LMFDB - Embedded newform 522.2.k.c.199.1

Error: no document with id 248694435 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [522,2,Mod(181,522)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("522.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(522, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	522.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-1,0,-1,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.16819098551$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + 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 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			199.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	522.199
Dual form			522.2.k.c.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(0.0440730 - 0.193096i) q^{5} +(-0.0990311 + 0.0476909i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.178448 + 0.0859360i) q^{10} +(0.832437 + 1.04384i) q^{11} +(2.45593 + 3.07964i) q^{13} +(-0.0244587 - 0.107160i) q^{14} +(0.623490 + 0.781831i) q^{16} +2.91185 q^{17} +(-1.16756 - 0.562269i) q^{19} +(-0.123490 + 0.154851i) q^{20} +(-1.20291 + 0.579289i) q^{22} +(1.73341 + 7.59455i) q^{23} +(4.46950 + 2.15240i) q^{25} +(-3.54892 + 1.70907i) q^{26} +0.109916 q^{28} +(1.39493 + 5.20136i) q^{29} +(2.07942 - 9.11052i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.647948 + 2.83885i) q^{34} +(0.00484434 + 0.0212244i) q^{35} +(-1.88740 + 2.36672i) q^{37} +(0.807979 - 1.01317i) q^{38} +(-0.123490 - 0.154851i) q^{40} -3.76271 q^{41} +(1.48307 + 6.49777i) q^{43} +(-0.297093 - 1.30165i) q^{44} -7.78986 q^{46} +(-0.500000 - 0.626980i) q^{47} +(-4.35690 + 5.46337i) q^{49} +(-3.09299 + 3.87849i) q^{50} +(-0.876510 - 3.84024i) q^{52} +(1.85474 - 8.12615i) q^{53} +(0.238250 - 0.114735i) q^{55} +(-0.0244587 + 0.107160i) q^{56} +(-5.38135 + 0.202542i) q^{58} +5.08815 q^{59} +(9.96346 - 4.79815i) q^{61} +(8.41939 + 4.05456i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(0.702907 - 0.338502i) q^{65} +(-6.85839 + 8.60015i) q^{67} +(-2.62349 - 1.26341i) q^{68} -0.0217703 q^{70} +(-6.82640 - 8.56003i) q^{71} +(-1.76875 - 7.74940i) q^{73} +(-1.88740 - 2.36672i) q^{74} +(0.807979 + 1.01317i) q^{76} +(-0.132219 - 0.0636733i) q^{77} +(3.04892 - 3.82322i) q^{79} +(0.178448 - 0.0859360i) q^{80} +(0.837282 - 3.66837i) q^{82} +(-10.5184 - 5.06540i) q^{83} +(0.128334 - 0.562269i) q^{85} -6.66487 q^{86} +1.33513 q^{88} +(-2.55765 + 11.2058i) q^{89} +(-0.390084 - 0.187854i) q^{91} +(1.73341 - 7.59455i) q^{92} +(0.722521 - 0.347948i) q^{94} +(-0.160030 + 0.200671i) q^{95} +(9.54288 + 4.59561i) q^{97} +(-4.35690 - 5.46337i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - q^{4} + 4 q^{5} - 5 q^{7} - q^{8} - 3 q^{10} + 6 q^{11} + 11 q^{13} + 9 q^{14} - q^{16} + 10 q^{17} - 6 q^{19} + 4 q^{20} + 6 q^{22} + 7 q^{23} + 17 q^{25} - 3 q^{26} + 2 q^{28} - 15 q^{29}+ \cdots - 18 q^{98}+O(q^{100}) $ 6 * q - q^2 - q^4 + 4 * q^5 - 5 * q^7 - q^8 - 3 * q^10 + 6 * q^11 + 11 * q^13 + 9 * q^14 - q^16 + 10 * q^17 - 6 * q^19 + 4 * q^20 + 6 * q^22 + 7 * q^23 + 17 * q^25 - 3 * q^26 + 2 * q^28 - 15 * q^29 + 4 * q^31 - q^32 + 10 * q^34 - 22 * q^35 - 13 * q^37 + 15 * q^38 + 4 * q^40 + 12 * q^41 - 7 * q^43 - 15 * q^44 - 3 * q^47 - 18 * q^49 - 4 * q^50 - 10 * q^52 + 22 * q^53 - 24 * q^55 + 9 * q^56 - 15 * q^58 + 38 * q^59 + 31 * q^61 + 18 * q^62 - q^64 - 9 * q^65 + 11 * q^67 - 11 * q^68 + 6 * q^70 - 23 * q^71 + 5 * q^73 - 13 * q^74 + 15 * q^76 - 12 * q^77 - 3 * q^80 - 16 * q^82 - 35 * q^83 - 26 * q^85 - 42 * q^86 + 6 * q^88 - 13 * q^89 - q^91 + 7 * q^92 + 4 * q^94 - 25 * q^95 + 20 * q^97 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$		0			0
$3$		0			0
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.0440730	−	0.193096i	0.0197100	−	0.0863553i	−0.964116	−	0.265480i	$-0.914469\pi$
$5$	0.0440730	−	0.193096i	0.0197100	−	0.0863553i	0.983826	+	0.179125i	$0.0573266\pi$
$6$		0			0
$7$	−0.0990311	+	0.0476909i	−0.0374302	+	0.0180255i	−0.452505	−	0.891762i	$-0.649470\pi$
$7$	−0.0990311	+	0.0476909i	−0.0374302	+	0.0180255i	0.415075	+	0.909787i	$0.363755\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$		0			0
$10$	0.178448	+	0.0859360i	0.0564302	+	0.0271753i
$11$	0.832437	+	1.04384i	0.250989	+	0.314731i	0.891325	−	0.453364i	$-0.149776\pi$
$11$	0.832437	+	1.04384i	0.250989	+	0.314731i	−0.640336	+	0.768095i	$0.721205\pi$
$12$		0			0
$13$	2.45593	+	3.07964i	0.681152	+	0.854137i	0.995460	−	0.0951839i	$-0.0303439\pi$
$13$	2.45593	+	3.07964i	0.681152	+	0.854137i	−0.314308	+	0.949321i	$0.601772\pi$
$14$	−0.0244587	−	0.107160i	−0.00653685	−	0.0286398i
$15$		0			0
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	2.91185			0.706228			0.353114	−	0.935580i	$-0.385123\pi$
$17$	2.91185			0.706228			0.353114	+	0.935580i	$0.385123\pi$
$18$		0			0
$19$	−1.16756	−	0.562269i	−0.267857	−	0.128993i	0.295135	−	0.955456i	$-0.404635\pi$
$19$	−1.16756	−	0.562269i	−0.267857	−	0.128993i	−0.562992	+	0.826462i	$0.690350\pi$
$20$	−0.123490	+	0.154851i	−0.0276132	+	0.0346258i
$21$		0			0
$22$	−1.20291	+	0.579289i	−0.256461	+	0.123505i
$23$	1.73341	+	7.59455i	0.361440	+	1.58357i	0.749542	+	0.661956i	$0.230274\pi$
$23$	1.73341	+	7.59455i	0.361440	+	1.58357i	−0.388102	+	0.921616i	$0.626869\pi$
$24$		0			0
$25$	4.46950	+	2.15240i	0.893900	+	0.430480i
$26$	−3.54892	+	1.70907i	−0.696000	+	0.335176i
$27$		0			0
$28$	0.109916			0.0207722
$29$	1.39493	+	5.20136i	0.259032	+	0.965869i
$29$	1.39493	+	5.20136i	0.259032	+	0.965869i
$30$		0			0
$31$	2.07942	−	9.11052i	0.373474	−	1.63630i	−0.343467	−	0.939165i	$-0.611601\pi$
$31$	2.07942	−	9.11052i	0.373474	−	1.63630i	0.716942	−	0.697133i	$-0.245541\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$		0			0
$34$	−0.647948	+	2.83885i	−0.111122	+	0.486858i
$35$	0.00484434	+	0.0212244i	0.000818843	+	0.00358758i
$36$		0			0
$37$	−1.88740	+	2.36672i	−0.310286	+	0.389086i	−0.912384	−	0.409336i	$-0.865760\pi$
$37$	−1.88740	+	2.36672i	−0.310286	+	0.389086i	0.602098	+	0.798422i	$0.294332\pi$
$38$	0.807979	−	1.01317i	0.131071	−	0.164358i
$39$		0			0
$40$	−0.123490	−	0.154851i	−0.0195255	−	0.0244841i
$41$	−3.76271			−0.587636			−0.293818	−	0.955861i	$-0.594926\pi$
$41$	−3.76271			−0.587636			−0.293818	+	0.955861i	$0.594926\pi$
$42$		0			0
$43$	1.48307	+	6.49777i	0.226167	+	0.990901i	0.952734	+	0.303806i	$0.0982574\pi$
$43$	1.48307	+	6.49777i	0.226167	+	0.990901i	−0.726567	+	0.687095i	$0.758885\pi$
$44$	−0.297093	−	1.30165i	−0.0447885	−	0.196231i
$45$		0			0
$46$	−7.78986			−1.14855
$47$	−0.500000	−	0.626980i	−0.0729325	−	0.0914545i	0.744027	−	0.668150i	$-0.232913\pi$
$47$	−0.500000	−	0.626980i	−0.0729325	−	0.0914545i	−0.816959	+	0.576695i	$0.804342\pi$
$48$		0			0
$49$	−4.35690	+	5.46337i	−0.622414	+	0.780482i
$50$	−3.09299	+	3.87849i	−0.437415	+	0.548501i
$51$		0			0
$52$	−0.876510	−	3.84024i	−0.121550	−	0.532546i
$53$	1.85474	−	8.12615i	0.254768	−	1.11621i	−0.671992	−	0.740558i	$-0.734561\pi$
$53$	1.85474	−	8.12615i	0.254768	−	1.11621i	0.926760	−	0.375654i	$-0.122582\pi$
$54$		0			0
$55$	0.238250	−	0.114735i	0.0321257	−	0.0154709i
$56$	−0.0244587	+	0.107160i	−0.00326843	+	0.0143199i
$57$		0			0
$58$	−5.38135	+	0.202542i	−0.706606	+	0.0265951i
$59$	5.08815			0.662420			0.331210	−	0.943557i	$-0.392543\pi$
$59$	5.08815			0.662420			0.331210	+	0.943557i	$0.392543\pi$
$60$		0			0
$61$	9.96346	−	4.79815i	1.27569	−	0.614340i	0.331411	−	0.943486i	$-0.392475\pi$
$61$	9.96346	−	4.79815i	1.27569	−	0.614340i	0.944279	+	0.329146i	$0.106761\pi$
$62$	8.41939	+	4.05456i	1.06926	+	0.514930i
$63$		0			0
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.702907	−	0.338502i	0.0871848	−	0.0419860i
$66$		0			0
$67$	−6.85839	+	8.60015i	−0.837885	+	1.05068i	0.160092	+	0.987102i	$0.448821\pi$
$67$	−6.85839	+	8.60015i	−0.837885	+	1.05068i	−0.997977	+	0.0635730i	$0.979750\pi$
$68$	−2.62349	−	1.26341i	−0.318145	−	0.153210i
$69$		0			0
$70$	−0.0217703			−0.00260204
$71$	−6.82640	−	8.56003i	−0.810144	−	1.01589i	−0.999423	−	0.0339653i	$-0.989186\pi$
$71$	−6.82640	−	8.56003i	−0.810144	−	1.01589i	0.189279	−	0.981923i	$-0.439385\pi$
$72$		0			0
$73$	−1.76875	−	7.74940i	−0.207017	−	0.906999i	−0.966539	−	0.256518i	$-0.917425\pi$
$73$	−1.76875	−	7.74940i	−0.207017	−	0.906999i	0.759523	−	0.650481i	$-0.225432\pi$
$74$	−1.88740	−	2.36672i	−0.219405	−	0.275125i
$75$		0			0
$76$	0.807979	+	1.01317i	0.0926815	+	0.116219i
$77$	−0.132219	−	0.0636733i	−0.0150678	−	0.00725625i
$78$		0			0
$79$	3.04892	−	3.82322i	0.343030	−	0.430146i	−0.580153	−	0.814508i	$-0.697007\pi$
$79$	3.04892	−	3.82322i	0.343030	−	0.430146i	0.923183	+	0.384362i	$0.125578\pi$
$80$	0.178448	−	0.0859360i	0.0199511	−	0.00960794i
$81$		0			0
$82$	0.837282	−	3.66837i	0.0924623	−	0.405104i
$83$	−10.5184	−	5.06540i	−1.15455	−	0.556000i	−0.244150	−	0.969737i	$-0.578509\pi$
$83$	−10.5184	−	5.06540i	−1.15455	−	0.556000i	−0.910396	+	0.413737i	$0.864223\pi$
$84$		0			0
$85$	0.128334	−	0.562269i	0.0139198	−	0.0609866i
$86$	−6.66487			−0.718692
$87$		0			0
$88$	1.33513			0.142325
$89$	−2.55765	+	11.2058i	−0.271110	+	1.18781i	0.637595	+	0.770372i	$0.279929\pi$
$89$	−2.55765	+	11.2058i	−0.271110	+	1.18781i	−0.908705	+	0.417439i	$0.862928\pi$
$90$		0			0
$91$	−0.390084	−	0.187854i	−0.0408919	−	0.0196925i
$92$	1.73341	−	7.59455i	0.180720	−	0.791786i
$93$		0			0
$94$	0.722521	−	0.347948i	0.0745223	−	0.0358881i
$95$	−0.160030	+	0.200671i	−0.0164187	+	0.0205884i
$96$		0			0
$97$	9.54288	+	4.59561i	0.968932	+	0.466613i	0.850285	−	0.526323i	$-0.176430\pi$
$97$	9.54288	+	4.59561i	0.968932	+	0.466613i	0.118648	+	0.992936i	$0.462144\pi$
$98$	−4.35690	−	5.46337i	−0.440113	−	0.551884i
$99$		0			0
$100$	−3.09299	−	3.87849i	−0.309299	−	0.387849i
$101$	1.32908	+	5.82310i	0.132249	+	0.579420i	0.997012	+	0.0772410i	$0.0246111\pi$
$101$	1.32908	+	5.82310i	0.132249	+	0.579420i	−0.864764	+	0.502179i	$0.832532\pi$
$102$		0			0
$103$	−8.97434	−	11.2535i	−0.884268	−	1.10884i	−0.993388	−	0.114809i	$-0.963374\pi$
$103$	−8.97434	−	11.2535i	−0.884268	−	1.10884i	0.109119	−	0.994029i	$-0.465197\pi$
$104$	3.93900			0.386251
$105$		0			0
$106$	7.50969	+	3.61648i	0.729405	+	0.351263i
$107$	10.2823	−	12.8936i	0.994030	−	1.24647i	0.0249596	−	0.999688i	$-0.492054\pi$
$107$	10.2823	−	12.8936i	0.994030	−	1.24647i	0.969070	−	0.246785i	$-0.0793743\pi$
$108$		0			0
$109$	−2.55980	+	1.23274i	−0.245185	+	0.118075i	−0.552441	−	0.833552i	$-0.686303\pi$
$109$	−2.55980	+	1.23274i	−0.245185	+	0.118075i	0.307256	+	0.951627i	$0.400589\pi$
$110$	0.0588430	+	0.257808i	0.00561046	+	0.0245810i
$111$		0			0
$112$	−0.0990311	−	0.0476909i	−0.00935756	−	0.00450636i
$113$	14.1223	−	6.80094i	1.32851	−	0.639778i	0.371125	−	0.928583i	$-0.378972\pi$
$113$	14.1223	−	6.80094i	1.32851	−	0.639778i	0.957388	+	0.288804i	$0.0932577\pi$
$114$		0			0
$115$	1.54288			0.143874
$116$	1.00000	−	5.29150i	0.0928477	−	0.491304i
$117$		0			0
$118$	−1.13222	+	4.96058i	−0.104229	+	0.456658i
$119$	−0.288364	+	0.138869i	−0.0264343	+	0.0127301i
$120$		0			0
$121$	2.05107	−	8.98634i	0.186461	−	0.816940i
$122$	2.46077	+	10.7813i	0.222788	+	0.976097i
$123$		0			0
$124$	−5.82640	+	7.30607i	−0.523226	+	0.656104i
$125$	1.23005	−	1.54244i	0.110019	−	0.137960i
$126$		0			0
$127$	−1.68867	−	2.11752i	−0.149845	−	0.187900i	0.701244	−	0.712922i	$-0.252629\pi$
$127$	−1.68867	−	2.11752i	−0.149845	−	0.187900i	−0.851089	+	0.525022i	$0.824057\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	0.173604	+	0.760607i	0.0152260	+	0.0667097i
$131$	−3.25182	−	14.2472i	−0.284113	−	1.24478i	−0.892466	−	0.451115i	$-0.851027\pi$
$131$	−3.25182	−	14.2472i	−0.284113	−	1.24478i	0.608353	−	0.793667i	$-0.291831\pi$
$132$		0			0
$133$	0.142440			0.0123511
$134$	−6.85839	−	8.60015i	−0.592474	−	0.742939i
$135$		0			0
$136$	1.81551	−	2.27658i	0.155679	−	0.195215i
$137$	0.993959	−	1.24639i	0.0849197	−	0.106486i	−0.737557	−	0.675285i	$-0.764021\pi$
$137$	0.993959	−	1.24639i	0.0849197	−	0.106486i	0.822476	+	0.568799i	$0.192592\pi$
$138$		0			0
$139$	−0.287168	−	1.25816i	−0.0243573	−	0.106716i	0.961288	−	0.275545i	$-0.0888585\pi$
$139$	−0.287168	−	1.25816i	−0.0243573	−	0.106716i	−0.985645	+	0.168829i	$0.946001\pi$
$140$	0.00484434	−	0.0212244i	0.000409421	−	0.00179379i
$141$		0			0
$142$	9.86443	−	4.75046i	0.827804	−	0.398650i
$143$	−1.17025	+	5.12721i	−0.0978613	+	0.428758i
$144$		0			0
$145$	1.06584	−	0.0401160i	0.0885135	−	0.00333145i
$146$	7.94869			0.657838
$147$		0			0
$148$	2.72737	−	1.31343i	0.224188	−	0.107963i
$149$	−6.03415	−	2.90589i	−0.494337	−	0.238060i	0.170069	−	0.985432i	$-0.445601\pi$
$149$	−6.03415	−	2.90589i	−0.494337	−	0.238060i	−0.664406	+	0.747372i	$0.731315\pi$
$150$		0			0
$151$	2.11260	+	9.25593i	0.171921	+	0.753237i	0.985207	+	0.171371i	$0.0548198\pi$
$151$	2.11260	+	9.25593i	0.171921	+	0.753237i	−0.813285	+	0.581865i	$0.802323\pi$
$152$	−1.16756	+	0.562269i	−0.0947018	+	0.0456060i
$153$		0			0
$154$	0.0914984	−	0.114735i	0.00737315	−	0.00924564i
$155$	−1.66756	−	0.803056i	−0.133942	−	0.0645030i
$156$		0			0
$157$	9.39373			0.749701			0.374851	−	0.927085i	$-0.377694\pi$
$157$	9.39373			0.749701			0.374851	+	0.927085i	$0.377694\pi$
$158$	3.04892	+	3.82322i	0.242559	+	0.304159i
$159$		0			0
$160$	0.0440730	+	0.193096i	0.00348428	+	0.0152656i
$161$	−0.533852	−	0.669429i	−0.0420734	−	0.0527584i
$162$		0			0
$163$	−10.1434	−	12.7194i	−0.794492	−	0.996262i	−0.999846	−	0.0175740i	$-0.994406\pi$
$163$	−10.1434	−	12.7194i	−0.794492	−	0.996262i	0.205353	−	0.978688i	$-0.434166\pi$
$164$	3.39008	+	1.63258i	0.264721	+	0.127483i
$165$		0			0
$166$	7.27897	−	9.12754i	0.564958	−	0.708435i
$167$	−12.3998	+	5.97142i	−0.959523	+	0.462082i	−0.847015	−	0.531569i	$-0.821603\pi$
$167$	−12.3998	+	5.97142i	−0.959523	+	0.462082i	−0.112508	+	0.993651i	$0.535888\pi$
$168$		0			0
$169$	−0.559802	+	2.45265i	−0.0430617	+	0.188666i
$170$	0.519614	+	0.250233i	0.0398526	+	0.0191920i
$171$		0			0
$172$	1.48307	−	6.49777i	0.113083	−	0.495450i
$173$	0.119605			0.00909340			0.00454670	−	0.999990i	$-0.498553\pi$
$173$	0.119605			0.00909340			0.00454670	+	0.999990i	$0.498553\pi$
$174$		0			0
$175$	−0.545269			−0.0412185
$176$	−0.297093	+	1.30165i	−0.0223943	+	0.0981157i
$177$		0			0
$178$	−10.3557	−	4.98704i	−0.776192	−	0.373795i
$179$	−2.82155	+	12.3620i	−0.210893	+	0.923981i	0.753069	+	0.657941i	$0.228572\pi$
$179$	−2.82155	+	12.3620i	−0.210893	+	0.923981i	−0.963962	+	0.266040i	$0.914285\pi$
$180$		0			0
$181$	−6.42812	+	3.09562i	−0.477798	+	0.230095i	−0.657252	−	0.753671i	$-0.728281\pi$
$181$	−6.42812	+	3.09562i	−0.477798	+	0.230095i	0.179454	+	0.983766i	$0.442567\pi$
$182$	0.269946	−	0.338502i	0.0200098	−	0.0250914i
$183$		0			0
$184$	7.01842	+	3.37989i	0.517405	+	0.249169i
$185$	0.373822	+	0.468758i	0.0274839	+	0.0344638i
$186$		0			0
$187$	2.42394	+	3.03952i	0.177256	+	0.222272i
$188$	0.178448	+	0.781831i	0.0130147	+	0.0570209i
$189$		0			0
$190$	−0.160030	−	0.200671i	−0.0116098	−	0.0145582i
$191$	−3.19806			−0.231404			−0.115702	−	0.993284i	$-0.536912\pi$
$191$	−3.19806			−0.231404			−0.115702	+	0.993284i	$0.536912\pi$
$192$		0			0
$193$	13.5782	+	6.53893i	0.977382	+	0.470682i	0.853204	−	0.521578i	$-0.174656\pi$
$193$	13.5782	+	6.53893i	0.977382	+	0.470682i	0.124178	+	0.992260i	$0.460371\pi$
$194$	−6.60388	+	8.28100i	−0.474131	+	0.594541i
$195$		0			0
$196$	6.29590	−	3.03194i	0.449707	−	0.216567i
$197$	−3.23072	−	14.1547i	−0.230179	−	1.00848i	−0.949491	−	0.313794i	$-0.898400\pi$
$197$	−3.23072	−	14.1547i	−0.230179	−	1.00848i	0.719312	−	0.694687i	$-0.244457\pi$
$198$		0			0
$199$	−23.9013	−	11.5102i	−1.69432	−	0.815939i	−0.994860	−	0.101264i	$-0.967711\pi$
$199$	−23.9013	−	11.5102i	−1.69432	−	0.815939i	−0.699456	−	0.714676i	$-0.746574\pi$
$200$	4.46950	−	2.15240i	0.316041	−	0.152198i
$201$		0			0
$202$	−5.97285			−0.420248
$203$	−0.386199	−	0.448572i	−0.0271058	−	0.0314835i
$204$		0			0
$205$	−0.165834	+	0.726566i	−0.0115823	+	0.0507455i
$206$	12.9683	−	6.24521i	0.903545	−	0.435124i
$207$		0			0
$208$	−0.876510	+	3.84024i	−0.0607750	+	0.266273i
$209$	−0.385002	−	1.68681i	−0.0266312	−	0.116679i
$210$		0			0
$211$	−10.4743	+	13.1344i	−0.721084	+	0.904210i	−0.998399	−	0.0565688i	$-0.981984\pi$
$211$	−10.4743	+	13.1344i	−0.721084	+	0.904210i	0.277315	+	0.960779i	$0.410555\pi$
$212$	−5.19687	+	6.51666i	−0.356922	+	0.447566i
$213$		0			0
$214$	10.2823	+	12.8936i	0.702885	+	0.881390i
$215$	1.32006			0.0900274
$216$		0			0
$217$	0.228562	+	1.00139i	0.0155158	+	0.0679791i
$218$	−0.632219	−	2.76993i	−0.0428193	−	0.187603i
$219$		0			0
$220$	−0.264438			−0.0178284
$221$	7.15130	+	8.96745i	0.481049	+	0.603216i
$222$		0			0
$223$	−0.893436	+	1.12033i	−0.0598289	+	0.0750231i	−0.810846	−	0.585260i	$-0.800992\pi$
$223$	−0.893436	+	1.12033i	−0.0598289	+	0.0750231i	0.751017	+	0.660283i	$0.229564\pi$
$224$	0.0685317	−	0.0859360i	0.00457896	−	0.00574184i
$225$		0			0
$226$	3.48792	+	15.2816i	0.232013	+	1.01651i
$227$	−2.98523	+	13.0791i	−0.198137	+	0.868093i	0.773908	+	0.633298i	$0.218299\pi$
$227$	−2.98523	+	13.0791i	−0.198137	+	0.868093i	−0.972045	+	0.234796i	$0.924558\pi$
$228$		0			0
$229$	−10.3693	+	4.99358i	−0.685221	+	0.329985i	−0.743899	−	0.668292i	$-0.767026\pi$
$229$	−10.3693	+	4.99358i	−0.685221	+	0.329985i	0.0586782	+	0.998277i	$0.481311\pi$
$230$	−0.343322	+	1.50419i	−0.0226380	+	0.0991836i
$231$		0			0
$232$	4.93631	+	2.15240i	0.324085	+	0.141312i
$233$	0.735562			0.0481883			0.0240941	−	0.999710i	$-0.492330\pi$
$233$	0.735562			0.0481883			0.0240941	+	0.999710i	$0.492330\pi$
$234$		0			0
$235$	−0.143104	+	0.0689153i	−0.00933508	+	0.00449554i
$236$	−4.58426	−	2.20766i	−0.298410	−	0.143707i
$237$		0			0
$238$	−0.0712201	−	0.312036i	−0.00461651	−	0.0202263i
$239$	0.0794168	−	0.0382451i	0.00513705	−	0.00247387i	−0.431313	−	0.902202i	$-0.641950\pi$
$239$	0.0794168	−	0.0382451i	0.00513705	−	0.00247387i	0.436450	+	0.899728i	$0.356235\pi$
$240$		0			0
$241$	−3.87382	+	4.85762i	−0.249535	+	0.312907i	−0.890785	−	0.454425i	$-0.849845\pi$
$241$	−3.87382	+	4.85762i	−0.249535	+	0.312907i	0.641250	+	0.767332i	$0.278416\pi$
$242$	8.30463	+	3.99930i	0.533842	+	0.257085i
$243$		0			0
$244$	−11.0586			−0.707955
$245$	0.862937	+	1.08209i	0.0551310	+	0.0691321i
$246$		0			0
$247$	−1.13587	−	4.97656i	−0.0722735	−	0.316651i
$248$	−5.82640	−	7.30607i	−0.369977	−	0.463936i
$249$		0			0
$250$	1.23005	+	1.54244i	0.0777954	+	0.0975524i
$251$	13.6869	+	6.59128i	0.863912	+	0.416038i	0.812723	−	0.582651i	$-0.197984\pi$
$251$	13.6869	+	6.59128i	0.863912	+	0.416038i	0.0511894	+	0.998689i	$0.483699\pi$
$252$		0			0
$253$	−6.48457	+	8.13139i	−0.407681	+	0.511216i
$254$	2.44020	−	1.17514i	0.153112	−	0.0737347i
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	4.98307	+	2.39972i	0.310836	+	0.149691i	0.582797	−	0.812618i	$-0.301958\pi$
$257$	4.98307	+	2.39972i	0.310836	+	0.149691i	−0.271962	+	0.962308i	$0.587672\pi$
$258$		0			0
$259$	0.0740400	−	0.324390i	0.00460062	−	0.0201566i
$260$	−0.780167			−0.0483839
$261$		0			0
$262$	14.6136			0.902829
$263$	0.486959	−	2.13351i	0.0300272	−	0.131558i	−0.957693	−	0.287793i	$-0.907079\pi$
$263$	0.486959	−	2.13351i	0.0300272	−	0.131558i	0.987720	+	0.156235i	$0.0499357\pi$
$264$		0			0
$265$	−1.48739	−	0.716287i	−0.0913694	−	0.0440012i
$266$	−0.0316959	+	0.138869i	−0.00194340	+	0.00851460i
$267$		0			0
$268$	9.91066	−	4.77272i	0.605390	−	0.291540i
$269$	−18.9901	+	23.8128i	−1.15785	+	1.45189i	−0.288642	+	0.957437i	$0.593204\pi$
$269$	−18.9901	+	23.8128i	−1.15785	+	1.45189i	−0.869203	+	0.494455i	$0.835368\pi$
$270$		0			0
$271$	−28.4218	−	13.6872i	−1.72650	−	0.831440i	−0.987477	−	0.157765i	$-0.949571\pi$
$271$	−28.4218	−	13.6872i	−1.72650	−	0.831440i	−0.739027	−	0.673676i	$-0.764714\pi$
$272$	1.81551	+	2.27658i	0.110082	+	0.138038i
$273$		0			0
$274$	0.993959	+	1.24639i	0.0600473	+	0.0752969i
$275$	1.47381	+	6.45719i	0.0888742	+	0.389383i
$276$		0			0
$277$	8.85504	+	11.1039i	0.532048	+	0.667166i	0.973118	−	0.230306i	$-0.0739727\pi$
$277$	8.85504	+	11.1039i	0.532048	+	0.667166i	−0.441071	+	0.897472i	$0.645401\pi$
$278$	1.29052			0.0774003
$279$		0			0
$280$	0.0196143	+	0.00944576i	0.00117218	+	0.000564492i
$281$	−12.9453	+	16.2329i	−0.772254	+	0.968376i	−0.999986	−	0.00534795i	$-0.998298\pi$
$281$	−12.9453	+	16.2329i	−0.772254	+	0.968376i	0.227732	+	0.973724i	$0.426869\pi$
$282$		0			0
$283$	15.6293	−	7.52667i	0.929065	−	0.447414i	0.0927662	−	0.995688i	$-0.470429\pi$
$283$	15.6293	−	7.52667i	0.929065	−	0.447414i	0.836299	+	0.548274i	$0.184715\pi$
$284$	2.43631	+	10.6742i	0.144569	+	0.633396i
$285$		0			0
$286$	−4.73825	−	2.28182i	−0.280179	−	0.134927i
$287$	0.372625	−	0.179447i	0.0219954	−	0.0105924i
$288$		0			0
$289$	−8.52111			−0.501242
$290$	−0.198062	+	1.04805i	−0.0116306	+	0.0615434i
$291$		0			0
$292$	−1.76875	+	7.74940i	−0.103508	+	0.453499i
$293$	15.7920	−	7.60503i	0.922579	−	0.444291i	0.0885879	−	0.996068i	$-0.471765\pi$
$293$	15.7920	−	7.60503i	0.922579	−	0.444291i	0.833991	+	0.551778i	$0.186050\pi$
$294$		0			0
$295$	0.224250	−	0.982503i	0.0130563	−	0.0572035i
$296$	0.673604	+	2.95125i	0.0391524	+	0.171538i
$297$		0			0
$298$	4.17576	−	5.23624i	0.241895	−	0.303327i
$299$	−19.1313	+	23.9899i	−1.10639	+	1.38737i
$300$		0			0
$301$	−0.456755	−	0.572753i	−0.0263269	−	0.0330129i
$302$	−9.49396			−0.546316
$303$		0			0
$304$	−0.288364	−	1.26341i	−0.0165388	−	0.0724613i
$305$	−0.487386	−	2.13538i	−0.0279076	−	0.122271i
$306$		0			0
$307$	30.3618			1.73284			0.866420	−	0.499316i	$-0.166415\pi$
$307$	30.3618			1.73284			0.866420	+	0.499316i	$0.166415\pi$
$308$	0.0914984	+	0.114735i	0.00521360	+	0.00653765i
$309$		0			0
$310$	1.15399	−	1.44706i	0.0655422	−	0.0821873i
$311$	14.8312	−	18.5978i	0.841003	−	1.05458i	−0.156754	−	0.987638i	$-0.550103\pi$
$311$	14.8312	−	18.5978i	0.841003	−	1.05458i	0.997757	−	0.0669461i	$-0.0213256\pi$
$312$		0			0
$313$	6.38069	+	27.9556i	0.360658	+	1.58015i	0.751529	+	0.659700i	$0.229317\pi$
$313$	6.38069	+	27.9556i	0.360658	+	1.58015i	−0.390871	+	0.920446i	$0.627826\pi$
$314$	−2.09030	+	9.15821i	−0.117963	+	0.516828i
$315$		0			0
$316$	−4.40581	+	2.12173i	−0.247846	+	0.119357i
$317$	−1.68180	+	7.36845i	−0.0944593	+	0.413853i	−0.999945	−	0.0105243i	$-0.996650\pi$
$317$	−1.68180	+	7.36845i	−0.0944593	+	0.413853i	0.905485	+	0.424378i	$0.139507\pi$
$318$		0			0
$319$	−4.26822	+	5.78589i	−0.238974	+	0.323948i
$320$	−0.198062			−0.0110720
$321$		0			0
$322$	0.771438	−	0.371505i	0.0429906	−	0.0207032i
$323$	−3.39977	−	1.63724i	−0.189168	−	0.0910987i
$324$		0			0
$325$	4.34817	+	19.0506i	0.241193	+	1.05674i
$326$	14.6576	−	7.05875i	0.811811	−	0.390948i
$327$		0			0
$328$	−2.34601	+	2.94180i	−0.129537	+	0.162434i
$329$	0.0794168	+	0.0382451i	0.00437839	+	0.00210852i
$330$		0			0
$331$	−11.1860			−0.614837			−0.307419	−	0.951574i	$-0.599465\pi$
$331$	−11.1860			−0.614837			−0.307419	+	0.951574i	$0.599465\pi$
$332$	7.27897	+	9.12754i	0.399485	+	0.500939i
$333$		0			0
$334$	−3.06249	−	13.4176i	−0.167572	−	0.734181i
$335$	1.35839	+	1.70336i	0.0742167	+	0.0930647i
$336$		0			0
$337$	−12.9641	−	16.2565i	−0.706201	−	0.885548i	0.291269	−	0.956641i	$-0.405923\pi$
$337$	−12.9641	−	16.2565i	−0.706201	−	0.885548i	−0.997470	+	0.0710934i	$0.977351\pi$
$338$	−2.26659	−	1.09153i	−0.123286	−	0.0593716i
$339$		0			0
$340$	−0.359584	+	0.450904i	−0.0195012	+	0.0244537i
$341$	11.2409	−	5.41335i	0.608731	−	0.293149i
$342$		0			0
$343$	0.342126	−	1.49895i	0.0184731	−	0.0809358i
$344$	6.00484	+	2.89178i	0.323760	+	0.155914i
$345$		0			0
$346$	−0.0266146	+	0.116606i	−0.00143081	+	0.00626879i
$347$	−0.0193774			−0.00104023			−0.000520116	−	1.00000i	$-0.500166\pi$
$347$	−0.0193774			−0.00104023			−0.000520116		1.00000i	$0.500166\pi$
$348$		0			0
$349$	29.0315			1.55402			0.777009	−	0.629489i	$-0.216736\pi$
$349$	29.0315			1.55402			0.777009	+	0.629489i	$0.216736\pi$
$350$	0.121334	−	0.531598i	0.00648557	−	0.0284151i
$351$		0			0
$352$	−1.20291	−	0.579289i	−0.0641151	−	0.0308762i
$353$	4.58761	−	20.0996i	0.244174	−	1.06980i	−0.693001	−	0.720937i	$-0.743712\pi$
$353$	4.58761	−	20.0996i	0.244174	−	1.06980i	0.937175	−	0.348860i	$-0.113431\pi$
$354$		0			0
$355$	−1.95377	+	0.940887i	−0.103695	+	0.0499371i
$356$	7.16637	−	8.98634i	0.379817	−	0.476275i
$357$		0			0
$358$	−11.4242	−	5.50162i	−0.603789	−	0.290770i
$359$	−13.0248	−	16.3325i	−0.687420	−	0.861998i	0.308594	−	0.951194i	$-0.400142\pi$
$359$	−13.0248	−	16.3325i	−0.687420	−	0.861998i	−0.996014	+	0.0891962i	$0.971570\pi$
$360$		0			0
$361$	−10.7992	−	13.5418i	−0.568382	−	0.712728i
$362$	−1.58761	−	6.95579i	−0.0834431	−	0.365588i
$363$		0			0
$364$	0.269946	+	0.338502i	0.0141490	+	0.0177423i
$365$	−1.57434			−0.0824045
$366$		0			0
$367$	−3.39008	−	1.63258i	−0.176961	−	0.0852199i	0.343306	−	0.939224i	$-0.388453\pi$
$367$	−3.39008	−	1.63258i	−0.176961	−	0.0852199i	−0.520267	+	0.854004i	$0.674168\pi$
$368$	−4.85690	+	6.09035i	−0.253183	+	0.317482i
$369$		0			0
$370$	−0.540188	+	0.260141i	−0.0280830	+	0.0135241i
$371$	0.203866	+	0.893196i	0.0105842	+	0.0463724i
$372$		0			0
$373$	−13.5271	−	6.51433i	−0.700409	−	0.337299i	0.0495609	−	0.998771i	$-0.484218\pi$
$373$	−13.5271	−	6.51433i	−0.700409	−	0.337299i	−0.749970	+	0.661472i	$0.769932\pi$
$374$	−3.50269	+	1.68681i	−0.181120	+	0.0872227i
$375$		0			0
$376$	−0.801938			−0.0413568
$377$	−12.5925	+	17.0700i	−0.648545	+	0.879152i
$378$		0			0
$379$	−5.24363	+	22.9738i	−0.269347	+	1.18009i	0.641428	+	0.767183i	$0.278342\pi$
$379$	−5.24363	+	22.9738i	−0.269347	+	1.18009i	−0.910775	+	0.412903i	$0.864515\pi$
$380$	0.231250	−	0.111364i	0.0118629	−	0.00571286i
$381$		0			0
$382$	0.711636	−	3.11788i	0.0364105	−	0.159525i
$383$	−5.96830	−	26.1488i	−0.304966	−	1.33614i	−0.862528	−	0.506009i	$-0.831120\pi$
$383$	−5.96830	−	26.1488i	−0.304966	−	1.33614i	0.557562	−	0.830135i	$-0.311737\pi$
$384$		0			0
$385$	−0.0181224	+	0.0227247i	−0.000923602	+	0.00115816i
$386$	−9.39642	+	11.7827i	−0.478265	+	0.599726i
$387$		0			0
$388$	−6.60388	−	8.28100i	−0.335261	−	0.420404i
$389$	18.4034			0.933090			0.466545	−	0.884497i	$-0.345498\pi$
$389$	18.4034			0.933090			0.466545	+	0.884497i	$0.345498\pi$
$390$		0			0
$391$	5.04743	+	22.1142i	0.255259	+	1.11836i
$392$	1.55496	+	6.81272i	0.0785372	+	0.344094i
$393$		0			0
$394$	14.5187			0.731442
$395$	−0.603875	−	0.757236i	−0.0303843	−	0.0381007i
$396$		0			0
$397$	18.0233	−	22.6005i	0.904562	−	1.13428i	−0.0858736	−	0.996306i	$-0.527368\pi$
$397$	18.0233	−	22.6005i	0.904562	−	1.13428i	0.990435	−	0.137978i	$-0.0440604\pi$
$398$	16.5402	−	20.7407i	0.829085	−	1.03964i
$399$		0			0
$400$	1.10388	+	4.83639i	0.0551938	+	0.241820i
$401$	3.41281	−	14.9525i	0.170428	−	0.746693i	−0.815395	−	0.578905i	$-0.803480\pi$
$401$	3.41281	−	14.9525i	0.170428	−	0.746693i	0.985823	−	0.167788i	$-0.0536625\pi$
$402$		0			0
$403$	33.1640	−	15.9709i	1.65202	−	0.795569i
$404$	1.32908	−	5.82310i	0.0661244	−	0.289710i
$405$		0			0
$406$	0.523262	−	0.276700i	0.0259691	−	0.0137324i
$407$	−4.04162			−0.200336
$408$		0			0
$409$	31.2913	−	15.0691i	1.54726	−	0.745120i	0.551246	−	0.834343i	$-0.314153\pi$
$409$	31.2913	−	15.0691i	1.54726	−	0.745120i	0.996012	+	0.0892229i	$0.0284383\pi$
$410$	−0.671448	−	0.323352i	−0.0331604	−	0.0159692i
$411$		0			0
$412$	3.20291	+	14.0329i	0.157796	+	0.691349i
$413$	−0.503885	+	0.242658i	−0.0247946	+	0.0119404i
$414$		0			0
$415$	−1.44169	+	1.80782i	−0.0707698	+	0.0887425i
$416$	−3.54892	−	1.70907i	−0.174000	−	0.0837940i
$417$		0			0
$418$	1.73019			0.0846261
$419$	13.6935	+	17.1711i	0.668972	+	0.838864i	0.994287	−	0.106742i	$-0.0340417\pi$
$419$	13.6935	+	17.1711i	0.668972	+	0.838864i	−0.325315	+	0.945606i	$0.605470\pi$
$420$		0			0
$421$	−8.99761	−	39.4211i	−0.438517	−	1.92127i	−0.385596	−	0.922668i	$-0.626004\pi$
$421$	−8.99761	−	39.4211i	−0.438517	−	1.92127i	−0.0529206	−	0.998599i	$-0.516853\pi$
$422$	−10.4743	−	13.1344i	−0.509883	−	0.639373i
$423$		0			0
$424$	−5.19687	−	6.51666i	−0.252382	−	0.316477i
$425$	13.0145	+	6.26747i	0.631298	+	0.304017i
$426$		0			0
$427$	−0.757865	+	0.950332i	−0.0366756	+	0.0459898i
$428$	−14.8584	+	7.15542i	−0.718207	+	0.345870i
$429$		0			0
$430$	−0.293741	+	1.28696i	−0.0141654	+	0.0620629i
$431$	−19.9121	−	9.58919i	−0.959134	−	0.461895i	−0.112255	−	0.993679i	$-0.535807\pi$
$431$	−19.9121	−	9.58919i	−0.959134	−	0.461895i	−0.846880	+	0.531785i	$0.821522\pi$
$432$		0			0
$433$	0.864961	−	3.78964i	0.0415674	−	0.182119i	−0.949882	−	0.312607i	$-0.898798\pi$
$433$	0.864961	−	3.78964i	0.0415674	−	0.182119i	0.991450	+	0.130489i	$0.0416547\pi$
$434$	−1.02715			−0.0493046
$435$		0			0
$436$	2.84117			0.136067
$437$	2.24632	−	9.84175i	0.107456	−	0.470795i
$438$		0			0
$439$	−9.15160	−	4.40718i	−0.436782	−	0.210343i	0.202553	−	0.979271i	$-0.435076\pi$
$439$	−9.15160	−	4.40718i	−0.436782	−	0.210343i	−0.639335	+	0.768928i	$0.720790\pi$
$440$	0.0588430	−	0.257808i	0.00280523	−	0.0122905i
$441$		0			0
$442$	−10.3339	+	4.97656i	−0.491535	+	0.236711i
$443$	−12.0312	+	15.0866i	−0.571618	+	0.716786i	−0.980658	−	0.195730i	$-0.937292\pi$
$443$	−12.0312	+	15.0866i	−0.571618	+	0.716786i	0.409040	+	0.912516i	$0.365864\pi$
$444$		0			0
$445$	2.05107	+	0.987745i	0.0972302	+	0.0468236i
$446$	−0.893436	−	1.12033i	−0.0423054	−	0.0530493i
$447$		0			0
$448$	0.0685317	+	0.0859360i	0.00323782	+	0.00406009i
$449$	4.81522	+	21.0968i	0.227244	+	0.995621i	0.951876	+	0.306485i	$0.0991529\pi$
$449$	4.81522	+	21.0968i	0.227244	+	0.995621i	−0.724631	+	0.689137i	$0.757990\pi$
$450$		0			0
$451$	−3.13222	−	3.92768i	−0.147490	−	0.184947i
$452$	−15.6746			−0.737269
$453$		0			0
$454$	−12.0869	−	5.82077i	−0.567269	−	0.273182i
$455$	−0.0534662	+	0.0670445i	−0.00250653	+	0.00314309i
$456$		0			0
$457$	−2.28017	+	1.09807i	−0.106662	+	0.0513656i	−0.486454	−	0.873706i	$-0.661710\pi$
$457$	−2.28017	+	1.09807i	−0.106662	+	0.0513656i	0.379792	+	0.925072i	$0.375996\pi$
$458$	−2.56100	−	11.2205i	−0.119668	−	0.524298i
$459$		0			0
$460$	−1.39008	−	0.669429i	−0.0648130	−	0.0312123i
$461$	9.69687	−	4.66976i	0.451628	−	0.217493i	−0.194221	−	0.980958i	$-0.562218\pi$
$461$	9.69687	−	4.66976i	0.451628	−	0.217493i	0.645849	+	0.763465i	$0.276504\pi$
$462$		0			0
$463$	−6.12392			−0.284603			−0.142301	−	0.989823i	$-0.545450\pi$
$463$	−6.12392			−0.284603			−0.142301	+	0.989823i	$0.545450\pi$
$464$	−3.19687	+	4.33360i	−0.148411	+	0.201182i
$465$		0			0
$466$	−0.163678	+	0.717120i	−0.00758223	+	0.0332199i
$467$	31.5013	−	15.1702i	1.45770	−	0.701993i	0.473790	−	0.880638i	$-0.342885\pi$
$467$	31.5013	−	15.1702i	1.45770	−	0.701993i	0.983914	+	0.178644i	$0.0571711\pi$
$468$		0			0
$469$	0.269045	−	1.17876i	0.0124234	−	0.0544303i
$470$	−0.0353438	−	0.154851i	−0.00163029	−	0.00714276i
$471$		0			0
$472$	3.17241	−	3.97807i	0.146022	−	0.183106i
$473$	−5.54809	+	6.95708i	−0.255101	+	0.319887i
$474$		0			0
$475$	−4.00820	−	5.02612i	−0.183909	−	0.230614i
$476$	0.320060			0.0146699
$477$		0			0
$478$	0.0196143	+	0.0859360i	0.000897139	+	0.00393062i
$479$	−6.86994	−	30.0992i	−0.313895	−	1.37527i	−0.848067	−	0.529889i	$-0.822233\pi$
$479$	−6.86994	−	30.0992i	−0.313895	−	1.37527i	0.534171	−	0.845376i	$-0.320624\pi$
$480$		0			0
$481$	−11.9239			−0.543685
$482$	−3.87382	−	4.85762i	−0.176448	−	0.221258i
$483$		0			0
$484$	−5.74698	+	7.20648i	−0.261226	+	0.327567i
$485$	1.30798	−	1.64015i	0.0593922	−	0.0744755i
$486$		0			0
$487$	0.0908344	+	0.397972i	0.00411610	+	0.0180338i	0.976944	−	0.213495i	$-0.0684845\pi$
$487$	0.0908344	+	0.397972i	0.00411610	+	0.0180338i	−0.972828	+	0.231528i	$0.925627\pi$
$488$	2.46077	−	10.7813i	0.111394	−	0.488048i
$489$		0			0
$490$	−1.24698	+	0.600514i	−0.0563328	+	0.0271284i
$491$	4.48643	−	19.6563i	0.202470	−	0.887077i	−0.766958	−	0.641698i	$-0.778230\pi$
$491$	4.48643	−	19.6563i	0.202470	−	0.887077i	0.969427	−	0.245379i	$-0.0789125\pi$
$492$		0			0
$493$	4.06183	+	15.1456i	0.182935	+	0.682124i
$494$	5.10454			0.229664
$495$		0			0
$496$	8.41939	−	4.05456i	0.378042	−	0.182055i
$497$	1.08426	+	0.522153i	0.0486358	+	0.0234217i
$498$		0			0
$499$	2.30947	+	10.1185i	0.103386	+	0.452964i	0.999950	+	0.0100487i	$0.00319865\pi$
$499$	2.30947	+	10.1185i	0.103386	+	0.452964i	−0.896563	+	0.442915i	$0.853944\pi$
$500$	−1.77748	+	0.855989i	−0.0794913	+	0.0382810i
$501$		0			0
$502$	−9.47166	+	11.8771i	−0.422741	+	0.530100i
$503$	20.7141	+	9.97538i	0.923596	+	0.444780i	0.834353	−	0.551230i	$-0.185841\pi$
$503$	20.7141	+	9.97538i	0.923596	+	0.444780i	0.0892420	+	0.996010i	$0.471556\pi$
$504$		0			0
$505$	1.18300			0.0526427
$506$	−6.48457	−	8.13139i	−0.288274	−	0.361484i
$507$		0			0
$508$	0.602679	+	2.64051i	0.0267396	+	0.117154i
$509$	−16.0262	−	20.0963i	−0.710351	−	0.890752i	0.287398	−	0.957811i	$-0.407210\pi$
$509$	−16.0262	−	20.0963i	−0.710351	−	0.890752i	−0.997749	+	0.0670594i	$0.978638\pi$
$510$		0			0
$511$	0.544737	+	0.683079i	0.0240977	+	0.0302176i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$		0			0
$514$	−3.44839	+	4.32415i	−0.152102	+	0.190730i
$515$	−2.56853	+	1.23694i	−0.113183	+	0.0545061i
$516$		0			0
$517$	0.238250	−	1.04384i	0.0104782	−	0.0459082i
$518$	0.299782	+	0.144367i	0.0131717	+	0.00634314i
$519$		0			0
$520$	0.173604	−	0.760607i	0.00761302	−	0.0333548i
$521$	−17.1535			−0.751507			−0.375753	−	0.926720i	$-0.622616\pi$
$521$	−17.1535			−0.751507			−0.375753	+	0.926720i	$0.622616\pi$
$522$		0			0
$523$	22.4494			0.981642			0.490821	−	0.871261i	$-0.336697\pi$
$523$	22.4494			0.981642			0.490821	+	0.871261i	$0.336697\pi$
$524$	−3.25182	+	14.2472i	−0.142057	+	0.622391i
$525$		0			0
$526$	1.97166	+	0.949500i	0.0859683	+	0.0414002i
$527$	6.05496	−	26.5285i	0.263758	−	1.15560i
$528$		0			0
$529$	−33.9502	+	16.3495i	−1.47609	+	0.710850i
$530$	1.02930	−	1.29071i	0.0447101	−	0.0560646i
$531$		0			0
$532$	−0.128334	−	0.0618025i	−0.00556399	−	0.00267948i
$533$	−9.24094	−	11.5878i	−0.400269	−	0.501922i
$534$		0			0
$535$	−2.03654	−	2.55374i	−0.0880473	−	0.110408i
$536$	2.44773	+	10.7242i	0.105726	+	0.463215i
$537$		0			0
$538$	−18.9901	−	23.8128i	−0.818720	−	1.02664i
$539$	−9.32975			−0.401861
$540$		0			0
$541$	11.2104	+	5.39866i	0.481974	+	0.232107i	0.659062	−	0.752088i	$-0.270953\pi$
$541$	11.2104	+	5.39866i	0.481974	+	0.232107i	−0.177088	+	0.984195i	$0.556668\pi$
$542$	19.6685	−	24.6635i	0.844835	−	1.05939i
$543$		0			0
$544$	−2.62349	+	1.26341i	−0.112481	+	0.0541681i
$545$	0.125219	+	0.548619i	0.00536378	+	0.0235003i
$546$		0			0
$547$	10.5988	+	5.10411i	0.453172	+	0.218236i	0.646524	−	0.762893i	$-0.276222\pi$
$547$	10.5988	+	5.10411i	0.453172	+	0.218236i	−0.193353	+	0.981129i	$0.561936\pi$
$548$	−1.43631	+	0.691692i	−0.0613562	+	0.0295476i
$549$		0			0
$550$	−6.62325			−0.282416
$551$	1.29590	−	6.85724i	0.0552071	−	0.292128i
$552$		0			0
$553$	−0.119605	+	0.524023i	−0.00508612	+	0.0222837i
$554$	−12.7959	+	6.16218i	−0.543646	+	0.261806i
$555$		0			0
$556$	−0.287168	+	1.25816i	−0.0121786	+	0.0533580i
$557$	7.28448	+	31.9154i	0.308653	+	1.35230i	0.856685	+	0.515841i	$0.172520\pi$
$557$	7.28448	+	31.9154i	0.308653	+	1.35230i	−0.548031	+	0.836458i	$0.684623\pi$
$558$		0			0
$559$	−16.3684	+	20.5254i	−0.692311	+	0.868131i
$560$	−0.0135735	+	0.0170207i	−0.000573587	+	0.000719255i
$561$		0			0
$562$	−12.9453	−	16.2329i	−0.546066	−	0.684745i
$563$	30.1105			1.26901			0.634503	−	0.772920i	$-0.281205\pi$
$563$	30.1105			1.26901			0.634503	+	0.772920i	$0.281205\pi$
$564$		0			0
$565$	−0.690825	−	3.02670i	−0.0290632	−	0.127334i
$566$	3.86012	+	16.9123i	0.162253	+	0.710876i
$567$		0			0
$568$	−10.9487			−0.459397
$569$	−9.71230	−	12.1788i	−0.407161	−	0.510563i	0.535400	−	0.844599i	$-0.320161\pi$
$569$	−9.71230	−	12.1788i	−0.407161	−	0.510563i	−0.942561	+	0.334035i	$0.891590\pi$
$570$		0			0
$571$	4.20589	−	5.27402i	0.176011	−	0.220711i	−0.685998	−	0.727603i	$-0.740634\pi$
$571$	4.20589	−	5.27402i	0.176011	−	0.220711i	0.862009	+	0.506892i	$0.169206\pi$
$572$	3.27897	−	4.11170i	0.137101	−	0.171919i
$573$		0			0
$574$	0.0920309	+	0.403214i	0.00384129	+	0.0168298i
$575$	−8.59903	+	37.6748i	−0.358604	+	1.57115i
$576$		0			0
$577$	16.8458	−	8.11250i	0.701299	−	0.337728i	−0.0490256	−	0.998798i	$-0.515612\pi$
$577$	16.8458	−	8.11250i	0.701299	−	0.337728i	0.750324	+	0.661070i	$0.229897\pi$
$578$	1.89612	−	8.30746i	0.0788684	−	0.345545i
$579$		0			0
$580$	−0.977697	−	0.426309i	−0.0405967	−	0.0177015i
$581$	1.28322			0.0532371
$582$		0			0
$583$	10.0264	−	4.82845i	0.415250	−	0.199974i
$584$	−7.16152	−	3.44881i	−0.296346	−	0.142713i
$585$		0			0
$586$	3.90030	+	17.0884i	0.161120	+	0.705913i
$587$	−14.6407	+	7.05059i	−0.604287	+	0.291009i	−0.710902	−	0.703291i	$-0.751713\pi$
$587$	−14.6407	+	7.05059i	−0.604287	+	0.291009i	0.106615	+	0.994300i	$0.465999\pi$
$588$		0			0
$589$	−7.55041	+	9.46791i	−0.311109	+	0.390119i
$590$	0.907969	+	0.437255i	0.0373805	+	0.0180015i
$591$		0			0
$592$	−3.02715			−0.124415
$593$	−19.4351	−	24.3709i	−0.798105	−	1.00079i	−0.999772	−	0.0213375i	$-0.993208\pi$
$593$	−19.4351	−	24.3709i	−0.798105	−	1.00079i	0.201668	−	0.979454i	$-0.435364\pi$
$594$		0			0
$595$	0.0141060	+	0.0618025i	0.000578290	+	0.00253365i
$596$	4.17576	+	5.23624i	0.171046	+	0.214485i
$597$		0			0
$598$	−19.1313	−	23.9899i	−0.782338	−	0.981021i
$599$	7.05280	+	3.39645i	0.288170	+	0.138775i	0.572384	−	0.819985i	$-0.306019\pi$
$599$	7.05280	+	3.39645i	0.288170	+	0.138775i	−0.284215	+	0.958761i	$0.591733\pi$
$600$		0			0
$601$	10.9566	−	13.7391i	0.446929	−	0.560431i	−0.506426	−	0.862283i	$-0.669034\pi$
$601$	10.9566	−	13.7391i	0.446929	−	0.560431i	0.953355	+	0.301853i	$0.0976051\pi$
$602$	0.660030	−	0.317854i	0.0269008	−	0.0129548i
$603$		0			0
$604$	2.11260	−	9.25593i	0.0859607	−	0.376618i
$605$	−1.64483	−	0.792110i	−0.0668720	−	0.0322038i
$606$		0			0
$607$	8.75504	−	38.3584i	0.355356	−	1.55692i	−0.409251	−	0.912422i	$-0.634210\pi$
$607$	8.75504	−	38.3584i	0.355356	−	1.55692i	0.764608	−	0.644496i	$-0.222933\pi$
$608$	1.29590			0.0525556
$609$		0			0
$610$	2.19029			0.0886824
$611$	0.702907	−	3.07964i	0.0284366	−	0.124589i
$612$		0			0
$613$	−22.6429	−	10.9042i	−0.914537	−	0.440418i	−0.0834193	−	0.996515i	$-0.526584\pi$
$613$	−22.6429	−	10.9042i	−0.914537	−	0.440418i	−0.831118	+	0.556097i	$0.812298\pi$
$614$	−6.75614	+	29.6006i	−0.272655	+	1.19458i
$615$		0			0
$616$	−0.132219	+	0.0636733i	−0.00532726	+	0.00256547i
$617$	7.87047	−	9.86926i	0.316853	−	0.397321i	−0.597744	−	0.801687i	$-0.703936\pi$
$617$	7.87047	−	9.86926i	0.316853	−	0.397321i	0.914597	+	0.404366i	$0.132508\pi$
$618$		0			0
$619$	19.5683	+	9.42359i	0.786516	+	0.378766i	0.783629	−	0.621230i	$-0.213367\pi$
$619$	19.5683	+	9.42359i	0.786516	+	0.378766i	0.00288757	+	0.999996i	$0.499081\pi$
$620$	1.15399	+	1.44706i	0.0463453	+	0.0581152i
$621$		0			0
$622$	14.8312	+	18.5978i	0.594679	+	0.745703i
$623$	−0.281127	−	1.23170i	−0.0112631	−	0.0493469i
$624$		0			0
$625$	15.2213	+	19.0869i	0.608853	+	0.763477i
$626$	−28.6746			−1.14607
$627$		0			0
$628$	−8.46346	−	4.07579i	−0.337729	−	0.162642i
$629$	−5.49582	+	6.89154i	−0.219133	+	0.274784i
$630$		0			0
$631$	35.4616	−	17.0774i	1.41170	−	0.679841i	0.436206	−	0.899847i	$-0.356322\pi$
$631$	35.4616	−	17.0774i	1.41170	−	0.679841i	0.975498	+	0.220006i	$0.0706078\pi$
$632$	−1.08815	−	4.76748i	−0.0432841	−	0.189640i
$633$		0			0
$634$	−6.80947	−	3.27927i	−0.270439	−	0.130236i
$635$	−0.483311	+	0.232750i	−0.0191796	+	0.00923642i
$636$		0			0
$637$	−27.5254			−1.09060
$638$	−4.69106	−	5.44869i	−0.185721	−	0.215716i
$639$		0			0
$640$	0.0440730	−	0.193096i	0.00174214	−	0.00763281i
$641$	−4.44020	+	2.13829i	−0.175377	+	0.0844572i	−0.519512	−	0.854463i	$-0.673886\pi$
$641$	−4.44020	+	2.13829i	−0.175377	+	0.0844572i	0.344135	+	0.938920i	$0.388172\pi$
$642$		0			0
$643$	1.56004	−	6.83498i	0.0615220	−	0.269545i	−0.934807	−	0.355157i	$-0.884427\pi$
$643$	1.56004	−	6.83498i	0.0615220	−	0.269545i	0.996329	+	0.0856119i	$0.0272845\pi$
$644$	0.190530	+	0.834764i	0.00750791	+	0.0328943i
$645$		0			0
$646$	2.35272	−	2.95021i	0.0925664	−	0.116075i
$647$	9.18329	−	11.5155i	0.361032	−	0.452720i	−0.567830	−	0.823146i	$-0.692217\pi$
$647$	9.18329	−	11.5155i	0.361032	−	0.452720i	0.928862	+	0.370426i	$0.120788\pi$
$648$		0			0
$649$	4.23556	+	5.31123i	0.166260	+	0.208484i
$650$	−19.5405			−0.766441
$651$		0			0
$652$	3.62014	+	15.8609i	0.141776	+	0.621159i
$653$	−5.56691	−	24.3902i	−0.217850	−	0.954463i	−0.959063	−	0.283193i	$-0.908606\pi$
$653$	−5.56691	−	24.3902i	−0.217850	−	0.954463i	0.741213	−	0.671270i	$-0.234251\pi$
$654$		0			0
$655$	−2.89440			−0.113093
$656$	−2.34601	−	2.94180i	−0.0915963	−	0.114858i
$657$		0			0
$658$	−0.0549581	+	0.0689153i	−0.00214249	+	0.00268660i
$659$	−30.3384	+	38.0432i	−1.18182	+	1.48195i	−0.341477	+	0.939890i	$0.610927\pi$
$659$	−30.3384	+	38.0432i	−1.18182	+	1.48195i	−0.840339	+	0.542061i	$0.817644\pi$
$660$		0			0
$661$	6.40528	+	28.0634i	0.249137	+	1.09154i	0.932417	+	0.361383i	$0.117695\pi$
$661$	6.40528	+	28.0634i	0.249137	+	1.09154i	−0.683281	+	0.730156i	$0.739448\pi$
$662$	2.48911	−	10.9055i	0.0967422	−	0.423855i
$663$		0			0
$664$	−10.5184	+	5.06540i	−0.408194	+	0.196576i
$665$	0.00627776	−	0.0275047i	0.000243441	−	0.00106659i
$666$		0			0
$667$	−37.0840	+	19.6099i	−1.43590	+	0.759299i
$668$	13.7627			0.532495
$669$		0			0
$670$	−1.96293	+	0.945296i	−0.0758345	+	0.0365200i
$671$	13.3025	+	6.40613i	0.513536	+	0.247306i
$672$		0			0
$673$	−5.14782	−	22.5541i	−0.198434	−	0.869395i	−0.971869	−	0.235520i	$-0.924321\pi$
$673$	−5.14782	−	22.5541i	−0.198434	−	0.869395i	0.773436	−	0.633875i	$-0.218537\pi$
$674$	18.7337	−	9.02168i	0.721595	−	0.347502i
$675$		0			0
$676$	1.56853	−	1.96688i	0.0603281	−	0.0756491i
$677$	−16.2690	−	7.83476i	−0.625270	−	0.301114i	0.0942895	−	0.995545i	$-0.469942\pi$
$677$	−16.2690	−	7.83476i	−0.625270	−	0.301114i	−0.719560	+	0.694431i	$0.755656\pi$
$678$		0			0
$679$	−1.16421			−0.0446783
$680$	−0.359584	−	0.450904i	−0.0137894	−	0.0172914i
$681$		0			0
$682$	2.77628	+	12.1637i	0.106309	+	0.465772i
$683$	27.5127	+	34.4998i	1.05274	+	1.32010i	0.945413	+	0.325875i	$0.105659\pi$
$683$	27.5127	+	34.4998i	1.05274	+	1.32010i	0.107330	+	0.994223i	$0.465770\pi$
$684$		0			0
$685$	−0.196866	−	0.246862i	−0.00752186	−	0.00943211i
$686$	1.38524	+	0.667096i	0.0528887	+	0.0254698i
$687$		0			0
$688$	−4.15548	+	5.21081i	−0.158426	+	0.198660i
$689$	29.5807	−	14.2453i	1.12693	−	0.542703i
$690$		0			0
$691$	−5.30702	+	23.2516i	−0.201889	+	0.884531i	0.767897	+	0.640573i	$0.221303\pi$
$691$	−5.30702	+	23.2516i	−0.201889	+	0.884531i	−0.969786	+	0.243958i	$0.921554\pi$
$692$	−0.107760	−	0.0518946i	−0.00409643	−	0.00197274i
$693$		0			0
$694$	0.00431187	−	0.0188915i	0.000163676	−	0.000717113i
$695$	−0.255603			−0.00969559
$696$		0			0
$697$	−10.9565			−0.415005
$698$	−6.46011	+	28.3036i	−0.244519	+	1.07131i
$699$		0			0
$700$	0.491271	+	0.236584i	0.0185683	+	0.00894202i
$701$	0.249668	−	1.09387i	0.00942983	−	0.0413148i	−0.969994	−	0.243128i	$-0.921826\pi$
$701$	0.249668	−	1.09387i	0.00942983	−	0.0413148i	0.979424	+	0.201814i	$0.0646835\pi$
$702$		0			0
$703$	3.53438	−	1.70207i	0.133302	−	0.0641948i
$704$	0.832437	−	1.04384i	0.0313737	−	0.0393413i
$705$		0			0
$706$	18.5749	+	8.94518i	0.699074	+	0.336656i
$707$	−0.409330	−	0.513283i	−0.0153944	−	0.0193040i
$708$		0			0
$709$	2.54623	+	3.19287i	0.0956256	+	0.119911i	0.827342	−	0.561698i	$-0.189852\pi$
$709$	2.54623	+	3.19287i	0.0956256	+	0.119911i	−0.731716	+	0.681609i	$0.761280\pi$
$710$	−0.482542	−	2.11415i	−0.0181095	−	0.0793427i
$711$		0			0
$712$	7.16637	+	8.98634i	0.268571	+	0.336777i
$713$	72.7948			2.72619
$714$		0			0
$715$	0.938469	+	0.451943i	0.0350967	+	0.0169017i
$716$	7.90581	−	9.91358i	0.295454	−	0.370488i
$717$		0			0
$718$	18.8213	−	9.06387i	0.702405	−	0.338261i
$719$	6.48062	+	28.3935i	0.241686	+	1.05890i	0.939481	+	0.342600i	$0.111308\pi$
$719$	6.48062	+	28.3935i	0.241686	+	1.05890i	−0.697795	+	0.716298i	$0.745835\pi$
$720$		0			0
$721$	1.42543	+	0.686450i	0.0530857	+	0.0255647i
$722$	15.6054	−	7.51515i	0.580772	−	0.279685i
$723$		0			0
$724$	7.13467			0.265158
$725$	−4.96077	+	26.2499i	−0.184238	+	0.974898i
$726$		0			0
$727$	3.52888	−	15.4610i	0.130879	−	0.573417i	−0.866377	−	0.499390i	$-0.833558\pi$
$727$	3.52888	−	15.4610i	0.130879	−	0.573417i	0.997256	−	0.0740276i	$-0.0235853\pi$
$728$	−0.390084	+	0.187854i	−0.0144575	+	0.00696235i
$729$		0			0
$730$	0.350323	−	1.53486i	0.0129660	−	0.0568079i
$731$	4.31850	+	18.9206i	0.159725	+	0.699802i
$732$		0			0
$733$	−13.3490	+	16.7391i	−0.493056	+	0.618273i	−0.964647	−	0.263544i	$-0.915108\pi$
$733$	−13.3490	+	16.7391i	−0.493056	+	0.618273i	0.471591	+	0.881817i	$0.343680\pi$
$734$	2.34601	−	2.94180i	0.0865928	−	0.108584i
$735$		0			0
$736$	−4.85690	−	6.09035i	−0.179028	−	0.224493i
$737$	−14.6864			−0.540980
$738$		0			0
$739$	7.48547	+	32.7960i	0.275357	+	1.20642i	0.903592	+	0.428395i	$0.140921\pi$
$739$	7.48547	+	32.7960i	0.275357	+	1.20642i	−0.628234	+	0.778024i	$0.716222\pi$
$740$	−0.133415	−	0.584531i	−0.00490445	−	0.0214878i
$741$		0			0
$742$	−0.916166			−0.0336335
$743$	−3.38972	−	4.25057i	−0.124357	−	0.155938i	0.715756	−	0.698351i	$-0.246082\pi$
$743$	−3.38972	−	4.25057i	−0.124357	−	0.155938i	−0.840112	+	0.542413i	$0.817511\pi$
$744$		0			0
$745$	−0.827060	+	1.03710i	−0.0303011	+	0.0379964i
$746$	9.36108	−	11.7384i	0.342733	−	0.429774i
$747$		0			0
$748$	−0.865093	−	3.79022i	−0.0316309	−	0.138584i
$749$	−0.403362	+	1.76724i	−0.0147385	+	0.0645737i
$750$		0			0
$751$	15.1341	−	7.28822i	0.552253	−	0.265951i	−0.136878	−	0.990588i	$-0.543707\pi$
$751$	15.1341	−	7.28822i	0.552253	−	0.265951i	0.689131	+	0.724637i	$0.257993\pi$
$752$	0.178448	−	0.781831i	0.00650733	−	0.0285105i
$753$		0			0
$754$	−13.8400	−	16.0752i	−0.504022	−	0.585423i
$755$	1.88040			0.0684346
$756$		0			0
$757$	−2.26271	+	1.08966i	−0.0822396	+	0.0396045i	−0.474551	−	0.880228i	$-0.657390\pi$
$757$	−2.26271	+	1.08966i	−0.0822396	+	0.0396045i	0.392312	+	0.919832i	$0.371675\pi$
$758$	−21.2310	−	10.2243i	−0.771145	−	0.371364i
$759$		0			0
$760$	0.0571141	+	0.250233i	0.00207174	+	0.00907691i
$761$	−48.2367	+	23.2296i	−1.74858	+	0.842071i	−0.769484	+	0.638666i	$0.779486\pi$
$761$	−48.2367	+	23.2296i	−1.74858	+	0.842071i	−0.979095	+	0.203405i	$0.934799\pi$
$762$		0			0
$763$	0.194710	−	0.244158i	0.00704897	−	0.00883913i
$764$	2.88135	+	1.38759i	0.104244	+	0.0502011i
$765$		0			0
$766$	26.8213			0.969094
$767$	12.4961	+	15.6696i	0.451209	+	0.565798i
$768$		0			0
$769$	−2.05658	−	9.01047i	−0.0741622	−	0.324926i	0.924215	−	0.381873i	$-0.124721\pi$
$769$	−2.05658	−	9.01047i	−0.0741622	−	0.324926i	−0.998377	+	0.0569466i	$0.981864\pi$
$770$	−0.0181224	−	0.0227247i	−0.000653085	−	0.000818943i
$771$		0			0
$772$	−9.39642	−	11.7827i	−0.338185	−	0.424070i
$773$	−33.7298	−	16.2434i	−1.21318	−	0.584235i	−0.285773	−	0.958297i	$-0.592250\pi$
$773$	−33.7298	−	16.2434i	−1.21318	−	0.584235i	−0.927404	+	0.374062i	$0.877965\pi$
$774$		0			0
$775$	28.9034	−	36.2437i	1.03824	−	1.30191i
$776$	9.54288	−	4.59561i	0.342569	−	0.164973i
$777$		0			0
$778$	−4.09515	+	17.9420i	−0.146818	+	0.643252i
$779$	4.39320	+	2.11565i	0.157403	+	0.0758011i
$780$		0			0
$781$	3.25278	−	14.2514i	0.116394	−	0.509954i
$782$	−22.6829			−0.811140
$783$		0			0
$784$	−6.98792			−0.249569
$785$	0.414010	−	1.81390i	0.0147766	−	0.0647407i
$786$		0			0
$787$	−23.3686	−	11.2537i	−0.833001	−	0.401152i	−0.0317612	−	0.999495i	$-0.510112\pi$
$787$	−23.3686	−	11.2537i	−0.833001	−	0.401152i	−0.801240	+	0.598343i	$0.795826\pi$
$788$	−3.23072	+	14.1547i	−0.115090	+	0.504240i
$789$		0			0
$790$	0.872625	−	0.420234i	0.0310466	−	0.0149513i
$791$	−1.07420	+	1.34701i	−0.0381943	+	0.0478941i
$792$		0			0
$793$	39.2461	+	18.8999i	1.39367	+	0.671156i
$794$	18.0233	+	22.6005i	0.639622	+	0.802060i
$795$		0			0
$796$	16.5402	+	20.7407i	0.586251	+	0.735136i
$797$	4.49300	+	19.6851i	0.159150	+	0.697283i	0.990033	+	0.140835i	$0.0449788\pi$
$797$	4.49300	+	19.6851i	0.159150	+	0.697283i	−0.830883	+	0.556447i	$0.812164\pi$
$798$		0			0
$799$	−1.45593	−	1.82567i	−0.0515070	−	0.0645877i
$800$	−4.96077			−0.175390
$801$		0			0
$802$	13.8182	+	6.65449i	0.487938	+	0.234978i
$803$	6.61679	−	8.29719i	0.233501	−	0.292801i
$804$		0			0
$805$	−0.152793	+	0.0735811i	−0.00538524	+	0.00259339i
$806$	8.19083	+	35.8863i	0.288510	+	1.26404i
$807$		0			0
$808$	5.38135	+	2.59152i	0.189315	+	0.0911695i
$809$	31.0306	−	14.9435i	1.09098	−	0.525387i	0.200166	−	0.979762i	$-0.435852\pi$
$809$	31.0306	−	14.9435i	1.09098	−	0.525387i	0.890810	+	0.454375i	$0.150138\pi$
$810$		0			0
$811$	32.7536			1.15013			0.575067	−	0.818106i	$-0.304976\pi$
$811$	32.7536			1.15013			0.575067	+	0.818106i	$0.304976\pi$
$812$	0.153325	+	0.571714i	0.00538066	+	0.0200632i
$813$		0			0
$814$	0.899345	−	3.94029i	0.0315220	−	0.138107i
$815$	−2.90312	+	1.39807i	−0.101692	+	0.0489723i
$816$		0			0
$817$	1.92191	−	8.42044i	0.0672392	−	0.294594i
$818$	7.72832	+	33.8600i	0.270215	+	1.18389i
$819$		0			0
$820$	0.464656	−	0.582660i	0.0162265	−	0.0203474i
$821$	−2.70978	+	3.39795i	−0.0945718	+	0.118589i	−0.826866	−	0.562399i	$-0.809878\pi$
$821$	−2.70978	+	3.39795i	−0.0945718	+	0.118589i	0.732294	+	0.680989i	$0.238450\pi$
$822$		0			0
$823$	8.36108	+	10.4845i	0.291449	+	0.365465i	0.905902	−	0.423488i	$-0.139195\pi$
$823$	8.36108	+	10.4845i	0.291449	+	0.365465i	−0.614453	+	0.788954i	$0.710623\pi$
$824$	−14.3937			−0.501429
$825$		0			0
$826$	−0.124449	−	0.545248i	−0.00433014	−	0.0189716i
$827$	−5.86174	−	25.6820i	−0.203833	−	0.893049i	−0.968577	−	0.248715i	$-0.919992\pi$
$827$	−5.86174	−	25.6820i	−0.203833	−	0.893049i	0.764744	−	0.644334i	$-0.222865\pi$
$828$		0			0
$829$	−10.3618			−0.359880			−0.179940	−	0.983678i	$-0.557590\pi$
$829$	−10.3618			−0.359880			−0.179940	+	0.983678i	$0.557590\pi$
$830$	−1.44169	−	1.80782i	−0.0500418	−	0.0627504i
$831$		0			0
$832$	2.45593	−	3.07964i	0.0851439	−	0.106767i
$833$	−12.6866	+	15.9085i	−0.439566	+	0.551199i
$834$		0			0
$835$	0.606564	+	2.65753i	0.0209910	+	0.0919676i
$836$	−0.385002	+	1.68681i	−0.0133156	+	0.0583394i
$837$		0			0
$838$	−19.7877	+	9.52925i	−0.683555	+	0.329183i
$839$	−5.93578	+	26.0064i	−0.204926	+	0.897839i	0.762959	+	0.646446i	$0.223746\pi$
$839$	−5.93578	+	26.0064i	−0.204926	+	0.897839i	−0.967885	+	0.251393i	$0.919112\pi$
$840$		0			0
$841$	−25.1084	+	14.5111i	−0.865805	+	0.500381i
$842$	40.4349			1.39348
$843$		0			0
$844$	15.1359	−	7.28905i	0.520998	−	0.250899i
$845$	0.448927	+	0.216192i	0.0154435	+	0.00743722i
$846$		0			0
$847$	0.225446	+	0.987745i	0.00774643	+	0.0339393i
$848$	7.50969	−	3.61648i	0.257884	−	0.124190i
$849$		0			0
$850$	−9.00634	+	11.2936i	−0.308915	+	0.387367i
$851$	−21.2458	−	10.2314i	−0.728296	−	0.350729i
$852$		0			0
$853$	−19.7071			−0.674758			−0.337379	−	0.941369i	$-0.609540\pi$
$853$	−19.7071			−0.674758			−0.337379	+	0.941369i	$0.609540\pi$
$854$	−0.757865	−	0.950332i	−0.0259336	−	0.0325197i
$855$		0			0
$856$	−3.66972	−	16.0781i	−0.125428	−	0.549538i
$857$	−1.34481	−	1.68634i	−0.0459380	−	0.0576044i	0.758332	−	0.651869i	$-0.226015\pi$
$857$	−1.34481	−	1.68634i	−0.0459380	−	0.0576044i	−0.804270	+	0.594264i	$0.797443\pi$
$858$		0			0
$859$	21.4799	+	26.9349i	0.732883	+	0.919006i	0.998990	−	0.0449372i	$-0.0143088\pi$
$859$	21.4799	+	26.9349i	0.732883	+	0.919006i	−0.266107	+	0.963944i	$0.585737\pi$
$860$	−1.18933	−	0.572753i	−0.0405559	−	0.0195307i
$861$		0			0
$862$	13.7796	−	17.2791i	0.469336	−	0.588529i
$863$	−8.63922	+	4.16043i	−0.294082	+	0.141623i	−0.575108	−	0.818078i	$-0.695040\pi$
$863$	−8.63922	+	4.16043i	−0.294082	+	0.141623i	0.281025	+	0.959700i	$0.409326\pi$
$864$		0			0
$865$	0.00527135	−	0.0230953i	0.000179231	−	0.000785263i
$866$	3.50216	+	1.68655i	0.119008	+	0.0573113i
$867$		0			0
$868$	0.228562	−	1.00139i	0.00775789	−	0.0339895i
$869$	6.52888			0.221477
$870$		0			0
$871$	−43.3290			−1.46815
$872$	−0.632219	+	2.76993i	−0.0214096	+	0.0938017i
$873$		0			0
$874$	9.09515	+	4.37999i	0.307648	+	0.148155i
$875$	−0.0482534	+	0.211412i	−0.00163126	+	0.00714702i
$876$		0			0
$877$	0.758824	−	0.365430i	0.0256237	−	0.0123397i	−0.421028	−	0.907048i	$-0.638331\pi$
$877$	0.758824	−	0.365430i	0.0256237	−	0.0123397i	0.446652	+	0.894708i	$0.352616\pi$
$878$	6.33310	−	7.94146i	0.213732	−	0.268011i
$879$		0			0
$880$	0.238250	+	0.114735i	0.00803142	+	0.00386773i
$881$	5.13019	+	6.43306i	0.172841	+	0.216735i	0.860705	−	0.509104i	$-0.170023\pi$
$881$	5.13019	+	6.43306i	0.172841	+	0.216735i	−0.687864	+	0.725839i	$0.741452\pi$
$882$		0			0
$883$	33.8568	+	42.4551i	1.13937	+	1.42873i	0.887404	+	0.460993i	$0.152507\pi$
$883$	33.8568	+	42.4551i	1.13937	+	1.42873i	0.251969	+	0.967735i	$0.418922\pi$
$884$	−2.55227	−	11.1822i	−0.0858421	−	0.376099i
$885$		0			0
$886$	−12.0312	−	15.0866i	−0.404195	−	0.506844i
$887$	13.5013			0.453328			0.226664	−	0.973973i	$-0.427218\pi$
$887$	13.5013			0.453328			0.226664	+	0.973973i	$0.427218\pi$
$888$		0			0
$889$	0.268217	+	0.129167i	0.00899572	+	0.00433211i
$890$	−1.41939	+	1.77985i	−0.0475780	+	0.0596609i
$891$		0			0
$892$	1.29105	−	0.621738i	0.0432276	−	0.0208173i
$893$	0.231250	+	1.01317i	0.00773849	+	0.0339045i
$894$		0			0
$895$	2.26271	+	1.08966i	0.0756340	+	0.0364234i
$896$	−0.0990311	+	0.0476909i	−0.00330840	+	0.00159324i
$897$		0			0
$898$	−21.6394			−0.722116
$899$	50.2878	−	1.89272i	1.67719	−	0.0631257i
$900$		0			0
$901$	5.40073	−	23.6622i	0.179924	−	0.788301i
$902$	4.52619	−	2.17970i	0.150706	−	0.0725760i
$903$		0			0
$904$	3.48792	−	15.2816i	0.116006	−	0.508257i
$905$	0.314446	+	1.37768i	0.0104525	+	0.0457956i
$906$		0			0
$907$	−28.9795	+	36.3391i	−0.962248	+	1.20662i	0.0161456	+	0.999870i	$0.494860\pi$
$907$	−28.9795	+	36.3391i	−0.962248	+	1.20662i	−0.978394	+	0.206751i	$0.933711\pi$
$908$	8.36443	−	10.4887i	0.277583	−	0.348078i
$909$		0			0
$910$	−0.0534662	−	0.0670445i	−0.00177239	−	0.00222250i
$911$	−21.1685			−0.701344			−0.350672	−	0.936498i	$-0.614047\pi$
$911$	−21.1685			−0.701344			−0.350672	+	0.936498i	$0.614047\pi$
$912$		0			0
$913$	−3.46844	−	15.1962i	−0.114788	−	0.502921i
$914$	−0.563155	−	2.46734i	−0.0186275	−	0.0816124i
$915$		0			0
$916$	11.5090			0.380269
$917$	1.00149	+	1.25583i	0.0330722	+	0.0414712i
$918$		0			0
$919$	−12.5699	+	15.7621i	−0.414641	+	0.519944i	−0.944664	−	0.328040i	$-0.893612\pi$
$919$	−12.5699	+	15.7621i	−0.414641	+	0.519944i	0.530023	+	0.847984i	$0.322183\pi$
$920$	0.961968	−	1.20627i	0.0317151	−	0.0397695i
$921$		0			0
$922$	2.39493	+	10.4929i	0.0788728	+	0.345564i
$923$	9.59664	−	42.0456i	0.315877	−	1.38395i
$924$		0			0
$925$	−13.5298	+	6.51563i	−0.444858	+	0.214232i
$926$	1.36270	−	5.97038i	0.0447811	−	0.196199i
$927$		0			0
$928$	−3.51357	−	4.08103i	−0.115339	−	0.133966i
$929$	−19.7952			−0.649461			−0.324730	−	0.945807i	$-0.605274\pi$
$929$	−19.7952			−0.649461			−0.324730	+	0.945807i	$0.605274\pi$
$930$		0			0
$931$	8.15883	−	3.92909i	0.267395	−	0.128771i
$932$	−0.662718	−	0.319148i	−0.0217081	−	0.0104541i
$933$		0			0
$934$	7.78017	+	34.0871i	0.254575	+	1.11537i
$935$	0.693750	−	0.334093i	0.0226881	−	0.0109260i
$936$		0			0
$937$	−34.9705	+	43.8516i	−1.14244	+	1.43257i	−0.257853	+	0.966184i	$0.583015\pi$
$937$	−34.9705	+	43.8516i	−1.14244	+	1.43257i	−0.884582	+	0.466384i	$0.845556\pi$
$938$	1.08934	+	0.524600i	0.0355683	+	0.0171288i
$939$		0			0
$940$	0.158834			0.00518058
$941$	1.50066	+	1.88177i	0.0489202	+	0.0613441i	0.805690	−	0.592338i	$-0.201795\pi$
$941$	1.50066	+	1.88177i	0.0489202	+	0.0613441i	−0.756769	+	0.653682i	$0.773223\pi$
$942$		0			0
$943$	−6.52230	−	28.5761i	−0.212395	−	0.930565i
$944$	3.17241	+	3.97807i	0.103253	+	0.129475i
$945$		0			0
$946$	−5.54809	−	6.95708i	−0.180384	−	0.226194i
$947$	2.16003	+	1.04022i	0.0701915	+	0.0338025i	0.468650	−	0.883384i	$-0.344740\pi$
$947$	2.16003	+	1.04022i	0.0701915	+	0.0338025i	−0.398459	+	0.917186i	$0.630455\pi$
$948$		0			0
$949$	19.5214	−	24.4791i	0.633692	−	0.794624i
$950$	5.79201	−	2.78929i	0.187918	−	0.0904964i
$951$		0			0
$952$	−0.0712201	+	0.312036i	−0.00230826	+	0.0101131i
$953$	−30.1634	−	14.5259i	−0.977090	−	0.470542i	−0.123987	−	0.992284i	$-0.539568\pi$
$953$	−30.1634	−	14.5259i	−0.977090	−	0.470542i	−0.853103	+	0.521742i	$0.825282\pi$
$954$		0			0
$955$	−0.140948	+	0.617534i	−0.00456098	+	0.0199829i
$956$	−0.0881460			−0.00285085
$957$		0			0
$958$	30.8732			0.997468
$959$	−0.0389917	+	0.170834i	−0.00125911	+	0.00551651i
$960$		0			0
$961$	−50.7476	−	24.4387i	−1.63702	−	0.788347i
$962$	2.65333	−	11.6250i	0.0855466	−	0.374804i
$963$		0			0
$964$	5.59783	−	2.69578i	0.180294	−	0.0868251i
$965$	1.86108	−	2.33372i	0.0599102	−	0.0751250i
$966$		0			0
$967$	−31.6906	−	15.2614i	−1.01910	−	0.490773i	−0.151723	−	0.988423i	$-0.548482\pi$
$967$	−31.6906	−	15.2614i	−1.01910	−	0.490773i	−0.867378	+	0.497650i	$0.834196\pi$
$968$	−5.74698	−	7.20648i	−0.184715	−	0.231625i
$969$		0			0
$970$	1.30798	+	1.64015i	0.0419967	+	0.0526621i
$971$	−6.12671	−	26.8429i	−0.196616	−	0.861429i	−0.972933	−	0.231087i	$-0.925772\pi$
$971$	−6.12671	−	26.8429i	−0.196616	−	0.861429i	0.776318	−	0.630342i	$-0.217085\pi$
$972$		0			0
$973$	0.0884415	+	0.110902i	0.00283530	+	0.00355536i
$974$	−0.408206			−0.0130798
$975$		0			0
$976$	9.96346	+	4.79815i	0.318923	+	0.153585i
$977$	7.08240	−	8.88105i	0.226586	−	0.284130i	−0.655523	−	0.755175i	$-0.727552\pi$
$977$	7.08240	−	8.88105i	0.226586	−	0.284130i	0.882109	+	0.471045i	$0.156123\pi$
$978$		0			0
$979$	−13.8262	+	6.65833i	−0.441886	+	0.212801i
$980$	−0.307979	−	1.34934i	−0.00983801	−	0.0431032i
$981$		0			0
$982$	18.1652	+	8.74788i	0.579674	+	0.279156i
$983$	−29.6589	+	14.2830i	−0.945972	+	0.455556i	−0.842272	−	0.539053i	$-0.818782\pi$
$983$	−29.6589	+	14.2830i	−0.945972	+	0.455556i	−0.103700	+	0.994609i	$0.533068\pi$
$984$		0			0
$985$	−2.87561			−0.0916245
$986$	−15.6697	+	0.589773i	−0.499026	+	0.0187822i
$987$		0			0
$988$	−1.13587	+	4.97656i	−0.0361367	+	0.158325i
$989$	−46.7769	+	22.5266i	−1.48742	+	0.716303i
$990$		0			0
$991$	−5.00258	+	21.9177i	−0.158912	+	0.696240i	0.831201	+	0.555972i	$0.187654\pi$
$991$	−5.00258	+	21.9177i	−0.158912	+	0.696240i	−0.990114	+	0.140269i	$0.955203\pi$
$992$	2.07942	+	9.11052i	0.0660215	+	0.289259i
$993$		0			0
$994$	−0.750332	+	0.940887i	−0.0237991	+	0.0298431i
$995$	−3.27599	+	4.10796i	−0.103856	+	0.130231i
$996$		0			0
$997$	−13.7943	−	17.2975i	−0.436871	−	0.547819i	0.513845	−	0.857883i	$-0.328221\pi$
$997$	−13.7943	−	17.2975i	−0.436871	−	0.547819i	−0.950716	+	0.310065i	$0.899649\pi$
$998$	−10.3787			−0.328531
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.2.k.c.199.1		6
3.2	odd	2		58.2.d.a.25.1	yes	6
12.11	even	2		464.2.u.b.257.1		6
29.7	even	7	inner	522.2.k.c.181.1		6
87.14	even	28		1682.2.b.g.1681.5		6
87.23	odd	14		1682.2.a.m.1.2		3
87.35	odd	14		1682.2.a.n.1.2		3
87.44	even	28		1682.2.b.g.1681.2		6
87.65	odd	14		58.2.d.a.7.1	✓	6
348.239	even	14		464.2.u.b.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.a.7.1	✓	6	87.65	odd	14
58.2.d.a.25.1	yes	6	3.2	odd	2
464.2.u.b.65.1		6	348.239	even	14
464.2.u.b.257.1		6	12.11	even	2
522.2.k.c.181.1		6	29.7	even	7	inner
522.2.k.c.199.1		6	1.1	even	1	trivial
1682.2.a.m.1.2		3	87.23	odd	14
1682.2.a.n.1.2		3	87.35	odd	14
1682.2.b.g.1681.2		6	87.44	even	28
1682.2.b.g.1681.5		6	87.14	even	28

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(0.0440730 - 0.193096i) q^{5} +(-0.0990311 + 0.0476909i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.178448 + 0.0859360i) q^{10} +(0.832437 + 1.04384i) q^{11} +(2.45593 + 3.07964i) q^{13} +(-0.0244587 - 0.107160i) q^{14} +(0.623490 + 0.781831i) q^{16} +2.91185 q^{17} +(-1.16756 - 0.562269i) q^{19} +(-0.123490 + 0.154851i) q^{20} +(-1.20291 + 0.579289i) q^{22} +(1.73341 + 7.59455i) q^{23} +(4.46950 + 2.15240i) q^{25} +(-3.54892 + 1.70907i) q^{26} +0.109916 q^{28} +(1.39493 + 5.20136i) q^{29} +(2.07942 - 9.11052i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.647948 + 2.83885i) q^{34} +(0.00484434 + 0.0212244i) q^{35} +(-1.88740 + 2.36672i) q^{37} +(0.807979 - 1.01317i) q^{38} +(-0.123490 - 0.154851i) q^{40} -3.76271 q^{41} +(1.48307 + 6.49777i) q^{43} +(-0.297093 - 1.30165i) q^{44} -7.78986 q^{46} +(-0.500000 - 0.626980i) q^{47} +(-4.35690 + 5.46337i) q^{49} +(-3.09299 + 3.87849i) q^{50} +(-0.876510 - 3.84024i) q^{52} +(1.85474 - 8.12615i) q^{53} +(0.238250 - 0.114735i) q^{55} +(-0.0244587 + 0.107160i) q^{56} +(-5.38135 + 0.202542i) q^{58} +5.08815 q^{59} +(9.96346 - 4.79815i) q^{61} +(8.41939 + 4.05456i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(0.702907 - 0.338502i) q^{65} +(-6.85839 + 8.60015i) q^{67} +(-2.62349 - 1.26341i) q^{68} -0.0217703 q^{70} +(-6.82640 - 8.56003i) q^{71} +(-1.76875 - 7.74940i) q^{73} +(-1.88740 - 2.36672i) q^{74} +(0.807979 + 1.01317i) q^{76} +(-0.132219 - 0.0636733i) q^{77} +(3.04892 - 3.82322i) q^{79} +(0.178448 - 0.0859360i) q^{80} +(0.837282 - 3.66837i) q^{82} +(-10.5184 - 5.06540i) q^{83} +(0.128334 - 0.562269i) q^{85} -6.66487 q^{86} +1.33513 q^{88} +(-2.55765 + 11.2058i) q^{89} +(-0.390084 - 0.187854i) q^{91} +(1.73341 - 7.59455i) q^{92} +(0.722521 - 0.347948i) q^{94} +(-0.160030 + 0.200671i) q^{95} +(9.54288 + 4.59561i) q^{97} +(-4.35690 - 5.46337i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - q^{4} + 4 q^{5} - 5 q^{7} - q^{8} - 3 q^{10} + 6 q^{11} + 11 q^{13} + 9 q^{14} - q^{16} + 10 q^{17} - 6 q^{19} + 4 q^{20} + 6 q^{22} + 7 q^{23} + 17 q^{25} - 3 q^{26} + 2 q^{28} - 15 q^{29}+ \cdots - 18 q^{98}+O(q^{100}) \) 6 * q - q^2 - q^4 + 4 * q^5 - 5 * q^7 - q^8 - 3 * q^10 + 6 * q^11 + 11 * q^13 + 9 * q^14 - q^16 + 10 * q^17 - 6 * q^19 + 4 * q^20 + 6 * q^22 + 7 * q^23 + 17 * q^25 - 3 * q^26 + 2 * q^28 - 15 * q^29 + 4 * q^31 - q^32 + 10 * q^34 - 22 * q^35 - 13 * q^37 + 15 * q^38 + 4 * q^40 + 12 * q^41 - 7 * q^43 - 15 * q^44 - 3 * q^47 - 18 * q^49 - 4 * q^50 - 10 * q^52 + 22 * q^53 - 24 * q^55 + 9 * q^56 - 15 * q^58 + 38 * q^59 + 31 * q^61 + 18 * q^62 - q^64 - 9 * q^65 + 11 * q^67 - 11 * q^68 + 6 * q^70 - 23 * q^71 + 5 * q^73 - 13 * q^74 + 15 * q^76 - 12 * q^77 - 3 * q^80 - 16 * q^82 - 35 * q^83 - 26 * q^85 - 42 * q^86 + 6 * q^88 - 13 * q^89 - q^91 + 7 * q^92 + 4 * q^94 - 25 * q^95 + 20 * q^97 - 18 * q^98

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