LMFDB - Embedded newform 375.2.g.c.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			76.1
Root			$0.623865 + 1.92006i$ of defining polynomial
Character	$\chi$	$=$	375.76
Dual form			375.2.g.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63330 - 1.18666i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} -1.01887 q^{7} +(0.0473123 - 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.63330 - 1.18666i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} -1.01887 q^{7} +(0.0473123 - 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.85061 - 2.79763i) q^{11} +(-1.67939 + 1.22015i) q^{12} +(-0.0840060 + 0.0610339i) q^{13} +(1.66412 + 1.20905i) q^{14} +(3.10871 - 2.25861i) q^{16} +(1.80397 - 5.55204i) q^{17} +2.01887 q^{18} +(-0.223853 + 0.688949i) q^{19} +(-0.314848 - 0.969003i) q^{21} +(2.96936 + 9.13874i) q^{22} +(-7.33901 - 5.33210i) q^{23} +0.153106 q^{24} +0.209634 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.653574 - 2.01149i) q^{28} +(-1.23251 - 3.79326i) q^{29} +(0.329605 - 1.01442i) q^{31} -8.06387 q^{32} +(1.47080 - 4.52666i) q^{33} +(-9.53482 + 6.92745i) q^{34} +(-1.67939 - 1.22015i) q^{36} +(3.25727 - 2.36655i) q^{37} +(1.18317 - 0.859623i) q^{38} +(-0.0840060 - 0.0610339i) q^{39} +(-5.83282 + 4.23780i) q^{41} +(-0.635638 + 1.95629i) q^{42} -8.62791 q^{43} +(3.05314 - 9.39661i) q^{44} +(5.65940 + 17.4179i) q^{46} +(2.53331 + 7.79673i) q^{47} +(3.10871 + 2.25861i) q^{48} -5.96190 q^{49} +5.83776 q^{51} +(-0.174383 - 0.126697i) q^{52} +(1.34954 + 4.15345i) q^{53} +(0.623865 + 1.92006i) q^{54} +(-0.0482051 + 0.148360i) q^{56} -0.724404 q^{57} +(-2.48827 + 7.65810i) q^{58} +(3.97458 - 2.88770i) q^{59} +(-5.63428 - 4.09354i) q^{61} +(-1.74212 + 1.26572i) q^{62} +(0.824283 - 0.598877i) q^{63} +(6.95331 + 5.05187i) q^{64} +(-7.77388 + 5.64805i) q^{66} +(3.06544 - 9.43446i) q^{67} +12.1183 q^{68} +(2.80325 - 8.62753i) q^{69} +(-3.33323 - 10.2586i) q^{71} +(0.0473123 + 0.145612i) q^{72} +(6.98275 + 5.07326i) q^{73} -8.12840 q^{74} -1.50375 q^{76} +(3.92327 + 2.85042i) q^{77} +(0.0647804 + 0.199374i) q^{78} +(0.767263 + 2.36139i) q^{79} +(0.309017 - 0.951057i) q^{81} +14.5556 q^{82} +(-1.31142 + 4.03614i) q^{83} +(1.71108 - 1.24317i) q^{84} +(14.0920 + 10.2384i) q^{86} +(3.22674 - 2.34436i) q^{87} +(-0.589550 + 0.428333i) q^{88} +(14.8659 + 10.8007i) q^{89} +(0.0855912 - 0.0621857i) q^{91} +(5.81910 - 17.9093i) q^{92} +1.06662 q^{93} +(5.11443 - 15.7406i) q^{94} +(-2.49187 - 7.66920i) q^{96} +(-2.07003 - 6.37090i) q^{97} +(9.73758 + 7.07477i) q^{98} +4.75961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−1.63330	−	1.18666i	−1.15492	−	0.839097i	−0.165791	−	0.986161i	$-0.553018\pi$
$2$	−1.63330	−	1.18666i	−1.15492	−	0.839097i	−0.989127	+	0.147064i	$0.953018\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.641469	+	1.97424i	0.320735	+	0.987119i
$5$		0			0
$5$		0			0
$6$	0.623865	−	1.92006i	0.254692	−	0.783861i
$7$	−1.01887			−0.385097			−0.192548	−	0.981287i	$-0.561675\pi$
$7$	−1.01887			−0.385097			−0.192548	+	0.981287i	$0.561675\pi$
$8$	0.0473123	−	0.145612i	0.0167274	−	0.0514817i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−3.85061	−	2.79763i	−1.16100	−	0.843517i	−0.171097	−	0.985254i	$-0.554731\pi$
$11$	−3.85061	−	2.79763i	−1.16100	−	0.843517i	−0.989904	+	0.141737i	$0.954731\pi$
$12$	−1.67939	+	1.22015i	−0.484797	+	0.352226i
$13$	−0.0840060	+	0.0610339i	−0.0232991	+	0.0169278i	−0.599374	−	0.800469i	$-0.704584\pi$
$13$	−0.0840060	+	0.0610339i	−0.0232991	+	0.0169278i	0.576075	+	0.817397i	$0.304584\pi$
$14$	1.66412	+	1.20905i	0.444755	+	0.323134i
$15$		0			0
$16$	3.10871	−	2.25861i	0.777177	−	0.564652i
$17$	1.80397	−	5.55204i	0.437527	−	1.34657i	−0.452949	−	0.891537i	$-0.649628\pi$
$17$	1.80397	−	5.55204i	0.437527	−	1.34657i	0.890475	−	0.455032i	$-0.150372\pi$
$18$	2.01887			0.475852
$19$	−0.223853	+	0.688949i	−0.0513554	+	0.158056i	−0.973445	−	0.228920i	$-0.926480\pi$
$19$	−0.223853	+	0.688949i	−0.0513554	+	0.158056i	0.922090	+	0.386976i	$0.126480\pi$
$20$		0			0
$21$	−0.314848	−	0.969003i	−0.0687055	−	0.211454i
$22$	2.96936	+	9.13874i	0.633069	+	1.94839i
$23$	−7.33901	−	5.33210i	−1.53029	−	1.11182i	−0.956077	−	0.293114i	$-0.905308\pi$
$23$	−7.33901	−	5.33210i	−1.53029	−	1.11182i	−0.574212	−	0.818707i	$-0.694692\pi$
$24$	0.153106			0.0312526
$25$		0			0
$26$	0.209634			0.0411126
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.653574	−	2.01149i	−0.123514	−	0.380136i
$29$	−1.23251	−	3.79326i	−0.228871	−	0.704391i	−0.997876	−	0.0651484i	$-0.979248\pi$
$29$	−1.23251	−	3.79326i	−0.228871	−	0.704391i	0.769005	−	0.639243i	$-0.220752\pi$
$30$		0			0
$31$	0.329605	−	1.01442i	0.0591988	−	0.182195i	−0.917084	−	0.398694i	$-0.869464\pi$
$31$	0.329605	−	1.01442i	0.0591988	−	0.182195i	0.976283	+	0.216498i	$0.0694636\pi$
$32$	−8.06387			−1.42550
$33$	1.47080	−	4.52666i	0.256034	−	0.787990i
$34$	−9.53482	+	6.92745i	−1.63521	+	1.18805i
$35$		0			0
$36$	−1.67939	−	1.22015i	−0.279898	−	0.203358i
$37$	3.25727	−	2.36655i	0.535493	−	0.389058i	−0.286916	−	0.957956i	$-0.592630\pi$
$37$	3.25727	−	2.36655i	0.535493	−	0.389058i	0.822408	+	0.568898i	$0.192630\pi$
$38$	1.18317	−	0.859623i	0.191935	−	0.139449i
$39$	−0.0840060	−	0.0610339i	−0.0134517	−	0.00977325i
$40$		0			0
$41$	−5.83282	+	4.23780i	−0.910934	+	0.661832i	−0.941251	−	0.337708i	$-0.890348\pi$
$41$	−5.83282	+	4.23780i	−0.910934	+	0.661832i	0.0303167	+	0.999540i	$0.490348\pi$
$42$	−0.635638	+	1.95629i	−0.0980810	+	0.301862i
$43$	−8.62791			−1.31574			−0.657872	−	0.753130i	$-0.728543\pi$
$43$	−8.62791			−1.31574			−0.657872	+	0.753130i	$0.728543\pi$
$44$	3.05314	−	9.39661i	0.460279	−	1.41659i
$45$		0			0
$46$	5.65940	+	17.4179i	0.834434	+	2.56812i
$47$	2.53331	+	7.79673i	0.369522	+	1.13727i	0.947101	+	0.320936i	$0.103997\pi$
$47$	2.53331	+	7.79673i	0.369522	+	1.13727i	−0.577579	+	0.816335i	$0.696003\pi$
$48$	3.10871	+	2.25861i	0.448703	+	0.326002i
$49$	−5.96190			−0.851700
$50$		0			0
$51$	5.83776			0.817451
$52$	−0.174383	−	0.126697i	−0.0241825	−	0.0175696i
$53$	1.34954	+	4.15345i	0.185373	+	0.570520i	0.999955	−	0.00952922i	$-0.00303329\pi$
$53$	1.34954	+	4.15345i	0.185373	+	0.570520i	−0.814581	+	0.580049i	$0.803033\pi$
$54$	0.623865	+	1.92006i	0.0848973	+	0.261287i
$55$		0			0
$56$	−0.0482051	+	0.148360i	−0.00644168	+	0.0198254i
$57$	−0.724404			−0.0959497
$58$	−2.48827	+	7.65810i	−0.326726	+	1.00556i
$59$	3.97458	−	2.88770i	0.517446	−	0.375947i	−0.298195	−	0.954505i	$-0.596384\pi$
$59$	3.97458	−	2.88770i	0.517446	−	0.375947i	0.815641	+	0.578558i	$0.196384\pi$
$60$		0			0
$61$	−5.63428	−	4.09354i	−0.721396	−	0.524125i	0.165434	−	0.986221i	$-0.447097\pi$
$61$	−5.63428	−	4.09354i	−0.721396	−	0.524125i	−0.886830	+	0.462096i	$0.847097\pi$
$62$	−1.74212	+	1.26572i	−0.221249	+	0.160747i
$63$	0.824283	−	0.598877i	0.103850	−	0.0754514i
$64$	6.95331	+	5.05187i	0.869163	+	0.631484i
$65$		0			0
$66$	−7.77388	+	5.64805i	−0.956898	+	0.695227i
$67$	3.06544	−	9.43446i	0.374503	−	1.15260i	−0.569310	−	0.822123i	$-0.692790\pi$
$67$	3.06544	−	9.43446i	0.374503	−	1.15260i	0.943813	−	0.330480i	$-0.107210\pi$
$68$	12.1183			1.46955
$69$	2.80325	−	8.62753i	0.337472	−	1.03863i
$70$		0			0
$71$	−3.33323	−	10.2586i	−0.395582	−	1.21748i	−0.928507	−	0.371314i	$-0.878907\pi$
$71$	−3.33323	−	10.2586i	−0.395582	−	1.21748i	0.532925	−	0.846162i	$-0.321093\pi$
$72$	0.0473123	+	0.145612i	0.00557581	+	0.0171606i
$73$	6.98275	+	5.07326i	0.817269	+	0.593781i	0.915929	−	0.401341i	$-0.131456\pi$
$73$	6.98275	+	5.07326i	0.817269	+	0.593781i	−0.0986599	+	0.995121i	$0.531456\pi$
$74$	−8.12840			−0.944907
$75$		0			0
$76$	−1.50375			−0.172491
$77$	3.92327	+	2.85042i	0.447098	+	0.324836i
$78$	0.0647804	+	0.199374i	0.00733493	+	0.0225746i
$79$	0.767263	+	2.36139i	0.0863238	+	0.265677i	0.984896	−	0.173149i	$-0.0553943\pi$
$79$	0.767263	+	2.36139i	0.0863238	+	0.265677i	−0.898572	+	0.438826i	$0.855394\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	14.5556			1.60740
$83$	−1.31142	+	4.03614i	−0.143947	+	0.443024i	−0.996874	−	0.0790064i	$-0.974825\pi$
$83$	−1.31142	+	4.03614i	−0.143947	+	0.443024i	0.852927	+	0.522030i	$0.174825\pi$
$84$	1.71108	−	1.24317i	0.186694	−	0.135641i
$85$		0			0
$86$	14.0920	+	10.2384i	1.51958	+	1.10404i
$87$	3.22674	−	2.34436i	0.345943	−	0.251342i
$88$	−0.589550	+	0.428333i	−0.0628463	+	0.0456605i
$89$	14.8659	+	10.8007i	1.57578	+	1.14487i	0.921344	+	0.388749i	$0.127093\pi$
$89$	14.8659	+	10.8007i	1.57578	+	1.14487i	0.654434	+	0.756120i	$0.272907\pi$
$90$		0			0
$91$	0.0855912	−	0.0621857i	0.00897240	−	0.00651883i
$92$	5.81910	−	17.9093i	0.606683	−	1.86718i
$93$	1.06662			0.110604
$94$	5.11443	−	15.7406i	0.527513	−	1.62352i
$95$		0			0
$96$	−2.49187	−	7.66920i	−0.254326	−	0.782734i
$97$	−2.07003	−	6.37090i	−0.210180	−	0.646867i	−0.999461	−	0.0328349i	$-0.989546\pi$
$97$	−2.07003	−	6.37090i	−0.210180	−	0.646867i	0.789281	−	0.614032i	$-0.210454\pi$
$98$	9.73758	+	7.07477i	0.983644	+	0.714659i
$99$	4.75961			0.478359
$100$		0			0
$101$	5.66147			0.563337			0.281669	−	0.959512i	$-0.409112\pi$
$101$	5.66147			0.563337			0.281669	+	0.959512i	$0.409112\pi$
$102$	−9.53482	−	6.92745i	−0.944088	−	0.685920i
$103$	−0.183707	−	0.565393i	−0.0181012	−	0.0557098i	0.941598	−	0.336739i	$-0.109324\pi$
$103$	−0.183707	−	0.565393i	−0.0181012	−	0.0557098i	−0.959699	+	0.281030i	$0.909324\pi$
$104$	0.00491278	+	0.0151200i	0.000481737	+	0.00148263i
$105$		0			0
$106$	2.72454	−	8.38527i	0.264631	−	0.814450i
$107$	−1.38651			−0.134039			−0.0670193	−	0.997752i	$-0.521349\pi$
$107$	−1.38651			−0.134039			−0.0670193	+	0.997752i	$0.521349\pi$
$108$	0.641469	−	1.97424i	0.0617254	−	0.189971i
$109$	7.16528	−	5.20588i	0.686309	−	0.498633i	−0.189136	−	0.981951i	$-0.560569\pi$
$109$	7.16528	−	5.20588i	0.686309	−	0.498633i	0.875445	+	0.483318i	$0.160569\pi$
$110$		0			0
$111$	3.25727	+	2.36655i	0.309167	+	0.224623i
$112$	−3.16737	+	2.30123i	−0.299288	+	0.217446i
$113$	5.33173	−	3.87373i	0.501567	−	0.364410i	−0.308048	−	0.951371i	$-0.599676\pi$
$113$	5.33173	−	3.87373i	0.501567	−	0.364410i	0.809615	+	0.586961i	$0.199676\pi$
$114$	1.18317	+	0.859623i	0.110814	+	0.0805111i
$115$		0			0
$116$	6.69819	−	4.86652i	0.621911	−	0.451845i
$117$	0.0320874	−	0.0987550i	0.00296649	−	0.00912990i
$118$	−9.91841			−0.913064
$119$	−1.83801	+	5.65681i	−0.168490	+	0.518559i
$120$		0			0
$121$	3.60125	+	11.0835i	0.327387	+	1.00759i
$122$	4.34482	+	13.3720i	0.393361	+	1.21064i
$123$	−5.83282	−	4.23780i	−0.525928	−	0.382109i
$124$	2.21414			0.198836
$125$		0			0
$126$	−2.05697			−0.183249
$127$	−5.89890	−	4.28580i	−0.523443	−	0.380303i	0.294457	−	0.955665i	$-0.404861\pi$
$127$	−5.89890	−	4.28580i	−0.523443	−	0.380303i	−0.817899	+	0.575362i	$0.804861\pi$
$128$	−0.378226	−	1.16406i	−0.0334308	−	0.102889i
$129$	−2.66617	−	8.20563i	−0.234743	−	0.722465i
$130$		0			0
$131$	−2.95230	+	9.08626i	−0.257944	+	0.793870i	0.735291	+	0.677751i	$0.237045\pi$
$131$	−2.95230	+	9.08626i	−0.257944	+	0.793870i	−0.993235	+	0.116119i	$0.962955\pi$
$132$	9.88018			0.859959
$133$	0.228077	−	0.701950i	0.0197768	−	0.0608668i
$134$	−16.2023	+	11.7717i	−1.39967	+	1.01692i
$135$		0			0
$136$	−0.723096	−	0.525360i	−0.0620050	−	0.0450493i
$137$	−5.01578	+	3.64418i	−0.428527	+	0.311343i	−0.781060	−	0.624457i	$-0.785320\pi$
$137$	−5.01578	+	3.64418i	−0.428527	+	0.311343i	0.352533	+	0.935799i	$0.385320\pi$
$138$	−14.8165	+	10.7648i	−1.26127	+	0.916363i
$139$	0.733399	+	0.532846i	0.0622061	+	0.0451954i	0.618454	−	0.785821i	$-0.287759\pi$
$139$	0.733399	+	0.532846i	0.0622061	+	0.0451954i	−0.556248	+	0.831017i	$0.687759\pi$
$140$		0			0
$141$	−6.63230	+	4.81865i	−0.558540	+	0.405803i
$142$	−6.72937	+	20.7109i	−0.564716	+	1.73802i
$143$	0.494225			0.0413291
$144$	−1.18742	+	3.65450i	−0.0989517	+	0.304542i
$145$		0			0
$146$	−5.38468	−	16.5723i	−0.445639	−	1.37154i
$147$	−1.84233	−	5.67011i	−0.151953	−	0.467663i
$148$	6.76157	+	4.91257i	0.555798	+	0.403811i
$149$	−4.89808			−0.401267			−0.200633	−	0.979666i	$-0.564300\pi$
$149$	−4.89808			−0.401267			−0.200633	+	0.979666i	$0.564300\pi$
$150$		0			0
$151$	−10.2626			−0.835161			−0.417581	−	0.908640i	$-0.637122\pi$
$151$	−10.2626			−0.835161			−0.417581	+	0.908640i	$0.637122\pi$
$152$	0.0897285	+	0.0651916i	0.00727794	+	0.00528773i
$153$	1.80397	+	5.55204i	0.145842	+	0.448856i
$154$	−3.02539	−	9.31119i	−0.243793	−	0.750317i
$155$		0			0
$156$	0.0666083	−	0.204999i	0.00533293	−	0.0164131i
$157$	8.89537			0.709928			0.354964	−	0.934880i	$-0.384493\pi$
$157$	8.89537			0.709928			0.354964	+	0.934880i	$0.384493\pi$
$158$	1.54900	−	4.76734i	0.123232	−	0.379269i
$159$	−3.53313	+	2.56697i	−0.280196	+	0.203574i
$160$		0			0
$161$	7.47750	+	5.43272i	0.589310	+	0.428159i
$162$	−1.63330	+	1.18666i	−0.128324	+	0.0932330i
$163$	9.52946	−	6.92356i	0.746405	−	0.542295i	−0.148305	−	0.988942i	$-0.547382\pi$
$163$	9.52946	−	6.92356i	0.746405	−	0.542295i	0.894710	+	0.446647i	$0.147382\pi$
$164$	−12.1080	−	8.79697i	−0.945476	−	0.686928i
$165$		0			0
$166$	6.93148	−	5.03602i	0.537987	−	0.390871i
$167$	−5.36954	+	16.5258i	−0.415508	+	1.27880i	0.496288	+	0.868158i	$0.334696\pi$
$167$	−5.36954	+	16.5258i	−0.415508	+	1.27880i	−0.911796	+	0.410644i	$0.865304\pi$
$168$	−0.155995			−0.0120353
$169$	−4.01389	+	12.3535i	−0.308761	+	0.950268i
$170$		0			0
$171$	−0.223853	−	0.688949i	−0.0171185	−	0.0526853i
$172$	−5.53454	−	17.0336i	−0.422004	−	1.29880i
$173$	−10.4845	−	7.61744i	−0.797123	−	0.579144i	0.112946	−	0.993601i	$-0.463971\pi$
$173$	−10.4845	−	7.61744i	−0.797123	−	0.579144i	−0.910069	+	0.414458i	$0.863971\pi$
$174$	−8.05221			−0.610436
$175$		0			0
$176$	−18.2892			−1.37860
$177$	3.97458	+	2.88770i	0.298748	+	0.217053i
$178$	−11.4636	−	35.2815i	−0.859237	−	2.64446i
$179$	0.339600	+	1.04518i	0.0253829	+	0.0781206i	0.962946	−	0.269696i	$-0.0869232\pi$
$179$	0.339600	+	1.04518i	0.0253829	+	0.0781206i	−0.937563	+	0.347817i	$0.886923\pi$
$180$		0			0
$181$	−4.62898	+	14.2465i	−0.344069	+	1.05894i	0.618011	+	0.786170i	$0.287939\pi$
$181$	−4.62898	+	14.2465i	−0.344069	+	1.05894i	−0.962080	+	0.272767i	$0.912061\pi$
$182$	−0.213590			−0.0158323
$183$	2.15210	−	6.62349i	0.159088	−	0.489623i
$184$	−1.12365	+	0.816376i	−0.0828363	+	0.0601841i
$185$		0			0
$186$	−1.74212	−	1.26572i	−0.127738	−	0.0928073i
$187$	−22.4789	+	16.3319i	−1.64382	+	1.19431i
$188$	−13.7676	+	10.0027i	−1.00410	+	0.729524i
$189$	0.824283	+	0.598877i	0.0599578	+	0.0435619i
$190$		0			0
$191$	10.3072	−	7.48861i	0.745802	−	0.541857i	−0.148721	−	0.988879i	$-0.547516\pi$
$191$	10.3072	−	7.48861i	0.745802	−	0.541857i	0.894523	+	0.447022i	$0.147516\pi$
$192$	−2.65593	+	8.17410i	−0.191675	+	0.589915i
$193$	4.38386			0.315557			0.157779	−	0.987475i	$-0.449567\pi$
$193$	4.38386			0.315557			0.157779	+	0.987475i	$0.449567\pi$
$194$	−4.17913	+	12.8620i	−0.300044	+	0.923440i
$195$		0			0
$196$	−3.82438	−	11.7702i	−0.273170	−	0.840730i
$197$	−0.995545	−	3.06397i	−0.0709296	−	0.218299i	0.909308	−	0.416125i	$-0.136612\pi$
$197$	−0.995545	−	3.06397i	−0.0709296	−	0.218299i	−0.980237	+	0.197826i	$0.936612\pi$
$198$	−7.77388	−	5.64805i	−0.552465	−	0.401390i
$199$	−2.70518			−0.191765			−0.0958825	−	0.995393i	$-0.530567\pi$
$199$	−2.70518			−0.191765			−0.0958825	+	0.995393i	$0.530567\pi$
$200$		0			0
$201$	9.91998			0.699701
$202$	−9.24688	−	6.71825i	−0.650608	−	0.472694i
$203$	1.25576	+	3.86484i	0.0881373	+	0.271259i
$204$	3.74475	+	11.5251i	0.262185	+	0.806921i
$205$		0			0
$206$	−0.370881	+	1.14145i	−0.0258405	+	0.0795289i
$207$	9.07152			0.630514
$208$	−0.123298	+	0.379473i	−0.00854920	+	0.0263117i
$209$	2.78940	−	2.02661i	0.192947	−	0.140184i
$210$		0			0
$211$	−21.3932	−	15.5431i	−1.47277	−	1.07003i	−0.979799	−	0.199983i	$-0.935911\pi$
$211$	−21.3932	−	15.5431i	−1.47277	−	1.07003i	−0.492970	−	0.870046i	$-0.664089\pi$
$212$	−7.33421	+	5.32862i	−0.503716	+	0.365971i
$213$	8.72652	−	6.34019i	0.597931	−	0.434423i
$214$	2.26458	+	1.64531i	0.154804	+	0.112471i
$215$		0			0
$216$	−0.123865	+	0.0899934i	−0.00842796	+	0.00612327i
$217$	−0.335825	+	1.03356i	−0.0227973	+	0.0701628i
$218$	−17.8807			−1.21103
$219$	−2.66717	+	8.20871i	−0.180231	+	0.554694i
$220$		0			0
$221$	0.187319	+	0.576508i	0.0126004	+	0.0387802i
$222$	−2.51181	−	7.73057i	−0.168582	−	0.518842i
$223$	−6.49839	−	4.72136i	−0.435164	−	0.316165i	0.348546	−	0.937292i	$-0.386675\pi$
$223$	−6.49839	−	4.72136i	−0.435164	−	0.316165i	−0.783711	+	0.621126i	$0.786675\pi$
$224$	8.21604			0.548957
$225$		0			0
$226$	−13.3051			−0.885044
$227$	13.3145	+	9.67356i	0.883715	+	0.642056i	0.934232	−	0.356667i	$-0.116087\pi$
$227$	13.3145	+	9.67356i	0.883715	+	0.642056i	−0.0505168	+	0.998723i	$0.516087\pi$
$228$	−0.464683	−	1.43015i	−0.0307744	−	0.0947138i
$229$	0.126476	+	0.389253i	0.00835776	+	0.0257226i	0.955148	−	0.296127i	$-0.0956953\pi$
$229$	0.126476	+	0.389253i	0.00835776	+	0.0257226i	−0.946791	+	0.321850i	$0.895695\pi$
$230$		0			0
$231$	−1.49856	+	4.61208i	−0.0985977	+	0.303453i
$232$	−0.610658			−0.0400917
$233$	5.70571	−	17.5604i	0.373794	−	1.15042i	−0.570495	−	0.821301i	$-0.693249\pi$
$233$	5.70571	−	17.5604i	0.373794	−	1.15042i	0.944289	−	0.329118i	$-0.106751\pi$
$234$	−0.169597	+	0.123220i	−0.0110869	+	0.00805512i
$235$		0			0
$236$	8.25058	+	5.99440i	0.537067	+	0.390202i
$237$	−2.00872	+	1.45942i	−0.130480	+	0.0947995i
$238$	9.71475	−	7.05818i	0.629714	−	0.457514i
$239$	3.73509	+	2.71370i	0.241603	+	0.175535i	0.701997	−	0.712180i	$-0.252292\pi$
$239$	3.73509	+	2.71370i	0.241603	+	0.175535i	−0.460394	+	0.887715i	$0.652292\pi$
$240$		0			0
$241$	23.6251	−	17.1646i	1.52183	−	1.10567i	0.561253	−	0.827644i	$-0.310319\pi$
$241$	23.6251	−	17.1646i	1.52183	−	1.10567i	0.960573	−	0.278028i	$-0.0896807\pi$
$242$	7.27047	−	22.3762i	0.467363	−	1.43840i
$243$	1.00000			0.0641500
$244$	4.46742	−	13.7493i	0.285997	−	0.880208i
$245$		0			0
$246$	4.49792	+	13.8432i	0.286777	+	0.882609i
$247$	−0.0232443	−	0.0715385i	−0.00147900	−	0.00455189i
$248$	−0.132118	−	0.0959892i	−0.00838949	−	0.00609532i
$249$	−4.24385			−0.268943
$250$		0			0
$251$	0.389664			0.0245954			0.0122977	−	0.999924i	$-0.496085\pi$
$251$	0.389664			0.0245954			0.0122977	+	0.999924i	$0.496085\pi$
$252$	1.71108	+	1.24317i	0.107788	+	0.0783124i
$253$	13.3424	+	41.0637i	0.838829	+	2.58165i
$254$	4.54888	+	14.0000i	0.285422	+	0.878438i
$255$		0			0
$256$	4.54826	−	13.9981i	0.284266	−	0.874882i
$257$	−8.03324			−0.501100			−0.250550	−	0.968104i	$-0.580611\pi$
$257$	−8.03324			−0.501100			−0.250550	+	0.968104i	$0.580611\pi$
$258$	−5.38265	+	16.5661i	−0.335109	+	1.03136i
$259$	−3.31874	+	2.41121i	−0.206216	+	0.149825i
$260$		0			0
$261$	3.22674	+	2.34436i	0.199730	+	0.145113i
$262$	15.6043	−	11.3372i	0.964038	−	0.700415i
$263$	−19.5888	+	14.2321i	−1.20790	+	0.877590i	−0.995038	−	0.0994928i	$-0.968278\pi$
$263$	−19.5888	+	14.2321i	−1.20790	+	0.877590i	−0.212860	+	0.977083i	$0.568278\pi$
$264$	−0.589550	−	0.428333i	−0.0362843	−	0.0263621i
$265$		0			0
$266$	−1.20550	+	0.875844i	−0.0739137	+	0.0537015i
$267$	−5.67825	+	17.4759i	−0.347503	+	1.06950i
$268$	20.5923			1.25787
$269$	8.15998	−	25.1138i	0.497523	−	1.53122i	−0.315465	−	0.948937i	$-0.602161\pi$
$269$	8.15998	−	25.1138i	0.497523	−	1.53122i	0.812988	−	0.582281i	$-0.197839\pi$
$270$		0			0
$271$	−3.21648	−	9.89932i	−0.195387	−	0.601341i	−0.999972	−	0.00750242i	$-0.997612\pi$
$271$	−3.21648	−	9.89932i	−0.195387	−	0.601341i	0.804584	−	0.593838i	$-0.202388\pi$
$272$	−6.93188	−	21.3341i	−0.420307	−	1.29357i
$273$	0.0855912	+	0.0621857i	0.00518022	+	0.00376365i
$274$	12.5167			0.756160
$275$		0			0
$276$	18.8310			1.13349
$277$	−19.8376	−	14.4129i	−1.19193	−	0.865987i	−0.198462	−	0.980109i	$-0.563595\pi$
$277$	−19.8376	−	14.4129i	−1.19193	−	0.865987i	−0.993467	+	0.114122i	$0.963595\pi$
$278$	−0.565553	−	1.74059i	−0.0339196	−	0.104394i
$279$	0.329605	+	1.01442i	0.0197329	+	0.0607318i
$280$		0			0
$281$	−4.45690	+	13.7169i	−0.265876	+	0.818283i	0.725614	+	0.688102i	$0.241556\pi$
$281$	−4.45690	+	13.7169i	−0.265876	+	0.818283i	−0.991490	+	0.130181i	$0.958444\pi$
$282$	16.5506			0.985576
$283$	−0.664155	+	2.04406i	−0.0394799	+	0.121507i	−0.968854	−	0.247633i	$-0.920347\pi$
$283$	−0.664155	+	2.04406i	−0.0394799	+	0.121507i	0.929374	+	0.369139i	$0.120347\pi$
$284$	18.1148	−	13.1612i	1.07492	−	0.780974i
$285$		0			0
$286$	−0.807217	−	0.586478i	−0.0477317	−	0.0346791i
$287$	5.94289	−	4.31776i	0.350798	−	0.254870i
$288$	6.52381	−	4.73982i	0.384419	−	0.279297i
$289$	−13.8176	−	10.0391i	−0.812800	−	0.590534i
$290$		0			0
$291$	5.41941	−	3.93743i	0.317692	−	0.230816i
$292$	−5.53662	+	17.0400i	−0.324006	+	0.997188i
$293$	9.02970			0.527521			0.263760	−	0.964588i	$-0.415037\pi$
$293$	9.02970			0.527521			0.263760	+	0.964588i	$0.415037\pi$
$294$	−3.71942	+	11.4472i	−0.216921	+	0.667615i
$295$		0			0
$296$	−0.190489	−	0.586266i	−0.0110720	−	0.0340760i
$297$	1.47080	+	4.52666i	0.0853445	+	0.262663i
$298$	8.00004	+	5.81237i	0.463430	+	0.336702i
$299$	0.941960			0.0544750
$300$		0			0
$301$	8.79072			0.506689
$302$	16.7620	+	12.1783i	0.964543	+	0.700781i
$303$	1.74949	+	5.38438i	0.100506	+	0.309324i
$304$	0.860173	+	2.64734i	0.0493343	+	0.151835i
$305$		0			0
$306$	3.64198	−	11.2089i	0.208198	−	0.640768i
$307$	−5.03454			−0.287336			−0.143668	−	0.989626i	$-0.545890\pi$
$307$	−5.03454			−0.287336			−0.143668	+	0.989626i	$0.545890\pi$
$308$	−3.11076	+	9.57393i	−0.177252	+	0.545525i
$309$	0.480952	−	0.349432i	0.0273604	−	0.0198785i
$310$		0			0
$311$	3.95737	+	2.87520i	0.224402	+	0.163038i	0.694306	−	0.719680i	$-0.255711\pi$
$311$	3.95737	+	2.87520i	0.224402	+	0.163038i	−0.469904	+	0.882718i	$0.655711\pi$
$312$	−0.0128618	+	0.00934465i	−0.000728157	+	0.000529037i
$313$	−2.56686	+	1.86494i	−0.145088	+	0.105412i	−0.657961	−	0.753052i	$-0.728581\pi$
$313$	−2.56686	+	1.86494i	−0.145088	+	0.105412i	0.512874	+	0.858464i	$0.328581\pi$
$314$	−14.5288	−	10.5558i	−0.819908	−	0.595698i
$315$		0			0
$316$	−4.16978	+	3.02952i	−0.234568	+	0.170424i
$317$	6.17888	−	19.0166i	0.347041	−	1.06808i	−0.613442	−	0.789740i	$-0.710215\pi$
$317$	6.17888	−	19.0166i	0.347041	−	1.06808i	0.960482	−	0.278341i	$-0.0897846\pi$
$318$	8.81680			0.494422
$319$	−5.86625	+	18.0545i	−0.328447	+	1.01086i
$320$		0			0
$321$	−0.428454	−	1.31865i	−0.0239140	−	0.0735996i
$322$	−5.76620	−	17.7465i	−0.321338	−	0.988976i
$323$	3.42125	+	2.48569i	0.190364	+	0.138307i
$324$	2.07584			0.115324
$325$		0			0
$326$	−23.7804			−1.31707
$327$	7.16528	+	5.20588i	0.396241	+	0.287886i
$328$	0.341111	+	1.04983i	0.0188347	+	0.0579672i
$329$	−2.58112	−	7.94386i	−0.142302	−	0.437959i
$330$		0			0
$331$	1.85943	−	5.72274i	0.102204	−	0.314550i	−0.886860	−	0.462037i	$-0.847119\pi$
$331$	1.85943	−	5.72274i	0.102204	−	0.314550i	0.989064	+	0.147487i	$0.0471186\pi$
$332$	−8.80954			−0.483486
$333$	−1.24417	+	3.82916i	−0.0681800	+	0.209836i
$334$	28.3806	−	20.6197i	1.55292	−	1.12826i
$335$		0			0
$336$	−3.16737	−	2.30123i	−0.172794	−	0.125542i
$337$	18.4566	−	13.4095i	1.00540	−	0.730463i	0.0421575	−	0.999111i	$-0.486577\pi$
$337$	18.4566	−	13.4095i	1.00540	−	0.730463i	0.963238	+	0.268648i	$0.0865769\pi$
$338$	21.2153	−	15.4138i	1.15396	−	0.838401i
$339$	5.33173	+	3.87373i	0.289580	+	0.210392i
$340$		0			0
$341$	−4.10715	+	2.98402i	−0.222415	+	0.161594i
$342$	−0.451931	+	1.39090i	−0.0244376	+	0.0752112i
$343$	13.2065			0.713084
$344$	−0.408206	+	1.25633i	−0.0220090	+	0.0677368i
$345$		0			0
$346$	8.08502	+	24.8831i	0.434654	+	1.33773i
$347$	−3.02549	−	9.31149i	−0.162417	−	0.499867i	0.836420	−	0.548089i	$-0.184644\pi$
$347$	−3.02549	−	9.31149i	−0.162417	−	0.499867i	−0.998837	+	0.0482222i	$0.984644\pi$
$348$	6.69819	+	4.86652i	0.359061	+	0.260873i
$349$	−1.28648			−0.0688639			−0.0344320	−	0.999407i	$-0.510962\pi$
$349$	−1.28648			−0.0688639			−0.0344320	+	0.999407i	$0.510962\pi$
$350$		0			0
$351$	0.103837			0.00554242
$352$	31.0508	+	22.5597i	1.65501	+	1.20244i
$353$	−0.359765	−	1.10724i	−0.0191484	−	0.0589326i	0.941026	−	0.338335i	$-0.109864\pi$
$353$	−0.359765	−	1.10724i	−0.0191484	−	0.0589326i	−0.960174	+	0.279402i	$0.909864\pi$
$354$	−3.06496	−	9.43297i	−0.162901	−	0.501357i
$355$		0			0
$356$	−11.7871	+	36.2770i	−0.624716	+	1.92268i
$357$	−5.94793			−0.314798
$358$	0.685609	−	2.11009i	0.0362356	−	0.111522i
$359$	−15.4121	+	11.1975i	−0.813418	+	0.590983i	−0.914820	−	0.403863i	$-0.867667\pi$
$359$	−15.4121	+	11.1975i	−0.813418	+	0.590983i	0.101402	+	0.994846i	$0.467667\pi$
$360$		0			0
$361$	14.9468	+	10.8595i	0.786673	+	0.571551i
$362$	24.4663	−	17.7758i	1.28592	−	0.934277i
$363$	−9.42821	+	6.84999i	−0.494853	+	0.359531i
$364$	0.177673	+	0.129087i	0.00931262	+	0.00676602i
$365$		0			0
$366$	−11.3749	+	8.26433i	−0.594575	+	0.431984i
$367$	−5.18204	+	15.9487i	−0.270500	+	0.832514i	0.719875	+	0.694104i	$0.244199\pi$
$367$	−5.18204	+	15.9487i	−0.270500	+	0.832514i	−0.990375	+	0.138410i	$0.955801\pi$
$368$	−34.8580			−1.81710
$369$	2.22794	−	6.85690i	0.115982	−	0.356956i
$370$		0			0
$371$	−1.37500	−	4.23183i	−0.0713866	−	0.219705i
$372$	0.684207	+	2.10577i	0.0354745	+	0.109179i
$373$	−13.7954	−	10.0229i	−0.714297	−	0.518967i	0.170260	−	0.985399i	$-0.445539\pi$
$373$	−13.7954	−	10.0229i	−0.714297	−	0.518967i	−0.884557	+	0.466432i	$0.845539\pi$
$374$	56.0953			2.90062
$375$		0			0
$376$	1.25516			0.0647298
$377$	0.335056	+	0.243432i	0.0172562	+	0.0125374i
$378$	−0.635638	−	1.95629i	−0.0326937	−	0.100621i
$379$	0.514857	+	1.58457i	0.0264464	+	0.0813938i	0.963409	−	0.268037i	$-0.0863750\pi$
$379$	0.514857	+	1.58457i	0.0264464	+	0.0813938i	−0.936962	+	0.349431i	$0.886375\pi$
$380$		0			0
$381$	2.25318	−	6.93457i	0.115434	−	0.355269i
$382$	−25.7212			−1.31601
$383$	−0.943618	+	2.90416i	−0.0482166	+	0.148396i	−0.972266	−	0.233877i	$-0.924859\pi$
$383$	−0.943618	+	2.90416i	−0.0482166	+	0.148396i	0.924049	+	0.382273i	$0.124859\pi$
$384$	0.990210	−	0.719429i	0.0505314	−	0.0367132i
$385$		0			0
$386$	−7.16016	−	5.20216i	−0.364443	−	0.264783i
$387$	6.98013	−	5.07136i	0.354820	−	0.257792i
$388$	11.2498	−	8.17347i	0.571123	−	0.414945i
$389$	−22.8730	−	16.6182i	−1.15971	−	0.842575i	−0.169965	−	0.985450i	$-0.554365\pi$
$389$	−22.8730	−	16.6182i	−1.15971	−	0.842575i	−0.989741	+	0.142875i	$0.954365\pi$
$390$		0			0
$391$	−42.8434	+	31.1276i	−2.16669	+	1.57419i
$392$	−0.282071	+	0.868127i	−0.0142468	+	0.0438470i
$393$	−9.55386			−0.481928
$394$	−2.00988	+	6.18576i	−0.101256	+	0.311634i
$395$		0			0
$396$	3.05314	+	9.39661i	0.153426	+	0.472197i
$397$	6.32814	+	19.4760i	0.317600	+	0.977472i	0.974671	+	0.223644i	$0.0717952\pi$
$397$	6.32814	+	19.4760i	0.317600	+	0.977472i	−0.657071	+	0.753829i	$0.728205\pi$
$398$	4.41837	+	3.21013i	0.221473	+	0.160909i
$399$	0.738074			0.0369499
$400$		0			0
$401$	25.5952			1.27816			0.639081	−	0.769139i	$-0.279315\pi$
$401$	25.5952			1.27816			0.639081	+	0.769139i	$0.279315\pi$
$402$	−16.2023	−	11.7717i	−0.808097	−	0.587117i
$403$	0.0342253	+	0.105335i	0.00170488	+	0.00524709i
$404$	3.63166	+	11.1771i	0.180682	+	0.556081i
$405$		0			0
$406$	2.53522	−	7.80262i	0.125821	−	0.387237i
$407$	−19.1632			−0.949885
$408$	0.276198	−	0.850050i	0.0136738	−	0.0420838i
$409$	9.74072	−	7.07705i	0.481648	−	0.349938i	−0.320316	−	0.947311i	$-0.603789\pi$
$409$	9.74072	−	7.07705i	0.481648	−	0.349938i	0.801963	+	0.597373i	$0.203789\pi$
$410$		0			0
$411$	−5.01578	−	3.64418i	−0.247410	−	0.179754i
$412$	0.998377	−	0.725364i	0.0491865	−	0.0357361i
$413$	−4.04958	+	2.94219i	−0.199267	+	0.144776i
$414$	−14.8165	−	10.7648i	−0.728192	−	0.529062i
$415$		0			0
$416$	0.677414	−	0.492170i	0.0332129	−	0.0241306i
$417$	−0.280134	+	0.862162i	−0.0137182	+	0.0422203i
$418$	−6.96083			−0.340465
$419$	−10.6934	+	32.9108i	−0.522405	+	1.60780i	0.246985	+	0.969019i	$0.420560\pi$
$419$	−10.6934	+	32.9108i	−0.522405	+	1.60780i	−0.769390	+	0.638779i	$0.779440\pi$
$420$		0			0
$421$	−4.62056	−	14.2206i	−0.225193	−	0.693071i	−0.998272	−	0.0587622i	$-0.981285\pi$
$421$	−4.62056	−	14.2206i	−0.225193	−	0.693071i	0.773079	−	0.634309i	$-0.218715\pi$
$422$	16.4972	+	50.7730i	0.803069	+	2.47159i
$423$	−6.63230	−	4.81865i	−0.322473	−	0.234291i
$424$	0.668643			0.0324722
$425$		0			0
$426$	−21.7767			−1.05508
$427$	5.74060	+	4.17079i	0.277807	+	0.201839i
$428$	−0.889401	−	2.73729i	−0.0429908	−	0.132312i
$429$	0.152724	+	0.470035i	0.00737357	+	0.0226935i
$430$		0			0
$431$	1.48670	−	4.57560i	0.0716119	−	0.220399i	−0.908845	−	0.417135i	$-0.863034\pi$
$431$	1.48670	−	4.57560i	0.0716119	−	0.220399i	0.980456	+	0.196736i	$0.0630342\pi$
$432$	−3.84257			−0.184876
$433$	−3.19632	+	9.83725i	−0.153605	+	0.472748i	−0.998017	−	0.0629466i	$-0.979950\pi$
$433$	−3.19632	+	9.83725i	−0.153605	+	0.472748i	0.844412	+	0.535695i	$0.179950\pi$
$434$	1.77499	−	1.28961i	0.0852024	−	0.0619032i
$435$		0			0
$436$	14.8739	+	10.8066i	0.712333	+	0.517540i
$437$	5.31641	−	3.86260i	0.254318	−	0.184773i
$438$	14.0973	−	10.2423i	0.673593	−	0.489394i
$439$	−24.8886	−	18.0826i	−1.18787	−	0.863037i	−0.194831	−	0.980837i	$-0.562416\pi$
$439$	−24.8886	−	18.0826i	−1.18787	−	0.863037i	−0.993037	+	0.117800i	$0.962416\pi$
$440$		0			0
$441$	4.82328	−	3.50432i	0.229680	−	0.166872i
$442$	0.378173	−	1.16390i	0.0179878	−	0.0553609i
$443$	17.7545			0.843543			0.421772	−	0.906702i	$-0.361408\pi$
$443$	17.7545			0.843543			0.421772	+	0.906702i	$0.361408\pi$
$444$	−2.58269	+	7.94870i	−0.122569	+	0.377229i
$445$		0			0
$446$	5.01117	+	15.4228i	0.237286	+	0.730290i
$447$	−1.51359	−	4.65836i	−0.0715904	−	0.220333i
$448$	−7.08452	−	5.14720i	−0.334712	−	0.243183i
$449$	−37.2184			−1.75645			−0.878223	−	0.478251i	$-0.841271\pi$
$449$	−37.2184			−1.75645			−0.878223	+	0.478251i	$0.841271\pi$
$450$		0			0
$451$	34.3157			1.61586
$452$	11.0678	+	8.04124i	0.520586	+	0.378228i
$453$	−3.17133	−	9.76034i	−0.149002	−	0.458581i
$454$	−10.2673	−	31.5996i	−0.481870	−	1.48304i
$455$		0			0
$456$	−0.0342732	+	0.105482i	−0.00160499	+	0.00493966i
$457$	27.6987			1.29569			0.647846	−	0.761772i	$-0.275670\pi$
$457$	27.6987			1.29569			0.647846	+	0.761772i	$0.275670\pi$
$458$	0.255338	−	0.785851i	0.0119312	−	0.0367204i
$459$	−4.72285	+	3.43135i	−0.220444	+	0.160162i
$460$		0			0
$461$	−7.94246	−	5.77053i	−0.369917	−	0.268760i	0.387259	−	0.921971i	$-0.373422\pi$
$461$	−7.94246	−	5.77053i	−0.369917	−	0.268760i	−0.757177	+	0.653210i	$0.773422\pi$
$462$	7.92057	−	5.75463i	0.368498	−	0.267730i
$463$	−3.01546	+	2.19086i	−0.140140	+	0.101818i	−0.655647	−	0.755068i	$-0.727604\pi$
$463$	−3.01546	+	2.19086i	−0.140140	+	0.101818i	0.515506	+	0.856886i	$0.327604\pi$
$464$	−12.3990	−	9.00840i	−0.575609	−	0.418204i
$465$		0			0
$466$	−30.1574	+	21.9106i	−1.39701	+	1.01499i
$467$	2.19379	−	6.75179i	0.101516	−	0.312436i	−0.887381	−	0.461038i	$-0.847477\pi$
$467$	2.19379	−	6.75179i	0.101516	−	0.312436i	0.988897	+	0.148602i	$0.0474773\pi$
$468$	0.215549			0.00996376
$469$	−3.12329	+	9.61249i	−0.144220	+	0.443864i
$470$		0			0
$471$	2.74882	+	8.46000i	0.126659	+	0.389816i
$472$	−0.232438	−	0.715372i	−0.0106988	−	0.0329277i
$473$	33.2227	+	24.1377i	1.52758	+	1.10985i
$474$	5.01268			0.230240
$475$		0			0
$476$	−12.3469			−0.565920
$477$	−3.53313	−	2.56697i	−0.161771	−	0.117534i
$478$	−2.88027	−	8.86457i	−0.131741	−	0.405456i
$479$	−8.79003	−	27.0529i	−0.401627	−	1.23608i	−0.923679	−	0.383166i	$-0.874834\pi$
$479$	−8.79003	−	27.0529i	−0.401627	−	1.23608i	0.522053	−	0.852913i	$-0.325166\pi$
$480$		0			0
$481$	−0.129191	+	0.397609i	−0.00589060	+	0.0181294i
$482$	−58.9555			−2.68535
$483$	−2.85615	+	8.79033i	−0.129959	+	0.399974i
$484$	−19.5714	+	14.2195i	−0.889610	+	0.646340i
$485$		0			0
$486$	−1.63330	−	1.18666i	−0.0740880	−	0.0538281i
$487$	−11.9236	+	8.66301i	−0.540310	+	0.392558i	−0.824200	−	0.566298i	$-0.808375\pi$
$487$	−11.9236	+	8.66301i	−0.540310	+	0.392558i	0.283890	+	0.958857i	$0.408375\pi$
$488$	−0.862641	+	0.626746i	−0.0390499	+	0.0283714i
$489$	9.52946	+	6.92356i	0.430937	+	0.313094i
$490$		0			0
$491$	22.9772	−	16.6939i	1.03695	−	0.753387i	0.0672603	−	0.997735i	$-0.478574\pi$
$491$	22.9772	−	16.6939i	1.03695	−	0.753387i	0.969687	+	0.244349i	$0.0785742\pi$
$492$	4.62484	−	14.2338i	0.208504	−	0.641709i
$493$	−23.2838			−1.04865
$494$	−0.0469272	+	0.144427i	−0.00211135	+	0.00649808i
$495$		0			0
$496$	−1.26653	−	3.89799i	−0.0568690	−	0.175025i
$497$	3.39613	+	10.4522i	0.152337	+	0.468846i
$498$	6.93148	+	5.03602i	0.310607	+	0.225669i
$499$	26.3842			1.18112			0.590559	−	0.806995i	$-0.298907\pi$
$499$	26.3842			1.18112			0.590559	+	0.806995i	$0.298907\pi$
$500$		0			0
$501$	−17.3762			−0.776312
$502$	−0.636439	−	0.462400i	−0.0284057	−	0.0206379i
$503$	−5.14796	−	15.8438i	−0.229536	−	0.706440i	−0.997799	−	0.0663060i	$-0.978879\pi$
$503$	−5.14796	−	15.8438i	−0.229536	−	0.706440i	0.768263	−	0.640134i	$-0.221121\pi$
$504$	−0.0482051	−	0.148360i	−0.00214723	−	0.00660848i
$505$		0			0
$506$	26.9366	−	82.9022i	1.19748	−	3.68545i
$507$	−12.9892			−0.576871
$508$	4.67723	−	14.3950i	0.207519	−	0.638677i
$509$	25.7073	−	18.6774i	1.13946	−	0.827863i	0.152413	−	0.988317i	$-0.451296\pi$
$509$	25.7073	−	18.6774i	1.13946	−	0.827863i	0.987043	+	0.160454i	$0.0512957\pi$
$510$		0			0
$511$	−7.11452	−	5.16900i	−0.314728	−	0.228663i
$512$	−26.0201	+	18.9047i	−1.14994	+	0.835479i
$513$	0.586055	−	0.425794i	0.0258750	−	0.0187993i
$514$	13.1207	+	9.53274i	0.578729	+	0.420471i
$515$		0			0
$516$	14.4896	−	10.5273i	0.637869	−	0.463439i
$517$	12.0576	−	37.1094i	0.530292	−	1.63207i
$518$	8.28179			0.363881
$519$	4.00473	−	12.3253i	0.175788	−	0.541020i
$520$		0			0
$521$	−0.183050	−	0.563371i	−0.00801958	−	0.0246817i	0.946967	−	0.321332i	$-0.104130\pi$
$521$	−0.183050	−	0.563371i	−0.00801958	−	0.0246817i	−0.954986	+	0.296650i	$0.904130\pi$
$522$	−2.48827	−	7.65810i	−0.108909	−	0.335186i
$523$	−13.9392	−	10.1274i	−0.609518	−	0.442840i	0.239727	−	0.970840i	$-0.422942\pi$
$523$	−13.9392	−	10.1274i	−0.609518	−	0.442840i	−0.849244	+	0.528000i	$0.822942\pi$
$524$	−19.8323			−0.866376
$525$		0			0
$526$	48.8832			2.13141
$527$	−5.03751	−	3.65997i	−0.219437	−	0.159431i
$528$	−5.65166	−	17.3940i	−0.245957	−	0.756978i
$529$	18.3224	+	56.3904i	0.796625	+	2.45176i
$530$		0			0
$531$	−1.51815	+	4.67240i	−0.0658823	+	0.202765i
$532$	1.53212			0.0664259
$533$	0.231343	−	0.712001i	0.0100206	−	0.0308402i
$534$	30.0122	−	21.8052i	1.29876	−	0.943601i
$535$		0			0
$536$	−1.22874	−	0.892732i	−0.0530735	−	0.0385602i
$537$	−0.889086	+	0.645959i	−0.0383669	+	0.0278752i
$538$	−43.1293	+	31.3353i	−1.85944	+	1.35096i
$539$	22.9569	+	16.6792i	0.988826	+	0.718424i
$540$		0			0
$541$	−11.9726	+	8.69863i	−0.514744	+	0.373983i	−0.814620	−	0.579995i	$-0.803055\pi$
$541$	−11.9726	+	8.69863i	−0.514744	+	0.373983i	0.299876	+	0.953978i	$0.403055\pi$
$542$	−6.49366	+	19.9854i	−0.278927	+	0.858448i
$543$	−14.9797			−0.642840
$544$	−14.5470	+	44.7710i	−0.623696	+	1.91954i
$545$		0			0
$546$	−0.0660028	−	0.203136i	−0.00282466	−	0.00869341i
$547$	−2.01110	−	6.18953i	−0.0859884	−	0.264645i	0.898812	−	0.438334i	$-0.144431\pi$
$547$	−2.01110	−	6.18953i	−0.0859884	−	0.264645i	−0.984801	+	0.173689i	$0.944431\pi$
$548$	−10.4119	−	7.56472i	−0.444776	−	0.323149i
$549$	6.96435			0.297231
$550$		0			0
$551$	2.88927			0.123087
$552$	−1.12365	−	0.816376i	−0.0478255	−	0.0347473i
$553$	−0.781741	−	2.40595i	−0.0332430	−	0.102311i
$554$	15.2976	+	47.0812i	0.649933	+	2.00029i
$555$		0			0
$556$	−0.581512	+	1.78971i	−0.0246616	+	0.0759006i
$557$	6.67224			0.282712			0.141356	−	0.989959i	$-0.454854\pi$
$557$	6.67224			0.282712			0.141356	+	0.989959i	$0.454854\pi$
$558$	0.665430	−	2.04798i	0.0281699	−	0.0866981i
$559$	0.724796	−	0.526595i	0.0306556	−	0.0222726i
$560$		0			0
$561$	−22.4789	−	16.3319i	−0.949061	−	0.689534i
$562$	23.5568	−	17.1150i	0.993684	−	0.721953i
$563$	16.2340	−	11.7947i	0.684181	−	0.497087i	−0.190561	−	0.981675i	$-0.561031\pi$
$563$	16.2340	−	11.7947i	0.684181	−	0.497087i	0.874742	+	0.484589i	$0.161031\pi$
$564$	−13.7676	−	10.0027i	−0.579719	−	0.421191i
$565$		0			0
$566$	3.51037	−	2.55043i	0.147552	−	0.107203i
$567$	−0.314848	+	0.969003i	−0.0132224	+	0.0406943i
$568$	−1.65149			−0.0692949
$569$	−6.67287	+	20.5370i	−0.279741	+	0.860955i	0.708185	+	0.706027i	$0.249514\pi$
$569$	−6.67287	+	20.5370i	−0.279741	+	0.860955i	−0.987926	+	0.154927i	$0.950486\pi$
$570$		0			0
$571$	−8.13758	−	25.0449i	−0.340547	−	1.04810i	−0.963925	−	0.266176i	$-0.914240\pi$
$571$	−8.13758	−	25.0449i	−0.340547	−	1.04810i	0.623377	−	0.781921i	$-0.285760\pi$
$572$	0.317030	+	0.975717i	0.0132557	+	0.0407968i
$573$	10.3072	+	7.48861i	0.430589	+	0.312841i
$574$	−14.8303			−0.619003
$575$		0			0
$576$	−8.59476			−0.358115
$577$	−7.42872	−	5.39728i	−0.309262	−	0.224692i	0.422318	−	0.906448i	$-0.361217\pi$
$577$	−7.42872	−	5.39728i	−0.309262	−	0.224692i	−0.731580	+	0.681756i	$0.761217\pi$
$578$	10.6553	+	32.7937i	0.443202	+	1.36404i
$579$	1.35469	+	4.16930i	0.0562989	+	0.173270i
$580$		0			0
$581$	1.33617	−	4.11230i	0.0554336	−	0.170607i
$582$	−13.5239			−0.560585
$583$	6.42327	−	19.7688i	0.266025	−	0.818740i
$584$	1.06910	−	0.776746i	0.0442397	−	0.0321420i
$585$		0			0
$586$	−14.7482	−	10.7152i	−0.609243	−	0.442641i
$587$	32.3422	−	23.4980i	1.33491	−	0.969865i	0.335290	−	0.942115i	$-0.391166\pi$
$587$	32.3422	−	23.4980i	1.33491	−	0.969865i	0.999615	−	0.0277503i	$-0.00883434\pi$
$588$	10.0123	−	7.27440i	0.412902	−	0.299991i
$589$	0.625101	+	0.454163i	0.0257568	+	0.0187134i
$590$		0			0
$591$	2.60637	−	1.89364i	0.107212	−	0.0778939i
$592$	4.78081	−	14.7138i	0.196490	−	0.604734i
$593$	41.6331			1.70967			0.854834	−	0.518902i	$-0.173659\pi$
$593$	41.6331			1.70967			0.854834	+	0.518902i	$0.173659\pi$
$594$	2.96936	−	9.13874i	0.121834	−	0.374967i
$595$		0			0
$596$	−3.14197	−	9.66999i	−0.128700	−	0.396098i
$597$	−0.835946	−	2.57278i	−0.0342130	−	0.105297i
$598$	−1.53850	−	1.11779i	−0.0629141	−	0.0457098i
$599$	39.0726			1.59646			0.798232	−	0.602350i	$-0.205769\pi$
$599$	39.0726			1.59646			0.798232	+	0.602350i	$0.205769\pi$
$600$		0			0
$601$	5.46965			0.223112			0.111556	−	0.993758i	$-0.464417\pi$
$601$	5.46965			0.223112			0.111556	+	0.993758i	$0.464417\pi$
$602$	−14.3579	−	10.4316i	−0.585184	−	0.425161i
$603$	3.06544	+	9.43446i	0.124834	+	0.384201i
$604$	−6.58316	−	20.2609i	−0.267865	−	0.824404i
$605$		0			0
$606$	3.53199	−	10.8704i	0.143477	−	0.441578i
$607$	−42.3108			−1.71734			−0.858671	−	0.512527i	$-0.828709\pi$
$607$	−42.3108			−1.71734			−0.858671	+	0.512527i	$0.828709\pi$
$608$	1.80512	−	5.55560i	0.0732074	−	0.225309i
$609$	−3.28763	+	2.38860i	−0.133222	+	0.0967911i
$610$		0			0
$611$	−0.688679	−	0.500355i	−0.0278610	−	0.0202422i
$612$	−9.80387	+	7.12293i	−0.396298	+	0.287927i
$613$	−27.5118	+	19.9885i	−1.11119	+	0.807327i	−0.982851	−	0.184403i	$-0.940965\pi$
$613$	−27.5118	+	19.9885i	−1.11119	+	0.807327i	−0.128340	+	0.991730i	$0.540965\pi$
$614$	8.22292	+	5.97430i	0.331850	+	0.241103i
$615$		0			0
$616$	0.600675	−	0.436416i	0.0242019	−	0.0175837i
$617$	−7.20543	+	22.1760i	−0.290080	+	0.892773i	0.694750	+	0.719251i	$0.255515\pi$
$617$	−7.20543	+	22.1760i	−0.290080	+	0.892773i	−0.984830	+	0.173522i	$0.944485\pi$
$618$	−1.20020			−0.0482790
$619$	10.9082	−	33.5721i	0.438439	−	1.34938i	−0.451083	−	0.892482i	$-0.648962\pi$
$619$	10.9082	−	33.5721i	0.438439	−	1.34938i	0.889521	−	0.456893i	$-0.151038\pi$
$620$		0			0
$621$	2.80325	+	8.62753i	0.112491	+	0.346211i
$622$	−3.05169	−	9.39213i	−0.122362	−	0.376590i
$623$	−15.1464	−	11.0045i	−0.606827	−	0.440885i
$624$	−0.399002			−0.0159729
$625$		0			0
$626$	6.40551			0.256016
$627$	2.78940	+	2.02661i	0.111398	+	0.0809352i
$628$	5.70610	+	17.5616i	0.227698	+	0.700783i
$629$	−7.26316	−	22.3537i	−0.289601	−	0.891301i
$630$		0			0
$631$	−1.08290	+	3.33282i	−0.0431095	+	0.132677i	−0.970295	−	0.241926i	$-0.922221\pi$
$631$	−1.08290	+	3.33282i	−0.0431095	+	0.132677i	0.927185	+	0.374603i	$0.122221\pi$
$632$	0.380149			0.0151215
$633$	8.17148	−	25.1492i	0.324787	−	0.999592i
$634$	−32.6583	+	23.7276i	−1.29703	+	0.942345i
$635$		0			0
$636$	−7.33421	−	5.32862i	−0.290820	−	0.211293i
$637$	0.500836	−	0.363878i	0.0198438	−	0.0144174i
$638$	31.0059	−	22.5271i	1.22753	−	0.891856i
$639$	8.72652	+	6.34019i	0.345216	+	0.250814i
$640$		0			0
$641$	7.51448	−	5.45959i	0.296804	−	0.215641i	−0.429409	−	0.903110i	$-0.641278\pi$
$641$	7.51448	−	5.45959i	0.296804	−	0.215641i	0.726214	+	0.687469i	$0.241278\pi$
$642$	−0.864993	+	2.66218i	−0.0341386	+	0.105068i
$643$	0.0291680			0.00115028			0.000575138	−	1.00000i	$-0.499817\pi$
$643$	0.0291680			0.00115028			0.000575138		1.00000i	$0.499817\pi$
$644$	−5.92891	+	18.2473i	−0.233632	+	0.719044i
$645$		0			0
$646$	−2.63826	−	8.11974i	−0.103801	−	0.319467i
$647$	0.260841	+	0.802787i	0.0102547	+	0.0315608i	0.956053	−	0.293194i	$-0.0947182\pi$
$647$	0.260841	+	0.802787i	0.0102547	+	0.0315608i	−0.945798	+	0.324755i	$0.894718\pi$
$648$	−0.123865	−	0.0899934i	−0.00486589	−	0.00353527i
$649$	−23.3833			−0.917874
$650$		0			0
$651$	−1.08675			−0.0425932
$652$	19.7816	+	14.3722i	0.774708	+	0.562858i
$653$	−11.7646	−	36.2077i	−0.460385	−	1.41692i	−0.864695	−	0.502297i	$-0.832489\pi$
$653$	−11.7646	−	36.2077i	−0.460385	−	1.41692i	0.404311	−	0.914622i	$-0.367511\pi$
$654$	−5.52543	−	17.0055i	−0.216061	−	0.664969i
$655$		0			0
$656$	−8.56103	+	26.3481i	−0.334252	+	1.02872i
$657$	−8.63115			−0.336733
$658$	−5.21094	+	16.0376i	−0.203144	+	0.625212i
$659$	−30.6086	+	22.2385i	−1.19234	+	0.866287i	−0.993510	−	0.113746i	$-0.963715\pi$
$659$	−30.6086	+	22.2385i	−1.19234	+	0.866287i	−0.198832	+	0.980034i	$0.563715\pi$
$660$		0			0
$661$	15.0165	+	10.9101i	0.584074	+	0.424355i	0.840191	−	0.542291i	$-0.182443\pi$
$661$	15.0165	+	10.9101i	0.584074	+	0.424355i	−0.256116	+	0.966646i	$0.582443\pi$
$662$	−9.82797	+	7.14044i	−0.381975	+	0.277521i
$663$	−0.490407	+	0.356302i	−0.0190458	+	0.0138376i
$664$	0.525665	+	0.381918i	0.0203998	+	0.0148213i
$665$		0			0
$666$	6.57601	−	4.77775i	0.254815	−	0.185134i
$667$	−11.1807	+	34.4106i	−0.432918	+	1.33239i
$668$	−36.0702			−1.39560
$669$	2.48216	−	7.63932i	0.0959660	−	0.295353i
$670$		0			0
$671$	10.2432	+	31.5253i	0.395433	+	1.21702i
$672$	2.53890	+	7.81392i	0.0979400	+	0.301428i
$673$	14.6923	+	10.6746i	0.566347	+	0.411475i	0.833776	−	0.552102i	$-0.186174\pi$
$673$	14.6923	+	10.6746i	0.566347	+	0.411475i	−0.267429	+	0.963578i	$0.586174\pi$
$674$	−46.0578			−1.77408
$675$		0			0
$676$	−26.9635			−1.03706
$677$	−4.56538	−	3.31695i	−0.175462	−	0.127481i	0.496588	−	0.867986i	$-0.334586\pi$
$677$	−4.56538	−	3.31695i	−0.175462	−	0.127481i	−0.672050	+	0.740506i	$0.734586\pi$
$678$	−4.11151	−	12.6539i	−0.157902	−	0.485971i
$679$	2.10909	+	6.49112i	0.0809396	+	0.249106i
$680$		0			0
$681$	−5.08569	+	15.6521i	−0.194884	+	0.599791i
$682$	10.2492			0.392464
$683$	−9.40859	+	28.9567i	−0.360010	+	1.10800i	0.593038	+	0.805175i	$0.297929\pi$
$683$	−9.40859	+	28.9567i	−0.360010	+	1.10800i	−0.953047	+	0.302821i	$0.902071\pi$
$684$	1.21656	−	0.883879i	0.0465162	−	0.0337960i
$685$		0			0
$686$	−21.5702	−	15.6717i	−0.823553	−	0.598346i
$687$	−0.331118	+	0.240572i	−0.0126330	+	0.00917838i
$688$	−26.8216	+	19.4871i	−1.02257	+	0.742937i
$689$	−0.366871	−	0.266547i	−0.0139767	−	0.0101546i
$690$		0			0
$691$	7.46294	−	5.42214i	0.283904	−	0.206268i	−0.436715	−	0.899600i	$-0.643858\pi$
$691$	7.46294	−	5.42214i	0.283904	−	0.206268i	0.720618	+	0.693332i	$0.243858\pi$
$692$	8.31316	−	25.5853i	0.316019	−	0.972607i
$693$	−4.84943			−0.184215
$694$	−6.10806	+	18.7987i	−0.231859	+	0.713588i
$695$		0			0
$696$	−0.188704	−	0.580771i	−0.00715280	−	0.0220141i
$697$	13.0062	+	40.0290i	0.492645	+	1.51620i
$698$	2.10121	+	1.52662i	0.0795322	+	0.0577835i
$699$	18.4641			0.698375
$700$		0			0
$701$	−19.9822			−0.754717			−0.377358	−	0.926067i	$-0.623168\pi$
$701$	−19.9822			−0.754717			−0.377358	+	0.926067i	$0.623168\pi$
$702$	−0.169597	−	0.123220i	−0.00640104	−	0.00465062i
$703$	0.901281	+	2.77386i	0.0339924	+	0.104618i
$704$	−12.6412	−	38.9056i	−0.476432	−	1.46631i
$705$		0			0
$706$	−0.726319	+	2.23538i	−0.0273354	+	0.0841296i
$707$	−5.76830			−0.216939
$708$	−3.15144	+	9.69914i	−0.118438	+	0.364516i
$709$	21.7026	−	15.7679i	0.815059	−	0.592175i	−0.100234	−	0.994964i	$-0.531959\pi$
$709$	21.7026	−	15.7679i	0.815059	−	0.592175i	0.915293	+	0.402789i	$0.131959\pi$
$710$		0			0
$711$	−2.00872	−	1.45942i	−0.0753329	−	0.0547325i
$712$	2.27605	−	1.65365i	0.0852985	−	0.0619730i
$713$	−7.82797	+	5.68735i	−0.293160	+	0.212993i
$714$	9.71475	+	7.05818i	0.363565	+	0.264146i
$715$		0			0
$716$	−1.84560	+	1.34090i	−0.0689732	+	0.0501120i
$717$	−1.42668	+	4.39086i	−0.0532802	+	0.163980i
$718$	38.4602			1.43532
$719$	11.9968	−	36.9223i	0.447404	−	1.37697i	−0.432421	−	0.901672i	$-0.642341\pi$
$719$	11.9968	−	36.9223i	0.447404	−	1.37697i	0.879825	−	0.475297i	$-0.157659\pi$
$720$		0			0
$721$	0.187174	+	0.576062i	0.00697072	+	0.0214537i
$722$	−11.5261	−	35.4736i	−0.428956	−	1.32019i
$723$	23.6251	+	17.1646i	0.878627	+	0.638360i
$724$	−31.0954			−1.15565
$725$		0			0
$726$	23.5277			0.873196
$727$	23.9278	+	17.3846i	0.887434	+	0.644759i	0.935208	−	0.354099i	$-0.115213\pi$
$727$	23.9278	+	17.3846i	0.887434	+	0.644759i	−0.0477734	+	0.998858i	$0.515213\pi$
$728$	−0.00500548	−	0.0154053i	−0.000185515	−	0.000570958i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−15.5645	+	47.9025i	−0.575673	+	1.77174i
$732$	14.4569			0.534341
$733$	15.1042	−	46.4859i	0.557886	−	1.71700i	−0.130311	−	0.991473i	$-0.541598\pi$
$733$	15.1042	−	46.4859i	0.557886	−	1.71700i	0.688197	−	0.725524i	$-0.258402\pi$
$734$	27.3895	−	19.8997i	1.01097	−	0.734510i
$735$		0			0
$736$	59.1808	+	42.9974i	2.18143	+	1.58490i
$737$	−38.1979	+	27.7524i	−1.40704	+	1.02227i
$738$	−11.7757	+	8.55556i	−0.433470	+	0.314934i
$739$	−17.6045	−	12.7904i	−0.647590	−	0.470502i	0.214859	−	0.976645i	$-0.431071\pi$
$739$	−17.6045	−	12.7904i	−0.647590	−	0.470502i	−0.862450	+	0.506143i	$0.831071\pi$
$740$		0			0
$741$	0.0608543	−	0.0442132i	0.00223554	−	0.00162421i
$742$	−2.77595	+	8.54351i	−0.101908	+	0.313642i
$743$	9.75724			0.357959			0.178979	−	0.983853i	$-0.442720\pi$
$743$	9.75724			0.357959			0.178979	+	0.983853i	$0.442720\pi$
$744$	0.0504645	−	0.155314i	0.00185012	−	0.00569408i
$745$		0			0
$746$	10.6382	+	32.7409i	0.389491	+	1.19873i
$747$	−1.31142	−	4.03614i	−0.0479824	−	0.147675i
$748$	−46.6626	−	33.9024i	−1.70615	−	1.23959i
$749$	1.41267			0.0516178
$750$		0			0
$751$	−17.6413			−0.643741			−0.321871	−	0.946784i	$-0.604312\pi$
$751$	−17.6413			−0.643741			−0.321871	+	0.946784i	$0.604312\pi$
$752$	25.4851	+	18.5160i	0.929346	+	0.675209i
$753$	0.120413	+	0.370593i	0.00438809	+	0.0135052i
$754$	−0.258375	−	0.795196i	−0.00940945	−	0.0289593i
$755$		0			0
$756$	−0.653574	+	2.01149i	−0.0237702	+	0.0731573i
$757$	44.2551			1.60848			0.804240	−	0.594305i	$-0.202573\pi$
$757$	44.2551			1.60848			0.804240	+	0.594305i	$0.202573\pi$
$758$	1.03943	−	3.19904i	0.0377538	−	0.116194i
$759$	−34.9308	+	25.3787i	−1.26791	+	0.921190i
$760$		0			0
$761$	−32.2600	−	23.4382i	−1.16942	−	0.849636i	−0.178483	−	0.983943i	$-0.557119\pi$
$761$	−32.2600	−	23.4382i	−1.16942	−	0.849636i	−0.990940	+	0.134307i	$0.957119\pi$
$762$	−11.9091	+	8.65248i	−0.431422	+	0.313446i
$763$	−7.30049	+	5.30412i	−0.264295	+	0.192022i
$764$	21.3960	+	15.5451i	0.774082	+	0.562403i
$765$		0			0
$766$	4.98747	−	3.62361i	0.180205	−	0.130926i
$767$	−0.157641	+	0.485169i	−0.00569208	+	0.0175184i
$768$	14.7185			0.531108
$769$	10.8980	−	33.5407i	0.392993	−	1.20951i	−0.537521	−	0.843250i	$-0.680639\pi$
$769$	10.8980	−	33.5407i	0.392993	−	1.20951i	0.930514	−	0.366257i	$-0.119361\pi$
$770$		0			0
$771$	−2.48241	−	7.64007i	−0.0894018	−	0.275150i
$772$	2.81211	+	8.65479i	0.101210	+	0.311493i
$773$	−18.8029	−	13.6611i	−0.676295	−	0.491357i	0.195832	−	0.980638i	$-0.437259\pi$
$773$	−18.8029	−	13.6611i	−0.676295	−	0.491357i	−0.872126	+	0.489281i	$0.837259\pi$
$774$	−17.4186			−0.626100
$775$		0			0
$776$	−1.02562			−0.0368176
$777$	−3.31874	−	2.41121i	−0.119059	−	0.0865015i
$778$	17.6383	+	54.2850i	0.632362	+	1.94621i
$779$	−1.61393	−	4.96717i	−0.0578250	−	0.177967i
$780$		0			0
$781$	−15.8649	+	48.8272i	−0.567691	+	1.74717i
$782$	106.914			3.82324
$783$	−1.23251	+	3.79326i	−0.0440462	+	0.135560i
$784$	−18.5338	+	13.4656i	−0.661922	+	0.480914i
$785$		0			0
$786$	15.6043	+	11.3372i	0.556588	+	0.404385i
$787$	5.52636	−	4.01513i	0.196993	−	0.143124i	−0.484916	−	0.874561i	$-0.661150\pi$
$787$	5.52636	−	4.01513i	0.196993	−	0.143124i	0.681909	+	0.731437i	$0.261150\pi$
$788$	5.41040	−	3.93089i	0.192738	−	0.140032i
$789$	−19.5888	−	14.2321i	−0.697381	−	0.506677i
$790$		0			0
$791$	−5.43235	+	3.94683i	−0.193152	+	0.140333i
$792$	0.225188	−	0.693058i	0.00800172	−	0.0246267i
$793$	0.723159			0.0256801
$794$	12.7757	−	39.3195i	0.453392	−	1.39540i
$795$		0			0
$796$	−1.73529	−	5.34067i	−0.0615056	−	0.189295i
$797$	−16.6649	−	51.2892i	−0.590301	−	1.81676i	−0.576852	−	0.816849i	$-0.695719\pi$
$797$	−16.6649	−	51.2892i	−0.590301	−	1.81676i	−0.0134488	−	0.999910i	$-0.504281\pi$
$798$	−1.20550	−	0.875844i	−0.0426741	−	0.0310046i
$799$	47.8578			1.69309
$800$		0			0
$801$	−18.3752			−0.649256
$802$	−41.8046	−	30.3728i	−1.47617	−	1.07250i
$803$	−12.6947	−	39.0703i	−0.447987	−	1.37876i
$804$	6.36336	+	19.5844i	0.224418	+	0.690689i
$805$		0			0
$806$	0.0690964	−	0.212657i	0.00243382	−	0.00749052i
$807$	26.4063			0.929544
$808$	0.267857	−	0.824380i	0.00942318	−	0.0290016i
$809$	14.8943	−	10.8214i	0.523656	−	0.380459i	−0.294323	−	0.955706i	$-0.595094\pi$
$809$	14.8943	−	10.8214i	0.523656	−	0.380459i	0.817980	+	0.575247i	$0.195094\pi$
$810$		0			0
$811$	9.53916	+	6.93060i	0.334965	+	0.243366i	0.742534	−	0.669808i	$-0.233624\pi$
$811$	9.53916	+	6.93060i	0.334965	+	0.243366i	−0.407569	+	0.913174i	$0.633624\pi$
$812$	−6.82459	+	4.95835i	−0.239496	+	0.174004i
$813$	8.42086	−	6.11811i	0.295333	−	0.214572i
$814$	31.2993	+	22.7403i	1.09704	+	0.797046i
$815$		0			0
$816$	18.1479	−	13.1852i	0.635304	−	0.461575i
$817$	1.93139	−	5.94419i	0.0675706	−	0.207961i
$818$	−24.3076			−0.849895
$819$	−0.0326929	+	0.100619i	−0.00114238	+	0.00351590i
$820$		0			0
$821$	−3.80899	−	11.7229i	−0.132935	−	0.409130i	0.862329	−	0.506349i	$-0.169005\pi$
$821$	−3.80899	−	11.7229i	−0.132935	−	0.409130i	−0.995263	+	0.0972189i	$0.969005\pi$
$822$	3.86787	+	11.9041i	0.134907	+	0.415202i
$823$	2.28023	+	1.65668i	0.0794839	+	0.0577484i	0.626818	−	0.779166i	$-0.284357\pi$
$823$	2.28023	+	1.65668i	0.0794839	+	0.0577484i	−0.547334	+	0.836914i	$0.684357\pi$
$824$	−0.0910197			−0.00317082
$825$		0			0
$826$	10.1056			0.351618
$827$	−30.2776	−	21.9979i	−1.05285	−	0.764943i	−0.0801008	−	0.996787i	$-0.525524\pi$
$827$	−30.2776	−	21.9979i	−1.05285	−	0.764943i	−0.972753	+	0.231844i	$0.925524\pi$
$828$	5.81910	+	17.9093i	0.202228	+	0.622393i
$829$	9.56205	+	29.4289i	0.332104	+	1.02211i	0.968131	+	0.250443i	$0.0805764\pi$
$829$	9.56205	+	29.4289i	0.332104	+	1.02211i	−0.636028	+	0.771666i	$0.719424\pi$
$830$		0			0
$831$	7.57731	−	23.3206i	0.262854	−	0.808981i
$832$	−0.892455			−0.0309403
$833$	−10.7551	+	33.1008i	−0.372642	+	1.14687i
$834$	1.48064	−	1.07575i	0.0512703	−	0.0372501i
$835$		0			0
$836$	5.79033	+	4.20692i	0.200263	+	0.145499i
$837$	−0.862918	+	0.626946i	−0.0298268	+	0.0216704i
$838$	56.5195	−	41.0638i	1.95243	−	1.41853i
$839$	21.5988	+	15.6924i	0.745672	+	0.541762i	0.894482	−	0.447103i	$-0.147544\pi$
$839$	21.5988	+	15.6924i	0.745672	+	0.541762i	−0.148810	+	0.988866i	$0.547544\pi$
$840$		0			0
$841$	10.5917	−	7.69534i	0.365232	−	0.265356i
$842$	−9.32832	+	28.7096i	−0.321475	+	0.989399i
$843$	−14.4228			−0.496748
$844$	16.9627	−	52.2057i	0.583879	−	1.79699i
$845$		0			0
$846$	5.11443	+	15.7406i	0.175838	+	0.541173i
$847$	−3.66921	−	11.2927i	−0.126076	−	0.388021i
$848$	13.5763	+	9.86378i	0.466213	+	0.338724i
$849$	−2.14925			−0.0737620
$850$		0			0
$851$	−36.5239			−1.25202
$852$	18.1148	+	13.1612i	0.620604	+	0.450895i
$853$	−9.04183	−	27.8279i	−0.309586	−	0.952808i	−0.977926	−	0.208952i	$-0.932995\pi$
$853$	−9.04183	−	27.8279i	−0.309586	−	0.952808i	0.668340	−	0.743856i	$-0.267005\pi$
$854$	−4.42681	−	13.6243i	−0.151482	−	0.466214i
$855$		0			0
$856$	−0.0655988	+	0.201892i	−0.00224212	+	0.00690054i
$857$	33.5284			1.14531			0.572654	−	0.819797i	$-0.305914\pi$
$857$	33.5284			1.14531			0.572654	+	0.819797i	$0.305914\pi$
$858$	0.308329	−	0.948941i	0.0105262	−	0.0323963i
$859$	20.8923	−	15.1792i	0.712837	−	0.517906i	−0.171251	−	0.985227i	$-0.554781\pi$
$859$	20.8923	−	15.1792i	0.712837	−	0.517906i	0.884088	+	0.467321i	$0.154781\pi$
$860$		0			0
$861$	5.94289	+	4.31776i	0.202533	+	0.147149i
$862$	−7.85792	+	5.70911i	−0.267642	+	0.194453i
$863$	−23.3713	+	16.9803i	−0.795569	+	0.578015i	−0.909611	−	0.415461i	$-0.863620\pi$
$863$	−23.3713	+	16.9803i	−0.795569	+	0.578015i	0.114042	+	0.993476i	$0.463620\pi$
$864$	6.52381	+	4.73982i	0.221944	+	0.161252i
$865$		0			0
$866$	16.8940	−	12.2742i	0.574083	−	0.417096i
$867$	5.27785	−	16.2436i	0.179245	−	0.551660i
$868$	−2.25592			−0.0765710
$869$	3.65187	−	11.2393i	0.123881	−	0.381267i
$870$		0			0
$871$	0.318307	+	0.979647i	0.0107854	+	0.0331941i
$872$	−0.419034	−	1.28965i	−0.0141903	−	0.0436732i
$873$	5.41941	+	3.93743i	0.183419	+	0.133262i
$874$	−13.2669			−0.448759
$875$		0			0
$876$	−17.9169			−0.605355
$877$	−12.2165	−	8.87581i	−0.412522	−	0.299715i	0.362100	−	0.932139i	$-0.382060\pi$
$877$	−12.2165	−	8.87581i	−0.412522	−	0.299715i	−0.774622	+	0.632425i	$0.782060\pi$
$878$	19.1926	+	59.0688i	0.647719	+	1.99347i
$879$	2.79033	+	8.58775i	0.0941155	+	0.289658i
$880$		0			0
$881$	11.3167	−	34.8292i	0.381269	−	1.17342i	−0.557882	−	0.829920i	$-0.688386\pi$
$881$	11.3167	−	34.8292i	0.381269	−	1.17342i	0.939151	−	0.343505i	$-0.111614\pi$
$882$	−12.0363			−0.405284
$883$	10.6753	−	32.8551i	0.359251	−	1.10566i	−0.594252	−	0.804279i	$-0.702552\pi$
$883$	10.6753	−	32.8551i	0.359251	−	1.10566i	0.953503	−	0.301383i	$-0.0974481\pi$
$884$	−1.01801	+	0.739625i	−0.0342392	+	0.0248763i
$885$		0			0
$886$	−28.9985	−	21.0686i	−0.974223	−	0.707814i
$887$	26.7267	−	19.4181i	0.897394	−	0.651995i	−0.0404016	−	0.999184i	$-0.512864\pi$
$887$	26.7267	−	19.4181i	0.897394	−	0.651995i	0.937795	+	0.347189i	$0.112864\pi$
$888$	0.498708	−	0.362332i	0.0167355	−	0.0121591i
$889$	6.01021	+	4.36668i	0.201576	+	0.146454i
$890$		0			0
$891$	−3.85061	+	2.79763i	−0.129000	+	0.0937241i
$892$	5.15257	−	15.8580i	0.172521	−	0.530964i
$893$	−5.93864			−0.198729
$894$	−3.05574	+	9.40461i	−0.102199	+	0.314537i
$895$		0			0
$896$	0.385364	+	1.18603i	0.0128741	+	0.0396224i
$897$	0.291082	+	0.895858i	0.00971894	+	0.0299118i
$898$	60.7889	+	44.1657i	2.02855	+	1.47383i
$899$	−4.25420			−0.141886
$900$		0			0
$901$	25.4947			0.849350
$902$	−56.0478	−	40.7211i	−1.86619	−	1.35587i
$903$	2.71648	+	8.36047i	0.0903989	+	0.278219i
$904$	−0.311806	−	0.959641i	−0.0103705	−	0.0319172i
$905$		0			0
$906$	−6.40250	+	19.7049i	−0.212709	+	0.654650i
$907$	44.2708			1.46999			0.734994	−	0.678074i	$-0.237185\pi$
$907$	44.2708			1.46999			0.734994	+	0.678074i	$0.237185\pi$
$908$	−10.5571	+	32.4913i	−0.350348	+	1.07826i
$909$	−4.58022	+	3.32773i	−0.151916	+	0.110374i
$910$		0			0
$911$	31.4581	+	22.8556i	1.04225	+	0.757241i	0.970724	−	0.240197i	$-0.0772121\pi$
$911$	31.4581	+	22.8556i	1.04225	+	0.757241i	0.0715293	+	0.997439i	$0.477212\pi$
$912$	−2.25196	+	1.63615i	−0.0745699	+	0.0541782i
$913$	16.3414	−	11.8727i	0.540821	−	0.392930i
$914$	−45.2403	−	32.8690i	−1.49642	−	1.08721i
$915$		0			0
$916$	−0.687348	+	0.499387i	−0.0227106	+	0.0165002i
$917$	3.00802	−	9.25772i	0.0993334	−	0.305717i
$918$	11.7857			0.388986
$919$	−8.81634	+	27.1339i	−0.290824	+	0.895065i	0.693768	+	0.720198i	$0.255949\pi$
$919$	−8.81634	+	27.1339i	−0.290824	+	0.895065i	−0.984592	+	0.174866i	$0.944051\pi$
$920$		0			0
$921$	−1.55576	−	4.78813i	−0.0512640	−	0.157774i
$922$	6.12474	+	18.8500i	0.201708	+	0.620793i
$923$	0.906137	+	0.658347i	0.0298259	+	0.0216698i
$924$	−10.0666			−0.331168
$925$		0			0
$926$	7.52497			0.247286
$927$	0.480952	+	0.349432i	0.0157965	+	0.0114768i
$928$	9.93877	+	30.5884i	0.326256	+	1.00411i
$929$	11.2447	+	34.6076i	0.368926	+	1.13544i	0.947486	+	0.319798i	$0.103615\pi$
$929$	11.2447	+	34.6076i	0.368926	+	1.13544i	−0.578559	+	0.815640i	$0.696385\pi$
$930$		0			0
$931$	1.33459	−	4.10745i	0.0437395	−	0.134616i
$932$	38.3284			1.25549
$933$	−1.51158	+	4.65217i	−0.0494870	+	0.152305i
$934$	−11.5952	+	8.42441i	−0.379407	+	0.275655i
$935$		0			0
$936$	−0.0128618	−	0.00934465i	−0.000420402	−	0.000305440i
$937$	−38.2951	+	27.8230i	−1.25105	+	0.908939i	−0.998282	−	0.0585890i	$-0.981340\pi$
$937$	−38.2951	+	27.8230i	−1.25105	+	0.908939i	−0.252765	+	0.967528i	$0.581340\pi$
$938$	16.5080	−	11.9938i	0.539007	−	0.391611i
$939$	−2.56686	−	1.86494i	−0.0837664	−	0.0608599i
$940$		0			0
$941$	−42.8175	+	31.1087i	−1.39581	+	1.01412i	−0.400611	+	0.916248i	$0.631202\pi$
$941$	−42.8175	+	31.1087i	−1.39581	+	1.01412i	−0.995199	+	0.0978679i	$0.968798\pi$
$942$	5.54951	−	17.0796i	0.180813	−	0.556485i
$943$	65.4035			2.12983
$944$	5.83362	−	17.9540i	0.189868	−	0.584354i
$945$		0			0
$946$	−25.6193	−	78.8482i	−0.832957	−	2.56358i
$947$	−5.85061	−	18.0063i	−0.190119	−	0.585127i	0.809880	−	0.586596i	$-0.199532\pi$
$947$	−5.85061	−	18.0063i	−0.190119	−	0.585127i	−0.999999	+	0.00146915i	$0.999532\pi$
$948$	−4.16978	−	3.02952i	−0.135428	−	0.0983942i
$949$	−0.896234			−0.0290930
$950$		0			0
$951$	19.9953			0.648392
$952$	0.736741	+	0.535274i	0.0238779	+	0.0173483i
$953$	3.53822	+	10.8895i	0.114614	+	0.352746i	0.991866	−	0.127284i	$-0.0406258\pi$
$953$	3.53822	+	10.8895i	0.114614	+	0.352746i	−0.877252	+	0.480030i	$0.840626\pi$
$954$	2.72454	+	8.38527i	0.0882103	+	0.271483i
$955$		0			0
$956$	−2.96155	+	9.11471i	−0.0957833	+	0.294791i
$957$	−18.9836			−0.613652
$958$	−17.7459	+	54.6163i	−0.573345	+	1.76457i
$959$	5.11043	−	3.71294i	0.165024	−	0.119897i
$960$		0			0
$961$	24.1591	+	17.5526i	0.779326	+	0.566214i
$962$	0.682835	−	0.496108i	0.0220155	−	0.0159952i
$963$	1.12171	−	0.814968i	0.0361465	−	0.0262620i
$964$	49.0419	+	35.6310i	1.57953	+	1.14760i
$965$		0			0
$966$	15.0961	−	10.9680i	0.485709	−	0.352888i
$967$	11.4313	−	35.1821i	0.367607	−	1.13138i	−0.580725	−	0.814100i	$-0.697231\pi$
$967$	11.4313	−	35.1821i	0.367607	−	1.13138i	0.948332	−	0.317279i	$-0.102769\pi$
$968$	1.78428			0.0573490
$969$	−1.30680	+	4.02192i	−0.0419805	+	0.129203i
$970$		0			0
$971$	−9.36004	−	28.8072i	−0.300378	−	0.924468i	−0.981362	−	0.192170i	$-0.938448\pi$
$971$	−9.36004	−	28.8072i	−0.300378	−	0.924468i	0.680984	−	0.732298i	$-0.261552\pi$
$972$	0.641469	+	1.97424i	0.0205751	+	0.0633237i
$973$	−0.747239	−	0.542901i	−0.0239554	−	0.0174046i
$974$	29.7549			0.953408
$975$		0			0
$976$	−26.7610			−0.856600
$977$	13.4629	+	9.78136i	0.430716	+	0.312934i	0.781935	−	0.623360i	$-0.214233\pi$
$977$	13.4629	+	9.78136i	0.430716	+	0.312934i	−0.351219	+	0.936293i	$0.614233\pi$
$978$	−7.34855	−	22.6165i	−0.234981	−	0.723196i
$979$	−27.0263	−	83.1783i	−0.863763	−	2.65839i
$980$		0			0
$981$	−2.73689	+	8.42329i	−0.0873822	+	0.268935i
$982$	−57.3388			−1.82975
$983$	−8.09305	+	24.9078i	−0.258128	+	0.794437i	0.735069	+	0.677992i	$0.237150\pi$
$983$	−8.09305	+	24.9078i	−0.258128	+	0.794437i	−0.993197	+	0.116445i	$0.962850\pi$
$984$	−0.893040	+	0.648831i	−0.0284691	+	0.0206840i
$985$		0			0
$986$	38.0294	+	27.6300i	1.21110	+	0.879917i
$987$	6.75745	−	4.90958i	0.215092	−	0.156274i
$988$	0.126324	−	0.0917795i	0.00401889	−	0.00291990i
$989$	63.3203	+	46.0049i	2.01347	+	1.46287i
$990$		0			0
$991$	20.0938	−	14.5990i	0.638300	−	0.463752i	−0.220966	−	0.975282i	$-0.570921\pi$
$991$	20.0938	−	14.5990i	0.638300	−	0.463752i	0.859266	+	0.511530i	$0.170921\pi$
$992$	−2.65789	+	8.18016i	−0.0843882	+	0.259720i
$993$	6.01724			0.190951
$994$	6.85635	−	21.1017i	0.217470	−	0.669305i
$995$		0			0
$996$	−2.72230	−	8.37837i	−0.0862593	−	0.265479i
$997$	−7.75208	−	23.8585i	−0.245511	−	0.755605i	−0.995552	−	0.0942136i	$-0.969966\pi$
$997$	−7.75208	−	23.8585i	−0.245511	−	0.755605i	0.750041	−	0.661391i	$-0.230034\pi$
$998$	−43.0933	−	31.3091i	−1.36409	−	0.991072i
$999$	−4.02621			−0.127384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.c.76.1		12
5.2	odd	4		375.2.i.d.49.5		24
5.3	odd	4		375.2.i.d.49.2		24
5.4	even	2		75.2.g.c.16.3	✓	12
15.14	odd	2		225.2.h.d.91.1		12
25.2	odd	20		375.2.i.d.199.2		24
25.6	even	5		1875.2.a.k.1.5		6
25.8	odd	20		1875.2.b.f.1249.4		12
25.11	even	5	inner	375.2.g.c.301.1		12
25.14	even	10		75.2.g.c.61.3	yes	12
25.17	odd	20		1875.2.b.f.1249.9		12
25.19	even	10		1875.2.a.j.1.2		6
25.23	odd	20		375.2.i.d.199.5		24
75.14	odd	10		225.2.h.d.136.1		12
75.44	odd	10		5625.2.a.p.1.5		6
75.56	odd	10		5625.2.a.q.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.3	✓	12	5.4	even	2
75.2.g.c.61.3	yes	12	25.14	even	10
225.2.h.d.91.1		12	15.14	odd	2
225.2.h.d.136.1		12	75.14	odd	10
375.2.g.c.76.1		12	1.1	even	1	trivial
375.2.g.c.301.1		12	25.11	even	5	inner
375.2.i.d.49.2		24	5.3	odd	4
375.2.i.d.49.5		24	5.2	odd	4
375.2.i.d.199.2		24	25.2	odd	20
375.2.i.d.199.5		24	25.23	odd	20
1875.2.a.j.1.2		6	25.19	even	10
1875.2.a.k.1.5		6	25.6	even	5
1875.2.b.f.1249.4		12	25.8	odd	20
1875.2.b.f.1249.9		12	25.17	odd	20
5625.2.a.p.1.5		6	75.44	odd	10
5625.2.a.q.1.2		6	75.56	odd	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.63330 - 1.18666i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} -1.01887 q^{7} +(0.0473123 - 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.63330 - 1.18666i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(0.623865 - 1.92006i) q^{6} -1.01887 q^{7} +(0.0473123 - 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.85061 - 2.79763i) q^{11} +(-1.67939 + 1.22015i) q^{12} +(-0.0840060 + 0.0610339i) q^{13} +(1.66412 + 1.20905i) q^{14} +(3.10871 - 2.25861i) q^{16} +(1.80397 - 5.55204i) q^{17} +2.01887 q^{18} +(-0.223853 + 0.688949i) q^{19} +(-0.314848 - 0.969003i) q^{21} +(2.96936 + 9.13874i) q^{22} +(-7.33901 - 5.33210i) q^{23} +0.153106 q^{24} +0.209634 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.653574 - 2.01149i) q^{28} +(-1.23251 - 3.79326i) q^{29} +(0.329605 - 1.01442i) q^{31} -8.06387 q^{32} +(1.47080 - 4.52666i) q^{33} +(-9.53482 + 6.92745i) q^{34} +(-1.67939 - 1.22015i) q^{36} +(3.25727 - 2.36655i) q^{37} +(1.18317 - 0.859623i) q^{38} +(-0.0840060 - 0.0610339i) q^{39} +(-5.83282 + 4.23780i) q^{41} +(-0.635638 + 1.95629i) q^{42} -8.62791 q^{43} +(3.05314 - 9.39661i) q^{44} +(5.65940 + 17.4179i) q^{46} +(2.53331 + 7.79673i) q^{47} +(3.10871 + 2.25861i) q^{48} -5.96190 q^{49} +5.83776 q^{51} +(-0.174383 - 0.126697i) q^{52} +(1.34954 + 4.15345i) q^{53} +(0.623865 + 1.92006i) q^{54} +(-0.0482051 + 0.148360i) q^{56} -0.724404 q^{57} +(-2.48827 + 7.65810i) q^{58} +(3.97458 - 2.88770i) q^{59} +(-5.63428 - 4.09354i) q^{61} +(-1.74212 + 1.26572i) q^{62} +(0.824283 - 0.598877i) q^{63} +(6.95331 + 5.05187i) q^{64} +(-7.77388 + 5.64805i) q^{66} +(3.06544 - 9.43446i) q^{67} +12.1183 q^{68} +(2.80325 - 8.62753i) q^{69} +(-3.33323 - 10.2586i) q^{71} +(0.0473123 + 0.145612i) q^{72} +(6.98275 + 5.07326i) q^{73} -8.12840 q^{74} -1.50375 q^{76} +(3.92327 + 2.85042i) q^{77} +(0.0647804 + 0.199374i) q^{78} +(0.767263 + 2.36139i) q^{79} +(0.309017 - 0.951057i) q^{81} +14.5556 q^{82} +(-1.31142 + 4.03614i) q^{83} +(1.71108 - 1.24317i) q^{84} +(14.0920 + 10.2384i) q^{86} +(3.22674 - 2.34436i) q^{87} +(-0.589550 + 0.428333i) q^{88} +(14.8659 + 10.8007i) q^{89} +(0.0855912 - 0.0621857i) q^{91} +(5.81910 - 17.9093i) q^{92} +1.06662 q^{93} +(5.11443 - 15.7406i) q^{94} +(-2.49187 - 7.66920i) q^{96} +(-2.07003 - 6.37090i) q^{97} +(9.73758 + 7.07477i) q^{98} +4.75961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

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