LMFDB - Embedded newform 546.2.bv.a.317.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.25
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-1.01561 + 1.40305i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.935798 + 0.250746i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(2.47599 + 0.932449i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.937080 - 2.84989i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.01561 + 1.40305i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.935798 + 0.250746i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(2.47599 + 0.932449i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.937080 - 2.84989i) q^{9} +(-0.839013 + 0.484404i) q^{10} +(0.989868 + 0.265234i) q^{11} +(-0.178019 + 1.72288i) q^{12} +(1.28292 + 3.36959i) q^{13} +(2.63296 + 0.259843i) q^{14} +(0.598595 - 1.56763i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.05787 + 3.56434i) q^{17} +(-1.64276 - 2.51025i) q^{18} +(0.715871 + 2.67167i) q^{19} +(-0.685051 + 0.685051i) q^{20} +(-3.82291 + 2.52693i) q^{21} +1.02479 q^{22} +(-0.318592 + 0.551817i) q^{23} +(0.273960 + 1.71025i) q^{24} +(-3.51728 + 2.03070i) q^{25} +(2.11132 + 2.92273i) q^{26} +(4.95024 + 1.57961i) q^{27} +(2.61050 - 0.430471i) q^{28} +3.48270i q^{29} +(0.172467 - 1.66914i) q^{30} +(-2.41212 - 0.646325i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.37745 + 1.11946i) q^{33} +(2.91027 + 2.91027i) q^{34} +(-2.55084 - 0.251738i) q^{35} +(-2.23648 - 1.99954i) q^{36} +(2.79469 - 0.748834i) q^{37} +(1.38296 + 2.39535i) q^{38} +(-6.03063 - 1.62219i) q^{39} +(-0.484404 + 0.839013i) q^{40} +(-0.0484181 - 0.0484181i) q^{41} +(-3.03863 + 3.43027i) q^{42} -8.67865i q^{43} +(0.989868 - 0.265234i) q^{44} +(1.59152 + 2.43195i) q^{45} +(-0.164915 + 0.615472i) q^{46} +(-0.867903 - 3.23906i) q^{47} +(0.707270 + 1.58107i) q^{48} +(5.26108 + 4.61748i) q^{49} +(-2.87185 + 2.87185i) q^{50} +(-7.09092 - 0.732681i) q^{51} +(2.79583 + 2.27669i) q^{52} +(6.87259 - 3.96789i) q^{53} +(5.19039 + 0.244568i) q^{54} -0.992823 q^{55} +(2.41013 - 1.09145i) q^{56} +(-4.47551 - 1.70897i) q^{57} +(0.901389 + 3.36403i) q^{58} +(5.60584 + 1.50208i) q^{59} +(-0.265415 - 1.65690i) q^{60} +(0.594016 - 1.02887i) q^{61} -2.49721 q^{62} +(0.337178 - 7.93009i) q^{63} -1.00000i q^{64} +(-2.04546 - 2.83157i) q^{65} +(-1.04078 + 1.43782i) q^{66} +(1.62806 + 0.436237i) q^{67} +(3.56434 + 2.05787i) q^{68} +(-0.450660 - 1.00743i) q^{69} +(-2.52907 + 0.417044i) q^{70} +(-8.55610 - 8.55610i) q^{71} +(-2.67779 - 1.35256i) q^{72} +(3.42226 - 12.7721i) q^{73} +(2.50565 - 1.44664i) q^{74} +(0.723009 - 6.99731i) q^{75} +(1.95579 + 1.95579i) q^{76} +(2.20359 + 1.57972i) q^{77} +(-6.24500 - 0.00607038i) q^{78} +(-0.0157356 + 0.0272549i) q^{79} +(-0.250746 + 0.935798i) q^{80} +(-7.24376 + 5.34115i) q^{81} +(-0.0592998 - 0.0342367i) q^{82} +(-6.06316 - 6.06316i) q^{83} +(-2.04727 + 4.09984i) q^{84} +(-2.81950 - 2.81950i) q^{85} +(-2.24620 - 8.38293i) q^{86} +(-4.88639 - 3.53706i) q^{87} +(0.887491 - 0.512393i) q^{88} +(-1.67059 - 6.23472i) q^{89} +(2.16672 + 1.93717i) q^{90} +(0.0345255 + 9.53933i) q^{91} +0.637183i q^{92} +(3.35659 - 2.72790i) q^{93} +(-1.67666 - 2.90406i) q^{94} +(-1.33982 - 2.32064i) q^{95} +(1.09238 + 1.34414i) q^{96} +(-8.64212 + 8.64212i) q^{97} +(6.27690 + 3.09847i) q^{98} +(-0.171696 - 3.06956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−1.01561	+	1.40305i	−0.586362	+	0.810049i
$3$	−1.01561	+	1.40305i	−0.586362	+	0.810049i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.935798	+	0.250746i	−0.418501	+	0.112137i	−0.461924	−	0.886920i	$-0.652841\pi$
$5$	−0.935798	+	0.250746i	−0.418501	+	0.112137i	0.0434222	+	0.999057i	$0.486174\pi$
$6$	−0.617867	+	1.61810i	−0.252243	+	0.660586i
$7$	2.47599	+	0.932449i	0.935837	+	0.352433i
$7$	2.47599	+	0.932449i	0.935837	+	0.352433i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.937080	−	2.84989i	−0.312360	−	0.949964i
$10$	−0.839013	+	0.484404i	−0.265319	+	0.153182i
$11$	0.989868	+	0.265234i	0.298456	+	0.0799712i	0.404940	−	0.914343i	$-0.367292\pi$
$11$	0.989868	+	0.265234i	0.298456	+	0.0799712i	−0.106483	+	0.994314i	$0.533959\pi$
$12$	−0.178019	+	1.72288i	−0.0513897	+	0.497352i
$13$	1.28292	+	3.36959i	0.355817	+	0.934555i
$13$	1.28292	+	3.36959i	0.355817	+	0.934555i
$14$	2.63296	+	0.259843i	0.703688	+	0.0694460i
$15$	0.598595	−	1.56763i	0.154557	−	0.404760i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.05787	+	3.56434i	0.499107	+	0.864479i	0.999999	−	0.00103068i	$-0.000328075\pi$
$17$	2.05787	+	3.56434i	0.499107	+	0.864479i	−0.500892	+	0.865510i	$0.666995\pi$
$18$	−1.64276	−	2.51025i	−0.387201	−	0.591672i
$19$	0.715871	+	2.67167i	0.164232	+	0.612922i	0.998137	+	0.0610140i	$0.0194334\pi$
$19$	0.715871	+	2.67167i	0.164232	+	0.612922i	−0.833905	+	0.551908i	$0.813900\pi$
$20$	−0.685051	+	0.685051i	−0.153182	+	0.153182i
$21$	−3.82291	+	2.52693i	−0.834227	+	0.551421i
$22$	1.02479			0.218485
$23$	−0.318592	+	0.551817i	−0.0664309	+	0.115062i	−0.897328	−	0.441365i	$-0.854495\pi$
$23$	−0.318592	+	0.551817i	−0.0664309	+	0.115062i	0.830897	+	0.556426i	$0.187828\pi$
$24$	0.273960	+	1.71025i	0.0559219	+	0.349103i
$25$	−3.51728	+	2.03070i	−0.703457	+	0.406141i
$26$	2.11132	+	2.92273i	0.414063	+	0.573194i
$27$	4.95024	+	1.57961i	0.952673	+	0.303996i
$28$	2.61050	−	0.430471i	0.493338	−	0.0813514i
$29$			3.48270i			0.646721i	0.946276	+	0.323361i	$0.104813\pi$
$29$			3.48270i			0.646721i	−0.946276	+	0.323361i	$0.895187\pi$
$30$	0.172467	−	1.66914i	0.0314880	−	0.304742i
$31$	−2.41212	−	0.646325i	−0.433229	−	0.116083i	0.0356126	−	0.999366i	$-0.488662\pi$
$31$	−2.41212	−	0.646325i	−0.433229	−	0.116083i	−0.468841	+	0.883282i	$0.655328\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−1.37745	+	1.11946i	−0.239784	+	0.194872i
$34$	2.91027	+	2.91027i	0.499107	+	0.499107i
$35$	−2.55084	−	0.251738i	−0.431170	−	0.0425515i
$36$	−2.23648	−	1.99954i	−0.372747	−	0.333256i
$37$	2.79469	−	0.748834i	0.459443	−	0.123107i	−0.0216713	−	0.999765i	$-0.506899\pi$
$37$	2.79469	−	0.748834i	0.459443	−	0.123107i	0.481115	+	0.876658i	$0.340232\pi$
$38$	1.38296	+	2.39535i	0.224345	+	0.388577i
$39$	−6.03063	−	1.62219i	−0.965674	−	0.259758i
$40$	−0.484404	+	0.839013i	−0.0765911	+	0.132660i
$41$	−0.0484181	−	0.0484181i	−0.00756163	−	0.00756163i	0.703316	−	0.710877i	$-0.251702\pi$
$41$	−0.0484181	−	0.0484181i	−0.00756163	−	0.00756163i	−0.710877	+	0.703316i	$0.751702\pi$
$42$	−3.03863	+	3.43027i	−0.468871	+	0.529302i
$43$		−	8.67865i		−	1.32348i	−0.749733	−	0.661741i	$-0.769818\pi$
$43$		−	8.67865i		−	1.32348i	0.749733	−	0.661741i	$-0.230182\pi$
$44$	0.989868	−	0.265234i	0.149228	−	0.0399856i
$45$	1.59152	+	2.43195i	0.237249	+	0.362534i
$46$	−0.164915	+	0.615472i	−0.0243154	+	0.0907463i
$47$	−0.867903	−	3.23906i	−0.126597	−	0.472465i	0.873295	−	0.487192i	$-0.161979\pi$
$47$	−0.867903	−	3.23906i	−0.126597	−	0.472465i	−0.999892	+	0.0147269i	$0.995312\pi$
$48$	0.707270	+	1.58107i	0.102086	+	0.228207i
$49$	5.26108	+	4.61748i	0.751582	+	0.659639i
$50$	−2.87185	+	2.87185i	−0.406141	+	0.406141i
$51$	−7.09092	−	0.732681i	−0.992928	−	0.102596i
$52$	2.79583	+	2.27669i	0.387712	+	0.315720i
$53$	6.87259	−	3.96789i	0.944023	−	0.545032i	0.0528037	−	0.998605i	$-0.483184\pi$
$53$	6.87259	−	3.96789i	0.944023	−	0.545032i	0.891219	+	0.453573i	$0.149851\pi$
$54$	5.19039	+	0.244568i	0.706323	+	0.0332814i
$55$	−0.992823			−0.133872
$56$	2.41013	−	1.09145i	0.322067	−	0.145851i
$57$	−4.47551	−	1.70897i	−0.592796	−	0.226358i
$58$	0.901389	+	3.36403i	0.118358	+	0.441719i
$59$	5.60584	+	1.50208i	0.729818	+	0.195554i	0.604548	−	0.796568i	$-0.293354\pi$
$59$	5.60584	+	1.50208i	0.729818	+	0.195554i	0.125270	+	0.992123i	$0.460020\pi$
$60$	−0.265415	−	1.65690i	−0.0342650	−	0.213905i
$61$	0.594016	−	1.02887i	0.0760560	−	0.131733i	−0.825489	−	0.564418i	$-0.809101\pi$
$61$	0.594016	−	1.02887i	0.0760560	−	0.131733i	0.901545	+	0.432685i	$0.142434\pi$
$62$	−2.49721			−0.317146
$63$	0.337178	−	7.93009i	0.0424804	−	0.999097i
$64$		−	1.00000i		−	0.125000i
$65$	−2.04546	−	2.83157i	−0.253708	−	0.351212i
$66$	−1.04078	+	1.43782i	−0.128111	+	0.176984i
$67$	1.62806	+	0.436237i	0.198899	+	0.0532948i	0.356893	−	0.934145i	$-0.383836\pi$
$67$	1.62806	+	0.436237i	0.198899	+	0.0532948i	−0.157994	+	0.987440i	$0.550503\pi$
$68$	3.56434	+	2.05787i	0.432239	+	0.249554i
$69$	−0.450660	−	1.00743i	−0.0542531	−	0.121280i
$70$	−2.52907	+	0.417044i	−0.302282	+	0.0498463i
$71$	−8.55610	−	8.55610i	−1.01542	−	1.01542i	−0.999879	−	0.0155429i	$-0.995052\pi$
$71$	−8.55610	−	8.55610i	−1.01542	−	1.01542i	−0.0155429	−	0.999879i	$-0.504948\pi$
$72$	−2.67779	−	1.35256i	−0.315581	−	0.159401i
$73$	3.42226	−	12.7721i	0.400545	−	1.49486i	−0.411581	−	0.911373i	$-0.635023\pi$
$73$	3.42226	−	12.7721i	0.400545	−	1.49486i	0.812126	−	0.583482i	$-0.198310\pi$
$74$	2.50565	−	1.44664i	0.291275	−	0.168168i
$75$	0.723009	−	6.99731i	0.0834859	−	0.807980i
$76$	1.95579	+	1.95579i	0.224345	+	0.224345i
$77$	2.20359	+	1.57972i	0.251122	+	0.180026i
$78$	−6.24500	−	0.00607038i	−0.707106	−	0.000687335i
$79$	−0.0157356	+	0.0272549i	−0.00177039	+	0.00306641i	−0.866909	−	0.498466i	$-0.833897\pi$
$79$	−0.0157356	+	0.0272549i	−0.00177039	+	0.00306641i	0.865139	+	0.501532i	$0.167230\pi$
$80$	−0.250746	+	0.935798i	−0.0280343	+	0.104625i
$81$	−7.24376	+	5.34115i	−0.804863	+	0.593461i
$82$	−0.0592998	−	0.0342367i	−0.00654856	−	0.00378082i
$83$	−6.06316	−	6.06316i	−0.665518	−	0.665518i	0.291157	−	0.956675i	$-0.405960\pi$
$83$	−6.06316	−	6.06316i	−0.665518	−	0.665518i	−0.956675	+	0.291157i	$0.905960\pi$
$84$	−2.04727	+	4.09984i	−0.223376	+	0.447329i
$85$	−2.81950	−	2.81950i	−0.305817	−	0.305817i
$86$	−2.24620	−	8.38293i	−0.242214	−	0.903955i
$87$	−4.88639	−	3.53706i	−0.523876	−	0.379213i
$88$	0.887491	−	0.512393i	0.0946069	−	0.0546213i
$89$	−1.67059	−	6.23472i	−0.177082	−	0.660879i	−0.996188	−	0.0872363i	$-0.972196\pi$
$89$	−1.67059	−	6.23472i	−0.177082	−	0.660879i	0.819106	−	0.573643i	$-0.194470\pi$
$90$	2.16672	+	1.93717i	0.228393	+	0.204196i
$91$	0.0345255	+	9.53933i	0.00361926	+	0.999993i
$92$			0.637183i			0.0664309i
$93$	3.35659	−	2.72790i	0.348062	−	0.282870i
$94$	−1.67666	−	2.90406i	−0.172934	−	0.299531i
$95$	−1.33982	−	2.32064i	−0.137463	−	0.238092i
$96$	1.09238	+	1.34414i	0.111491	+	0.137185i
$97$	−8.64212	+	8.64212i	−0.877475	+	0.877475i	−0.993273	−	0.115798i	$-0.963057\pi$
$97$	−8.64212	+	8.64212i	−0.877475	+	0.877475i	0.115798	+	0.993273i	$0.463057\pi$
$98$	6.27690	+	3.09847i	0.634063	+	0.312993i
$99$	−0.171696	−	3.06956i	−0.0172561	−	0.308503i
$100$	−2.03070	+	3.51728i	−0.203070	+	0.351728i
$101$	5.68164	+	9.84089i	0.565344	+	0.979205i	0.997018	+	0.0771748i	$0.0245900\pi$
$101$	5.68164	+	9.84089i	0.565344	+	0.979205i	−0.431673	+	0.902030i	$0.642077\pi$
$102$	−7.03894	+	1.12755i	−0.696959	+	0.111644i
$103$	−12.5991	−	7.27409i	−1.24143	−	0.716738i	−0.272042	−	0.962285i	$-0.587699\pi$
$103$	−12.5991	−	7.27409i	−1.24143	−	0.716738i	−0.969385	+	0.245548i	$0.921032\pi$
$104$	3.28982	+	1.47550i	0.322593	+	0.144685i
$105$	2.94385	−	3.32327i	0.287290	−	0.324318i
$106$	5.61145	−	5.61145i	0.545032	−	0.545032i
$107$	7.41867	+	4.28317i	0.717189	+	0.414070i	0.813717	−	0.581261i	$-0.197440\pi$
$107$	7.41867	+	4.28317i	0.717189	+	0.414070i	−0.0965279	+	0.995330i	$0.530774\pi$
$108$	5.07683	−	1.10714i	0.488519	−	0.106534i
$109$	0.938198	+	0.251389i	0.0898631	+	0.0240787i	0.303470	−	0.952841i	$-0.401855\pi$
$109$	0.938198	+	0.251389i	0.0898631	+	0.0240787i	−0.213607	+	0.976920i	$0.568521\pi$
$110$	−0.958993	+	0.256961i	−0.0914364	+	0.0245003i
$111$	−1.78766	+	4.68160i	−0.169677	+	0.444357i
$112$	2.04552	−	1.67805i	0.193284	−	0.158561i
$113$		−	8.13853i		−	0.765608i	−0.923829	−	0.382804i	$-0.874958\pi$
$113$		−	8.13853i		−	0.765608i	0.923829	−	0.382804i	$-0.125042\pi$
$114$	−4.76533	−	0.492385i	−0.446314	−	0.0461161i
$115$	0.159771	−	0.596274i	0.0148987	−	0.0556029i
$116$	1.74135	+	3.01611i	0.161680	+	0.280039i
$117$	8.40076	−	6.81375i	0.776651	−	0.629931i
$118$	5.80359			0.534264
$119$	1.77171	+	10.7441i	0.162412	+	0.984913i
$120$	−0.685209	−	1.53175i	−0.0625508	−	0.139829i
$121$	−8.61679	−	4.97491i	−0.783345	−	0.452264i
$122$	0.307485	−	1.14755i	0.0278384	−	0.103894i
$123$	0.117107	−	0.0187590i	0.0105591	−	0.00169144i
$124$	−2.41212	+	0.646325i	−0.216614	+	0.0580417i
$125$	6.20753	−	6.20753i	0.555218	−	0.555218i
$126$	−1.72677	−	7.74715i	−0.153833	−	0.690171i
$127$		−	20.2101i		−	1.79335i	−0.442687	−	0.896676i	$-0.645975\pi$
$127$		−	20.2101i		−	1.79335i	0.442687	−	0.896676i	$-0.354025\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	12.1766	+	8.81411i	1.07209	+	0.776039i
$130$	−2.70863	−	2.20568i	−0.237562	−	0.193451i
$131$	3.53443	+	2.04060i	0.308805	+	0.178288i	0.646391	−	0.763006i	$-0.276277\pi$
$131$	3.53443	+	2.04060i	0.308805	+	0.178288i	−0.337587	+	0.941294i	$0.609611\pi$
$132$	−0.633182	+	1.65820i	−0.0551114	+	0.144328i
$133$	−0.718703	+	7.28254i	−0.0623194	+	0.631476i
$134$	1.68549			0.145604
$135$	−5.02850	−	0.236939i	−0.432784	−	0.0203925i
$136$	3.97550	+	1.06523i	0.340897	+	0.0913429i
$137$	17.4258	+	4.66924i	1.48879	+	0.398920i	0.909328	−	0.416079i	$-0.136596\pi$
$137$	17.4258	+	4.66924i	1.48879	+	0.398920i	0.579462	+	0.814999i	$0.303263\pi$
$138$	−0.696046	−	0.856462i	−0.0592514	−	0.0729069i
$139$	−19.1544			−1.62465			−0.812326	−	0.583204i	$-0.801799\pi$
$139$	−19.1544			−1.62465			−0.812326	+	0.583204i	$0.801799\pi$
$140$	−2.33496	+	1.05741i	−0.197340	+	0.0893671i
$141$	5.42600	+	2.07190i	0.456951	+	0.174486i
$142$	−10.4790	−	6.05008i	−0.879381	−	0.507711i
$143$	0.376189	+	3.67572i	0.0314585	+	0.307379i
$144$	−2.93662	−	0.613411i	−0.244718	−	0.0511176i
$145$	−0.873274	−	3.25910i	−0.0725215	−	0.270654i
$146$		−	13.2226i		−	1.09431i
$147$	−11.8217	+	2.69199i	−0.975039	+	0.222032i
$148$	2.04585	−	2.04585i	0.168168	−	0.168168i
$149$	19.7448	−	5.29060i	1.61756	−	0.433423i	0.667274	−	0.744812i	$-0.267461\pi$
$149$	19.7448	−	5.29060i	1.61756	−	0.433423i	0.950282	+	0.311389i	$0.100794\pi$
$150$	−1.11266	−	6.94601i	−0.0908487	−	0.567140i
$151$	0.0427232	−	0.159445i	0.00347676	−	0.0129755i	−0.964166	−	0.265301i	$-0.914529\pi$
$151$	0.0427232	−	0.159445i	0.00347676	−	0.0129755i	0.967642	+	0.252325i	$0.0811954\pi$
$152$	2.39535	+	1.38296i	0.194289	+	0.112173i
$153$	8.22959	−	9.20478i	0.665323	−	0.744162i
$154$	2.53736	+	0.955562i	0.204467	+	0.0770014i
$155$	2.41932			0.194324
$156$	−6.03377	+	1.61046i	−0.483088	+	0.128940i
$157$	2.07855	+	3.60015i	0.165886	+	0.287323i	0.936970	−	0.349411i	$-0.113618\pi$
$157$	2.07855	+	3.60015i	0.165886	+	0.287323i	−0.771083	+	0.636734i	$0.780285\pi$
$158$	−0.00814535	+	0.0303989i	−0.000648009	+	0.00241840i
$159$	−1.41272	+	13.6724i	−0.112036	+	1.08429i
$160$			0.968809i			0.0765911i
$161$	−1.30337	+	1.06922i	−0.102720	+	0.0842666i
$162$	−5.61455	+	7.03398i	−0.441120	+	0.552642i
$163$	−9.85619	+	2.64096i	−0.771997	+	0.206856i	−0.623253	−	0.782020i	$-0.714189\pi$
$163$	−9.85619	+	2.64096i	−0.771997	+	0.206856i	−0.148743	+	0.988876i	$0.547523\pi$
$164$	−0.0661403	−	0.0177222i	−0.00516469	−	0.00138387i
$165$	1.00832	−	1.39298i	0.0784975	−	0.108443i
$166$	−7.42583	−	4.28730i	−0.576356	−	0.332759i
$167$	−18.0695	+	18.0695i	−1.39826	+	1.39826i	−0.593220	+	0.805040i	$0.702144\pi$
$167$	−18.0695	+	18.0695i	−1.39826	+	1.39826i	−0.805040	+	0.593220i	$0.797856\pi$
$168$	−0.916395	+	4.49001i	−0.0707014	+	0.346412i
$169$	−9.70824	+	8.64581i	−0.746788	+	0.665062i
$170$	−3.45316	−	1.99368i	−0.264845	−	0.152909i
$171$	6.94313	−	4.54372i	0.530954	−	0.347467i
$172$	−4.33933	−	7.51593i	−0.330870	−	0.573084i
$173$	2.51736	−	4.36020i	0.191392	−	0.331500i	−0.754320	−	0.656507i	$-0.772033\pi$
$173$	2.51736	−	4.36020i	0.191392	−	0.331500i	0.945712	+	0.325007i	$0.105367\pi$
$174$	−5.63535	−	2.15185i	−0.427215	−	0.163131i
$175$	−10.6023	+	1.74832i	−0.801458	+	0.132161i
$176$	0.724634	−	0.724634i	0.0546213	−	0.0546213i
$177$	−7.80083	+	6.33973i	−0.586346	+	0.476523i
$178$	−3.22733	−	5.58990i	−0.241898	−	0.418980i
$179$	−1.24867	−	2.16277i	−0.0933302	−	0.161653i	0.815580	−	0.578644i	$-0.196418\pi$
$179$	−1.24867	−	2.16277i	−0.0933302	−	0.161653i	−0.908910	+	0.416991i	$0.863085\pi$
$180$	2.59427	+	1.31037i	0.193365	+	0.0976695i
$181$		−	0.778086i		−	0.0578347i	−0.999582	−	0.0289173i	$-0.990794\pi$
$181$		−	0.778086i		−	0.0578347i	0.999582	−	0.0289173i	$-0.00920596\pi$
$182$	2.50231	+	9.20535i	0.185484	+	0.682346i
$183$	0.840259	+	1.87836i	0.0621138	+	0.138852i
$184$	0.164915	+	0.615472i	0.0121577	+	0.0453732i
$185$	−2.42749	+	1.40151i	−0.178473	+	0.103041i
$186$	2.53618	−	3.50370i	0.185962	−	0.256904i
$187$	1.09164	+	4.07404i	0.0798283	+	0.297923i
$188$	−2.37115	−	2.37115i	−0.172934	−	0.172934i
$189$	10.7838	+	8.52694i	0.784409	+	0.620244i
$190$	−1.89479	−	1.89479i	−0.137463	−	0.137463i
$191$	−18.0065	−	10.3961i	−1.30291	−	0.752234i	−0.322006	−	0.946738i	$-0.604357\pi$
$191$	−18.0065	−	10.3961i	−1.30291	−	0.752234i	−0.980902	+	0.194503i	$0.937690\pi$
$192$	1.40305	+	1.01561i	0.101256	+	0.0732952i
$193$	−5.49236	+	20.4978i	−0.395349	+	1.47546i	0.425837	+	0.904800i	$0.359980\pi$
$193$	−5.49236	+	20.4978i	−0.395349	+	1.47546i	−0.821185	+	0.570662i	$0.806687\pi$
$194$	−6.11090	+	10.5844i	−0.438737	+	0.759915i
$195$	6.05021	+	0.00588104i	0.433264	+	0.000421150i
$196$	6.86496	+	1.36831i	0.490355	+	0.0977366i
$197$	2.00709	+	2.00709i	0.142999	+	0.142999i	0.774982	−	0.631983i	$-0.217759\pi$
$197$	2.00709	+	2.00709i	0.142999	+	0.142999i	−0.631983	+	0.774982i	$0.717759\pi$
$198$	−0.960307	−	2.92053i	−0.0682460	−	0.207553i
$199$	11.4097	−	6.58738i	0.808811	−	0.466967i	−0.0377317	−	0.999288i	$-0.512013\pi$
$199$	11.4097	−	6.58738i	0.808811	−	0.466967i	0.846543	+	0.532321i	$0.178680\pi$
$200$	−1.05117	+	3.92302i	−0.0743289	+	0.277399i
$201$	−2.26553	+	1.84119i	−0.159798	+	0.129868i
$202$	8.03505	+	8.03505i	0.565344	+	0.565344i
$203$	−3.24744	+	8.62314i	−0.227926	+	0.605226i
$204$	−6.50726	+	2.91094i	−0.455599	+	0.203807i
$205$	0.0574501	+	0.0331689i	0.00401249	+	0.00231661i
$206$	−14.0525	−	3.76535i	−0.979082	−	0.262344i
$207$	1.87116	+	0.390855i	0.130055	+	0.0271663i
$208$	3.55961	+	0.573754i	0.246814	+	0.0397827i
$209$			2.83447i			0.196064i
$210$	1.98341	−	3.97196i	0.136869	−	0.274091i
$211$	14.0500			0.967244			0.483622	−	0.875277i	$-0.339321\pi$
$211$	14.0500			0.967244			0.483622	+	0.875277i	$0.339321\pi$
$212$	3.96789	−	6.87259i	0.272516	−	0.472011i
$213$	20.6943	−	3.31496i	1.41795	−	0.227137i
$214$	8.27445	+	2.21713i	0.565629	+	0.151560i
$215$	2.17614	+	8.12146i	0.148411	+	0.553879i
$216$	4.61730	−	2.38340i	0.314167	−	0.162169i
$217$	−5.36972	−	3.84947i	−0.364520	−	0.261319i
$218$	0.971294			0.0657843
$219$	14.4441	+	17.7730i	0.976042	+	1.20099i
$220$	−0.859810	+	0.496411i	−0.0579683	+	0.0334680i
$221$	−9.37027	+	11.5069i	−0.630312	+	0.774040i
$222$	−0.515058	+	4.98475i	−0.0345684	+	0.334555i
$223$	3.20158	−	3.20158i	0.214394	−	0.214394i	−0.591737	−	0.806131i	$-0.701558\pi$
$223$	3.20158	−	3.20158i	0.214394	−	0.214394i	0.806131	+	0.591737i	$0.201558\pi$
$224$	1.54151	−	2.15029i	0.102997	−	0.143672i
$225$	9.08326	+	8.12094i	0.605551	+	0.541396i
$226$	−2.10641	−	7.86122i	−0.140116	−	0.522920i
$227$	5.74340	−	21.4347i	0.381203	−	1.42267i	−0.462863	−	0.886430i	$-0.653178\pi$
$227$	5.74340	−	21.4347i	0.381203	−	1.42267i	0.844066	−	0.536239i	$-0.180155\pi$
$228$	−4.73039	+	0.757750i	−0.313278	+	0.0501832i
$229$	0.206162	−	0.0552409i	0.0136236	−	0.00365042i	−0.252001	−	0.967727i	$-0.581089\pi$
$229$	0.206162	−	0.0552409i	0.0136236	−	0.00365042i	0.265624	+	0.964077i	$0.414422\pi$
$230$		−	0.617309i		−	0.0407041i
$231$	−4.45440	+	1.48736i	−0.293078	+	0.0978611i
$232$	2.46264	+	2.46264i	0.161680	+	0.161680i
$233$	2.96602	−	5.13730i	0.194310	−	0.336556i	−0.752364	−	0.658748i	$-0.771086\pi$
$233$	2.96602	−	5.13730i	0.194310	−	0.336556i	0.946674	+	0.322192i	$0.104420\pi$
$234$	6.35099	−	8.75585i	0.415177	−	0.572388i
$235$	1.62436	+	2.81348i	0.105962	+	0.183531i
$236$	5.60584	−	1.50208i	0.364909	−	0.0977771i
$237$	−0.0222586	−	0.0497581i	−0.00144585	−	0.00323213i
$238$	4.49213	+	9.91948i	0.291181	+	0.642985i
$239$	16.2577	+	16.2577i	1.05162	+	1.05162i	0.998593	+	0.0530291i	$0.0168876\pi$
$239$	16.2577	+	16.2577i	1.05162	+	1.05162i	0.0530291	+	0.998593i	$0.483112\pi$
$240$	−1.05831	−	1.30221i	−0.0683135	−	0.0840575i
$241$	−1.02561	+	3.82763i	−0.0660653	+	0.246559i	−0.991059	−	0.133423i	$-0.957403\pi$
$241$	−1.02561	+	3.82763i	−0.0660653	+	0.246559i	0.924994	+	0.379982i	$0.124070\pi$
$242$	−9.61078	−	2.57520i	−0.617804	−	0.165540i
$243$	−0.137057	−	15.5879i	−0.00879224	−	0.999961i
$244$		−	1.18803i		−	0.0760560i
$245$	−6.08112	−	3.00183i	−0.388508	−	0.191780i
$246$	0.108261	−	0.0484292i	0.00690247	−	0.00308773i
$247$	−8.08401	+	5.83972i	−0.514373	+	0.371572i
$248$	−2.16264	+	1.24860i	−0.137328	+	0.0792864i
$249$	14.6647	−	2.34910i	0.929337	−	0.148868i
$250$	4.38939	−	7.60264i	0.277609	−	0.480833i
$251$	−25.5203			−1.61082			−0.805412	−	0.592715i	$-0.798056\pi$
$251$	−25.5203			−1.61082			−0.805412	+	0.592715i	$0.798056\pi$
$252$	−3.67304	−	7.03625i	−0.231380	−	0.443242i
$253$	−0.461724	+	0.461724i	−0.0290284	+	0.0290284i
$254$	−5.23075	−	19.5214i	−0.328206	−	1.22488i
$255$	6.81939	−	1.09238i	0.427047	−	0.0684075i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.41632	−	9.38134i	0.337861	−	0.585192i	−0.646169	−	0.763194i	$-0.723630\pi$
$257$	5.41632	−	9.38134i	0.337861	−	0.585192i	0.984030	+	0.178002i	$0.0569634\pi$
$258$	14.0429	+	5.36225i	0.874273	+	0.333839i
$259$	7.61787	+	0.751796i	0.473351	+	0.0467143i
$260$	−3.18721	−	1.42948i	−0.197662	−	0.0886523i
$261$	9.92532	−	3.26357i	0.614362	−	0.202010i
$262$	3.94215	+	1.05629i	0.243547	+	0.0652581i
$263$	−1.97029	+	1.13755i	−0.121493	+	0.0701440i	−0.559515	−	0.828820i	$-0.689013\pi$
$263$	−1.97029	+	1.13755i	−0.121493	+	0.0701440i	0.438022	+	0.898964i	$0.355679\pi$
$264$	−0.182432	+	1.76558i	−0.0112279	+	0.108664i
$265$	−5.43642	+	5.43642i	−0.333957	+	0.333957i
$266$	1.19065	+	7.22040i	0.0730032	+	0.442711i
$267$	10.4443	+	3.98812i	0.639179	+	0.244069i
$268$	1.62806	−	0.436237i	0.0994494	−	0.0266474i
$269$	−14.0370	+	8.10427i	−0.855852	+	0.494126i	−0.862621	−	0.505851i	$-0.831179\pi$
$269$	−14.0370	+	8.10427i	−0.855852	+	0.494126i	0.00676921	+	0.999977i	$0.497845\pi$
$270$	−4.91848	+	1.07261i	−0.299329	+	0.0652767i
$271$	31.3351	−	8.39621i	1.90347	−	0.510033i	0.907533	−	0.419980i	$-0.137963\pi$
$271$	31.3351	−	8.39621i	1.90347	−	0.510033i	0.995937	−	0.0900530i	$-0.0287036\pi$
$272$	4.11574			0.249554
$273$	−13.4192	−	9.63978i	−0.812166	−	0.583426i
$274$	18.0406			1.08987
$275$	−4.02026	+	1.07723i	−0.242431	+	0.0649591i
$276$	−0.893998	−	0.647128i	−0.0538123	−	0.0389526i
$277$	−24.4046	+	14.0900i	−1.46633	+	0.846585i	−0.999291	−	0.0376525i	$-0.988012\pi$
$277$	−24.4046	+	14.0900i	−1.46633	+	0.846585i	−0.467037	+	0.884238i	$0.654679\pi$
$278$	−18.5017	+	4.95751i	−1.10966	+	0.297332i
$279$	0.418390	+	7.47993i	0.0250484	+	0.447812i
$280$	−1.98172	+	1.62571i	−0.118430	+	0.0971546i
$281$	13.0253	−	13.0253i	0.777021	−	0.777021i	−0.202302	−	0.979323i	$-0.564842\pi$
$281$	13.0253	−	13.0253i	0.777021	−	0.777021i	0.979323	+	0.202302i	$0.0648422\pi$
$282$	5.77736	+	0.596955i	0.344037	+	0.0355482i
$283$	17.8732	−	10.3191i	1.06245	−	0.613408i	0.136344	−	0.990662i	$-0.456465\pi$
$283$	17.8732	−	10.3191i	1.06245	−	0.613408i	0.926110	+	0.377254i	$0.123132\pi$
$284$	−11.6878	−	3.13175i	−0.693546	−	0.185835i
$285$	4.61669	+	0.477027i	0.273469	+	0.0282567i
$286$	1.31472	+	3.45311i	0.0777409	+	0.204187i
$287$	−0.0747354	−	0.165030i	−0.00441149	−	0.00974142i
$288$	−2.99532	+	0.167543i	−0.176501	+	0.00987258i
$289$	0.0303301	−	0.0525333i	0.00178413	−	0.00309020i
$290$	−1.68704	−	2.92203i	−0.0990662	−	0.171588i
$291$	−3.34829	−	20.9023i	−0.196280	−	1.22532i
$292$	−3.42226	−	12.7721i	−0.200273	−	0.747428i
$293$	−21.8967	+	21.8967i	−1.27922	+	1.27922i	−0.338117	+	0.941104i	$0.609790\pi$
$293$	−21.8967	+	21.8967i	−1.27922	+	1.27922i	−0.941104	+	0.338117i	$0.890210\pi$
$294$	−10.7222	+	5.65995i	−0.625330	+	0.330095i
$295$	−5.62257			−0.327359
$296$	1.44664	−	2.50565i	0.0840840	−	0.145638i
$297$	4.48111	+	2.87657i	0.260021	+	0.166916i
$298$	17.7027	−	10.2207i	1.02549	−	0.592067i
$299$	−2.26812	−	0.365586i	−0.131169	−	0.0211424i
$300$	−2.87251	−	6.42136i	−0.165845	−	0.370737i
$301$	8.09240	−	21.4883i	0.466438	−	1.23856i
$302$		−	0.165070i		−	0.00949869i
$303$	−19.5775	−	2.02288i	−1.12470	−	0.116212i
$304$	2.67167	+	0.715871i	0.153231	+	0.0410580i
$305$	−0.297895	+	1.11176i	−0.0170574	+	0.0636591i
$306$	5.56680	−	11.0211i	0.318233	−	0.630035i
$307$	11.4023	+	11.4023i	0.650764	+	0.650764i	0.953177	−	0.302413i	$-0.0977921\pi$
$307$	11.4023	+	11.4023i	0.650764	+	0.650764i	−0.302413	+	0.953177i	$0.597792\pi$
$308$	2.69822	+	0.266284i	0.153746	+	0.0151729i
$309$	23.0016	−	10.2895i	1.30852	−	0.585349i
$310$	2.33688	−	0.626165i	0.132726	−	0.0355638i
$311$	−8.76323	−	15.1784i	−0.496917	−	0.860686i	0.503077	−	0.864242i	$-0.332201\pi$
$311$	−8.76323	−	15.1784i	−0.496917	−	0.860686i	−0.999994	+	0.00355622i	$0.998868\pi$
$312$	−5.41136	+	3.11724i	−0.306358	+	0.176479i
$313$	2.56506	−	4.44282i	0.144986	−	0.251123i	−0.784382	−	0.620278i	$-0.787020\pi$
$313$	2.56506	−	4.44282i	0.144986	−	0.251123i	0.929368	+	0.369155i	$0.120353\pi$
$314$	2.93951	+	2.93951i	0.165886	+	0.165886i
$315$	1.67291	+	7.50550i	0.0942578	+	0.422887i
$316$			0.0314712i			0.00177039i
$317$	26.0000	−	6.96668i	1.46031	−	0.391288i	0.560711	−	0.828012i	$-0.310528\pi$
$317$	26.0000	−	6.96668i	1.46031	−	0.391288i	0.899596	+	0.436724i	$0.143861\pi$
$318$	2.17409	+	13.5722i	0.121917	+	0.761088i
$319$	−0.923732	+	3.44741i	−0.0517191	+	0.193018i
$320$	0.250746	+	0.935798i	0.0140171	+	0.0523127i
$321$	−13.5439	+	6.05871i	−0.755949	+	0.338164i
$322$	−0.982225	+	1.37013i	−0.0547372	+	0.0763542i
$323$	−8.04955	+	8.04955i	−0.447889	+	0.447889i
$324$	−3.60271	+	8.24745i	−0.200150	+	0.458192i
$325$	−11.3550	−	9.24657i	−0.629863	−	0.512907i
$326$	−8.83682	+	5.10194i	−0.489426	+	0.282570i
$327$	−1.30555	+	1.06102i	−0.0721972	+	0.0586747i
$328$	−0.0684735			−0.00378082
$329$	0.871336	−	8.82915i	0.0480383	−	0.486767i
$330$	0.613432	−	1.60648i	0.0337683	−	0.0884340i
$331$	1.39711	+	5.21409i	0.0767922	+	0.286592i	0.993634	−	0.112659i	$-0.0359367\pi$
$331$	1.39711	+	5.21409i	0.0767922	+	0.286592i	−0.916841	+	0.399251i	$0.869270\pi$
$332$	−8.28243	−	2.21927i	−0.454557	−	0.121798i
$333$	−4.75294	−	7.26283i	−0.260459	−	0.398001i
$334$	−12.7771	+	22.1305i	−0.699130	+	1.21093i
$335$	−1.63292			−0.0892158
$336$	0.276931	+	4.57420i	0.0151078	+	0.249543i
$337$			24.6635i			1.34350i	0.740776	+	0.671752i	$0.234458\pi$
$337$			24.6635i			1.34350i	−0.740776	+	0.671752i	$0.765542\pi$
$338$	−7.13974	+	10.8639i	−0.388351	+	0.590918i
$339$	11.4187	+	8.26556i	0.620181	+	0.448923i
$340$	−3.85150	−	1.03201i	−0.208877	−	0.0559684i
$341$	−2.21625	−	1.27955i	−0.120017	−	0.0692916i
$342$	5.53055	−	6.18591i	0.299058	−	0.334496i
$343$	8.72082	+	16.3385i	0.470880	+	0.882197i
$344$	−6.13673	−	6.13673i	−0.330870	−	0.330870i
$345$	0.674336	+	0.829748i	0.0363050	+	0.0446721i
$346$	1.30308	−	4.86317i	0.0700542	−	0.261446i
$347$	22.4958	−	12.9880i	1.20764	−	0.697230i	0.245395	−	0.969423i	$-0.421082\pi$
$347$	22.4958	−	12.9880i	1.20764	−	0.697230i	0.962243	+	0.272193i	$0.0877489\pi$
$348$	−6.00027	−	0.619988i	−0.321648	−	0.0332348i
$349$	20.0901	+	20.0901i	1.07540	+	1.07540i	0.996916	+	0.0784823i	$0.0250074\pi$
$349$	20.0901	+	20.0901i	1.07540	+	1.07540i	0.0784823	+	0.996916i	$0.474993\pi$
$350$	−9.78853	+	4.43282i	−0.523219	+	0.236944i
$351$	1.02812	+	18.7068i	0.0548772	+	0.998493i
$352$	0.512393	−	0.887491i	0.0273107	−	0.0473034i
$353$	3.41201	−	12.7338i	0.181603	−	0.677752i	−0.813729	−	0.581244i	$-0.802566\pi$
$353$	3.41201	−	12.7338i	0.181603	−	0.677752i	0.995332	−	0.0965075i	$-0.0307672\pi$
$354$	−5.89418	+	8.14271i	−0.313272	+	0.432780i
$355$	10.1522	+	5.86137i	0.538822	+	0.311089i
$356$	−4.56413	−	4.56413i	−0.241898	−	0.241898i
$357$	−16.8739	−	8.42604i	−0.893061	−	0.445953i
$358$	−1.76589	−	1.76589i	−0.0933302	−	0.0933302i
$359$	2.37583	+	8.86671i	0.125391	+	0.467967i	0.999853	−	0.0171272i	$-0.00545203\pi$
$359$	2.37583	+	8.86671i	0.125391	+	0.467967i	−0.874462	+	0.485094i	$0.838785\pi$
$360$	2.84502	+	0.594278i	0.149946	+	0.0313212i
$361$	9.82916	−	5.67487i	0.517324	−	0.298677i
$362$	−0.201384	−	0.751574i	−0.0105845	−	0.0395018i
$363$	15.7313	−	7.03720i	0.825680	−	0.369357i
$364$	4.79956	+	8.24404i	0.251566	+	0.432105i
$365$			12.8102i			0.670515i
$366$	1.29778	+	1.59688i	0.0678362	+	0.0834702i
$367$	−7.46508	−	12.9299i	−0.389674	−	0.674935i	0.602732	−	0.797944i	$-0.294079\pi$
$367$	−7.46508	−	12.9299i	−0.389674	−	0.674935i	−0.992406	+	0.123009i	$0.960746\pi$
$368$	0.318592	+	0.551817i	0.0166077	+	0.0287654i
$369$	−0.0926146	+	0.183358i	−0.00482133	+	0.00954523i
$370$	−1.98204	+	1.98204i	−0.103041	+	0.103041i
$371$	20.7163	−	3.41613i	1.07554	−	0.177356i
$372$	1.54294	−	4.04072i	0.0799978	−	0.209502i
$373$	−10.8093	+	18.7223i	−0.559686	+	0.969404i	0.437837	+	0.899054i	$0.355745\pi$
$373$	−10.8093	+	18.7223i	−0.559686	+	0.969404i	−0.997522	+	0.0703493i	$0.977589\pi$
$374$	2.10888	+	3.65269i	0.109048	+	0.188876i
$375$	2.40504	+	15.0139i	0.124196	+	0.775313i
$376$	−2.90406	−	1.67666i	−0.149765	−	0.0864671i
$377$	−11.7353	+	4.46802i	−0.604397	+	0.230115i
$378$	12.6233	+	5.44533i	0.649274	+	0.280077i
$379$	14.4640	−	14.4640i	0.742967	−	0.742967i	−0.230181	−	0.973148i	$-0.573932\pi$
$379$	14.4640	−	14.4640i	0.742967	−	0.742967i	0.973148	+	0.230181i	$0.0739318\pi$
$380$	−2.32064	−	1.33982i	−0.119046	−	0.0687313i
$381$	28.3557	+	20.5255i	1.45270	+	1.05155i
$382$	−20.0837	−	5.38141i	−1.02757	−	0.275337i
$383$	−27.8016	+	7.44941i	−1.42059	+	0.380647i	−0.885695	−	0.464268i	$-0.846317\pi$
$383$	−27.8016	+	7.44941i	−1.42059	+	0.380647i	−0.534900	+	0.844915i	$0.679651\pi$
$384$	1.61810	+	0.617867i	0.0825732	+	0.0315304i
$385$	−2.45822	−	0.925757i	−0.125283	−	0.0471809i
$386$			21.2209i			1.08011i
$387$	−24.7332	+	8.13259i	−1.25726	+	0.413403i
$388$	−3.16324	+	11.8054i	−0.160589	+	0.599326i
$389$	2.90415	+	5.03013i	0.147246	+	0.255038i	0.930209	−	0.367031i	$-0.119626\pi$
$389$	2.90415	+	5.03013i	0.147246	+	0.255038i	−0.782963	+	0.622069i	$0.786292\pi$
$390$	5.84557	−	1.56023i	0.296002	−	0.0790052i
$391$	−2.62248			−0.132625
$392$	6.98519	−	0.455095i	0.352805	−	0.0229858i
$393$	−6.45266	+	2.88652i	−0.325494	+	0.145605i
$394$	2.45817	+	1.41923i	0.123841	+	0.0714997i
$395$	0.00789129	−	0.0294507i	0.000397054	−	0.00148183i
$396$	−1.68347	−	2.57247i	−0.0845978	−	0.129272i
$397$	−20.5855	+	5.51587i	−1.03316	+	0.276834i	−0.735275	−	0.677769i	$-0.762947\pi$
$397$	−20.5855	+	5.51587i	−1.03316	+	0.276834i	−0.297882	+	0.954603i	$0.596280\pi$
$398$	9.31597	−	9.31597i	0.466967	−	0.466967i
$399$	−9.48782	−	8.40458i	−0.474985	−	0.420755i
$400$			4.06141i			0.203070i
$401$	1.52226	+	5.68116i	0.0760181	+	0.283703i	0.993462	−	0.114161i	$-0.0364180\pi$
$401$	1.52226	+	5.68116i	0.0760181	+	0.283703i	−0.917444	+	0.397865i	$0.869751\pi$
$402$	−1.71180	+	2.36482i	−0.0853766	+	0.117946i
$403$	−0.916700	−	8.95702i	−0.0456641	−	0.446181i
$404$	9.84089	+	5.68164i	0.489602	+	0.282672i
$405$	5.43942	−	6.81458i	0.270287	−	0.338619i
$406$	−0.904955	+	9.16981i	−0.0449122	+	0.455090i
$407$	2.96499			0.146969
$408$	−5.53212	+	4.49596i	−0.273881	+	0.222583i
$409$	0.349927	+	0.0937626i	0.0173028	+	0.00463626i	0.267460	−	0.963569i	$-0.413816\pi$
$409$	0.349927	+	0.0937626i	0.0173028	+	0.00463626i	−0.250157	+	0.968205i	$0.580482\pi$
$410$	0.0640773	+	0.0171695i	0.00316455	+	0.000847939i
$411$	−24.2490	+	19.7072i	−1.19611	+	0.972082i
$412$	−14.5482			−0.716738
$413$	12.4794	+	8.94630i	0.614071	+	0.440219i
$414$	1.90857	−	0.106756i	0.0938009	−	0.00524676i
$415$	7.19421	+	4.15358i	0.353150	+	0.203891i
$416$	3.58682	−	0.367090i	0.175858	−	0.0179981i
$417$	19.4533	−	26.8745i	0.952634	−	1.31605i
$418$	0.733615	+	2.73789i	0.0358823	+	0.133914i
$419$			4.19355i			0.204869i	0.994740	+	0.102434i	$0.0326631\pi$
$419$			4.19355i			0.204869i	−0.994740	+	0.102434i	$0.967337\pi$
$420$	0.887812	−	4.34997i	0.0433208	−	0.212257i
$421$	−1.34291	+	1.34291i	−0.0654495	+	0.0654495i	−0.739074	−	0.673624i	$-0.764737\pi$
$421$	−1.34291	+	1.34291i	−0.0654495	+	0.0654495i	0.673624	+	0.739074i	$0.264737\pi$
$422$	13.5713	−	3.63642i	0.660640	−	0.177018i
$423$	−8.41767	+	5.50868i	−0.409281	+	0.267841i
$424$	2.05393	−	7.66538i	0.0997477	−	0.372264i
$425$	−14.4762	−	8.35786i	−0.702201	−	0.405416i
$426$	19.1311	−	8.55807i	0.926907	−	0.414640i
$427$	2.43015	−	1.99357i	0.117603	−	0.0964758i
$428$	8.56634			0.414070
$429$	−5.53927	−	3.20528i	−0.267438	−	0.154752i
$430$	4.20398	+	7.28150i	0.202734	+	0.351145i
$431$	−8.43634	+	31.4848i	−0.406364	+	1.51657i	0.395162	+	0.918611i	$0.370688\pi$
$431$	−8.43634	+	31.4848i	−0.406364	+	1.51657i	−0.801526	+	0.597960i	$0.795978\pi$
$432$	3.84310	−	3.49723i	0.184901	−	0.168260i
$433$		−	21.9098i		−	1.05292i	−0.850201	−	0.526458i	$-0.823520\pi$
$433$		−	21.9098i		−	1.05292i	0.850201	−	0.526458i	$-0.176480\pi$
$434$	−6.18306	−	2.32852i	−0.296797	−	0.111772i
$435$	5.45958	+	2.08473i	0.261767	+	0.0999551i
$436$	0.938198	−	0.251389i	0.0449315	−	0.0120394i
$437$	−1.70234	−	0.456141i	−0.0814340	−	0.0218202i
$438$	18.5519	+	13.4290i	0.886445	+	0.641662i
$439$	−5.86906	−	3.38851i	−0.280115	−	0.161725i	0.353360	−	0.935487i	$-0.385039\pi$
$439$	−5.86906	−	3.38851i	−0.280115	−	0.161725i	−0.633476	+	0.773763i	$0.718372\pi$
$440$	−0.702032	+	0.702032i	−0.0334680	+	0.0334680i
$441$	8.22926	−	19.3204i	0.391869	−	0.920021i
$442$	−6.07277	+	13.5400i	−0.288852	+	0.644034i
$443$	−30.3397	−	17.5166i	−1.44148	−	0.832240i	−0.443533	−	0.896258i	$-0.646275\pi$
$443$	−30.3397	−	17.5166i	−1.44148	−	0.832240i	−0.997949	+	0.0640182i	$0.979608\pi$
$444$	0.792641	+	4.94821i	0.0376171	+	0.234832i
$445$	3.12666	+	5.41554i	0.148218	+	0.256721i
$446$	2.26386	−	3.92112i	0.107197	−	0.185671i
$447$	−12.6300	+	33.0760i	−0.597379	+	1.56444i
$448$	0.932449	−	2.47599i	0.0440541	−	0.116980i
$449$	−2.14151	+	2.14151i	−0.101064	+	0.101064i	−0.755831	−	0.654767i	$-0.772767\pi$
$449$	−2.14151	+	2.14151i	−0.101064	+	0.101064i	0.654767	+	0.755831i	$0.272767\pi$
$450$	10.8756	+	5.49331i	0.512681	+	0.258957i
$451$	−0.0350854	−	0.0607696i	−0.00165210	−	0.00286153i
$452$	−4.06926	−	7.04817i	−0.191402	−	0.331518i
$453$	0.180319	+	0.221876i	0.00847212	+	0.0104247i
$454$		−	22.1908i		−	1.04147i
$455$	−2.42426	−	8.91822i	−0.113651	−	0.418093i
$456$	−4.37309	+	1.95625i	−0.204789	+	0.0916096i
$457$	−8.21302	−	30.6514i	−0.384189	−	1.43381i	−0.839441	−	0.543451i	$-0.817118\pi$
$457$	−8.21302	−	30.6514i	−0.384189	−	1.43381i	0.455252	−	0.890363i	$-0.349549\pi$
$458$	0.184840	−	0.106717i	0.00863698	−	0.00498657i
$459$	4.55670	+	20.8949i	0.212688	+	0.975292i
$460$	−0.159771	−	0.596274i	−0.00744937	−	0.0278014i
$461$	−11.2027	−	11.2027i	−0.521764	−	0.521764i	0.396340	−	0.918104i	$-0.370280\pi$
$461$	−11.2027	−	11.2027i	−0.521764	−	0.521764i	−0.918104	+	0.396340i	$0.870280\pi$
$462$	−3.91767	+	2.58956i	−0.182266	+	0.120477i
$463$	−17.5213	−	17.5213i	−0.814284	−	0.814284i	0.170989	−	0.985273i	$-0.445304\pi$
$463$	−17.5213	−	17.5213i	−0.814284	−	0.814284i	−0.985273	+	0.170989i	$0.945304\pi$
$464$	3.01611	+	1.74135i	0.140019	+	0.0808402i
$465$	−2.45708	+	3.39441i	−0.113944	+	0.157412i
$466$	1.53533	−	5.72991i	0.0711226	−	0.265433i
$467$	17.3288	−	30.0144i	0.801882	−	1.38890i	−0.116495	−	0.993191i	$-0.537166\pi$
$467$	17.3288	−	30.0144i	0.801882	−	1.38890i	0.918376	−	0.395708i	$-0.129501\pi$
$468$	3.86840	−	10.1013i	0.178817	−	0.466931i
$469$	3.62429	+	2.59820i	0.167354	+	0.119974i
$470$	2.29720	+	2.29720i	0.105962	+	0.105962i
$471$	−7.16217	−	0.740043i	−0.330015	−	0.0340994i
$472$	5.02606	−	2.90180i	0.231343	−	0.133566i
$473$	2.30188	−	8.59072i	0.105840	−	0.395002i
$474$	−0.0343785	−	0.0423016i	−0.00157906	−	0.00194298i
$475$	−7.94328	−	7.94328i	−0.364463	−	0.364463i
$476$	6.90641	+	8.41884i	0.316555	+	0.385877i
$477$	−17.7482	−	15.8679i	−0.812635	−	0.726541i
$478$	19.9115	+	11.4959i	0.910731	+	0.525811i
$479$	5.30314	+	1.42097i	0.242307	+	0.0649259i	0.377929	−	0.925835i	$-0.376637\pi$
$479$	5.30314	+	1.42097i	0.242307	+	0.0649259i	−0.135622	+	0.990761i	$0.543303\pi$
$480$	−1.35928	−	0.983930i	−0.0620425	−	0.0449101i
$481$	6.10861	+	8.45624i	0.278529	+	0.385572i
$482$			3.96265i			0.180494i
$483$	−0.176456	−	2.91460i	−0.00802901	−	0.132619i
$484$	−9.94981			−0.452264
$485$	5.92030	−	10.2543i	0.268827	−	0.465622i
$486$	−4.16682	−	15.0212i	−0.189011	−	0.681377i
$487$	−23.9967	−	6.42991i	−1.08740	−	0.291367i	−0.329774	−	0.944060i	$-0.606972\pi$
$487$	−23.9967	−	6.42991i	−1.08740	−	0.291367i	−0.757622	+	0.652693i	$0.773639\pi$
$488$	−0.307485	−	1.14755i	−0.0139192	−	0.0519472i
$489$	6.30464	−	16.5109i	0.285106	−	0.746648i
$490$	−6.65084	−	1.32563i	−0.300454	−	0.0598860i
$491$	−13.7326			−0.619744			−0.309872	−	0.950778i	$-0.600286\pi$
$491$	−13.7326			−0.619744			−0.309872	+	0.950778i	$0.600286\pi$
$492$	0.0920378	−	0.0747991i	0.00414938	−	0.00337220i
$493$	−12.4135	+	7.16695i	−0.559077	+	0.322783i
$494$	−6.29712	+	7.73303i	−0.283321	+	0.347925i
$495$	0.930354	+	2.82944i	0.0418163	+	0.127174i
$496$	−1.76579	+	1.76579i	−0.0792864	+	0.0792864i
$497$	−13.2067	−	29.1630i	−0.592402	−	1.30814i
$498$	13.5570	−	6.06456i	0.607504	−	0.271759i
$499$	6.69439	+	24.9838i	0.299682	+	1.11843i	0.937427	+	0.348181i	$0.113201\pi$
$499$	6.69439	+	24.9838i	0.299682	+	1.11843i	−0.637745	+	0.770247i	$0.720133\pi$
$500$	2.27211	−	8.47965i	0.101612	−	0.379221i
$501$	−7.00082	−	43.7039i	−0.312774	−	1.95255i
$502$	−24.6507	+	6.60513i	−1.10021	+	0.294801i
$503$			23.5158i			1.04852i	0.851559	+	0.524260i	$0.175658\pi$
$503$			23.5158i			1.04852i	−0.851559	+	0.524260i	$0.824342\pi$
$504$	−5.36900	−	5.84584i	−0.239154	−	0.260394i
$505$	−7.78443	−	7.78443i	−0.346403	−	0.346403i
$506$	−0.326488	+	0.565494i	−0.0145142	+	0.0251393i
$507$	−2.27070	−	22.4019i	−0.100845	−	0.994902i
$508$	−10.1050	−	17.5024i	−0.448338	−	0.776544i
$509$	−36.3055	+	9.72802i	−1.60921	+	0.431187i	−0.947808	−	0.318843i	$-0.896706\pi$
$509$	−36.3055	+	9.72802i	−1.60921	+	0.431187i	−0.661404	+	0.750030i	$0.730039\pi$
$510$	6.30429	−	2.82015i	0.279159	−	0.124878i
$511$	20.3828	−	28.4324i	0.901681	−	1.25778i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.676453	+	14.3562i	−0.0298661	+	0.633840i
$514$	2.80369	−	10.4635i	0.123666	−	0.461526i
$515$	13.6142	+	3.64790i	0.599912	+	0.160746i
$516$	14.9523	+	1.54497i	0.658236	+	0.0680134i
$517$		−	3.43644i		−	0.151134i
$518$	7.55288	−	1.24547i	0.331854	−	0.0547228i
$519$	3.56091	+	7.96024i	0.156307	+	0.349416i
$520$	−3.44858	−	0.555858i	−0.151230	−	0.0243760i
$521$	−35.6395	+	20.5765i	−1.56139	+	0.901472i	−0.564278	+	0.825585i	$0.690845\pi$
$521$	−35.6395	+	20.5765i	−1.56139	+	0.901472i	−0.997116	+	0.0758870i	$0.975821\pi$
$522$	8.74245	−	5.72123i	0.382647	−	0.250411i
$523$	14.4894	−	25.0964i	0.633578	−	1.09739i	−0.353236	−	0.935534i	$-0.614919\pi$
$523$	14.4894	−	25.0964i	0.633578	−	1.09739i	0.986814	−	0.161855i	$-0.0517478\pi$
$524$	4.08121			0.178288
$525$	8.31481	−	16.6511i	0.362888	−	0.726715i
$526$	−1.60873	+	1.60873i	−0.0701440	+	0.0701440i
$527$	−2.66011	−	9.92765i	−0.115876	−	0.432455i
$528$	0.280751	+	1.75264i	0.0122181	+	0.0762738i
$529$	11.2970	+	19.5670i	0.491174	+	0.850738i
$530$	−3.84413	+	6.65823i	−0.166978	+	0.289215i
$531$	−0.972353	−	17.3836i	−0.0421965	−	0.754384i
$532$	3.01885	+	6.66621i	0.130884	+	0.289017i
$533$	0.101032	−	0.225265i	0.00437620	−	0.00975732i
$534$	11.1206	+	1.14905i	0.481235	+	0.0497244i
$535$	−8.01636	−	2.14798i	−0.346577	−	0.0928651i
$536$	1.45968	−	0.842744i	0.0630484	−	0.0364010i
$537$	4.30262	+	0.444576i	0.185672	+	0.0191849i
$538$	−11.4612	+	11.4612i	−0.494126	+	0.494126i
$539$	3.98306	+	5.96611i	0.171562	+	0.256978i
$540$	−4.47328	+	2.30905i	−0.192499	+	0.0993659i
$541$	6.93022	−	1.85695i	0.297953	−	0.0798364i	−0.106745	−	0.994286i	$-0.534043\pi$
$541$	6.93022	−	1.85695i	0.297953	−	0.0798364i	0.404699	+	0.914450i	$0.367376\pi$
$542$	28.0943	−	16.2202i	1.20675	−	0.696718i
$543$	1.09169	+	0.790231i	0.0468490	+	0.0339121i
$544$	3.97550	−	1.06523i	0.170448	−	0.0456715i
$545$	−0.940998			−0.0403079
$546$	−15.4569	−	5.83817i	−0.661494	−	0.249851i
$547$	3.41524			0.146025			0.0730126	−	0.997331i	$-0.476739\pi$
$547$	3.41524			0.146025			0.0730126	+	0.997331i	$0.476739\pi$
$548$	17.4258	−	4.66924i	0.744395	−	0.199460i
$549$	−3.48880	−	0.728752i	−0.148898	−	0.0311024i
$550$	−3.60447	+	2.08104i	−0.153695	+	0.0887358i
$551$	−9.30461	+	2.49316i	−0.396390	+	0.106212i
$552$	−1.03102	−	0.393694i	−0.0438833	−	0.0167567i
$553$	−0.0643750	+	0.0528102i	−0.00273751	+	0.00224572i
$554$	−19.9262	+	19.9262i	−0.846585	+	0.846585i
$555$	0.498993	−	4.82927i	0.0211811	−	0.204991i
$556$	−16.5882	+	9.57718i	−0.703495	+	0.406163i
$557$	4.28820	+	1.14902i	0.181697	+	0.0486855i	0.348520	−	0.937301i	$-0.386684\pi$
$557$	4.28820	+	1.14902i	0.181697	+	0.0486855i	−0.166823	+	0.985987i	$0.553351\pi$
$558$	2.34008	+	7.11677i	0.0990636	+	0.301277i
$559$	29.2435	−	11.1340i	1.23687	−	0.470918i
$560$	−1.49343	+	2.08322i	−0.0631089	+	0.0880321i
$561$	−6.82475	−	2.60601i	−0.288141	−	0.110026i
$562$	9.21024	−	15.9526i	0.388511	−	0.672920i
$563$	−11.0361	−	19.1151i	−0.465116	−	0.805605i	0.534090	−	0.845427i	$-0.320654\pi$
$563$	−11.0361	−	19.1151i	−0.465116	−	0.805605i	−0.999207	+	0.0398220i	$0.987321\pi$
$564$	5.73500	−	0.918676i	0.241487	−	0.0386832i
$565$	2.04071	+	7.61602i	0.0858531	+	0.320408i
$566$	14.5934	−	14.5934i	0.613408	−	0.613408i
$567$	−22.9159	+	6.47021i	−0.962375	+	0.271723i
$568$	−12.1002			−0.507711
$569$	21.7766	−	37.7183i	0.912925	−	1.58123i	0.103013	−	0.994680i	$-0.467152\pi$
$569$	21.7766	−	37.7183i	0.912925	−	1.58123i	0.809912	−	0.586552i	$-0.199515\pi$
$570$	4.58285	−	0.734115i	0.191954	−	0.0307487i
$571$	29.0000	−	16.7431i	1.21361	−	0.700678i	0.250067	−	0.968229i	$-0.419548\pi$
$571$	29.0000	−	16.7431i	1.21361	−	0.700678i	0.963544	+	0.267550i	$0.0862142\pi$
$572$	2.16365	+	2.99517i	0.0904667	+	0.125234i
$573$	32.8738	−	14.7057i	1.37332	−	0.614338i
$574$	−0.114902	−	0.140064i	−0.00479591	−	0.00584616i
$575$		−	2.58786i		−	0.107921i
$576$	−2.84989	+	0.937080i	−0.118745	+	0.0390450i
$577$	−13.5027	−	3.61803i	−0.562124	−	0.150621i	−0.0334420	−	0.999441i	$-0.510647\pi$
$577$	−13.5027	−	3.61803i	−0.562124	−	0.150621i	−0.528682	+	0.848820i	$0.677314\pi$
$578$	0.0157000	−	0.0585933i	0.000653035	−	0.00243716i
$579$	−23.1812	−	28.5237i	−0.963379	−	1.18541i
$580$	−2.38583	−	2.38583i	−0.0990662	−	0.0990662i
$581$	−9.35875	−	20.6659i	−0.388266	−	0.857367i
$582$	−8.64412	−	19.3235i	−0.358310	−	0.800984i
$583$	7.85538	−	2.10484i	0.325336	−	0.0871736i
$584$	−6.61130	−	11.4511i	−0.273578	−	0.473850i
$585$	−6.15289	+	8.48275i	−0.254391	+	0.350719i
$586$	−15.4833	+	26.8179i	−0.639610	+	1.10784i
$587$	16.7060	+	16.7060i	0.689531	+	0.689531i	0.962128	−	0.272597i	$-0.0878826\pi$
$587$	16.7060	+	16.7060i	0.689531	+	0.689531i	−0.272597	+	0.962128i	$0.587883\pi$
$588$	−8.89192	+	8.24219i	−0.366697	+	0.339902i
$589$		−	6.90705i		−	0.284600i
$590$	−5.43099	+	1.45523i	−0.223590	+	0.0599108i
$591$	−4.85446	+	0.777624i	−0.199686	+	0.0319872i
$592$	0.748834	−	2.79469i	0.0307769	−	0.114861i
$593$	6.86959	+	25.6377i	0.282100	+	1.05281i	0.950932	+	0.309399i	$0.100128\pi$
$593$	6.86959	+	25.6377i	0.282100	+	1.05281i	−0.668832	+	0.743413i	$0.733205\pi$
$594$	5.07294	+	1.61876i	0.208145	+	0.0664185i
$595$	−4.35201	−	9.61009i	−0.178415	−	0.393975i
$596$	14.4542	−	14.4542i	0.592067	−	0.592067i
$597$	−2.34536	+	22.6985i	−0.0959893	+	0.928989i
$598$	−2.28546	+	0.233904i	−0.0934593	+	0.00956503i
$599$	−32.0100	+	18.4810i	−1.30789	+	0.755112i	−0.981744	−	0.190206i	$-0.939084\pi$
$599$	−32.0100	+	18.4810i	−1.30789	+	0.755112i	−0.326148	+	0.945319i	$0.605751\pi$
$600$	−4.43660	−	5.45909i	−0.181124	−	0.222867i
$601$	10.4935			0.428041			0.214020	−	0.976829i	$-0.431344\pi$
$601$	10.4935			0.428041			0.214020	+	0.976829i	$0.431344\pi$
$602$	2.25509	−	22.8505i	0.0919105	−	0.931319i
$603$	−0.282392	−	5.04857i	−0.0114999	−	0.205594i
$604$	−0.0427232	−	0.159445i	−0.00173838	−	0.00648773i
$605$	9.31101	+	2.49488i	0.378546	+	0.101431i
$606$	−19.4340	+	3.11309i	−0.789453	+	0.126460i
$607$	13.3739	−	23.1642i	0.542829	−	0.940207i	−0.455911	−	0.890025i	$-0.650686\pi$
$607$	13.3739	−	23.1642i	0.542829	−	0.940207i	0.998740	−	0.0501821i	$-0.0159802\pi$
$608$	2.76591			0.112173
$609$	−8.80054	−	13.3140i	−0.356616	−	0.539512i
$610$			1.15098i			0.0466017i
$611$	9.80084	−	7.07992i	0.396499	−	0.286423i
$612$	2.52464	−	12.0864i	0.102053	−	0.488562i
$613$	5.79912	+	1.55387i	0.234224	+	0.0627602i	0.374022	−	0.927420i	$-0.377979\pi$
$613$	5.79912	+	1.55387i	0.234224	+	0.0627602i	−0.139798	+	0.990180i	$0.544645\pi$
$614$	13.9649	+	8.06265i	0.563578	+	0.325382i
$615$	−0.104884	+	0.0469187i	−0.00422934	+	0.00189194i
$616$	2.67520	−	0.441141i	0.107787	−	0.0177741i
$617$	−18.6670	−	18.6670i	−0.751503	−	0.751503i	0.223257	−	0.974760i	$-0.428331\pi$
$617$	−18.6670	−	18.6670i	−0.751503	−	0.751503i	−0.974760	+	0.223257i	$0.928331\pi$
$618$	19.5548	−	15.8922i	0.786608	−	0.639276i
$619$	−5.95707	+	22.2321i	−0.239435	+	0.893583i	0.736665	+	0.676258i	$0.236400\pi$
$619$	−5.95707	+	22.2321i	−0.239435	+	0.893583i	−0.976099	+	0.217324i	$0.930267\pi$
$620$	2.09519	−	1.20966i	0.0841448	−	0.0485810i
$621$	−2.44876	+	2.22837i	−0.0982652	+	0.0894216i
$622$	−12.3931	−	12.3931i	−0.496917	−	0.496917i
$623$	1.67720	−	16.9949i	0.0671955	−	0.680885i
$624$	−4.42017	+	4.41159i	−0.176948	+	0.176605i
$625$	5.90105	−	10.2209i	0.236042	−	0.408836i
$626$	1.32777	−	4.95532i	0.0530686	−	0.198055i
$627$	−3.97689	−	2.87871i	−0.158822	−	0.114965i
$628$	3.60015	+	2.07855i	0.143662	+	0.0829431i
$629$	8.42020	+	8.42020i	0.335735	+	0.335735i
$630$	3.55847	+	6.81678i	0.141773	+	0.271587i
$631$	1.85070	+	1.85070i	0.0736750	+	0.0736750i	0.742984	−	0.669309i	$-0.233410\pi$
$631$	1.85070	+	1.85070i	0.0736750	+	0.0736750i	−0.669309	+	0.742984i	$0.733410\pi$
$632$	0.00814535	+	0.0303989i	0.000324005	+	0.00120920i
$633$	−14.2693	+	19.7128i	−0.567155	+	0.783515i
$634$	23.3110	−	13.4586i	0.925797	−	0.534509i
$635$	5.06760	+	18.9125i	0.201101	+	0.750521i
$636$	5.61274	+	12.5470i	0.222560	+	0.497521i
$637$	−8.80946	+	23.6515i	−0.349043	+	0.937107i
$638$			3.56903i			0.141299i
$639$	−16.3662	+	32.4017i	−0.647437	+	1.28179i
$640$	0.484404	+	0.839013i	0.0191478	+	0.0331649i
$641$	16.8365	+	29.1616i	0.665001	+	1.15181i	0.979285	+	0.202486i	$0.0649021\pi$
$641$	16.8365	+	29.1616i	0.665001	+	1.15181i	−0.314285	+	0.949329i	$0.601765\pi$
$642$	−11.5143	+	9.35770i	−0.454435	+	0.369319i
$643$	−2.15687	+	2.15687i	−0.0850587	+	0.0850587i	−0.748356	−	0.663297i	$-0.769157\pi$
$643$	−2.15687	+	2.15687i	−0.0850587	+	0.0850587i	0.663297	+	0.748356i	$0.269157\pi$
$644$	−0.594141	+	1.57766i	−0.0234124	+	0.0621685i
$645$	−13.6049	−	5.19500i	−0.535692	−	0.204553i
$646$	−5.69189	+	9.85864i	−0.223944	+	0.387883i
$647$	−20.9209	−	36.2361i	−0.822487	−	1.42459i	−0.903825	−	0.427902i	$-0.859253\pi$
$647$	−20.9209	−	36.2361i	−0.822487	−	1.42459i	0.0813383	−	0.996687i	$-0.474081\pi$
$648$	−1.34535	+	8.89888i	−0.0528504	+	0.349581i
$649$	5.15064	+	2.97372i	0.202180	+	0.116729i
$650$	−13.3613	−	5.99260i	−0.524073	−	0.235049i
$651$	10.8545	−	3.62441i	0.425422	−	0.142052i
$652$	−7.21523	+	7.21523i	−0.282570	+	0.282570i
$653$	11.1683	+	6.44801i	0.437049	+	0.252330i	0.702345	−	0.711837i	$-0.252136\pi$
$653$	11.1683	+	6.44801i	0.437049	+	0.252330i	−0.265296	+	0.964167i	$0.585470\pi$
$654$	−0.986454	+	1.36277i	−0.0385734	+	0.0532886i
$655$	−3.81919	−	1.02335i	−0.149228	−	0.0399855i
$656$	−0.0661403	+	0.0177222i	−0.00258234	+	0.000691937i
$657$	−39.6059	+	2.21536i	−1.54517	+	0.0864293i
$658$	−1.44351	−	8.75383i	−0.0562738	−	0.341260i
$659$		−	39.5546i		−	1.54083i	−0.637543	−	0.770415i	$-0.720049\pi$
$659$		−	39.5546i		−	1.54083i	0.637543	−	0.770415i	$-0.279951\pi$
$660$	0.176742	−	1.71051i	0.00687965	−	0.0665816i
$661$	−11.1046	+	41.4429i	−0.431919	+	1.61194i	0.316414	+	0.948621i	$0.397521\pi$
$661$	−11.1046	+	41.4429i	−0.431919	+	1.61194i	−0.748333	+	0.663323i	$0.769146\pi$
$662$	2.69901	+	4.67483i	0.104900	+	0.181692i
$663$	−6.62824	−	24.8335i	−0.257420	−	0.964452i
$664$	−8.57460			−0.332759
$665$	−1.15351	−	6.99519i	−0.0447311	−	0.271262i
$666$	−6.47074	−	5.78521i	−0.250736	−	0.224172i
$667$	−1.92181	−	1.10956i	−0.0744129	−	0.0429623i
$668$	−6.61390	+	24.6834i	−0.255899	+	0.955030i
$669$	1.24042	+	7.74353i	0.0479573	+	0.299382i
$670$	−1.57728	+	0.422630i	−0.0609355	+	0.0163276i
$671$	0.860888	−	0.860888i	0.0332342	−	0.0332342i
$672$	1.45138	+	4.34666i	0.0559884	+	0.167676i
$673$			17.9661i			0.692541i	0.938135	+	0.346271i	$0.112552\pi$
$673$			17.9661i			0.692541i	−0.938135	+	0.346271i	$0.887448\pi$
$674$	6.38338	+	23.8231i	0.245878	+	0.917631i
$675$	−20.6191	+	4.49654i	−0.793630	+	0.173072i
$676$	−4.08468	+	12.3416i	−0.157103	+	0.474677i
$677$	4.04856	+	2.33744i	0.155599	+	0.0898350i	0.575778	−	0.817606i	$-0.304699\pi$
$677$	4.04856	+	2.33744i	0.155599	+	0.0898350i	−0.420179	+	0.907441i	$0.638033\pi$
$678$	13.1689	+	5.02853i	0.505750	+	0.193119i
$679$	−29.4562	+	13.3395i	−1.13042	+	0.511923i
$680$	−3.98737			−0.152909
$681$	24.2408	+	29.8275i	0.928909	+	1.14299i
$682$	−2.47190	−	0.662345i	−0.0946541	−	0.0253625i
$683$	49.3429	+	13.2214i	1.88805	+	0.505902i	0.998826	+	0.0484369i	$0.0154240\pi$
$683$	49.3429	+	13.2214i	1.88805	+	0.505902i	0.889227	+	0.457466i	$0.151243\pi$
$684$	3.74107	−	7.40654i	0.143043	−	0.283196i
$685$	−17.4779			−0.667795
$686$	12.6524	+	13.5247i	0.483070	+	0.516375i
$687$	−0.131874	+	0.345358i	−0.00503131	+	0.0131762i
$688$	−7.51593	−	4.33933i	−0.286542	−	0.165435i
$689$	22.1871	+	18.0673i	0.845262	+	0.688310i
$690$	0.866113	+	0.626944i	0.0329724	+	0.0238673i
$691$	−3.35934	−	12.5372i	−0.127795	−	0.476938i	0.872129	−	0.489277i	$-0.162739\pi$
$691$	−3.35934	−	12.5372i	−0.127795	−	0.476938i	−0.999924	+	0.0123385i	$0.996072\pi$
$692$		−	5.03473i		−	0.191392i
$693$	2.43709	−	7.76031i	0.0925775	−	0.294790i
$694$	18.3677	−	18.3677i	0.697230	−	0.697230i
$695$	17.9246	−	4.80288i	0.679919	−	0.182184i
$696$	−5.95628	+	0.954122i	−0.225772	+	0.0361659i
$697$	0.0729402	−	0.272216i	0.00276281	−	0.0103109i
$698$	24.6052	+	14.2058i	0.931322	+	0.537699i
$699$	4.19555	+	9.37895i	0.158690	+	0.354744i
$700$	−8.30770	+	6.81524i	−0.314001	+	0.257592i
$701$	−34.1302			−1.28908			−0.644541	−	0.764570i	$-0.722951\pi$
$701$	−34.1302			−1.28908			−0.644541	+	0.764570i	$0.722951\pi$
$702$	5.83476	+	17.8032i	0.220219	+	0.671940i
$703$	4.00127	+	6.93040i	0.150911	+	0.261385i
$704$	0.265234	−	0.989868i	0.00999639	−	0.0373071i
$705$	−5.59716	−	0.578336i	−0.210801	−	0.0217814i
$706$		−	13.1830i		−	0.496149i
$707$	4.89156	+	29.6638i	0.183966	+	1.11562i
$708$	−3.58585	+	9.39078i	−0.134764	+	0.352927i
$709$	26.0559	−	6.98166i	0.978550	−	0.262202i	0.266116	−	0.963941i	$-0.414259\pi$
$709$	26.0559	−	6.98166i	0.978550	−	0.262202i	0.712434	+	0.701739i	$0.247593\pi$
$710$	11.3233	+	3.03407i	0.424956	+	0.113867i
$711$	0.0924190	+	0.0193048i	0.00346598	+	0.000723986i
$712$	−5.58990	−	3.22733i	−0.209490	−	0.120949i
$713$	1.12513	−	1.12513i	0.0421365	−	0.0421365i
$714$	−18.4797	−	3.77165i	−0.691587	−	0.141150i
$715$	−1.27371	−	3.34540i	−0.0476341	−	0.125111i
$716$	−2.16277	−	1.24867i	−0.0808263	−	0.0466651i
$717$	−39.3217	+	6.29885i	−1.46850	+	0.235235i
$718$	4.58974	+	7.94967i	0.171288	+	0.296679i
$719$	0.115201	−	0.199534i	0.00429627	−	0.00744135i	−0.863869	−	0.503716i	$-0.831966\pi$
$719$	0.115201	−	0.199534i	0.00429627	−	0.00744135i	0.868166	+	0.496275i	$0.165299\pi$
$720$	2.90189	−	0.162317i	0.108147	−	0.00604921i
$721$	−24.4126	−	29.7586i	−0.909171	−	1.10827i
$722$	8.02547	−	8.02547i	0.298677	−	0.298677i
$723$	−4.32872	−	5.32635i	−0.160987	−	0.198089i
$724$	−0.389043	−	0.673842i	−0.0144587	−	0.0250432i
$725$	−7.07234	−	12.2496i	−0.262660	−	0.454940i
$726$	13.3739	−	10.8690i	0.496353	−	0.403386i
$727$		−	19.6490i		−	0.728740i	−0.931254	−	0.364370i	$-0.881284\pi$
$727$		−	19.6490i		−	0.728740i	0.931254	−	0.364370i	$-0.118716\pi$
$728$	6.76974	+	6.72091i	0.250903	+	0.249094i
$729$	22.0097	+	15.6389i	0.815173	+	0.579217i
$730$	3.31552	+	12.3737i	0.122713	+	0.457970i
$731$	30.9336	−	17.8595i	1.14412	−	0.660559i
$732$	1.66686	+	1.20658i	0.0616091	+	0.0445963i
$733$	−2.63809	−	9.84548i	−0.0974401	−	0.363651i	0.899938	−	0.436018i	$-0.143612\pi$
$733$	−2.63809	−	9.84548i	−0.0974401	−	0.363651i	−0.997378	+	0.0723665i	$0.976945\pi$
$734$	−10.5572	−	10.5572i	−0.389674	−	0.389674i
$735$	10.3877	−	5.48341i	0.383157	−	0.202259i
$736$	0.450556	+	0.450556i	0.0166077	+	0.0166077i
$737$	1.49586	+	0.863633i	0.0551006	+	0.0318123i
$738$	−0.0420024	+	0.201080i	−0.00154613	+	0.00740187i
$739$	−6.99720	+	26.1139i	−0.257396	+	0.960616i	0.709345	+	0.704861i	$0.248991\pi$
$739$	−6.99720	+	26.1139i	−0.257396	+	0.960616i	−0.966742	+	0.255755i	$0.917676\pi$
$740$	−1.40151	+	2.42749i	−0.0515207	+	0.0892364i
$741$	0.0167901	−	17.2731i	0.000616801	−	0.634543i
$742$	19.1263	−	8.66151i	0.702148	−	0.317974i
$743$	19.6477	+	19.6477i	0.720804	+	0.720804i	0.968769	−	0.247965i	$-0.0797618\pi$
$743$	19.6477	+	19.6477i	0.720804	+	0.720804i	−0.247965	+	0.968769i	$0.579762\pi$
$744$	0.444551	−	4.30238i	0.0162980	−	0.157733i
$745$	−17.1505	+	9.90187i	−0.628347	+	0.362776i
$746$	−5.59532	+	20.8820i	−0.204859	+	0.764545i
$747$	−11.5977	+	22.9610i	−0.424337	+	0.840100i
$748$	2.98241	+	2.98241i	0.109048	+	0.109048i
$749$	14.3747	+	17.5226i	0.525241	+	0.640263i
$750$	6.20896	+	13.8798i	0.226719	+	0.506819i
$751$	29.8497	+	17.2337i	1.08923	+	0.628867i	0.933371	−	0.358912i	$-0.116852\pi$
$751$	29.8497	+	17.2337i	1.08923	+	0.628867i	0.155859	+	0.987779i	$0.450185\pi$
$752$	−3.23906	−	0.867903i	−0.118116	−	0.0316492i
$753$	25.9186	−	35.8061i	0.944526	−	1.30485i
$754$	−10.1790	+	7.35309i	−0.370697	+	0.267784i
$755$			0.159921i			0.00582012i
$756$	13.6026	+	1.99262i	0.494720	+	0.0724710i
$757$	17.4476			0.634144			0.317072	−	0.948401i	$-0.397300\pi$
$757$	17.4476			0.634144			0.317072	+	0.948401i	$0.397300\pi$
$758$	10.2276	−	17.7147i	0.371483	−	0.643428i
$759$	−0.178890	−	1.11675i	−0.00649328	−	0.0405355i
$760$	−2.58833	−	0.693542i	−0.0938887	−	0.0251574i
$761$	12.8087	+	47.8027i	0.464314	+	1.73284i	0.659152	+	0.752009i	$0.270915\pi$
$761$	12.8087	+	47.8027i	0.464314	+	1.73284i	−0.194838	+	0.980835i	$0.562418\pi$
$762$	32.7018	+	12.4871i	1.18466	+	0.452361i
$763$	2.08856	+	1.49726i	0.0756111	+	0.0542045i
$764$	−20.7922			−0.752234
$765$	−5.39316	+	10.6773i	−0.194990	+	0.386040i
$766$	−24.9262	+	14.3912i	−0.900621	+	0.519974i
$767$	2.13044	+	20.8164i	0.0769258	+	0.751637i
$768$	1.72288	+	0.178019i	0.0621690	+	0.00642372i
$769$	16.7245	−	16.7245i	0.603100	−	0.603100i	−0.338034	−	0.941134i	$-0.609762\pi$
$769$	16.7245	−	16.7245i	0.603100	−	0.603100i	0.941134	+	0.338034i	$0.109762\pi$
$770$	−2.61406	−	0.257978i	−0.0942043	−	0.00929688i
$771$	7.66160	+	17.1271i	0.275926	+	0.616818i
$772$	5.49236	+	20.4978i	0.197674	+	0.737731i
$773$	−2.65097	+	9.89355i	−0.0953487	+	0.355846i	−0.997072	−	0.0764673i	$-0.975636\pi$
$773$	−2.65097	+	9.89355i	−0.0953487	+	0.355846i	0.901723	+	0.432313i	$0.142303\pi$
$774$	−21.7856	+	14.2569i	−0.783067	+	0.512454i
$775$	9.79659	−	2.62499i	0.351904	−	0.0942924i
$776$			12.2218i			0.438737i
$777$	−8.79158	+	9.92469i	−0.315396	+	0.356046i
$778$	4.10709	+	4.10709i	0.147246	+	0.147246i
$779$	0.0946958	−	0.164018i	0.00339283	−	0.00587655i
$780$	5.24257	−	3.02001i	0.187714	−	0.108134i
$781$	−6.20004	−	10.7388i	−0.221855	−	0.384264i
$782$	−2.53312	+	0.678748i	−0.0905843	+	0.0242720i
$783$	−5.50130	+	17.2402i	−0.196600	+	0.616114i
$784$	6.62939	−	2.24749i	0.236764	−	0.0802674i
$785$	−2.84783	−	2.84783i	−0.101643	−	0.101643i
$786$	−5.48571	+	4.45823i	−0.195669	+	0.159020i
$787$	−8.25238	+	30.7983i	−0.294166	+	1.09784i	0.647712	+	0.761885i	$0.275726\pi$
$787$	−8.25238	+	30.7983i	−0.294166	+	1.09784i	−0.941878	+	0.335956i	$0.890941\pi$
$788$	2.74174	+	0.734646i	0.0976704	+	0.0261707i
$789$	0.405010	−	3.91970i	0.0144187	−	0.139545i
$790$		−	0.0304896i		−	0.00108477i
$791$	7.58877	−	20.1509i	0.269825	−	0.716485i
$792$	−2.29192	−	2.04910i	−0.0814397	−	0.0728116i
$793$	4.22893	+	0.681638i	0.150174	+	0.0242057i
$794$	−18.4565	+	10.6558i	−0.654995	+	0.378162i
$795$	−2.10628	−	13.1488i	−0.0747020	−	0.466341i
$796$	6.58738	−	11.4097i	0.233484	−	0.404406i
$797$	−49.1361			−1.74049			−0.870245	−	0.492620i	$-0.836039\pi$
$797$	−49.1361			−1.74049			−0.870245	+	0.492620i	$0.836039\pi$
$798$	−11.3398	−	5.66257i	−0.401424	−	0.200453i
$799$	9.75906	−	9.75906i	0.345251	−	0.345251i
$800$	1.05117	+	3.92302i	0.0371645	+	0.138700i
$801$	−16.2028	+	10.6034i	−0.572498	+	0.374654i
$802$	2.94078	+	5.09359i	0.103843	+	0.179861i
$803$	6.77517	−	11.7349i	0.239091	−	0.414117i
$804$	−1.04141	+	2.72729i	−0.0367276	+	0.0961839i
$805$	0.951588	−	1.32739i	0.0335391	−	0.0467844i
$806$	−3.20371	−	8.41456i	−0.112846	−	0.296390i
$807$	2.88543	−	27.9253i	0.101572	−	0.983019i
$808$	10.9761	+	2.94103i	0.386137	+	0.103465i
$809$	18.2677	−	10.5468i	0.642257	−	0.370807i	−0.143226	−	0.989690i	$-0.545748\pi$
$809$	18.2677	−	10.5468i	0.642257	−	0.370807i	0.785483	+	0.618883i	$0.212414\pi$
$810$	3.49034	−	7.99021i	0.122638	−	0.280747i
$811$	1.50378	−	1.50378i	0.0528049	−	0.0528049i	−0.680211	−	0.733016i	$-0.738112\pi$
$811$	1.50378	−	1.50378i	0.0528049	−	0.0528049i	0.733016	+	0.680211i	$0.238112\pi$
$812$	1.49920	+	9.09158i	0.0526117	+	0.319052i
$813$	−20.0439	+	52.4918i	−0.702970	+	1.84097i
$814$	2.86396	−	0.767395i	0.100382	−	0.0268972i
$815$	8.56119	−	4.94281i	0.299885	−	0.173139i
$816$	−4.17998	+	5.77458i	−0.146329	+	0.202151i
$817$	23.1865	−	6.21279i	0.811191	−	0.217358i
$818$	0.362271			0.0126665
$819$	27.1537	−	9.03751i	0.948827	−	0.315796i
$820$	0.0663377			0.00231661
$821$	−35.4726	+	9.50486i	−1.23800	+	0.331722i	−0.817691	−	0.575658i	$-0.804746\pi$
$821$	−35.4726	+	9.50486i	−1.23800	+	0.331722i	−0.420312	+	0.907380i	$0.638079\pi$
$822$	−18.3221	+	25.3117i	−0.639058	+	0.882849i
$823$	−35.4546	+	20.4697i	−1.23587	+	0.713530i	−0.968248	−	0.249993i	$-0.919572\pi$
$823$	−35.4546	+	20.4697i	−1.23587	+	0.713530i	−0.267623	+	0.963524i	$0.586238\pi$
$824$	−14.0525	+	3.76535i	−0.489541	+	0.131172i
$825$	2.57161	−	6.73465i	0.0895320	−	0.234470i
$826$	14.3697	+	5.41156i	0.499984	+	0.188292i
$827$	−4.37880	+	4.37880i	−0.152266	+	0.152266i	−0.779129	−	0.626863i	$-0.784338\pi$
$827$	−4.37880	+	4.37880i	−0.152266	+	0.152266i	0.626863	+	0.779129i	$0.284338\pi$
$828$	1.81590	−	0.597091i	0.0631070	−	0.0207504i
$829$	−1.09178	+	0.630338i	−0.0379190	+	0.0218925i	−0.518840	−	0.854872i	$-0.673636\pi$
$829$	−1.09178	+	0.630338i	−0.0379190	+	0.0218925i	0.480921	+	0.876764i	$0.340303\pi$
$830$	8.02409	+	2.15005i	0.278520	+	0.0746293i
$831$	5.01658	−	48.5506i	0.174023	−	1.68420i
$832$	3.36959	−	1.28292i	0.116819	−	0.0444772i
$833$	−5.63162	+	28.2544i	−0.195124	+	0.978958i
$834$	11.8349	−	30.9936i	0.409807	−	1.07322i
$835$	12.3785	−	21.4403i	0.428377	−	0.741971i
$836$	1.41723	+	2.45472i	0.0490161	+	0.0848983i
$837$	−10.9196	−	7.00966i	−0.377437	−	0.242289i
$838$	1.08537	+	4.05066i	0.0374935	+	0.139928i
$839$	30.2143	−	30.2143i	1.04311	−	1.04311i	0.0440850	−	0.999028i	$-0.485963\pi$
$839$	30.2143	−	30.2143i	1.04311	−	1.04311i	0.999028	−	0.0440850i	$-0.0140372\pi$
$840$	−0.268293	−	4.43153i	−0.00925699	−	0.152902i
$841$	16.8708			0.581751
$842$	−0.949582	+	1.64472i	−0.0327248	+	0.0566810i
$843$	5.04648	+	31.5036i	0.173810	+	1.08504i
$844$	12.1677	−	7.02502i	0.418829	−	0.241811i
$845$	6.91705	−	10.5250i	0.237954	−	0.362072i
$846$	−6.70509	+	7.49963i	−0.230526	+	0.257843i
$847$	−16.6963	−	20.3526i	−0.573690	−	0.699322i
$848$		−	7.93578i		−	0.272516i
$849$	−3.67400	+	35.5572i	−0.126091	+	1.22032i
$850$	−16.1461	−	4.32635i	−0.553808	−	0.148392i
$851$	−0.477144	+	1.78073i	−0.0163563	+	0.0610425i
$852$	16.2643	−	13.2180i	0.557205	−	0.452840i
$853$	12.0364	+	12.0364i	0.412120	+	0.412120i	0.882476	−	0.470356i	$-0.155875\pi$
$853$	12.0364	+	12.0364i	0.412120	+	0.412120i	−0.470356	+	0.882476i	$0.655875\pi$
$854$	1.83136	−	2.55461i	0.0626680	−	0.0874171i
$855$	−5.35804	+	5.99296i	−0.183241	+	0.204955i
$856$	8.27445	−	2.21713i	0.282815	−	0.0757800i
$857$	3.54715	+	6.14385i	0.121168	+	0.209870i	0.920229	−	0.391381i	$-0.128003\pi$
$857$	3.54715	+	6.14385i	0.121168	+	0.209870i	−0.799060	+	0.601251i	$0.794669\pi$
$858$	−6.18011	−	1.66240i	−0.210985	−	0.0567533i
$859$	−19.5791	+	33.9120i	−0.668030	+	1.15706i	0.310424	+	0.950598i	$0.399529\pi$
$859$	−19.5791	+	33.9120i	−0.668030	+	1.15706i	−0.978454	+	0.206464i	$0.933804\pi$
$860$	5.94532	+	5.94532i	0.202734	+	0.202734i
$861$	0.307447	+	0.0627488i	0.0104778	+	0.00213847i
$862$			32.5955i			1.11021i
$863$	−12.3696	+	3.31443i	−0.421067	+	0.112824i	−0.463130	−	0.886290i	$-0.653274\pi$
$863$	−12.3696	+	3.31443i	−0.421067	+	0.112824i	0.0420631	+	0.999115i	$0.486607\pi$
$864$	2.80700	−	4.37273i	0.0954960	−	0.148763i
$865$	−1.26244	+	4.71149i	−0.0429242	+	0.160195i
$866$	−5.67067	−	21.1632i	−0.192697	−	0.719155i
$867$	0.0429032	+	0.0959079i	0.00145707	+	0.00325720i
$868$	−6.57505	−	0.648882i	−0.223172	−	0.0220245i
$869$	−0.0228051	+	0.0228051i	−0.000773610	+	0.000773610i
$870$	5.81312	+	0.600650i	0.197083	+	0.0203639i
$871$	0.618727	+	6.04554i	0.0209647	+	0.204845i
$872$	0.841165	−	0.485647i	0.0284855	−	0.0164461i
$873$	32.7275	+	16.5308i	1.10766	+	0.559481i
$874$	−1.76239			−0.0596138
$875$	21.1580	−	9.58159i	0.715271	−	0.323917i
$876$	21.3955	+	8.16981i	0.722886	+	0.276032i
$877$	4.40030	+	16.4221i	0.148588	+	0.554536i	0.999569	+	0.0293413i	$0.00934098\pi$
$877$	4.40030	+	16.4221i	0.148588	+	0.554536i	−0.850982	+	0.525195i	$0.823992\pi$
$878$	−6.54609	−	1.75402i	−0.220920	−	0.0591953i
$879$	−8.48363	−	52.9606i	−0.286146	−	1.78632i
$880$	−0.496411	+	0.859810i	−0.0167340	+	0.0289842i
$881$	−31.1168			−1.04835			−0.524175	−	0.851610i	$-0.675626\pi$
$881$	−31.1168			−1.04835			−0.524175	+	0.851610i	$0.675626\pi$
$882$	2.94835	−	20.7920i	0.0992762	−	0.700103i
$883$			36.5043i			1.22847i	0.789124	+	0.614234i	$0.210535\pi$
$883$			36.5043i			1.22847i	−0.789124	+	0.614234i	$0.789465\pi$
$884$	−2.36142	+	14.6504i	−0.0794233	+	0.492747i
$885$	5.71033	−	7.88873i	0.191951	−	0.265177i
$886$	−33.8395	−	9.06727i	−1.13686	−	0.304621i
$887$	29.2300	+	16.8760i	0.981449	+	0.566640i	0.902707	−	0.430255i	$-0.141576\pi$
$887$	29.2300	+	16.8760i	0.981449	+	0.566640i	0.0787416	+	0.996895i	$0.474910\pi$
$888$	2.04632	+	4.57445i	0.0686701	+	0.153509i
$889$	18.8449	−	50.0400i	0.632036	−	1.67829i
$890$	4.42177	+	4.42177i	0.148218	+	0.148218i
$891$	−8.58703	+	3.36574i	−0.287676	+	0.112757i
$892$	1.17186	−	4.37344i	0.0392368	−	0.146434i
$893$	8.03237	−	4.63749i	0.268793	−	0.155188i
$894$	−3.63895	+	35.2179i	−0.121705	+	1.17786i
$895$	1.71081	+	1.71081i	0.0571861	+	0.0571861i
$896$	0.259843	−	2.63296i	0.00868074	−	0.0879610i
$897$	2.81646	−	2.81099i	0.0940388	−	0.0938562i
$898$	−1.51427	+	2.62280i	−0.0505320	+	0.0875240i
$899$	2.25096	−	8.40068i	0.0750736	−	0.280178i
$900$	11.9268	+	2.49131i	0.397560	+	0.0830438i
$901$	28.2858	+	16.3308i	0.942337	+	0.544059i
$902$	−0.0496182	−	0.0496182i	−0.00165210	−	0.00165210i
$903$	21.9303	+	33.1777i	0.729796	+	1.10408i
$904$	−5.75481	−	5.75481i	−0.191402	−	0.191402i
$905$	0.195102	+	0.728131i	0.00648542	+	0.0242039i
$906$	0.231600	+	0.167646i	0.00769441	+	0.00556967i
$907$	7.54896	−	4.35840i	0.250659	−	0.144718i	−0.369407	−	0.929268i	$-0.620439\pi$
$907$	7.54896	−	4.35840i	0.250659	−	0.144718i	0.620066	+	0.784550i	$0.287106\pi$
$908$	−5.74340	−	21.4347i	−0.190601	−	0.711334i
$909$	22.7213	−	25.4137i	0.753618	−	0.842921i
$910$	−4.64986	−	7.98690i	−0.154141	−	0.264763i
$911$			1.75437i			0.0581250i	0.999578	+	0.0290625i	$0.00925219\pi$
$911$			1.75437i			0.0581250i	−0.999578	+	0.0290625i	$0.990748\pi$
$912$	−3.71777	+	3.02143i	−0.123108	+	0.100049i
$913$	−4.39357	−	7.60989i	−0.145406	−	0.251850i
$914$	−15.8663	−	27.4813i	−0.524812	−	0.909001i
$915$	−1.25730	−	1.54707i	−0.0415652	−	0.0511446i
$916$	0.150921	−	0.150921i	0.00498657	−	0.00498657i
$917$	6.84846	+	8.34820i	0.226156	+	0.275682i
$918$	9.80944	+	19.0036i	0.323760	+	0.627212i
$919$	18.9448	−	32.8134i	0.624932	−	1.08241i	−0.363621	−	0.931547i	$-0.618460\pi$
$919$	18.9448	−	32.8134i	0.624932	−	1.08241i	0.988554	−	0.150868i	$-0.0482068\pi$
$920$	−0.308654	−	0.534605i	−0.0101760	−	0.0176254i
$921$	−27.5783	+	4.41769i	−0.908734	+	0.145568i
$922$	−13.7205	−	7.92154i	−0.451861	−	0.260882i
$923$	17.8538	−	39.8073i	0.587663	−	1.31027i
$924$	−3.11395	+	3.51529i	−0.102441	+	0.115645i
$925$	−8.30904	+	8.30904i	−0.273200	+	0.273200i
$926$	−21.4591	−	12.3894i	−0.705191	−	0.407142i
$927$	−8.92402	+	42.7225i	−0.293103	+	1.40319i
$928$	3.36403	+	0.901389i	0.110430	+	0.0295896i
$929$	10.8581	−	2.90941i	0.356242	−	0.0954547i	−0.0762595	−	0.997088i	$-0.524298\pi$
$929$	10.8581	−	2.90941i	0.356242	−	0.0954547i	0.432501	+	0.901633i	$0.357631\pi$
$930$	−1.49482	+	3.91469i	−0.0490169	+	0.128368i
$931$	−8.57010	+	17.3613i	−0.280874	+	0.568995i
$932$		−	5.93204i		−	0.194310i
$933$	30.1959	+	3.12005i	0.988571	+	0.102146i
$934$	8.97005	−	33.4767i	0.293509	−	1.09539i
$935$	−2.04310	−	3.53875i	−0.0668166	−	0.115730i
$936$	1.12219	−	10.7583i	0.0366799	−	0.351646i
$937$	−12.1574			−0.397164			−0.198582	−	0.980084i	$-0.563634\pi$
$937$	−12.1574			−0.397164			−0.198582	+	0.980084i	$0.563634\pi$
$938$	4.17326	+	1.57163i	0.136262	+	0.0513156i
$939$	3.62839	+	8.11107i	0.118408	+	0.264695i
$940$	2.81348	+	1.62436i	0.0917655	+	0.0529809i
$941$	−4.68365	+	17.4796i	−0.152683	+	0.569819i	0.846610	+	0.532214i	$0.178640\pi$
$941$	−4.68365	+	17.4796i	−0.152683	+	0.569819i	−0.999293	+	0.0376056i	$0.988027\pi$
$942$	−7.10966	+	1.13888i	−0.231645	+	0.0371067i
$943$	0.0421435	−	0.0112923i	0.00137238	−	0.000367728i
$944$	4.10376	−	4.10376i	0.133566	−	0.133566i
$945$	−12.2296	−	5.27548i	−0.397829	−	0.171611i
$946$		−	8.89377i		−	0.289161i
$947$	2.77214	+	10.3457i	0.0900823	+	0.336192i	0.996228	−	0.0867739i	$-0.0276558\pi$
$947$	2.77214	+	10.3457i	0.0900823	+	0.336192i	−0.906146	+	0.422966i	$0.860989\pi$
$948$	−0.0441556	−	0.0319624i	−0.00143411	−	0.00103809i
$949$	47.4270	−	4.85389i	1.53955	−	0.157564i
$950$	−9.72849	−	5.61675i	−0.315634	−	0.182231i
$951$	−16.6313	+	43.5547i	−0.539305	+	1.41236i
$952$	8.85004	+	6.34446i	0.286831	+	0.205625i
$953$	−4.17491			−0.135238			−0.0676192	−	0.997711i	$-0.521540\pi$
$953$	−4.17491			−0.135238			−0.0676192	+	0.997711i	$0.521540\pi$
$954$	−21.2504	−	10.7336i	−0.688007	−	0.347514i
$955$	19.4573	+	5.21356i	0.629622	+	0.168707i
$956$	22.2084	+	5.95072i	0.718271	+	0.192460i
$957$	−3.89873	−	4.79726i	−0.126028	−	0.155073i
$958$	5.49022			0.177381
$959$	38.7924	+	27.8097i	1.25267	+	0.898023i
$960$	−1.56763	−	0.598595i	−0.0505950	−	0.0193196i
$961$	−21.4462	−	12.3820i	−0.691813	−	0.399419i
$962$	8.08910	+	6.58708i	0.260803	+	0.212376i
$963$	5.25469	−	25.1561i	0.169330	−	0.810643i
$964$	1.02561	+	3.82763i	0.0330327	+	0.123280i
$965$		−	20.5590i		−	0.661816i
$966$	−0.924798	−	2.76962i	−0.0297549	−	0.0891111i
$967$	1.37016	−	1.37016i	0.0440615	−	0.0440615i	−0.684733	−	0.728794i	$-0.740081\pi$
$967$	1.37016	−	1.37016i	0.0440615	−	0.0440615i	0.728794	+	0.684733i	$0.240081\pi$
$968$	−9.61078	+	2.57520i	−0.308902	+	0.0827701i
$969$	−3.11870	−	19.4691i	−0.100187	−	0.625437i
$970$	3.06457	−	11.4371i	0.0983975	−	0.367224i
$971$	17.8130	+	10.2843i	0.571645	+	0.330039i	0.757806	−	0.652480i	$-0.226271\pi$
$971$	17.8130	+	10.2843i	0.571645	+	0.330039i	−0.186161	+	0.982519i	$0.559605\pi$
$972$	−7.91262	−	13.4309i	−0.253797	−	0.430798i
$973$	−47.4261	−	17.8605i	−1.52041	−	0.572581i
$974$	−24.8432			−0.796029
$975$	24.5056	−	6.54074i	0.784808	−	0.209471i
$976$	−0.594016	−	1.02887i	−0.0190140	−	0.0329332i
$977$	9.04912	−	33.7718i	0.289507	−	1.08045i	−0.655976	−	0.754782i	$-0.727743\pi$
$977$	9.04912	−	33.7718i	0.289507	−	1.08045i	0.945483	−	0.325673i	$-0.105591\pi$
$978$	1.81649	−	17.5800i	0.0580849	−	0.562148i
$979$		−	6.61465i		−	0.211405i
$980$	−6.76732	+	0.440900i	−0.216174	+	0.0140840i
$981$	−0.162734	−	2.90933i	−0.00519569	−	0.0928879i
$982$	−13.2647	+	3.55426i	−0.423293	+	0.113421i
$983$	−17.9548	−	4.81096i	−0.572668	−	0.153446i	−0.0391479	−	0.999233i	$-0.512464\pi$
$983$	−17.9548	−	4.81096i	−0.572668	−	0.153446i	−0.533520	+	0.845788i	$0.679131\pi$
$984$	0.0695422	−	0.0960715i	0.00221693	−	0.00306265i
$985$	−2.38150	−	1.37496i	−0.0758809	−	0.0438099i
$986$	−10.1356	+	10.1356i	−0.322783	+	0.322783i
$987$	11.5028	+	10.1895i	0.366137	+	0.324335i
$988$	−4.08110	+	9.09935i	−0.129837	+	0.289489i
$989$	4.78903	+	2.76494i	0.152282	+	0.0879201i
$990$	1.63096	+	2.49223i	0.0518355	+	0.0792083i
$991$	12.7044	+	22.0047i	0.403569	+	0.699001i	0.994154	−	0.107974i	$-0.0344364\pi$
$991$	12.7044	+	22.0047i	0.403569	+	0.699001i	−0.590585	+	0.806975i	$0.701103\pi$
$992$	−1.24860	+	2.16264i	−0.0396432	+	0.0686640i
$993$	−8.73453	−	3.33526i	−0.277182	−	0.105841i
$994$	−20.3046	−	24.7511i	−0.644024	−	0.785058i
$995$	−9.02539	+	9.02539i	−0.286124	+	0.286124i
$996$	11.5254	−	9.36673i	0.365198	−	0.296796i
$997$	−13.2786	−	22.9991i	−0.420536	−	0.728390i	0.575456	−	0.817833i	$-0.304825\pi$
$997$	−13.2786	−	22.9991i	−0.420536	−	0.728390i	−0.995992	+	0.0894429i	$0.971491\pi$
$998$	12.9326	+	22.3999i	0.409373	+	0.709055i
$999$	15.0172	+	0.707601i	0.475124	+	0.0223875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.25	yes	144
3.2	odd	2	inner	546.2.bv.a.317.18	✓	144
7.4	even	3	inner	546.2.bv.a.473.18	yes	144
13.8	odd	4	inner	546.2.bv.a.359.25	yes	144
21.11	odd	6	inner	546.2.bv.a.473.25	yes	144
39.8	even	4	inner	546.2.bv.a.359.18	yes	144
91.60	odd	12	inner	546.2.bv.a.515.18	yes	144
273.242	even	12	inner	546.2.bv.a.515.25	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.18	✓	144	3.2	odd	2	inner
546.2.bv.a.317.25	yes	144	1.1	even	1	trivial
546.2.bv.a.359.18	yes	144	39.8	even	4	inner
546.2.bv.a.359.25	yes	144	13.8	odd	4	inner
546.2.bv.a.473.18	yes	144	7.4	even	3	inner
546.2.bv.a.473.25	yes	144	21.11	odd	6	inner
546.2.bv.a.515.18	yes	144	91.60	odd	12	inner
546.2.bv.a.515.25	yes	144	273.242	even	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.01561 + 1.40305i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.935798 + 0.250746i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(2.47599 + 0.932449i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.937080 - 2.84989i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.01561 + 1.40305i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.935798 + 0.250746i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(2.47599 + 0.932449i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.937080 - 2.84989i) q^{9} +(-0.839013 + 0.484404i) q^{10} +(0.989868 + 0.265234i) q^{11} +(-0.178019 + 1.72288i) q^{12} +(1.28292 + 3.36959i) q^{13} +(2.63296 + 0.259843i) q^{14} +(0.598595 - 1.56763i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.05787 + 3.56434i) q^{17} +(-1.64276 - 2.51025i) q^{18} +(0.715871 + 2.67167i) q^{19} +(-0.685051 + 0.685051i) q^{20} +(-3.82291 + 2.52693i) q^{21} +1.02479 q^{22} +(-0.318592 + 0.551817i) q^{23} +(0.273960 + 1.71025i) q^{24} +(-3.51728 + 2.03070i) q^{25} +(2.11132 + 2.92273i) q^{26} +(4.95024 + 1.57961i) q^{27} +(2.61050 - 0.430471i) q^{28} +3.48270i q^{29} +(0.172467 - 1.66914i) q^{30} +(-2.41212 - 0.646325i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.37745 + 1.11946i) q^{33} +(2.91027 + 2.91027i) q^{34} +(-2.55084 - 0.251738i) q^{35} +(-2.23648 - 1.99954i) q^{36} +(2.79469 - 0.748834i) q^{37} +(1.38296 + 2.39535i) q^{38} +(-6.03063 - 1.62219i) q^{39} +(-0.484404 + 0.839013i) q^{40} +(-0.0484181 - 0.0484181i) q^{41} +(-3.03863 + 3.43027i) q^{42} -8.67865i q^{43} +(0.989868 - 0.265234i) q^{44} +(1.59152 + 2.43195i) q^{45} +(-0.164915 + 0.615472i) q^{46} +(-0.867903 - 3.23906i) q^{47} +(0.707270 + 1.58107i) q^{48} +(5.26108 + 4.61748i) q^{49} +(-2.87185 + 2.87185i) q^{50} +(-7.09092 - 0.732681i) q^{51} +(2.79583 + 2.27669i) q^{52} +(6.87259 - 3.96789i) q^{53} +(5.19039 + 0.244568i) q^{54} -0.992823 q^{55} +(2.41013 - 1.09145i) q^{56} +(-4.47551 - 1.70897i) q^{57} +(0.901389 + 3.36403i) q^{58} +(5.60584 + 1.50208i) q^{59} +(-0.265415 - 1.65690i) q^{60} +(0.594016 - 1.02887i) q^{61} -2.49721 q^{62} +(0.337178 - 7.93009i) q^{63} -1.00000i q^{64} +(-2.04546 - 2.83157i) q^{65} +(-1.04078 + 1.43782i) q^{66} +(1.62806 + 0.436237i) q^{67} +(3.56434 + 2.05787i) q^{68} +(-0.450660 - 1.00743i) q^{69} +(-2.52907 + 0.417044i) q^{70} +(-8.55610 - 8.55610i) q^{71} +(-2.67779 - 1.35256i) q^{72} +(3.42226 - 12.7721i) q^{73} +(2.50565 - 1.44664i) q^{74} +(0.723009 - 6.99731i) q^{75} +(1.95579 + 1.95579i) q^{76} +(2.20359 + 1.57972i) q^{77} +(-6.24500 - 0.00607038i) q^{78} +(-0.0157356 + 0.0272549i) q^{79} +(-0.250746 + 0.935798i) q^{80} +(-7.24376 + 5.34115i) q^{81} +(-0.0592998 - 0.0342367i) q^{82} +(-6.06316 - 6.06316i) q^{83} +(-2.04727 + 4.09984i) q^{84} +(-2.81950 - 2.81950i) q^{85} +(-2.24620 - 8.38293i) q^{86} +(-4.88639 - 3.53706i) q^{87} +(0.887491 - 0.512393i) q^{88} +(-1.67059 - 6.23472i) q^{89} +(2.16672 + 1.93717i) q^{90} +(0.0345255 + 9.53933i) q^{91} +0.637183i q^{92} +(3.35659 - 2.72790i) q^{93} +(-1.67666 - 2.90406i) q^{94} +(-1.33982 - 2.32064i) q^{95} +(1.09238 + 1.34414i) q^{96} +(-8.64212 + 8.64212i) q^{97} +(6.27690 + 3.09847i) q^{98} +(-0.171696 - 3.06956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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