LMFDB - Embedded newform 27.7.f.a.2.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,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, 7, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.56069 + 0.804173i) q^{2} +(-8.77856 - 25.5331i) q^{3} +(-39.9871 - 14.5541i) q^{4} +(33.6911 + 40.1515i) q^{5} +(-19.5033 - 123.508i) q^{6} +(-487.528 + 177.446i) q^{7} +(-427.344 - 246.727i) q^{8} +(-574.874 + 448.287i) q^{9} +O(q^{10})$	\(q+(4.56069 + 0.804173i) q^{2} +(-8.77856 - 25.5331i) q^{3} +(-39.9871 - 14.5541i) q^{4} +(33.6911 + 40.1515i) q^{5} +(-19.5033 - 123.508i) q^{6} +(-487.528 + 177.446i) q^{7} +(-427.344 - 246.727i) q^{8} +(-574.874 + 448.287i) q^{9} +(121.366 + 210.212i) q^{10} +(881.622 - 1050.68i) q^{11} +(-20.5819 + 1148.76i) q^{12} +(-481.717 - 2731.95i) q^{13} +(-2366.16 + 417.219i) q^{14} +(729.432 - 1212.71i) q^{15} +(335.685 + 281.674i) q^{16} +(-580.302 + 335.037i) q^{17} +(-2982.32 + 1582.20i) q^{18} +(-949.519 + 1644.62i) q^{19} +(-762.841 - 2095.89i) q^{20} +(8810.53 + 10890.4i) q^{21} +(4865.73 - 4082.84i) q^{22} +(1104.04 - 3033.33i) q^{23} +(-2548.23 + 13077.3i) q^{24} +(2236.20 - 12682.1i) q^{25} -12847.0i q^{26} +(16492.7 + 10743.0i) q^{27} +22077.4 q^{28} +(-30279.8 - 5339.14i) q^{29} +(4301.94 - 4944.21i) q^{30} +(41276.6 + 15023.4i) q^{31} +(21604.4 + 25747.1i) q^{32} +(-34566.4 - 13287.1i) q^{33} +(-2916.01 + 1061.34i) q^{34} +(-23550.1 - 13596.7i) q^{35} +(29512.0 - 9558.91i) q^{36} +(-20486.2 - 35483.2i) q^{37} +(-5653.02 + 6737.01i) q^{38} +(-65526.3 + 36282.3i) q^{39} +(-4491.23 - 25471.0i) q^{40} +(-101063. + 17820.1i) q^{41} +(31424.4 + 56752.8i) q^{42} +(6122.43 + 5137.33i) q^{43} +(-50545.2 + 29182.3i) q^{44} +(-37367.6 - 7978.77i) q^{45} +(7474.52 - 12946.3i) q^{46} +(-66616.3 - 183027. i) q^{47} +(4245.15 - 11043.8i) q^{48} +(116073. - 97396.4i) q^{49} +(20397.2 - 56041.0i) q^{50} +(13648.7 + 11875.7i) q^{51} +(-20498.7 + 116254. i) q^{52} +130003. i q^{53} +(66578.9 + 62258.4i) q^{54} +71889.1 q^{55} +(252123. + 44456.1i) q^{56} +(50327.5 + 9806.78i) q^{57} +(-133803. - 48700.4i) q^{58} +(79673.2 + 94950.9i) q^{59} +(-46817.8 + 37876.5i) q^{60} +(-327414. + 119169. i) q^{61} +(176168. + 101711. i) q^{62} +(200721. - 320561. i) q^{63} +(63803.1 + 110510. i) q^{64} +(93462.4 - 111384. i) q^{65} +(-146961. - 88395.7i) q^{66} +(22791.5 + 129257. i) q^{67} +(28080.8 - 4951.40i) q^{68} +(-87142.1 - 1561.30i) q^{69} +(-96470.7 - 80948.6i) q^{70} +(384533. - 222011. i) q^{71} +(356273. - 49735.7i) q^{72} +(-85249.1 + 147656. i) q^{73} +(-64896.8 - 178302. i) q^{74} +(-343444. + 54233.7i) q^{75} +(61904.5 - 51944.0i) q^{76} +(-243378. + 668675. i) q^{77} +(-328023. + 112778. i) q^{78} +(34940.5 - 198158. i) q^{79} +22968.2i q^{80} +(129519. - 515417. i) q^{81} -475247. q^{82} +(-428288. - 75518.8i) q^{83} +(-193808. - 563704. i) q^{84} +(-33003.3 - 12012.2i) q^{85} +(23791.2 + 28353.3i) q^{86} +(129488. + 820005. i) q^{87} +(-635986. + 231480. i) q^{88} +(426526. + 246255. i) q^{89} +(-164006. - 66438.7i) q^{90} +(719624. + 1.24642e6i) q^{91} +(-88294.9 + 105226. i) q^{92} +(21245.6 - 1.18580e6i) q^{93} +(-156631. - 888300. i) q^{94} +(-98024.2 + 17284.3i) q^{95} +(467746. - 777647. i) q^{96} +(-425098. - 356700. i) q^{97} +(607695. - 350853. i) q^{98} +(-35817.1 + 999226. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	4.56069	+	0.804173i	0.570087	+	0.100522i	0.451259	−	0.892393i	$-0.350975\pi$
$2$	4.56069	+	0.804173i	0.570087	+	0.100522i	0.118828	+	0.992915i	$0.462086\pi$
$3$	−8.77856	−	25.5331i	−0.325132	−	0.945669i
$3$	−8.77856	−	25.5331i	−0.325132	−	0.945669i
$4$	−39.9871	−	14.5541i	−0.624798	−	0.227408i
$5$	33.6911	+	40.1515i	0.269529	+	0.321212i	0.883784	−	0.467896i	$-0.154988\pi$
$5$	33.6911	+	40.1515i	0.269529	+	0.321212i	−0.614255	+	0.789108i	$0.710543\pi$
$6$	−19.5033	−	123.508i	−0.0902931	−	0.571796i
$7$	−487.528	+	177.446i	−1.42137	+	0.517335i	−0.934444	−	0.356111i	$-0.884103\pi$
$7$	−487.528	+	177.446i	−1.42137	+	0.517335i	−0.486922	+	0.873446i	$0.661880\pi$
$8$	−427.344	−	246.727i	−0.834656	−	0.481889i
$9$	−574.874	+	448.287i	−0.788579	+	0.614934i
$10$	121.366	+	210.212i	0.121366	+	0.210212i
$11$	881.622	−	1050.68i	0.662376	−	0.789389i	−0.325349	−	0.945594i	$-0.605482\pi$
$11$	881.622	−	1050.68i	0.662376	−	0.789389i	0.987725	+	0.156205i	$0.0499262\pi$
$12$	−20.5819	+	1148.76i	−0.0119108	+	0.664790i
$13$	−481.717	−	2731.95i	−0.219261	−	1.24349i	−0.873357	−	0.487080i	$-0.838062\pi$
$13$	−481.717	−	2731.95i	−0.219261	−	1.24349i	0.654096	−	0.756411i	$-0.273049\pi$
$14$	−2366.16	+	417.219i	−0.862305	+	0.152048i
$15$	729.432	−	1212.71i	0.216128	−	0.359322i
$16$	335.685	+	281.674i	0.0819545	+	0.0687680i
$17$	−580.302	+	335.037i	−0.118116	+	0.0681941i	−0.557894	−	0.829912i	$-0.688390\pi$
$17$	−580.302	+	335.037i	−0.118116	+	0.0681941i	0.439778	+	0.898106i	$0.355057\pi$
$18$	−2982.32	+	1582.20i	−0.511372	+	0.271296i
$19$	−949.519	+	1644.62i	−0.138434	+	0.239775i	−0.926904	−	0.375298i	$-0.877540\pi$
$19$	−949.519	+	1644.62i	−0.138434	+	0.239775i	0.788470	+	0.615073i	$0.210874\pi$
$20$	−762.841	−	2095.89i	−0.0953551	−	0.261986i
$21$	8810.53	+	10890.4i	0.951358	+	1.17594i
$22$	4865.73	−	4082.84i	0.456962	−	0.383437i
$23$	1104.04	−	3033.33i	0.0907407	−	0.249308i	−0.886018	−	0.463652i	$-0.846539\pi$
$23$	1104.04	−	3033.33i	0.0907407	−	0.249308i	0.976758	+	0.214343i	$0.0687612\pi$
$24$	−2548.23	+	13077.3i	−0.184334	+	0.945985i
$25$	2236.20	−	12682.1i	0.143117	−	0.811656i
$26$		−	12847.0i		−	0.730939i
$27$	16492.7	+	10743.0i	0.837916	+	0.545800i
$28$	22077.4			1.00571
$29$	−30279.8	−	5339.14i	−1.24153	−	0.218916i	−0.485961	−	0.873981i	$-0.661530\pi$
$29$	−30279.8	−	5339.14i	−1.24153	−	0.218916i	−0.755573	+	0.655065i	$0.772641\pi$
$30$	4301.94	−	4944.21i	0.159331	−	0.183119i
$31$	41276.6	+	15023.4i	1.38554	+	0.504295i	0.923852	−	0.382749i	$-0.125023\pi$
$31$	41276.6	+	15023.4i	1.38554	+	0.504295i	0.461686	+	0.887044i	$0.347245\pi$
$32$	21604.4	+	25747.1i	0.659313	+	0.785738i
$33$	−34566.4	−	13287.1i	−0.961860	−	0.369733i
$34$	−2916.01	+	1061.34i	−0.0741911	+	0.0270034i
$35$	−23550.1	−	13596.7i	−0.549274	−	0.317123i
$36$	29512.0	−	9558.91i	0.632544	−	0.204881i
$37$	−20486.2	−	35483.2i	−0.404443	−	0.700515i	0.589814	−	0.807539i	$-0.299201\pi$
$37$	−20486.2	−	35483.2i	−0.404443	−	0.700515i	−0.994256	+	0.107024i	$0.965868\pi$
$38$	−5653.02	+	6737.01i	−0.103022	+	0.122777i
$39$	−65526.3	+	36282.3i	−1.10464	+	0.611647i
$40$	−4491.23	−	25471.0i	−0.0701754	−	0.397985i
$41$	−101063.	+	17820.1i	−1.46636	+	0.258558i	−0.849112	−	0.528212i	$-0.822862\pi$
$41$	−101063.	+	17820.1i	−1.46636	+	0.258558i	−0.617245	+	0.786771i	$0.711751\pi$
$42$	31424.4	+	56752.8i	0.424149	+	0.766019i
$43$	6122.43	+	5137.33i	0.0770049	+	0.0646148i	0.680478	−	0.732769i	$-0.261772\pi$
$43$	6122.43	+	5137.33i	0.0770049	+	0.0646148i	−0.603473	+	0.797384i	$0.706217\pi$
$44$	−50545.2	+	29182.3i	−0.593365	+	0.342579i
$45$	−37367.6	−	7978.77i	−0.410069	−	0.0875585i
$46$	7474.52	−	12946.3i	0.0767909	−	0.133006i
$47$	−66616.3	−	183027.i	−0.641633	−	1.76287i	−0.646534	−	0.762885i	$-0.723782\pi$
$47$	−66616.3	−	183027.i	−0.641633	−	1.76287i	0.00490102	−	0.999988i	$-0.498440\pi$
$48$	4245.15	−	11043.8i	0.0383857	−	0.0998604i
$49$	116073.	−	97396.4i	0.986600	−	0.827856i
$50$	20397.2	−	56041.0i	0.163178	−	0.448328i
$51$	13648.7	+	11875.7i	0.102892	+	0.0895262i
$52$	−20498.7	+	116254.i	−0.145786	+	0.826793i
$53$			130003.i			0.873224i	0.899650	+	0.436612i	$0.143822\pi$
$53$			130003.i			0.873224i	−0.899650	+	0.436612i	$0.856178\pi$
$54$	66578.9	+	62258.4i	0.422820	+	0.395382i
$55$	71889.1			0.432091
$56$	252123.	+	44456.1i	1.43565	+	0.253144i
$57$	50327.5	+	9806.78i	0.271757	+	0.0529544i
$58$	−133803.	−	48700.4i	−0.685776	−	0.249602i
$59$	79673.2	+	94950.9i	0.387933	+	0.462320i	0.924301	−	0.381664i	$-0.124649\pi$
$59$	79673.2	+	94950.9i	0.387933	+	0.462320i	−0.536369	+	0.843984i	$0.680204\pi$
$60$	−46817.8	+	37876.5i	−0.216749	+	0.175354i
$61$	−327414.	+	119169.i	−1.44247	+	0.525017i	−0.940478	−	0.339855i	$-0.889622\pi$
$61$	−327414.	+	119169.i	−1.44247	+	0.525017i	−0.501993	+	0.864872i	$0.667400\pi$
$62$	176168.	+	101711.i	0.739184	+	0.426768i
$63$	200721.	−	320561.i	0.802732	−	1.28200i
$64$	63803.1	+	110510.i	0.243390	+	0.421563i
$65$	93462.4	−	111384.i	0.340328	−	0.405587i
$66$	−146961.	−	88395.7i	−0.511177	−	0.307467i
$67$	22791.5	+	129257.i	0.0757789	+	0.429764i	0.998968	+	0.0454177i	$0.0144619\pi$
$67$	22791.5	+	129257.i	0.0757789	+	0.429764i	−0.923189	+	0.384346i	$0.874427\pi$
$68$	28080.8	−	4951.40i	0.0893063	−	0.0157471i
$69$	−87142.1	−	1561.30i	−0.265265	−	0.00475268i
$70$	−96470.7	−	80948.6i	−0.281256	−	0.236002i
$71$	384533.	−	222011.i	1.07438	−	0.620295i	0.145007	−	0.989431i	$-0.453679\pi$
$71$	384533.	−	222011.i	1.07438	−	0.620295i	0.929376	+	0.369135i	$0.120346\pi$
$72$	356273.	−	49735.7i	0.954521	−	0.133251i
$73$	−85249.1	+	147656.i	−0.219140	+	0.379561i	−0.954545	−	0.298066i	$-0.903658\pi$
$73$	−85249.1	+	147656.i	−0.219140	+	0.379561i	0.735405	+	0.677627i	$0.236992\pi$
$74$	−64896.8	−	178302.i	−0.160150	−	0.440010i
$75$	−343444.	+	54233.7i	−0.814089	+	0.128554i
$76$	61904.5	−	51944.0i	0.141020	−	0.118330i
$77$	−243378.	+	668675.i	−0.533100	+	1.46468i
$78$	−328023.	+	112778.i	−0.691226	+	0.237651i
$79$	34940.5	−	198158.i	0.0708677	−	0.401910i	−0.928653	−	0.370950i	$-0.879032\pi$
$79$	34940.5	−	198158.i	0.0708677	−	0.401910i	0.999521	−	0.0309607i	$-0.00985668\pi$
$80$			22968.2i			0.0448597i
$81$	129519.	−	515417.i	0.243713	−	0.969848i
$82$	−475247.			−0.861942
$83$	−428288.	−	75518.8i	−0.749034	−	0.132075i	−0.213916	−	0.976852i	$-0.568622\pi$
$83$	−428288.	−	75518.8i	−0.749034	−	0.132075i	−0.535118	+	0.844777i	$0.679733\pi$
$84$	−193808.	−	563704.i	−0.326989	−	0.951071i
$85$	−33003.3	−	12012.2i	−0.0537404	−	0.0195599i
$86$	23791.2	+	28353.3i	0.0374043	+	0.0445767i
$87$	129488.	+	820005.i	0.196640	+	1.24526i
$88$	−635986.	+	231480.i	−0.933253	+	0.339676i
$89$	426526.	+	246255.i	0.605028	+	0.349313i	0.771017	−	0.636815i	$-0.219748\pi$
$89$	426526.	+	246255.i	0.605028	+	0.349313i	−0.165989	+	0.986128i	$0.553082\pi$
$90$	−164006.	−	66438.7i	−0.224973	−	0.0911368i
$91$	719624.	+	1.24642e6i	0.954952	+	1.65402i
$92$	−88294.9	+	105226.i	−0.113389	+	0.135132i
$93$	21245.6	−	1.18580e6i	0.0264132	−	1.47422i
$94$	−156631.	−	888300.i	−0.188580	−	1.06949i
$95$	−98024.2	+	17284.3i	−0.114331	+	0.0201596i
$96$	467746.	−	777647.i	0.528685	−	0.878960i
$97$	−425098.	−	356700.i	−0.465773	−	0.390830i	0.379477	−	0.925201i	$-0.376104\pi$
$97$	−425098.	−	356700.i	−0.465773	−	0.390830i	−0.845250	+	0.534371i	$0.820548\pi$
$98$	607695.	−	350853.i	0.645665	−	0.372775i
$99$	−35817.1	+	999226.i	−0.0369135	+	1.02981i
$100$	−273996.	+	474575.i	−0.273996	+	0.474575i
$101$	−332058.	−	912323.i	−0.322293	−	0.885492i	−0.990000	−	0.141068i	$-0.954946\pi$
$101$	−332058.	−	912323.i	−0.322293	−	0.885492i	0.667707	−	0.744424i	$-0.267276\pi$
$102$	52697.6	+	65137.5i	0.0496581	+	0.0613806i
$103$	1.29424e6	−	1.08600e6i	1.18441	−	0.993841i	0.184474	−	0.982837i	$-0.440942\pi$
$103$	1.29424e6	−	1.08600e6i	1.18441	−	0.993841i	0.999939	−	0.0110038i	$-0.00350270\pi$
$104$	−468187.	+	1.28633e6i	−0.416217	+	1.14355i
$105$	−140428.	+	720665.i	−0.121307	+	0.622538i
$106$	−104545.	+	592903.i	−0.0877779	+	0.497813i
$107$			580796.i			0.474103i	0.971497	+	0.237051i	$0.0761810\pi$
$107$			580796.i			0.474103i	−0.971497	+	0.237051i	$0.923819\pi$
$108$	−503141.	−	669617.i	−0.399409	−	0.531563i
$109$	2.20532e6			1.70291			0.851455	−	0.524428i	$-0.175721\pi$
$109$	2.20532e6			1.70291			0.851455	+	0.524428i	$0.175721\pi$
$110$	327864.	+	57811.3i	0.246329	+	0.0434345i
$111$	−726155.	+	834567.i	−0.530958	+	0.610228i
$112$	−213638.	−	77757.9i	−0.152063	−	0.0553465i
$113$	−1.45482e6	−	1.73379e6i	−1.00827	−	1.20160i	−0.979381	−	0.202021i	$-0.935249\pi$
$113$	−1.45482e6	−	1.73379e6i	−1.00827	−	1.20160i	−0.0288843	−	0.999583i	$-0.509195\pi$
$114$	221642.	+	85197.7i	0.149602	+	0.0575060i
$115$	158989.	−	57867.4i	0.104538	−	0.0380487i
$116$	1.13309e6	+	654192.i	0.725925	+	0.419113i
$117$	1.50162e6	+	1.35458e6i	0.937570	+	0.845760i
$118$	287008.	+	497113.i	0.174682	+	0.302558i
$119$	223463.	−	266312.i	0.132606	−	0.158034i
$120$	−610926.	+	338274.i	−0.353545	+	0.195760i
$121$	−19034.9	−	107952.i	−0.0107447	−	0.0609363i
$122$	−1.58907e6	+	280195.i	−0.875109	+	0.154305i
$123$	1.34219e6	+	2.42401e6i	0.721270	+	1.30262i
$124$	−1.43188e6	−	1.20149e6i	−0.751001	−	0.630165i
$125$	1.29380e6	−	746973.i	0.662423	−	0.382450i
$126$	1.17321e6	−	1.30057e6i	0.586496	−	0.650162i
$127$	375450.	−	650298.i	0.183291	−	0.317469i	−0.759708	−	0.650264i	$-0.774658\pi$
$127$	375450.	−	650298.i	0.183291	−	0.317469i	0.942999	+	0.332795i	$0.107992\pi$
$128$	−533591.	−	1.46603e6i	−0.254436	−	0.699057i
$129$	77425.6	−	201423.i	0.0360674	−	0.0938294i
$130$	515826.	−	432829.i	0.234786	−	0.197009i
$131$	392438.	−	1.07822e6i	0.174565	−	0.479614i	−0.821296	−	0.570502i	$-0.806748\pi$
$131$	392438.	−	1.07822e6i	0.174565	−	0.479614i	0.995861	+	0.0908886i	$0.0289707\pi$
$132$	1.18883e6	+	1.03439e6i	0.516888	+	0.449743i
$133$	171087.	−	970285.i	0.0727216	−	0.412424i
$134$			607830.i			0.252620i
$135$	124311.	+	1.02415e6i	0.0505252	+	0.416258i
$136$	330651.			0.131448
$137$	−3.04388e6	−	536719.i	−1.18377	−	0.208730i	−0.453097	−	0.891461i	$-0.649681\pi$
$137$	−3.04388e6	−	536719.i	−1.18377	−	0.208730i	−0.730670	+	0.682731i	$0.760792\pi$
$138$	−396173.	−	77198.0i	−0.150747	−	0.0293744i
$139$	−2.31754e6	−	843514.i	−0.862943	−	0.314086i	−0.127637	−	0.991821i	$-0.540739\pi$
$139$	−2.31754e6	−	843514.i	−0.862943	−	0.314086i	−0.735306	+	0.677735i	$0.762961\pi$
$140$	743813.	+	886442.i	0.271069	+	0.323047i
$141$	−4.08844e6	+	3.30763e6i	−1.45848	+	1.17994i
$142$	1.93227e6	−	703290.i	0.674845	−	0.245623i
$143$	−3.29509e6	−	1.90242e6i	−1.12683	−	0.650577i
$144$	−319247.	−	11443.4i	−0.106915	−	0.00383236i
$145$	−805785.	−	1.39566e6i	−0.264311	−	0.457800i
$146$	−507536.	+	604858.i	−0.163083	+	0.194355i
$147$	−3.50578e6	−	2.10869e6i	−1.10365	−	0.663835i
$148$	302758.	+	1.71703e6i	0.0933923	+	0.529654i
$149$	−2.36386e6	+	416812.i	−0.714599	+	0.126003i	−0.519116	−	0.854704i	$-0.673739\pi$
$149$	−2.36386e6	+	416812.i	−0.714599	+	0.126003i	−0.195483	+	0.980707i	$0.562627\pi$
$150$	−1.60996e6	−	28845.1i	−0.477024	−	0.00854669i
$151$	1.41913e6	+	1.19079e6i	0.412185	+	0.345864i	0.825181	−	0.564869i	$-0.191073\pi$
$151$	1.41913e6	+	1.19079e6i	0.412185	+	0.345864i	−0.412996	+	0.910733i	$0.635518\pi$
$152$	811542.	−	468544.i	0.231090	−	0.133420i
$153$	183408.	−	452746.i	0.0512086	−	0.126410i
$154$	−1.64770e6	+	2.85390e6i	−0.451145	+	0.781406i
$155$	787440.	+	2.16347e6i	0.211457	+	0.580974i
$156$	3.14826e6	−	497147.i	0.829272	−	0.130952i
$157$	2.87783e6	−	2.41478e6i	0.743645	−	0.623993i	−0.190169	−	0.981751i	$-0.560903\pi$
$157$	2.87783e6	−	2.41478e6i	0.743645	−	0.623993i	0.933814	+	0.357759i	$0.116459\pi$
$158$	318706.	−	875638.i	0.0808014	−	0.222000i
$159$	3.31937e6	−	1.14124e6i	0.825780	−	0.283913i
$160$	−305909.	+	1.73490e6i	−0.0746848	+	0.423559i
$161$			1.67474e6i			0.401301i
$162$	1.00518e6	−	2.24650e6i	0.236428	−	0.528399i
$163$	−1.07497e6			−0.248217			−0.124109	−	0.992269i	$-0.539607\pi$
$163$	−1.07497e6			−0.248217			−0.124109	+	0.992269i	$0.539607\pi$
$164$	4.30056e6	+	758306.i	0.974976	+	0.171915i
$165$	−631083.	−	1.83555e6i	−0.140486	−	0.408615i
$166$	−1.89256e6	−	688836.i	−0.413738	−	0.150588i
$167$	4.63008e6	+	5.51792e6i	0.994121	+	1.18475i	0.982774	+	0.184811i	$0.0591674\pi$
$167$	4.63008e6	+	5.51792e6i	0.994121	+	1.18475i	0.0113468	+	0.999936i	$0.496388\pi$
$168$	−1.07818e6	−	6.82773e6i	−0.227385	−	1.43995i
$169$	−2.69579e6	+	981187.i	−0.558503	+	0.203279i
$170$	−140858.	−	81324.4i	−0.0286705	−	0.0165529i
$171$	−191406.	−	1.37110e6i	−0.0382795	−	0.274209i
$172$	−170049.	−	294533.i	−0.0334186	−	0.0578827i
$173$	5.65055e6	−	6.73406e6i	1.09132	−	1.30059i	0.140761	−	0.990044i	$-0.455045\pi$
$173$	5.65055e6	−	6.73406e6i	1.09132	−	1.30059i	0.950560	−	0.310542i	$-0.100511\pi$
$174$	−68870.3	+	3.84392e6i	−0.0130733	+	0.729670i
$175$	1.16018e6	+	6.57970e6i	0.216476	+	1.22770i
$176$	591896.	−	104367.i	0.108569	−	0.0191437i
$177$	1.72497e6	−	2.86783e6i	0.311072	−	0.517171i
$178$	1.74722e6	+	1.46609e6i	0.309805	+	0.259957i
$179$	271703.	−	156868.i	0.0473734	−	0.0273511i	−0.476126	−	0.879377i	$-0.657959\pi$
$179$	271703.	−	156868.i	0.0473734	−	0.0273511i	0.523500	+	0.852026i	$0.324626\pi$
$180$	1.37810e6	+	862900.i	0.236299	+	0.147959i
$181$	2.06868e6	−	3.58306e6i	0.348865	−	0.604252i	−0.637183	−	0.770712i	$-0.719901\pi$
$181$	2.06868e6	−	3.58306e6i	0.348865	−	0.604252i	0.986048	+	0.166461i	$0.0532339\pi$
$182$	2.27964e6	+	6.26326e6i	0.378140	+	1.03893i
$183$	5.91696e6	+	7.31374e6i	0.965485	+	1.19340i
$184$	−1.22021e6	+	1.02388e6i	−0.195876	+	0.164359i
$185$	734500.	−	2.01802e6i	0.116005	−	0.318721i
$186$	1.05048e6	−	5.39099e6i	0.163249	−	0.837779i
$187$	−159591.	+	905086.i	−0.0244053	+	0.138409i
$188$			8.28825e6i			1.24735i
$189$	−9.94695e6	−	2.31094e6i	−1.47335	−	0.342298i
$190$	−460958.			−0.0672049
$191$	−7.70219e6	−	1.35810e6i	−1.10539	−	0.194910i	−0.408971	−	0.912548i	$-0.634112\pi$
$191$	−7.70219e6	−	1.35810e6i	−1.10539	−	0.194910i	−0.696416	+	0.717638i	$0.745223\pi$
$192$	2.26157e6	−	2.59921e6i	0.319525	−	0.367230i
$193$	3.45608e6	+	1.25791e6i	0.480741	+	0.174975i	0.571012	−	0.820942i	$-0.306551\pi$
$193$	3.45608e6	+	1.25791e6i	0.480741	+	0.174975i	−0.0902707	+	0.995917i	$0.528773\pi$
$194$	−1.65190e6	−	1.96865e6i	−0.226244	−	0.269627i
$195$	−3.66444e6	−	1.40859e6i	−0.494202	−	0.189968i
$196$	−6.05892e6	+	2.20527e6i	−0.804687	+	0.292882i
$197$	−8.00860e6	−	4.62377e6i	−1.04751	−	0.604780i	−0.125559	−	0.992086i	$-0.540072\pi$
$197$	−8.00860e6	−	4.62377e6i	−1.04751	−	0.604780i	−0.921951	+	0.387306i	$0.873406\pi$
$198$	−966902.	+	4.52836e6i	−0.124562	+	0.583372i
$199$	−1.15503e6	−	2.00058e6i	−0.146567	−	0.253861i	0.783390	−	0.621531i	$-0.213489\pi$
$199$	−1.15503e6	−	2.00058e6i	−0.146567	−	0.253861i	−0.929956	+	0.367670i	$0.880156\pi$
$200$	−4.08465e6	+	4.86789e6i	−0.510581	+	0.608487i
$201$	3.10025e6	−	1.71663e6i	0.381776	−	0.211392i
$202$	−780751.	−	4.42786e6i	−0.0947237	−	0.537205i
$203$	1.57096e7	−	2.77004e6i	1.87793	−	0.331129i
$204$	−372933.	−	673522.i	−0.0439279	−	0.0793343i
$205$	−4.12043e6	−	3.45745e6i	−0.478278	−	0.401323i
$206$	6.77597e6	−	3.91211e6i	0.775121	−	0.447516i
$207$	725117.	+	2.23871e6i	0.0817518	+	0.252399i
$208$	607813.	−	1.05276e6i	0.0675430	−	0.116988i
$209$	890842.	+	2.44757e6i	0.0975802	+	0.268099i
$210$	−1.21999e6	+	3.17380e6i	−0.131734	+	0.342706i
$211$	−8.53147e6	+	7.15875e6i	−0.908189	+	0.762061i	−0.971774	−	0.235915i	$-0.924191\pi$
$211$	−8.53147e6	+	7.15875e6i	−0.908189	+	0.762061i	0.0635844	+	0.997976i	$0.479747\pi$
$212$	1.89208e6	−	5.19844e6i	0.198578	−	0.545589i
$213$	−9.04426e6	−	7.86938e6i	−0.935910	−	0.814333i
$214$	−467061.	+	2.64883e6i	−0.0476576	+	0.270280i
$215$			418907.i			0.0421505i
$216$	−4.39747e6	−	8.66014e6i	−0.436356	−	0.859337i
$217$	−2.27893e7			−2.23025
$218$	1.00578e7	+	1.77346e6i	0.970806	+	0.171179i
$219$	4.51847e6	+	880465.i	0.430189	+	0.0838262i
$220$	−2.87464e6	−	1.04628e6i	−0.269970	−	0.0982609i
$221$	1.19485e6	+	1.42396e6i	0.110697	+	0.131923i
$222$	−3.98291e6	+	3.22225e6i	−0.364033	+	0.294510i
$223$	1.89700e7	−	6.90452e6i	1.71062	−	0.622614i	0.713655	−	0.700498i	$-0.247039\pi$
$223$	1.89700e7	−	6.90452e6i	1.71062	−	0.622614i	0.996962	+	0.0778837i	$0.0248163\pi$
$224$	−1.51014e7	−	8.71882e6i	−1.34361	−	0.775736i
$225$	4.39969e6	+	8.29308e6i	0.386256	+	0.728062i
$226$	−5.24073e6	−	9.07722e6i	−0.454011	−	0.786371i
$227$	−6.97671e6	+	8.31452e6i	−0.596449	+	0.710820i	−0.976832	−	0.214009i	$-0.931348\pi$
$227$	−6.97671e6	+	8.31452e6i	−0.596449	+	0.710820i	0.380383	+	0.924829i	$0.375792\pi$
$228$	−1.86972e6	−	1.12462e6i	−0.157751	−	0.0948855i
$229$	3.45692e6	+	1.96052e7i	0.287861	+	1.63254i	0.694883	+	0.719123i	$0.255456\pi$
$229$	3.45692e6	+	1.96052e7i	0.287861	+	1.63254i	−0.407021	+	0.913419i	$0.633433\pi$
$230$	771637.	−	136060.i	0.0634205	−	0.0111827i
$231$	1.92098e7	+	344176.i	1.55843	+	0.0279219i
$232$	1.16226e7	+	9.75248e6i	0.930760	+	0.781000i
$233$	−1.53852e6	+	888262.i	−0.121628	+	0.0702220i	−0.559580	−	0.828777i	$-0.689037\pi$
$233$	−1.53852e6	+	888262.i	−0.121628	+	0.0702220i	0.437952	+	0.898999i	$0.355704\pi$
$234$	5.75913e6	+	7.38539e6i	0.449479	+	0.576403i
$235$	5.10443e6	−	8.84113e6i	0.393318	−	0.681246i
$236$	−1.80398e6	−	4.95638e6i	−0.137244	−	0.377076i
$237$	−5.36630e6	+	847399.i	−0.403116	+	0.0636565i
$238$	1.23331e6	−	1.03487e6i	0.0914829	−	0.0767633i
$239$	−2.49246e6	+	6.84799e6i	−0.182572	+	0.501614i	−0.996890	−	0.0788060i	$-0.974889\pi$
$239$	−2.49246e6	+	6.84799e6i	−0.182572	+	0.501614i	0.814318	+	0.580420i	$0.197111\pi$
$240$	586448.	−	201628.i	0.0424225	−	0.0145853i
$241$	2.96144e6	−	1.67952e7i	0.211569	−	1.19987i	−0.675193	−	0.737641i	$-0.735940\pi$
$241$	2.96144e6	−	1.67952e7i	0.211569	−	1.19987i	0.886762	−	0.462226i	$-0.152949\pi$
$242$		−	507645.i		−	0.0358191i
$243$	−1.42972e7	+	1.21760e6i	−0.996393	+	0.0848569i
$244$	1.48267e7			1.02065
$245$	7.82123e6	+	1.37909e6i	0.531835	+	0.0937768i
$246$	4.17198e6	+	1.21345e7i	0.280245	+	0.815111i
$247$	4.95041e6	+	1.80180e6i	0.328511	+	0.119568i
$248$	−1.39326e7	−	1.66042e7i	−0.913433	−	1.08859i
$249$	1.83153e6	+	1.15985e7i	0.118636	+	0.751280i
$250$	6.50130e6	−	2.36628e6i	0.416083	−	0.151442i
$251$	−1.75560e7	−	1.01360e7i	−1.11021	−	0.640980i	−0.171326	−	0.985214i	$-0.554805\pi$
$251$	−1.75560e7	−	1.01360e7i	−1.11021	−	0.640980i	−0.938884	+	0.344234i	$0.888139\pi$
$252$	−1.26917e7	+	9.89701e6i	−0.793084	+	0.618447i
$253$	−2.21370e6	−	3.83424e6i	−0.136697	−	0.236765i
$254$	2.23526e6	−	2.66388e6i	0.136404	−	0.162560i
$255$	−16987.3	+	948125.i	−0.00102448	+	0.0571801i
$256$	−2.67275e6	−	1.51579e7i	−0.159309	−	0.903483i
$257$	6.05735e6	−	1.06807e6i	0.356848	−	0.0629219i	0.00764954	−	0.999971i	$-0.497565\pi$
$257$	6.05735e6	−	1.06807e6i	0.356848	−	0.0629219i	0.349198	+	0.937049i	$0.386454\pi$
$258$	515093.	−	856363.i	0.0299935	−	0.0498654i
$259$	1.62840e7	+	1.36639e7i	0.937261	+	0.786456i
$260$	−5.35839e6	+	3.09367e6i	−0.304870	+	0.176017i
$261$	1.98005e7	−	1.05047e7i	1.11367	−	0.590829i
$262$	2.65686e6	−	4.60182e6i	0.147729	−	0.255874i
$263$	4.80336e6	+	1.31971e7i	0.264045	+	0.725457i	0.998885	+	0.0472164i	$0.0150350\pi$
$263$	4.80336e6	+	1.31971e7i	0.264045	+	0.725457i	−0.734840	+	0.678241i	$0.762743\pi$
$264$	1.14934e7	+	1.42066e7i	0.624652	+	0.772109i
$265$	−5.21982e6	+	4.37995e6i	−0.280490	+	0.235359i
$266$	1.56055e6	−	4.28759e6i	0.0829152	−	0.227808i
$267$	2.54336e6	−	1.30523e7i	0.133621	−	0.685729i
$268$	969855.	−	5.50032e6i	0.0503851	−	0.285748i
$269$			2.97652e7i			1.52916i	0.644530	+	0.764579i	$0.277053\pi$
$269$			2.97652e7i			1.52916i	−0.644530	+	0.764579i	$0.722947\pi$
$270$	−256651.	+	4.77080e6i	−0.0130392	+	0.242382i
$271$	2.58564e7			1.29915			0.649577	−	0.760296i	$-0.274946\pi$
$271$	2.58564e7			1.29915			0.649577	+	0.760296i	$0.274946\pi$
$272$	−289170.	−	50988.5i	−0.0143697	−	0.00253376i
$273$	2.55078e7	−	2.93160e7i	1.25367	−	1.44084i
$274$	−1.34506e7	−	4.89562e6i	−0.653868	−	0.237988i
$275$	−1.13533e7	−	1.35304e7i	−0.545915	−	0.650596i
$276$	3.46184e6	+	1.33071e6i	0.164657	+	0.0632930i
$277$	2.67350e6	−	973074.i	0.125788	−	0.0457833i	−0.278359	−	0.960477i	$-0.589790\pi$
$277$	2.67350e6	−	973074.i	0.125788	−	0.0457833i	0.404147	+	0.914694i	$0.367568\pi$
$278$	−9.89124e6	−	5.71071e6i	−0.460380	−	0.265800i
$279$	−3.04636e7	+	9.86716e6i	−1.40271	+	0.454338i
$280$	6.70933e6	+	1.16209e7i	0.305636	+	0.529377i
$281$	−2.10351e7	+	2.50686e7i	−0.948037	+	1.12983i	0.0433756	+	0.999059i	$0.486189\pi$
$281$	−2.10351e7	+	2.50686e7i	−0.948037	+	1.12983i	−0.991413	+	0.130768i	$0.958256\pi$
$282$	−2.13060e7	+	1.17973e7i	−0.950069	+	0.526059i
$283$	−466638.	−	2.64643e6i	−0.0205883	−	0.116762i	0.972782	−	0.231724i	$-0.0744366\pi$
$283$	−466638.	−	2.64643e6i	−0.0205883	−	0.116762i	−0.993370	+	0.114962i	$0.963325\pi$
$284$	−1.86075e7	+	3.28101e6i	−0.812333	+	0.143236i
$285$	1.30183e6	+	2.35113e6i	0.0562368	+	0.101564i
$286$	−1.34980e7	−	1.13262e7i	−0.576995	−	0.484156i
$287$	4.61089e7	−	2.66210e7i	1.95047	−	1.12610i
$288$	−2.39619e7	−	5.11637e6i	−1.00310	−	0.214183i
$289$	−1.18443e7	+	2.05149e7i	−0.490699	+	0.849916i
$290$	−2.55259e6	−	7.01317e6i	−0.104661	−	0.287555i
$291$	−5.37589e6	+	1.39854e7i	−0.218158	+	0.567538i
$292$	5.55786e6	−	4.66360e6i	0.223233	−	0.187315i
$293$	6.75527e6	−	1.85600e7i	0.268559	−	0.737860i	−0.729962	−	0.683488i	$-0.760462\pi$
$293$	6.75527e6	−	1.85600e7i	0.268559	−	0.737860i	0.998521	−	0.0543722i	$-0.0173157\pi$
$294$	−1.42930e7	−	1.24363e7i	−0.562448	−	0.489384i
$295$	−1.12814e6	+	6.39800e6i	−0.0439438	+	0.249217i
$296$			2.02180e7i			0.779585i
$297$	2.58277e7	−	7.85724e6i	0.985863	−	0.299917i
$298$	−1.11160e7			−0.420049
$299$	−8.81875e6	−	1.55498e6i	−0.329908	−	0.0581717i
$300$	1.45226e7	+	2.82987e6i	0.537876	+	0.104810i
$301$	−3.89645e6	−	1.41819e6i	−0.142880	−	0.0520039i
$302$	5.51463e6	+	6.57207e6i	0.200214	+	0.238606i
$303$	−2.03794e7	+	1.64873e7i	−0.732594	+	0.592684i
$304$	−781985.	+	284619.i	−0.0278341	+	0.0101308i
$305$	−1.58157e7	−	9.13122e6i	−0.557430	−	0.321832i
$306$	1.20055e6	−	1.91734e6i	0.0419002	−	0.0669169i
$307$	−1.21010e7	−	2.09596e7i	−0.418223	−	0.724383i	0.577538	−	0.816364i	$-0.304014\pi$
$307$	−1.21010e7	−	2.09596e7i	−0.418223	−	0.724383i	−0.995761	+	0.0919806i	$0.970680\pi$
$308$	1.94639e7	−	2.31962e7i	0.666160	−	0.793898i
$309$	−3.90904e7	−	2.35124e7i	−1.32494	−	0.796934i
$310$	1.85147e6	+	1.05002e7i	0.0621485	+	0.352462i
$311$	1.00580e6	−	177349.i	0.0334371	−	0.00589587i	−0.156905	−	0.987614i	$-0.550152\pi$
$311$	1.00580e6	−	177349.i	0.0334371	−	0.00589587i	0.190342	+	0.981718i	$0.439040\pi$
$312$	3.69541e7	+	662094.i	1.21674	+	0.0218000i
$313$	−2.63950e7	−	2.21480e7i	−0.860773	−	0.722274i	0.101361	−	0.994850i	$-0.467680\pi$
$313$	−2.63950e7	−	2.21480e7i	−0.860773	−	0.722274i	−0.962134	+	0.272575i	$0.912125\pi$
$314$	1.50668e7	−	8.69882e6i	0.486667	−	0.280977i
$315$	1.96335e7	−	2.74084e6i	0.628155	−	0.0876903i
$316$	−4.28118e6	+	7.41522e6i	−0.135676	+	0.234997i
$317$	−2.74105e6	−	7.53099e6i	−0.0860478	−	0.236414i	0.889204	−	0.457511i	$-0.151259\pi$
$317$	−2.74105e6	−	7.53099e6i	−0.0860478	−	0.236414i	−0.975252	+	0.221096i	$0.929037\pi$
$318$	1.60564e7	−	2.53549e6i	0.499306	−	0.0788461i
$319$	−3.23050e7	+	2.71071e7i	−0.995172	+	0.835048i
$320$	−2.28756e6	+	6.28501e6i	−0.0698107	+	0.191803i
$321$	1.48295e7	−	5.09855e6i	0.448344	−	0.154146i
$322$	−1.34678e6	+	7.63799e6i	−0.0403395	+	0.228776i
$323$		−	1.27250e6i		−	0.0377615i
$324$	−1.26805e7	+	1.87250e7i	−0.372822	+	0.550537i
$325$	−3.57241e7			−1.04067
$326$	−4.90259e6	−	864459.i	−0.141505	−	0.0249512i
$327$	−1.93595e7	−	5.63085e7i	−0.553670	−	1.61039i
$328$	4.75853e7	+	1.73196e7i	1.34850	+	0.490814i
$329$	6.49547e7	+	7.74099e7i	1.82399	+	2.17375i
$330$	−1.40208e6	−	8.87888e6i	−0.0390148	−	0.247068i
$331$	−3.43454e7	+	1.25007e7i	−0.947074	+	0.344707i	−0.768956	−	0.639302i	$-0.779223\pi$
$331$	−3.43454e7	+	1.25007e7i	−0.947074	+	0.344707i	−0.178119	+	0.984009i	$0.557001\pi$
$332$	1.60269e7	+	9.25313e6i	0.437961	+	0.252857i
$333$	2.76836e7	+	1.12146e7i	0.749705	+	0.303706i
$334$	1.66790e7	+	2.88889e7i	0.447642	+	0.775339i
$335$	−4.42199e6	+	5.26993e6i	−0.117621	+	0.140175i
$336$	−109962.	+	6.13743e6i	−0.00289885	+	0.161796i
$337$	−8.02577e6	−	4.55164e7i	−0.209699	−	1.18926i	−0.889871	−	0.456212i	$-0.849206\pi$
$337$	−8.02577e6	−	4.55164e7i	−0.209699	−	1.18926i	0.680172	−	0.733053i	$-0.261905\pi$
$338$	−1.30837e7	+	2.30701e6i	−0.338829	+	0.0597447i
$339$	−3.14977e7	+	5.23663e7i	−0.808500	+	1.34416i
$340$	1.14488e6	+	960667.i	0.0291288	+	0.0244420i
$341$	5.21751e7	−	3.01233e7i	1.31583	−	0.759696i
$342$	229662.	−	6.40711e6i	0.00574131	−	0.160171i
$343$	−8.78691e6	+	1.52194e7i	−0.217748	+	0.377150i
$344$	−1.34886e6	−	3.70597e6i	−0.0331354	−	0.0910389i
$345$	−2.87323e6	−	3.55149e6i	−0.0699701	−	0.0864875i
$346$	3.11858e7	−	2.61680e7i	0.752885	−	0.631745i
$347$	−5.85569e6	+	1.60884e7i	−0.140149	+	0.385056i	−0.989833	−	0.142237i	$-0.954571\pi$
$347$	−5.85569e6	+	1.60884e7i	−0.140149	+	0.385056i	0.849684	+	0.527293i	$0.176793\pi$
$348$	6.75659e6	−	3.46742e7i	0.160321	−	0.822751i
$349$	−2.94112e6	+	1.66799e7i	−0.0691890	+	0.392390i	0.930472	+	0.366362i	$0.119397\pi$
$349$	−2.94112e6	+	1.66799e7i	−0.0691890	+	0.392390i	−0.999661	+	0.0260279i	$0.991714\pi$
$350$			3.09410e7i			0.721655i
$351$	2.14045e7	−	5.02323e7i	0.494975	−	1.16161i
$352$	4.60987e7			1.05697
$353$	2.70845e7	+	4.77572e6i	0.615739	+	0.108571i	0.472814	−	0.881162i	$-0.343238\pi$
$353$	2.70845e7	+	4.77572e6i	0.615739	+	0.108571i	0.142925	+	0.989734i	$0.454349\pi$
$354$	1.01733e7	−	1.16921e7i	0.229325	−	0.263563i
$355$	2.18694e7	+	7.95982e6i	0.488824	+	0.177917i
$356$	−1.34715e7	−	1.60547e7i	−0.298584	−	0.355838i
$357$	−8.76145e6	−	3.36784e6i	−0.192562	−	0.0740197i
$358$	1.36530e6	−	496929.i	0.0297563	−	0.0108304i
$359$	−1.22350e7	−	7.06389e6i	−0.264436	−	0.152672i	0.361920	−	0.932209i	$-0.382121\pi$
$359$	−1.22350e7	−	7.06389e6i	−0.264436	−	0.152672i	−0.626357	+	0.779537i	$0.715455\pi$
$360$	1.40002e7	+	1.26293e7i	0.300073	+	0.270689i
$361$	2.17198e7	+	3.76197e7i	0.461672	+	0.799639i
$362$	1.23160e7	−	1.46776e7i	0.259624	−	0.309407i
$363$	−2.58926e6	+	1.43369e6i	−0.0541321	+	0.0299733i
$364$	−1.06351e7	−	6.03144e7i	−0.220514	−	1.25060i
$365$	−8.80075e6	+	1.55181e6i	−0.180984	+	0.0319124i
$366$	2.11039e7	+	3.81140e7i	0.430448	+	0.777394i
$367$	−1.56183e7	−	1.31053e7i	−0.315962	−	0.265124i	0.470989	−	0.882139i	$-0.343897\pi$
$367$	−1.56183e7	−	1.31053e7i	−0.315962	−	0.265124i	−0.786951	+	0.617015i	$0.788342\pi$
$368$	1.22502e6	−	707266.i	0.0245810	−	0.0141919i
$369$	5.01099e7	−	5.55494e7i	0.997342	−	1.10561i
$370$	4.97267e6	−	8.61292e6i	0.0981713	−	0.170038i
$371$	−2.30685e7	−	6.33801e7i	−0.451749	−	1.24117i
$372$	−1.81078e7	+	4.71075e7i	−0.351753	+	0.915085i
$373$	−1.94046e7	+	1.62824e7i	−0.373919	+	0.313755i	−0.810310	−	0.586002i	$-0.800701\pi$
$373$	−1.94046e7	+	1.62824e7i	−0.373919	+	0.313755i	0.436390	+	0.899757i	$0.356257\pi$
$374$	−1.45569e6	+	3.99948e6i	−0.0278263	+	0.0764520i
$375$	−3.04302e7	−	2.64772e7i	−0.577046	−	0.502086i
$376$	−1.66896e7	+	9.46514e7i	−0.313966	+	1.78059i
$377$			8.52948e7i			1.59184i
$378$	−4.35066e7	−	1.85386e7i	−0.805526	−	0.343243i
$379$	−3.41464e7			−0.627230			−0.313615	−	0.949550i	$-0.601540\pi$
$379$	−3.41464e7			−0.627230			−0.313615	+	0.949550i	$0.601540\pi$
$380$	4.17126e6	+	735506.i	0.0760181	+	0.0134040i
$381$	−1.99000e7	−	3.87770e6i	−0.359814	−	0.0701132i
$382$	−3.40352e7	−	1.23878e7i	−0.610574	−	0.222231i
$383$	−3.71091e7	−	4.42250e7i	−0.660518	−	0.787175i	0.326942	−	0.945044i	$-0.393982\pi$
$383$	−3.71091e7	−	4.42250e7i	−0.660518	−	0.787175i	−0.987460	+	0.157870i	$0.949537\pi$
$384$	−3.27480e7	+	2.64938e7i	−0.578351	+	0.467898i
$385$	−3.50480e7	+	1.27564e7i	−0.614159	+	0.223536i
$386$	1.47505e7	+	8.51622e6i	0.256475	+	0.148076i
$387$	−5.82262e6	−	208711.i	−0.100458	−	0.00360091i
$388$	1.18070e7	+	2.04503e7i	0.202136	+	0.350110i
$389$	2.18970e7	−	2.60958e7i	0.371993	−	0.443324i	−0.547277	−	0.836952i	$-0.684336\pi$
$389$	2.18970e7	−	2.60958e7i	0.371993	−	0.443324i	0.919270	+	0.393627i	$0.128780\pi$
$390$	−1.55797e7	−	9.37099e6i	−0.262642	−	0.157976i
$391$	375602.	+	2.13014e6i	0.00628344	+	0.0356351i
$392$	−7.36332e7	+	1.29835e7i	−1.22241	+	0.215543i
$393$	−3.09752e7	−	554972.i	−0.510312	−	0.00914311i
$394$	−3.28065e7	−	2.75279e7i	−0.536378	−	0.450075i
$395$	9.13352e6	−	5.27324e6i	0.148199	−	0.0855630i
$396$	1.59751e7	−	3.94349e7i	0.257251	−	0.635031i
$397$	2.23743e7	−	3.87534e7i	0.357584	−	0.619354i	−0.629973	−	0.776617i	$-0.716934\pi$
$397$	2.23743e7	−	3.87534e7i	0.357584	−	0.619354i	0.987557	+	0.157264i	$0.0502672\pi$
$398$	−3.65895e6	−	1.00529e7i	−0.0580373	−	0.159456i
$399$	−2.62762e7	+	4.14932e6i	−0.413661	+	0.0653218i
$400$	4.32288e6	−	3.62733e6i	0.0675450	−	0.0566770i
$401$	−3.43165e7	+	9.42839e7i	−0.532195	+	1.46219i	0.324259	+	0.945968i	$0.394885\pi$
$401$	−3.43165e7	+	9.42839e7i	−0.532195	+	1.46219i	−0.856454	+	0.516224i	$0.827337\pi$
$402$	1.55198e7	−	5.33587e6i	0.238895	−	0.0821348i
$403$	2.11597e7	−	1.20003e8i	0.323292	−	1.83348i
$404$			4.13140e7i			0.626546i
$405$	2.50584e7	−	1.21646e7i	0.377215	−	0.183119i
$406$	7.38745e7			1.10387
$407$	−5.53425e7	−	9.75837e6i	−0.820872	−	0.144742i
$408$	−2.90264e6	−	8.44253e6i	−0.0427379	−	0.124306i
$409$	7.85514e7	+	2.85904e7i	1.14811	+	0.417878i	0.844836	−	0.535025i	$-0.179698\pi$
$409$	7.85514e7	+	2.85904e7i	1.14811	+	0.417878i	0.303275	+	0.952903i	$0.401920\pi$
$410$	−1.60116e7	−	1.90819e7i	−0.232318	−	0.276866i
$411$	1.30168e7	+	8.24312e7i	0.187491	+	1.18732i
$412$	−6.75587e7	+	2.45893e7i	−0.966027	+	0.351605i
$413$	−5.56916e7	−	3.21536e7i	−0.790568	−	0.456435i
$414$	1.50673e6	+	1.07932e7i	0.0212341	+	0.152107i
$415$	−1.13973e7	−	1.97407e7i	−0.159462	−	0.276197i
$416$	5.99326e7	−	7.14248e7i	0.832497	−	0.992132i
$417$	−1.19287e6	+	6.65786e7i	−0.0164507	+	0.918177i
$418$	2.09459e6	+	1.18790e7i	0.0286794	+	0.162649i
$419$	3.70435e7	−	6.53177e6i	0.503582	−	0.0887951i	0.0839143	−	0.996473i	$-0.473258\pi$
$419$	3.70435e7	−	6.53177e6i	0.503582	−	0.0887951i	0.419667	+	0.907678i	$0.362147\pi$
$420$	1.61040e7	−	2.67735e7i	0.217363	−	0.361374i
$421$	8.79853e7	+	7.38284e7i	1.17914	+	0.989412i	0.999984	+	0.00559091i	$0.00177965\pi$
$421$	8.79853e7	+	7.38284e7i	1.17914	+	0.989412i	0.179151	+	0.983822i	$0.442665\pi$
$422$	−4.46663e7	+	2.57881e7i	−0.594350	+	0.343148i
$423$	1.20344e8	+	7.53541e7i	1.59003	+	0.995602i
$424$	3.20752e7	−	5.55559e7i	0.420797	−	0.728841i
$425$	2.95131e6	+	8.10867e6i	0.0384458	+	0.105629i
$426$	−3.49197e7	−	4.31630e7i	−0.451692	−	0.558319i
$427$	1.38477e8	−	1.16196e8i	1.77867	−	1.49248i
$428$	8.45298e6	−	2.32244e7i	0.107815	−	0.296219i
$429$	−1.96485e7	+	1.00834e8i	−0.248861	+	1.27713i
$430$	−336874.	+	1.91051e6i	−0.00423704	+	0.0240294i
$431$		−	1.42123e8i		−	1.77514i	−0.460675	−	0.887569i	$-0.652393\pi$
$431$		−	1.42123e8i		−	1.77514i	0.460675	−	0.887569i	$-0.347607\pi$
$432$	2.51035e6	+	8.25182e6i	0.0311374	+	0.102352i
$433$	−3.45368e7			−0.425420			−0.212710	−	0.977115i	$-0.568229\pi$
$433$	−3.45368e7			−0.425420			−0.212710	+	0.977115i	$0.568229\pi$
$434$	−1.03935e8	−	1.83266e7i	−1.27143	−	0.224188i
$435$	−2.85618e7	+	3.28260e7i	−0.346991	+	0.398796i
$436$	−8.81842e7	−	3.20964e7i	−1.06398	−	0.387255i
$437$	3.94035e6	+	4.69593e6i	0.0472162	+	0.0562701i
$438$	1.98993e7	+	7.64916e6i	0.236818	+	0.0910315i
$439$	8.89712e7	−	3.23829e7i	1.05161	−	0.382756i	0.242342	−	0.970191i	$-0.422084\pi$
$439$	8.89712e7	−	3.23829e7i	1.05161	−	0.382756i	0.809271	+	0.587435i	$0.199862\pi$
$440$	−3.07214e7	−	1.77370e7i	−0.360647	−	0.208220i
$441$	−2.30655e7	+	1.08024e8i	−0.268935	+	1.25952i
$442$	4.30422e6	+	7.45512e6i	0.0498457	+	0.0863352i
$443$	−2.46172e7	+	2.93377e7i	−0.283158	+	0.337454i	−0.888811	−	0.458275i	$-0.848468\pi$
$443$	−2.46172e7	+	2.93377e7i	−0.283158	+	0.337454i	0.605653	+	0.795729i	$0.292912\pi$
$444$	4.11832e7	−	2.28034e7i	0.470513	−	0.260526i
$445$	4.48263e6	+	2.54223e7i	0.0508690	+	0.288492i
$446$	9.20688e7	−	1.62342e7i	1.03779	−	0.182990i
$447$	3.13937e7	+	5.66975e7i	0.351496	+	0.634806i
$448$	−5.07154e7	−	4.25553e7i	−0.564035	−	0.473282i
$449$	1.31025e8	−	7.56475e7i	1.44749	−	0.835710i	0.449160	−	0.893451i	$-0.351723\pi$
$449$	1.31025e8	−	7.56475e7i	1.44749	−	0.835710i	0.998332	+	0.0577415i	$0.0183899\pi$
$450$	1.33966e7	+	4.13603e7i	0.147013	+	0.453885i
$451$	−7.03761e7	+	1.21895e8i	−0.767177	+	1.32879i
$452$	3.29404e7	+	9.05029e7i	0.356708	+	0.980048i
$453$	1.79467e7	−	4.66882e7i	0.193059	−	0.502242i
$454$	−3.85049e7	+	3.23095e7i	−0.411480	+	0.345273i
$455$	−2.58009e7	+	7.08875e7i	−0.273906	+	0.752550i
$456$	−1.90875e7	−	1.66080e7i	−0.201305	−	0.175155i
$457$	307977.	−	1.74662e6i	0.00322678	−	0.0183000i	−0.983152	−	0.182791i	$-0.941487\pi$
$457$	307977.	−	1.74662e6i	0.00322678	−	0.0183000i	0.986379	+	0.164491i	$0.0525980\pi$
$458$			9.21932e7i			0.959627i
$459$	−1.31700e7	−	708497.i	−0.136191	−	0.00732656i
$460$	−7.19973e6			−0.0739678
$461$	−7.31707e7	−	1.29020e7i	−0.746852	−	0.131690i	−0.212746	−	0.977108i	$-0.568241\pi$
$461$	−7.31707e7	−	1.29020e7i	−0.746852	−	0.131690i	−0.534106	+	0.845418i	$0.679352\pi$
$462$	8.73333e7	+	1.70177e7i	0.885633	+	0.172574i
$463$	5.04325e7	+	1.83559e7i	0.508121	+	0.184941i	0.583343	−	0.812226i	$-0.301744\pi$
$463$	5.04325e7	+	1.83559e7i	0.508121	+	0.184941i	−0.0752219	+	0.997167i	$0.523967\pi$
$464$	−8.66058e6	−	1.03213e7i	−0.0866948	−	0.103319i
$465$	4.83275e7	−	3.90979e7i	0.480657	−	0.388862i
$466$	−7.73101e6	+	2.81386e6i	−0.0763974	+	0.0278064i
$467$	5.63621e7	+	3.25407e7i	0.553396	+	0.319504i	0.750491	−	0.660881i	$-0.229817\pi$
$467$	5.63621e7	+	3.25407e7i	0.553396	+	0.319504i	−0.197094	+	0.980385i	$0.563151\pi$
$468$	−4.03309e7	−	7.60205e7i	−0.393460	−	0.741640i
$469$	−3.40476e7	−	5.89722e7i	−0.330041	−	0.571648i
$470$	3.03895e7	−	3.62168e7i	0.292705	−	0.348832i
$471$	−8.69200e7	−	5.22814e7i	−0.831873	−	0.500362i
$472$	−1.06209e7	−	6.02342e7i	−0.101003	−	0.572819i
$473$	1.07953e7	−	1.90351e6i	0.102012	−	0.0179875i
$474$	−2.51555e7	−	450703.i	−0.236210	−	0.00423209i
$475$	1.87339e7	+	1.57196e7i	0.174802	+	0.146677i
$476$	−1.28116e7	+	7.39676e6i	−0.118790	+	0.0685837i
$477$	−5.82786e7	−	7.47353e7i	−0.536975	−	0.688605i
$478$	−1.68743e7	+	2.92272e7i	−0.154505	+	0.267611i
$479$	−1.81967e7	−	4.99951e7i	−0.165572	−	0.454905i	0.828964	−	0.559302i	$-0.188931\pi$
$479$	−1.81967e7	−	4.99951e7i	−0.165572	−	0.454905i	−0.994536	+	0.104397i	$0.966709\pi$
$480$	4.69826e7	−	7.41909e6i	0.424829	−	0.0670853i
$481$	−8.70698e7	+	7.30602e7i	−0.782406	+	0.656517i
$482$	2.70124e7	−	7.42161e7i	0.241225	−	0.662761i
$483$	4.27613e7	−	1.47018e7i	0.379498	−	0.130476i
$484$	−810000.	+	4.59374e6i	−0.00714412	+	0.0405163i
$485$		−	2.90860e7i		−	0.254952i
$486$	−6.61841e7	−	5.94427e6i	−0.576560	−	0.0517833i
$487$	7.90455e7			0.684369			0.342185	−	0.939633i	$-0.388833\pi$
$487$	7.90455e7			0.684369			0.342185	+	0.939633i	$0.388833\pi$
$488$	1.69320e8	+	2.98557e7i	1.45697	+	0.256902i
$489$	9.43665e6	+	2.74472e7i	0.0807033	+	0.234731i
$490$	3.45612e7	+	1.25792e7i	0.293765	+	0.106922i
$491$	−5.67709e7	−	6.76570e7i	−0.479603	−	0.571568i	0.470939	−	0.882166i	$-0.343915\pi$
$491$	−5.67709e7	−	6.76570e7i	−0.479603	−	0.571568i	−0.950541	+	0.310598i	$0.899471\pi$
$492$	−1.83909e7	−	1.16463e8i	−0.154421	−	0.977899i
$493$	1.93602e7	−	7.04654e6i	0.161573	−	0.0588078i
$494$	2.11283e7	+	1.21985e7i	0.175261	+	0.101187i
$495$	−4.13272e7	+	3.22269e7i	−0.340738	+	0.265707i
$496$	9.62424e6	+	1.66697e7i	0.0788717	+	0.136610i
$497$	−1.48076e8	+	1.76470e8i	−1.20619	+	1.43748i
$498$	−974127.	+	5.43698e7i	−0.00788729	+	0.440220i
$499$	1.88863e7	+	1.07109e8i	0.152000	+	0.862036i	0.961477	+	0.274885i	$0.0886396\pi$
$499$	1.88863e7	+	1.07109e8i	0.152000	+	0.862036i	−0.809477	+	0.587152i	$0.800249\pi$
$500$	−6.26067e7	+	1.10392e7i	−0.500853	+	0.0883140i
$501$	1.00244e8	−	1.66659e8i	0.797158	−	1.32531i
$502$	−7.19166e7	−	6.03452e7i	−0.568484	−	0.477014i
$503$	−1.03125e8	+	5.95392e7i	−0.810326	+	0.467842i	−0.847069	−	0.531483i	$-0.821635\pi$
$503$	−1.03125e8	+	5.95392e7i	−0.810326	+	0.467842i	0.0367432	+	0.999325i	$0.488302\pi$
$504$	−1.64868e8	+	8.74667e7i	−1.28779	+	0.683205i
$505$	2.54437e7	−	4.40699e7i	0.197564	−	0.342190i
$506$	−7.01262e6	−	1.92670e7i	−0.0541288	−	0.148718i
$507$	4.87178e7	+	6.02183e7i	0.373821	+	0.462067i
$508$	−2.44777e7	+	2.05392e7i	−0.186715	+	0.156672i
$509$	3.64720e7	−	1.00206e8i	0.276571	−	0.759871i	−0.721175	−	0.692753i	$-0.756397\pi$
$509$	3.64720e7	−	1.00206e8i	0.276571	−	0.759871i	0.997745	−	0.0671179i	$-0.0213803\pi$
$510$	−839931.	+	4.31045e6i	−0.00633188	+	0.0324946i
$511$	1.53605e7	−	8.71135e7i	0.115118	−	0.652864i
$512$			2.85673e7i			0.212843i
$513$	−3.33282e7	+	1.69235e7i	−0.246865	+	0.125354i
$514$	2.84846e7			0.209759
$515$	8.72089e7	+	1.53773e7i	0.638468	+	0.112579i
$516$	−6.02755e6	+	6.92745e6i	−0.0438724	+	0.0504225i
$517$	−2.51032e8	−	9.13683e7i	−1.81659	−	0.661186i
$518$	6.32780e7	+	7.54118e7i	0.455264	+	0.542563i
$519$	−2.21545e8	−	8.51605e7i	−1.58475	−	0.609166i
$520$	−6.74221e7	+	2.45396e7i	−0.479504	+	0.174525i
$521$	−4.33858e7	−	2.50488e7i	−0.306785	−	0.177123i	0.338702	−	0.940894i	$-0.390012\pi$
$521$	−4.33858e7	−	2.50488e7i	−0.306785	−	0.177123i	−0.645487	+	0.763771i	$0.723346\pi$
$522$	9.87516e7	−	3.19856e7i	0.694277	−	0.224876i
$523$	2.03058e7	+	3.51706e7i	0.141943	+	0.245852i	0.928228	−	0.372011i	$-0.121332\pi$
$523$	2.03058e7	+	3.51706e7i	0.141943	+	0.245852i	−0.786285	+	0.617864i	$0.787998\pi$
$524$	−3.13849e7	+	3.74031e7i	−0.218136	+	0.259964i
$525$	1.57815e8	−	8.73831e7i	1.09061	−	0.603879i
$526$	1.12939e7	+	6.40507e7i	0.0776043	+	0.440116i
$527$	−2.89863e7	+	5.11106e6i	−0.198044	+	0.0349204i
$528$	−7.86080e6	−	1.41967e7i	−0.0534029	−	0.0964464i
$529$	1.05420e8	+	8.84578e7i	0.712124	+	0.597543i
$530$	−2.73282e7	+	1.57780e7i	−0.183562	+	0.105980i
$531$	−8.83673e7	−	1.88683e7i	−0.590212	−	0.126023i
$532$	−2.09629e7	+	3.63089e7i	−0.139225	+	0.241145i
$533$	9.73673e7	+	2.67514e8i	0.643030	+	1.76671i
$534$	2.20958e7	−	5.74821e7i	0.145106	−	0.377493i
$535$	−2.33199e7	+	1.95677e7i	−0.152288	+	0.127785i
$536$	2.21514e7	−	6.08604e7i	0.143849	−	0.395222i
$537$	−6.39047e6	−	5.56033e6i	−0.0412676	−	0.0359069i
$538$	−2.39364e7	+	1.35750e8i	−0.153714	+	0.871753i
$539$		−	2.07821e8i		−	1.32716i
$540$	9.93477e6	−	4.27620e7i	0.0630923	−	0.271567i
$541$	−1.68168e8			−1.06207			−0.531033	−	0.847351i	$-0.678196\pi$
$541$	−1.68168e8			−1.06207			−0.531033	+	0.847351i	$0.678196\pi$
$542$	1.17923e8	+	2.07930e7i	0.740630	+	0.130593i
$543$	−1.09646e8	−	2.13656e7i	−0.684849	−	0.133449i
$544$	−2.11633e7	−	7.70280e6i	−0.131458	−	0.0478467i
$545$	7.42996e7	+	8.85469e7i	0.458984	+	0.546995i
$546$	1.39908e8	−	1.13189e8i	0.859539	−	0.695384i
$547$	1.76730e8	−	6.43244e7i	1.07981	−	0.393019i	0.259974	−	0.965616i	$-0.416286\pi$
$547$	1.76730e8	−	6.43244e7i	1.07981	−	0.393019i	0.819837	+	0.572597i	$0.194064\pi$
$548$	1.13905e8	+	6.57628e7i	0.692149	+	0.399612i
$549$	1.34800e8	−	2.15282e8i	0.814651	−	1.30104i
$550$	−4.08983e7	−	7.08379e7i	−0.245820	−	0.425772i
$551$	3.75321e7	−	4.47290e7i	0.224361	−	0.267383i
$552$	3.68544e7	+	2.21675e7i	0.219115	+	0.131795i
$553$	1.81277e7	+	1.02807e8i	0.107193	+	0.607924i
$554$	1.29755e7	−	2.28794e6i	0.0763125	−	0.0134560i
$555$	−5.79741e7	−	1.03870e6i	−0.339121	−	0.00607593i
$556$	8.03949e7	+	6.74594e7i	0.467740	+	0.392480i
$557$	−1.56494e8	+	9.03520e7i	−0.905592	+	0.522844i	−0.879010	−	0.476803i	$-0.841796\pi$
$557$	−1.56494e8	+	9.03520e7i	−0.905592	+	0.522844i	−0.0265818	+	0.999647i	$0.508462\pi$
$558$	−1.46870e8	+	2.05030e7i	−0.845339	+	0.118009i
$559$	1.10857e7	−	1.92009e7i	0.0634638	−	0.109922i
$560$	−4.07561e6	−	1.11976e7i	−0.0232075	−	0.0637621i
$561$	2.45106e7	−	3.87050e6i	0.138824	−	0.0219219i
$562$	−1.16094e8	+	9.74146e7i	−0.654036	+	0.548801i
$563$	8.98132e7	−	2.46760e8i	0.503286	−	1.38277i	−0.384762	−	0.923016i	$-0.625716\pi$
$563$	8.98132e7	−	2.46760e8i	0.503286	−	1.38277i	0.888048	−	0.459751i	$-0.152061\pi$
$564$	2.11624e8	−	7.27589e7i	1.17958	−	0.405554i
$565$	2.05997e7	−	1.16827e8i	0.114213	−	0.647734i
$566$		−	1.24448e7i		−	0.0686341i
$567$	2.83144e7	+	2.74263e8i	0.155331	+	1.50459i
$568$	−2.19104e8			−1.19565
$569$	5.06397e7	+	8.92915e6i	0.274887	+	0.0484700i	0.309392	−	0.950934i	$-0.399874\pi$
$569$	5.06397e7	+	8.92915e6i	0.274887	+	0.0484700i	−0.0345050	+	0.999405i	$0.510985\pi$
$570$	4.04655e6	+	1.17697e7i	0.0218504	+	0.0635535i
$571$	6.92271e7	+	2.51966e7i	0.371850	+	0.135342i	0.521184	−	0.853445i	$-0.325491\pi$
$571$	6.92271e7	+	2.51966e7i	0.371850	+	0.135342i	−0.149334	+	0.988787i	$0.547713\pi$
$572$	1.04073e8	+	1.24029e8i	0.556096	+	0.662730i
$573$	3.29376e7	+	2.08583e8i	0.175077	+	1.10870i
$574$	2.31696e8	−	8.43306e7i	1.22513	−	0.445912i
$575$	−3.60002e7	−	2.07847e7i	−0.189366	−	0.109330i
$576$	−8.62191e7	−	3.49274e7i	−0.451165	−	0.182767i
$577$	−9.09157e7	−	1.57471e8i	−0.473273	−	0.819732i	0.526259	−	0.850324i	$-0.323594\pi$
$577$	−9.09157e7	−	1.57471e8i	−0.473273	−	0.819732i	−0.999532	+	0.0305920i	$0.990261\pi$
$578$	−7.05157e7	+	8.40373e7i	−0.365176	+	0.435200i
$579$	1.77889e6	−	9.92868e7i	0.00916460	−	0.511512i
$580$	1.19084e7	+	6.75359e7i	0.0610337	+	0.346139i
$581$	2.22203e8	−	3.91804e7i	1.13298	−	0.199775i
$582$	−3.57644e7	+	5.94599e7i	−0.181419	+	0.301616i
$583$	1.36591e8	+	1.14613e8i	0.689313	+	0.578402i
$584$	7.28613e7	−	4.20665e7i	0.365813	−	0.211202i
$585$	−3.79704e6	+	1.05930e8i	−0.0189661	+	0.529116i
$586$	4.57342e7	−	7.92139e7i	0.227273	−	0.393648i
$587$	−3.57857e7	−	9.83204e7i	−0.176927	−	0.486104i	0.819252	−	0.573434i	$-0.194389\pi$
$587$	−3.57857e7	−	9.83204e7i	−0.176927	−	0.486104i	−0.996179	+	0.0873294i	$0.972167\pi$
$588$	1.09496e8	+	1.35344e8i	0.538599	+	0.665742i
$589$	−6.39007e7	+	5.36191e7i	−0.312723	+	0.262406i
$590$	−1.02902e7	+	2.82721e7i	−0.0501035	+	0.137658i
$591$	−4.77550e7	+	2.45074e8i	−0.231343	+	1.18723i
$592$	3.11775e6	−	1.76816e7i	0.0150271	−	0.0852230i
$593$		−	1.65827e8i		−	0.795225i	−0.917553	−	0.397612i	$-0.869839\pi$
$593$		−	1.65827e8i		−	0.795225i	0.917553	−	0.397612i	$-0.130161\pi$
$594$	1.24111e8	−	1.50645e7i	0.592176	−	0.0718780i
$595$	1.82216e7			0.0865037
$596$	1.00590e8	+	1.77367e7i	0.475134	+	0.0837790i
$597$	−4.09413e7	+	4.70538e7i	−0.192415	+	0.221142i
$598$	−3.89691e7	−	1.41836e7i	−0.182229	−	0.0663259i
$599$	−9.62910e7	−	1.14755e8i	−0.448028	−	0.533939i	0.494005	−	0.869459i	$-0.335532\pi$
$599$	−9.62910e7	−	1.14755e8i	−0.448028	−	0.533939i	−0.942033	+	0.335520i	$0.891088\pi$
$600$	1.60149e8	+	6.15604e7i	0.741433	+	0.285002i
$601$	−7.71302e7	+	2.80731e7i	−0.355305	+	0.129320i	−0.513505	−	0.858087i	$-0.671653\pi$
$601$	−7.71302e7	+	2.80731e7i	−0.355305	+	0.129320i	0.158200	+	0.987407i	$0.449431\pi$
$602$	−1.66301e7	−	9.60137e6i	−0.0762262	−	0.0440092i
$603$	−7.10464e7	−	6.40893e7i	−0.324034	−	0.292303i
$604$	−3.94161e7	−	6.82706e7i	−0.178880	−	0.309830i
$605$	3.69315e6	−	4.40132e6i	0.0166775	−	0.0198754i
$606$	−1.06203e8	+	5.88052e7i	−0.477220	+	0.264239i
$607$	5.03298e7	+	2.85434e8i	0.225040	+	1.27626i	0.862609	+	0.505871i	$0.168829\pi$
$607$	5.03298e7	+	2.85434e8i	0.225040	+	1.27626i	−0.637570	+	0.770393i	$0.720060\pi$
$608$	−6.28578e7	+	1.10835e7i	−0.279672	+	0.0493137i
$609$	−2.08636e8	−	3.76798e8i	−0.923712	−	1.66823i
$610$	−6.47877e7	−	5.43633e7i	−0.285432	−	0.239506i
$611$	−4.67930e8	+	2.70159e8i	−2.05143	+	1.18440i
$612$	−1.39232e7	+	1.54347e7i	−0.0607416	+	0.0673353i
$613$	1.51128e8	−	2.61762e8i	0.656091	−	1.13638i	−0.325528	−	0.945533i	$-0.605542\pi$
$613$	1.51128e8	−	2.61762e8i	0.656091	−	1.13638i	0.981619	−	0.190851i	$-0.0611248\pi$
$614$	−3.83340e7	−	1.05322e8i	−0.165607	−	0.455002i
$615$	−5.21078e7	+	1.35558e8i	−0.224015	+	0.582776i
$616$	2.68986e8	−	2.25706e8i	1.15077	−	0.965609i
$617$	−2.27681e7	+	6.25548e7i	−0.0969329	+	0.266321i	−0.978676	−	0.205408i	$-0.934148\pi$
$617$	−2.27681e7	+	6.25548e7i	−0.0969329	+	0.266321i	0.881743	+	0.471729i	$0.156370\pi$
$618$	−1.59371e8	−	1.38668e8i	−0.675219	−	0.587506i
$619$	−1.42750e7	+	8.09574e7i	−0.0601871	+	0.341338i	−1.00000		0.000351585i	$-0.999888\pi$
$619$	−1.42750e7	+	8.09574e7i	−0.0601871	+	0.341338i	0.939813	+	0.341690i	$0.110999\pi$
$620$		−	9.79716e7i		−	0.411079i
$621$	5.07956e7	−	3.81671e7i	0.212105	−	0.159373i
$622$	4.72975e6			0.0196547
$623$	−2.51640e8	−	4.43710e7i	−1.04068	−	0.183500i
$624$	−3.22160e7	−	6.27758e6i	−0.132592	−	0.0258368i
$625$	−1.15499e8	−	4.20381e7i	−0.473083	−	0.172188i
$626$	−1.02569e8	−	1.22237e8i	−0.418111	−	0.498285i
$627$	5.46736e7	−	4.42320e7i	0.221807	−	0.179446i
$628$	−1.50221e8	+	5.46760e7i	−0.606529	+	0.220759i
$629$	2.37764e7	+	1.37273e7i	0.0955419	+	0.0551612i
$630$	9.17467e7	+	3.28865e6i	0.366918	+	0.0131521i
$631$	−4.43309e7	−	7.67834e7i	−0.176449	−	0.305618i	0.764213	−	0.644964i	$-0.223128\pi$
$631$	−4.43309e7	−	7.67834e7i	−0.176449	−	0.305618i	−0.940662	+	0.339346i	$0.889794\pi$
$632$	−6.38224e7	+	7.60606e7i	−0.252826	+	0.301307i
$633$	2.57679e8	+	1.54991e8i	1.01594	+	0.611076i
$634$	−6.44489e6	−	3.65508e7i	−0.0252899	−	0.143426i
$635$	3.87598e7	−	6.83440e6i	0.151377	−	0.0266919i
$636$	−1.49342e8	−	2.67571e6i	−0.580510	−	0.0104008i
$637$	−3.21996e8	−	2.70187e8i	−1.24575	−	1.04531i
$638$	−1.69132e8	+	9.76485e7i	−0.651274	+	0.376013i
$639$	−1.21534e8	+	3.00009e8i	−0.465795	+	1.14983i
$640$	4.08860e7	−	7.08167e7i	0.155968	−	0.270144i
$641$	6.95470e7	+	1.91079e8i	0.264061	+	0.725501i	0.998883	+	0.0472419i	$0.0150432\pi$
$641$	6.95470e7	+	1.91079e8i	0.264061	+	0.725501i	−0.734823	+	0.678259i	$0.762735\pi$
$642$	7.17330e7	−	1.13275e7i	0.271090	−	0.0428082i
$643$	2.61570e8	−	2.19483e8i	0.983909	−	0.825597i	−0.000765804	−	1.00000i	$-0.500244\pi$
$643$	2.61570e8	−	2.19483e8i	0.983909	−	0.825597i	0.984674	+	0.174402i	$0.0557993\pi$
$644$	2.43744e7	−	6.69681e7i	0.0912591	−	0.250732i
$645$	1.06960e7	−	3.67740e6i	0.0398604	−	0.0137045i
$646$	1.02331e6	−	5.80348e6i	0.00379585	−	0.0215274i
$647$		−	1.53729e8i		−	0.567600i	−0.958883	−	0.283800i	$-0.908405\pi$
$647$		−	1.53729e8i		−	0.567600i	0.958883	−	0.283800i	$-0.0915952\pi$
$648$	−1.82516e8	+	1.88304e8i	−0.670775	+	0.692046i
$649$	1.70004e8			0.621908
$650$	−1.62927e8	−	2.87284e7i	−0.593270	−	0.104610i
$651$	2.00058e8	+	5.81882e8i	0.725124	+	2.10907i
$652$	4.29848e7	+	1.56452e7i	0.155086	+	0.0564466i
$653$	−1.44486e8	−	1.72191e8i	−0.518902	−	0.618403i	0.441419	−	0.897301i	$-0.354475\pi$
$653$	−1.44486e8	−	1.72191e8i	−0.518902	−	0.618403i	−0.960321	+	0.278898i	$0.910031\pi$
$654$	−4.30110e7	−	2.72374e8i	−0.153761	−	0.973717i
$655$	5.65137e7	−	2.05693e7i	0.201108	−	0.0731974i
$656$	−3.89448e7	−	2.24848e7i	−0.137955	−	0.0796484i
$657$	−1.71847e7	−	1.23100e8i	−0.0605961	−	0.434070i
$658$	2.33987e8	+	4.05278e8i	0.821324	+	1.42258i
$659$	1.81674e8	−	2.16511e8i	0.634800	−	0.756525i	−0.348740	−	0.937220i	$-0.613390\pi$
$659$	1.81674e8	−	2.16511e8i	0.634800	−	0.756525i	0.983539	+	0.180695i	$0.0578347\pi$
$660$	−1.47962e6	+	8.25831e7i	−0.00514656	+	0.287250i
$661$	−3.77695e7	−	2.14201e8i	−0.130779	−	0.741682i	−0.977707	−	0.209975i	$-0.932662\pi$
$661$	−3.77695e7	−	2.14201e8i	−0.130779	−	0.741682i	0.846928	−	0.531707i	$-0.178449\pi$
$662$	−1.66691e8	+	2.93922e7i	−0.574565	+	0.101311i
$663$	2.58691e7	−	4.30084e7i	0.0887648	−	0.147575i
$664$	1.64394e8	+	1.37943e8i	0.561540	+	0.471188i
$665$	4.47226e7	−	2.58206e7i	0.152076	−	0.0878013i
$666$	1.17238e8	+	7.34090e7i	0.396868	+	0.248500i
$667$	−4.96255e7	+	8.59539e7i	−0.167235	+	0.289660i
$668$	−1.04835e8	−	2.88032e8i	−0.351704	−	0.966299i
$669$	−3.42823e8	−	4.23750e8i	−1.14496	−	1.41525i
$670$	−2.44053e7	+	2.04785e7i	−0.0811446	+	0.0680884i
$671$	−1.63447e8	+	4.49068e8i	−0.541016	+	1.48643i
$672$	−9.00493e7	+	4.62125e8i	−0.296737	+	1.52283i
$673$	−6.17420e7	+	3.50157e8i	−0.202552	+	1.14873i	0.698695	+	0.715420i	$0.253765\pi$
$673$	−6.17420e7	+	3.50157e8i	−0.202552	+	1.14873i	−0.901246	+	0.433307i	$0.857346\pi$
$674$		−	2.14041e8i		−	0.699063i
$675$	1.73125e8	−	1.85139e8i	0.562921	−	0.601986i
$676$	1.22077e8			0.395179
$677$	−1.26944e7	−	2.23836e6i	−0.0409115	−	0.00721380i	0.153155	−	0.988202i	$-0.451057\pi$
$677$	−1.26944e7	−	2.23836e6i	−0.0409115	−	0.00721380i	−0.194066	+	0.980988i	$0.562168\pi$
$678$	−1.85763e8	+	2.13497e8i	−0.596033	+	0.685019i
$679$	2.70542e8	+	9.84694e7i	0.864223	+	0.314552i
$680$	1.11400e7	+	1.32762e7i	0.0354290	+	0.0422226i
$681$	2.73540e8	+	1.05147e8i	0.866124	+	0.332933i
$682$	2.62179e8	−	9.54254e7i	0.826504	−	0.300823i
$683$	5.32739e8	+	3.07577e8i	1.67206	+	0.965366i	0.966481	+	0.256738i	$0.0826476\pi$
$683$	5.32739e8	+	3.07577e8i	1.67206	+	0.965366i	0.705582	+	0.708628i	$0.250686\pi$
$684$	−1.23014e7	+	5.76122e7i	−0.0384404	+	0.180031i
$685$	−8.10018e7	−	1.40299e8i	−0.252013	−	0.436499i
$686$	−5.23134e7	+	6.23447e7i	−0.162047	+	0.193120i
$687$	4.70233e8	−	2.60371e8i	1.45025	−	0.803013i
$688$	608161.	+	3.44905e6i	0.00186747	+	0.0105909i
$689$	3.55162e8	−	6.26246e7i	1.08585	−	0.191464i
$690$	−1.02479e7	−	1.85078e7i	−0.0311952	−	0.0563389i
$691$	4.00671e7	+	3.36203e7i	0.121438	+	0.101898i	0.701484	−	0.712685i	$-0.252521\pi$
$691$	4.00671e7	+	3.36203e7i	0.121438	+	0.101898i	−0.580046	+	0.814583i	$0.696966\pi$
$692$	−3.23957e8	+	1.87037e8i	−0.977619	+	0.564429i
$693$	−1.59847e8	−	4.93507e8i	−0.480290	−	1.48284i
$694$	−3.96438e7	+	6.86652e7i	−0.118603	+	0.205427i
$695$	−4.42120e7	−	1.21472e8i	−0.131700	−	0.361843i
$696$	1.46981e8	−	3.82372e8i	0.435948	−	1.13412i
$697$	5.26766e7	−	4.42009e7i	0.155568	−	0.130537i
$698$	−2.68271e7	+	7.37069e7i	−0.0788875	+	0.216742i
$699$	3.61860e7	+	3.14853e7i	0.105952	+	0.0921885i
$700$	4.93695e7	−	2.79988e8i	0.143934	−	0.816293i
$701$			2.39326e8i			0.694761i	0.937724	+	0.347380i	$0.112929\pi$
$701$			2.39326e8i			0.694761i	−0.937724	+	0.347380i	$0.887071\pi$
$702$	1.38015e8	−	2.11881e8i	0.398946	−	0.612465i
$703$	7.78083e7			0.223955
$704$	1.72361e8	+	3.03919e7i	0.493993	+	0.0871042i
$705$	−2.70550e8	−	5.27193e7i	−0.772113	−	0.150453i
$706$	1.19683e8	+	4.35612e7i	0.340111	+	0.123790i
$707$	3.23776e8	+	3.85861e8i	0.916191	+	1.09187i
$708$	−1.10715e8	+	8.95709e7i	−0.311966	+	0.252387i
$709$	−3.85457e8	+	1.40295e8i	−1.08153	+	0.393643i	−0.820475	−	0.571682i	$-0.806291\pi$
$709$	−3.85457e8	+	1.40295e8i	−1.08153	+	0.393643i	−0.261051	+	0.965325i	$0.584069\pi$
$710$	9.33387e7	+	5.38891e7i	0.260787	+	0.150566i
$711$	6.87450e7	+	1.29579e8i	0.191264	+	0.360517i
$712$	−1.21515e8	−	2.10471e8i	−0.336660	−	0.583112i
$713$	9.11421e7	−	1.08619e8i	0.251449	−	0.299666i
$714$	−3.72500e7	−	2.24054e7i	−0.102337	−	0.0615543i
$715$	−3.46302e7	−	1.96398e8i	−0.0947407	−	0.537301i
$716$	−1.31477e7	+	2.31829e6i	−0.0358187	+	0.00631580i
$717$	1.96730e8	+	3.52475e6i	0.533720	+	0.00956250i
$718$	−5.01196e7	−	4.20553e7i	−0.135405	−	0.113618i
$719$	4.79822e8	−	2.77026e8i	1.29090	−	0.745304i	0.312089	−	0.950053i	$-0.398971\pi$
$719$	4.79822e8	−	2.77026e8i	1.29090	−	0.745304i	0.978814	+	0.204749i	$0.0656379\pi$
$720$	−1.02963e7	−	1.32038e7i	−0.0275858	−	0.0353754i
$721$	−4.38274e8	+	7.59112e8i	−1.16934	+	2.02535i
$722$	6.88044e7	+	1.89039e8i	0.182812	+	0.502272i
$723$	−4.54829e8	+	7.18227e7i	−1.20346	+	0.190041i
$724$	−1.34869e8	+	1.13168e8i	−0.355382	+	0.298201i
$725$	−1.35423e8	+	3.72072e8i	−0.355369	+	0.976367i
$726$	−1.29617e7	+	4.45639e6i	−0.0338730	+	0.0116459i
$727$	4.10034e7	−	2.32542e8i	0.106713	−	0.605198i	−0.883810	−	0.467847i	$-0.845030\pi$
$727$	4.10034e7	−	2.32542e8i	0.106713	−	0.605198i	0.990522	−	0.137351i	$-0.0438590\pi$
$728$		−	7.10202e8i		−	1.84072i
$729$	1.56598e8	+	3.54361e8i	0.404206	+	0.914668i
$730$	−4.13854e7			−0.106385
$731$	−5.27405e6	−	929958.i	−0.0135018	−	0.00238074i
$732$	−1.30157e8	−	3.78571e8i	−0.331845	−	0.965194i
$733$	−1.37415e8	−	5.00149e7i	−0.348917	−	0.126995i	0.161616	−	0.986854i	$-0.448329\pi$
$733$	−1.37415e8	−	5.00149e7i	−0.348917	−	0.126995i	−0.510532	+	0.859859i	$0.670552\pi$
$734$	−6.06912e7	−	7.23290e7i	−0.153475	−	0.182904i
$735$	−3.34466e7	−	2.11806e8i	−0.0842346	−	0.533429i
$736$	1.01951e8	−	3.71073e7i	0.255717	−	0.0930735i
$737$	1.55901e8	+	9.00093e7i	0.389445	+	0.224846i
$738$	2.73207e8	−	2.13047e8i	0.679709	−	0.530037i
$739$	1.93674e8	+	3.35454e8i	0.479887	+	0.831188i	0.999734	−	0.0230714i	$-0.00734449\pi$
$739$	1.93674e8	+	3.35454e8i	0.479887	+	0.831188i	−0.519847	+	0.854259i	$0.674011\pi$
$740$	−5.87410e7	+	7.00049e7i	−0.144959	+	0.172756i
$741$	2.54804e6	−	1.42216e8i	0.00626257	−	0.349538i
$742$	−5.42396e7	−	3.07608e8i	−0.132772	−	0.752985i
$743$	−2.29493e8	+	4.04659e7i	−0.559505	+	0.0986558i	−0.446247	−	0.894910i	$-0.647240\pi$
$743$	−2.29493e8	+	4.04659e7i	−0.559505	+	0.0986558i	−0.113258	+	0.993566i	$0.536129\pi$
$744$	−3.01648e8	+	5.01503e8i	−0.732457	+	1.21774i
$745$	−9.63766e7	−	8.08696e7i	−0.233079	−	0.195576i
$746$	−1.01592e8	+	5.86543e7i	−0.244706	+	0.141281i
$747$	2.80066e8	−	1.48582e8i	0.671890	−	0.356455i
$748$	1.95543e7	−	3.38691e7i	0.0467237	−	0.0809279i
$749$	−1.03060e8	−	2.83155e8i	−0.245270	−	0.673873i
$750$	−1.17490e8	−	1.45226e8i	−0.278496	−	0.344238i
$751$	−4.47426e8	+	3.75435e8i	−1.05633	+	0.886369i	−0.993745	−	0.111670i	$-0.964380\pi$
$751$	−4.47426e8	+	3.75435e8i	−1.05633	+	0.886369i	−0.0625883	+	0.998039i	$0.519936\pi$
$752$	2.91917e7	−	8.02035e7i	0.0686445	−	0.188599i
$753$	−1.04686e8	+	5.37238e8i	−0.245190	+	1.25829i
$754$	−6.85918e7	+	3.89003e8i	−0.160014	+	0.907485i
$755$			9.70996e7i			0.225619i
$756$	3.64116e8	+	2.37177e8i	0.842703	+	0.548918i
$757$	3.77019e7			0.0869113			0.0434556	−	0.999055i	$-0.486163\pi$
$757$	3.77019e7			0.0869113			0.0434556	+	0.999055i	$0.486163\pi$
$758$	−1.55731e8	−	2.74596e7i	−0.357576	−	0.0630502i
$759$

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(4.56069 + 0.804173i) q^{2} +(-8.77856 - 25.5331i) q^{3} +(-39.9871 - 14.5541i) q^{4} +(33.6911 + 40.1515i) q^{5} +(-19.5033 - 123.508i) q^{6} +(-487.528 + 177.446i) q^{7} +(-427.344 - 246.727i) q^{8} +(-574.874 + 448.287i) q^{9} +O(q^{10})\)	\(q+(4.56069 + 0.804173i) q^{2} +(-8.77856 - 25.5331i) q^{3} +(-39.9871 - 14.5541i) q^{4} +(33.6911 + 40.1515i) q^{5} +(-19.5033 - 123.508i) q^{6} +(-487.528 + 177.446i) q^{7} +(-427.344 - 246.727i) q^{8} +(-574.874 + 448.287i) q^{9} +(121.366 + 210.212i) q^{10} +(881.622 - 1050.68i) q^{11} +(-20.5819 + 1148.76i) q^{12} +(-481.717 - 2731.95i) q^{13} +(-2366.16 + 417.219i) q^{14} +(729.432 - 1212.71i) q^{15} +(335.685 + 281.674i) q^{16} +(-580.302 + 335.037i) q^{17} +(-2982.32 + 1582.20i) q^{18} +(-949.519 + 1644.62i) q^{19} +(-762.841 - 2095.89i) q^{20} +(8810.53 + 10890.4i) q^{21} +(4865.73 - 4082.84i) q^{22} +(1104.04 - 3033.33i) q^{23} +(-2548.23 + 13077.3i) q^{24} +(2236.20 - 12682.1i) q^{25} -12847.0i q^{26} +(16492.7 + 10743.0i) q^{27} +22077.4 q^{28} +(-30279.8 - 5339.14i) q^{29} +(4301.94 - 4944.21i) q^{30} +(41276.6 + 15023.4i) q^{31} +(21604.4 + 25747.1i) q^{32} +(-34566.4 - 13287.1i) q^{33} +(-2916.01 + 1061.34i) q^{34} +(-23550.1 - 13596.7i) q^{35} +(29512.0 - 9558.91i) q^{36} +(-20486.2 - 35483.2i) q^{37} +(-5653.02 + 6737.01i) q^{38} +(-65526.3 + 36282.3i) q^{39} +(-4491.23 - 25471.0i) q^{40} +(-101063. + 17820.1i) q^{41} +(31424.4 + 56752.8i) q^{42} +(6122.43 + 5137.33i) q^{43} +(-50545.2 + 29182.3i) q^{44} +(-37367.6 - 7978.77i) q^{45} +(7474.52 - 12946.3i) q^{46} +(-66616.3 - 183027. i) q^{47} +(4245.15 - 11043.8i) q^{48} +(116073. - 97396.4i) q^{49} +(20397.2 - 56041.0i) q^{50} +(13648.7 + 11875.7i) q^{51} +(-20498.7 + 116254. i) q^{52} +130003. i q^{53} +(66578.9 + 62258.4i) q^{54} +71889.1 q^{55} +(252123. + 44456.1i) q^{56} +(50327.5 + 9806.78i) q^{57} +(-133803. - 48700.4i) q^{58} +(79673.2 + 94950.9i) q^{59} +(-46817.8 + 37876.5i) q^{60} +(-327414. + 119169. i) q^{61} +(176168. + 101711. i) q^{62} +(200721. - 320561. i) q^{63} +(63803.1 + 110510. i) q^{64} +(93462.4 - 111384. i) q^{65} +(-146961. - 88395.7i) q^{66} +(22791.5 + 129257. i) q^{67} +(28080.8 - 4951.40i) q^{68} +(-87142.1 - 1561.30i) q^{69} +(-96470.7 - 80948.6i) q^{70} +(384533. - 222011. i) q^{71} +(356273. - 49735.7i) q^{72} +(-85249.1 + 147656. i) q^{73} +(-64896.8 - 178302. i) q^{74} +(-343444. + 54233.7i) q^{75} +(61904.5 - 51944.0i) q^{76} +(-243378. + 668675. i) q^{77} +(-328023. + 112778. i) q^{78} +(34940.5 - 198158. i) q^{79} +22968.2i q^{80} +(129519. - 515417. i) q^{81} -475247. q^{82} +(-428288. - 75518.8i) q^{83} +(-193808. - 563704. i) q^{84} +(-33003.3 - 12012.2i) q^{85} +(23791.2 + 28353.3i) q^{86} +(129488. + 820005. i) q^{87} +(-635986. + 231480. i) q^{88} +(426526. + 246255. i) q^{89} +(-164006. - 66438.7i) q^{90} +(719624. + 1.24642e6i) q^{91} +(-88294.9 + 105226. i) q^{92} +(21245.6 - 1.18580e6i) q^{93} +(-156631. - 888300. i) q^{94} +(-98024.2 + 17284.3i) q^{95} +(467746. - 777647. i) q^{96} +(-425098. - 356700. i) q^{97} +(607695. - 350853. i) q^{98} +(-35817.1 + 999226. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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