LMFDB - Embedded newform 630.2.bi.b.509.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(479,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 1]))

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

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

chi := DirichletCharacter("630.479");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.23
Character	$\chi$	$=$	630.509
Dual form			630.2.bi.b.479.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.69918 + 0.335859i) q^{3} +1.00000 q^{4} +(0.325622 + 2.21223i) q^{5} +(1.69918 + 0.335859i) q^{6} +(-1.75469 - 1.98017i) q^{7} +1.00000 q^{8} +(2.77440 + 1.14137i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.69918 + 0.335859i) q^{3} +1.00000 q^{4} +(0.325622 + 2.21223i) q^{5} +(1.69918 + 0.335859i) q^{6} +(-1.75469 - 1.98017i) q^{7} +1.00000 q^{8} +(2.77440 + 1.14137i) q^{9} +(0.325622 + 2.21223i) q^{10} +(0.702519 + 0.405599i) q^{11} +(1.69918 + 0.335859i) q^{12} +(0.0126841 - 0.0219696i) q^{13} +(-1.75469 - 1.98017i) q^{14} +(-0.189708 + 3.86833i) q^{15} +1.00000 q^{16} +(2.78721 - 1.60920i) q^{17} +(2.77440 + 1.14137i) q^{18} +(1.22111 + 0.705008i) q^{19} +(0.325622 + 2.21223i) q^{20} +(-2.31646 - 3.95398i) q^{21} +(0.702519 + 0.405599i) q^{22} +(1.76983 + 3.06543i) q^{23} +(1.69918 + 0.335859i) q^{24} +(-4.78794 + 1.44070i) q^{25} +(0.0126841 - 0.0219696i) q^{26} +(4.33085 + 2.87119i) q^{27} +(-1.75469 - 1.98017i) q^{28} +(-4.38175 + 2.52980i) q^{29} +(-0.189708 + 3.86833i) q^{30} -3.34408i q^{31} +1.00000 q^{32} +(1.05748 + 0.925132i) q^{33} +(2.78721 - 1.60920i) q^{34} +(3.80923 - 4.52656i) q^{35} +(2.77440 + 1.14137i) q^{36} +(-9.76868 - 5.63995i) q^{37} +(1.22111 + 0.705008i) q^{38} +(0.0289313 - 0.0330701i) q^{39} +(0.325622 + 2.21223i) q^{40} +(-0.973106 + 1.68547i) q^{41} +(-2.31646 - 3.95398i) q^{42} +(-2.76069 + 1.59389i) q^{43} +(0.702519 + 0.405599i) q^{44} +(-1.62156 + 6.50927i) q^{45} +(1.76983 + 3.06543i) q^{46} -7.51607i q^{47} +(1.69918 + 0.335859i) q^{48} +(-0.842147 + 6.94916i) q^{49} +(-4.78794 + 1.44070i) q^{50} +(5.27643 - 1.79820i) q^{51} +(0.0126841 - 0.0219696i) q^{52} +(-5.33975 - 9.24872i) q^{53} +(4.33085 + 2.87119i) q^{54} +(-0.668524 + 1.68621i) q^{55} +(-1.75469 - 1.98017i) q^{56} +(1.83810 + 1.60805i) q^{57} +(-4.38175 + 2.52980i) q^{58} -3.60215 q^{59} +(-0.189708 + 3.86833i) q^{60} +0.608585i q^{61} -3.34408i q^{62} +(-2.60810 - 7.49652i) q^{63} +1.00000 q^{64} +(0.0527320 + 0.0209065i) q^{65} +(1.05748 + 0.925132i) q^{66} +1.01578i q^{67} +(2.78721 - 1.60920i) q^{68} +(1.97770 + 5.80312i) q^{69} +(3.80923 - 4.52656i) q^{70} -10.9830i q^{71} +(2.77440 + 1.14137i) q^{72} +(-6.25999 - 10.8426i) q^{73} +(-9.76868 - 5.63995i) q^{74} +(-8.61943 + 0.839937i) q^{75} +(1.22111 + 0.705008i) q^{76} +(-0.429545 - 2.10281i) q^{77} +(0.0289313 - 0.0330701i) q^{78} +1.69131 q^{79} +(0.325622 + 2.21223i) q^{80} +(6.39456 + 6.33321i) q^{81} +(-0.973106 + 1.68547i) q^{82} +(14.5567 - 8.40429i) q^{83} +(-2.31646 - 3.95398i) q^{84} +(4.46750 + 5.64197i) q^{85} +(-2.76069 + 1.59389i) q^{86} +(-8.29502 + 2.82693i) q^{87} +(0.702519 + 0.405599i) q^{88} +(-2.31249 + 4.00536i) q^{89} +(-1.62156 + 6.50927i) q^{90} +(-0.0657602 + 0.0134330i) q^{91} +(1.76983 + 3.06543i) q^{92} +(1.12314 - 5.68218i) q^{93} -7.51607i q^{94} +(-1.16202 + 2.93094i) q^{95} +(1.69918 + 0.335859i) q^{96} +(3.19146 + 5.52778i) q^{97} +(-0.842147 + 6.94916i) q^{98} +(1.48613 + 1.92712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.69918	+	0.335859i	0.981020	+	0.193908i
$3$	1.69918	+	0.335859i	0.981020	+	0.193908i
$4$	1.00000			0.500000
$5$	0.325622	+	2.21223i	0.145623	+	0.989340i
$5$	0.325622	+	2.21223i	0.145623	+	0.989340i
$6$	1.69918	+	0.335859i	0.693686	+	0.137114i
$7$	−1.75469	−	1.98017i	−0.663209	−	0.748434i
$7$	−1.75469	−	1.98017i	−0.663209	−	0.748434i
$8$	1.00000			0.353553
$9$	2.77440	+	1.14137i	0.924799	+	0.380456i
$10$	0.325622	+	2.21223i	0.102971	+	0.699569i
$11$	0.702519	+	0.405599i	0.211817	+	0.122293i	0.602156	−	0.798379i	$-0.294309\pi$
$11$	0.702519	+	0.405599i	0.211817	+	0.122293i	−0.390338	+	0.920671i	$0.627642\pi$
$12$	1.69918	+	0.335859i	0.490510	+	0.0969541i
$13$	0.0126841	−	0.0219696i	0.00351795	−	0.00609326i	−0.864261	−	0.503044i	$-0.832214\pi$
$13$	0.0126841	−	0.0219696i	0.00351795	−	0.00609326i	0.867779	+	0.496950i	$0.165547\pi$
$14$	−1.75469	−	1.98017i	−0.468960	−	0.529223i
$15$	−0.189708	+	3.86833i	−0.0489825	+	0.998800i
$16$	1.00000			0.250000
$17$	2.78721	−	1.60920i	0.675999	−	0.390288i	−0.122347	−	0.992487i	$-0.539042\pi$
$17$	2.78721	−	1.60920i	0.675999	−	0.390288i	0.798346	+	0.602199i	$0.205709\pi$
$18$	2.77440	+	1.14137i	0.653932	+	0.269023i
$19$	1.22111	+	0.705008i	0.280142	+	0.161740i	0.633488	−	0.773753i	$-0.281623\pi$
$19$	1.22111	+	0.705008i	0.280142	+	0.161740i	−0.353346	+	0.935493i	$0.614956\pi$
$20$	0.325622	+	2.21223i	0.0728113	+	0.494670i
$21$	−2.31646	−	3.95398i	−0.505494	−	0.862830i
$22$	0.702519	+	0.405599i	0.149777	+	0.0864741i
$23$	1.76983	+	3.06543i	0.369035	+	0.639187i	0.989415	−	0.145114i	$-0.0463550\pi$
$23$	1.76983	+	3.06543i	0.369035	+	0.639187i	−0.620380	+	0.784301i	$0.713022\pi$
$24$	1.69918	+	0.335859i	0.346843	+	0.0685569i
$25$	−4.78794	+	1.44070i	−0.957588	+	0.288141i
$26$	0.0126841	−	0.0219696i	0.00248756	−	0.00430859i
$27$	4.33085	+	2.87119i	0.833473	+	0.552561i
$28$	−1.75469	−	1.98017i	−0.331605	−	0.374217i
$29$	−4.38175	+	2.52980i	−0.813670	+	0.469773i	−0.848229	−	0.529630i	$-0.822331\pi$
$29$	−4.38175	+	2.52980i	−0.813670	+	0.469773i	0.0345586	+	0.999403i	$0.488997\pi$
$30$	−0.189708	+	3.86833i	−0.0346358	+	0.706258i
$31$		−	3.34408i		−	0.600615i	−0.953842	−	0.300307i	$-0.902911\pi$
$31$		−	3.34408i		−	0.600615i	0.953842	−	0.300307i	$-0.0970893\pi$
$32$	1.00000			0.176777
$33$	1.05748	+	0.925132i	0.184083	+	0.161045i
$34$	2.78721	−	1.60920i	0.478003	−	0.275975i
$35$	3.80923	−	4.52656i	0.643877	−	0.765129i
$36$	2.77440	+	1.14137i	0.462400	+	0.190228i
$37$	−9.76868	−	5.63995i	−1.60596	−	0.927202i	−0.990261	−	0.139222i	$-0.955540\pi$
$37$	−9.76868	−	5.63995i	−1.60596	−	0.927202i	−0.615700	−	0.787981i	$-0.711127\pi$
$38$	1.22111	+	0.705008i	0.198090	+	0.114367i
$39$	0.0289313	−	0.0330701i	0.00463271	−	0.00529545i
$40$	0.325622	+	2.21223i	0.0514854	+	0.349785i
$41$	−0.973106	+	1.68547i	−0.151974	+	0.263226i	−0.931953	−	0.362579i	$-0.881896\pi$
$41$	−0.973106	+	1.68547i	−0.151974	+	0.263226i	0.779979	+	0.625805i	$0.215230\pi$
$42$	−2.31646	−	3.95398i	−0.357438	−	0.610113i
$43$	−2.76069	+	1.59389i	−0.421002	+	0.243065i	−0.695506	−	0.718521i	$-0.744820\pi$
$43$	−2.76069	+	1.59389i	−0.421002	+	0.243065i	0.274504	+	0.961586i	$0.411486\pi$
$44$	0.702519	+	0.405599i	0.105909	+	0.0611464i
$45$	−1.62156	+	6.50927i	−0.241728	+	0.970344i
$46$	1.76983	+	3.06543i	0.260947	+	0.451973i
$47$		−	7.51607i		−	1.09633i	−0.836370	−	0.548166i	$-0.815326\pi$
$47$		−	7.51607i		−	1.09633i	0.836370	−	0.548166i	$-0.184674\pi$
$48$	1.69918	+	0.335859i	0.245255	+	0.0484771i
$49$	−0.842147	+	6.94916i	−0.120307	+	0.992737i
$50$	−4.78794	+	1.44070i	−0.677117	+	0.203746i
$51$	5.27643	−	1.79820i	0.738848	−	0.251798i
$52$	0.0126841	−	0.0219696i	0.00175897	−	0.00304663i
$53$	−5.33975	−	9.24872i	−0.733471	−	1.27041i	−0.955391	−	0.295344i	$-0.904566\pi$
$53$	−5.33975	−	9.24872i	−0.733471	−	1.27041i	0.221920	−	0.975065i	$-0.428768\pi$
$54$	4.33085	+	2.87119i	0.589354	+	0.390719i
$55$	−0.668524	+	1.68621i	−0.0901438	+	0.227368i
$56$	−1.75469	−	1.98017i	−0.234480	−	0.264611i
$57$	1.83810	+	1.60805i	0.243462	+	0.212992i
$58$	−4.38175	+	2.52980i	−0.575352	+	0.332179i
$59$	−3.60215			−0.468960			−0.234480	−	0.972121i	$-0.575339\pi$
$59$	−3.60215			−0.468960			−0.234480	+	0.972121i	$0.575339\pi$
$60$	−0.189708	+	3.86833i	−0.0244912	+	0.499400i
$61$			0.608585i			0.0779214i	0.999241	+	0.0389607i	$0.0124047\pi$
$61$			0.608585i			0.0779214i	−0.999241	+	0.0389607i	$0.987595\pi$
$62$		−	3.34408i		−	0.424699i
$63$	−2.60810	−	7.49652i	−0.328590	−	0.944473i
$64$	1.00000			0.125000
$65$	0.0527320	+	0.0209065i	0.00654060	+	0.00259313i
$66$	1.05748	+	0.925132i	0.130167	+	0.113876i
$67$			1.01578i			0.124097i	0.998073	+	0.0620487i	$0.0197634\pi$
$67$			1.01578i			0.124097i	−0.998073	+	0.0620487i	$0.980237\pi$
$68$	2.78721	−	1.60920i	0.337999	−	0.195144i
$69$	1.97770	+	5.80312i	0.238087	+	0.698614i
$70$	3.80923	−	4.52656i	0.455290	−	0.541028i
$71$		−	10.9830i		−	1.30344i	−0.758460	−	0.651720i	$-0.774048\pi$
$71$		−	10.9830i		−	1.30344i	0.758460	−	0.651720i	$-0.225952\pi$
$72$	2.77440	+	1.14137i	0.326966	+	0.134511i
$73$	−6.25999	−	10.8426i	−0.732676	−	1.26903i	−0.955735	−	0.294228i	$-0.904938\pi$
$73$	−6.25999	−	10.8426i	−0.732676	−	1.26903i	0.223059	−	0.974805i	$-0.428396\pi$
$74$	−9.76868	−	5.63995i	−1.13559	−	0.655631i
$75$	−8.61943	+	0.839937i	−0.995286	+	0.0969876i
$76$	1.22111	+	0.705008i	0.140071	+	0.0808700i
$77$	−0.429545	−	2.10281i	−0.0489511	−	0.239637i
$78$	0.0289313	−	0.0330701i	0.00327582	−	0.00374445i
$79$	1.69131			0.190288			0.0951438	−	0.995464i	$-0.469669\pi$
$79$	1.69131			0.190288			0.0951438	+	0.995464i	$0.469669\pi$
$80$	0.325622	+	2.21223i	0.0364057	+	0.247335i
$81$	6.39456	+	6.33321i	0.710507	+	0.703690i
$82$	−0.973106	+	1.68547i	−0.107462	+	0.186129i
$83$	14.5567	−	8.40429i	1.59780	−	0.922491i	0.605891	−	0.795548i	$-0.292817\pi$
$83$	14.5567	−	8.40429i	1.59780	−	0.922491i	0.991910	−	0.126943i	$-0.0405165\pi$
$84$	−2.31646	−	3.95398i	−0.252747	−	0.431415i
$85$	4.46750	+	5.64197i	0.484568	+	0.611958i
$86$	−2.76069	+	1.59389i	−0.297693	+	0.171873i
$87$	−8.29502	+	2.82693i	−0.889319	+	0.303079i
$88$	0.702519	+	0.405599i	0.0748887	+	0.0432370i
$89$	−2.31249	+	4.00536i	−0.245124	+	0.424567i	−0.962166	−	0.272462i	$-0.912162\pi$
$89$	−2.31249	+	4.00536i	−0.245124	+	0.424567i	0.717043	+	0.697029i	$0.245495\pi$
$90$	−1.62156	+	6.50927i	−0.170928	+	0.686137i
$91$	−0.0657602	+	0.0134330i	−0.00689354	+	0.00140816i
$92$	1.76983	+	3.06543i	0.184517	+	0.319593i
$93$	1.12314	−	5.68218i	0.116464	−	0.589215i
$94$		−	7.51607i		−	0.775224i
$95$	−1.16202	+	2.93094i	−0.119221	+	0.300709i
$96$	1.69918	+	0.335859i	0.173421	+	0.0342785i
$97$	3.19146	+	5.52778i	0.324044	+	0.561261i	0.981318	−	0.192391i	$-0.0616240\pi$
$97$	3.19146	+	5.52778i	0.324044	+	0.561261i	−0.657274	+	0.753651i	$0.728291\pi$
$98$	−0.842147	+	6.94916i	−0.0850697	+	0.701971i
$99$	1.48613	+	1.92712i	0.149362	+	0.193683i
$100$	−4.78794	+	1.44070i	−0.478794	+	0.144070i
$101$	9.45788	−	16.3815i	0.941094	−	1.63002i	0.177706	−	0.984084i	$-0.443132\pi$
$101$	9.45788	−	16.3815i	0.941094	−	1.63002i	0.763388	−	0.645940i	$-0.223534\pi$
$102$	5.27643	−	1.79820i	0.522444	−	0.178048i
$103$	4.09618	+	7.09479i	0.403609	+	0.699071i	0.994158	−	0.107930i	$-0.0344224\pi$
$103$	4.09618	+	7.09479i	0.403609	+	0.699071i	−0.590550	+	0.807001i	$0.701089\pi$
$104$	0.0126841	−	0.0219696i	0.00124378	−	0.00215429i
$105$	7.99284	−	6.41206i	0.780021	−	0.625753i
$106$	−5.33975	−	9.24872i	−0.518642	−	0.898315i
$107$	0.859971	−	1.48951i	0.0831365	−	0.143997i	−0.821459	−	0.570267i	$-0.806840\pi$
$107$	0.859971	−	1.48951i	0.0831365	−	0.143997i	0.904596	+	0.426271i	$0.140173\pi$
$108$	4.33085	+	2.87119i	0.416736	+	0.276280i
$109$	6.77465	+	11.7340i	0.648894	+	1.12392i	0.983387	+	0.181519i	$0.0581014\pi$
$109$	6.77465	+	11.7340i	0.648894	+	1.12392i	−0.334494	+	0.942398i	$0.608565\pi$
$110$	−0.668524	+	1.68621i	−0.0637413	+	0.160773i
$111$	−14.7045	−	12.8642i	−1.39569	−	1.22101i
$112$	−1.75469	−	1.98017i	−0.165802	−	0.187108i
$113$	−3.60588	+	6.24558i	−0.339213	+	0.587534i	−0.984285	−	0.176588i	$-0.943494\pi$
$113$	−3.60588	+	6.24558i	−0.339213	+	0.587534i	0.645072	+	0.764122i	$0.276827\pi$
$114$	1.83810	+	1.60805i	0.172154	+	0.150608i
$115$	−6.20515	+	4.91344i	−0.578633	+	0.458181i
$116$	−4.38175	+	2.52980i	−0.406835	+	0.234886i
$117$	0.0602662	−	0.0464751i	0.00557161	−	0.00429662i
$118$	−3.60215			−0.331605
$119$	−8.07717	−	2.69552i	−0.740433	−	0.247098i
$120$	−0.189708	+	3.86833i	−0.0173179	+	0.353129i
$121$	−5.17098	−	8.95640i	−0.470089	−	0.814218i
$122$			0.608585i			0.0550987i
$123$	−2.21956	+	2.53708i	−0.200131	+	0.228761i
$124$		−	3.34408i		−	0.300307i
$125$	−4.74623	−	10.1229i	−0.424516	−	0.905421i
$126$	−2.60810	−	7.49652i	−0.232348	−	0.667843i
$127$			16.3712i			1.45271i	0.687318	+	0.726356i	$0.258788\pi$
$127$			16.3712i			1.45271i	−0.687318	+	0.726356i	$0.741212\pi$
$128$	1.00000			0.0883883
$129$	−5.22622	+	1.78109i	−0.460143	+	0.156816i
$130$	0.0527320	+	0.0209065i	0.00462490	+	0.00183362i
$131$	9.56546	+	16.5679i	0.835738	+	1.44754i	0.893428	+	0.449207i	$0.148293\pi$
$131$	9.56546	+	16.5679i	0.835738	+	1.44754i	−0.0576893	+	0.998335i	$0.518373\pi$
$132$	1.05748	+	0.925132i	0.0920417	+	0.0805224i
$133$	−0.746630	−	3.65507i	−0.0647410	−	0.316935i
$134$			1.01578i			0.0877502i
$135$	−4.94151	+	10.5158i	−0.425298	+	0.905053i
$136$	2.78721	−	1.60920i	0.239002	−	0.137988i
$137$	−7.97550	+	13.8140i	−0.681393	+	1.18021i	0.293163	+	0.956062i	$0.405292\pi$
$137$	−7.97550	+	13.8140i	−0.681393	+	1.18021i	−0.974556	+	0.224145i	$0.928041\pi$
$138$	1.97770	+	5.80312i	0.168353	+	0.493994i
$139$	−5.11887	−	2.95538i	−0.434177	−	0.250672i	0.266948	−	0.963711i	$-0.413985\pi$
$139$	−5.11887	−	2.95538i	−0.434177	−	0.250672i	−0.701124	+	0.713039i	$0.747318\pi$
$140$	3.80923	−	4.52656i	0.321939	−	0.382564i
$141$	2.52434	−	12.7711i	0.212588	−	1.07552i
$142$		−	10.9830i		−	0.921671i
$143$	0.0178217	−	0.0102894i	0.00149032	−	0.000860439i
$144$	2.77440	+	1.14137i	0.231200	+	0.0951139i
$145$	−7.02331	−	8.86968i	−0.583254	−	0.736587i
$146$	−6.25999	−	10.8426i	−0.518080	−	0.897342i
$147$	−3.76489	+	11.5250i	−0.310523	+	0.950566i
$148$	−9.76868	−	5.63995i	−0.802981	−	0.463601i
$149$	−9.81170	+	5.66479i	−0.803806	+	0.464078i	−0.844800	−	0.535082i	$-0.820281\pi$
$149$	−9.81170	+	5.66479i	−0.803806	+	0.464078i	0.0409943	+	0.999159i	$0.486947\pi$
$150$	−8.61943	+	0.839937i	−0.703773	+	0.0685806i
$151$	−6.13048	+	10.6183i	−0.498892	+	0.864105i	−0.999999	−	0.00127950i	$-0.999593\pi$
$151$	−6.13048	+	10.6183i	−0.498892	+	0.864105i	0.501108	+	0.865385i	$0.332926\pi$
$152$	1.22111	+	0.705008i	0.0990451	+	0.0571837i
$153$	9.56952	−	1.28332i	0.773650	−	0.103751i
$154$	−0.429545	−	2.10281i	−0.0346137	−	0.169449i
$155$	7.39788	−	1.08891i	0.594212	−	0.0874631i
$156$	0.0289313	−	0.0330701i	0.00231635	−	0.00264773i
$157$	−2.81134			−0.224369			−0.112185	−	0.993687i	$-0.535785\pi$
$157$	−2.81134			−0.224369			−0.112185	+	0.993687i	$0.535785\pi$
$158$	1.69131			0.134554
$159$	−5.96691	−	17.5086i	−0.473207	−	1.38852i
$160$	0.325622	+	2.21223i	0.0257427	+	0.174892i
$161$	2.96458	−	8.88343i	0.233642	−	0.700113i
$162$	6.39456	+	6.33321i	0.502404	+	0.497584i
$163$	−15.9183	−	9.19043i	−1.24682	−	0.719850i	−0.276343	−	0.961059i	$-0.589123\pi$
$163$	−15.9183	−	9.19043i	−1.24682	−	0.719850i	−0.970473	+	0.241209i	$0.922456\pi$
$164$	−0.973106	+	1.68547i	−0.0759868	+	0.131613i
$165$	−1.70227	+	2.64063i	−0.132521	+	0.205573i
$166$	14.5567	−	8.40429i	1.12982	−	0.652299i
$167$	7.45421	+	4.30369i	0.576824	+	0.333029i	0.759870	−	0.650075i	$-0.225262\pi$
$167$	7.45421	+	4.30369i	0.576824	+	0.333029i	−0.183046	+	0.983104i	$0.558596\pi$
$168$	−2.31646	−	3.95398i	−0.178719	−	0.305057i
$169$	6.49968	+	11.2578i	0.499975	+	0.865983i
$170$	4.46750	+	5.64197i	0.342642	+	0.432719i
$171$	2.58317	+	3.34971i	0.197540	+	0.256159i
$172$	−2.76069	+	1.59389i	−0.210501	+	0.121533i
$173$		−	3.90551i		−	0.296930i	−0.988918	−	0.148465i	$-0.952567\pi$
$173$		−	3.90551i		−	0.296930i	0.988918	−	0.148465i	$-0.0474332\pi$
$174$	−8.29502	+	2.82693i	−0.628844	+	0.214309i
$175$	11.2542	+	6.95295i	0.850736	+	0.525594i
$176$	0.702519	+	0.405599i	0.0529543	+	0.0305732i
$177$	−6.12068	−	1.20981i	−0.460059	−	0.0909352i
$178$	−2.31249	+	4.00536i	−0.173329	+	0.300214i
$179$	16.4704	−	9.50922i	1.23106	−	0.710752i	0.263808	−	0.964575i	$-0.415021\pi$
$179$	16.4704	−	9.50922i	1.23106	−	0.710752i	0.967251	+	0.253823i	$0.0816880\pi$
$180$	−1.62156	+	6.50927i	−0.120864	+	0.485172i
$181$		−	14.5366i		−	1.08049i	−0.841506	−	0.540247i	$-0.818331\pi$
$181$		−	14.5366i		−	1.08049i	0.841506	−	0.540247i	$-0.181669\pi$
$182$	−0.0657602	+	0.0134330i	−0.00487447	+	0.000995718i
$183$	−0.204399	+	1.03409i	−0.0151096	+	0.0764424i
$184$	1.76983	+	3.06543i	0.130473	+	0.225987i
$185$	9.29598	−	23.4471i	0.683454	−	1.72386i
$186$	1.12314	−	5.68218i	0.0823526	−	0.416638i
$187$	2.61076			0.190918
$188$		−	7.51607i		−	0.548166i
$189$	−1.91385	−	13.6139i	−0.139212	−	0.990263i
$190$	−1.16202	+	2.93094i	−0.0843019	+	0.212633i
$191$		−	2.54057i		−	0.183829i	−0.995767	−	0.0919146i	$-0.970701\pi$
$191$		−	2.54057i		−	0.183829i	0.995767	−	0.0919146i	$-0.0292987\pi$
$192$	1.69918	+	0.335859i	0.122627	+	0.0242385i
$193$			7.82427i			0.563203i	0.959531	+	0.281602i	$0.0908657\pi$
$193$			7.82427i			0.563203i	−0.959531	+	0.281602i	$0.909134\pi$
$194$	3.19146	+	5.52778i	0.229134	+	0.396871i
$195$	0.0825793	+	0.0532343i	0.00591363	+	0.00381219i
$196$	−0.842147	+	6.94916i	−0.0601534	+	0.496368i
$197$	2.27493			0.162082			0.0810412	−	0.996711i	$-0.474175\pi$
$197$	2.27493			0.162082			0.0810412	+	0.996711i	$0.474175\pi$
$198$	1.48613	+	1.92712i	0.105615	+	0.136955i
$199$	−17.5140	+	10.1117i	−1.24154	+	0.716801i	−0.969407	−	0.245460i	$-0.921061\pi$
$199$	−17.5140	+	10.1117i	−1.24154	+	0.716801i	−0.272128	+	0.962261i	$0.587728\pi$
$200$	−4.78794	+	1.44070i	−0.338559	+	0.101873i
$201$	−0.341159	+	1.72599i	−0.0240635	+	0.121742i
$202$	9.45788	−	16.3815i	0.665454	−	1.15260i
$203$	12.6980	+	4.23759i	0.891227	+	0.297421i
$204$	5.27643	−	1.79820i	0.369424	−	0.125899i
$205$	−4.04551	−	1.60391i	−0.282551	−	0.112022i
$206$	4.09618	+	7.09479i	0.285394	+	0.494318i
$207$	1.41142	+	10.5248i	0.0981008	+	0.731521i
$208$	0.0126841	−	0.0219696i	0.000879487	−	0.00152332i
$209$	0.571902	+	0.990563i	0.0395593	+	0.0685186i
$210$	7.99284	−	6.41206i	0.551558	−	0.442474i
$211$	2.65419	−	4.59719i	0.182722	−	0.316483i	−0.760085	−	0.649824i	$-0.774843\pi$
$211$	2.65419	−	4.59719i	0.182722	−	0.316483i	0.942806	+	0.333341i	$0.108176\pi$
$212$	−5.33975	−	9.24872i	−0.366735	−	0.635204i
$213$	3.68873	−	18.6620i	0.252748	−	1.27870i
$214$	0.859971	−	1.48951i	0.0587864	−	0.101821i
$215$	−4.42499	−	5.58829i	−0.301782	−	0.381118i
$216$	4.33085	+	2.87119i	0.294677	+	0.195360i
$217$	−6.62185	+	5.86782i	−0.449520	+	0.398333i
$218$	6.77465	+	11.7340i	0.458837	+	0.794729i
$219$	−6.99523	−	20.5260i	−0.472694	−	1.38702i
$220$	−0.668524	+	1.68621i	−0.0450719	+	0.113684i
$221$		−	0.0816452i		−	0.00549205i
$222$	−14.7045	−	12.8642i	−0.986900	−	0.863386i
$223$	4.61986	+	8.00184i	0.309369	+	0.535843i	0.978224	−	0.207550i	$-0.0665489\pi$
$223$	4.61986	+	8.00184i	0.309369	+	0.535843i	−0.668856	+	0.743392i	$0.733216\pi$
$224$	−1.75469	−	1.98017i	−0.117240	−	0.132306i
$225$	−14.9280	−	1.46771i	−0.995201	−	0.0978473i
$226$	−3.60588	+	6.24558i	−0.239860	+	0.415450i
$227$	−5.11105	−	2.95087i	−0.339232	−	0.195856i	0.320700	−	0.947181i	$-0.396082\pi$
$227$	−5.11105	−	2.95087i	−0.339232	−	0.195856i	−0.659933	+	0.751325i	$0.729415\pi$
$228$	1.83810	+	1.60805i	0.121731	+	0.106496i
$229$	−17.9965	+	10.3903i	−1.18924	+	0.686609i	−0.958134	−	0.286319i	$-0.907568\pi$
$229$	−17.9965	+	10.3903i	−1.18924	+	0.686609i	−0.231108	+	0.972928i	$0.574235\pi$
$230$	−6.20515	+	4.91344i	−0.409156	+	0.323983i
$231$	−0.0236257	−	3.71730i	−0.00155446	−	0.244581i
$232$	−4.38175	+	2.52980i	−0.287676	+	0.166090i
$233$	−14.0861	+	24.3978i	−0.922811	+	1.59836i	−0.127767	+	0.991804i	$0.540781\pi$
$233$	−14.0861	+	24.3978i	−0.922811	+	1.59836i	−0.795044	+	0.606551i	$0.792552\pi$
$234$	0.0602662	−	0.0464751i	0.00393972	−	0.00303817i
$235$	16.6273	−	2.44740i	1.08465	−	0.159651i
$236$	−3.60215			−0.234480
$237$	2.87384	+	0.568042i	0.186676	+	0.0368983i
$238$	−8.07717	−	2.69552i	−0.523565	−	0.174724i
$239$	7.81549	+	4.51228i	0.505542	+	0.291875i	0.730999	−	0.682378i	$-0.239054\pi$
$239$	7.81549	+	4.51228i	0.505542	+	0.291875i	−0.225457	+	0.974253i	$0.572388\pi$
$240$	−0.189708	+	3.86833i	−0.0122456	+	0.249700i
$241$	−2.13074	−	1.23018i	−0.137253	−	0.0792429i	0.429801	−	0.902923i	$-0.358584\pi$
$241$	−2.13074	−	1.23018i	−0.137253	−	0.0792429i	−0.567054	+	0.823681i	$0.691917\pi$
$242$	−5.17098	−	8.95640i	−0.332403	−	0.575739i
$243$	8.73843	+	12.9089i	0.560570	+	0.828107i
$244$			0.608585i			0.0389607i
$245$	−15.6474	+	0.399775i	−0.999674	+	0.0255407i
$246$	−2.21956	+	2.53708i	−0.141514	+	0.161758i
$247$	0.0309774	−	0.0178848i	0.00197105	−	0.00113799i
$248$		−	3.34408i		−	0.212349i
$249$	27.5570	−	9.39139i	1.74635	−	0.595155i
$250$	−4.74623	−	10.1229i	−0.300178	−	0.640229i
$251$	28.8906			1.82356			0.911780	−	0.410679i	$-0.134708\pi$
$251$	28.8906			1.82356			0.911780	+	0.410679i	$0.134708\pi$
$252$	−2.60810	−	7.49652i	−0.164295	−	0.472236i
$253$			2.87136i			0.180521i
$254$			16.3712i			1.02722i
$255$	5.69616	+	11.0872i	0.356707	+	0.694304i
$256$	1.00000			0.0625000
$257$	−2.25121	+	1.29974i	−0.140427	+	0.0810754i	−0.568567	−	0.822637i	$-0.692502\pi$
$257$	−2.25121	+	1.29974i	−0.140427	+	0.0810754i	0.428141	+	0.903712i	$0.359169\pi$
$258$	−5.22622	+	1.78109i	−0.325370	+	0.110886i
$259$	5.97292	+	29.2400i	0.371139	+	1.81689i
$260$	0.0527320	+	0.0209065i	0.00327030	+	0.00129656i
$261$	−15.0441	+	2.01750i	−0.931209	+	0.124880i
$262$	9.56546	+	16.5679i	0.590956	+	1.02357i
$263$	−8.11154	+	14.0496i	−0.500179	+	0.866336i	0.499821	+	0.866129i	$0.333399\pi$
$263$	−8.11154	+	14.0496i	−0.500179	+	0.866336i	−1.00000		0.000206827i	$0.999934\pi$
$264$	1.05748	+	0.925132i	0.0650833	+	0.0569379i
$265$	18.7216	−	14.8244i	1.15006	−	0.910653i
$266$	−0.746630	−	3.65507i	−0.0457788	−	0.224107i
$267$	−5.27457	+	6.02914i	−0.322798	+	0.368977i
$268$			1.01578i			0.0620487i
$269$	−3.04488	−	5.27389i	−0.185650	−	0.321555i	0.758145	−	0.652085i	$-0.226106\pi$
$269$	−3.04488	−	5.27389i	−0.185650	−	0.321555i	−0.943795	+	0.330531i	$0.892772\pi$
$270$	−4.94151	+	10.5158i	−0.300731	+	0.639969i
$271$	−16.3148	−	9.41937i	−0.991055	−	0.572186i	−0.0854657	−	0.996341i	$-0.527238\pi$
$271$	−16.3148	−	9.41937i	−0.991055	−	0.572186i	−0.905590	+	0.424155i	$0.860571\pi$
$272$	2.78721	−	1.60920i	0.169000	−	0.0975720i
$273$	−0.116250		0.000738837i	−0.00703575		4.47165e-5i
$274$	−7.97550	+	13.8140i	−0.481818	+	0.834532i
$275$	−3.94797	−	0.929864i	−0.238071	−	0.0560729i
$276$	1.97770	+	5.80312i	0.119043	+	0.349307i
$277$	14.9277	+	8.61850i	0.896917	+	0.517835i	0.876199	−	0.481950i	$-0.160071\pi$
$277$	14.9277	+	8.61850i	0.896917	+	0.517835i	0.0207184	+	0.999785i	$0.493405\pi$
$278$	−5.11887	−	2.95538i	−0.307009	−	0.177252i
$279$	3.81682	−	9.27781i	0.228507	−	0.555448i
$280$	3.80923	−	4.52656i	0.227645	−	0.270514i
$281$	6.70985	−	3.87393i	0.400276	−	0.231099i	−0.286327	−	0.958132i	$-0.592434\pi$
$281$	6.70985	−	3.87393i	0.400276	−	0.231099i	0.686603	+	0.727032i	$0.259101\pi$
$282$	2.52434	−	12.7711i	0.150322	−	0.760510i
$283$	0.773573			0.0459842			0.0229921	−	0.999736i	$-0.492681\pi$
$283$	0.773573			0.0459842			0.0229921	+	0.999736i	$0.492681\pi$
$284$		−	10.9830i		−	0.651720i
$285$	−2.95886	+	4.58992i	−0.175268	+	0.271883i
$286$	0.0178217	−	0.0102894i	0.00105382	−	0.000608422i
$287$	5.04501	−	1.03055i	0.297797	−	0.0608317i
$288$	2.77440	+	1.14137i	0.163483	+	0.0672557i
$289$	−3.32096	+	5.75207i	−0.195351	+	0.338357i
$290$	−7.02331	−	8.86968i	−0.412423	−	0.520846i
$291$	3.56631	+	10.4645i	0.209061	+	0.613443i
$292$	−6.25999	−	10.8426i	−0.366338	−	0.634516i
$293$	22.8864	+	13.2135i	1.33704	+	0.771939i	0.986367	−	0.164560i	$-0.0526203\pi$
$293$	22.8864	+	13.2135i	1.33704	+	0.771939i	0.350671	+	0.936499i	$0.385954\pi$
$294$	−3.76489	+	11.5250i	−0.219573	+	0.672152i
$295$	−1.17294	−	7.96879i	−0.0682912	−	0.463961i
$296$	−9.76868	−	5.63995i	−0.567793	−	0.327815i
$297$	1.87795	+	3.77365i	0.108970	+	0.218970i
$298$	−9.81170	+	5.66479i	−0.568377	+	0.328152i
$299$	0.0897950			0.00519298
$300$	−8.61943	+	0.839937i	−0.497643	+	0.0484938i
$301$	8.00032	+	2.66987i	0.461131	+	0.153889i
$302$	−6.13048	+	10.6183i	−0.352770	+	0.611015i
$303$	21.5725	−	24.6586i	1.23931	−	1.41660i
$304$	1.22111	+	0.705008i	0.0700355	+	0.0404350i
$305$	−1.34633	+	0.198169i	−0.0770907	+	0.0113471i
$306$	9.56952	−	1.28332i	0.547053	−	0.0733627i
$307$	16.0600			0.916592			0.458296	−	0.888800i	$-0.348460\pi$
$307$	16.0600			0.916592			0.458296	+	0.888800i	$0.348460\pi$
$308$	−0.429545	−	2.10281i	−0.0244756	−	0.119818i
$309$	4.57728	+	13.4310i	0.260393	+	0.764065i
$310$	7.39788	−	1.08891i	0.420172	−	0.0618458i
$311$	20.0672			1.13791			0.568954	−	0.822369i	$-0.307348\pi$
$311$	20.0672			1.13791			0.568954	+	0.822369i	$0.307348\pi$
$312$	0.0289313	−	0.0330701i	0.00163791	−	0.00187222i
$313$	−10.1545			−0.573969			−0.286984	−	0.957935i	$-0.592653\pi$
$313$	−10.1545			−0.573969			−0.286984	+	0.957935i	$0.592653\pi$
$314$	−2.81134			−0.158653
$315$	15.7348	−	8.21075i	0.886555	−	0.462624i
$316$	1.69131			0.0951438
$317$	−26.9529			−1.51383			−0.756913	−	0.653515i	$-0.773294\pi$
$317$	−26.9529			−1.51383			−0.756913	+	0.653515i	$0.773294\pi$
$318$	−5.96691	−	17.5086i	−0.334608	−	0.981833i
$319$	−4.10435			−0.229799
$320$	0.325622	+	2.21223i	0.0182028	+	0.123668i
$321$	1.96151	−	2.24212i	0.109481	−	0.125143i
$322$	2.96458	−	8.88343i	0.165210	−	0.495054i
$323$	4.53799			0.252501
$324$	6.39456	+	6.33321i	0.355254	+	0.351845i
$325$	−0.0290792	+	0.123463i	−0.00161303	+	0.00684850i
$326$	−15.9183	−	9.19043i	−0.881632	−	0.509011i
$327$	7.57034	+	22.2135i	0.418641	+	1.22841i
$328$	−0.973106	+	1.68547i	−0.0537308	+	0.0930644i
$329$	−14.8831	+	13.1884i	−0.820532	+	0.727098i
$330$	−1.70227	+	2.64063i	−0.0937067	+	0.145362i
$331$	20.1804			1.10921			0.554606	−	0.832113i	$-0.312869\pi$
$331$	20.1804			1.10921			0.554606	+	0.832113i	$0.312869\pi$
$332$	14.5567	−	8.40429i	0.798900	−	0.461245i
$333$	−20.6650	−	26.7971i	−1.13243	−	1.46847i
$334$	7.45421	+	4.30369i	0.407876	+	0.235487i
$335$	−2.24714	+	0.330761i	−0.122775	+	0.0180714i
$336$	−2.31646	−	3.95398i	−0.126373	−	0.215708i
$337$	18.8483	+	10.8821i	1.02673	+	0.592786i	0.916048	−	0.401070i	$-0.131361\pi$
$337$	18.8483	+	10.8821i	1.02673	+	0.592786i	0.110687	+	0.993855i	$0.464695\pi$
$338$	6.49968	+	11.2578i	0.353536	+	0.612342i
$339$	−8.22466	+	9.40126i	−0.446702	+	0.510607i
$340$	4.46750	+	5.64197i	0.242284	+	0.305979i
$341$	1.35636	−	2.34928i	0.0734508	−	0.127221i
$342$	2.58317	+	3.34971i	0.139682	+	0.181131i
$343$	15.2382	−	10.5260i	0.822786	−	0.568351i
$344$	−2.76069	+	1.59389i	−0.148847	+	0.0859366i
$345$	−12.1939	+	6.26475i	−0.656496	+	0.337283i
$346$		−	3.90551i		−	0.209961i
$347$	9.89335			0.531103			0.265551	−	0.964097i	$-0.414446\pi$
$347$	9.89335			0.531103			0.265551	+	0.964097i	$0.414446\pi$
$348$	−8.29502	+	2.82693i	−0.444660	+	0.151539i
$349$	29.2025	−	16.8601i	1.56318	−	0.902500i	0.566242	−	0.824239i	$-0.308397\pi$
$349$	29.2025	−	16.8601i	1.56318	−	0.902500i	0.996933	−	0.0782606i	$-0.0249366\pi$
$350$	11.2542	+	6.95295i	0.601561	+	0.371651i
$351$	0.118012	−	0.0587284i	0.00629901	−	0.00313469i
$352$	0.702519	+	0.405599i	0.0374444	+	0.0216185i
$353$	15.0879	+	8.71103i	0.803050	+	0.463641i	0.844537	−	0.535498i	$-0.179876\pi$
$353$	15.0879	+	8.71103i	0.803050	+	0.463641i	−0.0414865	+	0.999139i	$0.513209\pi$
$354$	−6.12068	−	1.20981i	−0.325311	−	0.0643009i
$355$	24.2969	−	3.57630i	1.28954	−	0.189810i
$356$	−2.31249	+	4.00536i	−0.122562	+	0.212284i
$357$	−12.8192	−	7.29295i	−0.678465	−	0.385984i
$358$	16.4704	−	9.50922i	0.870490	−	0.502578i
$359$	29.8414	+	17.2289i	1.57497	+	0.909309i	0.995546	+	0.0942818i	$0.0300555\pi$
$359$	29.8414	+	17.2289i	1.57497	+	0.909309i	0.579423	+	0.815027i	$0.303278\pi$
$360$	−1.62156	+	6.50927i	−0.0854638	+	0.343068i
$361$	−8.50593	−	14.7327i	−0.447680	−	0.775405i
$362$		−	14.5366i		−	0.764025i
$363$	−5.77832	−	16.9552i	−0.303283	−	0.889918i
$364$	−0.0657602	+	0.0134330i	−0.00344677	+	0.000704079i
$365$	21.9480	−	17.3791i	1.14881	−	0.909666i
$366$	−0.204399	+	1.03409i	−0.0106841	+	0.0540529i
$367$	−12.2578	+	21.2311i	−0.639852	+	1.10826i	0.345613	+	0.938377i	$0.387671\pi$
$367$	−12.2578	+	21.2311i	−0.639852	+	1.10826i	−0.985465	+	0.169879i	$0.945662\pi$
$368$	1.76983	+	3.06543i	0.0922587	+	0.159797i
$369$	−4.62352	+	3.56549i	−0.240691	+	0.185612i
$370$	9.29598	−	23.4471i	0.483275	−	1.21896i
$371$	−8.94444	+	26.8022i	−0.464372	+	1.39150i
$372$	1.12314	−	5.68218i	0.0582321	−	0.294607i
$373$	−18.8999	+	10.9119i	−0.978600	+	0.564995i	−0.901847	−	0.432055i	$-0.857789\pi$
$373$	−18.8999	+	10.9119i	−0.978600	+	0.564995i	−0.0767531	+	0.997050i	$0.524455\pi$
$374$	2.61076			0.134999
$375$	−4.66481	−	18.7947i	−0.240890	−	0.970552i
$376$		−	7.51607i		−	0.387612i
$377$			0.128353i			0.00661054i
$378$	−1.91385	−	13.6139i	−0.0984376	−	0.700221i
$379$	30.0822			1.54522			0.772610	−	0.634881i	$-0.218951\pi$
$379$	30.0822			1.54522			0.772610	+	0.634881i	$0.218951\pi$
$380$	−1.16202	+	2.93094i	−0.0596104	+	0.150354i
$381$	−5.49843	+	27.8176i	−0.281693	+	1.42514i
$382$		−	2.54057i		−	0.129987i
$383$	−26.4753	+	15.2855i	−1.35282	+	0.781054i	−0.988644	−	0.150275i	$-0.951984\pi$
$383$	−26.4753	+	15.2855i	−1.35282	+	0.781054i	−0.364180	+	0.931328i	$0.618651\pi$
$384$	1.69918	+	0.335859i	0.0867107	+	0.0171392i
$385$	4.51203	−	1.63497i	0.229954	−	0.0833259i
$386$			7.82427i			0.398245i
$387$	−9.47847	+	1.27111i	−0.481817	+	0.0646143i
$388$	3.19146	+	5.52778i	0.162022	+	0.280630i
$389$	−18.1559	−	10.4823i	−0.920543	−	0.531476i	−0.0367349	−	0.999325i	$-0.511696\pi$
$389$	−18.1559	−	10.4823i	−0.920543	−	0.531476i	−0.883808	+	0.467849i	$0.845029\pi$
$390$	0.0825793	+	0.0532343i	0.00418157	+	0.00269562i
$391$	9.86578	+	5.69601i	0.498934	+	0.288060i
$392$	−0.842147	+	6.94916i	−0.0425349	+	0.350985i
$393$	10.6889	+	31.3644i	0.539186	+	1.58212i
$394$	2.27493			0.114609
$395$	0.550729	+	3.74158i	0.0277102	+	0.188259i
$396$	1.48613	+	1.92712i	0.0746808	+	0.0968417i
$397$	15.9516	−	27.6289i	0.800586	−	1.38666i	−0.118645	−	0.992937i	$-0.537855\pi$
$397$	15.9516	−	27.6289i	0.800586	−	1.38666i	0.919231	−	0.393719i	$-0.128812\pi$
$398$	−17.5140	+	10.1117i	−0.877898	+	0.506855i
$399$	−0.0410660	−	6.46138i	−0.00205587	−	0.323473i
$400$	−4.78794	+	1.44070i	−0.239397	+	0.0720352i
$401$	−7.49269	+	4.32591i	−0.374167	+	0.216026i	−0.675277	−	0.737564i	$-0.735976\pi$
$401$	−7.49269	+	4.32591i	−0.374167	+	0.216026i	0.301110	+	0.953589i	$0.402643\pi$
$402$	−0.341159	+	1.72599i	−0.0170155	+	0.0860847i
$403$	−0.0734680	−	0.0424168i	−0.00365970	−	0.00211293i
$404$	9.45788	−	16.3815i	0.470547	−	0.815012i
$405$	−11.9283	+	16.2085i	−0.592723	+	0.805407i
$406$	12.6980	+	4.23759i	0.630193	+	0.210308i
$407$	−4.57512	−	7.92434i	−0.226780	−	0.392795i
$408$	5.27643	−	1.79820i	0.261222	−	0.0890242i
$409$		−	25.3709i		−	1.25451i	−0.778814	−	0.627255i	$-0.784178\pi$
$409$		−	25.3709i		−	1.25451i	0.778814	−	0.627255i	$-0.215822\pi$
$410$	−4.04551	−	1.60391i	−0.199794	−	0.0792114i
$411$	−18.1913	+	20.7937i	−0.897312	+	1.02568i
$412$	4.09618	+	7.09479i	0.201804	+	0.349535i
$413$	6.32064	+	7.13287i	0.311019	+	0.350985i
$414$	1.41142	+	10.5248i	0.0693677	+	0.517263i
$415$	23.3322	+	29.4661i	1.14533	+	1.44643i
$416$	0.0126841	−	0.0219696i	0.000621891	−	0.00107715i
$417$	−7.70527	−	6.74093i	−0.377329	−	0.330105i
$418$	0.571902	+	0.990563i	0.0279726	+	0.0484500i
$419$	−4.57468	+	7.92357i	−0.223488	+	0.387092i	−0.955865	−	0.293808i	$-0.905078\pi$
$419$	−4.57468	+	7.92357i	−0.223488	+	0.387092i	0.732377	+	0.680899i	$0.238411\pi$
$420$	7.99284	−	6.41206i	0.390011	−	0.312877i
$421$	−15.3068	−	26.5121i	−0.746007	−	1.29212i	−0.949723	−	0.313092i	$-0.898635\pi$
$421$	−15.3068	−	26.5121i	−0.746007	−	1.29212i	0.203716	−	0.979030i	$-0.434698\pi$
$422$	2.65419	−	4.59719i	0.129204	−	0.223787i
$423$	8.57860	−	20.8526i	0.417106	−	1.01389i
$424$	−5.33975	−	9.24872i	−0.259321	−	0.449157i
$425$	−11.0266	+	11.7203i	−0.534870	+	0.568518i
$426$	3.68873	−	18.6620i	0.178720	−	0.904177i
$427$	1.20510	−	1.06788i	0.0583190	−	0.0516782i
$428$	0.859971	−	1.48951i	0.0415683	−	0.0719983i
$429$	0.0337379	−	0.0114978i	0.00162888	−	0.000555121i
$430$	−4.42499	−	5.58829i	−0.213392	−	0.269491i
$431$	2.69929	−	1.55843i	0.130020	−	0.0750671i	−0.433579	−	0.901115i	$-0.642750\pi$
$431$	2.69929	−	1.55843i	0.130020	−	0.0750671i	0.563599	+	0.826048i	$0.309416\pi$
$432$	4.33085	+	2.87119i	0.208368	+	0.138140i
$433$	−25.2574			−1.21379			−0.606896	−	0.794781i	$-0.707585\pi$
$433$	−25.2574			−1.21379			−0.606896	+	0.794781i	$0.707585\pi$
$434$	−6.62185	+	5.86782i	−0.317859	+	0.281664i
$435$	−8.95487	−	17.4300i	−0.429353	−	0.835704i
$436$	6.77465	+	11.7340i	0.324447	+	0.561959i
$437$			4.99097i			0.238751i
$438$	−6.99523	−	20.5260i	−0.334245	−	0.980770i
$439$		−	8.30193i		−	0.396230i	−0.980179	−	0.198115i	$-0.936518\pi$
$439$		−	8.30193i		−	0.396230i	0.980179	−	0.198115i	$-0.0634819\pi$
$440$	−0.668524	+	1.68621i	−0.0318706	+	0.0803867i
$441$	−10.2680	+	18.3185i	−0.488952	+	0.872311i
$442$		−	0.0816452i		−	0.00388346i
$443$	8.64635			0.410800			0.205400	−	0.978678i	$-0.434150\pi$
$443$	8.64635			0.410800			0.205400	+	0.978678i	$0.434150\pi$
$444$	−14.7045	−	12.8642i	−0.697844	−	0.610506i
$445$	−9.61378	−	3.81154i	−0.455737	−	0.180684i
$446$	4.61986	+	8.00184i	0.218757	+	0.378898i
$447$	−18.5744	+	6.33013i	−0.878538	+	0.299405i
$448$	−1.75469	−	1.98017i	−0.0829012	−	0.0935542i
$449$		−	9.83537i		−	0.464160i	−0.972697	−	0.232080i	$-0.925447\pi$
$449$		−	9.83537i		−	0.464160i	0.972697	−	0.232080i	$-0.0745531\pi$
$450$	−14.9280	−	1.46771i	−0.703714	−	0.0691885i
$451$	−1.36725	+	0.789382i	−0.0643813	+	0.0371705i
$452$	−3.60588	+	6.24558i	−0.169607	+	0.293767i
$453$	−13.9830	+	15.9834i	−0.656980	+	0.750965i
$454$	−5.11105	−	2.95087i	−0.239874	−	0.138491i
$455$	−0.0511298	−	0.141103i	−0.00239700	−	0.00661500i
$456$	1.83810	+	1.60805i	0.0860768	+	0.0753040i
$457$		−	22.6172i		−	1.05799i	−0.848625	−	0.528994i	$-0.822569\pi$
$457$		−	22.6172i		−	1.05799i	0.848625	−	0.528994i	$-0.177431\pi$
$458$	−17.9965	+	10.3903i	−0.840921	+	0.485506i
$459$	16.6913	+	1.03342i	0.779084	+	0.0482358i
$460$	−6.20515	+	4.91344i	−0.289317	+	0.229090i
$461$	16.1968	+	28.0536i	0.754358	+	1.30659i	0.945693	+	0.325061i	$0.105385\pi$
$461$	16.1968	+	28.0536i	0.754358	+	1.30659i	−0.191335	+	0.981525i	$0.561282\pi$
$462$	−0.0236257	−	3.71730i	−0.00109917	−	0.172945i
$463$	−8.77792	−	5.06793i	−0.407944	−	0.235527i	0.281962	−	0.959426i	$-0.409015\pi$
$463$	−8.77792	−	5.06793i	−0.407944	−	0.235527i	−0.689906	+	0.723899i	$0.742348\pi$
$464$	−4.38175	+	2.52980i	−0.203418	+	0.117443i
$465$	12.9360	+	0.634400i	0.599894	+	0.0294196i
$466$	−14.0861	+	24.3978i	−0.652526	+	1.13021i
$467$	7.39730	+	4.27083i	0.342306	+	0.197631i	0.661291	−	0.750129i	$-0.270009\pi$
$467$	7.39730	+	4.27083i	0.342306	+	0.197631i	−0.318985	+	0.947760i	$0.603342\pi$
$468$	0.0602662	−	0.0464751i	0.00278580	−	0.00214831i
$469$	2.01142	−	1.78238i	0.0928788	−	0.0823026i
$470$	16.6273	−	2.44740i	0.766960	−	0.112890i
$471$	−4.77696	−	0.944213i	−0.220111	−	0.0435071i
$472$	−3.60215			−0.165802
$473$	−2.58592			−0.118901
$474$	2.87384	+	0.568042i	0.132000	+	0.0260910i
$475$	−6.86231	−	1.61628i	−0.314864	−	0.0741600i
$476$	−8.07717	−	2.69552i	−0.370217	−	0.123549i
$477$	−4.25841	−	31.7542i	−0.194979	−	1.45393i
$478$	7.81549	+	4.51228i	0.357472	+	0.206387i
$479$	9.04091	−	15.6593i	0.413090	−	0.715493i	−0.582136	−	0.813091i	$-0.697783\pi$
$479$	9.04091	−	15.6593i	0.413090	−	0.715493i	0.995226	+	0.0975988i	$0.0311162\pi$
$480$	−0.189708	+	3.86833i	−0.00865896	+	0.176564i
$481$	−0.247815	+	0.143076i	−0.0112994	+	0.00652370i
$482$	−2.13074	−	1.23018i	−0.0970523	−	0.0560332i
$483$	8.02093	−	14.0988i	0.364965	−	0.641519i
$484$	−5.17098	−	8.95640i	−0.235044	−	0.407109i
$485$	−11.1895	+	8.86023i	−0.508090	+	0.402322i
$486$	8.73843	+	12.9089i	0.396383	+	0.585560i
$487$	30.5288	−	17.6258i	1.38339	−	0.798701i	0.390832	−	0.920462i	$-0.372187\pi$
$487$	30.5288	−	17.6258i	1.38339	−	0.798701i	0.992559	+	0.121761i	$0.0388540\pi$
$488$			0.608585i			0.0275494i
$489$	−23.9613	−	20.9625i	−1.08357	−	0.947955i
$490$	−15.6474	+	0.399775i	−0.706876	+	0.0180600i
$491$	−5.16468	−	2.98183i	−0.233079	−	0.134568i	0.378913	−	0.925432i	$-0.376298\pi$
$491$	−5.16468	−	2.98183i	−0.233079	−	0.134568i	−0.611992	+	0.790864i	$0.709631\pi$
$492$	−2.21956	+	2.53708i	−0.100065	+	0.114380i
$493$	−8.14191	+	14.1022i	−0.366693	+	0.635131i
$494$	0.0309774	−	0.0178848i	0.00139374	−	0.000804677i
$495$	−3.77933	+	3.91518i	−0.169868	+	0.175974i
$496$		−	3.34408i		−	0.150154i
$497$	−21.7482	+	19.2717i	−0.975538	+	0.864453i
$498$	27.5570	−	9.39139i	1.23486	−	0.420838i
$499$	−15.2148	−	26.3528i	−0.681109	−	1.17972i	−0.974643	−	0.223767i	$-0.928165\pi$
$499$	−15.2148	−	26.3528i	−0.681109	−	1.17972i	0.293534	−	0.955949i	$-0.405169\pi$
$500$	−4.74623	−	10.1229i	−0.212258	−	0.452710i
$501$	11.2206	+	9.81629i	0.501299	+	0.438559i
$502$	28.8906			1.28945
$503$			23.6075i			1.05261i	0.850297	+	0.526304i	$0.176423\pi$
$503$			23.6075i			1.05261i	−0.850297	+	0.526304i	$0.823577\pi$
$504$	−2.60810	−	7.49652i	−0.116174	−	0.333922i
$505$	39.3194	+	15.5888i	1.74969	+	0.693694i
$506$			2.87136i			0.127648i
$507$	7.26307	+	21.3119i	0.322564	+	0.946495i
$508$			16.3712i			0.726356i
$509$	1.10906	+	1.92096i	0.0491584	+	0.0851449i	0.889558	−	0.456823i	$-0.151013\pi$
$509$	1.10906	+	1.92096i	0.0491584	+	0.0851449i	−0.840399	+	0.541968i	$0.817679\pi$
$510$	5.69616	+	11.0872i	0.252230	+	0.490947i
$511$	−10.4859	+	31.4212i	−0.463869	+	1.38999i
$512$	1.00000			0.0441942
$513$	3.26423	+	6.55932i	0.144119	+	0.289601i
$514$	−2.25121	+	1.29974i	−0.0992966	+	0.0573289i
$515$	−14.3615	+	11.3719i	−0.632844	+	0.501107i
$516$	−5.22622	+	1.78109i	−0.230072	+	0.0784081i
$517$	3.04851	−	5.28018i	0.134073	−	0.232222i
$518$	5.97292	+	29.2400i	0.262435	+	1.28473i
$519$	1.31170	−	6.63614i	0.0575772	−	0.291294i
$520$	0.0527320	+	0.0209065i	0.00231245	+	0.000916809i
$521$	−5.51885	−	9.55893i	−0.241785	−	0.418785i	0.719438	−	0.694557i	$-0.244400\pi$
$521$	−5.51885	−	9.55893i	−0.241785	−	0.418785i	−0.961223	+	0.275773i	$0.911066\pi$
$522$	−15.0441	+	2.01750i	−0.658464	+	0.0883036i
$523$	11.2452	−	19.4773i	0.491718	−	0.851681i	−0.508236	−	0.861218i	$-0.669702\pi$
$523$	11.2452	−	19.4773i	0.491718	−	0.851681i	0.999955	+	0.00953656i	$0.00303563\pi$
$524$	9.56546	+	16.5679i	0.417869	+	0.723771i
$525$	16.7876	+	15.5941i	0.732671	+	0.680582i
$526$	−8.11154	+	14.0496i	−0.353680	+	0.612592i
$527$	−5.38129	−	9.32067i	−0.234413	−	0.406015i
$528$	1.05748	+	0.925132i	0.0460208	+	0.0402612i
$529$	5.23542	−	9.06801i	0.227627	−	0.394261i
$530$	18.7216	−	14.8244i	0.813213	−	0.643929i
$531$	−9.99379	−	4.11137i	−0.433694	−	0.178418i
$532$	−0.746630	−	3.65507i	−0.0323705	−	0.158468i
$533$	0.0246860	+	0.0427574i	0.00106927	+	0.00185203i
$534$	−5.27457	+	6.02914i	−0.228253	+	0.260906i
$535$	3.57517	+	1.41744i	0.154568	+	0.0612811i
$536$			1.01578i			0.0438751i
$537$	31.1799	−	10.6261i	1.34551	−	0.458550i
$538$	−3.04488	−	5.27389i	−0.131274	−	0.227374i
$539$	−3.41020	+	4.54034i	−0.146888	+	0.195566i
$540$	−4.94151	+	10.5158i	−0.212649	+	0.452527i
$541$	10.9885	−	19.0326i	0.472433	−	0.818277i	−0.527070	−	0.849822i	$-0.676709\pi$
$541$	10.9885	−	19.0326i	0.472433	−	0.818277i	0.999502	+	0.0315447i	$0.0100427\pi$
$542$	−16.3148	−	9.41937i	−0.700782	−	0.404597i
$543$	4.88224	−	24.7002i	0.209517	−	1.05999i
$544$	2.78721	−	1.60920i	0.119501	−	0.0689938i
$545$	−23.7524	+	18.8080i	−1.01744	+	0.805645i
$546$	−0.116250		0.000738837i	−0.00497503		3.16193e-5i
$547$	−13.4100	+	7.74227i	−0.573371	+	0.331036i	−0.758494	−	0.651679i	$-0.774065\pi$
$547$	−13.4100	+	7.74227i	−0.573371	+	0.331036i	0.185124	+	0.982715i	$0.440731\pi$
$548$	−7.97550	+	13.8140i	−0.340696	+	0.590104i
$549$	−0.694619	+	1.68846i	−0.0296456	+	0.0720616i
$550$	−3.94797	−	0.929864i	−0.168342	−	0.0396495i
$551$	−7.13413			−0.303924
$552$	1.97770	+	5.80312i	0.0841764	+	0.246997i
$553$	−2.96772	−	3.34909i	−0.126200	−	0.142418i
$554$	14.9277	+	8.61850i	0.634216	+	0.366165i
$555$	23.6704	−	36.7186i	1.00475	−	1.55862i
$556$	−5.11887	−	2.95538i	−0.217088	−	0.125336i
$557$	−6.99648	−	12.1183i	−0.296451	−	0.513467i	0.678871	−	0.734258i	$-0.262470\pi$
$557$	−6.99648	−	12.1183i	−0.296451	−	0.513467i	−0.975321	+	0.220790i	$0.929136\pi$
$558$	3.81682	−	9.27781i	0.161579	−	0.392761i
$559$			0.0808683i			0.00342036i
$560$	3.80923	−	4.52656i	0.160969	−	0.191282i
$561$	4.43614	+	0.876847i	0.187294	+	0.0370205i
$562$	6.70985	−	3.87393i	0.283038	−	0.163412i
$563$			6.35679i			0.267907i	0.990988	+	0.133953i	$0.0427672\pi$
$563$			6.35679i			0.267907i	−0.990988	+	0.133953i	$0.957233\pi$
$564$	2.52434	−	12.7711i	0.106294	−	0.537762i
$565$	−14.9908	−	5.94336i	−0.630668	−	0.250039i
$566$	0.773573			0.0325157
$567$	1.32037	−	23.7751i	0.0554505	−	0.998461i
$568$		−	10.9830i		−	0.460835i
$569$		−	27.5953i		−	1.15686i	−0.815734	−	0.578428i	$-0.803666\pi$
$569$		−	27.5953i		−	1.15686i	0.815734	−	0.578428i	$-0.196334\pi$
$570$	−2.95886	+	4.58992i	−0.123933	+	0.192250i
$571$	−23.1754			−0.969861			−0.484931	−	0.874553i	$-0.661155\pi$
$571$	−23.1754			−0.969861			−0.484931	+	0.874553i	$0.661155\pi$
$572$	0.0178217	−	0.0102894i	0.000745162	−	0.000430219i
$573$	0.853273	−	4.31687i	0.0356460	−	0.180340i
$574$	5.04501	−	1.03055i	0.210575	−	0.0430145i
$575$	−12.8902	−	12.1273i	−0.537559	−	0.505744i
$576$	2.77440	+	1.14137i	0.115600	+	0.0475569i
$577$	14.2815	+	24.7363i	0.594546	+	1.02978i	0.993611	+	0.112862i	$0.0360017\pi$
$577$	14.2815	+	24.7363i	0.594546	+	1.02978i	−0.399064	+	0.916923i	$0.630665\pi$
$578$	−3.32096	+	5.75207i	−0.138134	+	0.239255i
$579$	−2.62785	+	13.2948i	−0.109210	+	0.552514i
$580$	−7.02331	−	8.86968i	−0.291627	−	0.368294i
$581$	−42.1843	−	14.0778i	−1.75010	−	0.584044i
$582$	3.56631	+	10.4645i	0.147828	+	0.433770i
$583$		−	8.66319i		−	0.358793i
$584$	−6.25999	−	10.8426i	−0.259040	−	0.448671i
$585$	0.122438	+	0.118189i	0.00506217	+	0.00488653i
$586$	22.8864	+	13.2135i	0.945429	+	0.545843i
$587$	−1.01410	+	0.585492i	−0.0418564	+	0.0241658i	−0.520782	−	0.853690i	$-0.674360\pi$
$587$	−1.01410	+	0.585492i	−0.0418564	+	0.0241658i	0.478926	+	0.877855i	$0.341026\pi$
$588$	−3.76489	+	11.5250i	−0.155262	+	0.475283i
$589$	2.35760	−	4.08349i	0.0971434	−	0.168257i
$590$	−1.17294	−	7.96879i	−0.0482892	−	0.328070i
$591$	3.86551	+	0.764057i	0.159006	+	0.0314291i
$592$	−9.76868	−	5.63995i	−0.401490	−	0.231801i
$593$	11.0764	+	6.39495i	0.454853	+	0.262609i	0.709877	−	0.704325i	$-0.248750\pi$
$593$	11.0764	+	6.39495i	0.454853	+	0.262609i	−0.255025	+	0.966935i	$0.582084\pi$
$594$	1.87795	+	3.77365i	0.0770533	+	0.154835i
$595$	3.33300	−	18.7463i	0.136640	−	0.768523i
$596$	−9.81170	+	5.66479i	−0.401903	+	0.232039i
$597$	−33.1555	+	11.2994i	−1.35696	+	0.462452i
$598$	0.0897950			0.00367199
$599$		−	36.8680i		−	1.50639i	−0.657800	−	0.753193i	$-0.728513\pi$
$599$		−	36.8680i		−	1.50639i	0.657800	−	0.753193i	$-0.271487\pi$
$600$	−8.61943	+	0.839937i	−0.351887	+	0.0342903i
$601$	11.3731	−	6.56624i	0.463917	−	0.267843i	−0.249773	−	0.968304i	$-0.580356\pi$
$601$	11.3731	−	6.56624i	0.463917	−	0.267843i	0.713690	+	0.700462i	$0.247023\pi$
$602$	8.00032	+	2.66987i	0.326069	+	0.108816i
$603$	−1.15938	+	2.81818i	−0.0472136	+	0.114765i
$604$	−6.13048	+	10.6183i	−0.249446	+	0.432053i
$605$	18.1298	−	14.3558i	0.737083	−	0.583647i
$606$	21.5725	−	24.6586i	0.876322	−	1.00169i
$607$	3.57009	+	6.18358i	0.144906	+	0.250984i	0.929338	−	0.369231i	$-0.120379\pi$
$607$	3.57009	+	6.18358i	0.144906	+	0.250984i	−0.784432	+	0.620215i	$0.787045\pi$
$608$	1.22111	+	0.705008i	0.0495225	+	0.0285919i
$609$	20.1530	+	11.4652i	0.816639	+	0.464592i
$610$	−1.34633	+	0.198169i	−0.0545114	+	0.00802362i
$611$	−0.165125	−	0.0953349i	−0.00668024	−	0.00385684i
$612$	9.56952	−	1.28332i	0.386825	−	0.0518753i
$613$	−7.59789	+	4.38664i	−0.306876	+	0.177175i	−0.645528	−	0.763737i	$-0.723362\pi$
$613$	−7.59789	+	4.38664i	−0.306876	+	0.177175i	0.338652	+	0.940912i	$0.390029\pi$
$614$	16.0600			0.648128
$615$	−6.33535	−	4.08404i	−0.255466	−	0.164685i
$616$	−0.429545	−	2.10281i	−0.0173068	−	0.0847245i
$617$	4.01634	−	6.95651i	0.161692	−	0.280059i	−0.773784	−	0.633450i	$-0.781638\pi$
$617$	4.01634	−	6.95651i	0.161692	−	0.280059i	0.935476	+	0.353391i	$0.114972\pi$
$618$	4.57728	+	13.4310i	0.184125	+	0.540276i
$619$	−39.1887	−	22.6256i	−1.57513	−	0.909400i	−0.995525	−	0.0944995i	$-0.969875\pi$
$619$	−39.1887	−	22.6256i	−1.57513	−	0.909400i	−0.579601	−	0.814900i	$-0.696792\pi$
$620$	7.39788	−	1.08891i	0.297106	−	0.0437316i
$621$	−1.13657	+	18.3574i	−0.0456091	+	0.736659i
$622$	20.0672			0.804622
$623$	11.9890	−	2.44902i	0.480329	−	0.0981178i
$624$	0.0289313	−	0.0330701i	0.00115818	−	0.00132386i
$625$	20.8487	−	13.7960i	0.833950	−	0.551840i
$626$	−10.1545			−0.405857
$627$	0.639072	+	1.87522i	0.0255221	+	0.0748890i
$628$	−2.81134			−0.112185
$629$	−36.3032			−1.44750
$630$	15.7348	−	8.21075i	0.626889	−	0.327124i
$631$	−43.0078			−1.71212			−0.856058	−	0.516881i	$-0.827093\pi$
$631$	−43.0078			−1.71212			−0.856058	+	0.516881i	$0.827093\pi$
$632$	1.69131			0.0672768
$633$	6.05393	−	6.91999i	0.240622	−	0.275045i
$634$	−26.9529			−1.07044
$635$	−36.2170	+	5.33084i	−1.43723	+	0.211548i
$636$	−5.96691	−	17.5086i	−0.236603	−	0.694261i
$637$	0.141988	+	0.106646i	0.00562577	+	0.00422546i
$638$	−4.10435			−0.162493
$639$	12.5356	−	30.4711i	0.495901	−	1.20542i
$640$	0.325622	+	2.21223i	0.0128713	+	0.0874461i
$641$	−2.22797	−	1.28632i	−0.0879994	−	0.0508065i	0.455355	−	0.890310i	$-0.349513\pi$
$641$	−2.22797	−	1.28632i	−0.0879994	−	0.0508065i	−0.543354	+	0.839504i	$0.682846\pi$
$642$	1.96151	−	2.24212i	0.0774146	−	0.0884893i
$643$	−17.2212	+	29.8280i	−0.679137	+	1.17630i	0.296104	+	0.955156i	$0.404313\pi$
$643$	−17.2212	+	29.8280i	−0.679137	+	1.17630i	−0.975241	+	0.221145i	$0.929021\pi$
$644$	2.96458	−	8.88343i	0.116821	−	0.350056i
$645$	−5.64196	−	10.9817i	−0.222152	−	0.432402i
$646$	4.53799			0.178545
$647$	−5.07916	+	2.93246i	−0.199683	+	0.115287i	−0.596507	−	0.802608i	$-0.703445\pi$
$647$	−5.07916	+	2.93246i	−0.199683	+	0.115287i	0.396825	+	0.917894i	$0.370112\pi$
$648$	6.39456	+	6.33321i	0.251202	+	0.248792i
$649$	−2.53058	−	1.46103i	−0.0993338	−	0.0573504i
$650$	−0.0290792	+	0.123463i	−0.00114058	+	0.00484262i
$651$	−13.2224	+	7.74644i	−0.518229	+	0.303607i
$652$	−15.9183	−	9.19043i	−0.623408	−	0.359925i
$653$	5.07241	+	8.78567i	0.198499	+	0.343810i	0.948042	−	0.318146i	$-0.103060\pi$
$653$	5.07241	+	8.78567i	0.198499	+	0.343810i	−0.749543	+	0.661956i	$0.769727\pi$
$654$	7.57034	+	22.2135i	0.296024	+	0.868617i
$655$	−33.5372	+	26.5559i	−1.31041	+	1.03762i
$656$	−0.973106	+	1.68547i	−0.0379934	+	0.0658065i
$657$	−4.99230	−	37.2267i	−0.194768	−	1.45235i
$658$	−14.8831	+	13.1884i	−0.580204	+	0.514136i
$659$	−8.24098	+	4.75793i	−0.321023	+	0.185343i	−0.651849	−	0.758349i	$-0.726006\pi$
$659$	−8.24098	+	4.75793i	−0.321023	+	0.185343i	0.330825	+	0.943692i	$0.392673\pi$
$660$	−1.70227	+	2.64063i	−0.0662607	+	0.102786i
$661$			12.3398i			0.479961i	0.970778	+	0.239980i	$0.0771410\pi$
$661$			12.3398i			0.479961i	−0.970778	+	0.239980i	$0.922859\pi$
$662$	20.1804			0.784332
$663$	0.0274213	−	0.138730i	0.00106495	−	0.00538781i
$664$	14.5567	−	8.40429i	0.564908	−	0.326150i
$665$	7.84275	−	2.84189i	0.304129	−	0.110204i
$666$	−20.6650	−	26.7971i	−0.800751	−	1.03837i
$667$	−15.5099	−	8.95463i	−0.600545	−	0.346725i
$668$	7.45421	+	4.30369i	0.288412	+	0.166515i
$669$	5.16247	+	15.1481i	0.199593	+	0.585661i
$670$	−2.24714	+	0.330761i	−0.0868148	+	0.0127784i
$671$	−0.246842	+	0.427542i	−0.00952922	+	0.0165051i
$672$	−2.31646	−	3.95398i	−0.0893595	−	0.152528i
$673$	−26.7585	+	15.4490i	−1.03146	+	0.595515i	−0.917403	−	0.397959i	$-0.869719\pi$
$673$	−26.7585	+	15.4490i	−1.03146	+	0.595515i	−0.114059	+	0.993474i	$0.536385\pi$
$674$	18.8483	+	10.8821i	0.726011	+	0.419163i
$675$	−24.8724	−	7.50761i	−0.957339	−	0.288968i
$676$	6.49968	+	11.2578i	0.249988	+	0.432991i
$677$		−	36.3021i		−	1.39520i	−0.716486	−	0.697601i	$-0.754251\pi$
$677$		−	36.3021i		−	1.39520i	0.716486	−	0.697601i	$-0.245749\pi$
$678$	−8.22466	+	9.40126i	−0.315866	+	0.361053i
$679$	5.34592	−	16.0192i	0.205158	−	0.614759i
$680$	4.46750	+	5.64197i	0.171321	+	0.216360i
$681$	−7.69350	−	6.73063i	−0.294816	−	0.257918i
$682$	1.35636	−	2.34928i	0.0519376	−	0.0899585i
$683$	−11.4960	−	19.9116i	−0.439882	−	0.761897i	0.557798	−	0.829977i	$-0.311646\pi$
$683$	−11.4960	−	19.9116i	−0.439882	−	0.761897i	−0.997680	+	0.0680791i	$0.978313\pi$
$684$	2.58317	+	3.34971i	0.0987700	+	0.128079i
$685$	−33.1567	−	13.1455i	−1.26685	−	0.502264i
$686$	15.2382	−	10.5260i	0.581798	−	0.401885i
$687$	−34.0689	+	11.6106i	−1.29981	+	0.442973i
$688$	−2.76069	+	1.59389i	−0.105250	+	0.0607663i
$689$	−0.270920			−0.0103212
$690$	−12.1939	+	6.26475i	−0.464213	+	0.238495i
$691$			3.73784i			0.142194i	0.997469	+	0.0710971i	$0.0226500\pi$
$691$			3.73784i			0.142194i	−0.997469	+	0.0710971i	$0.977350\pi$
$692$		−	3.90551i		−	0.148465i
$693$	1.20835	−	6.32429i	0.0459012	−	0.240240i
$694$	9.89335			0.375546
$695$	4.87117	−	12.2865i	0.184774	−	0.466052i
$696$	−8.29502	+	2.82693i	−0.314422	+	0.107155i
$697$			6.26368i			0.237254i
$698$	29.2025	−	16.8601i	1.10533	−	0.638164i
$699$	−32.1290	+	36.7253i	−1.21523	+	1.38908i
$700$	11.2542	+	6.95295i	0.425368	+	0.262797i
$701$			46.5565i			1.75842i	0.476438	+	0.879208i	$0.341928\pi$
$701$			46.5565i			1.75842i	−0.476438	+	0.879208i	$0.658072\pi$
$702$	0.118012	−	0.0587284i	0.00445407	−	0.00221656i
$703$	−7.95242	−	13.7740i	−0.299931	−	0.519496i
$704$	0.702519	+	0.405599i	0.0264772	+	0.0152866i
$705$	29.0747	+	1.42586i	1.09502	+	0.0537011i
$706$	15.0879	+	8.71103i	0.567842	+	0.327844i
$707$	−49.0338	+	10.0162i	−1.84411	+	0.376700i
$708$	−6.12068	−	1.20981i	−0.230029	−	0.0454676i
$709$	29.0412			1.09066			0.545332	−	0.838220i	$-0.316403\pi$
$709$	29.0412			1.09066			0.545332	+	0.838220i	$0.316403\pi$
$710$	24.2969	−	3.57630i	0.911846	−	0.134216i
$711$	4.69237	+	1.93041i	0.175978	+	0.0723959i
$712$	−2.31249	+	4.00536i	−0.0866644	+	0.150107i
$713$	10.2511	−	5.91845i	0.383905	−	0.221648i
$714$	−12.8192	−	7.29295i	−0.479747	−	0.272932i
$715$	0.0285656	+	0.0360752i	0.00106829	+	0.00134914i
$716$	16.4704	−	9.50922i	0.615530	−	0.355376i
$717$	11.7644	+	10.2921i	0.439350	+	0.384364i
$718$	29.8414	+	17.2289i	1.11367	+	0.642978i
$719$	−4.05625	+	7.02563i	−0.151273	+	0.262012i	−0.931696	−	0.363240i	$-0.881670\pi$
$719$	−4.05625	+	7.02563i	−0.151273	+	0.262012i	0.780423	+	0.625252i	$0.215004\pi$
$720$	−1.62156	+	6.50927i	−0.0604321	+	0.242586i
$721$	6.86138	−	20.5603i	0.255531	−	0.765705i
$722$	−8.50593	−	14.7327i	−0.316558	−	0.548294i
$723$	−3.20733	−	2.80592i	−0.119282	−	0.104353i
$724$		−	14.5366i		−	0.540247i
$725$	17.3349	−	18.4253i	0.643800	−	0.684300i
$726$	−5.77832	−	16.9552i	−0.214453	−	0.629267i
$727$	−5.53873	−	9.59336i	−0.205420	−	0.355798i	0.744846	−	0.667236i	$-0.232523\pi$
$727$	−5.53873	−	9.59336i	−0.205420	−	0.355798i	−0.950267	+	0.311438i	$0.899189\pi$
$728$	−0.0657602	+	0.0134330i	−0.00243723	+	0.000497859i
$729$	10.5125	+	24.8694i	0.389354	+	0.921088i
$730$	21.9480	−	17.3791i	0.812332	−	0.643231i
$731$	−5.12976	+	8.88500i	−0.189731	+	0.328624i
$732$	−0.204399	+	1.03409i	−0.00755480	+	0.0382212i
$733$	−21.5792	−	37.3763i	−0.797047	−	1.38053i	−0.921531	−	0.388304i	$-0.873061\pi$
$733$	−21.5792	−	37.3763i	−0.797047	−	1.38053i	0.124484	−	0.992222i	$-0.460272\pi$
$734$	−12.2578	+	21.2311i	−0.452444	+	0.783656i
$735$	−26.7219	−	4.57602i	−0.985652	−	0.168789i
$736$	1.76983	+	3.06543i	0.0652367	+	0.112993i
$737$	−0.412000	+	0.713605i	−0.0151762	+	0.0262860i
$738$	−4.62352	+	3.56549i	−0.170194	+	0.131247i
$739$	19.9836	+	34.6126i	0.735108	+	1.27324i	0.954676	+	0.297647i	$0.0962017\pi$
$739$	19.9836	+	34.6126i	0.735108	+	1.27324i	−0.219568	+	0.975597i	$0.570465\pi$
$740$	9.29598	−	23.4471i	0.341727	−	0.861932i
$741$	0.0586429	−	0.0199854i	0.00215430	−	0.000734183i
$742$	−8.94444	+	26.8022i	−0.328361	+	0.983940i
$743$	21.8276	−	37.8065i	0.800777	−	1.38699i	−0.118328	−	0.992975i	$-0.537754\pi$
$743$	21.8276	−	37.8065i	0.800777	−	1.38699i	0.919105	−	0.394012i	$-0.128913\pi$
$744$	1.12314	−	5.68218i	0.0411763	−	0.208319i
$745$	−15.7267	−	19.8612i	−0.576183	−	0.727657i
$746$	−18.8999	+	10.9119i	−0.691975	+	0.399512i
$747$	49.9783	−	6.70236i	1.82861	−	0.245227i
$748$	2.61076			0.0954588
$749$	−4.45847	+	0.910741i	−0.162909	+	0.0332777i
$750$	−4.66481	−	18.7947i	−0.170335	−	0.686284i
$751$	18.5297	+	32.0944i	0.676159	+	1.17114i	0.976129	+	0.217193i	$0.0696900\pi$
$751$	18.5297	+	32.0944i	0.676159	+	1.17114i	−0.299970	+	0.953949i	$0.596977\pi$
$752$		−	7.51607i		−	0.274083i
$753$	49.0903	+	9.70317i	1.78895	+	0.353603i
$754$			0.128353i			0.00467436i
$755$	−25.4864	−	10.1045i	−0.927544	−	0.367740i
$756$	−1.91385	−	13.6139i	−0.0696059	−	0.495131i
$757$		−	15.5973i		−	0.566892i	−0.958988	−	0.283446i	$-0.908522\pi$
$757$		−	15.5973i		−	0.566892i	0.958988	−	0.283446i	$-0.0914777\pi$
$758$	30.0822			1.09264
$759$	−0.964373	+	4.87895i	−0.0350045	+	0.177095i
$760$	−1.16202	+	2.93094i	−0.0421509	+	0.106317i
$761$	7.35947	+	12.7470i	0.266781	+	0.462077i	0.968029	−	0.250840i	$-0.0807068\pi$
$761$	7.35947	+	12.7470i	0.266781	+	0.462077i	−0.701248	+	0.712917i	$0.747373\pi$
$762$	−5.49843	+	27.8176i	−0.199187	+	1.00773i
$763$	11.3480	−	34.0045i	0.410825	−	1.23105i
$764$		−	2.54057i		−	0.0919146i
$765$	5.95506	+	20.7521i	0.215306	+	0.750295i
$766$	−26.4753	+	15.2855i	−0.956592	+	0.552288i
$767$	−0.0456901	+	0.0791376i	−0.00164978	+	0.00285749i
$768$	1.69918	+	0.335859i	0.0613137	+	0.0121193i
$769$	27.7329	+	16.0116i	1.00007	+	0.577393i	0.908270	−	0.418384i	$-0.137403\pi$
$769$	27.7329	+	16.0116i	1.00007	+	0.577393i	0.0918044	+	0.995777i	$0.470737\pi$
$770$	4.51203	−	1.63497i	0.162602	−	0.0589203i
$771$	−4.26173	+	1.45239i	−0.153482	+	0.0523067i
$772$			7.82427i			0.281602i
$773$	−40.9220	+	23.6263i	−1.47186	+	0.849780i	−0.999500	−	0.0316250i	$-0.989932\pi$
$773$	−40.9220	+	23.6263i	−1.47186	+	0.849780i	−0.472362	+	0.881405i	$0.656598\pi$
$774$	−9.47847	+	1.27111i	−0.340696	+	0.0456892i
$775$	4.81783	+	16.0113i	0.173062	+	0.575142i
$776$	3.19146	+	5.52778i	0.114567	+	0.198436i
$777$	0.328521	+	51.6900i	0.0117856	+	1.85437i
$778$	−18.1559	−	10.4823i	−0.650922	−	0.375810i
$779$	−2.37654	+	1.37209i	−0.0851483	+	0.0491604i
$780$	0.0825793	+	0.0532343i	0.00295681	+	0.00190609i
$781$	4.45469	−	7.71574i	0.159401	−	0.276091i
$782$	9.86578	+	5.69601i	0.352799	+	0.203689i
$783$	−26.2402	−	1.62462i	−0.937750	−	0.0580593i
$784$	−0.842147	+	6.94916i	−0.0300767	+	0.248184i
$785$	−0.915435	−	6.21934i	−0.0326733	−	0.221978i
$786$	10.6889	+	31.3644i	0.381262	+	1.11873i
$787$	−3.35453			−0.119576			−0.0597880	−	0.998211i	$-0.519042\pi$
$787$	−3.35453			−0.119576			−0.0597880	+	0.998211i	$0.519042\pi$
$788$	2.27493			0.0810412
$789$	−18.5016	+	21.1484i	−0.658675	+	0.752903i
$790$	0.550729	+	3.74158i	0.0195941	+	0.133119i
$791$	18.6945	−	3.81876i	0.664700	−	0.135780i
$792$	1.48613	+	1.92712i	0.0528073	+	0.0684774i
$793$	0.0133704	+	0.00771938i	0.000474795	+	0.000274123i
$794$	15.9516	−	27.6289i	0.566100	−	0.980514i
$795$	36.7901	−	18.9014i	1.30481	−	0.670363i
$796$	−17.5140	+	10.1117i	−0.620768	+	0.358400i
$797$	20.4799	+	11.8241i	0.725434	+	0.418830i	0.816749	−	0.576992i	$-0.195774\pi$
$797$	20.4799	+	11.8241i	0.725434	+	0.418830i	−0.0913154	+	0.995822i	$0.529107\pi$
$798$	−0.0410660	−	6.46138i	−0.00145372	−	0.228730i
$799$	−12.0949	−	20.9489i	−0.427885	−	0.741119i
$800$	−4.78794	+	1.44070i	−0.169279	+	0.0509366i
$801$	−10.9874	+	8.47305i	−0.388219	+	0.299381i
$802$	−7.49269	+	4.32591i	−0.264576	+	0.152753i
$803$		−	10.1562i		−	0.358404i
$804$	−0.341159	+	1.72599i	−0.0120318	+	0.0608710i
$805$	20.6176	+	3.66570i	0.726673	+	0.129199i
$806$	−0.0734680	−	0.0424168i	−0.00258780	−	0.00149407i
$807$	−3.40251	−	9.98392i	−0.119774	−	0.351451i
$808$	9.45788	−	16.3815i	0.332727	−	0.576300i
$809$	−43.8535	+	25.3188i	−1.54181	+	0.890162i	−0.543081	+	0.839680i	$0.682742\pi$
$809$	−43.8535	+	25.3188i	−1.54181	+	0.890162i	−0.998725	+	0.0504816i	$0.983924\pi$
$810$	−11.9283	+	16.2085i	−0.419118	+	0.569508i
$811$			15.9122i			0.558754i	0.960181	+	0.279377i	$0.0901280\pi$
$811$			15.9122i			0.558754i	−0.960181	+	0.279377i	$0.909872\pi$
$812$	12.6980	+	4.23759i	0.445614	+	0.148710i
$813$	−24.5582	−	21.4846i	−0.861293	−	0.753500i
$814$	−4.57512	−	7.92434i	−0.160358	−	0.277748i
$815$	15.1480	−	38.2076i	0.530612	−	1.33835i
$816$	5.27643	−	1.79820i	0.184712	−	0.0629496i
$817$	−4.49481			−0.157254
$818$		−	25.3709i		−	0.887073i
$819$	−0.197777	−	0.0377881i	−0.00691088	−	0.00132042i
$820$	−4.04551	−	1.60391i	−0.141275	−	0.0560109i
$821$		−	0.879168i		−	0.0306832i	−0.999882	−	0.0153416i	$-0.995116\pi$
$821$		−	0.879168i		−	0.0306832i	0.999882	−	0.0153416i	$-0.00488357\pi$
$822$	−18.1913	+	20.7937i	−0.634495	+	0.725264i
$823$			21.3612i			0.744604i	0.928112	+	0.372302i	$0.121431\pi$
$823$			21.3612i			0.744604i	−0.928112	+	0.372302i	$0.878569\pi$
$824$	4.09618	+	7.09479i	0.142697	+	0.247159i
$825$	−6.39598	−	2.90596i	−0.222680	−	0.101173i
$826$	6.32064	+	7.13287i	0.219923	+	0.248184i
$827$	3.54960			0.123432			0.0617159	−	0.998094i	$-0.480343\pi$
$827$	3.54960			0.123432			0.0617159	+	0.998094i	$0.480343\pi$
$828$	1.41142	+	10.5248i	0.0490504	+	0.365760i
$829$	−22.4132	+	12.9403i	−0.778443	+	0.449434i	−0.835878	−	0.548915i	$-0.815041\pi$
$829$	−22.4132	+	12.9403i	−0.778443	+	0.449434i	0.0574354	+	0.998349i	$0.481708\pi$
$830$	23.3322	+	29.4661i	0.809873	+	1.02278i
$831$	22.4701	+	19.6579i	0.779481	+	0.681926i
$832$	0.0126841	−	0.0219696i	0.000439743	−	0.000761658i
$833$	8.83533	+	20.7240i	0.306126	+	0.718043i
$834$	−7.70527	−	6.74093i	−0.266812	−	0.233419i
$835$	−7.09350	+	17.8918i	−0.245481	+	0.619172i
$836$	0.571902	+	0.990563i	0.0197796	+	0.0342593i
$837$	9.60149	−	14.4827i	0.331876	−	0.500596i
$838$	−4.57468	+	7.92357i	−0.158030	+	0.273715i
$839$	1.80168	+	3.12060i	0.0622009	+	0.107735i	0.895449	−	0.445164i	$-0.146855\pi$
$839$	1.80168	+	3.12060i	0.0622009	+	0.107735i	−0.833248	+	0.552899i	$0.813521\pi$
$840$	7.99284	−	6.41206i	0.275779	−	0.221237i
$841$	−1.70019	+	2.94482i	−0.0586273	+	0.101545i
$842$	−15.3068	−	26.5121i	−0.527506	−	0.913668i
$843$	12.7023	−	4.32893i	0.437491	−	0.149096i
$844$	2.65419	−	4.59719i	0.0913609	−	0.158242i
$845$	−22.7884	+	18.0446i	−0.783944	+	0.620752i
$846$	8.57860	−	20.8526i	0.294938	−	0.716926i
$847$	−8.66174	+	25.9551i	−0.297621	+	0.891827i
$848$	−5.33975	−	9.24872i	−0.183368	−	0.317602i
$849$	1.31444	+	0.259811i	0.0451114	+	0.00891671i
$850$	−11.0266	+	11.7203i	−0.378210	+	0.402003i
$851$		−	39.9270i		−	1.36868i
$852$	3.68873	−	18.6620i	0.126374	−	0.639350i
$853$	−9.42803	−	16.3298i	−0.322810	−	0.559122i	0.658257	−	0.752793i	$-0.271294\pi$
$853$	−9.42803	−	16.3298i	−0.322810	−	0.559122i	−0.981067	+	0.193671i	$0.937961\pi$
$854$	1.20510	−	1.06788i	0.0412378	−	0.0365420i
$855$	−6.56919	+	6.80531i	−0.224662	+	0.232737i
$856$	0.859971	−	1.48951i	0.0293932	−	0.0509105i
$857$	33.4494	+	19.3120i	1.14261	+	0.659687i	0.947076	−	0.321010i	$-0.104022\pi$
$857$	33.4494	+	19.3120i	1.14261	+	0.659687i	0.195535	+	0.980697i	$0.437356\pi$
$858$	0.0337379	−	0.0114978i	0.00115179	−	0.000392530i
$859$	11.1581	−	6.44215i	0.380710	−	0.219803i	−0.297417	−	0.954748i	$-0.596125\pi$
$859$	11.1581	−	6.44215i	0.380710	−	0.219803i	0.678127	+	0.734944i	$0.262792\pi$
$860$	−4.42499	−	5.58829i	−0.150891	−	0.190559i
$861$	8.91848	−	0.0566823i	0.303941	−	0.00193173i
$862$	2.69929	−	1.55843i	0.0919380	−	0.0530805i
$863$	26.0756	−	45.1643i	0.887625	−	1.53741i	0.0449489	−	0.998989i	$-0.485688\pi$
$863$	26.0756	−	45.1643i	0.887625	−	1.53741i	0.842676	−	0.538422i	$-0.180979\pi$
$864$	4.33085	+	2.87119i	0.147339	+	0.0976798i
$865$	8.63988	−	1.27172i	0.293765	−	0.0432398i
$866$	−25.2574			−0.858280
$867$	−7.57478	+	8.65841i	−0.257253	+	0.294055i
$868$	−6.62185	+	5.86782i	−0.224760	+	0.199167i
$869$	1.18818	+	0.685995i	0.0403062	+	0.0232708i
$870$	−8.95487	−	17.4300i	−0.303599	−	0.590932i
$871$	0.0223163	+	0.0128843i	0.000756159	+	0.000436568i
$872$	6.77465	+	11.7340i	0.229419	+	0.397365i
$873$	2.54517	+	18.9789i	0.0861409	+	0.642338i
$874$			4.99097i			0.168822i
$875$	−11.7169	+	27.1609i	−0.396105	+	0.918205i
$876$	−6.99523	−	20.5260i	−0.236347	−	0.693509i
$877$	6.40124	−	3.69575i	0.216154	−	0.124797i	−0.388014	−	0.921653i	$-0.626839\pi$
$877$	6.40124	−	3.69575i	0.216154	−	0.124797i	0.604168	+	0.796857i	$0.293505\pi$
$878$		−	8.30193i		−	0.280177i
$879$	34.4502	+	30.1386i	1.16198	+	1.01655i
$880$	−0.668524	+	1.68621i	−0.0225359	+	0.0568420i
$881$	33.1517			1.11691			0.558454	−	0.829535i	$-0.311395\pi$
$881$	33.1517			1.11691			0.558454	+	0.829535i	$0.311395\pi$
$882$	−10.2680	+	18.3185i	−0.345741	+	0.616817i
$883$		−	23.0244i		−	0.774834i	−0.921905	−	0.387417i	$-0.873367\pi$
$883$		−	23.0244i		−	0.774834i	0.921905	−	0.387417i	$-0.126633\pi$
$884$		−	0.0816452i		−	0.00274602i
$885$	0.683357	−	13.9343i	0.0229708	−	0.468397i
$886$	8.64635			0.290480
$887$	−2.26079	+	1.30527i	−0.0759099	+	0.0438266i	−0.537475	−	0.843280i	$-0.680622\pi$
$887$	−2.26079	+	1.30527i	−0.0759099	+	0.0438266i	0.461565	+	0.887107i	$0.347288\pi$
$888$	−14.7045	−	12.8642i	−0.493450	−	0.431693i
$889$	32.4178	−	28.7264i	1.08726	−	0.963453i
$890$	−9.61378	−	3.81154i	−0.322255	−	0.127763i
$891$	1.92355	+	7.04283i	0.0644415	+	0.235944i
$892$	4.61986	+	8.00184i	0.154684	+	0.267921i
$893$	5.29889	−	9.17795i	0.177321	−	0.307128i
$894$	−18.5744	+	6.33013i	−0.621220	+	0.211711i
$895$	26.3997	+	33.3400i	0.882446	+	1.11443i
$896$	−1.75469	−	1.98017i	−0.0586200	−	0.0661528i
$897$	0.152577	+	0.0301584i	0.00509441	+	0.00100696i
$898$		−	9.83537i		−	0.328211i
$899$	8.45987	+	14.6529i	0.282152	+	0.488702i
$900$	−14.9280	−	1.46771i	−0.497601	−	0.0489237i
$901$	−29.7660	−	17.1854i	−0.991651	−	0.572530i
$902$	−1.36725	+	0.789382i	−0.0455244	+	0.0262835i
$903$	12.6972	+	7.22355i	0.422538	+	0.240385i
$904$	−3.60588	+	6.24558i	−0.119930	+	0.207725i
$905$	32.1583	−	4.73343i	1.06898	−	0.157345i
$906$	−13.9830	+	15.9834i	−0.464555	+	0.531013i
$907$	−30.2468	−	17.4630i	−1.00433	−	0.579849i	−0.0948025	−	0.995496i	$-0.530222\pi$
$907$	−30.2468	−	17.4630i	−1.00433	−	0.579849i	−0.909526	+	0.415647i	$0.863555\pi$
$908$	−5.11105	−	2.95087i	−0.169616	−	0.0979280i
$909$	44.9373	−	34.6540i	1.49047	−	1.14940i
$910$	−0.0511298	−	0.141103i	−0.00169494	−	0.00467751i
$911$	−8.52724	+	4.92320i	−0.282520	+	0.163113i	−0.634564	−	0.772871i	$-0.718820\pi$
$911$	−8.52724	+	4.92320i	−0.282520	+	0.163113i	0.352044	+	0.935984i	$0.385487\pi$
$912$	1.83810	+	1.60805i	0.0608655	+	0.0532480i
$913$	13.6351			0.451256
$914$		−	22.6172i		−	0.748111i
$915$	−2.35421	−	0.115454i	−0.0778278	−	0.00381678i
$916$	−17.9965	+	10.3903i	−0.594621	+	0.343305i
$917$	16.0228	−	48.0127i	0.529120	−	1.58552i
$918$	16.6913	+	1.03342i	0.550896	+	0.0341078i
$919$	−25.5841	+	44.3130i	−0.843943	+	1.46175i	0.0425930	+	0.999093i	$0.486438\pi$
$919$	−25.5841	+	44.3130i	−0.843943	+	1.46175i	−0.886536	+	0.462660i	$0.846895\pi$
$920$	−6.20515	+	4.91344i	−0.204578	+	0.161991i
$921$	27.2887	+	5.39389i	0.899194	+	0.177735i
$922$	16.1968	+	28.0536i	0.533412	+	0.923896i
$923$	−0.241291	−	0.139310i	−0.00794220	−	0.00458543i
$924$	−0.0236257	−	3.71730i	−0.000777229	−	0.122290i
$925$	54.8974	+	12.9300i	1.80501	+	0.425135i
$926$	−8.77792	−	5.06793i	−0.288460	−	0.166543i
$927$	3.26667	+	24.3590i	0.107292	+	0.800055i
$928$	−4.38175	+	2.52980i	−0.143838	+	0.0830449i
$929$	20.7644			0.681256			0.340628	−	0.940198i	$-0.389360\pi$
$929$	20.7644			0.681256			0.340628	+	0.940198i	$0.389360\pi$
$930$	12.9360	+	0.634400i	0.424189	+	0.0208028i
$931$	−5.92757	+	7.89196i	−0.194268	+	0.258649i
$932$	−14.0861	+	24.3978i	−0.461405	+	0.799178i
$933$	34.0977	+	6.73975i	1.11631	+	0.220650i
$934$	7.39730	+	4.27083i	0.242047	+	0.139746i
$935$	0.850121	+	5.77560i	0.0278019	+	0.188882i
$936$	0.0602662	−	0.0464751i	0.00196986	−	0.00151909i
$937$	−44.4914			−1.45347			−0.726735	−	0.686918i	$-0.758963\pi$
$937$	−44.4914			−1.45347			−0.726735	+	0.686918i	$0.758963\pi$
$938$	2.01142	−	1.78238i	0.0656752	−	0.0581967i
$939$	−17.2544	−	3.41049i	−0.563075	−	0.111297i
$940$	16.6273	−	2.44740i	0.542323	−	0.0798254i
$941$	27.4464			0.894729			0.447364	−	0.894352i	$-0.352363\pi$
$941$	27.4464			0.894729			0.447364	+	0.894352i	$0.352363\pi$
$942$	−4.77696	−	0.944213i	−0.155642	−	0.0307641i
$943$	−6.88892			−0.224334
$944$	−3.60215			−0.117240
$945$	29.4938	−	8.66685i	0.959434	−	0.281933i
$946$	−2.58592			−0.0840754
$947$	44.2729			1.43868			0.719338	−	0.694660i	$-0.244445\pi$
$947$	44.2729			1.43868			0.719338	+	0.694660i	$0.244445\pi$
$948$	2.87384	+	0.568042i	0.0933379	+	0.0184492i
$949$	−0.317610			−0.0103101
$950$	−6.86231	−	1.61628i	−0.222643	−	0.0524390i
$951$	−45.7978	−	9.05238i	−1.48509	−	0.293543i
$952$	−8.07717	−	2.69552i	−0.261783	−	0.0873622i
$953$	23.6733			0.766855			0.383427	−	0.923571i	$-0.374744\pi$
$953$	23.6733			0.766855			0.383427	+	0.923571i	$0.374744\pi$
$954$	−4.25841	−	31.7542i	−0.137871	−	1.02808i
$955$	5.62033	−	0.827266i	0.181870	−	0.0267697i
$956$	7.81549	+	4.51228i	0.252771	+	0.145937i
$957$	−6.97400	−	1.37848i	−0.225438	−	0.0445600i
$958$	9.04091	−	15.6593i	0.292099	−	0.505930i
$959$	41.3485	−	8.44635i	1.33521	−	0.272747i
$960$	−0.189708	+	3.86833i	−0.00612281	+	0.124850i
$961$	19.8171			0.639262
$962$	−0.247815	+	0.143076i	−0.00798986	+	0.00461295i
$963$	4.08598	−	3.15096i	0.131669	−	0.101538i
$964$	−2.13074	−	1.23018i	−0.0686264	−	0.0396214i
$965$	−17.3091	+	2.54776i	−0.557200	+	0.0820152i
$966$	8.02093	−	14.0988i	0.258069	−	0.453623i
$967$	27.8500	+	16.0792i	0.895596	+	0.517073i	0.875769	−	0.482731i	$-0.160355\pi$
$967$	27.8500	+	16.0792i	0.895596	+	0.517073i	0.0198274	+	0.999803i	$0.493688\pi$
$968$	−5.17098	−	8.95640i	−0.166202	−	0.287870i
$969$	7.71085	+	1.52412i	0.247708	+	0.0489619i
$970$	−11.1895	+	8.86023i	−0.359274	+	0.284485i
$971$	6.17807	−	10.7007i	0.198264	−	0.343403i	−0.749702	−	0.661776i	$-0.769803\pi$
$971$	6.17807	−	10.7007i	0.198264	−	0.343403i	0.947966	+	0.318373i	$0.103136\pi$
$972$	8.73843	+	12.9089i	0.280285	+	0.414053i
$973$	3.12986	+	15.3220i	0.100339	+	0.491201i
$974$	30.5288	−	17.6258i	0.978205	−	0.564767i
$975$	−0.0908769	+	0.200019i	−0.00291039	+	0.00640573i
$976$			0.608585i			0.0194803i
$977$	−8.36325			−0.267564			−0.133782	−	0.991011i	$-0.542712\pi$
$977$	−8.36325			−0.267564			−0.133782	+	0.991011i	$0.542712\pi$
$978$	−23.9613	−	20.9625i	−0.766197	−	0.670305i
$979$	−3.24914	+	1.87589i	−0.103843	+	0.0599538i
$980$	−15.6474	+	0.399775i	−0.499837	+	0.0127703i
$981$	5.40273	+	40.2873i	0.172496	+	1.28627i
$982$	−5.16468	−	2.98183i	−0.164812	−	0.0951541i
$983$	−29.2857	−	16.9081i	−0.934068	−	0.539285i	−0.0459724	−	0.998943i	$-0.514639\pi$
$983$	−29.2857	−	16.9081i	−0.934068	−	0.539285i	−0.888096	+	0.459658i	$0.847972\pi$
$984$	−2.21956	+	2.53708i	−0.0707569	+	0.0808792i
$985$	0.740769	+	5.03268i	0.0236029	+	0.160355i
$986$	−8.14191	+	14.1022i	−0.259291	+	0.449106i
$987$	−29.7184	+	17.4107i	−0.945948	+	0.554189i
$988$	0.0309774	−	0.0178848i	0.000985524	−	0.000568993i
$989$	−9.77190	−	5.64181i	−0.310728	−	0.179399i
$990$	−3.77933	+	3.91518i	−0.120115	+	0.124432i
$991$	6.51443	+	11.2833i	0.206938	+	0.358427i	0.950748	−	0.309964i	$-0.100317\pi$
$991$	6.51443	+	11.2833i	0.206938	+	0.358427i	−0.743811	+	0.668390i	$0.766984\pi$
$992$		−	3.34408i		−	0.106175i
$993$	34.2900	+	6.77775i	1.08816	+	0.215085i
$994$	−21.7482	+	19.2717i	−0.689810	+	0.611261i
$995$	−28.0724	−	35.4524i	−0.889955	−	1.12392i
$996$	27.5570	−	9.39139i	0.873176	−	0.297577i
$997$	−11.5259	+	19.9634i	−0.365027	+	0.632246i	−0.988781	−	0.149375i	$-0.952274\pi$
$997$	−11.5259	+	19.9634i	−0.365027	+	0.632246i	0.623753	+	0.781621i	$0.285607\pi$
$998$	−15.2148	−	26.3528i	−0.481617	−	0.834185i
$999$	−26.1133	−	52.4735i	−0.826190	−	1.66019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.509.23	yes	48
3.2	odd	2		1890.2.bi.a.719.11		48
5.4	even	2		630.2.bi.a.509.2	yes	48
7.3	odd	6		630.2.r.a.59.15	✓	48
9.2	odd	6		630.2.r.b.299.10	yes	48
9.7	even	3		1890.2.r.a.89.4		48
15.14	odd	2		1890.2.bi.b.719.6		48
21.17	even	6		1890.2.r.b.1529.4		48
35.24	odd	6		630.2.r.b.59.10	yes	48
45.29	odd	6		630.2.r.a.299.15	yes	48
45.34	even	6		1890.2.r.b.89.4		48
63.38	even	6		630.2.bi.a.479.2	yes	48
63.52	odd	6		1890.2.bi.b.899.6		48
105.59	even	6		1890.2.r.a.1529.4		48
315.164	even	6	inner	630.2.bi.b.479.23	yes	48
315.304	odd	6		1890.2.bi.a.899.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.15	✓	48	7.3	odd	6
630.2.r.a.299.15	yes	48	45.29	odd	6
630.2.r.b.59.10	yes	48	35.24	odd	6
630.2.r.b.299.10	yes	48	9.2	odd	6
630.2.bi.a.479.2	yes	48	63.38	even	6
630.2.bi.a.509.2	yes	48	5.4	even	2
630.2.bi.b.479.23	yes	48	315.164	even	6	inner
630.2.bi.b.509.23	yes	48	1.1	even	1	trivial
1890.2.r.a.89.4		48	9.7	even	3
1890.2.r.a.1529.4		48	105.59	even	6
1890.2.r.b.89.4		48	45.34	even	6
1890.2.r.b.1529.4		48	21.17	even	6
1890.2.bi.a.719.11		48	3.2	odd	2
1890.2.bi.a.899.11		48	315.304	odd	6
1890.2.bi.b.719.6		48	15.14	odd	2
1890.2.bi.b.899.6		48	63.52	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.69918 + 0.335859i) q^{3} +1.00000 q^{4} +(0.325622 + 2.21223i) q^{5} +(1.69918 + 0.335859i) q^{6} +(-1.75469 - 1.98017i) q^{7} +1.00000 q^{8} +(2.77440 + 1.14137i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.69918 + 0.335859i) q^{3} +1.00000 q^{4} +(0.325622 + 2.21223i) q^{5} +(1.69918 + 0.335859i) q^{6} +(-1.75469 - 1.98017i) q^{7} +1.00000 q^{8} +(2.77440 + 1.14137i) q^{9} +(0.325622 + 2.21223i) q^{10} +(0.702519 + 0.405599i) q^{11} +(1.69918 + 0.335859i) q^{12} +(0.0126841 - 0.0219696i) q^{13} +(-1.75469 - 1.98017i) q^{14} +(-0.189708 + 3.86833i) q^{15} +1.00000 q^{16} +(2.78721 - 1.60920i) q^{17} +(2.77440 + 1.14137i) q^{18} +(1.22111 + 0.705008i) q^{19} +(0.325622 + 2.21223i) q^{20} +(-2.31646 - 3.95398i) q^{21} +(0.702519 + 0.405599i) q^{22} +(1.76983 + 3.06543i) q^{23} +(1.69918 + 0.335859i) q^{24} +(-4.78794 + 1.44070i) q^{25} +(0.0126841 - 0.0219696i) q^{26} +(4.33085 + 2.87119i) q^{27} +(-1.75469 - 1.98017i) q^{28} +(-4.38175 + 2.52980i) q^{29} +(-0.189708 + 3.86833i) q^{30} -3.34408i q^{31} +1.00000 q^{32} +(1.05748 + 0.925132i) q^{33} +(2.78721 - 1.60920i) q^{34} +(3.80923 - 4.52656i) q^{35} +(2.77440 + 1.14137i) q^{36} +(-9.76868 - 5.63995i) q^{37} +(1.22111 + 0.705008i) q^{38} +(0.0289313 - 0.0330701i) q^{39} +(0.325622 + 2.21223i) q^{40} +(-0.973106 + 1.68547i) q^{41} +(-2.31646 - 3.95398i) q^{42} +(-2.76069 + 1.59389i) q^{43} +(0.702519 + 0.405599i) q^{44} +(-1.62156 + 6.50927i) q^{45} +(1.76983 + 3.06543i) q^{46} -7.51607i q^{47} +(1.69918 + 0.335859i) q^{48} +(-0.842147 + 6.94916i) q^{49} +(-4.78794 + 1.44070i) q^{50} +(5.27643 - 1.79820i) q^{51} +(0.0126841 - 0.0219696i) q^{52} +(-5.33975 - 9.24872i) q^{53} +(4.33085 + 2.87119i) q^{54} +(-0.668524 + 1.68621i) q^{55} +(-1.75469 - 1.98017i) q^{56} +(1.83810 + 1.60805i) q^{57} +(-4.38175 + 2.52980i) q^{58} -3.60215 q^{59} +(-0.189708 + 3.86833i) q^{60} +0.608585i q^{61} -3.34408i q^{62} +(-2.60810 - 7.49652i) q^{63} +1.00000 q^{64} +(0.0527320 + 0.0209065i) q^{65} +(1.05748 + 0.925132i) q^{66} +1.01578i q^{67} +(2.78721 - 1.60920i) q^{68} +(1.97770 + 5.80312i) q^{69} +(3.80923 - 4.52656i) q^{70} -10.9830i q^{71} +(2.77440 + 1.14137i) q^{72} +(-6.25999 - 10.8426i) q^{73} +(-9.76868 - 5.63995i) q^{74} +(-8.61943 + 0.839937i) q^{75} +(1.22111 + 0.705008i) q^{76} +(-0.429545 - 2.10281i) q^{77} +(0.0289313 - 0.0330701i) q^{78} +1.69131 q^{79} +(0.325622 + 2.21223i) q^{80} +(6.39456 + 6.33321i) q^{81} +(-0.973106 + 1.68547i) q^{82} +(14.5567 - 8.40429i) q^{83} +(-2.31646 - 3.95398i) q^{84} +(4.46750 + 5.64197i) q^{85} +(-2.76069 + 1.59389i) q^{86} +(-8.29502 + 2.82693i) q^{87} +(0.702519 + 0.405599i) q^{88} +(-2.31249 + 4.00536i) q^{89} +(-1.62156 + 6.50927i) q^{90} +(-0.0657602 + 0.0134330i) q^{91} +(1.76983 + 3.06543i) q^{92} +(1.12314 - 5.68218i) q^{93} -7.51607i q^{94} +(-1.16202 + 2.93094i) q^{95} +(1.69918 + 0.335859i) q^{96} +(3.19146 + 5.52778i) q^{97} +(-0.842147 + 6.94916i) q^{98} +(1.48613 + 1.92712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

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