LMFDB - Embedded newform 115.4.g.a.6.9

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			6.9
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.857442 - 1.87754i) q^{2} +(-4.53505 - 1.33161i) q^{3} +(2.44895 + 2.82624i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-6.38869 + 7.37294i) q^{6} +(1.83914 - 12.7915i) q^{7} +(23.2498 - 6.82676i) q^{8} +(-3.92038 - 2.51948i) q^{9} +O(q^{10})$	\(q+(0.857442 - 1.87754i) q^{2} +(-4.53505 - 1.33161i) q^{3} +(2.44895 + 2.82624i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-6.38869 + 7.37294i) q^{6} +(1.83914 - 12.7915i) q^{7} +(23.2498 - 6.82676i) q^{8} +(-3.92038 - 2.51948i) q^{9} +(-1.46873 - 10.2153i) q^{10} +(-0.872387 - 1.91026i) q^{11} +(-7.34265 - 16.0782i) q^{12} +(-8.93876 - 62.1704i) q^{13} +(-22.4395 - 14.4210i) q^{14} +(-22.6752 + 6.65805i) q^{15} +(2.86022 - 19.8933i) q^{16} +(11.3782 - 13.1312i) q^{17} +(-8.09191 + 5.20035i) q^{18} +(-38.9485 - 44.9490i) q^{19} +(17.9408 + 5.26791i) q^{20} +(-25.3738 + 55.5610i) q^{21} -4.33461 q^{22} +(-65.8584 - 88.4854i) q^{23} -114.530 q^{24} +(10.3854 - 22.7408i) q^{25} +(-124.392 - 36.5247i) q^{26} +(97.9946 + 113.092i) q^{27} +(40.6557 - 26.1279i) q^{28} +(5.07537 - 5.85729i) q^{29} +(-6.94197 + 48.2825i) q^{30} +(12.9633 - 3.80635i) q^{31} +(128.180 + 82.3762i) q^{32} +(1.41259 + 9.82481i) q^{33} +(-14.8981 - 32.6223i) q^{34} +(-26.8421 - 58.7760i) q^{35} +(-2.48018 - 17.2500i) q^{36} +(311.189 + 199.989i) q^{37} +(-117.790 + 34.5861i) q^{38} +(-42.2491 + 293.849i) q^{39} +(79.3408 - 91.5642i) q^{40} +(33.4303 - 21.4843i) q^{41} +(82.5611 + 95.2806i) q^{42} +(213.228 + 62.6094i) q^{43} +(3.26242 - 7.14371i) q^{44} -23.3008 q^{45} +(-222.604 + 47.7804i) q^{46} -85.8592 q^{47} +(-39.4613 + 86.4082i) q^{48} +(168.866 + 49.5837i) q^{49} +(-33.7918 - 38.9978i) q^{50} +(-69.0865 + 44.3992i) q^{51} +(153.818 - 177.515i) q^{52} +(64.1751 - 446.348i) q^{53} +(296.359 - 87.0188i) q^{54} +(-8.83332 - 5.67683i) q^{55} +(-44.5648 - 309.955i) q^{56} +(116.779 + 255.710i) q^{57} +(-6.64544 - 14.5515i) q^{58} +(31.7657 + 220.935i) q^{59} +(-74.3477 - 47.7804i) q^{60} +(-405.433 + 119.046i) q^{61} +(3.96867 - 27.6027i) q^{62} +(-39.4379 + 45.5138i) q^{63} +(399.830 - 256.955i) q^{64} +(-205.658 - 237.342i) q^{65} +(19.6576 + 5.77201i) q^{66} +(-291.985 + 639.358i) q^{67} +64.9767 q^{68} +(180.843 + 488.983i) q^{69} -133.370 q^{70} +(-416.668 + 912.376i) q^{71} +(-108.348 - 31.8138i) q^{72} +(328.131 + 378.684i) q^{73} +(642.313 - 412.790i) q^{74} +(-77.3800 + 89.3013i) q^{75} +(31.6536 - 220.156i) q^{76} +(-26.0395 + 7.64589i) q^{77} +(515.485 + 331.282i) q^{78} +(87.5788 + 609.124i) q^{79} +(-41.7447 - 91.4081i) q^{80} +(-241.547 - 528.913i) q^{81} +(-11.6731 - 81.1882i) q^{82} +(-859.520 - 552.380i) q^{83} +(-219.168 + 64.3535i) q^{84} +(12.3636 - 85.9911i) q^{85} +(300.382 - 346.659i) q^{86} +(-30.8167 + 19.8047i) q^{87} +(-33.3238 - 38.4577i) q^{88} +(-21.6078 - 6.34464i) q^{89} +(-19.9791 + 43.7481i) q^{90} -811.691 q^{91} +(88.7971 - 402.828i) q^{92} -63.8575 q^{93} +(-73.6193 + 161.204i) q^{94} +(-285.334 - 83.7817i) q^{95} +(-471.609 - 544.266i) q^{96} +(1340.02 - 861.181i) q^{97} +(237.888 - 274.538i) q^{98} +(-1.39277 + 9.68691i) 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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.857442	−	1.87754i	0.303152	−	0.663809i	−0.695342	−	0.718679i	$-0.744747\pi$
$2$	0.857442	−	1.87754i	0.303152	−	0.663809i	0.998494	+	0.0548697i	$0.0174743\pi$
$3$	−4.53505	−	1.33161i	−0.872770	−	0.256268i	−0.185477	−	0.982649i	$-0.559383\pi$
$3$	−4.53505	−	1.33161i	−0.872770	−	0.256268i	−0.687293	+	0.726380i	$0.741201\pi$
$4$	2.44895	+	2.82624i	0.306119	+	0.353280i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	−6.38869	+	7.37294i	−0.434695	+	0.501665i
$7$	1.83914	−	12.7915i	0.0993041	−	0.690675i	−0.877973	−	0.478710i	$-0.841105\pi$
$7$	1.83914	−	12.7915i	0.0993041	−	0.690675i	0.977277	−	0.211965i	$-0.0679864\pi$
$8$	23.2498	−	6.82676i	1.02751	−	0.301703i
$9$	−3.92038	−	2.51948i	−0.145199	−	0.0933139i
$10$	−1.46873	−	10.2153i	−0.0464454	−	0.323035i
$11$	−0.872387	−	1.91026i	−0.0239122	−	0.0523605i	0.897299	−	0.441423i	$-0.145526\pi$
$11$	−0.872387	−	1.91026i	−0.0239122	−	0.0523605i	−0.921211	+	0.389063i	$0.872799\pi$
$12$	−7.34265	−	16.0782i	−0.176637	−	0.386781i
$13$	−8.93876	−	62.1704i	−0.190705	−	1.32638i	−0.830148	−	0.557544i	$-0.811744\pi$
$13$	−8.93876	−	62.1704i	−0.190705	−	1.32638i	0.639443	−	0.768839i	$-0.279165\pi$
$14$	−22.4395	−	14.4210i	−0.428372	−	0.275298i
$15$	−22.6752	+	6.65805i	−0.390315	+	0.114607i
$16$	2.86022	−	19.8933i	0.0446909	−	0.310832i
$17$	11.3782	−	13.1312i	0.162331	−	0.187340i	−0.668757	−	0.743481i	$-0.733173\pi$
$17$	11.3782	−	13.1312i	0.162331	−	0.187340i	0.831088	+	0.556141i	$0.187719\pi$
$18$	−8.09191	+	5.20035i	−0.105960	+	0.0680964i
$19$	−38.9485	−	44.9490i	−0.470285	−	0.542737i	0.470206	−	0.882557i	$-0.344180\pi$
$19$	−38.9485	−	44.9490i	−0.470285	−	0.542737i	−0.940491	+	0.339819i	$0.889634\pi$
$20$	17.9408	+	5.26791i	0.200585	+	0.0588970i
$21$	−25.3738	+	55.5610i	−0.263668	+	0.577352i
$22$	−4.33461			−0.0420064
$23$	−65.8584	−	88.4854i	−0.597062	−	0.802195i
$23$	−65.8584	−	88.4854i	−0.597062	−	0.802195i
$24$	−114.530			−0.974094
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	−124.392	−	36.5247i	−0.938278	−	0.275503i
$27$	97.9946	+	113.092i	0.698484	+	0.806093i
$28$	40.6557	−	26.1279i	0.274400	−	0.176346i
$29$	5.07537	−	5.85729i	0.0324991	−	0.0375059i	−0.739267	−	0.673412i	$-0.764828\pi$
$29$	5.07537	−	5.85729i	0.0324991	−	0.0375059i	0.771766	+	0.635906i	$0.219373\pi$
$30$	−6.94197	+	48.2825i	−0.0422475	+	0.293838i
$31$	12.9633	−	3.80635i	0.0751055	−	0.0220530i	−0.243964	−	0.969784i	$-0.578448\pi$
$31$	12.9633	−	3.80635i	0.0751055	−	0.0220530i	0.319069	+	0.947731i	$0.396630\pi$
$32$	128.180	+	82.3762i	0.708101	+	0.455069i
$33$	1.41259	+	9.82481i	0.00745155	+	0.0518266i
$34$	−14.8981	−	32.6223i	−0.0751472	−	0.164549i
$35$	−26.8421	−	58.7760i	−0.129633	−	0.283856i
$36$	−2.48018	−	17.2500i	−0.0114823	−	0.0798611i
$37$	311.189	+	199.989i	1.38268	+	0.888595i	0.999386	−	0.0350317i	$-0.0111532\pi$
$37$	311.189	+	199.989i	1.38268	+	0.888595i	0.383294	+	0.923626i	$0.374790\pi$
$38$	−117.790	+	34.5861i	−0.502842	+	0.147648i
$39$	−42.2491	+	293.849i	−0.173468	+	1.20650i
$40$	79.3408	−	91.5642i	0.313622	−	0.361939i
$41$	33.4303	−	21.4843i	0.127340	−	0.0818364i	−0.475420	−	0.879759i	$-0.657704\pi$
$41$	33.4303	−	21.4843i	0.127340	−	0.0818364i	0.602760	+	0.797922i	$0.294068\pi$
$42$	82.5611	+	95.2806i	0.303320	+	0.350050i
$43$	213.228	+	62.6094i	0.756209	+	0.222043i	0.637040	−	0.770831i	$-0.280159\pi$
$43$	213.228	+	62.6094i	0.756209	+	0.222043i	0.119169	+	0.992874i	$0.461977\pi$
$44$	3.26242	−	7.14371i	0.0111779	−	0.0244762i
$45$	−23.3008			−0.0771885
$46$	−222.604	+	47.7804i	−0.713505	+	0.153149i
$47$	−85.8592			−0.266465			−0.133232	−	0.991085i	$-0.542536\pi$
$47$	−85.8592			−0.266465			−0.133232	+	0.991085i	$0.542536\pi$
$48$	−39.4613	+	86.4082i	−0.118661	+	0.259832i
$49$	168.866	+	49.5837i	0.492322	+	0.144559i
$50$	−33.7918	−	38.9978i	−0.0955777	−	0.110303i
$51$	−69.0865	+	44.3992i	−0.189687	+	0.121905i
$52$	153.818	−	177.515i	0.410206	−	0.473403i
$53$	64.1751	−	446.348i	0.166323	−	1.15680i	−0.720080	−	0.693891i	$-0.755895\pi$
$53$	64.1751	−	446.348i	0.166323	−	1.15680i	0.886404	−	0.462913i	$-0.153196\pi$
$54$	296.359	−	87.0188i	0.746839	−	0.219292i
$55$	−8.83332	−	5.67683i	−0.0216561	−	0.0139175i
$56$	−44.5648	−	309.955i	−0.106343	−	0.739634i
$57$	116.779	+	255.710i	0.271364	+	0.594204i
$58$	−6.64544	−	14.5515i	−0.0150446	−	0.0329432i
$59$	31.7657	+	220.935i	0.0700939	+	0.487514i	0.994385	+	0.105825i	$0.0337484\pi$
$59$	31.7657	+	220.935i	0.0700939	+	0.487514i	−0.924291	+	0.381689i	$0.875343\pi$
$60$	−74.3477	−	47.7804i	−0.159971	−	0.102807i
$61$	−405.433	+	119.046i	−0.850989	+	0.249873i	−0.678010	−	0.735053i	$-0.737157\pi$
$61$	−405.433	+	119.046i	−0.850989	+	0.249873i	−0.172979	+	0.984925i	$0.555339\pi$
$62$	3.96867	−	27.6027i	0.00812938	−	0.0565411i
$63$	−39.4379	+	45.5138i	−0.0788685	+	0.0910191i
$64$	399.830	−	256.955i	0.780918	−	0.501866i
$65$	−205.658	−	237.342i	−0.392442	−	0.452903i
$66$	19.6576	+	5.77201i	0.0366620	+	0.0107649i
$67$	−291.985	+	639.358i	−0.532413	+	1.16582i	0.432110	+	0.901821i	$0.357769\pi$
$67$	−291.985	+	639.358i	−0.532413	+	1.16582i	−0.964523	+	0.264001i	$0.914958\pi$
$68$	64.9767			0.115876
$69$	180.843	+	488.983i	0.315520	+	0.853140i
$70$	−133.370			−0.227724
$71$	−416.668	+	912.376i	−0.696471	+	1.52506i	0.147728	+	0.989028i	$0.452804\pi$
$71$	−416.668	+	912.376i	−0.696471	+	1.52506i	−0.844199	+	0.536030i	$0.819923\pi$
$72$	−108.348	−	31.8138i	−0.177346	−	0.0520736i
$73$	328.131	+	378.684i	0.526094	+	0.607145i	0.955146	−	0.296135i	$-0.0956977\pi$
$73$	328.131	+	378.684i	0.526094	+	0.607145i	−0.429052	+	0.903280i	$0.641152\pi$
$74$	642.313	−	412.790i	1.00902	−	0.648457i
$75$	−77.3800	+	89.3013i	−0.119134	+	0.137488i
$76$	31.6536	−	220.156i	0.0477752	−	0.332284i
$77$	−26.0395	+	7.64589i	−0.0385387	+	0.0113160i
$78$	515.485	+	331.282i	0.748298	+	0.480902i
$79$	87.5788	+	609.124i	0.124726	+	0.867491i	0.952089	+	0.305822i	$0.0989313\pi$
$79$	87.5788	+	609.124i	0.124726	+	0.867491i	−0.827362	+	0.561669i	$0.810160\pi$
$80$	−41.7447	−	91.4081i	−0.0583400	−	0.127747i
$81$	−241.547	−	528.913i	−0.331340	−	0.725533i
$82$	−11.6731	−	81.1882i	−0.0157205	−	0.109338i
$83$	−859.520	−	552.380i	−1.13668	−	0.730501i	−0.169737	−	0.985489i	$-0.554292\pi$
$83$	−859.520	−	552.380i	−1.13668	−	0.730501i	−0.966944	+	0.254989i	$0.917928\pi$
$84$	−219.168	+	64.3535i	−0.284681	+	0.0835898i
$85$	12.3636	−	85.9911i	0.0157768	−	0.109730i
$86$	300.382	−	346.659i	0.376640	−	0.434666i
$87$	−30.8167	+	19.8047i	−0.0379758	+	0.0244056i
$88$	−33.3238	−	38.4577i	−0.0403673	−	0.0465864i
$89$	−21.6078	−	6.34464i	−0.0257351	−	0.00755652i	0.268840	−	0.963185i	$-0.413360\pi$
$89$	−21.6078	−	6.34464i	−0.0257351	−	0.00755652i	−0.294575	+	0.955628i	$0.595178\pi$
$90$	−19.9791	+	43.7481i	−0.0233998	+	0.0512384i
$91$	−811.691			−0.935037
$92$	88.7971	−	402.828i	0.100628	−	0.456497i
$93$	−63.8575			−0.0712013
$94$	−73.6193	+	161.204i	−0.0807792	+	0.176882i
$95$	−285.334	−	83.7817i	−0.308155	−	0.0904823i
$96$	−471.609	−	544.266i	−0.501389	−	0.578634i
$97$	1340.02	−	861.181i	1.40267	−	0.901440i	0.402765	−	0.915303i	$-0.368049\pi$
$97$	1340.02	−	861.181i	1.40267	−	0.901440i	0.999904	+	0.0138630i	$0.00441288\pi$
$98$	237.888	−	274.538i	0.245208	−	0.282985i
$99$	−1.39277	+	9.68691i	−0.00141392	+	0.00983405i
$100$	89.7042	−	26.3395i	0.0897042	−	0.0263395i
$101$	186.040	+	119.561i	0.183284	+	0.117790i	0.629066	−	0.777352i	$-0.283438\pi$
$101$	186.040	+	119.561i	0.183284	+	0.117790i	−0.445781	+	0.895142i	$0.647074\pi$
$102$	24.1234	+	167.782i	0.0234174	+	0.162872i
$103$	69.2627	+	151.664i	0.0662588	+	0.145086i	0.939864	−	0.341549i	$-0.110951\pi$
$103$	69.2627	+	151.664i	0.0662588	+	0.145086i	−0.873605	+	0.486635i	$0.838224\pi$
$104$	−632.247	−	1384.43i	−0.596124	−	1.30533i
$105$	43.4635	+	302.295i	0.0403962	+	0.280962i
$106$	−783.008	−	503.209i	−0.717476	−	0.461094i
$107$	−200.095	+	58.7533i	−0.180785	+	0.0530832i	−0.370872	−	0.928684i	$-0.620941\pi$
$107$	−200.095	+	58.7533i	−0.180785	+	0.0530832i	0.190087	+	0.981767i	$0.439123\pi$
$108$	−79.6406	+	553.912i	−0.0709576	+	0.493521i
$109$	104.937	−	121.104i	0.0922126	−	0.106419i	−0.707768	−	0.706445i	$-0.750298\pi$
$109$	104.937	−	121.104i	0.0922126	−	0.106419i	0.799980	+	0.600026i	$0.204843\pi$
$110$	−18.2325	+	11.7173i	−0.0158037	+	0.0101564i
$111$	−1144.95	−	1321.34i	−0.979043	−	1.12988i
$112$	−249.204	−	73.1729i	−0.210246	−	0.0617338i
$113$	−17.0412	+	37.3150i	−0.0141867	+	0.0310646i	−0.916593	−	0.399822i	$-0.869072\pi$
$113$	−17.0412	+	37.3150i	−0.0141867	+	0.0310646i	0.902406	+	0.430887i	$0.141799\pi$
$114$	580.236			0.476703
$115$	−516.212	−	194.165i	−0.418583	−	0.157443i
$116$	28.9834			0.0231987
$117$	−121.593	+	266.253i	−0.0960797	+	0.210385i
$118$	442.051	+	129.798i	0.344866	+	0.101262i
$119$	−147.041	−	169.695i	−0.113271	−	0.130722i
$120$	−481.742	+	309.597i	−0.366474	+	0.235518i
$121$	868.732	−	1002.57i	0.652691	−	0.753245i
$122$	−124.122	+	863.290i	−0.0921107	+	0.640644i
$123$	−180.217	+	52.9164i	−0.132111	+	0.0387911i
$124$	42.5040	+	27.3157i	0.0307820	+	0.0197824i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	51.6381	+	113.072i	0.0365102	+	0.0799462i
$127$	−274.568	−	601.220i	−0.191842	−	0.420076i	0.789129	−	0.614227i	$-0.210532\pi$
$127$	−274.568	−	601.220i	−0.191842	−	0.420076i	−0.980972	+	0.194151i	$0.937805\pi$
$128$	33.8619	+	235.515i	0.0233828	+	0.162631i
$129$	−883.628	−	567.873i	−0.603094	−	0.387585i
$130$	−621.958	+	182.623i	−0.419610	+	0.123209i
$131$	333.965	−	2322.77i	0.222738	−	1.54917i	−0.504879	−	0.863190i	$-0.668463\pi$
$131$	333.965	−	2322.77i	0.222738	−	1.54917i	0.727617	−	0.685984i	$-0.240628\pi$
$132$	−24.3079	+	28.0528i	−0.0160283	+	0.0184976i
$133$	−646.596	+	415.542i	−0.421556	+	0.270918i
$134$	950.058	+	1096.43i	0.612482	+	0.706841i
$135$	717.902	+	210.795i	0.457682	+	0.134388i
$136$	174.899	−	382.975i	0.110275	−	0.241469i
$137$	2278.52			1.42093			0.710463	−	0.703734i	$-0.248485\pi$
$137$	2278.52			1.42093			0.710463	+	0.703734i	$0.248485\pi$
$138$	1073.15	+	79.7360i	0.661973	+	0.0491854i
$139$	514.710			0.314080			0.157040	−	0.987592i	$-0.449805\pi$
$139$	514.710			0.314080			0.157040	+	0.987592i	$0.449805\pi$
$140$	100.380	−	219.802i	0.0605976	−	0.132690i
$141$	389.375	+	114.331i	0.232563	+	0.0682865i
$142$	1355.75	+	1564.62i	0.801212	+	0.924648i
$143$	−110.964	+	71.3120i	−0.0648899	+	0.0417022i
$144$	−61.3337	+	70.7829i	−0.0354940	+	0.0409623i
$145$	5.51492	−	38.3571i	0.00315855	−	0.0219682i
$146$	992.347	−	291.379i	0.562515	−	0.165169i
$147$	−699.791	−	449.729i	−0.392638	−	0.252333i
$148$	196.870	+	1369.26i	0.109342	+	0.760489i
$149$	611.245	+	1338.44i	0.336075	+	0.735901i	0.999928	−	0.0119617i	$-0.00380761\pi$
$149$	611.245	+	1338.44i	0.336075	+	0.735901i	−0.663854	+	0.747862i	$0.731080\pi$
$150$	101.318	+	221.855i	0.0551503	+	0.120762i
$151$	256.644	+	1785.00i	0.138314	+	0.961993i	0.934252	+	0.356614i	$0.116069\pi$
$151$	256.644	+	1785.00i	0.138314	+	0.961993i	−0.795938	+	0.605378i	$0.793022\pi$
$152$	−1212.40	−	779.164i	−0.646966	−	0.415780i
$153$	−77.6908	+	22.8121i	−0.0410518	+	0.0120539i
$154$	−7.97194	+	55.4461i	−0.00417141	+	0.0290128i
$155$	44.2376	−	51.0529i	0.0229242	−	0.0264559i
$156$	−933.952	+	600.215i	−0.479334	+	0.308049i
$157$	1643.63	+	1896.85i	0.835516	+	0.964236i	0.999754	−	0.0221843i	$-0.00706206\pi$
$157$	1643.63	+	1896.85i	0.835516	+	0.964236i	−0.164238	+	0.986421i	$0.552517\pi$
$158$	1218.75	+	357.856i	0.613659	+	0.180187i
$159$	−885.399	+	1938.75i	−0.441614	+	0.967000i
$160$	761.839			0.376429
$161$	−1252.98	+	679.689i	−0.613347	+	0.332715i
$162$	−1200.17			−0.582061
$163$	−1207.42	+	2643.88i	−0.580200	+	1.27046i	0.360986	+	0.932571i	$0.382440\pi$
$163$	−1207.42	+	2643.88i	−0.580200	+	1.27046i	−0.941186	+	0.337889i	$0.890287\pi$
$164$	142.589	+	41.8679i	0.0678922	+	0.0199350i
$165$	32.5002	+	37.5072i	0.0153342	+	0.0176966i
$166$	−1774.10	+	1140.15i	−0.829500	+	0.533087i
$167$	1936.53	−	2234.87i	0.897323	−	1.03557i	−0.101846	−	0.994800i	$-0.532475\pi$
$167$	1936.53	−	2234.87i	0.897323	−	1.03557i	0.999169	−	0.0407653i	$-0.0129796\pi$
$168$	−210.636	+	1465.00i	−0.0967315	+	0.672783i
$169$	−1677.25	+	492.486i	−0.763429	+	0.224163i
$170$	−150.850	−	96.9456i	−0.0680570	−	0.0437376i
$171$	39.4452	+	274.347i	0.0176400	+	0.122689i
$172$	345.236	+	755.961i	0.153046	+	0.335125i
$173$	−1586.81	−	3474.63i	−0.697358	−	1.52700i	−0.843146	−	0.537685i	$-0.819299\pi$
$173$	−1586.81	−	3474.63i	−0.697358	−	1.52700i	0.145788	−	0.989316i	$-0.453428\pi$
$174$	10.7605	+	74.8408i	0.00468822	+	0.0326073i
$175$	−271.788	−	174.668i	−0.117402	−	0.0754494i
$176$	−40.4965	+	11.8909i	−0.0173440	+	0.00509265i
$177$	150.141	−	1044.25i	0.0637586	−	0.443451i
$178$	−30.4398	+	35.1294i	−0.0128177	+	0.0147925i
$179$	−1087.42	+	698.842i	−0.454064	+	0.291810i	−0.747613	−	0.664135i	$-0.768800\pi$
$179$	−1087.42	+	698.842i	−0.454064	+	0.291810i	0.293548	+	0.955944i	$0.405164\pi$
$180$	−57.0625	−	65.8537i	−0.0236288	−	0.0272691i
$181$	3240.62	+	951.532i	1.33079	+	0.390756i	0.868376	−	0.495907i	$-0.165164\pi$
$181$	3240.62	+	951.532i	1.33079	+	0.390756i	0.462417	+	0.886663i	$0.346982\pi$
$182$	−695.978	+	1523.98i	−0.283458	+	0.620686i
$183$	1997.18			0.806753
$184$	−2135.26	−	1607.67i	−0.855510	−	0.644125i
$185$	1849.56			0.735038
$186$	−54.7542	+	119.895i	−0.0215848	+	0.0472641i
$187$	−35.0103	−	10.2799i	−0.0136909	−	0.00402002i
$188$	−210.265	−	242.659i	−0.0815699	−	0.0941367i
$189$	1626.84	−	1045.50i	0.626111	−	0.402377i
$190$	−401.961	+	463.888i	−0.153481	+	0.177126i
$191$	−450.514	+	3133.39i	−0.170670	+	1.18704i	0.706802	+	0.707411i	$0.250137\pi$
$191$	−450.514	+	3133.39i	−0.170670	+	1.18704i	−0.877473	+	0.479627i	$0.840772\pi$
$192$	−2155.41	+	632.886i	−0.810174	+	0.237889i
$193$	−2753.95	−	1769.86i	−1.02712	−	0.660088i	−0.0853493	−	0.996351i	$-0.527201\pi$
$193$	−2753.95	−	1769.86i	−1.02712	−	0.660088i	−0.941768	+	0.336263i	$0.890837\pi$
$194$	−467.906	−	3254.36i	−0.173163	−	1.20438i
$195$	616.622	+	1350.21i	0.226447	+	0.495850i
$196$	273.410	+	598.685i	0.0996393	+	0.218180i
$197$	−123.704	−	860.384i	−0.0447390	−	0.311166i	−0.999887	−	0.0150375i	$-0.995213\pi$
$197$	−123.704	−	860.384i	−0.0447390	−	0.311166i	0.955148	−	0.296129i	$-0.0956958\pi$
$198$	16.9933	+	10.9209i	0.00609930	+	0.00391978i
$199$	926.003	−	271.899i	0.329862	−	0.0968563i	−0.112608	−	0.993639i	$-0.535920\pi$
$199$	926.003	−	271.899i	0.329862	−	0.0968563i	0.442470	+	0.896783i	$0.354102\pi$
$200$	86.2121	−	599.618i	0.0304806	−	0.211997i
$201$	2175.54	−	2510.71i	0.763437	−	0.881054i
$202$	383.999	−	246.781i	0.133753	−	0.0859577i
$203$	−65.5891	−	75.6939i	−0.0226771	−	0.0261708i
$204$	−294.672	−	86.5236i	−0.101133	−	0.0296954i
$205$	82.5402	−	180.738i	0.0281213	−	0.0615769i
$206$	344.144			0.116396
$207$	35.2530	+	512.825i	0.0118370	+	0.172192i
$208$	−1262.34			−0.420805
$209$	−51.8862	+	113.615i	−0.0171724	+	0.0376024i
$210$	604.837	+	177.596i	0.198751	+	0.0583586i
$211$	−485.967	−	560.835i	−0.158556	−	0.182983i	0.670913	−	0.741536i	$-0.265902\pi$
$211$	−485.967	−	560.835i	−0.158556	−	0.182983i	−0.829469	+	0.558553i	$0.811357\pi$
$212$	1418.65	−	911.709i	0.459590	−	0.295361i
$213$	3104.54	−	3582.83i	0.998683	−	1.15254i
$214$	−61.2588	+	426.064i	−0.0195681	+	0.136099i
$215$	1066.14	−	313.047i	0.338187	−	0.0993006i
$216$	3050.41	+	1960.38i	0.960898	+	0.617532i
$217$	−24.8477	−	172.820i	−0.00777315	−	0.0540634i
$218$	−137.400	−	300.864i	−0.0426876	−	0.0934727i
$219$	−983.832	−	2154.29i	−0.303567	−	0.664720i
$220$	−5.58828	−	38.8674i	−0.00171255	−	0.0119111i
$221$	−918.080	−	590.014i	−0.279442	−	0.179587i
$222$	−3462.60	+	1016.71i	−1.04682	+	0.307374i
$223$	162.714	−	1131.70i	0.0488615	−	0.339839i	−0.950697	−	0.310122i	$-0.899630\pi$
$223$	162.714	−	1131.70i	0.0488615	−	0.339839i	0.999558	−	0.0297175i	$-0.00946075\pi$
$224$	1289.45	−	1488.11i	0.384622	−	0.443877i
$225$	−98.0095	+	62.9869i	−0.0290398	+	0.0186628i
$226$	55.4484	+	63.9908i	0.0163202	+	0.0188345i
$227$	−740.935	−	217.558i	−0.216641	−	0.0636117i	0.171611	−	0.985165i	$-0.445103\pi$
$227$	−740.935	−	217.558i	−0.216641	−	0.0636117i	−0.388252	+	0.921553i	$0.626921\pi$
$228$	−436.712	+	956.266i	−0.126851	+	0.277764i
$229$	−62.5216			−0.0180417			−0.00902084	−	0.999959i	$-0.502871\pi$
$229$	−62.5216			−0.0180417			−0.00902084	+	0.999959i	$0.502871\pi$
$230$	−807.174	+	802.722i	−0.231406	+	0.230130i
$231$	128.272			0.0365353
$232$	78.0152	−	170.829i	0.0220774	−	0.0483427i
$233$	−1638.72	−	481.173i	−0.460757	−	0.135290i	0.0431126	−	0.999070i	$-0.486273\pi$
$233$	−1638.72	−	481.173i	−0.460757	−	0.135290i	−0.503870	+	0.863780i	$0.668091\pi$
$234$	395.640	+	456.592i	0.110529	+	0.127557i
$235$	−361.147	+	232.095i	−0.100249	+	0.0644264i
$236$	−546.623	+	630.837i	−0.150772	+	0.174000i
$237$	413.941	−	2879.03i	0.113453	−	0.789083i
$238$	−444.688	+	130.572i	−0.121113	+	0.0355619i
$239$	−1867.53	−	1200.19i	−0.505442	−	0.324828i	0.262948	−	0.964810i	$-0.415305\pi$
$239$	−1867.53	−	1200.19i	−0.505442	−	0.324828i	−0.768390	+	0.639982i	$0.778942\pi$
$240$	67.5942	+	470.128i	0.0181799	+	0.126444i
$241$	2241.55	+	4908.31i	0.599133	+	1.31192i	0.929763	+	0.368158i	$0.120011\pi$
$241$	2241.55	+	4908.31i	0.599133	+	1.31192i	−0.330631	+	0.943760i	$0.607261\pi$
$242$	−1137.47	−	2490.72i	−0.302147	−	0.661610i
$243$	−183.880	−	1278.91i	−0.0485428	−	0.337623i
$244$	−1329.34	−	854.313i	−0.348779	−	0.224147i
$245$	844.332	−	247.918i	0.220173	−	0.0646487i
$246$	−55.1729	+	383.736i	−0.0142996	+	0.0994558i
$247$	−2446.35	+	2823.23i	−0.630192	+	0.727280i
$248$	275.408	−	176.994i	0.0705179	−	0.0453191i
$249$	3162.41	+	3649.61i	0.804857	+	0.928855i
$250$	−247.557	−	72.6892i	−0.0626274	−	0.0183891i
$251$	2582.64	−	5655.19i	0.649461	−	1.42212i	−0.242563	−	0.970136i	$-0.577988\pi$
$251$	2582.64	−	5655.19i	0.649461	−	1.42212i	0.892025	−	0.451987i	$-0.149285\pi$
$252$	−225.214			−0.0562983
$253$	−111.576	+	203.000i	−0.0277263	+	0.0504447i
$254$	−1364.24			−0.337008
$255$	−170.576	+	373.510i	−0.0418898	+	0.0917259i
$256$	4119.44	+	1209.58i	1.00572	+	0.295307i
$257$	−4876.94	−	5628.29i	−1.18372	−	1.36608i	−0.915296	−	0.402781i	$-0.868044\pi$
$257$	−4876.94	−	5628.29i	−1.18372	−	1.36608i	−0.268421	−	0.963302i	$-0.586502\pi$
$258$	−1823.86	+	1172.13i	−0.440111	+	0.282842i
$259$	3130.48	−	3612.76i	0.751036	−	0.866742i
$260$	167.139	−	1162.48i	0.0398674	−	0.277284i
$261$	−34.6547	+	10.1755i	−0.00821866	+	0.00241322i
$262$	−4074.74	−	2618.68i	−0.960833	−	0.617490i
$263$	65.1366	+	453.035i	0.0152718	+	0.106218i	0.996032	−	0.0890009i	$-0.0283674\pi$
$263$	65.1366	+	453.035i	0.0152718	+	0.106218i	−0.980760	+	0.195219i	$0.937458\pi$
$264$	99.9142	+	218.782i	0.0232928	+	0.0510041i
$265$	−936.632	−	2050.94i	−0.217120	−	0.475427i
$266$	225.777	+	1570.31i	0.0520423	+	0.361962i
$267$	89.5440	+	57.5464i	0.0205244	+	0.0131902i
$268$	−2522.04	+	740.537i	−0.574843	+	0.168789i
$269$	−810.352	+	5636.12i	−0.183673	+	1.27747i	0.664313	+	0.747454i	$0.268724\pi$
$269$	−810.352	+	5636.12i	−0.183673	+	1.27747i	−0.847986	+	0.530019i	$0.822185\pi$
$270$	1011.33	−	1167.14i	0.227955	−	0.263074i
$271$	−3398.40	+	2184.02i	−0.761764	+	0.489556i	−0.862936	−	0.505313i	$-0.831377\pi$
$271$	−3398.40	+	2184.02i	−0.761764	+	0.489556i	0.101172	+	0.994869i	$0.467741\pi$
$272$	−228.678	−	263.909i	−0.0509766	−	0.0588302i
$273$	3681.06	+	1080.86i	0.816072	+	0.239621i
$274$	1953.70	−	4278.00i	0.430756	−	0.943225i
$275$	−52.5010			−0.0115125
$276$	−939.109	+	1708.60i	−0.204810	+	0.372629i
$277$	−6611.73			−1.43415			−0.717076	−	0.696995i	$-0.754520\pi$
$277$	−6611.73			−1.43415			−0.717076	+	0.696995i	$0.754520\pi$
$278$	441.334	−	966.388i	0.0952140	−	0.208490i
$279$	−60.4109	−	17.7382i	−0.0129631	−	0.00380631i
$280$	−1025.32	−	1183.29i	−0.218838	−	0.252553i
$281$	2985.00	−	1918.34i	0.633702	−	0.407256i	−0.183977	−	0.982931i	$-0.558897\pi$
$281$	2985.00	−	1918.34i	0.633702	−	0.407256i	0.817679	+	0.575675i	$0.195261\pi$
$282$	548.527	−	633.034i	0.115831	−	0.133676i
$283$	1313.76	−	9137.39i	0.275954	−	1.91930i	−0.104551	−	0.994520i	$-0.533340\pi$
$283$	1313.76	−	9137.39i	0.275954	−	1.91930i	0.380504	−	0.924779i	$-0.375750\pi$
$284$	−3598.99	+	1056.76i	−0.751975	+	0.220800i
$285$	1182.44	+	759.908i	0.245760	+	0.157941i
$286$	38.7460	+	269.484i	0.00801084	+	0.0557166i
$287$	−213.334	−	467.136i	−0.0438770	−	0.0960772i
$288$	−294.969	−	645.892i	−0.0603515	−	0.132151i
$289$	656.229	+	4564.17i	0.133570	+	0.928999i
$290$	−67.2881	−	43.2435i	−0.0136252	−	0.00875636i
$291$	−7223.83	+	2121.11i	−1.45522	+	0.427291i
$292$	−266.674	+	1854.76i	−0.0534448	+	0.371717i
$293$	−481.218	+	555.355i	−0.0959490	+	0.110731i	−0.801693	−	0.597736i	$-0.796067\pi$
$293$	−481.218	+	555.355i	−0.0959490	+	0.110731i	0.705744	+	0.708467i	$0.250613\pi$
$294$	−1444.41	+	928.268i	−0.286530	+	0.184142i
$295$	730.848	+	843.444i	0.144243	+	0.166465i
$296$	8600.37	+	2525.30i	1.68880	+	0.495878i
$297$	130.546	−	285.855i	0.0255051	−	0.0558485i
$298$	3037.07			0.590379
$299$	−4912.48	+	4885.39i	−0.950155	+	0.944915i
$300$	−441.887			−0.0850411
$301$	1193.02	−	2612.36i	0.228454	−	0.500245i
$302$	3571.45	+	1048.67i	0.680510	+	0.199816i
$303$	−684.494	−	789.948i	−0.129779	−	0.149773i
$304$	−1005.58	+	646.249i	−0.189718	+	0.121924i
$305$	−1383.55	+	1596.71i	−0.259744	+	0.299761i
$306$	−23.7849	+	165.427i	−0.00444343	+	0.0309047i
$307$	−9238.18	+	2712.57i	−1.71743	+	0.504283i	−0.984405	−	0.175920i	$-0.943710\pi$
$307$	−9238.18	+	2712.57i	−1.71743	+	0.504283i	−0.733024	+	0.680202i	$0.761892\pi$
$308$	−85.3786	−	54.8695i	−0.0157951	−	0.0101509i
$309$	−112.152	−	780.035i	−0.0206476	−	0.143607i
$310$	−57.9225	−	126.833i	−0.0106122	−	0.0232374i
$311$	1235.07	+	2704.42i	0.225191	+	0.493099i	0.988177	−	0.153315i	$-0.0489950\pi$
$311$	1235.07	+	2704.42i	0.225191	+	0.493099i	−0.762987	+	0.646414i	$0.776268\pi$
$312$	1023.75	+	7120.35i	0.185765	+	1.29202i
$313$	7019.06	+	4510.87i	1.26754	+	0.814600i	0.989298	−	0.145911i	$-0.0466112\pi$
$313$	7019.06	+	4510.87i	1.26754	+	0.814600i	0.278244	+	0.960510i	$0.410248\pi$
$314$	4970.72	−	1459.54i	0.893357	−	0.262313i
$315$	−42.8534	+	298.052i	−0.00766513	+	0.0533122i
$316$	−1507.05	+	1739.23i	−0.268286	+	0.309618i
$317$	5146.97	−	3307.76i	0.911933	−	0.586064i	0.00162630	−	0.999999i	$-0.499482\pi$
$317$	5146.97	−	3307.76i	0.911933	−	0.586064i	0.910306	+	0.413935i	$0.135846\pi$
$318$	2880.90	+	3324.74i	0.508028	+	0.586295i
$319$	−15.6167	−	4.58546i	−0.00274096	−	0.000804817i
$320$	987.190	−	2161.64i	0.172455	−	0.377624i
$321$	985.679			0.171387
$322$	201.782	+	2935.31i	0.0349219	+	0.508008i
$323$	−1033.40			−0.178018
$324$	903.300	−	1977.95i	0.154887	−	0.339155i
$325$	−1506.64	−	442.389i	−0.257148	−	0.0755056i
$326$	3928.70	+	4533.96i	0.667455	+	0.770284i
$327$	−637.159	+	409.477i	−0.107752	+	0.0692482i
$328$	630.580	−	727.728i	0.106152	−	0.122506i
$329$	−157.907	+	1098.27i	−0.0264611	+	0.184041i
$330$	98.2882	−	28.8600i	0.0163957	−	0.00481422i
$331$	7704.43	+	4951.34i	1.27938	+	0.822206i	0.990811	−	0.135254i	$-0.0431850\pi$
$331$	7704.43	+	4951.34i	1.27938	+	0.822206i	0.288567	+	0.957460i	$0.406821\pi$
$332$	−543.763	−	3781.96i	−0.0898882	−	0.625186i
$333$	−716.112	−	1568.07i	−0.117846	−	0.258047i
$334$	−2535.59	−	5552.17i	−0.415393	−	0.909584i
$335$	500.148	+	3478.61i	0.0815702	+	0.567333i
$336$	1032.71	+	663.685i	0.167676	+	0.107759i
$337$	2055.22	−	603.467i	0.332210	−	0.0975458i	−0.111373	−	0.993779i	$-0.535525\pi$
$337$	2055.22	−	603.467i	0.332210	−	0.0975458i	0.443584	+	0.896233i	$0.353707\pi$
$338$	−513.487	+	3571.38i	−0.0826332	+	0.574726i
$339$	126.971	−	146.533i	0.0203426	−	0.0234766i
$340$	273.309	−	175.645i	0.0435949	−	0.0280168i
$341$	−18.5801	−	21.4426i	−0.00295064	−	0.00340522i
$342$	548.919	+	161.177i	0.0867898	+	0.0254838i
$343$	2786.18	−	6100.89i	0.438600	−	0.960400i
$344$	5384.93			0.844000
$345$	2082.49	+	1567.94i	0.324979	+	0.244681i
$346$	−7884.34			−1.22504
$347$	−2012.19	+	4406.08i	−0.311297	+	0.681644i	−0.999017	−	0.0443313i	$-0.985884\pi$
$347$	−2012.19	+	4406.08i	−0.311297	+	0.681644i	0.687720	+	0.725976i	$0.258612\pi$
$348$	−131.441	−	38.5946i	−0.0202471	−	0.00594509i
$349$	−483.427	−	557.905i	−0.0741469	−	0.0855701i	0.717464	−	0.696596i	$-0.245303\pi$
$349$	−483.427	−	557.905i	−0.0741469	−	0.0855701i	−0.791611	+	0.611025i	$0.790757\pi$
$350$	−560.988	+	360.525i	−0.0856745	+	0.0550597i
$351$	6155.01	−	7103.26i	0.935984	−	1.08018i
$352$	45.5376	−	316.721i	0.00689535	−	0.0479582i
$353$	−2985.17	+	876.525i	−0.450098	+	0.132161i	−0.498922	−	0.866647i	$-0.666271\pi$
$353$	−2985.17	+	876.525i	−0.450098	+	0.132161i	0.0488244	+	0.998807i	$0.484453\pi$
$354$	−1831.88	−	1177.28i	−0.275038	−	0.176756i
$355$	713.721	+	4964.04i	0.106705	+	0.742152i
$356$	−34.9851	−	76.6066i	−0.00520844	−	0.0114049i
$357$	440.872	+	965.375i	0.0653598	+	0.143118i
$358$	379.702	+	2640.89i	0.0560555	+	0.389875i
$359$	1472.71	+	946.452i	0.216509	+	0.139142i	0.644400	−	0.764688i	$-0.277107\pi$
$359$	1472.71	+	946.452i	0.216509	+	0.139142i	−0.427892	+	0.903830i	$0.640743\pi$
$360$	−541.740	+	159.069i	−0.0793117	+	0.0232880i
$361$	472.713	−	3287.79i	0.0689186	−	0.479339i
$362$	4565.18	−	5268.50i	0.662819	−	0.764934i
$363$	−5274.77	+	3389.89i	−0.762682	+	0.490146i
$364$	−1987.79	−	2294.03i	−0.286232	−	0.330330i
$365$	2403.87	+	705.840i	0.344724	+	0.101220i
$366$	1712.47	−	3749.78i	0.244568	−	0.535530i
$367$	7515.57			1.06896			0.534482	−	0.845180i	$-0.320507\pi$
$367$	7515.57			1.06896			0.534482	+	0.845180i	$0.320507\pi$
$368$	−1948.63	+	1057.05i	−0.276031	+	0.149735i
$369$	−185.189			−0.0261261
$370$	1585.89	−	3472.61i	0.222828	−	0.487925i
$371$	−5591.42	−	1641.79i	−0.782459	−	0.229751i
$372$	−156.384	−	180.477i	−0.0217960	−	0.0251540i
$373$	−3548.93	+	2280.76i	−0.492645	+	0.316604i	−0.763268	−	0.646082i	$-0.776407\pi$
$373$	−3548.93	+	2280.76i	−0.492645	+	0.316604i	0.270623	+	0.962685i	$0.412770\pi$
$374$	−49.3202	+	56.9186i	−0.00681896	+	0.00786949i
$375$	−84.0814	+	584.799i	−0.0115785	+	0.0805304i
$376$	−1996.21	+	586.140i	−0.273794	+	0.0803933i
$377$	−409.518	−	263.181i	−0.0559449	−	0.0359536i
$378$	−568.055	−	3950.91i	−0.0772952	−	0.537600i
$379$	−2102.58	−	4604.01i	−0.284966	−	0.623990i	0.711970	−	0.702210i	$-0.247803\pi$
$379$	−2102.58	−	4604.01i	−0.284966	−	0.623990i	−0.996936	+	0.0782207i	$0.975076\pi$
$380$	−461.982	−	1011.60i	−0.0623663	−	0.136563i
$381$	444.588	+	3092.18i	0.0597820	+	0.415793i
$382$	5496.77	+	3532.56i	0.736228	+	0.473145i
$383$	−8130.89	+	2387.44i	−1.08478	+	0.318519i	−0.774787	−	0.632222i	$-0.782143\pi$
$383$	−8130.89	+	2387.44i	−1.08478	+	0.318519i	−0.309988	+	0.950741i	$0.600325\pi$
$384$	160.049	−	1113.16i	0.0212694	−	0.147932i
$385$	−88.8608	+	102.551i	−0.0117630	+	0.0135753i
$386$	−5684.32	+	3653.09i	−0.749545	+	0.481703i
$387$	−678.192	−	782.675i	−0.0890812	−	0.102805i
$388$	5715.56	+	1678.24i	0.747844	+	0.219587i
$389$	−4948.15	+	10834.9i	−0.644939	+	1.41222i	0.250977	+	0.967993i	$0.419248\pi$
$389$	−4948.15	+	10834.9i	−0.644939	+	1.41222i	−0.895915	+	0.444225i	$0.853479\pi$
$390$	3063.79			0.397798
$391$	−1911.27	−	142.010i	−0.247205	−	0.0183676i
$392$	4264.61			0.549478
$393$	−4607.57	+	10089.2i	−0.591403	+	1.29499i
$394$	−1721.47	−	505.470i	−0.220118	−	0.0646325i
$395$	2014.97	+	2325.39i	0.256668	+	0.296211i
$396$	−30.7883	+	19.7865i	−0.00390700	+	0.00251088i
$397$	7491.73	−	8645.92i	0.947102	−	1.09301i	−0.0484529	−	0.998825i	$-0.515429\pi$
$397$	7491.73	−	8645.92i	0.947102	−	1.09301i	0.995554	−	0.0941879i	$-0.0300255\pi$
$398$	283.494	−	1971.74i	0.0357042	−	0.248328i
$399$	3485.68	−	1023.49i	0.437350	−	0.128417i
$400$	−422.684	−	271.643i	−0.0528355	−	0.0339553i
$401$	−566.134	−	3937.55i	−0.0705022	−	0.490354i	−0.994227	−	0.107297i	$-0.965780\pi$
$401$	−566.134	−	3937.55i	−0.0705022	−	0.490354i	0.923725	−	0.383057i	$-0.125129\pi$
$402$	−2848.55	−	6237.45i	−0.353414	−	0.773870i
$403$	−352.518	−	771.907i	−0.0435736	−	0.0954129i
$404$	117.696	+	818.594i	0.0144940	+	0.100808i
$405$	−2445.77	−	1571.80i	−0.300077	−	0.192848i
$406$	−198.357	+	58.2429i	−0.0242470	+	0.00711957i
$407$	110.554	−	768.921i	0.0134643	−	0.0936461i
$408$	−1303.15	+	1503.91i	−0.158126	+	0.182487i
$409$	4033.63	−	2592.26i	0.487653	−	0.313396i	−0.273608	−	0.961841i	$-0.588217\pi$
$409$	4033.63	−	2592.26i	0.487653	−	0.313396i	0.761261	+	0.648446i	$0.224581\pi$
$410$	−268.568	−	309.944i	−0.0323504	−	0.0373343i
$411$	−10333.2	−	3034.10i	−1.24014	−	0.364139i
$412$	−259.018	+	567.171i	−0.0309731	+	0.0678216i
$413$	2884.51			0.343674
$414$	993.075	+	373.529i	0.117891	+	0.0443429i
$415$	−5108.56			−0.604264
$416$	3975.59	−	8705.34i	0.468557	−	1.02600i
$417$	−2334.24	−	685.394i	−0.274120	−	0.0804889i
$418$	168.827	+	194.836i	0.0197550	+	0.0227985i
$419$	−10909.4	+	7011.02i	−1.27197	+	0.817448i	−0.989876	−	0.141937i	$-0.954667\pi$
$419$	−10909.4	+	7011.02i	−1.27197	+	0.817448i	−0.282099	+	0.959385i	$0.591031\pi$
$420$	−747.918	+	863.143i	−0.0868920	+	0.100279i
$421$	1014.77	−	7057.90i	0.117475	−	0.817057i	−0.842845	−	0.538157i	$-0.819121\pi$
$421$	1014.77	−	7057.90i	0.117475	−	0.817057i	0.960320	−	0.278901i	$-0.0899701\pi$
$422$	−1469.68	+	431.536i	−0.169533	+	0.0497793i
$423$	336.601	+	216.320i	0.0386905	+	0.0248649i
$424$	−1555.05	−	10815.6i	−0.178113	−	1.23880i
$425$	−180.447	−	395.123i	−0.0205952	−	0.0450971i
$426$	−4064.93	−	8900.96i	−0.462316	−	1.01233i
$427$	777.126	+	5405.03i	0.0880743	+	0.612571i
$428$	−656.075	−	421.634i	−0.0740948	−	0.0476178i
$429$	598.185	−	175.643i	0.0673209	−	0.0197672i
$430$	326.396	−	2270.14i	0.0366052	−	0.254595i
$431$	−1143.82	+	1320.04i	−0.127833	+	0.147527i	−0.816058	−	0.577971i	$-0.803845\pi$
$431$	−1143.82	+	1320.04i	−0.127833	+	0.147527i	0.688225	+	0.725498i	$0.258390\pi$
$432$	2530.05	−	1625.96i	0.281776	−	0.181086i
$433$	6537.09	+	7544.21i	0.725526	+	0.837301i	0.991960	−	0.126552i	$-0.0403910\pi$
$433$	6537.09	+	7544.21i	0.725526	+	0.837301i	−0.266434	+	0.963853i	$0.585846\pi$
$434$	−345.781	−	101.530i	−0.0382442	−	0.0112295i
$435$	−76.0871	+	166.608i	−0.00838643	+	0.0183637i
$436$	599.256			0.0658237
$437$	−1412.24	+	6406.65i	−0.154592	+	0.701308i
$438$	−4888.34			−0.533274
$439$	1735.84	−	3800.95i	0.188717	−	0.413233i	−0.791497	−	0.611173i	$-0.790698\pi$
$439$	1735.84	−	3800.95i	0.188717	−	0.413233i	0.980214	+	0.197940i	$0.0634251\pi$
$440$	−244.128	−	71.6823i	−0.0264507	−	0.00776664i
$441$	−537.096	−	619.842i	−0.0579955	−	0.0669303i
$442$	−1894.97	+	1217.83i	−0.203925	+	0.131054i
$443$	−3546.33	+	4092.68i	−0.380341	+	0.438937i	−0.913352	−	0.407172i	$-0.866515\pi$
$443$	−3546.33	+	4092.68i	−0.380341	+	0.438937i	0.533011	+	0.846108i	$0.321061\pi$
$444$	930.505	−	6471.80i	0.0994590	−	0.691753i
$445$	−108.039	+	31.7232i	−0.0115091	+	0.00337938i
$446$	−1985.29	−	1275.87i	−0.210776	−	0.135458i
$447$	−989.744	−	6883.82i	−0.104728	−	0.728397i
$448$	−2551.50	−	5587.00i	−0.269078	−	0.589198i
$449$	3446.68	+	7547.19i	0.362270	+	0.793260i	0.999740	+	0.0227854i	$0.00725344\pi$
$449$	3446.68	+	7547.19i	0.362270	+	0.793260i	−0.637471	+	0.770475i	$0.720019\pi$
$450$	34.2227	+	238.024i	0.00358505	+	0.0249346i
$451$	−70.2049	−	45.1179i	−0.00732997	−	0.00471069i
$452$	−147.194	+	43.2201i	−0.0153173	+	0.00449757i
$453$	1213.03	−	8436.79i	0.125812	−	0.875044i
$454$	−1043.78	+	1204.59i	−0.107901	+	0.124525i
$455$	−3414.19	+	2194.17i	−0.351780	+	0.226075i
$456$	4460.76	+	5147.99i	0.458101	+	0.528677i
$457$	−2158.24	−	633.717i	−0.220915	−	0.0648665i	0.169402	−	0.985547i	$-0.445816\pi$
$457$	−2158.24	−	633.717i	−0.220915	−	0.0648665i	−0.390317	+	0.920681i	$0.627635\pi$
$458$	−53.6087	+	117.387i	−0.00546936	+	0.0119762i
$459$	2600.04			0.264400
$460$	−715.422	−	1934.44i	−0.0725146	−	0.196073i
$461$	−13866.1			−1.40089			−0.700445	−	0.713706i	$-0.747015\pi$
$461$	−13866.1			−1.40089			−0.700445	+	0.713706i	$0.747015\pi$
$462$	109.986	−	240.835i	0.0110757	−	0.0242525i
$463$	3574.99	+	1049.71i	0.358842	+	0.105365i	0.456184	−	0.889886i	$-0.349216\pi$
$463$	3574.99	+	1049.71i	0.358842	+	0.105365i	−0.0973422	+	0.995251i	$0.531034\pi$
$464$	−102.004	−	117.719i	−0.0102056	−	0.0117779i
$465$	−268.602	+	172.620i	−0.0267873	+	0.0172152i
$466$	−2308.53	+	2664.19i	−0.229486	+	0.264841i
$467$	−1569.43	+	10915.7i	−0.155513	+	1.08162i	0.751262	+	0.660005i	$0.229446\pi$
$467$	−1569.43	+	10915.7i	−0.155513	+	1.08162i	−0.906775	+	0.421615i	$0.861463\pi$
$468$	−1050.27	+	308.387i	−0.103737	+	0.0304598i
$469$	7641.34	+	4910.79i	0.752333	+	0.483495i
$470$	126.104	+	877.074i	0.0123761	+	0.0860775i
$471$	−4928.07	−	10791.0i	−0.482110	−	1.05567i
$472$	2246.82	+	4919.85i	0.219107	+	0.479776i
$473$	−66.4171	−	461.941i	−0.00645637	−	0.0449050i
$474$	−5050.54	−	3245.79i	−0.489408	−	0.314523i
$475$	−1426.67	+	418.909i	−0.137811	+	0.0404649i
$476$	119.501	−	831.148i	0.0115070	−	0.0800328i
$477$	−1376.15	+	1588.17i	−0.132096	+	0.152447i
$478$	−3854.70	+	2477.27i	−0.368849	+	0.237045i
$479$	12514.6	+	14442.6i	1.19375	+	1.37766i	0.907790	+	0.419424i	$0.137768\pi$
$479$	12514.6	+	14442.6i	1.19375	+	1.37766i	0.285963	+	0.958241i	$0.407686\pi$
$480$	−3454.97	−	1014.47i	−0.328536	−	0.0964669i
$481$	9651.76	−	21134.4i	0.914932	−	2.00342i
$482$	11137.5			1.05249
$483$	6587.42	−	1413.94i	0.620575	−	0.133202i
$484$	4960.98			0.465907
$485$	3308.55	−	7244.72i	0.309760	−	0.678280i
$486$	−2558.87	−	751.353i	−0.238833	−	0.0701277i
$487$	6485.65	+	7484.84i	0.603476	+	0.696448i	0.972482	−	0.232979i	$-0.0748473\pi$
$487$	6485.65	+	7484.84i	0.603476	+	0.696448i	−0.369006	+	0.929427i	$0.620302\pi$
$488$	−8613.54	+	5535.59i	−0.799010	+	0.513492i
$489$	8996.34	−	10382.3i	0.831960	−	0.960133i
$490$	258.490	−	1797.84i	0.0238314	−	0.165751i
$491$	−15800.7	+	4639.49i	−1.45229	+	0.426430i	−0.910298	−	0.413954i	$-0.864147\pi$
$491$	−15800.7	+	4639.49i	−1.45229	+	0.426430i	−0.541991	+	0.840384i	$0.682329\pi$
$492$	−590.896	−	379.746i	−0.0541456	−	0.0347973i
$493$	−19.1644	−	133.291i	−0.00175075	−	0.0121768i
$494$	3203.13	+	7013.87i	0.291732	+	0.638803i
$495$	20.3273	+	44.5107i	0.00184575	+	0.00404163i
$496$	−38.6431	−	268.768i	−0.00349823	−	0.0243308i
$497$	10904.3	+	7007.79i	0.984158	+	0.632480i
$498$	9563.86	−	2808.20i	0.860576	−	0.252688i
$499$	2838.65	−	19743.2i	0.254660	−	1.77120i	−0.314779	−	0.949165i	$-0.601931\pi$
$499$	2838.65	−	19743.2i	0.254660	−	1.77120i	0.569439	−	0.822033i	$-0.307160\pi$
$500$	306.119	−	353.280i	0.0273801	−	0.0315983i
$501$	−11758.2	+	7556.54i	−1.04854	+	0.673855i
$502$	−8403.37	−	9698.00i	−0.747133	−	0.862237i
$503$	10041.4	+	2948.42i	0.890108	+	0.261359i	0.694646	−	0.719352i	$-0.255561\pi$
$503$	10041.4	+	2948.42i	0.890108	+	0.261359i	0.195462	+	0.980711i	$0.437379\pi$
$504$	−606.213	+	1327.42i	−0.0535771	+	0.117318i
$505$	1105.73			0.0974347
$506$	285.470	+	383.550i	0.0250804	+	0.0336974i
$507$	8262.22			0.723744
$508$	1026.79	−	2248.35i	0.0896779	−	0.196367i
$509$	−15242.2	−	4475.53i	−1.32731	−	0.389733i	−0.460184	−	0.887823i	$-0.652217\pi$
$509$	−15242.2	−	4475.53i	−1.32731	−	0.389733i	−0.867125	+	0.498090i	$0.834035\pi$
$510$	555.019	+	640.526i	0.0481895	+	0.0556137i
$511$	5447.41	−	3500.84i	0.471583	−	0.303068i
$512$	4556.68	−	5258.69i	0.393318	−	0.453913i
$513$	1266.62	−	8809.52i	0.109011	−	0.758187i
$514$	−14749.0	+	4330.70i	−1.26566	+	0.371633i
$515$	701.316	+	450.709i	0.0600072	+	0.0385643i
$516$	−559.015	−	3888.04i	−0.0476924	−	0.331708i
$517$	74.9025	+	164.014i	0.00637177	+	0.0139522i
$518$	−4098.89	−	8975.32i	−0.347674	−	0.761299i
$519$	2569.41	+	17870.6i	0.217311	+	1.51143i
$520$	−6401.79	−	4114.18i	−0.539879	−	0.346959i
$521$	1786.15	−	524.461i	0.150197	−	0.0441019i	−0.205770	−	0.978600i	$-0.565970\pi$
$521$	1786.15	−	524.461i	0.150197	−	0.0441019i	0.355967	+	0.934499i	$0.384152\pi$
$522$	−10.6095	+	73.7904i	−0.000889585	+	0.00618720i
$523$	617.377	−	712.492i	0.0516176	−	0.0595699i	−0.729354	−	0.684137i	$-0.760179\pi$
$523$	617.377	−	712.492i	0.0516176	−	0.0595699i	0.780971	+	0.624567i	$0.214725\pi$
$524$	7382.58	−	4744.49i	0.615476	−	0.395542i
$525$	999.984	+	1154.04i	0.0831293	+	0.0959363i
$526$	906.440	+	266.155i	0.0751382	+	0.0220626i
$527$	97.5171	−	213.533i	0.00806056	−	0.0176502i
$528$	199.488			0.0164424
$529$	−3492.35	+	11655.0i	−0.287034	+	0.957920i
$530$	−4653.82			−0.381413
$531$	432.107	−	946.183i	0.0353142	−	0.0773274i
$532$	−2757.90	−	809.793i	−0.224756	−	0.0659943i
$533$	−1634.52	−	1886.33i	−0.132831	−	0.153295i
$534$	184.824	−	118.779i	0.0149778	−	0.00962563i
$535$	−682.833	+	788.031i	−0.0551803	+	0.0636814i
$536$	−2423.85	+	16858.3i	−0.195326	+	1.35852i
$537$	5862.08	−	1721.26i	0.471076	−	0.138320i
$538$	9887.19	+	6354.11i	0.792318	+	0.509192i
$539$	−52.5992	−	365.835i	−0.00420335	−	0.0292350i
$540$	1162.35	+	2545.19i	0.0926287	+	0.202829i
$541$	4680.77	+	10249.5i	0.371982	+	0.814526i	0.999359	+	0.0358106i	$0.0114013\pi$
$541$	4680.77	+	10249.5i	0.371982	+	0.814526i	−0.627377	+	0.778716i	$0.715871\pi$
$542$	1186.64	+	8253.29i	0.0940419	+	0.654076i
$543$	−13429.3	−	8630.49i	−1.06134	−	0.682080i
$544$	2540.16	−	745.859i	0.200199	−	0.0587839i
$545$	114.025	−	793.064i	0.00896203	−	0.0623323i
$546$	5185.64	−	5984.55i	0.406456	−	0.469075i
$547$	3760.78	−	2416.91i	0.293966	−	0.188920i	−0.385342	−	0.922774i	$-0.625917\pi$
$547$	3760.78	−	2416.91i	0.293966	−	0.188920i	0.679308	+	0.733853i	$0.262280\pi$
$548$	5579.98	+	6439.64i	0.434972	+	0.501985i
$549$	1889.38	+	554.773i	0.146880	+	0.0431277i
$550$	−45.0165	+	98.5724i	−0.00349002	+	0.00764208i
$551$	−460.958			−0.0356397
$552$	7542.74	+	10134.2i	0.581594	+	0.781414i
$553$	7952.66			0.611540
$554$	−5669.17	+	12413.8i	−0.434766	+	0.952004i
$555$	−8387.82	−	2462.89i	−0.641519	−	0.188367i
$556$	1260.50	+	1454.69i	0.0961459	+	0.110958i
$557$	−10237.9	+	6579.48i	−0.778802	+	0.500506i	−0.868636	−	0.495451i	$-0.835003\pi$
$557$	−10237.9	+	6579.48i	−0.778802	+	0.500506i	0.0898337	+	0.995957i	$0.471366\pi$
$558$	−85.1030	+	98.2141i	−0.00645645	+	0.00745114i
$559$	1986.46	−	13816.1i	0.150301	−	1.04537i
$560$	−1246.02	+	365.864i	−0.0940249	+	0.0276082i
$561$	145.084	+	93.2400i	0.0109188	+	0.00701711i
$562$	−1042.29	−	7249.32i	−0.0782323	−	0.544118i
$563$	−1744.95	−	3820.92i	−0.130624	−	0.286026i	0.833008	−	0.553262i	$-0.186617\pi$
$563$	−1744.95	−	3820.92i	−0.130624	−	0.286026i	−0.963631	+	0.267236i	$0.913890\pi$
$564$	630.434	+	1380.46i	0.0470675	+	0.103063i
$565$	29.1902	+	203.022i	0.00217353	+	0.0151172i
$566$	−16029.3	−	10301.4i	−1.19039	−	0.765019i
$567$	−7209.82	+	2116.99i	−0.534011	+	0.156800i
$568$	−3458.89	+	24057.1i	−0.255513	+	1.77713i
$569$	4353.75	−	5024.49i	0.320771	−	0.370189i	−0.572347	−	0.820011i	$-0.693967\pi$
$569$	4353.75	−	5024.49i	0.320771	−	0.370189i	0.893118	+	0.449822i	$0.148513\pi$
$570$	2440.63	−	1568.50i	0.179345	−	0.115258i
$571$	13437.1	+	15507.3i	0.984811	+	1.13653i	0.990633	+	0.136549i	$0.0436013\pi$
$571$	13437.1	+	15507.3i	0.984811	+	1.13653i	−0.00582222	+	0.999983i	$0.501853\pi$
$572$	−473.289	−	138.970i	−0.0345965	−	0.0101585i
$573$	6215.56	−	13610.2i	0.453156	−	0.992274i
$574$	−1059.99			−0.0770783
$575$	−2696.19	+	578.718i	−0.195546	+	0.0419725i
$576$	−2214.88			−0.160220
$577$	−5946.10	+	13020.2i	−0.429011	+	0.939404i	0.564475	+	0.825450i	$0.309079\pi$
$577$	−5946.10	+	13020.2i	−0.429011	+	0.939404i	−0.993486	+	0.113954i	$0.963649\pi$
$578$	9132.08	+	2681.42i	0.657170	+	0.192963i
$579$	10132.5	+	11693.6i	0.727278	+	0.839323i
$580$	121.912	−	78.3482i	0.00872780	−	0.00560902i
$581$	−8646.53	+	9978.63i	−0.617416	+	0.712536i
$582$	−2211.56	+	15381.7i	−0.157512	+	1.09552i
$583$	−908.627	+	266.797i	−0.0645480	+	0.0189530i
$584$	10214.2	+	6564.26i	0.723743	+	0.465121i
$585$	208.280	+	1448.62i	0.0147202	+	0.102381i
$586$	630.083	+	1379.69i	0.0444172	+	0.0972602i
$587$	−3895.56	−	8530.09i	−0.273913	−	0.599786i	0.721818	−	0.692083i	$-0.243307\pi$
$587$	−3895.56	−	8530.09i	−0.273913	−	0.599786i	−0.995732	+	0.0922963i	$0.970579\pi$
$588$	−442.714	−	3079.14i	−0.0310497	−	0.215955i
$589$	−675.992	−	434.433i	−0.0472899	−	0.0303914i
$590$	2210.26	−	648.990i	0.154229	−	0.0452856i
$591$	−584.690	+	4066.61i	−0.0406953	+	0.283042i
$592$	4868.50	−	5618.55i	0.337997	−	0.390069i
$593$	16566.2	−	10646.4i	1.14720	−	0.737263i	0.178123	−	0.984008i	$-0.442998\pi$
$593$	16566.2	−	10646.4i	1.14720	−	0.737263i	0.969080	+	0.246746i	$0.0793612\pi$
$594$	−424.768	−	490.209i	−0.0293408	−	0.0338611i
$595$	−1077.21	−	316.299i	−0.0742210	−	0.0217933i
$596$	−2285.84	+	5005.29i	−0.157100	+	0.344001i
$597$	−4561.53			−0.312715
$598$	4960.33	+	13412.3i	0.339202	+	0.917174i
$599$	10662.0			0.727275			0.363638	−	0.931540i	$-0.381535\pi$
$599$	10662.0			0.727275			0.363638	+	0.931540i	$0.381535\pi$
$600$	−1189.43	+	2604.49i	−0.0809307	+	0.177213i
$601$	−16785.0	−	4928.51i	−1.13922	−	0.334506i	−0.342896	−	0.939373i	$-0.611408\pi$
$601$	−16785.0	−	4928.51i	−1.13922	−	0.334506i	−0.796326	+	0.604868i	$0.793226\pi$
$602$	−3881.84	−	4479.89i	−0.262811	−	0.303300i
$603$	2755.54	−	1770.88i	0.186093	−	0.119595i
$604$	−4416.32	+	5096.70i	−0.297512	+	0.343347i
$605$	943.967	−	6565.44i	0.0634342	−	0.441195i
$606$	−2070.07	+	607.827i	−0.138764	+	0.0407447i
$607$	−4317.04	−	2774.39i	−0.288671	−	0.185518i	0.388288	−	0.921538i	$-0.373066\pi$
$607$	−4317.04	−	2774.39i	−0.288671	−	0.185518i	−0.676960	+	0.736020i	$0.736703\pi$
$608$	−1289.69	−	8969.99i	−0.0860261	−	0.598324i
$609$	196.655	+	430.615i	0.0130852	+	0.0286525i
$610$	1811.56	+	3966.76i	0.120242	+	0.263294i
$611$	767.474	+	5337.90i	0.0508162	+	0.353434i
$612$	−254.733	−	163.707i	−0.0168251	−	0.0108129i
$613$	−20293.0	+	5958.58i	−1.33708	+	0.392601i	−0.870626	−	0.491945i	$-0.836286\pi$
$613$	−20293.0	+	5958.58i	−1.33708	+	0.392601i	−0.466451	+	0.884547i	$0.654468\pi$
$614$	−2828.25	+	19670.9i	−0.185894	+	1.29292i
$615$	−614.996	+	709.743i	−0.0403236	+	0.0465359i
$616$	−553.217	+	355.531i	−0.0361847	+	0.0232545i
$617$	4743.49	+	5474.28i	0.309507	+	0.357190i	0.889098	−	0.457718i	$-0.151333\pi$
$617$	4743.49	+	5474.28i	0.309507	+	0.357190i	−0.579591	+	0.814908i	$0.696788\pi$
$618$	−1560.71	−	458.265i	−0.101587	−	0.0298287i
$619$	2772.72	−	6071.42i	0.180041	−	0.394234i	−0.797997	−	0.602661i	$-0.794107\pi$
$619$	2772.72	−	6071.42i	0.180041	−	0.394234i	0.978038	+	0.208427i	$0.0668344\pi$
$620$	252.623			0.0163639
$621$	3553.21	−	16119.1i	0.229606	−	1.04161i
$622$	6136.65			0.395591
$623$	−120.897	+	264.728i	−0.00777470	+	0.0170242i
$624$	5724.77	+	1680.94i	0.367266	+	0.107839i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	14487.8	−	9310.72i	0.924996	−	0.594459i
$627$	386.597	−	446.157i	0.0246239	−	0.0284175i
$628$	−1335.78	+	9290.58i	−0.0848783	+	0.590342i
$629$	6166.88	−	1810.76i	0.390922	−	0.114785i
$630$	522.859	+	336.021i	0.0330654	+	0.0212499i
$631$	2541.03	+	17673.3i	0.160312	+	1.11499i	0.898045	+	0.439903i	$0.144987\pi$
$631$	2541.03	+	17673.3i	0.160312	+	1.11499i	−0.737733	+	0.675092i	$0.764104\pi$
$632$	6194.53	+	13564.1i	0.389882	+	0.853722i
$633$	1457.07	+	3190.53i	0.0914901	+	0.200335i
$634$	−1797.20	−	12499.8i	−0.112581	−	0.783016i
$635$	−2780.13	−	1786.68i	−0.173742	−	0.111657i
$636$	−7647.67	+	2245.56i	−0.476808	+	0.140004i
$637$	1573.18	−	10941.7i	0.0978520	−	0.680575i
$638$	−21.9998	+	25.3891i	−0.00136517	+	0.00157549i
$639$	3932.21	−	2527.08i	0.243436	−	0.156447i
$640$	779.077	+	899.103i	0.0481183	+	0.0555315i
$641$	24019.3	+	7052.70i	1.48004	+	0.434578i	0.919347	−	0.393447i	$-0.128718\pi$
$641$	24019.3	+	7052.70i	1.48004	+	0.434578i	0.560691	+	0.828025i	$0.310536\pi$
$642$	845.163	−	1850.65i	0.0519562	−	0.113768i
$643$	8767.81			0.537743			0.268872	−	0.963176i	$-0.413349\pi$
$643$	8767.81			0.537743			0.268872	+	0.963176i	$0.413349\pi$
$644$	−4989.46	−	1876.70i	−0.305298	−	0.114833i
$645$	−5251.85			−0.320607
$646$	−886.081	+	1940.25i	−0.0539666	+	0.118170i
$647$	−16494.7	−	4843.27i	−1.00228	−	0.294295i	−0.260886	−	0.965370i	$-0.584015\pi$
$647$	−16494.7	−	4843.27i	−1.00228	−	0.294295i	−0.741389	+	0.671075i	$0.765833\pi$
$648$	−9226.68	−	10648.2i	−0.559349	−	0.645523i
$649$	394.332	−	253.422i	0.0238504	−	0.0153277i
$650$	−2122.46	+	2449.44i	−0.128076	+	0.147808i
$651$	−117.443	+	816.833i	−0.00707058	+	0.0491770i
$652$	−10429.2	+	3062.28i	−0.626438	+	0.183939i
$653$	−26295.3	−	16898.9i	−1.57582	−	1.01272i	−0.977363	−	0.211567i	$-0.932143\pi$
$653$	−26295.3	−	16898.9i	−1.57582	−	1.01272i	−0.598460	−	0.801153i	$-0.704220\pi$
$654$	222.482	+	1547.39i	0.0133023	+	0.0925197i
$655$	−4874.19	−	10673.0i	−0.290764	−	0.636684i
$656$	−331.776	−	726.487i	−0.0197464	−	0.0432387i
$657$	−332.315	−	2311.30i	−0.0197334	−	0.137249i
$658$	1926.64	+	1238.18i	0.114146	+	0.0733573i
$659$	14625.9	−	4294.55i	0.864559	−	0.253857i	0.180759	−	0.983527i	$-0.442145\pi$
$659$	14625.9	−	4294.55i	0.864559	−	0.253857i	0.683799	+	0.729670i	$0.260326\pi$
$660$	−26.4130	+	183.707i	−0.00155777	+	0.0108345i
$661$	9838.14	−	11353.8i	0.578910	−	0.668097i	−0.388460	−	0.921465i	$-0.626993\pi$
$661$	9838.14	−	11353.8i	0.578910	−	0.668097i	0.967370	+	0.253368i	$0.0815384\pi$
$662$	15902.4	−	10219.9i	0.933633	−	0.600010i
$663$	3377.87	+	3898.26i	0.197866	+	0.228350i
$664$	−23754.6	−	6974.99i	−1.38834	−	0.407654i
$665$	−1596.46	+	3495.76i	−0.0930949	+	0.203849i
$666$	−3558.13			−0.207019
$667$	−852.541	−	63.3448i	−0.0494910	−	0.00367724i
$668$	11058.7			0.640532
$669$	−2244.90	+	4915.64i	−0.129735	+	0.284080i
$670$	6960.06	+	2043.66i	0.401329	+	0.117841i
$671$	581.103	+	670.629i	0.0334325	+	0.0385832i
$672$	−7829.32	+	5031.60i	−0.449438	+	0.288836i
$673$	−9552.95	+	11024.7i	−0.547161	+	0.631457i	−0.960219	−	0.279247i	$-0.909915\pi$
$673$	−9552.95	+	11024.7i	−0.547161	+	0.631457i	0.413058	+	0.910705i	$0.364461\pi$
$674$	629.201	−	4376.19i	0.0359583	−	0.250096i
$675$	3589.51	−	1053.97i	0.204682	−	0.0601000i
$676$	−5499.39	−	3534.24i	−0.312892	−	0.201084i
$677$	−1779.38	−	12375.9i	−0.101015	−	0.702576i	−0.975896	−	0.218237i	$-0.929969\pi$
$677$	−1779.38	−	12375.9i	−0.101015	−	0.702576i	0.874881	−	0.484339i	$-0.160940\pi$
$678$	−166.250	−	364.037i	−0.00941711	−	0.0206206i
$679$	−8551.30	−	18724.7i	−0.483312	−	1.05831i
$680$	−299.588	−	2083.68i	−0.0168951	−	0.117508i
$681$	3070.47	+	1973.27i	0.172777	+	0.111037i
$682$	−56.1906	+	16.4991i	−0.00315491	+	0.000926366i
$683$	3755.80	−	26122.1i	0.210412	−	1.46345i	−0.561371	−	0.827564i	$-0.689726\pi$
$683$	3755.80	−	26122.1i	0.210412	−	1.46345i	0.771783	−	0.635885i	$-0.219365\pi$
$684$	−678.771	+	783.344i	−0.0379437	+	0.0437893i
$685$	9584.06	−	6159.30i	0.534581	−	0.343554i
$686$	−9065.66	−	10462.3i	−0.504560	−	0.582294i
$687$	283.538	+	83.2544i	0.0157462	+	0.00462351i
$688$	1855.38	−	4062.72i	0.102814	−	0.225131i
$689$	−28323.3			−1.56608
$690$	4729.48	−	2565.54i	0.260940	−	0.141549i
$691$	−13670.9			−0.752628			−0.376314	−	0.926492i	$-0.622809\pi$
$691$	−13670.9			−0.752628			−0.376314	+	0.926492i	$0.622809\pi$
$692$	5934.11	−	12993.9i	0.325984	−	0.713806i
$693$	121.348	+	35.6311i	0.00665173	+	0.00195312i
$694$	6547.24	+	7555.91i	0.358112	+	0.413283i
$695$	2165.01	−	1391.37i	0.118163	−	0.0759390i
$696$	−581.280	+	670.833i	−0.0316572	+	0.0365343i
$697$	98.2630	−	683.434i	0.00533999	−	0.0371405i
$698$	−1462.00	+	429.281i	−0.0792800	+	0.0232787i
$699$	6790.96	+	4364.28i	0.367464	+	0.236155i
$700$	−171.943	−	1195.89i	−0.00928406	−	0.0645721i
$701$	−5761.60	−	12616.1i	−0.310432	−	0.679750i	0.688535	−	0.725203i	$-0.258254\pi$
$701$	−5761.60	−	12616.1i	−0.310432	−	0.679750i	−0.998966	+	0.0454529i	$0.985527\pi$
$702$	−8059.07	−	17646.9i	−0.433291	−	0.948774i
$703$	−3131.05	−	21776.9i	−0.167980	−	1.16832i
$704$	−839.658	−	539.616i	−0.0449514	−	0.0288885i
$705$	1946.88	−	571.655i	0.104005	−	0.0305387i
$706$	−913.903	+	6356.33i	−0.0487184	+	0.338844i
$707$	1871.52	−	2159.84i	0.0995553	−	0.114893i
$708$	3318.99	−	2132.99i	0.176180	−	0.113224i
$709$	−22355.4	−	25799.5i	−1.18417	−	1.36660i	−0.914973	−	0.403515i	$-0.867788\pi$
$709$	−22355.4	−	25799.5i	−1.18417	−	1.36660i	−0.269194	−	0.963086i	$-0.586757\pi$
$710$	9932.14	+	2916.34i	0.524995	+	0.154152i
$711$	1191.33	−	2608.65i	0.0628388	−	0.137598i
$712$	−545.692			−0.0287228
$713$	−1190.55	−	896.379i	−0.0625334	−	0.0470823i
$714$	2190.55			0.114817
$715$	−273.972	+	599.915i	−0.0143300	+	0.0313784i
$716$	−4638.13	−	1361.88i	−0.242088	−	0.0710835i
$717$	6871.16	+	7929.74i	0.357891	+	0.413029i
$718$	3039.76	−	1953.54i	0.157998	−	0.101539i
$719$	8462.68	−	9766.45i	0.438949	−	0.506575i	−0.492567	−	0.870275i	$-0.663941\pi$
$719$	8462.68	−	9766.45i	0.438949	−	0.506575i	0.931516	+	0.363700i	$0.118487\pi$
$720$	−66.6454	+	463.529i	−0.00344962	+	0.0239927i
$721$	2067.39	−	607.041i	0.106787	−	0.0313556i
$722$	−5767.62	−	3706.62i	−0.297297	−	0.191061i
$723$	−3629.58	−	25244.3i	−0.186702	−	1.29854i
$724$	5246.86	+	11489.0i	0.269334	+	0.589760i
$725$	−80.4899	−	176.248i	−0.00412320	−	0.00902854i
$726$	1841.83	+	12810.2i	0.0941553	+	0.654864i
$727$	24163.4	+	15528.9i	1.23270	+	0.792207i	0.984309	−	0.176454i	$-0.0564627\pi$
$727$	24163.4	+	15528.9i	1.23270	+	0.792207i	0.248389	+	0.968660i	$0.420099\pi$
$728$	−18871.7	+	5541.22i	−0.960757	+	0.282104i
$729$	−3103.36	+	21584.4i	−0.157667	+	1.09660i
$730$	3386.42	−	3908.13i	0.171694	−	0.198146i
$731$	3248.30	−	2087.55i	0.164354	−	0.105624i
$732$	4890.99	+	5644.50i	0.246962	+	0.285009i
$733$	2716.88	+	797.747i	0.136903	+	0.0401984i	0.349466	−	0.936949i	$-0.386363\pi$
$733$	2716.88	+	797.747i	0.136903	+	0.0401984i	−0.212563	+	0.977147i	$0.568181\pi$
$734$	6444.17	−	14110.8i	0.324058	−	0.709588i
$735$	−4159.22			−0.208728
$736$	−1152.63	−	16767.2i	−0.0577260	−	0.839739i
$737$	1476.07			0.0737742
$738$	−158.789	+	347.699i	−0.00792017	+	0.0173428i
$739$	−25919.9	−	7610.76i	−1.29023	−	0.378845i	−0.436565	−	0.899673i	$-0.643805\pi$
$739$	−25919.9	−	7610.76i	−1.29023	−	0.378845i	−0.853662	+	0.520828i	$0.825623\pi$
$740$	4529.47	+	5227.29i	0.225009	+	0.259674i
$741$	14853.7	−	9545.92i	0.736391	−	0.473250i
$742$	−7876.84	+	9090.36i	−0.389714	+	0.449754i
$743$	−4104.10	+	28544.7i	−0.202645	+	1.40942i	0.593752	+	0.804648i	$0.297646\pi$
$743$	−4104.10	+	28544.7i	−0.202645	+	1.40942i	−0.796396	+	0.604775i	$0.793263\pi$
$744$	−1484.68	+	435.940i	−0.0731598	+	0.0214816i
$745$	6189.13	+	3977.51i	0.304365	+	0.195604i
$746$	1239.21	+	8618.86i	0.0608184	+	0.423001i
$747$	1977.94	+	4331.08i	0.0968794	+	0.212136i
$748$	−56.6848	−	124.122i	−0.00277086	−	0.00606733i
$749$	383.539	+	2667.57i	0.0187106	+	0.130135i
$750$	1025.89	+	659.298i	0.0499468	+	0.0320989i
$751$	2738.31	−	804.040i	0.133052	−	0.0390677i	−0.214528	−	0.976718i	$-0.568821\pi$
$751$	2738.31	−	804.040i	0.133052	−	0.0390677i	0.347581	+	0.937650i	$0.387003\pi$
$752$	−245.576	+	1708.02i	−0.0119086	+	0.0828258i
$753$	−19242.9	+	22207.5i	−0.931276	+	1.07475i
$754$	−845.270	+	543.222i	−0.0408262	+	0.0262374i
$755$	5904.72	+	6814.41i	0.284629	+	0.328479i
$756$	6938.89	+	2037.44i	0.333816	+	0.0980172i
$757$	−5734.07	+	12555.9i	−0.275308	+	0.602841i	−0.995894	−	0.0905246i	$-0.971146\pi$
$757$	−5734.07	+	12555.9i	−0.275308	+	0.602841i	0.720586	+	0.693366i	$0.243873\pi$
$758$	−10447.0			−0.500598
$759$	776.321	−	772.040i	0.0371261	−	0.0369213i
$760$	−7205.93			−0.343930
$761$	−1668.83	+	3654.23i	−0.0794941	+	0.174068i	−0.945206	−	0.326475i	$-0.894139\pi$
$761$	−1668.83	+	3654.23i	−0.0794941	+	0.174068i	0.865712	+	0.500543i	$0.166866\pi$
$762$	6186.89	+	1816.63i	0.294130	+	0.0863645i
$763$	−1356.11	−	1565.03i	−0.0643439	−	0.0742568i
$764$	−9959.00	+	6400.26i</

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)

\(f(q)\)	\(=\)	\(q+(0.857442 - 1.87754i) q^{2} +(-4.53505 - 1.33161i) q^{3} +(2.44895 + 2.82624i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-6.38869 + 7.37294i) q^{6} +(1.83914 - 12.7915i) q^{7} +(23.2498 - 6.82676i) q^{8} +(-3.92038 - 2.51948i) q^{9} +O(q^{10})\)	\(q+(0.857442 - 1.87754i) q^{2} +(-4.53505 - 1.33161i) q^{3} +(2.44895 + 2.82624i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-6.38869 + 7.37294i) q^{6} +(1.83914 - 12.7915i) q^{7} +(23.2498 - 6.82676i) q^{8} +(-3.92038 - 2.51948i) q^{9} +(-1.46873 - 10.2153i) q^{10} +(-0.872387 - 1.91026i) q^{11} +(-7.34265 - 16.0782i) q^{12} +(-8.93876 - 62.1704i) q^{13} +(-22.4395 - 14.4210i) q^{14} +(-22.6752 + 6.65805i) q^{15} +(2.86022 - 19.8933i) q^{16} +(11.3782 - 13.1312i) q^{17} +(-8.09191 + 5.20035i) q^{18} +(-38.9485 - 44.9490i) q^{19} +(17.9408 + 5.26791i) q^{20} +(-25.3738 + 55.5610i) q^{21} -4.33461 q^{22} +(-65.8584 - 88.4854i) q^{23} -114.530 q^{24} +(10.3854 - 22.7408i) q^{25} +(-124.392 - 36.5247i) q^{26} +(97.9946 + 113.092i) q^{27} +(40.6557 - 26.1279i) q^{28} +(5.07537 - 5.85729i) q^{29} +(-6.94197 + 48.2825i) q^{30} +(12.9633 - 3.80635i) q^{31} +(128.180 + 82.3762i) q^{32} +(1.41259 + 9.82481i) q^{33} +(-14.8981 - 32.6223i) q^{34} +(-26.8421 - 58.7760i) q^{35} +(-2.48018 - 17.2500i) q^{36} +(311.189 + 199.989i) q^{37} +(-117.790 + 34.5861i) q^{38} +(-42.2491 + 293.849i) q^{39} +(79.3408 - 91.5642i) q^{40} +(33.4303 - 21.4843i) q^{41} +(82.5611 + 95.2806i) q^{42} +(213.228 + 62.6094i) q^{43} +(3.26242 - 7.14371i) q^{44} -23.3008 q^{45} +(-222.604 + 47.7804i) q^{46} -85.8592 q^{47} +(-39.4613 + 86.4082i) q^{48} +(168.866 + 49.5837i) q^{49} +(-33.7918 - 38.9978i) q^{50} +(-69.0865 + 44.3992i) q^{51} +(153.818 - 177.515i) q^{52} +(64.1751 - 446.348i) q^{53} +(296.359 - 87.0188i) q^{54} +(-8.83332 - 5.67683i) q^{55} +(-44.5648 - 309.955i) q^{56} +(116.779 + 255.710i) q^{57} +(-6.64544 - 14.5515i) q^{58} +(31.7657 + 220.935i) q^{59} +(-74.3477 - 47.7804i) q^{60} +(-405.433 + 119.046i) q^{61} +(3.96867 - 27.6027i) q^{62} +(-39.4379 + 45.5138i) q^{63} +(399.830 - 256.955i) q^{64} +(-205.658 - 237.342i) q^{65} +(19.6576 + 5.77201i) q^{66} +(-291.985 + 639.358i) q^{67} +64.9767 q^{68} +(180.843 + 488.983i) q^{69} -133.370 q^{70} +(-416.668 + 912.376i) q^{71} +(-108.348 - 31.8138i) q^{72} +(328.131 + 378.684i) q^{73} +(642.313 - 412.790i) q^{74} +(-77.3800 + 89.3013i) q^{75} +(31.6536 - 220.156i) q^{76} +(-26.0395 + 7.64589i) q^{77} +(515.485 + 331.282i) q^{78} +(87.5788 + 609.124i) q^{79} +(-41.7447 - 91.4081i) q^{80} +(-241.547 - 528.913i) q^{81} +(-11.6731 - 81.1882i) q^{82} +(-859.520 - 552.380i) q^{83} +(-219.168 + 64.3535i) q^{84} +(12.3636 - 85.9911i) q^{85} +(300.382 - 346.659i) q^{86} +(-30.8167 + 19.8047i) q^{87} +(-33.3238 - 38.4577i) q^{88} +(-21.6078 - 6.34464i) q^{89} +(-19.9791 + 43.7481i) q^{90} -811.691 q^{91} +(88.7971 - 402.828i) q^{92} -63.8575 q^{93} +(-73.6193 + 161.204i) q^{94} +(-285.334 - 83.7817i) q^{95} +(-471.609 - 544.266i) q^{96} +(1340.02 - 861.181i) q^{97} +(237.888 - 274.538i) q^{98} +(-1.39277 + 9.68691i) 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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