LMFDB - Embedded newform 177.4.e.a.133.3

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			133.3
Character	$\chi$	$=$	177.133
Dual form			177.4.e.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.04316 + 0.439720i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(8.34080 - 1.83595i) q^{4} +(2.28067 - 1.73372i) q^{5} +(8.85787 + 8.39062i) q^{6} +(2.30882 + 5.79471i) q^{7} +(-2.08305 + 0.701862i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})$	\(q+(-4.04316 + 0.439720i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(8.34080 - 1.83595i) q^{4} +(2.28067 - 1.73372i) q^{5} +(8.85787 + 8.39062i) q^{6} +(2.30882 + 5.79471i) q^{7} +(-2.08305 + 0.701862i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-8.45878 + 8.01258i) q^{10} +(-41.5638 - 19.2295i) q^{11} +(-20.3970 - 15.5054i) q^{12} +(6.71107 + 40.9357i) q^{13} +(-11.8830 - 22.4137i) q^{14} +(-8.39357 - 1.84756i) q^{15} +(-53.8955 + 24.9347i) q^{16} +(-20.7342 + 52.0389i) q^{17} +(1.98165 - 36.5493i) q^{18} +(46.0877 - 67.9743i) q^{19} +(15.8396 - 18.6479i) q^{20} +(8.76543 - 16.5333i) q^{21} +(176.505 + 59.4713i) q^{22} +(-9.16527 - 169.043i) q^{23} +(5.65042 + 3.39974i) q^{24} +(-31.2454 + 112.536i) q^{25} +(-45.1342 - 162.559i) q^{26} +(23.1351 - 13.9200i) q^{27} +(29.8963 + 44.0937i) q^{28} +(194.923 + 21.1992i) q^{29} +(34.7489 + 3.77917i) q^{30} +(177.887 + 262.363i) q^{31} +(222.012 - 133.580i) q^{32} +(36.7556 + 132.382i) q^{33} +(60.9491 - 219.519i) q^{34} +(15.3121 + 9.21299i) q^{35} +(4.16135 + 76.7516i) q^{36} +(237.937 + 80.1704i) q^{37} +(-156.450 + 295.096i) q^{38} +(80.5650 - 94.8485i) q^{39} +(-3.53393 + 5.21216i) q^{40} +(10.3693 - 191.251i) q^{41} +(-28.1700 + 70.7013i) q^{42} +(432.349 - 200.026i) q^{43} +(-381.980 - 84.0801i) q^{44} +(12.0772 + 22.7800i) q^{45} +(111.388 + 679.439i) q^{46} +(-135.112 - 102.710i) q^{47} +(161.687 + 74.8042i) q^{48} +(220.768 - 209.123i) q^{49} +(76.8458 - 468.738i) q^{50} +(159.255 - 53.6594i) q^{51} +(131.132 + 329.116i) q^{52} +(50.7048 + 48.0301i) q^{53} +(-87.4182 + 66.4536i) q^{54} +(-128.132 + 28.2040i) q^{55} +(-8.87649 - 10.4502i) q^{56} +(-244.932 + 26.6380i) q^{57} -797.427 q^{58} +(240.142 + 384.332i) q^{59} -73.4012 q^{60} +(-442.794 + 48.1568i) q^{61} +(-834.589 - 982.555i) q^{62} +(-54.8271 + 12.0684i) q^{63} +(-460.688 + 350.206i) q^{64} +(86.2770 + 81.7259i) q^{65} +(-206.820 - 519.078i) q^{66} +(513.930 - 173.163i) q^{67} +(-77.3991 + 472.113i) q^{68} +(-368.715 + 349.265i) q^{69} +(-65.9604 - 30.5165i) q^{70} +(219.953 + 167.204i) q^{71} +(-3.20054 - 19.5224i) q^{72} +(-367.606 - 693.379i) q^{73} +(-997.271 - 219.516i) q^{74} +(317.995 - 147.120i) q^{75} +(259.611 - 651.575i) q^{76} +(15.4657 - 285.248i) q^{77} +(-284.030 + 418.913i) q^{78} +(-295.863 + 348.317i) q^{79} +(-79.6882 + 150.308i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(42.1720 + 777.816i) q^{82} +(1.75052 + 1.05325i) q^{83} +(42.7563 - 153.994i) q^{84} +(42.9331 + 154.631i) q^{85} +(-1660.10 + 998.848i) q^{86} +(-330.100 - 486.862i) q^{87} +(100.076 + 10.8839i) q^{88} +(1078.35 + 117.277i) q^{89} +(-58.8469 - 86.7927i) q^{90} +(-221.716 + 133.402i) q^{91} +(-386.801 - 1393.13i) q^{92} +(254.405 - 916.286i) q^{93} +(591.444 + 355.860i) q^{94} +(-12.7376 - 234.931i) q^{95} +(-736.610 - 248.193i) q^{96} +(274.295 - 517.375i) q^{97} +(-800.646 + 942.593i) q^{98} +(231.304 - 341.147i) 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 $

$2$	−4.04316	+	0.439720i	−1.42947	+	0.155464i	−0.789885	−	0.613255i	$-0.789860\pi$
$2$	−4.04316	+	0.439720i	−1.42947	+	0.155464i	−0.639587	+	0.768719i	$0.720894\pi$
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$4$	8.34080	−	1.83595i	1.04260	−	0.229494i
$5$	2.28067	−	1.73372i	0.203990	−	0.155069i	−0.498192	−	0.867067i	$-0.666003\pi$
$5$	2.28067	−	1.73372i	0.203990	−	0.155069i	0.702182	+	0.711998i	$0.252209\pi$
$6$	8.85787	+	8.39062i	0.602702	+	0.570909i
$7$	2.30882	+	5.79471i	0.124665	+	0.312885i	0.978042	−	0.208409i	$-0.0668286\pi$
$7$	2.30882	+	5.79471i	0.124665	+	0.312885i	−0.853377	+	0.521294i	$0.825449\pi$
$8$	−2.08305	+	0.701862i	−0.0920588	+	0.0310182i
$9$	−1.45604	+	8.88144i	−0.0539273	+	0.328942i
$10$	−8.45878	+	8.01258i	−0.267490	+	0.253380i
$11$	−41.5638	−	19.2295i	−1.13927	−	0.527082i	−0.242750	−	0.970089i	$-0.578050\pi$
$11$	−41.5638	−	19.2295i	−1.13927	−	0.527082i	−0.896518	+	0.443007i	$0.853912\pi$
$12$	−20.3970	−	15.5054i	−0.490677	−	0.373003i
$13$	6.71107	+	40.9357i	0.143178	+	0.873348i	0.956542	+	0.291593i	$0.0941854\pi$
$13$	6.71107	+	40.9357i	0.143178	+	0.873348i	−0.813364	+	0.581755i	$0.802366\pi$
$14$	−11.8830	−	22.4137i	−0.226847	−	0.427880i
$15$	−8.39357	−	1.84756i	−0.144481	−	0.0318026i
$16$	−53.8955	+	24.9347i	−0.842118	+	0.389605i
$17$	−20.7342	+	52.0389i	−0.295811	+	0.742429i	0.703680	+	0.710517i	$0.251539\pi$
$17$	−20.7342	+	52.0389i	−0.295811	+	0.742429i	−0.999491	+	0.0319118i	$0.989840\pi$
$18$	1.98165	−	36.5493i	0.0259488	−	0.478597i
$19$	46.0877	−	67.9743i	0.556487	−	0.820757i	−0.440546	−	0.897730i	$-0.645215\pi$
$19$	46.0877	−	67.9743i	0.556487	−	0.820757i	0.997033	+	0.0769733i	$0.0245256\pi$
$20$	15.8396	−	18.6479i	0.177092	−	0.208489i
$21$	8.76543	−	16.5333i	0.0910844	−	0.171803i
$22$	176.505	+	59.4713i	1.71049	+	0.576333i
$23$	−9.16527	−	169.043i	−0.0830909	−	1.53252i	−0.681791	−	0.731547i	$-0.738798\pi$
$23$	−9.16527	−	169.043i	−0.0830909	−	1.53252i	0.598700	−	0.800974i	$-0.295684\pi$
$24$	5.65042	+	3.39974i	0.0480578	+	0.0289154i
$25$	−31.2454	+	112.536i	−0.249963	+	0.900285i
$26$	−45.1342	−	162.559i	−0.340444	−	1.22617i
$27$	23.1351	−	13.9200i	0.164902	−	0.0992184i
$28$	29.8963	+	44.0937i	0.201781	+	0.297604i
$29$	194.923	+	21.1992i	1.24815	+	0.135744i	0.708236	−	0.705976i	$-0.249491\pi$
$29$	194.923	+	21.1992i	1.24815	+	0.135744i	0.539914	+	0.841720i	$0.318457\pi$
$30$	34.7489	+	3.77917i	0.211475	+	0.0229993i
$31$	177.887	+	262.363i	1.03062	+	1.52006i	0.843070	+	0.537803i	$0.180746\pi$
$31$	177.887	+	262.363i	1.03062	+	1.52006i	0.187554	+	0.982254i	$0.439944\pi$
$32$	222.012	−	133.580i	1.22645	−	0.737932i
$33$	36.7556	+	132.382i	0.193889	+	0.698324i
$34$	60.9491	−	219.519i	0.307432	−	1.10727i
$35$	15.3121	+	9.21299i	0.0739491	+	0.0444937i
$36$	4.16135	+	76.7516i	0.0192655	+	0.355331i
$37$	237.937	+	80.1704i	1.05721	+	0.356215i	0.793615	−	0.608420i	$-0.208196\pi$
$37$	237.937	+	80.1704i	1.05721	+	0.356215i	0.263592	+	0.964634i	$0.415093\pi$
$38$	−156.450	+	295.096i	−0.667884	+	1.25976i
$39$	80.5650	−	94.8485i	0.330788	−	0.389434i
$40$	−3.53393	+	5.21216i	−0.0139691	+	0.0206029i
$41$	10.3693	−	191.251i	0.0394979	−	0.728496i	−0.909978	−	0.414656i	$-0.863902\pi$
$41$	10.3693	−	191.251i	0.0394979	−	0.728496i	0.949476	−	0.313840i	$-0.101615\pi$
$42$	−28.1700	+	70.7013i	−0.103493	+	0.259749i
$43$	432.349	−	200.026i	1.53331	−	0.709387i	0.541937	−	0.840419i	$-0.317691\pi$
$43$	432.349	−	200.026i	1.53331	−	0.709387i	0.991378	+	0.131032i	$0.0418292\pi$
$44$	−381.980	−	84.0801i	−1.30876	−	0.288081i
$45$	12.0772	+	22.7800i	0.0400081	+	0.0754633i
$46$	111.388	+	679.439i	0.357029	+	2.17778i
$47$	−135.112	−	102.710i	−0.419323	−	0.318761i	0.374148	−	0.927369i	$-0.377935\pi$
$47$	−135.112	−	102.710i	−0.419323	−	0.318761i	−0.793471	+	0.608608i	$0.791728\pi$
$48$	161.687	+	74.8042i	0.486197	+	0.224939i
$49$	220.768	−	209.123i	0.643640	−	0.609688i
$50$	76.8458	−	468.738i	0.217353	−	1.32579i
$51$	159.255	−	53.6594i	0.437259	−	0.147330i
$52$	131.132	+	329.116i	0.349706	+	0.877695i
$53$	50.7048	+	48.0301i	0.131412	+	0.124480i	0.750583	−	0.660776i	$-0.229773\pi$
$53$	50.7048	+	48.0301i	0.131412	+	0.124480i	−0.619171	+	0.785256i	$0.712531\pi$
$54$	−87.4182	+	66.4536i	−0.220298	+	0.167466i
$55$	−128.132	+	28.2040i	−0.314133	+	0.0691459i
$56$	−8.87649	−	10.4502i	−0.0211816	−	0.0249369i
$57$	−244.932	+	26.6380i	−0.569158	+	0.0618997i
$58$	−797.427			−1.80530
$59$	240.142	+	384.332i	0.529894	+	0.848064i
$59$	240.142	+	384.332i	0.529894	+	0.848064i
$60$	−73.4012			−0.157934
$61$	−442.794	+	48.1568i	−0.929410	+	0.101079i	−0.560285	−	0.828300i	$-0.689308\pi$
$61$	−442.794	+	48.1568i	−0.929410	+	0.101079i	−0.369126	+	0.929380i	$0.620343\pi$
$62$	−834.589	−	982.555i	−1.70956	−	2.01265i
$63$	−54.8271	+	12.0684i	−0.109644	+	0.0241345i
$64$	−460.688	+	350.206i	−0.899781	+	0.683996i
$65$	86.2770	+	81.7259i	0.164636	+	0.155952i
$66$	−206.820	−	519.078i	−0.385723	−	0.968092i
$67$	513.930	−	173.163i	0.937113	−	0.315750i	0.191015	−	0.981587i	$-0.438822\pi$
$67$	513.930	−	173.163i	0.937113	−	0.315750i	0.746097	+	0.665837i	$0.231925\pi$
$68$	−77.3991	+	472.113i	−0.138030	+	0.841943i
$69$	−368.715	+	349.265i	−0.643305	+	0.609371i
$70$	−65.9604	−	30.5165i	−0.112625	−	0.0521061i
$71$	219.953	+	167.204i	0.367657	+	0.279486i	0.772648	−	0.634835i	$-0.218932\pi$
$71$	219.953	+	167.204i	0.367657	+	0.279486i	−0.404990	+	0.914321i	$0.632725\pi$
$72$	−3.20054	−	19.5224i	−0.00523871	−	0.0319547i
$73$	−367.606	−	693.379i	−0.589384	−	1.11170i	−0.981443	−	0.191756i	$-0.938582\pi$
$73$	−367.606	−	693.379i	−0.589384	−	1.11170i	0.392058	−	0.919940i	$-0.371763\pi$
$74$	−997.271	−	219.516i	−1.56663	−	0.344841i
$75$	317.995	−	147.120i	0.489585	−	0.226506i
$76$	259.611	−	651.575i	0.391835	−	0.983431i
$77$	15.4657	−	285.248i	0.0228893	−	0.422169i
$78$	−284.030	+	418.913i	−0.412309	+	0.608110i
$79$	−295.863	+	348.317i	−0.421357	+	0.496060i	−0.931353	−	0.364117i	$-0.881371\pi$
$79$	−295.863	+	348.317i	−0.421357	+	0.496060i	0.509996	+	0.860177i	$0.329647\pi$
$80$	−79.6882	+	150.308i	−0.111368	+	0.210062i
$81$	−76.7599	−	25.8634i	−0.105295	−	0.0354779i
$82$	42.1720	+	777.816i	0.0567941	+	1.04751i
$83$	1.75052	+	1.05325i	0.00231500	+	0.00139289i	0.516711	−	0.856160i	$-0.327156\pi$
$83$	1.75052	+	1.05325i	0.00231500	+	0.00139289i	−0.514396	+	0.857553i	$0.671984\pi$
$84$	42.7563	−	153.994i	0.0555369	−	0.200026i
$85$	42.9331	+	154.631i	0.0547853	+	0.197319i
$86$	−1660.10	+	998.848i	−2.08155	+	1.25242i
$87$	−330.100	−	486.862i	−0.406787	−	0.599966i
$88$	100.076	+	10.8839i	0.121229	+	0.0131844i
$89$	1078.35	+	117.277i	1.28432	+	0.139678i	0.724696	−	0.689069i	$-0.241980\pi$
$89$	1078.35	+	117.277i	1.28432	+	0.139678i	0.559623	+	0.828747i	$0.310946\pi$
$90$	−58.8469	−	86.7927i	−0.0689223	−	0.101653i
$91$	−221.716	+	133.402i	−0.255408	+	0.153674i
$92$	−386.801	−	1393.13i	−0.438335	−	1.57874i
$93$	254.405	−	916.286i	0.283663	−	1.02166i
$94$	591.444	+	355.860i	0.648966	+	0.390470i
$95$	−12.7376	−	234.931i	−0.0137563	−	0.253720i
$96$	−736.610	−	248.193i	−0.783125	−	0.263865i
$97$	274.295	−	517.375i	0.287118	−	0.541562i	−0.697435	−	0.716648i	$-0.745676\pi$
$97$	274.295	−	517.375i	0.287118	−	0.541562i	0.984553	+	0.175086i	$0.0560204\pi$
$98$	−800.646	+	942.593i	−0.825280	+	0.971595i
$99$	231.304	−	341.147i	0.234817	−	0.346329i
$100$	−54.0017	+	996.003i	−0.0540017	+	0.996003i
$101$	−147.925	+	371.264i	−0.145734	+	0.365764i	−0.983664	−	0.180013i	$-0.942386\pi$
$101$	−147.925	+	371.264i	−0.145734	+	0.365764i	0.837931	+	0.545777i	$0.183765\pi$
$102$	−620.299	+	286.981i	−0.602145	+	0.278582i
$103$	1015.31	+	223.487i	0.971278	+	0.213794i	0.672147	−	0.740418i	$-0.265372\pi$
$103$	1015.31	+	223.487i	0.971278	+	0.213794i	0.299131	+	0.954212i	$0.403303\pi$
$104$	−42.7107	−	80.5610i	−0.0402705	−	0.0759582i
$105$	−8.67317	−	52.9040i	−0.00806110	−	0.0491705i
$106$	−226.127	−	171.897i	−0.207202	−	0.157511i
$107$	1122.02	+	519.102i	1.01374	+	0.469005i	0.855172	−	0.518344i	$-0.173451\pi$
$107$	1122.02	+	519.102i	1.01374	+	0.469005i	0.158565	+	0.987349i	$0.449313\pi$
$108$	167.409	−	158.579i	0.149157	−	0.141289i
$109$	−208.261	+	1270.34i	−0.183007	+	1.11630i	0.722313	+	0.691566i	$0.243079\pi$
$109$	−208.261	+	1270.34i	−0.183007	+	1.11630i	−0.905320	+	0.424730i	$0.860369\pi$
$110$	505.656	−	170.375i	0.438295	−	0.147679i
$111$	−278.804	−	699.744i	−0.238404	−	0.598349i
$112$	−268.925	−	254.739i	−0.226884	−	0.214916i
$113$	663.976	−	504.741i	0.552758	−	0.420195i	−0.291155	−	0.956676i	$-0.594040\pi$
$113$	663.976	−	504.741i	0.552758	−	0.420195i	0.843913	+	0.536480i	$0.180246\pi$
$114$	978.585	−	215.403i	0.803973	−	0.176968i
$115$	−313.978	−	369.643i	−0.254596	−	0.299734i
$116$	1664.74	−	181.051i	1.33247	−	0.144915i
$117$	−373.340			−0.295002
$118$	−1139.93	−	1448.32i	−0.889313	−	1.12990i
$119$	−349.422			−0.269172
$120$	18.7810	−	2.04255i	0.0142872	−	0.00155382i
$121$	496.105	+	584.060i	0.372731	+	0.438813i
$122$	1769.11	−	389.411i	1.31285	−	0.288980i
$123$	−457.431	+	347.730i	−0.335327	+	0.254909i
$124$	1965.40	+	1861.73i	1.42337	+	1.34829i
$125$	256.393	+	643.499i	0.183460	+	0.460450i
$126$	216.368	−	72.9029i	0.152981	−	0.0515453i
$127$	123.747	−	754.826i	0.0864630	−	0.527401i	−0.907709	−	0.419599i	$-0.862171\pi$
$127$	123.747	−	754.826i	0.0864630	−	0.527401i	0.994172	−	0.107802i	$-0.0343812\pi$
$128$	203.799	−	193.049i	0.140730	−	0.133307i
$129$	−1297.05	−	600.077i	−0.885260	−	0.409565i
$130$	−384.768	−	292.493i	−0.259588	−	0.197333i
$131$	142.372	+	868.429i	0.0949547	+	0.579198i	0.990854	+	0.134940i	$0.0430843\pi$
$131$	142.372	+	868.429i	0.0949547	+	0.579198i	−0.895899	+	0.444258i	$0.853467\pi$
$132$	549.617	+	1036.69i	0.362409	+	0.683577i
$133$	500.300	+	110.124i	0.326177	+	0.0717969i
$134$	−2001.76	+	926.111i	−1.29049	+	0.597044i
$135$	28.6304	−	71.8568i	0.0182527	−	0.0458108i
$136$	6.66628	−	122.952i	0.00420315	−	0.0775226i
$137$	−928.269	+	1369.09i	−0.578886	+	0.853793i	−0.998547	−	0.0538883i	$-0.982839\pi$
$137$	−928.269	+	1369.09i	−0.578886	+	0.853793i	0.419661	+	0.907681i	$0.362149\pi$
$138$	1337.19	−	1574.27i	0.824851	−	0.971090i
$139$	199.779	−	376.823i	0.121907	−	0.229940i	−0.815046	−	0.579396i	$-0.803289\pi$
$139$	199.779	−	376.823i	0.121907	−	0.229940i	0.936953	+	0.349456i	$0.113633\pi$
$140$	144.630	+	48.7315i	0.0873104	+	0.0294183i
$141$	27.5652	+	508.411i	0.0164639	+	0.303659i
$142$	−962.829	−	579.315i	−0.569006	−	0.342359i
$143$	508.234	−	1830.49i	0.297208	−	1.07044i
$144$	−142.982	−	514.976i	−0.0827444	−	0.298018i
$145$	481.310	−	289.595i	0.275660	−	0.165859i
$146$	1791.18	+	2641.80i	1.01534	+	1.49751i
$147$	−906.924	−	98.6339i	−0.508856	−	0.0553414i
$148$	2131.78	+	231.845i	1.18399	+	0.128767i
$149$	971.328	+	1432.60i	0.534056	+	0.787673i	0.995013	−	0.0997495i	$-0.0318041\pi$
$149$	971.328	+	1432.60i	0.534056	+	0.787673i	−0.460957	+	0.887422i	$0.652494\pi$
$150$	−1221.01	+	734.658i	−0.664634	+	0.399897i
$151$	829.055	+	2985.99i	0.446805	+	1.60925i	0.753507	+	0.657440i	$0.228361\pi$
$151$	829.055	+	2985.99i	0.446805	+	1.60925i	−0.306702	+	0.951806i	$0.599225\pi$
$152$	−48.2945	+	173.941i	−0.0257711	+	0.0928191i
$153$	−431.991	−	259.920i	−0.228264	−	0.137342i
$154$	62.8989	+	1160.10i	0.0329126	+	0.607037i
$155$	860.566	+	289.959i	0.445951	+	0.150258i
$156$	497.840	−	939.026i	0.255507	−	0.481937i
$157$	1570.87	−	1849.37i	0.798527	−	0.940099i	−0.200690	−	0.979655i	$-0.564318\pi$
$157$	1570.87	−	1849.37i	0.798527	−	0.940099i	0.999217	+	0.0395559i	$0.0125943\pi$
$158$	1043.06	−	1538.40i	0.525199	−	0.774610i
$159$	11.3435	−	209.218i	0.00565783	−	0.104353i
$160$	274.746	−	689.559i	0.135753	−	0.340715i
$161$	958.397	−	443.402i	0.469144	−	0.217049i
$162$	321.725	+	70.8170i	0.156032	+	0.0343451i
$163$	−1453.13	−	2740.89i	−0.698267	−	1.31707i	−0.938136	−	0.346267i	$-0.887449\pi$
$163$	−1453.13	−	2740.89i	−0.698267	−	1.31707i	0.239869	−	0.970805i	$-0.422896\pi$
$164$	−264.638	−	1614.22i	−0.126005	−	0.768595i
$165$	313.341	+	238.196i	0.147840	+	0.112385i
$166$	−7.54077	−	3.48873i	−0.00352577	−	0.00163119i
$167$	1461.59	−	1384.49i	0.677252	−	0.641527i	−0.269684	−	0.962949i	$-0.586919\pi$
$167$	1461.59	−	1384.49i	0.677252	−	0.641527i	0.946936	+	0.321421i	$0.104161\pi$
$168$	−6.65471	+	40.5919i	−0.00305608	+	0.0186413i
$169$	451.299	−	152.060i	0.205416	−	0.0692127i
$170$	−241.580	−	606.320i	−0.108990	−	0.273545i
$171$	536.604	+	508.298i	0.239972	+	0.227313i
$172$	3238.90	−	2462.15i	1.43584	−	1.09149i
$173$	−2895.09	+	637.258i	−1.27231	+	0.280057i	−0.799264	−	0.600980i	$-0.794777\pi$
$173$	−2895.09	+	637.258i	−1.27231	+	0.280057i	−0.473047	+	0.881037i	$0.656846\pi$
$174$	1548.73	+	1823.31i	0.674764	+	0.794394i
$175$	−724.252	+	78.7671i	−0.312847	+	0.0340242i
$176$	2719.58			1.16475
$177$	412.377	−	1295.51i	0.175119	−	0.550151i
$178$	−4411.49			−1.85761
$179$	−1977.60	+	215.077i	−0.825768	+	0.0898077i	−0.511237	−	0.859440i	$-0.670813\pi$
$179$	−1977.60	+	215.077i	−0.825768	+	0.0898077i	−0.314531	+	0.949247i	$0.601847\pi$
$180$	142.557	+	167.831i	0.0590308	+	0.0694965i
$181$	−3710.52	+	816.747i	−1.52376	+	0.335405i	−0.896372	−	0.443302i	$-0.853807\pi$
$181$	−3710.52	+	816.747i	−1.52376	+	0.335405i	−0.627388	+	0.778707i	$0.715876\pi$
$182$	837.773	−	636.859i	0.341208	−	0.259380i
$183$	970.087	+	918.915i	0.391863	+	0.371192i
$184$	137.737	+	345.693i	0.0551853	+	0.138505i
$185$	681.651	−	229.675i	0.270897	−	0.0912759i
$186$	−625.692	+	3816.55i	−0.246656	+	1.50453i
$187$	1862.47	−	1764.23i	0.728328	−	0.689909i
$188$	−1315.52	−	608.622i	−0.510340	−	0.236108i
$189$	134.077	+	101.923i	0.0516015	+	0.0392264i
$190$	154.804	+	944.261i	0.0591086	+	0.360547i
$191$	−245.856	−	463.733i	−0.0931387	−	0.175678i	0.832565	−	0.553927i	$-0.186871\pi$
$191$	−245.856	−	463.733i	−0.0931387	−	0.175678i	−0.925704	+	0.378249i	$0.876526\pi$
$192$	1695.47	+	373.201i	0.637292	+	0.140279i
$193$	−4499.90	+	2081.88i	−1.67829	+	0.776460i	−0.679194	+	0.733959i	$0.737670\pi$
$193$	−4499.90	+	2081.88i	−1.67829	+	0.776460i	−0.999096	+	0.0425005i	$0.986468\pi$
$194$	−881.517	+	2212.44i	−0.326233	+	0.818784i
$195$	19.3015	−	355.996i	0.00708827	−	0.130735i
$196$	1457.45	−	2149.57i	0.531140	−	0.783372i
$197$	−1108.50	+	1305.03i	−0.400901	+	0.471977i	−0.925158	−	0.379583i	$-0.876067\pi$
$197$	−1108.50	+	1305.03i	−0.400901	+	0.471977i	0.524257	+	0.851560i	$0.324343\pi$
$198$	−785.188	+	1481.02i	−0.281823	+	0.531574i
$199$	156.720	+	52.8050i	0.0558270	+	0.0188103i	0.347076	−	0.937837i	$-0.387174\pi$
$199$	156.720	+	52.8050i	0.0558270	+	0.0188103i	−0.291250	+	0.956647i	$0.594071\pi$
$200$	−13.8988	−	256.348i	−0.00491395	−	0.0906325i
$201$	−1394.07	−	838.783i	−0.489204	−	0.294344i
$202$	434.832	−	1566.12i	0.151459	−	0.545506i
$203$	327.201	+	1178.47i	0.113128	+	0.407450i
$204$	1229.80	−	739.947i	0.422075	−	0.253954i
$205$	−307.927	−	454.158i	−0.104910	−	0.154731i
$206$	−4203.34	−	457.140i	−1.42165	−	0.154614i
$207$	1514.69	+	164.733i	0.508592	+	0.0553127i
$208$	−1382.42	−	2038.91i	−0.460834	−	0.679679i
$209$	−3222.69	+	1939.03i	−1.06659	+	0.641748i
$210$	58.3300	+	210.086i	0.0191674	+	0.0690347i
$211$	930.642	−	3351.87i	0.303640	−	1.09361i	−0.641547	−	0.767084i	$-0.721707\pi$
$211$	930.642	−	3351.87i	0.303640	−	1.09361i	0.945187	−	0.326529i	$-0.105879\pi$
$212$	511.099	+	307.518i	0.165578	+	0.0996248i
$213$	−44.8743	−	827.658i	−0.0144354	−	0.266245i
$214$	−4764.77	−	1605.44i	−1.52202	−	0.512829i
$215$	639.257	−	1205.77i	0.202777	−	0.382477i
$216$	−38.4218	+	45.2337i	−0.0121031	+	0.0142489i
$217$	−1109.61	+	1636.55i	−0.347121	+	0.511965i
$218$	283.440	−	5227.75i	0.0880597	−	1.62417i
$219$	−871.452	+	2187.18i	−0.268891	+	0.674867i
$220$	−1016.94	+	470.488i	−0.311647	+	0.144183i
$221$	−2269.40	−	499.533i	−0.690753	−	0.152046i
$222$	1434.94	+	2706.58i	0.433814	+	0.818260i
$223$	−197.821	−	1206.65i	−0.0594039	−	0.362347i	−0.999755	−	0.0221416i	$-0.992952\pi$
$223$	−197.821	−	1206.65i	−0.0594039	−	0.362347i	0.940351	−	0.340206i	$-0.110497\pi$
$224$	1286.64	+	978.081i	0.383783	+	0.291744i
$225$	−953.984	−	441.360i	−0.282662	−	0.130773i
$226$	−2462.61	+	2332.71i	−0.724826	+	0.686592i
$227$	109.224	−	666.235i	0.0319358	−	0.194800i	−0.966040	−	0.258392i	$-0.916807\pi$
$227$	109.224	−	666.235i	0.0319358	−	0.194800i	0.997976	+	0.0635922i	$0.0202557\pi$
$228$	−1994.02	+	671.865i	−0.579199	+	0.195155i
$229$	1519.63	+	3813.99i	0.438516	+	1.10059i	0.967704	+	0.252087i	$0.0811170\pi$
$229$	1519.63	+	3813.99i	0.438516	+	1.10059i	−0.529189	+	0.848504i	$0.677504\pi$
$230$	1432.00	+	1356.46i	0.410536	+	0.388880i
$231$	−682.252	+	518.634i	−0.194324	+	0.147721i
$232$	−420.914	+	92.6503i	−0.119114	+	0.0262189i
$233$	1061.50	+	1249.69i	0.298459	+	0.351373i	0.890866	−	0.454266i	$-0.150098\pi$
$233$	1061.50	+	1249.69i	0.298459	+	0.351373i	−0.592407	+	0.805639i	$0.701822\pi$
$234$	1509.47	−	164.165i	0.421698	−	0.0458624i
$235$	−486.218			−0.134967
$236$	2708.59	+	2764.75i	0.747093	+	0.762584i
$237$	1371.04			0.375774
$238$	1412.77	−	153.648i	0.384774	−	0.0418467i
$239$	−383.572	−	451.576i	−0.103813	−	0.122218i	0.707802	−	0.706411i	$-0.249687\pi$
$239$	−383.572	−	451.576i	−0.103813	−	0.122218i	−0.811615	+	0.584193i	$0.801411\pi$
$240$	498.444	−	109.716i	0.134060	−	0.0295089i
$241$	2018.02	−	1534.06i	0.539386	−	0.410031i	−0.299696	−	0.954035i	$-0.596885\pi$
$241$	2018.02	−	1534.06i	0.539386	−	0.410031i	0.839083	+	0.544004i	$0.183092\pi$
$242$	−2262.66	−	2143.30i	−0.601029	−	0.569325i
$243$	89.9436	+	225.741i	0.0237444	+	0.0595939i
$244$	−3604.85	+	1214.61i	−0.945807	+	0.318679i
$245$	140.940	−	859.693i	0.0367522	−	0.224179i
$246$	1696.56	−	1607.07i	0.439711	−	0.416516i
$247$	3091.88	+	1430.45i	0.796483	+	0.368492i
$248$	−554.690	−	421.664i	−0.142028	−	0.107967i
$249$	−0.991540	−	6.04813i	−0.000252355	−	0.00153930i
$250$	−1319.60	−	2489.03i	−0.333835	−	0.629679i
$251$	−5836.21	−	1284.65i	−1.46764	−	0.323052i	−0.591970	−	0.805960i	$-0.701650\pi$
$251$	−5836.21	−	1284.65i	−1.46764	−	0.323052i	−0.875672	+	0.482907i	$0.839581\pi$
$252$	−435.145	+	201.320i	−0.108776	+	0.0503252i
$253$	−2869.67	+	7202.33i	−0.713101	+	1.78975i
$254$	−168.418	+	3106.29i	−0.0416044	+	0.767347i
$255$	270.179	−	398.484i	0.0663501	−	0.0978591i
$256$	2257.96	−	2658.28i	0.551261	−	0.648994i
$257$	2303.68	−	4345.20i	0.559143	−	1.05465i	−0.429315	−	0.903155i	$-0.641245\pi$
$257$	2303.68	−	4345.20i	0.559143	−	1.05465i	0.988457	−	0.151500i	$-0.0484103\pi$
$258$	5508.03	+	1855.87i	1.32913	+	0.447835i
$259$	84.7910	+	1563.88i	0.0203423	+	0.375192i
$260$	869.665	+	523.260i	0.207440	+	0.124812i
$261$	−472.095	+	1700.33i	−0.111961	+	0.403249i
$262$	−957.497	−	3448.59i	−0.225780	−	0.813186i
$263$	3155.04	−	1898.33i	0.739727	−	0.445079i	−0.0951870	−	0.995459i	$-0.530345\pi$
$263$	3155.04	−	1898.33i	0.739727	−	0.445079i	0.834914	+	0.550380i	$0.185517\pi$
$264$	−169.478	−	249.961i	−0.0395099	−	0.0582728i
$265$	198.912	+	21.6330i	0.0461097	+	0.00501473i
$266$	−2071.22	−	225.258i	−0.477422	−	0.0519228i
$267$	−1826.17	−	2693.39i	−0.418575	−	0.617352i
$268$	3968.67	−	2387.87i	0.904572	−	0.544263i
$269$	1500.20	+	5403.25i	0.340034	+	1.22469i	0.913967	+	0.405788i	$0.133003\pi$
$269$	1500.20	+	5403.25i	0.340034	+	1.22469i	−0.573933	+	0.818902i	$0.694583\pi$
$270$	−84.1603	+	303.118i	−0.0189697	+	0.0683228i
$271$	−114.416	−	68.8416i	−0.0256467	−	0.0154311i	0.502673	−	0.864477i	$-0.332350\pi$
$271$	−114.416	−	68.8416i	−0.0256467	−	0.0154311i	−0.528319	+	0.849046i	$0.677178\pi$
$272$	−180.095	−	3321.67i	−0.0401467	−	0.740462i
$273$	735.630	+	247.863i	0.163086	+	0.0549499i
$274$	3151.12	−	5943.64i	0.694767	−	1.31047i
$275$	3462.67	−	4076.58i	0.759299	−	0.893915i
$276$	−2434.15	+	3590.10i	−0.530864	+	0.782965i
$277$	6.67177	−	123.054i	0.00144718	−	0.0266916i	−0.997721	−	0.0674799i	$-0.978504\pi$
$277$	6.67177	−	123.054i	0.00144718	−	0.0266916i	0.999168	+	0.0407883i	$0.0129869\pi$
$278$	−642.041	+	1611.40i	−0.138515	+	0.347645i
$279$	−2589.17	+	1197.88i	−0.555590	+	0.257043i
$280$	−38.3622	−	8.44415i	−0.00818778	−	0.00180227i
$281$	−1161.97	−	2191.70i	−0.246680	−	0.465288i	0.728992	−	0.684522i	$-0.239989\pi$
$281$	−1161.97	−	2191.70i	−0.246680	−	0.465288i	−0.975672	+	0.219234i	$0.929644\pi$
$282$	−335.009	−	2043.47i	−0.0707429	−	0.431513i
$283$	7261.84	+	5520.30i	1.52534	+	1.15953i	0.936182	+	0.351516i	$0.114334\pi$
$283$	7261.84	+	5520.30i	1.52534	+	1.15953i	0.589159	+	0.808017i	$0.299459\pi$
$284$	2141.57	+	990.794i	0.447460	+	0.207017i
$285$	−512.427	+	485.397i	−0.106504	+	0.100886i
$286$	−1249.97	+	7624.46i	−0.258434	+	1.57638i
$287$	1132.18	−	381.477i	0.232860	−	0.0784595i
$288$	863.125	+	2166.28i	0.176598	+	0.443227i
$289$	1288.67	+	1220.70i	0.262299	+	0.248463i
$290$	−1818.67	+	1382.52i	−0.368263	+	0.279946i
$291$	−1715.70	+	377.653i	−0.345621	+	0.0760770i
$292$	−4339.14	−	5108.43i	−0.869620	−	1.02380i
$293$	−3238.36	+	352.192i	−0.645689	+	0.0702229i	−0.425103	−	0.905145i	$-0.639762\pi$
$293$	−3238.36	+	352.192i	−0.645689	+	0.0702229i	−0.220585	+	0.975368i	$0.570797\pi$
$294$	3710.21			0.735999
$295$	1214.01	+	460.197i	0.239601	+	0.0908261i
$296$	−551.905			−0.108374
$297$	−1229.26	+	133.690i	−0.240164	+	0.0261194i
$298$	−4557.17	−	5365.12i	−0.885873	−	1.04293i
$299$	6858.40	−	1509.65i	1.32653	−	0.291991i
$300$	2382.23	−	1810.92i	0.458460	−	0.348512i
$301$	2157.31	+	2043.51i	0.413107	+	0.391316i
$302$	−4665.00	−	11708.3i	−0.888876	−	2.23091i
$303$	1136.18	−	382.825i	0.215419	−	0.0725832i
$304$	−789.001	+	4812.70i	−0.148856	+	0.907984i
$305$	−926.380	+	877.513i	−0.173916	+	0.164742i
$306$	1860.90	+	860.943i	0.347649	+	0.160839i
$307$	889.228	+	675.973i	0.165312	+	0.125667i	0.684560	−	0.728957i	$-0.259995\pi$
$307$	889.228	+	675.973i	0.165312	+	0.125667i	−0.519247	+	0.854624i	$0.673788\pi$
$308$	−394.704	−	2407.59i	−0.0730206	−	0.445406i
$309$	−1460.90	−	2755.54i	−0.268956	−	0.507306i
$310$	−3606.91	−	793.940i	−0.660834	−	0.145461i
$311$	−9253.56	+	4281.15i	−1.68721	+	0.780585i	−0.688753	+	0.724996i	$0.741841\pi$
$311$	−9253.56	+	4281.15i	−1.68721	+	0.780585i	−0.998454	+	0.0555887i	$0.982296\pi$
$312$	−101.251	+	254.120i	−0.0183724	+	0.0461112i
$313$	187.474	−	3457.76i	0.0338552	−	0.624422i	−0.931541	−	0.363635i	$-0.881535\pi$
$313$	187.474	−	3457.76i	0.0338552	−	0.624422i	0.965397	−	0.260786i	$-0.0839818\pi$
$314$	−5538.06	+	8168.02i	−0.995320	+	1.46799i
$315$	−104.120	+	122.579i	−0.0186237	+	0.0219256i
$316$	−1828.25	+	3448.44i	−0.325465	+	0.613892i
$317$	2950.84	+	994.255i	0.522826	+	0.176161i	0.568326	−	0.822804i	$-0.307591\pi$
$317$	2950.84	+	994.255i	0.522826	+	0.176161i	−0.0454996	+	0.998964i	$0.514488\pi$
$318$	46.1338	+	850.889i	0.00813540	+	0.150049i
$319$	−7694.10	−	4629.39i	−1.35043	−	0.812526i
$320$	−443.519	+	1597.41i	−0.0774796	+	0.279056i
$321$	−992.223	−	3573.66i	−0.172525	−	0.621378i
$322$	−3679.98	+	2214.17i	−0.636885	+	0.383201i
$323$	2581.72	+	3807.75i	0.444739	+	0.655940i
$324$	−687.723	−	74.7944i	−0.117922	−	0.0128248i
$325$	−4816.42	−	523.817i	−0.822052	−	0.0894035i
$326$	7080.44	+	10442.9i	1.20291	+	1.77416i
$327$	3309.09	−	1991.01i	0.559611	−	0.336707i
$328$	112.632	+	405.663i	0.0189605	+	0.0682896i
$329$	283.223	−	1020.08i	0.0474607	−	0.170938i
$330$	−1371.63	−	825.280i	−0.228805	−	0.137667i
$331$	−445.974	−	8225.51i	−0.0740573	−	1.36591i	−0.765482	−	0.643458i	$-0.777499\pi$
$331$	−445.974	−	8225.51i	−0.0740573	−	1.36591i	0.691424	−	0.722449i	$-0.256984\pi$
$332$	16.5345	+	5.57111i	0.00273327	+	0.000920947i
$333$	−1058.47	+	1996.50i	−0.174186	+	0.328550i
$334$	−5300.65	+	6240.40i	−0.868379	+	1.02233i
$335$	871.890	−	1285.94i	0.142198	−	0.209727i
$336$	−60.1628	+	1109.64i	−0.00976830	+	0.180166i
$337$	3862.40	−	9693.90i	0.624328	−	1.56694i	−0.187005	−	0.982359i	$-0.559878\pi$
$337$	3862.40	−	9693.90i	0.624328	−	1.56694i	0.811332	−	0.584585i	$-0.198743\pi$
$338$	−1757.81	+	813.249i	−0.282876	+	0.130873i
$339$	−2443.63	−	537.884i	−0.391504	−	0.0861765i
$340$	641.992	+	1210.93i	0.102403	+	0.193152i
$341$	−2348.54	−	14325.5i	−0.372964	−	2.27498i
$342$	−2393.08	−	1819.18i	−0.378372	−	0.287631i
$343$	3663.32	+	1694.83i	0.576678	+	0.266800i
$344$	−760.214	+	720.113i	−0.119151	+	0.112866i
$345$	−235.389	+	1435.81i	−0.0367331	+	0.224062i
$346$	11425.1	−	3849.57i	1.77519	−	0.598133i
$347$	3732.99	+	9369.10i	0.577514	+	1.44945i	0.869937	+	0.493163i	$0.164159\pi$
$347$	3732.99	+	9369.10i	0.577514	+	1.44945i	−0.292423	+	0.956289i	$0.594461\pi$
$348$	−3647.16	−	3454.77i	−0.561805	−	0.532170i
$349$	3319.15	−	2523.15i	0.509083	−	0.386995i	−0.318864	−	0.947800i	$-0.603301\pi$
$349$	3319.15	−	2523.15i	0.509083	−	0.386995i	0.827948	+	0.560805i	$0.189508\pi$
$350$	2893.63	−	636.936i	0.441917	−	0.0972733i
$351$	725.085	+	853.636i	0.110263	+	0.129811i
$352$	−11796.3	+	1282.93i	−1.78621	+	0.194262i
$353$	−10385.0			−1.56583			−0.782916	−	0.622127i	$-0.786269\pi$
$353$	−10385.0			−1.56583			−0.782916	+	0.622127i	$0.786269\pi$
$354$	−1097.64	+	5419.30i	−0.164799	+	0.813651i
$355$	791.528			0.118338
$356$	9209.58	−	1001.60i	1.37109	−	0.149115i
$357$	678.633	+	798.949i	0.100608	+	0.118445i
$358$	7901.16	−	1739.18i	1.16645	−	0.256755i
$359$	−6826.10	+	5189.06i	−1.00353	+	0.762865i	−0.971601	−	0.236626i	$-0.923959\pi$
$359$	−6826.10	+	5189.06i	−1.00353	+	0.762865i	−0.0319302	+	0.999490i	$0.510165\pi$
$360$	−41.1459	−	38.9755i	−0.00602383	−	0.00570608i
$361$	42.3500	+	106.290i	0.00617437	+	0.0154965i
$362$	14643.1	−	4933.82i	2.12603	−	0.716343i
$363$	371.931	−	2268.68i	0.0537777	−	0.328029i
$364$	−1604.37	+	1519.74i	−0.231022	+	0.218835i
$365$	−2040.52	−	944.044i	−0.292618	−	0.135380i
$366$	−4326.28	−	3288.75i	−0.617864	−	0.469688i
$367$	−350.758	−	2139.53i	−0.0498894	−	0.304312i	0.950081	−	0.312003i	$-0.101000\pi$
$367$	−350.758	−	2139.53i	−0.0498894	−	0.304312i	−0.999970	+	0.00769143i	$0.997552\pi$
$368$	4709.02	+	8882.15i	0.667050	+	1.25819i
$369$	1683.48	+	370.563i	0.237503	+	0.0522784i
$370$	−2655.03	+	1228.35i	−0.373050	+	0.172591i
$371$	−161.252	+	404.713i	−0.0225655	+	0.0566351i
$372$	439.692	−	8109.64i	0.0612821	−	1.13028i
$373$	−4889.62	+	7211.65i	−0.678753	+	1.00109i	0.319809	+	0.947482i	$0.396381\pi$
$373$	−4889.62	+	7211.65i	−0.678753	+	1.00109i	−0.998562	+	0.0536037i	$0.982929\pi$
$374$	−6754.50	+	7952.01i	−0.933869	+	1.09944i
$375$	973.394	−	1836.02i	0.134042	−	0.252831i
$376$	353.534	+	119.120i	0.0484897	+	0.0163381i
$377$	440.340	+	8121.60i	0.0601556	+	1.10951i
$378$	−586.912	−	353.133i	−0.0798612	−	0.0480509i
$379$	−803.241	+	2893.01i	−0.108865	+	0.392095i	−0.997827	−	0.0658848i	$-0.979013\pi$
$379$	−803.241	+	2893.01i	−0.108865	+	0.392095i	0.888963	+	0.457980i	$0.151427\pi$
$380$	−537.563	−	1936.13i	−0.0725694	−	0.261371i
$381$	−1966.24	+	1183.04i	−0.264392	+	0.159079i
$382$	1197.95	+	1766.84i	0.160451	+	0.236647i
$383$	13749.2	+	1495.32i	1.83434	+	0.199497i	0.958884	−	0.283797i	$-0.0915942\pi$
$383$	13749.2	+	1495.32i	1.83434	+	0.199497i	0.875458	+	0.483294i	$0.160560\pi$
$384$	−837.214	−	91.0525i	−0.111260	−	0.0121003i
$385$	−459.269	−	677.370i	−0.0607961	−	0.0896675i
$386$	17278.4	−	10396.0i	2.27836	−	1.37084i
$387$	1147.00	+	4131.12i	0.150660	+	0.542627i
$388$	1337.97	−	4818.92i	0.175064	−	0.630524i
$389$	3280.25	+	1973.66i	0.427546	+	0.257246i	0.713024	−	0.701139i	$-0.247325\pi$
$389$	3280.25	+	1973.66i	0.427546	+	0.257246i	−0.285478	+	0.958385i	$0.592152\pi$
$390$	78.4993	+	1447.84i	0.0101922	+	0.187985i
$391$	8986.87	+	3028.03i	1.16237	+	0.391647i
$392$	−313.097	+	590.563i	−0.0403413	+	0.0760917i
$393$	1709.14	−	2012.16i	0.219376	−	0.258270i
$394$	3908.00	−	5763.87i	0.499701	−	0.737004i
$395$	−70.8821	+	1307.34i	−0.00902903	+	0.166531i
$396$	1302.93	−	3270.11i	0.165340	−	0.414972i
$397$	−685.128	+	316.974i	−0.0866135	+	0.0400717i	−0.462718	−	0.886506i	$-0.653126\pi$
$397$	−685.128	+	316.974i	−0.0866135	+	0.0400717i	0.376104	+	0.926577i	$0.377264\pi$
$398$	−656.862	−	144.586i	−0.0827274	−	0.0182097i
$399$	−719.864	−	1357.81i	−0.0903215	−	0.170364i
$400$	−1122.06	−	6844.26i	−0.140257	−	0.855533i
$401$	1137.69	+	864.847i	0.141679	+	0.107702i	0.673613	−	0.739084i	$-0.264741\pi$
$401$	1137.69	+	864.847i	0.141679	+	0.107702i	−0.531934	+	0.846786i	$0.678535\pi$
$402$	6005.27	+	2778.33i	0.745064	+	0.344703i
$403$	−9546.21	+	9042.65i	−1.17998	+	1.11773i
$404$	−552.192	+	3368.22i	−0.0680015	+	0.414791i
$405$	−219.904	+	74.0944i	−0.0269806	+	0.00909082i
$406$	−1841.12	−	4620.86i	−0.225057	−	0.564851i
$407$	−8347.95	−	7907.59i	−1.01669	−	0.963059i
$408$	−294.076	+	223.551i	−0.0356836	+	0.0271260i
$409$	10099.1	−	2222.98i	1.22095	−	0.268751i	0.442678	−	0.896681i	$-0.354028\pi$
$409$	10099.1	−	2222.98i	1.22095	−	0.268751i	0.778270	+	0.627929i	$0.216097\pi$
$410$	1444.70	+	1700.83i	0.174021	+	0.204873i
$411$	4933.26	−	536.524i	0.592067	−	0.0643912i
$412$	8878.83			1.06172
$413$	−1672.65	+	2278.91i	−0.199287	+	0.271520i
$414$	−6196.58			−0.735617
$415$	5.81842	−	0.632791i	0.000688229	−	7.48494e-5i
$416$	6958.13	+	8191.74i	0.820073	+	0.965464i
$417$	−1249.60	+	275.058i	−0.146746	+	0.0323013i
$418$	12177.2	−	9256.87i	1.42490	−	1.08318i
$419$	−2732.37	−	2588.24i	−0.318580	−	0.301775i	0.511652	−	0.859193i	$-0.329034\pi$
$419$	−2732.37	−	2588.24i	−0.318580	−	0.301775i	−0.830232	+	0.557418i	$0.811792\pi$
$420$	−169.470	−	425.339i	−0.0196888	−	0.0494152i
$421$	10852.6	−	3656.66i	1.25635	−	0.423313i	0.389103	−	0.921194i	$-0.372785\pi$
$421$	10852.6	−	3656.66i	1.25635	−	0.423313i	0.867245	+	0.497882i	$0.165889\pi$
$422$	−2288.85	+	13961.4i	−0.264027	+	1.61049i
$423$	1108.94	−	1050.44i	0.127467	−	0.120743i
$424$	−139.331	−	64.4615i	−0.0159588	−	0.00738332i
$425$	−5208.38	−	3959.31i	−0.594456	−	0.451894i
$426$	545.371	+	3326.62i	0.0620266	+	0.378345i
$427$	−1301.39	−	2454.68i	−0.147491	−	0.278198i
$428$	10311.6	+	2269.75i	1.16456	+	0.256338i
$429$	−5172.47	+	2393.04i	−0.582119	+	0.269317i
$430$	−2054.42	+	5156.20i	−0.230402	+	0.578265i
$431$	427.557	−	7885.83i	0.0477835	−	0.881315i	−0.872149	−	0.489240i	$-0.837274\pi$
$431$	427.557	−	7885.83i	0.0477835	−	0.881315i	0.919933	−	0.392076i	$-0.128243\pi$
$432$	−899.791	+	1327.09i	−0.100211	+	0.147800i
$433$	−8986.36	+	10579.6i	−0.997360	+	1.17418i	−0.0126609	+	0.999920i	$0.504030\pi$
$433$	−8986.36	+	10579.6i	−0.997360	+	1.17418i	−0.984699	+	0.174263i	$0.944246\pi$
$434$	3766.70	−	7104.75i	0.416607	−	0.785804i
$435$	−1596.94	−	538.070i	−0.176017	−	0.0593069i
$436$	595.210	+	10978.0i	0.0653793	+	1.20585i
$437$	−11913.0	−	7167.82i	−1.30407	−	0.784630i
$438$	2561.67	−	9226.30i	0.279455	−	1.00651i
$439$	2612.09	+	9407.91i	0.283983	+	1.02281i	0.958626	+	0.284669i	$0.0918838\pi$
$439$	2612.09	+	9407.91i	0.283983	+	1.02281i	−0.674643	+	0.738144i	$0.735702\pi$
$440$	247.110	−	148.681i	0.0267739	−	0.0161093i
$441$	1535.87	+	2265.23i	0.165842	+	0.244599i
$442$	9395.19	+	1021.79i	1.01105	+	0.109958i
$443$	13370.4	+	1454.11i	1.43396	+	0.155953i	0.791877	−	0.610681i	$-0.209104\pi$
$443$	13370.4	+	1454.11i	1.43396	+	0.155953i	0.642085	+	0.766634i	$0.278070\pi$
$444$	−3610.14	−	5324.56i	−0.385878	−	0.569127i
$445$	2662.68	−	1602.08i	0.283648	−	0.170665i
$446$	1330.41	+	4791.70i	0.141248	+	0.508730i
$447$	1389.15	−	5003.27i	0.146990	−	0.529410i
$448$	−3092.99	−	1860.99i	−0.326183	−	0.196258i
$449$	269.613	+	4972.72i	0.0283381	+	0.522666i	0.977898	+	0.209081i	$0.0670473\pi$
$449$	269.613	+	4972.72i	0.0283381	+	0.522666i	−0.949560	+	0.313585i	$0.898470\pi$
$450$	4051.18	+	1365.00i	0.424388	+	0.142993i
$451$	−4108.64	+	7749.71i	−0.428976	+	0.809134i
$452$	4611.41	−	5428.98i	0.479873	−	0.564950i
$453$	5217.26	−	7694.88i	0.541122	−	0.798095i
$454$	−148.652	+	2741.72i	−0.0153669	+	0.283426i
$455$	−274.380	+	688.641i	−0.0282706	+	0.0709539i
$456$	491.510	−	227.397i	0.0504760	−	0.0233527i
$457$	1845.15	+	406.148i	0.188867	+	0.0415728i	0.308397	−	0.951258i	$-0.400208\pi$
$457$	1845.15	+	406.148i	0.188867	+	0.0415728i	−0.119529	+	0.992831i	$0.538139\pi$
$458$	−7821.20	−	14752.3i	−0.797949	−	1.50509i
$459$	244.691	+	1492.55i	0.0248827	+	0.151778i
$460$	−3297.47	−	2506.67i	−0.334229	−	0.254074i
$461$	−4233.11	−	1958.45i	−0.427669	−	0.197861i	0.194233	−	0.980955i	$-0.437778\pi$
$461$	−4233.11	−	1958.45i	−0.427669	−	0.197861i	−0.621903	+	0.783094i	$0.713640\pi$
$462$	2530.40	−	2396.92i	0.254815	−	0.241374i
$463$	1985.93	−	12113.6i	0.199339	−	1.21591i	−0.677644	−	0.735390i	$-0.736999\pi$
$463$	1985.93	−	12113.6i	0.199339	−	1.21591i	0.876982	−	0.480522i	$-0.159553\pi$
$464$	−11034.1	+	3717.82i	−1.10398	+	0.371973i
$465$	−1008.37	−	2530.82i	−0.100564	−	0.252396i
$466$	−4841.31	−	4585.93i	−0.481265	−	0.455878i
$467$	3773.61	−	2868.63i	0.373923	−	0.284249i	−0.401287	−	0.915952i	$-0.631437\pi$
$467$	3773.61	−	2868.63i	0.373923	−	0.284249i	0.775210	+	0.631703i	$0.217644\pi$
$468$	−3113.95	+	685.433i	−0.307570	+	0.0677012i
$469$	2190.01	+	2578.27i	0.215618	+	0.253846i
$470$	1965.85	−	213.800i	0.192932	−	0.0209826i
$471$	−7279.42			−0.712140
$472$	−769.975	−	632.037i	−0.0750868	−	0.0616353i
$473$	−21816.4			−2.12076
$474$	−5543.32	+	602.872i	−0.537158	+	0.0584195i
$475$	6209.50	+	7310.39i	0.599814	+	0.706155i
$476$	−2914.46	+	641.522i	−0.280639	+	0.0617733i
$477$	−500.405	+	380.398i	−0.0480334	+	0.0365141i
$478$	1749.41	+	1657.13i	0.167398	+	0.158568i
$479$	985.587	+	2473.64i	0.0940138	+	0.235957i	0.968462	−	0.249163i	$-0.0801554\pi$
$479$	985.587	+	2473.64i	0.0940138	+	0.235957i	−0.874448	+	0.485120i	$0.838776\pi$
$480$	−2110.27	+	711.032i	−0.200667	+	0.0676125i
$481$	−1685.02	+	10278.2i	−0.159730	+	0.974312i
$482$	−7484.62	+	7089.80i	−0.707292	+	0.669983i
$483$	−2875.19	−	1330.20i	−0.270861	−	0.125313i
$484$	5210.22	+	3960.71i	0.489315	+	0.371967i
$485$	−271.408	−	1655.52i	−0.0254103	−	0.154996i
$486$	−462.919	−	873.158i	−0.0432066	−	0.0814964i
$487$	607.158	+	133.646i	0.0564948	+	0.0124354i	0.243128	−	0.969994i	$-0.421827\pi$
$487$	607.158	+	133.646i	0.0564948	+	0.0124354i	−0.186633	+	0.982430i	$0.559758\pi$
$488$	888.565	−	411.094i	0.0824251	−	0.0381339i
$489$	−3444.80	+	8645.79i	−0.318567	+	0.799542i
$490$	−191.817	+	3537.85i	−0.0176845	+	0.326171i
$491$	8714.39	−	12852.8i	0.800967	−	1.18134i	−0.179326	−	0.983790i	$-0.557392\pi$
$491$	8714.39	−	12852.8i	0.800967	−	1.18134i	0.980293	−	0.197548i	$-0.0632979\pi$
$492$	−3176.93	+	3740.17i	−0.291112	+	0.342723i
$493$	−5144.76	+	9704.05i	−0.469997	+	0.886508i
$494$	−13129.9	−	4423.99i	−1.19584	−	0.402925i
$495$	−63.9269	−	1179.06i	−0.00580465	−	0.107060i
$496$	−16129.2	−	9704.64i	−1.46013	−	0.878531i
$497$	−461.067	+	1660.61i	−0.0416130	+	0.149877i
$498$	6.66843	+	24.0175i	0.000600040	+	0.00216115i
$499$	2974.18	−	1789.51i	0.266819	−	0.160540i	−0.375857	−	0.926678i	$-0.622652\pi$
$499$	2974.18	−	1789.51i	0.266819	−	0.160540i	0.642676	+	0.766138i	$0.277824\pi$
$500$	3319.96	+	4896.57i	0.296946	+	0.437963i
$501$	−6004.26	−	653.002i	−0.535430	−	0.0582315i
$502$	24161.6	+	2627.73i	2.14818	+	0.233628i
$503$	−7782.21	−	11477.9i	−0.689845	−	1.01744i	−0.997816	−	0.0660491i	$-0.978961\pi$
$503$	−7782.21	−	11477.9i	−0.689845	−	1.01744i	0.307972	−	0.951395i	$-0.400350\pi$
$504$	105.737	−	63.6201i	0.00934508	−	0.00562275i
$505$	306.300	+	1103.19i	0.0269905	+	0.0972108i
$506$	8435.52	−	30382.0i	0.741116	−	2.66926i
$507$	−1224.18	−	736.564i	−0.107234	−	0.0645206i
$508$	−353.669	−	6523.05i	−0.0308889	−	0.569711i
$509$	−14303.0	−	4819.25i	−1.24552	−	0.419665i	−0.382088	−	0.924126i	$-0.624795\pi$
$509$	−14303.0	−	4819.25i	−1.24552	−	0.419665i	−0.863435	+	0.504461i	$0.831691\pi$
$510$	−917.155	+	1729.94i	−0.0796320	+	0.150202i
$511$	3169.19	−	3731.06i	0.274358	−	0.322999i
$512$	−9220.68	+	13599.5i	−0.795899	+	1.17386i
$513$	120.047	−	2214.13i	0.0103318	−	0.190558i
$514$	−7403.47	+	18581.3i	−0.635317	+	1.59453i
$515$	2703.06	−	1250.57i	0.231284	−	0.107003i
$516$	−11920.1	−	2623.82i	−1.01696	−	0.223851i
$517$	3640.73	+	6867.14i	0.309708	+	0.584171i
$518$	−1030.49	−	6285.72i	−0.0874077	−	0.533164i
$519$	7079.81	+	5381.93i	0.598785	+	0.455184i
$520$	−237.080	−	109.685i	−0.0199935	−	0.00925000i
$521$	−5364.59	+	5081.61i	−0.451107	+	0.427312i	−0.879222	−	0.476413i	$-0.841937\pi$
$521$	−5364.59	+	5081.61i	−0.451107	+	0.427312i	0.428114	+	0.903725i	$0.359178\pi$
$522$	1161.08	−	7082.30i	0.0973550	−	0.593839i
$523$	−2594.98	+	874.350i	−0.216961	+	0.0731026i	−0.425683	−	0.904872i	$-0.639966\pi$
$523$	−2594.98	+	874.350i	−0.216961	+	0.0731026i	0.208722	+	0.977975i	$0.433070\pi$
$524$	2781.89	+	6982.01i	0.231922	+	0.582081i
$525$	1586.71	+	1503.01i	0.131904	+	0.124946i
$526$	−11921.6	+	9062.56i	−0.988225	+	0.751229i
$527$	−17341.4	+	3817.14i	−1.43340	+	0.315516i
$528$	−5281.86	−	6218.29i	−0.435348	−	0.512531i
$529$	−16396.0	+	1783.17i	−1.34758	+	0.146558i
$530$	−813.745			−0.0666921
$531$	−3763.08	+	1573.20i	−0.307540	+	0.128571i
$532$	4375.09			0.356549
$533$	7898.58	−	859.022i	0.641886	−	0.0698093i
$534$	8567.81	+	10086.8i	0.694317	+	0.817414i
$535$	3458.94	−	761.371i	0.279520	−	0.0615270i
$536$	−949.007	+	721.416i	−0.0764754	+	0.0581351i
$537$	4332.57	+	4104.03i	0.348165	+	0.329799i
$538$	−8441.47	−	21186.5i	−0.676464	−	1.69780i
$539$	−13197.3	+	4446.69i	−1.05463	+	0.355348i
$540$	106.875	−	651.908i	0.00851697	−	0.0519512i
$541$	−2822.63	+	2673.73i	−0.224315	+	0.212482i	−0.791601	−	0.611039i	$-0.790752\pi$
$541$	−2822.63	+	2673.73i	−0.224315	+	0.212482i	0.567286	+	0.823521i	$0.307993\pi$
$542$	492.872	+	228.027i	0.0390603	+	0.0180712i
$543$	9073.89	+	6897.79i	0.717124	+	0.545143i
$544$	2348.12	+	14322.9i	0.185064	+	1.12884i
$545$	1727.44	+	3258.29i	0.135771	+	0.256092i
$546$	−3083.26	−	678.676i	−0.241669	−	0.0531954i
$547$	−19695.4	+	9112.06i	−1.53952	+	0.712255i	−0.992198	−	0.124670i	$-0.960213\pi$
$547$	−19695.4	+	9112.06i	−1.53952	+	0.712255i	−0.547317	+	0.836926i	$0.684351\pi$
$548$	−5228.92	+	13123.6i	−0.407607	+	1.02302i
$549$	217.024	−	4002.77i	0.0168713	−	0.311173i
$550$	−12207.6	+	18004.8i	−0.946424	+	1.39587i
$551$	10424.6	−	12272.8i	0.805992	−	0.948887i
$552$	522.916	−	986.325i	0.0403203	−	0.0760521i
$553$	−2701.50	−	910.240i	−0.207738	−	0.0699952i
$554$	27.1341	+	500.459i	0.00208090	+	0.0383799i
$555$	−1849.02	−	1112.52i	−0.141417	−	0.0850881i
$556$	974.488	−	3509.79i	0.0743300	−	0.267713i
$557$	−4946.15	−	17814.4i	−0.376257	−	1.35515i	−0.873196	−	0.487369i	$-0.837957\pi$
$557$	−4946.15	−	17814.4i	−0.376257	−	1.35515i	0.496939	−	0.867785i	$-0.334457\pi$
$558$	9941.69	−	5981.72i	0.754239	−	0.453811i
$559$	11089.7	+	16356.1i	0.839079	+	1.23755i
$560$	−1054.98	−	114.736i	−0.0796088	−	0.00865798i
$561$	−7651.10	−	832.107i	−0.575810	−	0.0626231i
$562$	5661.75	+	8350.45i	0.424958	+	0.626766i
$563$	−2710.66	+	1630.95i	−0.202914	+	0.122089i	−0.613384	−	0.789785i	$-0.710192\pi$
$563$	−2710.66	+	1630.95i	−0.202914	+	0.122089i	0.410470	+	0.911874i	$0.365365\pi$
$564$	1163.33	+	4189.95i	0.0868532	+	0.312817i
$565$	639.231	−	2302.30i	0.0475976	−	0.171431i
$566$	−31788.1	−	19126.3i	−2.36070	−	1.42038i
$567$	−27.3540	−	504.516i	−0.00202604	−	0.0373680i
$568$	−575.529	−	193.918i	−0.0425152	−	0.0143250i
$569$	3992.37	−	7530.41i	0.294146	−	0.554817i	−0.691758	−	0.722129i	$-0.743164\pi$
$569$	3992.37	−	7530.41i	0.294146	−	0.554817i	0.985904	+	0.167311i	$0.0535085\pi$
$570$	1858.39	−	2187.86i	0.136560	−	0.160771i
$571$	8139.38	−	12004.7i	0.596537	−	0.879826i	−0.402835	−	0.915273i	$-0.631975\pi$
$571$	8139.38	−	12004.7i	0.596537	−	0.879826i	0.999372	+	0.0354470i	$0.0112855\pi$
$572$	878.387	−	16200.9i	0.0642084	−	1.18425i
$573$	−582.828	+	1462.79i	−0.0424922	+	0.106647i
$574$	−4409.85	+	2040.22i	−0.320669	+	0.148357i
$575$	19309.8	+	4250.40i	1.40048	+	0.308268i
$576$	−2439.55	−	4601.49i	−0.176472	−	0.332862i
$577$	−2907.37	−	17734.2i	−0.209767	−	1.27952i	−0.856237	−	0.516582i	$-0.827204\pi$
$577$	−2907.37	−	17734.2i	−0.209767	−	1.27952i	0.646471	−	0.762939i	$-0.276244\pi$
$578$	−5747.08	−	4368.82i	−0.413576	−	0.314392i
$579$	13499.7	+	6245.63i	0.968961	+	0.448289i
$580$	3482.83	−	3299.11i	0.249339	−	0.236187i
$581$	−2.06166	+	12.5755i	−0.000147215	+	0.000897971i
$582$	6770.76	−	2281.34i	0.482229	−	0.162482i
$583$	−1183.89	−	2971.34i	−0.0841024	−	0.211081i
$584$	1252.40	+	1186.34i	0.0887408	+	0.0840598i
$585$	−851.467	+	647.268i	−0.0601774	+	0.0457457i
$586$	12938.3	−	2847.94i	0.912077	−	0.200763i
$587$	−7291.62	−	8584.36i	−0.512704	−	0.603602i	0.443510	−	0.896269i	$-0.353733\pi$
$587$	−7291.62	−	8584.36i	−0.512704	−	0.603602i	−0.956214	+	0.292667i	$0.905457\pi$
$588$	−7745.56	+	842.381i	−0.543234	+	0.0590803i
$589$	26032.3			1.82113
$590$	−5110.79	−	1326.82i	−0.356624	−	0.0925839i
$591$	5136.82			0.357530
$592$	−14822.8	+	1612.08i	−1.02908	+	0.111919i
$593$	−2676.96	−	3151.56i	−0.185378	−	0.218244i	0.661621	−	0.749839i	$-0.269869\pi$
$593$	−2676.96	−	3151.56i	−0.185378	−	0.218244i	−0.846999	+	0.531594i	$0.821593\pi$
$594$	4911.30	−	1081.06i	0.339247	−	0.0746740i
$595$	−796.918	+	605.802i	−0.0549083	+	0.0417402i
$596$	10731.8	+	10165.7i	0.737573	+	0.698666i
$597$	−183.637	−	460.893i	−0.0125892	−	0.0315965i
$598$	−27065.8	+	9119.53i	−1.85084	+	0.623621i
$599$	−2027.63	+	12368.0i	−0.138308	+	0.843643i	0.822974	+	0.568079i	$0.192313\pi$
$599$	−2027.63	+	12368.0i	−0.138308	+	0.843643i	−0.961283	+	0.275564i	$0.911135\pi$
$600$	−559.142	+	529.647i	−0.0380448	+	0.0360379i
$601$	20672.1	+	9563.92i	1.40305	+	0.649119i	0.967922	−	0.251251i	$-0.0808420\pi$
$601$	20672.1	+	9563.92i	1.40305	+	0.649119i	0.435125	+	0.900370i	$0.356704\pi$
$602$	−9620.91	−	7313.63i	−0.651361	−	0.495151i
$603$	789.637	+	4816.57i	0.0533275	+	0.325283i
$604$	12397.1	+	23383.4i	0.835151	+	1.57526i
$605$	2144.05	+	471.942i	0.144080	+	0.0317143i
$606$	−4425.44	+	2047.42i	−0.296652	+	0.137246i
$607$	5642.30	−	14161.1i	0.377288	−	0.946921i	−0.610626	−	0.791919i	$-0.709082\pi$
$607$	5642.30	−	14161.1i	0.377288	−	0.946921i	0.987914	−	0.155002i	$-0.0495385\pi$
$608$	1152.00	−	21247.5i	0.0768420	−	1.41727i
$609$	2059.08	−	3036.91i	0.137008	−	0.202072i
$610$	3359.64	−	3955.27i	0.222996	−	0.262532i
$611$	3297.75	−	6220.21i	0.218351	−	0.411854i
$612$	−4080.35	−	1374.83i	−0.269507	−	0.0908075i
$613$	774.928	+	14292.7i	0.0510588	+	0.941724i	0.906073	+	0.423120i	$0.139065\pi$
$613$	774.928	+	14292.7i	0.0510588	+	0.941724i	−0.855015	+	0.518604i	$0.826452\pi$
$614$	−3892.53	−	2342.06i	−0.255846	−	0.153938i
$615$	−440.384	+	1586.12i	−0.0288748	+	0.103997i
$616$	167.989	+	605.041i	0.0109878	+	0.0395743i
$617$	−19634.4	+	11813.6i	−1.28112	+	0.770825i	−0.982983	−	0.183698i	$-0.941193\pi$
$617$	−19634.4	+	11813.6i	−1.28112	+	0.770825i	−0.298138	+	0.954523i	$0.596365\pi$
$618$	7118.30	+	10498.7i	0.463334	+	0.683366i
$619$	−8981.12	−	976.756i	−0.583169	−	0.0634235i	−0.188221	−	0.982127i	$-0.560272\pi$
$619$	−8981.12	−	976.756i	−0.583169	−	0.0634235i	−0.394949	+	0.918703i	$0.629238\pi$
$620$	7710.17	+	838.531i	0.499432	+	0.0543165i
$621$	−2565.12	−	3783.26i	−0.165756	−	0.244472i
$622$	35531.1	−	21378.3i	2.29046	−	1.37812i
$623$	1810.12	+	6519.47i	0.116406	+	0.419257i
$624$	−1977.07	+	7120.77i	−0.126837	+	0.456825i
$625$	−10808.9	−	6503.52i	−0.691772	−	0.416225i
$626$	762.457	+	14062.7i	0.0486804	+	0.897856i
$627$	10692.5	+	3602.73i	0.681051	+	0.229473i
$628$	9706.94	−	18309.2i	0.616798	−	1.16340i
$629$	−9105.42	+	10719.7i	−0.577197	+	0.679529i
$630$	367.072	−	541.390i	0.0232135	−	0.0342373i
$631$	1408.41	−	25976.6i	0.0888557	−	1.63885i	−0.526198	−	0.850362i	$-0.676383\pi$
$631$	1408.41	−	25976.6i	0.0888557	−	1.63885i	0.615054	−	0.788485i	$-0.289134\pi$
$632$	371.828	−	933.218i	0.0234027	−	0.0587365i
$633$	−9471.46	+	4381.96i	−0.594719	+	0.275146i
$634$	−12367.9	−	2722.38i	−0.774752	−	0.170536i
$635$	−1026.43	−	1936.06i	−0.0641460	−	0.120992i
$636$	−289.500	−	1765.87i	−0.0180494	−	0.110096i
$637$	10042.2	+	7633.88i	0.624625	+	0.474828i
$638$	33144.1	+	15334.1i	2.05672	+	0.951540i
$639$	−1805.27	+	1710.05i	−0.111761	+	0.105866i
$640$	130.106	−	793.613i	0.00803578	−	0.0490161i
$641$	27681.9	−	9327.10i	1.70572	−	0.574725i	0.713662	−	0.700490i	$-0.247035\pi$
$641$	27681.9	−	9327.10i	1.70572	−	0.574725i	0.992060	+	0.125766i	$0.0401388\pi$
$642$	5583.12	+	14012.6i	0.343222	+	0.861421i
$643$	6021.19	+	5703.58i	0.369289	+	0.349809i	0.849730	−	0.527218i	$-0.176765\pi$
$643$	6021.19	+	5703.58i	0.369289	+	0.349809i	−0.480441	+	0.877027i	$0.659523\pi$
$644$	7179.74	−	5457.89i	0.439319	−	0.333961i
$645$	−3998.51	+	880.138i	−0.244095	+	0.0537293i
$646$	−12112.6	−	14260.1i	−0.737717	−	0.868507i
$647$	447.793	−	48.7005i	0.0272095	−	0.00295922i	−0.0945041	−	0.995524i	$-0.530127\pi$
$647$	447.793	−	48.7005i	0.0272095	−	0.00295922i	0.121714	+	0.992565i	$0.461161\pi$
$648$	178.047			0.0107938
$649$	−2590.70	−	20592.1i	−0.156693	−	1.24547i
$650$	19703.9			1.18900
$651$	5896.99	−	641.336i	0.355025	−	0.0386113i
$652$	−17152.4	−	20193.3i	−1.03027	−	1.21293i
$653$	28072.6	−	6179.25i	1.68234	−	0.370311i	0.731945	−	0.681363i	$-0.238613\pi$
$653$	28072.6	−	6179.25i	1.68234	−	0.370311i	0.950393	+	0.311053i	$0.100682\pi$
$654$	−12503.7	+	9505.04i	−0.747603	+	0.568313i
$655$	1830.32	+	1733.77i	0.109185	+	0.103426i
$656$	4209.92	+	10566.1i	0.250564	+	0.628868i
$657$	6693.45	−	2255.29i	0.397468	−	0.133923i
$658$	−696.566	+	4248.87i	−0.0412690	+	0.251730i
$659$	6517.26	−	6173.47i	0.385245	−	0.364923i	−0.470430	−	0.882437i	$-0.655901\pi$
$659$	6517.26	−	6173.47i	0.385245	−	0.364923i	0.855675	+	0.517514i	$0.173143\pi$
$660$	3050.83	+	1411.46i	0.179929	+	0.0832442i
$661$	−12534.9	−	9528.75i	−0.737593	−	0.560704i	0.167523	−	0.985868i	$-0.446423\pi$
$661$	−12534.9	−	9528.75i	−0.737593	−	0.560704i	−0.905116	+	0.425164i	$0.860216\pi$
$662$	5420.07	+	33060.9i	0.318213	+	1.94101i
$663$	3265.36	+	6159.12i	0.191276	+	0.360785i
$664$	−4.38567	−	0.965358i	−0.000256321	−	5.64204e-5i
$665$	1331.95	−	616.224i	0.0776702	−	0.0359341i
$666$	3401.68	−	8537.58i	0.197917	−	0.496733i
$667$	1797.06	−	33144.8i	0.104321	−	1.92410i
$668$	9648.97	−	14231.2i	0.558877	−	0.824282i
$669$	−2374.80	+	2795.83i	−0.137242	+	0.161574i
$670$	−2959.74	+	5582.65i	−0.170664	+	0.321906i
$671$	19330.2	+	6513.12i	1.11212	+	0.374719i
$672$	−262.497	−	4841.48i	−0.0150685	−	0.277923i
$673$	10696.8	+	6436.06i	0.612677	+	0.368636i	0.787818	−	0.615908i	$-0.211211\pi$
$673$	10696.8	+	6436.06i	0.612677	+	0.368636i	−0.175141	+	0.984543i	$0.556038\pi$
$674$	−11353.7	+	40892.3i	−0.648855	+	2.33696i
$675$	843.625	+	3038.46i	0.0481054	+	0.173260i
$676$	3485.02	−	2096.87i	0.198283	−	0.119303i
$677$	15621.4	+	23039.8i	0.886822	+	1.30796i	0.950734	+	0.310009i	$0.100332\pi$
$677$	15621.4	+	23039.8i	0.886822	+	1.30796i	−0.0639121	+	0.997956i	$0.520358\pi$
$678$	10116.5	+	1100.24i	0.573041	+	0.0623220i
$679$	3631.34	+	394.932i	0.205240	+	0.0223212i
$680$	−197.962	−	291.972i	−0.0111640	−	0.0164656i
$681$	−1735.47	+	1044.20i	−0.0976552	+	0.0587572i
$682$	15794.7	+	56887.4i	0.886819	+	3.19403i
$683$	5544.33	−	19968.9i	0.310612	−	1.11872i	−0.629260	−	0.777195i	$-0.716642\pi$
$683$	5544.33	−	19968.9i	0.310612	−	1.11872i	0.939872	−	0.341528i	$-0.110944\pi$
$684$	5408.92	+	3254.44i	0.302361	+	0.181925i
$685$	256.552	+	4731.82i	0.0143100	+	0.263932i
$686$	−15556.6	−	5241.64i	−0.865824	−	0.291730i
$687$	5769.26	−	10882.0i	0.320395	−	0.604329i
$688$	−18314.1	+	21561.0i	−1.01485	+	1.19477i
$689$	−1625.86	+	2397.97i	−0.0898991	+	0.132591i
$690$	320.361	−	5908.71i	0.0176753	−	0.326001i
$691$	−3620.65	+	9087.14i	−0.199328	+	0.500276i	−0.994331	−	0.106330i	$-0.966090\pi$
$691$	−3620.65	+	9087.14i	−0.199328	+	0.500276i	0.795003	+	0.606606i	$0.207469\pi$
$692$	−22977.4	+	10630.5i	−1.26224	+	0.583975i
$693$	2510.89	+	552.689i	0.137635	+	0.0302957i
$694$	−19212.9	−	36239.3i	−1.05088	−	1.98217i
$695$	−197.676	−	1205.77i	−0.0107889	−	0.0658094i
$696$	1029.33	+	782.473i	0.0560582	+	0.0426143i
$697$	9737.48	+	4505.04i	0.529173	+	0.244821i
$698$	−12310.4	+	11661.0i	−0.667556	+	0.632343i
$699$	795.804	−	4854.19i	0.0430616	−	0.262664i
$700$	−5896.23	+	1986.67i	−0.318366	+	0.107270i
$701$	6214.89	+	15598.2i	0.334855	+	0.840422i	0.995932	+	0.0901045i	$0.0287201\pi$
$701$	6214.89	+	15598.2i	0.334855	+	0.840422i	−0.661078	+	0.750318i	$0.729901\pi$
$702$	−3306.99	−	3132.55i	−0.177798	−	0.168420i
$703$	16415.5	−	12478.8i	0.880687	−	0.669481i
$704$	25882.2	−	5697.11i	1.38561	−	0.304997i
$705$	944.312	+	1111.73i	0.0504466	+	0.0593903i
$706$	41988.3	−	4566.50i	2.23831	−	0.243431i
$707$	−2492.90			−0.132610
$708$	1061.05	−	11562.7i	0.0563232	−	0.613777i
$709$	−12984.4			−0.687785			−0.343893	−	0.939009i	$-0.611746\pi$
$709$	−12984.4			−0.687785			−0.343893	+	0.939009i	$0.611746\pi$
$710$	−3200.27	+	348.051i	−0.169161	+	0.0183973i
$711$	−2662.77	−	3134.86i	−0.140452	−	0.165353i
$712$	−2328.56	+	512.555i	−0.122565	+	0.0269787i
$713$	42720.4	−	32475.2i	2.24388	−	1.70576i
$714$	−3095.14	−	2931.87i	−0.162230	−	0.153673i
$715$	−2014.45	−	5055.90i	−0.105365	−	0.264447i
$716$	−16099.9	+	5424.68i	−0.840336	+	0.283142i
$717$	−287.564	+	1754.07i	−0.0149781	+	0.0913623i
$718$	25317.3	−	23981.8i	1.31592	−	1.24651i
$719$	12965.8	+	5998.63i	0.672523	+	0.311142i	0.726267	−	0.687412i	$-0.241253\pi$
$719$	12965.8	+	5998.63i	0.672523	+	0.311142i	−0.0537442	+	0.998555i	$0.517116\pi$
$720$	−1218.92	−	926.600i	−0.0630924	−	0.0479616i
$721$	1049.13	+	6399.43i	0.0541911	+	0.330551i
$722$	−217.966	−	411.127i	−0.0112352	−	0.0211919i
$723$	−7426.92	−	1634.79i	−0.382033	−	0.0840919i
$724$	−29449.2	+	13624.6i	−1.51170	+	0.699387i
$725$	−8476.11	+	21273.4i	−0.434200	+	1.08976i
$726$	−506.192	+	9336.16i	−0.0258768	+	0.477269i
$727$	−2498.75	+	3685.39i	−0.127474	+	0.188010i	−0.886070	−	0.463551i	$-0.846575\pi$
$727$	−2498.75	+	3685.39i	−0.127474	+	0.188010i	0.758596	+	0.651561i	$0.225886\pi$
$728$	368.216	−	433.498i	0.0187459	−	0.0220694i
$729$	341.470	−	644.080i	0.0173485	−	0.0327227i
$730$	8665.25	+	2919.66i	0.439336	+	0.148030i
$731$	1444.72	+	26646.3i	0.0730984	+	1.34822i
$732$	9778.39	+	5883.46i	0.493743	+	0.297075i
$733$	−32.6765	+	117.690i	−0.00164657	+	0.00593041i	−0.964369	−	0.264562i	$-0.914773\pi$
$733$	−32.6765	+	117.690i	−0.00164657	+	0.00593041i	0.962722	+	0.270492i	$0.0871865\pi$
$734$	2358.96	+	8496.21i	0.118625	+	0.427249i
$735$	−2239.40	+	1347.40i	−0.112383	+	0.0676187i
$736$	−24615.6	−	36305.3i	−1.23280	−	1.81825i
$737$	−24690.7	−	2685.28i	−1.23405	−	0.134211i
$738$	−6969.53	−	757.982i	−0.347631	−	0.0378072i
$739$	11410.4	+	16829.1i	0.567981	+	0.837710i	0.997874	−	0.0651703i	$-0.0207591\pi$
$739$	11410.4	+	16829.1i	0.567981	+	0.837710i	−0.429893	+	0.902880i	$0.641449\pi$
$740$	5263.85	−	3167.15i	0.261490	−	0.157334i
$741$	−2734.20	−	9847.70i	−0.135551	−	0.488211i
$742$	474.008	−	1707.22i	0.0234520	−	0.0844665i
$743$	−11212.7	−	6746.45i	−0.553638	−	0.333113i	0.211089	−	0.977467i	$-0.432299\pi$
$743$	−11212.7	−	6746.45i	−0.553638	−	0.333113i	−0.764728	+	0.644354i	$0.777127\pi$
$744$	113.166	+	2087.23i	0.00557645	+	0.102852i
$745$	4699.02	+	1583.28i	0.231086	+	0.0778618i
$746$	16598.4	−	31307.9i	0.814625	−	1.53655i
$747$	−11.9032	+	14.0136i	−0.000583021	+	0.000686385i
$748$	12295.5	−	18134.5i	0.601026	−	0.886447i
$749$	−417.498	+	7700.30i	−0.0203672	+	0.375651i
$750$	−3128.25	+	7851.32i	−0.152304	+	0.382253i
$751$	−5025.67	+	2325.12i	−0.244193	+	0.112976i	−0.538169	−	0.842837i	$-0.680884\pi$
$751$	−5025.67	+	2325.12i	−0.244193	+	0.112976i	0.293975	+	0.955813i	$0.405022\pi$
$752$	9842.99	+	2166.61i	0.477310	+	0.105064i
$753$	8397.52	+	15839.4i	0.406404	+	0.766560i
$754$	−5351.59	−	32643.3i	−0.258479	−	1.57665i
$755$	7067.68	+	5372.71i	0.340688	+	0.258984i
$756$	1305.44	+	603.959i	0.0628019	+	0.0290553i
$757$	−1078.05	+	1021.19i	−0.0517603	+	0.0490299i	−0.713142	−	0.701019i	$-0.752729\pi$
$757$	−1078.05	+	1021.19i	−0.0517603	+	0.0490299i	0.661382	+	0.750049i	$0.269970\pi$
$758$	1975.51	−	12050.1i	0.0946621	−	0.577414i
$759$	22041.4	−	7426.60i	1.05409	−	0.355163i
$760$	191.422	+	480.433i	0.00913632	+	0.0229304i
$761$	−2930.08	−	2775.52i	−0.139573	−	0.132211i	0.614728	−	0.788739i	$-0.289266\pi$
$761$	−2930.08	−	2775.52i	−0.139573	−	0.132211i	−0.754302	+	0.656528i	$0.772024\pi$
$762$	7429.59	−	5647.83i	0.353210	−	0.268503i
$763$	−7842.08	+	1726.17i	−0.372087	+	0.0819025i
$764$	−2902.03	−	3416.53i	−0.137424	−	0.161788i
$765$	−1435.86	+	156.159i	−0.0678610	+	0.00738032i
$766$	−56247.9			−2.65316
$767$	−14121.3	+	12409.6i	−0.664786	+	0.584207i
$768$	−10463.4			−0.491624
$769$	8276.60	−	900.135i	0.388117	−	0.0422103i	0.0880194	−	0.996119i	$-0.471946\pi$
$769$	8276.60	−	900.135i	0.388117	−	0.0422103i	0.300098	+	0.953908i	$0.402981\pi$
$770$	2154.75	+	2536.77i	0.100846	+	0.118726i
$771$	−14409.4	+	3171.74i	−0.673074	+	0.148155i
$772$	−33710.6	+	25626.1i	−1.57159	+	1.19469i
$773$	−20399.5	−	19323.4i	−0.949184	−	0.899115i	0.0458199	−	0.998950i	$-0.485410\pi$
$773$	−20399.5	−	19323.4i	−0.949184	−	0.899115i	−0.995004	+	0.0998348i	$0.968169\pi$
$774$	−6454.04	−	16198.4i	−0.299723	−	0.752248i
$775$	−35083.3	+	11820.9i	−1.62610	+	0.547898i
$776$	−208.245	+	1270.24i	−0.00963344	+	0.0587614i
$777$	3411.11	−	3231.17i	0.157494	−	0.149186i
$778$	−14130.4	−	6537.43i	−0.651157	−	0.301258i
$779$	−12522.2	−	9519.16i	−0.575938	−	0.437817i
$780$	−492.600	−	3004.73i	−0.0226127	−	0.137932i
$781$	−5926.85	−	11179.2i	−0.271548	−	0.512195i
$782$	−37666.8	−	8291.09i	−1.72246	−	0.379142i
$783$	4804.67	−	2222.88i	0.219291	−	0.101455i
$784$	−6684.01	+	16775.6i	−0.304483	+	0.764194i
$785$	376.344	−	6941.25i	0.0171112	−	0.315597i
$786$	−6025.55	+	8887.01i	−0.273440	+	0.403294i
$787$	−12468.1	+	14678.6i	−0.564727	+	0.664848i	−0.968210	−	0.250139i	$-0.919524\pi$
$787$	−12468.1	+	14678.6i	−0.564727	+	0.664848i	0.403483	+	0.914987i	$0.367799\pi$
$788$	−6849.83	+	12920.1i	−0.309664	+	0.584088i
$789$	−10468.1	−	3527.11i	−0.472337	−	0.159149i
$790$	−288.278	−	5316.97i	−0.0129829	−	0.239455i
$791$	4457.84	+	2682.19i	0.200382	+	0.120566i
$792$	−242.379	+	872.971i	−0.0108745	+	0.0391663i
$793$	−4942.96	−	17802.9i	−0.221349	−	0.797226i
$794$	2630.70	−	1582.84i	0.117582	−	0.0707467i
$795$	−336.855	−	496.824i	−0.0150277	−	0.0221642i
$796$	1404.12	+	152.707i	0.0625221	+	0.00679968i
$797$	31357.3	+	3410.31i	1.39364	+	0.151567i	0.773934	−	0.633267i	$-0.218286\pi$
$797$	31357.3	+	3410.31i	1.39364	+	0.151567i	0.619706	+	0.784834i	$0.287252\pi$
$798$	3507.58	+	5173.29i	0.155598	+	0.229489i
$799$	8146.35	−	4901.49i	0.360697	−	0.217024i
$800$	8095.67	+	29158.0i	0.357781	+	1.28861i
$801$	−2611.70	+	9406.50i	−0.115206	+	0.414934i
$802$	−4980.14	−	2996.45i	−0.219270	−	0.131931i
$803$	1945.81	+	35888.3i	0.0855119	+	1.57717i
$804$	−13167.6	−	4436.69i	−0.577595	−	0.194614i
$805$	1417.06	−	2672.85i	0.0620430	−	0.117026i
$806$	34620.6	−	40758.5i	1.51298	−	1.78121i
$807$	9440.81	−	13924.2i	0.411812	−	0.607377i
$808$	47.5596	−	877.185i	0.00207072	−	0.0381922i
$809$	−289.271	+	726.015i	−0.0125713	+	0.0315517i	−0.935128	−	0.354309i	$-0.884716\pi$
$809$	−289.271	+	726.015i	−0.0125713	+	0.0315517i	0.922557	+	0.385861i	$0.126095\pi$
$810$	856.527	−	396.272i	0.0371547	−	0.0171896i
$811$	−27385.5	−	6028.01i	−1.18574	−	0.261001i	−0.422044	−	0.906576i	$-0.638687\pi$
$811$	−27385.5	−	6028.01i	−1.18574	−	0.261001i	−0.763698	+	0.645574i	$0.776618\pi$
$812$	4892.73	+	9228.66i	0.211455	+	0.398846i
$813$	64.8080	+	395.311i	0.00279571	+	0.0170531i
$814$	37229.2	+	28300.9i	1.60305	+	1.21861i
$815$	−8066.05	−	3731.75i	−0.346676	−	0.160390i
$816$	−7245.17	+	6862.99i	−0.310823	+	0.294427i
$817$	6329.35	−	38607.3i	0.271035	−	1.65324i
$818$	−39854.7	+	13428.6i	−1.70353	+	0.573986i
$819$	−861.976	−	2163.40i	−0.0367764	−	0.0923018i
$820$	−3402.17	−	3222.71i	−0.144889	−	0.137246i
$821$	−31844.0	+	24207.2i	−1.35367	+	1.02903i	−0.358233	+	0.933632i	$0.616621\pi$
$821$	−31844.0	+	24207.2i	−1.35367	+	1.02903i	−0.995439	+	0.0954026i	$0.969586\pi$
$822$	−19710.0	+	4338.50i	−0.836333	+	0.184091i
$823$	−29157.4	−	34326.8i	−1.23495	−	1.45390i	−0.846468	−	0.532440i	$-0.821275\pi$
$823$	−29157.4	−	34326.8i	−1.23495	−	1.45390i	−0.388483	−	0.921456i	$-0.627001\pi$
$824$	−2271.80	+	247.074i	−0.0960462	+	0.0104457i
$825$	−16046.1			−0.677156
$826$	5760.70	−	9949.47i	0.242664	−	0.419112i
$827$	5686.98			0.239124			0.119562	−	0.992827i	$-0.461851\pi$
$827$	5686.98			0.239124			0.119562	+	0.992827i	$0.461851\pi$
$828$	12936.2	−	1406.90i	0.542952	−	0.0590496i
$829$	8634.85	+	10165.7i	0.361762	+	0.425899i	0.912689	−	0.408654i	$-0.134002\pi$
$829$	8634.85	+	10165.7i	0.361762	+	0.425899i	−0.550927	+	0.834553i	$0.685726\pi$
$830$	−23.2465	+	5.11695i	−0.000972168	+	0.000213990i
$831$	−294.318	+	223.735i	−0.0122861	+	0.00933967i
$832$	−17427.6	−	16508.3i	−0.726196	−	0.687889i
$833$	6305.08	+	15824.5i	0.262254	+	0.658209i
$834$	4931.39	−	1661.58i	0.204748	−	0.0689877i
$835$	933.085	−	5691.56i	0.0386715	−	0.235886i
$836$	−23319.9	+	22089.7i	−0.964754	+	0.913863i
$837$	7767.51	+	3593.63i	0.320770	+	0.148404i
$838$	12185.5	+	9263.17i	0.502316	+	0.381851i
$839$	818.409	+	4992.08i	0.0336765	+	0.205418i	0.998305	−	0.0581944i	$-0.0185343\pi$
$839$	818.409	+	4992.08i	0.0336765	+	0.205418i	−0.964629	+	0.263612i	$0.915086\pi$
$840$	55.1980	+	104.114i	0.00226728	+	0.00427654i
$841$	13726.9	+	3021.52i	0.562831	+	0.123889i
$842$	−42270.8	+	19556.5i	−1.73010	+	0.800431i
$843$	−2754.57	+	6913.45i	−0.112541	+	0.282458i
$844$	1608.44	−	29665.9i	0.0655981	−	1.20988i
$845$	765.636	−	1129.23i	0.0311700	−	0.0459723i
$846$	−4021.71	+	4734.73i	−0.163439	+	0.192415i
$847$	−2239.04	+	4223.28i	−0.0908316	+	0.171327i
$848$	−3930.38	−	1324.30i	−0.159162	−	0.0536281i
$849$	−1481.54	−	27325.4i	−0.0598897	−	1.10460i
$850$	22799.3	+	13717.9i	0.920011	+	0.553552i
$851$	11371.5	−	40956.5i	0.458062	−	1.64979i
$852$	−1893.83	−	6820.94i	−0.0761519	−	0.274274i
$853$	−3245.75	+	1952.90i	−0.130284	+	0.0783893i	−0.579204	−	0.815183i	$-0.696636\pi$
$853$	−3245.75	+	1952.90i	−0.130284	+	0.0783893i	0.448920	+	0.893572i	$0.351809\pi$
$854$	6341.09	+	9352.42i	0.254084	+	0.374746i
$855$	2105.07	+	228.940i	0.0842010	+	0.00915741i
$856$	−2701.57	−	293.813i	−0.107871	−	0.0117317i
$857$	6500.40	+	9587.37i	0.259101	+	0.382145i	0.934883	−	0.354956i	$-0.115504\pi$
$857$	6500.40	+	9587.37i	0.259101	+	0.382145i	−0.675782	+	0.737101i	$0.736194\pi$
$858$	19860.8	−	11949.9i	0.790254	−	0.475480i
$859$	−5718.52	−	20596.3i	−0.227140	−	0.818085i	−0.985988	−	0.166817i	$-0.946651\pi$
$859$	−5718.52	−	20596.3i	−0.227140	−	0.818085i	0.758848	−	0.651268i	$-0.225763\pi$
$860$	3118.19	−	11230.7i	0.123639	−	0.445307i
$861$	−3071.12	−	1847.83i	−0.121561	−	0.0731405i
$862$	1738.87	+	32071.6i	0.0687080	+	1.26724i
$863$	36417.7	+	12270.6i	1.43647	+	0.484003i	0.926534	−	0.376210i	$-0.122773\pi$
$863$	36417.7	+	12270.6i	1.43647	+	0.484003i	0.509935	+	0.860213i	$0.329669\pi$
$864$	3276.84	−	6180.78i	0.129028	−	0.243373i
$865$	−5497.94	+	6472.67i	−0.216110	+	0.254425i
$866$	31681.2	−	46726.3i	1.24315	−	1.83352i
$867$	288.297	−	5317.32i	0.0112931	−	0.208288i
$868$	−6250.41	+	15687.3i	−0.244416	+	0.613437i
$869$	18995.2	−	8788.09i	0.741503	−	0.343056i
$870$	6693.26	+	1473.30i	0.260831	+	0.0574132i
$871$	10537.6	+	19876.0i	0.409934	+	0.773217i
$872$	−457.783	−	2792.35i	−0.0177781	−	0.108441i
$873$	4195.65	+	3189.45i	0.162659	+	0.123650i
$874$	51318.0	+	23742.2i	1.98611	+	0.918871i
$875$	−3136.92	+	2971.45i	−0.121197	+	0.114804i
$876$	−3253.06	+	19842.8i	−0.125469	+	0.765325i
$877$	−17559.9	+	5916.60i	−0.676116	+	0.227810i	−0.636352	−	0.771399i	$-0.719557\pi$
$877$	−17559.9	+	5916.60i	−0.676116	+	0.227810i	−0.0397646	+	0.999209i	$0.512661\pi$
$878$	−14697.9	−	36889.1i	−0.564956	−	1.41793i
$879$	7094.68	+	6720.44i	0.272239	+	0.257878i
$880$	6202.49	−	4715.01i	0.237597	−	0.180617i
$881$	33966.8	−	7476.65i	1.29894	−	0.285919i	0.488926	−	0.872325i	$-0.337389\pi$
$881$	33966.8	−	7476.65i	1.29894	−	0.285919i	0.810017	+	0.586406i	$0.199458\pi$
$882$	−7205.81	−	8483.34i	−0.275093	−	0.323865i
$883$	10293.4	−	1119.48i	0.392301	−	0.0426653i	0.0901571	−	0.995928i	$-0.471263\pi$
$883$	10293.4	−	1119.48i	0.392301	−	0.0426653i	0.302144	+	0.953262i	$0.402298\pi$
$884$	−19845.7			−0.755073
$885$	−1305.57	−	3669.59i	−0.0495889	−	0.139381i
$886$	−54697.9			−2.07405
$887$	45337.5	−	4930.75i	1.71622	−	0.186650i	0.803518	−	0.595281i	$-0.202959\pi$
$887$	45337.5	−	4930.75i	1.71622	−	0.186650i	0.912700	+	0.408631i	$0.133994\pi$
$888$	1071.89	+	1261.92i	0.0405069	+	0.0476884i
$889$	4659.71	−	1025.68i	0.175795	−	0.0386954i
$890$	−10061.2	+	7648.30i	−0.378934	+	0.288058i
$891$	2693.09	+	2551.03i	0.101259	+	0.0959179i
$892$	−3865.34	−	9701.27i	−0.145091	−	0.364151i
$893$	−13208.6	+	4450.51i	−0.494972	+	0.166776i
$894$	−3416.52	+	20839.8i	−0.127814	+	0.779629i
$895$	−4137.37	+	3919.12i	−0.154522	+	0.146371i
$896$	1589.20	+	735.242i	0.0592538	+	0.0274137i
$897$	−16771.9	−	12749.7i	−0.624300	−	0.474581i
$898$	−3276.69	−	19986.9i	−0.121765	−	0.742731i
$899$	29112.3	+	54911.7i	1.08003	+	2.03716i
$900$	−8767.31	−	1929.83i	−0.324715	−	0.0714752i
$901$	−3550.76	+	1642.76i	−0.131291	+	0.0607415i
$902$	13204.2	−	33139.9i	0.487417	−	1.22333i
$903$	482.624	−	8901.48i	0.0177860	−	0.328043i
$904$	−1028.84	+	1517.42i	−0.0378525	+	0.0558282i
$905$	−7046.47	+	8295.75i	−0.258821	+	0.304707i
$906$	−17710.6	+	33405.8i	−0.649443	+	1.22498i
$907$	−29782.4	−	10034.8i	−1.09031	−	0.367367i	−0.283975	−	0.958832i	$-0.591653\pi$
$907$	−29782.4	−	10034.8i	−1.09031	−	0.367367i	−0.806331	+	0.591465i	$0.798550\pi$
$908$	−312.161	−	5757.46i	−0.0114090	−	0.210427i
$909$	−3081.97	−	1854.36i	−0.112456	−	0.0676626i
$910$	806.551	−	2904.94i	0.0293812	−	0.105822i
$911$	7372.66	+	26553.9i	0.268131	+	0.965720i	0.967897	+	0.251348i	$0.0808738\pi$
$911$	7372.66	+	26553.9i	0.268131	+	0.965720i	−0.699766	+	0.714372i	$0.746712\pi$
$912$	12536.5	−	7542.98i	0.455182	−	0.273874i
$913$	−52.5048	−	77.4388i	−0.00190324	−	0.00280706i
$914$	−7638.81	−	830.771i	−0.276444	−	0.0300651i
$915$	3805.60	+	413.884i	0.137496	+	0.0149536i
$916$	19677.2	+	29021.8i	0.709776	+	1.04684i
$917$	−4703.58	+	2830.05i	−0.169385	+	0.101916i
$918$	−1645.63	−	5927.01i	−0.0591653	−	0.213094i
$919$	2505.89	−	9025.39i	0.0899473	−	0.323961i	−0.904864	−	0.425701i	$-0.860027\pi$
$919$	2505.89	−	9025.39i	0.0899473	−	0.323961i	0.994811	+	0.101741i	$0.0324412\pi$
$920$	913.470	+	549.617i	0.0327350	+	0.0196960i
$921$	−181.418	−	3346.05i	−0.00649068	−	0.119714i
$922$	17976.3	+	6056.92i	0.642102	+	0.216349i
$923$	−5368.50	+	10126.1i	−0.191448	+	0.361109i
$924$	−4738.34	+	5578.41i	−0.168701	+	0.198610i
$925$	−16456.5	+	24271.5i	−0.584957	+	0.862747i
$926$	−2702.82	+	49850.5i	−0.0959180	+	1.76910i
$927$	−3463.22	+	8692.02i	−0.122704	+	0.307965i
$928$	46107.0	−	21331.4i	1.63097	−	0.754565i
$929$	−39481.7	−	8690.59i	−1.39435	−	0.306920i	−0.546637	−	0.837370i	$-0.684092\pi$
$929$	−39481.7	−	8690.59i	−1.39435	−	0.306920i	−0.847717	+	0.530449i	$0.822023\pi$
$930$	5189.85	+	9789.10i	0.182991	+	0.345158i
$931$	−4040.27	−	24644.6i	−0.142228	−	0.867555i
$932$	11148.1	+	8474.56i	0.391811	+	0.297847i
$933$	27760.7	+	12843.5i	0.974109	+	0.450671i
$934$	−13995.9	+	13257.6i	−0.490322	+	0.464458i
$935$	1189.01	−	7252.64i	0.0415880	−	0.253676i
$936$	777.686	−	262.033i	0.0271575	−	0.00915044i
$937$	399.763	+	1003.33i	0.0139378	+	0.0349812i	0.935781	−	0.352582i	$-0.114696\pi$
$937$	399.763	+	1003.33i	0.0139378	+	0.0349812i	−0.921843	+	0.387563i	$0.873317\pi$
$938$	−9988.25	−	9461.38i	−0.347684	−	0.329344i
$939$	−8270.22	+	6286.86i	−0.287421	+	0.218492i
$940$	−4055.45	+	892.671i	−0.140717	+	0.0309742i
$941$	13507.9	+	15902.7i	0.467954	+	0.550919i	0.944620	−	0.328166i	$-0.106431\pi$
$941$	13507.9	+	15902.7i	0.467954	+	0.550919i	−0.476666	+	0.879085i	$0.658155\pi$
$942$	29431.9	−	3200.91i	1.01798	−	0.110713i
$943$	−32424.7			−1.11972
$944$	−22525.8	−	14725.9i	−0.776643	−	0.507720i
$945$	482.492			0.0166090
$946$	88207.3	−	9593.12i	3.03157	−	0.329703i
$947$	−24522.3	−	28869.8i	−0.841464	−	0.990648i	−0.999995	−	0.00329380i	$-0.998952\pi$
$947$	−24522.3	−	28869.8i	−0.841464	−	0.990648i	0.158531	−	0.987354i	$-0.449324\pi$
$948$	11435.5	−	2517.15i	0.391782	−	0.0862377i
$949$	25916.9	−	19701.5i	0.886511	−	0.673908i
$950$	−28320.5	−	26826.6i	−0.967199	−	0.916180i
$951$	−3457.66	−	8678.06i	−0.117899	−	0.295905i
$952$	727.865	−	245.246i	0.0247797	−	0.00834924i
$953$	−2574.69	+	15704.9i	−0.0875155	+	0.533821i	0.906287	+	0.422663i	$0.138904\pi$
$953$	−2574.69	+	15704.9i	−0.0875155	+	0.533821i	−0.993803	+	0.111159i	$0.964544\pi$
$954$	1855.95	−	1758.05i	0.0629858	−	0.0596633i
$955$	−1364.70	−	631.379i	−0.0462416	−	0.0213936i
$956$	−4028.37	−	3062.29i	−0.136283	−	0.103600i
$957$	4358.14	+	26583.5i	0.147209	+	0.897932i
$958$	−5072.59	−	9567.92i	−0.171073	−	0.322678i
$959$	−10076.7	−	2218.05i	−0.339306	−	0.0746868i
$960$	4513.85	−	2088.33i	0.151754	−	0.0702088i
$961$	−26163.9	+	65666.5i	−0.878250	+	2.20424i
$962$	2293.29	−	42297.2i	0.0768592	−	1.41758i
$963$	−6244.08	+	9209.32i	−0.208943	+	0.308169i
$964$	14015.5	−	16500.3i	0.468265	−	0.551284i
$965$	−6653.41	+	12549.7i	−0.221949	+	0.418641i
$966$	12209.8	+	4113.95i	0.406670	+	0.137023i
$967$	−6.50970	−	120.064i	−0.000216482	−	0.00399277i	0.998423	−	0.0561352i	$-0.0178778\pi$
$967$	−6.50970	−	120.064i	−0.000216482	−	0.00399277i	−0.998640	+	0.0521424i	$0.983395\pi$
$968$	−1443.34	−	868.431i	−0.0479244	−	0.0288351i
$969$	3692.26	−	13298.3i	0.122407	−	0.440870i
$970$	1825.31	+	6574.17i	0.0604197	+	0.217612i
$971$	−32522.1	+	19567.9i	−1.07485	+	0.646718i	−0.938967	−	0.344006i	$-0.888216\pi$
$971$	−32522.1	+	19567.9i	−1.07485	+	0.646718i	−0.135887	+	0.990724i	$0.543388\pi$
$972$	1164.65	+	1717.73i	0.0384323	+	0.0566834i
$973$	2644.83	+	287.643i	0.0871423	+	0.00947730i
$974$	−2513.60	−	273.371i	−0.0826910	−	0.00899318i
$975$	8156.55	+	12030.0i	0.267916	+	0.395147i
$976$	22663.9	−	13636.4i	0.743292	−	0.447224i
$977$	−5127.31	−	18466.9i	−0.167899	−	0.604717i	−0.998831	−	0.0483430i	$-0.984606\pi$
$977$	−5127.31	−	18466.9i	−0.167899	−	0.604717i	0.830932	−	0.556374i	$-0.187808\pi$
$978$	10126.1	−	36471.0i	0.331082	−	1.19245i
$979$	−42564.9	−	25610.5i	−1.38956	−	0.836072i
$980$	−402.804	−	7429.29i	−0.0131297	−	0.242163i
$981$	−10979.2	−	3699.32i	−0.357328	−	0.120398i
$982$	−29582.0	+	55797.6i	−0.961304	+	1.81321i
$983$	12810.8	−	15082.1i	0.415668	−	0.489362i	−0.513985	−	0.857799i	$-0.671831\pi$
$983$	12810.8	−	15082.1i	0.415668	−	0.489362i	0.929653	+	0.368437i	$0.120107\pi$
$984$	708.794	−	1045.39i	0.0229629	−	0.0338678i
$985$	−265.572	+	4898.18i	−0.00859068	+	0.158446i
$986$	16534.0	−	41497.2i	0.534027	−	1.34031i
$987$	−2882.45	+	1333.56i	−0.0929579	+	0.0430069i
$988$	28415.0	+	6254.61i	0.914980	+	0.201402i
$989$	−37775.6	−	71252.4i	−1.21455	−	2.29089i
$990$	776.924	+	4739.03i	0.0249417	+	0.152138i
$991$	−42074.2	−	31984.0i	−1.34867	−	1.02523i	−0.995988	−	0.0894877i	$-0.971477\pi$
$991$	−42074.2	−	31984.0i	−1.34867	−	1.02523i	−0.352681	−	0.935744i	$-0.614730\pi$
$992$	74539.3	+	34485.6i	2.38571	+	1.10375i
$993$	−17941.4	+	16995.0i	−0.573366	+	0.543121i
$994$	1133.96	−	6916.86i	0.0361842	−	0.220714i
$995$	448.976	−	151.278i	0.0143050	−	0.00481992i
$996$	−19.3743	−	48.6258i	−0.000616364	−	0.00154696i
$997$	−8718.76	−	8258.85i	−0.276957	−	0.262347i	0.536595	−	0.843840i	$-0.319710\pi$
$997$	−8718.76	−	8258.85i	−0.276957	−	0.262347i	−0.813552	+	0.581493i	$0.802469\pi$
$998$	−11238.2	+	8543.06i	−0.356452	+	0.270968i
$999$	6620.68	−	1457.32i	0.209679	−	0.0461538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.133.3	yes	420
59.4	even	29	inner	177.4.e.a.4.3	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.4.3	✓	420	59.4	even	29	inner
177.4.e.a.133.3	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)

\(f(q)\)	\(=\)	\(q+(-4.04316 + 0.439720i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(8.34080 - 1.83595i) q^{4} +(2.28067 - 1.73372i) q^{5} +(8.85787 + 8.39062i) q^{6} +(2.30882 + 5.79471i) q^{7} +(-2.08305 + 0.701862i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})\)	\(q+(-4.04316 + 0.439720i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(8.34080 - 1.83595i) q^{4} +(2.28067 - 1.73372i) q^{5} +(8.85787 + 8.39062i) q^{6} +(2.30882 + 5.79471i) q^{7} +(-2.08305 + 0.701862i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-8.45878 + 8.01258i) q^{10} +(-41.5638 - 19.2295i) q^{11} +(-20.3970 - 15.5054i) q^{12} +(6.71107 + 40.9357i) q^{13} +(-11.8830 - 22.4137i) q^{14} +(-8.39357 - 1.84756i) q^{15} +(-53.8955 + 24.9347i) q^{16} +(-20.7342 + 52.0389i) q^{17} +(1.98165 - 36.5493i) q^{18} +(46.0877 - 67.9743i) q^{19} +(15.8396 - 18.6479i) q^{20} +(8.76543 - 16.5333i) q^{21} +(176.505 + 59.4713i) q^{22} +(-9.16527 - 169.043i) q^{23} +(5.65042 + 3.39974i) q^{24} +(-31.2454 + 112.536i) q^{25} +(-45.1342 - 162.559i) q^{26} +(23.1351 - 13.9200i) q^{27} +(29.8963 + 44.0937i) q^{28} +(194.923 + 21.1992i) q^{29} +(34.7489 + 3.77917i) q^{30} +(177.887 + 262.363i) q^{31} +(222.012 - 133.580i) q^{32} +(36.7556 + 132.382i) q^{33} +(60.9491 - 219.519i) q^{34} +(15.3121 + 9.21299i) q^{35} +(4.16135 + 76.7516i) q^{36} +(237.937 + 80.1704i) q^{37} +(-156.450 + 295.096i) q^{38} +(80.5650 - 94.8485i) q^{39} +(-3.53393 + 5.21216i) q^{40} +(10.3693 - 191.251i) q^{41} +(-28.1700 + 70.7013i) q^{42} +(432.349 - 200.026i) q^{43} +(-381.980 - 84.0801i) q^{44} +(12.0772 + 22.7800i) q^{45} +(111.388 + 679.439i) q^{46} +(-135.112 - 102.710i) q^{47} +(161.687 + 74.8042i) q^{48} +(220.768 - 209.123i) q^{49} +(76.8458 - 468.738i) q^{50} +(159.255 - 53.6594i) q^{51} +(131.132 + 329.116i) q^{52} +(50.7048 + 48.0301i) q^{53} +(-87.4182 + 66.4536i) q^{54} +(-128.132 + 28.2040i) q^{55} +(-8.87649 - 10.4502i) q^{56} +(-244.932 + 26.6380i) q^{57} -797.427 q^{58} +(240.142 + 384.332i) q^{59} -73.4012 q^{60} +(-442.794 + 48.1568i) q^{61} +(-834.589 - 982.555i) q^{62} +(-54.8271 + 12.0684i) q^{63} +(-460.688 + 350.206i) q^{64} +(86.2770 + 81.7259i) q^{65} +(-206.820 - 519.078i) q^{66} +(513.930 - 173.163i) q^{67} +(-77.3991 + 472.113i) q^{68} +(-368.715 + 349.265i) q^{69} +(-65.9604 - 30.5165i) q^{70} +(219.953 + 167.204i) q^{71} +(-3.20054 - 19.5224i) q^{72} +(-367.606 - 693.379i) q^{73} +(-997.271 - 219.516i) q^{74} +(317.995 - 147.120i) q^{75} +(259.611 - 651.575i) q^{76} +(15.4657 - 285.248i) q^{77} +(-284.030 + 418.913i) q^{78} +(-295.863 + 348.317i) q^{79} +(-79.6882 + 150.308i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(42.1720 + 777.816i) q^{82} +(1.75052 + 1.05325i) q^{83} +(42.7563 - 153.994i) q^{84} +(42.9331 + 154.631i) q^{85} +(-1660.10 + 998.848i) q^{86} +(-330.100 - 486.862i) q^{87} +(100.076 + 10.8839i) q^{88} +(1078.35 + 117.277i) q^{89} +(-58.8469 - 86.7927i) q^{90} +(-221.716 + 133.402i) q^{91} +(-386.801 - 1393.13i) q^{92} +(254.405 - 916.286i) q^{93} +(591.444 + 355.860i) q^{94} +(-12.7376 - 234.931i) q^{95} +(-736.610 - 248.193i) q^{96} +(274.295 - 517.375i) q^{97} +(-800.646 + 942.593i) q^{98} +(231.304 - 341.147i) 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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