LMFDB - Embedded newform 75.2.g.c.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(16,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, 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("75.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.g (of order $5$, degree $4$, 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:	$0.598878015160$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.3
Root			$0.623865 + 1.92006i$ of defining polynomial
Character	$\chi$	$=$	75.16
Dual form			75.2.g.c.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63330 + 1.18666i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(-2.07079 + 0.843702i) q^{5} +(0.623865 - 1.92006i) q^{6} +1.01887 q^{7} +(-0.0473123 + 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.63330 + 1.18666i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(-2.07079 + 0.843702i) q^{5} +(0.623865 - 1.92006i) q^{6} +1.01887 q^{7} +(-0.0473123 + 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-4.38341 - 1.07931i) q^{10} +(-3.85061 - 2.79763i) q^{11} +(1.67939 - 1.22015i) q^{12} +(0.0840060 - 0.0610339i) q^{13} +(1.66412 + 1.20905i) q^{14} +(1.44232 + 1.70872i) q^{15} +(3.10871 - 2.25861i) q^{16} +(-1.80397 + 5.55204i) q^{17} -2.01887 q^{18} +(-0.223853 + 0.688949i) q^{19} +(-2.99402 - 3.54702i) q^{20} +(-0.314848 - 0.969003i) q^{21} +(-2.96936 - 9.13874i) q^{22} +(7.33901 + 5.33210i) q^{23} +0.153106 q^{24} +(3.57633 - 3.49426i) q^{25} +0.209634 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.653574 + 2.01149i) q^{28} +(-1.23251 - 3.79326i) q^{29} +(0.328065 + 4.50239i) q^{30} +(0.329605 - 1.01442i) q^{31} +8.06387 q^{32} +(-1.47080 + 4.52666i) q^{33} +(-9.53482 + 6.92745i) q^{34} +(-2.10987 + 0.859623i) q^{35} +(-1.67939 - 1.22015i) q^{36} +(-3.25727 + 2.36655i) q^{37} +(-1.18317 + 0.859623i) q^{38} +(-0.0840060 - 0.0610339i) q^{39} +(-0.0248796 - 0.341450i) q^{40} +(-5.83282 + 4.23780i) q^{41} +(0.635638 - 1.95629i) q^{42} +8.62791 q^{43} +(3.05314 - 9.39661i) q^{44} +(1.17939 - 1.89975i) q^{45} +(5.65940 + 17.4179i) q^{46} +(-2.53331 - 7.79673i) q^{47} +(-3.10871 - 2.25861i) q^{48} -5.96190 q^{49} +(9.98773 - 1.46327i) q^{50} +5.83776 q^{51} +(0.174383 + 0.126697i) q^{52} +(-1.34954 - 4.15345i) q^{53} +(0.623865 + 1.92006i) q^{54} +(10.3342 + 2.54454i) q^{55} +(-0.0482051 + 0.148360i) q^{56} +0.724404 q^{57} +(2.48827 - 7.65810i) q^{58} +(3.97458 - 2.88770i) q^{59} +(-2.44822 + 3.94357i) q^{60} +(-5.63428 - 4.09354i) q^{61} +(1.74212 - 1.26572i) q^{62} +(-0.824283 + 0.598877i) q^{63} +(6.95331 + 5.05187i) q^{64} +(-0.122464 + 0.197264i) q^{65} +(-7.77388 + 5.64805i) q^{66} +(-3.06544 + 9.43446i) q^{67} -12.1183 q^{68} +(2.80325 - 8.62753i) q^{69} +(-4.46613 - 1.09967i) q^{70} +(-3.33323 - 10.2586i) q^{71} +(-0.0473123 - 0.145612i) q^{72} +(-6.98275 - 5.07326i) q^{73} -8.12840 q^{74} +(-4.42838 - 2.32151i) q^{75} -1.50375 q^{76} +(-3.92327 - 2.85042i) q^{77} +(-0.0647804 - 0.199374i) q^{78} +(0.767263 + 2.36139i) q^{79} +(-4.53188 + 7.29992i) q^{80} +(0.309017 - 0.951057i) q^{81} -14.5556 q^{82} +(1.31142 - 4.03614i) q^{83} +(1.71108 - 1.24317i) q^{84} +(-0.948634 - 13.0191i) q^{85} +(14.0920 + 10.2384i) q^{86} +(-3.22674 + 2.34436i) q^{87} +(0.589550 - 0.428333i) q^{88} +(14.8659 + 10.8007i) q^{89} +(4.18065 - 1.70333i) q^{90} +(0.0855912 - 0.0621857i) q^{91} +(-5.81910 + 17.9093i) q^{92} -1.06662 q^{93} +(5.11443 - 15.7406i) q^{94} +(-0.117715 - 1.61553i) q^{95} +(-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} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23} + 6 q^{24} + 4 q^{25} - 56 q^{26} + 3 q^{27} + q^{28} - q^{29} + 19 q^{30} + 13 q^{31} - 32 q^{32} - q^{33} - 25 q^{34} - 10 q^{35} + 8 q^{37} - 22 q^{38} + 2 q^{39} - 28 q^{40} + 8 q^{41} - 16 q^{42} - 4 q^{43} + 33 q^{44} - 6 q^{45} - 22 q^{46} - 13 q^{47} - 16 q^{48} - 28 q^{49} + 81 q^{50} + 26 q^{51} + 44 q^{52} + 44 q^{53} + 9 q^{55} + 45 q^{56} - 22 q^{57} + 41 q^{58} - 22 q^{59} + 14 q^{60} - 8 q^{61} + 41 q^{62} + 3 q^{63} + 49 q^{64} - 38 q^{65} - 3 q^{66} - 6 q^{67} - 100 q^{68} + 6 q^{69} - 45 q^{70} - 21 q^{71} + 9 q^{72} - 16 q^{73} - 44 q^{74} - 4 q^{75} - 52 q^{76} + q^{77} - 19 q^{78} + 10 q^{79} - 99 q^{80} - 3 q^{81} + 26 q^{82} - 10 q^{83} - 6 q^{84} + 23 q^{85} + 56 q^{86} - 4 q^{87} - 16 q^{88} + 57 q^{89} + 16 q^{90} - 7 q^{91} + 3 q^{92} + 22 q^{93} - 23 q^{94} + 21 q^{95} - 23 q^{96} + 4 q^{97} - 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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	0.989127	−	0.147064i	$-0.0469823\pi$
$2$	1.63330	+	1.18666i	1.15492	+	0.839097i	0.165791	+	0.986161i	$0.446982\pi$
$3$	−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
$5$	−2.07079	+	0.843702i	−0.926085	+	0.377315i
$5$	−2.07079	+	0.843702i	−0.926085	+	0.377315i
$6$	0.623865	−	1.92006i	0.254692	−	0.783861i
$7$	1.01887			0.385097			0.192548	−	0.981287i	$-0.438325\pi$
$7$	1.01887			0.385097			0.192548	+	0.981287i	$0.438325\pi$
$8$	−0.0473123	+	0.145612i	−0.0167274	+	0.0514817i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−4.38341	−	1.07931i	−1.38616	−	0.341307i
$11$	−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	−0.576075	−	0.817397i	$-0.695416\pi$
$13$	0.0840060	−	0.0610339i	0.0232991	−	0.0169278i	0.599374	+	0.800469i	$0.295416\pi$
$14$	1.66412	+	1.20905i	0.444755	+	0.323134i
$15$	1.44232	+	1.70872i	0.372405	+	0.441189i
$16$	3.10871	−	2.25861i	0.777177	−	0.564652i
$17$	−1.80397	+	5.55204i	−0.437527	+	1.34657i	0.452949	+	0.891537i	$0.350372\pi$
$17$	−1.80397	+	5.55204i	−0.437527	+	1.34657i	−0.890475	+	0.455032i	$0.849628\pi$
$18$	−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	$0.126480\pi$
$20$	−2.99402	−	3.54702i	−0.669482	−	0.793138i
$21$	−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	$0.0946916\pi$
$23$	7.33901	+	5.33210i	1.53029	+	1.11182i	0.574212	+	0.818707i	$0.305308\pi$
$24$	0.153106			0.0312526
$25$	3.57633	−	3.49426i	0.715267	−	0.698852i
$26$	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	$-0.220752\pi$
$30$	0.328065	+	4.50239i	0.0598963	+	0.822021i
$31$	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
$35$	−2.10987	+	0.859623i	−0.356632	+	0.145303i
$36$	−1.67939	−	1.22015i	−0.279898	−	0.203358i
$37$	−3.25727	+	2.36655i	−0.535493	+	0.389058i	−0.822408	−	0.568898i	$-0.807370\pi$
$37$	−3.25727	+	2.36655i	−0.535493	+	0.389058i	0.286916	+	0.957956i	$0.407370\pi$
$38$	−1.18317	+	0.859623i	−0.191935	+	0.139449i
$39$	−0.0840060	−	0.0610339i	−0.0134517	−	0.00977325i
$40$	−0.0248796	−	0.341450i	−0.00393381	−	0.0539880i
$41$	−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	$-0.271457\pi$
$43$	8.62791			1.31574			0.657872	+	0.753130i	$0.271457\pi$
$44$	3.05314	−	9.39661i	0.460279	−	1.41659i
$45$	1.17939	−	1.89975i	0.175813	−	0.283198i
$46$	5.65940	+	17.4179i	0.834434	+	2.56812i
$47$	−2.53331	−	7.79673i	−0.369522	−	1.13727i	−0.947101	−	0.320936i	$-0.896003\pi$
$47$	−2.53331	−	7.79673i	−0.369522	−	1.13727i	0.577579	−	0.816335i	$-0.303997\pi$
$48$	−3.10871	−	2.25861i	−0.448703	−	0.326002i
$49$	−5.96190			−0.851700
$50$	9.98773	−	1.46327i	1.41248	−	0.206938i
$51$	5.83776			0.817451
$52$	0.174383	+	0.126697i	0.0241825	+	0.0175696i
$53$	−1.34954	−	4.15345i	−0.185373	−	0.570520i	0.814581	−	0.580049i	$-0.196967\pi$
$53$	−1.34954	−	4.15345i	−0.185373	−	0.570520i	−0.999955	+	0.00952922i	$0.996967\pi$
$54$	0.623865	+	1.92006i	0.0848973	+	0.261287i
$55$	10.3342	+	2.54454i	1.39346	+	0.343105i
$56$	−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	$0.196384\pi$
$60$	−2.44822	+	3.94357i	−0.316063	+	0.509113i
$61$	−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
$65$	−0.122464	+	0.197264i	−0.0151898	+	0.0244676i
$66$	−7.77388	+	5.64805i	−0.956898	+	0.695227i
$67$	−3.06544	+	9.43446i	−0.374503	+	1.15260i	0.569310	+	0.822123i	$0.307210\pi$
$67$	−3.06544	+	9.43446i	−0.374503	+	1.15260i	−0.943813	+	0.330480i	$0.892790\pi$
$68$	−12.1183			−1.46955
$69$	2.80325	−	8.62753i	0.337472	−	1.03863i
$70$	−4.46613	−	1.09967i	−0.533804	−	0.131436i
$71$	−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	0.0986599	−	0.995121i	$-0.468544\pi$
$73$	−6.98275	−	5.07326i	−0.817269	−	0.593781i	−0.915929	+	0.401341i	$0.868544\pi$
$74$	−8.12840			−0.944907
$75$	−4.42838	−	2.32151i	−0.511346	−	0.268065i
$76$	−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	$0.855394\pi$
$80$	−4.53188	+	7.29992i	−0.506680	+	0.816156i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−14.5556			−1.60740
$83$	1.31142	−	4.03614i	0.143947	−	0.443024i	−0.852927	−	0.522030i	$-0.825175\pi$
$83$	1.31142	−	4.03614i	0.143947	−	0.443024i	0.996874	+	0.0790064i	$0.0251748\pi$
$84$	1.71108	−	1.24317i	0.186694	−	0.135641i
$85$	−0.948634	−	13.0191i	−0.102894	−	1.41212i
$86$	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	$0.272907\pi$
$90$	4.18065	−	1.70333i	0.440680	−	0.179546i
$91$	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
$95$	−0.117715	−	1.61553i	−0.0120773	−	0.165750i
$96$	−2.49187	−	7.66920i	−0.254326	−	0.782734i
$97$	2.07003	+	6.37090i	0.210180	+	0.646867i	0.999461	+	0.0328349i	$0.0104535\pi$
$97$	2.07003	+	6.37090i	0.210180	+	0.646867i	−0.789281	+	0.614032i	$0.789546\pi$
$98$	−9.73758	−	7.07477i	−0.983644	−	0.714659i
$99$	4.75961			0.478359
$100$	9.19261	+	4.81908i	0.919261	+	0.481908i
$101$	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	0.959699	−	0.281030i	$-0.0906759\pi$
$103$	0.183707	+	0.565393i	0.0181012	+	0.0557098i	−0.941598	+	0.336739i	$0.890676\pi$
$104$	0.00491278	+	0.0151200i	0.000481737	+	0.00148263i
$105$	1.46953	+	1.74096i	0.143412	+	0.169901i
$106$	2.72454	−	8.38527i	0.264631	−	0.814450i
$107$	1.38651			0.134039			0.0670193	−	0.997752i	$-0.478651\pi$
$107$	1.38651			0.134039			0.0670193	+	0.997752i	$0.478651\pi$
$108$	−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	$0.160569\pi$
$110$	13.8593	+	16.4191i	1.32143	+	1.56550i
$111$	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	−0.809615	−	0.586961i	$-0.800324\pi$
$113$	−5.33173	+	3.87373i	−0.501567	+	0.364410i	0.308048	+	0.951371i	$0.400324\pi$
$114$	1.18317	+	0.859623i	0.110814	+	0.0805111i
$115$	−19.6963	−	4.84972i	−1.83668	−	0.452239i
$116$	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
$120$	−0.317050	+	0.129176i	−0.0289426	+	0.0117921i
$121$	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
$125$	−4.45772	+	10.2532i	−0.398710	+	0.917077i
$126$	−2.05697			−0.183249
$127$	5.89890	+	4.28580i	0.523443	+	0.380303i	0.817899	−	0.575362i	$-0.195139\pi$
$127$	5.89890	+	4.28580i	0.523443	+	0.380303i	−0.294457	+	0.955665i	$0.595139\pi$
$128$	0.378226	+	1.16406i	0.0334308	+	0.102889i
$129$	−2.66617	−	8.20563i	−0.234743	−	0.722465i
$130$	−0.434107	+	0.176868i	−0.0380737	+	0.0155124i
$131$	−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
$135$	−2.17122	−	0.534610i	−0.186869	−	0.0460119i
$136$	−0.723096	−	0.525360i	−0.0620050	−	0.0450493i
$137$	5.01578	−	3.64418i	0.428527	−	0.311343i	−0.352533	−	0.935799i	$-0.614680\pi$
$137$	5.01578	−	3.64418i	0.428527	−	0.311343i	0.781060	+	0.624457i	$0.214680\pi$
$138$	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	$0.687759\pi$
$140$	−3.05051	−	3.61396i	−0.257816	−	0.305435i
$141$	−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
$145$	5.75264	+	6.81518i	0.477731	+	0.565970i
$146$	−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	$0.564300\pi$
$150$	−4.47803	−	9.04672i	−0.365630	−	0.738662i
$151$	−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
$155$	0.173326	+	2.37874i	0.0139219	+	0.191065i
$156$	0.0666083	−	0.204999i	0.00533293	−	0.0164131i
$157$	−8.89537			−0.709928			−0.354964	−	0.934880i	$-0.615507\pi$
$157$	−8.89537			−0.709928			−0.354964	+	0.934880i	$0.615507\pi$
$158$	−1.54900	+	4.76734i	−0.123232	+	0.379269i
$159$	−3.53313	+	2.56697i	−0.280196	+	0.203574i
$160$	−16.6986	+	6.80350i	−1.32014	+	0.537864i
$161$	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	−0.894710	−	0.446647i	$-0.852618\pi$
$163$	−9.52946	+	6.92356i	−0.746405	+	0.542295i	0.148305	+	0.988942i	$0.452618\pi$
$164$	−12.1080	−	8.79697i	−0.945476	−	0.686928i
$165$	−0.773434	−	10.6147i	−0.0602118	−	0.826351i
$166$	6.93148	−	5.03602i	0.537987	−	0.390871i
$167$	5.36954	−	16.5258i	0.415508	−	1.27880i	−0.496288	−	0.868158i	$-0.665304\pi$
$167$	5.36954	−	16.5258i	0.415508	−	1.27880i	0.911796	−	0.410644i	$-0.134696\pi$
$168$	0.155995			0.0120353
$169$	−4.01389	+	12.3535i	−0.308761	+	0.950268i
$170$	13.8999	−	22.3898i	1.06607	−	1.71722i
$171$	−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	0.910069	−	0.414458i	$-0.136029\pi$
$173$	10.4845	+	7.61744i	0.797123	+	0.579144i	−0.112946	+	0.993601i	$0.536029\pi$
$174$	−8.05221			−0.610436
$175$	3.64382	−	3.56020i	0.275447	−	0.269126i
$176$	−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	$0.886923\pi$
$180$	4.50710	+	1.10976i	0.335939	+	0.0827168i
$181$	−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
$185$	4.74847	−	7.64879i	0.349114	−	0.562350i
$186$	−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
$190$	1.72483	−	2.77834i	0.125132	−	0.201562i
$191$	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	$-0.550433\pi$
$193$	−4.38386			−0.315557			−0.157779	+	0.987475i	$0.550433\pi$
$194$	−4.17913	+	12.8620i	−0.300044	+	0.923440i
$195$	0.225453	+	0.0555124i	0.0161450	+	0.00397532i
$196$	−3.82438	−	11.7702i	−0.273170	−	0.840730i
$197$	0.995545	+	3.06397i	0.0709296	+	0.218299i	0.980237	−	0.197826i	$-0.0633880\pi$
$197$	0.995545	+	3.06397i	0.0709296	+	0.218299i	−0.909308	+	0.416125i	$0.863388\pi$
$198$	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	$0.530567\pi$
$200$	0.339602	+	0.686080i	0.0240135	+	0.0485132i
$201$	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
$205$	8.50311	−	13.6967i	0.593883	−	0.956622i
$206$	−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
$210$	0.334256	+	4.58736i	0.0230659	+	0.316558i
$211$	−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
$215$	−17.8666	+	7.27939i	−1.21849	+	0.496450i
$216$	−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
$220$	1.60552	+	22.0343i	0.108244	+	1.48555i
$221$	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	0.783711	−	0.621126i	$-0.213325\pi$
$223$	6.49839	+	4.72136i	0.435164	+	0.316165i	−0.348546	+	0.937292i	$0.613325\pi$
$224$	8.21604			0.548957
$225$	−0.839441	+	4.92903i	−0.0559627	+	0.328602i
$226$	−13.3051			−0.885044
$227$	−13.3145	−	9.67356i	−0.883715	−	0.642056i	0.0505168	−	0.998723i	$-0.483913\pi$
$227$	−13.3145	−	9.67356i	−0.883715	−	0.642056i	−0.934232	+	0.356667i	$0.883913\pi$
$228$	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	$0.895695\pi$
$230$	−26.4149	−	31.2938i	−1.74175	−	2.06346i
$231$	−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	$0.306751\pi$
$233$	−5.70571	+	17.5604i	−0.373794	+	1.15042i	−0.944289	+	0.329118i	$0.893249\pi$
$234$	−0.169597	+	0.123220i	−0.0110869	+	0.00805512i
$235$	11.8241	+	14.0080i	0.771318	+	0.913783i
$236$	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	$0.652292\pi$
$240$	8.34307	+	2.05428i	0.538543	+	0.132603i
$241$	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
$245$	12.3458	−	5.03007i	0.788747	−	0.321359i
$246$	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
$250$	−19.4479	+	11.4568i	−1.22999	+	0.724592i
$251$	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
$255$	−12.0888	+	4.92533i	−0.757029	+	0.308436i
$256$	4.54826	−	13.9981i	0.284266	−	0.874882i
$257$	8.03324			0.501100			0.250550	−	0.968104i	$-0.419389\pi$
$257$	8.03324			0.501100			0.250550	+	0.968104i	$0.419389\pi$
$258$	5.38265	−	16.5661i	0.335109	−	1.03136i
$259$	−3.31874	+	2.41121i	−0.206216	+	0.149825i
$260$	−0.468004	−	0.115235i	−0.0290244	−	0.00714655i
$261$	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	0.212860	−	0.977083i	$-0.431722\pi$
$263$	19.5888	−	14.2321i	1.20790	−	0.877590i	0.995038	+	0.0994928i	$0.0317220\pi$
$264$	−0.589550	−	0.428333i	−0.0362843	−	0.0263621i
$265$	6.29888	+	7.46231i	0.386937	+	0.458406i
$266$	−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	$-0.197839\pi$
$270$	−2.91185	−	3.44968i	−0.177210	−	0.209941i
$271$	−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
$275$	−23.5467	+	3.44976i	−1.41992	+	0.208028i
$276$	18.8310			1.13349
$277$	19.8376	+	14.4129i	1.19193	+	0.865987i	0.993467	−	0.114122i	$-0.0364054\pi$
$277$	19.8376	+	14.4129i	1.19193	+	0.865987i	0.198462	+	0.980109i	$0.436405\pi$
$278$	0.565553	+	1.74059i	0.0339196	+	0.104394i
$279$	0.329605	+	1.01442i	0.0197329	+	0.0607318i
$280$	−0.0253491	−	0.347893i	−0.00151490	−	0.0207906i
$281$	−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	−0.929374	−	0.369139i	$-0.879653\pi$
$283$	0.664155	−	2.04406i	0.0394799	−	0.121507i	0.968854	+	0.247633i	$0.0796526\pi$
$284$	18.1148	−	13.1612i	1.07492	−	0.780974i
$285$	−1.50009	+	0.611181i	−0.0888576	+	0.0362033i
$286$	−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
$290$	1.30848	+	17.9577i	0.0768366	+	1.05451i
$291$	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	$-0.584963\pi$
$293$	−9.02970			−0.527521			−0.263760	+	0.964588i	$0.584963\pi$
$294$	−3.71942	+	11.4472i	−0.216921	+	0.667615i
$295$	−5.79416	+	9.33318i	−0.337349	+	0.543399i
$296$	−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
$300$	1.74254	−	10.2319i	0.100606	−	0.590737i
$301$	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
$305$	15.1211	+	3.72321i	0.865834	+	0.213190i
$306$	3.64198	−	11.2089i	0.208198	−	0.640768i
$307$	5.03454			0.287336			0.143668	−	0.989626i	$-0.454110\pi$
$307$	5.03454			0.287336			0.143668	+	0.989626i	$0.454110\pi$
$308$	3.11076	−	9.57393i	0.177252	−	0.545525i
$309$	0.480952	−	0.349432i	0.0273604	−	0.0198785i
$310$	−2.53967	+	4.09088i	−0.144243	+	0.232346i
$311$	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	−0.512874	−	0.858464i	$-0.671419\pi$
$313$	2.56686	−	1.86494i	0.145088	−	0.105412i	0.657961	+	0.753052i	$0.271419\pi$
$314$	−14.5288	−	10.5558i	−0.819908	−	0.595698i
$315$	1.20164	−	1.93560i	0.0677049	−	0.109059i
$316$	−4.16978	+	3.02952i	−0.234568	+	0.170424i
$317$	−6.17888	+	19.0166i	−0.347041	+	1.06808i	0.613442	+	0.789740i	$0.289785\pi$
$317$	−6.17888	+	19.0166i	−0.347041	+	1.06808i	−0.960482	+	0.278341i	$0.910215\pi$
$318$	−8.81680			−0.494422
$319$	−5.86625	+	18.0545i	−0.328447	+	1.01086i
$320$	−18.6611	−	4.59484i	−1.04319	−	0.256860i
$321$	−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
$325$	0.0871652	−	0.511816i	0.00483505	−	0.0283905i
$326$	−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
$330$	11.3328	−	18.2548i	0.623849	−	1.00489i
$331$	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
$335$	−1.61199	−	22.1231i	−0.0880725	−	1.20871i
$336$	−3.16737	−	2.30123i	−0.172794	−	0.125542i
$337$	−18.4566	+	13.4095i	−1.00540	+	0.730463i	−0.963238	−	0.268648i	$-0.913423\pi$
$337$	−18.4566	+	13.4095i	−1.00540	+	0.730463i	−0.0421575	+	0.999111i	$0.513423\pi$
$338$	−21.2153	+	15.4138i	−1.15396	+	0.838401i
$339$	5.33173	+	3.87373i	0.289580	+	0.210392i
$340$	25.0943	−	10.2242i	1.36093	−	0.554485i
$341$	−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
$345$	1.47412	+	20.2309i	0.0793638	+	1.08919i
$346$	8.08502	+	24.8831i	0.434654	+	1.33773i
$347$	3.02549	+	9.31149i	0.162417	+	0.499867i	0.998837	−	0.0482222i	$-0.0153555\pi$
$347$	3.02549	+	9.31149i	0.162417	+	0.499867i	−0.836420	+	0.548089i	$0.815356\pi$
$348$	−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	$0.510962\pi$
$350$	10.1762	−	1.49089i	0.543941	−	0.0796912i
$351$	0.103837			0.00554242
$352$	−31.0508	−	22.5597i	−1.65501	−	1.20244i
$353$	0.359765	+	1.10724i	0.0191484	+	0.0589326i	0.960174	−	0.279402i	$-0.0901363\pi$
$353$	0.359765	+	1.10724i	0.0191484	+	0.0589326i	−0.941026	+	0.338335i	$0.890136\pi$
$354$	−3.06496	−	9.43297i	−0.162901	−	0.501357i
$355$	15.5577	+	18.4312i	0.825715	+	0.978228i
$356$	−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	$0.467667\pi$
$360$	0.220827	+	0.261615i	0.0116386	+	0.0137883i
$361$	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
$365$	18.7401	+	4.61430i	0.980903	+	0.241523i
$366$	−11.3749	+	8.26433i	−0.594575	+	0.431984i
$367$	5.18204	−	15.9487i	0.270500	−	0.832514i	−0.719875	−	0.694104i	$-0.755801\pi$
$367$	5.18204	−	15.9487i	0.270500	−	0.832514i	0.990375	−	0.138410i	$-0.0441992\pi$
$368$	34.8580			1.81710
$369$	2.22794	−	6.85690i	0.115982	−	0.356956i
$370$	16.8322	−	6.85795i	0.875065	−	0.356528i
$371$	−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	0.884557	−	0.466432i	$-0.154461\pi$
$373$	13.7954	+	10.0229i	0.714297	+	0.518967i	−0.170260	+	0.985399i	$0.554461\pi$
$374$	56.0953			2.90062
$375$	11.1289	+	1.07112i	0.574695	+	0.0553124i
$376$	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	$0.886375\pi$
$380$	3.11394	−	1.26871i	0.159742	−	0.0650836i
$381$	2.25318	−	6.93457i	0.115434	−	0.355269i
$382$	25.7212			1.31601
$383$	0.943618	−	2.90416i	0.0482166	−	0.148396i	−0.924049	−	0.382273i	$-0.875141\pi$
$383$	0.943618	−	2.90416i	0.0482166	−	0.148396i	0.972266	+	0.233877i	$0.0751414\pi$
$384$	0.990210	−	0.719429i	0.0505314	−	0.0367132i
$385$	10.5292	+	2.59255i	0.536616	+	0.132129i
$386$	−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	$0.954365\pi$
$390$	0.302358	+	0.358205i	0.0153105	+	0.0181384i
$391$	−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
$395$	−3.58115	−	4.24260i	−0.180187	−	0.213468i
$396$	3.05314	+	9.39661i	0.153426	+	0.472197i
$397$	−6.32814	−	19.4760i	−0.317600	−	0.977472i	−0.974671	−	0.223644i	$-0.928205\pi$
$397$	−6.32814	−	19.4760i	−0.317600	−	0.977472i	0.657071	−	0.753829i	$-0.271795\pi$
$398$	−4.41837	−	3.21013i	−0.221473	−	0.160909i
$399$	0.738074			0.0369499
$400$	3.22561	−	18.9402i	0.161281	−	0.947008i
$401$	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
$405$	0.162499	+	2.23016i	0.00807466	+	0.110817i
$406$	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	$0.203789\pi$
$410$	30.1415	−	12.2806i	1.48858	−	0.606495i
$411$	−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
$415$	0.689623	+	9.46444i	0.0338523	+	0.464591i
$416$	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	$0.779440\pi$
$420$	−2.49442	+	4.01799i	−0.121715	+	0.196058i
$421$	−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
$425$	12.9487	+	26.1595i	0.628103	+	1.26892i
$426$	−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
$430$	−37.8197	−	9.31217i	−1.82383	−	0.449073i
$431$	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	−0.844412	−	0.535695i	$-0.820050\pi$
$433$	3.19632	−	9.83725i	0.153605	−	0.472748i	0.998017	+	0.0629466i	$0.0200498\pi$
$434$	1.77499	−	1.28961i	0.0852024	−	0.0619032i
$435$	4.70395	−	7.57709i	0.225537	−	0.363294i
$436$	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	$0.962416\pi$
$440$	−0.859449	+	1.38439i	−0.0409726	+	0.0659984i
$441$	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	$-0.638592\pi$
$443$	−17.7545			−0.843543			−0.421772	+	0.906702i	$0.638592\pi$
$444$	−2.58269	+	7.94870i	−0.122569	+	0.377229i
$445$	−39.8966	−	9.82356i	−1.89128	−	0.465682i
$446$	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	$0.841271\pi$
$450$	−7.22015	+	7.05445i	−0.340361	+	0.332550i
$451$	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
$455$	−0.124775	+	0.200987i	−0.00584955	+	0.00942241i
$456$	−0.0342732	+	0.105482i	−0.00160499	+	0.00493966i
$457$	−27.6987			−1.29569			−0.647846	−	0.761772i	$-0.724330\pi$
$457$	−27.6987			−1.29569			−0.647846	+	0.761772i	$0.724330\pi$
$458$	−0.255338	+	0.785851i	−0.0119312	+	0.0367204i
$459$	−4.72285	+	3.43135i	−0.220444	+	0.160162i
$460$	−3.06003	−	41.9960i	−0.142674	−	1.95808i
$461$	−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	−0.515506	−	0.856886i	$-0.672396\pi$
$463$	3.01546	−	2.19086i	0.140140	−	0.101818i	0.655647	+	0.755068i	$0.272396\pi$
$464$	−12.3990	−	9.00840i	−0.575609	−	0.418204i
$465$	2.20875	−	0.899914i	0.102429	−	0.0417325i
$466$	−30.1574	+	21.9106i	−1.39701	+	1.01499i
$467$	−2.19379	+	6.75179i	−0.101516	+	0.312436i	−0.988897	−	0.148602i	$-0.952523\pi$
$467$	−2.19379	+	6.75179i	−0.101516	+	0.312436i	0.887381	+	0.461038i	$0.152523\pi$
$468$	−0.215549			−0.00996376
$469$	−3.12329	+	9.61249i	−0.144220	+	0.443864i
$470$	2.68947	+	36.9105i	0.124056	+	1.70255i
$471$	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
$475$	1.60679	+	3.24611i	0.0737247	+	0.148942i
$476$	−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	$-0.325166\pi$
$480$	11.6307	+	13.7789i	0.530865	+	0.628917i
$481$	−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
$485$	−9.66174	−	11.4463i	−0.438717	−	0.519750i
$486$	−1.63330	−	1.18666i	−0.0740880	−	0.0538281i
$487$	11.9236	−	8.66301i	0.540310	−	0.392558i	−0.283890	−	0.958857i	$-0.591625\pi$
$487$	11.9236	−	8.66301i	0.540310	−	0.392558i	0.824200	+	0.566298i	$0.191625\pi$
$488$	0.862641	−	0.626746i	0.0390499	−	0.0283714i
$489$	9.52946	+	6.92356i	0.430937	+	0.313094i
$490$	26.1335	+	6.43473i	1.18059	+	0.290691i
$491$	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
$495$	−9.85615	+	4.01569i	−0.443001	+	0.180492i
$496$	−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	$0.298907\pi$
$500$	−23.1018	−	2.22347i	−1.03314	−	0.0994366i
$501$	−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	$0.0211213\pi$
$503$	5.14796	+	15.8438i	0.229536	+	0.706440i	−0.768263	+	0.640134i	$0.778879\pi$
$504$	−0.0482051	−	0.148360i	−0.00214723	−	0.00660848i
$505$	−11.7237	+	4.77659i	−0.521698	+	0.212556i
$506$	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	$0.0512957\pi$
$510$	−25.5893	−	6.30075i	−1.13311	−	0.279002i
$511$	−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
$515$	−0.857442	−	1.01581i	−0.0377834	−	0.0447621i
$516$	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
$520$	−0.0229301	−	0.0271653i	−0.00100555	−	0.00119128i
$521$	−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	0.849244	−	0.528000i	$-0.177058\pi$
$523$	13.9392	+	10.1274i	0.609518	+	0.442840i	−0.239727	+	0.970840i	$0.577058\pi$
$524$	−19.8323			−0.866376
$525$	−4.51195	−	2.36532i	−0.196918	−	0.103231i
$526$	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
$530$	1.43273	+	19.6628i	0.0622336	+	0.854099i
$531$	−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
$535$	−2.87116	+	1.16980i	−0.124131	+	0.0505748i
$536$	−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
$540$	−0.337322	−	4.62944i	−0.0145160	−	0.199219i
$541$	−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
$545$	−10.4456	+	16.8256i	−0.447439	+	0.720731i
$546$	−0.0660028	−	0.203136i	−0.00282466	−	0.00869341i
$547$	2.01110	+	6.18953i	0.0859884	+	0.264645i	0.984801	−	0.173689i	$-0.0555687\pi$
$547$	2.01110	+	6.18953i	0.0859884	+	0.264645i	−0.898812	+	0.438334i	$0.855569\pi$
$548$	10.4119	+	7.56472i	0.444776	+	0.323149i
$549$	6.96435			0.297231
$550$	−42.5525	−	22.3075i	−1.81445	−	0.951194i
$551$	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
$555$	−8.74179	−	2.15245i	−0.371068	−	0.0913665i
$556$	−0.581512	+	1.78971i	−0.0246616	+	0.0759006i
$557$	−6.67224			−0.282712			−0.141356	−	0.989959i	$-0.545146\pi$
$557$	−6.67224			−0.282712			−0.141356	+	0.989959i	$0.545146\pi$
$558$	−0.665430	+	2.04798i	−0.0281699	+	0.0866981i
$559$	0.724796	−	0.526595i	0.0306556	−	0.0222726i
$560$	−4.61740	+	7.43768i	−0.195121	+	0.314299i
$561$	−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	−0.874742	−	0.484589i	$-0.838969\pi$
$563$	−16.2340	+	11.7947i	−0.684181	+	0.497087i	0.190561	+	0.981675i	$0.438969\pi$
$564$	−13.7676	−	10.0027i	−0.579719	−	0.421191i
$565$	7.77262	−	12.5201i	0.326997	−	0.526724i
$566$	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	$0.950486\pi$
$570$	−3.17536	−	0.781855i	−0.133001	−	0.0327483i
$571$	−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
$575$	44.8785	−	6.57502i	1.87156	−	0.274197i
$576$	−8.59476			−0.358115
$577$	7.42872	+	5.39728i	0.309262	+	0.224692i	0.731580	−	0.681756i	$-0.238783\pi$
$577$	7.42872	+	5.39728i	0.309262	+	0.224692i	−0.422318	+	0.906448i	$0.638783\pi$
$578$	−10.6553	−	32.7937i	−0.443202	−	1.36404i
$579$	1.35469	+	4.16930i	0.0562989	+	0.173270i
$580$	−9.76465	+	15.7288i	−0.405455	+	0.653103i
$581$	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
$585$	−0.0168735	−	0.231573i	−0.000697633	−	0.00957437i
$586$	−14.7482	−	10.7152i	−0.609243	−	0.442641i
$587$	−32.3422	+	23.4980i	−1.33491	+	0.969865i	−0.335290	+	0.942115i	$0.608834\pi$
$587$	−32.3422	+	23.4980i	−1.33491	+	0.969865i	−0.999615	+	0.0277503i	$0.991166\pi$
$588$	−10.0123	+	7.27440i	−0.412902	+	0.299991i
$589$	0.625101	+	0.454163i	0.0257568	+	0.0187134i
$590$	−20.5389	+	8.36819i	−0.845575	+	0.344513i
$591$	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	$-0.826341\pi$
$593$	−41.6331			−1.70967			−0.854834	+	0.518902i	$0.826341\pi$
$594$	2.96936	−	9.13874i	0.121834	−	0.374967i
$595$	−0.966535	−	13.2648i	−0.0396241	−	0.543804i
$596$	−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	$0.205769\pi$
$600$	0.547558	−	0.534991i	0.0223539	−	0.0218409i
$601$	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
$605$	−16.8086	−	19.9132i	−0.683368	−	0.809589i
$606$	3.53199	−	10.8704i	0.143477	−	0.441578i
$607$	42.3108			1.71734			0.858671	−	0.512527i	$-0.171291\pi$
$607$	42.3108			1.71734			0.858671	+	0.512527i	$0.171291\pi$
$608$	−1.80512	+	5.55560i	−0.0732074	+	0.225309i
$609$	−3.28763	+	2.38860i	−0.133222	+	0.0967911i
$610$	20.2792	+	24.0248i	0.821079	+	0.972736i
$611$	−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	0.128340	−	0.991730i	$-0.459035\pi$
$613$	27.5118	−	19.9885i	1.11119	−	0.807327i	0.982851	+	0.184403i	$0.0590353\pi$
$614$	8.22292	+	5.97430i	0.331850	+	0.241103i
$615$	−15.6540	−	3.85441i	−0.631230	−	0.155425i
$616$	0.600675	−	0.436416i	0.0242019	−	0.0175837i
$617$	7.20543	−	22.1760i	0.290080	−	0.892773i	−0.694750	−	0.719251i	$-0.744485\pi$
$617$	7.20543	−	22.1760i	0.290080	−	0.892773i	0.984830	−	0.173522i	$-0.0555149\pi$
$618$	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	$-0.151038\pi$
$620$	−4.58502	+	1.86807i	−0.184139	+	0.0750237i
$621$	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
$625$	0.580320	−	24.9933i	0.0232128	−	0.999731i
$626$	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
$630$	4.25954	−	1.73547i	0.169704	−	0.0691427i
$631$	−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
$635$	−15.8313	−	3.89808i	−0.628247	−	0.154690i
$636$	−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
$640$	−1.76535	−	2.09141i	−0.0697815	−	0.0826704i
$641$	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	$-0.500183\pi$
$643$	−0.0291680			−0.00115028			−0.000575138		1.00000i	$0.500183\pi$
$644$	−5.92891	+	18.2473i	−0.233632	+	0.719044i
$645$	12.4442	+	14.7427i	0.489989	+	0.580492i
$646$	−2.63826	−	8.11974i	−0.103801	−	0.319467i
$647$	−0.260841	−	0.802787i	−0.0102547	−	0.0315608i	0.945798	−	0.324755i	$-0.105282\pi$
$647$	−0.260841	−	0.802787i	−0.0102547	−	0.0315608i	−0.956053	+	0.293194i	$0.905282\pi$
$648$	0.123865	+	0.0899934i	0.00486589	+	0.00353527i
$649$	−23.3833			−0.917874
$650$	0.749720	−	0.732514i	0.0294064	−	0.0287316i
$651$	−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	$0.167511\pi$
$653$	11.7646	+	36.2077i	0.460385	+	1.41692i	−0.404311	+	0.914622i	$0.632489\pi$
$654$	−5.52543	−	17.0055i	−0.216061	−	0.664969i
$655$	−1.55250	−	21.3066i	−0.0606611	−	0.832517i
$656$	−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	$0.563715\pi$
$660$	20.4598	−	8.33593i	0.796395	−	0.324476i
$661$	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
$665$	−0.119937	−	1.64602i	−0.00465094	−	0.0638299i
$666$	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
$670$	23.6198	−	38.0465i	0.912511	−	1.46987i
$671$	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	0.267429	−	0.963578i	$-0.413826\pi$
$673$	−14.6923	−	10.6746i	−0.566347	−	0.411475i	−0.833776	+	0.552102i	$0.813826\pi$
$674$	−46.0578			−1.77408
$675$	4.94719	−	0.724798i	0.190417	−	0.0278975i
$676$	−26.9635			−1.03706
$677$	4.56538	+	3.31695i	0.175462	+	0.127481i	0.672050	−	0.740506i	$-0.265414\pi$
$677$	4.56538	+	3.31695i	0.175462	+	0.127481i	−0.496588	+	0.867986i	$0.665414\pi$
$678$	4.11151	+	12.6539i	0.157902	+	0.485971i
$679$	2.10909	+	6.49112i	0.0809396	+	0.249106i
$680$	1.94063	+	0.477832i	0.0744196	+	0.0183240i
$681$	−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	$-0.702071\pi$
$683$	9.40859	−	28.9567i	0.360010	−	1.10800i	0.953047	−	0.302821i	$-0.0979286\pi$
$684$	1.21656	−	0.883879i	0.0465162	−	0.0337960i
$685$	−7.31202	+	11.7781i	−0.279378	+	0.450020i
$686$	−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
$690$	−21.5996	+	34.7924i	−0.822281	+	1.32452i
$691$	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
$695$	−1.96828	−	0.484640i	−0.0746610	−	0.0183835i
$696$	−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
$700$	9.36607	+	4.91001i	0.354004	+	0.185581i
$701$	−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
$705$	9.66859	−	15.5741i	0.364140	−	0.586554i
$706$	−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	$0.131959\pi$
$710$	3.53870	+	48.5654i	0.132805	+	1.82263i
$711$	−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
$715$	1.02343	−	0.416978i	0.0382743	−	0.0155941i
$716$	−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	$-0.157659\pi$
$720$	−0.624416	−	8.56954i	−0.0232706	−	0.319368i
$721$	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
$725$	−17.6625	−	9.25928i	−0.655968	−	0.343881i
$726$	23.5277			0.873196
$727$	−23.9278	−	17.3846i	−0.887434	−	0.644759i	0.0477734	−	0.998858i	$-0.484787\pi$
$727$	−23.9278	−	17.3846i	−0.887434	−	0.644759i	−0.935208	+	0.354099i	$0.884787\pi$
$728$	0.00500548	+	0.0154053i	0.000185515	+	0.000570958i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	25.1326	+	29.7747i	0.930201	+	1.10201i
$731$	−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	$0.458402\pi$
$733$	−15.1042	+	46.4859i	−0.557886	+	1.71700i	−0.688197	+	0.725524i	$0.741598\pi$
$734$	27.3895	−	19.8997i	1.01097	−	0.734510i
$735$	−8.59896	−	10.1872i	−0.317177	−	0.375761i
$736$	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	$0.831071\pi$
$740$	18.1465	+	4.46814i	0.667080	+	0.164252i
$741$	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	$-0.557280\pi$
$743$	−9.75724			−0.357959			−0.178979	+	0.983853i	$0.557280\pi$
$744$	0.0504645	−	0.155314i	0.00185012	−	0.00569408i
$745$	10.1429	−	4.13252i	0.371607	−	0.151404i
$746$	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
$750$	16.9058	+	14.9557i	0.617313	+	0.546106i
$751$	−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
$755$	21.2517	−	8.65861i	0.773430	−	0.315119i
$756$	−0.653574	+	2.01149i	−0.0237702	+	0.0731573i
$757$	−44.2551			−1.60848			−0.804240	−	0.594305i	$-0.797427\pi$
$757$	−44.2551			−1.60848			−0.804240	+	0.594305i	$0.797427\pi$
$758$	−1.03943	+	3.19904i	−0.0377538	+	0.116194i
$759$	−34.9308	+	25.3787i	−1.26791	+	0.921190i
$760$	0.240811	+	0.0592939i	0.00873514	+	0.00215081i
$761$	−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
$765$	8.41991	+	9.97510i	0.304422	+	0.360650i
$766$	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	$-0.119361\pi$
$770$	14.1208	+	16.7290i	0.508879	+	0.602871i
$771$	−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	0.872126	−	0.489281i	$-0.162741\pi$
$773$	18.8029	+	13.6611i	0.676295	+	0.491357i	−0.195832	+	0.980638i	$0.562741\pi$
$774$	−17.4186			−0.626100
$775$	−2.36587	−	4.77963i	−0.0849845	−	0.171689i
$776$	−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
$780$	0.0350266	+	0.480708i	0.00125415	+	0.0172121i
$781$	−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
$785$	18.4204	−	7.50504i	0.657453	−	0.267866i
$786$	15.6043	+	11.3372i	0.556588	+	0.404385i
$787$	−5.52636	+	4.01513i	−0.196993	+	0.143124i	−0.681909	−	0.731437i	$-0.738850\pi$
$787$	−5.52636	+	4.01513i	−0.196993	+	0.143124i	0.484916	+	0.874561i	$0.338850\pi$
$788$	−5.41040	+	3.93089i	−0.192738	+	0.140032i
$789$	−19.5888	−	14.2321i	−0.697381	−	0.506677i
$790$	−0.814558	−	11.1791i	−0.0289807	−	0.397733i
$791$	−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
$795$	5.15062	−	8.29657i	0.182674	−	0.294249i
$796$	−1.73529	−	5.34067i	−0.0615056	−	0.189295i
$797$	16.6649	+	51.2892i	0.590301	+	1.81676i	0.576852	+	0.816849i	$0.304281\pi$
$797$	16.6649	+	51.2892i	0.590301	+	1.81676i	0.0134488	+	0.999910i	$0.495719\pi$
$798$	1.20550	+	0.875844i	0.0426741	+	0.0310046i
$799$	47.8578			1.69309
$800$	28.8391	−	28.1772i	1.01962	−	0.996216i
$801$	−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
$805$	−20.0679	−	4.94124i	−0.707301	−	0.174156i
$806$	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	$0.195094\pi$
$810$	−2.38103	+	3.83535i	−0.0836609	+	0.134760i
$811$	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
$815$	13.8921	−	22.3773i	0.486618	−	0.783841i
$816$	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
$820$	32.4951	+	8.00113i	1.13478	+	0.279412i
$821$	−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	0.547334	−	0.836914i	$-0.315643\pi$
$823$	−2.28023	−	1.65668i	−0.0794839	−	0.0577484i	−0.626818	+	0.779166i	$0.715643\pi$
$824$	−0.0910197			−0.00317082
$825$	10.5572	+	21.3282i	0.367556	+	0.742553i
$826$	10.1056			0.351618
$827$	30.2776	+	21.9979i	1.05285	+	0.764943i	0.972753	−	0.231844i	$-0.0744758\pi$
$827$	30.2776	+	21.9979i	1.05285	+	0.764943i	0.0801008	+	0.996787i	$0.474476\pi$
$828$	−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	$0.719424\pi$
$830$	−10.1047	+	16.2766i	−0.350741	+	0.564970i
$831$	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
$835$	2.82363	+	38.7517i	0.0977156	+	1.34106i
$836$	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	$0.547544\pi$
$840$	−0.323033	+	0.131613i	−0.0111457	+	0.00454109i
$841$	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
$845$	−2.11074	−	28.9680i	−0.0726117	−	0.996529i
$846$	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
$850$	−9.89339	+	58.0920i	−0.339341	+	1.99254i
$851$	−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	$0.0670053\pi$
$853$	9.04183	+	27.8279i	0.309586	+	0.952808i	−0.668340	+	0.743856i	$0.732995\pi$
$854$	−4.42681	−	13.6243i	−0.151482	−	0.466214i
$855$	1.04482	+	1.23780i	0.0357321	+	0.0423320i
$856$	−0.0655988	+	0.201892i	−0.00224212	+	0.00690054i
$857$	−33.5284			−1.14531			−0.572654	−	0.819797i	$-0.694086\pi$
$857$	−33.5284			−1.14531			−0.572654	+	0.819797i	$0.694086\pi$
$858$	−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	$0.154781\pi$
$860$	−25.8321	−	30.6034i	−0.880867	−	1.04357i
$861$	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	−0.114042	−	0.993476i	$-0.536380\pi$
$863$	23.3713	−	16.9803i	0.795569	−	0.578015i	0.909611	+	0.415461i	$0.136380\pi$
$864$	6.52381	+	4.73982i	0.221944	+	0.161252i
$865$	−28.1381	−	6.92831i	−0.956723	−	0.235570i
$866$	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
$870$	16.6744	−	6.79366i	0.565316	−	0.230327i
$871$	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
$875$	−4.54184	+	10.4467i	−0.153542	+	0.353163i
$876$	−17.9169			−0.605355
$877$	12.2165	+	8.87581i	0.412522	+	0.299715i	0.774622	−	0.632425i	$-0.217940\pi$
$877$	12.2165	+	8.87581i	0.412522	+	0.299715i	−0.362100	+	0.932139i	$0.617940\pi$
$878$	−19.1926	−	59.0688i	−0.647719	−	1.99347i
$879$	2.79033	+	8.58775i	0.0941155	+	0.289658i
$880$	37.8730	−	15.4306i	1.27670	−	0.520166i
$881$	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	$0.297448\pi$
$883$	−10.6753	+	32.8551i	−0.359251	+	1.10566i	−0.953503	+	0.301383i	$0.902552\pi$
$884$	−1.01801	+	0.739625i	−0.0342392	+	0.0248763i
$885$	10.6669	+	2.62646i	0.358563	+	0.0882874i
$886$	−28.9985	−	21.0686i	−0.974223	−	0.707814i
$887$	−26.7267	+	19.4181i	−0.897394	+	0.651995i	−0.937795	−	0.347189i	$-0.887136\pi$
$887$	−26.7267	+	19.4181i	−0.897394	+	0.651995i	0.0404016	+	0.999184i	$0.487136\pi$
$888$	−0.498708	+	0.362332i	−0.0167355	+	0.0121591i
$889$	6.01021	+	4.36668i	0.201576	+	0.146454i
$890$	−53.5059	−	63.3886i	−1.79352	−	2.12479i
$891$	−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
$895$	−1.58506	−	1.87783i	−0.0529828	−	0.0627690i
$896$	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
$900$	−10.2696	+	1.50456i	−0.342319	+	0.0501521i
$901$	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
$905$	−2.43419	−	33.4071i	−0.0809153	−	1.11049i
$906$	−6.40250	+	19.7049i	−0.212709	+	0.654650i
$907$	−44.2708			−1.46999			−0.734994	−	0.678074i	$-0.762815\pi$
$907$	−44.2708			−1.46999			−0.734994	+	0.678074i	$0.762815\pi$
$908$	10.5571	−	32.4913i	0.350348	−	1.07826i
$909$	−4.58022	+	3.32773i	−0.151916	+	0.110374i
$910$	−0.442299	+	0.180206i	−0.0146621	+	0.00597377i
$911$	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
$915$	−1.13170	−	15.5316i	−0.0374130	−	0.513459i
$916$	−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	$0.944051\pi$
$920$	1.63805	−	2.63857i	0.0540051	−	0.0869909i
$921$	−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
$925$	−3.37977	+	19.8453i	−0.111126	+	0.652510i
$926$	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	$0.696385\pi$
$930$	4.67545	+	1.15122i	0.153314	+	0.0377499i
$931$	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
$935$	−32.7699	+	52.7855i	−1.07169	+	1.72627i
$936$	−0.0128618	−	0.00934465i	−0.000420402	−	0.000305440i
$937$	38.2951	−	27.8230i	1.25105	−	0.908939i	0.252765	−	0.967528i	$-0.418660\pi$
$937$	38.2951	−	27.8230i	1.25105	−	0.908939i	0.998282	+	0.0585890i	$0.0186602\pi$
$938$	−16.5080	+	11.9938i	−0.539007	+	0.391611i
$939$	−2.56686	−	1.86494i	−0.0837664	−	0.0608599i
$940$	−20.0704	+	32.3293i	−0.654625	+	1.05446i
$941$	−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
$945$	−2.21219	−	0.544698i	−0.0719626	−	0.0177190i
$946$	−25.6193	−	78.8482i	−0.832957	−	2.56358i
$947$	5.85061	+	18.0063i	0.190119	+	0.585127i	0.999999	−	0.00146915i	$-0.000467646\pi$
$947$	5.85061	+	18.0063i	0.190119	+	0.585127i	−0.809880	+	0.586596i	$0.800468\pi$
$948$	4.16978	+	3.02952i	0.135428	+	0.0983942i
$949$	−0.896234			−0.0290930
$950$	−1.22766	+	7.20860i	−0.0398307	+	0.233878i
$951$	19.9953			0.648392
$952$	−0.736741	−	0.535274i	−0.0238779	−	0.0173483i
$953$	−3.53822	−	10.8895i	−0.114614	−	0.352746i	0.877252	−	0.480030i	$-0.159374\pi$
$953$	−3.53822	−	10.8895i	−0.114614	−	0.352746i	−0.991866	+	0.127284i	$0.959374\pi$
$954$	2.72454	+	8.38527i	0.0882103	+	0.271483i
$955$	−15.0259	+	24.2035i	−0.486225	+	0.783208i
$956$	−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
$960$	1.39664	+	19.1677i	0.0450765	+	0.618633i
$961$	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
$965$	9.07805	−	3.69867i	0.292233	−	0.119065i
$966$	15.0961	−	10.9680i	0.485709	−	0.352888i
$967$	−11.4313	+	35.1821i	−0.367607	+	1.13138i	0.580725	+	0.814100i	$0.302769\pi$
$967$	−11.4313	+	35.1821i	−0.367607	+	1.13138i	−0.948332	+	0.317279i	$0.897231\pi$
$968$	−1.78428			−0.0573490
$969$	−1.30680	+	4.02192i	−0.0419805	+	0.129203i
$970$	−2.19763	−	30.1605i	−0.0705617	−	0.968395i
$971$	−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
$975$	−0.513702	+	0.0752610i	−0.0164516	+	0.00241028i
$976$	−26.7610			−0.856600
$977$	−13.4629	−	9.78136i	−0.430716	−	0.312934i	0.351219	−	0.936293i	$-0.385767\pi$
$977$	−13.4629	−	9.78136i	−0.430716	−	0.312934i	−0.781935	+	0.623360i	$0.785767\pi$
$978$	7.34855	+	22.6165i	0.234981	+	0.723196i
$979$	−27.0263	−	83.1783i	−0.863763	−	2.65839i
$980$	17.8500	+	21.1470i	0.570198	+	0.675516i
$981$	−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	$-0.762850\pi$
$983$	8.09305	−	24.9078i	0.258128	−	0.794437i	0.993197	−	0.116445i	$-0.0371497\pi$
$984$	−0.893040	+	0.648831i	−0.0284691	+	0.0206840i
$985$	−4.64664	−	5.50490i	−0.148054	−	0.175401i
$986$	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
$990$	−20.8633	−	5.13709i	−0.663080	−	0.163267i
$991$	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
$995$	5.60185	−	2.28236i	0.177591	−	0.0723558i
$996$	−2.72230	−	8.37837i	−0.0862593	−	0.265479i
$997$	7.75208	+	23.8585i	0.245511	+	0.755605i	0.995552	+	0.0942136i	$0.0300337\pi$
$997$	7.75208	+	23.8585i	0.245511	+	0.755605i	−0.750041	+	0.661391i	$0.769966\pi$
$998$	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	75.2.g.c.16.3	✓	12
3.2	odd	2		225.2.h.d.91.1		12
5.2	odd	4		375.2.i.d.49.2		24
5.3	odd	4		375.2.i.d.49.5		24
5.4	even	2		375.2.g.c.76.1		12
25.2	odd	20		375.2.i.d.199.5		24
25.6	even	5		1875.2.a.j.1.2		6
25.8	odd	20		1875.2.b.f.1249.9		12
25.11	even	5	inner	75.2.g.c.61.3	yes	12
25.14	even	10		375.2.g.c.301.1		12
25.17	odd	20		1875.2.b.f.1249.4		12
25.19	even	10		1875.2.a.k.1.5		6
25.23	odd	20		375.2.i.d.199.2		24
75.11	odd	10		225.2.h.d.136.1		12
75.44	odd	10		5625.2.a.q.1.2		6
75.56	odd	10		5625.2.a.p.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.3	✓	12	1.1	even	1	trivial
75.2.g.c.61.3	yes	12	25.11	even	5	inner
225.2.h.d.91.1		12	3.2	odd	2
225.2.h.d.136.1		12	75.11	odd	10
375.2.g.c.76.1		12	5.4	even	2
375.2.g.c.301.1		12	25.14	even	10
375.2.i.d.49.2		24	5.2	odd	4
375.2.i.d.49.5		24	5.3	odd	4
375.2.i.d.199.2		24	25.23	odd	20
375.2.i.d.199.5		24	25.2	odd	20
1875.2.a.j.1.2		6	25.6	even	5
1875.2.a.k.1.5		6	25.19	even	10
1875.2.b.f.1249.4		12	25.17	odd	20
1875.2.b.f.1249.9		12	25.8	odd	20
5625.2.a.p.1.5		6	75.56	odd	10
5625.2.a.q.1.2		6	75.44	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63330 + 1.18666i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(-2.07079 + 0.843702i) q^{5} +(0.623865 - 1.92006i) q^{6} +1.01887 q^{7} +(-0.0473123 + 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.63330 + 1.18666i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.641469 + 1.97424i) q^{4} +(-2.07079 + 0.843702i) q^{5} +(0.623865 - 1.92006i) q^{6} +1.01887 q^{7} +(-0.0473123 + 0.145612i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-4.38341 - 1.07931i) q^{10} +(-3.85061 - 2.79763i) q^{11} +(1.67939 - 1.22015i) q^{12} +(0.0840060 - 0.0610339i) q^{13} +(1.66412 + 1.20905i) q^{14} +(1.44232 + 1.70872i) q^{15} +(3.10871 - 2.25861i) q^{16} +(-1.80397 + 5.55204i) q^{17} -2.01887 q^{18} +(-0.223853 + 0.688949i) q^{19} +(-2.99402 - 3.54702i) q^{20} +(-0.314848 - 0.969003i) q^{21} +(-2.96936 - 9.13874i) q^{22} +(7.33901 + 5.33210i) q^{23} +0.153106 q^{24} +(3.57633 - 3.49426i) q^{25} +0.209634 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.653574 + 2.01149i) q^{28} +(-1.23251 - 3.79326i) q^{29} +(0.328065 + 4.50239i) q^{30} +(0.329605 - 1.01442i) q^{31} +8.06387 q^{32} +(-1.47080 + 4.52666i) q^{33} +(-9.53482 + 6.92745i) q^{34} +(-2.10987 + 0.859623i) q^{35} +(-1.67939 - 1.22015i) q^{36} +(-3.25727 + 2.36655i) q^{37} +(-1.18317 + 0.859623i) q^{38} +(-0.0840060 - 0.0610339i) q^{39} +(-0.0248796 - 0.341450i) q^{40} +(-5.83282 + 4.23780i) q^{41} +(0.635638 - 1.95629i) q^{42} +8.62791 q^{43} +(3.05314 - 9.39661i) q^{44} +(1.17939 - 1.89975i) q^{45} +(5.65940 + 17.4179i) q^{46} +(-2.53331 - 7.79673i) q^{47} +(-3.10871 - 2.25861i) q^{48} -5.96190 q^{49} +(9.98773 - 1.46327i) q^{50} +5.83776 q^{51} +(0.174383 + 0.126697i) q^{52} +(-1.34954 - 4.15345i) q^{53} +(0.623865 + 1.92006i) q^{54} +(10.3342 + 2.54454i) q^{55} +(-0.0482051 + 0.148360i) q^{56} +0.724404 q^{57} +(2.48827 - 7.65810i) q^{58} +(3.97458 - 2.88770i) q^{59} +(-2.44822 + 3.94357i) q^{60} +(-5.63428 - 4.09354i) q^{61} +(1.74212 - 1.26572i) q^{62} +(-0.824283 + 0.598877i) q^{63} +(6.95331 + 5.05187i) q^{64} +(-0.122464 + 0.197264i) q^{65} +(-7.77388 + 5.64805i) q^{66} +(-3.06544 + 9.43446i) q^{67} -12.1183 q^{68} +(2.80325 - 8.62753i) q^{69} +(-4.46613 - 1.09967i) q^{70} +(-3.33323 - 10.2586i) q^{71} +(-0.0473123 - 0.145612i) q^{72} +(-6.98275 - 5.07326i) q^{73} -8.12840 q^{74} +(-4.42838 - 2.32151i) q^{75} -1.50375 q^{76} +(-3.92327 - 2.85042i) q^{77} +(-0.0647804 - 0.199374i) q^{78} +(0.767263 + 2.36139i) q^{79} +(-4.53188 + 7.29992i) q^{80} +(0.309017 - 0.951057i) q^{81} -14.5556 q^{82} +(1.31142 - 4.03614i) q^{83} +(1.71108 - 1.24317i) q^{84} +(-0.948634 - 13.0191i) q^{85} +(14.0920 + 10.2384i) q^{86} +(-3.22674 + 2.34436i) q^{87} +(0.589550 - 0.428333i) q^{88} +(14.8659 + 10.8007i) q^{89} +(4.18065 - 1.70333i) q^{90} +(0.0855912 - 0.0621857i) q^{91} +(-5.81910 + 17.9093i) q^{92} -1.06662 q^{93} +(5.11443 - 15.7406i) q^{94} +(-0.117715 - 1.61553i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23} + 6 q^{24} + 4 q^{25} - 56 q^{26} + 3 q^{27} + q^{28} - q^{29} + 19 q^{30} + 13 q^{31} - 32 q^{32} - q^{33} - 25 q^{34} - 10 q^{35} + 8 q^{37} - 22 q^{38} + 2 q^{39} - 28 q^{40} + 8 q^{41} - 16 q^{42} - 4 q^{43} + 33 q^{44} - 6 q^{45} - 22 q^{46} - 13 q^{47} - 16 q^{48} - 28 q^{49} + 81 q^{50} + 26 q^{51} + 44 q^{52} + 44 q^{53} + 9 q^{55} + 45 q^{56} - 22 q^{57} + 41 q^{58} - 22 q^{59} + 14 q^{60} - 8 q^{61} + 41 q^{62} + 3 q^{63} + 49 q^{64} - 38 q^{65} - 3 q^{66} - 6 q^{67} - 100 q^{68} + 6 q^{69} - 45 q^{70} - 21 q^{71} + 9 q^{72} - 16 q^{73} - 44 q^{74} - 4 q^{75} - 52 q^{76} + q^{77} - 19 q^{78} + 10 q^{79} - 99 q^{80} - 3 q^{81} + 26 q^{82} - 10 q^{83} - 6 q^{84} + 23 q^{85} + 56 q^{86} - 4 q^{87} - 16 q^{88} + 57 q^{89} + 16 q^{90} - 7 q^{91} + 3 q^{92} + 22 q^{93} - 23 q^{94} + 21 q^{95} - 23 q^{96} + 4 q^{97} - 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

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