LMFDB - Embedded newform 450.2.h.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	450.361
Dual form			450.2.h.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(1.80902 + 1.31433i) q^{10} +(-0.618034 + 0.449028i) q^{11} +(-1.50000 - 1.08981i) q^{13} +(-1.61803 + 1.17557i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.354102 - 1.08981i) q^{17} +(-2.23607 - 6.88191i) q^{19} -2.23607 q^{20} +(0.236068 - 0.726543i) q^{22} +(4.85410 - 3.52671i) q^{23} +(-4.04508 + 2.93893i) q^{25} +1.85410 q^{26} +(0.618034 - 1.90211i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-3.00000 - 9.23305i) q^{31} +1.00000 q^{32} +(0.927051 + 0.673542i) q^{34} +(-1.38197 - 4.25325i) q^{35} +(7.16312 + 5.20431i) q^{37} +(5.85410 + 4.25325i) q^{38} +(1.80902 - 1.31433i) q^{40} +(4.11803 + 2.99193i) q^{41} +3.23607 q^{43} +(0.236068 + 0.726543i) q^{44} +(-1.85410 + 5.70634i) q^{46} +(-2.85410 + 8.78402i) q^{47} -3.00000 q^{49} +(1.54508 - 4.75528i) q^{50} +(-1.50000 + 1.08981i) q^{52} +(3.57295 - 10.9964i) q^{53} +(1.38197 + 1.00406i) q^{55} +(0.618034 + 1.90211i) q^{56} +(1.11803 + 3.44095i) q^{58} +(-7.23607 - 5.25731i) q^{59} +(1.73607 - 1.26133i) q^{61} +(7.85410 + 5.70634i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-1.28115 + 3.94298i) q^{65} +(1.14590 + 3.52671i) q^{67} -1.14590 q^{68} +(3.61803 + 2.62866i) q^{70} +(-2.52786 + 7.77997i) q^{71} +(7.97214 - 5.79210i) q^{73} -8.85410 q^{74} -7.23607 q^{76} +(-1.23607 + 0.898056i) q^{77} +(-0.690983 + 2.12663i) q^{80} -5.09017 q^{82} +(-1.85410 - 5.70634i) q^{83} +(-2.07295 + 1.50609i) q^{85} +(-2.61803 + 1.90211i) q^{86} +(-0.618034 - 0.449028i) q^{88} +(2.92705 - 2.12663i) q^{89} +(-3.00000 - 2.17963i) q^{91} +(-1.85410 - 5.70634i) q^{92} +(-2.85410 - 8.78402i) q^{94} +(-13.0902 + 9.51057i) q^{95} +(-2.20820 + 6.79615i) q^{97} +(2.42705 - 1.76336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8} + 5 q^{10} + 2 q^{11} - 6 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{22} + 6 q^{23} - 5 q^{25} - 6 q^{26} - 2 q^{28} - 12 q^{31} + 4 q^{32} - 3 q^{34} - 10 q^{35} + 13 q^{37} + 10 q^{38} + 5 q^{40} + 12 q^{41} + 4 q^{43} - 8 q^{44} + 6 q^{46} + 2 q^{47} - 12 q^{49} - 5 q^{50} - 6 q^{52} + 21 q^{53} + 10 q^{55} - 2 q^{56} - 20 q^{59} - 2 q^{61} + 18 q^{62} - q^{64} + 15 q^{65} + 18 q^{67} - 18 q^{68} + 10 q^{70} - 28 q^{71} + 14 q^{73} - 22 q^{74} - 20 q^{76} + 4 q^{77} - 5 q^{80} + 2 q^{82} + 6 q^{83} - 15 q^{85} - 6 q^{86} + 2 q^{88} + 5 q^{89} - 12 q^{91} + 6 q^{92} + 2 q^{94} - 30 q^{95} + 18 q^{97} + 3 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8 + 5 * q^10 + 2 * q^11 - 6 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 8 * q^22 + 6 * q^23 - 5 * q^25 - 6 * q^26 - 2 * q^28 - 12 * q^31 + 4 * q^32 - 3 * q^34 - 10 * q^35 + 13 * q^37 + 10 * q^38 + 5 * q^40 + 12 * q^41 + 4 * q^43 - 8 * q^44 + 6 * q^46 + 2 * q^47 - 12 * q^49 - 5 * q^50 - 6 * q^52 + 21 * q^53 + 10 * q^55 - 2 * q^56 - 20 * q^59 - 2 * q^61 + 18 * q^62 - q^64 + 15 * q^65 + 18 * q^67 - 18 * q^68 + 10 * q^70 - 28 * q^71 + 14 * q^73 - 22 * q^74 - 20 * q^76 + 4 * q^77 - 5 * q^80 + 2 * q^82 + 6 * q^83 - 15 * q^85 - 6 * q^86 + 2 * q^88 + 5 * q^89 - 12 * q^91 + 6 * q^92 + 2 * q^94 - 30 * q^95 + 18 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$	1.80902	+	1.31433i	0.572061	+	0.415627i
$11$	−0.618034	+	0.449028i	−0.186344	+	0.135387i	−0.677046	−	0.735940i	$-0.736740\pi$
$11$	−0.618034	+	0.449028i	−0.186344	+	0.135387i	0.490702	+	0.871327i	$0.336740\pi$
$12$		0			0
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	0.360011	−	0.932948i	$-0.382773\pi$
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	−0.776037	+	0.630688i	$0.782773\pi$
$14$	−1.61803	+	1.17557i	−0.432438	+	0.314184i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.354102	−	1.08981i	−0.0858823	−	0.264319i	0.898888	−	0.438178i	$-0.144376\pi$
$17$	−0.354102	−	1.08981i	−0.0858823	−	0.264319i	−0.984770	+	0.173860i	$0.944376\pi$
$18$		0			0
$19$	−2.23607	−	6.88191i	−0.512989	−	1.57882i	−0.786911	−	0.617066i	$-0.788321\pi$
$19$	−2.23607	−	6.88191i	−0.512989	−	1.57882i	0.273922	−	0.961752i	$-0.411679\pi$
$20$	−2.23607			−0.500000
$21$		0			0
$22$	0.236068	−	0.726543i	0.0503299	−	0.154899i
$23$	4.85410	−	3.52671i	1.01215	−	0.735370i	0.0474912	−	0.998872i	$-0.484877\pi$
$23$	4.85410	−	3.52671i	1.01215	−	0.735370i	0.964659	+	0.263501i	$0.0848774\pi$
$24$		0			0
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	1.85410			0.363619
$27$		0			0
$28$	0.618034	−	1.90211i	0.116797	−	0.359466i
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	−0.791982	−	0.610544i	$-0.790951\pi$
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	0.999596	−	0.0284251i	$-0.00904922\pi$
$30$		0			0
$31$	−3.00000	−	9.23305i	−0.538816	−	1.65830i	−0.735256	−	0.677789i	$-0.762938\pi$
$31$	−3.00000	−	9.23305i	−0.538816	−	1.65830i	0.196440	−	0.980516i	$-0.437062\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.927051	+	0.673542i	0.158988	+	0.115511i
$35$	−1.38197	−	4.25325i	−0.233595	−	0.718931i
$36$		0			0
$37$	7.16312	+	5.20431i	1.17761	+	0.855583i	0.991900	−	0.127021i	$-0.0405417\pi$
$37$	7.16312	+	5.20431i	1.17761	+	0.855583i	0.185710	+	0.982605i	$0.440542\pi$
$38$	5.85410	+	4.25325i	0.949661	+	0.689969i
$39$		0			0
$40$	1.80902	−	1.31433i	0.286031	−	0.207813i
$41$	4.11803	+	2.99193i	0.643129	+	0.467260i	0.860924	−	0.508734i	$-0.169886\pi$
$41$	4.11803	+	2.99193i	0.643129	+	0.467260i	−0.217795	+	0.975995i	$0.569886\pi$
$42$		0			0
$43$	3.23607			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$44$	0.236068	+	0.726543i	0.0355886	+	0.109530i
$45$		0			0
$46$	−1.85410	+	5.70634i	−0.273372	+	0.841354i
$47$	−2.85410	+	8.78402i	−0.416314	+	1.28128i	0.494757	+	0.869031i	$0.335257\pi$
$47$	−2.85410	+	8.78402i	−0.416314	+	1.28128i	−0.911071	+	0.412250i	$0.864743\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	1.54508	−	4.75528i	0.218508	−	0.672499i
$51$		0			0
$52$	−1.50000	+	1.08981i	−0.208013	+	0.151130i
$53$	3.57295	−	10.9964i	0.490782	−	1.51047i	−0.332646	−	0.943052i	$-0.607941\pi$
$53$	3.57295	−	10.9964i	0.490782	−	1.51047i	0.823428	−	0.567421i	$-0.192059\pi$
$54$		0			0
$55$	1.38197	+	1.00406i	0.186344	+	0.135387i
$56$	0.618034	+	1.90211i	0.0825883	+	0.254181i
$57$		0			0
$58$	1.11803	+	3.44095i	0.146805	+	0.451820i
$59$	−7.23607	−	5.25731i	−0.942056	−	0.684444i	0.00685884	−	0.999976i	$-0.497817\pi$
$59$	−7.23607	−	5.25731i	−0.942056	−	0.684444i	−0.948915	+	0.315533i	$0.897817\pi$
$60$		0			0
$61$	1.73607	−	1.26133i	0.222281	−	0.161496i	−0.471072	−	0.882095i	$-0.656133\pi$
$61$	1.73607	−	1.26133i	0.222281	−	0.161496i	0.693353	+	0.720598i	$0.256133\pi$
$62$	7.85410	+	5.70634i	0.997472	+	0.724706i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.28115	+	3.94298i	−0.158907	+	0.489067i
$66$		0			0
$67$	1.14590	+	3.52671i	0.139994	+	0.430856i	0.996333	−	0.0855568i	$-0.0272669\pi$
$67$	1.14590	+	3.52671i	0.139994	+	0.430856i	−0.856340	+	0.516413i	$0.827267\pi$
$68$	−1.14590			−0.138961
$69$		0			0
$70$	3.61803	+	2.62866i	0.432438	+	0.314184i
$71$	−2.52786	+	7.77997i	−0.300002	+	0.923312i	0.681493	+	0.731825i	$0.261331\pi$
$71$	−2.52786	+	7.77997i	−0.300002	+	0.923312i	−0.981495	+	0.191487i	$0.938669\pi$
$72$		0			0
$73$	7.97214	−	5.79210i	0.933068	−	0.677914i	−0.0136741	−	0.999907i	$-0.504353\pi$
$73$	7.97214	−	5.79210i	0.933068	−	0.677914i	0.946742	+	0.321993i	$0.104353\pi$
$74$	−8.85410			−1.02927
$75$		0			0
$76$	−7.23607			−0.830034
$77$	−1.23607	+	0.898056i	−0.140863	+	0.102343i
$78$		0			0
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$	−0.690983	+	2.12663i	−0.0772542	+	0.237764i
$81$		0			0
$82$	−5.09017			−0.562115
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	−0.999771	−	0.0213936i	$-0.993190\pi$
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	0.796257	−	0.604959i	$-0.206810\pi$
$84$		0			0
$85$	−2.07295	+	1.50609i	−0.224843	+	0.163358i
$86$	−2.61803	+	1.90211i	−0.282310	+	0.205110i
$87$		0			0
$88$	−0.618034	−	0.449028i	−0.0658826	−	0.0478665i
$89$	2.92705	−	2.12663i	0.310267	−	0.225422i	−0.421744	−	0.906715i	$-0.638582\pi$
$89$	2.92705	−	2.12663i	0.310267	−	0.225422i	0.732011	+	0.681293i	$0.238582\pi$
$90$		0			0
$91$	−3.00000	−	2.17963i	−0.314485	−	0.228487i
$92$	−1.85410	−	5.70634i	−0.193303	−	0.594927i
$93$		0			0
$94$	−2.85410	−	8.78402i	−0.294378	−	0.906003i
$95$	−13.0902	+	9.51057i	−1.34302	+	0.975763i
$96$		0			0
$97$	−2.20820	+	6.79615i	−0.224209	+	0.690045i	0.774162	+	0.632988i	$0.218172\pi$
$97$	−2.20820	+	6.79615i	−0.224209	+	0.690045i	−0.998371	+	0.0570570i	$0.981828\pi$
$98$	2.42705	−	1.76336i	0.245169	−	0.178126i
$99$		0			0
$100$	1.54508	+	4.75528i	0.154508	+	0.475528i
$101$	−17.3262			−1.72403			−0.862013	−	0.506887i	$-0.830796\pi$
$101$	−17.3262			−1.72403			−0.862013	+	0.506887i	$0.830796\pi$
$102$		0			0
$103$	−4.85410	+	14.9394i	−0.478289	+	1.47202i	0.363181	+	0.931718i	$0.381691\pi$
$103$	−4.85410	+	14.9394i	−0.478289	+	1.47202i	−0.841470	+	0.540303i	$0.818309\pi$
$104$	0.572949	−	1.76336i	0.0561823	−	0.172911i
$105$		0			0
$106$	3.57295	+	10.9964i	0.347035	+	1.06807i
$107$	6.94427			0.671328			0.335664	−	0.941982i	$-0.391039\pi$
$107$	6.94427			0.671328			0.335664	+	0.941982i	$0.391039\pi$
$108$		0			0
$109$	14.2082	+	10.3229i	1.36090	+	0.988751i	0.998387	+	0.0567720i	$0.0180808\pi$
$109$	14.2082	+	10.3229i	1.36090	+	0.988751i	0.362512	+	0.931979i	$0.381919\pi$
$110$	−1.70820			−0.162871
$111$		0			0
$112$	−1.61803	−	1.17557i	−0.152890	−	0.111081i
$113$	6.92705	+	5.03280i	0.651642	+	0.473446i	0.863830	−	0.503783i	$-0.168059\pi$
$113$	6.92705	+	5.03280i	0.651642	+	0.473446i	−0.212188	+	0.977229i	$0.568059\pi$
$114$		0			0
$115$	−10.8541	−	7.88597i	−1.01215	−	0.735370i
$116$	−2.92705	−	2.12663i	−0.271770	−	0.197452i
$117$		0			0
$118$	8.94427			0.823387
$119$	−0.708204	−	2.17963i	−0.0649209	−	0.199806i
$120$		0			0
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$	−0.663119	+	2.04087i	−0.0600360	+	0.184772i
$123$		0			0
$124$	−9.70820			−0.871822
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$		0			0
$127$	−11.0902	+	8.05748i	−0.984093	+	0.714986i	−0.958620	−	0.284690i	$-0.908109\pi$
$127$	−11.0902	+	8.05748i	−0.984093	+	0.714986i	−0.0254737	+	0.999675i	$0.508109\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	−1.28115	−	3.94298i	−0.112365	−	0.345823i
$131$	1.61803	+	4.97980i	0.141368	+	0.435087i	0.996526	−	0.0832809i	$-0.0265399\pi$
$131$	1.61803	+	4.97980i	0.141368	+	0.435087i	−0.855158	+	0.518368i	$0.826540\pi$
$132$		0			0
$133$	−4.47214	−	13.7638i	−0.387783	−	1.19347i
$134$	−3.00000	−	2.17963i	−0.259161	−	0.188291i
$135$		0			0
$136$	0.927051	−	0.673542i	0.0794940	−	0.0577557i
$137$	11.3541	+	8.24924i	0.970046	+	0.704780i	0.955462	−	0.295114i	$-0.0953575\pi$
$137$	11.3541	+	8.24924i	0.970046	+	0.704780i	0.0145842	+	0.999894i	$0.495358\pi$
$138$		0			0
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	−0.943681	−	0.330855i	$-0.892663\pi$
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	0.0230486	+	0.999734i	$0.492663\pi$
$140$	−4.47214			−0.377964
$141$		0			0
$142$	−2.52786	−	7.77997i	−0.212134	−	0.652880i
$143$	1.41641			0.118446
$144$		0			0
$145$	−8.09017			−0.671852
$146$	−3.04508	+	9.37181i	−0.252013	+	0.775616i
$147$		0			0
$148$	7.16312	−	5.20431i	0.588805	−	0.427792i
$149$	22.0344			1.80513			0.902566	−	0.430552i	$-0.141681\pi$
$149$	22.0344			1.80513			0.902566	+	0.430552i	$0.141681\pi$
$150$		0			0
$151$	10.9443			0.890632			0.445316	−	0.895373i	$-0.353091\pi$
$151$	10.9443			0.890632			0.445316	+	0.895373i	$0.353091\pi$
$152$	5.85410	−	4.25325i	0.474830	−	0.344984i
$153$		0			0
$154$	0.472136	−	1.45309i	0.0380458	−	0.117093i
$155$	−17.5623	+	12.7598i	−1.41064	+	1.02489i
$156$		0			0
$157$	11.1459			0.889540			0.444770	−	0.895645i	$-0.353286\pi$
$157$	11.1459			0.889540			0.444770	+	0.895645i	$0.353286\pi$
$158$		0			0
$159$		0			0
$160$	−0.690983	−	2.12663i	−0.0546270	−	0.168125i
$161$	9.70820	−	7.05342i	0.765114	−	0.555888i
$162$		0			0
$163$	−9.32624	−	6.77591i	−0.730487	−	0.530730i	0.159230	−	0.987241i	$-0.449099\pi$
$163$	−9.32624	−	6.77591i	−0.730487	−	0.530730i	−0.889718	+	0.456511i	$0.849099\pi$
$164$	4.11803	−	2.99193i	0.321564	−	0.233630i
$165$		0			0
$166$	4.85410	+	3.52671i	0.376751	+	0.273726i
$167$	0.763932	+	2.35114i	0.0591148	+	0.181937i	0.976253	−	0.216632i	$-0.0695071\pi$
$167$	0.763932	+	2.35114i	0.0591148	+	0.181937i	−0.917139	+	0.398569i	$0.869507\pi$
$168$		0			0
$169$	−2.95492	−	9.09429i	−0.227301	−	0.699561i
$170$	0.791796	−	2.43690i	0.0607280	−	0.186902i
$171$		0			0
$172$	1.00000	−	3.07768i	0.0762493	−	0.234671i
$173$	−17.8713	+	12.9843i	−1.35873	+	0.987176i	−0.360207	+	0.932872i	$0.617294\pi$
$173$	−17.8713	+	12.9843i	−1.35873	+	0.987176i	−0.998524	+	0.0543039i	$0.982706\pi$
$174$		0			0
$175$	−8.09017	+	5.87785i	−0.611559	+	0.444324i
$176$	0.763932			0.0575835
$177$		0			0
$178$	−1.11803	+	3.44095i	−0.0838002	+	0.257910i
$179$	8.09017	−	24.8990i	0.604688	−	1.86104i	0.105764	−	0.994391i	$-0.466271\pi$
$179$	8.09017	−	24.8990i	0.604688	−	1.86104i	0.498923	−	0.866646i	$-0.333729\pi$
$180$		0			0
$181$	2.79180	+	8.59226i	0.207513	+	0.638658i	0.999601	+	0.0282515i	$0.00899392\pi$
$181$	2.79180	+	8.59226i	0.207513	+	0.638658i	−0.792088	+	0.610407i	$0.791006\pi$
$182$	3.70820			0.274870
$183$		0			0
$184$	4.85410	+	3.52671i	0.357849	+	0.259993i
$185$	6.11803	−	18.8294i	0.449807	−	1.38436i
$186$		0			0
$187$	0.708204	+	0.514540i	0.0517890	+	0.0376269i
$188$	7.47214	+	5.42882i	0.544962	+	0.395938i
$189$		0			0
$190$	5.00000	−	15.3884i	0.362738	−	1.11639i
$191$	−4.23607	−	3.07768i	−0.306511	−	0.222693i	0.423887	−	0.905715i	$-0.360665\pi$
$191$	−4.23607	−	3.07768i	−0.306511	−	0.222693i	−0.730398	+	0.683022i	$0.760665\pi$
$192$		0			0
$193$	4.61803			0.332413			0.166207	−	0.986091i	$-0.446848\pi$
$193$	4.61803			0.332413			0.166207	+	0.986091i	$0.446848\pi$
$194$	−2.20820	−	6.79615i	−0.158540	−	0.487935i
$195$		0			0
$196$	−0.927051	+	2.85317i	−0.0662179	+	0.203798i
$197$	−0.718847	+	2.21238i	−0.0512157	+	0.157626i	−0.973393	−	0.229141i	$-0.926408\pi$
$197$	−0.718847	+	2.21238i	−0.0512157	+	0.157626i	0.922177	+	0.386767i	$0.126408\pi$
$198$		0			0
$199$	16.1803			1.14699			0.573497	−	0.819208i	$-0.305586\pi$
$199$	16.1803			1.14699			0.573497	+	0.819208i	$0.305586\pi$
$200$	−4.04508	−	2.93893i	−0.286031	−	0.207813i
$201$		0			0
$202$	14.0172	−	10.1841i	0.986248	−	0.716551i
$203$	2.23607	−	6.88191i	0.156941	−	0.483015i
$204$		0			0
$205$	3.51722	−	10.8249i	0.245653	−	0.756043i
$206$	−4.85410	−	14.9394i	−0.338201	−	1.04088i
$207$		0			0
$208$	0.572949	+	1.76336i	0.0397269	+	0.122267i
$209$	4.47214	+	3.24920i	0.309344	+	0.224752i
$210$		0			0
$211$	6.47214	−	4.70228i	0.445560	−	0.323718i	−0.342280	−	0.939598i	$-0.611199\pi$
$211$	6.47214	−	4.70228i	0.445560	−	0.323718i	0.787840	+	0.615880i	$0.211199\pi$
$212$	−9.35410	−	6.79615i	−0.642442	−	0.466762i
$213$		0			0
$214$	−5.61803	+	4.08174i	−0.384041	+	0.279022i
$215$	−2.23607	−	6.88191i	−0.152499	−	0.469342i
$216$		0			0
$217$	−6.00000	−	18.4661i	−0.407307	−	1.25356i
$218$	−17.5623			−1.18947
$219$		0			0
$220$	1.38197	−	1.00406i	0.0931721	−	0.0676935i
$221$	−0.656541	+	2.02063i	−0.0441637	+	0.135922i
$222$		0			0
$223$	12.7082	−	9.23305i	0.851004	−	0.618291i	−0.0744185	−	0.997227i	$-0.523710\pi$
$223$	12.7082	−	9.23305i	0.851004	−	0.618291i	0.925423	+	0.378936i	$0.123710\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	−8.56231			−0.569556
$227$	0.763932	−	0.555029i	0.0507039	−	0.0368386i	−0.562145	−	0.827039i	$-0.690024\pi$
$227$	0.763932	−	0.555029i	0.0507039	−	0.0368386i	0.612849	+	0.790200i	$0.290024\pi$
$228$		0			0
$229$	2.86475	−	8.81678i	0.189308	−	0.582629i	−0.810688	−	0.585478i	$-0.800907\pi$
$229$	2.86475	−	8.81678i	0.189308	−	0.582629i	0.999996	+	0.00284891i	$0.000906837\pi$
$230$	13.4164			0.884652
$231$		0			0
$232$	3.61803			0.237536
$233$	3.37132	+	10.3759i	0.220863	+	0.679746i	0.998685	+	0.0512616i	$0.0163242\pi$
$233$	3.37132	+	10.3759i	0.220863	+	0.679746i	−0.777823	+	0.628484i	$0.783676\pi$
$234$		0			0
$235$	20.6525			1.34722
$236$	−7.23607	+	5.25731i	−0.471028	+	0.342222i
$237$		0			0
$238$	1.85410	+	1.34708i	0.120184	+	0.0873185i
$239$	−21.7082	+	15.7719i	−1.40419	+	1.02020i	−0.410051	+	0.912063i	$0.634489\pi$
$239$	−21.7082	+	15.7719i	−1.40419	+	1.02020i	−0.994136	+	0.108139i	$0.965511\pi$
$240$		0			0
$241$	5.78115	+	4.20025i	0.372397	+	0.270562i	0.758204	−	0.652017i	$-0.226077\pi$
$241$	5.78115	+	4.20025i	0.372397	+	0.270562i	−0.385807	+	0.922579i	$0.626077\pi$
$242$	−3.21885	−	9.90659i	−0.206915	−	0.636820i
$243$		0			0
$244$	−0.663119	−	2.04087i	−0.0424518	−	0.130653i
$245$	2.07295	+	6.37988i	0.132436	+	0.407596i
$246$		0			0
$247$	−4.14590	+	12.7598i	−0.263797	+	0.811884i
$248$	7.85410	−	5.70634i	0.498736	−	0.362353i
$249$		0			0
$250$	−11.1803			−0.707107
$251$	3.52786			0.222677			0.111338	−	0.993783i	$-0.464486\pi$
$251$	3.52786			0.222677			0.111338	+	0.993783i	$0.464486\pi$
$252$		0			0
$253$	−1.41641	+	4.35926i	−0.0890488	+	0.274064i
$254$	4.23607	−	13.0373i	0.265795	−	0.818031i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.38197			0.585231			0.292615	−	0.956230i	$-0.405474\pi$
$257$	9.38197			0.585231			0.292615	+	0.956230i	$0.405474\pi$
$258$		0			0
$259$	14.3262	+	10.4086i	0.890189	+	0.646760i
$260$	3.35410	+	2.43690i	0.208013	+	0.151130i
$261$		0			0
$262$	−4.23607	−	3.07768i	−0.261705	−	0.190140i
$263$	−6.85410	−	4.97980i	−0.422642	−	0.307067i	0.356058	−	0.934464i	$-0.384121\pi$
$263$	−6.85410	−	4.97980i	−0.422642	−	0.307067i	−0.778700	+	0.627396i	$0.784121\pi$
$264$		0			0
$265$	−25.8541			−1.58820
$266$	11.7082	+	8.50651i	0.717876	+	0.521567i
$267$		0			0
$268$	3.70820			0.226515
$269$	4.04508	+	12.4495i	0.246633	+	0.759059i	0.995364	+	0.0961842i	$0.0306638\pi$
$269$	4.04508	+	12.4495i	0.246633	+	0.759059i	−0.748730	+	0.662875i	$0.769336\pi$
$270$		0			0
$271$	1.79837	−	5.53483i	0.109243	−	0.336217i	−0.881460	−	0.472260i	$-0.843438\pi$
$271$	1.79837	−	5.53483i	0.109243	−	0.336217i	0.990703	+	0.136043i	$0.0434385\pi$
$272$	−0.354102	+	1.08981i	−0.0214706	+	0.0660797i
$273$		0			0
$274$	−14.0344			−0.847852
$275$	1.18034	−	3.63271i	0.0711772	−	0.219061i
$276$		0			0
$277$	23.3435	−	16.9600i	1.40257	−	1.01903i	0.408222	−	0.912883i	$-0.366149\pi$
$277$	23.3435	−	16.9600i	1.40257	−	1.01903i	0.994351	−	0.106146i	$-0.0338510\pi$
$278$	4.14590	−	12.7598i	0.248654	−	0.765280i
$279$		0			0
$280$	3.61803	−	2.62866i	0.216219	−	0.157092i
$281$	−1.57295	−	4.84104i	−0.0938343	−	0.288792i	0.893114	−	0.449831i	$-0.148516\pi$
$281$	−1.57295	−	4.84104i	−0.0938343	−	0.288792i	−0.986948	+	0.161038i	$0.948516\pi$
$282$		0			0
$283$	−0.381966	−	1.17557i	−0.0227055	−	0.0698804i	0.939062	−	0.343749i	$-0.111697\pi$
$283$	−0.381966	−	1.17557i	−0.0227055	−	0.0698804i	−0.961767	+	0.273868i	$0.911697\pi$
$284$	6.61803	+	4.80828i	0.392708	+	0.285319i
$285$		0			0
$286$	−1.14590	+	0.832544i	−0.0677584	+	0.0492293i
$287$	8.23607	+	5.98385i	0.486160	+	0.353216i
$288$		0			0
$289$	12.6910	−	9.22054i	0.746528	−	0.542385i
$290$	6.54508	−	4.75528i	0.384341	−	0.279240i
$291$		0			0
$292$	−3.04508	−	9.37181i	−0.178200	−	0.548444i
$293$	4.20163			0.245462			0.122731	−	0.992440i	$-0.460835\pi$
$293$	4.20163			0.245462			0.122731	+	0.992440i	$0.460835\pi$
$294$		0			0
$295$	−6.18034	+	19.0211i	−0.359833	+	1.10745i
$296$	−2.73607	+	8.42075i	−0.159031	+	0.489446i
$297$		0			0
$298$	−17.8262	+	12.9515i	−1.03265	+	0.750261i
$299$	−11.1246			−0.643353
$300$		0			0
$301$	6.47214			0.373048
$302$	−8.85410	+	6.43288i	−0.509496	+	0.370171i
$303$		0			0
$304$	−2.23607	+	6.88191i	−0.128247	+	0.394705i
$305$	−3.88197	−	2.82041i	−0.222281	−	0.161496i
$306$		0			0
$307$	−29.7082			−1.69554			−0.847768	−	0.530367i	$-0.822054\pi$
$307$	−29.7082			−1.69554			−0.847768	+	0.530367i	$0.822054\pi$
$308$	0.472136	+	1.45309i	0.0269024	+	0.0827972i
$309$		0			0
$310$	6.70820	−	20.6457i	0.381000	−	1.17260i
$311$	10.2361	−	7.43694i	0.580434	−	0.421710i	−0.258446	−	0.966026i	$-0.583211\pi$
$311$	10.2361	−	7.43694i	0.580434	−	0.421710i	0.838881	+	0.544315i	$0.183211\pi$
$312$		0			0
$313$	−14.8541	−	10.7921i	−0.839603	−	0.610008i	0.0826564	−	0.996578i	$-0.473660\pi$
$313$	−14.8541	−	10.7921i	−0.839603	−	0.610008i	−0.922260	+	0.386570i	$0.873660\pi$
$314$	−9.01722	+	6.55139i	−0.508871	+	0.369717i
$315$		0			0
$316$		0			0
$317$	−3.38197	−	10.4086i	−0.189950	−	0.584606i	0.810048	−	0.586363i	$-0.199441\pi$
$317$	−3.38197	−	10.4086i	−0.189950	−	0.584606i	−0.999998	+	0.00175672i	$0.999441\pi$
$318$		0			0
$319$	0.854102	+	2.62866i	0.0478205	+	0.147176i
$320$	1.80902	+	1.31433i	0.101127	+	0.0734732i
$321$		0			0
$322$	−3.70820	+	11.4127i	−0.206650	+	0.636004i
$323$	−6.70820	+	4.87380i	−0.373254	+	0.271185i
$324$		0			0
$325$	9.27051			0.514235
$326$	11.5279			0.638469
$327$		0			0
$328$	−1.57295	+	4.84104i	−0.0868516	+	0.267302i
$329$	−5.70820	+	17.5680i	−0.314703	+	0.968558i
$330$		0			0
$331$	−7.27051	−	22.3763i	−0.399623	−	1.22991i	−0.925302	−	0.379231i	$-0.876189\pi$
$331$	−7.27051	−	22.3763i	−0.399623	−	1.22991i	0.525679	−	0.850683i	$-0.323811\pi$
$332$	−6.00000			−0.329293
$333$		0			0
$334$	−2.00000	−	1.45309i	−0.109435	−	0.0795093i
$335$	6.70820	−	4.87380i	0.366508	−	0.266284i
$336$		0			0
$337$	20.0902	+	14.5964i	1.09438	+	0.795115i	0.980134	−	0.198338i	$-0.0635543\pi$
$337$	20.0902	+	14.5964i	1.09438	+	0.795115i	0.114248	+	0.993452i	$0.463554\pi$
$338$	7.73607	+	5.62058i	0.420787	+	0.305719i
$339$		0			0
$340$	0.791796	+	2.43690i	0.0429412	+	0.132159i
$341$	6.00000	+	4.35926i	0.324918	+	0.236067i
$342$		0			0
$343$	−20.0000			−1.07990
$344$	1.00000	+	3.07768i	0.0539164	+	0.165938i
$345$		0			0
$346$	6.82624	−	21.0090i	0.366981	−	1.12945i
$347$	0.236068	−	0.726543i	0.0126728	−	0.0390028i	−0.944520	−	0.328453i	$-0.893473\pi$
$347$	0.236068	−	0.726543i	0.0126728	−	0.0390028i	0.957193	+	0.289451i	$0.0934726\pi$
$348$		0			0
$349$	−9.79837			−0.524495			−0.262247	−	0.965001i	$-0.584464\pi$
$349$	−9.79837			−0.524495			−0.262247	+	0.965001i	$0.584464\pi$
$350$	3.09017	−	9.51057i	0.165177	−	0.508361i
$351$		0			0
$352$	−0.618034	+	0.449028i	−0.0329413	+	0.0239333i
$353$	−3.56231	+	10.9637i	−0.189602	+	0.583536i	−0.999997	−	0.00234791i	$-0.999253\pi$
$353$	−3.56231	+	10.9637i	−0.189602	+	0.583536i	0.810395	+	0.585884i	$0.199253\pi$
$354$		0			0
$355$	18.2918			0.970828
$356$	−1.11803	−	3.44095i	−0.0592557	−	0.182370i
$357$		0			0
$358$	8.09017	+	24.8990i	0.427579	+	1.31595i
$359$	6.38197	+	4.63677i	0.336827	+	0.244719i	0.743322	−	0.668934i	$-0.233249\pi$
$359$	6.38197	+	4.63677i	0.336827	+	0.244719i	−0.406495	+	0.913653i	$0.633249\pi$
$360$		0			0
$361$	−26.9894	+	19.6089i	−1.42049	+	1.03205i
$362$	−7.30902	−	5.31031i	−0.384153	−	0.279104i
$363$		0			0
$364$	−3.00000	+	2.17963i	−0.157243	+	0.114244i
$365$	−17.8262	−	12.9515i	−0.933068	−	0.677914i
$366$		0			0
$367$	−1.09017	−	3.35520i	−0.0569064	−	0.175140i	0.918563	−	0.395274i	$-0.129350\pi$
$367$	−1.09017	−	3.35520i	−0.0569064	−	0.175140i	−0.975470	+	0.220134i	$0.929350\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	6.11803	+	18.8294i	0.318061	+	0.978892i
$371$	7.14590	−	21.9928i	0.370997	−	1.14181i
$372$		0			0
$373$	−23.7984	+	17.2905i	−1.23223	+	0.895270i	−0.997056	−	0.0766827i	$-0.975567\pi$
$373$	−23.7984	+	17.2905i	−1.23223	+	0.895270i	−0.235178	+	0.971952i	$0.575567\pi$
$374$	−0.875388			−0.0452652
$375$		0			0
$376$	−9.23607			−0.476314
$377$	−5.42705	+	3.94298i	−0.279507	+	0.203074i
$378$		0			0
$379$	7.23607	−	22.2703i	0.371692	−	1.14395i	−0.573992	−	0.818861i	$-0.694606\pi$
$379$	7.23607	−	22.2703i	0.371692	−	1.14395i	0.945684	−	0.325089i	$-0.105394\pi$
$380$	5.00000	+	15.3884i	0.256495	+	0.789409i
$381$		0			0
$382$	5.23607			0.267901
$383$	−3.56231	−	10.9637i	−0.182025	−	0.560216i	0.817859	−	0.575419i	$-0.195161\pi$
$383$	−3.56231	−	10.9637i	−0.182025	−	0.560216i	−0.999884	+	0.0152022i	$0.995161\pi$
$384$		0			0
$385$	2.76393	+	2.00811i	0.140863	+	0.102343i
$386$	−3.73607	+	2.71441i	−0.190161	+	0.138160i
$387$		0			0
$388$	5.78115	+	4.20025i	0.293494	+	0.213236i
$389$	−25.0623	+	18.2088i	−1.27071	+	0.923224i	−0.999231	−	0.0392200i	$-0.987513\pi$
$389$	−25.0623	+	18.2088i	−1.27071	+	0.923224i	−0.271479	+	0.962444i	$0.587513\pi$
$390$		0			0
$391$	−5.56231	−	4.04125i	−0.281298	−	0.204375i
$392$	−0.927051	−	2.85317i	−0.0468231	−	0.144107i
$393$		0			0
$394$	−0.718847	−	2.21238i	−0.0362150	−	0.111458i
$395$		0			0
$396$		0			0
$397$	−7.67376	+	23.6174i	−0.385135	+	1.18532i	0.551247	+	0.834342i	$0.314152\pi$
$397$	−7.67376	+	23.6174i	−0.385135	+	1.18532i	−0.936382	+	0.350982i	$0.885848\pi$
$398$	−13.0902	+	9.51057i	−0.656151	+	0.476722i
$399$		0			0
$400$	5.00000			0.250000
$401$	14.9098			0.744561			0.372281	−	0.928120i	$-0.378576\pi$
$401$	14.9098			0.744561			0.372281	+	0.928120i	$0.378576\pi$
$402$		0			0
$403$	−5.56231	+	17.1190i	−0.277078	+	0.852759i
$404$	−5.35410	+	16.4782i	−0.266377	+	0.819823i
$405$		0			0
$406$	2.23607	+	6.88191i	0.110974	+	0.341543i
$407$	−6.76393			−0.335276
$408$		0			0
$409$	21.0172	+	15.2699i	1.03923	+	0.755048i	0.970136	−	0.242562i	$-0.0779877\pi$
$409$	21.0172	+	15.2699i	1.03923	+	0.755048i	0.0690987	+	0.997610i	$0.477988\pi$
$410$	3.51722	+	10.8249i	0.173703	+	0.534603i
$411$		0			0
$412$	12.7082	+	9.23305i	0.626088	+	0.454880i
$413$	−14.4721	−	10.5146i	−0.712127	−	0.517391i
$414$		0			0
$415$	−10.8541	+	7.88597i	−0.532807	+	0.387107i
$416$	−1.50000	−	1.08981i	−0.0735436	−	0.0534325i
$417$		0			0
$418$	−5.52786			−0.270377
$419$	0.652476	+	2.00811i	0.0318755	+	0.0981028i	0.965729	−	0.259554i	$-0.0835757\pi$
$419$	0.652476	+	2.00811i	0.0318755	+	0.0981028i	−0.933853	+	0.357657i	$0.883576\pi$
$420$		0			0
$421$	0.0278640	−	0.0857567i	0.00135801	−	0.00417953i	−0.950375	−	0.311106i	$-0.899301\pi$
$421$	0.0278640	−	0.0857567i	0.00135801	−	0.00417953i	0.951733	+	0.306926i	$0.0993006\pi$
$422$	−2.47214	+	7.60845i	−0.120342	+	0.370374i
$423$		0			0
$424$	11.5623			0.561515
$425$	4.63525	+	3.36771i	0.224843	+	0.163358i
$426$		0			0
$427$	3.47214	−	2.52265i	0.168028	−	0.122080i
$428$	2.14590	−	6.60440i	0.103726	−	0.319235i
$429$		0			0
$430$	5.85410	+	4.25325i	0.282310	+	0.205110i
$431$	3.00000	+	9.23305i	0.144505	+	0.444740i	0.996947	−	0.0780813i	$-0.0248794\pi$
$431$	3.00000	+	9.23305i	0.144505	+	0.444740i	−0.852442	+	0.522822i	$0.824879\pi$
$432$		0			0
$433$	−9.22542	−	28.3929i	−0.443346	−	1.36448i	−0.884288	−	0.466942i	$-0.845356\pi$
$433$	−9.22542	−	28.3929i	−0.443346	−	1.36448i	0.440942	−	0.897535i	$-0.354644\pi$
$434$	15.7082	+	11.4127i	0.754018	+	0.547826i
$435$		0			0
$436$	14.2082	−	10.3229i	0.680450	−	0.494376i
$437$	−35.1246	−	25.5195i	−1.68024	−	1.22076i
$438$		0			0
$439$	−12.2361	+	8.89002i	−0.583996	+	0.424298i	−0.840162	−	0.542335i	$-0.817540\pi$
$439$	−12.2361	+	8.89002i	−0.583996	+	0.424298i	0.256167	+	0.966633i	$0.417540\pi$
$440$	−0.527864	+	1.62460i	−0.0251649	+	0.0774497i
$441$		0			0
$442$	−0.656541	−	2.02063i	−0.0312285	−	0.0961114i
$443$	28.0689			1.33359			0.666796	−	0.745240i	$-0.267665\pi$
$443$	28.0689			1.33359			0.666796	+	0.745240i	$0.267665\pi$
$444$		0			0
$445$	−6.54508	−	4.75528i	−0.310267	−	0.225422i
$446$	−4.85410	+	14.9394i	−0.229848	+	0.707401i
$447$		0			0
$448$	−1.61803	+	1.17557i	−0.0764449	+	0.0555405i
$449$	19.7984			0.934343			0.467172	−	0.884167i	$-0.345273\pi$
$449$	19.7984			0.934343			0.467172	+	0.884167i	$0.345273\pi$
$450$		0			0
$451$	−3.88854			−0.183104
$452$	6.92705	−	5.03280i	0.325821	−	0.236723i
$453$		0			0
$454$	−0.291796	+	0.898056i	−0.0136947	+	0.0421479i
$455$	−2.56231	+	7.88597i	−0.120123	+	0.369700i
$456$		0			0
$457$	−3.52786			−0.165027			−0.0825133	−	0.996590i	$-0.526295\pi$
$457$	−3.52786			−0.165027			−0.0825133	+	0.996590i	$0.526295\pi$
$458$	2.86475	+	8.81678i	0.133861	+	0.411981i
$459$		0			0
$460$	−10.8541	+	7.88597i	−0.506075	+	0.367685i
$461$	11.2533	−	8.17599i	0.524118	−	0.380794i	−0.294035	−	0.955795i	$-0.594998\pi$
$461$	11.2533	−	8.17599i	0.524118	−	0.380794i	0.818153	+	0.575001i	$0.194998\pi$
$462$		0			0
$463$	20.7984	+	15.1109i	0.966582	+	0.702263i	0.954670	−	0.297666i	$-0.0962081\pi$
$463$	20.7984	+	15.1109i	0.966582	+	0.702263i	0.0119123	+	0.999929i	$0.496208\pi$
$464$	−2.92705	+	2.12663i	−0.135885	+	0.0987262i
$465$		0			0
$466$	−8.82624	−	6.41264i	−0.408868	−	0.297060i
$467$	−11.7984	−	36.3117i	−0.545964	−	1.68030i	−0.718688	−	0.695333i	$-0.755257\pi$
$467$	−11.7984	−	36.3117i	−0.545964	−	1.68030i	0.172724	−	0.984970i	$-0.444743\pi$
$468$		0			0
$469$	2.29180	+	7.05342i	0.105825	+	0.325697i
$470$	−16.7082	+	12.1392i	−0.770692	+	0.559940i
$471$		0			0
$472$	2.76393	−	8.50651i	0.127220	−	0.391544i
$473$	−2.00000	+	1.45309i	−0.0919601	+	0.0668129i
$474$		0			0
$475$	29.2705	+	21.2663i	1.34302	+	0.975763i
$476$	−2.29180			−0.105044
$477$		0			0
$478$	8.29180	−	25.5195i	0.379258	−	1.16724i
$479$	1.38197	−	4.25325i	0.0631436	−	0.194336i	−0.914508	−	0.404568i	$-0.867422\pi$
$479$	1.38197	−	4.25325i	0.0631436	−	0.194336i	0.977652	+	0.210232i	$0.0674219\pi$
$480$		0			0
$481$	−5.07295	−	15.6129i	−0.231307	−	0.711888i
$482$	−7.14590			−0.325487
$483$		0			0
$484$	8.42705	+	6.12261i	0.383048	+	0.278300i
$485$	15.9787			0.725556
$486$		0			0
$487$	−19.1803	−	13.9353i	−0.869144	−	0.631470i	0.0612130	−	0.998125i	$-0.480503\pi$
$487$	−19.1803	−	13.9353i	−0.869144	−	0.631470i	−0.930357	+	0.366655i	$0.880503\pi$
$488$	1.73607	+	1.26133i	0.0785881	+	0.0570976i
$489$		0			0
$490$	−5.42705	−	3.94298i	−0.245169	−	0.178126i
$491$	−4.76393	−	3.46120i	−0.214993	−	0.156202i	0.475077	−	0.879944i	$-0.342420\pi$
$491$	−4.76393	−	3.46120i	−0.214993	−	0.156202i	−0.690070	+	0.723743i	$0.742420\pi$
$492$		0			0
$493$	−4.14590			−0.186722
$494$	−4.14590	−	12.7598i	−0.186533	−	0.574089i
$495$		0			0
$496$	−3.00000	+	9.23305i	−0.134704	+	0.414576i
$497$	−5.05573	+	15.5599i	−0.226780	+	0.697958i
$498$		0			0
$499$	−6.58359			−0.294722			−0.147361	−	0.989083i	$-0.547078\pi$
$499$	−6.58359			−0.294722			−0.147361	+	0.989083i	$0.547078\pi$
$500$	9.04508	−	6.57164i	0.404508	−	0.293893i
$501$		0			0
$502$	−2.85410	+	2.07363i	−0.127385	+	0.0925505i
$503$	−9.41641	+	28.9807i	−0.419857	+	1.29219i	0.487977	+	0.872857i	$0.337735\pi$
$503$	−9.41641	+	28.9807i	−0.419857	+	1.29219i	−0.907834	+	0.419330i	$0.862265\pi$
$504$		0			0
$505$	11.9721	+	36.8464i	0.532753	+	1.63965i
$506$	−1.41641	−	4.35926i	−0.0629670	−	0.193793i
$507$		0			0
$508$	4.23607	+	13.0373i	0.187945	+	0.578436i
$509$	23.2533	+	16.8945i	1.03068	+	0.748836i	0.968445	−	0.249226i	$-0.0801761\pi$
$509$	23.2533	+	16.8945i	1.03068	+	0.748836i	0.0622385	+	0.998061i	$0.480176\pi$
$510$		0			0
$511$	15.9443	−	11.5842i	0.705333	−	0.512454i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	−7.59017	+	5.51458i	−0.334788	+	0.243238i
$515$	35.1246			1.54778
$516$		0			0
$517$	−2.18034	−	6.71040i	−0.0958912	−	0.295123i
$518$	−17.7082			−0.778054
$519$		0			0
$520$	−4.14590			−0.181810
$521$	8.42705	−	25.9358i	0.369196	−	1.13627i	−0.578116	−	0.815955i	$-0.696212\pi$
$521$	8.42705	−	25.9358i	0.369196	−	1.13627i	0.947312	−	0.320313i	$-0.103788\pi$
$522$		0			0
$523$	12.7082	−	9.23305i	0.555691	−	0.403733i	−0.274188	−	0.961676i	$-0.588409\pi$
$523$	12.7082	−	9.23305i	0.555691	−	0.403733i	0.829879	+	0.557943i	$0.188409\pi$
$524$	5.23607			0.228739
$525$		0			0
$526$	8.47214			0.369403
$527$	−9.00000	+	6.53888i	−0.392046	+	0.284838i
$528$		0			0
$529$	4.01722	−	12.3637i	0.174662	−	0.537554i
$530$	20.9164	−	15.1967i	0.908551	−	0.660101i
$531$		0			0
$532$	−14.4721			−0.627447
$533$	−2.91641	−	8.97578i	−0.126324	−	0.388784i
$534$		0			0
$535$	−4.79837	−	14.7679i	−0.207452	−	0.638471i
$536$	−3.00000	+	2.17963i	−0.129580	+	0.0941456i
$537$		0			0
$538$	−10.5902	−	7.69421i	−0.456575	−	0.331721i
$539$	1.85410	−	1.34708i	0.0798618	−	0.0580230i
$540$		0			0
$541$	9.92705	+	7.21242i	0.426797	+	0.310086i	0.780367	−	0.625322i	$-0.215032\pi$
$541$	9.92705	+	7.21242i	0.426797	+	0.310086i	−0.353570	+	0.935408i	$0.615032\pi$
$542$	1.79837	+	5.53483i	0.0772468	+	0.237741i
$543$		0			0
$544$	−0.354102	−	1.08981i	−0.0151820	−	0.0467254i
$545$	12.1353	−	37.3485i	0.519817	−	1.59983i
$546$		0			0
$547$	0.618034	−	1.90211i	0.0264252	−	0.0813285i	−0.936974	−	0.349399i	$-0.886386\pi$
$547$	0.618034	−	1.90211i	0.0264252	−	0.0813285i	0.963399	+	0.268070i	$0.0863859\pi$
$548$	11.3541	−	8.24924i	0.485023	−	0.352390i
$549$		0			0
$550$	1.18034	+	3.63271i	0.0503299	+	0.154899i
$551$	−26.1803			−1.11532
$552$		0			0
$553$		0			0
$554$	−8.91641	+	27.4419i	−0.378822	+	1.16589i
$555$		0			0
$556$	4.14590	+	12.7598i	0.175825	+	0.541134i
$557$	−6.27051			−0.265690			−0.132845	−	0.991137i	$-0.542411\pi$
$557$	−6.27051			−0.265690			−0.132845	+	0.991137i	$0.542411\pi$
$558$		0			0
$559$	−4.85410	−	3.52671i	−0.205307	−	0.149164i
$560$	−1.38197	+	4.25325i	−0.0583987	+	0.179733i
$561$		0			0
$562$	4.11803	+	2.99193i	0.173709	+	0.126207i
$563$	1.23607	+	0.898056i	0.0520941	+	0.0378485i	0.613528	−	0.789673i	$-0.289750\pi$
$563$	1.23607	+	0.898056i	0.0520941	+	0.0378485i	−0.561434	+	0.827522i	$0.689750\pi$
$564$		0			0
$565$	5.91641	−	18.2088i	0.248905	−	0.766051i
$566$	1.00000	+	0.726543i	0.0420331	+	0.0305389i
$567$		0			0
$568$	−8.18034			−0.343239
$569$	−7.29837	−	22.4621i	−0.305964	−	0.941660i	−0.979316	−	0.202338i	$-0.935146\pi$
$569$	−7.29837	−	22.4621i	−0.305964	−	0.941660i	0.673352	−	0.739322i	$-0.264854\pi$
$570$		0			0
$571$	6.27051	−	19.2986i	0.262413	−	0.807623i	−0.729866	−	0.683591i	$-0.760417\pi$
$571$	6.27051	−	19.2986i	0.262413	−	0.807623i	0.992278	−	0.124032i	$-0.0395827\pi$
$572$	0.437694	−	1.34708i	0.0183009	−	0.0563244i
$573$		0			0
$574$	−10.1803			−0.424919
$575$	−9.27051	+	28.5317i	−0.386607	+	1.18985i
$576$		0			0
$577$	20.0902	−	14.5964i	0.836365	−	0.607655i	−0.0849881	−	0.996382i	$-0.527085\pi$
$577$	20.0902	−	14.5964i	0.836365	−	0.607655i	0.921353	+	0.388727i	$0.127085\pi$
$578$	−4.84752	+	14.9191i	−0.201630	+	0.620555i
$579$		0			0
$580$	−2.50000	+	7.69421i	−0.103807	+	0.319485i
$581$	−3.70820	−	11.4127i	−0.153842	−	0.473478i
$582$		0			0
$583$	2.72949	+	8.40051i	0.113044	+	0.347913i
$584$	7.97214	+	5.79210i	0.329889	+	0.239679i
$585$		0			0
$586$	−3.39919	+	2.46965i	−0.140419	+	0.102020i
$587$	16.0902	+	11.6902i	0.664112	+	0.482506i	0.868049	−	0.496478i	$-0.165374\pi$
$587$	16.0902	+	11.6902i	0.664112	+	0.482506i	−0.203937	+	0.978984i	$0.565374\pi$
$588$		0			0
$589$	−56.8328	+	41.2915i	−2.34176	+	1.70138i
$590$	−6.18034	−	19.0211i	−0.254441	−	0.783088i
$591$		0			0
$592$	−2.73607	−	8.42075i	−0.112452	−	0.346091i
$593$	−23.0344			−0.945911			−0.472956	−	0.881086i	$-0.656813\pi$
$593$	−23.0344			−0.945911			−0.472956	+	0.881086i	$0.656813\pi$
$594$		0			0
$595$	−4.14590	+	3.01217i	−0.169965	+	0.123487i
$596$	6.80902	−	20.9560i	0.278908	−	0.858391i
$597$		0			0
$598$	9.00000	−	6.53888i	0.368037	−	0.267395i
$599$	−18.9443			−0.774042			−0.387021	−	0.922071i	$-0.626496\pi$
$599$	−18.9443			−0.774042			−0.387021	+	0.922071i	$0.626496\pi$
$600$		0			0
$601$	−8.32624			−0.339634			−0.169817	−	0.985476i	$-0.554318\pi$
$601$	−8.32624			−0.339634			−0.169817	+	0.985476i	$0.554318\pi$
$602$	−5.23607	+	3.80423i	−0.213406	+	0.155049i
$603$		0			0
$604$	3.38197	−	10.4086i	0.137610	−	0.423521i
$605$	23.2918			0.946946
$606$		0			0
$607$	−24.1803			−0.981450			−0.490725	−	0.871315i	$-0.663268\pi$
$607$	−24.1803			−0.981450			−0.490725	+	0.871315i	$0.663268\pi$
$608$	−2.23607	−	6.88191i	−0.0906845	−	0.279098i
$609$		0			0
$610$	4.79837			0.194280
$611$	13.8541	−	10.0656i	0.560477	−	0.407210i
$612$		0			0
$613$	1.16312	+	0.845055i	0.0469779	+	0.0341315i	0.611026	−	0.791610i	$-0.290757\pi$
$613$	1.16312	+	0.845055i	0.0469779	+	0.0341315i	−0.564048	+	0.825742i	$0.690757\pi$
$614$	24.0344	−	17.4620i	0.969951	−	0.704711i
$615$		0			0
$616$	−1.23607	−	0.898056i	−0.0498026	−	0.0361837i
$617$	−3.28115	−	10.0984i	−0.132094	−	0.406544i	0.863032	−	0.505148i	$-0.168562\pi$
$617$	−3.28115	−	10.0984i	−0.132094	−	0.406544i	−0.995127	+	0.0986041i	$0.968562\pi$
$618$		0			0
$619$	−7.23607	−	22.2703i	−0.290842	−	0.895120i	−0.984586	−	0.174899i	$-0.944040\pi$
$619$	−7.23607	−	22.2703i	−0.290842	−	0.895120i	0.693744	−	0.720221i	$-0.255960\pi$
$620$	6.70820	+	20.6457i	0.269408	+	0.829152i
$621$		0			0
$622$	−3.90983	+	12.0332i	−0.156770	+	0.482488i
$623$	5.85410	−	4.25325i	0.234540	−	0.170403i
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	18.3607			0.733840
$627$		0			0
$628$	3.44427	−	10.6004i	0.137441	−	0.423001i
$629$	3.13525	−	9.64932i	0.125011	−	0.384744i
$630$		0			0
$631$	−0.888544	−	2.73466i	−0.0353724	−	0.108865i	0.931811	−	0.362943i	$-0.118228\pi$
$631$	−0.888544	−	2.73466i	−0.0353724	−	0.108865i	−0.967184	+	0.254078i	$0.918228\pi$
$632$		0			0
$633$		0			0
$634$	8.85410	+	6.43288i	0.351641	+	0.255482i
$635$	24.7984	+	18.0171i	0.984093	+	0.714986i
$636$		0			0
$637$	4.50000	+	3.26944i	0.178296	+	0.129540i
$638$	−2.23607	−	1.62460i	−0.0885268	−	0.0643185i
$639$		0			0
$640$	−2.23607			−0.0883883
$641$	−7.32624	−	5.32282i	−0.289369	−	0.210239i	0.433625	−	0.901094i	$-0.357234\pi$
$641$	−7.32624	−	5.32282i	−0.289369	−	0.210239i	−0.722994	+	0.690855i	$0.757234\pi$
$642$		0			0
$643$	31.7771			1.25317			0.626583	−	0.779355i	$-0.284453\pi$
$643$	31.7771			1.25317			0.626583	+	0.779355i	$0.284453\pi$
$644$	−3.70820	−	11.4127i	−0.146124	−	0.449723i
$645$		0			0
$646$	2.56231	−	7.88597i	0.100813	−	0.310269i
$647$	0.0344419	−	0.106001i	0.00135405	−	0.00416733i	−0.950377	−	0.311100i	$-0.899303\pi$
$647$	0.0344419	−	0.106001i	0.00135405	−	0.00416733i	0.951731	+	0.306933i	$0.0993026\pi$
$648$		0			0
$649$	6.83282			0.268211
$650$	−7.50000	+	5.44907i	−0.294174	+	0.213730i
$651$		0			0
$652$	−9.32624	+	6.77591i	−0.365244	+	0.265365i
$653$	−5.93769	+	18.2743i	−0.232360	+	0.715130i	0.765101	+	0.643911i	$0.222689\pi$
$653$	−5.93769	+	18.2743i	−0.232360	+	0.715130i	−0.997461	+	0.0712197i	$0.977311\pi$
$654$		0			0
$655$	9.47214	−	6.88191i	0.370107	−	0.268898i
$656$	−1.57295	−	4.84104i	−0.0614133	−	0.189011i
$657$		0			0
$658$	−5.70820	−	17.5680i	−0.222529	−	0.684874i
$659$	17.0344	+	12.3762i	0.663568	+	0.482110i	0.867866	−	0.496799i	$-0.165491\pi$
$659$	17.0344	+	12.3762i	0.663568	+	0.482110i	−0.204298	+	0.978909i	$0.565491\pi$
$660$		0			0
$661$	26.2705	−	19.0866i	1.02180	−	0.742384i	0.0551524	−	0.998478i	$-0.482436\pi$
$661$	26.2705	−	19.0866i	1.02180	−	0.742384i	0.966652	+	0.256094i	$0.0824355\pi$
$662$	19.0344	+	13.8293i	0.739795	+	0.537492i
$663$		0			0
$664$	4.85410	−	3.52671i	0.188376	−	0.136863i
$665$	−26.1803	+	19.0211i	−1.01523	+	0.737608i
$666$		0			0
$667$	−6.70820	−	20.6457i	−0.259743	−	0.799406i
$668$	2.47214			0.0956498
$669$		0			0
$670$	−2.56231	+	7.88597i	−0.0989905	+	0.304661i
$671$	−0.506578	+	1.55909i	−0.0195562	+	0.0601879i
$672$		0			0
$673$	−4.69098	+	3.40820i	−0.180824	+	0.131376i	−0.674515	−	0.738261i	$-0.735647\pi$
$673$	−4.69098	+	3.40820i	−0.180824	+	0.131376i	0.493691	+	0.869637i	$0.335647\pi$
$674$	−24.8328			−0.956524
$675$		0			0
$676$	−9.56231			−0.367781
$677$	22.2705	−	16.1805i	0.855925	−	0.621866i	−0.0708481	−	0.997487i	$-0.522571\pi$
$677$	22.2705	−	16.1805i	0.855925	−	0.621866i	0.926773	+	0.375621i	$0.122571\pi$
$678$		0			0
$679$	−4.41641	+	13.5923i	−0.169486	+	0.521625i
$680$	−2.07295	−	1.50609i	−0.0794940	−	0.0577557i
$681$		0			0
$682$	−7.41641			−0.283989
$683$	2.29180	+	7.05342i	0.0876931	+	0.269892i	0.985281	−	0.170945i	$-0.0546819\pi$
$683$	2.29180	+	7.05342i	0.0876931	+	0.269892i	−0.897588	+	0.440836i	$0.854682\pi$
$684$		0			0
$685$	9.69756	−	29.8460i	0.370525	−	1.14036i
$686$	16.1803	−	11.7557i	0.617768	−	0.448835i
$687$		0			0
$688$	−2.61803	−	1.90211i	−0.0998116	−	0.0725174i
$689$	−17.3435	+	12.6008i	−0.660733	+	0.480051i
$690$		0			0
$691$	1.47214	+	1.06957i	0.0560027	+	0.0406883i	0.615434	−	0.788188i	$-0.288981\pi$
$691$	1.47214	+	1.06957i	0.0560027	+	0.0406883i	−0.559432	+	0.828876i	$0.688981\pi$
$692$	6.82624	+	21.0090i	0.259495	+	0.798642i
$693$		0			0
$694$	0.236068	+	0.726543i	0.00896102	+	0.0275792i
$695$	24.2705	+	17.6336i	0.920633	+	0.668879i
$696$		0			0
$697$	1.80244	−	5.54734i	0.0682723	−	0.210120i
$698$	7.92705	−	5.75934i	0.300043	−	0.217994i
$699$		0			0
$700$	3.09017	+	9.51057i	0.116797	+	0.359466i
$701$	−49.1591			−1.85671			−0.928356	−	0.371692i	$-0.878778\pi$
$701$	−49.1591			−1.85671			−0.928356	+	0.371692i	$0.878778\pi$
$702$		0			0
$703$	19.7984	−	60.9331i	0.746710	−	2.29814i
$704$	0.236068	−	0.726543i	0.00889715	−	0.0273826i
$705$		0			0
$706$	−3.56231	−	10.9637i	−0.134069	−	0.412622i
$707$	−34.6525			−1.30324
$708$		0			0
$709$	4.20820	+	3.05744i	0.158042	+	0.114825i	0.663996	−	0.747736i	$-0.268859\pi$
$709$	4.20820	+	3.05744i	0.158042	+	0.114825i	−0.505953	+	0.862561i	$0.668859\pi$
$710$	−14.7984	+	10.7516i	−0.555373	+	0.403502i
$711$		0			0
$712$	2.92705	+	2.12663i	0.109696	+	0.0796987i
$713$	−47.1246	−	34.2380i	−1.76483	−	1.28222i
$714$		0			0
$715$	−0.978714	−	3.01217i	−0.0366018	−	0.112649i
$716$	−21.1803	−	15.3884i	−0.791546	−	0.575092i
$717$		0			0
$718$	−7.88854			−0.294398
$719$	6.90983	+	21.2663i	0.257693	+	0.793098i	0.993287	+	0.115675i	$0.0369032\pi$
$719$	6.90983	+	21.2663i	0.257693	+	0.793098i	−0.735594	+	0.677423i	$0.763097\pi$
$720$		0			0
$721$	−9.70820	+	29.8788i	−0.361552	+	1.11274i
$722$	10.3090	−	31.7279i	0.383662	−	1.18079i
$723$		0			0
$724$	9.03444			0.335762
$725$	5.59017	+	17.2048i	0.207614	+	0.638969i
$726$		0			0
$727$	−19.1803	+	13.9353i	−0.711359	+	0.516833i	−0.883612	−	0.468220i	$-0.844895\pi$
$727$	−19.1803	+	13.9353i	−0.711359	+	0.516833i	0.172253	+	0.985053i	$0.444895\pi$
$728$	1.14590	−	3.52671i	0.0424698	−	0.130709i
$729$		0			0
$730$	22.0344			0.815531
$731$	−1.14590	−	3.52671i	−0.0423826	−	0.130440i
$732$		0			0
$733$	11.8541	+	36.4832i	0.437841	+	1.34754i	0.890147	+	0.455674i	$0.150602\pi$
$733$	11.8541	+	36.4832i	0.437841	+	1.34754i	−0.452306	+	0.891863i	$0.649398\pi$
$734$	2.85410	+	2.07363i	0.105347	+	0.0765389i
$735$		0			0
$736$	4.85410	−	3.52671i	0.178925	−	0.129996i
$737$	−2.29180	−	1.66509i	−0.0844194	−	0.0613343i
$738$		0			0
$739$	−17.5623	+	12.7598i	−0.646040	+	0.469375i	−0.861920	−	0.507044i	$-0.830738\pi$
$739$	−17.5623	+	12.7598i	−0.646040	+	0.469375i	0.215880	+	0.976420i	$0.430738\pi$
$740$	−16.0172	−	11.6372i	−0.588805	−	0.427792i
$741$		0			0
$742$	7.14590	+	21.9928i	0.262334	+	0.807382i
$743$	24.6525			0.904412			0.452206	−	0.891914i	$-0.350637\pi$
$743$	24.6525			0.904412			0.452206	+	0.891914i	$0.350637\pi$
$744$		0			0
$745$	−15.2254	−	46.8590i	−0.557816	−	1.71678i
$746$	9.09017	−	27.9767i	0.332815	−	1.02430i
$747$		0			0
$748$	0.708204	−	0.514540i	0.0258945	−	0.0188135i
$749$	13.8885			0.507476
$750$		0			0
$751$	19.2361			0.701934			0.350967	−	0.936388i	$-0.385853\pi$
$751$	19.2361			0.701934			0.350967	+	0.936388i	$0.385853\pi$
$752$	7.47214	−	5.42882i	0.272481	−	0.197969i
$753$		0			0
$754$	2.07295	−	6.37988i	0.0754924	−	0.232342i
$755$	−7.56231	−	23.2744i	−0.275220	−	0.847042i
$756$		0			0
$757$	−22.1459			−0.804906			−0.402453	−	0.915441i	$-0.631842\pi$
$757$	−22.1459			−0.804906			−0.402453	+	0.915441i	$0.631842\pi$
$758$	7.23607	+	22.2703i	0.262826	+	0.808895i
$759$		0			0
$760$	−13.0902	−	9.51057i	−0.474830	−	0.344984i
$761$	−36.5344	+	26.5438i	−1.32437	+	0.962213i	−0.324506	+	0.945884i	$0.605198\pi$
$761$	−36.5344	+	26.5438i	−1.32437	+	0.962213i	−0.999867	+	0.0163292i	$0.994802\pi$
$762$		0			0
$763$	28.4164	+	20.6457i	1.02874	+	0.747426i
$764$	−4.23607	+	3.07768i	−0.153256	+	0.111347i
$765$		0			0
$766$	9.32624	+	6.77591i	0.336971	+	0.244824i
$767$	5.12461	+	15.7719i	0.185039	+	0.569492i
$768$		0			0
$769$	13.0902	+	40.2874i	0.472044	+	1.45280i	0.849904	+	0.526938i	$0.176660\pi$
$769$	13.0902	+	40.2874i	0.472044	+	1.45280i	−0.377860	+	0.925863i	$0.623340\pi$
$770$	−3.41641			−0.123119
$771$		0			0
$772$	1.42705	−	4.39201i	0.0513607	−	0.158072i
$773$	2.35410	−	1.71036i	0.0846712	−	0.0615172i	−0.544644	−	0.838667i	$-0.683335\pi$
$773$	2.35410	−	1.71036i	0.0846712	−	0.0615172i	0.629315	+	0.777150i	$0.283335\pi$
$774$		0			0
$775$	39.2705	+	28.5317i	1.41064	+	1.02489i
$776$	−7.14590			−0.256523
$777$		0			0
$778$	9.57295	−	29.4625i	0.343207	−	1.05628i
$779$	11.3820	−	35.0301i	0.407801	−	1.25508i
$780$		0			0
$781$	−1.93112	−	5.94336i	−0.0691008	−	0.212670i
$782$	6.87539			0.245863
$783$		0			0
$784$	2.42705	+	1.76336i	0.0866804	+	0.0629770i
$785$	−7.70163	−	23.7032i	−0.274883	−	0.846002i
$786$		0			0
$787$	29.5623	+	21.4783i	1.05378	+	0.765618i	0.972928	−	0.231108i	$-0.0742351\pi$
$787$	29.5623	+	21.4783i	1.05378	+	0.765618i	0.0808543	+	0.996726i	$0.474235\pi$
$788$	1.88197	+	1.36733i	0.0670423	+	0.0487091i
$789$		0			0
$790$		0			0
$791$	13.8541	+	10.0656i	0.492595	+	0.357891i
$792$		0			0
$793$	−3.97871			−0.141288
$794$	−7.67376	−	23.6174i	−0.272332	−	0.838151i
$795$		0			0
$796$	5.00000	−	15.3884i	0.177220	−	0.545428i
$797$	−0.718847	+	2.21238i	−0.0254629	+	0.0783667i	−0.962980	−	0.269571i	$-0.913118\pi$
$797$	−0.718847	+	2.21238i	−0.0254629	+	0.0783667i	0.937518	+	0.347938i	$0.113118\pi$
$798$		0			0
$799$	10.5836			0.374421
$800$	−4.04508	+	2.93893i	−0.143015	+	0.103907i
$801$		0			0
$802$	−12.0623	+	8.76378i	−0.425935	+	0.309460i
$803$	−2.32624	+	7.15942i	−0.0820912	+	0.252651i
$804$		0			0
$805$	−21.7082	−	15.7719i	−0.765114	−	0.555888i
$806$	−5.56231	−	17.1190i	−0.195924	−	0.602992i
$807$		0			0
$808$	−5.35410	−	16.4782i	−0.188357	−	0.579702i
$809$	−34.9615	−	25.4010i	−1.22918	−	0.893052i	−0.232352	−	0.972632i	$-0.574642\pi$
$809$	−34.9615	−	25.4010i	−1.22918	−	0.893052i	−0.996829	+	0.0795797i	$0.974642\pi$
$810$		0			0
$811$	−19.1803	+	13.9353i	−0.673513	+	0.489336i	−0.871199	−	0.490930i	$-0.836657\pi$
$811$	−19.1803	+	13.9353i	−0.673513	+	0.489336i	0.197686	+	0.980265i	$0.436657\pi$
$812$	−5.85410	−	4.25325i	−0.205439	−	0.149260i
$813$		0			0
$814$	5.47214	−	3.97574i	0.191798	−	0.139350i
$815$	−7.96556	+	24.5155i	−0.279021	+	0.858739i
$816$		0			0
$817$	−7.23607	−	22.2703i	−0.253158	−	0.779140i
$818$	−25.9787			−0.908324
$819$		0			0
$820$	−9.20820	−	6.69015i	−0.321564	−	0.233630i
$821$	−2.72949	+	8.40051i	−0.0952599	+	0.293180i	−0.987321	−	0.158734i	$-0.949259\pi$
$821$	−2.72949	+	8.40051i	−0.0952599	+	0.293180i	0.892061	+	0.451914i	$0.149259\pi$
$822$		0			0
$823$	−20.7082	+	15.0454i	−0.721843	+	0.524449i	−0.886972	−	0.461822i	$-0.847196\pi$
$823$	−20.7082	+	15.0454i	−0.721843	+	0.524449i	0.165130	+	0.986272i	$0.447196\pi$
$824$	−15.7082			−0.547221
$825$		0			0
$826$	17.8885			0.622422
$827$	15.5623	−	11.3067i	0.541154	−	0.393172i	−0.283359	−	0.959014i	$-0.591449\pi$
$827$	15.5623	−	11.3067i	0.541154	−	0.393172i	0.824514	+	0.565842i	$0.191449\pi$
$828$		0			0
$829$	14.1697	−	43.6098i	0.492134	−	1.51463i	−0.329242	−	0.944245i	$-0.606793\pi$
$829$	14.1697	−	43.6098i	0.492134	−	1.51463i	0.821376	−	0.570387i	$-0.193207\pi$
$830$	4.14590	−	12.7598i	0.143906	−	0.442898i
$831$		0			0
$832$	1.85410			0.0642794
$833$	1.06231	+	3.26944i	0.0368067	+	0.113279i
$834$		0			0
$835$	4.47214	−	3.24920i	0.154765	−	0.112443i
$836$	4.47214	−	3.24920i	0.154672	−	0.112376i
$837$		0			0
$838$	−1.70820	−	1.24108i	−0.0590089	−	0.0428725i
$839$	28.4164	−	20.6457i	0.981043	−	0.712770i	0.0231018	−	0.999733i	$-0.492646\pi$
$839$	28.4164	−	20.6457i	0.981043	−	0.712770i	0.957942	+	0.286963i	$0.0926458\pi$
$840$		0			0
$841$	12.8713	+	9.35156i	0.443839	+	0.322468i
$842$	0.0278640	+	0.0857567i	0.000960258	+	0.00295537i
$843$		0			0
$844$	−2.47214	−	7.60845i	−0.0850944	−	0.261894i
$845$	−17.2984	+	12.5680i	−0.595082	+	0.432352i
$846$		0			0
$847$	−6.43769	+	19.8132i	−0.221202	+	0.680789i
$848$	−9.35410	+	6.79615i	−0.321221	+	0.233381i
$849$		0			0
$850$	−5.72949			−0.196520
$851$	53.1246			1.82109
$852$		0			0
$853$	−12.1910	+	37.5200i	−0.417411	+	1.28466i	0.492665	+	0.870219i	$0.336023\pi$
$853$	−12.1910	+	37.5200i	−0.417411	+	1.28466i	−0.910076	+	0.414441i	$0.863977\pi$
$854$	−1.32624	+	4.08174i	−0.0453829	+	0.139674i
$855$		0			0
$856$	2.14590	+	6.60440i	0.0733453	+	0.225734i
$857$	39.3050			1.34263			0.671316	−	0.741171i	$-0.265729\pi$
$857$	39.3050			1.34263			0.671316	+	0.741171i	$0.265729\pi$
$858$		0			0
$859$	−44.0689	−	32.0179i	−1.50361	−	1.09244i	−0.968915	−	0.247393i	$-0.920426\pi$
$859$	−44.0689	−	32.0179i	−1.50361	−	1.09244i	−0.534696	−	0.845045i	$-0.679574\pi$
$860$	−7.23607			−0.246748
$861$		0			0
$862$	−7.85410	−	5.70634i	−0.267512	−	0.194359i
$863$	−8.23607	−	5.98385i	−0.280359	−	0.203693i	0.438715	−	0.898626i	$-0.355434\pi$
$863$	−8.23607	−	5.98385i	−0.280359	−	0.203693i	−0.719074	+	0.694934i	$0.755434\pi$
$864$		0			0
$865$	39.9615	+	29.0337i	1.35873	+	0.987176i
$866$	24.1525	+	17.5478i	0.820735	+	0.596299i
$867$		0			0
$868$	−19.4164			−0.659036
$869$		0			0
$870$		0			0
$871$	2.12461	−	6.53888i	0.0719897	−	0.221562i
$872$	−5.42705	+	16.7027i	−0.183783	+	0.565626i
$873$		0			0
$874$	43.4164			1.46858
$875$	18.0902	+	13.1433i	0.611559	+	0.444324i
$876$		0			0
$877$	23.4443	−	17.0333i	0.791657	−	0.575172i	−0.116798	−	0.993156i	$-0.537263\pi$
$877$	23.4443	−	17.0333i	0.791657	−	0.575172i	0.908455	+	0.417983i	$0.137263\pi$
$878$	4.67376	−	14.3844i	0.157732	−	0.485449i
$879$		0			0
$880$	−0.527864	−	1.62460i	−0.0177943	−	0.0547652i
$881$	13.2016	+	40.6304i	0.444774	+	1.36887i	0.882731	+	0.469878i	$0.155702\pi$
$881$	13.2016	+	40.6304i	0.444774	+	1.36887i	−0.437957	+	0.898996i	$0.644298\pi$
$882$		0			0
$883$	6.12461	+	18.8496i	0.206110	+	0.634340i	0.999666	+	0.0258434i	$0.00822713\pi$
$883$	6.12461	+	18.8496i	0.206110	+	0.634340i	−0.793556	+	0.608497i	$0.791773\pi$
$884$	1.71885	+	1.24882i	0.0578111	+	0.0420022i
$885$		0			0
$886$	−22.7082	+	16.4985i	−0.762897	+	0.554277i
$887$	38.9787	+	28.3197i	1.30878	+	0.950882i	1.00000		0.000252175i	$-8.02698e-5\pi$
$887$	38.9787	+	28.3197i	1.30878	+	0.950882i	0.308777	+	0.951134i	$0.400080\pi$
$888$		0			0
$889$	−22.1803	+	16.1150i	−0.743905	+	0.540478i
$890$	8.09017			0.271183
$891$		0			0
$892$	−4.85410	−	14.9394i	−0.162527	−	0.500208i
$893$	66.8328			2.23647
$894$		0			0
$895$	−58.5410			−1.95681
$896$	0.618034	−	1.90211i	0.0206471	−	0.0635451i
$897$		0			0
$898$	−16.0172	+	11.6372i	−0.534502	+	0.388338i
$899$	−35.1246			−1.17147
$900$		0			0
$901$	−13.2492			−0.441396
$902$	3.14590	−	2.28563i	0.104747	−	0.0761031i
$903$		0			0
$904$	−2.64590	+	8.14324i	−0.0880013	+	0.270840i
$905$	16.3435	−	11.8742i	0.543275	−	0.394712i
$906$		0			0
$907$	33.7082			1.11926			0.559631	−	0.828742i	$-0.310943\pi$
$907$	33.7082			1.11926			0.559631	+	0.828742i	$0.310943\pi$
$908$	−0.291796	−	0.898056i	−0.00968359	−	0.0298030i
$909$		0			0
$910$	−2.56231	−	7.88597i	−0.0849396	−	0.261417i
$911$	−1.67376	+	1.21606i	−0.0554542	+	0.0402898i	−0.615167	−	0.788397i	$-0.710911\pi$
$911$	−1.67376	+	1.21606i	−0.0554542	+	0.0402898i	0.559713	+	0.828687i	$0.310911\pi$
$912$		0			0
$913$	3.70820	+	2.69417i	0.122724	+	0.0891639i
$914$	2.85410	−	2.07363i	0.0944053	−	0.0685895i
$915$		0			0
$916$	−7.50000	−	5.44907i	−0.247807	−	0.180042i
$917$	3.23607	+	9.95959i	0.106864	+	0.328895i
$918$		0			0
$919$	−5.85410	−	18.0171i	−0.193109	−	0.594328i	−0.999993	−	0.00361909i	$-0.998848\pi$
$919$	−5.85410	−	18.0171i	−0.193109	−	0.594328i	0.806884	−	0.590709i	$-0.201152\pi$
$920$	4.14590	−	12.7598i	0.136686	−	0.420677i
$921$		0			0
$922$	−4.29837	+	13.2290i	−0.141559	+	0.435675i
$923$	12.2705	−	8.91505i	0.403889	−	0.293442i
$924$		0			0
$925$	−44.2705			−1.45561
$926$	−25.7082			−0.844824
$927$		0			0
$928$	1.11803	−	3.44095i	0.0367013	−	0.112955i
$929$	−4.93769	+	15.1967i	−0.162000	+	0.498586i	−0.998803	−	0.0489190i	$-0.984422\pi$
$929$	−4.93769	+	15.1967i	−0.162000	+	0.498586i	0.836802	+	0.547505i	$0.184422\pi$
$930$		0			0
$931$	6.70820	+	20.6457i	0.219853	+	0.676636i
$932$	10.9098			0.357363
$933$		0			0
$934$	30.8885	+	22.4418i	1.01070	+	0.734319i
$935$	0.604878	−	1.86162i	0.0197816	−	0.0608816i
$936$		0			0
$937$	−19.3435	−	14.0538i	−0.631923	−	0.459119i	0.225143	−	0.974326i	$-0.427715\pi$
$937$	−19.3435	−	14.0538i	−0.631923	−	0.459119i	−0.857066	+	0.515207i	$0.827715\pi$
$938$	−6.00000	−	4.35926i	−0.195907	−	0.142335i
$939$		0			0
$940$	6.38197	−	19.6417i	0.208157	−	0.640641i
$941$	30.1976	+	21.9398i	0.984412	+	0.715217i	0.958690	−	0.284452i	$-0.0918115\pi$
$941$	30.1976	+	21.9398i	0.984412	+	0.715217i	0.0257220	+	0.999669i	$0.491812\pi$
$942$		0			0
$943$	30.5410			0.994552
$944$	2.76393	+	8.50651i	0.0899583	+	0.276863i
$945$		0			0
$946$	0.763932	−	2.35114i	0.0248376	−	0.0764422i
$947$	2.14590	−	6.60440i	0.0697323	−	0.214614i	−0.910117	−	0.414351i	$-0.864009\pi$
$947$	2.14590	−	6.60440i	0.0697323	−	0.214614i	0.979850	+	0.199737i	$0.0640087\pi$
$948$		0			0
$949$	−18.2705			−0.593086
$950$	−36.1803			−1.17385
$951$		0			0
$952$	1.85410	−	1.34708i	0.0600918	−	0.0436592i
$953$	−15.4098	+	47.4266i	−0.499173	+	1.53630i	0.311177	+	0.950352i	$0.399277\pi$
$953$	−15.4098	+	47.4266i	−0.499173	+	1.53630i	−0.810350	+	0.585946i	$0.800723\pi$
$954$		0			0
$955$	−3.61803	+	11.1352i	−0.117077	+	0.360325i
$956$	8.29180	+	25.5195i	0.268176	+	0.825360i
$957$		0			0
$958$	1.38197	+	4.25325i	0.0446493	+	0.137416i
$959$	22.7082	+	16.4985i	0.733286	+	0.532764i
$960$		0			0
$961$	−51.1697	+	37.1770i	−1.65064	+	1.19926i
$962$	13.2812	+	9.64932i	0.428202	+	0.311107i
$963$		0			0
$964$	5.78115	−	4.20025i	0.186198	−	0.135281i
$965$	−3.19098	−	9.82084i	−0.102721	−	0.316144i
$966$		0			0
$967$	7.12461	+	21.9273i	0.229112	+	0.705134i	0.997848	+	0.0655682i	$0.0208860\pi$
$967$	7.12461	+	21.9273i	0.229112	+	0.705134i	−0.768736	+	0.639566i	$0.779114\pi$
$968$	−10.4164			−0.334796
$969$		0			0
$970$	−12.9271	+	9.39205i	−0.415063	+	0.301561i
$971$	−11.6738	+	35.9281i	−0.374629	+	1.15299i	0.569100	+	0.822268i	$0.307292\pi$
$971$	−11.6738	+	35.9281i	−0.374629	+	1.15299i	−0.943729	+	0.330721i	$0.892708\pi$
$972$		0			0
$973$	−21.7082	+	15.7719i	−0.695933	+	0.505625i
$974$	23.7082			0.759660
$975$		0			0
$976$	−2.14590			−0.0686885
$977$	−0.354102	+	0.257270i	−0.0113287	+	0.00823080i	−0.593435	−	0.804882i	$-0.702229\pi$
$977$	−0.354102	+	0.257270i	−0.0113287	+	0.00823080i	0.582106	+	0.813113i	$0.302229\pi$
$978$		0			0
$979$	−0.854102	+	2.62866i	−0.0272972	+	0.0840122i
$980$	6.70820			0.214286
$981$		0			0
$982$	5.88854			0.187911
$983$	−7.58359	−	23.3399i	−0.241879	−	0.744427i	−0.996134	−	0.0878456i	$-0.972002\pi$
$983$	−7.58359	−	23.3399i	−0.241879	−	0.744427i	0.754255	−	0.656582i	$-0.227998\pi$
$984$		0			0
$985$	5.20163			0.165738
$986$	3.35410	−	2.43690i	0.106816	−	0.0776066i
$987$		0			0
$988$	10.8541	+	7.88597i	0.345315	+	0.250886i
$989$	15.7082	−	11.4127i	0.499492	−	0.362902i
$990$		0			0
$991$	5.29180	+	3.84471i	0.168099	+	0.122131i	0.668654	−	0.743573i	$-0.266871\pi$
$991$	5.29180	+	3.84471i	0.168099	+	0.122131i	−0.500555	+	0.865705i	$0.666871\pi$
$992$	−3.00000	−	9.23305i	−0.0952501	−	0.293150i
$993$		0			0
$994$	−5.05573	−	15.5599i	−0.160358	−	0.493531i
$995$	−11.1803	−	34.4095i	−0.354441	−	1.09086i
$996$		0			0
$997$	7.85410	−	24.1724i	0.248742	−	0.765549i	−0.746257	−	0.665658i	$-0.768151\pi$
$997$	7.85410	−	24.1724i	0.248742	−	0.765549i	0.994998	−	0.0998904i	$-0.0318492\pi$
$998$	5.32624	−	3.86974i	0.168599	−	0.122494i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.b.361.1		4
3.2	odd	2		150.2.g.b.61.1	✓	4
15.2	even	4		750.2.h.a.199.2		8
15.8	even	4		750.2.h.a.199.1		8
15.14	odd	2		750.2.g.a.301.1		4
25.16	even	5	inner	450.2.h.b.91.1		4
75.29	odd	10		3750.2.a.g.1.2		2
75.38	even	20		750.2.h.a.49.2		8
75.41	odd	10		150.2.g.b.91.1	yes	4
75.47	even	20		3750.2.c.c.1249.2		4
75.53	even	20		3750.2.c.c.1249.4		4
75.59	odd	10		750.2.g.a.451.1		4
75.62	even	20		750.2.h.a.49.1		8
75.71	odd	10		3750.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.b.61.1	✓	4	3.2	odd	2
150.2.g.b.91.1	yes	4	75.41	odd	10
450.2.h.b.91.1		4	25.16	even	5	inner
450.2.h.b.361.1		4	1.1	even	1	trivial
750.2.g.a.301.1		4	15.14	odd	2
750.2.g.a.451.1		4	75.59	odd	10
750.2.h.a.49.1		8	75.62	even	20
750.2.h.a.49.2		8	75.38	even	20
750.2.h.a.199.1		8	15.8	even	4
750.2.h.a.199.2		8	15.2	even	4
3750.2.a.b.1.2		2	75.71	odd	10
3750.2.a.g.1.2		2	75.29	odd	10
3750.2.c.c.1249.2		4	75.47	even	20
3750.2.c.c.1249.4		4	75.53	even	20

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(1.80902 + 1.31433i) q^{10} +(-0.618034 + 0.449028i) q^{11} +(-1.50000 - 1.08981i) q^{13} +(-1.61803 + 1.17557i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.354102 - 1.08981i) q^{17} +(-2.23607 - 6.88191i) q^{19} -2.23607 q^{20} +(0.236068 - 0.726543i) q^{22} +(4.85410 - 3.52671i) q^{23} +(-4.04508 + 2.93893i) q^{25} +1.85410 q^{26} +(0.618034 - 1.90211i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-3.00000 - 9.23305i) q^{31} +1.00000 q^{32} +(0.927051 + 0.673542i) q^{34} +(-1.38197 - 4.25325i) q^{35} +(7.16312 + 5.20431i) q^{37} +(5.85410 + 4.25325i) q^{38} +(1.80902 - 1.31433i) q^{40} +(4.11803 + 2.99193i) q^{41} +3.23607 q^{43} +(0.236068 + 0.726543i) q^{44} +(-1.85410 + 5.70634i) q^{46} +(-2.85410 + 8.78402i) q^{47} -3.00000 q^{49} +(1.54508 - 4.75528i) q^{50} +(-1.50000 + 1.08981i) q^{52} +(3.57295 - 10.9964i) q^{53} +(1.38197 + 1.00406i) q^{55} +(0.618034 + 1.90211i) q^{56} +(1.11803 + 3.44095i) q^{58} +(-7.23607 - 5.25731i) q^{59} +(1.73607 - 1.26133i) q^{61} +(7.85410 + 5.70634i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-1.28115 + 3.94298i) q^{65} +(1.14590 + 3.52671i) q^{67} -1.14590 q^{68} +(3.61803 + 2.62866i) q^{70} +(-2.52786 + 7.77997i) q^{71} +(7.97214 - 5.79210i) q^{73} -8.85410 q^{74} -7.23607 q^{76} +(-1.23607 + 0.898056i) q^{77} +(-0.690983 + 2.12663i) q^{80} -5.09017 q^{82} +(-1.85410 - 5.70634i) q^{83} +(-2.07295 + 1.50609i) q^{85} +(-2.61803 + 1.90211i) q^{86} +(-0.618034 - 0.449028i) q^{88} +(2.92705 - 2.12663i) q^{89} +(-3.00000 - 2.17963i) q^{91} +(-1.85410 - 5.70634i) q^{92} +(-2.85410 - 8.78402i) q^{94} +(-13.0902 + 9.51057i) q^{95} +(-2.20820 + 6.79615i) q^{97} +(2.42705 - 1.76336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8} + 5 q^{10} + 2 q^{11} - 6 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{22} + 6 q^{23} - 5 q^{25} - 6 q^{26} - 2 q^{28} - 12 q^{31} + 4 q^{32} - 3 q^{34} - 10 q^{35} + 13 q^{37} + 10 q^{38} + 5 q^{40} + 12 q^{41} + 4 q^{43} - 8 q^{44} + 6 q^{46} + 2 q^{47} - 12 q^{49} - 5 q^{50} - 6 q^{52} + 21 q^{53} + 10 q^{55} - 2 q^{56} - 20 q^{59} - 2 q^{61} + 18 q^{62} - q^{64} + 15 q^{65} + 18 q^{67} - 18 q^{68} + 10 q^{70} - 28 q^{71} + 14 q^{73} - 22 q^{74} - 20 q^{76} + 4 q^{77} - 5 q^{80} + 2 q^{82} + 6 q^{83} - 15 q^{85} - 6 q^{86} + 2 q^{88} + 5 q^{89} - 12 q^{91} + 6 q^{92} + 2 q^{94} - 30 q^{95} + 18 q^{97} + 3 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8 + 5 * q^10 + 2 * q^11 - 6 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 8 * q^22 + 6 * q^23 - 5 * q^25 - 6 * q^26 - 2 * q^28 - 12 * q^31 + 4 * q^32 - 3 * q^34 - 10 * q^35 + 13 * q^37 + 10 * q^38 + 5 * q^40 + 12 * q^41 + 4 * q^43 - 8 * q^44 + 6 * q^46 + 2 * q^47 - 12 * q^49 - 5 * q^50 - 6 * q^52 + 21 * q^53 + 10 * q^55 - 2 * q^56 - 20 * q^59 - 2 * q^61 + 18 * q^62 - q^64 + 15 * q^65 + 18 * q^67 - 18 * q^68 + 10 * q^70 - 28 * q^71 + 14 * q^73 - 22 * q^74 - 20 * q^76 + 4 * q^77 - 5 * q^80 + 2 * q^82 + 6 * q^83 - 15 * q^85 - 6 * q^86 + 2 * q^88 + 5 * q^89 - 12 * q^91 + 6 * q^92 + 2 * q^94 - 30 * q^95 + 18 * q^97 + 3 * q^98

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