LMFDB - Embedded newform 570.2.q.c.49.2

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
Defining polynomial:	$x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} - 11968 x^{8} + 10368 x^{7} + 9344 x^{6} + 18176 x^{5} + 56320 x^{4} + 28160 x^{3} + 8192 x^{2} + 4096 x + 1024$
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-1.19457 + 0.320085i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.c.349.2

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34502 - 1.78632i) q^{5} +(-0.500000 - 0.866025i) q^{6} +4.03495i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34502 - 1.78632i) q^{5} +(-0.500000 - 0.866025i) q^{6} +4.03495i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.271659 + 2.21950i) q^{10} -1.47054 q^{11} +1.00000i q^{12} +(-4.38320 + 2.53064i) q^{13} +(2.01747 - 3.49437i) q^{14} +(-0.271659 - 2.21950i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0812933 - 0.0469347i) q^{17} -1.00000i q^{18} +(-4.00172 - 1.72807i) q^{19} +(0.874489 - 2.05798i) q^{20} +(-2.01747 + 3.49437i) q^{21} +(1.27352 + 0.735269i) q^{22} +(-2.22178 + 1.28274i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.38186 + 4.80525i) q^{25} +5.06128 q^{26} +1.00000i q^{27} +(-3.49437 + 2.01747i) q^{28} +(2.10491 + 3.64581i) q^{29} +(-0.874489 + 2.05798i) q^{30} +4.26558 q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.27352 - 0.735269i) q^{33} +(0.0469347 + 0.0812933i) q^{34} +(7.20770 - 5.42707i) q^{35} +(-0.500000 + 0.866025i) q^{36} +1.53807i q^{37} +(2.60156 + 3.49741i) q^{38} -5.06128 q^{39} +(-1.78632 + 1.34502i) q^{40} +(-3.88123 + 6.72248i) q^{41} +(3.49437 - 2.01747i) q^{42} +(-3.97202 - 2.29325i) q^{43} +(-0.735269 - 1.27352i) q^{44} +(0.874489 - 2.05798i) q^{45} +2.56549 q^{46} +(3.49530 - 2.01801i) q^{47} +(-0.866025 + 0.500000i) q^{48} -9.28080 q^{49} +(3.59936 - 3.47054i) q^{50} +(-0.0469347 - 0.0812933i) q^{51} +(-4.38320 - 2.53064i) q^{52} +(-9.22964 + 5.32873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.97790 + 2.62685i) q^{55} +4.03495 q^{56} +(-2.60156 - 3.49741i) q^{57} -4.20982i q^{58} +(-3.07599 + 5.32777i) q^{59} +(1.78632 - 1.34502i) q^{60} +(0.653722 + 1.13228i) q^{61} +(-3.69410 - 2.13279i) q^{62} +(-3.49437 + 2.01747i) q^{63} -1.00000 q^{64} +(10.4160 + 4.42603i) q^{65} +(0.735269 + 1.27352i) q^{66} +(9.31187 - 5.37621i) q^{67} -0.0938694i q^{68} -2.56549 q^{69} +(-8.95558 + 1.09613i) q^{70} +(4.33806 - 7.51373i) q^{71} +(0.866025 - 0.500000i) q^{72} +(11.0108 + 6.35711i) q^{73} +(0.769037 - 1.33201i) q^{74} +(-3.59936 + 3.47054i) q^{75} +(-0.504306 - 4.32963i) q^{76} -5.93355i q^{77} +(4.38320 + 2.53064i) q^{78} +(-6.48112 + 11.2256i) q^{79} +(2.21950 - 0.271659i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.72248 - 3.88123i) q^{82} -2.06328i q^{83} -4.03495 q^{84} +(0.0255005 + 0.208344i) q^{85} +(2.29325 + 3.97202i) q^{86} +4.20982i q^{87} +1.47054i q^{88} +(-0.813846 - 1.40962i) q^{89} +(-1.78632 + 1.34502i) q^{90} +(-10.2110 - 17.6860i) q^{91} +(-2.22178 - 1.28274i) q^{92} +(3.69410 + 2.13279i) q^{93} -4.03603 q^{94} +(2.29549 + 9.47263i) q^{95} +1.00000 q^{96} +(10.3479 + 5.97438i) q^{97} +(8.03741 + 4.64040i) q^{98} +(-0.735269 - 1.27352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20q + 10q^{4} - 10q^{6} + 10q^{9} + O(q^{10}) $	$ 20q + 10q^{4} - 10q^{6} + 10q^{9} - 2q^{10} + 12q^{11} + 10q^{14} + 2q^{15} - 10q^{16} + 6q^{19} - 10q^{21} + 10q^{24} + 14q^{25} + 8q^{29} + 40q^{31} + 12q^{34} + 2q^{35} - 10q^{36} + 2q^{40} - 14q^{41} + 6q^{44} + 44q^{46} - 8q^{49} - 8q^{50} - 12q^{51} + 10q^{54} + 20q^{56} + 8q^{59} - 2q^{60} + 16q^{61} - 20q^{64} + 40q^{65} - 6q^{66} - 44q^{69} + 8q^{70} - 4q^{71} + 26q^{74} + 8q^{75} + 8q^{79} - 10q^{81} - 20q^{84} - 16q^{85} - 20q^{86} - 2q^{89} + 2q^{90} - 44q^{91} - 32q^{94} - 80q^{95} + 20q^{96} + 6q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.34502	−	1.78632i	−0.601509	−	0.798866i
$5$	−1.34502	−	1.78632i	−0.601509	−	0.798866i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$			4.03495i			1.52507i	0.646949	+	0.762533i	$0.276045\pi$
$7$			4.03495i			1.52507i	−0.646949	+	0.762533i	$0.723955\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.271659	+	2.21950i	0.0859061	+	0.701869i
$11$	−1.47054			−0.443384			−0.221692	−	0.975117i	$-0.571158\pi$
$11$	−1.47054			−0.443384			−0.221692	+	0.975117i	$0.571158\pi$
$12$			1.00000i			0.288675i
$13$	−4.38320	+	2.53064i	−1.21568	+	0.701874i	−0.963991	−	0.265934i	$-0.914320\pi$
$13$	−4.38320	+	2.53064i	−1.21568	+	0.701874i	−0.251690	+	0.967808i	$0.580986\pi$
$14$	2.01747	−	3.49437i	0.539192	−	0.933909i
$15$	−0.271659	−	2.21950i	−0.0701421	−	0.573074i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0812933	−	0.0469347i	−0.0197165	−	0.0113833i	0.490109	−	0.871661i	$-0.336957\pi$
$17$	−0.0812933	−	0.0469347i	−0.0197165	−	0.0113833i	−0.509826	+	0.860278i	$0.670290\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−4.00172	−	1.72807i	−0.918058	−	0.396447i
$19$	−4.00172	−	1.72807i	−0.918058	−	0.396447i
$20$	0.874489	−	2.05798i	0.195542	−	0.460178i
$21$	−2.01747	+	3.49437i	−0.440249	+	0.762533i
$22$	1.27352	+	0.735269i	0.271516	+	0.156760i
$23$	−2.22178	+	1.28274i	−0.463273	+	0.267471i	−0.713419	−	0.700737i	$-0.752855\pi$
$23$	−2.22178	+	1.28274i	−0.463273	+	0.267471i	0.250147	+	0.968208i	$0.419521\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−1.38186	+	4.80525i	−0.276373	+	0.961051i
$26$	5.06128			0.992599
$27$			1.00000i			0.192450i
$28$	−3.49437	+	2.01747i	−0.660373	+	0.381267i
$29$	2.10491	+	3.64581i	0.390872	+	0.677011i	0.992565	−	0.121717i	$-0.0388401\pi$
$29$	2.10491	+	3.64581i	0.390872	+	0.677011i	−0.601693	+	0.798728i	$0.705507\pi$
$30$	−0.874489	+	2.05798i	−0.159659	+	0.375733i
$31$	4.26558			0.766120			0.383060	−	0.923723i	$-0.374870\pi$
$31$	4.26558			0.766120			0.383060	+	0.923723i	$0.374870\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.27352	−	0.735269i	−0.221692	−	0.127994i
$34$	0.0469347	+	0.0812933i	0.00804924	+	0.0139417i
$35$	7.20770	−	5.42707i	1.21832	−	0.917342i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$			1.53807i			0.252858i	0.991976	+	0.126429i	$0.0403515\pi$
$37$			1.53807i			0.252858i	−0.991976	+	0.126429i	$0.959648\pi$
$38$	2.60156	+	3.49741i	0.422028	+	0.567356i
$39$	−5.06128			−0.810454
$40$	−1.78632	+	1.34502i	−0.282442	+	0.212666i
$41$	−3.88123	+	6.72248i	−0.606146	+	1.04987i	0.385724	+	0.922614i	$0.373952\pi$
$41$	−3.88123	+	6.72248i	−0.606146	+	1.04987i	−0.991869	+	0.127261i	$0.959382\pi$
$42$	3.49437	−	2.01747i	0.539192	−	0.311303i
$43$	−3.97202	−	2.29325i	−0.605727	−	0.349717i	0.165564	−	0.986199i	$-0.447056\pi$
$43$	−3.97202	−	2.29325i	−0.605727	−	0.349717i	−0.771291	+	0.636482i	$0.780389\pi$
$44$	−0.735269	−	1.27352i	−0.110846	−	0.191991i
$45$	0.874489	−	2.05798i	0.130361	−	0.306785i
$46$	2.56549			0.378261
$47$	3.49530	−	2.01801i	0.509842	−	0.294358i	−0.222927	−	0.974835i	$-0.571561\pi$
$47$	3.49530	−	2.01801i	0.509842	−	0.294358i	0.732769	+	0.680478i	$0.238228\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−9.28080			−1.32583
$50$	3.59936	−	3.47054i	0.509026	−	0.490808i
$51$	−0.0469347	−	0.0812933i	−0.00657218	−	0.0113833i
$52$	−4.38320	−	2.53064i	−0.607840	−	0.350937i
$53$	−9.22964	+	5.32873i	−1.26779	+	0.731958i	−0.974569	−	0.224087i	$-0.928060\pi$
$53$	−9.22964	+	5.32873i	−1.26779	+	0.731958i	−0.293219	+	0.956045i	$0.594727\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.97790	+	2.62685i	0.266700	+	0.354204i
$56$	4.03495			0.539192
$57$	−2.60156	−	3.49741i	−0.344584	−	0.463244i
$58$		−	4.20982i		−	0.552777i
$59$	−3.07599	+	5.32777i	−0.400460	+	0.693617i	−0.993781	−	0.111349i	$-0.964483\pi$
$59$	−3.07599	+	5.32777i	−0.400460	+	0.693617i	0.593321	+	0.804966i	$0.297816\pi$
$60$	1.78632	−	1.34502i	0.230613	−	0.173641i
$61$	0.653722	+	1.13228i	0.0837005	+	0.144974i	0.904837	−	0.425759i	$-0.139993\pi$
$61$	0.653722	+	1.13228i	0.0837005	+	0.144974i	−0.821136	+	0.570732i	$0.806659\pi$
$62$	−3.69410	−	2.13279i	−0.469151	−	0.270864i
$63$	−3.49437	+	2.01747i	−0.440249	+	0.254178i
$64$	−1.00000			−0.125000
$65$	10.4160	+	4.42603i	1.29195	+	0.548982i
$66$	0.735269	+	1.27352i	0.0905054	+	0.156760i
$67$	9.31187	−	5.37621i	1.13763	−	0.656808i	0.191784	−	0.981437i	$-0.438573\pi$
$67$	9.31187	−	5.37621i	1.13763	−	0.656808i	0.945842	+	0.324629i	$0.105239\pi$
$68$		−	0.0938694i		−	0.0113833i
$69$	−2.56549			−0.308849
$70$	−8.95558	+	1.09613i	−1.07040	+	0.131013i
$71$	4.33806	−	7.51373i	0.514833	−	0.891716i	−0.485019	−	0.874503i	$-0.661187\pi$
$71$	4.33806	−	7.51373i	0.514833	−	0.891716i	0.999852	−	0.0172126i	$-0.00547923\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	11.0108	+	6.35711i	1.28872	+	0.744044i	0.978426	−	0.206596i	$-0.0662386\pi$
$73$	11.0108	+	6.35711i	1.28872	+	0.744044i	0.310296	+	0.950640i	$0.399572\pi$
$74$	0.769037	−	1.33201i	0.0893987	−	0.154843i
$75$	−3.59936	+	3.47054i	−0.415618	+	0.400743i
$76$	−0.504306	−	4.32963i	−0.0578479	−	0.496642i
$77$		−	5.93355i		−	0.676190i
$78$	4.38320	+	2.53064i	0.496300	+	0.286539i
$79$	−6.48112	+	11.2256i	−0.729183	+	1.26298i	0.228046	+	0.973650i	$0.426766\pi$
$79$	−6.48112	+	11.2256i	−0.729183	+	1.26298i	−0.957229	+	0.289332i	$0.906567\pi$
$80$	2.21950	−	0.271659i	0.248148	−	0.0303724i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.72248	−	3.88123i	0.742374	−	0.428610i
$83$		−	2.06328i		−	0.226475i	−0.993568	−	0.113237i	$-0.963878\pi$
$83$		−	2.06328i		−	0.226475i	0.993568	−	0.113237i	$-0.0361221\pi$
$84$	−4.03495			−0.440249
$85$	0.0255005	+	0.208344i	0.00276592	+	0.0225980i
$86$	2.29325	+	3.97202i	0.247287	+	0.428314i
$87$			4.20982i			0.451340i
$88$			1.47054i			0.156760i
$89$	−0.813846	−	1.40962i	−0.0862675	−	0.149420i	0.819663	−	0.572846i	$-0.194161\pi$
$89$	−0.813846	−	1.40962i	−0.0862675	−	0.149420i	−0.905931	+	0.423426i	$0.860827\pi$
$90$	−1.78632	+	1.34502i	−0.188294	+	0.141777i
$91$	−10.2110	−	17.6860i	−1.07040	−	1.85399i
$92$	−2.22178	−	1.28274i	−0.231636	−	0.133735i
$93$	3.69410	+	2.13279i	0.383060	+	0.221160i
$94$	−4.03603			−0.416285
$95$	2.29549	+	9.47263i	0.235513	+	0.971871i
$96$	1.00000			0.102062
$97$	10.3479	+	5.97438i	1.05067	+	0.606607i	0.922838	−	0.385188i	$-0.125864\pi$
$97$	10.3479	+	5.97438i	1.05067	+	0.606607i	0.127836	+	0.991795i	$0.459197\pi$
$98$	8.03741	+	4.64040i	0.811901	+	0.468751i
$99$	−0.735269	−	1.27352i	−0.0738974	−	0.127994i
$100$	−4.85240	+	1.20590i	−0.485240	+	0.120590i
$101$	−0.252103	−	0.436656i	−0.0250852	−	0.0434489i	0.853210	−	0.521567i	$-0.174652\pi$
$101$	−0.252103	−	0.436656i	−0.0250852	−	0.0434489i	−0.878295	+	0.478118i	$0.841319\pi$
$102$			0.0938694i			0.00929446i
$103$			5.33797i			0.525966i	0.964800	+	0.262983i	$0.0847063\pi$
$103$			5.33797i			0.525966i	−0.964800	+	0.262983i	$0.915294\pi$
$104$	2.53064	+	4.38320i	0.248150	+	0.429808i
$105$	8.95558	−	1.09613i	0.873976	−	0.106971i
$106$	10.6575			1.03514
$107$		−	17.9275i		−	1.73312i	−0.499076	−	0.866558i	$-0.666327\pi$
$107$		−	17.9275i		−	1.73312i	0.499076	−	0.866558i	$-0.333673\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−4.43631	+	7.68392i	−0.424922	+	0.735986i	−0.996413	−	0.0846222i	$-0.973032\pi$
$109$	−4.43631	+	7.68392i	−0.424922	+	0.735986i	0.571492	+	0.820608i	$0.306365\pi$
$110$	−0.399485	−	3.26387i	−0.0380894	−	0.311198i
$111$	−0.769037	+	1.33201i	−0.0729937	+	0.126429i
$112$	−3.49437	−	2.01747i	−0.330187	−	0.190633i
$113$		−	15.8667i		−	1.49261i	−0.665603	−	0.746306i	$-0.731826\pi$
$113$		−	15.8667i		−	1.49261i	0.665603	−	0.746306i	$-0.268174\pi$
$114$	0.504306	+	4.32963i	0.0472326	+	0.405507i
$115$	5.27972	+	2.24349i	0.492336	+	0.209207i
$116$	−2.10491	+	3.64581i	−0.195436	+	0.338505i
$117$	−4.38320	−	2.53064i	−0.405227	−	0.233958i
$118$	5.32777	−	3.07599i	0.490461	−	0.283168i
$119$	0.189379	−	0.328014i	0.0173604	−	0.0300690i
$120$	−2.21950	+	0.271659i	−0.202612	+	0.0247990i
$121$	−8.83752			−0.803410
$122$		−	1.30744i		−	0.118370i
$123$	−6.72248	+	3.88123i	−0.606146	+	0.349958i
$124$	2.13279	+	3.69410i	0.191530	+	0.331740i
$125$	10.4423	−	3.99469i	0.933991	−	0.357296i
$126$	4.03495			0.359462
$127$	5.77290	−	3.33298i	0.512262	−	0.295755i	−0.221501	−	0.975160i	$-0.571096\pi$
$127$	5.77290	−	3.33298i	0.512262	−	0.295755i	0.733763	+	0.679406i	$0.237762\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.29325	−	3.97202i	−0.201909	−	0.349717i
$130$	−6.80751	−	9.04106i	−0.597058	−	0.792953i
$131$	−3.53784	+	6.12771i	−0.309102	+	0.535381i	−0.978166	−	0.207824i	$-0.933362\pi$
$131$	−3.53784	+	6.12771i	−0.309102	+	0.535381i	0.669064	+	0.743205i	$0.266695\pi$
$132$		−	1.47054i		−	0.127994i
$133$	6.97268	−	16.1467i	0.604608	−	1.40010i
$134$	−10.7524			−0.928867
$135$	1.78632	−	1.34502i	0.153742	−	0.115761i
$136$	−0.0469347	+	0.0812933i	−0.00402462	+	0.00697084i
$137$	16.3302	−	9.42826i	1.39519	−	0.805511i	0.401302	−	0.915946i	$-0.368558\pi$
$137$	16.3302	−	9.42826i	1.39519	−	0.805511i	0.993883	+	0.110435i	$0.0352245\pi$
$138$	2.22178	+	1.28274i	0.189130	+	0.109194i
$139$	−9.99616	−	17.3139i	−0.847864	−	1.46854i	−0.883111	−	0.469164i	$-0.844555\pi$
$139$	−9.99616	−	17.3139i	−0.847864	−	1.46854i	0.0352474	−	0.999379i	$-0.488778\pi$
$140$	8.30383	+	3.52852i	0.701802	+	0.298214i
$141$	4.03603			0.339895
$142$	−7.51373	+	4.33806i	−0.630538	+	0.364042i
$143$	6.44566	−	3.72141i	0.539014	−	0.311200i
$144$	−1.00000			−0.0833333
$145$	3.68144	−	8.66372i	0.305727	−	0.719483i
$146$	−6.35711	−	11.0108i	−0.526119	−	0.911264i
$147$	−8.03741	−	4.64040i	−0.662914	−	0.382734i
$148$	−1.33201	+	0.769037i	−0.109491	+	0.0632144i
$149$	6.10397	−	10.5724i	0.500056	−	0.866123i	−0.499944	−	0.866058i	$-0.666646\pi$
$149$	6.10397	−	10.5724i	0.500056	−	0.866123i	1.00000		6.51503e-5i	$-2.07380e-5\pi$
$150$	4.85240	−	1.20590i	0.396197	−	0.0984611i
$151$	19.9109			1.62032			0.810161	−	0.586207i	$-0.199380\pi$
$151$	19.9109			1.62032			0.810161	+	0.586207i	$0.199380\pi$
$152$	−1.72807	+	4.00172i	−0.140165	+	0.324582i
$153$		−	0.0938694i		−	0.00758889i
$154$	−2.96677	+	5.13860i	−0.239069	+	0.414080i
$155$	−5.73727	−	7.61968i	−0.460828	−	0.612027i
$156$	−2.53064	−	4.38320i	−0.202613	−	0.350937i
$157$	14.0594	+	8.11721i	1.12206	+	0.647824i	0.941927	−	0.335817i	$-0.109012\pi$
$157$	14.0594	+	8.11721i	1.12206	+	0.647824i	0.180137	+	0.983641i	$0.442346\pi$
$158$	11.2256	−	6.48112i	0.893063	−	0.515610i
$159$	−10.6575			−0.845192
$160$	−2.05798	−	0.874489i	−0.162697	−	0.0691344i
$161$	−5.17581	−	8.96476i	−0.407911	−	0.706522i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$		−	2.05750i		−	0.161156i	−0.996748	−	0.0805780i	$-0.974323\pi$
$163$		−	2.05750i		−	0.161156i	0.996748	−	0.0805780i	$-0.0256766\pi$
$164$	−7.76245			−0.606146
$165$	0.399485	+	3.26387i	0.0310999	+	0.254092i
$166$	−1.03164	+	1.78686i	−0.0800709	+	0.138687i
$167$	−18.8169	+	10.8639i	−1.45609	+	0.840676i	−0.998816	−	0.0486476i	$-0.984509\pi$
$167$	−18.8169	+	10.8639i	−1.45609	+	0.840676i	−0.457278	+	0.889324i	$0.651176\pi$
$168$	3.49437	+	2.01747i	0.269596	+	0.155651i
$169$	6.30829	−	10.9263i	0.485253	−	0.840483i
$170$	0.0820878	−	0.193181i	0.00629584	−	0.0148163i
$171$	−0.504306	−	4.32963i	−0.0385652	−	0.331095i
$172$		−	4.58649i		−	0.349717i
$173$	−20.0963	−	11.6026i	−1.52790	−	0.882132i	−0.999450	−	0.0331655i	$-0.989441\pi$
$173$	−20.0963	−	11.6026i	−1.52790	−	0.882132i	−0.528447	−	0.848966i	$-0.677226\pi$
$174$	2.10491	−	3.64581i	0.159573	−	0.276388i
$175$	−19.3889	−	5.57575i	−1.46567	−	0.421487i
$176$	0.735269	−	1.27352i	0.0554230	−	0.0959955i
$177$	−5.32777	+	3.07599i	−0.400460	+	0.231206i
$178$			1.62769i			0.122001i
$179$	−6.37559			−0.476534			−0.238267	−	0.971200i	$-0.576579\pi$
$179$	−6.37559			−0.476534			−0.238267	+	0.971200i	$0.576579\pi$
$180$	2.21950	−	0.271659i	0.165432	−	0.0202483i
$181$	4.39603	+	7.61415i	0.326755	+	0.565955i	0.981866	−	0.189577i	$-0.0607116\pi$
$181$	4.39603	+	7.61415i	0.326755	+	0.565955i	−0.655111	+	0.755532i	$0.727378\pi$
$182$			20.4220i			1.51378i
$183$			1.30744i			0.0966491i
$184$	1.28274	+	2.22178i	0.0945652	+	0.163792i
$185$	2.74749	−	2.06873i	0.201999	−	0.152096i
$186$	−2.13279	−	3.69410i	−0.156384	−	0.270864i
$187$	0.119545	+	0.0690193i	0.00874200	+	0.00504719i
$188$	3.49530	+	2.01801i	0.254921	+	0.147179i
$189$	−4.03495			−0.293499
$190$	2.74836	−	9.35128i	0.199387	−	0.678413i
$191$	12.9659			0.938177			0.469088	−	0.883151i	$-0.344583\pi$
$191$	12.9659			0.938177			0.469088	+	0.883151i	$0.344583\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−5.29710	−	3.05828i	−0.381294	−	0.220140i	0.297087	−	0.954850i	$-0.403985\pi$
$193$	−5.29710	−	3.05828i	−0.381294	−	0.220140i	−0.678381	+	0.734710i	$0.737318\pi$
$194$	−5.97438	−	10.3479i	−0.428936	−	0.742939i
$195$	6.80751	+	9.04106i	0.487496	+	0.647444i
$196$	−4.64040	−	8.03741i	−0.331457	−	0.574101i
$197$			7.34941i			0.523624i	0.965119	+	0.261812i	$0.0843200\pi$
$197$			7.34941i			0.523624i	−0.965119	+	0.261812i	$0.915680\pi$
$198$			1.47054i			0.104507i
$199$	1.71780	+	2.97531i	0.121771	+	0.210914i	0.920466	−	0.390822i	$-0.127809\pi$
$199$	1.71780	+	2.97531i	0.121771	+	0.210914i	−0.798695	+	0.601736i	$0.794476\pi$
$200$	4.80525	+	1.38186i	0.339783	+	0.0977125i
$201$	10.7524			0.758417
$202$			0.504207i			0.0354759i
$203$	−14.7107	+	8.49321i	−1.03249	+	0.596106i
$204$	0.0469347	−	0.0812933i	0.00328609	−	0.00569167i
$205$	17.2288	−	2.10874i	1.20331	−	0.147281i
$206$	2.66899	−	4.62282i	0.185957	−	0.322087i
$207$	−2.22178	−	1.28274i	−0.154424	−	0.0891569i
$208$		−	5.06128i		−	0.350937i
$209$	5.88469	+	2.54120i	0.407052	+	0.175778i
$210$	−8.30383	−	3.52852i	−0.573019	−	0.243491i
$211$	2.01970	−	3.49822i	0.139042	−	0.240827i	−0.788092	−	0.615557i	$-0.788931\pi$
$211$	2.01970	−	3.49822i	0.139042	−	0.240827i	0.927134	+	0.374730i	$0.122264\pi$
$212$	−9.22964	−	5.32873i	−0.633894	−	0.365979i
$213$	7.51373	−	4.33806i	0.514833	−	0.297239i
$214$	−8.96375	+	15.5257i	−0.612749	+	1.06131i
$215$	1.24596	+	10.1797i	0.0849739	+	0.694253i
$216$	1.00000			0.0680414
$217$			17.2114i			1.16838i
$218$	7.68392	−	4.43631i	0.520421	−	0.300465i
$219$	6.35711	+	11.0108i	0.429574	+	0.744044i
$220$	−1.28597	+	3.02634i	−0.0867001	+	0.204035i
$221$	0.475100			0.0319587
$222$	1.33201	−	0.769037i	0.0893987	−	0.0516144i
$223$	−15.6334	−	9.02593i	−1.04689	−	0.604421i	−0.125111	−	0.992143i	$-0.539929\pi$
$223$	−15.6334	−	9.02593i	−1.04689	−	0.604421i	−0.921776	+	0.387722i	$0.873262\pi$
$224$	2.01747	+	3.49437i	0.134798	+	0.233477i
$225$	−4.85240	+	1.20590i	−0.323494	+	0.0803931i
$226$	−7.93334	+	13.7409i	−0.527718	+	0.914034i
$227$			26.8513i			1.78219i	0.453820	+	0.891093i	$0.350061\pi$
$227$			26.8513i			1.78219i	−0.453820	+	0.891093i	$0.649939\pi$
$228$	1.72807	−	4.00172i	0.114444	−	0.265020i
$229$	13.7131			0.906190			0.453095	−	0.891462i	$-0.350320\pi$
$229$	13.7131			0.906190			0.453095	+	0.891462i	$0.350320\pi$
$230$	−3.45062	−	4.58278i	−0.227527	−	0.302180i
$231$	2.96677	−	5.13860i	0.195199	−	0.338095i
$232$	3.64581	−	2.10491i	0.239359	−	0.138194i
$233$	−0.00572506	−	0.00330537i	−0.000375061	−	0.000216542i	0.499812	−	0.866134i	$-0.333402\pi$
$233$	−0.00572506	−	0.00330537i	−0.000375061	−	0.000216542i	−0.500188	+	0.865917i	$0.666736\pi$
$234$	2.53064	+	4.38320i	0.165433	+	0.286539i
$235$	−8.30605	−	3.52946i	−0.541827	−	0.230237i
$236$	−6.15198			−0.400460
$237$	−11.2256	+	6.48112i	−0.729183	+	0.420994i
$238$	−0.328014	+	0.189379i	−0.0212620	+	0.0122756i
$239$	4.67499			0.302400			0.151200	−	0.988503i	$-0.451686\pi$
$239$	4.67499			0.302400			0.151200	+	0.988503i	$0.451686\pi$
$240$	2.05798	+	0.874489i	0.132842	+	0.0564480i
$241$	13.9044	+	24.0831i	0.895659	+	1.55133i	0.832987	+	0.553292i	$0.186629\pi$
$241$	13.9044	+	24.0831i	0.895659	+	1.55133i	0.0626717	+	0.998034i	$0.480038\pi$
$242$	7.65351	+	4.41876i	0.491986	+	0.284049i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−0.653722	+	1.13228i	−0.0418503	+	0.0724868i
$245$	12.4828	+	16.5785i	0.797498	+	1.05916i
$246$	7.76245			0.494916
$247$	21.9135	−	2.55244i	1.39432	−	0.162408i
$248$		−	4.26558i		−	0.270864i
$249$	1.03164	−	1.78686i	0.0653776	−	0.113237i
$250$	−11.0407	−	1.76166i	−0.698274	−	0.111417i
$251$	3.03259	+	5.25259i	0.191415	+	0.331541i	0.945719	−	0.324984i	$-0.105359\pi$
$251$	3.03259	+	5.25259i	0.191415	+	0.331541i	−0.754304	+	0.656525i	$0.772026\pi$
$252$	−3.49437	−	2.01747i	−0.220124	−	0.127089i
$253$	3.26721	−	1.88633i	0.205408	−	0.118592i
$254$	−6.66597			−0.418260
$255$	−0.0820878	+	0.193181i	−0.00514054	+	0.0120975i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.11707	+	0.644941i	−0.0696809	+	0.0402303i	−0.534436	−	0.845209i	$-0.679476\pi$
$257$	−1.11707	+	0.644941i	−0.0696809	+	0.0402303i	0.464755	+	0.885439i	$0.346142\pi$
$258$			4.58649i			0.285543i
$259$	−6.20604			−0.385625
$260$	1.37494	+	11.2335i	0.0852704	+	0.696675i
$261$	−2.10491	+	3.64581i	−0.130291	+	0.225670i
$262$	6.12771	−	3.53784i	0.378571	−	0.218568i
$263$	24.4863	+	14.1372i	1.50989	+	0.871737i	0.999933	+	0.0115378i	$0.00367269\pi$
$263$	24.4863	+	14.1372i	1.50989	+	0.871737i	0.509959	+	0.860199i	$0.329661\pi$
$264$	−0.735269	+	1.27352i	−0.0452527	+	0.0783800i
$265$	21.9328	+	9.31984i	1.34732	+	0.572513i
$266$	−14.1119	+	10.4971i	−0.865255	+	0.643621i
$267$		−	1.62769i		−	0.0996131i
$268$	9.31187	+	5.37621i	0.568813	+	0.328404i
$269$	−13.8782	+	24.0377i	−0.846169	+	1.46561i	0.0384337	+	0.999261i	$0.487763\pi$
$269$	−13.8782	+	24.0377i	−0.846169	+	1.46561i	−0.884602	+	0.466346i	$0.845570\pi$
$270$	−2.21950	+	0.271659i	−0.135075	+	0.0165326i
$271$	−5.42826	+	9.40202i	−0.329743	+	0.571132i	−0.982461	−	0.186469i	$-0.940296\pi$
$271$	−5.42826	+	9.40202i	−0.329743	+	0.571132i	0.652718	+	0.757601i	$0.273629\pi$
$272$	0.0812933	−	0.0469347i	0.00492913	−	0.00284584i
$273$		−	20.4220i		−	1.23600i
$274$	−18.8565			−1.13916
$275$	2.03208	−	7.06631i	0.122539	−	0.426115i
$276$	−1.28274	−	2.22178i	−0.0772122	−	0.133735i
$277$			24.5237i			1.47349i	0.676173	+	0.736743i	$0.263637\pi$
$277$			24.5237i			1.47349i	−0.676173	+	0.736743i	$0.736363\pi$
$278$			19.9923i			1.19906i
$279$	2.13279	+	3.69410i	0.127687	+	0.221160i
$280$	−5.42707	−	7.20770i	−0.324329	−	0.430742i
$281$	3.29709	+	5.71073i	0.196688	+	0.340674i	0.947453	−	0.319896i	$-0.103648\pi$
$281$	3.29709	+	5.71073i	0.196688	+	0.340674i	−0.750765	+	0.660570i	$0.770315\pi$
$282$	−3.49530	−	2.01801i	−0.208142	−	0.120171i
$283$	−20.4709	−	11.8189i	−1.21687	−	0.702559i	−0.252621	−	0.967565i	$-0.581293\pi$
$283$	−20.4709	−	11.8189i	−1.21687	−	0.702559i	−0.964247	+	0.265006i	$0.914626\pi$
$284$	8.67611			0.514833
$285$	−2.74836	+	9.35128i	−0.162799	+	0.553922i
$286$	−7.44281			−0.440103
$287$	−27.1248	−	15.6605i	−1.60113	−	0.924412i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−8.49559	−	14.7148i	−0.499741	−	0.865577i
$290$	−7.52008	+	5.66228i	−0.441595	+	0.332501i
$291$	5.97438	+	10.3479i	0.350225	+	0.606607i
$292$			12.7142i			0.744044i
$293$			23.0123i			1.34439i	0.740374	+	0.672195i	$0.234648\pi$
$293$			23.0123i			1.34439i	−0.740374	+	0.672195i	$0.765352\pi$
$294$	4.64040	+	8.03741i	0.270634	+	0.468751i
$295$	13.6544	−	1.67124i	0.794987	−	0.0973034i
$296$	1.53807			0.0893987
$297$		−	1.47054i		−	0.0853293i
$298$	−10.5724	+	6.10397i	−0.612442	+	0.353593i
$299$	6.49233	−	11.2451i	0.375461	−	0.650318i
$300$	−4.80525	−	1.38186i	−0.277431	−	0.0797819i
$301$	9.25313	−	16.0269i	0.533341	−	0.923774i
$302$	−17.2433	−	9.95543i	−0.992241	−	0.572870i
$303$		−	0.504207i		−	0.0289659i
$304$	3.49741	−	2.60156i	0.200590	−	0.149209i
$305$	1.14335	−	2.69069i	0.0654678	−	0.154068i
$306$	−0.0469347	+	0.0812933i	−0.00268308	+	0.00464723i
$307$	−22.0807	−	12.7483i	−1.26021	−	0.727584i	−0.287097	−	0.957902i	$-0.592690\pi$
$307$	−22.0807	−	12.7483i	−1.26021	−	0.727584i	−0.973116	+	0.230318i	$0.926023\pi$
$308$	5.13860	−	2.96677i	0.292799	−	0.169048i
$309$	−2.66899	+	4.62282i	−0.151833	+	0.262983i
$310$	1.15878	+	9.46747i	0.0658144	+	0.537716i
$311$	−30.3172			−1.71913			−0.859565	−	0.511027i	$-0.829265\pi$
$311$	−30.3172			−1.71913			−0.859565	+	0.511027i	$0.829265\pi$
$312$			5.06128i			0.286539i
$313$	6.54063	−	3.77623i	0.369698	−	0.213445i	−0.303628	−	0.952791i	$-0.598198\pi$
$313$	6.54063	−	3.77623i	0.369698	−	0.213445i	0.673327	+	0.739345i	$0.264865\pi$
$314$	−8.11721	−	14.0594i	−0.458081	−	0.793419i
$315$	8.30383	+	3.52852i	0.467868	+	0.198809i
$316$	−12.9622			−0.729183
$317$	−12.1344	+	7.00579i	−0.681535	+	0.393484i	−0.800433	−	0.599422i	$-0.795397\pi$
$317$	−12.1344	+	7.00579i	−0.681535	+	0.393484i	0.118898	+	0.992906i	$0.462064\pi$
$318$	9.22964	+	5.32873i	0.517572	+	0.298821i
$319$	−3.09535	−	5.36131i	−0.173307	−	0.300176i
$320$	1.34502	+	1.78632i	0.0751887	+	0.0998582i
$321$	8.96375	−	15.5257i	0.500308	−	0.866558i
$322$			10.3516i			0.576873i
$323$	0.244207	+	0.328300i	0.0135880	+	0.0182671i
$324$	−1.00000			−0.0555556
$325$	−6.10339	−	24.5594i	−0.338555	−	1.36231i
$326$	−1.02875	+	1.78185i	−0.0569773	+	0.0986875i
$327$	−7.68392	+	4.43631i	−0.424922	+	0.245329i
$328$	6.72248	+	3.88123i	0.371187	+	0.214305i
$329$	8.14258	+	14.1034i	0.448915	+	0.777544i
$330$	1.28597	−	3.02634i	0.0707903	−	0.166594i
$331$	−2.20541			−0.121220			−0.0606102	−	0.998162i	$-0.519305\pi$
$331$	−2.20541			−0.121220			−0.0606102	+	0.998162i	$0.519305\pi$
$332$	1.78686	−	1.03164i	0.0980665	−	0.0566187i
$333$	−1.33201	+	0.769037i	−0.0729937	+	0.0421429i
$334$	21.7279			1.18890
$335$	−22.1282	−	9.40287i	−1.20899	−	0.513734i
$336$	−2.01747	−	3.49437i	−0.110062	−	0.190633i
$337$	−3.35026	−	1.93428i	−0.182500	−	0.105367i	0.405966	−	0.913888i	$-0.366935\pi$
$337$	−3.35026	−	1.93428i	−0.182500	−	0.105367i	−0.588467	+	0.808521i	$0.700268\pi$
$338$	−10.9263	+	6.30829i	−0.594311	+	0.343126i
$339$	7.93334	−	13.7409i	0.430880	−	0.746306i
$340$	−0.167681	+	0.126256i	−0.00909376	+	0.00684719i
$341$	−6.27270			−0.339685
$342$	−1.72807	+	4.00172i	−0.0934434	+	0.216388i
$343$		−	9.20290i		−	0.496910i
$344$	−2.29325	+	3.97202i	−0.123644	+	0.214157i
$345$	3.45062	+	4.58278i	0.185775	+	0.246729i
$346$	11.6026	+	20.0963i	0.623761	+	1.08039i
$347$	−10.6406	−	6.14337i	−0.571219	−	0.329793i	0.186417	−	0.982471i	$-0.440312\pi$
$347$	−10.6406	−	6.14337i	−0.571219	−	0.329793i	−0.757636	+	0.652677i	$0.773646\pi$
$348$	−3.64581	+	2.10491i	−0.195436	+	0.112835i
$349$	23.1329			1.23828			0.619139	−	0.785282i	$-0.287482\pi$
$349$	23.1329			1.23828			0.619139	+	0.785282i	$0.287482\pi$
$350$	14.0034	+	14.5232i	0.748515	+	0.776298i
$351$	−2.53064	−	4.38320i	−0.135076	−	0.233958i
$352$	−1.27352	+	0.735269i	−0.0678791	+	0.0391900i
$353$		−	2.27216i		−	0.120935i	−0.998170	−	0.0604674i	$-0.980741\pi$
$353$		−	2.27216i		−	0.120935i	0.998170	−	0.0604674i	$-0.0192591\pi$
$354$	6.15198			0.326974
$355$	−19.2567	+	2.35694i	−1.02204	+	0.125094i
$356$	0.813846	−	1.40962i	0.0431338	−	0.0747098i
$357$	0.328014	−	0.189379i	0.0173604	−	0.0100230i
$358$	5.52142	+	3.18779i	0.291816	+	0.168480i
$359$	−10.3404	+	17.9101i	−0.545746	+	0.945260i	0.452813	+	0.891605i	$0.350420\pi$
$359$	−10.3404	+	17.9101i	−0.545746	+	0.945260i	−0.998560	+	0.0536549i	$0.982913\pi$
$360$	−2.05798	−	0.874489i	−0.108465	−	0.0460896i
$361$	13.0275	+	13.8305i	0.685660	+	0.727922i
$362$		−	8.79207i		−	0.462101i
$363$	−7.65351	−	4.41876i	−0.401705	−	0.231925i
$364$	10.2110	−	17.6860i	0.535202	−	0.926997i
$365$	−3.45394	−	28.2193i	−0.180787	−	1.47707i
$366$	0.653722	−	1.13228i	0.0341706	−	0.0591852i
$367$	31.7744	−	18.3450i	1.65861	−	0.957600i	0.685255	−	0.728304i	$-0.259691\pi$
$367$	31.7744	−	18.3450i	1.65861	−	0.957600i	0.973357	−	0.229296i	$-0.0736424\pi$
$368$		−	2.56549i		−	0.133735i
$369$	−7.76245			−0.404097
$370$	−3.41376	+	0.417831i	−0.177473	+	0.0217220i
$371$	−21.5012	−	37.2411i	−1.11628	−	1.93346i
$372$			4.26558i			0.221160i
$373$			19.5380i			1.01164i	0.862640	+	0.505819i	$0.168810\pi$
$373$			19.5380i			1.01164i	−0.862640	+	0.505819i	$0.831190\pi$
$374$	−0.0690193	−	0.119545i	−0.00356890	−	0.00618152i
$375$	11.0407	+	1.76166i	0.570138	+	0.0909719i
$376$	−2.01801	−	3.49530i	−0.104071	−	0.180256i
$377$	−18.4525	−	10.6536i	−0.950352	−	0.548686i
$378$	3.49437	+	2.01747i	0.179731	+	0.103768i
$379$	−3.46802			−0.178140			−0.0890701	−	0.996025i	$-0.528390\pi$
$379$	−3.46802			−0.178140			−0.0890701	+	0.996025i	$0.528390\pi$
$380$	−7.05579	+	6.72427i	−0.361954	+	0.344948i
$381$	6.66597			0.341508
$382$	−11.2288	−	6.48293i	−0.574514	−	0.331696i
$383$	21.7388	+	12.5509i	1.11080	+	0.641322i	0.939037	−	0.343816i	$-0.111720\pi$
$383$	21.7388	+	12.5509i	1.11080	+	0.641322i	0.171765	+	0.985138i	$0.445053\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−10.5992	+	7.98072i	−0.540185	+	0.406735i
$386$	3.05828	+	5.29710i	0.155662	+	0.269615i
$387$		−	4.58649i		−	0.233145i
$388$			11.9488i			0.606607i
$389$	7.02074	+	12.1603i	0.355965	+	0.616550i	0.987283	−	0.158974i	$-0.0508188\pi$
$389$	7.02074	+	12.1603i	0.355965	+	0.616550i	−0.631317	+	0.775525i	$0.717485\pi$
$390$	−1.37494	−	11.2335i	−0.0696230	−	0.568832i
$391$	0.240821			0.0121788
$392$			9.28080i			0.468751i
$393$	−6.12771	+	3.53784i	−0.309102	+	0.178460i
$394$	3.67471	−	6.36478i	0.185129	−	0.320653i
$395$	28.7698	−	3.52131i	1.44756	−	0.177176i
$396$	0.735269	−	1.27352i	0.0369487	−	0.0639970i
$397$	26.6267	+	15.3729i	1.33635	+	0.771544i	0.986265	−	0.165172i	$-0.0528179\pi$
$397$	26.6267	+	15.3729i	1.33635	+	0.771544i	0.350089	+	0.936716i	$0.386151\pi$
$398$		−	3.43559i		−	0.172211i
$399$	14.1119	−	10.4971i	0.706478	−	0.525514i
$400$	−3.47054	−	3.59936i	−0.173527	−	0.179968i
$401$	−19.3518	+	33.5183i	−0.966381	+	1.67382i	−0.260525	+	0.965467i	$0.583896\pi$
$401$	−19.3518	+	33.5183i	−0.966381	+	1.67382i	−0.705857	+	0.708355i	$0.749438\pi$
$402$	−9.31187	−	5.37621i	−0.464434	−	0.268141i
$403$	−18.6969	+	10.7946i	−0.931357	+	0.537719i
$404$	0.252103	−	0.436656i	0.0125426	−	0.0217244i
$405$	2.21950	−	0.271659i	0.110288	−	0.0134988i
$406$	16.9864			0.843022
$407$		−	2.26180i		−	0.112113i
$408$	−0.0812933	+	0.0469347i	−0.00402462	+	0.00232361i
$409$	−10.3920	−	17.9994i	−0.513850	−	0.890014i	−0.999871	−	0.0160671i	$-0.994885\pi$
$409$	−10.3920	−	17.9994i	−0.513850	−	0.890014i	0.486021	−	0.873947i	$-0.338448\pi$
$410$	−15.9749	−	6.78818i	−0.788946	−	0.335244i
$411$	18.8565			0.930123
$412$	−4.62282	+	2.66899i	−0.227750	+	0.131491i
$413$	−21.4973	−	12.4115i	−1.05781	−	0.610728i
$414$	1.28274	+	2.22178i	0.0630435	+	0.109194i
$415$	−3.68568	+	2.77515i	−0.180923	+	0.136227i
$416$	−2.53064	+	4.38320i	−0.124075	+	0.214904i
$417$		−	19.9923i		−	0.979029i
$418$	−3.82569	−	5.14308i	−0.187121	−	0.251556i
$419$	36.2672			1.77177			0.885883	−	0.463908i	$-0.153553\pi$
$419$	36.2672			1.77177			0.885883	+	0.463908i	$0.153553\pi$
$420$	5.42707	+	7.20770i	0.264814	+	0.351700i
$421$	10.7212	−	18.5697i	0.522519	−	0.905030i	−0.477137	−	0.878829i	$-0.658326\pi$
$421$	10.7212	−	18.5697i	0.522519	−	0.905030i	0.999657	−	0.0262013i	$-0.00834109\pi$
$422$	−3.49822	+	2.01970i	−0.170291	+	0.0983174i
$423$	3.49530	+	2.01801i	0.169947	+	0.0981192i
$424$	5.32873	+	9.22964i	0.258786	+	0.448231i
$425$	0.337869	−	0.325778i	0.0163891	−	0.0158025i
$426$	−8.67611			−0.420359
$427$	−4.56869	+	2.63773i	−0.221094	+	0.127649i
$428$	15.5257	−	8.96375i	0.750461	−	0.433279i
$429$	7.44281			0.359342
$430$	4.01084	−	9.43890i	0.193420	−	0.455184i
$431$	2.91216	+	5.04400i	0.140274	+	0.242961i	0.927600	−	0.373576i	$-0.121868\pi$
$431$	2.91216	+	5.04400i	0.140274	+	0.242961i	−0.787326	+	0.616537i	$0.788535\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−27.3690	+	15.8015i	−1.31527	+	0.759371i	−0.982963	−	0.183801i	$-0.941160\pi$
$433$	−27.3690	+	15.8015i	−1.31527	+	0.759371i	−0.332305	+	0.943172i	$0.607826\pi$
$434$	8.60569	−	14.9055i	0.413086	−	0.715486i
$435$	7.52008	−	5.66228i	0.360560	−	0.271486i
$436$	−8.87262			−0.424922
$437$	11.1076	−	1.29379i	0.531349	−	0.0618904i
$438$		−	12.7142i		−	0.607509i
$439$	−0.932951	+	1.61592i	−0.0445273	+	0.0771236i	−0.887430	−	0.460942i	$-0.847512\pi$
$439$	−0.932951	+	1.61592i	−0.0445273	+	0.0771236i	0.842903	+	0.538066i	$0.180845\pi$
$440$	2.62685	−	1.97790i	0.125230	−	0.0942926i
$441$	−4.64040	−	8.03741i	−0.220971	−	0.382734i
$442$	−0.411448	−	0.237550i	−0.0195706	−	0.0112991i
$443$	13.6368	−	7.87318i	0.647902	−	0.374066i	−0.139750	−	0.990187i	$-0.544630\pi$
$443$	13.6368	−	7.87318i	0.647902	−	0.374066i	0.787652	+	0.616121i	$0.211297\pi$
$444$	−1.53807			−0.0729937
$445$	−1.42340	+	3.34975i	−0.0674755	+	0.158794i
$446$	9.02593	+	15.6334i	0.427390	+	0.740262i
$447$	10.5724	−	6.10397i	0.500056	−	0.288708i
$448$		−	4.03495i		−	0.190633i
$449$	−29.7436			−1.40369			−0.701845	−	0.712330i	$-0.747640\pi$
$449$	−29.7436			−1.40369			−0.701845	+	0.712330i	$0.747640\pi$
$450$	4.80525	+	1.38186i	0.226522	+	0.0651417i
$451$	5.70749	−	9.88567i	0.268755	−	0.465498i
$452$	13.7409	−	7.93334i	0.646320	−	0.373153i
$453$	17.2433	+	9.95543i	0.810161	+	0.467747i
$454$	13.4257	−	23.2539i	0.630098	−	1.09136i
$455$	−17.8588	+	42.0280i	−0.837234	+	1.97030i
$456$	−3.49741	+	2.60156i	−0.163781	+	0.121829i
$457$		−	12.7891i		−	0.598250i	−0.954214	−	0.299125i	$-0.903305\pi$
$457$		−	12.7891i		−	0.598250i	0.954214	−	0.299125i	$-0.0966948\pi$
$458$	−11.8759	−	6.85657i	−0.554926	−	0.320387i
$459$	0.0469347	−	0.0812933i	0.00219073	−	0.00379445i
$460$	0.696938	+	5.69412i	0.0324949	+	0.265490i
$461$	5.96303	−	10.3283i	0.277726	−	0.481035i	−0.693093	−	0.720848i	$-0.743753\pi$
$461$	5.96303	−	10.3283i	0.277726	−	0.481035i	0.970819	+	0.239813i	$0.0770860\pi$
$462$	−5.13860	+	2.96677i	−0.239069	+	0.138027i
$463$		−	19.3208i		−	0.897913i	−0.893554	−	0.448956i	$-0.851796\pi$
$463$		−	19.3208i		−	0.897913i	0.893554	−	0.448956i	$-0.148204\pi$
$464$	−4.20982			−0.195436
$465$	−1.15878	−	9.46747i	−0.0537372	−	0.439043i
$466$	0.00330537	+	0.00572506i	0.000153118	+	0.000265208i
$467$			26.7009i			1.23557i	0.786347	+	0.617785i	$0.211970\pi$
$467$			26.7009i			1.23557i	−0.786347	+	0.617785i	$0.788030\pi$
$468$		−	5.06128i		−	0.233958i
$469$	21.6927	+	37.5729i	1.00168	+	1.73496i
$470$	5.42852	+	7.20963i	0.250399	+	0.332555i
$471$	8.11721	+	14.0594i	0.374021	+	0.647824i
$472$	5.32777	+	3.07599i	0.245231	+	0.141584i
$473$	5.84101	+	3.37231i	0.268570	+	0.155059i
$474$	12.9622			0.595375
$475$	13.8337	−	16.8413i	0.634732	−	0.772733i
$476$	0.378758			0.0173604
$477$	−9.22964	−	5.32873i	−0.422596	−	0.243986i
$478$	−4.04866	−	2.33750i	−0.185182	−	0.106915i
$479$	−6.79124	−	11.7628i	−0.310299	−	0.537454i	0.668128	−	0.744047i	$-0.267096\pi$
$479$	−6.79124	−	11.7628i	−0.310299	−	0.537454i	−0.978427	+	0.206592i	$0.933763\pi$
$480$	−1.34502	−	1.78632i	−0.0613913	−	0.0815339i
$481$	−3.89231	−	6.74168i	−0.177474	−	0.307394i
$482$		−	27.8087i		−	1.26665i
$483$		−	10.3516i		−	0.471015i
$484$	−4.41876	−	7.65351i	−0.200853	−	0.347887i
$485$	−3.24599	−	26.5204i	−0.147393	−	1.20423i
$486$	1.00000			0.0453609
$487$			8.03640i			0.364164i	0.983283	+	0.182082i	$0.0582837\pi$
$487$			8.03640i			0.364164i	−0.983283	+	0.182082i	$0.941716\pi$
$488$	1.13228	−	0.653722i	0.0512559	−	0.0295926i
$489$	1.02875	−	1.78185i	0.0465217	−	0.0805780i
$490$	−2.52121	−	20.5988i	−0.113897	−	0.930558i
$491$	10.3390	−	17.9077i	0.466593	−	0.808163i	−0.532679	−	0.846317i	$-0.678815\pi$
$491$	10.3390	−	17.9077i	0.466593	−	0.808163i	0.999272	+	0.0381546i	$0.0121479\pi$
$492$	−6.72248	−	3.88123i	−0.303073	−	0.174979i
$493$		−	0.395174i		−	0.0177977i
$494$	−20.2538	−	8.74626i	−0.911263	−	0.393513i
$495$	−1.28597	+	3.02634i	−0.0578000	+	0.136024i
$496$	−2.13279	+	3.69410i	−0.0957650	+	0.165870i
$497$	30.3175	+	17.5038i	1.35993	+	0.785154i
$498$	−1.78686	+	1.03164i	−0.0800709	+	0.0462290i
$499$	−0.551160	+	0.954638i	−0.0246733	+	0.0427355i	−0.878098	−	0.478480i	$-0.841188\pi$
$499$	−0.551160	+	0.954638i	−0.0246733	+	0.0427355i	0.853425	+	0.521216i	$0.174521\pi$
$500$	8.68068	+	7.04598i	0.388212	+	0.315106i
$501$	−21.7279			−0.970729
$502$		−	6.06517i		−	0.270702i
$503$	−21.0518	+	12.1543i	−0.938653	+	0.541932i	−0.889538	−	0.456861i	$-0.848974\pi$
$503$	−21.0518	+	12.1543i	−0.938653	+	0.541932i	−0.0491154	+	0.998793i	$0.515640\pi$
$504$	2.01747	+	3.49437i	0.0898654	+	0.155651i
$505$	−0.440923	+	1.03765i	−0.0196208	+	0.0461746i
$506$	−3.77265			−0.167715
$507$	10.9263	−	6.30829i	0.485253	−	0.280161i
$508$	5.77290	+	3.33298i	0.256131	+	0.147877i
$509$	−4.96728	−	8.60358i	−0.220171	−	0.381347i	0.734689	−	0.678404i	$-0.237328\pi$
$509$	−4.96728	−	8.60358i	−0.220171	−	0.381347i	−0.954860	+	0.297057i	$0.903995\pi$
$510$	0.167681	−	0.126256i	0.00742502	−	0.00559071i
$511$	−25.6506	+	44.4282i	−1.13472	+	1.96539i
$512$			1.00000i			0.0441942i
$513$	1.72807	−	4.00172i	0.0762962	−	0.176680i
$514$	1.28988			0.0568942
$515$	9.53531	−	7.17966i	0.420176	−	0.316373i
$516$	2.29325	−	3.97202i	0.100955	−	0.174858i
$517$	−5.13998	+	2.96757i	−0.226056	+	0.130513i
$518$	5.37459	+	3.10302i	0.236146	+	0.136339i
$519$	−11.6026	−	20.0963i	−0.509299	−	0.882132i
$520$	4.42603	−	10.4160i	0.194094	−	0.456772i
$521$	−20.9057			−0.915895			−0.457947	−	0.888979i	$-0.651415\pi$
$521$	−20.9057			−0.915895			−0.457947	+	0.888979i	$0.651415\pi$
$522$	3.64581	−	2.10491i	0.159573	−	0.0921295i
$523$	−27.3676	+	15.8007i	−1.19670	+	0.690916i	−0.959818	−	0.280622i	$-0.909459\pi$
$523$	−27.3676	+	15.8007i	−1.19670	+	0.690916i	−0.236883	+	0.971538i	$0.576126\pi$
$524$	−7.07568			−0.309102
$525$	−14.0034	−	14.5232i	−0.611160	−	0.633845i
$526$	−14.1372	−	24.4863i	−0.616411	−	1.06766i
$527$	−0.346763	−	0.200204i	−0.0151052	−	0.00872101i
$528$	1.27352	−	0.735269i	0.0554230	−	0.0319985i
$529$	−8.20913	+	14.2186i	−0.356919	+	0.618202i
$530$	−14.3345	−	19.0376i	−0.622649	−	0.826942i
$531$	−6.15198			−0.266973
$532$	17.4698	−	2.03485i	0.757413	−	0.0882218i
$533$		−	39.2880i		−	1.70175i
$534$	−0.813846	+	1.40962i	−0.0352186	+	0.0610003i
$535$	−32.0242	+	24.1128i	−1.38453	+	1.04249i
$536$	−5.37621	−	9.31187i	−0.232217	−	0.402211i
$537$	−5.52142	−	3.18779i	−0.238267	−	0.137563i
$538$	24.0377	−	13.8782i	1.03634	−	0.598332i
$539$	13.6478			0.587851
$540$	2.05798	+	0.874489i	0.0885612	+	0.0376320i
$541$	−2.50615	−	4.34078i	−0.107748	−	0.186625i	0.807110	−	0.590402i	$-0.201031\pi$
$541$	−2.50615	−	4.34078i	−0.107748	−	0.186625i	−0.914858	+	0.403777i	$0.867697\pi$
$542$	9.40202	−	5.42826i	0.403851	−	0.233164i
$543$			8.79207i			0.377304i
$544$	−0.0938694			−0.00402462
$545$	19.6928	−	2.41033i	0.843548	−	0.103247i
$546$	−10.2110	+	17.6860i	−0.436991	+	0.756890i
$547$	30.7554	−	17.7566i	1.31500	−	0.759218i	0.332084	−	0.943250i	$-0.392248\pi$
$547$	30.7554	−	17.7566i	1.31500	−	0.759218i	0.982920	+	0.184032i	$0.0589150\pi$
$548$	16.3302	+	9.42826i	0.697593	+	0.402755i
$549$	−0.653722	+	1.13228i	−0.0279002	+	0.0483245i
$550$	−5.29299	+	5.10356i	−0.225694	+	0.217617i
$551$	−2.12304	−	18.2270i	−0.0904445	−	0.776495i
$552$			2.56549i			0.109194i
$553$	−45.2948	−	26.1510i	−1.92613	−	1.11205i
$554$	12.2618	−	21.2381i	0.520956	−	0.902322i
$555$	3.41376	−	0.417831i	0.144906	−	0.0177360i
$556$	9.99616	−	17.3139i	0.423932	−	0.734271i
$557$	8.45640	−	4.88231i	0.358309	−	0.206870i	−0.310030	−	0.950727i	$-0.600339\pi$
$557$	8.45640	−	4.88231i	0.358309	−	0.206870i	0.668339	+	0.743857i	$0.267006\pi$
$558$		−	4.26558i		−	0.180576i
$559$	23.2135			0.981828
$560$	1.09613	+	8.95558i	0.0463199	+	0.378443i
$561$	0.0690193	+	0.119545i	0.00291400	+	0.00504719i
$562$		−	6.59418i		−	0.278159i
$563$			11.5237i			0.485665i	0.970068	+	0.242833i	$0.0780766\pi$
$563$			11.5237i			0.485665i	−0.970068	+	0.242833i	$0.921923\pi$
$564$	2.01801	+	3.49530i	0.0849737	+	0.147179i
$565$	−28.3429	+	21.3409i	−1.19240	+	0.897820i
$566$	11.8189	+	20.4709i	0.496784	+	0.860456i
$567$	−3.49437	−	2.01747i	−0.146750	−	0.0847259i
$568$	−7.51373	−	4.33806i	−0.315269	−	0.182021i
$569$	−1.93925			−0.0812978			−0.0406489	−	0.999173i	$-0.512943\pi$
$569$	−1.93925			−0.0812978			−0.0406489	+	0.999173i	$0.512943\pi$
$570$	7.05579	−	6.72427i	0.295535	−	0.281649i
$571$	−38.0052			−1.59047			−0.795235	−	0.606301i	$-0.792652\pi$
$571$	−38.0052			−1.59047			−0.795235	+	0.606301i	$0.792652\pi$
$572$	6.44566	+	3.72141i	0.269507	+	0.155600i
$573$	11.2288	+	6.48293i	0.469088	+	0.270828i
$574$	15.6605	+	27.1248i	0.653658	+	1.13217i
$575$	−3.09372	−	12.4488i	−0.129017	−	0.519150i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$			28.3094i			1.17854i	0.807938	+	0.589268i	$0.200584\pi$
$577$			28.3094i			1.17854i	−0.807938	+	0.589268i	$0.799416\pi$
$578$			16.9912i			0.706740i
$579$	−3.05828	−	5.29710i	−0.127098	−	0.220140i
$580$	9.34372	−	1.14364i	0.387977	−	0.0474869i
$581$	8.32524			0.345389
$582$		−	11.9488i		−	0.495292i
$583$	13.5725	−	7.83611i	0.562117	−	0.324539i
$584$	6.35711	−	11.0108i	0.263059	−	0.455632i
$585$	1.37494	+	11.2335i	0.0568469	+	0.464450i
$586$	11.5061	−	19.9292i	0.475314	−	0.823267i
$587$	−9.39980	−	5.42698i	−0.387971	−	0.223995i	0.293309	−	0.956018i	$-0.405243\pi$
$587$	−9.39980	−	5.42698i	−0.387971	−	0.223995i	−0.681281	+	0.732022i	$0.738577\pi$
$588$		−	9.28080i		−	0.382734i
$589$	−17.0696	−	7.37122i	−0.703342	−	0.303726i
$590$	−12.6606	−	5.37984i	−0.521230	−	0.221484i
$591$	−3.67471	+	6.36478i	−0.151157	+	0.261812i
$592$	−1.33201	−	0.769037i	−0.0547453	−	0.0316072i
$593$	24.0190	−	13.8674i	0.986341	−	0.569464i	0.0821625	−	0.996619i	$-0.473817\pi$
$593$	24.0190	−	13.8674i	0.986341	−	0.569464i	0.904179	+	0.427155i	$0.140484\pi$
$594$	−0.735269	+	1.27352i	−0.0301685	+	0.0522533i
$595$	−0.840656	+	0.102893i	−0.0344635	+	0.00421821i
$596$	12.2079			0.500056
$597$			3.43559i			0.140609i
$598$	−11.2451	+	6.49233i	−0.459844	+	0.265491i
$599$	15.6071	+	27.0323i	0.637690	+	1.10451i	0.985938	+	0.167109i	$0.0534433\pi$
$599$	15.6071	+	27.0323i	0.637690	+	1.10451i	−0.348248	+	0.937402i	$0.613223\pi$
$600$	3.47054	+	3.59936i	0.141684	+	0.146943i
$601$	42.3271			1.72656			0.863280	−	0.504726i	$-0.168406\pi$
$601$	42.3271			1.72656			0.863280	+	0.504726i	$0.168406\pi$
$602$	−16.0269	+	9.25313i	−0.653207	+	0.377129i
$603$	9.31187	+	5.37621i	0.379209	+	0.218936i
$604$	9.95543	+	17.2433i	0.405081	+	0.701620i
$605$	11.8866	+	15.7866i	0.483259	+	0.641817i
$606$	−0.252103	+	0.436656i	−0.0102410	+	0.0177379i
$607$			12.9882i			0.527176i	0.964635	+	0.263588i	$0.0849059\pi$
$607$			12.9882i			0.527176i	−0.964635	+	0.263588i	$0.915094\pi$
$608$	−4.32963	+	0.504306i	−0.175590	+	0.0204523i
$609$	−16.9864			−0.688324
$610$	−2.33551	+	1.75853i	−0.0945621	+	0.0712009i
$611$	−10.2137	+	17.6907i	−0.413204	+	0.715690i
$612$	0.0812933	−	0.0469347i	0.00328609	−	0.00189722i
$613$	23.2303	+	13.4120i	0.938264	+	0.541707i	0.889416	−	0.457099i	$-0.151112\pi$
$613$	23.2303	+	13.4120i	0.938264	+	0.541707i	0.0488484	+	0.998806i	$0.484445\pi$
$614$	12.7483	+	22.0807i	0.514480	+	0.891105i
$615$	15.9749	+	6.78818i	0.644172	+	0.273726i
$616$	−5.93355			−0.239069
$617$	−11.9663	+	6.90877i	−0.481747	+	0.278136i	−0.721144	−	0.692785i	$-0.756383\pi$
$617$	−11.9663	+	6.90877i	−0.481747	+	0.278136i	0.239398	+	0.970922i	$0.423050\pi$
$618$	4.62282	−	2.66899i	0.185957	−	0.107362i
$619$	36.2091			1.45537			0.727684	−	0.685912i	$-0.240597\pi$
$619$	36.2091			1.45537			0.727684	+	0.685912i	$0.240597\pi$
$620$	3.73020	−	8.77846i	0.149808	−	0.352551i
$621$	−1.28274	−	2.22178i	−0.0514748	−	0.0891569i
$622$	26.2555	+	15.1586i	1.05275	+	0.607804i
$623$	5.68775	−	3.28383i	0.227875	−	0.131564i
$624$	2.53064	−	4.38320i	0.101307	−	0.175468i
$625$	−21.1809	−	13.2804i	−0.847236	−	0.531216i
$626$	−7.55247			−0.301857
$627$	3.82569	+	5.14308i	0.152783	+	0.205395i
$628$			16.2344i			0.647824i
$629$	0.0721890	−	0.125035i	0.00287837	−	0.00498547i
$630$	−5.42707	−	7.20770i	−0.216220	−	0.287162i
$631$	−1.00438	−	1.73963i	−0.0399836	−	0.0692536i	0.845341	−	0.534227i	$-0.179397\pi$
$631$	−1.00438	−	1.73963i	−0.0399836	−	0.0692536i	−0.885325	+	0.464973i	$0.846064\pi$
$632$	11.2256	+	6.48112i	0.446532	+	0.257805i
$633$	3.49822	−	2.01970i	0.139042	−	0.0802758i
$634$	14.0116			0.556471
$635$	−13.7184	−	5.82932i	−0.544399	−	0.231329i
$636$	−5.32873	−	9.22964i	−0.211298	−	0.365979i
$637$	40.6796	−	23.4864i	1.61178	−	0.930564i
$638$			6.19071i			0.245093i
$639$	8.67611			0.343222
$640$	−0.271659	−	2.21950i	−0.0107383	−	0.0877336i
$641$	−8.04795	+	13.9395i	−0.317875	+	0.550575i	−0.980044	−	0.198779i	$-0.936302\pi$
$641$	−8.04795	+	13.9395i	−0.317875	+	0.550575i	0.662170	+	0.749354i	$0.269636\pi$
$642$	−15.5257	+	8.96375i	−0.612749	+	0.353771i
$643$	34.6016	+	19.9773i	1.36455	+	0.787826i	0.990226	−	0.139470i	$-0.0445399\pi$
$643$	34.6016	+	19.9773i	1.36455	+	0.787826i	0.374328	+	0.927296i	$0.377873\pi$
$644$	5.17581	−	8.96476i	0.203955	−	0.353261i
$645$	−4.01084	+	9.43890i	−0.157927	+	0.371656i
$646$	−0.0473389	−	0.406420i	−0.00186252	−	0.0159904i
$647$		−	32.2985i		−	1.26979i	−0.772600	−	0.634893i	$-0.781044\pi$
$647$		−	32.2985i		−	1.26979i	0.772600	−	0.634893i	$-0.218956\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	4.52336	−	7.83470i	0.177558	−	0.307539i
$650$	−6.99400	+	24.3207i	−0.274327	+	0.953938i
$651$	−8.60569	+	14.9055i	−0.337283	+	0.584192i
$652$	1.78185	−	1.02875i	0.0697826	−	0.0402890i
$653$		−	25.3382i		−	0.991559i	−0.868448	−	0.495780i	$-0.834882\pi$
$653$		−	25.3382i		−	0.991559i	0.868448	−	0.495780i	$-0.165118\pi$
$654$	8.87262			0.346947
$655$	15.7045	−	1.92217i	0.613625	−	0.0751054i
$656$	−3.88123	−	6.72248i	−0.151536	−	0.262469i
$657$			12.7142i			0.496029i
$658$		−	16.2852i		−	0.634862i
$659$	2.44914	+	4.24204i	0.0954051	+	0.165247i	0.909778	−	0.415096i	$-0.136252\pi$
$659$	2.44914	+	4.24204i	0.0954051	+	0.165247i	−0.814372	+	0.580343i	$0.802919\pi$
$660$	−2.62685	+	1.97790i	−0.102250	+	0.0769896i
$661$	−24.1271	−	41.7893i	−0.938435	−	1.62542i	−0.768391	−	0.639980i	$-0.778942\pi$
$661$	−24.1271	−	41.7893i	−0.938435	−	1.62542i	−0.170044	−	0.985437i	$-0.554391\pi$
$662$	1.90994	+	1.10271i	0.0742320	+	0.0428579i
$663$	0.411448	+	0.237550i	0.0159793	+	0.00922567i
$664$	−2.06328			−0.0800709
$665$	−38.2216	+	9.26219i	−1.48217	+	0.359172i
$666$	1.53807			0.0595991
$667$	−9.35330	−	5.40013i	−0.362161	−	0.209094i
$668$	−18.8169	−	10.8639i	−0.728047	−	0.420338i
$669$	−9.02593	−	15.6334i	−0.348963	−	0.604421i
$670$	14.4622	+	19.2072i	0.558723	+	0.742040i
$671$	−0.961324	−	1.66506i	−0.0371115	−	0.0642790i
$672$			4.03495i			0.155651i
$673$			11.3374i			0.437025i	0.975834	+	0.218512i	$0.0701204\pi$
$673$			11.3374i			0.437025i	−0.975834	+	0.218512i	$0.929880\pi$
$674$	1.93428	+	3.35026i	0.0745055	+	0.129047i
$675$	−4.80525	−	1.38186i	−0.184954	−	0.0531880i
$676$	12.6166			0.485253
$677$			30.8182i			1.18444i	0.805776	+	0.592220i	$0.201748\pi$
$677$			30.8182i			1.18444i	−0.805776	+	0.592220i	$0.798252\pi$
$678$	−13.7409	+	7.93334i	−0.527718	+	0.304678i
$679$	−24.1063	+	41.7534i	−0.925116	+	1.60235i
$680$	0.208344	−	0.0255005i	0.00798961	−	0.000977899i
$681$	−13.4257	+	23.2539i	−0.514473	+	0.891093i
$682$	5.43231	+	3.13635i	0.208014	+	0.120097i
$683$		−	10.5683i		−	0.404386i	−0.979346	−	0.202193i	$-0.935193\pi$
$683$		−	10.5683i		−	0.404386i	0.979346	−	0.202193i	$-0.0648069\pi$
$684$	3.49741	−	2.60156i	0.133727	−	0.0994730i
$685$	−38.8063	−	16.4898i	−1.48271	−	0.630043i
$686$	−4.60145	+	7.96995i	−0.175684	+	0.304294i
$687$	11.8759	+	6.85657i	0.453095	+	0.261595i
$688$	3.97202	−	2.29325i	0.151432	−	0.0874292i
$689$	26.9702	−	46.7138i	1.02748	−	1.77965i
$690$	−0.696938	−	5.69412i	−0.0265320	−	0.216771i
$691$	−0.570970			−0.0217207			−0.0108604	−	0.999941i	$-0.503457\pi$
$691$	−0.570970			−0.0217207			−0.0108604	+	0.999941i	$0.503457\pi$
$692$		−	23.2053i		−	0.882132i
$693$	5.13860	−	2.96677i	0.195199	−	0.112698i
$694$	6.14337	+	10.6406i	0.233199	+	0.403913i
$695$	−17.4831	+	41.1438i	−0.663171	+	1.56067i
$696$	4.20982			0.159573
$697$	0.631035	−	0.364328i	0.0239022	−	0.0137999i
$698$	−20.0337	−	11.5665i	−0.758287	−	0.437797i
$699$	−0.00330537	−	0.00572506i	−0.000125020	−	0.000216542i
$700$	−4.86573	−	19.5792i	−0.183907	−	0.740024i
$701$	3.36247	−	5.82398i	0.126999	−	0.219969i	−0.795514	−	0.605936i	$-0.792799\pi$
$701$	3.36247	−	5.82398i	0.126999	−	0.219969i	0.922513	+	0.385967i	$0.126132\pi$
$702$			5.06128i			0.191026i
$703$	2.65790	−	6.15494i	0.100245	−	0.232138i
$704$	1.47054			0.0554230
$705$	−5.42852	−	7.20963i	−0.204450	−	0.271530i
$706$	−1.13608	+	1.96775i	−0.0427569	+	0.0740571i
$707$	1.76188	−	1.01722i	0.0662625	−	0.0382566i
$708$	−5.32777	−	3.07599i	−0.200230	−	0.115603i
$709$	−15.4517	−	26.7632i	−0.580302	−	1.00511i	−0.995443	−	0.0953554i	$-0.969601\pi$
$709$	−15.4517	−	26.7632i	−0.580302	−	1.00511i	0.415141	−	0.909757i	$-0.363732\pi$
$710$	17.8552	+	7.58716i	0.670095	+	0.284741i
$711$	−12.9622			−0.486122
$712$	−1.40962	+	0.813846i	−0.0528278	+	0.0305002i
$713$	−9.47717	+	5.47164i	−0.354923	+	0.204915i
$714$	−0.378758			−0.0141747
$715$	−15.3171	−	6.50866i	−0.572828	−	0.243410i
$716$	−3.18779	−	5.52142i	−0.119133	−	0.206345i
$717$	4.04866	+	2.33750i	0.151200	+	0.0872954i
$718$	17.9101	−	10.3404i	0.668400	−	0.385901i
$719$	−11.7185	+	20.2970i	−0.437025	+	0.756949i	−0.997458	−	0.0712504i	$-0.977301\pi$
$719$	−11.7185	+	20.2970i	−0.437025	+	0.756949i	0.560434	+	0.828199i	$0.310634\pi$
$720$	1.34502	+	1.78632i	0.0501258	+	0.0665721i
$721$	−21.5384			−0.802133
$722$	−4.36691	−	18.4914i	−0.162520	−	0.688177i
$723$			27.8087i			1.03422i
$724$	−4.39603	+	7.61415i	−0.163377	+	0.282978i
$725$	−20.4278	+	5.07661i	−0.758668	+	0.188541i
$726$	4.41876	+	7.65351i	0.163995	+	0.284049i
$727$	−34.0238	−	19.6436i	−1.26187	−	0.728543i	−0.288436	−	0.957499i	$-0.593135\pi$
$727$	−34.0238	−	19.6436i	−1.26187	−	0.728543i	−0.973437	+	0.228957i	$0.926469\pi$
$728$	−17.6860	+	10.2110i	−0.655486	+	0.378445i
$729$	−1.00000			−0.0370370
$730$	−11.1184	+	26.1656i	−0.411512	+	0.968432i
$731$	0.215266	+	0.372851i	0.00796189	+	0.0137904i
$732$	−1.13228	+	0.653722i	−0.0418503	+	0.0241623i
$733$			45.2875i			1.67273i	0.548171	+	0.836366i	$0.315324\pi$
$733$			45.2875i			1.67273i	−0.548171	+	0.836366i	$0.684676\pi$
$734$	−36.6899			−1.35425
$735$	2.52121	+	20.5988i	0.0929963	+	0.759797i
$736$	−1.28274	+	2.22178i	−0.0472826	+	0.0818959i
$737$	−13.6935	+	7.90592i	−0.504405	+	0.291218i
$738$	6.72248	+	3.88123i	0.247458	+	0.142870i
$739$	15.7422	−	27.2663i	0.579086	−	1.00301i	−0.416499	−	0.909136i	$-0.636743\pi$
$739$	15.7422	−	27.2663i	0.579086	−	1.00301i	0.995585	−	0.0938695i	$-0.0299237\pi$
$740$	3.16532	+	1.34503i	0.116359	+	0.0494442i
$741$	20.2538	+	8.74626i	0.744043	+	0.321302i
$742$			43.0023i			1.57866i
$743$	40.4415	+	23.3489i	1.48365	+	0.856587i	0.999827	−	0.0185770i	$-0.00591359\pi$
$743$	40.4415	+	23.3489i	1.48365	+	0.856587i	0.483826	+	0.875164i	$0.339247\pi$
$744$	2.13279	−	3.69410i	0.0781918	−	0.135432i
$745$	−27.0956	+	3.31640i	−0.992705	+	0.121503i
$746$	9.76898	−	16.9204i	0.357668	−	0.619499i
$747$	1.78686	−	1.03164i	0.0653776	−	0.0377458i
$748$			0.138039i			0.00504719i
$749$	72.3365			2.64312
$750$	−8.68068	−	7.04598i	−0.316973	−	0.257283i
$751$	−14.8807	−	25.7741i	−0.543004	−	0.940510i	−0.998730	−	0.0503901i	$-0.983954\pi$
$751$	−14.8807	−	25.7741i	−0.543004	−	0.940510i	0.455726	−	0.890120i	$-0.349380\pi$
$752$			4.03603i			0.147179i
$753$			6.06517i			0.221027i
$754$	10.6536	+	18.4525i	0.387980	+	0.672000i
$755$	−26.7804	−	35.5671i	−0.974639	−	1.29442i
$756$	−2.01747	−	3.49437i	−0.0733748	−	0.127089i
$757$	11.2784	+	6.51161i	0.409922	+	0.236668i	0.690756	−	0.723088i	$-0.257278\pi$
$757$	11.2784	+	6.51161i	0.409922	+	0.236668i	−0.280834	+	0.959756i	$0.590611\pi$
$758$	3.00339	+	1.73401i	0.109088	+	0.0629820i
$759$	3.77265			0.136939
$760$	9.47263	−	2.29549i	0.343608	−	0.0832662i
$761$	43.4538			1.57520			0.787600	−	0.616187i	$-0.211324\pi$
$761$	43.4538			1.57520			0.787600	+	0.616187i	$0.211324\pi$
$762$	−5.77290	−	3.33298i	−0.209130	−	0.120741i
$763$	−31.0042	−	17.9003i	−1.12243	−	0.648034i
$764$	6.48293	+	11.2288i	0.234544	+	0.406242i
$765$	−0.167681	+	0.126256i	−0.00606251	+	0.00456479i
$766$	−12.5509	−	21.7388i	−0.453483	−	0.785456i
$767$		−	31.1369i		−	1.12429i
$768$		−	1.00000i		−	0.0360844i
$769$	−23.6418	−	40.9487i	−0.852544	−	1.47665i	−0.878905	−	0.476996i	$-0.841725\pi$
$769$	−23.6418	−	40.9487i	−0.852544	−	1.47665i	0.0263617	−	0.999652i	$-0.491608\pi$
$770$	13.1695	−	1.61190i	0.474597	−	0.0580889i
$771$	−1.28988			−0.0464539
$772$		−	6.11656i		−	0.220140i
$773$	−11.4692	+	6.62172i	−0.412517	+	0.238167i	−0.691871	−	0.722022i	$-0.743213\pi$
$773$	−11.4692	+	6.62172i	−0.412517	+	0.238167i	0.279354	+	0.960188i	$0.409880\pi$
$774$	−2.29325	+	3.97202i	−0.0824290	+	0.142771i
$775$	−5.89445	+	20.4972i

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34502 - 1.78632i) q^{5} +(-0.500000 - 0.866025i) q^{6} +4.03495i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34502 - 1.78632i) q^{5} +(-0.500000 - 0.866025i) q^{6} +4.03495i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.271659 + 2.21950i) q^{10} -1.47054 q^{11} +1.00000i q^{12} +(-4.38320 + 2.53064i) q^{13} +(2.01747 - 3.49437i) q^{14} +(-0.271659 - 2.21950i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0812933 - 0.0469347i) q^{17} -1.00000i q^{18} +(-4.00172 - 1.72807i) q^{19} +(0.874489 - 2.05798i) q^{20} +(-2.01747 + 3.49437i) q^{21} +(1.27352 + 0.735269i) q^{22} +(-2.22178 + 1.28274i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.38186 + 4.80525i) q^{25} +5.06128 q^{26} +1.00000i q^{27} +(-3.49437 + 2.01747i) q^{28} +(2.10491 + 3.64581i) q^{29} +(-0.874489 + 2.05798i) q^{30} +4.26558 q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.27352 - 0.735269i) q^{33} +(0.0469347 + 0.0812933i) q^{34} +(7.20770 - 5.42707i) q^{35} +(-0.500000 + 0.866025i) q^{36} +1.53807i q^{37} +(2.60156 + 3.49741i) q^{38} -5.06128 q^{39} +(-1.78632 + 1.34502i) q^{40} +(-3.88123 + 6.72248i) q^{41} +(3.49437 - 2.01747i) q^{42} +(-3.97202 - 2.29325i) q^{43} +(-0.735269 - 1.27352i) q^{44} +(0.874489 - 2.05798i) q^{45} +2.56549 q^{46} +(3.49530 - 2.01801i) q^{47} +(-0.866025 + 0.500000i) q^{48} -9.28080 q^{49} +(3.59936 - 3.47054i) q^{50} +(-0.0469347 - 0.0812933i) q^{51} +(-4.38320 - 2.53064i) q^{52} +(-9.22964 + 5.32873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.97790 + 2.62685i) q^{55} +4.03495 q^{56} +(-2.60156 - 3.49741i) q^{57} -4.20982i q^{58} +(-3.07599 + 5.32777i) q^{59} +(1.78632 - 1.34502i) q^{60} +(0.653722 + 1.13228i) q^{61} +(-3.69410 - 2.13279i) q^{62} +(-3.49437 + 2.01747i) q^{63} -1.00000 q^{64} +(10.4160 + 4.42603i) q^{65} +(0.735269 + 1.27352i) q^{66} +(9.31187 - 5.37621i) q^{67} -0.0938694i q^{68} -2.56549 q^{69} +(-8.95558 + 1.09613i) q^{70} +(4.33806 - 7.51373i) q^{71} +(0.866025 - 0.500000i) q^{72} +(11.0108 + 6.35711i) q^{73} +(0.769037 - 1.33201i) q^{74} +(-3.59936 + 3.47054i) q^{75} +(-0.504306 - 4.32963i) q^{76} -5.93355i q^{77} +(4.38320 + 2.53064i) q^{78} +(-6.48112 + 11.2256i) q^{79} +(2.21950 - 0.271659i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.72248 - 3.88123i) q^{82} -2.06328i q^{83} -4.03495 q^{84} +(0.0255005 + 0.208344i) q^{85} +(2.29325 + 3.97202i) q^{86} +4.20982i q^{87} +1.47054i q^{88} +(-0.813846 - 1.40962i) q^{89} +(-1.78632 + 1.34502i) q^{90} +(-10.2110 - 17.6860i) q^{91} +(-2.22178 - 1.28274i) q^{92} +(3.69410 + 2.13279i) q^{93} -4.03603 q^{94} +(2.29549 + 9.47263i) q^{95} +1.00000 q^{96} +(10.3479 + 5.97438i) q^{97} +(8.03741 + 4.64040i) q^{98} +(-0.735269 - 1.27352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20q + 10q^{4} - 10q^{6} + 10q^{9} + O(q^{10}) \)	\( 20q + 10q^{4} - 10q^{6} + 10q^{9} - 2q^{10} + 12q^{11} + 10q^{14} + 2q^{15} - 10q^{16} + 6q^{19} - 10q^{21} + 10q^{24} + 14q^{25} + 8q^{29} + 40q^{31} + 12q^{34} + 2q^{35} - 10q^{36} + 2q^{40} - 14q^{41} + 6q^{44} + 44q^{46} - 8q^{49} - 8q^{50} - 12q^{51} + 10q^{54} + 20q^{56} + 8q^{59} - 2q^{60} + 16q^{61} - 20q^{64} + 40q^{65} - 6q^{66} - 44q^{69} + 8q^{70} - 4q^{71} + 26q^{74} + 8q^{75} + 8q^{79} - 10q^{81} - 20q^{84} - 16q^{85} - 20q^{86} - 2q^{89} + 2q^{90} - 44q^{91} - 32q^{94} - 80q^{95} + 20q^{96} + 6q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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