LMFDB - Embedded newform 675.2.l.b.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
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			601.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	675.601
Dual form			675.2.l.b.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826352 - 0.300767i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(-0.939693 + 0.788496i) q^{4} +1.52314i q^{6} +(2.87939 + 2.41609i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^7 - 6 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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	$-0.510477\pi$
$2$	0.826352	−	0.300767i	0.584319	−	0.212675i	0.617229	+	0.786784i	$0.288255\pi$
$3$	−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	$-0.0263186\pi$
$7$	2.87939	+	2.41609i	1.08831	+	0.913197i	0.0917216	+	0.995785i	$0.470763\pi$
$8$	−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	−0.999859	−	0.0168083i	$-0.994649\pi$
$11$	−0.180922	+	1.02606i	−0.0545501	+	0.309369i	0.945309	+	0.326177i	$0.105761\pi$
$12$	−0.726682	−	1.99654i	−0.209775	−	0.576352i
$13$	−2.99273	−	1.08926i	−0.830033	−	0.302107i	−0.108160	−	0.994133i	$-0.534496\pi$
$13$	−2.99273	−	1.08926i	−0.830033	−	0.302107i	−0.721872	+	0.692026i	$0.756718\pi$
$14$	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	$-0.148595\pi$
$17$	0.233956	+	0.405223i	0.0567426	+	0.0982810i	−0.836259	+	0.548335i	$0.815262\pi$
$18$	−2.47906	−	0.902302i	−0.584319	−	0.212675i
$19$	−2.34730	+	4.06564i	−0.538507	+	0.932721i	0.460478	+	0.887671i	$0.347678\pi$
$19$	−2.34730	+	4.06564i	−0.538507	+	0.932721i	−0.998985	+	0.0450499i	$0.985655\pi$
$20$		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	$-0.533093\pi$
$23$	4.11334	−	3.45150i	0.857691	−	0.719688i	0.961469	+	0.274912i	$0.0886488\pi$
$24$	−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	−0.794275	−	0.607558i	$-0.792149\pi$
$29$	−5.45084	+	1.98394i	−1.01220	+	0.368409i	−0.217920	+	0.975967i	$0.569927\pi$
$30$		0			0
$31$	−3.14543	+	2.63933i	−0.564936	+	0.474037i	−0.879961	−	0.475046i	$-0.842431\pi$
$31$	−3.14543	+	2.63933i	−0.564936	+	0.474037i	0.315025	+	0.949083i	$0.397987\pi$
$32$	−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	$-0.286589\pi$
$37$	−2.23783	−	3.87603i	−0.367896	−	0.637215i	−0.989236	+	0.146326i	$0.953255\pi$
$38$	−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	−0.320682	−	0.947187i	$-0.603912\pi$
$41$	−7.52481	−	2.73881i	−1.17518	−	0.427730i	−0.854497	+	0.519457i	$0.826134\pi$
$42$	−3.68004	+	4.38571i	−0.567843	+	0.676729i
$43$	−2.11334	+	11.9854i	−0.322281	+	1.82775i	0.205847	+	0.978584i	$0.434005\pi$
$43$	−2.11334	+	11.9854i	−0.322281	+	1.82775i	−0.528128	+	0.849165i	$0.677106\pi$
$44$	−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	$-0.196386\pi$
$47$	2.65657	+	2.22913i	0.387501	+	0.325152i	−0.428138	+	0.903714i	$0.640830\pi$
$48$	−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	$-0.292388\pi$
$53$	8.83750			1.21392			0.606962	+	0.794731i	$0.292388\pi$
$54$	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	0.606586	+	0.795018i	$0.292538\pi$
$59$	2.36959	+	13.4386i	0.308494	+	1.74955i	−0.298093	+	0.954537i	$0.596350\pi$
$60$		0			0
$61$	7.46064	+	6.26022i	0.955237	+	0.801539i	0.980172	−	0.198150i	$-0.0634934\pi$
$61$	7.46064	+	6.26022i	0.955237	+	0.801539i	−0.0249349	+	0.999689i	$0.507938\pi$
$62$	−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	$-0.353370\pi$
$67$	1.71301	+	0.623485i	0.209278	+	0.0761708i	−0.235254	+	0.971934i	$0.575592\pi$
$68$	−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	0.541754	−	0.840537i	$-0.317760\pi$
$71$	−3.85117	−	6.67042i	−0.457049	−	0.791633i	−0.998803	+	0.0489043i	$0.984427\pi$
$72$	7.99912	−	2.91144i	0.942706	−	0.343117i
$73$	−0.407604	+	0.705990i	−0.0477064	+	0.0826299i	−0.888893	−	0.458116i	$-0.848525\pi$
$73$	−0.407604	+	0.705990i	−0.0477064	+	0.0826299i	0.841186	+	0.540746i	$0.181858\pi$
$74$	−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	−0.118566	−	0.992946i	$-0.537830\pi$
$79$	3.81180	−	1.38738i	0.428861	−	0.156093i	0.547427	+	0.836853i	$0.315607\pi$
$80$		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	$-0.227919\pi$
$83$	15.9820	−	5.81699i	1.75426	−	0.638498i	0.999840	+	0.0178968i	$0.00569704\pi$
$84$	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	−0.447164	−	0.894452i	$-0.647566\pi$
$89$	5.19846	−	9.00400i	0.551036	−	0.954422i	0.998200	−	0.0599704i	$-0.0191006\pi$
$90$		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	0.882102	+	0.471059i	$0.156128\pi$
$97$	−1.06283	+	6.02763i	−0.107914	+	0.612013i	−0.990016	+	0.140954i	$0.954983\pi$
$98$	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	0.715043	−	0.699080i	$-0.246407\pi$
$101$	1.51501	+	1.27125i	0.150750	+	0.126494i	−0.564294	+	0.825574i	$0.690851\pi$
$102$	−0.617211	+	0.356347i	−0.0611130	+	0.0352836i
$103$	−2.07650	−	11.7764i	−0.204604	−	1.16037i	−0.898062	−	0.439870i	$-0.855025\pi$
$103$	−2.07650	−	11.7764i	−0.204604	−	1.16037i	0.693458	−	0.720497i	$-0.256086\pi$
$104$	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	$-0.0221360\pi$
$107$	20.6382			1.99517			0.997583	+	0.0694862i	$0.0221360\pi$
$108$	−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	0.995065	+	0.0992218i	$0.0316353\pi$
$113$	0.998656	+	5.66366i	0.0939456	+	0.532792i	−0.901120	+	0.433570i	$0.857254\pi$
$114$	−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	−0.00826966	+	0.999966i	$0.502632\pi$
$127$	−9.80587	+	16.9843i	−0.870131	+	1.50711i	−0.861861	+	0.507145i	$0.830701\pi$
$128$	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	0.212621	−	0.977135i	$-0.431800\pi$
$131$	13.8701	−	11.6384i	1.21183	−	1.01685i	0.999211	−	0.0397131i	$-0.0126444\pi$
$132$	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	$-0.825498\pi$
$137$	−13.7208	+	4.99395i	−1.17224	+	0.426662i	−0.318787	+	0.947826i	$0.603275\pi$
$138$	5.25712	+	6.26519i	0.447516	+	0.533329i
$139$	−16.9440	+	14.2177i	−1.43717	+	1.20593i	−0.495859	+	0.868403i	$0.665147\pi$
$139$	−16.9440	+	14.2177i	−1.43717	+	1.20593i	−0.941315	+	0.337529i	$0.890409\pi$
$140$		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	0.826401	−	0.563082i	$-0.190384\pi$
$149$	13.3969	+	4.87608i	1.09752	+	0.399464i	0.271118	+	0.962546i	$0.412607\pi$
$150$		0			0
$151$	0.805407	−	4.56769i	0.0655431	−	0.371713i	−0.934339	−	0.356384i	$-0.884009\pi$
$151$	0.805407	−	4.56769i	0.0655431	−	0.371713i	0.999883	−	0.0153290i	$-0.00487956\pi$
$152$	−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	0.938954	+	0.344043i	$0.111797\pi$
$157$	2.18392	+	12.3856i	0.174295	+	0.988478i	−0.764659	+	0.644436i	$0.777092\pi$
$158$	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	$-0.419310\pi$
$163$	6.40373			0.501579			0.250790	+	0.968042i	$0.419310\pi$
$164$	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	0.984056	+	0.177859i	$0.0569172\pi$
$167$	1.55303	+	8.80769i	0.120177	+	0.681560i	−0.863879	+	0.503700i	$0.831972\pi$
$168$		−	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	0.918175	+	0.396176i	$0.129663\pi$
$173$	−1.05391	+	5.97702i	−0.0801274	+	0.454425i	−0.998302	+	0.0582491i	$0.981448\pi$
$174$	−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	0.790790	−	0.612087i	$-0.209670\pi$
$179$	−1.80200	−	3.12116i	−0.134688	−	0.233287i	−0.925478	+	0.378801i	$0.876337\pi$
$180$		0			0
$181$	−5.56283	+	9.63511i	−0.413482	+	0.716172i	−0.995268	−	0.0971701i	$-0.969021\pi$
$181$	−5.56283	+	9.63511i	−0.413482	+	0.716172i	0.581786	+	0.813342i	$0.302354\pi$
$182$	−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	−0.663134	−	0.748500i	$-0.730774\pi$
$191$	−9.53596	+	3.47081i	−0.689998	+	0.251139i	−0.0268635	+	0.999639i	$0.508552\pi$
$192$	8.60014	−	1.51644i	0.620661	−	0.109439i
$193$	−0.269915	+	0.226485i	−0.0194289	+	0.0163028i	−0.652450	−	0.757831i	$-0.726259\pi$
$193$	−0.269915	+	0.226485i	−0.0194289	+	0.0163028i	0.633021	+	0.774134i	$0.281814\pi$
$194$	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	−0.165428	−	0.986222i	$-0.552901\pi$
$197$	10.8268	−	18.7526i	0.771379	−	1.33607i	0.936807	−	0.349846i	$-0.113766\pi$
$198$	1.37433	−	2.38041i	0.0976696	−	0.169169i
$199$	−12.0209	−	20.8209i	−0.852142	−	1.47595i	−0.879271	−	0.476322i	$-0.841970\pi$
$199$	−12.0209	−	20.8209i	−0.852142	−	1.47595i	0.0271290	−	0.999632i	$-0.491364\pi$
$200$		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	−0.998702	−	0.0509266i	$-0.983783\pi$
$211$	−1.12789	−	6.39657i	−0.0776471	−	0.440358i	0.921055	−	0.389432i	$-0.127329\pi$
$212$	−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	$-0.215644\pi$
$223$	4.43763	+	3.72362i	0.297166	+	0.249352i	−0.481998	+	0.876173i	$0.660089\pi$
$224$	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	0.815045	+	0.579398i	$0.196712\pi$
$227$	−2.24510	+	12.7326i	−0.149013	+	0.845092i	−0.964057	+	0.265694i	$0.914399\pi$
$228$	9.82295	+	1.73205i	0.650541	+	0.114708i
$229$	1.17365	+	0.427173i	0.0775569	+	0.0282284i	0.380507	−	0.924778i	$-0.375749\pi$
$229$	1.17365	+	0.427173i	0.0775569	+	0.0282284i	−0.302950	+	0.953006i	$0.597972\pi$
$230$		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	$-0.170644\pi$
$233$	−0.190722	−	0.330341i	−0.0124946	−	0.0216413i	−0.872205	+	0.489140i	$0.837311\pi$
$234$	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	−0.717326	−	0.696738i	$-0.754634\pi$
$239$	−2.40760	+	2.02022i	−0.155735	+	0.130677i	0.561591	+	0.827415i	$0.310190\pi$
$240$		0			0
$241$	7.05778	−	2.56882i	0.454632	−	0.165472i	−0.104546	−	0.994520i	$-0.533339\pi$
$241$	7.05778	−	2.56882i	0.454632	−	0.165472i	0.559178	+	0.829048i	$0.311117\pi$
$242$	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	−0.999856	−	0.0169841i	$-0.994594\pi$
$251$	−7.68732	+	13.3148i	−0.485219	+	0.840424i	0.514637	+	0.857408i	$0.327927\pi$
$252$	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	$-0.200502\pi$
$257$	16.8084	+	6.11776i	1.04848	+	0.381615i	0.240391	+	0.970676i	$0.422724\pi$
$258$	−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	$-0.315941\pi$
$263$	−2.97178	−	2.49362i	−0.183248	−	0.153763i	−0.729797	+	0.683664i	$0.760386\pi$
$264$	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	$-0.101033\pi$
$277$	13.4422	+	11.2794i	0.807665	+	0.677711i	−0.142385	+	0.989811i	$0.545477\pi$
$278$	−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	−0.934972	−	0.354721i	$-0.884576\pi$
$281$	1.08853	−	6.17334i	0.0649360	−	0.368270i	0.999908	−	0.0135494i	$-0.00431304\pi$
$282$	−3.39528	+	4.04633i	−0.202186	+	0.240956i
$283$	5.95084	+	2.16593i	0.353741	+	0.128751i	0.512777	−	0.858522i	$-0.328617\pi$
$283$	5.95084	+	2.16593i	0.353741	+	0.128751i	−0.159037	+	0.987273i	$0.550839\pi$
$284$	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	$-0.764904\pi$
$293$	−3.50593	+	2.94182i	−0.204819	+	0.171863i	0.534608	+	0.845100i	$0.320459\pi$
$294$	−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	$-0.129800\pi$
$307$	2.02481	+	3.50708i	0.115562	+	0.200160i	−0.802442	+	0.596730i	$0.796466\pi$
$308$	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	0.469962	−	0.882687i	$-0.344268\pi$
$311$	4.63088	+	1.68550i	0.262593	+	0.0955761i	−0.207369	+	0.978263i	$0.566490\pi$
$312$	5.35339	+	14.7083i	0.303076	+	0.832694i
$313$	−2.40033	+	13.6129i	−0.135675	+	0.769449i	0.838713	+	0.544574i	$0.183309\pi$
$313$	−2.40033	+	13.6129i	−0.135675	+	0.769449i	−0.974388	+	0.224875i	$0.927803\pi$
$314$	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	$-0.421042\pi$
$317$	−11.8669	−	9.95751i	−0.666511	−	0.559269i	−0.912031	+	0.410122i	$0.865486\pi$
$318$			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	0.454927	−	0.890529i	$-0.349665\pi$
$331$	−6.24170	−	5.23741i	−0.343075	−	0.287874i	−0.798002	+	0.602655i	$0.794110\pi$
$332$	−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	$-0.438483\pi$
$337$	−5.35369	−	1.94858i	−0.291634	−	0.106146i	−0.483694	+	0.875237i	$0.660705\pi$
$338$	−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	$-0.468490\pi$
$347$	20.4158	−	17.1309i	1.09598	−	0.919635i	0.997148	+	0.0754694i	$0.0240455\pi$
$348$	7.92205	+	9.44113i	0.424666	+	0.506098i
$349$	7.47906	−	2.72215i	0.400345	−	0.145714i	−0.133998	−	0.990982i	$-0.542782\pi$
$349$	7.47906	−	2.72215i	0.400345	−	0.145714i	0.534342	+	0.845268i	$0.320559\pi$
$350$		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	$-0.486268\pi$
$353$	13.4966	−	4.91236i	0.718351	−	0.261459i	0.675226	+	0.737611i	$0.264046\pi$
$354$	−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	−0.453168	−	0.891425i	$-0.649706\pi$
$359$	10.3341	−	17.8992i	0.545413	−	0.944682i	0.998581	−	0.0532573i	$-0.0169603\pi$
$360$		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	$-0.889147\pi$
$367$	1.15002	−	6.52206i	0.0600303	−	0.340449i	1.00000		0.000810039i	$0.000257843\pi$
$368$	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	−0.702318	−	0.711864i	$-0.747851\pi$
$373$	−5.52023	−	31.3068i	−0.285827	−	1.62100i	0.416491	−	0.909140i	$-0.363260\pi$
$374$	−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	−0.887408	−	0.460985i	$-0.847496\pi$
$383$	−4.13294	−	23.4391i	−0.211183	−	1.19768i	0.676224	−	0.736696i	$-0.263615\pi$
$384$	−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	−0.959049	−	0.283241i	$-0.908591\pi$
$389$	0.769915	−	4.36640i	0.0390362	−	0.221385i	0.998085	+	0.0618550i	$0.0197016\pi$
$390$		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	$-0.676608\pi$
$397$	9.41875	−	16.3138i	0.472713	−	0.818764i	0.999512	+	0.0312263i	$0.00994125\pi$
$398$	−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	−0.800692	−	0.599076i	$-0.795535\pi$
$401$	−7.00387	+	5.87695i	−0.349757	+	0.293481i	0.450936	+	0.892556i	$0.351090\pi$
$402$	−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	0.0594360	−	0.998232i	$-0.481070\pi$
$409$	21.2920	−	17.8661i	1.05282	−	0.883424i	0.993388	+	0.114808i	$0.0366253\pi$
$410$		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	0.150701	−	0.988579i	$-0.451847\pi$
$419$	−7.55943	−	2.75141i	−0.369302	−	0.134415i	−0.520003	+	0.854164i	$0.674069\pi$
$420$		0			0
$421$	−3.44862	+	19.5581i	−0.168075	+	0.953202i	0.777762	+	0.628559i	$0.216355\pi$
$421$	−3.44862	+	19.5581i	−0.168075	+	0.953202i	−0.945837	+	0.324643i	$0.894756\pi$
$422$	−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	$-0.470726\pi$
$433$	3.82201			0.183674			0.0918372	+	0.995774i	$0.470726\pi$
$434$	−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	0.961379	+	0.275229i	$0.0887536\pi$
$439$	29.3200	+	24.6024i	1.39937	+	1.17421i	0.437989	+	0.898980i	$0.355691\pi$
$440$		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	−0.878852	−	0.477095i	$-0.841690\pi$
$443$	2.31892	−	13.1512i	0.110175	−	0.624834i	0.989027	−	0.147738i	$-0.0471993\pi$
$444$	−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	0.772780	−	0.634674i	$-0.218866\pi$
$449$	−3.45929	−	5.99167i	−0.163254	−	0.282764i	−0.936034	+	0.351910i	$0.885532\pi$
$450$		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	$-0.548844\pi$
$457$	7.80928	−	2.84234i	0.365303	−	0.132959i	0.518148	+	0.855291i	$0.326622\pi$
$458$	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	0.261359	−	0.965242i	$-0.415829\pi$
$461$	23.2319	−	8.45572i	1.08202	−	0.393822i	0.820658	+	0.571420i	$0.193607\pi$
$462$	−3.83420	−	4.56942i	−0.178383	−	0.212589i
$463$	0.0983261	−	0.0825054i	0.00456960	−	0.00383435i	−0.640500	−	0.767958i	$-0.721273\pi$
$463$	0.0983261	−	0.0825054i	0.00456960	−	0.00383435i	0.645070	+	0.764124i	$0.276828\pi$
$464$	−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	−0.129627	+	0.991563i	$0.541378\pi$
$467$	−19.9577	+	34.5678i	−0.923532	+	1.59960i	−0.793905	+	0.608042i	$0.791955\pi$
$468$	−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	0.487360	−	0.873201i	$-0.337960\pi$
$479$	−6.30200	−	5.28801i	−0.287946	−	0.241615i	−0.775306	+	0.631586i	$0.782404\pi$
$480$		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	$-0.520551\pi$
$487$	−2.84760			−0.129037			−0.0645186	+	0.997917i	$0.520551\pi$
$488$	−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	−0.592996	−	0.805205i	$-0.702055\pi$
$491$	−6.89481	−	39.1024i	−0.311158	−	1.76467i	0.281838	−	0.959462i	$-0.409056\pi$
$492$			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	0.985938	−	0.167111i	$-0.0534438\pi$
$499$	36.4962	+	13.2835i	1.63379	+	0.594652i	0.647856	+	0.761763i	$0.275666\pi$
$500$		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	−0.992162	−	0.124961i	$-0.960120\pi$
$503$	−13.5530	−	23.4745i	−0.604300	−	1.04668i	0.387862	−	0.921718i	$-0.373214\pi$
$504$	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	−0.909024	−	0.416744i	$-0.863171\pi$
$509$	−14.8105	+	12.4275i	−0.656462	+	0.550837i	0.252562	+	0.967581i	$0.418727\pi$
$510$		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	0.461856	+	0.886955i	$0.347184\pi$
$521$	−12.2618	+	21.2380i	−0.537198	+	0.930454i	−0.999053	+	0.0434986i	$0.986150\pi$
$522$	15.3030			0.669796
$523$	−4.31521	−	7.47416i	−0.188691	−	0.326822i	0.756123	−	0.654429i	$-0.227091\pi$
$523$	−4.31521	−	7.47416i	−0.188691	−	0.326822i	−0.944814	+	0.327607i	$0.893758\pi$
$524$	−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	$-0.438451\pi$
$547$	−17.3289	−	14.5407i	−0.740929	−	0.621714i	−0.933087	+	0.359651i	$0.882896\pi$
$548$	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	−0.684084	−	0.729403i	$-0.739798\pi$
$557$	−22.9807	−	39.8037i	−0.973724	−	1.68654i	−0.289640	−	0.957136i	$-0.593535\pi$
$558$	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	$-0.702890\pi$
$563$	2.20645	−	1.85143i	0.0929909	−	0.0780286i	0.688098	+	0.725618i	$0.258446\pi$
$564$	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	−0.949035	−	0.315172i	$-0.897938\pi$
$569$	−35.1472	+	12.7925i	−1.47345	+	0.536292i	−0.524414	+	0.851463i	$0.675716\pi$
$570$		0			0
$571$	−19.2324	+	16.1379i	−0.804849	+	0.675349i	−0.949372	−	0.314153i	$-0.898280\pi$
$571$	−19.2324	+	16.1379i	−0.804849	+	0.675349i	0.144523	+	0.989501i	$0.453835\pi$
$572$	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	$-0.198397\pi$
$577$	−2.39053	−	4.14052i	−0.0995190	−	0.172372i	−0.911486	+	0.411332i	$0.865064\pi$
$578$	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	$-0.116513\pi$
$587$	18.0116	+	15.1135i	0.743419	+	0.623802i	−0.190335	+	0.981719i	$0.560957\pi$
$588$	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	$-0.519507\pi$
$593$	−2.98276			−0.122487			−0.0612437	+	0.998123i	$0.519507\pi$
$594$	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	−0.861703	−	0.507412i	$-0.830602\pi$
$599$	−5.51930	−	31.3015i	−0.225512	−	1.27894i	0.636191	−	0.771532i	$-0.280509\pi$
$600$		0			0
$601$	28.2763	+	23.7266i	1.15341	+	0.967830i	0.999794	−	0.0202999i	$-0.00646211\pi$
$601$	28.2763	+	23.7266i	1.15341	+	0.967830i	0.153621	+	0.988130i	$0.450907\pi$
$602$	−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	$-0.168703\pi$
$607$	29.5355	+	10.7501i	1.19881	+	0.436331i	0.336002	+	0.941861i	$0.390925\pi$
$608$	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	−0.486703	−	0.873567i	$-0.661801\pi$
$613$	12.7057	−	22.0070i	0.513180	−	0.888854i	0.999883	−	0.0152863i	$-0.00486596\pi$
$614$	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	$-0.867219\pi$
$617$	−16.7422	+	14.0483i	−0.674014	+	0.565565i	0.240236	+	0.970714i	$0.422775\pi$
$618$	17.9372	−	3.16281i	0.721539	−	0.127227i
$619$	37.8619	−	13.7806i	1.52180	−	0.553889i	0.560202	−	0.828356i	$-0.310724\pi$
$619$	37.8619	−	13.7806i	1.52180	−	0.553889i	0.961597	+	0.274467i	$0.0885014\pi$
$620$		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	0.997830	+	0.0658432i	$0.0209737\pi$
$631$	13.9650	+	24.1880i	0.555937	+	0.962911i	−0.441893	+	0.897068i	$0.645693\pi$
$632$	−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	0.0400580	−	0.999197i	$-0.487246\pi$
$641$	−23.7230	−	19.9060i	−0.937003	−	0.786239i	−0.977061	+	0.212958i	$0.931690\pi$
$642$			31.4348i			1.24063i
$643$	5.70068	+	32.3302i	0.224813	+	1.27498i	0.863042	+	0.505132i	$0.168556\pi$
$643$	5.70068	+	32.3302i	0.224813	+	1.27498i	−0.638229	+	0.769846i	$0.720333\pi$
$644$	−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	$-0.429785\pi$
$647$	11.1310			0.437606			0.218803	+	0.975769i	$0.429785\pi$
$648$	−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	$-0.0244240\pi$
$653$	0.866592	+	4.91469i	0.0339124	+	0.192327i	−0.963145	+	0.268982i	$0.913313\pi$
$654$			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	−0.824748	−	0.565500i	$-0.808683\pi$
$659$	3.68825	−	20.9171i	0.143674	−	0.814815i	0.968422	−	0.249315i	$-0.0802056\pi$
$660$		0			0
$661$	−1.06506	−	0.387648i	−0.0414258	−	0.0150778i	0.321224	−	0.947003i	$-0.395906\pi$
$661$	−1.06506	−	0.387648i	−0.0414258	−	0.0150778i	−0.362650	+	0.931925i	$0.618128\pi$
$662$	−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	$-0.290590\pi$
$673$	41.2083	−	14.9986i	1.58846	−	0.578154i	0.977023	+	0.213136i	$0.0683678\pi$
$674$	−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	$-0.673547\pi$
$677$	−9.53033	+	3.46876i	−0.366280	+	0.133315i	0.152321	+	0.988331i	$0.451325\pi$
$678$	−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	$-0.802459\pi$
$683$	2.53091	−	4.38366i	0.0968425	−	0.167736i	0.910376	+	0.413782i	$0.135792\pi$
$684$	−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	−0.792901	−	0.609350i	$-0.791430\pi$
$691$	4.22147	−	23.9411i	0.160592	−	0.910763i	0.953494	−	0.301413i	$-0.0974584\pi$
$692$	−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	0.513150	−	0.858299i	$-0.328479\pi$
$709$	−6.47044	−	5.42934i	−0.243002	−	0.203903i	−0.756152	+	0.654396i	$0.772923\pi$
$710$		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	0.999397	−	0.0347347i	$-0.0110586\pi$
$719$	12.5924	+	21.8107i	0.469617	+	0.813401i	−0.529779	+	0.848135i	$0.677725\pi$
$720$		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	$-0.682936\pi$
$727$	−11.3375	+	4.12651i	−0.420484	+	0.153044i	0.123108	+	0.992393i	$0.460714\pi$
$728$	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	$-0.990688\pi$
$733$	−30.9818	+	25.9968i	−1.14434	+	0.960214i	−0.144767	+	0.989466i	$0.546243\pi$
$734$	−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	0.775295	−	0.631599i	$-0.217601\pi$
$739$	−4.33140	−	7.50221i	−0.159333	−	0.275973i	−0.934628	+	0.355626i	$0.884268\pi$
$740$		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	$-0.284633\pi$
$743$	16.4804	+	5.99837i	0.604607	+	0.220059i	−0.0215347	+	0.999768i	$0.506855\pi$
$744$	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	−0.922979	−	0.384849i	$-0.874253\pi$
$751$	−5.13253	−	29.1080i	−0.187289	−	1.06217i	0.735691	−	0.677318i	$-0.236858\pi$
$752$	−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	$-0.342589\pi$
$757$	26.1165			0.949220			0.474610	+	0.880196i	$0.342589\pi$
$758$	−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	−0.999922	−	0.0124897i	$-0.996024\pi$
$761$	−1.78136	−	10.1026i	−0.0645744	−	0.366220i	0.935348	−	0.353730i	$-0.115087\pi$
$762$	−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	−0.188827	−	0.982010i	$-0.560468\pi$
$769$	−26.7520	−	9.73692i	−0.964700	−	0.351122i	−0.775874	+	0.630888i	$0.782691\pi$
$770$		0			0
$771$	−19.9145	+	23.7331i	−0.717202	+	0.854728i
$772$	0.0750542	−	0.425653i	0.00270126	−	0.0153196i
$773$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.826352 - 0.300767i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(-0.939693 + 0.788496i) q^{4} +1.52314i q^{6} +(2.87939 + 2.41609i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^7 - 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{7} - 6 q^{8} - 18 q^{11} + 9 q^{12} - 6 q^{14} - 18 q^{16} + 6 q^{17} - 18 q^{18} - 12 q^{19} - 36 q^{22} + 18 q^{23} + 18 q^{24} + 12 q^{26} + 27 q^{27} - 36 q^{28} - 21 q^{29} - 3 q^{31} - 9 q^{32} + 9 q^{34} - 18 q^{36} + 6 q^{37} + 12 q^{38} - 9 q^{39} - 18 q^{41} + 18 q^{42} - 6 q^{43} - 27 q^{44} - 9 q^{46} - 6 q^{47} + 9 q^{48} - 12 q^{49} + 9 q^{51} + 36 q^{52} + 48 q^{53} + 27 q^{54} - 48 q^{56} - 18 q^{57} - 27 q^{58} + 36 q^{61} - 15 q^{62} - 18 q^{63} - 12 q^{64} + 18 q^{67} - 12 q^{68} + 36 q^{69} + 3 q^{71} - 9 q^{72} - 6 q^{73} + 12 q^{74} - 6 q^{76} - 18 q^{77} - 27 q^{78} - 12 q^{79} - 36 q^{82} + 18 q^{83} + 36 q^{84} + 3 q^{86} - 18 q^{88} + 3 q^{89} - 63 q^{92} + 9 q^{93} + 27 q^{94} + 27 q^{96} + 3 q^{97} + 9 q^{98} - 27 q^{99}+O(q^{100}) \) 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

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