LMFDB - Embedded newform 115.4.g.a.16.2

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			16.2
Character	$\chi$	$=$	115.16
Dual form			115.4.g.a.36.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.78120 + 3.20967i) q^{2} +(0.620793 - 0.398960i) q^{3} +(-1.42842 - 9.93487i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.446019 + 3.10213i) q^{6} +(-1.32223 + 0.388243i) q^{7} +(7.27793 + 4.67724i) q^{8} +(-10.9900 + 24.0647i) q^{9} +O(q^{10})$	\(q+(-2.78120 + 3.20967i) q^{2} +(0.620793 - 0.398960i) q^{3} +(-1.42842 - 9.93487i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.446019 + 3.10213i) q^{6} +(-1.32223 + 0.388243i) q^{7} +(7.27793 + 4.67724i) q^{8} +(-10.9900 + 24.0647i) q^{9} +(-20.3748 - 5.98259i) q^{10} +(-14.8819 - 17.1746i) q^{11} +(-4.85037 - 5.59762i) q^{12} +(-74.9993 - 22.0218i) q^{13} +(2.43126 - 5.32372i) q^{14} +(3.10397 + 1.99480i) q^{15} +(41.7900 - 12.2706i) q^{16} +(11.2099 - 77.9669i) q^{17} +(-46.6745 - 102.203i) q^{18} +(15.1094 + 105.088i) q^{19} +(42.2184 - 27.1322i) q^{20} +(-0.665941 + 0.768537i) q^{21} +96.5144 q^{22} +(-34.9765 - 104.612i) q^{23} +6.38412 q^{24} +(-16.3715 + 18.8937i) q^{25} +(279.271 - 179.476i) q^{26} +(5.61387 + 39.0453i) q^{27} +(5.74585 + 12.5817i) q^{28} +(37.5529 - 261.186i) q^{29} +(-15.0354 + 4.41479i) q^{30} +(-169.450 - 108.899i) q^{31} +(-105.592 + 231.215i) q^{32} +(-16.0906 - 4.72462i) q^{33} +(219.071 + 252.821i) q^{34} +(-4.51217 - 5.20732i) q^{35} +(254.778 + 74.8096i) q^{36} +(55.8043 - 122.194i) q^{37} +(-379.321 - 243.775i) q^{38} +(-55.3449 + 16.2507i) q^{39} +(-6.15603 + 42.8161i) q^{40} +(154.173 + 337.593i) q^{41} +(-0.614638 - 4.27490i) q^{42} +(-376.985 + 242.274i) q^{43} +(-149.370 + 172.382i) q^{44} -132.277 q^{45} +(433.046 + 178.683i) q^{46} -376.918 q^{47} +(21.0474 - 24.2901i) q^{48} +(-286.952 + 184.413i) q^{49} +(-15.1103 - 105.094i) q^{50} +(-24.1466 - 52.8737i) q^{51} +(-111.653 + 776.565i) q^{52} +(-236.779 + 69.5246i) q^{53} +(-140.936 - 90.5740i) q^{54} +(47.2021 - 103.358i) q^{55} +(-11.4390 - 3.35880i) q^{56} +(51.3058 + 59.2101i) q^{57} +(733.879 + 846.942i) q^{58} +(-93.6935 - 27.5109i) q^{59} +(15.3843 - 33.6869i) q^{60} +(650.166 + 417.836i) q^{61} +(820.804 - 241.010i) q^{62} +(5.18838 - 36.0860i) q^{63} +(-303.706 - 665.024i) q^{64} +(-55.6206 - 386.850i) q^{65} +(59.9155 - 38.5054i) q^{66} +(-147.259 + 169.945i) q^{67} -790.604 q^{68} +(-63.4491 - 50.9881i) q^{69} +29.2630 q^{70} +(178.320 - 205.792i) q^{71} +(-192.541 + 123.738i) q^{72} +(56.5199 + 393.104i) q^{73} +(237.001 + 518.960i) q^{74} +(-2.62549 + 18.2607i) q^{75} +(1022.46 - 300.220i) q^{76} +(26.3453 + 16.9311i) q^{77} +(101.766 - 222.835i) q^{78} +(-17.1560 - 5.03745i) q^{79} +(142.610 + 164.580i) q^{80} +(-448.703 - 517.830i) q^{81} +(-1512.35 - 444.066i) q^{82} +(362.501 - 793.767i) q^{83} +(8.58656 + 5.51825i) q^{84} +(377.890 - 110.958i) q^{85} +(270.851 - 1883.81i) q^{86} +(-80.8901 - 177.125i) q^{87} +(-27.9795 - 194.602i) q^{88} +(-535.468 + 344.125i) q^{89} +(367.889 - 424.566i) q^{90} +107.717 q^{91} +(-989.344 + 496.917i) q^{92} -148.640 q^{93} +(1048.28 - 1209.78i) q^{94} +(-446.575 + 286.996i) q^{95} +(26.6944 + 185.664i) q^{96} +(241.129 + 528.000i) q^{97} +(206.165 - 1433.91i) q^{98} +(576.855 - 169.380i) 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 $

$2$	−2.78120	+	3.20967i	−0.983301	+	1.13479i	0.00756923	+	0.999971i	$0.497591\pi$
$2$	−2.78120	+	3.20967i	−0.983301	+	1.13479i	−0.990870	+	0.134819i	$0.956955\pi$
$3$	0.620793	−	0.398960i	0.119472	−	0.0767798i	−0.479540	−	0.877520i	$-0.659197\pi$
$3$	0.620793	−	0.398960i	0.119472	−	0.0767798i	0.599012	+	0.800740i	$0.295560\pi$
$4$	−1.42842	−	9.93487i	−0.178552	−	1.24186i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$6$	−0.446019	+	3.10213i	−0.0303477	+	0.211073i
$7$	−1.32223	+	0.388243i	−0.0713940	+	0.0209632i	−0.317234	−	0.948347i	$-0.602754\pi$
$7$	−1.32223	+	0.388243i	−0.0713940	+	0.0209632i	0.245841	+	0.969310i	$0.420936\pi$
$8$	7.27793	+	4.67724i	0.321642	+	0.206707i
$9$	−10.9900	+	24.0647i	−0.407037	+	0.891286i
$10$	−20.3748	−	5.98259i	−0.644309	−	0.189186i
$11$	−14.8819	−	17.1746i	−0.407915	−	0.470759i	0.514203	−	0.857669i	$-0.328088\pi$
$11$	−14.8819	−	17.1746i	−0.407915	−	0.470759i	−0.922118	+	0.386910i	$0.873542\pi$
$12$	−4.85037	−	5.59762i	−0.116682	−	0.134658i
$13$	−74.9993	−	22.0218i	−1.60008	−	0.469827i	−0.644513	−	0.764593i	$-0.722940\pi$
$13$	−74.9993	−	22.0218i	−1.60008	−	0.469827i	−0.955569	+	0.294766i	$0.904758\pi$
$14$	2.43126	−	5.32372i	0.0464130	−	0.101630i
$15$	3.10397	+	1.99480i	0.0534294	+	0.0343370i
$16$	41.7900	−	12.2706i	0.652968	−	0.191729i
$17$	11.2099	−	77.9669i	0.159930	−	1.11234i	−0.738828	−	0.673894i	$-0.764620\pi$
$17$	11.2099	−	77.9669i	0.159930	−	1.11234i	0.898758	−	0.438445i	$-0.144470\pi$
$18$	−46.6745	−	102.203i	−0.611183	−	1.33830i
$19$	15.1094	+	105.088i	0.182439	+	1.26889i	0.850973	+	0.525209i	$0.176013\pi$
$19$	15.1094	+	105.088i	0.182439	+	1.26889i	−0.668534	+	0.743681i	$0.733078\pi$
$20$	42.2184	−	27.1322i	0.472017	−	0.303347i
$21$	−0.665941	+	0.768537i	−0.00692001	+	0.00798612i
$22$	96.5144			0.935315
$23$	−34.9765	−	104.612i	−0.317092	−	0.948395i
$23$	−34.9765	−	104.612i	−0.317092	−	0.948395i
$24$	6.38412			0.0542980
$25$	−16.3715	+	18.8937i	−0.130972	+	0.151150i
$26$	279.271	−	179.476i	2.10652	−	1.35378i
$27$	5.61387	+	39.0453i	0.0400144	+	0.278307i
$28$	5.74585	+	12.5817i	0.0387808	+	0.0849182i
$29$	37.5529	−	261.186i	0.240462	−	1.67245i	−0.409368	−	0.912369i	$-0.634251\pi$
$29$	37.5529	−	261.186i	0.240462	−	1.67245i	0.649830	−	0.760080i	$-0.274840\pi$
$30$	−15.0354	+	4.41479i	−0.0915024	+	0.0268675i
$31$	−169.450	−	108.899i	−0.981747	−	0.630930i	−0.0518130	−	0.998657i	$-0.516500\pi$
$31$	−169.450	−	108.899i	−0.981747	−	0.630930i	−0.929934	+	0.367726i	$0.880136\pi$
$32$	−105.592	+	231.215i	−0.583321	+	1.27729i
$33$	−16.0906	−	4.72462i	−0.0848791	−	0.0249227i
$34$	219.071	+	252.821i	1.10501	+	1.27525i
$35$	−4.51217	−	5.20732i	−0.0217913	−	0.0251485i
$36$	254.778	+	74.8096i	1.17953	+	0.346341i
$37$	55.8043	−	122.194i	0.247951	−	0.542936i	−0.744204	−	0.667952i	$-0.767171\pi$
$37$	55.8043	−	122.194i	0.247951	−	0.542936i	0.992155	+	0.125016i	$0.0398983\pi$
$38$	−379.321	−	243.775i	−1.61932	−	1.04067i
$39$	−55.3449	+	16.2507i	−0.227238	+	0.0667231i
$40$	−6.15603	+	42.8161i	−0.0243339	+	0.169246i
$41$	154.173	+	337.593i	0.587265	+	1.28593i	0.937081	+	0.349112i	$0.113517\pi$
$41$	154.173	+	337.593i	0.587265	+	1.28593i	−0.349816	+	0.936818i	$0.613756\pi$
$42$	−0.614638	−	4.27490i	−0.00225811	−	0.0157055i
$43$	−376.985	+	242.274i	−1.33697	+	0.859219i	−0.996705	−	0.0811107i	$-0.974153\pi$
$43$	−376.985	+	242.274i	−1.33697	+	0.859219i	−0.340265	+	0.940329i	$0.610517\pi$
$44$	−149.370	+	172.382i	−0.511782	+	0.590628i
$45$	−132.277			−0.438194
$46$	433.046	+	178.683i	1.38803	+	0.572725i
$47$	−376.918			−1.16977			−0.584884	−	0.811117i	$-0.698860\pi$
$47$	−376.918			−1.16977			−0.584884	+	0.811117i	$0.698860\pi$
$48$	21.0474	−	24.2901i	0.0632904	−	0.0730410i
$49$	−286.952	+	184.413i	−0.836596	+	0.537648i
$50$	−15.1103	−	105.094i	−0.0427383	−	0.297252i
$51$	−24.1466	−	52.8737i	−0.0662980	−	0.145172i
$52$	−111.653	+	776.565i	−0.297760	+	2.07097i
$53$	−236.779	+	69.5246i	−0.613662	+	0.180187i	−0.573770	−	0.819016i	$-0.694520\pi$
$53$	−236.779	+	69.5246i	−0.613662	+	0.180187i	−0.0398923	+	0.999204i	$0.512701\pi$
$54$	−140.936	−	90.5740i	−0.355166	−	0.228251i
$55$	47.2021	−	103.358i	0.115722	−	0.253397i
$56$	−11.4390	−	3.35880i	−0.0272965	−	0.00801498i
$57$	51.3058	+	59.2101i	0.119221	+	0.137589i
$58$	733.879	+	846.942i	1.66143	+	1.91740i
$59$	−93.6935	−	27.5109i	−0.206743	−	0.0607053i	0.176721	−	0.984261i	$-0.443451\pi$
$59$	−93.6935	−	27.5109i	−0.206743	−	0.0607053i	−0.383464	+	0.923556i	$0.625269\pi$
$60$	15.3843	−	33.6869i	0.0331017	−	0.0724827i
$61$	650.166	+	417.836i	1.36468	+	0.877024i	0.998565	−	0.0535479i	$-0.0170530\pi$
$61$	650.166	+	417.836i	1.36468	+	0.877024i	0.366110	+	0.930572i	$0.380689\pi$
$62$	820.804	−	241.010i	1.68133	−	0.493682i
$63$	5.18838	−	36.0860i	0.0103758	−	0.0721652i
$64$	−303.706	−	665.024i	−0.593177	−	1.29888i
$65$	−55.6206	−	386.850i	−0.106137	−	0.738197i
$66$	59.9155	−	38.5054i	0.111744	−	0.0718133i
$67$	−147.259	+	169.945i	−0.268515	+	0.309883i	−0.873954	−	0.486009i	$-0.838452\pi$
$67$	−147.259	+	169.945i	−0.268515	+	0.309883i	0.605439	+	0.795892i	$0.292998\pi$
$68$	−790.604			−1.40992
$69$	−63.4491	−	50.9881i	−0.110701	−	0.0889602i
$70$	29.2630			0.0499657
$71$	178.320	−	205.792i	0.298066	−	0.343986i	−0.586885	−	0.809670i	$-0.699646\pi$
$71$	178.320	−	205.792i	0.298066	−	0.343986i	0.884951	+	0.465684i	$0.154192\pi$
$72$	−192.541	+	123.738i	−0.315155	+	0.202538i
$73$	56.5199	+	393.104i	0.0906185	+	0.630265i	0.983626	+	0.180223i	$0.0576820\pi$
$73$	56.5199	+	393.104i	0.0906185	+	0.630265i	−0.893007	+	0.450042i	$0.851409\pi$
$74$	237.001	+	518.960i	0.372308	+	0.815241i
$75$	−2.62549	+	18.2607i	−0.00404221	+	0.0281142i
$76$	1022.46	−	300.220i	1.54321	−	0.453127i
$77$	26.3453	+	16.9311i	0.0389912	+	0.0250581i
$78$	101.766	−	222.835i	0.147727	−	0.323476i
$79$	−17.1560	−	5.03745i	−0.0244329	−	0.00717414i	0.269493	−	0.963002i	$-0.413144\pi$
$79$	−17.1560	−	5.03745i	−0.0244329	−	0.00717414i	−0.293926	+	0.955828i	$0.594962\pi$
$80$	142.610	+	164.580i	0.199303	+	0.230008i
$81$	−448.703	−	517.830i	−0.615504	−	0.710330i
$82$	−1512.35	−	444.066i	−2.03672	−	0.598035i
$83$	362.501	−	793.767i	0.479394	−	1.04973i	−0.503236	−	0.864149i	$-0.667857\pi$
$83$	362.501	−	793.767i	0.479394	−	1.04973i	0.982630	−	0.185577i	$-0.0594155\pi$
$84$	8.58656	+	5.51825i	0.0111532	+	0.00716774i
$85$	377.890	−	110.958i	0.482211	−	0.141590i
$86$	270.851	−	1883.81i	0.339612	−	2.36205i
$87$	−80.8901	−	177.125i	−0.0996820	−	0.218273i
$88$	−27.9795	−	194.602i	−0.0338935	−	0.235734i
$89$	−535.468	+	344.125i	−0.637748	+	0.409855i	−0.819171	−	0.573550i	$-0.805566\pi$
$89$	−535.468	+	344.125i	−0.637748	+	0.409855i	0.181423	+	0.983405i	$0.441930\pi$
$90$	367.889	−	424.566i	0.430877	−	0.497258i
$91$	107.717			0.124085
$92$	−989.344	+	496.917i	−1.12116	+	0.563121i
$93$	−148.640			−0.165734
$94$	1048.28	−	1209.78i	1.15023	−	1.32744i
$95$	−446.575	+	286.996i	−0.482291	+	0.309950i
$96$	26.6944	+	185.664i	0.0283801	+	0.197388i
$97$	241.129	+	528.000i	0.252402	+	0.552683i	0.992841	−	0.119440i	$-0.0381099\pi$
$97$	241.129	+	528.000i	0.252402	+	0.552683i	−0.740440	+	0.672123i	$0.765383\pi$
$98$	206.165	−	1433.91i	0.212509	−	1.47803i
$99$	576.855	−	169.380i	0.585617	−	0.171953i
$100$	211.092	+	135.661i	0.211092	+	0.135661i
$101$	−492.191	+	1077.75i	−0.484900	+	1.06178i	0.496188	+	0.868215i	$0.334733\pi$
$101$	−492.191	+	1077.75i	−0.484900	+	1.06178i	−0.981087	+	0.193567i	$0.937994\pi$
$102$	236.863	+	69.5494i	0.229931	+	0.0675139i
$103$	896.395	+	1034.50i	0.857519	+	0.989630i	1.00000		0.000167937i	$-5.34561e-5\pi$
$103$	896.395	+	1034.50i	0.857519	+	0.989630i	−0.142481	+	0.989798i	$0.545508\pi$
$104$	−442.838	−	511.063i	−0.417537	−	0.481864i
$105$	−4.87864	−	1.43250i	−0.00453435	−	0.00133140i
$106$	435.378	−	953.344i	0.398940	−	0.873556i
$107$	−285.804	−	183.675i	−0.258221	−	0.165949i	0.405125	−	0.914261i	$-0.367228\pi$
$107$	−285.804	−	183.675i	−0.258221	−	0.165949i	−0.663346	+	0.748312i	$0.730864\pi$
$108$	379.891	−	111.546i	0.338473	−	0.0993846i
$109$	−200.052	+	1391.40i	−0.175794	+	1.22267i	0.690571	+	0.723264i	$0.257359\pi$
$109$	−200.052	+	1391.40i	−0.175794	+	1.22267i	−0.866366	+	0.499410i	$0.833550\pi$
$110$	200.468	+	438.963i	0.173762	+	0.380486i
$111$	−14.1077	−	98.1211i	−0.0120634	−	0.0839031i
$112$	−50.4922	+	32.4493i	−0.0425988	+	0.0273766i
$113$	−540.066	+	623.269i	−0.449603	+	0.518869i	−0.934626	−	0.355632i	$-0.884266\pi$
$113$	−540.066	+	623.269i	−0.449603	+	0.518869i	0.485023	+	0.874501i	$0.338811\pi$
$114$	−332.736			−0.273365
$115$	403.143	−	376.365i	0.326898	−	0.305185i
$116$	−2648.49			−2.11988
$117$	1354.19	−	1562.82i	1.07004	−	1.23489i
$118$	348.881	−	224.212i	0.272179	−	0.174919i
$119$	15.4479	+	107.443i	0.0119001	+	0.0827669i
$120$	13.2603	+	29.0360i	0.0100874	+	0.0220884i
$121$	115.924	−	806.270i	0.0870955	−	0.605763i
$122$	−3149.35	+	924.734i	−2.33712	+	0.686242i
$123$	230.396	+	148.066i	0.168895	+	0.108542i
$124$	−839.852	+	1839.02i	−0.608233	+	1.33185i
$125$	−119.937	−	35.2166i	−0.0858197	−	0.0251989i
$126$	101.394	+	117.015i	0.0716898	+	0.0827345i
$127$	−194.963	−	224.999i	−0.136222	−	0.157208i	0.683540	−	0.729913i	$-0.260440\pi$
$127$	−194.963	−	224.999i	−0.136222	−	0.157208i	−0.819762	+	0.572705i	$0.805894\pi$
$128$	1028.06	+	301.867i	0.709913	+	0.208449i
$129$	−137.373	+	300.804i	−0.0937595	+	0.205305i
$130$	1396.35	+	897.381i	0.942063	+	0.605427i
$131$	1112.24	−	326.584i	0.741811	−	0.217815i	0.111074	−	0.993812i	$-0.464571\pi$
$131$	1112.24	−	326.584i	0.741811	−	0.217815i	0.630737	+	0.775997i	$0.282753\pi$
$132$	−23.9544	+	166.606i	−0.0157952	+	0.109858i
$133$	−60.7780	−	133.085i	−0.0396250	−	0.0867666i
$134$	−135.914	−	945.303i	−0.0876208	−	0.609416i
$135$	−165.924	+	106.633i	−0.105781	+	0.0679814i
$136$	446.255	−	515.006i	0.281368	−	0.324716i
$137$	−1191.25			−0.742885			−0.371443	−	0.928456i	$-0.621137\pi$
$137$	−1191.25			−0.742885			−0.371443	+	0.928456i	$0.621137\pi$
$138$	340.120	−	61.8427i	0.209804	−	0.0381478i
$139$	−2773.78			−1.69258			−0.846290	−	0.532722i	$-0.821169\pi$
$139$	−2773.78			−1.69258			−0.846290	+	0.532722i	$0.821169\pi$
$140$	−45.2888	+	52.2661i	−0.0273400	+	0.0315521i
$141$	−233.988	+	150.375i	−0.139754	+	0.0898146i
$142$	164.582	+	1144.70i	0.0972637	+	0.676484i
$143$	737.917	+	1615.81i	0.431522	+	0.944902i
$144$	−163.982	+	1140.52i	−0.0948969	+	0.660022i
$145$	1265.92	−	371.707i	0.725025	−	0.212887i
$146$	−1418.93	−	911.890i	−0.804324	−	0.516908i
$147$	−104.565	+	228.965i	−0.0586691	+	0.128467i
$148$	−1293.70	−	379.864i	−0.718522	−	0.210977i
$149$	952.687	+	1099.46i	0.523807	+	0.604505i	0.954580	−	0.297955i	$-0.0963046\pi$
$149$	952.687	+	1099.46i	0.523807	+	0.604505i	−0.430773	+	0.902460i	$0.641759\pi$
$150$	−51.3088	−	59.2135i	−0.0279290	−	0.0322317i
$151$	−868.606	−	255.046i	−0.468120	−	0.137452i	0.0391614	−	0.999233i	$-0.487531\pi$
$151$	−868.606	−	255.046i	−0.468120	−	0.137452i	−0.507281	+	0.861780i	$0.669350\pi$
$152$	−381.558	+	835.495i	−0.203608	+	0.445840i
$153$	1753.05	+	1126.62i	0.926314	+	0.595306i
$154$	−127.615	+	37.4710i	−0.0667759	+	0.0196072i
$155$	143.329	−	996.878i	0.0742742	−	0.516588i
$156$	240.505	+	526.632i	0.123434	+	0.270284i
$157$	−512.442	−	3564.11i	−0.260493	−	1.81177i	−0.529148	−	0.848530i	$-0.677488\pi$
$157$	−512.442	−	3564.11i	−0.260493	−	1.81177i	0.268655	−	0.963237i	$-0.413421\pi$
$158$	63.8827	−	41.0549i	0.0321660	−	0.0206719i
$159$	−119.253	+	137.626i	−0.0594805	+	0.0686442i
$160$	−1270.93			−0.627972
$161$	86.8620	+	124.742i	0.0425198	+	0.0610624i
$162$	2909.99			1.41130
$163$	1659.34	−	1914.99i	0.797361	−	0.920204i	−0.200872	−	0.979617i	$-0.564378\pi$
$163$	1659.34	−	1914.99i	0.797361	−	0.920204i	0.998233	+	0.0594137i	$0.0189231\pi$
$164$	3133.72	−	2013.92i	1.49209	−	0.958906i
$165$	−11.9330	−	82.9959i	−0.00563020	−	0.0391589i
$166$	1539.54	+	3371.13i	0.719830	+	1.57621i
$167$	61.2265	−	425.839i	0.0283703	−	0.197320i	−0.970707	−	0.240266i	$-0.922765\pi$
$167$	61.2265	−	425.839i	0.0283703	−	0.197320i	0.999077	+	0.0429461i	$0.0136744\pi$
$168$	−8.44130	+	2.47859i	−0.00387655	+	0.00113826i
$169$	3291.71	+	2115.45i	1.49827	+	0.962882i
$170$	−694.845	+	1521.50i	−0.313484	+	0.686433i
$171$	−2694.97	−	791.316i	−1.20520	−	0.353880i
$172$	2945.45	+	3399.23i	1.30575	+	1.50691i
$173$	−87.6326	−	101.133i	−0.0385120	−	0.0444452i	0.736167	−	0.676800i	$-0.236634\pi$
$173$	−87.6326	−	101.133i	−0.0385120	−	0.0444452i	−0.774679	+	0.632355i	$0.782088\pi$
$174$	793.483	+	232.988i	0.345711	+	0.101510i
$175$	14.3116	−	31.3381i	0.00618204	−	0.0135368i
$176$	−832.658	−	535.117i	−0.356613	−	0.229182i
$177$	−69.1401	+	20.3014i	−0.0293609	+	0.00862115i
$178$	384.715	−	2675.75i	0.161998	−	1.12672i
$179$	−1049.51	−	2298.11i	−0.438235	−	0.959601i	−0.991919	−	0.126874i	$-0.959506\pi$
$179$	−1049.51	−	2298.11i	−0.438235	−	0.959601i	0.553684	−	0.832727i	$-0.313222\pi$
$180$	188.947	+	1314.16i	0.0782406	+	0.544175i
$181$	509.405	−	327.375i	0.209192	−	0.134440i	−0.431850	−	0.901946i	$-0.642139\pi$
$181$	509.405	−	327.375i	0.209192	−	0.134440i	0.641042	+	0.767506i	$0.278503\pi$
$182$	−299.581	+	345.735i	−0.122013	+	0.140811i
$183$	570.318			0.230378
$184$	234.738	−	924.951i	0.0940497	−	0.370589i
$185$	671.669			0.266930
$186$	413.397	−	477.085i	0.162966	−	0.188073i
$187$	−1505.88	+	967.769i	−0.588881	+	0.378451i
$188$	538.397	+	3744.63i	0.208865	+	1.45269i
$189$	−22.5819	−	49.4475i	−0.00869097	−	0.0190306i
$190$	320.849	−	2231.55i	0.122510	−	0.852073i
$191$	2386.69	−	700.795i	0.904161	−	0.265486i	0.203580	−	0.979058i	$-0.434742\pi$
$191$	2386.69	−	700.795i	0.904161	−	0.265486i	0.700581	+	0.713573i	$0.252924\pi$
$192$	−453.857	−	291.676i	−0.170595	−	0.109635i
$193$	−1310.79	+	2870.22i	−0.488872	+	1.07048i	0.491055	+	0.871128i	$0.336611\pi$
$193$	−1310.79	+	2870.22i	−0.488872	+	1.07048i	−0.979928	+	0.199353i	$0.936116\pi$
$194$	−2365.33	−	694.524i	−0.875366	−	0.257031i
$195$	−188.866	−	217.964i	−0.0693590	−	0.0800446i
$196$	2242.01	+	2587.42i	0.817059	+	0.942936i
$197$	816.111	+	239.632i	0.295155	+	0.0866653i	0.425958	−	0.904743i	$-0.359937\pi$
$197$	816.111	+	239.632i	0.295155	+	0.0866653i	−0.130803	+	0.991408i	$0.541755\pi$
$198$	−1060.69	+	2322.59i	−0.380708	+	0.833633i
$199$	−3654.09	−	2348.34i	−1.30167	−	0.836531i	−0.308275	−	0.951297i	$-0.599752\pi$
$199$	−3654.09	−	2348.34i	−1.30167	−	0.836531i	−0.993393	+	0.114766i	$0.963388\pi$
$200$	−207.521	+	60.9337i	−0.0733698	+	0.0215433i
$201$	−23.6158	+	164.251i	−0.00828720	+	0.0576387i
$202$	−2090.34	−	4577.20i	−0.728097	−	1.59431i
$203$	51.7500	+	359.929i	0.0178923	+	0.124444i
$204$	−490.802	+	315.419i	−0.168446	+	0.108254i
$205$	−1215.20	+	1402.41i	−0.414015	+	0.477798i
$206$	−5813.44			−1.96622
$207$	2901.85	+	307.984i	0.974359	+	0.103412i
$208$	−3404.44			−1.13488
$209$	1580.00	−	1823.41i	0.522922	−	0.603484i
$210$	18.1663	−	11.6748i	0.00596949	−	0.00383636i
$211$	416.355	+	2895.81i	0.135844	+	0.944815i	0.937737	+	0.347347i	$0.112917\pi$
$211$	416.355	+	2895.81i	0.135844	+	0.944815i	−0.801893	+	0.597468i	$0.796173\pi$
$212$	1028.94	+	2253.06i	0.333338	+	0.729909i
$213$	28.5970	−	198.897i	0.00919923	−	0.0639821i
$214$	1384.41	−	406.500i	0.442226	−	0.129849i
$215$	−1884.93	−	1211.37i	−0.597911	−	0.384254i
$216$	−141.767	+	310.426i	−0.0446575	+	0.0977863i
$217$	266.332	+	78.2022i	0.0833171	+	0.0244641i
$218$	−3909.54	−	4511.85i	−1.21462	−	1.40175i
$219$	191.920	+	221.487i	0.0592180	+	0.0683412i
$220$	−1094.28	−	321.308i	−0.335346	−	0.0984664i
$221$	−2557.71	+	5600.60i	−0.778508	+	1.70469i
$222$	354.173	+	227.613i	0.107074	+	0.0688125i
$223$	16.5331	−	4.85456i	0.00496475	−	0.00145778i	−0.279249	−	0.960219i	$-0.590086\pi$
$223$	16.5331	−	4.85456i	0.00496475	−	0.00145778i	0.284214	+	0.958761i	$0.408267\pi$
$224$	49.8502	−	346.716i	0.0148695	−	0.103419i
$225$	−274.750	−	601.618i	−0.0814073	−	0.178257i
$226$	−498.460	−	3466.87i	−0.146713	−	1.02041i
$227$	3307.75	−	2125.76i	0.967151	−	0.621550i	0.0411831	−	0.999152i	$-0.486887\pi$
$227$	3307.75	−	2125.76i	0.967151	−	0.621550i	0.925968	+	0.377601i	$0.123251\pi$
$228$	514.958	−	594.294i	0.149579	−	0.172623i
$229$	−4523.02			−1.30520			−0.652598	−	0.757704i	$-0.726321\pi$
$229$	−4523.02			−1.30520			−0.652598	+	0.757704i	$0.726321\pi$
$230$	86.7905	+	2340.70i	0.0248817	+	0.671049i
$231$	23.1098			0.00658231
$232$	1494.94	−	1725.25i	0.423049	−	0.488225i
$233$	2106.89	−	1354.02i	0.592391	−	0.380706i	−0.209827	−	0.977739i	$-0.567290\pi$
$233$	2106.89	−	1354.02i	0.592391	−	0.380706i	0.802217	+	0.597032i	$0.203654\pi$
$234$	1249.87	+	8693.01i	0.349172	+	2.42855i
$235$	−782.887	−	1714.28i	−0.217319	−	0.475862i
$236$	−139.484	+	970.130i	−0.0384729	+	0.267585i
$237$	−12.6601	+	3.71733i	−0.00346987	+	0.00101885i
$238$	−387.819	−	249.236i	−0.105624	−	0.0678807i
$239$	1076.14	−	2356.41i	0.291254	−	0.637756i	−0.706281	−	0.707931i	$-0.749629\pi$
$239$	1076.14	−	2356.41i	0.291254	−	0.637756i	0.997535	+	0.0701752i	$0.0223558\pi$
$240$	154.192	+	45.2749i	0.0414711	+	0.0121770i
$241$	380.033	+	438.582i	0.101577	+	0.117226i	0.804262	−	0.594275i	$-0.202561\pi$
$241$	380.033	+	438.582i	0.101577	+	0.117226i	−0.702685	+	0.711501i	$0.748016\pi$
$242$	2265.45	+	2614.47i	0.601772	+	0.694482i
$243$	−1507.07	−	442.515i	−0.397853	−	0.116820i
$244$	3222.44	−	7056.16i	0.845474	−	1.85133i
$245$	−1434.76	−	922.066i	−0.374137	−	0.240443i
$246$	−1116.02	+	327.693i	−0.289247	+	0.0849307i
$247$	1181.04	−	8214.29i	0.304241	−	2.11604i
$248$	−723.899	−	1585.12i	−0.185353	−	0.405867i
$249$	−91.6427	−	637.389i	−0.0233238	−	0.162220i
$250$	446.601	−	287.013i	0.112982	−	0.0726092i
$251$	3631.67	−	4191.17i	0.913264	−	1.05396i	−0.0850766	−	0.996374i	$-0.527114\pi$
$251$	3631.67	−	4191.17i	0.913264	−	1.05396i	0.998340	−	0.0575882i	$-0.0183410\pi$
$252$	−365.921			−0.0914716
$253$	−1276.15	+	2157.53i	−0.317119	+	0.536138i
$254$	1264.40			0.312346
$255$	190.324	−	219.645i	0.0467393	−	0.0539400i
$256$	1092.13	−	701.867i	0.266632	−	0.171354i
$257$	249.852	+	1737.76i	0.0606433	+	0.421784i	0.997416	+	0.0718447i	$0.0228886\pi$
$257$	249.852	+	1737.76i	0.0606433	+	0.421784i	−0.936772	+	0.349939i	$0.886202\pi$
$258$	−583.422	−	1277.52i	−0.140784	−	0.308274i
$259$	−26.3453	+	183.235i	−0.00632052	+	0.0439602i
$260$	−3763.85	+	1105.17i	−0.897786	+	0.263614i
$261$	5872.66	+	3774.13i	1.39275	+	0.895069i
$262$	−2045.14	+	4478.23i	−0.482249	+	1.05598i
$263$	−3720.48	−	1092.43i	−0.872300	−	0.256130i	−0.185207	−	0.982700i	$-0.559295\pi$
$263$	−3720.48	−	1092.43i	−0.872300	−	0.256130i	−0.687093	+	0.726569i	$0.741114\pi$
$264$	−95.0078	−	109.645i	−0.0221490	−	0.0255613i
$265$	−808.017	−	932.501i	−0.187306	−	0.216163i
$266$	596.196	+	175.059i	0.137425	+	0.0403517i
$267$	−195.123	+	427.261i	−0.0447242	+	0.0979323i
$268$	1898.73	+	1220.24i	0.432774	+	0.278127i
$269$	1084.10	−	318.321i	0.245721	−	0.0721502i	−0.156553	−	0.987670i	$-0.550038\pi$
$269$	1084.10	−	318.321i	0.245721	−	0.0721502i	0.402274	+	0.915519i	$0.368220\pi$
$270$	119.211	−	829.128i	0.0268701	−	0.186886i
$271$	2166.22	+	4743.36i	0.485566	+	1.06324i	0.980895	+	0.194537i	$0.0623203\pi$
$271$	2166.22	+	4743.36i	0.485566	+	1.06324i	−0.495329	+	0.868706i	$0.664952\pi$
$272$	−488.241	−	3395.79i	−0.108838	−	0.756985i
$273$	66.8697	−	42.9746i	0.0148247	−	0.00952725i
$274$	3313.10	−	3823.52i	0.730480	−	0.843019i
$275$	568.132			0.124581
$276$	−415.929	+	703.191i	−0.0907100	+	0.153359i
$277$	7079.26			1.53557			0.767783	−	0.640710i	$-0.221360\pi$
$277$	7079.26			1.53557			0.767783	+	0.640710i	$0.221360\pi$
$278$	7714.42	−	8902.91i	1.66432	−	1.92072i
$279$	4482.88	−	2880.97i	0.961947	−	0.618205i
$280$	−8.48336	−	59.0030i	−0.00181063	−	0.0125932i
$281$	−1434.12	−	3140.29i	−0.304458	−	0.666669i	0.694127	−	0.719852i	$-0.255791\pi$
$281$	−1434.12	−	3140.29i	−0.304458	−	0.666669i	−0.998585	+	0.0531833i	$0.983063\pi$
$282$	168.112	−	1169.25i	0.0354998	−	0.246907i
$283$	−6386.15	+	1875.14i	−1.34140	+	0.393871i	−0.872170	−	0.489203i	$-0.837288\pi$
$283$	−6386.15	+	1875.14i	−1.34140	+	0.393871i	−0.469233	+	0.883074i	$0.655469\pi$
$284$	−2299.23	−	1477.63i	−0.480403	−	0.308736i
$285$	−162.731	+	356.331i	−0.0338223	+	0.0740604i
$286$	−7238.52	−	2125.42i	−1.49658	−	0.439436i
$287$	−334.922	−	386.520i	−0.0688843	−	0.0794967i
$288$	−4403.67	−	5082.10i	−0.901002	−	1.03981i
$289$	−1239.19	−	363.858i	−0.252226	−	0.0740603i
$290$	−2327.70	+	5096.96i	−0.471336	+	1.03208i
$291$	360.342	+	231.578i	0.0725898	+	0.0466506i
$292$	3824.71	−	1123.04i	0.766521	−	0.225071i
$293$	−256.395	+	1783.26i	−0.0511220	+	0.355561i	0.948164	+	0.317781i	$0.102938\pi$
$293$	−256.395	+	1783.26i	−0.0511220	+	0.355561i	−0.999286	+	0.0377800i	$0.987971\pi$
$294$	−444.087	−	972.415i	−0.0880941	−	0.192899i
$295$	−69.4845	−	483.275i	−0.0137137	−	0.0953810i
$296$	977.672	−	628.312i	0.191980	−	0.123378i
$297$	587.044	−	677.485i	0.114693	−	0.132362i
$298$	−6178.51			−1.20105
$299$	319.474	+	8616.07i	0.0617914	+	1.66649i
$300$	185.168			0.0356356
$301$	404.402	−	466.705i	0.0774397	−	0.0893702i
$302$	3234.37	−	2078.61i	0.616283	−	0.396061i
$303$	124.429	+	865.424i	0.0235916	+	0.164083i
$304$	1920.92	+	4206.24i	0.362410	+	0.793566i
$305$	−549.943	+	3824.94i	−0.103245	+	0.718082i
$306$	−8491.67	+	2493.38i	−1.58639	+	0.465807i
$307$	−3717.39	−	2389.02i	−0.691083	−	0.444132i	0.147388	−	0.989079i	$-0.452914\pi$
$307$	−3717.39	−	2389.02i	−0.691083	−	0.444132i	−0.838471	+	0.544947i	$0.816550\pi$
$308$	130.576	−	285.922i	0.0241567	−	0.0528958i
$309$	969.198	+	284.582i	0.178433	+	0.0523926i
$310$	2801.02	+	3232.55i	0.513185	+	0.592247i
$311$	−3032.38	−	3499.56i	−0.552896	−	0.638076i	0.408659	−	0.912687i	$-0.365996\pi$
$311$	−3032.38	−	3499.56i	−0.552896	−	0.638076i	−0.961556	+	0.274611i	$0.911451\pi$
$312$	−478.805	−	140.590i	−0.0868813	−	0.0255107i
$313$	1871.39	−	4097.78i	0.337947	−	0.740001i	−0.662008	−	0.749497i	$-0.730295\pi$
$313$	1871.39	−	4097.78i	0.337947	−	0.740001i	0.999955	+	0.00949590i	$0.00302269\pi$
$314$	12864.8	+	8267.73i	2.31212	+	1.48591i
$315$	174.902	−	51.3557i	0.0312844	−	0.00918593i
$316$	−25.5405	+	177.638i	−0.00454672	+	0.0316232i
$317$	2385.92	+	5224.43i	0.422734	+	0.925657i	0.994450	+	0.105206i	$0.0335503\pi$
$317$	2385.92	+	5224.43i	0.422734	+	0.925657i	−0.571717	+	0.820451i	$0.693722\pi$
$318$	−110.066	−	765.528i	−0.0194095	−	0.134996i
$319$	−5044.63	+	3241.99i	−0.885408	+	0.569017i
$320$	2393.82	−	2762.61i	0.418182	−	0.482608i
$321$	−250.704			−0.0435917
$322$	−641.961	−	68.1337i	−0.111103	−	0.0117917i
$323$	8362.79			1.44061
$324$	−4503.64	+	5197.48i	−0.772229	+	0.891200i
$325$	1643.93	−	1056.49i	0.280581	−	0.180318i
$326$	1531.51	+	10651.9i	0.260192	+	1.80967i
$327$	430.920	+	943.582i	0.0728743	+	0.159573i
$328$	−456.939	+	3178.08i	−0.0769215	+	0.535001i
$329$	498.374	−	146.336i	0.0835144	−	0.0245220i
$330$	299.577	+	192.527i	0.0499733	+	0.0321159i
$331$	568.654	−	1245.18i	0.0944292	−	0.206771i	−0.856523	−	0.516109i	$-0.827380\pi$
$331$	568.654	−	1245.18i	0.0944292	−	0.206771i	0.950952	+	0.309338i	$0.100107\pi$
$332$	−8403.78	−	2467.57i	−1.38921	−	0.407909i
$333$	2327.28	+	2685.83i	0.382986	+	0.441990i
$334$	1196.52	+	1380.86i	0.196020	+	0.226219i
$335$	−1078.81	−	316.766i	−0.175945	−	0.0516620i
$336$	−18.3992	+	40.2887i	−0.00298738	+	0.00654145i
$337$	−896.894	−	576.399i	−0.144976	−	0.0931704i	0.466142	−	0.884710i	$-0.345644\pi$
$337$	−896.894	−	576.399i	−0.144976	−	0.0931704i	−0.611118	+	0.791539i	$0.709280\pi$
$338$	−15944.8	+	4681.81i	−2.56592	+	0.753423i
$339$	−86.6100	+	602.386i	−0.0138761	+	0.0965107i
$340$	−1642.14	−	3595.79i	−0.261934	−	0.573556i
$341$	651.441	+	4530.87i	0.103453	+	0.719532i
$342$	10035.1	−	6449.17i	1.58666	−	1.01968i
$343$	617.356	−	712.467i	0.0971840	−	0.112156i
$344$	−3876.84			−0.607632
$345$	100.114	−	394.483i	0.0156230	−	0.0615601i
$346$	568.328			0.0883049
$347$	−6342.37	+	7319.48i	−0.981200	+	1.13236i	0.00999489	+	0.999950i	$0.496818\pi$
$347$	−6342.37	+	7319.48i	−0.981200	+	1.13236i	−0.991194	+	0.132415i	$0.957727\pi$
$348$	−1644.17	+	1056.64i	−0.253266	+	0.162764i
$349$	52.3968	+	364.428i	0.00803650	+	0.0558951i	0.993445	−	0.114311i	$-0.0364659\pi$
$349$	52.3968	+	364.428i	0.00803650	+	0.0558951i	−0.985409	+	0.170206i	$0.945557\pi$
$350$	60.7815	+	133.093i	0.00928260	+	0.0203260i
$351$	438.812	−	3052.00i	0.0667294	−	0.464113i
$352$	5542.45	−	1627.41i	0.839243	−	0.246424i
$353$	8328.91	+	5352.67i	1.25582	+	0.807064i	0.987706	−	0.156324i	$-0.0499644\pi$
$353$	8328.91	+	5352.67i	1.25582	+	0.807064i	0.268110	+	0.963388i	$0.413601\pi$
$354$	127.131	−	278.379i	0.0190875	−	0.0417957i
$355$	1306.36	+	383.582i	0.195308	+	0.0573476i
$356$	4183.71	+	4828.26i	0.622854	+	0.718812i
$357$	52.4553	+	60.5366i	0.00777655	+	0.00897462i
$358$	10295.1	+	3022.90i	1.51986	+	0.446272i
$359$	1366.65	−	2992.55i	0.200917	−	0.439947i	−0.782175	−	0.623059i	$-0.785890\pi$
$359$	1366.65	−	2992.55i	0.200917	−	0.439947i	0.983092	+	0.183112i	$0.0586171\pi$
$360$	−962.704	−	618.692i	−0.140942	−	0.0905776i
$361$	−4234.10	+	1243.24i	−0.617306	+	0.181257i
$362$	−365.990	+	2545.52i	−0.0531381	+	0.369584i
$363$	−249.704	−	546.776i	−0.0361049	−	0.0790587i
$364$	−153.864	−	1070.15i	−0.0221557	−	0.154096i
$365$	−1670.51	+	1073.57i	−0.239557	+	0.153954i
$366$	−1586.17	+	1830.53i	−0.226531	+	0.261431i
$367$	372.890			0.0530373			0.0265186	−	0.999648i	$-0.491558\pi$
$367$	372.890			0.0530373			0.0265186	+	0.999648i	$0.491558\pi$
$368$	−2745.32	−	3942.54i	−0.388885	−	0.558476i
$369$	−9818.44			−1.38517
$370$	−1868.04	+	2155.84i	−0.262473	+	0.302910i
$371$	286.085	−	183.856i	0.0400345	−	0.0257286i
$372$	212.320	+	1476.72i	0.0295922	+	0.205818i
$373$	4409.63	+	9655.75i	0.612123	+	1.34036i	0.921112	+	0.389298i	$0.127282\pi$
$373$	4409.63	+	9655.75i	0.612123	+	1.34036i	−0.308989	+	0.951066i	$0.599990\pi$
$374$	1081.92	−	7524.93i	0.149585	−	1.04039i
$375$	−88.5059	+	25.9877i	−0.0121878	+	0.00357866i
$376$	−2743.18	−	1762.93i	−0.376247	−	0.241799i
$377$	−8568.23	+	18761.8i	−1.17052	+	2.56308i
$378$	221.515	+	65.0427i	0.0301415	+	0.00885036i
$379$	−6368.85	−	7350.04i	−0.863181	−	0.996164i	−0.999985	−	0.00556577i	$-0.998228\pi$
$379$	−6368.85	−	7350.04i	−0.863181	−	0.996164i	0.136804	−	0.990598i	$-0.456317\pi$
$380$	3489.17	+	4026.72i	0.471028	+	0.543595i
$381$	−210.797	−	61.8957i	−0.0283451	−	0.00832287i
$382$	−4388.53	+	9609.54i	−0.587792	+	1.28709i
$383$	−4806.32	−	3088.84i	−0.641231	−	0.412094i	0.179221	−	0.983809i	$-0.442642\pi$
$383$	−4806.32	−	3088.84i	−0.641231	−	0.412094i	−0.820453	+	0.571714i	$0.806279\pi$
$384$	758.648	−	222.759i	0.100819	−	0.0296032i
$385$	−22.2842	+	154.990i	−0.00294989	+	0.0205169i
$386$	−5566.91	−	12189.8i	−0.734063	−	1.60737i
$387$	−1687.19	−	11734.6i	−0.221614	−	1.54136i
$388$	4901.18	−	3149.79i	0.641287	−	0.412130i
$389$	6228.64	−	7188.24i	0.811838	−	0.936911i	−0.187130	−	0.982335i	$-0.559919\pi$
$389$	6228.64	−	7188.24i	0.811838	−	0.936911i	0.998968	+	0.0454246i	$0.0144641\pi$
$390$	1224.87			0.159035
$391$	−8548.35	+	1554.32i	−1.10565	+	0.201036i
$392$	−2950.96			−0.380220
$393$	560.180	−	646.482i	0.0719016	−	0.0829789i
$394$	−3038.90	+	1952.99i	−0.388573	+	0.249721i
$395$	−12.7231	−	88.4913i	−0.00162068	−	0.0112721i
$396$	−2506.76	−	5489.03i	−0.318104	−	0.696551i
$397$	−325.658	+	2265.00i	−0.0411695	+	0.286340i	0.958828	+	0.283988i	$0.0916577\pi$
$397$	−325.658	+	2265.00i	−0.0411695	+	0.286340i	−0.999997	+	0.00235193i	$0.999251\pi$
$398$	17700.2	−	5197.24i	2.22922	−	0.654557i
$399$	−90.8263	−	58.3705i	−0.0113960	−	0.00732376i
$400$	−452.327	+	990.458i	−0.0565409	+	0.123807i
$401$	−5841.56	−	1715.24i	−0.727465	−	0.213603i	−0.103029	−	0.994678i	$-0.532853\pi$
$401$	−5841.56	−	1715.24i	−0.727465	−	0.213603i	−0.624437	+	0.781075i	$0.714671\pi$
$402$	−461.512	−	532.614i	−0.0572591	−	0.0660805i
$403$	10310.5	+	11899.0i	1.27445	+	1.47079i
$404$	11410.3	+	3350.38i	1.40516	+	0.412593i
$405$	1423.19	−	3116.34i	0.174614	−	0.382351i
$406$	−1299.18	−	834.932i	−0.158811	−	0.102062i
$407$	−2929.12	+	860.066i	−0.356735	+	0.104747i
$408$	71.5656	−	497.750i	0.00868389	−	0.0603978i
$409$	−5174.16	−	11329.8i	−0.625539	−	1.36974i	−0.911421	−	0.411475i	$-0.865014\pi$
$409$	−5174.16	−	11329.8i	−0.625539	−	1.36974i	0.285882	−	0.958265i	$-0.407713\pi$
$410$	−1121.58	−	7800.76i	−0.135100	−	0.939639i
$411$	−739.519	+	475.260i	−0.0887538	+	0.0570386i
$412$	8997.15	−	10383.3i	1.07587	−	1.24162i
$413$	134.566			0.0160328
$414$	−9059.13	+	8457.41i	−1.07544	+	1.00401i
$415$	4363.12			0.516090
$416$	13011.1	−	15015.6i	1.53347	−	1.76972i
$417$	−1721.94	+	1106.63i	−0.202216	+	0.129956i
$418$	1458.28	+	10142.5i	0.170638	+	1.18681i
$419$	−4361.89	−	9551.21i	−0.508574	−	1.11362i	−0.973587	−	0.228317i	$-0.926678\pi$
$419$	−4361.89	−	9551.21i	−0.508574	−	1.11362i	0.465013	−	0.885304i	$-0.346050\pi$
$420$	−7.26294	+	50.5149i	−0.000843798	+	0.00586874i
$421$	3381.01	−	992.753i	0.391402	−	0.114926i	−0.0801092	−	0.996786i	$-0.525527\pi$
$421$	3381.01	−	992.753i	0.391402	−	0.114926i	0.471511	+	0.881860i	$0.343709\pi$
$422$	−10452.6	−	6717.46i	−1.20574	−	0.774884i
$423$	4142.32	−	9070.42i	0.476139	−	1.04260i
$424$	−2048.44	−	601.477i	−0.234625	−	0.0688923i
$425$	1289.56	+	1488.23i	0.147183	+	0.169859i
$426$	558.859	+	644.958i	0.0635606	+	0.0733528i
$427$	−1021.89	−	300.055i	−0.115815	−	0.0340063i
$428$	−1416.54	+	3101.79i	−0.159979	+	0.350305i
$429$	1102.74	+	708.687i	0.124104	+	0.0797569i
$430$	9130.45	−	2680.94i	1.02397	−	0.300666i
$431$	−1383.39	+	9621.69i	−0.154607	+	1.07531i	0.753763	+	0.657147i	$0.228237\pi$
$431$	−1383.39	+	9621.69i	−0.154607	+	1.07531i	−0.908370	+	0.418168i	$0.862672\pi$
$432$	713.715	+	1562.82i	0.0794875	+	0.174053i
$433$	188.145	+	1308.58i	0.0208815	+	0.145234i	0.997595	−	0.0693145i	$-0.0220812\pi$
$433$	188.145	+	1308.58i	0.0208815	+	0.145234i	−0.976713	+	0.214548i	$0.931172\pi$
$434$	−991.725	+	637.343i	−0.109687	+	0.0704918i
$435$	637.576	−	735.802i	0.0702746	−	0.0811012i
$436$	14109.1			1.54978
$437$	10465.0	−	5256.25i	1.14556	−	0.575379i
$438$	−1244.67			−0.135782
$439$	2281.28	−	2632.74i	0.248018	−	0.286228i	−0.618067	−	0.786126i	$-0.712084\pi$
$439$	2281.28	−	2632.74i	0.248018	−	0.286228i	0.866084	+	0.499898i	$0.166629\pi$
$440$	826.965	−	531.458i	0.0896000	−	0.0575824i
$441$	−1284.25	−	8932.13i	−0.138672	−	0.964488i
$442$	−10862.6	−	23785.8i	−1.16896	−	2.55967i
$443$	−282.091	+	1961.99i	−0.0302541	+	0.210422i	−0.999341	−	0.0362978i	$-0.988444\pi$
$443$	−282.091	+	1961.99i	−0.0302541	+	0.210422i	0.969087	+	0.246719i	$0.0793526\pi$
$444$	−954.669	+	280.316i	−0.102042	+	0.0299622i
$445$	−2677.34	−	1720.62i	−0.285209	−	0.183293i
$446$	−30.4003	+	66.5673i	−0.00322757	+	0.00706739i
$447$	1030.06	+	302.454i	0.108994	+	0.0320035i
$448$	659.762	+	761.406i	0.0695778	+	0.0802970i
$449$	−5264.97	−	6076.10i	−0.553384	−	0.638639i	0.408284	−	0.912855i	$-0.366127\pi$
$449$	−5264.97	−	6076.10i	−0.553384	−	0.638639i	−0.961668	+	0.274216i	$0.911582\pi$
$450$	2695.13	+	791.361i	0.282332	+	0.0829003i
$451$	3503.64	−	7671.90i	0.365809	−	0.801010i
$452$	6963.54	+	4475.20i	0.724640	+	0.465698i
$453$	−640.978	+	188.208i	−0.0664807	+	0.0195205i
$454$	−2376.51	+	16529.0i	−0.245672	+	1.70868i
$455$	223.735	+	489.912i	0.0230525	+	0.0504779i
$456$	96.4603	+	670.896i	0.00990607	+	0.0688982i
$457$	−7675.11	+	4932.50i	−0.785616	+	0.504885i	−0.870893	−	0.491472i	$-0.836459\pi$
$457$	−7675.11	+	4932.50i	−0.785616	+	0.504885i	0.0852768	+	0.996357i	$0.472823\pi$
$458$	12579.4	−	14517.4i	1.28340	−	1.48112i
$459$	3107.17			0.315971
$460$	−4315.00	−	3467.56i	−0.437365	−	0.351470i
$461$	9726.44			0.982658			0.491329	−	0.870974i	$-0.336511\pi$
$461$	9726.44			0.982658			0.491329	+	0.870974i	$0.336511\pi$
$462$	−64.2729	+	74.1749i	−0.00647239	+	0.00746954i
$463$	−9782.97	+	6287.14i	−0.981973	+	0.631076i	−0.929995	−	0.367573i	$-0.880189\pi$
$463$	−9782.97	+	6287.14i	−0.981973	+	0.631076i	−0.0519779	+	0.998648i	$0.516553\pi$
$464$	−1635.59	−	11375.8i	−0.163643	−	1.13816i
$465$	−308.736	−	676.038i	−0.0307899	−	0.0674205i
$466$	−1513.73	+	10528.2i	−0.150477	+	1.04659i
$467$	−10451.0	+	3068.70i	−1.03558	+	0.304074i	−0.754978	−	0.655750i	$-0.772353\pi$
$467$	−10451.0	+	3068.70i	−1.03558	+	0.304074i	−0.280603	+	0.959824i	$0.590535\pi$
$468$	−17460.8	−	11221.3i	−1.72462	−	1.10835i
$469$	128.730	−	281.880i	0.0126742	−	0.0277527i
$470$	7679.64	+	2254.95i	0.753693	+	0.221304i
$471$	−1740.06	−	2008.14i	−0.170229	−	0.196454i
$472$	−553.220	−	638.449i	−0.0539491	−	0.0622606i
$473$	9771.22	+	2869.09i	0.949855	+	0.278903i
$474$	23.2787	−	50.9732i	0.00225575	−	0.00493940i
$475$	−2232.88	−	1434.98i	−0.215687	−	0.138614i
$476$	1045.36	−	306.946i	0.100660	−	0.0295564i
$477$	929.109	−	6462.10i	0.0891844	−	0.620291i
$478$	4570.36	+	10007.7i	0.437329	+	0.957618i
$479$	133.609	+	929.272i	0.0127448	+	0.0886420i	0.995201	−	0.0978511i	$-0.0311969\pi$
$479$	133.609	+	929.272i	0.0127448	+	0.0886420i	−0.982456	+	0.186493i	$0.940288\pi$
$480$	−788.983	+	507.048i	−0.0750249	+	0.0482156i
$481$	−6876.22	+	7935.59i	−0.651827	+	0.752249i
$482$	−2464.65			−0.232908
$483$	103.690	+	42.7846i	0.00976827	+	0.00403057i
$484$	−8175.78			−0.767823
$485$	−1900.58	+	2193.39i	−0.177940	+	0.205354i
$486$	5611.77	−	3606.47i	0.523776	−	0.336611i
$487$	740.065	+	5147.26i	0.0688615	+	0.478942i	0.994847	+	0.101384i	$0.0323271\pi$
$487$	740.065	+	5147.26i	0.0688615	+	0.478942i	−0.925986	+	0.377558i	$0.876764\pi$
$488$	2777.54	+	6081.96i	0.257650	+	0.564175i
$489$	266.108	−	1850.82i	0.0246090	−	0.171160i
$490$	6949.88	−	2040.67i	0.640742	−	0.188139i
$491$	−9750.97	−	6266.57i	−0.896243	−	0.575980i	0.00943089	−	0.999956i	$-0.496998\pi$
$491$	−9750.97	−	6266.57i	−0.896243	−	0.575980i	−0.905674	+	0.423975i	$0.860634\pi$
$492$	1141.92	−	2500.45i	0.104638	−	0.229124i
$493$	−19942.9	−	5855.76i	−1.82187	−	0.534950i
$494$	23080.5	+	26636.3i	2.10210	+	2.42596i
$495$	1968.54	+	2271.81i	0.178746	+	0.206284i
$496$	−8417.58	−	2471.62i	−0.762017	−	0.223748i
$497$	−155.883	+	341.337i	−0.0140691	+	0.0308069i
$498$	2300.69	+	1478.56i	0.207020	+	0.133044i
$499$	−17542.2	+	5150.86i	−1.57374	+	0.462093i	−0.948088	−	0.318007i	$-0.896986\pi$
$499$	−17542.2	+	5150.86i	−1.57374	+	0.462093i	−0.625655	+	0.780100i	$0.715168\pi$
$500$	−178.552	+	1241.86i	−0.0159702	+	0.111075i
$501$	−131.884	−	288.785i	−0.0117607	−	0.0257524i
$502$	3351.90	+	23313.0i	0.298013	+	2.07273i
$503$	−3594.16	+	2309.83i	−0.318600	+	0.204752i	−0.690159	−	0.723657i	$-0.742460\pi$
$503$	−3594.16	+	2309.83i	−0.318600	+	0.204752i	0.371559	+	0.928409i	$0.378823\pi$
$504$	206.543	−	238.364i	0.0182543	−	0.0210666i
$505$	−5924.09			−0.522017
$506$	−3375.74	−	10096.6i	−0.296581	−	0.887048i
$507$	2887.45			0.252931
$508$	−1956.85	+	2258.33i	−0.170908	+	0.197238i
$509$	11962.0	−	7687.52i	1.04166	−	0.669437i	0.0962667	−	0.995356i	$-0.469310\pi$
$509$	11962.0	−	7687.52i	1.04166	−	0.669437i	0.945398	+	0.325918i	$0.105673\pi$
$510$	175.661	+	1221.75i	0.0152518	+	0.106079i
$511$	−227.353	−	497.833i	−0.0196820	−	0.0430975i
$512$	−2004.54	+	13941.9i	−0.173025	+	1.20342i
$513$	−4018.39	+	1179.90i	−0.345840	+	0.101548i
$514$	−6272.52	−	4031.10i	−0.538267	−	0.345923i
$515$	−2843.17	+	6225.67i	−0.243272	+	0.532691i
$516$	3184.67	+	935.105i	0.271700	+	0.0797785i
$517$	5609.25	+	6473.43i	0.477166	+	0.550679i
$518$	−514.854	−	594.173i	−0.0436706	−	0.0503985i
$519$	−94.7499	−	27.8211i	−0.00801360	−	0.00235300i
$520$	1404.59	−	3075.62i	0.118452	−	0.259374i
$521$	7783.86	+	5002.38i	0.654543	+	0.420649i	0.825324	−	0.564660i	$-0.190993\pi$
$521$	7783.86	+	5002.38i	0.654543	+	0.420649i	−0.170781	+	0.985309i	$0.554629\pi$
$522$	−28446.7	+	8352.72i	−2.38521	+	0.700361i
$523$	1219.78	−	8483.74i	0.101983	−	0.709308i	−0.873112	−	0.487520i	$-0.837902\pi$
$523$	1219.78	−	8483.74i	0.101983	−	0.709308i	0.975095	−	0.221788i	$-0.0711892\pi$
$524$	−4833.32	−	10583.5i	−0.402948	−	0.882333i
$525$	−3.61807	−	25.1642i	−0.000300773	−	0.00209192i
$526$	13853.7	−	8903.26i	1.14839	−	0.738024i
$527$	−10390.1	+	11990.8i	−0.858819	+	0.991130i
$528$	−730.399			−0.0602017
$529$	−9720.29	+	7317.92i	−0.798906	+	0.601456i
$530$	5240.27			0.429477
$531$	1691.73	−	1952.36i	0.138258	−	0.159558i
$532$	−1235.37	+	793.923i	−0.100677	+	0.0647010i
$533$	−4128.51	−	28714.4i	−0.335508	−	2.33351i
$534$	−828.690	−	1814.58i	−0.0671553	−	0.147049i
$535$	241.747	−	1681.39i	0.0195358	−	0.135874i
$536$	−1866.61	+	548.087i	−0.150420	+	0.0441674i
$537$	−1568.38	−	1007.94i	−0.126035	−	0.0809976i
$538$	−1993.40	+	4364.93i	−0.159742	+	0.349787i
$539$	7437.62	+	2183.88i	0.594362	+	0.174520i
$540$	1296.39	+	1496.12i	0.103311	+	0.119227i
$541$	8381.14	+	9672.35i	0.666051	+	0.768663i	0.983753	−	0.179527i	$-0.0574567\pi$
$541$	8381.14	+	9672.35i	0.666051	+	0.768663i	−0.317702	+	0.948190i	$0.602911\pi$
$542$	−21249.3	−	6239.36i	−1.68401	−	0.494471i
$543$	185.626	−	406.464i	0.0146703	−	0.0321235i
$544$	16843.4	+	10824.6i	1.32749	+	0.853128i
$545$	−6743.81	+	1980.16i	−0.530043	+	0.155635i
$546$	−48.0436	+	334.150i	−0.00376571	+	0.0261911i
$547$	7493.59	+	16408.7i	0.585745	+	1.28260i	0.937979	+	0.346691i	$0.112695\pi$
$547$	7493.59	+	16408.7i	0.585745	+	1.28260i	−0.352234	+	0.935912i	$0.614578\pi$
$548$	1701.60	+	11834.9i	0.132644	+	0.922558i
$549$	−17200.4	+	11054.0i	−1.33715	+	0.859335i
$550$	−1580.09	+	1823.52i	−0.122500	+	0.141373i
$551$	28015.0			2.16602
$552$	−223.294	−	667.855i	−0.0172174	−	0.0514960i
$553$	24.6400			0.00189475
$554$	−19688.8	+	22722.1i	−1.50992	+	1.74254i
$555$	416.968	−	267.969i	0.0318906	−	0.0204949i
$556$	3962.12	+	27557.1i	0.302214	+	2.10195i
$557$	−10695.5	−	23419.9i	−0.813616	−	1.78157i	−0.591014	−	0.806662i	$-0.701272\pi$
$557$	−10695.5	−	23419.9i	−0.813616	−	1.78157i	−0.222603	−	0.974909i	$-0.571455\pi$
$558$	−3220.79	+	22401.1i	−0.244350	+	1.69949i
$559$	33609.0	−	9868.48i	2.54295	−	0.746677i
$560$	−252.461	−	162.247i	−0.0190507	−	0.0122432i
$561$	−548.738	+	1201.57i	−0.0412972	+	0.0904283i
$562$	14067.9	+	4130.70i	1.05590	+	0.310041i
$563$	−9641.05	−	11126.4i	−0.721708	−	0.832896i	0.269803	−	0.962915i	$-0.413041\pi$
$563$	−9641.05	−	11126.4i	−0.721708	−	0.832896i	−0.991511	+	0.130020i	$0.958496\pi$
$564$	1828.19	+	2109.84i	0.136491	+	0.157518i
$565$	−3956.49	−	1161.73i	−0.294603	−	0.0865032i
$566$	11742.5	−	25712.6i	0.872041	−	1.90950i
$567$	794.334	+	510.488i	0.0588340	+	0.0378103i
$568$	2260.34	−	663.695i	0.166975	−	0.0490282i
$569$	−2242.82	+	15599.2i	−0.165244	+	1.14930i	0.723309	+	0.690525i	$0.242620\pi$
$569$	−2242.82	+	15599.2i	−0.165244	+	1.14930i	−0.888553	+	0.458774i	$0.848289\pi$
$570$	−691.119	−	1513.34i	−0.0507856	−	0.111205i
$571$	−2169.64	−	15090.2i	−0.159013	−	1.10596i	−0.900456	−	0.434947i	$-0.856767\pi$
$571$	−2169.64	−	15090.2i	−0.159013	−	1.10596i	0.741443	−	0.671016i	$-0.234142\pi$
$572$	14998.8	−	9639.16i	1.09639	−	0.704604i
$573$	1202.05	−	1387.24i	0.0876378	−	0.101139i
$574$	2172.08			0.157946
$575$	2549.13	+	1051.82i	0.184880	+	0.0762850i
$576$	19341.4			1.39911
$577$	10893.8	−	12572.1i	0.785985	−	0.907075i	−0.211541	−	0.977369i	$-0.567848\pi$
$577$	10893.8	−	12572.1i	0.785985	−	0.907075i	0.997526	+	0.0702938i	$0.0223937\pi$
$578$	4614.29	−	2965.42i	0.332057	−	0.213400i
$579$	331.375	+	2304.76i	0.0237849	+	0.165428i
$580$	−5501.11	−	12045.8i	−0.393830	−	0.862367i
$581$	−171.137	+	1190.29i	−0.0122203	+	0.0849937i
$582$	−1745.47	+	512.516i	−0.124316	+	0.0365026i
$583$	4717.78	+	3031.93i	0.335147	+	0.215386i
$584$	−1427.30	+	3125.34i	−0.101133	+	0.221451i
$585$	9920.71	+	2912.98i	0.701147	+	0.205875i
$586$	−5010.61	−	5782.55i	−0.353219	−	0.407636i
$587$	17574.4	+	20281.9i	1.23573	+	1.42611i	0.868289	+	0.496059i	$0.165220\pi$
$587$	17574.4	+	20281.9i	1.23573	+	1.42611i	0.367439	+	0.930047i	$0.380235\pi$
$588$	2424.10	+	711.780i	0.170014	+	0.0499206i
$589$	8883.72	−	19452.6i	0.621473	−	1.36084i
$590$	1744.41	+	1121.06i	0.121722	+	0.0782260i
$591$	602.240	−	176.834i	0.0419168	−	0.0123079i
$592$	832.657	−	5791.25i	0.0578074	−	0.402059i
$593$	4717.19	+	10329.2i	0.326664	+	0.715294i	0.999704	−	0.0243116i	$-0.00773937\pi$
$593$	4717.19	+	10329.2i	0.326664	+	0.715294i	−0.673041	+	0.739606i	$0.735012\pi$
$594$	541.819	+	3768.44i	0.0374261	+	0.260304i
$595$	−456.580	+	293.426i	−0.0314588	+	0.0202173i
$596$	9562.15	−	11035.3i	0.657183	−	0.758430i
$597$	−3205.33			−0.219741
$598$	−28543.3	−	22937.6i	−1.95187	−	1.56854i
$599$	−16435.3			−1.12108			−0.560540	−	0.828128i	$-0.689406\pi$
$599$	−16435.3			−1.12108			−0.560540	+	0.828128i	$0.689406\pi$
$600$	−104.518	+	120.620i	−0.00711153	+	0.00820714i
$601$	−21395.4	+	13750.0i	−1.45214	+	0.933232i	−0.453009	+	0.891506i	$0.649649\pi$
$601$	−21395.4	+	13750.0i	−1.45214	+	0.933232i	−0.999129	+	0.0417263i	$0.986714\pi$
$602$	373.248	+	2595.99i	0.0252698	+	0.175756i
$603$	−2471.32	−	5411.43i	−0.166899	−	0.365457i
$604$	−1293.11	+	8993.80i	−0.0871126	+	0.605882i
$605$	3907.83	−	1147.44i	0.262605	−	0.0771077i
$606$	−3123.79	−	2007.54i	−0.209398	−	0.134572i
$607$	−4673.03	+	10232.5i	−0.312475	+	0.684225i	−0.999084	−	0.0428025i	$-0.986371\pi$
$607$	−4673.03	+	10232.5i	−0.312475	+	0.684225i	0.686609	+	0.727027i	$0.259099\pi$
$608$	−25893.4	−	7603.00i	−1.72717	−	0.507142i
$609$	175.723	+	202.795i	0.0116924	+	0.0134937i
$610$	−10747.3	−	12403.0i	−0.713352	−	0.823252i
$611$	28268.6	+	8300.41i	1.87173	+	0.549588i
$612$	8688.73	−	19025.7i	0.573890	−	1.25664i
$613$	8317.46	+	5345.30i	0.548024	+	0.352194i	0.785170	−	0.619280i	$-0.212576\pi$
$613$	8317.46	+	5345.30i	0.548024	+	0.352194i	−0.237146	+	0.971474i	$0.576212\pi$
$614$	18006.7	−	5287.26i	1.18354	−	0.347518i
$615$	−194.880	+	1355.42i	−0.0127778	+	0.0888714i
$616$	112.548	+	246.447i	0.00736153	+	0.0161195i
$617$	1651.86	+	11488.9i	0.107782	+	0.749637i	0.970001	+	0.243102i	$0.0781649\pi$
$617$	1651.86	+	11488.9i	0.107782	+	0.749637i	−0.862219	+	0.506535i	$0.830926\pi$
$618$	−3608.94	+	2319.33i	−0.234908	+	0.150966i
$619$	14995.8	−	17306.1i	0.973719	−	1.12373i	−0.0185757	−	0.999827i	$-0.505913\pi$
$619$	14995.8	−	17306.1i	0.973719	−	1.12373i	0.992294	−	0.123904i	$-0.0395414\pi$
$620$	−10108.6			−0.654792
$621$	3888.25	−	1952.95i	0.251256	−	0.126198i
$622$	19666.1			1.26775
$623$	574.411	−	662.905i	0.0369395	−	0.0426304i
$624$	−2113.46	+	1358.24i	−0.135586	+	0.0871361i
$625$	−88.9468	−	618.638i	−0.00569259	−	0.0395929i
$626$	7947.82	+	17403.3i	0.507442	+	1.11114i
$627$	253.383	−	1762.32i	0.0161390	−	0.112249i
$628$	−34677.0	+	10182.1i	−2.20345	+	0.646990i
$629$	−8901.55	−	5720.68i	−0.564274	−	0.362637i
$630$	−321.600	+	704.207i	−0.0203379	+	0.0445338i
$631$	−3247.73	−	953.619i	−0.204897	−	0.0601632i	0.177673	−	0.984089i	$-0.443143\pi$
$631$	−3247.73	−	953.619i	−0.204897	−	0.0601632i	−0.382571	+	0.923926i	$0.624961\pi$
$632$	−101.299	−	116.905i	−0.00637570	−	0.00735795i
$633$	1413.78	+	1631.59i	0.0887723	+	0.102449i
$634$	−23404.4	−	6872.16i	−1.46610	−	0.430486i
$635$	618.380	−	1354.06i	0.0386451	−	0.0846211i
$636$	1537.64	+	988.179i	0.0958668	+	0.0616098i
$637$	25582.3	−	7511.66i	1.59122	−	0.467225i
$638$	3624.39	−	25208.2i	0.224908	−	1.56427i
$639$	2992.59	+	6552.87i	0.185266	+	0.405677i
$640$	762.428	+	5302.80i	0.0470900	+	0.327518i
$641$	−6203.31	+	3986.63i	−0.382240	+	0.245651i	−0.717624	−	0.696431i	$-0.754770\pi$
$641$	−6203.31	+	3986.63i	−0.382240	+	0.245651i	0.335384	+	0.942082i	$0.391134\pi$
$642$	697.257	−	804.677i	0.0428638	−	0.0494674i
$643$	30423.3			1.86591			0.932953	−	0.359998i	$-0.117223\pi$
$643$	30423.3			1.86591			0.932953	+	0.359998i	$0.117223\pi$
$644$	1115.22	−	1041.15i	0.0682389	−	0.0637064i
$645$	−1653.44			−0.100937
$646$	−23258.5	+	26841.8i	−1.41656	+	1.63479i
$647$	−10816.9	+	6951.57i	−0.657271	+	0.422402i	−0.826317	−	0.563206i	$-0.809568\pi$
$647$	−10816.9	+	6951.57i	−0.657271	+	0.422402i	0.169046	+	0.985608i	$0.445931\pi$
$648$	−843.608	−	5867.42i	−0.0511420	−	0.355701i
$649$	921.849	+	2018.57i	0.0557561	+	0.122089i
$650$	−1181.10	+	8214.76i	−0.0712719	+	0.495707i
$651$	196.537	−	57.7084i	0.0118324	−	0.00347430i
$652$	−21395.4	−	13750.0i	−1.28513	−	0.825905i
$653$	1165.32	−	2551.69i	0.0698352	−	0.152918i	−0.871495	−	0.490404i	$-0.836849\pi$
$653$	1165.32	−	2551.69i	0.0698352	−	0.152918i	0.941331	+	0.337486i	$0.109577\pi$
$654$	−4227.06	−	1241.18i	−0.252739	−	0.0742108i
$655$	3795.57	+	4380.32i	0.226420	+	0.261303i
$656$	10585.4	+	12216.2i	0.630015	+	0.727076i
$657$	−10081.1	−	2960.08i	−0.598632	−	0.175774i
$658$	−916.385	+	2006.60i	−0.0542924	+	0.118884i
$659$	−7497.30	−	4818.22i	−0.443176	−	0.284812i	0.299961	−	0.953952i	$-0.403026\pi$
$659$	−7497.30	−	4818.22i	−0.443176	−	0.284812i	−0.743137	+	0.669140i	$0.766663\pi$
$660$	−807.508	+	237.106i	−0.0476246	+	0.0139838i
$661$	1049.99	−	7302.83i	0.0617849	−	0.429723i	−0.935327	−	0.353783i	$-0.884895\pi$
$661$	1049.99	−	7302.83i	0.0617849	−	0.429723i	0.997112	−	0.0759403i	$-0.0241958\pi$
$662$	2415.08	+	5288.28i	0.141789	+	0.310476i
$663$	646.606	+	4497.24i	0.0378764	+	0.263436i
$664$	6350.90	−	4081.47i	0.371179	−	0.238542i
$665$	479.053	−	552.856i	0.0279351	−	0.0322389i
$666$	−15093.3			−0.878156
$667$	−28636.6	+	5206.90i	−1.66239	+	0.302267i
$668$	−4318.12			−0.250109
$669$	8.32688	−	9.60973i	0.000481219	−	0.000555357i
$670$	4017.08	−	2581.62i	0.231632	−	0.148861i
$671$	−2499.52	−	17384.6i	−0.143805	−	1.00018i
$672$	−107.379	−	235.127i	−0.00616404	−	0.0134974i
$673$	485.324	−	3375.50i	0.0277977	−	0.193337i	−0.971191	−	0.238303i	$-0.923409\pi$
$673$	485.324	−	3375.50i	0.0277977	−	0.193337i	0.998989	+	0.0449658i	$0.0143179\pi$
$674$	4344.49	−	1275.66i	0.248284	−	0.0729027i
$675$	−829.620	−	533.164i	−0.0473068	−	0.0304022i
$676$	16314.8	−	35724.4i	0.928244	−	2.03257i
$677$	11464.0	+	3366.13i	0.650808	+	0.191095i	0.590440	−	0.807082i	$-0.298954\pi$
$677$	11464.0	+	3366.13i	0.650808	+	0.191095i	0.0603684	+	0.998176i	$0.480772\pi$
$678$	−1692.58	−	1953.34i	−0.0958749	−	0.110646i
$679$	−523.822	−	604.523i	−0.0296059	−	0.0341671i
$680$	3269.23	+	959.934i	0.184367	+	0.0541350i
$681$	1205.34	−	2639.32i	0.0678247	−	0.148515i
$682$	−16354.4	−	10510.3i	−0.918243	−	0.590119i
$683$	−22390.2	+	6574.36i	−1.25438	+	0.368318i	−0.840398	−	0.541969i	$-0.817679\pi$
$683$	−22390.2	+	6574.36i	−1.25438	+	0.368318i	−0.413977	+	0.910287i	$0.635861\pi$
$684$	−4012.07	+	27904.5i	−0.224277	+	1.55988i
$685$	−2474.31	−	5417.99i	−0.138013	−	0.302206i
$686$	569.796	+	3963.02i	0.0317127	+	0.220567i
$687$	−2807.86	+	1804.50i	−0.155934	+	0.100213i
$688$	−12781.4	+	14750.5i	−0.708262	+	0.817378i
$689$	19289.3			1.06657
$690$	987.724	+	1418.47i	0.0544957	+	0.0782610i
$691$	8373.85			0.461007			0.230504	−	0.973071i	$-0.425963\pi$
$691$	8373.85			0.461007			0.230504	+	0.973071i	$0.425963\pi$
$692$	−879.571	+	1015.08i	−0.0483183	+	0.0557623i
$693$	−696.977	+	447.920i	−0.0382048	+	0.0245528i
$694$	−5853.77	−	40713.8i	−0.320181	−	2.22691i
$695$	−5761.34	−	12615.6i	−0.314446	−	0.688541i
$696$	239.742	−	1667.44i	0.0130566	−	0.0908107i
$697$	28049.3	−	8236.03i	1.52431	−	0.447578i
$698$	−1315.42	−	845.369i	−0.0713315	−	0.0458420i
$699$	767.746	−	1681.13i	0.0415434	−	0.0909673i
$700$	−331.783	−	97.4202i	−0.0179146	−	0.00526020i
$701$	3162.63	+	3649.87i	0.170401	+	0.196653i	0.834526	−	0.550968i	$-0.185741\pi$
$701$	3162.63	+	3649.87i	0.170401	+	0.196653i	−0.664125	+	0.747621i	$0.731196\pi$
$702$	8575.50	+	9896.65i	0.461056	+	0.532087i
$703$	13684.4	+	4018.09i	0.734162	+	0.215569i
$704$	−6901.82	+	15112.9i	−0.369492	+	0.809074i
$705$	−1169.94	−	751.875i	−0.0625000	−	0.0401663i
$706$	−40344.6	+	11846.2i	−2.15069	+	0.631501i
$707$	232.364	−	1616.13i	0.0123606	−	0.0859699i
$708$	300.452	+	657.899i	0.0159487	+	0.0349228i
$709$	−1865.71	−	12976.3i	−0.0988266	−	0.687354i	−0.977655	−	0.210216i	$-0.932583\pi$
$709$	−1865.71	−	12976.3i	−0.0988266	−	0.687354i	0.878828	−	0.477138i	$-0.158326\pi$
$710$	−4864.41	+	3126.17i	−0.257124	+	0.165244i
$711$	309.769	−	357.492i	0.0163393	−	0.0188566i
$712$	−5506.65			−0.289846
$713$	−5465.36	+	21535.4i	−0.287068	+	1.13115i
$714$	−340.191			−0.0178310
$715$	−5816.26	+	6712.33i	−0.304218	+	0.351086i
$716$	−21332.3	+	13709.4i	−1.11344	+	0.715565i
$717$	−272.055	−	1892.18i	−0.0141702	−	0.0985562i
$718$	5804.18	+	12709.4i	0.301685	+	0.660599i
$719$	57.9513	−	403.060i	0.00300587	−	0.0209063i	−0.988263	−	0.152760i	$-0.951184\pi$
$719$	57.9513	−	403.060i	0.00300587	−	0.0209063i	0.991269	+	0.131854i	$0.0420929\pi$
$720$	−5527.86	+	1623.13i	−0.286127	+	0.0840144i
$721$	−1586.88	−	1019.83i	−0.0819674	−	0.0526773i
$722$	7785.46	−	17047.8i	0.401309	−	0.878743i
$723$	410.898	+	120.651i	0.0211362	+	0.00620615i
$724$	−3980.07	−	4593.25i	−0.204307	−	0.235783i
$725$	4319.98	+	4985.53i	0.221297	+	0.255390i
$726$	2449.45	+	719.223i	0.125217	+	0.0367670i
$727$	−1398.53	+	3062.36i	−0.0713462	+	0.156226i	−0.941945	−	0.335767i	$-0.891004\pi$
$727$	−1398.53	+	3062.36i	−0.0713462	+	0.156226i	0.870599	+	0.491994i	$0.163732\pi$
$728$	783.953	+	503.816i	0.0399110	+	0.0256493i
$729$	16638.6	−	4885.52i	0.845327	−	0.248210i
$730$	1200.20	−	8347.58i	0.0608512	−	0.423230i
$731$	14663.4	+	32108.3i	0.741920	+	1.62458i
$732$	−814.654	−	5666.04i	−0.0411345	−	0.286097i
$733$	22548.6	−	14491.1i	1.13622	−	0.730207i	0.169374	−	0.985552i	$-0.445825\pi$
$733$	22548.6	−	14491.1i	1.13622	−	0.730207i	0.966850	+	0.255345i	$0.0821890\pi$
$734$	−1037.08	+	1196.85i	−0.0521516	+	0.0601862i
$735$	−1258.56			−0.0631600
$736$	27881.1	+	2959.12i	1.39635	+	0.148199i
$737$	5110.24			0.255411
$738$	27307.0	−	31514.0i	1.36204	−	1.57188i
$739$	9857.72	−	6335.17i	0.490693	−	0.315349i	−0.271791	−	0.962356i	$-0.587616\pi$
$739$	9857.72	−	6335.17i	0.490693	−	0.315349i	0.762484	+	0.647007i	$0.223980\pi$
$740$	−959.425	−	6672.95i	−0.0476610	−	0.331490i
$741$	−2543.99	−	5570.57i	−0.126121	−	0.276167i
$742$	−205.542	+	1429.58i	−0.0101694	+	0.0707297i
$743$	−15166.3	+	4453.22i	−0.748852	+	0.219883i	−0.633822	−	0.773479i	$-0.718515\pi$
$743$	−15166.3	+	4453.22i	−0.748852	+	0.219883i	−0.115030	+	0.993362i	$0.536697\pi$
$744$	−1081.79	−	695.224i	−0.0533069	−	0.0342583i
$745$	−3021.72	+	6616.63i	−0.148600	+	0.325389i
$746$	−43255.8	−	12701.1i	−2.12293	−	0.623349i
$747$	15117.9	+	17447.0i	0.740476	+	0.854554i
$748$	11765.7	+	13578.3i	0.575128	+	0.663734i
$749$	449.210	+	131.900i	0.0219143	+	0.00643461i
$750$	162.740	−	356.351i	0.00792324	−	0.0173495i
$751$	−15381.1	−	9884.81i	−0.747355	−	0.480296i	0.110700	−	0.993854i	$-0.464691\pi$
$751$	−15381.1	−	9884.81i	−0.747355	−	0.480296i	−0.858055	+	0.513558i	$0.828327\pi$
$752$	−15751.4	+	4625.02i	−0.763822	+	0.224278i
$753$	582.409	−	4050.75i	0.0281862	−	0.196039i
$754$	−36389.3	−	79681.4i	−1.75759	−	3.84858i
$755$	−644.171	−	4480.31i	−0.0310514	−	0.215967i
$756$	−458.998	+	294.980i	−0.0220815	+	0.0141909i
$757$	1439.20	−	1660.92i	0.0690997	−	0.0797453i	−0.720147	−	0.693821i	$-0.755926\pi$
$757$	1439.20	−	1660.92i	0.0690997	−	0.0797453i	0.789247	+	0.614076i	$0.210471\pi$
$758$	41304.2			1.97920
$759$	68.5408	+	1848.52i	0.00327783	+	0.0884017i
$760$	−4592.49			−0.219194
$761$	106.841	−	123.301i	0.00508931	−	0.00587338i	−0.753199	−	0.657792i	$-0.771490\pi$
$761$	106.841	−	123.301i	0.00508931	−	0.00587338i	0.758289	+	0.651919i	$0.226036\pi$
$762$	784.934	−	504.446i	0.0373165	−	0.0239818i
$763$	−275.683	−	1917.42i	−0.0130805	−	0.0909768i
$764$	−10371.5	−	22710.4i	−0.491136	−	1.0754

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)

\(f(q)\)	\(=\)	\(q+(-2.78120 + 3.20967i) q^{2} +(0.620793 - 0.398960i) q^{3} +(-1.42842 - 9.93487i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.446019 + 3.10213i) q^{6} +(-1.32223 + 0.388243i) q^{7} +(7.27793 + 4.67724i) q^{8} +(-10.9900 + 24.0647i) q^{9} +O(q^{10})\)	\(q+(-2.78120 + 3.20967i) q^{2} +(0.620793 - 0.398960i) q^{3} +(-1.42842 - 9.93487i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.446019 + 3.10213i) q^{6} +(-1.32223 + 0.388243i) q^{7} +(7.27793 + 4.67724i) q^{8} +(-10.9900 + 24.0647i) q^{9} +(-20.3748 - 5.98259i) q^{10} +(-14.8819 - 17.1746i) q^{11} +(-4.85037 - 5.59762i) q^{12} +(-74.9993 - 22.0218i) q^{13} +(2.43126 - 5.32372i) q^{14} +(3.10397 + 1.99480i) q^{15} +(41.7900 - 12.2706i) q^{16} +(11.2099 - 77.9669i) q^{17} +(-46.6745 - 102.203i) q^{18} +(15.1094 + 105.088i) q^{19} +(42.2184 - 27.1322i) q^{20} +(-0.665941 + 0.768537i) q^{21} +96.5144 q^{22} +(-34.9765 - 104.612i) q^{23} +6.38412 q^{24} +(-16.3715 + 18.8937i) q^{25} +(279.271 - 179.476i) q^{26} +(5.61387 + 39.0453i) q^{27} +(5.74585 + 12.5817i) q^{28} +(37.5529 - 261.186i) q^{29} +(-15.0354 + 4.41479i) q^{30} +(-169.450 - 108.899i) q^{31} +(-105.592 + 231.215i) q^{32} +(-16.0906 - 4.72462i) q^{33} +(219.071 + 252.821i) q^{34} +(-4.51217 - 5.20732i) q^{35} +(254.778 + 74.8096i) q^{36} +(55.8043 - 122.194i) q^{37} +(-379.321 - 243.775i) q^{38} +(-55.3449 + 16.2507i) q^{39} +(-6.15603 + 42.8161i) q^{40} +(154.173 + 337.593i) q^{41} +(-0.614638 - 4.27490i) q^{42} +(-376.985 + 242.274i) q^{43} +(-149.370 + 172.382i) q^{44} -132.277 q^{45} +(433.046 + 178.683i) q^{46} -376.918 q^{47} +(21.0474 - 24.2901i) q^{48} +(-286.952 + 184.413i) q^{49} +(-15.1103 - 105.094i) q^{50} +(-24.1466 - 52.8737i) q^{51} +(-111.653 + 776.565i) q^{52} +(-236.779 + 69.5246i) q^{53} +(-140.936 - 90.5740i) q^{54} +(47.2021 - 103.358i) q^{55} +(-11.4390 - 3.35880i) q^{56} +(51.3058 + 59.2101i) q^{57} +(733.879 + 846.942i) q^{58} +(-93.6935 - 27.5109i) q^{59} +(15.3843 - 33.6869i) q^{60} +(650.166 + 417.836i) q^{61} +(820.804 - 241.010i) q^{62} +(5.18838 - 36.0860i) q^{63} +(-303.706 - 665.024i) q^{64} +(-55.6206 - 386.850i) q^{65} +(59.9155 - 38.5054i) q^{66} +(-147.259 + 169.945i) q^{67} -790.604 q^{68} +(-63.4491 - 50.9881i) q^{69} +29.2630 q^{70} +(178.320 - 205.792i) q^{71} +(-192.541 + 123.738i) q^{72} +(56.5199 + 393.104i) q^{73} +(237.001 + 518.960i) q^{74} +(-2.62549 + 18.2607i) q^{75} +(1022.46 - 300.220i) q^{76} +(26.3453 + 16.9311i) q^{77} +(101.766 - 222.835i) q^{78} +(-17.1560 - 5.03745i) q^{79} +(142.610 + 164.580i) q^{80} +(-448.703 - 517.830i) q^{81} +(-1512.35 - 444.066i) q^{82} +(362.501 - 793.767i) q^{83} +(8.58656 + 5.51825i) q^{84} +(377.890 - 110.958i) q^{85} +(270.851 - 1883.81i) q^{86} +(-80.8901 - 177.125i) q^{87} +(-27.9795 - 194.602i) q^{88} +(-535.468 + 344.125i) q^{89} +(367.889 - 424.566i) q^{90} +107.717 q^{91} +(-989.344 + 496.917i) q^{92} -148.640 q^{93} +(1048.28 - 1209.78i) q^{94} +(-446.575 + 286.996i) q^{95} +(26.6944 + 185.664i) q^{96} +(241.129 + 528.000i) q^{97} +(206.165 - 1433.91i) q^{98} +(576.855 - 169.380i) 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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