LMFDB - Embedded newform 27.5.f.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,5,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.f (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:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	27.11
Dual form			27.5.f.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.868224 - 1.03471i) q^{2} +(-7.41018 + 5.10776i) q^{3} +(2.46156 + 13.9602i) q^{4} +(-3.20330 + 8.80100i) q^{5} +(-1.14866 + 12.1021i) q^{6} +(-7.41386 + 42.0461i) q^{7} +(35.2980 + 20.3793i) q^{8} +(28.8216 - 75.6988i) q^{9} +(6.32529 + 10.9557i) q^{10} +(-6.44259 - 17.7009i) q^{11} +(-89.5460 - 90.8746i) q^{12} +(-37.7989 + 31.7171i) q^{13} +(37.0686 + 44.1766i) q^{14} +(-21.2163 - 81.5787i) q^{15} +(-161.398 + 58.7439i) q^{16} +(390.443 - 225.422i) q^{17} +(-53.3026 - 95.5455i) q^{18} +(-57.0245 + 98.7692i) q^{19} +(-130.749 - 23.0546i) q^{20} +(-159.823 - 349.437i) q^{21} +(-23.9089 - 8.70211i) q^{22} +(608.929 - 107.371i) q^{23} +(-365.657 + 29.2792i) q^{24} +(411.581 + 345.358i) q^{25} +66.6484i q^{26} +(173.078 + 708.156i) q^{27} -605.222 q^{28} +(-179.539 + 213.967i) q^{29} +(-102.831 - 48.8759i) q^{30} +(211.710 + 1200.67i) q^{31} +(-302.391 + 830.812i) q^{32} +(138.152 + 98.2595i) q^{33} +(105.745 - 599.712i) q^{34} +(-346.299 - 199.936i) q^{35} +(1127.72 + 216.019i) q^{36} +(-1105.90 - 1915.47i) q^{37} +(52.6874 + 144.758i) q^{38} +(118.094 - 428.097i) q^{39} +(-292.429 + 245.377i) q^{40} +(-348.778 - 415.658i) q^{41} +(-500.328 - 138.019i) q^{42} +(3152.26 - 1147.33i) q^{43} +(231.249 - 133.512i) q^{44} +(573.901 + 496.145i) q^{45} +(417.590 - 723.286i) q^{46} +(-3962.16 - 698.636i) q^{47} +(895.936 - 1259.68i) q^{48} +(543.294 + 197.743i) q^{49} +(714.690 - 126.019i) q^{50} +(-1741.85 + 3664.71i) q^{51} +(-535.821 - 449.607i) q^{52} -3918.45i q^{53} +(883.006 + 435.753i) q^{54} +176.423 q^{55} +(-1118.57 + 1333.05i) q^{56} +(-81.9277 - 1023.17i) q^{57} +(65.5128 + 371.542i) q^{58} +(-1539.61 + 4230.04i) q^{59} +(1086.63 - 496.995i) q^{60} +(208.280 - 1181.21i) q^{61} +(1426.15 + 823.390i) q^{62} +(2969.16 + 1773.06i) q^{63} +(-776.940 - 1345.70i) q^{64} +(-158.060 - 434.267i) q^{65} +(221.617 - 57.6364i) q^{66} +(-2416.30 + 2027.52i) q^{67} +(4108.04 + 4895.77i) q^{68} +(-3963.85 + 3905.90i) q^{69} +(-507.540 + 184.729i) q^{70} +(2478.15 - 1430.76i) q^{71} +(2560.04 - 2084.65i) q^{72} +(-1176.80 + 2038.28i) q^{73} +(-2942.13 - 518.776i) q^{74} +(-4813.90 - 456.907i) q^{75} +(-1519.21 - 552.947i) q^{76} +(792.017 - 139.654i) q^{77} +(-340.424 - 493.877i) q^{78} +(3852.86 + 3232.93i) q^{79} -1608.63i q^{80} +(-4899.63 - 4363.53i) q^{81} -732.903 q^{82} +(7265.33 - 8658.48i) q^{83} +(4484.80 - 3091.33i) q^{84} +(733.235 + 4158.38i) q^{85} +(1549.72 - 4257.81i) q^{86} +(237.530 - 2502.57i) q^{87} +(133.321 - 756.101i) q^{88} +(-982.504 - 567.249i) q^{89} +(1011.64 - 163.055i) q^{90} +(-1053.34 - 1824.44i) q^{91} +(2997.83 + 8236.48i) q^{92} +(-7701.53 - 7815.80i) q^{93} +(-4162.93 + 3493.11i) q^{94} +(-686.601 - 818.260i) q^{95} +(-2002.81 - 7701.01i) q^{96} +(1751.37 - 637.447i) q^{97} +(676.307 - 390.466i) q^{98} +(-1525.62 - 22.4713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.868224	−	1.03471i	0.217056	−	0.258677i	−0.646519	−	0.762898i	$-0.723776\pi$
$2$	0.868224	−	1.03471i	0.217056	−	0.258677i	0.863575	+	0.504221i	$0.168220\pi$
$3$	−7.41018	+	5.10776i	−0.823354	+	0.567529i
$3$	−7.41018	+	5.10776i	−0.823354	+	0.567529i
$4$	2.46156	+	13.9602i	0.153848	+	0.872513i
$5$	−3.20330	+	8.80100i	−0.128132	+	0.352040i	−0.987126	−	0.159946i	$-0.948868\pi$
$5$	−3.20330	+	8.80100i	−0.128132	+	0.352040i	0.858994	+	0.511986i	$0.171090\pi$
$6$	−1.14866	+	12.1021i	−0.0319071	+	0.336168i
$7$	−7.41386	+	42.0461i	−0.151303	+	0.858083i	0.810785	+	0.585344i	$0.199041\pi$
$7$	−7.41386	+	42.0461i	−0.151303	+	0.858083i	−0.962088	+	0.272739i	$0.912070\pi$
$8$	35.2980	+	20.3793i	0.551531	+	0.318427i
$9$	28.8216	−	75.6988i	0.355823	−	0.934554i
$10$	6.32529	+	10.9557i	0.0632529	+	0.109557i
$11$	−6.44259	−	17.7009i	−0.0532445	−	0.146288i	0.910219	−	0.414127i	$-0.135913\pi$
$11$	−6.44259	−	17.7009i	−0.0532445	−	0.146288i	−0.963464	+	0.267838i	$0.913691\pi$
$12$	−89.5460	−	90.8746i	−0.621847	−	0.631074i
$13$	−37.7989	+	31.7171i	−0.223662	+	0.187675i	−0.747732	−	0.664000i	$-0.768857\pi$
$13$	−37.7989	+	31.7171i	−0.223662	+	0.187675i	0.524070	+	0.851675i	$0.324413\pi$
$14$	37.0686	+	44.1766i	0.189125	+	0.225391i
$15$	−21.2163	−	81.5787i	−0.0942947	−	0.362572i
$16$	−161.398	+	58.7439i	−0.630459	+	0.229468i
$17$	390.443	−	225.422i	1.35101	−	0.780008i	0.362622	−	0.931936i	$-0.381882\pi$
$17$	390.443	−	225.422i	1.35101	−	0.780008i	0.988391	+	0.151929i	$0.0485484\pi$
$18$	−53.3026	−	95.5455i	−0.164514	−	0.294894i
$19$	−57.0245	+	98.7692i	−0.157962	+	0.273599i	−0.934134	−	0.356923i	$-0.883826\pi$
$19$	−57.0245	+	98.7692i	−0.157962	+	0.273599i	0.776171	+	0.630522i	$0.217159\pi$
$20$	−130.749	−	23.0546i	−0.326872	−	0.0576364i
$21$	−159.823	−	349.437i	−0.362411	−	0.792375i
$22$	−23.9089	−	8.70211i	−0.0493985	−	0.0179796i
$23$	608.929	−	107.371i	1.15109	−	0.202969i	0.434641	−	0.900604i	$-0.356875\pi$
$23$	608.929	−	107.371i	1.15109	−	0.202969i	0.716454	+	0.697635i	$0.245764\pi$
$24$	−365.657	+	29.2792i	−0.634822	+	0.0508320i
$25$	411.581	+	345.358i	0.658530	+	0.552572i
$26$			66.6484i			0.0985923i
$27$	173.078	+	708.156i	0.237418	+	0.971408i
$28$	−605.222			−0.771967
$29$	−179.539	+	213.967i	−0.213483	+	0.254419i	−0.862150	−	0.506653i	$-0.830882\pi$
$29$	−179.539	+	213.967i	−0.213483	+	0.254419i	0.648667	+	0.761072i	$0.275327\pi$
$30$	−102.831	−	48.8759i	−0.114256	−	0.0543065i
$31$	211.710	+	1200.67i	0.220302	+	1.24939i	0.871465	+	0.490457i	$0.163170\pi$
$31$	211.710	+	1200.67i	0.220302	+	1.24939i	−0.651164	+	0.758937i	$0.725719\pi$
$32$	−302.391	+	830.812i	−0.295303	+	0.811340i
$33$	138.152	+	98.2595i	0.126862	+	0.0902291i
$34$	105.745	−	599.712i	0.0914752	−	0.518782i
$35$	−346.299	−	199.936i	−0.282693	−	0.163213i
$36$	1127.72	+	216.019i	0.870152	+	0.166681i
$37$	−1105.90	−	1915.47i	−0.807816	−	1.39918i	−0.914374	−	0.404871i	$-0.867316\pi$
$37$	−1105.90	−	1915.47i	−0.807816	−	1.39918i	0.106558	−	0.994306i	$-0.466017\pi$
$38$	52.6874	+	144.758i	0.0364871	+	0.100248i
$39$	118.094	−	428.097i	0.0776422	−	0.281458i
$40$	−292.429	+	245.377i	−0.182768	+	0.153360i
$41$	−348.778	−	415.658i	−0.207483	−	0.247268i	0.652260	−	0.757995i	$-0.273821\pi$
$41$	−348.778	−	415.658i	−0.207483	−	0.247268i	−0.859743	+	0.510727i	$0.829376\pi$
$42$	−500.328	−	138.019i	−0.283633	−	0.0782423i
$43$	3152.26	−	1147.33i	1.70485	−	0.620513i	0.708484	−	0.705727i	$-0.249379\pi$
$43$	3152.26	−	1147.33i	1.70485	−	0.620513i	0.996363	+	0.0852133i	$0.0271572\pi$
$44$	231.249	−	133.512i	0.119447	−	0.0689626i
$45$	573.901	+	496.145i	0.283408	+	0.245010i
$46$	417.590	−	723.286i	0.197349	−	0.341818i
$47$	−3962.16	−	698.636i	−1.79364	−	0.316268i	−0.825077	−	0.565020i	$-0.808868\pi$
$47$	−3962.16	−	698.636i	−1.79364	−	0.316268i	−0.968567	+	0.248752i	$0.919980\pi$
$48$	895.936	−	1259.68i	0.388861	−	0.546737i
$49$	543.294	+	197.743i	0.226278	+	0.0823585i
$50$	714.690	−	126.019i	0.285876	−	0.0504076i
$51$	−1741.85	+	3664.71i	−0.669685	+	1.40896i
$52$	−535.821	−	449.607i	−0.198159	−	0.166275i
$53$		−	3918.45i		−	1.39496i	−0.716603	−	0.697482i	$-0.754304\pi$
$53$		−	3918.45i		−	1.39496i	0.716603	−	0.697482i	$-0.245696\pi$
$54$	883.006	+	435.753i	0.302814	+	0.149435i
$55$	176.423			0.0583216
$56$	−1118.57	+	1333.05i	−0.356685	+	0.425081i
$57$	−81.9277	−	1023.17i	−0.0252163	−	0.314917i
$58$	65.5128	+	371.542i	0.0194747	+	0.110446i
$59$	−1539.61	+	4230.04i	−0.442290	+	1.21518i	0.495693	+	0.868498i	$0.334914\pi$
$59$	−1539.61	+	4230.04i	−0.442290	+	1.21518i	−0.937982	+	0.346683i	$0.887308\pi$
$60$	1086.63	−	496.995i	0.301842	−	0.138054i
$61$	208.280	−	1181.21i	0.0559742	−	0.317446i	−0.943946	−	0.330101i	$-0.892917\pi$
$61$	208.280	−	1181.21i	0.0559742	−	0.317446i	0.999920	+	0.0126552i	$0.00402839\pi$
$62$	1426.15	+	823.390i	0.371008	+	0.214201i
$63$	2969.16	+	1773.06i	0.748088	+	0.446726i
$64$	−776.940	−	1345.70i	−0.189683	−	0.328540i
$65$	−158.060	−	434.267i	−0.0374108	−	0.102785i
$66$	221.617	−	57.6364i	0.0508763	−	0.0132315i
$67$	−2416.30	+	2027.52i	−0.538271	+	0.451663i	−0.870946	−	0.491378i	$-0.836493\pi$
$67$	−2416.30	+	2027.52i	−0.538271	+	0.451663i	0.332675	+	0.943042i	$0.392049\pi$
$68$	4108.04	+	4895.77i	0.888417	+	1.05877i
$69$	−3963.85	+	3905.90i	−0.832567	+	0.820395i
$70$	−507.540	+	184.729i	−0.103580	+	0.0376999i
$71$	2478.15	−	1430.76i	0.491599	−	0.283825i	−0.233639	−	0.972323i	$-0.575063\pi$
$71$	2478.15	−	1430.76i	0.491599	−	0.283825i	0.725237	+	0.688499i	$0.241730\pi$
$72$	2560.04	−	2084.65i	0.493834	−	0.402132i
$73$	−1176.80	+	2038.28i	−0.220830	+	0.382488i	−0.955060	−	0.296412i	$-0.904210\pi$
$73$	−1176.80	+	2038.28i	−0.220830	+	0.382488i	0.734231	+	0.678900i	$0.237543\pi$
$74$	−2942.13	−	518.776i	−0.537277	−	0.0947364i
$75$	−4813.90	−	456.907i	−0.855804	−	0.0812278i
$76$	−1519.21	−	552.947i	−0.263021	−	0.0957317i
$77$	792.017	−	139.654i	0.133584	−	0.0235544i
$78$	−340.424	−	493.877i	−0.0559539	−	0.0811763i
$79$	3852.86	+	3232.93i	0.617347	+	0.518015i	0.896968	−	0.442095i	$-0.145765\pi$
$79$	3852.86	+	3232.93i	0.617347	+	0.518015i	−0.279622	+	0.960110i	$0.590209\pi$
$80$		−	1608.63i		−	0.251349i
$81$	−4899.63	−	4363.53i	−0.746781	−	0.665070i
$82$	−732.903			−0.108998
$83$	7265.33	−	8658.48i	1.05463	−	1.25686i	0.0892470	−	0.996010i	$-0.471554\pi$
$83$	7265.33	−	8658.48i	1.05463	−	1.25686i	0.965380	−	0.260846i	$-0.0840016\pi$
$84$	4484.80	−	3091.33i	0.635601	−	0.438113i
$85$	733.235	+	4158.38i	0.101486	+	0.575555i
$86$	1549.72	−	4257.81i	0.209534	−	0.575691i
$87$	237.530	−	2502.57i	0.0313819	−	0.330635i
$88$	133.321	−	756.101i	0.0172160	−	0.0976370i
$89$	−982.504	−	567.249i	−0.124038	−	0.0716133i	0.436697	−	0.899609i	$-0.356148\pi$
$89$	−982.504	−	567.249i	−0.124038	−	0.0716133i	−0.560735	+	0.827995i	$0.689481\pi$
$90$	1011.64	−	163.055i	0.124894	−	0.0201303i
$91$	−1053.34	−	1824.44i	−0.127200	−	0.220317i
$92$	2997.83	+	8236.48i	0.354186	+	0.973119i
$93$	−7701.53	−	7815.80i	−0.890453	−	0.903666i
$94$	−4162.93	+	3493.11i	−0.471133	+	0.395327i
$95$	−686.601	−	818.260i	−0.0760777	−	0.0906659i
$96$	−2002.81	−	7701.01i	−0.217319	−	0.835613i
$97$	1751.37	−	637.447i	0.186138	−	0.0677486i	−0.247270	−	0.968947i	$-0.579533\pi$
$97$	1751.37	−	637.447i	0.186138	−	0.0677486i	0.433407	+	0.901198i	$0.357311\pi$
$98$	676.307	−	390.466i	0.0704193	−	0.0406566i
$99$	−1525.62	−	22.4713i	−0.155660	−	0.00229276i
$100$	−3808.13	+	6595.88i	−0.380813	+	0.659588i
$101$	−845.823	−	149.141i	−0.0829157	−	0.0146203i	0.132036	−	0.991245i	$-0.457848\pi$
$101$	−845.823	−	149.141i	−0.0829157	−	0.0146203i	−0.214952	+	0.976625i	$0.568960\pi$
$102$	2279.59	+	4984.09i	0.219107	+	0.479056i
$103$	4752.33	+	1729.71i	0.447952	+	0.163041i	0.556139	−	0.831089i	$-0.312282\pi$
$103$	4752.33	+	1729.71i	0.447952	+	0.163041i	−0.108187	+	0.994131i	$0.534504\pi$
$104$	−1980.60	+	349.233i	−0.183117	+	0.0322886i
$105$	3587.36	−	287.250i	0.325384	−	0.0260544i
$106$	−4054.46	−	3402.09i	−0.360845	−	0.302785i
$107$			10768.0i			0.940518i	0.882529	+	0.470259i	$0.155839\pi$
$107$			10768.0i			0.940518i	−0.882529	+	0.470259i	$0.844161\pi$
$108$	−9459.96	+	4159.37i	−0.811039	+	0.356599i
$109$	2700.53			0.227298			0.113649	−	0.993521i	$-0.463746\pi$
$109$	2700.53			0.227298			0.113649	+	0.993521i	$0.463746\pi$
$110$	153.175	−	182.546i	0.0126591	−	0.0150865i
$111$	17978.7	+	8545.35i	1.45919	+	0.693560i
$112$	−1273.37	−	7221.65i	−0.101512	−	0.575706i
$113$	4381.95	−	12039.3i	0.343171	−	0.942855i	−0.641297	−	0.767293i	$-0.721603\pi$
$113$	4381.95	−	12039.3i	0.343171	−	0.942855i	0.984468	−	0.175562i	$-0.0561744\pi$
$114$	−1129.81	−	803.565i	−0.0869352	−	0.0618317i
$115$	−1005.61	+	5703.13i	−0.0760389	+	0.431238i
$116$	−3428.96	−	1979.71i	−0.254828	−	0.147125i
$117$	1311.52	+	3775.47i	0.0958082	+	0.275803i
$118$	3040.14	+	5265.67i	0.218338	+	0.378173i
$119$	6583.44	+	18087.8i	0.464899	+	1.27730i
$120$	913.624	−	3311.94i	0.0634461	−	0.229996i
$121$	10943.8	−	9182.97i	0.747479	−	0.627210i
$122$	−1041.38	−	1241.07i	−0.0699664	−	0.0833827i
$123$	4707.59	+	1298.63i	0.311163	+	0.0858368i
$124$	−16240.4	+	5911.03i	−1.05622	+	0.384433i
$125$	−9427.31	+	5442.86i	−0.603348	+	0.348343i
$126$	4412.49	−	1532.81i	0.277935	−	0.0965486i
$127$	5755.85	−	9969.42i	0.356863	−	0.618105i	−0.630572	−	0.776131i	$-0.717180\pi$
$127$	5755.85	−	9969.42i	0.356863	−	0.618105i	0.987435	+	0.158026i	$0.0505129\pi$
$128$	−15998.2	−	2820.91i	−0.976450	−	0.172174i
$129$	−17498.6	+	24602.9i	−1.05153	+	1.47845i
$130$	−586.572	−	213.495i	−0.0347084	−	0.0126328i
$131$	−20719.2	+	3653.35i	−1.20734	+	0.212887i	−0.740869	−	0.671650i	$-0.765586\pi$
$131$	−20719.2	+	3653.35i	−1.20734	+	0.212887i	−0.466471	+	0.884536i	$0.654475\pi$
$132$	−1031.65	+	2170.51i	−0.0592087	+	0.124570i
$133$	−3730.09	−	3129.92i	−0.210871	−	0.176941i
$134$			4260.51i			0.237275i
$135$	−6786.90	−	745.180i	−0.372395	−	0.0408878i
$136$	18375.8			0.993502
$137$	21898.4	−	26097.6i	1.16673	−	1.39046i	0.261686	−	0.965153i	$-0.415722\pi$
$137$	21898.4	−	26097.6i	1.16673	−	1.39046i	0.905049	−	0.425307i	$-0.139834\pi$
$138$	599.956	+	7492.63i	0.0315037	+	0.393438i
$139$	−2943.24	−	16692.0i	−0.152334	−	0.863928i	−0.961183	−	0.275912i	$-0.911020\pi$
$139$	−2943.24	−	16692.0i	−0.152334	−	0.863928i	0.808849	−	0.588016i	$-0.200091\pi$
$140$	1938.71	−	5326.56i	0.0989136	−	0.271763i
$141$	32928.8	−	15060.7i	1.65629	−	0.757544i
$142$	671.168	−	3806.38i	0.0332855	−	0.188771i
$143$	804.942	+	464.734i	0.0393634	+	0.0227265i
$144$	−204.895	+	13910.7i	−0.00988112	+	0.670848i
$145$	−1308.00	−	2265.52i	−0.0622117	−	0.107754i
$146$	1087.30	+	2987.33i	0.0510086	+	0.140145i
$147$	−5035.93	+	1309.70i	−0.233048	+	0.0606091i
$148$	24018.2	−	20153.6i	1.09652	−	0.920090i
$149$	−17955.5	−	21398.5i	−0.808768	−	0.963852i	0.191075	−	0.981575i	$-0.438803\pi$
$149$	−17955.5	−	21398.5i	−0.808768	−	0.963852i	−0.999843	+	0.0177231i	$0.994358\pi$
$150$	−4652.31	+	4584.29i	−0.206769	+	0.203746i
$151$	−3119.16	+	1135.28i	−0.136799	+	0.0497908i	−0.409512	−	0.912305i	$-0.634301\pi$
$151$	−3119.16	+	1135.28i	−0.136799	+	0.0497908i	0.272713	+	0.962095i	$0.412079\pi$
$152$	−4025.70	+	2324.24i	−0.174243	+	0.100599i
$153$	−5811.01	−	36053.1i	−0.248238	−	1.54014i
$154$	543.147	−	940.758i	0.0229021	−	0.0396676i
$155$	−11245.2	−	1982.84i	−0.468064	−	0.0825324i
$156$	6267.02	+	594.828i	0.257520	+	0.0244423i
$157$	−20046.5	−	7296.35i	−0.813280	−	0.296010i	−0.0983021	−	0.995157i	$-0.531341\pi$
$157$	−20046.5	−	7296.35i	−0.813280	−	0.296010i	−0.714978	+	0.699147i	$0.753563\pi$
$158$	6690.29	−	1179.68i	0.267998	−	0.0472552i
$159$	20014.5	+	29036.4i	0.791681	+	1.14855i
$160$	−6343.32	−	5322.68i	−0.247786	−	0.207917i
$161$			26399.1i			1.01845i
$162$	−8768.95	+	1281.17i	−0.334132	+	0.0488176i
$163$	−3741.11			−0.140807			−0.0704036	−	0.997519i	$-0.522429\pi$
$163$	−3741.11			−0.140807			−0.0704036	+	0.997519i	$0.522429\pi$
$164$	4944.13	−	5892.18i	0.183824	−	0.219073i
$165$	−1307.33	+	901.125i	−0.0480193	+	0.0330992i
$166$	−2651.08	−	15035.0i	−0.0962069	−	0.545616i
$167$	−4391.73	+	12066.2i	−0.157472	+	0.432650i	−0.993190	−	0.116509i	$-0.962830\pi$
$167$	−4391.73	+	12066.2i	−0.157472	+	0.432650i	0.835718	+	0.549159i	$0.185052\pi$
$168$	1479.86	−	15591.5i	0.0524325	−	0.552421i
$169$	−4536.78	+	25729.4i	−0.158845	+	0.900856i
$170$	4939.33	+	2851.72i	0.170911	+	0.0986755i
$171$	5833.18	+	7163.37i	0.199486	+	0.244977i
$172$	23776.4	+	41182.0i	0.803693	+	1.39204i
$173$	14623.8	+	40178.7i	0.488618	+	1.34247i	0.901932	+	0.431878i	$0.142149\pi$
$173$	14623.8	+	40178.7i	0.488618	+	1.34247i	−0.413314	+	0.910588i	$0.635629\pi$
$174$	−2383.21	−	2418.57i	−0.0787161	−	0.0798840i
$175$	−17572.4	+	14745.0i	−0.573791	+	0.481468i
$176$	2079.64	+	2478.41i	0.0671370	+	0.0800108i
$177$	−10197.2	−	39209.4i	−0.325489	−	1.25154i
$178$	−1439.97	+	524.107i	−0.0454479	+	0.0165417i
$179$	−23006.7	+	13282.9i	−0.718040	+	0.414561i	−0.814031	−	0.580822i	$-0.802731\pi$
$179$	−23006.7	+	13282.9i	−0.718040	+	0.414561i	0.0959908	+	0.995382i	$0.469398\pi$
$180$	−5513.60	+	9233.07i	−0.170173	+	0.284971i
$181$	−8497.75	+	14718.5i	−0.259386	+	0.449270i	−0.966078	−	0.258252i	$-0.916854\pi$
$181$	−8497.75	+	14718.5i	−0.259386	+	0.449270i	0.706692	+	0.707522i	$0.250187\pi$
$182$	−2802.30	−	494.122i	−0.0846004	−	0.0149173i
$183$	4489.97	+	9816.86i	0.134073	+	0.293137i
$184$	23682.1	+	8619.59i	0.699496	+	0.254596i
$185$	20400.6	−	3597.18i	0.596074	−	0.105104i
$186$	−14773.7	+	1182.97i	−0.427036	+	0.0341940i
$187$	−6505.63	−	5458.87i	−0.186040	−	0.156106i
$188$		−	57032.3i		−	1.61363i
$189$	−31058.4	+	2027.07i	−0.869471	+	0.0567474i
$190$	−1442.78			−0.0399663
$191$	33917.8	−	40421.7i	0.929739	−	1.10802i	−0.0641834	−	0.997938i	$-0.520444\pi$
$191$	33917.8	−	40421.7i	0.929739	−	1.10802i	0.993923	−	0.110082i	$-0.0351113\pi$
$192$	12630.8	+	6003.46i	0.342632	+	0.162854i
$193$	8157.94	+	46266.0i	0.219011	+	1.24207i	0.873809	+	0.486269i	$0.161643\pi$
$193$	8157.94	+	46266.0i	0.219011	+	1.24207i	−0.654798	+	0.755804i	$0.727246\pi$
$194$	861.010	−	2365.61i	0.0228773	−	0.0628549i
$195$	3389.39	+	2410.67i	0.0891358	+	0.0633969i
$196$	−1423.18	+	8071.25i	−0.0370465	+	0.210101i
$197$	20705.7	+	11954.4i	0.533528	+	0.308032i	0.742452	−	0.669899i	$-0.233663\pi$
$197$	20705.7	+	11954.4i	0.533528	+	0.308032i	−0.208924	+	0.977932i	$0.566996\pi$
$198$	−1347.83	+	1559.06i	−0.0343800	+	0.0397680i
$199$	−9654.27	−	16721.7i	−0.243789	−	0.422254i	0.718002	−	0.696041i	$-0.245057\pi$
$199$	−9654.27	−	16721.7i	−0.243789	−	0.422254i	−0.961790	+	0.273787i	$0.911724\pi$
$200$	7489.85	+	20578.2i	0.187246	+	0.514455i
$201$	7549.16	−	27366.1i	0.186856	−	0.677363i
$202$	−888.682	+	745.693i	−0.0217793	+	0.0182750i
$203$	−7665.38	−	9135.24i	−0.186012	−	0.221681i
$204$	−55447.7	−	15295.7i	−1.33237	−	0.367544i
$205$	4775.45	−	1738.12i	0.113633	−	0.0413592i
$206$	5915.83	−	3415.50i	0.139406	−	0.0804860i
$207$	9422.50	−	49189.8i	0.219900	−	1.14798i
$208$	4237.47	−	7339.51i	0.0979444	−	0.169645i
$209$	2115.69	+	373.053i	0.0484349	+	0.00854038i
$210$	2817.41	−	3961.27i	0.0638869	−	0.0898247i
$211$	−27331.4	−	9947.83i	−0.613900	−	0.223441i	0.0163089	−	0.999867i	$-0.494808\pi$
$211$	−27331.4	−	9947.83i	−0.613900	−	0.223441i	−0.630209	+	0.776426i	$0.717031\pi$
$212$	54702.4	−	9645.51i	1.21712	−	0.214612i
$213$	−11055.6	+	23260.0i	−0.243681	+	0.512684i
$214$	11141.7	+	9349.02i	0.243291	+	0.204145i
$215$			31418.3i			0.679682i
$216$	−8322.44	+	28523.7i	−0.178379	+	0.611362i
$217$	−52053.0			−1.10542
$218$	2344.67	−	2794.26i	0.0493365	−	0.0587969i
$219$	−1690.72	−	21114.8i	−0.0352521	−	0.440250i
$220$	434.276	+	2462.90i	0.00897263	+	0.0508863i
$221$	−7608.58	+	20904.4i	−0.155783	+	0.428010i
$222$	24451.5	−	11183.4i	0.496134	−	0.226918i
$223$	14655.3	−	83114.6i	0.294704	−	1.67135i	−0.373699	−	0.927550i	$-0.621911\pi$
$223$	14655.3	−	83114.6i	0.294704	−	1.67135i	0.668403	−	0.743800i	$-0.266978\pi$
$224$	−32690.5	−	18873.9i	−0.651517	−	0.376153i
$225$	38005.6	−	21202.5i	0.750728	−	0.418814i
$226$	−8652.67	−	14986.9i	−0.169408	−	0.293423i
$227$	1755.16	+	4822.25i	0.0340615	+	0.0935832i	0.955558	−	0.294804i	$-0.0952544\pi$
$227$	1755.16	+	4822.25i	0.0340615	+	0.0935832i	−0.921496	+	0.388387i	$0.873032\pi$
$228$	14081.9	−	3662.31i	0.270890	−	0.0704507i
$229$	−46872.0	+	39330.2i	−0.893804	+	0.749990i	−0.968969	−	0.247181i	$-0.920496\pi$
$229$	−46872.0	+	39330.2i	−0.893804	+	0.749990i	0.0751658	+	0.997171i	$0.476051\pi$
$230$	5027.98	+	5992.11i	0.0950468	+	0.113272i
$231$	−5155.67	+	5080.29i	−0.0966187	+	0.0952060i
$232$	−10697.9	+	3893.71i	−0.198757	+	0.0723415i
$233$	65323.4	−	37714.5i	1.20325	−	0.694699i	0.241976	−	0.970282i	$-0.422204\pi$
$233$	65323.4	−	37714.5i	1.20325	−	0.694699i	0.961277	+	0.275584i	$0.0888711\pi$
$234$	5045.21	+	1920.91i	0.0921398	+	0.0350814i
$235$	18840.7	−	32633.0i	0.341162	−	0.590910i
$236$	−62842.1	−	11080.8i	−1.12831	−	0.198951i
$237$	−45063.5	−	4277.16i	−0.802283	−	0.0761480i
$238$	24431.5	+	8892.36i	0.431318	+	0.156987i
$239$	−57194.9	+	10085.0i	−1.00129	+	0.176555i	−0.650182	−	0.759778i	$-0.725307\pi$
$239$	−57194.9	+	10085.0i	−1.00129	+	0.176555i	−0.351112	+	0.936334i	$0.614196\pi$
$240$	8216.51	+	11920.3i	0.142648	+	0.206949i
$241$	54221.6	+	45497.3i	0.933552	+	0.783343i	0.976452	−	0.215736i	$-0.0692152\pi$
$241$	54221.6	+	45497.3i	0.933552	+	0.783343i	−0.0428999	+	0.999079i	$0.513660\pi$
$242$		−	19296.6i		−	0.329495i
$243$	58595.0	+	7308.43i	0.992311	+	0.123769i
$244$	17002.7			0.285587
$245$	−3480.67	+	4148.10i	−0.0579869	+	0.0691061i
$246$	5430.94	−	3743.49i	0.0897439	−	0.0618595i
$247$	−977.207	−	5542.02i	−0.0160174	−	0.0908394i
$248$	−16995.8	+	46695.7i	−0.276337	+	0.759230i
$249$	−9611.99	+	101270.i	−0.155030	+	1.63337i
$250$	−2553.24	+	14480.1i	−0.0408519	+	0.231682i
$251$	−8013.71	−	4626.72i	−0.127200	−	0.0734388i	0.435050	−	0.900406i	$-0.356731\pi$
$251$	−8013.71	−	4626.72i	−0.127200	−	0.0734388i	−0.562250	+	0.826967i	$0.690064\pi$
$252$	−17443.5	+	45814.6i	−0.274683	+	0.721444i
$253$	−5823.63	−	10086.8i	−0.0909815	−	0.157585i
$254$	−5318.09	−	14611.3i	−0.0824305	−	0.226476i
$255$	−26673.4	−	27069.2i	−0.410202	−	0.416289i
$256$	2236.65	−	1876.78i	0.0341286	−	0.0286373i
$257$	51197.8	+	61015.2i	0.775149	+	0.923787i	0.998704	−	0.0509044i	$-0.0162104\pi$
$257$	51197.8	+	61015.2i	0.775149	+	0.923787i	−0.223554	+	0.974692i	$0.571766\pi$
$258$	10264.2	+	39466.7i	0.154200	+	0.592914i
$259$	88737.2	−	32297.7i	1.32284	−	0.481473i
$260$	5673.39	−	3275.53i	0.0839259	−	0.0484546i
$261$	11022.4	+	19757.8i	0.161806	+	0.290039i
$262$	−14208.7	+	24610.2i	−0.206992	+	0.358520i
$263$	−112009.	−	19750.3i	−1.61936	−	0.285537i	−0.710831	−	0.703363i	$-0.751681\pi$
$263$	−112009.	−	19750.3i	−1.61936	−	0.285537i	−0.908527	+	0.417826i	$0.862792\pi$
$264$	2874.05	+	6283.82i	0.0412369	+	0.0901604i
$265$	34486.3	+	12552.0i	0.491083	+	0.178739i
$266$	−6477.11	+	1142.09i	−0.0915414	+	0.0161412i
$267$	10177.9	−	814.974i	0.142770	−	0.0114320i
$268$	−34252.4	−	28741.2i	−0.476894	−	0.400161i
$269$		−	225.820i		−	0.00312074i	−0.999999	−	0.00156037i	$-0.999503\pi$
$269$		−	225.820i		−	0.00312074i	0.999999	−	0.00156037i	$-0.000496682\pi$
$270$	−6663.59	+	6375.48i	−0.0914073	+	0.0874552i
$271$	−23425.8			−0.318974			−0.159487	−	0.987200i	$-0.550984\pi$
$271$	−23425.8			−0.318974			−0.159487	+	0.987200i	$0.550984\pi$
$272$	−49774.3	+	59318.7i	−0.672771	+	0.801778i
$273$	17124.3	+	8139.24i	0.229767	+	0.109209i
$274$	−7990.62	−	45317.0i	−0.106434	−	0.603616i
$275$	3461.48	−	9510.34i	0.0457717	−	0.125757i
$276$	−64284.4	−	45721.6i	−0.843893	−	0.600210i
$277$	−5680.28	+	32214.5i	−0.0740304	+	0.419847i	0.925159	+	0.379581i	$0.123932\pi$
$277$	−5680.28	+	32214.5i	−0.0740304	+	0.419847i	−0.999189	+	0.0402664i	$0.987179\pi$
$278$	−19826.7	−	11447.0i	−0.256544	−	0.148115i
$279$	96991.0	+	18579.0i	1.24601	+	0.238679i
$280$	−8149.10	−	14114.7i	−0.103943	−	0.180034i
$281$	−18690.8	−	51352.6i	−0.236710	−	0.650355i	−0.999991	−	0.00428802i	$-0.998635\pi$
$281$	−18690.8	−	51352.6i	−0.236710	−	0.650355i	0.763281	−	0.646067i	$-0.223587\pi$
$282$	13006.1	−	47147.8i	0.163549	−	0.592875i
$283$	39160.2	−	32859.3i	0.488959	−	0.410285i	−0.364694	−	0.931127i	$-0.618827\pi$
$283$	39160.2	−	32859.3i	0.488959	−	0.410285i	0.853653	+	0.520842i	$0.174382\pi$
$284$	26073.8	+	31073.6i	0.323272	+	0.385260i
$285$	9267.31	+	2556.46i	0.114094	+	0.0314738i
$286$	1179.73	−	429.388i	0.0144229	−	0.00524950i
$287$	20062.6	−	11583.1i	0.243570	−	0.140625i
$288$	54176.1	+	46836.0i	0.653165	+	0.564670i
$289$	59869.9	−	103698.i	0.716824	−	1.24158i
$290$	−3479.80	−	613.582i	−0.0413769	−	0.00729586i
$291$	−9722.06	+	13669.2i	−0.114808	+	0.161420i
$292$	−31351.6	−	11411.0i	−0.367700	−	0.133832i
$293$	−16271.7	+	2869.13i	−0.189538	+	0.0334207i	−0.267611	−	0.963527i	$-0.586234\pi$
$293$	−16271.7	+	2869.13i	−0.189538	+	0.0334207i	0.0780733	+	0.996948i	$0.475123\pi$
$294$	−3017.15	+	6347.83i	−0.0349062	+	0.0734397i
$295$	−32296.8	−	27100.2i	−0.371121	−	0.311407i
$296$		−	90149.9i		−	1.02892i
$297$	11419.9	−	7625.98i	0.129464	−	0.0864536i
$298$	−37730.6			−0.424875
$299$	−19611.4	+	23371.9i	−0.219364	+	0.261428i
$300$	−5471.19	−	68327.7i	−0.0607910	−	0.759197i
$301$	24870.3	+	141046.i	0.274503	+	1.55679i
$302$	−1533.44	+	4213.09i	−0.0168133	+	0.0461942i
$303$	7029.48	−	3215.09i	0.0765664	−	0.0350194i
$304$	3401.52	−	19291.0i	0.0368066	−	0.208740i
$305$	9728.68	+	5616.86i	0.104581	+	0.0603801i
$306$	−42349.7	−	25289.5i	−0.452280	−	0.270083i
$307$	−51266.0	−	88795.3i	−0.543942	−	0.942135i	−0.998673	−	0.0515059i	$-0.983598\pi$
$307$	−51266.0	−	88795.3i	−0.543942	−	0.942135i	0.454731	−	0.890629i	$-0.349735\pi$
$308$	3899.19	+	10712.9i	0.0411030	+	0.112930i
$309$	−44050.5	+	11456.3i	−0.461354	+	0.119985i
$310$	−11815.1	+	9914.01i	−0.122945	+	0.103163i
$311$	−19903.6	−	23720.2i	−0.205784	−	0.245243i	0.653275	−	0.757121i	$-0.273395\pi$
$311$	−19903.6	−	23720.2i	−0.205784	−	0.245243i	−0.859058	+	0.511877i	$0.828950\pi$
$312$	12892.8	−	12704.3i	0.132446	−	0.130509i
$313$	60314.9	−	21952.8i	0.615652	−	0.224079i	−0.0153222	−	0.999883i	$-0.504877\pi$
$313$	60314.9	−	21952.8i	0.615652	−	0.224079i	0.630975	+	0.775803i	$0.282655\pi$
$314$	−24954.5	+	14407.5i	−0.253098	+	0.146126i
$315$	−25115.8	+	20451.9i	−0.253120	+	0.206117i
$316$	−35648.4	+	61744.8i	−0.356998	+	0.618338i
$317$	99398.3	+	17526.6i	0.989146	+	0.174413i	0.644735	−	0.764406i	$-0.276968\pi$
$317$	99398.3	+	17526.6i	0.989146	+	0.174413i	0.344411	+	0.938819i	$0.388079\pi$
$318$	47421.3	+	4500.95i	0.468942	+	0.0445092i
$319$	4944.09	+	1799.50i	0.0485853	+	0.0176836i
$320$	14332.3	−	2527.17i	0.139964	−	0.0246794i
$321$	−55000.3	−	79792.8i	−0.533771	−	0.774379i
$322$	27315.4	+	22920.4i	0.263449	+	0.221060i
$323$			51418.3i			0.492848i
$324$	48855.0	−	79140.9i	0.465392	−	0.753895i
$325$	−26511.1			−0.250992
$326$	−3248.12	+	3870.96i	−0.0305630	+	0.0364236i
$327$	−20011.4	+	13793.7i	−0.187147	+	0.128998i
$328$	−3840.36	−	21779.8i	−0.0356964	−	0.202444i
$329$	58749.8	−	161414.i	0.542769	−	1.49124i
$330$	−202.649	+	2135.08i	−0.00186087	+	0.0196059i
$331$	−194.082	+	1100.69i	−0.00177145	+	0.0100464i	−0.985681	−	0.168623i	$-0.946068\pi$
$331$	−194.082	+	1100.69i	−0.00177145	+	0.0100464i	0.983909	+	0.178669i	$0.0571792\pi$
$332$	138758.	+	80112.1i	1.25887	+	0.726812i
$333$	−176873.	+	28508.2i	−1.59505	+	0.257088i
$334$	8671.99	+	15020.3i	0.0777366	+	0.134644i
$335$	−10104.0	−	27760.6i	−0.0900337	−	0.247366i
$336$	46322.4	+	47009.7i	0.410310	+	0.416398i
$337$	−93620.4	+	78556.9i	−0.824349	+	0.691711i	−0.953986	−	0.299851i	$-0.903063\pi$
$337$	−93620.4	+	78556.9i	−0.824349	+	0.691711i	0.129637	+	0.991561i	$0.458619\pi$
$338$	22683.5	+	27033.1i	0.198553	+	0.236626i
$339$	29022.8	+	111595.i	0.252546	+	0.971062i
$340$	−56247.0	+	20472.2i	−0.486565	+	0.177095i
$341$	19888.9	−	11482.9i	0.171042	−	0.0987510i
$342$	12476.5	+	183.770i	0.106670	+	0.00157117i
$343$	−63597.2	+	110154.i	−0.540567	+	0.936290i
$344$	134650.	+	23742.5i	1.13786	+	0.200636i
$345$	−21678.4	−	47397.6i	−0.182133	−	0.398216i
$346$	54270.0	+	19752.7i	0.453323	+	0.164996i
$347$	−18668.4	+	3291.75i	−0.155042	+	0.0273381i	−0.250630	−	0.968083i	$-0.580638\pi$
$347$	−18668.4	+	3291.75i	−0.155042	+	0.0273381i	0.0955884	+	0.995421i	$0.469527\pi$
$348$	35521.1	−	2844.28i	0.293311	−	0.0234862i
$349$	95678.3	+	80283.6i	0.785530	+	0.659138i	0.944635	−	0.328124i	$-0.106416\pi$
$349$	95678.3	+	80283.6i	0.785530	+	0.659138i	−0.159105	+	0.987262i	$0.550861\pi$
$350$			30984.2i			0.252932i
$351$	−29002.8	−	21278.0i	−0.235410	−	0.172710i
$352$	16654.3			0.134413
$353$	−25396.8	+	30266.7i	−0.203812	+	0.242893i	−0.858262	−	0.513212i	$-0.828456\pi$
$353$	−25396.8	+	30266.7i	−0.203812	+	0.242893i	0.654450	+	0.756105i	$0.272900\pi$
$354$	−49423.8	−	23491.3i	−0.394393	−	0.187457i
$355$	4653.86	+	26393.3i	0.0369281	+	0.209429i
$356$	5500.42	−	15112.3i	0.0434006	−	0.119242i
$357$	−141173.	−	100408.i	−1.10768	−	0.787826i
$358$	−6231.01	+	35337.8i	−0.0486175	+	0.275723i
$359$	−89204.5	−	51502.2i	−0.692146	−	0.399611i	0.112269	−	0.993678i	$-0.464188\pi$
$359$	−89204.5	−	51502.2i	−0.692146	−	0.399611i	−0.804415	+	0.594067i	$0.797521\pi$
$360$	10146.5	+	29208.7i	0.0782906	+	0.225375i
$361$	58656.9	+	101597.i	0.450096	+	0.779589i
$362$	7851.45	+	21571.7i	0.0599146	+	0.164614i
$363$	−34191.5	+	123946.i	−0.259480	+	0.940631i
$364$	22876.7	−	19195.9i	0.172660	−	0.144879i
$365$	−14169.2	−	16886.2i	−0.106356	−	0.126750i
$366$	14055.9	+	3877.43i	0.104929	+	0.0289455i
$367$	−189399.	+	68935.5i	−1.40619	+	0.511812i	−0.930010	−	0.367534i	$-0.880202\pi$
$367$	−189399.	+	68935.5i	−1.40619	+	0.511812i	−0.476183	+	0.879346i	$0.657980\pi$
$368$	−91972.3	+	53100.2i	−0.679143	+	0.392104i
$369$	−41517.2	+	14422.2i	−0.304912	+	0.105920i
$370$	13990.3	−	24231.9i	0.102193	−	0.177004i
$371$	164756.	+	29050.8i	1.19699	+	0.211062i
$372$	90152.5	−	126754.i	0.651466	−	0.915959i
$373$	−100938.	−	36738.3i	−0.725497	−	0.264059i	−0.0472394	−	0.998884i	$-0.515042\pi$
$373$	−100938.	−	36738.3i	−0.725497	−	0.264059i	−0.678257	+	0.734824i	$0.737265\pi$
$374$	−11296.7	+	1991.91i	−0.0807622	+	0.0142405i
$375$	42057.3	−	88485.0i	0.299074	−	0.629227i
$376$	−125619.	−	105407.i	−0.888543	−	0.745576i
$377$		−	13782.2i		−	0.0969694i
$378$	−24868.2	+	33896.3i	−0.174045	+	0.237230i
$379$	221758.			1.54384			0.771918	−	0.635722i	$-0.219297\pi$
$379$	221758.			1.54384			0.771918	+	0.635722i	$0.219297\pi$
$380$	9732.96	−	11599.3i	0.0674028	−	0.0803275i
$381$	8269.50	+	103275.i	0.0569678	+	0.711450i
$382$	−12376.4	−	70190.1i	−0.0848141	−	0.481005i
$383$	−42635.0	+	117139.i	−0.290649	+	0.798552i	0.705323	+	0.708886i	$0.250802\pi$
$383$	−42635.0	+	117139.i	−0.290649	+	0.798552i	−0.995972	+	0.0896658i	$0.971420\pi$
$384$	132958.	−	60811.3i	0.901678	−	0.412403i
$385$	−1307.97	+	7417.89i	−0.00882425	+	0.0500448i
$386$	54954.8	+	31728.1i	0.368834	+	0.212946i
$387$	4001.81	−	271690.i	0.0267199	−	1.81406i
$388$	13210.0	+	22880.4i	0.0877484	+	0.151985i
$389$	−74280.1	−	204083.i	−0.490877	−	1.34867i	−0.899878	−	0.436141i	$-0.856345\pi$
$389$	−74280.1	−	204083.i	−0.490877	−	1.34867i	0.409001	−	0.912534i	$-0.365877\pi$
$390$	5437.09	−	1414.03i	0.0357468	−	0.00929673i
$391$	213548.	−	179188.i	1.39683	−	1.17208i
$392$	15147.3	+	18051.9i	0.0985743	+	0.117476i
$393$	134872.	−	132900.i	0.873249	−	0.860481i
$394$	30346.5	−	11045.2i	0.195486	−	0.0711512i
$395$	−40794.9	+	23553.0i	−0.261464	+	0.150956i
$396$	−3441.70	−	21353.3i	−0.0219474	−	0.136168i
$397$	−59824.4	+	103619.i	−0.379575	+	0.657443i	−0.991000	−	0.133859i	$-0.957263\pi$
$397$	−59824.4	+	103619.i	−0.379575	+	0.657443i	0.611426	+	0.791302i	$0.290596\pi$
$398$	−25684.2	−	4528.81i	−0.162143	−	0.0285903i
$399$	43627.5	+	4140.86i	0.274040	+	0.0260103i
$400$	−86715.9	−	31562.0i	−0.541974	−	0.197262i
$401$	78697.1	−	13876.4i	0.489407	−	0.0862956i	0.0765013	−	0.997069i	$-0.475625\pi$
$401$	78697.1	−	13876.4i	0.489407	−	0.0862956i	0.412906	+	0.910774i	$0.364514\pi$
$402$	−21761.6	−	31571.1i	−0.134660	−	0.195361i
$403$	−46084.1	−	38669.1i	−0.283753	−	0.238097i
$404$		−	12175.0i		−	0.0745943i
$405$	54098.4	−	29143.9i	0.329818	−	0.177680i
$406$	−16107.6			−0.0977188
$407$	−26780.7	+	31916.0i	−0.161671	+	0.192672i
$408$	−136168.	+	93859.2i	−0.818003	+	0.563841i
$409$	−44493.9	−	252337.i	−0.265983	−	1.50846i	−0.766222	−	0.642576i	$-0.777866\pi$
$409$	−44493.9	−	252337.i	−0.265983	−	1.50846i	0.500239	−	0.865887i	$-0.333245\pi$
$410$	2347.71	−	6450.27i	0.0139661	−	0.0383716i
$411$	−28971.5	+	305240.i	−0.171509	+	1.80700i
$412$	−12448.9	+	70601.2i	−0.0733393	+	0.415928i
$413$	−166442.	−	96095.6i	−0.975807	−	0.563382i
$414$	−42716.3	−	52457.3i	−0.249226	−	0.306059i
$415$	52930.2	+	91677.9i	0.307332	+	0.532314i
$416$	−14920.9	−	40994.7i	−0.0862198	−	0.236887i
$417$	107068.	+	108657.i	0.615729	+	0.624865i
$418$	2222.89	−	1865.23i	0.0127223	−	0.0106753i
$419$	−194699.	−	232033.i	−1.10901	−	1.32167i	−0.941962	−	0.335718i	$-0.891021\pi$
$419$	−194699.	−	232033.i	−1.10901	−	1.32167i	−0.167048	−	0.985949i	$-0.553423\pi$
$420$	12840.6	+	49373.2i	0.0727924	+	0.279893i
$421$	−61184.4	+	22269.3i	−0.345205	+	0.125644i	−0.508803	−	0.860883i	$-0.669912\pi$
$421$	−61184.4	+	22269.3i	−0.345205	+	0.125644i	0.163599	+	0.986527i	$0.447690\pi$
$422$	−34022.9	+	19643.1i	−0.191050	+	0.110303i
$423$	−167082.	+	279795.i	−0.933788	+	1.56372i
$424$	79855.4	−	138314.i	0.444194	−	0.769366i
$425$	238550.	+	42062.9i	1.32069	+	0.232874i
$426$	14468.6	+	31634.2i	0.0797274	+	0.174316i
$427$	48121.3	+	17514.7i	0.263926	+	0.0960611i
$428$	−150323.	+	26506.1i	−0.820614	+	0.144696i
$429$	−8338.52	+	667.688i	−0.0453079	+	0.00362793i
$430$	32508.8	+	27278.1i	0.175818	+	0.147529i
$431$			247253.i			1.33103i	0.746385	+	0.665514i	$0.231788\pi$
$431$			247253.i			1.33103i	−0.746385	+	0.665514i	$0.768212\pi$
$432$	−69534.2	−	104127.i	−0.372590	−	0.557953i
$433$	229960.			1.22652			0.613262	−	0.789880i	$-0.289857\pi$
$433$	229960.			1.22652			0.613262	+	0.789880i	$0.289857\pi$
$434$	−45193.6	+	53859.7i	−0.239937	+	0.285946i
$435$	21264.3	+	10107.0i	0.112376	+	0.0534126i
$436$	6647.52	+	37700.0i	0.0349693	+	0.198321i
$437$	−24118.9	+	66266.2i	−0.126298	+	0.347000i
$438$	−23315.6	−	16583.0i	−0.121534	−	0.0864400i
$439$	13862.8	−	78620.1i	0.0719322	−	0.407948i	−0.927487	−	0.373857i	$-0.878035\pi$
$439$	13862.8	−	78620.1i	0.0719322	−	0.407948i	0.999419	−	0.0340912i	$-0.0108537\pi$
$440$	6227.38	+	3595.38i	0.0321662	+	0.0185712i
$441$	30627.5	−	35427.4i	0.157483	−	0.182164i
$442$	15024.0	+	26022.4i	0.0769028	+	0.133199i
$443$	−37093.8	−	101914.i	−0.189014	−	0.519312i	0.808599	−	0.588360i	$-0.200226\pi$
$443$	−37093.8	−	101914.i	−0.189014	−	0.519312i	−0.997613	+	0.0690480i	$0.978004\pi$
$444$	−75039.2	+	272021.i	−0.380647	+	1.37987i
$445$	8139.62	−	6829.95i	0.0411040	−	0.0344903i
$446$	−73275.3	−	87326.1i	−0.368373	−	0.439010i
$447$	242352.	+	66854.6i	1.21292	+	0.334592i
$448$	62341.5	−	22690.5i	0.310614	−	0.113054i
$449$	26892.6	−	15526.5i	0.133395	−	0.0770158i	−0.431817	−	0.901961i	$-0.642127\pi$
$449$	26892.6	−	15526.5i	0.133395	−	0.0770158i	0.565213	+	0.824945i	$0.308794\pi$
$450$	11059.0	−	57733.2i	0.0546124	−	0.285102i
$451$	−5110.47	+	8851.59i	−0.0251251	+	0.0435179i
$452$	178858.	+	31537.4i	0.875449	+	0.154365i
$453$	17314.8	−	24344.5i	0.0843763	−	0.118633i
$454$	6513.49	+	2370.72i	0.0316011	+	0.0115019i
$455$	19431.1	−	3426.22i	0.0938586	−	0.0165498i
$456$	17959.5	−	37785.3i	0.0863704	−	0.181716i
$457$	−126339.	−	106011.i	−0.604930	−	0.507597i	0.288096	−	0.957602i	$-0.406978\pi$
$457$	−126339.	−	106011.i	−0.604930	−	0.507597i	−0.893026	+	0.450005i	$0.851422\pi$
$458$			82646.3i			0.393996i
$459$	227211.	+	237479.i	1.07846	+	1.12720i
$460$	−82092.2			−0.387959
$461$	−188614.	+	224781.i	−0.887507	+	1.05769i	0.110455	+	0.993881i	$0.464769\pi$
$461$	−188614.	+	224781.i	−0.887507	+	1.05769i	−0.997962	+	0.0638087i	$0.979675\pi$
$462$	780.345	+	9745.45i	0.00365597	+	0.0456581i
$463$	−12545.1	−	71146.6i	−0.0585209	−	0.331889i	0.941465	−	0.337109i	$-0.109449\pi$
$463$	−12545.1	−	71146.6i	−0.0585209	−	0.331889i	−0.999986	+	0.00522092i	$0.998338\pi$
$464$	16408.0	−	45080.5i	0.0762112	−	0.209389i
$465$	93457.2	−	42744.8i	0.432222	−	0.197687i
$466$	17691.8	−	100335.i	0.0814706	−	0.462043i
$467$	35163.8	+	20301.9i	0.161236	+	0.0930898i	0.578447	−	0.815720i	$-0.303659\pi$
$467$	35163.8	+	20301.9i	0.161236	+	0.0930898i	−0.417211	+	0.908810i	$0.636992\pi$
$468$	−49478.0	+	27602.6i	−0.225902	+	0.126026i
$469$	−67335.0	−	116628.i	−0.306123	−	0.530220i
$470$	−17407.7	−	47827.4i	−0.0788038	−	0.216512i
$471$	185817.	−	48325.6i	0.837611	−	0.217839i
$472$	−140551.	+	117936.i	−0.630883	+	0.529374i
$473$	−40617.4	−	48406.0i	−0.181548	−	0.216360i
$474$	−43550.8	+	42914.0i	−0.193838	+	0.191004i
$475$	−57580.9	+	20957.7i	−0.255206	+	0.0928875i
$476$	−236304.	+	136430.i	−1.04294	+	0.602140i
$477$	−296622.	−	112936.i	−1.30367	−	0.496359i
$478$	−39222.9	+	67936.1i	−0.171666	+	0.297334i
$479$	54719.7	+	9648.55i	0.238491	+	0.0420524i	0.291616	−	0.956535i	$-0.405807\pi$
$479$	54719.7	+	9648.55i	0.238491	+	0.0420524i	−0.0531249	+	0.998588i	$0.516918\pi$
$480$	74192.2	+	7041.88i	0.322015	+	0.0305637i
$481$	102555.	+	37327.0i	0.443268	+	0.161337i
$482$	94153.0	−	16601.7i	0.405266	−	0.0714593i
$483$	−134840.	−	195622.i	−0.577997	−	0.838541i
$484$	155135.	+	130174.i	0.662246	+	0.555691i
$485$			17455.7i			0.0742087i
$486$	58435.7	−	54283.4i	0.247403	−	0.229824i
$487$	−138957.			−0.585898			−0.292949	−	0.956128i	$-0.594637\pi$
$487$	−138957.			−0.585898			−0.292949	+	0.956128i	$0.594637\pi$
$488$	31424.2	−	37449.9i	0.131955	−	0.157258i
$489$	27722.3	−	19108.7i	0.115934	−	0.0799121i
$490$	1270.07	+	7202.95i	0.00528977	+	0.0299998i
$491$	−4504.33	+	12375.5i	−0.0186839	+	0.0513335i	−0.948684	−	0.316226i	$-0.897584\pi$
$491$	−4504.33	+	12375.5i	−0.0186839	+	0.0513335i	0.930000	+	0.367559i	$0.119807\pi$
$492$	−6541.06	+	68915.6i	−0.0270220	+	0.284700i
$493$	−21867.0	+	124014.i	−0.0899695	+	0.510242i
$494$	−6582.81	−	3800.59i	−0.0269748	−	0.0155739i
$495$	5084.79	−	13355.0i	0.0207521	−	0.0545046i
$496$	−104701.	−	181348.i	−0.425588	−	0.737140i
$497$	41785.2	+	114804.i	0.169165	+	0.464776i
$498$	96440.1	+	97871.0i	0.388865	+	0.394635i
$499$	134809.	−	113118.i	0.541398	−	0.454287i	−0.330618	−	0.943765i	$-0.607257\pi$
$499$	134809.	−	113118.i	0.541398	−	0.454287i	0.872016	+	0.489478i	$0.162813\pi$
$500$	−99189.4	−	118209.i	−0.396758	−	0.472837i
$501$	−29087.6	−	111845.i	−0.115886	−	0.445594i
$502$	−11745.0	+	4274.83i	−0.0466064	+	0.0169633i
$503$	293462.	−	169430.i	1.15989	−	0.669661i	0.208610	−	0.977999i	$-0.433106\pi$
$503$	293462.	−	169430.i	1.15989	−	0.669661i	0.951277	+	0.308338i	$0.0997728\pi$
$504$	68671.8	+	123095.i	0.270344	+	0.484595i
$505$	4022.02	−	6966.34i	0.0157711	−	0.0273163i
$506$	−15493.1	−	2731.86i	−0.0605116	−	0.0106698i
$507$	−97800.9	−	213832.i	−0.380476	−	0.831872i
$508$	153344.	+	55812.5i	0.594207	+	0.216274i
$509$	267722.	−	47206.7i	1.03335	−	0.182208i	0.368847	−	0.929490i	$-0.379753\pi$
$509$	267722.	−	47206.7i	1.03335	−	0.182208i	0.664507	+	0.747282i	$0.268642\pi$
$510$	−51167.2	+	4097.10i	−0.196721	+	0.0157520i
$511$	−76977.0	−	64591.4i	−0.294794	−	0.247362i
$512$		−	263863.i		−	1.00656i
$513$	−79813.7	−	23287.5i	−0.303279	−	0.0884886i
$514$	107584.			0.407214
$515$	−30446.3	+	36284.4i	−0.114794	+	0.136806i
$516$	−386535.	−	183722.i	−1.45174	−	0.690020i
$517$	13160.1	+	74634.7i	0.0492355	+	0.279228i
$518$	43625.0	−	119859.i	0.162583	−	0.446694i
$519$	−313588.	−	223036.i	−1.16419	−	0.828020i
$520$	3270.86	−	18549.9i	0.0120964	−	0.0686019i
$521$	−212819.	−	122871.i	−0.784035	−	0.452663i	0.0538237	−	0.998550i	$-0.482859\pi$
$521$	−212819.	−	122871.i	−0.784035	−	0.452663i	−0.837858	+	0.545888i	$0.816192\pi$
$522$	30013.5	+	5749.19i	0.110148	+	0.0210992i
$523$	145495.	+	252005.i	0.531920	+	0.921312i	0.999306	+	0.0372584i	$0.0118625\pi$
$523$	145495.	+	252005.i	0.531920	+	0.921312i	−0.467386	+	0.884053i	$0.654804\pi$
$524$	−102003.	−	280251.i	−0.371493	−	1.02067i
$525$	54900.7	−	199018.i	0.199186	−	0.722061i
$526$	−117685.	+	98749.4i	−0.425353	+	0.356914i
$527$	353318.	+	421068.i	1.27217	+	1.51611i
$528$	−28069.6	−	7743.22i	−0.100686	−	0.0277750i
$529$	96301.8	−	35051.0i	0.344130	−	0.125253i
$530$	42929.5	−	24785.3i	0.152828	−	0.0882354i
$531$	275835.	+	238463.i	0.978275	+	0.845732i
$532$	34512.4	−	59777.3i	0.121942	−	0.211209i
$533$	26366.9	+	4649.19i	0.0928121	+	0.0163653i
$534$	7993.44	−	11238.8i	0.0280318	−	0.0394127i
$535$	−94769.0	−	34493.1i	−0.331100	−	0.120510i
$536$	−126610.	+	22324.8i	−0.440695	+	0.0777065i
$537$	102638.	−	215942.i	0.355926	−	0.748838i
$538$	−233.658	−	196.062i	−0.000807266	−	0.000677376i
$539$		−	10890.7i		−	0.0374869i
$540$	−6303.50	−	96580.8i	−0.0216169	−	0.331210i
$541$	−462829.			−1.58134			−0.790671	−	0.612241i	$-0.790268\pi$
$541$	−462829.			−1.58134			−0.790671	+	0.612241i	$0.790268\pi$
$542$	−20338.8	+	24238.9i	−0.0692353	+	0.0825114i
$543$	−12208.8	−	152471.i	−0.0414070	−	0.517117i
$544$	69217.2	+	392550.i	0.233892	+	1.32647i
$545$	−8650.61	+	23767.4i	−0.0291242	+	0.0800181i
$546$	23289.4	−	10652.0i	0.0781221	−	0.0357309i
$547$	−65549.2	+	371748.i	−0.219075	+	1.24244i	0.654618	+	0.755960i	$0.272829\pi$
$547$	−65549.2	+	371748.i	−0.219075	+	1.24244i	−0.873693	+	0.486477i	$0.838282\pi$
$548$	418232.	+	241466.i	1.39269	+	0.804072i
$549$	−83413.6	−	49811.1i	−0.276753	−	0.165265i
$550$	−6835.10	−	11838.7i	−0.0225954	−	0.0391363i
$551$	−10895.2	−	29934.3i	−0.0358865	−	0.0985974i
$552$	−219516.	+	57089.8i	−0.720423	+	0.187362i
$553$	−164497.	+	138029.i	−0.537907	+	0.451358i
$554$	28400.8	+	33846.8i	0.0925362	+	0.110280i
$555$	−132799.	+	130857.i	−0.431130	+	0.424826i
$556$	225778.	−	82176.5i	0.730352	−	0.265826i
$557$	153585.	−	88672.5i	0.495039	−	0.285811i	−0.231624	−	0.972805i	$-0.574404\pi$
$557$	153585.	−	88672.5i	0.495039	−	0.285811i	0.726662	+	0.686995i	$0.241070\pi$
$558$	103434.	−	84226.7i	0.332196	−	0.270509i
$559$	−82762.2	+	143348.i	−0.264855	+	0.458742i
$560$	67636.8	+	11926.2i	0.215678	+	0.0380299i
$561$	76090.5	+	7222.06i	0.241771	+	0.0229475i
$562$	−69362.9	−	25246.0i	−0.219611	−	0.0799319i
$563$	−134655.	+	23743.4i	−0.424822	+	0.0749076i	−0.381972	−	0.924174i	$-0.624755\pi$
$563$	−134655.	+	23743.4i	−0.424822	+	0.0749076i	−0.0428501	+	0.999082i	$0.513644\pi$
$564$	291307.	+	422620.i	0.915784	+	1.32859i
$565$	91921.3	+	77131.1i	0.287951	+	0.241620i
$566$		−	69048.7i		−	0.215537i
$567$	219794.	−	173660.i	0.683676	−	0.540173i
$568$	116632.			0.361510
$569$	−301401.	+	359196.i	−0.930938	+	1.10945i	0.0628350	+	0.998024i	$0.479986\pi$
$569$	−301401.	+	359196.i	−0.930938	+	1.10945i	−0.993773	+	0.111425i	$0.964459\pi$
$570$	10691.3	−	7369.39i	0.0329064	−	0.0226820i
$571$	−16388.9	−	92946.2i	−0.0502664	−	0.285075i	0.949305	−	0.314357i	$-0.101789\pi$
$571$	−16388.9	−	92946.2i	−0.0502664	−	0.285075i	−0.999571	+	0.0292821i	$0.990678\pi$
$572$	−4506.36	+	12381.1i	−0.0137732	+	0.0378415i
$573$	−44873.1	+	472776.i	−0.136671	+	1.43995i
$574$	5433.64	−	30815.7i	0.0164918	−	0.0935294i
$575$	287705.	+	166107.i	0.870186	+	0.502402i
$576$	−124261.	+	20028.2i	−0.374531	+	0.0603666i
$577$	−151696.	−	262746.i	−0.455641	−	0.789194i	0.543083	−	0.839679i	$-0.317257\pi$
$577$	−151696.	−	262746.i	−0.455641	−	0.789194i	−0.998725	+	0.0504846i	$0.983923\pi$
$578$	−55316.5	−	151981.i	−0.165577	−	0.454918i
$579$	−296767.	−	301171.i	−0.885236	−	0.898371i
$580$	28407.5	−	23836.7i	0.0844455	−	0.0708582i
$581$	310191.	+	369671.i	0.918919	+	1.09512i
$582$	5702.70	+	21927.4i	0.0168358	+	0.0647353i
$583$	−69360.0	+	25245.0i	−0.204067	+	0.0742741i
$584$	−83077.5	+	47964.8i	−0.243589	+	0.140636i
$585$	−37429.1	−	551.304i	−0.109370	−	0.00161094i
$586$	−11158.7	+	19327.5i	−0.0324952	+	0.0562833i
$587$	−498455.	−	87891.1i	−1.44661	−	0.255076i	−0.605456	−	0.795879i	$-0.707009\pi$
$587$	−498455.	−	87891.1i	−1.44661	−	0.255076i	−0.841149	+	0.540803i	$0.818120\pi$
$588$	−30680.0	−	67078.7i	−0.0887360	−	0.194013i
$589$	−130662.	−	47557.0i	−0.376632	−	0.137083i
$590$	−56081.7	+	9888.71i	−0.161108	+	0.0284077i
$591$	−214493.	+	17175.1i	−0.614099	+	0.0491727i
$592$	291012.	+	244188.i	0.830362	+	0.696756i
$593$		−	382244.i		−	1.08701i	−0.839407	−	0.543503i	$-0.817098\pi$
$593$		−	382244.i		−	1.08701i	0.839407	−	0.543503i	$-0.182902\pi$
$594$	2024.36	−	18437.3i	0.00573740	−	0.0522547i
$595$	−180280.			−0.509229
$596$	254529.	−	303336.i	0.716547	−	0.853947i
$597$	156950.	+	74599.1i	0.440366	+	0.209308i
$598$	7156.08	+	40584.1i	0.0200112	+	0.113489i
$599$	−99670.1	+	273841.i	−0.277787	+	0.763213i	0.719826	+	0.694155i	$0.244222\pi$
$599$	−99670.1	+	273841.i	−0.277787	+	0.763213i	−0.997613	+	0.0690580i	$0.978001\pi$
$600$	−160610.	−	114232.i	−0.446138	−	0.317311i
$601$	95074.7	−	539196.i	0.263218	−	1.49279i	−0.510843	−	0.859674i	$-0.670667\pi$
$601$	95074.7	−	539196.i	0.263218	−	1.49279i	0.774061	−	0.633111i	$-0.218222\pi$
$602$	167535.	+	96726.4i	0.462288	+	0.266902i
$603$	83838.9	+	241347.i	0.230574	+	0.663755i
$604$	−23526.7	−	40749.5i	−0.0644893	−	0.111699i
$605$	45762.9	+	125733.i	0.125027	+	0.343508i
$606$	2776.48	−	10064.9i	0.00756048	−	0.0274072i
$607$	−172994.	+	145159.i	−0.469519	+	0.393973i	−0.846619	−	0.532199i	$-0.821366\pi$
$607$	−172994.	+	145159.i	−0.469519	+	0.393973i	0.377100	+	0.926173i	$0.376921\pi$
$608$	−64815.0	−	77243.5i	−0.175335	−	0.208956i
$609$	103462.	+	28540.9i	0.278964	+	0.0769544i
$610$	14258.5	−	5189.67i	0.0383190	−	0.0139470i
$611$	171924.	−	99260.4i	0.460526	−	0.265885i
$612$	489005.	−	169870.i	1.30560	−	0.453537i
$613$	295834.	−	512400.i	0.787277	−	1.36360i	−0.140352	−	0.990102i	$-0.544823\pi$
$613$	295834.	−	512400.i	0.787277	−	1.36360i	0.927629	−	0.373502i	$-0.121843\pi$
$614$	−136388.	−	24048.8i	−0.361775	−	0.0637906i
$615$	−26509.0	+	37271.6i	−0.0700880	+	0.0985435i
$616$	30802.7	+	11211.3i	0.0811759	+	0.0295456i
$617$	111685.	−	19693.0i	0.293375	−	0.0517300i	−0.0250234	−	0.999687i	$-0.507966\pi$
$617$	111685.	−	19693.0i	0.293375	−	0.0517300i	0.318399	+	0.947957i	$0.396855\pi$
$618$	−26391.8	+	55526.1i	−0.0691022	+	0.145385i
$619$	−171675.	−	144052.i	−0.448049	−	0.375958i	0.390662	−	0.920534i	$-0.372246\pi$
$619$	−171675.	−	144052.i	−0.448049	−	0.375958i	−0.838711	+	0.544576i	$0.816690\pi$
$620$		−	161867.i		−	0.421090i
$621$	181427.	+	412633.i	0.470456	+	1.06999i
$622$	−41824.3			−0.108105
$623$	31134.8	−	37105.0i	0.0802176	−	0.0955996i
$624$	6088.02	+	76031.1i	0.0156353	+	0.195264i
$625$	40607.1	+	230294.i	0.103954	+	0.589554i
$626$	29652.0	−	81468.3i	0.0756669	−	0.207893i
$627$	−17583.1	+	8042.02i	−0.0447260	+	0.0204564i
$628$	52512.7	−	297814.i	0.133151	−	0.755138i
$629$	−863581.	−	498589.i	−2.18274	−	1.26021i
$630$	−644.324	+	43744.4i	−0.00162339	+	0.110215i
$631$	36775.4	+	63696.9i	0.0923633	+	0.159978i	0.908505	−	0.417874i	$-0.137225\pi$
$631$	36775.4	+	63696.9i	0.0923633	+	0.159978i	−0.816142	+	0.577852i	$0.803891\pi$
$632$	70113.4	+	192635.i	0.175536	+	0.482282i
$633$	253342.	−	65887.1i	0.632266	−	0.164435i
$634$	104435.	−	87631.3i	0.259817	−	0.218012i
$635$	69303.1	+	82592.3i	0.171872	+	0.204829i
$636$	−356088.	+	350881.i	−0.880325	+	0.867454i
$637$	−26807.7	+	9757.21i	−0.0660665	+	0.0240462i
$638$	6154.54	−	3553.32i	0.0151201	−	0.00872958i
$639$	−36882.6	−	228830.i	−0.0903274	−	0.560416i
$640$	76073.7	−	131764.i	0.185727	−	0.321688i
$641$	−337744.	−	59553.3i	−0.821999	−	0.144941i	−0.253197	−	0.967415i	$-0.581482\pi$
$641$	−337744.	−	59553.3i	−0.821999	−	0.144941i	−0.568802	+	0.822474i	$0.692593\pi$
$642$	−130315.	−	12368.7i	−0.316172	−	0.0300092i
$643$	201474.	+	73330.5i	0.487300	+	0.177363i	0.573973	−	0.818874i	$-0.305401\pi$
$643$	201474.	+	73330.5i	0.487300	+	0.177363i	−0.0866731	+	0.996237i	$0.527624\pi$
$644$	−368537.	+	64983.1i	−0.888607	+	0.156685i
$645$	−160477.	−	232815.i	−0.385739	−	0.559618i
$646$	53203.0	+	44642.6i	0.127489	+	0.106976i
$647$			20926.3i			0.0499902i	0.999688	+	0.0249951i	$0.00795701\pi$
$647$			20926.3i			0.0499902i	−0.999688	+	0.0249951i	$0.992043\pi$
$648$	−84021.4	−	253875.i	−0.200097	−	0.604602i
$649$	84794.5			0.201316
$650$	−23017.5	+	27431.2i	−0.0544794	+	0.0649260i
$651$	385722.	−	265874.i	0.910149	−	0.627356i
$652$	−9208.96	−	52226.6i	−0.0216628	−	0.122856i
$653$	64062.7	−	176011.i	0.150238	−	0.412774i	−0.841629	−	0.540056i	$-0.818403\pi$
$653$	64062.7	−	176011.i	0.150238	−	0.412774i	0.991867	+	0.127282i	$0.0406252\pi$
$654$	−3101.98	+	32682.0i	−0.00725243	+	0.0764105i
$655$	34216.6	−	194052.i	0.0797544	−	0.452310i
$656$	80709.3	+	46597.5i	0.187550	+	0.108282i
$657$	120378.	+	147829.i	0.278879	+	0.342475i
$658$	−116008.	−	200932.i	−0.267940	−	0.464085i
$659$	−34435.2	−	94610.0i	−0.0792925	−	0.217854i	0.893712	−	0.448642i	$-0.148092\pi$
$659$	−34435.2	−	94610.0i	−0.0792925	−	0.217854i	−0.973004	+	0.230787i	$0.925870\pi$
$660$	−15798.0	−	16032.4i	−0.0362671	−	0.0368052i
$661$	377130.	−	316450.i	0.863154	−	0.724272i	−0.0994911	−	0.995038i	$-0.531721\pi$
$661$	377130.	−	316450.i	0.863154	−	0.724272i	0.962645	+	0.270766i	$0.0872770\pi$
$662$	970.390	+	1156.47i	0.00221427	+	0.00263886i
$663$	−50393.7	−	193768.i	−0.114643	−	0.440814i
$664$	432906.	−	157565.i	0.981877	−	0.357374i
$665$	39495.0	−	22802.4i	0.0893097	−	0.0515630i
$666$	−124068.	+	207764.i	−0.279711	+	0.468405i
$667$	−86353.0	+	149568.i	−0.194100	+	0.336191i
$668$	−179257.	−	31607.8i	−0.401720	−	0.0708340i
$669$	315930.	+	690750.i	0.705893	+	1.54337i
$670$	−37496.7	−	13647.7i	−0.0835302	−	0.0304025i
$671$	−22250.4	+	3923.34i	−0.0494188	+	0.00871387i
$672$	338646.	−	27116.3i	0.749906	−	0.0600471i
$673$	133890.	+	112347.i	0.295609	+	0.248045i	0.778514	−	0.627628i	$-0.215974\pi$
$673$	133890.	+	112347.i	0.295609	+	0.248045i	−0.482905	+	0.875673i	$0.660418\pi$
$674$			165075.i			0.363380i
$675$	−173332.	+	351238.i	−0.380426	+	0.770892i
$676$	−370355.			−0.810447
$677$	−66906.1	+	79735.6i	−0.145978	+	0.173970i	−0.834079	−	0.551645i	$-0.814000\pi$
$677$	−66906.1	+	79735.6i	−0.145978	+	0.173970i	0.688101	+	0.725615i	$0.258445\pi$
$678$	140667.	+	66859.7i	0.306008	+	0.145447i
$679$	13817.7	+	78364.3i	0.0299707	+	0.169972i
$680$	−58863.2	+	161725.i	−0.127299	+	0.349752i
$681$	−37636.9	−	26768.9i	−0.0811558	−	0.0577212i
$682$	5386.60	−	30548.9i	0.0115810	−	0.0656791i
$683$	−316965.	−	183000.i	−0.679469	−	0.392292i	0.120186	−	0.992751i	$-0.461651\pi$
$683$	−316965.	−	183000.i	−0.679469	−	0.392292i	−0.799655	+	0.600460i	$0.794984\pi$
$684$	−85643.5	+	99065.5i	−0.183055	+	0.211744i
$685$	159537.	+	276327.i	0.340001	+	0.588900i
$686$	58760.3	+	161443.i	0.124864	+	0.343060i
$687$	146440.	−	530855.i	0.310276	−	1.12477i
$688$	−441369.	+	370352.i	−0.932448	+	0.782417i
$689$	124282.	+	148113.i	0.261800	+	0.312001i
$690$	−67864.5	−	18720.9i	−0.142542	−	0.0393214i
$691$	126437.	−	46019.3i	0.264800	−	0.0963793i	−0.206208	−	0.978508i	$-0.566112\pi$
$691$	126437.	−	46019.3i	0.264800	−	0.0963793i	0.471008	+	0.882129i	$0.343890\pi$
$692$	−524905.	+	303054.i	−1.09615	+	0.632860i
$693$	12255.6	−	63979.8i	0.0255192	−	0.133222i
$694$	−12802.4	+	22174.4i	−0.0265810	+	0.0460397i
$695$	156334.	+	27565.9i	0.323656	+	0.0570693i
$696$	59385.1	−	83495.2i	0.122591	−	0.172363i
$697$	−229877.	−	83668.2i	−0.473183	−	0.172224i
$698$	166140.	−	29295.0i	0.341008	−	0.0601289i
$699$	−291422.	+	613127.i	−0.596442	+	1.25486i
$700$	−249098.	−	209018.i	−0.508363	−	0.426567i
$701$			730976.i			1.48753i	0.668439	+	0.743767i	$0.266963\pi$
$701$			730976.i			1.48753i	−0.668439	+	0.743767i	$0.733037\pi$
$702$	−47197.5	+	11535.4i	−0.0957733	+	0.0234076i
$703$	252253.			0.510418
$704$	−18814.5	+	22422.3i	−0.0379619	+	0.0452413i
$705$	27068.6	+	338050.i	0.0544613	+	0.680148i
$706$	9267.14	+	52556.5i	0.0185924	+	0.105443i
$707$	12541.6	−	34457.8i	0.0250908	−	0.0689365i
$708$	522270.	−	238872.i	1.04191	−	0.476539i
$709$	−84369.5	+	478483.i	−0.167839	+	0.951863i	0.778250	+	0.627955i	$0.216108\pi$
$709$	−84369.5	+	478483.i	−0.167839	+	0.951863i	−0.946089	+	0.323908i	$0.895003\pi$
$710$	31350.0	+	18099.9i	0.0621901	+	0.0359055i
$711$	355775.	−	198479.i	0.703779	−	0.392622i
$712$	−23120.3	−	40045.5i	−0.0456072	−	0.0789940i
$713$	257833.	+	708390.i	0.507177	+	1.39346i
$714$	−226462.	+	58896.4i	−0.444221	+	0.115529i
$715$	−6668.59	+	5595.61i	−0.0130443	+	0.0109455i
$716$	−242065.	−	288482.i	−0.472178	−	0.562720i
$717$	372313.	−	366870.i	0.724219	−	0.713630i
$718$	−130739.	+	47585.2i	−0.253605	+	0.0923045i
$719$	555622.	−	320788.i	1.07479	−	0.620527i	0.145300	−	0.989388i	$-0.453585\pi$
$719$	555622.	−	320788.i	1.07479	−	0.620527i	0.929485	+	0.368860i	$0.120252\pi$
$720$	−121772.	−	46363.4i	−0.234899	−	0.0894356i
$721$	−107960.	+	186993.i	−0.207680	+	0.359712i
$722$	156050.	+	27515.9i	0.299358	+	0.0527849i
$723$	−634181.	−	60192.7i	−1.21321	−	0.115151i
$724$	−226391.	−	82399.7i	−0.431900	−	0.157199i
$725$	−147790.	+	26059.4i	−0.281170	+	0.0495779i
$726$	98562.2	+	142991.i	0.186998	+	0.271291i
$727$	−204709.	−	171771.i	−0.387318	−	0.324999i	0.428249	−	0.903661i	$-0.359131\pi$
$727$	−204709.	−	171771.i	−0.387318	−	0.324999i	−0.815567	+	0.578662i	$0.803575\pi$
$728$		−	85865.6i		−	0.162015i
$729$	−471529.	+	245132.i	−0.887265	+	0.461259i
$730$	−29774.4			−0.0558724
$731$	972144.	−	1.15856e6i	1.81927	−	2.16812i
$732$	−125993.	+	86845.6i	−0.235139	+	0.162079i
$733$	−68087.6	−	386144.i	−0.126724	−	0.718690i	−0.980269	−	0.197670i	$-0.936663\pi$
$733$	−68087.6	−	386144.i	−0.126724	−	0.718690i	0.853544	−	0.521020i	$-0.174448\pi$
$734$	−93112.3	+	255824.i	−0.172828	+	0.474842i
$735$	4604.90	−	48516.6i	0.00852405	−	0.0898080i
$736$	−94929.8	+	538373.i	−0.175245	+	0.993866i
$737$	51456.0	+	29708.1i	0.0947330	+	0.0546941i
$738$	−21123.4	+	55479.9i	−0.0387839	+	0.101864i
$739$	169462.	+	293516.i	0.310301	+	0.537456i	0.978427	−	0.206591i	$-0.0662370\pi$
$739$	169462.	+	293516.i	0.310301	+	0.537456i	−0.668127	+	0.744047i	$0.732904\pi$
$740$	100435.	+	275942.i	0.183409	+	0.503912i
$741$	35548.6	+	36076.0i	0.0647419	+	0.0657026i
$742$	173104.	−	145251.i	0.314412	−	0.263823i
$743$	−445339.	−	530734.i	−0.806701	−	0.961389i	0.193103	−	0.981178i	$-0.438145\pi$
$743$	−445339.	−	530734.i	−0.806701	−	0.961389i	−0.999804	+	0.0197896i	$0.993700\pi$
$744$	−112568.	−	432834.i	−0.203362	−	0.781944i
$745$	245845.	−	89480.2i	0.442944	−	0.161218i
$746$	−125650.	+	72544.0i	−0.225780	+	0.130354i
$747$	−446038.	−	799528.i	−0.799339	−	1.43282i
$748$	60193.0	−	104257.i	0.107583	−	0.186339i
$749$	−452752.	−	79832.4i	−0.807043	−	0.142303i
$750$	−55041.1	−	120342.i	−0.0978509	−	0.213941i
$751$	688146.	+	250465.i	1.22012	+	0.444086i	0.870201	−	0.492696i	$-0.163989\pi$
$751$	688146.	+	250465.i	1.22012	+	0.444086i	0.349914	+	0.936782i	$0.386211\pi$
$752$	680524.	−	119995.i	1.20339	−	0.212191i
$753$	83015.2	−	6647.26i	0.146409	−	0.0117234i
$754$	−14260.5	−	11966.0i	−0.0250838	−	0.0210478i
$755$		−	31088.3i		−	0.0545385i
$756$	−104750.	−	428591.i	−0.183279	−	0.749894i
$757$	347674.			0.606709			0.303355	−	0.952878i	$-0.401893\pi$
$757$	347674.			0.606709			0.303355	+	0.952878i	$0.401893\pi$
$758$	192536.	−	229455.i	0.335099	−	0.399355i
$759$	94675.3	+	44999.5i	0.164344	+	0.0781132i
$760$	−7560.09	−	42875.4i	−0.0130888	−	0.0742303i
$761$	227751.	−	625741.i	0.393270	−	1.08050i	−0.572229	−	0.820094i	$-0.693921\pi$
$761$	227751.	−	625741.i	0.393270	−	1.08050i	0.965499	−	0.260407i	$-0.0838566\pi$
$762$	114039.	+	81109.1i	0.196401	+	0.139688i
$763$	−20021.4	+	113547.i	−0.0343910	+	0.195041i
$764$	647786.	+	373999.i	1.10980	+	0.640743i
$765$	335918.	+	64346.3i	0.573997	+	0.109951i
$766$	84187.8	+	145818.i	0.143480	+	0.248515i
$767$	−75969.0	−	208723.i	−0.129135	−	0.354797i
$768$	−6987.90	+	25331.5i	−0.0118474	+	0.0429476i
$769$	−69815.7	+	58582.4i	−0.118059	+	0.0990636i	−0.699906	−	0.714235i	$-0.746775\pi$
$769$	−69815.7	+	58582.4i	−0.118059	+	0.0990636i	0.581847	+	0.813299i	$0.302330\pi$
$770$	6539.74	+	7793.76i	0.0110301	+	0.0131452i
$771$	−691036.	−	190628.i	−1.16250	−	0.320684i
$772$	−625802.	+	227773.i	−1.05003	+	0.382180i
$773$	−75723.2	+	43718.8i	−0.126727	+	0.0731660i	−0.562024	−	0.827121i	$-0.689977\pi$
$773$	−75723.2	+	43718.8i	−0.126727	+	0.0731660i	0.435296	+	0.900287i	$0.356644\pi$
$774$	−277646.	−	240029.i	−0.463457	−	0.400665i
$775$	−327524.	+	567288.i	−0.545305	+	0.944497i
$776$	74810.7	+	13191.1i	0.124234	+	0.0219058i
$777$	−492590.	+	692580.i	−0.815913	+	1.14717i
$778$	−275658.	−	100331.i	−0.455419	−	0.165759i
$779$	60943.1	−	10745.9i	0.100427	−	0.0177080i
$780$	−25310.2	+	53250.6i	−0.0416013	+	0.0875256i
$781$	−41291.4	−	34647.6i	−0.0676951	−	0.0568029i
$782$		−	376536.i		−	0.615734i
$783$	−182596.	−	90109.0i	−0.297829	−	0.146975i
$784$	−99302.4			−0.161558
$785$	128430.	−	153057.i	0.208415	−	0.248379i
$786$	−20413.9	−	254941.i	−0.0330430	−	0.412662i
$787$	−152733.	−	866190.i	−0.246594	−	1.39850i	−0.816762	−	0.576975i	$-0.804233\pi$
$787$	−152733.	−	866190.i	−0.246594	−	1.39850i	0.570168	−	0.821528i	$-0.306878\pi$
$788$	−115918.	+	318482.i	−0.186680	+	0.512900i
$789$	930890.	−	425764.i	1.49535	−	0.683934i
$790$	−11048.7	+	62660.1i	−0.0177034	+	0.100401i
$791$	473719.	+	273502.i	0.757125	+	0.437126i
$792$	−53393.4	−	31884.3i	−0.0851211	−	0.0508308i
$793$	29591.9	+	51254.7i	0.0470572	+	0.0815055i
$794$	55274.4	+	151865.i	0.0876765	+	0.240889i
$795$	−319662.	+	83135.1i	−0.505774	+	0.131538i
$796$	209674.	−	175937.i	0.330916	−	0.277672i
$797$	−123272.	−	146910.i	−0.194065	−	0.231278i	0.660233	−	0.751061i	$-0.270457\pi$
$797$	−123272.	−	146910.i	−0.194065	−	0.231278i	−0.854299	+	0.519783i	$0.826013\pi$
$798$	42163.0	−	41546.6i	0.0662104	−	0.0652423i
$799$	−1.70449e6	+	620382.i	−2.66993	+	0.971775i
$800$	−411386.	+	237514.i	−0.642790	+	0.371115i
$801$	−71257.5	+	58025.4i	−0.111062	+	0.0904384i
$802$	53968.7	−	93476.4i	0.0839060	−	0.145329i
$803$	43660.9	+	7698.60i	0.0677114	+	0.0119393i
$804$	400620.	+	38024.4i	0.619755	+	0.0588235i
$805$	−232339.	−	84564.3i	−0.358533	−	0.130495i
$806$	−80022.6	+	14110.1i	−0.123181	+	0.0217201i
$807$	1153.43	+	1673.37i	0.00177111	+	0.00256948i
$808$	−26816.5	−	22501.7i	−0.0410751	−	0.0344661i
$809$			342800.i			0.523774i	0.965099	+	0.261887i	$0.0843447\pi$
$809$			342800.i			0.523774i	−0.965099	+	0.261887i	$0.915655\pi$
$810$	16814.0	−	81279.5i	0.0256272	−	0.123883i
$811$	1.12925e6			1.71691			0.858453	−	0.512892i	$-0.171426\pi$
$811$	1.12925e6			1.71691			0.858453	+	0.512892i	$0.171426\pi$
$812$	108661.	−	129497.i	0.164802	−	0.196403i
$813$	173589.	−	119653.i	0.262629	−	0.181027i
$814$	9772.12	+	55420.5i	0.0147482	+	0.0836414i
$815$	11983.9	−	32925.5i	0.0180419	−	0.0495697i
$816$	65851.2	−	693798.i	0.0988970	−	1.04196i
$817$	−66435.1	+	376772.i	−0.0995299	+	0.564462i
$818$	−299726.	−	173047.i	−0.447938	−	0.258617i
$819$	−168467.	+	27153.4i	−0.251158	+	0.0404815i
$820$	36019.6	+	62387.7i	0.0535687	+	0.0927836i
$821$	391161.	+	1.07471e6i	0.580323	+	1.59442i	0.787631	+	0.616148i	$0.211308\pi$
$821$	391161.	+	1.07471e6i	0.580323	+	1.59442i	−0.207308	+	0.978276i	$0.566470\pi$
$822$	290680.	+	294993.i	0.430202	+	0.436585i
$823$	474071.	−	397792.i	0.699912	−	0.587296i	−0.221837	−	0.975084i	$-0.571205\pi$
$823$	474071.	−	397792.i	0.699912	−	0.587296i	0.921749	+	0.387788i	$0.126761\pi$
$824$	132497.	+	157904.i	0.195143	+	0.232562i
$825$	22926.3	+	88153.8i	0.0336842	+	0.129519i
$826$	−243940.	+	88787.0i	−0.357539	+	0.130134i
$827$	106515.	−	61496.6i	0.155740	−	0.0899167i	−0.420104	−	0.907476i	$-0.638007\pi$
$827$	106515.	−	61496.6i	0.155740	−	0.0899167i	0.575845	+	0.817559i	$0.304673\pi$
$828$	709894.	+	10456.2i	1.03546	+	0.0152516i
$829$	235237.	−	407442.i	0.342291	−	0.592866i	−0.642567	−	0.766230i	$-0.722130\pi$
$829$	235237.	−	407442.i	0.342291	−	0.592866i	0.984858	+	0.173364i	$0.0554637\pi$
$830$	140815.	+	24829.5i	0.204406	+	0.0360423i
$831$	−122452.	−	267729.i	−0.177322	−	0.387697i
$832$	72049.1	+	26223.7i	0.104084	+	0.0378833i
$833$	256701.	−	45263.3i	0.369945	−	0.0652313i
$834$	205388.	−	16446.0i	0.295286	−	0.0236444i
$835$	−92126.5	−	77303.3i	−0.132133	−	0.110873i
$836$			30453.7i			0.0435740i
$837$	−813618.	+	357733.i	−1.16137	+	0.510632i
$838$	−409129.			−0.582602
$839$	42223.1	−	50319.5i	0.0599827	−	0.0714846i	−0.735219	−	0.677830i	$-0.762921\pi$
$839$	42223.1	−	50319.5i	0.0599827	−	0.0714846i	0.795202	+	0.606345i	$0.207365\pi$
$840$	132481.	+	62968.6i	0.187756	+	0.0892412i
$841$	109271.	+	619705.i	0.154494	+	0.876179i
$842$	−30079.5	+	82642.8i	−0.0424274	+	0.116568i
$843$	400799.	+	285064.i	0.563991	+	0.401132i
$844$	71595.7	−	406040.i	0.100508	−	0.570011i
$845$	−211911.	−	122347.i	−0.296784	−	0.171348i
$846$	144442.	+	415806.i	0.201815	+	0.580965i
$847$	304972.	+	528227.i	0.425102	+	0.736298i
$848$	230185.	+	632428.i	0.320100	+	0.879467i
$849$	−122347.	+	443514.i	−0.169737	+	0.615308i
$850$	250638.	−	210310.i	0.346904	−	0.291087i
$851$	−879080.	−	1.04765e6i	−1.21386	−	1.44662i
$852$	−351928.	−	97082.1i	−0.484813	−	0.133740i
$853$	913792.	−	332593.i	1.25588	−	0.457104i	0.373498	−	0.927631i	$-0.378158\pi$
$853$	913792.	−	332593.i	1.25588	−	0.457104i	0.882386	+	0.470527i	$0.155936\pi$
$854$	59902.7	−	34584.8i	0.0821355	−	0.0474209i
$855$	−81730.3	+	28391.4i	−0.111802	+	0.0388377i
$856$	−219444.	+	380089.i	−0.299486	+	0.518725i
$857$	−1.09569e6	−	193200.i	−1.49185	−	0.263054i	−0.632550	−	0.774519i	$-0.717992\pi$
$857$	−1.09569e6	−	193200.i	−1.49185	−	0.263054i	−0.859304	+	0.511465i	$0.829103\pi$
$858$	−6548.84	+	9207.64i	−0.00889589	+	0.0125076i
$859$	507014.	+	184538.i	0.687122	+	0.250092i	0.661903	−	0.749590i	$-0.269749\pi$
$859$	507014.	+	184538.i	0.687122	+	0.250092i	0.0252197	+	0.999682i	$0.491971\pi$
$860$	−438606.	+	77338.0i	−0.593031	+	0.104567i
$861$	−89503.5	+	188308.i	−0.120735	+	0.254017i
$862$	255835.	+	214671.i	0.344307	+	0.288908i
$863$			924852.i			1.24180i	0.783891	+	0.620899i	$0.213232\pi$
$863$			924852.i			1.24180i	−0.783891	+	0.620899i	$0.786768\pi$
$864$	−640682.	−	70344.8i	−0.858252	−	0.0942334i
$865$	−400457.			−0.535209
$866$	199656.	−	237941.i	0.266224	−	0.317274i
$867$	86015.8	+	1.07422e6i	0.114430	+	1.42907i
$868$	−128132.	−	726670.i	−0.170066	−	0.964491i
$869$	32403.3	−	89027.4i	0.0429092	−	0.117892i
$870$	28919.9	−	13227.2i	0.0382084	−	0.0174755i
$871$	27026.7	−	153276.i	0.0356251	−	0.202040i
$872$	95323.4	+	55035.0i	0.125362	+	0.0723779i
$873$	2223.37	−	150949.i	0.00291732	−	0.198062i
$874$	47625.6	+	82490.0i	0.0623473	+	0.107989i
$875$	−158958.	−	436734.i	−0.207619	−	0.570428i
$876$	290606.	−	75578.3i	0.378700	−	0.0984893i
$877$	−732255.	+	614435.i	−0.952057	+	0.798871i	−0.979643	−	0.200748i	$-0.935663\pi$
$877$	−732255.	+	614435.i	−0.952057	+	0.798871i	0.0275855	+	0.999619i	$0.491218\pi$
$878$	−69312.9	−	82603.9i	−0.0899135	−	0.107155i
$879$	105921.	−	104372.i	0.137090	−	0.135085i
$880$	−28474.2	+	10363.8i	−0.0367694	+	0.0133830i
$881$	−1.16480e6	+	672499.i	−1.50072	+	0.866443i	−0.500724	+	0.865607i	$0.666933\pi$
$881$	−1.16480e6	+	672499.i	−1.50072	+	0.866443i	−1.00000		0.000835760i	$0.999734\pi$
$882$	−10065.6	−	62449.5i	−0.0129390	−	0.0802771i
$883$	−195760.	+	339066.i	−0.251074	+	0.434873i	−0.963822	−	0.266547i	$-0.914117\pi$
$883$	−195760.	+	339066.i	−0.251074	+	0.434873i	0.712748	+	0.701421i	$0.247450\pi$
$884$	−310559.	−	54759.9i	−0.397411	−	0.0700742i
$885$	377746.	+	35853.4i	0.482296	+	0.0457767i
$886$	−137657.	−	50103.2i	−0.175361	−	0.0638261i
$887$	−163507.	+	28830.7i	−0.207821	+	0.0366444i	−0.276589	−	0.960988i	$-0.589204\pi$
$887$	−163507.	+	28830.7i	−0.207821	+	0.0366444i	0.0687684	+	0.997633i	$0.478093\pi$
$888$	460464.	+	668027.i	0.583942	+	0.847166i
$889$	376502.	+	315923.i	0.476391	+	0.399740i
$890$		−	14352.1i		−	0.0181190i
$891$	−45671.9	+	114840.i	−0.0575299	+	0.144657i
$892$	1.19637e6			1.50361
$893$	294944.	−	351500.i	0.369859	−	0.440781i
$894$	279590.	−	192719.i	0.349822	−	0.241129i
$895$	−43205.6	−	245031.i	−0.0539379	−	0.305897i
$896$	237216.	−	651746.i	0.295480	−	0.811825i
$897$	25945.8	−	273361.i	0.0322464	−	0.339743i
$898$	7283.44	−	41306.5i	0.00903200	−	0.0512230i
$899$	−294913.	−	170268.i	−0.364901	−	0.210675i
$900$	389544.	+	478375.i	0.480918	+	0.590587i
$901$	−883306.	−	1.52993e6i	−1.08808	−	1.88461i
$902$	4721.79	+	12973.0i	0.00580355	+	0.0159451i
$903$	−904724.	−	918148.i	−1.10953	−	1.12600i
$904$	400027.	−	335663.i	0.489500	−	0.410739i
$905$	−102317.	−	121937.i	−0.124925	−	0.148880i
$906$	−10156.4	−	39052.2i	−0.0123732	−	0.0475762i
$907$	1.28533e6	−	467822.i	1.56243	−	0.568678i	0.591138	−	0.806570i	$-0.298679\pi$
$907$	1.28533e6	−	467822.i	1.56243	−	0.568678i	0.971292	+	0.237892i	$0.0764565\pi$
$908$	−62999.2	+	36372.6i	−0.0764123	+	0.0441167i
$909$	−35667.8	+	59729.3i	−0.0431667	+	0.0722870i
$910$	13325.4	−	23080.2i	0.0160915	−	0.0278713i
$911$	950257.	+	167556.i	1.14500	+	0.201894i	0.713791	−	0.700359i	$-0.246977\pi$
$911$	950257.	+	167556.i	1.14500	+	0.201894i	0.431207	+	0.902253i	$0.358088\pi$
$912$	73327.6	+	160324.i	0.0881613	+	0.192756i
$913$	−200070.	−	72819.6i	−0.240016	−	0.0873588i
$914$	−219381.	+	38682.8i	−0.262607	+	0.0463048i
$915$	−100781.	+	8069.81i	−0.120375	+	0.00963876i
$916$	−664436.	−	557528.i	−0.791886	−	0.664471i
$917$		−	898246.i		−	1.06821i
$918$	442992.	−	28912.5i	0.525666	−	0.0343084i
$919$	−1.00521e6			−1.19021			−0.595107	−	0.803647i	$-0.702890\pi$
$919$	−1.00521e6			−1.19021			−0.595107	+	0.803647i	$0.702890\pi$
$920$	−151722.	+	180815.i	−0.179256	+	0.213629i
$921$	833435.	+	396135.i	0.982545	+	0.467008i
$922$	68824.1	+	390321.i	0.0809616	+	0.459156i
$923$	−48291.9	+	132681.i	−0.0566853	+	0.155742i
$924$	−83612.9	−	59468.8i	−0.0979330	−	0.0696538i
$925$	206356.	−	1.17030e6i	0.241176	−	1.36778i
$926$	−84508.0	−	48790.7i	−0.0985543	−	0.0569004i
$927$	267906.	−	309893.i	0.311762	−	0.360622i
$928$	−123475.	−	213865.i	−0.143378	−	0.248338i
$929$	100931.	+	277305.i	0.116948	+	0.321312i	0.984331	−	0.176328i	$-0.0564221\pi$
$929$	100931.	+	277305.i	0.116948	+	0.321312i	−0.867383	+	0.497641i	$0.834200\pi$
$930$	36913.4	−	133813.i	0.0426793	−	0.154715i
$931$	−50511.9	+	42384.5i	−0.0582766	+	0.0488999i
$932$	687300.	+	819092.i	0.791251	+	0.942976i
$933$	268646.	+	74108.2i	0.308615	+	0.0851339i
$934$	51536.6	−	18757.8i	0.0590775	−	0.0215024i
$935$	68883.0	−	39769.6i	0.0787932	−	0.0454913i
$936$	−30647.5	+	159994.i	−0.0349820	+	0.182622i
$937$	848848.	−	1.47025e6i	0.966831	−	1.67460i	0.262219	−	0.965008i	$-0.415546\pi$
$937$	848848.	−	1.47025e6i	0.966831	−	1.67460i	0.704612	−	0.709592i	$-0.251121\pi$
$938$	−179138.	−	31586.8i	−0.203602	−	0.0359004i
$939$	−334814.	+	470748.i	−0.379728	+	0.533897i
$940$	501941.	+	182692.i	0.568064	+	0.206758i
$941$	−921233.	+	162438.i	−1.04038	+	0.183446i	−0.667635	−	0.744489i	$-0.732693\pi$
$941$	−921233.	+	162438.i	−1.04038	+	0.183446i	−0.372741	+	0.927935i	$0.621582\pi$
$942$	111327.	−	234224.i	0.125459	−	0.263954i
$943$	−257011.	−	215658.i	−0.289020	−	0.242517i
$944$		−	773162.i		−	0.867613i
$945$	81649.1	−	279838.i	0.0914297	−	0.313360i
$946$	−85351.1			−0.0953734
$947$	3750.59	−	4469.77i	0.00418215	−	0.00498409i	−0.763949	−	0.645276i	$-0.776742\pi$
$947$	3750.59	−	4469.77i	0.00418215	−	0.00498409i	0.768131	+	0.640292i	$0.221187\pi$
$948$	−51216.5	−	639624.i	−0.0569892	−	0.711718i
$949$	−20166.4	−	114369.i	−0.0223922	−	0.126992i
$950$	−28308.0	+	77775.5i	−0.0313662	+	0.0861779i
$951$	−826081.	+	377827.i	−0.913401	+	0.417765i
$952$	−136236.	+	772631.i	−0.150320	+	0.852507i
$953$	−532595.	−	307494.i	−0.586423	−	0.338571i	0.177259	−	0.984164i	$-0.443277\pi$
$953$	−532595.	−	307494.i	−0.586423	−	0.338571i	−0.763682	+	0.645593i	$0.776610\pi$
$954$	−374391.	+	208864.i	−0.411366	+	0.229491i
$955$	247102.	+	427993.i	0.270938	+	0.469278i
$956$	−281578.	−	773628.i	−0.308093	−	0.846479i
$957$	−45828.0	+	11918.6i	−0.0500389	+	0.0130137i
$958$	57492.4	−	48241.8i	0.0626440	−	0.0525645i
$959$	934948.	+	1.11423e6i	1.01660	+	1.21154i
$960$	−93296.6	+	91932.5i	−0.101233	+	0.0997532i
$961$	−528956.	+	192524.i	−0.572760	+	0.208468i
$962$	127663.	−	73706.4i	0.137948	−	0.0796444i
$963$	815124.	+	310351.i	0.878964	+	0.334657i
$964$	−501682.	+	868939.i	−0.539852	+	0.935051i
$965$	−433319.	−	76405.9i	−0.465322	−	0.0820488i
$966$	−319484.	−	30323.5i	−0.342369	−	0.0324956i
$967$	−1.36323e6	−	496176.i	−1.45786	−	0.530619i	−0.513087	−	0.858337i	$-0.671498\pi$
$967$	−1.36323e6	−	496176.i	−1.45786	−	0.530619i	−0.944776	+	0.327718i	$0.893720\pi$
$968$	573439.	−	101113.i	0.611979	−	0.107908i
$969$	−262632.	−	381019.i	−0.279705	−	0.405788i
$970$	18061.6	+	15155.5i	0.0191961	+	0.0161074i
$971$			1.14407e6i			1.21343i	0.794921	+	0.606713i	$0.207512\pi$
$971$			1.14407e6i			1.21343i	−0.794921	+	0.606713i	$0.792488\pi$
$972$	42208.0	+	835988.i	0.0446747	+	0.884846i
$973$	723652.			0.764371
$974$	−120646.	+	143780.i	−0.127173	+	0.151559i
$975$	196452.	−	135412.i	0.206655	−	0.142445i
$976$	35773.3	+	202880.i	0.0375542	+	0.212981i
$977$	−87019.9	+	239085.i	−0.0911653	+	0.250474i	−0.976892	−	0.213732i	$-0.931438\pi$
$977$	−87019.9	+	239085.i	−0.0911653	+	0.250474i	0.885727	+	0.464206i	$0.153660\pi$
$978$	4297.24	−	45275.1i	0.00449275	−	0.0473349i
$979$	−3710.93	+	21045.7i	−0.00387184	+	0.0219583i
$980$	−66476.2	−	38380.0i	−0.0692172	−	0.0399625i
$981$	77833.7	−	204427.i	0.0808779	−	0.212422i
$982$	8894.31	+	15405.4i	0.00922336	+	0.0159753i
$983$	80074.8	+	220004.i	0.0828684	+	0.227679i	0.974206	−	0.225662i	$-0.0724543\pi$
$983$	80074.8	+	220004.i	0.0828684	+	0.227679i	−0.891337	+	0.453341i	$0.850232\pi$
$984$	139703.	+	141776.i	0.144284	+	0.146424i
$985$	−171537.	+	143937.i	−0.176802	+	0.148354i
$986$	109333.	+	130298.i	0.112460	+	0.134024i
$987$	389116.	+	1.49619e6i	0.399433	+	1.53586i
$988$	74962.3	−	27284.0i	0.0767943	−	0.0279508i
$989$	1.79631e6	−	1.03710e6i	1.83650	−	1.06030i
$990$	−9403.80	−	16856.4i	−0.00959474	−	0.0171987i
$991$	−638655.	+	1.10618e6i	−0.650308	+	1.12637i	0.332740	+	0.943019i	$0.392027\pi$
$991$	−638655.	+	1.10618e6i	−0.650308	+	1.12637i	−0.983048	+	0.183348i	$0.941306\pi$
$992$	−1.06155e6	−	187180.i	−1.07874	−	0.190211i
$993$	−4183.89	−	9147.66i	−0.00424309	−	0.00927708i
$994$	155068.	+	56440.0i	0.156945	+	0.0571234i
$995$	178093.	−	31402.6i	0.179888	−	0.0317190i
$996$	−1.43742e6	+	115098.i	−1.44899	+	0.116024i
$997$	1.09814e6	+	921445.i	1.10475	+	0.926999i	0.997736	−	0.0672585i	$-0.0214252\pi$
$997$	1.09814e6	+	921445.i	1.10475	+	0.926999i	0.107018	+	0.994257i	$0.465870\pi$
$998$		−	237699.i		−	0.238653i
$999$	1.16505e6	−	1.11468e6i	1.16738	−	1.11691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.11.7	yes	66
3.2	odd	2		81.5.f.a.35.5		66
27.5	odd	18	inner	27.5.f.a.5.7	✓	66
27.22	even	9		81.5.f.a.44.5		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.5.7	✓	66	27.5	odd	18	inner
27.5.f.a.11.7	yes	66	1.1	even	1	trivial
81.5.f.a.35.5		66	3.2	odd	2
81.5.f.a.44.5		66	27.22	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.868224 - 1.03471i) q^{2} +(-7.41018 + 5.10776i) q^{3} +(2.46156 + 13.9602i) q^{4} +(-3.20330 + 8.80100i) q^{5} +(-1.14866 + 12.1021i) q^{6} +(-7.41386 + 42.0461i) q^{7} +(35.2980 + 20.3793i) q^{8} +(28.8216 - 75.6988i) q^{9} +(6.32529 + 10.9557i) q^{10} +(-6.44259 - 17.7009i) q^{11} +(-89.5460 - 90.8746i) q^{12} +(-37.7989 + 31.7171i) q^{13} +(37.0686 + 44.1766i) q^{14} +(-21.2163 - 81.5787i) q^{15} +(-161.398 + 58.7439i) q^{16} +(390.443 - 225.422i) q^{17} +(-53.3026 - 95.5455i) q^{18} +(-57.0245 + 98.7692i) q^{19} +(-130.749 - 23.0546i) q^{20} +(-159.823 - 349.437i) q^{21} +(-23.9089 - 8.70211i) q^{22} +(608.929 - 107.371i) q^{23} +(-365.657 + 29.2792i) q^{24} +(411.581 + 345.358i) q^{25} +66.6484i q^{26} +(173.078 + 708.156i) q^{27} -605.222 q^{28} +(-179.539 + 213.967i) q^{29} +(-102.831 - 48.8759i) q^{30} +(211.710 + 1200.67i) q^{31} +(-302.391 + 830.812i) q^{32} +(138.152 + 98.2595i) q^{33} +(105.745 - 599.712i) q^{34} +(-346.299 - 199.936i) q^{35} +(1127.72 + 216.019i) q^{36} +(-1105.90 - 1915.47i) q^{37} +(52.6874 + 144.758i) q^{38} +(118.094 - 428.097i) q^{39} +(-292.429 + 245.377i) q^{40} +(-348.778 - 415.658i) q^{41} +(-500.328 - 138.019i) q^{42} +(3152.26 - 1147.33i) q^{43} +(231.249 - 133.512i) q^{44} +(573.901 + 496.145i) q^{45} +(417.590 - 723.286i) q^{46} +(-3962.16 - 698.636i) q^{47} +(895.936 - 1259.68i) q^{48} +(543.294 + 197.743i) q^{49} +(714.690 - 126.019i) q^{50} +(-1741.85 + 3664.71i) q^{51} +(-535.821 - 449.607i) q^{52} -3918.45i q^{53} +(883.006 + 435.753i) q^{54} +176.423 q^{55} +(-1118.57 + 1333.05i) q^{56} +(-81.9277 - 1023.17i) q^{57} +(65.5128 + 371.542i) q^{58} +(-1539.61 + 4230.04i) q^{59} +(1086.63 - 496.995i) q^{60} +(208.280 - 1181.21i) q^{61} +(1426.15 + 823.390i) q^{62} +(2969.16 + 1773.06i) q^{63} +(-776.940 - 1345.70i) q^{64} +(-158.060 - 434.267i) q^{65} +(221.617 - 57.6364i) q^{66} +(-2416.30 + 2027.52i) q^{67} +(4108.04 + 4895.77i) q^{68} +(-3963.85 + 3905.90i) q^{69} +(-507.540 + 184.729i) q^{70} +(2478.15 - 1430.76i) q^{71} +(2560.04 - 2084.65i) q^{72} +(-1176.80 + 2038.28i) q^{73} +(-2942.13 - 518.776i) q^{74} +(-4813.90 - 456.907i) q^{75} +(-1519.21 - 552.947i) q^{76} +(792.017 - 139.654i) q^{77} +(-340.424 - 493.877i) q^{78} +(3852.86 + 3232.93i) q^{79} -1608.63i q^{80} +(-4899.63 - 4363.53i) q^{81} -732.903 q^{82} +(7265.33 - 8658.48i) q^{83} +(4484.80 - 3091.33i) q^{84} +(733.235 + 4158.38i) q^{85} +(1549.72 - 4257.81i) q^{86} +(237.530 - 2502.57i) q^{87} +(133.321 - 756.101i) q^{88} +(-982.504 - 567.249i) q^{89} +(1011.64 - 163.055i) q^{90} +(-1053.34 - 1824.44i) q^{91} +(2997.83 + 8236.48i) q^{92} +(-7701.53 - 7815.80i) q^{93} +(-4162.93 + 3493.11i) q^{94} +(-686.601 - 818.260i) q^{95} +(-2002.81 - 7701.01i) q^{96} +(1751.37 - 637.447i) q^{97} +(676.307 - 390.466i) q^{98} +(-1525.62 - 22.4713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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