LMFDB - Embedded newform 333.3.r.a.38.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(38,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("333.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.r (of order $6$, degree $2$, 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:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.15
Character	$\chi$	$=$	333.38
Dual form			333.3.r.a.149.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45006 - 1.41454i) q^{2} +(-0.985391 - 2.83355i) q^{3} +(2.00185 + 3.46731i) q^{4} +(-6.74188 + 3.89243i) q^{5} +(-1.59391 + 8.33624i) q^{6} +(-4.88663 + 8.46390i) q^{7} -0.0104923i q^{8} +(-7.05801 + 5.58431i) q^{9} +O(q^{10})$	\(q+(-2.45006 - 1.41454i) q^{2} +(-0.985391 - 2.83355i) q^{3} +(2.00185 + 3.46731i) q^{4} +(-6.74188 + 3.89243i) q^{5} +(-1.59391 + 8.33624i) q^{6} +(-4.88663 + 8.46390i) q^{7} -0.0104923i q^{8} +(-7.05801 + 5.58431i) q^{9} +22.0240 q^{10} +(-7.41762 - 4.28257i) q^{11} +(7.85220 - 9.08901i) q^{12} +(1.86262 + 3.22616i) q^{13} +(23.9451 - 13.8247i) q^{14} +(17.6728 + 15.2679i) q^{15} +(7.99258 - 13.8435i) q^{16} -29.7354i q^{17} +(25.1918 - 3.69803i) q^{18} -10.1250 q^{19} +(-26.9925 - 15.5841i) q^{20} +(28.7981 + 5.50628i) q^{21} +(12.1157 + 20.9851i) q^{22} +(-21.4344 + 12.3751i) q^{23} +(-0.0297306 + 0.0103391i) q^{24} +(17.8020 - 30.8339i) q^{25} -10.5390i q^{26} +(22.7783 + 14.4965i) q^{27} -39.1293 q^{28} +(-5.80095 - 3.34918i) q^{29} +(-21.7022 - 62.4061i) q^{30} +(19.0900 + 33.0648i) q^{31} +(-39.2009 + 22.6326i) q^{32} +(-4.82561 + 25.2382i) q^{33} +(-42.0619 + 72.8534i) q^{34} -76.0835i q^{35} +(-33.4917 - 13.2934i) q^{36} +6.08276 q^{37} +(24.8068 + 14.3222i) q^{38} +(7.30607 - 8.45687i) q^{39} +(0.0408407 + 0.0707382i) q^{40} +(-22.3561 + 12.9073i) q^{41} +(-62.7682 - 54.2268i) q^{42} +(17.5817 - 30.4524i) q^{43} -34.2923i q^{44} +(25.8478 - 65.1215i) q^{45} +70.0206 q^{46} +(1.49929 + 0.865618i) q^{47} +(-47.1022 - 9.00606i) q^{48} +(-23.2584 - 40.2847i) q^{49} +(-87.2318 + 50.3633i) q^{50} +(-84.2567 + 29.3010i) q^{51} +(-7.45740 + 12.9166i) q^{52} +44.5247i q^{53} +(-35.3023 - 67.7381i) q^{54} +66.6783 q^{55} +(0.0888062 + 0.0512723i) q^{56} +(9.97708 + 28.6897i) q^{57} +(9.47511 + 16.4114i) q^{58} +(92.8752 - 53.6215i) q^{59} +(-17.5603 + 91.8412i) q^{60} +(25.3318 - 43.8759i) q^{61} -108.014i q^{62} +(-12.7751 - 87.0268i) q^{63} +64.1186 q^{64} +(-25.1152 - 14.5003i) q^{65} +(47.5235 - 55.0090i) q^{66} +(34.1225 + 59.1019i) q^{67} +(103.102 - 59.5259i) q^{68} +(56.1868 + 48.5410i) q^{69} +(-107.623 + 186.409i) q^{70} -66.4225i q^{71} +(0.0585925 + 0.0740551i) q^{72} -63.1355 q^{73} +(-14.9031 - 8.60432i) q^{74} +(-104.911 - 20.0593i) q^{75} +(-20.2688 - 35.1065i) q^{76} +(72.4944 - 41.8547i) q^{77} +(-29.8629 + 10.3851i) q^{78} +(72.9298 - 126.318i) q^{79} +124.442i q^{80} +(18.6310 - 78.8282i) q^{81} +73.0317 q^{82} +(-67.1042 - 38.7426i) q^{83} +(38.5577 + 110.875i) q^{84} +(115.743 + 200.472i) q^{85} +(-86.1524 + 49.7401i) q^{86} +(-3.77387 + 19.7375i) q^{87} +(-0.0449342 + 0.0778283i) q^{88} +66.6090i q^{89} +(-155.446 + 122.989i) q^{90} -36.4079 q^{91} +(-85.8170 - 49.5465i) q^{92} +(74.8797 - 86.6741i) q^{93} +(-2.44890 - 4.24163i) q^{94} +(68.2616 - 39.4108i) q^{95} +(102.759 + 88.7757i) q^{96} +(-79.1353 + 137.066i) q^{97} +131.600i q^{98} +(76.2688 - 11.1959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9}+O(q^{10}) $ 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9	$ 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9} - 12 q^{12} + 72 q^{14} - 18 q^{15} - 288 q^{16} - 90 q^{18} - 24 q^{19} + 32 q^{21} - 24 q^{22} + 144 q^{23} - 48 q^{24} + 360 q^{25} - 50 q^{27} - 216 q^{29} + 28 q^{30} + 36 q^{32} - 110 q^{33} + 60 q^{34} - 10 q^{36} + 36 q^{38} + 88 q^{39} - 60 q^{40} + 108 q^{41} + 278 q^{42} - 60 q^{43} + 64 q^{45} - 216 q^{46} + 90 q^{47} - 238 q^{48} - 552 q^{49} - 522 q^{50} + 90 q^{51} - 18 q^{52} + 216 q^{54} + 48 q^{55} + 432 q^{56} - 264 q^{57} + 138 q^{58} - 270 q^{59} - 458 q^{60} + 96 q^{61} + 148 q^{63} - 636 q^{64} - 54 q^{65} - 224 q^{66} + 84 q^{67} - 72 q^{68} + 410 q^{69} - 216 q^{70} - 636 q^{72} - 72 q^{73} + 344 q^{75} + 84 q^{76} + 432 q^{77} - 384 q^{78} + 108 q^{79} + 556 q^{81} - 204 q^{82} - 180 q^{83} - 308 q^{84} + 60 q^{85} + 72 q^{86} + 126 q^{87} + 168 q^{88} - 206 q^{90} + 168 q^{91} - 36 q^{92} + 70 q^{93} - 186 q^{94} - 864 q^{95} + 932 q^{96} - 180 q^{97} + 128 q^{99}+O(q^{100}) $ 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9 - 12 * q^12 + 72 * q^14 - 18 * q^15 - 288 * q^16 - 90 * q^18 - 24 * q^19 + 32 * q^21 - 24 * q^22 + 144 * q^23 - 48 * q^24 + 360 * q^25 - 50 * q^27 - 216 * q^29 + 28 * q^30 + 36 * q^32 - 110 * q^33 + 60 * q^34 - 10 * q^36 + 36 * q^38 + 88 * q^39 - 60 * q^40 + 108 * q^41 + 278 * q^42 - 60 * q^43 + 64 * q^45 - 216 * q^46 + 90 * q^47 - 238 * q^48 - 552 * q^49 - 522 * q^50 + 90 * q^51 - 18 * q^52 + 216 * q^54 + 48 * q^55 + 432 * q^56 - 264 * q^57 + 138 * q^58 - 270 * q^59 - 458 * q^60 + 96 * q^61 + 148 * q^63 - 636 * q^64 - 54 * q^65 - 224 * q^66 + 84 * q^67 - 72 * q^68 + 410 * q^69 - 216 * q^70 - 636 * q^72 - 72 * q^73 + 344 * q^75 + 84 * q^76 + 432 * q^77 - 384 * q^78 + 108 * q^79 + 556 * q^81 - 204 * q^82 - 180 * q^83 - 308 * q^84 + 60 * q^85 + 72 * q^86 + 126 * q^87 + 168 * q^88 - 206 * q^90 + 168 * q^91 - 36 * q^92 + 70 * q^93 - 186 * q^94 - 864 * q^95 + 932 * q^96 - 180 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.45006	−	1.41454i	−1.22503	−	0.707271i	−0.259043	−	0.965866i	$-0.583407\pi$
$2$	−2.45006	−	1.41454i	−1.22503	−	0.707271i	−0.965986	+	0.258595i	$0.916740\pi$
$3$	−0.985391	−	2.83355i	−0.328464	−	0.944517i
$3$	−0.985391	−	2.83355i	−0.328464	−	0.944517i
$4$	2.00185	+	3.46731i	0.500464	+	0.866828i
$5$	−6.74188	+	3.89243i	−1.34838	+	0.778485i	−0.988020	−	0.154329i	$-0.950678\pi$
$5$	−6.74188	+	3.89243i	−1.34838	+	0.778485i	−0.360357	+	0.932815i	$0.617345\pi$
$6$	−1.59391	+	8.33624i	−0.265652	+	1.38937i
$7$	−4.88663	+	8.46390i	−0.698091	+	1.20913i	0.271037	+	0.962569i	$0.412633\pi$
$7$	−4.88663	+	8.46390i	−0.698091	+	1.20913i	−0.969128	+	0.246560i	$0.920700\pi$
$8$		−	0.0104923i		−	0.00131154i
$9$	−7.05801	+	5.58431i	−0.784223	+	0.620479i
$10$	22.0240			2.20240
$11$	−7.41762	−	4.28257i	−0.674329	−	0.389324i	0.123386	−	0.992359i	$-0.460625\pi$
$11$	−7.41762	−	4.28257i	−0.674329	−	0.389324i	−0.797715	+	0.603034i	$0.793958\pi$
$12$	7.85220	−	9.08901i	0.654350	−	0.757418i
$13$	1.86262	+	3.22616i	0.143279	+	0.248166i	0.928729	−	0.370758i	$-0.120902\pi$
$13$	1.86262	+	3.22616i	0.143279	+	0.248166i	−0.785451	+	0.618924i	$0.787569\pi$
$14$	23.9451	−	13.8247i	1.71036	−	0.987478i
$15$	17.6728	+	15.2679i	1.17818	+	1.01786i
$16$	7.99258	−	13.8435i	0.499536	−	0.865222i
$17$		−	29.7354i		−	1.74914i	−0.484899	−	0.874570i	$-0.661144\pi$
$17$		−	29.7354i		−	1.74914i	0.484899	−	0.874570i	$-0.338856\pi$
$18$	25.1918	−	3.69803i	1.39954	−	0.205446i
$19$	−10.1250			−0.532895			−0.266447	−	0.963849i	$-0.585850\pi$
$19$	−10.1250			−0.532895			−0.266447	+	0.963849i	$0.585850\pi$
$20$	−26.9925	−	15.5841i	−1.34963	−	0.779207i
$21$	28.7981	+	5.50628i	1.37134	+	0.262204i
$22$	12.1157	+	20.9851i	0.550715	+	0.953867i
$23$	−21.4344	+	12.3751i	−0.931929	+	0.538050i	−0.887421	−	0.460959i	$-0.847505\pi$
$23$	−21.4344	+	12.3751i	−0.931929	+	0.538050i	−0.0445080	+	0.999009i	$0.514172\pi$
$24$	−0.0297306	+	0.0103391i	−0.00123877	+	0.000430794i
$25$	17.8020	−	30.8339i	0.712079	−	1.23336i
$26$		−	10.5390i		−	0.405348i
$27$	22.7783	+	14.4965i	0.843641	+	0.536907i
$28$	−39.1293			−1.39748
$29$	−5.80095	−	3.34918i	−0.200033	−	0.115489i	0.396638	−	0.917975i	$-0.370177\pi$
$29$	−5.80095	−	3.34918i	−0.200033	−	0.115489i	−0.596671	+	0.802486i	$0.703510\pi$
$30$	−21.7022	−	62.4061i	−0.723408	−	2.08020i
$31$	19.0900	+	33.0648i	0.615806	+	1.06661i	0.990243	+	0.139354i	$0.0445027\pi$
$31$	19.0900	+	33.0648i	0.615806	+	1.06661i	−0.374437	+	0.927252i	$0.622164\pi$
$32$	−39.2009	+	22.6326i	−1.22503	+	0.707270i
$33$	−4.82561	+	25.2382i	−0.146231	+	0.764794i
$34$	−42.0619	+	72.8534i	−1.23712	+	2.14275i
$35$		−	76.0835i		−	2.17381i
$36$	−33.4917	−	13.2934i	−0.930324	−	0.369260i
$37$	6.08276			0.164399
$37$	6.08276			0.164399
$38$	24.8068	+	14.3222i	0.652811	+	0.376901i
$39$	7.30607	−	8.45687i	0.187335	−	0.216843i
$40$	0.0408407	+	0.0707382i	0.00102102	+	0.00176845i
$41$	−22.3561	+	12.9073i	−0.545271	+	0.314813i	−0.747213	−	0.664585i	$-0.768608\pi$
$41$	−22.3561	+	12.9073i	−0.545271	+	0.314813i	0.201941	+	0.979398i	$0.435275\pi$
$42$	−62.7682	−	54.2268i	−1.49448	−	1.29112i
$43$	17.5817	−	30.4524i	0.408877	−	0.708195i	−0.585887	−	0.810392i	$-0.699254\pi$
$43$	17.5817	−	30.4524i	0.408877	−	0.708195i	0.994764	+	0.102197i	$0.0325872\pi$
$44$		−	34.2923i		−	0.779371i
$45$	25.8478	−	65.1215i	0.574395	−	1.44715i
$46$	70.0206			1.52219
$47$	1.49929	+	0.865618i	0.0318999	+	0.0184174i	0.515865	−	0.856670i	$-0.327471\pi$
$47$	1.49929	+	0.865618i	0.0318999	+	0.0184174i	−0.483965	+	0.875087i	$0.660804\pi$
$48$	−47.1022	−	9.00606i	−0.981296	−	0.187626i
$49$	−23.2584	−	40.2847i	−0.474661	−	0.822137i
$50$	−87.2318	+	50.3633i	−1.74464	+	1.00727i
$51$	−84.2567	+	29.3010i	−1.65209	+	0.574529i
$52$	−7.45740	+	12.9166i	−0.143412	+	0.248396i
$53$			44.5247i			0.840089i	0.907504	+	0.420044i	$0.137986\pi$
$53$			44.5247i			0.840089i	−0.907504	+	0.420044i	$0.862014\pi$
$54$	−35.3023	−	67.7381i	−0.653746	−	1.25441i
$55$	66.6783			1.21233
$56$	0.0888062	+	0.0512723i	0.00158583	+	0.000915577i
$57$	9.97708	+	28.6897i	0.175036	+	0.503328i
$58$	9.47511	+	16.4114i	0.163364	+	0.282955i
$59$	92.8752	−	53.6215i	1.57416	−	0.908840i	0.578506	−	0.815678i	$-0.303636\pi$
$59$	92.8752	−	53.6215i	1.57416	−	0.908840i	0.995651	−	0.0931613i	$-0.0296972\pi$
$60$	−17.5603	+	91.8412i	−0.292671	+	1.53069i
$61$	25.3318	−	43.8759i	0.415275	−	0.719277i	−0.580183	−	0.814486i	$-0.697019\pi$
$61$	25.3318	−	43.8759i	0.415275	−	0.719277i	0.995457	+	0.0952097i	$0.0303522\pi$
$62$		−	108.014i		−	1.74216i
$63$	−12.7751	−	87.0268i	−0.202779	−	1.38138i
$64$	64.1186			1.00185
$65$	−25.1152	−	14.5003i	−0.386387	−	0.223081i
$66$	47.5235	−	55.0090i	0.720053	−	0.833470i
$67$	34.1225	+	59.1019i	0.509291	+	0.882118i	0.999942	+	0.0107621i	$0.00342575\pi$
$67$	34.1225	+	59.1019i	0.509291	+	0.882118i	−0.490651	+	0.871356i	$0.663241\pi$
$68$	103.102	−	59.5259i	1.51620	−	0.875381i
$69$	56.1868	+	48.5410i	0.814302	+	0.703493i
$70$	−107.623	+	186.409i	−1.53747	+	2.66298i
$71$		−	66.4225i		−	0.935528i	−0.883853	−	0.467764i	$-0.845060\pi$
$71$		−	66.4225i		−	0.935528i	0.883853	−	0.467764i	$-0.154940\pi$
$72$	0.0585925	+	0.0740551i	0.000813785	+	0.00102854i
$73$	−63.1355			−0.864870			−0.432435	−	0.901665i	$-0.642346\pi$
$73$	−63.1355			−0.864870			−0.432435	+	0.901665i	$0.642346\pi$
$74$	−14.9031	−	8.60432i	−0.201393	−	0.116275i
$75$	−104.911	−	20.0593i	−1.39882	−	0.267458i
$76$	−20.2688	−	35.1065i	−0.266694	−	0.461928i
$77$	72.4944	−	41.8547i	0.941486	−	0.543567i
$78$	−29.8629	+	10.3851i	−0.382857	+	0.133142i
$79$	72.9298	−	126.318i	0.923162	−	1.59896i	0.128670	−	0.991687i	$-0.458929\pi$
$79$	72.9298	−	126.318i	0.923162	−	1.59896i	0.794491	−	0.607276i	$-0.207738\pi$
$80$			124.442i			1.55553i
$81$	18.6310	−	78.8282i	0.230013	−	0.973188i
$82$	73.0317			0.890631
$83$	−67.1042	−	38.7426i	−0.808484	−	0.466778i	0.0379452	−	0.999280i	$-0.487919\pi$
$83$	−67.1042	−	38.7426i	−0.808484	−	0.466778i	−0.846429	+	0.532501i	$0.821252\pi$
$84$	38.5577	+	110.875i	0.459020	+	1.31994i
$85$	115.743	+	200.472i	1.36168	+	2.35850i
$86$	−86.1524	+	49.7401i	−1.00177	+	0.578373i
$87$	−3.77387	+	19.7375i	−0.0433778	+	0.226868i
$88$	−0.0449342	+	0.0778283i	−0.000510616	+	0.000884413i
$89$			66.6090i			0.748416i	0.927345	+	0.374208i	$0.122085\pi$
$89$			66.6090i			0.748416i	−0.927345	+	0.374208i	$0.877915\pi$
$90$	−155.446	+	122.989i	−1.72717	+	1.36654i
$91$	−36.4079			−0.400086
$92$	−85.8170	−	49.5465i	−0.932793	−	0.538548i
$93$	74.8797	−	86.6741i	0.805158	−	0.931980i
$94$	−2.44890	−	4.24163i	−0.0260522	−	0.0451237i
$95$	68.2616	−	39.4108i	0.718543	−	0.414851i
$96$	102.759	+	88.7757i	1.07041	+	0.924747i
$97$	−79.1353	+	137.066i	−0.815828	+	1.41306i	0.0929043	+	0.995675i	$0.470385\pi$
$97$	−79.1353	+	137.066i	−0.815828	+	1.41306i	−0.908732	+	0.417380i	$0.862948\pi$
$98$			131.600i			1.34286i
$99$	76.2688	−	11.1959i	0.770392	−	0.113090i
$100$	142.548			1.42548
$101$	156.708	+	90.4754i	1.55156	+	0.895796i	0.998015	+	0.0629790i	$0.0200601\pi$
$101$	156.708	+	90.4754i	1.55156	+	0.895796i	0.553549	+	0.832817i	$0.313273\pi$
$102$	247.881	+	47.3955i	2.43021	+	0.464662i
$103$	−30.7637	−	53.2843i	−0.298677	−	0.517323i	0.677157	−	0.735839i	$-0.263212\pi$
$103$	−30.7637	−	53.2843i	−0.298677	−	0.517323i	−0.975833	+	0.218516i	$0.929879\pi$
$104$	0.0338500	−	0.0195433i	0.000325481	−	0.000187916i
$105$	−215.586	+	74.9720i	−2.05320	+	0.714019i
$106$	62.9820	−	109.088i	0.594170	−	1.02913i
$107$			153.014i			1.43004i	0.699106	+	0.715018i	$0.253581\pi$
$107$			153.014i			1.43004i	−0.699106	+	0.715018i	$0.746419\pi$
$108$	−4.66505	+	107.999i	−0.0431950	+	0.999995i
$109$	−147.196			−1.35042			−0.675212	−	0.737624i	$-0.735948\pi$
$109$	−147.196			−1.35042			−0.675212	+	0.737624i	$0.735948\pi$
$110$	−163.366	−	94.3193i	−1.48514	−	0.857448i
$111$	−5.99390	−	17.2358i	−0.0539991	−	0.155278i
$112$	78.1136	+	135.297i	0.697443	+	1.20801i
$113$	20.1920	−	11.6578i	0.178690	−	0.103167i	−0.407987	−	0.912988i	$-0.633769\pi$
$113$	20.1920	−	11.6578i	0.178690	−	0.103167i	0.586677	+	0.809821i	$0.300436\pi$
$114$	16.1383	−	84.4044i	0.141564	−	0.740389i
$115$	96.3387	−	166.863i	0.837728	−	1.45099i
$116$		−	26.8183i		−	0.231192i
$117$	−31.1623	−	12.3688i	−0.266344	−	0.105716i
$118$	−303.400			−2.57118
$119$	251.677	+	145.306i	2.11494	+	1.22106i
$120$	0.160196	−	0.185429i	0.00133497	−	0.00154524i
$121$	−23.8192	−	41.2561i	−0.196853	−	0.340960i
$122$	−124.128	+	71.6656i	−1.01745	+	0.587423i
$123$	58.6030	+	50.6285i	0.476447	+	0.411613i
$124$	−76.4307	+	132.382i	−0.616377	+	1.06760i
$125$			82.5503i			0.660403i
$126$	−91.8032	+	231.291i	−0.728597	+	1.83565i
$127$	87.9862			0.692805			0.346403	−	0.938086i	$-0.387403\pi$
$127$	87.9862			0.692805			0.346403	+	0.938086i	$0.387403\pi$
$128$	−0.290772	−	0.167878i	−0.00227166	−	0.00131154i
$129$	−103.613	−	19.8111i	−0.803203	−	0.153575i
$130$	41.0224	+	71.0529i	0.315557	+	0.546561i
$131$	102.224	−	59.0188i	0.780333	−	0.450525i	−0.0562154	−	0.998419i	$-0.517903\pi$
$131$	102.224	−	59.0188i	0.780333	−	0.450525i	0.836548	+	0.547893i	$0.184570\pi$
$132$	−97.1690	+	33.7913i	−0.736128	+	0.255995i
$133$	49.4772	−	85.6970i	0.372009	−	0.644338i
$134$		−	193.071i		−	1.44083i
$135$	−209.995	−	9.07078i	−1.55552	−	0.0671910i
$136$	−0.311994			−0.00229407
$137$	13.8507	+	7.99671i	0.101100	+	0.0583702i	0.549698	−	0.835364i	$-0.314743\pi$
$137$	13.8507	+	7.99671i	0.101100	+	0.0583702i	−0.448597	+	0.893734i	$0.648076\pi$
$138$	−68.9976	−	198.407i	−0.499983	−	1.43773i
$139$	2.46650	+	4.27210i	0.0177446	+	0.0307345i	0.874761	−	0.484554i	$-0.161018\pi$
$139$	2.46650	+	4.27210i	0.0177446	+	0.0307345i	−0.857017	+	0.515289i	$0.827685\pi$
$140$	263.805	−	152.308i	1.88432	−	1.08791i
$141$	0.975381	−	5.10130i	0.00691760	−	0.0361794i
$142$	−93.9574	+	162.739i	−0.661672	+	1.14605i
$143$		−	31.9073i		−	0.223128i
$144$	20.8949	+	142.341i	0.145104	+	0.988478i
$145$	52.1458			0.359626
$146$	154.686	+	89.3078i	1.05949	+	0.611697i
$147$	−91.2302	+	105.600i	−0.620614	+	0.718368i
$148$	12.1768	+	21.0908i	0.0822757	+	0.142506i
$149$	87.4103	−	50.4664i	0.586647	−	0.338701i	−0.177124	−	0.984189i	$-0.556679\pi$
$149$	87.4103	−	50.4664i	0.586647	−	0.338701i	0.763770	+	0.645488i	$0.223346\pi$
$150$	228.664	+	197.548i	1.52443	+	1.31699i
$151$	25.2355	−	43.7092i	0.167123	−	0.289465i	−0.770284	−	0.637700i	$-0.779886\pi$
$151$	25.2355	−	43.7092i	0.167123	−	0.289465i	0.937407	+	0.348236i	$0.113219\pi$
$152$			0.106235i			0.000698915i
$153$	166.051	+	209.873i	1.08530	+	1.37172i
$154$	−236.821			−1.53780
$155$	−257.405	−	148.613i	−1.66068	−	0.958791i
$156$	43.9483	+	8.40303i	0.281720	+	0.0538656i
$157$	−23.4726	−	40.6557i	−0.149507	−	0.258953i	0.781538	−	0.623857i	$-0.214435\pi$
$157$	−23.4726	−	40.6557i	−0.149507	−	0.258953i	−0.931045	+	0.364904i	$0.881102\pi$
$158$	−357.364	+	206.324i	−2.26180	+	1.30585i
$159$	126.163	−	43.8742i	0.793478	−	0.275939i
$160$	176.192	−	305.173i	1.10120	−	1.90733i
$161$		−	241.891i		−	1.50243i
$162$	−157.153	+	166.779i	−0.970079	+	1.02950i
$163$	−108.247			−0.664092			−0.332046	−	0.943263i	$-0.607739\pi$
$163$	−108.247			−0.664092			−0.332046	+	0.943263i	$0.607739\pi$
$164$	−89.5074	−	51.6771i	−0.545777	−	0.315104i
$165$	−65.7042	−	188.936i	−0.398207	−	1.14507i
$166$	109.606	+	189.843i	0.660277	+	1.14363i
$167$	13.0109	−	7.51186i	0.0779097	−	0.0449812i	−0.460539	−	0.887639i	$-0.652344\pi$
$167$	13.0109	−	7.51186i	0.0779097	−	0.0449812i	0.538449	+	0.842658i	$0.319011\pi$
$168$	0.0577738	−	0.302160i	0.000343892	−	0.00179857i
$169$	77.5613	−	134.340i	0.458942	−	0.794912i
$170$		−	654.892i		−	3.85231i
$171$	71.4624	−	56.5411i	0.417909	−	0.330650i
$172$	140.784			0.818512
$173$	41.9988	+	24.2480i	0.242768	+	0.140162i	0.616448	−	0.787395i	$-0.288571\pi$
$173$	41.9988	+	24.2480i	0.242768	+	0.140162i	−0.373680	+	0.927558i	$0.621904\pi$
$174$	37.1658	−	43.0198i	0.213596	−	0.247240i
$175$	173.984	+	301.348i	0.994192	+	1.72199i
$176$	−118.572	+	68.4575i	−0.673704	+	0.388963i
$177$	−243.458	−	210.328i	−1.37547	−	1.18830i
$178$	94.2212	−	163.196i	0.529333	−	0.916831i
$179$		−	294.510i		−	1.64531i	−0.568543	−	0.822653i	$-0.692493\pi$
$179$		−	294.510i		−	1.64531i	0.568543	−	0.822653i	$-0.307507\pi$
$180$	277.540	−	40.7415i	1.54189	−	0.226342i
$181$	−191.428			−1.05761			−0.528806	−	0.848743i	$-0.677360\pi$
$181$	−191.428			−1.05761			−0.528806	+	0.848743i	$0.677360\pi$
$182$	89.2013	+	51.5004i	0.490117	+	0.282969i
$183$	−149.286	−	28.5439i	−0.815771	−	0.155978i
$184$	0.129844	+	0.224897i	0.000705676	+	0.00122227i
$185$	−41.0093	+	23.6767i	−0.221672	+	0.127982i
$186$	−306.064	+	106.436i	−1.64550	+	0.572238i
$187$	−127.344	+	220.566i	−0.680983	+	1.17950i
$188$			6.93136i			0.0368690i
$189$	−234.006	+	121.954i	−1.23813	+	0.645260i
$190$	−222.993			−1.17365
$191$	185.801	+	107.272i	0.972782	+	0.561636i	0.900083	−	0.435718i	$-0.143505\pi$
$191$	185.801	+	107.272i	0.972782	+	0.561636i	0.0726989	+	0.997354i	$0.476839\pi$
$192$	−63.1819	−	181.683i	−0.329072	−	0.946267i
$193$	−123.541	−	213.979i	−0.640109	−	1.10870i	−0.985408	−	0.170209i	$-0.945556\pi$
$193$	−123.541	−	213.979i	−0.640109	−	1.10870i	0.345299	−	0.938493i	$-0.387778\pi$
$194$	387.772	−	223.880i	1.99882	−	1.15402i
$195$	−16.3389	+	85.4536i	−0.0837894	+	0.438223i
$196$	93.1199	−	161.288i	0.475101	−	0.822900i
$197$			313.602i			1.59189i	0.605369	+	0.795945i	$0.293026\pi$
$197$			313.602i			1.59189i	−0.605369	+	0.795945i	$0.706974\pi$
$198$	−202.700	−	80.4549i	−1.02374	−	0.406338i
$199$	248.216			1.24732			0.623658	−	0.781697i	$-0.285646\pi$
$199$	248.216			1.24732			0.623658	+	0.781697i	$0.285646\pi$
$200$	−0.323520	−	0.186785i	−0.00161760	−	0.000933923i
$201$	133.844	−	154.926i	0.665892	−	0.770778i
$202$	−255.962	−	443.340i	−1.26714	−	2.19475i
$203$	56.6943	−	32.7325i	0.279282	−	0.161244i
$204$	−270.265	−	233.488i	−1.32483	−	1.14455i
$205$	100.482	−	174.039i	0.490154	−	0.848972i
$206$			174.066i			0.844981i
$207$	82.1774	−	207.040i	0.396992	−	1.00019i
$208$	59.5487			0.286292
$209$	75.1034	+	43.3610i	0.359347	+	0.207469i
$210$	634.250	+	121.270i	3.02024	+	0.577477i
$211$	185.666	+	321.584i	0.879936	+	1.52409i	0.851410	+	0.524500i	$0.175748\pi$
$211$	185.666	+	321.584i	0.879936	+	1.52409i	0.0285253	+	0.999593i	$0.490919\pi$
$212$	−154.381	+	89.1320i	−0.728213	+	0.420434i
$213$	−188.211	+	65.4521i	−0.883622	+	0.307287i
$214$	216.444	−	374.893i	1.01142	−	1.75183i
$215$			273.742i			1.27322i
$216$	0.152102	−	0.238998i	0.000704178	−	0.00110647i
$217$	−373.143			−1.71955
$218$	360.639	+	208.215i	1.65431	+	0.955115i
$219$	62.2132	+	178.898i	0.284078	+	0.816884i
$220$	133.480	+	231.195i	0.606729	+	1.05088i
$221$	95.9311	−	55.3858i	0.434077	−	0.250615i
$222$	−9.69538	+	50.7073i	−0.0436729	+	0.228411i
$223$	65.8091	−	113.985i	0.295108	−	0.511143i	−0.679902	−	0.733303i	$-0.737978\pi$
$223$	65.8091	−	113.985i	0.295108	−	0.511143i	0.975010	+	0.222161i	$0.0713109\pi$
$224$		−	442.390i		−	1.97495i
$225$	46.5396	+	317.038i	0.206843	+	1.40906i
$226$	−65.9620			−0.291867
$227$	149.747	+	86.4563i	0.659677	+	0.380865i	0.792154	−	0.610321i	$-0.208960\pi$
$227$	149.747	+	86.4563i	0.659677	+	0.380865i	−0.132477	+	0.991186i	$0.542293\pi$
$228$	−79.5035	+	92.0263i	−0.348700	+	0.403624i
$229$	98.0985	+	169.912i	0.428378	+	0.741972i	0.996729	−	0.0808139i	$-0.0257520\pi$
$229$	98.0985	+	169.912i	0.428378	+	0.741972i	−0.568352	+	0.822786i	$0.692419\pi$
$230$	−472.071	+	272.550i	−2.05248	+	1.18500i
$231$	−190.033	−	164.173i	−0.822652	−	0.710707i
$232$	−0.0351408	+	0.0608656i	−0.000151469	+	0.000262352i
$233$		−	56.2884i		−	0.241581i	−0.992678	−	0.120791i	$-0.961457\pi$
$233$		−	56.2884i		−	0.241581i	0.992678	−	0.120791i	$-0.0385430\pi$
$234$	58.8532	+	74.3846i	0.251509	+	0.317883i
$235$	−13.4774			−0.0573507
$236$	371.845	+	214.685i	1.57562	+	0.909682i
$237$	−429.793	−	82.1775i	−1.81347	−	0.346741i
$238$	−411.083	−	712.016i	−1.72724	−	2.99166i
$239$	−338.807	+	195.611i	−1.41760	+	0.818454i	−0.996088	−	0.0883663i	$-0.971835\pi$
$239$	−338.807	+	195.611i	−1.41760	+	0.818454i	−0.421517	+	0.906821i	$0.638502\pi$
$240$	352.613	−	122.624i	1.46922	−	0.510934i
$241$	94.8088	−	164.214i	0.393398	−	0.681385i	−0.599498	−	0.800376i	$-0.704633\pi$
$241$	94.8088	−	164.214i	0.393398	−	0.681385i	0.992895	+	0.118992i	$0.0379663\pi$
$242$			134.773i			0.556914i
$243$	−241.722	+	24.8846i	−0.994743	+	0.102406i
$244$	202.842			0.831319
$245$	313.611	+	181.063i	1.28004	+	0.739034i
$246$	−71.9648	−	206.939i	−0.292540	−	0.841216i
$247$	−18.8591	−	32.6649i	−0.0763525	−	0.132246i
$248$	0.346927	−	0.200299i	0.00139890	−	0.000807656i
$249$	−43.6553	+	228.320i	−0.175322	+	0.916946i
$250$	116.771	−	202.253i	0.467083	−	0.809012i
$251$		−	59.4015i		−	0.236659i	−0.992974	−	0.118330i	$-0.962246\pi$
$251$		−	59.4015i		−	0.236659i	0.992974	−	0.118330i	$-0.0377540\pi$
$252$	276.175	−	218.510i	1.09593	−	0.867104i
$253$	211.989			0.837903
$254$	−215.571	−	124.460i	−0.848706	−	0.490001i
$255$	453.997	−	525.507i	1.78038	−	2.06081i
$256$	−127.762	−	221.291i	−0.499072	−	0.864417i
$257$	−359.457	+	207.533i	−1.39867	+	0.807520i	−0.994253	−	0.107057i	$-0.965857\pi$
$257$	−359.457	+	207.533i	−1.39867	+	0.807520i	−0.404413	+	0.914577i	$0.632524\pi$
$258$	225.835	+	195.104i	0.875329	+	0.756216i
$259$	−29.7242	+	51.4839i	−0.114765	+	0.198780i
$260$		−	116.110i		−	0.446575i
$261$	59.6460	−	8.75574i	0.228529	−	0.0335469i
$262$	−333.938			−1.27457
$263$	−81.7971	−	47.2256i	−0.311016	−	0.179565i	0.336365	−	0.941732i	$-0.390802\pi$
$263$	−81.7971	−	47.2256i	−0.311016	−	0.179565i	−0.647381	+	0.762167i	$0.724136\pi$
$264$	0.264808	+	0.0506320i	0.00100306	+	0.000191788i
$265$	−173.309	−	300.180i	−0.653997	−	1.13276i
$266$	−242.444	+	139.975i	−0.911443	+	0.526222i
$267$	188.740	−	65.6359i	0.706892	−	0.245827i
$268$	−136.617	+	236.627i	−0.509764	+	0.882936i
$269$			180.492i			0.670974i	0.942045	+	0.335487i	$0.108901\pi$
$269$			180.492i			0.670974i	−0.942045	+	0.335487i	$0.891099\pi$
$270$	501.669	+	319.271i	1.85804	+	1.18248i
$271$	−21.0825			−0.0777952			−0.0388976	−	0.999243i	$-0.512385\pi$
$271$	−21.0825			−0.0777952			−0.0388976	+	0.999243i	$0.512385\pi$
$272$	−411.643	−	237.662i	−1.51339	−	0.873758i
$273$	35.8760	+	103.163i	0.131414	+	0.377888i
$274$	−22.6234	−	39.1848i	−0.0825670	−	0.143010i
$275$	−264.097	+	152.476i	−0.960352	+	0.554460i
$276$	−55.8291	+	291.989i	−0.202279	+	1.05793i
$277$	133.832	−	231.803i	0.483147	−	0.836836i	−0.516665	−	0.856187i	$-0.672827\pi$
$277$	133.832	−	231.803i	0.483147	−	0.836836i	0.999813	+	0.0193517i	$0.00616021\pi$
$278$		−	13.9558i		−	0.0502009i
$279$	−319.381	−	126.767i	−1.14474	−	0.454364i
$280$	−0.798295			−0.00285105
$281$	385.644	+	222.652i	1.37240	+	0.792355i	0.991230	−	0.132151i	$-0.0421883\pi$
$281$	385.644	+	222.652i	1.37240	+	0.792355i	0.381169	+	0.924505i	$0.375522\pi$
$282$	−9.60573	+	11.1188i	−0.0340629	+	0.0394282i
$283$	−184.755	−	320.005i	−0.652845	−	1.13076i	−0.982429	−	0.186634i	$-0.940242\pi$
$283$	−184.755	−	320.005i	−0.652845	−	1.13076i	0.329585	−	0.944126i	$-0.393091\pi$
$284$	230.308	−	132.968i	0.810942	−	0.468198i
$285$	−178.937	−	154.587i	−0.627849	−	0.542412i
$286$	−45.1341	+	78.1746i	−0.157812	+	0.273338i
$287$		−	252.293i		−	0.879071i
$288$	150.293	−	378.651i	0.521849	−	1.31476i
$289$	−595.193			−2.05949
$290$	−127.760	−	73.7624i	−0.440552	−	0.254353i
$291$	466.363	+	89.1699i	1.60262	+	0.306426i
$292$	−126.388	−	218.911i	−0.432836	−	0.749694i
$293$	−384.419	+	221.944i	−1.31201	+	0.757490i	−0.982429	−	0.186637i	$-0.940241\pi$
$293$	−384.419	+	221.944i	−1.31201	+	0.757490i	−0.329582	+	0.944127i	$0.606908\pi$
$294$	372.895	−	129.677i	1.26835	−	0.441079i
$295$	−417.436	+	723.020i	−1.41504	+	2.45092i
$296$		−	0.0638225i		−	0.000215616i
$297$	−106.879	−	205.079i	−0.359861	−	0.690503i
$298$	−285.547			−0.958212
$299$	−79.8484	−	46.1005i	−0.267051	−	0.154182i
$300$	−140.465	−	403.917i	−0.468218	−	1.34639i
$301$	171.831	+	297.620i	0.570866	+	0.988769i
$302$	−123.657	+	71.3933i	−0.409460	+	0.236402i
$303$	101.948	−	533.193i	0.336462	−	1.75971i
$304$	−80.9248	+	140.166i	−0.266200	+	0.461072i
$305$			394.408i			1.29314i
$306$	−109.962	−	749.087i	−0.359354	−	2.44800i
$307$	505.611			1.64694			0.823471	−	0.567359i	$-0.192035\pi$
$307$	505.611			1.64694			0.823471	+	0.567359i	$0.192035\pi$
$308$	290.247	+	167.574i	0.942359	+	0.544071i
$309$	−120.669	+	139.676i	−0.390516	+	0.452027i
$310$	420.438	+	728.219i	1.35625	+	2.34909i
$311$	242.956	−	140.271i	0.781208	−	0.451031i	−0.0556502	−	0.998450i	$-0.517723\pi$
$311$	242.956	−	140.271i	0.781208	−	0.451031i	0.836858	+	0.547420i	$0.184390\pi$
$312$	−0.0887324	−	0.0766579i	−0.000284399	−	0.000245698i
$313$	−85.9765	+	148.916i	−0.274685	+	0.475769i	−0.970056	−	0.242883i	$-0.921907\pi$
$313$	−85.9765	+	148.916i	−0.274685	+	0.475769i	0.695370	+	0.718652i	$0.255240\pi$
$314$			132.812i			0.422967i
$315$	424.874	+	536.998i	1.34880	+	1.70476i
$316$	583.979			1.84804
$317$	323.531	+	186.790i	1.02060	+	0.589244i	0.914278	−	0.405087i	$-0.132759\pi$
$317$	323.531	+	186.790i	1.02060	+	0.589244i	0.106323	+	0.994332i	$0.466092\pi$
$318$	−371.168	−	70.9684i	−1.16720	−	0.223171i
$319$	28.6862	+	49.6859i	0.0899254	+	0.155755i
$320$	−432.280	+	249.577i	−1.35088	+	0.779928i
$321$	433.572	−	150.778i	1.35069	−	0.469715i
$322$	−342.165	+	592.647i	−1.06262	+	1.84052i
$323$			301.071i			0.932107i
$324$	310.619	−	93.2030i	0.958700	−	0.287663i
$325$	132.634			0.408103
$326$	265.212	+	153.120i	0.813532	+	0.469693i
$327$	145.046	+	417.088i	0.443565	+	1.27550i
$328$	0.135428	+	0.234568i	0.000412890	+	0.000715147i
$329$	−14.6530	+	8.45992i	−0.0445380	+	0.0257140i
$330$	−106.279	+	555.846i	−0.322058	+	1.68438i
$331$	87.3106	−	151.226i	0.263778	−	0.456877i	−0.703465	−	0.710730i	$-0.748365\pi$
$331$	87.3106	−	151.226i	0.263778	−	0.456877i	0.967243	+	0.253853i	$0.0816980\pi$
$332$		−	310.228i		−	0.934422i
$333$	−42.9322	+	33.9680i	−0.128926	+	0.102006i
$334$	−42.5034			−0.127256
$335$	−460.100	−	265.639i	−1.37343	−	0.792952i
$336$	306.398	−	354.659i	0.911898	−	1.05553i
$337$	153.954	+	266.656i	0.456836	+	0.791264i	0.998792	−	0.0491436i	$-0.0156492\pi$
$337$	153.954	+	266.656i	0.456836	+	0.791264i	−0.541955	+	0.840407i	$0.682316\pi$
$338$	−380.059	+	219.427i	−1.12444	+	0.649193i
$339$	−52.9300	−	45.7274i	−0.156136	−	0.134889i
$340$	−463.400	+	802.633i	−1.36294	+	2.36069i
$341$		−	327.016i		−	0.958992i
$342$	−255.067	+	37.4425i	−0.745809	+	0.109481i
$343$	−24.2689			−0.0707549
$344$	−0.319517	−	0.184473i	−0.000928829	−	0.000536260i
$345$	−567.747	−	108.555i	−1.64564	−	0.314651i
$346$	−68.5997	−	118.818i	−0.198265	−	0.343405i
$347$	411.298	−	237.463i	1.18530	−	0.684332i	0.228064	−	0.973646i	$-0.426761\pi$
$347$	411.298	−	237.463i	1.18530	−	0.684332i	0.957234	+	0.289314i	$0.0934273\pi$
$348$	−75.9910	+	26.4265i	−0.218365	+	0.0759382i
$349$	246.779	−	427.434i	0.707103	−	1.22474i	−0.258824	−	0.965924i	$-0.583335\pi$
$349$	246.779	−	427.434i	0.707103	−	1.22474i	0.965927	−	0.258814i	$-0.0833316\pi$
$350$		−	984.428i		−	2.81265i
$351$	−4.34060	+	100.488i	−0.0123664	+	0.286291i
$352$	387.703			1.10143
$353$	−324.713	−	187.473i	−0.919866	−	0.531085i	−0.0362738	−	0.999342i	$-0.511549\pi$
$353$	−324.713	−	187.473i	−0.919866	−	0.531085i	−0.883592	+	0.468257i	$0.844882\pi$
$354$	298.967	+	859.698i	0.844540	+	2.42852i
$355$	258.545	+	447.813i	0.728295	+	1.26144i
$356$	−230.954	+	133.342i	−0.648748	+	0.374555i
$357$	163.731	−	856.323i	0.458631	−	2.39866i
$358$	−416.596	+	721.566i	−1.16368	+	2.01555i
$359$		−	196.425i		−	0.547144i	−0.961852	−	0.273572i	$-0.911795\pi$
$359$		−	196.425i		−	0.547144i	0.961852	−	0.273572i	$-0.0882052\pi$
$360$	−0.683278	−	0.271204i	−0.00189799	−	0.000753344i
$361$	−258.484			−0.716023
$362$	469.009	+	270.783i	1.29561	+	0.748018i
$363$	−93.4300	+	108.146i	−0.257383	+	0.297924i
$364$	−72.8832	−	126.237i	−0.200229	−	0.346806i
$365$	425.652	−	245.751i	1.16617	−	0.673289i
$366$	325.383	+	281.106i	0.889025	+	0.768048i
$367$	−112.558	+	194.956i	−0.306697	+	0.531216i	−0.977638	−	0.210296i	$-0.932557\pi$
$367$	−112.558	+	194.956i	−0.306697	+	0.531216i	0.670940	+	0.741511i	$0.265891\pi$
$368$			395.637i			1.07510i
$369$	85.7114	−	215.943i	0.232280	−	0.585213i
$370$	133.967			0.362072
$371$	−376.853	−	217.576i	−1.01578	−	0.586458i
$372$	450.425	+	86.1224i	1.21082	+	0.231512i
$373$	38.4374	+	66.5756i	0.103049	+	0.178487i	0.912940	−	0.408095i	$-0.133807\pi$
$373$	38.4374	+	66.5756i	0.103049	+	0.178487i	−0.809890	+	0.586582i	$0.800473\pi$
$374$	623.999	−	360.266i	1.66845	−	0.963278i
$375$	233.910	−	81.3443i	0.623761	−	0.216918i
$376$	0.00908237	−	0.0157311i	2.41552e−5	−	4.18381e-5i
$377$		−	24.9531i		−	0.0661885i
$378$	745.838	+	32.2166i	1.97312	+	0.0852291i
$379$	491.457			1.29672			0.648360	−	0.761334i	$-0.275455\pi$
$379$	491.457			1.29672			0.648360	+	0.761334i	$0.275455\pi$
$380$	273.299	+	157.789i	0.719209	+	0.415235i
$381$	−86.7008	−	249.313i	−0.227561	−	0.654366i
$382$	−303.483	−	525.648i	−0.794457	−	1.37604i
$383$	352.611	−	203.580i	0.920655	−	0.531541i	0.0368113	−	0.999322i	$-0.488280\pi$
$383$	352.611	−	203.580i	0.920655	−	0.531541i	0.883844	+	0.467782i	$0.154947\pi$
$384$	−0.189165	+	0.989343i	−0.000492617	+	0.00257641i
$385$	−325.833	+	564.359i	−0.846319	+	1.46587i
$386$			699.016i			1.81092i
$387$	45.9637	+	313.115i	0.118769	+	0.809083i
$388$	−633.669			−1.63317
$389$	−342.669	−	197.840i	−0.880897	−	0.508586i	−0.00994327	−	0.999951i	$-0.503165\pi$
$389$	−342.669	−	197.840i	−0.880897	−	0.508586i	−0.870954	+	0.491364i	$0.836498\pi$
$390$	160.909	−	186.254i	0.412587	−	0.477574i
$391$	367.979	+	637.359i	0.941124	+	1.63007i
$392$	−0.422682	+	0.244035i	−0.00107827	+	0.000622539i
$393$	−267.963	−	231.499i	−0.681840	−	0.589056i
$394$	443.604	−	768.344i	1.12590	−	1.95011i
$395$			1135.50i			2.87467i
$396$	191.499	+	242.035i	0.483583	+	0.611201i
$397$	−41.0806			−0.103478			−0.0517388	−	0.998661i	$-0.516476\pi$
$397$	−41.0806			−0.103478			−0.0517388	+	0.998661i	$0.516476\pi$
$398$	−608.144	−	351.112i	−1.52800	−	0.882191i
$399$	−291.581	−	55.7510i	−0.730780	−	0.139727i
$400$	−284.567	−	492.885i	−0.711418	−	1.23221i
$401$	−141.681	+	81.7996i	−0.353320	+	0.203989i	−0.666146	−	0.745821i	$-0.732057\pi$
$401$	−141.681	+	81.7996i	−0.353320	+	0.203989i	0.312827	+	0.949810i	$0.398724\pi$
$402$	−547.076	+	190.250i	−1.36089	+	0.473259i
$403$	−71.1149	+	123.175i	−0.176464	+	0.305644i
$404$			724.474i			1.79325i
$405$	181.225	+	603.970i	0.447469	+	1.49128i
$406$	−185.206			−0.456172
$407$	−45.1196	−	26.0498i	−0.110859	−	0.0640045i
$408$	0.307436	+	0.884051i	0.000753520	+	0.00216679i
$409$	−253.518	−	439.105i	−0.619848	−	1.07361i	−0.989513	−	0.144443i	$-0.953861\pi$
$409$	−253.518	−	439.105i	−0.619848	−	1.07361i	0.369666	−	0.929165i	$-0.379472\pi$
$410$	−492.371	+	284.271i	−1.20091	+	0.693343i
$411$	9.01072	−	47.1266i	0.0219239	−	0.114663i
$412$	123.169	−	213.335i	0.298954	−	0.517803i
$413$			1048.12i			2.53781i
$414$	−494.206	+	391.016i	−1.19373	+	0.944484i
$415$	603.211			1.45352
$416$	−146.033	−	84.3122i	−0.351041	−	0.202674i
$417$	9.67474	−	11.1986i	0.0232008	−	0.0268552i
$418$	−122.672	−	212.474i	−0.293473	−	0.508311i
$419$	−424.386	+	245.019i	−1.01285	+	0.584772i	−0.912026	−	0.410132i	$-0.865483\pi$
$419$	−424.386	+	245.019i	−1.01285	+	0.584772i	−0.100828	+	0.994904i	$0.532149\pi$
$420$	−691.524	−	597.423i	−1.64649	−	1.42243i
$421$	106.603	−	184.642i	0.253214	−	0.438579i	−0.711195	−	0.702995i	$-0.751846\pi$
$421$	106.603	−	184.642i	0.253214	−	0.438579i	0.964409	+	0.264416i	$0.0851791\pi$
$422$		−	1050.53i		−	2.48941i
$423$	−15.4159	+	2.26298i	−0.0364442	+	0.00534983i
$424$	0.467169			0.00110181
$425$	−916.859	−	529.349i	−2.15731	−	1.24553i
$426$	553.714	+	105.871i	1.29980	+	0.248525i
$427$	247.574	+	428.811i	0.579799	+	1.00424i
$428$	−530.547	+	306.311i	−1.23960	+	0.715681i
$429$	−90.4108	+	31.4411i	−0.210748	+	0.0732893i
$430$	387.219	−	670.684i	0.900510	−	1.55973i
$431$		−	142.684i		−	0.331054i	−0.986205	−	0.165527i	$-0.947068\pi$
$431$		−	142.684i		−	0.331054i	0.986205	−	0.165527i	$-0.0529325\pi$
$432$	382.740	−	199.468i	0.885973	−	0.461732i
$433$	−462.506			−1.06814			−0.534072	−	0.845439i	$-0.679339\pi$
$433$	−462.506			−1.06814			−0.534072	+	0.845439i	$0.679339\pi$
$434$	914.222	+	527.826i	2.10650	+	1.21619i
$435$	−51.3840	−	147.758i	−0.118124	−	0.339673i
$436$	−294.665	−	510.376i	−0.675838	−	1.17059i
$437$	217.023	−	125.298i	0.496620	−	0.286724i
$438$	100.632	−	526.313i	0.229754	−	1.20163i
$439$	−270.251	+	468.089i	−0.615606	+	1.06626i	0.374671	+	0.927158i	$0.377756\pi$
$439$	−270.251	+	468.089i	−0.615606	+	1.06626i	−0.990278	+	0.139104i	$0.955578\pi$
$440$		−	0.699612i		−	0.00159003i
$441$	389.120	+	154.448i	0.882359	+	0.350222i
$442$	−313.382			−0.709010
$443$	289.124	+	166.926i	0.652649	+	0.376807i	0.789471	−	0.613788i	$-0.210355\pi$
$443$	289.124	+	166.926i	0.652649	+	0.376807i	−0.136821	+	0.990596i	$0.543689\pi$
$444$	47.7631	−	55.2863i	0.107574	−	0.124519i
$445$	−259.271	−	449.070i	−0.582631	−	1.00915i
$446$	−322.472	+	186.180i	−0.723032	+	0.417443i
$447$	−229.132	−	197.952i	−0.512600	−	0.442847i
$448$	−313.324	+	542.694i	−0.699385	+	1.21137i
$449$		−	634.474i		−	1.41308i	−0.707672	−	0.706541i	$-0.750255\pi$
$449$		−	634.474i		−	1.41308i	0.707672	−	0.706541i	$-0.249745\pi$
$450$	334.439	−	842.593i	0.743197	−	1.87243i
$451$	221.106			0.490257
$452$	80.8427	+	46.6746i	0.178856	+	0.103262i
$453$	−148.719	−	28.4354i	−0.328298	−	0.0627714i
$454$	−244.592	−	423.646i	−0.538749	−	0.933140i
$455$	245.457	−	141.715i	0.539467	−	0.311461i
$456$	0.301022	−	0.104683i	0.000660137	−	0.000229568i
$457$	404.725	−	701.004i	0.885612	−	1.53393i	0.0406022	−	0.999175i	$-0.487072\pi$
$457$	404.725	−	701.004i	0.885612	−	1.53393i	0.845010	−	0.534750i	$-0.179594\pi$
$458$		−	555.057i		−	1.21192i
$459$	431.059	−	677.322i	0.939126	−	1.47565i
$460$	771.424			1.67701
$461$	50.1321	+	28.9438i	0.108746	+	0.0627848i	0.553387	−	0.832924i	$-0.313335\pi$
$461$	50.1321	+	28.9438i	0.108746	+	0.0627848i	−0.444640	+	0.895709i	$0.646668\pi$
$462$	233.361	+	671.043i	0.505110	+	1.45247i
$463$	−48.2724	−	83.6102i	−0.104260	−	0.180584i	0.809176	−	0.587567i	$-0.199914\pi$
$463$	−48.2724	−	83.6102i	−0.104260	−	0.180584i	−0.913436	+	0.406983i	$0.866581\pi$
$464$	−92.7291	+	53.5372i	−0.199847	+	0.115382i
$465$	−167.457	+	875.811i	−0.360123	+	1.88346i
$466$	−79.6223	+	137.910i	−0.170863	+	0.295944i
$467$		−	489.296i		−	1.04774i	−0.851797	−	0.523871i	$-0.824487\pi$
$467$		−	489.296i		−	1.04774i	0.851797	−	0.523871i	$-0.175513\pi$
$468$	−19.4958	−	132.810i	−0.0416578	−	0.283782i
$469$	−666.977			−1.42213
$470$	33.0204	+	19.0644i	0.0702563	+	0.0405625i
$471$	−92.0703	+	106.572i	−0.195478	+	0.226268i
$472$	−0.562616	−	0.974480i	−0.00119198	−	0.00206458i
$473$	−260.829	+	150.590i	−0.551435	+	0.318371i
$474$	936.774	+	809.299i	1.97632	+	1.70738i
$475$	−180.245	+	312.194i	−0.379463	+	0.657250i
$476$			1163.53i			2.44438i
$477$	−248.640	−	314.256i	−0.521257	−	0.658817i
$478$	1106.80			2.31548
$479$	−744.556	−	429.870i	−1.55440	−	0.897432i	−0.997775	−	0.0666661i	$-0.978764\pi$
$479$	−744.556	−	429.870i	−1.55440	−	0.897432i	−0.556622	−	0.830766i	$-0.687903\pi$
$480$	−1038.34	−	198.534i	−2.16321	−	0.413612i
$481$	11.3299	+	19.6240i	0.0235549	+	0.0407983i
$482$	−464.574	+	268.222i	−0.963847	+	0.556477i
$483$	−685.411	+	238.357i	−1.41907	+	0.493493i
$484$	95.3653	−	165.178i	0.197036	−	0.341276i
$485$		−	1232.11i		−	2.54044i
$486$	627.434	+	280.958i	1.29102	+	0.578102i
$487$	−59.4085			−0.121989			−0.0609944	−	0.998138i	$-0.519427\pi$
$487$	−59.4085			−0.121989			−0.0609944	+	0.998138i	$0.519427\pi$
$488$	−0.460361	−	0.265790i	−0.000943363	−	0.000544651i
$489$	106.666	+	306.723i	0.218130	+	0.627246i
$490$	−512.243	−	887.231i	−1.04539	−	1.81068i
$491$	451.865	−	260.884i	0.920295	−	0.531333i	0.0365660	−	0.999331i	$-0.488358\pi$
$491$	451.865	−	260.884i	0.920295	−	0.531333i	0.883729	+	0.467999i	$0.155025\pi$
$492$	−58.2300	+	304.546i	−0.118354	+	0.618996i
$493$	−99.5892	+	172.494i	−0.202006	+	0.349885i
$494$			106.708i			0.216008i
$495$	−470.616	+	372.352i	−0.950740	+	0.752227i
$496$	610.312			1.23047
$497$	562.193	+	324.582i	1.13117	+	0.653083i
$498$	429.925	−	497.644i	0.863304	−	0.999285i
$499$	−112.438	−	194.747i	−0.225326	−	0.390276i	0.731091	−	0.682280i	$-0.239011\pi$
$499$	−112.438	−	194.747i	−0.225326	−	0.390276i	−0.956417	+	0.292004i	$0.905678\pi$
$500$	−286.228	+	165.254i	−0.572456	+	0.330507i
$501$	−34.1061	−	29.4650i	−0.0680760	−	0.0588124i
$502$	−84.0259	+	145.537i	−0.167382	+	0.289915i
$503$		−	487.943i		−	0.970065i	−0.874496	−	0.485033i	$-0.838808\pi$
$503$		−	487.943i		−	0.970065i	0.874496	−	0.485033i	$-0.161192\pi$
$504$	−0.913115	+	0.134041i	−0.00181174	+	0.000265954i
$505$	−1408.68			−2.78946
$506$	−519.386	−	299.868i	−1.02646	−	0.592624i
$507$	−457.087	−	87.3963i	−0.901553	−	0.172379i
$508$	176.136	+	305.076i	0.346724	+	0.600543i
$509$	−62.1255	+	35.8681i	−0.122054	+	0.0704679i	−0.559784	−	0.828639i	$-0.689116\pi$
$509$	−62.1255	+	35.8681i	−0.122054	+	0.0704679i	0.437730	+	0.899106i	$0.355783\pi$
$510$	−1855.67	+	645.324i	−3.63857	+	1.26534i
$511$	308.520	−	534.373i	0.603758	−	1.04574i
$512$			724.243i			1.41454i
$513$	−230.630	−	146.777i	−0.449572	−	0.286115i
$514$	1174.25			2.28454
$515$	414.810	+	239.491i	0.805457	+	0.465031i
$516$	−138.727	−	398.919i	−0.268851	−	0.773098i
$517$	−7.41413	−	12.8417i	−0.0143407	−	0.0248388i
$518$	145.652	−	84.0923i	0.281182	−	0.162340i
$519$	27.3228	−	142.900i	0.0526450	−	0.275336i
$520$	−0.152142	+	0.263517i	−0.000292580	+	0.000506764i
$521$		−	678.395i		−	1.30210i	−0.759034	−	0.651051i	$-0.774328\pi$
$521$		−	678.395i		−	1.30210i	0.759034	−	0.651051i	$-0.225672\pi$
$522$	−158.522	−	62.9197i	−0.303681	−	0.120536i
$523$	520.212			0.994668			0.497334	−	0.867559i	$-0.334312\pi$
$523$	520.212			0.994668			0.497334	+	0.867559i	$0.334312\pi$
$524$	409.274	+	236.294i	0.781056	+	0.450943i
$525$	682.444	−	789.937i	1.29989	−	1.50464i
$526$	133.605	+	231.411i	0.254002	+	0.439944i
$527$	983.194	−	567.648i	1.86564	−	1.07713i
$528$	310.817	+	268.522i	0.588669	+	0.508564i
$529$	41.7882	−	72.3792i	0.0789947	−	0.136823i
$530$			980.612i			1.85021i
$531$	−356.075	+	897.105i	−0.670575	+	1.68946i
$532$	396.184			0.744708
$533$	−83.2821	−	48.0830i	−0.156252	−	0.0902119i
$534$	−555.269	−	106.169i	−1.03983	−	0.198818i
$535$	−595.595	−	1031.60i	−1.11326	−	1.92823i
$536$	0.620118	−	0.358025i	0.00115694	−	0.000667958i
$537$	−834.509	+	290.207i	−1.55402	+	0.540423i
$538$	255.313	−	442.216i	0.474560	−	0.821962i
$539$			398.423i			0.739189i
$540$	−388.929	−	746.278i	−0.720238	−	1.38200i
$541$	−517.808			−0.957131			−0.478565	−	0.878052i	$-0.658843\pi$
$541$	−517.808			−0.957131			−0.478565	+	0.878052i	$0.658843\pi$
$542$	51.6533	+	29.8220i	0.0953013	+	0.0550222i
$543$	188.631	+	542.420i	0.347387	+	0.998933i
$544$	672.990	+	1165.65i	1.23711	+	2.14274i
$545$	992.380	−	572.951i	1.82088	−	1.05129i
$546$	58.0308	−	303.505i	0.106284	−	0.555869i
$547$	−175.109	+	303.297i	−0.320125	+	0.554473i	−0.980514	−	0.196451i	$-0.937058\pi$
$547$	−175.109	+	303.297i	−0.320125	+	0.554473i	0.660388	+	0.750924i	$0.270392\pi$
$548$			64.0330i			0.116849i
$549$	66.2246	+	451.137i	0.120628	+	0.821743i
$550$	862.737			1.56861
$551$	58.7346	+	33.9105i	0.106596	+	0.0615435i
$552$	0.509309	−	0.589532i	0.000922662	−	0.00106799i
$553$	712.762	+	1234.54i	1.28890	+	2.23244i
$554$	−655.791	+	378.621i	−1.18374	+	0.683432i
$555$	107.499	+	92.8710i	0.193692	+	0.167335i
$556$	−9.87514	+	17.1042i	−0.0177610	+	0.0307630i
$557$		−	186.143i		−	0.334188i	−0.985941	−	0.167094i	$-0.946562\pi$
$557$		−	186.143i		−	0.334188i	0.985941	−	0.167094i	$-0.0534384\pi$
$558$	603.185	+	762.366i	1.08098	+	1.36625i
$559$	130.992			0.234333
$560$	−1053.27	−	608.103i	−1.88083	−	1.08590i
$561$	750.468	+	143.491i	1.33773	+	0.255778i
$562$	−629.900	−	1091.02i	−1.12082	−	1.94131i
$563$	−641.417	+	370.322i	−1.13928	+	0.657766i	−0.946253	−	0.323427i	$-0.895165\pi$
$563$	−641.417	+	370.322i	−1.13928	+	0.657766i	−0.193031	+	0.981193i	$0.561832\pi$
$564$	19.6404	−	6.83010i	0.0348233	−	0.0121101i
$565$	−90.7545	+	157.191i	−0.160628	+	0.278215i
$566$			1045.37i			1.84695i
$567$	576.151	+	542.896i	1.01614	+	0.957488i
$568$	−0.696928			−0.00122699
$569$	842.066	+	486.167i	1.47990	+	0.854423i	0.999741	−	0.0227555i	$-0.00724393\pi$
$569$	842.066	+	486.167i	1.47990	+	0.854423i	0.480164	+	0.877179i	$0.340577\pi$
$570$	219.735	+	631.862i	0.385500	+	1.10853i
$571$	81.4578	+	141.089i	0.142658	+	0.247091i	0.928497	−	0.371340i	$-0.121102\pi$
$571$	81.4578	+	141.089i	0.142658	+	0.247091i	−0.785839	+	0.618432i	$0.787768\pi$
$572$	110.632	−	63.8737i	0.193413	−	0.111667i
$573$	120.875	−	632.183i	0.210951	−	1.10329i
$574$	−356.879	+	618.133i	−0.621741	+	1.07689i
$575$			881.208i			1.53254i
$576$	−452.550	+	358.058i	−0.785677	+	0.621629i
$577$	33.3873			0.0578637			0.0289318	−	0.999581i	$-0.490789\pi$
$577$	33.3873			0.0578637			0.0289318	+	0.999581i	$0.490789\pi$
$578$	1458.26	+	841.925i	2.52293	+	1.45662i
$579$	−484.585	+	560.913i	−0.836935	+	0.968762i
$580$	104.388	+	180.806i	0.179980	+	0.311734i
$581$	655.827	−	378.642i	1.12879	−	0.651707i
$582$	−1016.48	−	878.162i	−1.74653	−	1.50887i
$583$	190.680	−	330.268i	0.327067	−	0.566497i
$584$			0.662440i			0.00113432i
$585$	258.237	−	37.9079i	0.441431	−	0.0647999i
$586$	1255.80			2.14300
$587$	737.495	+	425.793i	1.25638	+	0.725371i	0.972369	−	0.233449i	$-0.0750013\pi$
$587$	737.495	+	425.793i	1.25638	+	0.725371i	0.284011	+	0.958821i	$0.408335\pi$
$588$	−548.778	−	104.928i	−0.933296	−	0.178449i
$589$	−193.286	−	334.781i	−0.328160	−	0.568389i
$590$	2045.48	−	1180.96i	3.46692	−	2.00163i
$591$	888.608	−	309.021i	1.50357	−	0.522878i
$592$	48.6169	−	84.2070i	0.0821232	−	0.142242i
$593$		−	934.963i		−	1.57667i	−0.615249	−	0.788333i	$-0.710945\pi$
$593$		−	934.963i		−	1.57667i	0.615249	−	0.788333i	$-0.289055\pi$
$594$	−28.2341	+	653.640i	−0.0475322	+	1.10040i
$595$	−2262.37			−3.80230
$596$	349.966	+	202.053i	0.587191	+	0.339015i
$597$	−244.590	−	703.333i	−0.409698	−	1.17811i
$598$	130.422	+	225.898i	0.218097	+	0.377755i
$599$	170.769	−	98.5937i	0.285091	−	0.164597i	−0.350635	−	0.936512i	$-0.614034\pi$
$599$	170.769	−	98.5937i	0.285091	−	0.164597i	0.635726	+	0.771915i	$0.280701\pi$
$600$	−0.210470	+	1.10077i	−0.000350783	+	0.00183461i
$601$	−469.718	+	813.575i	−0.781561	+	1.35370i	0.149471	+	0.988766i	$0.452243\pi$
$601$	−469.718	+	813.575i	−0.781561	+	1.35370i	−0.931032	+	0.364937i	$0.881091\pi$
$602$		−	972.247i		−	1.61503i
$603$	−570.880	−	226.591i	−0.946734	−	0.375774i
$604$	202.071			0.334555
$605$	321.173	+	185.429i	0.530864	+	0.306495i
$606$	−1004.00	+	1162.14i	−1.65677	+	1.91773i
$607$	−178.157	−	308.577i	−0.293504	−	0.508364i	0.681132	−	0.732161i	$-0.261488\pi$
$607$	−178.157	−	308.577i	−0.293504	−	0.508364i	−0.974636	+	0.223797i	$0.928155\pi$
$608$	396.909	−	229.155i	0.652811	−	0.376900i
$609$	−148.615	−	128.392i	−0.244031	−	0.210824i
$610$	557.906	−	966.322i	0.914601	−	1.58413i
$611$			6.44928i			0.0105553i
$612$	−395.283	+	995.887i	−0.645888	+	1.62727i
$613$	967.944			1.57903			0.789513	−	0.613733i	$-0.210333\pi$
$613$	967.944			1.57903			0.789513	+	0.613733i	$0.210333\pi$
$614$	−1238.78	−	715.208i	−2.01755	−	1.16483i
$615$	−592.162	−	113.223i	−0.962866	−	0.184102i
$616$	−0.439154	−	0.760637i	−0.000712912	−	0.00123480i
$617$	933.276	−	538.827i	1.51260	−	0.873302i	0.512712	−	0.858561i	$-0.328641\pi$
$617$	933.276	−	538.827i	1.51260	−	0.873302i	0.999891	−	0.0147408i	$-0.00469231\pi$
$618$	493.225	−	171.523i	0.798098	−	0.277545i
$619$	−98.7425	+	171.027i	−0.159519	+	0.276296i	−0.934695	−	0.355449i	$-0.884328\pi$
$619$	−98.7425	+	171.027i	−0.159519	+	0.276296i	0.775176	+	0.631745i	$0.217661\pi$
$620$		−	1190.00i		−	1.91936i
$621$	−667.635	−	28.8386i	−1.07510	−	0.0464390i
$622$	−793.674			−1.27600
$623$	−563.772	−	325.494i	−0.904931	−	0.522462i
$624$	−58.6787	−	168.734i	−0.0940364	−	0.270407i
$625$	123.728	+	214.304i	0.197965	+	0.342886i
$626$	421.295	−	243.235i	0.672995	−	0.388554i
$627$	48.8593	−	255.537i	0.0779255	−	0.407555i
$628$	93.9774	−	162.774i	0.149645	−	0.259194i
$629$		−	180.873i		−	0.287557i
$630$	−281.359	−	1916.68i	−0.446601	−	3.04234i
$631$	474.359			0.751758			0.375879	−	0.926669i	$-0.377341\pi$
$631$	474.359			0.751758			0.375879	+	0.926669i	$0.377341\pi$
$632$	−1.32537	−	0.765205i	−0.00209711	−	0.00121077i
$633$	728.269	−	842.981i	1.15050	−	1.33172i
$634$	−528.446	−	915.295i	−0.833511	−	1.44368i
$635$	−593.193	+	342.480i	−0.934162	+	0.539339i
$636$	404.686	+	349.617i	0.636298	+	0.549712i
$637$	86.6433	−	150.071i	0.136018	−	0.235590i
$638$		−	162.311i		−	0.254406i
$639$	370.924	+	468.811i	0.580475	+	0.733663i
$640$	2.61380			0.00408407
$641$	−614.256	−	354.641i	−0.958277	−	0.553261i	−0.0626347	−	0.998037i	$-0.519950\pi$
$641$	−614.256	−	354.641i	−0.958277	−	0.553261i	−0.895642	+	0.444775i	$0.853284\pi$
$642$	−1275.56	−	243.890i	−1.98685	−	0.379891i
$643$	−50.4415	−	87.3672i	−0.0784471	−	0.135874i	0.824133	−	0.566396i	$-0.191663\pi$
$643$	−50.4415	−	87.3672i	−0.0784471	−	0.135874i	−0.902580	+	0.430522i	$0.858329\pi$
$644$	838.713	−	484.231i	1.30235	−	0.751911i
$645$	775.662	−	269.743i	1.20258	−	0.418206i
$646$	425.877	−	737.641i	0.659252	−	1.14186i
$647$			40.9503i			0.0632926i	0.999499	+	0.0316463i	$0.0100750\pi$
$647$			40.9503i			0.0632926i	−0.999499	+	0.0316463i	$0.989925\pi$
$648$	−0.827093	−	0.195483i	−0.00127638	−	0.000301672i
$649$	−918.551			−1.41533
$650$	−324.960	−	187.616i	−0.499938	−	0.288640i
$651$	367.692	+	1057.32i	0.564810	+	1.62415i
$652$	−216.695	−	375.327i	−0.332354	−	0.575654i
$653$	384.480	−	221.980i	0.588790	−	0.339938i	−0.175829	−	0.984421i	$-0.556261\pi$
$653$	384.480	−	221.980i	0.588790	−	0.339938i	0.764619	+	0.644483i	$0.222927\pi$
$654$	234.618	−	1227.06i	0.358742	−	1.87624i
$655$	−459.453	+	795.796i	−0.701455	+	1.21496i
$656$			412.651i			0.629041i
$657$	445.611	−	352.568i	0.678252	−	0.536634i
$658$	47.8676			0.0727471
$659$	53.6851	+	30.9951i	0.0814644	+	0.0470335i	0.540179	−	0.841550i	$-0.318357\pi$
$659$	53.6851	+	30.9951i	0.0814644	+	0.0470335i	−0.458714	+	0.888584i	$0.651690\pi$
$660$	523.571	−	606.040i	0.793290	−	0.918243i
$661$	−150.128	−	260.030i	−0.227123	−	0.393388i	0.729831	−	0.683627i	$-0.239599\pi$
$661$	−150.128	−	260.030i	−0.227123	−	0.393388i	−0.956954	+	0.290239i	$0.906265\pi$
$662$	−427.832	+	247.009i	−0.646272	+	0.373125i
$663$	−251.468	−	217.249i	−0.379288	−	0.327675i
$664$	−0.406501	+	0.704080i	−0.000612200	+	0.00106036i
$665$			770.345i			1.15841i
$666$	153.236	−	22.4942i	0.230083	−	0.0337751i
$667$	165.786			0.248555
$668$	52.0920	+	30.0753i	0.0779820	+	0.0450229i
$669$	−387.829	−	74.1540i	−0.579715	−	0.110843i
$670$	751.514	+	1301.66i	1.12166	+	1.94278i
$671$	−375.803	+	216.970i	−0.560064	+	0.323353i
$672$	−1253.53	+	435.927i	−1.86538	+	0.648701i
$673$	80.0580	−	138.665i	0.118957	−	0.206039i	−0.800398	−	0.599469i	$-0.795378\pi$
$673$	80.0580	−	138.665i	0.118957	−	0.206039i	0.919355	+	0.393430i	$0.128712\pi$
$674$		−	871.096i		−	1.29243i
$675$	852.483	−	444.279i	1.26294	−	0.658190i
$676$	621.065			0.918736
$677$	878.333	+	507.106i	1.29739	+	0.749048i	0.979953	−	0.199231i	$-0.0638445\pi$
$677$	878.333	+	507.106i	1.29739	+	0.749048i	0.317437	+	0.948279i	$0.397178\pi$
$678$	64.9983	+	186.906i	0.0958677	+	0.275673i
$679$	−773.411	−	1339.59i	−1.13904	−	1.97288i
$680$	2.10343	−	1.21441i	0.00309327	−	0.00178590i
$681$	97.4192	−	509.508i	0.143053	−	0.748176i
$682$	−462.578	+	801.209i	−0.678267	+	1.17479i
$683$			250.462i			0.366708i	0.983047	+	0.183354i	$0.0586955\pi$
$683$			250.462i			0.366708i	−0.983047	+	0.183354i	$0.941304\pi$
$684$	339.103	+	134.595i	0.495765	+	0.196777i
$685$	−124.506			−0.181761
$686$	59.4603	+	34.3294i	0.0866768	+	0.0500428i
$687$	384.788	−	445.396i	0.560098	−	0.648321i
$688$	−281.046	−	486.786i	−0.408497	−	0.707538i
$689$	−143.644	+	82.9328i	−0.208482	+	0.120367i
$690$	1237.46	+	1069.07i	1.79342	+	1.54937i
$691$	153.580	−	266.008i	0.222258	−	0.384961i	−0.733236	−	0.679975i	$-0.761991\pi$
$691$	153.580	−	266.008i	0.222258	−	0.384961i	0.955493	+	0.295013i	$0.0953241\pi$
$692$			194.164i			0.280584i
$693$	−277.937	+	700.242i	−0.401064	+	1.01045i
$694$	−1343.61			−1.93603
$695$	−33.2577	−	19.2013i	−0.0478528	−	0.0276278i
$696$	0.207093	+	0.0395968i	0.000297548	+	5.68919e-5i
$697$	383.804	+	664.768i	0.550651	+	0.953756i
$698$	−1209.25	+	698.158i	−1.73244	+	1.00023i
$699$	−159.496	+	55.4661i	−0.228177	+	0.0793506i
$700$	−696.580	+	1206.51i	−0.995114	+	1.72359i
$701$		−	178.483i		−	0.254612i	−0.991863	−	0.127306i	$-0.959367\pi$
$701$		−	178.483i		−	0.254612i	0.991863	−	0.127306i	$-0.0406331\pi$
$702$	152.779	−	240.061i	0.217634	−	0.341968i
$703$	−61.5880			−0.0876074
$704$	−475.608	−	274.592i	−0.675579	−	0.390046i
$705$	13.2805	+	38.1889i	0.0188376	+	0.0541687i
$706$	530.377	+	918.639i	0.751242	+	1.30119i
$707$	−1531.55	+	884.240i	−2.16626	+	1.25069i
$708$	241.908	−	1265.19i	0.341678	−	1.78699i
$709$	−207.150	+	358.794i	−0.292172	+	0.506057i	−0.974323	−	0.225155i	$-0.927711\pi$
$709$	−207.150	+	358.794i	−0.292172	+	0.506057i	0.682151	+	0.731211i	$0.261045\pi$
$710$		−	1462.89i		−	2.06041i
$711$	190.660	+	1298.82i	0.268157	+	1.82675i
$712$	0.698885			0.000981581
$713$	−818.363	−	472.482i	−1.14777	−	0.662668i
$714$	−1612.46	+	1866.44i	−2.25834	+	2.61406i
$715$	124.197	+	215.115i	0.173702	+	0.300860i
$716$	1021.16	−	589.566i	1.42620	−	0.823416i
$717$	888.130	+	767.275i	1.23868	+	1.07012i
$718$	−277.851	+	481.252i	−0.386979	+	0.670267i
$719$		−	465.750i		−	0.647774i	−0.946096	−	0.323887i	$-0.895010\pi$
$719$		−	465.750i		−	0.647774i	0.946096	−	0.323887i	$-0.104990\pi$
$720$	−694.923	−	878.314i	−0.965171	−	1.21988i
$721$	601.324			0.834013
$722$	633.302	+	365.637i	0.877149	+	0.506422i
$723$	−558.731	−	106.831i	−0.772796	−	0.147761i
$724$	−383.211	−	663.740i	−0.529297	−	0.916768i
$725$	−206.537	+	119.244i	−0.284878	+	0.164475i
$726$	381.887	−	132.804i	0.526014	−	0.182926i
$727$	−111.997	+	193.985i	−0.154054	+	0.266830i	−0.932714	−	0.360616i	$-0.882566\pi$
$727$	−111.997	+	193.985i	−0.154054	+	0.266830i	0.778660	+	0.627446i	$0.215900\pi$
$728$			0.382004i			0.000524731i
$729$	308.703	+	660.412i	0.423461	+	0.905914i
$730$	−1390.50			−1.90479
$731$	−905.514	−	522.799i	−1.23873	−	0.715183i
$732$	−199.879	−	574.763i	−0.273058	−	0.785195i
$733$	177.218	+	306.951i	0.241771	+	0.418760i	0.961219	−	0.275787i	$-0.0889384\pi$
$733$	177.218	+	306.951i	0.241771	+	0.418760i	−0.719448	+	0.694546i	$0.755605\pi$
$734$	551.547	−	318.436i	0.751426	−	0.433836i
$735$	204.023	−	1067.05i	0.277582	−	1.45177i
$736$	560.164	−	970.233i	0.761093	−	1.31825i
$737$		−	584.528i		−	0.793118i
$738$	−515.459	+	407.832i	−0.698453	+	0.552617i
$739$	210.580			0.284953			0.142476	−	0.989798i	$-0.454494\pi$
$739$	210.580			0.284953			0.142476	+	0.989798i	$0.454494\pi$
$740$	−164.189	−	94.7947i	−0.221877	−	0.128101i
$741$	−73.9740	+	85.6258i	−0.0998299	+	0.115554i
$742$	615.540	+	1066.15i	0.829569	+	1.43686i
$743$	492.221	−	284.184i	0.662478	−	0.382482i	−0.130742	−	0.991416i	$-0.541736\pi$
$743$	492.221	−	284.184i	0.662478	−	0.382482i	0.793221	+	0.608934i	$0.208403\pi$
$744$	−0.909415	−	0.785664i	−0.00122233	−	0.00105600i
$745$	−392.873	+	680.477i	−0.527347	+	0.913392i
$746$		−	217.485i		−	0.291535i
$747$	689.973	−	101.285i	0.923658	−	0.135588i
$748$	−1019.69			−1.36323
$749$	−1295.09	−	747.723i	−1.72910	−	0.998295i
$750$	−688.159	−	131.578i	−0.917545	−	0.175437i
$751$	611.157	+	1058.55i	0.813791	+	1.40953i	0.910193	+	0.414185i	$0.135933\pi$
$751$	611.157	+	1058.55i	0.813791	+	1.40953i	−0.0964019	+	0.995342i	$0.530733\pi$
$752$	23.9664	−	13.8370i	0.0318703	−	0.0184003i
$753$	−168.317	+	58.5337i	−0.223529	+	0.0777340i
$754$	−35.2971	+	61.1364i	−0.0468132	+	0.0810828i
$755$			392.909i			0.520410i
$756$	−891.300	−	567.238i	−1.17897	−	0.750315i
$757$	524.073			0.692303			0.346152	−	0.938179i	$-0.387488\pi$
$757$	524.073			0.692303			0.346152	+	0.938179i	$0.387488\pi$
$758$	−1204.10	−	695.186i	−1.58852	−	0.917132i
$759$	−208.892	−	600.683i	−0.275221	−	0.791413i
$760$	−0.413512	−	0.716224i	−0.000544095	−	0.000942400i
$761$	70.9477	−	40.9617i	0.0932295	−	0.0538261i	−0.452660	−	0.891683i	$-0.649525\pi$
$761$	70.9477	−	40.9617i	0.0932295	−	0.0538261i	0.545890	+	0.837857i	$0.316192\pi$
$762$	−140.242	+	733.474i	−0.184045	+	0.962564i
$763$	719.294	−	1245.85i	0.942719	−	1.63284i
$764$			858.976i			1.12431i
$765$	−1936.41	−	768.593i	−2.53126	−	1.00470i
$766$	−1151.89			−1.50377
$767$	345.983	+	199.754i	0.451086	+	0.260435i
$768$	−501.143	+	580.079i	−0.652530	+	0.755311i
$769$	283.661	+	491.315i	0.368870	+	0.638901i	0.989389	−	0.145290i	$-0.0464115\pi$
$769$	283.661	+	491.315i	0.368870	+	0.638901i	−0.620519	+	0.784191i	$0.713078\pi$
$770$	1596.62	−	921.808i	2.07353	−	1.19715i
$771$	942.260	+	814.039i	1.22213	+	1.05582i
$772$	494.622	−	856.711i	0.640703	−	1.10973i
$773$			770.346i			0.996567i	0.867014	+	0.498284i	$0.166036\pi$
$773$			770.346i			0.996567i	−0.867014	+	0.498284i	$0.833964\pi$
$774$	330.300	−	832.167i	0.426745	−	1.07515i
$775$	1359.36			1.75401
$776$	1.43815	+	0.830315i	0.00185328	+	0.00106999i
$777$	175.172	+	33.4934i	0.225447	+	0.0431060i
$778$	559.706	+	969.439i	0.719416	+	1.24607i
$779$	226.356	−	130.687i	0.290572	−	0.167762i
$780$	−329.002	+	114.413i	−0.421798	+	0.146684i
$781$	−284.459	+	492.697i	−0.364224	+	0.630854i
$782$		−	2082.09i		−	2.66252i
$783$	−83.5845	−	160.382i	−0.106749	−	0.204830i
$784$	−743.578			−0.948442
$785$	316.499	+	182.731i	0.403183	+	0.232778i
$786$	329.060	+	946.231i	0.418651	+	1.20386i
$787$	−573.327	−	993.032i	−0.728497	−	1.26179i	−0.957518	−	0.288373i	$-0.906886\pi$
$787$	−573.327	−	993.032i	−0.728497	−	1.26179i	0.229021	−	0.973422i	$-0.426448\pi$
$788$	−1087.36	+	627.786i	−1.37990	+	0.796683i
$789$	−53.2139	+	278.312i	−0.0674448	+	0.352740i
$790$	1606.21	−	2782.03i	2.03317	−	3.52156i
$791$			227.870i			0.288079i
$792$	−0.117471	−	0.800239i	−0.000148322	−	0.00101040i
$793$	188.734			0.238000
$794$	100.650	+	58.1102i	0.126763	+	0.0731867i
$795$	−679.799	+	786.875i	−0.855093	+	0.989780i
$796$	496.892	+	860.643i	0.624237	+	1.08121i
$797$	−1205.35	+	695.910i	−1.51236	+	0.873162i	−0.512465	+	0.858708i	$0.671268\pi$
$797$	−1205.35	+	695.910i	−1.51236	+	0.873162i	−0.999896	+	0.0144540i	$0.995399\pi$
$798$	635.528	+	549.047i	0.796401	+	0.688028i
$799$	25.7395	−	44.5821i	0.0322146	−	0.0557973i
$800$			1611.62i			2.01453i
$801$	−371.965	−	470.127i	−0.464376	−	0.586925i
$802$	462.836			0.577102
$803$	468.316	+	270.382i	0.583208	+	0.336715i
$804$	805.115	+	153.940i	1.00139	+	0.191468i
$805$	941.544	+	1630.80i	1.16962	+	2.02584i
$806$	348.471	−	201.190i	0.432346	−	0.249615i
$807$	511.433	−	177.855i	0.633746	−	0.220390i
$808$	0.949299	−	1.64423i	0.00117488	−	0.00203494i
$809$		−	910.861i		−	1.12591i	−0.826488	−	0.562955i	$-0.809664\pi$
$809$		−	910.861i		−	1.12591i	0.826488	−	0.562955i	$-0.190336\pi$
$810$	410.330	−	1736.11i	0.506580	−	2.14335i
$811$	249.797			0.308011			0.154006	−	0.988070i	$-0.450783\pi$
$811$	249.797			0.308011			0.154006	+	0.988070i	$0.450783\pi$
$812$	226.987	+	131.051i	0.279541	+	0.161393i
$813$	20.7745	+	59.7383i	0.0255529	+	0.0734788i
$814$	73.6972	+	127.647i	0.0905370	+	0.156815i
$815$	729.789	−	421.344i	0.895447	−	0.516986i
$816$	−267.799	+	1400.60i	−0.328185	+	1.71642i
$817$	−178.015	+	308.331i	−0.217888	+	0.377394i
$818$			1434.44i			1.75360i
$819$	256.967	−	203.313i	0.313757	−	0.248245i
$820$	804.598			0.981217
$821$	169.344	+	97.7711i	0.206266	+	0.119088i	0.599575	−	0.800319i	$-0.295336\pi$
$821$	169.344	+	97.7711i	0.206266	+	0.119088i	−0.393309	+	0.919406i	$0.628670\pi$
$822$	−88.7393	+	102.717i	−0.107955	+	0.124960i
$823$	−493.457	−	854.693i	−0.599583	−	1.03851i	−0.992882	−	0.119098i	$-0.962000\pi$
$823$	−493.457	−	854.693i	−0.599583	−	1.03851i	0.393299	−	0.919411i	$-0.371334\pi$
$824$	−0.559077	+	0.322783i	−0.000678492	+	0.000391727i
$825$	692.288	+	598.083i	0.839137	+	0.724949i
$826$	1482.60	−	2567.94i	1.79492	−	3.10889i
$827$		−	385.959i		−	0.466698i	−0.972393	−	0.233349i	$-0.925032\pi$
$827$		−	385.959i		−	0.466698i	0.972393	−	0.233349i	$-0.0749684\pi$
$828$	882.380	−	129.529i	1.06568	−	0.156436i
$829$	−588.604			−0.710017			−0.355009	−	0.934863i	$-0.615522\pi$
$829$	−588.604			−0.710017			−0.355009	+	0.934863i	$0.615522\pi$
$830$	−1477.90	−	853.267i	−1.78060	−	1.02803i
$831$	−788.703	−	150.802i	−0.949102	−	0.181471i
$832$	119.429	+	206.857i	0.143544	+	0.248626i
$833$	−1197.88	+	691.597i	−1.43803	+	0.830249i
$834$	−39.5446	+	13.7520i	−0.0474156	+	0.0164892i
$835$	−58.4787	+	101.288i	−0.0700344	+	0.121303i
$836$			347.210i			0.415322i
$837$	−44.4866	+	1029.90i	−0.0531501	+	1.23046i
$838$	1386.36			1.65437
$839$	−604.019	−	348.731i	−0.719927	−	0.415650i	0.0947986	−	0.995496i	$-0.469779\pi$
$839$	−604.019	−	348.731i	−0.719927	−	0.415650i	−0.814726	+	0.579846i	$0.803113\pi$
$840$	0.786632	+	2.26201i	0.000936467	+	0.00269287i
$841$	−398.066	−	689.470i	−0.473325	−	0.819822i
$842$	−522.367	+	301.588i	−0.620388	+	0.358181i
$843$	250.885	−	1312.14i	0.297609	−	1.55651i
$844$	−743.354	+	1287.53i	−0.880752	+	1.52551i
$845$			1207.61i			1.42912i
$846$	40.9709	+	16.2620i	0.0484290	+	0.0192222i
$847$	465.584			0.549686
$848$	616.380	+	355.867i	0.726863	+	0.419655i
$849$	−724.695	+	838.843i	−0.853586	+	0.988036i
$850$	1497.57	+	2593.87i	1.76185	+	3.05161i
$851$	−130.380	+	75.2750i	−0.153208	+	0.0884548i
$852$	−603.715	−	521.563i	−0.708586	−	0.612163i
$853$	378.986	−	656.422i	0.444297	−	0.769545i	−0.553706	−	0.832712i	$-0.686787\pi$
$853$	378.986	−	656.422i	0.444297	−	0.769545i	0.998003	+	0.0631670i	$0.0201201\pi$
$854$		−	1400.81i		−	1.64030i
$855$	−261.709	+	659.356i	−0.306092	+	0.771176i
$856$	1.60547			0.00187555
$857$	−675.747	−	390.143i	−0.788503	−	0.455243i	0.0509321	−	0.998702i	$-0.483781\pi$
$857$	−675.747	−	390.143i	−0.788503	−	0.455243i	−0.839435	+	0.543460i	$0.817114\pi$
$858$	265.986	+	50.8573i	0.310007	+	0.0592742i
$859$	608.798	+	1054.47i	0.708729	+	1.22755i	0.965329	+	0.261037i	$0.0840644\pi$
$859$	608.798	+	1054.47i	0.708729	+	1.22755i	−0.256600	+	0.966518i	$0.582602\pi$
$860$	−949.149	+	547.992i	−1.10366	+	0.637200i
$861$	−714.886	+	248.608i	−0.830297	+	0.288743i
$862$	−201.833	+	349.584i	−0.234145	+	0.405550i
$863$			120.779i			0.139952i	0.997549	+	0.0699761i	$0.0222923\pi$
$863$			120.779i			0.139952i	−0.997549	+	0.0699761i	$0.977708\pi$
$864$	−1221.02	−	52.7424i	−1.41322	−	0.0610444i
$865$	−377.535			−0.436457
$866$	1133.17	+	654.234i	1.30851	+	0.755466i
$867$	586.497	+	1686.51i	0.676468	+	1.94522i
$868$	−746.978	−	1293.80i	−0.860573	−	1.49056i
$869$	−1081.93	+	624.653i	−1.24503	+	0.718819i
$870$	−83.1157	+	434.700i	−0.0955353	+	0.499655i
$871$	−127.115	+	220.169i	−0.145941	+	0.252778i
$872$			1.54443i			0.00177114i
$873$	−206.883	−	1409.33i	−0.236979	−	1.61435i
$874$	−708.958			−0.811165
$875$	−698.698	−	403.393i	−0.798512	−	0.461021i
$876$	−495.753	+	573.840i	−0.565928	+	0.655068i
$877$	250.866	+	434.513i	0.286051	+	0.495454i	0.972863	−	0.231380i	$-0.0743241\pi$
$877$	250.866	+	434.513i	0.286051	+	0.495454i	−0.686813	+	0.726834i	$0.740991\pi$
$878$	1324.26	−	764.563i	1.50827	−	0.870801i
$879$	1007.69	+	870.569i	1.14641	+	0.990408i
$880$	532.932	−	923.065i	0.605604	−	1.04894i
$881$			704.397i			0.799542i	0.916615	+	0.399771i	$0.130910\pi$
$881$			704.397i			0.799542i	−0.916615	+	0.399771i	$0.869090\pi$
$882$	−734.894	−	928.833i	−0.833213	−	1.05310i
$883$	852.644			0.965622			0.482811	−	0.875725i	$-0.339616\pi$
$883$	852.644			0.965622			0.482811	+	0.875725i	$0.339616\pi$
$884$	384.080	+	221.749i	0.434480	+	0.250847i
$885$	2460.05	+	470.368i	2.77972	+	0.531489i
$886$	−472.246	−	817.955i	−0.533010	−	0.923200i
$887$	498.625	−	287.882i	0.562148	−	0.324556i	−0.191859	−	0.981422i	$-0.561452\pi$
$887$	498.625	−	287.882i	0.562148	−	0.324556i	0.754007	+	0.656866i	$0.228118\pi$
$888$	−0.180844	+	0.0628901i	−0.000203653	+	7.08221e-5i
$889$	−429.957	+	744.707i	−0.483641	+	0.837690i
$890$			1467.00i			1.64831i
$891$	−475.785	+	504.929i	−0.533990	+	0.566700i
$892$	526.961			0.590764
$893$	−15.1804	−	8.76438i	−0.0169993	−	0.00981454i
$894$	281.375	+	809.112i	0.314738	+	0.905047i
$895$	1146.36	+	1985.55i	1.28085	+	2.21849i
$896$	2.84180	−	1.64071i	0.00317165	−	0.00183115i
$897$	−51.9462	+	271.681i	−0.0579110	+	0.302878i
$898$	−897.489	+	1554.50i	−0.999431	+	1.73107i
$899$		−	255.743i		−	0.284475i
$900$	−1006.10	+	796.031i	−1.11789	+	0.884479i
$901$	1323.96			1.46943
$902$	−541.722	−	312.763i	−0.600579	−	0.346744i
$903$	673.999	−	780.162i	0.746400	−	0.863967i
$904$	−0.122318	−	0.211861i	−0.000135308	−	0.000234360i
$905$	1290.58	−	745.119i	1.42606	−	0.823336i
$906$	324.147	+	280.038i	0.357778	+	0.309092i
$907$	186.349	−	322.767i	0.205457	−	0.355862i	−0.744821	−	0.667264i	$-0.767465\pi$
$907$	186.349	−	322.767i	0.205457	−	0.355862i	0.950278	+	0.311402i	$0.100799\pi$
$908$			692.291i			0.762436i
$909$	−1611.29	+	236.529i	−1.77259	+	0.260208i
$910$	−801.847			−0.881150
$911$	1325.68	+	765.381i	1.45519	+	0.840155i	0.998769	−	0.0496083i	$-0.0157973\pi$
$911$	1325.68	+	765.381i	1.45519	+	0.840155i	0.456422	+	0.889763i	$0.349131\pi$
$912$	476.910	+	91.1864i	0.522927	+	0.0999850i
$913$	331.836	+	574.756i	0.363456	+	0.629525i
$914$	−1983.20	+	1145.00i	−2.16980	+	1.25274i
$915$	1117.57	−	388.646i	1.22139	−	0.424750i
$916$	−392.758	+	680.276i	−0.428775	+	0.742660i
$917$			1153.61i			1.25803i
$918$	−2014.22	+	1049.73i	−2.19414	+	1.14349i
$919$	−219.714			−0.239080			−0.119540	−	0.992829i	$-0.538142\pi$
$919$	−219.714			−0.239080			−0.119540	+	0.992829i	$0.538142\pi$
$920$	−1.75079	−	1.01082i	−0.00190303	−	0.00109872i
$921$	−498.224	−	1432.67i	−0.540960	−	1.55556i
$922$	−81.8844	−	141.828i	−0.0888117	−	0.153826i
$923$	214.290	−	123.720i	0.232166	−	0.134041i
$924$	188.823	−	987.554i	0.204354	−	1.06878i
$925$	108.285	−	187.556i	0.117065	−	0.202763i
$926$			273.133i			0.294960i
$927$	514.686	+	204.287i	0.555217	+	0.220374i
$928$	303.203			0.326728
$929$	65.4384	+	37.7809i	0.0704397	+	0.0406684i	0.534806	−	0.844975i	$-0.320385\pi$
$929$	65.4384	+	37.7809i	0.0704397	+	0.0406684i	−0.464367	+	0.885643i	$0.653718\pi$
$930$	1649.15	−	1908.91i	1.77328	−	2.05259i
$931$	235.491	+	407.883i	0.252945	+	0.438113i
$932$	195.170	−	112.681i	0.209409	−	0.120903i
$933$	−636.870	−	550.206i	−0.682604	−	0.589717i
$934$	−692.129	+	1198.80i	−0.741038	+	1.28351i
$935$		−	1982.71i		−	2.12054i
$936$	−0.129778	+	0.326966i	−0.000138652	+	0.000349322i
$937$	−139.060			−0.148410			−0.0742048	−	0.997243i	$-0.523642\pi$
$937$	−139.060			−0.148410			−0.0742048	+	0.997243i	$0.523642\pi$
$938$	1634.13	+	943.467i	1.74215	+	1.00583i
$939$	506.680	+	96.8786i	0.539596	+	0.103172i
$940$	−26.9798	−	46.7304i	−0.0287019	−	0.0497132i
$941$	568.245	−	328.076i	0.603873	−	0.348647i	−0.166690	−	0.986009i	$-0.553308\pi$
$941$	568.245	−	328.076i	0.603873	−	0.348647i	0.770564	+	0.637363i	$0.219975\pi$
$942$	376.329	−	130.871i	0.399500	−	0.138929i
$943$	319.460	−	553.320i	0.338770	−	0.586766i
$944$		−	1714.30i		−	1.81599i
$945$	1102.94	−	1733.05i	1.16714	−	1.83392i
$946$	852.061			0.900699
$947$	−1121.88	−	647.720i	−1.18467	−	0.683970i	−0.227581	−	0.973759i	$-0.573082\pi$
$947$	−1121.88	−	647.720i	−1.18467	−	0.683970i	−0.957091	+	0.289789i	$0.906415\pi$
$948$	−575.448	−	1654.73i	−0.607012	−	1.74550i
$949$	−117.598	−	203.685i	−0.123918	−	0.214632i
$950$	883.222	−	509.928i	0.929707	−	0.536767i
$951$	210.476	−	1100.80i	0.221321	−	1.15752i
$952$	1.52460	−	2.64069i	0.00160147	−	0.00277383i
$953$			78.4217i			0.0822893i	0.999153	+	0.0411446i	$0.0131004\pi$
$953$			78.4217i			0.0822893i	−0.999153	+	0.0411446i	$0.986900\pi$
$954$	164.654	+	1121.66i	0.172593	+	1.17574i
$955$	−1670.20			−1.74890
$956$	−1356.49	−	783.168i	−1.41892	−	0.819213i
$957$	112.520	−	130.244i	0.117576	−	0.136096i
$958$	1216.14	+	2106.41i	1.26945	+	2.19876i
$959$	−135.367	+	78.1540i	−0.141154	+	0.0814953i
$960$	1133.15	+	978.957i	1.18037	+	1.01975i
$961$	−248.354	+	430.162i	−0.258433	+	0.447619i
$962$		−	64.1065i		−	0.0666387i
$963$	−854.476	−	1079.97i	−0.887306	−	1.12147i
$964$	759.174			0.787525
$965$	1665.80	+	961.749i	1.72622	+	0.996631i
$966$	2016.46	+	385.553i	2.08743	+	0.399123i
$967$	−356.274	−	617.085i	−0.368433	−	0.638144i	0.620888	−	0.783899i	$-0.286772\pi$
$967$	−356.274	−	617.085i	−0.368433	−	0.638144i	−0.989321	+	0.145755i	$0.953439\pi$
$968$	−0.432874	+	0.249920i	−0.000447184	+	0.000258182i
$969$	853.099	−	296.672i	0.880391	−	0.306163i
$970$	−1742.88	+	3018.75i	−1.79678	+	3.11211i
$971$		−	901.726i		−	0.928657i	−0.885663	−	0.464328i	$-0.846296\pi$
$971$		−	901.726i		−	0.928657i	0.885663	−	0.464328i	$-0.153704\pi$
$972$	−570.176	−	788.312i	−0.586601	−	0.811021i
$973$	−48.2115			−0.0495493
$974$	145.554	+	84.0358i	0.149440	+	0.0862791i
$975$	−130.696	−	375.824i	−0.134047	−	0.385460i
$976$	−404.932	−	701.363i	−0.414889	−	0.718609i
$977$	−1506.63	+	869.851i	−1.54209	+	0.890328i	−0.543387	+	0.839482i	$0.682859\pi$
$977$	−1506.63	+	869.851i	−1.54209	+	0.890328i	−0.998706	+	0.0508462i	$0.983808\pi$
$978$	172.536	−	902.373i	0.176417	−	0.922672i
$979$	285.258	−	494.081i	0.291377	−	0.504679i
$980$			1449.85i			1.47944i
$981$	1038.91	−	821.989i	1.05903	−	0.837909i
$982$	−1476.13			−1.50318
$983$	−125.891	−	72.6834i	−0.128069	−	0.0739404i	0.434597	−	0.900625i	$-0.356891\pi$
$983$	−125.891	−	72.6834i	−0.128069	−	0.0739404i	−0.562666	+	0.826685i	$0.690224\pi$
$984$	0.531211	−	0.614884i	0.000539849	−	0.000624882i
$985$	−1220.67	−	2114.27i	−1.23926	−	2.14647i
$986$	487.998	−	281.746i	0.494927	−	0.285746i
$987$	38.4105	+	33.1837i	0.0389164	+	0.0336208i
$988$	75.5062	−	130.781i	0.0764233	−	0.132369i
$989$			870.304i			0.879984i
$990$	1679.74	−	246.578i	1.69671	−	0.249069i
$991$	659.178			0.665164			0.332582	−	0.943074i	$-0.392080\pi$
$991$	659.178			0.665164			0.332582	+	0.943074i	$0.392080\pi$
$992$	−1496.69	−	864.113i	−1.50876	−	0.871082i
$993$	−514.542	−	98.3818i	−0.518170	−	0.0990754i
$994$	−918.271	−	1590.49i	−0.923814	−	1.60009i
$995$	−1673.44	+	966.163i	−1.68185	+	0.971018i
$996$	−879.047	+	305.696i	−0.882577	+	0.306924i
$997$	271.323	−	469.945i	0.272139	−	0.471359i	−0.697270	−	0.716809i	$-0.745602\pi$
$997$	271.323	−	469.945i	0.272139	−	0.471359i	0.969409	+	0.245449i	$0.0789355\pi$
$998$			636.190i			0.637465i
$999$	138.555	+	88.1788i	0.138694	+	0.0882670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.r.a.38.15	✓	144
9.5	odd	6	inner	333.3.r.a.149.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
333.3.r.a.38.15	✓	144	1.1	even	1	trivial
333.3.r.a.149.15	yes	144	9.5	odd	6	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.45006 - 1.41454i) q^{2} +(-0.985391 - 2.83355i) q^{3} +(2.00185 + 3.46731i) q^{4} +(-6.74188 + 3.89243i) q^{5} +(-1.59391 + 8.33624i) q^{6} +(-4.88663 + 8.46390i) q^{7} -0.0104923i q^{8} +(-7.05801 + 5.58431i) q^{9} +O(q^{10})\)	\(q+(-2.45006 - 1.41454i) q^{2} +(-0.985391 - 2.83355i) q^{3} +(2.00185 + 3.46731i) q^{4} +(-6.74188 + 3.89243i) q^{5} +(-1.59391 + 8.33624i) q^{6} +(-4.88663 + 8.46390i) q^{7} -0.0104923i q^{8} +(-7.05801 + 5.58431i) q^{9} +22.0240 q^{10} +(-7.41762 - 4.28257i) q^{11} +(7.85220 - 9.08901i) q^{12} +(1.86262 + 3.22616i) q^{13} +(23.9451 - 13.8247i) q^{14} +(17.6728 + 15.2679i) q^{15} +(7.99258 - 13.8435i) q^{16} -29.7354i q^{17} +(25.1918 - 3.69803i) q^{18} -10.1250 q^{19} +(-26.9925 - 15.5841i) q^{20} +(28.7981 + 5.50628i) q^{21} +(12.1157 + 20.9851i) q^{22} +(-21.4344 + 12.3751i) q^{23} +(-0.0297306 + 0.0103391i) q^{24} +(17.8020 - 30.8339i) q^{25} -10.5390i q^{26} +(22.7783 + 14.4965i) q^{27} -39.1293 q^{28} +(-5.80095 - 3.34918i) q^{29} +(-21.7022 - 62.4061i) q^{30} +(19.0900 + 33.0648i) q^{31} +(-39.2009 + 22.6326i) q^{32} +(-4.82561 + 25.2382i) q^{33} +(-42.0619 + 72.8534i) q^{34} -76.0835i q^{35} +(-33.4917 - 13.2934i) q^{36} +6.08276 q^{37} +(24.8068 + 14.3222i) q^{38} +(7.30607 - 8.45687i) q^{39} +(0.0408407 + 0.0707382i) q^{40} +(-22.3561 + 12.9073i) q^{41} +(-62.7682 - 54.2268i) q^{42} +(17.5817 - 30.4524i) q^{43} -34.2923i q^{44} +(25.8478 - 65.1215i) q^{45} +70.0206 q^{46} +(1.49929 + 0.865618i) q^{47} +(-47.1022 - 9.00606i) q^{48} +(-23.2584 - 40.2847i) q^{49} +(-87.2318 + 50.3633i) q^{50} +(-84.2567 + 29.3010i) q^{51} +(-7.45740 + 12.9166i) q^{52} +44.5247i q^{53} +(-35.3023 - 67.7381i) q^{54} +66.6783 q^{55} +(0.0888062 + 0.0512723i) q^{56} +(9.97708 + 28.6897i) q^{57} +(9.47511 + 16.4114i) q^{58} +(92.8752 - 53.6215i) q^{59} +(-17.5603 + 91.8412i) q^{60} +(25.3318 - 43.8759i) q^{61} -108.014i q^{62} +(-12.7751 - 87.0268i) q^{63} +64.1186 q^{64} +(-25.1152 - 14.5003i) q^{65} +(47.5235 - 55.0090i) q^{66} +(34.1225 + 59.1019i) q^{67} +(103.102 - 59.5259i) q^{68} +(56.1868 + 48.5410i) q^{69} +(-107.623 + 186.409i) q^{70} -66.4225i q^{71} +(0.0585925 + 0.0740551i) q^{72} -63.1355 q^{73} +(-14.9031 - 8.60432i) q^{74} +(-104.911 - 20.0593i) q^{75} +(-20.2688 - 35.1065i) q^{76} +(72.4944 - 41.8547i) q^{77} +(-29.8629 + 10.3851i) q^{78} +(72.9298 - 126.318i) q^{79} +124.442i q^{80} +(18.6310 - 78.8282i) q^{81} +73.0317 q^{82} +(-67.1042 - 38.7426i) q^{83} +(38.5577 + 110.875i) q^{84} +(115.743 + 200.472i) q^{85} +(-86.1524 + 49.7401i) q^{86} +(-3.77387 + 19.7375i) q^{87} +(-0.0449342 + 0.0778283i) q^{88} +66.6090i q^{89} +(-155.446 + 122.989i) q^{90} -36.4079 q^{91} +(-85.8170 - 49.5465i) q^{92} +(74.8797 - 86.6741i) q^{93} +(-2.44890 - 4.24163i) q^{94} +(68.2616 - 39.4108i) q^{95} +(102.759 + 88.7757i) q^{96} +(-79.1353 + 137.066i) q^{97} +131.600i q^{98} +(76.2688 - 11.1959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9}+O(q^{10}) \) 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9	\( 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9} - 12 q^{12} + 72 q^{14} - 18 q^{15} - 288 q^{16} - 90 q^{18} - 24 q^{19} + 32 q^{21} - 24 q^{22} + 144 q^{23} - 48 q^{24} + 360 q^{25} - 50 q^{27} - 216 q^{29} + 28 q^{30} + 36 q^{32} - 110 q^{33} + 60 q^{34} - 10 q^{36} + 36 q^{38} + 88 q^{39} - 60 q^{40} + 108 q^{41} + 278 q^{42} - 60 q^{43} + 64 q^{45} - 216 q^{46} + 90 q^{47} - 238 q^{48} - 552 q^{49} - 522 q^{50} + 90 q^{51} - 18 q^{52} + 216 q^{54} + 48 q^{55} + 432 q^{56} - 264 q^{57} + 138 q^{58} - 270 q^{59} - 458 q^{60} + 96 q^{61} + 148 q^{63} - 636 q^{64} - 54 q^{65} - 224 q^{66} + 84 q^{67} - 72 q^{68} + 410 q^{69} - 216 q^{70} - 636 q^{72} - 72 q^{73} + 344 q^{75} + 84 q^{76} + 432 q^{77} - 384 q^{78} + 108 q^{79} + 556 q^{81} - 204 q^{82} - 180 q^{83} - 308 q^{84} + 60 q^{85} + 72 q^{86} + 126 q^{87} + 168 q^{88} - 206 q^{90} + 168 q^{91} - 36 q^{92} + 70 q^{93} - 186 q^{94} - 864 q^{95} + 932 q^{96} - 180 q^{97} + 128 q^{99}+O(q^{100}) \) 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9 - 12 * q^12 + 72 * q^14 - 18 * q^15 - 288 * q^16 - 90 * q^18 - 24 * q^19 + 32 * q^21 - 24 * q^22 + 144 * q^23 - 48 * q^24 + 360 * q^25 - 50 * q^27 - 216 * q^29 + 28 * q^30 + 36 * q^32 - 110 * q^33 + 60 * q^34 - 10 * q^36 + 36 * q^38 + 88 * q^39 - 60 * q^40 + 108 * q^41 + 278 * q^42 - 60 * q^43 + 64 * q^45 - 216 * q^46 + 90 * q^47 - 238 * q^48 - 552 * q^49 - 522 * q^50 + 90 * q^51 - 18 * q^52 + 216 * q^54 + 48 * q^55 + 432 * q^56 - 264 * q^57 + 138 * q^58 - 270 * q^59 - 458 * q^60 + 96 * q^61 + 148 * q^63 - 636 * q^64 - 54 * q^65 - 224 * q^66 + 84 * q^67 - 72 * q^68 + 410 * q^69 - 216 * q^70 - 636 * q^72 - 72 * q^73 + 344 * q^75 + 84 * q^76 + 432 * q^77 - 384 * q^78 + 108 * q^79 + 556 * q^81 - 204 * q^82 - 180 * q^83 - 308 * q^84 + 60 * q^85 + 72 * q^86 + 126 * q^87 + 168 * q^88 - 206 * q^90 + 168 * q^91 - 36 * q^92 + 70 * q^93 - 186 * q^94 - 864 * q^95 + 932 * q^96 - 180 * q^97 + 128 * q^99

Introduction

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