LMFDB - Embedded newform 930.2.o.e.161.8

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.8
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.18

$q$-expansion

$f(q)$	$=$	$q-1.00000i q^{2} +(1.29636 + 1.14867i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.14867 - 1.29636i) q^{6} +(1.71736 + 2.97455i) q^{7} +1.00000i q^{8} +(0.361105 + 2.97819i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.29636 + 1.14867i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.14867 - 1.29636i) q^{6} +(1.71736 + 2.97455i) q^{7} +1.00000i q^{8} +(0.361105 + 2.97819i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.402897 - 0.697837i) q^{11} +(-1.29636 - 1.14867i) q^{12} +(-2.61618 - 1.51045i) q^{13} +(2.97455 - 1.71736i) q^{14} +(0.548346 + 1.64296i) q^{15} +1.00000 q^{16} +(1.94308 + 3.36552i) q^{17} +(2.97819 - 0.361105i) q^{18} +(-1.37995 - 2.39014i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.19047 + 5.82877i) q^{21} +(-0.697837 - 0.402897i) q^{22} -0.142267 q^{23} +(-1.14867 + 1.29636i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.51045 + 2.61618i) q^{26} +(-2.95284 + 4.27560i) q^{27} +(-1.71736 - 2.97455i) q^{28} +7.20137 q^{29} +(1.64296 - 0.548346i) q^{30} +(-1.97991 + 5.20384i) q^{31} -1.00000i q^{32} +(1.32389 - 0.441853i) q^{33} +(3.36552 - 1.94308i) q^{34} +3.43472i q^{35} +(-0.361105 - 2.97819i) q^{36} +(-9.28550 + 5.36099i) q^{37} +(-2.39014 + 1.37995i) q^{38} +(-1.65650 - 4.96323i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.634427 - 0.366287i) q^{41} +(5.82877 + 1.19047i) q^{42} +(-0.711673 + 0.410885i) q^{43} +(-0.402897 + 0.697837i) q^{44} +(-1.17637 + 2.75974i) q^{45} +0.142267i q^{46} +4.88227i q^{47} +(1.29636 + 1.14867i) q^{48} +(-2.39863 + 4.15456i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-1.34694 + 6.59489i) q^{51} +(2.61618 + 1.51045i) q^{52} +(6.79605 - 11.7711i) q^{53} +(4.27560 + 2.95284i) q^{54} +(0.697837 - 0.402897i) q^{55} +(-2.97455 + 1.71736i) q^{56} +(0.956575 - 4.68359i) q^{57} -7.20137i q^{58} +(11.5957 - 6.69476i) q^{59} +(-0.548346 - 1.64296i) q^{60} -10.6269i q^{61} +(5.20384 + 1.97991i) q^{62} +(-8.23862 + 6.18874i) q^{63} -1.00000 q^{64} +(-1.51045 - 2.61618i) q^{65} +(-0.441853 - 1.32389i) q^{66} +(-0.342847 + 0.593829i) q^{67} +(-1.94308 - 3.36552i) q^{68} +(-0.184430 - 0.163418i) q^{69} +3.43472 q^{70} +(9.83676 + 5.67926i) q^{71} +(-2.97819 + 0.361105i) q^{72} +(0.721718 + 0.416684i) q^{73} +(5.36099 + 9.28550i) q^{74} +(-0.346599 + 1.69702i) q^{75} +(1.37995 + 2.39014i) q^{76} +2.76767 q^{77} +(-4.96323 + 1.65650i) q^{78} +(2.81725 - 1.62654i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-8.73921 + 2.15088i) q^{81} +(-0.366287 + 0.634427i) q^{82} +(0.934238 - 1.61815i) q^{83} +(1.19047 - 5.82877i) q^{84} +3.88616i q^{85} +(0.410885 + 0.711673i) q^{86} +(9.33558 + 8.27202i) q^{87} +(0.697837 + 0.402897i) q^{88} -7.24740 q^{89} +(2.75974 + 1.17637i) q^{90} -10.3760i q^{91} +0.142267 q^{92} +(-8.54419 + 4.47178i) q^{93} +4.88227 q^{94} -2.75989i q^{95} +(1.14867 - 1.29636i) q^{96} +16.1867 q^{97} +(4.15456 + 2.39863i) q^{98} +(2.22378 + 0.947909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) $	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.29636	+	1.14867i	0.748454	+	0.663186i
$3$	1.29636	+	1.14867i	0.748454	+	0.663186i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	1.14867	−	1.29636i	0.468943	−	0.529237i
$7$	1.71736	+	2.97455i	0.649100	+	1.12427i	0.983338	+	0.181786i	$0.0581877\pi$
$7$	1.71736	+	2.97455i	0.649100	+	1.12427i	−0.334238	+	0.942489i	$0.608479\pi$
$8$			1.00000i			0.353553i
$9$	0.361105	+	2.97819i	0.120368	+	0.992729i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.402897	−	0.697837i	0.121478	−	0.210406i	−0.798873	−	0.601500i	$-0.794570\pi$
$11$	0.402897	−	0.697837i	0.121478	−	0.210406i	0.920351	+	0.391094i	$0.127903\pi$
$12$	−1.29636	−	1.14867i	−0.374227	−	0.331593i
$13$	−2.61618	−	1.51045i	−0.725599	−	0.418925i	0.0912110	−	0.995832i	$-0.470926\pi$
$13$	−2.61618	−	1.51045i	−0.725599	−	0.418925i	−0.816810	+	0.576907i	$0.804260\pi$
$14$	2.97455	−	1.71736i	0.794982	−	0.458983i
$15$	0.548346	+	1.64296i	0.141582	+	0.424210i
$16$	1.00000			0.250000
$17$	1.94308	+	3.36552i	0.471267	+	0.816258i	0.999460	−	0.0328666i	$-0.0104637\pi$
$17$	1.94308	+	3.36552i	0.471267	+	0.816258i	−0.528193	+	0.849124i	$0.677130\pi$
$18$	2.97819	−	0.361105i	0.701966	−	0.0851132i
$19$	−1.37995	−	2.39014i	−0.316581	−	0.548335i	0.663191	−	0.748450i	$-0.269202\pi$
$19$	−1.37995	−	2.39014i	−0.316581	−	0.548335i	−0.979772	+	0.200115i	$0.935868\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−1.19047	+	5.82877i	−0.259781	+	1.27194i
$22$	−0.697837	−	0.402897i	−0.148779	−	0.0858978i
$23$	−0.142267			−0.0296648			−0.0148324	−	0.999890i	$-0.504721\pi$
$23$	−0.142267			−0.0296648			−0.0148324	+	0.999890i	$0.504721\pi$
$24$	−1.14867	+	1.29636i	−0.234472	+	0.264619i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.51045	+	2.61618i	−0.296225	+	0.513076i
$27$	−2.95284	+	4.27560i	−0.568274	+	0.822839i
$28$	−1.71736	−	2.97455i	−0.324550	−	0.562137i
$29$	7.20137			1.33726			0.668631	−	0.743595i	$-0.266881\pi$
$29$	7.20137			1.33726			0.668631	+	0.743595i	$0.266881\pi$
$30$	1.64296	−	0.548346i	0.299962	−	0.100114i
$31$	−1.97991	+	5.20384i	−0.355603	+	0.934637i
$31$	−1.97991	+	5.20384i	−0.355603	+	0.934637i
$32$		−	1.00000i		−	0.176777i
$33$	1.32389	−	0.441853i	0.230459	−	0.0769168i
$34$	3.36552	−	1.94308i	0.577181	−	0.333236i
$35$			3.43472i			0.580573i
$36$	−0.361105	−	2.97819i	−0.0601841	−	0.496365i
$37$	−9.28550	+	5.36099i	−1.52653	+	0.881341i	−0.527024	+	0.849851i	$0.676692\pi$
$37$	−9.28550	+	5.36099i	−1.52653	+	0.881341i	−0.999504	+	0.0314905i	$0.989975\pi$
$38$	−2.39014	+	1.37995i	−0.387732	+	0.223857i
$39$	−1.65650	−	4.96323i	−0.265253	−	0.794753i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−0.634427	−	0.366287i	−0.0990809	−	0.0572044i	0.449641	−	0.893209i	$-0.351552\pi$
$41$	−0.634427	−	0.366287i	−0.0990809	−	0.0572044i	−0.548722	+	0.836005i	$0.684885\pi$
$42$	5.82877	+	1.19047i	0.899399	+	0.183693i
$43$	−0.711673	+	0.410885i	−0.108529	+	0.0626594i	−0.553282	−	0.832994i	$-0.686625\pi$
$43$	−0.711673	+	0.410885i	−0.108529	+	0.0626594i	0.444753	+	0.895653i	$0.353291\pi$
$44$	−0.402897	+	0.697837i	−0.0607389	+	0.105203i
$45$	−1.17637	+	2.75974i	−0.175363	+	0.411398i
$46$			0.142267i			0.0209761i
$47$			4.88227i			0.712152i	0.934457	+	0.356076i	$0.115886\pi$
$47$			4.88227i			0.712152i	−0.934457	+	0.356076i	$0.884114\pi$
$48$	1.29636	+	1.14867i	0.187114	+	0.165797i
$49$	−2.39863	+	4.15456i	−0.342662	+	0.593508i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−1.34694	+	6.59489i	−0.188609	+	0.923469i
$52$	2.61618	+	1.51045i	0.362799	+	0.209462i
$53$	6.79605	−	11.7711i	0.933509	−	1.61688i	0.156237	−	0.987720i	$-0.450064\pi$
$53$	6.79605	−	11.7711i	0.933509	−	1.61688i	0.777272	−	0.629165i	$-0.216603\pi$
$54$	4.27560	+	2.95284i	0.581835	+	0.401831i
$55$	0.697837	−	0.402897i	0.0940964	−	0.0543266i
$56$	−2.97455	+	1.71736i	−0.397491	+	0.229492i
$57$	0.956575	−	4.68359i	0.126701	−	0.620356i
$58$		−	7.20137i		−	0.945587i
$59$	11.5957	−	6.69476i	1.50963	−	0.871584i	0.509690	−	0.860358i	$-0.329760\pi$
$59$	11.5957	−	6.69476i	1.50963	−	0.871584i	0.999937	−	0.0112259i	$-0.00357339\pi$
$60$	−0.548346	−	1.64296i	−0.0707911	−	0.212105i
$61$		−	10.6269i		−	1.36064i	−0.732916	−	0.680319i	$-0.761841\pi$
$61$		−	10.6269i		−	1.36064i	0.732916	−	0.680319i	$-0.238159\pi$
$62$	5.20384	+	1.97991i	0.660888	+	0.251449i
$63$	−8.23862	+	6.18874i	−1.03797	+	0.779708i
$64$	−1.00000			−0.125000
$65$	−1.51045	−	2.61618i	−0.187349	−	0.324498i
$66$	−0.441853	−	1.32389i	−0.0543884	−	0.162959i
$67$	−0.342847	+	0.593829i	−0.0418854	+	0.0725477i	−0.886208	−	0.463287i	$-0.846670\pi$
$67$	−0.342847	+	0.593829i	−0.0418854	+	0.0725477i	0.844323	+	0.535835i	$0.180003\pi$
$68$	−1.94308	−	3.36552i	−0.235633	−	0.408129i
$69$	−0.184430	−	0.163418i	−0.0222027	−	0.0196733i
$70$	3.43472			0.410527
$71$	9.83676	+	5.67926i	1.16741	+	0.674004i	0.953068	−	0.302755i	$-0.0979065\pi$
$71$	9.83676	+	5.67926i	1.16741	+	0.674004i	0.214340	+	0.976759i	$0.431240\pi$
$72$	−2.97819	+	0.361105i	−0.350983	+	0.0425566i
$73$	0.721718	+	0.416684i	0.0844707	+	0.0487692i	0.541640	−	0.840610i	$-0.317803\pi$
$73$	0.721718	+	0.416684i	0.0844707	+	0.0487692i	−0.457170	+	0.889380i	$0.651137\pi$
$74$	5.36099	+	9.28550i	0.623202	+	1.07942i
$75$	−0.346599	+	1.69702i	−0.0400218	+	0.195955i
$76$	1.37995	+	2.39014i	0.158291	+	0.274168i
$77$	2.76767			0.315405
$78$	−4.96323	+	1.65650i	−0.561975	+	0.187562i
$79$	2.81725	−	1.62654i	0.316966	−	0.183000i	−0.333074	−	0.942901i	$-0.608086\pi$
$79$	2.81725	−	1.62654i	0.316966	−	0.183000i	0.650039	+	0.759901i	$0.274752\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	−8.73921	+	2.15088i	−0.971023	+	0.238986i
$82$	−0.366287	+	0.634427i	−0.0404496	+	0.0700608i
$83$	0.934238	−	1.61815i	0.102546	−	0.177615i	−0.810187	−	0.586172i	$-0.800634\pi$
$83$	0.934238	−	1.61815i	0.102546	−	0.177615i	0.912733	+	0.408557i	$0.133968\pi$
$84$	1.19047	−	5.82877i	0.129891	−	0.635971i
$85$			3.88616i			0.421514i
$86$	0.410885	+	0.711673i	0.0443069	+	0.0767417i
$87$	9.33558	+	8.27202i	1.00088	+	0.886853i
$88$	0.697837	+	0.402897i	0.0743897	+	0.0429489i
$89$	−7.24740			−0.768222			−0.384111	−	0.923287i	$-0.625492\pi$
$89$	−7.24740			−0.768222			−0.384111	+	0.923287i	$0.625492\pi$
$90$	2.75974	+	1.17637i	0.290902	+	0.124000i
$91$		−	10.3760i		−	1.08770i
$92$	0.142267			0.0148324
$93$	−8.54419	+	4.47178i	−0.885991	+	0.463702i
$94$	4.88227			0.503567
$95$		−	2.75989i		−	0.283159i
$96$	1.14867	−	1.29636i	0.117236	−	0.132309i
$97$	16.1867			1.64351			0.821755	−	0.569841i	$-0.192995\pi$
$97$	16.1867			1.64351			0.821755	+	0.569841i	$0.192995\pi$
$98$	4.15456	+	2.39863i	0.419674	+	0.242299i
$99$	2.22378	+	0.947909i	0.223498	+	0.0952685i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			3.07118i			0.305594i	0.988258	+	0.152797i	$0.0488281\pi$
$101$			3.07118i			0.305594i	−0.988258	+	0.152797i	$0.951172\pi$
$102$	6.59489	+	1.34694i	0.652991	+	0.133367i
$103$	−0.368713	+	0.638630i	−0.0363304	+	0.0629261i	−0.883619	−	0.468207i	$-0.844900\pi$
$103$	−0.368713	+	0.638630i	−0.0363304	+	0.0629261i	0.847288	+	0.531133i	$0.178234\pi$
$104$	1.51045	−	2.61618i	0.148112	−	0.256538i
$105$	−3.94536	+	4.45263i	−0.385028	+	0.434532i
$106$	−11.7711	−	6.79605i	−1.14331	−	0.660090i
$107$	−1.85660	+	1.07191i	−0.179484	+	0.103625i	−0.587050	−	0.809551i	$-0.699711\pi$
$107$	−1.85660	+	1.07191i	−0.179484	+	0.103625i	0.407566	+	0.913176i	$0.366378\pi$
$108$	2.95284	−	4.27560i	0.284137	−	0.411420i
$109$	−14.2883			−1.36857			−0.684284	−	0.729216i	$-0.739885\pi$
$109$	−14.2883			−1.36857			−0.684284	+	0.729216i	$0.739885\pi$
$110$	−0.402897	−	0.697837i	−0.0384147	−	0.0665362i
$111$	−18.1954	−	3.71622i	−1.72703	−	0.352728i
$112$	1.71736	+	2.97455i	0.162275	+	0.281069i
$113$	−13.2560	−	7.65337i	−1.24702	−	0.719968i	−0.276508	−	0.961012i	$-0.589177\pi$
$113$	−13.2560	−	7.65337i	−1.24702	−	0.719968i	−0.970514	+	0.241043i	$0.922510\pi$
$114$	−4.68359	−	0.956575i	−0.438658	−	0.0895915i
$115$	−0.123207	−	0.0711336i	−0.0114891	−	0.00663324i
$116$	−7.20137			−0.668631
$117$	3.55370	−	8.33692i	0.328540	−	0.770749i
$118$	−6.69476	−	11.5957i	−0.616303	−	1.06747i
$119$	−6.67393	+	11.5596i	−0.611798	+	1.05967i
$120$	−1.64296	+	0.548346i	−0.149981	+	0.0500569i
$121$	5.17535	+	8.96397i	0.470486	+	0.814906i
$122$	−10.6269			−0.962117
$123$	−0.401704	−	1.20359i	−0.0362204	−	0.108524i
$124$	1.97991	−	5.20384i	0.177802	−	0.467319i
$125$			1.00000i			0.0894427i
$126$	6.18874	+	8.23862i	0.551337	+	0.733955i
$127$	9.01862	−	5.20690i	0.800273	−	0.462038i	−0.0432935	−	0.999062i	$-0.513785\pi$
$127$	9.01862	−	5.20690i	0.800273	−	0.462038i	0.843567	+	0.537024i	$0.180452\pi$
$128$			1.00000i			0.0883883i
$129$	−1.39456	−	0.284824i	−0.122784	−	0.0250774i
$130$	−2.61618	+	1.51045i	−0.229455	+	0.132476i
$131$	14.0976	−	8.13923i	1.23171	−	0.711128i	0.264323	−	0.964434i	$-0.414852\pi$
$131$	14.0976	−	8.13923i	1.23171	−	0.711128i	0.967386	+	0.253307i	$0.0815182\pi$
$132$	−1.32389	+	0.441853i	−0.115229	+	0.0384584i
$133$	4.73972	−	8.20944i	0.410986	−	0.711849i
$134$	0.593829	+	0.342847i	0.0512990	+	0.0296175i
$135$	−4.69503	+	2.22636i	−0.404084	+	0.191614i
$136$	−3.36552	+	1.94308i	−0.288591	+	0.166618i
$137$	3.25803	−	5.64307i	0.278352	−	0.482120i	−0.692623	−	0.721299i	$-0.743545\pi$
$137$	3.25803	−	5.64307i	0.278352	−	0.482120i	0.970975	+	0.239180i	$0.0768785\pi$
$138$	−0.163418	+	0.184430i	−0.0139111	+	0.0156997i
$139$		−	16.3232i		−	1.38452i	−0.721648	−	0.692260i	$-0.756615\pi$
$139$		−	16.3232i		−	1.38452i	0.721648	−	0.692260i	$-0.243385\pi$
$140$		−	3.43472i		−	0.290286i
$141$	−5.60812	+	6.32918i	−0.472289	+	0.533013i
$142$	5.67926	−	9.83676i	0.476593	−	0.825483i
$143$	−2.10810	+	1.21711i	−0.176288	+	0.101780i
$144$	0.361105	+	2.97819i	0.0300921	+	0.248182i
$145$	6.23657	+	3.60069i	0.517919	+	0.299021i
$146$	0.416684	−	0.721718i	0.0344850	−	0.0597298i
$147$	−7.88172	+	2.63056i	−0.650073	+	0.216965i
$148$	9.28550	−	5.36099i	0.763264	−	0.440671i
$149$	−2.68851	+	1.55221i	−0.220251	+	0.127162i	−0.606067	−	0.795414i	$-0.707253\pi$
$149$	−2.68851	+	1.55221i	−0.220251	+	0.127162i	0.385815	+	0.922576i	$0.373920\pi$
$150$	1.69702	+	0.346599i	0.138561	+	0.0282997i
$151$		−	19.8572i		−	1.61596i	−0.589212	−	0.807979i	$-0.700562\pi$
$151$		−	19.8572i		−	1.61596i	0.589212	−	0.807979i	$-0.299438\pi$
$152$	2.39014	−	1.37995i	0.193866	−	0.111928i
$153$	−9.32148	+	7.00217i	−0.753597	+	0.566092i
$154$		−	2.76767i		−	0.223025i
$155$	−4.31658	+	3.51670i	−0.346716	+	0.282468i
$156$	1.65650	+	4.96323i	0.132626	+	0.397377i
$157$	1.70330			0.135938			0.0679690	−	0.997687i	$-0.478348\pi$
$157$	1.70330			0.135938			0.0679690	+	0.997687i	$0.478348\pi$
$158$	−1.62654	−	2.81725i	−0.129401	−	0.224129i
$159$	22.3313	−	7.45317i	1.77098	−	0.591074i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.244324	−	0.423181i	−0.0192554	−	0.0333513i
$162$	2.15088	+	8.73921i	0.168989	+	0.686617i
$163$	2.96548			0.232274			0.116137	−	0.993233i	$-0.462949\pi$
$163$	2.96548			0.232274			0.116137	+	0.993233i	$0.462949\pi$
$164$	0.634427	+	0.366287i	0.0495405	+	0.0286022i
$165$	1.36745	+	0.279287i	0.106455	+	0.0217424i
$166$	−1.61815	−	0.934238i	−0.125593	−	0.0725109i
$167$	11.5431	+	19.9933i	0.893235	+	1.54713i	0.835974	+	0.548768i	$0.184903\pi$
$167$	11.5431	+	19.9933i	0.893235	+	1.54713i	0.0572603	+	0.998359i	$0.481764\pi$
$168$	−5.82877	−	1.19047i	−0.449700	−	0.0918466i
$169$	−1.93705	−	3.35507i	−0.149004	−	0.258083i
$170$	3.88616			0.298055
$171$	6.61997	−	4.97283i	0.506242	−	0.380282i
$172$	0.711673	−	0.410885i	0.0542646	−	0.0313297i
$173$	−11.7703	−	6.79559i	−0.894880	−	0.516659i	−0.0193444	−	0.999813i	$-0.506158\pi$
$173$	−11.7703	−	6.79559i	−0.894880	−	0.516659i	−0.875536	+	0.483154i	$0.839491\pi$
$174$	8.27202	−	9.33558i	0.627100	−	0.707729i
$175$	−1.71736	+	2.97455i	−0.129820	+	0.224855i
$176$	0.402897	−	0.697837i	0.0303695	−	0.0526015i
$177$	22.7223	+	4.64079i	1.70791	+	0.348823i
$178$			7.24740i			0.543215i
$179$	−1.61838	−	2.80311i	−0.120963	−	0.209514i	0.799185	−	0.601086i	$-0.205265\pi$
$179$	−1.61838	−	2.80311i	−0.120963	−	0.209514i	−0.920148	+	0.391571i	$0.871932\pi$
$180$	1.17637	−	2.75974i	0.0876813	−	0.205699i
$181$	−14.2426	−	8.22298i	−1.05865	−	0.611209i	−0.133588	−	0.991037i	$-0.542650\pi$
$181$	−14.2426	−	8.22298i	−1.05865	−	0.611209i	−0.925057	+	0.379827i	$0.875983\pi$
$182$	−10.3760			−0.769118
$183$	12.2069	−	13.7763i	0.902357	−	1.01838i
$184$		−	0.142267i		−	0.0104881i
$185$	−10.7220			−0.788295
$186$	4.47178	+	8.54419i	0.327887	+	0.626490i
$187$	3.13144			0.228994
$188$		−	4.88227i		−	0.356076i
$189$	−17.7891	−	1.44064i	−1.29396	−	0.104791i
$190$	−2.75989			−0.200224
$191$	−11.6288	−	6.71391i	−0.841433	−	0.485802i	0.0163179	−	0.999867i	$-0.494806\pi$
$191$	−11.6288	−	6.71391i	−0.841433	−	0.485802i	−0.857751	+	0.514065i	$0.828139\pi$
$192$	−1.29636	−	1.14867i	−0.0935568	−	0.0828983i
$193$	7.75886	+	13.4387i	0.558495	+	0.967341i	0.997622	+	0.0689165i	$0.0219542\pi$
$193$	7.75886	+	13.4387i	0.558495	+	0.967341i	−0.439128	+	0.898425i	$0.644712\pi$
$194$		−	16.1867i		−	1.16214i
$195$	1.04704	−	5.12654i	0.0749803	−	0.367119i
$196$	2.39863	−	4.15456i	0.171331	−	0.296754i
$197$	2.76263	−	4.78502i	0.196829	−	0.340918i	−0.750669	−	0.660678i	$-0.770269\pi$
$197$	2.76263	−	4.78502i	0.196829	−	0.340918i	0.947499	+	0.319760i	$0.103602\pi$
$198$	0.947909	−	2.22378i	0.0673650	−	0.158037i
$199$	−13.6901	−	7.90400i	−0.970467	−	0.560299i	−0.0710885	−	0.997470i	$-0.522647\pi$
$199$	−13.6901	−	7.90400i	−0.970467	−	0.560299i	−0.899379	+	0.437171i	$0.855981\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−1.12657	+	0.375997i	−0.0794620	+	0.0265208i
$202$	3.07118			0.216088
$203$	12.3673	+	21.4208i	0.868017	+	1.50345i
$204$	1.34694	−	6.59489i	0.0943046	−	0.461735i
$205$	−0.366287	−	0.634427i	−0.0255826	−	0.0443103i
$206$	0.638630	+	0.368713i	0.0444954	+	0.0256895i
$207$	−0.0513733	−	0.423698i	−0.00357069	−	0.0294491i
$208$	−2.61618	−	1.51045i	−0.181400	−	0.104731i
$209$	−2.22390			−0.153831
$210$	4.45263	+	3.94536i	0.307261	+	0.272256i
$211$	−8.66050	−	15.0004i	−0.596214	−	1.03267i	−0.993374	−	0.114923i	$-0.963338\pi$
$211$	−8.66050	−	15.0004i	−0.596214	−	1.03267i	0.397161	−	0.917749i	$-0.369996\pi$
$212$	−6.79605	+	11.7711i	−0.466754	+	0.808442i
$213$	6.22839	+	18.6616i	0.426762	+	1.27867i
$214$	1.07191	+	1.85660i	0.0732740	+	0.126914i
$215$	−0.821770			−0.0560442
$216$	−4.27560	−	2.95284i	−0.290918	−	0.200915i
$217$	−18.8793	+	3.04750i	−1.28161	+	0.206877i
$218$			14.2883i			0.967724i
$219$	0.456974	+	1.36919i	0.0308794	+	0.0925214i
$220$	−0.697837	+	0.402897i	−0.0470482	+	0.0271633i
$221$		−	11.7397i		−	0.789701i
$222$	−3.71622	+	18.1954i	−0.249417	+	1.22119i
$223$	0.150848	−	0.0870923i	0.0101016	−	0.00583213i	−0.494941	−	0.868927i	$-0.664810\pi$
$223$	0.150848	−	0.0870923i	0.0101016	−	0.00583213i	0.505042	+	0.863095i	$0.331477\pi$
$224$	2.97455	−	1.71736i	0.198746	−	0.114746i
$225$	−2.39863	+	1.80182i	−0.159909	+	0.120121i
$226$	−7.65337	+	13.2560i	−0.509095	+	0.881778i
$227$	−19.6588	−	11.3500i	−1.30480	−	0.753327i	−0.323577	−	0.946202i	$-0.604886\pi$
$227$	−19.6588	−	11.3500i	−1.30480	−	0.753327i	−0.981223	+	0.192875i	$0.938219\pi$
$228$	−0.956575	+	4.68359i	−0.0633507	+	0.310178i
$229$	4.32320	−	2.49600i	0.285685	−	0.164940i	−0.350309	−	0.936634i	$-0.613924\pi$
$229$	4.32320	−	2.49600i	0.285685	−	0.164940i	0.635994	+	0.771694i	$0.280590\pi$
$230$	−0.0711336	+	0.123207i	−0.00469041	+	0.00812403i
$231$	3.58790	+	3.17914i	0.236066	+	0.209172i
$232$			7.20137i			0.472793i
$233$		−	2.46821i		−	0.161698i	−0.996726	−	0.0808491i	$-0.974237\pi$
$233$		−	2.46821i		−	0.161698i	0.996726	−	0.0808491i	$-0.0257632\pi$
$234$	−8.33692	−	3.55370i	−0.545002	−	0.232313i
$235$	−2.44113	+	4.22817i	−0.159242	+	0.275815i
$236$	−11.5957	+	6.69476i	−0.754814	+	0.435792i
$237$	5.52054	+	1.12751i	0.358597	+	0.0732399i
$238$	11.5596	+	6.67393i	0.749297	+	0.432607i
$239$	−6.74918	+	11.6899i	−0.436568	+	0.756158i	−0.997422	−	0.0717566i	$-0.977140\pi$
$239$	−6.74918	+	11.6899i	−0.436568	+	0.756158i	0.560854	+	0.827915i	$0.310473\pi$
$240$	0.548346	+	1.64296i	0.0353956	+	0.106053i
$241$	−6.84964	+	3.95464i	−0.441224	+	0.254741i	−0.704117	−	0.710084i	$-0.748657\pi$
$241$	−6.84964	+	3.95464i	−0.441224	+	0.254741i	0.262892	+	0.964825i	$0.415324\pi$
$242$	8.96397	−	5.17535i	0.576226	−	0.332684i
$243$	−13.7998	−	7.25017i	−0.885259	−	0.465099i
$244$			10.6269i			0.680319i
$245$	−4.15456	+	2.39863i	−0.265425	+	0.153243i
$246$	−1.20359	+	0.401704i	−0.0767380	+	0.0256117i
$247$			8.33739i			0.530495i
$248$	−5.20384	−	1.97991i	−0.330444	−	0.125725i
$249$	3.06983	−	1.02457i	0.194543	−	0.0649295i
$250$	1.00000			0.0632456
$251$	−9.52107	−	16.4910i	−0.600965	−	1.04090i	−0.992675	−	0.120813i	$-0.961450\pi$
$251$	−9.52107	−	16.4910i	−0.600965	−	1.04090i	0.391711	−	0.920089i	$-0.371883\pi$
$252$	8.23862	−	6.18874i	0.518985	−	0.389854i
$253$	−0.0573189	+	0.0992793i	−0.00360361	+	0.00624164i
$254$	−5.20690	−	9.01862i	−0.326710	−	0.565879i
$255$	−4.46393	+	5.03787i	−0.279542	+	0.315484i
$256$	1.00000			0.0625000
$257$	−3.10579	−	1.79313i	−0.193734	−	0.111852i	0.399995	−	0.916517i	$-0.369012\pi$
$257$	−3.10579	−	1.79313i	−0.193734	−	0.111852i	−0.593729	+	0.804665i	$0.702345\pi$
$258$	−0.284824	+	1.39456i	−0.0177324	+	0.0868214i
$259$	−31.8931	−	18.4135i	−1.98174	−	1.14416i
$260$	1.51045	+	2.61618i	0.0936744	+	0.162249i
$261$	2.60045	+	21.4470i	0.160964	+	1.32754i
$262$	−8.13923	−	14.0976i	−0.502843	−	0.870950i
$263$	16.7103			1.03040			0.515200	−	0.857070i	$-0.327718\pi$
$263$	16.7103			1.03040			0.515200	+	0.857070i	$0.327718\pi$
$264$	0.441853	+	1.32389i	0.0271942	+	0.0814795i
$265$	11.7711	−	6.79605i	0.723093	−	0.417478i
$266$	−8.20944	−	4.73972i	−0.503353	−	0.290611i
$267$	−9.39524	−	8.32488i	−0.574979	−	0.509474i
$268$	0.342847	−	0.593829i	0.0209427	−	0.0362739i
$269$	−9.69936	+	16.7998i	−0.591381	+	1.02430i	0.402666	+	0.915347i	$0.368084\pi$
$269$	−9.69936	+	16.7998i	−0.591381	+	1.02430i	−0.994047	+	0.108954i	$0.965250\pi$
$270$	2.22636	+	4.69503i	0.135492	+	0.285731i
$271$			4.62368i			0.280869i	0.990090	+	0.140434i	$0.0448499\pi$
$271$			4.62368i			0.280869i	−0.990090	+	0.140434i	$0.955150\pi$
$272$	1.94308	+	3.36552i	0.117817	+	0.204064i
$273$	11.9186	−	13.4510i	0.721345	−	0.814091i
$274$	−5.64307	−	3.25803i	−0.340910	−	0.196825i
$275$	0.805793			0.0485911
$276$	0.184430	+	0.163418i	0.0111014	+	0.00983663i
$277$			23.9855i			1.44115i	0.693377	+	0.720575i	$0.256122\pi$
$277$			23.9855i			1.44115i	−0.693377	+	0.720575i	$0.743878\pi$
$278$	−16.3232			−0.979003
$279$	−16.2130	−	4.01743i	−0.970645	−	0.240517i
$280$	−3.43472			−0.205263
$281$		−	9.55099i		−	0.569764i	−0.958563	−	0.284882i	$-0.908046\pi$
$281$		−	9.55099i		−	0.569764i	0.958563	−	0.284882i	$-0.0919544\pi$
$282$	6.32918	+	5.60812i	0.376897	+	0.333959i
$283$	12.9772			0.771415			0.385708	−	0.922621i	$-0.373957\pi$
$283$	12.9772			0.771415			0.385708	+	0.922621i	$0.373957\pi$
$284$	−9.83676	−	5.67926i	−0.583704	−	0.337002i
$285$	3.17021	−	3.57782i	0.187787	−	0.211932i
$286$	1.21711	+	2.10810i	0.0719695	+	0.124655i
$287$		−	2.51618i		−	0.148525i
$288$	2.97819	−	0.361105i	0.175491	−	0.0212783i
$289$	0.948867	−	1.64349i	0.0558157	−	0.0966757i
$290$	3.60069	−	6.23657i	0.211440	−	0.366224i
$291$	20.9838	+	18.5932i	1.23009	+	1.08995i
$292$	−0.721718	−	0.416684i	−0.0422354	−	0.0243846i
$293$	14.6795	−	8.47522i	0.857586	−	0.495128i	−0.00561696	−	0.999984i	$-0.501788\pi$
$293$	14.6795	−	8.47522i	0.857586	−	0.495128i	0.863203	+	0.504857i	$0.168455\pi$
$294$	2.63056	+	7.88172i	0.153417	+	0.459671i
$295$	13.3895			0.779568
$296$	−5.36099	−	9.28550i	−0.311601	−	0.539709i
$297$	1.79398	+	3.78322i	0.104097	+	0.219525i
$298$	1.55221	+	2.68851i	0.0899171	+	0.155741i
$299$	0.372197	+	0.214888i	0.0215247	+	0.0124273i
$300$	0.346599	−	1.69702i	0.0200109	−	0.0979774i
$301$	−2.44440	−	1.41127i	−0.140893	−	0.0813444i
$302$	−19.8572			−1.14265
$303$	−3.52778	+	3.98136i	−0.202666	+	0.228723i
$304$	−1.37995	−	2.39014i	−0.0791454	−	0.137084i
$305$	5.31346	−	9.20319i	0.304248	−	0.526973i
$306$	7.00217	+	9.32148i	0.400287	+	0.532874i
$307$	10.7499	+	18.6193i	0.613527	+	1.06266i	0.990641	+	0.136493i	$0.0435831\pi$
$307$	10.7499	+	18.6193i	0.613527	+	1.06266i	−0.377114	+	0.926167i	$0.623084\pi$
$308$	−2.76767			−0.157703
$309$	−1.21156	+	0.404364i	−0.0689233	+	0.0230035i
$310$	3.51670	+	4.31658i	0.199735	+	0.245165i
$311$		−	0.500059i		−	0.0283557i	−0.999899	−	0.0141779i	$-0.995487\pi$
$311$		−	0.500059i		−	0.0283557i	0.999899	−	0.0141779i	$-0.00451310\pi$
$312$	4.96323	−	1.65650i	0.280988	−	0.0937810i
$313$	−13.0279	+	7.52167i	−0.736381	+	0.425150i	−0.820752	−	0.571284i	$-0.806445\pi$
$313$	−13.0279	+	7.52167i	−0.736381	+	0.425150i	0.0843707	+	0.996434i	$0.473112\pi$
$314$		−	1.70330i		−	0.0961226i
$315$	−10.2292	+	1.24029i	−0.576352	+	0.0698825i
$316$	−2.81725	+	1.62654i	−0.158483	+	0.0915001i
$317$	−8.13168	+	4.69483i	−0.456721	+	0.263688i	−0.710664	−	0.703531i	$-0.751606\pi$
$317$	−8.13168	+	4.69483i	−0.456721	+	0.263688i	0.253944	+	0.967219i	$0.418272\pi$
$318$	−7.45317	−	22.3313i	−0.417953	−	1.25228i
$319$	2.90141	−	5.02539i	0.162448	−	0.281368i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−3.63809	−	0.743042i	−0.203058	−	0.0414726i
$322$	−0.423181	+	0.244324i	−0.0235829	+	0.0136156i
$323$	5.36270	−	9.28847i	0.298389	−	0.516824i
$324$	8.73921	−	2.15088i	0.485511	−	0.119493i
$325$		−	3.02091i		−	0.167570i
$326$		−	2.96548i		−	0.164243i
$327$	−18.5228	−	16.4125i	−1.02431	−	0.907615i
$328$	0.366287	−	0.634427i	0.0202248	−	0.0350304i
$329$	−14.5225	+	8.38460i	−0.800654	+	0.462258i
$330$	0.279287	−	1.36745i	0.0153742	−	0.0752754i
$331$	19.1463	+	11.0541i	1.05238	+	0.607591i	0.923314	−	0.384045i	$-0.125469\pi$
$331$	19.1463	+	11.0541i	1.05238	+	0.607591i	0.129064	+	0.991636i	$0.458803\pi$
$332$	−0.934238	+	1.61815i	−0.0512730	+	0.0888074i
$333$	−19.3191	−	25.7181i	−1.05868	−	1.40934i
$334$	19.9933	−	11.5431i	1.09398	−	0.631612i
$335$	−0.593829	+	0.342847i	−0.0324443	+	0.0187317i
$336$	−1.19047	+	5.82877i	−0.0649453	+	0.317986i
$337$			1.64170i			0.0894289i	0.999000	+	0.0447145i	$0.0142378\pi$
$337$			1.64170i			0.0894289i	−0.999000	+	0.0447145i	$0.985762\pi$
$338$	−3.35507	+	1.93705i	−0.182492	+	0.105362i
$339$	−8.39338	−	25.1484i	−0.455866	−	1.36587i
$340$		−	3.88616i		−	0.210757i
$341$	2.83373	+	3.47827i	0.153455	+	0.188359i
$342$	−4.97283	−	6.61997i	−0.268900	−	0.357967i
$343$	7.56576			0.408512
$344$	−0.410885	−	0.711673i	−0.0221534	−	0.0383709i
$345$	−0.0780116	−	0.233739i	−0.00420000	−	0.0125841i
$346$	−6.79559	+	11.7703i	−0.365333	+	0.632776i
$347$	4.05019	+	7.01513i	0.217425	+	0.376592i	0.954020	−	0.299743i	$-0.0969008\pi$
$347$	4.05019	+	7.01513i	0.217425	+	0.376592i	−0.736595	+	0.676334i	$0.763567\pi$
$348$	−9.33558	−	8.27202i	−0.500440	−	0.443427i
$349$	10.2078			0.546409			0.273205	−	0.961956i	$-0.411916\pi$
$349$	10.2078			0.546409			0.273205	+	0.961956i	$0.411916\pi$
$350$	2.97455	+	1.71736i	0.158996	+	0.0917966i
$351$	14.1833	−	6.72562i	0.757047	−	0.358987i
$352$	−0.697837	−	0.402897i	−0.0371948	−	0.0214745i
$353$	−2.18441	−	3.78351i	−0.116265	−	0.201376i	0.802020	−	0.597297i	$-0.203759\pi$
$353$	−2.18441	−	3.78351i	−0.116265	−	0.201376i	−0.918285	+	0.395921i	$0.870425\pi$
$354$	4.64079	−	22.7223i	0.246655	−	1.20767i
$355$	5.67926	+	9.83676i	0.301424	+	0.522081i
$356$	7.24740			0.384111
$357$	−21.9300	+	7.31924i	−1.16066	+	0.387375i
$358$	−2.80311	+	1.61838i	−0.148149	+	0.0855339i
$359$	−5.77578	−	3.33465i	−0.304834	−	0.175996i	0.339778	−	0.940506i	$-0.389648\pi$
$359$	−5.77578	−	3.33465i	−0.304834	−	0.175996i	−0.644612	+	0.764509i	$0.722981\pi$
$360$	−2.75974	−	1.17637i	−0.145451	−	0.0620000i
$361$	5.69149	−	9.85796i	0.299552	−	0.518840i
$362$	−8.22298	+	14.2426i	−0.432190	+	0.748576i
$363$	−3.58754	+	17.5653i	−0.188297	+	0.921940i
$364$			10.3760i			0.543848i
$365$	0.416684	+	0.721718i	0.0218103	+	0.0377765i
$366$	−13.7763	−	12.2069i	−0.720100	−	0.638062i
$367$	12.6325	+	7.29338i	0.659411	+	0.380711i	0.792053	−	0.610453i	$-0.209013\pi$
$367$	12.6325	+	7.29338i	0.659411	+	0.380711i	−0.132642	+	0.991164i	$0.542346\pi$
$368$	−0.142267			−0.00741619
$369$	0.861776	−	2.02171i	0.0448623	−	0.105246i
$370$			10.7220i			0.557409i
$371$	46.6850			2.42376
$372$	8.54419	−	4.47178i	0.442996	−	0.231851i
$373$	−21.3294			−1.10439			−0.552197	−	0.833714i	$-0.686210\pi$
$373$	−21.3294			−1.10439			−0.552197	+	0.833714i	$0.686210\pi$
$374$		−	3.13144i		−	0.161923i
$375$	−1.14867	+	1.29636i	−0.0593172	+	0.0669438i
$376$	−4.88227			−0.251784
$377$	−18.8401	−	10.8773i	−0.970316	−	0.560212i
$378$	−1.44064	+	17.7891i	−0.0740985	+	0.914971i
$379$	−15.6454	−	27.0986i	−0.803650	−	1.39196i	−0.917199	−	0.398430i	$-0.869555\pi$
$379$	−15.6454	−	27.0986i	−0.803650	−	1.39196i	0.113549	−	0.993532i	$-0.463778\pi$
$380$			2.75989i			0.141580i
$381$	17.6724	+	3.60941i	0.905385	+	0.184916i
$382$	−6.71391	+	11.6288i	−0.343514	+	0.594983i
$383$	11.8065	−	20.4494i	0.603282	−	1.04491i	−0.389039	−	0.921221i	$-0.627193\pi$
$383$	11.8065	−	20.4494i	0.603282	−	1.04491i	0.992320	−	0.123693i	$-0.0394739\pi$
$384$	−1.14867	+	1.29636i	−0.0586179	+	0.0661547i
$385$	2.39687	+	1.38383i	0.122156	+	0.0705268i
$386$	13.4387	−	7.75886i	0.684013	−	0.394915i
$387$	−1.48068	−	1.97112i	−0.0752672	−	0.100198i
$388$	−16.1867			−0.821755
$389$	12.7612	+	22.1030i	0.647018	+	1.12067i	0.983832	+	0.179096i	$0.0573173\pi$
$389$	12.7612	+	22.1030i	0.647018	+	1.12067i	−0.336814	+	0.941571i	$0.609349\pi$
$390$	−5.12654	−	1.04704i	−0.259592	−	0.0530191i
$391$	−0.276437	−	0.478802i	−0.0139800	−	0.0242141i
$392$	−4.15456	−	2.39863i	−0.209837	−	0.121149i
$393$	27.6248	+	5.64209i	1.39349	+	0.284606i
$394$	−4.78502	−	2.76263i	−0.241066	−	0.139179i
$395$	3.25308			0.163680
$396$	−2.22378	−	0.947909i	−0.111749	−	0.0476342i
$397$	10.1941	+	17.6566i	0.511625	+	0.886161i	0.999909	+	0.0134762i	$0.00428974\pi$
$397$	10.1941	+	17.6566i	0.511625	+	0.886161i	−0.488284	+	0.872685i	$0.662377\pi$
$398$	−7.90400	+	13.6901i	−0.396192	+	0.686224i
$399$	15.5744	−	5.19801i	0.779693	−	0.260226i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	7.15181			0.357144			0.178572	−	0.983927i	$-0.442852\pi$
$401$	7.15181			0.357144			0.178572	+	0.983927i	$0.442852\pi$
$402$	0.375997	+	1.12657i	0.0187531	+	0.0561881i
$403$	13.0400	−	10.6236i	0.649568	−	0.529201i
$404$		−	3.07118i		−	0.152797i
$405$	−8.64381	−	2.50689i	−0.429515	−	0.124568i
$406$	21.4208	−	12.3673i	1.06310	−	0.613780i
$407$			8.63969i			0.428254i
$408$	−6.59489	−	1.34694i	−0.326496	−	0.0666834i
$409$	−4.97254	+	2.87090i	−0.245876	+	0.141957i	−0.617875	−	0.786277i	$-0.712006\pi$
$409$	−4.97254	+	2.87090i	−0.245876	+	0.141957i	0.371998	+	0.928233i	$0.378673\pi$
$410$	−0.634427	+	0.366287i	−0.0313321	+	0.0180896i
$411$	10.7056	−	3.57305i	0.528069	−	0.176245i
$412$	0.368713	−	0.638630i	0.0181652	−	0.0314630i
$413$	39.8278	+	22.9946i	1.95980	+	1.13149i
$414$	−0.423698	+	0.0513733i	−0.0208236	+	0.00252486i
$415$	1.61815	−	0.934238i	0.0794318	−	0.0458599i
$416$	−1.51045	+	2.61618i	−0.0740561	+	0.128269i
$417$	18.7501	−	21.1608i	0.918194	−	1.03625i
$418$			2.22390i			0.108775i
$419$			9.62101i			0.470017i	0.971993	+	0.235008i	$0.0755118\pi$
$419$			9.62101i			0.470017i	−0.971993	+	0.235008i	$0.924488\pi$
$420$	3.94536	−	4.45263i	0.192514	−	0.217266i
$421$	−17.3075	+	29.9775i	−0.843516	+	1.46101i	0.0433873	+	0.999058i	$0.486185\pi$
$421$	−17.3075	+	29.9775i	−0.843516	+	1.46101i	−0.886904	+	0.461955i	$0.847148\pi$
$422$	−15.0004	+	8.66050i	−0.730209	+	0.421587i
$423$	−14.5403	+	1.76301i	−0.706974	+	0.0857204i
$424$	11.7711	+	6.79605i	0.571655	+	0.330045i
$425$	−1.94308	+	3.36552i	−0.0942533	+	0.163252i
$426$	18.6616	−	6.22839i	0.904157	−	0.301767i
$427$	31.6103	−	18.2502i	1.52973	−	0.883191i
$428$	1.85660	−	1.07191i	0.0897419	−	0.0518125i
$429$	−4.13093	−	0.843700i	−0.199443	−	0.0407342i
$430$			0.821770i			0.0396293i
$431$	32.5014	−	18.7647i	1.56554	−	0.903864i	0.568860	−	0.822434i	$-0.307385\pi$
$431$	32.5014	−	18.7647i	1.56554	−	0.903864i	0.996679	−	0.0814300i	$-0.0259487\pi$
$432$	−2.95284	+	4.27560i	−0.142069	+	0.205710i
$433$			0.00668506i			0.000321263i	1.00000		0.000160632i	$5.11307e-5\pi$
$433$			0.00668506i			0.000321263i	−1.00000		0.000160632i	$0.999949\pi$
$434$	3.04750	+	18.8793i	0.146284	+	0.906236i
$435$	3.94884	+	11.8316i	0.189332	+	0.567280i
$436$	14.2883			0.684284
$437$	0.196321	+	0.340038i	0.00939131	+	0.0162662i
$438$	1.36919	−	0.456974i	0.0654225	−	0.0218351i
$439$	−10.4394	+	18.0815i	−0.498244	+	0.862984i	−0.999998	−	0.00202667i	$-0.999355\pi$
$439$	−10.4394	+	18.0815i	−0.498244	+	0.862984i	0.501754	+	0.865010i	$0.332688\pi$
$440$	0.402897	+	0.697837i	0.0192073	+	0.0332681i
$441$	−13.2392	−	5.64335i	−0.630438	−	0.268731i
$442$	−11.7397			−0.558403
$443$	23.3341	+	13.4719i	1.10864	+	0.640071i	0.938476	−	0.345345i	$-0.112238\pi$
$443$	23.3341	+	13.4719i	1.10864	+	0.640071i	0.170160	+	0.985416i	$0.445571\pi$
$444$	18.1954	+	3.71622i	0.863515	+	0.176364i
$445$	−6.27643	−	3.62370i	−0.297531	−	0.171780i
$446$	−0.0870923	−	0.150848i	−0.00412394	−	0.00714288i
$447$	−5.26826	−	1.07599i	−0.249180	−	0.0508925i
$448$	−1.71736	−	2.97455i	−0.0811375	−	0.140534i
$449$	−22.2082			−1.04807			−0.524035	−	0.851697i	$-0.675574\pi$
$449$	−22.2082			−1.04807			−0.524035	+	0.851697i	$0.675574\pi$
$450$	1.80182	+	2.39863i	0.0849386	+	0.113073i
$451$	−0.511217	+	0.295151i	−0.0240723	+	0.0138981i
$452$	13.2560	+	7.65337i	0.623511	+	0.359984i
$453$	22.8094	−	25.7421i	1.07168	−	1.20947i
$454$	−11.3500	+	19.6588i	−0.532683	+	0.922633i
$455$	5.18798	−	8.98585i	0.243216	−	0.421263i
$456$	4.68359	+	0.956575i	0.219329	+	0.0447957i
$457$		−	35.8276i		−	1.67594i	−0.545714	−	0.837972i	$-0.683741\pi$
$457$		−	35.8276i		−	1.67594i	0.545714	−	0.837972i	$-0.316259\pi$
$458$	−2.49600	−	4.32320i	−0.116630	−	0.202010i
$459$	−20.1272	−	1.62999i	−0.939457	−	0.0760815i
$460$	0.123207	+	0.0711336i	0.00574455	+	0.00331662i
$461$	−11.0236			−0.513419			−0.256710	−	0.966489i	$-0.582638\pi$
$461$	−11.0236			−0.513419			−0.256710	+	0.966489i	$0.582638\pi$
$462$	3.17914	−	3.58790i	0.147907	−	0.166924i
$463$			6.77239i			0.314740i	0.987540	+	0.157370i	$0.0503015\pi$
$463$			6.77239i			0.314740i	−0.987540	+	0.157370i	$0.949699\pi$
$464$	7.20137			0.334315
$465$	−9.63538	−	0.399418i	−0.446830	−	0.0185226i
$466$	−2.46821			−0.114338
$467$			19.9229i			0.921923i	0.887420	+	0.460962i	$0.152495\pi$
$467$			19.9229i			0.921923i	−0.887420	+	0.460962i	$0.847505\pi$
$468$	−3.55370	+	8.33692i	−0.164270	+	0.385374i
$469$	−2.35516			−0.108751
$470$	4.22817	+	2.44113i	0.195031	+	0.112601i
$471$	2.20809	+	1.95653i	0.101743	+	0.0901522i
$472$	6.69476	+	11.5957i	0.308151	+	0.533734i
$473$			0.662176i			0.0304469i
$474$	1.12751	−	5.52054i	0.0517884	−	0.253567i
$475$	1.37995	−	2.39014i	0.0633163	−	0.109667i
$476$	6.67393	−	11.5596i	0.305899	−	0.529833i
$477$	37.5106	+	15.9893i	1.71749	+	0.732100i
$478$	11.6899	+	6.74918i	0.534684	+	0.308700i
$479$	10.4505	−	6.03362i	0.477497	−	0.275683i	−0.241876	−	0.970307i	$-0.577763\pi$
$479$	10.4505	−	6.03362i	0.477497	−	0.275683i	0.719373	+	0.694624i	$0.244429\pi$
$480$	1.64296	−	0.548346i	0.0749905	−	0.0250284i
$481$	32.3901			1.47686
$482$	3.95464	+	6.84964i	0.180129	+	0.311993i
$483$	0.169364	−	0.829243i	0.00770635	−	0.0377319i
$484$	−5.17535	−	8.96397i	−0.235243	−	0.407453i
$485$	14.0181	+	8.09335i	0.636528	+	0.367500i
$486$	−7.25017	+	13.7998i	−0.328874	+	0.625972i
$487$	−25.6391	−	14.8027i	−1.16182	−	0.670776i	−0.210079	−	0.977684i	$-0.567372\pi$
$487$	−25.6391	−	14.8027i	−1.16182	−	0.670776i	−0.951739	+	0.306909i	$0.900705\pi$
$488$	10.6269			0.481058
$489$	3.84433	+	3.40636i	0.173847	+	0.154041i
$490$	2.39863	+	4.15456i	0.108359	+	0.187684i
$491$	16.7692	−	29.0451i	0.756784	−	1.31079i	−0.187698	−	0.982227i	$-0.560103\pi$
$491$	16.7692	−	29.0451i	0.756784	−	1.31079i	0.944482	−	0.328562i	$-0.106564\pi$
$492$	0.401704	+	1.20359i	0.0181102	+	0.0542620i
$493$	13.9929	+	24.2363i	0.630207	+	1.09155i
$494$	8.33739			0.375117
$495$	1.45189	+	1.93280i	0.0652578	+	0.0868730i
$496$	−1.97991	+	5.20384i	−0.0889008	+	0.233659i
$497$			39.0133i			1.74998i
$498$	−1.02457	−	3.06983i	−0.0459121	−	0.137562i
$499$	33.0134	−	19.0603i	1.47788	−	0.853256i	0.478195	−	0.878254i	$-0.341291\pi$
$499$	33.0134	−	19.0603i	1.47788	−	0.853256i	0.999688	+	0.0249976i	$0.00795783\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−8.00167	+	39.1778i	−0.357488	+	1.75034i
$502$	−16.4910	+	9.52107i	−0.736029	+	0.424946i
$503$	−23.7159	+	13.6924i	−1.05744	+	0.610513i	−0.924723	−	0.380642i	$-0.875703\pi$
$503$	−23.7159	+	13.6924i	−1.05744	+	0.610513i	−0.132716	+	0.991154i	$0.542370\pi$
$504$	−6.18874	−	8.23862i	−0.275668	−	0.366978i
$505$	−1.53559	+	2.65972i	−0.0683329	+	0.118356i
$506$	0.0992793	+	0.0573189i	0.00441350	+	0.00254814i
$507$	1.34276	−	6.57443i	0.0596341	−	0.291981i
$508$	−9.01862	+	5.20690i	−0.400137	+	0.231019i
$509$	8.81251	−	15.2637i	0.390608	−	0.676552i	−0.601922	−	0.798555i	$-0.705598\pi$
$509$	8.81251	−	15.2637i	0.390608	−	0.676552i	0.992530	+	0.122002i	$0.0389316\pi$
$510$	5.03787	+	4.46393i	0.223081	+	0.197666i
$511$			2.86238i			0.126624i
$512$		−	1.00000i		−	0.0441942i
$513$	14.2940	+	1.15760i	0.631097	+	0.0511091i
$514$	−1.79313	+	3.10579i	−0.0790915	+	0.136991i
$515$	−0.638630	+	0.368713i	−0.0281414	+	0.0162474i
$516$	1.39456	+	0.284824i	0.0613920	+	0.0125387i
$517$	3.40703	+	1.96705i	0.149841	+	0.0865107i
$518$	−18.4135	+	31.8931i	−0.809041	+	1.40130i
$519$	−7.45267	−	22.3298i	−0.327136	−	0.980168i
$520$	2.61618	−	1.51045i	0.114727	−	0.0662378i
$521$	−9.89159	+	5.71091i	−0.433359	+	0.250200i	−0.700776	−	0.713381i	$-0.747163\pi$
$521$	−9.89159	+	5.71091i	−0.433359	+	0.250200i	0.267418	+	0.963581i	$0.413830\pi$
$522$	21.4470	−	2.60045i	0.938712	−	0.113819i
$523$		−	39.2997i		−	1.71846i	−0.511592	−	0.859229i	$-0.670944\pi$
$523$		−	39.2997i		−	1.71846i	0.511592	−	0.859229i	$-0.329056\pi$
$524$	−14.0976	+	8.13923i	−0.615855	+	0.355564i
$525$	−5.64310	+	1.88341i	−0.246285	+	0.0821988i
$526$		−	16.7103i		−	0.728602i
$527$	−21.3607	+	3.44805i	−0.930488	+	0.150199i
$528$	1.32389	−	0.441853i	0.0576147	−	0.0192292i
$529$	−22.9798			−0.999120
$530$	−6.79605	−	11.7711i	−0.295201	−	0.511304i
$531$	24.1255	+	32.1166i	1.04696	+	1.39374i
$532$	−4.73972	+	8.20944i	−0.205493	+	0.355924i
$533$	1.10652	+	1.91655i	0.0479287	+	0.0830149i
$534$	−8.32488	+	9.39524i	−0.360253	+	0.406572i
$535$	−2.14381			−0.0926850
$536$	−0.593829	−	0.342847i	−0.0256495	−	0.0148087i
$537$	1.12186	−	5.49283i	0.0484116	−	0.237033i
$538$	16.7998	+	9.69936i	0.724290	+	0.418169i
$539$	1.93280	+	3.34771i	0.0832517	+	0.144196i
$540$	4.69503	−	2.22636i	0.202042	−	0.0958071i
$541$	0.345486	+	0.598400i	0.0148536	+	0.0257272i	0.873357	−	0.487081i	$-0.161938\pi$
$541$	0.345486	+	0.598400i	0.0148536	+	0.0257272i	−0.858503	+	0.512808i	$0.828605\pi$
$542$	4.62368			0.198604
$543$	−9.01807	−	27.0201i	−0.387003	−	1.15954i
$544$	3.36552	−	1.94308i	0.144295	−	0.0833089i
$545$	−12.3740	−	7.14414i	−0.530044	−	0.306021i
$546$	−13.4510	−	11.9186i	−0.575650	−	0.510068i
$547$	−7.88536	+	13.6578i	−0.337153	+	0.583967i	−0.983896	−	0.178741i	$-0.942797\pi$
$547$	−7.88536	+	13.6578i	−0.337153	+	0.583967i	0.646743	+	0.762708i	$0.276131\pi$
$548$	−3.25803	+	5.64307i	−0.139176	+	0.241060i
$549$	31.6490	−	3.83743i	1.35075	−	0.163778i
$550$		−	0.805793i		−	0.0343591i
$551$	−9.93751	−	17.2123i	−0.423352	−	0.733268i
$552$	0.163418	−	0.184430i	0.00695555	−	0.00784985i
$553$	9.67646	+	5.58671i	0.411485	+	0.237571i
$554$	23.9855			1.01905
$555$	−13.8996	−	12.3160i	−0.590003	−	0.522787i
$556$			16.3232i			0.692260i
$557$	30.0547			1.27346			0.636729	−	0.771088i	$-0.280287\pi$
$557$	30.0547			1.27346			0.636729	+	0.771088i	$0.280287\pi$
$558$	−4.01743	+	16.2130i	−0.170071	+	0.686350i
$559$	2.48249			0.104998
$560$			3.43472i			0.145143i
$561$	4.05948	+	3.59700i	0.171391	+	0.151866i
$562$	−9.55099			−0.402884
$563$	20.8367	+	12.0301i	0.878162	+	0.507007i	0.870052	−	0.492960i	$-0.164085\pi$
$563$	20.8367	+	12.0301i	0.878162	+	0.507007i	0.00811024	+	0.999967i	$0.497418\pi$
$564$	5.60812	−	6.32918i	0.236145	−	0.266507i
$565$	−7.65337	−	13.2560i	−0.321980	−	0.557685i
$566$		−	12.9772i		−	0.545473i
$567$	−21.4062	−	22.3014i	−0.898977	−	0.936570i
$568$	−5.67926	+	9.83676i	−0.238296	+	0.412741i
$569$	−1.61547	+	2.79807i	−0.0677239	+	0.117301i	−0.897899	−	0.440201i	$-0.854907\pi$
$569$	−1.61547	+	2.79807i	−0.0677239	+	0.117301i	0.830175	+	0.557503i	$0.188240\pi$
$570$	−3.57782	−	3.17021i	−0.149858	−	0.132786i
$571$	16.0871	+	9.28786i	0.673222	+	0.388685i	0.797296	−	0.603588i	$-0.206263\pi$
$571$	16.0871	+	9.28786i	0.673222	+	0.388685i	−0.124074	+	0.992273i	$0.539596\pi$
$572$	2.10810	−	1.21711i	0.0881442	−	0.0508901i
$573$	−7.36309	−	22.0614i	−0.307597	−	0.921627i
$574$	−2.51618			−0.105023
$575$	−0.0711336	−	0.123207i	−0.00296648	−	0.00513809i
$576$	−0.361105	−	2.97819i	−0.0150460	−	0.124091i
$577$	11.7194	+	20.2986i	0.487886	+	0.845043i	0.999903	−	0.0139325i	$-0.00443500\pi$
$577$	11.7194	+	20.2986i	0.487886	+	0.845043i	−0.512017	+	0.858975i	$0.671102\pi$
$578$	−1.64349	−	0.948867i	−0.0683600	−	0.0394677i
$579$	−5.37842	+	26.3338i	−0.223519	+	1.09440i
$580$	−6.23657	−	3.60069i	−0.258960	−	0.149510i
$581$	6.41768			0.266250
$582$	18.5932	−	20.9838i	0.770713	−	0.869806i
$583$	−5.47621	−	9.48507i	−0.226801	−	0.392831i
$584$	−0.416684	+	0.721718i	−0.0172425	+	0.0298649i
$585$	7.24606	−	5.44313i	0.299588	−	0.225046i
$586$	−8.47522	−	14.6795i	−0.350108	−	0.606405i
$587$	−13.2705			−0.547732			−0.273866	−	0.961768i	$-0.588302\pi$
$587$	−13.2705			−0.547732			−0.273866	+	0.961768i	$0.588302\pi$
$588$	7.88172	−	2.63056i	0.325037	−	0.108483i
$589$	15.1701	−	2.44875i	0.625072	−	0.100899i
$590$		−	13.3895i		−	0.551238i
$591$	9.07779	−	3.02975i	0.373410	−	0.124627i
$592$	−9.28550	+	5.36099i	−0.381632	+	0.220335i
$593$			28.5918i			1.17412i	0.809542	+	0.587062i	$0.199716\pi$
$593$			28.5918i			1.17412i	−0.809542	+	0.587062i	$0.800284\pi$
$594$	3.78322	−	1.79398i	0.155228	−	0.0736080i
$595$	−11.5596	+	6.67393i	−0.473897	+	0.273605i
$596$	2.68851	−	1.55221i	0.110126	−	0.0635810i
$597$	−8.66824	−	25.9719i	−0.354768	−	1.06296i
$598$	0.214888	−	0.372197i	0.00878743	−	0.0152203i
$599$	22.8692	+	13.2035i	0.934410	+	0.539482i	0.888203	−	0.459450i	$-0.151954\pi$
$599$	22.8692	+	13.2035i	0.934410	+	0.539482i	0.0462061	+	0.998932i	$0.485287\pi$
$600$	−1.69702	−	0.346599i	−0.0692805	−	0.0141498i
$601$	−32.0608	+	18.5103i	−1.30779	+	0.755051i	−0.981726	−	0.190298i	$-0.939055\pi$
$601$	−32.0608	+	18.5103i	−1.30779	+	0.755051i	−0.326060	+	0.945349i	$0.605721\pi$
$602$	−1.41127	+	2.44440i	−0.0575192	+	0.0996261i
$603$	−1.89234	−	0.806629i	−0.0770619	−	0.0328485i
$604$			19.8572i			0.807979i
$605$			10.3507i			0.420816i
$606$	3.98136	+	3.52778i	0.161732	+	0.143306i
$607$	−1.23539	+	2.13976i	−0.0501429	+	0.0868500i	−0.890007	−	0.455946i	$-0.849301\pi$
$607$	−1.23539	+	2.13976i	−0.0501429	+	0.0868500i	0.839865	+	0.542796i	$0.182634\pi$
$608$	−2.39014	+	1.37995i	−0.0969329	+	0.0559642i
$609$	−8.57300	+	41.9752i	−0.347396	+	1.70092i
$610$	−9.20319	−	5.31346i	−0.372626	−	0.215136i
$611$	7.37444	−	12.7729i	0.298338	−	0.516737i
$612$	9.32148	−	7.00217i	0.376799	−	0.283046i
$613$	−20.7979	+	12.0077i	−0.840021	+	0.484986i	−0.857271	−	0.514865i	$-0.827842\pi$
$613$	−20.7979	+	12.0077i	−0.840021	+	0.484986i	0.0172504	+	0.999851i	$0.494509\pi$
$614$	18.6193	−	10.7499i	0.751414	−	0.433829i
$615$	0.253909	−	1.24319i	0.0102386	−	0.0501303i
$616$			2.76767i			0.111513i
$617$	20.4157	−	11.7870i	0.821903	−	0.474526i	−0.0291690	−	0.999574i	$-0.509286\pi$
$617$	20.4157	−	11.7870i	0.821903	−	0.474526i	0.851072	+	0.525048i	$0.175953\pi$
$618$	0.404364	+	1.21156i	0.0162659	+	0.0487362i
$619$		−	4.54430i		−	0.182651i	−0.995821	−	0.0913255i	$-0.970890\pi$
$619$		−	4.54430i		−	0.182651i	0.995821	−	0.0913255i	$-0.0291104\pi$
$620$	4.31658	−	3.51670i	0.173358	−	0.141234i
$621$	0.420092	−	0.608277i	0.0168577	−	0.0244093i
$622$	−0.500059			−0.0200505
$623$	−12.4464	−	21.5577i	−0.498653	−	0.863693i
$624$	−1.65650	−	4.96323i	−0.0663132	−	0.198688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	7.52167	+	13.0279i	0.300626	+	0.520700i
$627$	−2.88298	−	2.55454i	−0.115135	−	0.102018i
$628$	−1.70330			−0.0679690
$629$	−36.0850	−	20.8337i	−1.43880	−	0.830693i
$630$	1.24029	+	10.2292i	0.0494144	+	0.407542i
$631$	−37.2561	−	21.5098i	−1.48314	−	0.856293i	−0.483326	−	0.875440i	$-0.660572\pi$
$631$	−37.2561	−	21.5098i	−1.48314	−	0.856293i	−0.999817	+	0.0191471i	$0.993905\pi$
$632$	1.62654	+	2.81725i	0.0647003	+	0.112064i
$633$	6.00344	−	29.3941i	0.238615	−	1.16831i
$634$	4.69483	+	8.13168i	0.186455	+	0.322950i
$635$	10.4138			0.413259
$636$	−22.3313	+	7.45317i	−0.885492	+	0.295537i
$637$	12.5505	−	7.24606i	0.497270	−	0.287099i
$638$	−5.02539	−	2.90141i	−0.198957	−	0.114868i
$639$	−13.3618	+	31.3465i	−0.528584	+	1.24005i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	16.6839	−	28.8974i	0.658976	−	1.14138i	−0.321906	−	0.946772i	$-0.604323\pi$
$641$	16.6839	−	28.8974i	0.658976	−	1.14138i	0.980881	−	0.194608i	$-0.0623433\pi$
$642$	−0.743042	+	3.63809i	−0.0293255	+	0.143584i
$643$			24.1854i			0.953778i	0.878963	+	0.476889i	$0.158236\pi$
$643$			24.1854i			0.953778i	−0.878963	+	0.476889i	$0.841764\pi$
$644$	0.244324	+	0.423181i	0.00962770	+	0.0166757i
$645$	−1.06531	−	0.943944i	−0.0419466	−	0.0371678i
$646$	−9.28847	−	5.36270i	−0.365450	−	0.210993i
$647$	23.9342			0.940952			0.470476	−	0.882413i	$-0.344082\pi$
$647$	23.9342			0.940952			0.470476	+	0.882413i	$0.344082\pi$
$648$	−2.15088	−	8.73921i	−0.0844944	−	0.343308i
$649$		−	10.7892i		−	0.423513i
$650$	−3.02091			−0.118490
$651$	−27.9750	−	17.7355i	−1.09643	−	0.695108i
$652$	−2.96548			−0.116137
$653$		−	21.4538i		−	0.839554i	−0.907627	−	0.419777i	$-0.862108\pi$
$653$		−	21.4538i		−	0.839554i	0.907627	−	0.419777i	$-0.137892\pi$
$654$	−16.4125	+	18.5228i	−0.641781	+	0.724297i
$655$	16.2785			0.636052
$656$	−0.634427	−	0.366287i	−0.0247702	−	0.0143011i
$657$	−0.980348	+	2.29988i	−0.0382470	+	0.0897268i
$658$	8.38460	+	14.5225i	0.326866	+	0.566148i
$659$		−	9.57650i		−	0.373047i	−0.982450	−	0.186524i	$-0.940278\pi$
$659$		−	9.57650i		−	0.373047i	0.982450	−	0.186524i	$-0.0597221\pi$
$660$	−1.36745	−	0.279287i	−0.0532277	−	0.0108712i
$661$	−14.2276	+	24.6429i	−0.553390	+	0.958499i	0.444637	+	0.895711i	$0.353333\pi$
$661$	−14.2276	+	24.6429i	−0.553390	+	0.958499i	−0.998027	+	0.0627884i	$0.980001\pi$
$662$	11.0541	−	19.1463i	0.429632	−	0.744144i
$663$	13.4851	−	15.2190i	0.523719	−	0.591055i
$664$	1.61815	+	0.934238i	0.0627963	+	0.0362555i
$665$	8.20944	−	4.73972i	0.318349	−	0.183799i
$666$	−25.7181	+	19.3191i	−0.996556	+	0.748599i
$667$	−1.02452			−0.0396695
$668$	−11.5431	−	19.9933i	−0.446617	−	0.773564i
$669$	0.295594	+	0.0603722i	0.0114283	+	0.00233412i
$670$	0.342847	+	0.593829i	0.0132453	+	0.0229416i
$671$	−7.41586	−	4.28155i	−0.286286	−	0.165287i
$672$	5.82877	+	1.19047i	0.224850	+	0.0459233i
$673$	−22.2226	−	12.8302i	−0.856618	−	0.494569i	0.00626006	−	0.999980i	$-0.498007\pi$
$673$	−22.2226	−	12.8302i	−0.856618	−	0.494569i	−0.862878	+	0.505412i	$0.831341\pi$
$674$	1.64170			0.0632358
$675$	−5.17920	−	0.419435i	−0.199347	−	0.0161441i
$676$	1.93705	+	3.35507i	0.0745020	+	0.129041i
$677$	−23.9003	+	41.3965i	−0.918563	+	1.59100i	−0.116964	+	0.993136i	$0.537316\pi$
$677$	−23.9003	+	41.3965i	−0.918563	+	1.59100i	−0.801599	+	0.597862i	$0.796017\pi$
$678$	−25.1484	+	8.39338i	−0.965817	+	0.322346i
$679$	27.7983	+	48.1481i	1.06680	+	1.84776i
$680$	−3.88616			−0.149028
$681$	−12.4475	−	37.2952i	−0.476988	−	1.42916i
$682$	3.47827	−	2.83373i	0.133190	−	0.108509i
$683$		−	19.5460i		−	0.747908i	−0.927447	−	0.373954i	$-0.878002\pi$
$683$		−	19.5460i		−	0.747908i	0.927447	−	0.373954i	$-0.121998\pi$
$684$	−6.61997	+	4.97283i	−0.253121	+	0.190141i
$685$	5.64307	−	3.25803i	0.215610	−	0.124483i
$686$		−	7.56576i		−	0.288862i
$687$	8.47151	+	1.73022i	0.323208	+	0.0660120i
$688$	−0.711673	+	0.410885i	−0.0271323	+	0.0156648i
$689$	−35.5594	+	20.5302i	−1.35471	+	0.782140i
$690$	−0.233739	+	0.0780116i	−0.00889830	+	0.00296985i
$691$	−18.2356	+	31.5851i	−0.693717	+	1.20155i	0.276895	+	0.960900i	$0.410695\pi$
$691$	−18.2356	+	31.5851i	−0.693717	+	1.20155i	−0.970611	+	0.240652i	$0.922639\pi$
$692$	11.7703	+	6.79559i	0.447440	+	0.258330i
$693$	0.999418	+	8.24264i	0.0379648	+	0.313112i
$694$	7.01513	−	4.05019i	0.266291	−	0.153743i
$695$	8.16162	−	14.1363i	0.309588	−	0.536222i
$696$	−8.27202	+	9.33558i	−0.313550	+	0.353864i
$697$		−	2.84690i		−	0.107834i
$698$		−	10.2078i		−	0.386370i
$699$	2.83517	−	3.19970i	0.107236	−	0.121024i
$700$	1.71736	−	2.97455i	0.0649100	−	0.112427i
$701$	−31.1895	+	18.0073i	−1.17801	+	0.680126i	−0.955554	−	0.294816i	$-0.904742\pi$
$701$	−31.1895	+	18.0073i	−1.17801	+	0.680126i	−0.222459	+	0.974942i	$0.571408\pi$
$702$	−6.72562	−	14.1833i	−0.253842	−	0.535313i
$703$	25.6270	+	14.7958i	0.966541	+	0.558033i
$704$	−0.402897	+	0.697837i	−0.0151847	+	0.0263007i
$705$	−8.02137	+	2.67717i	−0.302102	+	0.100828i
$706$	−3.78351	+	2.18441i	−0.142394	+	0.0822114i
$707$	−9.13539	+	5.27432i	−0.343572	+	0.198361i
$708$	−22.7223	−	4.64079i	−0.853955	−	0.174412i
$709$			45.8983i			1.72375i	0.507122	+	0.861874i	$0.330709\pi$
$709$			45.8983i			1.72375i	−0.507122	+	0.861874i	$0.669291\pi$
$710$	9.83676	−	5.67926i	0.369167	−	0.213139i
$711$	5.86147	+	7.80295i	0.219822	+	0.292634i
$712$		−	7.24740i		−	0.271608i
$713$	0.281677	−	0.740335i	0.0105489	−	0.0277258i
$714$	7.31924	+	21.9300i	0.273916	+	0.820710i
$715$	−2.43423			−0.0910350
$716$	1.61838	+	2.80311i	0.0604816	+	0.104757i
$717$	−22.1773	+	7.40176i	−0.828225	+	0.276424i
$718$	−3.33465	+	5.77578i	−0.124448	+	0.215550i
$719$	−4.43050	−	7.67386i	−0.165230	−	0.286187i	0.771507	−	0.636221i	$-0.219503\pi$
$719$	−4.43050	−	7.67386i	−0.165230	−	0.286187i	−0.936737	+	0.350034i	$0.886170\pi$
$720$	−1.17637	+	2.75974i	−0.0438407	+	0.102849i
$721$	−2.53285			−0.0943282
$722$	−9.85796	−	5.69149i	−0.366875	−	0.211815i
$723$	−13.4222	−	2.74135i	−0.499177	−	0.101952i
$724$	14.2426	+	8.22298i	0.529323	+	0.305605i
$725$	3.60069	+	6.23657i	0.133726	+	0.231620i
$726$	17.5653	+	3.58754i	0.651910	+	0.133146i
$727$	−4.07367	−	7.05581i	−0.151084	−	0.261685i	0.780542	−	0.625103i	$-0.214943\pi$
$727$	−4.07367	−	7.05581i	−0.151084	−	0.261685i	−0.931626	+	0.363418i	$0.881610\pi$
$728$	10.3760			0.384559
$729$	−9.56148	−	25.2503i	−0.354129	−	0.935197i
$730$	0.721718	−	0.416684i	0.0267120	−	0.0154222i
$731$	−2.76568	−	1.59677i	−0.102292	−	0.0590585i
$732$	−12.2069	+	13.7763i	−0.451178	+	0.509188i
$733$	−8.01155	+	13.8764i	−0.295913	+	0.512537i	−0.975197	−	0.221339i	$-0.928957\pi$
$733$	−8.01155	+	13.8764i	−0.295913	+	0.512537i	0.679284	+	0.733876i	$0.262291\pi$
$734$	7.29338	−	12.6325i	0.269203	−	0.466274i
$735$	−8.14105	−	1.66273i	−0.300287	−	0.0613306i
$736$			0.142267i			0.00524404i
$737$	0.276264	+	0.478503i	0.0101763	+	0.0176259i
$738$	−2.02171	−	0.861776i	−0.0744202	−	0.0317224i
$739$	26.4217	+	15.2546i	0.971938	+	0.561149i	0.899827	−	0.436248i	$-0.143693\pi$
$739$	26.4217	+	15.2546i	0.971938	+	0.561149i	0.0721115	+	0.997397i	$0.477026\pi$
$740$	10.7220			0.394148
$741$	−9.57693	+	10.8083i	−0.351817	+	0.397052i
$742$		−	46.6850i		−	1.71386i
$743$	1.95284			0.0716426			0.0358213	−	0.999358i	$-0.488595\pi$
$743$	1.95284			0.0716426			0.0358213	+	0.999358i	$0.488595\pi$
$744$	−4.47178	−	8.54419i	−0.163943	−	0.313245i
$745$	−3.10442			−0.113737
$746$			21.3294i			0.780924i
$747$	5.15651	+	2.19802i	0.188667	+	0.0804212i
$748$	−3.13144			−0.114497
$749$	−6.37688	−	3.68169i	−0.233006	−	0.134526i
$750$	1.29636	+	1.14867i	0.0473364	+	0.0419436i
$751$	20.1487	+	34.8986i	0.735238	+	1.27347i	0.954619	+	0.297830i	$0.0962628\pi$
$751$	20.1487	+	34.8986i	0.735238	+	1.27347i	−0.219381	+	0.975639i	$0.570404\pi$
$752$			4.88227i			0.178038i
$753$	6.59998	−	32.3149i	0.240517	−	1.17762i
$754$	−10.8773	+	18.8401i	−0.396130	+	0.686117i
$755$	9.92861	−	17.1969i	0.361339	−	0.625858i
$756$	17.7891	+	1.44064i	0.646982	+	0.0523955i
$757$	−41.1044	−	23.7316i	−1.49396	−	0.862540i	−0.493987	−	0.869469i	$-0.664461\pi$
$757$	−41.1044	−	23.7316i	−1.49396	−	0.862540i	−0.999976	+	0.00692880i	$0.997794\pi$
$758$	−27.0986	+	15.6454i	−0.984266	+	0.568266i
$759$	−0.188345	+	0.0628612i	−0.00683651	+	0.00228172i
$760$	2.75989			0.100112
$761$	7.70000	+	13.3368i	0.279125	+	0.483458i	0.971167	−	0.238398i	$-0.0766224\pi$
$761$	7.70000	+	13.3368i	0.279125	+	0.483458i	−0.692043	+	0.721856i	$0.743289\pi$
$762$	3.60941	−	17.6724i	0.130755	−	0.640204i
$763$	−24.5381	−	42.5012i	−0.888338	−	1.53865i
$764$	11.6288	+	6.71391i	0.420717	+	0.242901i
$765$	−11.5737	+	1.40331i	−0.418449	+	0.0507368i
$766$	−20.4494	−	11.8065i	−0.738866	−	0.426585i
$767$	−40.4485			−1.46051
$768$	1.29636	+	1.14867i	0.0467784	+	0.0414491i
$769$	−3.29403	−	5.70542i	−0.118786	−	0.205743i	0.800501	−	0.599331i	$-0.204567\pi$
$769$	−3.29403	−	5.70542i	−0.118786	−	0.205743i	−0.919287	+	0.393589i	$0.871233\pi$
$770$	1.38383	−	2.39687i	0.0498699	−	0.0863773i
$771$	−1.96651	−	5.89208i	−0.0708221	−	0.212198i
$772$	−7.75886	−	13.4387i	−0.279247	−	0.483671i
$773$	−24.5515			−0.883057			−0.441529	−	0.897247i	$-0.645564\pi$
$773$	−24.5515			−0.883057			−0.441529	+	0.897247i	$0.645564\pi$
$774$	−1.97112	+	1.48068i	−0.0708506	+	0.0532220i
$775$	−5.49661	+	0.887263i	−0.197444	+	0.0318714i
$776$

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.29636 + 1.14867i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.14867 - 1.29636i) q^{6} +(1.71736 + 2.97455i) q^{7} +1.00000i q^{8} +(0.361105 + 2.97819i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.29636 + 1.14867i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.14867 - 1.29636i) q^{6} +(1.71736 + 2.97455i) q^{7} +1.00000i q^{8} +(0.361105 + 2.97819i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.402897 - 0.697837i) q^{11} +(-1.29636 - 1.14867i) q^{12} +(-2.61618 - 1.51045i) q^{13} +(2.97455 - 1.71736i) q^{14} +(0.548346 + 1.64296i) q^{15} +1.00000 q^{16} +(1.94308 + 3.36552i) q^{17} +(2.97819 - 0.361105i) q^{18} +(-1.37995 - 2.39014i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.19047 + 5.82877i) q^{21} +(-0.697837 - 0.402897i) q^{22} -0.142267 q^{23} +(-1.14867 + 1.29636i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.51045 + 2.61618i) q^{26} +(-2.95284 + 4.27560i) q^{27} +(-1.71736 - 2.97455i) q^{28} +7.20137 q^{29} +(1.64296 - 0.548346i) q^{30} +(-1.97991 + 5.20384i) q^{31} -1.00000i q^{32} +(1.32389 - 0.441853i) q^{33} +(3.36552 - 1.94308i) q^{34} +3.43472i q^{35} +(-0.361105 - 2.97819i) q^{36} +(-9.28550 + 5.36099i) q^{37} +(-2.39014 + 1.37995i) q^{38} +(-1.65650 - 4.96323i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.634427 - 0.366287i) q^{41} +(5.82877 + 1.19047i) q^{42} +(-0.711673 + 0.410885i) q^{43} +(-0.402897 + 0.697837i) q^{44} +(-1.17637 + 2.75974i) q^{45} +0.142267i q^{46} +4.88227i q^{47} +(1.29636 + 1.14867i) q^{48} +(-2.39863 + 4.15456i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-1.34694 + 6.59489i) q^{51} +(2.61618 + 1.51045i) q^{52} +(6.79605 - 11.7711i) q^{53} +(4.27560 + 2.95284i) q^{54} +(0.697837 - 0.402897i) q^{55} +(-2.97455 + 1.71736i) q^{56} +(0.956575 - 4.68359i) q^{57} -7.20137i q^{58} +(11.5957 - 6.69476i) q^{59} +(-0.548346 - 1.64296i) q^{60} -10.6269i q^{61} +(5.20384 + 1.97991i) q^{62} +(-8.23862 + 6.18874i) q^{63} -1.00000 q^{64} +(-1.51045 - 2.61618i) q^{65} +(-0.441853 - 1.32389i) q^{66} +(-0.342847 + 0.593829i) q^{67} +(-1.94308 - 3.36552i) q^{68} +(-0.184430 - 0.163418i) q^{69} +3.43472 q^{70} +(9.83676 + 5.67926i) q^{71} +(-2.97819 + 0.361105i) q^{72} +(0.721718 + 0.416684i) q^{73} +(5.36099 + 9.28550i) q^{74} +(-0.346599 + 1.69702i) q^{75} +(1.37995 + 2.39014i) q^{76} +2.76767 q^{77} +(-4.96323 + 1.65650i) q^{78} +(2.81725 - 1.62654i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-8.73921 + 2.15088i) q^{81} +(-0.366287 + 0.634427i) q^{82} +(0.934238 - 1.61815i) q^{83} +(1.19047 - 5.82877i) q^{84} +3.88616i q^{85} +(0.410885 + 0.711673i) q^{86} +(9.33558 + 8.27202i) q^{87} +(0.697837 + 0.402897i) q^{88} -7.24740 q^{89} +(2.75974 + 1.17637i) q^{90} -10.3760i q^{91} +0.142267 q^{92} +(-8.54419 + 4.47178i) q^{93} +4.88227 q^{94} -2.75989i q^{95} +(1.14867 - 1.29636i) q^{96} +16.1867 q^{97} +(4.15456 + 2.39863i) q^{98} +(2.22378 + 0.947909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) \)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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