LMFDB - Embedded newform 162.4.e.b.19.1

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			19.1
Character	$\chi$	$=$	162.19
Dual form			162.4.e.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-3.05422 - 17.3214i) q^{5} +(-19.9833 - 16.7680i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-3.05422 - 17.3214i) q^{5} +(-19.9833 - 16.7680i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(17.5886 + 30.4643i) q^{10} +(-11.6982 + 66.3439i) q^{11} +(9.80676 + 3.56937i) q^{13} +(49.0263 + 17.8441i) q^{14} +(2.77837 - 15.7569i) q^{16} +(22.6291 + 39.1948i) q^{17} +(-19.3348 + 33.4888i) q^{19} +(-53.8945 - 45.2229i) q^{20} +(-23.3964 - 132.688i) q^{22} +(-42.9723 + 36.0581i) q^{23} +(-173.240 + 63.0541i) q^{25} -20.8723 q^{26} -104.345 q^{28} +(140.522 - 51.1459i) q^{29} +(-179.336 + 150.481i) q^{31} +(5.55674 + 31.5138i) q^{32} +(-69.3397 - 58.1829i) q^{34} +(-229.411 + 397.351i) q^{35} +(40.0816 + 69.4234i) q^{37} +(13.4298 - 76.1641i) q^{38} +(132.223 + 48.1252i) q^{40} +(-268.482 - 97.7195i) q^{41} +(27.0319 - 153.306i) q^{43} +(134.735 + 233.367i) q^{44} +(56.0964 - 97.1618i) q^{46} +(-444.971 - 373.375i) q^{47} +(58.6056 + 332.369i) q^{49} +(282.452 - 237.006i) q^{50} +(39.2271 - 14.2775i) q^{52} +53.6540 q^{53} +1184.90 q^{55} +(196.105 - 71.3764i) q^{56} +(-229.109 + 192.246i) q^{58} +(46.6462 + 264.544i) q^{59} +(-103.379 - 86.7454i) q^{61} +(234.106 - 405.484i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(31.8743 - 180.768i) q^{65} +(-540.576 - 196.754i) q^{67} +(170.115 + 61.9169i) q^{68} +(159.347 - 903.701i) q^{70} +(97.3794 + 168.666i) q^{71} +(-124.173 + 215.074i) q^{73} +(-122.817 - 103.056i) q^{74} +(26.8596 + 152.328i) q^{76} +(1346.22 - 1129.61i) q^{77} +(53.9300 - 19.6289i) q^{79} -281.417 q^{80} +571.426 q^{82} +(14.2898 - 5.20107i) q^{83} +(609.793 - 511.677i) q^{85} +(54.0638 + 306.611i) q^{86} +(-412.851 - 346.423i) q^{88} +(-393.099 + 680.868i) q^{89} +(-136.120 - 235.767i) q^{91} +(-38.9642 + 220.977i) q^{92} +(1091.67 + 397.337i) q^{94} +(639.124 + 232.622i) q^{95} +(-16.1918 + 91.8285i) q^{97} +(-337.496 - 584.561i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	−3.05422	−	17.3214i	−0.273178	−	1.54927i	−0.744690	−	0.667410i	$-0.767403\pi$
$5$	−3.05422	−	17.3214i	−0.273178	−	1.54927i	0.471512	−	0.881859i	$-0.343708\pi$
$6$		0			0
$7$	−19.9833	−	16.7680i	−1.07900	−	0.905385i	−0.0831589	−	0.996536i	$-0.526501\pi$
$7$	−19.9833	−	16.7680i	−1.07900	−	0.905385i	−0.995837	+	0.0911512i	$0.970945\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$		0			0
$10$	17.5886	+	30.4643i	0.556199	+	0.963366i
$11$	−11.6982	+	66.3439i	−0.320650	+	1.81849i	0.217982	+	0.975953i	$0.430053\pi$
$11$	−11.6982	+	66.3439i	−0.320650	+	1.81849i	−0.538631	+	0.842542i	$0.681058\pi$
$12$		0			0
$13$	9.80676	+	3.56937i	0.209224	+	0.0761512i	0.444506	−	0.895776i	$-0.353379\pi$
$13$	9.80676	+	3.56937i	0.209224	+	0.0761512i	−0.235282	+	0.971927i	$0.575601\pi$
$14$	49.0263	+	17.8441i	0.935916	+	0.340645i
$15$		0			0
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	22.6291	+	39.1948i	0.322845	+	0.559184i	0.981074	−	0.193634i	$-0.0620273\pi$
$17$	22.6291	+	39.1948i	0.322845	+	0.559184i	−0.658229	+	0.752818i	$0.728694\pi$
$18$		0			0
$19$	−19.3348	+	33.4888i	−0.233458	+	0.404361i	−0.958823	−	0.284003i	$-0.908337\pi$
$19$	−19.3348	+	33.4888i	−0.233458	+	0.404361i	0.725366	+	0.688364i	$0.241671\pi$
$20$	−53.8945	−	45.2229i	−0.602559	−	0.505607i
$21$		0			0
$22$	−23.3964	−	132.688i	−0.226734	−	1.28587i
$23$	−42.9723	+	36.0581i	−0.389580	+	0.326897i	−0.816450	−	0.577417i	$-0.804061\pi$
$23$	−42.9723	+	36.0581i	−0.389580	+	0.326897i	0.426869	+	0.904313i	$0.359616\pi$
$24$		0			0
$25$	−173.240	+	63.0541i	−1.38592	+	0.504433i
$26$	−20.8723			−0.157438
$27$		0			0
$28$	−104.345			−0.704265
$29$	140.522	−	51.1459i	0.899803	−	0.327502i	0.149629	−	0.988742i	$-0.452192\pi$
$29$	140.522	−	51.1459i	0.899803	−	0.327502i	0.750174	+	0.661241i	$0.229970\pi$
$30$		0			0
$31$	−179.336	+	150.481i	−1.03902	+	0.871842i	−0.991897	−	0.127047i	$-0.959450\pi$
$31$	−179.336	+	150.481i	−1.03902	+	0.871842i	−0.0471247	+	0.998889i	$0.515006\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$		0			0
$34$	−69.3397	−	58.1829i	−0.349755	−	0.293479i
$35$	−229.411	+	397.351i	−1.10793	+	1.91899i
$36$		0			0
$37$	40.0816	+	69.4234i	0.178091	+	0.308463i	0.941227	−	0.337775i	$-0.109674\pi$
$37$	40.0816	+	69.4234i	0.178091	+	0.308463i	−0.763135	+	0.646239i	$0.776341\pi$
$38$	13.4298	−	76.1641i	0.0573315	−	0.325143i
$39$		0			0
$40$	132.223	+	48.1252i	0.522656	+	0.190231i
$41$	−268.482	−	97.7195i	−1.02268	−	0.372225i	−0.224391	−	0.974499i	$-0.572039\pi$
$41$	−268.482	−	97.7195i	−1.02268	−	0.372225i	−0.798289	+	0.602274i	$0.794261\pi$
$42$		0			0
$43$	27.0319	−	153.306i	0.0958681	−	0.543695i	−0.898610	−	0.438749i	$-0.855422\pi$
$43$	27.0319	−	153.306i	0.0958681	−	0.543695i	0.994478	−	0.104946i	$-0.0334670\pi$
$44$	134.735	+	233.367i	0.461637	+	0.799579i
$45$		0			0
$46$	56.0964	−	97.1618i	0.179804	−	0.311429i
$47$	−444.971	−	373.375i	−1.38097	−	1.15877i	−0.968851	−	0.247643i	$-0.920344\pi$
$47$	−444.971	−	373.375i	−1.38097	−	1.15877i	−0.412120	−	0.911130i	$-0.635212\pi$
$48$		0			0
$49$	58.6056	+	332.369i	0.170862	+	0.969006i
$50$	282.452	−	237.006i	0.798896	−	0.670353i
$51$		0			0
$52$	39.2271	−	14.2775i	0.104612	−	0.0380756i
$53$	53.6540			0.139056			0.0695278	−	0.997580i	$-0.477851\pi$
$53$	53.6540			0.139056			0.0695278	+	0.997580i	$0.477851\pi$
$54$		0			0
$55$	1184.90			2.90493
$56$	196.105	−	71.3764i	0.467958	−	0.170323i
$57$		0			0
$58$	−229.109	+	192.246i	−0.518681	+	0.435225i
$59$	46.6462	+	264.544i	0.102929	+	0.583740i	0.992027	+	0.126023i	$0.0402214\pi$
$59$	46.6462	+	264.544i	0.102929	+	0.583740i	−0.889098	+	0.457717i	$0.848667\pi$
$60$		0			0
$61$	−103.379	−	86.7454i	−0.216989	−	0.182076i	0.527814	−	0.849360i	$-0.323012\pi$
$61$	−103.379	−	86.7454i	−0.216989	−	0.182076i	−0.744803	+	0.667285i	$0.767456\pi$
$62$	234.106	−	405.484i	0.479541	−	0.830589i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	31.8743	−	180.768i	0.0608234	−	0.344947i
$66$		0			0
$67$	−540.576	−	196.754i	−0.985699	−	0.358765i	−0.201646	−	0.979458i	$-0.564629\pi$
$67$	−540.576	−	196.754i	−0.985699	−	0.358765i	−0.784053	+	0.620693i	$0.786851\pi$
$68$	170.115	+	61.9169i	0.303375	+	0.110420i
$69$		0			0
$70$	159.347	−	903.701i	0.272080	−	1.54304i
$71$	97.3794	+	168.666i	0.162772	+	0.281929i	0.935862	−	0.352367i	$-0.114623\pi$
$71$	97.3794	+	168.666i	0.162772	+	0.281929i	−0.773090	+	0.634297i	$0.781290\pi$
$72$		0			0
$73$	−124.173	+	215.074i	−0.199087	+	0.344829i	−0.948233	−	0.317577i	$-0.897131\pi$
$73$	−124.173	+	215.074i	−0.199087	+	0.344829i	0.749146	+	0.662405i	$0.230464\pi$
$74$	−122.817	−	103.056i	−0.192935	−	0.161892i
$75$		0			0
$76$	26.8596	+	152.328i	0.0405395	+	0.229911i
$77$	1346.22	−	1129.61i	1.99242	−	1.67184i
$78$		0			0
$79$	53.9300	−	19.6289i	0.0768051	−	0.0279548i	−0.303332	−	0.952885i	$-0.598099\pi$
$79$	53.9300	−	19.6289i	0.0768051	−	0.0279548i	0.380137	+	0.924930i	$0.375877\pi$
$80$	−281.417			−0.393292
$81$		0			0
$82$	571.426			0.769554
$83$	14.2898	−	5.20107i	0.0188977	−	0.00687821i	−0.332554	−	0.943084i	$-0.607910\pi$
$83$	14.2898	−	5.20107i	0.0188977	−	0.00687821i	0.351452	+	0.936206i	$0.385688\pi$
$84$		0			0
$85$	609.793	−	511.677i	0.778133	−	0.652931i
$86$	54.0638	+	306.611i	0.0677890	+	0.384450i
$87$		0			0
$88$	−412.851	−	346.423i	−0.500115	−	0.419646i
$89$	−393.099	+	680.868i	−0.468185	+	0.810920i	−0.999339	−	0.0363554i	$-0.988425\pi$
$89$	−393.099	+	680.868i	−0.468185	+	0.810920i	0.531154	+	0.847275i	$0.321759\pi$
$90$		0			0
$91$	−136.120	−	235.767i	−0.156805	−	0.271595i
$92$	−38.9642	+	220.977i	−0.0441554	+	0.250418i
$93$		0			0
$94$	1091.67	+	397.337i	1.19785	+	0.435981i
$95$	639.124	+	232.622i	0.690239	+	0.251227i
$96$		0			0
$97$	−16.1918	+	91.8285i	−0.0169488	+	0.0961214i	−0.992109	−	0.125381i	$-0.959985\pi$
$97$	−16.1918	+	91.8285i	−0.0169488	+	0.0961214i	0.975160	+	0.221502i	$0.0710959\pi$
$98$	−337.496	−	584.561i	−0.347880	−	0.602547i
$99$		0			0
$100$	−368.715	+	638.634i	−0.368715	+	0.638634i
$101$	−242.615	−	203.578i	−0.239021	−	0.200562i	0.515407	−	0.856946i	$-0.327641\pi$
$101$	−242.615	−	203.578i	−0.239021	−	0.200562i	−0.754427	+	0.656383i	$0.772085\pi$
$102$		0			0
$103$	232.624	+	1319.28i	0.222535	+	1.26206i	0.867341	+	0.497714i	$0.165827\pi$
$103$	232.624	+	1319.28i	0.222535	+	1.26206i	−0.644806	+	0.764346i	$0.723062\pi$
$104$	−63.9564	+	53.6658i	−0.0603023	+	0.0505996i
$105$		0			0
$106$	−100.837	+	36.7015i	−0.0923972	+	0.0336298i
$107$	−687.948			−0.621556			−0.310778	−	0.950483i	$-0.600590\pi$
$107$	−687.948			−0.621556			−0.310778	+	0.950483i	$0.600590\pi$
$108$		0			0
$109$	−109.408			−0.0961408			−0.0480704	−	0.998844i	$-0.515307\pi$
$109$	−109.408			−0.0961408			−0.0480704	+	0.998844i	$0.515307\pi$
$110$	−2226.88	+	810.516i	−1.93022	+	0.702543i
$111$		0			0
$112$	−319.733	+	268.287i	−0.269749	+	0.226346i
$113$	−87.2131	−	494.610i	−0.0726046	−	0.411761i	−0.999349	−	0.0360693i	$-0.988516\pi$
$113$	−87.2131	−	494.610i	−0.0726046	−	0.411761i	0.926745	−	0.375692i	$-0.122595\pi$
$114$		0			0
$115$	755.822	+	634.210i	0.612876	+	0.514264i
$116$	299.081	−	518.023i	0.239388	−	0.414632i
$117$		0			0
$118$	−268.625	−	465.272i	−0.209567	−	0.362981i
$119$	205.013	−	1162.69i	0.157928	−	0.895657i
$120$		0			0
$121$	−3013.93	−	1096.98i	−2.26441	−	0.824179i
$122$	253.627	+	92.3125i	0.188215	+	0.0685048i
$123$		0			0
$124$	−162.609	+	922.199i	−0.117764	+	0.667870i
$125$	522.009	+	904.146i	0.373519	+	0.646954i
$126$		0			0
$127$	733.787	−	1270.96i	0.512701	−	0.888024i	−0.487190	−	0.873296i	$-0.661978\pi$
$127$	733.787	−	1270.96i	0.512701	−	0.888024i	0.999892	−	0.0147287i	$-0.00468846\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$		0			0
$130$	63.7486	+	361.536i	0.0430086	+	0.243914i
$131$	−1014.53	+	851.288i	−0.676638	+	0.567766i	−0.915022	−	0.403405i	$-0.867827\pi$
$131$	−1014.53	+	851.288i	−0.676638	+	0.567766i	0.238384	+	0.971171i	$0.423382\pi$
$132$		0			0
$133$	947.911	−	345.011i	0.618002	−	0.224934i
$134$	1150.54			0.741726
$135$		0			0
$136$	−362.066			−0.228286
$137$	−322.884	+	117.520i	−0.201356	+	0.0732877i	−0.440730	−	0.897640i	$-0.645280\pi$
$137$	−322.884	+	117.520i	−0.201356	+	0.0732877i	0.239373	+	0.970928i	$0.423058\pi$
$138$		0			0
$139$	−2099.41	+	1761.62i	−1.28108	+	1.07495i	−0.287984	+	0.957635i	$0.592985\pi$
$139$	−2099.41	+	1761.62i	−1.28108	+	1.07495i	−0.993095	+	0.117317i	$0.962571\pi$
$140$	318.694	+	1807.40i	0.192390	+	1.09110i
$141$		0			0
$142$	−298.388	−	250.377i	−0.176339	−	0.147966i
$143$	−351.528	+	608.864i	−0.205568	+	0.356054i
$144$		0			0
$145$	−1315.10	−	2277.82i	−0.753195	−	1.30457i
$146$	86.2496	−	489.146i	0.0488909	−	0.277274i
$147$		0			0
$148$	301.315	+	109.670i	0.167351	+	0.0609108i
$149$	−2767.25	−	1007.20i	−1.52149	−	0.553776i	−0.559969	−	0.828514i	$-0.689187\pi$
$149$	−2767.25	−	1007.20i	−1.52149	−	0.553776i	−0.961519	+	0.274737i	$0.911409\pi$
$150$		0			0
$151$	−96.0620	+	544.795i	−0.0517710	+	0.293608i	−0.999690	−	0.0249041i	$-0.992072\pi$
$151$	−96.0620	+	544.795i	−0.0517710	+	0.293608i	0.947919	+	0.318512i	$0.103183\pi$
$152$	−154.678	−	267.910i	−0.0825398	−	0.142963i
$153$		0			0
$154$	−1757.37	+	3043.85i	−0.919563	+	1.59273i
$155$	3154.26	+	2646.74i	1.63456	+	1.37156i
$156$		0			0
$157$	−445.103	−	2524.30i	−0.226261	−	1.28319i	−0.860259	−	0.509857i	$-0.829698\pi$
$157$	−445.103	−	2524.30i	−0.226261	−	1.28319i	0.633997	−	0.773335i	$-0.281413\pi$
$158$	−87.9283	+	73.7806i	−0.0442734	+	0.0371498i
$159$		0			0
$160$	528.891	−	192.501i	0.261328	−	0.0951157i
$161$	1463.35			0.716323
$162$		0			0
$163$	2629.48			1.26354			0.631769	−	0.775156i	$-0.282329\pi$
$163$	2629.48			1.26354			0.631769	+	0.775156i	$0.282329\pi$
$164$	−1073.93	+	390.878i	−0.511340	+	0.186113i
$165$		0			0
$166$	−23.2983	+	19.5496i	−0.0108934	+	0.00914064i
$167$	159.156	+	902.620i	0.0737478	+	0.418244i	0.999222	+	0.0394342i	$0.0125556\pi$
$167$	159.156	+	902.620i	0.0737478	+	0.418244i	−0.925474	+	0.378810i	$0.876333\pi$
$168$		0			0
$169$	−1599.57	−	1342.20i	−0.728069	−	0.610922i
$170$	−796.028	+	1378.76i	−0.359133	+	0.622036i
$171$		0			0
$172$	−311.341	−	539.259i	−0.138021	−	0.239059i
$173$	−190.899	+	1082.64i	−0.0838945	+	0.475789i	0.913695	+	0.406400i	$0.133216\pi$
$173$	−190.899	+	1082.64i	−0.0838945	+	0.475789i	−0.997590	+	0.0693891i	$0.977895\pi$
$174$		0			0
$175$	4519.19	+	1644.85i	1.95210	+	0.710508i
$176$	1012.87	+	368.656i	0.433797	+	0.157889i
$177$		0			0
$178$	273.044	−	1548.51i	0.114975	−	0.652054i
$179$	−68.2981	−	118.296i	−0.0285187	−	0.0493958i	0.851414	−	0.524495i	$-0.175746\pi$
$179$	−68.2981	−	118.296i	−0.0285187	−	0.0493958i	−0.879932	+	0.475099i	$0.842412\pi$
$180$		0			0
$181$	−1422.88	+	2464.50i	−0.584320	+	1.01207i	0.410640	+	0.911797i	$0.365305\pi$
$181$	−1422.88	+	2464.50i	−0.584320	+	1.01207i	−0.994960	+	0.100274i	$0.968028\pi$
$182$	417.097	+	349.986i	0.169875	+	0.142542i
$183$		0			0
$184$	−77.9283	−	441.953i	−0.0312226	−	0.177072i
$185$	1080.09	−	906.303i	0.429242	−	0.360177i
$186$		0			0
$187$	−2865.06	+	1042.80i	−1.12039	+	0.407790i
$188$	−2323.47			−0.901365
$189$		0			0
$190$	−1360.28			−0.519396
$191$	4697.17	−	1709.63i	1.77945	−	0.647667i	0.779682	−	0.626175i	$-0.215381\pi$
$191$	4697.17	−	1709.63i	1.77945	−	0.647667i	0.999769	−	0.0214922i	$-0.00684170\pi$
$192$		0			0
$193$	3289.12	−	2759.90i	1.22671	−	1.02934i	0.228269	−	0.973598i	$-0.426693\pi$
$193$	3289.12	−	2759.90i	1.22671	−	1.02934i	0.998445	−	0.0557378i	$-0.0177511\pi$
$194$	−32.3837	−	183.657i	−0.0119846	−	0.0679681i
$195$		0			0
$196$	1034.15	+	867.754i	0.376876	+	0.316237i
$197$	2730.00	−	4728.50i	0.987332	−	1.71011i	0.356256	−	0.934388i	$-0.384053\pi$
$197$	2730.00	−	4728.50i	0.987332	−	1.71011i	0.631076	−	0.775721i	$-0.282614\pi$
$198$		0			0
$199$	−1628.39	−	2820.45i	−0.580067	−	1.00471i	−0.995471	−	0.0950685i	$-0.969693\pi$
$199$	−1628.39	−	2820.45i	−0.580067	−	1.00471i	0.415404	−	0.909637i	$-0.363640\pi$
$200$	256.107	−	1452.46i	0.0905475	−	0.513521i
$201$		0			0
$202$	595.223	+	216.643i	0.207325	+	0.0754603i
$203$	−3665.71	−	1334.21i	−1.26740	−	0.461296i
$204$		0			0
$205$	−872.631	+	4948.93i	−0.297303	+	1.68609i
$206$	−1339.63	−	2320.30i	−0.453089	−	0.784773i
$207$		0			0
$208$	83.4891	−	144.607i	0.0278314	−	0.0482054i
$209$	−1995.59	−	1674.50i	−0.660469	−	0.554200i
$210$		0			0
$211$	−903.933	−	5126.46i	−0.294926	−	1.67261i	−0.667504	−	0.744606i	$-0.732637\pi$
$211$	−903.933	−	5126.46i	−0.294926	−	1.67261i	0.372578	−	0.928001i	$-0.378474\pi$
$212$	164.405	−	137.952i	0.0532613	−	0.0446916i
$213$		0			0
$214$	1292.92	−	470.584i	0.413001	−	0.150320i
$215$	−2738.02			−0.868519
$216$		0			0
$217$	6106.97			1.91045
$218$	205.619	−	74.8392i	0.0638820	−	0.0232512i
$219$		0			0
$220$	3630.73	−	3046.54i	1.11265	−	0.933627i
$221$	82.0178	+	465.146i	0.0249643	+	0.141580i
$222$		0			0
$223$	3504.62	+	2940.72i	1.05241	+	0.883074i	0.993345	−	0.115181i	$-0.0367447\pi$
$223$	3504.62	+	2940.72i	1.05241	+	0.883074i	0.0590615	+	0.998254i	$0.481189\pi$
$224$	417.381	−	722.925i	0.124498	−	0.215636i
$225$		0			0
$226$	502.240	+	869.905i	0.147825	+	0.256041i
$227$	−884.820	+	5018.06i	−0.258712	+	1.46723i	0.527651	+	0.849462i	$0.323073\pi$
$227$	−884.820	+	5018.06i	−0.258712	+	1.46723i	−0.786362	+	0.617766i	$0.788038\pi$
$228$		0			0
$229$	−393.358	−	143.171i	−0.113510	−	0.0413143i	0.284641	−	0.958634i	$-0.408126\pi$
$229$	−393.358	−	143.171i	−0.113510	−	0.0413143i	−0.398151	+	0.917320i	$0.630348\pi$
$230$	−1854.31	−	674.912i	−0.531606	−	0.193489i
$231$		0			0
$232$	−207.739	+	1178.15i	−0.0587878	+	0.333402i
$233$	−940.018	−	1628.16i	−0.264303	−	0.457786i	0.703078	−	0.711113i	$-0.251809\pi$
$233$	−940.018	−	1628.16i	−0.264303	−	0.457786i	−0.967381	+	0.253327i	$0.918475\pi$
$234$		0			0
$235$	−5108.32	+	8847.87i	−1.41800	+	2.45605i
$236$	823.114	+	690.675i	0.227035	+	0.190505i
$237$		0			0
$238$	410.026	+	2325.37i	0.111672	+	0.633325i
$239$	−3065.35	+	2572.14i	−0.829628	+	0.696141i	−0.955206	−	0.295943i	$-0.904366\pi$
$239$	−3065.35	+	2572.14i	−0.829628	+	0.696141i	0.125577	+	0.992084i	$0.459922\pi$
$240$		0			0
$241$	2245.24	−	817.200i	0.600118	−	0.218425i	−0.0240558	−	0.999711i	$-0.507658\pi$
$241$	2245.24	−	817.200i	0.600118	−	0.218425i	0.624174	+	0.781286i	$0.285436\pi$
$242$	6414.72			1.70394
$243$		0			0
$244$	−539.808			−0.141630
$245$	5578.09	−	2030.26i	1.45458	−	0.529422i
$246$		0			0
$247$	−309.145	+	259.404i	−0.0796374	+	0.0668237i
$248$	−325.217	−	1844.40i	−0.0832714	−	0.472255i
$249$		0			0
$250$	−1599.53	−	1342.16i	−0.404652	−	0.339543i
$251$	−1159.88	+	2008.96i	−0.291676	+	0.505198i	−0.974206	−	0.225660i	$-0.927546\pi$
$251$	−1159.88	+	2008.96i	−0.291676	+	0.505198i	0.682530	+	0.730858i	$0.260880\pi$
$252$		0			0
$253$	−1889.53	−	3272.77i	−0.469541	−	0.813269i
$254$	−509.683	+	2890.56i	−0.125907	+	0.714054i
$255$		0			0
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	2508.32	+	912.952i	0.608811	+	0.221589i	0.627983	−	0.778227i	$-0.283881\pi$
$257$	2508.32	+	912.952i	0.608811	+	0.221589i	−0.0191718	+	0.999816i	$0.506103\pi$
$258$		0			0
$259$	363.127	−	2059.39i	0.0871182	−	0.494072i
$260$	−367.114	−	635.859i	−0.0875670	−	0.151670i
$261$		0			0
$262$	1324.37	−	2293.88i	0.312289	−	0.540901i
$263$	−3414.21	−	2864.86i	−0.800491	−	0.671692i	0.147827	−	0.989013i	$-0.452772\pi$
$263$	−3414.21	−	2864.86i	−0.800491	−	0.671692i	−0.948318	+	0.317321i	$0.897217\pi$
$264$		0			0
$265$	−163.871	−	929.360i	−0.0379869	−	0.215434i
$266$	−1545.49	+	1296.82i	−0.356240	+	0.298921i
$267$		0			0
$268$	−2162.30	+	787.014i	−0.492850	+	0.179383i
$269$	1546.84			0.350604			0.175302	−	0.984515i	$-0.443910\pi$
$269$	1546.84			0.350604			0.175302	+	0.984515i	$0.443910\pi$
$270$		0			0
$271$	−3866.49			−0.866689			−0.433344	−	0.901228i	$-0.642667\pi$
$271$	−3866.49			−0.866689			−0.433344	+	0.901228i	$0.642667\pi$
$272$	680.461	−	247.668i	0.151688	−	0.0552098i
$273$		0			0
$274$	526.434	−	441.731i	0.116070	−	0.0973939i
$275$	−2156.66	−	12231.0i	−0.472914	−	2.68203i
$276$		0			0
$277$	1213.38	+	1018.15i	0.263195	+	0.220847i	0.764829	−	0.644233i	$-0.222823\pi$
$277$	1213.38	+	1018.15i	0.263195	+	0.220847i	−0.501634	+	0.865080i	$0.667268\pi$
$278$	2740.59	−	4746.84i	0.591258	−	1.02409i
$279$		0			0
$280$	−1835.28	−	3178.81i	−0.391712	−	0.678464i
$281$	19.2304	−	109.061i	0.00408253	−	0.0231532i	−0.982698	−	0.185213i	$-0.940703\pi$
$281$	19.2304	−	109.061i	0.00408253	−	0.0231532i	0.986781	+	0.162060i	$0.0518137\pi$
$282$		0			0
$283$	−387.990	−	141.217i	−0.0814969	−	0.0296624i	0.300950	−	0.953640i	$-0.402696\pi$
$283$	−387.990	−	141.217i	−0.0814969	−	0.0296624i	−0.382447	+	0.923977i	$0.624919\pi$
$284$	732.054	+	266.446i	0.152956	+	0.0556713i
$285$		0			0
$286$	244.169	−	1384.75i	0.0504825	−	0.286300i
$287$	3726.60	+	6454.66i	0.766460	+	1.32755i
$288$		0			0
$289$	1432.35	−	2480.90i	0.291542	−	0.504965i
$290$	4029.70	+	3381.32i	0.815974	+	0.684683i
$291$		0			0
$292$	172.499	+	978.292i	0.0345711	+	0.196062i
$293$	−6159.02	+	5168.03i	−1.22803	+	1.03044i	−0.229669	+	0.973269i	$0.573764\pi$
$293$	−6159.02	+	5168.03i	−1.22803	+	1.03044i	−0.998364	+	0.0571736i	$0.981791\pi$
$294$		0			0
$295$	4439.79	−	1615.95i	0.876252	−	0.318930i
$296$	−641.306			−0.125930
$297$		0			0
$298$	5889.69			1.14490
$299$	−550.124	+	200.229i	−0.106403	+	0.0387275i
$300$		0			0
$301$	−3110.81	+	2610.28i	−0.595695	+	0.499847i
$302$	−192.124	−	1089.59i	−0.0366076	−	0.207612i
$303$		0			0
$304$	473.961	+	397.701i	0.0894195	+	0.0750319i
$305$	−1186.81	+	2055.61i	−0.222807	+	0.385914i
$306$		0			0
$307$	−1272.25	−	2203.61i	−0.236519	−	0.409663i	0.723194	−	0.690645i	$-0.242673\pi$
$307$	−1272.25	−	2203.61i	−0.236519	−	0.409663i	−0.959713	+	0.280982i	$0.909340\pi$
$308$	1220.65	−	6922.67i	0.225822	−	1.28070i
$309$		0			0
$310$	−7738.55	−	2816.60i	−1.41781	−	0.516039i
$311$	6110.44	+	2224.02i	1.11412	+	0.405507i	0.832503	−	0.554020i	$-0.186907\pi$
$311$	6110.44	+	2224.02i	1.11412	+	0.405507i	0.281617	+	0.959527i	$0.409129\pi$
$312$		0			0
$313$	−507.754	+	2879.62i	−0.0916932	+	0.520018i	0.904017	+	0.427496i	$0.140604\pi$
$313$	−507.754	+	2879.62i	−0.0916932	+	0.520018i	−0.995711	+	0.0925222i	$0.970507\pi$
$314$	2563.24	+	4439.67i	0.460676	+	0.797914i
$315$		0			0
$316$	114.782	−	198.809i	0.0204336	−	0.0353920i
$317$	−3100.53	−	2601.65i	−0.549347	−	0.460957i	0.325373	−	0.945586i	$-0.394510\pi$
$317$	−3100.53	−	2601.65i	−0.549347	−	0.460957i	−0.874720	+	0.484629i	$0.838955\pi$
$318$		0			0
$319$	1749.36	+	9921.10i	0.307038	+	1.74130i
$320$	−862.312	+	723.566i	−0.150640	+	0.126402i
$321$		0			0
$322$	−2750.20	+	1000.99i	−0.475970	+	0.173239i
$323$	−1750.11			−0.301483
$324$		0			0
$325$	−1923.98			−0.328380
$326$	−4941.81	+	1798.67i	−0.839575	+	0.305580i
$327$		0			0
$328$	1750.95	−	1469.22i	0.294756	−	0.247330i
$329$	2631.24	+	14922.5i	0.440927	+	2.50062i
$330$		0			0
$331$	7486.13	+	6281.61i	1.24313	+	1.04311i	0.997273	+	0.0738005i	$0.0235128\pi$
$331$	7486.13	+	6281.61i	1.24313	+	1.04311i	0.245854	+	0.969307i	$0.420932\pi$
$332$	30.4138	−	52.6783i	0.00502764	−	0.00870813i
$333$		0			0
$334$	−916.544	−	1587.50i	−0.150153	−	0.260072i
$335$	−1757.00	+	9964.44i	−0.286553	+	1.62512i
$336$		0			0
$337$	1985.16	+	722.539i	0.320886	+	0.116793i	0.497441	−	0.867498i	$-0.334273\pi$
$337$	1985.16	+	722.539i	0.320886	+	0.116793i	−0.176555	+	0.984291i	$0.556495\pi$
$338$	3924.32	+	1428.34i	0.631523	+	0.229856i
$339$		0			0
$340$	552.915	−	3135.74i	0.0881942	−	0.500174i
$341$	−7885.56	−	13658.2i	−1.25228	−	2.16901i
$342$		0			0
$343$	−71.7839	+	124.333i	−0.0113002	+	0.0195725i
$344$	954.004	+	800.505i	0.149525	+	0.125466i
$345$		0			0
$346$	−381.797	−	2165.28i	−0.0593224	−	0.336434i
$347$	2478.10	−	2079.37i	0.383375	−	0.321690i	−0.430651	−	0.902519i	$-0.641716\pi$
$347$	2478.10	−	2079.37i	0.383375	−	0.321690i	0.814026	+	0.580829i	$0.197271\pi$
$348$		0			0
$349$	−10368.7	+	3773.91i	−1.59033	+	0.578833i	−0.977417	−	0.211318i	$-0.932225\pi$
$349$	−10368.7	+	3773.91i	−1.59033	+	0.578833i	−0.612913	+	0.790151i	$0.710002\pi$
$350$	−9618.43			−1.46893
$351$		0			0
$352$	−2155.76			−0.326427
$353$	−7212.68	+	2625.20i	−1.08751	+	0.395822i	−0.822699	−	0.568477i	$-0.807533\pi$
$353$	−7212.68	+	2625.20i	−1.08751	+	0.395822i	−0.264814	+	0.964299i	$0.585311\pi$
$354$		0			0
$355$	2624.11	−	2201.89i	0.392319	−	0.329195i
$356$	546.088	+	3097.02i	0.0812994	+	0.461072i
$357$		0			0
$358$	209.278	+	175.605i	0.0308957	+	0.0259246i
$359$	−2346.73	+	4064.65i	−0.345002	+	0.597561i	−0.985354	−	0.170521i	$-0.945455\pi$
$359$	−2346.73	+	4064.65i	−0.345002	+	0.597561i	0.640352	+	0.768081i	$0.278788\pi$
$360$		0			0
$361$	2681.83	+	4645.07i	0.390995	+	0.677223i
$362$	988.322	−	5605.05i	0.143495	−	0.813799i
$363$		0			0
$364$	−1023.29	−	372.447i	−0.147349	−	0.0536306i
$365$	4104.62	+	1493.96i	0.588619	+	0.214240i
$366$		0			0
$367$	2255.96	−	12794.2i	0.320873	−	1.81976i	−0.216344	−	0.976317i	$-0.569413\pi$
$367$	2255.96	−	12794.2i	0.320873	−	1.81976i	0.537217	−	0.843444i	$-0.319475\pi$
$368$	448.771	+	777.295i	0.0635702	+	0.110107i
$369$		0			0
$370$	−1409.96	+	2442.12i	−0.198109	+	0.343134i
$371$	−1072.18	−	899.668i	−0.150040	−	0.125899i
$372$		0			0
$373$	−303.523	−	1721.36i	−0.0421336	−	0.238951i	0.956467	−	0.291841i	$-0.0942679\pi$
$373$	−303.523	−	1721.36i	−0.0421336	−	0.238951i	−0.998600	+	0.0528899i	$0.983157\pi$
$374$	4671.23	−	3919.63i	0.645838	−	0.541923i
$375$		0			0
$376$	4366.70	−	1589.35i	0.598924	−	0.217990i
$377$	1560.63			0.213200
$378$		0			0
$379$	292.225			0.0396058			0.0198029	−	0.999804i	$-0.493696\pi$
$379$	292.225			0.0396058			0.0198029	+	0.999804i	$0.493696\pi$
$380$	2556.50	−	930.488i	0.345120	−	0.125613i
$381$		0			0
$382$	−7658.33	+	6426.11i	−1.02574	+	0.860702i
$383$	−377.147	−	2138.91i	−0.0503167	−	0.285360i	0.949259	−	0.314496i	$-0.101836\pi$
$383$	−377.147	−	2138.91i	−0.0503167	−	0.285360i	−0.999575	+	0.0291359i	$0.990724\pi$
$384$		0			0
$385$	−23678.1	−	19868.3i	−3.13441	−	2.63008i
$386$	−4293.64	+	7436.80i	−0.566167	+	0.980630i
$387$		0			0
$388$	186.490	+	323.011i	0.0244011	+	0.0422639i
$389$	−229.370	+	1300.82i	−0.0298960	+	0.169548i	−0.996100	−	0.0882294i	$-0.971879\pi$
$389$	−229.370	+	1300.82i	−0.0298960	+	0.169548i	0.966204	+	0.257778i	$0.0829903\pi$
$390$		0			0
$391$	−2385.72	−	868.329i	−0.308570	−	0.112310i
$392$	−2537.14	−	923.445i	−0.326901	−	0.118982i
$393$		0			0
$394$	−1896.24	+	10754.1i	−0.242465	+	1.37509i
$395$	−504.714	−	874.190i	−0.0642909	−	0.111355i
$396$		0			0
$397$	−2908.54	+	5037.74i	−0.367696	+	0.636869i	−0.989205	−	0.146539i	$-0.953187\pi$
$397$	−2908.54	+	5037.74i	−0.367696	+	0.636869i	0.621509	+	0.783407i	$0.286520\pi$
$398$	4989.67	+	4186.83i	0.628416	+	0.527304i
$399$		0			0
$400$	512.214	+	2904.91i	0.0640268	+	0.363114i
$401$	10559.4	−	8860.38i	1.31499	−	1.10341i	0.327647	−	0.944800i	$-0.393744\pi$
$401$	10559.4	−	8860.38i	1.31499	−	1.10341i	0.987342	−	0.158607i	$-0.0507002\pi$
$402$		0			0
$403$	−2295.83	+	835.612i	−0.283780	+	0.103287i
$404$	−1266.85			−0.156010
$405$		0			0
$406$	7801.92			0.953702
$407$	−5074.70	+	1847.04i	−0.618043	+	0.224949i
$408$		0			0
$409$	−11891.1	+	9977.82i	−1.43760	+	1.20629i	−0.496551	+	0.868008i	$0.665400\pi$
$409$	−11891.1	+	9977.82i	−1.43760	+	1.20629i	−0.941046	+	0.338279i	$0.890155\pi$
$410$	−1745.26	−	9897.87i	−0.210225	−	1.19225i
$411$		0			0
$412$	4104.86	+	3444.39i	0.490854	+	0.411875i
$413$	3503.72	−	6068.61i	0.417449	−	0.723044i
$414$		0			0
$415$	−133.734	−	231.634i	−0.0158187	−	0.0273987i
$416$	−57.9909	+	328.883i	−0.00683471	+	0.0387616i
$417$		0			0
$418$	4895.92	+	1781.97i	0.572888	+	0.208514i
$419$	5607.82	+	2041.08i	0.653842	+	0.237979i	0.647576	−	0.762001i	$-0.275783\pi$
$419$	5607.82	+	2041.08i	0.653842	+	0.237979i	0.00626665	+	0.999980i	$0.498005\pi$
$420$		0			0
$421$	1002.92	−	5687.85i	0.116103	−	0.658454i	−0.870095	−	0.492884i	$-0.835943\pi$
$421$	1002.92	−	5687.85i	0.116103	−	0.658454i	0.986198	−	0.165570i	$-0.0529463\pi$
$422$	5205.54	+	9016.27i	0.600479	+	1.04006i
$423$		0			0
$424$	−214.616	+	371.726i	−0.0245818	+	0.0425769i
$425$	−6391.65	−	5363.23i	−0.729507	−	0.612129i
$426$		0			0
$427$	611.311	+	3466.92i	0.0692820	+	0.392918i
$428$	−2108.00	+	1768.82i	−0.238070	+	0.199764i
$429$		0			0
$430$	5145.80	−	1872.92i	0.577099	−	0.210047i
$431$	11485.9			1.28366			0.641829	−	0.766848i	$-0.278176\pi$
$431$	11485.9			1.28366			0.641829	+	0.766848i	$0.278176\pi$
$432$		0			0
$433$	15025.6			1.66763			0.833815	−	0.552044i	$-0.186152\pi$
$433$	15025.6			1.66763			0.833815	+	0.552044i	$0.186152\pi$
$434$	−11477.4	+	4177.42i	−1.26943	+	0.462033i
$435$		0			0
$436$	−335.244	+	281.303i	−0.0368241	+	0.0308991i
$437$	−376.681	−	2136.27i	−0.0412336	−	0.233848i
$438$		0			0
$439$	3401.60	+	2854.28i	0.369817	+	0.310313i	0.808689	−	0.588236i	$-0.200177\pi$
$439$	3401.60	+	2854.28i	0.369817	+	0.310313i	−0.438872	+	0.898550i	$0.644622\pi$
$440$	−4739.58	+	8209.20i	−0.513524	+	0.889450i
$441$		0			0
$442$	−472.321	−	818.085i	−0.0508281	−	0.0880369i
$443$	2399.35	−	13607.4i	0.257328	−	1.45938i	−0.532696	−	0.846306i	$-0.678821\pi$
$443$	2399.35	−	13607.4i	0.257328	−	1.45938i	0.790025	−	0.613075i	$-0.210068\pi$
$444$		0			0
$445$	12994.2	+	4729.49i	1.38423	+	0.503819i
$446$	−8598.10	−	3129.45i	−0.912852	−	0.332251i
$447$		0			0
$448$	−289.910	+	1644.16i	−0.0305736	+	0.173391i
$449$	5639.84	+	9768.50i	0.592786	+	1.02673i	0.993855	+	0.110687i	$0.0353052\pi$
$449$	5639.84	+	9768.50i	0.592786	+	1.02673i	−0.401070	+	0.916048i	$0.631362\pi$
$450$		0			0
$451$	9623.86	−	16669.0i	1.00481	−	1.74038i
$452$	−1538.95	−	1291.33i	−0.160147	−	0.134379i
$453$		0			0
$454$	−1769.64	−	10036.1i	−0.182937	−	1.03749i
$455$	−3668.07	+	3077.87i	−0.377938	+	0.317127i
$456$		0			0
$457$	14967.4	−	5447.71i	1.53205	−	0.557621i	0.567929	−	0.823078i	$-0.307745\pi$
$457$	14967.4	−	5447.71i	1.53205	−	0.557621i	0.964123	+	0.265456i	$0.0855226\pi$
$458$	837.206			0.0854149
$459$		0			0
$460$	3946.62			0.400026
$461$	1211.14	−	440.819i	0.122361	−	0.0445358i	−0.280114	−	0.959967i	$-0.590372\pi$
$461$	1211.14	−	440.819i	0.122361	−	0.0445358i	0.402475	+	0.915431i	$0.368150\pi$
$462$		0			0
$463$	−31.8257	+	26.7049i	−0.00319453	+	0.00268053i	−0.644383	−	0.764703i	$-0.722886\pi$
$463$	−31.8257	+	26.7049i	−0.00319453	+	0.00268053i	0.641189	+	0.767383i	$0.278441\pi$
$464$	−415.479	−	2356.30i	−0.0415692	−	0.235751i
$465$		0			0
$466$	2880.38	+	2416.93i	0.286333	+	0.240262i
$467$	2292.38	−	3970.52i	0.227149	−	0.393434i	−0.729813	−	0.683647i	$-0.760393\pi$
$467$	2292.38	−	3970.52i	0.227149	−	0.393434i	0.956962	+	0.290213i	$0.0937262\pi$
$468$		0			0
$469$	7503.33	+	12996.1i	0.738745	+	1.27954i
$470$	3548.20	−	20122.8i	0.348226	−	1.97489i
$471$		0			0
$472$	−2019.40	−	735.001i	−0.196929	−	0.0716761i
$473$	9854.66	+	3586.80i	0.957966	+	0.348671i
$474$		0			0
$475$	1237.94	−	7020.72i	0.119580	−	0.678174i
$476$	−2361.24	−	4089.79i	−0.227368	−	0.393814i
$477$		0			0
$478$	4001.53	−	6930.86i	0.382899	−	0.663201i
$479$	−3164.99	−	2655.74i	−0.301904	−	0.253328i	0.479232	−	0.877688i	$-0.340915\pi$
$479$	−3164.99	−	2655.74i	−0.301904	−	0.253328i	−0.781136	+	0.624360i	$0.785360\pi$
$480$		0			0
$481$	145.273	+	823.885i	0.0137711	+	0.0780996i
$482$	−3660.67	+	3071.67i	−0.345931	+	0.290271i
$483$		0			0
$484$	−12055.7	+	4387.93i	−1.13221	+	0.412089i
$485$	1640.05			0.153548
$486$		0			0
$487$	−12221.6			−1.13719			−0.568597	−	0.822617i	$-0.692513\pi$
$487$	−12221.6			−1.13719			−0.568597	+	0.822617i	$0.692513\pi$
$488$	1014.51	−	369.250i	0.0941077	−	0.0342524i
$489$		0			0
$490$	−9094.60	+	7631.28i	−0.838474	+	0.703563i
$491$	−1467.91	−	8324.93i	−0.134920	−	0.765171i	−0.974915	−	0.222577i	$-0.928553\pi$
$491$	−1467.91	−	8324.93i	−0.134920	−	0.765171i	0.839995	−	0.542594i	$-0.182558\pi$
$492$		0			0
$493$	5184.54	+	4350.35i	0.473631	+	0.397424i
$494$	403.560	−	698.987i	0.0367551	−	0.0636618i
$495$		0			0
$496$	1872.85	+	3243.87i	0.169543	+	0.293658i
$497$	882.227	−	5003.36i	0.0796243	−	0.451572i
$498$		0			0
$499$	−9453.06	−	3440.63i	−0.848050	−	0.308665i	−0.118805	−	0.992918i	$-0.537906\pi$
$499$	−9453.06	−	3440.63i	−0.848050	−	0.308665i	−0.729245	+	0.684253i	$0.760129\pi$
$500$	3924.22	+	1428.30i	0.350993	+	0.127751i
$501$		0			0
$502$	805.641	−	4569.02i	0.0716286	−	0.406226i
$503$	1202.67	+	2083.09i	0.106609	+	0.184653i	0.914395	−	0.404824i	$-0.132667\pi$
$503$	1202.67	+	2083.09i	0.106609	+	0.184653i	−0.807785	+	0.589477i	$0.799334\pi$
$504$		0			0
$505$	−2785.25	+	4824.20i	−0.245430	+	0.425097i
$506$	5789.87	+	4858.27i	0.508678	+	0.426831i
$507$		0			0
$508$	−1019.37	−	5781.11i	−0.0890296	−	0.504912i
$509$	−793.245	+	665.612i	−0.0690766	+	0.0579621i	−0.676672	−	0.736284i	$-0.736579\pi$
$509$	−793.245	+	665.612i	−0.0690766	+	0.0579621i	0.607596	+	0.794247i	$0.292134\pi$
$510$		0			0
$511$	6087.73	−	2215.75i	0.527017	−	0.191818i
$512$	512.000			0.0441942
$513$		0			0
$514$	−5338.59			−0.458123
$515$	22141.2	−	8058.73i	1.89448	−	0.689534i
$516$		0			0
$517$	29976.5	−	25153.3i	2.55003	−	2.13973i
$518$	726.254	+	4118.79i	0.0616019	+	0.349361i
$519$		0			0
$520$	1124.90	+	943.904i	0.0948657	+	0.0796018i
$521$	−4877.00	+	8447.21i	−0.410106	+	0.710324i	−0.994901	−	0.100857i	$-0.967842\pi$
$521$	−4877.00	+	8447.21i	−0.410106	+	0.710324i	0.584795	+	0.811181i	$0.301175\pi$
$522$		0			0
$523$	−6379.17	−	11049.0i	−0.533349	−	0.923788i	−0.999241	−	0.0389464i	$-0.987600\pi$
$523$	−6379.17	−	11049.0i	−0.533349	−	0.923788i	0.465892	−	0.884842i	$-0.345733\pi$
$524$	−919.897	+	5217.00i	−0.0766907	+	0.434934i
$525$		0			0
$526$	8376.30	+	3048.72i	0.694342	+	0.252720i
$527$	−9956.27	−	3623.79i	−0.822964	−	0.299534i
$528$		0			0
$529$	−1566.34	+	8883.16i	−0.128737	+	0.730102i
$530$	943.697	+	1634.53i	0.0773426	+	0.133961i
$531$		0			0
$532$	2017.49	−	3494.40i	0.164416	−	0.284777i
$533$	−2284.14	−	1916.62i	−0.185623	−	0.155757i
$534$		0			0
$535$	2101.15	+	11916.2i	0.169795	+	0.962958i
$536$	3525.45	−	2958.21i	0.284098	−	0.238386i
$537$		0			0
$538$	−2907.10	+	1058.10i	−0.232963	+	0.0847916i
$539$	−22736.2			−1.81692
$540$		0			0
$541$	−9012.43			−0.716220			−0.358110	−	0.933679i	$-0.616579\pi$
$541$	−9012.43			−0.716220			−0.358110	+	0.933679i	$0.616579\pi$
$542$	7266.63	−	2644.84i	0.575882	−	0.209604i
$543$		0			0
$544$	−1109.43	+	930.926i	−0.0874386	+	0.0733697i
$545$	334.155	+	1895.09i	0.0262636	+	0.148948i
$546$		0			0
$547$	−18528.2	−	15547.0i	−1.44828	−	1.21525i	−0.933826	−	0.357728i	$-0.883551\pi$
$547$	−18528.2	−	15547.0i	−1.44828	−	1.21525i	−0.514451	−	0.857520i	$-0.672004\pi$
$548$	−687.211	+	1190.28i	−0.0535697	+	0.0927855i
$549$		0			0
$550$	12419.7	+	21511.5i	0.962868	+	1.66774i
$551$	−1004.15	+	5694.81i	−0.0776373	+	0.440303i
$552$		0			0
$553$	−1406.84	−	512.047i	−0.108182	−	0.0393751i
$554$	−2976.87	−	1083.49i	−0.228294	−	0.0830923i
$555$		0			0
$556$	−1903.59	+	10795.8i	−0.145198	+	0.823461i
$557$	2492.09	+	4316.42i	0.189575	+	0.328353i	0.945109	−	0.326757i	$-0.105956\pi$
$557$	2492.09	+	4316.42i	0.189575	+	0.328353i	−0.755534	+	0.655110i	$0.772622\pi$
$558$		0			0
$559$	812.300	−	1406.94i	0.0614609	−	0.106453i
$560$	5623.64	+	4718.79i	0.424361	+	0.356081i
$561$		0			0
$562$	38.4608	+	218.122i	0.00288678	+	0.0163718i
$563$	16347.9	−	13717.5i	1.22377	−	1.02687i	0.225152	−	0.974324i	$-0.427712\pi$
$563$	16347.9	−	13717.5i	1.22377	−	1.02687i	0.998619	−	0.0525417i	$-0.0167323\pi$
$564$		0			0
$565$	−8300.95	+	3021.30i	−0.618095	+	0.224968i
$566$	825.781			0.0613254
$567$		0			0
$568$	−1558.07			−0.115097
$569$	−11141.3	+	4055.12i	−0.820860	+	0.298769i	−0.718102	−	0.695938i	$-0.754989\pi$
$569$	−11141.3	+	4055.12i	−0.820860	+	0.298769i	−0.102758	+	0.994706i	$0.532767\pi$
$570$		0			0
$571$	−5636.09	+	4729.24i	−0.413070	+	0.346607i	−0.825520	−	0.564373i	$-0.809118\pi$
$571$	−5636.09	+	4729.24i	−0.413070	+	0.346607i	0.412449	+	0.910981i	$0.364673\pi$
$572$	488.337	+	2769.50i	0.0356965	+	0.202445i
$573$		0			0
$574$	−11419.0	−	9581.65i	−0.830345	−	0.696742i
$575$	5170.90	−	8956.27i	0.375029	−	0.649569i
$576$		0			0
$577$	13363.2	+	23145.7i	0.964152	+	1.66996i	0.711876	+	0.702305i	$0.247846\pi$
$577$	13363.2	+	23145.7i	0.964152	+	1.66996i	0.252276	+	0.967655i	$0.418821\pi$
$578$	−994.897	+	5642.34i	−0.0715956	+	0.406039i
$579$		0			0
$580$	−9886.33	−	3598.33i	−0.707772	−	0.257608i
$581$	−372.769	−	135.677i	−0.0266180	−	0.00968817i
$582$		0			0
$583$	−627.656	+	3559.61i	−0.0445881	+	0.252872i
$584$	−993.384	−	1720.59i	−0.0703879	−	0.121915i
$585$		0			0
$586$	8040.03	−	13925.7i	0.566776	−	0.981684i
$587$	−8902.77	−	7470.31i	−0.625991	−	0.525269i	0.273689	−	0.961818i	$-0.411756\pi$
$587$	−8902.77	−	7470.31i	−0.625991	−	0.525269i	−0.899680	+	0.436549i	$0.856200\pi$
$588$		0			0
$589$	−1572.00	−	8915.24i	−0.109971	−	0.623678i
$590$	−7238.70	+	6073.99i	−0.505106	+	0.423834i
$591$		0			0
$592$	1205.26	−	438.679i	0.0836755	−	0.0304554i
$593$	7823.32			0.541763			0.270881	−	0.962613i	$-0.412685\pi$
$593$	7823.32			0.541763			0.270881	+	0.962613i	$0.412685\pi$
$594$		0			0
$595$	−20765.4			−1.43076
$596$	−11069.0	+	4028.78i	−0.760744	+	0.276888i
$597$		0			0
$598$	896.931	−	752.614i	0.0613348	−	0.0514660i
$599$	3920.24	+	22232.8i	0.267407	+	1.51654i	0.762093	+	0.647468i	$0.224172\pi$
$599$	3920.24	+	22232.8i	0.267407	+	1.51654i	−0.494686	+	0.869072i	$0.664717\pi$
$600$		0			0
$601$	6511.80	+	5464.05i	0.441967	+	0.370854i	0.836445	−	0.548051i	$-0.184630\pi$
$601$	6511.80	+	5464.05i	0.441967	+	0.370854i	−0.394478	+	0.918905i	$0.629075\pi$
$602$	4060.87	−	7033.64i	0.274932	−	0.476195i
$603$		0			0
$604$	1106.40	+	1916.34i	0.0745343	+	0.129097i
$605$	−9796.00	+	55555.9i	−0.658287	+	3.73333i
$606$		0			0
$607$	−11396.5	−	4147.98i	−0.762058	−	0.277366i	−0.0683874	−	0.997659i	$-0.521785\pi$
$607$	−11396.5	−	4147.98i	−0.762058	−	0.277366i	−0.693671	+	0.720292i	$0.744008\pi$
$608$	−1162.80	−	423.224i	−0.0775620	−	0.0282303i
$609$		0			0
$610$	824.346	−	4675.10i	0.0547161	−	0.310310i
$611$	−3031.01	−	5249.86i	−0.200690	−	0.347605i
$612$		0			0
$613$	−78.2443	+	135.523i	−0.00515540	+	0.00892941i	−0.868592	−	0.495529i	$-0.834974\pi$
$613$	−78.2443	+	135.523i	−0.00515540	+	0.00892941i	0.863436	+	0.504458i	$0.168308\pi$
$614$	3898.41	+	3271.16i	0.256233	+	0.215005i
$615$		0			0
$616$	2441.31	+	13845.3i	0.159680	+	0.905593i
$617$	−15669.5	+	13148.3i	−1.02242	+	0.857910i	−0.989929	−	0.141562i	$-0.954788\pi$
$617$	−15669.5	+	13148.3i	−1.02242	+	0.857910i	−0.0324881	+	0.999472i	$0.510343\pi$
$618$		0			0
$619$	−9312.88	+	3389.61i	−0.604711	+	0.220097i	−0.626187	−	0.779673i	$-0.715386\pi$
$619$	−9312.88	+	3389.61i	−0.604711	+	0.220097i	0.0214764	+	0.999769i	$0.493163\pi$
$620$	16470.4			1.06688
$621$		0			0
$622$	−13005.2			−0.838361
$623$	19272.2	−	7014.50i	1.23936	−	0.451092i
$624$		0			0
$625$	−3586.57	+	3009.49i	−0.229541	+	0.192608i
$626$	−1015.51	−	5759.23i	−0.0648368	−	0.367708i
$627$		0			0
$628$	−7854.23	−	6590.49i	−0.499073	−	0.418772i
$629$	−1814.02	+	3141.98i	−0.114992	+	0.199172i
$630$		0			0
$631$	727.004	+	1259.21i	0.0458662	+	0.0794425i	0.888047	−	0.459753i	$-0.152062\pi$
$631$	727.004	+	1259.21i	0.0458662	+	0.0794425i	−0.842181	+	0.539195i	$0.818729\pi$
$632$	−79.7269	+	452.154i	−0.00501799	+	0.0284584i
$633$		0			0
$634$	7606.73	+	2768.62i	0.476501	+	0.173432i
$635$	−24255.8	−	8828.40i	−1.51585	−	0.551724i
$636$		0			0
$637$	−611.617	+	3468.65i	−0.0380426	+	0.215750i
$638$	−10074.1	−	17448.9i	−0.625140	−	1.08277i
$639$		0			0
$640$	1125.67	−	1949.71i	0.0695249	−	0.120421i
$641$	−22893.6	−	19210.0i	−1.41068	−	1.18370i	−0.956118	−	0.292981i	$-0.905353\pi$
$641$	−22893.6	−	19210.0i	−1.41068	−	1.18370i	−0.454558	−	0.890717i	$-0.650203\pi$
$642$		0			0
$643$	2153.84	+	12215.0i	0.132098	+	0.749165i	0.976837	+	0.213986i	$0.0686446\pi$
$643$	2153.84	+	12215.0i	0.132098	+	0.749165i	−0.844739	+	0.535179i	$0.820244\pi$
$644$	4483.96	−	3762.49i	0.274368	−	0.230222i
$645$		0			0
$646$	3289.14	−	1197.15i	0.200324	−	0.0729121i
$647$	−16789.0			−1.02016			−0.510080	−	0.860127i	$-0.670384\pi$
$647$	−16789.0			−1.02016			−0.510080	+	0.860127i	$0.670384\pi$
$648$		0			0
$649$	−18096.5			−1.09453
$650$	3615.91	−	1316.08i	0.218196	−	0.0794169i
$651$		0			0
$652$	8057.19	−	6760.79i	0.483963	−	0.406093i
$653$	3456.64	+	19603.6i	0.207150	+	1.17481i	0.894020	+	0.448026i	$0.147873\pi$
$653$	3456.64	+	19603.6i	0.207150	+	1.17481i	−0.686870	+	0.726780i	$0.741016\pi$
$654$		0			0
$655$	17844.1	+	14972.9i	1.06447	+	0.893193i
$656$	−2285.70	+	3958.95i	−0.136039	+	0.235627i
$657$		0			0
$658$	−15152.7	−	26245.3i	−0.897742	−	1.55493i
$659$	241.662	−	1370.53i	0.0142850	−	0.0810141i	−0.976832	−	0.214008i	$-0.931348\pi$
$659$	241.662	−	1370.53i	0.0142850	−	0.0810141i	0.991117	+	0.132994i	$0.0424592\pi$
$660$		0			0
$661$	−9178.93	−	3340.86i	−0.540120	−	0.196587i	0.0575316	−	0.998344i	$-0.481677\pi$
$661$	−9178.93	−	3340.86i	−0.540120	−	0.196587i	−0.597651	+	0.801756i	$0.703899\pi$
$662$	−18366.2	−	6684.75i	−1.07828	−	0.392463i
$663$		0			0
$664$	−21.1252	+	119.807i	−0.00123467	+	0.00700214i
$665$	−8871.19	−	15365.4i	−0.517309	−	0.896005i
$666$		0			0
$667$	−4194.34	+	7264.81i	−0.243487	+	0.421731i
$668$	2808.45	+	2356.57i	0.162668	+	0.136495i
$669$		0			0
$670$	−3514.00	−	19928.9i	−0.202623	−	1.14913i
$671$	6964.38	−	5843.81i	0.400681	−	0.336211i
$672$		0			0
$673$	−3889.50	+	1415.66i	−0.222777	+	0.0810844i	−0.450997	−	0.892525i	$-0.648932\pi$
$673$	−3889.50	+	1415.66i	−0.222777	+	0.0810844i	0.228220	+	0.973610i	$0.426709\pi$
$674$	−4225.13			−0.241463
$675$		0			0
$676$	−8352.35			−0.475213
$677$	7323.52	−	2665.54i	0.415754	−	0.151322i	−0.125669	−	0.992072i	$-0.540108\pi$
$677$	7323.52	−	2665.54i	0.415754	−	0.151322i	0.541424	+	0.840750i	$0.317886\pi$
$678$		0			0
$679$	1863.34	−	1563.53i	0.105315	−	0.0883694i
$680$	1105.83	+	6271.48i	0.0623627	+	0.353677i
$681$		0			0
$682$	24162.8	+	20275.0i	1.35666	+	1.13837i
$683$	3230.85	−	5595.99i	0.181003	−	0.313506i	−0.761219	−	0.648494i	$-0.775399\pi$
$683$	3230.85	−	5595.99i	0.181003	−	0.313506i	0.942222	+	0.334988i	$0.108732\pi$
$684$		0			0
$685$	3021.77	+	5233.85i	0.168548	+	0.291935i
$686$	49.8606	−	282.773i	0.00277505	−	0.0157381i
$687$		0			0
$688$	−2340.52	−	851.879i	−0.129697	−	0.0472058i
$689$	526.172	+	191.511i	0.0290937	+	0.0105892i
$690$		0			0
$691$	−303.637	+	1722.01i	−0.0167162	+	0.0948023i	−0.992024	−	0.126046i	$-0.959771\pi$
$691$	−303.637	+	1722.01i	−0.0167162	+	0.0948023i	0.975308	+	0.220848i	$0.0708825\pi$
$692$	2198.68	+	3808.23i	0.120782	+	0.209201i
$693$		0			0
$694$	−3234.92	+	5603.05i	−0.176940	+	0.306468i
$695$	36925.7	+	30984.3i	2.01535	+	1.69108i
$696$		0			0
$697$	−2245.42	−	12734.4i	−0.122025	−	0.692038i
$698$	16905.3	−	14185.3i	0.916728	−	0.769226i
$699$		0			0
$700$	18076.7	−	6579.40i	0.976052	−	0.355254i
$701$	17432.8			0.939267			0.469633	−	0.882862i	$-0.344386\pi$
$701$	17432.8			0.939267			0.469633	+	0.882862i	$0.344386\pi$
$702$		0			0
$703$	−3099.87			−0.166307
$704$	4051.50	−	1474.62i	0.216898	−	0.0789446i
$705$		0			0
$706$	11759.7	−	9867.53i	0.626885	−	0.526019i
$707$	1434.65	+	8136.33i	0.0763164	+	0.432812i
$708$		0			0
$709$	21475.5	+	18020.1i	1.13756	+	0.954525i	0.999356	−	0.0358787i	$-0.0114230\pi$
$709$	21475.5	+	18020.1i	1.13756	+	0.954525i	0.138203	+	0.990404i	$0.455867\pi$
$710$	−3425.53	+	5933.19i	−0.181067	+	0.313618i
$711$		0			0
$712$	−3144.79	−	5446.94i	−0.165528	−	0.286703i
$713$	2280.44	−	12933.0i	0.119780	−	0.679306i
$714$		0			0
$715$	11620.0	+	4229.33i	0.607780	+	0.221214i
$716$	−513.434	−	186.875i	−0.0267988	−	0.00975396i
$717$		0			0
$718$	1630.02	−	9244.31i	0.0847240	−	0.480494i
$719$	10255.0	+	17762.1i	0.531913	+	0.921301i	0.999306	+	0.0372512i	$0.0118602\pi$
$719$	10255.0	+	17762.1i	0.531913	+	0.921301i	−0.467392	+	0.884050i	$0.654807\pi$
$720$		0			0
$721$	17473.0	−	30264.1i	0.902536	−	1.56324i
$722$	−8217.62	−	6895.40i	−0.423585	−	0.355430i
$723$		0			0
$724$	1976.64	+	11210.1i	0.101466	+	0.575443i
$725$	−21119.0	+	17721.0i	−1.08185	+	0.907780i
$726$		0			0
$727$	17758.2	−	6463.45i	0.905935	−	0.329734i	0.153307	−	0.988179i	$-0.451008\pi$
$727$	17758.2	−	6463.45i	0.905935	−	0.329734i	0.752629	+	0.658445i	$0.228786\pi$
$728$	2177.92			0.110878
$729$		0			0
$730$	−8736.10			−0.442928
$731$	6620.49	−	2409.66i	0.334976	−	0.121921i
$732$		0			0
$733$	4761.15	−	3995.08i	0.239914	−	0.201312i	−0.514901	−	0.857250i	$-0.672171\pi$
$733$	4761.15	−	3995.08i	0.239914	−	0.201312i	0.754815	+	0.655938i	$0.227727\pi$
$734$	4511.93	+	25588.4i	0.226891	+	1.28677i
$735$		0			0
$736$	−1375.11	−	1153.86i	−0.0688688	−	0.0577877i
$737$	19377.2	−	33562.2i	0.968477	−	1.67745i
$738$		0			0
$739$	−10206.1	−	17677.6i	−0.508037	−	0.879946i	−0.999957	−	0.00930516i	$-0.997038\pi$
$739$	−10206.1	−	17677.6i	−0.508037	−	0.879946i	0.491920	−	0.870640i	$-0.336295\pi$
$740$	979.346	−	5554.14i	0.0486506	−	0.275911i
$741$		0			0
$742$	2630.45	+	957.407i	0.130144	+	0.0473686i
$743$	−22160.3	−	8065.69i	−1.09419	−	0.398252i	−0.269018	−	0.963135i	$-0.586699\pi$
$743$	−22160.3	−	8065.69i	−1.09419	−	0.398252i	−0.825171	+	0.564883i	$0.808921\pi$
$744$		0			0
$745$	−8994.21	+	51008.7i	−0.442312	+	2.50847i
$746$	1747.92	+	3027.48i	0.0857853	+	0.148585i
$747$		0			0
$748$	−6097.86	+	10561.8i	−0.298075	+	0.516280i
$749$	13747.5	+	11535.5i	0.670656	+	0.562747i
$750$		0			0
$751$	−2054.84	−	11653.6i	−0.0998430	−	0.566238i	−0.993155	−	0.116801i	$-0.962736\pi$
$751$	−2054.84	−	11653.6i	−0.0998430	−	0.566238i	0.893312	−	0.449436i	$-0.148375\pi$
$752$	−7119.53	+	5974.00i	−0.345243	+	0.289693i
$753$		0			0
$754$	−2933.02	+	1067.53i	−0.141663	+	0.0515612i
$755$	9729.98			0.469020
$756$		0			0
$757$	−22961.8			−1.10246			−0.551230	−	0.834354i	$-0.685841\pi$
$757$	−22961.8			−1.10246			−0.551230	+	0.834354i	$0.685841\pi$
$758$	−549.204	+	199.894i	−0.0263166	+	0.00957845i
$759$		0			0
$760$	−4168.15	+	3497.49i	−0.198940	+	0.166931i
$761$	−4614.73	−	26171.4i	−0.219821	−	1.24667i	−0.872342	−	0.488897i	$-0.837399\pi$
$761$	−4614.73	−	26171.4i	−0.219821	−	1.24667i	0.652520	−	0.757771i	$-0.273712\pi$
$762$		0			0
$763$	2186.32	+	1834.54i	0.103736	+	0.0870445i
$764$	9997.25	−	17315.7i	0.473413	−	0.819976i
$765$		0			0
$766$	2171.90	+	3761.84i	0.102446	+	0.177442i
$767$	−486.806	+	2760.82i	−0.0229173	+	0.129970i
$768$		0			0
$769$	21031.5	+	7654.83i	0.986234	+	0.358960i	0.784261	−	0.620431i	$-0.213042\pi$
$769$	21031.5	+	7654.83i	0.986234	+	0.358960i	0.201973	+	0.979391i	$0.435265\pi$
$770$	58091.0	+	21143.4i	2.71877	+	0.989552i
$771$		0			0
$772$	2982.33	−	16913.6i	0.139037	−	0.788517i
$773$	−9257.45	−	16034.4i	−0.430747	−	0.746075i	0.566191	−	0.824274i	$-0.308416\pi$
$773$	−9257.45	−	16034.4i	−0.430747	−	0.746075i	−0.996938	+	0.0781987i	$0.975083\pi$
$774$		0			0
$775$	21579.7	−	37377.1i	1.00021	−	1.73242i
$776$	−571.439	−	479.495i	−0.0264349	−	0.0221815i
$777$		0			0
$778$	−458.740	−	2601.65i	−0.0211396	−	0.119889i
$779$	8463.55	−	7101.76i	0.389266	−	0.326633i
$780$		0			0
$781$	−12329.1	+	4487.44i	−0.564880	+	0.205599i
$782$	5077.65			0.232195
$783$		0			0
$784$	5399.94			0.245989
$785$	−42364.9	+	15419.6i	−1.92620	+	0.701080i
$786$		0			0
$787$	−28809.0	+	24173.6i	−1.30487	+	1.09491i	−0.315585	+	0.948897i	$0.602201\pi$
$787$	−28809.0	+	24173.6i	−1.30487	+	1.09491i	−0.989282	+	0.146016i	$0.953355\pi$
$788$	−3792.48	−	21508.2i	−0.171448	−	0.972332i
$789$		0			0
$790$	1546.53	+	1297.70i	0.0696496	+	0.0584430i
$791$	−6550.80	+	11346.3i	−0.294462	+	0.510024i
$792$		0			0
$793$	−704.188	−	1219.69i	−0.0315340	−	0.0546185i
$794$	2020.25	−	11457.4i	0.0902972	−	0.512101i
$795$		0			0
$796$	−12241.5	−	4455.53i	−0.545085	−	0.198395i
$797$	−12422.1	−	4521.28i	−0.552088	−	0.200944i	0.0508860	−	0.998704i	$-0.483795\pi$
$797$	−12422.1	−	4521.28i	−0.552088	−	0.200944i	−0.602974	+	0.797761i	$0.706018\pi$
$798$		0			0
$799$	4565.05	−	25889.7i	0.202127	−	1.14632i
$800$	−2949.72	−	5109.07i	−0.130361	−	0.225791i
$801$		0			0
$802$	−13784.3	+	23875.1i	−0.606908	+	1.05120i
$803$	−12816.2	−	10754.1i	−0.563232	−	0.472608i
$804$		0			0
$805$	−4469.39	−	25347.2i	−0.195684	−	1.10978i
$806$	3743.15	−	3140.87i	0.163582	−	0.137261i
$807$		0			0
$808$	2380.89	−	866.574i	0.103663	−	0.0377302i
$809$	7792.70			0.338661			0.169330	−	0.985559i	$-0.445839\pi$
$809$	7792.70			0.338661			0.169330	+	0.985559i	$0.445839\pi$
$810$		0			0
$811$	7296.44			0.315922			0.157961	−	0.987445i	$-0.449508\pi$
$811$	7296.44			0.315922			0.157961	+	0.987445i	$0.449508\pi$
$812$	−14662.8	+	5336.83i	−0.633700	+	0.230648i
$813$		0			0
$814$	8273.87	−	6942.60i	0.356264	−	0.298941i
$815$	−8031.02	−	45546.2i	−0.345171	−	1.95756i
$816$		0			0
$817$	4611.36	+	3869.39i	0.197468	+	0.165695i
$818$	15522.7	−	26886.2i	0.663496	−	1.14921i
$819$		0			0
$820$	10050.6	+	17408.1i	0.428025	+	0.741361i
$821$	2630.91	−	14920.6i	0.111838	−	0.634267i	−0.876429	−	0.481532i	$-0.840081\pi$
$821$	2630.91	−	14920.6i	0.111838	−	0.634267i	0.988267	−	0.152735i	$-0.0488082\pi$
$822$		0			0
$823$	28105.4	+	10229.5i	1.19039	+	0.433267i	0.859860	−	0.510529i	$-0.170550\pi$
$823$	28105.4	+	10229.5i	1.19039	+	0.433267i	0.330530	+	0.943796i	$0.392773\pi$
$824$	−10070.7	−	3665.44i	−0.425764	−	0.154966i
$825$		0			0
$826$	−2433.66	+	13801.9i	−0.102515	+	0.581394i
$827$	−8696.60	−	15063.0i	−0.365672	−	0.633362i	0.623212	−	0.782053i	$-0.285827\pi$
$827$	−8696.60	−	15063.0i	−0.365672	−	0.633362i	−0.988884	+	0.148691i	$0.952494\pi$
$828$		0			0
$829$	7158.61	−	12399.1i	0.299914	−	0.519466i	−0.676202	−	0.736716i	$-0.736375\pi$
$829$	7158.61	−	12399.1i	0.299914	−	0.519466i	0.976116	+	0.217250i	$0.0697087\pi$
$830$	409.785	+	343.850i	0.0171371	+	0.0143798i
$831$		0			0
$832$	−115.982	−	657.766i	−0.00483287	−	0.0274086i
$833$	−11700.9	+	9818.26i	−0.486691	+	0.408382i
$834$		0			0
$835$	15148.5	−	5513.60i	0.627827	−	0.228510i
$836$	−10420.3			−0.431091
$837$		0			0
$838$	−11935.4			−0.492008
$839$	20317.0	−	7394.78i	0.836019	−	0.304286i	0.111692	−	0.993743i	$-0.464373\pi$
$839$	20317.0	−	7394.78i	0.836019	−	0.304286i	0.724327	+	0.689457i	$0.242151\pi$
$840$		0			0
$841$	−1552.50	+	1302.70i	−0.0636557	+	0.0534135i
$842$	2005.84	+	11375.7i	0.0820973	+	0.465597i
$843$		0			0
$844$	−15950.7	−	13384.2i	−0.650529	−	0.545858i
$845$	−18363.2	+	31806.0i	−0.747591	+	1.29487i
$846$		0			0
$847$	41834.1	+	72458.9i	1.69709	+	2.93945i
$848$	149.071	−	845.422i	0.00603668	−	0.0342357i
$849$		0			0
$850$	15681.0	+	5707.43i	0.632771	+	0.230310i
$851$	−4225.67	−	1538.02i	−0.170217	−	0.0619537i
$852$		0			0
$853$	5682.85	−	32229.0i	0.228109	−	1.29367i	−0.628543	−	0.777775i	$-0.716348\pi$
$853$	5682.85	−	32229.0i	0.228109	−	1.29367i	0.856652	−	0.515895i	$-0.172541\pi$
$854$	−3520.40	−	6097.51i	−0.141060	−	0.244324i
$855$		0			0
$856$	2751.79	−	4766.25i	0.109877	−	0.190312i
$857$	35391.7	+	29697.2i	1.41069	+	1.18371i	0.956113	+	0.292999i	$0.0946531\pi$
$857$	35391.7	+	29697.2i	1.41069	+	1.18371i	0.454575	+	0.890709i	$0.349791\pi$
$858$		0			0
$859$	−1599.38	−	9070.55i	−0.0635276	−	0.360283i	−0.999956	−	0.00942318i	$-0.997000\pi$
$859$	−1599.38	−	9070.55i	−0.0635276	−	0.360283i	0.936428	−	0.350860i	$-0.114111\pi$
$860$	−8389.79	+	7039.87i	−0.332662	+	0.279137i
$861$		0			0
$862$	−21586.4	+	7856.82i	−0.852943	+	0.310446i
$863$	−29481.0			−1.16286			−0.581428	−	0.813598i	$-0.697506\pi$
$863$	−29481.0			−1.16286			−0.581428	+	0.813598i	$0.697506\pi$
$864$		0			0
$865$	19335.8			0.760044
$866$	−28238.9	+	10278.1i	−1.10808	+	0.403308i
$867$		0			0
$868$	18712.9	−	15701.9i	0.731746	−	0.614008i
$869$	671.374	+	3807.55i	0.0262081	+	0.148633i
$870$		0			0
$871$	−4599.01	−	3859.03i	−0.178911	−	0.150124i
$872$	437.630	−	757.998i	0.0169955	−	0.0294370i
$873$		0			0
$874$	2169.22	+	3757.20i	0.0839531	+	0.145411i
$875$	4729.24	−	26820.8i	0.182717	−	1.03624i
$876$		0			0
$877$	−14551.8	−	5296.44i	−0.560297	−	0.203932i	0.0463184	−	0.998927i	$-0.485251\pi$
$877$	−14551.8	−	5296.44i	−0.560297	−	0.203932i	−0.606616	+	0.794995i	$0.707473\pi$
$878$	−8345.37	−	3037.47i	−0.320777	−	0.116753i
$879$		0			0
$880$	3292.08	−	18670.3i	0.126109	−	0.715200i
$881$	−392.119	−	679.170i	−0.0149952	−	0.0259725i	0.858430	−	0.512930i	$-0.171440\pi$
$881$	−392.119	−	679.170i	−0.0149952	−	0.0259725i	−0.873426	+	0.486958i	$0.838107\pi$
$882$		0			0
$883$	−12611.5	+	21843.8i	−0.480647	+	0.832506i	−0.999753	−	0.0222040i	$-0.992932\pi$
$883$	−12611.5	+	21843.8i	−0.480647	+	0.832506i	0.519106	+	0.854710i	$0.326265\pi$
$884$	1447.28	+	1214.41i	0.0550647	+	0.0462048i
$885$		0			0
$886$	4798.70	+	27214.8i	0.181959	+	1.03194i
$887$	12898.6	−	10823.2i	0.488266	−	0.409704i	−0.365139	−	0.930953i	$-0.618978\pi$
$887$	12898.6	−	10823.2i	0.488266	−	0.409704i	0.853404	+	0.521250i	$0.174534\pi$
$888$		0			0
$889$	−35974.8	+	13093.8i	−1.35721	+	0.493983i
$890$	−27656.2			−1.04162
$891$		0			0
$892$	18299.8			0.686909
$893$	21107.3	−	7682.42i	0.790961	−	0.287886i
$894$		0			0
$895$	−1840.45	+	1544.32i	−0.0687367	+	0.0576769i
$896$	−579.820	−	3288.32i	−0.0216188	−	0.122606i
$897$		0			0
$898$	−17281.5	−	14500.9i	−0.642194	−	0.538865i
$899$	−17504.2	+	30318.1i	−0.649385	+	1.12477i
$900$		0			0
$901$	1214.14	+	2102.96i	0.0448934	+	0.0777577i
$902$	−6684.66	+	37910.6i	−0.246757	+	1.39943i
$903$		0			0
$904$	3775.61	+	1374.21i	0.138910	+	0.0505592i
$905$	47034.3	+	17119.1i	1.72759	+	0.628793i
$906$		0			0
$907$	−3959.61	+	22456.1i	−0.144958	+	0.822096i	0.822443	+	0.568847i	$0.192610\pi$
$907$	−3959.61	+	22456.1i	−0.144958	+	0.822096i	−0.967401	+	0.253249i	$0.918501\pi$
$908$	10191.0	+	17651.2i	0.372465	+	0.645129i
$909$		0			0
$910$	4788.32	−	8293.62i	0.174430	−	0.302122i
$911$	25939.9	+	21766.1i	0.943387	+	0.791596i	0.978172	−	0.207799i	$-0.0666300\pi$
$911$	25939.9	+	21766.1i	0.943387	+	0.791596i	−0.0347844	+	0.999395i	$0.511074\pi$
$912$		0			0
$913$	177.894	+	1008.89i	0.00644844	+	0.0365709i
$914$	−24403.2	+	20476.7i	−0.883134	+	0.741037i
$915$		0			0
$916$	−1573.43	+	572.682i	−0.0567551	+	0.0206572i
$917$	34547.9			1.24414
$918$		0			0
$919$	−22106.5			−0.793501			−0.396750	−	0.917927i	$-0.629862\pi$
$919$	−22106.5			−0.793501			−0.396750	+	0.917927i	$0.629862\pi$
$920$	−7417.22	+	2699.65i	−0.265803	+	0.0967443i
$921$		0			0
$922$	−1974.66	+	1656.94i	−0.0705336	+	0.0591847i
$923$	352.945	+	2001.65i	0.0125865	+	0.0713816i
$924$		0			0
$925$	−11321.2	−	9499.57i	−0.402419	−	0.337669i
$926$	41.5455	−	71.9589i	0.00147437	−	0.00255369i
$927$		0			0
$928$	2392.65	+	4144.19i	0.0846363	+	0.146594i
$929$	8676.21	−	49205.2i	0.306412	−	1.73775i	−0.310369	−	0.950616i	$-0.600452\pi$
$929$	8676.21	−	49205.2i	0.306412	−	1.73775i	0.616781	−	0.787135i	$-0.288436\pi$
$930$		0			0
$931$	−12263.8	−	4463.64i	−0.431717	−	0.157132i
$932$	−7066.62	−	2572.04i	−0.248364	−	0.0903970i
$933$		0			0
$934$	−1592.27	+	9030.21i	−0.0557823	+	0.316357i
$935$	26813.1	+	46441.7i	0.937844	+	1.62439i
$936$		0			0
$937$	−11796.8	+	20432.7i	−0.411298	+	0.712388i	−0.995032	−	0.0995564i	$-0.968258\pi$
$937$	−11796.8	+	20432.7i	−0.411298	+	0.712388i	0.583734	+	0.811945i	$0.301591\pi$
$938$	−22991.5	−	19292.2i	−0.800320	−	0.671548i
$939$		0			0
$940$	7096.40	+	40245.7i	0.246233	+	1.39646i
$941$	37871.9	−	31778.3i	1.31200	−	1.10090i	0.324059	−	0.946037i	$-0.394952\pi$
$941$	37871.9	−	31778.3i	1.31200	−	1.10090i	0.987937	−	0.154858i	$-0.0494921\pi$
$942$		0			0
$943$	15060.9	−	5481.71i	0.520095	−	0.189299i
$944$	4298.00			0.148186
$945$		0			0
$946$	−20974.2			−0.720857
$947$	1547.77	−	563.344i	0.0531108	−	0.0193307i	−0.315328	−	0.948983i	$-0.602115\pi$
$947$	1547.77	−	563.344i	0.0531108	−	0.0193307i	0.368439	+	0.929652i	$0.379892\pi$
$948$		0			0
$949$	−1985.41	+	1665.96i	−0.0679128	+	0.0569856i
$950$	2475.88	+	14041.4i	0.0845561	+	0.479541i
$951$		0			0
$952$	7235.27	+	6071.11i	0.246320	+	0.206687i
$953$	−12756.7	+	22095.3i	−0.433611	+	0.751037i	−0.997181	−	0.0750316i	$-0.976094\pi$
$953$	−12756.7	+	22095.3i	−0.433611	+	0.751037i	0.563570	+	0.826068i	$0.309428\pi$
$954$		0			0
$955$	−43959.3	−	76139.8i	−1.48952	−	2.57992i
$956$	−2779.44	+	15763.0i	−0.0940307	+	0.533275i
$957$		0			0
$958$	7764.88	+	2826.18i	0.261870	+	0.0953130i
$959$	8422.85	+	3065.67i	0.283616	+	0.103228i
$960$		0			0
$961$	4343.77	−	24634.7i	0.145808	−	0.826918i
$962$	−836.595	−	1449.02i	−0.0280384	−	0.0485639i
$963$		0			0
$964$	4778.66	−	8276.89i	0.159658	−	0.276536i
$965$	−57850.9	−	48542.7i	−1.92983	−	1.61932i
$966$		0			0
$967$	−7518.20	−	42637.9i	−0.250020	−	1.41793i	−0.808540	−	0.588442i	$-0.799742\pi$
$967$	−7518.20	−	42637.9i	−0.250020	−	1.41793i	0.558520	−	0.829491i	$-0.311369\pi$
$968$	19655.9	−	16493.2i	0.652648	−	0.547636i
$969$		0			0
$970$	−3082.28	+	1121.86i	−0.102027	+	0.0371348i
$971$	−43297.6			−1.43098			−0.715492	−	0.698621i	$-0.753798\pi$
$971$	−43297.6			−1.43098			−0.715492	+	0.698621i	$0.753798\pi$
$972$		0			0
$973$	71491.9			2.35552
$974$	22969.1	−	8360.06i	0.755623	−	0.275024i
$975$		0			0
$976$	−1654.07	+	1387.93i	−0.0542473	+	0.0455189i
$977$	3658.96	+	20751.0i	0.119816	+	0.679511i	0.984252	+	0.176769i	$0.0565644\pi$
$977$	3658.96	+	20751.0i	0.119816	+	0.679511i	−0.864436	+	0.502742i	$0.832324\pi$
$978$		0			0
$979$	−40572.9	−	34044.7i	−1.32453	−	1.11141i
$980$	11872.2	−	20563.2i	0.386982	−	0.670272i
$981$		0			0
$982$	8453.35	+	14641.6i	0.274702	+	0.475798i
$983$	805.909	−	4570.54i	0.0261490	−	0.148299i	−0.968938	−	0.247305i	$-0.920455\pi$
$983$	805.909	−	4570.54i	0.0261490	−	0.148299i	0.995087	+	0.0990060i	$0.0315663\pi$
$984$		0			0
$985$	−90242.0	−	32845.4i	−2.91914	−	1.06248i
$986$	−12719.6	−	4629.54i	−0.410825	−	0.149528i
$987$		0			0
$988$	−280.310	+	1589.72i	−0.00902617	+	0.0511899i
$989$	4366.28	+	7562.62i	0.140384	+	0.243152i
$990$		0			0
$991$	26697.7	−	46241.8i	0.855782	−	1.48226i	−0.0201352	−	0.999797i	$-0.506410\pi$
$991$	26697.7	−	46241.8i	0.855782	−	1.48226i	0.875917	−	0.482461i	$-0.160257\pi$
$992$	−5738.75	−	4815.38i	−0.183675	−	0.154121i
$993$		0			0
$994$	1764.45	+	10006.7i	0.0563029	+	0.319310i
$995$	−43880.6	+	36820.2i	−1.39810	+	1.17314i
$996$		0			0
$997$	−10141.5	+	3691.19i	−0.322150	+	0.117253i	−0.498033	−	0.867158i	$-0.665944\pi$
$997$	−10141.5	+	3691.19i	−0.322150	+	0.117253i	0.175883	+	0.984411i	$0.443722\pi$
$998$	20119.5			0.638147
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.19.1		30
3.2	odd	2		54.4.e.b.7.5	✓	30
27.2	odd	18		1458.4.a.i.1.14		15
27.4	even	9	inner	162.4.e.b.145.1		30
27.23	odd	18		54.4.e.b.31.5	yes	30
27.25	even	9		1458.4.a.j.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.7.5	✓	30	3.2	odd	2
54.4.e.b.31.5	yes	30	27.23	odd	18
162.4.e.b.19.1		30	1.1	even	1	trivial
162.4.e.b.145.1		30	27.4	even	9	inner
1458.4.a.i.1.14		15	27.2	odd	18
1458.4.a.j.1.2		15	27.25	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)

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-3.05422 - 17.3214i) q^{5} +(-19.9833 - 16.7680i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-3.05422 - 17.3214i) q^{5} +(-19.9833 - 16.7680i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(17.5886 + 30.4643i) q^{10} +(-11.6982 + 66.3439i) q^{11} +(9.80676 + 3.56937i) q^{13} +(49.0263 + 17.8441i) q^{14} +(2.77837 - 15.7569i) q^{16} +(22.6291 + 39.1948i) q^{17} +(-19.3348 + 33.4888i) q^{19} +(-53.8945 - 45.2229i) q^{20} +(-23.3964 - 132.688i) q^{22} +(-42.9723 + 36.0581i) q^{23} +(-173.240 + 63.0541i) q^{25} -20.8723 q^{26} -104.345 q^{28} +(140.522 - 51.1459i) q^{29} +(-179.336 + 150.481i) q^{31} +(5.55674 + 31.5138i) q^{32} +(-69.3397 - 58.1829i) q^{34} +(-229.411 + 397.351i) q^{35} +(40.0816 + 69.4234i) q^{37} +(13.4298 - 76.1641i) q^{38} +(132.223 + 48.1252i) q^{40} +(-268.482 - 97.7195i) q^{41} +(27.0319 - 153.306i) q^{43} +(134.735 + 233.367i) q^{44} +(56.0964 - 97.1618i) q^{46} +(-444.971 - 373.375i) q^{47} +(58.6056 + 332.369i) q^{49} +(282.452 - 237.006i) q^{50} +(39.2271 - 14.2775i) q^{52} +53.6540 q^{53} +1184.90 q^{55} +(196.105 - 71.3764i) q^{56} +(-229.109 + 192.246i) q^{58} +(46.6462 + 264.544i) q^{59} +(-103.379 - 86.7454i) q^{61} +(234.106 - 405.484i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(31.8743 - 180.768i) q^{65} +(-540.576 - 196.754i) q^{67} +(170.115 + 61.9169i) q^{68} +(159.347 - 903.701i) q^{70} +(97.3794 + 168.666i) q^{71} +(-124.173 + 215.074i) q^{73} +(-122.817 - 103.056i) q^{74} +(26.8596 + 152.328i) q^{76} +(1346.22 - 1129.61i) q^{77} +(53.9300 - 19.6289i) q^{79} -281.417 q^{80} +571.426 q^{82} +(14.2898 - 5.20107i) q^{83} +(609.793 - 511.677i) q^{85} +(54.0638 + 306.611i) q^{86} +(-412.851 - 346.423i) q^{88} +(-393.099 + 680.868i) q^{89} +(-136.120 - 235.767i) q^{91} +(-38.9642 + 220.977i) q^{92} +(1091.67 + 397.337i) q^{94} +(639.124 + 232.622i) q^{95} +(-16.1918 + 91.8285i) q^{97} +(-337.496 - 584.561i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more