LMFDB - Embedded newform 162.4.e.b.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	162.91
Dual form			162.4.e.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(9.84993 + 8.26508i) q^{5} +(-26.8516 - 9.77320i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(9.84993 + 8.26508i) q^{5} +(-26.8516 - 9.77320i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-12.8582 + 22.2710i) q^{10} +(-25.0993 + 21.0608i) q^{11} +(-14.0621 + 79.7503i) q^{13} +(9.92397 - 56.2816i) q^{14} +(12.2567 - 10.2846i) q^{16} +(17.5008 - 30.3123i) q^{17} +(-39.1734 - 67.8503i) q^{19} +(-48.3309 - 17.5910i) q^{20} +(-50.1986 - 42.1217i) q^{22} +(-86.5749 + 31.5107i) q^{23} +(7.00370 + 39.7200i) q^{25} -161.961 q^{26} +114.300 q^{28} +(15.2117 + 86.2697i) q^{29} +(-266.051 + 96.8348i) q^{31} +(24.5134 + 20.5692i) q^{32} +(65.7816 + 23.9425i) q^{34} +(-183.711 - 318.196i) q^{35} +(-85.7217 + 148.474i) q^{37} +(120.034 - 100.721i) q^{38} +(17.8624 - 101.303i) q^{40} +(6.15632 - 34.9142i) q^{41} +(275.616 - 231.270i) q^{43} +(65.5297 - 113.501i) q^{44} +(-92.1310 - 159.576i) q^{46} +(244.565 + 89.0144i) q^{47} +(362.742 + 304.377i) q^{49} +(-75.8007 + 27.5892i) q^{50} +(-56.2485 - 319.001i) q^{52} +420.091 q^{53} -421.296 q^{55} +(39.6959 + 225.126i) q^{56} +(-164.635 + 59.9223i) q^{58} +(571.246 + 479.332i) q^{59} +(153.387 + 55.8282i) q^{61} +(-283.126 - 490.389i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-797.654 + 669.311i) q^{65} +(-66.4139 + 376.652i) q^{67} +(-24.3119 + 137.880i) q^{68} +(562.922 - 472.348i) q^{70} +(-167.370 + 289.894i) q^{71} +(-50.6730 - 87.7682i) q^{73} +(-322.208 - 117.274i) q^{74} +(240.068 + 201.441i) q^{76} +(879.790 - 320.217i) q^{77} +(93.7010 + 531.405i) q^{79} +205.731 q^{80} +70.9057 q^{82} +(113.048 + 641.125i) q^{83} +(422.916 - 153.929i) q^{85} +(551.233 + 462.539i) q^{86} +(246.311 + 89.6499i) q^{88} +(95.2928 + 165.052i) q^{89} +(1157.01 - 2004.00i) q^{91} +(282.306 - 236.883i) q^{92} +(-90.3876 + 512.613i) q^{94} +(174.933 - 992.092i) q^{95} +(81.2556 - 68.1816i) q^{97} +(-473.527 + 820.172i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.347296	+	1.96962i	0.122788	+	0.696364i
$2$	0.347296	+	1.96962i	0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	+	1.36808i	−0.469846	+	0.171010i
$5$	9.84993	+	8.26508i	0.881005	+	0.739251i	0.966385	−	0.257097i	$-0.0827661\pi$
$5$	9.84993	+	8.26508i	0.881005	+	0.739251i	−0.0853805	+	0.996348i	$0.527211\pi$
$6$		0			0
$7$	−26.8516	−	9.77320i	−1.44985	−	0.527703i	−0.507303	−	0.861768i	$-0.669357\pi$
$7$	−26.8516	−	9.77320i	−1.44985	−	0.527703i	−0.942550	+	0.334065i	$0.891580\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$		0			0
$10$	−12.8582	+	22.2710i	−0.406611	+	0.704271i
$11$	−25.0993	+	21.0608i	−0.687975	+	0.577280i	−0.918325	−	0.395828i	$-0.870458\pi$
$11$	−25.0993	+	21.0608i	−0.687975	+	0.577280i	0.230349	+	0.973108i	$0.426013\pi$
$12$		0			0
$13$	−14.0621	+	79.7503i	−0.300010	+	1.70144i	0.346099	+	0.938198i	$0.387506\pi$
$13$	−14.0621	+	79.7503i	−0.300010	+	1.70144i	−0.646109	+	0.763245i	$0.723605\pi$
$14$	9.92397	−	56.2816i	0.189449	−	1.07442i
$15$		0			0
$16$	12.2567	−	10.2846i	0.191511	−	0.160697i
$17$	17.5008	−	30.3123i	0.249681	−	0.432460i	−0.713756	−	0.700394i	$-0.753008\pi$
$17$	17.5008	−	30.3123i	0.249681	−	0.432460i	0.963437	+	0.267934i	$0.0863410\pi$
$18$		0			0
$19$	−39.1734	−	67.8503i	−0.473000	−	0.819259i	0.526523	−	0.850161i	$-0.323495\pi$
$19$	−39.1734	−	67.8503i	−0.473000	−	0.819259i	−0.999522	+	0.0309016i	$0.990162\pi$
$20$	−48.3309	−	17.5910i	−0.540356	−	0.196674i
$21$		0			0
$22$	−50.1986	−	42.1217i	−0.486472	−	0.408199i
$23$	−86.5749	+	31.5107i	−0.784874	+	0.285671i	−0.703204	−	0.710989i	$-0.748248\pi$
$23$	−86.5749	+	31.5107i	−0.784874	+	0.285671i	−0.0816706	+	0.996659i	$0.526026\pi$
$24$		0			0
$25$	7.00370	+	39.7200i	0.0560296	+	0.317760i
$26$	−161.961			−1.22166
$27$		0			0
$28$	114.300			0.771451
$29$	15.2117	+	86.2697i	0.0974047	+	0.552410i	0.993984	+	0.109526i	$0.0349334\pi$
$29$	15.2117	+	86.2697i	0.0974047	+	0.552410i	−0.896579	+	0.442883i	$0.853956\pi$
$30$		0			0
$31$	−266.051	+	96.8348i	−1.54143	+	0.561034i	−0.966387	−	0.257091i	$-0.917236\pi$
$31$	−266.051	+	96.8348i	−1.54143	+	0.561034i	−0.575040	+	0.818125i	$0.695014\pi$
$32$	24.5134	+	20.5692i	0.135419	+	0.113630i
$33$		0			0
$34$	65.7816	+	23.9425i	0.331807	+	0.120768i
$35$	−183.711	−	318.196i	−0.887222	−	1.53671i
$36$		0			0
$37$	−85.7217	+	148.474i	−0.380880	+	0.659704i	−0.991188	−	0.132460i	$-0.957712\pi$
$37$	−85.7217	+	148.474i	−0.380880	+	0.659704i	0.610308	+	0.792164i	$0.291046\pi$
$38$	120.034	−	100.721i	0.512424	−	0.429975i
$39$		0			0
$40$	17.8624	−	101.303i	0.0706073	−	0.400434i
$41$	6.15632	−	34.9142i	0.0234501	−	0.132992i	−0.970835	−	0.239748i	$-0.922935\pi$
$41$	6.15632	−	34.9142i	0.0234501	−	0.132992i	0.994285	+	0.106756i	$0.0340463\pi$
$42$		0			0
$43$	275.616	−	231.270i	0.977468	−	0.820193i	−0.00623765	−	0.999981i	$-0.501986\pi$
$43$	275.616	−	231.270i	0.977468	−	0.820193i	0.983705	+	0.179788i	$0.0575411\pi$
$44$	65.5297	−	113.501i	0.224522	−	0.388884i
$45$		0			0
$46$	−92.1310	−	159.576i	−0.295304	−	0.511481i
$47$	244.565	+	89.0144i	0.759010	+	0.276257i	0.692392	−	0.721521i	$-0.256557\pi$
$47$	244.565	+	89.0144i	0.759010	+	0.276257i	0.0666180	+	0.997779i	$0.478779\pi$
$48$		0			0
$49$	362.742	+	304.377i	1.05756	+	0.887396i
$50$	−75.8007	+	27.5892i	−0.214397	+	0.0780340i
$51$		0			0
$52$	−56.2485	−	319.001i	−0.150005	−	0.850721i
$53$	420.091			1.08875			0.544377	−	0.838841i	$-0.316766\pi$
$53$	420.091			1.08875			0.544377	+	0.838841i	$0.316766\pi$
$54$		0			0
$55$	−421.296			−1.03286
$56$	39.6959	+	225.126i	0.0947247	+	0.537211i
$57$		0			0
$58$	−164.635	+	59.9223i	−0.372718	+	0.135658i
$59$	571.246	+	479.332i	1.26051	+	1.05769i	0.995628	+	0.0934084i	$0.0297762\pi$
$59$	571.246	+	479.332i	1.26051	+	1.05769i	0.264878	+	0.964282i	$0.414668\pi$
$60$		0			0
$61$	153.387	+	55.8282i	0.321954	+	0.117182i	0.497941	−	0.867211i	$-0.334090\pi$
$61$	153.387	+	55.8282i	0.321954	+	0.117182i	−0.175987	+	0.984392i	$0.556312\pi$
$62$	−283.126	−	490.389i	−0.579952	−	1.00451i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−797.654	+	669.311i	−1.52210	+	1.27720i
$66$		0			0
$67$	−66.4139	+	376.652i	−0.121101	+	0.686796i	0.862447	+	0.506148i	$0.168931\pi$
$67$	−66.4139	+	376.652i	−0.121101	+	0.686796i	−0.983548	+	0.180649i	$0.942180\pi$
$68$	−24.3119	+	137.880i	−0.0433566	+	0.245888i
$69$		0			0
$70$	562.922	−	472.348i	0.961173	−	0.806520i
$71$	−167.370	+	289.894i	−0.279763	+	0.484565i	−0.971326	−	0.237752i	$-0.923589\pi$
$71$	−167.370	+	289.894i	−0.279763	+	0.484565i	0.691562	+	0.722317i	$0.256923\pi$
$72$		0			0
$73$	−50.6730	−	87.7682i	−0.0812442	−	0.140719i	0.822540	−	0.568707i	$-0.192556\pi$
$73$	−50.6730	−	87.7682i	−0.0812442	−	0.140719i	−0.903785	+	0.427988i	$0.859223\pi$
$74$	−322.208	−	117.274i	−0.506161	−	0.184228i
$75$		0			0
$76$	240.068	+	201.441i	0.362339	+	0.304038i
$77$	879.790	−	320.217i	1.30210	−	0.473924i
$78$		0			0
$79$	93.7010	+	531.405i	0.133445	+	0.756807i	0.975930	+	0.218086i	$0.0699812\pi$
$79$	93.7010	+	531.405i	0.133445	+	0.756807i	−0.842484	+	0.538721i	$0.818908\pi$
$80$	205.731			0.287518
$81$		0			0
$82$	70.9057			0.0954905
$83$	113.048	+	641.125i	0.149501	+	0.847863i	0.963642	+	0.267196i	$0.0860971\pi$
$83$	113.048	+	641.125i	0.149501	+	0.847863i	−0.814141	+	0.580667i	$0.802792\pi$
$84$		0			0
$85$	422.916	−	153.929i	0.539666	−	0.196422i
$86$	551.233	+	462.539i	0.691174	+	0.579964i
$87$		0			0
$88$	246.311	+	89.6499i	0.298373	+	0.108599i
$89$	95.2928	+	165.052i	0.113495	+	0.196578i	0.917177	−	0.398480i	$-0.130462\pi$
$89$	95.2928	+	165.052i	0.113495	+	0.196578i	−0.803682	+	0.595059i	$0.797129\pi$
$90$		0			0
$91$	1157.01	−	2004.00i	1.33283	−	2.30853i
$92$	282.306	−	236.883i	0.319918	−	0.268443i
$93$		0			0
$94$	−90.3876	+	512.613i	−0.0991784	+	0.562468i
$95$	174.933	−	992.092i	0.188923	−	1.07144i
$96$		0			0
$97$	81.2556	−	68.1816i	0.0850542	−	0.0713690i	−0.599269	−	0.800548i	$-0.704542\pi$
$97$	81.2556	−	68.1816i	0.0850542	−	0.0713690i	0.684323	+	0.729179i	$0.260098\pi$
$98$	−473.527	+	820.172i	−0.488096	+	0.845407i
$99$		0			0
$100$	−80.6654	−	139.717i	−0.0806654	−	0.139717i
$101$	139.530	+	50.7848i	0.137463	+	0.0500325i	0.409836	−	0.912159i	$-0.365586\pi$
$101$	139.530	+	50.7848i	0.137463	+	0.0500325i	−0.272372	+	0.962192i	$0.587808\pi$
$102$		0			0
$103$	128.849	+	108.117i	0.123261	+	0.103428i	0.702335	−	0.711847i	$-0.252141\pi$
$103$	128.849	+	108.117i	0.123261	+	0.103428i	−0.579073	+	0.815275i	$0.696586\pi$
$104$	608.775	−	221.576i	0.573993	−	0.208916i
$105$		0			0
$106$	145.896	+	827.418i	0.133686	+	0.758169i
$107$	−118.530			−0.107091			−0.0535454	−	0.998565i	$-0.517052\pi$
$107$	−118.530			−0.107091			−0.0535454	+	0.998565i	$0.517052\pi$
$108$		0			0
$109$	−1672.23			−1.46946			−0.734729	−	0.678361i	$-0.762690\pi$
$109$	−1672.23			−1.46946			−0.734729	+	0.678361i	$0.762690\pi$
$110$	−146.315	−	829.791i	−0.126823	−	0.719250i
$111$		0			0
$112$	−429.626	+	156.371i	−0.362463	+	0.131926i
$113$	−1693.00	−	1420.59i	−1.40942	−	1.18264i	−0.956733	−	0.290968i	$-0.906023\pi$
$113$	−1693.00	−	1420.59i	−1.40942	−	1.18264i	−0.452682	−	0.891672i	$-0.649533\pi$
$114$		0			0
$115$	−1113.19	−	405.170i	−0.902661	−	0.328542i
$116$	−175.201	−	303.457i	−0.140233	−	0.242890i
$117$		0			0
$118$	−745.708	+	1291.60i	−0.581763	+	1.00764i
$119$	−766.174	+	642.896i	−0.590211	+	0.495246i
$120$		0			0
$121$	−44.7084	+	253.554i	−0.0335901	+	0.190499i
$122$	−56.6895	+	321.502i	−0.0420691	+	0.238585i
$123$		0			0
$124$	867.549	−	727.960i	0.628292	−	0.527199i
$125$	544.333	−	942.813i	0.389493	−	0.674622i
$126$		0			0
$127$	−520.657	−	901.805i	−0.363786	−	0.630096i	0.624794	−	0.780789i	$-0.285183\pi$
$127$	−520.657	−	901.805i	−0.363786	−	0.630096i	−0.988581	+	0.150693i	$0.951850\pi$
$128$	−120.281	−	43.7786i	−0.0830579	−	0.0302306i
$129$		0			0
$130$	−1595.31	−	1338.62i	−1.07629	−	0.903114i
$131$	1002.18	−	364.763i	0.668402	−	0.243278i	0.0145423	−	0.999894i	$-0.495371\pi$
$131$	1002.18	−	364.763i	0.668402	−	0.243278i	0.653860	+	0.756616i	$0.273149\pi$
$132$		0			0
$133$	388.756	+	2204.74i	0.253454	+	1.43741i
$134$	−764.925			−0.493130
$135$		0			0
$136$	−280.013			−0.176551
$137$	22.1477	+	125.606i	0.0138118	+	0.0783303i	0.990935	−	0.134346i	$-0.0428932\pi$
$137$	22.1477	+	125.606i	0.0138118	+	0.0783303i	−0.977123	+	0.212676i	$0.931782\pi$
$138$		0			0
$139$	1225.92	−	446.197i	0.748063	−	0.272273i	0.0602728	−	0.998182i	$-0.480803\pi$
$139$	1225.92	−	446.197i	0.748063	−	0.272273i	0.687791	+	0.725909i	$0.258581\pi$
$140$	1125.84	+	944.696i	0.679652	+	0.570296i
$141$		0			0
$142$	−629.107	−	228.976i	−0.371785	−	0.135319i
$143$	−1326.66	−	2297.84i	−0.775809	−	1.34374i
$144$		0			0
$145$	−563.192	+	975.477i	−0.322555	+	0.558682i
$146$	155.271	−	130.288i	0.0880160	−	0.0738542i
$147$		0			0
$148$	119.083	−	675.355i	0.0661391	−	0.375094i
$149$	−476.343	+	2701.47i	−0.261903	+	1.48533i	0.515809	+	0.856704i	$0.327492\pi$
$149$	−476.343	+	2701.47i	−0.261903	+	1.48533i	−0.777712	+	0.628621i	$0.783620\pi$
$150$		0			0
$151$	841.500	−	706.102i	0.453512	−	0.380541i	−0.387225	−	0.921985i	$-0.626566\pi$
$151$	841.500	−	706.102i	0.453512	−	0.380541i	0.840737	+	0.541444i	$0.182122\pi$
$152$	−313.387	+	542.802i	−0.167231	+	0.289652i
$153$		0			0
$154$	936.253	+	1621.64i	0.489905	+	0.848541i
$155$	−3420.94	−	1245.12i	−1.77275	−	0.645228i
$156$		0			0
$157$	1540.55	+	1292.68i	0.783118	+	0.657114i	0.944032	−	0.329855i	$-0.107000\pi$
$157$	1540.55	+	1292.68i	0.783118	+	0.657114i	−0.160914	+	0.986968i	$0.551444\pi$
$158$	−1014.12	+	369.110i	−0.510628	+	0.185853i
$159$		0			0
$160$	71.4496	+	405.211i	0.0353037	+	0.200217i
$161$	2632.64			1.28870
$162$		0			0
$163$	1314.97			0.631877			0.315939	−	0.948780i	$-0.397681\pi$
$163$	1314.97			0.631877			0.315939	+	0.948780i	$0.397681\pi$
$164$	24.6253	+	139.657i	0.0117251	+	0.0664962i
$165$		0			0
$166$	−1223.51	+	445.321i	−0.572065	+	0.208215i
$167$	−3231.03	−	2711.16i	−1.49715	−	1.25626i	−0.885060	−	0.465477i	$-0.845883\pi$
$167$	−3231.03	−	2711.16i	−1.49715	−	1.25626i	−0.612094	−	0.790785i	$-0.709673\pi$
$168$		0			0
$169$	−4097.86	−	1491.50i	−1.86521	−	0.678881i
$170$	450.057	+	779.522i	0.203046	+	0.351686i
$171$		0			0
$172$	−719.583	+	1246.36i	−0.318998	+	0.552521i
$173$	2366.00	−	1985.31i	1.03979	−	0.872486i	0.0478055	−	0.998857i	$-0.484777\pi$
$173$	2366.00	−	1985.31i	1.03979	−	0.872486i	0.991983	+	0.126370i	$0.0403328\pi$
$174$		0			0
$175$	200.130	−	1135.00i	0.0864481	−	0.490272i
$176$	−91.0329	+	516.273i	−0.0389878	+	0.221111i
$177$		0			0
$178$	−291.994	+	245.012i	−0.122954	+	0.103171i
$179$	−1502.85	+	2603.02i	−0.627534	+	1.08692i	0.360511	+	0.932755i	$0.382602\pi$
$179$	−1502.85	+	2603.02i	−0.627534	+	1.08692i	−0.988045	+	0.154166i	$0.950731\pi$
$180$		0			0
$181$	−693.483	−	1201.15i	−0.284786	−	0.493263i	0.687772	−	0.725927i	$-0.258589\pi$
$181$	−693.483	−	1201.15i	−0.284786	−	0.493263i	−0.972557	+	0.232664i	$0.925256\pi$
$182$	4348.92	+	1582.88i	1.77123	+	0.644675i
$183$		0			0
$184$	564.612	+	473.766i	0.226216	+	0.189818i
$185$	−2071.50	+	753.966i	−0.823244	+	0.299636i
$186$		0			0
$187$	199.144	+	1129.40i	0.0778761	+	0.441657i
$188$	−1041.04			−0.403861
$189$		0			0
$190$	2014.79			0.769308
$191$	−265.636	−	1506.50i	−0.100632	−	0.570714i	−0.992875	−	0.119158i	$-0.961980\pi$
$191$	−265.636	−	1506.50i	−0.100632	−	0.570714i	0.892243	−	0.451555i	$-0.149131\pi$
$192$		0			0
$193$	−336.885	+	122.616i	−0.125645	+	0.0457311i	−0.404078	−	0.914725i	$-0.632407\pi$
$193$	−336.885	+	122.616i	−0.125645	+	0.0457311i	0.278432	+	0.960456i	$0.410185\pi$
$194$	162.511	+	136.363i	0.0601424	+	0.0504655i
$195$		0			0
$196$	−1779.88	−	647.822i	−0.648643	−	0.236087i
$197$	2543.28	+	4405.08i	0.919802	+	1.59314i	0.799715	+	0.600380i	$0.204984\pi$
$197$	2543.28	+	4405.08i	0.919802	+	1.59314i	0.120087	+	0.992763i	$0.461683\pi$
$198$		0			0
$199$	−998.330	+	1729.16i	−0.355627	+	0.615963i	−0.987225	−	0.159332i	$-0.949066\pi$
$199$	−998.330	+	1729.16i	−0.355627	+	0.615963i	0.631598	+	0.775296i	$0.282399\pi$
$200$	247.173	−	207.403i	0.0873889	−	0.0733280i
$201$		0			0
$202$	−51.5683	+	292.458i	−0.0179620	+	0.101868i
$203$	434.673	−	2465.15i	0.150286	−	0.852313i
$204$		0			0
$205$	349.208	−	293.020i	0.118974	−	0.0998314i
$206$	−168.201	+	291.332i	−0.0568889	+	0.0985344i
$207$		0			0
$208$	647.845	+	1122.10i	0.215961	+	0.374056i
$209$	2412.21	+	877.973i	0.798354	+	0.290577i
$210$		0			0
$211$	−4592.55	−	3853.61i	−1.49841	−	1.25731i	−0.883243	−	0.468916i	$-0.844645\pi$
$211$	−4592.55	−	3853.61i	−1.49841	−	1.25731i	−0.615165	−	0.788398i	$-0.710911\pi$
$212$	−1579.03	+	574.718i	−0.511547	+	0.186188i
$213$		0			0
$214$	−41.1650	−	233.458i	−0.0131494	−	0.0745742i
$215$	4626.27			1.46748
$216$		0			0
$217$	8090.31			2.53090
$218$	−580.760	−	3293.66i	−0.180431	−	1.02328i
$219$		0			0
$220$	1583.56	−	576.367i	0.485288	−	0.176630i
$221$	2171.32	+	1821.95i	0.660899	+	0.554560i
$222$		0			0
$223$	−1291.28	−	469.986i	−0.387759	−	0.141133i	0.140782	−	0.990041i	$-0.455038\pi$
$223$	−1291.28	−	469.986i	−0.387759	−	0.141133i	−0.528541	+	0.848908i	$0.677261\pi$
$224$	−457.199	−	791.892i	−0.136374	−	0.236208i
$225$		0			0
$226$	2210.05	−	3827.92i	0.650489	−	1.12668i
$227$	372.172	−	312.289i	0.108819	−	0.0913100i	−0.586755	−	0.809765i	$-0.699595\pi$
$227$	372.172	−	312.289i	0.108819	−	0.0913100i	0.695574	+	0.718455i	$0.255150\pi$
$228$		0			0
$229$	76.5704	−	434.253i	0.0220957	−	0.125311i	−0.971765	−	0.235952i	$-0.924179\pi$
$229$	76.5704	−	434.253i	0.0220957	−	0.125311i	0.993860	+	0.110641i	$0.0352903\pi$
$230$	411.420	−	2333.28i	0.117949	−	0.668921i
$231$		0			0
$232$	536.847	−	450.468i	0.151921	−	0.127477i
$233$	1199.80	−	2078.11i	0.337345	−	0.584298i	−0.646588	−	0.762840i	$-0.723805\pi$
$233$	1199.80	−	2078.11i	0.337345	−	0.584298i	0.983932	+	0.178542i	$0.0571379\pi$
$234$		0			0
$235$	1673.24	+	2898.13i	0.464468	+	0.804483i
$236$	−2802.95	−	1020.19i	−0.773120	−	0.281393i
$237$		0			0
$238$	−1532.35	−	1285.79i	−0.417342	−	0.350192i
$239$	−2897.51	+	1054.61i	−0.784203	+	0.285427i	−0.702924	−	0.711265i	$-0.748123\pi$
$239$	−2897.51	+	1054.61i	−0.784203	+	0.285427i	−0.0812789	+	0.996691i	$0.525900\pi$
$240$		0			0
$241$	446.533	+	2532.41i	0.119352	+	0.676876i	0.984503	+	0.175366i	$0.0561109\pi$
$241$	446.533	+	2532.41i	0.119352	+	0.676876i	−0.865152	+	0.501510i	$0.832778\pi$
$242$	−514.931			−0.136781
$243$		0			0
$244$	−652.923			−0.171308
$245$	1057.29	+	5996.19i	0.275705	+	1.56360i
$246$		0			0
$247$	5961.94	−	2169.97i	1.53583	−	0.558996i
$248$	1735.10	+	1455.92i	0.444269	+	0.372786i
$249$		0			0
$250$	2046.02	+	744.692i	0.517608	+	0.188394i
$251$	662.417	+	1147.34i	0.166579	+	0.288524i	0.937215	−	0.348752i	$-0.113395\pi$
$251$	662.417	+	1147.34i	0.166579	+	0.288524i	−0.770636	+	0.637276i	$0.780061\pi$
$252$		0			0
$253$	1509.33	−	2614.24i	0.375062	−	0.649627i
$254$	1595.39	−	1338.69i	0.394108	−	0.330696i
$255$		0			0
$256$	44.4539	−	252.111i	0.0108530	−	0.0615505i
$257$	−423.468	+	2401.61i	−0.102783	+	0.582911i	0.889300	+	0.457325i	$0.151192\pi$
$257$	−423.468	+	2401.61i	−0.102783	+	0.582911i	−0.992083	+	0.125586i	$0.959919\pi$
$258$		0			0
$259$	3752.84	−	3149.01i	0.900348	−	0.755481i
$260$	2082.53	−	3607.04i	0.496741	−	0.860381i
$261$		0			0
$262$	1066.50	+	1847.22i	0.251482	+	0.435580i
$263$	3784.74	+	1377.53i	0.887366	+	0.322975i	0.745179	−	0.666865i	$-0.232364\pi$
$263$	3784.74	+	1377.53i	0.887366	+	0.322975i	0.142188	+	0.989840i	$0.454586\pi$
$264$		0			0
$265$	4137.87	+	3472.08i	0.959197	+	0.804862i
$266$	−4207.48	+	1531.40i	−0.969839	+	0.352993i
$267$		0			0
$268$	−265.656	−	1506.61i	−0.0605504	−	0.343398i
$269$	−8253.30			−1.87068			−0.935339	−	0.353753i	$-0.884905\pi$
$269$	−8253.30			−1.87068			−0.935339	+	0.353753i	$0.884905\pi$
$270$		0			0
$271$	−5266.67			−1.18054			−0.590271	−	0.807205i	$-0.700979\pi$
$271$	−5266.67			−1.18054			−0.590271	+	0.807205i	$0.700979\pi$
$272$	−97.2475	−	551.518i	−0.0216783	−	0.122944i
$273$		0			0
$274$	−239.704	+	87.2451i	−0.0528505	+	0.0192360i
$275$	−1012.32	−	849.440i	−0.221983	−	0.186266i
$276$		0			0
$277$	−8086.78	−	2943.35i	−1.75411	−	0.638442i	−0.754270	−	0.656564i	$-0.772009\pi$
$277$	−8086.78	−	2943.35i	−1.75411	−	0.638442i	−0.999836	+	0.0181216i	$0.994231\pi$
$278$	1304.59	+	2259.62i	0.281454	+	0.487493i
$279$		0			0
$280$	−1469.69	+	2545.57i	−0.313680	+	0.543311i
$281$	1841.57	−	1545.26i	0.390956	−	0.328051i	−0.426029	−	0.904709i	$-0.640088\pi$
$281$	1841.57	−	1545.26i	0.390956	−	0.328051i	0.816986	+	0.576658i	$0.195643\pi$
$282$		0			0
$283$	532.826	−	3021.81i	0.111920	−	0.634727i	−0.876310	−	0.481748i	$-0.840002\pi$
$283$	532.826	−	3021.81i	0.111920	−	0.634727i	0.988229	−	0.152979i	$-0.0488868\pi$
$284$	232.508	−	1318.62i	0.0485804	−	0.275513i
$285$		0			0
$286$	4065.12	−	3411.04i	0.840473	−	0.705241i
$287$	−506.531	+	877.338i	−0.104180	+	0.180445i
$288$		0			0
$289$	1843.94	+	3193.80i	0.375319	+	0.650072i
$290$	−2116.91	−	770.492i	−0.428652	−	0.156017i
$291$		0			0
$292$	310.542	+	260.576i	0.0622367	+	0.0522228i
$293$	3743.91	−	1362.67i	0.746490	−	0.271700i	0.0593623	−	0.998237i	$-0.481093\pi$
$293$	3743.91	−	1362.67i	0.746490	−	0.271700i	0.687128	+	0.726536i	$0.258871\pi$
$294$		0			0
$295$	1665.02	+	9442.78i	0.328614	+	1.86366i
$296$	1371.55			0.269323
$297$		0			0
$298$	−5486.30			−1.06649
$299$	−1295.56	−	7347.48i	−0.250582	−	1.42112i
$300$		0			0
$301$	−9661.00	+	3516.32i	−1.85000	+	0.673346i
$302$	1683.00	+	1412.20i	0.320681	+	0.269083i
$303$		0			0
$304$	−1177.95	−	428.739i	−0.222237	−	0.0808877i
$305$	1049.43	+	1817.66i	0.197016	+	0.341242i
$306$		0			0
$307$	−2401.88	+	4160.18i	−0.446524	+	0.773401i	−0.998157	−	0.0606852i	$-0.980671\pi$
$307$	−2401.88	+	4160.18i	−0.446524	+	0.773401i	0.551633	+	0.834087i	$0.314005\pi$
$308$	−2868.85	+	2407.25i	−0.530739	+	0.445343i
$309$		0			0
$310$	1264.33	−	7170.35i	0.231642	−	1.31371i
$311$	−964.126	+	5467.83i	−0.175790	+	0.996952i	0.761439	+	0.648236i	$0.224493\pi$
$311$	−964.126	+	5467.83i	−0.175790	+	0.996952i	−0.937229	+	0.348715i	$0.886618\pi$
$312$		0			0
$313$	−4992.45	+	4189.16i	−0.901565	+	0.756503i	−0.970496	−	0.241119i	$-0.922486\pi$
$313$	−4992.45	+	4189.16i	−0.901565	+	0.756503i	0.0689306	+	0.997621i	$0.478041\pi$
$314$	−2011.05	+	3483.24i	−0.361433	+	0.626021i
$315$		0			0
$316$	−1079.21	−	1869.24i	−0.192120	−	0.332762i
$317$	1798.05	+	654.437i	0.318576	+	0.115952i	0.496359	−	0.868118i	$-0.334670\pi$
$317$	1798.05	+	654.437i	0.318576	+	0.115952i	−0.177783	+	0.984070i	$0.556892\pi$
$318$		0			0
$319$	−2198.71	−	1844.94i	−0.385907	−	0.323815i
$320$	−773.295	+	281.456i	−0.135089	+	0.0491684i
$321$		0			0
$322$	914.306	+	5185.28i	0.158237	+	0.897406i
$323$	−2742.27			−0.472396
$324$		0			0
$325$	−3266.17			−0.557459
$326$	456.683	+	2589.98i	0.0775868	+	0.440017i
$327$		0			0
$328$	−266.518	+	97.0047i	−0.0448659	+	0.0163298i
$329$	−5697.02	−	4780.37i	−0.954671	−	0.801064i
$330$		0			0
$331$	−173.211	−	63.0436i	−0.0287629	−	0.0104689i	0.327599	−	0.944817i	$-0.393761\pi$
$331$	−173.211	−	63.0436i	−0.0287629	−	0.0104689i	−0.356362	+	0.934348i	$0.615983\pi$
$332$	−1302.03	−	2255.18i	−0.215236	−	0.372799i
$333$		0			0
$334$	4217.81	−	7305.47i	0.690983	−	1.19682i
$335$	−3767.23	+	3161.08i	−0.614405	+	0.515547i
$336$		0			0
$337$	−326.925	+	1854.08i	−0.0528449	+	0.299699i	−0.999763	−	0.0217769i	$-0.993068\pi$
$337$	−326.925	+	1854.08i	−0.0528449	+	0.299699i	0.946918	+	0.321475i	$0.104179\pi$
$338$	1514.51	−	8589.21i	0.243723	−	1.38222i
$339$		0			0
$340$	−1379.06	+	1157.16i	−0.219970	+	0.184577i
$341$	4638.29	−	8033.75i	0.736591	−	1.27581i
$342$		0			0
$343$	−1864.89	−	3230.09i	−0.293571	−	0.508479i
$344$	−2704.75	−	984.448i	−0.423925	−	0.154296i
$345$		0			0
$346$	4731.99	+	3970.61i	0.735242	+	0.616941i
$347$	8916.44	−	3245.32i	1.37942	−	0.502069i	0.457419	−	0.889251i	$-0.348774\pi$
$347$	8916.44	−	3245.32i	1.37942	−	0.502069i	0.922003	+	0.387182i	$0.126552\pi$
$348$		0			0
$349$	300.422	+	1703.78i	0.0460779	+	0.261321i	0.999140	−	0.0414526i	$-0.0131985\pi$
$349$	300.422	+	1703.78i	0.0460779	+	0.261321i	−0.953063	+	0.302773i	$0.902087\pi$
$350$	2305.01			0.352023
$351$		0			0
$352$	−1048.47			−0.158761
$353$	−247.341	−	1402.74i	−0.0372935	−	0.211502i	0.960467	−	0.278395i	$-0.0898025\pi$
$353$	−247.341	−	1402.74i	−0.0372935	−	0.211502i	−0.997760	+	0.0668931i	$0.978691\pi$
$354$		0			0
$355$	−4044.58	+	1472.11i	−0.604688	+	0.220088i
$356$	−583.988	−	490.024i	−0.0869419	−	0.0729529i
$357$		0			0
$358$	−5648.89	−	2056.03i	−0.833947	−	0.303532i
$359$	4871.46	+	8437.62i	0.716172	+	1.24045i	0.962506	+	0.271262i	$0.0874409\pi$
$359$	4871.46	+	8437.62i	0.716172	+	1.24045i	−0.246333	+	0.969185i	$0.579226\pi$
$360$		0			0
$361$	360.390	−	624.214i	0.0525427	−	0.0910066i
$362$	2124.96	−	1783.05i	0.308523	−	0.258881i
$363$		0			0
$364$	−1607.30	+	9115.44i	−0.231443	+	1.31258i
$365$	226.285	−	1283.33i	0.0324502	−	0.184034i
$366$		0			0
$367$	5317.40	−	4461.83i	0.756311	−	0.634620i	−0.180853	−	0.983510i	$-0.557886\pi$
$367$	5317.40	−	4461.83i	0.756311	−	0.634620i	0.937164	+	0.348890i	$0.113441\pi$
$368$	−737.048	+	1276.61i	−0.104406	+	0.180836i
$369$		0			0
$370$	−2204.45	−	3818.22i	−0.309740	−	0.536486i
$371$	−11280.1	−	4105.63i	−1.57853	−	0.574539i
$372$		0			0
$373$	5211.60	+	4373.05i	0.723449	+	0.607046i	0.928337	−	0.371740i	$-0.121239\pi$
$373$	5211.60	+	4373.05i	0.723449	+	0.607046i	−0.204888	+	0.978785i	$0.565683\pi$
$374$	−2155.32	+	784.473i	−0.297992	+	0.108460i
$375$		0			0
$376$	−361.550	−	2050.45i	−0.0495892	−	0.281234i
$377$	−7093.94			−0.969116
$378$		0			0
$379$	283.583			0.0384345			0.0192172	−	0.999815i	$-0.493883\pi$
$379$	283.583			0.0384345			0.0192172	+	0.999815i	$0.493883\pi$
$380$	699.731	+	3968.37i	0.0944616	+	0.535719i
$381$		0			0
$382$	2874.97	−	1046.40i	0.385068	−	0.140153i
$383$	3036.67	+	2548.07i	0.405135	+	0.339949i	0.822475	−	0.568802i	$-0.192593\pi$
$383$	3036.67	+	2548.07i	0.405135	+	0.339949i	−0.417339	+	0.908751i	$0.637037\pi$
$384$		0			0
$385$	11312.5	+	4117.41i	1.49750	+	0.545046i
$386$	−358.505	−	620.950i	−0.0472732	−	0.0818796i
$387$		0			0
$388$	−212.143	+	367.443i	−0.0277576	+	0.0480776i
$389$	−4980.47	+	4179.11i	−0.649151	+	0.544702i	−0.906813	−	0.421533i	$-0.861492\pi$
$389$	−4980.47	+	4179.11i	−0.649151	+	0.544702i	0.257662	+	0.966235i	$0.417048\pi$
$390$		0			0
$391$	−559.970	+	3175.75i	−0.0724268	+	0.410753i
$392$	657.816	−	3730.66i	0.0847570	−	0.480681i
$393$		0			0
$394$	−7793.05	+	6539.15i	−0.996468	+	0.836136i
$395$	−3469.15	+	6008.75i	−0.441904	+	0.765400i
$396$		0			0
$397$	−4527.68	−	7842.16i	−0.572387	−	0.991403i	−0.996320	−	0.0857095i	$-0.972684\pi$
$397$	−4527.68	−	7842.16i	−0.572387	−	0.991403i	0.423933	−	0.905693i	$-0.360649\pi$
$398$	−3752.49	−	1365.80i	−0.472602	−	0.172013i
$399$		0			0
$400$	494.346	+	414.806i	0.0617933	+	0.0518507i
$401$	3866.10	−	1407.14i	0.481455	−	0.175235i	−0.0898792	−	0.995953i	$-0.528648\pi$
$401$	3866.10	−	1407.14i	0.481455	−	0.175235i	0.571335	+	0.820717i	$0.306426\pi$
$402$		0			0
$403$	−3981.36	−	22579.4i	−0.492123	−	2.79097i
$404$	−593.940			−0.0731426
$405$		0			0
$406$	5006.36			0.611974
$407$	−975.437	−	5531.98i	−0.118798	−	0.673734i
$408$		0			0
$409$	4818.78	−	1753.89i	0.582575	−	0.212040i	−0.0338855	−	0.999426i	$-0.510788\pi$
$409$	4818.78	−	1753.89i	0.582575	−	0.212040i	0.616461	+	0.787386i	$0.288566\pi$
$410$	698.416	+	586.041i	0.0841276	+	0.0705915i
$411$		0			0
$412$	−632.228	−	230.112i	−0.0756011	−	0.0275166i
$413$	−10654.3	−	18453.8i	−1.26940	−	2.19867i
$414$		0			0
$415$	−4185.44	+	7249.39i	−0.495072	+	0.857490i
$416$	−1985.11	+	1665.71i	−0.233962	+	0.196317i
$417$		0			0
$418$	−891.517	+	5056.04i	−0.104319	+	0.591625i
$419$	−1912.98	+	10849.0i	−0.223043	+	1.26494i	0.643348	+	0.765574i	$0.277545\pi$
$419$	−1912.98	+	10849.0i	−0.223043	+	1.26494i	−0.866391	+	0.499366i	$0.833566\pi$
$420$		0			0
$421$	11841.3	−	9936.05i	1.37081	−	1.15025i	0.398333	−	0.917241i	$-0.369589\pi$
$421$	11841.3	−	9936.05i	1.37081	−	1.15025i	0.972476	−	0.233005i	$-0.0748557\pi$
$422$	5995.15	−	10383.9i	0.691562	−	1.19782i
$423$		0			0
$424$	−1680.36	−	2910.48i	−0.192466	−	0.333361i
$425$	1326.57	+	482.834i	0.151408	+	0.0551079i
$426$		0			0
$427$	−3573.07	−	2998.16i	−0.404948	−	0.339792i
$428$	445.526	−	162.158i	0.0503162	−	0.0183136i
$429$		0			0
$430$	1606.69	+	9111.96i	0.180189	+	1.02190i
$431$	−279.832			−0.0312738			−0.0156369	−	0.999878i	$-0.504978\pi$
$431$	−279.832			−0.0312738			−0.0156369	+	0.999878i	$0.504978\pi$
$432$		0			0
$433$	−5698.49			−0.632453			−0.316226	−	0.948684i	$-0.602416\pi$
$433$	−5698.49			−0.632453			−0.316226	+	0.948684i	$0.602416\pi$
$434$	2809.73	+	15934.8i	0.310764	+	1.76243i
$435$		0			0
$436$	6285.54	−	2287.75i	0.690419	−	0.251292i
$437$	5529.44	+	4639.75i	0.605284	+	0.507893i
$438$		0			0
$439$	12303.0	+	4477.94i	1.33757	+	0.486835i	0.909045	−	0.416697i	$-0.136812\pi$
$439$	12303.0	+	4477.94i	1.33757	+	0.486835i	0.428522	+	0.903532i	$0.359035\pi$
$440$	1685.18	+	2918.82i	0.182586	+	0.316249i
$441$		0			0
$442$	−2834.45	+	4909.42i	−0.305025	+	0.528319i
$443$	488.373	−	409.794i	0.0523777	−	0.0439501i	−0.616223	−	0.787572i	$-0.711338\pi$
$443$	488.373	−	409.794i	0.0523777	−	0.0439501i	0.668601	+	0.743622i	$0.266894\pi$
$444$		0			0
$445$	−425.539	+	2413.35i	−0.0453315	+	0.257088i
$446$	477.236	−	2706.54i	0.0506677	−	0.287351i
$447$		0			0
$448$	1400.94	−	1175.53i	0.147741	−	0.123970i
$449$	667.345	−	1155.88i	0.0701424	−	0.121490i	−0.828821	−	0.559514i	$-0.810988\pi$
$449$	667.345	−	1155.88i	0.0701424	−	0.121490i	0.898964	+	0.438023i	$0.144321\pi$
$450$		0			0
$451$	580.803	+	1005.98i	0.0606407	+	0.105033i
$452$	8307.08	+	3023.53i	0.864452	+	0.314635i
$453$		0			0
$454$	744.344	+	624.578i	0.0769466	+	0.0645659i
$455$	27959.6	−	10176.5i	2.88081	−	1.04853i
$456$		0			0
$457$	373.957	+	2120.82i	0.0382779	+	0.217085i	0.997947	−	0.0640480i	$-0.0204011\pi$
$457$	373.957	+	2120.82i	0.0382779	+	0.217085i	−0.959669	+	0.281133i	$0.909290\pi$
$458$	881.903			0.0899752
$459$		0			0
$460$	4738.55			0.480296
$461$	1579.50	+	8957.77i	0.159576	+	0.905000i	0.954482	+	0.298268i	$0.0964089\pi$
$461$	1579.50	+	8957.77i	0.159576	+	0.905000i	−0.794906	+	0.606732i	$0.792480\pi$
$462$		0			0
$463$	281.903	−	102.604i	0.0282963	−	0.0102990i	−0.327833	−	0.944736i	$-0.606318\pi$
$463$	281.903	−	102.604i	0.0282963	−	0.0102990i	0.356130	+	0.934437i	$0.384096\pi$
$464$	1073.69	+	900.937i	0.107425	+	0.0901400i
$465$		0			0
$466$	4509.76	+	1641.42i	0.448306	+	0.163170i
$467$	−4102.46	−	7105.67i	−0.406508	−	0.704093i	0.587988	−	0.808870i	$-0.299920\pi$
$467$	−4102.46	−	7105.67i	−0.406508	−	0.704093i	−0.994496	+	0.104777i	$0.966587\pi$
$468$		0			0
$469$	5464.42	−	9464.65i	0.538003	−	0.931848i
$470$	−5127.10	+	4302.15i	−0.503182	+	0.422220i
$471$		0			0
$472$	1035.93	−	5875.04i	0.101022	−	0.572925i
$473$	−2047.05	+	11609.4i	−0.198993	+	1.12855i
$474$		0			0
$475$	2420.65	−	2031.17i	0.233826	−	0.196203i
$476$	2000.34	−	3464.69i	0.192616	−	0.333621i
$477$		0			0
$478$	−3083.47	−	5340.72i	−0.295051	−	0.511044i
$479$	15057.0	+	5480.29i	1.43626	+	0.522757i	0.938720	−	0.344681i	$-0.112013\pi$
$479$	15057.0	+	5480.29i	1.43626	+	0.522757i	0.497544	+	0.867439i	$0.334235\pi$
$480$		0			0
$481$	−10635.4	−	8924.20i	−1.00818	−	0.845963i
$482$	−4832.80	+	1759.00i	−0.456697	+	0.166224i
$483$		0			0
$484$	−178.834	−	1014.22i	−0.0167950	−	0.0952494i
$485$	1363.89			0.127693
$486$		0			0
$487$	4635.78			0.431349			0.215675	−	0.976465i	$-0.430805\pi$
$487$	4635.78			0.431349			0.215675	+	0.976465i	$0.430805\pi$
$488$	−226.758	−	1286.01i	−0.0210345	−	0.119293i
$489$		0			0
$490$	−11443.0	+	4164.91i	−1.05498	+	0.383982i
$491$	−3147.50	−	2641.06i	−0.289297	−	0.242749i	0.486576	−	0.873638i	$-0.338246\pi$
$491$	−3147.50	−	2641.06i	−0.289297	−	0.242749i	−0.775873	+	0.630890i	$0.782690\pi$
$492$		0			0
$493$	2881.25	+	1048.69i	0.263215	+	0.0958024i
$494$	6344.57	+	10989.1i	0.577845	+	1.00086i
$495$		0			0
$496$	−2265.01	+	3923.11i	−0.205044	+	0.355147i
$497$	7327.36	−	6148.39i	0.661322	−	0.554915i
$498$		0			0
$499$	−2162.88	+	12266.3i	−0.194036	+	1.10043i	0.719750	+	0.694233i	$0.244256\pi$
$499$	−2162.88	+	12266.3i	−0.194036	+	1.10043i	−0.913786	+	0.406197i	$0.866855\pi$
$500$	−756.180	+	4288.51i	−0.0676348	+	0.383576i
$501$		0			0
$502$	−2029.76	+	1703.17i	−0.180464	+	0.151427i
$503$	912.509	−	1580.51i	0.0808882	−	0.140102i	−0.822744	−	0.568413i	$-0.807558\pi$
$503$	912.509	−	1580.51i	0.0808882	−	0.140102i	0.903632	+	0.428310i	$0.140891\pi$
$504$		0			0
$505$	954.623	+	1653.46i	0.0841191	+	0.145699i
$506$	5673.22	+	2064.88i	0.498430	+	0.181414i
$507$		0			0
$508$	3190.77	+	2677.38i	0.278676	+	0.233837i
$509$	−20932.1	+	7618.64i	−1.82278	+	0.663439i	−0.828086	+	0.560601i	$0.810570\pi$
$509$	−20932.1	+	7618.64i	−1.82278	+	0.663439i	−0.994698	+	0.102838i	$0.967208\pi$
$510$		0			0
$511$	502.877	+	2851.96i	0.0435342	+	0.246895i
$512$	512.000			0.0441942
$513$		0			0
$514$	−4877.31			−0.418539
$515$	375.559	+	2129.90i	0.0321342	+	0.182242i
$516$		0			0
$517$	−8013.13	+	2916.54i	−0.681658	+	0.248103i
$518$	7505.68	+	6298.01i	0.636642	+	0.534206i
$519$		0			0
$520$	7827.74	+	2849.06i	0.660133	+	0.240269i
$521$	−1666.20	−	2885.94i	−0.140111	−	0.242679i	0.787428	−	0.616407i	$-0.211412\pi$
$521$	−1666.20	−	2885.94i	−0.140111	−	0.242679i	−0.927538	+	0.373729i	$0.878079\pi$
$522$		0			0
$523$	−590.155	+	1022.18i	−0.0493417	+	0.0854623i	−0.889641	−	0.456660i	$-0.849046\pi$
$523$	−590.155	+	1022.18i	−0.0493417	+	0.0854623i	0.840300	+	0.542122i	$0.182379\pi$
$524$	−3267.93	+	2742.12i	−0.272443	+	0.228607i
$525$		0			0
$526$	−1398.78	+	7932.90i	−0.115950	+	0.657587i
$527$	−1720.83	+	9759.32i	−0.142240	+	0.806685i
$528$		0			0
$529$	−2818.18	+	2364.73i	−0.231625	+	0.194356i
$530$	−5401.60	+	9355.85i	−0.442699	+	0.766778i
$531$		0			0
$532$	−4477.51	−	7755.27i	−0.364896	−	0.632018i
$533$	2697.85	+	981.937i	0.219244	+	0.0797982i
$534$		0			0
$535$	−1167.51	−	979.658i	−0.0943475	−	0.0791669i
$536$	2875.18	−	1046.48i	0.231695	−	0.0843302i
$537$		0			0
$538$	−2866.34	−	16255.8i	−0.229696	−	1.30267i
$539$	−15515.0			−1.23985
$540$		0			0
$541$	10346.8			0.822266			0.411133	−	0.911575i	$-0.365133\pi$
$541$	10346.8			0.822266			0.411133	+	0.911575i	$0.365133\pi$
$542$	−1829.09	−	10373.3i	−0.144956	−	0.822088i
$543$		0			0
$544$	1052.51	−	383.081i	0.0829518	−	0.0301920i
$545$	−16471.4	−	13821.1i	−1.29460	−	1.08630i
$546$		0			0
$547$	5753.49	+	2094.10i	0.449729	+	0.163688i	0.556948	−	0.830548i	$-0.311972\pi$
$547$	5753.49	+	2094.10i	0.449729	+	0.163688i	−0.107219	+	0.994235i	$0.534195\pi$
$548$	−255.088	−	441.825i	−0.0198847	−	0.0344413i
$549$		0			0
$550$	1321.49	−	2288.90i	0.102452	−	0.177452i
$551$	5257.53	−	4411.59i	0.406494	−	0.341089i
$552$		0			0
$553$	2677.50	−	15184.9i	0.205893	−	1.16768i
$554$	2988.75	−	16950.1i	0.229206	−	1.29989i
$555$		0			0
$556$	−3997.50	+	3354.30i	−0.304913	+	0.255853i
$557$	3638.43	−	6301.95i	0.276778	−	0.479393i	−0.693804	−	0.720164i	$-0.744067\pi$
$557$	3638.43	−	6301.95i	0.276778	−	0.479393i	0.970582	+	0.240770i	$0.0774001\pi$
$558$		0			0
$559$	14568.1	+	25232.6i	1.10226	+	1.90917i
$560$	−5524.21	−	2010.65i	−0.416858	−	0.151724i
$561$		0			0
$562$	3683.14	+	3090.52i	0.276448	+	0.231967i
$563$	−737.926	+	268.583i	−0.0552395	+	0.0201055i	−0.369492	−	0.929234i	$-0.620468\pi$
$563$	−737.926	+	268.583i	−0.0552395	+	0.0201055i	0.314253	+	0.949339i	$0.398246\pi$
$564$		0			0
$565$	−4934.60	−	27985.5i	−0.367434	−	2.08382i
$566$	6136.85			0.455744
$567$		0			0
$568$	2677.93			0.197823
$569$	26.7098	+	151.479i	0.00196790	+	0.0111605i	0.985776	−	0.168065i	$-0.0537519\pi$
$569$	26.7098	+	151.479i	0.00196790	+	0.0111605i	−0.983808	+	0.179226i	$0.942641\pi$
$570$		0			0
$571$	−5932.33	+	2159.19i	−0.434781	+	0.158247i	−0.550133	−	0.835077i	$-0.685423\pi$
$571$	−5932.33	+	2159.19i	−0.434781	+	0.158247i	0.115351	+	0.993325i	$0.463201\pi$
$572$	8130.23	+	6822.07i	0.594304	+	0.498681i
$573$		0			0
$574$	−1903.93	−	692.976i	−0.138447	−	0.0503907i
$575$	−1857.95	−	3218.06i	−0.134751	−	0.233395i
$576$		0			0
$577$	10039.6	−	17389.1i	0.724355	−	1.25462i	−0.234884	−	0.972023i	$-0.575471\pi$
$577$	10039.6	−	17389.1i	0.724355	−	1.25462i	0.959239	−	0.282596i	$-0.0911957\pi$
$578$	−5650.17	+	4741.05i	−0.406602	+	0.341180i
$579$		0			0
$580$	782.378	−	4437.08i	0.0560111	−	0.317655i
$581$	3230.33	−	18320.1i	0.230665	−	1.30817i
$582$		0			0
$583$	−10544.0	+	8847.46i	−0.749036	+	0.628515i
$584$	−405.384	+	702.146i	−0.0287242	+	0.0497517i
$585$		0			0
$586$	3984.19	+	6900.82i	0.280862	+	0.486468i
$587$	−17224.7	−	6269.29i	−1.21114	−	0.440820i	−0.344043	−	0.938954i	$-0.611797\pi$
$587$	−17224.7	−	6269.29i	−1.21114	−	0.440820i	−0.867100	+	0.498134i	$0.834019\pi$
$588$		0			0
$589$	16992.4	+	14258.3i	1.18873	+	0.997460i
$590$	−18020.4	+	6558.89i	−1.25744	+	0.457670i
$591$		0			0
$592$	476.333	+	2701.42i	0.0330696	+	0.187547i
$593$	21220.8			1.46954			0.734768	−	0.678318i	$-0.237291\pi$
$593$	21220.8			1.46954			0.734768	+	0.678318i	$0.237291\pi$
$594$		0			0
$595$	−12860.4			−0.886089
$596$	−1905.37	−	10805.9i	−0.130951	−	0.742663i
$597$		0			0
$598$	14021.8	−	5103.51i	0.958851	−	0.348993i
$599$	11019.1	+	9246.12i	0.751633	+	0.630695i	0.935934	−	0.352175i	$-0.114558\pi$
$599$	11019.1	+	9246.12i	0.751633	+	0.630695i	−0.184302	+	0.982870i	$0.559002\pi$
$600$		0			0
$601$	−18632.2	−	6781.56i	−1.26460	−	0.460275i	−0.379287	−	0.925279i	$-0.623831\pi$
$601$	−18632.2	−	6781.56i	−1.26460	−	0.460275i	−0.885309	+	0.465004i	$0.846053\pi$
$602$	−10281.0	−	17807.3i	−0.696052	−	1.20560i
$603$		0			0
$604$	−2197.00	+	3805.31i	−0.148004	+	0.256351i
$605$	−2536.02	+	2127.97i	−0.170419	+	0.142999i
$606$		0			0
$607$	687.783	−	3900.61i	0.0459905	−	0.260825i	−0.953139	−	0.302531i	$-0.902168\pi$
$607$	687.783	−	3900.61i	0.0459905	−	0.260825i	0.999130	+	0.0417063i	$0.0132794\pi$
$608$	435.353	−	2469.01i	0.0290393	−	0.164690i
$609$		0			0
$610$	−3215.63	+	2698.23i	−0.213438	+	0.179095i
$611$	−10538.0	+	18252.4i	−0.697746	+	1.20853i
$612$		0			0
$613$	2965.54	+	5136.46i	0.195395	+	0.338433i	0.947030	−	0.321146i	$-0.104068\pi$
$613$	2965.54	+	5136.46i	0.195395	+	0.338433i	−0.751635	+	0.659579i	$0.770735\pi$
$614$	−9028.13	−	3285.97i	−0.593397	−	0.215979i
$615$		0			0
$616$	−5737.69	−	4814.49i	−0.375289	−	0.314905i
$617$	−2013.24	+	732.759i	−0.131361	+	0.0478116i	−0.406864	−	0.913489i	$-0.633378\pi$
$617$	−2013.24	+	732.759i	−0.131361	+	0.0478116i	0.275503	+	0.961300i	$0.411156\pi$
$618$		0			0
$619$	2700.08	+	15312.9i	0.175324	+	0.994311i	0.937769	+	0.347258i	$0.112887\pi$
$619$	2700.08	+	15312.9i	0.175324	+	0.994311i	−0.762446	+	0.647052i	$0.776002\pi$
$620$	14561.9			0.943261
$621$		0			0
$622$	−11104.4			−0.715826
$623$	−945.683	−	5363.23i	−0.0608154	−	0.344901i
$624$		0			0
$625$	17891.6	−	6512.02i	1.14506	−	0.416769i
$626$	−9984.90	−	8378.32i	−0.637503	−	0.534928i
$627$		0			0
$628$	−7559.07	−	2751.28i	−0.480318	−	0.174822i
$629$	3000.40	+	5196.85i	0.190197	+	0.329431i
$630$		0			0
$631$	−12251.4	+	21220.1i	−0.772934	+	1.33876i	0.163014	+	0.986624i	$0.447879\pi$
$631$	−12251.4	+	21220.1i	−0.772934	+	1.33876i	−0.935948	+	0.352138i	$0.885455\pi$
$632$	3306.88	−	2774.80i	0.208134	−	0.174645i
$633$		0			0
$634$	−664.533	+	3768.75i	−0.0416277	+	0.236083i
$635$	2325.05	−	13186.0i	0.145302	−	0.824047i
$636$		0			0
$637$	−29375.1	+	24648.6i	−1.82713	+	1.53315i
$638$	2870.22	−	4971.36i	0.178108	−	0.308492i
$639$		0			0
$640$	−822.923	−	1425.34i	−0.0508264	−	0.0880339i
$641$	−16021.1	−	5831.21i	−0.987201	−	0.359312i	−0.202565	−	0.979269i	$-0.564928\pi$
$641$	−16021.1	−	5831.21i	−0.987201	−	0.359312i	−0.784636	+	0.619957i	$0.787150\pi$
$642$		0			0
$643$	−22223.5	−	18647.8i	−1.36300	−	1.14369i	−0.975042	−	0.222019i	$-0.928735\pi$
$643$	−22223.5	−	18647.8i	−1.36300	−	1.14369i	−0.387960	−	0.921676i	$-0.626820\pi$
$644$	−9895.48	+	3601.66i	−0.605492	+	0.220381i
$645$		0			0
$646$	−952.379	−	5401.21i	−0.0580044	−	0.328959i
$647$	7519.09			0.456887			0.228443	−	0.973557i	$-0.426636\pi$
$647$	7519.09			0.456887			0.228443	+	0.973557i	$0.426636\pi$
$648$		0			0
$649$	−24433.0			−1.47778
$650$	−1134.33	−	6433.09i	−0.0684492	−	0.388195i
$651$		0			0
$652$	−4942.65	+	1798.98i	−0.296885	+	0.108057i
$653$	187.437	+	157.278i	0.0112327	+	0.00942537i	0.648387	−	0.761311i	$-0.275444\pi$
$653$	187.437	+	157.278i	0.0112327	+	0.00942537i	−0.637154	+	0.770737i	$0.719888\pi$
$654$		0			0
$655$	12886.2	+	4690.18i	0.768709	+	0.279787i
$656$	−283.623	−	491.249i	−0.0168805	−	0.0292379i
$657$		0			0
$658$	7436.93	−	12881.1i	0.440610	−	0.763160i
$659$	10259.1	−	8608.38i	0.606429	−	0.508854i	−0.287076	−	0.957908i	$-0.592683\pi$
$659$	10259.1	−	8608.38i	0.606429	−	0.508854i	0.893505	+	0.449054i	$0.148239\pi$
$660$		0			0
$661$	−2699.84	+	15311.5i	−0.158868	+	0.900984i	0.796296	+	0.604907i	$0.206790\pi$
$661$	−2699.84	+	15311.5i	−0.158868	+	0.900984i	−0.955164	+	0.296077i	$0.904322\pi$
$662$	64.0162	−	363.054i	0.00375840	−	0.0213149i
$663$		0			0
$664$	3989.66	−	3347.72i	0.233176	−	0.195658i
$665$	−14393.1	+	24929.7i	−0.839312	+	1.45373i
$666$		0			0
$667$	−4035.36	−	6989.46i	−0.234258	−	0.405746i
$668$	15853.8	+	5770.31i	0.918266	+	0.334221i
$669$		0			0
$670$	−7534.46	−	6322.16i	−0.434450	−	0.364547i
$671$	−5025.69	+	1829.20i	−0.289143	+	0.105239i
$672$		0			0
$673$	−4330.11	−	24557.3i	−0.248014	−	1.40656i	−0.813387	−	0.581723i	$-0.802379\pi$
$673$	−4330.11	−	24557.3i	−0.248014	−	1.40656i	0.565373	−	0.824835i	$-0.308732\pi$
$674$	−3765.37			−0.215188
$675$		0			0
$676$	17443.4			0.992457
$677$	172.817	+	980.091i	0.00981075	+	0.0556395i	0.989320	−	0.145759i	$-0.0465624\pi$
$677$	172.817	+	980.091i	0.00981075	+	0.0556395i	−0.979509	+	0.201399i	$0.935451\pi$
$678$		0			0
$679$	−2848.20	+	1036.66i	−0.160978	+	0.0585911i
$680$	−2758.11	−	2314.33i	−0.155542	−	0.130515i
$681$		0			0
$682$	17434.3	+	6345.55i	0.978875	+	0.356281i
$683$	14258.4	+	24696.4i	0.798806	+	1.38357i	0.920394	+	0.390992i	$0.127868\pi$
$683$	14258.4	+	24696.4i	0.798806	+	1.38357i	−0.121589	+	0.992581i	$0.538799\pi$
$684$		0			0
$685$	−819.990	+	1420.26i	−0.0457375	+	0.0792198i
$686$	5714.36	−	4794.92i	0.318040	−	0.266867i
$687$		0			0
$688$	999.635	−	5669.21i	0.0553935	−	0.314152i
$689$	−5907.37	+	33502.4i	−0.326637	+	1.85245i
$690$		0			0
$691$	−13038.6	+	10940.7i	−0.717815	+	0.602319i	−0.926780	−	0.375605i	$-0.877435\pi$
$691$	−13038.6	+	10940.7i	−0.717815	+	0.602319i	0.208965	+	0.977923i	$0.432991\pi$
$692$	−6177.18	+	10699.2i	−0.339337	+	0.587749i
$693$		0			0
$694$	9488.68	+	16434.9i	0.518999	+	0.898933i
$695$	15763.0	+	5737.28i	0.860325	+	0.313133i
$696$		0			0
$697$	−950.590	−	797.640i	−0.0516588	−	0.0433469i
$698$	−3251.45	+	1183.43i	−0.176317	+	0.0641740i
$699$		0			0
$700$	800.521	+	4539.98i	0.0432241	+	0.245136i
$701$	10252.7			0.552408			0.276204	−	0.961099i	$-0.410923\pi$
$701$	10252.7			0.552408			0.276204	+	0.961099i	$0.410923\pi$
$702$		0			0
$703$	13432.0			0.720624
$704$	−364.131	−	2065.09i	−0.0194939	−	0.110556i
$705$		0			0
$706$	2676.95	−	974.332i	0.142703	−	0.0519398i
$707$	−3250.29	−	2727.31i	−0.172899	−	0.145079i
$708$		0			0
$709$	9794.94	+	3565.07i	0.518839	+	0.188842i	0.588148	−	0.808753i	$-0.299857\pi$
$709$	9794.94	+	3565.07i	0.518839	+	0.188842i	−0.0693093	+	0.997595i	$0.522080\pi$
$710$	−4304.15	−	7455.02i	−0.227510	−	0.394059i
$711$		0			0
$712$	762.343	−	1320.42i	0.0401264	−	0.0695010i
$713$	19982.0	−	16766.9i	1.04956	−	0.880682i
$714$		0			0
$715$	5924.32	−	33598.5i	0.309870	−	1.75736i
$716$	2087.74	−	11840.2i	0.108970	−	0.618001i
$717$		0			0
$718$	−14927.0	+	12525.3i	−0.775866	+	0.651029i
$719$	4312.15	−	7468.86i	0.223666	−	0.387401i	−0.732252	−	0.681033i	$-0.761531\pi$
$719$	4312.15	−	7468.86i	0.223666	−	0.387401i	0.955918	+	0.293632i	$0.0948642\pi$
$720$		0			0
$721$	−2403.16	−	4162.40i	−0.124131	−	0.215001i
$722$	1354.62	+	493.043i	0.0698253	+	0.0254143i
$723$		0			0
$724$	4249.91	+	3566.10i	0.218158	+	0.183057i
$725$	−3320.09	+	1208.41i	−0.170076	+	0.0619026i
$726$		0			0
$727$	5181.28	+	29384.5i	0.264323	+	1.49905i	0.770955	+	0.636889i	$0.219779\pi$
$727$	5181.28	+	29384.5i	0.264323	+	1.49905i	−0.506632	+	0.862162i	$0.669110\pi$
$728$	−18512.1			−0.942451
$729$		0			0
$730$	2606.25			0.132139
$731$	−2186.80	−	12402.0i	−0.110645	−	0.627502i
$732$		0			0
$733$	2524.51	−	918.846i	0.127210	−	0.0463006i	−0.277631	−	0.960688i	$-0.589549\pi$
$733$	2524.51	−	918.846i	0.127210	−	0.0463006i	0.404841	+	0.914387i	$0.367327\pi$
$734$	10634.8	+	8923.66i	0.534792	+	0.448744i
$735$		0			0
$736$	−2770.40	−	1008.34i	−0.138747	−	0.0504999i
$737$	−6265.66	−	10852.4i	−0.313159	−	0.542408i
$738$		0			0
$739$	918.993	−	1591.74i	0.0457452	−	0.0792330i	−0.842246	−	0.539093i	$-0.818767\pi$
$739$	918.993	−	1591.74i	0.0457452	−	0.0792330i	0.887991	+	0.459860i	$0.152100\pi$
$740$	6754.83	−	5667.97i	0.335557	−	0.281566i
$741$		0			0
$742$	4168.97	−	23643.4i	0.206264	−	1.16978i
$743$	5339.52	−	30281.9i	0.263645	−	1.49520i	−0.509222	−	0.860635i	$-0.670067\pi$
$743$	5339.52	−	30281.9i	0.263645	−	1.49520i	0.772867	−	0.634568i	$-0.218822\pi$
$744$		0			0
$745$	−27019.8	+	22672.3i	−1.32877	+	1.11497i
$746$	−6803.26	+	11783.6i	−0.333894	+	0.578322i
$747$		0			0
$748$	−2293.65	−	3972.71i	−0.112118	−	0.194193i
$749$	3182.72	+	1158.42i	0.155266	+	0.0565121i
$750$		0			0
$751$	6925.93	+	5811.55i	0.336526	+	0.282379i	0.795353	−	0.606147i	$-0.207286\pi$
$751$	6925.93	+	5811.55i	0.336526	+	0.282379i	−0.458827	+	0.888526i	$0.651730\pi$
$752$	3913.04	−	1424.23i	0.189753	−	0.0690643i
$753$		0			0
$754$	−2463.70	−	13972.3i	−0.118996	−	0.674858i
$755$	14124.7			0.680862
$756$		0			0
$757$	40810.8			1.95944			0.979719	−	0.200378i	$-0.0642170\pi$
$757$	40810.8			1.95944			0.979719	+	0.200378i	$0.0642170\pi$
$758$	98.4873	+	558.549i	0.00471929	+	0.0267644i
$759$		0			0
$760$	−7573.15	+	2756.40i	−0.361456	+	0.131559i
$761$	−26217.9	−	21999.4i	−1.24888	−	1.04793i	−0.996776	−	0.0802335i	$-0.974433\pi$
$761$	−26217.9	−	21999.4i	−1.24888	−	1.04793i	−0.252103	−	0.967700i	$-0.581122\pi$
$762$		0			0
$763$	44902.2	+	16343.1i	2.13050	+	0.775437i
$764$	3059.47	+	5299.17i	0.144879	+	0.250939i
$765$		0			0
$766$	−3964.10	+	6866.02i	−0.186983	+	0.323863i
$767$	−46259.8	+	38816.6i	−2.17776	+	1.82736i
$768$		0			0
$769$	1792.99	−	10168.6i	0.0840792	−	0.476837i	−0.913472	−	0.406901i	$-0.866609\pi$
$769$	1792.99	−	10168.6i	0.0840792	−	0.476837i	0.997551	−	0.0699359i	$-0.0222795\pi$
$770$	−4180.93	+	23711.2i	−0.195676	+	1.10973i
$771$		0			0
$772$	1098.52	−	921.771i	0.0512134	−	0.0429732i
$773$	1752.80	−	3035.94i	0.0815575	−	0.141262i	−0.822362	−	0.568965i	$-0.807344\pi$
$773$	1752.80	−	3035.94i	0.0815575	−	0.141262i	0.903919	+	0.427703i	$0.140677\pi$
$774$		0			0
$775$	−5709.62	−	9889.35i	−0.264639	−	0.458369i
$776$	−797.398	−	290.229i	−0.0368878	−	0.0134261i
$777$		0			0
$778$	−9960.93	−	8358.22i	−0.459019	−	0.385163i
$779$	−2610.11	+	950.001i	−0.120047	+	0.0436936i
$780$		0			0
$781$	−1904.53	−	10801.1i	−0.0872590	−	0.494870i
$782$	−6449.48			−0.294927
$783$		0			0
$784$	7576.42			0.345136
$785$	4490.27	+	25465.6i	0.204159	+	1.15784i
$786$		0			0
$787$	13679.9	−	4979.09i	0.619615	−	0.225521i	−0.0130902	−	0.999914i	$-0.504167\pi$
$787$	13679.9	−	4979.09i	0.619615	−	0.225521i	0.632705	+	0.774393i	$0.281945\pi$
$788$	−15586.1	−	13078.3i	−0.704609	−	0.591237i
$789$		0			0
$790$	−13039.8	−	4746.08i	−0.587258	−	0.213744i
$791$	31576.0	+	54691.3i	1.41936	+	2.45841i
$792$		0			0
$793$	−6609.27	+	11447.6i	−0.295967	+	0.512630i
$794$	13873.6	−	11641.3i	0.620095	−	0.520322i
$795$		0			0
$796$	1386.86	−	7865.30i	0.0617539	−	0.350224i
$797$	−6652.78	+	37729.8i	−0.295676	+	1.67686i	0.368767	+	0.929522i	$0.379780\pi$
$797$	−6652.78	+	37729.8i	−0.295676	+	1.67686i	−0.664443	+	0.747339i	$0.731331\pi$
$798$		0			0
$799$	6978.32	−	5855.51i	0.308980	−	0.259265i
$800$	−645.323	+	1117.73i	−0.0285195	+	0.0493973i
$801$		0			0
$802$	4114.21	+	7126.03i	0.181145	+	0.313752i
$803$	3120.33	+	1135.71i	0.137128	+	0.0499106i
$804$		0			0
$805$	25931.3	+	21759.0i	1.13535	+	0.952674i
$806$	43090.0	−	15683.5i	1.88310	−	0.685393i
$807$		0			0
$808$	−206.273	−	1169.83i	−0.00898102	−	0.0509339i
$809$	26029.1			1.13119			0.565597	−	0.824682i	$-0.308646\pi$
$809$	26029.1			1.13119			0.565597	+	0.824682i	$0.308646\pi$
$810$		0			0
$811$	−6998.53			−0.303023			−0.151512	−	0.988455i	$-0.548414\pi$
$811$	−6998.53			−0.303023			−0.151512	+	0.988455i	$0.548414\pi$
$812$	1738.69	+	9860.60i	0.0751429	+	0.426157i
$813$		0			0
$814$	10557.1	−	3842.47i	0.454578	−	0.165453i
$815$	12952.3	+	10868.3i	0.556687	+	0.467116i
$816$		0			0
$817$	−26488.6	−	9641.04i	−1.13429	−	0.412849i
$818$	5128.04	+	8882.02i	0.219190	+	0.379649i
$819$		0			0
$820$	−911.718	+	1579.14i	−0.0388275	+	0.0672512i
$821$	25659.8	−	21531.1i	1.09078	−	0.915275i	0.0940110	−	0.995571i	$-0.470031\pi$
$821$	25659.8	−	21531.1i	1.09078	−	0.915275i	0.996771	+	0.0802964i	$0.0255867\pi$
$822$		0			0
$823$	−2221.26	+	12597.4i	−0.0940805	+	0.533557i	0.900945	+	0.433934i	$0.142875\pi$
$823$	−2221.26	+	12597.4i	−0.0940805	+	0.533557i	−0.995025	+	0.0996232i	$0.968236\pi$
$824$	233.662	−	1325.16i	0.00987865	−	0.0560246i
$825$		0			0
$826$	32646.6	−	27393.8i	1.37521	−	1.15394i
$827$	5508.42	−	9540.87i	0.231616	−	0.401171i	−0.726668	−	0.686989i	$-0.758932\pi$
$827$	5508.42	−	9540.87i	0.231616	−	0.401171i	0.958284	+	0.285818i	$0.0922653\pi$
$828$		0			0
$829$	−13983.6	−	24220.4i	−0.585852	−	1.01473i	−0.994769	−	0.102154i	$-0.967427\pi$
$829$	−13983.6	−	24220.4i	−0.585852	−	1.01473i	0.408916	−	0.912572i	$-0.365907\pi$
$830$	−15732.1	−	5726.02i	−0.657915	−	0.239461i
$831$		0			0
$832$	−3970.22	−	3331.41i	−0.165436	−	0.138817i
$833$	15574.7	−	5668.71i	0.647815	−	0.235785i
$834$		0			0
$835$	−9417.53	−	53409.5i	−0.390308	−	2.21355i
$836$	−10268.1			−0.424795
$837$		0			0
$838$	−22032.8			−0.908246
$839$	−2828.20	−	16039.5i	−0.116377	−	0.660006i	−0.986059	−	0.166394i	$-0.946788\pi$
$839$	−2828.20	−	16039.5i	−0.116377	−	0.660006i	0.869683	−	0.493612i	$-0.164324\pi$
$840$		0			0
$841$	15707.1	−	5716.92i	0.644024	−	0.234406i
$842$	23682.6	+	19872.1i	0.969308	+	0.813346i
$843$		0			0
$844$	22534.4	+	8201.85i	0.919035	+	0.334501i
$845$	−28036.3	−	48560.3i	−1.14140	−	1.97695i
$846$		0			0
$847$	3678.53	−	6371.40i	0.149227	−	0.258470i
$848$	5148.93	−	4320.47i	0.208508	−	0.174959i
$849$		0			0
$850$	−490.282	+	2780.53i	−0.0197842	+	0.112202i
$851$	2742.82	−	15555.3i	0.110485	−	0.626591i
$852$		0			0
$853$	3114.18	−	2613.11i	0.125003	−	0.104890i	−0.578143	−	0.815935i	$-0.696222\pi$
$853$	3114.18	−	2613.11i	0.125003	−	0.104890i	0.703146	+	0.711045i	$0.251778\pi$
$854$	4664.31	−	8078.82i	0.186896	−	0.323714i
$855$		0			0
$856$	474.119	+	821.199i	0.0189311	+	0.0327897i
$857$	5806.41	+	2113.36i	0.231439	+	0.0842368i	0.455136	−	0.890422i	$-0.349591\pi$
$857$	5806.41	+	2113.36i	0.231439	+	0.0842368i	−0.223697	+	0.974659i	$0.571813\pi$
$858$		0			0
$859$	31567.2	+	26488.0i	1.25385	+	1.05211i	0.996309	+	0.0858395i	$0.0273572\pi$
$859$	31567.2	+	26488.0i	1.25385	+	1.05211i	0.257543	+	0.966267i	$0.417087\pi$
$860$	−17389.1	+	6329.10i	−0.689491	+	0.250954i
$861$		0			0
$862$	−97.1846	−	551.161i	−0.00384005	−	0.0217780i
$863$	1054.85			0.0416077			0.0208038	−	0.999784i	$-0.493377\pi$
$863$	1054.85			0.0416077			0.0208038	+	0.999784i	$0.493377\pi$
$864$		0			0
$865$	39713.6			1.56105
$866$	−1979.07	−	11223.8i	−0.0776575	−	0.440418i
$867$		0			0
$868$	−30409.6	+	11068.2i	−1.18914	+	0.432810i
$869$	−13543.7	−	11364.5i	−0.528697	−	0.443629i
$870$		0			0
$871$	−29104.2	−	10593.1i	−1.13221	−	0.412092i
$872$	6688.93	+	11585.6i	0.259766	+	0.449928i
$873$		0			0
$874$	−7218.17	+	12502.2i	−0.279357	+	0.483861i
$875$	−23830.6	+	19996.2i	−0.920708	+	0.772566i
$876$		0			0
$877$	−3533.02	+	20036.7i	−0.136034	+	0.771486i	0.838101	+	0.545516i	$0.183666\pi$
$877$	−3533.02	+	20036.7i	−0.136034	+	0.771486i	−0.974134	+	0.225970i	$0.927445\pi$
$878$	−4547.02	+	25787.4i	−0.174777	+	0.991211i
$879$		0			0
$880$	−5163.70	+	4332.86i	−0.197805	+	0.165978i
$881$	18965.9	−	32849.9i	0.725287	−	1.25623i	−0.233569	−	0.972340i	$-0.575040\pi$
$881$	18965.9	−	32849.9i	0.725287	−	1.25623i	0.958856	−	0.283894i	$-0.0916263\pi$
$882$		0			0
$883$	−6886.26	−	11927.3i	−0.262447	−	0.454572i	0.704444	−	0.709759i	$-0.251196\pi$
$883$	−6886.26	−	11927.3i	−0.262447	−	0.454572i	−0.966892	+	0.255187i	$0.917863\pi$
$884$	−10654.1	−	3877.76i	−0.405356	−	0.147538i
$885$		0			0
$886$	976.746	+	819.587i	0.0370366	+	0.0310774i
$887$	18273.2	−	6650.91i	0.691719	−	0.251765i	0.0278478	−	0.999612i	$-0.491135\pi$
$887$	18273.2	−	6650.91i	0.691719	−	0.251765i	0.663871	+	0.747847i	$0.268912\pi$
$888$		0			0
$889$	5166.99	+	29303.4i	0.194933	+	1.10552i
$890$	−4901.17			−0.184593
$891$		0			0
$892$	5496.59			0.206322
$893$	−3540.79	−	20080.8i	−0.132685	−	0.752496i
$894$		0			0
$895$	−36317.2	+	13218.4i	−1.35637	+	0.493678i
$896$	2801.88	+	2351.05i	0.104469	+	0.0876598i
$897$		0			0
$898$	2508.40	+	912.981i	0.0932141	+	0.0339272i
$899$	−12401.0	−	21479.2i	−0.460063	−	0.796852i
$900$		0			0
$901$	7351.94	−	12733.9i	0.271841	−	0.470842i
$902$	−1779.68	+	1493.33i	−0.0656951	+	0.0551248i
$903$		0			0
$904$	−3070.17	+	17411.8i	−0.112956	+	0.640607i
$905$	3096.82	−	17562.9i	0.113748	−	0.645095i
$906$		0			0
$907$	−13866.8	+	11635.6i	−0.507652	+	0.425971i	−0.860302	−	0.509785i	$-0.829725\pi$
$907$	−13866.8	+	11635.6i	−0.507652	+	0.425971i	0.352650	+	0.935755i	$0.385281\pi$
$908$	−971.671	+	1682.98i	−0.0355133	+	0.0615108i
$909$		0			0
$910$	29754.0	+	51535.5i	1.08389	+	1.87734i
$911$	13109.1	+	4771.32i	0.476755	+	0.173525i	0.569210	−	0.822192i	$-0.307249\pi$
$911$	13109.1	+	4771.32i	0.476755	+	0.173525i	−0.0924550	+	0.995717i	$0.529471\pi$
$912$		0			0
$913$	−16340.1	−	13710.9i	−0.592308	−	0.497005i
$914$	−4047.32	+	1473.10i	−0.146470	+	0.0533107i
$915$		0			0
$916$	306.282	+	1737.01i	0.0110479	+	0.0626555i
$917$	−30475.0			−1.09746
$918$		0			0
$919$	−15001.8			−0.538481			−0.269241	−	0.963073i	$-0.586773\pi$
$919$	−15001.8			−0.538481			−0.269241	+	0.963073i	$0.586773\pi$
$920$	1645.68	+	9333.12i	0.0589744	+	0.334461i
$921$		0			0
$922$	−17094.8	+	6222.01i	−0.610616	+	0.222246i
$923$	−20765.5	−	17424.4i	−0.740527	−	0.621376i
$924$		0			0
$925$	−6497.76	−	2364.99i	−0.230968	−	0.0840654i
$926$	299.995	+	519.607i	0.0106463	+	0.0184399i
$927$		0			0
$928$	−1401.61	+	2427.66i	−0.0495798	+	0.0858747i
$929$	−31855.1	+	26729.6i	−1.12501	+	0.943993i	−0.998847	−	0.0480169i	$-0.984710\pi$
$929$	−31855.1	+	26729.6i	−1.12501	+	0.943993i	−0.126160	+	0.992010i	$0.540265\pi$
$930$		0			0
$931$	6442.22	−	36535.7i	0.226783	−	1.28615i
$932$	−1666.74	+	9452.55i	−0.0585793	+	0.332219i
$933$		0			0
$934$	12570.7	−	10548.0i	0.440391	−	0.369532i
$935$	−7373.03	+	12770.5i	−0.257886	+	0.446672i
$936$		0			0
$937$	−13121.4	−	22727.0i	−0.457479	−	0.792377i	0.541348	−	0.840799i	$-0.317914\pi$
$937$	−13121.4	−	22727.0i	−0.457479	−	0.792377i	−0.998827	+	0.0484217i	$0.984581\pi$
$938$	20539.5	+	7475.76i	0.714966	+	0.260226i
$939$		0			0
$940$	−10254.2	−	8604.30i	−0.355803	−	0.298555i
$941$	−31682.2	+	11531.4i	−1.09757	+	0.399482i	−0.826419	−	0.563056i	$-0.809626\pi$
$941$	−31682.2	+	11531.4i	−1.09757	+	0.399482i	−0.271148	+	0.962538i	$0.587403\pi$
$942$		0			0
$943$	567.188	+	3216.69i	0.0195866	+	0.111081i
$944$	11931.3			0.411368
$945$		0			0
$946$	−23577.0			−0.810312
$947$	3113.38	+	17656.8i	0.106833	+	0.605882i	0.990472	+	0.137713i	$0.0439750\pi$
$947$	3113.38	+	17656.8i	0.106833	+	0.605882i	−0.883639	+	0.468169i	$0.844914\pi$
$948$		0			0
$949$	7712.11	−	2806.98i	0.263800	−	0.0960152i
$950$	4841.31	+	4062.34i	0.165340	+	0.138736i
$951$		0			0
$952$	7518.81	+	2736.62i	0.255973	+	0.0931665i
$953$	5908.93	+	10234.6i	0.200849	+	0.347881i	0.948802	−	0.315871i	$-0.102297\pi$
$953$	5908.93	+	10234.6i	0.200849	+	0.347881i	−0.747953	+	0.663751i	$0.768963\pi$
$954$		0			0
$955$	9834.82	−	17034.4i	0.333243	−	0.577194i
$956$	9448.30	−	7928.06i	0.319644	−	0.268213i
$957$		0			0
$958$	−5564.83	+	31559.7i	−0.187674	+	1.06435i
$959$	632.870	−	3589.19i	0.0213102	−	0.120856i
$960$		0			0
$961$	38585.2	−	32376.8i	1.29520	−	1.08680i
$962$	13883.6	−	24047.1i	0.465306	−	0.805934i
$963$		0			0
$964$	−5142.96	−	8907.87i	−0.171829	−	0.297617i
$965$	−4331.73	−	1576.62i	−0.144501	−	0.0525940i
$966$		0			0
$967$	−32299.3	−	27102.3i	−1.07412	−	0.901295i	−0.0787024	−	0.996898i	$-0.525078\pi$
$967$	−32299.3	−	27102.3i	−1.07412	−	0.901295i	−0.995420	+	0.0956028i	$0.969522\pi$
$968$	1935.51	−	704.467i	0.0642660	−	0.0233909i
$969$		0			0
$970$	473.674	+	2686.34i	0.0156791	+	0.0889207i
$971$	−30707.9			−1.01490			−0.507448	−	0.861682i	$-0.669411\pi$
$971$	−30707.9			−1.01490			−0.507448	+	0.861682i	$0.669411\pi$
$972$		0			0
$973$	−37278.6			−1.22826
$974$	1609.99	+	9130.70i	0.0529644	+	0.300376i
$975$		0			0
$976$	2454.19	−	893.252i	0.0804884	−	0.0292954i
$977$	6792.22	+	5699.35i	0.222418	+	0.186631i	0.747187	−	0.664614i	$-0.231404\pi$
$977$	6792.22	+	5699.35i	0.222418	+	0.186631i	−0.524769	+	0.851245i	$0.675848\pi$
$978$		0			0
$979$	−5867.92	−	2135.75i	−0.191562	−	0.0697230i
$980$	−12177.4	−	21091.8i	−0.396931	−	0.687504i
$981$		0			0
$982$	4108.77	−	7116.59i	0.133519	−	0.231262i
$983$	11807.1	−	9907.35i	0.383101	−	0.321460i	−0.430817	−	0.902439i	$-0.641775\pi$
$983$	11807.1	−	9907.35i	0.383101	−	0.321460i	0.813919	+	0.580979i	$0.197330\pi$
$984$		0			0
$985$	−11357.2	+	64410.2i	−0.367383	+	2.08353i
$986$	−1064.87	+	6039.16i	−0.0343938	+	0.195057i
$987$		0			0
$988$	−19440.9	+	16312.8i	−0.626009	+	0.525284i
$989$	−16574.0	+	28707.0i	−0.532884	+	0.922982i
$990$		0			0
$991$	18226.8	+	31569.8i	0.584253	+	1.01196i	0.994968	+	0.100192i	$0.0319456\pi$
$991$	18226.8	+	31569.8i	0.584253	+	1.01196i	−0.410716	+	0.911764i	$0.634721\pi$
$992$	−8513.65	−	3098.71i	−0.272488	−	0.0991777i
$993$		0			0
$994$	14654.7	+	12296.8i	0.467625	+	0.392384i
$995$	−24125.1	+	8780.82i	−0.768660	+	0.279770i
$996$		0			0
$997$	4496.36	+	25500.1i	0.142830	+	0.810027i	0.969084	+	0.246730i	$0.0793562\pi$
$997$	4496.36	+	25500.1i	0.142830	+	0.810027i	−0.826255	+	0.563297i	$0.809533\pi$
$998$	−24911.0			−0.790125
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.91.4		30
3.2	odd	2		54.4.e.b.13.3	✓	30
27.2	odd	18		54.4.e.b.25.3	yes	30
27.5	odd	18		1458.4.a.i.1.5		15
27.22	even	9		1458.4.a.j.1.11		15
27.25	even	9	inner	162.4.e.b.73.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.13.3	✓	30	3.2	odd	2
54.4.e.b.25.3	yes	30	27.2	odd	18
162.4.e.b.73.4		30	27.25	even	9	inner
162.4.e.b.91.4		30	1.1	even	1	trivial
1458.4.a.i.1.5		15	27.5	odd	18
1458.4.a.j.1.11		15	27.22	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(9.84993 + 8.26508i) q^{5} +(-26.8516 - 9.77320i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(0.347296 + 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(9.84993 + 8.26508i) q^{5} +(-26.8516 - 9.77320i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-12.8582 + 22.2710i) q^{10} +(-25.0993 + 21.0608i) q^{11} +(-14.0621 + 79.7503i) q^{13} +(9.92397 - 56.2816i) q^{14} +(12.2567 - 10.2846i) q^{16} +(17.5008 - 30.3123i) q^{17} +(-39.1734 - 67.8503i) q^{19} +(-48.3309 - 17.5910i) q^{20} +(-50.1986 - 42.1217i) q^{22} +(-86.5749 + 31.5107i) q^{23} +(7.00370 + 39.7200i) q^{25} -161.961 q^{26} +114.300 q^{28} +(15.2117 + 86.2697i) q^{29} +(-266.051 + 96.8348i) q^{31} +(24.5134 + 20.5692i) q^{32} +(65.7816 + 23.9425i) q^{34} +(-183.711 - 318.196i) q^{35} +(-85.7217 + 148.474i) q^{37} +(120.034 - 100.721i) q^{38} +(17.8624 - 101.303i) q^{40} +(6.15632 - 34.9142i) q^{41} +(275.616 - 231.270i) q^{43} +(65.5297 - 113.501i) q^{44} +(-92.1310 - 159.576i) q^{46} +(244.565 + 89.0144i) q^{47} +(362.742 + 304.377i) q^{49} +(-75.8007 + 27.5892i) q^{50} +(-56.2485 - 319.001i) q^{52} +420.091 q^{53} -421.296 q^{55} +(39.6959 + 225.126i) q^{56} +(-164.635 + 59.9223i) q^{58} +(571.246 + 479.332i) q^{59} +(153.387 + 55.8282i) q^{61} +(-283.126 - 490.389i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-797.654 + 669.311i) q^{65} +(-66.4139 + 376.652i) q^{67} +(-24.3119 + 137.880i) q^{68} +(562.922 - 472.348i) q^{70} +(-167.370 + 289.894i) q^{71} +(-50.6730 - 87.7682i) q^{73} +(-322.208 - 117.274i) q^{74} +(240.068 + 201.441i) q^{76} +(879.790 - 320.217i) q^{77} +(93.7010 + 531.405i) q^{79} +205.731 q^{80} +70.9057 q^{82} +(113.048 + 641.125i) q^{83} +(422.916 - 153.929i) q^{85} +(551.233 + 462.539i) q^{86} +(246.311 + 89.6499i) q^{88} +(95.2928 + 165.052i) q^{89} +(1157.01 - 2004.00i) q^{91} +(282.306 - 236.883i) q^{92} +(-90.3876 + 512.613i) q^{94} +(174.933 - 992.092i) q^{95} +(81.2556 - 68.1816i) q^{97} +(-473.527 + 820.172i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Introduction

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