LMFDB - Embedded newform 27.4.e.a.4.5

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			4.5
Character	$\chi$	$=$	27.4
Dual form			27.4.e.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.932125 - 0.339266i) q^{2} +(1.23404 - 5.04749i) q^{3} +(-5.37460 - 4.50982i) q^{4} +(0.0250883 - 0.142283i) q^{5} +(-2.86272 + 4.28623i) q^{6} +(19.4381 - 16.3105i) q^{7} +(7.44756 + 12.8996i) q^{8} +(-23.9543 - 12.4576i) q^{9} +O(q^{10})$	\(q+(-0.932125 - 0.339266i) q^{2} +(1.23404 - 5.04749i) q^{3} +(-5.37460 - 4.50982i) q^{4} +(0.0250883 - 0.142283i) q^{5} +(-2.86272 + 4.28623i) q^{6} +(19.4381 - 16.3105i) q^{7} +(7.44756 + 12.8996i) q^{8} +(-23.9543 - 12.4576i) q^{9} +(-0.0716572 + 0.124114i) q^{10} +(11.3027 + 64.1008i) q^{11} +(-29.3957 + 21.5629i) q^{12} +(24.9207 - 9.07040i) q^{13} +(-23.6524 + 8.60876i) q^{14} +(-0.687211 - 0.302215i) q^{15} +(7.18090 + 40.7249i) q^{16} +(34.5011 - 59.7576i) q^{17} +(18.1020 + 19.7389i) q^{18} +(-15.9760 - 27.6712i) q^{19} +(-0.776510 + 0.651569i) q^{20} +(-58.3398 - 118.241i) q^{21} +(11.2117 - 63.5846i) q^{22} +(-25.9254 - 21.7540i) q^{23} +(74.3009 - 21.6730i) q^{24} +(117.442 + 42.7454i) q^{25} -26.3065 q^{26} +(-92.4400 + 105.536i) q^{27} -178.030 q^{28} +(40.6547 + 14.7971i) q^{29} +(0.538036 + 0.514850i) q^{30} +(-48.7783 - 40.9298i) q^{31} +(27.8152 - 157.748i) q^{32} +(337.496 + 22.0525i) q^{33} +(-52.4331 + 43.9966i) q^{34} +(-1.83304 - 3.17491i) q^{35} +(72.5633 + 174.984i) q^{36} +(-128.992 + 223.421i) q^{37} +(5.50371 + 31.2131i) q^{38} +(-15.0297 - 136.980i) q^{39} +(2.02223 - 0.736032i) q^{40} +(-356.758 + 129.849i) q^{41} +(14.2647 + 130.009i) q^{42} +(51.2384 + 290.587i) q^{43} +(228.336 - 395.489i) q^{44} +(-2.37347 + 3.09575i) q^{45} +(16.7854 + 29.0731i) q^{46} +(-228.972 + 192.130i) q^{47} +(214.420 + 14.0105i) q^{48} +(52.2461 - 296.302i) q^{49} +(-94.9686 - 79.6881i) q^{50} +(-259.050 - 247.887i) q^{51} +(-174.845 - 63.6383i) q^{52} +340.033 q^{53} +(121.970 - 67.0111i) q^{54} +9.40401 q^{55} +(355.165 + 129.269i) q^{56} +(-159.385 + 46.4912i) q^{57} +(-32.8751 - 27.5855i) q^{58} +(53.1307 - 301.319i) q^{59} +(2.33055 + 4.72349i) q^{60} +(515.642 - 432.675i) q^{61} +(31.5814 + 54.7005i) q^{62} +(-668.816 + 148.555i) q^{63} +(85.9670 - 148.899i) q^{64} +(-0.665344 - 3.77335i) q^{65} +(-307.107 - 135.057i) q^{66} +(161.847 - 58.9077i) q^{67} +(-454.926 + 165.580i) q^{68} +(-141.796 + 104.013i) q^{69} +(0.631481 + 3.58131i) q^{70} +(-523.492 + 906.714i) q^{71} +(-17.7040 - 401.778i) q^{72} +(87.6625 + 151.836i) q^{73} +(196.036 - 164.494i) q^{74} +(360.685 - 540.038i) q^{75} +(-38.9277 + 220.770i) q^{76} +(1265.22 + 1061.65i) q^{77} +(-32.4632 + 132.782i) q^{78} +(-85.3554 - 31.0668i) q^{79} +5.97461 q^{80} +(418.618 + 596.825i) q^{81} +376.597 q^{82} +(-909.434 - 331.007i) q^{83} +(-219.695 + 898.603i) q^{84} +(-7.63691 - 6.40813i) q^{85} +(50.8258 - 288.247i) q^{86} +(124.858 - 186.944i) q^{87} +(-742.694 + 623.194i) q^{88} +(-240.117 - 415.895i) q^{89} +(3.26266 - 2.08039i) q^{90} +(336.469 - 582.781i) q^{91} +(41.2320 + 233.838i) q^{92} +(-266.787 + 195.699i) q^{93} +(278.614 - 101.407i) q^{94} +(-4.33794 + 1.57888i) q^{95} +(-761.904 - 335.063i) q^{96} +(-174.496 - 989.614i) q^{97} +(-149.225 + 258.466i) q^{98} +(527.792 - 1676.29i) 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 $

$2$	−0.932125	−	0.339266i	−0.329556	−	0.119949i	0.171943	−	0.985107i	$-0.444996\pi$
$2$	−0.932125	−	0.339266i	−0.329556	−	0.119949i	−0.501499	+	0.865158i	$0.667218\pi$
$3$	1.23404	−	5.04749i	0.237490	−	0.971390i
$3$	1.23404	−	5.04749i	0.237490	−	0.971390i
$4$	−5.37460	−	4.50982i	−0.671825	−	0.563728i
$5$	0.0250883	−	0.142283i	0.00224397	−	0.0127262i	−0.983665	−	0.180008i	$-0.942388\pi$
$5$	0.0250883	−	0.142283i	0.00224397	−	0.0127262i	0.985909	+	0.167281i	$0.0534989\pi$
$6$	−2.86272	+	4.28623i	−0.194783	+	0.291641i
$7$	19.4381	−	16.3105i	1.04956	−	0.880685i	0.0565125	−	0.998402i	$-0.482002\pi$
$7$	19.4381	−	16.3105i	1.04956	−	0.880685i	0.993047	+	0.117717i	$0.0375575\pi$
$8$	7.44756	+	12.8996i	0.329139	+	0.570085i
$9$	−23.9543	−	12.4576i	−0.887197	−	0.461392i
$10$	−0.0716572	+	0.124114i	−0.00226600	+	0.00392483i
$11$	11.3027	+	64.1008i	0.309808	+	1.75701i	0.599960	+	0.800030i	$0.295183\pi$
$11$	11.3027	+	64.1008i	0.309808	+	1.75701i	−0.290152	+	0.956981i	$0.593706\pi$
$12$	−29.3957	+	21.5629i	−0.707152	+	0.518724i
$13$	24.9207	−	9.07040i	0.531674	−	0.193514i	−0.0622116	−	0.998063i	$-0.519815\pi$
$13$	24.9207	−	9.07040i	0.531674	−	0.193514i	0.593886	+	0.804549i	$0.297593\pi$
$14$	−23.6524	+	8.60876i	−0.451526	+	0.164342i
$15$	−0.687211	−	0.302215i	−0.0118291	−	0.00520211i
$16$	7.18090	+	40.7249i	0.112202	+	0.636327i
$17$	34.5011	−	59.7576i	0.492220	−	0.852550i	−0.507740	−	0.861511i	$-0.669519\pi$
$17$	34.5011	−	59.7576i	0.492220	−	0.852550i	0.999960	+	0.00896013i	$0.00285214\pi$
$18$	18.1020	+	19.7389i	0.237038	+	0.258472i
$19$	−15.9760	−	27.6712i	−0.192902	−	0.334116i	0.753309	−	0.657667i	$-0.228457\pi$
$19$	−15.9760	−	27.6712i	−0.192902	−	0.334116i	−0.946211	+	0.323551i	$0.895123\pi$
$20$	−0.776510	+	0.651569i	−0.00868165	+	0.00728477i
$21$	−58.3398	−	118.241i	−0.606228	−	1.22869i
$22$	11.2117	−	63.5846i	0.108652	−	0.616195i
$23$	−25.9254	−	21.7540i	−0.235036	−	0.197219i	0.517661	−	0.855586i	$-0.326803\pi$
$23$	−25.9254	−	21.7540i	−0.235036	−	0.197219i	−0.752697	+	0.658367i	$0.771247\pi$
$24$	74.3009	−	21.6730i	0.631942	−	0.184332i
$25$	117.442	+	42.7454i	0.939536	+	0.341963i
$26$	−26.3065			−0.198428
$27$	−92.4400	+	105.536i	−0.658892	+	0.752238i
$28$	−178.030			−1.20159
$29$	40.6547	+	14.7971i	0.260324	+	0.0947501i	0.468885	−	0.883259i	$-0.344656\pi$
$29$	40.6547	+	14.7971i	0.260324	+	0.0947501i	−0.208561	+	0.978009i	$0.566878\pi$
$30$	0.538036	+	0.514850i	0.00327438	+	0.00313328i
$31$	−48.7783	−	40.9298i	−0.282608	−	0.237136i	0.490454	−	0.871467i	$-0.336831\pi$
$31$	−48.7783	−	40.9298i	−0.282608	−	0.237136i	−0.773061	+	0.634331i	$0.781276\pi$
$32$	27.8152	−	157.748i	0.153658	−	0.871441i
$33$	337.496	+	22.0525i	1.78032	+	0.116329i
$34$	−52.4331	+	43.9966i	−0.264476	+	0.221922i
$35$	−1.83304	−	3.17491i	−0.00885257	−	0.0153331i
$36$	72.5633	+	174.984i	0.335941	+	0.810112i
$37$	−128.992	+	223.421i	−0.573140	+	0.992707i	0.423101	+	0.906082i	$0.360941\pi$
$37$	−128.992	+	223.421i	−0.573140	+	0.992707i	−0.996241	+	0.0866247i	$0.972392\pi$
$38$	5.50371	+	31.2131i	0.0234953	+	0.133248i
$39$	−15.0297	−	136.980i	−0.0617096	−	0.562420i
$40$	2.02223	−	0.736032i	0.00799357	−	0.00290942i
$41$	−356.758	+	129.849i	−1.35893	+	0.494612i	−0.915725	−	0.401806i	$-0.868383\pi$
$41$	−356.758	+	129.849i	−1.35893	+	0.494612i	−0.443210	+	0.896418i	$0.646160\pi$
$42$	14.2647	+	130.009i	0.0524070	+	0.477637i
$43$	51.2384	+	290.587i	0.181716	+	1.03056i	0.930103	+	0.367299i	$0.119718\pi$
$43$	51.2384	+	290.587i	0.181716	+	1.03056i	−0.748387	+	0.663262i	$0.769171\pi$
$44$	228.336	−	395.489i	0.782339	−	1.35505i
$45$	−2.37347	+	3.09575i	−0.00786259	+	0.0102553i
$46$	16.7854	+	29.0731i	0.0538014	+	0.0931868i
$47$	−228.972	+	192.130i	−0.710618	+	0.596279i	−0.924772	−	0.380521i	$-0.875745\pi$
$47$	−228.972	+	192.130i	−0.710618	+	0.596279i	0.214155	+	0.976800i	$0.431300\pi$
$48$	214.420	+	14.0105i	0.644768	+	0.0421301i
$49$	52.2461	−	296.302i	0.152321	−	0.863856i
$50$	−94.9686	−	79.6881i	−0.268612	−	0.225392i
$51$	−259.050	−	247.887i	−0.711261	−	0.680610i
$52$	−174.845	−	63.6383i	−0.466281	−	0.169712i
$53$	340.033			0.881268			0.440634	−	0.897687i	$-0.354754\pi$
$53$	340.033			0.881268			0.440634	+	0.897687i	$0.354754\pi$
$54$	121.970	−	67.0111i	0.307372	−	0.168871i
$55$	9.40401			0.0230552
$56$	355.165	+	129.269i	0.847516	+	0.308471i
$57$	−159.385	+	46.4912i	−0.370369	+	0.108034i
$58$	−32.8751	−	27.5855i	−0.0744262	−	0.0624510i
$59$	53.1307	−	301.319i	0.117238	−	0.664889i	−0.868380	−	0.495899i	$-0.834839\pi$
$59$	53.1307	−	301.319i	0.117238	−	0.664889i	0.985618	−	0.168989i	$-0.0540504\pi$
$60$	2.33055	+	4.72349i	0.00501454	+	0.0101633i
$61$	515.642	−	432.675i	1.08232	−	0.908170i	0.0862041	−	0.996277i	$-0.472526\pi$
$61$	515.642	−	432.675i	1.08232	−	0.908170i	0.996111	+	0.0881073i	$0.0280818\pi$
$62$	31.5814	+	54.7005i	0.0646909	+	0.112048i
$63$	−668.816	+	148.555i	−1.33751	+	0.297083i
$64$	85.9670	−	148.899i	0.167904	−	0.290819i
$65$	−0.665344	−	3.77335i	−0.00126963	−	0.00720041i
$66$	−307.107	−	135.057i	−0.572761	−	0.251884i
$67$	161.847	−	58.9077i	0.295117	−	0.107414i	−0.190219	−	0.981742i	$-0.560920\pi$
$67$	161.847	−	58.9077i	0.295117	−	0.107414i	0.485335	+	0.874328i	$0.338698\pi$
$68$	−454.926	+	165.580i	−0.811292	+	0.295286i
$69$	−141.796	+	104.013i	−0.247395	+	0.181474i
$70$	0.631481	+	3.58131i	0.00107823	+	0.00611497i
$71$	−523.492	+	906.714i	−0.875028	+	1.51559i	−0.0182959	+	0.999833i	$0.505824\pi$
$71$	−523.492	+	906.714i	−0.875028	+	1.51559i	−0.856732	+	0.515761i	$0.827509\pi$
$72$	−17.7040	−	401.778i	−0.0289783	−	0.657639i
$73$	87.6625	+	151.836i	0.140550	+	0.243439i	0.927704	−	0.373317i	$-0.121780\pi$
$73$	87.6625	+	151.836i	0.140550	+	0.243439i	−0.787154	+	0.616756i	$0.788446\pi$
$74$	196.036	−	164.494i	0.307956	−	0.258405i
$75$	360.685	−	540.038i	0.555310	−	0.831443i
$76$	−38.9277	+	220.770i	−0.0587542	+	0.333211i
$77$	1265.22	+	1061.65i	1.87254	+	1.57124i
$78$	−32.4632	+	132.782i	−0.0471248	+	0.192751i
$79$	−85.3554	−	31.0668i	−0.121560	−	0.0442442i	0.280524	−	0.959847i	$-0.409492\pi$
$79$	−85.3554	−	31.0668i	−0.121560	−	0.0442442i	−0.402084	+	0.915603i	$0.631714\pi$
$80$	5.97461			0.00834978
$81$	418.618	+	596.825i	0.574235	+	0.818690i
$82$	376.597			0.507173
$83$	−909.434	−	331.007i	−1.20269	−	0.437744i	−0.338528	−	0.940956i	$-0.609929\pi$
$83$	−909.434	−	331.007i	−1.20269	−	0.437744i	−0.864163	+	0.503213i	$0.832151\pi$
$84$	−219.695	+	898.603i	−0.285365	+	1.16721i
$85$	−7.63691	−	6.40813i	−0.00974517	−	0.00817717i
$86$	50.8258	−	288.247i	0.0637289	−	0.361425i
$87$	124.858	−	186.944i	0.153864	−	0.230374i
$88$	−742.694	+	623.194i	−0.899675	+	0.754917i
$89$	−240.117	−	415.895i	−0.285982	−	0.495335i	0.686865	−	0.726785i	$-0.258986\pi$
$89$	−240.117	−	415.895i	−0.285982	−	0.495335i	−0.972847	+	0.231450i	$0.925653\pi$
$90$	3.26266	−	2.08039i	0.00382127	−	0.00243658i
$91$	336.469	−	582.781i	0.387599	−	0.671342i
$92$	41.2320	+	233.838i	0.0467254	+	0.264993i
$93$	−266.787	+	195.699i	−0.297468	+	0.218205i
$94$	278.614	−	101.407i	0.305711	−	0.111270i
$95$	−4.33794	+	1.57888i	−0.00468488	+	0.00170516i
$96$	−761.904	−	335.063i	−0.810016	−	0.356221i
$97$	−174.496	−	989.614i	−0.182653	−	1.03588i	−0.928934	−	0.370246i	$-0.879273\pi$
$97$	−174.496	−	989.614i	−0.182653	−	1.03588i	0.746281	−	0.665631i	$-0.231838\pi$
$98$	−149.225	+	258.466i	−0.153817	+	0.266418i
$99$	527.792	−	1676.29i	0.535809	−	1.70176i
$100$	−438.429	−	759.382i	−0.438429	−	0.759382i
$101$	981.349	−	823.450i	0.966811	−	0.811251i	−0.0152366	−	0.999884i	$-0.504850\pi$
$101$	981.349	−	823.450i	0.966811	−	0.811251i	0.982048	+	0.188633i	$0.0604057\pi$
$102$	157.368	+	318.949i	0.152762	+	0.309614i
$103$	−242.163	+	1373.38i	−0.231661	+	1.31381i	0.617872	+	0.786278i	$0.287995\pi$
$103$	−242.163	+	1373.38i	−0.231661	+	1.31381i	−0.849533	+	0.527535i	$0.823116\pi$
$104$	302.603	+	253.914i	0.285314	+	0.239407i
$105$	−18.2874	+	5.33428i	−0.0169968	+	0.00495783i
$106$	−316.954	−	115.362i	−0.290427	−	0.105707i
$107$	−968.304			−0.874855			−0.437427	−	0.899254i	$-0.644110\pi$
$107$	−968.304			−0.874855			−0.437427	+	0.899254i	$0.644110\pi$
$108$	972.777	−	150.326i	0.866717	−	0.133936i
$109$	196.304			0.172501			0.0862503	−	0.996274i	$-0.472512\pi$
$109$	196.304			0.172501			0.0862503	+	0.996274i	$0.472512\pi$
$110$	−8.76572	−	3.19046i	−0.00759798	−	0.00276544i
$111$	968.534	+	926.796i	0.828190	+	0.792501i
$112$	803.827	+	674.491i	0.678166	+	0.569049i
$113$	369.850	−	2097.52i	0.307898	−	1.74618i	−0.301640	−	0.953422i	$-0.597534\pi$
$113$	369.850	−	2097.52i	0.307898	−	1.74618i	0.609538	−	0.792757i	$-0.291355\pi$
$114$	164.340	+	10.7382i	0.135016	+	0.00882213i
$115$	−3.74565	+	3.14297i	−0.00303725	+	0.00254855i
$116$	−151.770	−	262.874i	−0.121479	−	0.210407i
$117$	−709.954	−	93.1766i	−0.560985	−	0.0736254i
$118$	−151.752	+	262.842i	−0.118389	+	0.205056i
$119$	−304.042	−	1724.31i	−0.234214	−	1.32829i
$120$	−1.21961	−	11.1155i	−0.000927786	−	0.00845584i
$121$	−2730.43	+	993.795i	−2.05141	+	0.746653i
$122$	−627.435	+	228.368i	−0.465617	+	0.169471i
$123$	215.161	+	1960.97i	0.157727	+	1.43752i
$124$	77.5773	+	439.963i	0.0561826	+	0.318628i
$125$	18.0582	−	31.2778i	0.0129214	−	0.0223805i
$126$	673.820	+	88.4343i	0.476418	+	0.0625266i
$127$	989.454	+	1713.78i	0.691337	+	1.19743i	0.971400	+	0.237449i	$0.0763114\pi$
$127$	989.454	+	1713.78i	0.691337	+	1.19743i	−0.280063	+	0.959982i	$0.590355\pi$
$128$	−1112.30	+	933.327i	−0.768078	+	0.644494i
$129$	1529.97	+	99.9702i	1.04423	+	0.0682317i
$130$	−0.659986	+	3.74297i	−0.000445266	+	0.00252523i
$131$	1556.74	+	1306.26i	1.03826	+	0.871207i	0.991811	−	0.127714i	$-0.0407638\pi$
$131$	1556.74	+	1306.26i	1.03826	+	0.871207i	0.0464529	+	0.998920i	$0.485208\pi$
$132$	−1714.45	−	1640.57i	−1.13048	−	1.08177i
$133$	−761.873	−	277.299i	−0.496713	−	0.180789i
$134$	−170.847			−0.110142
$135$	12.6968	+	15.8003i	0.00809457	+	0.0100732i
$136$	1027.80			0.648035
$137$	−215.623	−	78.4805i	−0.134467	−	0.0489419i	0.273910	−	0.961755i	$-0.411683\pi$
$137$	−215.623	−	78.4805i	−0.134467	−	0.0489419i	−0.408377	+	0.912813i	$0.633905\pi$
$138$	167.460	−	48.8467i	0.103298	−	0.0301312i
$139$	−603.337	−	506.260i	−0.368161	−	0.308924i	0.439872	−	0.898060i	$-0.355024\pi$
$139$	−603.337	−	506.260i	−0.368161	−	0.308924i	−0.808034	+	0.589136i	$0.799468\pi$
$140$	−4.46646	+	25.3306i	−0.00269632	+	0.0152916i
$141$	687.217	+	1392.83i	0.410454	+	0.831897i
$142$	795.577	−	667.568i	0.470164	−	0.394515i
$143$	863.091	+	1494.92i	0.504722	+	0.874205i
$144$	335.320	−	1064.99i	0.194051	−	0.616316i
$145$	3.12533	−	5.41323i	0.00178996	−	0.00310031i
$146$	−30.1997	−	171.271i	−0.0171188	−	0.0970855i
$147$	−1431.11	−	629.360i	−0.802966	−	0.353121i
$148$	1700.87	−	619.066i	0.944666	−	0.343830i
$149$	−502.378	+	182.851i	−0.276217	+	0.100535i	−0.476415	−	0.879221i	$-0.658064\pi$
$149$	−502.378	+	182.851i	−0.276217	+	0.100535i	0.200197	+	0.979756i	$0.435842\pi$
$150$	−519.420	+	381.015i	−0.282736	+	0.207398i
$151$	−180.053	−	1021.13i	−0.0970364	−	0.550321i	−0.994104	−	0.108428i	$-0.965418\pi$
$151$	−180.053	−	1021.13i	−0.0970364	−	0.550321i	0.897068	−	0.441893i	$-0.145693\pi$
$152$	237.964	−	412.165i	0.126983	−	0.219941i
$153$	−1570.89	+	1001.65i	−0.830056	+	0.529274i
$154$	−819.164	−	1418.83i	−0.428637	−	0.742421i
$155$	−7.04738	+	5.91345i	−0.00365199	+	0.00306439i
$156$	−536.978	+	803.995i	−0.275594	+	0.412635i
$157$	206.727	−	1172.41i	0.105087	−	0.595977i	−0.886099	−	0.463496i	$-0.846595\pi$
$157$	206.727	−	1172.41i	0.105087	−	0.595977i	0.991186	−	0.132480i	$-0.0422942\pi$
$158$	69.0221	+	57.9164i	0.0347538	+	0.0291619i
$159$	419.614	−	1716.32i	0.209293	−	0.856054i
$160$	−21.7469	−	7.91524i	−0.0107453	−	0.00391097i
$161$	−858.761			−0.420372
$162$	−187.722	−	698.339i	−0.0910421	−	0.338683i
$163$	−1238.39			−0.595082			−0.297541	−	0.954709i	$-0.596167\pi$
$163$	−1238.39			−0.595082			−0.297541	+	0.954709i	$0.596167\pi$
$164$	2503.03	+	911.029i	1.19179	+	0.433777i
$165$	11.6049	−	47.4666i	0.00547539	−	0.0223956i
$166$	735.407	+	617.080i	0.343847	+	0.288522i
$167$	−13.9583	+	79.1617i	−0.00646784	+	0.0366809i	−0.987871	−	0.155278i	$-0.950373\pi$
$167$	−13.9583	+	79.1617i	−0.00646784	+	0.0366809i	0.981403	+	0.191959i	$0.0614839\pi$
$168$	1090.77	−	1633.17i	0.500922	−	0.750010i
$169$	−1144.23	+	960.123i	−0.520815	+	0.437015i
$170$	4.94450	+	8.56413i	0.00223074	+	0.00386376i
$171$	37.9773	+	861.865i	0.0169836	+	0.385430i
$172$	1035.11	−	1792.87i	0.458875	−	0.794795i
$173$	160.324	+	909.241i	0.0704577	+	0.399586i	0.999557	+	0.0297557i	$0.00947292\pi$
$173$	160.324	+	909.241i	0.0704577	+	0.399586i	−0.929099	+	0.369830i	$0.879416\pi$
$174$	−179.807	+	131.895i	−0.0783397	+	0.0574653i
$175$	2980.05	−	1084.65i	1.28726	−	0.468525i
$176$	−2529.34	+	920.603i	−1.08327	+	0.394279i
$177$	−1455.34	−	640.016i	−0.618023	−	0.271788i
$178$	82.7202	+	469.130i	0.0348323	+	0.197544i
$179$	435.913	−	755.023i	0.182020	−	0.315269i	−0.760548	−	0.649282i	$-0.775070\pi$
$179$	435.913	−	755.023i	0.182020	−	0.315269i	0.942568	+	0.334013i	$0.108403\pi$
$180$	26.7177	−	5.93446i	0.0110635	−	0.00245738i
$181$	−125.378	−	217.160i	−0.0514875	−	0.0891790i	0.839133	−	0.543926i	$-0.183063\pi$
$181$	−125.378	−	217.160i	−0.0514875	−	0.0891790i	−0.890621	+	0.454747i	$0.849730\pi$
$182$	−511.349	+	429.073i	−0.208262	+	0.174753i
$183$	−1547.60	−	3136.64i	−0.625148	−	1.26703i
$184$	87.5359	−	496.441i	0.0350719	−	0.198903i
$185$	28.5528	+	23.9586i	0.0113472	+	0.00952147i
$186$	315.073	−	91.9042i	0.124206	−	0.0362298i
$187$	4220.47	+	1536.12i	1.65043	+	0.600709i
$188$	2097.11			0.813550
$189$	−75.5120	+	3559.17i	−0.0290619	+	1.36979i
$190$	4.57917			0.00174846
$191$	−1963.89	−	714.797i	−0.743989	−	0.270790i	−0.0579152	−	0.998322i	$-0.518445\pi$
$191$	−1963.89	−	714.797i	−0.743989	−	0.270790i	−0.686074	+	0.727531i	$0.740668\pi$
$192$	−645.481	−	617.665i	−0.242623	−	0.232167i
$193$	−1899.00	−	1593.45i	−0.708255	−	0.594296i	0.215854	−	0.976426i	$-0.430746\pi$
$193$	−1899.00	−	1593.45i	−0.708255	−	0.594296i	−0.924109	+	0.382129i	$0.875191\pi$
$194$	−173.090	+	981.645i	−0.0640576	+	0.363289i
$195$	−19.8670	−	1.29814i	−0.00729593	−	0.000476726i
$196$	−1617.07	+	1356.89i	−0.589313	+	0.494492i
$197$	891.507	+	1544.14i	0.322423	+	0.558452i	0.980987	−	0.194072i	$-0.0621694\pi$
$197$	891.507	+	1544.14i	0.322423	+	0.558452i	−0.658565	+	0.752524i	$0.728836\pi$
$198$	−1060.68	+	1383.45i	−0.380703	+	0.496555i
$199$	−2167.76	+	3754.67i	−0.772202	+	1.33749i	0.164151	+	0.986435i	$0.447511\pi$
$199$	−2167.76	+	3754.67i	−0.772202	+	1.33749i	−0.936354	+	0.351058i	$0.885822\pi$
$200$	323.260	+	1833.30i	0.114290	+	0.648169i
$201$	−97.6101	−	889.618i	−0.0342532	−	0.312183i
$202$	−1194.11	+	434.620i	−0.415927	+	0.151385i
$203$	1031.60	−	375.472i	0.356670	−	0.129817i
$204$	274.366	+	2500.57i	0.0941639	+	0.858209i
$205$	9.52489	+	54.0183i	0.00324511	+	0.0184039i
$206$	691.666	−	1198.00i	0.233935	−	0.405188i
$207$	350.023	+	844.071i	0.117528	+	0.283415i
$208$	548.344	+	949.760i	0.182793	+	0.316606i
$209$	1593.17	−	1336.83i	0.527282	−	0.442442i
$210$	18.8559	+	1.23207i	0.00619609	+	0.000404861i
$211$	459.648	−	2606.80i	0.149969	−	0.850517i	−0.813273	−	0.581882i	$-0.802316\pi$
$211$	459.648	−	2606.80i	0.149969	−	0.850517i	0.963242	−	0.268635i	$-0.0865725\pi$
$212$	−1827.54	−	1533.49i	−0.592058	−	0.496795i
$213$	3930.62	+	3761.24i	1.26442	+	1.20993i
$214$	902.581	+	328.513i	0.288314	+	0.104938i
$215$	42.6311			0.0135229
$216$	−2049.82	−	406.448i	−0.645706	−	0.128034i
$217$	−1615.74			−0.505456
$218$	−182.980	−	66.5994i	−0.0568486	−	0.0206912i
$219$	874.569	−	255.104i	0.269853	−	0.0787140i
$220$	−50.5428	−	42.4104i	−0.0154891	−	0.0129969i
$221$	317.766	−	1802.14i	0.0967207	−	0.548530i
$222$	−588.365	−	1192.48i	−0.177876	−	0.360514i
$223$	2524.84	−	2118.59i	0.758187	−	0.636194i	−0.179467	−	0.983764i	$-0.557437\pi$
$223$	2524.84	−	2118.59i	0.758187	−	0.636194i	0.937654	+	0.347570i	$0.112993\pi$
$224$	−2032.27	−	3520.00i	−0.606191	−	1.04995i
$225$	−2280.74	−	2486.98i	−0.675774	−	0.736882i
$226$	−1056.36	+	1829.68i	−0.310922	+	0.538532i
$227$	669.392	+	3796.31i	0.195723	+	1.11000i	0.911386	+	0.411554i	$0.135014\pi$
$227$	669.392	+	3796.31i	0.195723	+	1.11000i	−0.715663	+	0.698446i	$0.753875\pi$
$228$	1066.30	+	468.926i	0.309725	+	0.136208i
$229$	−1449.35	+	527.520i	−0.418235	+	0.152225i	−0.542561	−	0.840016i	$-0.682545\pi$
$229$	−1449.35	+	527.520i	−0.418235	+	0.152225i	0.124326	+	0.992241i	$0.460323\pi$
$230$	4.55772	−	1.65887i	0.00130664	−	0.000475578i
$231$	6919.97	−	5076.08i	1.97100	−	1.44581i
$232$	111.902	+	634.630i	0.0316670	+	0.179593i
$233$	1201.12	−	2080.39i	0.337715	−	0.584940i	−0.646287	−	0.763094i	$-0.723679\pi$
$233$	1201.12	−	2080.39i	0.337715	−	0.584940i	0.984003	+	0.178154i	$0.0570125\pi$
$234$	630.154	+	327.715i	0.176045	+	0.0915531i
$235$	21.5923	+	37.3990i	0.00599374	+	0.0103815i
$236$	−1644.45	+	1379.86i	−0.453580	+	0.380599i
$237$	−262.141	+	392.493i	−0.0718477	+	0.107575i
$238$	−301.593	+	1710.42i	−0.0821403	+	0.465841i
$239$	−5500.18	−	4615.20i	−1.48861	−	1.24909i	−0.896355	−	0.443336i	$-0.853795\pi$
$239$	−5500.18	−	4615.20i	−1.48861	−	1.24909i	−0.592251	−	0.805753i	$-0.701761\pi$
$240$	7.37289	−	30.1568i	0.00198299	−	0.00811089i
$241$	−1960.54	−	713.578i	−0.524023	−	0.190729i	0.0664447	−	0.997790i	$-0.478834\pi$
$241$	−1960.54	−	713.578i	−0.524023	−	0.190729i	−0.590468	+	0.807061i	$0.701057\pi$
$242$	2882.26			0.765615
$243$	3529.06	−	1376.46i	0.931643	−	0.363375i
$244$	−4722.66			−1.23909
$245$	−40.8480	−	14.8675i	−0.0106518	−	0.00387693i
$246$	464.735	−	1900.87i	0.120449	−	0.492663i
$247$	−649.121	−	544.677i	−0.167217	−	0.140312i
$248$	164.697	−	934.045i	0.0421705	−	0.239161i
$249$	−2793.03	+	4181.88i	−0.710847	+	1.06432i
$250$	−27.4440	+	23.0282i	−0.00694284	+	0.00582574i
$251$	−1447.18	−	2506.59i	−0.363925	−	0.630337i	0.624678	−	0.780883i	$-0.285230\pi$
$251$	−1447.18	−	2506.59i	−0.363925	−	0.630337i	−0.988603	+	0.150545i	$0.951897\pi$
$252$	4264.58	+	2217.82i	1.06604	+	0.554402i
$253$	1101.42	−	1907.72i	0.273699	−	0.474061i
$254$	−340.866	−	1933.15i	−0.0842042	−	0.477546i
$255$	−41.7692	+	30.6394i	−0.0102576	+	0.00752436i
$256$	60.9233	−	22.1743i	0.0148739	−	0.00541364i
$257$	−259.176	+	94.3324i	−0.0629065	+	0.0228961i	−0.373282	−	0.927718i	$-0.621768\pi$
$257$	−259.176	+	94.3324i	−0.0629065	+	0.0228961i	0.310375	+	0.950614i	$0.399545\pi$
$258$	−1392.20	−	612.250i	−0.335949	−	0.147740i
$259$	1136.75	+	6446.81i	0.272718	+	1.54666i
$260$	−13.4412	+	23.2808i	−0.00320611	+	0.00555314i
$261$	−789.519	−	860.913i	−0.187241	−	0.204173i
$262$	−1007.90	−	1745.74i	−0.237666	−	0.411650i
$263$	−165.731	+	139.065i	−0.0388571	+	0.0326050i	−0.662009	−	0.749496i	$-0.730296\pi$
$263$	−165.731	+	139.065i	−0.0388571	+	0.0326050i	0.623152	+	0.782101i	$0.285852\pi$
$264$	2229.05	+	4517.78i	0.519655	+	1.05322i
$265$	8.53086	−	48.3809i	0.00197753	−	0.0112152i
$266$	616.083	+	516.955i	0.142009	+	0.119160i
$267$	−2395.54	+	698.759i	−0.549081	+	0.160162i
$268$	−1135.53	−	413.299i	−0.258819	−	0.0942023i
$269$	1941.22			0.439993			0.219996	−	0.975501i	$-0.429395\pi$
$269$	1941.22			0.439993			0.219996	+	0.975501i	$0.429395\pi$
$270$	−6.47450	−	19.0355i	−0.00145935	−	0.00429061i
$271$	4238.26			0.950023			0.475011	−	0.879980i	$-0.342444\pi$
$271$	4238.26			0.950023			0.475011	+	0.879980i	$0.342444\pi$
$272$	2681.37	+	975.940i	0.597728	+	0.217555i
$273$	−2526.37	−	2417.50i	−0.560083	−	0.535947i
$274$	174.362	+	146.307i	0.0384438	+	0.0322582i
$275$	−1412.60	+	8011.26i	−0.309757	+	1.75672i
$276$	1231.18	+	80.4469i	0.268508	+	0.0175447i
$277$	1020.73	−	856.496i	0.221407	−	0.185783i	−0.525336	−	0.850895i	$-0.676061\pi$
$277$	1020.73	−	856.496i	0.221407	−	0.185783i	0.746744	+	0.665112i	$0.231616\pi$
$278$	390.629	+	676.590i	0.0842748	+	0.145968i
$279$	658.563	+	1588.10i	0.141316	+	0.340779i
$280$	27.3033	−	47.2907i	0.00582745	−	0.0100934i
$281$	448.263	+	2542.23i	0.0951643	+	0.539703i	0.994697	+	0.102850i	$0.0327961\pi$
$281$	448.263	+	2542.23i	0.0951643	+	0.539703i	−0.899533	+	0.436854i	$0.856093\pi$
$282$	−168.032	−	1531.44i	−0.0354828	−	0.323390i
$283$	119.523	−	43.5028i	0.0251056	−	0.00913771i	−0.329437	−	0.944178i	$-0.606859\pi$
$283$	119.523	−	43.5028i	0.0251056	−	0.00913771i	0.354542	+	0.935040i	$0.384637\pi$
$284$	6902.68	−	2512.37i	1.44225	−	0.524936i
$285$	2.61621	+	23.8441i	0.000543758	+	0.00495580i
$286$	−297.335	−	1686.27i	−0.0614747	−	0.348640i
$287$	−4816.80	+	8342.94i	−0.990686	+	1.71592i
$288$	−2631.45	+	3432.22i	−0.538401	+	0.702242i
$289$	75.8493	+	131.375i	0.0154385	+	0.0267403i
$290$	−4.74973	+	3.98549i	−0.000961771	+	0.000807022i
$291$	−5210.40	−	340.455i	−1.04962	−	0.0685836i
$292$	213.602	−	1211.40i	0.0428087	−	0.242780i
$293$	1169.51	+	981.339i	0.233187	+	0.195667i	0.751892	−	0.659286i	$-0.229141\pi$
$293$	1169.51	+	981.339i	0.233187	+	0.195667i	−0.518705	+	0.854953i	$0.673586\pi$
$294$	1120.45	+	1072.17i	0.222266	+	0.212688i
$295$	−41.5396	−	15.1192i	−0.00819841	−	0.00298398i
$296$	−3842.71			−0.754570
$297$	−7809.76	−	4732.63i	−1.52582	−	0.924630i
$298$	530.314			0.103088
$299$	−843.398	−	306.972i	−0.163127	−	0.0593734i
$300$	−4374.01	+	1275.86i	−0.841779	+	0.245540i
$301$	5735.61	+	4812.75i	1.09832	+	0.921602i
$302$	−178.603	+	1012.91i	−0.0340313	+	0.193001i
$303$	−2945.33	−	5969.52i	−0.558432	−	1.13181i
$304$	1012.18	−	849.323i	0.190963	−	0.160237i
$305$	−48.6257	−	84.2221i	−0.00912885	−	0.0158116i
$306$	1804.09	−	400.719i	0.337036	−	0.0748613i
$307$	1999.50	−	3463.24i	0.371719	−	0.643836i	−0.618111	−	0.786091i	$-0.712102\pi$
$307$	1999.50	−	3463.24i	0.371719	−	0.643836i	0.989830	+	0.142255i	$0.0454352\pi$
$308$	−2012.22	−	11411.8i	−0.372262	−	2.11120i
$309$	6633.27	+	2917.11i	1.22121	+	0.537051i
$310$	8.57527	−	3.12114i	0.00157111	−	0.000571836i
$311$	6718.66	−	2445.39i	1.22502	−	0.445870i	0.353129	−	0.935575i	$-0.385118\pi$
$311$	6718.66	−	2445.39i	1.22502	−	0.445870i	0.871888	+	0.489705i	$0.162895\pi$
$312$	1655.05	−	1214.04i	0.300316	−	0.220294i
$313$	−1557.46	−	8832.81i	−0.281255	−	1.59508i	−0.718362	−	0.695669i	$-0.755108\pi$
$313$	−1557.46	−	8832.81i	−0.281255	−	1.59508i	0.437107	−	0.899410i	$-0.356003\pi$
$314$	−590.454	+	1022.70i	−0.106119	+	0.183803i
$315$	4.35741	+	98.8881i	0.000779405	+	0.0176880i
$316$	318.645	+	551.910i	0.0567253	+	0.0982511i
$317$	469.124	−	393.641i	0.0831186	−	0.0697448i	−0.600282	−	0.799789i	$-0.704945\pi$
$317$	469.124	−	393.641i	0.0831186	−	0.0697448i	0.683400	+	0.730044i	$0.260500\pi$
$318$	−973.420	+	1457.46i	−0.171656	+	0.257014i
$319$	−488.998	+	2773.25i	−0.0858265	+	0.486746i
$320$	−19.0290	−	15.9673i	−0.00332424	−	0.00278937i
$321$	−1194.92	+	4887.50i	−0.207770	+	0.849825i
$322$	800.473	+	291.348i	0.138536	+	0.0504230i
$323$	−2204.75			−0.379801
$324$	441.674	−	5095.59i	0.0757329	−	0.873729i
$325$	3314.46			0.565701
$326$	1154.34	+	420.144i	0.196113	+	0.0713793i
$327$	242.247	−	990.845i	0.0409672	−	0.167565i
$328$	−4331.98	−	3634.96i	−0.729249	−	0.611912i
$329$	−1317.04	+	7469.31i	−0.220702	+	1.25166i
$330$	−26.9210	+	40.3077i	−0.00449077	+	0.00672384i
$331$	−2453.42	+	2058.67i	−0.407409	+	0.341857i	−0.823349	−	0.567535i	$-0.807897\pi$
$331$	−2453.42	+	2058.67i	−0.407409	+	0.341857i	0.415940	+	0.909392i	$0.363453\pi$
$332$	3395.06	+	5880.42i	0.561229	+	0.972078i
$333$	5873.20	−	3744.96i	0.966514	−	0.616284i
$334$	39.8678	−	69.0530i	0.00653134	−	0.0113126i
$335$	−4.32107	−	24.5060i	−0.000704732	−	0.00399674i
$336$	4396.44	−	3224.96i	0.713826	−	0.523620i
$337$	2923.35	−	1064.01i	0.472537	−	0.171989i	−0.0947645	−	0.995500i	$-0.530210\pi$
$337$	2923.35	−	1064.01i	0.472537	−	0.171989i	0.567301	+	0.823510i	$0.307988\pi$
$338$	1392.30	−	506.757i	0.224057	−	0.0815501i
$339$	−10130.8	−	4455.23i	−1.62310	−	0.713790i
$340$	12.1458	+	68.8823i	0.00193735	+	0.0109873i
$341$	2072.31	−	3589.34i	0.329096	−	0.570011i
$342$	257.002	−	816.251i	0.0406347	−	0.129058i
$343$	534.474	+	925.736i	0.0841367	+	0.145729i
$344$	−3366.85	+	2825.12i	−0.527698	+	0.442791i
$345$	11.2419	+	22.7847i	0.00175432	+	0.00355561i
$346$	159.033	−	901.919i	0.0247100	−	0.140137i
$347$	−1464.76	−	1229.08i	−0.226607	−	0.190146i	0.522414	−	0.852692i	$-0.325031\pi$
$347$	−1464.76	−	1229.08i	−0.226607	−	0.190146i	−0.749021	+	0.662546i	$0.769476\pi$
$348$	−1514.14	+	441.663i	−0.233238	+	0.0680335i
$349$	−7952.27	−	2894.39i	−1.21970	−	0.443934i	−0.349642	−	0.936883i	$-0.613697\pi$
$349$	−7952.27	−	2894.39i	−1.21970	−	0.443934i	−0.870058	+	0.492949i	$0.835919\pi$
$350$	−3145.76			−0.480423
$351$	−1346.42	+	3468.50i	−0.204748	+	0.527450i
$352$	10426.1			1.57873
$353$	−2673.18	−	972.958i	−0.403057	−	0.146701i	0.132534	−	0.991178i	$-0.457689\pi$
$353$	−2673.18	−	972.958i	−0.403057	−	0.146701i	−0.535591	+	0.844478i	$0.679911\pi$
$354$	1139.42	+	1090.32i	0.171073	+	0.163701i
$355$	115.876	+	97.2318i	0.0173242	+	0.0145367i
$356$	−585.080	+	3318.15i	−0.0871044	+	0.493994i
$357$	−9078.62	−	593.210i	−1.34591	−	0.0879440i
$358$	−662.479	+	555.886i	−0.0978019	+	0.0820656i
$359$	645.056	+	1117.27i	0.0948323	+	0.164254i	0.909539	−	0.415619i	$-0.136435\pi$
$359$	645.056	+	1117.27i	0.0948323	+	0.164254i	−0.814706	+	0.579874i	$0.803102\pi$
$360$	−57.6103	−	7.56096i	−0.00843425	−	0.00110694i
$361$	2919.04	−	5055.92i	0.425578	−	0.737122i
$362$	43.1925	+	244.957i	0.00627113	+	0.0355654i
$363$	1646.72	+	15008.2i	0.238100	+	2.17004i
$364$	−4436.63	+	1614.80i	−0.638853	+	0.232523i
$365$	23.8029	−	8.66356i	0.00341343	−	0.00124239i
$366$	378.406	+	3448.79i	0.0540426	+	0.492544i
$367$	377.155	+	2138.95i	0.0536439	+	0.304230i	0.999811	−	0.0194492i	$-0.00619127\pi$
$367$	377.155	+	2138.95i	0.0536439	+	0.304230i	−0.946167	+	0.323679i	$0.895080\pi$
$368$	699.763	−	1212.02i	0.0991240	−	0.171688i
$369$	10163.5	+	1333.89i	1.43385	+	0.188183i
$370$	−18.4864	−	32.0194i	−0.00259747	−	0.00449895i
$371$	6609.61	−	5546.12i	0.924943	−	0.776119i
$372$	2316.44	+	151.359i	0.322854	+	0.0210958i
$373$	−2074.53	+	11765.3i	−0.287977	+	1.63320i	0.406478	+	0.913660i	$0.366757\pi$
$373$	−2074.53	+	11765.3i	−0.287977	+	1.63320i	−0.694455	+	0.719536i	$0.744354\pi$
$374$	−3412.85	−	2863.72i	−0.471856	−	0.395935i
$375$	−135.590	−	129.747i	−0.0186715	−	0.0178669i
$376$	−4183.68	−	1522.74i	−0.573821	−	0.208854i
$377$	1147.36			0.156743
$378$	1277.89	−	3291.97i	0.173882	−	0.447938i
$379$	−9629.88			−1.30515			−0.652577	−	0.757722i	$-0.726312\pi$
$379$	−9629.88			−1.30515			−0.652577	+	0.757722i	$0.726312\pi$
$380$	30.4352	+	11.0775i	0.00410866	+	0.00149543i
$381$	9871.33	−	2879.39i	1.32736	−	0.387179i
$382$	1588.08	+	1332.56i	0.212705	+	0.178481i
$383$	330.744	−	1875.74i	0.0441259	−	0.250250i	−0.954764	−	0.297366i	$-0.903892\pi$
$383$	330.744	−	1875.74i	0.0441259	−	0.250250i	0.998889	+	0.0471156i	$0.0150029\pi$
$384$	3338.34	+	6766.06i	0.443644	+	0.899164i
$385$	182.796	−	153.384i	0.0241978	−	0.0203044i
$386$	1229.50	+	2129.56i	0.162125	+	0.280808i
$387$	2392.63	−	7599.13i	0.314275	−	0.998153i
$388$	−3525.14	+	6105.72i	−0.461242	+	0.798895i
$389$	578.319	+	3279.81i	0.0753777	+	0.427488i	0.999021	+	0.0442354i	$0.0140852\pi$
$389$	578.319	+	3279.81i	0.0753777	+	0.427488i	−0.923643	+	0.383253i	$0.874804\pi$
$390$	18.0781	+	7.95023i	0.00234724	+	0.00103224i
$391$	−2194.43	+	798.705i	−0.283828	+	0.103305i
$392$	4211.27	−	1532.78i	0.542606	−	0.197492i
$393$	8514.38	−	6245.64i	1.09286	−	0.801656i
$394$	−307.124	−	1741.79i	−0.0392708	−	0.222716i
$395$	−6.56170	+	11.3652i	−0.000835836	+	0.00144771i
$396$	−10396.5	+	6629.16i	−1.31930	+	0.841232i
$397$	3181.07	+	5509.77i	0.402149	+	0.696542i	0.993985	−	0.109516i	$-0.0349301\pi$
$397$	3181.07	+	5509.77i	0.402149	+	0.696542i	−0.591836	+	0.806058i	$0.701597\pi$
$398$	3294.45	−	2764.37i	0.414914	−	0.348155i
$399$	−2339.84	+	3503.35i	−0.293581	+	0.439566i
$400$	−897.463	+	5089.76i	−0.112183	+	0.636220i
$401$	−5662.64	−	4751.52i	−0.705184	−	0.591720i	0.218059	−	0.975936i	$-0.430027\pi$
$401$	−5662.64	−	4751.52i	−0.705184	−	0.591720i	−0.923243	+	0.384216i	$0.874472\pi$
$402$	−210.832	+	862.351i	−0.0261576	+	0.106990i
$403$	−1586.84	−	577.562i	−0.196144	−	0.0713906i
$404$	−8987.97			−1.10685
$405$	95.4204	−	44.5888i	0.0117074	−	0.00547070i
$406$	−1088.96			−0.133114
$407$	−15779.4	−	5743.24i	−1.92176	−	0.699464i
$408$	1268.34	−	5187.79i	0.153902	−	0.629495i
$409$	−751.921	−	630.937i	−0.0909049	−	0.0762783i	0.596203	−	0.802834i	$-0.296675\pi$
$409$	−751.921	−	630.937i	−0.0909049	−	0.0762783i	−0.687108	+	0.726556i	$0.741120\pi$
$410$	9.44818	−	53.5833i	0.00113808	−	0.00645437i
$411$	−662.217	+	991.509i	−0.0794762	+	0.118996i
$412$	7495.22	−	6289.23i	0.896269	−	0.752059i
$413$	−3881.91	−	6723.67i	−0.462509	−	0.801090i
$414$	−39.9014	−	905.531i	−0.00473683	−	0.107499i
$415$	−69.9128	+	121.092i	−0.00826960	+	0.0143234i
$416$	−737.660	−	4183.48i	−0.0869393	−	0.493057i
$417$	−3299.88	+	2420.60i	−0.387520	+	0.284262i
$418$	−1938.58	+	705.584i	−0.226839	+	0.0825628i
$419$	10352.9	−	3768.16i	1.20710	−	0.439348i	0.341401	−	0.939918i	$-0.389098\pi$
$419$	10352.9	−	3768.16i	1.20710	−	0.439348i	0.865696	+	0.500570i	$0.166876\pi$
$420$	122.344	+	53.8033i	0.0142138	+	0.00625079i
$421$	1782.27	+	10107.7i	0.206324	+	1.17012i	0.895343	+	0.445378i	$0.146931\pi$
$421$	1782.27	+	10107.7i	0.206324	+	1.17012i	−0.689019	+	0.724743i	$0.741958\pi$
$422$	−1312.85	+	2273.92i	−0.151442	+	0.262305i
$423$	7878.35	−	1749.91i	0.905576	−	0.201144i
$424$	2532.42	+	4386.28i	0.290059	+	0.502397i
$425$	6606.24	−	5543.29i	0.753999	−	0.632680i
$426$	−2387.77	−	4839.47i	−0.271568	−	0.550406i
$427$	2965.96	−	16820.8i	0.336142	−	1.90636i
$428$	5204.25	+	4366.88i	0.587749	+	0.493180i
$429$	8610.67	−	2511.66i	0.969061	−	0.282667i
$430$	−39.7375	−	14.4633i	−0.00445654	−	0.00162205i
$431$	4696.43			0.524870			0.262435	−	0.964950i	$-0.415474\pi$
$431$	4696.43			0.524870			0.262435	+	0.964950i	$0.415474\pi$
$432$	−4961.75	−	3006.77i	−0.552598	−	0.334868i
$433$	3775.87			0.419068			0.209534	−	0.977801i	$-0.432805\pi$
$433$	3775.87			0.419068			0.209534	+	0.977801i	$0.432805\pi$
$434$	1506.08	+	548.167i	0.166576	+	0.0606287i
$435$	−23.4665	−	22.4552i	−0.00258651	−	0.00247505i
$436$	−1055.06	−	885.299i	−0.115890	−	0.0972434i
$437$	−187.776	+	1064.93i	−0.0205550	+	0.116573i
$438$	−901.756	−	58.9220i	−0.0983734	−	0.00642786i
$439$	−8372.61	+	7025.45i	−0.910257	+	0.763796i	−0.972168	−	0.234285i	$-0.924725\pi$
$439$	−8372.61	+	7025.45i	−0.910257	+	0.763796i	0.0619108	+	0.998082i	$0.480281\pi$
$440$	70.0369	+	121.308i	0.00758836	+	0.0131434i
$441$	−4942.73	+	6446.86i	−0.533714	+	0.696130i
$442$	−907.603	+	1572.02i	−0.0976703	+	0.169170i
$443$	386.089	+	2189.62i	0.0414078	+	0.234835i	0.998487	−	0.0549918i	$-0.0175133\pi$
$443$	386.089	+	2189.62i	0.0414078	+	0.234835i	−0.957079	+	0.289827i	$0.906402\pi$
$444$	−1025.79	−	9349.07i	−0.109644	−	0.999296i
$445$	−65.1988	+	23.7304i	−0.00694544	+	0.00252793i
$446$	−3072.23	+	1118.20i	−0.326176	+	0.118718i
$447$	302.984	+	2761.39i	0.0320596	+	0.292191i
$448$	−757.587	−	4296.49i	−0.0798942	−	0.453103i
$449$	5908.73	−	10234.2i	0.621048	−	1.07569i	−0.368243	−	0.929729i	$-0.620041\pi$
$449$	5908.73	−	10234.2i	0.621048	−	1.07569i	0.989291	−	0.145957i	$-0.0466260\pi$
$450$	1282.19	+	3091.95i	0.134317	+	0.323902i
$451$	−12355.8	−	21400.8i	−1.29005	−	2.23443i
$452$	−11447.2	+	9605.38i	−1.19122	+	0.999555i
$453$	−5376.34	−	351.297i	−0.557621	−	0.0364357i
$454$	664.001	−	3765.74i	0.0686413	−	0.389284i
$455$	−74.4784	−	62.4948i	−0.00767384	−	0.00643912i
$456$	−1786.74	−	1709.75i	−0.183491	−	0.175584i
$457$	8361.42	+	3043.31i	0.855866	+	0.311510i	0.732430	−	0.680843i	$-0.238386\pi$
$457$	8361.42	+	3043.31i	0.855866	+	0.311510i	0.123436	+	0.992352i	$0.460609\pi$
$458$	1529.94			0.156091
$459$	3117.30	+	9165.10i	0.317001	+	0.932005i
$460$	34.3056			0.00347719
$461$	18161.1	+	6610.10i	1.83481	+	0.667816i	0.991453	+	0.130461i	$0.0416457\pi$
$461$	18161.1	+	6610.10i	1.83481	+	0.667816i	0.843356	+	0.537355i	$0.180577\pi$
$462$	−8172.42	+	2383.83i	−0.822977	+	0.240056i
$463$	7603.20	+	6379.84i	0.763177	+	0.640381i	0.938952	−	0.344049i	$-0.111799\pi$
$463$	7603.20	+	6379.84i	0.763177	+	0.640381i	−0.175775	+	0.984430i	$0.556243\pi$
$464$	−310.673	+	1761.92i	−0.0310833	+	0.176282i
$465$	21.1514	+	42.8690i	0.00210940	+	0.00427527i
$466$	−1825.40	+	1531.69i	−0.181459	+	0.152262i
$467$	2648.73	+	4587.73i	0.262459	+	0.454593i	0.966895	−	0.255175i	$-0.0821332\pi$
$467$	2648.73	+	4587.73i	0.262459	+	0.454593i	−0.704436	+	0.709768i	$0.748800\pi$
$468$	3395.51	+	3702.55i	0.335379	+	0.365706i
$469$	2185.20	−	3784.87i	0.215145	−	0.372642i
$470$	−7.43856	−	42.1862i	−0.000730032	−	0.00414022i
$471$	−5662.61	−	2490.25i	−0.553969	−	0.243619i
$472$	4282.58	−	1558.73i	0.417631	−	0.152005i
$473$	−18047.8	+	6568.84i	−1.75441	+	0.638553i
$474$	377.508	−	276.917i	0.0365813	−	0.0268338i
$475$	−693.433	−	3932.65i	−0.0669829	−	0.379879i
$476$	−6142.22	+	10638.6i	−0.591446	+	1.02441i
$477$	−8145.27	−	4235.99i	−0.781858	−	0.406610i
$478$	3561.08	+	6167.97i	0.340753	+	0.590201i
$479$	−6181.20	+	5186.64i	−0.589616	+	0.494747i	−0.888089	−	0.459671i	$-0.847967\pi$
$479$	−6181.20	+	5186.64i	−0.589616	+	0.494747i	0.298473	+	0.954418i	$0.403523\pi$
$480$	−66.7886	+	99.9998i	−0.00635098	+	0.00950905i
$481$	−1188.06	+	6737.82i	−0.112621	+	0.638707i
$482$	1585.38	+	1330.29i	0.149817	+	0.125712i
$483$	−1059.74	+	4334.59i	−0.0998343	+	0.408345i
$484$	19156.8	+	6972.51i	1.79910	+	0.654818i
$485$	−145.183			−0.0135926
$486$	−3756.51	+	85.7482i	−0.350615	+	0.00800333i
$487$	−16598.7			−1.54447			−0.772235	−	0.635337i	$-0.780861\pi$
$487$	−16598.7			−1.54447			−0.772235	+	0.635337i	$0.780861\pi$
$488$	9421.59	+	3429.18i	0.873966	+	0.318098i
$489$	−1528.22	+	6250.77i	−0.141326	+	0.578057i
$490$	33.0314	+	27.7167i	0.00304532	+	0.00255533i
$491$	703.737	−	3991.09i	0.0646827	−	0.366834i	−0.935235	−	0.354027i	$-0.884812\pi$
$491$	703.737	−	3991.09i	0.0646827	−	0.366834i	0.999918	−	0.0128070i	$-0.00407669\pi$
$492$	7687.24	−	11509.8i	0.704406	−	1.05468i
$493$	2286.87	−	1918.91i	0.208916	−	0.175301i
$494$	420.272	+	727.932i	0.0382772	+	0.0662980i
$495$	−225.267	−	117.151i	−0.0204545	−	0.0106375i
$496$	1316.59	−	2280.40i	0.119187	−	0.206438i
$497$	4613.28	+	26163.2i	0.416366	+	2.36133i
$498$	4022.22	−	2950.46i	0.361928	−	0.265489i
$499$	9423.94	−	3430.03i	0.845438	−	0.307714i	0.117259	−	0.993101i	$-0.462589\pi$
$499$	9423.94	−	3430.03i	0.845438	−	0.307714i	0.728179	+	0.685387i	$0.240367\pi$
$500$	−238.113	+	86.6660i	−0.0212975	+	0.00775164i
$501$	382.343	+	168.143i	0.0340954	+	0.0149942i
$502$	498.553	+	2827.44i	0.0443258	+	0.251384i
$503$	3131.16	−	5423.33i	0.277558	−	0.480744i	−0.693219	−	0.720727i	$-0.743808\pi$
$503$	3131.16	−	5423.33i	0.277558	−	0.480744i	0.970777	+	0.239982i	$0.0771417\pi$
$504$	−6897.35	−	7521.05i	−0.609588	−	0.664711i
$505$	−92.5424	−	160.288i	−0.00815462	−	0.0141242i
$506$	−1673.89	+	1404.56i	−0.147062	+	0.123400i
$507$	3434.19	+	6960.31i	0.300824	+	0.609701i
$508$	2410.95	−	13673.2i	0.210568	−	1.19419i
$509$	−8942.03	−	7503.25i	−0.778681	−	0.653391i	0.164235	−	0.986421i	$-0.447484\pi$
$509$	−8942.03	−	7503.25i	−0.778681	−	0.653391i	−0.942916	+	0.333030i	$0.891929\pi$
$510$	49.3290	−	14.3889i	0.00428299	−	0.00124931i
$511$	4180.51	+	1521.58i	0.361908	+	0.131724i
$512$	11551.7			0.997103
$513$	4397.12	+	871.883i	0.378436	+	0.0750382i
$514$	273.589			0.0234776
$515$	189.332	+	68.9114i	0.0162000	+	0.00589631i
$516$	−7772.11	−	7437.18i	−0.663078	−	0.634503i
$517$	−14903.7	−	12505.7i	−1.26782	−	1.06383i
$518$	1127.59	−	6394.89i	0.0956439	−	0.542424i
$519$	4787.23	+	312.804i	0.404886	+	0.0264558i
$520$	43.7194	−	36.6849i	0.00368696	−	0.00309373i
$521$	−6768.24	−	11722.9i	−0.569140	−	0.985780i	−0.996651	−	0.0817697i	$-0.973943\pi$
$521$	−6768.24	−	11722.9i	−0.569140	−	0.985780i	0.427511	−	0.904010i	$-0.359391\pi$
$522$	443.853	+	1070.34i	0.0372163	+	0.0897459i
$523$	−8123.42	+	14070.2i	−0.679183	+	1.17638i	0.296045	+	0.955174i	$0.404332\pi$
$523$	−8123.42	+	14070.2i	−0.679183	+	1.17638i	−0.975227	+	0.221205i	$0.929001\pi$
$524$	−2475.84	−	14041.2i	−0.206408	−	1.17060i
$525$	−1797.27	−	16380.3i	−0.149408	−	1.36170i
$526$	201.662	−	73.3990i	0.0167165	−	0.00608431i
$527$	−4128.77	+	1502.75i	−0.341275	+	0.124214i
$528$	1525.44	+	13902.9i	0.125732	+	1.14592i
$529$	−1913.89	−	10854.2i	−0.157301	−	0.892101i
$530$	−24.3658	+	42.2029i	−0.00199695	+	0.00345882i
$531$	−5026.42	+	6556.01i	−0.410787	+	0.535794i
$532$	2844.19	+	4926.29i	0.231788	+	0.401469i
$533$	−7712.89	+	6471.88i	−0.626796	+	0.525944i
$534$	2470.01	+	161.394i	0.200164	+	0.0130790i
$535$	−24.2931	+	137.773i	−0.00196315	+	0.0111335i
$536$	1965.25	+	1649.04i	0.158369	+	0.132888i
$537$	−3273.04	−	3131.99i	−0.263021	−	0.251686i
$538$	−1809.46	−	658.589i	−0.145002	−	0.0527765i
$539$	19583.7			1.56499
$540$	3.01654	−	142.181i	0.000240391	−	0.0113305i
$541$	13385.4			1.06374			0.531872	−	0.846825i	$-0.321489\pi$
$541$	13385.4			1.06374			0.531872	+	0.846825i	$0.321489\pi$
$542$	−3950.59	−	1437.90i	−0.313086	−	0.113954i
$543$	−1250.84	+	364.858i	−0.0988554	+	0.0288353i
$544$	−8466.97	−	7104.63i	−0.667313	−	0.559942i
$545$	4.92495	−	27.9308i	0.000387085	−	0.00219527i
$546$	1534.72	+	3110.52i	0.120293	+	0.243806i
$547$	2600.12	−	2181.76i	0.203242	−	0.170540i	−0.535486	−	0.844544i	$-0.679872\pi$
$547$	2600.12	−	2181.76i	0.203242	−	0.170540i	0.738727	+	0.674004i	$0.235427\pi$
$548$	804.956	+	1394.22i	0.0627482	+	0.108683i
$549$	−17741.9	+	3940.78i	−1.37925	+	0.306354i
$550$	4034.67	−	6988.25i	0.312798	−	0.541782i
$551$	−240.045	−	1361.36i	−0.0185594	−	0.105256i
$552$	−2397.76	−	1054.46i	−0.184883	−	0.0813060i
$553$	−2165.87	+	788.311i	−0.166550	+	0.0606191i
$554$	−1242.03	+	452.062i	−0.0952505	+	0.0346684i
$555$	156.166	−	114.554i	0.0119439	−	0.00876134i
$556$	959.552	+	5441.89i	0.0731908	+	0.415085i
$557$	4007.81	−	6941.73i	0.304877	−	0.528062i	−0.672357	−	0.740227i	$-0.734718\pi$
$557$	4007.81	−	6941.73i	0.304877	−	0.528062i	0.977234	+	0.212165i	$0.0680513\pi$
$558$	−75.0738	−	1703.74i	−0.00569557	−	0.129256i
$559$	3912.64	+	6776.89i	0.296041	+	0.512759i
$560$	116.135	−	97.4490i	0.00876359	−	0.00735352i
$561$	12961.8	−	19407.1i	0.975485	−	1.46055i
$562$	444.654	−	2521.76i	0.0333747	−	0.189277i
$563$	10180.9	+	8542.80i	0.762121	+	0.639496i	0.938678	−	0.344795i	$-0.112051\pi$
$563$	10180.9	+	8542.80i	0.762121	+	0.639496i	−0.176557	+	0.984290i	$0.556496\pi$
$564$	2587.91	−	10585.1i	0.193210	−	0.790274i
$565$	−289.162	−	105.247i	−0.0215312	−	0.00783673i
$566$	−126.169			−0.00936978
$567$	17871.7	+	4773.29i	1.32370	+	0.353544i
$568$	−15594.9			−1.15202
$569$	−4874.08	−	1774.02i	−0.359107	−	0.130704i	0.156165	−	0.987731i	$-0.450087\pi$
$569$	−4874.08	−	1774.02i	−0.359107	−	0.130704i	−0.515272	+	0.857027i	$0.672309\pi$
$570$	5.65086	−	23.1133i	0.000415243	−	0.00169844i
$571$	8263.96	+	6934.28i	0.605667	+	0.508215i	0.893262	−	0.449537i	$-0.148411\pi$
$571$	8263.96	+	6934.28i	0.605667	+	0.508215i	−0.287595	+	0.957752i	$0.592856\pi$
$572$	2103.05	−	11927.0i	0.153729	−	0.871839i
$573$	−6031.44	+	9030.62i	−0.439733	+	0.658394i
$574$	7320.34	−	6142.49i	0.532308	−	0.446660i
$575$	−2114.85	−	3663.03i	−0.153383	−	0.265668i
$576$	−3914.20	+	2495.84i	−0.283146	+	0.180544i
$577$	−7471.95	+	12941.8i	−0.539101	+	0.933750i	0.459852	+	0.887996i	$0.347903\pi$
$577$	−7471.95	+	12941.8i	−0.539101	+	0.933750i	−0.998953	+	0.0457545i	$0.985431\pi$
$578$	−26.1301	−	148.191i	−0.00188039	−	0.0106642i
$579$	−10386.4	+	7618.82i	−0.745497	+	0.546852i
$580$	−41.2101	+	14.9993i	−0.00295027	+	0.00107381i
$581$	−23076.6	+	8399.19i	−1.64781	+	0.599754i
$582$	4741.24	+	2085.06i	0.337682	+	0.148502i
$583$	3843.30	+	21796.4i	0.273024	+	1.54840i
$584$	−1305.74	+	2261.61i	−0.0925206	+	0.160250i
$585$	−31.0690	+	98.6766i	−0.00219580	+	0.00697398i
$586$	−757.199	−	1311.51i	−0.0533782	−	0.0924537i
$587$	16327.7	−	13700.6i	1.14807	−	0.963346i	0.148398	−	0.988928i	$-0.452588\pi$
$587$	16327.7	−	13700.6i	1.14807	−	0.963346i	0.999673	+	0.0255816i	$0.00814376\pi$
$588$	4853.34	+	9836.61i	0.340388	+	0.689889i
$589$	−353.296	+	2003.64i	−0.0247153	+	0.140168i
$590$	33.5907	+	28.1859i	0.00234391	+	0.00196677i
$591$	8894.16	−	2594.35i	0.619047	−	0.180571i
$592$	−10025.1	−	3648.83i	−0.695993	−	0.253321i
$593$	−13235.6			−0.916564			−0.458282	−	0.888807i	$-0.651535\pi$
$593$	−13235.6			−0.916564			−0.458282	+	0.888807i	$0.651535\pi$
$594$	5674.06	+	7060.99i	0.391935	+	0.487738i
$595$	−252.967			−0.0174297
$596$	3524.70	+	1282.89i	0.242244	+	0.0881696i
$597$	16276.5	+	15575.1i	1.11584	+	1.06775i
$598$	682.008	+	572.272i	0.0466377	+	0.0391337i
$599$	4450.42	−	25239.6i	0.303571	−	1.72164i	−0.326584	−	0.945168i	$-0.605898\pi$
$599$	4450.42	−	25239.6i	0.303571	−	1.72164i	0.630155	−	0.776469i	$-0.282991\pi$
$600$	9652.46	+	630.706i	0.656767	+	0.0429141i
$601$	−15034.1	+	12615.1i	−1.02039	+	0.856207i	−0.989676	−	0.143321i	$-0.954222\pi$
$601$	−15034.1	+	12615.1i	−1.02039	+	0.856207i	−0.0307119	+	0.999528i	$0.509777\pi$
$602$	−3713.51	−	6431.98i	−0.251414	−	0.435462i
$603$	−4610.79	−	605.135i	−0.311386	−	0.0408673i
$604$	−3637.41	+	6300.17i	−0.245040	+	0.424421i
$605$	72.8982	+	413.426i	0.00489873	+	0.0277821i
$606$	720.167	+	6563.59i	0.0482752	+	0.439980i
$607$	−4560.36	+	1659.84i	−0.304941	+	0.110990i	−0.489959	−	0.871746i	$-0.662988\pi$
$607$	−4560.36	+	1659.84i	−0.304941	+	0.110990i	0.185017	+	0.982735i	$0.440766\pi$
$608$	−4809.43	+	1750.49i	−0.320803	+	0.116763i
$609$	−622.157	−	5670.33i	−0.0413975	−	0.377296i
$610$	16.7515	+	95.0026i	0.00111188	+	0.00630581i
$611$	−3963.45	+	6864.90i	−0.262429	+	0.454540i
$612$	12960.2	+	1700.93i	0.856018	+	0.112347i
$613$	−5518.81	−	9558.86i	−0.363626	−	0.629819i	0.624929	−	0.780682i	$-0.285128\pi$
$613$	−5518.81	−	9558.86i	−0.363626	−	0.629819i	−0.988555	+	0.150863i	$0.951795\pi$
$614$	−3038.75	+	2549.81i	−0.199729	+	0.167593i
$615$	284.411	+	18.5838i	0.0186481	+	0.00121849i
$616$	−4271.95	+	24227.4i	−0.279419	+	1.58466i
$617$	4066.26	+	3412.00i	0.265318	+	0.222628i	0.765735	−	0.643156i	$-0.222375\pi$
$617$	4066.26	+	3412.00i	0.265318	+	0.222628i	−0.500417	+	0.865785i	$0.666820\pi$
$618$	−5193.36	−	4969.56i	−0.338038	−	0.323471i
$619$	−11334.4	−	4125.37i	−0.735972	−	0.267872i	−0.0532815	−	0.998580i	$-0.516968\pi$
$619$	−11334.4	−	4125.37i	−0.735972	−	0.267872i	−0.682691	+	0.730708i	$0.739190\pi$
$620$	64.5454			0.00418098
$621$	4692.38	−	725.126i	0.303219	−	0.0468572i
$622$	−7092.27			−0.457193
$623$	−11450.9	−	4167.78i	−0.736388	−	0.268023i
$624$	5470.58	−	1595.72i	0.350959	−	0.102372i
$625$	11963.4	+	10038.5i	0.765661	+	0.642466i
$626$	−1544.92	+	8761.68i	−0.0986380	+	0.559404i
$627$	−4781.60	−	9691.22i	−0.304560	−	0.617273i
$628$	−6398.43	+	5368.92i	−0.406569	+	0.341152i
$629$	8900.74	+	15416.5i	0.564222	+	0.977261i
$630$	29.4877	−	93.6544i	0.00186479	−	0.00592267i
$631$	10634.3	−	18419.2i	0.670913	−	1.16206i	−0.306732	−	0.951796i	$-0.599236\pi$
$631$	10634.3	−	18419.2i	0.670913	−	1.16206i	0.977646	−	0.210260i	$-0.0674310\pi$
$632$	−234.941	−	1332.42i	−0.0147871	−	0.0838620i
$633$	−12590.5	−	5536.95i	−0.790568	−	0.347668i
$634$	−570.831	+	207.766i	−0.0357580	+	0.0130149i
$635$	268.666	−	97.7864i	0.0167900	−	0.00611108i
$636$	−9995.54	+	7332.12i	−0.623190	+	0.457135i
$637$	−1385.57	−	7857.96i	−0.0861826	−	0.488766i
$638$	1396.68	−	2419.11i	0.0866691	−	0.150115i
$639$	23835.3	−	15198.3i	1.47560	−	0.940899i
$640$	104.891	+	181.676i	0.00647839	+	0.0112209i
$641$	12391.8	−	10398.0i	0.763569	−	0.640711i	−0.175484	−	0.984482i	$-0.556149\pi$
$641$	12391.8	−	10398.0i	0.763569	−	0.640711i	0.939053	+	0.343772i	$0.111705\pi$
$642$	2771.98	−	4150.37i	0.170407	−	0.255143i
$643$	4441.03	−	25186.3i	0.272375	−	1.54472i	−0.474804	−	0.880092i	$-0.657481\pi$
$643$	4441.03	−	25186.3i	0.272375	−	1.54472i	0.747179	−	0.664623i	$-0.231408\pi$
$644$	4615.50	+	3872.86i	0.282416	+	0.236975i
$645$	52.6083	−	215.180i	0.00321155	−	0.0131360i
$646$	2055.10	+	747.997i	0.125166	+	0.0455566i
$647$	−9723.13			−0.590813			−0.295406	−	0.955372i	$-0.595455\pi$
$647$	−9723.13			−0.590813			−0.295406	+	0.955372i	$0.595455\pi$
$648$	−4581.10	+	9844.87i	−0.277720	+	0.596826i
$649$	19915.3			1.20454
$650$	−3089.49	−	1124.48i	−0.186430	−	0.0678551i
$651$	−1993.89	+	8155.45i	−0.120041	+	0.490994i
$652$	6655.86	+	5584.93i	0.399791	+	0.335464i
$653$	−1116.67	+	6332.96i	−0.0669199	+	0.379522i	0.932893	+	0.360155i	$0.117276\pi$
$653$	−1116.67	+	6332.96i	−0.0669199	+	0.379522i	−0.999812	+	0.0193669i	$0.993835\pi$
$654$	−561.964	+	841.405i	−0.0336002	+	0.0503082i
$655$	224.914	−	188.725i	0.0134170	−	0.0112582i
$656$	−7849.95	−	13596.5i	−0.467209	−	0.809230i
$657$	−208.387	−	4729.18i	−0.0123744	−	0.280827i
$658$	3761.73	−	6515.51i	0.222869	−	0.386020i
$659$	−1673.21	−	9489.25i	−0.0989060	−	0.560924i	−0.993480	−	0.114004i	$-0.963632\pi$
$659$	−1673.21	−	9489.25i	−0.0989060	−	0.560924i	0.894574	−	0.446919i	$-0.147479\pi$
$660$	−276.438	+	202.778i	−0.0163035	+	0.0119593i
$661$	5660.47	−	2060.24i	0.333082	−	0.121232i	−0.170065	−	0.985433i	$-0.554398\pi$
$661$	5660.47	−	2060.24i	0.333082	−	0.121232i	0.503147	+	0.864201i	$0.332176\pi$
$662$	2985.33	−	1086.57i	0.175269	−	0.0637928i
$663$	−8704.16	−	3827.83i	−0.509867	−	0.224224i
$664$	−2503.22	−	14196.5i	−0.146301	−	0.829715i
$665$	−58.5690	+	101.445i	−0.00341535	+	0.00591557i
$666$	−6745.10	+	1498.20i	−0.392443	+	0.0871682i
$667$	−732.095	−	1268.02i	−0.0424990	−	0.0736104i
$668$	432.026	−	362.513i	0.0250233	−	0.0209971i
$669$	−7577.82	−	15358.5i	−0.437931	−	0.887585i
$670$	−4.28627	+	24.3087i	−0.000247154	+	0.00140168i
$671$	33563.0	+	28162.7i	1.93097	+	1.62028i
$672$	−20275.0	+	5914.06i	−1.16388	+	0.339494i
$673$	6650.68	+	2420.65i	0.380928	+	0.138647i	0.525385	−	0.850865i	$-0.323921\pi$
$673$	6650.68	+	2420.65i	0.380928	+	0.138647i	−0.144457	+	0.989511i	$0.546143\pi$
$674$	−3085.91			−0.176357
$675$	−15367.5	+	8442.98i	−0.876290	+	0.481437i
$676$	10479.8			0.596254
$677$	−20674.0	−	7524.74i	−1.17366	−	0.427177i	−0.319702	−	0.947518i	$-0.603583\pi$
$677$	−20674.0	−	7524.74i	−1.17366	−	0.427177i	−0.853959	+	0.520341i	$0.825805\pi$
$678$	7931.68	+	7589.87i	0.449283	+	0.429922i
$679$	−19533.0	−	16390.1i	−1.10399	−	0.926355i
$680$	25.7857	−	146.238i	0.00145417	−	0.00824700i
$681$	19987.9	+	1306.04i	1.12472	+	0.0734911i
$682$	−3149.39	+	2642.65i	−0.176828	+	0.148376i
$683$	16442.5	+	28479.2i	0.921163	+	1.59550i	0.797618	+	0.603162i	$0.206093\pi$
$683$	16442.5	+	28479.2i	0.921163	+	1.59550i	0.123545	+	0.992339i	$0.460574\pi$
$684$	3682.75	−	4803.45i	0.205867	−	0.268515i
$685$	−16.5761	+	28.7106i	−0.000924582	+	0.00160142i
$686$	−184.126	−	1044.23i	−0.0102478	−	0.0581180i
$687$	874.102	+	7966.56i	0.0485430	+	0.442421i
$688$	−11466.2	+	4173.36i	−0.635385	+	0.231261i
$689$	8473.88	−	3084.24i	0.468547	−	0.170537i
$690$	−2.74876	−	25.0522i	−0.000151657	−	0.00138220i
$691$	−3790.16	−	21495.0i	−0.208660	−	1.18337i	−0.891575	−	0.452874i	$-0.850399\pi$
$691$	−3790.16	−	21495.0i	−0.208660	−	1.18337i	0.682914	−	0.730498i	$-0.260712\pi$
$692$	3238.84	−	5609.84i	0.177922	−	0.308171i
$693$	−17081.9	−	41192.6i	−0.936348	−	2.25797i
$694$	948.356	+	1642.60i	0.0518719	+	0.0898448i
$695$	−87.1688	+	73.1433i	−0.00475756	+	0.00399207i
$696$	3341.38	+	218.330i	0.181975	+	0.0118905i
$697$	−4549.06	+	25799.0i	−0.247214	+	1.40202i
$698$	6430.55	+	5395.87i	0.348710	+	0.292603i
$699$	−9018.54	−	8629.90i	−0.488001	−	0.466971i
$700$	−20908.2	−	7609.94i	−1.12893	−	0.410898i
$701$	−34790.7			−1.87450			−0.937251	−	0.348656i	$-0.886638\pi$
$701$	−34790.7			−1.87450			−0.937251	+	0.348656i	$0.886638\pi$
$702$	2431.77	−	2776.28i	0.130743	−	0.149265i
$703$	8243.09			0.442239
$704$	10516.2	+	3827.59i	0.562990	+	0.204912i
$705$	215.417	−	62.8354i	0.0115079	−	0.00335676i
$706$	2161.65	+	1813.84i	0.115233	+	0.0966922i
$707$	5644.69	−	32012.6i	0.300269	−	1.70291i
$708$	4935.51	+	10003.2i	0.261989	+	0.530991i
$709$	25726.9	−	21587.5i	1.36276	−	1.14349i	0.387638	−	0.921812i	$-0.373291\pi$
$709$	25726.9	−	21587.5i	1.36276	−	1.14349i	0.975120	−	0.221678i	$-0.0711533\pi$
$710$	−75.0239	−	129.945i	−0.00396563	−	0.00686867i
$711$	1657.61	+	1807.51i	0.0874337	+	0.0953401i
$712$	3576.57	−	6194.80i	0.188255	−	0.326068i
$713$	374.209	+	2122.25i	0.0196553	+	0.111471i
$714$	8261.16	+	3633.01i	0.433006	+	0.190423i
$715$	234.355	−	85.2981i	0.0122579	−	0.00446150i
$716$	−5747.88	+	2092.06i	−0.300012	+	0.109195i
$717$	−30082.6	+	22066.8i	−1.56688	+	1.14937i
$718$	−222.222	−	1260.28i	−0.0115505	−	0.0655060i
$719$	−16437.6	+	28470.8i	−0.852601	+	1.47675i	0.0262517	+	0.999655i	$0.491643\pi$
$719$	−16437.6	+	28470.8i	−0.852601	+	1.47675i	−0.878853	+	0.477093i	$0.841690\pi$
$720$	−143.118	−	74.4292i	−0.00740789	−	0.00385252i
$721$	17693.3	+	30645.7i	0.913914	+	1.58295i
$722$	−4436.21	+	3722.42i	−0.228669	+	0.191876i
$723$	−6021.16	+	9015.23i	−0.309722	+	0.463734i
$724$	−305.501	+	1732.58i	−0.0156821	+	0.0889377i
$725$	4142.06	+	3475.60i	0.212182	+	0.178042i
$726$	3556.82	−	14548.2i	0.181826	−	0.743711i
$727$	27323.1	+	9944.80i	1.39389	+	0.507334i	0.926359	−	0.376642i	$-0.122921\pi$
$727$	27323.1	+	9944.80i	1.39389	+	0.507334i	0.467531	+	0.883977i	$0.345144\pi$
$728$	10023.5			0.510296
$729$	−2592.70	−	19511.5i	−0.131723	−	0.991287i
$730$	−25.1266			−0.00127394
$731$	19132.6	+	6963.70i	0.968050	+	0.352341i
$732$	−5827.93	+	23837.6i	−0.294271	+	1.20364i
$733$	28106.1	+	23583.8i	1.41627	+	1.18839i	0.953305	+	0.302008i	$0.0976570\pi$
$733$	28106.1	+	23583.8i	1.41627	+	1.18839i	0.462960	+	0.886379i	$0.346787\pi$
$734$	374.118	−	2121.73i	0.0188133	−	0.106695i
$735$	−125.451	+	187.833i	−0.00629570	+	0.00942628i
$736$	−4152.76	+	3484.58i	−0.207980	+	0.174516i
$737$	5605.34	+	9708.73i	0.280157	+	0.485245i
$738$	−9021.12	−	4691.49i	−0.449962	−	0.234005i
$739$	5259.61	−	9109.91i	0.261810	−	0.453469i	−0.704913	−	0.709294i	$-0.749014\pi$
$739$	5259.61	−	9109.91i	0.261810	−	0.453469i	0.966723	+	0.255825i	$0.0823472\pi$
$740$	−45.4105	−	257.536i	−0.00225584	−	0.0127935i
$741$	−3550.29	+	2604.28i	−0.176010	+	0.129110i
$742$	−8042.60	+	2927.27i	−0.397915	+	0.144829i
$743$	−9957.03	+	3624.06i	−0.491639	+	0.178942i	−0.575930	−	0.817499i	$-0.695360\pi$
$743$	−9957.03	+	3624.06i	−0.491639	+	0.178942i	0.0842905	+	0.996441i	$0.473138\pi$
$744$	−4511.34	−	1983.95i	−0.222303	−	0.0977625i
$745$	13.4127	+	76.0672i	0.000659601	+	0.00374079i
$746$	5925.28	−	10262.9i	0.290804	−	0.503688i
$747$	17661.3	+	19258.4i	0.865052	+	0.943276i
$748$	−15755.7	−	27289.6i	−0.770166	−	1.33397i
$749$	−18822.0	+	15793.5i	−0.918212	+	0.770472i
$750$	82.3680	+	166.941i	0.00401020	+	0.00812776i
$751$	−1478.72	+	8386.24i	−0.0718499	+	0.407481i	0.927577	+	0.373632i	$0.121888\pi$
$751$	−1478.72	+	8386.24i	−0.0718499	+	0.407481i	−0.999427	+	0.0338490i	$0.989223\pi$
$752$	−9468.72	−	7945.20i	−0.459161	−	0.385281i
$753$	−14437.9	+	4211.41i	−0.698732	+	0.203814i
$754$	−1069.48	−	389.260i	−0.0516556	−	0.0188011i
$755$	−149.807			−0.00722122
$756$	16457.1	−	18788.5i	0.791716	−	0.903879i
$757$	2716.53			0.130428			0.0652139	−	0.997871i	$-0.479227\pi$
$757$	2716.53			0.130428			0.0652139	+	0.997871i	$0.479227\pi$
$758$	8976.26	+	3267.09i	0.430122	+	0.156552i
$759$	−8270.00	−	7913.62i	−0.395497	−	0.378453i
$760$	−52.6739	−	44.1987i	−0.00251406	−	0.00210955i
$761$	−4597.56	+	26074.0i	−0.219003	+	1.24203i	0.654821	+	0.755784i	$0.272744\pi$
$761$	−4597.56	+	26074.0i	−0.219003	+	1.24203i	−0.873824	+	0.486243i	$0.838367\pi$
$762$	−10178.2	−	665.058i	−0.483881	−	0.0316174i
$763$	3815.79	−	3201.83i	0.181050	−	0.151919i
$764$	7331.50	+	12698.5i	0.347179	+	0.601331i
$765$	103.107	+	248.640i	0.00487301	+	0.0117511i
$766$	−944.670	+	1636.22i	−0.0445592	+	0.0771787i
$767$	−1409.03	−	7991.01i	−0.0663327	−	0.376191i
$768$	−36.7428	−	334.874i	−0.00172636	−	0.0157340i
$769$	−19780.3	+	7199.44i	−0.927563	+	0.337605i	−0.761243	−	0.648466i	$-0.775411\pi$
$769$	−19780.3	+	7199.44i	−0.927563	+	0.337605i	−0.166320	+	0.986072i	$0.553188\pi$
$770$	−222.427	+	80.9568i	−0.0104100	+	0.00378894i
$771$	156.309	+	1424.60i	0.00730134	+	0.0665443i
$772$	3020.19	+	17128.3i	0.140802	+	0.798526i
$773$	906.569	−	1570.22i	0.0421824	−	0.0730621i	−0.844163	−	0.536086i	$-0.819902\pi$
$773$	906.569	−	1570.22i	0.0421824	−	0.0730621i	0.886346	+	0.463024i	$0.153236\pi$
$774$	−4808.36	+	6271.60i	−0.223298	+	0.291251i
$775$	−3979.05	−	6891.92i	−0.184428	−	0.319439i
$776$	11466.0	−	9621.12i	0.530420	−	0.445075i
$777$	33943.0	+	2217.88i	1.56718	+	0.102402i
$778$	573.662	−	3253.40i	0.0264355	−	0.149923i
$779$	9292.64	+	7797.45i	0.427398	+	0.358630i
$780$	100.923	+	96.5737i	0.00463284	+	0.00443320i
$781$	−64038.0	−	23307.9i	−2.93401	−	1.06789i
$782$	2316.45			0.105929
$783$	−5319.75	+	2922.69i	−0.242800	+	0.133395i
$784$	12442.1			0.566785
$785$	−161.627	−	58.8275i	−0.00734869	−	0.00267470i
$786$	−10055.4	+	2933.08i	−0.456316	+	0.133104i
$787$	−26253.8	−	22029.6i	−1.18913	−	0.997801i	−0.999874	−	0.0158739i	$-0.994947\pi$
$787$	−26253.8	−	22029.6i	−1.18913	−	0.997801i	−0.189259	−	0.981927i	$-0.560609\pi$
$788$	2172.29	−	12319.7i	0.0982037	−	0.556941i
$789$	497.410	+	1008.14i	0.0224439	+	0.0454887i
$790$	9.97216	−	8.36763i	0.000449106	−	0.000376844i
$791$	−27022.5	−	46804.3i	−1.21468	−	2.10388i
$792$	25554.2	−	5676.02i	1.14650	−	0.254657i
$793$	8925.64	−	15459.7i	0.399696	−	0.692293i
$794$	−1095.88	−	6215.02i	−0.0489813	−	0.277787i
$795$	−233.675	−	102.763i	−0.0104246	−	0.00458445i
$796$	28583.7	−	10403.6i	1.27277	−	0.463249i
$797$	21326.9	−	7762.37i	0.947853	−	0.344990i	0.178591	−	0.983923i	$-0.442846\pi$
$797$	21326.9	−	7762.37i	0.947853	−	0.344990i	0.769262	+	0.638933i	$0.220624\pi$
$798$	3369.60	−	2471.73i	0.149477	−	0.109647i
$799$	3581.47	+	20311.5i	0.158578	+	0.899338i
$800$	10009.6	−	17337.2i	0.442368	−	0.766204i
$801$	570.795	+	12953.8i	0.0251786	+	0.571409i
$802$	3666.26	+	6350.15i	0.161422	+	0.279591i
$803$	−8741.98	+	7335.39i	−0.384181	+	0.322366i
$804$	−3487.40	+	5221.54i	−0.152974	+	0.229042i
$805$	−21.5449	+	122.187i	−0.000943300	+	0.00534972i
$806$	1283.19	+	1076.72i	0.0560773	+	0.0470544i
$807$	2395.53	−	9798.27i	0.104494	−	0.427405i
$808$	17930.8	+	6526.27i	0.780697	+	0.284150i
$809$	14635.7			0.636049			0.318024	−	0.948083i	$-0.396981\pi$
$809$	14635.7			0.636049			0.318024	+	0.948083i	$0.396981\pi$
$810$	−104.071	+	9.18946i	−0.00451443	+	0.000398623i
$811$	−21636.5			−0.936821			−0.468410	−	0.883511i	$-0.655173\pi$
$811$	−21636.5			−0.936821			−0.468410	+	0.883511i	$0.655173\pi$
$812$	−7237.74	−	2634.32i	−0.312802	−	0.113851i
$813$	5230.17	−	21392.6i	0.225621	−	0.922842i
$814$	12759.9	+	10706.8i	0.549428	+	0.461025i
$815$	−31.0692	+	176.202i	−0.00133534	+	0.00757311i
$816$	8234.96	−	12329.9i	0.353286	−	0.528960i
$817$	7222.31	−	6060.24i	0.309274	−	0.259511i
$818$	486.829	+	843.213i	0.0208088	+	0.0360419i
$819$	−15319.9	+	9768.54i	−0.653628	+	0.416777i
$820$	192.421	−	333.282i	0.00819466	−	0.0141936i
$821$	−4957.32	−	28114.4i	−0.210733	−	1.19513i	−0.888160	−	0.459535i	$-0.848016\pi$
$821$	−4957.32	−	28114.4i	−0.210733	−	1.19513i	0.677427	−	0.735590i	$-0.263095\pi$
$822$	953.654	−	699.543i	0.0404653	−	0.0296829i
$823$	13978.4	−	5087.71i	0.592048	−	0.215488i	−0.0285819	−	0.999591i	$-0.509099\pi$
$823$	13978.4	−	5087.71i	0.592048	−	0.215488i	0.620630	+	0.784104i	$0.286877\pi$
$824$	−19519.5	+	7104.51i	−0.825234	+	0.300361i
$825$	38693.6	+	17016.3i	1.63289	+	0.718098i
$826$	1337.32	+	7584.30i	0.0563332	+	0.319481i
$827$	−11642.5	+	20165.4i	−0.489540	+	0.847908i	−0.999928	−	0.0120362i	$-0.996169\pi$
$827$	−11642.5	+	20165.4i	−0.489540	+	0.847908i	0.510387	+	0.859945i	$0.329502\pi$
$828$	1925.37	−	6115.09i	0.0808108	−	0.256659i
$829$	−938.107	−	1624.85i	−0.0393026	−	0.0680740i	0.845705	−	0.533651i	$-0.179180\pi$
$829$	−938.107	−	1624.85i	−0.0393026	−	0.0680740i	−0.885008	+	0.465577i	$0.845847\pi$
$830$	106.250	−	89.1543i	0.00444336	−	0.00372842i
$831$	−3063.53	−	6209.08i	−0.127885	−	0.259195i
$832$	791.784	−	4490.43i	0.0329930	−	0.187113i
$833$	−15903.8	−	13344.9i	−0.661505	−	0.555069i
$834$	3897.13	−	1136.76i	0.161806	−	0.0471976i
$835$	10.9132	+	3.97206i	0.000452294	+	0.000164621i
$836$	−14591.5			−0.603659
$837$	8828.63	−	1364.31i	0.364590	−	0.0563411i
$838$	−10928.6			−0.450506
$839$	−11244.6	−	4092.71i	−0.462703	−	0.168410i	0.100141	−	0.994973i	$-0.468071\pi$
$839$	−11244.6	−	4092.71i	−0.462703	−	0.168410i	−0.562844	+	0.826563i	$0.690293\pi$
$840$	−205.006	−	196.172i	−0.00842070	−	0.00805782i
$841$	−17249.2	−	14473.8i	−0.707254	−	0.593456i
$842$	1767.91	−	10026.3i	0.0723591	−	0.410369i
$843$	13385.0	+	874.598i	0.546863	+	0.0357328i
$844$	−14226.6	+	11937.5i	−0.580214	+	0.486857i
$845$	107.902	+	186.892i	0.00439284	+	0.00760862i
$846$	−7937.30	−	1041.72i	−0.322565	−	0.0423344i
$847$	−36865.1	+	63852.2i	−1.49551	+	2.59031i
$848$	2441.75	+	13847.8i	0.0988796	+	0.560774i
$849$	−72.0842	−	656.975i	−0.00291393	−	0.0265575i
$850$	−8038.49	+	2925.77i	−0.324374	+	0.118063i
$851$	8204.48	−	2986.19i	0.330489	−	0.120288i
$852$	−4163.00	−	37941.6i	−0.167397	−	1.52565i
$853$	−144.419	−	819.040i	−0.00579696	−	0.0328762i	0.981772	−	0.190062i	$-0.0608689\pi$
$853$	−144.419	−	819.040i	−0.00579696	−	0.0328762i	−0.987569	+	0.157186i	$0.949758\pi$
$854$	−8471.36	+	14672.8i	−0.339443	+	0.587932i
$855$	123.581	+	16.2192i	0.00494315	+	0.000648755i
$856$	−7211.50	−	12490.7i	−0.287949	−	0.498742i
$857$	21526.8	−	18063.1i	0.858041	−	0.719982i	−0.103504	−	0.994629i	$-0.533006\pi$
$857$	21526.8	−	18063.1i	0.858041	−	0.719982i	0.961545	+	0.274647i	$0.0885611\pi$
$858$	−8878.34	−	580.123i	−0.353265	−	0.0230829i
$859$	−2789.69	+	15821.1i	−0.110807	+	0.628416i	0.877935	+	0.478781i	$0.158921\pi$
$859$	−2789.69	+	15821.1i	−0.110807	+	0.628416i	−0.988741	+	0.149635i	$0.952190\pi$
$860$	−229.125	−	192.259i	−0.00908500	−	0.00762322i
$861$	36166.8	+	34608.3i	1.43155	+	1.36986i
$862$	−4377.66	−	1593.34i	−0.172974	−	0.0629574i
$863$	11092.1			0.437521			0.218760	−	0.975779i	$-0.429799\pi$
$863$	11092.1			0.437521			0.218760	+	0.975779i	$0.429799\pi$
$864$	14076.8	+	17517.7i	0.554286	+	0.689773i
$865$	133.392			0.00524330
$866$	−3519.58	−	1281.02i	−0.138107	−	0.0502667i
$867$	756.714	−	220.727i	0.0296417	−	0.00864624i
$868$	8683.98	+	7286.72i	0.339578	+	0.284939i
$869$	1026.66	−	5822.49i	0.0400772	−	0.227289i
$870$	14.2554	+	28.8924i	0.000555521	+	0.00112591i
$871$	3499.04	−	2936.04i	0.136120	−	0.114218i
$872$	1461.99	+	2532.24i	0.0567766	+	0.0983400i
$873$	−8148.27	+	25879.3i	−0.315896	+	1.00330i
$874$	536.324	−	928.941i	0.0207568	−	0.0359518i
$875$	−159.139	−	902.519i	−0.00614842	−	0.0348694i
$876$	−5850.93	−	2573.07i	−0.225667	−	0.0992419i
$877$	−16696.7	+	6077.10i	−0.642882	+	0.233990i	−0.642828	−	0.766010i	$-0.722239\pi$
$877$	−16696.7	+	6077.10i	−0.642882	+	0.233990i	−5.32658e−5		1.00000i	$0.500017\pi$
$878$	10187.8	−	3708.06i	0.391597	−	0.142530i
$879$	6396.52	−	4692.10i	0.245449	−	0.180046i
$880$	67.5293	+	382.977i	0.00258683	+	0.0146706i
$881$	8846.20	−	15322.1i	0.338293	−	0.585940i	−0.645819	−	0.763491i	$-0.723484\pi$
$881$	8846.20	−	15322.1i	0.338293	−	0.585940i	0.984112	+	0.177550i	$0.0568172\pi$
$882$	6794.44	−	4332.38i	0.259389	−	0.165396i
$883$	16120.6	+	27921.6i	0.614383	+	1.06414i	0.990492	+	0.137567i	$0.0439283\pi$
$883$	16120.6	+	27921.6i	0.614383	+	1.06414i	−0.376110	+	0.926575i	$0.622738\pi$
$884$	−9835.21	+	8252.72i	−0.374201	+	0.313992i
$885$	−127.575	+	191.013i	−0.00484565	+	0.00725518i
$886$	382.980	−	2171.99i	0.0145220	−	0.0823583i
$887$	−28081.0	−	23562.7i	−1.06298	−	0.891950i	−0.0685857	−	0.997645i	$-0.521849\pi$
$887$	−28081.0	−	23562.7i	−1.06298	−	0.891950i	−0.994399	+	0.105696i	$0.966293\pi$
$888$	−4742.04	+	19396.0i	−0.179203	+	0.732982i
$889$	47185.8	+	17174.2i	1.78016	+	0.647925i
$890$	68.8244			0.00259214
$891$	−33525.5	+	33579.5i	−1.26054	+	1.26257i
$892$	−23124.5			−0.868009
$893$	8974.52	+	3266.46i	0.336306	+	0.122405i
$894$	654.427	−	2676.75i	0.0244825	−	0.100139i
$895$	−96.4905	−	80.9652i	−0.00360371	−	0.00302387i
$896$	−6397.89	+	36284.2i	−0.238547	+	1.35287i
$897$	−2590.22	+	3878.23i	−0.0964158	+	0.144359i
$898$	−8979.81	+	7534.95i	−0.333697	+	0.280005i
$899$	−1377.42	−	2385.77i	−0.0511008	−	0.0885092i
$900$	1042.21	+	23652.2i	0.0386005	+	0.876009i
$901$	11731.5	−	20319.6i	0.433778	−	0.751325i
$902$	4256.56	+	24140.2i	0.157126	+	0.891109i
$903$	31370.2	−	23011.3i	1.15608	−	0.848027i
$904$	29811.6	−	10850.5i	1.09681	−	0.399207i
$905$	−34.0437	+	12.3909i	−0.00125044	+	0.000455124i
$906$	4892.24	+	2151.46i	0.179397	+	0.0788935i
$907$	1216.77	+	6900.66i	0.0445449	+	0.252627i	0.998946	−	0.0459004i	$-0.0146157\pi$
$907$	1216.77	+	6900.66i	0.0445449	+	0.252627i	−0.954401	+	0.298527i	$0.903505\pi$
$908$	13523.0	−	23422.5i	0.494246	−	0.856060i
$909$	−33765.7	+	7499.94i	−1.23206	+	0.273660i
$910$	48.2208	+	83.5209i	0.00175660	+	0.00304252i
$911$	9740.35	−	8173.13i	0.354240	−	0.297242i	−0.448250	−	0.893908i	$-0.647953\pi$
$911$	9740.35	−	8173.13i	0.354240	−	0.297242i	0.802490	+	0.596666i	$0.203508\pi$
$912$	−3037.88	−	6157.08i	−0.110301	−	0.223554i
$913$	10938.7	−	62036.7i	0.396517	−	2.24876i
$914$	−6761.40	−	5673.49i	−0.244691	−	0.205320i
$915$	−485.116	+	141.504i	−0.0175273	+	0.00511256i
$916$	10168.7	+	3701.10i	0.366794	+	0.133502i
$917$	51565.7			1.85698
$918$	203.689	−	9600.62i	0.00732324	−	0.345172i
$919$	−361.452			−0.0129741			−0.00648705	−	0.999979i	$-0.502065\pi$
$919$	−361.452			−0.0129741			−0.00648705	+	0.999979i	$0.502065\pi$
$920$	−68.4389	−	24.9097i	−0.00245257	−	0.000892662i
$921$	−15013.2	−	14366.2i	−0.537136	−	0.513989i
$922$	−14685.8	−	12322.9i	−0.524569	−	0.440166i
$923$	−4821.53	+	27344.2i	−0.171942	+	0.975132i
$924$	−60084.3	−	3925.99i	−2.13921	−	0.139779i
$925$	−24699.3	+	20725.2i	−0.877954	+	0.736691i
$926$	−4922.67	−	8526.32i	−0.174697	−	0.302584i
$927$	22909.8	−	29881.5i	0.811711	−	1.05872i
$928$	3465.02	−	6001.60i	0.122570	−	0.212298i
$929$	7553.19	+	42836.3i	0.266751	+	1.51282i	0.764001	+	0.645215i	$0.223232\pi$
$929$	7553.19	+	42836.3i	0.266751	+	1.51282i	−0.497250	+	0.867607i	$0.665657\pi$
$930$	−5.17174	−	47.1352i	−0.000182353	−	0.00166196i
$931$	−9033.71	+	3288.00i	−0.318011	+	0.115746i
$932$	−15837.7	+	5764.46i	−0.556633	+	0.202598i
$933$	−4052.02	−	36930.1i	−0.142184	−	1.29586i
$934$	−912.485	−	5174.96i	−0.0319673	−	0.181295i
$935$	324.449	−	561.961i	0.0113482	−	0.0196557i
$936$	−4085.49	−	9852.02i	−0.142669	−	0.344042i
$937$	−9081.40	−	15729.4i	−0.316624	−	0.548408i	0.663158	−	0.748480i	$-0.269216\pi$
$937$	−9081.40	−	15729.4i	−0.316624	−	0.548408i	−0.979781	+	0.200072i	$0.935883\pi$
$938$	−3320.95	+	2786.61i	−0.115600	+	0.0970001i
$939$	−46505.5	−	3038.73i	−1.61624	−	0.105607i
$940$	52.6129	−	298.383i	0.00182558	−	0.0103534i
$941$	−17833.6	−	14964.2i	−0.617810	−	0.518405i	0.279304	−	0.960203i	$-0.409896\pi$
$941$	−17833.6	−	14964.2i	−0.617810	−	0.518405i	−0.897114	+	0.441798i	$0.854341\pi$
$942$	4433.41	+	4242.35i	0.153342	+	0.146734i
$943$	12073.9	+	4394.53i	0.416945	+	0.151756i
$944$	12652.7			0.436241
$945$	504.514	+	100.037i	0.0173670	+	0.00344362i
$946$	19051.4			0.654770
$947$	−24501.6	−	8917.84i	−0.840753	−	0.306009i	−0.114489	−	0.993425i	$-0.536523\pi$
$947$	−24501.6	−	8917.84i	−0.840753	−	0.306009i	−0.726265	+	0.687415i	$0.758745\pi$
$948$	3178.98	−	927.282i	0.108912	−	0.0317687i
$949$	3561.82	+	2988.72i	0.121835	+	0.102232i
$950$	−687.849	+	3900.98i	−0.0234913	+	0.133226i
$951$	−1407.99	−	2853.66i	−0.0480095	−	0.0973043i
$952$	19978.4	−	16763.9i	0.680151	−	0.570715i
$953$	3326.12	+	5761.01i	0.113057	+	0.195821i	0.917001	−	0.398884i	$-0.130602\pi$
$953$	3326.12	+	5761.01i	0.113057	+	0.195821i	−0.803944	+	0.594705i	$0.797269\pi$
$954$	6155.28	+	6711.89i	0.208894	+	0.227783i
$955$	−150.974	+	261.495i	−0.00511561	+	0.00886049i
$956$	8747.53	+	49609.7i	0.295936	+	1.67834i
$957$	13394.5	+	5890.50i	0.452437	+	0.198968i
$958$	7521.30	−	2737.53i	0.253656	−	0.0923232i
$959$	−5471.37	+	1991.42i	−0.184233	+	0.0670554i
$960$	−104.077	+	76.3447i	−0.00349904	+	0.00256668i
$961$	−4469.08	−	25345.4i	−0.150015	−	0.850775i
$962$	3393.33	−	5877.42i	0.113727	−	0.196981i
$963$	23195.1	+	12062.7i	0.776168	+	0.403651i
$964$	7319.01	+	12676.9i	0.244532	+	0.423543i
$965$	−274.364	+	230.218i	−0.00915241	+	0.00767979i
$966$	2458.39	−	3680.84i	0.0818814	−	0.122598i
$967$	3644.82	−	20670.8i	0.121209	−	0.687412i	−0.862278	−	0.506435i	$-0.830963\pi$
$967$	3644.82	−	20670.8i	0.121209	−	0.687412i	0.983487	−	0.180977i	$-0.0579259\pi$
$968$	−33154.5	−	27820.0i	−1.10085	−	0.923727i
$969$	−2720.74	+	11128.5i	−0.0901990	+	0.368935i
$970$	135.329	+	49.2556i	0.00447953	+	0.00163041i
$971$	26526.7			0.876706			0.438353	−	0.898803i	$-0.355562\pi$
$971$	26526.7			0.876706			0.438353	+	0.898803i	$0.355562\pi$
$972$	−25174.9	−	8517.49i	−0.830746	−	0.281068i
$973$	−19985.1			−0.658472
$974$	15472.0	+	5631.36i	0.508990	+	0.185257i
$975$	4090.16	−	16729.7i	0.134349	−	0.549517i
$976$	21323.4	+	17892.5i	0.699330	+	0.586808i
$977$	3383.79	−	19190.4i	0.110805	−	0.628409i	−0.877936	−	0.478777i	$-0.841080\pi$
$977$	3383.79	−	19190.4i	0.110805	−	0.628409i	0.988742	−	0.149632i	$-0.0478087\pi$
$978$	3545.17	−	5308.03i	0.115912	−	0.173550i
$979$	23945.2	−	20092.4i	0.781709	−	0.655931i
$980$	152.492	+	264.124i	0.00497059	+	0.00860931i
$981$	−4702.34	−	2445.48i	−0.153042	−	0.0795903i
$982$	−2010.01	+	3481.44i	−0.0653178	+	0.113134i
$983$	−2050.48	−	11628.9i	−0.0665313	−	0.377318i	−0.999834	−	0.0182269i	$-0.994198\pi$
$983$	−2050.48	−	11628.9i	−0.0665313	−	0.377318i	0.933303	−	0.359091i	$-0.116913\pi$
$984$	−23693.3	+	17379.9i	−0.767595	+	0.563061i
$985$	242.070	−	88.1065i	0.00783046	−	0.00285006i
$986$	−2782.67	+	1012.81i	−0.0898767	+	0.0327124i
$987$	36076.0	+	15865.2i	1.16344	+	0.511645i
$988$	1032.37	+	5854.84i	0.0332429	+	0.188530i
$989$	4993.07	−	8648.25i	0.160536	−	0.278057i
$990$	170.231	+	185.625i	0.00546495	+	0.00595914i
$991$	−12690.3	−	21980.2i	−0.406781	−	0.704566i	0.587746	−	0.809046i	$-0.300016\pi$
$991$	−12690.3	−	21980.2i	−0.406781	−	0.704566i	−0.994527	+	0.104480i	$0.966682\pi$
$992$	−7813.35	+	6556.18i	−0.250075	+	0.209838i
$993$	7363.49	+	14924.1i	0.235320	+	0.476941i
$994$	4576.13	−	25952.5i	0.146022	−	0.828133i
$995$	479.839	+	402.633i	0.0152884	+	0.0128285i
$996$	33871.0	−	9879.88i	1.07755	−	0.314313i
$997$	13484.2	+	4907.86i	0.428335	+	0.155901i	0.547186	−	0.837011i	$-0.315699\pi$
$997$	13484.2	+	4907.86i	0.428335	+	0.155901i	−0.118851	+	0.992912i	$0.537921\pi$
$998$	−9947.99			−0.315529
$999$	−11654.9	−	34266.3i	−0.369115	−	1.08522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.4.5	✓	48
3.2	odd	2		81.4.e.a.64.4		48
9.2	odd	6		243.4.e.b.28.5		48
9.4	even	3		243.4.e.d.109.4		48
9.5	odd	6		243.4.e.a.109.5		48
9.7	even	3		243.4.e.c.28.4		48
27.2	odd	18		243.4.e.a.136.5		48
27.7	even	9	inner	27.4.e.a.7.5	yes	48
27.11	odd	18		243.4.e.b.217.5		48
27.13	even	9		729.4.a.d.1.14		24
27.14	odd	18		729.4.a.c.1.11		24
27.16	even	9		243.4.e.c.217.4		48
27.20	odd	18		81.4.e.a.19.4		48
27.25	even	9		243.4.e.d.136.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.5	✓	48	1.1	even	1	trivial
27.4.e.a.7.5	yes	48	27.7	even	9	inner
81.4.e.a.19.4		48	27.20	odd	18
81.4.e.a.64.4		48	3.2	odd	2
243.4.e.a.109.5		48	9.5	odd	6
243.4.e.a.136.5		48	27.2	odd	18
243.4.e.b.28.5		48	9.2	odd	6
243.4.e.b.217.5		48	27.11	odd	18
243.4.e.c.28.4		48	9.7	even	3
243.4.e.c.217.4		48	27.16	even	9
243.4.e.d.109.4		48	9.4	even	3
243.4.e.d.136.4		48	27.25	even	9
729.4.a.c.1.11		24	27.14	odd	18
729.4.a.d.1.14		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)

\(f(q)\)	\(=\)	\(q+(-0.932125 - 0.339266i) q^{2} +(1.23404 - 5.04749i) q^{3} +(-5.37460 - 4.50982i) q^{4} +(0.0250883 - 0.142283i) q^{5} +(-2.86272 + 4.28623i) q^{6} +(19.4381 - 16.3105i) q^{7} +(7.44756 + 12.8996i) q^{8} +(-23.9543 - 12.4576i) q^{9} +O(q^{10})\)	\(q+(-0.932125 - 0.339266i) q^{2} +(1.23404 - 5.04749i) q^{3} +(-5.37460 - 4.50982i) q^{4} +(0.0250883 - 0.142283i) q^{5} +(-2.86272 + 4.28623i) q^{6} +(19.4381 - 16.3105i) q^{7} +(7.44756 + 12.8996i) q^{8} +(-23.9543 - 12.4576i) q^{9} +(-0.0716572 + 0.124114i) q^{10} +(11.3027 + 64.1008i) q^{11} +(-29.3957 + 21.5629i) q^{12} +(24.9207 - 9.07040i) q^{13} +(-23.6524 + 8.60876i) q^{14} +(-0.687211 - 0.302215i) q^{15} +(7.18090 + 40.7249i) q^{16} +(34.5011 - 59.7576i) q^{17} +(18.1020 + 19.7389i) q^{18} +(-15.9760 - 27.6712i) q^{19} +(-0.776510 + 0.651569i) q^{20} +(-58.3398 - 118.241i) q^{21} +(11.2117 - 63.5846i) q^{22} +(-25.9254 - 21.7540i) q^{23} +(74.3009 - 21.6730i) q^{24} +(117.442 + 42.7454i) q^{25} -26.3065 q^{26} +(-92.4400 + 105.536i) q^{27} -178.030 q^{28} +(40.6547 + 14.7971i) q^{29} +(0.538036 + 0.514850i) q^{30} +(-48.7783 - 40.9298i) q^{31} +(27.8152 - 157.748i) q^{32} +(337.496 + 22.0525i) q^{33} +(-52.4331 + 43.9966i) q^{34} +(-1.83304 - 3.17491i) q^{35} +(72.5633 + 174.984i) q^{36} +(-128.992 + 223.421i) q^{37} +(5.50371 + 31.2131i) q^{38} +(-15.0297 - 136.980i) q^{39} +(2.02223 - 0.736032i) q^{40} +(-356.758 + 129.849i) q^{41} +(14.2647 + 130.009i) q^{42} +(51.2384 + 290.587i) q^{43} +(228.336 - 395.489i) q^{44} +(-2.37347 + 3.09575i) q^{45} +(16.7854 + 29.0731i) q^{46} +(-228.972 + 192.130i) q^{47} +(214.420 + 14.0105i) q^{48} +(52.2461 - 296.302i) q^{49} +(-94.9686 - 79.6881i) q^{50} +(-259.050 - 247.887i) q^{51} +(-174.845 - 63.6383i) q^{52} +340.033 q^{53} +(121.970 - 67.0111i) q^{54} +9.40401 q^{55} +(355.165 + 129.269i) q^{56} +(-159.385 + 46.4912i) q^{57} +(-32.8751 - 27.5855i) q^{58} +(53.1307 - 301.319i) q^{59} +(2.33055 + 4.72349i) q^{60} +(515.642 - 432.675i) q^{61} +(31.5814 + 54.7005i) q^{62} +(-668.816 + 148.555i) q^{63} +(85.9670 - 148.899i) q^{64} +(-0.665344 - 3.77335i) q^{65} +(-307.107 - 135.057i) q^{66} +(161.847 - 58.9077i) q^{67} +(-454.926 + 165.580i) q^{68} +(-141.796 + 104.013i) q^{69} +(0.631481 + 3.58131i) q^{70} +(-523.492 + 906.714i) q^{71} +(-17.7040 - 401.778i) q^{72} +(87.6625 + 151.836i) q^{73} +(196.036 - 164.494i) q^{74} +(360.685 - 540.038i) q^{75} +(-38.9277 + 220.770i) q^{76} +(1265.22 + 1061.65i) q^{77} +(-32.4632 + 132.782i) q^{78} +(-85.3554 - 31.0668i) q^{79} +5.97461 q^{80} +(418.618 + 596.825i) q^{81} +376.597 q^{82} +(-909.434 - 331.007i) q^{83} +(-219.695 + 898.603i) q^{84} +(-7.63691 - 6.40813i) q^{85} +(50.8258 - 288.247i) q^{86} +(124.858 - 186.944i) q^{87} +(-742.694 + 623.194i) q^{88} +(-240.117 - 415.895i) q^{89} +(3.26266 - 2.08039i) q^{90} +(336.469 - 582.781i) q^{91} +(41.2320 + 233.838i) q^{92} +(-266.787 + 195.699i) q^{93} +(278.614 - 101.407i) q^{94} +(-4.33794 + 1.57888i) q^{95} +(-761.904 - 335.063i) q^{96} +(-174.496 - 989.614i) q^{97} +(-149.225 + 258.466i) q^{98} +(527.792 - 1676.29i) 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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