LMFDB - Embedded newform 27.4.e.a.4.1

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			4.1
Character	$\chi$	$=$	27.4
Dual form			27.4.e.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.97861 - 1.81207i) q^{2} +(-3.67671 - 3.67176i) q^{3} +(15.3746 + 12.9008i) q^{4} +(-1.82513 + 10.3508i) q^{5} +(11.6515 + 24.9427i) q^{6} +(-5.92244 + 4.96952i) q^{7} +(-31.9745 - 55.3815i) q^{8} +(0.0364268 + 27.0000i) q^{9} +O(q^{10})$	\(q+(-4.97861 - 1.81207i) q^{2} +(-3.67671 - 3.67176i) q^{3} +(15.3746 + 12.9008i) q^{4} +(-1.82513 + 10.3508i) q^{5} +(11.6515 + 24.9427i) q^{6} +(-5.92244 + 4.96952i) q^{7} +(-31.9745 - 55.3815i) q^{8} +(0.0364268 + 27.0000i) q^{9} +(27.8430 - 48.2255i) q^{10} +(2.99161 + 16.9662i) q^{11} +(-9.15933 - 103.884i) q^{12} +(-67.4795 + 24.5605i) q^{13} +(38.4906 - 14.0094i) q^{14} +(44.7163 - 31.3556i) q^{15} +(30.9527 + 175.541i) q^{16} +(-23.3676 + 40.4738i) q^{17} +(48.7444 - 134.488i) q^{18} +(-21.3371 - 36.9569i) q^{19} +(-161.595 + 135.595i) q^{20} +(40.0220 + 3.47427i) q^{21} +(15.8499 - 89.8892i) q^{22} +(36.3731 + 30.5207i) q^{23} +(-85.7862 + 321.025i) q^{24} +(13.6527 + 4.96918i) q^{25} +380.460 q^{26} +(99.0034 - 99.4049i) q^{27} -155.166 q^{28} +(-139.582 - 50.8038i) q^{29} +(-279.443 + 75.0787i) q^{30} +(-120.570 - 101.170i) q^{31} +(75.1539 - 426.219i) q^{32} +(51.2966 - 73.3644i) q^{33} +(189.679 - 159.160i) q^{34} +(-40.6295 - 70.3723i) q^{35} +(-347.762 + 415.584i) q^{36} +(35.3750 - 61.2713i) q^{37} +(39.2606 + 222.658i) q^{38} +(338.283 + 157.466i) q^{39} +(631.603 - 229.885i) q^{40} +(-219.420 + 79.8623i) q^{41} +(-192.958 - 89.8195i) q^{42} +(71.5802 + 405.951i) q^{43} +(-172.884 + 299.444i) q^{44} +(-279.539 - 48.9015i) q^{45} +(-125.782 - 217.861i) q^{46} +(327.908 - 275.147i) q^{47} +(530.740 - 759.065i) q^{48} +(-49.1821 + 278.926i) q^{49} +(-58.9671 - 49.4792i) q^{50} +(234.526 - 63.0106i) q^{51} +(-1354.32 - 492.933i) q^{52} +43.9296 q^{53} +(-673.027 + 315.498i) q^{54} -181.075 q^{55} +(464.587 + 169.096i) q^{56} +(-57.2464 + 214.224i) q^{57} +(602.866 + 505.864i) q^{58} +(-57.9243 + 328.505i) q^{59} +(1092.01 + 94.7962i) q^{60} +(292.335 - 245.298i) q^{61} +(416.943 + 722.167i) q^{62} +(-134.393 - 159.725i) q^{63} +(-433.502 + 750.847i) q^{64} +(-131.063 - 743.296i) q^{65} +(-388.327 + 272.300i) q^{66} +(-230.604 + 83.9331i) q^{67} +(-881.413 + 320.808i) q^{68} +(-21.6691 - 245.769i) q^{69} +(74.7591 + 423.980i) q^{70} +(403.252 - 698.452i) q^{71} +(1494.14 - 865.329i) q^{72} +(175.470 + 303.922i) q^{73} +(-287.146 + 240.944i) q^{74} +(-31.9515 - 68.3997i) q^{75} +(148.726 - 843.464i) q^{76} +(-102.032 - 85.6147i) q^{77} +(-1398.84 - 1396.95i) q^{78} +(999.930 + 363.945i) q^{79} -1873.49 q^{80} +(-728.997 + 1.96705i) q^{81} +1237.12 q^{82} +(-959.423 - 349.201i) q^{83} +(570.502 + 569.733i) q^{84} +(-376.289 - 315.744i) q^{85} +(379.241 - 2150.78i) q^{86} +(326.665 + 699.303i) q^{87} +(843.961 - 708.167i) q^{88} +(320.730 + 555.520i) q^{89} +(1303.10 + 750.005i) q^{90} +(277.590 - 480.799i) q^{91} +(165.481 + 938.488i) q^{92} +(71.8288 + 814.676i) q^{93} +(-2131.11 + 775.661i) q^{94} +(421.478 - 153.406i) q^{95} +(-1841.29 + 1291.14i) q^{96} +(60.5209 + 343.231i) q^{97} +(750.290 - 1299.54i) q^{98} +(-457.979 + 81.3913i) 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 $

$2$	−4.97861	−	1.81207i	−1.76020	−	0.640662i	−0.760245	−	0.649637i	$-0.774921\pi$
$2$	−4.97861	−	1.81207i	−1.76020	−	0.640662i	−0.999960	+	0.00897504i	$0.997143\pi$
$3$	−3.67671	−	3.67176i	−0.707584	−	0.706630i
$3$	−3.67671	−	3.67176i	−0.707584	−	0.706630i
$4$	15.3746	+	12.9008i	1.92183	+	1.61260i
$5$	−1.82513	+	10.3508i	−0.163245	+	0.925808i	0.787611	+	0.616173i	$0.211318\pi$
$5$	−1.82513	+	10.3508i	−0.163245	+	0.925808i	−0.950856	+	0.309635i	$0.899793\pi$
$6$	11.6515	+	24.9427i	0.792781	+	1.69713i
$7$	−5.92244	+	4.96952i	−0.319782	+	0.268329i	−0.788521	−	0.615008i	$-0.789153\pi$
$7$	−5.92244	+	4.96952i	−0.319782	+	0.268329i	0.468739	+	0.883337i	$0.344708\pi$
$8$	−31.9745	−	55.3815i	−1.41309	−	2.44754i
$9$	0.0364268	+	27.0000i	0.00134914	+	0.999999i
$10$	27.8430	−	48.2255i	0.880474	−	1.52503i
$11$	2.99161	+	16.9662i	0.0820003	+	0.465047i	0.997964	+	0.0637848i	$0.0203171\pi$
$11$	2.99161	+	16.9662i	0.0820003	+	0.465047i	−0.915963	+	0.401262i	$0.868572\pi$
$12$	−9.15933	−	103.884i	−0.220339	−	2.49907i
$13$	−67.4795	+	24.5605i	−1.43965	+	0.523990i	−0.939681	−	0.342053i	$-0.888878\pi$
$13$	−67.4795	+	24.5605i	−1.43965	+	0.523990i	−0.499970	+	0.866043i	$0.666656\pi$
$14$	38.4906	−	14.0094i	0.734790	−	0.267442i
$15$	44.7163	−	31.3556i	0.769712	−	0.539733i
$16$	30.9527	+	175.541i	0.483635	+	2.74283i
$17$	−23.3676	+	40.4738i	−0.333380	+	0.577432i	−0.983172	−	0.182680i	$-0.941523\pi$
$17$	−23.3676	+	40.4738i	−0.333380	+	0.577432i	0.649792	+	0.760112i	$0.274856\pi$
$18$	48.7444	−	134.488i	0.638287	−	1.76107i
$19$	−21.3371	−	36.9569i	−0.257635	−	0.446237i	0.707973	−	0.706239i	$-0.249610\pi$
$19$	−21.3371	−	36.9569i	−0.257635	−	0.446237i	−0.965608	+	0.260003i	$0.916276\pi$
$20$	−161.595	+	135.595i	−1.80669	+	1.51599i
$21$	40.0220	+	3.47427i	0.415882	+	0.0361023i
$22$	15.8499	−	89.8892i	0.153600	−	0.871111i
$23$	36.3731	+	30.5207i	0.329753	+	0.276696i	0.792599	−	0.609743i	$-0.208727\pi$
$23$	36.3731	+	30.5207i	0.329753	+	0.276696i	−0.462846	+	0.886439i	$0.653172\pi$
$24$	−85.7862	+	321.025i	−0.729627	+	2.73037i
$25$	13.6527	+	4.96918i	0.109222	+	0.0397535i
$26$	380.460			2.86978
$27$	99.0034	−	99.4049i	0.705674	−	0.708536i
$28$	−155.166			−1.04727
$29$	−139.582	−	50.8038i	−0.893785	−	0.325311i	−0.146026	−	0.989281i	$-0.546648\pi$
$29$	−139.582	−	50.8038i	−0.893785	−	0.325311i	−0.747760	+	0.663969i	$0.768870\pi$
$30$	−279.443	+	75.0787i	−1.70064	+	0.456914i
$31$	−120.570	−	101.170i	−0.698548	−	0.586151i	0.222812	−	0.974861i	$-0.428476\pi$
$31$	−120.570	−	101.170i	−0.698548	−	0.586151i	−0.921360	+	0.388710i	$0.872921\pi$
$32$	75.1539	−	426.219i	0.415171	−	2.35455i
$33$	51.2966	−	73.3644i	0.270594	−	0.387003i
$34$	189.679	−	159.160i	0.956756	−	0.802814i
$35$	−40.6295	−	70.3723i	−0.196218	−	0.339860i
$36$	−347.762	+	415.584i	−1.61001	+	1.92400i
$37$	35.3750	−	61.2713i	0.157179	−	0.272242i	−0.776671	−	0.629906i	$-0.783093\pi$
$37$	35.3750	−	61.2713i	0.157179	−	0.272242i	0.933850	+	0.357664i	$0.116427\pi$
$38$	39.2606	+	222.658i	0.167603	+	0.950524i
$39$	338.283	+	157.466i	1.38894	+	0.646533i
$40$	631.603	−	229.885i	2.49663	−	0.908700i
$41$	−219.420	+	79.8623i	−0.835796	+	0.304205i	−0.724235	−	0.689553i	$-0.757807\pi$
$41$	−219.420	+	79.8623i	−0.835796	+	0.304205i	−0.111561	+	0.993758i	$0.535585\pi$
$42$	−192.958	−	89.8195i	−0.708907	−	0.329987i
$43$	71.5802	+	405.951i	0.253858	+	1.43970i	0.798988	+	0.601347i	$0.205369\pi$
$43$	71.5802	+	405.951i	0.253858	+	1.43970i	−0.545131	+	0.838351i	$0.683520\pi$
$44$	−172.884	+	299.444i	−0.592346	+	1.02597i
$45$	−279.539	−	48.9015i	−0.926027	−	0.161996i
$46$	−125.782	−	217.861i	−0.403165	−	0.698301i
$47$	327.908	−	275.147i	1.01767	−	0.853923i	0.0283334	−	0.999599i	$-0.490980\pi$
$47$	327.908	−	275.147i	1.01767	−	0.853923i	0.989332	+	0.145676i	$0.0465356\pi$
$48$	530.740	−	759.065i	1.59595	−	2.28253i
$49$	−49.1821	+	278.926i	−0.143388	+	0.813194i
$50$	−58.9671	−	49.4792i	−0.166784	−	0.139948i
$51$	234.526	−	63.0106i	0.643925	−	0.173005i
$52$	−1354.32	−	492.933i	−3.61175	−	1.31457i
$53$	43.9296			0.113853			0.0569263	−	0.998378i	$-0.481870\pi$
$53$	43.9296			0.113853			0.0569263	+	0.998378i	$0.481870\pi$
$54$	−673.027	+	315.498i	−1.69606	+	0.795070i
$55$	−181.075			−0.443930
$56$	464.587	+	169.096i	1.10863	+	0.403507i
$57$	−57.2464	+	214.224i	−0.133026	+	0.497802i
$58$	602.866	+	505.864i	1.36483	+	1.14523i
$59$	−57.9243	+	328.505i	−0.127815	+	0.724876i	0.851781	+	0.523899i	$0.175523\pi$
$59$	−57.9243	+	328.505i	−0.127815	+	0.724876i	−0.979596	+	0.200978i	$0.935588\pi$
$60$	1092.01	+	94.7962i	2.34963	+	0.203969i
$61$	292.335	−	245.298i	0.613601	−	0.514872i	−0.282184	−	0.959360i	$-0.591059\pi$
$61$	292.335	−	245.298i	0.613601	−	0.514872i	0.895785	+	0.444488i	$0.146614\pi$
$62$	416.943	+	722.167i	0.854062	+	1.47928i
$63$	−134.393	−	159.725i	−0.268760	−	0.319420i
$64$	−433.502	+	750.847i	−0.846683	+	1.46650i
$65$	−131.063	−	743.296i	−0.250098	−	1.41838i
$66$	−388.327	+	272.300i	−0.724238	+	0.507846i
$67$	−230.604	+	83.9331i	−0.420490	+	0.153046i	−0.543595	−	0.839348i	$-0.682937\pi$
$67$	−230.604	+	83.9331i	−0.420490	+	0.153046i	0.123105	+	0.992394i	$0.460715\pi$
$68$	−881.413	+	320.808i	−1.57187	+	0.572113i
$69$	−21.6691	−	245.769i	−0.0378065	−	0.428799i
$70$	74.7591	+	423.980i	0.127649	+	0.723932i
$71$	403.252	−	698.452i	0.674045	−	1.16748i	−0.302703	−	0.953085i	$-0.597889\pi$
$71$	403.252	−	698.452i	0.674045	−	1.16748i	0.976747	−	0.214394i	$-0.0687778\pi$
$72$	1494.14	−	865.329i	2.44563	−	1.41639i
$73$	175.470	+	303.922i	0.281331	+	0.487280i	0.971713	−	0.236166i	$-0.0758908\pi$
$73$	175.470	+	303.922i	0.281331	+	0.487280i	−0.690382	+	0.723445i	$0.742557\pi$
$74$	−287.146	+	240.944i	−0.451081	+	0.378502i
$75$	−31.9515	−	68.3997i	−0.0491925	−	0.105308i
$76$	148.726	−	843.464i	0.224474	−	1.27305i
$77$	−102.032	−	85.6147i	−0.151008	−	0.126710i
$78$	−1398.84	−	1396.95i	−2.03061	−	2.02787i
$79$	999.930	+	363.945i	1.42406	+	0.518316i	0.935223	−	0.354058i	$-0.115199\pi$
$79$	999.930	+	363.945i	1.42406	+	0.518316i	0.488838	+	0.872374i	$0.337421\pi$
$80$	−1873.49			−2.61829
$81$	−728.997	+	1.96705i	−0.999996	+	0.00269828i
$82$	1237.12			1.66606
$83$	−959.423	−	349.201i	−1.26880	−	0.461805i	−0.382087	−	0.924126i	$-0.624794\pi$
$83$	−959.423	−	349.201i	−1.26880	−	0.461805i	−0.886712	+	0.462321i	$0.847017\pi$
$84$	570.502	+	569.733i	0.741034	+	0.740035i
$85$	−376.289	−	315.744i	−0.480168	−	0.402909i
$86$	379.241	−	2150.78i	0.475518	−	2.69680i
$87$	326.665	+	699.303i	0.402553	+	0.861760i
$88$	843.961	−	708.167i	1.02235	−	0.857851i
$89$	320.730	+	555.520i	0.381992	+	0.661629i	0.991347	−	0.131268i	$-0.0419049\pi$
$89$	320.730	+	555.520i	0.381992	+	0.661629i	−0.609355	+	0.792897i	$0.708572\pi$
$90$	1303.10	+	750.005i	1.52621	+	0.878416i
$91$	277.590	−	480.799i	0.319773	−	0.553862i
$92$	165.481	+	938.488i	0.187528	+	1.06352i
$93$	71.8288	+	814.676i	0.0800892	+	0.908366i
$94$	−2131.11	+	775.661i	−2.33838	+	0.851099i
$95$	421.478	−	153.406i	0.455187	−	0.165674i
$96$	−1841.29	+	1291.14i	−1.95756	+	1.37267i
$97$	60.5209	+	343.231i	0.0633501	+	0.359277i	0.999960	+	0.00890345i	$0.00283410\pi$
$97$	60.5209	+	343.231i	0.0633501	+	0.359277i	−0.936610	+	0.350373i	$0.886055\pi$
$98$	750.290	−	1299.54i	0.773375	−	1.33952i
$99$	−457.979	+	81.3913i	−0.464936	+	0.0826276i
$100$	145.799	+	252.531i	0.145799	+	0.252531i
$101$	−98.7810	+	82.8871i	−0.0973176	+	0.0816592i	−0.690148	−	0.723668i	$-0.742455\pi$
$101$	−98.7810	+	82.8871i	−0.0973176	+	0.0816592i	0.592831	+	0.805327i	$0.298010\pi$
$102$	−1281.79	−	111.271i	−1.24428	−	0.108014i
$103$	−52.2596	+	296.379i	−0.0499932	+	0.283525i	−0.999548	−	0.0300770i	$-0.990425\pi$
$103$	−52.2596	+	296.379i	−0.0499932	+	0.283525i	0.949554	+	0.313602i	$0.101536\pi$
$104$	3517.83	+	2951.81i	3.31684	+	2.78316i
$105$	−109.007	+	407.920i	−0.101314	+	0.379133i
$106$	−218.708	−	79.6033i	−0.200404	−	0.0729411i
$107$	−117.488			−0.106149			−0.0530746	−	0.998591i	$-0.516902\pi$
$107$	−117.488			−0.106149			−0.0530746	+	0.998591i	$0.516902\pi$
$108$	2804.54	−	251.086i	2.49877	−	0.223711i
$109$	−1412.88			−1.24156			−0.620778	−	0.783987i	$-0.713183\pi$
$109$	−1412.88			−1.24156			−0.620778	+	0.783987i	$0.713183\pi$
$110$	901.501	+	328.120i	0.781407	+	0.284409i
$111$	−355.037	+	95.3886i	−0.303591	+	0.0815665i
$112$	−1055.67	−	885.813i	−0.890639	−	0.747335i
$113$	−386.315	+	2190.90i	−0.321606	+	1.82392i	0.210918	+	0.977504i	$0.432355\pi$
$113$	−386.315	+	2190.90i	−0.321606	+	1.82392i	−0.532524	+	0.846415i	$0.678756\pi$
$114$	673.196	−	962.806i	0.553076	−	0.791009i
$115$	−382.301	+	320.788i	−0.309998	+	0.260119i
$116$	−1490.61	−	2581.82i	−1.19310	−	2.06651i
$117$	−665.592	−	1821.05i	−0.525932	−	1.43894i
$118$	883.655	−	1530.53i	0.689381	−	1.19404i
$119$	−62.7424	−	355.830i	−0.0483326	−	0.274108i
$120$	−3166.31	−	1473.87i	−2.40869	−	1.12121i
$121$	971.827	−	353.716i	0.730148	−	0.265752i
$122$	−1899.92	+	691.513i	−1.40992	+	0.513169i
$123$	1099.98	+	512.026i	0.806356	+	0.375348i
$124$	−548.536	−	3110.90i	−0.397258	−	2.25296i
$125$	−733.261	+	1270.05i	−0.524679	+	0.908770i
$126$	379.657	+	1038.74i	0.268433	+	0.734428i
$127$	−22.1073	−	38.2910i	−0.0154465	−	0.0267542i	0.858199	−	0.513317i	$-0.171584\pi$
$127$	−22.1073	−	38.2910i	−0.0154465	−	0.0267542i	−0.873645	+	0.486563i	$0.838250\pi$
$128$	866.504	−	727.083i	0.598351	−	0.502076i
$129$	1227.37	−	1755.39i	0.837708	−	1.19809i
$130$	−694.389	+	3938.08i	−0.468477	+	2.65686i
$131$	933.316	+	783.145i	0.622475	+	0.522319i	0.898580	−	0.438809i	$-0.144599\pi$
$131$	933.316	+	783.145i	0.622475	+	0.522319i	−0.276105	+	0.961127i	$0.589044\pi$
$132$	1735.13	−	466.181i	1.14412	−	0.307393i
$133$	310.026	+	112.840i	0.202125	+	0.0735675i
$134$	1300.18			0.838198
$135$	848.230	+	1206.20i	0.540771	+	0.768984i
$136$	2988.67			1.88438
$137$	2196.19	+	799.346i	1.36958	+	0.498487i	0.919004	−	0.394249i	$-0.128995\pi$
$137$	2196.19	+	799.346i	1.36958	+	0.498487i	0.450579	+	0.892737i	$0.351218\pi$
$138$	−337.468	+	1262.85i	−0.208168	+	0.778995i
$139$	−1556.50	−	1306.06i	−0.949791	−	0.796969i	0.0294717	−	0.999566i	$-0.490618\pi$
$139$	−1556.50	−	1306.06i	−0.949791	−	0.796969i	−0.979262	+	0.202597i	$0.935062\pi$
$140$	283.199	−	1606.10i	0.170962	−	0.969574i
$141$	−2215.90	−	192.360i	−1.32349	−	0.114891i
$142$	−3273.27	+	2746.60i	−1.93442	+	1.62317i
$143$	−618.572	−	1071.40i	−0.361731	−	0.626537i
$144$	−4738.48	+	842.115i	−2.74218	+	0.487335i
$145$	780.618	−	1352.07i	0.447082	−	0.774368i
$146$	−322.868	−	1831.07i	−0.183019	−	1.03795i
$147$	1204.98	−	844.945i	0.676086	−	0.474081i
$148$	1334.33	−	485.656i	0.741088	−	0.269734i
$149$	308.716	−	112.363i	0.169738	−	0.0617797i	−0.255753	−	0.966742i	$-0.582323\pi$
$149$	308.716	−	112.363i	0.169738	−	0.0617797i	0.425492	+	0.904962i	$0.360101\pi$
$150$	35.1293	+	398.434i	0.0191219	+	0.216880i
$151$	−58.5847	−	332.251i	−0.0315732	−	0.179061i	0.964943	−	0.262459i	$-0.0845336\pi$
$151$	−58.5847	−	332.251i	−0.0315732	−	0.179061i	−0.996516	+	0.0833988i	$0.973422\pi$
$152$	−1364.49	+	2363.36i	−0.728122	+	1.26114i
$153$	−1093.64	−	629.449i	−0.577881	−	0.332601i
$154$	352.836	+	611.131i	0.184626	+	0.319781i
$155$	1267.25	−	1063.35i	0.656698	−	0.551035i
$156$	3169.53	+	6785.12i	1.62670	+	3.48233i
$157$	621.913	−	3527.04i	0.316141	−	1.79292i	−0.249611	−	0.968346i	$-0.580303\pi$
$157$	621.913	−	3527.04i	0.316141	−	1.79292i	0.565751	−	0.824576i	$-0.308586\pi$
$158$	−4318.77	−	3623.88i	−2.17457	−	1.82468i
$159$	−161.516	−	161.299i	−0.0805603	−	0.0804517i
$160$	4274.56	+	1555.81i	2.11209	+	0.768736i
$161$	−367.091			−0.179695
$162$	3632.96	+	1311.20i	1.76193	+	0.635910i
$163$	−3292.80			−1.58228			−0.791142	−	0.611633i	$-0.790513\pi$
$163$	−3292.80			−1.58228			−0.791142	+	0.611633i	$0.790513\pi$
$164$	−4403.79	−	1602.85i	−2.09682	−	0.763179i
$165$	665.760	+	664.863i	0.314117	+	0.313694i
$166$	4143.82	+	3477.07i	1.93748	+	1.62574i
$167$	266.163	−	1509.49i	0.123331	−	0.699447i	−0.858954	−	0.512053i	$-0.828885\pi$
$167$	266.163	−	1509.49i	0.123331	−	0.699447i	0.982285	−	0.187393i	$-0.0600039\pi$
$168$	−1087.27	−	2327.57i	−0.499316	−	1.06890i
$169$	2267.27	−	1902.46i	1.03198	−	0.865937i
$170$	1301.25	+	2253.83i	0.587066	+	1.01683i
$171$	997.058	−	577.447i	0.445889	−	0.258237i
$172$	−4136.59	+	7164.79i	−1.83379	+	3.17622i
$173$	443.834	+	2517.11i	0.195052	+	1.10620i	0.912344	+	0.409424i	$0.134270\pi$
$173$	443.834	+	2517.11i	0.195052	+	1.10620i	−0.717292	+	0.696773i	$0.754619\pi$
$174$	−359.154	−	4073.49i	−0.156479	−	1.77477i
$175$	−105.552	+	38.4178i	−0.0455941	+	0.0165949i
$176$	−2885.68	+	1050.30i	−1.23589	+	0.449826i
$177$	1419.16	−	995.134i	0.602659	−	0.422592i
$178$	−590.149	−	3346.90i	−0.248503	−	1.40933i
$179$	−1334.64	+	2311.66i	−0.557292	+	0.965259i	0.440429	+	0.897788i	$0.354826\pi$
$179$	−1334.64	+	2311.66i	−0.557292	+	0.965259i	−0.997721	+	0.0674712i	$0.978507\pi$
$180$	−3666.93	−	4358.13i	−1.51843	−	1.80464i
$181$	2344.91	+	4061.51i	0.962961	+	1.66790i	0.714997	+	0.699128i	$0.246428\pi$
$181$	2344.91	+	4061.51i	0.962961	+	1.66790i	0.247964	+	0.968769i	$0.420238\pi$
$182$	−2253.25	+	1890.70i	−0.917704	+	0.770045i
$183$	−1975.51	−	171.492i	−0.797997	−	0.0692733i
$184$	527.268	−	2990.29i	0.211254	−	1.19808i
$185$	569.645	+	477.989i	0.226385	+	0.189959i
$186$	1118.64	−	4186.11i	0.440982	−	1.65022i
$187$	−756.595	−	275.378i	−0.295870	−	0.107688i
$188$	8591.09			3.33282
$189$	−92.3473	+	1080.72i	−0.0355411	+	0.415930i
$190$	−2376.36			−0.907363
$191$	−701.355	−	255.272i	−0.265698	−	0.0967060i	0.205736	−	0.978608i	$-0.434041\pi$
$191$	−701.355	−	255.272i	−0.265698	−	0.0967060i	−0.471434	+	0.881901i	$0.656263\pi$
$192$	4350.79	−	1168.94i	1.63537	−	0.439379i
$193$	1817.39	+	1524.97i	0.677816	+	0.568755i	0.915367	−	0.402620i	$-0.131900\pi$
$193$	1817.39	+	1524.97i	0.677816	+	0.568755i	−0.237551	+	0.971375i	$0.576345\pi$
$194$	320.647	−	1818.48i	0.118666	−	0.672986i
$195$	−2247.32	+	3214.12i	−0.825302	+	1.18035i
$196$	−4354.53	+	3653.88i	−1.58693	+	1.33159i
$197$	−106.817	−	185.012i	−0.0386313	−	0.0669114i	0.846063	−	0.533082i	$-0.178966\pi$
$197$	−106.817	−	185.012i	−0.0386313	−	0.0669114i	−0.884695	+	0.466171i	$0.845633\pi$
$198$	2427.58	+	424.673i	0.871318	+	0.152425i
$199$	−495.139	+	857.607i	−0.176379	+	0.305498i	−0.940638	−	0.339412i	$-0.889772\pi$
$199$	−495.139	+	857.607i	−0.176379	+	0.305498i	0.764258	+	0.644910i	$0.223105\pi$
$200$	−161.338	−	914.996i	−0.0570418	−	0.323500i
$201$	1156.05	+	538.125i	0.405678	+	0.188838i
$202$	641.989	−	233.665i	0.223615	−	0.0813891i
$203$	1079.14	−	392.774i	0.373107	−	0.135800i
$204$	4418.63	+	2056.81i	1.51650	+	0.705911i
$205$	−426.172	−	2416.94i	−0.145196	−	0.823446i
$206$	797.239	−	1380.86i	0.269642	−	0.467034i
$207$	−822.733	+	983.186i	−0.276251	+	0.330126i
$208$	−6400.06	−	11085.2i	−2.13348	−	3.69530i
$209$	563.187	−	472.570i	0.186395	−	0.156404i
$210$	1281.88	−	1833.35i	0.421230	−	0.602443i
$211$	−32.5611	+	184.663i	−0.0106237	+	0.0602499i	−0.989659	−	0.143442i	$-0.954183\pi$
$211$	−32.5611	+	184.663i	−0.0106237	+	0.0602499i	0.979035	+	0.203692i	$0.0652941\pi$
$212$	675.400	+	566.728i	0.218805	+	0.183599i
$213$	−4047.19	+	1087.37i	−1.30192	+	0.349789i
$214$	584.925	+	212.895i	0.186844	+	0.0680057i
$215$	−4332.58			−1.37432
$216$	−8670.78	−	2304.53i	−2.73135	−	0.725942i
$217$	1216.84			0.380664
$218$	7034.19	+	2560.24i	2.18539	+	0.795417i
$219$	470.777	−	1761.72i	0.145261	−	0.543588i
$220$	−2783.96	−	2336.02i	−0.853156	−	0.715883i
$221$	582.774	−	3305.07i	0.177383	−	1.00599i
$222$	1940.44	+	168.448i	0.586639	+	0.0509255i
$223$	−4364.88	+	3662.57i	−1.31073	+	1.09984i	−0.322553	+	0.946551i	$0.604541\pi$
$223$	−4364.88	+	3662.57i	−1.31073	+	1.09984i	−0.988182	+	0.153286i	$0.951015\pi$
$224$	1673.01	+	2897.74i	0.499030	+	0.864345i
$225$	−133.670	+	368.804i	−0.0396061	+	0.109275i
$226$	5893.37	−	10207.6i	1.73461	−	3.00443i
$227$	37.0599	+	210.177i	0.0108359	+	0.0614534i	0.989746	−	0.142837i	$-0.0456224\pi$
$227$	37.0599	+	210.177i	0.0108359	+	0.0614534i	−0.978910	+	0.204290i	$0.934511\pi$
$228$	−3643.82	+	2555.09i	−1.05841	+	0.742171i
$229$	234.649	−	85.4054i	0.0677121	−	0.0246452i	−0.307942	−	0.951405i	$-0.599640\pi$
$229$	234.649	−	85.4054i	0.0677121	−	0.0246452i	0.375654	+	0.926760i	$0.377418\pi$
$230$	2484.62	−	904.326i	0.712307	−	0.259259i
$231$	60.7847	+	689.416i	0.0173132	+	0.196365i
$232$	1649.49	+	9354.71i	0.466785	+	2.64727i
$233$	1003.25	−	1737.68i	0.282082	−	0.488580i	−0.689815	−	0.723985i	$-0.742308\pi$
$233$	1003.25	−	1737.68i	0.282082	−	0.488580i	0.971897	+	0.235405i	$0.0756417\pi$
$234$	13.8589	+	10272.4i	0.00387174	+	2.86978i
$235$	2249.53	+	3896.30i	0.624440	+	1.08156i
$236$	−5128.55	+	4303.36i	−1.41458	+	1.18697i
$237$	−2340.14	−	5009.62i	−0.641385	−	1.37304i
$238$	−332.417	+	1885.23i	−0.0905352	+	0.513451i
$239$	425.681	+	357.189i	0.115209	+	0.0966720i	0.698572	−	0.715540i	$-0.253819\pi$
$239$	425.681	+	357.189i	0.115209	+	0.0966720i	−0.583363	+	0.812212i	$0.698264\pi$
$240$	6888.29	+	6879.01i	1.85266	+	1.85016i
$241$	1581.82	+	575.735i	0.422797	+	0.153885i	0.544651	−	0.838663i	$-0.316662\pi$
$241$	1581.82	+	575.735i	0.422797	+	0.153885i	−0.121855	+	0.992548i	$0.538884\pi$
$242$	−5479.31			−1.45547
$243$	2687.54	+	2669.47i	0.709488	+	0.704718i
$244$	7659.08			2.00952
$245$	−2797.35	−	1018.15i	−0.729454	−	0.265500i
$246$	−4548.54	−	4542.41i	−1.17888	−	1.17729i
$247$	2347.50	+	1969.78i	0.604728	+	0.507427i
$248$	−1747.79	+	9912.21i	−0.447519	+	2.53801i
$249$	2245.34	+	4806.68i	0.571456	+	1.22334i
$250$	5952.02	−	4994.34i	1.50576	−	1.26348i
$251$	−2273.12	−	3937.15i	−0.571625	−	0.990083i	−0.996399	−	0.0847837i	$-0.972980\pi$
$251$	−2273.12	−	3937.15i	−0.571625	−	0.990083i	0.424775	−	0.905299i	$-0.360353\pi$
$252$	−5.65221	−	4189.49i	−0.00141292	−	1.04727i
$253$	−409.007	+	708.421i	−0.101637	+	0.176040i
$254$	40.6779	+	230.696i	0.0100487	+	0.0569888i
$255$	224.172	+	2542.54i	0.0550517	+	0.624393i
$256$	886.225	−	322.560i	0.216364	−	0.0787499i
$257$	271.381	−	98.7746i	0.0658688	−	0.0239743i	−0.308876	−	0.951102i	$-0.599953\pi$
$257$	271.381	−	98.7746i	0.0658688	−	0.0239743i	0.374744	+	0.927128i	$0.377730\pi$
$258$	−9291.50	+	6515.33i	−2.24211	+	1.57220i
$259$	94.9825	+	538.673i	0.0227874	+	0.129234i
$260$	7574.10	−	13118.7i	1.80664	−	3.12919i
$261$	1366.62	−	3770.57i	0.324105	−	0.894223i
$262$	−3227.51	−	5590.21i	−0.761054	−	1.31818i
$263$	5409.82	−	4539.37i	1.26838	−	1.06430i	0.273642	−	0.961832i	$-0.411772\pi$
$263$	5409.82	−	4539.37i	1.26838	−	1.06430i	0.994737	−	0.102464i	$-0.0326726\pi$
$264$	−5703.22	−	495.091i	−1.32958	−	0.115419i
$265$	−80.1773	+	454.708i	−0.0185859	+	0.105406i
$266$	−1339.02	−	1123.57i	−0.308650	−	0.258988i
$267$	860.503	−	3220.13i	0.197236	−	0.738085i
$268$	−4628.26	−	1684.55i	−1.05491	−	0.383956i
$269$	−1328.59			−0.301135			−0.150567	−	0.988600i	$-0.548110\pi$
$269$	−1328.59			−0.301135			−0.150567	+	0.988600i	$0.548110\pi$
$270$	−2037.30	−	7542.23i	−0.459208	−	1.70002i
$271$	−7645.70			−1.71381			−0.856906	−	0.515473i	$-0.827616\pi$
$271$	−7645.70			−1.71381			−0.856906	+	0.515473i	$0.827616\pi$
$272$	−7828.11	−	2849.20i	−1.74503	−	0.635140i
$273$	−2786.00	+	748.520i	−0.617641	+	0.165943i
$274$	−9485.48	−	7959.27i	−2.09138	−	1.75488i
$275$	−43.4648	+	246.501i	−0.00953100	+	0.0540530i
$276$	2837.47	−	4058.15i	0.618825	−	0.885044i
$277$	3555.09	−	2983.08i	0.771137	−	0.647061i	−0.169863	−	0.985468i	$-0.554333\pi$
$277$	3555.09	−	2983.08i	0.771137	−	0.647061i	0.941000	+	0.338407i	$0.109888\pi$
$278$	5382.55	+	9322.86i	1.16124	+	2.01132i
$279$	2727.20	−	3259.07i	0.585208	−	0.699338i
$280$	−2598.22	+	4500.25i	−0.554547	+	0.960504i
$281$	1176.55	+	6672.53i	0.249775	+	1.41655i	0.809136	+	0.587622i	$0.199936\pi$
$281$	1176.55	+	6672.53i	0.249775	+	1.41655i	−0.559360	+	0.828925i	$0.688953\pi$
$282$	10683.5	+	4973.04i	2.25601	+	1.05014i
$283$	3336.58	−	1214.42i	0.700844	−	0.255087i	0.0330731	−	0.999453i	$-0.489471\pi$
$283$	3336.58	−	1214.42i	0.700844	−	0.255087i	0.667771	+	0.744366i	$0.267248\pi$
$284$	15210.5	−	5536.15i	3.17808	−	1.15673i
$285$	−2112.92	−	983.537i	−0.439153	−	0.204420i
$286$	1138.18	+	6454.97i	0.235323	+	1.33458i
$287$	902.625	−	1563.39i	0.185646	−	0.321547i
$288$	11510.6	+	2013.63i	2.35511	+	0.411994i
$289$	1364.41	+	2363.23i	0.277715	+	0.481016i
$290$	−6336.43	+	5316.90i	−1.28306	+	1.07662i
$291$	1037.74	−	1484.18i	0.209050	−	0.298983i
$292$	−1223.07	+	6936.39i	−0.245120	+	1.39014i
$293$	−3307.11	−	2775.00i	−0.659398	−	0.553300i	0.250509	−	0.968114i	$-0.419402\pi$
$293$	−3307.11	−	2775.00i	−0.659398	−	0.553300i	−0.909906	+	0.414814i	$0.863847\pi$
$294$	−7530.20	+	2023.16i	−1.49378	+	0.401336i
$295$	−3294.58	−	1199.13i	−0.650231	−	0.236665i
$296$	−4524.40			−0.888430
$297$	1982.71	+	1382.33i	0.387368	+	0.270071i
$298$	−1740.59			−0.338354
$299$	−3204.05	−	1166.18i	−0.619715	−	0.225558i
$300$	391.171	−	1463.82i	0.0752809	−	0.281712i
$301$	−2441.31	−	2048.51i	−0.467492	−	0.392272i
$302$	−310.389	+	1760.30i	−0.0591420	+	0.335411i
$303$	667.530	+	57.9476i	0.126563	+	0.0109868i
$304$	5827.02	−	4889.45i	1.09935	−	0.922465i
$305$	2005.49	+	3473.61i	0.376505	+	0.652126i
$306$	4304.22	+	5115.54i	0.804104	+	0.955672i
$307$	1988.83	−	3444.76i	0.369735	−	0.640400i	−0.619789	−	0.784769i	$-0.712782\pi$
$307$	1988.83	−	3444.76i	0.369735	−	0.640400i	0.989524	+	0.144369i	$0.0461151\pi$
$308$	−464.196	−	2632.59i	−0.0858767	−	0.487031i
$309$	1280.38	−	897.816i	0.235722	−	0.165291i
$310$	−8236.02	+	2997.66i	−1.50895	+	0.549213i
$311$	−257.322	+	93.6574i	−0.0469176	+	0.0170766i	−0.365372	−	0.930861i	$-0.619058\pi$
$311$	−257.322	+	93.6574i	−0.0469176	+	0.0170766i	0.318455	+	0.947938i	$0.396836\pi$
$312$	−2095.72	−	23769.6i	−0.380279	−	4.31310i
$313$	757.654	+	4296.87i	0.136822	+	0.775954i	0.973574	+	0.228372i	$0.0733403\pi$
$313$	757.654	+	4296.87i	0.136822	+	0.775954i	−0.836752	+	0.547581i	$0.815549\pi$
$314$	−9487.50	+	16432.8i	−1.70513	+	2.95337i
$315$	1898.57	−	1099.56i	0.339595	−	0.196677i
$316$	10678.3	+	18495.4i	1.90096	+	3.29256i
$317$	−2682.95	+	2251.26i	−0.475361	+	0.398875i	−0.848745	−	0.528802i	$-0.822642\pi$
$317$	−2682.95	+	2251.26i	−0.475361	+	0.398875i	0.373385	+	0.927677i	$0.378197\pi$
$318$	511.843	+	1095.72i	0.0902602	+	0.193223i
$319$	444.374	−	2520.17i	0.0779943	−	0.442327i
$320$	−6980.70	−	5857.50i	−1.21948	−	1.02326i
$321$	431.968	+	431.386i	0.0751094	+	0.0750081i
$322$	1827.60	+	665.193i	0.316299	+	0.115124i
$323$	1994.38			0.343562
$324$	−11233.4	−	9374.43i	−1.92617	−	1.60741i
$325$	−1043.32			−0.178072
$326$	16393.6	+	5966.77i	2.78514	+	1.01371i
$327$	5194.76	+	5187.76i	0.878504	+	0.877320i
$328$	11438.8	+	9598.25i	1.92561	+	1.61578i
$329$	−574.666	+	3259.09i	−0.0962989	+	0.546138i
$330$	−2109.79	−	4516.49i	−0.351939	−	0.753409i
$331$	−1407.45	+	1180.99i	−0.233718	+	0.196112i	−0.752123	−	0.659022i	$-0.770970\pi$
$331$	−1407.45	+	1180.99i	−0.233718	+	0.196112i	0.518406	+	0.855135i	$0.326526\pi$
$332$	−10245.8	−	17746.2i	−1.69370	−	2.93358i
$333$	1655.61	+	952.892i	0.272453	+	0.156811i
$334$	−4060.41	+	7032.84i	−0.665197	+	1.15216i
$335$	−447.895	−	2540.14i	−0.0730481	−	0.414276i
$336$	628.910	+	7133.05i	0.102113	+	1.15815i
$337$	−7159.67	+	2605.91i	−1.15731	+	0.421225i	−0.848134	−	0.529781i	$-0.822274\pi$
$337$	−7159.67	+	2605.91i	−1.15731	+	0.421225i	−0.309172	+	0.951006i	$0.600052\pi$
$338$	−14735.2	+	5363.19i	−2.37127	+	0.863073i
$339$	9464.83	−	6636.86i	1.51640	−	1.06332i
$340$	−1711.94	−	9708.89i	−0.273067	−	1.54864i
$341$	1355.78	−	2348.28i	0.215307	−	0.372922i
$342$	−6010.34	+	1068.15i	−0.950297	+	0.168885i
$343$	−2420.75	−	4192.86i	−0.381073	−	0.660039i
$344$	20193.5	−	16944.3i	3.16500	−	2.65575i
$345$	2583.47	+	224.268i	0.403157	+	0.0349976i
$346$	2351.49	−	13335.9i	0.365366	−	2.07209i
$347$	1615.14	+	1355.27i	0.249871	+	0.209667i	0.759117	−	0.650954i	$-0.225631\pi$
$347$	1615.14	+	1355.27i	0.249871	+	0.209667i	−0.509246	+	0.860621i	$0.670075\pi$
$348$	−3999.25	+	14965.8i	−0.616040	+	2.30531i
$349$	−9721.75	−	3538.43i	−1.49110	−	0.542716i	−0.537360	−	0.843353i	$-0.680578\pi$
$349$	−9721.75	−	3538.43i	−1.49110	−	0.542716i	−0.953739	+	0.300637i	$0.902801\pi$
$350$	595.117			0.0908867
$351$	−4239.26	+	9139.37i	−0.644659	+	1.38981i
$352$	7456.16			1.12902
$353$	−6092.76	−	2217.58i	−0.918654	−	0.334363i	−0.160951	−	0.986962i	$-0.551456\pi$
$353$	−6092.76	−	2217.58i	−0.918654	−	0.334363i	−0.757703	+	0.652600i	$0.773678\pi$
$354$	−8868.69	+	2382.77i	−1.33154	+	0.357748i
$355$	6493.58	+	5448.76i	0.970827	+	0.814621i
$356$	−2235.58	+	12678.6i	−0.332824	+	1.88754i
$357$	−1075.83	+	1538.66i	−0.159493	+	0.228108i
$358$	10833.5	−	9090.39i	1.59935	−	1.34202i
$359$	3087.26	+	5347.29i	0.453870	+	0.786126i	0.998622	−	0.0524709i	$-0.0167097\pi$
$359$	3087.26	+	5347.29i	0.453870	+	0.786126i	−0.544752	+	0.838597i	$0.683376\pi$
$360$	6229.89	+	17044.9i	0.912067	+	2.49540i
$361$	2518.96	−	4362.96i	0.367249	−	0.636093i
$362$	−4314.68	−	24469.8i	−0.626450	−	3.55277i
$363$	−4871.89	−	2267.80i	−0.704429	−	0.327902i
$364$	10470.5	−	3810.97i	1.50771	−	0.548761i
$365$	−3466.11	+	1261.56i	−0.497053	+	0.180913i
$366$	9524.51	+	4433.53i	1.36026	+	0.633182i
$367$	−445.507	−	2526.60i	−0.0633659	−	0.359366i	−0.999960	−	0.00894945i	$-0.997151\pi$
$367$	−445.507	−	2526.60i	−0.0633659	−	0.359366i	0.936594	−	0.350416i	$-0.113960\pi$
$368$	−4231.79	+	7329.68i	−0.599450	+	1.03828i
$369$	−2164.27	−	5921.42i	−0.305332	−	0.835385i
$370$	−1969.89	−	3411.96i	−0.276784	−	0.479403i
$371$	−260.171	+	218.309i	−0.0364080	+	0.0305500i
$372$	−9405.67	+	13452.0i	−1.31092	+	1.87487i
$373$	−1466.84	+	8318.89i	−0.203620	+	1.15479i	0.695976	+	0.718065i	$0.254972\pi$
$373$	−1466.84	+	8318.89i	−0.203620	+	1.15479i	−0.899596	+	0.436722i	$0.856139\pi$
$374$	3267.79	+	2742.00i	0.451800	+	0.379105i
$375$	7359.28	−	1977.24i	1.01342	−	0.272277i
$376$	−25722.8	−	9362.33i	−3.52806	−	1.28411i
$377$	10666.7			1.45720
$378$	2418.10	−	5213.14i	0.329030	−	0.709352i
$379$	5435.86			0.736731			0.368366	−	0.929681i	$-0.379917\pi$
$379$	5435.86			0.736731			0.368366	+	0.929681i	$0.379917\pi$
$380$	8459.12	+	3078.87i	1.14196	+	0.415639i
$381$	−59.3129	+	221.958i	−0.00797557	+	0.0298458i
$382$	3029.20	+	2541.80i	0.405726	+	0.340445i
$383$	771.662	−	4376.31i	0.102951	−	0.583862i	−0.889069	−	0.457774i	$-0.848647\pi$
$383$	771.662	−	4376.31i	0.102951	−	0.583862i	0.992019	−	0.126088i	$-0.0402421\pi$
$384$	−5855.56	−	508.315i	−0.778165	−	0.0675517i
$385$	1072.41	−	899.856i	0.141961	−	0.119119i
$386$	−6284.72	−	10885.5i	−0.828715	−	1.43538i
$387$	−10958.1	+	1947.45i	−1.43935	+	0.255800i
$388$	−3497.48	+	6057.81i	−0.457623	+	0.792626i
$389$	1569.27	+	8899.75i	0.204537	+	1.15999i	0.898167	+	0.439655i	$0.144899\pi$
$389$	1569.27	+	8899.75i	0.204537	+	1.15999i	−0.693629	+	0.720332i	$0.743989\pi$
$390$	17012.7	−	11929.6i	2.20890	−	1.54891i
$391$	−2085.24	+	758.965i	−0.269706	+	0.0981651i
$392$	17019.9	−	6194.74i	2.19295	−	0.798167i
$393$	−556.018	−	6306.31i	−0.0713674	−	0.809443i
$394$	196.545	+	1114.66i	0.0251314	+	0.142527i
$395$	−5592.14	+	9685.87i	−0.712332	+	1.23379i
$396$	−8091.27	−	4656.95i	−1.02677	−	0.590961i
$397$	−1572.55	−	2723.74i	−0.198801	−	0.344334i	0.749339	−	0.662187i	$-0.230372\pi$
$397$	−1572.55	−	2723.74i	−0.198801	−	0.344334i	−0.948140	+	0.317853i	$0.897038\pi$
$398$	4019.15	−	3372.46i	0.506185	−	0.424740i
$399$	−725.554	−	1553.22i	−0.0910354	−	0.194883i
$400$	−449.709	+	2550.42i	−0.0562136	+	0.318803i
$401$	−3836.22	−	3218.97i	−0.477734	−	0.400867i	0.371872	−	0.928284i	$-0.378716\pi$
$401$	−3836.22	−	3218.97i	−0.477734	−	0.400867i	−0.849606	+	0.527417i	$0.823160\pi$
$402$	−4780.39	−	4773.95i	−0.593095	−	0.592296i
$403$	10620.8	+	3865.65i	1.31280	+	0.477821i
$404$	−2588.03			−0.318711
$405$	1310.16	−	7549.33i	0.160746	−	0.926245i
$406$	−6084.34			−0.743746
$407$	1145.37	+	416.881i	0.139494	+	0.0507716i
$408$	−10988.5	−	10973.7i	−1.33336	−	1.33156i
$409$	−9402.56	−	7889.68i	−1.13674	−	0.953838i	−0.137413	−	0.990514i	$-0.543879\pi$
$409$	−9402.56	−	7889.68i	−1.13674	−	0.953838i	−0.999327	+	0.0366758i	$0.988323\pi$
$410$	−2257.91	+	12805.3i	−0.271976	+	1.54245i
$411$	−5139.74	−	11002.8i	−0.616848	−	1.32051i
$412$	−4627.01	+	3882.52i	−0.553292	+	0.464267i
$413$	−1289.46	−	2233.41i	−0.153632	−	0.266099i
$414$	5877.66	−	3404.05i	0.697757	−	0.404106i
$415$	5365.60	−	9293.50i	0.634668	−	1.09928i
$416$	5396.82	+	30606.9i	0.636060	+	3.60727i
$417$	927.277	+	10517.1i	0.108894	+	1.23507i
$418$	−3660.22	+	1332.21i	−0.428295	+	0.155887i
$419$	−4345.44	+	1581.61i	−0.506656	+	0.184408i	−0.582685	−	0.812698i	$-0.697998\pi$
$419$	−4345.44	+	1581.61i	−0.506656	+	0.184408i	0.0760294	+	0.997106i	$0.475776\pi$
$420$	−6938.45	+	4865.34i	−0.806100	+	0.565248i
$421$	640.488	+	3632.39i	0.0741460	+	0.420503i	0.999175	+	0.0406068i	$0.0129291\pi$
$421$	640.488	+	3632.39i	0.0741460	+	0.420503i	−0.925029	+	0.379896i	$0.875960\pi$
$422$	496.730	−	860.362i	0.0572996	−	0.0992459i
$423$	7440.92	+	8843.48i	0.855295	+	1.01651i
$424$	−1404.63	−	2432.89i	−0.160884	−	0.278659i
$425$	−520.153	+	436.460i	−0.0593673	+	0.0498151i
$426$	22119.7	+	1920.19i	2.51574	+	0.218389i
$427$	−512.323	+	2905.53i	−0.0580633	+	0.329294i
$428$	−1806.33	−	1515.69i	−0.204000	−	0.171177i
$429$	−1659.60	+	6210.47i	−0.186775	+	0.698938i
$430$	21570.2	+	7850.92i	2.41909	+	0.880477i
$431$	9457.15			1.05693			0.528463	−	0.848956i	$-0.322769\pi$
$431$	9457.15			1.05693			0.528463	+	0.848956i	$0.322769\pi$
$432$	20514.1	+	14302.3i	2.28468	+	1.59287i
$433$	5424.25			0.602016			0.301008	−	0.953622i	$-0.402677\pi$
$433$	5424.25			0.602016			0.301008	+	0.953622i	$0.402677\pi$
$434$	−6058.15	−	2204.99i	−0.670047	−	0.243877i
$435$	−7834.58	+	2104.94i	−0.863539	+	0.232009i
$436$	−21722.5	−	18227.4i	−2.38605	−	2.00214i
$437$	351.854	−	1995.46i	0.0385159	−	0.218434i
$438$	−5536.16	+	7917.82i	−0.603945	+	0.863763i
$439$	−5489.82	+	4606.51i	−0.596845	+	0.500812i	−0.890430	−	0.455121i	$-0.849596\pi$
$439$	−5489.82	+	4606.51i	−0.596845	+	0.500812i	0.293585	+	0.955933i	$0.405152\pi$
$440$	5789.79	+	10028.2i	0.627312	+	1.08654i
$441$	−7532.78	−	1317.76i	−0.813387	−	0.142291i
$442$	−8890.42	+	15398.7i	−0.956728	+	1.65710i
$443$	−1218.10	−	6908.21i	−0.130641	−	0.740901i	−0.977797	−	0.209556i	$-0.932798\pi$
$443$	−1218.10	−	6908.21i	−0.130641	−	0.740901i	0.847156	−	0.531345i	$-0.178313\pi$
$444$	−6689.15	−	3113.71i	−0.714984	−	0.332815i
$445$	−6335.47	+	2305.92i	−0.674899	+	0.245643i
$446$	28367.8	−	10325.0i	3.01179	−	1.09620i
$447$	−1547.63	−	720.402i	−0.163759	−	0.0762278i
$448$	−1163.96	−	6601.15i	−0.122750	−	0.696149i
$449$	8938.47	−	15481.9i	0.939493	−	1.62725i	0.173073	−	0.984909i	$-0.444630\pi$
$449$	8938.47	−	15481.9i	0.939493	−	1.62725i	0.766420	−	0.642340i	$-0.222036\pi$
$450$	1333.79	−	1593.91i	0.139723	−	0.166973i
$451$	−2011.38	−	3483.81i	−0.210005	−	0.363739i
$452$	−34203.9	+	28700.5i	−3.55933	+	2.98663i
$453$	−1004.54	+	1436.70i	−0.104189	+	0.149011i
$454$	196.348	−	1113.54i	0.0202975	−	0.115113i
$455$	4470.04	+	3750.81i	0.460569	+	0.386463i
$456$	13694.5	−	3679.33i	1.40637	−	0.377852i
$457$	10778.5	+	3923.06i	1.10328	+	0.401560i	0.828523	−	0.559955i	$-0.189182\pi$
$457$	10778.5	+	3923.06i	1.10328	+	0.401560i	0.274754	+	0.961515i	$0.411404\pi$
$458$	−1322.99			−0.134976
$459$	1709.83	+	6329.89i	0.173873	+	0.643691i
$460$	−10016.2			−1.01523
$461$	−3260.04	−	1186.56i	−0.329361	−	0.119877i	0.172047	−	0.985089i	$-0.444962\pi$
$461$	−3260.04	−	1186.56i	−0.329361	−	0.119877i	−0.501407	+	0.865211i	$0.667184\pi$
$462$	946.644	−	3542.48i	0.0953287	−	0.356734i
$463$	1341.68	+	1125.80i	0.134672	+	0.113003i	0.707636	−	0.706578i	$-0.249762\pi$
$463$	1341.68	+	1125.80i	0.134672	+	0.113003i	−0.572963	+	0.819581i	$0.694206\pi$
$464$	4597.72	−	26075.0i	0.460008	−	2.60883i
$465$	−8563.69	−	743.405i	−0.854046	−	0.0741389i
$466$	−8143.58	+	6833.27i	−0.809536	+	0.679282i
$467$	1743.80	+	3020.36i	0.172792	+	0.299284i	0.939395	−	0.342837i	$-0.111388\pi$
$467$	1743.80	+	3020.36i	0.172792	+	0.299284i	−0.766603	+	0.642121i	$0.778055\pi$
$468$	13259.9	−	36584.7i	1.30969	−	3.61352i
$469$	948.634	−	1643.08i	0.0933984	−	0.161771i
$470$	−4139.18	−	23474.5i	−0.406226	−	2.30382i
$471$	−15237.0	+	10684.4i	−1.49063	+	1.04525i
$472$	20045.2	−	7295.86i	1.95478	−	0.711481i
$473$	−6673.33	+	2428.89i	−0.648710	+	0.236111i
$474$	2572.88	+	29181.4i	0.249317	+	2.82773i
$475$	−107.663	−	610.590i	−0.0103999	−	0.0589806i
$476$	3625.86	−	6280.17i	0.349141	−	0.604729i
$477$	1.60021	+	1186.10i	0.000153603	+	0.113853i
$478$	−1472.05	−	2549.66i	−0.140858	−	0.243973i
$479$	−436.975	+	366.666i	−0.0416825	+	0.0349757i	−0.663391	−	0.748273i	$-0.730883\pi$
$479$	−436.975	+	366.666i	−0.0416825	+	0.0349757i	0.621708	+	0.783249i	$0.286439\pi$
$480$	−10003.8	−	21415.4i	−0.951265	−	2.03641i
$481$	−882.232	+	5003.39i	−0.0836306	+	0.474293i
$482$	−6831.99	−	5732.72i	−0.645620	−	0.541739i
$483$	1349.69	+	1347.87i	0.127149	+	0.126978i
$484$	19504.7	+	7099.13i	1.83177	+	0.666710i
$485$	−3663.19			−0.342963
$486$	−8542.94	−	18160.2i	−0.797357	−	1.69499i
$487$	7682.70			0.714859			0.357429	−	0.933940i	$-0.383653\pi$
$487$	7682.70			0.714859			0.357429	+	0.933940i	$0.383653\pi$
$488$	−22932.3	−	8346.66i	−2.12724	−	0.774253i
$489$	12106.7	+	12090.4i	1.11960	+	1.11809i
$490$	12082.0	+	10138.0i	1.11389	+	0.934667i
$491$	−1915.90	+	10865.6i	−0.176096	+	0.998691i	0.760775	+	0.649016i	$0.224819\pi$
$491$	−1915.90	+	10865.6i	−0.176096	+	0.998691i	−0.936871	+	0.349675i	$0.886292\pi$
$492$	10306.2	+	22062.8i	0.944389	+	2.02169i
$493$	5317.92	−	4462.27i	0.485816	−	0.407648i
$494$	−8117.90	−	14060.6i	−0.739355	−	1.28060i
$495$	−6.59598	−	4889.02i	−0.000598924	−	0.443929i
$496$	14027.6	−	24296.5i	1.26987	−	2.19948i
$497$	1082.74	+	6140.51i	0.0977212	+	0.554205i
$498$	−2468.65	−	27999.3i	−0.222134	−	2.51943i
$499$	15257.5	−	5553.26i	1.36877	−	0.498192i	0.450017	−	0.893020i	$-0.351418\pi$
$499$	15257.5	−	5553.26i	1.36877	−	0.498192i	0.918755	+	0.394828i	$0.129196\pi$
$500$	−27658.2	+	10066.8i	−2.47383	+	0.900400i
$501$	−6521.07	+	4572.66i	−0.581517	+	0.407768i
$502$	4182.58	+	23720.6i	0.371868	+	2.10897i
$503$	2644.10	−	4579.72i	0.234383	−	0.405963i	−0.724710	−	0.689054i	$-0.758026\pi$
$503$	2644.10	−	4579.72i	0.234383	−	0.405963i	0.959093	+	0.283091i	$0.0913597\pi$
$504$	−4548.66	+	12550.0i	−0.402011	+	1.10917i
$505$	−677.663	−	1173.75i	−0.0597141	−	0.103428i
$506$	3319.99	−	2785.80i	0.291683	−	0.244751i
$507$	−15321.5	−	1330.04i	−1.34211	−	0.116507i
$508$	154.094	−	873.912i	0.0134583	−	0.0763260i
$509$	−361.081	−	302.983i	−0.0314433	−	0.0263841i	0.626931	−	0.779075i	$-0.284311\pi$
$509$	−361.081	−	302.983i	−0.0314433	−	0.0263841i	−0.658374	+	0.752691i	$0.728755\pi$
$510$	3491.19	−	13064.5i	0.303122	−	1.13433i
$511$	−2549.56	−	927.963i	−0.220716	−	0.0803340i
$512$	−14045.8			−1.21239
$513$	−5786.14	−	1537.85i	−0.497981	−	0.132354i
$514$	−1530.09			−0.131302
$515$	−2972.39	−	1081.86i	−0.254329	−	0.0925681i
$516$	41516.4	−	11154.3i	3.54197	−	0.951630i
$517$	5649.19	+	4740.23i	0.480563	+	0.403240i
$518$	503.229	−	2853.96i	0.0426846	−	0.242076i
$519$	7610.35	−	10884.3i	0.643655	−	0.920556i
$520$	−36974.2	+	31025.0i	−3.11813	+	2.61642i
$521$	2841.59	+	4921.79i	0.238949	+	0.413872i	0.960413	−	0.278580i	$-0.0898637\pi$
$521$	2841.59	+	4921.79i	0.238949	+	0.413872i	−0.721464	+	0.692452i	$0.756530\pi$
$522$	−13636.4	+	16295.8i	−1.14339	+	1.36637i
$523$	296.307	−	513.218i	0.0247736	−	0.0429091i	−0.853373	−	0.521301i	$-0.825447\pi$
$523$	296.307	−	513.218i	0.0247736	−	0.0429091i	0.878146	+	0.478392i	$0.158780\pi$
$524$	4246.15	+	24081.1i	0.353996	+	2.00761i
$525$	529.145	+	246.310i	0.0439881	+	0.0204759i
$526$	−35159.0	+	12796.8i	−2.91446	+	1.06078i
$527$	6912.17	−	2515.82i	0.571345	−	0.207952i
$528$	14466.2	+	6733.84i	1.19235	+	0.555024i
$529$	−1721.28	−	9761.89i	−0.141472	−	0.802325i
$530$	1223.13	−	2118.53i	0.100244	−	0.173628i
$531$	−8871.73	−	1551.99i	−0.725048	−	0.126837i
$532$	3310.80	+	5734.47i	0.269814	+	0.467332i
$533$	12844.9	−	10778.1i	1.04385	−	0.875897i
$534$	−10119.2	+	14472.5i	−0.820038	+	1.17282i
$535$	214.431	−	1216.10i	0.0173283	−	0.0982737i
$536$	12021.8	+	10087.5i	0.968775	+	0.812898i
$537$	13394.9	−	3598.84i	1.07641	−	0.289202i
$538$	6614.51	+	2407.48i	0.530059	+	0.192926i
$539$	−4879.45			−0.389931
$540$	−2519.72	+	29487.7i	−0.200799	+	2.34990i
$541$	14198.0			1.12831			0.564157	−	0.825667i	$-0.309201\pi$
$541$	14198.0			1.12831			0.564157	+	0.825667i	$0.309201\pi$
$542$	38064.9	+	13854.5i	3.01666	+	1.09797i
$543$	6291.29	−	23542.9i	0.497210	−	1.86063i
$544$	15494.5	+	13001.5i	1.22118	+	1.02469i
$545$	2578.70	−	14624.5i	0.202678	−	1.14944i
$546$	15226.8	+	1321.82i	1.19349	+	0.103606i
$547$	−1932.93	+	1621.92i	−0.151090	+	0.126780i	−0.715199	−	0.698921i	$-0.753664\pi$
$547$	−1932.93	+	1621.92i	−0.151090	+	0.126780i	0.564109	+	0.825700i	$0.309220\pi$
$548$	23453.3	+	40622.3i	1.82824	+	3.16660i
$549$	6633.69	+	7884.10i	0.515699	+	0.612905i
$550$	663.070	−	1148.47i	0.0514062	−	0.0890382i
$551$	1100.73	+	6242.53i	0.0851044	+	0.482651i
$552$	−12918.2	+	9058.42i	−0.996079	+	0.698464i
$553$	−7730.66	+	2813.73i	−0.594468	+	0.216369i
$554$	−23105.0	+	8409.52i	−1.77191	+	0.644921i
$555$	−339.363	−	3849.03i	−0.0259552	−	0.294382i
$556$	−7081.36	−	40160.4i	−0.540138	−	3.06327i
$557$	2857.54	−	4949.40i	0.217375	−	0.376504i	−0.736630	−	0.676296i	$-0.763584\pi$
$557$	2857.54	−	4949.40i	0.217375	−	0.376504i	0.954005	+	0.299792i	$0.0969173\pi$
$558$	−19483.3	+	11283.8i	−1.47813	+	0.856057i
$559$	−14800.6	−	25635.4i	−1.11985	−	1.93964i
$560$	11095.7	−	9310.36i	0.837280	−	0.702562i
$561$	1770.66	+	3790.52i	0.133257	+	0.285269i
$562$	6233.49	−	35351.9i	0.467872	−	2.65343i
$563$	2884.11	+	2420.05i	0.215898	+	0.181160i	0.744322	−	0.667820i	$-0.232773\pi$
$563$	2884.11	+	2420.05i	0.215898	+	0.181160i	−0.528424	+	0.848980i	$0.677217\pi$
$564$	−31587.0	−	31544.4i	−2.35825	−	2.35507i
$565$	−21972.6	−	7997.38i	−1.63610	−	0.595491i
$566$	−18812.1			−1.39705
$567$	4307.67	−	3634.42i	0.319057	−	0.269191i
$568$	−51575.1			−3.80994
$569$	−16673.4	−	6068.61i	−1.22844	−	0.447116i	−0.355378	−	0.934723i	$-0.615648\pi$
$569$	−16673.4	−	6068.61i	−1.22844	−	0.447116i	−0.873064	+	0.487606i	$0.837870\pi$
$570$	8737.18	+	8725.40i	0.642035	+	0.641170i
$571$	2080.29	+	1745.57i	0.152465	+	0.127933i	0.715829	−	0.698275i	$-0.246049\pi$
$571$	2080.29	+	1745.57i	0.152465	+	0.127933i	−0.563364	+	0.826209i	$0.690493\pi$
$572$	4311.62	−	24452.4i	0.315171	−	1.78743i
$573$	1641.38	+	3513.77i	0.119668	+	0.256177i
$574$	−7326.79	+	6147.90i	−0.532777	+	0.447053i
$575$	344.929	+	597.435i	0.0250166	+	0.0433300i
$576$	−20288.6	−	11677.2i	−1.46764	−	0.844704i
$577$	−11533.7	+	19977.0i	−0.832158	+	1.44134i	0.0641648	+	0.997939i	$0.479562\pi$
$577$	−11533.7	+	19977.0i	−0.832158	+	1.44134i	−0.896323	+	0.443401i	$0.853772\pi$
$578$	−2510.55	−	14238.0i	−0.180666	−	1.02461i
$579$	−1082.70	−	12279.9i	−0.0777123	−	0.881407i
$580$	29444.5	−	10716.9i	2.10796	−	0.767236i
$581$	7417.49	−	2699.75i	0.529655	−	0.192779i
$582$	−7855.94	+	5508.69i	−0.559518	+	0.392341i
$583$	131.420	+	745.320i	0.00933595	+	0.0529468i
$584$	11221.1	−	19435.6i	0.795091	−	1.37714i
$585$	20064.2	−	3565.78i	1.41804	−	0.252012i
$586$	11436.3	+	19808.3i	0.806196	+	1.39637i
$587$	1349.11	−	1132.04i	0.0948617	−	0.0795984i	−0.594123	−	0.804374i	$-0.702501\pi$
$587$	1349.11	−	1132.04i	0.0948617	−	0.0795984i	0.688985	+	0.724775i	$0.258057\pi$
$588$	29426.5	+	2554.49i	2.06383	+	0.179159i
$589$	−1166.33	+	6614.56i	−0.0815919	+	0.462731i
$590$	14229.5	+	11940.0i	0.992917	+	0.833156i
$591$	−286.584	+	1072.44i	−0.0199467	+	0.0746434i
$592$	11850.6	+	4313.26i	0.822730	+	0.299449i
$593$	18645.1			1.29117			0.645583	−	0.763690i	$-0.276614\pi$
$593$	18645.1			1.29117			0.645583	+	0.763690i	$0.276614\pi$
$594$	−7366.24	−	10474.9i	−0.508822	−	0.723553i
$595$	3797.65			0.261661
$596$	6195.97	+	2255.15i	0.425834	+	0.154991i
$597$	4969.41	−	1335.14i	0.340677	−	0.0915305i
$598$	13838.5	+	11611.9i	0.946319	+	0.794056i
$599$	−3807.30	+	21592.3i	−0.259703	+	1.47285i	0.524002	+	0.851717i	$0.324438\pi$
$599$	−3807.30	+	21592.3i	−0.259703	+	1.47285i	−0.783705	+	0.621133i	$0.786673\pi$
$600$	−2766.45	+	3956.57i	−0.188233	+	0.269211i
$601$	1101.22	−	924.033i	0.0747416	−	0.0627156i	−0.604651	−	0.796490i	$-0.706688\pi$
$601$	1101.22	−	924.033i	0.0747416	−	0.0627156i	0.679393	+	0.733775i	$0.262243\pi$
$602$	8442.32	+	14622.5i	0.571567	+	0.989983i
$603$	−2274.59	−	6223.25i	−0.153613	−	0.420283i
$604$	3385.59	−	5864.02i	0.228076	−	0.395039i
$605$	1887.55	+	10704.8i	0.126843	+	0.719360i
$606$	−3218.37	−	1498.11i	−0.215738	−	0.100423i
$607$	6222.24	−	2264.71i	0.416067	−	0.151436i	−0.125500	−	0.992094i	$-0.540053\pi$
$607$	6222.24	−	2264.71i	0.416067	−	0.151436i	0.541567	+	0.840658i	$0.317831\pi$
$608$	−17355.3	+	6316.81i	−1.15765	+	0.421350i
$609$	−5409.85	−	2518.22i	−0.359964	−	0.167559i
$610$	−3690.14	−	20927.8i	−0.244934	−	1.38909i
$611$	−15369.3	+	26620.4i	−1.01764	+	1.76260i
$612$	−8693.92	−	23786.5i	−0.574234	−	1.57110i
$613$	9789.40	+	16955.7i	0.645008	+	1.11719i	0.984300	+	0.176506i	$0.0564795\pi$
$613$	9789.40	+	16955.7i	0.645008	+	1.11719i	−0.339291	+	0.940681i	$0.610187\pi$
$614$	−16143.8	+	13546.2i	−1.06109	+	0.890360i
$615$	−7307.50	+	10451.2i	−0.479133	+	0.685257i
$616$	−1479.06	+	8388.16i	−0.0967419	+	0.548651i
$617$	−20133.5	−	16894.0i	−1.31369	−	1.10232i	−0.987603	−	0.156975i	$-0.949826\pi$
$617$	−20133.5	−	16894.0i	−1.31369	−	1.10232i	−0.326086	−	0.945340i	$-0.605730\pi$
$618$	−8001.39	+	2149.75i	−0.520814	+	0.139928i
$619$	2516.77	+	916.028i	0.163421	+	0.0594802i	0.422435	−	0.906393i	$-0.361175\pi$
$619$	2516.77	+	916.028i	0.163421	+	0.0594802i	−0.259014	+	0.965873i	$0.583398\pi$
$620$	33201.6			2.15066
$621$	6634.97	−	594.017i	0.428747	−	0.0383850i
$622$	1450.82			0.0935249
$623$	−4660.17	−	1696.16i	−0.299688	−	0.109078i
$624$	−17171.1	+	64256.6i	−1.10159	+	4.12231i
$625$	−10416.5	−	8740.49i	−0.666657	−	0.559392i
$626$	4014.15	−	22765.4i	0.256290	−	1.45349i
$627$	−3805.84	−	330.381i	−0.242409	−	0.0210433i
$628$	55063.5	−	46203.7i	3.49884	−	2.93588i
$629$	1653.26	+	2863.52i	0.104801	+	0.181520i
$630$	−11444.7	+	2033.94i	−0.723760	+	0.128625i
$631$	−12842.2	+	22243.3i	−0.810206	+	1.40332i	0.102514	+	0.994732i	$0.467311\pi$
$631$	−12842.2	+	22243.3i	−0.810206	+	1.40332i	−0.912720	+	0.408586i	$0.866022\pi$
$632$	−11816.5	−	67014.6i	−0.743725	−	4.21788i
$633$	797.755	−	559.396i	0.0500915	−	0.0351248i
$634$	17436.8	−	6346.47i	1.09228	−	0.397556i
$635$	436.693	−	158.943i	0.0272908	−	0.00993303i
$636$	−402.366	−	4563.60i	−0.0250862	−	0.284526i
$637$	−3531.78	−	20029.7i	−0.219677	−	1.24585i
$638$	−6779.08	+	11741.7i	−0.420668	+	0.728619i
$639$	18872.9	+	10862.3i	1.16839	+	0.672469i
$640$	5944.44	+	10296.1i	0.367148	+	0.635919i
$641$	−9033.33	+	7579.86i	−0.556622	+	0.467062i	−0.877176	−	0.480169i	$-0.840575\pi$
$641$	−9033.33	+	7579.86i	−0.556622	+	0.467062i	0.320554	+	0.947230i	$0.396131\pi$
$642$	−1368.90	−	2930.46i	−0.0841530	−	0.180149i
$643$	−192.033	+	1089.07i	−0.0117776	+	0.0667943i	−0.990130	−	0.140151i	$-0.955241\pi$
$643$	−192.033	+	1089.07i	−0.0117776	+	0.0667943i	0.978352	+	0.206945i	$0.0663523\pi$
$644$	−5643.88	−	4735.78i	−0.345342	−	0.289776i
$645$	15929.7	+	15908.2i	0.972449	+	0.971138i
$646$	−9929.25	−	3613.95i	−0.604739	−	0.220107i
$647$	−26901.6			−1.63464			−0.817318	−	0.576187i	$-0.804540\pi$
$647$	−26901.6			−1.63464			−0.817318	+	0.576187i	$0.804540\pi$
$648$	23418.3	+	40310.1i	1.41969	+	2.44372i
$649$	−5746.78			−0.347582
$650$	5194.31	+	1890.57i	0.313442	+	0.114084i
$651$	−4473.95	−	4467.92i	−0.269352	−	0.268989i
$652$	−50625.6	−	42479.9i	−3.04087	−	2.55160i
$653$	3265.90	−	18521.9i	0.195719	−	1.10998i	−0.715672	−	0.698437i	$-0.753879\pi$
$653$	3265.90	−	18521.9i	0.195719	−	1.10998i	0.911391	−	0.411542i	$-0.135010\pi$
$654$	−16462.1	−	35241.1i	−0.984282	−	2.10709i
$655$	−9809.64	+	8231.27i	−0.585182	+	0.491026i
$656$	−20810.8	−	36045.3i	−1.23860	−	2.14532i
$657$	−8199.50	+	4748.75i	−0.486900	+	0.281988i
$658$	8766.72	−	15184.4i	0.519396	−	0.899620i
$659$	5061.07	+	28702.7i	0.299167	+	1.69666i	0.649764	+	0.760136i	$0.274868\pi$
$659$	5061.07	+	28702.7i	0.299167	+	1.69666i	−0.350597	+	0.936526i	$0.614021\pi$
$660$	1658.53	+	18810.9i	0.0978152	+	1.10941i
$661$	7174.42	−	2611.28i	0.422167	−	0.153656i	−0.122196	−	0.992506i	$-0.538994\pi$
$661$	7174.42	−	2611.28i	0.422167	−	0.153656i	0.544363	+	0.838850i	$0.316771\pi$
$662$	9147.19	−	3329.30i	0.537033	−	0.195464i
$663$	−14278.1	+	10012.0i	−0.836374	+	0.586477i
$664$	11337.8	+	64299.9i	0.662639	+	3.75801i
$665$	−1733.83	+	3003.08i	−0.101105	+	0.175119i
$666$	−6515.94	−	7744.15i	−0.379111	−	0.450570i
$667$	−3526.48	−	6108.04i	−0.204716	−	0.354579i
$668$	23565.8	−	19774.1i	1.36495	−	1.14533i
$669$	29496.5	+	2560.56i	1.70463	+	0.147977i
$670$	−2373.00	+	13458.0i	−0.136832	+	0.776010i
$671$	5036.33	+	4225.99i	0.289755	+	0.243133i
$672$	4488.61	−	16797.0i	0.257666	−	0.964225i
$673$	3739.18	+	1360.95i	0.214167	+	0.0779506i	0.446876	−	0.894596i	$-0.352537\pi$
$673$	3739.18	+	1360.95i	0.214167	+	0.0779506i	−0.232708	+	0.972547i	$0.574759\pi$
$674$	40367.3			2.30696
$675$	1845.63	−	865.181i	0.105242	−	0.0493346i
$676$	59401.7			3.37971
$677$	21293.0	+	7750.03i	1.20880	+	0.439967i	0.866287	−	0.499546i	$-0.166500\pi$
$677$	21293.0	+	7750.03i	1.20880	+	0.439967i	0.342513	+	0.939513i	$0.388722\pi$
$678$	−59148.1	+	15891.5i	−3.35040	+	0.900159i
$679$	−2064.13	−	1732.01i	−0.116663	−	0.0978915i
$680$	−5454.72	+	30935.3i	−0.307616	+	1.74458i
$681$	635.460	−	908.835i	0.0357575	−	0.0511404i
$682$	−11005.1	+	9234.40i	−0.617900	+	0.518480i
$683$	−17182.9	−	29761.6i	−0.962643	−	1.66735i	−0.715819	−	0.698286i	$-0.753947\pi$
$683$	−17182.9	−	29761.6i	−0.962643	−	1.66735i	−0.246823	−	0.969060i	$-0.579387\pi$
$684$	22778.9	+	3984.86i	1.27335	+	0.222756i
$685$	−12282.2	+	21273.5i	−0.685081	+	1.18659i
$686$	4454.23	+	25261.2i	0.247906	+	1.40594i
$687$	−1176.33	−	547.564i	−0.0653270	−	0.0304088i
$688$	−69045.6	+	25130.5i	−3.82607	+	1.39258i
$689$	−2964.35	+	1078.93i	−0.163908	+	0.0596577i
$690$	−12455.7	−	5797.95i	−0.687217	−	0.319890i
$691$	4226.20	+	23968.0i	0.232666	+	1.31952i	0.847473	+	0.530838i	$0.178123\pi$
$691$	4226.20	+	23968.0i	0.232666	+	1.31952i	−0.614807	+	0.788677i	$0.710766\pi$
$692$	−25649.0	+	44425.4i	−1.40900	+	2.44046i
$693$	2307.88	−	2757.97i	0.126507	−	0.151178i
$694$	−5585.33	−	9674.08i	−0.305499	−	0.529140i
$695$	16359.7	−	13727.4i	0.892888	−	0.749222i
$696$	28283.5	−	40451.1i	1.54035	−	2.20301i
$697$	1894.98	−	10747.0i	0.102980	−	0.584031i
$698$	41988.9	+	35232.9i	2.27694	+	1.91058i
$699$	−10069.0	+	2705.26i	−0.544842	+	0.146384i
$700$	−2118.44	−	771.050i	−0.114385	−	0.0416328i
$701$	−11818.5			−0.636775			−0.318388	−	0.947961i	$-0.603141\pi$
$701$	−11818.5			−0.636775			−0.318388	+	0.947961i	$0.603141\pi$
$702$	37666.8	−	37819.5i	2.02513	−	2.03334i
$703$	−3019.20			−0.161979
$704$	−14035.9	−	5108.66i	−0.751418	−	0.273494i
$705$	6035.39	−	22585.3i	0.322420	−	1.20654i
$706$	26315.1	+	22081.0i	1.40280	+	1.17709i
$707$	173.116	−	981.789i	0.00920890	−	0.0522263i
$708$	34657.1	+	3008.55i	1.83968	+	0.159701i
$709$	−4683.60	+	3930.01i	−0.248091	+	0.208173i	−0.758350	−	0.651848i	$-0.773994\pi$
$709$	−4683.60	+	3930.01i	−0.248091	+	0.208173i	0.510259	+	0.860021i	$0.329550\pi$
$710$	−22455.5	−	38894.1i	−1.18696	−	2.05587i
$711$	−9790.07	+	27011.3i	−0.516394	+	1.42476i
$712$	20510.4	−	35525.0i	1.07958	−	1.86988i
$713$	−1297.72	−	7359.75i	−0.0681628	−	0.386571i
$714$	8144.30	−	5710.89i	0.426881	−	0.299335i
$715$	12218.9	−	4447.30i	0.639104	−	0.232615i
$716$	−50341.8	+	18322.9i	−2.62760	+	0.956368i
$717$	−253.597	−	2876.28i	−0.0132088	−	0.149814i
$718$	−5680.62	−	32216.4i	−0.295263	−	1.67452i
$719$	981.181	−	1699.45i	0.0508927	−	0.0881488i	−0.839457	−	0.543426i	$-0.817127\pi$
$719$	981.181	−	1699.45i	0.0508927	−	0.0881488i	0.890350	+	0.455278i	$0.150460\pi$
$720$	−68.2453	−	50584.3i	−0.00353244	−	2.61828i
$721$	−1163.36	−	2014.99i	−0.0600911	−	0.104081i
$722$	−20446.9	+	17157.0i	−1.05395	+	0.884372i
$723$	−3701.94	−	7924.87i	−0.190424	−	0.407647i
$724$	−16344.7	+	92695.4i	−0.839014	+	4.75828i
$725$	−1653.22	−	1387.22i	−0.0846885	−	0.0710621i
$726$	20145.8	+	20118.7i	1.02987	+	1.02848i
$727$	−13937.2	−	5072.74i	−0.711009	−	0.258786i	−0.0389053	−	0.999243i	$-0.512387\pi$
$727$	−13937.2	−	5072.74i	−0.711009	−	0.258786i	−0.672104	+	0.740457i	$0.734609\pi$
$728$	−35503.2			−1.80747
$729$	−79.6652	−	19682.8i	−0.00404741	−	0.999992i
$730$	19542.4			0.990819
$731$	−18103.1	−	6588.97i	−0.915959	−	0.333382i
$732$	−28160.2	−	28122.3i	−1.42190	−	1.41999i
$733$	4524.21	+	3796.27i	0.227975	+	0.191294i	0.749619	−	0.661869i	$-0.230237\pi$
$733$	4524.21	+	3796.27i	0.227975	+	0.191294i	−0.521644	+	0.853163i	$0.674681\pi$
$734$	−2360.35	+	13386.2i	−0.118695	+	0.673153i
$735$	6546.65	+	14014.6i	0.328540	+	0.703317i
$736$	15742.1	−	13209.2i	0.788398	−	0.661544i
$737$	−2113.91	−	3661.39i	−0.105654	−	0.182997i
$738$	45.0644	+	33402.3i	0.00224776	+	1.66606i
$739$	8336.35	−	14439.0i	0.414963	−	0.718737i	−0.580462	−	0.814288i	$-0.697128\pi$
$739$	8336.35	−	14439.0i	0.414963	−	0.718737i	0.995425	+	0.0955508i	$0.0304612\pi$
$740$	2591.62	+	14697.8i	0.128743	+	0.730138i
$741$	−1398.51	−	15861.8i	−0.0693326	−	0.786365i
$742$	1690.88	−	615.429i	0.0836578	−	0.0304489i
$743$	28551.4	−	10391.9i	1.40976	−	0.513110i	0.478699	−	0.877979i	$-0.341108\pi$
$743$	28551.4	−	10391.9i	1.40976	−	0.513110i	0.931059	+	0.364869i	$0.118886\pi$
$744$	42821.3	−	30026.9i	2.11009	−	1.47962i
$745$	599.609	+	3400.55i	0.0294872	+	0.167230i
$746$	22377.2	−	38758.5i	1.09824	−	1.90221i
$747$	9393.48	−	25917.1i	0.460093	−	1.26942i
$748$	−8079.75	−	13994.5i	−0.394953	−	0.684079i
$749$	695.814	−	583.857i	0.0339446	−	0.0284829i
$750$	−40221.9	−	3491.62i	−1.95826	−	0.169995i
$751$	4130.46	−	23425.0i	0.200696	−	1.13820i	−0.703375	−	0.710819i	$-0.748324\pi$
$751$	4130.46	−	23425.0i	0.200696	−	1.13820i	0.904071	−	0.427383i	$-0.140564\pi$
$752$	58449.3	+	49044.8i	2.83435	+	2.37830i
$753$	−6098.66	+	22822.1i	−0.295150	+	1.10449i
$754$	−53105.4	−	19328.8i	−2.56497	−	0.933572i
$755$	3546.00			0.170930
$756$	−15362.0	+	15424.3i	−0.739034	+	0.742032i
$757$	14027.2			0.673482			0.336741	−	0.941597i	$-0.390675\pi$
$757$	14027.2			0.673482			0.336741	+	0.941597i	$0.390675\pi$
$758$	−27063.0	−	9850.13i	−1.29680	−	0.471996i
$759$	4104.95	−	1102.89i	0.196311	−	0.0527434i
$760$	−21972.4	−	18437.0i	−1.04871	−	0.879976i
$761$	−258.313	+	1464.97i	−0.0123047	+	0.0697832i	−0.990342	−	0.138648i	$-0.955724\pi$
$761$	−258.313	+	1464.97i	−0.0123047	+	0.0697832i	0.978037	+	0.208431i	$0.0668356\pi$
$762$	697.498	−	997.562i	0.0331597	−	0.0474250i
$763$	8367.72	−	7021.35i	0.397027	−	0.333145i
$764$	−7489.83	−	12972.8i	−0.354676	−	0.614317i
$765$	8511.38	−	10171.3i	0.402261	−	0.480711i
$766$	−11772.0	+	20389.6i	−0.555272	+	0.961760i
$767$	−4159.56	−	23590.0i	−0.195819	−	1.11054i
$768$	−4442.76	−	2068.04i	−0.208742	−	0.0971668i
$769$	−11591.8	+	4219.08i	−0.543578	+	0.197846i	−0.599191	−	0.800606i	$-0.704511\pi$
$769$	−11591.8	+	4219.08i	−0.543578	+	0.197846i	0.0556126	+	0.998452i	$0.482289\pi$
$770$	−6969.69	+	2536.76i	−0.326195	+	0.118725i
$771$	−1360.47	−	633.279i	−0.0635486	−	0.0295810i
$772$	8268.27	+	46891.7i	0.385468	+	2.18610i
$773$	9153.38	−	15854.1i	0.425905	−	0.737689i	−0.570600	−	0.821228i	$-0.693289\pi$
$773$	9153.38	−	15854.1i	0.425905	−	0.737689i	0.996504	+	0.0835397i	$0.0266225\pi$
$774$	58084.9	+	10161.1i	2.69744	+	0.471880i
$775$	−1143.37	−	1980.38i	−0.0529951	−	0.0917902i
$776$	17073.5	−	14326.4i	0.789825	−	0.662742i
$777$	1628.65	−	2329.30i	0.0751963	−	0.107546i
$778$	8314.17	−	47152.0i	0.383133	−	2.17285i
$779$	7633.24	+	6405.05i	0.351078	+	0.294589i
$780$	−76016.5	+	20423.5i	−3.48952	+	0.937538i
$781$	13056.5	+	4752.17i	0.598204	+	0.217729i
$782$	11756.9			0.537629
$783$	−18869.3	+	8845.41i	−0.861216	+	0.403716i
$784$	−50485.3			−2.29980
$785$	35372.8	+	12874.7i	1.60829	+	0.585371i
$786$	−8659.25	+	32404.2i	−0.392958	+	1.47051i
$787$	25909.7	+	21740.8i	1.17354	+	0.984720i	1.00000		0.000105582i	$-3.36078e-5\pi$
$787$	25909.7	+	21740.8i	1.17354	+	0.984720i	0.173544	+	0.984826i	$0.444478\pi$
$788$	744.542	−	4222.51i	0.0336589	−	0.190889i
$789$	−36557.8	−	3173.55i	−1.64955	−	0.143195i
$790$	45392.5	−	38088.8i	2.04429	−	1.71537i
$791$	−8599.81	−	14895.3i	−0.386566	−	0.669553i
$792$	19151.2	+	22761.1i	0.859230	+	1.02119i
$793$	−13702.0	+	23732.5i	−0.613583	+	1.06276i
$794$	2893.53	+	16410.0i	0.129329	+	0.733463i
$795$	1964.37	−	1377.44i	0.0876338	−	0.0614500i
$796$	−18676.4	+	6797.66i	−0.831618	+	0.302684i
$797$	3588.01	−	1305.93i	0.159465	−	0.0580406i	−0.261054	−	0.965324i	$-0.584070\pi$
$797$	3588.01	−	1305.93i	0.159465	−	0.0580406i	0.420519	+	0.907284i	$0.361848\pi$
$798$	797.715	+	9047.63i	0.0353870	+	0.401357i
$799$	3473.86	+	19701.2i	0.153812	+	0.872314i
$800$	3144.01	−	5445.59i	0.138947	−	0.240663i
$801$	−14987.3	+	8679.93i	−0.661113	+	0.382884i
$802$	13266.0	+	22977.5i	0.584090	+	1.01167i
$803$	−4631.48	+	3886.27i	−0.203539	+	0.170789i
$804$	10831.5	+	23187.4i	0.475123	+	1.01711i
$805$	669.990	−	3799.70i	0.0293342	−	0.166363i
$806$	−45872.0	−	38491.1i	−2.00468	−	1.68212i
$807$	4884.83	+	4878.24i	0.213078	+	0.212791i
$808$	7748.89	+	2820.37i	0.337383	+	0.122797i
$809$	−28520.8			−1.23948			−0.619738	−	0.784808i	$-0.712761\pi$
$809$	−28520.8			−1.23948			−0.619738	+	0.784808i	$0.712761\pi$
$810$	−20202.6	+	35211.1i	−0.876356	+	1.52740i
$811$	19863.7			0.860061			0.430031	−	0.902814i	$-0.358503\pi$
$811$	19863.7			0.860061			0.430031	+	0.902814i	$0.358503\pi$
$812$	21658.5	+	7883.04i	0.936038	+	0.340690i
$813$	28111.0	+	28073.1i	1.21267	+	1.21103i
$814$	−4946.94	−	4150.98i	−0.213010	−	0.178737i
$815$	6009.80	−	34083.3i	0.258300	−	1.46489i
$816$	18320.1	+	39218.6i	0.785948	+	1.68251i
$817$	13475.4	−	11307.2i	0.577043	−	0.484197i
$818$	32515.0	+	56317.7i	1.38981	+	2.40722i
$819$	12991.7	+	7477.40i	0.554293	+	0.319025i
$820$	24628.3	−	42657.5i	1.04885	−	1.81666i
$821$	−2839.99	−	16106.4i	−0.120726	−	0.684673i	−0.983755	−	0.179518i	$-0.942546\pi$
$821$	−2839.99	−	16106.4i	−0.120726	−	0.684673i	0.863028	−	0.505155i	$-0.168565\pi$
$822$	5650.92	+	64092.3i	0.239779	+	2.71956i
$823$	−11834.3	+	4307.32i	−0.501235	+	0.182435i	−0.580250	−	0.814439i	$-0.697045\pi$
$823$	−11834.3	+	4307.32i	−0.501235	+	0.182435i	0.0790142	+	0.996873i	$0.474823\pi$
$824$	18084.9	−	6582.37i	0.764585	−	0.278286i
$825$	1064.90	−	746.721i	0.0449394	−	0.0315121i
$826$	2372.63	+	13455.9i	0.0999447	+	0.566815i
$827$	−20001.2	+	34643.0i	−0.841002	+	1.45666i	0.0480464	+	0.998845i	$0.484700\pi$
$827$	−20001.2	+	34643.0i	−0.841002	+	1.45666i	−0.889048	+	0.457813i	$0.848633\pi$
$828$	−25333.1	+	4502.16i	−1.06327	+	0.188962i
$829$	−955.816	−	1655.52i	−0.0400445	−	0.0693591i	0.845309	−	0.534278i	$-0.179417\pi$
$829$	−955.816	−	1655.52i	−0.0400445	−	0.0693591i	−0.885353	+	0.464919i	$0.846083\pi$
$830$	−43553.7	+	36545.9i	−1.82141	+	1.52834i
$831$	−24024.2	−	2085.52i	−1.00288	−	0.0870586i
$832$	10811.3	−	61313.9i	0.450497	−	2.55490i
$833$	−10139.9	−	8508.40i	−0.421762	−	0.353900i
$834$	14441.1	−	54040.9i	0.599587	−	2.24374i
$835$	15138.7	+	5510.03i	0.627420	+	0.228362i
$836$	14755.3			0.610436
$837$	−21993.6	+	1969.05i	−0.908257	+	0.0813146i
$838$	24500.2			1.00996
$839$	−584.784	−	212.844i	−0.0240632	−	0.00875828i	0.329961	−	0.943995i	$-0.392965\pi$
$839$	−584.784	−	212.844i	−0.0240632	−	0.00875828i	−0.354024	+	0.935236i	$0.615187\pi$
$840$	26076.7	−	7006.09i	1.07111	−	0.287777i
$841$	−1780.87	−	1494.33i	−0.0730195	−	0.0612706i
$842$	3393.38	−	19244.8i	0.138888	−	0.787673i
$843$	20174.1	−	28853.0i	0.824237	−	1.17882i
$844$	−2882.92	+	2419.06i	−0.117576	+	0.0986580i
$845$	15554.0	+	26940.4i	0.633225	+	1.09678i
$846$	−21020.5	−	57511.7i	−0.854253	−	2.33723i
$847$	−3997.79	+	6924.38i	−0.162179	+	0.280903i
$848$	1359.74	+	7711.45i	0.0550632	+	0.312279i
$849$	−16726.7	−	7786.04i	−0.676158	−	0.314742i
$850$	3380.53	−	1230.41i	0.136413	−	0.0496504i
$851$	3156.74	−	1148.96i	0.127158	−	0.0462818i
$852$	−76251.9	−	35494.2i	−3.06613	−	1.42724i
$853$	−196.105	−	1112.17i	−0.00787163	−	0.0446422i	0.980619	−	0.195925i	$-0.0627708\pi$
$853$	−196.105	−	1112.17i	−0.00787163	−	0.0446422i	−0.988491	+	0.151282i	$0.951660\pi$
$854$	7815.66	−	13537.1i	0.313169	−	0.542425i
$855$	4157.30	+	11374.3i	0.166288	+	0.454963i
$856$	3756.61	+	6506.64i	0.149998	+	0.259804i
$857$	−10301.7	+	8644.14i	−0.410617	+	0.344549i	−0.824580	−	0.565745i	$-0.808589\pi$
$857$	−10301.7	+	8644.14i	−0.410617	+	0.344549i	0.413963	+	0.910294i	$0.364144\pi$
$858$	19516.3	−	27912.2i	0.776544	−	1.11061i
$859$	2493.03	−	14138.7i	0.0990234	−	0.561590i	−0.894417	−	0.447235i	$-0.852409\pi$
$859$	2493.03	−	14138.7i	0.0990234	−	0.561590i	0.993440	−	0.114355i	$-0.0364801\pi$
$860$	−66611.8	−	55893.9i	−2.64121	−	2.21624i
$861$	−9059.09	+	2433.93i	−0.358575	+	0.0963391i
$862$	−47083.5	−	17137.0i	−1.86041	−	0.677132i
$863$	8498.08			0.335201			0.167600	−	0.985855i	$-0.446398\pi$
$863$	8498.08			0.335201			0.167600	+	0.985855i	$0.446398\pi$
$864$	−34927.8	−	49667.8i	−1.37531	−	1.95571i
$865$	−26864.2			−1.05597
$866$	−27005.2	−	9829.09i	−1.05967	−	0.385688i
$867$	3660.66	−	13698.7i	0.143394	−	0.536601i
$868$	18708.4	+	15698.2i	0.731571	+	0.613861i
$869$	−3183.38	+	18053.8i	−0.124268	+	0.704757i
$870$	42819.6	+	3717.13i	1.66864	+	0.144853i
$871$	13499.6	−	11327.5i	0.525164	−	0.440665i
$872$	45176.3	+	78247.6i	1.75443	+	3.03876i
$873$	−9265.02	+	1646.57i	−0.359191	+	0.0638348i
$874$	−5367.65	+	9297.04i	−0.207738	+	0.359814i
$875$	−1968.82	−	11165.7i	−0.0760666	−	0.431395i
$876$	29965.6	−	21012.3i	1.15576	−	0.810433i
$877$	−6538.82	+	2379.93i	−0.251768	+	0.0916359i	−0.464821	−	0.885405i	$-0.653881\pi$
$877$	−6538.82	+	2379.93i	−0.251768	+	0.0916359i	0.213054	+	0.977041i	$0.431659\pi$
$878$	35679.0	−	12986.1i	1.37142	−	0.499156i
$879$	1970.19	+	22345.8i	0.0756006	+	0.857456i
$880$	−5604.75	−	31786.1i	−0.214700	−	1.21762i
$881$	16834.7	−	29158.5i	0.643785	−	1.11507i	−0.340795	−	0.940137i	$-0.610696\pi$
$881$	16834.7	−	29158.5i	0.643785	−	1.11507i	0.984581	−	0.174931i	$-0.0559703\pi$
$882$	35114.9	+	20210.5i	1.34057	+	0.771567i
$883$	8647.05	+	14977.1i	0.329554	+	0.570805i	0.982423	−	0.186666i	$-0.0597682\pi$
$883$	8647.05	+	14977.1i	0.329554	+	0.570805i	−0.652869	+	0.757471i	$0.726435\pi$
$884$	51598.1	−	43296.0i	1.96316	−	1.64729i
$885$	7710.32	+	16505.8i	0.292858	+	0.626932i
$886$	−6453.67	+	36600.6i	−0.244712	+	1.38783i
$887$	27090.3	+	22731.4i	1.02548	+	0.860482i	0.990306	−	0.138899i	$-0.0443565\pi$
$887$	27090.3	+	22731.4i	1.02548	+	0.860482i	0.0351756	+	0.999381i	$0.488801\pi$
$888$	16634.9	+	16612.5i	0.628638	+	0.627791i
$889$	321.217	+	116.914i	0.0121184	+	0.00441075i
$890$	35720.3			1.34534
$891$	−2214.25	−	12362.5i	−0.0832548	−	0.464824i
$892$	−114359.			−4.29261
$893$	−17165.2	−	6247.62i	−0.643238	−	0.234119i
$894$	6399.64	+	6391.01i	0.239414	+	0.239091i
$895$	−21491.7	−	18033.7i	−0.802669	−	0.673519i
$896$	−1518.57	+	8612.22i	−0.0566203	+	0.321110i
$897$	7498.44	+	16052.2i	0.279114	+	0.597510i
$898$	−72555.3	+	60881.1i	−2.69622	+	2.26239i
$899$	11689.6	+	20247.0i	0.433670	+	0.751139i
$900$	−6813.01	+	3945.76i	−0.252334	+	0.146139i
$901$	−1026.53	+	1778.00i	−0.0379563	+	0.0657422i
$902$	3700.98	+	20989.3i	0.136618	+	0.774797i
$903$	1454.40	+	16495.7i	0.0535984	+	0.607909i
$904$	133688.	−	48658.4i	4.91857	−	1.79021i
$905$	−46319.8	+	16859.0i	−1.70135	+	0.619241i
$906$	7604.62	−	5332.46i	0.278859	−	0.195540i
$907$	−4931.98	−	27970.6i	−0.180555	−	1.02398i	−0.931534	−	0.363654i	$-0.881529\pi$
$907$	−4931.98	−	27970.6i	−0.180555	−	1.02398i	0.750979	−	0.660326i	$-0.229582\pi$
$908$	−2141.68	+	3709.49i	−0.0782754	+	0.135577i
$909$	−2241.55	−	2664.07i	−0.0817904	−	0.0972073i
$910$	−15457.9	−	26773.8i	−0.563103	−	0.975323i
$911$	28442.4	−	23866.0i	1.03440	−	0.867966i	0.0430334	−	0.999074i	$-0.486298\pi$
$911$	28442.4	−	23866.0i	1.03440	−	0.867966i	0.991368	+	0.131108i	$0.0418534\pi$
$912$	−39377.1	−	3418.29i	−1.42972	−	0.124113i
$913$	3054.42	−	17322.5i	0.110719	−	0.627919i
$914$	−46553.2	−	39062.7i	−1.68473	−	1.41365i
$915$	5380.64	−	20135.2i	0.194403	−	0.727484i
$916$	4709.45	+	1714.10i	0.169874	+	0.0618290i
$917$	−9419.37			−0.339209
$918$	2957.62	−	34612.4i	0.106336	−	1.24442i
$919$	3295.52			0.118291			0.0591453	−	0.998249i	$-0.481162\pi$
$919$	3295.52			0.118291			0.0591453	+	0.998249i	$0.481162\pi$
$920$	29989.6	+	10915.3i	1.07471	+	0.391161i
$921$	−19960.7	+	5362.88i	−0.714144	+	0.191871i
$922$	14080.4	+	11814.8i	0.502941	+	0.422018i
$923$	−10056.9	+	57035.3i	−0.358641	+	2.03395i
$924$	−7959.50	+	11383.7i	−0.283386	+	0.405298i
$925$	787.433	−	660.735i	0.0279899	−	0.0234863i
$926$	−4639.68	−	8036.16i	−0.164654	−	0.285188i
$927$	−8004.13	−	1400.21i	−0.283593	−	0.0496106i
$928$	−32143.7	+	55674.5i	−1.13703	+	1.96940i
$929$	−972.944	−	5517.84i	−0.0343609	−	0.194870i	0.962795	−	0.270231i	$-0.0871002\pi$
$929$	−972.944	−	5517.84i	−0.0343609	−	0.194870i	−0.997156	+	0.0753611i	$0.975989\pi$
$930$	41288.2	+	19219.1i	1.45580	+	0.677654i
$931$	11357.6	−	4133.84i	0.399819	−	0.145522i
$932$	37842.1	−	13773.4i	1.33000	−	0.484080i
$933$	1289.98	+	600.471i	0.0452650	+	0.0210702i
$934$	−3208.63	−	18197.1i	−0.112409	−	0.637501i
$935$	4231.28	−	7328.79i	0.147998	−	0.256339i
$936$	−79570.6	+	95088.8i	−2.77868	+	3.32059i
$937$	−10184.1	−	17639.4i	−0.355071	−	0.615001i	0.632059	−	0.774920i	$-0.282210\pi$
$937$	−10184.1	−	17639.4i	−0.355071	−	0.615001i	−0.987130	+	0.159919i	$0.948877\pi$
$938$	−7700.25	+	6461.28i	−0.268041	+	0.224913i
$939$	12991.4	−	18580.3i	0.451499	−	0.645734i
$940$	−15679.9	+	88925.0i	−0.544065	+	3.08555i
$941$	35769.2	+	30013.9i	1.23915	+	1.03977i	0.997590	+	0.0693863i	$0.0221041\pi$
$941$	35769.2	+	30013.9i	1.23915	+	1.03977i	0.241562	+	0.970385i	$0.422340\pi$
$942$	95220.1	−	25583.0i	3.29346	−	0.884862i
$943$	−10418.4	−	3792.00i	−0.359779	−	0.130949i
$944$	−59459.1			−2.05003
$945$	−11017.8	−	2928.33i	−0.379269	−	0.100803i
$946$	37625.2			1.29313
$947$	21803.4	+	7935.80i	0.748169	+	0.272311i	0.687835	−	0.725867i	$-0.258561\pi$
$947$	21803.4	+	7935.80i	0.748169	+	0.272311i	0.0603340	+	0.998178i	$0.480783\pi$
$948$	28649.5	−	107211.i	0.981532	−	3.67304i
$949$	−19305.1	−	16198.9i	−0.660348	−	0.554098i
$950$	−570.415	+	3234.98i	−0.0194807	+	0.110481i
$951$	18130.5	+	1573.89i	0.618214	+	0.0536665i
$952$	−17700.2	+	14852.3i	−0.602592	+	0.505635i
$953$	−494.246	−	856.060i	−0.0167998	−	0.0290981i	0.857503	−	0.514478i	$-0.172014\pi$
$953$	−494.246	−	856.060i	−0.0167998	−	0.0290981i	−0.874303	+	0.485380i	$0.838681\pi$
$954$	2141.32	−	5908.02i	0.0726706	−	0.200502i
$955$	3922.35	−	6793.71i	0.132905	−	0.230198i
$956$	1936.65	+	10983.3i	0.0655185	+	0.371574i
$957$	−10887.3	+	7634.31i	−0.367749	+	0.257871i
$958$	2839.95	−	1033.66i	0.0957773	−	0.0348601i
$959$	−16979.2	+	6179.91i	−0.571726	+	0.208091i
$960$	4158.71	+	47167.8i	0.139814	+	1.58576i
$961$	−871.456	−	4942.27i	−0.0292523	−	0.165898i
$962$	13458.8	−	23311.2i	0.451068	−	0.781273i
$963$	−4.27970	−	3172.16i	−0.000143210	−	0.106149i
$964$	16892.4	+	29258.5i	0.564386	+	0.977545i
$965$	−19101.7	+	16028.2i	−0.637208	+	0.534681i
$966$	−4277.15	−	9156.24i	−0.142458	−	0.304966i
$967$	−6043.22	+	34272.8i	−0.200969	+	1.13975i	0.702690	+	0.711497i	$0.251982\pi$
$967$	−6043.22	+	34272.8i	−0.200969	+	1.13975i	−0.903658	+	0.428254i	$0.859129\pi$
$968$	−50663.1	−	42511.4i	−1.68220	−	1.41154i
$969$	−7332.77	−	7322.88i	−0.243099	−	0.242771i
$970$	18237.6	+	6637.94i	0.603684	+	0.219723i
$971$	14774.2			0.488288			0.244144	−	0.969739i	$-0.421493\pi$
$971$	14774.2			0.488288			0.244144	+	0.969739i	$0.421493\pi$
$972$	6881.47	+	75713.5i	0.227082	+	2.49847i
$973$	15708.8			0.517576
$974$	−38249.2	−	13921.6i	−1.25830	−	0.457983i
$975$	3836.01	+	3830.83i	0.126000	+	0.125831i
$976$	52108.4	+	43724.2i	1.70897	+	1.43399i
$977$	−3177.36	+	18019.7i	−0.104046	+	0.590073i	0.887551	+	0.460709i	$0.152405\pi$
$977$	−3177.36	+	18019.7i	−0.104046	+	0.590073i	−0.991597	+	0.129364i	$0.958706\pi$
$978$	−38365.9	−	82131.3i	−1.25440	−	2.68535i
$979$	−8465.59	+	7103.47i	−0.276365	+	0.231898i
$980$	−29873.2	−	51741.9i	−0.973739	−	1.68656i
$981$	−51.4668	−	38147.8i	−0.00167503	−	1.24155i
$982$	29227.7	−	50623.8i	0.949789	−	1.64508i
$983$	−4635.49	−	26289.2i	−0.150406	−	0.852996i	−0.962866	−	0.269979i	$-0.912983\pi$
$983$	−4635.49	−	26289.2i	−0.150406	−	0.852996i	0.812460	−	0.583017i	$-0.198128\pi$
$984$	−6814.57	−	77290.3i	−0.220773	−	2.50399i
$985$	2109.98	−	767.971i	0.0682534	−	0.0248422i
$986$	−34561.8	+	12579.5i	−1.11630	+	0.406300i
$987$	14079.5	−	9872.71i	0.454057	−	0.318391i
$988$	10680.0	+	60569.4i	0.343903	+	1.95037i
$989$	−9786.32	+	16950.4i	−0.314648	+	0.544986i
$990$	−8826.38	+	24352.5i	−0.283354	+	0.781790i
$991$	−19989.7	−	34623.2i	−0.640762	−	1.10983i	−0.985263	−	0.171046i	$-0.945285\pi$
$991$	−19989.7	−	34623.2i	−0.640762	−	1.10983i	0.344501	−	0.938786i	$-0.388048\pi$
$992$	−52181.9	+	43785.8i	−1.67014	+	1.40141i
$993$	9511.11	+	825.650i	0.303954	+	0.0263859i
$994$	5736.48	−	32533.2i	0.183048	−	1.03812i
$995$	−7973.26	−	6690.36i	−0.254039	−	0.213164i
$996$	−27488.9	+	102868.i	−0.874518	+	3.27257i
$997$	48576.7	+	17680.5i	1.54307	+	0.561631i	0.966779	−	0.255614i	$-0.0822775\pi$
$997$	48576.7	+	17680.5i	1.54307	+	0.561631i	0.576290	+	0.817245i	$0.304500\pi$
$998$	−86023.8			−2.72849
$999$	−2588.42	−	9582.51i	−0.0819760	−	0.303481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.4.1	✓	48
3.2	odd	2		81.4.e.a.64.8		48
9.2	odd	6		243.4.e.b.28.1		48
9.4	even	3		243.4.e.d.109.8		48
9.5	odd	6		243.4.e.a.109.1		48
9.7	even	3		243.4.e.c.28.8		48
27.2	odd	18		243.4.e.a.136.1		48
27.7	even	9	inner	27.4.e.a.7.1	yes	48
27.11	odd	18		243.4.e.b.217.1		48
27.13	even	9		729.4.a.d.1.23		24
27.14	odd	18		729.4.a.c.1.2		24
27.16	even	9		243.4.e.c.217.8		48
27.20	odd	18		81.4.e.a.19.8		48
27.25	even	9		243.4.e.d.136.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.1	✓	48	1.1	even	1	trivial
27.4.e.a.7.1	yes	48	27.7	even	9	inner
81.4.e.a.19.8		48	27.20	odd	18
81.4.e.a.64.8		48	3.2	odd	2
243.4.e.a.109.1		48	9.5	odd	6
243.4.e.a.136.1		48	27.2	odd	18
243.4.e.b.28.1		48	9.2	odd	6
243.4.e.b.217.1		48	27.11	odd	18
243.4.e.c.28.8		48	9.7	even	3
243.4.e.c.217.8		48	27.16	even	9
243.4.e.d.109.8		48	9.4	even	3
243.4.e.d.136.8		48	27.25	even	9
729.4.a.c.1.2		24	27.14	odd	18
729.4.a.d.1.23		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)

\(f(q)\)	\(=\)	\(q+(-4.97861 - 1.81207i) q^{2} +(-3.67671 - 3.67176i) q^{3} +(15.3746 + 12.9008i) q^{4} +(-1.82513 + 10.3508i) q^{5} +(11.6515 + 24.9427i) q^{6} +(-5.92244 + 4.96952i) q^{7} +(-31.9745 - 55.3815i) q^{8} +(0.0364268 + 27.0000i) q^{9} +O(q^{10})\)	\(q+(-4.97861 - 1.81207i) q^{2} +(-3.67671 - 3.67176i) q^{3} +(15.3746 + 12.9008i) q^{4} +(-1.82513 + 10.3508i) q^{5} +(11.6515 + 24.9427i) q^{6} +(-5.92244 + 4.96952i) q^{7} +(-31.9745 - 55.3815i) q^{8} +(0.0364268 + 27.0000i) q^{9} +(27.8430 - 48.2255i) q^{10} +(2.99161 + 16.9662i) q^{11} +(-9.15933 - 103.884i) q^{12} +(-67.4795 + 24.5605i) q^{13} +(38.4906 - 14.0094i) q^{14} +(44.7163 - 31.3556i) q^{15} +(30.9527 + 175.541i) q^{16} +(-23.3676 + 40.4738i) q^{17} +(48.7444 - 134.488i) q^{18} +(-21.3371 - 36.9569i) q^{19} +(-161.595 + 135.595i) q^{20} +(40.0220 + 3.47427i) q^{21} +(15.8499 - 89.8892i) q^{22} +(36.3731 + 30.5207i) q^{23} +(-85.7862 + 321.025i) q^{24} +(13.6527 + 4.96918i) q^{25} +380.460 q^{26} +(99.0034 - 99.4049i) q^{27} -155.166 q^{28} +(-139.582 - 50.8038i) q^{29} +(-279.443 + 75.0787i) q^{30} +(-120.570 - 101.170i) q^{31} +(75.1539 - 426.219i) q^{32} +(51.2966 - 73.3644i) q^{33} +(189.679 - 159.160i) q^{34} +(-40.6295 - 70.3723i) q^{35} +(-347.762 + 415.584i) q^{36} +(35.3750 - 61.2713i) q^{37} +(39.2606 + 222.658i) q^{38} +(338.283 + 157.466i) q^{39} +(631.603 - 229.885i) q^{40} +(-219.420 + 79.8623i) q^{41} +(-192.958 - 89.8195i) q^{42} +(71.5802 + 405.951i) q^{43} +(-172.884 + 299.444i) q^{44} +(-279.539 - 48.9015i) q^{45} +(-125.782 - 217.861i) q^{46} +(327.908 - 275.147i) q^{47} +(530.740 - 759.065i) q^{48} +(-49.1821 + 278.926i) q^{49} +(-58.9671 - 49.4792i) q^{50} +(234.526 - 63.0106i) q^{51} +(-1354.32 - 492.933i) q^{52} +43.9296 q^{53} +(-673.027 + 315.498i) q^{54} -181.075 q^{55} +(464.587 + 169.096i) q^{56} +(-57.2464 + 214.224i) q^{57} +(602.866 + 505.864i) q^{58} +(-57.9243 + 328.505i) q^{59} +(1092.01 + 94.7962i) q^{60} +(292.335 - 245.298i) q^{61} +(416.943 + 722.167i) q^{62} +(-134.393 - 159.725i) q^{63} +(-433.502 + 750.847i) q^{64} +(-131.063 - 743.296i) q^{65} +(-388.327 + 272.300i) q^{66} +(-230.604 + 83.9331i) q^{67} +(-881.413 + 320.808i) q^{68} +(-21.6691 - 245.769i) q^{69} +(74.7591 + 423.980i) q^{70} +(403.252 - 698.452i) q^{71} +(1494.14 - 865.329i) q^{72} +(175.470 + 303.922i) q^{73} +(-287.146 + 240.944i) q^{74} +(-31.9515 - 68.3997i) q^{75} +(148.726 - 843.464i) q^{76} +(-102.032 - 85.6147i) q^{77} +(-1398.84 - 1396.95i) q^{78} +(999.930 + 363.945i) q^{79} -1873.49 q^{80} +(-728.997 + 1.96705i) q^{81} +1237.12 q^{82} +(-959.423 - 349.201i) q^{83} +(570.502 + 569.733i) q^{84} +(-376.289 - 315.744i) q^{85} +(379.241 - 2150.78i) q^{86} +(326.665 + 699.303i) q^{87} +(843.961 - 708.167i) q^{88} +(320.730 + 555.520i) q^{89} +(1303.10 + 750.005i) q^{90} +(277.590 - 480.799i) q^{91} +(165.481 + 938.488i) q^{92} +(71.8288 + 814.676i) q^{93} +(-2131.11 + 775.661i) q^{94} +(421.478 - 153.406i) q^{95} +(-1841.29 + 1291.14i) q^{96} +(60.5209 + 343.231i) q^{97} +(750.290 - 1299.54i) q^{98} +(-457.979 + 81.3913i) 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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