LMFDB - Embedded newform 675.2.u.a.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			274.2
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	675.274
Dual form			675.2.u.a.574.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	0.300767	−	0.826352i	0.212675	−	0.584319i	−0.786784	−	0.617229i	$-0.788255\pi$
$2$	0.300767	−	0.826352i	0.212675	−	0.584319i	0.999458	+	0.0329100i	$0.0104775\pi$
$3$	1.62760	−	0.592396i	0.939693	−	0.342020i
$3$	1.62760	−	0.592396i	0.939693	−	0.342020i
$4$	0.939693	+	0.788496i	0.469846	+	0.394248i
$5$		0			0
$5$		0			0
$6$		−	1.52314i		−	0.621819i
$7$	−2.41609	−	2.87939i	−0.913197	−	1.08831i	−0.995785	−	0.0917216i	$-0.970763\pi$
$7$	−2.41609	−	2.87939i	−0.913197	−	1.08831i	0.0825881	−	0.996584i	$-0.473681\pi$
$8$	2.45734	−	1.41875i	0.868802	−	0.501603i
$9$	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	$0.994649\pi$
$12$	1.99654	+	0.726682i	0.576352	+	0.209775i
$13$	−1.08926	−	2.99273i	−0.302107	−	0.830033i	−0.994133	−	0.108160i	$-0.965504\pi$
$13$	−1.08926	−	2.99273i	−0.302107	−	0.830033i	0.692026	−	0.721872i	$-0.256718\pi$
$14$	−3.10607	+	1.13052i	−0.830131	+	0.302143i
$15$		0			0
$16$	−0.00727396	−	0.0412527i	−0.00181849	−	0.0103132i
$17$	−0.405223	−	0.233956i	−0.0982810	−	0.0567426i	0.450054	−	0.893001i	$-0.351405\pi$
$17$	−0.405223	−	0.233956i	−0.0982810	−	0.0567426i	−0.548335	+	0.836259i	$0.684738\pi$
$18$	−0.902302	−	2.47906i	−0.212675	−	0.584319i
$19$	2.34730	+	4.06564i	0.538507	+	0.932721i	0.998985	+	0.0450499i	$0.0143447\pi$
$19$	2.34730	+	4.06564i	0.538507	+	0.932721i	−0.460478	+	0.887671i	$0.652322\pi$
$20$		0			0
$21$	−5.63816	−	3.25519i	−1.23035	−	0.710341i
$22$	−0.902302	−	0.159100i	−0.192372	−	0.0339203i
$23$	−3.45150	+	4.11334i	−0.719688	+	0.857691i	−0.994600	−	0.103778i	$-0.966907\pi$
$23$	−3.45150	+	4.11334i	−0.719688	+	0.857691i	0.274912	+	0.961469i	$0.411351\pi$
$24$	3.15910	−	3.76487i	0.644849	−	0.768501i
$25$		0			0
$26$	−2.80066			−0.549255
$27$	2.59808	−	4.50000i	0.500000	−	0.866025i
$28$		−	4.61081i		−	0.871362i
$29$	5.45084	+	1.98394i	1.01220	+	0.368409i	0.794275	−	0.607558i	$-0.207851\pi$
$29$	5.45084	+	1.98394i	1.01220	+	0.368409i	0.217920	+	0.975967i	$0.430073\pi$
$30$		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	$0.842431\pi$
$32$	5.55250	+	0.979055i	0.981553	+	0.173074i
$33$	−0.902302	−	1.56283i	−0.157071	−	0.272054i
$34$	−0.315207	+	0.264490i	−0.0540576	+	0.0453597i
$35$		0			0
$36$	3.68004			0.613341
$37$	3.87603	+	2.23783i	0.637215	+	0.367896i	0.783541	−	0.621340i	$-0.213411\pi$
$37$	3.87603	+	2.23783i	0.637215	+	0.367896i	−0.146326	+	0.989236i	$0.546745\pi$
$38$	4.06564	−	0.716881i	0.659533	−	0.116294i
$39$	−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	$0.603912\pi$
$42$	−4.38571	+	3.68004i	−0.676729	+	0.567843i
$43$	11.9854	−	2.11334i	1.82775	−	0.322281i	0.849165	−	0.528128i	$-0.177106\pi$
$43$	11.9854	−	2.11334i	1.82775	−	0.322281i	0.978584	+	0.205847i	$0.0659948\pi$
$44$	0.639033	−	1.10684i	0.0963379	−	0.166862i
$45$		0			0
$46$	2.36097	+	4.08931i	0.348106	+	0.602937i
$47$	−2.22913	−	2.65657i	−0.325152	−	0.387501i	0.578561	−	0.815639i	$-0.303614\pi$
$47$	−2.22913	−	2.65657i	−0.325152	−	0.387501i	−0.903714	+	0.428138i	$0.859170\pi$
$48$	−0.0362770	−	0.0628336i	−0.00523613	−	0.00906925i
$49$	−1.23783	+	7.02006i	−0.176832	+	1.00287i
$50$		0			0
$51$	−0.798133	−	0.140732i	−0.111761	−	0.0197065i
$52$	1.33618	−	3.67112i	0.185295	−	0.509093i
$53$			8.83750i			1.21392i	0.794731	+	0.606962i	$0.207612\pi$
$53$			8.83750i			1.21392i	−0.794731	+	0.606962i	$0.792388\pi$
$54$	−2.93717	−	3.50038i	−0.399698	−	0.476341i
$55$		0			0
$56$	−10.0223	−	3.64781i	−1.33928	−	0.487460i
$57$	6.22892	+	5.22668i	0.825040	+	0.692291i
$58$	3.27887	−	3.90760i	0.430537	−	0.513094i
$59$	−2.36959	+	13.4386i	−0.308494	+	1.74955i	0.298093	+	0.954537i	$0.403650\pi$
$59$	−2.36959	+	13.4386i	−0.308494	+	1.74955i	−0.606586	+	0.795018i	$0.707462\pi$
$60$		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	$0.0634934\pi$
$62$	−3.12706	+	1.80541i	−0.397137	+	0.229287i
$63$	−11.1050	−	1.95811i	−1.39910	−	0.246699i
$64$	2.52094	−	4.36640i	0.315118	−	0.545801i
$65$		0			0
$66$	−1.56283	+	0.275570i	−0.192372	+	0.0339203i
$67$	−0.623485	−	1.71301i	−0.0761708	−	0.209278i	0.895763	−	0.444532i	$-0.146630\pi$
$67$	−0.623485	−	1.71301i	−0.0761708	−	0.209278i	−0.971934	+	0.235254i	$0.924408\pi$
$68$	−0.196312	−	0.539363i	−0.0238063	−	0.0654074i
$69$	−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	$0.317760\pi$
$72$	2.91144	−	7.99912i	0.343117	−	0.942706i
$73$	0.705990	−	0.407604i	0.0826299	−	0.0477064i	−0.458116	−	0.888893i	$-0.651475\pi$
$73$	0.705990	−	0.407604i	0.0826299	−	0.0477064i	0.540746	+	0.841186i	$0.318142\pi$
$74$	3.01501	−	2.52990i	0.350488	−	0.294095i
$75$		0			0
$76$	−1.00000	+	5.67128i	−0.114708	+	0.650541i
$77$	−2.51730	+	3.00000i	−0.286873	+	0.341882i
$78$	−4.55834	+	1.65910i	−0.516130	+	0.187856i
$79$	−3.81180	−	1.38738i	−0.428861	−	0.156093i	0.118566	−	0.992946i	$-0.462170\pi$
$79$	−3.81180	−	1.38738i	−0.428861	−	0.156093i	−0.547427	+	0.836853i	$0.684393\pi$
$80$		0			0
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$			7.04189i			0.777647i
$83$	−5.81699	+	15.9820i	−0.638498	+	1.75426i	0.0178968	+	0.999840i	$0.494303\pi$
$83$	−5.81699	+	15.9820i	−0.638498	+	1.75426i	−0.656394	+	0.754418i	$0.727919\pi$
$84$	−2.73143	−	7.50454i	−0.298023	−	0.818812i
$85$		0			0
$86$	1.85844	−	10.5397i	0.200401	−	1.13653i
$87$	10.0470			1.07716
$88$	−1.90031	−	2.26470i	−0.202574	−	0.241418i
$89$	−5.19846	−	9.00400i	−0.551036	−	0.954422i	−0.998200	−	0.0599704i	$-0.980899\pi$
$89$	−5.19846	−	9.00400i	−0.551036	−	0.954422i	0.447164	−	0.894452i	$-0.352434\pi$
$90$		0			0
$91$	−5.98545	+	10.3671i	−0.627446	+	1.08677i
$92$	−6.48670	+	1.14378i	−0.676286	+	0.119247i
$93$	−6.68302	−	2.43242i	−0.692996	−	0.252230i
$94$	−2.86571	+	1.04303i	−0.295576	+	0.107581i
$95$		0			0
$96$	9.61721	−	1.69577i	0.981553	−	0.173074i
$97$	−6.02763	+	1.06283i	−0.612013	+	0.107914i	−0.471059	−	0.882102i	$-0.656128\pi$
$97$	−6.02763	+	1.06283i	−0.612013	+	0.107914i	−0.140954	+	0.990016i	$0.545017\pi$
$98$	5.42874	+	3.13429i	0.548386	+	0.316611i
$99$	−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	$0.246407\pi$
$102$	−0.356347	+	0.617211i	−0.0352836	+	0.0611130i
$103$	−11.7764	−	2.07650i	−1.16037	−	0.204604i	−0.439870	−	0.898062i	$-0.644975\pi$
$103$	−11.7764	−	2.07650i	−1.16037	−	0.204604i	−0.720497	+	0.693458i	$0.756086\pi$
$104$	−6.92262	−	5.80877i	−0.678819	−	0.569596i
$105$		0			0
$106$	7.30288	+	2.65803i	0.709319	+	0.258171i
$107$		−	20.6382i		−	1.99517i	−0.0694862	−	0.997583i	$-0.522136\pi$
$107$		−	20.6382i		−	1.99517i	0.0694862	−	0.997583i	$-0.477864\pi$
$108$	5.98962	−	2.18004i	0.576352	−	0.209775i
$109$	−0.433763			−0.0415469			−0.0207735	−	0.999784i	$-0.506613\pi$
$109$	−0.433763			−0.0415469			−0.0207735	+	0.999784i	$0.506613\pi$
$110$		0			0
$111$	7.63429	+	1.34613i	0.724614	+	0.127769i
$112$	−0.101208	+	0.120615i	−0.00956324	+	0.0113970i
$113$	5.66366	+	0.998656i	0.532792	+	0.0939456i	0.433570	−	0.901120i	$-0.357254\pi$
$113$	5.66366	+	0.998656i	0.532792	+	0.0939456i	0.0992218	+	0.995065i	$0.468365\pi$
$114$	6.19253	−	3.57526i	0.579984	−	0.334854i
$115$		0			0
$116$	3.55778	+	6.16226i	0.330332	+	0.572151i
$117$	−8.27433	−	4.77719i	−0.764962	−	0.441651i
$118$	10.3923	+	6.00000i	0.956689	+	0.552345i
$119$	0.305407	+	1.73205i	0.0279966	+	0.158777i
$120$		0			0
$121$	9.31655	−	3.39095i	0.846959	−	0.308268i
$122$	−2.92923	−	8.04798i	−0.265200	−	0.728630i
$123$	−10.6249	+	8.91534i	−0.958014	+	0.803870i
$124$	−0.874638	−	4.96032i	−0.0785448	−	0.445450i
$125$		0			0
$126$	−4.95811	+	8.58770i	−0.441704	+	0.765053i
$127$	−16.9843	+	9.80587i	−1.50711	+	0.870131i	−0.507145	+	0.861861i	$0.669299\pi$
$127$	−16.9843	+	9.80587i	−1.50711	+	0.870131i	−0.999966	+	0.00826966i	$0.997368\pi$
$128$	4.39831	+	5.24170i	0.388759	+	0.463305i
$129$	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	$0.431800\pi$
$132$	0.384401	−	2.18004i	0.0334578	−	0.189749i
$133$	6.03525	−	16.5817i	0.523323	−	1.43782i
$134$	−1.60307			−0.138484
$135$		0			0
$136$	−1.32770			−0.113849
$137$	−4.99395	+	13.7208i	−0.426662	+	1.17224i	0.521165	+	0.853456i	$0.325498\pi$
$137$	−4.99395	+	13.7208i	−0.426662	+	1.17224i	−0.947826	+	0.318787i	$0.896725\pi$
$138$	6.26519	+	5.25712i	0.533329	+	0.447516i
$139$	16.9440	+	14.2177i	1.43717	+	1.20593i	0.941315	+	0.337529i	$0.109591\pi$
$139$	16.9440	+	14.2177i	1.43717	+	1.20593i	0.495859	+	0.868403i	$0.334853\pi$
$140$		0			0
$141$	−5.20187	−	3.00330i	−0.438076	−	0.252923i
$142$	4.35381	+	5.18866i	0.365363	+	0.435423i
$143$	−2.87365	+	1.65910i	−0.240306	+	0.138741i
$144$	−0.0962667	−	0.0807773i	−0.00802222	−	0.00673144i
$145$		0			0
$146$	−0.124485	−	0.705990i	−0.0103025	−	0.0584282i
$147$	2.14398	+	12.1591i	0.176832	+	1.00287i
$148$	1.87776	+	5.15910i	0.154351	+	0.424075i
$149$	−13.3969	+	4.87608i	−1.09752	+	0.399464i	−0.826401	−	0.563082i	$-0.809616\pi$
$149$	−13.3969	+	4.87608i	−1.09752	+	0.399464i	−0.271118	+	0.962546i	$0.587393\pi$
$150$		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	$0.884009\pi$
$152$	11.5362	+	6.66044i	0.935712	+	0.540233i
$153$	−1.38241	+	0.243756i	−0.111761	+	0.0197065i
$154$	1.72193	+	2.98248i	0.138757	+	0.240335i
$155$		0			0
$156$		−	6.76665i		−	0.541765i
$157$	−12.3856	−	2.18392i	−0.988478	−	0.174295i	−0.344043	−	0.938954i	$-0.611797\pi$
$157$	−12.3856	−	2.18392i	−0.988478	−	0.174295i	−0.644436	+	0.764659i	$0.722908\pi$
$158$	−2.29293	+	2.73261i	−0.182416	+	0.217395i
$159$	5.23530	+	14.3839i	0.415186	+	1.14071i
$160$		0			0
$161$	20.1830			1.59065
$162$	−6.85413	−	3.95723i	−0.538511	−	0.310910i
$163$			6.40373i			0.501579i	0.968042	+	0.250790i	$0.0806902\pi$
$163$			6.40373i			0.501579i	−0.968042	+	0.250790i	$0.919310\pi$
$164$	−9.23055	−	3.35965i	−0.720785	−	0.262344i
$165$		0			0
$166$	11.4572	+	9.61376i	0.889254	+	0.746173i
$167$	−8.80769	−	1.55303i	−0.681560	−	0.120177i	−0.177859	−	0.984056i	$-0.556917\pi$
$167$	−8.80769	−	1.55303i	−0.681560	−	0.120177i	−0.503700	+	0.863879i	$0.668028\pi$
$168$	−18.4732			−1.42524
$169$	2.18866	−	1.83651i	0.168359	−	0.141270i
$170$		0			0
$171$	13.2344	+	4.81694i	1.01206	+	0.368360i
$172$	12.9289	+	7.46451i	0.985820	+	0.569163i
$173$	5.97702	−	1.05391i	0.454425	−	0.0801274i	0.0582491	−	0.998302i	$-0.481448\pi$
$173$	5.97702	−	1.05391i	0.454425	−	0.0801274i	0.396176	+	0.918175i	$0.370337\pi$
$174$	3.02182	−	8.30239i	0.229084	−	0.629402i
$175$		0			0
$176$	−0.0410117	+	0.0149270i	−0.00309137	+	0.00112517i
$177$	4.10424	+	23.2763i	0.308494	+	1.74955i
$178$	−9.00400	+	1.58765i	−0.674878	+	0.118999i
$179$	1.80200	−	3.12116i	0.134688	−	0.233287i	−0.790790	−	0.612087i	$-0.790330\pi$
$179$	1.80200	−	3.12116i	0.134688	−	0.233287i	0.925478	+	0.378801i	$0.123663\pi$
$180$		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	$0.969021\pi$
$182$	6.76665	+	8.06418i	0.501577	+	0.597757i
$183$	8.43437	−	14.6088i	0.623486	−	1.07991i
$184$	−2.64573	+	15.0047i	−0.195046	+	1.10616i
$185$		0			0
$186$	−4.02007	+	4.79093i	−0.294766	+	0.351288i
$187$	−0.166739	+	0.458111i	−0.0121931	+	0.0335004i
$188$		−	4.25402i		−	0.310256i
$189$	−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	$0.730774\pi$
$192$	1.51644	−	8.60014i	0.109439	−	0.620661i
$193$	0.226485	−	0.269915i	0.0163028	−	0.0194289i	−0.757831	−	0.652450i	$-0.773741\pi$
$193$	0.226485	−	0.269915i	0.0163028	−	0.0194289i	0.774134	+	0.633021i	$0.218186\pi$
$194$	−0.934640	+	5.30061i	−0.0671033	+	0.380561i
$195$		0			0
$196$	−6.69846	+	5.62068i	−0.478462	+	0.401477i
$197$	18.7526	−	10.8268i	1.33607	−	0.771379i	0.349846	−	0.936807i	$-0.386234\pi$
$197$	18.7526	−	10.8268i	1.33607	−	0.771379i	0.986222	+	0.165428i	$0.0529007\pi$
$198$	−2.38041	+	1.37433i	−0.169169	+	0.0976696i
$199$	12.0209	−	20.8209i	0.852142	−	1.47595i	−0.0271290	−	0.999632i	$-0.508636\pi$
$199$	12.0209	−	20.8209i	0.852142	−	1.47595i	0.879271	−	0.476322i	$-0.158030\pi$
$200$		0			0
$201$	−2.02956	−	2.41874i	−0.143154	−	0.170605i
$202$	−0.594831	−	1.63429i	−0.0418522	−	0.114988i
$203$	−7.45718	−	20.4884i	−0.523392	−	1.43801i
$204$	−0.639033	−	0.761570i	−0.0447413	−	0.0533206i
$205$		0			0
$206$	−5.25789	+	9.10694i	−0.366335	+	0.634510i
$207$			16.1088i			1.11964i
$208$	−0.115535	+	0.0667040i	−0.00801089	+	0.00462509i
$209$	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	$0.983783\pi$
$212$	−6.96833	+	8.30453i	−0.478587	+	0.570357i
$213$	−2.31661	+	13.1382i	−0.158732	+	0.900212i
$214$	−17.0544	−	6.20729i	−1.16581	−	0.424321i
$215$		0			0
$216$		−	14.7441i		−	1.00321i
$217$			15.4338i			1.04771i
$218$	−0.130462	+	0.358441i	−0.00883598	+	0.0242767i
$219$	0.907604	−	1.08164i	0.0613302	−	0.0730905i
$220$		0			0
$221$	−0.258770	+	1.46756i	−0.0174068	+	0.0987188i
$222$	3.40852	−	5.90373i	0.228765	−	0.396233i
$223$	3.72362	+	4.43763i	0.249352	+	0.297166i	0.876173	−	0.481998i	$-0.160089\pi$
$223$	3.72362	+	4.43763i	0.249352	+	0.297166i	−0.626821	+	0.779164i	$0.715644\pi$
$224$	−10.5963	−	18.3533i	−0.707993	−	1.22628i
$225$		0			0
$226$	2.52869	−	4.37981i	0.168206	−	0.291341i
$227$	−12.7326	+	2.24510i	−0.845092	+	0.149013i	−0.579398	−	0.815045i	$-0.696712\pi$
$227$	−12.7326	+	2.24510i	−0.845092	+	0.149013i	−0.265694	+	0.964057i	$0.585601\pi$
$228$	1.73205	+	9.82295i	0.114708	+	0.650541i
$229$	−1.17365	+	0.427173i	−0.0775569	+	0.0282284i	−0.380507	−	0.924778i	$-0.624251\pi$
$229$	−1.17365	+	0.427173i	−0.0775569	+	0.0282284i	0.302950	+	0.953006i	$0.402028\pi$
$230$		0			0
$231$	−2.31996	+	6.37402i	−0.152642	+	0.419380i
$232$	16.2093	−	2.85814i	1.06419	−	0.187646i
$233$	−0.330341	−	0.190722i	−0.0216413	−	0.0124946i	0.489140	−	0.872205i	$-0.337311\pi$
$233$	−0.330341	−	0.190722i	−0.0216413	−	0.0124946i	−0.510782	+	0.859710i	$0.670644\pi$
$234$	−6.43629	+	5.40069i	−0.420753	+	0.353054i
$235$		0			0
$236$	−12.8229	+	10.7597i	−0.834703	+	0.700399i
$237$	−7.02595			−0.456385
$238$	1.52314	+	0.268571i	0.0987305	+	0.0174089i
$239$	2.40760	+	2.02022i	0.155735	+	0.130677i	0.717326	−	0.696738i	$-0.245366\pi$
$239$	2.40760	+	2.02022i	0.155735	+	0.130677i	−0.561591	+	0.827415i	$0.689810\pi$
$240$		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	$0.533339\pi$
$242$		−	8.71864i		−	0.560455i
$243$	−2.70691	−	15.3516i	−0.173648	−	0.984808i
$244$	11.9469			0.764819
$245$		0			0
$246$	4.17159	+	11.4613i	0.265971	+	0.730749i
$247$	9.61051	−	11.4534i	0.611502	−	0.728760i
$248$	−11.4739	−	2.02317i	−0.728596	−	0.128471i
$249$			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	$0.994594\pi$
$252$	−8.89132	−	10.5963i	−0.560101	−	0.667502i
$253$	4.84499	+	2.79726i	0.304602	+	0.175862i
$254$	2.99479	+	16.9843i	0.187910	+	1.06569i
$255$		0			0
$256$	15.1300	−	5.50687i	0.945625	−	0.344179i
$257$	−6.11776	−	16.8084i	−0.381615	−	1.04848i	−0.970676	−	0.240391i	$-0.922724\pi$
$257$	−6.11776	−	16.8084i	−0.381615	−	1.04848i	0.589061	−	0.808089i	$-0.299498\pi$
$258$	−3.21891	−	18.2554i	−0.200401	−	1.13653i
$259$	−2.92127	−	16.5674i	−0.181519	−	1.02945i
$260$		0			0
$261$	16.3525	−	5.95183i	1.01220	−	0.368409i
$262$	13.7890	−	7.96110i	0.851890	−	0.491839i
$263$	−2.49362	−	2.97178i	−0.153763	−	0.183248i	0.683664	−	0.729797i	$-0.260386\pi$
$263$	−2.49362	−	2.97178i	−0.153763	−	0.183248i	−0.837427	+	0.546549i	$0.815941\pi$
$264$	−4.43453	−	2.56028i	−0.272927	−	0.157574i
$265$		0			0
$266$	−11.8871	−	9.97448i	−0.728846	−	0.611575i
$267$	−13.7949	−	11.5753i	−0.844236	−	0.708398i
$268$	0.764818	−	2.10132i	0.0467187	−	0.128358i
$269$	19.8084			1.20774			0.603870	−	0.797083i	$-0.293625\pi$
$269$	19.8084			1.20774			0.603870	+	0.797083i	$0.293625\pi$
$270$		0			0
$271$	−14.7888			−0.898356			−0.449178	−	0.893442i	$-0.648283\pi$
$271$	−14.7888			−0.898356			−0.449178	+	0.893442i	$0.648283\pi$
$272$	−0.00670372	+	0.0184183i	−0.000406473	+	0.00111677i
$273$	−3.60046	+	20.4192i	−0.217910	+	1.23583i
$274$	9.83615	+	8.25351i	0.594224	+	0.498613i
$275$		0			0
$276$	−9.88016	+	5.70431i	−0.594716	+	0.343359i
$277$	−11.2794	−	13.4422i	−0.677711	−	0.807665i	0.312100	−	0.950049i	$-0.398967\pi$
$277$	−11.2794	−	13.4422i	−0.677711	−	0.807665i	−0.989811	+	0.142385i	$0.954523\pi$
$278$	16.8451	−	9.72550i	1.01030	−	0.583297i
$279$	−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	$0.884576\pi$
$282$	−4.04633	+	3.39528i	−0.240956	+	0.202186i
$283$	2.16593	+	5.95084i	0.128751	+	0.353741i	0.987273	−	0.159037i	$-0.0508389\pi$
$283$	2.16593	+	5.95084i	0.128751	+	0.353741i	−0.858522	+	0.512777i	$0.828617\pi$
$284$	−8.87851	+	3.23151i	−0.526843	+	0.191755i
$285$		0			0
$286$	0.506701	+	2.87365i	0.0299619	+	0.169922i
$287$	26.0667	+	15.0496i	1.53867	+	0.888352i
$288$	14.6484	−	8.45723i	0.863163	−	0.498347i
$289$	−8.39053	−	14.5328i	−0.493561	−	0.854872i
$290$		0			0
$291$	−9.18092	+	5.30061i	−0.538195	+	0.310727i
$292$	0.984808	+	0.173648i	0.0576315	+	0.0101620i
$293$	2.94182	−	3.50593i	0.171863	−	0.204819i	−0.673237	−	0.739427i	$-0.735096\pi$
$293$	2.94182	−	3.50593i	0.171863	−	0.204819i	0.845100	+	0.534608i	$0.179541\pi$
$294$	10.6925	+	1.88538i	0.623601	+	0.109958i
$295$		0			0
$296$	12.6996			0.738152
$297$	−5.08732	−	1.85163i	−0.295196	−	0.107443i
$298$			12.5371i			0.726257i
$299$	16.0697	+	5.84889i	0.929335	+	0.338250i
$300$		0			0
$301$	−35.0428	−	29.4044i	−2.01983	−	1.69484i
$302$	4.01676	+	0.708263i	0.231139	+	0.0407560i
$303$	1.71275	−	2.96657i	0.0983948	−	0.170425i
$304$	0.150644	−	0.126406i	0.00864004	−	0.00724985i
$305$		0			0
$306$	−0.214355	+	1.21567i	−0.0122539	+	0.0694952i
$307$	−3.50708	−	2.02481i	−0.200160	−	0.115562i	0.396570	−	0.918004i	$-0.370200\pi$
$307$	−3.50708	−	2.02481i	−0.200160	−	0.115562i	−0.596730	+	0.802442i	$0.703534\pi$
$308$	−4.73097	+	0.834198i	−0.269572	+	0.0475329i
$309$	−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	$0.344268\pi$
$312$	−14.7083	−	5.35339i	−0.832694	−	0.303076i
$313$	13.6129	−	2.40033i	0.769449	−	0.135675i	0.224875	−	0.974388i	$-0.427803\pi$
$313$	13.6129	−	2.40033i	0.769449	−	0.135675i	0.544574	+	0.838713i	$0.316691\pi$
$314$	−5.52987	+	9.57801i	−0.312068	+	0.540518i
$315$		0			0
$316$	−2.48798	−	4.30930i	−0.139960	−	0.242417i
$317$	9.95751	+	11.8669i	0.559269	+	0.666511i	0.969392	−	0.245519i	$-0.0789584\pi$
$317$	9.95751	+	11.8669i	0.559269	+	0.666511i	−0.410122	+	0.912031i	$0.634514\pi$
$318$	13.4607			0.754841
$319$	1.04947	−	5.95183i	0.0587589	−	0.333238i
$320$		0			0
$321$	−12.2260	−	33.5906i	−0.682387	−	1.87484i
$322$	6.07040	−	16.6783i	0.338290	−	0.929445i
$323$		−	2.19665i		−	0.122225i
$324$	8.45723	−	7.09646i	0.469846	−	0.394248i
$325$		0			0
$326$	5.29174	+	1.92603i	0.293082	+	0.106673i
$327$	−0.705990	+	0.256959i	−0.0390414	+	0.0142099i
$328$	−14.6054	+	17.4060i	−0.806447	+	0.961086i
$329$	−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	$0.349665\pi$
$332$	−18.0680	+	10.4315i	−0.991608	+	0.572505i
$333$	13.2230	−	2.33157i	0.724614	−	0.127769i
$334$	−3.93242	+	6.81115i	−0.215172	+	0.372689i
$335$		0			0
$336$	−0.0932736	+	0.256267i	−0.00508849	+	0.0139805i
$337$	1.94858	+	5.35369i	0.106146	+	0.291634i	0.981383	−	0.192060i	$-0.0615169\pi$
$337$	1.94858	+	5.35369i	0.106146	+	0.291634i	−0.875237	+	0.483694i	$0.839295\pi$
$338$	−0.859322	−	2.36097i	−0.0467409	−	0.128420i
$339$	9.80974	−	1.72972i	0.532792	−	0.0939456i
$340$		0			0
$341$	−2.13903	+	3.70491i	−0.115835	+	0.200632i
$342$	7.96097	−	9.48751i	0.430480	−	0.513026i
$343$	0.417822	−	0.241230i	0.0225603	−	0.0130252i
$344$	26.4538	−	22.1974i	1.42629	−	1.19680i
$345$		0			0
$346$	0.926794	−	5.25611i	0.0498247	−	0.282570i
$347$	17.1309	−	20.4158i	0.919635	−	1.09598i	−0.0754694	−	0.997148i	$-0.524046\pi$
$347$	17.1309	−	20.4158i	0.919635	−	1.09598i	0.995104	−	0.0988301i	$-0.0315100\pi$
$348$	9.44113	+	7.92205i	0.506098	+	0.424666i
$349$	−7.47906	−	2.72215i	−0.400345	−	0.145714i	0.133998	−	0.990982i	$-0.457218\pi$
$349$	−7.47906	−	2.72215i	−0.400345	−	0.145714i	−0.534342	+	0.845268i	$0.679441\pi$
$350$		0			0
$351$	−16.2973	−	2.87365i	−0.869883	−	0.153384i
$352$		−	5.87433i		−	0.313103i
$353$	−4.91236	+	13.4966i	−0.261459	+	0.718351i	0.737611	+	0.675226i	$0.235954\pi$
$353$	−4.91236	+	13.4966i	−0.261459	+	0.718351i	−0.999070	+	0.0431256i	$0.986268\pi$
$354$	20.4688	+	3.60921i	1.08791	+	0.191827i
$355$		0			0
$356$	2.21466	−	12.5600i	0.117377	−	0.665677i
$357$	1.52314	+	2.63816i	0.0806131	+	0.139626i
$358$	−2.03719	−	2.42783i	−0.107669	−	0.128315i
$359$	−10.3341	−	17.8992i	−0.545413	−	0.944682i	−0.998581	−	0.0532573i	$-0.983040\pi$
$359$	−10.3341	−	17.8992i	−0.545413	−	0.944682i	0.453168	−	0.891425i	$-0.350294\pi$
$360$		0			0
$361$	−1.51960	+	2.63203i	−0.0799790	+	0.138528i
$362$	−9.63511	+	1.69893i	−0.506410	+	0.0892938i
$363$	13.1548	−	11.0382i	0.690447	−	0.579354i
$364$	−13.7989	+	5.02239i	−0.723259	+	0.263245i
$365$		0			0
$366$	−9.53519	−	11.3636i	−0.498412	−	0.593985i
$367$	6.52206	−	1.15002i	0.340449	−	0.0600303i	−0.000810039	−	1.00000i	$-0.500258\pi$
$367$	6.52206	−	1.15002i	0.340449	−	0.0600303i	0.341259	+	0.939969i	$0.389147\pi$
$368$	0.194792	+	0.112463i	0.0101543	+	0.00586256i
$369$	−12.0116	+	20.8047i	−0.625300	+	1.08305i
$370$		0			0
$371$	25.4466	−	21.3522i	1.32112	−	1.10855i
$372$	−4.36203	−	7.55525i	−0.226161	−	0.391722i
$373$	−31.3068	−	5.52023i	−1.62100	−	0.285827i	−0.711864	−	0.702318i	$-0.752149\pi$
$373$	−31.3068	−	5.52023i	−1.62100	−	0.285827i	−0.909140	+	0.416491i	$0.863260\pi$
$374$	0.328411	+	0.275570i	0.0169817	+	0.0142494i
$375$		0			0
$376$	−9.24675	−	3.36554i	−0.476865	−	0.173565i
$377$		−	18.4739i		−	0.951454i
$378$	−2.98248	+	16.9145i	−0.153402	+	0.869986i
$379$	34.1925			1.75635			0.878176	−	0.478337i	$-0.158760\pi$
$379$	34.1925			1.75635			0.878176	+	0.478337i	$0.158760\pi$
$380$		0			0
$381$	−21.8346	+	26.0214i	−1.11862	+	1.33312i
$382$	−5.73621	+	6.83615i	−0.293490	+	0.349768i
$383$	−23.4391	−	4.13294i	−1.19768	−	0.211183i	−0.460985	−	0.887408i	$-0.652504\pi$
$383$	−23.4391	−	4.13294i	−1.19768	−	0.211183i	−0.736696	+	0.676224i	$0.763615\pi$
$384$	10.2638	+	5.92582i	0.523774	+	0.302401i
$385$		0			0
$386$	−0.154925	−	0.268338i	−0.00788548	−	0.0136581i
$387$	23.4686	−	27.9688i	1.19298	−	1.42174i
$388$	−6.50216	−	3.75402i	−0.330097	−	0.190582i
$389$	−0.769915	−	4.36640i	−0.0390362	−	0.221385i	0.959049	−	0.283241i	$-0.0914095\pi$
$389$	−0.769915	−	4.36640i	−0.0390362	−	0.221385i	−0.998085	+	0.0618550i	$0.980298\pi$
$390$		0			0
$391$	2.36097	−	0.859322i	0.119399	−	0.0434578i
$392$	6.91793	+	19.0069i	0.349408	+	0.959992i
$393$	29.4694	+	10.7260i	1.48653	+	0.541053i
$394$	−3.30659	−	18.7526i	−0.166584	−	0.944742i
$395$		0			0
$396$	−0.665802	−	3.77595i	−0.0334578	−	0.189749i
$397$	16.3138	−	9.41875i	0.818764	−	0.472713i	−0.0312263	−	0.999512i	$-0.509941\pi$
$397$	16.3138	−	9.41875i	0.818764	−	0.472713i	0.849990	+	0.526799i	$0.176608\pi$
$398$	−13.5899	−	16.1958i	−0.681199	−	0.811821i
$399$		−	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	$0.795535\pi$
$402$	−2.60916	+	0.949655i	−0.130133	+	0.0473645i
$403$	−4.47259	+	12.2883i	−0.222795	+	0.612125i
$404$	2.42602			0.120699
$405$		0			0
$406$	−19.1735			−0.951567
$407$	1.59489	−	4.38191i	0.0790555	−	0.217203i
$408$	−2.16095	+	0.786522i	−0.106983	+	0.0389386i
$409$	−21.2920	−	17.8661i	−1.05282	−	0.883424i	−0.0594360	−	0.998232i	$-0.518930\pi$
$409$	−21.2920	−	17.8661i	−1.05282	−	0.883424i	−0.993388	+	0.114808i	$0.963375\pi$
$410$		0			0
$411$			25.2902i			1.24747i
$412$	−9.42892	−	11.2369i	−0.464530	−	0.553605i
$413$	44.4200	−	25.6459i	2.18577	−	1.26195i
$414$	13.3115	+	4.84499i	0.654224	+	0.238118i
$415$		0			0
$416$	−3.11809	−	17.6836i	−0.152877	−	0.867008i
$417$	36.0006	+	13.1031i	1.76295	+	0.641663i
$418$	−1.47113	−	4.04189i	−0.0719552	−	0.197695i
$419$	7.55943	−	2.75141i	0.369302	−	0.134415i	−0.150701	−	0.988579i	$-0.548153\pi$
$419$	7.55943	−	2.75141i	0.369302	−	0.134415i	0.520003	+	0.854164i	$0.325931\pi$
$420$		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	$-0.216355\pi$
$422$	4.94659	+	2.85591i	0.240796	+	0.139024i
$423$	−10.2457	−	1.80659i	−0.498162	−	0.0878394i
$424$	12.5382	+	21.7168i	0.608908	+	1.05466i
$425$		0			0
$426$	10.1600	+	5.86587i	0.492253	+	0.284202i
$427$	−36.0512	−	6.35679i	−1.74464	−	0.307627i
$428$	16.2731	−	19.3935i	0.786590	−	0.937421i
$429$	−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	$0.545337\pi$
$432$	−0.204535	−	0.0744448i	−0.00984071	−	0.00358173i
$433$			3.82201i			0.183674i	0.995774	+	0.0918372i	$0.0292739\pi$
$433$			3.82201i			0.183674i	−0.995774	+	0.0918372i	$0.970726\pi$
$434$	12.7537	+	4.64197i	0.612198	+	0.222822i
$435$		0			0
$436$	−0.407604	−	0.342020i	−0.0195207	−	0.0163798i
$437$	−24.8250	−	4.37733i	−1.18754	−	0.209396i
$438$	−0.620838	−	1.07532i	−0.0296648	−	0.0513809i
$439$	−29.3200	+	24.6024i	−1.39937	+	1.17421i	−0.437989	+	0.898980i	$0.644309\pi$
$439$	−29.3200	+	24.6024i	−1.39937	+	1.17421i	−0.961379	+	0.275229i	$0.911246\pi$
$440$		0			0
$441$	10.6925	+	18.5200i	0.509168	+	0.881905i
$442$	1.13489	+	0.655230i	0.0539813	+	0.0311661i
$443$	−13.1512	+	2.31892i	−0.624834	+	0.110175i	−0.477095	−	0.878852i	$-0.658310\pi$
$443$	−13.1512	+	2.31892i	−0.624834	+	0.110175i	−0.147738	+	0.989027i	$0.547199\pi$
$444$	6.11246	+	7.28455i	0.290085	+	0.345709i
$445$		0			0
$446$	4.78699	−	1.74232i	0.226670	−	0.0825013i
$447$	−18.9162	+	15.8726i	−0.894706	+	0.750747i
$448$	−18.6634	+	3.29086i	−0.881762	+	0.155478i
$449$	3.45929	−	5.99167i	0.163254	−	0.282764i	−0.772780	−	0.634674i	$-0.781134\pi$
$449$	3.45929	−	5.99167i	0.163254	−	0.282764i	0.936034	+	0.351910i	$0.114468\pi$
$450$		0			0
$451$	4.17159	+	7.22540i	0.196432	+	0.340231i
$452$	4.53466	+	5.40420i	0.213293	+	0.254192i
$453$	4.01676	+	6.95723i	0.188724	+	0.326879i
$454$	−1.97431	+	11.1969i	−0.0926589	+	0.525494i
$455$		0			0
$456$	22.7219	+	4.00649i	1.06405	+	0.187621i
$457$	2.84234	−	7.80928i	0.132959	−	0.365303i	−0.855291	−	0.518148i	$-0.826622\pi$
$457$	2.84234	−	7.80928i	0.132959	−	0.365303i	0.988250	+	0.152846i	$0.0488438\pi$
$458$			1.09833i			0.0513214i
$459$	−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	$0.415829\pi$
$462$	4.56942	+	3.83420i	0.212589	+	0.178383i
$463$	−0.0825054	+	0.0983261i	−0.00383435	+	0.00456960i	−0.767958	−	0.640500i	$-0.778727\pi$
$463$	−0.0825054	+	0.0983261i	−0.00383435	+	0.00456960i	0.764124	+	0.645070i	$0.223172\pi$
$464$	0.0421938	−	0.239293i	0.00195880	−	0.0111089i
$465$		0			0
$466$	−0.256959	+	0.215615i	−0.0119034	+	0.00998815i
$467$	−34.5678	+	19.9577i	−1.59960	+	0.923532i	−0.608042	+	0.793905i	$0.708045\pi$
$467$	−34.5678	+	19.9577i	−1.59960	+	0.923532i	−0.991563	+	0.129627i	$0.958622\pi$
$468$	−4.00854	−	11.0134i	−0.185295	−	0.509093i
$469$	−3.42602	+	5.93404i	−0.158199	+	0.274009i
$470$		0			0
$471$	−21.4525	+	3.78265i	−0.988478	+	0.174295i
$472$	13.2431	+	36.3851i	0.609562	+	1.67476i
$473$	−4.33683	−	11.9153i	−0.199408	−	0.547868i
$474$	−2.11318	+	5.80591i	−0.0970615	+	0.266674i
$475$		0			0
$476$	−1.07873	+	1.86841i	−0.0494433	+	0.0856383i
$477$	17.0419	+	20.3097i	0.780295	+	0.929919i
$478$	2.39354	−	1.38191i	0.109478	−	0.0632072i
$479$	6.30200	−	5.28801i	0.287946	−	0.241615i	−0.487360	−	0.873201i	$-0.662040\pi$
$479$	6.30200	−	5.28801i	0.287946	−	0.241615i	0.775306	+	0.631586i	$0.217596\pi$
$480$		0			0
$481$	2.47519	−	14.0375i	0.112859	−	0.640054i
$482$	4.24550	−	5.05959i	0.193377	−	0.230458i
$483$	32.8498	−	11.9564i	1.49472	−	0.544033i
$484$	11.4284	+	4.15961i	0.519475	+	0.189073i
$485$		0			0
$486$	−13.5000	−	2.38041i	−0.612372	−	0.107978i
$487$			2.84760i			0.129037i	0.997917	+	0.0645186i	$0.0205512\pi$
$487$			2.84760i			0.129037i	−0.997917	+	0.0645186i	$0.979449\pi$
$488$	9.45168	−	25.9683i	0.427857	−	1.17553i
$489$	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	$0.702055\pi$
$492$	−17.0138			−0.767043
$493$	−1.74465	−	2.07919i	−0.0785751	−	0.0936421i
$494$	−6.57398	−	11.3865i	−0.295777	−	0.512301i
$495$		0			0
$496$	−0.0859997	+	0.148956i	−0.00386150	+	0.00668831i
$497$	28.5115	−	5.02734i	1.27891	−	0.225507i
$498$	24.3429	+	8.86009i	1.09083	+	0.397030i
$499$	−36.4962	+	13.2835i	−1.63379	+	0.594652i	−0.985938	−	0.167111i	$-0.946556\pi$
$499$	−36.4962	+	13.2835i	−1.63379	+	0.594652i	−0.647856	+	0.761763i	$0.724334\pi$
$500$		0			0
$501$	−15.2554	+	2.68993i	−0.681560	+	0.120177i
$502$	−13.3148	+	2.34776i	−0.594270	+	0.104786i
$503$	−23.4745	−	13.5530i	−1.04668	−	0.604300i	−0.124961	−	0.992162i	$-0.539880\pi$
$503$	−23.4745	−	13.5530i	−1.04668	−	0.604300i	−0.921718	+	0.387862i	$0.873214\pi$
$504$	−30.0669	+	10.9434i	−1.33928	+	0.487460i
$505$		0			0
$506$	3.76873	−	3.16234i	0.167541	−	0.140583i
$507$	2.47432	−	4.28564i	0.109888	−	0.190332i
$508$	−23.6919	−	4.17752i	−1.05116	−	0.185347i
$509$	14.8105	+	12.4275i	0.656462	+	0.550837i	0.909024	−	0.416744i	$-0.136829\pi$
$509$	14.8105	+	12.4275i	0.656462	+	0.550837i	−0.252562	+	0.967581i	$0.581273\pi$
$510$		0			0
$511$	−2.87939	−	1.04801i	−0.127377	−	0.0463613i
$512$		−	0.473897i		−	0.0209435i
$513$	24.3938			1.07701
$514$	−15.7297			−0.693806
$515$		0			0
$516$	25.4650	+	4.49016i	1.12103	+	0.197668i
$517$	−2.32251	+	2.76786i	−0.102144	+	0.121730i
$518$	−14.5691	−	2.56893i	−0.640130	−	0.112872i
$519$	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	$-0.347184\pi$
$522$		−	15.3030i		−	0.669796i
$523$	−7.47416	−	4.31521i	−0.326822	−	0.188691i	0.327607	−	0.944814i	$-0.393758\pi$
$523$	−7.47416	−	4.31521i	−0.326822	−	0.188691i	−0.654429	+	0.756123i	$0.727091\pi$
$524$	3.85679	+	21.8730i	0.168485	+	0.955524i
$525$		0			0
$526$	−3.20574	+	1.16679i	−0.139777	+	0.0508746i
$527$	0.657115	+	1.80541i	0.0286244	+	0.0786448i
$528$	−0.0579078	+	0.0485904i	−0.00252011	+	0.00211462i
$529$	−1.01279	−	5.74384i	−0.0440345	−	0.249732i
$530$		0			0
$531$	20.4688	+	35.4531i	0.888272	+	1.53853i
$532$	18.7459	−	10.8229i	0.812738	−	0.469234i
$533$	16.3930	+	19.5364i	0.710060	+	0.846217i
$534$	−13.7144	+	7.91799i	−0.593478	+	0.342645i
$535$		0			0
$536$	−3.96245	−	3.32489i	−0.171152	−	0.143613i
$537$	1.08397	−	6.14749i	0.0467767	−	0.265284i
$538$	5.95772	−	16.3687i	0.256856	−	0.705705i
$539$	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	$0.346510\pi$
$542$	−4.44799	+	12.2208i	−0.191058	+	0.524926i
$543$	−14.7618	−	12.3867i	−0.633491	−	0.531562i
$544$	−2.02094	−	1.69577i	−0.0866473	−	0.0727057i
$545$		0			0
$546$	15.7906	+	9.11668i	0.675773	+	0.390158i
$547$	14.5407	+	17.3289i	0.621714	+	0.740929i	0.981364	−	0.192158i	$-0.0615485\pi$
$547$	14.5407	+	17.3289i	0.621714	+	0.740929i	−0.359651	+	0.933087i	$0.617104\pi$
$548$	−15.5115	+	8.95558i	−0.662620	+	0.382564i
$549$	5.07357	−	28.7736i	0.216535	−	1.22803i
$550$		0			0
$551$	4.72874	+	26.8180i	0.201451	+	1.14249i
$552$	4.58255	+	25.9889i	0.195046	+	1.10616i
$553$	5.21485	+	14.3277i	0.221758	+	0.609276i
$554$	−14.5005	+	5.27774i	−0.616066	+	0.224230i
$555$		0			0
$556$	4.71156	+	26.7206i	0.199815	+	1.13321i
$557$	39.8037	+	22.9807i	1.68654	+	0.973724i	0.957136	+	0.289640i	$0.0935354\pi$
$557$	39.8037	+	22.9807i	1.68654	+	0.973724i	0.729403	+	0.684084i	$0.239798\pi$
$558$	−3.70491	+	10.1792i	−0.156842	+	0.430919i
$559$	−19.3799	−	33.5669i	−0.819680	−	1.41973i
$560$		0			0
$561$			0.844395i			0.0356504i
$562$	5.42874	+	0.957234i	0.228998	+	0.0403785i
$563$	−1.85143	+	2.20645i	−0.0780286	+	0.0929909i	−0.803646	−	0.595107i	$-0.797110\pi$
$563$	−1.85143	+	2.20645i	−0.0780286	+	0.0929909i	0.725618	+	0.688098i	$0.241554\pi$
$564$	−2.52007	−	6.92383i	−0.106114	−	0.291546i
$565$		0			0
$566$	5.56893			0.234079
$567$	−29.2967	+	16.9145i	−1.23035	+	0.710341i
$568$			21.8553i			0.917030i
$569$	35.1472	+	12.7925i	1.47345	+	0.536292i	0.949035	−	0.315172i	$-0.102062\pi$
$569$	35.1472	+	12.7925i	1.47345	+	0.536292i	0.524414	+	0.851463i	$0.324284\pi$
$570$		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	$0.898280\pi$
$572$	−4.00854	−	0.706813i	−0.167605	−	0.0295533i
$573$	−17.5768			−0.734280
$574$	20.2763	−	17.0138i	0.846317	−	0.710144i
$575$		0			0
$576$	−2.62654	−	14.8959i	−0.109439	−	0.620661i
$577$	4.14052	+	2.39053i	0.172372	+	0.0995190i	0.583704	−	0.811967i	$-0.301603\pi$
$577$	4.14052	+	2.39053i	0.172372	+	0.0995190i	−0.411332	+	0.911486i	$0.634936\pi$
$578$	−14.5328	+	2.56253i	−0.604486	+	0.106587i
$579$	0.208730	−	0.573481i	0.00867453	−	0.0238331i
$580$		0			0
$581$	60.0729	−	21.8647i	2.49224	−	0.907102i
$582$	1.61884	+	9.18092i	0.0671033	+	0.380561i
$583$	9.06781	−	1.59890i	0.375550	−	0.0662196i
$584$	1.15657	−	2.00324i	0.0478594	−	0.0828949i
$585$		0			0
$586$	−2.01233	−	3.48545i	−0.0831284	−	0.143983i
$587$	−15.1135	−	18.0116i	−0.623802	−	0.743419i	0.357917	−	0.933753i	$-0.383487\pi$
$587$	−15.1135	−	18.0116i	−0.623802	−	0.743419i	−0.981719	+	0.190335i	$0.939043\pi$
$588$	−7.57272	+	13.1163i	−0.312294	+	0.540908i
$589$	3.34730	−	18.9835i	0.137923	−	0.782200i
$590$		0			0
$591$	24.1079	−	28.7307i	0.991666	−	1.18182i
$592$	0.0641222	−	0.176174i	0.00263541	−	0.00724072i
$593$		−	2.98276i		−	0.122487i	−0.998123	−	0.0612437i	$-0.980493\pi$
$593$		−	2.98276i		−	0.122487i	0.998123	−	0.0612437i	$-0.0195067\pi$
$594$	−3.06020	+	3.64701i	−0.125562	+	0.149638i
$595$		0			0
$596$	−16.4338	−	5.98140i	−0.673153	−	0.245008i
$597$	7.23102	−	41.0091i	0.295946	−	1.67839i
$598$	9.66648	−	11.5201i	0.395292	−	0.471091i
$599$	5.51930	−	31.3015i	0.225512	−	1.27894i	−0.636191	−	0.771532i	$-0.719491\pi$
$599$	5.51930	−	31.3015i	0.225512	−	1.27894i	0.861703	−	0.507412i	$-0.169398\pi$
$600$		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	$0.00646211\pi$
$602$	−34.8381	+	20.1138i	−1.41990	+	0.819778i
$603$	−4.73616	−	2.73442i	−0.192871	−	0.111354i
$604$	−2.84477	+	4.92729i	−0.115752	+	0.200488i
$605$		0			0
$606$	−1.93629	−	2.30758i	−0.0786564	−	0.0937390i
$607$	−10.7501	−	29.5355i	−0.436331	−	1.19881i	−0.941861	−	0.336002i	$-0.890925\pi$
$607$	−10.7501	−	29.5355i	−0.436331	−	1.19881i	0.505530	−	0.862809i	$-0.331297\pi$
$608$	9.05288	+	24.8726i	0.367143	+	1.00872i
$609$	−24.2746	−	28.9293i	−0.983655	−	1.17227i
$610$		0			0
$611$	−5.52229	+	9.56488i	−0.223408	+	0.386954i
$612$	−1.49124	−	0.860967i	−0.0602797	−	0.0348025i
$613$	−22.0070	+	12.7057i	−0.888854	+	0.513180i	−0.873567	−	0.486703i	$-0.838199\pi$
$613$	−22.0070	+	12.7057i	−0.888854	+	0.513180i	−0.0152863	+	0.999883i	$0.504866\pi$
$614$	−2.72803	+	2.28909i	−0.110094	+	0.0923800i
$615$		0			0
$616$	−1.92962	+	10.9434i	−0.0777468	+	0.440924i
$617$	−14.0483	+	16.7422i	−0.565565	+	0.674014i	−0.970714	−	0.240236i	$-0.922775\pi$
$617$	−14.0483	+	16.7422i	−0.565565	+	0.674014i	0.405149	+	0.914250i	$0.367219\pi$
$618$	−3.16281	+	17.9372i	−0.127227	+	0.721539i
$619$	−37.8619	−	13.7806i	−1.52180	−	0.553889i	−0.560202	−	0.828356i	$-0.689276\pi$
$619$	−37.8619	−	13.7806i	−1.52180	−	0.553889i	−0.961597	+	0.274467i	$0.911499\pi$
$620$		0			0
$621$	9.54277	+	26.2185i	0.382938	+	1.05211i
$622$		−	4.33368i		−	0.173765i
$623$	−13.3660	+	36.7229i	−0.535499	+	1.47127i
$624$	−0.148529	+	0.177009i	−0.00594590	+	0.00708605i
$625$		0			0
$626$	2.11081	−	11.9710i	0.0843651	−	0.478458i
$627$	4.23594	−	7.33687i	0.169167	−	0.293006i
$628$	−9.91665	−	11.8182i	−0.395717	−	0.471598i
$629$	−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	$-0.0209737\pi$
$632$	−11.3353	+	1.99871i	−0.450892	+	0.0795045i
$633$	1.95356	+	11.0792i	0.0776471	+	0.440358i
$634$	12.8011	−	4.65923i	0.508398	−	0.185042i
$635$		0			0
$636$	−6.42205	+	17.6444i	−0.254651	+	0.699647i
$637$	22.3574	−	3.94222i	0.885834	−	0.156196i
$638$	−4.60266	−	2.65735i	−0.182221	−	0.105205i
$639$	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	$0.487246\pi$
$642$	−31.4348			−1.24063
$643$	32.3302	+	5.70068i	1.27498	+	0.224813i	0.769846	−	0.638229i	$-0.220333\pi$
$643$	32.3302	+	5.70068i	1.27498	+	0.224813i	0.505132	+	0.863042i	$0.331444\pi$
$644$	18.9659	+	15.9142i	0.747359	+	0.627109i
$645$		0			0
$646$	−1.81521	−	0.660681i	−0.0714184	−	0.0259942i
$647$		−	11.1310i		−	0.437606i	−0.975769	−	0.218803i	$-0.929785\pi$
$647$		−	11.1310i		−	0.437606i	0.975769	−	0.218803i	$-0.0702153\pi$
$648$	−8.73433	−	23.9974i	−0.343117	−	0.942706i
$649$	14.2175			0.558086
$650$		0			0
$651$	9.14290	+	25.1199i	0.358339	+	0.984527i
$652$	−5.04932	+	6.01754i	−0.197746	+	0.235665i
$653$	4.91469	+	0.866592i	0.192327	+	0.0339124i	0.268982	−	0.963145i	$-0.413313\pi$
$653$	4.91469	+	0.866592i	0.192327	+	0.0339124i	−0.0766550	+	0.997058i	$0.524424\pi$
$654$			0.660681i			0.0258347i
$655$		0			0
$656$	0.167718	+	0.290497i	0.00654830	+	0.0113420i
$657$	0.836452	−	2.29813i	0.0326331	−	0.0896587i
$658$	9.92713	+	5.73143i	0.387000	+	0.223434i
$659$	−3.68825	−	20.9171i	−0.143674	−	0.814815i	−0.968422	−	0.249315i	$-0.919794\pi$
$659$	−3.68825	−	20.9171i	−0.143674	−	0.814815i	0.824748	−	0.565500i	$-0.191317\pi$
$660$		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	$0.395906\pi$
$662$	2.45064	+	6.73308i	0.0952468	+	0.261689i
$663$	0.448204	+	2.54189i	0.0174068	+	0.0987188i
$664$	8.38016	+	47.5262i	0.325213	+	1.84438i
$665$		0			0
$666$	2.05035	−	11.6281i	0.0794493	−	0.450579i
$667$	−26.9742	+	15.5736i	−1.04445	+	0.603011i
$668$	−7.05196	−	8.40420i	−0.272849	−	0.325168i
$669$	8.68938	+	5.01681i	0.335951	+	0.193961i
$670$		0			0
$671$	−7.77316	−	6.52245i	−0.300079	−	0.251796i
$672$	−28.1188	−	23.5945i	−1.08471	−	0.910178i
$673$	−14.9986	+	41.2083i	−0.578154	+	1.58846i	0.213136	+	0.977023i	$0.431632\pi$
$673$	−14.9986	+	41.2083i	−0.578154	+	1.58846i	−0.791290	+	0.611441i	$0.790590\pi$
$674$	5.01010			0.192982
$675$		0			0
$676$	3.50475			0.134798
$677$	−3.46876	+	9.53033i	−0.133315	+	0.366280i	−0.988331	−	0.152321i	$-0.951325\pi$
$677$	−3.46876	+	9.53033i	−0.133315	+	0.366280i	0.855016	+	0.518602i	$0.173547\pi$
$678$	1.52109	−	8.62654i	0.0584172	−	0.331300i
$679$	17.6236	+	14.7880i	0.676332	+	0.567510i
$680$		0			0
$681$	−19.3935	+	11.1969i	−0.743161	+	0.429064i
$682$	2.41821	+	2.88191i	0.0925981	+	0.110354i
$683$	−4.38366	+	2.53091i	−0.167736	+	0.0968425i	−0.581518	−	0.813534i	$-0.697541\pi$
$683$	−4.38366	+	2.53091i	−0.167736	+	0.0968425i	0.413782	+	0.910376i	$0.364208\pi$
$684$	8.63816	+	14.9617i	0.330288	+	0.572076i
$685$		0			0
$686$	−0.0736733	−	0.417822i	−0.00281286	−	0.0159525i
$687$	−1.65717	+	1.39053i	−0.0632249	+	0.0530520i
$688$	−0.174362	−	0.479055i	−0.00664749	−	0.0182638i
$689$	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	$0.791430\pi$
$692$	6.44757	+	3.72251i	0.245100	+	0.141508i
$693$			11.7487i			0.446295i
$694$	−11.7182	−	20.2966i	−0.444818	−	0.770447i
$695$		0			0
$696$	24.6890	−	14.2542i	0.935835	−	0.540305i
$697$	3.68999	+	0.650644i	0.139768	+	0.0246449i
$698$	−4.49891	+	5.36160i	−0.170286	+	0.202939i
$699$	−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	$0.155926\pi$
$702$	−7.27633	+	12.6030i	−0.274627	+	0.475668i
$703$			21.0114i			0.792459i
$704$	−4.93629	−	1.79666i	−0.186043	−	0.0677143i
$705$		0			0
$706$	9.67546	+	8.11867i	0.364141	+	0.305550i
$707$	−7.32083	−	1.29086i	−0.275328	−	0.0485478i
$708$	−14.4965	+	25.1088i	−0.544814	+	0.943645i
$709$	6.47044	−	5.42934i	0.243002	−	0.203903i	−0.513150	−	0.858299i	$-0.671521\pi$
$709$	6.47044	−	5.42934i	0.243002	−	0.203903i	0.756152	+	0.654396i	$0.227077\pi$
$710$		0			0
$711$	−11.4354	+	4.16215i	−0.428861	+	0.156093i
$712$	−25.5488	−	14.7506i	−0.957483	−	0.552803i
$713$	21.7129	−	3.82857i	0.813155	−	0.143381i
$714$	2.63816	−	0.465178i	0.0987305	−	0.0174089i
$715$		0			0
$716$	4.15435	−	1.51206i	0.155255	−	0.0565084i
$717$	5.11538	+	1.86184i	0.191037	+	0.0695318i
$718$	−17.8992	+	3.15611i	−0.667991	+	0.117785i
$719$	−12.5924	+	21.8107i	−0.469617	+	0.813401i	−0.999397	−	0.0347347i	$-0.988941\pi$
$719$	−12.5924	+	21.8107i	−0.469617	+	0.813401i	0.529779	+	0.848135i	$0.322275\pi$
$720$		0			0
$721$	22.4739	+	38.9259i	0.836972	+	1.44968i
$722$	1.71793	+	2.04735i	0.0639348	+	0.0761946i
$723$	13.0090			0.483809
$724$	2.36989	−	13.4403i	0.0880763	−	0.499505i
$725$		0			0
$726$	−5.16489	−	14.1904i	−0.191687	−	0.526656i
$727$	−4.12651	+	11.3375i	−0.153044	+	0.420484i	−0.992393	−	0.123108i	$-0.960714\pi$
$727$	−4.12651	+	11.3375i	−0.153044	+	0.420484i	0.839349	+	0.543592i	$0.182936\pi$
$728$			33.9674i			1.25892i
$729$	−13.5000	−	23.3827i	−0.500000	−	0.866025i
$730$		0			0
$731$	−5.35117	−	1.94767i	−0.197920	−	0.0720370i
$732$	19.4447	−	7.07728i	0.718695	−	0.261584i
$733$	25.9968	−	30.9818i	0.960214	−	1.14434i	−0.0292515	−	0.999572i	$-0.509312\pi$
$733$	25.9968	−	30.9818i	0.960214	−	1.14434i	0.989466	−	0.144767i	$-0.0462432\pi$
$734$	1.01131	−	5.73540i	0.0373280	−	0.211698i
$735$		0			0
$736$	−23.1917	+	19.4601i	−0.854856	+	0.717309i
$737$	−1.64485	+	0.949655i	−0.0605889	+	0.0349810i
$738$	13.5793	+	16.1832i	0.499862	+	0.595712i
$739$	4.33140	−	7.50221i	0.159333	−	0.275973i	−0.775295	−	0.631599i	$-0.782399\pi$
$739$	4.33140	−	7.50221i	0.159333	−	0.275973i	0.934628	+	0.355626i	$0.115732\pi$
$740$		0			0
$741$	8.85710	−	24.3347i	0.325374	−	0.893957i
$742$	−9.99093	−	27.4499i	−0.366779	−	1.00772i
$743$	5.99837	+	16.4804i	0.220059	+	0.604607i	0.999768	−	0.0215347i	$-0.00685525\pi$
$743$	5.99837	+	16.4804i	0.220059	+	0.604607i	−0.779709	+	0.626142i	$0.784633\pi$
$744$	−19.8735	+	3.50423i	−0.728596	+	0.128471i
$745$		0			0
$746$	−13.9777	+	24.2101i	−0.511760	+	0.886395i
$747$	17.4510	+	47.9461i	0.638498	+	1.75426i
$748$	−0.517902	+	0.299011i	−0.0189364	+	0.0109329i
$749$	−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	$0.874253\pi$
$752$	−0.0933762	+	0.111281i	−0.00340508	+	0.00405802i
$753$	−20.3995	−	17.1172i	−0.743399	−	0.623786i
$754$	−15.2659	−	5.55635i	−0.555953	−	0.202350i
$755$		0			0
$756$	−20.7487	−	11.9792i	−0.754622	−	0.435681i
$757$		−	26.1165i		−	0.949220i	−0.880196	−	0.474610i	$-0.842589\pi$
$757$		−	26.1165i		−	0.949220i	0.880196	−	0.474610i	$-0.157411\pi$
$758$	10.2840	−	28.2551i	0.373532	−	1.02627i
$759$	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	$0.996024\pi$
$762$	14.9357	+	25.8694i	0.541064	+	0.937150i
$763$	1.04801	+	1.24897i	0.0379405	+	0.0452158i
$764$	−6.22416	−	10.7806i	−0.225182	−	0.390027i
$765$		0			0
$766$	−10.4650	+	18.1259i	−0.378115	+	0.654914i
$767$	42.7991	−	7.54664i	1.54539	−	0.272493i
$768$	21.3633	−	17.9259i	0.770881	−	0.646846i
$769$	26.7520	−	9.73692i	0.964700	−	0.351122i	0.188827	−	0.982010i	$-0.439532\pi$
$769$	26.7520	−	9.73692i	0.964700	−	0.351122i	0.775874	+	0.630888i	$0.217309\pi$
$770$		0			0
$771$	−19.9145	−	23.7331i	−0.717202	−	0.854728i
$772$	0.425653	−	0.0750542i	0.0153196	−	0.00270126i
$773$	−21.5514	−	12.4427i	−0.775149	−	0.447532i	0.0595595	−	0.998225i	$-0.481030\pi$
$773$	−21.5514	−	12.4427i	−0.775149	−	0.447532i	−0.834708	+	0.550692i	$0.814364\pi$
$774$	−16.0535	−	27.8055i	−0.5

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.u (of order \(18\), degree \(6\), not minimal)

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

Introduction

L-functions

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