LMFDB - Embedded newform 675.2.l.a.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] 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("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	675.301
Dual form			675.2.l.a.601.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.826352 - 0.300767i) q^{2} +(0.592396 + 1.62760i) q^{3} +(-0.939693 - 0.788496i) q^{4} -1.52314i q^{6} +(-2.87939 + 2.41609i) q^{7} +(1.41875 + 2.45734i) q^{8} +(-2.29813 + 1.92836i) q^{9} +(-0.180922 - 1.02606i) q^{11} +(0.726682 - 1.99654i) q^{12} +(2.99273 - 1.08926i) q^{13} +(3.10607 - 1.13052i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(-0.233956 + 0.405223i) q^{17} +(2.47906 - 0.902302i) q^{18} +(-2.34730 - 4.06564i) q^{19} +(-5.63816 - 3.25519i) q^{21} +(-0.159100 + 0.902302i) q^{22} +(-4.11334 - 3.45150i) q^{23} +(-3.15910 + 3.76487i) q^{24} -2.80066 q^{26} +(-4.50000 - 2.59808i) q^{27} +4.61081 q^{28} +(-5.45084 - 1.98394i) q^{29} +(-3.14543 - 2.63933i) q^{31} +(0.979055 - 5.55250i) q^{32} +(1.56283 - 0.902302i) q^{33} +(0.315207 - 0.264490i) q^{34} +3.68004 q^{36} +(2.23783 - 3.87603i) q^{37} +(0.716881 + 4.06564i) q^{38} +(3.54576 + 4.22567i) q^{39} +(-7.52481 + 2.73881i) q^{41} +(3.68004 + 4.38571i) q^{42} +(2.11334 + 11.9854i) q^{43} +(-0.639033 + 1.10684i) q^{44} +(2.36097 + 4.08931i) q^{46} +(-2.65657 + 2.22913i) q^{47} +(0.0628336 - 0.0362770i) q^{48} +(1.23783 - 7.02006i) q^{49} +(-0.798133 - 0.140732i) q^{51} +(-3.67112 - 1.33618i) q^{52} -8.83750 q^{53} +(2.93717 + 3.50038i) q^{54} +(-10.0223 - 3.64781i) q^{56} +(5.22668 - 6.22892i) q^{57} +(3.90760 + 3.27887i) q^{58} +(2.36959 - 13.4386i) q^{59} +(7.46064 - 6.26022i) q^{61} +(1.80541 + 3.12706i) q^{62} +(1.95811 - 11.1050i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-1.56283 + 0.275570i) q^{66} +(-1.71301 + 0.623485i) q^{67} +(0.539363 - 0.196312i) q^{68} +(3.18092 - 8.73951i) q^{69} +(-3.85117 + 6.67042i) q^{71} +(-7.99912 - 2.91144i) q^{72} +(0.407604 + 0.705990i) q^{73} +(-3.01501 + 2.52990i) q^{74} +(-1.00000 + 5.67128i) q^{76} +(3.00000 + 2.51730i) q^{77} +(-1.65910 - 4.55834i) q^{78} +(3.81180 + 1.38738i) q^{79} +(1.56283 - 8.86327i) q^{81} +7.04189 q^{82} +(-15.9820 - 5.81699i) q^{83} +(2.73143 + 7.50454i) q^{84} +(1.85844 - 10.5397i) q^{86} -10.0470i q^{87} +(2.26470 - 1.90031i) q^{88} +(5.19846 + 9.00400i) q^{89} +(-5.98545 + 10.3671i) q^{91} +(1.14378 + 6.48670i) q^{92} +(2.43242 - 6.68302i) q^{93} +(2.86571 - 1.04303i) q^{94} +(9.61721 - 1.69577i) q^{96} +(1.06283 + 6.02763i) q^{97} +(-3.13429 + 5.42874i) q^{98} +(2.39440 + 2.00914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31}+ \cdots - 27 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8 - 18 * q^11 - 9 * q^12 - 6 * q^14 - 18 * q^16 - 6 * q^17 + 18 * q^18 - 12 * q^19 + 36 * q^22 - 18 * q^23 + 18 * q^24 + 12 * q^26 - 27 * q^27 + 36 * q^28 - 21 * q^29 - 3 * q^31 + 9 * q^32 + 9 * q^34 - 18 * q^36 - 6 * q^37 - 12 * q^38 - 9 * q^39 - 18 * q^41 - 18 * q^42 + 6 * q^43 - 27 * q^44 - 9 * q^46 + 6 * q^47 - 9 * q^48 - 12 * q^49 + 9 * q^51 - 36 * q^52 - 48 * q^53 + 27 * q^54 - 48 * q^56 + 18 * q^57 + 27 * q^58 + 36 * q^61 + 15 * q^62 + 18 * q^63 - 12 * q^64 - 18 * q^67 + 12 * q^68 + 36 * q^69 + 3 * q^71 + 9 * q^72 + 6 * q^73 + 12 * q^74 - 6 * q^76 + 18 * q^77 + 27 * q^78 - 12 * q^79 + 36 * q^82 - 18 * q^83 + 36 * q^84 + 3 * q^86 + 18 * q^88 + 3 * q^89 + 63 * q^92 - 9 * q^93 + 27 * q^94 + 27 * q^96 - 3 * q^97 - 9 * q^98 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	−0.826352	−	0.300767i	−0.584319	−	0.212675i	0.0329100	−	0.999458i	$-0.489523\pi$
$2$	−0.826352	−	0.300767i	−0.584319	−	0.212675i	−0.617229	+	0.786784i	$0.711745\pi$
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$4$	−0.939693	−	0.788496i	−0.469846	−	0.394248i
$5$		0			0
$5$		0			0
$6$		−	1.52314i		−	0.621819i
$7$	−2.87939	+	2.41609i	−1.08831	+	0.913197i	−0.996584	−	0.0825881i	$-0.973681\pi$
$7$	−2.87939	+	2.41609i	−1.08831	+	0.913197i	−0.0917216	+	0.995785i	$0.529237\pi$
$8$	1.41875	+	2.45734i	0.501603	+	0.868802i
$9$	−2.29813	+	1.92836i	−0.766044	+	0.642788i
$10$		0			0
$11$	−0.180922	−	1.02606i	−0.0545501	−	0.309369i	0.945309	−	0.326177i	$-0.105761\pi$
$11$	−0.180922	−	1.02606i	−0.0545501	−	0.309369i	−0.999859	+	0.0168083i	$0.994649\pi$
$12$	0.726682	−	1.99654i	0.209775	−	0.576352i
$13$	2.99273	−	1.08926i	0.830033	−	0.302107i	0.108160	−	0.994133i	$-0.465504\pi$
$13$	2.99273	−	1.08926i	0.830033	−	0.302107i	0.721872	+	0.692026i	$0.243282\pi$
$14$	3.10607	−	1.13052i	0.830131	−	0.302143i
$15$		0			0
$16$	−0.00727396	−	0.0412527i	−0.00181849	−	0.0103132i
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	−0.893001	−	0.450054i	$-0.851405\pi$
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	0.836259	+	0.548335i	$0.184738\pi$
$18$	2.47906	−	0.902302i	0.584319	−	0.212675i
$19$	−2.34730	−	4.06564i	−0.538507	−	0.932721i	−0.998985	−	0.0450499i	$-0.985655\pi$
$19$	−2.34730	−	4.06564i	−0.538507	−	0.932721i	0.460478	−	0.887671i	$-0.347678\pi$
$20$		0			0
$21$	−5.63816	−	3.25519i	−1.23035	−	0.710341i
$22$	−0.159100	+	0.902302i	−0.0339203	+	0.192372i
$23$	−4.11334	−	3.45150i	−0.857691	−	0.719688i	0.103778	−	0.994600i	$-0.466907\pi$
$23$	−4.11334	−	3.45150i	−0.857691	−	0.719688i	−0.961469	+	0.274912i	$0.911351\pi$
$24$	−3.15910	+	3.76487i	−0.644849	+	0.768501i
$25$		0			0
$26$	−2.80066			−0.549255
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$	4.61081			0.871362
$29$	−5.45084	−	1.98394i	−1.01220	−	0.368409i	−0.217920	−	0.975967i	$-0.569927\pi$
$29$	−5.45084	−	1.98394i	−1.01220	−	0.368409i	−0.794275	+	0.607558i	$0.792149\pi$
$30$		0			0
$31$	−3.14543	−	2.63933i	−0.564936	−	0.474037i	0.315025	−	0.949083i	$-0.397987\pi$
$31$	−3.14543	−	2.63933i	−0.564936	−	0.474037i	−0.879961	+	0.475046i	$0.842431\pi$
$32$	0.979055	−	5.55250i	0.173074	−	0.981553i
$33$	1.56283	−	0.902302i	0.272054	−	0.157071i
$34$	0.315207	−	0.264490i	0.0540576	−	0.0453597i
$35$		0			0
$36$	3.68004			0.613341
$37$	2.23783	−	3.87603i	0.367896	−	0.637215i	−0.621340	−	0.783541i	$-0.713411\pi$
$37$	2.23783	−	3.87603i	0.367896	−	0.637215i	0.989236	+	0.146326i	$0.0467448\pi$
$38$	0.716881	+	4.06564i	0.116294	+	0.659533i
$39$	3.54576	+	4.22567i	0.567776	+	0.676649i
$40$		0			0
$41$	−7.52481	+	2.73881i	−1.17518	+	0.427730i	−0.854497	−	0.519457i	$-0.826134\pi$
$41$	−7.52481	+	2.73881i	−1.17518	+	0.427730i	−0.320682	+	0.947187i	$0.603912\pi$
$42$	3.68004	+	4.38571i	0.567843	+	0.676729i
$43$	2.11334	+	11.9854i	0.322281	+	1.82775i	0.528128	+	0.849165i	$0.322894\pi$
$43$	2.11334	+	11.9854i	0.322281	+	1.82775i	−0.205847	+	0.978584i	$0.565995\pi$
$44$	−0.639033	+	1.10684i	−0.0963379	+	0.166862i
$45$		0			0
$46$	2.36097	+	4.08931i	0.348106	+	0.602937i
$47$	−2.65657	+	2.22913i	−0.387501	+	0.325152i	−0.815639	−	0.578561i	$-0.803614\pi$
$47$	−2.65657	+	2.22913i	−0.387501	+	0.325152i	0.428138	+	0.903714i	$0.359170\pi$
$48$	0.0628336	−	0.0362770i	0.00906925	−	0.00523613i
$49$	1.23783	−	7.02006i	0.176832	−	1.00287i
$50$		0			0
$51$	−0.798133	−	0.140732i	−0.111761	−	0.0197065i
$52$	−3.67112	−	1.33618i	−0.509093	−	0.185295i
$53$	−8.83750			−1.21392			−0.606962	−	0.794731i	$-0.707612\pi$
$53$	−8.83750			−1.21392			−0.606962	+	0.794731i	$0.707612\pi$
$54$	2.93717	+	3.50038i	0.399698	+	0.476341i
$55$		0			0
$56$	−10.0223	−	3.64781i	−1.33928	−	0.487460i
$57$	5.22668	−	6.22892i	0.692291	−	0.825040i
$58$	3.90760	+	3.27887i	0.513094	+	0.430537i
$59$	2.36959	−	13.4386i	0.308494	−	1.74955i	−0.298093	−	0.954537i	$-0.596350\pi$
$59$	2.36959	−	13.4386i	0.308494	−	1.74955i	0.606586	−	0.795018i	$-0.292538\pi$
$60$		0			0
$61$	7.46064	−	6.26022i	0.955237	−	0.801539i	−0.0249349	−	0.999689i	$-0.507938\pi$
$61$	7.46064	−	6.26022i	0.955237	−	0.801539i	0.980172	+	0.198150i	$0.0634934\pi$
$62$	1.80541	+	3.12706i	0.229287	+	0.397137i
$63$	1.95811	−	11.1050i	0.246699	−	1.39910i
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$		0			0
$66$	−1.56283	+	0.275570i	−0.192372	+	0.0339203i
$67$	−1.71301	+	0.623485i	−0.209278	+	0.0761708i	−0.444532	−	0.895763i	$-0.646630\pi$
$67$	−1.71301	+	0.623485i	−0.209278	+	0.0761708i	0.235254	+	0.971934i	$0.424408\pi$
$68$	0.539363	−	0.196312i	0.0654074	−	0.0238063i
$69$	3.18092	−	8.73951i	0.382938	−	1.05211i
$70$		0			0
$71$	−3.85117	+	6.67042i	−0.457049	+	0.791633i	−0.998803	−	0.0489043i	$-0.984427\pi$
$71$	−3.85117	+	6.67042i	−0.457049	+	0.791633i	0.541754	+	0.840537i	$0.317760\pi$
$72$	−7.99912	−	2.91144i	−0.942706	−	0.343117i
$73$	0.407604	+	0.705990i	0.0477064	+	0.0826299i	0.888893	−	0.458116i	$-0.151475\pi$
$73$	0.407604	+	0.705990i	0.0477064	+	0.0826299i	−0.841186	+	0.540746i	$0.818142\pi$
$74$	−3.01501	+	2.52990i	−0.350488	+	0.294095i
$75$		0			0
$76$	−1.00000	+	5.67128i	−0.114708	+	0.650541i
$77$	3.00000	+	2.51730i	0.341882	+	0.286873i
$78$	−1.65910	−	4.55834i	−0.187856	−	0.516130i
$79$	3.81180	+	1.38738i	0.428861	+	0.156093i	0.547427	−	0.836853i	$-0.315607\pi$
$79$	3.81180	+	1.38738i	0.428861	+	0.156093i	−0.118566	+	0.992946i	$0.537830\pi$
$80$		0			0
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$	7.04189			0.777647
$83$	−15.9820	−	5.81699i	−1.75426	−	0.638498i	−0.754418	−	0.656394i	$-0.772081\pi$
$83$	−15.9820	−	5.81699i	−1.75426	−	0.638498i	−0.999840	+	0.0178968i	$0.994303\pi$
$84$	2.73143	+	7.50454i	0.298023	+	0.818812i
$85$		0			0
$86$	1.85844	−	10.5397i	0.200401	−	1.13653i
$87$		−	10.0470i		−	1.07716i
$88$	2.26470	−	1.90031i	0.241418	−	0.202574i
$89$	5.19846	+	9.00400i	0.551036	+	0.954422i	0.998200	+	0.0599704i	$0.0191006\pi$
$89$	5.19846	+	9.00400i	0.551036	+	0.954422i	−0.447164	+	0.894452i	$0.647566\pi$
$90$		0			0
$91$	−5.98545	+	10.3671i	−0.627446	+	1.08677i
$92$	1.14378	+	6.48670i	0.119247	+	0.676286i
$93$	2.43242	−	6.68302i	0.252230	−	0.692996i
$94$	2.86571	−	1.04303i	0.295576	−	0.107581i
$95$		0			0
$96$	9.61721	−	1.69577i	0.981553	−	0.173074i
$97$	1.06283	+	6.02763i	0.107914	+	0.612013i	0.990016	+	0.140954i	$0.0450170\pi$
$97$	1.06283	+	6.02763i	0.107914	+	0.612013i	−0.882102	+	0.471059i	$0.843872\pi$
$98$	−3.13429	+	5.42874i	−0.316611	+	0.548386i
$99$	2.39440	+	2.00914i	0.240646	+	0.201926i
$100$		0			0
$101$	1.51501	−	1.27125i	0.150750	−	0.126494i	−0.564294	−	0.825574i	$-0.690851\pi$
$101$	1.51501	−	1.27125i	0.150750	−	0.126494i	0.715043	+	0.699080i	$0.246407\pi$
$102$	0.617211	+	0.356347i	0.0611130	+	0.0352836i
$103$	2.07650	−	11.7764i	0.204604	−	1.16037i	−0.693458	−	0.720497i	$-0.743914\pi$
$103$	2.07650	−	11.7764i	0.204604	−	1.16037i	0.898062	−	0.439870i	$-0.144975\pi$
$104$	6.92262	+	5.80877i	0.678819	+	0.569596i
$105$		0			0
$106$	7.30288	+	2.65803i	0.709319	+	0.258171i
$107$	−20.6382			−1.99517			−0.997583	−	0.0694862i	$-0.977864\pi$
$107$	−20.6382			−1.99517			−0.997583	+	0.0694862i	$0.977864\pi$
$108$	2.18004	+	5.98962i	0.209775	+	0.576352i
$109$	0.433763			0.0415469			0.0207735	−	0.999784i	$-0.493387\pi$
$109$	0.433763			0.0415469			0.0207735	+	0.999784i	$0.493387\pi$
$110$		0			0
$111$	7.63429	+	1.34613i	0.724614	+	0.127769i
$112$	0.120615	+	0.101208i	0.0113970	+	0.00956324i
$113$	−0.998656	+	5.66366i	−0.0939456	+	0.532792i	0.901120	+	0.433570i	$0.142746\pi$
$113$	−0.998656	+	5.66366i	−0.0939456	+	0.532792i	−0.995065	+	0.0992218i	$0.968365\pi$
$114$	−6.19253	+	3.57526i	−0.579984	+	0.334854i
$115$		0			0
$116$	3.55778	+	6.16226i	0.330332	+	0.572151i
$117$	−4.77719	+	8.27433i	−0.441651	+	0.764962i
$118$	−6.00000	+	10.3923i	−0.552345	+	0.956689i
$119$	−0.305407	−	1.73205i	−0.0279966	−	0.158777i
$120$		0			0
$121$	9.31655	−	3.39095i	0.846959	−	0.308268i
$122$	−8.04798	+	2.92923i	−0.728630	+	0.265200i
$123$	−8.91534	−	10.6249i	−0.803870	−	0.958014i
$124$	0.874638	+	4.96032i	0.0785448	+	0.445450i
$125$		0			0
$126$	−4.95811	+	8.58770i	−0.441704	+	0.765053i
$127$	9.80587	+	16.9843i	0.870131	+	1.50711i	0.861861	+	0.507145i	$0.169299\pi$
$127$	9.80587	+	16.9843i	0.870131	+	1.50711i	0.00826966	+	0.999966i	$0.497368\pi$
$128$	−5.24170	+	4.39831i	−0.463305	+	0.388759i
$129$	−18.2554	+	10.5397i	−1.60730	+	0.927972i
$130$		0			0
$131$	13.8701	+	11.6384i	1.21183	+	1.01685i	0.999211	+	0.0397131i	$0.0126444\pi$
$131$	13.8701	+	11.6384i	1.21183	+	1.01685i	0.212621	+	0.977135i	$0.431800\pi$
$132$	−2.18004	−	0.384401i	−0.189749	−	0.0334578i
$133$	16.5817	+	6.03525i	1.43782	+	0.523323i
$134$	1.60307			0.138484
$135$		0			0
$136$	−1.32770			−0.113849
$137$	13.7208	+	4.99395i	1.17224	+	0.426662i	0.853456	−	0.521165i	$-0.174502\pi$
$137$	13.7208	+	4.99395i	1.17224	+	0.426662i	0.318787	+	0.947826i	$0.396725\pi$
$138$	−5.25712	+	6.26519i	−0.447516	+	0.533329i
$139$	−16.9440	−	14.2177i	−1.43717	−	1.20593i	−0.941315	−	0.337529i	$-0.890409\pi$
$139$	−16.9440	−	14.2177i	−1.43717	−	1.20593i	−0.495859	−	0.868403i	$-0.665147\pi$
$140$		0			0
$141$	−5.20187	−	3.00330i	−0.438076	−	0.252923i
$142$	5.18866	−	4.35381i	0.435423	−	0.365363i
$143$	−1.65910	−	2.87365i	−0.138741	−	0.240306i
$144$	0.0962667	+	0.0807773i	0.00802222	+	0.00673144i
$145$		0			0
$146$	−0.124485	−	0.705990i	−0.0103025	−	0.0584282i
$147$	12.1591	−	2.14398i	1.00287	−	0.176832i
$148$	−5.15910	+	1.87776i	−0.424075	+	0.154351i
$149$	13.3969	−	4.87608i	1.09752	−	0.399464i	0.271118	−	0.962546i	$-0.412607\pi$
$149$	13.3969	−	4.87608i	1.09752	−	0.399464i	0.826401	+	0.563082i	$0.190384\pi$
$150$		0			0
$151$	0.805407	+	4.56769i	0.0655431	+	0.371713i	0.999883	+	0.0153290i	$0.00487956\pi$
$151$	0.805407	+	4.56769i	0.0655431	+	0.371713i	−0.934339	+	0.356384i	$0.884009\pi$
$152$	6.66044	−	11.5362i	0.540233	−	0.935712i
$153$	−0.243756	−	1.38241i	−0.0197065	−	0.111761i
$154$	−1.72193	−	2.98248i	−0.138757	−	0.240335i
$155$		0			0
$156$		−	6.76665i		−	0.541765i
$157$	−2.18392	+	12.3856i	−0.174295	+	0.988478i	0.764659	+	0.644436i	$0.222908\pi$
$157$	−2.18392	+	12.3856i	−0.174295	+	0.988478i	−0.938954	+	0.344043i	$0.888203\pi$
$158$	−2.73261	−	2.29293i	−0.217395	−	0.182416i
$159$	−5.23530	−	14.3839i	−0.415186	−	1.14071i
$160$		0			0
$161$	20.1830			1.59065
$162$	−3.95723	+	6.85413i	−0.310910	+	0.538511i
$163$	−6.40373			−0.501579			−0.250790	−	0.968042i	$-0.580690\pi$
$163$	−6.40373			−0.501579			−0.250790	+	0.968042i	$0.580690\pi$
$164$	9.23055	+	3.35965i	0.720785	+	0.262344i
$165$		0			0
$166$	11.4572	+	9.61376i	0.889254	+	0.746173i
$167$	−1.55303	+	8.80769i	−0.120177	+	0.681560i	0.863879	+	0.503700i	$0.168028\pi$
$167$	−1.55303	+	8.80769i	−0.120177	+	0.681560i	−0.984056	+	0.177859i	$0.943083\pi$
$168$		−	18.4732i		−	1.42524i
$169$	−2.18866	+	1.83651i	−0.168359	+	0.141270i
$170$		0			0
$171$	13.2344	+	4.81694i	1.01206	+	0.368360i
$172$	7.46451	−	12.9289i	0.569163	−	0.985820i
$173$	1.05391	+	5.97702i	0.0801274	+	0.454425i	0.998302	+	0.0582491i	$0.0185518\pi$
$173$	1.05391	+	5.97702i	0.0801274	+	0.454425i	−0.918175	+	0.396176i	$0.870337\pi$
$174$	−3.02182	+	8.30239i	−0.229084	+	0.629402i
$175$		0			0
$176$	−0.0410117	+	0.0149270i	−0.00309137	+	0.00112517i
$177$	23.2763	−	4.10424i	1.74955	−	0.308494i
$178$	−1.58765	−	9.00400i	−0.118999	−	0.674878i
$179$	−1.80200	+	3.12116i	−0.134688	+	0.233287i	−0.925478	−	0.378801i	$-0.876337\pi$
$179$	−1.80200	+	3.12116i	−0.134688	+	0.233287i	0.790790	+	0.612087i	$0.209670\pi$
$180$		0			0
$181$	−5.56283	−	9.63511i	−0.413482	−	0.716172i	0.581786	−	0.813342i	$-0.302354\pi$
$181$	−5.56283	−	9.63511i	−0.413482	−	0.716172i	−0.995268	+	0.0971701i	$0.969021\pi$
$182$	8.06418	−	6.76665i	0.597757	−	0.501577i
$183$	14.6088	+	8.43437i	1.07991	+	0.623486i
$184$	2.64573	−	15.0047i	0.195046	−	1.10616i
$185$		0			0
$186$	−4.02007	+	4.79093i	−0.294766	+	0.351288i
$187$	0.458111	+	0.166739i	0.0335004	+	0.0121931i
$188$	4.25402			0.310256
$189$	19.2344	−	3.39155i	1.39910	−	0.246699i
$190$		0			0
$191$	−9.53596	−	3.47081i	−0.689998	−	0.251139i	−0.0268635	−	0.999639i	$-0.508552\pi$
$191$	−9.53596	−	3.47081i	−0.689998	−	0.251139i	−0.663134	+	0.748500i	$0.730774\pi$
$192$	−8.60014	−	1.51644i	−0.620661	−	0.109439i
$193$	0.269915	+	0.226485i	0.0194289	+	0.0163028i	0.652450	−	0.757831i	$-0.273741\pi$
$193$	0.269915	+	0.226485i	0.0194289	+	0.0163028i	−0.633021	+	0.774134i	$0.718186\pi$
$194$	0.934640	−	5.30061i	0.0671033	−	0.380561i
$195$		0			0
$196$	−6.69846	+	5.62068i	−0.478462	+	0.401477i
$197$	−10.8268	−	18.7526i	−0.771379	−	1.33607i	−0.936807	−	0.349846i	$-0.886234\pi$
$197$	−10.8268	−	18.7526i	−0.771379	−	1.33607i	0.165428	−	0.986222i	$-0.447099\pi$
$198$	−1.37433	−	2.38041i	−0.0976696	−	0.169169i
$199$	−12.0209	+	20.8209i	−0.852142	+	1.47595i	0.0271290	+	0.999632i	$0.491364\pi$
$199$	−12.0209	+	20.8209i	−0.852142	+	1.47595i	−0.879271	+	0.476322i	$0.841970\pi$
$200$		0			0
$201$	−2.02956	−	2.41874i	−0.143154	−	0.170605i
$202$	−1.63429	+	0.594831i	−0.114988	+	0.0418522i
$203$	20.4884	−	7.45718i	1.43801	−	0.523392i
$204$	0.639033	+	0.761570i	0.0447413	+	0.0533206i
$205$		0			0
$206$	−5.25789	+	9.10694i	−0.366335	+	0.634510i
$207$	16.1088			1.11964
$208$	−0.0667040	−	0.115535i	−0.00462509	−	0.00801089i
$209$	−3.74691	+	3.14403i	−0.259179	+	0.217477i
$210$		0			0
$211$	−1.12789	+	6.39657i	−0.0776471	+	0.440358i	0.921055	+	0.389432i	$0.127329\pi$
$211$	−1.12789	+	6.39657i	−0.0776471	+	0.440358i	−0.998702	+	0.0509266i	$0.983783\pi$
$212$	8.30453	+	6.96833i	0.570357	+	0.478587i
$213$	−13.1382	−	2.31661i	−0.900212	−	0.158732i
$214$	17.0544	+	6.20729i	1.16581	+	0.424321i
$215$		0			0
$216$		−	14.7441i		−	1.00321i
$217$	15.4338			1.04771
$218$	−0.358441	−	0.130462i	−0.0242767	−	0.00883598i
$219$	−0.907604	+	1.08164i	−0.0613302	+	0.0730905i
$220$		0			0
$221$	−0.258770	+	1.46756i	−0.0174068	+	0.0987188i
$222$	−5.90373	−	3.40852i	−0.396233	−	0.228765i
$223$	−4.43763	+	3.72362i	−0.297166	+	0.249352i	−0.779164	−	0.626821i	$-0.784356\pi$
$223$	−4.43763	+	3.72362i	−0.297166	+	0.249352i	0.481998	+	0.876173i	$0.339911\pi$
$224$	10.5963	+	18.3533i	0.707993	+	1.22628i
$225$		0			0
$226$	2.52869	−	4.37981i	0.168206	−	0.291341i
$227$	2.24510	+	12.7326i	0.149013	+	0.845092i	0.964057	+	0.265694i	$0.0856011\pi$
$227$	2.24510	+	12.7326i	0.149013	+	0.845092i	−0.815045	+	0.579398i	$0.803288\pi$
$228$	−9.82295	+	1.73205i	−0.650541	+	0.114708i
$229$	1.17365	−	0.427173i	0.0775569	−	0.0282284i	−0.302950	−	0.953006i	$-0.597972\pi$
$229$	1.17365	−	0.427173i	0.0775569	−	0.0282284i	0.380507	+	0.924778i	$0.375749\pi$
$230$		0			0
$231$	−2.31996	+	6.37402i	−0.152642	+	0.419380i
$232$	−2.85814	−	16.2093i	−0.187646	−	1.06419i
$233$	0.190722	−	0.330341i	0.0124946	−	0.0216413i	−0.859710	−	0.510782i	$-0.829356\pi$
$233$	0.190722	−	0.330341i	0.0124946	−	0.0216413i	0.872205	+	0.489140i	$0.162689\pi$
$234$	6.43629	−	5.40069i	0.420753	−	0.353054i
$235$		0			0
$236$	−12.8229	+	10.7597i	−0.834703	+	0.700399i
$237$			7.02595i			0.456385i
$238$	−0.268571	+	1.52314i	−0.0174089	+	0.0987305i
$239$	−2.40760	−	2.02022i	−0.155735	−	0.130677i	0.561591	−	0.827415i	$-0.310190\pi$
$239$	−2.40760	−	2.02022i	−0.155735	−	0.130677i	−0.717326	+	0.696738i	$0.754634\pi$
$240$		0			0
$241$	7.05778	+	2.56882i	0.454632	+	0.165472i	0.559178	−	0.829048i	$-0.311117\pi$
$241$	7.05778	+	2.56882i	0.454632	+	0.165472i	−0.104546	+	0.994520i	$0.533339\pi$
$242$	−8.71864			−0.560455
$243$	15.3516	−	2.70691i	0.984808	−	0.173648i
$244$	−11.9469			−0.764819
$245$		0			0
$246$	4.17159	+	11.4613i	0.265971	+	0.730749i
$247$	−11.4534	−	9.61051i	−0.728760	−	0.611502i
$248$	2.02317	−	11.4739i	0.128471	−	0.728596i
$249$		−	29.4583i		−	1.86684i
$250$		0			0
$251$	−7.68732	−	13.3148i	−0.485219	−	0.840424i	0.514637	−	0.857408i	$-0.327927\pi$
$251$	−7.68732	−	13.3148i	−0.485219	−	0.840424i	−0.999856	+	0.0169841i	$0.994594\pi$
$252$	−10.5963	+	8.89132i	−0.667502	+	0.560101i
$253$	−2.79726	+	4.84499i	−0.175862	+	0.304602i
$254$	−2.99479	−	16.9843i	−0.187910	−	1.06569i
$255$		0			0
$256$	15.1300	−	5.50687i	0.945625	−	0.344179i
$257$	−16.8084	+	6.11776i	−1.04848	+	0.381615i	−0.808089	−	0.589061i	$-0.799498\pi$
$257$	−16.8084	+	6.11776i	−1.04848	+	0.381615i	−0.240391	+	0.970676i	$0.577276\pi$
$258$	18.2554	−	3.21891i	1.13653	−	0.200401i
$259$	2.92127	+	16.5674i	0.181519	+	1.02945i
$260$		0			0
$261$	16.3525	−	5.95183i	1.01220	−	0.368409i
$262$	−7.96110	−	13.7890i	−0.491839	−	0.851890i
$263$	2.97178	−	2.49362i	0.183248	−	0.153763i	−0.546549	−	0.837427i	$-0.684059\pi$
$263$	2.97178	−	2.49362i	0.183248	−	0.153763i	0.729797	+	0.683664i	$0.239614\pi$
$264$	4.43453	+	2.56028i	0.272927	+	0.157574i
$265$		0			0
$266$	−11.8871	−	9.97448i	−0.728846	−	0.611575i
$267$	−11.5753	+	13.7949i	−0.708398	+	0.844236i
$268$	2.10132	+	0.764818i	0.128358	+	0.0467187i
$269$	−19.8084			−1.20774			−0.603870	−	0.797083i	$-0.706375\pi$
$269$	−19.8084			−1.20774			−0.603870	+	0.797083i	$0.706375\pi$
$270$		0			0
$271$	−14.7888			−0.898356			−0.449178	−	0.893442i	$-0.648283\pi$
$271$	−14.7888			−0.898356			−0.449178	+	0.893442i	$0.648283\pi$
$272$	0.0184183	+	0.00670372i	0.00111677	+	0.000406473i
$273$	−20.4192	−	3.60046i	−1.23583	−	0.217910i
$274$	−9.83615	−	8.25351i	−0.594224	−	0.498613i
$275$		0			0
$276$	−9.88016	+	5.70431i	−0.594716	+	0.343359i
$277$	−13.4422	+	11.2794i	−0.807665	+	0.677711i	−0.950049	−	0.312100i	$-0.898967\pi$
$277$	−13.4422	+	11.2794i	−0.807665	+	0.677711i	0.142385	+	0.989811i	$0.454523\pi$
$278$	9.72550	+	16.8451i	0.583297	+	1.01030i
$279$	12.3182			0.737471
$280$		0			0
$281$	1.08853	+	6.17334i	0.0649360	+	0.368270i	0.999908	+	0.0135494i	$0.00431304\pi$
$281$	1.08853	+	6.17334i	0.0649360	+	0.368270i	−0.934972	+	0.354721i	$0.884576\pi$
$282$	3.39528	+	4.04633i	0.202186	+	0.240956i
$283$	−5.95084	+	2.16593i	−0.353741	+	0.128751i	−0.512777	−	0.858522i	$-0.671383\pi$
$283$	−5.95084	+	2.16593i	−0.353741	+	0.128751i	0.159037	+	0.987273i	$0.449161\pi$
$284$	8.87851	−	3.23151i	0.526843	−	0.191755i
$285$		0			0
$286$	0.506701	+	2.87365i	0.0299619	+	0.169922i
$287$	15.0496	−	26.0667i	0.888352	−	1.53867i
$288$	8.45723	+	14.6484i	0.498347	+	0.863163i
$289$	8.39053	+	14.5328i	0.493561	+	0.854872i
$290$		0			0
$291$	−9.18092	+	5.30061i	−0.538195	+	0.310727i
$292$	0.173648	−	0.984808i	0.0101620	−	0.0576315i
$293$	3.50593	+	2.94182i	0.204819	+	0.171863i	0.739427	−	0.673237i	$-0.235096\pi$
$293$	3.50593	+	2.94182i	0.204819	+	0.171863i	−0.534608	+	0.845100i	$0.679541\pi$
$294$	−10.6925	−	1.88538i	−0.623601	−	0.109958i
$295$		0			0
$296$	12.6996			0.738152
$297$	−1.85163	+	5.08732i	−0.107443	+	0.295196i
$298$	−12.5371			−0.726257
$299$	−16.0697	−	5.84889i	−0.929335	−	0.338250i
$300$		0			0
$301$	−35.0428	−	29.4044i	−2.01983	−	1.69484i
$302$	0.708263	−	4.01676i	0.0407560	−	0.231139i
$303$	2.96657	+	1.71275i	0.170425	+	0.0983948i
$304$	−0.150644	+	0.126406i	−0.00864004	+	0.00724985i
$305$		0			0
$306$	−0.214355	+	1.21567i	−0.0122539	+	0.0694952i
$307$	−2.02481	+	3.50708i	−0.115562	+	0.200160i	−0.918004	−	0.396570i	$-0.870200\pi$
$307$	−2.02481	+	3.50708i	−0.115562	+	0.200160i	0.802442	+	0.596730i	$0.203534\pi$
$308$	−0.834198	−	4.73097i	−0.0475329	−	0.269572i
$309$	20.3974	−	3.59661i	1.16037	−	0.204604i
$310$		0			0
$311$	4.63088	−	1.68550i	0.262593	−	0.0955761i	−0.207369	−	0.978263i	$-0.566490\pi$
$311$	4.63088	−	1.68550i	0.262593	−	0.0955761i	0.469962	+	0.882687i	$0.344268\pi$
$312$	−5.35339	+	14.7083i	−0.303076	+	0.832694i
$313$	2.40033	+	13.6129i	0.135675	+	0.769449i	0.974388	+	0.224875i	$0.0721975\pi$
$313$	2.40033	+	13.6129i	0.135675	+	0.769449i	−0.838713	+	0.544574i	$0.816691\pi$
$314$	5.52987	−	9.57801i	0.312068	−	0.540518i
$315$		0			0
$316$	−2.48798	−	4.30930i	−0.139960	−	0.242417i
$317$	11.8669	−	9.95751i	0.666511	−	0.559269i	−0.245519	−	0.969392i	$-0.578958\pi$
$317$	11.8669	−	9.95751i	0.666511	−	0.559269i	0.912031	+	0.410122i	$0.134514\pi$
$318$			13.4607i			0.754841i
$319$	−1.04947	+	5.95183i	−0.0587589	+	0.333238i
$320$		0			0
$321$	−12.2260	−	33.5906i	−0.682387	−	1.87484i
$322$	−16.6783	−	6.07040i	−0.929445	−	0.338290i
$323$	2.19665			0.122225
$324$	−8.45723	+	7.09646i	−0.469846	+	0.394248i
$325$		0			0
$326$	5.29174	+	1.92603i	0.293082	+	0.106673i
$327$	0.256959	+	0.705990i	0.0142099	+	0.0390414i
$328$	−17.4060	−	14.6054i	−0.961086	−	0.806447i
$329$	2.26352	−	12.8370i	0.124792	−	0.707729i
$330$		0			0
$331$	−6.24170	+	5.23741i	−0.343075	+	0.287874i	−0.798002	−	0.602655i	$-0.794110\pi$
$331$	−6.24170	+	5.23741i	−0.343075	+	0.287874i	0.454927	+	0.890529i	$0.349665\pi$
$332$	10.4315	+	18.0680i	0.572505	+	0.991608i
$333$	2.33157	+	13.2230i	0.127769	+	0.724614i
$334$	3.93242	−	6.81115i	0.215172	−	0.372689i
$335$		0			0
$336$	−0.0932736	+	0.256267i	−0.00508849	+	0.0139805i
$337$	5.35369	−	1.94858i	0.291634	−	0.106146i	−0.192060	−	0.981383i	$-0.561517\pi$
$337$	5.35369	−	1.94858i	0.291634	−	0.106146i	0.483694	+	0.875237i	$0.339295\pi$
$338$	2.36097	−	0.859322i	0.128420	−	0.0467409i
$339$	−9.80974	+	1.72972i	−0.532792	+	0.0939456i
$340$		0			0
$341$	−2.13903	+	3.70491i	−0.115835	+	0.200632i
$342$	−9.48751	−	7.96097i	−0.513026	−	0.430480i
$343$	0.241230	+	0.417822i	0.0130252	+	0.0225603i
$344$	−26.4538	+	22.1974i	−1.42629	+	1.19680i
$345$		0			0
$346$	0.926794	−	5.25611i	0.0498247	−	0.282570i
$347$	−20.4158	−	17.1309i	−1.09598	−	0.919635i	−0.0988301	−	0.995104i	$-0.531510\pi$
$347$	−20.4158	−	17.1309i	−1.09598	−	0.919635i	−0.997148	+	0.0754694i	$0.975954\pi$
$348$	−7.92205	+	9.44113i	−0.424666	+	0.506098i
$349$	7.47906	+	2.72215i	0.400345	+	0.145714i	0.534342	−	0.845268i	$-0.320559\pi$
$349$	7.47906	+	2.72215i	0.400345	+	0.145714i	−0.133998	+	0.990982i	$0.542782\pi$
$350$		0			0
$351$	−16.2973	−	2.87365i	−0.869883	−	0.153384i
$352$	−5.87433			−0.313103
$353$	−13.4966	−	4.91236i	−0.718351	−	0.261459i	−0.0431256	−	0.999070i	$-0.513732\pi$
$353$	−13.4966	−	4.91236i	−0.718351	−	0.261459i	−0.675226	+	0.737611i	$0.735954\pi$
$354$	−20.4688	−	3.60921i	−1.08791	−	0.191827i
$355$		0			0
$356$	2.21466	−	12.5600i	0.117377	−	0.665677i
$357$	2.63816	−	1.52314i	0.139626	−	0.0806131i
$358$	2.42783	−	2.03719i	0.128315	−	0.107669i
$359$	10.3341	+	17.8992i	0.545413	+	0.944682i	0.998581	+	0.0532573i	$0.0169603\pi$
$359$	10.3341	+	17.8992i	0.545413	+	0.944682i	−0.453168	+	0.891425i	$0.649706\pi$
$360$		0			0
$361$	−1.51960	+	2.63203i	−0.0799790	+	0.138528i
$362$	1.69893	+	9.63511i	0.0892938	+	0.506410i
$363$	11.0382	+	13.1548i	0.579354	+	0.690447i
$364$	13.7989	−	5.02239i	0.723259	−	0.263245i
$365$		0			0
$366$	−9.53519	−	11.3636i	−0.498412	−	0.593985i
$367$	−1.15002	−	6.52206i	−0.0600303	−	0.340449i	0.939969	−	0.341259i	$-0.110853\pi$
$367$	−1.15002	−	6.52206i	−0.0600303	−	0.340449i	−1.00000		0.000810039i	$0.999742\pi$
$368$	−0.112463	+	0.194792i	−0.00586256	+	0.0101543i
$369$	12.0116	−	20.8047i	0.625300	−	1.08305i
$370$		0			0
$371$	25.4466	−	21.3522i	1.32112	−	1.10855i
$372$	−7.55525	+	4.36203i	−0.391722	+	0.226161i
$373$	5.52023	−	31.3068i	0.285827	−	1.62100i	−0.416491	−	0.909140i	$-0.636740\pi$
$373$	5.52023	−	31.3068i	0.285827	−	1.62100i	0.702318	−	0.711864i	$-0.252149\pi$
$374$	−0.328411	−	0.275570i	−0.0169817	−	0.0142494i
$375$		0			0
$376$	−9.24675	−	3.36554i	−0.476865	−	0.173565i
$377$	−18.4739			−0.951454
$378$	−16.9145	−	2.98248i	−0.869986	−	0.153402i
$379$	−34.1925			−1.75635			−0.878176	−	0.478337i	$-0.841240\pi$
$379$	−34.1925			−1.75635			−0.878176	+	0.478337i	$0.841240\pi$
$380$		0			0
$381$	−21.8346	+	26.0214i	−1.11862	+	1.33312i
$382$	6.83615	+	5.73621i	0.349768	+	0.293490i
$383$	4.13294	−	23.4391i	0.211183	−	1.19768i	−0.676224	−	0.736696i	$-0.736385\pi$
$383$	4.13294	−	23.4391i	0.211183	−	1.19768i	0.887408	−	0.460985i	$-0.152504\pi$
$384$	−10.2638	−	5.92582i	−0.523774	−	0.302401i
$385$		0			0
$386$	−0.154925	−	0.268338i	−0.00788548	−	0.0136581i
$387$	−27.9688	−	23.4686i	−1.42174	−	1.19298i
$388$	3.75402	−	6.50216i	0.190582	−	0.330097i
$389$	0.769915	+	4.36640i	0.0390362	+	0.221385i	0.998085	−	0.0618550i	$-0.0197016\pi$
$389$	0.769915	+	4.36640i	0.0390362	+	0.221385i	−0.959049	+	0.283241i	$0.908591\pi$
$390$		0			0
$391$	2.36097	−	0.859322i	0.119399	−	0.0434578i
$392$	19.0069	−	6.91793i	0.959992	−	0.349408i
$393$	−10.7260	+	29.4694i	−0.541053	+	1.48653i
$394$	3.30659	+	18.7526i	0.166584	+	0.944742i
$395$		0			0
$396$	−0.665802	−	3.77595i	−0.0334578	−	0.189749i
$397$	−9.41875	−	16.3138i	−0.472713	−	0.818764i	0.526799	−	0.849990i	$-0.323392\pi$
$397$	−9.41875	−	16.3138i	−0.472713	−	0.818764i	−0.999512	+	0.0312263i	$0.990059\pi$
$398$	16.1958	−	13.5899i	0.811821	−	0.681199i
$399$			30.5636i			1.53009i
$400$		0			0
$401$	−7.00387	−	5.87695i	−0.349757	−	0.293481i	0.450936	−	0.892556i	$-0.351090\pi$
$401$	−7.00387	−	5.87695i	−0.349757	−	0.293481i	−0.800692	+	0.599076i	$0.795535\pi$
$402$	0.949655	+	2.60916i	0.0473645	+	0.130133i
$403$	−12.2883	−	4.47259i	−0.612125	−	0.222795i
$404$	−2.42602			−0.120699
$405$		0			0
$406$	−19.1735			−0.951567
$407$	−4.38191	−	1.59489i	−0.217203	−	0.0790555i
$408$	−0.786522	−	2.16095i	−0.0389386	−	0.106983i
$409$	21.2920	+	17.8661i	1.05282	+	0.883424i	0.993388	−	0.114808i	$-0.0366253\pi$
$409$	21.2920	+	17.8661i	1.05282	+	0.883424i	0.0594360	+	0.998232i	$0.481070\pi$
$410$		0			0
$411$			25.2902i			1.24747i
$412$	−11.2369	+	9.42892i	−0.553605	+	0.464530i
$413$	25.6459	+	44.4200i	1.26195	+	2.18577i
$414$	−13.3115	−	4.84499i	−0.654224	−	0.238118i
$415$		0			0
$416$	−3.11809	−	17.6836i	−0.152877	−	0.867008i
$417$	13.1031	−	36.0006i	0.641663	−	1.76295i
$418$	4.04189	−	1.47113i	0.197695	−	0.0719552i
$419$	−7.55943	+	2.75141i	−0.369302	+	0.134415i	−0.520003	−	0.854164i	$-0.674069\pi$
$419$	−7.55943	+	2.75141i	−0.369302	+	0.134415i	0.150701	+	0.988579i	$0.451847\pi$
$420$		0			0
$421$	−3.44862	−	19.5581i	−0.168075	−	0.953202i	−0.945837	−	0.324643i	$-0.894756\pi$
$421$	−3.44862	−	19.5581i	−0.168075	−	0.953202i	0.777762	−	0.628559i	$-0.216355\pi$
$422$	2.85591	−	4.94659i	0.139024	−	0.240796i
$423$	1.80659	−	10.2457i	0.0878394	−	0.498162i
$424$	−12.5382	−	21.7168i	−0.608908	−	1.05466i
$425$		0			0
$426$	10.1600	+	5.86587i	0.492253	+	0.284202i
$427$	−6.35679	+	36.0512i	−0.307627	+	1.74464i
$428$	19.3935	+	16.2731i	0.937421	+	0.786590i
$429$	3.69429	−	4.40268i	0.178362	−	0.212563i
$430$		0			0
$431$	−5.89393			−0.283901			−0.141950	−	0.989874i	$-0.545337\pi$
$431$	−5.89393			−0.283901			−0.141950	+	0.989874i	$0.545337\pi$
$432$	−0.0744448	+	0.204535i	−0.00358173	+	0.00984071i
$433$	−3.82201			−0.183674			−0.0918372	−	0.995774i	$-0.529274\pi$
$433$	−3.82201			−0.183674			−0.0918372	+	0.995774i	$0.529274\pi$
$434$	−12.7537	−	4.64197i	−0.612198	−	0.222822i
$435$		0			0
$436$	−0.407604	−	0.342020i	−0.0195207	−	0.0163798i
$437$	−4.37733	+	24.8250i	−0.209396	+	1.18754i
$438$	1.07532	−	0.620838i	0.0513809	−	0.0296648i
$439$	29.3200	−	24.6024i	1.39937	−	1.17421i	0.437989	−	0.898980i	$-0.355691\pi$
$439$	29.3200	−	24.6024i	1.39937	−	1.17421i	0.961379	−	0.275229i	$-0.0887536\pi$
$440$		0			0
$441$	10.6925	+	18.5200i	0.509168	+	0.881905i
$442$	0.655230	−	1.13489i	0.0311661	−	0.0539813i
$443$	−2.31892	−	13.1512i	−0.110175	−	0.624834i	−0.989027	−	0.147738i	$-0.952801\pi$
$443$	−2.31892	−	13.1512i	−0.110175	−	0.624834i	0.878852	−	0.477095i	$-0.158310\pi$
$444$	−6.11246	−	7.28455i	−0.290085	−	0.345709i
$445$		0			0
$446$	4.78699	−	1.74232i	0.226670	−	0.0825013i
$447$	15.8726	+	18.9162i	0.750747	+	0.894706i
$448$	−3.29086	−	18.6634i	−0.155478	−	0.881762i
$449$	−3.45929	+	5.99167i	−0.163254	+	0.282764i	−0.936034	−	0.351910i	$-0.885532\pi$
$449$	−3.45929	+	5.99167i	−0.163254	+	0.282764i	0.772780	+	0.634674i	$0.218866\pi$
$450$		0			0
$451$	4.17159	+	7.22540i	0.196432	+	0.340231i
$452$	5.40420	−	4.53466i	0.254192	−	0.213293i
$453$	−6.95723	+	4.01676i	−0.326879	+	0.188724i
$454$	1.97431	−	11.1969i	0.0926589	−	0.525494i
$455$		0			0
$456$	22.7219	+	4.00649i	1.06405	+	0.187621i
$457$	−7.80928	−	2.84234i	−0.365303	−	0.132959i	0.152846	−	0.988250i	$-0.451156\pi$
$457$	−7.80928	−	2.84234i	−0.365303	−	0.132959i	−0.518148	+	0.855291i	$0.673378\pi$
$458$	−1.09833			−0.0513214
$459$	2.10560	−	1.21567i	0.0982810	−	0.0567426i
$460$		0			0
$461$	23.2319	+	8.45572i	1.08202	+	0.393822i	0.820658	−	0.571420i	$-0.193607\pi$
$461$	23.2319	+	8.45572i	1.08202	+	0.393822i	0.261359	+	0.965242i	$0.415829\pi$
$462$	3.83420	−	4.56942i	0.178383	−	0.212589i
$463$	−0.0983261	−	0.0825054i	−0.00456960	−	0.00383435i	0.640500	−	0.767958i	$-0.278727\pi$
$463$	−0.0983261	−	0.0825054i	−0.00456960	−	0.00383435i	−0.645070	+	0.764124i	$0.723172\pi$
$464$	−0.0421938	+	0.239293i	−0.00195880	+	0.0111089i
$465$		0			0
$466$	−0.256959	+	0.215615i	−0.0119034	+	0.00998815i
$467$	19.9577	+	34.5678i	0.923532	+	1.59960i	0.793905	+	0.608042i	$0.208045\pi$
$467$	19.9577	+	34.5678i	0.923532	+	1.59960i	0.129627	+	0.991563i	$0.458622\pi$
$468$	11.0134	−	4.00854i	0.509093	−	0.185295i
$469$	3.42602	−	5.93404i	0.158199	−	0.274009i
$470$		0			0
$471$	−21.4525	+	3.78265i	−0.988478	+	0.174295i
$472$	36.3851	−	13.2431i	1.67476	−	0.609562i
$473$	11.9153	−	4.33683i	0.547868	−	0.199408i
$474$	2.11318	−	5.80591i	0.0970615	−	0.266674i
$475$		0			0
$476$	−1.07873	+	1.86841i	−0.0494433	+	0.0856383i
$477$	20.3097	−	17.0419i	0.929919	−	0.780295i
$478$	1.38191	+	2.39354i	0.0632072	+	0.109478i
$479$	−6.30200	+	5.28801i	−0.287946	+	0.241615i	−0.775306	−	0.631586i	$-0.782404\pi$
$479$	−6.30200	+	5.28801i	−0.287946	+	0.241615i	0.487360	+	0.873201i	$0.337960\pi$
$480$		0			0
$481$	2.47519	−	14.0375i	0.112859	−	0.640054i
$482$	−5.05959	−	4.24550i	−0.230458	−	0.193377i
$483$	11.9564	+	32.8498i	0.544033	+	1.49472i
$484$	−11.4284	−	4.15961i	−0.519475	−	0.189073i
$485$		0			0
$486$	−13.5000	−	2.38041i	−0.612372	−	0.107978i
$487$	2.84760			0.129037			0.0645186	−	0.997917i	$-0.479449\pi$
$487$	2.84760			0.129037			0.0645186	+	0.997917i	$0.479449\pi$
$488$	25.9683	+	9.45168i	1.17553	+	0.427857i
$489$	−3.79355	−	10.4227i	−0.171550	−	0.471330i
$490$		0			0
$491$	−6.89481	+	39.1024i	−0.311158	+	1.76467i	0.281838	+	0.959462i	$0.409056\pi$
$491$	−6.89481	+	39.1024i	−0.311158	+	1.76467i	−0.592996	+	0.805205i	$0.702055\pi$
$492$			17.0138i			0.767043i
$493$	2.07919	−	1.74465i	0.0936421	−	0.0785751i
$494$	6.57398	+	11.3865i	0.295777	+	0.512301i
$495$		0			0
$496$	−0.0859997	+	0.148956i	−0.00386150	+	0.00668831i
$497$	−5.02734	−	28.5115i	−0.225507	−	1.27891i
$498$	−8.86009	+	24.3429i	−0.397030	+	1.09083i
$499$	36.4962	−	13.2835i	1.63379	−	0.594652i	0.647856	−	0.761763i	$-0.275666\pi$
$499$	36.4962	−	13.2835i	1.63379	−	0.594652i	0.985938	+	0.167111i	$0.0534438\pi$
$500$		0			0
$501$	−15.2554	+	2.68993i	−0.681560	+	0.120177i
$502$	2.34776	+	13.3148i	0.104786	+	0.594270i
$503$	13.5530	−	23.4745i	0.604300	−	1.04668i	−0.387862	−	0.921718i	$-0.626786\pi$
$503$	13.5530	−	23.4745i	0.604300	−	1.04668i	0.992162	−	0.124961i	$-0.0398804\pi$
$504$	30.0669	−	10.9434i	1.33928	−	0.487460i
$505$		0			0
$506$	3.76873	−	3.16234i	0.167541	−	0.140583i
$507$	−4.28564	−	2.47432i	−0.190332	−	0.109888i
$508$	4.17752	−	23.6919i	0.185347	−	1.05116i
$509$	−14.8105	−	12.4275i	−0.656462	−	0.550837i	0.252562	−	0.967581i	$-0.418727\pi$
$509$	−14.8105	−	12.4275i	−0.656462	−	0.550837i	−0.909024	+	0.416744i	$0.863171\pi$
$510$		0			0
$511$	−2.87939	−	1.04801i	−0.127377	−	0.0463613i
$512$	−0.473897			−0.0209435
$513$			24.3938i			1.07701i
$514$	15.7297			0.693806
$515$		0			0
$516$	25.4650	+	4.49016i	1.12103	+	0.197668i
$517$	2.76786	+	2.32251i	0.121730	+	0.102144i
$518$	2.56893	−	14.5691i	0.112872	−	0.640130i
$519$	−9.10385	+	5.25611i	−0.399614	+	0.230718i
$520$		0			0
$521$	−12.2618	−	21.2380i	−0.537198	−	0.930454i	−0.999053	−	0.0434986i	$-0.986150\pi$
$521$	−12.2618	−	21.2380i	−0.537198	−	0.930454i	0.461856	−	0.886955i	$-0.347184\pi$
$522$	−15.3030			−0.669796
$523$	4.31521	−	7.47416i	0.188691	−	0.326822i	−0.756123	−	0.654429i	$-0.772909\pi$
$523$	4.31521	−	7.47416i	0.188691	−	0.326822i	0.944814	+	0.327607i	$0.106242\pi$
$524$	−3.85679	−	21.8730i	−0.168485	−	0.955524i
$525$		0			0
$526$	−3.20574	+	1.16679i	−0.139777	+	0.0508746i
$527$	1.80541	−	0.657115i	0.0786448	−	0.0286244i
$528$	−0.0485904	−	0.0579078i	−0.00211462	−	0.00252011i
$529$	1.01279	+	5.74384i	0.0440345	+	0.249732i
$530$		0			0
$531$	20.4688	+	35.4531i	0.888272	+	1.53853i
$532$	−10.8229	−	18.7459i	−0.469234	−	0.812738i
$533$	−19.5364	+	16.3930i	−0.846217	+	0.710060i
$534$	13.7144	−	7.91799i	0.593478	−	0.342645i
$535$		0			0
$536$	−3.96245	−	3.32489i	−0.171152	−	0.143613i
$537$	−6.14749	−	1.08397i	−0.265284	−	0.0467767i
$538$	16.3687	+	5.95772i	0.705705	+	0.256856i
$539$	−7.42696			−0.319902
$540$		0			0
$541$	21.5722			0.927462			0.463731	−	0.885976i	$-0.346510\pi$
$541$	21.5722			0.927462			0.463731	+	0.885976i	$0.346510\pi$
$542$	12.2208	+	4.44799i	0.524926	+	0.191058i
$543$	12.3867	−	14.7618i	0.531562	−	0.633491i
$544$	2.02094	+	1.69577i	0.0866473	+	0.0727057i
$545$		0			0
$546$	15.7906	+	9.11668i	0.675773	+	0.390158i
$547$	17.3289	−	14.5407i	0.740929	−	0.621714i	−0.192158	−	0.981364i	$-0.561549\pi$
$547$	17.3289	−	14.5407i	0.740929	−	0.621714i	0.933087	+	0.359651i	$0.117104\pi$
$548$	−8.95558	−	15.5115i	−0.382564	−	0.662620i
$549$	−5.07357	+	28.7736i	−0.216535	+	1.22803i
$550$		0			0
$551$	4.72874	+	26.8180i	0.201451	+	1.14249i
$552$	25.9889	−	4.58255i	1.10616	−	0.195046i
$553$	−14.3277	+	5.21485i	−0.609276	+	0.221758i
$554$	14.5005	−	5.27774i	0.616066	−	0.224230i
$555$		0			0
$556$	4.71156	+	26.7206i	0.199815	+	1.13321i
$557$	22.9807	−	39.8037i	0.973724	−	1.68654i	0.289640	−	0.957136i	$-0.406465\pi$
$557$	22.9807	−	39.8037i	0.973724	−	1.68654i	0.684084	−	0.729403i	$-0.260202\pi$
$558$	−10.1792	−	3.70491i	−0.430919	−	0.156842i
$559$	19.3799	+	33.5669i	0.819680	+	1.41973i
$560$		0			0
$561$			0.844395i			0.0356504i
$562$	0.957234	−	5.42874i	0.0403785	−	0.228998i
$563$	−2.20645	−	1.85143i	−0.0929909	−	0.0780286i	0.595107	−	0.803646i	$-0.297110\pi$
$563$	−2.20645	−	1.85143i	−0.0929909	−	0.0780286i	−0.688098	+	0.725618i	$0.741554\pi$
$564$	2.52007	+	6.92383i	0.106114	+	0.291546i
$565$		0			0
$566$	5.56893			0.234079
$567$	16.9145	+	29.2967i	0.710341	+	1.23035i
$568$	−21.8553			−0.917030
$569$	−35.1472	−	12.7925i	−1.47345	−	0.536292i	−0.524414	−	0.851463i	$-0.675716\pi$
$569$	−35.1472	−	12.7925i	−1.47345	−	0.536292i	−0.949035	+	0.315172i	$0.897938\pi$
$570$		0			0
$571$	−19.2324	−	16.1379i	−0.804849	−	0.675349i	0.144523	−	0.989501i	$-0.453835\pi$
$571$	−19.2324	−	16.1379i	−0.804849	−	0.675349i	−0.949372	+	0.314153i	$0.898280\pi$
$572$	−0.706813	+	4.00854i	−0.0295533	+	0.167605i
$573$		−	17.5768i		−	0.734280i
$574$	−20.2763	+	17.0138i	−0.846317	+	0.710144i
$575$		0			0
$576$	−2.62654	−	14.8959i	−0.109439	−	0.620661i
$577$	2.39053	−	4.14052i	0.0995190	−	0.172372i	−0.811967	−	0.583704i	$-0.801603\pi$
$577$	2.39053	−	4.14052i	0.0995190	−	0.172372i	0.911486	+	0.411332i	$0.134936\pi$
$578$	−2.56253	−	14.5328i	−0.106587	−	0.604486i
$579$	−0.208730	+	0.573481i	−0.00867453	+	0.0238331i
$580$		0			0
$581$	60.0729	−	21.8647i	2.49224	−	0.907102i
$582$	9.18092	−	1.61884i	0.380561	−	0.0671033i
$583$	1.59890	+	9.06781i	0.0662196	+	0.375550i
$584$	−1.15657	+	2.00324i	−0.0478594	+	0.0828949i
$585$		0			0
$586$	−2.01233	−	3.48545i	−0.0831284	−	0.143983i
$587$	−18.0116	+	15.1135i	−0.743419	+	0.623802i	−0.933753	−	0.357917i	$-0.883487\pi$
$587$	−18.0116	+	15.1135i	−0.743419	+	0.623802i	0.190335	+	0.981719i	$0.439043\pi$
$588$	−13.1163	−	7.57272i	−0.540908	−	0.312294i
$589$	−3.34730	+	18.9835i	−0.137923	+	0.782200i
$590$		0			0
$591$	24.1079	−	28.7307i	0.991666	−	1.18182i
$592$	−0.176174	−	0.0641222i	−0.00724072	−	0.00263541i
$593$	2.98276			0.122487			0.0612437	−	0.998123i	$-0.480493\pi$
$593$	2.98276			0.122487			0.0612437	+	0.998123i	$0.480493\pi$
$594$	3.06020	−	3.64701i	0.125562	−	0.149638i
$595$		0			0
$596$	−16.4338	−	5.98140i	−0.673153	−	0.245008i
$597$	−41.0091	−	7.23102i	−1.67839	−	0.295946i
$598$	11.5201	+	9.66648i	0.471091	+	0.395292i
$599$	−5.51930	+	31.3015i	−0.225512	+	1.27894i	0.636191	+	0.771532i	$0.280509\pi$
$599$	−5.51930	+	31.3015i	−0.225512	+	1.27894i	−0.861703	+	0.507412i	$0.830602\pi$
$600$		0			0
$601$	28.2763	−	23.7266i	1.15341	−	0.967830i	0.153621	−	0.988130i	$-0.450907\pi$
$601$	28.2763	−	23.7266i	1.15341	−	0.967830i	0.999794	+	0.0202999i	$0.00646211\pi$
$602$	20.1138	+	34.8381i	0.819778	+	1.41990i
$603$	2.73442	−	4.73616i	0.111354	−	0.192871i
$604$	2.84477	−	4.92729i	0.115752	−	0.200488i
$605$		0			0
$606$	−1.93629	−	2.30758i	−0.0786564	−	0.0937390i
$607$	−29.5355	+	10.7501i	−1.19881	+	0.436331i	−0.862809	−	0.505530i	$-0.831297\pi$
$607$	−29.5355	+	10.7501i	−1.19881	+	0.436331i	−0.336002	+	0.941861i	$0.609075\pi$
$608$	−24.8726	+	9.05288i	−1.00872	+	0.367143i
$609$	24.2746	+	28.9293i	0.983655	+	1.17227i
$610$		0			0
$611$	−5.52229	+	9.56488i	−0.223408	+	0.386954i
$612$	−0.860967	+	1.49124i	−0.0348025	+	0.0602797i
$613$	−12.7057	−	22.0070i	−0.513180	−	0.888854i	−0.999883	−	0.0152863i	$-0.995134\pi$
$613$	−12.7057	−	22.0070i	−0.513180	−	0.888854i	0.486703	−	0.873567i	$-0.338199\pi$
$614$	2.72803	−	2.28909i	0.110094	−	0.0923800i
$615$		0			0
$616$	−1.92962	+	10.9434i	−0.0777468	+	0.440924i
$617$	16.7422	+	14.0483i	0.674014	+	0.565565i	0.914250	−	0.405149i	$-0.132781\pi$
$617$	16.7422	+	14.0483i	0.674014	+	0.565565i	−0.240236	+	0.970714i	$0.577225\pi$
$618$	−17.9372	−	3.16281i	−0.721539	−	0.127227i
$619$	37.8619	+	13.7806i	1.52180	+	0.553889i	0.961597	−	0.274467i	$-0.0885014\pi$
$619$	37.8619	+	13.7806i	1.52180	+	0.553889i	0.560202	+	0.828356i	$0.310724\pi$
$620$		0			0
$621$	9.54277	+	26.2185i	0.382938	+	1.05211i
$622$	−4.33368			−0.173765
$623$	−36.7229	−	13.3660i	−1.47127	−	0.535499i
$624$	0.148529	−	0.177009i	0.00594590	−	0.00708605i
$625$		0			0
$626$	2.11081	−	11.9710i	0.0843651	−	0.478458i
$627$	−7.33687	−	4.23594i	−0.293006	−	0.169167i
$628$	11.8182	−	9.91665i	0.471598	−	0.395717i
$629$	1.04710	+	1.81364i	0.0417508	+	0.0723144i
$630$		0			0
$631$	13.9650	−	24.1880i	0.555937	−	0.962911i	−0.441893	−	0.897068i	$-0.645693\pi$
$631$	13.9650	−	24.1880i	0.555937	−	0.962911i	0.997830	−	0.0658432i	$-0.0209737\pi$
$632$	1.99871	+	11.3353i	0.0795045	+	0.450892i
$633$	−11.0792	+	1.95356i	−0.440358	+	0.0776471i
$634$	−12.8011	+	4.65923i	−0.508398	+	0.185042i
$635$		0			0
$636$	−6.42205	+	17.6444i	−0.254651	+	0.699647i
$637$	−3.94222	−	22.3574i	−0.156196	−	0.885834i
$638$	2.65735	−	4.60266i	0.105205	−	0.182221i
$639$	−4.01249	−	22.7560i	−0.158732	−	0.900212i
$640$		0			0
$641$	−23.7230	+	19.9060i	−0.937003	+	0.786239i	−0.977061	−	0.212958i	$-0.931690\pi$
$641$	−23.7230	+	19.9060i	−0.937003	+	0.786239i	0.0400580	+	0.999197i	$0.487246\pi$
$642$			31.4348i			1.24063i
$643$	−5.70068	+	32.3302i	−0.224813	+	1.27498i	0.638229	+	0.769846i	$0.279667\pi$
$643$	−5.70068	+	32.3302i	−0.224813	+	1.27498i	−0.863042	+	0.505132i	$0.831444\pi$
$644$	−18.9659	−	15.9142i	−0.747359	−	0.627109i
$645$		0			0
$646$	−1.81521	−	0.660681i	−0.0714184	−	0.0259942i
$647$	−11.1310			−0.437606			−0.218803	−	0.975769i	$-0.570215\pi$
$647$	−11.1310			−0.437606			−0.218803	+	0.975769i	$0.570215\pi$
$648$	23.9974	−	8.73433i	0.942706	−	0.343117i
$649$	−14.2175			−0.558086
$650$		0			0
$651$	9.14290	+	25.1199i	0.358339	+	0.984527i
$652$	6.01754	+	5.04932i	0.235665	+	0.197746i
$653$	−0.866592	+	4.91469i	−0.0339124	+	0.192327i	−0.997058	−	0.0766550i	$-0.975576\pi$
$653$	−0.866592	+	4.91469i	−0.0339124	+	0.192327i	0.963145	+	0.268982i	$0.0866871\pi$
$654$		−	0.660681i		−	0.0258347i
$655$		0			0
$656$	0.167718	+	0.290497i	0.00654830	+	0.0113420i
$657$	−2.29813	−	0.836452i	−0.0896587	−	0.0326331i
$658$	−5.73143	+	9.92713i	−0.223434	+	0.387000i
$659$	3.68825	+	20.9171i	0.143674	+	0.814815i	0.968422	+	0.249315i	$0.0802056\pi$
$659$	3.68825	+	20.9171i	0.143674	+	0.814815i	−0.824748	+	0.565500i	$0.808683\pi$
$660$		0			0
$661$	−1.06506	+	0.387648i	−0.0414258	+	0.0150778i	−0.362650	−	0.931925i	$-0.618128\pi$
$661$	−1.06506	+	0.387648i	−0.0414258	+	0.0150778i	0.321224	+	0.947003i	$0.395906\pi$
$662$	6.73308	−	2.45064i	0.261689	−	0.0952468i
$663$	−2.54189	+	0.448204i	−0.0987188	+	0.0174068i
$664$	−8.38016	−	47.5262i	−0.325213	−	1.84438i
$665$		0			0
$666$	2.05035	−	11.6281i	0.0794493	−	0.450579i
$667$	15.5736	+	26.9742i	0.603011	+	1.04445i
$668$	8.40420	−	7.05196i	0.325168	−	0.272849i
$669$	−8.68938	−	5.01681i	−0.335951	−	0.193961i
$670$		0			0
$671$	−7.77316	−	6.52245i	−0.300079	−	0.251796i
$672$	−23.5945	+	28.1188i	−0.910178	+	1.08471i
$673$	−41.2083	−	14.9986i	−1.58846	−	0.578154i	−0.611441	−	0.791290i	$-0.709410\pi$
$673$	−41.2083	−	14.9986i	−1.58846	−	0.578154i	−0.977023	+	0.213136i	$0.931632\pi$
$674$	−5.01010			−0.192982
$675$		0			0
$676$	3.50475			0.134798
$677$	9.53033	+	3.46876i	0.366280	+	0.133315i	0.518602	−	0.855016i	$-0.326453\pi$
$677$	9.53033	+	3.46876i	0.366280	+	0.133315i	−0.152321	+	0.988331i	$0.548675\pi$
$678$	8.62654	+	1.52109i	0.331300	+	0.0584172i
$679$	−17.6236	−	14.7880i	−0.676332	−	0.567510i
$680$		0			0
$681$	−19.3935	+	11.1969i	−0.743161	+	0.429064i
$682$	2.88191	−	2.41821i	0.110354	−	0.0925981i
$683$	−2.53091	−	4.38366i	−0.0968425	−	0.167736i	0.813534	−	0.581518i	$-0.197541\pi$
$683$	−2.53091	−	4.38366i	−0.0968425	−	0.167736i	−0.910376	+	0.413782i	$0.864208\pi$
$684$	−8.63816	−	14.9617i	−0.330288	−	0.572076i
$685$		0			0
$686$	−0.0736733	−	0.417822i	−0.00281286	−	0.0159525i
$687$	1.39053	+	1.65717i	0.0530520	+	0.0632249i
$688$	0.479055	−	0.174362i	0.0182638	−	0.00664749i
$689$	−26.4482	+	9.62636i	−1.00760	+	0.366735i
$690$		0			0
$691$	4.22147	+	23.9411i	0.160592	+	0.910763i	0.953494	+	0.301413i	$0.0974584\pi$
$691$	4.22147	+	23.9411i	0.160592	+	0.910763i	−0.792901	+	0.609350i	$0.791430\pi$
$692$	3.72251	−	6.44757i	0.141508	−	0.245100i
$693$	−11.7487			−0.446295
$694$	11.7182	+	20.2966i	0.444818	+	0.770447i
$695$		0			0
$696$	24.6890	−	14.2542i	0.935835	−	0.540305i
$697$	0.650644	−	3.68999i	0.0246449	−	0.139768i
$698$	−5.36160	−	4.49891i	−0.202939	−	0.170286i
$699$	0.650644	+	0.114726i	0.0246096	+	0.00433934i
$700$		0			0
$701$	46.7256			1.76480			0.882400	−	0.470500i	$-0.155926\pi$
$701$	46.7256			1.76480			0.882400	+	0.470500i	$0.155926\pi$
$702$	12.6030	+	7.27633i	0.475668	+	0.274627i
$703$	−21.0114			−0.792459
$704$	4.93629	+	1.79666i	0.186043	+	0.0677143i
$705$		0			0
$706$	9.67546	+	8.11867i	0.364141	+	0.305550i
$707$	−1.29086	+	7.32083i	−0.0485478	+	0.275328i
$708$	−25.1088	−	14.4965i	−0.943645	−	0.544814i
$709$	−6.47044	+	5.42934i	−0.243002	+	0.203903i	−0.756152	−	0.654396i	$-0.772923\pi$
$709$	−6.47044	+	5.42934i	−0.243002	+	0.203903i	0.513150	+	0.858299i	$0.328479\pi$
$710$		0			0
$711$	−11.4354	+	4.16215i	−0.428861	+	0.156093i
$712$	−14.7506	+	25.5488i	−0.552803	+	0.957483i
$713$	3.82857	+	21.7129i	0.143381	+	0.813155i
$714$	−2.63816	+	0.465178i	−0.0987305	+	0.0174089i
$715$		0			0
$716$	4.15435	−	1.51206i	0.155255	−	0.0565084i
$717$	1.86184	−	5.11538i	0.0695318	−	0.191037i
$718$	−3.15611	−	17.8992i	−0.117785	−	0.667991i
$719$	12.5924	−	21.8107i	0.469617	−	0.813401i	−0.529779	−	0.848135i	$-0.677725\pi$
$719$	12.5924	−	21.8107i	0.469617	−	0.813401i	0.999397	+	0.0347347i	$0.0110586\pi$
$720$		0			0
$721$	22.4739	+	38.9259i	0.836972	+	1.44968i
$722$	2.04735	−	1.71793i	0.0761946	−	0.0639348i
$723$			13.0090i			0.483809i
$724$	−2.36989	+	13.4403i	−0.0880763	+	0.499505i
$725$		0			0
$726$	−5.16489	−	14.1904i	−0.191687	−	0.526656i
$727$	11.3375	+	4.12651i	0.420484	+	0.153044i	0.543592	−	0.839349i	$-0.317064\pi$
$727$	11.3375	+	4.12651i	0.420484	+	0.153044i	−0.123108	+	0.992393i	$0.539286\pi$
$728$	−33.9674			−1.25892
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$		0			0
$731$	−5.35117	−	1.94767i	−0.197920	−	0.0720370i
$732$	−7.07728	−	19.4447i	−0.261584	−	0.718695i
$733$	30.9818	+	25.9968i	1.14434	+	0.960214i	0.999572	−	0.0292515i	$-0.00931236\pi$
$733$	30.9818	+	25.9968i	1.14434	+	0.960214i	0.144767	+	0.989466i	$0.453757\pi$
$734$	−1.01131	+	5.73540i	−0.0373280	+	0.211698i
$735$		0			0
$736$	−23.1917	+	19.4601i	−0.854856	+	0.717309i
$737$	0.949655	+	1.64485i	0.0349810	+	0.0605889i
$738$	−16.1832	+	13.5793i	−0.595712	+	0.499862i
$739$	−4.33140	+	7.50221i	−0.159333	+	0.275973i	−0.934628	−	0.355626i	$-0.884268\pi$
$739$	−4.33140	+	7.50221i	−0.159333	+	0.275973i	0.775295	+	0.631599i	$0.217601\pi$
$740$		0			0
$741$	8.85710	−	24.3347i	0.325374	−	0.893957i
$742$	−27.4499	+	9.99093i	−1.00772	+	0.366779i
$743$	−16.4804	+	5.99837i	−0.604607	+	0.220059i	−0.626142	−	0.779709i	$-0.715367\pi$
$743$	−16.4804	+	5.99837i	−0.604607	+	0.220059i	0.0215347	+	0.999768i	$0.493145\pi$
$744$	19.8735	−	3.50423i	0.728596	−	0.128471i
$745$		0			0
$746$	−13.9777	+	24.2101i	−0.511760	+	0.886395i
$747$	47.9461	−	17.4510i	1.75426	−	0.638498i
$748$	−0.299011	−	0.517902i	−0.0109329	−	0.0189364i
$749$	59.4252	−	49.8637i	2.17135	−	1.82198i
$750$		0			0
$751$	−5.13253	+	29.1080i	−0.187289	+	1.06217i	0.735691	+	0.677318i	$0.236858\pi$
$751$	−5.13253	+	29.1080i	−0.187289	+	1.06217i	−0.922979	+	0.384849i	$0.874253\pi$
$752$	0.111281	+	0.0933762i	0.00405802	+	0.00340508i
$753$	17.1172	−	20.3995i	0.623786	−	0.743399i
$754$	15.2659	+	5.55635i	0.555953	+	0.202350i
$755$		0			0
$756$	−20.7487	−	11.9792i	−0.754622	−	0.435681i
$757$	−26.1165			−0.949220			−0.474610	−	0.880196i	$-0.657411\pi$
$757$	−26.1165			−0.949220			−0.474610	+	0.880196i	$0.657411\pi$
$758$	28.2551	+	10.2840i	1.02627	+	0.373532i
$759$	−9.54277	−	1.68265i	−0.346380	−	0.0610762i
$760$		0			0
$761$	−1.78136	+	10.1026i	−0.0645744	+	0.366220i	0.935348	+	0.353730i	$0.115087\pi$
$761$	−1.78136	+	10.1026i	−0.0645744	+	0.366220i	−0.999922	+	0.0124897i	$0.996024\pi$
$762$	25.8694	−	14.9357i	0.937150	−	0.541064i
$763$	−1.24897	+	1.04801i	−0.0452158	+	0.0379405i
$764$	6.22416	+	10.7806i	0.225182	+	0.390027i
$765$		0			0
$766$	−10.4650	+	18.1259i	−0.378115	+	0.654914i
$767$	−7.54664	−	42.7991i	−0.272493	−	1.54539i
$768$	17.9259	+	21.3633i	0.646846	+	0.770881i
$769$	−26.7520	+	9.73692i	−0.964700	+	0.351122i	−0.775874	−	0.630888i	$-0.782691\pi$
$769$	−26.7520	+	9.73692i	−0.964700	+	0.351122i	−0.188827	+	0.982010i	$0.560468\pi$
$770$		0			0
$771$	−19.9145	−	23.7331i	−0.717202	−	0.854728i
$772$	−0.0750542	−	0.425653i	−0.00270126	−	0.0153196i
$773$	12.4427	−	21.5514i	0.447532	−	0.775149i	−0.550692	−	0.834708i	$-0.685636\pi$
$773$	12.4427	−	21.5514i	0.447532	−	0.775149i	0.998225	+	0.0595595i	$0.0189696\pi$
$774$	16.0535	+	27.8055i	0.577031	+	0.999447i
$775$		0			0
$776$	−13.3041	+	11.1634i	−0.477588	+	0.400744i
$777$	−25.2344	+	14.5691i	−0.905280	+	0.522664i
$778$	0.677052	−	3.83975i	0.0242735	−	0.137662i
$779$	28.7980	+	24.1644i	1.03179	+	0.865778i
$780$		0			0
$781$	7.54101	+	2.74470i	0.269839	+	0.0982132i
$782$	−2.20945			−0.0790096
$783$	19.3743	+	23.0894i	0.692382	+	0.825149i
$784$	−0.298600			−0.0106643
$785$		0			0
$786$	17.7268	−	21.1260i	0.632296	−	0.753541i
$787$	−0.539830	−	0.452971i	−0.0192428	−	0.0161467i	0.633115	−	0.774057i	$-0.281776\pi$
$787$	−0.539830	−	0.452971i	−0.0192428	−	0.0161467i	−0.652358	+	0.757911i	$0.726220\pi$
$788$	−4.61246	+	26.1586i	−0.164312	+	0.931861i
$789$	5.81908	+	3.35965i	0.207165	+	0.119607i
$790$		0			0
$791$	−10.8084	−	18.7207i	−0.384302	−	0.665631i
$792$	−1.54010	+	8.73433i	−0.0547250	+	0.310361i
$793$	15.5086	−	26.8617i	0.550727	−	0.953887i
$794$	2.87655	+	16.3138i	0.102085	+	0.578953i
$795$		0			0
$796$	27.7132	−	10.0868i	0.982267	−	0.357516i
$797$	−11.2819	+	4.10629i	−0.399627	+	0.145452i	−0.534012	−	0.845477i	$-0.679316\pi$
$797$	−11.2819	+	4.10629i	−0.399627	+	0.145452i	0.134385	+	0.990929i	$0.457094\pi$
$798$	9.19253	−	25.2563i	0.325412	−	0.894063i
$799$	−0.281774	−	1.59802i	−0.00996846	−	0.0565340i
$800$		0			0
$801$	−29.3097	−	10.6679i	−1.03561	−	0.376931i
$802$	4.02007	+	6.96296i	0.141954	+	0.245871i
$803$	0.650644	−	0.545955i	0.0229607	−	0.0192663i
$804$			3.87317i			0.136596i
$805$		0			0
$806$	8.80928	+	7.39186i	0.310294	+	0.260367i
$807$	−11.7344	−	32.2401i	−0.413071	−	1.13490i
$808$	5.27332	+	1.91933i	0.185515	+	0.0675218i
$809$	−20.6750			−0.726894			−0.363447	−	0.931615i	$-0.618400\pi$
$809$	−20.6750			−0.726894			−0.363447	+	0.931615i	$0.618400\pi$
$810$		0			0
$811$	22.5877			0.793162			0.396581	−	0.918000i	$-0.370197\pi$
$811$	22.5877			0.793162			0.396581	+	0.918000i	$0.370197\pi$
$812$	−25.1328	−	9.14759i	−0.881988	−	0.321017i
$813$	−8.76083	−	24.0702i	−0.307256	−	0.844178i
$814$	3.14131	+	2.63587i	0.110103	+	0.0923873i
$815$		0			0
$816$			0.0339488i			0.00118845i
$817$	43.7674	−	36.7252i	1.53123	−	1.28485i
$818$	−12.2212	−	21.1677i	−0.427303	−	0.740110i
$819$	−6.23618	−	35.3671i	−0.217910	−	1.23583i
$820$		0			0
$821$	−2.09199	−	11.8642i	−0.0730108	−	0.414065i	−0.999305	−	0.0372648i	$-0.988135\pi$
$821$	−2.09199	−	11.8642i	−0.0730108	−	0.414065i	0.926295	−	0.376800i	$-0.122976\pi$
$822$	7.60648	−	20.8986i	0.265306	−	0.728923i
$823$	0.0231661	−	0.00843175i	0.000807518	−	0.000293912i	−0.341616	−	0.939839i	$-0.610974\pi$
$823$	0.0231661	−	0.00843175i	0.000807518	−	0.000293912i	0.342424	+	0.939546i	$0.388752\pi$
$824$	31.8848	−	11.6051i	1.11076	−	0.404283i
$825$		0			0
$826$	−7.83244	−	44.4200i	−0.272526	−	1.54557i
$827$	14.7126	−	25.4830i	0.511607	−	0.886130i	−0.488302	−	0.872675i	$-0.662384\pi$
$827$	14.7126	−	25.4830i	0.511607	−	0.886130i	0.999909	−	0.0134552i	$-0.00428304\pi$
$828$	−15.1373	−	12.7017i	−0.526057	−	0.441414i
$829$	−16.6766	−	28.8848i	−0.579204	−	1.00321i	−0.995571	−	0.0940137i	$-0.970030\pi$
$829$	−16.6766	−	28.8848i	−0.579204	−	1.00321i	0.416367	−	0.909197i	$-0.363303\pi$
$830$		0			0
$831$	−26.3214	−	15.1966i	−0.913078	−	0.527166i
$832$	−2.78833	+	15.8134i	−0.0966681	+	0.548232i
$833$	2.55509	+	2.14398i	0.0885287	+	0.0742844i
$834$	−21.6556	+	25.8081i	−0.749872	+	0.893662i
$835$		0			0
$836$	6.00000			0.207514
$837$	7.29726	+	20.0490i	0.252230	+	0.692996i
$838$	7.07428			0.244377
$839$	50.4154	+	18.3497i	1.74053	+	0.633502i	0.999288	−	0.0377323i	$-0.0120134\pi$
$839$	50.4154	+	18.3497i	1.74053	+	0.633502i	0.741245	+	0.671235i	$0.234236\pi$
$840$		0			0
$841$	3.56031	+	2.98745i	0.122769	+	0.103016i
$842$	−3.03266	+	17.1991i	−0.104512	+	0.592719i
$843$	−9.40286	+	5.42874i	−0.323852	+	0.186976i
$844$	6.10354	−	5.12148i	0.210093	−	0.176289i
$845$		0			0
$846$	−4.57444	+	7.92317i	−0.157273	+	0.272404i
$847$	−18.6331	+	32.2735i	−0.640241	+	1.10893i
$848$	0.0642836	+	0.364570i	0.00220751	+	0.0125194i
$849$	−7.05051	−	8.40247i	−0.241973	−	0.288372i
$850$		0			0
$851$	−22.5831	+	8.21956i	−0.774137	+	0.281763i
$852$	10.5192	+	12.5363i	0.360382	+	0.429486i
$853$	1.93464	+	10.9719i	0.0662408	+	0.375670i	0.999849	+	0.0173748i	$0.00553086\pi$
$853$	1.93464	+	10.9719i	0.0662408	+	0.375670i	−0.933608	+	0.358296i	$0.883358\pi$
$854$	16.0960	−	27.8790i	0.550792	−	0.954001i
$855$		0			0
$856$	−29.2803	−	50.7150i	−1.00078	−	1.73340i
$857$	13.0189	−	10.9241i	0.444717	−	0.373162i	−0.392754	−	0.919643i	$-0.628478\pi$
$857$	13.0189	−	10.9241i	0.444717	−	0.373162i	0.837471	+	0.546482i	$0.184033\pi$
$858$	−4.37696	+	2.52704i	−0.149427	+	0.0862718i
$859$	2.88578	−	16.3661i	0.0984616	−	0.558404i	−0.895170	−	0.445725i	$-0.852946\pi$
$859$	2.88578	−	16.3661i	0.0984616	−	0.558404i	0.993632	−	0.112678i	$-0.0359430\pi$
$860$		0			0
$861$	51.3414	+	9.05288i	1.74971	+	0.308521i
$862$	4.87046	+	1.77270i	0.165889	+	0.0603785i
$863$	19.9121			0.677816			0.338908	−	0.940820i	$-0.389942\pi$
$863$	19.9121			0.677816			0.338908	+	0.940820i	$0.389942\pi$
$864$	−18.8316	+	22.4426i	−0.640663	+	0.763512i
$865$		0			0
$866$	3.15833	+	1.14954i	0.107324	+	0.0390629i
$867$	−18.6830	+	22.2656i	−0.634509	+	0.756179i
$868$	−14.5030	−	12.1695i	−0.492264	−	0.413058i
$869$	0.733899	−	4.16215i	0.0248958	−	0.141191i
$870$		0			0
$871$	−4.44743	+	3.73184i	−0.150696	+	0.126449i
$872$	0.615400	+	1.06590i	0.0208401	+	0.0360961i
$873$	−14.0660	−	11.8028i	−0.476062	−	0.399463i
$874$	11.0838	−	19.1977i	0.374914	−	0.649371i
$875$		0			0
$876$	1.70574	−	0.300767i	0.0576315	−	0.0101620i
$877$	39.8153	−	14.4916i	1.34447	−	0.489346i	0.433250	−	0.901274i	$-0.357367\pi$
$877$	39.8153	−	14.4916i	1.34447	−	0.489346i	0.911216	+	0.411928i	$0.135145\pi$
$878$	−31.6282	+	11.5117i	−1.06740	+	0.388502i
$879$	−2.71120	+	7.44896i	−0.0914465	+	0.251247i
$880$		0			0
$881$	−13.9881	+	24.2282i	−0.471272	+	0.816268i	−0.999460	−	0.0328600i	$-0.989538\pi$
$881$	−13.9881	+	24.2282i	−0.471272	+	0.816268i	0.528188	+	0.849128i	$0.322872\pi$
$882$	−3.26558	−	18.5200i	−0.109958	−	0.623601i
$883$	14.7340	+	25.5200i	0.495837	+	0.858815i	0.999988	−	0.00480027i	$-0.00152798\pi$
$883$	14.7340	+	25.5200i	0.495837	+	0.858815i	−0.504151	+	0.863615i	$0.668195\pi$
$884$	1.40033	−	1.17502i	0.0470982	−	0.0395201i
$885$		0			0
$886$	−2.03922	+	11.5650i	−0.0685089	+	0.388534i
$887$	−26.2147	−	21.9967i	−0.880202	−	0.738577i	0.0860185	−	0.996294i	$-0.472586\pi$
$887$	−26.2147	−	21.9967i	−0.880202	−	0.738577i	−0.966221	+	0.257716i	$0.917030\pi$
$888$	7.52322	+	20.6699i	0.252463	+	0.693636i
$889$	−69.2704	−	25.2124i	−2.32326	−	0.845596i
$890$		0			0
$891$	−9.37700			−0.314141
$892$	7.10607			0.237929
$893$	15.2986	+	5.56824i	0.511948	+	0.186334i
$894$	−7.42696	−	20.4054i	−0.248395	−	0.682458i
$895$		0			0
$896$	4.46616	−	25.3288i	0.149204	−	0.846177i
$897$		−	29.6198i		−	0.988977i
$898$	4.66069	−	3.91079i	0.155529	−	0.130505i
$899$	11.9089	+	20.6269i	0.397186	+	0.687946i
$900$		0			0
$901$	2.06758	−	3.58116i	0.0688811	−	0.119306i
$902$	−1.27403	−	7.22540i	−0.0424207	−	0.240580i
$903$	27.0993	−	74.4546i	0.901807	−	2.47769i
$904$	−15.3344	+	5.58126i	−0.510014	+	0.185630i
$905$		0			0
$906$	6.95723	−	1.22675i	0.231139	−	0.0407560i
$907$	−2.00222	−	11.3552i	−0.0664827	−	0.377042i	−0.999836	−	0.0180842i	$-0.994243\pi$
$907$	−2.00222	−	11.3552i	−0.0664827	−	0.377042i	0.933354	−	0.358958i	$-0.116868\pi$
$908$	7.92989	−	13.7350i	0.263163	−	0.455811i
$909$	−1.03028	+	5.84300i	−0.0341722	+	0.193800i
$910$		0			0
$911$	0.770544	−	0.646563i	0.0255293	−	0.0214216i	−0.629934	−	0.776649i	$-0.716918\pi$
$911$	0.770544	−	0.646563i	0.0255293	−	0.0214216i	0.655463	+	0.755227i	$0.272474\pi$
$912$	−0.294978	−	0.170306i	−0.00976770	−	0.00563939i
$913$	−3.07708	+	17.4510i	−0.101836	+	0.577543i
$914$	5.59833	+	4.69755i	0.185176	+	0.155381i
$915$		0			0
$916$	−1.43969	−	0.524005i	−0.0475688	−	0.0173136i
$917$	−68.0565			−2.24743
$918$	−2.10560	+	0.371274i	−0.0694952	+	0.0122539i
$919$	36.9469			1.21876			0.609382	−	0.792877i	$-0.291418\pi$
$919$	36.9469			1.21876			0.609382	+	0.792877i	$0.291418\pi$
$920$		0			0
$921$	−6.90760	−	1.21800i	−0.227613	−	0.0401344i
$922$	−16.6545	−	13.9748i	−0.548487	−	0.460235i
$923$	−4.25965	+	24.1577i	−0.140208	+	0.795159i
$924$	7.20594	−	4.16035i	0.237058	−	0.136865i
$925$		0			0
$926$	0.0564370	+	0.0977517i	0.00185463	+	0.00321232i
$927$	17.9372	+	31.0681i	0.589134	+	1.02041i
$928$	−16.3525	+	28.3234i	−0.536797	+	0.929760i
$929$	−2.23530	−	12.6770i	−0.0733378	−	0.415919i	−0.999269	−	0.0382273i	$-0.987829\pi$
$929$	−2.23530	−	12.6770i	−0.0733378	−	0.415919i	0.925931	−	0.377692i	$-0.123282\pi$
$930$		0			0
$931$	−31.4466	+	11.4456i	−1.03062	+	0.375115i
$932$	−0.439693	+	0.160035i	−0.0144026	+	0.00524212i
$933$	5.48663	+	6.53872i	0.179624	+	0.214068i
$934$	−6.09523	−	34.5678i	−0.199442	−	1.13109i
$935$		0			0
$936$	−27.1105			−0.886135
$937$	5.01367	+	8.68393i	0.163789	+	0.283692i	0.936225	−	0.351402i	$-0.114295\pi$
$937$	5.01367	+	8.68393i	0.163789	+	0.283692i	−0.772435	+	0.635094i	$0.780962\pi$
$938$	−4.61587	+	3.87317i	−0.150713	+	0.126464i
$939$	−20.7344	+	11.9710i	−0.676642	+	0.390660i
$940$		0			0
$941$	−12.9526	−	10.8686i	−0.422244	−	0.354305i	0.406772	−	0.913530i	$-0.366654\pi$
$941$	−12.9526	−	10.8686i	−0.422244	−	0.354305i	−0.829016	+	0.559225i	$0.811099\pi$
$942$	18.8650	+	3.32641i	0.614655	+	0.108380i
$943$	40.4051	+	14.7063i	1.31577	+	0.478902i
$944$	−0.571614			−0.0186044
$945$		0			0
$946$	−11.1506			−0.362539
$947$	−9.21853	−	3.35527i	−0.299562	−	0.109032i	0.187866	−	0.982195i	$-0.439843\pi$
$947$	−9.21853	−	3.35527i	−0.299562	−	0.109032i	−0.487428	+	0.873163i	$0.662065\pi$
$948$	5.53994	−	6.60224i	0.179929	−	0.214431i
$949$	1.98886	+	1.66885i	0.0645610	+	0.0541731i
$950$		0			0
$951$	23.2367	+	13.4157i	0.753502	+	0.435034i
$952$	3.82295	−	3.20783i	0.123902	−	0.103967i
$953$	9.77972	+	16.9390i	0.316796	+	0.548707i	0.979818	−	0.199893i	$-0.0640596\pi$
$953$	9.77972	+	16.9390i	0.316796	+	0.548707i	−0.663022	+	0.748600i	$0.730726\pi$
$954$	−21.9086	+	7.97409i	−0.709319	+	0.258171i
$955$		0			0
$956$	0.669473	+	3.79677i	0.0216523	+	0.122796i
$957$	−10.3089	+	1.81773i	−0.333238	+	0.0587589i
$958$	6.79813	−	2.47432i	0.219638	−	0.0799416i
$959$	−51.5732	+	18.7711i	−1.66538	+	0.606150i
$960$		0			0
$961$	−2.45542	−	13.9254i	−0.0792072	−	0.449206i
$962$	−6.26739	+	10.8554i	−0.202069	+	0.349993i
$963$	47.4292	−	39.7979i	1.52839	−	1.28247i
$964$	−4.60664	−	7.97893i	−0.148370	−	0.256984i
$965$		0			0
$966$		−	30.7416i		−	0.989094i
$967$	3.74123	−	21.2176i	0.120310	−	0.682311i	−0.863674	−	0.504051i	$-0.831842\pi$
$967$	3.74123	−	21.2176i	0.120310	−	0.682311i	0.983983	−	0.178260i	$-0.0570467\pi$
$968$	21.5506	+	18.0831i	0.692661	+	0.581212i
$969$	1.30129	+	3.57526i	0.0418034	+	0.114854i
$970$		0			0
$971$	−45.7056			−1.46676			−0.733382	−	0.679817i	$-0.762059\pi$
$971$	−45.7056			−1.46676			−0.733382	+	0.679817i	$0.762059\pi$
$972$	−16.5602	−	9.56104i	−0.531169	−	0.306670i
$973$	83.1397			2.66534
$974$	−2.35312	−	0.856466i	−0.0753988	−	0.0274429i
$975$		0			0
$976$	−0.312519	−	0.262235i	−0.0100035	−	0.00839393i
$977$	−1.53580	+	8.70994i	−0.0491345	+	0.278656i	−0.999469	−	0.0325737i	$-0.989630\pi$
$977$	−1.53580	+	8.70994i	−0.0491345	+	0.278656i	0.950335	+	0.311229i	$0.100741\pi$
$978$			9.75378i			0.311892i
$979$	8.29813	−	6.96296i	0.265209	−	0.222537i
$980$		0			0
$981$	−0.996845	+	0.836452i	−0.0318268	+	0.0267059i
$982$	17.4583	−	30.2386i	0.557116	−	0.964953i
$983$	0.854160	+	4.84418i	0.0272435	+	0.154505i	0.995395	−	0.0958604i	$-0.0305602\pi$
$983$	0.854160	+	4.84418i	0.0272435	+	0.154505i	−0.968151	+	0.250366i	$0.919449\pi$
$984$	13.4604	−	36.9821i	0.429102	−	1.17895i
$985$		0			0
$986$	−2.24288	+	0.816341i	−0.0714278	+	0.0259976i
$987$	22.2344	−	3.92053i	0.707729	−	0.124792i
$988$	3.18479	+	18.0619i	0.101322	+	0.574624i
$989$	32.6746	−	56.5940i	1.03899	−	1.79959i
$990$		0			0
$991$	16.2515	+	28.1484i	0.516246	+	0.894164i	0.999822	+	0.0188617i	$0.00600424\pi$
$991$	16.2515	+	28.1484i	0.516246	+	0.894164i	−0.483576	+	0.875302i	$0.660662\pi$
$992$	−17.7344	+	14.8809i	−0.563068	+	0.472471i
$993$	−12.2219	−	7.05634i	−0.387851	−	0.223926i
$994$	−4.42097	+	25.0726i	−0.140225	+	0.795253i
$995$		0			0
$996$	−23.2277	+	27.6817i	−0.735999	+	0.877129i
$997$	26.9024	+	9.79169i	0.852009	+	0.310106i	0.730859	−	0.682528i	$-0.239120\pi$
$997$	26.9024	+	9.79169i	0.852009	+	0.310106i	0.121150	+	0.992634i	$0.461342\pi$
$998$	−34.1539			−1.08112
$999$	−20.1404	+	11.6281i	−0.637215	+	0.367896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.a.301.1	✓	6
5.2	odd	4		675.2.u.a.274.2		12
5.3	odd	4		675.2.u.a.274.1		12
5.4	even	2		675.2.l.b.301.1	yes	6
27.7	even	9	inner	675.2.l.a.601.1	yes	6
135.7	odd	36		675.2.u.a.574.1		12
135.34	even	18		675.2.l.b.601.1	yes	6
135.88	odd	36		675.2.u.a.574.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.a.301.1	✓	6	1.1	even	1	trivial
675.2.l.a.601.1	yes	6	27.7	even	9	inner
675.2.l.b.301.1	yes	6	5.4	even	2
675.2.l.b.601.1	yes	6	135.34	even	18
675.2.u.a.274.1		12	5.3	odd	4
675.2.u.a.274.2		12	5.2	odd	4
675.2.u.a.574.1		12	135.7	odd	36
675.2.u.a.574.2		12	135.88	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.826352 - 0.300767i) q^{2} +(0.592396 + 1.62760i) q^{3} +(-0.939693 - 0.788496i) q^{4} -1.52314i q^{6} +(-2.87939 + 2.41609i) q^{7} +(1.41875 + 2.45734i) q^{8} +(-2.29813 + 1.92836i) q^{9} +(-0.180922 - 1.02606i) q^{11} +(0.726682 - 1.99654i) q^{12} +(2.99273 - 1.08926i) q^{13} +(3.10607 - 1.13052i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(-0.233956 + 0.405223i) q^{17} +(2.47906 - 0.902302i) q^{18} +(-2.34730 - 4.06564i) q^{19} +(-5.63816 - 3.25519i) q^{21} +(-0.159100 + 0.902302i) q^{22} +(-4.11334 - 3.45150i) q^{23} +(-3.15910 + 3.76487i) q^{24} -2.80066 q^{26} +(-4.50000 - 2.59808i) q^{27} +4.61081 q^{28} +(-5.45084 - 1.98394i) q^{29} +(-3.14543 - 2.63933i) q^{31} +(0.979055 - 5.55250i) q^{32} +(1.56283 - 0.902302i) q^{33} +(0.315207 - 0.264490i) q^{34} +3.68004 q^{36} +(2.23783 - 3.87603i) q^{37} +(0.716881 + 4.06564i) q^{38} +(3.54576 + 4.22567i) q^{39} +(-7.52481 + 2.73881i) q^{41} +(3.68004 + 4.38571i) q^{42} +(2.11334 + 11.9854i) q^{43} +(-0.639033 + 1.10684i) q^{44} +(2.36097 + 4.08931i) q^{46} +(-2.65657 + 2.22913i) q^{47} +(0.0628336 - 0.0362770i) q^{48} +(1.23783 - 7.02006i) q^{49} +(-0.798133 - 0.140732i) q^{51} +(-3.67112 - 1.33618i) q^{52} -8.83750 q^{53} +(2.93717 + 3.50038i) q^{54} +(-10.0223 - 3.64781i) q^{56} +(5.22668 - 6.22892i) q^{57} +(3.90760 + 3.27887i) q^{58} +(2.36959 - 13.4386i) q^{59} +(7.46064 - 6.26022i) q^{61} +(1.80541 + 3.12706i) q^{62} +(1.95811 - 11.1050i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-1.56283 + 0.275570i) q^{66} +(-1.71301 + 0.623485i) q^{67} +(0.539363 - 0.196312i) q^{68} +(3.18092 - 8.73951i) q^{69} +(-3.85117 + 6.67042i) q^{71} +(-7.99912 - 2.91144i) q^{72} +(0.407604 + 0.705990i) q^{73} +(-3.01501 + 2.52990i) q^{74} +(-1.00000 + 5.67128i) q^{76} +(3.00000 + 2.51730i) q^{77} +(-1.65910 - 4.55834i) q^{78} +(3.81180 + 1.38738i) q^{79} +(1.56283 - 8.86327i) q^{81} +7.04189 q^{82} +(-15.9820 - 5.81699i) q^{83} +(2.73143 + 7.50454i) q^{84} +(1.85844 - 10.5397i) q^{86} -10.0470i q^{87} +(2.26470 - 1.90031i) q^{88} +(5.19846 + 9.00400i) q^{89} +(-5.98545 + 10.3671i) q^{91} +(1.14378 + 6.48670i) q^{92} +(2.43242 - 6.68302i) q^{93} +(2.86571 - 1.04303i) q^{94} +(9.61721 - 1.69577i) q^{96} +(1.06283 + 6.02763i) q^{97} +(-3.13429 + 5.42874i) q^{98} +(2.39440 + 2.00914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31}+ \cdots - 27 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8 - 18 * q^11 - 9 * q^12 - 6 * q^14 - 18 * q^16 - 6 * q^17 + 18 * q^18 - 12 * q^19 + 36 * q^22 - 18 * q^23 + 18 * q^24 + 12 * q^26 - 27 * q^27 + 36 * q^28 - 21 * q^29 - 3 * q^31 + 9 * q^32 + 9 * q^34 - 18 * q^36 - 6 * q^37 - 12 * q^38 - 9 * q^39 - 18 * q^41 - 18 * q^42 + 6 * q^43 - 27 * q^44 - 9 * q^46 + 6 * q^47 - 9 * q^48 - 12 * q^49 + 9 * q^51 - 36 * q^52 - 48 * q^53 + 27 * q^54 - 48 * q^56 + 18 * q^57 + 27 * q^58 + 36 * q^61 + 15 * q^62 + 18 * q^63 - 12 * q^64 - 18 * q^67 + 12 * q^68 + 36 * q^69 + 3 * q^71 + 9 * q^72 + 6 * q^73 + 12 * q^74 - 6 * q^76 + 18 * q^77 + 27 * q^78 - 12 * q^79 + 36 * q^82 - 18 * q^83 + 36 * q^84 + 3 * q^86 + 18 * q^88 + 3 * q^89 + 63 * q^92 - 9 * q^93 + 27 * q^94 + 27 * q^96 - 3 * q^97 - 9 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

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Database

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