LMFDB - Embedded newform 108.3.j.a.7.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(7,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("108.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			7.15
Character	$\chi$	$=$	108.7
Dual form			108.3.j.a.31.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.619770 - 1.90155i) q^{2} +(2.41946 + 1.77376i) q^{3} +(-3.23177 + 2.35705i) q^{4} +(0.463207 + 2.62698i) q^{5} +(1.87339 - 5.70004i) q^{6} +(4.34885 - 5.18275i) q^{7} +(6.48499 + 4.68454i) q^{8} +(2.70753 + 8.58308i) q^{9} +O(q^{10})$	\(q+(-0.619770 - 1.90155i) q^{2} +(2.41946 + 1.77376i) q^{3} +(-3.23177 + 2.35705i) q^{4} +(0.463207 + 2.62698i) q^{5} +(1.87339 - 5.70004i) q^{6} +(4.34885 - 5.18275i) q^{7} +(6.48499 + 4.68454i) q^{8} +(2.70753 + 8.58308i) q^{9} +(4.70825 - 2.50894i) q^{10} +(18.5390 + 3.26893i) q^{11} +(-12.0000 - 0.0296259i) q^{12} +(-4.76031 - 1.73261i) q^{13} +(-12.5505 - 5.05742i) q^{14} +(-3.53893 + 7.17748i) q^{15} +(4.88867 - 15.2349i) q^{16} +(7.37511 + 12.7741i) q^{17} +(14.6431 - 10.4680i) q^{18} +(-28.7994 - 16.6273i) q^{19} +(-7.68889 - 7.39799i) q^{20} +(19.7148 - 4.82562i) q^{21} +(-5.27392 - 37.2789i) q^{22} +(-11.3558 - 13.5334i) q^{23} +(7.38089 + 22.8369i) q^{24} +(16.8059 - 6.11683i) q^{25} +(-0.344344 + 10.1258i) q^{26} +(-8.67361 + 25.5689i) q^{27} +(-1.83848 + 26.9999i) q^{28} +(-38.2238 + 13.9123i) q^{29} +(15.8416 + 2.28106i) q^{30} +(4.43128 + 5.28100i) q^{31} +(-31.9997 + 0.146076i) q^{32} +(39.0561 + 40.7929i) q^{33} +(19.7196 - 21.9411i) q^{34} +(15.6294 + 9.02364i) q^{35} +(-28.9808 - 21.3568i) q^{36} +(-4.65176 - 8.05708i) q^{37} +(-13.7687 + 65.0686i) q^{38} +(-8.44411 - 12.6356i) q^{39} +(-9.30229 + 19.2059i) q^{40} +(-20.9136 - 7.61194i) q^{41} +(-21.3948 - 34.4979i) q^{42} +(-42.0191 - 7.40910i) q^{43} +(-67.6189 + 33.1329i) q^{44} +(-21.2934 + 11.0884i) q^{45} +(-18.6963 + 29.9813i) q^{46} +(35.0594 - 41.7822i) q^{47} +(38.8509 - 28.1887i) q^{48} +(0.560291 + 3.17757i) q^{49} +(-22.0472 - 28.1661i) q^{50} +(-4.81442 + 43.9880i) q^{51} +(19.4681 - 5.62087i) q^{52} +25.6875 q^{53} +(53.9961 + 0.646439i) q^{54} +50.2159i q^{55} +(52.4810 - 13.2378i) q^{56} +(-40.1859 - 91.3124i) q^{57} +(50.1449 + 64.0619i) q^{58} +(15.3255 - 2.70230i) q^{59} +(-5.48065 - 31.5374i) q^{60} +(-48.6391 - 40.8131i) q^{61} +(7.29569 - 11.6993i) q^{62} +(56.2586 + 23.2941i) q^{63} +(20.1102 + 60.7584i) q^{64} +(2.34652 - 13.3078i) q^{65} +(53.3639 - 99.5492i) q^{66} +(11.8552 - 32.5718i) q^{67} +(-53.9437 - 23.8994i) q^{68} +(-3.46997 - 52.8860i) q^{69} +(7.47225 - 35.3127i) q^{70} +(23.7276 - 13.6991i) q^{71} +(-22.6495 + 68.3447i) q^{72} +(18.2594 - 31.6262i) q^{73} +(-12.4379 + 13.8391i) q^{74} +(51.5108 + 15.0102i) q^{75} +(132.264 - 14.1458i) q^{76} +(97.5656 - 81.8672i) q^{77} +(-18.7938 + 23.8881i) q^{78} +(-43.9448 - 120.737i) q^{79} +(42.2861 + 5.78553i) q^{80} +(-66.3386 + 46.4779i) q^{81} +(-1.51282 + 44.4859i) q^{82} +(-0.482480 - 1.32560i) q^{83} +(-52.3396 + 62.0640i) q^{84} +(-30.1410 + 25.2913i) q^{85} +(11.9534 + 84.4932i) q^{86} +(-117.158 - 34.1397i) q^{87} +(104.912 + 108.046i) q^{88} +(-34.1806 + 59.2025i) q^{89} +(34.2821 + 33.6182i) q^{90} +(-29.6815 + 17.1366i) q^{91} +(68.5982 + 16.9705i) q^{92} +(1.35405 + 20.6372i) q^{93} +(-101.180 - 40.7718i) q^{94} +(30.3396 - 83.3573i) q^{95} +(-77.6809 - 56.4064i) q^{96} +(-19.7333 + 111.913i) q^{97} +(5.69505 - 3.03478i) q^{98} +(22.1375 + 167.973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$

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 $

$2$	−0.619770	−	1.90155i	−0.309885	−	0.950774i
$2$	−0.619770	−	1.90155i	−0.309885	−	0.950774i
$3$	2.41946	+	1.77376i	0.806485	+	0.591254i
$3$	2.41946	+	1.77376i	0.806485	+	0.591254i
$4$	−3.23177	+	2.35705i	−0.807942	+	0.589262i
$5$	0.463207	+	2.62698i	0.0926415	+	0.525396i	0.995445	+	0.0953418i	$0.0303944\pi$
$5$	0.463207	+	2.62698i	0.0926415	+	0.525396i	−0.902803	+	0.430054i	$0.858494\pi$
$6$	1.87339	−	5.70004i	0.312232	−	0.950006i
$7$	4.34885	−	5.18275i	0.621264	−	0.740393i	−0.360023	−	0.932943i	$-0.617231\pi$
$7$	4.34885	−	5.18275i	0.621264	−	0.740393i	0.981287	+	0.192550i	$0.0616757\pi$
$8$	6.48499	+	4.68454i	0.810624	+	0.585567i
$9$	2.70753	+	8.58308i	0.300837	+	0.953676i
$10$	4.70825	−	2.50894i	0.470825	−	0.250894i
$11$	18.5390	+	3.26893i	1.68537	+	0.297176i	0.932547	−	0.361049i	$-0.117581\pi$
$11$	18.5390	+	3.26893i	1.68537	+	0.297176i	0.752821	+	0.658225i	$0.228693\pi$
$12$	−12.0000	−	0.0296259i	−0.999997	−	0.00246882i
$13$	−4.76031	−	1.73261i	−0.366177	−	0.133278i	0.152377	−	0.988322i	$-0.451307\pi$
$13$	−4.76031	−	1.73261i	−0.366177	−	0.133278i	−0.518554	+	0.855045i	$0.673530\pi$
$14$	−12.5505	−	5.05742i	−0.896467	−	0.361245i
$15$	−3.53893	+	7.17748i	−0.235929	+	0.478499i
$16$	4.88867	−	15.2349i	0.305542	−	0.952179i
$17$	7.37511	+	12.7741i	0.433830	+	0.751416i	0.997199	−	0.0747894i	$-0.0238284\pi$
$17$	7.37511	+	12.7741i	0.433830	+	0.751416i	−0.563369	+	0.826205i	$0.690495\pi$
$18$	14.6431	−	10.4680i	0.813505	−	0.581557i
$19$	−28.7994	−	16.6273i	−1.51576	−	0.875123i	−0.999829	−	0.0184912i	$-0.994114\pi$
$19$	−28.7994	−	16.6273i	−1.51576	−	0.875123i	−0.515928	−	0.856632i	$-0.672553\pi$
$20$	−7.68889	−	7.39799i	−0.384445	−	0.369900i
$21$	19.7148	−	4.82562i	0.938801	−	0.229791i
$22$	−5.27392	−	37.2789i	−0.239723	−	1.69449i
$23$	−11.3558	−	13.5334i	−0.493732	−	0.588407i	0.460430	−	0.887696i	$-0.347695\pi$
$23$	−11.3558	−	13.5334i	−0.493732	−	0.588407i	−0.954163	+	0.299289i	$0.903251\pi$
$24$	7.38089	+	22.8369i	0.307537	+	0.951536i
$25$	16.8059	−	6.11683i	0.672234	−	0.244673i
$26$	−0.344344	+	10.1258i	−0.0132440	+	0.389453i
$27$	−8.67361	+	25.5689i	−0.321245	+	0.946996i
$28$	−1.83848	+	26.9999i	−0.0656600	+	0.964282i
$29$	−38.2238	+	13.9123i	−1.31806	+	0.479735i	−0.902836	−	0.429984i	$-0.858519\pi$
$29$	−38.2238	+	13.9123i	−1.31806	+	0.479735i	−0.415224	+	0.909719i	$0.636297\pi$
$30$	15.8416	+	2.28106i	0.528055	+	0.0760352i
$31$	4.43128	+	5.28100i	0.142945	+	0.170355i	0.832767	−	0.553624i	$-0.186756\pi$
$31$	4.43128	+	5.28100i	0.142945	+	0.170355i	−0.689822	+	0.723979i	$0.742311\pi$
$32$	−31.9997	+	0.146076i	−0.999990	+	0.00456489i
$33$	39.0561	+	40.7929i	1.18352	+	1.23615i
$34$	19.7196	−	21.9411i	0.579989	−	0.645327i
$35$	15.6294	+	9.02364i	0.446555	+	0.257818i
$36$	−28.9808	−	21.3568i	−0.805023	−	0.593244i
$37$	−4.65176	−	8.05708i	−0.125723	−	0.217759i	0.796292	−	0.604912i	$-0.206792\pi$
$37$	−4.65176	−	8.05708i	−0.125723	−	0.217759i	−0.922015	+	0.387153i	$0.873458\pi$
$38$	−13.7687	+	65.0686i	−0.362333	+	1.71233i
$39$	−8.44411	−	12.6356i	−0.216516	−	0.323991i
$40$	−9.30229	+	19.2059i	−0.232557	+	0.480146i
$41$	−20.9136	−	7.61194i	−0.510089	−	0.185657i	0.0741374	−	0.997248i	$-0.476380\pi$
$41$	−20.9136	−	7.61194i	−0.510089	−	0.185657i	−0.584226	+	0.811591i	$0.698602\pi$
$42$	−21.3948	−	34.4979i	−0.509400	−	0.821379i
$43$	−42.0191	−	7.40910i	−0.977188	−	0.172305i	−0.337824	−	0.941209i	$-0.609691\pi$
$43$	−42.0191	−	7.40910i	−0.977188	−	0.172305i	−0.639363	+	0.768905i	$0.720802\pi$
$44$	−67.6189	+	33.1329i	−1.53679	+	0.753021i
$45$	−21.2934	+	11.0884i	−0.473187	+	0.246408i
$46$	−18.6963	+	29.9813i	−0.406442	+	0.651767i
$47$	35.0594	−	41.7822i	0.745945	−	0.888982i	−0.250928	−	0.968006i	$-0.580736\pi$
$47$	35.0594	−	41.7822i	0.745945	−	0.888982i	0.996873	+	0.0790235i	$0.0251802\pi$
$48$	38.8509	−	28.1887i	0.809395	−	0.587265i
$49$	0.560291	+	3.17757i	0.0114345	+	0.0648483i
$50$	−22.0472	−	28.1661i	−0.440944	−	0.563322i
$51$	−4.81442	+	43.9880i	−0.0944004	+	0.862510i
$52$	19.4681	−	5.62087i	0.374386	−	0.108094i
$53$	25.6875			0.484670			0.242335	−	0.970193i	$-0.422087\pi$
$53$	25.6875			0.484670			0.242335	+	0.970193i	$0.422087\pi$
$54$	53.9961	+	0.646439i	0.999928	+	0.0119711i
$55$			50.2159i			0.913016i
$56$	52.4810	−	13.2378i	0.937161	−	0.236389i
$57$	−40.1859	−	91.3124i	−0.705016	−	1.60197i
$58$	50.1449	+	64.0619i	0.864567	+	1.10452i
$59$	15.3255	−	2.70230i	0.259755	−	0.0458018i	−0.0422541	−	0.999107i	$-0.513454\pi$
$59$	15.3255	−	2.70230i	0.259755	−	0.0458018i	0.302009	+	0.953305i	$0.402343\pi$
$60$	−5.48065	−	31.5374i	−0.0913441	−	0.525623i
$61$	−48.6391	−	40.8131i	−0.797363	−	0.669067i	0.150193	−	0.988657i	$-0.452010\pi$
$61$	−48.6391	−	40.8131i	−0.797363	−	0.669067i	−0.947556	+	0.319590i	$0.896455\pi$
$62$	7.29569	−	11.6993i	0.117672	−	0.188698i
$63$	56.2586	+	23.2941i	0.892994	+	0.369747i
$64$	20.1102	+	60.7584i	0.314222	+	0.949349i
$65$	2.34652	−	13.3078i	0.0361003	−	0.204735i
$66$	53.3639	−	99.5492i	0.808544	−	1.50832i
$67$	11.8552	−	32.5718i	0.176943	−	0.486147i	−0.819239	−	0.573453i	$-0.805604\pi$
$67$	11.8552	−	32.5718i	0.176943	−	0.486147i	0.996182	+	0.0873060i	$0.0278258\pi$
$68$	−53.9437	−	23.8994i	−0.793290	−	0.351461i
$69$	−3.46997	−	52.8860i	−0.0502894	−	0.766463i
$70$	7.47225	−	35.3127i	0.106746	−	0.504467i
$71$	23.7276	−	13.6991i	0.334192	−	0.192946i	−0.323509	−	0.946225i	$-0.604863\pi$
$71$	23.7276	−	13.6991i	0.334192	−	0.192946i	0.657701	+	0.753279i	$0.271529\pi$
$72$	−22.6495	+	68.3447i	−0.314576	+	0.949232i
$73$	18.2594	−	31.6262i	0.250129	−	0.433235i	−0.713432	−	0.700724i	$-0.752860\pi$
$73$	18.2594	−	31.6262i	0.250129	−	0.433235i	0.963561	+	0.267489i	$0.0861938\pi$
$74$	−12.4379	+	13.8391i	−0.168080	+	0.187015i
$75$	51.5108	+	15.0102i	0.686811	+	0.200136i
$76$	132.264	−	14.1458i	1.74032	−	0.186129i
$77$	97.5656	−	81.8672i	1.26709	−	1.06321i
$78$	−18.7938	+	23.8881i	−0.240947	+	0.306257i
$79$	−43.9448	−	120.737i	−0.556263	−	1.52832i	−0.825015	−	0.565111i	$-0.808833\pi$
$79$	−43.9448	−	120.737i	−0.556263	−	1.52832i	0.268752	−	0.963209i	$-0.413389\pi$
$80$	42.2861	+	5.78553i	0.528577	+	0.0723192i
$81$	−66.3386	+	46.4779i	−0.818995	+	0.573801i
$82$	−1.51282	+	44.4859i	−0.0184490	+	0.542511i
$83$	−0.482480	−	1.32560i	−0.00581301	−	0.0159711i	0.936752	−	0.349993i	$-0.113816\pi$
$83$	−0.482480	−	1.32560i	−0.00581301	−	0.0159711i	−0.942565	+	0.334022i	$0.891594\pi$
$84$	−52.3396	+	62.0640i	−0.623090	+	0.738857i
$85$	−30.1410	+	25.2913i	−0.354600	+	0.297545i
$86$	11.9534	+	84.4932i	0.138993	+	0.982479i
$87$	−117.158	−	34.1397i	−1.34664	−	0.392410i
$88$	104.912	+	108.046i	1.19218	+	1.22779i
$89$	−34.1806	+	59.2025i	−0.384052	+	0.665197i	−0.991637	−	0.129057i	$-0.958805\pi$
$89$	−34.1806	+	59.2025i	−0.384052	+	0.665197i	0.607585	+	0.794254i	$0.292138\pi$
$90$	34.2821	+	33.6182i	0.380912	+	0.373536i
$91$	−29.6815	+	17.1366i	−0.326171	+	0.188315i
$92$	68.5982	+	16.9705i	0.745633	+	0.184462i
$93$	1.35405	+	20.6372i	0.0145597	+	0.221905i
$94$	−101.180	−	40.7718i	−1.07638	−	0.433742i
$95$	30.3396	−	83.3573i	0.319364	−	0.877446i
$96$	−77.6809	−	56.4064i	−0.809176	−	0.587567i
$97$	−19.7333	+	111.913i	−0.203436	+	1.15375i	0.696445	+	0.717610i	$0.254764\pi$
$97$	−19.7333	+	111.913i	−0.203436	+	1.15375i	−0.899881	+	0.436135i	$0.856347\pi$
$98$	5.69505	−	3.03478i	0.0581127	−	0.0309672i
$99$	22.1375	+	167.973i	0.223611	+	1.69670i
$100$	−39.8950	+	59.3804i	−0.398950	+	0.593804i
$101$	−129.982	−	109.068i	−1.28695	−	1.07988i	−0.992245	−	0.124296i	$-0.960333\pi$
$101$	−129.982	−	109.068i	−1.28695	−	1.07988i	−0.294710	−	0.955587i	$-0.595223\pi$
$102$	86.6291	−	18.1076i	0.849305	−	0.177526i
$103$	−13.3003	+	2.34520i	−0.129129	+	0.0227689i	−0.237839	−	0.971305i	$-0.576439\pi$
$103$	−13.3003	+	2.34520i	−0.129129	+	0.0227689i	0.108710	+	0.994073i	$0.465328\pi$
$104$	−22.7541	−	33.5358i	−0.218789	−	0.322460i
$105$	21.8089	+	49.5552i	0.207703	+	0.471954i
$106$	−15.9204	−	48.8461i	−0.150192	−	0.460812i
$107$			161.176i			1.50632i	0.657838	+	0.753159i	$0.271471\pi$
$107$			161.176i			1.50632i	−0.657838	+	0.753159i	$0.728529\pi$
$108$	−32.2360	−	103.077i	−0.298481	−	0.954416i
$109$	67.0064			0.614738			0.307369	−	0.951590i	$-0.400551\pi$
$109$	67.0064			0.614738			0.307369	+	0.951590i	$0.400551\pi$
$110$	95.4879	−	31.1223i	0.868072	−	0.282930i
$111$	3.03663	−	27.7449i	0.0273571	−	0.249954i
$112$	−57.6985	−	91.5908i	−0.515165	−	0.817775i
$113$	−2.48868	−	14.1140i	−0.0220237	−	0.124903i	0.971814	−	0.235750i	$-0.0757547\pi$
$113$	−2.48868	−	14.1140i	−0.0220237	−	0.124903i	−0.993837	+	0.110847i	$0.964644\pi$
$114$	−148.729	+	133.008i	−1.30464	+	1.16674i
$115$	30.2918	−	36.1003i	0.263407	−	0.313916i
$116$	90.7384	−	135.057i	0.782228	−	1.16428i
$117$	1.98247	−	45.5492i	0.0169441	−	0.389309i
$118$	−14.6369	−	27.4674i	−0.124041	−	0.232775i
$119$	98.2781	+	17.3291i	0.825866	+	0.145623i
$120$	−56.5731	+	29.9676i	−0.471443	+	0.249730i
$121$	219.307	+	79.8214i	1.81246	+	0.659681i
$122$	−47.4629	+	117.784i	−0.389041	+	0.965446i
$123$	−37.0978	−	55.5126i	−0.301608	−	0.451322i
$124$	−26.7684	−	6.62223i	−0.215875	−	0.0534051i
$125$	57.1972	+	99.0685i	0.457578	+	0.792548i
$126$	9.42733	−	121.415i	0.0748201	−	0.963615i
$127$	−123.798	−	71.4751i	−0.974791	−	0.562796i	−0.0740975	−	0.997251i	$-0.523608\pi$
$127$	−123.798	−	71.4751i	−0.974791	−	0.562796i	−0.900693	+	0.434455i	$0.856941\pi$
$128$	103.071	−	75.8968i	0.805244	−	0.592944i
$129$	−88.5213	−	92.4579i	−0.686211	−	0.716728i
$130$	−26.7597	+	3.78575i	−0.205844	+	0.0291211i
$131$	−50.1592	−	59.7775i	−0.382895	−	0.456316i	0.539831	−	0.841774i	$-0.318488\pi$
$131$	−50.1592	−	59.7775i	−0.382895	−	0.456316i	−0.922726	+	0.385457i	$0.874044\pi$
$132$	−222.371	−	39.7763i	−1.68463	−	0.301336i
$133$	−211.420	+	76.9504i	−1.58962	+	0.578575i
$134$	−69.2844	−	2.35613i	−0.517048	−	0.0175831i
$135$	−71.1867	−	10.9417i	−0.527309	−	0.0810496i
$136$	−12.0131	+	117.389i	−0.0883314	+	0.863152i
$137$	206.641	−	75.2110i	1.50833	−	0.548985i	0.550125	−	0.835083i	$-0.314580\pi$
$137$	206.641	−	75.2110i	1.50833	−	0.548985i	0.958201	+	0.286097i	$0.0923580\pi$
$138$	−98.4146	+	39.3755i	−0.713149	+	0.285329i
$139$	127.475	+	151.919i	0.917089	+	1.09294i	0.995380	+	0.0960135i	$0.0306092\pi$
$139$	127.475	+	151.919i	0.917089	+	1.09294i	−0.0782911	+	0.996931i	$0.524946\pi$
$140$	−71.7798	+	7.67690i	−0.512713	+	0.0548350i
$141$	158.936	−	38.9030i	1.12721	−	0.275908i
$142$	−40.7553	−	36.6289i	−0.287009	−	0.257950i
$143$	−82.5878	−	47.6821i	−0.577537	−	0.333441i
$144$	143.998	+	0.711019i	0.999988	+	0.00493763i
$145$	−54.2529	−	93.9688i	−0.374158	−	0.648060i
$146$	−71.4553	−	15.1201i	−0.489420	−	0.103563i
$147$	−4.28065	+	8.68181i	−0.0291201	+	0.0590599i
$148$	34.0243	+	15.0742i	0.229894	+	0.101853i
$149$	207.161	+	75.4005i	1.39034	+	0.506044i	0.925297	−	0.379243i	$-0.123816\pi$
$149$	207.161	+	75.4005i	1.39034	+	0.506044i	0.465046	+	0.885286i	$0.346038\pi$
$150$	−3.38225	−	107.253i	−0.0225484	−	0.715021i
$151$	103.590	+	18.2656i	0.686023	+	0.120964i	0.505786	−	0.862659i	$-0.331202\pi$
$151$	103.590	+	18.2656i	0.686023	+	0.120964i	0.180237	+	0.983623i	$0.442314\pi$
$152$	−108.872	−	242.740i	−0.716266	−	1.59697i
$153$	−89.6726	+	97.8874i	−0.586095	+	0.639787i
$154$	−216.143	−	134.787i	−1.40352	−	0.875238i
$155$	−11.8205	+	14.0871i	−0.0762611	+	0.0908845i
$156$	57.0722	+	20.9323i	0.365847	+	0.134181i
$157$	46.2911	+	262.530i	0.294848	+	1.67216i	0.667820	+	0.744322i	$0.267227\pi$
$157$	46.2911	+	262.530i	0.294848	+	1.67216i	−0.372973	+	0.927842i	$0.621662\pi$
$158$	−202.352	+	158.392i	−1.28071	+	1.00248i
$159$	62.1498	+	45.5636i	0.390879	+	0.286563i
$160$	−15.2062	−	83.9948i	−0.0950389	−	0.524968i
$161$	−119.525			−0.742391
$162$	129.495	+	97.3404i	0.799349	+	0.600867i
$163$			179.334i			1.10021i	0.835096	+	0.550104i	$0.185412\pi$
$163$			179.334i			1.10021i	−0.835096	+	0.550104i	$0.814588\pi$
$164$	85.5298	−	24.6944i	0.521523	−	0.150575i
$165$	−89.0711	+	121.495i	−0.539825	+	0.736334i
$166$	−2.22167	+	1.73903i	−0.0133835	+	0.0104761i
$167$	−190.029	+	33.5073i	−1.13790	+	0.200642i	−0.710687	−	0.703508i	$-0.751616\pi$
$167$	−190.029	+	33.5073i	−1.13790	+	0.200642i	−0.427213	+	0.904151i	$0.640505\pi$
$168$	150.456	+	61.0607i	0.895573	+	0.363457i
$169$	−109.803	−	92.1356i	−0.649721	−	0.545181i
$170$	66.7732	+	41.6398i	0.392783	+	0.244940i
$171$	64.7386	−	292.207i	0.378588	−	1.70881i
$172$	153.260	−	75.0964i	0.891044	−	0.436607i
$173$	−43.0667	+	244.244i	−0.248941	+	1.41181i	0.562219	+	0.826988i	$0.309948\pi$
$173$	−43.0667	+	244.244i	−0.248941	+	1.41181i	−0.811160	+	0.584825i	$0.801163\pi$
$174$	7.69270	+	243.940i	0.0442109	+	1.40195i
$175$	41.3841	−	113.702i	0.236480	−	0.649724i
$176$	140.433	−	266.459i	0.797915	−	1.51397i
$177$	41.8727	+	20.6457i	0.236569	+	0.116643i
$178$	133.761	+	28.3041i	0.751464	+	0.159012i
$179$	−24.5003	+	14.1453i	−0.136873	+	0.0790238i	−0.566873	−	0.823805i	$-0.691847\pi$
$179$	−24.5003	+	14.1453i	−0.136873	+	0.0790238i	0.430000	+	0.902829i	$0.358514\pi$
$180$	42.6797	−	86.0247i	0.237109	−	0.477915i
$181$	134.243	−	232.516i	0.741676	−	1.28462i	−0.210056	−	0.977689i	$-0.567365\pi$
$181$	134.243	−	232.516i	0.741676	−	1.28462i	0.951732	−	0.306931i	$-0.0993019\pi$
$182$	50.9819	+	45.8201i	0.280120	+	0.251759i
$183$	−45.2875	−	185.020i	−0.247473	−	1.01104i
$184$	−10.2450	−	140.961i	−0.0556792	−	0.766091i
$185$	19.0111	−	15.9522i	0.102762	−	0.0862280i
$186$	38.4034	−	15.3651i	0.206470	−	0.0826081i
$187$	94.9700	+	260.928i	0.507861	+	1.39534i
$188$	−14.8214	+	217.667i	−0.0788373	+	1.15780i
$189$	94.7971	+	156.148i	0.501572	+	0.826182i
$190$	−177.312	−	6.02978i	−0.933219	−	0.0317357i
$191$	−10.7627	−	29.5704i	−0.0563494	−	0.154819i	0.908324	−	0.418267i	$-0.137362\pi$
$191$	−10.7627	−	29.5704i	−0.0563494	−	0.154819i	−0.964674	+	0.263448i	$0.915140\pi$
$192$	−59.1152	+	182.673i	−0.307892	+	0.951421i
$193$	178.497	−	149.777i	0.924855	−	0.776045i	−0.0500319	−	0.998748i	$-0.515932\pi$
$193$	178.497	−	149.777i	0.924855	−	0.776045i	0.974886	+	0.222703i	$0.0714879\pi$
$194$	225.039	−	31.8367i	1.15999	−	0.164107i
$195$	29.2822	−	28.0354i	0.150165	−	0.143771i
$196$	−9.30040	−	8.94853i	−0.0474510	−	0.0456558i
$197$	−126.054	+	218.332i	−0.639867	+	1.10828i	0.345595	+	0.938384i	$0.387677\pi$
$197$	−126.054	+	218.332i	−0.639867	+	1.10828i	−0.985462	+	0.169898i	$0.945656\pi$
$198$	305.688	−	146.200i	1.54388	−	0.738384i
$199$	258.347	−	149.157i	1.29823	−	0.749531i	0.318128	−	0.948048i	$-0.396946\pi$
$199$	258.347	−	149.157i	1.29823	−	0.749531i	0.980098	+	0.198517i	$0.0636124\pi$
$200$	137.640	+	39.0601i	0.688202	+	0.195300i
$201$	86.4578	−	57.7778i	0.430138	−	0.287452i
$202$	−126.839	+	314.765i	−0.627917	+	1.55824i
$203$	−94.1252	+	258.607i	−0.463671	+	1.27393i
$204$	−88.1226	−	153.507i	−0.431974	−	0.752485i
$205$	10.3091	−	58.4656i	0.0502881	−	0.285198i
$206$	12.7026	+	23.8377i	0.0616633	+	0.115717i
$207$	85.4117	−	134.110i	0.412617	−	0.647875i
$208$	−49.6676	+	64.0524i	−0.238787	+	0.307944i
$209$	−479.560	−	402.398i	−2.29454	−	1.92535i
$210$	80.7151	−	72.1834i	0.384357	−	0.343730i
$211$	−79.4973	+	14.0175i	−0.376764	+	0.0664337i	−0.358824	−	0.933405i	$-0.616822\pi$
$211$	−79.4973	+	14.0175i	−0.376764	+	0.0664337i	−0.0179406	+	0.999839i	$0.505711\pi$
$212$	−83.0162	+	60.5467i	−0.391586	+	0.285598i
$213$	81.7070	+	8.94270i	0.383601	+	0.0419845i
$214$	306.484	−	99.8921i	1.43217	−	0.466786i
$215$		−	113.815i		−	0.529373i
$216$	−176.027	+	125.182i	−0.814939	+	0.579547i
$217$	46.6411			0.214936
$218$	−41.5286	−	127.416i	−0.190498	−	0.584477i
$219$	100.275	−	44.1303i	0.457877	−	0.201508i
$220$	−118.361	−	162.286i	−0.538005	−	0.737664i
$221$	−12.9753	−	73.5867i	−0.0587119	−	0.332971i
$222$	−54.6402	+	11.4211i	−0.246127	+	0.0514466i
$223$	−86.4593	+	103.038i	−0.387710	+	0.462055i	−0.924232	−	0.381832i	$-0.875293\pi$
$223$	−86.4593	+	103.038i	−0.387710	+	0.462055i	0.536522	+	0.843886i	$0.319738\pi$
$224$	−138.405	+	166.482i	−0.617878	+	0.743222i
$225$	98.0036	+	127.685i	0.435571	+	0.567487i
$226$	−25.2961	+	13.4798i	−0.111929	+	0.0596451i
$227$	−301.128	−	53.0971i	−1.32656	−	0.233908i	−0.534922	−	0.844902i	$-0.679659\pi$
$227$	−301.128	−	53.0971i	−1.32656	−	0.233908i	−0.791635	+	0.610994i	$0.790770\pi$
$228$	345.099	+	200.381i	1.51359	+	0.878862i
$229$	−208.128	−	75.7525i	−0.908858	−	0.330797i	−0.155061	−	0.987905i	$-0.549557\pi$
$229$	−208.128	−	75.7525i	−0.908858	−	0.330797i	−0.753797	+	0.657108i	$0.771780\pi$
$230$	−87.4205	−	35.2274i	−0.380089	−	0.153162i
$231$	381.269	−	25.0159i	1.65051	−	0.108294i
$232$	−313.054	−	88.8394i	−1.34937	−	0.382929i
$233$	42.1249	+	72.9625i	0.180794	+	0.313144i	0.942151	−	0.335189i	$-0.108800\pi$
$233$	42.1249	+	72.9625i	0.180794	+	0.313144i	−0.761357	+	0.648332i	$0.775467\pi$
$234$	−87.8427	+	24.4603i	−0.375396	+	0.104531i
$235$	126.001	+	72.7465i	0.536173	+	0.309560i
$236$	−43.1591	+	44.8562i	−0.182878	+	0.190069i
$237$	107.837	−	370.066i	0.455008	−	1.56146i
$238$	−27.9578	−	197.621i	−0.117470	−	0.830339i
$239$	80.0260	+	95.3713i	0.334837	+	0.399043i	0.907023	−	0.421081i	$-0.138349\pi$
$239$	80.0260	+	95.3713i	0.334837	+	0.399043i	−0.572186	+	0.820124i	$0.693905\pi$
$240$	92.0473	+	89.0034i	0.383530	+	0.370848i
$241$	−142.642	+	51.9174i	−0.591876	+	0.215425i	−0.620554	−	0.784164i	$-0.713092\pi$
$241$	−142.642	+	51.9174i	−0.591876	+	0.215425i	0.0286786	+	0.999589i	$0.490870\pi$
$242$	15.8639	−	466.495i	0.0655535	−	1.92766i
$243$	−242.944	−	5.21777i	−0.999769	−	0.0214723i
$244$	253.389	+	17.2538i	1.03848	+	0.0707123i
$245$	−8.08788	+	2.94375i	−0.0330117	+	0.0120153i
$246$	−82.5677	+	104.948i	−0.335641	+	0.426619i
$247$	108.285	+	129.049i	0.438402	+	0.522467i
$248$	3.99780	+	55.0057i	0.0161202	+	0.221797i
$249$	1.18397	−	4.06304i	0.00475488	−	0.0163174i
$250$	152.934	−	170.163i	0.611737	−	0.680652i
$251$	18.3430	+	10.5903i	0.0730796	+	0.0421925i	0.536095	−	0.844158i	$-0.319899\pi$
$251$	18.3430	+	10.5903i	0.0730796	+	0.0421925i	−0.463015	+	0.886350i	$0.653232\pi$
$252$	−236.720	+	57.3232i	−0.939365	+	0.227473i
$253$	−166.287	−	288.017i	−0.657260	−	1.13841i
$254$	−59.1867	+	279.707i	−0.233018	+	1.10121i
$255$	−117.786	+	7.72819i	−0.461905	+	0.0303066i
$256$	−208.202	−	148.956i	−0.813288	−	0.581861i
$257$	36.6814	+	13.3509i	0.142729	+	0.0519491i	0.412397	−	0.911004i	$-0.364692\pi$
$257$	36.6814	+	13.3509i	0.142729	+	0.0519491i	−0.269668	+	0.962953i	$0.586914\pi$
$258$	−120.950	+	225.630i	−0.468799	+	0.874535i
$259$	−61.9877	−	10.9301i	−0.239335	−	0.0422011i
$260$	23.7837	+	48.5386i	0.0914756	+	0.186687i
$261$	−222.902	−	290.410i	−0.854032	−	1.11268i
$262$	−82.5825	+	132.428i	−0.315200	+	0.505452i
$263$	−247.344	+	294.773i	−0.940472	+	1.12081i	0.0520376	+	0.998645i	$0.483428\pi$
$263$	−247.344	+	294.773i	−0.940472	+	1.12081i	−0.992510	+	0.122166i	$0.961016\pi$
$264$	62.1824	+	447.501i	0.235539	+	1.69508i
$265$	11.8987	+	67.4806i	0.0449006	+	0.254644i
$266$	277.356	+	354.333i	1.04269	+	1.33208i
$267$	−187.710	+	82.6096i	−0.703033	+	0.309399i
$268$	38.4601	+	133.208i	0.143508	+	0.497044i
$269$	128.494			0.477672			0.238836	−	0.971060i	$-0.423234\pi$
$269$	128.494			0.477672			0.238836	+	0.971060i	$0.423234\pi$
$270$	23.3132	+	142.146i	0.0863453	+	0.526467i
$271$		−	173.624i		−	0.640678i	−0.947303	−	0.320339i	$-0.896203\pi$
$271$		−	173.624i		−	0.640678i	0.947303	−	0.320339i	$-0.103797\pi$
$272$	230.666	−	49.9106i	0.848035	−	0.183495i
$273$	−102.210	−	11.1867i	−0.374394	−	0.0409768i
$274$	−271.087	−	346.323i	−0.989369	−	1.26395i
$275$	331.560	−	58.4630i	1.20567	−	0.212593i
$276$	135.869	+	162.736i	0.492278	+	0.589624i
$277$	123.403	+	103.547i	0.445498	+	0.373818i	0.837762	−	0.546035i	$-0.183864\pi$
$277$	123.403	+	103.547i	0.445498	+	0.373818i	−0.392264	+	0.919853i	$0.628308\pi$
$278$	209.876	−	336.556i	0.754950	−	1.21063i
$279$	−33.3294	+	52.3325i	−0.119460	+	0.187572i
$280$	59.0850	+	131.735i	0.211018	+	0.470481i
$281$	−14.1148	+	80.0493i	−0.0502308	+	0.284873i	−0.999568	−	0.0293859i	$-0.990645\pi$
$281$	−14.1148	+	80.0493i	−0.0502308	+	0.284873i	0.949337	+	0.314259i	$0.101756\pi$
$282$	−172.480	−	278.114i	−0.611631	−	0.986220i
$283$	109.608	−	301.145i	0.387306	−	1.06412i	−0.580903	−	0.813973i	$-0.697300\pi$
$283$	109.608	−	301.145i	0.387306	−	1.06412i	0.968209	−	0.250142i	$-0.0804774\pi$
$284$	−44.3927	+	100.200i	−0.156312	+	0.352815i
$285$	221.261	−	147.864i	0.776356	−	0.518821i
$286$	−39.4843	+	186.597i	−0.138057	+	0.652435i
$287$	−130.401	+	75.2871i	−0.454359	+	0.262324i
$288$	−87.8938	−	274.260i	−0.305187	−	0.952293i
$289$	35.7154	−	61.8609i	0.123583	−	0.214052i
$290$	−145.062	+	161.404i	−0.500213	+	0.556564i
$291$	−246.252	+	235.767i	−0.846226	+	0.810196i
$292$	15.5342	+	145.247i	0.0531995	+	0.497420i
$293$	−38.6454	+	32.4274i	−0.131896	+	0.110674i	−0.706349	−	0.707864i	$-0.749659\pi$
$293$	−38.6454	+	32.4274i	−0.131896	+	0.110674i	0.574453	+	0.818537i	$0.305215\pi$
$294$	19.1619	+	2.75914i	0.0651765	+	0.00938484i
$295$	14.1978	+	39.0081i	0.0481281	+	0.132231i
$296$	7.57709	−	74.0414i	0.0255983	−	0.250140i
$297$	−244.383	+	445.669i	−0.822840	+	1.50057i
$298$	14.9853	−	440.658i	0.0502863	−	1.47872i
$299$	30.6093	+	84.0982i	0.102372	+	0.281265i
$300$	−201.851	+	72.9039i	−0.672836	+	0.243013i
$301$	−221.134	+	185.553i	−0.734665	+	0.616457i
$302$	−29.4687	−	208.301i	−0.0975786	−	0.689738i
$303$	−121.026	−	494.444i	−0.399424	−	1.63183i
$304$	−394.106	+	357.469i	−1.29640	+	1.17589i
$305$	84.6851	−	146.679i	0.277656	−	0.480915i
$306$	241.714	+	109.849i	0.789915	+	0.358984i
$307$	−109.109	+	62.9942i	−0.355404	+	0.205193i	−0.667063	−	0.745001i	$-0.732449\pi$
$307$	−109.109	+	62.9942i	−0.355404	+	0.205193i	0.311659	+	0.950194i	$0.399115\pi$
$308$	−122.345	+	494.542i	−0.397223	+	1.60566i
$309$	−36.3393	−	17.9175i	−0.117603	−	0.0579853i
$310$	34.1133	+	13.7464i	0.110043	+	0.0443433i
$311$	78.4332	−	215.493i	0.252197	−	0.692905i	−0.747396	−	0.664378i	$-0.768696\pi$
$311$	78.4332	−	215.493i	0.252197	−	0.692905i	0.999593	−	0.0285262i	$-0.00908142\pi$
$312$	4.43210	−	121.499i	0.0142055	−	0.389419i
$313$	51.3526	−	291.235i	0.164066	−	0.930463i	−0.785957	−	0.618281i	$-0.787829\pi$
$313$	51.3526	−	291.235i	0.164066	−	0.930463i	0.950023	−	0.312181i	$-0.101060\pi$
$314$	470.523	−	250.733i	1.49848	−	0.798513i
$315$	−35.1336	+	158.580i	−0.111535	+	0.503429i
$316$	426.603	+	286.615i	1.35001	+	0.907010i
$317$	144.559	+	121.299i	0.456021	+	0.382647i	0.841665	−	0.540001i	$-0.181576\pi$
$317$	144.559	+	121.299i	0.456021	+	0.382647i	−0.385643	+	0.922648i	$0.626020\pi$
$318$	48.1227	−	146.420i	0.151329	−	0.460440i
$319$	−754.110	+	132.970i	−2.36398	+	0.416834i
$320$	−150.296	+	80.9729i	−0.469674	+	0.253040i
$321$	−285.888	+	389.958i	−0.890617	+	1.21482i
$322$	74.0780	+	227.282i	0.230056	+	0.705846i
$323$		−	490.514i		−	1.51862i
$324$	104.840	−	306.569i	0.323582	−	0.946200i
$325$	−90.5991			−0.278766
$326$	341.012	−	111.146i	1.04605	−	0.340938i
$327$	162.119	+	118.853i	0.495777	+	0.363466i
$328$	−99.9663	−	147.334i	−0.304775	−	0.449189i
$329$	−64.0787	−	363.408i	−0.194768	−	1.10459i
$330$	286.232	+	94.0739i	0.867371	+	0.285072i
$331$	114.150	−	136.038i	0.344863	−	0.410992i	−0.565536	−	0.824724i	$-0.691330\pi$
$331$	114.150	−	136.038i	0.344863	−	0.410992i	0.910399	+	0.413732i	$0.135775\pi$
$332$	4.68377	+	3.14681i	0.0141077	+	0.00947835i
$333$	56.5598	−	61.7412i	0.169849	−	0.185409i
$334$	181.490	+	340.583i	0.543384	+	1.01971i
$335$	91.0570	+	16.0558i	0.271812	+	0.0479278i
$336$	22.8616	−	323.943i	0.0680405	−	0.964117i
$337$	337.952	+	123.004i	1.00282	+	0.364998i	0.790673	−	0.612238i	$-0.209731\pi$
$337$	337.952	+	123.004i	1.00282	+	0.364998i	0.212151	+	0.977237i	$0.431953\pi$
$338$	−107.148	+	265.898i	−0.317005	+	0.786682i
$339$	19.0137	−	38.5626i	0.0560875	−	0.113754i
$340$	37.7960	−	152.779i	0.111165	−	0.449351i
$341$	64.8885	+	112.390i	0.190289	+	0.329590i
$342$	−595.768	+	57.9974i	−1.74201	+	0.169583i
$343$	306.005	+	176.672i	0.892144	+	0.515079i
$344$	−237.785	−	244.888i	−0.691236	−	0.711883i
$345$	137.323	−	33.6127i	0.398038	−	0.0974281i
$346$	491.132	−	69.4815i	1.41946	−	0.200814i
$347$	178.381	+	212.586i	0.514065	+	0.612639i	0.959167	−	0.282841i	$-0.0912770\pi$
$347$	178.381	+	212.586i	0.514065	+	0.612639i	−0.445102	+	0.895480i	$0.646833\pi$
$348$	459.096	−	165.815i	1.31924	−	0.476479i
$349$	49.7907	−	18.1223i	0.142667	−	0.0519265i	−0.269700	−	0.962944i	$-0.586924\pi$
$349$	49.7907	−	18.1223i	0.142667	−	0.0519265i	0.412367	+	0.911018i	$0.364702\pi$
$350$	−241.858	−	8.22479i	−0.691023	−	0.0234994i
$351$	85.5900	−	106.688i	0.243846	−	0.303954i
$352$	−593.721	−	101.897i	−1.68671	−	0.289479i
$353$	−128.371	+	46.7231i	−0.363657	+	0.132360i	−0.517385	−	0.855753i	$-0.673094\pi$
$353$	−128.371	+	46.7231i	−0.363657	+	0.132360i	0.153728	+	0.988113i	$0.450872\pi$
$354$	13.3074	−	92.4185i	0.0375916	−	0.261069i
$355$	46.9782	+	55.9864i	0.132333	+	0.157708i
$356$	−29.0793	−	271.894i	−0.0816834	−	0.763748i
$357$	207.042	+	216.249i	0.579949	+	0.605740i
$358$	42.0825	+	37.8217i	0.117549	+	0.105647i
$359$	166.650	+	96.2154i	0.464206	+	0.268009i	0.713811	−	0.700338i	$-0.246968\pi$
$359$	166.650	+	96.2154i	0.464206	+	0.268009i	−0.249605	+	0.968348i	$0.580301\pi$
$360$	−190.032	−	27.8419i	−0.527866	−	0.0773387i
$361$	372.437	+	645.079i	1.03168	+	1.78692i
$362$	−525.341	−	111.163i	−1.45122	−	0.307081i
$363$	389.020	+	582.124i	1.07168	+	1.60365i
$364$	55.5320	−	125.342i	0.152561	−	0.344347i
$365$	91.5392	+	33.3176i	0.250792	+	0.0912810i
$366$	−323.756	+	200.786i	−0.884579	+	0.548596i
$367$	239.898	+	42.3005i	0.653673	+	0.115260i	0.490642	−	0.871361i	$-0.336762\pi$
$367$	239.898	+	42.3005i	0.653673	+	0.115260i	0.163030	+	0.986621i	$0.447873\pi$
$368$	−261.694	+	106.845i	−0.711125	+	0.290338i
$369$	8.70964	−	200.113i	0.0236034	−	0.542312i
$370$	−42.1163	−	26.2638i	−0.113828	−	0.0709831i
$371$	111.711	−	133.132i	0.301108	−	0.358847i
$372$	−53.0188	−	63.5031i	−0.142524	−	0.170707i
$373$	−68.4605	−	388.259i	−0.183540	−	1.04091i	−0.927817	−	0.373037i	$-0.878317\pi$
$373$	−68.4605	−	388.259i	−0.183540	−	1.04091i	0.744276	−	0.667872i	$-0.232795\pi$
$374$	437.307	−	342.305i	1.16927	−	0.915255i
$375$	−37.3379	+	341.146i	−0.0995677	+	0.909723i
$376$	423.090	−	106.720i	1.12524	−	0.283829i
$377$	206.061			0.546582
$378$	238.171	−	277.037i	0.630083	−	0.732903i
$379$		−	353.110i		−	0.931690i	−0.884866	−	0.465845i	$-0.845751\pi$
$379$		−	353.110i		−	0.931690i	0.884866	−	0.465845i	$-0.154249\pi$
$380$	98.4265	+	340.903i	0.259017	+	0.897114i
$381$	−172.745	−	392.520i	−0.453399	−	1.03024i
$382$	−49.5591	+	38.7927i	−0.129736	+	0.101552i
$383$	−45.9409	+	8.10062i	−0.119950	+	0.0211504i	−0.233301	−	0.972405i	$-0.574953\pi$
$383$	−45.9409	+	8.10062i	−0.119950	+	0.0211504i	0.113351	+	0.993555i	$0.463842\pi$
$384$	383.999	−	0.804893i	0.999998	−	0.00209607i
$385$	260.257	+	218.381i	0.675991	+	0.567224i
$386$	−395.435	−	246.593i	−1.02444	−	0.638843i
$387$	−50.1750	−	380.713i	−0.129651	−	0.983756i
$388$	−200.011	−	408.190i	−0.515493	−	1.05204i
$389$	−28.7035	+	162.786i	−0.0737880	+	0.418472i	0.925430	+	0.378920i	$0.123704\pi$
$389$	−28.7035	+	162.786i	−0.0737880	+	0.418472i	−0.999217	+	0.0395526i	$0.987407\pi$
$390$	−71.4589	−	38.3059i	−0.183228	−	0.0982203i
$391$	89.1256	−	244.870i	0.227943	−	0.626267i
$392$	−11.2520	+	23.2312i	−0.0287040	+	0.0592633i
$393$	−15.3270	−	233.599i	−0.0390000	−	0.594401i
$394$	493.292	+	104.382i	1.25201	+	0.264929i
$395$	296.819	−	171.368i	0.751440	−	0.433844i
$396$	−467.463	−	490.671i	−1.18046	−	1.23907i
$397$	−330.658	+	572.717i	−0.832892	+	1.44261i	0.0628427	+	0.998023i	$0.479983\pi$
$397$	−330.658	+	572.717i	−0.832892	+	1.44261i	−0.895735	+	0.444588i	$0.853350\pi$
$398$	−443.744	−	398.816i	−1.11494	−	1.00205i
$399$	−648.012	−	188.830i	−1.62409	−	0.473258i
$400$	−11.0308	−	285.938i	−0.0275770	−	0.714845i
$401$	322.430	−	270.551i	0.804065	−	0.674690i	−0.145119	−	0.989414i	$-0.546356\pi$
$401$	322.430	−	270.551i	0.804065	−	0.674690i	0.949183	+	0.314724i	$0.101912\pi$
$402$	−163.451	−	128.595i	−0.406595	−	0.319887i
$403$	−11.9444	−	32.8169i	−0.0296386	−	0.0814314i
$404$	677.152	+	46.1087i	1.67612	+	0.114131i
$405$	−152.825	−	152.741i	−0.377346	−	0.377139i
$406$	550.089	+	18.7067i	1.35490	+	0.0460757i
$407$	−59.9011	−	164.577i	−0.147177	−	0.404366i
$408$	−237.285	+	262.708i	−0.581581	+	0.643893i
$409$	−298.130	+	250.161i	−0.728925	+	0.611640i	−0.929838	−	0.367969i	$-0.880053\pi$
$409$	−298.130	+	250.161i	−0.728925	+	0.611640i	0.200914	+	0.979609i	$0.435609\pi$
$410$	−117.564	+	16.6321i	−0.286742	+	0.0405660i
$411$	633.364	+	184.562i	1.54103	+	0.449055i
$412$	37.4557	−	38.9286i	0.0909120	−	0.0944868i
$413$	52.6430	−	91.1803i	0.127465	−	0.220776i
$414$	−307.953	−	79.2970i	−0.743847	−	0.191539i
$415$	3.25884	−	1.88149i	0.00785263	−	0.00453372i
$416$	152.581	+	54.7476i	0.366782	+	0.131605i
$417$	38.9522	+	593.673i	0.0934106	+	1.42368i
$418$	−467.963	+	1161.30i	−1.11953	+	2.77823i
$419$	1.34000	−	3.68161i	0.00319809	−	0.00878667i	−0.938083	−	0.346410i	$-0.887401\pi$
$419$	1.34000	−	3.68161i	0.00319809	−	0.00878667i	0.941281	+	0.337623i	$0.109623\pi$
$420$	−187.285	−	108.746i	−0.445917	−	0.258920i
$421$	−74.4542	+	422.251i	−0.176851	+	1.00297i	0.759135	+	0.650933i	$0.225622\pi$
$421$	−74.4542	+	422.251i	−0.176851	+	1.00297i	−0.935986	+	0.352038i	$0.885489\pi$
$422$	75.9250	+	142.480i	0.179917	+	0.337631i
$423$	453.544	+	187.791i	1.07221	+	0.443951i
$424$	166.583	+	120.334i	0.392885	+	0.283807i
$425$	202.082	+	169.567i	0.475487	+	0.398981i
$426$	−33.6346	−	160.912i	−0.0789544	−	0.377728i
$427$	−423.048	+	74.5948i	−0.990746	+	0.174695i
$428$	−379.899	−	520.884i	−0.887615	−	1.21702i
$429$	−115.241	−	261.856i	−0.268626	−	0.610386i
$430$	−216.425	+	70.5393i	−0.503314	+	0.164045i
$431$			112.825i			0.261775i	0.991397	+	0.130887i	$0.0417826\pi$
$431$			112.825i			0.261775i	−0.991397	+	0.130887i	$0.958217\pi$
$432$	347.136	+	257.139i	0.803556	+	0.595229i
$433$	164.343			0.379546			0.189773	−	0.981828i	$-0.439225\pi$
$433$	164.343			0.379546			0.189773	+	0.981828i	$0.439225\pi$
$434$	−28.9068	−	88.6903i	−0.0666055	−	0.204355i
$435$	35.4159	−	323.585i	0.0814158	−	0.743874i
$436$	−216.549	+	157.937i	−0.496673	+	0.362241i
$437$	102.018	+	578.570i	0.233450	+	1.32396i
$438$	−146.063	−	163.327i	−0.333478	−	0.372893i
$439$	−424.795	+	506.251i	−0.967642	+	1.15319i	0.0205222	+	0.999789i	$0.493467\pi$
$439$	−424.795	+	506.251i	−0.967642	+	1.15319i	−0.988164	+	0.153401i	$0.950977\pi$
$440$	−235.238	+	325.650i	−0.534632	+	0.740113i
$441$	−25.7563	+	13.4124i	−0.0584044	+	0.0304136i
$442$	−131.887	+	70.2800i	−0.298387	+	0.159005i
$443$	−230.174	−	40.5858i	−0.519580	−	0.0916159i	−0.0922926	−	0.995732i	$-0.529420\pi$
$443$	−230.174	−	40.5858i	−0.519580	−	0.0916159i	−0.427287	+	0.904116i	$0.640531\pi$
$444$	55.5822	+	96.8225i	0.125185	+	0.218069i
$445$	−171.357	−	62.3687i	−0.385071	−	0.140154i
$446$	249.517	+	100.547i	0.559455	+	0.225441i
$447$	367.475	+	549.883i	0.822091	+	1.23016i
$448$	402.352	+	160.003i	0.898107	+	0.357149i
$449$	−122.709	−	212.538i	−0.273294	−	0.473360i	0.696409	−	0.717645i	$-0.254780\pi$
$449$	−122.709	−	212.538i	−0.273294	−	0.473360i	−0.969703	+	0.244285i	$0.921447\pi$
$450$	182.059	−	265.494i	0.404574	−	0.589986i
$451$	−362.836	−	209.483i	−0.804514	−	0.464487i
$452$	41.3102	+	39.7473i	0.0913943	+	0.0879365i
$453$	218.231	+	227.936i	0.481747	+	0.503170i
$454$	85.6639	+	605.518i	0.188687	+	1.33374i
$455$	−58.7663	−	70.0350i	−0.129157	−	0.153923i
$456$	167.151	−	780.412i	0.366560	−	1.71143i
$457$	429.197	−	156.215i	0.939162	−	0.341827i	0.173327	−	0.984864i	$-0.444548\pi$
$457$	429.197	−	156.215i	0.939162	−	0.341827i	0.765835	+	0.643037i	$0.222326\pi$
$458$	−15.0553	+	442.715i	−0.0328718	+	0.966627i
$459$	−390.588	+	77.7762i	−0.850954	+	0.169447i
$460$	−12.8059	+	188.067i	−0.0278389	+	0.408841i
$461$	613.064	−	223.137i	1.32986	−	0.484029i	0.423254	−	0.906011i	$-0.360888\pi$
$461$	613.064	−	223.137i	1.32986	−	0.484029i	0.906604	+	0.421982i	$0.138666\pi$
$462$	−283.868	−	709.496i	−0.614433	−	1.53571i
$463$	153.827	+	183.324i	0.332240	+	0.395948i	0.906140	−	0.422977i	$-0.139015\pi$
$463$	153.827	+	183.324i	0.332240	+	0.395948i	−0.573901	+	0.818925i	$0.694570\pi$
$464$	25.0888	+	650.346i	0.0540707	+	1.40161i
$465$	−53.5863	+	13.1164i	−0.115239	+	0.0282072i
$466$	112.634	−	125.323i	0.241704	−	0.268932i
$467$	81.5519	+	47.0840i	0.174629	+	0.100822i	0.584767	−	0.811201i	$-0.301186\pi$
$467$	81.5519	+	47.0840i	0.174629	+	0.100822i	−0.410138	+	0.912024i	$0.634519\pi$
$468$	100.955	+	151.877i	0.215715	+	0.324524i
$469$	−117.255	−	203.092i	−0.250012	−	0.433033i
$470$	60.2395	−	284.682i	0.128169	−	0.605707i
$471$	−353.667	+	717.289i	−0.750884	+	1.52291i
$472$	112.045	+	54.2686i	0.237383	+	0.114976i
$473$	−754.774	−	274.715i	−1.59572	−	0.580793i
$474$	−770.533	+	24.2989i	−1.62560	+	0.0512635i
$475$	−585.705	−	103.276i	−1.23306	−	0.217422i
$476$	−358.458	+	175.642i	−0.753062	+	0.368997i
$477$	69.5497	+	220.478i	0.145807	+	0.462218i
$478$	131.755	−	211.282i	0.275639	−	0.442012i
$479$	220.464	−	262.739i	0.460260	−	0.548516i	−0.485137	−	0.874438i	$-0.661230\pi$
$479$	220.464	−	262.739i	0.460260	−	0.548516i	0.945397	+	0.325922i	$0.105675\pi$
$480$	112.196	−	230.194i	0.233742	−	0.479571i
$481$	8.18402	+	46.4139i	0.0170146	+	0.0964945i
$482$	187.129	+	239.064i	0.388234	+	0.495983i
$483$	−289.185	−	212.009i	−0.598727	−	0.438942i
$484$	−896.894	+	258.953i	−1.85309	+	0.535028i
$485$	−303.135			−0.625020
$486$	140.648	+	465.203i	0.289398	+	0.957209i
$487$		−	446.412i		−	0.916656i	−0.888783	−	0.458328i	$-0.848448\pi$
$487$		−	446.412i		−	0.916656i	0.888783	−	0.458328i	$-0.151552\pi$
$488$	−124.234	−	492.524i	−0.254578	−	1.00927i
$489$	−318.096	+	433.890i	−0.650503	+	0.887301i
$490$	10.6103	+	13.5550i	0.0216537	+	0.0276633i
$491$	−5.90542	+	1.04128i	−0.0120273	+	0.00212074i	−0.179659	−	0.983729i	$-0.557499\pi$
$491$	−5.90542	+	1.04128i	−0.0120273	+	0.00212074i	0.167631	+	0.985850i	$0.446388\pi$
$492$	250.737	+	91.9626i	0.509629	+	0.186916i
$493$	−459.621	−	385.668i	−0.932295	−	0.782288i
$494$	178.282	−	285.891i	0.360894	−	0.578726i
$495$	−431.007	+	135.961i	−0.870721	+	0.274669i
$496$	102.118	−	41.6929i	0.205884	−	0.0840583i
$497$	32.1885	−	182.550i	0.0647655	−	0.367304i
$498$	−8.45985	+	0.266783i	−0.0169877	+	0.000535709i
$499$	274.772	−	754.929i	0.550645	−	1.51288i	−0.282188	−	0.959359i	$-0.591060\pi$
$499$	274.772	−	754.929i	0.550645	−	1.51288i	0.832833	−	0.553525i	$-0.186718\pi$
$500$	−418.357	−	185.350i	−0.836714	−	0.370700i
$501$	−519.201	−	255.998i	−1.03633	−	0.510973i
$502$	8.76958	−	41.4436i	0.0174693	−	0.0825570i
$503$	127.666	−	73.7082i	0.253810	−	0.146537i	−0.367698	−	0.929945i	$-0.619854\pi$
$503$	127.666	−	73.7082i	0.253810	−	0.146537i	0.621508	+	0.783408i	$0.286521\pi$
$504$	255.715	+	414.607i	0.507371	+	0.822634i
$505$	226.311	−	391.982i	0.448141	−	0.776203i
$506$	−444.619	+	494.707i	−0.878694	+	0.977682i
$507$	−102.237	−	417.682i	−0.201650	−	0.823831i
$508$	568.558	−	60.8077i	1.11921	−	0.119700i
$509$	−519.941	+	436.282i	−1.02149	+	0.857136i	−0.989815	−	0.142362i	$-0.954530\pi$
$509$	−519.941	+	436.282i	−1.02149	+	0.857136i	−0.0316799	+	0.999498i	$0.510086\pi$
$510$	87.6956	+	219.185i	0.171952	+	0.429775i
$511$	−84.5035	−	232.171i	−0.165369	−	0.454347i
$512$	−154.210	+	488.225i	−0.301192	+	0.953564i
$513$	674.937	−	592.150i	1.31567	−	1.15429i
$514$	2.65340	−	78.0259i	0.00516226	−	0.151801i
$515$	−12.3216	−	33.8533i	−0.0239254	−	0.0657345i
$516$	504.008	+	90.1537i	0.976759	+	0.174717i
$517$	786.551	−	659.995i	1.52138	−	1.27659i
$518$	17.6340	+	124.647i	0.0340425	+	0.240631i
$519$	−537.428	+	514.546i	−1.03551	+	0.991419i
$520$	77.5580	−	75.3085i	0.149150	−	0.144824i
$521$	107.426	−	186.067i	0.206192	−	0.357135i	−0.744320	−	0.667823i	$-0.767226\pi$
$521$	107.426	−	186.067i	0.206192	−	0.357135i	0.950512	+	0.310688i	$0.100559\pi$
$522$	−414.080	+	603.847i	−0.793256	+	1.15680i
$523$	−535.275	+	309.041i	−1.02347	+	0.590901i	−0.915107	−	0.403210i	$-0.867894\pi$
$523$	−535.275	+	309.041i	−1.02347	+	0.590901i	−0.108363	+	0.994111i	$0.534561\pi$
$524$	303.001	+	74.9593i	0.578247	+	0.143052i
$525$	301.807	−	201.691i	0.574870	−	0.384173i
$526$	713.822	+	287.645i	1.35708	+	0.546854i
$527$	−34.7786	+	95.5535i	−0.0659936	+	0.181316i
$528$	812.406	−	395.591i	1.53865	−	0.749225i
$529$	37.6630	−	213.598i	0.0711966	−	0.403776i
$530$	120.943	−	64.4483i	0.228195	−	0.121601i
$531$	64.6884	+	124.224i	0.121824	+	0.233943i
$532$	501.884	−	747.012i	0.943390	−	1.40416i
$533$	86.3668	+	72.4704i	0.162039	+	0.135967i
$534$	273.423	+	305.740i	0.512028	+	0.572547i
$535$	−423.406	+	74.6579i	−0.791414	+	0.139548i
$536$	229.465	−	155.692i	0.428106	−	0.290470i
$537$	−84.3678	−	9.23392i	−0.157109	−	0.0171954i
$538$	−79.6366	−	244.337i	−0.148024	−	0.454158i
$539$			60.7406i			0.112691i
$540$	255.849	−	132.429i	0.473794	−	0.245239i
$541$	−647.938			−1.19767			−0.598834	−	0.800873i	$-0.704369\pi$
$541$	−647.938			−1.19767			−0.598834	+	0.800873i	$0.704369\pi$
$542$	−330.154	+	107.607i	−0.609140	+	0.198536i
$543$	737.224	−	324.447i	1.35769	−	0.597508i
$544$	−237.867	−	407.689i	−0.437256	−	0.749428i
$545$	31.0379	+	176.024i	0.0569502	+	0.322981i
$546$	42.0744	+	201.289i	0.0770594	+	0.368662i
$547$	431.014	−	513.662i	0.787960	−	0.939054i	−0.211304	−	0.977420i	$-0.567771\pi$
$547$	431.014	−	513.662i	0.787960	−	0.939054i	0.999264	+	0.0383666i	$0.0122155\pi$
$548$	−490.539	+	730.126i	−0.895144	+	1.33235i
$549$	218.610	−	527.976i	0.398197	−	0.961705i
$550$	−316.661	−	594.244i	−0.575748	−	1.08044i
$551$	1332.15	+	234.893i	2.41769	+	0.426304i
$552$	225.244	−	359.220i	0.408050	−	0.650761i
$553$	−816.861	−	297.313i	−1.47714	−	0.537637i
$554$	120.419	−	298.832i	0.217363	−	0.539409i
$555$	74.2918	−	4.87445i	0.133859	−	0.00878280i
$556$	−770.052	−	190.503i	−1.38498	−	0.342631i
$557$	−334.348	−	579.107i	−0.600265	−	1.03969i	−0.992781	−	0.119944i	$-0.961728\pi$
$557$	−334.348	−	579.107i	−0.600265	−	1.03969i	0.392515	−	0.919745i	$-0.371605\pi$
$558$	120.169	+	30.9433i	0.215357	+	0.0554540i
$559$	187.187	+	108.072i	0.334860	+	0.193331i
$560$	213.881	−	193.998i	0.381930	−	0.346425i
$561$	−233.049	+	799.757i	−0.415416	+	1.42559i
$562$	160.965	−	22.7721i	0.286415	−	0.0405198i
$563$	−30.5238	−	36.3768i	−0.0542163	−	0.0646125i	0.738255	−	0.674522i	$-0.235650\pi$
$563$	−30.5238	−	36.3768i	−0.0542163	−	0.0646125i	−0.792471	+	0.609910i	$0.791206\pi$
$564$	−421.949	+	500.346i	−0.748137	+	0.887138i
$565$	35.9245	−	13.0754i	0.0635831	−	0.0231424i
$566$	−640.573	−	21.7838i	−1.13175	−	0.0384872i
$567$	−47.6129	+	545.942i	−0.0839734	+	0.962860i
$568$	218.048	+	22.3141i	0.383887	+	0.0392853i
$569$	114.639	−	41.7252i	0.201475	−	0.0733307i	−0.239312	−	0.970943i	$-0.576922\pi$
$569$	114.639	−	41.7252i	0.201475	−	0.0733307i	0.440786	+	0.897612i	$0.354700\pi$
$570$	−418.302	−	329.097i	−0.733863	−	0.577364i
$571$	604.450	+	720.356i	1.05858	+	1.26157i	0.963958	+	0.266056i	$0.0857205\pi$
$571$	604.450	+	720.356i	1.05858	+	1.26157i	0.0946241	+	0.995513i	$0.469835\pi$
$572$	379.293	−	40.5657i	0.663100	−	0.0709191i
$573$	26.4109	−	90.6348i	0.0460923	−	0.158176i
$574$	223.981	+	201.303i	0.390210	+	0.350702i
$575$	−273.626	−	157.978i	−0.475871	−	0.274744i
$576$	−467.045	+	337.113i	−0.810842	+	0.585265i
$577$	−71.2440	−	123.398i	−0.123473	−	0.213862i	0.797662	−	0.603105i	$-0.206070\pi$
$577$	−71.2440	−	123.398i	−0.123473	−	0.213862i	−0.921135	+	0.389243i	$0.872737\pi$
$578$	−139.767	−	29.5750i	−0.241811	−	0.0511678i
$579$	697.534	−	45.7668i	1.20472	−	0.0790445i
$580$	396.822	+	175.809i	0.684175	+	0.303119i
$581$	−8.96850	−	3.26427i	−0.0154363	−	0.00561836i
$582$	600.942	+	322.138i	1.03255	+	0.553502i
$583$	476.222	+	83.9708i	0.816848	+	0.144032i
$584$	266.566	−	119.559i	0.456449	−	0.204724i
$585$	120.575	−	15.8908i	0.206111	−	0.0271638i
$586$	85.6135	+	53.3886i	0.146098	+	0.0911068i
$587$	109.295	−	130.253i	0.186192	−	0.221895i	−0.664871	−	0.746958i	$-0.731514\pi$
$587$	109.295	−	130.253i	0.186192	−	0.221895i	0.851064	+	0.525063i	$0.175958\pi$
$588$	−6.62933	−	38.1473i	−0.0112744	−	0.0648764i
$589$	−39.8093	−	225.770i	−0.0675880	−	0.383311i
$590$	65.3764	−	51.1739i	0.110808	−	0.0867354i
$591$	−692.250	+	304.654i	−1.17132	+	0.515489i
$592$	−145.489	+	31.4805i	−0.245759	+	0.0531765i
$593$	−669.024			−1.12820			−0.564101	−	0.825706i	$-0.690777\pi$
$593$	−669.024			−1.12820			−0.564101	+	0.825706i	$0.690777\pi$
$594$	998.924	+	188.494i	1.68169	+	0.317330i
$595$			266.202i			0.447398i
$596$	−847.219	+	244.611i	−1.42151	+	0.410422i
$597$	889.627	+	97.3684i	1.49016	+	0.163096i
$598$	140.946	−	110.327i	0.235696	−	0.184493i
$599$	483.540	−	85.2611i	0.807245	−	0.142339i	0.245229	−	0.969465i	$-0.421137\pi$
$599$	483.540	−	85.2611i	0.807245	−	0.142339i	0.562016	+	0.827126i	$0.310026\pi$
$600$	263.731	+	338.645i	0.439552	+	0.564409i
$601$	231.159	+	193.966i	0.384624	+	0.322738i	0.814515	−	0.580143i	$-0.197003\pi$
$601$	231.159	+	193.966i	0.384624	+	0.322738i	−0.429890	+	0.902881i	$0.641448\pi$
$602$	489.891	+	305.496i	0.813773	+	0.507469i
$603$	311.665	+	13.5648i	0.516857	+	0.0224955i
$604$	−377.830	+	185.135i	−0.625547	+	0.306515i
$605$	−108.104	+	613.090i	−0.178685	+	1.01337i
$606$	−865.200	+	536.577i	−1.42772	+	0.885441i
$607$	66.6834	−	183.211i	0.109857	−	0.301830i	−0.872566	−	0.488496i	$-0.837546\pi$
$607$	66.6834	−	183.211i	0.109857	−	0.301830i	0.982424	+	0.186665i	$0.0597680\pi$
$608$	924.000	+	527.862i	1.51974	+	0.868195i
$609$	−686.439	+	458.732i	−1.12716	+	0.753255i
$610$	−331.402	−	70.1256i	−0.543283	−	0.114960i
$611$	−239.286	+	138.152i	−0.391630	+	0.226107i
$612$	59.0760	−	527.712i	0.0965295	−	0.862274i
$613$	−296.011	+	512.707i	−0.482890	+	0.836389i	−0.999807	−	0.0196459i	$-0.993746\pi$
$613$	−296.011	+	512.707i	−0.482890	+	0.836389i	0.516917	+	0.856035i	$0.327079\pi$
$614$	187.409	+	168.434i	0.305227	+	0.274323i
$615$	128.646	−	123.169i	0.209181	−	0.200275i
$616$	1016.22	−	73.8587i	1.64971	−	0.119900i
$617$	−272.885	+	228.978i	−0.442277	+	0.371114i	−0.836561	−	0.547874i	$-0.815437\pi$
$617$	−272.885	+	228.978i	−0.442277	+	0.371114i	0.394284	+	0.918989i	$0.370993\pi$
$618$	−11.5489	+	80.2056i	−0.0186875	+	0.129783i
$619$	−190.318	−	522.895i	−0.307461	−	0.844741i	−0.993150	−	0.116847i	$-0.962721\pi$
$619$	−190.318	−	522.895i	−0.307461	−	0.844741i	0.685689	−	0.727894i	$-0.259501\pi$
$620$	4.99712	−	73.3876i	0.00805987	−	0.118367i
$621$	444.529	−	172.973i	0.715828	−	0.278540i
$622$	−458.381	−	15.5880i	−0.736948	−	0.0250612i
$623$	158.186	+	434.612i	0.253910	+	0.697612i
$624$	−233.782	+	66.8734i	−0.374651	+	0.107169i
$625$	108.750	−	91.2519i	0.174000	−	0.146003i
$626$	−585.624	+	82.8494i	−0.935501	+	0.132347i
$627$	−446.514	−	1824.21i	−0.712143	−	2.90943i
$628$	−768.397	−	739.326i	−1.22356	−	1.17727i
$629$	68.6145	−	118.844i	0.109085	−	0.188941i
$630$	323.323	−	31.4751i	0.513211	−	0.0499605i
$631$	−716.677	+	413.773i	−1.13578	+	0.655742i	−0.945382	−	0.325965i	$-0.894311\pi$
$631$	−716.677	+	413.773i	−1.13578	+	0.655742i	−0.190397	+	0.981707i	$0.560978\pi$
$632$	280.617	−	988.841i	0.444014	−	1.56462i
$633$	−217.204	−	107.095i	−0.343134	−	0.169186i
$634$	141.063	−	350.063i	0.222497	−	0.552150i
$635$	130.419	−	358.324i	0.205385	−	0.564289i
$636$	−308.249	−	0.761016i	−0.484669	−	0.00119657i
$637$	2.83833	−	16.0970i	0.00445578	−	0.0252700i
$638$	720.224	+	1351.57i	1.12888	+	2.11844i
$639$	181.824	+	166.565i	0.284545	+	0.260665i
$640$	247.123	+	235.610i	0.386129	+	0.368141i
$641$	18.1457	+	15.2260i	0.0283084	+	0.0237536i	0.656832	−	0.754037i	$-0.271896\pi$
$641$	18.1457	+	15.2260i	0.0283084	+	0.0237536i	−0.628524	+	0.777790i	$0.716340\pi$
$642$	918.709	+	301.945i	1.43101	+	0.470320i
$643$	511.335	−	90.1621i	0.795233	−	0.140221i	0.238751	−	0.971081i	$-0.423262\pi$
$643$	511.335	−	90.1621i	0.795233	−	0.140221i	0.556482	+	0.830860i	$0.312151\pi$
$644$	386.277	−	281.726i	0.599809	−	0.437462i
$645$	201.881	−	275.371i	0.312994	−	0.426931i
$646$	−932.736	+	304.006i	−1.44386	+	0.470597i
$647$			728.461i			1.12591i	0.826489	+	0.562953i	$0.190335\pi$
$647$			728.461i			1.12591i	−0.826489	+	0.562953i	$0.809665\pi$
$648$	−647.932	−	9.35693i	−0.999896	−	0.0144397i
$649$	292.954			0.451393
$650$	56.1506	+	172.279i	0.0863856	+	0.265044i
$651$	112.846	+	82.7303i	0.173343	+	0.127082i
$652$	−422.698	−	579.566i	−0.648310	−	0.888905i
$653$	101.708	+	576.816i	0.155755	+	0.883332i	0.958092	+	0.286460i	$0.0924786\pi$
$653$	101.708	+	576.816i	0.155755	+	0.883332i	−0.802337	+	0.596871i	$0.796410\pi$
$654$	125.529	−	381.939i	0.191940	−	0.584004i
$655$	133.800	−	159.457i	0.204275	−	0.243445i
$656$	−218.207	+	281.404i	−0.332632	+	0.428970i
$657$	320.888	+	71.0930i	0.488414	+	0.108209i
$658$	−651.325	+	347.079i	−0.989855	+	0.527475i
$659$	−1165.69	−	205.543i	−1.76888	−	0.311901i	−0.808064	−	0.589095i	$-0.799485\pi$
$659$	−1165.69	−	205.543i	−1.76888	−	0.311901i	−0.960814	+	0.277194i	$0.910596\pi$
$660$	1.48769	−	602.589i	0.00225408	−	0.913013i
$661$	−112.165	−	40.8248i	−0.169690	−	0.0617622i	0.255778	−	0.966736i	$-0.417668\pi$
$661$	−112.165	−	40.8248i	−0.169690	−	0.0617622i	−0.425468	+	0.904973i	$0.639891\pi$
$662$	−329.430	−	132.749i	−0.497628	−	0.200527i
$663$	99.1322	−	201.055i	0.149521	−	0.303250i
$664$	3.08096	−	10.8567i	0.00463999	−	0.0163505i
$665$	−300.078	−	519.751i	−0.451246	−	0.781580i
$666$	−152.458	−	69.2858i	−0.228916	−	0.104033i
$667$	622.344	+	359.310i	0.933049	+	0.538696i
$668$	535.153	−	556.196i	0.801127	−	0.832628i
$669$	−391.950	+	95.9380i	−0.585874	+	0.143405i
$670$	−25.9035	−	183.100i	−0.0386620	−	0.273284i
$671$	−768.308	−	915.634i	−1.14502	−	1.36458i
$672$	−630.163	+	157.298i	−0.937742	+	0.234074i
$673$	989.622	−	360.193i	1.47046	−	0.535205i	0.522237	−	0.852800i	$-0.325098\pi$
$673$	989.622	−	360.193i	1.47046	−	0.535205i	0.948226	+	0.317595i	$0.102875\pi$
$674$	24.4463	−	718.866i	0.0362704	−	1.06657i
$675$	10.6332	+	482.762i	0.0157529	+	0.715203i
$676$	572.026	+	38.9505i	0.846192	+	0.0576190i
$677$	529.374	−	192.676i	0.781940	−	0.284603i	0.0799588	−	0.996798i	$-0.474521\pi$
$677$	529.374	−	192.676i	0.781940	−	0.284603i	0.701982	+	0.712195i	$0.252299\pi$
$678$	−85.1127	−	12.2555i	−0.125535	−	0.0180759i
$679$	494.202	+	588.967i	0.727838	+	0.867404i
$680$	−313.942	+	22.8172i	−0.461680	+	0.0335548i
$681$	−634.385	−	662.597i	−0.931550	−	0.972976i
$682$	173.499	−	193.045i	0.254398	−	0.283057i
$683$	226.467	+	130.751i	0.331577	+	0.191436i	0.656541	−	0.754290i	$-0.272019\pi$
$683$	226.467	+	130.751i	0.331577	+	0.191436i	−0.324964	+	0.945726i	$0.605352\pi$
$684$	479.524	+	1096.94i	0.701058	+	1.60371i
$685$	293.295	+	508.002i	0.428168	+	0.741609i
$686$	146.298	−	691.380i	0.213262	−	1.00784i
$687$	−369.190	−	552.450i	−0.537395	−	0.804149i
$688$	−318.294	+	603.934i	−0.462636	+	0.877811i
$689$	−122.280	−	44.5065i	−0.177475	−	0.0645957i
$690$	−149.025	−	240.294i	−0.215978	−	0.348252i
$691$	−720.416	−	127.029i	−1.04257	−	0.183833i	−0.373959	−	0.927445i	$-0.622000\pi$
$691$	−720.416	−	127.029i	−1.04257	−	0.183833i	−0.668611	+	0.743612i	$0.733111\pi$
$692$	−436.512	−	890.849i	−0.630797	−	1.28735i
$693$	966.835	+	615.755i	1.39514	+	0.888536i
$694$	293.687	−	470.953i	0.423180	−	0.678607i
$695$	−340.041	+	405.245i	−0.489268	+	0.583087i
$696$	−599.839	−	770.226i	−0.861837	−	1.10665i
$697$	−57.0050	−	323.291i	−0.0817862	−	0.463832i
$698$	−65.3193	−	83.4478i	−0.0935807	−	0.119553i
$699$	−27.4988	+	251.249i	−0.0393402	+	0.359441i
$700$	134.257	+	465.002i	0.191795	+	0.664289i
$701$	980.935			1.39934			0.699668	−	0.714468i	$-0.253331\pi$
$701$	980.935			1.39934			0.699668	+	0.714468i	$0.253331\pi$
$702$	−255.918	−	96.6315i	−0.364556	−	0.137652i
$703$			309.385i			0.440093i
$704$	174.209	+	1192.14i	0.247456	+	1.69338i
$705$	175.818	+	399.502i	0.249387	+	0.566670i
$706$	168.407	+	215.146i	0.238536	+	0.304739i
$707$	−1130.55	+	199.346i	−1.59908	+	0.281960i
$708$	−183.986	+	31.9735i	−0.259867	+	0.0451603i
$709$	−36.9636	−	31.0162i	−0.0521349	−	0.0437464i	0.616348	−	0.787474i	$-0.288612\pi$
$709$	−36.9636	−	31.0162i	−0.0521349	−	0.0437464i	−0.668483	+	0.743728i	$0.733056\pi$
$710$	77.3452	−	124.030i	0.108937	−	0.174690i
$711$	917.316	−	704.081i	1.29018	−	0.990269i
$712$	−498.997	+	223.808i	−0.700839	+	0.314337i
$713$	21.1487	−	119.940i	0.0296616	−	0.168219i
$714$	282.890	−	527.725i	0.396204	−	0.739110i
$715$	87.0046	−	239.043i	0.121685	−	0.334326i
$716$	45.8383	−	103.463i	0.0640200	−	0.144501i
$717$	24.4533	+	372.694i	0.0341050	+	0.519796i
$718$	79.6735	−	376.524i	0.110966	−	0.524407i
$719$	−1170.39	+	675.725i	−1.62780	+	0.939813i	−0.643057	+	0.765818i	$0.722334\pi$
$719$	−1170.39	+	675.725i	−1.62780	+	0.939813i	−0.984747	+	0.173994i	$0.944333\pi$
$720$	64.8332	+	378.610i	0.0900461	+	0.525847i
$721$	−45.6863	+	79.1311i	−0.0633652	+	0.109752i
$722$	995.824	−	1108.01i	1.37926	−	1.53464i
$723$	−437.205	−	127.401i	−0.604710	−	0.176212i
$724$	114.208	+	1067.86i	0.157746	+	1.47494i
$725$	−557.284	+	467.617i	−0.768667	+	0.644988i
$726$	865.833	−	1100.52i	1.19261	−	1.51587i
$727$	264.383	+	726.385i	0.363662	+	0.999154i	0.977724	+	0.209896i	$0.0673126\pi$
$727$	264.383	+	726.385i	0.363662	+	0.999154i	−0.614061	+	0.789258i	$0.710465\pi$
$728$	−272.762	−	27.9133i	−0.374673	−	0.0383424i
$729$	−578.537	−	443.549i	−0.793604	−	0.608435i
$730$	6.62163	−	194.716i	0.00907073	−	0.266734i
$731$	−215.251	−	591.397i	−0.294461	−	0.809025i
$732$	582.459	+	491.196i	0.795709	+	0.671033i
$733$	−1060.19	+	889.603i	−1.44637	+	1.21365i	−0.511190	+	0.859468i	$0.670795\pi$
$733$	−1060.19	+	889.603i	−1.44637	+	1.21365i	−0.935178	+	0.354179i	$0.884760\pi$
$734$	−68.2452	−	482.394i	−0.0929771	−	0.657212i
$735$	−24.7898	−	7.22371i	−0.0337276	−	0.00982818i
$736$	365.360	+	431.404i	0.496413	+	0.586147i
$737$	326.259	−	565.097i	0.442685	−	0.766753i
$738$	−385.922	+	107.462i	−0.522930	+	0.145613i
$739$	295.927	−	170.854i	0.400442	−	0.231196i	−0.286232	−	0.958160i	$-0.592403\pi$
$739$	295.927	−	170.854i	0.400442	−	0.231196i	0.686675	+	0.726965i	$0.259070\pi$
$740$	−23.8394	+	96.3637i	−0.0322153	+	0.130221i
$741$	33.0884	+	504.302i	0.0446537	+	0.680569i
$742$	−322.392	−	129.913i	−0.434491	−	0.175085i
$743$	−191.604	+	526.428i	−0.257879	+	0.708517i	0.741419	+	0.671043i	$0.234153\pi$
$743$	−191.604	+	526.428i	−0.257879	+	0.708517i	−0.999298	+	0.0374741i	$0.988069\pi$
$744$	−87.8947	+	140.175i	−0.118138	+	0.188407i
$745$	−102.117	+	579.134i	−0.137070	+	0.777361i
$746$	−695.863	+	370.812i	−0.932792	+	0.497067i
$747$	10.0714	−	7.73027i	0.0134825	−	0.0103484i
$748$	−921.940	−	619.410i	−1.23254	−	0.828088i
$749$	835.336	+	700.930i	1.11527	+	0.935821i
$750$	671.846	−	140.432i	0.895795	−	0.187243i
$751$	−732.986	+	129.245i	−0.976013	+	0.172097i	−0.638835	−	0.769344i	$-0.720583\pi$
$751$	−732.986	+	129.245i	−0.976013	+	0.172097i	−0.337178	+	0.941441i	$0.609472\pi$
$752$	−465.152	−	738.384i	−0.618553	−	0.981894i
$753$	25.5953	+	58.1589i	0.0339911	+	0.0772363i
$754$	−127.711	−	391.836i	−0.169378	−	0.519676i
$755$			280.588i			0.371640i
$756$	−674.411	−	281.195i	−0.892079	−	0.371950i
$757$	−34.0389			−0.0449655			−0.0224828	−	0.999747i	$-0.507157\pi$
$757$	−34.0389			−0.0449655			−0.0224828	+	0.999747i	$0.507157\pi$
$758$	−671.456	+	218.847i	−0.885826	+	0.288717i
$759$	108.551	−	991.798i	0.143018	−	1.30672i
$760$	587.242	−	398.445i	0.772687	−	0.524269i
$761$	27.3928	+	155.352i	0.0359958	+	0.204142i	0.997502	−	0.0706419i	$-0.0225048\pi$
$761$	27.3928	+	155.352i	0.0359958	+	0.204142i	−0.961506	+	0.274784i	$0.911394\pi$
$762$	−639.333	+	571.755i	−0.839020	+	0.750335i
$763$	291.401	−	347.278i	0.381914	−	0.455148i
$764$	104.481	+	70.1964i	0.136756	+	0.0918801i
$765$	−298.685	−	190.226i	−0.390438	−	0.248661i
$766$	43.8765	+	82.3383i	0.0572800	+	0.107491i
$767$	−77.6362	−	13.6894i	−0.101221	−	0.0178479i
$768$	−239.522	−	729.694i	−0.311877	−	0.950122i
$769$	271.545	+	98.8342i	0.353114	+	0.128523i	0.512486	−	0.858696i	$-0.328725\pi$
$769$	271.545	+	98.8342i	0.353114	+	0.128523i	−0.159372	+	0.987219i	$0.550947\pi$
$770$	253.963	−	630.237i	0.329822	−	0.818489i
$771$	65.0675	+	97.3660i	0.0843937	+	0.126285i
$772$	−223.830	+	904.769i	−0.289936	+	1.17198i
$773$	514.374	+	890.922i	0.665426	+	1.15255i	0.979170	+	0.203043i	$0.0650832\pi$
$773$	514.374	+	890.922i	0.665426	+	1.15255i	−0.313744	+	0.949508i	$0.601583\pi$
$774$	−692.848	+	331.365i	−0.895152	+	0.428120i
$775$	106.774	+	61.6463i	0.137774	+	0.0795436i
$776$	−652.233	+	633.315i	−0.840506	+	0.816128i
$777$	−130.589	−	136.396i	−0.168068	−	0.175542i
$778$	327.334	−	46.3087i	0.420738	−	0.0595227i
$779$	475.734	+	566.957i	0.610698	+	0.727801i
$780$	−28.5524	+	159.623i	−0.0366057	+	0.204645i
$781$	484.669	−	176.405i	0.620575	−	0.225871i
$782$	−520.870	−	17.7131i	−0.666075	−	0.0226510i
$783$	−24.1845	−	1098.01i	−0.0308870	−	1.40231i
$784$	51.1489	+	6.99812i	0.0652409	+	0.00892617i
$785$	−668.218	+	243.212i	−0.851233	+	0.309824i
$786$	−434.701	+	173.923i	−0.553055	+	0.221276i
$787$	541.136	+	644.900i	0.687593	+	0.819441i	0.991062	−	0.133400i	$-0.0425894\pi$
$787$	541.136	+	644.900i	0.687593	+	0.819441i	−0.303469	+	0.952841i	$0.598145\pi$
$788$	−107.241	−	1002.71i	−0.136092	−	1.27248i
$789$	−1121.30	+	274.461i	−1.42116	+	0.347859i
$790$	−509.825	−	458.206i	−0.645348	−	0.580008i
$791$	−83.9724	−	48.4815i	−0.106160	−	0.0612914i
$792$	−643.314	+	1193.01i	−0.812265	+	1.50632i
$793$	160.824	+	278.555i	0.202805	+	0.351268i
$794$	1293.98	+	273.810i	1.62970	+	0.344848i
$795$	−90.9064	+	184.372i	−0.114348	+	0.231914i
$796$	−483.349	+	1090.98i	−0.607222	+	1.37057i
$797$	50.5238	+	18.3892i	0.0633925	+	0.0230730i	0.373522	−	0.927621i	$-0.378150\pi$
$797$	50.5238	+	18.3892i	0.0633925	+	0.0230730i	−0.310129	+	0.950694i	$0.600372\pi$
$798$	42.5491	+	1349.26i	0.0533197	+	1.69080i
$799$	792.295	+	139.703i	0.991609	+	0.174847i
$800$	−536.888	+	198.191i	−0.671110	+	0.247739i
$801$	−600.685	−	133.082i	−0.749919	−	0.166145i
$802$	−714.298	−	445.437i	−0.890646	−	0.555407i
$803$	441.896	−	526.631i	0.550306	−	0.655829i
$804$	−143.227	+	390.510i	−0.178143	+	0.485709i
$805$	−55.3648	−	313.990i	−0.0687762	−	0.390049i
$806$	−55.0001	+	43.0517i	−0.0682383	+	0.0534140i
$807$	310.885	+	227.918i	0.385235	+	0.282426i
$808$	−332.001	−	1316.21i	−0.410892	−	1.62898i
$809$	491.114			0.607063			0.303531	−	0.952821i	$-0.401834\pi$
$809$	491.114			0.607063			0.303531	+	0.952821i	$0.401834\pi$
$810$	−195.728	+	385.268i	−0.241640	+	0.475640i
$811$			1304.91i			1.60901i	0.593943	+	0.804507i	$0.297570\pi$
$811$			1304.91i			1.60901i	−0.593943	+	0.804507i	$0.702430\pi$
$812$	−305.357	−	1057.62i	−0.376056	−	1.30248i
$813$	307.967	−	420.075i	0.378803	−	0.516697i
$814$	−275.826	+	215.905i	−0.338852	+	0.265239i
$815$	−471.107	+	83.0688i	−0.578045	+	0.101925i
$816$	646.615	+	288.390i	0.792420	+	0.353419i
$817$	1086.93	+	912.043i	1.33039	+	1.11633i
$818$	660.465	+	411.867i	0.807415	+	0.503504i
$819$	−227.449	−	208.361i	−0.277715	−	0.254409i
$820$	104.490	+	213.246i	0.127426	+	0.260056i
$821$	227.261	−	1288.86i	0.276810	−	1.56987i	−0.456341	−	0.889805i	$-0.650840\pi$
$821$	227.261	−	1288.86i	0.276810	−	1.56987i	0.733152	−	0.680065i	$-0.238049\pi$
$822$	−41.5873	−	1318.76i	−0.0505929	−	1.60433i
$823$	45.6295	−	125.366i	0.0554428	−	0.152328i	−0.908879	−	0.417059i	$-0.863061\pi$
$823$	45.6295	−	125.366i	0.0554428	−	0.152328i	0.964322	+	0.264731i	$0.0852831\pi$
$824$	−97.2385	−	47.0971i	−0.118008	−	0.0571567i
$825$	905.894	+	446.660i	1.09805	+	0.541406i
$826$	−206.010	−	43.5923i	−0.249407	−	0.0527752i
$827$	1078.20	−	622.498i	1.30375	−	0.752718i	0.322701	−	0.946501i	$-0.395409\pi$
$827$	1078.20	−	622.498i	1.30375	−	0.752718i	0.981044	+	0.193783i	$0.0620757\pi$
$828$	40.0727	+	634.732i	0.0483970	+	0.766585i
$829$	−494.673	+	856.798i	−0.596710	+	1.03353i	0.396593	+	0.917995i	$0.370193\pi$
$829$	−494.673	+	856.798i	−0.596710	+	1.03353i	−0.993303	+	0.115538i	$0.963141\pi$
$830$	−5.59748	−	5.03075i	−0.00674395	−	0.00606114i
$831$	114.900	+	469.416i	0.138267	+	0.564881i
$832$	9.53976	−	324.072i	0.0114661	−	0.389509i
$833$	−36.4583	+	30.5921i	−0.0437674	+	0.0367252i
$834$	1104.76	−	442.010i	1.32465	−	0.529988i
$835$	−176.046	−	483.682i	−0.210833	−	0.579260i
$836$	2498.30	+	170.114i	2.98839	+	0.203486i
$837$	−173.465	+	67.4977i	−0.207246	+	0.0806425i
$838$	−7.83126	−	0.266315i	−0.00934518	−	0.000317799i
$839$	−11.0695	−	30.4133i	−0.0131937	−	0.0362495i	0.932921	−	0.360081i	$-0.117251\pi$
$839$	−11.0695	−	30.4133i	−0.0131937	−	0.0362495i	−0.946115	+	0.323832i	$0.895029\pi$
$840$	−90.7129	+	423.529i	−0.107992	+	0.504201i
$841$	623.260	−	522.977i	0.741094	−	0.621852i
$842$	849.074	−	120.120i	1.00840	−	0.142661i
$843$	−176.139	+	168.639i	−0.208943	+	0.200047i
$844$	223.877	−	232.680i	0.265257	−	0.275687i
$845$	191.177	−	331.128i	0.226245	−	0.391867i
$846$	76.0010	−	978.823i	0.0898357	−	1.15700i
$847$	1367.43	−	789.486i	1.61444	−	0.932096i
$848$	125.578	−	391.346i	0.148087	−	0.461493i
$849$	799.350	−	534.188i	0.941520	−	0.629197i
$850$	197.195	−	489.361i	0.231994	−	0.575719i
$851$	−56.2148	+	154.449i	−0.0660574	+	0.181491i
$852$	−285.136	+	163.686i	−0.334667	+	0.192120i
$853$	156.148	−	885.558i	0.183057	−	1.03817i	−0.745369	−	0.666652i	$-0.767727\pi$
$853$	156.148	−	885.558i	0.183057	−	1.03817i	0.928426	−	0.371517i	$-0.121162\pi$
$854$	404.038	+	758.215i	0.473113	+	0.887840i
$855$	797.608	+	34.7148i	0.932875	+	0.0406021i
$856$	−755.035	+	1045.23i	−0.882051	+	1.22106i
$857$	936.816	+	786.082i	1.09313	+	0.917249i	0.996944	−	0.0781141i	$-0.0248899\pi$
$857$	936.816	+	786.082i	1.09313	+	0.917249i	0.0961902	+	0.995363i	$0.469334\pi$
$858$	−426.509	+	381.426i	−0.497096	+	0.444553i
$859$	256.657	−	45.2555i	0.298785	−	0.0526839i	−0.0222459	−	0.999753i	$-0.507082\pi$
$859$	256.657	−	45.2555i	0.298785	−	0.0526839i	0.321031	+	0.947069i	$0.395971\pi$
$860$	268.268	+	367.824i	0.311939	+	0.427703i
$861$	−449.041	−	49.1468i	−0.521534	−	0.0570811i
$862$	214.542	−	69.9256i	0.248889	−	0.0811201i
$863$			545.581i			0.632191i	0.948727	+	0.316095i	$0.102372\pi$
$863$			545.581i			0.632191i	−0.948727	+	0.316095i	$0.897628\pi$
$864$	273.818	−	819.463i	0.316918	−	0.948453i
$865$	−661.572			−0.764823
$866$	−101.855	−	312.507i	−0.117616	−	0.360862i
$867$	196.138	−	86.3190i	0.226227	−	0.0995606i
$868$	−150.733	+	109.935i	−0.173656	+	0.126653i
$869$	−420.012	−	2382.01i	−0.483328	−	2.74109i
$870$	−637.262	+	133.203i	−0.732485	+	0.153107i
$871$	−112.869	+	134.512i	−0.129585	+	0.154433i
$872$	434.536	+	313.894i	0.498321	+	0.359970i
$873$	−1013.99	+	133.636i	−1.16150	+	0.153076i
$874$	1036.95	−	552.572i	1.18644	−	0.632233i
$875$	762.189	+	134.395i	0.871074	+	0.153594i
$876$	−220.049	+	378.972i	−0.251197	+	0.432617i
$877$	−555.246	−	202.093i	−0.633119	−	0.230437i	0.00546906	−	0.999985i	$-0.498259\pi$
$877$	−555.246	−	202.093i	−0.633119	−	0.230437i	−0.638588	+	0.769548i	$0.720481\pi$
$878$	1225.94	+	494.008i	1.39628	+	0.562652i
$879$	−151.019	+	9.90872i	−0.171808	+	0.0112727i
$880$	765.032	+	245.489i	0.869355	+	0.278965i
$881$	−515.317	−	892.555i	−0.584922	−	1.01312i	−0.994885	−	0.101013i	$-0.967792\pi$
$881$	−515.317	−	892.555i	−0.584922	−	1.01312i	0.409963	−	0.912102i	$-0.365542\pi$
$882$	41.4673	+	40.6643i	0.0470151	+	0.0461046i
$883$	−1233.98	−	712.438i	−1.39748	−	0.806838i	−0.403356	−	0.915043i	$-0.632156\pi$
$883$	−1233.98	−	712.438i	−1.39748	−	0.806838i	−0.994129	+	0.108205i	$0.965490\pi$
$884$	215.380	+	207.232i	0.243643	+	0.234425i
$885$	−34.8402	+	119.562i	−0.0393675	+	0.135098i
$886$	65.4789	+	462.840i	0.0739040	+	0.522393i
$887$	−116.721	−	139.102i	−0.131590	−	0.156823i	0.696226	−	0.717823i	$-0.254861\pi$
$887$	−116.721	−	139.102i	−0.131590	−	0.156823i	−0.827816	+	0.561000i	$0.810417\pi$
$888$	149.664	−	165.700i	0.168541	−	0.186599i
$889$	−908.818	+	330.783i	−1.02229	+	0.372084i
$890$	−12.3953	+	364.497i	−0.0139274	+	0.409547i
$891$	−1381.79	+	644.799i	−1.55083	+	0.723680i
$892$	36.5508	−	536.784i	0.0409762	−	0.601776i
$893$	−1704.42	+	620.356i	−1.90864	+	0.694688i
$894$	817.879	−	1039.57i	0.914853	−	1.16283i
$895$	−48.5080	−	57.8096i	−0.0541989	−	0.0645918i
$896$	54.8867	−	864.256i	0.0612575	−	0.964572i
$897$	−75.1126	+	257.766i	−0.0837376	+	0.287364i
$898$	−328.101	+	365.062i	−0.365368	+	0.406528i
$899$	−242.851	−	140.210i	−0.270135	−	0.155962i
$900$	−617.683	−	181.648i	−0.686315	−	0.201831i
$901$	189.448	+	328.134i	0.210265	+	0.364189i
$902$	−173.468	+	819.782i	−0.192315	+	0.908849i
$903$	−864.152	+	56.6990i	−0.956979	+	0.0627896i
$904$	49.9786	−	103.188i	0.0552860	−	0.114146i
$905$	672.998	+	244.951i	0.743644	+	0.270664i
$906$	298.178	−	556.245i	0.329115	−	0.613957i
$907$	576.345	+	101.625i	0.635441	+	0.112045i	0.482083	−	0.876125i	$-0.339880\pi$
$907$	576.345	+	101.625i	0.635441	+	0.112045i	0.153358	+	0.988171i	$0.450991\pi$
$908$	1098.33	−	538.176i	1.20961	−	0.592705i
$909$	584.210	−	1410.96i	0.642695	−	1.55221i
$910$	−96.7533	+	155.153i	−0.106322	+	0.170497i
$911$	88.0696	−	104.957i	0.0966735	−	0.115211i	−0.715539	−	0.698573i	$-0.753819\pi$
$911$	88.0696	−	104.957i	0.0966735	−	0.115211i	0.812212	+	0.583362i	$0.198263\pi$
$912$	−1587.59	+	165.830i	−1.74078	+	0.181831i
$913$	−4.61141	−	26.1526i	−0.00505083	−	0.0286447i
$914$	−563.054	−	719.322i	−0.616033	−	0.787004i
$915$	465.066	−	204.672i	0.508268	−	0.223685i
$916$	851.175	−	245.753i	0.929231	−	0.268290i
$917$	−527.947			−0.575733
$918$	389.970	+	694.518i	0.424804	+	0.756556i
$919$		−	654.910i		−	0.712633i	−0.934365	−	0.356316i	$-0.884033\pi$
$919$		−	654.910i		−	0.712633i	0.934365	−	0.356316i	$-0.115967\pi$
$920$	365.555	−	92.2074i	0.397343	−	0.100225i
$921$	−375.722	−	41.1221i	−0.407950	−	0.0446494i
$922$	−804.265	−	1027.48i	−0.872305	−	1.11440i
$923$	−136.686	+	24.1014i	−0.148089	+	0.0261121i
$924$	−1173.21	+	979.513i	−1.26971	+	1.06008i
$925$	−127.461	−	106.952i	−0.137795	−	0.115624i
$926$	253.262	−	406.128i	0.273501	−	0.438583i
$927$	−56.1400	−	107.808i	−0.0605609	−	0.116298i
$928$	1221.12	−	450.773i	1.31586	−	0.485747i
$929$	78.7080	−	446.375i	0.0847234	−	0.480490i	−0.912693	−	0.408647i	$-0.866001\pi$
$929$	78.7080	−	446.375i	0.0847234	−	0.480490i	0.997416	−	0.0718432i	$-0.0228881\pi$
$930$	58.1526	+	93.7677i	0.0625297	+	0.100826i
$931$	36.6984	−	100.828i	0.0394183	−	0.108301i
$932$	−308.114	−	136.508i	−0.330594	−	0.146467i
$933$	572.000	−	382.255i	0.613076	−	0.409705i
$934$	38.9891	−	184.256i	0.0417442	−	0.197276i
$935$	−641.461	+	370.348i	−0.686055	+	0.396094i
$936$	226.233	−	286.099i	0.241702	−	0.305662i
$937$	−245.002	+	424.356i	−0.261475	+	0.452888i	−0.966634	−	0.256161i	$-0.917542\pi$
$937$	−245.002	+	424.356i	−0.261475	+	0.452888i	0.705159	+	0.709049i	$0.250875\pi$
$938$	−313.519	+	348.838i	−0.334242	+	0.371895i
$939$	640.827	−	613.542i	0.682457	−	0.653400i
$940$	−578.672	+	61.8894i	−0.615609	+	0.0658398i
$941$	251.005	−	210.618i	0.266743	−	0.223824i	−0.499599	−	0.866257i	$-0.666519\pi$
$941$	251.005	−	210.618i	0.266743	−	0.223824i	0.766342	+	0.642433i	$0.222075\pi$
$942$	1583.15	+	227.960i	1.68063	+	0.241995i
$943$	134.477	+	369.472i	0.142605	+	0.391805i
$944$	33.7522	−	246.693i	0.0357544	−	0.261327i
$945$	−366.288	+	321.359i	−0.387606	+	0.340063i
$946$	−54.5977	+	1605.50i	−0.0577143	+	1.69714i
$947$	422.437	+	1160.64i	0.446079	+	1.22559i	0.935432	+	0.353507i	$0.115011\pi$
$947$	422.437	+	1160.64i	0.446079	+	1.22559i	−0.489353	+	0.872086i	$0.662767\pi$
$948$	523.759	+	1450.14i	0.552488	+	1.52969i
$949$	−141.716	+	118.914i	−0.149332	+	0.125304i
$950$	166.619	+	1177.75i	0.175388	+	1.23974i
$951$	134.597	+	549.891i	0.141532	+	0.578224i
$952$	556.154	+	572.766i	0.584195	+	0.601645i
$953$	25.7103	−	44.5315i	0.0269782	−	0.0467277i	−0.852221	−	0.523182i	$-0.824745\pi$
$953$	25.7103	−	44.5315i	0.0269782	−	0.0467277i	0.879199	+	0.476454i	$0.158078\pi$
$954$	376.145	−	268.898i	0.394282	−	0.281864i
$955$	72.6954	−	41.9707i	0.0761209	−	0.0439484i
$956$	−483.420	−	119.593i	−0.505670	−	0.125097i
$957$	−2060.39	−	1015.90i	−2.15297	−	1.06154i
$958$	−636.249	−	256.386i	−0.664143	−	0.267626i
$959$	508.848	−	1398.05i	0.530603	−	1.45782i
$960$	−507.261	−	70.6789i	−0.528397	−	0.0736239i
$961$	158.623	−	899.597i	0.165061	−	0.936105i
$962$	83.1860	−	44.3282i	0.0864719	−	0.0460792i
$963$	−1383.39	+	436.389i	−1.43654	+	0.453156i
$964$	338.614	−	503.999i	0.351260	−	0.522821i
$965$	476.141	+	399.530i	0.493411	+	0.414021i
$966$	−223.917	+	681.297i	−0.231798	+	0.705276i
$967$	−74.2039	+	13.0841i	−0.0767362	+	0.0135307i	−0.211884	−	0.977295i	$-0.567960\pi$
$967$	−74.2039	+	13.0841i	−0.0767362	+	0.0135307i	0.135148	+	0.990825i	$0.456849\pi$
$968$	1048.28	+	1544.99i	1.08293	+	1.59607i
$969$	870.056	−	1186.78i	0.897890	−	1.22474i
$970$	187.874	+	576.425i	0.193684	+	0.594253i
$971$		−	1155.37i		−	1.18988i	−0.803770	−	0.594940i	$-0.797176\pi$
$971$		−	1155.37i		−	1.18988i	0.803770	−	0.594940i	$-0.202824\pi$
$972$	797.437	−	555.768i	0.820409	−	0.571777i
$973$	1341.73			1.37896
$974$	−848.873	+	276.673i	−0.871533	+	0.284058i
$975$	−219.200	−	160.701i	−0.224821	−	0.164822i
$976$	−859.562	+	541.489i	−0.880699	+	0.554804i
$977$	117.331	+	665.415i	0.120093	+	0.681080i	0.984102	+	0.177604i	$0.0568346\pi$
$977$	117.331	+	665.415i	0.120093	+	0.681080i	−0.864009	+	0.503476i	$0.832054\pi$
$978$	1022.21	+	335.962i	1.04520	+	0.343520i
$979$	−827.205	+	985.824i	−0.844949	+	1.00697i
$980$	19.1996	−	28.5770i	0.0195914	−	0.0291602i
$981$	181.422	+	575.121i	0.184936	+	0.586260i
$982$	5.64005	+	10.5841i	0.00574344	+	0.0107781i
$983$	−355.871	−	62.7497i	−0.362026	−	0.0638349i	−0.0103231	−	0.999947i	$-0.503286\pi$
$983$	−355.871	−	62.7497i	−0.362026	−	0.0638349i	−0.351702	+	0.936112i	$0.614397\pi$
$984$	19.4717	−	533.785i	0.0197883	−	0.542464i
$985$	−631.942	−	230.008i	−0.641565	−	0.233511i
$986$	−448.507	+	1113.02i	−0.454875	+	1.12882i
$987$	489.565	−	992.911i	0.496013	−	1.00599i
$988$	−654.128	−	161.824i	−0.662073	−	0.163790i
$989$	376.892	+	652.796i	0.381084	+	0.660057i
$990$	525.662	+	735.316i	0.530971	+	0.742744i
$991$	−1393.22	−	804.374i	−1.40587	−	0.811679i	−0.410883	−	0.911688i	$-0.634779\pi$
$991$	−1393.22	−	804.374i	−1.40587	−	0.811679i	−0.994987	+	0.100009i	$0.968113\pi$
$992$	−142.571	−	168.343i	−0.143721	−	0.169701i
$993$	517.480	−	126.664i	0.521128	−	0.127557i
$994$	−367.077	+	51.9311i	−0.369293	+	0.0522446i
$995$	511.500	+	609.582i	0.514070	+	0.612645i
$996$	5.75047	+	15.9215i	0.00577356	+	0.0159854i
$997$	−833.657	+	303.426i	−0.836165	+	0.304339i	−0.724387	−	0.689394i	$-0.757877\pi$
$997$	−833.657	+	303.426i	−0.836165	+	0.304339i	−0.111779	+	0.993733i	$0.535655\pi$
$998$	−1605.83	−	54.6090i	−1.60905	−	0.0547184i
$999$	246.358	−	49.0564i	0.246605	−	0.0491055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.7.15	✓	204
3.2	odd	2		324.3.j.a.19.20		204
4.3	odd	2	inner	108.3.j.a.7.23	yes	204
12.11	even	2		324.3.j.a.19.12		204
27.4	even	9	inner	108.3.j.a.31.23	yes	204
27.23	odd	18		324.3.j.a.307.12		204
108.23	even	18		324.3.j.a.307.20		204
108.31	odd	18	inner	108.3.j.a.31.15	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.15	✓	204	1.1	even	1	trivial
108.3.j.a.7.23	yes	204	4.3	odd	2	inner
108.3.j.a.31.15	yes	204	108.31	odd	18	inner
108.3.j.a.31.23	yes	204	27.4	even	9	inner
324.3.j.a.19.12		204	12.11	even	2
324.3.j.a.19.20		204	3.2	odd	2
324.3.j.a.307.12		204	27.23	odd	18
324.3.j.a.307.20		204	108.23	even	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.619770 - 1.90155i) q^{2} +(2.41946 + 1.77376i) q^{3} +(-3.23177 + 2.35705i) q^{4} +(0.463207 + 2.62698i) q^{5} +(1.87339 - 5.70004i) q^{6} +(4.34885 - 5.18275i) q^{7} +(6.48499 + 4.68454i) q^{8} +(2.70753 + 8.58308i) q^{9} +O(q^{10})\)	\(q+(-0.619770 - 1.90155i) q^{2} +(2.41946 + 1.77376i) q^{3} +(-3.23177 + 2.35705i) q^{4} +(0.463207 + 2.62698i) q^{5} +(1.87339 - 5.70004i) q^{6} +(4.34885 - 5.18275i) q^{7} +(6.48499 + 4.68454i) q^{8} +(2.70753 + 8.58308i) q^{9} +(4.70825 - 2.50894i) q^{10} +(18.5390 + 3.26893i) q^{11} +(-12.0000 - 0.0296259i) q^{12} +(-4.76031 - 1.73261i) q^{13} +(-12.5505 - 5.05742i) q^{14} +(-3.53893 + 7.17748i) q^{15} +(4.88867 - 15.2349i) q^{16} +(7.37511 + 12.7741i) q^{17} +(14.6431 - 10.4680i) q^{18} +(-28.7994 - 16.6273i) q^{19} +(-7.68889 - 7.39799i) q^{20} +(19.7148 - 4.82562i) q^{21} +(-5.27392 - 37.2789i) q^{22} +(-11.3558 - 13.5334i) q^{23} +(7.38089 + 22.8369i) q^{24} +(16.8059 - 6.11683i) q^{25} +(-0.344344 + 10.1258i) q^{26} +(-8.67361 + 25.5689i) q^{27} +(-1.83848 + 26.9999i) q^{28} +(-38.2238 + 13.9123i) q^{29} +(15.8416 + 2.28106i) q^{30} +(4.43128 + 5.28100i) q^{31} +(-31.9997 + 0.146076i) q^{32} +(39.0561 + 40.7929i) q^{33} +(19.7196 - 21.9411i) q^{34} +(15.6294 + 9.02364i) q^{35} +(-28.9808 - 21.3568i) q^{36} +(-4.65176 - 8.05708i) q^{37} +(-13.7687 + 65.0686i) q^{38} +(-8.44411 - 12.6356i) q^{39} +(-9.30229 + 19.2059i) q^{40} +(-20.9136 - 7.61194i) q^{41} +(-21.3948 - 34.4979i) q^{42} +(-42.0191 - 7.40910i) q^{43} +(-67.6189 + 33.1329i) q^{44} +(-21.2934 + 11.0884i) q^{45} +(-18.6963 + 29.9813i) q^{46} +(35.0594 - 41.7822i) q^{47} +(38.8509 - 28.1887i) q^{48} +(0.560291 + 3.17757i) q^{49} +(-22.0472 - 28.1661i) q^{50} +(-4.81442 + 43.9880i) q^{51} +(19.4681 - 5.62087i) q^{52} +25.6875 q^{53} +(53.9961 + 0.646439i) q^{54} +50.2159i q^{55} +(52.4810 - 13.2378i) q^{56} +(-40.1859 - 91.3124i) q^{57} +(50.1449 + 64.0619i) q^{58} +(15.3255 - 2.70230i) q^{59} +(-5.48065 - 31.5374i) q^{60} +(-48.6391 - 40.8131i) q^{61} +(7.29569 - 11.6993i) q^{62} +(56.2586 + 23.2941i) q^{63} +(20.1102 + 60.7584i) q^{64} +(2.34652 - 13.3078i) q^{65} +(53.3639 - 99.5492i) q^{66} +(11.8552 - 32.5718i) q^{67} +(-53.9437 - 23.8994i) q^{68} +(-3.46997 - 52.8860i) q^{69} +(7.47225 - 35.3127i) q^{70} +(23.7276 - 13.6991i) q^{71} +(-22.6495 + 68.3447i) q^{72} +(18.2594 - 31.6262i) q^{73} +(-12.4379 + 13.8391i) q^{74} +(51.5108 + 15.0102i) q^{75} +(132.264 - 14.1458i) q^{76} +(97.5656 - 81.8672i) q^{77} +(-18.7938 + 23.8881i) q^{78} +(-43.9448 - 120.737i) q^{79} +(42.2861 + 5.78553i) q^{80} +(-66.3386 + 46.4779i) q^{81} +(-1.51282 + 44.4859i) q^{82} +(-0.482480 - 1.32560i) q^{83} +(-52.3396 + 62.0640i) q^{84} +(-30.1410 + 25.2913i) q^{85} +(11.9534 + 84.4932i) q^{86} +(-117.158 - 34.1397i) q^{87} +(104.912 + 108.046i) q^{88} +(-34.1806 + 59.2025i) q^{89} +(34.2821 + 33.6182i) q^{90} +(-29.6815 + 17.1366i) q^{91} +(68.5982 + 16.9705i) q^{92} +(1.35405 + 20.6372i) q^{93} +(-101.180 - 40.7718i) q^{94} +(30.3396 - 83.3573i) q^{95} +(-77.6809 - 56.4064i) q^{96} +(-19.7333 + 111.913i) q^{97} +(5.69505 - 3.03478i) q^{98} +(22.1375 + 167.973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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