LMFDB - Embedded newform 432.2.y.e.253.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.4
Character	$\chi$	$=$	432.253
Dual form			432.2.y.e.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24122 + 0.677764i) q^{2} +(1.08127 - 1.68251i) q^{4} +(-1.10094 - 4.10876i) q^{5} +(1.63313 - 0.942891i) q^{7} +(-0.201751 + 2.82122i) q^{8} +O(q^{10})$	\(q+(-1.24122 + 0.677764i) q^{2} +(1.08127 - 1.68251i) q^{4} +(-1.10094 - 4.10876i) q^{5} +(1.63313 - 0.942891i) q^{7} +(-0.201751 + 2.82122i) q^{8} +(4.15129 + 4.35372i) q^{10} +(1.18389 + 0.317223i) q^{11} +(-2.31428 + 0.620109i) q^{13} +(-1.38803 + 2.27722i) q^{14} +(-1.66171 - 3.63851i) q^{16} -3.44622 q^{17} +(-4.17726 - 4.17726i) q^{19} +(-8.10347 - 2.59034i) q^{20} +(-1.68448 + 0.408656i) q^{22} +(1.34867 + 0.778655i) q^{23} +(-11.3397 + 6.54701i) q^{25} +(2.45225 - 2.33823i) q^{26} +(0.179434 - 3.76729i) q^{28} +(0.343336 - 1.28135i) q^{29} +(1.25840 - 2.17961i) q^{31} +(4.52860 + 3.38996i) q^{32} +(4.27753 - 2.33572i) q^{34} +(-5.67210 - 5.67210i) q^{35} +(5.77154 - 5.77154i) q^{37} +(8.01610 + 2.35371i) q^{38} +(11.8139 - 2.27705i) q^{40} +(3.43245 + 1.98173i) q^{41} +(-2.96053 - 0.793272i) q^{43} +(1.81384 - 1.64891i) q^{44} +(-2.20175 - 0.0524044i) q^{46} +(-0.230692 - 0.399570i) q^{47} +(-1.72191 + 2.98244i) q^{49} +(9.63783 - 15.8120i) q^{50} +(-1.45902 + 4.56431i) q^{52} +(-5.61507 + 5.61507i) q^{53} -5.21358i q^{55} +(2.33062 + 4.79766i) q^{56} +(0.442294 + 1.82314i) q^{58} +(-2.92766 - 10.9262i) q^{59} +(1.27078 - 4.74261i) q^{61} +(-0.0846915 + 3.55828i) q^{62} +(-7.91859 - 1.13837i) q^{64} +(5.09576 + 8.82612i) q^{65} +(0.286572 - 0.0767867i) q^{67} +(-3.72630 + 5.79831i) q^{68} +(10.8847 + 3.19600i) q^{70} -13.9935i q^{71} -0.0279090i q^{73} +(-3.25203 + 11.0755i) q^{74} +(-11.5450 + 2.51154i) q^{76} +(2.23256 - 0.598214i) q^{77} +(2.19067 + 3.79435i) q^{79} +(-13.1203 + 10.8333i) q^{80} +(-5.60358 - 0.133372i) q^{82} +(0.915902 - 3.41819i) q^{83} +(3.79408 + 14.1597i) q^{85} +(4.21233 - 1.02191i) q^{86} +(-1.13381 + 3.27603i) q^{88} -4.74894i q^{89} +(-3.19483 + 3.19483i) q^{91} +(2.76838 - 1.42722i) q^{92} +(0.557154 + 0.339601i) q^{94} +(-12.5645 + 21.7623i) q^{95} +(4.17352 + 7.22875i) q^{97} +(0.115887 - 4.86893i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.24122	+	0.677764i	−0.877677	+	0.479252i
$2$	−1.24122	+	0.677764i	−0.877677	+	0.479252i
$3$		0			0
$3$		0			0
$4$	1.08127	−	1.68251i	0.540636	−	0.841257i
$5$	−1.10094	−	4.10876i	−0.492355	−	1.83750i	−0.544365	−	0.838849i	$-0.683229\pi$
$5$	−1.10094	−	4.10876i	−0.492355	−	1.83750i	0.0520092	−	0.998647i	$-0.483437\pi$
$6$		0			0
$7$	1.63313	−	0.942891i	0.617267	−	0.356379i	−0.158537	−	0.987353i	$-0.550678\pi$
$7$	1.63313	−	0.942891i	0.617267	−	0.356379i	0.775804	+	0.630974i	$0.217344\pi$
$8$	−0.201751	+	2.82122i	−0.0713297	+	0.997453i
$9$		0			0
$10$	4.15129	+	4.35372i	1.31275	+	1.37677i
$11$	1.18389	+	0.317223i	0.356957	+	0.0956464i	0.432841	−	0.901470i	$-0.357511\pi$
$11$	1.18389	+	0.317223i	0.356957	+	0.0956464i	−0.0758838	+	0.997117i	$0.524178\pi$
$12$		0			0
$13$	−2.31428	+	0.620109i	−0.641865	+	0.171987i	−0.565048	−	0.825058i	$-0.691142\pi$
$13$	−2.31428	+	0.620109i	−0.641865	+	0.171987i	−0.0768171	+	0.997045i	$0.524476\pi$
$14$	−1.38803	+	2.27722i	−0.370966	+	0.608612i
$15$		0			0
$16$	−1.66171	−	3.63851i	−0.415426	−	0.909627i
$17$	−3.44622			−0.835831			−0.417915	−	0.908486i	$-0.637239\pi$
$17$	−3.44622			−0.835831			−0.417915	+	0.908486i	$0.637239\pi$
$18$		0			0
$19$	−4.17726	−	4.17726i	−0.958328	−	0.958328i	0.0408377	−	0.999166i	$-0.486997\pi$
$19$	−4.17726	−	4.17726i	−0.958328	−	0.958328i	−0.999166	+	0.0408377i	$0.986997\pi$
$20$	−8.10347	−	2.59034i	−1.81199	−	0.579218i
$21$		0			0
$22$	−1.68448	+	0.408656i	−0.359132	+	0.0871257i
$23$	1.34867	+	0.778655i	0.281217	+	0.162361i	0.633974	−	0.773354i	$-0.281422\pi$
$23$	1.34867	+	0.778655i	0.281217	+	0.162361i	−0.352757	+	0.935715i	$0.614756\pi$
$24$		0			0
$25$	−11.3397	+	6.54701i	−2.26795	+	1.30940i
$26$	2.45225	−	2.33823i	0.480925	−	0.458564i
$27$		0			0
$28$	0.179434	−	3.76729i	0.0339099	−	0.711951i
$29$	0.343336	−	1.28135i	0.0637558	−	0.237940i	−0.926693	−	0.375818i	$-0.877362\pi$
$29$	0.343336	−	1.28135i	0.0637558	−	0.237940i	0.990449	+	0.137878i	$0.0440283\pi$
$30$		0			0
$31$	1.25840	−	2.17961i	0.226015	−	0.391469i	−0.730609	−	0.682796i	$-0.760764\pi$
$31$	1.25840	−	2.17961i	0.226015	−	0.391469i	0.956623	+	0.291327i	$0.0940969\pi$
$32$	4.52860	+	3.38996i	0.800551	+	0.599265i
$33$		0			0
$34$	4.27753	−	2.33572i	0.733590	−	0.400573i
$35$	−5.67210	−	5.67210i	−0.958760	−	0.958760i
$36$		0			0
$37$	5.77154	−	5.77154i	0.948836	−	0.948836i	−0.0499178	−	0.998753i	$-0.515896\pi$
$37$	5.77154	−	5.77154i	0.948836	−	0.948836i	0.998753	+	0.0499178i	$0.0158959\pi$
$38$	8.01610	+	2.35371i	1.30038	+	0.381823i
$39$		0			0
$40$	11.8139	−	2.27705i	1.86793	−	0.360033i
$41$	3.43245	+	1.98173i	0.536058	+	0.309493i	0.743480	−	0.668758i	$-0.233174\pi$
$41$	3.43245	+	1.98173i	0.536058	+	0.309493i	−0.207422	+	0.978252i	$0.566507\pi$
$42$		0			0
$43$	−2.96053	−	0.793272i	−0.451477	−	0.120973i	0.0259136	−	0.999664i	$-0.491751\pi$
$43$	−2.96053	−	0.793272i	−0.451477	−	0.120973i	−0.477390	+	0.878691i	$0.658417\pi$
$44$	1.81384	−	1.64891i	0.273447	−	0.248583i
$45$		0			0
$46$	−2.20175	−	0.0524044i	−0.324630	−	0.00772660i
$47$	−0.230692	−	0.399570i	−0.0336498	−	0.0582832i	0.848710	−	0.528858i	$-0.177380\pi$
$47$	−0.230692	−	0.399570i	−0.0336498	−	0.0582832i	−0.882360	+	0.470575i	$0.844046\pi$
$48$		0			0
$49$	−1.72191	+	2.98244i	−0.245988	+	0.426063i
$50$	9.63783	−	15.8120i	1.36300	−	2.23615i
$51$		0			0
$52$	−1.45902	+	4.56431i	−0.202330	+	0.632956i
$53$	−5.61507	+	5.61507i	−0.771289	+	0.771289i	−0.978332	−	0.207043i	$-0.933616\pi$
$53$	−5.61507	+	5.61507i	−0.771289	+	0.771289i	0.207043	+	0.978332i	$0.433616\pi$
$54$		0			0
$55$		−	5.21358i		−	0.702999i
$56$	2.33062	+	4.79766i	0.311442	+	0.641115i
$57$		0			0
$58$	0.442294	+	1.82314i	0.0580761	+	0.239390i
$59$	−2.92766	−	10.9262i	−0.381148	−	1.42247i	−0.844150	−	0.536108i	$-0.819894\pi$
$59$	−2.92766	−	10.9262i	−0.381148	−	1.42247i	0.463001	−	0.886358i	$-0.346773\pi$
$60$		0			0
$61$	1.27078	−	4.74261i	0.162707	−	0.607229i	−0.835615	−	0.549316i	$-0.814888\pi$
$61$	1.27078	−	4.74261i	0.162707	−	0.607229i	0.998322	−	0.0579138i	$-0.0184448\pi$
$62$	−0.0846915	+	3.55828i	−0.0107558	+	0.451902i
$63$		0			0
$64$	−7.91859	−	1.13837i	−0.989824	−	0.142296i
$65$	5.09576	+	8.82612i	0.632052	+	1.09475i
$66$		0			0
$67$	0.286572	−	0.0767867i	0.0350103	−	0.00938099i	−0.241271	−	0.970458i	$-0.577564\pi$
$67$	0.286572	−	0.0767867i	0.0350103	−	0.00938099i	0.276282	+	0.961077i	$0.410898\pi$
$68$	−3.72630	+	5.79831i	−0.451880	+	0.703148i
$69$		0			0
$70$	10.8847	+	3.19600i	1.30097	+	0.381995i
$71$		−	13.9935i		−	1.66073i	−0.557221	−	0.830364i	$-0.688133\pi$
$71$		−	13.9935i		−	1.66073i	0.557221	−	0.830364i	$-0.311867\pi$
$72$		0			0
$73$		−	0.0279090i		−	0.00326650i	−0.999999	−	0.00163325i	$-0.999480\pi$
$73$		−	0.0279090i		−	0.00326650i	0.999999	−	0.00163325i	$-0.000519880\pi$
$74$	−3.25203	+	11.0755i	−0.378040	+	1.28750i
$75$		0			0
$76$	−11.5450	+	2.51154i	−1.32431	+	0.288094i
$77$	2.23256	−	0.598214i	0.254424	−	0.0681728i
$78$		0			0
$79$	2.19067	+	3.79435i	0.246470	+	0.426898i	0.962544	−	0.271126i	$-0.0873960\pi$
$79$	2.19067	+	3.79435i	0.246470	+	0.426898i	−0.716074	+	0.698024i	$0.754063\pi$
$80$	−13.1203	+	10.8333i	−1.46690	+	1.21120i
$81$		0			0
$82$	−5.60358	−	0.133372i	−0.618812	−	0.0147285i
$83$	0.915902	−	3.41819i	0.100533	−	0.375195i	−0.897267	−	0.441489i	$-0.854451\pi$
$83$	0.915902	−	3.41819i	0.100533	−	0.375195i	0.997800	+	0.0662931i	$0.0211172\pi$
$84$		0			0
$85$	3.79408	+	14.1597i	0.411526	+	1.53584i
$86$	4.21233	−	1.02191i	0.454227	−	0.110196i
$87$		0			0
$88$	−1.13381	+	3.27603i	−0.120864	+	0.349226i
$89$		−	4.74894i		−	0.503386i	−0.967807	−	0.251693i	$-0.919013\pi$
$89$		−	4.74894i		−	0.503386i	0.967807	−	0.251693i	$-0.0809874\pi$
$90$		0			0
$91$	−3.19483	+	3.19483i	−0.334909	+	0.334909i
$92$	2.76838	−	1.42722i	0.288623	−	0.148798i
$93$		0			0
$94$	0.557154	+	0.339601i	0.0574660	+	0.0350271i
$95$	−12.5645	+	21.7623i	−1.28909	+	2.23276i
$96$		0			0
$97$	4.17352	+	7.22875i	0.423757	+	0.733968i	0.996303	−	0.0859041i	$-0.0273779\pi$
$97$	4.17352	+	7.22875i	0.423757	+	0.733968i	−0.572547	+	0.819872i	$0.694045\pi$
$98$	0.115887	−	4.86893i	0.0117063	−	0.491836i
$99$		0			0
$100$	−1.24591	+	26.1584i	−0.124591	+	2.61584i
$101$	7.20785	+	1.93134i	0.717208	+	0.192175i	0.598926	−	0.800805i	$-0.295594\pi$
$101$	7.20785	+	1.93134i	0.717208	+	0.192175i	0.118282	+	0.992980i	$0.462261\pi$
$102$		0			0
$103$	12.2204	+	7.05547i	1.20411	+	0.695196i	0.961468	−	0.274919i	$-0.0886509\pi$
$103$	12.2204	+	7.05547i	1.20411	+	0.695196i	0.242647	+	0.970115i	$0.421984\pi$
$104$	−1.28256	−	6.65420i	−0.125765	−	0.652498i
$105$		0			0
$106$	3.16386	−	10.7753i	0.307302	−	1.04659i
$107$	3.84992	−	3.84992i	0.372186	−	0.372186i	−0.496087	−	0.868273i	$-0.665230\pi$
$107$	3.84992	−	3.84992i	0.372186	−	0.372186i	0.868273	+	0.496087i	$0.165230\pi$
$108$		0			0
$109$	2.08616	+	2.08616i	0.199818	+	0.199818i	0.799922	−	0.600104i	$-0.204874\pi$
$109$	2.08616	+	2.08616i	0.199818	+	0.199818i	−0.600104	+	0.799922i	$0.704874\pi$
$110$	3.53358	+	6.47122i	0.336914	+	0.617007i
$111$		0			0
$112$	−6.14450	−	4.37536i	−0.580601	−	0.413433i
$113$	2.04799	−	3.54722i	0.192658	−	0.333694i	−0.753472	−	0.657480i	$-0.771622\pi$
$113$	2.04799	−	3.54722i	0.192658	−	0.333694i	0.946130	+	0.323786i	$0.104956\pi$
$114$		0			0
$115$	1.71451	−	6.39862i	0.159878	−	0.596674i
$116$	−1.78464	−	1.96315i	−0.165700	−	0.182274i
$117$		0			0
$118$	11.0392	+	11.5775i	1.01624	+	1.06580i
$119$	−5.62814	+	3.24941i	−0.515931	+	0.297873i
$120$		0			0
$121$	−8.22531	−	4.74888i	−0.747755	−	0.431717i
$122$	1.63705	+	6.74793i	0.148212	+	0.610929i
$123$		0			0
$124$	−2.30655	−	4.47402i	−0.207134	−	0.401779i
$125$	24.3454	+	24.3454i	2.17752	+	2.17752i
$126$		0			0
$127$	4.89832			0.434656			0.217328	−	0.976099i	$-0.430266\pi$
$127$	4.89832			0.434656			0.217328	+	0.976099i	$0.430266\pi$
$128$	10.6003	−	3.95397i	0.936942	−	0.349485i
$129$		0			0
$130$	−12.3070	−	7.50146i	−1.07940	−	0.657922i
$131$	17.7751	−	4.76283i	1.55302	−	0.416130i	0.622574	−	0.782561i	$-0.286087\pi$
$131$	17.7751	−	4.76283i	1.55302	−	0.416130i	0.930446	+	0.366430i	$0.119420\pi$
$132$		0			0
$133$	−10.7607	−	2.88332i	−0.933072	−	0.250016i
$134$	−0.303657	+	0.289538i	−0.0262319	+	0.0250123i
$135$		0			0
$136$	0.695278	−	9.72255i	0.0596196	−	0.833702i
$137$	−13.4198	+	7.74793i	−1.14653	+	0.661950i	−0.948040	−	0.318153i	$-0.896938\pi$
$137$	−13.4198	+	7.74793i	−1.14653	+	0.661950i	−0.198492	+	0.980103i	$0.563604\pi$
$138$		0			0
$139$	−1.90836	−	7.12209i	−0.161865	−	0.604088i	−0.998419	−	0.0562039i	$-0.982100\pi$
$139$	−1.90836	−	7.12209i	−0.161865	−	0.604088i	0.836555	−	0.547884i	$-0.184566\pi$
$140$	−15.6765	+	3.41031i	−1.32490	+	0.288224i
$141$		0			0
$142$	9.48432	+	17.3691i	0.795907	+	1.45758i
$143$	−2.93657			−0.245568
$144$		0			0
$145$	−5.64274			−0.468604
$146$	0.0189157	+	0.0346413i	0.00156548	+	0.00286694i
$147$		0			0
$148$	−3.47010	−	15.9513i	−0.285240	−	1.31119i
$149$	1.99897	+	7.46026i	0.163762	+	0.611168i	0.998195	+	0.0600585i	$0.0191287\pi$
$149$	1.99897	+	7.46026i	0.163762	+	0.611168i	−0.834433	+	0.551110i	$0.814205\pi$
$150$		0			0
$151$	3.36540	−	1.94301i	0.273872	−	0.158120i	−0.356774	−	0.934191i	$-0.616123\pi$
$151$	3.36540	−	1.94301i	0.273872	−	0.158120i	0.630646	+	0.776071i	$0.282790\pi$
$152$	12.6277	−	10.9422i	1.02424	−	0.887530i
$153$		0			0
$154$	−2.36566	+	2.25567i	−0.190631	+	0.181767i
$155$	−10.3409	−	2.77084i	−0.830602	−	0.222559i
$156$		0			0
$157$	6.23351	−	1.67026i	0.497488	−	0.133302i	−0.00134577	−	0.999999i	$-0.500428\pi$
$157$	6.23351	−	1.67026i	0.497488	−	0.133302i	0.498834	+	0.866698i	$0.333762\pi$
$158$	−5.29079	−	3.22488i	−0.420913	−	0.256558i
$159$		0			0
$160$	8.94281	−	22.3391i	0.706991	−	1.76606i
$161$	2.93675			0.231448
$162$		0			0
$163$	10.5783	+	10.5783i	0.828556	+	0.828556i	0.987317	−	0.158761i	$-0.0507499\pi$
$163$	10.5783	+	10.5783i	0.828556	+	0.828556i	−0.158761	+	0.987317i	$0.550750\pi$
$164$	7.04569	−	3.63236i	0.550176	−	0.283640i
$165$		0			0
$166$	1.17989	+	4.86351i	0.0915773	+	0.377481i
$167$	18.7147	+	10.8050i	1.44819	+	0.836112i	0.998374	−	0.0570092i	$-0.0181564\pi$
$167$	18.7147	+	10.8050i	1.44819	+	0.836112i	0.449815	+	0.893122i	$0.351490\pi$
$168$		0			0
$169$	−6.28698	+	3.62979i	−0.483614	+	0.279215i
$170$	−14.3062	−	15.0039i	−1.09724	−	1.15074i
$171$		0			0
$172$	−4.53583	+	4.12339i	−0.345854	+	0.314406i
$173$	5.00981	−	18.6969i	0.380889	−	1.42150i	−0.463657	−	0.886015i	$-0.653463\pi$
$173$	5.00981	−	18.6969i	0.380889	−	1.42150i	0.844546	−	0.535483i	$-0.179870\pi$
$174$		0			0
$175$	−12.3462	+	21.3843i	−0.933287	+	1.61650i
$176$	−0.813064	−	4.83474i	−0.0612870	−	0.364432i
$177$		0			0
$178$	3.21866	+	5.89449i	0.241249	+	0.441811i
$179$	2.88152	+	2.88152i	0.215375	+	0.215375i	0.806546	−	0.591171i	$-0.201334\pi$
$179$	2.88152	+	2.88152i	0.215375	+	0.215375i	−0.591171	+	0.806546i	$0.701334\pi$
$180$		0			0
$181$	−9.50186	+	9.50186i	−0.706268	+	0.706268i	−0.965748	−	0.259480i	$-0.916449\pi$
$181$	−9.50186	+	9.50186i	−0.706268	+	0.706268i	0.259480	+	0.965748i	$0.416449\pi$
$182$	1.80016	−	6.13084i	0.133437	−	0.454448i
$183$		0			0
$184$	−2.46885	+	3.64780i	−0.182006	+	0.268920i
$185$	−30.0680	−	17.3598i	−2.21065	−	1.27632i
$186$		0			0
$187$	−4.07996	−	1.09322i	−0.298356	−	0.0799442i
$188$	−0.921721	−	0.0439012i	−0.0672234	−	0.00320182i
$189$		0			0
$190$	0.845602	−	35.5276i	0.0613464	−	2.57744i
$191$	−2.36417	−	4.09487i	−0.171066	−	0.296294i	0.767727	−	0.640777i	$-0.221388\pi$
$191$	−2.36417	−	4.09487i	−0.171066	−	0.296294i	−0.938793	+	0.344483i	$0.888054\pi$
$192$		0			0
$193$	9.76542	−	16.9142i	0.702931	−	1.21751i	−0.264503	−	0.964385i	$-0.585208\pi$
$193$	9.76542	−	16.9142i	0.702931	−	1.21751i	0.967433	−	0.253127i	$-0.0814589\pi$
$194$	−10.0797	−	6.14383i	−0.723677	−	0.441101i
$195$		0			0
$196$	3.15615	+	6.12198i	0.225439	+	0.437284i
$197$	−6.89966	+	6.89966i	−0.491581	+	0.491581i	−0.908804	−	0.417223i	$-0.863003\pi$
$197$	−6.89966	+	6.89966i	−0.491581	+	0.491581i	0.417223	+	0.908804i	$0.363003\pi$
$198$		0			0
$199$		−	24.4752i		−	1.73500i	−0.497438	−	0.867500i	$-0.665726\pi$
$199$		−	24.4752i		−	1.73500i	0.497438	−	0.867500i	$-0.334274\pi$
$200$	−16.1828	−	33.3128i	−1.14429	−	2.35557i
$201$		0			0
$202$	−10.2555	+	2.48800i	−0.721578	+	0.175055i
$203$	−0.647456	−	2.41634i	−0.0454425	−	0.169594i
$204$		0			0
$205$	4.36352	−	16.2849i	0.304762	−	1.13739i
$206$	−19.9502	−	0.474841i	−1.39000	−	0.0330837i
$207$		0			0
$208$	6.10192	+	7.39008i	0.423092	+	0.512410i
$209$	−3.62030	−	6.27055i	−0.250422	−	0.433743i
$210$		0			0
$211$	21.1840	−	5.67623i	1.45837	−	0.390768i	0.559441	−	0.828870i	$-0.311016\pi$
$211$	21.1840	−	5.67623i	1.45837	−	0.390768i	0.898925	+	0.438102i	$0.144349\pi$
$212$	3.37602	+	15.5189i	0.231866	+	1.06584i
$213$		0			0
$214$	−2.16927	+	7.38795i	−0.148288	+	0.505030i
$215$			13.0375i			0.889148i
$216$		0			0
$217$		−	4.74612i		−	0.322188i
$218$	−4.00332	−	1.17547i	−0.271139	−	0.0796126i
$219$		0			0
$220$	−8.77193	−	5.63730i	−0.591403	−	0.380066i
$221$	7.97551	−	2.13703i	0.536491	−	0.143752i
$222$		0			0
$223$	−1.56986	−	2.71908i	−0.105126	−	0.182083i	0.808664	−	0.588271i	$-0.200191\pi$
$223$	−1.56986	−	2.71908i	−0.105126	−	0.182083i	−0.913790	+	0.406188i	$0.866858\pi$
$224$	10.5922	+	1.26628i	0.707719	+	0.0846068i
$225$		0			0
$226$	−0.137832	+	5.79094i	−0.00916844	+	0.385208i
$227$	−3.64479	+	13.6026i	−0.241913	+	0.902833i	0.732996	+	0.680233i	$0.238121\pi$
$227$	−3.64479	+	13.6026i	−0.241913	+	0.902833i	−0.974910	+	0.222601i	$0.928545\pi$
$228$		0			0
$229$	−4.91218	−	18.3325i	−0.324606	−	1.21145i	−0.914707	−	0.404117i	$-0.867579\pi$
$229$	−4.91218	−	18.3325i	−0.324606	−	1.21145i	0.590101	−	0.807330i	$-0.299088\pi$
$230$	2.20867	+	9.10415i	0.145636	+	0.600310i
$231$		0			0
$232$	3.54569	+	1.22714i	0.232786	+	0.0805656i
$233$			12.6802i			0.830708i	0.909660	+	0.415354i	$0.136342\pi$
$233$			12.6802i			0.830708i	−0.909660	+	0.415354i	$0.863658\pi$
$234$		0			0
$235$	−1.38776	+	1.38776i	−0.0905275	+	0.0905275i
$236$	−21.5490	−	6.88832i	−1.40272	−	0.448391i
$237$		0			0
$238$	4.78344	−	7.84779i	0.310065	−	0.508697i
$239$	3.69405	−	6.39829i	0.238948	−	0.413871i	−0.721464	−	0.692451i	$-0.756531\pi$
$239$	3.69405	−	6.39829i	0.238948	−	0.413871i	0.960413	+	0.278581i	$0.0898640\pi$
$240$		0			0
$241$	11.1955	+	19.3912i	0.721167	+	1.24910i	0.960533	+	0.278168i	$0.0897271\pi$
$241$	11.1955	+	19.3912i	0.721167	+	1.24910i	−0.239366	+	0.970929i	$0.576940\pi$
$242$	13.4281	+	0.319605i	0.863189	+	0.0205450i
$243$		0			0
$244$	−6.60546	−	7.26615i	−0.422871	−	0.465168i
$245$	14.1499	+	3.79145i	0.904003	+	0.242227i
$246$		0			0
$247$	12.2577	+	7.07698i	0.779938	+	0.450297i
$248$	5.89527	+	3.98996i	0.374350	+	0.253362i
$249$		0			0
$250$	−46.7185	−	13.7176i	−2.95474	−	0.867579i
$251$	7.52339	−	7.52339i	0.474872	−	0.474872i	−0.428615	−	0.903487i	$-0.640998\pi$
$251$	7.52339	−	7.52339i	0.474872	−	0.474872i	0.903487	+	0.428615i	$0.140998\pi$
$252$		0			0
$253$	1.34967	+	1.34967i	0.0848533	+	0.0848533i
$254$	−6.07991	+	3.31991i	−0.381487	+	0.208309i
$255$		0			0
$256$	−10.4775	+	12.0923i	−0.654842	+	0.755766i
$257$	−2.21664	+	3.83934i	−0.138270	+	0.239491i	−0.926842	−	0.375452i	$-0.877488\pi$
$257$	−2.21664	+	3.83934i	−0.138270	+	0.239491i	0.788572	+	0.614943i	$0.210821\pi$
$258$		0			0
$259$	3.98377	−	14.8676i	0.247539	−	0.923830i
$260$	20.3600	+	0.969736i	1.26267	+	0.0601405i
$261$		0			0
$262$	−18.8348	+	17.9591i	−1.16362	+	1.10952i
$263$	−4.61948	+	2.66706i	−0.284850	+	0.164458i	−0.635617	−	0.772005i	$-0.719254\pi$
$263$	−4.61948	+	2.66706i	−0.284850	+	0.164458i	0.350767	+	0.936463i	$0.385921\pi$
$264$		0			0
$265$	29.2529	+	16.8891i	1.79699	+	1.03749i
$266$	15.3107	−	3.71438i	0.938757	−	0.227743i
$267$		0			0
$268$	0.180667	−	0.565189i	0.0110360	−	0.0345244i
$269$	−20.6406	−	20.6406i	−1.25848	−	1.25848i	−0.951818	−	0.306663i	$-0.900788\pi$
$269$	−20.6406	−	20.6406i	−1.25848	−	1.25848i	−0.306663	−	0.951818i	$-0.599212\pi$
$270$		0			0
$271$	23.2339			1.41136			0.705680	−	0.708530i	$-0.250642\pi$
$271$	23.2339			1.41136			0.705680	+	0.708530i	$0.250642\pi$
$272$	5.72660	+	12.5391i	0.347226	+	0.760294i
$273$		0			0
$274$	11.4057	−	18.7124i	0.689044	−	1.13046i
$275$	−15.5019	+	4.15373i	−0.934801	+	0.250479i
$276$		0			0
$277$	19.0092	+	5.09351i	1.14215	+	0.306039i	0.779817	−	0.626007i	$-0.215312\pi$
$277$	19.0092	+	5.09351i	1.14215	+	0.306039i	0.362338	+	0.932047i	$0.381979\pi$
$278$	7.19579	+	7.54668i	0.431575	+	0.452620i
$279$		0			0
$280$	17.1466	−	14.8579i	1.02471	−	0.887929i
$281$	16.3011	−	9.41146i	0.972444	−	0.561441i	0.0724633	−	0.997371i	$-0.476914\pi$
$281$	16.3011	−	9.41146i	0.972444	−	0.561441i	0.899980	+	0.435930i	$0.143581\pi$
$282$		0			0
$283$	−3.43848	−	12.8326i	−0.204397	−	0.762819i	−0.989633	−	0.143622i	$-0.954125\pi$
$283$	−3.43848	−	12.8326i	−0.204397	−	0.762819i	0.785236	−	0.619197i	$-0.212542\pi$
$284$	−23.5443	−	15.1308i	−1.39710	−	0.897848i
$285$		0			0
$286$	3.64494	−	1.99030i	0.215530	−	0.117689i
$287$	7.47420			0.441188
$288$		0			0
$289$	−5.12358			−0.301387
$290$	7.00390	−	3.82445i	0.411283	−	0.224579i
$291$		0			0
$292$	−0.0469573	−	0.0301772i	−0.00274797	−	0.00176599i
$293$	−2.20679	−	8.23584i	−0.128922	−	0.481143i	0.871027	−	0.491235i	$-0.163454\pi$
$293$	−2.20679	−	8.23584i	−0.128922	−	0.481143i	−0.999949	+	0.0100919i	$0.996788\pi$
$294$		0			0
$295$	−41.6699	+	24.0581i	−2.42611	+	1.40072i
$296$	15.1184	+	17.4472i	0.878738	+	1.01410i
$297$		0			0
$298$	−7.53746	−	7.90502i	−0.436634	−	0.457925i
$299$	−3.60405	−	0.965702i	−0.208427	−	0.0558480i
$300$		0			0
$301$	−5.58291	+	1.49594i	−0.321794	+	0.0862244i
$302$	−2.86031	+	4.69266i	−0.164592	+	0.270032i
$303$		0			0
$304$	−8.25760	+	22.1403i	−0.473606	+	1.26984i
$305$	−20.8853			−1.19589
$306$		0			0
$307$	−7.13558	−	7.13558i	−0.407249	−	0.407249i	0.473529	−	0.880778i	$-0.342980\pi$
$307$	−7.13558	−	7.13558i	−0.407249	−	0.407249i	−0.880778	+	0.473529i	$0.842980\pi$
$308$	1.40750	−	4.40315i	0.0802000	−	0.250893i
$309$		0			0
$310$	14.7134	−	3.56947i	0.835663	−	0.202732i
$311$	−10.0741	−	5.81630i	−0.571252	−	0.329812i	0.186397	−	0.982474i	$-0.440319\pi$
$311$	−10.0741	−	5.81630i	−0.571252	−	0.329812i	−0.757649	+	0.652662i	$0.773652\pi$
$312$		0			0
$313$	5.76956	−	3.33106i	0.326115	−	0.188282i	−0.328000	−	0.944678i	$-0.606375\pi$
$313$	5.76956	−	3.33106i	0.326115	−	0.188282i	0.654115	+	0.756395i	$0.273041\pi$
$314$	−6.60513	+	6.29802i	−0.372749	+	0.355418i
$315$		0			0
$316$	8.75276	+	0.416890i	0.492381	+	0.0234519i
$317$	−0.708583	+	2.64447i	−0.0397980	+	0.148528i	−0.982966	−	0.183789i	$-0.941164\pi$
$317$	−0.708583	+	2.64447i	−0.0397980	+	0.148528i	0.943168	+	0.332317i	$0.107830\pi$
$318$		0			0
$319$	0.812945	−	1.40806i	0.0455162	−	0.0788364i
$320$	4.04061	+	33.7889i	0.225877	+	1.88886i
$321$		0			0
$322$	−3.64516	+	1.99042i	−0.203137	+	0.110922i
$323$	14.3957	+	14.3957i	0.801000	+	0.801000i
$324$		0			0
$325$	22.1835	−	22.1835i	1.23052	−	1.23052i
$326$	−20.2996	−	5.96044i	−1.12429	−	0.330118i
$327$		0			0
$328$	−6.28339	+	9.28389i	−0.346942	+	0.512617i
$329$	−0.753501	−	0.435034i	−0.0415418	−	0.0239842i
$330$		0			0
$331$	−19.6789	−	5.27295i	−1.08165	−	0.289827i	−0.326379	−	0.945239i	$-0.605829\pi$
$331$	−19.6789	−	5.27295i	−1.08165	−	0.289827i	−0.755272	+	0.655412i	$0.772495\pi$
$332$	−4.76082	−	5.23701i	−0.261284	−	0.287418i
$333$		0			0
$334$	−30.5524	−	0.727186i	−1.67175	−	0.0397898i
$335$	−0.630997	−	1.09292i	−0.0344751	−	0.0597126i
$336$		0			0
$337$	−0.514533	+	0.891197i	−0.0280284	+	0.0485466i	−0.879699	−	0.475530i	$-0.842256\pi$
$337$	−0.514533	+	0.891197i	−0.0280284	+	0.0485466i	0.851671	+	0.524077i	$0.175590\pi$
$338$	5.34341	−	8.76647i	0.290643	−	0.476833i
$339$		0			0
$340$	27.9263	+	8.92688i	1.51452	+	0.484128i
$341$	2.18123	−	2.18123i	0.118120	−	0.118120i
$342$		0			0
$343$			19.6948i			1.06342i
$344$	2.83529	−	8.19227i	0.152868	−	0.441698i
$345$		0			0
$346$	6.45378	+	26.6025i	0.346957	+	1.43016i
$347$	8.08026	+	30.1559i	0.433771	+	1.61886i	0.743990	+	0.668191i	$0.232931\pi$
$347$	8.08026	+	30.1559i	0.433771	+	1.61886i	−0.310219	+	0.950665i	$0.600402\pi$
$348$		0			0
$349$	4.62320	−	17.2540i	0.247474	−	0.923587i	−0.724649	−	0.689118i	$-0.757998\pi$
$349$	4.62320	−	17.2540i	0.247474	−	0.923587i	0.972124	−	0.234469i	$-0.0753352\pi$
$350$	0.830915	−	34.9105i	0.0444143	−	1.86605i
$351$		0			0
$352$	4.28601	+	5.44992i	0.228445	+	0.290482i
$353$	1.02827	+	1.78101i	0.0547291	+	0.0947935i	0.892092	−	0.451854i	$-0.149237\pi$
$353$	1.02827	+	1.78101i	0.0547291	+	0.0947935i	−0.837363	+	0.546647i	$0.815904\pi$
$354$		0			0
$355$	−57.4962	+	15.4061i	−3.05158	+	0.817668i
$356$	−7.99015	−	5.13489i	−0.423477	−	0.272149i
$357$		0			0
$358$	−5.52961	−	1.62362i	−0.292249	−	0.0858110i
$359$			4.76579i			0.251529i	0.992060	+	0.125764i	$0.0401383\pi$
$359$			4.76579i			0.251529i	−0.992060	+	0.125764i	$0.959862\pi$
$360$		0			0
$361$			15.8989i			0.836785i
$362$	5.35391	−	18.2340i	0.281395	−	0.958356i
$363$		0			0
$364$	1.92087	+	8.82983i	0.100681	+	0.462809i
$365$	−0.114672	+	0.0307261i	−0.00600218	+	0.00160828i
$366$		0			0
$367$	8.61021	+	14.9133i	0.449449	+	0.778469i	0.998350	−	0.0574187i	$-0.0182870\pi$
$367$	8.61021	+	14.9133i	0.449449	+	0.778469i	−0.548901	+	0.835887i	$0.684954\pi$
$368$	0.592049	−	6.20104i	0.0308627	−	0.323252i
$369$		0			0
$370$	49.0870	+	1.16833i	2.55191	+	0.0607387i
$371$	−3.87577	+	14.4646i	−0.201220	+	0.750963i
$372$		0			0
$373$	4.29744	+	16.0383i	0.222513	+	0.830430i	0.983386	+	0.181529i	$0.0581046\pi$
$373$	4.29744	+	16.0383i	0.222513	+	0.830430i	−0.760872	+	0.648901i	$0.775229\pi$
$374$	5.80508	−	1.40832i	0.300174	−	0.0728224i
$375$		0			0
$376$	1.17382	−	0.570219i	0.0605350	−	0.0294068i
$377$			3.17830i			0.163691i
$378$		0			0
$379$	−22.5741	+	22.5741i	−1.15955	+	1.15955i	−0.174981	+	0.984572i	$0.555987\pi$
$379$	−22.5741	+	22.5741i	−1.15955	+	1.15955i	−0.984572	+	0.174981i	$0.944013\pi$
$380$	23.0297	+	44.6708i	1.18140	+	2.29156i
$381$		0			0
$382$	5.70983	+	3.48030i	0.292140	+	0.178067i
$383$	12.6153	−	21.8504i	0.644614	−	1.11650i	−0.339777	−	0.940506i	$-0.610352\pi$
$383$	12.6153	−	21.8504i	0.644614	−	1.11650i	0.984391	−	0.175997i	$-0.0563150\pi$
$384$		0			0
$385$	−4.91584	−	8.51448i	−0.250534	−	0.433938i
$386$	−0.657224	+	27.6130i	−0.0334518	+	1.40546i
$387$		0			0
$388$	16.6752	+	0.794231i	0.846554	+	0.0403210i
$389$	−7.09570	−	1.90129i	−0.359766	−	0.0963991i	0.0744082	−	0.997228i	$-0.476293\pi$
$389$	−7.09570	−	1.90129i	−0.359766	−	0.0963991i	−0.434175	+	0.900829i	$0.642960\pi$
$390$		0			0
$391$	−4.64781	−	2.68342i	−0.235050	−	0.135706i
$392$	−8.06674	−	5.45962i	−0.407432	−	0.275752i
$393$		0			0
$394$	3.88768	−	13.2404i	0.195858	−	0.667040i
$395$	13.1783	−	13.1783i	0.663073	−	0.663073i
$396$		0			0
$397$	−2.23236	−	2.23236i	−0.112039	−	0.112039i	0.648865	−	0.760904i	$-0.275244\pi$
$397$	−2.23236	−	2.23236i	−0.112039	−	0.112039i	−0.760904	+	0.648865i	$0.775244\pi$
$398$	16.5884	+	30.3792i	0.831501	+	1.52277i
$399$		0			0
$400$	42.6647	+	30.3806i	2.13323	+	1.51903i
$401$	−9.10949	+	15.7781i	−0.454906	+	0.787921i	−0.998683	−	0.0513094i	$-0.983661\pi$
$401$	−9.10949	+	15.7781i	−0.454906	+	0.787921i	0.543777	+	0.839230i	$0.316994\pi$
$402$		0			0
$403$	−1.56069	+	5.82456i	−0.0777433	+	0.290142i
$404$	11.0431	−	10.0390i	0.549417	−	0.499460i
$405$		0			0
$406$	2.44134	+	2.56039i	0.121162	+	0.127070i
$407$	8.66376	−	5.00202i	0.429447	−	0.247941i
$408$		0			0
$409$	−22.6986	−	13.1050i	−1.12237	−	0.648002i	−0.180368	−	0.983599i	$-0.557729\pi$
$409$	−22.6986	−	13.1050i	−1.12237	−	0.648002i	−0.942006	+	0.335597i	$0.891062\pi$
$410$	5.62121	+	23.1706i	0.277612	+	1.14432i
$411$		0			0
$412$	25.0845	−	12.9322i	1.23583	−	0.637122i
$413$	−15.0834	−	15.0834i	−0.742207	−	0.742207i
$414$		0			0
$415$	−15.0529			−0.738918
$416$	−12.5826	−	5.03707i	−0.616912	−	0.246963i
$417$		0			0
$418$	8.74356	+	5.32944i	0.427661	+	0.260671i
$419$	−11.2202	+	3.00645i	−0.548144	+	0.146875i	−0.522254	−	0.852790i	$-0.674909\pi$
$419$	−11.2202	+	3.00645i	−0.548144	+	0.146875i	−0.0258901	+	0.999665i	$0.508242\pi$
$420$		0			0
$421$	−9.74548	−	2.61129i	−0.474966	−	0.127267i	0.0133918	−	0.999910i	$-0.495737\pi$
$421$	−9.74548	−	2.61129i	−0.474966	−	0.127267i	−0.488358	+	0.872644i	$0.662404\pi$
$422$	−22.4469	+	21.4032i	−1.09270	+	1.04189i
$423$		0			0
$424$	−14.7085	−	16.9742i	−0.714309	−	0.824341i
$425$	39.0793	−	22.5624i	1.89562	−	1.09444i
$426$		0			0
$427$	−2.39641	−	8.94353i	−0.115970	−	0.432808i
$428$	−2.31474	−	10.6404i	−0.111887	−	0.514321i
$429$		0			0
$430$	−8.83633	−	16.1824i	−0.426126	−	0.780385i
$431$	4.07825			0.196442			0.0982211	−	0.995165i	$-0.468685\pi$
$431$	4.07825			0.196442			0.0982211	+	0.995165i	$0.468685\pi$
$432$		0			0
$433$	−25.1331			−1.20782			−0.603910	−	0.797052i	$-0.706392\pi$
$433$	−25.1331			−1.20782			−0.603910	+	0.797052i	$0.706392\pi$
$434$	3.21675	+	5.89100i	0.154409	+	0.282777i
$435$		0			0
$436$	5.76570	−	1.25429i	0.276127	−	0.0600696i
$437$	−2.38110	−	8.88638i	−0.113903	−	0.425093i
$438$		0			0
$439$	13.5272	−	7.80991i	0.645616	−	0.372747i	−0.141158	−	0.989987i	$-0.545083\pi$
$439$	13.5272	−	7.80991i	0.645616	−	0.372747i	0.786775	+	0.617240i	$0.211749\pi$
$440$	14.7087	+	1.05185i	0.701209	+	0.0501448i
$441$		0			0
$442$	−8.45098	+	8.05805i	−0.401972	+	0.383282i
$443$	−32.6709	−	8.75415i	−1.55224	−	0.415922i	−0.622045	−	0.782982i	$-0.713698\pi$
$443$	−32.6709	−	8.75415i	−1.55224	−	0.415922i	−0.930197	+	0.367060i	$0.880364\pi$
$444$		0			0
$445$	−19.5123	+	5.22830i	−0.924970	+	0.247845i
$446$	3.79144	+	2.31099i	0.179530	+	0.109428i
$447$		0			0
$448$	−14.0055	+	5.60726i	−0.661697	+	0.264918i
$449$	28.0284			1.32274			0.661370	−	0.750060i	$-0.269975\pi$
$449$	28.0284			1.32274			0.661370	+	0.750060i	$0.269975\pi$
$450$		0			0
$451$	3.43500	+	3.43500i	0.161748	+	0.161748i
$452$	−3.75381	−	7.28127i	−0.176565	−	0.342482i
$453$		0			0
$454$	−4.69532	−	19.3541i	−0.220362	−	0.908334i
$455$	16.6441	+	9.60949i	0.780289	+	0.450500i
$456$		0			0
$457$	14.8363	−	8.56574i	0.694012	−	0.400688i	−0.111101	−	0.993809i	$-0.535438\pi$
$457$	14.8363	−	8.56574i	0.694012	−	0.400688i	0.805113	+	0.593121i	$0.202104\pi$
$458$	18.5222	+	19.4254i	0.865488	+	0.907692i
$459$		0			0
$460$	−8.91192	−	9.80332i	−0.415521	−	0.457082i
$461$	−2.43727	+	9.09603i	−0.113515	+	0.423644i	−0.999172	−	0.0406970i	$-0.987042\pi$
$461$	−2.43727	+	9.09603i	−0.113515	+	0.423644i	0.885656	+	0.464341i	$0.153709\pi$
$462$		0			0
$463$	−0.777204	+	1.34616i	−0.0361197	+	0.0625612i	−0.883520	−	0.468393i	$-0.844833\pi$
$463$	−0.777204	+	1.34616i	−0.0361197	+	0.0625612i	0.847400	+	0.530954i	$0.178166\pi$
$464$	−5.23271	+	0.879991i	−0.242922	+	0.0408526i
$465$		0			0
$466$	−8.59420	−	15.7390i	−0.398118	−	0.729094i
$467$	−9.81211	−	9.81211i	−0.454050	−	0.454050i	0.442646	−	0.896696i	$-0.354040\pi$
$467$	−9.81211	−	9.81211i	−0.454050	−	0.454050i	−0.896696	+	0.442646i	$0.854040\pi$
$468$		0			0
$469$	0.395609	−	0.395609i	0.0182675	−	0.0182675i
$470$	0.781946	−	2.66309i	0.0360685	−	0.122839i
$471$		0			0
$472$	31.4158	−	6.05521i	1.44603	−	0.278713i
$473$	−3.25331	−	1.87830i	−0.149587	−	0.0863643i
$474$		0			0
$475$	74.7175	+	20.0205i	3.42828	+	0.918604i
$476$	−0.618370	+	12.9829i	−0.0283429	+	0.595071i
$477$		0			0
$478$	−0.248614	+	10.4454i	−0.0113713	+	0.477761i
$479$	11.7030	+	20.2702i	0.534724	+	0.926169i	0.999177	+	0.0405710i	$0.0129177\pi$
$479$	11.7030	+	20.2702i	0.534724	+	0.926169i	−0.464453	+	0.885598i	$0.653749\pi$
$480$		0			0
$481$	−9.77797	+	16.9359i	−0.445837	+	0.772212i
$482$	−27.0388	−	16.4809i	−1.23158	−	0.750684i
$483$		0			0
$484$	−16.8838	+	8.70436i	−0.767448	+	0.395653i
$485$	25.1064	−	25.1064i	1.14002	−	1.14002i
$486$		0			0
$487$		−	21.0301i		−	0.952967i	−0.879183	−	0.476483i	$-0.841911\pi$
$487$		−	21.0301i		−	0.952967i	0.879183	−	0.476483i	$-0.158089\pi$
$488$	13.1236	+	4.54198i	0.594077	+	0.205606i
$489$		0			0
$490$	−20.1329	+	4.88425i	−0.909511	+	0.220648i
$491$	6.82214	+	25.4606i	0.307879	+	1.14902i	0.930439	+	0.366447i	$0.119426\pi$
$491$	6.82214	+	25.4606i	0.307879	+	1.14902i	−0.622560	+	0.782572i	$0.713907\pi$
$492$		0			0
$493$	−1.18321	+	4.41580i	−0.0532891	+	0.198877i
$494$	−20.0110	−	0.476289i	−0.900339	−	0.0214292i
$495$		0			0
$496$	−10.0216	−	0.956819i	−0.449983	−	0.0429625i
$497$	−13.1944	−	22.8533i	−0.591849	−	1.02511i
$498$		0			0
$499$	12.8466	−	3.44223i	0.575092	−	0.154095i	0.0404610	−	0.999181i	$-0.487117\pi$
$499$	12.8466	−	3.44223i	0.575092	−	0.154095i	0.534631	+	0.845086i	$0.320451\pi$
$500$	67.2854	−	14.6375i	3.00909	−	0.654608i
$501$		0			0
$502$	−4.23912	+	14.4373i	−0.189201	+	0.644368i
$503$		−	7.97796i		−	0.355720i	−0.984056	−	0.177860i	$-0.943083\pi$
$503$		−	7.97796i		−	0.355720i	0.984056	−	0.177860i	$-0.0569174\pi$
$504$		0			0
$505$		−	31.7417i		−	1.41249i
$506$	−2.59001	−	0.760486i	−0.115140	−	0.0338077i
$507$		0			0
$508$	5.29641	−	8.24149i	0.234990	−	0.365657i
$509$	−33.3037	+	8.92371i	−1.47616	+	0.395536i	−0.905039	−	0.425328i	$-0.860159\pi$
$509$	−33.3037	+	8.92371i	−1.47616	+	0.395536i	−0.571123	+	0.820865i	$0.693492\pi$
$510$		0			0
$511$	−0.0263151	−	0.0455792i	−0.00116411	−	0.00201630i
$512$	4.80918	−	22.1104i	0.212538	−	0.977153i
$513$		0			0
$514$	0.149183	−	6.26784i	0.00658016	−	0.276463i
$515$	15.5353	−	57.9785i	0.684567	−	2.55484i
$516$		0			0
$517$	−0.146362	−	0.546229i	−0.00643697	−	0.0240231i
$518$	5.13200	+	21.1541i	0.225487	+	0.929458i
$519$		0			0
$520$	−25.9285	+	12.5956i	−1.13704	+	0.552354i
$521$		−	20.0111i		−	0.876703i	−0.898804	−	0.438352i	$-0.855562\pi$
$521$		−	20.0111i		−	0.876703i	0.898804	−	0.438352i	$-0.144438\pi$
$522$		0			0
$523$	−11.2432	+	11.2432i	−0.491633	+	0.491633i	−0.908820	−	0.417188i	$-0.863016\pi$
$523$	−11.2432	+	11.2432i	−0.491633	+	0.491633i	0.417188	+	0.908820i	$0.363016\pi$
$524$	11.2062	−	35.0568i	0.489545	−	1.53146i
$525$		0			0
$526$	3.92617	−	6.44134i	0.171189	−	0.280856i
$527$	−4.33671	+	7.51140i	−0.188910	+	0.327202i
$528$		0			0
$529$	−10.2874	−	17.8183i	−0.447278	−	0.774708i
$530$	−47.7562	−	1.13666i	−2.07440	−	0.0493733i
$531$		0			0
$532$	−16.4865	+	14.9874i	−0.714780	+	0.649786i
$533$	−9.17253	−	2.45777i	−0.397306	−	0.106458i
$534$		0			0
$535$	−20.0569	−	11.5799i	−0.867137	−	0.500642i
$536$	0.158816	+	0.823975i	0.00685982	+	0.0355903i
$537$		0			0
$538$	39.6091	+	11.6301i	1.70767	+	0.501411i
$539$	−2.98466	+	2.98466i	−0.128559	+	0.128559i
$540$		0			0
$541$	9.38252	+	9.38252i	0.403386	+	0.403386i	0.879424	−	0.476038i	$-0.157928\pi$
$541$	9.38252	+	9.38252i	0.403386	+	0.403386i	−0.476038	+	0.879424i	$0.657928\pi$
$542$	−28.8385	+	15.7471i	−1.23872	+	0.676397i
$543$		0			0
$544$	−15.6065	−	11.6825i	−0.669125	−	0.500884i
$545$	6.27481	−	10.8683i	0.268783	−	0.465546i
$546$		0			0
$547$	−9.70067	+	36.2034i	−0.414770	+	1.54794i	0.370524	+	0.928823i	$0.379178\pi$
$547$	−9.70067	+	36.2034i	−0.414770	+	1.54794i	−0.785295	+	0.619122i	$0.787489\pi$
$548$	−1.47445	+	30.9566i	−0.0629854	+	1.32240i
$549$		0			0
$550$	16.4261	−	15.6624i	0.700411	−	0.667845i
$551$	−6.78671	+	3.91831i	−0.289123	+	0.166926i
$552$		0			0
$553$	7.15532	+	4.13113i	0.304275	+	0.175673i
$554$	−27.0469	+	6.56160i	−1.14911	+	0.278776i
$555$		0			0
$556$	−14.0465	−	4.49007i	−0.595703	−	0.190421i
$557$	−9.01169	−	9.01169i	−0.381838	−	0.381838i	0.489926	−	0.871764i	$-0.337024\pi$
$557$	−9.01169	−	9.01169i	−0.381838	−	0.381838i	−0.871764	+	0.489926i	$0.837024\pi$
$558$		0			0
$559$	7.34341			0.310593
$560$	−11.2126	+	30.0633i	−0.473819	+	1.27041i
$561$		0			0
$562$	−13.8546	+	22.7300i	−0.584420	+	0.958809i
$563$	16.4015	−	4.39477i	0.691241	−	0.185218i	0.103937	−	0.994584i	$-0.466856\pi$
$563$	16.4015	−	4.39477i	0.691241	−	0.185218i	0.587304	+	0.809366i	$0.300189\pi$
$564$		0			0
$565$	−16.8294	−	4.50942i	−0.708018	−	0.189713i
$566$	12.9654	+	13.5976i	0.544976	+	0.571551i
$567$		0			0
$568$	39.4789	+	2.82321i	1.65650	+	0.118459i
$569$	−14.1855	+	8.19001i	−0.594688	+	0.343343i	−0.766949	−	0.641708i	$-0.778226\pi$
$569$	−14.1855	+	8.19001i	−0.594688	+	0.343343i	0.172261	+	0.985051i	$0.444893\pi$
$570$		0			0
$571$	−9.58794	−	35.7827i	−0.401243	−	1.49746i	−0.810881	−	0.585211i	$-0.801012\pi$
$571$	−9.58794	−	35.7827i	−0.401243	−	1.49746i	0.409638	−	0.912248i	$-0.365655\pi$
$572$	−3.17523	+	4.94082i	−0.132763	+	0.206586i
$573$		0			0
$574$	−9.27715	+	5.06575i	−0.387221	+	0.211440i
$575$	−20.3914			−0.850382
$576$		0			0
$577$	−2.14863			−0.0894487			−0.0447243	−	0.998999i	$-0.514241\pi$
$577$	−2.14863			−0.0894487			−0.0447243	+	0.998999i	$0.514241\pi$
$578$	6.35950	−	3.47258i	0.264520	−	0.144440i
$579$		0			0
$580$	−6.10133	+	9.49399i	−0.253344	+	0.394216i
$581$	−1.72719	−	6.44597i	−0.0716560	−	0.267424i
$582$		0			0
$583$	−8.42888	+	4.86642i	−0.349088	+	0.201546i
$584$	0.0787375	+	0.00563067i	0.00325818	+	0.000232999i
$585$		0			0
$586$	8.32107	+	8.72684i	0.343740	+	0.360502i
$587$	21.6014	+	5.78807i	0.891585	+	0.238899i	0.675399	−	0.737453i	$-0.263972\pi$
$587$	21.6014	+	5.78807i	0.891585	+	0.238899i	0.216186	+	0.976352i	$0.430638\pi$
$588$		0			0
$589$	−14.3614	+	3.84813i	−0.591752	+	0.158559i
$590$	35.4159	−	58.1038i	1.45805	−	2.39210i
$591$		0			0
$592$	−30.5904	−	11.4092i	−1.25726	−	0.468915i
$593$	−10.7128			−0.439921			−0.219960	−	0.975509i	$-0.570593\pi$
$593$	−10.7128			−0.439921			−0.219960	+	0.975509i	$0.570593\pi$
$594$		0			0
$595$	19.5473	+	19.5473i	0.801361	+	0.801361i
$596$	14.7134	+	4.70327i	0.602685	+	0.192653i
$597$		0			0
$598$	5.12795	−	1.24404i	0.209697	−	0.0508727i
$599$	−23.8944	−	13.7955i	−0.976300	−	0.563667i	−0.0751489	−	0.997172i	$-0.523943\pi$
$599$	−23.8944	−	13.7955i	−0.976300	−	0.563667i	−0.901151	+	0.433505i	$0.857277\pi$
$600$		0			0
$601$	−9.37490	+	5.41260i	−0.382410	+	0.220785i	−0.678866	−	0.734262i	$-0.737528\pi$
$601$	−9.37490	+	5.41260i	−0.382410	+	0.220785i	0.296456	+	0.955046i	$0.404195\pi$
$602$	5.91575	−	5.64069i	0.241108	−	0.229897i
$603$		0			0
$604$	0.369760	−	7.76325i	0.0150453	−	0.315882i
$605$	−10.4565	+	39.0241i	−0.425116	+	1.58655i
$606$		0			0
$607$	19.0270	−	32.9557i	0.772282	−	1.33763i	−0.164028	−	0.986456i	$-0.552449\pi$
$607$	19.0270	−	32.9557i	0.772282	−	1.33763i	0.936310	−	0.351175i	$-0.114218\pi$
$608$	−4.75640	−	33.0778i	−0.192898	−	1.34148i
$609$		0			0
$610$	25.9234	−	14.1553i	1.04961	−	0.573133i
$611$	0.781661	+	0.781661i	0.0316226	+	0.0316226i
$612$		0			0
$613$	−34.9758	+	34.9758i	−1.41266	+	1.41266i	−0.673168	+	0.739489i	$0.735067\pi$
$613$	−34.9758	+	34.9758i	−1.41266	+	1.41266i	−0.739489	+	0.673168i	$0.764933\pi$
$614$	13.6931	+	4.02061i	0.552608	+	0.162259i
$615$		0			0
$616$	1.23727	+	6.41925i	0.0498511	+	0.258639i
$617$	11.9478	+	6.89807i	0.481001	+	0.277706i	0.720834	−	0.693108i	$-0.243759\pi$
$617$	11.9478	+	6.89807i	0.481001	+	0.277706i	−0.239833	+	0.970814i	$0.577093\pi$
$618$		0			0
$619$	32.9231	+	8.82171i	1.32329	+	0.354574i	0.850209	−	0.526445i	$-0.176475\pi$
$619$	32.9231	+	8.82171i	1.32329	+	0.354574i	0.473080	+	0.881019i	$0.343142\pi$
$620$	−15.8433	+	14.4027i	−0.636282	+	0.578426i
$621$		0			0
$622$	16.4463	+	0.391444i	0.659438	+	0.0156955i
$623$	−4.47773	−	7.75565i	−0.179396	−	0.310724i
$624$		0			0
$625$	40.4916	−	70.1335i	1.61966	−	2.80534i
$626$	−4.90364	+	8.04499i	−0.195989	+	0.321542i
$627$		0			0
$628$	3.92987	−	12.2940i	0.156819	−	0.490583i
$629$	−19.8900	+	19.8900i	−0.793066	+	0.793066i
$630$		0			0
$631$			7.97657i			0.317542i	0.987315	+	0.158771i	$0.0507532\pi$
$631$			7.97657i			0.317542i	−0.987315	+	0.158771i	$0.949247\pi$
$632$	−11.1467	+	5.41486i	−0.443392	+	0.215391i
$633$		0			0
$634$	−0.912816	−	3.76263i	−0.0362526	−	0.149433i
$635$	−5.39276	−	20.1260i	−0.214005	−	0.798677i
$636$		0			0
$637$	2.13555	−	7.96998i	0.0846135	−	0.315782i
$638$	−0.0547121	+	2.29871i	−0.00216607	+	0.0910066i
$639$		0			0
$640$	−27.9162	−	39.2010i	−1.10349	−	1.54956i
$641$	18.6956	+	32.3818i	0.738434	+	1.27900i	0.953200	+	0.302339i	$0.0977676\pi$
$641$	18.6956	+	32.3818i	0.738434	+	1.27900i	−0.214767	+	0.976665i	$0.568899\pi$
$642$		0			0
$643$	12.4765	−	3.34308i	0.492026	−	0.131838i	−0.00427070	−	0.999991i	$-0.501359\pi$
$643$	12.4765	−	3.34308i	0.492026	−	0.131838i	0.496297	+	0.868153i	$0.334693\pi$
$644$	3.17542	−	4.94112i	0.125129	−	0.194707i
$645$		0			0
$646$	−27.6252	−	8.11141i	−1.08690	−	0.319139i
$647$		−	4.85394i		−	0.190828i	−0.995438	−	0.0954140i	$-0.969582\pi$
$647$		−	4.85394i		−	0.190828i	0.995438	−	0.0954140i	$-0.0304175\pi$
$648$		0			0
$649$		−	13.8641i		−	0.544215i
$650$	−12.4995	+	42.5698i	−0.490270	+	1.66973i
$651$		0			0
$652$	29.2361	−	6.36013i	1.14498	−	0.249082i
$653$	37.4249	−	10.0280i	1.46455	−	0.392425i	0.563492	−	0.826121i	$-0.309458\pi$
$653$	37.4249	−	10.0280i	1.46455	−	0.392425i	0.901059	+	0.433696i	$0.142791\pi$
$654$		0			0
$655$	−39.1387	−	67.7902i	−1.52928	−	2.64878i
$656$	1.50680	−	15.7820i	0.0588307	−	0.616185i
$657$		0			0
$658$	1.23011	+	0.0292783i	0.0479548	+	0.00114139i
$659$	−9.85502	+	36.7794i	−0.383897	+	1.43272i	0.456001	+	0.889979i	$0.349281\pi$
$659$	−9.85502	+	36.7794i	−0.383897	+	1.43272i	−0.839898	+	0.542744i	$0.817385\pi$
$660$		0			0
$661$	3.10339	+	11.5820i	0.120708	+	0.450488i	0.999650	−	0.0264400i	$-0.00841709\pi$
$661$	3.10339	+	11.5820i	0.120708	+	0.450488i	−0.878943	+	0.476927i	$0.841750\pi$
$662$	27.9997	−	6.79276i	1.08824	−	0.264008i
$663$		0			0
$664$	9.45870	+	3.27359i	0.367069	+	0.127040i
$665$			47.3876i			1.83761i
$666$		0			0
$667$	1.46077	−	1.46077i	0.0565613	−	0.0565613i
$668$	38.4152	−	19.8047i	1.48633	−	0.766267i
$669$		0			0
$670$	1.52395	+	0.928890i	0.0588753	+	0.0358861i
$671$	3.00893	−	5.21163i	0.116159	−	0.201193i
$672$		0			0
$673$	14.9076	+	25.8207i	0.574645	+	0.995314i	0.996080	+	0.0884554i	$0.0281931\pi$
$673$	14.9076	+	25.8207i	0.574645	+	0.995314i	−0.421435	+	0.906858i	$0.638474\pi$
$674$	0.0346286	−	1.45491i	0.00133385	−	0.0560409i
$675$		0			0
$676$	−0.690758	+	14.5027i	−0.0265676	+	0.557797i
$677$	−27.4303	−	7.34993i	−1.05423	−	0.282481i	−0.310233	−	0.950661i	$-0.600407\pi$
$677$	−27.4303	−	7.34993i	−1.05423	−	0.282481i	−0.744000	+	0.668180i	$0.767074\pi$
$678$		0			0
$679$	13.6318	+	7.87034i	0.523142	+	0.302036i
$680$	−40.7131	+	7.84721i	−1.56128	+	0.300927i
$681$		0			0
$682$	−1.22903	+	4.18575i	−0.0470621	+	0.160281i
$683$	−34.9639	+	34.9639i	−1.33786	+	1.33786i	−0.439721	+	0.898134i	$0.644923\pi$
$683$	−34.9639	+	34.9639i	−1.33786	+	1.33786i	−0.898134	+	0.439721i	$0.855077\pi$
$684$		0			0
$685$	46.6088	+	46.6088i	1.78083	+	1.78083i
$686$	−13.3484	−	24.4456i	−0.509645	−	0.933338i
$687$		0			0
$688$	2.03321	+	12.0901i	0.0775153	+	0.460931i
$689$	9.51288	−	16.4768i	0.362412	−	0.627716i
$690$		0			0
$691$	−3.37585	+	12.5989i	−0.128424	+	0.479283i	−0.999939	−	0.0110856i	$-0.996471\pi$
$691$	−3.37585	+	12.5989i	−0.128424	+	0.479283i	0.871515	+	0.490369i	$0.163138\pi$
$692$	−26.0408	−	28.6455i	−0.989922	−	1.08894i
$693$		0			0
$694$	−30.4680	−	31.9538i	−1.15655	−	1.21295i
$695$	−27.1620	+	15.6820i	−1.03031	+	0.594851i
$696$		0			0
$697$	−11.8290	−	6.82946i	−0.448054	−	0.258684i
$698$	5.95574	+	24.5495i	0.225428	+	0.929214i
$699$		0			0
$700$	22.6297	+	43.8949i	0.855324	+	1.65907i
$701$	1.18582	+	1.18582i	0.0447879	+	0.0447879i	0.729146	−	0.684358i	$-0.239917\pi$
$701$	1.18582	+	1.18582i	0.0447879	+	0.0447879i	−0.684358	+	0.729146i	$0.739917\pi$
$702$		0			0
$703$	−48.2184			−1.81859
$704$	−9.01365	−	3.85967i	−0.339715	−	0.145467i
$705$		0			0
$706$	−2.48341	−	1.51371i	−0.0934644	−	0.0569691i
$707$	13.5924	−	3.64208i	0.511196	−	0.136975i
$708$		0			0
$709$	13.3909	+	3.58808i	0.502906	+	0.134753i	0.501349	−	0.865245i	$-0.332837\pi$
$709$	13.3909	+	3.58808i	0.502906	+	0.134753i	0.00155784	+	0.999999i	$0.499504\pi$
$710$	60.9239	−	58.0912i	2.28643	−	2.18012i
$711$		0			0
$712$	13.3978	+	0.958103i	0.502104	+	0.0359064i
$713$	3.39432	−	1.95971i	0.127118	−	0.0733919i
$714$		0			0
$715$	3.23299	+	12.0657i	0.120907	+	0.451231i
$716$	7.96391	−	1.73250i	0.297625	−	0.0647464i
$717$		0			0
$718$	−3.23008	−	5.91541i	−0.120546	−	0.220761i
$719$	−22.9314			−0.855198			−0.427599	−	0.903968i	$-0.640641\pi$
$719$	−22.9314			−0.855198			−0.427599	+	0.903968i	$0.640641\pi$
$720$		0			0
$721$	26.6101			0.991013
$722$	−10.7757	−	19.7341i	−0.401031	−	0.734428i
$723$		0			0
$724$	5.71293	+	26.2611i	0.212319	+	0.975986i
$725$	4.49564	+	16.7780i	0.166964	+	0.623118i
$726$		0			0
$727$	14.6244	−	8.44338i	0.542387	−	0.313147i	−0.203659	−	0.979042i	$-0.565283\pi$
$727$	14.6244	−	8.44338i	0.542387	−	0.313147i	0.746046	+	0.665894i	$0.231950\pi$
$728$	−8.36877	−	9.65789i	−0.310167	−	0.357945i
$729$		0			0
$730$	0.121508	−	0.115858i	0.00449721	−	0.00428811i
$731$	10.2026	+	2.73379i	0.377358	+	0.101113i
$732$		0			0
$733$	−39.1181	+	10.4817i	−1.44486	+	0.387149i	−0.894232	−	0.447603i	$-0.852278\pi$
$733$	−39.1181	+	10.4817i	−1.44486	+	0.387149i	−0.550626	+	0.834752i	$0.685611\pi$
$734$	−20.7949	−	12.6751i	−0.767554	−	0.467845i
$735$		0			0
$736$	3.46798	+	8.09815i	0.127831	+	0.298502i
$737$	0.363629			0.0133945
$738$		0			0
$739$	20.2719	+	20.2719i	0.745713	+	0.745713i	0.973671	−	0.227958i	$-0.0732050\pi$
$739$	20.2719	+	20.2719i	0.745713	+	0.745713i	−0.227958	+	0.973671i	$0.573205\pi$
$740$	−61.7198	+	31.8192i	−2.26886	+	1.16970i
$741$		0			0
$742$	−4.99287	−	20.5806i	−0.183294	−	0.755538i
$743$	−33.3722	−	19.2674i	−1.22431	−	0.706853i	−0.258473	−	0.966019i	$-0.583219\pi$
$743$	−33.3722	−	19.2674i	−1.22431	−	0.706853i	−0.965833	+	0.259165i	$0.916553\pi$
$744$		0			0
$745$	28.4517	−	16.4266i	1.04239	−	0.601824i
$746$	−16.2043	−	16.9944i	−0.593280	−	0.622210i
$747$		0			0
$748$	−6.25090	+	5.68251i	−0.228555	+	0.207773i
$749$	2.65738	−	9.91749i	0.0970987	−	0.362377i
$750$		0			0
$751$	−2.59701	+	4.49815i	−0.0947663	+	0.164140i	−0.909511	−	0.415680i	$-0.863544\pi$
$751$	−2.59701	+	4.49815i	−0.0947663	+	0.164140i	0.814745	+	0.579820i	$0.196877\pi$
$752$	−1.07050	+	1.50334i	−0.0390369	+	0.0548212i
$753$		0			0
$754$	−2.15414	−	3.94497i	−0.0784490	−	0.143667i
$755$	−11.6885	−	11.6885i	−0.425388	−	0.425388i
$756$		0			0
$757$	16.3310	−	16.3310i	0.593562	−	0.593562i	−0.345030	−	0.938592i	$-0.612131\pi$
$757$	16.3310	−	16.3310i	0.593562	−	0.593562i	0.938592	+	0.345030i	$0.112131\pi$
$758$	12.7196	−	43.3194i	0.461996	−	1.57343i
$759$		0			0
$760$	−58.8613	−	39.8377i	−2.13512	−	1.44506i
$761$	30.2706	+	17.4767i	1.09731	+	0.633530i	0.935512	−	0.353294i	$-0.114939\pi$
$761$	30.2706	+	17.4767i	1.09731	+	0.633530i	0.161794	+	0.986824i	$0.448272\pi$
$762$		0			0
$763$	5.37400	+	1.43996i	0.194552	+	0.0521300i
$764$	−9.44599	−	0.449908i	−0.341744	−	0.0162771i
$765$		0			0
$766$	−0.849026	+	35.6715i	−0.0306766	+	1.28886i
$767$	13.5508	+	23.4707i	0.489292	+	0.847478i
$768$		0			0
$769$	−11.5439	+	19.9946i	−0.416284	+	0.721024i	−0.995562	−	0.0941052i	$-0.970001\pi$
$769$	−11.5439	+	19.9946i	−0.416284	+	0.721024i	0.579279	+	0.815130i	$0.303334\pi$
$770$	11.8725	+	7.23659i	0.427854	+	0.260789i
$771$		0			0
$772$	−17.8993	−	34.7193i	−0.644211	−	1.24958i
$773$	−14.4736	+	14.4736i	−0.520581	+	0.520581i	−0.917747	−	0.397166i	$-0.869994\pi$
$773$	−14.4736	+	14.4736i	−0.520581	+	0.520581i	0.397166	+	0.917747i	$0.369994\pi$
$774$		0			0
$775$			32.9549i			1.18378i
$776$	−21.2359	+	10.3160i	−0.762325	+	0.370323i
$777$		0			0
$778$	10.0960	−	2.44929i	0.361958	−	0.0878113i
$779$	−6.06004	−	22.6164i	−0.217124	−	0.810316i
$780$		0			0
$781$	4.43908	−	16.5669i	0.158843	−	0.592809i
$782$	7.58770	+	0.180597i	0.271335	+	0.00645813i
$783$		0			0
$784$	13.7130	+	1.30925i	0.489749	+	0.0467591i
$785$	−13.7254	−	23.7732i	−0.489882	−	0.848501i
$786$		0			0
$787$	−33.2907	+	8.92022i	−1.18669	+	0.317971i	−0.797575	−	0.603220i	$-0.793884\pi$
$787$	−33.2907	+	8.92022i	−1.18669	+	0.317971i	−0.389110	+	0.921191i	$0.627218\pi$
$788$	4.14837	+	19.0692i	0.147780	+	0.679312i
$789$		0			0
$790$	−7.42544	+	25.2890i	−0.264185	+	0.899743i
$791$		−	7.72411i		−	0.274638i
$792$		0			0
$793$			11.7637i			0.417743i
$794$	4.28387	+	1.25784i	0.152029	+	0.0446392i
$795$		0			0
$796$	−41.1798	−	26.4643i	−1.45958	−	0.938002i
$797$	−19.0745	+	5.11099i	−0.675652	+	0.181040i	−0.580299	−	0.814403i	$-0.697064\pi$
$797$	−19.0745	+	5.11099i	−0.675652	+	0.181040i	−0.0953525	+	0.995444i	$0.530398\pi$
$798$		0			0
$799$	0.795014	+	1.37700i	0.0281256	+	0.0487149i
$800$	−73.5472	−	8.79247i	−2.60029	−	0.310861i
$801$		0			0
$802$	0.613079	−	25.7582i	0.0216486	−	0.909555i
$803$	0.00885339	−	0.0330413i	0.000312429	−	0.00116600i
$804$		0			0
$805$	−3.23318	−	12.0664i	−0.113955	−	0.425285i
$806$	−2.01052	−	8.28736i	−0.0708175	−	0.291910i
$807$		0			0
$808$	−6.90293	+	19.9453i	−0.242844	+	0.701673i
$809$		−	2.32596i		−	0.0817763i	−0.999164	−	0.0408882i	$-0.986981\pi$
$809$		−	2.32596i		−	0.0817763i	0.999164	−	0.0408882i	$-0.0130187\pi$
$810$		0			0
$811$	34.5092	−	34.5092i	1.21178	−	1.21178i	0.241343	−	0.970440i	$-0.422412\pi$
$811$	34.5092	−	34.5092i	1.21178	−	1.21178i	0.970440	−	0.241343i	$-0.0775878\pi$
$812$	−4.76560	−	1.52336i	−0.167240	−	0.0534595i
$813$		0			0
$814$	−7.36347	+	12.0806i	−0.258089	+	0.423425i
$815$	31.8177	−	55.1098i	1.11452	−	1.93041i
$816$		0			0
$817$	9.05319	+	15.6806i	0.316731	+	0.548594i
$818$	37.0562	+	0.881984i	1.29564	+	0.0308378i
$819$		0			0
$820$	−22.6814	−	24.9501i	−0.792069	−	0.871294i
$821$	51.3558	+	13.7607i	1.79233	+	0.480253i	0.992738	−	0.120294i	$-0.0383836\pi$
$821$	51.3558	+	13.7607i	1.79233	+	0.480253i	0.799590	+	0.600547i	$0.205050\pi$
$822$		0			0
$823$	8.35343	+	4.82286i	0.291182	+	0.168114i	0.638475	−	0.769643i	$-0.279566\pi$
$823$	8.35343	+	4.82286i	0.291182	+	0.168114i	−0.347293	+	0.937757i	$0.612899\pi$
$824$	−22.3705	+	33.0531i	−0.779314	+	1.15146i
$825$		0			0
$826$	28.9449	+	8.49890i	1.00712	+	0.295714i
$827$	18.2747	−	18.2747i	0.635475	−	0.635475i	−0.313961	−	0.949436i	$-0.601656\pi$
$827$	18.2747	−	18.2747i	0.635475	−	0.635475i	0.949436	+	0.313961i	$0.101656\pi$
$828$		0			0
$829$	6.63529	+	6.63529i	0.230453	+	0.230453i	0.812882	−	0.582429i	$-0.197897\pi$
$829$	6.63529	+	6.63529i	0.230453	+	0.230453i	−0.582429	+	0.812882i	$0.697897\pi$
$830$	18.6840	−	10.2023i	0.648532	−	0.354128i
$831$		0			0
$832$	19.0317	−	2.27589i	0.659807	−	0.0789022i
$833$	5.93409	−	10.2782i	0.205604	−	0.356117i
$834$		0			0
$835$	23.7912	−	88.7900i	0.823329	−	3.07271i
$836$	−14.4648	−	0.688953i	−0.500276	−	0.0238279i
$837$		0			0
$838$	11.8891	−	11.3363i	0.410704	−	0.391608i
$839$	34.7829	−	20.0819i	1.20084	−	0.693306i	0.240099	−	0.970749i	$-0.422820\pi$
$839$	34.7829	−	20.0819i	1.20084	−	0.693306i	0.960742	+	0.277443i	$0.0894869\pi$
$840$		0			0
$841$	23.5908	+	13.6201i	0.813475	+	0.469660i
$842$	13.8662	−	3.36394i	0.477860	−	0.115929i
$843$		0			0
$844$	13.3553	−	41.7799i	0.459708	−	1.43812i
$845$	21.8355	+	21.8355i	0.751166	+	0.751166i
$846$		0			0
$847$	−17.9107			−0.615419
$848$	29.7611	+	11.0999i	1.02200	+	0.381171i
$849$		0			0
$850$	−33.2141	+	54.4915i	−1.13923	+	1.86904i
$851$	12.2779	−	3.28987i	0.420883	−	0.112775i
$852$		0			0
$853$	−2.70204	−	0.724010i	−0.0925162	−	0.0247896i	0.212264	−	0.977212i	$-0.431916\pi$
$853$	−2.70204	−	0.724010i	−0.0925162	−	0.0247896i	−0.304780	+	0.952423i	$0.598583\pi$
$854$	9.03609	+	9.47672i	0.309209	+	0.324287i
$855$		0			0
$856$	10.0848	+	11.6382i	0.344690	+	0.397786i
$857$	−32.4678	+	18.7453i	−1.10908	+	0.640326i	−0.938590	−	0.345033i	$-0.887868\pi$
$857$	−32.4678	+	18.7453i	−1.10908	+	0.640326i	−0.170488	+	0.985360i	$0.554534\pi$
$858$		0			0
$859$	12.4963	+	46.6369i	0.426369	+	1.59123i	0.760916	+	0.648850i	$0.224750\pi$
$859$	12.4963	+	46.6369i	0.426369	+	1.59123i	−0.334547	+	0.942379i	$0.608583\pi$
$860$	21.9357	+	14.0970i	0.748002	+	0.480705i
$861$		0			0
$862$	−5.06202	+	2.76409i	−0.172413	+	0.0941453i
$863$	40.4745			1.37777			0.688883	−	0.724872i	$-0.258101\pi$
$863$	40.4745			1.37777			0.688883	+	0.724872i	$0.258101\pi$
$864$		0			0
$865$	−82.3366			−2.79953
$866$	31.1958	−	17.0343i	1.06008	−	0.578850i
$867$		0			0
$868$	−7.98542	−	5.13184i	−0.271043	−	0.174186i
$869$	1.38986	+	5.18704i	0.0471479	+	0.175958i
$870$		0			0
$871$	−0.615591	+	0.355412i	−0.0208585	+	0.0120427i
$872$	−6.30641	+	5.46464i	−0.213562	+	0.185056i
$873$		0			0
$874$	8.97835	+	9.41616i	0.303697	+	0.318506i
$875$	62.7143	+	16.8042i	2.12013	+	0.568087i
$876$		0			0
$877$	31.1530	−	8.34743i	1.05196	−	0.281873i	0.308901	−	0.951094i	$-0.400039\pi$
$877$	31.1530	−	8.34743i	1.05196	−	0.281873i	0.743063	+	0.669222i	$0.233372\pi$
$878$	−11.4970	+	18.8621i	−0.388003	+	0.636564i
$879$		0			0
$880$	−18.9697	+	8.66344i	−0.639467	+	0.292045i
$881$	44.0930			1.48553			0.742765	−	0.669552i	$-0.233514\pi$
$881$	44.0930			1.48553			0.742765	+	0.669552i	$0.233514\pi$
$882$		0			0
$883$	−28.6867	−	28.6867i	−0.965385	−	0.965385i	0.0340356	−	0.999421i	$-0.489164\pi$
$883$	−28.6867	−	28.6867i	−0.965385	−	0.965385i	−0.999421	+	0.0340356i	$0.989164\pi$
$884$	5.02810	−	15.7296i	0.169113	−	0.529044i
$885$		0			0
$886$	46.4852	−	11.2773i	1.56170	−	0.378869i
$887$	6.66474	+	3.84789i	0.223780	+	0.129199i	0.607699	−	0.794167i	$-0.292093\pi$
$887$	6.66474	+	3.84789i	0.223780	+	0.129199i	−0.383919	+	0.923367i	$0.625426\pi$
$888$		0			0
$889$	7.99961	−	4.61858i	0.268298	−	0.154902i
$890$	20.6755	−	19.7142i	0.693045	−	0.660822i
$891$		0			0
$892$	−6.27233	−	0.298748i	−0.210013	−	0.0100028i
$893$	−0.705446	+	2.63276i	−0.0236069	+	0.0881020i
$894$		0			0
$895$	8.66712	−	15.0119i	0.289710	−	0.501792i
$896$	13.5835	−	16.4523i	0.453794	−	0.549632i
$897$		0			0
$898$	−34.7895	+	18.9966i	−1.16094	+	0.633926i
$899$	−2.36078	−	2.36078i	−0.0787364	−	0.0787364i
$900$		0			0
$901$	19.3508	−	19.3508i	0.644667	−	0.644667i
$902$	−6.59173	−	1.93548i	−0.219481	−	0.0644446i
$903$		0			0
$904$	9.59430	+	6.49348i	0.319102	+	0.215970i
$905$	49.5019	+	28.5799i	1.64550	+	0.950029i
$906$		0			0
$907$	−30.2432	−	8.10365i	−1.00421	−	0.269077i	−0.281002	−	0.959707i	$-0.590667\pi$
$907$	−30.2432	−	8.10365i	−1.00421	−	0.269077i	−0.723208	+	0.690630i	$0.757333\pi$
$908$	18.9455	+	20.8405i	0.628728	+	0.691615i
$909$		0			0
$910$	−27.1721	−	0.646730i	−0.900745	−	0.0214389i
$911$	−11.1615	−	19.3322i	−0.369796	−	0.640506i	0.619737	−	0.784809i	$-0.287239\pi$
$911$	−11.1615	−	19.3322i	−0.369796	−	0.640506i	−0.989533	+	0.144304i	$0.953906\pi$
$912$		0			0
$913$	2.16866	−	3.75623i	0.0717722	−	0.124313i
$914$	−12.6096	+	20.6875i	−0.417089	+	0.684282i
$915$		0			0
$916$	−36.1561	−	11.5576i	−1.19463	−	0.381874i
$917$	24.5383	−	24.5383i	0.810327	−	0.810327i
$918$		0			0
$919$		−	51.8070i		−	1.70895i	−0.519489	−	0.854477i	$-0.673877\pi$
$919$		−	51.8070i		−	1.70895i	0.519489	−	0.854477i	$-0.326123\pi$
$920$	17.7060	+	6.12793i	0.583750	+	0.202032i
$921$		0			0
$922$	−3.13976	−	12.9421i	−0.103403	−	0.426225i
$923$	8.67752	+	32.3849i	0.285624	+	1.06596i
$924$		0			0
$925$	−27.6615	+	103.234i	−0.909505	+	3.39432i
$926$	0.0523067	−	2.19764i	0.00171890	−	0.0722190i
$927$		0			0
$928$	5.89853	−	4.63881i	0.193629	−	0.152276i
$929$	13.9260	+	24.1206i	0.456899	+	0.791372i	0.998795	−	0.0490736i	$-0.0156269\pi$
$929$	13.9260	+	24.1206i	0.456899	+	0.791372i	−0.541897	+	0.840445i	$0.682294\pi$
$930$		0			0
$931$	19.6513	−	5.26555i	0.644046	−	0.172571i
$932$	21.3346	+	13.7107i	0.698839	+	0.449110i
$933$		0			0
$934$	18.8293	+	5.52872i	0.616114	+	0.180905i
$935$			17.9671i			0.587589i
$936$		0			0
$937$			35.0104i			1.14374i	0.820344	+	0.571870i	$0.193782\pi$
$937$			35.0104i			1.14374i	−0.820344	+	0.571870i	$0.806218\pi$
$938$	−0.222910	+	0.759169i	−0.00727825	+	0.0247877i
$939$		0			0
$940$	0.834381	+	3.83547i	0.0272145	+	0.125099i
$941$	−25.0151	+	6.70277i	−0.815468	+	0.218504i	−0.642364	−	0.766400i	$-0.722046\pi$
$941$	−25.0151	+	6.70277i	−0.815468	+	0.218504i	−0.173104	+	0.984904i	$0.555380\pi$
$942$		0			0
$943$	3.08616	+	5.34539i	0.100499	+	0.174070i
$944$	−34.8900	+	28.8084i	−1.13557	+	0.937633i
$945$		0			0
$946$	5.31113	+	0.126412i	0.172680	+	0.00411000i
$947$	−5.18039	+	19.3335i	−0.168340	+	0.628254i	0.829250	+	0.558877i	$0.188768\pi$
$947$	−5.18039	+	19.3335i	−0.168340	+	0.628254i	−0.997591	+	0.0693768i	$0.977899\pi$
$948$		0			0
$949$	0.0173066	+	0.0645892i	0.000561797	+	0.00209665i
$950$	−106.310	+	25.7910i	−3.44916	+	0.836770i
$951$		0			0
$952$	−8.03182	−	16.5338i	−0.260313	−	0.535864i
$953$		−	6.37793i		−	0.206601i	−0.994650	−	0.103301i	$-0.967060\pi$
$953$		−	6.37793i		−	0.206601i	0.994650	−	0.103301i	$-0.0329404\pi$
$954$		0			0
$955$	−14.2220	+	14.2220i	−0.460215	+	0.460215i
$956$	−6.77093	−	13.1336i	−0.218988	−	0.424770i
$957$		0			0
$958$	−28.2645	−	17.2280i	−0.913183	−	0.556610i
$959$	−14.6109	+	25.3068i	−0.471810	+	0.817199i
$960$		0			0
$961$	12.3329	+	21.3612i	0.397835	+	0.689070i
$962$	0.658068	−	27.6484i	0.0212170	−	0.891421i
$963$		0			0
$964$	44.7314	+	2.13053i	1.44070	+	0.0686199i
$965$	−80.2477	−	21.5023i	−2.58326	−	0.692183i
$966$		0			0
$967$	32.7206	+	18.8912i	1.05222	+	0.607501i	0.923271	−	0.384149i	$-0.125505\pi$
$967$	32.7206	+	18.8912i	1.05222	+	0.607501i	0.128952	+	0.991651i	$0.458839\pi$
$968$	15.0571	−	22.2473i	0.483954	−	0.715056i
$969$		0			0
$970$	−14.1464	+	48.1789i	−0.454215	+	1.54693i
$971$	−39.2528	+	39.2528i	−1.25968	+	1.25968i	−0.308436	+	0.951245i	$0.599806\pi$
$971$	−39.2528	+	39.2528i	−1.25968	+	1.25968i	−0.951245	+	0.308436i	$0.900194\pi$
$972$		0			0
$973$	−9.83195	−	9.83195i	−0.315198	−	0.315198i
$974$	14.2535	+	26.1031i	0.456711	+	0.836398i
$975$		0			0
$976$	−19.3677	+	3.25709i	−0.619945	+	0.104257i
$977$	13.9657	−	24.1893i	0.446803	−	0.773885i	−0.551373	−	0.834259i	$-0.685896\pi$
$977$	13.9657	−	24.1893i	0.446803	−	0.773885i	0.998176	+	0.0603737i	$0.0192293\pi$
$978$		0			0
$979$	1.50647	−	5.62224i	0.0481471	−	0.179687i
$980$	21.6790	−	19.7078i	0.692511	−	0.629542i
$981$		0			0
$982$	−25.7240	−	26.9784i	−0.820887	−	0.860916i
$983$	31.3818	−	18.1183i	1.00092	−	0.577883i	0.0924017	−	0.995722i	$-0.470546\pi$
$983$	31.3818	−	18.1183i	1.00092	−	0.577883i	0.908521	+	0.417839i	$0.137212\pi$
$984$		0			0
$985$	35.9452	+	20.7530i	1.14531	+	0.661245i
$986$	−1.52424	−	6.28293i	−0.0485418	−	0.200089i
$987$		0			0
$988$	25.1610	−	12.9716i	0.800478	−	0.412681i
$989$	−3.37509	−	3.37509i	−0.107322	−	0.107322i
$990$		0			0
$991$	52.0673			1.65397			0.826985	−	0.562223i	$-0.190054\pi$
$991$	52.0673			1.65397			0.826985	+	0.562223i	$0.190054\pi$
$992$	13.0875	−	5.60466i	0.415530	−	0.177948i
$993$		0			0
$994$	31.8663	+	19.4234i	1.01074	+	0.616073i
$995$	−100.563	+	26.9457i	−3.18805	+	0.854236i
$996$		0			0
$997$	−52.9980	−	14.2008i	−1.67846	−	0.449743i	−0.711091	−	0.703100i	$-0.751798\pi$
$997$	−52.9980	−	14.2008i	−1.67846	−	0.449743i	−0.967373	+	0.253357i	$0.918465\pi$
$998$	−13.6125	+	12.9795i	−0.430895	+	0.410860i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.253.4		72
3.2	odd	2		144.2.x.e.13.15	✓	72
4.3	odd	2		1728.2.bc.e.145.1		72
9.2	odd	6		144.2.x.e.61.4	yes	72
9.7	even	3	inner	432.2.y.e.397.15		72
12.11	even	2		576.2.bb.e.337.16		72
16.5	even	4	inner	432.2.y.e.37.15		72
16.11	odd	4		1728.2.bc.e.1009.18		72
36.7	odd	6		1728.2.bc.e.721.18		72
36.11	even	6		576.2.bb.e.529.6		72
48.5	odd	4		144.2.x.e.85.4	yes	72
48.11	even	4		576.2.bb.e.49.6		72
144.11	even	12		576.2.bb.e.241.16		72
144.43	odd	12		1728.2.bc.e.1585.1		72
144.101	odd	12		144.2.x.e.133.15	yes	72
144.133	even	12	inner	432.2.y.e.181.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.15	✓	72	3.2	odd	2
144.2.x.e.61.4	yes	72	9.2	odd	6
144.2.x.e.85.4	yes	72	48.5	odd	4
144.2.x.e.133.15	yes	72	144.101	odd	12
432.2.y.e.37.15		72	16.5	even	4	inner
432.2.y.e.181.4		72	144.133	even	12	inner
432.2.y.e.253.4		72	1.1	even	1	trivial
432.2.y.e.397.15		72	9.7	even	3	inner
576.2.bb.e.49.6		72	48.11	even	4
576.2.bb.e.241.16		72	144.11	even	12
576.2.bb.e.337.16		72	12.11	even	2
576.2.bb.e.529.6		72	36.11	even	6
1728.2.bc.e.145.1		72	4.3	odd	2
1728.2.bc.e.721.18		72	36.7	odd	6
1728.2.bc.e.1009.18		72	16.11	odd	4
1728.2.bc.e.1585.1		72	144.43	odd	12

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.24122 + 0.677764i) q^{2} +(1.08127 - 1.68251i) q^{4} +(-1.10094 - 4.10876i) q^{5} +(1.63313 - 0.942891i) q^{7} +(-0.201751 + 2.82122i) q^{8} +O(q^{10})\)	\(q+(-1.24122 + 0.677764i) q^{2} +(1.08127 - 1.68251i) q^{4} +(-1.10094 - 4.10876i) q^{5} +(1.63313 - 0.942891i) q^{7} +(-0.201751 + 2.82122i) q^{8} +(4.15129 + 4.35372i) q^{10} +(1.18389 + 0.317223i) q^{11} +(-2.31428 + 0.620109i) q^{13} +(-1.38803 + 2.27722i) q^{14} +(-1.66171 - 3.63851i) q^{16} -3.44622 q^{17} +(-4.17726 - 4.17726i) q^{19} +(-8.10347 - 2.59034i) q^{20} +(-1.68448 + 0.408656i) q^{22} +(1.34867 + 0.778655i) q^{23} +(-11.3397 + 6.54701i) q^{25} +(2.45225 - 2.33823i) q^{26} +(0.179434 - 3.76729i) q^{28} +(0.343336 - 1.28135i) q^{29} +(1.25840 - 2.17961i) q^{31} +(4.52860 + 3.38996i) q^{32} +(4.27753 - 2.33572i) q^{34} +(-5.67210 - 5.67210i) q^{35} +(5.77154 - 5.77154i) q^{37} +(8.01610 + 2.35371i) q^{38} +(11.8139 - 2.27705i) q^{40} +(3.43245 + 1.98173i) q^{41} +(-2.96053 - 0.793272i) q^{43} +(1.81384 - 1.64891i) q^{44} +(-2.20175 - 0.0524044i) q^{46} +(-0.230692 - 0.399570i) q^{47} +(-1.72191 + 2.98244i) q^{49} +(9.63783 - 15.8120i) q^{50} +(-1.45902 + 4.56431i) q^{52} +(-5.61507 + 5.61507i) q^{53} -5.21358i q^{55} +(2.33062 + 4.79766i) q^{56} +(0.442294 + 1.82314i) q^{58} +(-2.92766 - 10.9262i) q^{59} +(1.27078 - 4.74261i) q^{61} +(-0.0846915 + 3.55828i) q^{62} +(-7.91859 - 1.13837i) q^{64} +(5.09576 + 8.82612i) q^{65} +(0.286572 - 0.0767867i) q^{67} +(-3.72630 + 5.79831i) q^{68} +(10.8847 + 3.19600i) q^{70} -13.9935i q^{71} -0.0279090i q^{73} +(-3.25203 + 11.0755i) q^{74} +(-11.5450 + 2.51154i) q^{76} +(2.23256 - 0.598214i) q^{77} +(2.19067 + 3.79435i) q^{79} +(-13.1203 + 10.8333i) q^{80} +(-5.60358 - 0.133372i) q^{82} +(0.915902 - 3.41819i) q^{83} +(3.79408 + 14.1597i) q^{85} +(4.21233 - 1.02191i) q^{86} +(-1.13381 + 3.27603i) q^{88} -4.74894i q^{89} +(-3.19483 + 3.19483i) q^{91} +(2.76838 - 1.42722i) q^{92} +(0.557154 + 0.339601i) q^{94} +(-12.5645 + 21.7623i) q^{95} +(4.17352 + 7.22875i) q^{97} +(0.115887 - 4.86893i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more