0.396392i
$580$	−9892.39	−	9370.57i	−0.708205	−	0.670848i
$581$	−465.591	−	2839.98i	−0.0332461	−	0.202792i
$582$	8555.10	+	2882.55i	0.609313	+	0.205301i
$583$	5940.82	−	14910.3i	0.422031	−	1.05922i
$584$	1425.82	−	1350.61i	0.101029	−	0.0956995i
$585$	−5780.05	−	4393.88i	−0.408505	−	0.310538i
$586$	23756.2	+	5229.13i	1.67467	+	0.368623i
$587$	7873.45	−	9269.34i	0.553615	−	0.651766i	−0.412171	−	0.911107i	$-0.635229\pi$
$587$	7873.45	−	9269.34i	0.553615	−	0.651766i	0.965786	+	0.259340i	$0.0835052\pi$
$588$	−4035.76	−	438.915i	−0.283047	−	0.0307833i
$589$	417.712			0.0292216
$590$	−28266.1	−	3147.70i	−1.97237	−	0.219642i
$591$	13063.1			0.909209
$592$	−10749.7	−	1169.10i	−0.746303	−	0.0811653i
$593$	−9670.79	+	11385.3i	−0.669699	+	0.788431i	−0.987142	−	0.159847i	$-0.948900\pi$
$593$	−9670.79	+	11385.3i	−0.669699	+	0.788431i	0.317443	+	0.948277i	$0.397176\pi$
$594$	3478.28	+	765.628i	0.240262	+	0.0528857i
$595$	4468.03	+	3396.51i	0.307851	+	0.234022i
$596$	−9693.52	+	9182.19i	−0.666211	+	0.631069i
$597$	5122.61	−	12856.8i	0.351180	−	0.881395i
$598$	−305.774	−	103.027i	−0.0209097	−	0.00704531i
$599$	2430.69	+	14826.5i	0.165802	+	1.01134i	0.930322	+	0.366745i	$0.119528\pi$
$599$	2430.69	+	14826.5i	0.165802	+	1.01134i	−0.764520	+	0.644600i	$0.777024\pi$
$600$	−2561.98	−	2426.84i	−0.174321	−	0.165126i
$601$	1847.20	−	854.607i	0.125373	−	0.0580036i	−0.356200	−	0.934410i	$-0.615928\pi$
$601$	1847.20	−	854.607i	0.125373	−	0.0580036i	0.481573	+	0.876406i	$0.340066\pi$
$602$	30412.4	−	23118.9i	2.05900	−	1.56521i
$603$	58.7900	−	358.603i	0.00397034	−	0.0242180i
$604$	10101.7	−	19053.9i	0.680518	−	1.28359i
$605$	6058.51	−	1333.58i	0.407130	−	0.0896160i
$606$	9703.59	+	4489.36i	0.650464	+	0.300937i
$607$	926.912	+	2326.37i	0.0619806	+	0.155559i	0.956705	−	0.291059i	$-0.0940075\pi$
$607$	926.912	+	2326.37i	0.0619806	+	0.155559i	−0.894725	+	0.446618i	$0.852628\pi$
$608$	31.5893	+	582.630i	0.00210710	+	0.0388631i
$609$	3026.42	+	4463.64i	0.201374	+	0.297005i
$610$	19410.7	+	22852.1i	1.28839	+	1.51681i
$611$	−5684.92	−	10722.9i	−0.376411	−	0.709986i
$612$	1790.67	−	603.347i	0.118274	−	0.0398511i
$613$	−132.760	+	2448.62i	−0.00874738	+	0.161336i	0.990896	+	0.134630i	$0.0429846\pi$
$613$	−132.760	+	2448.62i	−0.00874738	+	0.161336i	−0.999643	+	0.0267060i	$0.991498\pi$
$614$	37260.2	−	22418.7i	2.44902	−	1.47353i
$615$	3019.06	+	10873.7i	0.197952	+	0.712958i
$616$	2605.20	−	9383.09i	0.170400	−	0.613726i
$617$	−3586.45	−	2157.89i	−0.234011	−	0.140800i	0.393719	−	0.919231i	$-0.371188\pi$
$617$	−3586.45	−	2157.89i	−0.234011	−	0.140800i	−0.627730	+	0.778431i	$0.716016\pi$
$618$	−5250.80	+	7744.35i	−0.341777	+	0.504083i
$619$	−5781.80	+	628.809i	−0.375428	+	0.0408303i	−0.293888	−	0.955840i	$-0.594949\pi$
$619$	−5781.80	+	628.809i	−0.375428	+	0.0408303i	−0.0815400	+	0.996670i	$0.525984\pi$
$620$	−26658.0	+	2899.24i	−1.72680	+	0.187800i
$621$	−19.5672	+	28.8594i	−0.00126442	+	0.00186488i
$622$	−6942.32	−	4177.06i	−0.447527	−	0.269268i
$623$	−1981.55	+	7136.88i	−0.127430	+	0.458962i
$624$	−1122.98	−	4044.59i	−0.0720432	−	0.259476i
$625$	16539.4	−	9951.45i	1.05852	−	0.636893i
$626$	1568.44	−	28928.2i	0.100140	−	1.84697i
$627$	215.720	−	72.6844i	0.0137400	−	0.00462956i
$628$	7316.37	+	13800.1i	0.464897	+	0.876888i
$629$	5204.98	+	6127.78i	0.329946	+	0.388443i
$630$	6807.89	+	10040.9i	0.430529	+	0.634982i
$631$	670.203	+	12361.2i	0.0422826	+	0.779858i	0.940393	+	0.340088i	$0.110457\pi$
$631$	670.203	+	12361.2i	0.0422826	+	0.779858i	−0.898111	+	0.439769i	$0.855060\pi$
$632$	−5766.08	−	14471.8i	−0.362915	−	0.910848i
$633$	−11127.4	−	5148.07i	−0.698694	−	0.323250i
$634$	25462.2	−	5604.65i	1.59500	−	0.351087i
$635$	17064.6	−	32187.2i	1.06644	−	2.01151i
$636$	2977.78	−	18163.7i	0.185655	−	1.13245i
$637$	5338.03	−	4057.87i	0.332026	−	0.252400i
$638$	−10019.8	+	4635.66i	−0.621769	+	0.287661i
$639$	3046.15	+	2885.47i	0.188582	+	0.178635i
$640$	−4054.58	−	24731.8i	−0.250424	−	1.52752i
$641$	−17611.8	−	5934.12i	−1.08522	−	0.365653i	−0.280832	−	0.959757i	$-0.590610\pi$
$641$	−17611.8	−	5934.12i	−1.08522	−	0.365653i	−0.804388	+	0.594104i	$0.797507\pi$
$642$	−7555.74	+	18963.5i	−0.464488	+	1.16578i
$643$	13351.2	−	12647.0i	0.818851	−	0.775657i	−0.158482	−	0.987362i	$-0.550660\pi$
$643$	13351.2	−	12647.0i	0.818851	−	0.775657i	0.977334	+	0.211705i	$0.0679015\pi$
$644$	252.544	+	191.979i	0.0154528	+	0.0117469i
$645$	−16825.5	−	3703.57i	−1.02714	−	0.226090i
$646$	132.876	−	156.433i	0.00809277	−	0.00952754i
$647$	−2825.36	−	307.276i	−0.171679	−	0.0186712i	0.0218757	−	0.999761i	$-0.493036\pi$
$647$	−2825.36	−	307.276i	−0.171679	−	0.0186712i	−0.193555	+	0.981089i	$0.562002\pi$
$648$	1227.44			0.0744109
$649$	−6382.07	+	11963.4i	−0.386007	+	0.723583i
$650$	19395.5			1.17039
$651$	10550.7	+	1147.46i	0.635202	+	0.0690824i
$652$	25484.8	−	30003.1i	1.53077	−	1.80216i
$653$	−11082.9	−	2439.54i	−0.664179	−	0.146197i	−0.129929	−	0.991523i	$-0.541475\pi$
$653$	−11082.9	−	2439.54i	−0.664179	−	0.146197i	−0.534250	+	0.845327i	$0.679406\pi$
$654$	−15554.7	−	11824.4i	−0.930024	−	0.706986i
$655$	20193.6	−	19128.4i	1.20463	−	1.14108i
$656$	−2414.90	+	6060.94i	−0.143729	+	0.360731i
$657$	1105.37	+	372.443i	0.0656387	+	0.0221163i
$658$	3280.70	+	20011.4i	0.194369	+	1.18560i
$659$	9526.89	+	9024.35i	0.563149	+	0.533443i	0.915444	−	0.402446i	$-0.131840\pi$
$659$	9526.89	+	9024.35i	0.563149	+	0.533443i	−0.352295	+	0.935889i	$0.614599\pi$
$660$	−13262.6	+	6135.92i	−0.782190	+	0.361879i
$661$	14465.3	−	10996.2i	0.851187	−	0.647055i	−0.0858417	−	0.996309i	$-0.527358\pi$
$661$	14465.3	−	10996.2i	0.851187	−	0.647055i	0.937028	+	0.349254i	$0.113565\pi$
$662$	−197.128	+	1202.43i	−0.0115734	+	0.0705945i
$663$	−1461.94	+	2757.51i	−0.0856366	+	0.161528i
$664$	1982.97	−	436.484i	0.115895	−	0.0255103i
$665$	703.702	+	325.567i	0.0410352	+	0.0189849i
$666$	6432.39	+	16144.1i	0.374249	+	0.939294i
$667$	−5.85151	−	107.925i	−0.000339687	−	0.00626517i
$668$	11873.9	+	17512.6i	0.687745	+	1.01435i
$669$	1207.92	+	1422.07i	0.0698069	+	0.0821831i
$670$	1186.91	+	2238.76i	0.0684395	+	0.129091i
$671$	13546.4	−	4564.30i	0.779361	−	0.262597i
$672$	−802.602	+	14803.1i	−0.0460730	+	0.849766i
$673$	25139.2	−	15125.8i	1.43989	−	0.866353i	0.440385	−	0.897809i	$-0.354842\pi$
$673$	25139.2	−	15125.8i	1.43989	−	0.866353i	0.999505	+	0.0314557i	$0.0100143\pi$
$674$	−5473.62	−	19714.2i	−0.312813	−	1.12665i
$675$	560.713	−	2019.51i	0.0319731	−	0.115157i
$676$	−9945.54	−	5984.03i	−0.565859	−	0.340466i
$677$	16624.3	−	24519.0i	0.943756	−	1.39194i	0.0238854	−	0.999715i	$-0.492396\pi$
$677$	16624.3	−	24519.0i	0.943756	−	1.39194i	0.919871	−	0.392222i	$-0.128293\pi$
$678$	14082.0	−	1531.50i	0.797661	−	0.0867509i
$679$	14574.2	−	1585.04i	0.823719	−	0.0895848i
$680$	−2222.16	+	3277.44i	−0.125318	+	0.184830i
$681$	−8086.74	−	4865.63i	−0.455043	−	0.273790i
$682$	−5812.48	+	20934.7i	−0.326351	+	1.17541i
$683$	4416.02	+	15905.1i	0.247400	+	0.891055i	0.978062	+	0.208315i	$0.0667979\pi$
$683$	4416.02	+	15905.1i	0.247400	+	0.891055i	−0.730662	+	0.682740i	$0.760788\pi$
$684$	223.681	−	134.584i	0.0125039	−	0.00752333i
$685$	1851.84	−	34155.2i	0.103292	−	1.90511i
$686$	20162.2	−	6793.45i	1.12215	−	0.378098i
$687$	−1225.56	−	2311.66i	−0.0680613	−	0.128377i
$688$	−6448.18	−	7591.39i	−0.357318	−	0.420667i
$689$	17061.2	+	25163.4i	0.943367	+	1.39136i
$690$	−13.1629	−	242.775i	−0.000726236	−	0.0133946i
$691$	5623.82	+	14114.7i	0.309609	+	0.777061i	0.998630	+	0.0523196i	$0.0166615\pi$
$691$	5623.82	+	14114.7i	0.309609	+	0.777061i	−0.689021	+	0.724741i	$0.741959\pi$
$692$	33414.1	+	15459.0i	1.83557	+	0.849224i
$693$	5648.41	−	1243.31i	0.309618	−	0.0681521i
$694$	−7208.28	+	13596.3i	−0.394269	+	0.743670i
$695$	−2974.30	+	18142.4i	−0.162333	+	0.990188i
$696$	−3029.01	+	2302.60i	−0.164963	+	0.125402i
$697$	4402.73	−	2036.92i	0.239262	−	0.110694i
$698$	36418.5	+	34497.4i	1.97487	+	1.87070i
$699$	−1484.56	−	9055.40i	−0.0803306	−	0.489995i
$700$	−18070.6	−	6088.70i	−0.975721	−	0.328759i
$701$	−8873.95	+	22271.9i	−0.478124	+	1.20000i	0.470162	+	0.882580i	$0.344196\pi$
$701$	−8873.95	+	22271.9i	−0.478124	+	1.20000i	−0.948285	+	0.317419i	$0.897184\pi$
$702$	−4897.69	+	4639.34i	−0.263321	+	0.249431i
$703$	884.246	+	672.187i	0.0474395	+	0.0360626i
$704$	−23868.2	−	5253.79i	−1.27779	−	0.281264i
$705$	5920.44	−	6970.08i	0.316279	−	0.372352i
$706$	39939.6	+	4343.70i	2.12911	+	0.231554i
$707$	17362.4			0.923596
$708$	−4198.45	+	14972.0i	−0.222864	+	0.794748i
$709$	7330.40			0.388292			0.194146	−	0.980973i	$-0.437806\pi$
$709$	7330.40			0.388292			0.194146	+	0.980973i	$0.437806\pi$
$710$	−29086.1	−	3163.31i	−1.53744	−	0.167207i
$711$	5989.75	−	7051.68i	0.315940	−	0.371953i
$712$	−5103.58	−	1123.38i	−0.268631	−	0.0591300i
$713$	−169.331	−	128.722i	−0.00889412	−	0.00676113i
$714$	3785.96	−	3586.25i	0.198440	−	0.187972i
$715$	8934.04	−	22422.8i	0.467293	−	1.17282i
$716$	−11721.6	−	3949.48i	−0.611813	−	0.206144i
$717$	2109.07	+	12864.7i	0.109853	+	0.670073i
$718$	−16795.2	−	15909.3i	−0.872969	−	0.826920i
$719$	12171.2	−	5631.00i	0.631306	−	0.292073i	−0.0780221	−	0.996952i	$-0.524860\pi$
$719$	12171.2	−	5631.00i	0.631306	−	0.292073i	0.709328	+	0.704878i	$0.248998\pi$
$720$	2518.00	−	1914.13i	0.130334	−	0.0990771i
$721$	−2458.16	+	14994.1i	−0.126972	+	0.774492i
$722$	−14151.2	+	26692.1i	−0.729438	+	1.37587i
$723$	3131.03	−	689.192i	0.161057	−	0.0354514i
$724$	−25840.5	−	11955.1i	−1.32646	−	0.613685i
$725$	2404.77	+	6035.51i	0.123187	+	0.309177i
$726$	−312.061	−	5755.62i	−0.0159527	−	0.294230i
$727$	−9454.38	−	13944.2i	−0.482316	−	0.711363i	0.506211	−	0.862410i	$-0.331046\pi$
$727$	−9454.38	−	13944.2i	−0.482316	−	0.711363i	−0.988527	+	0.151047i	$0.951735\pi$
$728$	11941.4	+	14058.5i	0.607935	+	0.715716i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−7707.78	+	2597.05i	−0.390792	+	0.131673i
$731$	−400.948	+	7395.05i	−0.0202867	+	0.374167i
$732$	14046.3	−	8451.37i	0.709243	−	0.426737i
$733$	−2347.43	−	8454.69i	−0.118287	−	0.426031i	0.880565	−	0.473925i	$-0.157163\pi$
$733$	−2347.43	−	8454.69i	−0.118287	−	0.426031i	−0.998852	+	0.0478932i	$0.984749\pi$
$734$	−7811.34	+	28133.9i	−0.392809	+	1.41477i
$735$	4329.29	+	2604.85i	0.217263	+	0.130723i
$736$	166.738	−	245.920i	0.00835061	−	0.0123162i
$737$	1200.98	−	130.615i	0.0600254	−	0.00652815i
$738$	10424.1	−	1133.69i	0.519941	−	0.0565470i
$739$	18942.9	−	27938.6i	0.942929	−	1.39072i	0.0225253	−	0.999746i	$-0.492829\pi$
$739$	18942.9	−	27938.6i	0.942929	−	1.39072i	0.920404	−	0.390970i	$-0.127860\pi$
$740$	−61097.5	−	36761.1i	−3.03512	−	1.82617i
$741$	−115.353	+	415.464i	−0.00571875	+	0.0205971i
$742$	−13589.7	−	48945.6i	−0.672362	−	2.42163i
$743$	−476.843	+	286.907i	−0.0235446	+	0.0141663i	−0.527278	−	0.849693i	$-0.676787\pi$
$743$	−476.843	+	286.907i	−0.0235446	+	0.0141663i	0.503733	+	0.863859i	$0.331960\pi$
$744$	−405.379	+	7476.78i	−0.0199757	+	0.368430i
$745$	15748.1	−	5306.14i	0.774448	−	0.260942i
$746$	5990.74	+	11299.7i	0.294017	+	0.554574i
$747$	780.695	+	919.105i	0.0382385	+	0.0450178i
$748$	3525.25	+	5199.36i	0.172321	+	0.254154i
$749$	1794.67	+	33100.7i	0.0875510	+	1.61478i
$750$	−3301.33	−	8285.72i	−0.160730	−	0.403402i
$751$	21258.9	+	9835.40i	1.03295	+	0.477895i	0.861746	−	0.507341i	$-0.169371\pi$
$751$	21258.9	+	9835.40i	1.03295	+	0.477895i	0.171207	+	0.985235i	$0.445233\pi$
$752$	5163.56	−	1136.58i	0.250393	−	0.0551157i
$753$	7601.51	−	14338.0i	0.367881	−	0.693898i
$754$	3383.19	−	20636.5i	0.163406	−	0.996735i
$755$	−21368.0	+	16243.6i	−1.03002	+	0.782998i
$756$	6019.53	−	2784.93i	0.289588	−	0.133978i
$757$	−6277.91	−	5946.75i	−0.301419	−	0.285520i	0.522009	−	0.852940i	$-0.325183\pi$
$757$	−6277.91	−	5946.75i	−0.301419	−	0.285520i	−0.823428	+	0.567420i	$0.807941\pi$
$758$	−5769.23	−	35190.7i	−0.276448	−	1.68626i
$759$	−109.847	−	37.0116i	−0.00525320	−	0.00177001i
$760$	−202.482	+	508.190i	−0.00966418	+	0.0242553i
$761$	−16113.0	+	15263.1i	−0.767538	+	0.727050i	−0.967533	−	0.252747i	$-0.918666\pi$
$761$	−16113.0	+	15263.1i	−0.767538	+	0.727050i	0.199995	+	0.979797i	$0.435907\pi$
$762$	−26947.9	−	20485.2i	−1.28113	−	0.973887i
$763$	−30987.3	−	6820.83i	−1.47027	−	0.323631i
$764$	−2852.11	+	3357.76i	−0.135060	+	0.159005i
$765$	−2337.99	−	254.272i	−0.110497	−	0.0120173i
$766$	−24888.1			−1.17395
$767$	−11972.0	−	22722.6i	−0.563604	−	1.06971i
$768$	−3682.49			−0.173021
$769$	−34701.2	−	3773.99i	−1.62725	−	0.176975i	−0.751501	−	0.659732i	$-0.770670\pi$
$769$	−34701.2	−	3773.99i	−1.62725	−	0.176975i	−0.875754	+	0.482757i	$0.839635\pi$
$770$	−26108.7	+	30737.5i	−1.22194	+	1.43858i
$771$	−5649.29	−	1243.50i	−0.263884	−	0.0580852i
$772$	−39918.0	−	30344.9i	−1.86098	−	1.41468i
$773$	−13818.1	+	13089.2i	−0.642953	+	0.609037i	−0.938079	−	0.346421i	$-0.887397\pi$
$773$	−13818.1	+	13089.2i	−0.642953	+	0.609037i	0.295126	+	0.955458i	$0.404638\pi$
$774$	−5925.09	+	14870.9i	−0.275159	+	0.690597i
$775$	12116.4	+	4082.49i	0.561591	+	0.189222i
$776$	1673.33	+	10206.9i	0.0774087	+	0.472172i
$777$	20488.2	+	19407.4i	0.945958	+	0.896059i
$778$	−11321.0	+	5237.65i	−0.521694	+	0.241361i
$779$	533.528	−	405.578i	0.0245387	−	0.0186538i
$780$	4478.11	−	27315.2i	0.205567	−	1.25390i
$781$	−6533.70	+	12323.9i	−0.299352	+	0.564638i
$782$	−102.072	+	22.4677i	−0.00466761	+	0.00102742i
$783$	−2050.92	−	948.856i	−0.0936065	−	0.0433070i
$784$	1081.20	+	2713.60i	0.0492528	+	0.123615i
$785$	−1052.47	−	19411.7i	−0.0478527	−	0.882590i
$786$	−14503.7	−	21391.3i	−0.658179	−	0.970742i
$787$	17950.4	+	21132.8i	0.813039	+	0.957183i	0.999681	−	0.0252446i	$-0.00803646\pi$
$787$	17950.4	+	21132.8i	0.813039	+	0.957183i	−0.186642	+	0.982428i	$0.559761\pi$
$788$	23327.4	+	44000.1i	1.05457	+	1.98914i
$789$	7121.09	−	2399.37i	0.321315	−	0.108264i
$790$	−3492.82	+	64421.2i	−0.157302	+	2.90127i
$791$	19710.0	−	11859.1i	0.885974	−	0.533073i
$792$	1091.65	+	3931.78i	0.0489776	+	0.176401i
$793$	−7243.72	+	26089.5i	−0.324378	+	1.16831i
$794$	9765.02	+	5875.42i	0.436458	+	0.262608i
$795$	−12855.8	+	18960.9i	−0.573522	+	0.845881i
$796$	52453.0	−	5704.60i	2.33561	−	0.254013i
$797$	5502.17	−	598.398i	0.244538	−	0.0265951i	0.0149710	−	0.999888i	$-0.495234\pi$
$797$	5502.17	−	598.398i	0.244538	−	0.0265951i	0.229567	+	0.973293i	$0.426269\pi$
$798$	404.300	−	596.298i	0.0179349	−	0.0264520i
$799$	−3368.50	−	2026.76i	−0.149147	−	0.0897391i
$800$	−4778.01	+	17208.9i	−0.211160	+	0.760531i
$801$	−830.324	−	2990.56i	−0.0366268	−	0.131918i
$802$	−13238.5	+	7965.37i	−0.582879	+	0.350707i
$803$	−209.935	+	3872.02i	−0.00922595	+	0.170163i
$804$	1312.86	−	442.355i	0.0575884	−	0.0194038i
$805$	−184.939	−	348.831i	−0.00809718	−	0.0152729i
$806$	−26642.4	−	31365.9i	−1.16432	−	1.37074i
$807$	1906.66	+	2812.12i	0.0831695	+	0.122666i
$808$	663.187	+	12231.8i	0.0288748	+	0.532564i
$809$	8505.42	+	21347.0i	0.369635	+	0.927714i	0.989699	+	0.143163i	$0.0457272\pi$
$809$	8505.42	+	21347.0i	0.369635	+	0.927714i	−0.620064	+	0.784551i	$0.712893\pi$
$810$	−4613.51	−	2134.44i	−0.200126	−	0.0925883i
$811$	6236.97	−	1372.86i	0.270049	−	0.0594423i	−0.0778814	−	0.996963i	$-0.524816\pi$
$811$	6236.97	−	1372.86i	0.270049	−	0.0594423i	0.347930	+	0.937520i	$0.386885\pi$
$812$	−9630.37	+	18164.8i	−0.416207	+	0.785049i
$813$	3633.21	−	22161.6i	0.156731	−	0.956016i
$814$	−45992.6	+	34962.7i	−1.98039	+	1.50546i
$815$	−44466.3	+	20572.3i	−1.91115	+	0.884192i
$816$	−987.103	−	935.034i	−0.0423475	−	0.0401136i
$817$	165.525	+	1009.66i	0.00708810	+	0.0432355i
$818$	64345.1	+	21680.4i	2.75033	+	0.926695i
$819$	−4054.93	+	10177.1i	−0.173004	+	0.434208i
$820$	−31234.4	+	29586.8i	−1.33018	+	1.26002i
$821$	−33327.1	−	25334.6i	−1.41672	−	1.07696i	−0.984538	−	0.175171i	$-0.943952\pi$
$821$	−33327.1	−	25334.6i	−1.41672	−	1.07696i	−0.432178	−	0.901788i	$-0.642255\pi$
$822$	−31039.2	−	6832.24i	−1.31705	−	0.289905i
$823$	16683.2	−	19641.0i	0.706609	−	0.831884i	−0.285353	−	0.958423i	$-0.592111\pi$
$823$	16683.2	−	19641.0i	0.706609	−	0.831884i	0.991962	+	0.126538i	$0.0403866\pi$
$824$	−10657.1	−	1159.03i	−0.450558	−	0.0490011i
$825$	6967.66			0.294040
$826$	6833.68	+	42365.8i	0.287862	+	1.78462i
$827$	1226.83			0.0515852			0.0257926	−	0.999667i	$-0.491789\pi$
$827$	1226.83			0.0515852			0.0257926	+	0.999667i	$0.491789\pi$
$828$	−132.149	−	14.3721i	−0.00554649	−	0.000603217i
$829$	−3530.47	+	4156.39i	−0.147911	+	0.174134i	−0.831128	−	0.556081i	$-0.812304\pi$
$829$	−3530.47	+	4156.39i	−0.147911	+	0.174134i	0.683217	+	0.730215i	$0.260580\pi$
$830$	−8212.31	−	1807.67i	−0.343438	−	0.0755964i
$831$	8442.22	+	6417.61i	0.352416	+	0.267899i
$832$	33608.3	−	31835.5i	1.40043	−	1.32656i
$833$	803.914	−	2017.67i	0.0334381	−	0.0839234i
$834$	16188.0	+	5454.38i	0.672116	+	0.226462i
$835$	−4260.34	−	25986.9i	−0.176569	−	1.07702i
$836$	630.043	+	596.809i	0.0260652	+	0.0246903i
$837$	−4036.11	+	1867.30i	−0.166677	+	0.0771128i
$838$	46075.0	−	35025.3i	1.89932	−	1.44383i
$839$	−1474.42	+	8993.56i	−0.0606706	+	0.370074i	0.938988	+	0.343950i	$0.111765\pi$
$839$	−1474.42	+	8993.56i	−0.0606706	+	0.370074i	−0.999659	+	0.0261246i	$0.991683\pi$
$840$	−6510.38	+	12279.9i	−0.267416	+	0.504400i
$841$	−16977.6	+	3737.06i	−0.696119	+	0.153227i
$842$	16201.1	+	7495.41i	0.663094	+	0.306780i
$843$	−8356.24	−	20972.6i	−0.341405	−	0.856862i
$844$	−2530.55	−	46673.3i	−0.103205	−	1.90351i
$845$	8106.95	+	11956.9i	0.330044	+	0.486779i
$846$	−5501.03	−	6476.31i	−0.223557	−	0.263192i
$847$	−4384.46	−	8269.96i	−0.177865	−	0.335489i
$848$	−12550.9	+	4228.89i	−0.508254	+	0.171251i
$849$	−389.939	+	7192.00i	−0.0157629	+	0.290729i
$850$	5383.17	−	3238.94i	0.217225	−	0.130700i
$851$	−151.313	−	544.980i	−0.00609511	−	0.0219526i
$852$	−4279.41	+	15413.1i	−0.172078	+	0.619768i
$853$	9731.23	+	5855.09i	0.390611	+	0.235023i	0.697288	−	0.716791i	$-0.254390\pi$
$853$	9731.23	+	5855.09i	0.390611	+	0.235023i	−0.306678	+	0.951813i	$0.599217\pi$
$854$	25388.5	−	37445.2i	1.01730	−	1.50041i
$855$	−322.996	+	35.1279i	−0.0129196	+	0.00140509i
$856$	−23250.7	+	2528.67i	−0.928379	+	0.100967i
$857$	3925.59	−	5789.82i	0.156471	−	0.230778i	−0.741371	−	0.671096i	$-0.765824\pi$
$857$	3925.59	−	5789.82i	0.156471	−	0.230778i	0.897842	+	0.440318i	$0.145134\pi$
$858$	−19216.9	−	11562.4i	−0.764630	−	0.460063i
$859$	−1493.35	+	5378.57i	−0.0593161	+	0.213637i	−0.987269	−	0.159061i	$-0.949153\pi$
$859$	−1493.35	+	5378.57i	−0.0593161	+	0.213637i	0.927953	+	0.372698i	$0.121567\pi$
$860$	−17571.4	−	63286.6i	−0.696722	−	2.50937i
$861$	14590.2	−	8778.65i	0.577507	−	0.347474i
$862$	−872.272	+	16088.1i	−0.0344660	+	0.635688i
$863$	−30192.0	+	10172.9i	−1.19090	+	0.401261i	−0.843846	−	0.536585i	$-0.819714\pi$
$863$	−30192.0	+	10172.9i	−1.19090	+	0.401261i	−0.347053	+	0.937846i	$0.612818\pi$
$864$	−2909.77	−	5488.41i	−0.114575	−	0.216111i
$865$	−29664.7	−	34924.0i	−1.16605	−	1.37278i
$866$	−21753.3	−	32083.8i	−0.853589	−	1.25895i
$867$	−743.221	−	13707.9i	−0.0291132	−	0.536961i
$868$	14976.0	+	37587.0i	0.585622	+	1.46980i
$869$	27915.4	+	12915.0i	1.08972	+	0.504158i
$870$	15389.1	−	3387.40i	0.599700	−	0.132004i
$871$	−1071.85	+	2021.72i	−0.0416971	+	0.0786491i
$872$	3621.63	−	22091.0i	0.140647	−	0.857906i
$873$	−4890.40	+	3717.59i	−0.189593	+	0.144125i
$874$	−13.1044	+	6.06272i	−0.000507164	+	0.000234639i
$875$	−10515.3	−	9960.59i	−0.406264	−	0.384834i
$876$	719.425	+	4388.30i	0.0277478	+	0.169254i
$877$	−34229.6	−	11533.3i	−1.31796	−	0.444073i	−0.429518	−	0.903058i	$-0.641317\pi$
$877$	−34229.6	−	11533.3i	−1.31796	−	0.444073i	−0.888444	+	0.458985i	$0.848213\pi$
$878$	−12236.9	+	30712.3i	−0.470359	+	1.18051i
$879$	−12016.8	+	11382.9i	−0.461112	+	0.436788i
$880$	8370.89	+	6363.38i	0.320662	+	0.243761i
$881$	9158.44	+	2015.93i	0.350234	+	0.0770922i	0.386603	−	0.922246i	$-0.373648\pi$
$881$	9158.44	+	2015.93i	0.350234	+	0.0770922i	−0.0363696	+	0.999338i	$0.511579\pi$
$882$	3039.22	−	3578.04i	0.116027	−	0.136598i
$883$	−1074.67	−	116.878i	−0.0409577	−	0.00445442i	0.0876172	−	0.996154i	$-0.472075\pi$
$883$	−1074.67	−	116.878i	−0.0409577	−	0.00445442i	−0.128575	+	0.991700i	$0.541040\pi$
$884$	−11898.7			−0.452713
$885$	12566.7	−	14717.8i	0.477317	−	0.559021i
$886$	73662.9			2.79317
$887$	29236.8	+	3179.70i	1.10674	+	0.120365i	0.643190	−	0.765706i	$-0.277610\pi$
$887$	29236.8	+	3179.70i	1.10674	+	0.120365i	0.463549	+	0.886072i	$0.346576\pi$
$888$	−12889.9	+	15175.1i	−0.487112	+	0.573473i
$889$	−53684.3	−	11816.8i	−2.02533	−	0.445808i
$890$	17229.1	+	13097.2i	0.648900	+	0.493281i
$891$	−1759.45	+	1666.64i	−0.0661548	+	0.0626651i
$892$	−2632.90	+	6608.08i	−0.0988296	+	0.248044i
$893$	−514.673	−	173.413i	−0.0192865	−	0.00649839i
$894$	−2498.03	−	15237.3i	−0.0934526	−	0.570035i
$895$	11176.4	+	10586.9i	0.417415	+	0.395397i
$896$	−34320.2	+	15878.2i	−1.27964	+	0.592024i
$897$	174.791	−	132.873i	0.00650625	−	0.00494592i
$898$	−8655.14	+	52794.0i	−0.321632	+	1.96187i
$899$	6457.19	−	12179.5i	0.239554	−	0.451847i
$900$	7803.57	−	1717.69i	0.289021	−	0.0636183i
$901$	8937.43	+	4134.90i	0.330465	+	0.152889i
$902$	12902.5	+	32382.7i	0.476280	+	1.19537i
$903$	1407.35	+	25957.0i	0.0518645	+	0.956585i
$904$	9107.53	+	13432.6i	0.335079	+	0.494205i
$905$	22941.0	+	27008.2i	0.842635	+	0.992027i
$906$	11681.9	+	22034.5i	0.428374	+	0.807999i
$907$	39500.1	−	13309.1i	1.44606	−	0.487235i	0.516625	−	0.856212i	$-0.327188\pi$
$907$	39500.1	−	13309.1i	1.44606	−	0.487235i	0.929439	+	0.368977i	$0.120292\pi$
$908$	1947.92	−	35927.2i	0.0711938	−	1.31309i
$909$	−6233.95	+	3750.84i	−0.227466	+	0.136862i
$910$	−20436.7	−	73606.2i	−0.744471	−	2.68134i
$911$	−9954.90	+	35854.3i	−0.362042	+	1.30396i	0.528452	+	0.848963i	$0.322773\pi$
$911$	−9954.90	+	35854.3i	−0.362042	+	1.30396i	−0.890494	+	0.454995i	$0.849641\pi$
$912$	−160.950	−	96.8404i	−0.00584385	−	0.00351613i
$913$	−2249.79	+	3318.19i	−0.0815522	+	0.120281i
$914$	30457.4	−	3312.44i	1.10223	−	0.119875i
$915$	−20282.9	+	2205.90i	−0.732821	+	0.0796991i
$916$	5597.77	−	8256.09i	0.201916	−	0.297805i
$917$	−35961.7	−	21637.4i	−1.29505	−	0.779205i
$918$	−584.596	+	2105.52i	−0.0210180	+	0.0757001i
$919$	−12706.4	−	45764.5i	−0.456090	−	1.64269i	−0.731853	−	0.681463i	$-0.761344\pi$
$919$	−12706.4	−	45764.5i	−0.456090	−	1.64269i	0.275763	−	0.961226i	$-0.411070\pi$
$920$	238.686	−	143.613i	0.00855352	−	0.00514648i
$921$	−1601.96	+	29546.4i	−0.0573141	+	1.05710i
$922$	73012.7	−	24600.8i	2.60797	−	0.878726i
$923$	−12375.9	−	23343.5i	−0.441342	−	0.832460i
$924$	14274.5	+	16805.2i	0.508220	+	0.598323i
$925$	19079.4	+	28140.0i	0.678190	+	1.00026i
$926$	−1267.15	−	23371.3i	−0.0449689	−	0.829403i
$927$	−2356.60	−	5914.63i	−0.0834963	−	0.209560i
$928$	17476.5	+	8085.51i	0.618206	+	0.286013i
$929$	50176.4	−	11044.7i	1.77205	−	0.390058i	0.795603	−	0.605818i	$-0.207154\pi$
$929$	50176.4	−	11044.7i	1.77205	−	0.390058i	0.976446	+	0.215761i	$0.0692231\pi$
$930$	14525.3	−	27397.7i	0.512156	−	0.966028i
$931$	48.5434	−	296.101i	0.00170886	−	0.0104236i
$932$	27850.1	−	21171.1i	0.978821	−	0.744080i
$933$	5003.62	−	2314.92i	0.175575	−	0.0812294i
$934$	−24228.7	−	22950.7i	−0.848810	−	0.804035i
$935$	−1264.86	−	7715.31i	−0.0442410	−	0.269858i
$936$	−7324.60	−	2467.94i	−0.255782	−	0.0861830i
$937$	−16219.8	+	40708.7i	−0.565506	+	1.41931i	0.316736	+	0.948514i	$0.397413\pi$
$937$	−16219.8	+	40708.7i	−0.565506	+	1.41931i	−0.882241	+	0.470798i	$0.843966\pi$
$938$	2775.75	−	2629.33i	0.0966219	−	0.0915251i
$939$	15693.8	+	11930.1i	0.545419	+	0.414616i
$940$	34049.7	+	7494.90i	1.18147	+	0.260060i
$941$	−5830.88	+	6864.64i	−0.201999	+	0.237812i	−0.853829	−	0.520553i	$-0.825726\pi$
$941$	−5830.88	+	6864.64i	−0.201999	+	0.237812i	0.651830	+	0.758365i	$0.274002\pi$
$942$	−17957.2	−	1952.96i	−0.621100	−	0.0675486i
$943$	−341.264			−0.0117848
$944$	10933.3	−	2377.13i	0.376957	−	0.0819586i
$945$	−8254.87			−0.284160
$946$	−52904.7	−	5753.73i	−1.81827	−	0.197748i
$947$	−5508.19	+	6484.74i	−0.189010	+	0.222519i	−0.848502	−	0.529192i	$-0.822495\pi$
$947$	−5508.19	+	6484.74i	−0.189010	+	0.222519i	0.659493	+	0.751711i	$0.270771\pi$
$948$	34448.3	+	7582.64i	1.18020	+	0.259781i
$949$	−5847.33	−	4445.03i	−0.200013	−	0.152046i
$950$	630.111	−	596.873i	0.0215195	−	0.0203843i
$951$	−6566.57	+	16480.9i	−0.223907	+	0.561964i
$952$	5661.98	+	1907.74i	0.192758	+	0.0649478i
$953$	885.046	+	5398.54i	0.0300834	+	0.183501i	0.997594	−	0.0693310i	$-0.0220864\pi$
$953$	885.046	+	5398.54i	0.0300834	+	0.183501i	−0.967510	+	0.252831i	$0.918638\pi$
$954$	15453.1	+	14638.0i	0.524438	+	0.496774i
$955$	4976.40	−	2302.33i	0.168621	−	0.0780122i
$956$	−39565.8	+	30077.1i	−1.33855	+	1.01754i
$957$	1215.38	−	7413.49i	0.0410530	−	0.250412i
$958$	−35308.1	+	66598.2i	−1.19077	+	2.24602i
$959$	−50404.8	+	11094.9i	−1.69724	+	0.373591i
$960$	31658.2	+	14646.7i	1.06434	+	0.492416i
$961$	985.326	+	2472.98i	0.0330746	+	0.0830110i
$962$	−5924.52	−	109271.i	−0.198559	−	3.66221i
$963$	−7795.17	−	11497.0i	−0.260847	−	0.384721i
$964$	7912.64	+	9315.48i	0.264366	+	0.311236i
$965$	29232.1	+	55137.5i	0.975143	+	1.83932i
$966$	−347.650	+	117.137i	−0.0115792	+	0.00390147i
$967$	−1511.15	+	27871.6i	−0.0502538	+	0.926877i	0.859347	+	0.511393i	$0.170871\pi$
$967$	−1511.15	+	27871.6i	−0.0502538	+	0.926877i	−0.909601	+	0.415484i	$0.863612\pi$
$968$	5658.67	−	3404.71i	0.187889	−	0.113049i
$969$	37.3643	+	134.574i	0.00123871	+	0.00446145i
$970$	11459.7	−	41274.0i	0.379327	−	1.36621i
$971$	−40572.4	−	24411.6i	−1.34092	−	0.806803i	−0.349425	−	0.936964i	$-0.613623\pi$
$971$	−40572.4	−	24411.6i	−1.34092	−	0.806803i	−0.991493	+	0.130161i	$0.958451\pi$
$972$	−1559.67	+	2300.33i	−0.0514674	+	0.0759087i
$973$	27577.3	−	2999.21i	0.908621	−	0.0988185i
$974$	−742.252	+	80.7248i	−0.0244182	+	0.00265564i
$975$	−7406.51	+	10923.8i	−0.243280	+	0.358811i
$976$	−10107.0	−	6081.20i	−0.331474	−	0.199441i
$977$	3902.70	−	14056.2i	0.127798	−	0.460286i	−0.871763	−	0.489928i	$-0.837023\pi$
$977$	3902.70	−	14056.2i	0.127798	−	0.460286i	0.999561	+	0.0296424i	$0.00943687\pi$
$978$	12178.9	+	43864.4i	0.398199	+	1.43418i
$979$	8841.03	−	5319.47i	0.288621	−	0.173658i
$980$	−1042.83	+	19233.9i	−0.0339919	+	0.626943i
$981$	12599.4	−	4245.25i	0.410061	−	0.138165i
$982$	−23721.4	−	44743.3i	−0.770855	−	1.45399i
$983$	10827.6	+	12747.2i	0.351319	+	0.413605i	0.909229	−	0.416297i	$-0.136672\pi$
$983$	10827.6	+	12747.2i	0.351319	+	0.413605i	−0.557910	+	0.829902i	$0.688396\pi$
$984$	6741.81	+	9943.42i	0.218416	+	0.322139i
$985$	−3355.68	−	61891.9i	−0.108549	−	2.00207i
$986$	−2507.20	−	6292.59i	−0.0809791	−	0.203242i
$987$	−12523.5	−	5793.97i	−0.403877	−	0.186853i
$988$	−1605.39	+	353.374i	−0.0516947	+	0.0113789i
$989$	244.036	−	460.301i	0.00784620	−	0.0147995i
$990$	2733.98	−	16676.5i	0.0877693	−	0.535369i
$991$	48815.4	−	37108.5i	1.56476	−	1.18950i	0.670529	−	0.741883i	$-0.266067\pi$
$991$	48815.4	−	37108.5i	1.56476	−	1.18950i	0.894227	−	0.447614i	$-0.147726\pi$
$992$	34393.0	−	15911.9i	1.10078	−	0.509277i
$993$	−601.944	−	570.192i	−0.0192368	−	0.0182220i
$994$	7142.01	+	43564.4i	0.227898	+	1.39012i
$995$	−62230.4	−	20967.9i	−1.98275	−	0.668067i
$996$	−1701.68	+	4270.90i	−0.0541364	+	0.135872i
$997$	−7366.62	+	6978.03i	−0.234005	+	0.221661i	−0.795712	−	0.605675i	$-0.792903\pi$
$997$	−7366.62	+	6978.03i	−0.234005	+	0.221661i	0.561707	+	0.827336i	$0.310145\pi$
$998$	53097.2	+	40363.4i	1.68413	+	1.28024i
$999$	−11548.9	−	2542.10i	−0.365756	−	0.0805089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.b.4.2	✓	420
59.15	even	29	inner	177.4.e.b.133.2	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.b.4.2	✓	420	1.1	even	1	trivial
177.4.e.b.133.2	yes	420	59.15	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)

\(f(q)\)	\(=\)	\(q+(-4.38291 - 0.476671i) q^{2} +(1.94216 - 2.28649i) q^{3} +(11.1698 + 2.45865i) q^{4} +(-11.3321 - 8.61446i) q^{5} +(-9.60221 + 9.09570i) q^{6} +(-7.94992 + 19.9528i) q^{7} +(-14.3603 - 4.83855i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(-4.38291 - 0.476671i) q^{2} +(1.94216 - 2.28649i) q^{3} +(11.1698 + 2.45865i) q^{4} +(-11.3321 - 8.61446i) q^{5} +(-9.60221 + 9.09570i) q^{6} +(-7.94992 + 19.9528i) q^{7} +(-14.3603 - 4.83855i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(45.5615 + 43.1581i) q^{10} +(27.1545 - 12.5630i) q^{11} +(27.3151 - 20.7644i) q^{12} +(-9.16870 + 55.9266i) q^{13} +(44.3547 - 83.6619i) q^{14} +(-41.7056 + 9.18010i) q^{15} +(-22.4070 - 10.3666i) q^{16} +(6.79469 + 17.0534i) q^{17} +(2.14817 + 39.6206i) q^{18} +(1.42321 + 2.09907i) q^{19} +(-105.397 - 124.083i) q^{20} +(30.1818 + 56.9289i) q^{21} +(-125.004 + 42.1188i) q^{22} +(0.0699143 - 1.28949i) q^{23} +(-38.9533 + 23.4374i) q^{24} +(20.7672 + 74.7965i) q^{25} +(66.8442 - 240.751i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-137.855 + 203.322i) q^{28} +(83.2049 - 9.04907i) q^{29} +(187.168 - 20.3558i) q^{30} +(92.4324 - 136.328i) q^{31} +(197.142 + 118.616i) q^{32} +(24.0132 - 86.4877i) q^{33} +(-21.6517 - 77.9824i) q^{34} +(261.972 - 157.623i) q^{35} +(5.57275 - 102.783i) q^{36} +(415.049 - 139.846i) q^{37} +(-5.23722 - 9.87845i) q^{38} +(110.068 + 129.582i) q^{39} +(121.051 + 178.537i) q^{40} +(-14.3068 - 263.874i) q^{41} +(-105.148 - 263.901i) q^{42} +(366.147 + 169.398i) q^{43} +(334.197 - 73.5623i) q^{44} +(-60.0088 + 113.189i) q^{45} +(-0.921092 + 5.61841i) q^{46} +(-170.485 + 129.599i) q^{47} +(-67.2211 + 31.0998i) q^{48} +(-85.8961 - 81.3651i) q^{49} +(-55.3673 - 337.726i) q^{50} +(52.1887 + 17.5844i) q^{51} +(-239.916 + 602.144i) q^{52} +(389.456 - 368.912i) q^{53} +(94.7641 + 72.0378i) q^{54} +(-415.941 - 91.5556i) q^{55} +(210.706 - 248.062i) q^{56} +(7.56359 + 0.822590i) q^{57} -368.993 q^{58} +(-361.484 + 273.329i) q^{59} -488.412 q^{60} +(474.964 + 51.6555i) q^{61} +(-470.106 + 553.452i) q^{62} +(188.785 + 41.5547i) q^{63} +(-650.278 - 494.328i) q^{64} +(585.678 - 554.784i) q^{65} +(-146.474 + 367.622i) q^{66} +(38.2631 + 12.8923i) q^{67} +(33.9667 + 207.188i) q^{68} +(-2.81263 - 2.66426i) q^{69} +(-1223.33 + 565.975i) q^{70} +(-371.141 + 282.134i) q^{71} +(-22.0641 + 134.585i) q^{72} +(-60.7073 + 114.506i) q^{73} +(-1885.78 + 415.092i) q^{74} +(211.354 + 97.7829i) q^{75} +(10.7360 + 26.9453i) q^{76} +(34.7910 + 641.683i) q^{77} +(-420.652 - 620.415i) q^{78} +(665.528 + 783.520i) q^{79} +(164.617 + 310.500i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-63.0753 + 1163.36i) q^{82} +(-114.811 + 69.0795i) q^{83} +(197.155 + 710.088i) q^{84} +(69.9074 - 251.784i) q^{85} +(-1524.04 - 916.986i) q^{86} +(140.906 - 207.822i) q^{87} +(-450.733 + 49.0202i) q^{88} +(342.833 - 37.2853i) q^{89} +(316.967 - 467.491i) q^{90} +(-1043.00 - 627.553i) q^{91} +(3.95134 - 14.2314i) q^{92} +(-132.193 - 476.115i) q^{93} +(808.996 - 486.757i) q^{94} +(1.95442 - 36.0471i) q^{95} +(654.096 - 220.390i) q^{96} +(-319.715 - 603.046i) q^{97} +(337.691 + 397.561i) q^{98} +(-151.115 - 222.879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Introduction

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