LMFDB - Embedded newform 115.4.g.a.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	115.16
Dual form			115.4.g.a.36.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69252 + 1.95327i) q^{2} +(-4.05620 + 2.60676i) q^{3} +(0.187875 + 1.30670i) q^{4} +(2.07708 + 4.54816i) q^{5} +(1.77348 - 12.3348i) q^{6} +(-18.0212 + 5.29151i) q^{7} +(-20.2644 - 13.0231i) q^{8} +(-1.55865 + 3.41296i) q^{9} +O(q^{10})$	\(q+(-1.69252 + 1.95327i) q^{2} +(-4.05620 + 2.60676i) q^{3} +(0.187875 + 1.30670i) q^{4} +(2.07708 + 4.54816i) q^{5} +(1.77348 - 12.3348i) q^{6} +(-18.0212 + 5.29151i) q^{7} +(-20.2644 - 13.0231i) q^{8} +(-1.55865 + 3.41296i) q^{9} +(-12.3993 - 3.64075i) q^{10} +(23.4071 + 27.0133i) q^{11} +(-4.16831 - 4.81049i) q^{12} +(12.6925 + 3.72685i) q^{13} +(20.1655 - 44.1563i) q^{14} +(-20.2810 - 13.0338i) q^{15} +(49.6021 - 14.5645i) q^{16} +(5.64595 - 39.2685i) q^{17} +(-4.02839 - 8.82094i) q^{18} +(-19.5882 - 136.239i) q^{19} +(-5.55284 + 3.56860i) q^{20} +(59.3040 - 68.4405i) q^{21} -92.3810 q^{22} +(-38.5347 - 103.354i) q^{23} +116.144 q^{24} +(-16.3715 + 18.8937i) q^{25} +(-28.7618 + 18.4841i) q^{26} +(-21.1017 - 146.765i) q^{27} +(-10.3002 - 22.5542i) q^{28} +(-37.7953 + 262.872i) q^{29} +(59.7844 - 17.5543i) q^{30} +(219.068 + 140.787i) q^{31} +(24.5491 - 53.7551i) q^{32} +(-165.361 - 48.5544i) q^{33} +(67.1459 + 77.4905i) q^{34} +(-61.4981 - 70.9726i) q^{35} +(-4.75254 - 1.39547i) q^{36} +(-165.735 + 362.908i) q^{37} +(299.265 + 192.326i) q^{38} +(-61.1983 + 17.9695i) q^{39} +(17.1406 - 119.216i) q^{40} +(-190.422 - 416.965i) q^{41} +(33.3096 + 231.673i) q^{42} +(-92.4431 + 59.4096i) q^{43} +(-30.9006 + 35.6612i) q^{44} -18.7601 q^{45} +(267.099 + 99.6600i) q^{46} -169.504 q^{47} +(-163.230 + 188.377i) q^{48} +(8.21491 - 5.27940i) q^{49} +(-9.19547 - 63.9559i) q^{50} +(79.4624 + 173.998i) q^{51} +(-2.48527 + 17.2855i) q^{52} +(-219.448 + 64.4356i) q^{53} +(322.387 + 207.185i) q^{54} +(-74.2423 + 162.568i) q^{55} +(434.101 + 127.464i) q^{56} +(434.597 + 501.552i) q^{57} +(-449.491 - 518.740i) q^{58} +(-847.937 - 248.977i) q^{59} +(13.2210 - 28.9499i) q^{60} +(161.787 + 103.974i) q^{61} +(-645.770 + 189.615i) q^{62} +(10.0290 - 69.7533i) q^{63} +(235.251 + 515.128i) q^{64} +(9.41294 + 65.4685i) q^{65} +(374.716 - 240.815i) q^{66} +(-116.268 + 134.180i) q^{67} +52.3728 q^{68} +(425.724 + 318.774i) q^{69} +242.715 q^{70} +(497.362 - 573.987i) q^{71} +(76.0323 - 48.8630i) q^{72} +(81.1694 + 564.545i) q^{73} +(-428.349 - 937.953i) q^{74} +(17.1547 - 119.313i) q^{75} +(174.344 - 51.1919i) q^{76} +(-564.766 - 362.953i) q^{77} +(68.4800 - 149.950i) q^{78} +(-610.161 - 179.160i) q^{79} +(169.269 + 195.347i) q^{80} +(401.834 + 463.741i) q^{81} +(1136.74 + 333.776i) q^{82} +(-68.2885 + 149.531i) q^{83} +(100.573 + 64.6343i) q^{84} +(190.326 - 55.8848i) q^{85} +(40.4186 - 281.118i) q^{86} +(-531.940 - 1164.79i) q^{87} +(-122.534 - 852.240i) q^{88} +(-701.025 + 450.521i) q^{89} +(31.7518 - 36.6435i) q^{90} -248.455 q^{91} +(127.813 - 69.7709i) q^{92} -1255.58 q^{93} +(286.888 - 331.087i) q^{94} +(578.952 - 372.070i) q^{95} +(40.5505 + 282.035i) q^{96} +(137.186 + 300.394i) q^{97} +(-3.59178 + 24.9814i) q^{98} +(-128.679 + 37.7834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) $ 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−1.69252	+	1.95327i	−0.598395	+	0.690584i	−0.971455	−	0.237223i	$-0.923763\pi$
$2$	−1.69252	+	1.95327i	−0.598395	+	0.690584i	0.373061	+	0.927807i	$0.378308\pi$
$3$	−4.05620	+	2.60676i	−0.780616	+	0.501672i	−0.869238	−	0.494394i	$-0.835390\pi$
$3$	−4.05620	+	2.60676i	−0.780616	+	0.501672i	0.0886218	+	0.996065i	$0.471754\pi$
$4$	0.187875	+	1.30670i	0.0234844	+	0.163337i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$6$	1.77348	−	12.3348i	0.120670	−	0.839279i
$7$	−18.0212	+	5.29151i	−0.973055	+	0.285715i	−0.729355	−	0.684136i	$-0.760180\pi$
$7$	−18.0212	+	5.29151i	−0.973055	+	0.285715i	−0.243701	+	0.969851i	$0.578361\pi$
$8$	−20.2644	−	13.0231i	−0.895567	−	0.575546i
$9$	−1.55865	+	3.41296i	−0.0577276	+	0.126406i
$10$	−12.3993	−	3.64075i	−0.392099	−	0.115131i
$11$	23.4071	+	27.0133i	0.641592	+	0.740437i	0.979655	−	0.200687i	$-0.0643173\pi$
$11$	23.4071	+	27.0133i	0.641592	+	0.740437i	−0.338064	+	0.941123i	$0.609772\pi$
$12$	−4.16831	−	4.81049i	−0.100274	−	0.115722i
$13$	12.6925	+	3.72685i	0.270790	+	0.0795110i	0.414308	−	0.910137i	$-0.364024\pi$
$13$	12.6925	+	3.72685i	0.270790	+	0.0795110i	−0.143519	+	0.989648i	$0.545842\pi$
$14$	20.1655	−	44.1563i	0.384961	−	0.842947i
$15$	−20.2810	−	13.0338i	−0.349102	−	0.224354i
$16$	49.6021	−	14.5645i	0.775033	−	0.227570i
$17$	5.64595	−	39.2685i	0.0805497	−	0.560235i	−0.909083	−	0.416615i	$-0.863216\pi$
$17$	5.64595	−	39.2685i	0.0805497	−	0.560235i	0.989633	−	0.143621i	$-0.0458745\pi$
$18$	−4.02839	−	8.82094i	−0.0527500	−	0.115506i
$19$	−19.5882	−	136.239i	−0.236519	−	1.64502i	−0.668915	−	0.743339i	$-0.733241\pi$
$19$	−19.5882	−	136.239i	−0.236519	−	1.64502i	0.432396	−	0.901684i	$-0.357668\pi$
$20$	−5.55284	+	3.56860i	−0.0620827	+	0.0398981i
$21$	59.3040	−	68.4405i	0.616248	−	0.711188i
$22$	−92.3810			−0.895259
$23$	−38.5347	−	103.354i	−0.349350	−	0.936992i
$23$	−38.5347	−	103.354i	−0.349350	−	0.936992i
$24$	116.144			0.987829
$25$	−16.3715	+	18.8937i	−0.130972	+	0.151150i
$26$	−28.7618	+	18.4841i	−0.216948	+	0.139424i
$27$	−21.1017	−	146.765i	−0.150408	−	1.04611i
$28$	−10.3002	−	22.5542i	−0.0695195	−	0.152226i
$29$	−37.7953	+	262.872i	−0.242014	+	1.68325i	0.399969	+	0.916529i	$0.369021\pi$
$29$	−37.7953	+	262.872i	−0.242014	+	1.68325i	−0.641983	+	0.766719i	$0.721888\pi$
$30$	59.7844	−	17.5543i	0.363837	−	0.106832i
$31$	219.068	+	140.787i	1.26922	+	0.815678i	0.989518	−	0.144409i	$-0.0461282\pi$
$31$	219.068	+	140.787i	1.26922	+	0.815678i	0.279701	+	0.960087i	$0.409765\pi$
$32$	24.5491	−	53.7551i	0.135616	−	0.296958i
$33$	−165.361	−	48.5544i	−0.872293	−	0.256128i
$34$	67.1459	+	77.4905i	0.338689	+	0.390868i
$35$	−61.4981	−	70.9726i	−0.297002	−	0.342759i
$36$	−4.75254	−	1.39547i	−0.0220025	−	0.00646052i
$37$	−165.735	+	362.908i	−0.736395	+	1.61248i	0.0529995	+	0.998595i	$0.483122\pi$
$37$	−165.735	+	362.908i	−0.736395	+	1.61248i	−0.789395	+	0.613886i	$0.789605\pi$
$38$	299.265	+	192.326i	1.27756	+	0.821037i
$39$	−61.1983	+	17.9695i	−0.251271	+	0.0737799i
$40$	17.1406	−	119.216i	0.0677542	−	0.471241i
$41$	−190.422	−	416.965i	−0.725338	−	1.58827i	−0.806270	−	0.591548i	$-0.798517\pi$
$41$	−190.422	−	416.965i	−0.725338	−	1.58827i	0.0809319	−	0.996720i	$-0.474210\pi$
$42$	33.3096	+	231.673i	0.122376	+	0.851142i
$43$	−92.4431	+	59.4096i	−0.327848	+	0.210695i	−0.694201	−	0.719781i	$-0.744242\pi$
$43$	−92.4431	+	59.4096i	−0.327848	+	0.210695i	0.366354	+	0.930476i	$0.380606\pi$
$44$	−30.9006	+	35.6612i	−0.105874	+	0.122185i
$45$	−18.7601			−0.0621465
$46$	267.099	+	99.6600i	0.856121	+	0.319436i
$47$	−169.504			−0.526058			−0.263029	−	0.964788i	$-0.584721\pi$
$47$	−169.504			−0.526058			−0.263029	+	0.964788i	$0.584721\pi$
$48$	−163.230	+	188.377i	−0.490838	+	0.566457i
$49$	8.21491	−	5.27940i	0.0239502	−	0.0153918i
$50$	−9.19547	−	63.9559i	−0.0260087	−	0.180895i
$51$	79.4624	+	173.998i	0.218176	+	0.477738i
$52$	−2.48527	+	17.2855i	−0.00662779	+	0.0460973i
$53$	−219.448	+	64.4356i	−0.568744	+	0.166998i	−0.553447	−	0.832885i	$-0.686688\pi$
$53$	−219.448	+	64.4356i	−0.568744	+	0.166998i	−0.0152976	+	0.999883i	$0.504870\pi$
$54$	322.387	+	207.185i	0.812431	+	0.522118i
$55$	−74.2423	+	162.568i	−0.182015	+	0.398557i
$56$	434.101	+	127.464i	1.03588	+	0.304161i
$57$	434.597	+	501.552i	1.00989	+	1.16548i
$58$	−449.491	−	518.740i	−1.01760	−	1.17438i
$59$	−847.937	−	248.977i	−1.87105	−	0.549390i	−0.998102	−	0.0615777i	$-0.980387\pi$
$59$	−847.937	−	248.977i	−1.87105	−	0.549390i	−0.872948	−	0.487812i	$-0.837795\pi$
$60$	13.2210	−	28.9499i	0.0284470	−	0.0622902i
$61$	161.787	+	103.974i	0.339586	+	0.218238i	0.699307	−	0.714821i	$-0.253492\pi$
$61$	161.787	+	103.974i	0.339586	+	0.218238i	−0.359722	+	0.933060i	$0.617128\pi$
$62$	−645.770	+	189.615i	−1.32279	+	0.388406i
$63$	10.0290	−	69.7533i	0.0200561	−	0.139494i
$64$	235.251	+	515.128i	0.459475	+	1.00611i
$65$	9.41294	+	65.4685i	0.0179620	+	0.124929i
$66$	374.716	−	240.815i	0.698854	−	0.449126i
$67$	−116.268	+	134.180i	−0.212006	+	0.244668i	−0.851786	−	0.523891i	$-0.824480\pi$
$67$	−116.268	+	134.180i	−0.212006	+	0.244668i	0.639780	+	0.768558i	$0.279026\pi$
$68$	52.3728			0.0933990
$69$	425.724	+	318.774i	0.742770	+	0.556173i
$70$	242.715			0.414428
$71$	497.362	−	573.987i	0.831353	−	0.959432i	−0.168301	−	0.985736i	$-0.553828\pi$
$71$	497.362	−	573.987i	0.831353	−	0.959432i	0.999654	+	0.0263033i	$0.00837358\pi$
$72$	76.0323	−	48.8630i	0.124451	−	0.0799800i
$73$	81.1694	+	564.545i	0.130139	+	0.905138i	0.945369	+	0.326001i	$0.105701\pi$
$73$	81.1694	+	564.545i	0.130139	+	0.905138i	−0.815230	+	0.579137i	$0.803390\pi$
$74$	−428.349	−	937.953i	−0.672899	−	1.47344i
$75$	17.1547	−	119.313i	0.0264114	−	0.183695i
$76$	174.344	−	51.1919i	0.263139	−	0.0772646i
$77$	−564.766	−	362.953i	−0.835858	−	0.537173i
$78$	68.4800	−	149.950i	0.0994082	−	0.217673i
$79$	−610.161	−	179.160i	−0.868968	−	0.255152i	−0.183292	−	0.983059i	$-0.558675\pi$
$79$	−610.161	−	179.160i	−0.868968	−	0.255152i	−0.685677	+	0.727906i	$0.740494\pi$
$80$	169.269	+	195.347i	0.236560	+	0.273005i
$81$	401.834	+	463.741i	0.551213	+	0.636134i
$82$	1136.74	+	333.776i	1.53087	+	0.449504i
$83$	−68.2885	+	149.531i	−0.0903089	+	0.197749i	−0.949397	−	0.314079i	$-0.898304\pi$
$83$	−68.2885	+	149.531i	−0.0903089	+	0.197749i	0.859088	+	0.511828i	$0.171032\pi$
$84$	100.573	+	64.6343i	0.130636	+	0.0839545i
$85$	190.326	−	55.8848i	0.242868	−	0.0713125i
$86$	40.4186	−	281.118i	0.0506797	−	0.352485i
$87$	−531.940	−	1164.79i	−0.655517	−	1.43538i
$88$	−122.534	−	852.240i	−0.148433	−	1.03238i
$89$	−701.025	+	450.521i	−0.834927	+	0.536575i	−0.886840	−	0.462077i	$-0.847104\pi$
$89$	−701.025	+	450.521i	−0.834927	+	0.536575i	0.0519132	+	0.998652i	$0.483468\pi$
$90$	31.7518	−	36.6435i	0.0371881	−	0.0429174i
$91$	−248.455			−0.286211
$92$	127.813	−	69.7709i	0.144842	−	0.0790665i
$93$	−1255.58			−1.39998
$94$	286.888	−	331.087i	0.314790	−	0.363287i
$95$	578.952	−	372.070i	0.625255	−	0.401827i
$96$	40.5505	+	282.035i	0.0431112	+	0.299845i
$97$	137.186	+	300.394i	0.143599	+	0.314437i	0.967742	−	0.251944i	$-0.0810700\pi$
$97$	137.186	+	300.394i	0.143599	+	0.314437i	−0.824143	+	0.566382i	$0.808343\pi$
$98$	−3.59178	+	24.9814i	−0.00370229	+	0.0257500i
$99$	−128.679	+	37.7834i	−0.130633	+	0.0383573i
$100$	−27.7642	−	17.8430i	−0.0277642	−	0.0178430i
$101$	408.762	−	895.063i	0.402706	−	0.881803i	−0.594283	−	0.804256i	$-0.702564\pi$
$101$	408.762	−	895.063i	0.402706	−	0.881803i	0.996989	−	0.0775468i	$-0.0247087\pi$
$102$	−474.357	−	139.284i	−0.460474	−	0.135207i
$103$	613.830	+	708.397i	0.587208	+	0.677674i	0.969139	−	0.246517i	$-0.0792860\pi$
$103$	613.830	+	708.397i	0.587208	+	0.677674i	−0.381930	+	0.924191i	$0.624741\pi$
$104$	−208.670	−	240.818i	−0.196748	−	0.227059i
$105$	434.457	+	127.568i	0.403797	+	0.118566i
$106$	245.559	−	537.698i	0.225007	−	0.492697i
$107$	−167.266	−	107.495i	−0.151123	−	0.0971211i	0.462894	−	0.886414i	$-0.346811\pi$
$107$	−167.266	−	107.495i	−0.151123	−	0.0971211i	−0.614017	+	0.789293i	$0.710447\pi$
$108$	187.813	−	55.1470i	0.167337	−	0.0491345i
$109$	−27.1092	+	188.549i	−0.0238220	+	0.165685i	−0.998260	−	0.0589728i	$-0.981217\pi$
$109$	−27.1092	+	188.549i	−0.0238220	+	0.165685i	0.974438	+	0.224658i	$0.0721266\pi$
$110$	−191.882	−	420.164i	−0.166321	−	0.364191i
$111$	−273.763	−	1904.06i	−0.234094	−	1.62816i
$112$	−816.823	+	524.940i	−0.689130	+	0.442877i
$113$	433.518	−	500.307i	0.360902	−	0.416503i	−0.546040	−	0.837759i	$-0.683865\pi$
$113$	433.518	−	500.307i	0.360902	−	0.416503i	0.906942	+	0.421256i	$0.138411\pi$
$114$	−1715.23			−1.40917
$115$	390.032	−	389.936i	0.316266	−	0.316189i
$116$	−350.596			−0.280621
$117$	−32.5027	+	37.5101i	−0.0256827	+	0.0296394i
$118$	1921.47	−	1234.85i	1.49903	−	0.963366i
$119$	106.042	+	737.542i	0.0816882	+	0.568154i
$120$	241.241	+	528.244i	0.183518	+	0.401849i
$121$	7.59835	−	52.8477i	0.00570875	−	0.0397052i
$122$	−476.917	+	140.035i	−0.353918	+	0.103920i
$123$	1859.32	+	1194.91i	1.36300	+	0.875947i
$124$	−142.808	+	312.706i	−0.103424	+	0.226467i
$125$	−119.937	−	35.2166i	−0.0858197	−	0.0251989i
$126$	119.273	+	137.648i	0.0843306	+	0.0973227i
$127$	−63.7917	−	73.6196i	−0.0445717	−	0.0514384i	0.733026	−	0.680201i	$-0.238107\pi$
$127$	−63.7917	−	73.6196i	−0.0445717	−	0.0514384i	−0.777598	+	0.628762i	$0.783562\pi$
$128$	−950.736	−	279.161i	−0.656516	−	0.192770i
$129$	220.101	−	481.954i	0.150224	−	0.328944i
$130$	−143.809	−	92.4204i	−0.0970222	−	0.0623524i
$131$	−2273.66	+	667.606i	−1.51642	+	0.445260i	−0.930861	−	0.365373i	$-0.880941\pi$
$131$	−2273.66	+	667.606i	−1.51642	+	0.445260i	−0.585554	+	0.810633i	$0.699123\pi$
$132$	32.3788	−	225.199i	0.0213501	−	0.148493i
$133$	1073.92	+	2351.55i	0.700153	+	1.53312i
$134$	−65.3047	−	454.204i	−0.0421005	−	0.292816i
$135$	623.682	−	400.816i	0.397615	−	0.255532i
$136$	−625.809	+	722.222i	−0.394579	+	0.455368i
$137$	−1614.76			−1.00699			−0.503496	−	0.863998i	$-0.667953\pi$
$137$	−1614.76			−1.00699			−0.503496	+	0.863998i	$0.667953\pi$
$138$	−1343.20	+	292.022i	−0.828554	+	0.180135i
$139$	548.916			0.334953			0.167476	−	0.985876i	$-0.446438\pi$
$139$	548.916			0.334953			0.167476	+	0.985876i	$0.446438\pi$
$140$	81.1858	−	93.6935i	0.0490104	−	0.0565610i
$141$	687.542	−	441.857i	0.410649	−	0.263908i
$142$	279.356	+	1942.96i	0.165092	+	1.14824i
$143$	196.420	+	430.101i	0.114864	+	0.251516i
$144$	−27.6041	+	191.991i	−0.0159746	+	0.111106i
$145$	−1274.09	+	374.106i	−0.729706	+	0.214261i
$146$	−1240.09	−	796.957i	−0.702948	−	0.451758i
$147$	−19.5592	+	42.8286i	−0.0109742	+	0.0240302i
$148$	−505.349	−	148.384i	−0.280672	−	0.0824127i
$149$	788.436	+	909.904i	0.433498	+	0.500283i	0.929902	−	0.367808i	$-0.119892\pi$
$149$	788.436	+	909.904i	0.433498	+	0.500283i	−0.496404	+	0.868092i	$0.665346\pi$
$150$	204.017	+	235.448i	0.111053	+	0.128161i
$151$	1451.88	+	426.311i	0.782467	+	0.229753i	0.648482	−	0.761230i	$-0.275404\pi$
$151$	1451.88	+	426.311i	0.782467	+	0.229753i	0.133985	+	0.990983i	$0.457223\pi$
$152$	−1377.32	+	3015.90i	−0.734968	+	1.60935i
$153$	125.222	+	80.4750i	0.0661671	+	0.0425230i
$154$	1664.82	−	488.835i	0.871137	−	0.255789i
$155$	−185.299	+	1288.78i	−0.0960229	+	0.667854i
$156$	−34.9783	−	76.5918i	−0.0179520	−	0.0393093i
$157$	−8.91074	−	61.9756i	−0.00452965	−	0.0315044i	0.987431	−	0.158049i	$-0.0505204\pi$
$157$	−8.91074	−	61.9756i	−0.00452965	−	0.0315044i	−0.991961	+	0.126545i	$0.959611\pi$
$158$	1382.65	−	888.578i	0.696190	−	0.447414i
$159$	722.155	−	833.412i	0.360193	−	0.415685i
$160$	295.477			0.145997
$161$	1241.34	+	1658.66i	0.607649	+	0.811931i
$162$	−1585.92			−0.769147
$163$	789.539	−	911.176i	0.379395	−	0.437846i	−0.533649	−	0.845706i	$-0.679180\pi$
$163$	789.539	−	911.176i	0.379395	−	0.437846i	0.913044	+	0.407861i	$0.133725\pi$
$164$	509.072	−	327.161i	0.242389	−	0.155774i
$165$	−122.634	−	852.940i	−0.0578610	−	0.402432i
$166$	−176.495	−	386.469i	−0.0825219	−	0.180698i
$167$	404.055	−	2810.26i	0.187226	−	1.30218i	−0.651924	−	0.758284i	$-0.726038\pi$
$167$	404.055	−	2810.26i	0.187226	−	1.30218i	0.839150	−	0.543900i	$-0.183053\pi$
$168$	−2093.07	+	614.580i	−0.961212	+	0.282237i
$169$	−1701.02	−	1093.18i	−0.774248	−	0.497579i
$170$	−212.972	+	466.344i	−0.0960837	+	0.210394i
$171$	495.510	+	145.495i	0.221594	+	0.0650659i
$172$	−94.9982	−	109.634i	−0.0421136	−	0.0486017i
$173$	2054.80	+	2371.37i	0.903027	+	1.04215i	0.998906	+	0.0467553i	$0.0148881\pi$
$173$	2054.80	+	2371.37i	0.903027	+	1.04215i	−0.0958798	+	0.995393i	$0.530566\pi$
$174$	3175.46	+	932.398i	1.38351	+	0.406235i
$175$	195.059	−	427.119i	0.0842574	−	0.184498i
$176$	1554.48	+	999.001i	0.665756	+	0.427855i
$177$	4088.43	−	1200.47i	1.73619	−	0.509790i
$178$	306.507	−	2131.80i	0.129066	−	0.897671i
$179$	212.640	+	465.616i	0.0887902	+	0.194424i	0.948818	−	0.315824i	$-0.102281\pi$
$179$	212.640	+	465.616i	0.0887902	+	0.194424i	−0.860027	+	0.510248i	$0.829554\pi$
$180$	−3.52455	−	24.5138i	−0.00145947	−	0.0101508i
$181$	−1164.66	+	748.481i	−0.478278	+	0.307371i	−0.757476	−	0.652863i	$-0.773568\pi$
$181$	−1164.66	+	748.481i	−0.478278	+	0.307371i	0.279198	+	0.960234i	$0.409931\pi$
$182$	420.514	−	485.299i	0.171267	−	0.197653i
$183$	−927.277			−0.374570
$184$	−565.112	+	2596.25i	−0.226416	+	1.04021i
$185$	−1994.81			−0.792764
$186$	2125.09	−	2452.49i	0.837738	−	0.966801i
$187$	1192.92	−	766.646i	0.466499	−	0.299800i
$188$	−31.8456	−	221.491i	−0.0123541	−	0.0859248i
$189$	1156.89	+	2533.23i	0.445244	+	0.974949i
$190$	−253.133	+	1760.58i	−0.0966538	+	0.672242i
$191$	−3469.31	+	1018.68i	−1.31430	+	0.385913i	−0.862432	−	0.506173i	$-0.831060\pi$
$191$	−3469.31	+	1018.68i	−1.31430	+	0.385913i	−0.451866	+	0.892086i	$0.649241\pi$
$192$	−2297.04	−	1476.22i	−0.863410	−	0.554880i
$193$	−1236.87	+	2708.38i	−0.461306	+	1.01012i	0.525882	+	0.850558i	$0.323735\pi$
$193$	−1236.87	+	2708.38i	−0.461306	+	1.01012i	−0.987188	+	0.159562i	$0.948992\pi$
$194$	−818.939	−	240.462i	−0.303074	−	0.0889907i
$195$	−208.842	−	241.016i	−0.0766946	−	0.0885103i
$196$	8.44196	+	9.74254i	0.00307652	+	0.00355049i
$197$	−1649.54	−	484.348i	−0.596572	−	0.175169i	−0.0305131	−	0.999534i	$-0.509714\pi$
$197$	−1649.54	−	484.348i	−0.596572	−	0.175169i	−0.566058	+	0.824365i	$0.691532\pi$
$198$	143.989	−	315.293i	0.0516812	−	0.113166i
$199$	−2018.99	−	1297.52i	−0.719207	−	0.462206i	0.129154	−	0.991625i	$-0.458774\pi$
$199$	−2018.99	−	1297.52i	−0.719207	−	0.462206i	−0.848361	+	0.529418i	$0.822410\pi$
$200$	577.814	−	169.661i	0.204288	−	0.0599844i
$201$	121.830	−	847.345i	0.0427523	−	0.297349i
$202$	1056.46	+	2313.33i	0.367982	+	0.805769i
$203$	−709.874	−	4937.28i	−0.245435	−	1.70704i
$204$	−212.434	+	136.523i	−0.0729088	+	0.0468556i
$205$	1500.90	−	1732.14i	0.511354	−	0.590134i
$206$	−2422.61			−0.819374
$207$	412.805	+	29.5752i	0.138609	+	0.00993053i
$208$	683.854			0.227965
$209$	3221.76	−	3718.11i	1.06629	−	1.23056i
$210$	−984.501	+	632.700i	−0.323510	+	0.207907i
$211$	236.640	+	1645.87i	0.0772083	+	0.536996i	0.991314	+	0.131519i	$0.0419854\pi$
$211$	236.640	+	1645.87i	0.0772083	+	0.536996i	−0.914105	+	0.405477i	$0.867106\pi$
$212$	−125.427	−	274.646i	−0.0406337	−	0.0889753i
$213$	−521.155	+	3624.71i	−0.167648	+	1.16601i
$214$	493.067	−	144.778i	0.157502	−	0.0462467i
$215$	−462.216	−	297.048i	−0.146618	−	0.0942256i
$216$	−1483.73	+	3248.91i	−0.467384	+	1.02343i
$217$	−4692.85	−	1377.95i	−1.46807	−	0.431065i
$218$	−322.404	−	372.074i	−0.100165	−	0.115596i
$219$	−1800.88	−	2078.32i	−0.555671	−	0.641278i
$220$	−226.375	−	66.4698i	−0.0693738	−	0.0203700i
$221$	218.009	−	477.373i	0.0663569	−	0.145301i
$222$	4182.49	+	2687.92i	1.26446	+	0.812619i
$223$	−1516.89	+	445.400i	−0.455510	+	0.133750i	−0.501435	−	0.865195i	$-0.667194\pi$
$223$	−1516.89	+	445.400i	−0.455510	+	0.133750i	0.0459255	+	0.998945i	$0.485376\pi$
$224$	−157.960	+	1098.63i	−0.0471167	+	0.327704i
$225$	−38.9662	−	85.3240i	−0.0115455	−	0.0252812i
$226$	243.496	+	1693.55i	0.0716687	+	0.498467i
$227$	859.460	−	552.342i	0.251297	−	0.161499i	−0.408928	−	0.912567i	$-0.634097\pi$
$227$	859.460	−	552.342i	0.251297	−	0.161499i	0.660225	+	0.751068i	$0.270461\pi$
$228$	−573.727	+	662.117i	−0.166649	+	0.192323i
$229$	−2116.30			−0.610695			−0.305347	−	0.952241i	$-0.598773\pi$
$229$	−2116.30			−0.610695			−0.305347	+	0.952241i	$0.598773\pi$
$230$	101.515	+	1421.81i	0.0291030	+	0.407615i
$231$	3236.94			0.921969
$232$	4189.32	−	4834.73i	1.18553	−	1.36817i
$233$	1109.98	−	713.342i	0.312092	−	0.200569i	−0.375213	−	0.926939i	$-0.622430\pi$
$233$	1109.98	−	713.342i	0.312092	−	0.200569i	0.687304	+	0.726370i	$0.258794\pi$
$234$	−18.2560	−	126.973i	−0.00510013	−	0.0354722i
$235$	−352.073	−	770.931i	−0.0977306	−	0.214000i
$236$	166.032	−	1154.77i	0.0457955	−	0.318515i
$237$	2941.96	−	863.838i	0.806334	−	0.236761i
$238$	−1620.09	−	1041.17i	−0.441240	−	0.283568i
$239$	−1353.07	+	2962.82i	−0.366205	+	0.801878i	0.633401	+	0.773824i	$0.281658\pi$
$239$	−1353.07	+	2962.82i	−0.366205	+	0.801878i	−0.999606	+	0.0280542i	$0.991069\pi$
$240$	−1195.81	−	351.122i	−0.321622	−	0.0944367i
$241$	1542.04	+	1779.60i	0.412163	+	0.475661i	0.923434	−	0.383758i	$-0.125370\pi$
$241$	1542.04	+	1779.60i	0.412163	+	0.475661i	−0.511271	+	0.859420i	$0.670825\pi$
$242$	90.3653	+	104.287i	0.0240037	+	0.0277018i
$243$	1002.46	+	294.349i	0.264641	+	0.0777057i
$244$	−105.467	+	230.941i	−0.0276715	+	0.0605922i
$245$	41.0745	+	26.3970i	0.0107108	+	0.00688344i
$246$	−5480.90	+	1609.34i	−1.42053	+	0.417104i
$247$	259.120	−	1802.22i	0.0667506	−	0.464261i
$248$	−2605.80	−	5705.90i	−0.667211	−	1.46099i
$249$	−112.800	−	784.539i	−0.0287084	−	0.199671i
$250$	271.782	−	174.664i	0.0687560	−	0.0441868i
$251$	−1211.29	+	1397.90i	−0.304606	+	0.351534i	−0.887329	−	0.461137i	$-0.847442\pi$
$251$	−1211.29	+	1397.90i	−0.304606	+	0.351534i	0.582723	+	0.812671i	$0.301987\pi$
$252$	93.0308			0.0232555
$253$	1889.95	−	3460.17i	0.469644	−	0.859838i
$254$	251.767			0.0621940
$255$	−626.323	+	722.815i	−0.153811	+	0.177508i
$256$	−1656.83	+	1064.78i	−0.404499	+	0.259956i
$257$	959.019	+	6670.12i	0.232770	+	1.61895i	0.686029	+	0.727574i	$0.259352\pi$
$257$	959.019	+	6670.12i	0.232770	+	1.61895i	−0.453259	+	0.891379i	$0.649739\pi$
$258$	568.861	+	1245.63i	0.137270	+	0.300580i
$259$	1066.41	−	7417.05i	0.255844	−	1.77943i
$260$	−83.7791	+	24.5998i	−0.0199837	+	0.00586774i
$261$	−838.263	−	538.719i	−0.198801	−	0.127762i
$262$	2544.19	−	5571.00i	0.599926	−	1.31365i
$263$	−6995.05	−	2053.93i	−1.64005	−	0.481563i	−0.673746	−	0.738963i	$-0.735316\pi$
$263$	−6995.05	−	2053.93i	−1.64005	−	0.481563i	−0.966305	+	0.257400i	$0.917134\pi$
$264$	2718.61	+	3137.44i	0.633783	+	0.731425i
$265$	−748.873	−	864.245i	−0.173596	−	0.200340i
$266$	−6410.82	−	1882.39i	−1.47772	−	0.433897i
$267$	1669.10	−	3654.81i	0.382573	−	0.837718i
$268$	−197.177	−	126.718i	−0.0449422	−	0.0288826i
$269$	1108.18	−	325.390i	0.251178	−	0.0737524i	−0.153720	−	0.988114i	$-0.549125\pi$
$269$	1108.18	−	325.390i	0.251178	−	0.0737524i	0.404898	+	0.914362i	$0.367307\pi$
$270$	−272.691	+	1896.61i	−0.0614645	+	0.427495i
$271$	−2550.63	−	5585.11i	−0.571734	−	1.25192i	−0.945869	−	0.324548i	$-0.894788\pi$
$271$	−2550.63	−	5585.11i	−0.571734	−	1.25192i	0.374135	−	0.927374i	$-0.377940\pi$
$272$	−291.874	−	2030.03i	−0.0650642	−	0.452531i
$273$	1007.78	−	647.664i	0.223421	−	0.143584i
$274$	2733.00	−	3154.05i	0.602579	−	0.695413i
$275$	−893.591			−0.195948
$276$	−336.559	+	616.183i	−0.0734003	+	0.134384i
$277$	7245.50			1.57162			0.785812	−	0.618465i	$-0.212245\pi$
$277$	7245.50			1.57162			0.785812	+	0.618465i	$0.212245\pi$
$278$	−929.049	+	1072.18i	−0.200434	+	0.231313i
$279$	−821.949	+	528.234i	−0.176376	+	0.113350i
$280$	321.936	+	2239.11i	0.0687119	+	0.477902i
$281$	2743.96	+	6008.44i	0.582530	+	1.27556i	0.939852	+	0.341582i	$0.110963\pi$
$281$	2743.96	+	6008.44i	0.582530	+	1.27556i	−0.357322	+	0.933981i	$0.616310\pi$
$282$	−300.612	+	2090.80i	−0.0634794	+	0.441509i
$283$	5361.34	−	1574.23i	1.12614	−	0.330666i	0.334953	−	0.942235i	$-0.391279\pi$
$283$	5361.34	−	1574.23i	1.12614	−	0.330666i	0.791191	+	0.611569i	$0.209461\pi$
$284$	843.470	+	542.065i	0.176235	+	0.113259i
$285$	−1378.45	+	3018.38i	−0.286499	+	0.627345i
$286$	−1172.55	−	344.291i	−0.242427	−	0.0711830i
$287$	5638.01	+	6506.61i	1.15959	+	1.33823i
$288$	145.200	+	167.570i	0.0297084	+	0.0342853i
$289$	3203.85	+	940.737i	0.652118	+	0.191479i
$290$	1425.69	−	3121.82i	0.288687	−	0.632136i
$291$	−1339.51	−	860.850i	−0.269840	−	0.173416i
$292$	−722.441	+	212.128i	−0.144787	+	0.0425132i
$293$	679.602	−	4726.73i	0.135504	−	0.942453i	−0.802703	−	0.596379i	$-0.796606\pi$
$293$	679.602	−	4726.73i	0.135504	−	0.942453i	0.938207	−	0.346074i	$-0.112485\pi$
$294$	−50.5516	−	110.692i	−0.0100280	−	0.0219582i
$295$	−628.843	−	4373.70i	−0.124111	−	0.863208i
$296$	8084.71	−	5195.73i	1.58755	−	1.02025i
$297$	3470.68	−	4005.37i	0.678078	−	0.782543i
$298$	−3111.73			−0.604891
$299$	−103.916	−	1455.44i	−0.0200990	−	0.281505i
$300$	159.130			0.0306245
$301$	1351.57	−	1559.80i	0.258815	−	0.298689i
$302$	−3290.03	+	2114.38i	−0.626888	+	0.402876i
$303$	675.197	+	4696.10i	0.128017	+	0.890376i
$304$	−2955.87	−	6472.46i	−0.557668	−	1.22112i
$305$	−136.848	+	951.796i	−0.0256914	+	0.178687i
$306$	−369.129	+	108.386i	−0.0689598	+	0.0202484i
$307$	5937.99	+	3816.11i	1.10391	+	0.709437i	0.959957	−	0.280148i	$-0.0903837\pi$
$307$	5937.99	+	3816.11i	1.10391	+	0.709437i	0.143948	+	0.989585i	$0.454020\pi$
$308$	368.165	−	806.169i	0.0681109	−	0.149142i
$309$	−4336.44	−	1273.29i	−0.798354	−	0.234418i
$310$	−2203.71	−	2543.22i	−0.403750	−	0.465952i
$311$	2956.24	+	3411.69i	0.539014	+	0.622055i	0.958288	−	0.285805i	$-0.0922609\pi$
$311$	2956.24	+	3411.69i	0.539014	+	0.622055i	−0.419274	+	0.907860i	$0.637715\pi$
$312$	1474.16	+	432.854i	0.267494	+	0.0785433i
$313$	−4320.07	+	9459.63i	−0.780142	+	1.70827i	−0.0772122	+	0.997015i	$0.524602\pi$
$313$	−4320.07	+	9459.63i	−0.780142	+	1.70827i	−0.702930	+	0.711259i	$0.748125\pi$
$314$	136.136	+	87.4896i	0.0244670	+	0.0157240i
$315$	338.080	−	99.2694i	0.0604720	−	0.0177562i
$316$	119.474	−	830.957i	0.0212687	−	0.147927i
$317$	845.924	+	1852.31i	0.149880	+	0.328190i	0.969648	−	0.244504i	$-0.0786253\pi$
$317$	845.924	+	1852.31i	0.149880	+	0.328190i	−0.819769	+	0.572695i	$0.805898\pi$
$318$	405.617	+	2821.13i	0.0715278	+	0.497487i
$319$	−7985.72	+	5132.11i	−1.40161	+	0.900762i
$320$	−1854.25	+	2139.92i	−0.323924	+	0.373829i
$321$	958.679			0.166692
$322$	−5340.80	−	382.639i	−0.924321	−	0.0662225i
$323$	−5460.50			−0.940651
$324$	−530.476	+	612.202i	−0.0909595	+	0.104973i
$325$	−278.210	+	178.794i	−0.0474840	+	0.0305161i
$326$	443.464	+	3084.36i	0.0753411	+	0.524009i
$327$	−381.542	−	835.460i	−0.0645239	−	0.141288i
$328$	−1571.41	+	10929.4i	−0.264533	+	1.83987i
$329$	3054.67	−	896.933i	0.511883	−	0.150302i
$330$	1873.58	+	1204.08i	0.312537	+	0.200855i
$331$	−4784.71	+	10477.1i	−0.794536	+	1.73979i	−0.131353	+	0.991336i	$0.541932\pi$
$331$	−4784.71	+	10477.1i	−0.794536	+	1.73979i	−0.663184	+	0.748456i	$0.730795\pi$
$332$	−208.222	−	61.1394i	−0.0344206	−	0.0101068i
$333$	−980.270	−	1131.29i	−0.161317	−	0.186169i
$334$	4805.33	+	5545.64i	0.787233	+	0.908515i
$335$	−851.770	−	250.102i	−0.138917	−	0.0407897i
$336$	1944.80	−	4258.53i	0.315767	−	0.691434i
$337$	−4012.09	−	2578.41i	−0.648524	−	0.416781i	0.174603	−	0.984639i	$-0.444136\pi$
$337$	−4012.09	−	2578.41i	−0.648524	−	0.416781i	−0.823127	+	0.567858i	$0.807772\pi$
$338$	5014.29	−	1472.33i	0.806927	−	0.236935i
$339$	−454.256	+	3159.42i	−0.0727782	+	0.506184i
$340$	108.782	+	238.200i	0.0173516	+	0.0379947i
$341$	1324.65	+	9213.15i	0.210363	+	1.46311i
$342$	−1122.85	+	721.612i	−0.177534	+	0.114094i
$343$	4098.66	−	4730.11i	0.645210	−	0.744612i
$344$	2647.00			0.414874
$345$	−565.576	+	2598.38i	−0.0882597	+	0.405484i
$346$	−8109.70			−1.26006
$347$	−2573.06	+	2969.47i	−0.398067	+	0.459394i	−0.919031	−	0.394185i	$-0.871027\pi$
$347$	−2573.06	+	2969.47i	−0.398067	+	0.459394i	0.520964	+	0.853579i	$0.325572\pi$
$348$	1422.09	−	913.920i	0.219057	−	0.140779i
$349$	785.624	+	5464.14i	0.120497	+	0.838076i	0.956995	+	0.290105i	$0.0936903\pi$
$349$	785.624	+	5464.14i	0.120497	+	0.838076i	−0.836498	+	0.547971i	$0.815401\pi$
$350$	504.137	+	1103.91i	0.0769922	+	0.168589i
$351$	279.140	−	1941.46i	0.0424484	−	0.295235i
$352$	2026.72	−	595.100i	0.306888	−	0.0901106i
$353$	929.847	+	597.576i	0.140200	+	0.0901014i	0.608861	−	0.793277i	$-0.291627\pi$
$353$	929.847	+	597.576i	0.140200	+	0.0901014i	−0.468660	+	0.883378i	$0.655263\pi$
$354$	−4574.89	+	10017.6i	−0.686872	+	1.50404i
$355$	3643.64	+	1069.87i	0.544745	+	0.159952i
$356$	−720.400	−	831.386i	−0.107250	−	0.123774i
$357$	−2352.73	−	2715.19i	−0.348794	−	0.402530i
$358$	−1269.37	−	372.721i	−0.187397	−	0.0550249i
$359$	1401.20	−	3068.20i	0.205996	−	0.451068i	−0.778231	−	0.627978i	$-0.783883\pi$
$359$	1401.20	−	3068.20i	0.205996	−	0.451068i	0.984227	+	0.176910i	$0.0566101\pi$
$360$	380.162	+	244.315i	0.0556563	+	0.0357682i
$361$	−11596.3	+	3404.97i	−1.69067	+	0.496424i
$362$	509.220	−	3541.71i	0.0739338	−	0.514221i
$363$	106.941	+	234.168i	0.0154626	+	0.0338585i
$364$	−46.6785	−	324.656i	−0.00672148	−	0.0467489i
$365$	−2399.05	+	1541.77i	−0.344033	+	0.221096i
$366$	1569.43	−	1811.22i	0.224141	−	0.258672i
$367$	−8095.00			−1.15138			−0.575689	−	0.817669i	$-0.695266\pi$
$367$	−8095.00			−1.15138			−0.575689	+	0.817669i	$0.695266\pi$
$368$	−3416.70	−	4565.34i	−0.483989	−	0.646698i
$369$	1719.88			0.242638
$370$	3376.25	−	3896.40i	0.474386	−	0.547470i
$371$	3613.76	−	2322.42i	0.505706	−	0.324997i
$372$	−235.892	−	1640.67i	−0.0328775	−	0.228668i
$373$	555.602	+	1216.60i	0.0771259	+	0.168882i	0.944267	−	0.329180i	$-0.106772\pi$
$373$	555.602	+	1216.60i	0.0771259	+	0.168882i	−0.867141	+	0.498062i	$0.834045\pi$
$374$	−521.579	+	3627.66i	−0.0721128	+	0.501556i
$375$	578.288	−	169.801i	0.0796338	−	0.0233826i
$376$	3434.89	+	2207.47i	0.471120	+	0.302770i
$377$	−1459.40	+	3195.65i	−0.199372	+	0.436563i
$378$	−6906.13	−	2027.82i	−0.939717	−	0.275926i
$379$	943.030	+	1088.32i	0.127811	+	0.147501i	0.816048	−	0.577984i	$-0.196161\pi$
$379$	943.030	+	1088.32i	0.127811	+	0.147501i	−0.688237	+	0.725486i	$0.741615\pi$
$380$	594.953	+	686.613i	0.0803170	+	0.0926908i
$381$	450.661	+	132.326i	0.0605986	+	0.0177933i
$382$	3882.11	−	8500.64i	0.519963	−	1.13856i
$383$	12266.7	+	7883.32i	1.63655	+	1.05175i	0.943773	+	0.330596i	$0.107250\pi$
$383$	12266.7	+	7883.32i	1.63655	+	1.05175i	0.692778	+	0.721151i	$0.256387\pi$
$384$	4584.09	−	1346.01i	0.609194	−	0.178876i
$385$	477.707	−	3322.53i	0.0632369	−	0.439823i
$386$	−3196.75	−	6999.91i	−0.421530	−	0.923021i
$387$	−58.6764	−	408.103i	−0.00770720	−	0.0536048i
$388$	−366.751	+	235.697i	−0.0479871	+	0.0308394i
$389$	6797.88	−	7845.17i	0.886032	−	1.02254i	−0.113548	−	0.993533i	$-0.536221\pi$
$389$	6797.88	−	7845.17i	0.886032	−	1.02254i	0.999579	−	0.0290025i	$-0.00923308\pi$
$390$	824.236			0.107018
$391$	−4276.12	+	929.665i	−0.553076	+	0.120243i
$392$	−235.224			−0.0303077
$393$	7482.12	−	8634.83i	0.960364	−	1.10832i
$394$	3737.93	−	2402.22i	0.477954	−	0.307163i
$395$	−452.505	−	3147.24i	−0.0576405	−	0.400898i
$396$	−73.5470	−	161.046i	−0.00933302	−	0.0204365i
$397$	414.776	−	2884.83i	0.0524358	−	0.364699i	−0.946662	−	0.322228i	$-0.895568\pi$
$397$	414.776	−	2884.83i	0.0524358	−	0.364699i	0.999098	−	0.0424705i	$-0.0135228\pi$
$398$	5951.58	−	1747.54i	0.749562	−	0.220091i
$399$	−10485.9	−	6738.91i	−1.31567	−	0.845533i
$400$	−536.884	+	1175.61i	−0.0671105	+	0.146951i
$401$	−4255.87	−	1249.63i	−0.529995	−	0.155620i	0.00577719	−	0.999983i	$-0.498161\pi$
$401$	−4255.87	−	1249.63i	−0.529995	−	0.155620i	−0.535772	+	0.844363i	$0.679979\pi$
$402$	1448.89	+	1672.11i	0.179762	+	0.207456i
$403$	2255.83	+	2603.37i	0.278836	+	0.321794i
$404$	1246.37	+	365.968i	0.153489	+	0.0450683i
$405$	−1274.53	+	2790.83i	−0.156375	+	0.342414i
$406$	10845.3	+	6969.85i	1.32572	+	0.851990i
$407$	−13682.7	+	4017.61i	−1.66640	+	0.489301i
$408$	655.746	−	4560.81i	0.0795693	−	0.553417i
$409$	−5767.10	−	12628.2i	−0.697224	−	1.52671i	−0.843305	−	0.537435i	$-0.819393\pi$
$409$	−5767.10	−	12628.2i	−0.697224	−	1.52671i	0.146081	−	0.989273i	$-0.453334\pi$
$410$	843.020	+	5863.33i	0.101546	+	0.706267i
$411$	6549.77	−	4209.28i	0.786074	−	0.505179i
$412$	−810.339	+	935.181i	−0.0968993	+	0.111828i
$413$	16598.3			1.97760
$414$	−756.448	+	756.263i	−0.0898005	+	0.0897785i
$415$	−821.931			−0.0972217
$416$	511.927	−	590.795i	0.0603348	−	0.0696301i
$417$	−2226.51	+	1430.89i	−0.261470	+	0.168036i
$418$	1809.58	+	12585.9i	0.211745	+	1.47272i
$419$	−2164.92	−	4740.52i	−0.252419	−	0.552720i	0.740425	−	0.672139i	$-0.234624\pi$
$419$	−2164.92	−	4740.52i	−0.252419	−	0.552720i	−0.992844	+	0.119419i	$0.961897\pi$
$420$	−85.0696	+	591.672i	−0.00988326	+	0.0687396i
$421$	375.995	−	110.402i	0.0435270	−	0.0127807i	−0.259897	−	0.965636i	$-0.583688\pi$
$421$	375.995	−	110.402i	0.0435270	−	0.0127807i	0.303424	+	0.952856i	$0.401870\pi$
$422$	−3615.33	−	2323.43i	−0.417042	−	0.268016i
$423$	264.197	−	578.510i	0.0303681	−	0.0664968i
$424$	5286.12	+	1552.14i	0.605464	+	0.177780i
$425$	649.495	+	749.557i	0.0741297	+	0.0855503i
$426$	−6197.97	−	7152.84i	−0.704912	−	0.813512i
$427$	−3465.79	−	1017.65i	−0.392789	−	0.115333i
$428$	109.039	−	238.762i	0.0123145	−	0.0269649i
$429$	−1917.89	−	1232.55i	−0.215843	−	0.138714i
$430$	1362.52	−	400.072i	0.152806	−	0.0448679i
$431$	1538.31	−	10699.2i	0.171921	−	1.19573i	−0.702901	−	0.711288i	$-0.748112\pi$
$431$	1538.31	−	10699.2i	0.171921	−	1.19573i	0.874821	−	0.484446i	$-0.160979\pi$
$432$	−3184.25	−	6972.53i	−0.354635	−	0.776541i
$433$	−117.587	−	817.838i	−0.0130505	−	0.0907685i	0.982255	−	0.187549i	$-0.0600545\pi$
$433$	−117.587	−	817.838i	−0.0130505	−	0.0907685i	−0.995306	+	0.0967809i	$0.969145\pi$
$434$	10634.2	−	6834.20i	1.17617	−	0.755881i
$435$	4192.76	−	4838.70i	0.462132	−	0.533328i
$436$	−251.470			−0.0276221
$437$	−13326.1	+	7274.46i	−1.45875	+	0.796304i
$438$	7107.53			0.775367
$439$	−9210.92	+	10630.0i	−1.00140	+	1.15567i	−0.0136023	+	0.999907i	$0.504330\pi$
$439$	−9210.92	+	10630.0i	−1.00140	+	1.15567i	−0.987794	+	0.155766i	$0.950216\pi$
$440$	3621.61	−	2327.47i	0.392394	−	0.252177i
$441$	5.21425	+	36.2659i	0.000563033	+	0.00391598i
$442$	563.454	+	1233.79i	0.0606352	+	0.132773i
$443$	382.373	−	2659.46i	0.0410092	−	0.285225i	−0.958989	−	0.283443i	$-0.908523\pi$
$443$	382.373	−	2659.46i	0.0410092	−	0.285225i	0.999998	−	0.00178260i	$-0.000567419\pi$
$444$	2436.60	−	715.450i	0.260441	−	0.0764725i
$445$	−3505.12	−	2252.61i	−0.373391	−	0.239964i
$446$	1697.38	−	3716.75i	0.180209	−	0.394603i
$447$	−5569.96	−	1635.49i	−0.589374	−	0.173056i
$448$	−6965.32	−	8038.41i	−0.734555	−	0.847722i
$449$	2018.68	+	2329.68i	0.212177	+	0.244865i	0.851855	−	0.523778i	$-0.175478\pi$
$449$	2018.68	+	2329.68i	0.212177	+	0.244865i	−0.639678	+	0.768643i	$0.720932\pi$
$450$	232.611	+	68.3009i	0.0243676	+	0.00715496i
$451$	6806.36	−	14903.9i	0.710641	−	1.55609i
$452$	735.197	+	472.482i	0.0765061	+	0.0491675i
$453$	−7000.42	+	2055.51i	−0.726067	+	0.213192i
$454$	−375.779	+	2613.60i	−0.0388463	+	0.270182i
$455$	−516.060	−	1130.01i	−0.0531720	−	0.116430i
$456$	−2275.07	−	15823.4i	−0.233640	−	1.62500i
$457$	−5572.57	+	3581.27i	−0.570402	+	0.366575i	−0.793825	−	0.608147i	$-0.791913\pi$
$457$	−5572.57	+	3581.27i	−0.570402	+	0.366575i	0.223423	+	0.974722i	$0.428277\pi$
$458$	3581.87	−	4133.70i	0.365437	−	0.421736i
$459$	−5882.38			−0.598183
$460$	582.806	+	436.395i	0.0590728	+	0.0442326i
$461$	7099.54			0.717264			0.358632	−	0.933479i	$-0.383243\pi$
$461$	7099.54			0.717264			0.358632	+	0.933479i	$0.383243\pi$
$462$	−5478.57	+	6322.61i	−0.551701	+	0.636697i
$463$	−6124.22	+	3935.80i	−0.614723	+	0.395058i	−0.810625	−	0.585565i	$-0.800873\pi$
$463$	−6124.22	+	3935.80i	−0.614723	+	0.395058i	0.195903	+	0.980623i	$0.437236\pi$
$464$	1953.87	+	13589.5i	0.195488	+	1.35965i
$465$	−2607.94	−	5710.59i	−0.260086	−	0.569510i
$466$	−485.314	+	3375.43i	−0.0482441	+	0.335545i
$467$	10303.4	−	3025.36i	1.02096	−	0.299779i	0.271927	−	0.962318i	$-0.412339\pi$
$467$	10303.4	−	3025.36i	1.02096	−	0.299779i	0.749028	+	0.662538i	$0.230521\pi$
$468$	−55.1209	−	35.4240i	−0.00544437	−	0.00349888i
$469$	1385.27	−	3033.33i	0.136388	−	0.298648i
$470$	2101.72	+	617.122i	0.206267	+	0.0605653i
$471$	197.699	+	228.157i	0.0193408	+	0.0223205i
$472$	13940.5	+	16088.1i	1.35945	+	1.56889i
$473$	−3768.67	−	1106.58i	−0.366350	−	0.107570i
$474$	−3292.01	+	7208.50i	−0.319002	+	0.698518i
$475$	2894.76	+	1860.35i	0.279622	+	0.179702i
$476$	−943.822	+	277.131i	−0.0908824	+	0.0266855i
$477$	122.125	−	849.398i	0.0117227	−	0.0815331i
$478$	−3497.08	−	7657.53i	−0.334629	−	0.732735i
$479$	−864.399	−	6012.03i	−0.0824539	−	0.573479i	−0.988606	−	0.150527i	$-0.951903\pi$
$479$	−864.399	−	6012.03i	−0.0824539	−	0.573479i	0.906152	−	0.422952i	$-0.139006\pi$
$480$	−1198.51	+	770.238i	−0.113968	+	0.0732425i
$481$	−3456.09	+	3988.55i	−0.327618	+	0.378092i
$482$	−6085.97			−0.575121
$483$	−9358.87	−	3491.98i	−0.881664	−	0.328966i
$484$	70.4835			0.00661941
$485$	−1081.30	+	1247.88i	−0.101235	+	0.116832i
$486$	−2271.62	+	1459.88i	−0.212022	+	0.136258i
$487$	494.952	+	3442.47i	0.0460542	+	0.320314i	0.999806	+	0.0197176i	$0.00627672\pi$
$487$	494.952	+	3442.47i	0.0460542	+	0.320314i	−0.953751	+	0.300597i	$0.902814\pi$
$488$	−1924.44	−	4213.94i	−0.178515	−	0.390894i
$489$	−827.308	+	5754.05i	−0.0765075	+	0.532121i
$490$	−121.080	+	35.5522i	−0.0111629	+	0.00327773i
$491$	−9367.85	−	6020.35i	−0.861029	−	0.553349i	0.0339678	−	0.999423i	$-0.489186\pi$
$491$	−9367.85	−	6020.35i	−0.861029	−	0.553349i	−0.894996	+	0.446073i	$0.852822\pi$
$492$	−1212.07	+	2654.06i	−0.111066	+	0.243200i
$493$	10109.2	+	2968.33i	0.923520	+	0.271170i
$494$	3081.65	+	3556.42i	0.280668	+	0.323908i
$495$	−439.120	−	506.772i	−0.0398727	−	0.0460155i
$496$	12916.7	+	3792.69i	1.16931	+	0.343341i
$497$	−5925.83	+	12975.7i	−0.534828	+	1.17111i
$498$	1723.33	+	1107.52i	0.155069	+	0.0996567i
$499$	14542.0	−	4269.92i	1.30459	−	0.383062i	0.445680	−	0.895192i	$-0.352962\pi$
$499$	14542.0	−	4269.92i	1.30459	−	0.383062i	0.858908	+	0.512131i	$0.171144\pi$
$500$	23.4844	−	163.337i	0.00210051	−	0.0146093i
$501$	5686.76	+	12452.3i	0.507117	+	1.11043i
$502$	−680.352	−	4731.95i	−0.0604892	−	0.420712i
$503$	−9871.58	+	6344.08i	−0.875054	+	0.562363i	−0.899295	−	0.437343i	$-0.855920\pi$
$503$	−9871.58	+	6344.08i	−0.875054	+	0.562363i	0.0242408	+	0.999706i	$0.492283\pi$
$504$	−1111.64	+	1282.90i	−0.0982466	+	0.113383i
$505$	4919.92			0.433532
$506$	3559.87	+	9547.96i	0.312758	+	0.838851i
$507$	9749.36			0.854012
$508$	84.2137	−	97.1878i	0.00735508	−	0.00848821i
$509$	−2721.43	+	1748.96i	−0.236985	+	0.152301i	−0.653743	−	0.756716i	$-0.726802\pi$
$509$	−2721.43	+	1748.96i	−0.236985	+	0.152301i	0.416759	+	0.909017i	$0.363166\pi$
$510$	−351.790	−	2446.75i	−0.0305442	−	0.212439i
$511$	−4450.07	−	9744.30i	−0.385244	−	0.843566i
$512$	1852.54	−	12884.7i	0.159905	−	1.11216i
$513$	−19581.8	+	5749.75i	−1.68530	+	0.494849i
$514$	−14651.7	−	9416.07i	−1.25731	−	0.808025i
$515$	−1946.93	+	4263.19i	−0.166587	+	0.364774i
$516$	671.121	+	197.059i	0.0572567	+	0.0168121i
$517$	−3967.60	−	4578.86i	−0.337514	−	0.389512i
$518$	12682.6	+	14636.5i	1.07575	+	1.24148i
$519$	−14516.3	−	4262.36i	−1.22773	−	0.360495i
$520$	661.856	−	1449.26i	0.0558160	−	0.122220i
$521$	−1089.83	−	700.392i	−0.0916438	−	0.0588959i	0.494016	−	0.869453i	$-0.335528\pi$
$521$	−1089.83	−	700.392i	−0.0916438	−	0.0588959i	−0.585660	+	0.810557i	$0.699165\pi$
$522$	2471.04	−	725.562i	0.207192	−	0.0608371i
$523$	−2678.05	+	18626.2i	−0.223906	+	1.55730i	0.499152	+	0.866515i	$0.333645\pi$
$523$	−2678.05	+	18626.2i	−0.223906	+	1.55730i	−0.723058	+	0.690787i	$0.757264\pi$
$524$	−1299.52	−	2845.56i	−0.108340	−	0.237231i
$525$	322.200	+	2240.95i	0.0267847	+	0.186292i
$526$	15851.1	−	10186.9i	1.31396	−	0.844429i
$527$	6765.32	−	7807.59i	0.559207	−	0.645359i
$528$	−8909.43			−0.734343
$529$	−9197.16	+	7965.44i	−0.755910	+	0.654676i
$530$	2955.58			0.242231
$531$	2171.38	−	2505.91i	0.177457	−	0.204797i
$532$	−2871.00	+	1845.08i	−0.233973	+	0.150366i
$533$	−862.957	−	6002.00i	−0.0701291	−	0.487759i
$534$	4313.85	+	9446.01i	0.349585	+	0.765485i
$535$	141.482	−	984.028i	0.0114333	−	0.0795201i
$536$	4103.54	−	1204.91i	0.330683	−	0.0970972i
$537$	−2076.26	−	1334.33i	−0.166848	−	0.107227i
$538$	−1240.03	+	2715.30i	−0.0993711	+	0.217592i
$539$	334.901	+	98.3359i	0.0267629	+	0.00785830i
$540$	640.920	+	739.661i	0.0510756	+	0.0589443i
$541$	−1303.48	−	1504.29i	−0.103587	−	0.119546i	0.701588	−	0.712582i	$-0.252475\pi$
$541$	−1303.48	−	1504.29i	−0.103587	−	0.119546i	−0.805176	+	0.593036i	$0.797929\pi$
$542$	15226.2	+	4470.81i	1.20668	+	0.354313i
$543$	2772.98	−	6071.98i	0.219153	−	0.479878i
$544$	−1972.28	−	1267.50i	−0.155442	−	0.0998967i
$545$	−913.859	+	268.333i	−0.0718264	+	0.0210901i
$546$	−440.631	+	3064.65i	−0.0345371	+	0.240211i
$547$	5244.30	+	11483.4i	0.409927	+	0.897614i	0.996167	+	0.0874768i	$0.0278804\pi$
$547$	5244.30	+	11483.4i	0.409927	+	0.897614i	−0.586240	+	0.810138i	$0.699392\pi$
$548$	−303.372	−	2110.00i	−0.0236486	−	0.164479i
$549$	−607.029	+	390.114i	−0.0471901	+	0.0303272i
$550$	1512.42	−	1745.42i	0.117254	−	0.135318i
$551$	36553.9			2.82622
$552$	−4475.59	−	12004.0i	−0.345098	−	0.925588i
$553$	11943.9			0.918455
$554$	−12263.1	+	14152.4i	−0.940452	+	1.08534i
$555$	8091.35	−	5199.99i	0.618844	−	0.397707i
$556$	103.128	+	717.268i	0.00786616	+	0.0547103i
$557$	3601.99	+	7887.26i	0.274006	+	0.599989i	0.995742	−	0.0921788i	$-0.0293831\pi$
$557$	3601.99	+	7887.26i	0.274006	+	0.599989i	−0.721737	+	0.692168i	$0.756656\pi$
$558$	359.378	−	2499.53i	0.0272647	−	0.189630i
$559$	−1394.74	+	409.534i	−0.105530	+	0.0309865i
$560$	−4084.11	−	2624.70i	−0.308188	−	0.198060i
$561$	−2840.28	+	6219.34i	−0.213755	+	0.468058i
$562$	−16380.3	−	4809.68i	−1.22947	−	0.361004i
$563$	−6112.95	−	7054.72i	−0.457602	−	0.528101i	0.479319	−	0.877641i	$-0.340884\pi$
$563$	−6112.95	−	7054.72i	−0.457602	−	0.528101i	−0.936922	+	0.349539i	$0.886338\pi$
$564$	706.546	+	815.397i	0.0527499	+	0.0608766i
$565$	3175.92	+	932.535i	0.236482	+	0.0694373i
$566$	−5999.26	+	13136.6i	−0.445526	+	0.975566i
$567$	−9695.44	−	6230.88i	−0.718113	−	0.461503i
$568$	−17553.8	+	5154.27i	−1.29673	+	0.380754i
$569$	−1868.87	+	12998.3i	−0.137693	+	0.957673i	0.797446	+	0.603391i	$0.206184\pi$
$569$	−1868.87	+	12998.3i	−0.137693	+	0.957673i	−0.935138	+	0.354282i	$0.884725\pi$
$570$	−3562.66	−	7801.13i	−0.261795	−	0.573252i
$571$	3364.72	+	23402.1i	0.246601	+	1.71515i	0.617583	+	0.786506i	$0.288112\pi$
$571$	3364.72	+	23402.1i	0.246601	+	1.71515i	−0.370982	+	0.928640i	$0.620979\pi$
$572$	−525.109	+	337.467i	−0.0383845	+	0.0246682i
$573$	11416.8	−	13175.7i	0.832361	−	0.960595i
$574$	−22251.6			−1.61805
$575$	2583.62	+	964.000i	0.187381	+	0.0699158i
$576$	−2124.78			−0.153703
$577$	104.108	−	120.147i	0.00751140	−	0.00866861i	−0.751981	−	0.659184i	$-0.770902\pi$
$577$	104.108	−	120.147i	0.00751140	−	0.00866861i	0.759493	+	0.650516i	$0.225447\pi$
$578$	−7260.08	+	4665.77i	−0.522456	+	0.335762i
$579$	−2043.08	−	14209.9i	−0.146645	−	1.01994i
$580$	−728.214	−	1594.57i	−0.0521335	−	0.114156i
$581$	439.398	−	3056.08i	0.0313757	−	0.218223i
$582$	3948.61	−	1159.42i	0.281229	−	0.0825762i
$583$	−6877.25	−	4419.74i	−0.488554	−	0.313974i
$584$	5707.29	−	12497.2i	0.404400	−	0.885512i
$585$	−238.113	−	69.9162i	−0.0168286	−	0.00494133i
$586$	8082.34	+	9327.52i	0.569758	+	0.657536i
$587$	6897.01	+	7959.57i	0.484957	+	0.559671i	0.944511	−	0.328479i	$-0.106536\pi$
$587$	6897.01	+	7959.57i	0.484957	+	0.559671i	−0.459554	+	0.888150i	$0.651991\pi$
$588$	−59.6388	−	17.5115i	−0.00418276	−	0.00122817i
$589$	14889.5	−	32603.4i	1.04161	−	2.28082i
$590$	9607.33	+	6174.25i	0.670385	+	0.430830i
$591$	7953.43	−	2335.34i	0.553571	−	0.162543i
$592$	−2935.21	+	20414.9i	−0.203778	+	1.41731i
$593$	10720.7	+	23475.1i	0.742408	+	1.62565i	0.779552	+	0.626337i	$0.215447\pi$
$593$	10720.7	+	23475.1i	0.742408	+	1.62565i	−0.0371442	+	0.999310i	$0.511826\pi$
$594$	1949.39	+	13558.3i	0.134654	+	0.936540i
$595$	−3134.20	+	2014.23i	−0.215949	+	0.138782i
$596$	−1040.84	+	1201.20i	−0.0715345	+	0.0825553i
$597$	11571.8			0.793300
$598$	3018.73	+	2260.37i	0.206430	+	0.154571i
$599$	7575.58			0.516744			0.258372	−	0.966045i	$-0.416814\pi$
$599$	7575.58			0.516744			0.258372	+	0.966045i	$0.416814\pi$
$600$	−1901.46	+	2194.40i	−0.129378	+	0.149310i
$601$	15224.6	−	9784.27i	1.03332	−	0.664074i	0.0899940	−	0.995942i	$-0.471315\pi$
$601$	15224.6	−	9784.27i	1.03332	−	0.664074i	0.943326	+	0.331868i	$0.107679\pi$
$602$	759.145	+	5279.97i	0.0513961	+	0.357467i
$603$	−276.731	−	605.957i	−0.0186888	−	0.0409228i
$604$	−284.288	+	1977.27i	−0.0191515	+	0.133202i
$605$	256.142	−	75.2101i	0.0172126	−	0.00505409i
$606$	−10315.5	−	6629.38i	−0.691484	−	0.444390i
$607$	−717.164	+	1570.37i	−0.0479552	+	0.105007i	−0.932093	−	0.362219i	$-0.882019\pi$
$607$	−717.164	+	1570.37i	−0.0479552	+	0.105007i	0.884138	+	0.467226i	$0.154747\pi$
$608$	−7804.43	−	2291.59i	−0.520578	−	0.152855i
$609$	15749.7	+	18176.1i	1.04796	+	1.20942i
$610$	−1627.50	−	1878.23i	−0.108025	−	0.124668i
$611$	−2151.43	−	631.717i	−0.142451	−	0.0418274i
$612$	−81.6306	+	178.746i	−0.00539170	+	0.0118062i
$613$	−8712.69	−	5599.31i	−0.574066	−	0.368930i	0.221165	−	0.975236i	$-0.429014\pi$
$613$	−8712.69	−	5599.31i	−0.574066	−	0.368930i	−0.795231	+	0.606307i	$0.792650\pi$
$614$	−17504.0	+	5139.65i	−1.15050	+	0.337816i
$615$	−1572.70	+	10938.4i	−0.103118	+	0.717201i
$616$	6717.85	+	14710.0i	0.439399	+	0.962149i
$617$	−1670.26	−	11616.9i	−0.108983	−	0.757990i	−0.968881	−	0.247526i	$-0.920383\pi$
$617$	−1670.26	−	11616.9i	−0.108983	−	0.757990i	0.859899	−	0.510465i	$-0.170527\pi$
$618$	9826.58	−	6315.16i	0.639617	−	0.411057i
$619$	3574.63	−	4125.34i	0.232111	−	0.267870i	−0.627731	−	0.778430i	$-0.716016\pi$
$619$	3574.63	−	4125.34i	0.232111	−	0.267870i	0.859842	+	0.510560i	$0.170562\pi$
$620$	−1718.86			−0.111341
$621$	−14355.6	+	7836.50i	−0.927653	+	0.506389i
$622$	−11667.4			−0.752124
$623$	10249.4	−	11828.4i	0.659123	−	0.760668i
$624$	−2773.85	+	1782.65i	−0.177953	+	0.114364i
$625$	−88.9468	−	618.638i	−0.00569259	−	0.0395929i
$626$	−11165.4	−	24448.8i	−0.712874	−	1.56098i
$627$	−3375.88	+	23479.8i	−0.215023	+	1.49552i
$628$	79.3093	−	23.2873i	0.00503947	−	0.00147972i
$629$	13315.1	+	8557.11i	0.844052	+	0.542439i
$630$	−378.307	+	828.376i	−0.0239240	+	0.0523862i
$631$	−13448.4	−	3948.79i	−0.848448	−	0.249127i	−0.171524	−	0.985180i	$-0.554869\pi$
$631$	−13448.4	−	3948.79i	−0.848448	−	0.249127i	−0.676924	+	0.736053i	$0.736687\pi$
$632$	10031.3	+	11576.8i	0.631368	+	0.728637i
$633$	−5250.24	−	6059.10i	−0.329666	−	0.380454i
$634$	−5049.81	−	1482.76i	−0.316330	−	0.0928830i
$635$	202.333	−	443.048i	0.0126447	−	0.0276879i
$636$	1224.69	+	787.062i	0.0763557	+	0.0490708i
$637$	123.943	−	36.3930i	0.00770928	−	0.00226365i
$638$	3491.57	−	24284.4i	0.216666	−	1.50694i
$639$	1183.78	+	2592.12i	0.0732859	+	0.160474i
$640$	−705.080	−	4903.94i	−0.0435480	−	0.302883i
$641$	5148.93	−	3309.02i	0.317271	−	0.203898i	−0.372306	−	0.928110i	$-0.621433\pi$
$641$	5148.93	−	3309.02i	0.317271	−	0.203898i	0.689577	+	0.724212i	$0.257796\pi$
$642$	−1622.58	+	1872.56i	−0.0997478	+	0.115115i
$643$	−15995.2			−0.981008			−0.490504	−	0.871439i	$-0.663187\pi$
$643$	−15995.2			−0.981008			−0.490504	+	0.871439i	$0.663187\pi$
$644$	−1934.16	+	1933.68i	−0.118348	+	0.118319i
$645$	2649.17			0.161723
$646$	9241.98	−	10665.8i	0.562881	−	0.649599i
$647$	1712.45	−	1100.52i	0.104054	−	0.0668717i	−0.487579	−	0.873079i	$-0.662120\pi$
$647$	1712.45	−	1100.52i	0.104054	−	0.0668717i	0.591633	+	0.806207i	$0.298483\pi$
$648$	−2103.56	−	14630.6i	−0.127524	−	0.886948i
$649$	−13122.1	−	28733.4i	−0.793663	−	1.73788i
$650$	121.641	−	846.030i	0.00734022	−	0.0510524i
$651$	22627.1	−	6643.93i	1.36225	−	0.399994i
$652$	1338.97	+	860.502i	0.0804264	+	0.0516869i
$653$	−7205.37	+	15777.5i	−0.431804	+	0.945518i	0.561227	+	0.827662i	$0.310329\pi$
$653$	−7205.37	+	15777.5i	−0.431804	+	0.945518i	−0.993031	+	0.117856i	$0.962398\pi$
$654$	2277.64	+	668.776i	0.136182	+	0.0399866i
$655$	−7758.94	−	8954.29i	−0.462850	−	0.534157i
$656$	−15518.2	−	17908.9i	−0.923603	−	1.06589i
$657$	−2053.29	−	602.899i	−0.121927	−	0.0358011i
$658$	−3418.13	+	7484.67i	−0.202512	+	0.443439i
$659$	23435.4	+	15061.0i	1.38530	+	0.890280i	0.999478	−	0.0322915i	$-0.0102805\pi$
$659$	23435.4	+	15061.0i	1.38530	+	0.890280i	0.385825	+	0.922572i	$0.373917\pi$
$660$	1091.50	−	320.492i	0.0643733	−	0.0189017i
$661$	−669.505	+	4656.51i	−0.0393960	+	0.274005i	−0.999992	−	0.00394255i	$-0.998745\pi$
$661$	−669.505	+	4656.51i	−0.0393960	+	0.274005i	0.960596	+	0.277948i	$0.0896541\pi$
$662$	−12366.3	−	27078.4i	−0.726027	−	1.58978i
$663$	360.110	+	2504.62i	0.0210943	+	0.146714i
$664$	3331.18	−	2140.82i	0.194691	−	0.125120i
$665$	−8464.61	+	9768.69i	−0.493600	+	0.569644i
$666$	3868.84			0.225097
$667$	28625.4	−	6223.40i	1.66174	−	0.361276i
$668$	3748.08			0.217092
$669$	4991.77	−	5760.81i	0.288480	−	0.332924i
$670$	1930.15	−	1240.43i	0.111296	−	0.0715255i
$671$	978.287	+	6804.13i	0.0562837	+	0.391462i
$672$	−2223.16	−	4868.05i	−0.127620	−	0.279448i
$673$	−835.412	+	5810.42i	−0.0478496	+	0.332801i	0.951809	+	0.306690i	$0.0992214\pi$
$673$	−835.412	+	5810.42i	−0.0478496	+	0.332801i	−0.999659	+	0.0261111i	$0.991688\pi$
$674$	11826.9	−	3472.68i	0.675896	−	0.198461i
$675$	3118.41	+	2004.08i	0.177819	+	0.114277i
$676$	1108.88	−	2428.11i	0.0630905	−	0.138149i
$677$	−2079.31	−	610.540i	−0.118042	−	0.0346602i	0.222178	−	0.975006i	$-0.428683\pi$
$677$	−2079.31	−	610.540i	−0.118042	−	0.0346602i	−0.340220	+	0.940346i	$0.610502\pi$
$678$	−5402.36	−	6234.66i	−0.306012	−	0.353157i
$679$	−4061.79	−	4687.56i	−0.229569	−	0.264937i
$680$	−4584.64	−	1346.17i	−0.258548	−	0.0759166i
$681$	−2046.32	+	4480.82i	−0.115147	+	0.252137i
$682$	−20237.7	−	13006.0i	−1.13628	−	0.730243i
$683$	−13294.7	+	3903.67i	−0.744813	+	0.218697i	−0.632053	−	0.774925i	$-0.717787\pi$
$683$	−13294.7	+	3903.67i	−0.744813	+	0.218697i	−0.112760	+	0.993622i	$0.535969\pi$
$684$	−97.0241	+	674.817i	−0.00542370	+	0.0377226i
$685$	−3353.97	−	7344.17i	−0.187078	−	0.409644i
$686$	2302.12	+	16011.6i	0.128127	+	0.891144i
$687$	8584.15	−	5516.70i	0.476718	−	0.306368i
$688$	−3720.10	+	4293.23i	−0.206145	+	0.237904i
$689$	−3025.48			−0.167288
$690$	−4118.08	−	5502.52i	−0.227207	−	0.303590i
$691$	3210.38			0.176742			0.0883709	−	0.996088i	$-0.471834\pi$
$691$	3210.38			0.176742			0.0883709	+	0.996088i	$0.471834\pi$
$692$	−2712.62	+	3130.53i	−0.149015	+	0.171972i
$693$	2119.02	−	1361.81i	0.116154	−	0.0746476i
$694$	−1445.23	−	10051.8i	−0.0790490	−	0.549798i
$695$	1140.14	+	2496.56i	0.0622273	+	0.136259i
$696$	−4389.72	+	30531.2i	−0.239069	+	1.66276i
$697$	−17448.7	+	5123.39i	−0.948229	+	0.278425i
$698$	−12002.6	−	7713.60i	−0.650867	−	0.418287i
$699$	−2642.80	+	5786.92i	−0.143004	+	0.313135i
$700$	594.762	+	174.638i	0.0321141	+	0.00942956i
$701$	−22706.9	−	26205.2i	−1.22344	−	1.41192i	−0.881492	−	0.472199i	$-0.843460\pi$
$701$	−22706.9	−	26205.2i	−1.22344	−	1.41192i	−0.341943	−	0.939721i	$-0.611085\pi$
$702$	3319.74	+	3831.19i	0.178484	+	0.205981i
$703$	52688.8	+	15470.8i	2.82674	+	0.830005i
$704$	−8408.74	+	18412.6i	−0.450165	+	0.985724i
$705$	3437.71	+	2209.28i	0.183648	+	0.118023i
$706$	−2741.01	+	804.832i	−0.146118	+	0.0429041i
$707$	−2630.15	+	18293.1i	−0.139911	+	0.973102i
$708$	2336.77	+	5116.80i	0.124041	+	0.271612i
$709$	−3651.57	−	25397.2i	−0.193424	−	1.34529i	−0.822861	−	0.568242i	$-0.807624\pi$
$709$	−3651.57	−	25397.2i	−0.193424	−	1.34529i	0.629437	−	0.777051i	$-0.283285\pi$
$710$	−8256.66	+	5306.24i	−0.436433	+	0.280478i
$711$	1562.49	−	1803.21i	0.0824162	−	0.0951134i
$712$	20073.0			1.05656
$713$	6109.15	−	28066.8i	0.320883	−	1.47421i
$714$	9285.52			0.486697
$715$	−1548.19	+	1786.70i	−0.0809775	+	0.0934530i
$716$	−568.471	+	365.334i	−0.0296714	+	0.0190687i
$717$	−2235.02	−	15544.9i	−0.116414	−	0.809674i
$718$	3621.46	+	7929.90i	0.188234	+	0.412174i
$719$	−592.093	+	4118.10i	−0.0307112	+	0.213601i	−0.999398	−	0.0346834i	$-0.988958\pi$
$719$	−592.093	+	4118.10i	−0.0307112	+	0.213601i	0.968687	+	0.248285i	$0.0798668\pi$
$720$	−930.541	+	273.231i	−0.0481656	+	0.0141427i
$721$	−14810.5	−	9518.11i	−0.765008	−	0.491641i
$722$	12976.1	−	28413.6i	0.668863	−	1.46460i
$723$	−10893.8	−	3198.71i	−0.560367	−	0.164539i
$724$	−1196.85	−	1381.24i	−0.0614372	−	0.0709023i
$725$	−4347.87	−	5017.72i	−0.222726	−	0.257039i
$726$	−638.392	−	187.449i	−0.0326349	−	0.00958247i
$727$	4883.06	−	10692.4i	0.249109	−	0.545474i	−0.743227	−	0.669039i	$-0.766706\pi$
$727$	4883.06	−	10692.4i	0.249109	−	0.545474i	0.992336	+	0.123566i	$0.0394330\pi$
$728$	5034.79	+	3235.66i	0.256321	+	0.164727i
$729$	−20730.0	+	6086.89i	−1.05320	+	0.309246i
$730$	1048.93	−	7295.46i	0.0531816	−	0.369886i
$731$	1810.99	+	3965.52i	0.0916306	+	0.200643i
$732$	−174.212	−	1211.67i	−0.00879654	−	0.0611813i
$733$	−4553.90	+	2926.62i	−0.229471	+	0.147472i	−0.650324	−	0.759657i	$-0.725367\pi$
$733$	−4553.90	+	2926.62i	−0.229471	+	0.147472i	0.420853	+	0.907129i	$0.361731\pi$
$734$	13700.9	−	15811.7i	0.688978	−	0.795123i
$735$	−235.417			−0.0118143
$736$	−6501.80	−	465.818i	−0.325624	−	0.0233292i
$737$	−6346.14			−0.317182
$738$	−2910.93	+	3359.39i	−0.145194	+	0.167562i
$739$	13537.3	−	8699.89i	0.673853	−	0.433059i	−0.158460	−	0.987365i	$-0.550653\pi$
$739$	13537.3	−	8699.89i	0.673853	−	0.433059i	0.832313	+	0.554306i	$0.187016\pi$
$740$	−374.775	−	2606.61i	−0.0186176	−	0.129488i
$741$	3646.91	+	7985.63i	0.180800	+	0.395897i
$742$	−1580.03	+	10989.4i	−0.0781736	+	0.543709i
$743$	−37065.3	+	10883.4i	−1.83014	+	0.537378i	−0.999802	−	0.0198831i	$-0.993671\pi$
$743$	−37065.3	+	10883.4i	−1.83014	+	0.537378i	−0.830338	+	0.557261i	$0.811852\pi$
$744$	25443.6	+	16351.6i	1.25377	+	0.805750i
$745$	−2500.75	+	5475.87i	−0.122980	+	0.269289i
$746$	−3316.71	−	973.873i	−0.162779	−	0.0477963i
$747$	−403.905	−	466.132i	−0.0197833	−	0.0228311i
$748$	1225.90	+	1414.76i	0.0599240	+	0.0691560i
$749$	3583.15	+	1052.11i	0.174800	+	0.0513260i
$750$	−647.096	+	1416.94i	−0.0315048	+	0.0689859i
$751$	−2763.26	−	1775.84i	−0.134265	−	0.0862866i	0.471784	−	0.881714i	$-0.343610\pi$
$751$	−2763.26	−	1775.84i	−0.134265	−	0.0862866i	−0.606049	+	0.795427i	$0.707246\pi$
$752$	−8407.76	+	2468.74i	−0.407712	+	0.119715i
$753$	1269.24	−	8827.73i	0.0614257	−	0.427225i
$754$	−3771.89	−	8259.29i	−0.182181	−	0.398920i
$755$	1076.74	+	7488.87i	0.0519026	+	0.360991i
$756$	−3092.82	+	1987.63i	−0.148789	+	0.0956211i
$757$	23962.4	−	27654.1i	1.15050	−	1.32775i	0.214100	−	0.976812i	$-0.431318\pi$
$757$	23962.4	−	27654.1i	1.15050	−	1.32775i	0.936400	−	0.350936i	$-0.114136\pi$
$758$	−3721.86			−0.178343
$759$	1353.84	+	18961.8i	0.0647448	+	0.906810i
$760$	−16577.6			−0.791227
$761$	3409.02	−	3934.22i	0.162388	−	0.187405i	−0.668724	−	0.743510i	$-0.733159\pi$
$761$	3409.02	−	3934.22i	0.162388	−	0.187405i	0.831112	+	0.556105i	$0.187705\pi$
$762$	−1021.22	+	656.297i	−0.0485497	+	0.0312010i
$763$	−509.167	−	3541.33i	−0.0241587	−	0.168027i
$764$	−1982.91	−	4341.96i	−0.0938994

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69252 + 1.95327i) q^{2} +(-4.05620 + 2.60676i) q^{3} +(0.187875 + 1.30670i) q^{4} +(2.07708 + 4.54816i) q^{5} +(1.77348 - 12.3348i) q^{6} +(-18.0212 + 5.29151i) q^{7} +(-20.2644 - 13.0231i) q^{8} +(-1.55865 + 3.41296i) q^{9} +O(q^{10})\)	\(q+(-1.69252 + 1.95327i) q^{2} +(-4.05620 + 2.60676i) q^{3} +(0.187875 + 1.30670i) q^{4} +(2.07708 + 4.54816i) q^{5} +(1.77348 - 12.3348i) q^{6} +(-18.0212 + 5.29151i) q^{7} +(-20.2644 - 13.0231i) q^{8} +(-1.55865 + 3.41296i) q^{9} +(-12.3993 - 3.64075i) q^{10} +(23.4071 + 27.0133i) q^{11} +(-4.16831 - 4.81049i) q^{12} +(12.6925 + 3.72685i) q^{13} +(20.1655 - 44.1563i) q^{14} +(-20.2810 - 13.0338i) q^{15} +(49.6021 - 14.5645i) q^{16} +(5.64595 - 39.2685i) q^{17} +(-4.02839 - 8.82094i) q^{18} +(-19.5882 - 136.239i) q^{19} +(-5.55284 + 3.56860i) q^{20} +(59.3040 - 68.4405i) q^{21} -92.3810 q^{22} +(-38.5347 - 103.354i) q^{23} +116.144 q^{24} +(-16.3715 + 18.8937i) q^{25} +(-28.7618 + 18.4841i) q^{26} +(-21.1017 - 146.765i) q^{27} +(-10.3002 - 22.5542i) q^{28} +(-37.7953 + 262.872i) q^{29} +(59.7844 - 17.5543i) q^{30} +(219.068 + 140.787i) q^{31} +(24.5491 - 53.7551i) q^{32} +(-165.361 - 48.5544i) q^{33} +(67.1459 + 77.4905i) q^{34} +(-61.4981 - 70.9726i) q^{35} +(-4.75254 - 1.39547i) q^{36} +(-165.735 + 362.908i) q^{37} +(299.265 + 192.326i) q^{38} +(-61.1983 + 17.9695i) q^{39} +(17.1406 - 119.216i) q^{40} +(-190.422 - 416.965i) q^{41} +(33.3096 + 231.673i) q^{42} +(-92.4431 + 59.4096i) q^{43} +(-30.9006 + 35.6612i) q^{44} -18.7601 q^{45} +(267.099 + 99.6600i) q^{46} -169.504 q^{47} +(-163.230 + 188.377i) q^{48} +(8.21491 - 5.27940i) q^{49} +(-9.19547 - 63.9559i) q^{50} +(79.4624 + 173.998i) q^{51} +(-2.48527 + 17.2855i) q^{52} +(-219.448 + 64.4356i) q^{53} +(322.387 + 207.185i) q^{54} +(-74.2423 + 162.568i) q^{55} +(434.101 + 127.464i) q^{56} +(434.597 + 501.552i) q^{57} +(-449.491 - 518.740i) q^{58} +(-847.937 - 248.977i) q^{59} +(13.2210 - 28.9499i) q^{60} +(161.787 + 103.974i) q^{61} +(-645.770 + 189.615i) q^{62} +(10.0290 - 69.7533i) q^{63} +(235.251 + 515.128i) q^{64} +(9.41294 + 65.4685i) q^{65} +(374.716 - 240.815i) q^{66} +(-116.268 + 134.180i) q^{67} +52.3728 q^{68} +(425.724 + 318.774i) q^{69} +242.715 q^{70} +(497.362 - 573.987i) q^{71} +(76.0323 - 48.8630i) q^{72} +(81.1694 + 564.545i) q^{73} +(-428.349 - 937.953i) q^{74} +(17.1547 - 119.313i) q^{75} +(174.344 - 51.1919i) q^{76} +(-564.766 - 362.953i) q^{77} +(68.4800 - 149.950i) q^{78} +(-610.161 - 179.160i) q^{79} +(169.269 + 195.347i) q^{80} +(401.834 + 463.741i) q^{81} +(1136.74 + 333.776i) q^{82} +(-68.2885 + 149.531i) q^{83} +(100.573 + 64.6343i) q^{84} +(190.326 - 55.8848i) q^{85} +(40.4186 - 281.118i) q^{86} +(-531.940 - 1164.79i) q^{87} +(-122.534 - 852.240i) q^{88} +(-701.025 + 450.521i) q^{89} +(31.7518 - 36.6435i) q^{90} -248.455 q^{91} +(127.813 - 69.7709i) q^{92} -1255.58 q^{93} +(286.888 - 331.087i) q^{94} +(578.952 - 372.070i) q^{95} +(40.5505 + 282.035i) q^{96} +(137.186 + 300.394i) q^{97} +(-3.59178 + 24.9814i) q^{98} +(-128.679 + 37.7834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

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