LMFDB - Embedded newform 27.4.e.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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([2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	27.4
Dual form			27.4.e.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12171 - 0.772239i) q^{2} +(-0.789571 + 5.13581i) q^{3} +(-2.22306 - 1.86537i) q^{4} +(-3.33920 + 18.9376i) q^{5} +(5.64131 - 10.2870i) q^{6} +(0.500915 - 0.420318i) q^{7} +(12.3077 + 21.3175i) q^{8} +(-25.7532 - 8.11018i) q^{9} +O(q^{10})$	\(q+(-2.12171 - 0.772239i) q^{2} +(-0.789571 + 5.13581i) q^{3} +(-2.22306 - 1.86537i) q^{4} +(-3.33920 + 18.9376i) q^{5} +(5.64131 - 10.2870i) q^{6} +(0.500915 - 0.420318i) q^{7} +(12.3077 + 21.3175i) q^{8} +(-25.7532 - 8.11018i) q^{9} +(21.7091 - 37.6013i) q^{10} +(-4.24549 - 24.0774i) q^{11} +(11.3355 - 9.94439i) q^{12} +(36.6094 - 13.3247i) q^{13} +(-1.38738 + 0.504965i) q^{14} +(-94.6232 - 32.1021i) q^{15} +(-5.61966 - 31.8707i) q^{16} +(-20.0093 + 34.6572i) q^{17} +(48.3777 + 37.0950i) q^{18} +(76.3151 + 132.182i) q^{19} +(42.7488 - 35.8705i) q^{20} +(1.76317 + 2.90448i) q^{21} +(-9.58578 + 54.3637i) q^{22} +(89.8865 + 75.4237i) q^{23} +(-119.201 + 46.3782i) q^{24} +(-230.019 - 83.7201i) q^{25} -87.9642 q^{26} +(61.9863 - 125.860i) q^{27} -1.89761 q^{28} +(-83.5721 - 30.4178i) q^{29} +(175.972 + 141.183i) q^{30} +(58.9074 + 49.4292i) q^{31} +(21.5068 - 121.971i) q^{32} +(127.009 - 2.79325i) q^{33} +(69.2176 - 58.0805i) q^{34} +(6.28713 + 10.8896i) q^{35} +(42.1224 + 66.0686i) q^{36} +(108.072 - 187.187i) q^{37} +(-59.8426 - 339.384i) q^{38} +(39.5276 + 198.540i) q^{39} +(-444.800 + 161.894i) q^{40} +(-48.1790 + 17.5357i) q^{41} +(-1.49797 - 7.52404i) q^{42} +(26.9611 + 152.904i) q^{43} +(-35.4752 + 61.4449i) q^{44} +(239.582 - 460.620i) q^{45} +(-132.468 - 229.441i) q^{46} +(100.384 - 84.2318i) q^{47} +(168.119 - 3.69736i) q^{48} +(-59.4871 + 337.368i) q^{49} +(423.381 + 355.259i) q^{50} +(-162.194 - 130.129i) q^{51} +(-106.240 - 38.6684i) q^{52} -362.751 q^{53} +(-228.711 + 219.170i) q^{54} +470.143 q^{55} +(15.1252 + 5.50514i) q^{56} +(-739.116 + 287.573i) q^{57} +(153.826 + 129.075i) q^{58} +(60.3962 - 342.524i) q^{59} +(150.471 + 247.872i) q^{60} +(279.664 - 234.666i) q^{61} +(-86.8132 - 150.365i) q^{62} +(-16.3090 + 6.76200i) q^{63} +(-269.271 + 466.392i) q^{64} +(130.092 + 737.786i) q^{65} +(-271.633 - 92.1548i) q^{66} +(749.971 - 272.967i) q^{67} +(109.131 - 39.7203i) q^{68} +(-458.334 + 402.088i) q^{69} +(-4.93007 - 27.9598i) q^{70} +(-185.178 + 320.737i) q^{71} +(-144.073 - 648.811i) q^{72} +(-253.302 - 438.733i) q^{73} +(-373.851 + 313.698i) q^{74} +(611.587 - 1115.23i) q^{75} +(76.9145 - 436.204i) q^{76} +(-12.2468 - 10.2763i) q^{77} +(69.4540 - 451.768i) q^{78} +(-143.391 - 52.1900i) q^{79} +622.318 q^{80} +(597.450 + 417.725i) q^{81} +115.763 q^{82} +(457.778 + 166.617i) q^{83} +(1.49830 - 9.74579i) q^{84} +(-589.508 - 494.656i) q^{85} +(60.8748 - 345.238i) q^{86} +(222.206 - 405.194i) q^{87} +(461.018 - 386.840i) q^{88} +(44.9643 + 77.8804i) q^{89} +(-864.032 + 792.287i) q^{90} +(12.7376 - 22.0621i) q^{91} +(-59.1301 - 335.343i) q^{92} +(-300.371 + 263.510i) q^{93} +(-278.032 + 101.195i) q^{94} +(-2758.03 + 1003.84i) q^{95} +(609.440 + 206.760i) q^{96} +(197.390 + 1119.46i) q^{97} +(386.743 - 669.858i) q^{98} +(-85.9370 + 654.500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−2.12171	−	0.772239i	−0.750137	−	0.273028i	−0.0614736	−	0.998109i	$-0.519580\pi$
$2$	−2.12171	−	0.772239i	−0.750137	−	0.273028i	−0.688663	+	0.725081i	$0.741802\pi$
$3$	−0.789571	+	5.13581i	−0.151953	+	0.988388i
$3$	−0.789571	+	5.13581i	−0.151953	+	0.988388i
$4$	−2.22306	−	1.86537i	−0.277883	−	0.233171i
$5$	−3.33920	+	18.9376i	−0.298667	+	1.69383i	0.353244	+	0.935531i	$0.385079\pi$
$5$	−3.33920	+	18.9376i	−0.298667	+	1.69383i	−0.651911	+	0.758295i	$0.726033\pi$
$6$	5.64131	−	10.2870i	0.383843	−	0.699939i
$7$	0.500915	−	0.420318i	0.0270469	−	0.0226950i	−0.629164	−	0.777273i	$-0.716603\pi$
$7$	0.500915	−	0.420318i	0.0270469	−	0.0226950i	0.656211	+	0.754578i	$0.272158\pi$
$8$	12.3077	+	21.3175i	0.543928	+	0.942110i
$9$	−25.7532	−	8.11018i	−0.953821	−	0.300377i
$10$	21.7091	−	37.6013i	0.686503	−	1.18906i
$11$	−4.24549	−	24.0774i	−0.116369	−	0.659964i	−0.986063	−	0.166372i	$-0.946795\pi$
$11$	−4.24549	−	24.0774i	−0.116369	−	0.659964i	0.869694	−	0.493592i	$-0.164316\pi$
$12$	11.3355	−	9.94439i	0.272689	−	0.239225i
$13$	36.6094	−	13.3247i	0.781047	−	0.284278i	0.0794378	−	0.996840i	$-0.474687\pi$
$13$	36.6094	−	13.3247i	0.781047	−	0.284278i	0.701609	+	0.712562i	$0.252465\pi$
$14$	−1.38738	+	0.504965i	−0.0264852	+	0.00963984i
$15$	−94.6232	−	32.1021i	−1.62877	−	0.552581i
$16$	−5.61966	−	31.8707i	−0.0878073	−	0.497980i
$17$	−20.0093	+	34.6572i	−0.285469	+	0.494448i	−0.972723	−	0.231970i	$-0.925483\pi$
$17$	−20.0093	+	34.6572i	−0.285469	+	0.494448i	0.687253	+	0.726418i	$0.258816\pi$
$18$	48.3777	+	37.0950i	0.633485	+	0.485743i
$19$	76.3151	+	132.182i	0.921467	+	1.59603i	0.797146	+	0.603786i	$0.206342\pi$
$19$	76.3151	+	132.182i	0.921467	+	1.59603i	0.124321	+	0.992242i	$0.460325\pi$
$20$	42.7488	−	35.8705i	0.477946	−	0.401045i
$21$	1.76317	+	2.90448i	0.0183216	+	0.0301814i
$22$	−9.58578	+	54.3637i	−0.0928953	+	0.526835i
$23$	89.8865	+	75.4237i	0.814897	+	0.683779i	0.951771	−	0.306809i	$-0.0992613\pi$
$23$	89.8865	+	75.4237i	0.814897	+	0.683779i	−0.136874	+	0.990588i	$0.543706\pi$
$24$	−119.201	+	46.3782i	−1.01382	+	0.394455i
$25$	−230.019	−	83.7201i	−1.84015	−	0.669761i
$26$	−87.9642			−0.663508
$27$	61.9863	−	125.860i	0.441825	−	0.897101i
$28$	−1.89761			−0.0128077
$29$	−83.5721	−	30.4178i	−0.535136	−	0.194774i	0.0602939	−	0.998181i	$-0.480796\pi$
$29$	−83.5721	−	30.4178i	−0.535136	−	0.194774i	−0.595430	+	0.803407i	$0.703018\pi$
$30$	175.972	+	141.183i	1.07093	+	0.859212i
$31$	58.9074	+	49.4292i	0.341293	+	0.286379i	0.797283	−	0.603606i	$-0.206270\pi$
$31$	58.9074	+	49.4292i	0.341293	+	0.286379i	−0.455990	+	0.889985i	$0.650715\pi$
$32$	21.5068	−	121.971i	0.118809	−	0.673801i
$33$	127.009	−	2.79325i	0.669983	−	0.0147346i
$34$	69.2176	−	58.0805i	0.349139	−	0.292962i
$35$	6.28713	+	10.8896i	0.0303634	+	0.0525910i
$36$	42.1224	+	66.0686i	0.195011	+	0.305873i
$37$	108.072	−	187.187i	0.480189	−	0.831711i	−0.519553	−	0.854438i	$-0.673901\pi$
$37$	108.072	−	187.187i	0.480189	−	0.831711i	0.999742	+	0.0227269i	$0.00723483\pi$
$38$	−59.8426	−	339.384i	−0.255467	−	1.44883i
$39$	39.5276	+	198.540i	0.162294	+	0.815174i
$40$	−444.800	+	161.894i	−1.75822	+	0.639941i
$41$	−48.1790	+	17.5357i	−0.183519	+	0.0667956i	−0.432145	−	0.901804i	$-0.642243\pi$
$41$	−48.1790	+	17.5357i	−0.183519	+	0.0667956i	0.248626	+	0.968600i	$0.420021\pi$
$42$	−1.49797	−	7.52404i	−0.00550338	−	0.0276425i
$43$	26.9611	+	152.904i	0.0956169	+	0.542271i	0.994557	+	0.104198i	$0.0332276\pi$
$43$	26.9611	+	152.904i	0.0956169	+	0.542271i	−0.898940	+	0.438073i	$0.855661\pi$
$44$	−35.4752	+	61.4449i	−0.121548	+	0.210527i
$45$	239.582	−	460.620i	0.793661	−	1.52589i
$46$	−132.468	−	229.441i	−0.424594	−	0.735418i
$47$	100.384	−	84.2318i	0.311542	−	0.261414i	−0.473587	−	0.880747i	$-0.657041\pi$
$47$	100.384	−	84.2318i	0.311542	−	0.261414i	0.785129	+	0.619332i	$0.212597\pi$
$48$	168.119	−	3.69736i	0.505540	−	0.0111181i
$49$	−59.4871	+	337.368i	−0.173432	+	0.983580i
$50$	423.381	+	355.259i	1.19750	+	1.00482i
$51$	−162.194	−	130.129i	−0.445328	−	0.357287i
$52$	−106.240	−	38.6684i	−0.283325	−	0.103122i
$53$	−362.751			−0.940144			−0.470072	−	0.882628i	$-0.655772\pi$
$53$	−362.751			−0.940144			−0.470072	+	0.882628i	$0.655772\pi$
$54$	−228.711	+	219.170i	−0.576363	+	0.552319i
$55$	470.143			1.15262
$56$	15.1252	+	5.50514i	0.0360928	+	0.0131367i
$57$	−739.116	+	287.573i	−1.71751	+	0.668246i
$58$	153.826	+	129.075i	0.348247	+	0.292214i
$59$	60.3962	−	342.524i	0.133270	−	0.755811i	−0.842779	−	0.538260i	$-0.819082\pi$
$59$	60.3962	−	342.524i	0.133270	−	0.755811i	0.976049	−	0.217551i	$-0.0698069\pi$
$60$	150.471	+	247.872i	0.323762	+	0.533336i
$61$	279.664	−	234.666i	0.587006	−	0.492556i	−0.300234	−	0.953866i	$-0.597065\pi$
$61$	279.664	−	234.666i	0.587006	−	0.492556i	0.887239	+	0.461310i	$0.152620\pi$
$62$	−86.8132	−	150.365i	−0.177827	−	0.308006i
$63$	−16.3090	+	6.76200i	−0.0326149	+	0.0135227i
$64$	−269.271	+	466.392i	−0.525921	+	0.910921i
$65$	130.092	+	737.786i	0.248244	+	1.40786i
$66$	−271.633	−	92.1548i	−0.506602	−	0.171871i
$67$	749.971	−	272.967i	1.36752	−	0.497735i	0.449146	−	0.893458i	$-0.351728\pi$
$67$	749.971	−	272.967i	1.36752	−	0.497735i	0.918370	+	0.395723i	$0.129506\pi$
$68$	109.131	−	39.7203i	0.194618	−	0.0708352i
$69$	−458.334	+	402.088i	−0.799665	+	0.701531i
$70$	−4.93007	−	27.9598i	−0.00841794	−	0.0477405i
$71$	−185.178	+	320.737i	−0.309529	+	0.536119i	−0.978259	−	0.207385i	$-0.933505\pi$
$71$	−185.178	+	320.737i	−0.309529	+	0.536119i	0.668731	+	0.743505i	$0.266838\pi$
$72$	−144.073	−	648.811i	−0.235821	−	1.06199i
$73$	−253.302	−	438.733i	−0.406121	−	0.703421i	0.588331	−	0.808620i	$-0.299785\pi$
$73$	−253.302	−	438.733i	−0.406121	−	0.703421i	−0.994451	+	0.105199i	$0.966452\pi$
$74$	−373.851	+	313.698i	−0.587288	+	0.492793i
$75$	611.587	−	1115.23i	0.941600	−	1.71701i
$76$	76.9145	−	436.204i	0.116088	−	0.658369i
$77$	−12.2468	−	10.2763i	−0.0181253	−	0.0152089i
$78$	69.4540	−	451.768i	0.100822	−	0.655803i
$79$	−143.391	−	52.1900i	−0.204212	−	0.0743270i	0.237889	−	0.971292i	$-0.423544\pi$
$79$	−143.391	−	52.1900i	−0.204212	−	0.0743270i	−0.442101	+	0.896965i	$0.645767\pi$
$80$	622.318			0.869716
$81$	597.450	+	417.725i	0.819547	+	0.573012i
$82$	115.763			0.155902
$83$	457.778	+	166.617i	0.605393	+	0.220345i	0.626486	−	0.779432i	$-0.284492\pi$
$83$	457.778	+	166.617i	0.605393	+	0.220345i	−0.0210932	+	0.999778i	$0.506715\pi$
$84$	1.49830	−	9.74579i	0.00194617	−	0.0126590i
$85$	−589.508	−	494.656i	−0.752248	−	0.631211i
$86$	60.8748	−	345.238i	0.0763290	−	0.432883i
$87$	222.206	−	405.194i	0.273828	−	0.499326i
$88$	461.018	−	386.840i	0.558462	−	0.468605i
$89$	44.9643	+	77.8804i	0.0535529	+	0.0927563i	0.891559	−	0.452904i	$-0.149612\pi$
$89$	44.9643	+	77.8804i	0.0535529	+	0.0927563i	−0.838006	+	0.545661i	$0.816279\pi$
$90$	−864.032	+	792.287i	−1.01197	+	0.927938i
$91$	12.7376	−	22.0621i	0.0146732	−	0.0254147i
$92$	−59.1301	−	335.343i	−0.0670080	−	0.380021i
$93$	−300.371	+	263.510i	−0.334914	+	0.293814i
$94$	−278.032	+	101.195i	−0.305072	+	0.111037i
$95$	−2758.03	+	1003.84i	−2.97861	+	1.08412i
$96$	609.440	+	206.760i	0.647924	+	0.219816i
$97$	197.390	+	1119.46i	0.206618	+	1.17179i	0.894873	+	0.446320i	$0.147266\pi$
$97$	197.390	+	1119.46i	0.206618	+	1.17179i	−0.688255	+	0.725468i	$0.741623\pi$
$98$	386.743	−	669.858i	0.398642	−	0.690468i
$99$	−85.9370	+	654.500i	−0.0872424	+	0.664442i
$100$	355.178	+	615.186i	0.355178	+	0.615186i
$101$	188.919	−	158.522i	0.186121	−	0.156174i	−0.544967	−	0.838458i	$-0.683458\pi$
$101$	188.919	−	158.522i	0.186121	−	0.156174i	0.731087	+	0.682284i	$0.239013\pi$
$102$	243.638	+	401.348i	0.236508	+	0.389601i
$103$	69.8300	−	396.026i	0.0668015	−	0.378850i	−0.933018	−	0.359831i	$-0.882834\pi$
$103$	69.8300	−	396.026i	0.0668015	−	0.378850i	0.999819	−	0.0190194i	$-0.00605442\pi$
$104$	734.626	+	616.425i	0.692654	+	0.581206i
$105$	−60.8913	+	23.6914i	−0.0565941	+	0.0220195i
$106$	769.651	+	280.130i	0.705237	+	0.256685i
$107$	1634.47			1.47673			0.738365	−	0.674401i	$-0.235598\pi$
$107$	1634.47			1.47673			0.738365	+	0.674401i	$0.235598\pi$
$108$	−372.575	+	164.167i	−0.331954	+	0.146268i
$109$	−1970.93			−1.73193			−0.865965	−	0.500104i	$-0.833295\pi$
$109$	−1970.93			−1.73193			−0.865965	+	0.500104i	$0.833295\pi$
$110$	−997.506	−	363.063i	−0.864623	−	0.314697i
$111$	876.026	+	702.837i	0.749087	+	0.600994i
$112$	−16.2108	−	13.6025i	−0.0136766	−	0.0114760i
$113$	407.313	−	2309.99i	0.339087	−	1.92306i	−0.0433162	−	0.999061i	$-0.513792\pi$
$113$	407.313	−	2309.99i	0.339087	−	1.92306i	0.382403	−	0.923996i	$-0.375097\pi$
$114$	1790.26	−	39.3724i	1.47082	−	0.0323471i
$115$	−1728.49	+	1450.37i	−1.40159	+	1.17607i
$116$	129.046	+	223.514i	0.103290	+	0.178903i
$117$	−1050.87	+	46.2451i	−0.830369	+	0.0365415i
$118$	−392.653	+	680.096i	−0.306328	+	0.530575i
$119$	4.54405	+	25.7706i	0.00350044	+	0.0198520i
$120$	−480.255	−	2412.23i	−0.365343	−	1.83505i
$121$	689.035	−	250.788i	0.517682	−	0.188421i
$122$	−774.584	+	281.926i	−0.574816	+	0.209216i
$123$	−52.0194	−	261.284i	−0.0381336	−	0.191538i
$124$	−38.7511	−	219.768i	−0.0280641	−	0.159160i
$125$	1151.68	−	1994.77i	0.824074	−	1.42734i
$126$	39.8248	−	1.75254i	0.0281577	−	0.00123912i
$127$	562.199	+	973.757i	0.392812	+	0.680370i	0.992819	−	0.119624i	$-0.0381690\pi$
$127$	562.199	+	973.757i	0.392812	+	0.680370i	−0.600007	+	0.799994i	$0.704836\pi$
$128$	172.467	−	144.717i	0.119095	−	0.0999323i
$129$	−806.574	+	17.7386i	−0.550503	+	0.0121070i
$130$	293.730	−	1665.83i	0.198168	−	1.12387i
$131$	−354.923	−	297.815i	−0.236715	−	0.198628i	0.516711	−	0.856160i	$-0.327156\pi$
$131$	−354.923	−	297.815i	−0.236715	−	0.198628i	−0.753427	+	0.657532i	$0.771601\pi$
$132$	−287.559	−	230.709i	−0.189612	−	0.152126i
$133$	93.7856	+	34.1352i	0.0611447	+	0.0222549i
$134$	−1802.02			−1.16172
$135$	2176.49	+	1594.14i	1.38758	+	1.01631i
$136$	−985.074			−0.621099
$137$	1596.78	+	581.180i	0.995781	+	0.362435i	0.787956	−	0.615731i	$-0.211139\pi$
$137$	1596.78	+	581.180i	0.995781	+	0.362435i	0.207825	+	0.978166i	$0.433362\pi$
$138$	1282.96	−	499.170i	0.791396	−	0.307914i
$139$	828.306	+	695.032i	0.505439	+	0.424114i	0.859521	−	0.511101i	$-0.170762\pi$
$139$	828.306	+	695.032i	0.505439	+	0.424114i	−0.354082	+	0.935214i	$0.615207\pi$
$140$	6.33652	−	35.9362i	0.00382524	−	0.0216940i
$141$	353.339	+	582.058i	0.211039	+	0.347647i
$142$	640.578	−	537.509i	0.378564	−	0.317653i
$143$	−476.249	−	824.887i	−0.278503	−	0.482381i
$144$	−113.753	+	866.348i	−0.0658293	+	0.501359i
$145$	855.102	−	1481.08i	0.489741	−	0.848256i
$146$	198.627	+	1126.47i	0.112593	+	0.638545i
$147$	−1685.69	−	571.890i	−0.945805	−	0.320876i
$148$	−589.425	+	214.533i	−0.327368	+	0.119152i
$149$	1177.72	−	428.656i	0.647536	−	0.235684i	0.00269001	−	0.999996i	$-0.499144\pi$
$149$	1177.72	−	428.656i	0.647536	−	0.235684i	0.644846	+	0.764313i	$0.276922\pi$
$150$	−2158.83	+	1893.91i	−1.17512	+	1.03091i
$151$	−395.026	−	2240.30i	−0.212892	−	1.20737i	−0.884526	−	0.466490i	$-0.845518\pi$
$151$	−395.026	−	2240.30i	−0.212892	−	1.20737i	0.671634	−	0.740883i	$-0.265593\pi$
$152$	−1878.52	+	3253.70i	−1.00242	+	1.73625i
$153$	796.380	−	730.253i	0.420807	−	0.385866i
$154$	18.0484	+	31.2607i	0.00944401	+	0.0163575i
$155$	−1132.77	+	950.508i	−0.587009	+	0.492559i
$156$	282.478	−	515.100i	0.144977	−	0.264365i
$157$	−160.719	+	911.484i	−0.0816993	+	0.463340i	0.916321	+	0.400445i	$0.131144\pi$
$157$	−160.719	+	911.484i	−0.0816993	+	0.463340i	−0.998020	+	0.0628948i	$0.979967\pi$
$158$	263.930	+	221.464i	0.132893	+	0.111511i
$159$	286.417	−	1863.02i	0.142858	−	0.929227i
$160$	2238.02	+	814.572i	1.10582	+	0.402485i
$161$	76.7274			0.0375588
$162$	−945.031	−	1347.67i	−0.458325	−	0.653596i
$163$	−177.938			−0.0855042			−0.0427521	−	0.999086i	$-0.513613\pi$
$163$	−177.938			−0.0855042			−0.0427521	+	0.999086i	$0.513613\pi$
$164$	139.816	+	50.8887i	0.0665717	+	0.0242301i
$165$	−371.211	+	2414.57i	−0.175144	+	1.13923i
$166$	−842.602	−	707.027i	−0.393968	−	0.330578i
$167$	−221.275	+	1254.91i	−0.102532	+	0.581486i	0.889646	+	0.456651i	$0.150951\pi$
$167$	−221.275	+	1254.91i	−0.102532	+	0.581486i	−0.992178	+	0.124835i	$0.960160\pi$
$168$	−40.2158	+	73.3337i	−0.0184685	+	0.0336775i
$169$	−520.302	+	436.585i	−0.236824	+	0.198719i
$170$	868.771	+	1504.76i	0.391951	+	0.678879i
$171$	−893.338	−	4023.02i	−0.399504	−	1.79911i
$172$	225.286	−	390.208i	0.0998717	−	0.172983i
$173$	297.016	+	1684.46i	0.130530	+	0.740272i	0.977869	+	0.209219i	$0.0670923\pi$
$173$	297.016	+	1684.46i	0.130530	+	0.740272i	−0.847339	+	0.531053i	$0.821797\pi$
$174$	−784.363	+	688.107i	−0.341738	+	0.299800i
$175$	−150.409	+	54.7444i	−0.0649706	+	0.0236474i
$176$	−743.504	+	270.613i	−0.318430	+	0.115899i
$177$	1711.45	+	580.631i	0.726783	+	0.246570i
$178$	−35.2588	−	199.963i	−0.0148470	−	0.0842013i
$179$	996.991	−	1726.84i	0.416305	−	0.721062i	−0.579259	−	0.815143i	$-0.696658\pi$
$179$	996.991	−	1726.84i	0.416305	−	0.721062i	0.995564	+	0.0940815i	$0.0299914\pi$
$180$	−1391.83	+	577.079i	−0.576340	+	0.238961i
$181$	−1479.11	−	2561.90i	−0.607412	−	1.05207i	−0.991665	−	0.128841i	$-0.958874\pi$
$181$	−1479.11	−	2561.90i	−0.607412	−	1.05207i	0.384253	−	0.923228i	$-0.374459\pi$
$182$	−44.0626	+	36.9729i	−0.0179458	+	0.0150583i
$183$	984.387	+	1621.59i	0.397639	+	0.655035i
$184$	−501.553	+	2844.45i	−0.200951	+	1.13965i
$185$	3183.98	+	2671.68i	1.26536	+	1.06176i
$186$	840.791	−	327.133i	0.331451	−	0.128960i
$187$	919.404	+	334.636i	0.359537	+	0.130861i
$188$	−380.283			−0.147526
$189$	−21.8512	−	89.0990i	−0.00840975	−	0.0342910i
$190$	6626.93			2.53036
$191$	−3169.67	−	1153.67i	−1.20078	−	0.437049i	−0.337285	−	0.941403i	$-0.609509\pi$
$191$	−3169.67	−	1153.67i	−1.20078	−	0.437049i	−0.863497	+	0.504354i	$0.831731\pi$
$192$	−2182.69	−	1751.18i	−0.820428	−	0.658231i
$193$	471.618	+	395.735i	0.175895	+	0.147594i	0.726485	−	0.687182i	$-0.241153\pi$
$193$	471.618	+	395.735i	0.175895	+	0.147594i	−0.550590	+	0.834776i	$0.685597\pi$
$194$	445.682	−	2527.59i	0.164939	−	0.935414i
$195$	−3891.85	+	85.5915i	−1.42924	+	0.0314325i
$196$	761.560	−	639.025i	0.277536	−	0.232881i
$197$	−403.273	−	698.489i	−0.145848	−	0.252616i	0.783841	−	0.620961i	$-0.213258\pi$
$197$	−403.273	−	698.489i	−0.145848	−	0.252616i	−0.929689	+	0.368346i	$0.879924\pi$
$198$	687.763	−	1322.29i	0.246855	−	0.474603i
$199$	308.855	−	534.953i	0.110021	−	0.190562i	−0.805758	−	0.592246i	$-0.798242\pi$
$199$	308.855	−	534.953i	0.110021	−	0.190562i	0.915778	+	0.401684i	$0.131575\pi$
$200$	−1046.30	−	5933.84i	−0.369921	−	2.09793i
$201$	809.753	+	4067.24i	0.284157	+	1.42727i
$202$	−523.249	+	190.447i	−0.182256	+	0.0663357i
$203$	−54.6477	+	19.8901i	−0.0188942	+	0.00687691i
$204$	117.830	+	591.836i	0.0404398	+	0.203122i
$205$	−171.204	−	970.947i	−0.0583289	−	0.330799i
$206$	−453.985	+	786.325i	−0.153547	+	0.265951i
$207$	−1703.16	−	2671.39i	−0.571874	−	0.896979i
$208$	−630.401	−	1091.89i	−0.210146	−	0.363984i
$209$	2858.59	−	2398.64i	0.946090	−	0.793864i
$210$	147.489	−	3.24365i	0.0484652	−	0.00106587i
$211$	−460.355	+	2610.80i	−0.150200	+	0.851825i	0.812844	+	0.582481i	$0.197918\pi$
$211$	−460.355	+	2610.80i	−0.150200	+	0.851825i	−0.963044	+	0.269344i	$0.913193\pi$
$212$	806.417	+	676.664i	0.261250	+	0.219215i
$213$	−1501.03	−	1204.28i	−0.482860	−	0.387399i
$214$	−3467.87	−	1262.20i	−1.10775	−	0.403188i
$215$	−2985.66			−0.947070
$216$	3445.93	−	227.648i	1.08549	−	0.0717105i
$217$	50.2836			0.0157303
$218$	4181.73	+	1522.02i	1.29918	+	0.472865i
$219$	2453.25	−	954.503i	0.756964	−	0.294518i
$220$	−1045.16	−	876.991i	−0.320293	−	0.268758i
$221$	−270.732	+	1535.40i	−0.0824045	+	0.467339i
$222$	−1315.91	−	2167.71i	−0.397830	−	0.655349i
$223$	−1414.76	+	1187.13i	−0.424841	+	0.356484i	−0.830001	−	0.557762i	$-0.811660\pi$
$223$	−1414.76	+	1187.13i	−0.424841	+	0.356484i	0.405160	+	0.914246i	$0.367216\pi$
$224$	−40.4935	−	70.1369i	−0.0120785	−	0.0209206i
$225$	5244.73	+	4021.55i	1.55399	+	1.19157i
$226$	−2648.06	+	4586.58i	−0.779409	+	1.34998i
$227$	218.634	+	1239.93i	0.0639261	+	0.362543i	0.999944	+	0.0105904i	$0.00337109\pi$
$227$	218.634	+	1239.93i	0.0639261	+	0.362543i	−0.936018	+	0.351953i	$0.885518\pi$
$228$	2179.53	+	739.433i	0.633084	+	0.214781i
$229$	−1908.52	+	694.645i	−0.550736	+	0.200452i	−0.602374	−	0.798214i	$-0.705778\pi$
$229$	−1908.52	+	694.645i	−0.550736	+	0.200452i	0.0516373	+	0.998666i	$0.483556\pi$
$230$	4787.39	−	1742.47i	1.37248	−	0.499543i
$231$	62.4467	−	54.7833i	0.0177865	−	0.0156038i
$232$	−380.147	−	2155.92i	−0.107577	−	0.610100i
$233$	−2199.86	+	3810.27i	−0.618531	+	1.07133i	0.371222	+	0.928544i	$0.378939\pi$
$233$	−2199.86	+	3810.27i	−0.618531	+	1.07133i	−0.989754	+	0.142784i	$0.954395\pi$
$234$	2265.36	+	713.406i	0.632868	+	0.199303i
$235$	1259.94	+	2182.29i	0.349743	+	0.605773i
$236$	−773.199	+	648.791i	−0.213267	+	0.178952i
$237$	381.255	−	695.221i	0.104494	−	0.190546i
$238$	10.2599	−	58.1868i	0.00279433	−	0.0158474i
$239$	−3904.23	−	3276.04i	−1.05667	−	0.886650i	−0.0628898	−	0.998020i	$-0.520032\pi$
$239$	−3904.23	−	3276.04i	−1.05667	−	0.886650i	−0.993779	+	0.111370i	$0.964476\pi$
$240$	−491.365	+	3196.11i	−0.132156	+	0.859617i
$241$	−3716.59	−	1352.73i	−0.993388	−	0.361564i	−0.206357	−	0.978477i	$-0.566161\pi$
$241$	−3716.59	−	1352.73i	−0.993388	−	0.361564i	−0.787031	+	0.616913i	$0.788383\pi$
$242$	−1655.60			−0.439777
$243$	−2617.09	+	2738.57i	−0.690890	+	0.722960i
$244$	−1059.45			−0.277969
$245$	−6190.28	−	2253.08i	−1.61422	−	0.587526i
$246$	−91.4035	+	594.540i	−0.0236897	+	0.154091i
$247$	4555.13	+	3822.21i	1.17342	+	0.984620i
$248$	−328.694	+	1864.12i	−0.0841618	+	0.477305i
$249$	−1217.16	+	2219.50i	−0.309778	+	0.564881i
$250$	−3983.96	+	3342.94i	−1.00787	+	0.845704i
$251$	−251.096	−	434.910i	−0.0631435	−	0.109368i	0.832725	−	0.553686i	$-0.186779\pi$
$251$	−251.096	−	434.910i	−0.0631435	−	0.109368i	−0.895869	+	0.444318i	$0.853446\pi$
$252$	48.8696	+	15.3900i	0.0122162	+	0.00384714i
$253$	1434.39	−	2484.44i	0.356441	−	0.617373i
$254$	−440.849	−	2500.18i	−0.108903	−	0.617619i
$255$	3005.92	−	2637.03i	0.738187	−	0.647598i
$256$	3570.83	−	1299.68i	0.871786	−	0.317304i
$257$	280.694	−	102.164i	0.0681291	−	0.0247970i	−0.307731	−	0.951473i	$-0.599570\pi$
$257$	280.694	−	102.164i	0.0681291	−	0.0247970i	0.375860	+	0.926676i	$0.377347\pi$
$258$	1725.01	+	585.231i	0.416258	+	0.141221i
$259$	−24.5429	−	139.189i	−0.00588810	−	0.0333931i
$260$	1087.04	−	1882.81i	0.259290	−	0.449104i
$261$	1905.55	+	1461.14i	0.451919	+	0.346522i
$262$	523.057	+	905.962i	0.123338	+	0.213628i
$263$	2351.88	−	1973.47i	0.551420	−	0.462696i	−0.324002	−	0.946057i	$-0.605028\pi$
$263$	2351.88	−	1973.47i	0.551420	−	0.462696i	0.875421	+	0.483360i	$0.160584\pi$
$264$	1622.73	+	2673.14i	0.378304	+	0.623183i
$265$	1211.30	−	6869.61i	0.280790	−	1.59244i
$266$	−172.625	−	144.850i	−0.0397907	−	0.0333884i
$267$	−435.482	+	169.436i	−0.0998167	+	0.0388364i
$268$	−2176.42	−	792.152i	−0.496067	−	0.180554i
$269$	6343.67			1.43785			0.718923	−	0.695090i	$-0.244635\pi$
$269$	6343.67			1.43785			0.718923	+	0.695090i	$0.244635\pi$
$270$	−3386.82	−	5063.07i	−0.763391	−	1.14122i
$271$	1232.62			0.276297			0.138148	−	0.990412i	$-0.455885\pi$
$271$	1232.62			0.276297			0.138148	+	0.990412i	$0.455885\pi$
$272$	1217.00	+	442.950i	0.271291	+	0.0987419i
$273$	103.250	+	82.8374i	0.0228900	+	0.0183646i
$274$	−2939.09	−	2466.19i	−0.648018	−	0.543751i
$275$	−1039.22	+	5893.69i	−0.227880	+	1.29237i
$276$	1768.95	−	38.9036i	0.385790	−	0.00848451i
$277$	4767.55	−	4000.45i	1.03413	−	0.867739i	0.0427944	−	0.999084i	$-0.486374\pi$
$277$	4767.55	−	4000.45i	1.03413	−	0.867739i	0.991337	+	0.131345i	$0.0419295\pi$
$278$	−1220.69	−	2114.30i	−0.263354	−	0.456142i
$279$	−1116.17	−	1750.71i	−0.239511	−	0.375671i
$280$	−154.760	+	268.052i	−0.0330310	+	0.0572114i
$281$	−97.3794	−	552.266i	−0.0206732	−	0.117244i	0.972725	−	0.231962i	$-0.0745145\pi$
$281$	−97.3794	−	552.266i	−0.0206732	−	0.117244i	−0.993398	+	0.114718i	$0.963403\pi$
$282$	−300.194	−	1507.82i	−0.0633912	−	0.318402i
$283$	−5865.99	+	2135.05i	−1.23215	+	0.448464i	−0.874332	−	0.485329i	$-0.838700\pi$
$283$	−5865.99	+	2135.05i	−1.23215	+	0.448464i	−0.357814	+	0.933793i	$0.616478\pi$
$284$	1009.95	−	367.593i	0.211020	−	0.0768051i
$285$	−2977.88	−	14957.3i	−0.618927	−	3.10875i
$286$	373.451	+	2117.95i	0.0772120	+	0.437891i
$287$	−16.7630	+	29.0344i	−0.00344770	+	0.00597159i
$288$	−1543.08	+	2966.72i	−0.315717	+	0.606998i
$289$	1655.75	+	2867.85i	0.337014	+	0.583726i
$290$	−2958.03	+	2482.08i	−0.598970	+	0.502595i
$291$	−5905.17	+	129.870i	−1.18958	+	0.0261618i
$292$	−255.292	+	1447.83i	−0.0511638	+	0.290164i
$293$	−3288.99	−	2759.79i	−0.655784	−	0.550268i	0.253036	−	0.967457i	$-0.418571\pi$
$293$	−3288.99	−	2759.79i	−0.655784	−	0.550268i	−0.908820	+	0.417189i	$0.863015\pi$
$294$	3134.91	+	2515.14i	0.621875	+	0.498932i
$295$	6284.89	+	2287.51i	1.24041	+	0.451472i
$296$	5320.48			1.04475
$297$	−3293.54	−	958.131i	−0.643469	−	0.187193i
$298$	−2829.81			−0.550089
$299$	4295.69	+	1563.50i	0.830856	+	0.302407i
$300$	−3439.92	+	1338.39i	−0.662013	+	0.257574i
$301$	77.7735	+	65.2597i	0.0148930	+	0.0124967i
$302$	−891.919	+	5058.32i	−0.169948	+	0.963821i
$303$	664.975	+	1095.42i	0.126079	+	0.207691i
$304$	3783.85	−	3175.03i	0.713878	−	0.599015i
$305$	3510.15	+	6079.76i	0.658985	+	1.14140i
$306$	−2253.62	+	934.388i	−0.421015	+	0.174560i
$307$	4087.53	−	7079.81i	0.759895	−	1.31618i	−0.183009	−	0.983111i	$-0.558584\pi$
$307$	4087.53	−	7079.81i	0.759895	−	1.31618i	0.942904	−	0.333066i	$-0.108083\pi$
$308$	8.05630	+	45.6896i	0.00149042	+	0.00845261i
$309$	1978.78	+	671.324i	0.364300	+	0.123593i
$310$	3137.43	−	1141.93i	0.574819	−	0.209217i
$311$	1506.25	−	548.232i	0.274636	−	0.0999594i	−0.201031	−	0.979585i	$-0.564429\pi$
$311$	1506.25	−	548.232i	0.274636	−	0.0999594i	0.475667	+	0.879626i	$0.342207\pi$
$312$	−3745.88	+	3286.19i	−0.679708	+	0.596295i
$313$	1895.60	+	10750.5i	0.342319	+	1.94139i	0.337297	+	0.941398i	$0.390487\pi$
$313$	1895.60	+	10750.5i	0.342319	+	1.94139i	0.00502124	+	0.999987i	$0.498402\pi$
$314$	1044.88	−	1809.79i	0.187790	−	0.325262i
$315$	−73.5966	−	331.432i	−0.0131641	−	0.0592828i
$316$	221.413	+	383.499i	0.0394160	+	0.0682705i
$317$	−1256.41	+	1054.26i	−0.222610	+	0.186792i	−0.747271	−	0.664519i	$-0.768636\pi$
$317$	−1256.41	+	1054.26i	−0.222610	+	0.186792i	0.524661	+	0.851311i	$0.324192\pi$
$318$	−2046.39	+	3731.60i	−0.360867	+	0.658043i
$319$	−377.575	+	2141.34i	−0.0662701	+	0.375836i
$320$	−7933.17	−	6656.72i	−1.38587	−	1.16288i
$321$	−1290.53	+	8394.33i	−0.224394	+	1.45958i
$322$	−162.793	−	59.2519i	−0.0281742	−	0.0102546i
$323$	−6108.06			−1.05220
$324$	−548.956	−	2043.10i	−0.0941283	−	0.350325i
$325$	−9536.40			−1.62764
$326$	377.533	+	137.411i	0.0641399	+	0.0233450i
$327$	1556.19	−	10122.3i	0.263172	−	1.71182i
$328$	−966.789	−	811.232i	−0.162750	−	0.136563i
$329$	14.8795	−	84.3860i	0.00249342	−	0.0141409i
$330$	2652.22	−	4836.34i	0.442425	−	0.806763i
$331$	5341.08	−	4481.69i	0.886925	−	0.744218i	−0.0806662	−	0.996741i	$-0.525705\pi$
$331$	5341.08	−	4481.69i	0.886925	−	0.744218i	0.967591	+	0.252523i	$0.0812603\pi$
$332$	−706.865	−	1224.33i	−0.116850	−	0.202390i
$333$	−4301.32	+	3944.16i	−0.707841	+	0.649066i
$334$	1438.57	−	2491.68i	0.235675	−	0.408200i
$335$	2665.03	+	15114.1i	0.434645	+	2.46499i
$336$	82.6593	−	72.5155i	0.0134209	−	0.0117739i
$337$	8810.91	−	3206.91i	1.42422	−	0.518372i	0.488948	−	0.872313i	$-0.337381\pi$
$337$	8810.91	−	3206.91i	1.42422	−	0.518372i	0.935268	+	0.353941i	$0.115158\pi$
$338$	1441.08	−	524.509i	0.231906	−	0.0844069i
$339$	11542.1	+	3915.79i	1.84920	+	0.627364i
$340$	387.796	+	2199.30i	0.0618565	+	0.350805i
$341$	940.034	−	1628.19i	0.149284	−	0.258567i
$342$	−1211.33	+	9225.55i	−0.191524	+	1.45866i
$343$	224.147	+	388.235i	0.0352852	+	0.0611157i
$344$	−2927.71	+	2456.64i	−0.458870	+	0.385038i
$345$	−6084.09	−	10022.4i	−0.949439	−	1.56402i
$346$	670.624	−	3803.30i	0.104199	−	0.590944i
$347$	1000.76	+	839.741i	0.154824	+	0.129913i	0.716909	−	0.697167i	$-0.245556\pi$
$347$	1000.76	+	839.741i	0.154824	+	0.129913i	−0.562085	+	0.827079i	$0.690001\pi$
$348$	−1249.82	+	486.275i	−0.192520	+	0.0749053i
$349$	−3710.11	−	1350.37i	−0.569048	−	0.207117i	0.0414413	−	0.999141i	$-0.486805\pi$
$349$	−3710.11	−	1350.37i	−0.569048	−	0.207117i	−0.610490	+	0.792024i	$0.709027\pi$
$350$	361.400			0.0551933
$351$	592.233	−	5433.60i	0.0900599	−	0.826279i
$352$	−3028.05			−0.458510
$353$	−1916.14	−	697.416i	−0.288911	−	0.105155i	0.193499	−	0.981100i	$-0.438016\pi$
$353$	−1916.14	−	697.416i	−0.288911	−	0.105155i	−0.482410	+	0.875945i	$0.660239\pi$
$354$	−3182.82	−	2553.58i	−0.477867	−	0.383393i
$355$	−5455.63	−	4577.81i	−0.815647	−	0.684409i
$356$	45.3175	−	257.008i	0.00674669	−	0.0382624i
$357$	−135.941	+	2.98968i	−0.0201534	+	0.000443224i
$358$	−3448.86	+	2893.93i	−0.509156	+	0.427232i
$359$	−3268.69	−	5661.54i	−0.480543	−	0.832325i	0.519208	−	0.854648i	$-0.326227\pi$
$359$	−3268.69	−	5661.54i	−0.480543	−	0.832325i	−0.999751	+	0.0223230i	$0.992894\pi$
$360$	12768.0	−	561.872i	1.86925	−	0.0822590i
$361$	−8218.48	+	14234.8i	−1.19820	+	2.07535i
$362$	1159.85	+	6577.83i	0.168399	+	0.955036i
$363$	743.960	+	3736.77i	0.107570	+	0.540302i
$364$	−69.4705	+	25.2852i	−0.0100034	+	0.00364094i
$365$	9154.35	−	3331.91i	1.31277	−	0.477809i
$366$	−836.328	−	4200.72i	−0.119441	−	0.599932i
$367$	−744.758	−	4223.73i	−0.105929	−	0.600755i	−0.990845	−	0.135004i	$-0.956895\pi$
$367$	−744.758	−	4223.73i	−0.105929	−	0.600755i	0.884916	−	0.465751i	$-0.154216\pi$
$368$	1898.67	−	3288.60i	0.268954	−	0.465843i
$369$	1382.98	−	60.8598i	0.195108	−	0.00858600i
$370$	−4692.31	−	8127.32i	−0.659302	−	1.14194i
$371$	−181.707	+	152.470i	−0.0254280	+	0.0213366i
$372$	1159.29	−	25.4956i	0.161576	−	0.00355346i
$373$	767.513	−	4352.78i	0.106542	−	0.604232i	−0.884051	−	0.467391i	$-0.845194\pi$
$373$	767.513	−	4352.78i	0.106542	−	0.604232i	0.990593	−	0.136841i	$-0.0436949\pi$
$374$	−1692.29	−	1420.00i	−0.233974	−	0.196327i
$375$	9335.41	+	7489.81i	1.28554	+	1.03139i
$376$	3031.10	+	1103.23i	0.415737	+	0.151316i
$377$	−3464.83			−0.473337
$378$	−22.4438	+	205.917i	−0.00305392	+	0.0280191i
$379$	2226.11			0.301709			0.150854	−	0.988556i	$-0.451798\pi$
$379$	2226.11			0.301709			0.150854	+	0.988556i	$0.451798\pi$
$380$	8003.80	+	2913.15i	1.08049	+	0.393266i
$381$	−5444.93	+	2118.50i	−0.732158	+	0.284866i
$382$	5834.21	+	4895.49i	0.781425	+	0.655693i
$383$	1312.12	−	7441.42i	0.175056	−	0.992791i	−0.763023	−	0.646371i	$-0.776286\pi$
$383$	1312.12	−	7441.42i	0.175056	−	0.992791i	0.938079	−	0.346420i	$-0.112603\pi$
$384$	607.066	+	1000.03i	0.0806751	+	0.132897i
$385$	235.502	−	197.609i	0.0311748	−	0.0261587i
$386$	−695.035	−	1203.84i	−0.0916485	−	0.158740i
$387$	545.745	−	4156.42i	0.0716842	−	0.545950i
$388$	1649.39	−	2856.83i	0.215812	−	0.373797i
$389$	−2407.96	−	13656.2i	−0.313852	−	1.77994i	−0.578585	−	0.815622i	$-0.696395\pi$
$389$	−2407.96	−	13656.2i	−0.313852	−	1.77994i	0.264733	−	0.964322i	$-0.414716\pi$
$390$	8323.46	+	2823.83i	1.08070	+	0.366642i
$391$	−4412.54	+	1606.03i	−0.570721	+	0.207726i
$392$	−7924.00	+	2884.10i	−1.02098	+	0.371605i
$393$	1809.76	−	1587.67i	0.232291	−	0.203785i
$394$	316.227	+	1793.41i	0.0404347	+	0.229317i
$395$	1467.16	−	2541.20i	0.186888	−	0.323700i
$396$	1411.93	−	1294.69i	0.179172	−	0.164295i
$397$	866.691	+	1501.15i	0.109567	+	0.189775i	0.915595	−	0.402102i	$-0.131720\pi$
$397$	866.691	+	1501.15i	0.109567	+	0.189775i	−0.806028	+	0.591877i	$0.798387\pi$
$398$	−1068.41	+	896.504i	−0.134559	+	0.112909i
$399$	−249.362	+	454.713i	−0.0312876	+	0.0570530i
$400$	−1375.59	+	7801.35i	−0.171949	+	0.975169i
$401$	−5076.09	−	4259.35i	−0.632139	−	0.530428i	0.269454	−	0.963013i	$-0.413157\pi$
$401$	−5076.09	−	4259.35i	−0.632139	−	0.530428i	−0.901593	+	0.432586i	$0.857601\pi$
$402$	1422.82	−	9254.82i	0.176527	−	1.14823i
$403$	2815.19	+	1024.65i	0.347977	+	0.126653i
$404$	−715.683			−0.0881350
$405$	−9905.70	+	9919.37i	−1.21535	+	1.21703i
$406$	131.306			0.0160508
$407$	−4965.79	−	1807.40i	−0.604779	−	0.220121i
$408$	777.786	−	5059.16i	0.0943778	−	0.613886i
$409$	−4235.35	−	3553.88i	−0.512041	−	0.429653i	0.349806	−	0.936822i	$-0.386248\pi$
$409$	−4235.35	−	3553.88i	−0.512041	−	0.429653i	−0.861847	+	0.507169i	$0.830692\pi$
$410$	−386.558	+	2192.28i	−0.0465627	+	0.264070i
$411$	−4245.60	+	7741.87i	−0.509538	+	0.929145i
$412$	−893.971	+	750.131i	−0.106900	+	0.0896997i
$413$	−113.716	−	196.961i	−0.0135486	−	0.0234669i
$414$	1550.66	+	6983.16i	0.184084	+	0.828995i
$415$	−4683.94	+	8112.82i	−0.554037	+	0.959621i
$416$	−837.880	−	4751.86i	−0.0987511	−	0.560045i
$417$	−4223.56	+	3705.25i	−0.495992	+	0.435124i
$418$	−7917.42	+	2881.70i	−0.926444	+	0.337198i
$419$	2789.83	−	1015.41i	0.325279	−	0.118392i	−0.174219	−	0.984707i	$-0.555740\pi$
$419$	2789.83	−	1015.41i	0.325279	−	0.118392i	0.499498	+	0.866315i	$0.333518\pi$
$420$	179.558	+	60.9173i	0.0208608	+	0.00707729i
$421$	1591.00	+	9023.02i	0.184182	+	1.04455i	0.927002	+	0.375057i	$0.122377\pi$
$421$	1591.00	+	9023.02i	0.184182	+	1.04455i	−0.742819	+	0.669492i	$0.766512\pi$
$422$	2992.90	−	5183.86i	0.345242	−	0.597977i
$423$	−3268.33	+	1355.11i	−0.375678	+	0.155763i
$424$	−4464.62	−	7732.94i	−0.511370	−	0.885719i
$425$	7504.04	−	6296.64i	0.856469	−	0.718663i
$426$	2254.76	+	3714.29i	0.256440	+	0.422436i
$427$	41.4537	−	235.096i	0.00469809	−	0.0266442i
$428$	−3633.53	−	3048.89i	−0.410358	−	0.344331i
$429$	4612.50	−	1794.62i	0.519099	−	0.201970i
$430$	6334.69	+	2305.64i	0.710432	+	0.258576i
$431$	13854.8			1.54840			0.774200	−	0.632941i	$-0.218152\pi$
$431$	13854.8			1.54840			0.774200	+	0.632941i	$0.218152\pi$
$432$	−4359.58	−	1268.26i	−0.485534	−	0.141248i
$433$	11703.3			1.29890			0.649449	−	0.760405i	$-0.274999\pi$
$433$	11703.3			1.29890			0.649449	+	0.760405i	$0.274999\pi$
$434$	−106.687	−	38.8309i	−0.0117999	−	0.00429480i
$435$	6931.39	+	5561.06i	0.763988	+	0.612949i
$436$	4381.49	+	3676.51i	0.481274	+	0.403837i
$437$	−3109.93	+	17637.3i	−0.340431	+	1.93068i
$438$	−5942.18	+	130.684i	−0.648238	+	0.0142564i
$439$	−10242.1	+	8594.13i	−1.11350	+	0.934340i	−0.998258	−	0.0589972i	$-0.981210\pi$
$439$	−10242.1	+	8594.13i	−1.11350	+	0.934340i	−0.115245	+	0.993337i	$0.536765\pi$
$440$	5786.37	+	10022.3i	0.626942	+	1.08589i
$441$	4268.09	−	8205.84i	0.460868	−	0.886064i
$442$	1760.11	−	3048.60i	0.189411	−	0.328070i
$443$	615.153	+	3488.71i	0.0659747	+	0.374161i	0.999862	+	0.0165945i	$0.00528243\pi$
$443$	615.153	+	3488.71i	0.0659747	+	0.374161i	−0.933888	+	0.357567i	$0.883606\pi$
$444$	−636.409	−	3196.56i	−0.0680239	−	0.341672i
$445$	−1625.01	+	591.455i	−0.173108	+	0.0630060i
$446$	3918.46	−	1426.20i	0.416019	−	0.151418i
$447$	1271.60	+	6387.02i	0.134552	+	0.675829i
$448$	61.1506	+	346.802i	0.00644887	+	0.0365734i
$449$	−6869.46	+	11898.3i	−0.722027	+	1.25059i	0.238159	+	0.971226i	$0.423456\pi$
$449$	−6869.46	+	11898.3i	−0.722027	+	1.25059i	−0.960186	+	0.279361i	$0.909877\pi$
$450$	−8022.19	−	12582.7i	−0.840377	−	1.31813i
$451$	626.757	+	1085.58i	0.0654387	+	0.113343i
$452$	−5214.47	+	4375.46i	−0.542628	+	0.455319i
$453$	11817.7	−	259.901i	1.22570	−	0.0269563i
$454$	493.648	−	2799.61i	0.0510309	−	0.289411i
$455$	375.269	+	314.888i	0.0386657	+	0.0324444i
$456$	−15227.2	−	12216.8i	−1.56376	−	1.25461i
$457$	−12604.5	−	4587.65i	−1.29018	−	0.469587i	−0.396393	−	0.918081i	$-0.629738\pi$
$457$	−12604.5	−	4587.65i	−1.29018	−	0.469587i	−0.893786	+	0.448494i	$0.851961\pi$
$458$	4585.76			0.467856
$459$	3121.64	+	4666.65i	0.317442	+	0.474554i
$460$	6548.03			0.663703
$461$	−14001.8	−	5096.23i	−1.41459	−	0.514870i	−0.482120	−	0.876105i	$-0.660133\pi$
$461$	−14001.8	−	5096.23i	−1.41459	−	0.514870i	−0.932475	+	0.361235i	$0.882355\pi$
$462$	−174.799	+	68.0105i	−0.0176026	+	0.00684877i
$463$	−4001.92	−	3358.01i	−0.401696	−	0.337063i	0.419453	−	0.907777i	$-0.362222\pi$
$463$	−4001.92	−	3358.01i	−0.401696	−	0.337063i	−0.821149	+	0.570714i	$0.806666\pi$
$464$	−499.788	+	2834.44i	−0.0500045	+	0.283590i
$465$	−3987.23	−	6568.20i	−0.397642	−	0.655038i
$466$	7609.91	−	6385.47i	0.756485	−	0.634767i
$467$	770.017	+	1333.71i	0.0763001	+	0.132156i	0.901651	−	0.432465i	$-0.142356\pi$
$467$	770.017	+	1333.71i	0.0763001	+	0.132156i	−0.825351	+	0.564620i	$0.809023\pi$
$468$	2422.42	+	1857.46i	0.239266	+	0.183464i
$469$	260.939	−	451.960i	0.0256909	−	0.0444980i
$470$	−987.987	−	5603.15i	−0.0969627	−	0.549903i
$471$	−4554.31	−	1545.10i	−0.445545	−	0.151156i
$472$	8045.10	−	2928.18i	0.784546	−	0.285551i
$473$	3567.06	−	1298.30i	0.346752	−	0.126207i
$474$	−1345.79	+	1180.64i	−0.130410	+	0.114406i
$475$	−6487.67	−	36793.4i	−0.626683	−	3.55410i
$476$	37.9700	−	65.7660i	0.00365621	−	0.00633273i
$477$	9341.97	+	2941.97i	0.896728	+	0.282398i
$478$	5753.76	+	9965.80i	0.550566	+	0.953609i
$479$	9129.50	−	7660.56i	0.870851	−	0.730730i	−0.0934265	−	0.995626i	$-0.529782\pi$
$479$	9129.50	−	7660.56i	0.870851	−	0.730730i	0.964277	+	0.264896i	$0.0853376\pi$
$480$	−5950.56	+	10850.9i	−0.565844	+	1.03182i
$481$	1462.25	−	8292.82i	0.138613	−	0.786113i
$482$	6840.88	+	5740.18i	0.646460	+	0.542444i
$483$	−60.5817	+	394.058i	−0.00570717	+	0.0371227i
$484$	−1999.58	−	727.788i	−0.187789	−	0.0683498i
$485$	−21858.9			−2.04652
$486$	7667.53	−	3789.42i	0.715650	−	0.353687i
$487$	8607.21			0.800883			0.400441	−	0.916322i	$-0.368857\pi$
$487$	8607.21			0.800883			0.400441	+	0.916322i	$0.368857\pi$
$488$	8444.52	+	3073.55i	0.783331	+	0.285109i
$489$	140.495	−	913.857i	0.0129926	−	0.0845113i
$490$	11394.1	+	9560.75i	1.05047	+	0.881451i
$491$	725.217	−	4112.91i	0.0666570	−	0.378031i	−0.933170	−	0.359435i	$-0.882969\pi$
$491$	725.217	−	4112.91i	0.0666570	−	0.378031i	0.999827	−	0.0185957i	$-0.00591952\pi$
$492$	−371.749	+	677.886i	−0.0340645	+	0.0621168i
$493$	2726.42	−	2287.74i	0.249070	−	0.208995i
$494$	−6713.00	−	11627.3i	−0.611401	−	1.05898i
$495$	−12107.7	−	3812.94i	−1.09939	−	0.346220i
$496$	1244.30	−	2155.20i	0.112643	−	0.195103i
$497$	42.0532	+	238.495i	0.00379546	+	0.0215251i
$498$	4296.45	−	3769.20i	0.386604	−	0.339160i
$499$	6630.01	−	2413.13i	0.594790	−	0.216486i	−0.0270449	−	0.999634i	$-0.508610\pi$
$499$	6630.01	−	2413.13i	0.594790	−	0.216486i	0.621835	+	0.783148i	$0.286387\pi$
$500$	−6281.23	+	2286.18i	−0.561810	+	0.204482i
$501$	−6270.29	−	2127.27i	−0.559154	−	0.189700i
$502$	196.897	+	1116.66i	0.0175059	+	0.0992807i
$503$	−3434.09	+	5948.02i	−0.304411	+	0.527255i	−0.977130	−	0.212643i	$-0.931793\pi$
$503$	−3434.09	+	5948.02i	−0.304411	+	0.527255i	0.672719	+	0.739898i	$0.265126\pi$
$504$	−344.875	−	264.443i	−0.0304801	−	0.0233715i
$505$	2371.18	+	4107.01i	0.208943	+	0.361900i
$506$	−4961.94	+	4163.56i	−0.435939	+	0.365796i
$507$	−1831.41	−	3016.89i	−0.160425	−	0.264270i
$508$	566.615	−	3213.43i	0.0494872	−	0.280656i
$509$	13507.1	+	11333.8i	1.17621	+	0.986959i	0.999997	+	0.00260759i	$0.000830024\pi$
$509$	13507.1	+	11333.8i	1.17621	+	0.986959i	0.176216	+	0.984352i	$0.443614\pi$
$510$	−8414.10	+	3273.73i	−0.730554	+	0.284242i
$511$	−311.290	−	113.300i	−0.0269485	−	0.00980844i
$512$	−10381.1			−0.896059
$513$	21366.8	−	1411.55i	1.83893	−	0.121485i
$514$	−674.445			−0.0578765
$515$	7266.58	+	2644.82i	0.621755	+	0.226300i
$516$	1826.15	+	1465.13i	0.155798	+	0.124997i
$517$	−2454.26	−	2059.37i	−0.208778	−	0.175185i
$518$	−55.4147	+	314.272i	−0.00470035	+	0.0266570i
$519$	−8885.58	+	195.416i	−0.751510	+	0.0165276i
$520$	−14126.6	+	11853.7i	−1.19133	+	0.999649i
$521$	10807.6	+	18719.2i	0.908805	+	1.57410i	0.815726	+	0.578439i	$0.196338\pi$
$521$	10807.6	+	18719.2i	0.908805	+	1.57410i	0.0930796	+	0.995659i	$0.470329\pi$
$522$	−2914.68	−	4571.65i	−0.244391	−	0.383325i
$523$	5278.59	−	9142.79i	0.441332	−	0.764410i	−0.556456	−	0.830877i	$-0.687839\pi$
$523$	5278.59	−	9142.79i	0.441332	−	0.764410i	0.997789	+	0.0664670i	$0.0211727\pi$
$524$	233.479	+	1324.12i	0.0194648	+	0.110391i
$525$	−162.399	−	815.698i	−0.0135003	−	0.0678095i
$526$	−6514.00	+	2370.90i	−0.539969	+	0.196533i
$527$	−2891.78	+	1052.52i	−0.239028	+	0.0869991i
$528$	−802.771	−	4032.17i	−0.0661669	−	0.332344i
$529$	278.065	+	1576.98i	0.0228540	+	0.129612i
$530$	−7875.00	+	13639.9i	−0.645411	+	1.11789i
$531$	−4333.32	+	8331.25i	−0.354144	+	0.680877i
$532$	−144.817	−	250.830i	−0.0118019	−	0.0204414i
$533$	−1530.14	+	1283.94i	−0.124349	+	0.104341i
$534$	1054.81	−	23.1979i	0.0854796	−	0.00187991i
$535$	−5457.82	+	30952.8i	−0.441051	+	2.50132i
$536$	15049.4	+	12627.9i	1.21275	+	1.01762i
$537$	8081.53	+	6483.82i	0.649430	+	0.521039i
$538$	−13459.4	−	4898.83i	−1.07858	−	0.392571i
$539$	8375.49			0.669309
$540$	−1864.82	−	7603.84i	−0.148609	−	0.605958i
$541$	−12500.9			−0.993450			−0.496725	−	0.867908i	$-0.665464\pi$
$541$	−12500.9			−0.993450			−0.496725	+	0.867908i	$0.665464\pi$
$542$	−2615.26	−	951.878i	−0.207260	−	0.0754366i
$543$	14325.3	−	5573.65i	1.13215	−	0.440494i
$544$	3796.84	+	3185.93i	0.299243	+	0.251095i
$545$	6581.32	−	37324.5i	0.517271	−	2.93359i
$546$	−155.096	−	255.490i	−0.0121565	−	0.0200256i
$547$	−1779.95	+	1493.56i	−0.139132	+	0.116746i	−0.709698	−	0.704506i	$-0.751168\pi$
$547$	−1779.95	+	1493.56i	−0.139132	+	0.116746i	0.570566	+	0.821252i	$0.306724\pi$
$548$	−2465.62	−	4270.58i	−0.192201	−	0.332902i
$549$	−9105.42	+	3775.27i	−0.707851	+	0.293487i
$550$	6756.25	−	11702.2i	0.523795	−	0.907240i
$551$	−2357.14	−	13368.0i	−0.182246	−	1.03357i
$552$	−14212.5	−	4821.77i	−1.09588	−	0.371790i
$553$	−93.7630	+	34.1269i	−0.00721014	+	0.00262428i
$554$	−13204.7	+	4806.10i	−1.01266	+	0.368577i
$555$	−16235.2	+	14242.9i	−1.24171	+	1.08933i
$556$	−544.885	−	3090.20i	−0.0415617	−	0.235708i
$557$	461.672	−	799.640i	0.0351197	−	0.0608291i	−0.847931	−	0.530106i	$-0.822152\pi$
$557$	461.672	−	799.640i	0.0351197	−	0.0608291i	0.883051	+	0.469277i	$0.155485\pi$
$558$	1016.23	+	4576.44i	0.0770974	+	0.347197i
$559$	3024.43	+	5238.47i	0.228837	+	0.396357i
$560$	311.729	−	261.571i	0.0235231	−	0.0197382i
$561$	−2444.56	+	4457.67i	−0.183974	+	0.335478i
$562$	−219.871	+	1246.95i	−0.0165030	+	0.0935931i
$563$	5914.16	+	4962.57i	0.442722	+	0.371488i	0.836727	−	0.547621i	$-0.184466\pi$
$563$	5914.16	+	4962.57i	0.442722	+	0.371488i	−0.394005	+	0.919108i	$0.628911\pi$
$564$	300.260	−	1953.06i	0.0224171	−	0.145813i
$565$	42385.4	+	15427.0i	3.15605	+	1.14871i
$566$	14094.7			1.04672
$567$	474.849	−	41.8738i	0.0351707	−	0.00310147i
$568$	−9116.42			−0.673445
$569$	−10199.1	−	3712.18i	−0.751441	−	0.273502i	−0.0622291	−	0.998062i	$-0.519821\pi$
$569$	−10199.1	−	3712.18i	−0.751441	−	0.273502i	−0.689212	+	0.724560i	$0.742043\pi$
$570$	−5232.43	+	34034.7i	−0.384496	+	2.50098i
$571$	−10739.6	−	9011.60i	−0.787108	−	0.660462i	0.157920	−	0.987452i	$-0.449521\pi$
$571$	−10739.6	−	9011.60i	−0.787108	−	0.660462i	−0.945028	+	0.326990i	$0.893966\pi$
$572$	−479.990	+	2722.16i	−0.0350863	+	0.198984i
$573$	8427.69	−	15367.9i	0.614436	−	1.12043i
$574$	57.9877	−	48.6574i	0.00421665	−	0.00353819i
$575$	−14361.1	−	24874.2i	−1.04157	−	1.80404i
$576$	10717.1	−	9827.22i	0.775254	−	0.710881i
$577$	7531.32	−	13044.6i	0.543384	−	0.941169i	−0.455322	−	0.890327i	$-0.650476\pi$
$577$	7531.32	−	13044.6i	0.543384	−	0.941169i	0.998707	−	0.0508427i	$-0.0161907\pi$
$578$	−1298.36	−	7363.37i	−0.0934337	−	0.529889i
$579$	−2404.80	+	2109.68i	−0.172608	+	0.151426i
$580$	−4663.71	+	1697.45i	−0.333879	+	0.121522i
$581$	299.340	−	108.951i	0.0213747	−	0.00777977i
$582$	12629.3	+	4284.65i	0.899489	+	0.305163i
$583$	1540.05	+	8734.08i	0.109404	+	0.620461i
$584$	6235.13	−	10799.6i	0.441800	−	0.765221i
$585$	2633.31	−	20055.4i	0.186109	−	1.41742i
$586$	4847.05	+	8395.34i	0.341689	+	0.591823i
$587$	20331.5	−	17060.2i	1.42959	−	1.19957i	0.483640	−	0.875267i	$-0.339314\pi$
$587$	20331.5	−	17060.2i	1.42959	−	1.19957i	0.945953	−	0.324304i	$-0.105130\pi$
$588$	2680.61	+	4415.79i	0.188004	+	0.309701i
$589$	−2038.11	+	11558.7i	−0.142578	+	0.808602i
$590$	−11568.2	−	9706.87i	−0.807212	−	0.677332i
$591$	3905.72	−	1519.63i	0.271844	−	0.105768i
$592$	−6573.10	−	2392.41i	−0.456339	−	0.166094i
$593$	−15784.3			−1.09306			−0.546530	−	0.837440i	$-0.684051\pi$
$593$	−15784.3			−1.09306			−0.546530	+	0.837440i	$0.684051\pi$
$594$	6248.02	+	4576.27i	0.431581	+	0.316105i
$595$	−503.206			−0.0346713
$596$	−3417.76	−	1243.96i	−0.234894	−	0.0854944i
$597$	2503.56	+	2008.61i	0.171631	+	0.137700i
$598$	−7906.80	−	6634.59i	−0.540690	−	0.453693i
$599$	−2810.24	+	15937.7i	−0.191692	+	1.08714i	0.725360	+	0.688369i	$0.241673\pi$
$599$	−2810.24	+	15937.7i	−0.191692	+	1.08714i	−0.917052	+	0.398768i	$0.869438\pi$
$600$	31301.2	−	688.393i	2.12978	−	0.0468392i
$601$	−896.588	+	752.327i	−0.0608529	+	0.0510616i	−0.672707	−	0.739909i	$-0.734868\pi$
$601$	−896.588	+	752.327i	−0.0608529	+	0.0510616i	0.611854	+	0.790971i	$0.290424\pi$
$602$	−114.617	−	198.522i	−0.00775984	−	0.0134404i
$603$	−21527.9	+	947.366i	−1.45387	+	0.0639796i
$604$	−3300.83	+	5717.21i	−0.222366	+	0.385149i
$605$	2448.49	+	13886.1i	0.164538	+	0.933139i
$606$	−564.958	−	2837.68i	−0.0378711	−	0.190219i
$607$	−19065.8	+	6939.39i	−1.27489	+	0.464022i	−0.888739	−	0.458414i	$-0.848418\pi$
$607$	−19065.8	+	6939.39i	−1.27489	+	0.464022i	−0.386151	+	0.922436i	$0.626196\pi$
$608$	17763.6	−	6465.43i	1.18489	−	0.431263i
$609$	−59.0038	−	296.365i	−0.00392603	−	0.0197197i
$610$	−2752.49	−	15610.1i	−0.182697	−	1.03612i
$611$	2552.61	−	4421.26i	0.169014	−	0.292741i
$612$	−3132.60	+	137.854i	−0.206908	+	0.00910526i
$613$	−10440.8	−	18084.0i	−0.687929	−	1.19153i	−0.972507	−	0.232874i	$-0.925187\pi$
$613$	−10440.8	−	18084.0i	−0.687929	−	1.19153i	0.284578	−	0.958653i	$-0.408146\pi$
$614$	−14139.9	+	11864.7i	−0.929378	+	0.779841i
$615$	5121.78	−	112.641i	0.335821	−	0.00738556i
$616$	68.3351	−	387.548i	0.00446965	−	0.0253486i
$617$	5761.74	+	4834.68i	0.375946	+	0.315457i	0.811109	−	0.584896i	$-0.198865\pi$
$617$	5761.74	+	4834.68i	0.375946	+	0.315457i	−0.435162	+	0.900352i	$0.643309\pi$
$618$	−3679.97	−	2952.44i	−0.239531	−	0.192176i
$619$	−18420.0	−	6704.35i	−1.19606	−	0.435332i	−0.334216	−	0.942497i	$-0.608471\pi$
$619$	−18420.0	−	6704.35i	−1.19606	−	0.435332i	−0.861849	+	0.507165i	$0.830694\pi$
$620$	4291.27			0.277970
$621$	15064.5	−	6637.86i	0.973461	−	0.428934i
$622$	−3619.20			−0.233307
$623$	55.2578	+	20.1122i	0.00355354	+	0.00129338i
$624$	6105.47	−	2375.50i	0.391690	−	0.152397i
$625$	10491.1	+	8803.10i	0.671432	+	0.563398i
$626$	4280.03	−	24273.3i	0.273266	−	1.54977i
$627$	10061.9	+	16575.1i	0.640884	+	1.05573i
$628$	2057.54	−	1726.48i	0.130740	−	0.109704i
$629$	4324.91	+	7490.97i	0.274158	+	0.474856i
$630$	−99.7942	+	760.037i	−0.00631094	+	0.0480644i
$631$	−9209.77	+	15951.8i	−0.581038	+	1.00639i	0.414318	+	0.910132i	$0.364020\pi$
$631$	−9209.77	+	15951.8i	−0.581038	+	1.00639i	−0.995357	+	0.0962559i	$0.969313\pi$
$632$	−652.247	−	3699.07i	−0.0410522	−	0.232818i
$633$	−13045.1	−	4425.71i	−0.819110	−	0.277893i
$634$	3479.88	−	1266.57i	0.217987	−	0.0793408i
$635$	−20317.9	+	7395.10i	−1.26975	+	0.462151i
$636$	−4111.95	+	3607.33i	−0.256367	+	0.224906i
$637$	2317.55	+	13143.5i	0.144152	+	0.817525i
$638$	2454.73	−	4251.71i	0.152325	−	0.263835i
$639$	7370.14	−	6758.16i	0.456273	−	0.418386i
$640$	2164.69	+	3749.35i	0.133698	+	0.231572i
$641$	−14688.2	+	12324.9i	−0.905069	+	0.759443i	−0.971174	−	0.238370i	$-0.923387\pi$
$641$	−14688.2	+	12324.9i	−0.905069	+	0.759443i	0.0661057	+	0.997813i	$0.478943\pi$
$642$	9220.55	−	16813.7i	0.566832	−	1.03362i
$643$	3093.64	−	17544.9i	0.189737	−	1.07605i	−0.729979	−	0.683470i	$-0.760470\pi$
$643$	3093.64	−	17544.9i	0.189737	−	1.07605i	0.919716	−	0.392584i	$-0.128419\pi$
$644$	−170.570	−	143.125i	−0.0104369	−	0.00875764i
$645$	2357.39	−	15333.8i	0.143910	−	0.936072i
$646$	12959.5	+	4716.88i	0.789296	+	0.287280i
$647$	8729.68			0.530447			0.265223	−	0.964187i	$-0.414554\pi$
$647$	8729.68			0.530447			0.265223	+	0.964187i	$0.414554\pi$
$648$	−1551.65	+	17877.4i	−0.0940656	+	1.08378i
$649$	−8503.49			−0.514316
$650$	20233.5	+	7364.38i	1.22096	+	0.444392i
$651$	−39.7025	+	258.247i	−0.00239026	+	0.0155476i
$652$	395.568	+	331.921i	0.0237602	+	0.0199371i
$653$	970.271	−	5502.68i	0.0581464	−	0.329765i	−0.941834	−	0.336080i	$-0.890899\pi$
$653$	970.271	−	5502.68i	0.0581464	−	0.329765i	0.999980	+	0.00631463i	$0.00201002\pi$
$654$	−11118.6	+	20274.8i	−0.664789	+	1.21225i
$655$	6825.05	−	5726.90i	0.407140	−	0.341631i
$656$	829.625	+	1436.95i	0.0493772	+	0.0855238i
$657$	2965.14	+	13353.1i	0.176075	+	0.792927i
$658$	−96.7362	+	167.552i	−0.00573126	+	0.00992683i
$659$	5652.44	+	32056.6i	0.334124	+	1.89491i	0.435712	+	0.900086i	$0.356496\pi$
$659$	5652.44	+	32056.6i	0.334124	+	1.89491i	−0.101588	+	0.994827i	$0.532392\pi$
$660$	5329.29	−	4675.29i	0.314307	−	0.275735i
$661$	14602.3	−	5314.82i	0.859252	−	0.312742i	0.125445	−	0.992101i	$-0.459964\pi$
$661$	14602.3	−	5314.82i	0.859252	−	0.312742i	0.733806	+	0.679359i	$0.237742\pi$
$662$	−14793.1	+	5384.26i	−0.868507	+	0.316111i
$663$	−7671.75	−	2602.73i	−0.449391	−	0.152461i
$664$	2082.31	+	11809.4i	0.121701	+	0.690199i
$665$	−959.606	+	1662.09i	−0.0559578	+	0.0969217i
$666$	12172.0	−	5046.72i	0.708190	−	0.293628i
$667$	−5217.78	−	9037.46i	−0.302899	−	0.524636i
$668$	2832.79	−	2376.99i	0.164078	−	0.137678i
$669$	−4979.81	−	8203.28i	−0.287788	−	0.474076i
$670$	6017.29	−	34125.8i	0.346968	−	1.96775i
$671$	−6837.46	−	5737.31i	−0.393379	−	0.330084i
$672$	392.182	−	152.589i	0.0225130	−	0.00875931i
$673$	3858.21	+	1404.28i	0.220985	+	0.0804321i	0.450140	−	0.892958i	$-0.351374\pi$
$673$	3858.21	+	1404.28i	0.220985	+	0.0804321i	−0.229155	+	0.973390i	$0.573596\pi$
$674$	−21170.7			−1.20989
$675$	−24795.0	+	23760.7i	−1.41387	+	1.35489i
$676$	1971.06			0.112145
$677$	−4112.42	−	1496.80i	−0.233461	−	0.0849729i	0.222640	−	0.974901i	$-0.428532\pi$
$677$	−4112.42	−	1496.80i	−0.233461	−	0.0849729i	−0.456102	+	0.889928i	$0.650755\pi$
$678$	−21465.0	−	17221.4i	−1.21587	−	0.975491i
$679$	569.403	+	477.786i	0.0321821	+	0.0270040i
$680$	3289.36	−	18654.9i	0.185502	−	1.05203i
$681$	−6540.69	+	143.846i	−0.368047	+	0.00809428i
$682$	−3251.83	+	2728.61i	−0.182579	+	0.153202i
$683$	6487.22	+	11236.2i	0.363436	+	0.629489i	0.988524	−	0.151065i	$-0.0482703\pi$
$683$	6487.22	+	11236.2i	0.363436	+	0.629489i	−0.625088	+	0.780554i	$0.714937\pi$
$684$	−5518.48	+	10609.8i	−0.308486	+	0.593095i
$685$	−16338.1	+	28298.4i	−0.911309	+	1.57843i
$686$	−175.765	−	996.816i	−0.00978244	−	0.0554790i
$687$	−2060.65	−	10350.3i	−0.114438	−	0.574800i
$688$	4721.64	−	1718.54i	0.261644	−	0.0952306i
$689$	−13280.1	+	4833.55i	−0.734296	+	0.267262i
$690$	5169.00	+	25962.9i	0.285189	+	1.43245i
$691$	−135.781	−	770.053i	−0.00747519	−	0.0423939i	0.980842	−	0.194805i	$-0.0624074\pi$
$691$	−135.781	−	770.053i	−0.00747519	−	0.0423939i	−0.988317	+	0.152411i	$0.951296\pi$
$692$	2481.86	−	4298.70i	0.136338	−	0.236145i
$693$	232.051	+	363.970i	0.0127199	+	0.0199510i
$694$	−1474.85	−	2554.51i	−0.0806694	−	0.139723i
$695$	−15928.1	+	13365.2i	−0.869333	+	0.729457i
$696$	11372.6	−	250.112i	0.619362	−	0.0136213i
$697$	356.291	−	2020.63i	0.0193622	−	0.109809i
$698$	6828.97	+	5730.19i	0.370316	+	0.310732i
$699$	−17831.9	−	14306.6i	−0.964900	−	0.774140i
$700$	436.488	+	158.869i	0.0235681	+	0.00857809i
$701$	15155.3			0.816556			0.408278	−	0.912858i	$-0.366129\pi$
$701$	15155.3			0.816556			0.408278	+	0.912858i	$0.366129\pi$
$702$	−5452.58	+	11071.2i	−0.293154	+	0.595234i
$703$	32990.2			1.76991
$704$	12372.7	+	4503.28i	0.662376	+	0.241085i
$705$	−12202.6	+	4747.77i	−0.651883	+	0.253633i
$706$	3526.91	+	2959.43i	0.188013	+	0.157761i
$707$	28.0029	−	158.812i	0.00148962	−	0.00844803i
$708$	−2721.57	−	4483.27i	−0.144468	−	0.237983i
$709$	13564.5	−	11382.0i	0.718515	−	0.602905i	−0.208459	−	0.978031i	$-0.566845\pi$
$709$	13564.5	−	11382.0i	0.718515	−	0.602905i	0.926974	+	0.375126i	$0.122400\pi$
$710$	8040.08	+	13925.8i	0.424984	+	0.736094i
$711$	3269.50	+	2506.98i	0.172455	+	0.132235i
$712$	−1106.81	+	1917.05i	−0.0582578	+	0.100905i
$713$	1566.85	+	8886.03i	0.0822986	+	0.466738i
$714$	290.736	+	98.6356i	0.0152388	+	0.00516995i
$715$	17211.6	−	6264.52i	0.900250	−	0.327664i
$716$	−5437.57	+	1979.11i	−0.283815	+	0.103300i
$717$	19907.8	−	17464.7i	1.03692	−	0.909669i
$718$	2563.15	+	14536.3i	0.133226	+	0.755559i
$719$	9827.59	−	17021.9i	0.509746	−	0.882906i	−0.490190	−	0.871615i	$-0.663073\pi$
$719$	9827.59	−	17021.9i	0.509746	−	0.882906i	0.999936	−	0.0112904i	$-0.00359394\pi$
$720$	−16026.7	−	5047.11i	−0.829553	−	0.261243i
$721$	−131.478	−	227.726i	−0.00679124	−	0.0117628i
$722$	28429.9	−	23855.5i	1.46545	−	1.22965i
$723$	9881.86	−	18019.6i	0.508313	−	0.926912i
$724$	−1490.73	+	8454.36i	−0.0765229	+	0.433983i
$725$	16676.6	+	13993.3i	0.854281	+	0.716827i
$726$	1307.21	−	8502.85i	0.0668254	−	0.434670i
$727$	−24052.7	−	8754.46i	−1.22705	−	0.446609i	−0.354463	−	0.935070i	$-0.615336\pi$
$727$	−24052.7	−	8754.46i	−1.22705	−	0.446609i	−0.872586	+	0.488461i	$0.837559\pi$
$728$	627.080			0.0319246
$729$	−11998.4	−	15603.2i	−0.609582	−	0.792723i
$730$	−21995.9			−1.11521
$731$	−5838.70	−	2125.11i	−0.295420	−	0.107524i
$732$	836.512	−	5441.14i	0.0422382	−	0.274741i
$733$	20321.3	+	17051.6i	1.02399	+	0.859231i	0.990124	−	0.140195i	$-0.0447730\pi$
$733$	20321.3	+	17051.6i	1.02399	+	0.859231i	0.0338680	+	0.999426i	$0.489217\pi$
$734$	−1681.57	+	9536.65i	−0.0845611	+	0.479570i
$735$	16459.1	−	30013.2i	0.825989	−	1.50619i
$736$	11132.7	−	9341.43i	0.557549	−	0.467839i
$737$	−9756.33	−	16898.5i	−0.487624	−	0.844590i
$738$	−2981.27	−	938.862i	−0.148702	−	0.0468293i
$739$	2964.87	−	5135.30i	0.147584	−	0.255622i	−0.782750	−	0.622336i	$-0.786184\pi$
$739$	2964.87	−	5135.30i	0.147584	−	0.255622i	0.930334	+	0.366714i	$0.119517\pi$
$740$	−2094.52	−	11878.6i	−0.104049	−	0.590091i
$741$	−23226.7	+	20376.4i	−1.15149	+	1.01018i
$742$	503.273	−	183.177i	0.0248999	−	0.00906283i
$743$	−34440.9	+	12535.5i	−1.70056	+	0.618953i	−0.995889	−	0.0905835i	$-0.971127\pi$
$743$	−34440.9	+	12535.5i	−1.70056	+	0.618953i	−0.704669	+	0.709536i	$0.748905\pi$
$744$	−9314.24	−	3159.97i	−0.458974	−	0.155712i
$745$	4185.04	+	23734.6i	0.205810	+	1.16720i
$746$	−4989.82	+	8642.63i	−0.244893	+	0.424168i
$747$	−10437.9	−	8003.58i	−0.511250	−	0.392016i
$748$	−1419.67	−	2458.95i	−0.0693962	−	0.120198i
$749$	818.730	−	686.996i	0.0399409	−	0.0335144i
$750$	−14023.1	−	23100.4i	−0.682735	−	1.12467i
$751$	6829.61	−	38732.6i	0.331846	−	1.88199i	−0.124551	−	0.992213i	$-0.539749\pi$
$751$	6829.61	−	38732.6i	0.331846	−	1.88199i	0.456396	−	0.889777i	$-0.349140\pi$
$752$	−3248.65	−	2725.94i	−0.157535	−	0.132187i
$753$	2431.88	−	946.188i	0.117693	−	0.0457915i
$754$	7351.36	+	2675.68i	0.355067	+	0.129234i
$755$	43744.9			2.10866
$756$	−117.626	+	238.833i	−0.00565876	+	0.0114898i
$757$	15815.2			0.759330			0.379665	−	0.925124i	$-0.376039\pi$
$757$	15815.2			0.759330			0.379665	+	0.925124i	$0.376039\pi$
$758$	−4723.16	−	1719.09i	−0.226323	−	0.0823748i
$759$	11627.1	+	9328.41i	0.556042	+	0.446113i
$760$	−55344.3	−	46439.4i	−2.64151	−	2.21649i
$761$	−767.663	+	4353.63i	−0.0365674	+	0.207384i	−0.997617	−	0.0689910i	$-0.978022\pi$
$761$	−767.663	+	4353.63i	−0.0365674	+	0.207384i	0.961050	+	0.276375i	$0.0891331\pi$
$762$	13188.5	−	290.049i	0.626995	−	0.0137892i
$763$	−987.266	+	828.415i	−0.0468433	+	0.0393062i
$764$	4894.36	+	8477.29i	0.231769	+	0.401436i
$765$	11169.9	+	17520.0i	0.527908	+	0.828020i
$766$	−8530.50	+	14775.3i	−0.402375	+	0.696934i
$767$	−2352.97	−	13344.4i	−0.110770	−	0.628209i
$768$	3855.47	+	19365.3i	0.181149	+	0.909878i
$769$	9351.80	−	3403.78i	0.438536	−	0.159614i	−0.113311	−	0.993560i	$-0.536145\pi$
$769$	9351.80	−	3403.78i	0.438536	−	0.159614i	0.551847	+	0.833945i	$0.313923\pi$
$770$	−652.268	+	237.406i	−0.0305274	+	0.0111111i
$771$	303.068	+	1522.26i	0.0141566	+	0.0711060i
$772$	−310.245	−	1759.49i	−0.0144637	−	0.0820276i
$773$	12142.6	−	21031.6i	0.564991	−	0.978594i	−0.432059	−	0.901845i	$-0.642213\pi$
$773$	12142.6	−	21031.6i	0.564991	−	0.978594i	0.997050	−	0.0767486i	$-0.0244539\pi$
$774$	−4367.66	+	8397.26i	−0.202832	+	0.389966i
$775$	−9411.61	−	16301.4i	−0.436226	−	0.755566i
$776$	−21434.6	+	17985.8i	−0.991569	+	0.832025i
$777$	734.229	−	16.1476i	0.0339000	−	0.000745547i
$778$	−5436.87	+	30834.0i	−0.250542	+	1.42089i
$779$	−5994.68	−	5030.13i	−0.275715	−	0.231352i
$780$	8811.48	+	7069.46i	0.404489	+	0.324522i
$781$	8508.67	+	3096.90i	0.389839	+	0.141890i
$782$	10602.4			0.484834
$783$	−9008.70	+	8632.89i	−0.411168	+	0.394016i
$784$	11086.5			0.505031
$785$	−16724.6	−	6087.26i	−0.760416	−	0.276769i
$786$	−5065.84	+	1971.00i	−0.229889	+	0.0894445i
$787$	12775.2	+	10719.7i	0.578637	+	0.485534i	0.884499	−	0.466541i	$-0.154500\pi$
$787$	12775.2	+	10719.7i	0.578637	+	0.485534i	−0.305862	+	0.952076i	$0.598945\pi$
$788$	−406.441	+	2305.04i	−0.0183742	+	0.104205i
$789$	8278.37	+	13637.0i	0.373533	+	0.615325i
$790$	−5075.30	+	4258.68i	−0.228571	+	0.191794i
$791$	−766.900	−	1328.31i	−0.0344726	−	0.0597083i
$792$	−15010.0	+	6223.41i	−0.673431	+	0.279216i
$793$	7111.47	−	12317.4i	0.318456	−	0.551582i
$794$	−679.617	−	3854.30i	−0.0303762	−	0.172272i
$795$	34324.6	+	11645.0i	1.53128	+	0.519506i
$796$	−1684.49	+	613.105i	−0.0750065	+	0.0273001i
$797$	1470.43	−	535.192i	0.0653516	−	0.0237860i	−0.309138	−	0.951017i	$-0.600040\pi$
$797$	1470.43	−	535.192i	0.0653516	−	0.0237860i	0.374489	+	0.927231i	$0.377818\pi$
$798$	880.221	−	772.202i	0.0390470	−	0.0342552i
$799$	910.630	+	5164.44i	0.0403201	+	0.228667i
$800$	−15158.4	+	26255.1i	−0.669913	+	1.16032i
$801$	−526.348	−	2370.34i	−0.0232180	−	0.104559i
$802$	7480.75	+	12957.0i	0.329370	+	0.570485i
$803$	−9488.13	+	7961.49i	−0.416973	+	0.349882i
$804$	5786.78	−	10552.2i	0.253836	−	0.462871i
$805$	−256.208	+	1453.03i	−0.0112176	+	0.0636181i
$806$	−5181.75	−	4348.00i	−0.226451	−	0.190015i
$807$	−5008.78	+	32579.9i	−0.218485	+	1.42115i
$808$	5704.46	+	2076.25i	0.248369	+	0.0903990i
$809$	−26781.3			−1.16388			−0.581941	−	0.813231i	$-0.697706\pi$
$809$	−26781.3			−1.16388			−0.581941	+	0.813231i	$0.697706\pi$
$810$	28677.1	−	13396.4i	1.24397	−	0.581115i
$811$	−29767.3			−1.28887			−0.644433	−	0.764661i	$-0.722906\pi$
$811$	−29767.3			−1.28887			−0.644433	+	0.764661i	$0.722906\pi$
$812$	158.588	+	57.7212i	0.00685386	+	0.00249460i
$813$	−973.242	+	6330.51i	−0.0419841	+	0.273088i
$814$	9140.20	+	7669.54i	0.393568	+	0.330242i
$815$	594.171	−	3369.71i	0.0255373	−	0.144829i
$816$	−3235.81	+	5900.52i	−0.138819	+	0.253137i
$817$	−18153.6	+	15232.6i	−0.777371	+	0.652292i
$818$	6241.74	+	10811.0i	0.266794	+	0.462100i
$819$	−506.960	+	464.865i	−0.0216296	+	0.0198336i
$820$	−1430.58	+	2477.84i	−0.0609244	+	0.105524i
$821$	961.362	+	5452.15i	0.0408669	+	0.231768i	0.998399	−	0.0565578i	$-0.0180125\pi$
$821$	961.362	+	5452.15i	0.0408669	+	0.231768i	−0.957532	+	0.288326i	$0.906901\pi$
$822$	14986.5	−	13147.4i	0.635905	−	0.557868i
$823$	−7932.73	+	2887.28i	−0.335987	+	0.122289i	−0.504504	−	0.863409i	$-0.668325\pi$
$823$	−7932.73	+	2887.28i	−0.335987	+	0.122289i	0.168517	+	0.985699i	$0.446102\pi$
$824$	9301.73	−	3385.55i	0.393254	−	0.143133i
$825$	−29448.3	−	9990.71i	−1.24274	−	0.421614i
$826$	89.1702	+	505.709i	0.00375621	+	0.0213025i
$827$	2458.99	−	4259.10i	0.103395	−	0.179085i	−0.809686	−	0.586863i	$-0.800363\pi$
$827$	2458.99	−	4259.10i	0.103395	−	0.179085i	0.913081	+	0.407778i	$0.133696\pi$
$828$	−1196.91	+	9115.70i	−0.0502360	+	0.382600i
$829$	−7243.05	−	12545.3i	−0.303452	−	0.525594i	0.673464	−	0.739220i	$-0.264806\pi$
$829$	−7243.05	−	12545.3i	−0.303452	−	0.525594i	−0.976915	+	0.213627i	$0.931472\pi$
$830$	16203.0	−	13595.9i	0.677607	−	0.568580i
$831$	16781.2	+	27643.9i	0.700523	+	1.15398i
$832$	−3643.32	+	20662.3i	−0.151814	+	0.860980i
$833$	−10501.9	−	8812.17i	−0.436819	−	0.366535i
$834$	11822.5	−	4599.86i	0.490863	−	0.190984i
$835$	−23026.1	−	8380.82i	−0.954314	−	0.347342i
$836$	−10829.2			−0.448009
$837$	9872.60	−	4350.14i	0.407703	−	0.179645i
$838$	−6703.34			−0.276328
$839$	33311.7	+	12124.5i	1.37074	+	0.498907i	0.919356	−	0.393426i	$-0.128710\pi$
$839$	33311.7	+	12124.5i	1.37074	+	0.498907i	0.451379	+	0.892332i	$0.350932\pi$
$840$	−1254.47	−	1006.46i	−0.0515279	−	0.0413409i
$841$	−12624.0	−	10592.8i	−0.517610	−	0.434327i
$842$	3592.28	−	20372.9i	0.147029	−	0.833842i
$843$	2913.22	−	64.0692i	0.119023	−	0.00261763i
$844$	5893.52	−	4945.25i	0.240359	−	0.201685i
$845$	−6530.46	−	11311.1i	−0.265864	−	0.460489i
$846$	7980.91	−	351.211i	0.324337	−	0.0142729i
$847$	239.737	−	415.237i	0.00972547	−	0.0168450i
$848$	2038.54	+	11561.1i	0.0825514	+	0.468173i
$849$	−6333.58	−	31812.4i	−0.256028	−	1.28598i
$850$	−20783.9	+	7564.71i	−0.838684	+	0.305256i
$851$	23832.6	−	8674.34i	0.960011	−	0.349416i
$852$	1090.46	+	5477.18i	0.0438481	+	0.220241i
$853$	−4342.16	−	24625.6i	−0.174294	−	0.988470i	−0.938956	−	0.344038i	$-0.888205\pi$
$853$	−4342.16	−	24625.6i	−0.174294	−	0.988470i	0.764662	−	0.644432i	$-0.222906\pi$
$854$	−269.503	+	466.792i	−0.0107988	+	0.0187041i
$855$	79169.2	−	3483.95i	3.16670	−	0.139355i
$856$	20116.5	+	34842.8i	0.803234	+	1.39124i
$857$	19697.9	−	16528.5i	0.785142	−	0.658812i	−0.159396	−	0.987215i	$-0.550955\pi$
$857$	19697.9	−	16528.5i	0.785142	−	0.658812i	0.944538	+	0.328403i	$0.106510\pi$
$858$	−11172.3	+	245.706i	−0.444539	+	0.00977653i
$859$	−5219.23	+	29599.7i	−0.207308	+	1.17570i	0.686457	+	0.727170i	$0.259165\pi$
$859$	−5219.23	+	29599.7i	−0.207308	+	1.17570i	−0.893766	+	0.448534i	$0.851946\pi$
$860$	6637.30	+	5569.36i	0.263175	+	0.220830i
$861$	−135.880	−	109.016i	−0.00537835	−	0.00431506i
$862$	−29395.8	−	10699.2i	−1.16151	−	0.422756i
$863$	−37340.0			−1.47285			−0.736423	−	0.676521i	$-0.763487\pi$
$863$	−37340.0			−1.47285			−0.736423	+	0.676521i	$0.763487\pi$
$864$	−14018.1	−	10267.4i	−0.551975	−	0.404286i
$865$	−32891.3			−1.29288
$866$	−24830.9	−	9037.71i	−0.974352	−	0.354635i
$867$	−16036.1	+	6239.26i	−0.628158	+	0.244402i
$868$	−111.784	−	93.7976i	−0.00437118	−	0.00366785i
$869$	−647.833	+	3674.05i	−0.0252891	+	0.143422i
$870$	−10411.9	−	17151.6i	−0.405744	−	0.668385i
$871$	23818.8	−	19986.3i	0.926599	−	0.777509i
$872$	−24257.5	−	42015.2i	−0.942045	−	1.63167i
$873$	3995.56	−	30430.4i	0.154902	−	1.17974i
$874$	20218.6	−	35019.6i	0.782498	−	1.35533i
$875$	−261.542	−	1483.28i	−0.0101048	−	0.0573074i
$876$	−7234.23	−	2454.30i	−0.279021	−	0.0946611i
$877$	−26702.4	+	9718.87i	−1.02814	+	0.374211i	−0.800371	−	0.599505i	$-0.795364\pi$
$877$	−26702.4	+	9718.87i	−1.02814	+	0.374211i	−0.227765	+	0.973716i	$0.573142\pi$
$878$	28367.4	−	10324.9i	1.09038	−	0.396866i
$879$	16770.6	−	14712.6i	0.643526	−	0.564554i
$880$	−2642.05	−	14983.8i	−0.101208	−	0.573981i
$881$	−6915.61	+	11978.2i	−0.264464	+	0.458065i	−0.967423	−	0.253165i	$-0.918528\pi$
$881$	−6915.61	+	11978.2i	−0.264464	+	0.458065i	0.702959	+	0.711230i	$0.251862\pi$
$882$	−15392.5	+	14114.4i	−0.587634	+	0.538840i
$883$	22236.2	+	38514.3i	0.847462	+	1.46785i	0.883466	+	0.468495i	$0.155204\pi$
$883$	22236.2	+	38514.3i	0.847462	+	1.46785i	−0.0360045	+	0.999352i	$0.511463\pi$
$884$	3465.94	−	2908.27i	0.131869	−	0.110651i
$885$	−16710.6	+	30471.9i	−0.634713	+	1.15740i
$886$	1388.94	−	7877.06i	0.0526662	−	0.298685i
$887$	−9063.98	−	7605.58i	−0.343110	−	0.287903i	0.454906	−	0.890539i	$-0.349673\pi$
$887$	−9063.98	−	7605.58i	−0.343110	−	0.287903i	−0.798016	+	0.602636i	$0.794117\pi$
$888$	−4200.90	+	27325.0i	−0.158753	+	1.03262i
$889$	690.902	+	251.468i	0.0260653	+	0.00948701i
$890$	3904.54			0.147057
$891$	7521.26	−	16158.5i	0.282797	−	0.607552i
$892$	5359.54			0.201178
$893$	18794.7	+	6840.71i	0.704300	+	0.256344i
$894$	2234.34	−	14533.4i	0.0835877	−	0.543701i
$895$	29373.0	+	24646.8i	1.09702	+	0.920506i
$896$	25.5643	−	144.982i	0.000953173	−	0.00540571i
$897$	−11421.6	+	20827.3i	−0.425146	+	0.775256i
$898$	23763.3	−	19939.8i	0.883064	−	0.740979i
$899$	−3419.49	−	5922.73i	−0.126859	−	0.219727i
$900$	−4157.68	−	18723.5i	−0.153988	−	0.693464i
$901$	7258.40	−	12571.9i	0.268382	−	0.464852i
$902$	−491.473	−	2787.28i	−0.0181422	−	0.102889i
$903$	−396.569	+	347.903i	−0.0146146	+	0.0128211i
$904$	54256.3	−	19747.7i	1.99617	−	0.726547i
$905$	53455.1	−	19456.1i	1.96344	−	0.714632i
$906$	−25274.4	−	8574.64i	−0.926805	−	0.314430i
$907$	4462.90	+	25310.4i	0.163383	+	0.926590i	0.950716	+	0.310062i	$0.100350\pi$
$907$	4462.90	+	25310.4i	0.163383	+	0.926590i	−0.787334	+	0.616527i	$0.788539\pi$
$908$	1826.90	−	3164.28i	0.0667707	−	0.115650i
$909$	−6150.92	+	2550.28i	−0.224437	+	0.0930554i
$910$	−553.043	−	957.898i	−0.0201464	−	0.0348945i
$911$	−17157.4	+	14396.7i	−0.623984	+	0.523585i	−0.899053	−	0.437840i	$-0.855744\pi$
$911$	−17157.4	+	14396.7i	−0.623984	+	0.523585i	0.275069	+	0.961424i	$0.411299\pi$
$912$	13318.7	+	21940.1i	0.483583	+	0.796611i
$913$	2068.22	−	11729.5i	0.0749705	−	0.425179i
$914$	23200.2	+	19467.3i	0.839601	+	0.704509i
$915$	−33996.0	+	13227.1i	−1.22828	+	0.477894i
$916$	5538.53	+	2015.86i	0.199780	+	0.0727139i
$917$	−302.963			−0.0109103
$918$	−3019.46	−	12311.9i	−0.108559	−	0.442651i
$919$	40681.8			1.46025			0.730124	−	0.683314i	$-0.239462\pi$
$919$	40681.8			1.46025			0.730124	+	0.683314i	$0.239462\pi$
$920$	−52192.1	−	18996.4i	−1.87035	−	0.680752i
$921$	33133.2	+	26582.8i	1.18542	+	0.951068i
$922$	25772.2	+	21625.4i	0.920566	+	0.772447i
$923$	−2505.50	+	14209.4i	−0.0893495	+	0.506726i
$924$	−241.014	+	5.30051i	−0.00858093	+	0.000188716i
$925$	−40530.0	+	34008.7i	−1.44067	+	1.20886i
$926$	5897.72	+	10215.2i	0.209299	+	0.362517i
$927$	−5010.18	+	9632.57i	−0.177514	+	0.341289i
$928$	−5507.46	+	9539.19i	−0.194818	+	0.337435i
$929$	−7262.46	−	41187.4i	−0.256484	−	1.45459i	−0.792235	−	0.610216i	$-0.791083\pi$
$929$	−7262.46	−	41187.4i	−0.256484	−	1.45459i	0.535751	−	0.844376i	$-0.320029\pi$
$930$	3387.52	+	17014.9i	0.119442	+	0.599936i
$931$	−49133.6	+	17883.2i	−1.72963	+	0.629535i
$932$	11998.0	−	4366.92i	0.421682	−	0.153480i
$933$	1626.32	+	8168.71i	0.0570669	+	0.286636i
$934$	−603.810	−	3424.38i	−0.0211534	−	0.119967i
$935$	−9407.26	+	16293.8i	−0.329038	+	0.569910i
$936$	−13919.6	−	21832.8i	−0.486087	−	0.762423i
$937$	−26219.7	−	45413.9i	−0.914153	−	1.58336i	−0.808137	−	0.588995i	$-0.799524\pi$
$937$	−26219.7	−	45413.9i	−0.914153	−	1.58336i	−0.106016	−	0.994364i	$-0.533810\pi$
$938$	−902.657	+	757.419i	−0.0314209	+	0.0263653i
$939$	−56709.2	+	1247.18i	−1.97086	+	0.0433442i
$940$	1269.84	−	7201.63i	0.0440613	−	0.249884i
$941$	−30508.3	−	25599.5i	−1.05690	−	0.886844i	−0.0630972	−	0.998007i	$-0.520098\pi$
$941$	−30508.3	−	25599.5i	−1.05690	−	0.886844i	−0.993802	+	0.111164i	$0.964542\pi$
$942$	8469.73	+	6795.28i	0.292950	+	0.235034i
$943$	−5653.25	−	2057.61i	−0.195223	−	0.0710553i
$944$	−11255.9			−0.388080
$945$	1760.28	−	116.289i	0.0605947	−	0.00400306i
$946$	−8570.87			−0.294570
$947$	48884.8	+	17792.6i	1.67745	+	0.610541i	0.992956	−	0.118481i	$-0.0378023\pi$
$947$	48884.8	+	17792.6i	1.67745	+	0.610541i	0.684491	+	0.729021i	$0.260025\pi$
$948$	−2144.40	+	834.337i	−0.0734671	+	0.0285844i
$949$	−15119.2	−	12686.5i	−0.517166	−	0.433954i
$950$	−14648.3	+	83074.9i	−0.500268	+	2.83716i
$951$	−4422.44	−	7285.12i	−0.150796	−	0.248408i
$952$	−493.439	+	414.044i	−0.0167988	+	0.0140959i
$953$	25938.1	+	44926.0i	0.881654	+	1.52707i	0.849502	+	0.527586i	$0.176903\pi$
$953$	25938.1	+	44926.0i	0.881654	+	1.52707i	0.0321519	+	0.999483i	$0.489764\pi$
$954$	−17549.0	−	13456.2i	−0.595567	−	0.456668i
$955$	32431.8	−	56173.5i	1.09892	−	1.90338i
$956$	2568.32	+	14565.7i	0.0868886	+	0.492770i
$957$	−10699.4	−	3629.89i	−0.361402	−	0.122610i
$958$	−25285.9	+	9203.32i	−0.852767	+	0.310382i
$959$	1044.13	−	380.033i	0.0351582	−	0.0127966i
$960$	40451.5	−	35487.3i	1.35996	−	1.19307i
$961$	−4146.31	−	23514.9i	−0.139180	−	0.789330i
$962$	−9506.50	+	16465.7i	−0.318609	+	0.551847i
$963$	−42092.7	−	13255.8i	−1.40854	−	0.443576i
$964$	5738.87	+	9940.01i	0.191739	+	0.332102i
$965$	−9069.08	+	7609.86i	−0.302533	+	0.253855i
$966$	432.843	−	789.292i	0.0144167	−	0.0262889i
$967$	−9130.66	+	51782.6i	−0.303642	+	1.72204i	0.326184	+	0.945306i	$0.394237\pi$
$967$	−9130.66	+	51782.6i	−0.303642	+	1.72204i	−0.629826	+	0.776736i	$0.716874\pi$
$968$	13826.6	+	11601.9i	0.459095	+	0.385227i
$969$	4822.75	−	31369.9i	0.159885	−	1.03998i
$970$	46378.2	+	16880.3i	1.53517	+	0.558755i
$971$	21515.9			0.711100			0.355550	−	0.934657i	$-0.384294\pi$
$971$	21515.9			0.711100			0.355550	+	0.934657i	$0.384294\pi$
$972$	10926.4	−	1206.17i	0.360560	−	0.0398023i
$973$	707.045			0.0232958
$974$	−18262.0	−	6646.82i	−0.600772	−	0.218663i
$975$	7529.67	−	48977.2i	0.247325	−	1.60874i
$976$	−9050.60	−	7594.35i	−0.296826	−	0.249067i
$977$	−3655.15	+	20729.4i	−0.119692	+	0.678804i	0.864628	+	0.502412i	$0.167554\pi$
$977$	−3655.15	+	20729.4i	−0.119692	+	0.678804i	−0.984320	+	0.176392i	$0.943557\pi$
$978$	−1003.80	+	1830.44i	−0.0328202	+	0.0598477i
$979$	1684.26	−	1413.26i	0.0549839	−	0.0461369i
$980$	9558.56	+	16555.9i	0.311568	+	0.539652i
$981$	50757.5	+	15984.6i	1.65195	+	0.520232i
$982$	−4714.85	+	8166.36i	−0.153215	+	0.265376i
$983$	−1817.84	−	10309.5i	−0.0589829	−	0.334509i	0.941010	−	0.338380i	$-0.109879\pi$
$983$	−1817.84	−	10309.5i	−0.0589829	−	0.334509i	−0.999993	+	0.00387121i	$0.998768\pi$
$984$	4929.69	−	4324.72i	0.159708	−	0.140109i
$985$	14574.3	−	5304.61i	0.471447	−	0.171593i
$986$	−7551.34	+	2748.46i	−0.243898	+	0.0887717i
$987$	421.642	+	143.047i	0.0135978	+	0.00461322i
$988$	−2996.50	−	16994.0i	−0.0964893	−	0.547218i
$989$	−9109.15	+	15777.5i	−0.292876	+	0.507275i
$990$	22744.4	+	17440.0i	0.730167	+	0.559877i
$991$	−6106.19	−	10576.2i	−0.195731	−	0.339016i	0.751409	−	0.659837i	$-0.229375\pi$
$991$	−6106.19	−	10576.2i	−0.195731	−	0.339016i	−0.947140	+	0.320821i	$0.896041\pi$
$992$	7295.84	−	6121.94i	0.233511	−	0.195939i
$993$	18800.0	+	30969.4i	0.600805	+	0.989712i
$994$	94.9508	−	538.493i	0.00302983	−	0.0171830i
$995$	9099.37	+	7635.28i	0.289919	+	0.243271i
$996$	6846.03	−	2663.64i	0.217796	−	0.0847395i
$997$	−7555.41	−	2749.94i	−0.240002	−	0.0873536i	0.219219	−	0.975676i	$-0.429649\pi$
$997$	−7555.41	−	2749.94i	−0.240002	−	0.0873536i	−0.459221	+	0.888322i	$0.651871\pi$
$998$	−15930.5			−0.505281
$999$	−16860.3	−	25205.0i	−0.533970	−	0.798249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.4.3	✓	48
3.2	odd	2		81.4.e.a.64.6		48
9.2	odd	6		243.4.e.b.28.3		48
9.4	even	3		243.4.e.d.109.6		48
9.5	odd	6		243.4.e.a.109.3		48
9.7	even	3		243.4.e.c.28.6		48
27.2	odd	18		243.4.e.a.136.3		48
27.7	even	9	inner	27.4.e.a.7.3	yes	48
27.11	odd	18		243.4.e.b.217.3		48
27.13	even	9		729.4.a.d.1.16		24
27.14	odd	18		729.4.a.c.1.9		24
27.16	even	9		243.4.e.c.217.6		48
27.20	odd	18		81.4.e.a.19.6		48
27.25	even	9		243.4.e.d.136.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.3	✓	48	1.1	even	1	trivial
27.4.e.a.7.3	yes	48	27.7	even	9	inner
81.4.e.a.19.6		48	27.20	odd	18
81.4.e.a.64.6		48	3.2	odd	2
243.4.e.a.109.3		48	9.5	odd	6
243.4.e.a.136.3		48	27.2	odd	18
243.4.e.b.28.3		48	9.2	odd	6
243.4.e.b.217.3		48	27.11	odd	18
243.4.e.c.28.6		48	9.7	even	3
243.4.e.c.217.6		48	27.16	even	9
243.4.e.d.109.6		48	9.4	even	3
243.4.e.d.136.6		48	27.25	even	9
729.4.a.c.1.9		24	27.14	odd	18
729.4.a.d.1.16		24	27.13	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12171 - 0.772239i) q^{2} +(-0.789571 + 5.13581i) q^{3} +(-2.22306 - 1.86537i) q^{4} +(-3.33920 + 18.9376i) q^{5} +(5.64131 - 10.2870i) q^{6} +(0.500915 - 0.420318i) q^{7} +(12.3077 + 21.3175i) q^{8} +(-25.7532 - 8.11018i) q^{9} +O(q^{10})\)	\(q+(-2.12171 - 0.772239i) q^{2} +(-0.789571 + 5.13581i) q^{3} +(-2.22306 - 1.86537i) q^{4} +(-3.33920 + 18.9376i) q^{5} +(5.64131 - 10.2870i) q^{6} +(0.500915 - 0.420318i) q^{7} +(12.3077 + 21.3175i) q^{8} +(-25.7532 - 8.11018i) q^{9} +(21.7091 - 37.6013i) q^{10} +(-4.24549 - 24.0774i) q^{11} +(11.3355 - 9.94439i) q^{12} +(36.6094 - 13.3247i) q^{13} +(-1.38738 + 0.504965i) q^{14} +(-94.6232 - 32.1021i) q^{15} +(-5.61966 - 31.8707i) q^{16} +(-20.0093 + 34.6572i) q^{17} +(48.3777 + 37.0950i) q^{18} +(76.3151 + 132.182i) q^{19} +(42.7488 - 35.8705i) q^{20} +(1.76317 + 2.90448i) q^{21} +(-9.58578 + 54.3637i) q^{22} +(89.8865 + 75.4237i) q^{23} +(-119.201 + 46.3782i) q^{24} +(-230.019 - 83.7201i) q^{25} -87.9642 q^{26} +(61.9863 - 125.860i) q^{27} -1.89761 q^{28} +(-83.5721 - 30.4178i) q^{29} +(175.972 + 141.183i) q^{30} +(58.9074 + 49.4292i) q^{31} +(21.5068 - 121.971i) q^{32} +(127.009 - 2.79325i) q^{33} +(69.2176 - 58.0805i) q^{34} +(6.28713 + 10.8896i) q^{35} +(42.1224 + 66.0686i) q^{36} +(108.072 - 187.187i) q^{37} +(-59.8426 - 339.384i) q^{38} +(39.5276 + 198.540i) q^{39} +(-444.800 + 161.894i) q^{40} +(-48.1790 + 17.5357i) q^{41} +(-1.49797 - 7.52404i) q^{42} +(26.9611 + 152.904i) q^{43} +(-35.4752 + 61.4449i) q^{44} +(239.582 - 460.620i) q^{45} +(-132.468 - 229.441i) q^{46} +(100.384 - 84.2318i) q^{47} +(168.119 - 3.69736i) q^{48} +(-59.4871 + 337.368i) q^{49} +(423.381 + 355.259i) q^{50} +(-162.194 - 130.129i) q^{51} +(-106.240 - 38.6684i) q^{52} -362.751 q^{53} +(-228.711 + 219.170i) q^{54} +470.143 q^{55} +(15.1252 + 5.50514i) q^{56} +(-739.116 + 287.573i) q^{57} +(153.826 + 129.075i) q^{58} +(60.3962 - 342.524i) q^{59} +(150.471 + 247.872i) q^{60} +(279.664 - 234.666i) q^{61} +(-86.8132 - 150.365i) q^{62} +(-16.3090 + 6.76200i) q^{63} +(-269.271 + 466.392i) q^{64} +(130.092 + 737.786i) q^{65} +(-271.633 - 92.1548i) q^{66} +(749.971 - 272.967i) q^{67} +(109.131 - 39.7203i) q^{68} +(-458.334 + 402.088i) q^{69} +(-4.93007 - 27.9598i) q^{70} +(-185.178 + 320.737i) q^{71} +(-144.073 - 648.811i) q^{72} +(-253.302 - 438.733i) q^{73} +(-373.851 + 313.698i) q^{74} +(611.587 - 1115.23i) q^{75} +(76.9145 - 436.204i) q^{76} +(-12.2468 - 10.2763i) q^{77} +(69.4540 - 451.768i) q^{78} +(-143.391 - 52.1900i) q^{79} +622.318 q^{80} +(597.450 + 417.725i) q^{81} +115.763 q^{82} +(457.778 + 166.617i) q^{83} +(1.49830 - 9.74579i) q^{84} +(-589.508 - 494.656i) q^{85} +(60.8748 - 345.238i) q^{86} +(222.206 - 405.194i) q^{87} +(461.018 - 386.840i) q^{88} +(44.9643 + 77.8804i) q^{89} +(-864.032 + 792.287i) q^{90} +(12.7376 - 22.0621i) q^{91} +(-59.1301 - 335.343i) q^{92} +(-300.371 + 263.510i) q^{93} +(-278.032 + 101.195i) q^{94} +(-2758.03 + 1003.84i) q^{95} +(609.440 + 206.760i) q^{96} +(197.390 + 1119.46i) q^{97} +(386.743 - 669.858i) q^{98} +(-85.9370 + 654.500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

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